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{"name": "AddConstMapClass.map_add_nsmul", "kind": "theorem", "module": "Mathlib.Algebra.AddConstMap.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
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{"name": "AddConstMapClass.map_const", "kind": "theorem", "module": "Mathlib.Algebra.AddConstMap.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
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{"name": "AddConstMapClass.map_add_zsmul", "kind": "theorem", "module": "Mathlib.Algebra.AddConstMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AddConstMapClass.map_add_int'", "kind": "theorem", "module": "Mathlib.Algebra.AddConstMap.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "AddConstMapClass.strictMono_iff_Icc", "kind": "theorem", "module": "Mathlib.Algebra.AddConstMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddConstMapClass.strictAnti_iff_Icc", "kind": "theorem", "module": "Mathlib.Algebra.AddConstMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AddConstMap.toFun_eq_coe", "kind": "theorem", "module": "Mathlib.Algebra.AddConstMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddConstMap.instAddConstMapClass", "kind": "instance", "module": "Mathlib.Algebra.AddConstMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AddConstMap.id", "kind": "definition", "module": "Mathlib.Algebra.AddConstMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddConstMap.instInhabited", "kind": "instance", "module": "Mathlib.Algebra.AddConstMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AddConstMap.id_comp", "kind": "theorem", "module": "Mathlib.Algebra.AddConstMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddConstMap.replaceConsts", "kind": "definition", "module": "Mathlib.Algebra.AddConstMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddConstMap.instVAddOfVAddAssocClass", "kind": "instance", "module": "Mathlib.Algebra.AddConstMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddConstMap.coe_vadd", "kind": "theorem", "module": "Mathlib.Algebra.AddConstMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddConstMap.instAddActionOfVAddAssocClass", "kind": "instance", "module": "Mathlib.Algebra.AddConstMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddConstMap.instMul", "kind": "instance", "module": "Mathlib.Algebra.AddConstMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AddConstMap.mul_def", "kind": "theorem", "module": "Mathlib.Algebra.AddConstMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AddConstMap.pow_apply", "kind": "theorem", "module": "Mathlib.Algebra.AddConstMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddConstMap.toEnd", "kind": "definition", "module": "Mathlib.Algebra.AddConstMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddConstMap.smul", "kind": "definition", "module": "Mathlib.Algebra.AddConstMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddConstMap.addLeftHom", "kind": "definition", "module": "Mathlib.Algebra.AddConstMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddConstMap.conjNeg", "kind": "definition", "module": "Mathlib.Algebra.AddConstMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddConstMap.conjNeg_symm", "kind": "theorem", "module": "Mathlib.Algebra.AddConstMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddConstMap.mkFract", "kind": "definition", "module": "Mathlib.Algebra.AddConstMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddConstMap.term_≃+c[_,_]_", "kind": "definition", "module": "Mathlib.Algebra.AddConstMap.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AddConstMap._aux_Mathlib_Algebra_AddConstMap_Equiv___unexpand_AddConstEquiv_1", "kind": "definition", "module": "Mathlib.Algebra.AddConstMap.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddConstEquiv.toEquiv_injective", "kind": "theorem", "module": "Mathlib.Algebra.AddConstMap.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AddConstEquiv.instAddConstMapClass", "kind": "instance", "module": "Mathlib.Algebra.AddConstMap.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AddConstEquiv.coe_toEquiv", "kind": "theorem", "module": "Mathlib.Algebra.AddConstMap.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddConstEquiv.symm", "kind": "definition", "module": "Mathlib.Algebra.AddConstMap.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddConstEquiv.Simps.symm_apply", "kind": "definition", "module": "Mathlib.Algebra.AddConstMap.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddConstEquiv.symm_symm", "kind": "theorem", "module": "Mathlib.Algebra.AddConstMap.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AddConstEquiv.symm_refl", "kind": "theorem", "module": "Mathlib.Algebra.AddConstMap.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AddConstEquiv.trans_refl", "kind": "theorem", "module": "Mathlib.Algebra.AddConstMap.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AddConstEquiv.self_trans_symm", "kind": "theorem", "module": "Mathlib.Algebra.AddConstMap.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddConstEquiv.symm_trans_self", "kind": "theorem", "module": "Mathlib.Algebra.AddConstMap.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddConstEquiv.coe_symm_toEquiv", "kind": "theorem", "module": "Mathlib.Algebra.AddConstMap.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddConstEquiv.toEquiv_symm", "kind": "theorem", "module": "Mathlib.Algebra.AddConstMap.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AddConstEquiv.instPowInt", "kind": "instance", "module": "Mathlib.Algebra.AddConstMap.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AddConstEquiv.toAddConstMapHom", "kind": "definition", "module": "Mathlib.Algebra.AddConstMap.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddConstEquiv.equivUnits", "kind": "definition", "module": "Mathlib.Algebra.AddConstMap.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.singleton_vsub_self", "kind": "theorem", "module": "Mathlib.Algebra.AddTorsor.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "vadd_vsub_vadd_comm", "kind": "theorem", "module": "Mathlib.Algebra.AddTorsor.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "Prod.fst_vsub", "kind": "theorem", "module": "Mathlib.Algebra.AddTorsor.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.snd_vsub", "kind": "theorem", "module": "Mathlib.Algebra.AddTorsor.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.mk_vsub_mk", "kind": "theorem", "module": "Mathlib.Algebra.AddTorsor.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instAddTorsor", "kind": "instance", "module": "Mathlib.Algebra.AddTorsor.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.vsub_apply", "kind": "theorem", "module": "Mathlib.Algebra.AddTorsor.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.vsub_def", "kind": "theorem", "module": "Mathlib.Algebra.AddTorsor.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.constVAdd_zero", "kind": "theorem", "module": "Mathlib.Algebra.AddTorsor.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.constVAdd_add", "kind": "theorem", "module": "Mathlib.Algebra.AddTorsor.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.constVAddHom", "kind": "definition", "module": "Mathlib.Algebra.AddTorsor.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.left_vsub_pointReflection", "kind": "theorem", "module": "Mathlib.Algebra.AddTorsor.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.right_vsub_pointReflection", "kind": "theorem", "module": "Mathlib.Algebra.AddTorsor.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.pointReflection_fixed_iff_of_injective_two_nsmul", "kind": "theorem", "module": "Mathlib.Algebra.AddTorsor.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Equiv.injective_pointReflection_left_of_injective_two_nsmul", "kind": "theorem", "module": "Mathlib.Algebra.AddTorsor.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.pointReflection_eq_subLeft", "kind": "theorem", "module": "Mathlib.Algebra.AddTorsor.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "addGroupIsAddTorsor", "kind": "instance", "module": "Mathlib.Algebra.AddTorsor.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "vsub_eq_sub", "kind": "theorem", "module": "Mathlib.Algebra.AddTorsor.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "vsub_vadd", "kind": "theorem", "module": "Mathlib.Algebra.AddTorsor.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "vadd_vsub", "kind": "theorem", "module": "Mathlib.Algebra.AddTorsor.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "vadd_right_cancel", "kind": "theorem", "module": "Mathlib.Algebra.AddTorsor.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "vadd_right_cancel_iff", "kind": "theorem", "module": "Mathlib.Algebra.AddTorsor.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "vadd_right_injective", "kind": "theorem", "module": "Mathlib.Algebra.AddTorsor.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "vadd_vsub_assoc", "kind": "theorem", "module": "Mathlib.Algebra.AddTorsor.Defs", "is_tactic_proof": true, "tactics": ["apply", "rw"], "tactic_count": 2}
{"name": "vsub_self", "kind": "theorem", "module": "Mathlib.Algebra.AddTorsor.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "eq_of_vsub_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.AddTorsor.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "vsub_eq_zero_iff_eq", "kind": "theorem", "module": "Mathlib.Algebra.AddTorsor.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "vsub_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.AddTorsor.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "vsub_add_vsub_cancel", "kind": "theorem", "module": "Mathlib.Algebra.AddTorsor.Defs", "is_tactic_proof": true, "tactics": ["apply", "rw"], "tactic_count": 2}
{"name": "neg_vsub_eq_vsub_rev", "kind": "theorem", "module": "Mathlib.Algebra.AddTorsor.Defs", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "vadd_vsub_eq_sub_vsub", "kind": "theorem", "module": "Mathlib.Algebra.AddTorsor.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "vsub_vadd_eq_vsub_sub", "kind": "theorem", "module": "Mathlib.Algebra.AddTorsor.Defs", "is_tactic_proof": true, "tactics": ["rw", "neg_vsub_eq_vsub_rev,"], "tactic_count": 2}
{"name": "vsub_sub_vsub_cancel_right", "kind": "theorem", "module": "Mathlib.Algebra.AddTorsor.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "eq_vadd_iff_vsub_eq", "kind": "theorem", "module": "Mathlib.Algebra.AddTorsor.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "vadd_eq_vadd_iff_neg_add_eq_vsub", "kind": "theorem", "module": "Mathlib.Algebra.AddTorsor.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "vadd_vsub_vadd_cancel_right", "kind": "theorem", "module": "Mathlib.Algebra.AddTorsor.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Equiv.vaddConst", "kind": "definition", "module": "Mathlib.Algebra.AddTorsor.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.coe_vaddConst", "kind": "theorem", "module": "Mathlib.Algebra.AddTorsor.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.coe_vaddConst_symm", "kind": "theorem", "module": "Mathlib.Algebra.AddTorsor.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.constVSub", "kind": "definition", "module": "Mathlib.Algebra.AddTorsor.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.coe_constVSub", "kind": "theorem", "module": "Mathlib.Algebra.AddTorsor.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.coe_constVSub_symm", "kind": "theorem", "module": "Mathlib.Algebra.AddTorsor.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.constVAdd", "kind": "definition", "module": "Mathlib.Algebra.AddTorsor.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.coe_constVAdd", "kind": "theorem", "module": "Mathlib.Algebra.AddTorsor.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.pointReflection", "kind": "definition", "module": "Mathlib.Algebra.AddTorsor.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.pointReflection_apply", "kind": "theorem", "module": "Mathlib.Algebra.AddTorsor.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.pointReflection_vsub_left", "kind": "theorem", "module": "Mathlib.Algebra.AddTorsor.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.pointReflection_vsub_right", "kind": "theorem", "module": "Mathlib.Algebra.AddTorsor.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Equiv.pointReflection_symm", "kind": "theorem", "module": "Mathlib.Algebra.AddTorsor.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.pointReflection_self", "kind": "theorem", "module": "Mathlib.Algebra.AddTorsor.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.pointReflection_involutive", "kind": "theorem", "module": "Mathlib.Algebra.AddTorsor.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddTorsor.subsingleton_iff", "kind": "theorem", "module": "Mathlib.Algebra.AddTorsor.Defs", "is_tactic_proof": true, "tactics": ["inhabit", "exact"], "tactic_count": 2}
{"name": "AffineAddMonoid.dim", "kind": "abbrev", "module": "Mathlib.Algebra.AffineMonoid.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineAddMonoid.embedding", "kind": "definition", "module": "Mathlib.Algebra.AffineMonoid.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineAddMonoid.embedding_injective", "kind": "theorem", "module": "Mathlib.Algebra.AffineMonoid.Embedding", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "irreducible_mem_submonoidClosure_subset", "kind": "theorem", "module": "Mathlib.Algebra.AffineMonoid.Irreducible", "is_tactic_proof": false, "tactics": ["refine", "obtain"], "tactic_count": 2}
{"name": "irreducible_subset_of_submonoidClosure_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.AffineMonoid.Irreducible", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Submonoid.FG.finite_irreducible_mem_submonoidClosure", "kind": "theorem", "module": "Mathlib.Algebra.AffineMonoid.Irreducible", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "finite_irreducible", "kind": "theorem", "module": "Mathlib.Algebra.AffineMonoid.Irreducible", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Submonoid.closure_irreducible", "kind": "theorem", "module": "Mathlib.Algebra.AffineMonoid.Irreducible", "is_tactic_proof": true, "tactics": ["classical", "obtain", "convert", "refine", "by_contra", "obtain", "simpa", "simp", "obtain", "hrirred", "simpa", "obtain", "obtain", "replace", "rw", "replace", "rw", "have", "rwa", "have", "simp", "rw", "refine", "simpa", "specialize", "simpa", "simp", "obtain", "obtain", "simp", "obtain", "simp"], "tactic_count": 32}
{"name": "AffineAddMonoid.to_twoUniqueSums", "kind": "instance", "module": "Mathlib.Algebra.AffineMonoid.UniqueSums", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMonoid.to_twoUniqueProds", "kind": "instance", "module": "Mathlib.Algebra.AffineMonoid.UniqueSums", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PUnit.algebra", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.algebraMap_pUnit", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.algebra", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.algebraMap_eq", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.down_algebraMap", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.ofSubsemiring", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.algebraMap_ofSubsemiring", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.coe_algebraMap_ofSubsemiring", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.algebraMap_ofSubsemiring_apply", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.ofSubring", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.algebraMap_ofSubring", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.coe_algebraMap_ofSubring", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.algebraMap_ofSubring_apply", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.algebraMapSubmonoid", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.mem_algebraMapSubmonoid_of_mem", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.algebraMapSubmonoid_self", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.algebraMapSubmonoid_powers", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Algebra.mul_sub_algebraMap_commutes", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Algebra.mul_sub_algebraMap_pow_commutes", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Algebra.semiringToRing", "kind": "abbrev", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.commSemiringToCommRing", "kind": "abbrev", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.instSubtypeMemSubringCenter", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.instAlgebra", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Module.algebraMap_end_eq_smul_id", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.algebraMap_end_apply", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.ker_algebraMap_end", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.algebraMap_isUnit_inv_apply_eq_iff", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.algebraMap_isUnit_inv_apply_eq_iff'", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.map_algebraMap_mul", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LinearMap.map_mul_algebraMap", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Semiring.toNatAlgebra", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nat_algebra_subsingleton", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "algebraMap_comp_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Ring.toIntAlgebra", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "algebraMap_int_eq", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "int_algebra_subsingleton", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "algebraMap_comp_intCast", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "NeZero.of_faithfulSMul", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "faithfulSMul_iff_algebraMap_injective", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "FaithfulSMul.algebraMap_injective", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FaithfulSMul.algebraMap_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FaithfulSMul.algebraMap_eq_one_iff", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "algebraMap.coe_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "algebraMap.lift_map_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.charZero_of_charZero", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFaithfulSMulNatOfCharZero", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "instFaithfulSMulIntOfCharZero", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "algebra_compatible_smul", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "algebraMap_smul", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isSMulRegular_algebraMap_iff", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsScalarTower.to_smulCommClass", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsScalarTower.to_smulCommClass'", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.to_smulCommClass", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instSMulCommClass", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smul_algebra_smul_comm", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NoZeroDivisors.of_faithfulSMul", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCancelMulZero.of_faithfulSMul", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDomain.of_faithfulSMul", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Module.isTorsionFree_iff_algebraMap_injective", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "Invertible.algebraMapOfInvertibleAlgebraMap", "kind": "abbrev", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUnit.algebraMap_of_algebraMap", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "injective_algebraMap_of_linearMap", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "surjective_algebraMap_of_linearMap", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bijective_algebraMap_of_linearMap", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bijective_algebraMap_of_linearEquiv", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.extendScalarsOfSurjectiveEquiv", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.extendScalarsOfSurjective", "kind": "abbrev", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.extendScalarsOfSurjective", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.extendScalarsOfSurjective_apply", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.extendScalarsOfSurjective_apply", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.extendScalarsOfSurjective_symm", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "algebraMap.coe_prod", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "algebraMap.coe_sum", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.mul", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.mul'", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingTheory.LinearMap.termμ", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "RingTheory.LinearMap._aux_Mathlib_Algebra_Algebra_Bilinear___unexpand_LinearMap_mul'_1", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingTheory.LinearMap.termμ[_]", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "RingTheory.LinearMap._aux_Mathlib_Algebra_Algebra_Bilinear___unexpand_LinearMap_mul'_2", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.mul_apply'", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.mul'_apply", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "NonUnitalAlgHom.lmul", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgHom.coe_lmul_eq_mul", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.commute_mulLeft_right", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Bilinear", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
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{"name": "LinearMap.pow_mulLeft", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.pow_mulRight", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.lmul", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.coe_lmul_eq_mul", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Algebra.lmul_isUnit_iff", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Bilinear", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "LinearMap.toSpanSingleton_one_eq_algebraLinearMap", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Bilinear", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "LinearMap.mul''", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.flip_mul", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Bilinear", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "LinearMap.mul'_comp_comm", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Bilinear", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "NonUnitalAlgHom.comp_mul'", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.comp_mul'", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "algebraMap", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.subsingleton", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "algebraMap.coeHTCT", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "RingHom.toAlgebra'", "kind": "abbrev", "module": "Mathlib.Algebra.Algebra.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.smul_toAlgebra'", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "IsScalarTower.right", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.smulOneHom_eq_algebraMap", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AlgEquiv.surjective", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.refl", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AlgEquiv.refl_toAlgHom", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.refl_toRingHom", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AlgEquiv.symm", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.invFun_eq_symm", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.coe_apply_coe_coe_symm_apply", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AlgEquiv.mk_coe'", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AlgEquiv.refl_symm", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.toRingEquiv_symm", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AlgEquiv.symm_toAddEquiv", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AlgEquiv.apply_symm_apply", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AlgEquiv.rightInverse_symm", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AlgHom.toRingHom_toAddMonoidHom", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "NonUnitalSubalgebra.instIsTorsionFree", "kind": "instance", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.coe_add", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.coe_mul", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.coe_zero", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.coe_neg", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.coe_sub", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.coe_smul", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.coe_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.toNonUnitalSubsemiring_subtype", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.toSubring_subtype", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.toSubmoduleEquiv", "kind": "definition", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.map", "kind": "definition", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.map_mono", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.map_injective", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.map_id", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.map_map", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.mem_map", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.map_toSubmodule", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.map_toNonUnitalSubsemiring", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.coe_map", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.comap", "kind": "definition", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.map_le", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.gc_map_comap", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.mem_comap", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.coe_comap", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.noZeroDivisors", "kind": "instance", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.toNonUnitalSubalgebra", "kind": "definition", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mem_toNonUnitalSubalgebra", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.coe_toNonUnitalSubalgebra", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.toNonUnitalSubalgebra_mk", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.toNonUnitalSubalgebra_toSubmodule", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.toSubmodule_toNonUnitalSubalgebra", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgHom.range", "kind": "definition", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgHom.mem_range", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgHom.mem_range_self", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgHom.coe_range", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "NonUnitalAlgHom.range_comp", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgHom.range_comp_le_range", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgHom.codRestrict", "kind": "definition", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgHom.subtype_comp_codRestrict", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgHom.coe_codRestrict", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgHom.injective_codRestrict", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgHom.rangeRestrict", "kind": "abbrev", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgHom.equalizer", "kind": "definition", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgHom.mem_equalizer", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgHom.fintypeRange", "kind": "instance", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgebra.span_eq_toSubmodule", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NonUnitalAlgebra.adjoin", "kind": "definition", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgebra.adjoin_toSubmodule", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgebra.subset_adjoin", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgebra.mem_adjoin_of_mem", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgebra.self_mem_adjoin_singleton", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgebra.gc", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgebra.gi", "kind": "definition", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgebra.instCompleteLatticeNonUnitalSubalgebra", "kind": "instance", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgebra.adjoin_le", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgebra.adjoin_le_iff", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgebra.adjoin_mono", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgebra.adjoin_union", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgebra.adjoin_eq", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgebra.adjoin_induction", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "NonUnitalAlgebra.adjoin_empty", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgebra.adjoin_univ", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgHom.map_adjoin", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgHom.map_adjoin_singleton", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "NonUnitalAlgebra.mem_top", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgebra.top_toSubmodule", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgebra.top_toNonUnitalSubsemiring", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgebra.toNonUnitalSubring_top", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgebra.toNonUnitalSubsemiring_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NonUnitalAlgebra.toSubmodule_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NonUnitalAlgebra.toNonUnitalSubring_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NonUnitalAlgebra.mem_sup_left", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "NonUnitalAlgebra.mem_sup_right", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "NonUnitalAlgebra.mul_mem_sup", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgebra.map_sup", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgebra.map_inf", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgebra.coe_inf", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "NonUnitalAlgebra.inf_toSubmodule", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgebra.inf_toNonUnitalSubsemiring", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgebra.coe_sInf", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgebra.mem_sInf", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NonUnitalAlgebra.sInf_toSubmodule", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgebra.sInf_toNonUnitalSubsemiring", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgebra.coe_iInf", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NonUnitalAlgebra.mem_iInf", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NonUnitalAlgebra.map_iInf", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": true, "tactics": ["apply", "simpa"], "tactic_count": 2}
{"name": "NonUnitalAlgebra.iInf_toSubmodule", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgebra.instInhabitedNonUnitalSubalgebra", "kind": "instance", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgebra.mem_bot", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgebra.toSubmodule_bot", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "NonUnitalAlgebra.coe_bot", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NonUnitalAlgebra.eq_top_iff", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgebra.range_id", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgebra.map_top", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "NonUnitalAlgebra.comap_top", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgebra.toTop", "kind": "definition", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgebra.range_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.range_val", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.subsingleton_of_subsingleton", "kind": "instance", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.prod", "kind": "definition", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.coe_prod", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.prod_toSubmodule", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.mem_prod", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.prod_mono", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.prod_top", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "NonUnitalSubalgebra.prod_inf_prod", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.inclusion", "kind": "definition", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.inclusion_injective", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.inclusion_self", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "NonUnitalSubalgebra.inclusion_right", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.inclusion_inclusion", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.coe_inclusion", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgHom.subsingleton", "kind": "instance", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.coe_iSup_of_directed", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.iSupLift", "kind": "definition", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": true, "tactics": ["subst", "exact", "let", "simp", "rw", "rfl)", "map_zero", "dsimp", "exact", "map_mul", "dsimp", "apply", "all_goals", "map_add", "dsimp", "apply", "all_goals", "map_smul", "dsimp", "apply", "all_goals"], "tactic_count": 21}
{"name": "NonUnitalSubalgebra.iSupLift_inclusion", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": true, "tactics": ["subst", "dsimp", "apply", "exact"], "tactic_count": 4}
{"name": "NonUnitalSubalgebra.iSupLift_comp_inclusion", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "NonUnitalSubalgebra.iSupLift_mk", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": true, "tactics": ["subst", "dsimp", "apply"], "tactic_count": 3}
{"name": "NonUnitalSubalgebra.iSupLift_of_mem", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": true, "tactics": ["subst", "dsimp", "apply"], "tactic_count": 3}
{"name": "Set.smul_mem_center", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.center", "kind": "definition", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.coe_center", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.center.instNonUnitalCommSemiring", "kind": "instance", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.center.instNonUnitalCommRing", "kind": "instance", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.center_toNonUnitalSubsemiring", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.center_toNonUnitalSubring", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra._example", "kind": "example", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": true, "tactics": ["with_reducible_and_instances"], "tactic_count": 1}
{"name": "NonUnitalSubalgebra.center_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.mem_center_iff", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smul_mem_centralizer", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.centralizer", "kind": "definition", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.coe_centralizer", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.mem_centralizer_iff", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.centralizer_le", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.centralizer_univ", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgebra.adjoin_le_centralizer_centralizer", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgebra.commute_of_mem_adjoin_of_forall_mem_commute", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "NonUnitalAlgebra.commute_of_mem_adjoin_singleton_of_commute", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgebra.commute_of_mem_adjoin_self", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgebra.adjoinNonUnitalCommSemiringOfComm", "kind": "abbrev", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgebra.adjoinNonUnitalCommRingOfComm", "kind": "abbrev", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nonUnitalSubalgebraOfNonUnitalSubsemiring", "kind": "definition", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_nonUnitalSubalgebraOfNonUnitalSubsemiring", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nonUnitalSubalgebraOfNonUnitalSubring", "kind": "definition", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_nonUnitalSubalgebraOfNonUnitalSubring", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.algebraMap_mem", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.mem_one'", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.one", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.one_eq_span", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.le_one_toAddSubmonoid", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "Submodule.toSubMulAction_one", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.one_eq_span_one_set", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.one_le", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Submodule.instAddCommMonoidWithOne", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.instSMul", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.smul_toAddSubmonoid", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.smul_mem_smul", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.smul_le", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.coe_set_smul", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.smul_induction_on", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.smul_induction_on'", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "Submodule.smul_mono", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.smul_mono_left", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.instCovariantClassHSMulLe_1", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.smul_bot", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.bot_smul", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.smul_sup", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.sup_smul", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.smul_assoc", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.smul_iSup", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.iSup_smul", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.one_smul", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": true, "tactics": ["refine", "obtain", "rw", "rw"], "tactic_count": 4}
{"name": "Submodule.smul_subset_smul", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mul", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mul_mem_mul", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mul_le", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mul_toAddSubmonoid", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mul_induction_on", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mul_induction_on'", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mul_bot", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.bot_mul", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.one_mul", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.instMulLeftMono", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.instMulRightMono", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mul_comm_of_commute", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mul_sup", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.sup_mul", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mul_subset_mul", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.restrictScalars_mul", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.iSup_mul", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mul_iSup", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.instNonUnitalSemiring", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.instPowNat", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mul_top_eq_top_of_mul_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.pow_eq_npowRec", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.pow_zero", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.pow_succ", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.pow_add", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.pow_one", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submodule.pow_succ'", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submodule.bot_pow", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.pow_toAddSubmonoid", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "cases", "zero", "succ"], "tactic_count": 7}
{"name": "Submodule.le_pow_toAddSubmonoid", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact", "exact"], "tactic_count": 4}
{"name": "Submodule.pow_subset_pow", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.pow_mem_pow", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.restrictScalars_pow", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.one_eq_range", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submodule.algebraMap_mem", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "Submodule.span_singleton_algebraMap_of_isUnit", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": true, "tactics": ["conv_rhs"], "tactic_count": 1}
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{"name": "Submodule.map_op_one", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": true, "tactics": ["ext", "induction", "simp"], "tactic_count": 3}
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{"name": "Submodule.map_unop_one", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submodule.comap_unop_one", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submodule.mul_eq_map₂", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.span_mul_span", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submodule.mul_def", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Submodule.mul_one", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": true, "tactics": ["conv_lhs", "rw", "simp"], "tactic_count": 3}
{"name": "Submodule.map_mul", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.map_op_mul", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": true, "tactics": ["apply", "simp_rw", "refine", "rw", "change", "exact", "refine", "rw", "exact"], "tactic_count": 9}
{"name": "Submodule.comap_unop_mul", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Submodule.map_unop_mul", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.comap_op_mul", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Submodule.instIsScalarTower", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.instSMulCommClass", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.instSMulCommClass_1", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.hasDistribPointwiseNeg", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mem_span_mul_finite_of_mem_span_mul", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": true, "tactics": ["classical", "obtain", "obtain", "use", "have", "have", "assumption"], "tactic_count": 7}
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{"name": "Submodule.mapHom_id", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Submodule.map_op_pow", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submodule.map_unop_pow", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submodule.span.ringHom", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.spanSingleton", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.spanSingleton_apply", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.span_singleton_eq_one_iff", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mker_spanSingleton", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "Submodule.ker_unitsMap_spanSingleton", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Submodule.pointwiseMulSemiringAction", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mul_mem_mul_rev", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mul_comm", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.instIdemCommSemiring", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.prod_span", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": true, "tactics": ["letI", "refine", "simp", "intro", "rw"], "tactic_count": 5}
{"name": "Submodule.prod_span_singleton", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submodule.moduleSet", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.setSemiring_smul_def", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.smul_le_smul", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.singleton_smul", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": true, "tactics": ["conv_lhs", "rw", "exact"], "tactic_count": 3}
{"name": "Submodule.instDiv", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mem_div_iff_forall_mul_mem", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mem_div_iff_smul_subset", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.le_div_iff", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.le_div_iff_mul_le", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submodule.one_le_one_div", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submodule.one_mem_div", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submodule.le_self_mul_one_div", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Submodule.mul_one_div_le_one", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Operations", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "rw", "exact"], "tactic_count": 5}
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{"name": "MulOpposite.instAlgebra", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.algebraMap_apply", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.opOp", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.toRingEquiv_opOp", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.fromOpposite", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.toLinearMap_fromOpposite", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.toRingHom_fromOpposite", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.toOpposite", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.toLinearMap_toOpposite", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.toRingHom_toOpposite", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.op", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.toRingHom_op", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.unop", "kind": "abbrev", "module": "Mathlib.Algebra.Algebra.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.toRingHom_unop", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.opComm", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.op", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.toAlgHom_op", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.toRingEquiv_op", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.unop", "kind": "abbrev", "module": "Mathlib.Algebra.Algebra.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.toAlgHom_unop", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.toRingEquiv_unop", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.opComm", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.moduleEndSelf", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.moduleEndSelfOp", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.toOpposite", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.toRingEquiv_toOpposite", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.toLinearEquiv_toOpposite", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.algebra", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.algebraMap_def", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.algebraMap_apply", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.algHom", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.evalAlgHom", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.algHom_evalAlgHom", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.algHom_comp", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instAlgebraForall", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi._example", "kind": "example", "module": "Mathlib.Algebra.Algebra.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.constAlgHom", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.constRingHom_eq_algebraMap", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.constAlgHom_eq_algebra_ofId", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.algebra", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.compLeft", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.piCongrRight", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.piCongrRight_refl", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.piCongrRight_symm", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.piCongrRight_trans", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.piMulOpposite", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.piCongrLeft'", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.piCongrLeft'_apply", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.piCongrLeft'_symm_apply", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.piCongrLeft", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.piCongrLeft_apply", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.piCongrLeft_symm_apply", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.funUnique", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.funUnique_apply", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.funUnique_symm_apply", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.sumArrowEquivProdArrow", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.sumArrowEquivProdArrow_apply", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.sumArrowEquivProdArrow_symm_apply_inr", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.algebra", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.algebraMap_apply", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.fst", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.snd", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.fst_apply", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.snd_apply", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.prod", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.coe_prod", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.fst_prod", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Prod", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "AlgHom.snd_prod", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Prod", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "AlgHom.prod_fst_snd", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.prod_comp", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.prodEquiv", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.prodMap", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.prodCongr", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.prodCongr_apply", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.prodCongr_symm_apply", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.prodUnique", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Subalgebra.coe_mk", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.mem_mk", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.ofClass", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.instCanLiftSetCoeAndForallForallForallMemForallHAddForallForallForallForallHMulForallCoeRingHomAlgebraMap", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.instSubsemiringClass", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.mem_toSubsemiring", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.mem_carrier", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.ext", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.coe_toSubsemiring", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.toSubsemiring_injective", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.toSubsemiring_inj", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.copy", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.copy_eq", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.instSMulMemClass", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "algebraMap_mem", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.algebraMap_mem", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.rangeS_le", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.range_subset", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.range_le", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.smul_mem", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.one_mem", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.mul_mem", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.pow_mem", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.zero_mem", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.add_mem", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.nsmul_mem", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.natCast_mem", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.list_prod_mem", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.list_sum_mem", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.multiset_sum_mem", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.sum_mem", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.multiset_prod_mem", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.prod_mem", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.toNonUnitalSubalgebra", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.one_mem_toNonUnitalSubalgebra", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.instSubringClass", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.neg_mem", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.sub_mem", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.zsmul_mem", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.intCast_mem", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.toAddSubmonoid", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.toSubring", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.mem_toSubring", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.coe_toSubring", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.toSubring_injective", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.toSubring_inj", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.instInhabitedSubtypeMem", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.toSemiring", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.toCommSemiring", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.toRing", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.toCommRing", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.toSubmodule", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.mem_toSubmodule", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.coe_toSubmodule", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.toSubmodule_injective", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.module'", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.instModuleSubtypeMem", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.instIsScalarTowerSubtypeMem", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.algebra'", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.algebra", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.mk_algebraMap", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.instIsTorsionFree", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.coe_add", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.coe_mul", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.coe_zero", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.coe_one", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.coe_neg", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.coe_sub", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.coe_smul", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.coe_algebraMap", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.coe_pow", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.coe_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.coe_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.val", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.coe_val", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.val_apply", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.toSubsemiring_subtype", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.toSubring_subtype", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.toSubmoduleEquiv", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.map", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.map_mono", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.map_injective", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.map_id", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.map_map", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.mem_map", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.map_toSubmodule", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.comap", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.map_le", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.gc_map_comap", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.mem_comap", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.noZeroDivisors", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.isDomain", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubalgebraClass.toAlgebra", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubalgebraClass.coe_algebraMap", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubalgebraClass.val", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubalgebraClass.coe_val", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.toSubalgebra", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mem_toSubalgebra", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.toSubalgebra_mk", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.toSubalgebra_toSubmodule", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.toSubmodule_toSubalgebra", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.range", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.mem_range", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.mem_range_self", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.range_comp", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.range_comp_le_range", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.codRestrict", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.val_comp_codRestrict", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.coe_codRestrict", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.injective_codRestrict", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.rangeRestrict", "kind": "abbrev", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.val_comp_rangeRestrict", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgHom.rangeRestrict_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.fintypeRange", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.ofLeftInverse", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.ofLeftInverse_apply", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.ofLeftInverse_symm_apply", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.ofInjective", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.ofInjective_apply", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.ofInjectiveField", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.subalgebraMap", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.subsingleton_of_subsingleton", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.range_val", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.inclusion", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.inclusion_injective", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.inclusion_self", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.inclusion_mk", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.inclusion_right", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.inclusion_inclusion", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.val_comp_inclusion", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.coe_inclusion", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.inclusion.isScalarTower_left", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.inclusion.isScalarTower_right", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.inclusion.faithfulSMul", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.equivOfEq", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.equivOfEq_symm", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.equivOfEq_rfl", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Subalgebra.equivOfEq_trans", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.range_comp_val", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgHom.subalgebraMap", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.subalgebraMap_coe_apply", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.subalgebraMap_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.equivMapOfInjective", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.coe_equivMapOfInjective_apply", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.instSMulSubtypeMem", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.smul_def", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.smulCommClass_left", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.smulCommClass_right", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.isScalarTower_left", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.isScalarTower_mid", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.isScalarTower_right", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.instFaithfulSMulSubtypeMem", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.instMulActionSubtypeMem", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.instDistribMulActionSubtypeMem", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.instSMulWithZeroSubtypeMem", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.instMulActionWithZeroSubtypeMem", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.moduleLeft", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.toAlgebra", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.algebraMap_eq", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.algebraMap_def", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.algebraMap_mk", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.algebraMap_apply", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.rangeS_algebraMap", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subalgebra.range_algebraMap", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subalgebra.setRange_algebraMap", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.instIsTorsionFree'", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.algebraMap_mem_center", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Subalgebra.center", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.center_toSubring", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.instCommSemiringSubtypeMemCenter", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.instCommRingSubtypeMemCenter", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.mem_center_iff", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.algebraMap_mem_centralizer", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.centralizer", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.coe_centralizer", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.mem_centralizer_iff", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.center_le_centralizer", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.centralizer_le", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.centralizer_univ", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.le_centralizer_centralizer", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.centralizer_centralizer_centralizer", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "subalgebraOfSubsemiring", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_subalgebraOfSubsemiring", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "subalgebraOfSubring", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_subalgebraOfSubring", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.equalizer", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.mem_equalizer", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.equalizer_toSubmodule", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.le_equalizer", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.comap_map_eq_self_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.toSubalgebra", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.toNonUnitalSubalgebra_toSubalgebra", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "NonUnitalSubalgebra.toSubalgebra_toNonUnitalSubalgebra", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Subalgebra.le_centralizer_iff", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Centralizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.centralizer_coe_sup", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Centralizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.centralizer_coe_iSup", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Centralizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.centralizer_coe_image_includeLeft_eq_center_tensorProduct", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Centralizer", "is_tactic_proof": true, "tactics": ["classical", "ext", "constructor", "intro", "rw", "let", "obtain", "refine", "rw", "intro", "suffices", "specialize", "simp", "refine", "simp", "rw", "sum_of_support_subset", "simpa", "rintro", "rw", "rintro", "induction", "zero", "tmul", "add"], "tactic_count": 25}
{"name": "Subalgebra.centralizer_coe_image_includeRight_eq_center_tensorProduct", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Centralizer", "is_tactic_proof": true, "tactics": ["have", "apply_fun", "convert", "ext", "simpa", "ext", "simp", "constructor", "rintro", "exact", "rintro", "refine", "rw"], "tactic_count": 13}
{"name": "Subalgebra.centralizer_coe_map_includeLeft_eq_center_tensorProduct", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Centralizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.centralizer_coe_map_includeRight_eq_center_tensorProduct", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Centralizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.centralizer_coe_range_includeLeft_eq_center_tensorProduct", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Centralizer", "is_tactic_proof": false, "tactics": ["rw", "centralizer_coe_map_includeLeft_eq_center_tensorProduct", "ext", "simp"], "tactic_count": 4}
{"name": "Subalgebra.centralizer_range_includeRight_eq_center_tensorProduct", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Centralizer", "is_tactic_proof": false, "tactics": ["rw", "centralizer_coe_map_includeRight_eq_center_tensorProduct", "ext", "simp"], "tactic_count": 4}
{"name": "Subalgebra.centralizer_tensorProduct_eq_center_tensorProduct_left", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Centralizer", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Subalgebra.centralizer_tensorProduct_eq_center_tensorProduct_right", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Centralizer", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Subalgebra.coe_iSup_of_directed", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Directed", "is_tactic_proof": false, "tactics": ["let", "algebraMap_mem", "have", "le_antisymm", "simp"], "tactic_count": 5}
{"name": "Subalgebra.iSupLift", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Subalgebra.Directed", "is_tactic_proof": false, "tactics": ["let", "intro", "rcases", "simp", "let", "map_one", "dsimp", "exact", "map_zero", "dsimp", "exact", "map_mul", "dsimp", "apply", "all_goals", "map_add", "dsimp", "apply", "all_goals", "commutes", "dsimp", "exact", "exact"], "tactic_count": 23}
{"name": "Subalgebra.iSupLift_inclusion", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Directed", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "exact"], "tactic_count": 3}
{"name": "Subalgebra.iSupLift_comp_inclusion", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Directed", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Subalgebra.iSupLift_mk", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Directed", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "Subalgebra.iSupLift_of_mem", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Directed", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "Subalgebra.isSimpleOrder_of_finrank_prime", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.IsSimpleOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.adjoin", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.gc", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.gi", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.instCompleteLatticeSubalgebra", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.instSubtypeMemSubalgebraMin", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.instSubtypeMemSubalgebraMin_1", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.sup_def", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.sSup_def", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.coe_top", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.mem_top", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.top_toSubmodule", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.top_toSubsemiring", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.top_toSubring", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.toSubmodule_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.toSubsemiring_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.toSubring_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.mem_sup_left", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.mem_sup_right", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.mul_mem_sup", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.map_sup", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.map_inf", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.coe_inf", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.mem_inf", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.inf_toSubmodule", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.inf_toSubsemiring", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.sup_toSubsemiring", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "congr", "rw", "rintro", "exact"], "tactic_count": 6}
{"name": "Algebra.coe_sInf", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.mem_sInf", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Algebra.sInf_toSubmodule", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.sInf_toSubsemiring", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.sSup_toSubsemiring", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": ["have", "rw", "congr", "exact", "rw", "congr", "rw", "rintro", "obtain", "simp", "exact"], "tactic_count": 11}
{"name": "Algebra.coe_iInf", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Algebra.mem_iInf", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Algebra.map_iInf", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": true, "tactics": ["apply", "simpa"], "tactic_count": 2}
{"name": "Algebra.iInf_toSubmodule", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.iInf_toSubsemiring", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Algebra.iSup_toSubsemiring", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Algebra.mem_iSup_of_mem", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.iSup_induction", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": ["let", "mul_mem", "add_mem", "algebraMap_mem", "suffices", "rwa"], "tactic_count": 6}
{"name": "Algebra.iSup_induction'", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": true, "tactics": ["refine", "exact", "iSup_induction"], "tactic_count": 3}
{"name": "Algebra.instInhabitedSubalgebra", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.mem_bot", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.toSubmodule_bot", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.coe_bot", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.toSubring_bot", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Algebra.eq_top_iff", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.range_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.range_ofId", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.range_id", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.map_top", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.map_bot", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.comap_top", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.toTop", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.surjective_algebraMap_iff", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.bijective_algebraMap_iff", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.botEquivOfInjective", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.botEquiv", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.topEquiv", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.subsingleton", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.subsingleton_left", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.subsingleton_right", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.instUnique", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.center_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.centralizer_eq_top_iff_subset", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.equalizer_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgHom.equalizer_same", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.eqOn_sup", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "AlgHom.ext_on_codisjoint", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.map_comap_eq", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.map_comap_eq_self", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Subalgebra.map_comap_eq_self_of_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.saturation", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.mem_saturation_iff", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.le_saturation", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.saturation_saturation", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.mem_saturation_of_mul_mem_left", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.mem_saturation_of_mul_mem_right", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.subset_adjoin", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.mem_adjoin_of_mem", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.adjoin_le", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.adjoin_singleton_le", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.adjoin_eq_sInf", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.adjoin_le_iff", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.adjoin_mono", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.adjoin_eq_of_le", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.adjoin_eq", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.adjoin_iUnion", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.adjoin_attach_biUnion", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Algebra.adjoin_induction", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.adjoin_induction₂", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": true, "tactics": ["induction", "mem", "induction", "mem", "algebraMap", "mul", "add", "algebraMap", "induction", "mem", "algebraMap", "mul", "add", "mul", "add"], "tactic_count": 15}
{"name": "Algebra.adjoin_adjoin_coe_preimage", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": ["refine", "eq_top_iff.2", "exact", "exact", "exact", "exact"], "tactic_count": 6}
{"name": "Algebra.adjoin_union", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.adjoin_empty", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.adjoin_univ", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.adjoin_singleton_algebraMap", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.adjoin_singleton_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Algebra.adjoin_singleton_zero", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.adjoin_singleton_one", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.adjoin_insert_algebraMap", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Algebra.adjoin_insert_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.adjoin_insert_zero", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.adjoin_insert_one", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.adjoin_eq_span", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": true, "tactics": ["apply", "intro", "rcases", "clear", "induction", "nil", "cons", "rw", "rw", "refine", "replace", "clear", "suffices", "rcases", "rw", "exact", "induction", "nil", "cons", "rw", "rcases", "rw", "rcases", "refine", "rw", "exact", "refine", "change", "exact"], "tactic_count": 29}
{"name": "Algebra.span_le_adjoin", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.adjoin_toSubmodule_le", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Algebra.adjoin_eq_span_of_subset", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.adjoin_span", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.adjoin_image", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.adjoin_insert_adjoin", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.mem_adjoin_of_map_mul", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": true, "tactics": ["induction", "mem", "algebraMap", "r", "have", "convert", "rw", "exact", "add", "mul"], "tactic_count": 10}
{"name": "Algebra.adjoin_le_centralizer_centralizer", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.adjoinCommSemiringOfComm", "kind": "abbrev", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.commute_of_mem_adjoin_of_forall_mem_commute", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": true, "tactics": ["induction", "mem", "algebraMap", "add", "mul"], "tactic_count": 5}
{"name": "Algebra.commute_of_mem_adjoin_singleton_of_commute", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.commute_of_mem_adjoin_self", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.self_mem_adjoin_singleton", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.adjoin_union_coe_submodule", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": true, "tactics": ["rw", "congr"], "tactic_count": 2}
{"name": "Algebra.adjoin_singleton_intCast", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Algebra.adjoin_insert_intCast", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Algebra.adjoin_eq_ring_closure", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.mem_adjoin_iff", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Algebra.adjoinCommRingOfComm", "kind": "abbrev", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.map_adjoin", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.map_adjoin_singleton", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgHom.adjoin_le_equalizer", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.ext_of_adjoin_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.eqOn_adjoin_iff", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": true, "tactics": ["have", "simp"], "tactic_count": 2}
{"name": "AlgHom.adjoin_ext", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.ext_of_eq_adjoin", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "Algebra.forall_mem_adjoin_smul_eq_self_iff", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.adjoin_nat", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.adjoin_int", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.closureEquivAdjoinNat", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.closureEquivAdjoinInt", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.adjoin_eq_span_of_eq_span", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Subalgebra.adjoin_eq_span_of_eq_span", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgebra.adjoin_le_algebra_adjoin", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.adjoin_nonUnitalSubalgebra", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.comap_map_eq", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": true, "tactics": ["apply", "intro", "rw", "obtain", "replace", "rw", "exact", "rw", "apply", "rw", "exact"], "tactic_count": 11}
{"name": "Subalgebra.comap_map_eq_self", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Lattice", "is_tactic_proof": true, "tactics": ["convert", "rwa"], "tactic_count": 2}
{"name": "Subalgebra.matrix", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Subalgebra.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.op", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Subalgebra.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.mem_op", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.unop", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Subalgebra.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.mem_unop", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.unop_op", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.op_unop", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.op_le_iff", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.le_op_iff", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.op_le_op_iff", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.unop_le_unop_iff", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.opEquiv", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Subalgebra.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.op_bot", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.unop_bot", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.op_top", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.unop_top", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.op_sup", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.unop_sup", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.op_inf", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.unop_inf", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.op_sSup", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.unop_sSup", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.op_sInf", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.unop_sInf", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.op_iSup", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.unop_iSup", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.op_iInf", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.unop_iInf", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.op_adjoin", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.MulOpposite", "is_tactic_proof": true, "tactics": ["apply", "simp_rw", "congr", "simp_rw", "congr", "rw"], "tactic_count": 6}
{"name": "Subalgebra.unop_adjoin", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.MulOpposite", "is_tactic_proof": true, "tactics": ["apply", "simp_rw", "congr", "simp"], "tactic_count": 4}
{"name": "Subalgebra.linearEquivOp", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Subalgebra.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.algEquivOpMop", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Subalgebra.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.mopAlgEquivOp", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Subalgebra.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.op_toSubring", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.unop_toSubring", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.ker_rangeRestrict", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.mem_of_finset_sum_eq_one_of_pow_smul_mem", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Operations", "is_tactic_proof": false, "tactics": ["suffices", "obtain", "exact", "choose", "let", "let", "have", "ext", "change", "simpa", "have", "rw", "apply", "intro", "exact", "let", "have", "apply", "rintro", "change", "rw", "refine", "exact"], "tactic_count": 23}
{"name": "Subalgebra.mem_of_span_eq_top_of_smul_pow_mem", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FixedPoints.subring", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Subalgebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FixedPoints.subalgebra", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Subalgebra.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.toIsOrderedRing", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Subalgebra.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.toIsStrictOrderedRing", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Subalgebra.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.pi", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Subalgebra.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.mem_pi", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.pi_toSubmodule", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.pi_top", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.pi_mono", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.mul_toSubmodule_le", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Pointwise", "is_tactic_proof": true, "tactics": ["rw", "intro", "simp", "exact"], "tactic_count": 4}
{"name": "Subalgebra.isIdempotentElem_toSubmodule", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Pointwise", "is_tactic_proof": true, "tactics": ["apply", "refine", "rw", "intro", "rw", "exact"], "tactic_count": 6}
{"name": "Subalgebra.mul_toSubmodule", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Pointwise", "is_tactic_proof": true, "tactics": ["refine", "rintro", "refine", "rcases", "rw", "exact", "rw", "exact", "rw", "exact", "have", "rwa", "isIdempotentElem_toSubmodule,"], "tactic_count": 13}
{"name": "Subalgebra.pointwiseMulAction", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Subalgebra.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.coe_pointwise_smul", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.pointwise_smul_toSubsemiring", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.pointwise_smul_toSubmodule", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.pointwise_smul_toSubring", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.smul_mem_pointwise_smul", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.instCovariantClassHSMulLe", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Subalgebra.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.prod", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Subalgebra.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.coe_prod", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.prod_toSubmodule", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.mem_prod", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.prod_top", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Prod", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Subalgebra.prod_mono", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.prod_inf_prod", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.rank_sup_eq_rank_left_mul_rank_of_free", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Rank", "is_tactic_proof": true, "tactics": ["rcases", "haveI", "nontriviality", "letI", "letI", "haveI", "rw", "change", "rw"], "tactic_count": 9}
{"name": "Subalgebra.finrank_sup_eq_finrank_left_mul_finrank_of_free", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Rank", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Subalgebra.finrank_left_dvd_finrank_sup_of_free", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Rank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.rank_sup_eq_rank_right_mul_rank_of_free", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Rank", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subalgebra.finrank_sup_eq_finrank_right_mul_finrank_of_free", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Rank", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subalgebra.finrank_right_dvd_finrank_sup_of_free", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Rank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.lmul_algebraMap", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Tower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsScalarTower.subalgebra", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Subalgebra.Tower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsScalarTower.subalgebra'", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Subalgebra.Tower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.restrictScalars", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Subalgebra.Tower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.coe_restrictScalars", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Tower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.restrictScalars_top", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Tower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.restrictScalars_toSubmodule", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Tower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.mem_restrictScalars", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Tower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.restrictScalars_injective", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Tower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.ofRestrictScalars", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Subalgebra.Tower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.range_isScalarTower_toAlgHom", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Tower", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "IsScalarTower.adjoin_range_toAlgHom", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Tower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitization.lift_range_le", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Unitization", "is_tactic_proof": true, "tactics": ["refine", "rintro", "exact", "rintro", "induction"], "tactic_count": 5}
{"name": "Unitization.lift_range", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Unitization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.unitization", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Subalgebra.Unitization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.unitization_apply", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Unitization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.unitization_range", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Unitization", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "AlgHomClass.unitization_injective'", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Unitization", "is_tactic_proof": true, "tactics": ["refine", "induction", "inl_add_inr", "a", "simp_rw", "rw", "by_cases", "ext", "simp", "simpa", "exact"], "tactic_count": 11}
{"name": "AlgHomClass.unitization_injective", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Unitization", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "NonUnitalSubalgebra.unitization_injective", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Unitization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.unitizationAlgEquiv", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Subalgebra.Unitization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.unitization", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Subalgebra.Unitization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.unitization_apply", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Unitization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.unitization_range", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Unitization", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "NonUnitalSubring.unitization", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Subalgebra.Unitization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.unitization_apply", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Unitization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.unitization_range", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Unitization", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "Unitization.starLift_range_le", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Unitization", "is_tactic_proof": true, "tactics": ["refine", "rintro", "exact", "rintro", "induction"], "tactic_count": 5}
{"name": "Unitization.starLift_range", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Unitization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.unitization", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Subalgebra.Unitization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.unitization_apply", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Unitization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.unitization_range", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Unitization", "is_tactic_proof": true, "tactics": ["rw", "simp", "rfl"], "tactic_count": 3}
{"name": "NonUnitalStarSubalgebra.unitization_injective", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Subalgebra.Unitization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.unitizationStarAlgEquiv", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Subalgebra.Unitization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.lsmul", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Tower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.lsmul_coe", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Tower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsScalarTower.algebraMap_smul", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Tower", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsScalarTower.of_algebraMap_smul", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Tower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsScalarTower.of_compHom", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Tower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsScalarTower.of_algebraMap_eq", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Tower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsScalarTower.of_algebraMap_eq'", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Tower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsScalarTower.algebraMap_eq", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Tower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsScalarTower.algebraMap_apply", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Tower", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsScalarTower.Algebra.ext", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Tower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsScalarTower.toAlgHom", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Tower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsScalarTower.toAlgHom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Tower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsScalarTower.coe_toAlgHom", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Tower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsScalarTower.coe_toAlgHom'", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Tower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.map_algebraMap", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Tower", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgHom.comp_algebraMap_of_tower", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Tower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsScalarTower.subsemiring", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Tower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsScalarTower.of_algHom", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Tower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.restrictScalars", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Tower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.restrictScalars_apply", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Tower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.coe_restrictScalars", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Tower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.coe_restrictScalars'", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Tower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.restrictScalars_injective", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Tower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.extendScalarsOfSurjective", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Tower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.restrictScalars_extendScalarsOfSurjective", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Tower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.restrictScalars", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Tower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.restrictScalars_apply", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Tower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.coe_restrictScalars", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Tower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.coe_restrictScalars'", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Tower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AlgEquiv.coe_restrictScalars_symm'", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Tower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.extendScalarsOfSurjective", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Tower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.restrictScalars_extendScalarsOfSurjective", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Tower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Algebra.algebraMapSubmonoid_map_map", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Tower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Equiv.algEquiv_symm_apply", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.TransferInstance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitization", "kind": "definition", "module": "Mathlib.Algebra.Algebra.Unitization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Unitization.instNontrivialLeft", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Unitization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitization.instNontrivialRight", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Unitization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitization.instCanLift", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Unitization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitization.instInhabited", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Unitization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitization.instZero", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Unitization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitization.instAdd", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Unitization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitization.instNeg", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Unitization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitization.instAddSemigroup", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Unitization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitization.instAddZeroClass", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Unitization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitization.instAddMonoid", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Unitization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Unitization.instIsScalarTower", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Unitization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitization.instSMulCommClass", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Unitization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitization.instIsCentralScalar", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Unitization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitization.instMulAction", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Unitization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitization.instDistribMulAction", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Unitization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitization.instModule", "kind": "instance", "module": "Mathlib.Algebra.Algebra.Unitization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Unitization.fst_zero", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Unitization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Unitization.fst_smul", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Unitization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Unitization.fst_one", "kind": "theorem", "module": "Mathlib.Algebra.Algebra.Unitization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Finset.smul_expect", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Expect", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.expect_sub_distrib", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Expect", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.expect_neg_distrib", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Expect", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.card_mul_expect", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Expect", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fintype.card_mul_expect", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Expect", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.expect_mul", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Expect", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.mul_expect", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Expect", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.expect_mul_expect", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Expect", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Finset.expect_pow", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Expect", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finset.expect_boole_mul", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Expect", "is_tactic_proof": true, "tactics": ["simp_rw", "rw", "simp"], "tactic_count": 3}
{"name": "Finset.expect_boole_mul'", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Expect", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Finset.expect_eq_sum_div_card", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Expect", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fintype.expect_eq_sum_div_card", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Expect", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.expect_div", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Expect", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Finset.expect_apply", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Expect", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "algebraMap.coe_expect", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Expect", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.expect_bijective", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Expect", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.expect_equiv", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Expect", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.expect_const", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Expect", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.expect_ite_zero", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Expect", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fintype.expect_ite_mem", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Expect", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fintype.expect_dite_eq", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Expect", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fintype.expect_dite_eq'", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Expect", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fintype.expect_ite_eq", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Expect", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fintype.expect_ite_eq'", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Expect", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fintype.expect_one", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Expect", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.expect_mul_expect", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Expect", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.sum_map_div", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Field", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.sum_div", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Field", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.dens_disjiUnion", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Field", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.dens_biUnion", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Field", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.dens_biUnion_le", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Field", "is_tactic_proof": true, "tactics": ["simp", "gcongr", "exact"], "tactic_count": 3}
{"name": "Finset.dens_eq_sum_dens_fiberwise", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Field", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.dens_eq_sum_dens_image", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_range", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.prod_ofFn", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.prod_univ_def", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.prod_univ_zero", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.prod_univ_succAbove", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.prod_univ_succ", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.prod_univ_castSucc", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Fin.prod_univ_getElem", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.prod_univ_fun_getElem", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.prod_cons", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Fin.prod_snoc", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.prod_univ_one", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.prod_univ_two", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.prod_univ_two'", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.prod_univ_three", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Fin.prod_univ_four", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Fin.prod_univ_five", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Fin.prod_univ_six", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Fin.prod_univ_seven", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Fin.prod_univ_eight", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Fin.prod_const", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.prod_congr'", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": true, "tactics": ["subst", "congr"], "tactic_count": 2}
{"name": "Fin.prod_univ_add", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": true, "tactics": ["rw", "apply", "intro", "simp"], "tactic_count": 4}
{"name": "Fin.prod_trunc", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "_private.Mathlib.Algebra.BigOperators.Fin.0.Fin.prod_insertNth_go", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.prod_insertNth", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.mul_prod_removeNth", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.prod_Icc_cast", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.prod_Ico_cast", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.prod_Ioc_cast", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.prod_Ioo_cast", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.prod_uIcc_cast", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.prod_Ici_cast", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.prod_Ioi_cast", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.prod_Iic_cast", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.prod_Iio_cast", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.prod_Icc_castLE", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "Fin.prod_Icc_castAdd", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.prod_Ico_castAdd", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "Fin.prod_Ioc_castSucc", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "Fin.prod_Iic_castSucc", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.prod_Iio_castSucc", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.prod_Icc_succ", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.prod_Ico_succ", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.prod_Ioc_succ", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.prod_Ioo_succ", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.prod_uIcc_succ", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.prod_Ici_succ", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.prod_Ioi_succ", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.prod_Ioi_zero", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.prod_prod_eq_prod_triangle_mul", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.sum_pow_mul_eq_add_pow", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Fin.sum_neg_one_pow", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "simp", "split_ifs", "simp", "simp"], "tactic_count": 7}
{"name": "Fin.partialProd", "kind": "definition", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.partialProd_zero", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.partialProd_succ", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.partialProd_succ'", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": true, "tactics": ["simp", "rfl"], "tactic_count": 2}
{"name": "Fin.partialProd_init", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.partialProd_left_inv", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.partialProd_right_inv", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.partialProd_contractNth", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": true, "tactics": ["ext", "refine", "simp", "intro", "simp", "rw", "rcases", "rw", "simp", "lia", "rw", "partialProd_succ,", "simp", "lia", "rw", "simp", "lia"], "tactic_count": 17}
{"name": "Fin.inv_partialProd_mul_eq_contractNth", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": true, "tactics": ["rcases", "rwa", "assumption", "rw", "exact", "rwa", "partialProd_right_inv,", "simp", "rw", "exact", "rwa", "partialProd_succ,", "exact", "rw", "exact"], "tactic_count": 15}
{"name": "finFunctionFinEquiv", "kind": "definition", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finFunctionFinEquiv_apply", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finFunctionFinEquiv_single", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": true, "tactics": ["rw", "rintro", "rw"], "tactic_count": 3}
{"name": "finPiFinEquiv", "kind": "definition", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finPiFinEquiv_apply", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finPiFinEquiv_single", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": true, "tactics": ["rw", "rintro", "rw"], "tactic_count": 3}
{"name": "finSigmaFinEquiv", "kind": "definition", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finSigmaFinEquiv_apply", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Fin", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rcases", "rw", "unfold", "simp", "finCongr_apply,", "by_cases", "conv", "simpa", "replace", "subst", "conv", "simp", "rfl"], "tactic_count": 16}
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{"name": "finprod_mem_eq_of_bijOn", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finprod", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "finprod_eq_of_bijective", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finprod", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "finprod_comp", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finprod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finprod_comp_equiv", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finprod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finprod_set_coe_eq_finprod_mem", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finprod", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "finprod_subtype_eq_finprod_cond", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finprod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finprod_mem_inter_mul_diff'", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finprod", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact", "exacts"], "tactic_count": 4}
{"name": "finprod_mem_inter_mul_diff", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finprod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finprod_mem_mul_diff'", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finprod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "finprod_mem_mul_diff", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finprod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finprod_mem_iUnion", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finprod", "is_tactic_proof": true, "tactics": ["cases", "lift", "classical", "rw", "simp", "exact"], "tactic_count": 6}
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{"name": "finprod_mem_sUnion", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finprod", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "finprod_option", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finprod", "is_tactic_proof": true, "tactics": ["replace", "convert", "simp", "rw", "exact"], "tactic_count": 5}
{"name": "finprod_mem_powerset_insert", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finprod", "is_tactic_proof": true, "tactics": ["rw", "finprod_mem_image"], "tactic_count": 2}
{"name": "finprod_mem_powerset_diff_elem", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finprod", "is_tactic_proof": false, "tactics": ["nth_rw", "exact"], "tactic_count": 2}
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{"name": "finprod_mem_induction", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finprod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finprod_cond_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finprod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "single_le_finprod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finprod", "is_tactic_proof": true, "tactics": ["classical", "calc", "f"], "tactic_count": 3}
{"name": "finprod_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finprod", "is_tactic_proof": true, "tactics": ["nontriviality", "rw", "refine", "simp"], "tactic_count": 4}
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{"name": "prod_finprod_comm", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finprod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "mul_finsum'", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finprod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_finsum_mem'", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finprod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finsum_mul'", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finprod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finsum_mem_mul'", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finprod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_finsum", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finprod", "is_tactic_proof": true, "tactics": ["by_cases", "simp_all", "by_cases", "exact", "simp"], "tactic_count": 5}
{"name": "mul_finsum_mem", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finprod", "is_tactic_proof": true, "tactics": ["rw", "congr", "ext", "by_cases"], "tactic_count": 4}
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{"name": "Finset.mulSupport_of_fiberwise_prod_subset_image", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finprod", "is_tactic_proof": true, "tactics": ["simp", "intro", "suffices", "exact"], "tactic_count": 4}
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{"name": "finprod_mem_finset_product₃", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finprod", "is_tactic_proof": true, "tactics": ["classical", "rw", "simp_rw", "simp"], "tactic_count": 4}
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{"name": "finprod_dmem", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finprod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finprod_emb_domain'", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finprod", "is_tactic_proof": true, "tactics": ["simp_rw", "rw", "intro", "rw"], "tactic_count": 4}
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{"name": "Nat.cast_finprod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finprod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.cast_finprod_mem", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finprod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.cast_finsum", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finprod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.cast_finsum_mem", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finprod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.prod", "kind": "definition", "module": "Mathlib.Algebra.BigOperators.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.prod_fun_one", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finsupp.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finsupp.prod_of_support_subset", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finsupp.Basic", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
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{"name": "Finsupp.prod_finsetProd_comm", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Finsupp.if_mem_support", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finsupp.Basic", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
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{"name": "Finsupp.prod_zpow", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.onFinset_prod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SubmonoidClass.finsuppProd_mem", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.prod_congr", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Finsupp.prod_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "map_finsuppProd", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.coe_finsuppProd", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.finsuppProd_apply", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.single_multiset_sum", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.single_finset_sum", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finsupp.Basic", "is_tactic_proof": true, "tactics": ["trans", "apply", "rw", "rfl"], "tactic_count": 4}
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{"name": "Finsupp.support_finset_sum", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finsupp.Basic", "is_tactic_proof": true, "tactics": ["rw", "induction", "empty", "cons", "rw", "exact"], "tactic_count": 6}
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{"name": "Finsupp.liftAddHom_apply", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.liftAddHom_symm_apply", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.liftAddHom_symm_apply_apply", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Finsupp.prod_finset_sum_index", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.prod_sum_index", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.multiset_sum_sum_index", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.support_sum_eq_biUnion", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finsupp.Basic", "is_tactic_proof": true, "tactics": ["classical", "refine", "simp", "intro", "simp", "intro", "rw", "rw", "intro", "exact"], "tactic_count": 10}
{"name": "Finsupp.multiset_map_sum", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.multiset_sum_sum", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.prod_add_index_of_disjoint", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finsupp.Basic", "is_tactic_proof": false, "tactics": ["have", "classical", "simp_rw"], "tactic_count": 3}
{"name": "Finsupp.prod_dvd_prod_of_subset_of_dvd", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finsupp.Basic", "is_tactic_proof": true, "tactics": ["classical", "simp", "rw", "apply", "apply", "exact"], "tactic_count": 6}
{"name": "Finsupp.indicator_eq_sum_attach_single", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finsupp.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "intro", "rw"], "tactic_count": 5}
{"name": "Finsupp.indicator_eq_sum_single", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.prod_indicator_index_eq_prod_attach", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finsupp.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw"], "tactic_count": 3}
{"name": "Finsupp.prod_attach_index", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.prod_indicator_index", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finsupp.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finsupp.prod_mul_eq_prod_mul_of_exists", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finsupp.Basic", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finset.sum_apply'", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.sum_apply'", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.sum_apply''", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finsupp.Basic", "is_tactic_proof": true, "tactics": ["classical", "unfold", "induction", "empty", "insert"], "tactic_count": 5}
{"name": "Finsupp.sum_sum_index'", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.sum_mul", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finsupp.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finsupp.mul_sum", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finsupp.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.card_finsuppSum", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.prod_pow_pos_of_zero_notMem_support", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.op_finsuppSum", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.unop_finsuppSum", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddOpposite.op_finsuppProd", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddOpposite.unop_finsuppProd", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.sum_cons", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finsupp.Fin", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finsupp.sum_cons'", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finsupp.Fin", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "congr"], "tactic_count": 3}
{"name": "Finsupp.ofSupportFinite_fin_two_eq", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finsupp.Fin", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "finTwoArrowEquiv'", "kind": "definition", "module": "Mathlib.Algebra.BigOperators.Finsupp.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finTwoArrowEquiv'_sum_eq", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Finsupp.Fin", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "List.smul_sum", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.GroupWithZero.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.smul_prod'", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.GroupWithZero.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.smul_sum", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.GroupWithZero.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.smul_sum", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.GroupWithZero.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smul_finsum_mem", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.GroupWithZero.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.smul_prod'", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.GroupWithZero.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.smul_prod'", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.GroupWithZero.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smul_finprod'", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.GroupWithZero.Action", "is_tactic_proof": true, "tactics": ["cases", "simp"], "tactic_count": 2}
{"name": "Finset.smul_prod_perm", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.GroupWithZero.Action", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "smul_finprod_perm", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.GroupWithZero.Action", "is_tactic_proof": true, "tactics": ["cases", "simp"], "tactic_count": 2}
{"name": "List.smul_prod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.GroupWithZero.Action", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "Multiset.smul_prod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.GroupWithZero.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.smul_prod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.GroupWithZero.Action", "is_tactic_proof": false, "tactics": ["have", "simp", "simp_rw"], "tactic_count": 3}
{"name": "Finset.prod_smul", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.GroupWithZero.Action", "is_tactic_proof": true, "tactics": ["induction", "empty", "cons"], "tactic_count": 3}
{"name": "Finset.prod_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.GroupWithZero.Finset", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finset.prod_ite_zero", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.GroupWithZero.Finset", "is_tactic_proof": true, "tactics": ["split_ifs", "exact", "push_neg", "rcases", "exact"], "tactic_count": 5}
{"name": "Finset.prod_boole", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.GroupWithZero.Finset", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.support_prod_subset", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.GroupWithZero.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.indicator_pi_one_apply", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.GroupWithZero.Finset", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finset.prod_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.GroupWithZero.Finset", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "insert"], "tactic_count": 4}
{"name": "Finset.prod_ne_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.GroupWithZero.Finset", "is_tactic_proof": true, "tactics": ["rw", "push_neg"], "tactic_count": 2}
{"name": "Finset.support_prod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.GroupWithZero.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.prod_ite_zero", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.GroupWithZero.Finset", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fintype.prod_boole", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.GroupWithZero.Finset", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Units.mk0_prod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.GroupWithZero.Finset", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "Finset.prod_eq_fold", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_cons", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_cons'", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["funext", "rw"], "tactic_count": 2}
{"name": "Finset.prod_insert", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_insert'", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["funext", "rw"], "tactic_count": 2}
{"name": "Finset.prod_insert_of_eq_one_if_notMem", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "Finset.prod_insert_one", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.prod_singleton", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_singleton'", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["funext", "simp"], "tactic_count": 2}
{"name": "Finset.prod_pair", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.prod_image", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_attach", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finset.prod_congr", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.prod_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_eq_one_iff", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "Finset.prod_disjUnion", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "rfl"], "tactic_count": 3}
{"name": "Finset.prod_disjiUnion", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["refine", "dsimp", "congr", "exact"], "tactic_count": 4}
{"name": "Finset.prod_union_inter", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_union", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.prod_filter_mul_prod_filter_not", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "Finset.prod_filter_not_mul_prod_filter", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.prod_filter_xor", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["classical", "simp"], "tactic_count": 2}
{"name": "IsCompl.prod_mul_prod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_mul_prod_compl", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_compl_mul_prod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_sdiff", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.prod_subset_one_on_sdiff", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finset.prod_subset", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_disjSum", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Finset.prod_sum_eq_prod_toLeft_mul_prod_toRight", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.prod_sumElim", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.prod_biUnion", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.prod_of_injOn", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["classical", "exact", "prod_subset"], "tactic_count": 3}
{"name": "Finset.prod_fiberwise_eq_prod_filter", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw", "intro", "simp_rw"], "tactic_count": 3}
{"name": "Finset.prod_fiberwise_eq_prod_filter'", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["calc", "prod_congr"], "tactic_count": 2}
{"name": "Finset.prod_fiberwise_of_maps_to", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw", "intro", "simp_rw"], "tactic_count": 3}
{"name": "Finset.prod_fiberwise_of_maps_to'", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["calc", "prod_congr"], "tactic_count": 2}
{"name": "Finset.prod_fiberwise", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_fiberwise'", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_diag", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.prod_image'", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_mul_distrib", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_mul_prod_comm", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Finset.prod_filter_of_ne", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_filter_ne_one", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_filter", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_eq_single_of_mem", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["calc", "refine", "intro", "rwa", "simpa"], "tactic_count": 5}
{"name": "Finset.prod_eq_single", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_ite_mem_eq", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.prod_eq_ite", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "replace", "simp"], "tactic_count": 4}
{"name": "Finset.prod_union_eq_left", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_union_eq_right", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.prod_congr_of_eq_on_inter", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["classical", "conv_lhs", "conv_rhs", "exact"], "tactic_count": 4}
{"name": "Finset.prod_eq_mul_of_mem", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["haveI", "have", "have", "rw", "exact"], "tactic_count": 5}
{"name": "Finset.prod_eq_mul", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["haveI", "exact", "rw", "apply", "exact", "rw", "apply", "exact", "rw", "exact", "prod_const_one"], "tactic_count": 11}
{"name": "Finset.prod_subtype_eq_prod_filter", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["have", "simp_all"], "tactic_count": 2}
{"name": "Finset.prod_subtype_of_mem", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "Finset.prod_subtype_map_embedding", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finset.prod_coe_sort", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_finset_coe", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_subtype", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["have", "subst", "rw", "congr"], "tactic_count": 4}
{"name": "Finset.prod_set_coe", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_congr_set", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw", "congr", "exact"], "tactic_count": 3}
{"name": "Finset.prod_extend_by_one", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_eq_prod_extend", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw", "congr", "rw"], "tactic_count": 3}
{"name": "Finset.prod_bij_ne_one", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["classical", "calc", "grind", "solve_by_elim", "intro", "refine", "obtain", "exact", "solve_by_elim"], "tactic_count": 9}
{"name": "Finset.exists_ne_one_of_prod_ne_one", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["contrapose", "exact"], "tactic_count": 2}
{"name": "Finset.prod_range_succ_comm", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.prod_range_succ", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.prod_range_succ'", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.eventually_constant_prod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["obtain", "clear", "induction", "zero", "succ"], "tactic_count": 5}
{"name": "Finset.prod_range_add", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Finset.prod_range_one", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.prod_list_map_count", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "simp", "by_cases", "rw", "mul_assoc,", "congr", "refine", "rw", "rw", "grind"], "tactic_count": 12}
{"name": "Finset.prod_list_count", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.prod_list_count_of_subset", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "rw"], "tactic_count": 4}
{"name": "Finset.prod_multiset_map_count", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["refine", "simp"], "tactic_count": 2}
{"name": "Finset.prod_multiset_count", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "Finset.prod_multiset_count_of_subset", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["revert", "refine", "simp", "apply"], "tactic_count": 4}
{"name": "Finset.prod_range_induction", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "exact"], "tactic_count": 5}
{"name": "Finset.prod_const", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_eq_pow_card", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.pow_card_mul_prod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_mul_pow_card", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.pow_eq_prod_const", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.prod_pow_eq_pow_sum", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_flip", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "simp"], "tactic_count": 5}
{"name": "Finset.prod_involution", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["classical", "induction", "obtain", "simp", "have", "suffices", "rw", "cases", "inl", "inr", "suffices", "ih", "grind"], "tactic_count": 13}
{"name": "Finset.prod_ninvolution", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_comp", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Finset.prod_partition", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["refine", "rfl"], "tactic_count": 2}
{"name": "Finset.prod_cancels_of_partition_cancels", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw", "intro", "obtain", "simp", "exact"], "tactic_count": 5}
{"name": "Finset.eq_of_card_le_one_of_prod_eq", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["intro", "by_cases", "exact", "have", "rw", "grind"], "tactic_count": 6}
{"name": "Finset.mul_prod_erase", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.prod_erase_mul", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.prod_erase", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "grind"], "tactic_count": 3}
{"name": "Finset.prod_erase_lt_of_one_lt", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["conv", "rw", "exact"], "tactic_count": 3}
{"name": "Finset.eq_one_of_prod_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["intro", "classical", "by_cases", "rw", "rw", "rw", "exact", "exact"], "tactic_count": 8}
{"name": "Finset.prod_mul_eq_prod_mul_of_exists", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["classical", "rw", "simp", "rw"], "tactic_count": 4}
{"name": "Finset.prod_biUnion_of_pairwise_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["classical", "let", "have", "rw", "swap", "intro", "have", "have", "simp", "exact", "exact"], "tactic_count": 11}
{"name": "Finset.prod_filter_of_pairwise_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["classical", "have", "simp", "exact", "rw", "mul_prod_erase"], "tactic_count": 6}
{"name": "Finset.prod_image_of_pairwise_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finset.prod_image_of_disjoint", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "rw"], "tactic_count": 3}
{"name": "Finset.prod_unique_nonempty", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.prod_dvd_prod_of_dvd", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_map_equiv", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.prod_comp_equiv", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.prod_sdiff_eq_prod_sdiff_iff", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_sdiff_ne_prod_sdiff_iff", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_insert_div", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.prod_erase_eq_div", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.prod_range_div", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "Finset.prod_range_div'", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "Finset.eq_prod_range_div", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.eq_prod_range_div'", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["conv_lhs", "simp"], "tactic_count": 2}
{"name": "Finset.prod_range_add_div_prod_range", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_sdiff_eq_div", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.prod_sdiff_div_prod_sdiff", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.sum_range_tsub", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["apply", "apply", "intro", "have", "have", "rw"], "tactic_count": 6}
{"name": "Finset.sum_tsub_distrib", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_eq_sum_ones", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.sum_const_nat", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "Finset.sum_card_fiberwise_eq_card_filter", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.card_disjiUnion", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_biUnion", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.card_biUnion_le", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_eq_sum_card_fiberwise", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.card_eq_sum_card_image", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.prod_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.prod_fiberwise", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw", "congr", "exact"], "tactic_count": 3}
{"name": "Fintype.prod_fiberwise'", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw", "congr", "exact"], "tactic_count": 3}
{"name": "Fintype.prod_unique", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fintype.prod_subsingleton", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "Fintype.prod_Prop", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fintype.prod_subtype_mul_prod_subtype", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["classical", "let", "rw", "exact", "simp", "simp"], "tactic_count": 6}
{"name": "Fintype.prod_subset", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.prod_toFinset", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sum_toFinset_count_eq_length", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Multiset.mem_sum", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "Finset.mem_sum", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.prod_map_prod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "insert"], "tactic_count": 4}
{"name": "Multiset.toFinset_sum_count_eq", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Multiset.sum_count_eq_card", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw", "congr", "simpa"], "tactic_count": 3}
{"name": "Multiset.toFinset_sum_count_nsmul_eq", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.exists_smul_of_dvd_count", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["use", "have", "apply", "intro", "rw", "rw"], "tactic_count": 6}
{"name": "Multiset.prod_sum", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "IsUnit.prod_iff", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "IsUnit.prod_univ_iff", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "nat_abs_sum_le", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Basic", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "Finset.prod", "kind": "definition", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_mk", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_val", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LibraryNote.operator_precedence_of_big_operators", "kind": "definition", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BigOperators.bigOpBinder", "kind": "definition", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BigOperators.bigOpBinderParenthesized", "kind": "definition", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BigOperators.bigOpBinderCollection", "kind": "definition", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BigOperators.bigOpBinders", "kind": "definition", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BigOperators.processBigOpBinder", "kind": "definition", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BigOperators.processBigOpBinders", "kind": "definition", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BigOperators.bigOpBindersPattern", "kind": "definition", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BigOperators.bigOpBindersProd", "kind": "definition", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BigOperators.bigsum", "kind": "definition", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BigOperators.bigprod", "kind": "definition", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BigOperators._aux_Mathlib_Algebra_BigOperators_Group_Finset_Defs___macroRules_BigOperators_bigsum_1", "kind": "definition", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BigOperators._aux_Mathlib_Algebra_BigOperators_Group_Finset_Defs___macroRules_BigOperators_bigprod_1", "kind": "definition", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.BigOperators.Group.Finset.Defs.0.BigOperators.FinsetResult", "kind": "inductive", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.BigOperators.Group.Finset.Defs.0.BigOperators.delabFinsetArg", "kind": "definition", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BigOperators.delabFinsetProd", "kind": "definition", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BigOperators.delabFinsetSum", "kind": "definition", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_eq_multiset_prod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_map_val", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sum_multiset_singleton", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "Finset.prod_empty", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_empty'", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_of_isEmpty", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.prod_const_one", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.prod_map", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "Finset.prod_map_toList", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "Equiv.Perm.prod_comp'", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "Finset.prod_bij", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_bij'", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": true, "tactics": ["refine", "rw", "simp"], "tactic_count": 3}
{"name": "Finset.prod_nbij", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_nbij'", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Finset.prod_bijective", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_hom_rel", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": true, "tactics": ["delta", "apply"], "tactic_count": 2}
{"name": "Finset.prod_coe_sort_eq_attach", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_ite_index", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_ite_irrel", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": true, "tactics": ["split_ifs"], "tactic_count": 1}
{"name": "Finset.prod_dite_irrel", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": true, "tactics": ["split_ifs"], "tactic_count": 1}
{"name": "Finset.ite_prod_one", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.ite_one_prod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.nonempty_of_prod_ne_one", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_range_zero", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.sum_filter_count_eq_countP", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.prod_mem_multiset", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": true, "tactics": ["refine"], "tactic_count": 1}
{"name": "Finset.prod_induction", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_induction_nonempty", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_pow", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_dvd_prod_of_subset", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.op_sum", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.unop_sum", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.op_prod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.unop_prod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_inv_distrib", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_div_distrib", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_zpow", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sum_nat_mod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_nat_mod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sum_int_mod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_int_mod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.prod_bijective", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.prod_equiv", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Bijective.prod_comp", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.prod_comp", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.prod_empty", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_attach_univ", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_erase_attach", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Multiset.card_sum", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.disjoint_list_sum_left", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "Multiset.disjoint_list_sum_right", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Multiset.disjoint_sum_left", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.disjoint_sum_right", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Multiset.disjoint_finset_sum_left", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "Multiset.disjoint_finset_sum_right", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Multiset.count_sum'", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "Multiset.toFinset_prod_dvd_prod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp"], "tactic_count": 3}
{"name": "Units.coe_prod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofMul_list_prod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "toMul_list_sum", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ofAdd_list_prod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "toAdd_list_sum", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ofMul_multiset_prod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "toMul_multiset_sum", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ofMul_prod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toMul_sum", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofAdd_multiset_prod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "toAdd_multiset_sum", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ofAdd_sum", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toAdd_prod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_eq_prod_range_intervalGapsWithin", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Gaps", "is_tactic_proof": true, "tactics": ["set", "symm", "apply", "exact", "intro", "rw", "apply", "intro", "obtain", "exact", "simp"], "tactic_count": 11}
{"name": "Finset.prod_intervalGapsWithin_mul_prod_eq_div", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Gaps", "is_tactic_proof": false, "tactics": ["rw", "prod_mul_distrib,", "prod_range_div", "simp"], "tactic_count": 4}
{"name": "Finset.prod_intervalGapsWithin_eq_div_div_prod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Gaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_mulIndicator_subset_of_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Indicator", "is_tactic_proof": true, "tactics": ["calc"], "tactic_count": 1}
{"name": "Finset.prod_mulIndicator_subset", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_mulIndicator_eq_prod_filter", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Indicator", "is_tactic_proof": false, "tactics": ["refine", "exact", "exact"], "tactic_count": 3}
{"name": "Finset.prod_mulIndicator_eq_prod_inter", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Indicator", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.mulIndicator_prod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mulIndicator_biUnion", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Indicator", "is_tactic_proof": true, "tactics": ["induction", "empty", "cons", "ext", "rw", "classical", "rw", "exact"], "tactic_count": 8}
{"name": "Finset.mulIndicator_biUnion_apply", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Indicator", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.prod_Icc_of_even_eq_range", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Interval", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "prod_range_succ"], "tactic_count": 5}
{"name": "Finset.prod_Icc_eq_prod_Ico_mul", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Interval", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.prod_Icc_succ_eq_mul_endpoints", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Interval", "is_tactic_proof": true, "tactics": ["induction", "rw", "grind", "rw", "grind"], "tactic_count": 5}
{"name": "Finset.prod_Ico_int_div", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Interval", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "simp", "rw", "simp"], "tactic_count": 6}
{"name": "MonoidHom.coe_finset_prod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.finset_prod_apply", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mulSupport_prod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Lemmas", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Finset.isSquare_prod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "use", "rw", "congr", "ext", "rw", "exact"], "tactic_count": 7}
{"name": "Finset.prod_univ_pi", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Pi", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "Finset.prod_apply_dite", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Piecewise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_apply_ite", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Piecewise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_dite", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Piecewise", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.prod_ite", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Piecewise", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.prod_dite_of_false", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Piecewise", "is_tactic_proof": true, "tactics": ["refine"], "tactic_count": 1}
{"name": "Finset.prod_ite_of_false", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Piecewise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_dite_of_true", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Piecewise", "is_tactic_proof": true, "tactics": ["refine"], "tactic_count": 1}
{"name": "Finset.prod_ite_of_true", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Piecewise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_apply_ite_of_false", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Piecewise", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Finset.prod_apply_ite_of_true", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Piecewise", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Finset.prod_ite_mem", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Piecewise", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.prod_attach_eq_prod_dite", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Piecewise", "is_tactic_proof": true, "tactics": ["rw", "congr", "simp", "ext", "apply"], "tactic_count": 5}
{"name": "Finset.prod_dite_eq", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Piecewise", "is_tactic_proof": true, "tactics": ["split_ifs", "rw", "intro", "rw", "exact", "simp", "rw", "grind"], "tactic_count": 8}
{"name": "Finset.prod_dite_eq'", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Piecewise", "is_tactic_proof": true, "tactics": ["split_ifs", "rw", "intro", "rw", "exact", "simp", "rw", "grind"], "tactic_count": 8}
{"name": "Finset.prod_ite_eq", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Piecewise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_ite_eq'", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Piecewise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_ite_eq_of_mem", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Piecewise", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.prod_ite_eq_of_mem'", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Piecewise", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.prod_pi_mulSingle'", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Piecewise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_pi_mulSingle", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Piecewise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_piecewise", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Piecewise", "is_tactic_proof": true, "tactics": ["simp", "rw"], "tactic_count": 2}
{"name": "Finset.prod_inter_mul_prod_diff", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Piecewise", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "Finset.prod_eq_mul_prod_diff_singleton", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Piecewise", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "Finset.prod_eq_prod_diff_singleton_mul", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Piecewise", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fintype.prod_eq_mul_prod_compl", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Piecewise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.prod_eq_prod_compl_mul", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Piecewise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.dvd_prod_of_mem", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Piecewise", "is_tactic_proof": true, "tactics": ["classical", "rw", "exact"], "tactic_count": 3}
{"name": "Finset.prod_update_of_notMem", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Piecewise", "is_tactic_proof": true, "tactics": ["apply", "intro", "have", "rintro", "exact", "simp"], "tactic_count": 6}
{"name": "Finset.prod_update_of_mem", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Piecewise", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Finset.prod_ite_one", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Piecewise", "is_tactic_proof": true, "tactics": ["split_ifs", "obtain", "rw", "exact", "push_neg", "rw", "exact"], "tactic_count": 7}
{"name": "Finset.prod_pow_boole", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Piecewise", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.prod_eq_prod_iff_single", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Piecewise", "is_tactic_proof": true, "tactics": ["classical", "rw"], "tactic_count": 2}
{"name": "Finset.card_filter", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Piecewise", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fintype.prod_ite_eq_ite_exists", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Piecewise", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fintype.prod_ite_mem", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Piecewise", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fintype.prod_dite_eq", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Piecewise", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fintype.prod_dite_eq'", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Piecewise", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fintype.prod_ite_eq", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Piecewise", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fintype.prod_ite_eq'", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Piecewise", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fintype.prod_pi_mulSingle", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Piecewise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.prod_pi_mulSingle'", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Piecewise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_powerset_insert", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Powerset", "is_tactic_proof": true, "tactics": ["rw", "exact", "aesop"], "tactic_count": 3}
{"name": "Finset.prod_powerset_cons", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Powerset", "is_tactic_proof": true, "tactics": ["classical", "simp_rw", "rw"], "tactic_count": 3}
{"name": "Finset.prod_powerset", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Powerset", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.prod_powersetCard", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Powerset", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.prod_preimage'", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Preimage", "is_tactic_proof": true, "tactics": ["classical", "calc"], "tactic_count": 2}
{"name": "Finset.prod_preimage", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Preimage", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finset.prod_preimage_of_bij", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Preimage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_sigma", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Sigma", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Finset.prod_sigma'", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_finset_product", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Sigma", "is_tactic_proof": true, "tactics": ["refine", "apply"], "tactic_count": 2}
{"name": "Finset.prod_finset_product'", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_finset_product_right", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Sigma", "is_tactic_proof": true, "tactics": ["refine", "apply"], "tactic_count": 2}
{"name": "Finset.prod_finset_product_right'", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_product", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_product'", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_product_right", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_product_right'", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_comm'", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Sigma", "is_tactic_proof": true, "tactics": ["classical", "have", "rintro", "simp", "exact"], "tactic_count": 5}
{"name": "Finset.prod_comm", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_comm_cycle", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Sigma", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Finset.card_sigma", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Finset.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.rel_prod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.prod_hom_nonempty", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.prod_hom", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Basic", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "List.prod_hom₂_nonempty", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Basic", "is_tactic_proof": true, "tactics": ["x"], "tactic_count": 1}
{"name": "List.prod_hom₂", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Basic", "is_tactic_proof": true, "tactics": ["simp", "rw"], "tactic_count": 2}
{"name": "List.prod_map_mul", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.prod_map_hom", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.prod_take_mul_prod_drop", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.prod_take_succ", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "List.length_pos_of_prod_ne_one", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Basic", "is_tactic_proof": true, "tactics": ["cases", "simp", "simp"], "tactic_count": 3}
{"name": "List.length_pos_of_one_lt_prod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.length_pos_of_prod_lt_one", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.prod_set", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.getElem?_zero_mul_tail_prod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "List.headI_mul_tail_prod_of_ne_nil", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Commute.list_prod_right", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Basic", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "rw", "rw", "exact"], "tactic_count": 6}
{"name": "Commute.list_prod_left", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.prod_range_succ", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.prod_range_succ'", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "List.prod_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Basic", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "List.exists_mem_ne_one_of_prod_ne_one", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "List.prod_erase_of_comm", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Basic", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "obtain", "simp", "rw", "mul_assoc,"], "tactic_count": 7}
{"name": "List.prod_map_eq_pow_single", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Basic", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "specialize", "rw", "simp", "split_ifs", "rw", "rw"], "tactic_count": 9}
{"name": "List.prod_eq_pow_single", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.prod_insertIdx", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Basic", "is_tactic_proof": true, "tactics": ["induction", "rfl", "obtain", "simp", "ih", "exact"], "tactic_count": 6}
{"name": "List.mul_prod_eraseIdx", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Basic", "is_tactic_proof": true, "tactics": ["rw", "prod_insertIdx", "insertIdx_eraseIdx_getElem"], "tactic_count": 3}
{"name": "List.CommMonoid.prod_insertIdx", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.CommMonoid.mul_prod_eraseIdx", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.prod_erase", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.prod_map_erase", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Perm.prod_eq", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.prod_reverse", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.prod_mul_prod_eq_prod_zipWith_mul_prod_drop", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.prod_mul_prod_eq_prod_zipWith_of_length_eq", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Basic", "is_tactic_proof": true, "tactics": ["apply", "rw"], "tactic_count": 2}
{"name": "List.prod_map_ite", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Basic", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "simp", "rw", "clear", "by_cases", "simp", "simp", "prod_cons,"], "tactic_count": 10}
{"name": "List.prod_map_filter_mul_prod_map_filter_not", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "List.eq_of_prod_take_eq", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Basic", "is_tactic_proof": true, "tactics": ["refine", "have", "rw", "convert"], "tactic_count": 4}
{"name": "List.prod_inv_reverse", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.prod_reverse_noncomm", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.prod_drop_succ", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.prod_range_div'", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "List.prod_inv", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.prod_range_div", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Basic", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "List.prod_set'", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Basic", "is_tactic_proof": true, "tactics": ["refine", "split_ifs", "rw", "prod_take_mul_prod_drop,", "simp"], "tactic_count": 5}
{"name": "List.prod_map_ite_eq", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Basic", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "simp", "rw", "clear", "by_cases", "simp", "mul_inv_cancel_left,", "simp"], "tactic_count": 10}
{"name": "List.sum_const_nat", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.headI_add_tail_sum", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "List.headI_le_sum", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.tail_sum", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.alternatingProd_nil", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.alternatingProd_singleton", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.alternatingProd_cons_cons'", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.alternatingProd_cons_cons", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.alternatingProd_cons'", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.alternatingProd_cons", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.sum_nat_mod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Basic", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "List.prod_nat_mod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Basic", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "List.sum_int_mod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Basic", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.prod_int_mod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Basic", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "map_list_prod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.map_list_prod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.prod_zpow", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.take_sum_flatten", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Basic", "is_tactic_proof": true, "tactics": ["induction", "simp", "cases"], "tactic_count": 3}
{"name": "List.drop_sum_flatten", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Basic", "is_tactic_proof": true, "tactics": ["induction", "simp", "cases"], "tactic_count": 3}
{"name": "List.length_le_sum_of_one_le", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Basic", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "rw", "exact"], "tactic_count": 5}
{"name": "List.alternatingSum", "kind": "definition", "module": "Mathlib.Algebra.BigOperators.Group.List.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.alternatingProd", "kind": "definition", "module": "Mathlib.Algebra.BigOperators.Group.List.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.prod_induction", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Defs", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "rw", "simp", "exact"], "tactic_count": 6}
{"name": "List.prod_map_one", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Defs", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.prod_induction_nonempty", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Defs", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "by_cases", "simp", "rw", "simp", "exact"], "tactic_count": 8}
{"name": "List.prod_replicate", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Defs", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "List.prod_eq_pow_card", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.prod_hom_rel", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.prod_isUnit", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.prod_isUnit_iff", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Lemmas", "is_tactic_proof": true, "tactics": ["refine", "induction", "nil", "cons", "rw", "exact"], "tactic_count": 6}
{"name": "List.Perm.prod_eq'", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Lemmas", "is_tactic_proof": true, "tactics": ["refine", "apply", "intro", "exact", "intros", "apply", "intro", "rw"], "tactic_count": 8}
{"name": "List.prod_rotate_eq_one_of_prod_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sum_map_count_dedup_filter_eq_countP", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Lemmas", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "simp_rw", "congr", "refine", "by_cases", "simp", "simp", "true", "false", "simp", "by_cases", "refine", "simp", "exact"], "tactic_count": 16}
{"name": "List.sum_map_count_dedup_eq_length", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Lemmas", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "List.length_sigma", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Lemmas", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "List.ranges_flatten", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.ranges_nodup", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.mem_mem_ranges_iff_lt_sum", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.drop_take_succ_flatten_eq_getElem", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Lemmas", "is_tactic_proof": false, "tactics": ["have", "simp", "append_nil]"], "tactic_count": 3}
{"name": "List.neg_one_mem_of_prod_eq_neg_one", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Lemmas", "is_tactic_proof": true, "tactics": ["obtain", "exact", "h₂", "h₁"], "tactic_count": 4}
{"name": "List.dvd_prod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Lemmas", "is_tactic_proof": true, "tactics": ["let", "rw", "exact"], "tactic_count": 3}
{"name": "List.Sublist.prod_dvd_prod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Lemmas", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact"], "tactic_count": 3}
{"name": "List.alternatingProd_append", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.alternatingProd_reverse", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.op_list_prod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Lemmas", "is_tactic_proof": true, "tactics": ["intro", "induction", "nil", "cons"], "tactic_count": 4}
{"name": "MulOpposite.unop_list_prod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "unop_map_list_prod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.List.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.prod_erase", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Multiset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.prod_map_erase", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Multiset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.prod_add", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Multiset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.prod_nsmul", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Multiset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.prod_filter_mul_prod_filter_not", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Multiset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.prod_map_eq_pow_single", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Multiset.Basic", "is_tactic_proof": true, "tactics": ["induction", "simp"], "tactic_count": 2}
{"name": "Multiset.prod_eq_pow_single", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Multiset.Basic", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "Multiset.prod_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Multiset.Basic", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "Multiset.prod_hom_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Multiset.Basic", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "Multiset.prod_hom", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Multiset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.prod_hom'", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Multiset.Basic", "is_tactic_proof": true, "tactics": ["convert", "exact"], "tactic_count": 2}
{"name": "Multiset.prod_hom₂_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Multiset.Basic", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "Multiset.prod_hom₂", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Multiset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.prod_map_mul", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Multiset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.prod_map_pow", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Multiset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.prod_map_prod_map", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Multiset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.prod_dvd_prod_of_le", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Multiset.Basic", "is_tactic_proof": true, "tactics": ["obtain", "simp"], "tactic_count": 2}
{"name": "map_multiset_prod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Multiset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "map_multiset_ne_zero_prod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Multiset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.map_multiset_prod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Multiset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulHom.map_multiset_ne_zero_prod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Multiset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.dvd_prod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Multiset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.fst_prod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Multiset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.snd_prod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Multiset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.prod_dvd_prod_of_dvd", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Multiset.Basic", "is_tactic_proof": true, "tactics": ["apply", "simp", "intro", "simp"], "tactic_count": 4}
{"name": "Multiset.sumAddMonoidHom", "kind": "definition", "module": "Mathlib.Algebra.BigOperators.Group.Multiset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.coe_sumAddMonoidHom", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Multiset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.prod_map_inv'", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Multiset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.prod_map_inv", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Multiset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.prod_map_div", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Multiset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.prod_map_zpow", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Multiset.Basic", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "Multiset.sum_map_singleton", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Multiset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.sum_nat_mod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Multiset.Basic", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "Multiset.prod_nat_mod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Multiset.Basic", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "Multiset.sum_int_mod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Multiset.Basic", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "Multiset.prod_int_mod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Multiset.Basic", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "Multiset.sum_map_tsub", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Multiset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.instIsAddTorsionFree", "kind": "instance", "module": "Mathlib.Algebra.BigOperators.Group.Multiset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.prod", "kind": "definition", "module": "Mathlib.Algebra.BigOperators.Group.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.prod_eq_foldr", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.prod_eq_foldl", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.prod_coe", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.prod_toList", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Multiset.Defs", "is_tactic_proof": true, "tactics": ["conv_rhs", "rw"], "tactic_count": 2}
{"name": "Multiset.prod_map_toList", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Multiset.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.prod_zero", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.prod_cons", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.prod_singleton", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Multiset.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.prod_pair", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Multiset.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.prod_replicate", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Multiset.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.pow_count", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Multiset.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.prod_hom_rel", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.prod_map_one", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Multiset.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.prod_induction", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Multiset.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Multiset.prod_induction_nonempty", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Group.Multiset.Defs", "is_tactic_proof": true, "tactics": ["induction", "empty", "cons", "rw", "by_cases", "simp", "have", "exact"], "tactic_count": 8}
{"name": "Finset.prod_Ico_add'", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Intervals", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Finset.prod_Ico_add", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Intervals", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "Finset.prod_Ico_add_right_sub_eq", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Intervals", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.prod_Ico_succ_top", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Intervals", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.prod_Ico_consecutive", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Intervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_Ioc_consecutive", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Intervals", "is_tactic_proof": true, "tactics": ["rw", "apply", "intro", "exact"], "tactic_count": 4}
{"name": "Finset.prod_Ioc_succ_top", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Intervals", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.prod_Icc_succ_top", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Intervals", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.prod_range_mul_prod_Ico", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Intervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_range_eq_mul_Ico", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Intervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_Ico_eq_mul_inv", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Intervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_Ico_eq_div", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Intervals", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.prod_range_div_prod_range", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Intervals", "is_tactic_proof": true, "tactics": ["rw", "congr", "apply", "simp", "tauto"], "tactic_count": 5}
{"name": "Finset.sum_Ico_Ico_comm", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Intervals", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp", "lia"], "tactic_count": 4}
{"name": "Finset.sum_Ico_Ico_comm'", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Intervals", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp", "lia"], "tactic_count": 4}
{"name": "Finset.prod_Ico_eq_prod_range", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Intervals", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "replace", "rw"], "tactic_count": 4}
{"name": "Finset.prod_Ico_reflect", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Intervals", "is_tactic_proof": false, "tactics": ["have", "intro", "exact", "rcases", "rw", "refine", "simp", "rintro", "rw", "have", "rw", "exact", "simp"], "tactic_count": 13}
{"name": "Finset.sum_Ico_reflect", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Intervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_range_reflect", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Intervals", "is_tactic_proof": true, "tactics": ["cases", "simp", "simp", "rw", "simp"], "tactic_count": 5}
{"name": "Finset.sum_range_reflect", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Intervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_Ico_id_eq_factorial", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Intervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sum_range_id_mul_two", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Intervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sum_range_id", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Intervals", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.prod_range_diag_flip", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Intervals", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp", "exact"], "tactic_count": 4}
{"name": "Finset.prod_range_succ_div_prod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Intervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_range_succ_div_top", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Intervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_Ico_div_bot", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Intervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Int.ModEq.listProd_map", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.ModEq", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
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{"name": "Int.ModEq.multisetProd_map", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.ModEq", "is_tactic_proof": true, "tactics": ["rcases", "simpa"], "tactic_count": 2}
{"name": "Int.ModEq.multisetProd_map_one", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.ModEq", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Int.ModEq.multisetProd_one", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.ModEq", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Int.ModEq.multisetSum_map", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.ModEq", "is_tactic_proof": true, "tactics": ["rcases", "simpa"], "tactic_count": 2}
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{"name": "Int.ModEq.multisetSum_zero", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.ModEq", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Int.ModEq.prod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.ModEq.prod_one", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.ModEq", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Int.ModEq.sum", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.ModEq.sum_zero", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.prod_modEq_ite", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.ModEq", "is_tactic_proof": false, "tactics": ["simp", "exact"], "tactic_count": 2}
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{"name": "Int.sum_modEq_ite", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.ModEq", "is_tactic_proof": false, "tactics": ["simp", "exact"], "tactic_count": 2}
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{"name": "_private.Mathlib.Algebra.BigOperators.Module.0.Finset.termG_", "kind": "definition", "module": "Mathlib.Algebra.BigOperators.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.BigOperators.Module.0.Finset._aux_Mathlib_Algebra_BigOperators_Module___macroRules__private_Mathlib_Algebra_BigOperators_Module_0_Finset_termG__1", "kind": "definition", "module": "Mathlib.Algebra.BigOperators.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sum_Ico_by_parts", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Module", "is_tactic_proof": false, "tactics": ["have", "rw", "simp", "have", "rw", "rw", "conv", "simp_rw", "conv_lhs", "have", "intro", "rw", "abel", "simp_rw", "abel"], "tactic_count": 15}
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{"name": "Finset.Nat.prod_antidiagonal_swap", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.NatAntidiagonal", "is_tactic_proof": true, "tactics": ["conv_lhs", "rfl"], "tactic_count": 2}
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{"name": "eqOn_fun_finsetProd", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Pi", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
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{"name": "Finset.natCast_card_filter", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Ring.Finset", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.sum_boole", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Ring.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sum_mul", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Ring.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Finset.sum_range_succ_mul_sum_range_succ", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Ring.Finset", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "Finset.sum_mul_boole", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Ring.Finset", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "Finset.sum_prod_piFinset", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Ring.Finset", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "Finset.prod_sub", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Ring.Finset", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.prod_sub_ordered", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Ring.Finset", "is_tactic_proof": true, "tactics": ["simp", "convert", "simp"], "tactic_count": 3}
{"name": "Finset.prod_one_sub_ordered", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Ring.Finset", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Finset.prod_range_natCast_sub", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Ring.Finset", "is_tactic_proof": true, "tactics": ["rw", "rcases", "exact", "rw", "rw"], "tactic_count": 5}
{"name": "Fintype.sum_pow", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Ring.Finset", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fintype.prod_sum", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Ring.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.prod_add", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Ring.Finset", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Nat.sum_div", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Ring.Finset", "is_tactic_proof": true, "tactics": ["obtain", "simp", "rw", "refine", "rw"], "tactic_count": 5}
{"name": "Nat.cast_list_sum", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Ring.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.cast_list_prod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Ring.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.cast_multiset_sum", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Ring.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.cast_multiset_prod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Ring.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.cast_sum", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Ring.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.cast_prod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Ring.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.sum_div", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Ring.Finset", "is_tactic_proof": true, "tactics": ["obtain", "simp", "rw", "refine", "rw"], "tactic_count": 5}
{"name": "Int.cast_list_sum", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Ring.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.cast_list_prod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Ring.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.cast_multiset_sum", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Ring.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.cast_multiset_prod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Ring.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.cast_sum", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Ring.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.cast_prod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Ring.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.list_sum_right", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Ring.List", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "rw", "exact"], "tactic_count": 5}
{"name": "Commute.list_sum_left", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Ring.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.prod_map_neg", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Ring.List", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.prod_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Ring.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.prod_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Ring.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.prod_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Ring.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sum_map_mul_left", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Ring.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sum_map_mul_right", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Ring.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.dvd_sum", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Ring.List", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "rw", "exact"], "tactic_count": 5}
{"name": "List.sum_zipWith_distrib_left", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Ring.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.prod_map_neg", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Ring.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.prod_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Ring.Multiset", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "Multiset.prod_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Ring.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.prod_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Ring.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.sum_map_mul_left", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Ring.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.sum_map_mul_right", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Ring.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.dvd_sum", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Ring.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.prod_map_sum", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Ring.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.prod_map_add", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Ring.Multiset", "is_tactic_proof": true, "tactics": ["refine", "simp", "simp", "sum_map_add,", "mul_assoc,", "exact"], "tactic_count": 6}
{"name": "Commute.multiset_sum_right", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Ring.Multiset", "is_tactic_proof": true, "tactics": ["induction", "rw", "exact"], "tactic_count": 3}
{"name": "Commute.multiset_sum_left", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Ring.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.even_sum_iff_even_card_odd", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Ring.Nat", "is_tactic_proof": true, "tactics": ["rw", "simp", "rw", "simp", "simp_rw"], "tactic_count": 5}
{"name": "Finset.odd_sum_iff_odd_card_odd", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Ring.Nat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.card_preimage_eq_sum_card_image_eq", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Ring.Nat", "is_tactic_proof": true, "tactics": ["classical", "let", "rw", "rw", "exact", "have", "rw", "refine", "simpa", "rw", "suffices", "congr_arg", "intro", "simpa"], "tactic_count": 14}
{"name": "Finset.sum_sym2_filter_not_isDiag", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Sym", "is_tactic_proof": true, "tactics": ["rw", "conv_rhs", "refine", "all_goals"], "tactic_count": 4}
{"name": "Finset.sum_count_of_mem_sym", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.Sym", "is_tactic_proof": true, "tactics": ["simp_all"], "tactic_count": 1}
{"name": "WithTop.coe_sum", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.sum_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.WithTop", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "WithTop.sum_ne_top", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.WithTop", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WithTop.sum_lt_top", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.WithTop", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WithTop.prod_ne_top", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.prod_lt_top", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.prod_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.WithTop", "is_tactic_proof": true, "tactics": ["classical", "refine", "refine", "intros", "simp_all"], "tactic_count": 5}
{"name": "WithTop.prod_eq_top_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.WithTop", "is_tactic_proof": true, "tactics": ["by_contra", "apply", "calc"], "tactic_count": 3}
{"name": "WithTop.prod_eq_top_ex_top", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.WithTop", "is_tactic_proof": true, "tactics": ["contrapose", "exact"], "tactic_count": 2}
{"name": "WithTop.prod_eq_top_iff", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.WithTop", "is_tactic_proof": true, "tactics": ["constructor", "exact", "exact"], "tactic_count": 3}
{"name": "WithBot.coe_sum", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.sum_eq_bot_iff", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.WithTop", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "WithBot.bot_lt_sum_iff", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.WithTop", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WithBot.sum_lt_bot", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.prod_ne_bot", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.bot_lt_prod", "kind": "theorem", "module": "Mathlib.Algebra.BigOperators.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCoeSortCSAType", "kind": "instance", "module": "Mathlib.Algebra.BrauerGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBrauerEquivalent", "kind": "abbrev", "module": "Mathlib.Algebra.BrauerGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBrauerEquivalent.refl", "kind": "theorem", "module": "Mathlib.Algebra.BrauerGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBrauerEquivalent.symm", "kind": "theorem", "module": "Mathlib.Algebra.BrauerGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBrauerEquivalent.trans", "kind": "theorem", "module": "Mathlib.Algebra.BrauerGroup.Defs", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "exact", "compAlgEquiv", "iso1.mapMatrix", "compAlgEquiv", "reindexAlgEquiv", "compAlgEquiv", "iso2.mapMatrix.trans"], "tactic_count": 9}
{"name": "IsBrauerEquivalent.is_eqv", "kind": "theorem", "module": "Mathlib.Algebra.BrauerGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Brauer.CSA_Setoid", "kind": "definition", "module": "Mathlib.Algebra.BrauerGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BrauerGroup", "kind": "abbrev", "module": "Mathlib.Algebra.BrauerGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgCat.instCoeSortType", "kind": "instance", "module": "Mathlib.Algebra.Category.AlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgCat.of", "kind": "abbrev", "module": "Mathlib.Algebra.Category.AlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgCat.coe_of", "kind": "theorem", "module": "Mathlib.Algebra.Category.AlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgCat.instCategory", "kind": "instance", "module": "Mathlib.Algebra.Category.AlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgCat.instConcreteCategoryAlgHomCarrier", "kind": "instance", "module": "Mathlib.Algebra.Category.AlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgCat.Hom.hom", "kind": "abbrev", "module": "Mathlib.Algebra.Category.AlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgCat.ofHom", "kind": "abbrev", "module": "Mathlib.Algebra.Category.AlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgCat.Hom.Simps.hom", "kind": "definition", "module": "Mathlib.Algebra.Category.AlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgCat.hom_id", "kind": "theorem", "module": "Mathlib.Algebra.Category.AlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgCat.id_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.AlgCat.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgCat.hom_comp", "kind": "theorem", "module": "Mathlib.Algebra.Category.AlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgCat.comp_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.AlgCat.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgCat.hom_ext", "kind": "theorem", "module": "Mathlib.Algebra.Category.AlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgCat.hom_ofHom", "kind": "theorem", "module": "Mathlib.Algebra.Category.AlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgCat.ofHom_hom", "kind": "theorem", "module": "Mathlib.Algebra.Category.AlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgCat.ofHom_id", "kind": "theorem", "module": "Mathlib.Algebra.Category.AlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgCat.ofHom_comp", "kind": "theorem", "module": "Mathlib.Algebra.Category.AlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgCat.ofHom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.AlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgCat.inv_hom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.AlgCat.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgCat.hom_inv_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.AlgCat.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgCat.instInhabited", "kind": "instance", "module": "Mathlib.Algebra.Category.AlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgCat.forget_obj", "kind": "theorem", "module": "Mathlib.Algebra.Category.AlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgCat.forget_map", "kind": "theorem", "module": "Mathlib.Algebra.Category.AlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgCat.instRingObjForget", "kind": "instance", "module": "Mathlib.Algebra.Category.AlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgCat.instAlgebraObjForget", "kind": "instance", "module": "Mathlib.Algebra.Category.AlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgCat.hasForgetToRing", "kind": "instance", "module": "Mathlib.Algebra.Category.AlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgCat.hasForgetToModule", "kind": "instance", "module": "Mathlib.Algebra.Category.AlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgCat.forget₂_module_obj", "kind": "theorem", "module": "Mathlib.Algebra.Category.AlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgCat.forget₂_module_map", "kind": "theorem", "module": "Mathlib.Algebra.Category.AlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgCat.free", "kind": "definition", "module": "Mathlib.Algebra.Category.AlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgCat.adj", "kind": "definition", "module": "Mathlib.Algebra.Category.AlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgCat.instIsRightAdjointForget", "kind": "instance", "module": "Mathlib.Algebra.Category.AlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.toAlgebraIso", "kind": "definition", "module": "Mathlib.Algebra.Category.AlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.toAlgEquiv", "kind": "definition", "module": "Mathlib.Algebra.Category.AlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "algEquivIsoAlgebraIso", "kind": "definition", "module": "Mathlib.Algebra.Category.AlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgCat.forget_reflects_isos", "kind": "instance", "module": "Mathlib.Algebra.Category.AlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgCat.semiringObj", "kind": "instance", "module": "Mathlib.Algebra.Category.AlgCat.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgCat.algebraObj", "kind": "instance", "module": "Mathlib.Algebra.Category.AlgCat.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgCat.sectionsSubalgebra", "kind": "definition", "module": "Mathlib.Algebra.Category.AlgCat.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgCat.instRingElemForallObjCompForgetSections", "kind": "instance", "module": "Mathlib.Algebra.Category.AlgCat.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgCat.instAlgebraElemForallObjCompForgetSections", "kind": "instance", "module": "Mathlib.Algebra.Category.AlgCat.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgCat.instSmallSubtypeForallCarrierObjMemSubalgebraSectionsSubalgebra", "kind": "instance", "module": "Mathlib.Algebra.Category.AlgCat.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgCat.limitSemiring", "kind": "instance", "module": "Mathlib.Algebra.Category.AlgCat.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgCat.limitAlgebra", "kind": "instance", "module": "Mathlib.Algebra.Category.AlgCat.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgCat.limitπAlgHom", "kind": "definition", "module": "Mathlib.Algebra.Category.AlgCat.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgCat.HasLimits.limitCone", "kind": "definition", "module": "Mathlib.Algebra.Category.AlgCat.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgCat.HasLimits.limitConeIsLimit", "kind": "definition", "module": "Mathlib.Algebra.Category.AlgCat.Limits", "is_tactic_proof": false, "tactics": ["refine", "congr", "ext", "simp", "intro", "ext", "simp", "apply", "ext", "simp", "apply", "intro", "ext", "simp", "apply", "intro", "simp", "apply", "apply", "ext", "exact"], "tactic_count": 21}
{"name": "AlgCat.hasLimitsOfSize", "kind": "theorem", "module": "Mathlib.Algebra.Category.AlgCat.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgCat.hasLimits", "kind": "instance", "module": "Mathlib.Algebra.Category.AlgCat.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgCat.forget₂Ring_preservesLimitsOfSize", "kind": "instance", "module": "Mathlib.Algebra.Category.AlgCat.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgCat.forget₂Ring_preservesLimits", "kind": "instance", "module": "Mathlib.Algebra.Category.AlgCat.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgCat.forget₂Module_preservesLimitsOfSize", "kind": "instance", "module": "Mathlib.Algebra.Category.AlgCat.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgCat.forget₂Module_preservesLimits", "kind": "instance", "module": "Mathlib.Algebra.Category.AlgCat.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgCat.forget_preservesLimitsOfSize", "kind": "instance", "module": "Mathlib.Algebra.Category.AlgCat.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgCat.forget_preservesLimits", "kind": "instance", "module": "Mathlib.Algebra.Category.AlgCat.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgCat.instMonoidalCategory.tensorObj", "kind": "abbrev", "module": "Mathlib.Algebra.Category.AlgCat.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgCat.instMonoidalCategory.tensorHom", "kind": "abbrev", "module": "Mathlib.Algebra.Category.AlgCat.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgCat.instMonoidalCategoryStruct", "kind": "instance", "module": "Mathlib.Algebra.Category.AlgCat.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgCat.hom_tensorHom", "kind": "theorem", "module": "Mathlib.Algebra.Category.AlgCat.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgCat.hom_whiskerLeft", "kind": "theorem", "module": "Mathlib.Algebra.Category.AlgCat.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgCat.hom_whiskerRight", "kind": "theorem", "module": "Mathlib.Algebra.Category.AlgCat.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgCat.hom_hom_leftUnitor", "kind": "theorem", "module": "Mathlib.Algebra.Category.AlgCat.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgCat.hom_inv_leftUnitor", "kind": "theorem", "module": "Mathlib.Algebra.Category.AlgCat.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgCat.hom_hom_rightUnitor", "kind": "theorem", "module": "Mathlib.Algebra.Category.AlgCat.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgCat.hom_inv_rightUnitor", "kind": "theorem", "module": "Mathlib.Algebra.Category.AlgCat.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgCat.hom_hom_associator", "kind": "theorem", "module": "Mathlib.Algebra.Category.AlgCat.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgCat.hom_inv_associator", "kind": "theorem", "module": "Mathlib.Algebra.Category.AlgCat.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgCat.instMonoidalCategory", "kind": "instance", "module": "Mathlib.Algebra.Category.AlgCat.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgCat._example", "kind": "example", "module": "Mathlib.Algebra.Category.AlgCat.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgCat.instBraidedCategory", "kind": "instance", "module": "Mathlib.Algebra.Category.AlgCat.Symmetric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgCat.instBraidedModuleCatForget₂", "kind": "instance", "module": "Mathlib.Algebra.Category.AlgCat.Symmetric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgCat.instSymmetricCategory", "kind": "instance", "module": "Mathlib.Algebra.Category.AlgCat.Symmetric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgCat.instCoeSortType", "kind": "instance", "module": "Mathlib.Algebra.Category.BialgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgCat.of", "kind": "definition", "module": "Mathlib.Algebra.Category.BialgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgCat.of_comul", "kind": "theorem", "module": "Mathlib.Algebra.Category.BialgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgCat.of_counit", "kind": "theorem", "module": "Mathlib.Algebra.Category.BialgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgCat.category", "kind": "instance", "module": "Mathlib.Algebra.Category.BialgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgCat.concreteCategory", "kind": "instance", "module": "Mathlib.Algebra.Category.BialgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgCat.Hom.toBialgHom", "kind": "abbrev", "module": "Mathlib.Algebra.Category.BialgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgCat.ofHom", "kind": "abbrev", "module": "Mathlib.Algebra.Category.BialgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgCat.Hom.toBialgHom_injective", "kind": "theorem", "module": "Mathlib.Algebra.Category.BialgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgCat.hom_ext", "kind": "theorem", "module": "Mathlib.Algebra.Category.BialgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgCat.toBialgHom_comp", "kind": "theorem", "module": "Mathlib.Algebra.Category.BialgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgCat.toBialgHom_id", "kind": "theorem", "module": "Mathlib.Algebra.Category.BialgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgCat.hasForget", "kind": "instance", "module": "Mathlib.Algebra.Category.BialgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgCat.hasForgetToAlgebra", "kind": "instance", "module": "Mathlib.Algebra.Category.BialgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgCat.forget₂_algebra_obj", "kind": "theorem", "module": "Mathlib.Algebra.Category.BialgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgCat.forget₂_algebra_map", "kind": "theorem", "module": "Mathlib.Algebra.Category.BialgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgCat.hasForgetToCoalgebra", "kind": "instance", "module": "Mathlib.Algebra.Category.BialgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgCat.forget₂_coalgebra_obj", "kind": "theorem", "module": "Mathlib.Algebra.Category.BialgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgCat.forget₂_coalgebra_map", "kind": "theorem", "module": "Mathlib.Algebra.Category.BialgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgEquiv.toBialgIso", "kind": "definition", "module": "Mathlib.Algebra.Category.BialgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgEquiv.toBialgIso_refl", "kind": "theorem", "module": "Mathlib.Algebra.Category.BialgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgEquiv.toBialgIso_symm", "kind": "theorem", "module": "Mathlib.Algebra.Category.BialgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgEquiv.toBialgIso_trans", "kind": "theorem", "module": "Mathlib.Algebra.Category.BialgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.toBialgEquiv", "kind": "definition", "module": "Mathlib.Algebra.Category.BialgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.toBialgEquiv_toBialgHom", "kind": "theorem", "module": "Mathlib.Algebra.Category.BialgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.toBialgEquiv_refl", "kind": "theorem", "module": "Mathlib.Algebra.Category.BialgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.toBialgEquiv_symm", "kind": "theorem", "module": "Mathlib.Algebra.Category.BialgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.toBialgEquiv_trans", "kind": "theorem", "module": "Mathlib.Algebra.Category.BialgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgCat.forget_reflects_isos", "kind": "instance", "module": "Mathlib.Algebra.Category.BialgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgCat.instMonoidalCategoryStruct", "kind": "instance", "module": "Mathlib.Algebra.Category.BialgCat.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgCat.MonoidalCategory.inducingFunctorData", "kind": "definition", "module": "Mathlib.Algebra.Category.BialgCat.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgCat.instMonoidalCategory", "kind": "instance", "module": "Mathlib.Algebra.Category.BialgCat.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgCat.instMonoidalAlgCatForget₂", "kind": "instance", "module": "Mathlib.Algebra.Category.BialgCat.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgCat.instMonoidalCoalgCatForget₂", "kind": "instance", "module": "Mathlib.Algebra.Category.BialgCat.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoolRing.instCoeSortType", "kind": "instance", "module": "Mathlib.Algebra.Category.BoolRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoolRing.coe_of", "kind": "theorem", "module": "Mathlib.Algebra.Category.BoolRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoolRing.instInhabited", "kind": "instance", "module": "Mathlib.Algebra.Category.BoolRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoolRing.instCategory", "kind": "instance", "module": "Mathlib.Algebra.Category.BoolRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoolRing.instConcreteCategoryRingHomCarrier", "kind": "instance", "module": "Mathlib.Algebra.Category.BoolRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoolRing.Hom.hom", "kind": "abbrev", "module": "Mathlib.Algebra.Category.BoolRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoolRing.ofHom", "kind": "abbrev", "module": "Mathlib.Algebra.Category.BoolRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoolRing.hom_ext", "kind": "theorem", "module": "Mathlib.Algebra.Category.BoolRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoolRing.hasForgetToCommRing", "kind": "instance", "module": "Mathlib.Algebra.Category.BoolRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoolRing.Iso.mk", "kind": "definition", "module": "Mathlib.Algebra.Category.BoolRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instBooleanAlgebraCarrierToBddLatToBddDistLat", "kind": "instance", "module": "Mathlib.Algebra.Category.BoolRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instBooleanRingCarrierToBddLatToBddDistLatOfAsBoolAlg", "kind": "instance", "module": "Mathlib.Algebra.Category.BoolRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoolRing.hasForgetToBoolAlg", "kind": "instance", "module": "Mathlib.Algebra.Category.BoolRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoolAlg.hasForgetToBoolRing", "kind": "instance", "module": "Mathlib.Algebra.Category.BoolRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "boolRingCatEquivBoolAlg", "kind": "definition", "module": "Mathlib.Algebra.Category.BoolRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgCat.instCoeSortType", "kind": "instance", "module": "Mathlib.Algebra.Category.CoalgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgCat.moduleCat_of_toModuleCat", "kind": "theorem", "module": "Mathlib.Algebra.Category.CoalgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgCat.of", "kind": "abbrev", "module": "Mathlib.Algebra.Category.CoalgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgCat.of_comul", "kind": "theorem", "module": "Mathlib.Algebra.Category.CoalgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgCat.of_counit", "kind": "theorem", "module": "Mathlib.Algebra.Category.CoalgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgCat.category", "kind": "instance", "module": "Mathlib.Algebra.Category.CoalgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgCat.concreteCategory", "kind": "instance", "module": "Mathlib.Algebra.Category.CoalgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgCat.Hom.toCoalgHom", "kind": "abbrev", "module": "Mathlib.Algebra.Category.CoalgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgCat.ofHom", "kind": "abbrev", "module": "Mathlib.Algebra.Category.CoalgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgCat.Hom.toCoalgHom_injective", "kind": "theorem", "module": "Mathlib.Algebra.Category.CoalgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgCat.hom_ext", "kind": "theorem", "module": "Mathlib.Algebra.Category.CoalgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgCat.toCoalgHom_comp", "kind": "theorem", "module": "Mathlib.Algebra.Category.CoalgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgCat.toCoalgHom_id", "kind": "theorem", "module": "Mathlib.Algebra.Category.CoalgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgCat.hasForgetToModule", "kind": "instance", "module": "Mathlib.Algebra.Category.CoalgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgCat.forget₂_obj", "kind": "theorem", "module": "Mathlib.Algebra.Category.CoalgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgCat.forget₂_map", "kind": "theorem", "module": "Mathlib.Algebra.Category.CoalgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgEquiv.toCoalgIso", "kind": "definition", "module": "Mathlib.Algebra.Category.CoalgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgEquiv.toCoalgIso_refl", "kind": "theorem", "module": "Mathlib.Algebra.Category.CoalgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgEquiv.toCoalgIso_symm", "kind": "theorem", "module": "Mathlib.Algebra.Category.CoalgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgEquiv.toCoalgIso_trans", "kind": "theorem", "module": "Mathlib.Algebra.Category.CoalgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.toCoalgEquiv", "kind": "definition", "module": "Mathlib.Algebra.Category.CoalgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.toCoalgEquiv_toCoalgHom", "kind": "theorem", "module": "Mathlib.Algebra.Category.CoalgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.toCoalgEquiv_refl", "kind": "theorem", "module": "Mathlib.Algebra.Category.CoalgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.toCoalgEquiv_symm", "kind": "theorem", "module": "Mathlib.Algebra.Category.CoalgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.toCoalgEquiv_trans", "kind": "theorem", "module": "Mathlib.Algebra.Category.CoalgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgCat.forget_reflects_isos", "kind": "instance", "module": "Mathlib.Algebra.Category.CoalgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgCat.MonoidalCategoryAux.tensorObj_comul", "kind": "theorem", "module": "Mathlib.Algebra.Category.CoalgCat.ComonEquivalence", "is_tactic_proof": true, "tactics": ["rw", "simp", "toComonObj_X,", "rfl"], "tactic_count": 4}
{"name": "CoalgCat.MonoidalCategoryAux.tensorHom_toLinearMap", "kind": "theorem", "module": "Mathlib.Algebra.Category.CoalgCat.ComonEquivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgCat.MonoidalCategoryAux.associator_hom_toLinearMap", "kind": "theorem", "module": "Mathlib.Algebra.Category.CoalgCat.ComonEquivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgCat.MonoidalCategoryAux.leftUnitor_hom_toLinearMap", "kind": "theorem", "module": "Mathlib.Algebra.Category.CoalgCat.ComonEquivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgCat.MonoidalCategoryAux.rightUnitor_hom_toLinearMap", "kind": "theorem", "module": "Mathlib.Algebra.Category.CoalgCat.ComonEquivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgCat.MonoidalCategoryAux.comul_tensorObj", "kind": "theorem", "module": "Mathlib.Algebra.Category.CoalgCat.ComonEquivalence", "is_tactic_proof": true, "tactics": ["rw", "simp", "rfl"], "tactic_count": 3}
{"name": "CoalgCat.MonoidalCategoryAux.comul_tensorObj_tensorObj_right", "kind": "theorem", "module": "Mathlib.Algebra.Category.CoalgCat.ComonEquivalence", "is_tactic_proof": true, "tactics": ["rw", "simp", "simp", "rfl"], "tactic_count": 4}
{"name": "CoalgCat.MonoidalCategoryAux.comul_tensorObj_tensorObj_left", "kind": "theorem", "module": "Mathlib.Algebra.Category.CoalgCat.ComonEquivalence", "is_tactic_proof": true, "tactics": ["rw", "dsimp", "simp", "simp", "rfl"], "tactic_count": 5}
{"name": "CoalgCat.MonoidalCategoryAux.counit_tensorObj", "kind": "theorem", "module": "Mathlib.Algebra.Category.CoalgCat.ComonEquivalence", "is_tactic_proof": true, "tactics": ["rw", "simp", "rfl"], "tactic_count": 3}
{"name": "CoalgCat.MonoidalCategoryAux.counit_tensorObj_tensorObj_right", "kind": "theorem", "module": "Mathlib.Algebra.Category.CoalgCat.ComonEquivalence", "is_tactic_proof": true, "tactics": ["rw", "simp", "rfl"], "tactic_count": 3}
{"name": "CoalgCat.MonoidalCategoryAux.counit_tensorObj_tensorObj_left", "kind": "theorem", "module": "Mathlib.Algebra.Category.CoalgCat.ComonEquivalence", "is_tactic_proof": true, "tactics": ["rw", "simp", "rfl"], "tactic_count": 3}
{"name": "CoalgCat.instMonoidalCategoryStruct", "kind": "instance", "module": "Mathlib.Algebra.Category.CoalgCat.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgCat.MonoidalCategory.inducingFunctorData", "kind": "definition", "module": "Mathlib.Algebra.Category.CoalgCat.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgCat.instMonoidalCategory", "kind": "instance", "module": "Mathlib.Algebra.Category.CoalgCat.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommAlgCat.instCoeSortType", "kind": "instance", "module": "Mathlib.Algebra.Category.CommAlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommAlgCat.of", "kind": "abbrev", "module": "Mathlib.Algebra.Category.CommAlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommAlgCat.coe_of", "kind": "theorem", "module": "Mathlib.Algebra.Category.CommAlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommAlgCat.instCategory", "kind": "instance", "module": "Mathlib.Algebra.Category.CommAlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommAlgCat.instConcreteCategoryAlgHomCarrier", "kind": "instance", "module": "Mathlib.Algebra.Category.CommAlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommAlgCat.Hom.hom", "kind": "abbrev", "module": "Mathlib.Algebra.Category.CommAlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommAlgCat.ofHom", "kind": "abbrev", "module": "Mathlib.Algebra.Category.CommAlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommAlgCat.Hom.Simps.hom", "kind": "definition", "module": "Mathlib.Algebra.Category.CommAlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommAlgCat.hom_id", "kind": "theorem", "module": "Mathlib.Algebra.Category.CommAlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommAlgCat.id_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.CommAlgCat.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CommAlgCat.hom_comp", "kind": "theorem", "module": "Mathlib.Algebra.Category.CommAlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommAlgCat.comp_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.CommAlgCat.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CommAlgCat.hom_ext", "kind": "theorem", "module": "Mathlib.Algebra.Category.CommAlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommAlgCat.hom_ofHom", "kind": "theorem", "module": "Mathlib.Algebra.Category.CommAlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommAlgCat.ofHom_hom", "kind": "theorem", "module": "Mathlib.Algebra.Category.CommAlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommAlgCat.ofHom_id", "kind": "theorem", "module": "Mathlib.Algebra.Category.CommAlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommAlgCat.ofHom_comp", "kind": "theorem", "module": "Mathlib.Algebra.Category.CommAlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommAlgCat.ofHom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.CommAlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommAlgCat.inv_hom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.CommAlgCat.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CommAlgCat.hom_inv_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.CommAlgCat.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CommAlgCat.instInhabited", "kind": "instance", "module": "Mathlib.Algebra.Category.CommAlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommAlgCat.forget_obj", "kind": "theorem", "module": "Mathlib.Algebra.Category.CommAlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommAlgCat.forget_map", "kind": "theorem", "module": "Mathlib.Algebra.Category.CommAlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommAlgCat.instCommRingObjForget", "kind": "instance", "module": "Mathlib.Algebra.Category.CommAlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommAlgCat.instAlgebraObjForget", "kind": "instance", "module": "Mathlib.Algebra.Category.CommAlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommAlgCat.hasForgetToCommRingCat", "kind": "instance", "module": "Mathlib.Algebra.Category.CommAlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommAlgCat.hasForgetToAlgCat", "kind": "instance", "module": "Mathlib.Algebra.Category.CommAlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommAlgCat.forget₂_commRingCat_obj", "kind": "theorem", "module": "Mathlib.Algebra.Category.CommAlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommAlgCat.forget₂_commRingCat_map", "kind": "theorem", "module": "Mathlib.Algebra.Category.CommAlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommAlgCat.forget₂_algCat_obj", "kind": "theorem", "module": "Mathlib.Algebra.Category.CommAlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommAlgCat.forget₂_algCat_map", "kind": "theorem", "module": "Mathlib.Algebra.Category.CommAlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommAlgCat.isoMk", "kind": "definition", "module": "Mathlib.Algebra.Category.CommAlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommAlgCat.algEquivOfIso", "kind": "definition", "module": "Mathlib.Algebra.Category.CommAlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommAlgCat.isoEquivAlgEquiv", "kind": "definition", "module": "Mathlib.Algebra.Category.CommAlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommAlgCat.reflectsIsomorphisms_forget", "kind": "instance", "module": "Mathlib.Algebra.Category.CommAlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommAlgCat.uliftFunctor", "kind": "definition", "module": "Mathlib.Algebra.Category.CommAlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommAlgCat.fullyFaithfulUliftFunctor", "kind": "definition", "module": "Mathlib.Algebra.Category.CommAlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommAlgCat.instFullUliftFunctor", "kind": "instance", "module": "Mathlib.Algebra.Category.CommAlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommAlgCat.instFaithfulUliftFunctor", "kind": "instance", "module": "Mathlib.Algebra.Category.CommAlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "commAlgCatEquivUnder", "kind": "definition", "module": "Mathlib.Algebra.Category.CommAlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instHasColimitsCommAlgCat", "kind": "instance", "module": "Mathlib.Algebra.Category.CommAlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instHasLimitsCommAlgCat", "kind": "instance", "module": "Mathlib.Algebra.Category.CommAlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FGAlgCat", "kind": "abbrev", "module": "Mathlib.Algebra.Category.CommAlgCat.FiniteType", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFiniteTypeCarrierObjCommAlgCat", "kind": "instance", "module": "Mathlib.Algebra.Category.CommAlgCat.FiniteType", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FGAlgCatSkeleton.eval", "kind": "definition", "module": "Mathlib.Algebra.Category.CommAlgCat.FiniteType", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.FiniteType.exists_fgAlgCatSkeleton", "kind": "theorem", "module": "Mathlib.Algebra.Category.CommAlgCat.FiniteType", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "FGAlgCat.uliftFunctor", "kind": "definition", "module": "Mathlib.Algebra.Category.CommAlgCat.FiniteType", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FGAlgCat.fullyFaithfulUliftFunctor", "kind": "definition", "module": "Mathlib.Algebra.Category.CommAlgCat.FiniteType", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFullFGAlgCatUliftFunctor", "kind": "instance", "module": "Mathlib.Algebra.Category.CommAlgCat.FiniteType", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFaithfulFGAlgCatUliftFunctor", "kind": "instance", "module": "Mathlib.Algebra.Category.CommAlgCat.FiniteType", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instEssentiallySmallFGAlgCat", "kind": "instance", "module": "Mathlib.Algebra.Category.CommAlgCat.FiniteType", "is_tactic_proof": false, "tactics": ["suffices", "exact", "rw", "refine", "let", "refine", "simp", "obtain", "exact", "refine", "obtain", "obtain", "let", "refine", "ext", "obtain", "exact"], "tactic_count": 17}
{"name": "FGAlgCat.equivUnder", "kind": "definition", "module": "Mathlib.Algebra.Category.CommAlgCat.FiniteType", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "essentiallySmall_of_le", "kind": "theorem", "module": "Mathlib.Algebra.Category.CommAlgCat.FiniteType", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommAlgCat.binaryCofan", "kind": "definition", "module": "Mathlib.Algebra.Category.CommAlgCat.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommAlgCat.binaryCofan_inl", "kind": "theorem", "module": "Mathlib.Algebra.Category.CommAlgCat.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommAlgCat.binaryCofan_inr", "kind": "theorem", "module": "Mathlib.Algebra.Category.CommAlgCat.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommAlgCat.binaryCofan_pt", "kind": "theorem", "module": "Mathlib.Algebra.Category.CommAlgCat.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommAlgCat.binaryCofanIsColimit", "kind": "definition", "module": "Mathlib.Algebra.Category.CommAlgCat.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommAlgCat.isInitialSelf", "kind": "definition", "module": "Mathlib.Algebra.Category.CommAlgCat.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommAlgCat.instMonoidalCategory", "kind": "instance", "module": "Mathlib.Algebra.Category.CommAlgCat.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommAlgCat.coe_tensorUnit", "kind": "theorem", "module": "Mathlib.Algebra.Category.CommAlgCat.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommAlgCat.coe_tensorObj", "kind": "theorem", "module": "Mathlib.Algebra.Category.CommAlgCat.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommAlgCat.tensorHom_hom", "kind": "theorem", "module": "Mathlib.Algebra.Category.CommAlgCat.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommAlgCat.whiskerRight_hom", "kind": "theorem", "module": "Mathlib.Algebra.Category.CommAlgCat.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommAlgCat.whiskerLeft_hom", "kind": "theorem", "module": "Mathlib.Algebra.Category.CommAlgCat.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommAlgCat.associator_hom_hom", "kind": "theorem", "module": "Mathlib.Algebra.Category.CommAlgCat.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommAlgCat.associator_inv_hom", "kind": "theorem", "module": "Mathlib.Algebra.Category.CommAlgCat.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommAlgCat.instBraidedCategory", "kind": "instance", "module": "Mathlib.Algebra.Category.CommAlgCat.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommAlgCat.braiding_hom_hom", "kind": "theorem", "module": "Mathlib.Algebra.Category.CommAlgCat.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommAlgCat.braiding_inv_hom", "kind": "theorem", "module": "Mathlib.Algebra.Category.CommAlgCat.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommAlgCat.instCartesianMonoidalCategoryOpposite", "kind": "instance", "module": "Mathlib.Algebra.Category.CommAlgCat.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommAlgCat.fst_unop_hom", "kind": "theorem", "module": "Mathlib.Algebra.Category.CommAlgCat.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommAlgCat.snd_unop_hom", "kind": "theorem", "module": "Mathlib.Algebra.Category.CommAlgCat.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommAlgCat.toUnit_unop_hom", "kind": "theorem", "module": "Mathlib.Algebra.Category.CommAlgCat.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommAlgCat.lift_unop_hom", "kind": "theorem", "module": "Mathlib.Algebra.Category.CommAlgCat.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommBialgCat.instCoeSortType", "kind": "instance", "module": "Mathlib.Algebra.Category.CommBialgCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommBialgCat.of", "kind": "abbrev", "module": "Mathlib.Algebra.Category.CommBialgCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommBialgCat.coe_of", "kind": "theorem", "module": "Mathlib.Algebra.Category.CommBialgCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommBialgCat.instCategory", "kind": "instance", "module": "Mathlib.Algebra.Category.CommBialgCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommBialgCat.instConcreteCategoryBialgHomCarrier", "kind": "instance", "module": "Mathlib.Algebra.Category.CommBialgCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommBialgCat.Hom.hom", "kind": "abbrev", "module": "Mathlib.Algebra.Category.CommBialgCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommBialgCat.ofHom", "kind": "abbrev", "module": "Mathlib.Algebra.Category.CommBialgCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommBialgCat.Hom.Simps.hom", "kind": "definition", "module": "Mathlib.Algebra.Category.CommBialgCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommBialgCat.hom_id", "kind": "theorem", "module": "Mathlib.Algebra.Category.CommBialgCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommBialgCat.hom_comp", "kind": "theorem", "module": "Mathlib.Algebra.Category.CommBialgCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommBialgCat.id_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.CommBialgCat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CommBialgCat.comp_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.CommBialgCat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CommBialgCat.hom_ext", "kind": "theorem", "module": "Mathlib.Algebra.Category.CommBialgCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommBialgCat.hom_ofHom", "kind": "theorem", "module": "Mathlib.Algebra.Category.CommBialgCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommBialgCat.ofHom_hom", "kind": "theorem", "module": "Mathlib.Algebra.Category.CommBialgCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommBialgCat.ofHom_id", "kind": "theorem", "module": "Mathlib.Algebra.Category.CommBialgCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommBialgCat.ofHom_comp", "kind": "theorem", "module": "Mathlib.Algebra.Category.CommBialgCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommBialgCat.ofHom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.CommBialgCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommBialgCat.inv_hom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.CommBialgCat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CommBialgCat.hom_inv_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.CommBialgCat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CommBialgCat.instInhabited", "kind": "instance", "module": "Mathlib.Algebra.Category.CommBialgCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommBialgCat.forget_obj", "kind": "theorem", "module": "Mathlib.Algebra.Category.CommBialgCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommBialgCat.forget_map", "kind": "theorem", "module": "Mathlib.Algebra.Category.CommBialgCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommBialgCat.instCommRingObjForget", "kind": "instance", "module": "Mathlib.Algebra.Category.CommBialgCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommBialgCat.instBialgebraObjForget", "kind": "instance", "module": "Mathlib.Algebra.Category.CommBialgCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommBialgCat.hasForgetToCommAlgCat", "kind": "instance", "module": "Mathlib.Algebra.Category.CommBialgCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommBialgCat.forget₂_commAlgCat_obj", "kind": "theorem", "module": "Mathlib.Algebra.Category.CommBialgCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommBialgCat.forget₂_commAlgCat_map", "kind": "theorem", "module": "Mathlib.Algebra.Category.CommBialgCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommBialgCat.ofSelfIso", "kind": "definition", "module": "Mathlib.Algebra.Category.CommBialgCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommBialgCat.isoMk", "kind": "definition", "module": "Mathlib.Algebra.Category.CommBialgCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommBialgCat.bialgEquivOfIso", "kind": "definition", "module": "Mathlib.Algebra.Category.CommBialgCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommBialgCat.isoEquivBialgEquiv", "kind": "definition", "module": "Mathlib.Algebra.Category.CommBialgCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommBialgCat.reflectsIsomorphisms_forget", "kind": "instance", "module": "Mathlib.Algebra.Category.CommBialgCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommAlgCat.monObjOpOf", "kind": "instance", "module": "Mathlib.Algebra.Category.CommBialgCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommAlgCat.one_op_of_unop_hom", "kind": "theorem", "module": "Mathlib.Algebra.Category.CommBialgCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommAlgCat.mul_op_of_unop_hom", "kind": "theorem", "module": "Mathlib.Algebra.Category.CommBialgCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsCommMonObjOppositeCommAlgCatOpOfOfIsCocomm", "kind": "instance", "module": "Mathlib.Algebra.Category.CommBialgCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsMonHomOppositeCommAlgCatOpOfHomToAlgHomBialgHom", "kind": "instance", "module": "Mathlib.Algebra.Category.CommBialgCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instBialgebraCarrierUnopCommAlgCatOfMonObjOpposite", "kind": "instance", "module": "Mathlib.Algebra.Category.CommBialgCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "commBialgCatEquivComonCommAlgCat", "kind": "definition", "module": "Mathlib.Algebra.Category.CommBialgCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "commBialgCatEquivComonCommAlgCat_functor_map_unop_hom", "kind": "theorem", "module": "Mathlib.Algebra.Category.CommBialgCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "commBialgCatEquivComonCommAlgCat_inverse_map_unop_hom", "kind": "theorem", "module": "Mathlib.Algebra.Category.CommBialgCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsCommMonObjOppositeCommAlgCatXUnopMonObjCommBialgCatFunctorCommBialgCatEquivComonCommAlgCatOfIsCocommCarrier", "kind": "instance", "module": "Mathlib.Algebra.Category.CommBialgCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousCohomology.Iobj", "kind": "abbrev", "module": "Mathlib.Algebra.Category.ContinuousCohomology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousCohomology.Iobj_ρ_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ContinuousCohomology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousCohomology.I", "kind": "definition", "module": "Mathlib.Algebra.Category.ContinuousCohomology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousCohomology.instAdditiveActionTopModuleCatI", "kind": "instance", "module": "Mathlib.Algebra.Category.ContinuousCohomology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousCohomology.instLinearActionTopModuleCatI", "kind": "instance", "module": "Mathlib.Algebra.Category.ContinuousCohomology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousCohomology.const", "kind": "definition", "module": "Mathlib.Algebra.Category.ContinuousCohomology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousCohomology.MultiInd.functor", "kind": "definition", "module": "Mathlib.Algebra.Category.ContinuousCohomology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousCohomology.MultiInd.d", "kind": "definition", "module": "Mathlib.Algebra.Category.ContinuousCohomology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousCohomology.MultiInd.d_zero", "kind": "theorem", "module": "Mathlib.Algebra.Category.ContinuousCohomology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousCohomology.MultiInd.d_succ", "kind": "theorem", "module": "Mathlib.Algebra.Category.ContinuousCohomology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousCohomology.MultiInd.d_comp_d", "kind": "theorem", "module": "Mathlib.Algebra.Category.ContinuousCohomology.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "rw", "rfl", "succ", "rw", "nth_rw", "rw", "rfl"], "tactic_count": 9}
{"name": "ContinuousCohomology.MultiInd.complex", "kind": "definition", "module": "Mathlib.Algebra.Category.ContinuousCohomology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousCohomology.invariants", "kind": "definition", "module": "Mathlib.Algebra.Category.ContinuousCohomology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousCohomology.instLinearActionTopModuleCatInvariants", "kind": "instance", "module": "Mathlib.Algebra.Category.ContinuousCohomology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousCohomology.instAdditiveActionTopModuleCatInvariants", "kind": "instance", "module": "Mathlib.Algebra.Category.ContinuousCohomology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousCohomology.homogeneousCochains", "kind": "definition", "module": "Mathlib.Algebra.Category.ContinuousCohomology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousCohomology", "kind": "definition", "module": "Mathlib.Algebra.Category.ContinuousCohomology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousCohomology.kerHomogeneousCochainsZeroEquiv", "kind": "definition", "module": "Mathlib.Algebra.Category.ContinuousCohomology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousCohomology.continuousCohomologyZeroIso", "kind": "definition", "module": "Mathlib.Algebra.Category.ContinuousCohomology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FGModuleCat.instIsIsoCoimageImageComparison", "kind": "instance", "module": "Mathlib.Algebra.Category.FGModuleCat.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FGModuleCat.instAbelian", "kind": "instance", "module": "Mathlib.Algebra.Category.FGModuleCat.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.isFG", "kind": "definition", "module": "Mathlib.Algebra.Category.FGModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.isFG_iff", "kind": "theorem", "module": "Mathlib.Algebra.Category.FGModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FGModuleCat", "kind": "abbrev", "module": "Mathlib.Algebra.Category.FGModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FGModuleCat.carrier", "kind": "definition", "module": "Mathlib.Algebra.Category.FGModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCoeSortFGModuleCatType", "kind": "instance", "module": "Mathlib.Algebra.Category.FGModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FGModuleCat.obj_carrier", "kind": "theorem", "module": "Mathlib.Algebra.Category.FGModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instAddCommGroupCarrier", "kind": "instance", "module": "Mathlib.Algebra.Category.FGModuleCat.Basic", "is_tactic_proof": true, "tactics": ["change", "infer_instance"], "tactic_count": 2}
{"name": "instModuleCarrier", "kind": "instance", "module": "Mathlib.Algebra.Category.FGModuleCat.Basic", "is_tactic_proof": true, "tactics": ["change", "infer_instance"], "tactic_count": 2}
{"name": "instFiniteCarrier", "kind": "instance", "module": "Mathlib.Algebra.Category.FGModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFiniteCarrierObjModuleCatIsFG", "kind": "instance", "module": "Mathlib.Algebra.Category.FGModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FGModuleCat.hom_hom_comp", "kind": "theorem", "module": "Mathlib.Algebra.Category.FGModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FGModuleCat.hom_hom_id", "kind": "theorem", "module": "Mathlib.Algebra.Category.FGModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FGModuleCat.instInhabited", "kind": "instance", "module": "Mathlib.Algebra.Category.FGModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FGModuleCat.of", "kind": "abbrev", "module": "Mathlib.Algebra.Category.FGModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FGModuleCat.of_carrier", "kind": "theorem", "module": "Mathlib.Algebra.Category.FGModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FGModuleCat.ofHom", "kind": "abbrev", "module": "Mathlib.Algebra.Category.FGModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FGModuleCat.hom_ext", "kind": "theorem", "module": "Mathlib.Algebra.Category.FGModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FGModuleCat.instFiniteCarrier", "kind": "instance", "module": "Mathlib.Algebra.Category.FGModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FGModuleCat.instFullModuleCatForget₂", "kind": "instance", "module": "Mathlib.Algebra.Category.FGModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FGModuleCat.isoToLinearEquiv", "kind": "definition", "module": "Mathlib.Algebra.Category.FGModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.toFGModuleCatIso", "kind": "definition", "module": "Mathlib.Algebra.Category.FGModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FGModuleCat.ulift", "kind": "definition", "module": "Mathlib.Algebra.Category.FGModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FGModuleCat.fullyFaithfulULift", "kind": "definition", "module": "Mathlib.Algebra.Category.FGModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FGModuleCat.instFaithfulUlift", "kind": "instance", "module": "Mathlib.Algebra.Category.FGModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FGModuleCat.instFullUlift", "kind": "instance", "module": "Mathlib.Algebra.Category.FGModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FGModuleCat.instIsMonoidalModuleCatIsFG", "kind": "instance", "module": "Mathlib.Algebra.Category.FGModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FGModuleCat.tensorUnit_obj", "kind": "theorem", "module": "Mathlib.Algebra.Category.FGModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FGModuleCat.tensorObj_obj", "kind": "theorem", "module": "Mathlib.Algebra.Category.FGModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FGModuleCat.instAdditiveModuleCatForget₂", "kind": "instance", "module": "Mathlib.Algebra.Category.FGModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FGModuleCat.instLinearModuleCatForget₂", "kind": "instance", "module": "Mathlib.Algebra.Category.FGModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FGModuleCat.Iso.conj_eq_conj", "kind": "theorem", "module": "Mathlib.Algebra.Category.FGModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FGModuleCat.Iso.conj_hom_eq_conj", "kind": "theorem", "module": "Mathlib.Algebra.Category.FGModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FGModuleCat.instFiniteHomModuleCatObjIsFG", "kind": "instance", "module": "Mathlib.Algebra.Category.FGModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FGModuleCat.instFiniteHom", "kind": "instance", "module": "Mathlib.Algebra.Category.FGModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FGModuleCat.instIsMonoidalClosedModuleCatIsFG", "kind": "instance", "module": "Mathlib.Algebra.Category.FGModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FGModuleCat.ihom_obj", "kind": "theorem", "module": "Mathlib.Algebra.Category.FGModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FGModuleCat.FGModuleCatDual", "kind": "definition", "module": "Mathlib.Algebra.Category.FGModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FGModuleCat.FGModuleCatDual_obj", "kind": "theorem", "module": "Mathlib.Algebra.Category.FGModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FGModuleCat.FGModuleCatDual_coe", "kind": "theorem", "module": "Mathlib.Algebra.Category.FGModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FGModuleCat.FGModuleCatCoevaluation", "kind": "definition", "module": "Mathlib.Algebra.Category.FGModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FGModuleCat.FGModuleCatCoevaluation_apply_one", "kind": "theorem", "module": "Mathlib.Algebra.Category.FGModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FGModuleCat.FGModuleCatEvaluation", "kind": "definition", "module": "Mathlib.Algebra.Category.FGModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FGModuleCat.FGModuleCatEvaluation_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.FGModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FGModuleCat.FGModuleCatEvaluation_apply'", "kind": "theorem", "module": "Mathlib.Algebra.Category.FGModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Category.FGModuleCat.Basic.0.FGModuleCat.coevaluation_evaluation", "kind": "theorem", "module": "Mathlib.Algebra.Category.FGModuleCat.Basic", "is_tactic_proof": true, "tactics": ["ext", "apply"], "tactic_count": 2}
{"name": "_private.Mathlib.Algebra.Category.FGModuleCat.Basic.0.FGModuleCat.evaluation_coevaluation", "kind": "theorem", "module": "Mathlib.Algebra.Category.FGModuleCat.Basic", "is_tactic_proof": true, "tactics": ["ext", "apply"], "tactic_count": 2}
{"name": "FGModuleCat.exactPairing", "kind": "instance", "module": "Mathlib.Algebra.Category.FGModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FGModuleCat.rightDual", "kind": "instance", "module": "Mathlib.Algebra.Category.FGModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FGModuleCat.rightRigidCategory", "kind": "instance", "module": "Mathlib.Algebra.Category.FGModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.comp_id_fgModuleCat", "kind": "theorem", "module": "Mathlib.Algebra.Category.FGModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.id_fgModuleCat_comp", "kind": "theorem", "module": "Mathlib.Algebra.Category.FGModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FGModuleCat.instFiniteCarrierSigmaObjModuleCatOfFinite", "kind": "instance", "module": "Mathlib.Algebra.Category.FGModuleCat.Colimits", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "FGModuleCat.instFiniteCarrierColimitModuleCatCompForget₂", "kind": "instance", "module": "Mathlib.Algebra.Category.FGModuleCat.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FGModuleCat.forget₂CreatesColimit", "kind": "definition", "module": "Mathlib.Algebra.Category.FGModuleCat.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FGModuleCat.instCreatesColimitsOfShapeModuleCatForget₂", "kind": "instance", "module": "Mathlib.Algebra.Category.FGModuleCat.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FGModuleCat.instHasColimitsOfShapeOfFinCategory", "kind": "instance", "module": "Mathlib.Algebra.Category.FGModuleCat.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FGModuleCat.instHasFiniteColimits", "kind": "instance", "module": "Mathlib.Algebra.Category.FGModuleCat.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FGModuleCat.instPreservesFiniteColimitsModuleCatForget₂", "kind": "instance", "module": "Mathlib.Algebra.Category.FGModuleCat.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FGModuleRepr.repr", "kind": "definition", "module": "Mathlib.Algebra.Category.FGModuleCat.EssentiallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FGModuleRepr.instCoeSortType", "kind": "instance", "module": "Mathlib.Algebra.Category.FGModuleCat.EssentiallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FGModuleRepr.instAddCommGroupRepr", "kind": "instance", "module": "Mathlib.Algebra.Category.FGModuleCat.EssentiallySmall", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "FGModuleRepr.instModuleRepr", "kind": "instance", "module": "Mathlib.Algebra.Category.FGModuleCat.EssentiallySmall", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "FGModuleRepr.instFiniteRepr", "kind": "instance", "module": "Mathlib.Algebra.Category.FGModuleCat.EssentiallySmall", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "FGModuleRepr.ofFinite", "kind": "definition", "module": "Mathlib.Algebra.Category.FGModuleCat.EssentiallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FGModuleRepr.ofFiniteEquiv", "kind": "definition", "module": "Mathlib.Algebra.Category.FGModuleCat.EssentiallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FGModuleRepr.instCategory", "kind": "instance", "module": "Mathlib.Algebra.Category.FGModuleCat.EssentiallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FGModuleRepr.instSmallCategory", "kind": "instance", "module": "Mathlib.Algebra.Category.FGModuleCat.EssentiallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FGModuleRepr.embed", "kind": "definition", "module": "Mathlib.Algebra.Category.FGModuleCat.EssentiallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FGModuleRepr.instIsEquivalenceFGModuleCatEmbed", "kind": "instance", "module": "Mathlib.Algebra.Category.FGModuleCat.EssentiallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instEssentiallySmallFGModuleCat", "kind": "instance", "module": "Mathlib.Algebra.Category.FGModuleCat.EssentiallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsEquivalenceFGModuleCatUlift", "kind": "instance", "module": "Mathlib.Algebra.Category.FGModuleCat.EssentiallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FGModuleCat.instFiniteCarrierPiObjModuleCatOfFinite", "kind": "instance", "module": "Mathlib.Algebra.Category.FGModuleCat.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FGModuleCat.instFiniteCarrierLimitModuleCatCompForget₂", "kind": "instance", "module": "Mathlib.Algebra.Category.FGModuleCat.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FGModuleCat.forget₂CreatesLimit", "kind": "definition", "module": "Mathlib.Algebra.Category.FGModuleCat.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FGModuleCat.instCreatesLimitsOfShapeModuleCatForget₂", "kind": "instance", "module": "Mathlib.Algebra.Category.FGModuleCat.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FGModuleCat.instHasLimitsOfShapeOfFinCategory", "kind": "instance", "module": "Mathlib.Algebra.Category.FGModuleCat.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FGModuleCat.instHasFiniteLimits", "kind": "instance", "module": "Mathlib.Algebra.Category.FGModuleCat.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FGModuleCat.instPreservesFiniteLimitsModuleCatForget₂", "kind": "instance", "module": "Mathlib.Algebra.Category.FGModuleCat.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpWithZero.instCoeSortType", "kind": "instance", "module": "Mathlib.Algebra.Category.GrpWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpWithZero.instInhabited", "kind": "instance", "module": "Mathlib.Algebra.Category.GrpWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpWithZero.instLargeCategory", "kind": "instance", "module": "Mathlib.Algebra.Category.GrpWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpWithZero.groupWithZeroConcreteCategory", "kind": "instance", "module": "Mathlib.Algebra.Category.GrpWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpWithZero.ofHom", "kind": "abbrev", "module": "Mathlib.Algebra.Category.GrpWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpWithZero.hom_id", "kind": "theorem", "module": "Mathlib.Algebra.Category.GrpWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpWithZero.hom_comp", "kind": "theorem", "module": "Mathlib.Algebra.Category.GrpWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpWithZero.coe_id", "kind": "theorem", "module": "Mathlib.Algebra.Category.GrpWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpWithZero.coe_comp", "kind": "theorem", "module": "Mathlib.Algebra.Category.GrpWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpWithZero.forget_map", "kind": "theorem", "module": "Mathlib.Algebra.Category.GrpWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpWithZero.hasForgetToBipointed", "kind": "instance", "module": "Mathlib.Algebra.Category.GrpWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpWithZero.hasForgetToMon", "kind": "instance", "module": "Mathlib.Algebra.Category.GrpWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpWithZero.Iso.mk", "kind": "definition", "module": "Mathlib.Algebra.Category.GrpWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instAdditiveFunctorColim", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.AB", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instPreservesHomologyFunctorAddCommGrpCatColim", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.AB", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instPreservesFiniteLimitsFunctorAddCommGrpCatColim", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.AB", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "instHasFilteredColimitsAddCommGrpCat", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.AB", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instAB5AddCommGrpCat", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.AB", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instAB4AddCommGrpCat", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.AB", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instHasExactLimitsOfShapeDiscreteAddCommGrpCat", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.AB", "is_tactic_proof": true, "tactics": ["apply", "exact", "preserves", "hf", "let", "let", "have", "simp", "limit.cone,", "iY]", "ext", "change", "simp", "change", "simp", "suffices", "suffices", "rw", "simp_rw", "refine", "funext", "exact"], "tactic_count": 22}
{"name": "instAB4StarAddCommGrpCat", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.AB", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.normalMono", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.normalEpi", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.instAbelian", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.free", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.Adjunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.free_obj_coe", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Adjunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.free_map_coe", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Adjunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.adj", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.Adjunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.instIsLeftAdjointFree", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Adjunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.instIsRightAdjointForget", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Adjunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat._example", "kind": "example", "module": "Mathlib.Algebra.Category.Grp.Adjunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.instPreservesMonomorphismsFree", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Adjunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.free", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.Adjunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.adj", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.Adjunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.instIsRightAdjointForget", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Adjunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.abelianize", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.Adjunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.abelianizeAdj", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.Adjunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonCat.units", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.Adjunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.forget₂MonAdj", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.Adjunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsRightAdjointGrpCatMonCatUnits", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Adjunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommMonCat.units", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.Adjunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.forget₂CommMonAdj", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.Adjunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsRightAdjointCommGrpCatCommMonCatUnits", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Adjunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.instCoeSortType", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.of", "kind": "abbrev", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.instCategory", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.instConcreteCategoryMonoidHomCarrier", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.Hom.hom", "kind": "abbrev", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.ofHom", "kind": "abbrev", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.Hom.Simps.hom", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.coe_id", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.coe_comp", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.forget_map", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.ext", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.coe_of", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.hom_id", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.id_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "GrpCat.hom_comp", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.comp_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "GrpCat.hom_ext", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.hom_ofHom", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.ofHom_hom", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.ofHom_id", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.ofHom_comp", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.ofHom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.inv_hom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "GrpCat.hom_inv_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "GrpCat.instInhabited", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.hasForgetToMonCat", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.forget₂_map_ofHom", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.instCoeMonCat", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.instOneHom", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.one_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.ofHom_injective", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": true, "tactics": ["intro", "ext", "apply"], "tactic_count": 3}
{"name": "GrpCat.fullyFaithfulForget₂ToMonCat", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.instFullMonCatForget₂", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat._example", "kind": "example", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "GrpCat.uliftFunctor", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ab", "kind": "abbrev", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.instCoeSortType", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.of", "kind": "abbrev", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.instCategory", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.instConcreteCategoryMonoidHomCarrier", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.Hom.hom", "kind": "abbrev", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.ofHom", "kind": "abbrev", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.Hom.Simps.hom", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.coe_id", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.coe_comp", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.forget_map", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.ext", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.instInhabited", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.coe_of", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.hom_id", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.id_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CommGrpCat.hom_comp", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.comp_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CommGrpCat.hom_ext", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.hom_ofHom", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.ofHom_hom", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.ofHom_id", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.ofHom_comp", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.ofHom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.inv_hom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CommGrpCat.hom_inv_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CommGrpCat.hasForgetToGroup", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.forget₂_grp_map_ofHom", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.instCoeGrpCat", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.fullyFaithfulForget₂ToGrp", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.instFullGrpCatForget₂", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.hasForgetToCommMonCat", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.forget₂_commMonCat_map_ofHom", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.instCoeCommMonCat", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.instOneHom", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.one_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.ofHom_injective", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": true, "tactics": ["intro", "ext", "apply"], "tactic_count": 3}
{"name": "CommGrpCat._example", "kind": "example", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CommGrpCat.uliftFunctor", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.asHom", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.asHom_injective", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.int_hom_ext", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.injective_of_mono", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.toGrpIso", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.toCommGrpIso", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.groupIsoToMulEquiv", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.commGroupIsoToMulEquiv", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mulEquivIsoGroupIso", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mulEquivIsoCommGroupIso", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Aut.isoPerm", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Aut.mulEquivPerm", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.forget_reflects_isos", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.forget_reflects_isos", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpMax", "kind": "abbrev", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddGrpMax", "kind": "abbrev", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpMax", "kind": "abbrev", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpMax", "kind": "abbrev", "module": "Mathlib.Algebra.Category.Grp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.instHasBinaryBiproducts", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.instHasFiniteBiproducts", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.binaryProductLimitCone", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.binaryProductLimitCone_cone_π_app_left", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.binaryProductLimitCone_cone_π_app_right", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.biprodIsoProd", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.biprodIsoProd_inv_comp_fst", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.biprodIsoProd_inv_comp_snd", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.HasLimit.lift", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.HasLimit.productLimitCone", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.biproductIsoPi", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.biproductIsoPi_inv_comp_π", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.binaryProductLimitCone", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.CartesianMonoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.cartesianMonoidalCategoryGrp", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.CartesianMonoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.instBraidedCategory", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.CartesianMonoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.instBraidedForget", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.CartesianMonoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "GrpCat.SurjectiveOfEpiAuxs.h_apply_fromCoset_nin_range", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.EpiMono", "is_tactic_proof": true, "tactics": ["change", "simp", "rw", "simp", "refine", "convert", "rw"], "tactic_count": 7}
{"name": "GrpCat.SurjectiveOfEpiAuxs.agree", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.EpiMono", "is_tactic_proof": true, "tactics": ["refine", "rintro", "change", "ext", "rw", "by_cases", "rw", "change", "simp", "rw", "simp", "rw", "have", "change", "dsimp", "simp", "have", "exact"], "tactic_count": 18}
{"name": "GrpCat.SurjectiveOfEpiAuxs.comp_eq", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.EpiMono", "is_tactic_proof": true, "tactics": ["ext", "simp", "have", "rw", "use", "rw"], "tactic_count": 6}
{"name": "GrpCat.SurjectiveOfEpiAuxs.g_ne_h", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.EpiMono", "is_tactic_proof": true, "tactics": ["intro", "apply", "replace", "simpa"], "tactic_count": 4}
{"name": "GrpCat.surjective_of_epi", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.EpiMono", "is_tactic_proof": true, "tactics": ["dsimp", "by_contra", "exact"], "tactic_count": 3}
{"name": "GrpCat.epi_iff_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.epi_iff_range_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddGrpCat.epi_iff_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.EpiMono", "is_tactic_proof": false, "tactics": ["have", "refine", "apply", "rwa"], "tactic_count": 4}
{"name": "AddGrpCat.epi_iff_range_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.forget_grp_preserves_mono", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.forget_grp_preserves_epi", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.ker_eq_bot_of_mono", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.mono_iff_ker_eq_bot", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.mono_iff_injective", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.range_eq_top_of_epi", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.epi_iff_range_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.epi_iff_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.EpiMono", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CommGrpCat.forget_commGrp_preserves_mono", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.forget_commGrp_preserves_epi", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.toAddGrp", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.EquivalenceGroupAddGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.toAddCommGrp", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.EquivalenceGroupAddGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddGrpCat.toGrp", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.EquivalenceGroupAddGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.toCommGrp", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.EquivalenceGroupAddGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupAddGroupEquivalence", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.EquivalenceGroupAddGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "commGroupAddCommGroupEquivalence", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.EquivalenceGroupAddGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.FilteredColimits.G", "kind": "abbrev", "module": "Mathlib.Algebra.Category.Grp.FilteredColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.FilteredColimits.G.mk", "kind": "abbrev", "module": "Mathlib.Algebra.Category.Grp.FilteredColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.FilteredColimits.G.mk_eq", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.FilteredColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.FilteredColimits.colimit_one_eq", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.FilteredColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.FilteredColimits.colimit_mul_mk_eq", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.FilteredColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.FilteredColimits.colimit_mul_mk_eq'", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.FilteredColimits", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "GrpCat.FilteredColimits.colimitInvAux", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.FilteredColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.FilteredColimits.colimitInvAux_eq_of_rel", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.FilteredColimits", "is_tactic_proof": true, "tactics": ["apply", "obtain", "use", "rw", "exact"], "tactic_count": 5}
{"name": "GrpCat.FilteredColimits.colimitInv", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.FilteredColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.FilteredColimits.colimit_inv_mk_eq", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.FilteredColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.FilteredColimits.colimitGroup", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.FilteredColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.FilteredColimits.colimit", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.FilteredColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.FilteredColimits.colimitCocone", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.FilteredColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.FilteredColimits.colimitCoconeIsColimit", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.FilteredColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.FilteredColimits.forget₂Mon_preservesFilteredColimits", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.FilteredColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.FilteredColimits.forget_preservesFilteredColimits", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.FilteredColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.FilteredColimits.G", "kind": "abbrev", "module": "Mathlib.Algebra.Category.Grp.FilteredColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.FilteredColimits.colimitCommGroup", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.FilteredColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.FilteredColimits.colimit", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.FilteredColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.FilteredColimits.colimitCocone", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.FilteredColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.FilteredColimits.colimitCoconeIsColimit", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.FilteredColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.FilteredColimits.forget₂Group_preservesFilteredColimits", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.FilteredColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.FilteredColimits.forget_preservesFilteredColimits", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.FilteredColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteGrp.instCoeSortType", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.FiniteGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteGrp.instCategory", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.FiniteGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteGrp.instConcreteCategoryMonoidHomCarrierToGrp", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.FiniteGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteGrp.instGroupCarrierToGrp", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.FiniteGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteGrp.instFiniteCarrierToGrp", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.FiniteGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteGrp.of", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.FiniteGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteGrp.ofHom", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.FiniteGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteGrp.ofHom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.FiniteGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uliftZMultiplesHom", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.ForgetCorepresentable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uliftZPowersHom", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.ForgetCorepresentable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.coyonedaObjIsoForget", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.ForgetCorepresentable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.coyonedaObjIsoForget", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.ForgetCorepresentable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddGrpCat.coyonedaObjIsoForget", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.ForgetCorepresentable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.coyonedaObjIsoForget", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.ForgetCorepresentable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.forget_isCorepresentable", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.ForgetCorepresentable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.forget_isCorepresentable", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.ForgetCorepresentable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddGrpCat.forget_isCorepresentable", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.ForgetCorepresentable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.forget_isCorepresentable", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.ForgetCorepresentable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.image", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.image.ι", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.instMonoι", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.factorThruImage", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.image.fac", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Images", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "AddCommGrpCat.image.lift", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.image.lift_fac", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Images", "is_tactic_proof": true, "tactics": ["ext", "change", "rw", "rfl"], "tactic_count": 4}
{"name": "AddCommGrpCat.monoFactorisation", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.isImage", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.imageIsoRange", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Baer.of_divisible", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Injective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.injective_as_module_iff", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Injective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.injective_of_divisible", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Injective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.isFinite", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.IsFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.prop_isFinite_iff", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.IsFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.instIsSerreClassIsFinite", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.IsFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.kernelCone", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.kernelIsLimit", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.cokernelCocone", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.cokernelIsColimit", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.isColimit_iff_bijective_desc", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.LargeColimits", "is_tactic_proof": true, "tactics": ["refine", "change", "rw", "refine", "apply", "apply", "refine", "ext", "rw", "exact", "set", "ι", "naturality", "u", "ext", "dsimp", "rw", "use", "refine", "dsimp", "rw", "change", "rw", "dsimp", "rw"], "tactic_count": 25}
{"name": "AddCommGrpCat.hasColimit_iff_small_quot", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.LargeColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Category.Grp.LeftExactFunctor.0.AddCommGrpCat.leftExactFunctorForgetEquivalence.instCartesianMonoidalCategory", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.LeftExactFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Category.Grp.LeftExactFunctor.0.AddCommGrpCat.leftExactFunctorForgetEquivalence.instBraidedCategory", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.LeftExactFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.leftExactFunctorForgetEquivalence.inverseAux", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.LeftExactFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.leftExactFunctorForgetEquivalence.instPreservesFiniteLimitsObjLeftExactFunctorTypeFunctorInverseAux", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.LeftExactFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.leftExactFunctorForgetEquivalence.inverse", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.LeftExactFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.leftExactFunctorForgetEquivalence.unitIsoAux", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.LeftExactFunctor", "is_tactic_proof": true, "tactics": ["letI", "letI", "refine", "erw", "cat_disch)", "dsimp", "have", "simp", "erw", "erw", "cat_disch"], "tactic_count": 11}
{"name": "AddCommGrpCat.leftExactFunctorForgetEquivalence.unitIso", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.LeftExactFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.leftExactFunctorForgetEquivalence", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.LeftExactFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.groupObj", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.sectionsSubgroup", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.sectionsGroup", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.sectionsπMonoidHom", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.limitGroup", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.instSmallElemForallObjCompMonCatForget₂ForgetSections", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.Forget₂.createsLimit", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.limitCone", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.limitConeIsLimit", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.hasLimit", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.hasLimit_iff_small_sections", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Limits", "is_tactic_proof": true, "tactics": ["constructor", "apply", "intro", "infer_instance"], "tactic_count": 4}
{"name": "GrpCat.hasLimitsOfShape", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.hasLimitsOfSize", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.hasLimits", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.forget₂Mon_preservesLimitsOfSize", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.forget₂Mon_preservesLimits", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.forget_preservesLimitsOfShape", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.forget_preservesLimitsOfSize", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.forget_preservesLimits", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.forget_createsLimit", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Limits", "is_tactic_proof": true, "tactics": ["set", "exact"], "tactic_count": 2}
{"name": "GrpCat.forget_createsLimitsOfShape", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.forget_createsLimitsOfSize", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.commGroupObj", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.limitCommGroup", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.instReflectsIsomorphismsGrpCatForget₂", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.Forget₂.createsLimit", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.limitCone", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.limitConeIsLimit", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.hasLimit", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.hasLimit_iff_small_sections", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Limits", "is_tactic_proof": true, "tactics": ["constructor", "apply", "intro", "infer_instance"], "tactic_count": 4}
{"name": "CommGrpCat.hasLimitsOfShape", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.hasLimitsOfSize", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.hasLimits", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.forget₂Group_preservesLimit", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.forget₂Group_preservesLimitsOfShape", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.forget₂Group_preservesLimitsOfSize", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.forget₂Group_preservesLimits", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.forget₂CommMon_preservesLimitsAux", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.forget₂CommMon_preservesLimitsOfShape", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.forget₂CommMon_preservesLimitsOfSize", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.forget_preservesLimitsOfShape", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.forget_preservesLimitsOfSize", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.forget_preservesLimits", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.forget_preservesLimits", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.forget_createsLimit", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Limits", "is_tactic_proof": true, "tactics": ["set", "exact"], "tactic_count": 2}
{"name": "CommGrpCat.forget_createsLimitsOfShape", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.forget_createsLimitsOfSize", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat._example", "kind": "example", "module": "Mathlib.Algebra.Category.Grp.Limits", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "AddCommGrpCat.kernelIsoKer", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.kernelIsoKer_hom_comp_subtype", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Limits", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "AddCommGrpCat.kernelIsoKer_inv_comp_ι", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Limits", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AddCommGrpCat.kernelIsoKerOver", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.instAddHom", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.hom_add", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.hom_add_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.instZeroHom_1", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.hom_zero", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.instSMulNatHom", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.hom_nsmul", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.instNegHom", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.hom_neg", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.instSubHom", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.hom_sub", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.instSMulIntHom", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.hom_zsmul", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.instAddCommGroupHom", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.instPreadditive", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.homAddEquiv", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.wellPowered_addCommGrp", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Subobject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.uliftFunctorFullyFaithful", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.Ulift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.instFaithfulUliftFunctor", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Ulift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.instFullUliftFunctor", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Ulift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.uliftFunctor_preservesLimit", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Ulift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.uliftFunctor_preservesLimitsOfShape", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Ulift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.uliftFunctor_preservesLimitsOfSize", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Ulift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.instCreatesLimitsOfSizeUliftFunctor", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Ulift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.uliftFunctorFullyFaithful", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.Ulift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.instFaithfulUliftFunctor", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Ulift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.instFullUliftFunctor", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Ulift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.uliftFunctor_preservesLimit", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Ulift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.uliftFunctor_preservesLimitsOfShape", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Ulift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.uliftFunctor_preservesLimitsOfSize", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Ulift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.instCreatesLimitsOfSizeUliftFunctor", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Ulift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.uliftFunctor_additive", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Ulift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.instPreservesColimitsOfSizeUliftFunctor", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Ulift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.instCreatesColimitsOfSizeUliftFunctor", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Ulift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.coyoneda", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.Yoneda", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.coyonedaForget", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.Yoneda", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.coyonedaType", "kind": "definition", "module": "Mathlib.Algebra.Category.Grp.Yoneda", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.forget₂_addCommGroup_full", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.ZModuleEquivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.forget₂_addCommGrp_essSurj", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.ZModuleEquivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.forget₂AddCommGroupIsEquivalence", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.ZModuleEquivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.isZero_of_subsingleton", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Zero", "is_tactic_proof": true, "tactics": ["refine", "ext", "have", "rw", "ext", "subsingleton"], "tactic_count": 6}
{"name": "GrpCat.instHasZeroObject", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.subsingleton_of_isZero", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GrpCat.isZero_iff_subsingleton", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.isZero_of_subsingleton", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Zero", "is_tactic_proof": true, "tactics": ["refine", "ext", "have", "rw", "ext", "subsingleton"], "tactic_count": 6}
{"name": "CommGrpCat.instHasZeroObject", "kind": "instance", "module": "Mathlib.Algebra.Category.Grp.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.subsingleton_of_isZero", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGrpCat.isZero_iff_subsingleton", "kind": "theorem", "module": "Mathlib.Algebra.Category.Grp.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HopfAlgCat.instCoeSortType", "kind": "instance", "module": "Mathlib.Algebra.Category.HopfAlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HopfAlgCat.of", "kind": "abbrev", "module": "Mathlib.Algebra.Category.HopfAlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HopfAlgCat.of_comul", "kind": "theorem", "module": "Mathlib.Algebra.Category.HopfAlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HopfAlgCat.of_counit", "kind": "theorem", "module": "Mathlib.Algebra.Category.HopfAlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HopfAlgCat.category", "kind": "instance", "module": "Mathlib.Algebra.Category.HopfAlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HopfAlgCat.concreteCategory", "kind": "instance", "module": "Mathlib.Algebra.Category.HopfAlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HopfAlgCat.Hom.toBialgHom", "kind": "abbrev", "module": "Mathlib.Algebra.Category.HopfAlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HopfAlgCat.ofHom", "kind": "abbrev", "module": "Mathlib.Algebra.Category.HopfAlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HopfAlgCat.Hom.toBialgHom_injective", "kind": "theorem", "module": "Mathlib.Algebra.Category.HopfAlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HopfAlgCat.hom_ext", "kind": "theorem", "module": "Mathlib.Algebra.Category.HopfAlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HopfAlgCat.toBialgHom_comp", "kind": "theorem", "module": "Mathlib.Algebra.Category.HopfAlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HopfAlgCat.toBialgHom_id", "kind": "theorem", "module": "Mathlib.Algebra.Category.HopfAlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HopfAlgCat.hasForgetToBialgebra", "kind": "instance", "module": "Mathlib.Algebra.Category.HopfAlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HopfAlgCat.forget₂_bialgebra_obj", "kind": "theorem", "module": "Mathlib.Algebra.Category.HopfAlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HopfAlgCat.forget₂_bialgebra_map", "kind": "theorem", "module": "Mathlib.Algebra.Category.HopfAlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgEquiv.toHopfAlgIso", "kind": "definition", "module": "Mathlib.Algebra.Category.HopfAlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgEquiv.toHopfAlgIso_refl", "kind": "theorem", "module": "Mathlib.Algebra.Category.HopfAlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgEquiv.toHopfAlgIso_symm", "kind": "theorem", "module": "Mathlib.Algebra.Category.HopfAlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgEquiv.toHopfAlgIso_trans", "kind": "theorem", "module": "Mathlib.Algebra.Category.HopfAlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.toHopfAlgEquiv", "kind": "definition", "module": "Mathlib.Algebra.Category.HopfAlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.toHopfAlgEquiv_toBialgHom", "kind": "theorem", "module": "Mathlib.Algebra.Category.HopfAlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.toHopfAlgEquiv_refl", "kind": "theorem", "module": "Mathlib.Algebra.Category.HopfAlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.toHopfAlgEquiv_symm", "kind": "theorem", "module": "Mathlib.Algebra.Category.HopfAlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.toHopfAlgEquiv_trans", "kind": "theorem", "module": "Mathlib.Algebra.Category.HopfAlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HopfAlgCat.forget_reflects_isos", "kind": "instance", "module": "Mathlib.Algebra.Category.HopfAlgCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HopfAlgCat.instMonoidalCategoryStruct", "kind": "instance", "module": "Mathlib.Algebra.Category.HopfAlgCat.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HopfAlgCat.MonoidalCategory.inducingFunctorData", "kind": "definition", "module": "Mathlib.Algebra.Category.HopfAlgCat.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HopfAlgCat.instMonoidalCategory", "kind": "instance", "module": "Mathlib.Algebra.Category.HopfAlgCat.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HopfAlgCat.instMonoidalBialgCatForget₂", "kind": "instance", "module": "Mathlib.Algebra.Category.HopfAlgCat.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instAB5ModuleCat", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.AB", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instAB4ModuleCat", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.AB", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instAB4StarModuleCat", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.AB", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.isSeparator", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.AB", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instHasSeparatorModuleCatOfSmall", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.AB", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsGrothendieckAbelianModuleCat", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.AB", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.normalMono", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.normalEpi", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.abelian", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.instHasLimitsOfSize", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.forget_reflectsLimitsOfSize", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.forget₂_reflectsLimitsOfSize", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.forget_reflectsLimits", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.forget₂_reflectsLimits", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.free", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Adjunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.freeMk", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Adjunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.free_hom_ext", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Adjunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.freeDesc", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Adjunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.freeDesc_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Adjunctions", "is_tactic_proof": true, "tactics": ["dsimp", "erw", "all_goals"], "tactic_count": 3}
{"name": "ModuleCat.free_map_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Adjunctions", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "ModuleCat.freeHomEquiv", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Adjunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.adj", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Adjunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.adj_homEquiv", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Adjunctions", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ModuleCat.instIsRightAdjointForget", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Adjunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.FreeMonoidal.εIso", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Adjunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.FreeMonoidal.εIso_hom_one", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Adjunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.FreeMonoidal.εIso_inv_freeMk", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Adjunctions", "is_tactic_proof": true, "tactics": ["dsimp", "erw", "rw"], "tactic_count": 3}
{"name": "ModuleCat.FreeMonoidal.μIso", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Adjunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.FreeMonoidal.μIso_hom_freeMk_tmul_freeMk", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Adjunctions", "is_tactic_proof": true, "tactics": ["dsimp", "erw", "rw"], "tactic_count": 3}
{"name": "ModuleCat.FreeMonoidal.μIso_inv_freeMk", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Adjunctions", "is_tactic_proof": true, "tactics": ["dsimp", "erw"], "tactic_count": 2}
{"name": "ModuleCat.instMonoidalFree", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Adjunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.free_ε_one", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Adjunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.free_η_freeMk", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Adjunctions", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "ModuleCat.free_μ_freeMk_tmul_freeMk", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Adjunctions", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "ModuleCat.free_δ_freeMk", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Adjunctions", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Free", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Adjunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Free.of", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Adjunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.categoryFree", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Adjunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Free.instPreadditive", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Adjunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Free.instLinear", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Adjunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Free.single_comp_single", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Adjunctions", "is_tactic_proof": true, "tactics": ["dsimp"], "tactic_count": 1}
{"name": "CategoryTheory.Free.embedding", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Adjunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Free.lift", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Adjunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Free.lift_map_single", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Adjunctions", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Free.lift_additive", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Adjunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Free.lift_linear", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Adjunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Free.embeddingLiftIso", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Adjunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Free.ext", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Adjunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Free.liftUnique", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Adjunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.moduleOfAlgebraModule", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.isScalarTower_of_algebra_moduleCat", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat._example", "kind": "example", "module": "Mathlib.Algebra.Category.ModuleCat.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.linearOverField", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.instCoeSortType", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.of", "kind": "abbrev", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.coe_of", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat._example", "kind": "example", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": true, "tactics": ["with_reducible"], "tactic_count": 1}
{"name": "ModuleCat._example", "kind": "example", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": true, "tactics": ["with_reducible"], "tactic_count": 1}
{"name": "ModuleCat.moduleCategory", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.instConcreteCategoryLinearMapIdCarrier", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.Hom.hom", "kind": "abbrev", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.ofHom", "kind": "abbrev", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.Hom.Simps.hom", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.hom_id", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.id_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ModuleCat.hom_comp", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.comp_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ModuleCat.hom_ext", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.hom_bijective", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.hom_injective", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.hom_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.hom_ofHom", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.ofHom_hom", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.ofHom_id", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.ofHom_comp", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.ofHom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.inv_hom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ModuleCat.hom_inv_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ModuleCat.homEquiv", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.equivalenceSemimoduleCat", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.forget_obj", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.forget_map", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.hasForgetToAddCommGroup", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.forget₂_obj", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.forget₂_obj_moduleCat_of", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.forget₂_map", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.instInhabited", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.of_coe", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.isZero_of_subsingleton", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.instHasZeroObject", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.term↟_", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat._aux_Mathlib_Algebra_Category_ModuleCat_Basic___macroRules_ModuleCat_term↟__1", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat._aux_Mathlib_Algebra_Category_ModuleCat_Basic___unexpand_ModuleCat_ofHom_1", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.toModuleIso", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.toLinearEquiv", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.toLinearEquiv_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.toLinearEquiv_symm", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.toLinearMap_toLinearEquiv", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "linearEquivIsoModuleIso", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.instAddHom", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.hom_add", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.instZeroHom", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.hom_zero", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.instSMulNatHom", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.hom_nsmul", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.instNegHom", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.hom_neg", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.instSubHom", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.hom_sub", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.instSMulIntHom", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.hom_zsmul", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.instAddCommGroupHom", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.hom_sum", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.instPreadditive", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.forget₂_addCommGrp_additive", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.homAddEquiv", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.subsingleton_of_isZero", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "simp"], "tactic_count": 3}
{"name": "ModuleCat.isZero_iff_subsingleton", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.isZero_of_iff_subsingleton", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.instSMulHom", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.hom_smul", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.Hom.instModule", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.homLinearEquiv", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.Algebra.instModuleCarrier", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.Algebra.instIsScalarTowerCarrier", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.Algebra.instSMulCommClassCarrier", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.Algebra.instLinear", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.instLinear", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.Iso.homCongr_eq_arrowCongr", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.Iso.conj_eq_conj", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.endRingEquiv", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.smul", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.smul_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "ModuleCat.smulNatTrans", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.mkOfSMul'", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.instAddCommGroupCarrierMkOfSMul'", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "ModuleCat.instSMulCarrierMkOfSMul'", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.mkOfSMul'_smul", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.instModuleCarrierMkOfSMul'", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.mkOfSMul", "kind": "abbrev", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.mkOfSMul_smul", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.homMk", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.forget₂_map_homMk", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.instReflectsIsomorphismsForget", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.instReflectsIsomorphismsAddCommGrpCatForget₂", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.ofHom₂", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.Hom.hom₂", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.Hom.hom₂_ofHom₂", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.ofHom₂_hom₂", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.comp_id_moduleCat", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LinearMap.id_moduleCat_comp", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ModuleCat.instHasBinaryBiproducts", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.instHasFiniteBiproducts", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.binaryProductLimitCone", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.binaryProductLimitCone_cone_π_app_left", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.binaryProductLimitCone_cone_π_app_right", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.biprodIsoProd", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.biprodIsoProd_inv_comp_fst", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.biprodIsoProd_inv_comp_snd", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.HasLimit.lift", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.HasLimit.productLimitCone", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.biproductIsoPi", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.biproductIsoPi_inv_comp_π", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Category.ModuleCat.Biproducts.0.lequivProdOfRightSplitExact'", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Category.ModuleCat.Biproducts.0.lequivProdOfLeftSplitExact'", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lequivProdOfRightSplitExact", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lequivProdOfLeftSplitExact", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.restrictScalars.map_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.ChangeOfRings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.restrictScalars.smul_def", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.ChangeOfRings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.restrictScalars.smul_def'", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.ChangeOfRings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.restrictScalarsCongr_symm", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.ChangeOfRings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.restrictScalarsCongr_hom_app", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.ChangeOfRings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.restrictScalarsCongr_inv_app", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.ChangeOfRings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.restrictScalarsId'App_hom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.ChangeOfRings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.restrictScalarsId'App_inv_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.ChangeOfRings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.restrictScalarsId'App_hom_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.ChangeOfRings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.restrictScalarsId'App_inv_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.ChangeOfRings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.restrictScalarsComp'App_hom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.ChangeOfRings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.restrictScalarsComp'App_inv_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.ChangeOfRings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.restrictScalarsComp'App_hom_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.ChangeOfRings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.restrictScalarsComp'App_inv_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.ChangeOfRings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ChangeOfRings.term_⊗ₜ[_,_]_", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.ChangeOfRings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ChangeOfRings._aux_Mathlib_Algebra_Category_ModuleCat_ChangeOfRings___macroRules_ChangeOfRings_term_⊗ₜ[_,_]__1", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.ChangeOfRings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.ExtendScalars.map'_id", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.ChangeOfRings", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ModuleCat.ExtendScalars.map'_comp", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.ChangeOfRings", "is_tactic_proof": true, "tactics": ["ext", "induction", "zero", "tmul", "add"], "tactic_count": 5}
{"name": "ModuleCat.ExtendScalars.smul_tmul", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.ChangeOfRings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.ExtendScalars.map_tmul", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.ChangeOfRings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.ExtendScalars.hom_ext", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.ChangeOfRings", "is_tactic_proof": true, "tactics": ["apply", "letI", "ext", "apply", "intro", "change", "have", "simp"], "tactic_count": 8}
{"name": "ModuleCat.CoextendScalars.smul_apply'", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.ChangeOfRings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.CoextendScalars.smul_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.ChangeOfRings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.CoextendScalars.map_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.ChangeOfRings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.RestrictionCoextensionAdj.HomEquiv.fromRestriction_hom_apply_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.ChangeOfRings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.RestrictionCoextensionAdj.HomEquiv.toRestriction_hom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.ChangeOfRings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.RestrictionCoextensionAdj.unit'", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.ChangeOfRings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.RestrictionCoextensionAdj.counit'", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.ChangeOfRings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.extendRestrictScalarsAdj_homEquiv_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.ChangeOfRings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.extendRestrictScalarsAdj_unit_app_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.ChangeOfRings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.extendScalarsId_inv_app_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.ChangeOfRings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.homEquiv_extendScalarsId", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.ChangeOfRings", "is_tactic_proof": true, "tactics": ["ext", "rw", "simp"], "tactic_count": 3}
{"name": "ModuleCat.extendScalarsId_hom_app_one_tmul", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.ChangeOfRings", "is_tactic_proof": true, "tactics": ["rw", "dsimp"], "tactic_count": 2}
{"name": "ModuleCat.homEquiv_extendScalarsComp", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.ChangeOfRings", "is_tactic_proof": true, "tactics": ["dsimp", "simp", "rfl"], "tactic_count": 3}
{"name": "ModuleCat.extendScalarsComp_hom_app_one_tmul", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.ChangeOfRings", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "ModuleCat.extendScalars_assoc", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.ChangeOfRings", "is_tactic_proof": true, "tactics": ["ext", "have", "have", "have", "have", "dsimp", "rw", "erw", "rw"], "tactic_count": 9}
{"name": "ModuleCat.extendScalars_assoc'", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.ChangeOfRings", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "ModuleCat.extendScalars_id_comp", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.ChangeOfRings", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "erw", "rw", "erw", "rfl"], "tactic_count": 6}
{"name": "ModuleCat.extendScalars_comp_id", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.ChangeOfRings", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "erw", "rfl"], "tactic_count": 4}
{"name": "ModuleCat.HasColimit.coconePointSMul", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.HasColimit.colimitCocone", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.HasColimit.isColimitColimitCocone", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.HasColimit.instHasColimit", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.HasColimit.instPreservesColimitAddCommGrpCatForget₂", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.HasColimit.reflectsColimit", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.hasColimitsOfShape", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.reflectsColimitsOfShape", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.hasColimitsOfSize", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.forget₂PreservesColimitsOfShape", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.forget₂PreservesColimitsOfSize", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.instPreservesColimitsOfSizeAddCommGrpCatForget₂OfHasColimitsOfSizeAddCommGrpMax", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.instHasFiniteColimits", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat._example", "kind": "example", "module": "Mathlib.Algebra.Category.ModuleCat.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat._example", "kind": "example", "module": "Mathlib.Algebra.Category.ModuleCat.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat._example", "kind": "example", "module": "Mathlib.Algebra.Category.ModuleCat.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat._example", "kind": "example", "module": "Mathlib.Algebra.Category.ModuleCat.Colimits", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "ModuleCat.instHasCoequalizers", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat._example", "kind": "example", "module": "Mathlib.Algebra.Category.ModuleCat.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.preservesFiniteLimits_tensorLeft_of_ringHomFlat", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Descent", "is_tactic_proof": true, "tactics": ["algebraize", "change", "infer_instance"], "tactic_count": 3}
{"name": "ModuleCat.preservesFiniteLimits_extendScalars_of_flat", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Descent", "is_tactic_proof": false, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "ModuleCat.reflectsIsomorphisms_extendScalars_of_faithfullyFlat", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Descent", "is_tactic_proof": true, "tactics": ["refine", "algebraize", "rw", "replace", "rwa"], "tactic_count": 5}
{"name": "comonadicExtendScalars", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Descent", "is_tactic_proof": true, "tactics": ["have", "have", "convert", "exact", "exact"], "tactic_count": 5}
{"name": "ModuleCat.Derivation", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Differentials.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.Derivation.d", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Differentials.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.Derivation.d_add", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Differentials.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ModuleCat.Derivation.d_mul", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Differentials.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ModuleCat.Derivation.d_map", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Differentials.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.KaehlerDifferential", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Differentials.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.KaehlerDifferential.D", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Differentials.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.KaehlerDifferential.d", "kind": "abbrev", "module": "Mathlib.Algebra.Category.ModuleCat.Differentials.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.KaehlerDifferential.ext", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Differentials.Basic", "is_tactic_proof": true, "tactics": ["rw", "have", "rw", "rintro", "rw", "apply", "rw", "ext", "exact"], "tactic_count": 9}
{"name": "CommRingCat.KaehlerDifferential.map", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Differentials.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.KaehlerDifferential.map_d", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Differentials.Basic", "is_tactic_proof": true, "tactics": ["algebraize", "have", "exact"], "tactic_count": 3}
{"name": "ModuleCat.Derivation.desc", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Differentials.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.Derivation.desc_d", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Differentials.Basic", "is_tactic_proof": true, "tactics": ["letI", "letI", "apply"], "tactic_count": 3}
{"name": "PresheafOfModules.Derivation.congr_d", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Differentials.Presheaf", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PresheafOfModules.Derivation.d_one", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Differentials.Presheaf", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "PresheafOfModules.Derivation.postcomp", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Differentials.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.Derivation.instSubsingletonUniversal", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Differentials.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.Derivation'", "kind": "abbrev", "module": "Mathlib.Algebra.Category.ModuleCat.Differentials.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.Derivation'.d_app", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Differentials.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.Derivation'.app", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Differentials.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.Derivation'.app_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Differentials.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.Derivation'.mk", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Differentials.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.Derivation'.mk_app", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Differentials.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.Derivation'.Universal.mk", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Differentials.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.DifferentialsConstruction.relativeDifferentials'", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Differentials.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.DifferentialsConstruction.relativeDifferentials'_map_d", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Differentials.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.DifferentialsConstruction.derivation'", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Differentials.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.DifferentialsConstruction.isUniversal'", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Differentials.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.DifferentialsConstruction.instHasDifferentials", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Differentials.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instEnoughInjectivesModuleCatInt", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.EnoughInjectives", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.enoughInjectives", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.EnoughInjectives", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instEnoughInjectivesModuleCatOfSmall", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.EnoughInjectives", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.ker_eq_bot_of_mono", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.range_eq_top_of_epi", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.mono_iff_ker_eq_bot", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.mono_iff_injective", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.EpiMono", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ModuleCat.epi_iff_range_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.epi_iff_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.EpiMono", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ModuleCat.uniqueOfEpiZero", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.mono_as_hom'_subtype", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.epi_as_hom''_mkQ", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.forget_preservesEpimorphisms", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.forget_preservesMonomorphisms", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.projectiveShortComplex", "kind": "abbrev", "module": "Mathlib.Algebra.Category.ModuleCat.Ext.DimensionShifting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.shortExact_projectiveShortComplex", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Ext.DimensionShifting", "is_tactic_proof": true, "tactics": ["apply", "refine", "simp"], "tactic_count": 3}
{"name": "instFreeCarrierX₂ModuleCatProjectiveShortComplex", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Ext.DimensionShifting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "precomp_extClass_surjective_of_projective_X₂", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Ext.DimensionShifting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "postcomp_extClass_surjective_of_projective_X₂", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Ext.DimensionShifting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.finite_ext", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Ext.Finite", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "obtain", "let", "exact"], "tactic_count": 6}
{"name": "instHasExtModuleCatOfSmall", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Ext.HasExt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.exteriorPower", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.ExteriorPower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.AlternatingMap", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.ExteriorPower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.instFunLikeAlternatingMapForallFinCarrier", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.ExteriorPower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.AlternatingMap.ext", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.ExteriorPower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.AlternatingMap.postcomp", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.ExteriorPower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.AlternatingMap.postcomp_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.ExteriorPower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.exteriorPower.mk", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.ExteriorPower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.exteriorPower.hom_ext", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.ExteriorPower", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "ModuleCat.exteriorPower.desc", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.ExteriorPower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.exteriorPower.desc_mk", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.ExteriorPower", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "ModuleCat.exteriorPower.map", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.ExteriorPower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.exteriorPower.map_mk", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.ExteriorPower", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "ModuleCat.exteriorPower.functor", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.ExteriorPower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.exteriorPower.iso₀", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.ExteriorPower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.exteriorPower.iso₀_hom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.ExteriorPower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.exteriorPower.iso₀_hom_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.ExteriorPower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.exteriorPower.iso₁", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.ExteriorPower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.exteriorPower.iso₁_hom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.ExteriorPower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.exteriorPower.iso₁_hom_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.ExteriorPower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.exteriorPower.natIso₀", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.ExteriorPower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.exteriorPower.natIso₁", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.ExteriorPower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.FilteredColimits.M", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.FilteredColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.FilteredColimits.M.mk", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.FilteredColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.FilteredColimits.M.mk_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.FilteredColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.FilteredColimits.M.mk_eq", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.FilteredColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.FilteredColimits.M.mk_map", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.FilteredColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.FilteredColimits.colimitSMulAux", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.FilteredColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.FilteredColimits.colimitSMulAux_eq_of_rel", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.FilteredColimits", "is_tactic_proof": true, "tactics": ["apply", "obtain", "use", "simp", "simp"], "tactic_count": 5}
{"name": "ModuleCat.FilteredColimits.colimitHasSMul", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.FilteredColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.FilteredColimits.colimit_zero_eq", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.FilteredColimits", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "ModuleCat.FilteredColimits.colimit_add_mk_eq", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.FilteredColimits", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "ModuleCat.FilteredColimits.colimit_add_mk_eq'", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.FilteredColimits", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "ModuleCat.FilteredColimits.colimit_smul_mk_eq", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.FilteredColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.FilteredColimits.colimitMulAction", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.FilteredColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.FilteredColimits.colimitSMulWithZero", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.FilteredColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.FilteredColimits.colimitModule", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.FilteredColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.FilteredColimits.colimit", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.FilteredColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.FilteredColimits.coconeMorphism", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.FilteredColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.FilteredColimits.colimitCocone", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.FilteredColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.FilteredColimits.colimitDesc", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.FilteredColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.FilteredColimits.ι_colimitDesc", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.FilteredColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.FilteredColimits.colimitCoconeIsColimit", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.FilteredColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.FilteredColimits.forget₂AddCommGroup_preservesFilteredColimits", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.FilteredColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.FilteredColimits.forget_preservesFilteredColimits", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.FilteredColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.FilteredColimits.forget_reflectsFilteredColimits", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.FilteredColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.disjoint_span_sum", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Free", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "ModuleCat.linearIndependent_leftExact", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Free", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "rw", "infer_instance", "exact"], "tactic_count": 6}
{"name": "ModuleCat.linearIndependent_shortExact", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Free", "is_tactic_proof": true, "tactics": ["apply", "dsimp", "convert", "ext", "apply"], "tactic_count": 5}
{"name": "ModuleCat.span_exact", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Free", "is_tactic_proof": true, "tactics": ["intro", "have", "rw", "obtain", "let", "have", "rw", "simp", "rw", "simp", "obtain", "have", "rw", "obtain", "rw", "rw", "simp", "have", "ext", "rw", "apply", "rw", "use", "rw", "rw", "use", "rw"], "tactic_count": 27}
{"name": "ModuleCat.span_rightExact", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Free", "is_tactic_proof": true, "tactics": ["refine", "simp", "convert", "simp", "rw", "rw"], "tactic_count": 6}
{"name": "ModuleCat.Basis.ofShortExact", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.free_shortExact", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.free_shortExact_rank_add", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Free", "is_tactic_proof": true, "tactics": ["haveI", "rw", "exact"], "tactic_count": 3}
{"name": "ModuleCat.free_shortExact_finrank_add", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Free", "is_tactic_proof": true, "tactics": ["apply", "rw", "simp"], "tactic_count": 3}
{"name": "ModuleCat.image", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.image.ι", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.instMonoι", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.factorThruImage", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.image.fac", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.image.lift", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.image.lift_fac", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Images", "is_tactic_proof": true, "tactics": ["ext", "change", "rw", "rfl"], "tactic_count": 4}
{"name": "ModuleCat.monoFactorisation", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.isImage", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.imageIsoRange", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.imageIsoRange_inv_image_ι", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.imageIsoRange_hom_subtype", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Images", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Module.injective_object_of_injective_module", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Injective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.injective_module_of_injective_object", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Injective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.injective_iff_injective_object", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Injective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.ulift_injective_of_injective", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Injective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.kernelCone", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.kernelIsLimit", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.cokernelCocone", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.cokernelIsColimit", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.hasKernels_moduleCat", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.hasCokernels_moduleCat", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.kernelIsoKer", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.kernelIsoKer_inv_kernel_ι", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.kernelIsoKer_hom_ker_subtype", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.cokernelIsoRangeQuotient", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.cokernel_π_cokernelIsoRangeQuotient_hom", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.range_mkQ_cokernelIsoRangeQuotient_inv", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.cokernel_π_ext", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Kernels", "is_tactic_proof": true, "tactics": ["subst", "simpa"], "tactic_count": 2}
{"name": "ModuleCat.instProjectiveObjFree", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.LeftResolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.projectiveResolution", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.LeftResolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.addCommGroupObj", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.moduleObj", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.sectionsSubmodule", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.instAddCommMonoidElemForallObjCompForgetSections", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.instModuleElemForallObjCompForgetSections", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.instSmallSubtypeForallCarrierObjMemSubmoduleSectionsSubmodule", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.limitAddCommMonoid", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.limitAddCommGroup", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.limitModule", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.limitπLinearMap", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.HasLimits.limitCone", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.HasLimits.limitConeIsLimit", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Limits", "is_tactic_proof": false, "tactics": ["refine", "intro", "simp", "rw", "rfl", "intro", "simp", "rw", "rfl"], "tactic_count": 9}
{"name": "ModuleCat.hasLimit", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.hasLimitsOfShape", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.hasLimitsOfSize", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.hasLimits", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.hasLimits'", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.forget₂AddCommGroup_preservesLimitsAux", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.forget₂AddCommGroup_preservesLimit", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.forget₂AddCommGroup_preservesLimitsOfSize", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.forget₂AddCommGroup_preservesLimits", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.forget_preservesLimitsOfSize", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.forget_preservesLimits", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.forget₂AddCommGroup_reflectsLimit", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.forget₂AddCommGroup_reflectsLimitOfShape", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.forget₂AddCommGroup_reflectsLimitOfSize", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.directLimitDiagram", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.directLimitCocone", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.directLimitIsColimit", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instSmallLocalizedModule", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.localizedModule", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.instModuleCarrierLocalizationLocalizedModule", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.instIsScalarTowerLocalizationCarrierLocalizedModule", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.localizedModuleMkLinearMap", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.localizedModule_isLocalizedModule", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Localization", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "ModuleCat.localizedModuleMap", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.localizedModule_functor", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.instAdditiveLocalizationLocalizedModule_functor", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.localizedModule_functor_map_exact", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Localization", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ModuleCat.instPreservesFiniteLimitsLocalizationLocalizedModule_functor", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Localization", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "ModuleCat.instPreservesFiniteColimitsLocalizationLocalizedModule_functor", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Localization", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "SemimoduleCat.MonoidalCategory.tensorObj", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.MonoidalCategory.tensorHom", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.MonoidalCategory.whiskerLeft", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.MonoidalCategory.whiskerRight", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.MonoidalCategory.id_tensorHom_id", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": false, "tactics": ["ext", "apply", "rfl"], "tactic_count": 3}
{"name": "SemimoduleCat.MonoidalCategory.tensorHom_comp_tensorHom", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": false, "tactics": ["ext", "apply", "rfl"], "tactic_count": 3}
{"name": "SemimoduleCat.MonoidalCategory.associator", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.MonoidalCategory.leftUnitor", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.MonoidalCategory.rightUnitor", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.MonoidalCategory.instMonoidalCategoryStruct", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.MonoidalCategory.associator_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": true, "tactics": ["ext", "apply", "intro", "rfl"], "tactic_count": 4}
{"name": "SemimoduleCat.MonoidalCategory.pentagon", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": true, "tactics": ["ext", "apply", "intro", "rfl"], "tactic_count": 4}
{"name": "SemimoduleCat.MonoidalCategory.leftUnitor_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": false, "tactics": ["ext", "apply", "ext", "simp"], "tactic_count": 4}
{"name": "SemimoduleCat.MonoidalCategory.rightUnitor_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": false, "tactics": ["ext", "apply", "ext", "simp"], "tactic_count": 4}
{"name": "SemimoduleCat.MonoidalCategory.triangle", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": true, "tactics": ["ext", "apply", "intro", "exact"], "tactic_count": 4}
{"name": "SemimoduleCat.monoidalCategory", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.instCommSemiringCarrierTensorUnit", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.hom_tensorHom", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.hom_whiskerLeft", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.hom_whiskerRight", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.hom_hom_leftUnitor", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.hom_inv_leftUnitor", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.hom_hom_rightUnitor", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.hom_inv_rightUnitor", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.hom_hom_associator", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.hom_inv_associator", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.MonoidalCategory.tensorHom_tmul", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.MonoidalCategory.whiskerLeft_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.MonoidalCategory.whiskerRight_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.MonoidalCategory.leftUnitor_hom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.MonoidalCategory.leftUnitor_inv_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.MonoidalCategory.rightUnitor_hom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.MonoidalCategory.rightUnitor_inv_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.MonoidalCategory.associator_hom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.MonoidalCategory.associator_inv_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.MonoidalCategory.tensorLift", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.MonoidalCategory.tensorLift_tmul", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.MonoidalCategory.tensor_ext", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.MonoidalCategory.tensor_ext₃'", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.MonoidalCategory.tensor_ext₃", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ModuleCat.MonoidalCategory.instMonoidalCategoryStruct", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.monoidalCategory", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.instCommRingCarrierTensorUnit", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.hom_tensorHom", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.hom_whiskerLeft", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.hom_whiskerRight", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.hom_hom_leftUnitor", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.hom_inv_leftUnitor", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.hom_hom_rightUnitor", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.hom_inv_rightUnitor", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.hom_hom_associator", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.hom_inv_associator", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.MonoidalCategory.tensorHom_tmul", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.MonoidalCategory.whiskerLeft_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.MonoidalCategory.whiskerRight_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.MonoidalCategory.leftUnitor_hom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.MonoidalCategory.leftUnitor_inv_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.MonoidalCategory.rightUnitor_hom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.MonoidalCategory.rightUnitor_inv_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.MonoidalCategory.associator_hom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.MonoidalCategory.associator_inv_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.MonoidalCategory.tensorLift", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.MonoidalCategory.tensorLift_tmul", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.MonoidalCategory.tensor_ext", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.MonoidalCategory.tensor_ext₃'", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.MonoidalCategory.tensor_ext₃", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ModuleCat.instMonoidalPreadditive", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": true, "tactics": ["refine", "intros", "ext", "refine", "simp", "erw", "simp", "intros", "ext", "refine", "simp", "erw", "simp", "intros", "ext", "refine", "simp", "erw", "erw", "simp", "intros", "ext", "refine", "simp", "erw", "erw", "simp"], "tactic_count": 27}
{"name": "ModuleCat.instMonoidalLinear", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": true, "tactics": ["refine", "intros", "ext", "refine", "simp", "erw", "simp", "intros", "ext", "refine", "simp", "erw", "simp"], "tactic_count": 13}
{"name": "ModuleCat.ofHom₂_compr₂", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.monoidalClosedHomEquiv", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Closed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.instMonoidalClosed", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Closed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.ihom_map_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Closed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.monoidalClosed_curry", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Closed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.monoidalClosed_uncurry", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Closed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.ihom_ev_app", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Closed", "is_tactic_proof": true, "tactics": ["rw", "ext", "apply", "apply"], "tactic_count": 4}
{"name": "ModuleCat.ihom_coev_app", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Closed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.monoidalClosed_pre_app", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Closed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.braiding", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Symmetric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.MonoidalCategory.braiding_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Symmetric", "is_tactic_proof": true, "tactics": ["ext", "apply", "intro", "rfl"], "tactic_count": 4}
{"name": "SemimoduleCat.MonoidalCategory.braiding_naturality_left", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Symmetric", "is_tactic_proof": true, "tactics": ["simp_rw", "apply"], "tactic_count": 2}
{"name": "SemimoduleCat.MonoidalCategory.braiding_naturality_right", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Symmetric", "is_tactic_proof": true, "tactics": ["simp_rw", "apply"], "tactic_count": 2}
{"name": "SemimoduleCat.MonoidalCategory.hexagon_forward", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Symmetric", "is_tactic_proof": true, "tactics": ["ext", "apply", "intro", "rfl"], "tactic_count": 4}
{"name": "SemimoduleCat.MonoidalCategory.hexagon_reverse", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Symmetric", "is_tactic_proof": true, "tactics": ["apply", "ext", "apply", "intro", "rfl"], "tactic_count": 5}
{"name": "SemimoduleCat.MonoidalCategory.symmetricCategory", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Symmetric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.MonoidalCategory.braiding_hom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Symmetric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.MonoidalCategory.braiding_inv_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Symmetric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.MonoidalCategory.tensorμ_eq_tensorTensorTensorComm", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Symmetric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.MonoidalCategory.tensorμ_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Symmetric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.MonoidalCategory.instBraidedCategory", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Symmetric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.MonoidalCategory.instBraidedSemimoduleCatFunctorEquivalenceSemimoduleCat", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Symmetric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.MonoidalCategory.symmetricCategory", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Symmetric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.MonoidalCategory.braiding_hom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Symmetric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.MonoidalCategory.braiding_inv_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Symmetric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.MonoidalCategory.tensorμ_eq_tensorTensorTensorComm", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Symmetric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.MonoidalCategory.tensorμ_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Monoidal.Symmetric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.map_smul", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PresheafOfModules.congr_map_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PresheafOfModules.instCategory", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.hom_ext", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.id_app", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "PresheafOfModules.comp_app", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "PresheafOfModules.naturality_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.presheaf", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.presheaf_obj_coe", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.presheaf_map_apply_coe", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.instModuleCarrierObjOppositeRingCatCarrierAbPresheaf", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.toPresheaf", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.toPresheaf_obj_coe", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.toPresheaf_map_app_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.instFaithfulFunctorOppositeAbToPresheaf", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.ofPresheaf", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.ofPresheaf_presheaf", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.homMk", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.instZeroHom", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.zero_app", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.instNegHom", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.instAddHom", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.instSubHom", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.neg_app", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.add_app", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.sub_app", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.instAddCommGroupHom", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.instPreadditive", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.instAdditiveFunctorOppositeAbToPresheaf", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.zsmul_app", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf", "is_tactic_proof": true, "tactics": ["ext", "change", "rw", "rfl"], "tactic_count": 4}
{"name": "PresheafOfModules.evaluation", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.instAdditiveModuleCatCarrierObjOppositeRingCatEvaluation", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.restriction", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.unit", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.unit_map_one", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.sections", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.sections.eval", "kind": "abbrev", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.sections_property", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.sectionsMk", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.sections_ext", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.sectionsMap", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.sectionsMap_comp", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.sectionsMap_id", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.unitHomEquiv", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.forgetToPresheafModuleCatObjObj", "kind": "abbrev", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.forgetToPresheafModuleCatObjObj_coe", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.forgetToPresheafModuleCatObjMap", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.forgetToPresheafModuleCatObjMap_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.forgetToPresheafModuleCatObj", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.forgetToPresheafModuleCatMap", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.forgetToPresheafModuleCat", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.instIsNormalEpiCategory", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.instIsNormalMonoCategory", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.instAbelian", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.restrictScalarsObj", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.ChangeOfRings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.restrictScalars", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.ChangeOfRings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.instAdditiveRestrictScalars", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.ChangeOfRings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.instFullRestrictScalarsIdFunctorOppositeRingCat", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.ChangeOfRings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.instFaithfulRestrictScalars", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.ChangeOfRings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.restrictScalarsCompToPresheaf", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.ChangeOfRings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.evaluationJointlyReflectsColimits", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.instHasColimitModuleCatCarrierObjOppositeRingCatCompEvaluationRestrictScalarsHomMap", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.colimitPresheafOfModules", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.colimitCocone", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.isColimitColimitCocone", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.hasColimit", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.evaluation_preservesColimit", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.toPresheaf_preservesColimit", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.hasColimitsOfShape", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.evaluation_preservesColimitsOfShape", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.toPresheaf_preservesColimitsOfShape", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.Finite.hasFiniteColimits", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.Finite.evaluation_preservesFiniteColimits", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.Finite.toPresheaf_preservesFiniteColimits", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.hasColimitsOfSize", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.evaluation_preservesColimitsOfSize", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.toPresheaf_preservesColimitsOfSize", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.epi_of_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.mono_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.instEpiModuleCatCarrierObjOppositeRingCatApp", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.instMonoModuleCatCarrierObjOppositeRingCatApp", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.surjective_of_epi", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.EpiMono", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "PresheafOfModules.injective_of_mono", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.EpiMono", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "PresheafOfModules.epi_iff_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.mono_iff_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.freeObj", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.free", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.freeObjDesc", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.freeAdjunctionUnit", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.freeHomEquiv", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.free_hom_ext", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.freeAdjunction", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.freeAdjunction_homEquiv", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Free", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PresheafOfModules.freeAdjunction_unit_app", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.freeYonedaEquiv", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Generator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.freeYonedaEquiv_symm_app", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Generator", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "rfl"], "tactic_count": 3}
{"name": "PresheafOfModules.freeYonedaEquiv_comp", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Generator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.freeYoneda", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Generator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.freeYoneda.instSmall", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Generator", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "PresheafOfModules.freeYoneda.isSeparating", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Generator", "is_tactic_proof": true, "tactics": ["intro", "ext", "obtain", "exact"], "tactic_count": 4}
{"name": "PresheafOfModules.freeYoneda.isDetecting", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Generator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.wellPowered", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Generator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.Elements", "kind": "abbrev", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Generator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.elementsMk", "kind": "abbrev", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Generator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.Elements.freeYoneda", "kind": "abbrev", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Generator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.Elements.fromFreeYoneda", "kind": "abbrev", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Generator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.Elements.fromFreeYoneda_app_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Generator", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "PresheafOfModules.freeYonedaCoproduct", "kind": "abbrev", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Generator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.ιFreeYonedaCoproduct", "kind": "abbrev", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Generator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.fromFreeYonedaCoproduct", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Generator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.freeYonedaCoproductMk", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Generator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.ι_fromFreeYonedaCoproduct", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Generator", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "PresheafOfModules.ι_fromFreeYonedaCoproduct_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Generator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.fromFreeYonedaCoproduct_app_mk", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Generator", "is_tactic_proof": true, "tactics": ["dsimp", "erw", "rw"], "tactic_count": 3}
{"name": "PresheafOfModules.instEpiFromFreeYonedaCoproduct", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Generator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.toFreeYonedaCoproduct", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Generator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.toFreeYonedaCoproduct_fromFreeYonedaCoproduct", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Generator", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PresheafOfModules.freeYonedaCoproductsCokernelCofork", "kind": "abbrev", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Generator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.isColimitFreeYonedaCoproductsCokernelCofork", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Generator", "is_tactic_proof": true, "tactics": ["let", "let", "let", "τ₂", "τ₃", "exact"], "tactic_count": 6}
{"name": "PresheafOfModules.evaluationJointlyReflectsLimits", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.instHasLimitModuleCatCarrierObjOppositeRingCatCompEvaluationRestrictScalarsHomMap", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Limits", "is_tactic_proof": true, "tactics": ["change", "infer_instance"], "tactic_count": 2}
{"name": "PresheafOfModules.limitPresheafOfModules", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.limitCone", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.isLimitLimitCone", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.hasLimit", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.evaluation_preservesLimit", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.toPresheaf_preservesLimit", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.hasLimitsOfShape", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.hasLimitsOfSize", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.instPreservesLimitsOfShapeModuleCatCarrierObjOppositeRingCatEvaluation", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.instPreservesLimitsOfSizeModuleCatCarrierObjOppositeRingCatEvaluation", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.instPreservesLimitsOfShapeFunctorOppositeAbToPresheaf", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.instPreservesLimitsOfSizeFunctorOppositeAbToPresheaf", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.hasFiniteLimits", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.evaluation_preservesFiniteLimits", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.toPresheaf_preservesFiniteLimits", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCommRingCarrierObjOppositeRingCatCompCommRingCatForget₂", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.Monoidal.tensorObjMap", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.Monoidal.tensorObj", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.Monoidal.tensorObj_map_tmul", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.Monoidal.tensorHom", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.monoidalCategoryStruct", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.monoidalCategory", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.pullback", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Pullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.pullbackPushforwardAdjunction", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Pullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.pullbackObjIsDefined", "kind": "abbrev", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Pullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.pushforwardCompCoyonedaFreeYonedaCorepresentableBy", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Pullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.pullbackObjIsDefined_free_yoneda", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Pullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.pullbackObjIsDefined_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Pullback", "is_tactic_proof": true, "tactics": ["ext", "simp", "apply", "rintro", "all_goals"], "tactic_count": 5}
{"name": "PresheafOfModules.instIsRightAdjointPushforward", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Pullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.instIsRightAdjointPushforwardIdFunctorOppositeRingCat", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Pullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.pullbackId", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Pullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.instIsRightAdjointPushforwardCompFunctorOppositeRingCatWhiskerLeftOp", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Pullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.pullbackComp", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Pullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.pullback_assoc", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Pullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.pullback_id_comp", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Pullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.pullback_comp_id", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Pullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.pushforward₀_obj", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Pushforward", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.pushforward₀", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Pushforward", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.pushforward₀CompToPresheaf", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Pushforward", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.pushforward", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Pushforward", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.pushforwardCompToPresheaf", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Pushforward", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.pushforward_obj_map_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Pushforward", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.pushforward_obj_map_apply'", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Pushforward", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.pushforward_map_app_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Pushforward", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.pushforward_map_app_apply'", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Pushforward", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.pushforwardId", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Pushforward", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.pushforwardComp", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Pushforward", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.pushforward_assoc", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Pushforward", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "PresheafOfModules.pushforward_comp_id", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Pushforward", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "PresheafOfModules.pushforward_id_comp", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Pushforward", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "PresheafOfModules.sheafification", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Sheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.sheafificationCompToSheaf", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Sheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.sheafificationCompForgetCompToPresheaf", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Sheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.sheafificationHomEquiv", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Sheafification", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "PresheafOfModules.toPresheaf_map_sheafificationHomEquiv_def", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Sheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.toPresheaf_map_sheafificationHomEquiv", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Sheafification", "is_tactic_proof": true, "tactics": ["rw", "dsimp"], "tactic_count": 2}
{"name": "PresheafOfModules.toSheaf_map_sheafificationHomEquiv_symm", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Sheafification", "is_tactic_proof": true, "tactics": ["obtain", "apply", "rw", "rfl"], "tactic_count": 4}
{"name": "PresheafOfModules.sheafificationAdjunction", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Sheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.sheafificationAdjunction_homEquiv_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Sheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.toPresheaf_map_sheafificationAdjunction_unit_app", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Sheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.instIsLeftAdjointSheafOfModulesSheafification", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Sheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.instPreservesFiniteLimitsSheafAddCommGrpCatCompSheafOfModulesSheafificationToSheaf", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Sheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.instReflectsIsomorphismsSheafOfModulesFunctorOppositeAddCommGrpCatCompSheafToSheafSheafToPresheaf", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Sheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.instReflectsIsomorphismsSheafOfModulesSheafAddCommGrpCatToSheaf", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Sheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.instReflectsFiniteLimitsSheafOfModulesSheafAddCommGrpCatToSheaf", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Sheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.instPreservesFiniteLimitsSheafOfModulesSheafification", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Sheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.FamilyOfElements.smul", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Sheafify", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.Sheafify.app_eq_of_isLocallyInjective", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Sheafify", "is_tactic_proof": true, "tactics": ["apply", "apply", "exact", "exact", "intro", "rw", "erw", "rfl"], "tactic_count": 8}
{"name": "CategoryTheory.Presieve.FamilyOfElements.isCompatible_map_smul_aux", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Sheafify", "is_tactic_proof": false, "tactics": ["rw", "rw", "rw", "erw"], "tactic_count": 4}
{"name": "CategoryTheory.Presieve.FamilyOfElements.isCompatible_map_smul", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Sheafify", "is_tactic_proof": true, "tactics": ["intro", "let", "let", "let", "let", "let", "let", "have", "have", "have", "have", "have", "rw", "have", "dsimp", "erw", "have", "have", "dsimp", "erw", "exact"], "tactic_count": 21}
{"name": "PresheafOfModules.Sheafify.SMulCandidate.mk'", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Sheafify", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.Sheafify.instNonemptySMulCandidate", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Sheafify", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.Sheafify.instSubsingletonSMulCandidate", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Sheafify", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.Sheafify.instUniqueSMulCandidate", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Sheafify", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.Sheafify.smulCandidate", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Sheafify", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.Sheafify.smul", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Sheafify", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.Sheafify.map_smul_eq", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Sheafify", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.Sheafify.one_smul", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Sheafify", "is_tactic_proof": true, "tactics": ["apply", "rintro", "rw"], "tactic_count": 3}
{"name": "PresheafOfModules.Sheafify.zero_smul", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Sheafify", "is_tactic_proof": true, "tactics": ["apply", "rintro", "rw"], "tactic_count": 3}
{"name": "PresheafOfModules.Sheafify.smul_zero", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Sheafify", "is_tactic_proof": true, "tactics": ["apply", "rintro", "rw"], "tactic_count": 3}
{"name": "PresheafOfModules.Sheafify.smul_add", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Sheafify", "is_tactic_proof": true, "tactics": ["let", "have", "refine", "all_goals", "apply", "rintro", "rw", "map_smul_eq"], "tactic_count": 8}
{"name": "PresheafOfModules.Sheafify.add_smul", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Sheafify", "is_tactic_proof": true, "tactics": ["let", "have", "refine", "all_goals", "apply", "rintro", "rw", "map_smul_eq"], "tactic_count": 8}
{"name": "PresheafOfModules.Sheafify.mul_smul", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Sheafify", "is_tactic_proof": true, "tactics": ["let", "have", "refine", "all_goals", "apply", "rintro", "rw", "map_smul_eq"], "tactic_count": 8}
{"name": "PresheafOfModules.Sheafify.module", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Sheafify", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.Sheafify.map_smul", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Sheafify", "is_tactic_proof": true, "tactics": ["let", "have", "apply", "all_goals", "apply", "rintro", "rw", "map_smul_eq", "map_smul_eq"], "tactic_count": 9}
{"name": "PresheafOfModules.sheafify", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Sheafify", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.toSheafify", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Sheafify", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.toSheafify_app_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Sheafify", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.toSheafify_app_apply'", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Sheafify", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.toPresheaf_map_toSheafify", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Sheafify", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.instIsLocallyInjectiveToSheafify", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Sheafify", "is_tactic_proof": true, "tactics": ["dsimp"], "tactic_count": 1}
{"name": "PresheafOfModules.instIsLocallySurjectiveToSheafify", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Sheafify", "is_tactic_proof": true, "tactics": ["dsimp"], "tactic_count": 1}
{"name": "PresheafOfModules.sheafifyHomEquiv'", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Sheafify", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.comp_toPresheaf_map_sheafifyHomEquiv'_symm_hom", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Sheafify", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.sheafifyHomEquiv", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Sheafify", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.sheafifyMap", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Presheaf.Sheafify", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.productCone", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.productConeIsLimit", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.piIsoPi", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.piIsoPi_inv_kernel_ι", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.piIsoPi_hom_ker_subtype", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.coproductCocone", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.coproductCoconeIsColimit", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.coprodIsoDirectSum", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.ι_coprodIsoDirectSum_hom", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.lof_coprodIsoDirectSum_inv", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.projective_of_categoryTheory_projective", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Projective", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact"], "tactic_count": 3}
{"name": "ModuleCat.projective_of_module_projective", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Projective", "is_tactic_proof": true, "tactics": ["refine", "intro", "have", "exact"], "tactic_count": 4}
{"name": "IsProjective.iff_projective", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Projective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.projective_of_free", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Projective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.enoughProjectives", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Projective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.moduleCatRestrictScalarsPseudofunctor", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Pseudofunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCat.moduleCatRestrictScalarsPseudofunctor", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Pseudofunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.moduleCatExtendScalarsPseudofunctor", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Pseudofunctor", "is_tactic_proof": false, "tactics": ["refine", "intros", "intros", "intros"], "tactic_count": 4}
{"name": "SemimoduleCat.instCoeSortType", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.of", "kind": "abbrev", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.coe_of", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat._example", "kind": "example", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": true, "tactics": ["with_reducible"], "tactic_count": 1}
{"name": "SemimoduleCat._example", "kind": "example", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": true, "tactics": ["with_reducible"], "tactic_count": 1}
{"name": "SemimoduleCat.moduleCategory", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.instConcreteCategoryLinearMapIdCarrier", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.Hom.hom", "kind": "abbrev", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.ofHom", "kind": "abbrev", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.Hom.Simps.hom", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.hom_id", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.id_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SemimoduleCat.hom_comp", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.comp_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SemimoduleCat.hom_ext", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.hom_bijective", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.hom_injective", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.hom_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.hom_ofHom", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.ofHom_hom", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.ofHom_id", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.ofHom_comp", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.ofHom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.inv_hom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SemimoduleCat.hom_inv_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SemimoduleCat.homEquiv", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.forget_obj", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.forget_map", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.hasForgetToAddCommMonoid", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.forget₂_obj", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.forget₂_obj_moduleCat_of", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.forget₂_map", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.instInhabited", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.of_coe", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.isZero_of_subsingleton", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.instHasZeroObject", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.term↟_", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat._aux_Mathlib_Algebra_Category_ModuleCat_Semi___macroRules_SemimoduleCat_term↟__1", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat._aux_Mathlib_Algebra_Category_ModuleCat_Semi___unexpand_SemimoduleCat_ofHom_1", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.toModuleIsoₛ", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.toLinearEquivₛ", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "linearEquivIsoModuleIsoₛ", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.instAddHom", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.hom_add", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.instZeroHom", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.hom_zero", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.instSMulNatHom", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.hom_nsmul", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.instAddCommMonoidHom", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.hom_sum", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.instHasZeroMorphisms", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.homAddEquiv", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.subsingleton_of_isZero", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": true, "tactics": ["refine", "rw", "simp"], "tactic_count": 3}
{"name": "SemimoduleCat.isZero_iff_subsingleton", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.isZero_of_iff_subsingleton", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.instSMulHom", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.hom_smul", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.Hom.instModule", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.homLinearEquiv", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.Algebra.instModuleCarrier", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.Algebra.instIsScalarTowerCarrier", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.Algebra.instSMulCommClassCarrier", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.Iso.homCongr_eq_arrowCongr", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.Iso.conj_eq_conj", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.instReflectsIsomorphismsForget", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.instReflectsIsomorphismsAddCommMonCatForget₂", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.ofHom₂", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.Hom.hom₂", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.Hom.hom₂_ofHom₂", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemimoduleCat.ofHom₂_hom₂", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.comp_id_semiModuleCat", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LinearMap.id_semiModuleCat_comp", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Semi", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SheafOfModules.instCategory", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.hom_ext", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.id_val", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.comp_val", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.forget", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.fullyFaithfulForget", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.instFaithfulPresheafOfModulesValRingCatForget", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.instFullPresheafOfModulesValRingCatForget", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.instReflectsIsomorphismsPresheafOfModulesValRingCatForget", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.evaluation", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.toSheaf", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.forgetToSheafModuleCat", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.toSheafCompSheafToPresheafIso", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.instFaithfulSheafAddCommGrpCatToSheaf", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.instAddCommGroupHom", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.add_val", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.instPreadditive", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.instAdditivePresheafOfModulesValRingCatForget", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.instAdditiveSheafAddCommGrpCatToSheaf", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.sections", "kind": "abbrev", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.sectionsMap", "kind": "abbrev", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.sectionsMap_comp", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.sectionsMap_id", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.sectionsFunctor", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.unit", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.unitHomEquiv", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.unitHomEquiv_apply_coe", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.unitHomEquiv_comp_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.unitHomEquiv_symm_comp", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.IsLocallySurjective", "kind": "abbrev", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.IsLocallyInjective", "kind": "abbrev", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.homEquivOfIsLocallyBijective", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.instAbelian", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian", "is_tactic_proof": true, "tactics": ["let", "exact"], "tactic_count": 2}
{"name": "SheafOfModules.restrictScalars", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.ChangeOfRings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.instAdditiveRestrictScalars", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.ChangeOfRings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.restrictHomEquivOfIsLocallySurjective", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.ChangeOfRings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.instHasColimitsOfShapeOfPresheafOfModulesValRingCat", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.instHasColimitsOfSizeOfPresheafOfModulesValRingCat", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.free", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.ιFree", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.freeCofan", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.freeCofan_inj", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.isColimitFreeCofan", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.freeHomEquiv", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.freeHomEquiv_comp_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.freeHomEquiv_symm_comp", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.freeSection", "kind": "abbrev", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.unitHomEquiv_symm_freeHomEquiv_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.Free", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SheafOfModules.freeMap", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.freeHomEquiv_freeMap", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.sectionMap_freeMap_freeSection", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.Free", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SheafOfModules.ιFree_freeMap", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.Free", "is_tactic_proof": true, "tactics": ["rw", "dsimp", "rw"], "tactic_count": 3}
{"name": "SheafOfModules.freeFunctor", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.mapFree", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.ιFree_mapFree_inv", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.Free", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SheafOfModules.map_ιFree_mapFree_hom", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.Free", "is_tactic_proof": false, "tactics": ["have", "rw", "simp"], "tactic_count": 3}
{"name": "SheafOfModules.GeneratingSections.π", "kind": "abbrev", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.Generators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.GeneratingSections.ofEpi", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.Generators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.GeneratingSections.opEpi_id", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.Generators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.GeneratingSections.opEpi_comp", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.Generators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.GeneratingSections.equivOfIso", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.Generators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.localGeneratorsDataOfIsFiniteType", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.Generators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresheafOfModules.isSheaf_of_isLimit", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.Limits", "is_tactic_proof": false, "tactics": ["let", "map", "exact"], "tactic_count": 3}
{"name": "SheafOfModules.instSmallElemForallObjCompModuleCatCarrierOppositeRingCatValPresheafOfModulesForgetEvaluationForgetSections", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.Limits", "is_tactic_proof": true, "tactics": ["solve_by_elim"], "tactic_count": 1}
{"name": "SheafOfModules.createsLimit", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.hasLimit", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.evaluationPreservesLimit", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.Limits", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "SheafOfModules.hasLimitsOfShape", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.evaluationPreservesLimitsOfShape", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.forgetPreservesLimitsOfShape", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.Finite.hasFiniteLimits", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.Finite.evaluationPreservesFiniteLimits", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.Finite.forgetPreservesFiniteLimits", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.hasLimitsOfSize", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.evaluationPreservesLimitsOfSize", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.forgetPreservesLimitsOfSize", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.instPreservesFiniteLimitsFunctorOppositeAddCommGrpCatCompSheafToSheafSheafToPresheaf", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.instPreservesFiniteLimitsSheafAddCommGrpCatToSheaf", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.pullback", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.PullbackContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.pullbackPushforwardAdjunction", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.PullbackContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.instIsLeftAdjointPullback", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.PullbackContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.PullbackConstruction.adjunction", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.PullbackContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.instIsRightAdjointPushforward", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.PullbackContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.pullbackIso", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.PullbackContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.sheafificationCompPullback", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.PullbackContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.instIsRightAdjointPushforwardIdSheafRingCat", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.PullbackContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.pullbackId", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.PullbackContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.conjugateEquiv_pullbackId_hom", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.PullbackContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.instIsRightAdjointPushforwardCompSheafRingCatMapSheafPushforwardContinuous", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.PullbackContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.pullbackComp", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.PullbackContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.conjugateEquiv_pullbackComp_inv", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.PullbackContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.pullback_assoc", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.PullbackContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.pullback_id_comp", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.PullbackContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.pullback_comp_id", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.PullbackContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.pushforwardSections", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.PullbackFree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.bijective_pushforwardSections", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.PullbackFree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.unitToPushforwardObjUnit", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.PullbackFree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.unitToPushforwardObjUnit_val_app_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.PullbackFree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.pushforwardSections_unitHomEquiv", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.PullbackFree", "is_tactic_proof": true, "tactics": ["ext", "have", "dsimp", "simp", "rfl"], "tactic_count": 5}
{"name": "SheafOfModules.pullbackObjUnitToUnit", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.PullbackFree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.pullbackPushforwardAdjunction_homEquiv_symm_unitToPushforwardObjUnit", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.PullbackFree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.pullbackPushforwardAdjunction_homEquiv_pullbackObjUnitToUnit", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.PullbackFree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.instIsIsoPullbackObjUnitToUnitOfFinal", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.PullbackFree", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "convert", "ext", "dsimp", "rw", "pullbackPushforwardAdjunction_homEquiv_pullbackObjUnitToUnit]"], "tactic_count": 8}
{"name": "SheafOfModules.pullbackObjFreeIso", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.PullbackFree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.pullback_map_ιFree_comp_pullbackObjFreeIso_hom", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.PullbackFree", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SheafOfModules.pullbackObjFreeIso_hom_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.PullbackFree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.freeFunctorCompPullbackIso", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.PullbackFree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.pushforward", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.PushforwardContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.over", "kind": "abbrev", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.PushforwardContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.pushforwardId", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.PushforwardContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.pushforwardCongr", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.PushforwardContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.pushforwardCongr_symm", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.PushforwardContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.pushforwardCongr_hom_app_val_app", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.PushforwardContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.pushforwardCongr_inv_app_val_app", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.PushforwardContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.pushforwardComp", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.PushforwardContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.pushforwardComp_hom_app_val_app", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.PushforwardContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.pushforwardComp_inv_app_val_app", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.PushforwardContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.pushforward_assoc", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.PushforwardContinuous", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "SheafOfModules.pushforward_comp_id", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.PushforwardContinuous", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "SheafOfModules.pushforward_id_comp", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.PushforwardContinuous", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "SheafOfModules.pushforwardNatTrans", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.PushforwardContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.pushforwardNatTrans_app_val_app", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.PushforwardContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.pushforwardNatTrans_id", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.PushforwardContinuous", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "SheafOfModules.pushforwardNatTrans_comp", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.PushforwardContinuous", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "SheafOfModules.pushforwardNatTrans_app_val_app_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.PushforwardContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.pushforwardNatIso", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.PushforwardContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.pushforwardPushforwardAdj", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.PushforwardContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.pushforwardPushforwardAdj_unit_app_val_app", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.PushforwardContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.pushforwardPushforwardAdj_counit_app_val_app", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.PushforwardContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.generatorsOfIsCokernelFree", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.Quasicoherent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.generatorsOfIsCokernelFree_π", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.Quasicoherent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.relationsOfIsCokernelFree", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.Quasicoherent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.presentationOfIsCokernelFree", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.Quasicoherent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.Presentation.isColimit", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.Quasicoherent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.Presentation.mapRelations", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.Quasicoherent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.Presentation.mapGenerators", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.Quasicoherent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.Presentation.mapRelations_mapGenerators", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.Quasicoherent", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SheafOfModules.Presentation.map", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.Quasicoherent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.Presentation.map_π_eq", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.Quasicoherent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.QuasicoherentData.localGeneratorsData", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.Quasicoherent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.QuasicoherentData.instIsFiniteTypeLocalGeneratorsDataOfIsFinitePresentation", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.Quasicoherent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.isQuasicoherent", "kind": "abbrev", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.Quasicoherent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.isFinitePresentation", "kind": "abbrev", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.Quasicoherent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.instIsQuasicoherentOfIsFinitePresentation", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.Quasicoherent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.instIsFiniteTypeOfIsFinitePresentation", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.Quasicoherent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SheafOfModules.quasicoherentDataOfIsFinitePresentation", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Sheaf.Quasicoherent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "simple_iff_isSimpleModule", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Simple", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "simple_iff_isSimpleModule'", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Simple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "simple_of_isSimpleModule", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Simple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isSimpleModule_of_simple", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Simple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "simple_of_finrank_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Simple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.subobjectModule", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Subobject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.wellPowered_moduleCat", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Subobject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.toKernelSubobject", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Subobject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.toKernelSubobject_arrow", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Subobject", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ModuleCat.cokernel_π_imageSubobject_ext", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Subobject", "is_tactic_proof": true, "tactics": ["subst", "simp"], "tactic_count": 2}
{"name": "ringEquivEndForget₂", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Tannaka", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.instCoeSortType", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.of", "kind": "abbrev", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.coe_of", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.instCategory", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.instConcreteCategoryContinuousLinearMapIdCarrier", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.Hom.hom", "kind": "abbrev", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.ofHom", "kind": "abbrev", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.hom_ofHom", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.ofHom_hom", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.hom_comp", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.hom_id", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.Hom.Simps.hom", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.ofIso", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.toContinuousLinearEquiv", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.instAddCommGroupHom", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.instPreadditive", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.hom_zero", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.hom_zero_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.hom_add", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.hom_neg", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.hom_sub", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.hom_nsmul", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.hom_zsmul", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.instModuleHom", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.instLinear", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.hom_smul", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.instTopologicalSpaceCarrier", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.instIsTopologicalAddGroupCarrier", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.instHasForget₂ModuleCat", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.instHasForget₂TopCat", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.instReflectsIsomorphismsTopCatForget₂", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.hom_forget₂_TopCat_map", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.forget₂_TopCat_obj", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.coinduced", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.toCoinduced", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.ofCocone", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.isColimit", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.instHasColimitOfModuleCatCompForget₂", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.instHasColimitsOfShapeOfModuleCat", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.instHasColimits", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.induced", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.fromInduced", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.ofCone", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.isLimit", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.hasLimit_of_hasLimit_forget₂", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.instHasLimitsOfShapeOfModuleCat", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.instHasLimits", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.instPreservesLimitTopCatForget₂OfHasLimitOfModuleCatCompForget", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.instPreservesLimitsOfShapeTopCatForget₂OfHasLimitsOfShapeOfModuleCatForget", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.instPreservesLimitsTopCatForget₂", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.withModuleTopology", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.withModuleTopologyAdj", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.instIsRightAdjointModuleCatForget₂", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.instIsLeftAdjointModuleCatWithModuleTopology", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.indiscrete", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.indiscreteAdj", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.instIsLeftAdjointModuleCatForget₂", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.instIsRightAdjointModuleCatIndiscrete", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.freeObj", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.coe_freeObj", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.freeMap", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.freeMap_map", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.free", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.freeAdj", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.instIsRightAdjointTopCatForget₂", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.instIsLeftAdjointTopCatFree", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.ker", "kind": "abbrev", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.kerι", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.instMonoKerι", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.kerι_comp", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Homology", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "TopModuleCat.kerι_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.isLimitKer", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.coker", "kind": "abbrev", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.cokerπ", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.hom_cokerπ", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.cokerπ_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.instEpiCokerπ", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.comp_cokerπ", "kind": "theorem", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Homology", "is_tactic_proof": true, "tactics": ["ext", "change", "simp"], "tactic_count": 3}
{"name": "TopModuleCat.isColimitCoker", "kind": "definition", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopModuleCat.instCategoryWithHomology", "kind": "instance", "module": "Mathlib.Algebra.Category.ModuleCat.Topology.Homology", "is_tactic_proof": true, "tactics": ["constructor", "intro", "let", "let", "let", "suffices", "have", "change", "rw", "infer_instance", "have", "refine", "refine", "isEmbedding_of_isOpenQuotientMap_of_isInducing", "rw", "suffices", "intro", "obtain", "obtain", "simpa", "rw", "isHomeomorph_iff_isEmbedding_surjective]", "exact"], "tactic_count": 23}
{"name": "MonCat.adjoinOne", "kind": "definition", "module": "Mathlib.Algebra.Category.MonCat.Adjunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonCat.hasForgetToSemigroup", "kind": "instance", "module": "Mathlib.Algebra.Category.MonCat.Adjunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonCat.adjoinOneAdj", "kind": "definition", "module": "Mathlib.Algebra.Category.MonCat.Adjunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonCat.free", "kind": "definition", "module": "Mathlib.Algebra.Category.MonCat.Adjunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonCat.adj", "kind": "definition", "module": "Mathlib.Algebra.Category.MonCat.Adjunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonCat.instIsRightAdjointForget", "kind": "instance", "module": "Mathlib.Algebra.Category.MonCat.Adjunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommMonCat.free", "kind": "definition", "module": "Mathlib.Algebra.Category.MonCat.Adjunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommMonCat.adj", "kind": "definition", "module": "Mathlib.Algebra.Category.MonCat.Adjunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommMonCat.instIsLeftAdjointFree", "kind": "instance", "module": "Mathlib.Algebra.Category.MonCat.Adjunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommMonCat.instIsRightAdjointForget", "kind": "instance", "module": "Mathlib.Algebra.Category.MonCat.Adjunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommMonCat.instIsRightAdjointForget", "kind": "instance", "module": "Mathlib.Algebra.Category.MonCat.Adjunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonCat.instCoeSortType", "kind": "instance", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonCat.of", "kind": "abbrev", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonCat.instCategory", "kind": "instance", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonCat.instConcreteCategoryMonoidHomCarrier", "kind": "instance", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonCat.Hom.hom", "kind": "abbrev", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonCat.ofHom", "kind": "abbrev", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonCat.Hom.Simps.hom", "kind": "definition", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonCat.coe_id", "kind": "theorem", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonCat.coe_comp", "kind": "theorem", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonCat.forget_map", "kind": "theorem", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonCat.ext", "kind": "theorem", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonCat.coe_of", "kind": "theorem", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonCat.hom_id", "kind": "theorem", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonCat.id_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MonCat.hom_comp", "kind": "theorem", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonCat.comp_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MonCat.hom_ext", "kind": "theorem", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonCat.hom_ofHom", "kind": "theorem", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonCat.ofHom_hom", "kind": "theorem", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonCat.ofHom_id", "kind": "theorem", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonCat.ofHom_comp", "kind": "theorem", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonCat.ofHom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonCat.inv_hom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MonCat.hom_inv_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MonCat.instInhabited", "kind": "instance", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonCat.instOneHom", "kind": "instance", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonCat.hom_one", "kind": "theorem", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonCat.oneHom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonCat.one_of", "kind": "theorem", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonCat.mul_of", "kind": "theorem", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonCat.uliftFunctor", "kind": "definition", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommMonCat.instCoeSortType", "kind": "instance", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommMonCat.of", "kind": "abbrev", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommMonCat.instCategory", "kind": "instance", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommMonCat.instConcreteCategoryMonoidHomCarrier", "kind": "instance", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommMonCat.Hom.hom", "kind": "abbrev", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommMonCat.ofHom", "kind": "abbrev", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommMonCat.Hom.Simps.hom", "kind": "definition", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommMonCat.coe_id", "kind": "theorem", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommMonCat.coe_comp", "kind": "theorem", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommMonCat.forget_map", "kind": "theorem", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommMonCat.ext", "kind": "theorem", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommMonCat.hom_id", "kind": "theorem", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommMonCat.id_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CommMonCat.hom_comp", "kind": "theorem", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommMonCat.comp_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CommMonCat.hom_ext", "kind": "theorem", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommMonCat.hom_ofHom", "kind": "theorem", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommMonCat.ofHom_hom", "kind": "theorem", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommMonCat.ofHom_id", "kind": "theorem", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommMonCat.ofHom_comp", "kind": "theorem", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommMonCat.ofHom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommMonCat.inv_hom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CommMonCat.hom_inv_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CommMonCat.instInhabited", "kind": "instance", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommMonCat.coe_of", "kind": "theorem", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommMonCat.hasForgetToMonCat", "kind": "instance", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommMonCat.coe_forget₂_obj", "kind": "theorem", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommMonCat.hom_forget₂_map", "kind": "theorem", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommMonCat.forget₂_map_ofHom", "kind": "theorem", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommMonCat.fullyFaithfulForgetToMonCat", "kind": "definition", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommMonCat.instFullMonCatForget₂", "kind": "instance", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommMonCat.instCoeMonCat", "kind": "instance", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommMonCat.uliftFunctor", "kind": "definition", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.toMonCatIso", "kind": "definition", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.toCommMonCatIso", "kind": "definition", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.monCatIsoToMulEquiv", "kind": "definition", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.commMonCatIsoToMulEquiv", "kind": "definition", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mulEquivIsoMonCatIso", "kind": "definition", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mulEquivIsoCommMonCatIso", "kind": "definition", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonCat.forget_reflects_isos", "kind": "instance", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommMonCat.forget_reflects_isos", "kind": "instance", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommMonCat.forget₂_full", "kind": "instance", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_example", "kind": "example", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonCat.equivalence", "kind": "definition", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommMonCat.equivalence", "kind": "definition", "module": "Mathlib.Algebra.Category.MonCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonCat.Colimits.Prequotient", "kind": "inductive", "module": "Mathlib.Algebra.Category.MonCat.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonCat.Colimits.instInhabitedPrequotient", "kind": "instance", "module": "Mathlib.Algebra.Category.MonCat.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonCat.Colimits.Relation", "kind": "inductive", "module": "Mathlib.Algebra.Category.MonCat.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonCat.Colimits.colimitSetoid", "kind": "definition", "module": "Mathlib.Algebra.Category.MonCat.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonCat.Colimits.ColimitType", "kind": "definition", "module": "Mathlib.Algebra.Category.MonCat.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonCat.Colimits.instInhabitedColimitType", "kind": "instance", "module": "Mathlib.Algebra.Category.MonCat.Colimits", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "MonCat.Colimits.monoidColimitType", "kind": "instance", "module": "Mathlib.Algebra.Category.MonCat.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonCat.Colimits.quot_one", "kind": "theorem", "module": "Mathlib.Algebra.Category.MonCat.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonCat.Colimits.quot_mul", "kind": "theorem", "module": "Mathlib.Algebra.Category.MonCat.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonCat.Colimits.colimit", "kind": "definition", "module": "Mathlib.Algebra.Category.MonCat.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonCat.Colimits.coconeFun", "kind": "definition", "module": "Mathlib.Algebra.Category.MonCat.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonCat.Colimits.coconeMorphism", "kind": "definition", "module": "Mathlib.Algebra.Category.MonCat.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonCat.Colimits.cocone_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Category.MonCat.Colimits", "is_tactic_proof": true, "tactics": ["ext", "apply", "apply"], "tactic_count": 3}
{"name": "MonCat.Colimits.cocone_naturality_components", "kind": "theorem", "module": "Mathlib.Algebra.Category.MonCat.Colimits", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
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{"name": "MonCat.Colimits.descFunLift", "kind": "definition", "module": "Mathlib.Algebra.Category.MonCat.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SemiRingCat.hom_inv_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SemiRingCat.instInhabited", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiRingCat.forget_obj_eq_coe", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiRingCat.forget_obj", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiRingCat.forget_map", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiRingCat.instSemiringObjForget", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiRingCat.hasForgetToMonCat", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiRingCat.hasForgetToAddCommMonCat", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.toSemiRingCatIso", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiRingCat.forgetReflectIsos", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCat.instCoeSortType", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCat.coe_of", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCat.of_carrier", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCat.instCategory", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCat.instConcreteCategoryRingHomCarrier", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCat.Hom.hom", "kind": "abbrev", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCat.ofHom", "kind": "abbrev", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCat.Hom.Simps.hom", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCat.hom_id", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCat.id_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RingCat.hom_comp", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCat.comp_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RingCat.hom_ext", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCat.hom_ofHom", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCat.ofHom_hom", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCat.ofHom_id", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCat.ofHom_comp", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCat.ofHom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCat.inv_hom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RingCat.hom_inv_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RingCat.instInhabited", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCat.forget_obj_eq_coe", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCat.forget_obj", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCat.forget_map", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCat.instRingObjForget", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCat.hasForgetToSemiRingCat", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCat.fullyFaithfulForget₂ToSemiRingCat", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCat.instFullSemiRingCatForget₂", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCat.hasForgetToAddCommGrp", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.toRingCatIso", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCat.forgetReflectIsos", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommSemiRingCat.instCoeSortType", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommSemiRingCat.coe_of", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommSemiRingCat.of_carrier", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommSemiRingCat.instCategory", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommSemiRingCat.instConcreteCategoryRingHomCarrier", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommSemiRingCat.Hom.hom", "kind": "abbrev", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommSemiRingCat.ofHom", "kind": "abbrev", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommSemiRingCat.Hom.Simps.hom", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommSemiRingCat.hom_id", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommSemiRingCat.id_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CommSemiRingCat.hom_comp", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommSemiRingCat.comp_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CommSemiRingCat.hom_ext", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommSemiRingCat.hom_ofHom", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommSemiRingCat.ofHom_hom", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommSemiRingCat.ofHom_id", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommSemiRingCat.ofHom_comp", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommSemiRingCat.ofHom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommSemiRingCat.inv_hom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CommSemiRingCat.hom_inv_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CommSemiRingCat.instInhabited", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommSemiRingCat.forget_obj_eq_coe", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommSemiRingCat.forget_obj", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommSemiRingCat.forget_map", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommSemiRingCat.instCommSemiringObjForget", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommSemiRingCat.hasForgetToSemiRingCat", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommSemiRingCat.fullyFaithfulForget₂ToSemiRingCat", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommSemiRingCat.instFullSemiRingCatForget₂", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommSemiRingCat.hasForgetToCommMonCat", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.toCommSemiRingCatIso", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommSemiRingCat.forgetReflectIsos", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.instCoeSortType", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.coe_of", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.of_carrier", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.instCategory", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.instConcreteCategoryRingHomCarrier", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.Hom.hom", "kind": "abbrev", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.ofHom", "kind": "abbrev", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.Hom.Simps.hom", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.hom_id", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.id_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CommRingCat.hom_comp", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.comp_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CommRingCat.hom_ext", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.hom_ofHom", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.ofHom_hom", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.ofHom_id", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.ofHom_comp", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.ofHom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.inv_hom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CommRingCat.hom_inv_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CommRingCat.instInhabited", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.forget_obj", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.forget_obj_eq_coe", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.forget_map", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.instCommRingObjForget", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.hasForgetToRingCat", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.fullyFaithfulForget₂ToRingCat", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.instFullRingCatForget₂", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.forgetToRingCat_map_hom", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.forgetToRingCat_obj", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.hasForgetToAddCommMonCat", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.instHasForget₂CommMonCat", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.toCommRingCatIso", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.forgetReflectIsos", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.semiRingCatIsoToRingEquiv", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.ringCatIsoToRingEquiv", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.commSemiRingCatIsoToRingEquiv", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.commRingCatIsoToRingEquiv", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.semiRingCatIsoToRingEquiv_toRingHom", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.ringCatIsoToRingEquiv_toRingHom", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.commSemiRingCatIsoToRingEquiv_toRingHom", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.commRingCatIsoToRingEquiv_toRingHom", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCat.forget_map_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.forget_map_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCat.Colimits.Prequotient", "kind": "inductive", "module": "Mathlib.Algebra.Category.Ring.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCat.Colimits.instInhabitedPrequotient", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCat.Colimits.Relation", "kind": "inductive", "module": "Mathlib.Algebra.Category.Ring.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCat.Colimits.colimitSetoid", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCat.Colimits.ColimitType", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCat.Colimits.ColimitType.instZero", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCat.Colimits.ColimitType.instAdd", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCat.Colimits.ColimitType.instNeg", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCat.Colimits.ColimitType.AddGroup", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCat.Colimits.InhabitedColimitType", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCat.Colimits.ColimitType.AddGroupWithOne", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCat.Colimits.instRingColimitType", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCat.Colimits.quot_zero", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCat.Colimits.quot_one", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCat.Colimits.quot_neg", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCat.Colimits.quot_add", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCat.Colimits.quot_mul", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCat.Colimits.colimit", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCat.Colimits.coconeFun", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCat.Colimits.coconeMorphism", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCat.Colimits.cocone_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Colimits", "is_tactic_proof": true, "tactics": ["ext", "apply", "apply"], "tactic_count": 3}
{"name": "RingCat.Colimits.cocone_naturality_components", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Colimits", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RingCat.Colimits.colimitCocone", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCat.Colimits.descFunLift", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCat.Colimits.descFun", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Colimits", "is_tactic_proof": true, "tactics": ["fapply", "exact", "intro", "induction", "refl", "symm", "trans", "map", "zero", "one", "neg", "add", "mul", "neg_1", "add_1", "add_2", "mul_1", "mul_2", "zero_add", "add_zero", "one_mul", "mul_one", "neg_add_cancel", "add_comm", "add_assoc", "mul_assoc", "left_distrib", "right_distrib", "zero_mul", "mul_zero"], "tactic_count": 30}
{"name": "RingCat.Colimits.descMorphism", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCat.Colimits.colimitIsColimit", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCat.Colimits.hasColimits_ringCat", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.Colimits.Prequotient", "kind": "inductive", "module": "Mathlib.Algebra.Category.Ring.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.Colimits.instInhabitedPrequotient", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.Colimits.Relation", "kind": "inductive", "module": "Mathlib.Algebra.Category.Ring.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.Colimits.colimitSetoid", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.Colimits.ColimitType", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.Colimits.ColimitType.instZero", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.Colimits.ColimitType.instAdd", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.Colimits.ColimitType.instNeg", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.Colimits.ColimitType.AddGroup", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.Colimits.InhabitedColimitType", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.Colimits.ColimitType.AddGroupWithOne", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.Colimits.instCommRingColimitType", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.Colimits.quot_zero", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.Colimits.quot_one", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.Colimits.quot_neg", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.Colimits.quot_add", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.Colimits.quot_mul", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.Colimits.colimit", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.Colimits.coconeFun", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.Colimits.coconeMorphism", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.Colimits.cocone_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Colimits", "is_tactic_proof": true, "tactics": ["ext", "apply", "apply"], "tactic_count": 3}
{"name": "CommRingCat.Colimits.cocone_naturality_components", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Colimits", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CommRingCat.Colimits.colimitCocone", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.Colimits.descFunLift", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.Colimits.descFun", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Colimits", "is_tactic_proof": true, "tactics": ["fapply", "exact", "intro", "induction", "refl", "symm", "trans", "map", "zero", "one", "neg", "add", "mul", "neg_1", "add_1", "add_2", "mul_1", "mul_2", "zero_add", "add_zero", "one_mul", "mul_one", "neg_add_cancel", "add_comm", "mul_comm", "add_assoc", "mul_assoc", "left_distrib", "right_distrib", "zero_mul", "mul_zero"], "tactic_count": 31}
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{"name": "CommRingCat.Colimits.colimitIsColimit", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.Colimits.hasColimits_commRingCat", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.pushoutCocone", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Constructions", "is_tactic_proof": true, "tactics": ["fapply", "exact", "exact", "exact", "ext", "trans", "exact", "exact"], "tactic_count": 8}
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{"name": "CommRingCat.pushoutCocone_inr", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.pushoutCocone_pt", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.pushoutCoconeIsColimit", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.isPushout_tensorProduct", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.isPushout_of_isPushout", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.isPushout_iff_isPushout", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.isPushout_of_isLocalization", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Constructions", "is_tactic_proof": true, "tactics": ["algebraize", "have", "have", "exact"], "tactic_count": 4}
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{"name": "CommRingCat.coproductCocone_inl", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.coproductCocone_inr", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.coproductCoconeIsColimit", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CommRingCat.punitIsTerminal", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.commRingCat_hasStrictTerminalObjects", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Constructions", "is_tactic_proof": true, "tactics": ["apply", "intro", "refine", "ext", "ext", "have", "replace", "rw", "exact"], "tactic_count": 9}
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{"name": "CommRingCat.zIsInitial", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.isInitial", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.prodFan", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.prodFanIsLimit", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.piFan", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.piFanIsLimit", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.piIsoPi", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.piEquivPi", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.equalizerFork", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.equalizerForkIsLimit", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Constructions", "is_tactic_proof": true, "tactics": ["fapply", "intro", "use", "constructor", "ext", "rfl", "intro", "ext", "exact"], "tactic_count": 9}
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{"name": "CommRingCat.pullbackConeIsLimit", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Constructions", "is_tactic_proof": true, "tactics": ["fapply", "intro", "refine", "intro", "exact", "intro", "ext", "rfl", "intro", "ext", "rfl", "intro", "refine", "change", "have", "have", "rw", "rfl"], "tactic_count": 18}
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{"name": "SemiRingCat.FilteredColimits.R", "kind": "abbrev", "module": "Mathlib.Algebra.Category.Ring.FilteredColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SemiRingCat.FilteredColimits.colimitCoconeIsColimit.descAddMonoidHom_quotMk", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.FilteredColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SemiRingCat.FilteredColimits.colimitCoconeIsColimit.descMonoidHom_quotMk", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.FilteredColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiRingCat.FilteredColimits.colimitCoconeIsColimit.descMonoidHom_apply_eq", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.FilteredColimits", "is_tactic_proof": true, "tactics": ["obtain", "rw"], "tactic_count": 2}
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{"name": "SemiRingCat.FilteredColimits.forget₂Mon_preservesFilteredColimits", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.FilteredColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiRingCat.FilteredColimits.forget_preservesFilteredColimits", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.FilteredColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommSemiRingCat.FilteredColimits.R", "kind": "abbrev", "module": "Mathlib.Algebra.Category.Ring.FilteredColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommSemiRingCat.FilteredColimits.colimitCommSemiring", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.FilteredColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommSemiRingCat.FilteredColimits.colimit", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.FilteredColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "RingCat.FilteredColimits.colimitRing", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.FilteredColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCat.FilteredColimits.colimit", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.FilteredColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CommRingCat.FilteredColimits.colimitCommRing", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.FilteredColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.FilteredColimits.colimit", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.FilteredColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.FilteredColimits.colimitCocone", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.FilteredColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.FilteredColimits.colimitCoconeIsColimit", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.FilteredColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.FilteredColimits.forget₂Ring_preservesFilteredColimits", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.FilteredColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.FilteredColimits.forget_preservesFilteredColimits", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.FilteredColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.FilteredColimits.nontrivial", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.FilteredColimits", "is_tactic_proof": true, "tactics": ["classical", "cases", "exact", "have", "refine", "have", "obtain", "exact"], "tactic_count": 8}
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{"name": "localization_unit_isIso", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "localization_unit_isIso'", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Instances", "is_tactic_proof": true, "tactics": ["cases", "exact"], "tactic_count": 2}
{"name": "IsLocalization.epi", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.epi", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.epi'", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Instances", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "CommRingCat.isLocalHom_comp", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLocalHom_of_iso", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLocalHom_of_isIso", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LibraryNote.change_elaboration_strategy_with_`by_apply`", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiRingCat.semiringObj", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiRingCat.sectionsSubsemiring", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiRingCat.sectionsSemiring", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiRingCat.limitSemiring", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiRingCat.limitπRingHom", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiRingCat.HasLimits.limitCone", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SemiRingCat.hasLimitsOfShape", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiRingCat.hasLimitsOfSize", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CommSemiRingCat.limitCommSemiring", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommSemiRingCat.instCreatesLimitSemiRingCatForget₂", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CommSemiRingCat.limitConeIsLimit", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "RingCat.limitRing", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "RingCat.limitConeIsLimit", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCat.hasLimit", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCat.hasLimitsOfShape", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCat.hasLimitsOfSize", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CommRingCat.limitCommRing", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.instCreatesLimitRingCatForget₂", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.limitCone", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.limitConeIsLimit", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.hasLimit", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.hasLimitsOfShape", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.hasLimitsOfSize", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CommRingCat.HomTopology.continuous_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.HomTopology.isEmbedding_hom", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CommRingCat.HomTopology.isClosedEmbedding_hom", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Topology", "is_tactic_proof": false, "tactics": ["let", "have", "convert", "ext", "simp"], "tactic_count": 5}
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{"name": "CommRingCat.HomTopology.isEmbedding_pushout", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.instCoeSortUnderType", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Under.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CommRingCat.toAlgHom", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Under.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.toAlgHom_id", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Under.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CommRingCat.toAlgHom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Under.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.mkUnder", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Under.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.mkUnder_ext", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Under.Basic", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "AlgHom.toUnder", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Under.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.toUnder_right", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Under.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AlgEquiv.toUnder", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Under.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.toUnder_hom_right_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Under.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.toUnder_inv_right_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Under.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.toUnder_trans", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Under.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.tensorProd", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Under.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.tensorProdObjIsoPushoutObj", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Under.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.pushout_inl_tensorProdObjIsoPushoutObj_inv_right", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Under.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CommRingCat.pushout_inr_tensorProdObjIsoPushoutObj_inv_right", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Under.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CommRingCat.tensorProdIsoPushout", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Under.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.tensorProdIsoPushout_app", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Under.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.Under.piFan", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Under.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.Under.piFanIsLimit", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Under.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.Under.tensorProductFan", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Under.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.Under.tensorProductFan'", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Under.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.Under.tensorProductFanIso", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Under.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.Under.tensorProductFanIsLimit", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Under.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.Under.piFanTensorProductIsLimit", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Under.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.Under.instPreservesLimitUnderDiscreteFunctorTensorProdOfFinite", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Under.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.Under.instPreservesFiniteProductsUnderTensorProd", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Under.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.Under.equalizer_comp", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Under.Limits", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "CommRingCat.Under.equalizerFork", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Under.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.Under.equalizerFork_ι", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Under.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.Under.equalizerFork'", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Under.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.Under.equalizerFork'_ι", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Under.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.Under.equalizerForkIsLimit", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Under.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.Under.equalizerFork'IsLimit", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Under.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.Under.tensorProdEqualizer", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Under.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.Under.tensorProdEqualizer_ι", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Under.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.Under.equalizerForkTensorProdIso", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Under.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.Under.tensorProdMapEqualizerForkIsLimit", "kind": "definition", "module": "Mathlib.Algebra.Category.Ring.Under.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.Under.instPreservesLimitUnderWalkingParallelPairParallelPairTensorProdOfFlatCarrier", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Under.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.Under.instPreservesLimitsOfShapeUnderWalkingParallelPairTensorProdOfFlatCarrier", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Under.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.Under.instPreservesFiniteLimitsUnderTensorProdOfFlatCarrier", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Under.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.Under.instPreservesFiniteProductsUnderPushout", "kind": "instance", "module": "Mathlib.Algebra.Category.Ring.Under.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRingCat.Under.preservesFiniteLimits_of_flat", "kind": "theorem", "module": "Mathlib.Algebra.Category.Ring.Under.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MagmaCat.instCoeSortType", "kind": "instance", "module": "Mathlib.Algebra.Category.Semigrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MagmaCat.of", "kind": "abbrev", "module": "Mathlib.Algebra.Category.Semigrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MagmaCat.instCategory", "kind": "instance", "module": "Mathlib.Algebra.Category.Semigrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MagmaCat.instConcreteCategoryMulHomCarrier", "kind": "instance", "module": "Mathlib.Algebra.Category.Semigrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MagmaCat.Hom.hom", "kind": "abbrev", "module": "Mathlib.Algebra.Category.Semigrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MagmaCat.ofHom", "kind": "abbrev", "module": "Mathlib.Algebra.Category.Semigrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MagmaCat.Hom.Simps.hom", "kind": "definition", "module": "Mathlib.Algebra.Category.Semigrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MagmaCat.coe_id", "kind": "theorem", "module": "Mathlib.Algebra.Category.Semigrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MagmaCat.coe_comp", "kind": "theorem", "module": "Mathlib.Algebra.Category.Semigrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MagmaCat.forget_map", "kind": "theorem", "module": "Mathlib.Algebra.Category.Semigrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MagmaCat.ext", "kind": "theorem", "module": "Mathlib.Algebra.Category.Semigrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MagmaCat.coe_of", "kind": "theorem", "module": "Mathlib.Algebra.Category.Semigrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MagmaCat.hom_id", "kind": "theorem", "module": "Mathlib.Algebra.Category.Semigrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MagmaCat.id_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.Semigrp.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MagmaCat.hom_comp", "kind": "theorem", "module": "Mathlib.Algebra.Category.Semigrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MagmaCat.comp_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.Semigrp.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MagmaCat.hom_ext", "kind": "theorem", "module": "Mathlib.Algebra.Category.Semigrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MagmaCat.hom_ofHom", "kind": "theorem", "module": "Mathlib.Algebra.Category.Semigrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MagmaCat.ofHom_hom", "kind": "theorem", "module": "Mathlib.Algebra.Category.Semigrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MagmaCat.ofHom_id", "kind": "theorem", "module": "Mathlib.Algebra.Category.Semigrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MagmaCat.ofHom_comp", "kind": "theorem", "module": "Mathlib.Algebra.Category.Semigrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MagmaCat.ofHom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.Semigrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MagmaCat.inv_hom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.Semigrp.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "MagmaCat.instInhabited", "kind": "instance", "module": "Mathlib.Algebra.Category.Semigrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Semigrp.instCoeSortType", "kind": "instance", "module": "Mathlib.Algebra.Category.Semigrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Semigrp.of", "kind": "abbrev", "module": "Mathlib.Algebra.Category.Semigrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Semigrp.instCategory", "kind": "instance", "module": "Mathlib.Algebra.Category.Semigrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Semigrp.instConcreteCategoryMulHomCarrier", "kind": "instance", "module": "Mathlib.Algebra.Category.Semigrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Semigrp.Hom.hom", "kind": "abbrev", "module": "Mathlib.Algebra.Category.Semigrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Semigrp.ofHom", "kind": "abbrev", "module": "Mathlib.Algebra.Category.Semigrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Semigrp.Hom.Simps.hom", "kind": "definition", "module": "Mathlib.Algebra.Category.Semigrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Semigrp.coe_id", "kind": "theorem", "module": "Mathlib.Algebra.Category.Semigrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Semigrp.coe_comp", "kind": "theorem", "module": "Mathlib.Algebra.Category.Semigrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Semigrp.forget_map", "kind": "theorem", "module": "Mathlib.Algebra.Category.Semigrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Semigrp.ext", "kind": "theorem", "module": "Mathlib.Algebra.Category.Semigrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Semigrp.coe_of", "kind": "theorem", "module": "Mathlib.Algebra.Category.Semigrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Semigrp.hom_id", "kind": "theorem", "module": "Mathlib.Algebra.Category.Semigrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Semigrp.id_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.Semigrp.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Semigrp.hom_comp", "kind": "theorem", "module": "Mathlib.Algebra.Category.Semigrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Semigrp.hom_ext", "kind": "theorem", "module": "Mathlib.Algebra.Category.Semigrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Semigrp.hom_ofHom", "kind": "theorem", "module": "Mathlib.Algebra.Category.Semigrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Semigrp.ofHom_hom", "kind": "theorem", "module": "Mathlib.Algebra.Category.Semigrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Semigrp.ofHom_id", "kind": "theorem", "module": "Mathlib.Algebra.Category.Semigrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Semigrp.ofHom_comp", "kind": "theorem", "module": "Mathlib.Algebra.Category.Semigrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Semigrp.ofHom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.Semigrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Semigrp.inv_hom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.Semigrp.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Semigrp.hom_inv_apply", "kind": "theorem", "module": "Mathlib.Algebra.Category.Semigrp.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Semigrp.mulEquiv_coe_eq", "kind": "theorem", "module": "Mathlib.Algebra.Category.Semigrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Semigrp.instInhabited", "kind": "instance", "module": "Mathlib.Algebra.Category.Semigrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Semigrp.hasForgetToMagmaCat", "kind": "instance", "module": "Mathlib.Algebra.Category.Semigrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.toMagmaCatIso", "kind": "definition", "module": "Mathlib.Algebra.Category.Semigrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.toSemigrpIso", "kind": "definition", "module": "Mathlib.Algebra.Category.Semigrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.magmaCatIsoToMulEquiv", "kind": "definition", "module": "Mathlib.Algebra.Category.Semigrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.semigrpIsoToMulEquiv", "kind": "definition", "module": "Mathlib.Algebra.Category.Semigrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mulEquivIsoMagmaIso", "kind": "definition", "module": "Mathlib.Algebra.Category.Semigrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mulEquivIsoSemigrpIso", "kind": "definition", "module": "Mathlib.Algebra.Category.Semigrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MagmaCat.forgetReflectsIsos", "kind": "instance", "module": "Mathlib.Algebra.Category.Semigrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Semigrp.forgetReflectsIsos", "kind": "instance", "module": "Mathlib.Algebra.Category.Semigrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Semigrp.forget₂_full", "kind": "instance", "module": "Mathlib.Algebra.Category.Semigrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_example", "kind": "example", "module": "Mathlib.Algebra.Category.Semigrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsCentral.center_eq_bot", "kind": "theorem", "module": "Mathlib.Algebra.Central.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsCentral.mem_center_iff", "kind": "theorem", "module": "Mathlib.Algebra.Central.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Algebra.IsCentral.self", "kind": "instance", "module": "Mathlib.Algebra.Central.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsCentral.baseField_essentially_unique", "kind": "theorem", "module": "Mathlib.Algebra.Central.Basic", "is_tactic_proof": false, "tactics": ["haveI", "out", "show", "simp", "rintro", "exact", "refine", "have", "rw", "simp", "obtain", "exact"], "tactic_count": 12}
{"name": "Algebra.IsCentral.of_algEquiv", "kind": "theorem", "module": "Mathlib.Algebra.Central.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsCentral.instMulOpposite", "kind": "instance", "module": "Mathlib.Algebra.Central.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.mem_subsemiringCenter_iff", "kind": "theorem", "module": "Mathlib.Algebra.Central.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.mem_subalgebraCenter_iff", "kind": "theorem", "module": "Mathlib.Algebra.Central.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsCentral.instEnd", "kind": "instance", "module": "Mathlib.Algebra.Central.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.subalgebraCenter_eq_scalarAlgHom_map", "kind": "theorem", "module": "Mathlib.Algebra.Central.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsCentral.matrix", "kind": "instance", "module": "Mathlib.Algebra.Central.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.TensorProduct.includeLeft_map_center_le", "kind": "theorem", "module": "Mathlib.Algebra.Central.TensorProduct", "is_tactic_proof": true, "tactics": ["intro", "simp", "obtain", "intro", "induction", "zero", "tmul", "add"], "tactic_count": 8}
{"name": "Algebra.TensorProduct.includeRight_map_center_le", "kind": "theorem", "module": "Mathlib.Algebra.Central.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsCentral.left_of_tensor", "kind": "theorem", "module": "Mathlib.Algebra.Central.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsCentral.right_of_tensor", "kind": "theorem", "module": "Mathlib.Algebra.Central.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsCentral.left_of_tensor_of_field", "kind": "theorem", "module": "Mathlib.Algebra.Central.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsCentral.right_of_tensor_of_field", "kind": "theorem", "module": "Mathlib.Algebra.Central.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CharP.of_ringHom_of_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Algebra", "is_tactic_proof": true, "tactics": ["have", "have", "obtain", "obtain", "have", "rw", "exact"], "tactic_count": 7}
{"name": "charP_of_injective_ringHom", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "charP_of_injective_algebraMap", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "charP_of_injective_algebraMap'", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "charZero_of_injective_ringHom", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "charZero_of_injective_algebraMap", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.charP", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Algebra", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "RingHom.charP_iff", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "expChar_of_injective_ringHom", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Algebra", "is_tactic_proof": true, "tactics": ["rcases", "haveI", "haveI"], "tactic_count": 3}
{"name": "RingHom.expChar", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Algebra", "is_tactic_proof": true, "tactics": ["cases", "zero", "prime"], "tactic_count": 3}
{"name": "RingHom.expChar_iff", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "expChar_of_injective_algebraMap", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ExpChar.of_injective_algebraMap'", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "algebraRat.charP_zero", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "algebraRat.charZero", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.charP_iff_charP", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Algebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Algebra.charP_iff", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.ringChar_eq", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Algebra", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "FreeAlgebra.charP", "kind": "instance", "module": "Mathlib.Algebra.CharP.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeAlgebra.charZero", "kind": "instance", "module": "Mathlib.Algebra.CharP.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractionRing.charP_of_isFractionRing", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractionRing.charZero_of_isFractionRing", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractionRing.charP", "kind": "instance", "module": "Mathlib.Algebra.CharP.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractionRing.charZero", "kind": "instance", "module": "Mathlib.Algebra.CharP.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CharP.natCast_eq_natCast'", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Basic", "is_tactic_proof": true, "tactics": ["wlog", "exact", "rw", "rw"], "tactic_count": 4}
{"name": "CharP.natCast_eq_natCast_mod", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CharP.natCast_eq_natCast", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Basic", "is_tactic_proof": true, "tactics": ["wlog", "rw", "rw", "zero_add,"], "tactic_count": 4}
{"name": "CharP.natCast_injOn_Iio", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CharP.intCast_eq_intCast", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CharP.intCast_eq_intCast_mod", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CharP.intCast_injOn_Ico", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Basic", "is_tactic_proof": true, "tactics": ["rintro", "lift", "lift", "norm_cast", "exact"], "tactic_count": 5}
{"name": "CharP.cast_ne_zero_of_ne_of_prime", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CharP.ringChar_of_prime_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CharP.charP_iff_prime_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ring.two_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Ring.neg_one_ne_one_of_char_ne_two", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ring.eq_self_iff_eq_zero_of_char_ne_two", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.lcm.charP", "kind": "instance", "module": "Mathlib.Algebra.CharP.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.charP", "kind": "instance", "module": "Mathlib.Algebra.CharP.Basic", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "Prod.charZero_of_left", "kind": "instance", "module": "Mathlib.Algebra.CharP.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.charZero_of_right", "kind": "instance", "module": "Mathlib.Algebra.CharP.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.charP", "kind": "instance", "module": "Mathlib.Algebra.CharP.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.charP", "kind": "instance", "module": "Mathlib.Algebra.CharP.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.cast_injOn_of_ringChar_ne_two", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Basic", "is_tactic_proof": false, "tactics": ["rintro", "simp", "exact", "exact"], "tactic_count": 4}
{"name": "CharZero.charZero_iff_forall_prime_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Basic", "is_tactic_proof": true, "tactics": ["refine", "let", "cases", "inl", "inr"], "tactic_count": 5}
{"name": "Fin.charP", "kind": "instance", "module": "Mathlib.Algebra.CharP.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instExpCharProd", "kind": "instance", "module": "Mathlib.Algebra.CharP.Basic", "is_tactic_proof": true, "tactics": ["obtain", "constructor", "obtain", "exact", "have"], "tactic_count": 5}
{"name": "instIsCharPOfIsLeftCancelAddOfCharP", "kind": "instance", "module": "Mathlib.Algebra.CharP.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isUnit_iff_not_dvd_char_of_ringChar_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.CharP.CharAndCard", "is_tactic_proof": true, "tactics": ["have", "have", "constructor", "rintro", "rcases", "have", "rintro", "rw", "nth_rw", "exact", "have", "apply_fun", "apply_fun", "rw", "norm_cast", "exact", "intro", "rcases", "apply_fun", "push_cast", "rw", "exact"], "tactic_count": 22}
{"name": "isUnit_iff_not_dvd_char", "kind": "theorem", "module": "Mathlib.Algebra.CharP.CharAndCard", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "prime_dvd_char_iff_dvd_card", "kind": "theorem", "module": "Mathlib.Algebra.CharP.CharAndCard", "is_tactic_proof": false, "tactics": ["refine", "h.trans", "by_contra", "rcases", "have", "rw", "rcases", "apply_fun", "rw", "exact"], "tactic_count": 10}
{"name": "not_isUnit_prime_of_dvd_card", "kind": "theorem", "module": "Mathlib.Algebra.CharP.CharAndCard", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "charP_of_card_eq_prime", "kind": "theorem", "module": "Mathlib.Algebra.CharP.CharAndCard", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "charP_of_card_eq_prime_pow", "kind": "theorem", "module": "Mathlib.Algebra.CharP.CharAndCard", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CharP.ofNat_eq_zero'", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Defs", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "CharP.congr", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CharP.cast_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CharP.cast_eq_mod", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CharP.cast_eq_iff_mod_eq", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Defs", "is_tactic_proof": true, "tactics": ["wlog", "simpa", "obtain", "rw", "constructor", "simp", "intro", "have", "simpa"], "tactic_count": 9}
{"name": "CharP.ofNat_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CharP.eq", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CharP.ofCharZero", "kind": "instance", "module": "Mathlib.Algebra.CharP.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CharP.intCast_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Defs", "is_tactic_proof": true, "tactics": ["rcases", "rw", "lift", "rw", "simp", "lift", "rw"], "tactic_count": 7}
{"name": "CharP.charP_to_charZero", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CharP.charP_zero_iff_charZero", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CharP.exists", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CharP.existsUnique", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ringChar", "kind": "definition", "module": "Mathlib.Algebra.CharP.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ringChar.spec", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Defs", "is_tactic_proof": true, "tactics": ["letI", "exact"], "tactic_count": 2}
{"name": "ringChar.eq", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ringChar.charP", "kind": "instance", "module": "Mathlib.Algebra.CharP.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ringChar.of_eq", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ringChar.eq_iff", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ringChar.dvd", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ringChar.eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ringChar.Nat.cast_ringChar", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ringChar.ringChar_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ringChar.ringChar_subsingleton", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CharP.neg_one_ne_one", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Defs", "is_tactic_proof": false, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CharP.ringChar_zero_iff_CharZero", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CharP.char_ne_one", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CharP.char_is_prime_of_two_le", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CharP.char_is_prime_or_zero", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CharP.char_prime_of_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CharP.exists'", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Defs", "is_tactic_proof": true, "tactics": ["obtain", "rcases", "exacts"], "tactic_count": 3}
{"name": "CharP.char_is_prime_of_pos", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CharP.CharOne.subsingleton", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CharP.false_of_nontrivial_of_char_one", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Defs", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "CharP.ringChar_ne_one", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CharP.nontrivial_of_char_ne_one", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NeZero.of_not_dvd", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NeZero.not_char_dvd", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Defs", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "ExpChar", "kind": "classInductive", "module": "Mathlib.Algebra.CharP.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "expChar_prime", "kind": "instance", "module": "Mathlib.Algebra.CharP.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "expChar_one", "kind": "instance", "module": "Mathlib.Algebra.CharP.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "expChar_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Defs", "is_tactic_proof": true, "tactics": ["cases", "exact", "exact"], "tactic_count": 3}
{"name": "ExpChar.eq", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Defs", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "exacts", "rcases", "exacts"], "tactic_count": 5}
{"name": "ExpChar.congr", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "expChar_one_of_char_zero", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Defs", "is_tactic_proof": true, "tactics": ["rcases", "rfl", "exact"], "tactic_count": 3}
{"name": "char_eq_expChar_iff", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Defs", "is_tactic_proof": true, "tactics": ["rcases", "rw", "decide", "exact"], "tactic_count": 4}
{"name": "expChar_is_prime_or_one", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Defs", "is_tactic_proof": true, "tactics": ["cases", "zero", "prime"], "tactic_count": 3}
{"name": "expChar_pos", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Defs", "is_tactic_proof": true, "tactics": ["rcases", "exacts"], "tactic_count": 2}
{"name": "expChar_pow_pos", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ringExpChar", "kind": "definition", "module": "Mathlib.Algebra.CharP.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ringExpChar.eq", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Defs", "is_tactic_proof": true, "tactics": ["rcases", "haveI", "rw", "rw", "exact"], "tactic_count": 5}
{"name": "ringExpChar.eq_one", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "char_zero_of_expChar_one", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Defs", "is_tactic_proof": true, "tactics": ["cases", "exact", "exact"], "tactic_count": 3}
{"name": "charZero_of_expChar_one'", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Defs", "is_tactic_proof": true, "tactics": ["cases", "assumption", "exact"], "tactic_count": 3}
{"name": "expChar_one_iff_char_zero", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Defs", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 5}
{"name": "ExpChar.exists", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Defs", "is_tactic_proof": true, "tactics": ["obtain", "exacts"], "tactic_count": 2}
{"name": "ExpChar.exists_unique", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ringExpChar.expChar", "kind": "instance", "module": "Mathlib.Algebra.CharP.Defs", "is_tactic_proof": true, "tactics": ["obtain", "rwa"], "tactic_count": 2}
{"name": "ringExpChar.of_eq", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ringExpChar.eq_iff", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "frobenius_def", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Frobenius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iterateFrobenius_def", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Frobenius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iterate_frobenius", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Frobenius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iterateFrobenius_eq_pow", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Frobenius", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "coe_iterateFrobenius", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Frobenius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iterateFrobenius_one_apply", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Frobenius", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "iterateFrobenius_one", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Frobenius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iterateFrobenius_zero_apply", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Frobenius", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "iterateFrobenius_zero", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Frobenius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iterateFrobenius_add_apply", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Frobenius", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "iterateFrobenius_add", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Frobenius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iterateFrobenius_mul_apply", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Frobenius", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "coe_iterateFrobenius_mul", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Frobenius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "frobenius_mul", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Frobenius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "frobenius_one", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Frobenius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.map_frobenius", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Frobenius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.map_frobenius", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Frobenius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.map_iterate_frobenius", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Frobenius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.map_iterateFrobenius", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Frobenius", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "RingHom.frobenius_comm", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Frobenius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.iterateFrobenius_comm", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Frobenius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.frobenius", "kind": "definition", "module": "Mathlib.Algebra.CharP.Frobenius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.iterateFrobenius", "kind": "definition", "module": "Mathlib.Algebra.CharP.Frobenius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.frobenius_def", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Frobenius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.iterateFrobenius_def", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Frobenius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "frobenius_zero", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Frobenius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "frobenius_add", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Frobenius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "frobenius_natCast", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Frobenius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "frobenius_sub", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Frobenius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.charP", "kind": "instance", "module": "Mathlib.Algebra.CharP.IntermediateField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.expChar", "kind": "instance", "module": "Mathlib.Algebra.CharP.IntermediateField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.charZero", "kind": "instance", "module": "Mathlib.Algebra.CharP.IntermediateField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.charP", "kind": "instance", "module": "Mathlib.Algebra.CharP.IntermediateField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.expChar", "kind": "instance", "module": "Mathlib.Algebra.CharP.IntermediateField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.charP'", "kind": "instance", "module": "Mathlib.Algebra.CharP.IntermediateField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.expChar'", "kind": "instance", "module": "Mathlib.Algebra.CharP.IntermediateField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Even.all", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Invertible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Odd.all", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Invertible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_ringChar_dvd_of_invertible", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Invertible", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CharP.intCast_mul_natCast_gcdA_eq_gcd", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Invertible", "is_tactic_proof": true, "tactics": ["suffices", "rw"], "tactic_count": 2}
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{"name": "invertibleOfCoprime", "kind": "definition", "module": "Mathlib.Algebra.CharP.Invertible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "invOf_eq_of_coprime", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Invertible", "is_tactic_proof": true, "tactics": ["letI", "convert"], "tactic_count": 2}
{"name": "CharP.isUnit_natCast_iff", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Invertible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CharP.isUnit_ofNat_iff", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Invertible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CharP.isUnit_intCast_iff", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Invertible", "is_tactic_proof": true, "tactics": ["obtain", "simp", "simp"], "tactic_count": 3}
{"name": "invertibleOfRingCharNotDvd", "kind": "definition", "module": "Mathlib.Algebra.CharP.Invertible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "invertibleOfCharPNotDvd", "kind": "definition", "module": "Mathlib.Algebra.CharP.Invertible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "invertibleOfPos", "kind": "instance", "module": "Mathlib.Algebra.CharP.Invertible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "invertibleSucc", "kind": "instance", "module": "Mathlib.Algebra.CharP.Invertible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "invertibleTwo", "kind": "instance", "module": "Mathlib.Algebra.CharP.Invertible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "invertibleThree", "kind": "instance", "module": "Mathlib.Algebra.CharP.Invertible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.add_pow_prime_pow_eq'", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Nat.Prime.dvd_add_pow_sub_pow_of_dvd", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
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{"name": "CharP.char_is_prime", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CharP.prime_ringChar", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Lemmas", "is_tactic_proof": true, "tactics": ["apply", "exact"], "tactic_count": 2}
{"name": "frobenius", "kind": "definition", "module": "Mathlib.Algebra.CharP.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iterateFrobenius", "kind": "definition", "module": "Mathlib.Algebra.CharP.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "list_sum_pow_char", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "multiset_sum_pow_char", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sum_pow_char", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "list_sum_pow_char_pow", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Module.charP_end", "kind": "theorem", "module": "Mathlib.Algebra.CharP.LinearMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCharPLinearMapSubtypeMemSubringCenterId", "kind": "instance", "module": "Mathlib.Algebra.CharP.LinearMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instExpCharLinearMapSubtypeMemSubringCenterId", "kind": "instance", "module": "Mathlib.Algebra.CharP.LinearMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "charP_zero_or_prime_power", "kind": "theorem", "module": "Mathlib.Algebra.CharP.LocalRing", "is_tactic_proof": true, "tactics": ["apply", "intro", "let", "haveI", "let", "let", "rcases", "let", "have", "have", "have", "rw", "have", "by_contra", "rw", "rw", "have", "rw", "have", "exact", "have", "rw", "have", "have", "absurd", "exact", "haveI", "haveI", "haveI", "have", "exact"], "tactic_count": 31}
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{"name": "EqualCharZero.pnatCast_one", "kind": "theorem", "module": "Mathlib.Algebra.CharP.MixedCharZero", "is_tactic_proof": true, "tactics": ["apply", "rw", "change", "rw", "rw"], "tactic_count": 5}
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{"name": "CharP.pi", "kind": "instance", "module": "Mathlib.Algebra.CharP.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CharP.pi'", "kind": "instance", "module": "Mathlib.Algebra.CharP.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CharP.ker_intAlgebraMap_eq_span", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Quotient", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CharP.quotient", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CharP.quotient'", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CharP.quotient_iff", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Quotient", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "CharP.quotient_iff_le_ker_natCast", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Quotient", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.natCast_mem_of_charP_quotient", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.index_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Quotient", "is_tactic_proof": true, "tactics": ["rw", "split_ifs", "simp", "letI", "exact"], "tactic_count": 5}
{"name": "iterateFrobenius_inj", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Reduced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "frobenius_inj", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Reduced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isSquare_of_charTwo'", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Reduced", "is_tactic_proof": true, "tactics": ["cases", "exact"], "tactic_count": 2}
{"name": "ExpChar.pow_prime_pow_mul_eq_one_iff", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Reduced", "is_tactic_proof": true, "tactics": ["rw", "convert", "apply"], "tactic_count": 3}
{"name": "CharP.subsemiring", "kind": "instance", "module": "Mathlib.Algebra.CharP.Subring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CharP.subring", "kind": "instance", "module": "Mathlib.Algebra.CharP.Subring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CharP.subring'", "kind": "instance", "module": "Mathlib.Algebra.CharP.Subring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CharP.charP_center_iff", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Subring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ExpChar.expChar_center_iff", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Subring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CharTwo.two_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Two", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CharTwo.of_one_ne_zero_of_two_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Two", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CharTwo.add_self_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Two", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CharTwo.two_nsmul", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Two", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CharTwo.add_cancel_left", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Two", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CharTwo.add_cancel_right", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Two", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CharTwo.neg_eq", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Two", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CharTwo.neg_eq'", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Two", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CharTwo.sub_eq_add", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Two", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CharTwo.add_eq_iff_eq_add", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Two", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CharTwo.eq_add_iff_add_eq", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Two", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CharTwo.two_zsmul", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Two", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CharTwo.add_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Two", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CharTwo.add_sq", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Two", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CharTwo.add_mul_self", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Two", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "_private.Mathlib.Algebra.CharP.Two.0.CharTwo.sqAddMonoidHom", "kind": "definition", "module": "Mathlib.Algebra.CharP.Two", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CharTwo.list_sum_sq", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Two", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CharTwo.list_sum_mul_self", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Two", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "CharTwo.multiset_sum_sq", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Two", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CharTwo.multiset_sum_mul_self", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Two", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "CharTwo.sum_sq", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Two", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CharTwo.sum_mul_self", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Two", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "CharTwo.CommRing.sq_injective", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Two", "is_tactic_proof": true, "tactics": ["intro", "rwa"], "tactic_count": 2}
{"name": "CharTwo.CommRing.sq_inj", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Two", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "neg_one_eq_one_iff", "kind": "theorem", "module": "Mathlib.Algebra.CharP.Two", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "CharZero.of_addMonoidHom", "kind": "theorem", "module": "Mathlib.Algebra.CharZero.AddMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "charZero_of_inj_zero", "kind": "theorem", "module": "Mathlib.Algebra.CharZero.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.cast_injective", "kind": "theorem", "module": "Mathlib.Algebra.CharZero.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.cast_inj", "kind": "theorem", "module": "Mathlib.Algebra.CharZero.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.cast_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.CharZero.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.cast_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.CharZero.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.cast_add_one_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.CharZero.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.cast_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.CharZero.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.cast_ne_one", "kind": "theorem", "module": "Mathlib.Algebra.CharZero.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OfNat.ofNat_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.CharZero.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OfNat.zero_ne_ofNat", "kind": "theorem", "module": "Mathlib.Algebra.CharZero.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OfNat.ofNat_ne_one", "kind": "theorem", "module": "Mathlib.Algebra.CharZero.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OfNat.one_ne_ofNat", "kind": "theorem", "module": "Mathlib.Algebra.CharZero.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OfNat.ofNat_eq_ofNat", "kind": "theorem", "module": "Mathlib.Algebra.CharZero.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NeZero.charZero", "kind": "instance", "module": "Mathlib.Algebra.CharZero.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NeZero.charZero_one", "kind": "instance", "module": "Mathlib.Algebra.CharZero.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NeZero.charZero_ofNat", "kind": "instance", "module": "Mathlib.Algebra.CharZero.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CharZero.infinite", "kind": "instance", "module": "Mathlib.Algebra.CharZero.Infinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroup.zsmul_mem_zmultiples_iff_exists_sub_div", "kind": "theorem", "module": "Mathlib.Algebra.CharZero.Quotient", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "have", "conv_rhs", "simp_rw", "natCast_zsmul,", "constructor", "rintro", "simp_rw", "refine", "rw", "exact", "rw", "nth_rewrite", "rfl", "rintro", "exact"], "tactic_count": 17}
{"name": "AddSubgroup.nsmul_mem_zmultiples_iff_exists_sub_div", "kind": "theorem", "module": "Mathlib.Algebra.CharZero.Quotient", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "QuotientAddGroup.zmultiples_zsmul_eq_zsmul_iff", "kind": "theorem", "module": "Mathlib.Algebra.CharZero.Quotient", "is_tactic_proof": true, "tactics": ["induction", "induction", "simp_rw", "sub_sub]", "exact"], "tactic_count": 5}
{"name": "QuotientAddGroup.zmultiples_nsmul_eq_nsmul_iff", "kind": "theorem", "module": "Mathlib.Algebra.CharZero.Quotient", "is_tactic_proof": false, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "DirectLimit.one_def", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.DirectLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectLimit.exists_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.DirectLimit", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "DirectLimit.mul_def", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.DirectLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectLimit.smul_def", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.DirectLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectLimit.npow_def", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.DirectLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectLimit.inv_def", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.DirectLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectLimit.div_def", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.DirectLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectLimit.zpow_def", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.DirectLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectLimit.inv₀_def", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.DirectLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectLimit.div₀_def", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.DirectLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectLimit.zpow₀_def", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.DirectLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectLimit.natCast_def", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.DirectLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectLimit.intCast_def", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.DirectLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectLimit.nnratCast_def", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.DirectLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectLimit.ratCast_def", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.DirectLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectLimit.Module.of_f", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.DirectLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectLimit.Module.lift_of", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.DirectLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectLimit.Module.hom_ext", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.DirectLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectLimit.Ring.of_f", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.DirectLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectLimit.Ring.lift_of", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.DirectLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectLimit.Ring.hom_ext", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.DirectLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.fgSystem", "kind": "definition", "module": "Mathlib.Algebra.Colimit.Finiteness", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.fgSystem.instIsDirectedOrderSubtypeSubmoduleFG", "kind": "instance", "module": "Mathlib.Algebra.Colimit.Finiteness", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.fgSystem.instDirectedSystemSubtypeSubmoduleFGMemValCoeLinearMapId", "kind": "instance", "module": "Mathlib.Algebra.Colimit.Finiteness", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.fgSystem.equiv", "kind": "definition", "module": "Mathlib.Algebra.Colimit.Finiteness", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.fgSystem.equiv_comp_of", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.Finiteness", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Module.DirectLimit.Eqv", "kind": "inductive", "module": "Mathlib.Algebra.Colimit.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.DirectLimit.quotMk_of", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.DirectLimit.of_f", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.DirectLimit.exists_of", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.DirectLimit.exists_of₂", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.DirectLimit.induction_on", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.DirectLimit.lift_of", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.DirectLimit.hom_ext", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.DirectLimit.lift_comp_of", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.Module", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Module.DirectLimit.lift_unique", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.Module", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Module.DirectLimit.lift_of'", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.Module", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Module.DirectLimit.lift_injective", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.Module", "is_tactic_proof": true, "tactics": ["cases", "apply", "intro", "obtain", "simp_rw", "rw"], "tactic_count": 6}
{"name": "Module.DirectLimit.map_apply_of", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.DirectLimit.map_id", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.Module", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Module.DirectLimit.map_comp", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.Module", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Module.DirectLimit.congr_apply_of", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.DirectLimit.congr_symm_apply_of", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.DirectLimit.linearEquiv_of", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.Module", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Module.DirectLimit.linearEquiv_symm_mk", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.DirectLimit.exists_eq_of_of_eq", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.Module", "is_tactic_proof": true, "tactics": ["have", "apply_fun", "simp_rw", "have", "exact"], "tactic_count": 5}
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{"name": "AddCommGroup.DirectLimit.of_f", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGroup.DirectLimit.induction_on", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGroup.DirectLimit.of.zero_exact", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGroup.DirectLimit.lift_of", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGroup.DirectLimit.hom_ext", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGroup.DirectLimit.lift_comp_of", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.Module", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "AddCommGroup.DirectLimit.lift_unique", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.Module", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AddCommGroup.DirectLimit.lift_of'", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.Module", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "AddCommGroup.DirectLimit.lift_injective", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGroup.DirectLimit.map_apply_of", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGroup.DirectLimit.map_id", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.Module", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "AddCommGroup.DirectLimit.map_comp", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.Module", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
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{"name": "Ring.DirectLimit.quotientMk_of", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ring.DirectLimit.of_f", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Ring.DirectLimit.induction_on", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ring.DirectLimit.lift_of", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ring.DirectLimit.hom_ext", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ring.DirectLimit.lift_comp_of", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.Ring", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
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{"name": "Ring.DirectLimit.of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ring.DirectLimit.map_apply_of", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ring.DirectLimit.map_id", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.Ring", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Ring.DirectLimit.map_comp", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.Ring", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Ring.DirectLimit.congr_apply_of", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ring.DirectLimit.congr_symm_apply_of", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.Ring", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Field.DirectLimit.exists_inv", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Field.DirectLimit.mul_inv_cancel", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.Ring", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Field.DirectLimit.inv_mul_cancel", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.Ring", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Field.DirectLimit.field", "kind": "abbrev", "module": "Mathlib.Algebra.Colimit.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.FG.exists_rTensor_fg_inclusion_eq", "kind": "theorem", "module": "Mathlib.Algebra.Colimit.TensorProduct", "is_tactic_proof": true, "tactics": ["classical", "lift", "apply_fun", "apply_fun", "simp_rw", "have", "exact"], "tactic_count": 7}
{"name": "GenContFract.instInhabitedPair.default", "kind": "definition", "module": "Mathlib.Algebra.ContinuedFractions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GenContFract.instInhabitedPair", "kind": "instance", "module": "Mathlib.Algebra.ContinuedFractions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GenContFract.Pair.instRepr", "kind": "instance", "module": "Mathlib.Algebra.ContinuedFractions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GenContFract.Pair.map", "kind": "definition", "module": "Mathlib.Algebra.ContinuedFractions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GenContFract.Pair.coeFn", "kind": "definition", "module": "Mathlib.Algebra.ContinuedFractions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GenContFract.Pair.instCoe", "kind": "instance", "module": "Mathlib.Algebra.ContinuedFractions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GenContFract.Pair.coe_toPair", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GenContFract.ofInteger", "kind": "definition", "module": "Mathlib.Algebra.ContinuedFractions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GenContFract.instInhabited", "kind": "instance", "module": "Mathlib.Algebra.ContinuedFractions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GenContFract.partNums", "kind": "definition", "module": "Mathlib.Algebra.ContinuedFractions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GenContFract.partDens", "kind": "definition", "module": "Mathlib.Algebra.ContinuedFractions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GenContFract.TerminatedAt", "kind": "definition", "module": "Mathlib.Algebra.ContinuedFractions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GenContFract.terminatedAtDecidable", "kind": "instance", "module": "Mathlib.Algebra.ContinuedFractions.Basic", "is_tactic_proof": true, "tactics": ["unfold", "infer_instance"], "tactic_count": 2}
{"name": "GenContFract.Terminates", "kind": "definition", "module": "Mathlib.Algebra.ContinuedFractions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GenContFract.coeFn", "kind": "definition", "module": "Mathlib.Algebra.ContinuedFractions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GenContFract.instCoe", "kind": "instance", "module": "Mathlib.Algebra.ContinuedFractions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GenContFract.coe_toGenContFract", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GenContFract.IsSimpContFract", "kind": "definition", "module": "Mathlib.Algebra.ContinuedFractions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpContFract", "kind": "definition", "module": "Mathlib.Algebra.ContinuedFractions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpContFract.ofInteger", "kind": "definition", "module": "Mathlib.Algebra.ContinuedFractions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpContFract.instInhabited", "kind": "instance", "module": "Mathlib.Algebra.ContinuedFractions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpContFract.instCoeGenContFract", "kind": "instance", "module": "Mathlib.Algebra.ContinuedFractions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpContFract.IsContFract", "kind": "definition", "module": "Mathlib.Algebra.ContinuedFractions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContFract", "kind": "definition", "module": "Mathlib.Algebra.ContinuedFractions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContFract.ofInteger", "kind": "definition", "module": "Mathlib.Algebra.ContinuedFractions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContFract.instInhabited", "kind": "instance", "module": "Mathlib.Algebra.ContinuedFractions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContFract.instCoeSimpContFract", "kind": "instance", "module": "Mathlib.Algebra.ContinuedFractions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContFract.instCoeGenContFract", "kind": "instance", "module": "Mathlib.Algebra.ContinuedFractions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GenContFract.nextNum", "kind": "definition", "module": "Mathlib.Algebra.ContinuedFractions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GenContFract.nextDen", "kind": "definition", "module": "Mathlib.Algebra.ContinuedFractions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GenContFract.nextConts", "kind": "definition", "module": "Mathlib.Algebra.ContinuedFractions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GenContFract.contsAux", "kind": "definition", "module": "Mathlib.Algebra.ContinuedFractions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GenContFract.conts", "kind": "definition", "module": "Mathlib.Algebra.ContinuedFractions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GenContFract.nums", "kind": "definition", "module": "Mathlib.Algebra.ContinuedFractions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GenContFract.dens", "kind": "definition", "module": "Mathlib.Algebra.ContinuedFractions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GenContFract.convs", "kind": "definition", "module": "Mathlib.Algebra.ContinuedFractions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GenContFract.convs'Aux", "kind": "definition", "module": "Mathlib.Algebra.ContinuedFractions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GenContFract.convs'", "kind": "definition", "module": "Mathlib.Algebra.ContinuedFractions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GenContFract.of_convs_eq_convs'", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Computation.ApproximationCorollaries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "GenContFract.of_one_le_get?_partDen", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Computation.Approximations", "is_tactic_proof": false, "tactics": ["obtain", "exists_s_b_of_partDen", "obtain", "rw", "exact"], "tactic_count": 5}
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{"name": "GenContFract.of_isSimpContFract", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Computation.Approximations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SimpContFract.of_isContFract", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Computation.Approximations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "GenContFract.fib_le_of_contsAux_b", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Computation.Approximations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "GenContFract.le_of_succ_succ_get?_contsAux_b", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Computation.Approximations", "is_tactic_proof": false, "tactics": ["obtain", "exists_s_b_of_partDen", "simp"], "tactic_count": 3}
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{"name": "GenContFract.IntFractPair.stream_isSeq", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Computation.Basic", "is_tactic_proof": true, "tactics": ["intro", "simp"], "tactic_count": 2}
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{"name": "GenContFract.compExactValue", "kind": "definition", "module": "Mathlib.Algebra.ContinuedFractions.Computation.CorrectnessTerminating", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GenContFract.compExactValue_correctness_of_stream_eq_some_aux_comp", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Computation.CorrectnessTerminating", "is_tactic_proof": true, "tactics": ["field_simp", "rw", "ring"], "tactic_count": 3}
{"name": "GenContFract.compExactValue_correctness_of_stream_eq_some", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Computation.CorrectnessTerminating", "is_tactic_proof": true, "tactics": ["let", "induction", "zero", "intro", "obtain", "have", "simpa", "cases", "inl", "suffices", "calc", "v", "inr", "simp", "succ", "intro", "obtain", "let", "set", "set", "cases", "inl", "suffices", "simpa", "obtain", "have", "cases", "have", "get?_of_eq_some_of_get?_intFractPair_stream_fr_ne_zero", "rw", "suffices", "simpa", "exact", "inr", "suffices", "grind", "obtain", "have", "cases", "have", "get?_of_eq_some_of_get?_intFractPair_stream_fr_ne_zero", "let", "let", "let", "let", "have", "simp", "ac_rfl", "rw", "have", "have", "let", "have", "dsimp", "have", "simp", "grind"], "tactic_count": 57}
{"name": "GenContFract.of_correctness_of_nth_stream_eq_none", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Computation.CorrectnessTerminating", "is_tactic_proof": true, "tactics": ["induction", "zero", "contradiction", "succ", "let", "change", "obtain", "cases", "zero", "succ", "have", "have", "rw", "exact", "simpa"], "tactic_count": 15}
{"name": "GenContFract.of_correctness_of_terminatedAt", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Computation.CorrectnessTerminating", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GenContFract.of_correctness_of_terminates", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Computation.CorrectnessTerminating", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GenContFract.of_correctness_atTop_of_terminates", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Computation.CorrectnessTerminating", "is_tactic_proof": true, "tactics": ["rw", "obtain", "use", "intro", "rw", "exact"], "tactic_count": 6}
{"name": "GenContFract.exists_gcf_pair_rat_eq_of_nth_contsAux", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Computation.TerminatesIffRat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GenContFract.exists_gcf_pair_rat_eq_nth_conts", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Computation.TerminatesIffRat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "GenContFract.exists_rat_eq_nth_num", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Computation.TerminatesIffRat", "is_tactic_proof": true, "tactics": ["rcases", "use", "simp"], "tactic_count": 3}
{"name": "GenContFract.exists_rat_eq_nth_den", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Computation.TerminatesIffRat", "is_tactic_proof": true, "tactics": ["rcases", "use", "simp"], "tactic_count": 3}
{"name": "GenContFract.exists_rat_eq_nth_conv", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Computation.TerminatesIffRat", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "use", "simp"], "tactic_count": 4}
{"name": "GenContFract.exists_rat_eq_of_terminates", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Computation.TerminatesIffRat", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "have", "use"], "tactic_count": 4}
{"name": "GenContFract.IntFractPair.coe_of_rat_eq", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Computation.TerminatesIffRat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "GenContFract.IntFractPair.coe_stream_nth_rat_eq", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Computation.TerminatesIffRat", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "cases", "none", "some", "obtain", "rcases", "simp", "replace", "have", "have", "simpa"], "tactic_count": 14}
{"name": "GenContFract.IntFractPair.coe_stream'_rat_eq", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Computation.TerminatesIffRat", "is_tactic_proof": true, "tactics": ["funext"], "tactic_count": 1}
{"name": "GenContFract.coe_of_h_rat_eq", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Computation.TerminatesIffRat", "is_tactic_proof": true, "tactics": ["simp_all"], "tactic_count": 1}
{"name": "GenContFract.coe_of_s_get?_rat_eq", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Computation.TerminatesIffRat", "is_tactic_proof": true, "tactics": ["simp", "simp", "rw", "rcases", "simp"], "tactic_count": 5}
{"name": "GenContFract.coe_of_s_rat_eq", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Computation.TerminatesIffRat", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "GenContFract.coe_of_rat_eq", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Computation.TerminatesIffRat", "is_tactic_proof": true, "tactics": ["rcases", "obtain", "simp"], "tactic_count": 3}
{"name": "GenContFract.of_terminates_iff_of_rat_terminates", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Computation.TerminatesIffRat", "is_tactic_proof": true, "tactics": ["constructor", "simp", "cases", "simp", "trivial"], "tactic_count": 5}
{"name": "GenContFract.IntFractPair.of_inv_fr_num_lt_num_of_pos", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Computation.TerminatesIffRat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GenContFract.IntFractPair.stream_succ_nth_fr_num_lt_nth_fr_num_rat", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Computation.TerminatesIffRat", "is_tactic_proof": false, "tactics": ["obtain", "succ_nth_stream_eq_some_iff.mp", "have", "cases", "rw", "obtain", "have", "exact"], "tactic_count": 8}
{"name": "GenContFract.IntFractPair.stream_nth_fr_num_le_fr_num_sub_n_rat", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Computation.TerminatesIffRat", "is_tactic_proof": true, "tactics": ["induction", "zero", "intro", "have", "simp", "succ", "intro", "suffices", "rw", "solve_by_elim", "rcases", "have", "exact"], "tactic_count": 13}
{"name": "GenContFract.IntFractPair.exists_nth_stream_eq_none_of_rat", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Computation.TerminatesIffRat", "is_tactic_proof": true, "tactics": ["let", "rcases", "use", "have", "stream_nth_fr_num_le_fr_num_sub_n_rat", "have", "have", "simp", "sub_self,", "have", "have", "lia"], "tactic_count": 12}
{"name": "GenContFract.terminates_of_rat", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Computation.TerminatesIffRat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GenContFract.terminates_iff_rat", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Computation.TerminatesIffRat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GenContFract.IntFractPair.stream_zero", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Computation.Translations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GenContFract.IntFractPair.stream_eq_none_of_fr_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Computation.Translations", "is_tactic_proof": true, "tactics": ["obtain", "change", "simp"], "tactic_count": 3}
{"name": "GenContFract.IntFractPair.succ_nth_stream_eq_none_iff", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Computation.Translations", "is_tactic_proof": true, "tactics": ["rw", "cases"], "tactic_count": 2}
{"name": "GenContFract.IntFractPair.succ_nth_stream_eq_some_iff", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Computation.Translations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "GenContFract.IntFractPair.stream_succ_of_some", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Computation.Translations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GenContFract.IntFractPair.stream_succ_of_int", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Computation.Translations", "is_tactic_proof": true, "tactics": ["induction", "zero", "refine", "simp", "succ"], "tactic_count": 5}
{"name": "GenContFract.IntFractPair.exists_succ_nth_stream_of_fr_zero", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Computation.Translations", "is_tactic_proof": true, "tactics": ["rcases", "refine", "simpa"], "tactic_count": 3}
{"name": "GenContFract.IntFractPair.stream_succ", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Computation.Translations", "is_tactic_proof": true, "tactics": ["induction", "zero", "have", "rw", "succ", "rcases", "rw", "rw", "obtain", "rw", "rcases", "rw", "rw"], "tactic_count": 13}
{"name": "GenContFract.IntFractPair.seq1_fst_eq_of", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Computation.Translations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GenContFract.of_h_eq_intFractPair_seq1_fst_b", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Computation.Translations", "is_tactic_proof": true, "tactics": ["cases", "simp"], "tactic_count": 2}
{"name": "GenContFract.of_h_eq_floor", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Computation.Translations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "GenContFract.IntFractPair.get?_seq1_eq_succ_get?_stream", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Computation.Translations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GenContFract.of_terminatedAt_iff_intFractPair_seq1_terminatedAt", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Computation.Translations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GenContFract.of_terminatedAt_n_iff_succ_nth_intFractPair_stream_eq_none", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Computation.Translations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "GenContFract.IntFractPair.exists_succ_get?_stream_of_gcf_of_get?_eq_some", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Computation.Translations", "is_tactic_proof": false, "tactics": ["obtain", "unfold", "simpa", "cases", "simp_all"], "tactic_count": 5}
{"name": "GenContFract.get?_of_eq_some_of_succ_get?_intFractPair_stream", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Computation.Translations", "is_tactic_proof": true, "tactics": ["unfold", "simp"], "tactic_count": 2}
{"name": "GenContFract.get?_of_eq_some_of_get?_intFractPair_stream_fr_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Computation.Translations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GenContFract.of_s_head_aux", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Computation.Translations", "is_tactic_proof": true, "tactics": ["rw", "simp", "rw", "split"], "tactic_count": 4}
{"name": "GenContFract.of_s_head", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Computation.Translations", "is_tactic_proof": true, "tactics": ["change", "rw", "rfl"], "tactic_count": 3}
{"name": "GenContFract.of_s_of_int", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Computation.Translations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GenContFract.of_s_succ", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Computation.Translations", "is_tactic_proof": true, "tactics": ["rcases", "obtain", "rw", "rcases", "rwa", "of_terminatedAt_n_iff_succ_nth_intFractPair_stream_eq_none,", "obtain", "obtain", "have", "rw", "rw"], "tactic_count": 11}
{"name": "GenContFract.of_s_tail", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Computation.Translations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GenContFract.convs'_of_int", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Computation.Translations", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "exact"], "tactic_count": 5}
{"name": "GenContFract.convs'_succ", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Computation.Translations", "is_tactic_proof": true, "tactics": ["rcases", "obtain", "rw", "floor_intCast]", "rw", "exact"], "tactic_count": 6}
{"name": "GenContFract.contsAux_recurrence", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.ContinuantsRecurrence", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "GenContFract.conts_recurrenceAux", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.ContinuantsRecurrence", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "GenContFract.conts_recurrence", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.ContinuantsRecurrence", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "GenContFract.nums_recurrence", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.ContinuantsRecurrence", "is_tactic_proof": false, "tactics": ["obtain", "exists_conts_a_of_num", "obtain", "exists_conts_a_of_num", "rw"], "tactic_count": 5}
{"name": "GenContFract.dens_recurrence", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.ContinuantsRecurrence", "is_tactic_proof": false, "tactics": ["obtain", "exists_conts_b_of_den", "obtain", "exists_conts_b_of_den", "rw"], "tactic_count": 5}
{"name": "GenContFract.squashSeq", "kind": "definition", "module": "Mathlib.Algebra.ContinuedFractions.ConvergentsEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GenContFract.squashSeq_eq_self_of_terminated", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.ConvergentsEquiv", "is_tactic_proof": true, "tactics": ["change", "cases"], "tactic_count": 2}
{"name": "GenContFract.squashSeq_nth_of_not_terminated", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.ConvergentsEquiv", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "GenContFract.squashSeq_nth_of_lt", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.ConvergentsEquiv", "is_tactic_proof": true, "tactics": ["cases", "none", "some", "obtain", "simp"], "tactic_count": 5}
{"name": "GenContFract.squashSeq_succ_n_tail_eq_squashSeq_tail_n", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.ConvergentsEquiv", "is_tactic_proof": true, "tactics": ["cases", "none", "cases", "simp", "some", "gp_succ_succ_n", "obtain", "s.ge_stable", "ext1", "rcases", "simp", "cases", "simp", "simp"], "tactic_count": 14}
{"name": "GenContFract.succ_succ_nth_conv'Aux_eq_succ_nth_conv'Aux_squashSeq", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.ConvergentsEquiv", "is_tactic_proof": true, "tactics": ["cases", "none", "some", "induction", "zero", "obtain", "have", "squashSeq_nth_of_not_terminated", "simp_all", "succ", "obtain", "suffices", "simpa", "have", "simp_all"], "tactic_count": 15}
{"name": "GenContFract.squashGCF", "kind": "definition", "module": "Mathlib.Algebra.ContinuedFractions.ConvergentsEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GenContFract.squashGCF_eq_self_of_terminated", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.ConvergentsEquiv", "is_tactic_proof": true, "tactics": ["cases", "zero", "change", "simp", "succ", "cases", "simp", "exact"], "tactic_count": 8}
{"name": "GenContFract.squashGCF_nth_of_lt", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.ConvergentsEquiv", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "GenContFract.succ_nth_conv'_eq_squashGCF_nth_conv'", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.ConvergentsEquiv", "is_tactic_proof": true, "tactics": ["cases", "zero", "succ"], "tactic_count": 3}
{"name": "GenContFract.contsAux_eq_contsAux_squashGCF_of_le", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.ConvergentsEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GenContFract.succ_nth_conv_eq_squashGCF_nth_conv", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.ConvergentsEquiv", "is_tactic_proof": true, "tactics": ["rcases", "have", "simp", "obtain", "have", "cases", "zero", "suffices", "simpa", "conts_recurrenceAux", "grind", "succ", "n", "obtain", "let", "set", "set", "let", "let", "let", "let", "set", "set", "let", "let", "let", "let", "have", "have", "rw", "rw", "have", "have", "contsAux_recurrence", "rw", "rw", "suffices", "obtain", "simp", "symm", "simpa", "grind"], "tactic_count": 42}
{"name": "GenContFract.convs_eq_convs'", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.ConvergentsEquiv", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "let", "suffices", "rcases", "have", "rw", "intro", "exact", "suffices", "rwa", "intro", "rcases", "obtain", "obtain", "suffices", "have", "squashSeq_nth_of_not_terminated", "grind", "have", "refine", "refine", "have", "exact", "refine", "exact", "have", "intro", "obtain", "exact", "exact"], "tactic_count": 32}
{"name": "ContFract.convs_eq_convs'", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.ConvergentsEquiv", "is_tactic_proof": true, "tactics": ["ext", "apply", "intro", "exact", "c.property"], "tactic_count": 5}
{"name": "SimpContFract.determinant_aux", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Determinant", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "let", "let", "set", "set", "let", "let", "let", "let", "change", "have", "obtain", "suffices", "simp", "have", "rw", "ring", "suffices", "exact"], "tactic_count": 21}
{"name": "SimpContFract.determinant", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Determinant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GenContFract.terminated_stable", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.TerminatedStable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GenContFract.contsAux_stable_step_of_terminated", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.TerminatedStable", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "GenContFract.contsAux_stable_of_terminated", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.TerminatedStable", "is_tactic_proof": true, "tactics": ["refine", "rcases", "refine", "exact"], "tactic_count": 4}
{"name": "GenContFract.convs'Aux_stable_step_of_terminated", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.TerminatedStable", "is_tactic_proof": true, "tactics": ["change", "induction", "zero", "succ", "cases", "none", "some", "gp_head", "have", "have", "rw", "simp"], "tactic_count": 12}
{"name": "GenContFract.convs'Aux_stable_of_terminated", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.TerminatedStable", "is_tactic_proof": true, "tactics": ["induction", "refl", "step", "refine", "exact"], "tactic_count": 5}
{"name": "GenContFract.conts_stable_of_terminated", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.TerminatedStable", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "GenContFract.nums_stable_of_terminated", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.TerminatedStable", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "GenContFract.dens_stable_of_terminated", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.TerminatedStable", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "GenContFract.convs_stable_of_terminated", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.TerminatedStable", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "GenContFract.convs'_stable_of_terminated", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.TerminatedStable", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "GenContFract.terminatedAt_iff_s_terminatedAt", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Translations", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "GenContFract.terminatedAt_iff_s_none", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Translations", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "GenContFract.partNum_none_iff_s_none", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Translations", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "GenContFract.terminatedAt_iff_partNum_none", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Translations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "GenContFract.partDen_none_iff_s_none", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Translations", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "GenContFract.terminatedAt_iff_partDen_none", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Translations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "GenContFract.partNum_eq_s_a", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Translations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "GenContFract.partDen_eq_s_b", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Translations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "GenContFract.exists_s_a_of_partNum", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Translations", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "GenContFract.exists_s_b_of_partDen", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Translations", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "GenContFract.nth_cont_eq_succ_nth_contAux", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Translations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GenContFract.num_eq_conts_a", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Translations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GenContFract.den_eq_conts_b", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Translations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GenContFract.conv_eq_num_div_den", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Translations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GenContFract.conv_eq_conts_a_div_conts_b", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Translations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GenContFract.exists_conts_a_of_num", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Translations", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "GenContFract.exists_conts_b_of_den", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Translations", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "GenContFract.zeroth_contAux_eq_one_zero", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Translations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GenContFract.first_contAux_eq_h_one", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Translations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GenContFract.zeroth_cont_eq_h_one", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Translations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GenContFract.zeroth_num_eq_h", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Translations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GenContFract.zeroth_den_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Translations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GenContFract.zeroth_conv_eq_h", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Translations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "GenContFract.second_contAux_eq", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Translations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "GenContFract.first_cont_eq", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Translations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "GenContFract.first_num_eq", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Translations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "GenContFract.first_den_eq", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Translations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "GenContFract.zeroth_conv'Aux_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Translations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GenContFract.zeroth_conv'_eq_h", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Translations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "GenContFract.convs'Aux_succ_none", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Translations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "GenContFract.convs'Aux_succ_some", "kind": "theorem", "module": "Mathlib.Algebra.ContinuedFractions.Translations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Cubic.instInhabited", "kind": "instance", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cubic.instZero", "kind": "instance", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cubic.toPoly", "kind": "definition", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cubic.C_mul_prod_X_sub_C_eq", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": true, "tactics": ["simp", "ring1"], "tactic_count": 2}
{"name": "Cubic.prod_X_sub_C_eq", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "_private.Mathlib.Algebra.CubicDiscriminant.0.Cubic.coeffs", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": false, "tactics": ["simp", "grind"], "tactic_count": 2}
{"name": "Cubic.coeff_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cubic.coeff_eq_a", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cubic.coeff_eq_b", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cubic.coeff_eq_c", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cubic.coeff_eq_d", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cubic.a_of_eq", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cubic.b_of_eq", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cubic.c_of_eq", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cubic.d_of_eq", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cubic.toPoly_injective", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cubic.of_a_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cubic.of_a_eq_zero'", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cubic.of_b_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cubic.of_b_eq_zero'", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cubic.of_c_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cubic.of_c_eq_zero'", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cubic.of_d_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cubic.of_d_eq_zero'", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cubic.zero", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cubic.toPoly_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "_private.Mathlib.Algebra.CubicDiscriminant.0.Cubic.ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": true, "tactics": ["contrapose", "rw", "exact"], "tactic_count": 3}
{"name": "Cubic.ne_zero_of_a_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cubic.ne_zero_of_b_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cubic.ne_zero_of_c_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cubic.ne_zero_of_d_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cubic.leadingCoeff_of_a_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cubic.leadingCoeff_of_a_ne_zero'", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Cubic.leadingCoeff_of_b_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cubic.leadingCoeff_of_b_ne_zero'", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Cubic.leadingCoeff_of_c_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cubic.leadingCoeff_of_c_ne_zero'", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Cubic.leadingCoeff_of_c_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cubic.leadingCoeff_of_c_eq_zero'", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cubic.monic_of_a_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": true, "tactics": ["nontriviality", "rw"], "tactic_count": 2}
{"name": "Cubic.monic_of_a_eq_one'", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cubic.monic_of_b_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": true, "tactics": ["nontriviality", "rw"], "tactic_count": 2}
{"name": "Cubic.monic_of_b_eq_one'", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cubic.monic_of_c_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": true, "tactics": ["nontriviality", "rw"], "tactic_count": 2}
{"name": "Cubic.monic_of_c_eq_one'", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cubic.monic_of_d_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cubic.monic_of_d_eq_one'", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cubic.equiv", "kind": "definition", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cubic.degree_of_a_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cubic.degree_of_a_ne_zero'", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Cubic.degree_of_a_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Cubic.degree_of_a_eq_zero'", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cubic.degree_of_b_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cubic.degree_of_b_ne_zero'", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Cubic.degree_of_b_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Cubic.degree_of_b_eq_zero'", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cubic.degree_of_c_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cubic.degree_of_c_ne_zero'", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Cubic.degree_of_c_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Cubic.degree_of_c_eq_zero'", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cubic.degree_of_d_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cubic.degree_of_d_ne_zero'", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Cubic.degree_of_d_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cubic.degree_of_d_eq_zero'", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cubic.degree_of_zero", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cubic.natDegree_of_a_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cubic.natDegree_of_a_ne_zero'", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Cubic.natDegree_of_a_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Cubic.natDegree_of_a_eq_zero'", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cubic.natDegree_of_b_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cubic.natDegree_of_b_ne_zero'", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Cubic.natDegree_of_b_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Cubic.natDegree_of_b_eq_zero'", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cubic.natDegree_of_c_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cubic.natDegree_of_c_ne_zero'", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Cubic.natDegree_of_c_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cubic.natDegree_of_c_eq_zero'", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cubic.natDegree_of_zero", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cubic.map", "kind": "definition", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cubic.map_toPoly", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Cubic.roots", "kind": "definition", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cubic.map_roots", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cubic.mem_roots_iff", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Cubic.card_roots_le", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": true, "tactics": ["apply", "by_cases", "exact", "exact"], "tactic_count": 4}
{"name": "Cubic.splits_iff_card_roots", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": true, "tactics": ["replace", "rw"], "tactic_count": 2}
{"name": "Cubic.splits_iff_roots_eq_three", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cubic.eq_prod_three_roots", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": false, "tactics": ["rw", "leadingCoeff_map,", "change", "rw"], "tactic_count": 4}
{"name": "Cubic.eq_sum_three_roots", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": true, "tactics": ["apply_fun", "rw", "exact"], "tactic_count": 3}
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{"name": "Cubic.c_eq_three_roots", "kind": "theorem", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": true, "tactics": ["injection"], "tactic_count": 1}
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{"name": "Cubic.discr", "kind": "definition", "module": "Mathlib.Algebra.CubicDiscriminant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AddChar.directSum", "kind": "definition", "module": "Mathlib.Algebra.DirectSum.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.directSum_injective", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.AddChar", "is_tactic_proof": true, "tactics": ["refine", "rintro", "simpa"], "tactic_count": 3}
{"name": "GradedMonoid.smulCommClass_right", "kind": "instance", "module": "Mathlib.Algebra.DirectSum.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GradedMonoid.isScalarTower_right", "kind": "instance", "module": "Mathlib.Algebra.DirectSum.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.instAlgebra", "kind": "instance", "module": "Mathlib.Algebra.DirectSum.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.algebraMap_apply", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.algebraMap_toAddMonoid_hom", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.toAlgebra", "kind": "definition", "module": "Mathlib.Algebra.DirectSum.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.algHom_ext'", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.algHom_ext", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.gMulLHom", "kind": "definition", "module": "Mathlib.Algebra.DirectSum.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.directSumGAlgebra", "kind": "instance", "module": "Mathlib.Algebra.DirectSum.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum", "kind": "definition", "module": "Mathlib.Algebra.DirectSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.term⨁_,_", "kind": "definition", "module": "Mathlib.Algebra.DirectSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum._aux_Mathlib_Algebra_DirectSum_Basic___macroRules_DirectSum_term⨁_,__1", "kind": "definition", "module": "Mathlib.Algebra.DirectSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum._aux_Mathlib_Algebra_DirectSum_Basic___delab_app_DirectSum_term⨁_,__1", "kind": "definition", "module": "Mathlib.Algebra.DirectSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDecidableEqDirectSum", "kind": "instance", "module": "Mathlib.Algebra.DirectSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.coeFnAddMonoidHom", "kind": "definition", "module": "Mathlib.Algebra.DirectSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.coeFnAddMonoidHom_apply", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.instAddCommGroup", "kind": "instance", "module": "Mathlib.Algebra.DirectSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.sub_apply", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.ext", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.zero_apply", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.add_apply", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.mk", "kind": "definition", "module": "Mathlib.Algebra.DirectSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "DirectSum.of_eq_same", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.of_eq_of_ne", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "DirectSum.mk_apply_of_notMem", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "DirectSum.support_zero", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "DirectSum.support_of_subset", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.sum_support_of", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.sum_univ_of", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Basic", "is_tactic_proof": true, "tactics": ["apply", "rw", "simp"], "tactic_count": 3}
{"name": "DirectSum.mk_injective", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "DirectSum.addHom_ext", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.addHom_ext'", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.toAddMonoid", "kind": "definition", "module": "Mathlib.Algebra.DirectSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.toAddMonoid_of", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.toAddMonoid.unique", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Basic", "is_tactic_proof": false, "tactics": ["congr", "apply", "simp"], "tactic_count": 3}
{"name": "DirectSum.toAddMonoid_injective", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.toAddMonoid_inj", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.fromAddMonoid", "kind": "definition", "module": "Mathlib.Algebra.DirectSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.fromAddMonoid_of", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Basic", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "DirectSum.fromAddMonoid_of_apply", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "DirectSum.setToSet", "kind": "definition", "module": "Mathlib.Algebra.DirectSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "DirectSum.uniqueOfIsEmpty", "kind": "instance", "module": "Mathlib.Algebra.DirectSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.equivCongrLeft", "kind": "definition", "module": "Mathlib.Algebra.DirectSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.equivCongrLeft_apply", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Basic", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "DirectSum.addEquivProdDirectSum", "kind": "definition", "module": "Mathlib.Algebra.DirectSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.sigmaCurry", "kind": "definition", "module": "Mathlib.Algebra.DirectSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.sigmaCurry_apply", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.sigmaUncurry", "kind": "definition", "module": "Mathlib.Algebra.DirectSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.sigmaUncurry_apply", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.sigmaCurryEquiv", "kind": "definition", "module": "Mathlib.Algebra.DirectSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.coeAddMonoidHom", "kind": "definition", "module": "Mathlib.Algebra.DirectSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.coeAddMonoidHom_eq_dfinsuppSum", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Basic", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "DirectSum.coeAddMonoidHom_of", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.coe_of_apply", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Basic", "is_tactic_proof": true, "tactics": ["obtain", "rw", "rw"], "tactic_count": 3}
{"name": "DirectSum.IsInternal", "kind": "definition", "module": "Mathlib.Algebra.DirectSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.IsInternal.addSubmonoid_iSup_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
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{"name": "DirectSum.finite_support", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Basic", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "DirectSum.map", "kind": "definition", "module": "Mathlib.Algebra.DirectSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.map_of", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.map_apply", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.map_id", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.map_comp", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.map_injective", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Basic", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "DirectSum.map_surjective", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Basic", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "DirectSum.map_eq_iff", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "DirectSum.addEquivProd", "kind": "definition", "module": "Mathlib.Algebra.DirectSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.instSubsingletonDecomposition", "kind": "instance", "module": "Mathlib.Algebra.DirectSum.Decomposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.Decomposition.ofAddHom", "kind": "abbrev", "module": "Mathlib.Algebra.DirectSum.Decomposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.IsInternal.chooseDecomposition", "kind": "definition", "module": "Mathlib.Algebra.DirectSum.Decomposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.Decomposition.isInternal", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Decomposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "DirectSum.SetLike.IsHomogeneous", "kind": "definition", "module": "Mathlib.Algebra.DirectSum.Decomposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.Decomposition.inductionOn", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Decomposition", "is_tactic_proof": false, "tactics": ["let", "haveI", "left_inv", "right_inv", "have", "exact"], "tactic_count": 6}
{"name": "DirectSum.Decomposition.decompose'_eq", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Decomposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.decompose_symm_of", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Decomposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.decompose_coe", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Decomposition", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "DirectSum.decompose_of_mem", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Decomposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.decompose_of_mem_same", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Decomposition", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "DirectSum.decompose_of_mem_ne", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Decomposition", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "DirectSum.degree_eq_of_mem_mem", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Decomposition", "is_tactic_proof": true, "tactics": ["contrapose"], "tactic_count": 1}
{"name": "DirectSum.decomposeAddEquiv", "kind": "definition", "module": "Mathlib.Algebra.DirectSum.Decomposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.decompose_zero", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Decomposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.decompose_symm_zero", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Decomposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.decompose_add", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Decomposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.decompose_symm_add", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Decomposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.decompose_sum", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Decomposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.decompose_symm_sum", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Decomposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.sum_support_decompose", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Decomposition", "is_tactic_proof": true, "tactics": ["conv_rhs", "rw", "simp_rw"], "tactic_count": 3}
{"name": "DirectSum.AddSubmonoidClass.IsHomogeneous.mem_iff", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Decomposition", "is_tactic_proof": true, "tactics": ["classical", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "DirectSum.AddSubmonoidClass.IsHomogeneous.ext", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Decomposition", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "DirectSum.addCommGroupSetLike", "kind": "instance", "module": "Mathlib.Algebra.DirectSum.Decomposition", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "DirectSum.decompose_neg", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Decomposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.decompose_symm_neg", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Decomposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.decompose_sub", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Decomposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.decompose_symm_sub", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Decomposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.Decomposition.ofLinearMap", "kind": "abbrev", "module": "Mathlib.Algebra.DirectSum.Decomposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.decomposeLinearEquiv", "kind": "definition", "module": "Mathlib.Algebra.DirectSum.Decomposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.decomposeLinearEquiv_apply", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Decomposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.decomposeLinearEquiv_symm_apply", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Decomposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.decompose_smul", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Decomposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.decomposeLinearEquiv_symm_comp_lof", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Decomposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.decompose_lhom_ext", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Decomposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finsuppLEquivDirectSum", "kind": "definition", "module": "Mathlib.Algebra.DirectSum.Finsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finsuppLEquivDirectSum_single", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Finsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finsuppLEquivDirectSum_apply", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Finsupp", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "finsuppLEquivDirectSum_symm_lof", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Finsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lmap_finsuppLEquivDirectSum_eq", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Finsupp", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "DirectSum.idempotent", "kind": "definition", "module": "Mathlib.Algebra.DirectSum.Idempotents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.decompose_eq_mul_idempotent", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Idempotents", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "DirectSum.isIdempotentElem_idempotent", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Idempotents", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "DirectSum.completeOrthogonalIdempotents_idempotent", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Idempotents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.algebraMap_mem_graded", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Internal", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SetLike.natCast_mem_graded", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Internal", "is_tactic_proof": true, "tactics": ["induction", "zero", "rw", "exact", "succ", "rw", "exact"], "tactic_count": 7}
{"name": "SetLike.intCast_mem_graded", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Internal", "is_tactic_proof": true, "tactics": ["cases", "rw", "exact", "rw", "exact"], "tactic_count": 5}
{"name": "SetLike.gnonUnitalNonAssocSemiring", "kind": "instance", "module": "Mathlib.Algebra.DirectSum.Internal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.gsemiring", "kind": "instance", "module": "Mathlib.Algebra.DirectSum.Internal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.gcommSemiring", "kind": "instance", "module": "Mathlib.Algebra.DirectSum.Internal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.gring", "kind": "instance", "module": "Mathlib.Algebra.DirectSum.Internal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.gcommRing", "kind": "instance", "module": "Mathlib.Algebra.DirectSum.Internal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.coeRingHom", "kind": "definition", "module": "Mathlib.Algebra.DirectSum.Internal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.coeRingHom_of", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Internal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.coe_mul_apply", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Internal", "is_tactic_proof": true, "tactics": ["rw", "simp_rw"], "tactic_count": 2}
{"name": "DirectSum.coe_mul_apply_eq_dfinsuppSum", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Internal", "is_tactic_proof": true, "tactics": ["rw", "iterate", "dsimp", "split_ifs", "subst", "rw", "rfl", "rw", "rfl"], "tactic_count": 9}
{"name": "DirectSum.coe_mul_apply_eq_sum_antidiagonal", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Internal", "is_tactic_proof": true, "tactics": ["classical", "rw", "apply", "aesop"], "tactic_count": 4}
{"name": "DirectSum.coe_of_mul_apply_aux", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Internal", "is_tactic_proof": true, "tactics": ["classical", "rw", "apply", "swap", "simp_rw", "exact", "simp_rw", "split_ifs", "rfl", "rw"], "tactic_count": 10}
{"name": "DirectSum.coe_mul_of_apply_aux", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Internal", "is_tactic_proof": true, "tactics": ["classical", "rw", "apply", "swap", "simp_rw", "exact", "simp_rw", "split_ifs", "rfl", "rw"], "tactic_count": 10}
{"name": "DirectSum.coe_of_mul_apply_add", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Internal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.coe_mul_of_apply_add", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Internal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.coe_of_mul_apply_of_mem_zero", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Internal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.coe_mul_of_apply_of_mem_zero", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Internal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.coe_of_mul_apply_of_not_le", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Internal", "is_tactic_proof": true, "tactics": ["classical", "rw", "apply", "swap", "simp_rw", "exact", "rw", "exact"], "tactic_count": 8}
{"name": "DirectSum.coe_mul_of_apply_of_not_le", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Internal", "is_tactic_proof": true, "tactics": ["classical", "rw", "apply", "swap", "simp_rw", "exact", "rw", "exact"], "tactic_count": 8}
{"name": "DirectSum.coe_mul_of_apply_of_le", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Internal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.coe_of_mul_apply_of_le", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Internal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.coe_mul_of_apply", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Internal", "is_tactic_proof": true, "tactics": ["split_ifs", "exacts"], "tactic_count": 2}
{"name": "DirectSum.coe_of_mul_apply", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Internal", "is_tactic_proof": true, "tactics": ["split_ifs", "exacts"], "tactic_count": 2}
{"name": "Submodule.galgebra", "kind": "instance", "module": "Mathlib.Algebra.DirectSum.Internal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.setLike.coe_galgebra_toFun", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Internal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.nat_power_gradedMonoid", "kind": "instance", "module": "Mathlib.Algebra.DirectSum.Internal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.coeAlgHom", "kind": "definition", "module": "Mathlib.Algebra.DirectSum.Internal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.iSup_eq_toSubmodule_range", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Internal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.coeAlgHom_of", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Internal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.GradeZero.subsemiring", "kind": "definition", "module": "Mathlib.Algebra.DirectSum.Internal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.GradeZero.instSemiring", "kind": "instance", "module": "Mathlib.Algebra.DirectSum.Internal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.GradeZero.coe_natCast", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Internal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.GradeZero.coe_ofNat", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Internal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.GradeZero.instCommSemiring", "kind": "instance", "module": "Mathlib.Algebra.DirectSum.Internal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.GradeZero.instAlgebraSubtypeMemOfNat", "kind": "instance", "module": "Mathlib.Algebra.DirectSum.Internal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.GradeZero.algebraMap_apply", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Internal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.GradeZero.subring", "kind": "definition", "module": "Mathlib.Algebra.DirectSum.Internal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.GradeZero.instRing", "kind": "instance", "module": "Mathlib.Algebra.DirectSum.Internal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.GradeZero.coe_intCast", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Internal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.GradeZero.instCommRing", "kind": "instance", "module": "Mathlib.Algebra.DirectSum.Internal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.GradeZero.subalgebra", "kind": "definition", "module": "Mathlib.Algebra.DirectSum.Internal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.GradeZero.instAlgebra", "kind": "instance", "module": "Mathlib.Algebra.DirectSum.Internal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.GradeZero.coe_algebraMap", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Internal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.homogeneous_zero_submodule", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Internal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.Homogeneous.smul", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Internal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_apply_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Internal", "is_tactic_proof": true, "tactics": ["classical", "rw", "apply", "obtain", "by_contra", "obtain", "apply", "all_goals"], "tactic_count": 8}
{"name": "listProd_apply_eq_zero'", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Internal", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "ih", "simp", "exact"], "tactic_count": 6}
{"name": "listProd_apply_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Internal", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "ih", "simp", "refine", "simpa"], "tactic_count": 7}
{"name": "multisetProd_apply_eq_zero'", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Internal", "is_tactic_proof": false, "tactics": ["have", "listProd_apply_eq_zero", "simpa"], "tactic_count": 3}
{"name": "multisetProd_apply_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Internal", "is_tactic_proof": false, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "finsetProd_apply_eq_zero'", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Internal", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "finsetProd_apply_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Internal", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "LinearMap.toMatrix_directSum_collectedBasis_eq_blockDiagonal'", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.LinearMap", "is_tactic_proof": true, "tactics": ["ext", "simp", "rcases", "simp", "simp"], "tactic_count": 5}
{"name": "LinearMap.diag_toMatrix_directSum_collectedBasis_eq_zero_of_mapsTo_ne", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.LinearMap", "is_tactic_proof": true, "tactics": ["ext", "simp", "by_cases", "let", "replace", "exact", "suffices", "simpa"], "tactic_count": 8}
{"name": "LinearMap.trace_eq_sum_trace_restrict", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.LinearMap", "is_tactic_proof": true, "tactics": ["let", "simp_rw"], "tactic_count": 2}
{"name": "LinearMap.trace_eq_sum_trace_restrict'", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.LinearMap", "is_tactic_proof": true, "tactics": ["let", "let", "rw", "exact"], "tactic_count": 4}
{"name": "LinearMap.trace_eq_zero_of_mapsTo_ne", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.LinearMap", "is_tactic_proof": true, "tactics": ["have", "let", "let", "let", "replace", "simp_rw", "diag_toMatrix_directSum_collectedBasis_eq_zero_of_mapsTo_ne"], "tactic_count": 7}
{"name": "LinearMap.trace_comp_eq_zero_of_commute_of_trace_restrict_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.LinearMap", "is_tactic_proof": false, "tactics": ["have", "suffices", "classical", "have", "have", "simp", "intro", "have", "have", "replace", "restrict_commute", "have", "rw"], "tactic_count": 13}
{"name": "LinearMap.mapsTo_biSup_of_mapsTo", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.LinearMap", "is_tactic_proof": true, "tactics": ["replace", "suffices", "simpa"], "tactic_count": 3}
{"name": "DirectSum.instModule", "kind": "instance", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.instSMulCommClass", "kind": "instance", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.instIsScalarTower", "kind": "instance", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.instIsCentralScalar", "kind": "instance", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.smul_apply", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.coeFnLinearMap", "kind": "definition", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.coeFnLinearMap_apply", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.lmk", "kind": "definition", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.lof", "kind": "definition", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.lof_eq_of", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.single_eq_lof", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.mk_smul", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.of_smul", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.support_smul", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.toModule", "kind": "definition", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.coe_toModule_eq_coe_toAddMonoid", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.toModule_lof", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.toModule.unique", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.linearMap_ext", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.lsetToSet", "kind": "definition", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.linearEquivFunOnFintype", "kind": "definition", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.linearEquivFunOnFintype_lof", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "DirectSum.linearEquivFunOnFintype_symm_single", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.linearEquivFunOnFintype_symm_coe", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.component", "kind": "definition", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.apply_eq_component", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.ext_component", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.ext_component_iff", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.lof_apply", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.component.lof_self", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.component.of", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.mker_map", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.mrange_map", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.lmap", "kind": "definition", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.lmap_apply", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.lmap_of", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.lmap_lof", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.lmap_id", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.lmap_comp", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.lmap_injective", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "DirectSum.lmap_surjective", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "DirectSum.lmap_eq_iff", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.toAddMonoidHom_lmap", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.lmap_eq_map", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.ker_lmap", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.range_lmap", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.ker_map", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "DirectSum.lequivCongrLeft", "kind": "definition", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.lequivCongrLeft_apply", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.sigmaLcurry", "kind": "definition", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.sigmaLcurry_apply", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.sigmaLuncurry", "kind": "definition", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.sigmaLuncurry_apply", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.sigmaLcurryEquiv", "kind": "definition", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.lequivProdDirectSum", "kind": "definition", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.coeLinearMap", "kind": "definition", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.coeLinearMap_eq_dfinsuppSum", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": true, "tactics": ["simp", "rw", "simp"], "tactic_count": 3}
{"name": "DirectSum.coeLinearMap_of", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.range_coeLinearMap", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.IsInternal.ofBijective_coeLinearMap_same", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "DirectSum.IsInternal.ofBijective_coeLinearMap_of_ne", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "DirectSum.IsInternal.ofBijective_coeLinearMap_of_mem", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.IsInternal.ofBijective_coeLinearMap_of_mem_ne", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.IsInternal.submodule_iSup_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "DirectSum.IsInternal.submodule_iSupIndep", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.IsInternal.collectedBasis", "kind": "definition", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.IsInternal.collectedBasis_coe", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DirectSum.IsInternal.collectedBasis_mem", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DirectSum.IsInternal.collectedBasis_repr_of_mem", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": true, "tactics": ["change", "simp"], "tactic_count": 2}
{"name": "DirectSum.IsInternal.collectedBasis_repr_of_mem_ne", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": true, "tactics": ["change", "simp"], "tactic_count": 2}
{"name": "DirectSum.IsInternal.isCompl", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.isInternal_submodule_of_iSupIndep_of_iSup_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.isInternal_submodule_iff_iSupIndep_and_iSup_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.isInternal_submodule_iff_isCompl", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "DirectSum.isInternal_ne_bot_iff", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DirectSum.isInternal_biSup_submodule_of_iSupIndep", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": true, "tactics": ["refine", "let", "have", "let", "suffices", "rw", "exact", "ext", "change", "rw"], "tactic_count": 10}
{"name": "DirectSum.IsInternal.addSubmonoid_iSupIndep", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.IsInternal.addSubgroup_iSupIndep", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.congrAddEquiv", "kind": "definition", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.coe_congrAddEquiv", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.congrLinearEquiv", "kind": "definition", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.coe_congrLinearEquiv", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.congrLinearEquiv_toAddEquiv", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.congrLinearEquiv_toLinearMap", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.of_eq_of_gradedMonoid_eq", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.instOne", "kind": "instance", "module": "Mathlib.Algebra.DirectSum.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.one_def", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.gMulHom", "kind": "definition", "module": "Mathlib.Algebra.DirectSum.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.mulHom", "kind": "definition", "module": "Mathlib.Algebra.DirectSum.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.instMul", "kind": "instance", "module": "Mathlib.Algebra.DirectSum.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.instNonUnitalNonAssocSemiring", "kind": "instance", "module": "Mathlib.Algebra.DirectSum.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.mulHom_apply", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.mulHom_of_of", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Ring", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DirectSum.of_mul_of", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.DirectSum.Ring.0.DirectSum.one_mul", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Ring", "is_tactic_proof": true, "tactics": ["suffices", "apply", "simp", "rw", "exact"], "tactic_count": 5}
{"name": "_private.Mathlib.Algebra.DirectSum.Ring.0.DirectSum.mul_one", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Ring", "is_tactic_proof": true, "tactics": ["suffices", "apply", "simp", "rw", "exact"], "tactic_count": 5}
{"name": "_private.Mathlib.Algebra.DirectSum.Ring.0.DirectSum.mul_assoc", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Ring", "is_tactic_proof": true, "tactics": ["suffices", "simpa", "ext", "dsimp", "simp_rw", "exact"], "tactic_count": 6}
{"name": "DirectSum.instNatCast", "kind": "instance", "module": "Mathlib.Algebra.DirectSum.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.semiring", "kind": "instance", "module": "Mathlib.Algebra.DirectSum.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.ofPow", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Ring", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "exact"], "tactic_count": 5}
{"name": "DirectSum.ofList_dProd", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Ring", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "rename_i", "simp", "rw", "rfl"], "tactic_count": 7}
{"name": "DirectSum.list_prod_ofFn_of_eq_dProd", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Ring", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "DirectSum.mul_eq_dfinsuppSum", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Ring", "is_tactic_proof": false, "tactics": ["change", "mulHom", "rw", "dsimp", "rw", "apply", "simp_rw", "funext", "simp"], "tactic_count": 9}
{"name": "DirectSum.mul_eq_sum_support_ghas_mul", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Ring", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "_private.Mathlib.Algebra.DirectSum.Ring.0.DirectSum.mul_comm", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Ring", "is_tactic_proof": true, "tactics": ["suffices", "apply", "rw", "exact"], "tactic_count": 4}
{"name": "DirectSum.commSemiring", "kind": "instance", "module": "Mathlib.Algebra.DirectSum.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.nonAssocRing", "kind": "instance", "module": "Mathlib.Algebra.DirectSum.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.ring", "kind": "instance", "module": "Mathlib.Algebra.DirectSum.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.commRing", "kind": "instance", "module": "Mathlib.Algebra.DirectSum.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.of_zero_one", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.of_zero_smul", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.of_zero_mul", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.GradeZero.nonUnitalNonAssocSemiring", "kind": "instance", "module": "Mathlib.Algebra.DirectSum.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.GradeZero.smulWithZero", "kind": "instance", "module": "Mathlib.Algebra.DirectSum.Ring", "is_tactic_proof": true, "tactics": ["letI", "exact"], "tactic_count": 2}
{"name": "DirectSum.of_zero_pow", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.instNatCastOfNat", "kind": "instance", "module": "Mathlib.Algebra.DirectSum.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.of_natCast", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.of_zero_ofNat", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.GradeZero.semiring", "kind": "instance", "module": "Mathlib.Algebra.DirectSum.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.ofZeroRingHom", "kind": "definition", "module": "Mathlib.Algebra.DirectSum.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.GradeZero.module", "kind": "instance", "module": "Mathlib.Algebra.DirectSum.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.GradeZero.commSemiring", "kind": "instance", "module": "Mathlib.Algebra.DirectSum.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.GradeZero.nonUnitalNonAssocRing", "kind": "instance", "module": "Mathlib.Algebra.DirectSum.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.instIntCastOfNat", "kind": "instance", "module": "Mathlib.Algebra.DirectSum.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.of_intCast", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Ring", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "DirectSum.GradeZero.ring", "kind": "instance", "module": "Mathlib.Algebra.DirectSum.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.GradeZero.commRing", "kind": "instance", "module": "Mathlib.Algebra.DirectSum.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.ringHom_ext'", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.ringHom_ext", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.toSemiring", "kind": "definition", "module": "Mathlib.Algebra.DirectSum.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.toSemiring_of", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.toSemiring_coe_addMonoidHom", "kind": "theorem", "module": "Mathlib.Algebra.DirectSum.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.liftRingHom", "kind": "definition", "module": "Mathlib.Algebra.DirectSum.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalNonAssocSemiring.directSumGNonUnitalNonAssocSemiring", "kind": "instance", "module": "Mathlib.Algebra.DirectSum.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Semiring.directSumGSemiring", "kind": "instance", "module": "Mathlib.Algebra.DirectSum.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ring.directSumGRing", "kind": "instance", "module": "Mathlib.Algebra.DirectSum.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_example", "kind": "example", "module": "Mathlib.Algebra.DirectSum.Ring", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CommSemiring.directSumGCommSemiring", "kind": "instance", "module": "Mathlib.Algebra.DirectSum.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRing.directSumGCommRing", "kind": "instance", "module": "Mathlib.Algebra.DirectSum.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "semigroupDvd", "kind": "instance", "module": "Mathlib.Algebra.Divisibility.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dvd.intro", "kind": "theorem", "module": "Mathlib.Algebra.Divisibility.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_eq_mul_right_of_dvd", "kind": "theorem", "module": "Mathlib.Algebra.Divisibility.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dvd_def", "kind": "theorem", "module": "Mathlib.Algebra.Divisibility.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dvd.elim", "kind": "theorem", "module": "Mathlib.Algebra.Divisibility.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dvd_trans", "kind": "theorem", "module": "Mathlib.Algebra.Divisibility.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsTransDvd", "kind": "instance", "module": "Mathlib.Algebra.Divisibility.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dvd_mul_right", "kind": "theorem", "module": "Mathlib.Algebra.Divisibility.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dvd_mul_of_dvd_left", "kind": "theorem", "module": "Mathlib.Algebra.Divisibility.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dvd_of_mul_right_dvd", "kind": "theorem", "module": "Mathlib.Algebra.Divisibility.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimal", "kind": "definition", "module": "Mathlib.Algebra.Divisibility.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_dvd_and_dvd_of_dvd_mul", "kind": "theorem", "module": "Mathlib.Algebra.Divisibility.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_dvd_mul_left", "kind": "theorem", "module": "Mathlib.Algebra.Divisibility.Basic", "is_tactic_proof": true, "tactics": ["obtain", "use", "rw"], "tactic_count": 3}
{"name": "IsLeftRegular.dvd_cancel_left", "kind": "theorem", "module": "Mathlib.Algebra.Divisibility.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dvd_refl", "kind": "theorem", "module": "Mathlib.Algebra.Divisibility.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dvd_rfl", "kind": "theorem", "module": "Mathlib.Algebra.Divisibility.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instReflDvd_mathlib", "kind": "instance", "module": "Mathlib.Algebra.Divisibility.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_dvd", "kind": "theorem", "module": "Mathlib.Algebra.Divisibility.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dvd_of_eq", "kind": "theorem", "module": "Mathlib.Algebra.Divisibility.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "pow_dvd_pow", "kind": "theorem", "module": "Mathlib.Algebra.Divisibility.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dvd_pow", "kind": "theorem", "module": "Mathlib.Algebra.Divisibility.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dvd_pow_self", "kind": "theorem", "module": "Mathlib.Algebra.Divisibility.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dvd.intro_left", "kind": "theorem", "module": "Mathlib.Algebra.Divisibility.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_eq_mul_left_of_dvd", "kind": "theorem", "module": "Mathlib.Algebra.Divisibility.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dvd_iff_exists_eq_mul_left", "kind": "theorem", "module": "Mathlib.Algebra.Divisibility.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dvd.elim_left", "kind": "theorem", "module": "Mathlib.Algebra.Divisibility.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dvd_mul_left", "kind": "theorem", "module": "Mathlib.Algebra.Divisibility.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dvd_mul_of_dvd_right", "kind": "theorem", "module": "Mathlib.Algebra.Divisibility.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mul_dvd_mul", "kind": "theorem", "module": "Mathlib.Algebra.Divisibility.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dvd_of_mul_left_dvd", "kind": "theorem", "module": "Mathlib.Algebra.Divisibility.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dvd_mul", "kind": "theorem", "module": "Mathlib.Algebra.Divisibility.Basic", "is_tactic_proof": true, "tactics": ["refine", "rintro", "gcongr"], "tactic_count": 3}
{"name": "mul_dvd_mul_right", "kind": "theorem", "module": "Mathlib.Algebra.Divisibility.Basic", "is_tactic_proof": true, "tactics": ["gcongr"], "tactic_count": 1}
{"name": "pow_dvd_pow_of_dvd", "kind": "theorem", "module": "Mathlib.Algebra.Divisibility.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "gcongr"], "tactic_count": 5}
{"name": "pow_dvd_pow_of_dvd_of_le", "kind": "theorem", "module": "Mathlib.Algebra.Divisibility.Basic", "is_tactic_proof": true, "tactics": ["trans"], "tactic_count": 1}
{"name": "instDecidableDvdOfFintypeOfDecidableEq", "kind": "instance", "module": "Mathlib.Algebra.Divisibility.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "map_dvd", "kind": "theorem", "module": "Mathlib.Algebra.Divisibility.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulHom.map_dvd", "kind": "theorem", "module": "Mathlib.Algebra.Divisibility.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.map_dvd", "kind": "theorem", "module": "Mathlib.Algebra.Divisibility.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "prod_dvd_iff", "kind": "theorem", "module": "Mathlib.Algebra.Divisibility.Prod", "is_tactic_proof": true, "tactics": ["cases", "simp"], "tactic_count": 2}
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{"name": "EuclideanDomain.gcd_dvd", "kind": "theorem", "module": "Mathlib.Algebra.EuclideanDomain.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "EuclideanDomain.gcd_dvd_right", "kind": "theorem", "module": "Mathlib.Algebra.EuclideanDomain.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanDomain.gcd_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.EuclideanDomain.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanDomain.dvd_gcd", "kind": "theorem", "module": "Mathlib.Algebra.EuclideanDomain.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "EuclideanDomain.gcd_one_left", "kind": "theorem", "module": "Mathlib.Algebra.EuclideanDomain.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanDomain.gcd_self", "kind": "theorem", "module": "Mathlib.Algebra.EuclideanDomain.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanDomain.xgcdAux_fst", "kind": "theorem", "module": "Mathlib.Algebra.EuclideanDomain.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanDomain.xgcdAux_val", "kind": "theorem", "module": "Mathlib.Algebra.EuclideanDomain.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "EuclideanDomain.instIsDomain", "kind": "instance", "module": "Mathlib.Algebra.EuclideanDomain.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanDomain.div_pow", "kind": "theorem", "module": "Mathlib.Algebra.EuclideanDomain.Basic", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "obtain", "simp"], "tactic_count": 4}
{"name": "EuclideanDomain.dvd_lcm_left", "kind": "theorem", "module": "Mathlib.Algebra.EuclideanDomain.Basic", "is_tactic_proof": false, "tactics": ["rw", "exact", "let"], "tactic_count": 3}
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{"name": "EuclideanDomain.lcm_zero_left", "kind": "theorem", "module": "Mathlib.Algebra.EuclideanDomain.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "_private.Mathlib.Algebra.EuclideanDomain.Defs.0.EuclideanDomain._aux_Mathlib_Algebra_EuclideanDomain_Defs___macroRules__private_Mathlib_Algebra_EuclideanDomain_Defs_0_EuclideanDomain_term_≺__1", "kind": "definition", "module": "Mathlib.Algebra.EuclideanDomain.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.EuclideanDomain.Defs.0.EuclideanDomain._aux_Mathlib_Algebra_EuclideanDomain_Defs___unexpand_EuclideanDomain_r_1", "kind": "definition", "module": "Mathlib.Algebra.EuclideanDomain.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanDomain.wellFoundedRelation", "kind": "instance", "module": "Mathlib.Algebra.EuclideanDomain.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanDomain.isWellFounded", "kind": "instance", "module": "Mathlib.Algebra.EuclideanDomain.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "EuclideanDomain.instMod", "kind": "instance", "module": "Mathlib.Algebra.EuclideanDomain.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanDomain.div_add_mod", "kind": "theorem", "module": "Mathlib.Algebra.EuclideanDomain.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanDomain.mod_add_div", "kind": "theorem", "module": "Mathlib.Algebra.EuclideanDomain.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanDomain.mod_add_div'", "kind": "theorem", "module": "Mathlib.Algebra.EuclideanDomain.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
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{"name": "EuclideanDomain.mul_right_not_lt", "kind": "theorem", "module": "Mathlib.Algebra.EuclideanDomain.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "EuclideanDomain.mod_zero", "kind": "theorem", "module": "Mathlib.Algebra.EuclideanDomain.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "EuclideanDomain.lt_one", "kind": "theorem", "module": "Mathlib.Algebra.EuclideanDomain.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "EuclideanDomain.gcdB", "kind": "definition", "module": "Mathlib.Algebra.EuclideanDomain.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanDomain.gcdA_zero_left", "kind": "theorem", "module": "Mathlib.Algebra.EuclideanDomain.Defs", "is_tactic_proof": true, "tactics": ["unfold", "rw"], "tactic_count": 2}
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{"name": "EuclideanDomain.lcm", "kind": "definition", "module": "Mathlib.Algebra.EuclideanDomain.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Field.toEuclideanDomain", "kind": "instance", "module": "Mathlib.Algebra.EuclideanDomain.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Field.mod_eq", "kind": "theorem", "module": "Mathlib.Algebra.EuclideanDomain.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Field.gcd_eq", "kind": "theorem", "module": "Mathlib.Algebra.EuclideanDomain.Field", "is_tactic_proof": true, "tactics": ["unfold", "split_ifs"], "tactic_count": 2}
{"name": "Field.gcd_zero_eq", "kind": "theorem", "module": "Mathlib.Algebra.EuclideanDomain.Field", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Field.gcd_eq_of_ne", "kind": "theorem", "module": "Mathlib.Algebra.EuclideanDomain.Field", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.euclideanDomain", "kind": "instance", "module": "Mathlib.Algebra.EuclideanDomain.Int", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.MulExact", "kind": "definition", "module": "Mathlib.Algebra.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.MulExact.apply_apply_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.MulExact.comp_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.MulExact.of_comp_of_mem_range", "kind": "theorem", "module": "Mathlib.Algebra.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MonoidHom.mulExact_iff", "kind": "theorem", "module": "Mathlib.Algebra.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Function.Exact.splitInjectiveEquiv", "kind": "definition", "module": "Mathlib.Algebra.Exact", "is_tactic_proof": false, "tactics": ["refine", "invFun", "left_inv", "right_inv", "have", "have", "constructor", "intro", "simp", "obtain", "suffices", "rw", "rintro", "obtain", "refine", "have", "have", "constructor", "rw", "ext", "ext", "rw", "intro", "rintro", "ext"], "tactic_count": 25}
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{"name": "Function.Exact.split_tfae", "kind": "theorem", "module": "Mathlib.Algebra.Exact", "is_tactic_proof": true, "tactics": ["tfae_have", "tfae_have", "tfae_finish"], "tactic_count": 3}
{"name": "Function.Exact.inr_fst", "kind": "theorem", "module": "Mathlib.Algebra.Exact", "is_tactic_proof": true, "tactics": ["rintro", "simp"], "tactic_count": 2}
{"name": "Function.Exact.inl_snd", "kind": "theorem", "module": "Mathlib.Algebra.Exact", "is_tactic_proof": true, "tactics": ["rintro", "simp"], "tactic_count": 2}
{"name": "Function.Exact.exact_mapQ_iff", "kind": "theorem", "module": "Mathlib.Algebra.Exact", "is_tactic_proof": true, "tactics": ["rw", "dsimp", "rw", "sup_comm,"], "tactic_count": 4}
{"name": "LinearMap.exact_iff_of_surjective_of_bijective_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.surjective_range_liftQ", "kind": "theorem", "module": "Mathlib.Algebra.Exact", "is_tactic_proof": true, "tactics": ["intro", "obtain", "exact"], "tactic_count": 3}
{"name": "LinearMap.ker_eq_bot_range_liftQ_iff", "kind": "theorem", "module": "Mathlib.Algebra.Exact", "is_tactic_proof": true, "tactics": ["simp", "constructor", "intro", "simpa", "intro", "obtain", "simpa"], "tactic_count": 7}
{"name": "LinearMap.injective_range_liftQ_of_exact", "kind": "theorem", "module": "Mathlib.Algebra.Exact", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Function.Exact.linearEquivOfSurjective", "kind": "definition", "module": "Mathlib.Algebra.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Exact.linearEquivOfSurjective_symm_apply", "kind": "theorem", "module": "Mathlib.Algebra.Exact", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Expr.instOne", "kind": "definition", "module": "Mathlib.Algebra.Expr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Expr.instZero", "kind": "definition", "module": "Mathlib.Algebra.Expr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Expr.instMul", "kind": "definition", "module": "Mathlib.Algebra.Expr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Expr.instAdd", "kind": "definition", "module": "Mathlib.Algebra.Expr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjAct.distribMulAction₀", "kind": "instance", "module": "Mathlib.Algebra.Field.Action.ConjAct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "add_div", "kind": "theorem", "module": "Mathlib.Algebra.Field.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "div_add_div_same", "kind": "theorem", "module": "Mathlib.Algebra.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "same_add_div", "kind": "theorem", "module": "Mathlib.Algebra.Field.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "div_add_same", "kind": "theorem", "module": "Mathlib.Algebra.Field.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "one_add_div", "kind": "theorem", "module": "Mathlib.Algebra.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "div_add_one", "kind": "theorem", "module": "Mathlib.Algebra.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_add_inv'", "kind": "theorem", "module": "Mathlib.Algebra.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_div_mul_add_mul_one_div_eq_one_div_add_one_div", "kind": "theorem", "module": "Mathlib.Algebra.Field.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "add_div_eq_mul_add_div", "kind": "theorem", "module": "Mathlib.Algebra.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "add_div'", "kind": "theorem", "module": "Mathlib.Algebra.Field.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "div_add'", "kind": "theorem", "module": "Mathlib.Algebra.Field.Basic", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Commute.div_add_div", "kind": "theorem", "module": "Mathlib.Algebra.Field.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Commute.one_div_add_one_div", "kind": "theorem", "module": "Mathlib.Algebra.Field.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Commute.inv_add_inv", "kind": "theorem", "module": "Mathlib.Algebra.Field.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "add_self_div_two", "kind": "theorem", "module": "Mathlib.Algebra.Field.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "add_halves", "kind": "theorem", "module": "Mathlib.Algebra.Field.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "div_neg_self", "kind": "theorem", "module": "Mathlib.Algebra.Field.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "neg_div_self", "kind": "theorem", "module": "Mathlib.Algebra.Field.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "div_sub_div_same", "kind": "theorem", "module": "Mathlib.Algebra.Field.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "same_sub_div", "kind": "theorem", "module": "Mathlib.Algebra.Field.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "one_sub_div", "kind": "theorem", "module": "Mathlib.Algebra.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "div_sub_same", "kind": "theorem", "module": "Mathlib.Algebra.Field.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "div_sub_one", "kind": "theorem", "module": "Mathlib.Algebra.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sub_div", "kind": "theorem", "module": "Mathlib.Algebra.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_sub_inv'", "kind": "theorem", "module": "Mathlib.Algebra.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_div_mul_sub_mul_one_div_eq_one_div_add_one_div", "kind": "theorem", "module": "Mathlib.Algebra.Field.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "DivisionRing.isDomain", "kind": "instance", "module": "Mathlib.Algebra.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.div_sub_div", "kind": "theorem", "module": "Mathlib.Algebra.Field.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Commute.inv_sub_inv", "kind": "theorem", "module": "Mathlib.Algebra.Field.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "sub_half", "kind": "theorem", "module": "Mathlib.Algebra.Field.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "half_sub", "kind": "theorem", "module": "Mathlib.Algebra.Field.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "div_add_div", "kind": "theorem", "module": "Mathlib.Algebra.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_div_add_one_div", "kind": "theorem", "module": "Mathlib.Algebra.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_add_inv", "kind": "theorem", "module": "Mathlib.Algebra.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Field.toGrindField", "kind": "instance", "module": "Mathlib.Algebra.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "div_sub_div", "kind": "theorem", "module": "Mathlib.Algebra.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_sub_inv", "kind": "theorem", "module": "Mathlib.Algebra.Field.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "sub_div'", "kind": "theorem", "module": "Mathlib.Algebra.Field.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "div_sub'", "kind": "theorem", "module": "Mathlib.Algebra.Field.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Field.isDomain", "kind": "instance", "module": "Mathlib.Algebra.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DivisionRing.ofIsUnitOrEqZero", "kind": "abbrev", "module": "Mathlib.Algebra.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Field.ofIsUnitOrEqZero", "kind": "abbrev", "module": "Mathlib.Algebra.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.divisionSemiring", "kind": "abbrev", "module": "Mathlib.Algebra.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.divisionRing", "kind": "abbrev", "module": "Mathlib.Algebra.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.semifield", "kind": "abbrev", "module": "Mathlib.Algebra.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.field", "kind": "abbrev", "module": "Mathlib.Algebra.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instRatCast", "kind": "instance", "module": "Mathlib.Algebra.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instDivisionSemiring", "kind": "instance", "module": "Mathlib.Algebra.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instDivisionRing", "kind": "instance", "module": "Mathlib.Algebra.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instSemifield", "kind": "instance", "module": "Mathlib.Algebra.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instField", "kind": "instance", "module": "Mathlib.Algebra.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toDual_ratCast", "kind": "theorem", "module": "Mathlib.Algebra.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofDual_ratCast", "kind": "theorem", "module": "Mathlib.Algebra.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lex.instRatCast", "kind": "instance", "module": "Mathlib.Algebra.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lex.instDivisionSemiring", "kind": "instance", "module": "Mathlib.Algebra.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lex.instDivisionRing", "kind": "instance", "module": "Mathlib.Algebra.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lex.instSemifield", "kind": "instance", "module": "Mathlib.Algebra.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lex.instField", "kind": "instance", "module": "Mathlib.Algebra.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toLex_ratCast", "kind": "theorem", "module": "Mathlib.Algebra.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofLex_ratCast", "kind": "theorem", "module": "Mathlib.Algebra.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.castRec", "kind": "definition", "module": "Mathlib.Algebra.Field.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.castRec", "kind": "definition", "module": "Mathlib.Algebra.Field.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DivisionRing.toDivisionSemiring", "kind": "instance", "module": "Mathlib.Algebra.Field.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Field.toSemifield", "kind": "instance", "module": "Mathlib.Algebra.Field.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.smulDivisionSemiring", "kind": "instance", "module": "Mathlib.Algebra.Field.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.cast_def", "kind": "theorem", "module": "Mathlib.Algebra.Field.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.smul_def", "kind": "theorem", "module": "Mathlib.Algebra.Field.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.smul_one_eq_cast", "kind": "theorem", "module": "Mathlib.Algebra.Field.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Rat.cast_def", "kind": "theorem", "module": "Mathlib.Algebra.Field.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.cast_mk'", "kind": "theorem", "module": "Mathlib.Algebra.Field.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.smulDivisionRing", "kind": "instance", "module": "Mathlib.Algebra.Field.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.smul_def", "kind": "theorem", "module": "Mathlib.Algebra.Field.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.smul_one_eq_cast", "kind": "theorem", "module": "Mathlib.Algebra.Field.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Rat.ofScientific_eq_ofScientific", "kind": "theorem", "module": "Mathlib.Algebra.Field.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalHom.isField", "kind": "theorem", "module": "Mathlib.Algebra.Field.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.isField", "kind": "theorem", "module": "Mathlib.Algebra.Field.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.geom_sum₂", "kind": "theorem", "module": "Mathlib.Algebra.Field.GeomSum", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "geom_sum_eq", "kind": "theorem", "module": "Mathlib.Algebra.Field.GeomSum", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "Commute.geom_sum₂_Ico", "kind": "theorem", "module": "Mathlib.Algebra.Field.GeomSum", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "geom_sum_Ico", "kind": "theorem", "module": "Mathlib.Algebra.Field.GeomSum", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "geom_sum_Ico'", "kind": "theorem", "module": "Mathlib.Algebra.Field.GeomSum", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "geom_sum_inv", "kind": "theorem", "module": "Mathlib.Algebra.Field.GeomSum", "is_tactic_proof": true, "tactics": ["have", "have", "have", "have", "rw", "rw", "simp", "mul_one,", "rw"], "tactic_count": 9}
{"name": "geom₂_sum", "kind": "theorem", "module": "Mathlib.Algebra.Field.GeomSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "geom_sum₂_Ico", "kind": "theorem", "module": "Mathlib.Algebra.Field.GeomSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Semifield.toIsField", "kind": "theorem", "module": "Mathlib.Algebra.Field.IsField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Field.toIsField", "kind": "theorem", "module": "Mathlib.Algebra.Field.IsField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsField.nontrivial", "kind": "theorem", "module": "Mathlib.Algebra.Field.IsField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsField.isDomain", "kind": "theorem", "module": "Mathlib.Algebra.Field.IsField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsDomain", "kind": "instance", "module": "Mathlib.Algebra.Field.IsField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_isField_of_subsingleton", "kind": "theorem", "module": "Mathlib.Algebra.Field.IsField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsField.toSemifield", "kind": "definition", "module": "Mathlib.Algebra.Field.IsField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsField.toField", "kind": "definition", "module": "Mathlib.Algebra.Field.IsField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniq_inv_of_isField", "kind": "theorem", "module": "Mathlib.Algebra.Field.IsField", "is_tactic_proof": true, "tactics": ["intro", "apply", "exact", "intro", "calc", "y"], "tactic_count": 6}
{"name": "Field.ofMinimalAxioms", "kind": "abbrev", "module": "Mathlib.Algebra.Field.MinimalAxioms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGroup.div_modEq_div", "kind": "theorem", "module": "Mathlib.Algebra.Field.ModEq", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AddCommGroup.mul_modEq_mul_right", "kind": "theorem", "module": "Mathlib.Algebra.Field.ModEq", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AddCommGroup.mul_modEq_mul_left", "kind": "theorem", "module": "Mathlib.Algebra.Field.ModEq", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Int.cast_negOnePow", "kind": "theorem", "module": "Mathlib.Algebra.Field.NegOnePow", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rw", "simp"], "tactic_count": 4}
{"name": "MulOpposite.instNNRatCast", "kind": "instance", "module": "Mathlib.Algebra.Field.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instRatCast", "kind": "instance", "module": "Mathlib.Algebra.Field.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.op_nnratCast", "kind": "theorem", "module": "Mathlib.Algebra.Field.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.unop_nnratCast", "kind": "theorem", "module": "Mathlib.Algebra.Field.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.op_ratCast", "kind": "theorem", "module": "Mathlib.Algebra.Field.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.unop_ratCast", "kind": "theorem", "module": "Mathlib.Algebra.Field.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instDivisionSemiring", "kind": "instance", "module": "Mathlib.Algebra.Field.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instDivisionRing", "kind": "instance", "module": "Mathlib.Algebra.Field.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instSemifield", "kind": "instance", "module": "Mathlib.Algebra.Field.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instField", "kind": "instance", "module": "Mathlib.Algebra.Field.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddOpposite.instDivisionSemiring", "kind": "instance", "module": "Mathlib.Algebra.Field.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddOpposite.instDivisionRing", "kind": "instance", "module": "Mathlib.Algebra.Field.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddOpposite.instSemifield", "kind": "instance", "module": "Mathlib.Algebra.Field.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddOpposite.instField", "kind": "instance", "module": "Mathlib.Algebra.Field.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Periodic.const_smul₀", "kind": "theorem", "module": "Mathlib.Algebra.Field.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Periodic.const_mul", "kind": "theorem", "module": "Mathlib.Algebra.Field.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Periodic.const_inv_smul₀", "kind": "theorem", "module": "Mathlib.Algebra.Field.Periodic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Function.Periodic.const_inv_mul", "kind": "theorem", "module": "Mathlib.Algebra.Field.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Periodic.mul_const", "kind": "theorem", "module": "Mathlib.Algebra.Field.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Periodic.mul_const'", "kind": "theorem", "module": "Mathlib.Algebra.Field.Periodic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Function.Periodic.mul_const_inv", "kind": "theorem", "module": "Mathlib.Algebra.Field.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Periodic.div_const", "kind": "theorem", "module": "Mathlib.Algebra.Field.Periodic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Function.Periodic.exists_mem_Ico₀", "kind": "theorem", "module": "Mathlib.Algebra.Field.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Periodic.exists_mem_Ico", "kind": "theorem", "module": "Mathlib.Algebra.Field.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Periodic.exists_mem_Ioc", "kind": "theorem", "module": "Mathlib.Algebra.Field.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Periodic.image_Ioc", "kind": "theorem", "module": "Mathlib.Algebra.Field.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Periodic.image_Icc", "kind": "theorem", "module": "Mathlib.Algebra.Field.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Periodic.image_uIcc", "kind": "theorem", "module": "Mathlib.Algebra.Field.Periodic", "is_tactic_proof": true, "tactics": ["cases", "inl", "rw", "inr"], "tactic_count": 4}
{"name": "Function.Antiperiodic.add_nat_mul_eq", "kind": "theorem", "module": "Mathlib.Algebra.Field.Periodic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Function.Antiperiodic.sub_nat_mul_eq", "kind": "theorem", "module": "Mathlib.Algebra.Field.Periodic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Function.Antiperiodic.nat_mul_sub_eq", "kind": "theorem", "module": "Mathlib.Algebra.Field.Periodic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Function.Antiperiodic.const_smul₀", "kind": "theorem", "module": "Mathlib.Algebra.Field.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Antiperiodic.const_mul", "kind": "theorem", "module": "Mathlib.Algebra.Field.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Antiperiodic.const_inv_smul₀", "kind": "theorem", "module": "Mathlib.Algebra.Field.Periodic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Function.Antiperiodic.const_inv_mul", "kind": "theorem", "module": "Mathlib.Algebra.Field.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Antiperiodic.mul_const", "kind": "theorem", "module": "Mathlib.Algebra.Field.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Antiperiodic.mul_const'", "kind": "theorem", "module": "Mathlib.Algebra.Field.Periodic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Function.Antiperiodic.mul_const_inv", "kind": "theorem", "module": "Mathlib.Algebra.Field.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Antiperiodic.div_inv", "kind": "theorem", "module": "Mathlib.Algebra.Field.Periodic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Int.fract_periodic", "kind": "theorem", "module": "Mathlib.Algebra.Field.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Odd.neg_zpow", "kind": "theorem", "module": "Mathlib.Algebra.Field.Power", "is_tactic_proof": true, "tactics": ["have", "obtain", "simp_rw"], "tactic_count": 3}
{"name": "Odd.neg_one_zpow", "kind": "theorem", "module": "Mathlib.Algebra.Field.Power", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Rat.instField", "kind": "instance", "module": "Mathlib.Algebra.Field.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.instDivisionRing", "kind": "instance", "module": "Mathlib.Algebra.Field.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.inv_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Field.Rat", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Rat.div_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Field.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.instInv", "kind": "instance", "module": "Mathlib.Algebra.Field.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.instDiv", "kind": "instance", "module": "Mathlib.Algebra.Field.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.instZPow", "kind": "instance", "module": "Mathlib.Algebra.Field.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.coe_inv", "kind": "theorem", "module": "Mathlib.Algebra.Field.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.coe_div", "kind": "theorem", "module": "Mathlib.Algebra.Field.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.coe_zpow", "kind": "theorem", "module": "Mathlib.Algebra.Field.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.inv_def", "kind": "theorem", "module": "Mathlib.Algebra.Field.Rat", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "NNRat.div_def", "kind": "theorem", "module": "Mathlib.Algebra.Field.Rat", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "NNRat.num_inv_of_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Field.Rat", "is_tactic_proof": false, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "NNRat.den_inv_of_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Field.Rat", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "NNRat.num_div_den", "kind": "theorem", "module": "Mathlib.Algebra.Field.Rat", "is_tactic_proof": true, "tactics": ["ext1", "rw", "exact"], "tactic_count": 3}
{"name": "NNRat.instSemifield", "kind": "instance", "module": "Mathlib.Algebra.Field.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Shrink.instNNRatCast", "kind": "instance", "module": "Mathlib.Algebra.Field.Shrink", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Shrink.instRatCast", "kind": "instance", "module": "Mathlib.Algebra.Field.Shrink", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Shrink.instDivisionRing", "kind": "instance", "module": "Mathlib.Algebra.Field.Shrink", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Shrink.instField", "kind": "instance", "module": "Mathlib.Algebra.Field.Shrink", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.list_prod_mem", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.list_sum_mem", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.multiset_sum_mem", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.sum_mem", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.instTop", "kind": "instance", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.instInhabited", "kind": "instance", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.mem_top", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.coe_top", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.topEquiv", "kind": "definition", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.comap", "kind": "definition", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.coe_comap", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.mem_comap", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.comap_comap", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.map", "kind": "definition", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.coe_map", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.mem_map", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": true, "tactics": ["unfold", "simp"], "tactic_count": 2}
{"name": "Subfield.map_map", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.map_le_iff_le_comap", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.gc_map_comap", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.fieldRange", "kind": "definition", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.coe_fieldRange", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.mem_fieldRange", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.fieldRange_eq_map", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "RingHom.map_fieldRange", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "RingHom.mem_fieldRange_self", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.fieldRange_eq_top_iff", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.fintypeFieldRange", "kind": "instance", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.instMin", "kind": "instance", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.coe_inf", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.mem_inf", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.instInfSet", "kind": "instance", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.coe_sInf", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.mem_sInf", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.coe_iInf", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Subfield.mem_iInf", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Subfield.sInf_toSubring", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Subfield.isGLB_sInf", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": true, "tactics": ["have", "refine", "convert", "exact"], "tactic_count": 4}
{"name": "Subfield.instCompleteLattice", "kind": "instance", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.closure", "kind": "definition", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.mem_closure", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.subset_closure", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.mem_closure_of_mem", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.subring_closure_le", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.notMem_of_notMem_closure", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.closure_le", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.closure_mono", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.closure_eq_of_le", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.closure_induction", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.gi", "kind": "definition", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.closure_eq", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.closure_empty", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.closure_univ", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.closure_union", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.closure_iUnion", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.closure_sUnion", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.map_sup", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.map_iSup", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.map_inf", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.map_iInf", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": true, "tactics": ["apply", "simpa"], "tactic_count": 2}
{"name": "Subfield.comap_inf", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.comap_iInf", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.map_bot", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.comap_top", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.mem_iSup_of_directed", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": ["let", "inv_mem", "have", "have", "le_antisymm", "exact"], "tactic_count": 6}
{"name": "Subfield.coe_iSup_of_directed", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.mem_sSup_of_directedOn", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": true, "tactics": ["haveI", "simp"], "tactic_count": 2}
{"name": "Subfield.coe_sSup_of_directedOn", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.rangeRestrictField", "kind": "definition", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.coe_rangeRestrictField", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.rangeRestrictField_bijective", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.rangeRestrictFieldEquiv", "kind": "definition", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.rangeRestrictFieldEquiv_apply_symm_apply", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RingHom.eqLocusField", "kind": "definition", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.mem_eqLocusField", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.eqOn_field_closure", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.eq_of_eqOn_subfield_top", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.eq_of_eqOn_of_field_closure_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.field_closure_preimage_le", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.map_field_closure", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.inclusion", "kind": "definition", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.fieldRange_subtype", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.subfieldCongr", "kind": "definition", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.closure_preimage_le", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.multiset_prod_mem", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.prod_mem", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.toAlgebra", "kind": "instance", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Field.Subfield.Basic.0.Subfield.commClosure", "kind": "definition", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Field.Subfield.Basic.0.Subfield.commClosure_eq_closure", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.mem_closure_iff", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subfield.map_comap_eq", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.map_comap_eq_self", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Subfield.map_comap_eq_self_of_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.comap_map", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.instSMulSubtypeMem", "kind": "instance", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.smul_def", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.smulCommClass_left", "kind": "instance", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.smulCommClass_right", "kind": "instance", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.instIsScalarTowerSubtypeMem", "kind": "instance", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.instFaithfulSMulSubtypeMem", "kind": "instance", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.instMulActionSubtypeMem", "kind": "instance", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.instDistribMulActionSubtypeMem", "kind": "instance", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.instMulDistribMulActionSubtypeMem", "kind": "instance", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.instSMulWithZeroSubtypeMem", "kind": "instance", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.instMulActionWithZeroSubtypeMem", "kind": "instance", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.instModuleSubtypeMem", "kind": "instance", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.instMulSemiringActionSubtypeMem", "kind": "instance", "module": "Mathlib.Algebra.Field.Subfield.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubfieldClass.toSubgroupClass", "kind": "instance", "module": "Mathlib.Algebra.Field.Subfield.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubfieldClass.nnratCast_mem", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "SubfieldClass.ratCast_mem", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "SubfieldClass.instNNRatCast", "kind": "instance", "module": "Mathlib.Algebra.Field.Subfield.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubfieldClass.instRatCast", "kind": "instance", "module": "Mathlib.Algebra.Field.Subfield.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubfieldClass.coe_nnratCast", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubfieldClass.coe_ratCast", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubfieldClass.nnqsmul_mem", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "SubfieldClass.qsmul_mem", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "SubfieldClass.ofScientific_mem", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubfieldClass.instSMulNNRat", "kind": "instance", "module": "Mathlib.Algebra.Field.Subfield.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubfieldClass.instSMulRat", "kind": "instance", "module": "Mathlib.Algebra.Field.Subfield.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubfieldClass.coe_nnqsmul", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubfieldClass.coe_qsmul", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubfieldClass.toDivisionRing", "kind": "instance", "module": "Mathlib.Algebra.Field.Subfield.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubfieldClass.toField", "kind": "instance", "module": "Mathlib.Algebra.Field.Subfield.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.toAddSubgroup", "kind": "definition", "module": "Mathlib.Algebra.Field.Subfield.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.instSetLike", "kind": "instance", "module": "Mathlib.Algebra.Field.Subfield.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.instPartialOrder", "kind": "instance", "module": "Mathlib.Algebra.Field.Subfield.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.instSubfieldClass", "kind": "instance", "module": "Mathlib.Algebra.Field.Subfield.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.mem_carrier", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.mem_mk", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.coe_set_mk", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.mk_le_mk", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.ext", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.copy", "kind": "definition", "module": "Mathlib.Algebra.Field.Subfield.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.coe_copy", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.copy_eq", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.coe_toSubring", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.mem_toSubring", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.toSubfield", "kind": "definition", "module": "Mathlib.Algebra.Field.Subfield.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.one_mem", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.zero_mem", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.mul_mem", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.add_mem", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.neg_mem", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.sub_mem", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.inv_mem", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.div_mem", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.pow_mem", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.zsmul_mem", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.intCast_mem", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.zpow_mem", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.instRingSubtypeMem", "kind": "instance", "module": "Mathlib.Algebra.Field.Subfield.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.instDivSubtypeMem", "kind": "instance", "module": "Mathlib.Algebra.Field.Subfield.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.instInvSubtypeMem", "kind": "instance", "module": "Mathlib.Algebra.Field.Subfield.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.instPowSubtypeMemInt", "kind": "instance", "module": "Mathlib.Algebra.Field.Subfield.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.toDivisionRing", "kind": "instance", "module": "Mathlib.Algebra.Field.Subfield.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.toField", "kind": "instance", "module": "Mathlib.Algebra.Field.Subfield.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.coe_add", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.coe_sub", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.coe_neg", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.coe_mul", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.coe_div", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.coe_inv", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.coe_zero", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.coe_one", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.subtype", "kind": "definition", "module": "Mathlib.Algebra.Field.Subfield.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.subtype_apply", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.subtype_injective", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.coe_subtype", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.toSubring_subtype_eq_subtype", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.mem_toSubmonoid", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.coe_toSubmonoid", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.mem_toAddSubgroup", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.coe_toAddSubgroup", "kind": "theorem", "module": "Mathlib.Algebra.Field.Subfield.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.nnratCast", "kind": "abbrev", "module": "Mathlib.Algebra.Field.TransferInstance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.ratCast", "kind": "abbrev", "module": "Mathlib.Algebra.Field.TransferInstance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.divisionRing", "kind": "abbrev", "module": "Mathlib.Algebra.Field.TransferInstance", "is_tactic_proof": true, "tactics": ["let", "let", "let", "let", "let", "let", "let", "let", "let", "let", "apply"], "tactic_count": 11}
{"name": "Equiv.field", "kind": "abbrev", "module": "Mathlib.Algebra.Field.TransferInstance", "is_tactic_proof": true, "tactics": ["let", "let", "let", "let", "let", "let", "let", "let", "let", "let", "let", "apply"], "tactic_count": 12}
{"name": "ULift.instNNRatCast", "kind": "instance", "module": "Mathlib.Algebra.Field.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.instRatCast", "kind": "instance", "module": "Mathlib.Algebra.Field.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.up_nnratCast", "kind": "theorem", "module": "Mathlib.Algebra.Field.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.down_nnratCast", "kind": "theorem", "module": "Mathlib.Algebra.Field.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.up_ratCast", "kind": "theorem", "module": "Mathlib.Algebra.Field.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.down_ratCast", "kind": "theorem", "module": "Mathlib.Algebra.Field.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.divisionSemiring", "kind": "instance", "module": "Mathlib.Algebra.Field.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.semifield", "kind": "instance", "module": "Mathlib.Algebra.Field.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.divisionRing", "kind": "instance", "module": "Mathlib.Algebra.Field.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.field", "kind": "instance", "module": "Mathlib.Algebra.Field.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Field.ZMod.0.ZMod.mul_inv_cancel_aux", "kind": "theorem", "module": "Mathlib.Algebra.Field.ZMod", "is_tactic_proof": true, "tactics": ["obtain", "apply", "apply", "rwa"], "tactic_count": 4}
{"name": "ZMod.instField", "kind": "instance", "module": "Mathlib.Algebra.Field.ZMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.instIsDomain", "kind": "instance", "module": "Mathlib.Algebra.Field.ZMod", "is_tactic_proof": true, "tactics": ["constructor"], "tactic_count": 1}
{"name": "MonoidHom.surjective_of_surjective_of_surjective_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.FiveLemma", "is_tactic_proof": true, "tactics": ["intro", "obtain", "obtain", "obtain", "obtain", "use", "simp"], "tactic_count": 7}
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{"name": "MonoidHom.injective_of_surjective_of_injective_of_right_exact", "kind": "theorem", "module": "Mathlib.Algebra.FiveLemma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.bijective_of_surjective_of_bijective_of_bijective_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.FiveLemma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.bijective_of_bijective_of_injective_of_left_exact", "kind": "theorem", "module": "Mathlib.Algebra.FiveLemma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.bijective_of_surjective_of_bijective_of_right_exact", "kind": "theorem", "module": "Mathlib.Algebra.FiveLemma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.surjective_of_surjective_of_surjective_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.FiveLemma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LinearMap.injective_of_surjective_of_injective_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.FiveLemma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.injective_of_surjective_of_injective_of_right_exact", "kind": "theorem", "module": "Mathlib.Algebra.FiveLemma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.bijective_of_surjective_of_bijective_of_bijective_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.FiveLemma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.bijective_of_bijective_of_injective_of_left_exact", "kind": "theorem", "module": "Mathlib.Algebra.FiveLemma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "instDecidableEqFreeAddMagma", "kind": "instance", "module": "Mathlib.Algebra.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "FreeMonoid.map_comp", "kind": "theorem", "module": "Mathlib.Algebra.FreeMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeMonoid.map_id", "kind": "theorem", "module": "Mathlib.Algebra.FreeMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeMonoid.map_symm_apply_map_eq", "kind": "theorem", "module": "Mathlib.Algebra.FreeMonoid.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FreeMonoid.map_apply_map_symm_eq", "kind": "theorem", "module": "Mathlib.Algebra.FreeMonoid.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FreeMonoid.uniqueUnits", "kind": "instance", "module": "Mathlib.Algebra.FreeMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeMonoid.map_surjective", "kind": "theorem", "module": "Mathlib.Algebra.FreeMonoid.Basic", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rcases", "induction", "one", "have", "simp", "mul_of", "simp", "use", "have", "simp", "rw", "exact", "intro", "induction", "one", "mul_of", "specialize", "rcases", "rcases", "use", "rfl"], "tactic_count": 23}
{"name": "FreeMonoid.reverse", "kind": "definition", "module": "Mathlib.Algebra.FreeMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeMonoid.reverse_of", "kind": "theorem", "module": "Mathlib.Algebra.FreeMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeMonoid.reverse_mul", "kind": "theorem", "module": "Mathlib.Algebra.FreeMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeMonoid.reverse_reverse", "kind": "theorem", "module": "Mathlib.Algebra.FreeMonoid.Basic", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "FreeMonoid.length_reverse", "kind": "theorem", "module": "Mathlib.Algebra.FreeMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeMonoid.freeMonoidCongr", "kind": "definition", "module": "Mathlib.Algebra.FreeMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeMonoid.freeMonoidCongr_of", "kind": "theorem", "module": "Mathlib.Algebra.FreeMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeMonoid.freeMonoidCongr_symm_of", "kind": "theorem", "module": "Mathlib.Algebra.FreeMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeMonoid.countP'", "kind": "definition", "module": "Mathlib.Algebra.FreeMonoid.Count", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeMonoid.countP'_one", "kind": "theorem", "module": "Mathlib.Algebra.FreeMonoid.Count", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeMonoid.countP'_mul", "kind": "theorem", "module": "Mathlib.Algebra.FreeMonoid.Count", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "FreeMonoid.countP", "kind": "definition", "module": "Mathlib.Algebra.FreeMonoid.Count", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeMonoid.countP_apply", "kind": "theorem", "module": "Mathlib.Algebra.FreeMonoid.Count", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeMonoid.countP_of", "kind": "theorem", "module": "Mathlib.Algebra.FreeMonoid.Count", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "FreeMonoid.count", "kind": "definition", "module": "Mathlib.Algebra.FreeMonoid.Count", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeMonoid.count_apply", "kind": "theorem", "module": "Mathlib.Algebra.FreeMonoid.Count", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeMonoid.count_of", "kind": "theorem", "module": "Mathlib.Algebra.FreeMonoid.Count", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FreeAddMonoid.countP", "kind": "definition", "module": "Mathlib.Algebra.FreeMonoid.Count", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeAddMonoid.countP_apply", "kind": "theorem", "module": "Mathlib.Algebra.FreeMonoid.Count", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeAddMonoid.countP_of", "kind": "theorem", "module": "Mathlib.Algebra.FreeMonoid.Count", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "FreeAddMonoid.count", "kind": "definition", "module": "Mathlib.Algebra.FreeMonoid.Count", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeAddMonoid.count_of", "kind": "theorem", "module": "Mathlib.Algebra.FreeMonoid.Count", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "simp"], "tactic_count": 3}
{"name": "FreeAddMonoid.count_apply", "kind": "theorem", "module": "Mathlib.Algebra.FreeMonoid.Count", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeMonoid.symbols", "kind": "definition", "module": "Mathlib.Algebra.FreeMonoid.Symbols", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeMonoid.symbols_one", "kind": "theorem", "module": "Mathlib.Algebra.FreeMonoid.Symbols", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeMonoid.symbols_of", "kind": "theorem", "module": "Mathlib.Algebra.FreeMonoid.Symbols", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeMonoid.symbols_mul", "kind": "theorem", "module": "Mathlib.Algebra.FreeMonoid.Symbols", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeMonoid.mem_symbols", "kind": "theorem", "module": "Mathlib.Algebra.FreeMonoid.Symbols", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeMonoid.instTwoUniqueProds", "kind": "instance", "module": "Mathlib.Algebra.FreeMonoid.UniqueProds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeAddMonoid.instTwoUniqueSums", "kind": "instance", "module": "Mathlib.Algebra.FreeMonoid.UniqueProds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeNonUnitalNonAssocAlgebra", "kind": "abbrev", "module": "Mathlib.Algebra.FreeNonUnitalNonAssocAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeNonUnitalNonAssocAlgebra.of", "kind": "definition", "module": "Mathlib.Algebra.FreeNonUnitalNonAssocAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeNonUnitalNonAssocAlgebra.lift", "kind": "definition", "module": "Mathlib.Algebra.FreeNonUnitalNonAssocAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeNonUnitalNonAssocAlgebra.lift_symm_apply", "kind": "theorem", "module": "Mathlib.Algebra.FreeNonUnitalNonAssocAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeNonUnitalNonAssocAlgebra.of_comp_lift", "kind": "theorem", "module": "Mathlib.Algebra.FreeNonUnitalNonAssocAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeNonUnitalNonAssocAlgebra.lift_unique", "kind": "theorem", "module": "Mathlib.Algebra.FreeNonUnitalNonAssocAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeNonUnitalNonAssocAlgebra.lift_of_apply", "kind": "theorem", "module": "Mathlib.Algebra.FreeNonUnitalNonAssocAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeNonUnitalNonAssocAlgebra.lift_comp_of", "kind": "theorem", "module": "Mathlib.Algebra.FreeNonUnitalNonAssocAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeNonUnitalNonAssocAlgebra.hom_ext", "kind": "theorem", "module": "Mathlib.Algebra.FreeNonUnitalNonAssocAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "normUnit_one", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "normalize", "kind": "definition", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "associated_normalize", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "normalize_associated", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "associated_normalize_iff", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "normalize_associated_iff", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associates.mk_normalize", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "normalize_apply", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "normalize_zero", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "normalize_one", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "normalize_coe_units", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "normalize_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "normalize_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "normUnit_mul_normUnit", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": true, "tactics": ["nontriviality", "obtain", "rw", "rw"], "tactic_count": 4}
{"name": "normalize_idem", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "normalize_eq_normalize", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": true, "tactics": ["nontriviality", "rcases", "refine", "suffices", "simpa", "calc", "a"], "tactic_count": 7}
{"name": "normalize_eq_normalize_iff", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "normalize_eq_normalize_iff_associated", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "dvd_antisymm_of_normalize_eq", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associated.eq_of_normalized", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dvd_normalize_iff", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "normalize_dvd_iff", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associates.out", "kind": "definition", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associates.out_mk", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associates.out_one", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associates.out_mul", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associates.dvd_out_iff", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associates.out_dvd_iff", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associates.out_top", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associates.normalize_out", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associates.mk_out", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associates.out_injective", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associates.out_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associates.out_zero", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "instNonemptyNormalizationMonoid", "kind": "instance", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instNonemptyGCDMonoid", "kind": "instance", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instNonemptyNormalizedGCDMonoid", "kind": "instance", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instNonemptyNormalizationMonoidOfNormalizedGCDMonoid", "kind": "instance", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instNonemptyGCDMonoidOfNormalizedGCDMonoid", "kind": "instance", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "gcd_isUnit_iff_isRelPrime", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "normalize_gcd", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "gcd_mul_lcm", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dvd_gcd_iff", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "gcd_comm", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "gcd_comm'", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "gcd_assoc", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "gcd_assoc'", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCommutativeGcd", "kind": "instance", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instAssociativeGcd", "kind": "instance", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "gcd_eq_normalize", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "gcd_zero_left", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "gcd_zero_left'", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "gcd_zero_right", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "gcd_zero_right'", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "gcd_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "gcd_ne_zero_of_left", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": true, "tactics": ["simp_all"], "tactic_count": 1}
{"name": "gcd_ne_zero_of_right", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": true, "tactics": ["simp_all"], "tactic_count": 1}
{"name": "gcd_one_left", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isUnit_gcd_one_left", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "gcd_one_left'", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "gcd_one_right", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isUnit_gcd_one_right", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "gcd_one_right'", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "gcd_dvd_gcd", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associated.gcd", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "gcd_same", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "gcd_mul_left", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "gcd_mul_left'", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": true, "tactics": ["obtain", "simp", "obtain", "apply", "rw", "gcongr", "exact", "dvd_gcd", "exact"], "tactic_count": 9}
{"name": "gcd_mul_right", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "gcd_mul_right'", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "gcd_eq_left_iff", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "gcd_eq_right_iff", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "gcd_dvd_gcd_mul_left", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": true, "tactics": ["grw"], "tactic_count": 1}
{"name": "gcd_dvd_gcd_mul_right", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": true, "tactics": ["grw"], "tactic_count": 1}
{"name": "gcd_dvd_gcd_mul_left_right", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": true, "tactics": ["grw"], "tactic_count": 1}
{"name": "gcd_dvd_gcd_mul_right_right", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": true, "tactics": ["grw"], "tactic_count": 1}
{"name": "Associated.gcd_eq_left", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associated.gcd_eq_right", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "dvd_gcd_mul_iff_dvd_mul", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "lcm_comm", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "instCommutativeLcm", "kind": "instance", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instAssociativeLcm", "kind": "instance", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "NormalizationMonoid.ofUniqueUnits", "kind": "instance", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniqueNormalizationMonoidOfUniqueUnits", "kind": "instance", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "subsingleton_gcdMonoid_of_unique_units", "kind": "instance", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "normUnit_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "normalizedGCDMonoidOfExistsLCM", "kind": "definition", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGroupWithZero.instNormalizedGCDMonoid", "kind": "instance", "module": "Mathlib.Algebra.GCDMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Finset.gcd_eq_gcd_filter_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Finset", "is_tactic_proof": true, "tactics": ["classical", "trans", "rw", "rw", "refine", "exact", "refine", "simp", "intro", "rw", "split_ifs", "simp"], "tactic_count": 12}
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{"name": "Finset.extract_gcd'", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.extract_gcd", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Finset", "is_tactic_proof": true, "tactics": ["classical", "by_cases", "refine", "rw", "choose", "refine", "simp", "rw"], "tactic_count": 8}
{"name": "Finset.gcd_div_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Finset", "is_tactic_proof": true, "tactics": ["obtain", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "Finset.gcd_div_id_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.gcd_eq_of_dvd_sub", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Finset", "is_tactic_proof": true, "tactics": ["classical", "revert", "refine", "simp", "intro", "rw", "gcd_assoc,", "exact"], "tactic_count": 8}
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{"name": "Finset.associated_lcm_prod", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.FinsetLemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "IsLocalization.surj_of_gcd_domain", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.IntegrallyClosed", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "use", "rw", "convert", "grind"], "tactic_count": 6}
{"name": "GCDMonoid.toIsIntegrallyClosed", "kind": "instance", "module": "Mathlib.Algebra.GCDMonoid.IntegrallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.lcm", "kind": "definition", "module": "Mathlib.Algebra.GCDMonoid.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.lcm_zero", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.lcm_cons", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.lcm_singleton", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.lcm_add", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.lcm_dvd", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.dvd_lcm", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.lcm_mono", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.normalize_lcm", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.lcm_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Multiset", "is_tactic_proof": true, "tactics": ["induction", "empty", "cons"], "tactic_count": 3}
{"name": "Multiset.lcm_ne_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.lcm_dedup", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.lcm_ndunion", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Multiset", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
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{"name": "Multiset.lcm_ndinsert", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Multiset", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Multiset.gcd", "kind": "definition", "module": "Mathlib.Algebra.GCDMonoid.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.gcd_zero", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.gcd_cons", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Multiset.dvd_gcd", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.gcd_dvd", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Multiset.normalize_gcd", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Multiset.gcd_dedup", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.gcd_ndunion", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Multiset", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
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{"name": "Multiset.extract_gcd'", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "lcm_eq_nat_lcm", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Nat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instNormalizedGCDMonoidNat", "kind": "instance", "module": "Mathlib.Algebra.GCDMonoid.Nat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Int.normalize_of_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.GCDMonoid.Nat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "List.dProd_nil", "kind": "theorem", "module": "Mathlib.Algebra.GradedMonoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.dProd_cons", "kind": "theorem", "module": "Mathlib.Algebra.GradedMonoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GradedMonoid.mk_list_dProd", "kind": "theorem", "module": "Mathlib.Algebra.GradedMonoid", "is_tactic_proof": true, "tactics": ["head"], "tactic_count": 1}
{"name": "GradedMonoid.list_prod_map_eq_dProd", "kind": "theorem", "module": "Mathlib.Algebra.GradedMonoid", "is_tactic_proof": true, "tactics": ["rw", "simp_rw"], "tactic_count": 2}
{"name": "GradedMonoid.list_prod_ofFn_eq_dProd", "kind": "theorem", "module": "Mathlib.Algebra.GradedMonoid", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "One.gOne", "kind": "instance", "module": "Mathlib.Algebra.GradedMonoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mul.gMul", "kind": "instance", "module": "Mathlib.Algebra.GradedMonoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monoid.gMonoid", "kind": "instance", "module": "Mathlib.Algebra.GradedMonoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommMonoid.gCommMonoid", "kind": "instance", "module": "Mathlib.Algebra.GradedMonoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.dProd_monoid", "kind": "theorem", "module": "Mathlib.Algebra.GradedMonoid", "is_tactic_proof": true, "tactics": ["rw", "rfl", "head", "rw", "rfl"], "tactic_count": 5}
{"name": "SetLike.one_mem_graded", "kind": "theorem", "module": "Mathlib.Algebra.GradedMonoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.gOne", "kind": "instance", "module": "Mathlib.Algebra.GradedMonoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.coe_gOne", "kind": "theorem", "module": "Mathlib.Algebra.GradedMonoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.mul_mem_graded", "kind": "theorem", "module": "Mathlib.Algebra.GradedMonoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.gMul", "kind": "instance", "module": "Mathlib.Algebra.GradedMonoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.coe_gMul", "kind": "theorem", "module": "Mathlib.Algebra.GradedMonoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.GradeZero.submonoid", "kind": "definition", "module": "Mathlib.Algebra.GradedMonoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.GradeZero.instMonoid", "kind": "instance", "module": "Mathlib.Algebra.GradedMonoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.GradeZero.instCommMonoid", "kind": "instance", "module": "Mathlib.Algebra.GradedMonoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.GradeZero.coe_one", "kind": "theorem", "module": "Mathlib.Algebra.GradedMonoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.GradeZero.coe_mul", "kind": "theorem", "module": "Mathlib.Algebra.GradedMonoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.GradeZero.coe_pow", "kind": "theorem", "module": "Mathlib.Algebra.GradedMonoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.pow_mem_graded", "kind": "theorem", "module": "Mathlib.Algebra.GradedMonoid", "is_tactic_proof": true, "tactics": ["rw", "exact", "n", "rw", "exact"], "tactic_count": 5}
{"name": "SetLike.list_prod_map_mem_graded", "kind": "theorem", "module": "Mathlib.Algebra.GradedMonoid", "is_tactic_proof": true, "tactics": ["rw", "exact", "head", "rw", "exact", "mul_mem_graded"], "tactic_count": 6}
{"name": "SetLike.list_prod_ofFn_mem_graded", "kind": "theorem", "module": "Mathlib.Algebra.GradedMonoid", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SetLike.gMonoid", "kind": "instance", "module": "Mathlib.Algebra.GradedMonoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.coe_gnpow", "kind": "theorem", "module": "Mathlib.Algebra.GradedMonoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.gCommMonoid", "kind": "instance", "module": "Mathlib.Algebra.GradedMonoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.coe_list_dProd", "kind": "theorem", "module": "Mathlib.Algebra.GradedMonoid", "is_tactic_proof": true, "tactics": ["head"], "tactic_count": 1}
{"name": "SetLike.list_dProd_eq", "kind": "theorem", "module": "Mathlib.Algebra.GradedMonoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.IsHomogeneousElem", "kind": "definition", "module": "Mathlib.Algebra.GradedMonoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.isHomogeneousElem_coe", "kind": "theorem", "module": "Mathlib.Algebra.GradedMonoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.isHomogeneousElem_one", "kind": "theorem", "module": "Mathlib.Algebra.GradedMonoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.IsHomogeneousElem.mul", "kind": "theorem", "module": "Mathlib.Algebra.GradedMonoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.homogeneousSubmonoid", "kind": "definition", "module": "Mathlib.Algebra.GradedMonoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.prod_mem_graded", "kind": "theorem", "module": "Mathlib.Algebra.GradedMonoid", "is_tactic_proof": true, "tactics": ["classical", "induction", "simp", "rw", "apply", "grind"], "tactic_count": 6}
{"name": "SetLike.prod_pow_mem_graded", "kind": "theorem", "module": "Mathlib.Algebra.GradedMonoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GradedMonoid.GMul.toGSMul", "kind": "instance", "module": "Mathlib.Algebra.GradedMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GradedMonoid.GSMul.toSMul", "kind": "instance", "module": "Mathlib.Algebra.GradedMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GradedMonoid.mk_smul_mk", "kind": "theorem", "module": "Mathlib.Algebra.GradedMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GradedMonoid.GMonoid.toGMulAction", "kind": "instance", "module": "Mathlib.Algebra.GradedMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GradedMonoid.GMulAction.toMulAction", "kind": "instance", "module": "Mathlib.Algebra.GradedMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.toGSMul", "kind": "instance", "module": "Mathlib.Algebra.GradedMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.coe_GSMul", "kind": "theorem", "module": "Mathlib.Algebra.GradedMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.GradedMul.toGradedSMul", "kind": "instance", "module": "Mathlib.Algebra.GradedMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.IsHomogeneousElem.graded_smul", "kind": "theorem", "module": "Mathlib.Algebra.GradedMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.bijective₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.injective₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.surjective₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DistribMulAction.toAddEquiv", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DistribMulAction.toAddAut", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smulMonoidWithZeroHom", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddAut.applyDistribMulAction", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUnit.smul_sub_iff_sub_inv_smul", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "smul_zpow₀'", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Subgroup.centerUnitsEquivUnitsCenter", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.Action.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjAct.instGroupWithZero", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Action.ConjAct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjAct.ofConjAct_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.ConjAct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjAct.toConjAct_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.ConjAct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjAct.mulAction₀", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Action.ConjAct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjAct.smulCommClass₀", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Action.ConjAct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjAct.smulCommClass₀'", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Action.ConjAct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smul_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smul_ite_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Defs", "is_tactic_proof": true, "tactics": ["split_ifs"], "tactic_count": 1}
{"name": "smul_eq_zero_of_right", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "right_ne_zero_of_smul", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.smulZeroClass", "kind": "abbrev", "module": "Mathlib.Algebra.GroupWithZero.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroHom.smulZeroClass", "kind": "abbrev", "module": "Mathlib.Algebra.GroupWithZero.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.smulZeroClassLeft", "kind": "abbrev", "module": "Mathlib.Algebra.GroupWithZero.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SMulZeroClass.compFun", "kind": "abbrev", "module": "Mathlib.Algebra.GroupWithZero.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SMulZeroClass.toZeroHom", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulZeroClass.toSMulWithZero", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulZeroClass.toOppositeSMulWithZero", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zero_smul", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smul_eq_zero_of_left", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "left_ne_zero_of_smul", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.smulWithZero", "kind": "abbrev", "module": "Mathlib.Algebra.GroupWithZero.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.smulWithZero", "kind": "abbrev", "module": "Mathlib.Algebra.GroupWithZero.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SMulWithZero.compHom", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoid.natSMulWithZero", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddGroup.intSMulWithZero", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulActionWithZero.toSMulWithZero", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZero.toMulActionWithZero", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZero.toOppositeMulActionWithZero", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulActionWithZero.subsingleton", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulActionWithZero.nontrivial", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ite_zero_smul", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "boole_smul", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Pi.single_apply_smul", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Function.Injective.mulActionWithZero", "kind": "abbrev", "module": "Mathlib.Algebra.GroupWithZero.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.mulActionWithZero", "kind": "abbrev", "module": "Mathlib.Algebra.GroupWithZero.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulActionWithZero.compHom", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smul_inv₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Defs", "is_tactic_proof": true, "tactics": ["obtain", "simp", "obtain", "simp", "refine", "rw"], "tactic_count": 6}
{"name": "smul_add", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.distribSMul", "kind": "abbrev", "module": "Mathlib.Algebra.GroupWithZero.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.distribSMul", "kind": "abbrev", "module": "Mathlib.Algebra.GroupWithZero.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.distribSMulLeft", "kind": "abbrev", "module": "Mathlib.Algebra.GroupWithZero.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DistribSMul.compFun", "kind": "abbrev", "module": "Mathlib.Algebra.GroupWithZero.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DistribSMul.toAddMonoidHom", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoid.nat_smulCommClass", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoid.nat_smulCommClass'", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DistribMulAction.toDistribSMul", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_example", "kind": "example", "module": "Mathlib.Algebra.GroupWithZero.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.distribMulAction", "kind": "abbrev", "module": "Mathlib.Algebra.GroupWithZero.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.distribMulAction", "kind": "abbrev", "module": "Mathlib.Algebra.GroupWithZero.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DistribMulAction.toAddMonoidHom", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DistribMulAction.toAddMonoidEnd", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddGroup.int_smulCommClass", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddGroup.int_smulCommClass'", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smul_neg", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smul_sub", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "smul_eq_zero_iff_eq", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smul_ne_zero_iff_ne", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instSMulZeroClass", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smul_inv₀'", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Defs", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "apply", "rw"], "tactic_count": 4}
{"name": "smul_div₀'", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Function.Surjective.distribMulActionLeft", "kind": "abbrev", "module": "Mathlib.Algebra.GroupWithZero.Action.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DistribMulAction.compHom", "kind": "abbrev", "module": "Mathlib.Algebra.GroupWithZero.Action.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulDistribMulAction.compHom", "kind": "abbrev", "module": "Mathlib.Algebra.GroupWithZero.Action.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoid.End.applyDistribMulAction", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Action.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoid.End.smul_def", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoid.End.applyFaithfulSMul", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Action.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DistribMulAction.toAddEquiv₀", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.Action.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRightCancelMulZero.faithfulSMul", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Action.Faithful", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroHom.instSMulZeroClass", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Action.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroHom.coe_smul", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroHom.smul_apply", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroHom.smul_comp", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroHom.instSMulCommClass", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Action.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroHom.instIsScalarTower", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Action.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroHom.instIsCentralScalar", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Action.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroHom.instSMulWithZero", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Action.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroHom.instMulActionWithZero", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Action.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.instSMulZeroClassOfDistribSMul", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Action.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.coe_smul", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.smul_apply", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.smul_comp", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.instSMulCommClass", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Action.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.instIsScalarTower", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Action.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.instIsCentralScalar", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Action.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.instDistribSMul", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Action.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.instDistribMulAction", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Action.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instSMulZeroClass", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Action.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instSMulWithZero", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Action.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instMulActionWithZero", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Action.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instDistribMulAction", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Action.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instMulDistribMulAction", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Action.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLeftCancelMulZero.toFaithfulSMul_opposite", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Action.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.smulZeroClass", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Action.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.smulZeroClass'", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Action.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.distribSMul", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Action.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.distribSMul'", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Action.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.distribMulAction", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Action.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.distribMulAction'", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Action.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.smulWithZero", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Action.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.smulWithZero'", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Action.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.mulActionWithZero", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Action.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.mulActionWithZero'", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Action.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.single_smul", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.single_smul'", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.single_smul₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.mulDistribMulAction", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Action.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.mulDistribMulAction'", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Action.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.smulZeroClass", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.Action.Pointwise.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.distribSMul", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.Action.Pointwise.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.distribMulAction", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.Action.Pointwise.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mulDistribMulAction", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.Action.Pointwise.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.instNoZeroDivisors", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Action.Pointwise.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.smul_zero_subset", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Pointwise.Finset", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.Nonempty.smul_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Pointwise.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.zero_mem_smul_finset", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Pointwise.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.zero_smul_subset", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Pointwise.Finset", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.Nonempty.zero_smul", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Pointwise.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.zero_smul_finset", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Pointwise.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.zero_smul_finset_subset", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Pointwise.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.smul_mem_smul_finset_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Pointwise.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inv_smul_mem_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Pointwise.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_inv_smul_finset_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Pointwise.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.smul_finset_subset_smul_finset_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Pointwise.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.smul_finset_subset_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Pointwise.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.subset_smul_finset_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Pointwise.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.smul_finset_inter₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Pointwise.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.smul_finset_sdiff₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Pointwise.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.smul_finset_symmDiff₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Pointwise.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.smul_finset_univ₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Pointwise.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.smul_univ₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Pointwise.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.smul_univ₀'", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Pointwise.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inv_smul_finset_distrib₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Pointwise.Finset", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "simp", "ext", "simp"], "tactic_count": 5}
{"name": "Finset.inv_op_smul_finset_distrib₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Pointwise.Finset", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "simp", "ext", "simp", "mul_inv_rev,"], "tactic_count": 6}
{"name": "Finset.smul_finset_neg", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Pointwise.Finset", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.smul_neg", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Pointwise.Finset", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.smul_set_pi₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Pointwise.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smul_set_pi₀'", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Pointwise.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smulZeroClassSet", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.Action.Pointwise.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smul_zero_subset", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Pointwise.Set", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.Nonempty.smul_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Pointwise.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.zero_mem_smul_set", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Pointwise.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.zero_smul_subset", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Pointwise.Set", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.Nonempty.zero_smul", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Pointwise.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.zero_smul_set", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Pointwise.Set", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.zero_smul_set_subset", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Pointwise.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subsingleton_zero_smul_set", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Pointwise.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.distribSMulSet", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.Action.Pointwise.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.distribMulActionSet", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.Action.Pointwise.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mulDistribMulActionSet", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.Action.Pointwise.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instNoZeroDivisors", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Action.Pointwise.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smul_mem_smul_set_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Pointwise.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_smul_set_iff_inv_smul_mem₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Pointwise.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_inv_smul_set_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Pointwise.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.preimage_smul₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Pointwise.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.preimage_smul_inv₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Pointwise.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smul_set_subset_smul_set_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Pointwise.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smul_set_subset_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Pointwise.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subset_smul_set_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Pointwise.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smul_set_inter₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Pointwise.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smul_set_sdiff₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Pointwise.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smul_set_symmDiff₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Pointwise.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smul_set_univ₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Pointwise.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smul_univ₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Pointwise.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smul_univ₀'", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Pointwise.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inv_smul_set_distrib₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Pointwise.Set", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "ext"], "tactic_count": 3}
{"name": "Set.inv_op_smul_set_distrib₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Pointwise.Set", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "ext"], "tactic_count": 3}
{"name": "Prod.smul_zero_mk", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Prod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Prod.smul_mk_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Prod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Prod.smulZeroClass", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Action.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.distribSMul", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Action.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.distribMulAction", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Action.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.mulDistribMulAction", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Action.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.smulWithZero", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Action.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.mulActionWithZero", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Action.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DistribMulAction.prodOfSMulCommClass", "kind": "abbrev", "module": "Mathlib.Algebra.GroupWithZero.Action.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DistribMulAction.prodEquiv", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.Action.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.smulZeroClass", "kind": "abbrev", "module": "Mathlib.Algebra.GroupWithZero.Action.TransferInstance", "is_tactic_proof": true, "tactics": ["letI", "exact"], "tactic_count": 2}
{"name": "Equiv.smulWithZero", "kind": "abbrev", "module": "Mathlib.Algebra.GroupWithZero.Action.TransferInstance", "is_tactic_proof": true, "tactics": ["letI", "exact"], "tactic_count": 2}
{"name": "Equiv.mulActionWithZero", "kind": "abbrev", "module": "Mathlib.Algebra.GroupWithZero.Action.TransferInstance", "is_tactic_proof": true, "tactics": ["letI", "exact"], "tactic_count": 2}
{"name": "Equiv.distribSMul", "kind": "abbrev", "module": "Mathlib.Algebra.GroupWithZero.Action.TransferInstance", "is_tactic_proof": true, "tactics": ["letI", "exact"], "tactic_count": 2}
{"name": "Equiv.distribMulAction", "kind": "abbrev", "module": "Mathlib.Algebra.GroupWithZero.Action.TransferInstance", "is_tactic_proof": true, "tactics": ["letI", "exact"], "tactic_count": 2}
{"name": "Units.smul_mk0", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_smul_smul₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smul_inv_smul₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_smul_eq_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_inv_smul_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Units.instSMulZeroClass", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Action.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.instDistribSMulUnits", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Action.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "IsUnit.smul_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Action.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "_private.Mathlib.Algebra.GroupWithZero.Associated.0._aux_Mathlib_Algebra_GroupWithZero_Associated___unexpand_Associated_1", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associated.refl", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associated.rfl", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associated.instRefl", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associated.symm", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associated.instSymm", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associated.comm", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associated.trans", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associated.instIsTrans", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associated.setoid", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associated.map", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Associated.of_eq", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unit_associated_one", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "associated_one_iff_isUnit", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "associated_zero_iff_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "associated_one_of_mul_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "associated_one_of_associated_mul_one", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "associated_mul_unit_left", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "associated_unit_mul_left", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "associated_mul_unit_right", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "associated_unit_mul_right", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "associated_mul_isUnit_left_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "associated_isUnit_mul_left_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "associated_mul_isUnit_right_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "associated_isUnit_mul_right_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "associated_mul_unit_left_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "associated_unit_mul_left_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "associated_mul_unit_right_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "associated_unit_mul_right_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associated.mul_left", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "Associated.mul_right", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "Associated.mul_mul", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Associated.dvd", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associated.dvd'", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associated.dvd_dvd", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "associated_of_dvd_dvd", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "by_cases", "simp_all", "have", "intro", "rw", "apply", "have", "have", "have", "have", "exact"], "tactic_count": 13}
{"name": "dvd_dvd_iff_associated", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDecidableRelAssociatedOfIsLeftCancelMulZeroOfDvd", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associated.dvd_iff_dvd_left", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associated.dvd_iff_dvd_right", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associated.eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": true, "tactics": ["obtain", "rw"], "tactic_count": 2}
{"name": "Associated.ne_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associated.prime", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "prime_mul_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": true, "tactics": ["refine", "rcases", "exact", "exact", "rintro", "exact", "exact"], "tactic_count": 7}
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{"name": "Irreducible.associated_of_dvd", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Irreducible.dvd_irreducible_iff_associated", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prime.associated_of_dvd", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prime.dvd_prime_iff_associated", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Irreducible.isUnit_iff_not_associated_of_dvd", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Associated.of_mul_left", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associated.of_mul_right", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Associated.of_pow_associated_of_prime", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": ["have", "rw", "apply", "rw", "exact"], "tactic_count": 5}
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{"name": "Irreducible.isRelPrime_iff_not_dvd", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": true, "tactics": ["refine", "contrapose", "suffices", "exact"], "tactic_count": 4}
{"name": "Irreducible.dvd_or_isRelPrime", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "associated_iff_eq", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "associated_eq_eq", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "prime_dvd_prime_iff_eq", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "Associates", "kind": "abbrev", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Associates.instInhabited", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associates.mk_eq_mk_iff_associated", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Associates.quot_mk_eq_mk", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associates.quot_out", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "Associates.mk_surjective", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associates.instOne", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associates.mk_one", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associates.one_eq_mk_one", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associates.mk_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Associates.instBot", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associates.bot_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associates.exists_rep", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associates.instUniqueOfSubsingleton", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associates.mk_injective", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associates.instMul", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associates.mk_mul_mk", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associates.instCommMonoid", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associates.instPreorder", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associates.mkMonoidHom", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associates.mkMonoidHom_apply", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associates.associated_map_mk", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associates.mk_pow", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "Associates.dvd_eq_le", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associates.uniqueUnits", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associates.coe_unit_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Associates.isUnit_iff_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associates.isUnit_iff_eq_bot", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Associates.isUnit_mk", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associates.mul_mono", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associates.one_le", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associates.le_mul_right", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associates.le_mul_left", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Associates.instOrderBot", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associates.mk_dvd_mk", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": true, "tactics": ["simp", "constructor", "rintro", "exact", "rintro", "use"], "tactic_count": 6}
{"name": "Associates.dvd_of_mk_le_mk", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associates.mk_le_mk_of_dvd", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associates.mk_le_mk_iff_dvd", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associates.isPrimal_mk", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": true, "tactics": ["simp_rw", "constructor", "obtain", "exact", "exact"], "tactic_count": 5}
{"name": "Associates.decompositionMonoid_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Associates.instDecompositionMonoid", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associates.mk_isRelPrime_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Associates.instZero", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associates.instTopOfZero", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associates.mk_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associates.mk_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associates.quot_out_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Associates.mk_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associates.instNontrivial", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associates.exists_non_zero_rep", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associates.instCommMonoidWithZero", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associates.instOrderTop", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associates.le_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associates.instBoundedOrder", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associates.instDecidableRelDvd", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associates.Prime.le_or_le", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associates.prime_mk", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Associates.irreducible_mk", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": ["simp", "apply", "constructor", "rintro", "exact", "rintro", "simpa"], "tactic_count": 7}
{"name": "Associates.mk_dvdNotUnit_mk_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": ["simp", "refine", "constructor", "rintro", "refine", "simpa", "rintro", "use"], "tactic_count": 8}
{"name": "Associates.dvdNotUnit_of_lt", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "apply", "apply", "rcases", "refine", "contrapose", "rcases", "simp"], "tactic_count": 9}
{"name": "Associates.irreducible_iff_prime_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Associates.instPartialOrder", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associates.instIsCancelMulZero", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "associates_irreducible_iff_prime", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associates.instNoZeroDivisors", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Associates.le_of_mul_le_mul_left", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associates.one_or_eq_of_le_of_prime", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "simpa"], "tactic_count": 3}
{"name": "Associates.dvdNotUnit_iff_lt", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associates.le_one_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "dvdNotUnit_of_dvdNotUnit_associated", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "refine", "rw"], "tactic_count": 4}
{"name": "isUnit_of_associated_mul", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": true, "tactics": ["obtain", "refine", "rwa"], "tactic_count": 3}
{"name": "DvdNotUnit.not_associated", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": true, "tactics": ["rintro", "obtain", "rcases", "exact"], "tactic_count": 4}
{"name": "dvd_prime_pow", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Associated", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "refine", "rw", "rcases", "rw", "rcases", "refine", "rw", "obtain", "exact"], "tactic_count": 12}
{"name": "left_ne_zero_of_mul", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "right_ne_zero_of_mul", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ne_zero_and_ne_zero_of_mul", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_eq_zero_of_ne_zero_imp_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "zero_mul_eq_const", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_zero_eq_const", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_zero_of_mul_self_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NeZero.mul", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_zero_of_zero_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "uniqueOfZeroEqOne", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "subsingleton_iff_zero_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_of_zero_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zero_ne_one_or_forall_eq_0", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "left_ne_zero_of_mul_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "right_ne_zero_of_mul_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsNilpotent", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsNilpotent.mk", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isNilpotent_of_subsingleton", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsNilpotent.zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_isNilpotent_one", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsNilpotent.pow_succ", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsNilpotent.of_pow", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsNilpotent.pow_of_pos", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": true, "tactics": ["cases", "zero", "succ"], "tactic_count": 3}
{"name": "IsNilpotent.pow_iff_pos", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_zero_of_pow_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isReduced_of_subsingleton", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsNilpotent.eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isNilpotent_iff_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_isNilpotent_of_not_isReduced", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "zero_pow", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zero_pow_eq", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": true, "tactics": ["split_ifs", "rw", "rw"], "tactic_count": 3}
{"name": "zero_pow_eq_one₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "pow_eq_zero_of_le", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ne_zero_pow", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "zero_pow_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pow_mul_eq_zero_of_le", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "isReduced_of_noZeroDivisors", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pow_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pow_ne_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pow_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NeZero.pow", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sq_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pow_eq_zero_iff'", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "exists_right_inv_of_exists_left_inv", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": true, "tactics": ["obtain", "exact", "obtain", "obtain", "refine", "conv_lhs"], "tactic_count": 6}
{"name": "mul_right_eq_self₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_left_eq_self₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_eq_left₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mul_eq_right₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "left_eq_mul₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "right_eq_mul₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "eq_zero_of_mul_eq_self_right", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_zero_of_mul_eq_self_left", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupWithZero.mul_right_injective", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupWithZero.mul_left_injective", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_mul_cancel_right₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_mul_cancel_left₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.GroupWithZero.Basic.0.inv_eq_of_mul", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "GroupWithZero.toDivisionMonoid", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsCancelMulZero", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zero_div", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "div_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mul_self_mul_inv", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "rw"], "tactic_count": 3}
{"name": "mul_inv_mul_cancel", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "rw"], "tactic_count": 3}
{"name": "inv_mul_mul_self", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "rw"], "tactic_count": 3}
{"name": "mul_self_div_self", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "div_self_mul_self", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "div_self_mul_self'", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_div_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "inv_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "zero_eq_inv", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "div_div_self", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ne_zero_of_one_div_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_zero_of_one_div_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_left_surjective₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_right_surjective₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zero_zpow", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zero_zpow_eq", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": true, "tactics": ["split_ifs", "rw", "rw"], "tactic_count": 3}
{"name": "zero_zpow_eq_one₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "zpow_add_one₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zpow_sub_one₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zpow_add₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "pred"], "tactic_count": 4}
{"name": "zpow_add'", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "by_cases", "simp", "by_cases", "subst", "simp", "rw", "exact"], "tactic_count": 9}
{"name": "zpow_one_add₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "div_mul_eq_mul_div₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "div_sq_cancel", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Basic", "is_tactic_proof": true, "tactics": ["obtain", "simp", "rw"], "tactic_count": 3}
{"name": "Set.zero_mem_center", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.zero_mem_centralizer", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Center", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.center_units_subset", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Center", "is_tactic_proof": true, "tactics": ["simp_rw", "intro", "obtain", "rw", "exact"], "tactic_count": 5}
{"name": "Set.center_units_eq", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inv_mem_centralizer₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Center", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact", "rintro", "rw"], "tactic_count": 5}
{"name": "Set.div_mem_centralizer₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Center", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Ring.mul_inverse_rev'", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Commute", "is_tactic_proof": true, "tactics": ["by_cases", "obtain", "rw", "obtain", "rw", "rw"], "tactic_count": 6}
{"name": "Ring.mul_inverse_rev", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Commute", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ring.inverse_pow", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Commute", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ring.inverse_pow_mul_eq_iff_eq_mul", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Commute", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Commute.ringInverse_ringInverse", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Commute", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.zero_right", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Commute", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.zero_left", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Commute", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.inv_left_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Commute", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.inv_left₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Commute", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.inv_right_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Commute", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.inv_right₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Commute", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.div_right", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Commute", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.div_left", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Commute", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "pow_inv_comm₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Commute", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupWithZero.isConj_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Conj", "is_tactic_proof": true, "tactics": ["rw", "congr", "exact"], "tactic_count": 3}
{"name": "GroupWithZero.conj_pow₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Conj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_left_cancel₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_right_injective₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_right_inj'", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_eq_mul_left_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Defs", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "mul_right_cancel₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_left_injective₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_left_inj'", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_eq_mul_right_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Defs", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "isCancelMulZero_iff_forall_isRegular", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Defs", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "pow_mul_apply_eq_pow_mul", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Defs", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "IsLeftCancelMulZero.to_noZeroDivisors", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRightCancelMulZero.to_noZeroDivisors", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLeftCancelMulZero.to_isRightCancelMulZero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRightCancelMulZero.to_isLeftCancelMulZero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLeftCancelMulZero.to_isCancelMulZero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRightCancelMulZero.to_isCancelMulZero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_div_cancel_right₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_div_cancel_left₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "inv_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_inv_cancel₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupWithZero.toMulDivCancelClass", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_zero_or_one_of_sq_eq_self", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_inv_cancel_right₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_inv_cancel_left₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_eq_zero_of_left", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_eq_zero_of_right", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "noZeroDivisors_iff_right_eq_zero_of_mul", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Defs", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "noZeroDivisors_iff_left_eq_zero_of_mul", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Defs", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "noZeroDivisors_iff_eq_zero_of_mul", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "mul_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zero_eq_mul", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mul_ne_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_eq_zero_comm", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_ne_zero_comm", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_self_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "zero_eq_mul_self", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "mul_self_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zero_ne_mul_self", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_eq_zero_iff_left", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "mul_eq_zero_iff_right", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "mul_ne_zero_iff_left", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "mul_ne_zero_iff_right", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "eq_zero_of_zero_dvd", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Divisibility", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zero_dvd_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Divisibility", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dvd_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Divisibility", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_dvd_mul_iff_left", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Divisibility", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_dvd_mul_iff_right", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Divisibility", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DvdNotUnit", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.Divisibility", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dvdNotUnit_of_dvd_of_not_dvd", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Divisibility", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "exact", "rcases", "refine", "rintro", "simp"], "tactic_count": 7}
{"name": "isRelPrime_zero_left", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Divisibility", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isRelPrime_zero_right", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Divisibility", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_isRelPrime_zero_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Divisibility", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRelPrime.ne_zero_or_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Divisibility", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isRelPrime_of_no_nonunits_factors", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Divisibility", "is_tactic_proof": true, "tactics": ["refine", "rintro"], "tactic_count": 2}
{"name": "dvd_and_not_dvd_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Divisibility", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ne_zero_of_dvd_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Divisibility", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "isPrimal_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Divisibility", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimal.mul", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Divisibility", "is_tactic_proof": true, "tactics": ["obtain", "intro", "obtain", "rw", "obtain", "exact"], "tactic_count": 6}
{"name": "dvd_antisymm", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Divisibility", "is_tactic_proof": true, "tactics": ["rintro", "rw", "obtain"], "tactic_count": 3}
{"name": "dvd_antisymm'", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Divisibility", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_of_forall_dvd", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Divisibility", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_of_forall_dvd'", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Divisibility", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pow_dvd_pow_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Divisibility", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "intro", "apply", "have", "rw", "exact", "rwa", "apply", "apply"], "tactic_count": 11}
{"name": "GroupWithZero.dvd_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Divisibility", "is_tactic_proof": true, "tactics": ["refine", "simp", "refine", "obtain", "simp", "rw"], "tactic_count": 6}
{"name": "MulEquivClass.toZeroHomClass", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquivClass.toMonoidWithZeroHomClass", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.toMonoidWithZeroHom", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.toMonoidWithZeroHom_apply", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.toMonoidWithZeroHom_injective", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.toMonoidWithZeroHom_surjective", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.toMonoidWithZeroHom_bijective", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.toMonoidWithZeroHom_inj", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Equiv", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NeZero.of_map", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NeZero.of_injective", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "term_→*₀_", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Algebra_GroupWithZero_Hom___macroRules_term_→*₀__1", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Algebra_GroupWithZero_Hom___unexpand_MonoidWithZeroHom_1", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHomClass.toMonoidWithZeroHom", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCoeTCMonoidWithZeroHomOfMonoidWithZeroHomClass", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.funLike", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.monoidWithZeroHomClass", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.instSubsingleton", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.coe_coe", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.coeToMonoidHom", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.coeToZeroHom", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.coe_mk", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.toZeroHom_coe", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.toMonoidHom_coe", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.ext", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.mk_coe", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.copy", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.coe_copy", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.copy_eq", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.map_one", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.map_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.map_mul", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.map_ite_zero_one", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Hom", "is_tactic_proof": true, "tactics": ["split_ifs"], "tactic_count": 1}
{"name": "MonoidWithZeroHom.map_ite_one_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Hom", "is_tactic_proof": true, "tactics": ["split_ifs"], "tactic_count": 1}
{"name": "MonoidWithZeroHom.id", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.comp", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.coe_comp", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.comp_apply", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.comp_assoc", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.cancel_right", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.cancel_left", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.toMonoidHom_injective", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.toZeroHom_injective", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.comp_id", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.id_comp", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.instInhabited", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.instMul", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.one", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.one_apply_def", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.one_apply_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.one_apply_of_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.one_apply_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Hom", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "MonoidWithZeroHom.one_apply_eq_one_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Hom", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "powMonoidWithZeroHom", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "coe_powMonoidWithZeroHom", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "powMonoidWithZeroHom_apply", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIdempotentElem.zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Idempotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIdempotentElem.instZeroSubtype", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Idempotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIdempotentElem.coe_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Idempotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIdempotentElem.iff_eq_zero_or_one", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Idempotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.indicator_mul", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Indicator", "is_tactic_proof": true, "tactics": ["funext", "simp", "split_ifs", "rfl", "rw"], "tactic_count": 5}
{"name": "Set.indicator_mul_left", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Indicator", "is_tactic_proof": true, "tactics": ["simp", "split_ifs", "rfl", "rw"], "tactic_count": 4}
{"name": "Set.indicator_mul_right", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Indicator", "is_tactic_proof": true, "tactics": ["simp", "split_ifs", "rfl", "rw"], "tactic_count": 4}
{"name": "Set.indicator_mul_const", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Indicator", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.indicator_const_mul", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Indicator", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.inter_indicator_mul", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Indicator", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "split_ifs"], "tactic_count": 3}
{"name": "Set.inter_indicator_one", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.indicator_prod_one", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Indicator", "is_tactic_proof": true, "tactics": ["simp_rw", "split_ifs"], "tactic_count": 2}
{"name": "Set.indicator_eq_zero_iff_notMem", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Indicator", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Set.indicator_eq_one_iff_mem", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Indicator", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Set.indicator_one_inj", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Indicator", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Function.support_one", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.mulSupport_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.support_mul_subset_left", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.support_mul_subset_right", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.support_mul", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.support_mul'", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.support_pow", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Indicator", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Function.support_pow'", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.support_inv", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.support_inv'", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.support_div", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Indicator", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Function.support_div'", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.mulSupport_one_add", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.mulSupport_one_add'", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.mulSupport_add_one", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.mulSupport_add_one'", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.mulSupport_one_sub'", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Indicator", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Function.mulSupport_one_sub", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.mulZeroClass", "kind": "abbrev", "module": "Mathlib.Algebra.GroupWithZero.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.mulZeroClass", "kind": "abbrev", "module": "Mathlib.Algebra.GroupWithZero.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.noZeroDivisors", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.isLeftCancelMulZero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.isRightCancelMulZero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.isCancelMulZero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.mulZeroOneClass", "kind": "abbrev", "module": "Mathlib.Algebra.GroupWithZero.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.mulZeroOneClass", "kind": "abbrev", "module": "Mathlib.Algebra.GroupWithZero.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.semigroupWithZero", "kind": "abbrev", "module": "Mathlib.Algebra.GroupWithZero.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.semigroupWithZero", "kind": "abbrev", "module": "Mathlib.Algebra.GroupWithZero.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.monoidWithZero", "kind": "abbrev", "module": "Mathlib.Algebra.GroupWithZero.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.monoidWithZero", "kind": "abbrev", "module": "Mathlib.Algebra.GroupWithZero.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.commMonoidWithZero", "kind": "abbrev", "module": "Mathlib.Algebra.GroupWithZero.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.commMonoidWithZero", "kind": "abbrev", "module": "Mathlib.Algebra.GroupWithZero.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.groupWithZero", "kind": "abbrev", "module": "Mathlib.Algebra.GroupWithZero.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.groupWithZero", "kind": "abbrev", "module": "Mathlib.Algebra.GroupWithZero.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.commGroupWithZero", "kind": "abbrev", "module": "Mathlib.Algebra.GroupWithZero.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.commGroupWithZero", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Invertible.ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Invertible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Invertible.toNeZero", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Invertible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ring.inverse_invertible", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Invertible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "invertibleOfNonzero", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.Invertible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "invOf_eq_inv", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Invertible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_mul_cancel_of_invertible", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Invertible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_inv_cancel_of_invertible", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Invertible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "invertibleInv", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Invertible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "div_mul_cancel_of_invertible", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Invertible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_div_cancel_of_invertible", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Invertible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "div_self_of_invertible", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Invertible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "invertibleDiv", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.Invertible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "invOf_div", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Invertible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.instMulZeroClass", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Nat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.instSemigroupWithZero", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Nat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.instMonoidWithZero", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Nat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.instCommMonoidWithZero", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Nat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.instIsCancelMulZero", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Nat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.instMulDivCancelClass", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Nat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.instMulZeroOneClass", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Nat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NeZero.one", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.NeZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "domain_nontrivial", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.NeZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.NeZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_mul_cancel₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.NeZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Irreducible.coe_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nonZeroDivisorsLeft", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_nonZeroDivisorsLeft_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "notMem_nonZeroDivisorsLeft_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "nonZeroDivisorsRight", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_nonZeroDivisorsRight_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "notMem_nonZeroDivisorsRight_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "nonZeroDivisorsLeft_eq_right", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "coe_nonZeroDivisorsLeft_eq", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": true, "tactics": ["ext", "simp", "refine", "contrapose", "exact"], "tactic_count": 5}
{"name": "coe_nonZeroDivisorsRight_eq", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": true, "tactics": ["ext", "simp", "refine", "contrapose", "exact"], "tactic_count": 5}
{"name": "nonZeroDivisors", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nonZeroDivisors.term_⁰", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nonZeroDivisors._aux_Mathlib_Algebra_GroupWithZero_NonZeroDivisors___macroRules_nonZeroDivisors_term_⁰_1", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nonZeroDivisors._aux_Mathlib_Algebra_GroupWithZero_NonZeroDivisors___unexpand_nonZeroDivisors_1", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nonZeroSMulDivisors", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nonZeroSMulDivisors.term_⁰[_]", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nonZeroSMulDivisors._aux_Mathlib_Algebra_GroupWithZero_NonZeroDivisors___macroRules_nonZeroSMulDivisors_term_⁰[_]_1", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nonZeroSMulDivisors._aux_Mathlib_Algebra_GroupWithZero_NonZeroDivisors___unexpand_nonZeroSMulDivisors_1", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nonZeroDivisorsLeft_eq_nonZeroSMulDivisors", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_nonZeroDivisors_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_nonZeroDivisors_iff'", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "notMem_nonZeroDivisors_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "mul_left_mem_nonZeroDivisorsLeft_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_right_mem_nonZeroDivisorsRight_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_right_mem_nonZeroDivisors_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_right_coe_nonZeroDivisors_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUnit.mem_nonZeroDivisors", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isUnit_le_nonZeroDivisors", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_mem_nonZeroDivisorsLeft_of_mem_nonZeroDivisorsLeft", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_mem_nonZeroDivisorsRight_of_mem_nonZeroDivisorsRight", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_mem_nonZeroDivisors_of_mem_nonZeroDivisors", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zero_notMem_nonZeroDivisorsLeft", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zero_notMem_nonZeroDivisorsRight", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zero_notMem_nonZeroDivisors", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nonZeroDivisors.ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nonZeroDivisors.coe_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instLeftCancelMonoidSubtypeMemSubmonoidNonZeroDivisorsOfIsLeftCancelMulZero", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instRightCancelMonoidSubtypeMemSubmonoidNonZeroDivisorsOfIsRightCancelMulZero", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_zero_of_ne_zero_of_mul_right_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_zero_of_ne_zero_of_mul_left_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_nonZeroDivisors_of_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_nonZeroDivisors_iff_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_nonZeroDivisors_of_noZeroDivisors", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "powers_le_nonZeroDivisors_of_noZeroDivisors", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLeftRegular.mem_nonZeroDivisorsLeft", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRightRegular.mem_nonZeroDivisorsRight", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRegular.mem_nonZeroDivisors", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "noZeroDivisors_iff_forall_mem_nonZeroDivisorsLeft", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "noZeroDivisors_iff_forall_mem_nonZeroDivisorsRight", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "noZeroDivisors_iff_forall_mem_nonZeroDivisors", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSMulRegular.mem_nonZeroSMulDivisors", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isSMulRegular_iff_mem_nonZeroSMulDivisors", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "map_ne_zero_of_mem_nonZeroDivisors", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "map_mem_nonZeroDivisors", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquivClass.map_nonZeroDivisors", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": true, "tactics": ["let", "change", "ext", "simp_rw", "h.symm.toEquiv_eq_coe,"], "tactic_count": 5}
{"name": "map_le_nonZeroDivisors_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": true, "tactics": ["cases", "simp", "refine", "rintro", "exact"], "tactic_count": 5}
{"name": "nonZeroDivisors_le_comap_nonZeroDivisors_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_nonZeroDivisors_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "comap_nonZeroDivisors_le_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nonZeroDivisorsLeft_eq_nonZeroDivisors", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "nonZeroDivisorsRight_eq_nonZeroDivisors", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mem_nonZeroDivisors_iff_right", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "notMem_nonZeroDivisors_iff_right", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "mul_left_mem_nonZeroDivisors_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mul_left_coe_nonZeroDivisors_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_mem_nonZeroDivisors", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nonZeroDivisors_dvd_iff_dvd_coe", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "prod_mem_nonZeroDivisors_of_mem_nonZeroDivisors", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nonZeroDivisorsEquivUnits", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isUnit_of_mem_nonZeroDivisors", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_nonZeroSMulDivisors_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitsNonZeroDivisorsEquiv", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nonZeroDivisors.associated_coe", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mk_mem_nonZeroDivisors_associates", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": true, "tactics": ["rw", "contrapose", "constructor", "rintro", "refine", "rwa", "rwa", "refine", "rw"], "tactic_count": 9}
{"name": "associatesNonZeroDivisorsEquiv", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "associatesNonZeroDivisorsEquiv_mk_mk", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "associatesNonZeroDivisorsEquiv_symm_mk_mk", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instMulZeroClass", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instMulZeroOneClass", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instSemigroupWithZero", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instMonoidWithZero", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instGroupWithZero", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instNoZeroDivisors", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instIsRightCancelMulZeroOfIsLeftCancelMulZero", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instIsLeftCancelMulZeroOfIsRightCancelMulZero", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instIsCancelMulZero", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.isLeftCancelMulZero_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.isRightCancelMulZero_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.isCancelMulZero_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddOpposite.instMulZeroClass", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddOpposite.instMulZeroOneClass", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddOpposite.instSemigroupWithZero", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddOpposite.instMonoidWithZero", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddOpposite.instNoZeroDivisors", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddOpposite.instGroupWithZero", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.mulZeroClass", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulHom.single", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.single_mul", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.single_mul_left_apply", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.single_mul_right_apply", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.single_mul_left", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.single_mul_right", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.mulZeroOneClass", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.monoidWithZero", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.commMonoidWithZero", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.semigroupWithZero", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_le_card_mul_left₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Pointwise.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_le_card_mul_right₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Pointwise.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_le_card_mul_self₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Pointwise.Finset", "is_tactic_proof": true, "tactics": ["obtain", "rw", "obtain", "obtain", "simp", "exact"], "tactic_count": 6}
{"name": "Finset.mul_zero_subset", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Pointwise.Finset", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.zero_mul_subset", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Pointwise.Finset", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.Nonempty.mul_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Pointwise.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Nonempty.zero_mul", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Pointwise.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.div_zero_subset", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Pointwise.Finset", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.zero_div_subset", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Pointwise.Finset", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.Nonempty.div_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Pointwise.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Nonempty.zero_div", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Pointwise.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inv_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Pointwise.Finset", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Set.mul_zero_subset", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.zero_mul_subset", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.Nonempty.mul_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nonempty.zero_mul", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.div_zero_subset", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.zero_div_subset", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.Nonempty.div_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nonempty.zero_div", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inv_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Cardinal.mk_smul_set₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Pointwise.Set.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.natCard_smul_set₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Pointwise.Set.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instMulZeroClass", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instSemigroupWithZero", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instMulZeroOneClass", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instMonoidWithZero", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instCommMonoidWithZero", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.toMonoidWithZeroHom_withZeroUnitsEquiv", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mulMonoidWithZeroHom", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "divMonoidWithZeroHom", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.one_apply_apply_eq", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.ProdHom", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rw", "rwa"], "tactic_count": 4}
{"name": "MonoidWithZeroHom.one_comp", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.ProdHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.inl", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.ProdHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.inr", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.ProdHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.fst", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.ProdHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.snd", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.ProdHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.inl_apply_unit", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.ProdHom", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MonoidWithZeroHom.inr_apply_unit", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.ProdHom", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MonoidWithZeroHom.fst_apply_coe", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.ProdHom", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "MonoidWithZeroHom.snd_apply_coe", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.ProdHom", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "MonoidWithZeroHom.fst_inl", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.ProdHom", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "MonoidWithZeroHom.fst_comp_inl", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.ProdHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.snd_comp_inl", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.ProdHom", "is_tactic_proof": true, "tactics": ["ext", "obtain"], "tactic_count": 2}
{"name": "MonoidWithZeroHom.snd_inl_apply_of_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.ProdHom", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MonoidWithZeroHom.fst_comp_inr", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.ProdHom", "is_tactic_proof": true, "tactics": ["ext", "obtain"], "tactic_count": 2}
{"name": "MonoidWithZeroHom.fst_inr_apply_of_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.ProdHom", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MonoidWithZeroHom.snd_inr", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.ProdHom", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "MonoidWithZeroHom.snd_comp_inr", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.ProdHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.inl_injective", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.ProdHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.inr_injective", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.ProdHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.fst_surjective", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.ProdHom", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "MonoidWithZeroHom.snd_surjective", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.ProdHom", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "MonoidWithZeroHom.inl_mul_inr_eq_mk_of_unit", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.ProdHom", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MonoidWithZeroHom.commute_inl_inr", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.ProdHom", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "simp"], "tactic_count": 3}
{"name": "MonoidWithZeroHom.mrange_nontrivial", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.range_nontrivial", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.valueMonoid", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.one_mem_valueMonoid", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.coe_one", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.mem_valueMonoid_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.valueMonoid_eq_closure", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.valueGroup", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.valueGroup_def", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.ValueMonoid₀", "kind": "abbrev", "module": "Mathlib.Algebra.GroupWithZero.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.ValueGroup₀", "kind": "abbrev", "module": "Mathlib.Algebra.GroupWithZero.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.mem_valueMonoid", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Range", "is_tactic_proof": true, "tactics": ["tauto"], "tactic_count": 1}
{"name": "MonoidWithZeroHom.mem_valueGroup", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Range", "is_tactic_proof": true, "tactics": ["suffices", "exact"], "tactic_count": 2}
{"name": "MonoidWithZeroHom.inv_mem_valueGroup", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.valueMonoid_eq_valueGroup", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Range", "is_tactic_proof": true, "tactics": ["rw", "apply", "simp", "intro", "use", "simp", "simp"], "tactic_count": 7}
{"name": "MonoidWithZeroHom.valueMonoid_eq_valueGroup'", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Range", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MonoidWithZeroHom.valueGroup_eq_range", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Range", "is_tactic_proof": true, "tactics": ["ext", "simp", "mem_valueMonoid_iff,", "constructor", "rintro", "simp", "rintro", "refine", "simpa"], "tactic_count": 9}
{"name": "MonoidWithZeroHom.mem_valueGroup_iff_of_comm", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Range", "is_tactic_proof": true, "tactics": ["refine", "simp", "induction", "mem", "obtain", "exact", "one", "mul", "obtain", "obtain", "refine", "simpa", "inv", "obtain", "exact", "have", "let", "have", "let", "have", "rw_mod_cast", "rw", "apply", "apply", "use", "apply", "use"], "tactic_count": 27}
{"name": "MonoidWithZeroHom.instCommGroupWithZeroValueGroup₀", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLeftRegular.subsingleton", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRightRegular.subsingleton", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRegular.subsingleton", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLeftRegular_zero_iff_subsingleton", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_isLeftRegular_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Regular", "is_tactic_proof": true, "tactics": ["rw", "push_neg", "exact"], "tactic_count": 3}
{"name": "isRightRegular_zero_iff_subsingleton", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_isRightRegular_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Regular", "is_tactic_proof": true, "tactics": ["rw", "push_neg", "exact"], "tactic_count": 3}
{"name": "isRegular_iff_subsingleton", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLeftRegular.ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Regular", "is_tactic_proof": true, "tactics": ["rintro", "rcases", "refine", "simp"], "tactic_count": 4}
{"name": "IsRightRegular.ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Regular", "is_tactic_proof": true, "tactics": ["rintro", "rcases", "refine", "simp"], "tactic_count": 4}
{"name": "IsRegular.ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_isLeftRegular_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_isRightRegular_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_isRegular_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLeftRegular.mul_left_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Regular", "is_tactic_proof": true, "tactics": ["conv_lhs", "exact"], "tactic_count": 2}
{"name": "IsRightRegular.mul_right_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Regular", "is_tactic_proof": true, "tactics": ["conv_lhs", "exact"], "tactic_count": 2}
{"name": "IsRegular.of_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isRegular_iff_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiconjBy.zero_right", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Semiconj", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SemiconjBy.zero_left", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Semiconj", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SemiconjBy.inv_symm_left_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Semiconj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiconjBy.inv_symm_left₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Semiconj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiconjBy.inv_right₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Semiconj", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "by_cases", "subst", "simp", "simp", "have", "rw", "exact"], "tactic_count": 9}
{"name": "SemiconjBy.inv_right_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Semiconj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiconjBy.div_right", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Semiconj", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SemiconjBy.zpow_right₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Semiconj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.zpow_right₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Semiconj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.zpow_left₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Semiconj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.zpow_zpow₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Semiconj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.zpow_self₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Semiconj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.self_zpow₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Semiconj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.zpow_zpow_self₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Semiconj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instSemigroupWithZeroShrink", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Shrink", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instMulZeroClassShrink", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Shrink", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instMulZeroOneClassShrink", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Shrink", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDistribMulActionShrink", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Shrink", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.smul_mem_pointwise_smul_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Subgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.mem_pointwise_smul_iff_inv_smul_mem₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Subgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.mem_inv_pointwise_smul_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Subgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.pointwise_smul_le_pointwise_smul_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Subgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.pointwise_smul_le_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Subgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.le_pointwise_smul_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Subgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroup.pointwiseMulAction", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.Subgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroup.pointwise_smul_def", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Subgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroup.coe_pointwise_smul", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Subgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroup.pointwise_smul_toAddSubmonoid", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Subgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroup.smul_mem_pointwise_smul", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Subgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroup.mem_smul_pointwise_iff_exists", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Subgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroup.pointwise_isCentralScalar", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Subgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroup.smul_mem_pointwise_smul_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Subgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroup.mem_pointwise_smul_iff_inv_smul_mem", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Subgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroup.mem_inv_pointwise_smul_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Subgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroup.pointwise_smul_le_pointwise_smul_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Subgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroup.pointwise_smul_le_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Subgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroup.le_pointwise_smul_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Subgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroup.smul_mem_pointwise_smul_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Subgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroup.mem_pointwise_smul_iff_inv_smul_mem₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Subgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroup.mem_inv_pointwise_smul_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Subgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroup.pointwise_smul_le_pointwise_smul_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Subgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroup.pointwise_smul_le_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Subgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroup.le_pointwise_smul_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Subgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulZeroMemClass.isLeftCancelMulZero", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Submonoid.CancelMulZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulZeroMemClass.isRightCancelMulZero", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Submonoid.CancelMulZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulZeroMemClass.isCancelMulZero", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Submonoid.CancelMulZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.instMulZeroOneClassSubtypeMemSubmonoidMrange", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Submonoid.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.val_mrange_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Submonoid.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.instMonoidWithZeroSubtypeMemSubmonoidMrange", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Submonoid.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.instCommMonoidWithZeroSubtypeMemSubmonoidMrange", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Submonoid.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.instGroupWithZeroSubtypeMemSubmonoidMrange", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Submonoid.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.instCommGroupWithZeroSubtypeMemSubmonoidMrange", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Submonoid.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.smul_mem_pointwise_smul_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.mem_pointwise_smul_iff_inv_smul_mem₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.mem_inv_pointwise_smul_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.pointwise_smul_le_pointwise_smul_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.pointwise_smul_le_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.le_pointwise_smul_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.pointwiseMulAction", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.coe_pointwise_smul", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.smul_mem_pointwise_smul", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.mem_smul_pointwise_iff_exists", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.smul_bot", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.smul_sup", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.smul_closure", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.pointwise_isCentralScalar", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.smul_mem_pointwise_smul_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.mem_pointwise_smul_iff_inv_smul_mem", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.mem_inv_pointwise_smul_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.pointwise_smul_le_pointwise_smul_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.pointwise_smul_le_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.le_pointwise_smul_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.smul_mem_pointwise_smul_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.mem_pointwise_smul_iff_inv_smul_mem₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.mem_inv_pointwise_smul_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.pointwise_smul_le_pointwise_smul_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.pointwise_smul_le_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.le_pointwise_smul_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.isPrimal", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.Submonoid.Primal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMulTorsionFree.mk'", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Torsion", "is_tactic_proof": true, "tactics": ["refine", "by_cases", "exact", "have", "grind"], "tactic_count": 5}
{"name": "UniqueFactorizationMonoid.instIsMulTorsionFree", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Torsion", "is_tactic_proof": true, "tactics": ["refine", "obtain", "have", "rwa", "associated_iff_normalizedFactors_eq_normalizedFactors", "replace", "rw", "pow_eq_one_iff_left", "rwa"], "tactic_count": 9}
{"name": "Equiv.semigroupWithZero", "kind": "abbrev", "module": "Mathlib.Algebra.GroupWithZero.TransferInstance", "is_tactic_proof": true, "tactics": ["let", "let", "apply"], "tactic_count": 3}
{"name": "Equiv.mulZeroClass", "kind": "abbrev", "module": "Mathlib.Algebra.GroupWithZero.TransferInstance", "is_tactic_proof": true, "tactics": ["let", "let", "apply"], "tactic_count": 3}
{"name": "Equiv.mulZeroOneClass", "kind": "abbrev", "module": "Mathlib.Algebra.GroupWithZero.TransferInstance", "is_tactic_proof": true, "tactics": ["let", "let", "let", "apply"], "tactic_count": 4}
{"name": "Equiv.monoidWithZero", "kind": "abbrev", "module": "Mathlib.Algebra.GroupWithZero.TransferInstance", "is_tactic_proof": true, "tactics": ["let", "let", "apply"], "tactic_count": 3}
{"name": "Equiv.commMonoidWithZero", "kind": "abbrev", "module": "Mathlib.Algebra.GroupWithZero.TransferInstance", "is_tactic_proof": true, "tactics": ["let", "apply"], "tactic_count": 2}
{"name": "ULift.mulZeroOneClass", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.monoidWithZero", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.commMonoidWithZero", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.groupWithZero", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.commGroupWithZero", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.mul_left_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.mul_right_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUnit.ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUnit.mul_right_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUnit.mul_left_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isUnit_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_isUnit_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ring.inverse", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ring.inverse_unit", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ring.inverse_of_isUnit", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ring.inverse_non_unit", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ring.mul_inverse_cancel", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": true, "tactics": ["rcases", "rw"], "tactic_count": 2}
{"name": "Ring.inverse_mul_cancel", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": true, "tactics": ["rcases", "rw"], "tactic_count": 2}
{"name": "Ring.mul_inverse_cancel_right", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ring.inverse_mul_cancel_right", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ring.mul_inverse_cancel_left", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ring.inverse_mul_cancel_left", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ring.inverse_mul_eq_iff_eq_mul", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ring.eq_mul_inverse_iff_mul_eq", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ring.inverse_one", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ring.inverse_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": true, "tactics": ["nontriviality", "exact"], "tactic_count": 2}
{"name": "IsUnit.ringInverse", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isUnit_ringInverse", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.mk0", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.val_mk0", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.mk0_val", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.mul_inv'", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.inv_mul'", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.mk0_inj", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.exists0", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.exists0'", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.exists_iff_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "GroupWithZero.eq_zero_or_unit", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsUnit.mk0", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isUnit_iff_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupWithZero.noZeroDivisors", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.mk0_mul", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "div_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "div_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "div_ne_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "div_self", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "div_self_eq_one₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_mul_inv_iff_mul_eq₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_inv_mul_iff_mul_eq₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_mul_eq_iff_eq_mul₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_inv_eq_iff_eq_mul₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_inv_eq_one₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_mul_eq_one₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_eq_one_iff_eq_inv₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_eq_one_iff_inv_eq₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_eq_of_eq_mul_inv₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "mul_eq_of_eq_inv_mul₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "eq_mul_of_inv_mul_eq₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_mul_of_mul_inv_eq₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "div_mul_cancel₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "mul_one_div_cancel", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_div_mul_cancel", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "div_left_inj'", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "div_eq_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_div_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "div_eq_iff_mul_eq", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_div_iff_mul_eq", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "div_eq_of_eq_mul", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_div_of_mul_eq", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "div_eq_one_iff_eq", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "div_mul_cancel_right₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_div_mul_right", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_mul_div", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "div_div_div_cancel_right₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "div_mul_div_cancel₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "div_mul_cancel_of_imp", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "mul_div_cancel_of_imp", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "divp_mk0", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pow_sub₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": true, "tactics": ["have", "have", "simpa"], "tactic_count": 3}
{"name": "pow_sub_of_lt", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact"], "tactic_count": 3}
{"name": "inv_pow_sub₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "inv_pow_sub_of_lt", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "zpow_sub₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "zpow_natCast_sub_natCast₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "zpow_natCast_sub_one₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "zpow_one_sub_natCast₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "zpow_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_zero_of_zpow_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zpow_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zpow_ne_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zpow_neg_mul_zpow_self", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ring.inverse_eq_inv", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": true, "tactics": ["obtain", "simp", "exact"], "tactic_count": 3}
{"name": "Ring.inverse_eq_inv'", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGroupWithZero.toDivisionCommMonoid", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "div_mul_cancel_left₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_div_cancel_left_of_imp", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mul_div_cancel_of_imp'", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mul_div_cancel₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_div_mul_left", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_eq_mul_of_div_eq_div", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "div_eq_div_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_inv_eq_mul_inv_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_mul_eq_inv_mul_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "div_eq_div_iff_div_eq_div'", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": true, "tactics": ["conv_lhs", "conv_rhs", "rw"], "tactic_count": 3}
{"name": "div_eq_div_of_div_eq_div", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "div_div_cancel₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "div_div_cancel_left'", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "div_helper", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "div_div_div_cancel_left'", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "div_mul_div_cancel₀'", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "groupWithZeroOfIsUnitOrEqZero", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "commGroupWithZeroOfIsUnitOrEqZero", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitsEquivNeZero", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.Units.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.mulLeft₀", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.Units.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mulLeft_bijective₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.mulRight₀", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.Units.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mulRight_bijective₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.divRight₀", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.Units.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.divLeft₀", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.Units.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLocalHom_of_exists_map_ne_one", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsLocalHomOfMonoidWithZeroHomClassOfNontrivial", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.Units.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.div_eq_div_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.mul_inv_eq_mul_inv_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.inv_mul_eq_inv_mul_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "map_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Lemmas", "is_tactic_proof": true, "tactics": ["refine", "intro", "lift", "apply", "rw"], "tactic_count": 5}
{"name": "map_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_on_inv₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Lemmas", "is_tactic_proof": true, "tactics": ["rcases", "rw", "exact"], "tactic_count": 3}
{"name": "map_inv₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Lemmas", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "apply", "rw"], "tactic_count": 4}
{"name": "map_div₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZero.inverse", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.Units.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZero.coe_inverse", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZero.inverse_apply", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "invMonoidWithZeroHom", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.Units.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "map_zpow₀", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.Units.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.one", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.coe_one", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.recZeroCoe_one", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.instMulZeroClass", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.coe_mul", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.unzero_mul", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WithZero.instNoZeroDivisors", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.instSemigroupWithZero", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.instCommSemigroup", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.instMulZeroOneClass", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.coeMonoidHom", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.monoidWithZeroHom_ext", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.lift'", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.lift'_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.lift'_coe", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.lift'_unique", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.lift'_surjective", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": true, "tactics": ["intro", "obtain", "exact"], "tactic_count": 3}
{"name": "WithZero.map'", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.map'_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.map'_coe", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.map'_id", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "WithZero.map'_map'", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "WithZero.map'_comp", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.map'_injective_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WithZero.map'_surjective_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": true, "tactics": ["simp", "refine", "obtain", "induction", "grind", "obtain", "use", "simp"], "tactic_count": 8}
{"name": "WithZero.pow", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.coe_pow", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.instMonoidWithZero", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.instCommMonoidWithZero", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.inv", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.coe_inv", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.inv_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.invOneClass", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.div", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.coe_div", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.instPowInt", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.coe_zpow", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.instDivInvMonoid", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.instDivInvOneMonoid", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.instInvolutiveInv", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.instDivisionMonoid", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.instDivisionCommMonoid", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.instGroupWithZero", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.unitsWithZeroEquiv", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.instNontrivialUnits", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.coe_unitsWithZeroEquiv_eq_units_val", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WithZero.withZeroUnitsEquiv", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.withZeroUnitsEquiv_symm_apply_coe", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MulEquiv.withZero", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.unzero", "kind": "abbrev", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.instCommGroupWithZero", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.instAddMonoidWithOne", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.term_ᵐ⁰", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero._aux_Mathlib_Algebra_GroupWithZero_WithZero___macroRules_WithZero_term_ᵐ⁰_1", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.exp", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.exp_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WithZero.exp_injective", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.exp_inj", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.expRecOn", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.expRecOn_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.expRecOn_exp", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.instCanLiftMultiplicativeExpNeOfNat", "kind": "instance", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.log", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.log_exp", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.exp_log", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": true, "tactics": ["lift"], "tactic_count": 1}
{"name": "WithZero.log_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.exp_zero", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.exp_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "WithZero.log_one", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.exp_add", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.log_mul", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": true, "tactics": ["lift"], "tactic_count": 1}
{"name": "WithZero.exp_nsmul", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.log_pow", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.expEquiv", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.logEquiv", "kind": "definition", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.logEquiv_symm", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.expEquiv_symm", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.coe_expEquiv_apply", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.logEquiv_apply", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": true, "tactics": ["obtain", "cases", "cases", "cases", "rfl"], "tactic_count": 5}
{"name": "WithZero.logEquiv_unitsMk0", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.exp_sub", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.log_div", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": true, "tactics": ["lift"], "tactic_count": 1}
{"name": "WithZero.exp_neg", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.log_inv", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.exp_zsmul", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MonoidWithZeroHom.map_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": true, "tactics": ["refine", "contrapose", "intro", "lift", "apply", "rw"], "tactic_count": 6}
{"name": "MonoidWithZeroHom.one_apply_val_unit", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.apply_one_apply_eq", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rw"], "tactic_count": 3}
{"name": "MonoidWithZeroHom.comp_one", "kind": "theorem", "module": "Mathlib.Algebra.GroupWithZero.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.toPerm", "kind": "definition", "module": "Mathlib.Algebra.Group.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.toPerm_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.bijective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.surjective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smul_left_cancel", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smul_left_cancel_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smul_eq_iff_eq_inv_smul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCancelSMul_iff_eq_one_of_smul_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "invOf_smul_smul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smul_invOf_smul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "invOf_smul_eq_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smul_eq_iff_eq_invOf_smul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "arrowAction", "kind": "definition", "module": "Mathlib.Algebra.Group.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "arrowMulDistribMulAction", "kind": "definition", "module": "Mathlib.Algebra.Group.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUnit.smul_bijective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Basic", "is_tactic_proof": true, "tactics": ["lift", "exact"], "tactic_count": 2}
{"name": "IsUnit.smul_left_cancel", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isUnit_smul_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.toFun", "kind": "definition", "module": "Mathlib.Algebra.Group.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.toFun_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.mulDistribMulAction", "kind": "abbrev", "module": "Mathlib.Algebra.Group.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.mulDistribMulAction", "kind": "abbrev", "module": "Mathlib.Algebra.Group.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulDistribMulAction.toMonoidHom", "kind": "definition", "module": "Mathlib.Algebra.Group.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smul_pow'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulDistribMulAction.toMonoidEnd", "kind": "definition", "module": "Mathlib.Algebra.Group.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smul_inv'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smul_div'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smul_zpow'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mul.toSMul", "kind": "definition", "module": "Mathlib.Algebra.Group.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mul.toSMulMulOpposite", "kind": "instance", "module": "Mathlib.Algebra.Group.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smul_eq_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "op_smul_eq_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.smul_eq_mul_unop", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LibraryNote.bundled_maps_over_different_rings", "kind": "definition", "module": "Mathlib.Algebra.Group.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SMulCommClass.symm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.smulCommClass", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.smulCommClass", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smulCommClass_self", "kind": "instance", "module": "Mathlib.Algebra.Group.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smul_assoc", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SMulCommClass.op_right", "kind": "instance", "module": "Mathlib.Algebra.Group.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SMul.comp.smulCommClass", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "smul_smul_smul_comm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "Function.Injective.mulAction", "kind": "abbrev", "module": "Mathlib.Algebra.Group.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "smul_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SMulCommClass.of_commMonoid", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsScalarTower.of_commMonoid", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isScalarTower_iff_smulCommClass_of_commMonoid", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "IsScalarTower.of_smul_one_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "IsLeftCancelSMul.left_cancel", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "instIsCancelSMul", "kind": "instance", "module": "Mathlib.Algebra.Group.Action.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AddAut.apply_faithfulSMul", "kind": "instance", "module": "Mathlib.Algebra.Group.Action.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MulAction.ofEndHom", "kind": "abbrev", "module": "Mathlib.Algebra.Group.Action.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddAction.toEndHom", "kind": "definition", "module": "Mathlib.Algebra.Group.Action.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddAction.ofEndHom", "kind": "abbrev", "module": "Mathlib.Algebra.Group.Action.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.toPermHom", "kind": "definition", "module": "Mathlib.Algebra.Group.Action.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.coe_toPermHom", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AddAction.coe_toPermHom", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "mulAutArrow", "kind": "definition", "module": "Mathlib.Algebra.Group.Action.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equidecomp.IsDecompOn", "kind": "definition", "module": "Mathlib.Algebra.Group.Action.Equidecomp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equidecomp.instCoeFunForall", "kind": "instance", "module": "Mathlib.Algebra.Group.Action.Equidecomp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Equidecomp.toPartialEquiv_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Equidecomp", "is_tactic_proof": true, "tactics": ["intro", "congr"], "tactic_count": 2}
{"name": "Equidecomp.IsDecompOn.mono", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Equidecomp", "is_tactic_proof": true, "tactics": ["intro", "rw", "exact"], "tactic_count": 3}
{"name": "Equidecomp.restr", "kind": "definition", "module": "Mathlib.Algebra.Group.Action.Equidecomp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equidecomp.toPartialEquiv_restr", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Equidecomp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equidecomp.source_restr", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Equidecomp", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "Equidecomp.refl", "kind": "definition", "module": "Mathlib.Algebra.Group.Action.Equidecomp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equidecomp.IsDecompOn.comp'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Equidecomp", "is_tactic_proof": true, "tactics": ["intro", "rcases", "rcases", "use", "rwa"], "tactic_count": 5}
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{"name": "Equidecomp.IsDecompOn.of_leftInvOn", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Equidecomp", "is_tactic_proof": true, "tactics": ["rintro", "rcases", "use", "rw"], "tactic_count": 4}
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{"name": "MulAction.compHom", "kind": "abbrev", "module": "Mathlib.Algebra.Group.Action.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Monoid.toOppositeMulAction", "kind": "instance", "module": "Mathlib.Algebra.Group.Action.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SMulCommClass.opposite_mid", "kind": "instance", "module": "Mathlib.Algebra.Group.Action.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Pi.isScalarTower'", "kind": "instance", "module": "Mathlib.Algebra.Group.Action.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Pi.smulCommClass''", "kind": "instance", "module": "Mathlib.Algebra.Group.Action.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Function.update_smul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Set.piecewise_smul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Finset.isScalarTower", "kind": "instance", "module": "Mathlib.Algebra.Group.Action.Pointwise.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.isScalarTower'", "kind": "instance", "module": "Mathlib.Algebra.Group.Action.Pointwise.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Finset.mulActionFinset", "kind": "definition", "module": "Mathlib.Algebra.Group.Action.Pointwise.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mul_singleton", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.singleton_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.smul_finset_subset_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.op_smul_finset_subset_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.biUnion_op_smul_finset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mul_subset_iff_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mul_subset_iff_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.op_smul_finset_mul_eq_mul_smul_finset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.pairwiseDisjoint_smul_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Finset", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Finset.image_smul_distrib", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.smul_mem_smul_finset_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mul_mem_smul_finset_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inv_smul_mem_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Finset", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.mem_inv_smul_finset_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Finset", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.smul_finset_subset_smul_finset_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.smul_finset_subset_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Finset", "is_tactic_proof": true, "tactics": ["simp_rw", "push_cast", "exact"], "tactic_count": 3}
{"name": "Finset.subset_smul_finset_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Finset", "is_tactic_proof": true, "tactics": ["simp_rw", "push_cast", "exact"], "tactic_count": 3}
{"name": "Finset.smul_finset_inter", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.smul_finset_sdiff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.smul_finset_symmDiff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.smul_finset_univ", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.smul_finset_eq_univ", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Finset", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.smul_univ", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_smul_finset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_dvd_card_smul_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_dvd_card_mul_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_dvd_card_mul_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inv_smul_finset_distrib", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Finset", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finset.inv_op_smul_finset_distrib", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Finset", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Fintype.piFinset_smul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.piFinset_smul_finset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.decidablePred_mem_vadd_set", "kind": "instance", "module": "Mathlib.Algebra.Group.Action.Pointwise.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smul_set_prod", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smul_set_pi", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smul_set_pi_of_isUnit", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["lift", "exact"], "tactic_count": 2}
{"name": "Set.smul_set_subset_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.op_smul_set_subset_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_op_smul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Set.iUnion_op_smul_set", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mul_subset_iff_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mul_subset_iff_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.pair_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.mul_pair", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.range_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_smul_distrib", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_op_smul_distrib", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.op_smul_set_mul_eq_mul_smul_set", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.pairwiseDisjoint_smul_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smulCommClass_set", "kind": "instance", "module": "Mathlib.Algebra.Group.Action.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smulCommClass_set'", "kind": "instance", "module": "Mathlib.Algebra.Group.Action.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smulCommClass_set''", "kind": "instance", "module": "Mathlib.Algebra.Group.Action.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smulCommClass", "kind": "instance", "module": "Mathlib.Algebra.Group.Action.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.isScalarTower", "kind": "instance", "module": "Mathlib.Algebra.Group.Action.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.isScalarTower'", "kind": "instance", "module": "Mathlib.Algebra.Group.Action.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.isScalarTower''", "kind": "instance", "module": "Mathlib.Algebra.Group.Action.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.isCentralScalar", "kind": "instance", "module": "Mathlib.Algebra.Group.Action.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mulAction", "kind": "definition", "module": "Mathlib.Algebra.Group.Action.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mulActionSet", "kind": "definition", "module": "Mathlib.Algebra.Group.Action.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smul_mem_smul_set_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_smul_set_iff_inv_smul_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_inv_smul_set_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.mem_smul_set_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.preimage_smul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.preimage_smul_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smul_set_subset_smul_set_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smul_set_subset_iff_subset_inv_smul_set", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["refine", "congr", "exact"], "tactic_count": 3}
{"name": "Set.subset_smul_set_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["refine"], "tactic_count": 1}
{"name": "Set.smul_set_inter", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smul_set_iInter", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smul_set_sdiff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smul_set_symmDiff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smul_set_univ", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smul_set_eq_univ", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.smul_univ", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smul_set_compl", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.smul_inter_nonempty_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "obtain", "exact", "rintro", "exact"], "tactic_count": 6}
{"name": "Set.smul_inter_ne_empty_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.smul_inter_nonempty_iff'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.smul_inter_ne_empty_iff'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.op_smul_inter_nonempty_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "obtain", "exact", "rintro", "have", "exact"], "tactic_count": 7}
{"name": "Set.op_smul_inter_ne_empty_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.iUnion_inv_smul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_smul_eq_setOf_exists", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.inv_smul_set_distrib", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Set.inv_op_smul_set_distrib", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Set.disjoint_smul_set", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.disjoint_smul_set_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.disjoint_smul_set_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.pairwise_disjoint_smul_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": ["simp_rw", "not_disjoint_iff_nonempty_inter]", "exact"], "tactic_count": 3}
{"name": "Set.exists_smul_inter_smul_subset_smul_inv_mul_inter_inv_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["obtain", "exact", "refine", "calc", "a"], "tactic_count": 5}
{"name": "Set.mem_invOf_smul_set", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smul_graphOn", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Set.smul_graphOn_univ", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.smul_div_smul_comm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.finite_smul_set", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Set.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.infinite_smul_set", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pointwise.Set.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.instIsPretransitiveOfSubsingleton", "kind": "instance", "module": "Mathlib.Algebra.Group.Action.Pretransitive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.exists_smul_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pretransitive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.surjective_smul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pretransitive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.Regular.isPretransitive", "kind": "instance", "module": "Mathlib.Algebra.Group.Action.Pretransitive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.Regular.isPretransitive_mulOpposite", "kind": "instance", "module": "Mathlib.Algebra.Group.Action.Pretransitive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.IsPretransitive.of_smul_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pretransitive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.IsPretransitive.of_isScalarTower", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Pretransitive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Additive.addAction_isPretransitive", "kind": "instance", "module": "Mathlib.Algebra.Group.Action.Pretransitive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiplicative.mulAction_isPretransitive", "kind": "instance", "module": "Mathlib.Algebra.Group.Action.Pretransitive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.isScalarTower", "kind": "instance", "module": "Mathlib.Algebra.Group.Action.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.smulCommClass", "kind": "instance", "module": "Mathlib.Algebra.Group.Action.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.isCentralScalar", "kind": "instance", "module": "Mathlib.Algebra.Group.Action.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.faithfulSMulLeft", "kind": "instance", "module": "Mathlib.Algebra.Group.Action.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.faithfulSMulRight", "kind": "instance", "module": "Mathlib.Algebra.Group.Action.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.smulCommClassBoth", "kind": "instance", "module": "Mathlib.Algebra.Group.Action.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.isScalarTowerBoth", "kind": "instance", "module": "Mathlib.Algebra.Group.Action.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.mulAction", "kind": "instance", "module": "Mathlib.Algebra.Group.Action.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smulMulHom", "kind": "definition", "module": "Mathlib.Algebra.Group.Action.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smulMonoidHom", "kind": "definition", "module": "Mathlib.Algebra.Group.Action.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.prodOfSMulCommClass", "kind": "abbrev", "module": "Mathlib.Algebra.Group.Action.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.prodEquiv", "kind": "definition", "module": "Mathlib.Algebra.Group.Action.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.instSMul_mathlib", "kind": "instance", "module": "Mathlib.Algebra.Group.Action.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.smul_def", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.smul_mk", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.instIsScalarTowerOfSMul", "kind": "instance", "module": "Mathlib.Algebra.Group.Action.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.instSMulCommClass", "kind": "instance", "module": "Mathlib.Algebra.Group.Action.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.instIsCentralScalar", "kind": "instance", "module": "Mathlib.Algebra.Group.Action.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.FaithfulSMul'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.instFaithfulSMulOfNonempty", "kind": "instance", "module": "Mathlib.Algebra.Group.Action.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.instMulAction", "kind": "instance", "module": "Mathlib.Algebra.Group.Action.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.instSMul", "kind": "instance", "module": "Mathlib.Algebra.Group.Action.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.smul_def", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.smul_inl", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.smul_inr", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.smul_swap", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Sum", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Sum.instIsScalarTower", "kind": "instance", "module": "Mathlib.Algebra.Group.Action.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.instSMulCommClass", "kind": "instance", "module": "Mathlib.Algebra.Group.Action.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.instIsCentralScalar", "kind": "instance", "module": "Mathlib.Algebra.Group.Action.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.FaithfulSMulLeft", "kind": "instance", "module": "Mathlib.Algebra.Group.Action.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.FaithfulSMulRight", "kind": "instance", "module": "Mathlib.Algebra.Group.Action.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.instMulAction", "kind": "instance", "module": "Mathlib.Algebra.Group.Action.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.mulAction", "kind": "abbrev", "module": "Mathlib.Algebra.Group.Action.TransferInstance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.smulCommClass", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.TransferInstance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.isScalarTower", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.TransferInstance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.isCentralScalar", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.TransferInstance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.mulDistribMulAction", "kind": "abbrev", "module": "Mathlib.Algebra.Group.Action.TransferInstance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.faithfulSMul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.TransferInstance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Additive.vadd", "kind": "instance", "module": "Mathlib.Algebra.Group.Action.TypeTags", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiplicative.smul", "kind": "instance", "module": "Mathlib.Algebra.Group.Action.TypeTags", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toMul_smul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.TypeTags", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofMul_vadd", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.TypeTags", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toAdd_vadd", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.TypeTags", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofAdd_smul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.TypeTags", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Additive.addAction", "kind": "instance", "module": "Mathlib.Algebra.Group.Action.TypeTags", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiplicative.mulAction", "kind": "instance", "module": "Mathlib.Algebra.Group.Action.TypeTags", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Additive.vaddCommClass", "kind": "instance", "module": "Mathlib.Algebra.Group.Action.TypeTags", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiplicative.smulCommClass", "kind": "instance", "module": "Mathlib.Algebra.Group.Action.TypeTags", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.instSMul", "kind": "instance", "module": "Mathlib.Algebra.Group.Action.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.smul_def", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.smul_mk_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.smul_isUnit", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUnit.inv_smul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.instFaithfulSMul", "kind": "instance", "module": "Mathlib.Algebra.Group.Action.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.instMulAction", "kind": "instance", "module": "Mathlib.Algebra.Group.Action.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.smulCommClass_left", "kind": "instance", "module": "Mathlib.Algebra.Group.Action.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.smulCommClass_right", "kind": "instance", "module": "Mathlib.Algebra.Group.Action.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.instIsScalarTower", "kind": "instance", "module": "Mathlib.Algebra.Group.Action.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.mulAction'", "kind": "instance", "module": "Mathlib.Algebra.Group.Action.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.smul_eq_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Units", "is_tactic_proof": false, "tactics": ["fail_if_success", "rfl", "ext", "rfl"], "tactic_count": 4}
{"name": "Units.val_smul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.smul_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.smulCommClass'", "kind": "instance", "module": "Mathlib.Algebra.Group.Action.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.isScalarTower'", "kind": "instance", "module": "Mathlib.Algebra.Group.Action.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.isScalarTower'_left", "kind": "instance", "module": "Mathlib.Algebra.Group.Action.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units._example", "kind": "example", "module": "Mathlib.Algebra.Group.Action.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.mulDistribMulActionRight", "kind": "abbrev", "module": "Mathlib.Algebra.Group.Action.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.coe_smul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.coe_inv_smul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUnit.smul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Action.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.instFunLike", "kind": "instance", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.ext", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.coe_mk", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "AddChar.map_zero_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.map_add_eq_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.toMonoidHom", "kind": "definition", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.toMonoidHom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.map_nsmul_eq_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.toMonoidHomEquiv", "kind": "definition", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.coe_toMonoidHomEquiv", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.coe_toMonoidHomEquiv_symm", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.toMonoidHomEquiv_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.toMonoidHomEquiv_symm_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.toAddMonoidHom", "kind": "definition", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.coe_toAddMonoidHom", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.toAddMonoidHom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.toAddMonoidHomEquiv", "kind": "definition", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.coe_toAddMonoidHomEquiv", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.coe_toAddMonoidHomEquiv_symm", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.toAddMonoidHomEquiv_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.toAddMonoidHomEquiv_symm_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.instOne", "kind": "instance", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.instZero", "kind": "instance", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.coe_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.coe_zero", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.one_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.zero_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.one_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.coe_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AddChar.toMonoidHomEquiv_zero", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.toMonoidHomEquiv_symm_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.toAddMonoidHomEquiv_zero", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.toAddMonoidHomEquiv_symm_zero", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.instInhabited", "kind": "instance", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.compAddChar", "kind": "definition", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.coe_compAddChar", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.compAddChar_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.compAddChar_injective_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "MonoidHom.compAddChar_injective_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "AddChar.compAddMonoidHom", "kind": "definition", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.coe_compAddMonoidHom", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.compAddMonoidHom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.compAddMonoidHom_injective_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "AddChar.compAddMonoidHom_injective_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": true, "tactics": ["rintro", "rw"], "tactic_count": 2}
{"name": "AddChar.eq_one_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.ne_one_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.ne_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.instDecidableEq", "kind": "instance", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.instCommMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.instAddCommMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.coe_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.coe_add", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.coe_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.coe_nsmul", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.coe_prod", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "AddChar.coe_sum", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "AddChar.mul_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.add_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.pow_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.nsmul_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.prod_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AddChar.sum_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AddChar.mul_eq_add", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.pow_eq_nsmul", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.prod_eq_sum", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.toMonoidHomEquiv_add", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.toMonoidHomEquiv_symm_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.toMonoidHomMulEquiv", "kind": "definition", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.toAddMonoidAddEquiv", "kind": "definition", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.doubleDualEmb", "kind": "definition", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.doubleDualEmb_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.sum_eq_ite", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": true, "tactics": ["split_ifs", "simp", "obtain", "refine", "rw", "exact"], "tactic_count": 6}
{"name": "AddChar.sum_eq_zero_iff_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "AddChar.sum_ne_zero_iff_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.instCommGroup", "kind": "instance", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.instAddCommGroup", "kind": "instance", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.inv_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.neg_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.div_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.sub_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.val_isUnit", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.map_neg_eq_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "AddChar.map_zsmul_eq_zpow", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.inv_apply'", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AddChar.neg_apply'", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.div_apply'", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AddChar.sub_apply'", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AddChar.zsmul_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "AddChar.zpow_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.map_sub_eq_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.injective_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.coe_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.mulShift", "kind": "definition", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.mulShift_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.inv_mulShift", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "AddChar.mulShift_spec'", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AddChar.pow_mulShift", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "AddChar.mulShift_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "AddChar.mulShift_mulShift", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "AddChar.mulShift_zero", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "AddChar.mulShift_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "AddChar.mulShift_unit_eq_one_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.AddChar", "is_tactic_proof": true, "tactics": ["refine", "ext1", "rw", "simpa", "solve_by_elim"], "tactic_count": 5}
{"name": "pow_dite", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["split_ifs"], "tactic_count": 1}
{"name": "dite_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["split_ifs"], "tactic_count": 1}
{"name": "pow_ite", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ite_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Semigroup.to_isAssociative", "kind": "instance", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "comp_mul_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "comp_mul_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Semigroup.to_isLawfulIdentity", "kind": "instance", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ite_mul_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "ite_one_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "eq_one_iff_eq_one_of_mul_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["constructor"], "tactic_count": 1}
{"name": "one_mul_eq_id", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_one_eq_id", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_left_comm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mul_right_comm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mul_mul_mul_comm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "mul_mul_mul_comm'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "mul_rotate", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "mul_rotate'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "pow_boole", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "pow_mul_pow_sub", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "pow_sub_mul_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mul_pow_sub_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "pow_sub_one_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "pow_eq_pow_mod", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["calc", "a"], "tactic_count": 2}
{"name": "pow_mul_pow_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_left_iterate", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_right_iterate", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_left_iterate_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "mul_right_iterate_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "mul_left_iterate_apply_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "mul_right_iterate_apply_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "pow_iterate", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_unique", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_eq_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "left_eq_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_ne_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "left_ne_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_eq_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "right_eq_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_ne_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "right_ne_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_iff_eq_of_mul_eq_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "ne_iff_ne_of_mul_eq_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "inv_involutive", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_inj", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_eq_iff_eq_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_comp_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "leftInverse_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "rightInverse_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_one_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mul_div_assoc'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "div_eq_mul_one_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "div_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "one_div_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_inv_of_mul_eq_one_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_one_div_of_mul_eq_one_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "eq_one_div_of_mul_eq_one_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "eq_of_div_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_of_inv_mul_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "eq_of_mul_inv_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "div_ne_one_of_ne", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_div_mul_one_div_rev", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "inv_div_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "inv_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "one_div_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "one_div_one_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "div_eq_div_iff_comm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DivisionMonoid.toDivInvOneMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_zpow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zpow_neg", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_zpow_neg_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "inv_zpow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_zpow'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "one_div_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "one_div_zpow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "inv_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_eq_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_ne_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_of_one_div_eq_one_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "zpow_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zpow_mul'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "zpow_comm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "div_div_eq_mul_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "div_inv_eq_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "div_mul_eq_div_div_swap", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "mul_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "inv_div'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "div_eq_inv_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "inv_mul_eq_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "inv_div_comm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "inv_mul'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "inv_div_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "inv_inv_div_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "one_div_mul_one_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "div_right_comm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "div_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "div_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "mul_div_left_comm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "mul_div_right_comm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "div_mul_eq_div_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "div_mul_eq_mul_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "one_div_mul_eq_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "mul_comm_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "div_mul_comm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "div_mul_eq_div_mul_one_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "div_div_div_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "div_div_div_comm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "div_mul_div_comm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "mul_div_mul_comm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "mul_zpow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "div_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "div_zpow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "div_eq_inv_self", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mul_left_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_right_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_mul_inv_of_mul_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "eq_inv_mul_of_mul_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "inv_mul_eq_of_eq_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "mul_inv_eq_of_eq_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "eq_mul_of_mul_inv_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "eq_mul_of_inv_mul_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "mul_eq_of_eq_inv_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mul_eq_of_eq_mul_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "mul_eq_one_iff_eq_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_eq_one_iff_inv_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mul_eq_one_iff_eq_inv'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mul_eq_one_iff_inv_eq'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "eq_inv_iff_mul_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_eq_iff_mul_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_mul_inv_iff_mul_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_inv_mul_iff_mul_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_mul_eq_iff_eq_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_inv_eq_iff_eq_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_inv_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "inv_mul_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "conj_eq_one_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "div_left_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "div_right_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "div_mul_cancel_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mul_div_mul_right_eq_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "eq_div_of_mul_eq'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "div_eq_of_eq_mul''", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "eq_mul_of_div_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "mul_eq_of_eq_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "div_right_inj", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "div_left_inj", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "div_mul_div_cancel", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "div_div_div_cancel_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "div_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "div_ne_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "div_eq_self", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "eq_div_iff_mul_eq'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "div_eq_iff_eq_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "eq_iff_eq_of_div_eq_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "leftInverse_div_mul_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "leftInverse_mul_left_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "leftInverse_mul_right_inv_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "leftInverse_inv_mul_mul_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pow_natAbs_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "pow_sub", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_pow_sub", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "zpow_add_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zpow_sub_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zpow_add", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "pred"], "tactic_count": 4}
{"name": "zpow_one_add", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mul_self_zpow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mul_zpow_self", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zpow_sub", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "zpow_natCast_sub_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "zpow_natCast_sub_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "zpow_one_sub_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "zpow_mul_comm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mul_zpow_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zpow_eq_zpow_emod", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zpow_eq_zpow_emod'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zpow_iterate", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zpow_induction_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "exact", "pred", "rw", "exact"], "tactic_count": 8}
{"name": "zpow_induction_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "exact", "pred", "rw", "exact"], "tactic_count": 8}
{"name": "div_eq_of_eq_mul'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mul_div_mul_left_eq_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw", "div_eq_mul_inv]"], "tactic_count": 2}
{"name": "eq_div_of_mul_eq''", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "eq_mul_of_div_eq'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "mul_eq_of_eq_div'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "div_div_self'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "div_eq_div_mul_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "div_div_cancel", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "div_div_cancel_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "eq_div_iff_mul_eq''", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "div_eq_iff_eq_mul'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "div_eq_iff_comm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mul_div_cancel_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mul_div_cancel", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "div_mul_cancel_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mul_mul_inv_cancel'_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mul_mul_div_cancel", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "div_mul_mul_cancel", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "div_mul_div_cancel'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mul_div_div_cancel", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "div_div_div_cancel_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "div_eq_div_iff_mul_eq_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "mul_inv_eq_mul_inv_iff_mul_eq_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "inv_mul_eq_inv_mul_iff_mul_eq_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "div_eq_div_iff_div_eq_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "const_div_involutive", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "multiplicative_of_symmetric_of_total", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": ["have", "intro", "obtain", "exact", "rw", "obtain", "rw", "rw", "obtain", "exact", "rw"], "tactic_count": 11}
{"name": "multiplicative_of_total", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["apply", "simp_rw", "exact", "exacts"], "tactic_count": 4}
{"name": "hom_coe_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommMonoid.toGrindNatModule", "kind": "instance", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGroup.toGrindIntModule", "kind": "instance", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRightCancelAdd.toGrindAddRightCancel", "kind": "instance", "module": "Mathlib.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMulCentral.mid_assoc", "kind": "theorem", "module": "Mathlib.Algebra.Group.Center", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsMulCentral.left_comm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Center", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsMulCentral.right_comm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Center", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.center", "kind": "definition", "module": "Mathlib.Algebra.Group.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.centralizer", "kind": "definition", "module": "Mathlib.Algebra.Group.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_center_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_centralizer_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mul_mem_center", "kind": "theorem", "module": "Mathlib.Algebra.Group.Center", "is_tactic_proof": true, "tactics": ["simp", "grind"], "tactic_count": 2}
{"name": "Set.center_subset_centralizer", "kind": "theorem", "module": "Mathlib.Algebra.Group.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.centralizer_union", "kind": "theorem", "module": "Mathlib.Algebra.Group.Center", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.centralizer_subset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subset_centralizer_centralizer", "kind": "theorem", "module": "Mathlib.Algebra.Group.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.centralizer_centralizer_centralizer", "kind": "theorem", "module": "Mathlib.Algebra.Group.Center", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "Set.decidableMemCentralizer", "kind": "instance", "module": "Mathlib.Algebra.Group.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.centralizer_centralizer_comm_of_comm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.centralizer_empty", "kind": "theorem", "module": "Mathlib.Algebra.Group.Center", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.centralizer_prod", "kind": "theorem", "module": "Mathlib.Algebra.Group.Center", "is_tactic_proof": true, "tactics": ["ext", "simp", "grind"], "tactic_count": 3}
{"name": "Set.prod_centralizer_subset_centralizer_prod", "kind": "theorem", "module": "Mathlib.Algebra.Group.Center", "is_tactic_proof": true, "tactics": ["simp_all"], "tactic_count": 1}
{"name": "Set.center_prod", "kind": "theorem", "module": "Mathlib.Algebra.Group.Center", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Set.center_pi", "kind": "theorem", "module": "Mathlib.Algebra.Group.Center", "is_tactic_proof": true, "tactics": ["classical", "ext", "simp", "refine", "exact"], "tactic_count": 5}
{"name": "Semigroup.mem_center_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mul_mem_centralizer", "kind": "theorem", "module": "Mathlib.Algebra.Group.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.centralizer_eq_top_iff_subset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.centralizer_univ", "kind": "theorem", "module": "Mathlib.Algebra.Group.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.decidableMemCenter", "kind": "instance", "module": "Mathlib.Algebra.Group.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.center_eq_univ", "kind": "theorem", "module": "Mathlib.Algebra.Group.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.centralizer_eq_univ", "kind": "theorem", "module": "Mathlib.Algebra.Group.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.one_mem_center", "kind": "theorem", "module": "Mathlib.Algebra.Group.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.one_mem_centralizer", "kind": "theorem", "module": "Mathlib.Algebra.Group.Center", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.subset_center_units", "kind": "theorem", "module": "Mathlib.Algebra.Group.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.units_inv_mem_center", "kind": "theorem", "module": "Mathlib.Algebra.Group.Center", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.invOf_mem_center", "kind": "theorem", "module": "Mathlib.Algebra.Group.Center", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.inv_mem_center", "kind": "theorem", "module": "Mathlib.Algebra.Group.Center", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw"], "tactic_count": 3}
{"name": "Set.div_mem_center", "kind": "theorem", "module": "Mathlib.Algebra.Group.Center", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.inv_mem_centralizer", "kind": "theorem", "module": "Mathlib.Algebra.Group.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.div_mem_centralizer", "kind": "theorem", "module": "Mathlib.Algebra.Group.Center", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "commutatorElement", "kind": "instance", "module": "Mathlib.Algebra.Group.Commutator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "commutatorElement_def", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commutator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiconjBy.function_semiconj_mul_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.function_commute_mul_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiconjBy.function_semiconj_mul_right_swap", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.function_commute_mul_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.inv_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.inv_inv_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.div_mul_div_comm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Commute.mul_div_mul_comm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.div_div_div_comm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Commute.inv_left_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.inv_right_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.inv_mul_cancel", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Commute.inv_mul_cancel_assoc", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Commute.conj_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.conj", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.zpow_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.zpow_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.zpow_zpow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.self_zpow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.zpow_self", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.zpow_zpow_self", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pow_inv_comm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute", "kind": "definition", "module": "Mathlib.Algebra.Group.Commute.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "commute_iff_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.refl", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.symm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.semiconjBy", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.symm_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.instRefl", "kind": "instance", "module": "Mathlib.Algebra.Group.Commute.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.on_refl", "kind": "instance", "module": "Mathlib.Algebra.Group.Commute.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.mul_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.mul_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.right_comm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Commute.left_comm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Commute.mul_mul_mul_comm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Commute.all", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.one_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.one_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.pow_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.pow_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.pow_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Commute.self_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.pow_self", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.pow_pow_self", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.mul_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.mul_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Commute.inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Commute.mul_zpow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.mul_inv_cancel", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Commute.mul_inv_cancel_assoc", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SemiconjBy.map", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Hom", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Commute.map", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiconjBy.of_map", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.of_map", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "semiconjBy_map_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "commute_map_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.units_inv_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.units_inv_right_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.units_inv_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.units_inv_left_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.units_val", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.units_of_val", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.units_val_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.leftOfMul", "kind": "definition", "module": "Mathlib.Algebra.Group.Commute.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.rightOfMul", "kind": "definition", "module": "Mathlib.Algebra.Group.Commute.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.isUnit_mul_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isUnit_mul_self_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.units_zpow_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.units_zpow_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.ofPow", "kind": "definition", "module": "Mathlib.Algebra.Group.Commute.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isUnit_pow_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isUnit_pow_succ_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isUnit_pow_iff_of_not_isUnit", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Units", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "Units.ofPowEqOne", "kind": "definition", "module": "Mathlib.Algebra.Group.Commute.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.pow_ofPowEqOne", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUnit.of_pow_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.commute_iff_inv_mul_cancel", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Units", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Units.commute_iff_inv_mul_cancel_assoc", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Units", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Units.commute_iff_mul_inv_cancel", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Units", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Units.commute_iff_mul_inv_cancel_assoc", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Units", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Commute.div_eq_div_iff_of_isUnit", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Units", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Commute.mul_inv_eq_mul_inv_iff_of_isUnit", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Units", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Commute.inv_mul_eq_inv_mul_iff_of_isUnit", "kind": "theorem", "module": "Mathlib.Algebra.Group.Commute.Units", "is_tactic_proof": true, "tactics": ["rw", "hbd.symm.left_comm,"], "tactic_count": 2}
{"name": "IsConj", "kind": "definition", "module": "Mathlib.Algebra.Group.Conj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsConj.refl", "kind": "theorem", "module": "Mathlib.Algebra.Group.Conj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsConj.symm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Conj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isConj_comm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Conj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsConj.trans", "kind": "theorem", "module": "Mathlib.Algebra.Group.Conj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsConj.pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Conj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isConj_iff_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.Conj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.map_isConj", "kind": "theorem", "module": "Mathlib.Algebra.Group.Conj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isConj_one_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Conj", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "isConj_one_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Conj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isConj_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Conj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "conj_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Conj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "conj_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Conj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "conj_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Conj", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "conj_zpow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Conj", "is_tactic_proof": true, "tactics": ["cases", "simp", "simp", "rw"], "tactic_count": 4}
{"name": "conj_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Conj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsConj.setoid", "kind": "definition", "module": "Mathlib.Algebra.Group.Conj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjClasses", "kind": "definition", "module": "Mathlib.Algebra.Group.Conj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjClasses.mk", "kind": "definition", "module": "Mathlib.Algebra.Group.Conj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjClasses.instInhabited", "kind": "instance", "module": "Mathlib.Algebra.Group.Conj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjClasses.mk_eq_mk_iff_isConj", "kind": "theorem", "module": "Mathlib.Algebra.Group.Conj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjClasses.quotient_mk_eq_mk", "kind": "theorem", "module": "Mathlib.Algebra.Group.Conj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjClasses.quot_mk_eq_mk", "kind": "theorem", "module": "Mathlib.Algebra.Group.Conj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjClasses.forall_isConj", "kind": "theorem", "module": "Mathlib.Algebra.Group.Conj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ConjClasses.instOne", "kind": "instance", "module": "Mathlib.Algebra.Group.Conj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjClasses.one_eq_mk_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Conj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjClasses.exists_rep", "kind": "theorem", "module": "Mathlib.Algebra.Group.Conj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjClasses.map", "kind": "definition", "module": "Mathlib.Algebra.Group.Conj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LibraryNote.slow-failing_instance_priority", "kind": "definition", "module": "Mathlib.Algebra.Group.Conj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjClasses.instDecidableEqOfDecidableRelIsConj", "kind": "instance", "module": "Mathlib.Algebra.Group.Conj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ConjClasses.mkEquiv", "kind": "definition", "module": "Mathlib.Algebra.Group.Conj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "conjugatesOf", "kind": "definition", "module": "Mathlib.Algebra.Group.Conj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_conjugatesOf_self", "kind": "theorem", "module": "Mathlib.Algebra.Group.Conj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsConj.conjugatesOf_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.Conj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isConj_iff_conjugatesOf_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.Conj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjClasses.carrier", "kind": "definition", "module": "Mathlib.Algebra.Group.Conj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjClasses.mem_carrier_mk", "kind": "theorem", "module": "Mathlib.Algebra.Group.Conj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ConjClasses.carrier_eq_preimage_mk", "kind": "theorem", "module": "Mathlib.Algebra.Group.Conj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFintypeConjClassesOfDecidableRelIsConj", "kind": "instance", "module": "Mathlib.Algebra.Group.ConjFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFiniteConjClasses", "kind": "instance", "module": "Mathlib.Algebra.Group.ConjFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDecidableRelIsConjOfDecidableEqOfFintype", "kind": "instance", "module": "Mathlib.Algebra.Group.ConjFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "conjugatesOf.fintype", "kind": "instance", "module": "Mathlib.Algebra.Group.ConjFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjClasses.instFintypeElemCarrier", "kind": "instance", "module": "Mathlib.Algebra.Group.ConjFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCancelMul_iff_forall_isRegular", "kind": "theorem", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsLeftRegular.all", "kind": "theorem", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRightRegular.all", "kind": "theorem", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRegular.all", "kind": "theorem", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_left_cancel", "kind": "theorem", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_left_cancel_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_right_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "mul_ne_mul_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_right_cancel", "kind": "theorem", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "mul_left_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_left_inj", "kind": "theorem", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_ne_mul_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_assoc", "kind": "theorem", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "isLeftRegular_iff_isRegular", "kind": "theorem", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "isRightRegular_iff_isRegular", "kind": "theorem", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CommMagma.IsRightCancelMul.toIsLeftCancelMul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommMagma.IsLeftCancelMul.toIsRightCancelMul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommMagma.IsLeftCancelMul.toIsCancelMul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommMagma.IsRightCancelMul.toIsCancelMul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LibraryNote.lower_cancel_priority", "kind": "definition", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_eq_one_comm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsDedekindFiniteMonoidOfCommutativeHMul", "kind": "instance", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LibraryNote.forgetful_inheritance", "kind": "definition", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "npowBinRec", "kind": "definition", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "nsmulRec'", "kind": "definition", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "npowRec'_succ", "kind": "theorem", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "npowRec'_two_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": true, "tactics": ["induction", "ind", "k"], "tactic_count": 3}
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{"name": "npowBinRecAuto", "kind": "abbrev", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "npowRec_eq_npowBinRec", "kind": "theorem", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": true, "tactics": ["funext", "rw", "k"], "tactic_count": 3}
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{"name": "Monoid.toNatPow", "kind": "instance", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "left_inv_eq_right_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "pow_succ'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "pow_mul_comm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "IsLeftRegular.mul_eq_one_symm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRightRegular.mul_eq_one_symm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsDedekindFiniteMonoidOfIsLeftCancelMul", "kind": "instance", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsDedekindFiniteMonoidOfIsRightCancelMul", "kind": "instance", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindFiniteMonoid.of_exists_self_mul_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindFiniteMonoid.of_exists_mul_self_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsDedekindFiniteMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CancelCommMonoid.toCancelMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CancelMonoid.toIsCancelMul", "kind": "instance", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DivInvMonoid.div'", "kind": "definition", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubNegMonoid.sub'", "kind": "definition", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DivInvMonoid.toZPow", "kind": "instance", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubNegMonoid.toZSMul", "kind": "instance", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_zpow_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "zpow_zero", "kind": "theorem", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zpow_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zpow_ofNat", "kind": "theorem", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zpow_negSucc", "kind": "theorem", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "negSucc_zsmul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "div_eq_mul_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_eq_one_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mul_div_assoc", "kind": "theorem", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "one_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zpow_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "zpow_two", "kind": "theorem", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "zpow_neg_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zpow_neg_coe_of_pos", "kind": "theorem", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_inv_rev", "kind": "theorem", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_eq_of_mul_eq_one_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_eq_of_mul_eq_one_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "eq_inv_of_mul_eq_one_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_mul_cancel", "kind": "theorem", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Group.Defs.0.inv_eq_of_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "div_self'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "inv_mul_cancel_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mul_inv_cancel_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mul_inv_cancel_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mul_div_cancel_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "inv_mul_cancel_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "div_mul_cancel", "kind": "theorem", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Group.toDivisionMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Group.toCancelMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGroup.toCancelCommMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGroup.toDivisionCommMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_mul_cancel_comm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mul_inv_cancel_comm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "inv_mul_cancel_comm_assoc", "kind": "theorem", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mul_inv_cancel_comm_assoc", "kind": "theorem", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CommMonoid.ofIsMulCommutative", "kind": "instance", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGroup.ofIsMulCommutative", "kind": "instance", "module": "Mathlib.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mulLeftEmbedding", "kind": "definition", "module": "Mathlib.Algebra.Group.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mulRightEmbedding", "kind": "definition", "module": "Mathlib.Algebra.Group.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mulLeftEmbedding_eq_mulRightEmbedding", "kind": "theorem", "module": "Mathlib.Algebra.Group.Embedding", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "Function.End", "kind": "definition", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instMonoidEnd", "kind": "instance", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInhabitedEnd", "kind": "instance", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.instOne", "kind": "instance", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.instMul", "kind": "instance", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.instInv", "kind": "instance", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.instPowNat", "kind": "instance", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.permGroup", "kind": "instance", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.default_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.equivUnitsEnd", "kind": "definition", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.toHomPerm", "kind": "definition", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.mul_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.one_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.inv_apply_self", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.apply_inv_self", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.one_def", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.mul_def", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.inv_def", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.coe_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.coe_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.coe_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.coe_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.iterate_eq_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.eq_inv_iff_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.inv_eq_iff_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.zpow_apply_comm", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Equiv.Perm.trans_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.mul_refl", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.one_symm", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.refl_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.one_trans", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.refl_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.inv_trans_self", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.mul_symm", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.self_trans_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.symm_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.sumCongr_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.sumCongr_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.sumCongr_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.sumCongrHom", "kind": "definition", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.sumCongrHom_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": true, "tactics": ["rintro", "rw", "constructor", "simpa", "simpa"], "tactic_count": 5}
{"name": "Equiv.Perm.sumCongr_swap_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.sumCongr_one_swap", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.sigmaCongrRight_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.sigmaCongrRight_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.sigmaCongrRight_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.sigmaCongrRightHom", "kind": "definition", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.sigmaCongrRightHom_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": true, "tactics": ["intro", "ext", "simpa"], "tactic_count": 3}
{"name": "Equiv.Perm.subtypeCongrHom", "kind": "definition", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.subtypeCongrHom_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": true, "tactics": ["rintro", "rw", "constructor"], "tactic_count": 3}
{"name": "Equiv.permCongr_eq_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.permCongr_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.permCongrHom", "kind": "definition", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.permCongrHom_symm", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.permCongrHom_trans", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.permCongrHom_coe_equiv", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.permCongrHom_coe", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.extendDomain_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.extendDomain_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.extendDomain_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.extendDomainHom", "kind": "definition", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.extendDomainHom_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.extendDomain_eq_one_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.extendDomain_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.extendDomain_zpow", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.subtypePerm", "kind": "definition", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.subtypePerm_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.subtypePerm_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Group.End.0.Equiv.Perm.inv_aux", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.subtypePerm_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.inv_subtypePerm", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Group.End.0.Equiv.Perm.pow_aux", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.subtypePerm_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "_private.Mathlib.Algebra.Group.End.0.Equiv.Perm.zpow_aux", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.subtypePerm_zpow", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": true, "tactics": ["cases", "ofNat", "negSucc"], "tactic_count": 3}
{"name": "Equiv.Perm.ofSubtype", "kind": "definition", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.ofSubtype_subtypePerm", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.ofSubtype_apply_of_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.ofSubtype_apply_coe", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.ofSubtype_apply_of_not_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.ofSubtype_apply_mem_iff_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.ofSubtype_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": true, "tactics": ["intro", "rw", "intro", "specialize", "rwa"], "tactic_count": 5}
{"name": "Equiv.Perm.subtypePerm_ofSubtype", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.ofSubtype_subtypePerm_of_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.ofSubtype_subtypePerm_of_not_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.subtypeEquivSubtypePerm", "kind": "definition", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.subtypeEquivSubtypePerm_apply_of_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.subtypeEquivSubtypePerm_apply_of_not_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.swap_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.swap_mul_self", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.swap_mul_eq_mul_swap", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.mul_swap_eq_swap_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Equiv.swap_apply_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Equiv.swap_mul_self_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Equiv.mul_swap_mul_self", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Equiv.swap_mul_involutive", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.mul_swap_involutive", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.swap_eq_one_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.swap_mul_eq_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Equiv.mul_swap_eq_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Equiv.swap_mul_swap_mul_swap", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": true, "tactics": ["nth_rewrite", "rw"], "tactic_count": 2}
{"name": "Equiv.addLeft_zero", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.addRight_zero", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.addLeft_add", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.addRight_add", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.inv_addLeft", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.inv_addRight", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.pow_addLeft", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Equiv.pow_addRight", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Equiv.zpow_addLeft", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.zpow_addRight", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.mulLeft_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.mulRight_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.mulLeft_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.mulRight_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.inv_mulLeft", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Equiv.pow_mulLeft", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Equiv.pow_mulRight", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Equiv.zpow_mulLeft", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.zpow_mulRight", "kind": "theorem", "module": "Mathlib.Algebra.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MonoidHom.precompEquiv", "kind": "definition", "module": "Mathlib.Algebra.Group.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Equiv.inv", "kind": "definition", "module": "Mathlib.Algebra.Group.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.inv_symm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EmbeddingLike.map_eq_one_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EmbeddingLike.map_ne_one_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "term_≃*_", "kind": "definition", "module": "Mathlib.Algebra.Group.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Algebra_Group_Equiv_Defs___macroRules_term_≃*__1", "kind": "definition", "module": "Mathlib.Algebra.Group.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Algebra_Group_Equiv_Defs___unexpand_MulEquiv_1", "kind": "definition", "module": "Mathlib.Algebra.Group.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "term_≃+_", "kind": "definition", "module": "Mathlib.Algebra.Group.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "_aux_Mathlib_Algebra_Group_Equiv_Defs___unexpand_AddEquiv_1", "kind": "definition", "module": "Mathlib.Algebra.Group.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MulEquivClass.instMonoidHomClass", "kind": "instance", "module": "Mathlib.Algebra.Group.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "instCoeTCMulEquivOfMulEquivClass", "kind": "instance", "module": "Mathlib.Algebra.Group.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.instEquivLike", "kind": "instance", "module": "Mathlib.Algebra.Group.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.instCoeFunForall", "kind": "instance", "module": "Mathlib.Algebra.Group.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MulEquiv.congr_arg", "kind": "theorem", "module": "Mathlib.Algebra.Group.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MulEquiv.map_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MulEquiv.surjective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.apply_eq_iff_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MulEquiv.instInhabited", "kind": "instance", "module": "Mathlib.Algebra.Group.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.coe_refl", "kind": "theorem", "module": "Mathlib.Algebra.Group.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MulEquiv.symm_map_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.symm", "kind": "definition", "module": "Mathlib.Algebra.Group.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.invFun_eq_symm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.coe_toEquiv_symm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.equivLike_inv_eq_symm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MulEquiv.mk_coe'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.symm_mk", "kind": "theorem", "module": "Mathlib.Algebra.Group.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.refl_symm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.apply_symm_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.symm_apply_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.symm_comp_self", "kind": "theorem", "module": "Mathlib.Algebra.Group.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.self_comp_symm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.apply_eq_iff_symm_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.symm_apply_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.eq_symm_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.eq_comp_symm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.comp_symm_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.eq_symm_comp", "kind": "theorem", "module": "Mathlib.Algebra.Group.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.symm_comp_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquivClass.apply_coe_symm_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquivClass.coe_symm_apply_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.Simps.symm_apply", "kind": "definition", "module": "Mathlib.Algebra.Group.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.trans", "kind": "definition", "module": "Mathlib.Algebra.Group.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.coe_trans", "kind": "theorem", "module": "Mathlib.Algebra.Group.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.trans_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.symm_trans_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.symm_trans_self", "kind": "theorem", "module": "Mathlib.Algebra.Group.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.self_trans_symm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.symmEquiv", "kind": "definition", "module": "Mathlib.Algebra.Group.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.cast", "kind": "definition", "module": "Mathlib.Algebra.Group.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.coe_monoidHom_refl", "kind": "theorem", "module": "Mathlib.Algebra.Group.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.coe_monoidHom_trans", "kind": "theorem", "module": "Mathlib.Algebra.Group.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.coe_monoidHom_comp_coe_monoidHom_symm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Equiv.Defs", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "MulEquiv.coe_monoidHom_symm_comp_coe_monoidHom", "kind": "theorem", "module": "Mathlib.Algebra.Group.Equiv.Defs", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "MulEquiv.comp_left_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.comp_right_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.map_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.map_eq_one_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.map_ne_one_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.ofBijective", "kind": "definition", "module": "Mathlib.Algebra.Group.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.ofBijective_apply_symm_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.toMonoidHom", "kind": "definition", "module": "Mathlib.Algebra.Group.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.coe_toMonoidHom", "kind": "theorem", "module": "Mathlib.Algebra.Group.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.toMonoidHom_eq_coe", "kind": "theorem", "module": "Mathlib.Algebra.Group.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.toMonoidHom_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.map_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.map_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulHom.toMulEquiv", "kind": "definition", "module": "Mathlib.Algebra.Group.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.toMulEquiv", "kind": "definition", "module": "Mathlib.Algebra.Group.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.decidableEqMulEquivFintype", "kind": "instance", "module": "Mathlib.Algebra.Group.Equiv.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.opMulEquiv", "kind": "definition", "module": "Mathlib.Algebra.Group.Equiv.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.coe_opMulEquiv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Equiv.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.coe_symm_opMulEquiv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Equiv.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.opAddEquiv", "kind": "definition", "module": "Mathlib.Algebra.Group.Equiv.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.opAddEquiv_toEquiv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Equiv.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddOpposite.opMulEquiv", "kind": "definition", "module": "Mathlib.Algebra.Group.Equiv.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddOpposite.opMulEquiv_toEquiv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Equiv.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.inv'", "kind": "definition", "module": "Mathlib.Algebra.Group.Equiv.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulHom.toOpposite", "kind": "definition", "module": "Mathlib.Algebra.Group.Equiv.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulHom.fromOpposite", "kind": "definition", "module": "Mathlib.Algebra.Group.Equiv.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.toOpposite", "kind": "definition", "module": "Mathlib.Algebra.Group.Equiv.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.fromOpposite", "kind": "definition", "module": "Mathlib.Algebra.Group.Equiv.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulHom.op", "kind": "definition", "module": "Mathlib.Algebra.Group.Equiv.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulHom.unop", "kind": "definition", "module": "Mathlib.Algebra.Group.Equiv.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddHom.mulOp", "kind": "definition", "module": "Mathlib.Algebra.Group.Equiv.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddHom.mulUnop", "kind": "definition", "module": "Mathlib.Algebra.Group.Equiv.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.op", "kind": "definition", "module": "Mathlib.Algebra.Group.Equiv.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.unop", "kind": "definition", "module": "Mathlib.Algebra.Group.Equiv.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.opOp", "kind": "definition", "module": "Mathlib.Algebra.Group.Equiv.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.mulOp", "kind": "definition", "module": "Mathlib.Algebra.Group.Equiv.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.mulUnop", "kind": "definition", "module": "Mathlib.Algebra.Group.Equiv.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddEquiv.mulOp", "kind": "definition", "module": "Mathlib.Algebra.Group.Equiv.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddEquiv.mulUnop", "kind": "definition", "module": "Mathlib.Algebra.Group.Equiv.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.op", "kind": "definition", "module": "Mathlib.Algebra.Group.Equiv.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.unop", "kind": "definition", "module": "Mathlib.Algebra.Group.Equiv.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.mul_op_ext", "kind": "theorem", "module": "Mathlib.Algebra.Group.Equiv.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddEquiv.toMultiplicative", "kind": "definition", "module": "Mathlib.Algebra.Group.Equiv.TypeTags", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.toAdditive", "kind": "definition", "module": "Mathlib.Algebra.Group.Equiv.TypeTags", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddEquiv.toMultiplicativeRight", "kind": "definition", "module": "Mathlib.Algebra.Group.Equiv.TypeTags", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.toAdditiveLeft", "kind": "abbrev", "module": "Mathlib.Algebra.Group.Equiv.TypeTags", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddEquiv.toMultiplicativeLeft", "kind": "definition", "module": "Mathlib.Algebra.Group.Equiv.TypeTags", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.toAdditiveRight", "kind": "abbrev", "module": "Mathlib.Algebra.Group.Equiv.TypeTags", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.toMultiplicative_toAdditive", "kind": "definition", "module": "Mathlib.Algebra.Group.Equiv.TypeTags", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddEquiv.toAdditive_toMultiplicative", "kind": "definition", "module": "Mathlib.Algebra.Group.Equiv.TypeTags", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monoidEndToAdditive", "kind": "definition", "module": "Mathlib.Algebra.Group.Equiv.TypeTags", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "addMonoidEndToMultiplicative", "kind": "definition", "module": "Mathlib.Algebra.Group.Equiv.TypeTags", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.piMultiplicative", "kind": "definition", "module": "Mathlib.Algebra.Group.Equiv.TypeTags", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.funMultiplicative", "kind": "abbrev", "module": "Mathlib.Algebra.Group.Equiv.TypeTags", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddEquiv.piAdditive", "kind": "definition", "module": "Mathlib.Algebra.Group.Equiv.TypeTags", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddEquiv.funAdditive", "kind": "abbrev", "module": "Mathlib.Algebra.Group.Equiv.TypeTags", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddEquiv.additiveMultiplicative", "kind": "definition", "module": "Mathlib.Algebra.Group.Equiv.TypeTags", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.multiplicativeAdditive", "kind": "definition", "module": "Mathlib.Algebra.Group.Equiv.TypeTags", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.prodMultiplicative", "kind": "definition", "module": "Mathlib.Algebra.Group.Equiv.TypeTags", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddEquiv.prodAdditive", "kind": "definition", "module": "Mathlib.Algebra.Group.Equiv.TypeTags", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.Monoid.End", "kind": "definition", "module": "Mathlib.Algebra.Group.Equiv.TypeTags", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.AddMonoid.End", "kind": "definition", "module": "Mathlib.Algebra.Group.Equiv.TypeTags", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSquare", "kind": "definition", "module": "Mathlib.Algebra.Group.Even", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isSquare_iff_exists_mul_self", "kind": "theorem", "module": "Mathlib.Algebra.Group.Even", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSquare.mul_self", "kind": "theorem", "module": "Mathlib.Algebra.Group.Even", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isSquare_op_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Even", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isSquare_unop_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Even", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDecidablePredMulOppositeIsSquare", "kind": "instance", "module": "Mathlib.Algebra.Group.Even", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "even_ofMul_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Even", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isSquare_toMul_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Even", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Additive.instDecidablePredEven", "kind": "instance", "module": "Mathlib.Algebra.Group.Even", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isSquare_ofAdd_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Even", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "even_toAdd_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Even", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiplicative.instDecidablePredIsSquare", "kind": "instance", "module": "Mathlib.Algebra.Group.Even", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSquare.one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Even", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSquare.map", "kind": "theorem", "module": "Mathlib.Algebra.Group.Even", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isSquare_subset_image_isSquare", "kind": "theorem", "module": "Mathlib.Algebra.Group.Even", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isSquare_iff_exists_sq", "kind": "theorem", "module": "Mathlib.Algebra.Group.Even", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsSquare.sq", "kind": "theorem", "module": "Mathlib.Algebra.Group.Even", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSquare.pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Even", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Even.isSquare_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Even", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "IsSquare.mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Even", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isSquare_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Even", "is_tactic_proof": true, "tactics": ["constructor"], "tactic_count": 1}
{"name": "IsSquare.zpow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Even", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "IsSquare.div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Even", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Even.isSquare_zpow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Even", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "_example", "kind": "example", "module": "Mathlib.Algebra.Group.Even", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "_example", "kind": "example", "module": "Mathlib.Algebra.Group.Even", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Function.Even", "kind": "definition", "module": "Mathlib.Algebra.Group.EvenFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Odd", "kind": "definition", "module": "Mathlib.Algebra.Group.EvenFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Even.const", "kind": "theorem", "module": "Mathlib.Algebra.Group.EvenFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Even.zero", "kind": "theorem", "module": "Mathlib.Algebra.Group.EvenFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Odd.zero", "kind": "theorem", "module": "Mathlib.Algebra.Group.EvenFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Even.left_comp", "kind": "theorem", "module": "Mathlib.Algebra.Group.EvenFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Even.comp_odd", "kind": "theorem", "module": "Mathlib.Algebra.Group.EvenFunction", "is_tactic_proof": true, "tactics": ["intro", "simp"], "tactic_count": 2}
{"name": "Function.Odd.comp_odd", "kind": "theorem", "module": "Mathlib.Algebra.Group.EvenFunction", "is_tactic_proof": true, "tactics": ["intro", "simp"], "tactic_count": 2}
{"name": "Function.Even.add", "kind": "theorem", "module": "Mathlib.Algebra.Group.EvenFunction", "is_tactic_proof": true, "tactics": ["intro", "simp"], "tactic_count": 2}
{"name": "Function.Odd.add", "kind": "theorem", "module": "Mathlib.Algebra.Group.EvenFunction", "is_tactic_proof": true, "tactics": ["intro", "simp"], "tactic_count": 2}
{"name": "Function.Even.smul_even", "kind": "theorem", "module": "Mathlib.Algebra.Group.EvenFunction", "is_tactic_proof": true, "tactics": ["intro", "simp"], "tactic_count": 2}
{"name": "Function.Even.smul_odd", "kind": "theorem", "module": "Mathlib.Algebra.Group.EvenFunction", "is_tactic_proof": true, "tactics": ["intro", "simp"], "tactic_count": 2}
{"name": "Function.Odd.smul_even", "kind": "theorem", "module": "Mathlib.Algebra.Group.EvenFunction", "is_tactic_proof": true, "tactics": ["intro", "simp"], "tactic_count": 2}
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{"name": "Function.Even.const_smul", "kind": "theorem", "module": "Mathlib.Algebra.Group.EvenFunction", "is_tactic_proof": true, "tactics": ["intro", "simp"], "tactic_count": 2}
{"name": "Function.Odd.const_smul", "kind": "theorem", "module": "Mathlib.Algebra.Group.EvenFunction", "is_tactic_proof": true, "tactics": ["intro", "simp"], "tactic_count": 2}
{"name": "Function.Even.mul_even", "kind": "theorem", "module": "Mathlib.Algebra.Group.EvenFunction", "is_tactic_proof": true, "tactics": ["intro", "simp"], "tactic_count": 2}
{"name": "Function.Even.mul_odd", "kind": "theorem", "module": "Mathlib.Algebra.Group.EvenFunction", "is_tactic_proof": true, "tactics": ["intro", "simp"], "tactic_count": 2}
{"name": "Function.Odd.mul_even", "kind": "theorem", "module": "Mathlib.Algebra.Group.EvenFunction", "is_tactic_proof": true, "tactics": ["intro", "simp"], "tactic_count": 2}
{"name": "Function.Odd.mul_odd", "kind": "theorem", "module": "Mathlib.Algebra.Group.EvenFunction", "is_tactic_proof": true, "tactics": ["intro", "simp"], "tactic_count": 2}
{"name": "Function.zero_of_even_and_odd", "kind": "theorem", "module": "Mathlib.Algebra.Group.EvenFunction", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "Function.Odd.sum_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Group.EvenFunction", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Function.Odd.map_zero", "kind": "theorem", "module": "Mathlib.Algebra.Group.EvenFunction", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Monoid.ext", "kind": "theorem", "module": "Mathlib.Algebra.Group.Ext", "is_tactic_proof": true, "tactics": ["have", "have", "let", "have", "ext", "exact", "rcases", "congr"], "tactic_count": 8}
{"name": "CommMonoid.toMonoid_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Ext", "is_tactic_proof": true, "tactics": ["rintro", "congr"], "tactic_count": 2}
{"name": "CommMonoid.ext", "kind": "theorem", "module": "Mathlib.Algebra.Group.Ext", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LeftCancelMonoid.toMonoid_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Ext", "is_tactic_proof": true, "tactics": ["rintro", "congr"], "tactic_count": 2}
{"name": "LeftCancelMonoid.ext", "kind": "theorem", "module": "Mathlib.Algebra.Group.Ext", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RightCancelMonoid.toMonoid_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Ext", "is_tactic_proof": true, "tactics": ["rintro", "congr"], "tactic_count": 2}
{"name": "RightCancelMonoid.ext", "kind": "theorem", "module": "Mathlib.Algebra.Group.Ext", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CancelMonoid.toLeftCancelMonoid_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Ext", "is_tactic_proof": true, "tactics": ["rintro", "congr"], "tactic_count": 2}
{"name": "CancelMonoid.ext", "kind": "theorem", "module": "Mathlib.Algebra.Group.Ext", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CancelCommMonoid.toCommMonoid_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Ext", "is_tactic_proof": true, "tactics": ["rintro", "grind"], "tactic_count": 2}
{"name": "CancelCommMonoid.ext", "kind": "theorem", "module": "Mathlib.Algebra.Group.Ext", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DivInvMonoid.ext", "kind": "theorem", "module": "Mathlib.Algebra.Group.Ext", "is_tactic_proof": true, "tactics": ["have", "have", "let", "have", "ext", "exact", "have", "ext", "exact", "rcases", "congr"], "tactic_count": 11}
{"name": "Group.toDivInvMonoid_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Ext", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "Group.ext", "kind": "theorem", "module": "Mathlib.Algebra.Group.Ext", "is_tactic_proof": true, "tactics": ["have", "let", "exact"], "tactic_count": 3}
{"name": "CommGroup.toGroup_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Ext", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "CommGroup.ext", "kind": "theorem", "module": "Mathlib.Algebra.Group.Ext", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.addCommSemigroup", "kind": "instance", "module": "Mathlib.Algebra.Group.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.addCommMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.instAddMonoidWithOne", "kind": "definition", "module": "Mathlib.Algebra.Group.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.addCommGroup", "kind": "instance", "module": "Mathlib.Algebra.Group.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.instInvolutiveNeg", "kind": "instance", "module": "Mathlib.Algebra.Group.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.instIsCancelAdd", "kind": "instance", "module": "Mathlib.Algebra.Group.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.instAddLeftCancelSemigroup", "kind": "instance", "module": "Mathlib.Algebra.Group.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.instAddRightCancelSemigroup", "kind": "instance", "module": "Mathlib.Algebra.Group.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.intCast_def'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.coe_sub_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Fin.Basic", "is_tactic_proof": true, "tactics": ["cases", "simp", "split_ifs", "simp", "rw", "conv_rhs", "rw", "rwa"], "tactic_count": 8}
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{"name": "Fin.sub_le_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Fin.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.lt_one_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Fin.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "Fin.neg_natCast_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Fin.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "Fin.insertNth_one_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Fin.Tuple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.insertNth_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Fin.Tuple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.insertNth_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Fin.Tuple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.insertNth_div_same", "kind": "theorem", "module": "Mathlib.Algebra.Group.Fin.Tuple", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
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{"name": "Matrix.empty_add_empty", "kind": "theorem", "module": "Mathlib.Algebra.Group.Fin.Tuple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Matrix.tail_neg", "kind": "theorem", "module": "Mathlib.Algebra.Group.Fin.Tuple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.apply_single", "kind": "theorem", "module": "Mathlib.Algebra.Group.Finsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.mapRange.zeroHom", "kind": "definition", "module": "Mathlib.Algebra.Group.Finsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.mapRange.zeroHom_id", "kind": "theorem", "module": "Mathlib.Algebra.Group.Finsupp", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finsupp.mapRange.zeroHom_comp", "kind": "theorem", "module": "Mathlib.Algebra.Group.Finsupp", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finsupp.instAdd", "kind": "instance", "module": "Mathlib.Algebra.Group.Finsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.coe_add", "kind": "theorem", "module": "Mathlib.Algebra.Group.Finsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.add_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Finsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.support_add", "kind": "theorem", "module": "Mathlib.Algebra.Group.Finsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.support_add_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.Finsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.instAddZeroClass", "kind": "instance", "module": "Mathlib.Algebra.Group.Finsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.instIsLeftCancelAdd", "kind": "instance", "module": "Mathlib.Algebra.Group.Finsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.addEquivFunOnFinite", "kind": "definition", "module": "Mathlib.Algebra.Group.Finsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddEquiv.finsuppUnique", "kind": "definition", "module": "Mathlib.Algebra.Group.Finsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.instIsRightCancelAdd", "kind": "instance", "module": "Mathlib.Algebra.Group.Finsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.instIsCancelAdd", "kind": "instance", "module": "Mathlib.Algebra.Group.Finsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.applyAddHom", "kind": "definition", "module": "Mathlib.Algebra.Group.Finsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.coeFnAddHom", "kind": "definition", "module": "Mathlib.Algebra.Group.Finsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.mapRange_add", "kind": "theorem", "module": "Mathlib.Algebra.Group.Finsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.mapRange_add'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Finsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.embDomain.addMonoidHom", "kind": "definition", "module": "Mathlib.Algebra.Group.Finsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.embDomain_add", "kind": "theorem", "module": "Mathlib.Algebra.Group.Finsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.single_add", "kind": "theorem", "module": "Mathlib.Algebra.Group.Finsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.single_add_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Finsupp", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finsupp.support_single_add", "kind": "theorem", "module": "Mathlib.Algebra.Group.Finsupp", "is_tactic_proof": true, "tactics": ["classical", "have", "rw", "rwa"], "tactic_count": 4}
{"name": "Finsupp.support_add_single", "kind": "theorem", "module": "Mathlib.Algebra.Group.Finsupp", "is_tactic_proof": true, "tactics": ["classical", "have", "rw", "rwa"], "tactic_count": 4}
{"name": "Finsupp.support_single_add_single", "kind": "theorem", "module": "Mathlib.Algebra.Group.Finsupp", "is_tactic_proof": true, "tactics": ["rw", "simp", "simp"], "tactic_count": 3}
{"name": "Finsupp.support_single_add_single_subset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Finsupp", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "AddEquiv.finsuppUnique_symm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Finsupp", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finsupp.addCommute_iff_inter", "kind": "theorem", "module": "Mathlib.Algebra.Group.Finsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.addCommute_of_disjoint", "kind": "theorem", "module": "Mathlib.Algebra.Group.Finsupp", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finsupp.singleAddHom", "kind": "definition", "module": "Mathlib.Algebra.Group.Finsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.update_eq_single_add_erase", "kind": "theorem", "module": "Mathlib.Algebra.Group.Finsupp", "is_tactic_proof": true, "tactics": ["classical", "ext", "rcases", "simp", "simp"], "tactic_count": 5}
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{"name": "fwdDiff_aux.shiftₗ", "kind": "definition", "module": "Mathlib.Algebra.Group.ForwardDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "fwdDiff_finset_sum", "kind": "theorem", "module": "Mathlib.Algebra.Group.ForwardDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Submonoid.exists_mulEquiv_eq_mgraph", "kind": "theorem", "module": "Mathlib.Algebra.Group.Graph", "is_tactic_proof": true, "tactics": ["simpa", "hG₁.injective.eq_iff.trans"], "tactic_count": 2}
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{"name": "MonoidHom.exists_mulEquiv_range_eq_graph", "kind": "theorem", "module": "Mathlib.Algebra.Group.Graph", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
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{"name": "Subgroup.exists_mulEquiv_eq_graph", "kind": "theorem", "module": "Mathlib.Algebra.Group.Graph", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
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{"name": "invMonoidHom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "invMonoidHom_comp_invMonoidHom", "kind": "theorem", "module": "Mathlib.Algebra.Group.Hom.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
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{"name": "OneHom.coe_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "OneHom.mul_comp", "kind": "theorem", "module": "Mathlib.Algebra.Group.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OneHom.instInv", "kind": "instance", "module": "Mathlib.Algebra.Group.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "OneHom.div_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MulHom.instMul", "kind": "instance", "module": "Mathlib.Algebra.Group.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MonoidHom.ofMapMulInv", "kind": "definition", "module": "Mathlib.Algebra.Group.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.coe_of_map_mul_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MonoidHom.comp_id", "kind": "theorem", "module": "Mathlib.Algebra.Group.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OneHom.id_comp", "kind": "theorem", "module": "Mathlib.Algebra.Group.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulHom.id_comp", "kind": "theorem", "module": "Mathlib.Algebra.Group.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.id_comp", "kind": "theorem", "module": "Mathlib.Algebra.Group.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.map_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.map_zpow'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OneHom.inverse", "kind": "definition", "module": "Mathlib.Algebra.Group.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulHom.inverse", "kind": "definition", "module": "Mathlib.Algebra.Group.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.mul_comm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.inverse", "kind": "definition", "module": "Mathlib.Algebra.Group.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monoid.End", "kind": "definition", "module": "Mathlib.Algebra.Group.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monoid.End.instFunLike", "kind": "instance", "module": "Mathlib.Algebra.Group.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monoid.End.instMonoidHomClass", "kind": "instance", "module": "Mathlib.Algebra.Group.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monoid.End.instOne", "kind": "instance", "module": "Mathlib.Algebra.Group.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monoid.End.instMul", "kind": "instance", "module": "Mathlib.Algebra.Group.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monoid.End.instMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monoid.End.instInhabited", "kind": "instance", "module": "Mathlib.Algebra.Group.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monoid.End.coe_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monoid.End.coe_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monoid.End.coe_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instOneOneHom", "kind": "instance", "module": "Mathlib.Algebra.Group.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instOneMulHom", "kind": "instance", "module": "Mathlib.Algebra.Group.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instOneMonoidHom", "kind": "instance", "module": "Mathlib.Algebra.Group.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OneHom.one_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.one_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OneHom.one_comp", "kind": "theorem", "module": "Mathlib.Algebra.Group.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OneHom.comp_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Hom.Defs", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "instInhabitedOneHom", "kind": "instance", "module": "Mathlib.Algebra.Group.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInhabitedMulHom", "kind": "instance", "module": "Mathlib.Algebra.Group.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInhabitedMonoidHom", "kind": "instance", "module": "Mathlib.Algebra.Group.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.one_comp", "kind": "theorem", "module": "Mathlib.Algebra.Group.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.comp_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Hom.Defs", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "MonoidHom.map_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.map_zpow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.map_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.map_mul_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Hom.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "iterate_map_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iterate_map_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iterate_map_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iterate_map_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iterate_map_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iterate_map_zpow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoid.End.instAddMonoidWithOne", "kind": "instance", "module": "Mathlib.Algebra.Group.Hom.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoid.End.natCast_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Hom.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoid.End.ofNat_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Hom.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoid.End.instSemiring", "kind": "instance", "module": "Mathlib.Algebra.Group.Hom.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoid.End.instRing", "kind": "instance", "module": "Mathlib.Algebra.Group.Hom.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroHom.instNatSMul", "kind": "instance", "module": "Mathlib.Algebra.Group.Hom.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.instNatSMul", "kind": "instance", "module": "Mathlib.Algebra.Group.Hom.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OneHom.instPow", "kind": "instance", "module": "Mathlib.Algebra.Group.Hom.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.instPow", "kind": "instance", "module": "Mathlib.Algebra.Group.Hom.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OneHom.pow_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Hom.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.pow_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Hom.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OneHom.instMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.Hom.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OneHom.instCommMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.Hom.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.instCommMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.Hom.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroHom.instIntSMul", "kind": "instance", "module": "Mathlib.Algebra.Group.Hom.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.instIntSMul", "kind": "instance", "module": "Mathlib.Algebra.Group.Hom.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OneHom.instIntPow", "kind": "instance", "module": "Mathlib.Algebra.Group.Hom.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.instIntPow", "kind": "instance", "module": "Mathlib.Algebra.Group.Hom.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OneHom.zpow_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Hom.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.zpow_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Hom.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OneHom.instGroup", "kind": "instance", "module": "Mathlib.Algebra.Group.Hom.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OneHom.instCommGroup", "kind": "instance", "module": "Mathlib.Algebra.Group.Hom.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.instCommGroup", "kind": "instance", "module": "Mathlib.Algebra.Group.Hom.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsLeftCancelMulOneHom", "kind": "instance", "module": "Mathlib.Algebra.Group.Hom.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsLeftCancelMulMonoidHom", "kind": "instance", "module": "Mathlib.Algebra.Group.Hom.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsRightCancelMulOneHom", "kind": "instance", "module": "Mathlib.Algebra.Group.Hom.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsRightCancelMulMonoidHom", "kind": "instance", "module": "Mathlib.Algebra.Group.Hom.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsCancelMulOneHom", "kind": "instance", "module": "Mathlib.Algebra.Group.Hom.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsCancelMulMonoidHom", "kind": "instance", "module": "Mathlib.Algebra.Group.Hom.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoid.End.instAddCommMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.Hom.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoid.End.zero_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Hom.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoid.End.one_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Hom.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoid.End.instAddCommGroup", "kind": "instance", "module": "Mathlib.Algebra.Group.Hom.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoid.End.instIntCast", "kind": "instance", "module": "Mathlib.Algebra.Group.Hom.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoid.End.intCast_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Hom.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.ext_iff₂", "kind": "theorem", "module": "Mathlib.Algebra.Group.Hom.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.flip", "kind": "definition", "module": "Mathlib.Algebra.Group.Hom.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.flip_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Hom.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.map_one₂", "kind": "theorem", "module": "Mathlib.Algebra.Group.Hom.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.map_mul₂", "kind": "theorem", "module": "Mathlib.Algebra.Group.Hom.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.map_inv₂", "kind": "theorem", "module": "Mathlib.Algebra.Group.Hom.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.map_div₂", "kind": "theorem", "module": "Mathlib.Algebra.Group.Hom.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.eval", "kind": "definition", "module": "Mathlib.Algebra.Group.Hom.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.compHom'", "kind": "definition", "module": "Mathlib.Algebra.Group.Hom.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.compHom", "kind": "definition", "module": "Mathlib.Algebra.Group.Hom.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.flipHom", "kind": "definition", "module": "Mathlib.Algebra.Group.Hom.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.compl₂", "kind": "definition", "module": "Mathlib.Algebra.Group.Hom.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.compl₂_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Hom.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.compr₂", "kind": "definition", "module": "Mathlib.Algebra.Group.Hom.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.compr₂_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Hom.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemigroupIdeal", "kind": "abbrev", "module": "Mathlib.Algebra.Group.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemigroupIdeal.mul_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemigroupIdeal.closure", "kind": "abbrev", "module": "Mathlib.Algebra.Group.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemigroupIdeal.mem_closure", "kind": "theorem", "module": "Mathlib.Algebra.Group.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemigroupIdeal.subset_closure", "kind": "theorem", "module": "Mathlib.Algebra.Group.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemigroupIdeal.mem_closure_of_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemigroupIdeal.closure_le", "kind": "theorem", "module": "Mathlib.Algebra.Group.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemigroupIdeal.closure_mono", "kind": "theorem", "module": "Mathlib.Algebra.Group.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemigroupIdeal.coe_closure", "kind": "theorem", "module": "Mathlib.Algebra.Group.Ideal", "is_tactic_proof": false, "tactics": ["let", "smul_mem", "y", "rintro", "exact", "simpa", "suffices", "refine", "rintro", "exact"], "tactic_count": 10}
{"name": "SemigroupIdeal.mem_closure'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Ideal", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "SemigroupIdeal.coe_closure'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Ideal", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SemigroupIdeal.mem_closure''", "kind": "theorem", "module": "Mathlib.Algebra.Group.Ideal", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "SemigroupIdeal.FG", "kind": "definition", "module": "Mathlib.Algebra.Group.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemigroupIdeal.fg_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIdempotentElem", "kind": "definition", "module": "Mathlib.Algebra.Group.Idempotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIdempotentElem.of_isIdempotent", "kind": "theorem", "module": "Mathlib.Algebra.Group.Idempotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIdempotentElem.eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.Idempotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIdempotentElem.mul_of_commute", "kind": "theorem", "module": "Mathlib.Algebra.Group.Idempotent", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsIdempotentElem.mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Idempotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIdempotentElem.one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Idempotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIdempotentElem.instOneSubtype", "kind": "instance", "module": "Mathlib.Algebra.Group.Idempotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIdempotentElem.coe_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Idempotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIdempotentElem.pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Idempotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIdempotentElem.pow_succ_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.Idempotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIdempotentElem.pow_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.Idempotent", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "IsIdempotentElem.iff_eq_one_of_isUnit", "kind": "theorem", "module": "Mathlib.Algebra.Group.Idempotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIdempotentElem.iff_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Idempotent", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsIdempotentElem.map", "kind": "theorem", "module": "Mathlib.Algebra.Group.Idempotent", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsIdempotentElem.mul_mul_self", "kind": "theorem", "module": "Mathlib.Algebra.Group.Idempotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIdempotentElem.mul_self_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Idempotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mulIndicator_union_mul_inter_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Indicator", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "Set.mulIndicator_union_mul_inter", "kind": "theorem", "module": "Mathlib.Algebra.Group.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mulIndicator_union_of_notMem_inter", "kind": "theorem", "module": "Mathlib.Algebra.Group.Indicator", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.mulIndicator_union_of_disjoint", "kind": "theorem", "module": "Mathlib.Algebra.Group.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mulIndicator_symmDiff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mulIndicator_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Indicator", "is_tactic_proof": true, "tactics": ["funext", "simp", "split_ifs", "rfl", "rw"], "tactic_count": 5}
{"name": "Set.mulIndicator_mul'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mulIndicator_compl_mul_self_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mulIndicator_compl_mul_self", "kind": "theorem", "module": "Mathlib.Algebra.Group.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mulIndicator_self_mul_compl_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mulIndicator_self_mul_compl", "kind": "theorem", "module": "Mathlib.Algebra.Group.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mulIndicator_mul_eq_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Indicator", "is_tactic_proof": true, "tactics": ["refine", "have", "rw"], "tactic_count": 3}
{"name": "Set.mulIndicator_mul_eq_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Indicator", "is_tactic_proof": true, "tactics": ["refine", "have", "rw"], "tactic_count": 3}
{"name": "Set.mulIndicator_mul_compl_eq_piecewise", "kind": "theorem", "module": "Mathlib.Algebra.Group.Indicator", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "rw", "rw"], "tactic_count": 4}
{"name": "Set.mulIndicatorHom", "kind": "definition", "module": "Mathlib.Algebra.Group.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mulIndicator_inv'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mulIndicator_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mulIndicator_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mulIndicator_div'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mulIndicator_compl", "kind": "theorem", "module": "Mathlib.Algebra.Group.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mulIndicator_compl'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Indicator", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.mulIndicator_diff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mulIndicator_diff'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Indicator", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.apply_mulIndicator_symmDiff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Indicator", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "Set.mulIndicator_singleton", "kind": "theorem", "module": "Mathlib.Algebra.Group.Indicator", "is_tactic_proof": true, "tactics": ["ext", "simp", "split_ifs"], "tactic_count": 3}
{"name": "map_mulIndicator", "kind": "theorem", "module": "Mathlib.Algebra.Group.Indicator", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Function.Injective.semigroup", "kind": "abbrev", "module": "Mathlib.Algebra.Group.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.commMagma", "kind": "abbrev", "module": "Mathlib.Algebra.Group.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.commSemigroup", "kind": "abbrev", "module": "Mathlib.Algebra.Group.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.isLeftCancelMul", "kind": "theorem", "module": "Mathlib.Algebra.Group.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.isRightCancelMul", "kind": "theorem", "module": "Mathlib.Algebra.Group.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.isCancelMul", "kind": "theorem", "module": "Mathlib.Algebra.Group.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.leftCancelSemigroup", "kind": "abbrev", "module": "Mathlib.Algebra.Group.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.rightCancelSemigroup", "kind": "abbrev", "module": "Mathlib.Algebra.Group.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.mulOneClass", "kind": "abbrev", "module": "Mathlib.Algebra.Group.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.monoid", "kind": "abbrev", "module": "Mathlib.Algebra.Group.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.leftCancelMonoid", "kind": "abbrev", "module": "Mathlib.Algebra.Group.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.rightCancelMonoid", "kind": "abbrev", "module": "Mathlib.Algebra.Group.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.cancelMonoid", "kind": "abbrev", "module": "Mathlib.Algebra.Group.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.commMonoid", "kind": "abbrev", "module": "Mathlib.Algebra.Group.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.cancelCommMonoid", "kind": "abbrev", "module": "Mathlib.Algebra.Group.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.involutiveInv", "kind": "abbrev", "module": "Mathlib.Algebra.Group.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.invOneClass", "kind": "abbrev", "module": "Mathlib.Algebra.Group.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.divInvMonoid", "kind": "abbrev", "module": "Mathlib.Algebra.Group.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.divInvOneMonoid", "kind": "abbrev", "module": "Mathlib.Algebra.Group.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.divisionMonoid", "kind": "abbrev", "module": "Mathlib.Algebra.Group.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.divisionCommMonoid", "kind": "abbrev", "module": "Mathlib.Algebra.Group.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.group", "kind": "abbrev", "module": "Mathlib.Algebra.Group.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.commGroup", "kind": "abbrev", "module": "Mathlib.Algebra.Group.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.semigroup", "kind": "abbrev", "module": "Mathlib.Algebra.Group.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.commMagma", "kind": "abbrev", "module": "Mathlib.Algebra.Group.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.commSemigroup", "kind": "abbrev", "module": "Mathlib.Algebra.Group.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.mulOneClass", "kind": "abbrev", "module": "Mathlib.Algebra.Group.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.monoid", "kind": "abbrev", "module": "Mathlib.Algebra.Group.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.commMonoid", "kind": "abbrev", "module": "Mathlib.Algebra.Group.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.involutiveInv", "kind": "abbrev", "module": "Mathlib.Algebra.Group.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.divInvMonoid", "kind": "abbrev", "module": "Mathlib.Algebra.Group.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.group", "kind": "abbrev", "module": "Mathlib.Algebra.Group.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.commGroup", "kind": "abbrev", "module": "Mathlib.Algebra.Group.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.instCommMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.Int.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.instAddCommGroup", "kind": "instance", "module": "Mathlib.Algebra.Group.Int.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.instIsAddTorsionFree", "kind": "instance", "module": "Mathlib.Algebra.Group.Int.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.instAddCommMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.Int.Defs", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Int.instAddMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.Int.Defs", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Int.instMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.Int.Defs", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Int.instCommSemigroup", "kind": "instance", "module": "Mathlib.Algebra.Group.Int.Defs", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Int.instSemigroup", "kind": "instance", "module": "Mathlib.Algebra.Group.Int.Defs", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Int.instAddGroup", "kind": "instance", "module": "Mathlib.Algebra.Group.Int.Defs", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Int.instAddCommSemigroup", "kind": "instance", "module": "Mathlib.Algebra.Group.Int.Defs", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Int.instAddSemigroup", "kind": "instance", "module": "Mathlib.Algebra.Group.Int.Defs", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Int.nsmul_eq_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Int.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.zsmul_eq_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Int.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zsmul_int_int", "kind": "theorem", "module": "Mathlib.Algebra.Group.Int.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zsmul_int_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Int.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.emod_two_ne_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Int.Even", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Int.one_emod_two", "kind": "theorem", "module": "Mathlib.Algebra.Group.Int.Even", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.emod_two_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Group.Int.Even", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Int.even_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Int.Even", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.not_even_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Int.Even", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Int.two_dvd_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Group.Int.Even", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Int.instDecidablePredEven", "kind": "instance", "module": "Mathlib.Algebra.Group.Int.Even", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.instDecidablePredIsSquare", "kind": "instance", "module": "Mathlib.Algebra.Group.Int.Even", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.not_even_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Int.Even", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Int.even_add", "kind": "theorem", "module": "Mathlib.Algebra.Group.Int.Even", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Int.two_not_dvd_two_mul_add_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Int.Even", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Int.even_sub", "kind": "theorem", "module": "Mathlib.Algebra.Group.Int.Even", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Int.even_add_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Int.Even", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Int.even_sub_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Int.Even", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Int.even_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Int.Even", "is_tactic_proof": true, "tactics": ["rcases", "simp"], "tactic_count": 2}
{"name": "Int.even_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Int.Even", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "Int.even_pow'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Int.Even", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Int.even_coe_nat", "kind": "theorem", "module": "Mathlib.Algebra.Group.Int.Even", "is_tactic_proof": true, "tactics": ["rw_mod_cast"], "tactic_count": 1}
{"name": "Int.two_mul_ediv_two_of_even", "kind": "theorem", "module": "Mathlib.Algebra.Group.Int.Even", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Int.ediv_two_mul_two_of_even", "kind": "theorem", "module": "Mathlib.Algebra.Group.Int.Even", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Int._example", "kind": "example", "module": "Mathlib.Algebra.Group.Int.Even", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Int._example", "kind": "example", "module": "Mathlib.Algebra.Group.Int.Even", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "Int.isSquare_sign_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Int.Even", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "pred", "rw", "norm_cast", "simp", "rintro"], "tactic_count": 8}
{"name": "Int.toAdd_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Int.TypeTags", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.toAdd_zpow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Int.TypeTags", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.ofAdd_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Int.TypeTags", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.units_natAbs", "kind": "theorem", "module": "Mathlib.Algebra.Group.Int.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.natAbs_of_isUnit", "kind": "theorem", "module": "Mathlib.Algebra.Group.Int.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.isUnit_eq_one_or", "kind": "theorem", "module": "Mathlib.Algebra.Group.Int.Units", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Int.isUnit_ne_iff_eq_neg", "kind": "theorem", "module": "Mathlib.Algebra.Group.Int.Units", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "Int.isUnit_eq_or_eq_neg", "kind": "theorem", "module": "Mathlib.Algebra.Group.Int.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.isUnit_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Int.Units", "is_tactic_proof": true, "tactics": ["refine", "rcases", "exact", "exact"], "tactic_count": 4}
{"name": "Int.eq_one_or_neg_one_of_mul_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Int.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.eq_one_or_neg_one_of_mul_eq_one'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Int.Units", "is_tactic_proof": true, "tactics": ["have", "obtain", "tauto"], "tactic_count": 3}
{"name": "Int.eq_of_mul_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Int.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.mul_eq_one_iff_eq_one_or_neg_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Int.Units", "is_tactic_proof": true, "tactics": ["refine", "rfl"], "tactic_count": 2}
{"name": "Int.eq_one_or_neg_one_of_mul_eq_neg_one'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Int.Units", "is_tactic_proof": true, "tactics": ["obtain", "exact", "simpa"], "tactic_count": 3}
{"name": "Int.mul_eq_neg_one_iff_eq_one_or_neg_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Int.Units", "is_tactic_proof": true, "tactics": ["refine", "obtain", "rfl"], "tactic_count": 3}
{"name": "Int.isUnit_iff_natAbs_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.Int.Units", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Int.ofNat_isUnit", "kind": "theorem", "module": "Mathlib.Algebra.Group.Int.Units", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Int.isUnit_mul_self", "kind": "theorem", "module": "Mathlib.Algebra.Group.Int.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.isUnit_add_isUnit_eq_isUnit_add_isUnit", "kind": "theorem", "module": "Mathlib.Algebra.Group.Int.Units", "is_tactic_proof": true, "tactics": ["rw", "lia"], "tactic_count": 2}
{"name": "Int.eq_one_or_neg_one_of_mul_eq_neg_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Int.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitOfInvertible", "kind": "definition", "module": "Mathlib.Algebra.Group.Invertible.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isUnit_of_invertible", "kind": "theorem", "module": "Mathlib.Algebra.Group.Invertible.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.invertible", "kind": "instance", "module": "Mathlib.Algebra.Group.Invertible.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "invOf_units", "kind": "theorem", "module": "Mathlib.Algebra.Group.Invertible.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUnit.nonempty_invertible", "kind": "theorem", "module": "Mathlib.Algebra.Group.Invertible.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUnit.invertible", "kind": "definition", "module": "Mathlib.Algebra.Group.Invertible.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nonempty_invertible_iff_isUnit", "kind": "theorem", "module": "Mathlib.Algebra.Group.Invertible.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.invOf_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Invertible.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.invOf_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Invertible.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "commute_invOf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Invertible.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "invertibleOfInvertibleMul", "kind": "abbrev", "module": "Mathlib.Algebra.Group.Invertible.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "invertibleOfMulInvertible", "kind": "abbrev", "module": "Mathlib.Algebra.Group.Invertible.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Invertible.mulLeft", "kind": "definition", "module": "Mathlib.Algebra.Group.Invertible.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Invertible.mulRight", "kind": "definition", "module": "Mathlib.Algebra.Group.Invertible.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MulOpposite.instCommSemigroup", "kind": "instance", "module": "Mathlib.Algebra.Group.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instMulOne", "kind": "instance", "module": "Mathlib.Algebra.Group.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instMulOneClass", "kind": "instance", "module": "Mathlib.Algebra.Group.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instLeftCancelMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instRightCancelMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instCancelMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instCommMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instCancelCommMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instDivInvMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instDivisionMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instDivisionCommMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instGroup", "kind": "instance", "module": "Mathlib.Algebra.Group.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instCommGroup", "kind": "instance", "module": "Mathlib.Algebra.Group.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.op_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.unop_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.op_zpow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.unop_zpow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.unop_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.op_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Opposite", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MulOpposite.semiconjBy_op", "kind": "theorem", "module": "Mathlib.Algebra.Group.Opposite", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MulOpposite.semiconjBy_unop", "kind": "theorem", "module": "Mathlib.Algebra.Group.Opposite", "is_tactic_proof": true, "tactics": ["conv_rhs"], "tactic_count": 1}
{"name": "SemiconjBy.op", "kind": "theorem", "module": "Mathlib.Algebra.Group.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiconjBy.unop", "kind": "theorem", "module": "Mathlib.Algebra.Group.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.op", "kind": "theorem", "module": "Mathlib.Algebra.Group.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.unop", "kind": "theorem", "module": "Mathlib.Algebra.Group.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.commute_op", "kind": "theorem", "module": "Mathlib.Algebra.Group.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.commute_unop", "kind": "theorem", "module": "Mathlib.Algebra.Group.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.isDedekindFiniteMonoid_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Opposite", "is_tactic_proof": true, "tactics": ["simp_rw", "simpa"], "tactic_count": 2}
{"name": "MulOpposite.instIsDedekindFiniteMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddOpposite.instSemigroup", "kind": "instance", "module": "Mathlib.Algebra.Group.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddOpposite.instLeftCancelSemigroup", "kind": "instance", "module": "Mathlib.Algebra.Group.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddOpposite.instRightCancelSemigroup", "kind": "instance", "module": "Mathlib.Algebra.Group.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddOpposite.instCommSemigroup", "kind": "instance", "module": "Mathlib.Algebra.Group.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddOpposite.instMulOneClass", "kind": "instance", "module": "Mathlib.Algebra.Group.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddOpposite.pow", "kind": "instance", "module": "Mathlib.Algebra.Group.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddOpposite.op_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddOpposite.unop_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddOpposite.instMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddOpposite.instCommMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddOpposite.instDivInvMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddOpposite.instGroup", "kind": "instance", "module": "Mathlib.Algebra.Group.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddOpposite.instCommGroup", "kind": "instance", "module": "Mathlib.Algebra.Group.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddOpposite.instMulTorsionFree", "kind": "instance", "module": "Mathlib.Algebra.Group.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ppow_add", "kind": "theorem", "module": "Mathlib.Algebra.Group.PNatPowAssoc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ppow_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.PNatPowAssoc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ppow_mul_assoc", "kind": "theorem", "module": "Mathlib.Algebra.Group.PNatPowAssoc", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ppow_mul_comm", "kind": "theorem", "module": "Mathlib.Algebra.Group.PNatPowAssoc", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "Prod.instPNatPowAssoc", "kind": "instance", "module": "Mathlib.Algebra.Group.PNatPowAssoc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ppow_eq_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.PNatPowAssoc", "is_tactic_proof": true, "tactics": ["induction", "one", "succ"], "tactic_count": 3}
{"name": "PUnit.commGroup", "kind": "instance", "module": "Mathlib.Algebra.Group.PUnit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PUnit.instOne_mathlib", "kind": "instance", "module": "Mathlib.Algebra.Group.PUnit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PUnit.instMul_mathlib", "kind": "instance", "module": "Mathlib.Algebra.Group.PUnit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PUnit.instDiv_mathlib", "kind": "instance", "module": "Mathlib.Algebra.Group.PUnit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PUnit.instInv_mathlib", "kind": "instance", "module": "Mathlib.Algebra.Group.PUnit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PUnit.one_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.PUnit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PUnit.mul_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.PUnit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PUnit.div_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.PUnit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PUnit.inv_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.PUnit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.semigroup", "kind": "instance", "module": "Mathlib.Algebra.Group.Pi.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Pi.mulOneClass", "kind": "instance", "module": "Mathlib.Algebra.Group.Pi.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.invOneClass", "kind": "instance", "module": "Mathlib.Algebra.Group.Pi.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Pi.divInvMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.Pi.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.divInvOneMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.Pi.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.involutiveInv", "kind": "instance", "module": "Mathlib.Algebra.Group.Pi.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.divisionMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.Pi.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.divisionCommMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.Pi.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.group", "kind": "instance", "module": "Mathlib.Algebra.Group.Pi.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Pi.instIsLeftCancelMul", "kind": "instance", "module": "Mathlib.Algebra.Group.Pi.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instIsRightCancelMul", "kind": "instance", "module": "Mathlib.Algebra.Group.Pi.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instIsCancelMul", "kind": "instance", "module": "Mathlib.Algebra.Group.Pi.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.leftCancelSemigroup", "kind": "instance", "module": "Mathlib.Algebra.Group.Pi.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.rightCancelSemigroup", "kind": "instance", "module": "Mathlib.Algebra.Group.Pi.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.leftCancelMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.Pi.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.rightCancelMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.Pi.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.cancelMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.Pi.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.cancelCommMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.Pi.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.extend_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pi.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.extend_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pi.Basic", "is_tactic_proof": true, "tactics": ["classical", "funext", "simp"], "tactic_count": 3}
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{"name": "Function.comp_eq_const_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pi.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.comp_eq_one_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pi.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Function.comp_ne_one_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pi.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniqueOfSurjectiveOne", "kind": "definition", "module": "Mathlib.Algebra.Group.Pi.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsingleton.pi_mulSingle_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pi.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.elim_one_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pi.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.elim_mulSingle_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pi.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Sum.elim_one_mulSingle", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pi.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Sum.elim_inv_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pi.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.elim_mul_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pi.Basic", "is_tactic_proof": true, "tactics": ["ext", "cases"], "tactic_count": 2}
{"name": "Sum.elim_div_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pi.Basic", "is_tactic_proof": true, "tactics": ["ext", "cases"], "tactic_count": 2}
{"name": "Set.range_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pi.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.preimage_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pi.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instIsMulTorsionFree", "kind": "instance", "module": "Mathlib.Algebra.Group.Pi.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.one_mono", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pi.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.one_anti", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pi.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulHom.coe_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pi.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.mulHom", "kind": "definition", "module": "Mathlib.Algebra.Group.Pi.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.mulHom_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pi.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.monoidHom", "kind": "definition", "module": "Mathlib.Algebra.Group.Pi.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.monoidHom_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pi.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.evalMulHom", "kind": "definition", "module": "Mathlib.Algebra.Group.Pi.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.constMulHom", "kind": "definition", "module": "Mathlib.Algebra.Group.Pi.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulHom.coeFn", "kind": "definition", "module": "Mathlib.Algebra.Group.Pi.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulHom.compLeft", "kind": "definition", "module": "Mathlib.Algebra.Group.Pi.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.evalMonoidHom", "kind": "definition", "module": "Mathlib.Algebra.Group.Pi.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.coe_evalMonoidHom", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pi.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.constMonoidHom", "kind": "definition", "module": "Mathlib.Algebra.Group.Pi.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.coeFn", "kind": "definition", "module": "Mathlib.Algebra.Group.Pi.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.compLeft", "kind": "definition", "module": "Mathlib.Algebra.Group.Pi.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OneHom.mulSingle", "kind": "definition", "module": "Mathlib.Algebra.Group.Pi.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OneHom.mulSingle_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pi.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OneHom.coe_mulSingle", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pi.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.mulSingle", "kind": "definition", "module": "Mathlib.Algebra.Group.Pi.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.mulSingle_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pi.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.coe_mulSingle", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pi.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.mulSingle_sup", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pi.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.mulSingle_inf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pi.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.mulSingle_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pi.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.mulSingle_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pi.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.mulSingle_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pi.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.mulSingle_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pi.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.mulSingle_zpow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pi.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.mulSingle_commute", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pi.Lemmas", "is_tactic_proof": true, "tactics": ["intro", "by_cases"], "tactic_count": 2}
{"name": "Pi.mulSingle_apply_commute", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pi.Lemmas", "is_tactic_proof": true, "tactics": ["obtain", "rfl", "exact"], "tactic_count": 3}
{"name": "Pi.update_eq_div_mul_mulSingle", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pi.Lemmas", "is_tactic_proof": true, "tactics": ["ext", "rcases", "simp", "simp"], "tactic_count": 4}
{"name": "Pi.mulSingle_mul_mulSingle_eq_mulSingle_mul_mulSingle", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pi.Lemmas", "is_tactic_proof": true, "tactics": ["refine", "have", "have", "have", "have", "grind", "aesop"], "tactic_count": 7}
{"name": "SemiconjBy.pi", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pi.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.semiconjBy_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pi.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.pi", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pi.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.commute_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pi.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.update_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pi.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.update_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pi.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.update_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pi.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.update_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pi.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.const_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pi.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.const_ne_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pi.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.piecewise_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pi.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.piecewise_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pi.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.piecewise_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pi.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.ExtendByOne.hom", "kind": "definition", "module": "Mathlib.Algebra.Group.Pi.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.mulSingle_mono", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pi.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.mulSingle_strictMono", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pi.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.mulSingle_comp_equiv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pi.Lemmas", "is_tactic_proof": true, "tactics": ["ext", "aesop"], "tactic_count": 2}
{"name": "Sigma.curry_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pi.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.uncurry_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pi.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.curry_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pi.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.uncurry_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pi.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.curry_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pi.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.uncurry_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pi.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.curry_mulSingle", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pi.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Sigma.uncurry_mulSingle_mulSingle", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pi.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MulEquiv.piUnits", "kind": "definition", "module": "Mathlib.Algebra.Group.Pi.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.isUnit_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pi.Units", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Pi.instSubsingletonUnits", "kind": "instance", "module": "Mathlib.Algebra.Group.Pi.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUnit.val_inv_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pi.Units", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.one", "kind": "definition", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.coe_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.coe_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.one_subset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.singleton_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.one_mem_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.one_nonempty", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.map_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.subset_one_iff_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Nonempty.subset_one_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.singletonOneHom", "kind": "definition", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.coe_singletonOneHom", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.singletonOneHom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.imageOneHom", "kind": "definition", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sup_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sup'_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inf_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inf'_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.max_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.min_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.max'_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.min'_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image_op_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.map_op_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.one_product_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finset.inv", "kind": "definition", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inv_def", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image_inv_eq_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inv_mem_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_inv_le", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inv_empty", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inv_nonempty_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inv_eq_empty", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inv_subset_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inv_singleton", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inv_insert", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sup_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sup'_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inf_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inf'_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image_op_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.map_op_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.mem_inv'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.inv_filter", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finset.inv_filter_univ", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.coe_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.preimage_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inv_univ", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finset.inv_inter", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inv_product", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mul", "kind": "definition", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mul_def", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image_mul_product", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.coe_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mul_mem_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_mul_le", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_mul_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.empty_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mul_empty", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mul_eq_empty", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mul_nonempty", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Nonempty.mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Nonempty.of_mul_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Nonempty.of_mul_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.singleton_mul_singleton", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mul_subset_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mul_subset_mul_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mul_subset_mul_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.instMulLeftMono", "kind": "instance", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.instMulRightMono", "kind": "instance", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mul_subset_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.union_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mul_union", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inter_mul_subset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mul_inter_subset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inter_mul_union_subset_union", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.union_mul_inter_subset_union", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.subset_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image_op_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.product_mul_product_comm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.map_op_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.singletonMulHom", "kind": "definition", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.coe_singletonMulHom", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.singletonMulHom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.imageMulHom", "kind": "definition", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sup_mul_le", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sup_mul_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sup_mul_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.le_inf_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inf_mul_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inf_mul_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_le_card_mul_left_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_le_card_mul_right_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.div", "kind": "definition", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.div_def", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image_div_product", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.coe_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.div_mem_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_div_le", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.empty_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.div_empty", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.div_eq_empty", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.div_nonempty", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Nonempty.div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Nonempty.of_div_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Nonempty.of_div_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.div_singleton", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.singleton_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.singleton_div_singleton", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.div_subset_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.div_subset_div_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.div_subset_div_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.div_subset_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.union_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.div_union", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inter_div_subset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.div_inter_subset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inter_div_union_subset_union", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.union_div_inter_subset_union", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.subset_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sup_div_le", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sup_div_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sup_div_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.le_inf_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inf_div_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inf_div_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.nsmul", "kind": "definition", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.npow", "kind": "definition", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.zsmul", "kind": "definition", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.zpow", "kind": "definition", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.semigroup", "kind": "definition", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.commSemigroup", "kind": "definition", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inter_mul_union_subset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.union_mul_inter_subset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mulOneClass", "kind": "definition", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.subset_mul_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.subset_mul_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.singletonMonoidHom", "kind": "definition", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.coe_singletonMonoidHom", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.singletonMonoidHom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.coeMonoidHom", "kind": "definition", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.coe_coeMonoidHom", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.coeMonoidHom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.imageMonoidHom", "kind": "definition", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.coe_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": true, "tactics": ["change", "induction", "zero", "succ"], "tactic_count": 4}
{"name": "Finset.monoid", "kind": "definition", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.pow_right_monotone", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.pow_subset_pow_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.pow_subset_pow_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.pow_subset_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.subset_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.pow_subset_pow_mul_of_sq_subset_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.empty_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Nonempty.pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.pow_eq_empty", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": true, "tactics": ["constructor", "contrapose", "rintro", "exact", "simp", "rintro", "exact"], "tactic_count": 7}
{"name": "Finset.singleton_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.pow_mem_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.one_mem_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.inter_pow_subset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "Finset.coe_list_prod", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_prod_list_ofFn", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Finset.mem_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.card_pow_le", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mul_univ_of_one_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.univ_mul_of_one_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.univ_mul_univ", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.univ_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUnit.finset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image_op_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.map_op_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.product_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.commMonoid", "kind": "definition", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.coe_zpow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mul_eq_one_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Finset.divisionMonoid", "kind": "definition", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.isUnit_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "obtain", "refine", "rw", "exact", "rintro", "exact"], "tactic_count": 8}
{"name": "Finset.isUnit_coe", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Finset.univ_div_univ", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.subset_div_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.inv_subset_div_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.empty_zpow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Finset.Nonempty.zpow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.zpow_eq_empty", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": true, "tactics": ["constructor", "contrapose", "rintro", "exact", "simp", "rintro", "exact"], "tactic_count": 7}
{"name": "Finset.singleton_zpow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Finset.divisionCommMonoid", "kind": "definition", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.one_mem_div_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.one_mem_inv_mul_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Finset.one_notMem_div_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.one_notMem_inv_mul_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Nonempty.one_mem_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.isUnit_singleton", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.isUnit_iff_singleton", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.isUnit_iff_singleton_aux", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.image_mul_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image_mul_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image_mul_left'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.image_mul_right'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.image_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.preimage_mul_left_singleton", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finset.preimage_mul_right_singleton", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finset.preimage_mul_left_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finset.preimage_mul_right_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finset.preimage_mul_left_one'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.preimage_mul_right_one'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.image_pow_of_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Nontrivial.mul_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "Finset.Nontrivial.mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_singleton_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.singleton_mul_inter", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_le_card_mul_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_le_card_mul_self", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Finset.Nontrivial.mul_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "Finset.card_mul_singleton", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inter_mul_singleton", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_le_card_mul_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_le_card_mul_self'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Finset.Nontrivial.pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Nonempty.card_pow_mono", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_pow_mono", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": true, "tactics": ["obtain", "simp", "exact"], "tactic_count": 3}
{"name": "Finset.card_le_card_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.card_le_card_div_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_le_card_div_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_le_card_div_self", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Fintype.piFinset_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.piFinset_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.piFinset_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instFintypeOne", "kind": "instance", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.toFinset_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.toFinset_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.coe_prod", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_inv_index", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_neg_index", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sum_inv_index", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.dens_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Density", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.dens_smul_finset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Density", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.Icc_mul_Icc_subset'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Iic_mul_Iic_subset'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ici_mul_Ici_subset'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Icc_mul_Ico_subset'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ico_mul_Icc_subset'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ioc_mul_Ico_subset'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ico_mul_Ioc_subset'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Iic_mul_Iio_subset'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Iio_mul_Iic_subset'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ioi_mul_Ici_subset'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ici_mul_Ioi_subset'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.smul", "kind": "definition", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.smul_def", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image_smul_product", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_smul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.coe_smul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.smul_mem_smul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_smul_le", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.empty_smul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.smul_empty", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.smul_eq_empty", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.smul_nonempty_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Nonempty.smul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Nonempty.of_smul_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Nonempty.of_smul_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.smul_singleton", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.singleton_smul_singleton", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.smul_subset_smul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.smul_subset_smul_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.smul_subset_smul_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.smul_subset_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.union_smul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.smul_union", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inter_smul_subset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.smul_inter_subset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inter_smul_union_subset_union", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.union_smul_inter_subset_union", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.subset_smul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.smulFinset", "kind": "definition", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.smul_finset_def", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image_smul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_smul_finset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.coe_smul_finset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.smul_mem_smul_finset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.smul_finset_card_le", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.smul_finset_empty", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.smul_finset_eq_empty", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.smul_finset_nonempty", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Nonempty.smul_finset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.singleton_smul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.smul_finset_subset_smul_finset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.smul_finset_singleton", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.smul_finset_union", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.smul_finset_insert", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.smul_finset_inter_subset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.smul_finset_subset_smul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.biUnion_smul_finset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.vsub", "kind": "definition", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.vsub_def", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image_vsub_product", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_vsub", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.coe_vsub", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.vsub_mem_vsub", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.vsub_card_le", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.empty_vsub", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.vsub_empty", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.vsub_eq_empty", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.vsub_nonempty", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Nonempty.vsub", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Nonempty.of_vsub_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Nonempty.of_vsub_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.vsub_singleton", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.singleton_vsub", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.singleton_vsub_singleton", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.vsub_subset_vsub", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.vsub_subset_vsub_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.vsub_subset_vsub_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.vsub_subset_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.union_vsub", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.vsub_union", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inter_vsub_subset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.vsub_inter_subset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.subset_vsub", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.op_smul_finset_smul_eq_smul_smul_finset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Finset.image_smul_comm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.toFinset_smul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.toFinset_smul_set", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.toFinset_vsub", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LibraryNote.pointwise_nat_action", "kind": "definition", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.one", "kind": "definition", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.singleton_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.one_mem_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.one_subset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.one_nonempty", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subset_one_iff_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nonempty.subset_one_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.singletonOneHom", "kind": "definition", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.coe_singletonOneHom", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_op_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.one_prod_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Set.inv", "kind": "definition", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inv_setOf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inv_preimage", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inv_empty", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inv_univ", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inter_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.union_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.compl_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inv_prod", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inv_mem_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.nonempty_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nonempty.inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_inv_eq_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inv_eq_empty", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.involutiveInv", "kind": "instance", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inv_subset_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inv_subset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.inv_singleton", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.inv_insert", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.inv_range", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.image_inv_of_apply_inv_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.image_inv_of_apply_inv_eq_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["conv_rhs"], "tactic_count": 1}
{"name": "Set.forall_inv_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Set.exists_inv_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Set.image_op_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.mul", "kind": "definition", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image2_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mul_mem_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_mul_prod", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.empty_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mul_empty", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mul_eq_empty", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mul_nonempty", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nonempty.mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nonempty.of_mul_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nonempty.of_mul_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mul_singleton", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.singleton_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.singleton_mul_singleton", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mul_subset_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mul_subset_mul_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mul_subset_mul_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instMulLeftMono", "kind": "instance", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instMulRightMono", "kind": "instance", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mul_subset_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.union_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mul_union", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inter_mul_subset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mul_inter_subset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inter_mul_union_subset_union", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.union_mul_inter_subset_union", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.singletonMulHom", "kind": "definition", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.coe_singletonMulHom", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.singletonMulHom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_op_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.prod_mul_prod_comm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Set.div", "kind": "definition", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image2_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.div_mem_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_div_prod", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.empty_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.div_empty", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.div_eq_empty", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.div_nonempty", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nonempty.div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nonempty.of_div_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nonempty.of_div_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.div_singleton", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.singleton_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.singleton_div_singleton", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.div_subset_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.div_subset_div_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.div_subset_div_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.div_subset_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.union_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.div_union", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inter_div_subset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.div_inter_subset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inter_div_union_subset_union", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.union_div_inter_subset_union", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.NSMul", "kind": "definition", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.NPow", "kind": "definition", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ZSMul", "kind": "definition", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ZPow", "kind": "definition", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.semigroup", "kind": "definition", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.commSemigroup", "kind": "definition", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inter_mul_union_subset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.union_mul_inter_subset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mulOneClass", "kind": "definition", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subset_mul_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subset_mul_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.singletonMonoidHom", "kind": "definition", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.coe_singletonMonoidHom", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.singletonMonoidHom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.monoid", "kind": "definition", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.pow_right_monotone", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.pow_subset_pow_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.pow_subset_pow_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.pow_subset_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subset_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.pow_subset_pow_mul_of_sq_subset_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.empty_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nonempty.pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.pow_eq_empty", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["constructor", "contrapose", "rintro", "exact", "simp", "rintro", "exact"], "tactic_count": 7}
{"name": "Set.singleton_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.pow_mem_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.one_mem_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.inter_pow_subset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "Set.mul_univ_of_one_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.univ_mul_of_one_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.univ_mul_univ", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.univ_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUnit.set", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.prod_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nontrivial.mul_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "Set.Nontrivial.mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nontrivial.mul_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "Set.Nontrivial.pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.commMonoid", "kind": "definition", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mul_eq_one_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["refine", "have", "obtain", "obtain", "have", "refine", "exact", "exact", "rintro", "rw"], "tactic_count": 10}
{"name": "Set.nonempty_image_mulLeft_inv_inter_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.nonempty_image_mulRight_inv_inter_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.divisionMonoid", "kind": "definition", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.isUnit_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "obtain", "refine", "rw", "exact", "rintro", "exact"], "tactic_count": 8}
{"name": "Set.univ_div_univ", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.subset_div_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.inv_subset_div_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.empty_zpow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Set.Nonempty.zpow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.zpow_eq_empty", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["constructor", "contrapose", "rintro", "exact", "simp", "rintro", "exact"], "tactic_count": 7}
{"name": "Set.singleton_zpow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Set.divisionCommMonoid", "kind": "definition", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.one_mem_div_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.one_mem_inv_mul_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Set.one_notMem_div_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.one_notMem_inv_mul_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nonempty.one_mem_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.isUnit_singleton", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.isUnit_iff_singleton", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.image_mul_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.image_mul_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.image_mul_left'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.image_mul_right'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.preimage_mul_left_singleton", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.preimage_mul_right_singleton", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.preimage_mul_left_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.preimage_mul_right_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.preimage_mul_left_one'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.preimage_mul_right_one'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.mul_univ", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.univ_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.image_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mul_subset_range", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["rintro", "obtain", "obtain", "exact"], "tactic_count": 4}
{"name": "Set.preimage_mul_preimage_subset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "Set.preimage_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_pow_of_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.preimage_pow_subset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.div_subset_range", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["rintro", "obtain", "obtain", "exact"], "tactic_count": 4}
{"name": "Set.preimage_div_preimage_subset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "Set.preimage_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inv_pi", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Set.MapsTo.mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.MapsTo.inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.MapsTo.div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_list_prod", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_multiset_prod", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_finset_prod", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_finset_prod", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.BigOperators", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "simp_rw", "exact", "insert", "rw", "simp_rw", "simp_rw", "constructor", "rintro", "refine", "intro", "obtain", "rwa", "rw", "exact", "rw", "rintro", "exact"], "tactic_count": 20}
{"name": "Set.mem_pow_iff_prod", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.BigOperators", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.mem_fintype_prod", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.BigOperators", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Set.list_prod_mem_list_prod", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.BigOperators", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "simp_rw", "exact"], "tactic_count": 5}
{"name": "Set.list_prod_subset_list_prod", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.BigOperators", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "simp_rw", "exact"], "tactic_count": 5}
{"name": "Set.list_prod_singleton", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.multiset_prod_mem_multiset_prod", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.BigOperators", "is_tactic_proof": true, "tactics": ["induction", "simp_rw", "exact"], "tactic_count": 3}
{"name": "Set.multiset_prod_subset_multiset_prod", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.BigOperators", "is_tactic_proof": true, "tactics": ["induction", "simp_rw", "exact"], "tactic_count": 3}
{"name": "Set.multiset_prod_singleton", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.finset_prod_mem_finset_prod", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.finset_prod_subset_finset_prod", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.finset_prod_singleton", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_finset_prod_pi", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.BigOperators", "is_tactic_proof": true, "tactics": ["ext", "simp_rw"], "tactic_count": 2}
{"name": "Set.image_fintype_prod_pi", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.BigOperators", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Cardinal.mk_mul_le", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.natCard_mul_le", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Card", "is_tactic_proof": true, "tactics": ["obtain", "simp", "simp", "refine", "aesop"], "tactic_count": 5}
{"name": "Cardinal.mk_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.encard_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Card", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.ncard_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Card", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.natCard_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Card", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Cardinal.mk_div_le", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.natCard_div_le", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.mk_smul_set", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.encard_smul_set", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Card", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.ncard_smul_set", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Card", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.natCard_smul_set", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Card", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.finite_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.fintypeMul", "kind": "instance", "module": "Mathlib.Algebra.Group.Pointwise.Set.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.decidableMemMul", "kind": "instance", "module": "Mathlib.Algebra.Group.Pointwise.Set.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.decidableMemPow", "kind": "instance", "module": "Mathlib.Algebra.Group.Pointwise.Set.Finite", "is_tactic_proof": true, "tactics": ["induction", "zero", "simp", "infer_instance", "succ", "rw", "infer_instance"], "tactic_count": 7}
{"name": "Set.Finite.smul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.smul_set", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Infinite.of_smul_set", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.vsub", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.finite_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.infinite_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.finite_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Finite", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.infinite_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.fintypeDiv", "kind": "instance", "module": "Mathlib.Algebra.Group.Pointwise.Set.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.finite_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.infinite_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Group.card_pow_eq_card_pow_card_univ", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Finite", "is_tactic_proof": true, "tactics": ["have", "rcases", "refine", "rw", "have", "refine", "rintro", "exact", "have", "monotone_nat_of_le_succ", "refine", "le_antisymm", "replace", "have", "refine", "exact", "convert", "rw", "intro", "rwa"], "tactic_count": 20}
{"name": "Set.iInter_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sInter_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sUnion_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_mul_left_image", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_mul_right_image", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mul_iUnion", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sUnion_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mul_sUnion", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion₂_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mul_iUnion₂", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iInter_mul_subset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mul_iInter_subset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mul_sInter_subset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sInter_mul_subset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iInter₂_mul_subset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mul_iInter₂_subset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_div_left_image", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_div_right_image", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.div_iUnion", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sUnion_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.div_sUnion", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion₂_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.div_iUnion₂", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iInter_div_subset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.div_iInter_subset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sInter_div_subset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.div_sInter_subset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iInter₂_div_subset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.div_iInter₂_subset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_smul_left_image", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_smul_right_image", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_smul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smul_iUnion", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sUnion_smul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smul_sUnion", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion₂_smul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smul_iUnion₂", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iInter_smul_subset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smul_iInter_subset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sInter_smul_subset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smul_sInter_subset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iInter₂_smul_subset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smul_iInter₂_subset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_smul_set", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smul_set_iUnion", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smul_set_iUnion₂", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smul_set_sUnion", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.smul_set_iInter_subset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smul_set_sInter_subset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smul_set_iInter₂_subset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_vsub_left_image", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_vsub_right_image", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_vsub", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.vsub_iUnion", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sUnion_vsub", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.vsub_sUnion", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion₂_vsub", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.vsub_iUnion₂", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iInter_vsub_subset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.vsub_iInter_subset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sInter_vsub_subset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.vsub_sInter_subset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iInter₂_vsub_subset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.vsub_iInter₂_subset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_prod_list_ofFn", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.ListOfFn", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "simp_rw", "exists_exists_eq_and,"], "tactic_count": 5}
{"name": "Set.mem_list_prod", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.ListOfFn", "is_tactic_proof": false, "tactics": ["induction", "simp", "and_left_comm,", "constructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 8}
{"name": "Set.mem_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.ListOfFn", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.smulSet", "kind": "definition", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smul", "kind": "definition", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image2_smul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_smul_prod", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_smul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smul_mem_smul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.empty_smul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smul_empty", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smul_eq_empty", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smul_nonempty", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nonempty.smul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nonempty.of_smul_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nonempty.of_smul_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smul_singleton", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.singleton_smul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.singleton_smul_singleton", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smul_subset_smul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smul_subset_smul_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smul_subset_smul_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smul_subset_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.union_smul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smul_union", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inter_smul_subset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smul_inter_subset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inter_smul_union_subset_union", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.union_smul_inter_subset_union", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smul_set_subset_smul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_smul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_smul_set", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smul_mem_smul_set", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smul_set_empty", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smul_set_eq_empty", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smul_set_nonempty", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smul_set_singleton", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smul_set_mono", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smul_set_subset_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smul_set_union", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smul_set_insert", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smul_set_inter_subset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nonempty.smul_set", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smul_set_pi_of_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smul_set_univ_pi", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.range_smul_range", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smul_set_range", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.range_smul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.vsub", "kind": "instance", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image2_vsub", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_vsub_prod", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_vsub", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.vsub_mem_vsub", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.empty_vsub", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.vsub_empty", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.vsub_eq_empty", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.vsub_nonempty", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nonempty.vsub", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nonempty.of_vsub_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nonempty.of_vsub_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.vsub_singleton", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.singleton_vsub", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.singleton_vsub_singleton", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.vsub_subset_vsub", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.vsub_subset_vsub_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.vsub_subset_vsub_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.vsub_subset_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.vsub_self_mono", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.union_vsub", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.vsub_union", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inter_vsub_subset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.vsub_inter_subset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inter_vsub_union_subset_union", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.union_vsub_inter_subset_union", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_smul_comm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.op_smul_set_smul_eq_smul_smul_set", "kind": "theorem", "module": "Mathlib.Algebra.Group.Pointwise.Set.Scalar", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "small_set_zero", "kind": "instance", "module": "Mathlib.Algebra.Group.Pointwise.Set.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "small_set_one", "kind": "instance", "module": "Mathlib.Algebra.Group.Pointwise.Set.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "small_neg", "kind": "instance", "module": "Mathlib.Algebra.Group.Pointwise.Set.Small", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "small_add", "kind": "instance", "module": "Mathlib.Algebra.Group.Pointwise.Set.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "small_sub", "kind": "instance", "module": "Mathlib.Algebra.Group.Pointwise.Set.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "small_mul", "kind": "instance", "module": "Mathlib.Algebra.Group.Pointwise.Set.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "small_div", "kind": "instance", "module": "Mathlib.Algebra.Group.Pointwise.Set.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.one_mk_mul_one_mk", "kind": "theorem", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Prod.mk_one_mul_mk_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Prod.fst_mul_snd", "kind": "theorem", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instInvolutiveInv", "kind": "instance", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instSemigroup", "kind": "instance", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instCommSemigroup", "kind": "instance", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instMulOneClass", "kind": "instance", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instIsMulTorsionFree", "kind": "instance", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instDivInvMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instDivisionMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instDivisionCommMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instGroup", "kind": "instance", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instIsLeftCancelMul", "kind": "instance", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instIsRightCancelMul", "kind": "instance", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instIsCancelMul", "kind": "instance", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instLeftCancelSemigroup", "kind": "instance", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instRightCancelSemigroup", "kind": "instance", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instLeftCancelMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instRightCancelMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instCancelMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instCommMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instCancelCommMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instCommGroup", "kind": "instance", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiconjBy.prod", "kind": "theorem", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.semiconjBy_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.prod", "kind": "theorem", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.commute_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulHom.fst", "kind": "definition", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulHom.snd", "kind": "definition", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulHom.coe_fst", "kind": "theorem", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulHom.coe_snd", "kind": "theorem", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulHom.prod", "kind": "definition", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulHom.coe_prod", "kind": "theorem", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulHom.prod_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulHom.fst_comp_prod", "kind": "theorem", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulHom.snd_comp_prod", "kind": "theorem", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulHom.prod_unique", "kind": "theorem", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulHom.prodMap", "kind": "definition", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulHom.prodMap_def", "kind": "theorem", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulHom.coe_prodMap", "kind": "theorem", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulHom.prod_comp_prodMap", "kind": "theorem", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulHom.coprod", "kind": "definition", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulHom.coprod_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulHom.comp_coprod", "kind": "theorem", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.fst", "kind": "definition", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.snd", "kind": "definition", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.inl", "kind": "definition", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.inr", "kind": "definition", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.coe_fst", "kind": "theorem", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.coe_snd", "kind": "theorem", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.inl_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.inr_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.fst_comp_inl", "kind": "theorem", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.snd_comp_inl", "kind": "theorem", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.fst_comp_inr", "kind": "theorem", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.snd_comp_inr", "kind": "theorem", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.commute_inl_inr", "kind": "theorem", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.prod", "kind": "definition", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.coe_prod", "kind": "theorem", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.prod_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.fst_comp_prod", "kind": "theorem", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.snd_comp_prod", "kind": "theorem", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.prod_unique", "kind": "theorem", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.prodMap", "kind": "definition", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.prodMap_def", "kind": "theorem", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.coe_prodMap", "kind": "theorem", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.prod_comp_prodMap", "kind": "theorem", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.coprod", "kind": "definition", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.coprod_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.coprod_comp_inl", "kind": "theorem", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.coprod_comp_inr", "kind": "theorem", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.coprod_unique", "kind": "theorem", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.coprod_inl_inr", "kind": "theorem", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.comp_coprod", "kind": "theorem", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.prodComm", "kind": "definition", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.coe_prodComm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.coe_prodComm_symm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.prodAssoc", "kind": "definition", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.coe_prodAssoc", "kind": "theorem", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.coe_prodAssoc_symm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.prodProdProdComm", "kind": "definition", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.prodProdProdComm_toEquiv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.prodProdProdComm_symm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.prodCongr", "kind": "definition", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.uniqueProd", "kind": "definition", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.prodUnique", "kind": "definition", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.prodUnits", "kind": "definition", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.isUnit_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instSubsingletonUnits", "kind": "instance", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.embedProduct", "kind": "definition", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.embedProduct_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mulMulHom", "kind": "definition", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mulMonoidHom", "kind": "definition", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "divMonoidHom", "kind": "definition", "module": "Mathlib.Algebra.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiconjBy.inv_inv_symm_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Semiconj.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "SemiconjBy.inv_symm_left_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Semiconj.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "SemiconjBy.inv_right_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Semiconj.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SemiconjBy.zpow_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Semiconj.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiconjBy.eq_one_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Semiconj.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SemiconjBy", "kind": "definition", "module": "Mathlib.Algebra.Group.Semiconj.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiconjBy.eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.Semiconj.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiconjBy.mul_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Semiconj.Defs", "is_tactic_proof": true, "tactics": ["unfold", "rw"], "tactic_count": 2}
{"name": "SemiconjBy.mul_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Semiconj.Defs", "is_tactic_proof": true, "tactics": ["unfold", "rw"], "tactic_count": 2}
{"name": "SemiconjBy.transitive", "kind": "theorem", "module": "Mathlib.Algebra.Group.Semiconj.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiconjBy.one_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Semiconj.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SemiconjBy.one_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Semiconj.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiconjBy.reflexive", "kind": "theorem", "module": "Mathlib.Algebra.Group.Semiconj.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiconjBy.pow_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Semiconj.Defs", "is_tactic_proof": true, "tactics": ["induction", "zero", "rw", "exact", "succ", "rw", "exact"], "tactic_count": 7}
{"name": "SemiconjBy.conj_mk", "kind": "theorem", "module": "Mathlib.Algebra.Group.Semiconj.Defs", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "SemiconjBy.conj_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Semiconj.Defs", "is_tactic_proof": true, "tactics": ["unfold", "simp", "repeat", "rw"], "tactic_count": 4}
{"name": "semiconjBy_iff_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.Semiconj.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiconjBy.units_inv_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Semiconj.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiconjBy.units_inv_right_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Semiconj.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiconjBy.units_inv_symm_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Semiconj.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiconjBy.units_inv_symm_left_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Semiconj.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiconjBy.units_val", "kind": "theorem", "module": "Mathlib.Algebra.Group.Semiconj.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiconjBy.units_of_val", "kind": "theorem", "module": "Mathlib.Algebra.Group.Semiconj.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiconjBy.units_val_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Semiconj.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiconjBy.units_zpow_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Semiconj.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.mk_semiconjBy", "kind": "theorem", "module": "Mathlib.Algebra.Group.Semiconj.Units", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "Units.conj_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Semiconj.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.conj_pow'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Semiconj.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Shrink.instOne", "kind": "instance", "module": "Mathlib.Algebra.Group.Shrink", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Shrink.instMul", "kind": "instance", "module": "Mathlib.Algebra.Group.Shrink", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Shrink.instDiv", "kind": "instance", "module": "Mathlib.Algebra.Group.Shrink", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Shrink.instInv", "kind": "instance", "module": "Mathlib.Algebra.Group.Shrink", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Shrink.instPow", "kind": "instance", "module": "Mathlib.Algebra.Group.Shrink", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "equivShrink_symm_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Shrink", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "equivShrink_symm_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Shrink", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "equivShrink_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Shrink", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "equivShrink_symm_smul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Shrink", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "equivShrink_smul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Shrink", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "equivShrink_symm_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Shrink", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "equivShrink_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Shrink", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "equivShrink_symm_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Shrink", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "equivShrink_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Shrink", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Shrink.mulEquiv", "kind": "definition", "module": "Mathlib.Algebra.Group.Shrink", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Shrink.instSemigroup", "kind": "instance", "module": "Mathlib.Algebra.Group.Shrink", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Shrink.instCommSemigroup", "kind": "instance", "module": "Mathlib.Algebra.Group.Shrink", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Shrink.instIsLeftCancelMul", "kind": "instance", "module": "Mathlib.Algebra.Group.Shrink", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Shrink.instIsRightCancelMul", "kind": "instance", "module": "Mathlib.Algebra.Group.Shrink", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Shrink.instIsCancelMul", "kind": "instance", "module": "Mathlib.Algebra.Group.Shrink", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Shrink.instMulOneClass", "kind": "instance", "module": "Mathlib.Algebra.Group.Shrink", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Shrink.instMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.Shrink", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Shrink.instCommMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.Shrink", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Shrink.instGroup", "kind": "instance", "module": "Mathlib.Algebra.Group.Shrink", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Shrink.instCommGroup", "kind": "instance", "module": "Mathlib.Algebra.Group.Shrink", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Shrink.instMulAction", "kind": "instance", "module": "Mathlib.Algebra.Group.Shrink", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.instMulAction", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Actions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.smul_def", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Actions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.mk_smul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Actions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.smulCommClass_left", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Actions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.smulCommClass_right", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Actions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.instIsScalarTowerSubtypeMem", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Actions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.instFaithfulSMulSubtypeMem", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Actions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.instDistribMulActionSubtypeMem", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Actions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.instMulDistribMulActionSubtypeMem", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Actions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.center.smulCommClass_left", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Actions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.center.smulCommClass_right", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Actions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "div_mem_comm_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.div_mem_comm_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.prod", "kind": "definition", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.coe_prod", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.mem_prod", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.prod_mono", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.prod_mono_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.prod_mono_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.prod_top", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.top_prod", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.top_prod_top", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.bot_prod_bot", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.le_prod_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Subgroup.prod_le_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Subgroup.prod_eq_bot_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Subgroup.closure_prod", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.prodEquiv", "kind": "definition", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.pi", "kind": "definition", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.coe_pi", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.mem_pi", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.pi_top", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.pi_empty", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.pi_bot", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.le_pi_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.mulSingle_mem_pi", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.pi_eq_bot_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Subgroup.instIsMulTorsionFree", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.normal_of_characteristic", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroup.normal_of_characteristic", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.normal_top", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.normal_bot", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.characteristic_iff_comap_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.characteristic_iff_comap_le", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.characteristic_iff_le_comap", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.characteristic_iff_map_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Subgroup.characteristic_iff_map_le", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Subgroup.characteristic_iff_le_map", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Subgroup.botCharacteristic", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.topCharacteristic", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.normalizer_eq_top_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.normalizer_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.le_normalizer_comap", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.le_normalizer_map", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.comap_normalizer_eq_of_le_range", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": true, "tactics": ["apply", "rw", "apply", "rw"], "tactic_count": 4}
{"name": "Subgroup.subgroupOf_normalizer_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.normal_subgroupOf_iff_le_normalizer", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subgroup.normal_subgroupOf_iff_le_normalizer_inf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.normal_in_normalizer", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.le_normalizer_of_normal_subgroupOf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.subset_normalizer_of_normal", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.le_normalizer_of_normal", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.inf_normalizer_le_normalizer_inf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormalizerCondition", "kind": "definition", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "normalizerCondition_iff_only_full_group_self_normalizing", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": true, "tactics": ["apply", "simp", "tauto"], "tactic_count": 3}
{"name": "Group.conjugatesOfSet", "kind": "definition", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Group.mem_conjugatesOfSet_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Group.subset_conjugatesOfSet", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Group.conjugatesOfSet_mono", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Group.conjugates_subset_normal", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": true, "tactics": ["rintro", "obtain", "exact"], "tactic_count": 3}
{"name": "Group.conjugatesOfSet_subset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Group.conj_mem_conjugatesOfSet", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.normalClosure", "kind": "definition", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.conjugatesOfSet_subset_normalClosure", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.subset_normalClosure", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.le_normalClosure", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.normalClosure_normal", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.normalClosure_le_normal", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": true, "tactics": ["intro", "refine", "exact", "exact", "exact", "exact"], "tactic_count": 6}
{"name": "Subgroup.normalClosure_subset_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.normalClosure_mono", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.normalClosure_eq_iInf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.normalClosure_eq_self", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.normalClosure_idempotent", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.closure_le_normalClosure", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Subgroup.normalClosure_closure_eq_normalClosure", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.normalCore", "kind": "definition", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.normalCore_le", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.normalCore_normal", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.normal_le_normalCore", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.normalCore_mono", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.normalCore_eq_iSup", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.normalCore_eq_self", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.normalCore_idempotent", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.prodMap_comap_prod", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.ker_prodMap", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MonoidHom.ker_fst", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.ker_snd", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.Normal.map", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Subgroup.comap_normalizer_eq_of_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.map_equiv_normalizer_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp", "rw", "intro", "simp"], "tactic_count": 5}
{"name": "Subgroup.map_normalizer_eq_of_bijective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.liftOfRightInverseAux", "kind": "definition", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.liftOfRightInverseAux_comp_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "apply", "rw", "simp"], "tactic_count": 5}
{"name": "MonoidHom.liftOfRightInverse", "kind": "definition", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.liftOfSurjective", "kind": "abbrev", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.liftOfRightInverse_comp_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.liftOfRightInverse_comp", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.eq_liftOfRightInverse", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Subgroup.Normal.comap", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.normal_comap", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.Normal.subgroupOf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.normal_subgroupOf", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.map_normalClosure", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": true, "tactics": ["have", "apply", "simp", "exact"], "tactic_count": 4}
{"name": "Subgroup.comap_normalClosure", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": true, "tactics": ["have", "simp_all"], "tactic_count": 2}
{"name": "Subgroup.Normal.of_map_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.Normal.of_map_subtype", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.normal_subgroupOf_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.prod_subgroupOf_prod_normal", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.prod_normal", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.inf_subgroupOf_inf_normal_of_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "Subgroup.inf_subgroupOf_inf_normal_of_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "Subgroup.normal_inf_normal", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.normal_iInf_normal", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "intro", "exact"], "tactic_count": 5}
{"name": "Subgroup.SubgroupNormal.mem_comm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "Subgroup.commute_of_normal_of_disjoint", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": ["suffices", "change", "rw", "simpa", "apply", "constructor", "suffices", "exact", "change", "apply", "apply"], "tactic_count": 11}
{"name": "Subgroup.normal_subgroupOf_of_le_normalizer", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Subgroup.normal_subgroupOf_sup_of_le_normalizer", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsConj.normalClosure_eq_top_of", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": true, "tactics": ["obtain", "have", "rintro", "exact", "have", "rintro", "refine", "have", "rwa", "simp", "rw", "rw", "grw", "refine", "rw", "simp", "mem_comap]", "exact"], "tactic_count": 18}
{"name": "ConjClasses.noncenter", "kind": "definition", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjClasses.mem_noncenter", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroup.inertia", "kind": "definition", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroup.mem_inertia", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroup.subgroupOf_inertia", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroup.inertia_map_subtype", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HasMemOrInvMem.inv_mem_of_notMem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": true, "tactics": ["have", "simp_all"], "tactic_count": 2}
{"name": "HasMemOrInvMem.mem_of_inv_notMem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": true, "tactics": ["have", "simp_all"], "tactic_count": 2}
{"name": "inv_mem_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "div_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "zpow_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_inv_mem_iff_exists_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "exact"], "tactic_count": 3}
{"name": "mul_mem_cancel_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_mem_cancel_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InvMemClass.inv", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InvMemClass.coe_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubgroupClass.subset_union", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "SubgroupClass.div", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroupClass.zsmul", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubgroupClass.zpow", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubgroupClass.coe_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubgroupClass.toGroup", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubgroupClass.toCommGroup", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubgroupClass.subtype", "kind": "definition", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubgroupClass.subtype_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubgroupClass.subtype_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubgroupClass.coe_subtype", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "SubgroupClass.coe_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubgroupClass.coe_zpow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubgroupClass.inclusion", "kind": "definition", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubgroupClass.inclusion_self", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": true, "tactics": ["cases", "rfl"], "tactic_count": 2}
{"name": "SubgroupClass.inclusion_mk", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubgroupClass.inclusion_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": true, "tactics": ["cases", "rfl"], "tactic_count": 2}
{"name": "SubgroupClass.inclusion_inclusion", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": true, "tactics": ["cases", "rfl"], "tactic_count": 2}
{"name": "SubgroupClass.coe_inclusion", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubgroupClass.subtype_comp_inclusion", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.instSetLike", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.instPartialOrder", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.ofClass", "kind": "definition", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.instCanLiftSetCoeAndMemOfNatForallForallForallForallHMulForallForallInv", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.instSubgroupClass", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.mem_carrier", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.mem_mk", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.coe_set_mk", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.mk_le_mk", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.coe_toSubmonoid", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.mem_toSubmonoid", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.toSubmonoid_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.toSubmonoid_inj", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.toSubmonoid_strictMono", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.toSubmonoid_mono", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.toSubmonoid_le", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.coe_nonempty", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.copy", "kind": "definition", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.copy_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.ext", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.one_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.mul_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.inv_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.div_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.inv_mem_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.exists_inv_mem_iff_exists_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.mul_mem_cancel_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.mul_mem_cancel_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.pow_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.zpow_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.ofDiv", "kind": "definition", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.mul", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.one", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.inv", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.div", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroup.nsmul", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.npow", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroup.zsmul", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.zpow", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.coe_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.coe_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.coe_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.coe_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.coe_mk", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.coe_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.coe_zpow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": true, "tactics": ["dsimp"], "tactic_count": 1}
{"name": "Subgroup.mk_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.toGroup", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.toCommGroup", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.subtype", "kind": "definition", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.subtype_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.subtype_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.coe_subtype", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.inclusion", "kind": "definition", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.coe_inclusion", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.inclusion_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.inclusion_inj", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.subtype_comp_inclusion", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.normal_of_comm", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.Normal.conj_mem'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "Subgroup.Normal.mem_comm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "Subgroup.Normal.mem_comm_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.normalizer", "kind": "definition", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.setNormalizer", "kind": "definition", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.mem_normalizer_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.mem_normalizer_iff''", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subgroup.mem_normalizer_iff'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.le_normalizer", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.commGroup_isMulCommutative", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.mul_comm_of_mem_isMulCommutative", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.injOn_iff_map_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.square", "kind": "definition", "module": "Mathlib.Algebra.Group.Subgroup.Even", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.mem_square", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Even", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.coe_square", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Even", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.square", "kind": "definition", "module": "Mathlib.Algebra.Group.Subgroup.Even", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.square_toSubsemigroup", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Even", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.mem_square", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Even", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.coe_square", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Even", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.square", "kind": "definition", "module": "Mathlib.Algebra.Group.Subgroup.Even", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.square_toSubmonoid", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Even", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.mem_square", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Even", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.coe_square", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Even", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.instFintypeSubtypeMemOfDecidablePred", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.instFiniteSubtypeMem", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.list_prod_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.multiset_prod_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.multiset_noncommProd_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.prod_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.noncommProd_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.val_list_prod", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.val_multiset_prod", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.val_finset_prod", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.fintypeBot", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.card_bot", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Finite", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Subgroup.card_top", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.eq_of_le_of_card_ge", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.eq_top_of_le_card", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.eq_top_of_card_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Finite", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "Subgroup.card_eq_iff_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.eq_bot_of_card_le", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.eq_bot_of_card_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.card_le_one_iff_eq_bot", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.eq_bot_iff_card", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.one_lt_card_iff_ne_bot", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.card_le_card_group", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.card_le_of_le", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.card_map_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Finite", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "Subgroup.card_subtype", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.pi_mem_of_mulSingle_mem_aux", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.pi_mem_of_mulSingle_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.pi_le_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.closure_pi", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.mem_normalizer_fintype", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Finite", "is_tactic_proof": true, "tactics": ["haveI", "exact", "have", "have", "let", "conj_injective"], "tactic_count": 6}
{"name": "MonoidHom.decidableMemRange", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.fintypeMrange", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.fintypeRange", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_coeSort_mrange", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_coeSort_range", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.exists_finsupp_of_mem_closure_range", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Finsupp", "is_tactic_proof": true, "tactics": ["classical", "induction", "mem", "one", "mul", "obtain", "use", "rw", "simp", "simp", "inv", "obtain", "use", "rw", "simp", "simp"], "tactic_count": 16}
{"name": "Subgroup.exists_of_mem_closure_range", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Finsupp", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Subgroup.mem_closure_range_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Finsupp", "is_tactic_proof": true, "tactics": ["refine", "rintro", "exact"], "tactic_count": 3}
{"name": "Subgroup.mem_closure_range_iff_of_fintype", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Finsupp", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Subgroup.mem_closure_iff_of_fintype", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Finsupp", "is_tactic_proof": true, "tactics": ["conv_lhs", "exact"], "tactic_count": 2}
{"name": "MonoidHom.range", "kind": "definition", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.coe_range", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.mem_range", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.range_eq_map", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "MonoidHom.range_isMulCommutative", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.restrict_range", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MonoidHom.rangeRestrict", "kind": "definition", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.coe_rangeRestrict", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.coe_comp_rangeRestrict", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.subtype_comp_rangeRestrict", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.rangeRestrict_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.rangeRestrict_injective_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "MonoidHom.map_range", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MonoidHom.range_comp", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.range_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.range_eq_top_of_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.range_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.range_subtype", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.inclusion_range", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.subgroupOf_range_eq_of_le", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": true, "tactics": ["ext", "refine", "simp"], "tactic_count": 3}
{"name": "MonoidHom.ofLeftInverse", "kind": "definition", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.ofLeftInverse_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.ofLeftInverse_symm_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.ofInjective", "kind": "definition", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.ofInjective_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.apply_ofInjective_symm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.coe_toAdditive_range", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.coe_toMultiplicative_range", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.ker", "kind": "definition", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.ker_toSubmonoid", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.mem_ker", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.div_mem_ker_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": true, "tactics": ["constructor", "rw", "rw"], "tactic_count": 3}
{"name": "MonoidHom.coe_ker", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.ker_toHomUnits", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "MonoidHom.eq_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": true, "tactics": ["constructor", "rw", "rw"], "tactic_count": 3}
{"name": "MonoidHom.decidableMemKer", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.comap_ker", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.comap_bot", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.ker_restrict", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.ker_codRestrict", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.ker_rangeRestrict", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.ker_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.ker_id", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.ker_eq_top_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MonoidHom.range_eq_bot_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MonoidHom.ker_eq_bot_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.ker_subtype", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.ker_inclusion", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.ker_prod", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.range_le_ker_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.normal_ker", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.coe_toAdditive_ker", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.coe_toMultiplicative_ker", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.eqLocus", "kind": "definition", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.eqLocus_same", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.eqOn_closure", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.eq_of_eqOn_top", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.eq_of_eqOn_dense", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.map_eq_bot_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.map_eq_bot_iff_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subgroup.map_le_range", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.map_subtype_le", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.ker_le_comap", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.map_comap_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.comap_map_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": true, "tactics": ["refine", "intro", "rcases", "rw", "exact"], "tactic_count": 5}
{"name": "Subgroup.map_comap_eq_self", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Subgroup.map_comap_eq_self_of_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.comap_le_comap_of_le_range", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.comap_le_comap_of_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.comap_lt_comap_of_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Subgroup.comap_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.comap_map_eq_self", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Subgroup.comap_map_eq_self_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.map_le_map_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subgroup.map_le_map_iff'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Subgroup.map_eq_map_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Subgroup.map_eq_range_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subgroup.map_le_map_iff_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subgroup.map_subtype_le_map_subtype", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.MapSubtype.orderIso", "kind": "definition", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.MapSubtype.orderIso_symm_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.forall", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Subgroup.map_lt_map_iff_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.map_subtype_lt_map_subtype", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.map_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.map_injective_of_ker_le", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": true, "tactics": ["apply_fun", "rwa"], "tactic_count": 2}
{"name": "Subgroup.ker_subgroupMap", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.closure_preimage_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Subgroup.comap_sup_eq_of_le_range", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.comap_sup_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.subgroupOf_sup", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": false, "tactics": ["refine", "simp", "rw"], "tactic_count": 3}
{"name": "Subgroup.codisjoint_subgroupOf_sup", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "is_tactic_proof": true, "tactics": ["rw", "exacts"], "tactic_count": 2}
{"name": "Subgroup.toAddSubgroup", "kind": "definition", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Additive.mem_toAddSubgroup", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroup.toSubgroup'", "kind": "abbrev", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroup.mem_toSubgroup'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroup.toSubgroup", "kind": "definition", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiplicative.mem_toSubgroup", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.toAddSubgroup'", "kind": "abbrev", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.mem_toAddSubgroup'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.instTop", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.topEquiv", "kind": "definition", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.instBot", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.instInhabited", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.mem_bot", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.mem_top", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.coe_top", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.coe_bot", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.instUniqueSubtypeMemBot", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.top_toSubmonoid", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.bot_toSubmonoid", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.eq_bot_iff_forall", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.eq_bot_of_subsingleton", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw"], "tactic_count": 3}
{"name": "Subgroup.coe_eq_univ", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.coe_eq_singleton", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.nontrivial_iff_exists_ne_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Subgroup.exists_ne_one_of_nontrivial", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Subgroup.nontrivial_iff_ne_bot", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Subgroup.bot_or_nontrivial", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": true, "tactics": ["have", "tauto"], "tactic_count": 2}
{"name": "Subgroup.bot_or_exists_ne_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "Subgroup.ne_bot_iff_exists_ne_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Subgroup.instMin", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.coe_inf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.mem_inf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.instInfSet", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.coe_sInf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.mem_sInf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.mem_iInf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Subgroup.coe_iInf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Subgroup.instCompleteLattice", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.mem_sup_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.mem_sup_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.mul_mem_sup", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.mem_iSup_of_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.mem_sSup_of_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.subsingleton_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.nontrivial_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.instUniqueOfSubsingleton", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.instNontrivial", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.instNontrivialSubtypeMemTop", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Subgroup.eq_top_iff'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.closure", "kind": "definition", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.mem_closure", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.subset_closure", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.mem_closure_of_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.notMem_of_notMem_closure", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.closure_le", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.closure_eq_of_le", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.closure_induction", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.closure_induction₂", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": true, "tactics": ["induction", "mem", "induction", "mem", "one", "mul", "inv", "one", "mul", "inv"], "tactic_count": 10}
{"name": "Subgroup.closure_closure_coe_preimage", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.gi", "kind": "definition", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.closure_mono", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.closure_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.closure_empty", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.closure_univ", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.closure_union", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.sup_eq_closure", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Subgroup.closure_iUnion", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.closure_eq_bot_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.iSup_eq_closure", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Subgroup.mem_closure_singleton", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": ["refine", "intro", "rw", "exact", "exact", "rintro", "exact", "rintro", "exact"], "tactic_count": 9}
{"name": "Subgroup.closure_singleton_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Subgroup.mem_closure_singleton_self", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Subgroup.le_closure_toSubmonoid", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.closure_eq_top_of_mclosure_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.closure_insert_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Subgroup.closure_union_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subgroup.closure_diff_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subgroup.toAddSubgroup_closure", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroup.toSubgroup_closure", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.toAddSubgroup'_closure", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroup.toSubgroup'_closure", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.mem_biSup_of_directedOn", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": true, "tactics": ["refine", "suffices", "simpa", "refine", "simp", "exact", "rintro", "rcases", "exact", "rintro", "exact", "apply", "simp"], "tactic_count": 13}
{"name": "Subgroup.mem_iSup_of_directed", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": true, "tactics": ["have", "rw", "simp", "simp", "rw", "intro", "simp", "intro", "refine", "simp", "exact"], "tactic_count": 11}
{"name": "Subgroup.mem_iSup_prop", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "Subgroup.coe_iSup_of_directed", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.mem_sSup_of_directedOn", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": true, "tactics": ["haveI", "simp"], "tactic_count": 2}
{"name": "Subgroup.mem_sup", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.mem_sup'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.forall_mem_sup", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Subgroup.exists_mem_sup", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Subgroup.mem_sup_of_normal_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": true, "tactics": ["constructor", "intro", "refine", "rintro", "exact", "exact", "exact", "rintro", "exact", "rintro", "exact", "rintro"], "tactic_count": 12}
{"name": "Subgroup.mem_sup_of_normal_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": true, "tactics": ["have", "exact", "h.trans"], "tactic_count": 3}
{"name": "Subgroup.mem_closure_pair", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": true, "tactics": ["rw", "simp_rw"], "tactic_count": 2}
{"name": "Subgroup.disjoint_def", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.disjoint_def'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.disjoint_iff_mul_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.mul_injective_of_disjoint", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "is_tactic_proof": true, "tactics": ["intro", "rw", "replace", "rwa", "eq_comm,"], "tactic_count": 5}
{"name": "Subgroup.comap", "kind": "definition", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.coe_comap", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.mem_comap", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.comap_mono", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.comap_comap", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.comap_id", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "Subgroup.toAddSubgroup_comap", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroup.toSubgroup_comap", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.map", "kind": "definition", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.coe_map", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.map_toSubmonoid", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.mem_map", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.mem_map_of_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.apply_coe_mem_map", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.map_mono", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.map_id", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.map_map", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.map_one_eq_bot", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.mem_map_equiv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.mem_map_iff_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.map_equiv_eq_comap_symm'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.map_equiv_eq_comap_symm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.comap_equiv_eq_map_symm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.comap_equiv_eq_map_symm'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.map_symm_eq_iff_map_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": true, "tactics": ["constructor", "rw", "rw"], "tactic_count": 3}
{"name": "Subgroup.map_le_iff_le_comap", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.gc_map_comap", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.map_sup", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.map_iSup", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.map_inf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.map_iInf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": true, "tactics": ["apply", "simpa"], "tactic_count": 2}
{"name": "Subgroup.comap_sup_comap_le", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.iSup_comap_le", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.comap_inf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.comap_iInf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.map_inf_le", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.map_inf_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Subgroup.map_bot", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.disjoint_map", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subgroup.map_top_of_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": true, "tactics": ["rw", "intro", "obtain", "exact"], "tactic_count": 4}
{"name": "Subgroup.codisjoint_map", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subgroup.map_equiv_top", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.comap_top", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.subgroupOf", "kind": "definition", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.subgroupOfEquivOfLe", "kind": "definition", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.comap_subtype", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.comap_inclusion_subgroupOf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.coe_subgroupOf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.mem_subgroupOf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.subgroupOf_map_subtype", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.map_subgroupOf_eq_of_le", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Subgroup.bot_subgroupOf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.top_subgroupOf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.subgroupOf_bot_eq_bot", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.subgroupOf_bot_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.subgroupOf_self", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.subgroupOf_inj", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Subgroup.inf_subgroupOf_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.inf_subgroupOf_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subgroup.subgroupOf_eq_bot", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subgroup.subgroupOf_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subgroup.map_isMulCommutative", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.comap_injective_isMulCommutative", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.subgroupOf_isMulCommutative", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.comapSubgroup", "kind": "definition", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.coe_comapSubgroup", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.symm_comapSubgroup", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.mapSubgroup", "kind": "definition", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.coe_mapSubgroup", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.symm_mapSubgroup", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.comap_toSubmonoid", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.map_comap_le", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.le_comap_map", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.map_eq_comap_of_inverse", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.equivMapOfInjective", "kind": "definition", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.coe_equivMapOfInjective_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.subgroupComap", "kind": "definition", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.subgroupComap_surjective_of_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.subgroupMap", "kind": "definition", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.subgroupMap_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.subgroupCongr", "kind": "definition", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.subgroupCongr_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.subgroupCongr_symm_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.subgroupMap", "kind": "definition", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.coe_subgroupMap_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.subgroupMap_symm_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.closure_preimage_le", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.map_closure", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.surjOn_iff_le_map", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.equivMapOfInjective_coe_mulEquiv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Map", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "Subgroup.op", "kind": "definition", "module": "Mathlib.Algebra.Group.Subgroup.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.mem_op", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.op_toSubmonoid", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.op_toSubsemigroup", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.MulOpposite", "is_tactic_proof": true, "tactics": ["dsimp"], "tactic_count": 1}
{"name": "Subgroup.unop", "kind": "definition", "module": "Mathlib.Algebra.Group.Subgroup.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.mem_unop", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.unop_toSubmonoid", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.unop_toSubsemigroup", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.MulOpposite", "is_tactic_proof": true, "tactics": ["dsimp"], "tactic_count": 1}
{"name": "Subgroup.unop_op", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.op_unop", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.op_le_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.le_op_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.op_le_op_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.unop_le_unop_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.opEquiv", "kind": "definition", "module": "Mathlib.Algebra.Group.Subgroup.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.op_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.unop_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.op_inj", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.unop_inj", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.equivOp", "kind": "definition", "module": "Mathlib.Algebra.Group.Subgroup.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.op_normalizer", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.MulOpposite", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Subgroup.unop_normalizer", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.MulOpposite", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subgroup.instSMul", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.MulOppositeLemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.op_bot", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.MulOppositeLemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.op_eq_bot", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.MulOppositeLemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.unop_bot", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.MulOppositeLemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.unop_eq_bot", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.MulOppositeLemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.op_top", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.MulOppositeLemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.op_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.MulOppositeLemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.unop_top", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.MulOppositeLemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.unop_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.MulOppositeLemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.op_sup", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.MulOppositeLemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.unop_sup", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.MulOppositeLemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.op_inf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.MulOppositeLemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.unop_inf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.MulOppositeLemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.op_sSup", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.MulOppositeLemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.unop_sSup", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.MulOppositeLemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.op_sInf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.MulOppositeLemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.unop_sInf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.MulOppositeLemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.op_iSup", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.MulOppositeLemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.unop_iSup", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.MulOppositeLemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.op_iInf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.MulOppositeLemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.unop_iInf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.MulOppositeLemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.op_closure", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.MulOppositeLemmas", "is_tactic_proof": true, "tactics": ["simp_rw", "congr", "exact"], "tactic_count": 3}
{"name": "Subgroup.unop_closure", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.MulOppositeLemmas", "is_tactic_proof": true, "tactics": ["rw", "simp_rw"], "tactic_count": 2}
{"name": "Subgroup.instEncodableSubtypeMulOppositeMemOp", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.MulOppositeLemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.instCountableSubtypeMulOppositeMemOp", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.MulOppositeLemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.smul_opposite_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.MulOppositeLemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.normal_op", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.MulOppositeLemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Subgroup.op.instNormal", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.MulOppositeLemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.normal_unop", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.MulOppositeLemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subgroup.unop.instNormal", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.MulOppositeLemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mabs_mem_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Order", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "instIsModularLatticeSubgroup", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.NormalizerCondition.normal_of_coatom", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.isCoatom_comap", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.isCoatom_map", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.isCoatom_comap_of_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Order", "is_tactic_proof": true, "tactics": ["refine", "rwa", "intro", "specialize", "rw", "rw", "exact"], "tactic_count": 7}
{"name": "Subgroup.toIsOrderedMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.strictMono_topEquiv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.strictMono_subsemigroupCongr", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.strictMono_symm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Order", "is_tactic_proof": true, "tactics": ["intro", "simp"], "tactic_count": 2}
{"name": "inv_coe_set", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smul_coe_set", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Pointwise", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "coe_set_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "op_smul_coe_set", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Pointwise", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "coe_div_coe", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Pointwise", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.mul_subgroupClosure", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Pointwise", "is_tactic_proof": true, "tactics": ["rw", "have", "simp"], "tactic_count": 3}
{"name": "Set.subgroupClosure_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Pointwise", "is_tactic_proof": true, "tactics": ["rw", "have", "simp"], "tactic_count": 3}
{"name": "Set.pow_mul_subgroupClosure", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subgroupClosure_mul_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.inv_subset_closure", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.closure_toSubmonoid", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Pointwise", "is_tactic_proof": true, "tactics": ["refine", "refine", "closure_induction", "rwa", "simp"], "tactic_count": 5}
{"name": "Subgroup.toSubmonoid_zpowers", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Pointwise", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submonoid.powers_le_zpowers", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Pointwise", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Subgroup.closure_induction_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Pointwise", "is_tactic_proof": true, "tactics": ["revert", "simp_rw", "intro", "induction", "one", "mul_left", "cases", "inl", "inr"], "tactic_count": 9}
{"name": "Subgroup.closure_induction_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.closure_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Pointwise", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Subgroup.closure_singleton_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Pointwise", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subgroup.closure_induction''", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.iSup_induction", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Pointwise", "is_tactic_proof": true, "tactics": ["rw", "induction", "one", "mem", "obtain", "exact", "inv_mem", "obtain", "exact", "mul"], "tactic_count": 10}
{"name": "Subgroup.iSup_induction'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Pointwise", "is_tactic_proof": true, "tactics": ["suffices", "refine", "exact", "exact", "rintro", "exact"], "tactic_count": 6}
{"name": "Subgroup.closure_mul_le", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.closure_pow_le", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.closure_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.sup_eq_closure_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.set_mul_normalizer_comm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Pointwise", "is_tactic_proof": true, "tactics": ["rw", "simp", "congr", "exact"], "tactic_count": 4}
{"name": "Subgroup.set_mul_normal_comm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.coe_mul_of_left_le_normalizer_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Pointwise", "is_tactic_proof": true, "tactics": ["rw", "refine", "induction", "one", "mem", "inv_mem", "obtain", "simpa", "mul_mem_mul", "mul", "obtain", "obtain", "refine", "exact", "simp"], "tactic_count": 15}
{"name": "Subgroup.coe_mul_of_right_le_normalizer_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Pointwise", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subgroup.mul_normal", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.normal_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.mul_inf_assoc", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Pointwise", "is_tactic_proof": true, "tactics": ["ext", "simp", "constructor", "rintro", "refine", "exact", "rintro", "refine", "suffices", "exact"], "tactic_count": 10}
{"name": "Subgroup.inf_mul_assoc", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Pointwise", "is_tactic_proof": true, "tactics": ["ext", "simp", "constructor", "rintro", "refine", "exact", "rintro", "refine", "suffices", "exact"], "tactic_count": 10}
{"name": "Subgroup.sup_normal", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.smul_mem_of_mem_closure_of_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Pointwise", "is_tactic_proof": true, "tactics": ["induction", "one", "mem", "inv_mem", "mul"], "tactic_count": 5}
{"name": "Subgroup.smul_opposite_image_mul_preimage'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Pointwise", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Subgroup.smul_opposite_image_mul_preimage", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.pointwiseMulAction", "kind": "definition", "module": "Mathlib.Algebra.Group.Subgroup.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.pointwise_smul_def", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.coe_pointwise_smul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.pointwise_smul_toSubmonoid", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.smul_mem_pointwise_smul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.instCovariantClassHSMulLe", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.mem_smul_pointwise_iff_exists", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.smul_bot", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.smul_sup", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.smul_closure", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.pointwise_isCentralScalar", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.conj_smul_le_of_le", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Pointwise", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "Subgroup.conj_smul_subgroupOf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Pointwise", "is_tactic_proof": true, "tactics": ["refine", "rintro", "exact", "rintro", "exact"], "tactic_count": 5}
{"name": "Subgroup.smul_mem_pointwise_smul_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.mem_pointwise_smul_iff_inv_smul_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.mem_inv_pointwise_smul_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.pointwise_smul_le_pointwise_smul_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.pointwise_smul_subset_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.subset_pointwise_smul_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.smul_inf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Pointwise", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Subgroup.equivSMul", "kind": "definition", "module": "Mathlib.Algebra.Group.Subgroup.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.subgroup_mul_singleton", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Pointwise", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Subgroup.singleton_mul_subgroup", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Pointwise", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Subgroup.Normal.conjAct", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.Normal.conj_smul_eq_self", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.Normal.of_conjugate_fixed", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Pointwise", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "mul_assoc,", "exact"], "tactic_count": 5}
{"name": "Subgroup.normalCore_eq_iInf_conjAct", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Pointwise", "is_tactic_proof": true, "tactics": ["ext", "simp", "refine", "simpa"], "tactic_count": 4}
{"name": "Subgroup.conjAct_pointwise_smul_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Pointwise", "is_tactic_proof": true, "tactics": ["rw", "simp", "mem_normalizer_iff,"], "tactic_count": 3}
{"name": "Subgroup.conjAct_pointwise_smul_eq_self", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.zpowers", "kind": "definition", "module": "Mathlib.Algebra.Group.Subgroup.ZPowers.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.mem_zpowers", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.ZPowers.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.coe_zpowers", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.ZPowers.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.decidableMemZPowers", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.ZPowers.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.zpowers_eq_closure", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.ZPowers.Basic", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "Subgroup.mem_zpowers_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.ZPowers.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.zpow_mem_zpowers", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.ZPowers.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.npow_mem_zpowers", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.ZPowers.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.forall_zpowers", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.ZPowers.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.exists_zpowers", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.ZPowers.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.forall_mem_zpowers", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.ZPowers.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.exists_mem_zpowers", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.ZPowers.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.map_zpowers", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.ZPowers.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.mem_zmultiples_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.ZPowers.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.zmultiples_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.ZPowers.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "ofMul_image_zpowers_eq_zmultiples_ofMul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.ZPowers.Basic", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "ofAdd_image_zmultiples_eq_zpowers_ofAdd", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.ZPowers.Basic", "is_tactic_proof": true, "tactics": ["symm", "rw", "exact"], "tactic_count": 3}
{"name": "Subgroup.zpowers_isMulCommutative", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.ZPowers.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.zpowers_le", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.ZPowers.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subgroup.zpowers_eq_bot", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.ZPowers.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subgroup.zpowers_ne_bot", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.ZPowers.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.zpowers_one_eq_bot", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.ZPowers.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.zpowers_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.ZPowers.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.zmultiples_natAbs", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.ZPowers.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Int.addSubgroupClosure_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.ZPowers.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Subgroup.range_zpowersHom", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.ZPowers.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.instCountableSubtypeMemZpowers", "kind": "instance", "module": "Mathlib.Algebra.Group.Subgroup.ZPowers.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroup.range_zmultiplesHom", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.ZPowers.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroup.intCast_mul_mem_zmultiples", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.ZPowers.Lemmas", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "AddSubgroup.intCast_mem_zmultiples_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.ZPowers.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.range_castAddHom", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subgroup.ZPowers.Lemmas", "is_tactic_proof": true, "tactics": ["ext", "simp_rw"], "tactic_count": 2}
{"name": "Submonoid.instInfSet", "kind": "instance", "module": "Mathlib.Algebra.Group.Submonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.coe_sInf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.mem_sInf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.mem_iInf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Submonoid.coe_iInf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Submonoid.instCompleteLattice", "kind": "instance", "module": "Mathlib.Algebra.Group.Submonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.closure", "kind": "definition", "module": "Mathlib.Algebra.Group.Submonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.mem_closure", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.subset_closure", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.mem_closure_of_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.notMem_of_notMem_closure", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.closure_le", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.closure_mono", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.closure_eq_of_le", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.closure_induction", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.closure_induction₂", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Basic", "is_tactic_proof": true, "tactics": ["induction", "mem", "induction", "mem", "one", "mul", "one", "mul"], "tactic_count": 8}
{"name": "Submonoid.dense_induction", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Basic", "is_tactic_proof": true, "tactics": ["induction", "mem", "one", "mul"], "tactic_count": 4}
{"name": "Submonoid._example", "kind": "example", "module": "Mathlib.Algebra.Group.Submonoid.Basic", "is_tactic_proof": true, "tactics": ["induction", "closure", "mem", "one", "mul"], "tactic_count": 5}
{"name": "Submonoid.closure_eq_one_union", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Basic", "is_tactic_proof": true, "tactics": ["apply", "intro", "induction", "mem", "one", "mul", "push", "obtain", "all_goals", "exact", "rintro", "exact", "exact"], "tactic_count": 13}
{"name": "Submonoid.gi", "kind": "definition", "module": "Mathlib.Algebra.Group.Submonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.closure_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.closure_empty", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.closure_univ", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.closure_union", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.sup_eq_closure", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Submonoid.closure_iUnion", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.closure_singleton_le_iff_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submonoid.closure_insert_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "Submonoid.mem_iSup", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Submonoid.iSup_eq_closure", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Submonoid.disjoint_def", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Submonoid.disjoint_def'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.closure_sdiff_eq_closure", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Basic", "is_tactic_proof": true, "tactics": ["refine", "by_cases", "exact", "rw", "exact"], "tactic_count": 5}
{"name": "Submonoid.closure_sdiff_singleton_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.eqOn_closureM", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.eq_of_eqOn_denseM", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUnit.submonoid", "kind": "definition", "module": "Mathlib.Algebra.Group.Submonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUnit.mem_submonoid_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Basic", "is_tactic_proof": true, "tactics": ["change", "rw"], "tactic_count": 2}
{"name": "MonoidHom.ofClosureMEqTopLeft", "kind": "definition", "module": "Mathlib.Algebra.Group.Submonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.coe_ofClosureMEqTopLeft", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.ofClosureMEqTopRight", "kind": "definition", "module": "Mathlib.Algebra.Group.Submonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.coe_ofClosureMEqTopRight", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubmonoidClass.coe_list_prod", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubmonoidClass.coe_multiset_prod", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubmonoidClass.coe_finset_prod", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "list_prod_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.BigOperators", "is_tactic_proof": true, "tactics": ["lift", "rw", "exact"], "tactic_count": 3}
{"name": "multiset_prod_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.BigOperators", "is_tactic_proof": true, "tactics": ["lift", "rw", "exact"], "tactic_count": 3}
{"name": "prod_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.coe_list_prod", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.coe_multiset_prod", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.coe_finset_prod", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.list_prod_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.multiset_prod_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.multiset_noncommProd_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.BigOperators", "is_tactic_proof": false, "tactics": ["induction", "h", "simp", "exact"], "tactic_count": 4}
{"name": "Submonoid.prod_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.noncommProd_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.BigOperators", "is_tactic_proof": true, "tactics": ["apply", "intro", "rw", "rintro", "exact"], "tactic_count": 5}
{"name": "Submonoid.mem_closure_iff_exists_finset_subset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.mem_closure_finset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pow_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.toSubsemigroup_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.toSubsemigroup_inj", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.instSetLike", "kind": "instance", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.instPartialOrder", "kind": "instance", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.ofClass", "kind": "definition", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.instCanLiftSetCoeAndMemOfNatForallForallForallForallHMul", "kind": "instance", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.instSubmonoidClass", "kind": "instance", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.mem_toSubsemigroup", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.mem_carrier", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.mem_mk", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.coe_set_mk", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.mk_le_mk", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.ext", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.copy", "kind": "definition", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.coe_copy", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.copy_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.one_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.mul_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.instTop", "kind": "instance", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.instBot", "kind": "instance", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.instInhabited", "kind": "instance", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.mem_bot", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.mem_top", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.coe_top", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.coe_bot", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.mk_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Submonoid.mk_eq_bot", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Submonoid.instMin", "kind": "instance", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.coe_inf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.mem_inf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.subsingleton_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.nontrivial_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.instUniqueOfSubsingleton", "kind": "instance", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.instNontrivial", "kind": "instance", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.eqLocusM", "kind": "definition", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.mem_eqLocusM", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.eqLocusM_same", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.eq_of_eqOn_topM", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OneMemClass.one", "kind": "instance", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OneMemClass.coe_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OneMemClass.coe_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OneMemClass.one_def", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoidClass.nSMul", "kind": "instance", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubmonoidClass.nPow", "kind": "instance", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubmonoidClass.coe_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubmonoidClass.mk_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubmonoidClass.toMulOneClass", "kind": "instance", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubmonoidClass.instIsDedekindFiniteMonoidSubtypeMem", "kind": "instance", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubmonoidClass.toMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubmonoidClass.toCommMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubmonoidClass.subtype", "kind": "definition", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubmonoidClass.subtype_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubmonoidClass.subtype_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubmonoidClass.coe_subtype", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.mul", "kind": "instance", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.one", "kind": "instance", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.coe_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.coe_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.mk_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Submonoid.mk_mul_mk", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.mul_def", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.one_def", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.toMulOneClass", "kind": "instance", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.pow_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.toMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.toCommMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.subtype", "kind": "definition", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.subtype_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.subtype_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.coe_subtype", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.instDistribMulActionSubtypeMem", "kind": "instance", "module": "Mathlib.Algebra.Group.Submonoid.DistribMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.distribMulAction", "kind": "instance", "module": "Mathlib.Algebra.Group.Submonoid.DistribMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.instMulDistribMulActionSubtypeMem", "kind": "instance", "module": "Mathlib.Algebra.Group.Submonoid.DistribMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.mulDistribMulAction", "kind": "instance", "module": "Mathlib.Algebra.Group.Submonoid.DistribMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.pi_mem_of_mulSingle_mem_aux", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Finite", "is_tactic_proof": true, "tactics": ["induction", "empty", "have", "exact", "insert", "ih", "have", "ext", "by_cases", "subst", "simp", "simp", "rw", "clear", "apply", "by_cases", "subst", "simp", "simpa", "have", "simp", "exact"], "tactic_count": 22}
{"name": "Submonoid.pi_mem_of_mulSingle_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Finite", "is_tactic_proof": true, "tactics": ["cases", "exact"], "tactic_count": 2}
{"name": "Submonoid.pi_le_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.closure_pi", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.exists_finsupp_of_mem_closure_range", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Finsupp", "is_tactic_proof": true, "tactics": ["classical", "induction", "mem", "one", "mul", "obtain", "use", "rw", "simp", "simp"], "tactic_count": 10}
{"name": "Submonoid.exists_of_mem_closure_range", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Finsupp", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Submonoid.mem_closure_range_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Finsupp", "is_tactic_proof": true, "tactics": ["refine", "rintro", "exact"], "tactic_count": 3}
{"name": "Submonoid.mem_closure_range_iff_of_fintype", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Finsupp", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Submonoid.mem_closure_iff_of_fintype", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Finsupp", "is_tactic_proof": true, "tactics": ["conv_lhs", "exact"], "tactic_count": 2}
{"name": "Submonoid.mem_closure_finset'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Finsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.mem_biSup_of_directedOn", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": true, "tactics": ["refine", "suffices", "simpa", "refine", "simp", "exact", "rintro", "rcases", "exact", "apply", "simp"], "tactic_count": 11}
{"name": "Submonoid.mem_iSup_of_directed", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": true, "tactics": ["have", "rw", "simp", "simp", "rw", "intro", "simp", "intro", "refine", "simp", "exact"], "tactic_count": 11}
{"name": "Submonoid.mem_iSup_prop", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "Submonoid.coe_iSup_of_directed", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.mem_sSup_of_directedOn", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": true, "tactics": ["haveI", "simp"], "tactic_count": 2}
{"name": "Submonoid.coe_sSup_of_directedOn", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.mem_sup_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Submonoid.mem_sup_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Submonoid.mul_mem_sup", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.mem_iSup_of_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Submonoid.mem_sSup_of_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Submonoid.iSup_induction", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": true, "tactics": ["rw", "refine", "obtain", "exact"], "tactic_count": 4}
{"name": "Submonoid.iSup_induction'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": true, "tactics": ["refine", "refine", "exact", "exact", "rintro", "exact"], "tactic_count": 6}
{"name": "FreeMonoid.closure_range_of", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.closure_singleton_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.mem_closure_singleton", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submonoid.mem_closure_singleton_self", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.closure_singleton_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Submonoid.card_bot", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.eq_bot_of_card_le", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.eq_bot_of_card_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.card_le_one_iff_eq_bot", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.eq_bot_iff_card", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeMonoid.mrange_lift", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submonoid.closure_eq_mrange", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submonoid.closure_eq_image_prod", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Submonoid.exists_list_of_mem_closure", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Submonoid.exists_multiset_of_mem_closure", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Submonoid.closure_induction_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": true, "tactics": ["simp_rw", "obtain", "induction", "one", "mul_of", "simp", "refine", "simp"], "tactic_count": 8}
{"name": "Submonoid.induction_of_closure_eq_top_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": true, "tactics": ["have", "induction", "one", "mul_left"], "tactic_count": 4}
{"name": "Submonoid.closure_induction_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.induction_of_closure_eq_top_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": true, "tactics": ["have", "induction", "one", "mul_right"], "tactic_count": 4}
{"name": "Submonoid.powers", "kind": "definition", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.mem_powers", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.coe_powers", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.mem_powers_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.decidableMemPowers", "kind": "instance", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.fintypePowers", "kind": "instance", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.powers_eq_closure", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "Submonoid.powers_le", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Submonoid.powers_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIdempotentElem.coe_powers", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.groupPowers", "kind": "abbrev", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.pow", "kind": "definition", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.pow_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.log", "kind": "definition", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.pow_log_eq_self", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.pow_right_injective_iff_pow_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.log_pow_eq_self", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.powLogEquiv", "kind": "definition", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.log_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.log_pow_int_eq_self", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.map_powers", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsScalarTower.of_mclosure_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": true, "tactics": ["refine", "intro", "rw", "clear", "intro", "rw"], "tactic_count": 6}
{"name": "SMulCommClass.of_mclosure_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": true, "tactics": ["refine", "intro", "rw", "clear", "intro", "rw"], "tactic_count": 6}
{"name": "Submonoid.sup_eq_range", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": true, "tactics": ["rw", "mrange_subtype,"], "tactic_count": 2}
{"name": "Submonoid.mem_sup", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Submonoid.forall_mem_sup", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": true, "tactics": ["simp", "aesop"], "tactic_count": 2}
{"name": "Submonoid.exists_mem_sup", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AddSubmonoid.closure_singleton_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.mem_closure_singleton", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AddSubmonoid.closure_singleton_zero", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AddSubmonoid.multiples", "kind": "definition", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.mem_closure_pair", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": true, "tactics": ["rw", "simp_rw"], "tactic_count": 2}
{"name": "ofMul_image_powers_eq_multiples_ofMul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "ofAdd_image_multiples_eq_powers_ofAdd", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": true, "tactics": ["symm", "rw", "exact"], "tactic_count": 3}
{"name": "Nat.addSubmonoidClosure_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Submonoid.instSMulSubtypeMem", "kind": "instance", "module": "Mathlib.Algebra.Group.Submonoid.MulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.instIsLeftCancelSMulSubtypeMem", "kind": "instance", "module": "Mathlib.Algebra.Group.Submonoid.MulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.instIsCancelSMulSubtypeMem", "kind": "instance", "module": "Mathlib.Algebra.Group.Submonoid.MulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.instSMulCommClassSubtypeMem", "kind": "instance", "module": "Mathlib.Algebra.Group.Submonoid.MulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.instSMulCommClassSubtypeMem_1", "kind": "instance", "module": "Mathlib.Algebra.Group.Submonoid.MulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.instIsScalarTowerSubtypeMem", "kind": "instance", "module": "Mathlib.Algebra.Group.Submonoid.MulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.instMulActionSubtypeMem", "kind": "instance", "module": "Mathlib.Algebra.Group.Submonoid.MulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.smul", "kind": "instance", "module": "Mathlib.Algebra.Group.Submonoid.MulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.smulCommClass_left", "kind": "instance", "module": "Mathlib.Algebra.Group.Submonoid.MulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.smulCommClass_right", "kind": "instance", "module": "Mathlib.Algebra.Group.Submonoid.MulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.isScalarTower", "kind": "instance", "module": "Mathlib.Algebra.Group.Submonoid.MulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.smul_def", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.MulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.mk_smul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.MulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.mulAction", "kind": "instance", "module": "Mathlib.Algebra.Group.Submonoid.MulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid._example", "kind": "example", "module": "Mathlib.Algebra.Group.Submonoid.MulAction", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Submonoid.op", "kind": "definition", "module": "Mathlib.Algebra.Group.Submonoid.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.mem_op", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.op_toSubsemigroup", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.unop", "kind": "definition", "module": "Mathlib.Algebra.Group.Submonoid.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.mem_unop", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.unop_toSubsemigroup", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.unop_op", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.op_unop", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.op_le_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.le_op_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.op_le_op_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.unop_le_unop_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.opEquiv", "kind": "definition", "module": "Mathlib.Algebra.Group.Submonoid.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.op_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.unop_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.op_inj", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.unop_inj", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.op_bot", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.op_eq_bot", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.unop_bot", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.unop_eq_bot", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.op_top", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.op_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.unop_top", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.unop_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.op_sup", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.unop_sup", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.op_inf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.unop_inf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.op_sSup", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.unop_sSup", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.op_sInf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.unop_sInf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.op_iSup", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.unop_iSup", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.op_iInf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.unop_iInf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.op_closure", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.MulOpposite", "is_tactic_proof": true, "tactics": ["simp_rw", "congr", "exact"], "tactic_count": 3}
{"name": "Submonoid.unop_closure", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.MulOpposite", "is_tactic_proof": true, "tactics": ["rw", "simp_rw"], "tactic_count": 2}
{"name": "Submonoid.equivOp", "kind": "definition", "module": "Mathlib.Algebra.Group.Submonoid.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.toAddSubmonoid", "kind": "definition", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.toSubmonoid'", "kind": "abbrev", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.toAddSubmonoid_closure", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.toSubmonoid'_closure", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.toSubmonoid", "kind": "definition", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.toAddSubmonoid'", "kind": "abbrev", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.toSubmonoid_closure", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.toAddSubmonoid'_closure", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.comap", "kind": "definition", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.coe_comap", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.mem_comap", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.comap_comap", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.comap_id", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.map", "kind": "definition", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.coe_map", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.map_coe_toMonoidHom", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.map_coe_toMulEquiv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.mem_map", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.mem_map_of_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.apply_coe_mem_map", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.map_map", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.mem_map_iff_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.map_le_iff_le_comap", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.gc_map_comap", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.map_le_of_le_comap", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.le_comap_of_map_le", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.le_comap_map", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.map_comap_le", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.monotone_map", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.monotone_comap", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.map_comap_map", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.comap_map_comap", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.map_sup", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.map_iSup", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.map_inf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.map_iInf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": true, "tactics": ["apply", "simpa"], "tactic_count": 2}
{"name": "Submonoid.comap_inf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.comap_iInf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.map_bot", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.disjoint_map", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submonoid.comap_top", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.map_id", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.gciMapComap", "kind": "definition", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.comap_map_eq_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.comap_surjective_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.map_injective_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.comap_inf_map_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.comap_iInf_map_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.comap_sup_map_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.comap_iSup_map_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.map_le_map_iff_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.map_strictMono_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.giMapComap", "kind": "definition", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.map_comap_eq_of_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.map_surjective_of_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.comap_injective_of_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.map_inf_comap_of_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.map_iInf_comap_of_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.map_sup_comap_of_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.map_iSup_comap_of_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.comap_le_comap_iff_of_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.comap_strictMono_of_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.topEquiv", "kind": "definition", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.topEquiv_toMonoidHom", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.equivMapOfInjective", "kind": "definition", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.coe_equivMapOfInjective_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.closure_closure_coe_preimage", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.prod", "kind": "definition", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.coe_prod", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.mem_prod", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.prod_mono", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.prod_top", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.top_prod", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.top_prod_top", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.bot_prod_bot", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.prodEquiv", "kind": "definition", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.map_inl", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.map_inr", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.prod_bot_sup_bot_prod", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.mem_map_equiv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.map_equiv_eq_comap_symm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.comap_equiv_eq_map_symm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.map_equiv_top", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.le_prod_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": true, "tactics": ["constructor", "intro", "constructor", "rintro", "exact", "rintro", "exact", "rintro", "exact"], "tactic_count": 9}
{"name": "Submonoid.prod_le_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": true, "tactics": ["constructor", "intro", "constructor", "rintro", "apply", "exact", "rintro", "apply", "exact", "rintro", "have", "apply", "simpa", "have", "apply", "simpa", "simpa"], "tactic_count": 17}
{"name": "Submonoid.closure_prod", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.closure_prod_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.closure_one_prod", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LibraryNote.range_copy_pattern", "kind": "definition", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.mrange", "kind": "definition", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.coe_mrange", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.mem_mrange", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.mrange_comp", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.mrange_eq_map", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.mrange_id", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MonoidHom.map_mrange", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MonoidHom.mrange_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.mrange_eq_top_of_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.mclosure_preimage_le", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.map_mclosure", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.mclosure_range", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MonoidHom.restrict", "kind": "definition", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.restrict_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.restrict_mrange", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MonoidHom.codRestrict", "kind": "definition", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.injective_codRestrict", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.mrangeRestrict", "kind": "definition", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.coe_mrangeRestrict", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.mrangeRestrict_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.mker", "kind": "definition", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.mem_mker", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.coe_mker", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.decidableMemMker", "kind": "instance", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.comap_mker", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.comap_bot'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.restrict_mker", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.mrangeRestrict_mker", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": true, "tactics": ["ext", "change", "simp"], "tactic_count": 3}
{"name": "MonoidHom.mker_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "MonoidHom.prod_map_comap_prod'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.mker_prod_map", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MonoidHom.mker_inl", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "MonoidHom.mker_inr", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "MonoidHom.mker_fst", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.mker_snd", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.submonoidComap", "kind": "definition", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.submonoidComap_surjective_of_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.submonoidMap", "kind": "definition", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.submonoidMap_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "Submonoid.surjOn_iff_le_map", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.mrange_inl", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Submonoid.mrange_inr", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Submonoid.mrange_inl'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.mrange_inr'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.mrange_fst", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.mrange_snd", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.prod_eq_bot_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Submonoid.prod_eq_top_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Submonoid.mrange_inl_sup_mrange_inr", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Submonoid.inclusion", "kind": "definition", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.coe_inclusion", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.inclusion_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.inclusion_inj", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.subtype_comp_inclusion", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.mrange_subtype", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.eq_top_iff'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.eq_bot_iff_forall", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.eq_bot_of_subsingleton", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": true, "tactics": ["rw", "intro", "simpa"], "tactic_count": 3}
{"name": "Submonoid.nontrivial_iff_exists_ne_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.bot_or_nontrivial", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Submonoid.bot_or_exists_ne_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.codisjoint_map", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submonoid.pi", "kind": "definition", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.coe_pi", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.mem_pi", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.pi_top", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.pi_empty", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.pi_bot", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.le_pi_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.mulSingle_mem_pi", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.pi_eq_bot_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Submonoid.le_comap_mulSingle_pi", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.iSup_map_mulSingle_le", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.submonoidCongr", "kind": "definition", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.ofLeftInverse'", "kind": "definition", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.submonoidMap", "kind": "definition", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.coe_submonoidMap_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.submonoidMap_symm_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.equivMapOfInjective_coe_mulEquiv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "Submonoid.faithfulSMul", "kind": "instance", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.unitsTypeEquivIsUnitSubmonoid", "kind": "definition", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.map_comap_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.map_comap_eq_self", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Submonoid.map_comap_eq_self_of_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "coe_mul_coe", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Pointwise", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "coe_set_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.mul_subset", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.mul_subset_closure", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.coe_mul_self_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Pointwise", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Submonoid.closure_mul_le", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.closure_pow_le", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.closure_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.sup_eq_closure_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.coe_sup", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Pointwise", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Submonoid.pow_smul_mem_closure_smul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Pointwise", "is_tactic_proof": true, "tactics": ["induction", "mem", "one", "mul", "obtain", "use", "rw", "exact"], "tactic_count": 8}
{"name": "Submonoid.inv", "kind": "definition", "module": "Mathlib.Algebra.Group.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.coe_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.mem_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.involutiveInv", "kind": "definition", "module": "Mathlib.Algebra.Group.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.inv_le_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.inv_le", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.invOrderIso", "kind": "definition", "module": "Mathlib.Algebra.Group.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.closure_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Pointwise", "is_tactic_proof": true, "tactics": ["apply", "rw", "exact", "rw", "exact"], "tactic_count": 5}
{"name": "Submonoid.mem_closure_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Pointwise", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submonoid.inv_inf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.inv_sup", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.inv_bot", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.inv_top", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.inv_iInf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.inv_iSup", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.pointwiseMulAction", "kind": "definition", "module": "Mathlib.Algebra.Group.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.coe_pointwise_smul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.smul_mem_pointwise_smul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.instCovariantClassHSMulLe", "kind": "instance", "module": "Mathlib.Algebra.Group.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.mem_smul_pointwise_iff_exists", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.smul_bot", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.smul_sup", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.smul_closure", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.pointwise_isCentralScalar", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.smul_mem_pointwise_smul_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.mem_pointwise_smul_iff_inv_smul_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.mem_inv_pointwise_smul_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.pointwise_smul_le_pointwise_smul_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.pointwise_smul_subset_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.subset_pointwise_smul_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.IsPWO.submonoid_closure", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Pointwise", "is_tactic_proof": true, "tactics": ["rw", "refine", "exact"], "tactic_count": 3}
{"name": "Submonoid.units", "kind": "definition", "module": "Mathlib.Algebra.Group.Submonoid.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.ofUnits", "kind": "definition", "module": "Mathlib.Algebra.Group.Submonoid.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.units_mono", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.ofUnits_units_le", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.ofUnits_mono", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.units_ofUnits_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofUnits_units_gci", "kind": "definition", "module": "Mathlib.Algebra.Group.Submonoid.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofUnits_units_gc", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofUnits_le_iff_le_units", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.mem_units_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.mem_units_of_val_mem_inv_val_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.val_mem_of_mem_units", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.inv_val_mem_of_mem_units", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.coe_inv_val_mul_coe_val", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.coe_val_mul_coe_inv_val", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.mk_inv_mul_mk_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.mk_mul_mk_inv_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.mul_mem_units", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.inv_mem_units", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.inv_mem_units_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.unitsEquivUnitsType", "kind": "definition", "module": "Mathlib.Algebra.Group.Submonoid.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.units_top", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.units_inf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.units_sInf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.units_iInf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.units_iInf₂", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.units_bot", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.units_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.units_left_inverse", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.unitsEquivIsUnitSubmonoid", "kind": "definition", "module": "Mathlib.Algebra.Group.Submonoid.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.instSubsingletonUnits", "kind": "instance", "module": "Mathlib.Algebra.Group.Submonoid.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.mem_ofUnits_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.mem_ofUnits", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.exists_mem_ofUnits_val_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.mem_of_mem_val_ofUnits", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.isUnit_of_mem_ofUnits", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.unit_of_mem_ofUnits", "kind": "definition", "module": "Mathlib.Algebra.Group.Submonoid.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.unit_of_mem_ofUnits_spec_eq_of_val_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.unit_of_mem_ofUnits_spec_val_eq_of_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.unit_of_mem_ofUnits_spec_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.unit_eq_unit_of_mem_ofUnits", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.unit_mem_of_mem_ofUnits", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.mem_ofUnits_of_isUnit_of_unit_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.mem_ofUnits_iff_exists_isUnit", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.ofUnitsEquivType", "kind": "definition", "module": "Mathlib.Algebra.Group.Submonoid.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.ofUnits_bot", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.ofUnits_inf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.ofUnits_sSup", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.ofUnits_iSup", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.ofUnits_iSup₂", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.ofUnits_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.ofUnits_sup_units", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.ofUnits_inf_units", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.ofUnits_right_inverse", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.ofUnits_strictMono", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.ofUnits_le_ofUnits_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.ofUnitsTopEquiv", "kind": "definition", "module": "Mathlib.Algebra.Group.Submonoid.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.mem_units_iff_val_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Units", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Subgroup.mem_ofUnits_iff_toUnits_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Units", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Subgroup.mem_iff_toUnits_mem_units", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Units", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Subgroup.val_mem_ofUnits_iff_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Submonoid.Units", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Subgroup.unitsEquivSelf", "kind": "definition", "module": "Mathlib.Algebra.Group.Submonoid.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.instInfSet", "kind": "instance", "module": "Mathlib.Algebra.Group.Subsemigroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.coe_sInf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.mem_sInf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.mem_iInf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Subsemigroup.coe_iInf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Subsemigroup.instCompleteLattice", "kind": "instance", "module": "Mathlib.Algebra.Group.Subsemigroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.closure", "kind": "definition", "module": "Mathlib.Algebra.Group.Subsemigroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.mem_closure", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.subset_closure", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.mem_closure_of_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.notMem_of_notMem_closure", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.closure_le", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.closure_mono", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.closure_eq_of_le", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.closure_induction", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.closure_induction₂", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Basic", "is_tactic_proof": true, "tactics": ["induction", "mem", "induction", "mem", "mul", "mul"], "tactic_count": 6}
{"name": "Subsemigroup.dense_induction", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Basic", "is_tactic_proof": true, "tactics": ["induction", "mem", "mul"], "tactic_count": 3}
{"name": "Subsemigroup._example", "kind": "example", "module": "Mathlib.Algebra.Group.Subsemigroup.Basic", "is_tactic_proof": true, "tactics": ["induction", "closure", "mem", "mul"], "tactic_count": 4}
{"name": "Subsemigroup.gi", "kind": "definition", "module": "Mathlib.Algebra.Group.Subsemigroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.closure_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.closure_empty", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.closure_univ", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.closure_union", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.closure_iUnion", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.closure_singleton_le_iff_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subsemigroup.mem_iSup", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Subsemigroup.iSup_eq_closure", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MulHom.eqOn_closure", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulHom.eq_of_eqOn_dense", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulHom.ofDense", "kind": "definition", "module": "Mathlib.Algebra.Group.Subsemigroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulHom.coe_ofDense", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.instSetLike", "kind": "instance", "module": "Mathlib.Algebra.Group.Subsemigroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.instPartialOrder", "kind": "instance", "module": "Mathlib.Algebra.Group.Subsemigroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.ofClass", "kind": "definition", "module": "Mathlib.Algebra.Group.Subsemigroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.instCanLiftSetCoeForallForallForallMemForallHMul", "kind": "instance", "module": "Mathlib.Algebra.Group.Subsemigroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.instMulMemClass", "kind": "instance", "module": "Mathlib.Algebra.Group.Subsemigroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.mem_carrier", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.mem_mk", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.coe_set_mk", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.mk_le_mk", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.ext", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.copy", "kind": "definition", "module": "Mathlib.Algebra.Group.Subsemigroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.coe_copy", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.copy_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.mul_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.instTop", "kind": "instance", "module": "Mathlib.Algebra.Group.Subsemigroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.instBot", "kind": "instance", "module": "Mathlib.Algebra.Group.Subsemigroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.instInhabited", "kind": "instance", "module": "Mathlib.Algebra.Group.Subsemigroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.notMem_bot", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.mem_top", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.coe_top", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.coe_bot", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.mk_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Subsemigroup.mk_eq_bot", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Subsemigroup.instMin", "kind": "instance", "module": "Mathlib.Algebra.Group.Subsemigroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.coe_inf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.mem_inf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.subsingleton_of_subsingleton", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Defs", "is_tactic_proof": true, "tactics": ["constructor", "have", "exact"], "tactic_count": 3}
{"name": "Subsemigroup.instNontrivialOfNonempty", "kind": "instance", "module": "Mathlib.Algebra.Group.Subsemigroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulHom.eqLocus", "kind": "definition", "module": "Mathlib.Algebra.Group.Subsemigroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulHom.mem_eqLocus", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulHom.eq_of_eqOn_top", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulMemClass.mul", "kind": "instance", "module": "Mathlib.Algebra.Group.Subsemigroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulMemClass.coe_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulMemClass.mk_mul_mk", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulMemClass.mul_def", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulMemClass.toSemigroup", "kind": "instance", "module": "Mathlib.Algebra.Group.Subsemigroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulMemClass.toCommSemigroup", "kind": "instance", "module": "Mathlib.Algebra.Group.Subsemigroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulMemClass.isLeftCancelMul", "kind": "instance", "module": "Mathlib.Algebra.Group.Subsemigroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulMemClass.isRightCancelMul", "kind": "instance", "module": "Mathlib.Algebra.Group.Subsemigroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulMemClass.isCancelMul", "kind": "instance", "module": "Mathlib.Algebra.Group.Subsemigroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulMemClass.subtype", "kind": "definition", "module": "Mathlib.Algebra.Group.Subsemigroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulMemClass.subtype_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulMemClass.subtype_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulMemClass.coe_subtype", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.mem_biSup_of_directedOn", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Membership", "is_tactic_proof": true, "tactics": ["refine", "suffices", "simpa", "refine", "simp", "rintro", "rcases", "exact", "apply", "simp"], "tactic_count": 10}
{"name": "Subsemigroup.mem_iSup_of_directed", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Membership", "is_tactic_proof": true, "tactics": ["have", "rw", "simp", "simp", "rw", "intro", "simp", "intro", "refine", "simp"], "tactic_count": 10}
{"name": "Subsemigroup.mem_iSup_prop", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Membership", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "simpa"], "tactic_count": 3}
{"name": "Subsemigroup.coe_iSup_of_directed", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Membership", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.mem_sSup_of_directed_on", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Membership", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Subsemigroup.coe_sSup_of_directed_on", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Membership", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.mem_sup_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Membership", "is_tactic_proof": true, "tactics": ["have", "tauto"], "tactic_count": 2}
{"name": "Subsemigroup.mem_sup_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Membership", "is_tactic_proof": true, "tactics": ["have", "tauto"], "tactic_count": 2}
{"name": "Subsemigroup.mul_mem_sup", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Membership", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.mem_iSup_of_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Membership", "is_tactic_proof": true, "tactics": ["have", "tauto"], "tactic_count": 2}
{"name": "Subsemigroup.mem_sSup_of_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Membership", "is_tactic_proof": true, "tactics": ["have", "tauto"], "tactic_count": 2}
{"name": "Subsemigroup.iSup_induction", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Membership", "is_tactic_proof": true, "tactics": ["rw", "refine", "obtain", "exact"], "tactic_count": 4}
{"name": "Subsemigroup.iSup_induction'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Membership", "is_tactic_proof": true, "tactics": ["refine", "refine", "exact", "rintro", "exact"], "tactic_count": 5}
{"name": "Subsemigroup.op", "kind": "definition", "module": "Mathlib.Algebra.Group.Subsemigroup.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.mem_op", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.unop", "kind": "definition", "module": "Mathlib.Algebra.Group.Subsemigroup.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.mem_unop", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.unop_op", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.op_unop", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.op_le_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.le_op_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.op_le_op_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.unop_le_unop_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.opEquiv", "kind": "definition", "module": "Mathlib.Algebra.Group.Subsemigroup.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.op_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.unop_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.op_inj", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.unop_inj", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.op_bot", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.op_eq_bot", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.unop_bot", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.unop_eq_bot", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.op_top", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.op_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.unop_top", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.unop_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.op_sup", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.unop_sup", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.op_inf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.unop_inf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.op_sSup", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.unop_sSup", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.op_sInf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.unop_sInf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.op_iSup", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.unop_iSup", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.op_iInf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.unop_iInf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.op_closure", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.MulOpposite", "is_tactic_proof": true, "tactics": ["simp_rw", "congr", "exact"], "tactic_count": 3}
{"name": "Subsemigroup.unop_closure", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.MulOpposite", "is_tactic_proof": true, "tactics": ["rw", "simp_rw"], "tactic_count": 2}
{"name": "Subsemigroup.equivOp", "kind": "definition", "module": "Mathlib.Algebra.Group.Subsemigroup.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.toAddSubsemigroup", "kind": "definition", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubsemigroup.toSubsemigroup'", "kind": "abbrev", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.toAddSubsemigroup_closure", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubsemigroup.toSubsemigroup'_closure", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubsemigroup.toSubsemigroup", "kind": "definition", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.toAddSubsemigroup'", "kind": "abbrev", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubsemigroup.toSubsemigroup_closure", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.toAddSubsemigroup'_closure", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.comap", "kind": "definition", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.coe_comap", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.mem_comap", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.comap_comap", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.comap_id", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.map", "kind": "definition", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.coe_map", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.mem_map", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.mem_map_of_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.apply_coe_mem_map", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.map_map", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.mem_map_iff_mem", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.map_le_iff_le_comap", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.gc_map_comap", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.map_le_of_le_comap", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.le_comap_of_map_le", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.le_comap_map", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.map_comap_le", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.monotone_map", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.monotone_comap", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.map_comap_map", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.comap_map_comap", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.map_sup", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.map_iSup", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.map_inf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.map_iInf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": true, "tactics": ["apply", "simpa"], "tactic_count": 2}
{"name": "Subsemigroup.comap_inf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.comap_iInf", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.map_bot", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.comap_top", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.map_id", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.gciMapComap", "kind": "definition", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.comap_map_eq_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.comap_surjective_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.map_injective_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.comap_inf_map_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.comap_iInf_map_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.comap_sup_map_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.comap_iSup_map_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.map_le_map_iff_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.map_strictMono_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.giMapComap", "kind": "definition", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.map_comap_eq_of_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.map_surjective_of_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.comap_injective_of_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.map_inf_comap_of_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.map_iInf_comap_of_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.map_sup_comap_of_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.map_iSup_comap_of_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.comap_le_comap_iff_of_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.comap_strictMono_of_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.topEquiv", "kind": "definition", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.topEquiv_toMulHom", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.equivMapOfInjective", "kind": "definition", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.coe_equivMapOfInjective_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.closure_closure_coe_preimage", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.prod", "kind": "definition", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.coe_prod", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.mem_prod", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.prod_mono", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.prod_top", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.top_prod", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.top_prod_top", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.bot_prod_bot", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.prodEquiv", "kind": "definition", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.mem_map_equiv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.map_equiv_eq_comap_symm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.comap_equiv_eq_map_symm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.map_equiv_top", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.le_prod_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": true, "tactics": ["constructor", "intro", "constructor", "rintro", "exact", "rintro", "exact", "rintro", "exact"], "tactic_count": 9}
{"name": "MulHom.srange", "kind": "definition", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulHom.coe_srange", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulHom.mem_srange", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Group.Subsemigroup.Operations.0.MulHom.srange_mk_aux_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulHom.srange_mk", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulHom.srange_eq_map", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulHom.map_srange", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MulHom.srange_eq_top_iff_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulHom.srange_eq_top_of_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulHom.mclosure_preimage_le", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulHom.map_mclosure", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulHom.restrict", "kind": "definition", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulHom.restrict_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulHom.codRestrict", "kind": "definition", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulHom.srangeRestrict", "kind": "definition", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulHom.coe_srangeRestrict", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulHom.srangeRestrict_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulHom.prod_map_comap_prod'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulHom.subsemigroupComap", "kind": "definition", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulHom.subsemigroupMap", "kind": "definition", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulHom.subsemigroupMap_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "Subsemigroup.srange_fst", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.srange_snd", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.prod_eq_top_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Subsemigroup.inclusion", "kind": "definition", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.range_subtype", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.eq_top_iff'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.subsemigroupCongr", "kind": "definition", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.ofLeftInverse", "kind": "definition", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.subsemigroupMap", "kind": "definition", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.map_comap_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.map_comap_eq_self", "kind": "theorem", "module": "Mathlib.Algebra.Group.Subsemigroup.Operations", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Function.mulSupport_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.mulSupport_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.Support", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Function.mulSupport_fun_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.mulSupport_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.mulSupport_mul_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.mulSupport_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instNoNatZeroDivisorsOfIsAddTorsionFree", "kind": "instance", "module": "Mathlib.Algebra.Group.Torsion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsingleton.to_isMulTorsionFree", "kind": "instance", "module": "Mathlib.Algebra.Group.Torsion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pow_left_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Torsion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pow_left_inj", "kind": "theorem", "module": "Mathlib.Algebra.Group.Torsion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pow_eq_one_iff_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Torsion", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "pow_eq_one_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Torsion", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "pow_eq_one_iff_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Torsion", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "sq_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.Torsion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zpow_left_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Torsion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zpow_left_inj", "kind": "theorem", "module": "Mathlib.Algebra.Group.Torsion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zpow_eq_zpow_iff'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Torsion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMulTorsionFree.zpow_eq_one_iff_left", "kind": "theorem", "module": "Mathlib.Algebra.Group.Torsion", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsMulTorsionFree.zpow_eq_one_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Torsion", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "IsMulTorsionFree.zpow_eq_one_iff_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Torsion", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "self_eq_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Torsion", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "inv_eq_self", "kind": "theorem", "module": "Mathlib.Algebra.Group.Torsion", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "self_ne_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Torsion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_ne_self", "kind": "theorem", "module": "Mathlib.Algebra.Group.Torsion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.one", "kind": "abbrev", "module": "Mathlib.Algebra.Group.TransferInstance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.one_def", "kind": "theorem", "module": "Mathlib.Algebra.Group.TransferInstance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.mul", "kind": "abbrev", "module": "Mathlib.Algebra.Group.TransferInstance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.mul_def", "kind": "theorem", "module": "Mathlib.Algebra.Group.TransferInstance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.div", "kind": "abbrev", "module": "Mathlib.Algebra.Group.TransferInstance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.div_def", "kind": "theorem", "module": "Mathlib.Algebra.Group.TransferInstance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Inv", "kind": "abbrev", "module": "Mathlib.Algebra.Group.TransferInstance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.inv_def", "kind": "theorem", "module": "Mathlib.Algebra.Group.TransferInstance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.smul", "kind": "abbrev", "module": "Mathlib.Algebra.Group.TransferInstance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.smul_def", "kind": "theorem", "module": "Mathlib.Algebra.Group.TransferInstance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.pow", "kind": "abbrev", "module": "Mathlib.Algebra.Group.TransferInstance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.pow_def", "kind": "theorem", "module": "Mathlib.Algebra.Group.TransferInstance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.mulEquiv", "kind": "definition", "module": "Mathlib.Algebra.Group.TransferInstance", "is_tactic_proof": true, "tactics": ["intros", "exact"], "tactic_count": 2}
{"name": "Equiv.mulEquiv_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.TransferInstance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.mulEquiv_symm_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.TransferInstance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.semigroup", "kind": "abbrev", "module": "Mathlib.Algebra.Group.TransferInstance", "is_tactic_proof": true, "tactics": ["let", "apply"], "tactic_count": 2}
{"name": "Equiv.commSemigroup", "kind": "abbrev", "module": "Mathlib.Algebra.Group.TransferInstance", "is_tactic_proof": true, "tactics": ["let", "apply"], "tactic_count": 2}
{"name": "Equiv.isLeftCancelMul", "kind": "theorem", "module": "Mathlib.Algebra.Group.TransferInstance", "is_tactic_proof": true, "tactics": ["letI"], "tactic_count": 1}
{"name": "Equiv.isRightCancelMul", "kind": "theorem", "module": "Mathlib.Algebra.Group.TransferInstance", "is_tactic_proof": true, "tactics": ["letI"], "tactic_count": 1}
{"name": "Equiv.isCancelMul", "kind": "theorem", "module": "Mathlib.Algebra.Group.TransferInstance", "is_tactic_proof": true, "tactics": ["letI"], "tactic_count": 1}
{"name": "Equiv.mulOneClass", "kind": "abbrev", "module": "Mathlib.Algebra.Group.TransferInstance", "is_tactic_proof": true, "tactics": ["let", "let", "apply"], "tactic_count": 3}
{"name": "Equiv.monoid", "kind": "abbrev", "module": "Mathlib.Algebra.Group.TransferInstance", "is_tactic_proof": true, "tactics": ["let", "let", "let", "apply"], "tactic_count": 4}
{"name": "Equiv.commMonoid", "kind": "abbrev", "module": "Mathlib.Algebra.Group.TransferInstance", "is_tactic_proof": true, "tactics": ["let", "let", "let", "apply"], "tactic_count": 4}
{"name": "Equiv.group", "kind": "abbrev", "module": "Mathlib.Algebra.Group.TransferInstance", "is_tactic_proof": true, "tactics": ["let", "let", "let", "let", "let", "let", "apply"], "tactic_count": 7}
{"name": "Equiv.commGroup", "kind": "abbrev", "module": "Mathlib.Algebra.Group.TransferInstance", "is_tactic_proof": true, "tactics": ["let", "let", "let", "let", "let", "let", "apply"], "tactic_count": 7}
{"name": "Finite.exists_type_univ_nonempty_mulEquiv", "kind": "theorem", "module": "Mathlib.Algebra.Group.TransferInstance", "is_tactic_proof": true, "tactics": ["obtain", "let", "let", "letI", "exact"], "tactic_count": 5}
{"name": "translate", "kind": "definition", "module": "Mathlib.Algebra.Group.Translate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "translate.termτ", "kind": "definition", "module": "Mathlib.Algebra.Group.Translate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "translate._aux_Mathlib_Algebra_Group_Translate___macroRules_translate_termτ_1", "kind": "definition", "module": "Mathlib.Algebra.Group.Translate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "translate._aux_Mathlib_Algebra_Group_Translate___unexpand_translate_1", "kind": "definition", "module": "Mathlib.Algebra.Group.Translate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "translate_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Translate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "translate_zero", "kind": "theorem", "module": "Mathlib.Algebra.Group.Translate", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "translate_translate", "kind": "theorem", "module": "Mathlib.Algebra.Group.Translate", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "translate_add", "kind": "theorem", "module": "Mathlib.Algebra.Group.Translate", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "translate_add'", "kind": "theorem", "module": "Mathlib.Algebra.Group.Translate", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "translate_comm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Translate", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "comp_translate", "kind": "theorem", "module": "Mathlib.Algebra.Group.Translate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "translate_eq_domAddActMk_vadd", "kind": "theorem", "module": "Mathlib.Algebra.Group.Translate", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "translate_smul_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Translate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "translate_zero_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Translate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "translate_add_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Translate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "translate_sub_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Translate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "translate_neg_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Translate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "translate_sum_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Translate", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "sum_translate", "kind": "theorem", "module": "Mathlib.Algebra.Group.Translate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "support_translate", "kind": "theorem", "module": "Mathlib.Algebra.Group.Translate", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "translate_prod_right", "kind": "theorem", "module": "Mathlib.Algebra.Group.Translate", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Additive", "kind": "definition", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiplicative", "kind": "definition", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Additive.ofMul", "kind": "definition", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Additive.toMul", "kind": "definition", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Additive.ofMul_symm_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Additive.toMul_symm_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Additive.ext", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Additive.forall", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Additive.exists", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Additive.rec", "kind": "definition", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiplicative.ofAdd", "kind": "definition", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiplicative.toAdd", "kind": "definition", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiplicative.ofAdd_symm_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiplicative.toAdd_symm_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiplicative.ext", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiplicative.forall", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiplicative.exists", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiplicative.rec", "kind": "definition", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toAdd_ofAdd", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofAdd_toAdd", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toMul_ofMul", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofMul_toMul", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instSubsingletonAdditive", "kind": "instance", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instSubsingletonMultiplicative", "kind": "instance", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInhabitedAdditive", "kind": "instance", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInhabitedMultiplicative", "kind": "instance", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instUniqueAdditive", "kind": "instance", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instUniqueMultiplicative", "kind": "instance", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDecidableEqMultiplicative", "kind": "instance", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDecidableEqAdditive", "kind": "instance", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Additive.instNontrivial", "kind": "instance", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiplicative.instNontrivial", "kind": "instance", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Additive.add", "kind": "instance", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiplicative.mul", "kind": "instance", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofAdd_add", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toAdd_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofMul_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toMul_add", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Additive.addSemigroup", "kind": "instance", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiplicative.semigroup", "kind": "instance", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Additive.addCommSemigroup", "kind": "instance", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiplicative.commSemigroup", "kind": "instance", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Additive.isLeftCancelAdd", "kind": "instance", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiplicative.isLeftCancelMul", "kind": "instance", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Additive.isRightCancelAdd", "kind": "instance", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiplicative.isRightCancelMul", "kind": "instance", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Additive.isCancelAdd", "kind": "instance", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiplicative.isCancelMul", "kind": "instance", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Additive.addLeftCancelSemigroup", "kind": "instance", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiplicative.leftCancelSemigroup", "kind": "instance", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Additive.addRightCancelSemigroup", "kind": "instance", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiplicative.rightCancelSemigroup", "kind": "instance", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instZeroAdditiveOfOne", "kind": "instance", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofMul_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofMul_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toMul_zero", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toMul_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instOneMultiplicativeOfZero", "kind": "instance", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofAdd_zero", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofAdd_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toAdd_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toAdd_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Additive.addZeroClass", "kind": "instance", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiplicative.mulOneClass", "kind": "instance", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Additive.addMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiplicative.monoid", "kind": "instance", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofMul_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toMul_nsmul", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofAdd_nsmul", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toAdd_pow", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isAddLeftRegular_ofMul", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLeftRegular_toMul", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isAddRightRegular_ofMul", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isRightRegular_toMul", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isAddRegular_ofMul", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "isRegular_toMul", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "isLeftRegular_ofAdd", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isAddLeftRegular_toAdd", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isRightRegular_ofAdd", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isAddRightRegular_toAdd", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isRegular_ofAdd", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "isAddRegular_toAdd", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Additive.addLeftCancelMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiplicative.leftCancelMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Additive.addRightCancelMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiplicative.rightCancelMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Additive.addCommMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiplicative.commMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Additive.instAddCancelCommMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiplicative.instCancelCommMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Additive.neg", "kind": "instance", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofMul_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toMul_neg", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiplicative.inv", "kind": "instance", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofAdd_neg", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toAdd_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Additive.sub", "kind": "instance", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiplicative.div", "kind": "instance", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofAdd_sub", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toAdd_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofMul_div", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toMul_sub", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Additive.involutiveNeg", "kind": "instance", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiplicative.involutiveInv", "kind": "instance", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Additive.subNegMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiplicative.divInvMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofMul_zpow", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toMul_zsmul", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofAdd_zsmul", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toAdd_zpow", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Additive.subtractionMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiplicative.divisionMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Additive.subtractionCommMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiplicative.divisionCommMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Additive.addGroup", "kind": "instance", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiplicative.group", "kind": "instance", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Additive.addCommGroup", "kind": "instance", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiplicative.commGroup", "kind": "instance", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsAddTorsionFreeAdditiveOfIsMulTorsionFree", "kind": "instance", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsMulTorsionFreeMultiplicativeOfIsAddTorsionFree", "kind": "instance", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Additive.coeToFun", "kind": "instance", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiplicative.coeToFun", "kind": "instance", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.mulSingle_multiplicativeOfAdd_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simp"], "tactic_count": 3}
{"name": "Pi.single_additiveOfMul_eq", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simp"], "tactic_count": 3}
{"name": "instFiniteAdditive", "kind": "instance", "module": "Mathlib.Algebra.Group.TypeTags.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFiniteMultiplicative", "kind": "instance", "module": "Mathlib.Algebra.Group.TypeTags.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInfiniteAdditive", "kind": "instance", "module": "Mathlib.Algebra.Group.TypeTags.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInfiniteMultiplicative", "kind": "instance", "module": "Mathlib.Algebra.Group.TypeTags.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Additive.fintype", "kind": "instance", "module": "Mathlib.Algebra.Group.TypeTags.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiplicative.fintype", "kind": "instance", "module": "Mathlib.Algebra.Group.TypeTags.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_multiplicative", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_additive", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.toMultiplicative", "kind": "definition", "module": "Mathlib.Algebra.Group.TypeTags.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.coe_toMultiplicative", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.toMultiplicative_id", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.toAdditive", "kind": "definition", "module": "Mathlib.Algebra.Group.TypeTags.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.coe_toAdditive", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.toAdditive_id", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.toMultiplicativeRight", "kind": "definition", "module": "Mathlib.Algebra.Group.TypeTags.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.coe_toMultiplicativeRight", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.toAdditiveLeft", "kind": "definition", "module": "Mathlib.Algebra.Group.TypeTags.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.coe_toAdditiveLeft", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.toMultiplicativeLeft", "kind": "definition", "module": "Mathlib.Algebra.Group.TypeTags.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.coe_toMultiplicativeLeft", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.toAdditiveRight", "kind": "definition", "module": "Mathlib.Algebra.Group.TypeTags.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.coe_toAdditiveRight", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiplicative.monoidHom_ext", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Additive.addMonoidHom_ext", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.toMultiplicative_add", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.toMultiplicativeLeftAddEquiv", "kind": "definition", "module": "Mathlib.Algebra.Group.TypeTags.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.toMultiplicativeRightAddEquiv", "kind": "definition", "module": "Mathlib.Algebra.Group.TypeTags.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.toAdditiveLeftMulEquiv", "kind": "definition", "module": "Mathlib.Algebra.Group.TypeTags.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.toAdditiveRightMulEquiv", "kind": "definition", "module": "Mathlib.Algebra.Group.TypeTags.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiplicative.ofAdd_image_setAdd", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Pointwise", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiplicative.ofAdd_image_nsmul", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Pointwise", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
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{"name": "Multiplicative.toAdd_image_nsmul", "kind": "theorem", "module": "Mathlib.Algebra.Group.TypeTags.Pointwise", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
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{"name": "ULift.one_down", "kind": "theorem", "module": "Mathlib.Algebra.Group.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ULift.mul_down", "kind": "theorem", "module": "Mathlib.Algebra.Group.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.div", "kind": "instance", "module": "Mathlib.Algebra.Group.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.div_down", "kind": "theorem", "module": "Mathlib.Algebra.Group.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.inv", "kind": "instance", "module": "Mathlib.Algebra.Group.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.inv_down", "kind": "theorem", "module": "Mathlib.Algebra.Group.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.smul", "kind": "instance", "module": "Mathlib.Algebra.Group.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.smul_down", "kind": "theorem", "module": "Mathlib.Algebra.Group.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.pow", "kind": "instance", "module": "Mathlib.Algebra.Group.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.pow_down", "kind": "theorem", "module": "Mathlib.Algebra.Group.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.ulift", "kind": "definition", "module": "Mathlib.Algebra.Group.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.semigroup", "kind": "instance", "module": "Mathlib.Algebra.Group.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.commSemigroup", "kind": "instance", "module": "Mathlib.Algebra.Group.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.mulOneClass", "kind": "instance", "module": "Mathlib.Algebra.Group.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.monoid", "kind": "instance", "module": "Mathlib.Algebra.Group.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.commMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.divInvMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.group", "kind": "instance", "module": "Mathlib.Algebra.Group.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.commGroup", "kind": "instance", "module": "Mathlib.Algebra.Group.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.leftCancelSemigroup", "kind": "instance", "module": "Mathlib.Algebra.Group.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.rightCancelSemigroup", "kind": "instance", "module": "Mathlib.Algebra.Group.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.leftCancelMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.rightCancelMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.cancelMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.cancelCommMonoid", "kind": "instance", "module": "Mathlib.Algebra.Group.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.nontrivial", "kind": "instance", "module": "Mathlib.Algebra.Group.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniqueMul", "kind": "definition", "module": "Mathlib.Algebra.Group.UniqueProds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniqueMul.mono", "kind": "theorem", "module": "Mathlib.Algebra.Group.UniqueProds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniqueMul.of_subsingleton", "kind": "theorem", "module": "Mathlib.Algebra.Group.UniqueProds.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "UniqueMul.of_card_le_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.UniqueProds.Basic", "is_tactic_proof": true, "tactics": ["rw", "obtain", "exact"], "tactic_count": 3}
{"name": "UniqueMul.mt", "kind": "theorem", "module": "Mathlib.Algebra.Group.UniqueProds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniqueMul.subsingleton", "kind": "theorem", "module": "Mathlib.Algebra.Group.UniqueProds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniqueMul.set_subsingleton", "kind": "theorem", "module": "Mathlib.Algebra.Group.UniqueProds.Basic", "is_tactic_proof": true, "tactics": ["rintro", "rcases", "rcases", "rfl"], "tactic_count": 4}
{"name": "UniqueMul.iff_existsUnique", "kind": "theorem", "module": "Mathlib.Algebra.Group.UniqueProds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniqueMul.iff_card_le_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.UniqueProds.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "have", "grind", "exact"], "tactic_count": 5}
{"name": "UniqueMul.exists_iff_exists_existsUnique", "kind": "theorem", "module": "Mathlib.Algebra.Group.UniqueProds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniqueMul.mulHom_preimage", "kind": "theorem", "module": "Mathlib.Algebra.Group.UniqueProds.Basic", "is_tactic_proof": true, "tactics": ["intro", "simp", "exact"], "tactic_count": 3}
{"name": "UniqueMul.of_mulHom_image", "kind": "theorem", "module": "Mathlib.Algebra.Group.UniqueProds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniqueMul.mulHom_image_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.UniqueProds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniqueMul.mulHom_map_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.UniqueProds.Basic", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "UniqueMul.of_mulOpposite", "kind": "theorem", "module": "Mathlib.Algebra.Group.UniqueProds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniqueMul.to_mulOpposite", "kind": "theorem", "module": "Mathlib.Algebra.Group.UniqueProds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniqueMul.iff_mulOpposite", "kind": "theorem", "module": "Mathlib.Algebra.Group.UniqueProds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniqueMul.of_image_filter", "kind": "theorem", "module": "Mathlib.Algebra.Group.UniqueProds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniqueMul_of_twoUniqueMul", "kind": "theorem", "module": "Mathlib.Algebra.Group.UniqueProds.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "rw", "obtain", "rw", "exact"], "tactic_count": 6}
{"name": "TwoUniqueProds.toUniqueProds", "kind": "instance", "module": "Mathlib.Algebra.Group.UniqueProds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiplicative.instUniqueProdsOfUniqueSums", "kind": "instance", "module": "Mathlib.Algebra.Group.UniqueProds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiplicative.instTwoUniqueProdsOfTwoUniqueSums", "kind": "instance", "module": "Mathlib.Algebra.Group.UniqueProds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Additive.instUniqueSumsOfUniqueProds", "kind": "instance", "module": "Mathlib.Algebra.Group.UniqueProds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Additive.instTwoUniqueSumsOfTwoUniqueProds", "kind": "instance", "module": "Mathlib.Algebra.Group.UniqueProds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Group.UniqueProds.Basic.0.I", "kind": "abbrev", "module": "Mathlib.Algebra.Group.UniqueProds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Group.UniqueProds.Basic.0.instMulI", "kind": "instance", "module": "Mathlib.Algebra.Group.UniqueProds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Group.UniqueProds.Basic.0.Prod.upMulHom", "kind": "definition", "module": "Mathlib.Algebra.Group.UniqueProds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Group.UniqueProds.Basic.0.downMulHom", "kind": "definition", "module": "Mathlib.Algebra.Group.UniqueProds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "isLocalHom_equiv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Units.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Units.map", "kind": "definition", "module": "Mathlib.Algebra.Group.Units.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Units.map_mk", "kind": "theorem", "module": "Mathlib.Algebra.Group.Units.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Units.map_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Units.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.map_id", "kind": "theorem", "module": "Mathlib.Algebra.Group.Units.Hom", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Units.coeHom", "kind": "definition", "module": "Mathlib.Algebra.Group.Units.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.coeHom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Group.Units.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.coeHom_injective", "kind": "theorem", "module": "Mathlib.Algebra.Group.Units.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.val_zpow_eq_zpow_val", "kind": "theorem", "module": "Mathlib.Algebra.Group.Units.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "map_units_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Units.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.liftRight", "kind": "definition", "module": "Mathlib.Algebra.Group.Units.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.coe_liftRight", "kind": "theorem", "module": "Mathlib.Algebra.Group.Units.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.mul_liftRight_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Units.Hom", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Units.liftRight_inv_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Units.Hom", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MonoidHom.toHomUnits", "kind": "definition", "module": "Mathlib.Algebra.Group.Units.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.coe_toHomUnits", "kind": "theorem", "module": "Mathlib.Algebra.Group.Units.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.toHomUnits_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Units.Hom", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
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{"name": "IsUnit.map", "kind": "theorem", "module": "Mathlib.Algebra.Group.Units.Hom", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "IsUnit.of_leftInverse", "kind": "theorem", "module": "Mathlib.Algebra.Group.Units.Hom", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "isUnit_map_of_leftInverse", "kind": "theorem", "module": "Mathlib.Algebra.Group.Units.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUnit.liftRight", "kind": "definition", "module": "Mathlib.Algebra.Group.Units.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUnit.coe_liftRight", "kind": "theorem", "module": "Mathlib.Algebra.Group.Units.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUnit.mul_liftRight_inv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Units.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUnit.liftRight_inv_mul", "kind": "theorem", "module": "Mathlib.Algebra.Group.Units.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUnit.of_map", "kind": "theorem", "module": "Mathlib.Algebra.Group.Units.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isUnit_map_iff", "kind": "theorem", "module": "Mathlib.Algebra.Group.Units.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLocalHom_of_leftInverse", "kind": "theorem", "module": "Mathlib.Algebra.Group.Units.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.isLocalHom_comp", "kind": "theorem", "module": "Mathlib.Algebra.Group.Units.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLocalHom_toMonoidHom", "kind": "theorem", "module": "Mathlib.Algebra.Group.Units.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.isLocalHom_of_comp", "kind": "theorem", "module": "Mathlib.Algebra.Group.Units.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.opEquiv", "kind": "definition", "module": "Mathlib.Algebra.Group.Units.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.coe_unop_opEquiv", "kind": "theorem", "module": "Mathlib.Algebra.Group.Units.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.coe_opEquiv_symm", "kind": "theorem", "module": "Mathlib.Algebra.Group.Units.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUnit.op", "kind": "theorem", "module": "Mathlib.Algebra.Group.Units.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "isUnit_unop", "kind": "theorem", "module": "Mathlib.Algebra.Group.Units.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithOne.instInvolutiveInv", "kind": "instance", "module": "Mathlib.Algebra.Group.WithOne.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithOne.coeMulHom", "kind": "definition", "module": "Mathlib.Algebra.Group.WithOne.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithOne.lift", "kind": "definition", "module": "Mathlib.Algebra.Group.WithOne.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithOne.lift_coe", "kind": "theorem", "module": "Mathlib.Algebra.Group.WithOne.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithOne.lift_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.WithOne.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithOne.lift_unique", "kind": "theorem", "module": "Mathlib.Algebra.Group.WithOne.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithOne.mapMulHom", "kind": "definition", "module": "Mathlib.Algebra.Group.WithOne.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithOne.mapMulHom_coe", "kind": "theorem", "module": "Mathlib.Algebra.Group.WithOne.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithOne.mapMulHom_id", "kind": "theorem", "module": "Mathlib.Algebra.Group.WithOne.Basic", "is_tactic_proof": true, "tactics": ["ext", "induction"], "tactic_count": 2}
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{"name": "WithOne.mapMulHom_injective'", "kind": "theorem", "module": "Mathlib.Algebra.Group.WithOne.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithOne.mapMulHom_inj", "kind": "theorem", "module": "Mathlib.Algebra.Group.WithOne.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithOne.mapMulHom_mapMulHom", "kind": "theorem", "module": "Mathlib.Algebra.Group.WithOne.Basic", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
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{"name": "MulEquiv.withOneCongr", "kind": "definition", "module": "Mathlib.Algebra.Group.WithOne.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.withOneCongr_refl", "kind": "theorem", "module": "Mathlib.Algebra.Group.WithOne.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.withOneCongr_symm", "kind": "theorem", "module": "Mathlib.Algebra.Group.WithOne.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "WithOne", "kind": "definition", "module": "Mathlib.Algebra.Group.WithOne.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "WithOne.instInvOneClass", "kind": "instance", "module": "Mathlib.Algebra.Group.WithOne.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithOne.inhabited", "kind": "instance", "module": "Mathlib.Algebra.Group.WithOne.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "WithOne.instCoeTC", "kind": "instance", "module": "Mathlib.Algebra.Group.WithOne.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "WithOne.recOneCoe_one", "kind": "theorem", "module": "Mathlib.Algebra.Group.WithOne.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Functor.mapHomologicalComplex_reflects_iso", "kind": "instance", "module": "Mathlib.Algebra.Homology.Additive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.NatTrans.mapHomologicalComplex_id", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Additive", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
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{"name": "CategoryTheory.Equivalence.mapHomologicalComplex", "kind": "definition", "module": "Mathlib.Algebra.Homology.Additive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ChainComplex.map_chain_complex_of", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Additive", "is_tactic_proof": true, "tactics": ["refine", "rintro", "simp"], "tactic_count": 3}
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{"name": "HomologicalComplex.singleMapHomologicalComplex", "kind": "definition", "module": "Mathlib.Algebra.Homology.Additive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.singleMapHomologicalComplex_hom_app_self", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Additive", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "ChainComplex.alternatingConstHomologyDataZero", "kind": "definition", "module": "Mathlib.Algebra.Homology.AlternatingConst", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "HomologicalComplex.mapBifunctor₁₂.ι_mapBifunctor₁₂Desc", "kind": "theorem", "module": "Mathlib.Algebra.Homology.BifunctorAssociator", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
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{"name": "CategoryTheory.CommSq.shortComplex", "kind": "definition", "module": "Mathlib.Algebra.Homology.CommSq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CommSq.isColimitEquivIsColimitCokernelCofork", "kind": "definition", "module": "Mathlib.Algebra.Homology.CommSq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPushout.isColimitCokernelCofork", "kind": "definition", "module": "Mathlib.Algebra.Homology.CommSq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPushout.epi_shortComplex_g", "kind": "theorem", "module": "Mathlib.Algebra.Homology.CommSq", "is_tactic_proof": true, "tactics": ["rw", "intro", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.CommSq.kernelFork", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.CommSq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CommSq.shortComplex'", "kind": "definition", "module": "Mathlib.Algebra.Homology.CommSq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CommSq.isLimitEquivIsLimitKernelFork", "kind": "definition", "module": "Mathlib.Algebra.Homology.CommSq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPullback.isLimitKernelFork", "kind": "definition", "module": "Mathlib.Algebra.Homology.CommSq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPullback.mono_shortComplex'_f", "kind": "theorem", "module": "Mathlib.Algebra.Homology.CommSq", "is_tactic_proof": true, "tactics": ["rw", "intro", "exact"], "tactic_count": 3}
{"name": "ComplexShape.refl", "kind": "definition", "module": "Mathlib.Algebra.Homology.ComplexShape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.symm", "kind": "definition", "module": "Mathlib.Algebra.Homology.ComplexShape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.symm_symm", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ComplexShape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.symm_bijective", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ComplexShape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.trans", "kind": "definition", "module": "Mathlib.Algebra.Homology.ComplexShape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.subsingleton_next", "kind": "instance", "module": "Mathlib.Algebra.Homology.ComplexShape", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "congr", "exact"], "tactic_count": 4}
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{"name": "ComplexShape.next", "kind": "definition", "module": "Mathlib.Algebra.Homology.ComplexShape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.prev", "kind": "definition", "module": "Mathlib.Algebra.Homology.ComplexShape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.next_eq'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ComplexShape", "is_tactic_proof": true, "tactics": ["apply", "rw", "rw", "exact"], "tactic_count": 4}
{"name": "ComplexShape.prev_eq'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ComplexShape", "is_tactic_proof": true, "tactics": ["apply", "rw", "exact"], "tactic_count": 3}
{"name": "ComplexShape.next_eq_self'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ComplexShape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.prev_eq_self'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ComplexShape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.next_eq_self", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ComplexShape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.prev_eq_self", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ComplexShape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.up'", "kind": "definition", "module": "Mathlib.Algebra.Homology.ComplexShape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.down'", "kind": "definition", "module": "Mathlib.Algebra.Homology.ComplexShape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.down'_mk", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ComplexShape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.up", "kind": "definition", "module": "Mathlib.Algebra.Homology.ComplexShape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.down", "kind": "definition", "module": "Mathlib.Algebra.Homology.ComplexShape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.down_mk", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ComplexShape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.instDecidableRelRelUp'", "kind": "instance", "module": "Mathlib.Algebra.Homology.ComplexShape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.instDecidableRelRelDown'", "kind": "instance", "module": "Mathlib.Algebra.Homology.ComplexShape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.instDecidableRelRelUp", "kind": "instance", "module": "Mathlib.Algebra.Homology.ComplexShape", "is_tactic_proof": true, "tactics": ["dsimp"], "tactic_count": 1}
{"name": "ComplexShape.instDecidableRelRelDown", "kind": "instance", "module": "Mathlib.Algebra.Homology.ComplexShape", "is_tactic_proof": true, "tactics": ["dsimp"], "tactic_count": 1}
{"name": "ComplexShape.π", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.ComplexShapeSigns", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.ε₁", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.ComplexShapeSigns", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.ε₂", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.ComplexShapeSigns", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.rel_π₁", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ComplexShapeSigns", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.next_π₁", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ComplexShapeSigns", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ComplexShape.prev_π₂", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ComplexShapeSigns", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ComplexShape.rel_add", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ComplexShapeSigns", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ComplexShape.instTensorSignsNatDown", "kind": "instance", "module": "Mathlib.Algebra.Homology.ComplexShapeSigns", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ComplexShape.instTensorSignsIntUp", "kind": "instance", "module": "Mathlib.Algebra.Homology.ComplexShapeSigns", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ComplexShape.σ", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.ComplexShapeSigns", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ComplexShape.σ_ε₁", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ComplexShapeSigns", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "DerivedCategory.Qh_obj_singleFunctors_obj", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.Basic", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
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{"name": "CategoryTheory.Functor.mapDerivedCategory", "kind": "definition", "module": "Mathlib.Algebra.Homology.DerivedCategory.ExactFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapDerivedCategoryFactors", "kind": "definition", "module": "Mathlib.Algebra.Homology.DerivedCategory.ExactFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instLiftingCochainComplexIntDerivedCategoryQQuasiIsoUpCompHomologicalComplexMapHomologicalComplexMapDerivedCategory", "kind": "instance", "module": "Mathlib.Algebra.Homology.DerivedCategory.ExactFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapDerivedCategoryFactorsh", "kind": "definition", "module": "Mathlib.Algebra.Homology.DerivedCategory.ExactFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapDerivedCategoryFactorsh_hom_app", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.ExactFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instLiftingHomotopyCategoryIntUpDerivedCategoryQhQuasiIsoCompMapHomotopyCategoryMapDerivedCategory", "kind": "instance", "module": "Mathlib.Algebra.Homology.DerivedCategory.ExactFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instCommShiftDerivedCategoryMapDerivedCategoryInt", "kind": "instance", "module": "Mathlib.Algebra.Homology.DerivedCategory.ExactFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instCommShiftHomotopyCategoryIntUpDerivedCategoryHomMapDerivedCategoryFactorsh", "kind": "instance", "module": "Mathlib.Algebra.Homology.DerivedCategory.ExactFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instCommShiftCochainComplexIntDerivedCategoryHomMapDerivedCategoryFactors", "kind": "instance", "module": "Mathlib.Algebra.Homology.DerivedCategory.ExactFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instIsTriangulatedDerivedCategoryMapDerivedCategory", "kind": "instance", "module": "Mathlib.Algebra.Homology.DerivedCategory.ExactFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instCommShiftHomologicalComplexIntUpFunctorQuasiIsoMapHomologicalComplexUpToQuasiIsoLocalizerMorphism", "kind": "instance", "module": "Mathlib.Algebra.Homology.DerivedCategory.ExactFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapDerivedCategorySingleFunctor", "kind": "definition", "module": "Mathlib.Algebra.Homology.DerivedCategory.ExactFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instLinearDerivedCategoryMapDerivedCategory", "kind": "instance", "module": "Mathlib.Algebra.Homology.DerivedCategory.ExactFunctor", "is_tactic_proof": false, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.HasExt", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.hasExt_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "simp", "constructor", "intro", "exact", "intro", "obtain", "refine", "exact", "suffices", "from", "constructor", "intro", "rw", "have", "have", "apply"], "tactic_count": 17}
{"name": "CategoryTheory.hasExt_of_hasDerivedCategory", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.HasExt.standard", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic", "is_tactic_proof": true, "tactics": ["letI", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.instSmallHomDerivedCategoryObjSingleFunctorOfHasExt", "kind": "instance", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic", "is_tactic_proof": false, "tactics": ["have", "inferInstance", "exact", "small_of_injective", "φ"], "tactic_count": 5}
{"name": "CategoryTheory.Abelian.Ext", "kind": "definition", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.Ext.comp", "kind": "definition", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.Ext.comp_assoc", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.Ext.comp_assoc_of_second_deg_zero", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic", "is_tactic_proof": true, "tactics": ["apply", "lia"], "tactic_count": 2}
{"name": "CategoryTheory.Abelian.Ext.comp_assoc_of_third_deg_zero", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic", "is_tactic_proof": true, "tactics": ["apply", "lia"], "tactic_count": 2}
{"name": "CategoryTheory.Abelian.Ext.homEquiv", "kind": "definition", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.Ext.hom", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.Ext.comp_hom", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Abelian.Ext.ext", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.Ext.mk₀", "kind": "definition", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.Ext.mk₀_hom", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Abelian.Ext.mk₀_comp_mk₀", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic", "is_tactic_proof": true, "tactics": ["letI"], "tactic_count": 1}
{"name": "CategoryTheory.Abelian.Ext.mk₀_comp_mk₀_assoc", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic", "is_tactic_proof": true, "tactics": ["rw", "lia"], "tactic_count": 2}
{"name": "CategoryTheory.Abelian.Ext.mk₀_bijective", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic", "is_tactic_proof": true, "tactics": ["letI", "have", "let", "have", "ext", "dsimp", "apply", "apply", "symm", "apply", "rw", "exact"], "tactic_count": 12}
{"name": "CategoryTheory.Abelian.Ext.homEquiv₀", "kind": "definition", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.Ext.mk₀_homEquiv₀_apply", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.Ext.instAddCommGroup", "kind": "instance", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.Ext.hom'", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic.0.CategoryTheory.Abelian.Ext.add_hom'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic.0.CategoryTheory.Abelian.Ext.neg_hom'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic.0.CategoryTheory.Abelian.Ext.zero_hom'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.Ext.add_comp", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic", "is_tactic_proof": true, "tactics": ["letI"], "tactic_count": 1}
{"name": "CategoryTheory.Abelian.Ext.comp_add", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic", "is_tactic_proof": true, "tactics": ["letI"], "tactic_count": 1}
{"name": "CategoryTheory.Abelian.Ext.neg_comp", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic", "is_tactic_proof": true, "tactics": ["letI"], "tactic_count": 1}
{"name": "CategoryTheory.Abelian.Ext.comp_neg", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic", "is_tactic_proof": true, "tactics": ["letI"], "tactic_count": 1}
{"name": "CategoryTheory.Abelian.Ext.zero_comp", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic", "is_tactic_proof": true, "tactics": ["letI"], "tactic_count": 1}
{"name": "CategoryTheory.Abelian.Ext.comp_zero", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic", "is_tactic_proof": true, "tactics": ["letI"], "tactic_count": 1}
{"name": "CategoryTheory.Abelian.Ext.mk₀_id_comp", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic", "is_tactic_proof": true, "tactics": ["letI"], "tactic_count": 1}
{"name": "CategoryTheory.Abelian.Ext.comp_mk₀_id", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic", "is_tactic_proof": true, "tactics": ["letI"], "tactic_count": 1}
{"name": "CategoryTheory.Abelian.Ext.mk₀_zero", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic", "is_tactic_proof": true, "tactics": ["letI"], "tactic_count": 1}
{"name": "CategoryTheory.Abelian.Ext.mk₀_add", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic", "is_tactic_proof": true, "tactics": ["letI"], "tactic_count": 1}
{"name": "CategoryTheory.Abelian.Ext.addEquiv₀", "kind": "definition", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.Ext.mk₀_addEquiv₀_apply", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.Ext.mk₀_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.Ext.biprod_ext", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic", "is_tactic_proof": true, "tactics": ["letI", "rw", "simp", "apply", "all_goals"], "tactic_count": 5}
{"name": "CategoryTheory.Abelian.Ext.zero_hom", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic", "is_tactic_proof": true, "tactics": ["let", "have", "have", "rw"], "tactic_count": 4}
{"name": "CategoryTheory.Abelian.Ext.add_hom", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic", "is_tactic_proof": true, "tactics": ["let", "let", "have", "have", "apply", "all_goals", "simp", "congr", "dsimp", "rw", "dsimp", "rw", "dsimp", "rw", "dsimp", "rw"], "tactic_count": 16}
{"name": "CategoryTheory.Abelian.Ext.neg_hom", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Abelian.Ext.homAddEquiv", "kind": "definition", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.Ext.homAddEquiv_apply", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.Ext.bilinearComp", "kind": "definition", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.Ext.postcomp", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.Ext.precomp", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.extFunctorObj", "kind": "definition", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.extFunctor", "kind": "definition", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.instAdditiveAddCommGrpCatExtFunctorObj", "kind": "instance", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.instAdditiveOppositeFunctorAddCommGrpCatExtFunctor", "kind": "instance", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.Ext.comp_sum", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.Ext.sum_comp", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.Ext.mk₀_sum", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.Ext.biproductAddEquiv", "kind": "definition", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.Ext.addEquivBiproduct", "kind": "definition", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.Ext.chgUniv", "kind": "definition", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.Ext.homEquiv_chgUniv", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.hasExt_iff_small_ext", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic", "is_tactic_proof": true, "tactics": ["letI", "simp", "constructor", "intro", "exact", "intro", "lift", "exact"], "tactic_count": 8}
{"name": "CochainComplex.isSplitMono_from_singleFunctor_obj_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.EnoughInjectives", "is_tactic_proof": true, "tactics": ["let", "let", "have", "rw", "dsimp", "rw", "dsimp", "rw", "exact", "retraction", "mkHomToSingle", "rintro", "apply", "id", "apply", "rw"], "tactic_count": 16}
{"name": "DerivedCategory.to_singleFunctor_obj_eq_zero_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.EnoughInjectives", "is_tactic_proof": true, "tactics": ["obtain", "have", "rw", "exact", "have", "rw", "have", "apply", "apply", "rw"], "tactic_count": 10}
{"name": "CategoryTheory.Abelian.Ext.eq_zero_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.EnoughInjectives", "is_tactic_proof": true, "tactics": ["let", "have", "letI", "apply", "simp", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.Abelian.Ext.subsingleton_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.EnoughInjectives", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.hasExt_of_enoughInjectives", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.EnoughInjectives", "is_tactic_proof": true, "tactics": ["letI", "have", "rw", "intro", "induction", "zero", "rw", "infer_instance", "succ", "let", "have", "have", "exact"], "tactic_count": 13}
{"name": "CochainComplex.isSplitEpi_to_singleFunctor_obj_of_projective", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.EnoughProjectives", "is_tactic_proof": true, "tactics": ["let", "let", "have", "rw", "dsimp", "rw", "dsimp", "rw", "cyclesMap_i]", "exact", "section_", "mkHomFromSingle", "rintro", "apply", "id", "apply", "rw", "rfl"], "tactic_count": 18}
{"name": "DerivedCategory.from_singleFunctor_obj_eq_zero_of_projective", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.EnoughProjectives", "is_tactic_proof": true, "tactics": ["obtain", "have", "rw", "exact", "have", "rw", "have", "apply", "apply", "rw"], "tactic_count": 10}
{"name": "CategoryTheory.Abelian.Ext.eq_zero_of_projective", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.EnoughProjectives", "is_tactic_proof": true, "tactics": ["letI", "apply", "simp", "apply", "from_singleFunctor_obj_eq_zero_of_projective"], "tactic_count": 5}
{"name": "CategoryTheory.Abelian.Ext.subsingleton_of_projective", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.EnoughProjectives", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.hasExt_of_enoughProjectives", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.EnoughProjectives", "is_tactic_proof": true, "tactics": ["letI", "have", "rw", "intro", "induction", "zero", "rw", "infer_instance", "succ", "let", "have", "have", "exact"], "tactic_count": 13}
{"name": "CategoryTheory.Abelian.Ext.hom_comp_singleFunctor_map_shift", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.ExactSequences", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Abelian.Ext.preadditiveCoyoneda_homologySequenceδ_singleTriangle_apply", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.ExactSequences", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "CategoryTheory.Abelian.Ext.covariant_sequence_exact₂'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.ExactSequences", "is_tactic_proof": true, "tactics": ["letI", "have", "rw", "apply", "all_goals"], "tactic_count": 5}
{"name": "CategoryTheory.Abelian.Ext.covariant_sequence_exact₃'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.ExactSequences", "is_tactic_proof": true, "tactics": ["letI", "have", "rw", "apply", "ext", "ext", "exact"], "tactic_count": 7}
{"name": "CategoryTheory.Abelian.Ext.covariant_sequence_exact₁'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.ExactSequences", "is_tactic_proof": true, "tactics": ["letI", "have", "rw", "apply", "ext", "exact", "ext"], "tactic_count": 7}
{"name": "CategoryTheory.Abelian.Ext.covariantSequence", "kind": "definition", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.ExactSequences", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.Ext.covariantSequence_exact", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.ExactSequences", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.Ext.covariant_sequence_exact₁", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.ExactSequences", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Abelian.Ext.covariant_sequence_exact₂", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.ExactSequences", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Abelian.Ext.covariant_sequence_exact₃", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.ExactSequences", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Abelian.Ext.postcomp_mk₀_injective_of_mono", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.ExactSequences", "is_tactic_proof": true, "tactics": ["rw", "intro", "obtain", "simpa"], "tactic_count": 4}
{"name": "CategoryTheory.Abelian.Ext.mono_postcomp_mk₀_of_mono", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.ExactSequences", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.Ext.singleFunctor_map_comp_hom", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.ExactSequences", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Abelian.Ext.preadditiveYoneda_homologySequenceδ_singleTriangle_apply", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.Ext.ExactSequences", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
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{"name": "DerivedCategory.HomologySequence.exact₃", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.HomologySequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DerivedCategory.HomologySequence.exact₁", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.HomologySequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DerivedCategory.HomologySequence.epi_homologyMap_mor₁_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.HomologySequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DerivedCategory.HomologySequence.mono_homologyMap_mor₁_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.HomologySequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DerivedCategory.HomologySequence.epi_homologyMap_mor₂_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.HomologySequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DerivedCategory.HomologySequence.mono_homologyMap_mor₂_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.HomologySequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.IsKInjective.Qh_map_bijective", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.KInjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.HomComplex.CohomologyClass.bijective_toSmallShiftedHom_of_isKInjective", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.KInjective", "is_tactic_proof": true, "tactics": ["letI", "rw", "convert", "ext", "obtain", "simp"], "tactic_count": 6}
{"name": "CochainComplex.HomComplex.CohomologyClass.equivOfIsKInjective", "kind": "definition", "module": "Mathlib.Algebra.Homology.DerivedCategory.KInjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.IsKProjective.Qh_map_bijective", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.KProjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.HomComplex.CohomologyClass.bijective_toSmallShiftedHom_of_isKProjective", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.KProjective", "is_tactic_proof": true, "tactics": ["letI", "rw", "convert", "ext", "obtain", "simp"], "tactic_count": 6}
{"name": "CochainComplex.HomComplex.CohomologyClass.equivOfIsKProjective", "kind": "definition", "module": "Mathlib.Algebra.Homology.DerivedCategory.KProjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DerivedCategory.instLinear", "kind": "instance", "module": "Mathlib.Algebra.Homology.DerivedCategory.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DerivedCategory.instLinearHomotopyCategoryIntUpQh", "kind": "instance", "module": "Mathlib.Algebra.Homology.DerivedCategory.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DerivedCategory.instLinearCochainComplexIntQ", "kind": "instance", "module": "Mathlib.Algebra.Homology.DerivedCategory.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DerivedCategory.instLinearShiftFunctorInt", "kind": "instance", "module": "Mathlib.Algebra.Homology.DerivedCategory.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DerivedCategory.instLinearSingleFunctor", "kind": "instance", "module": "Mathlib.Algebra.Homology.DerivedCategory.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DerivedCategory.triangleOfSESδ", "kind": "definition", "module": "Mathlib.Algebra.Homology.DerivedCategory.ShortExact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DerivedCategory.triangleOfSES", "kind": "definition", "module": "Mathlib.Algebra.Homology.DerivedCategory.ShortExact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DerivedCategory.triangleOfSESIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.DerivedCategory.ShortExact", "is_tactic_proof": true, "tactics": ["have", "refine", "dsimp", "simp", "dsimp", "simp", "dsimp", "rw"], "tactic_count": 8}
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{"name": "CategoryTheory.ShortComplex.ShortExact.singleδ", "kind": "definition", "module": "Mathlib.Algebra.Homology.DerivedCategory.SingleTriangle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.ShortExact.singleTriangle", "kind": "definition", "module": "Mathlib.Algebra.Homology.DerivedCategory.SingleTriangle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.ShortExact.singleTriangleIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.DerivedCategory.SingleTriangle", "is_tactic_proof": true, "tactics": ["let", "refine", "cat_disch", "cat_disch", "simp"], "tactic_count": 5}
{"name": "CategoryTheory.ShortComplex.ShortExact.singleTriangle_distinguished", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.SingleTriangle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.HomComplex.CohomologyClass.toSmallShiftedHom", "kind": "definition", "module": "Mathlib.Algebra.Homology.DerivedCategory.SmallShiftedHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.HomComplex.CohomologyClass.toSmallShiftedHom_mk", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.SmallShiftedHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.HomComplex.CohomologyClass.equiv_toSmallShiftedHom_mk", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.SmallShiftedHom", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DerivedCategory.TStructure.t", "kind": "definition", "module": "Mathlib.Algebra.Homology.DerivedCategory.TStructure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DerivedCategory.IsLE", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.DerivedCategory.TStructure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DerivedCategory.IsGE", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.DerivedCategory.TStructure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DerivedCategory.isGE_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.TStructure", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "apply", "exact", "intro", "have", "rw", "intro", "rw", "apply", "exact", "exact", "inferInstance⟩"], "tactic_count": 13}
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{"name": "DerivedCategory.isZero_of_isLE", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.TStructure", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
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{"name": "DerivedCategory.instIsGEObjCochainComplexIntQOfIsGE", "kind": "instance", "module": "Mathlib.Algebra.Homology.DerivedCategory.TStructure", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "DerivedCategory.instIsLEObjCochainComplexIntQOfIsLE", "kind": "instance", "module": "Mathlib.Algebra.Homology.DerivedCategory.TStructure", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "DerivedCategory.instIsGEObjSingleFunctor", "kind": "instance", "module": "Mathlib.Algebra.Homology.DerivedCategory.TStructure", "is_tactic_proof": true, "tactics": ["let", "dsimp", "exact"], "tactic_count": 3}
{"name": "DerivedCategory.instIsLEObjSingleFunctor", "kind": "instance", "module": "Mathlib.Algebra.Homology.DerivedCategory.TStructure", "is_tactic_proof": true, "tactics": ["let", "dsimp", "exact"], "tactic_count": 3}
{"name": "DerivedCategory.exists_iso_Q_obj_of_isLE", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.TStructure", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "DerivedCategory.exists_iso_Q_obj_of_isGE", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.TStructure", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "DerivedCategory.exists_iso_Q_obj_of_isGE_of_isLE", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.TStructure", "is_tactic_proof": true, "tactics": ["obtain", "have", "rw", "exact", "exact"], "tactic_count": 5}
{"name": "DerivedCategory.exists_iso_singleFunctor_obj_of_isGE_of_isLE", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DerivedCategory.TStructure", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.DifferentialObject.objEqToHom", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.DifferentialObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.DifferentialObject.objEqToHom_refl", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DifferentialObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.DifferentialObject.objEqToHom_d", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DifferentialObject", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "CategoryTheory.DifferentialObject.d_squared_apply", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DifferentialObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.DifferentialObject.eqToHom_f'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DifferentialObject", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "HomologicalComplex.d_eqToHom", "kind": "theorem", "module": "Mathlib.Algebra.Homology.DifferentialObject", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "HomologicalComplex.dgoToHomologicalComplex", "kind": "definition", "module": "Mathlib.Algebra.Homology.DifferentialObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.homologicalComplexToDGO", "kind": "definition", "module": "Mathlib.Algebra.Homology.DifferentialObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.dgoEquivHomologicalComplexUnitIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.DifferentialObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.dgoEquivHomologicalComplexCounitIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.DifferentialObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.dgoEquivHomologicalComplex", "kind": "definition", "module": "Mathlib.Algebra.Homology.DifferentialObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.double", "kind": "definition", "module": "Mathlib.Algebra.Homology.Double", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.isZero_double_X", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Double", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "exact"], "tactic_count": 3}
{"name": "HomologicalComplex.doubleXIso₀", "kind": "definition", "module": "Mathlib.Algebra.Homology.Double", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.doubleXIso₁", "kind": "definition", "module": "Mathlib.Algebra.Homology.Double", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.double_d", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Double", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.double_d_eq_zero₀", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Double", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.double_d_eq_zero₁", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Double", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.from_double_hom_ext", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Double", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "obtain", "simp", "apply"], "tactic_count": 5}
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{"name": "HomologicalComplex.mkHomFromDouble_f₁", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Double", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
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{"name": "HomologicalComplex.evalCompCoyonedaCorepresentableBySingle", "kind": "definition", "module": "Mathlib.Algebra.Homology.Double", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.evalCompCoyonedaCorepresentative", "kind": "definition", "module": "Mathlib.Algebra.Homology.Double", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.evalCompCoyonedaCorepresentable", "kind": "definition", "module": "Mathlib.Algebra.Homology.Double", "is_tactic_proof": true, "tactics": ["dsimp", "classical", "split_ifs", "exact", "apply", "obtain"], "tactic_count": 6}
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{"name": "ComplexShape.Embedding.AreComplementary.Boundary.fst", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.AreComplementary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ComplexShape.Embedding.embeddingUpInt_areComplementary", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.AreComplementary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.shortComplexTruncLEX₃ToTruncGE", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.AreComplementary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.g_shortComplexTruncLEX₃ToTruncGE", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.AreComplementary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ComplexShape.Embedding.op", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.Embedding.rel_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.Basic", "is_tactic_proof": true, "tactics": ["constructor", "apply", "exact"], "tactic_count": 3}
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{"name": "ComplexShape.Embedding.mk'", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.Embedding.instIsRelIffMk'", "kind": "instance", "module": "Mathlib.Algebra.Homology.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.Embedding.mem_next", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.Embedding.mem_prev", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.Embedding.instIsTruncLEOpOfIsTruncGE", "kind": "instance", "module": "Mathlib.Algebra.Homology.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.Embedding.instIsTruncGEOpOfIsTruncLE", "kind": "instance", "module": "Mathlib.Algebra.Homology.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.Embedding.r", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.Embedding.r_eq_some", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.Basic", "is_tactic_proof": true, "tactics": ["have", "have", "dsimp", "rw"], "tactic_count": 4}
{"name": "ComplexShape.Embedding.r_eq_none", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.Embedding.r_f", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.Embedding.f_eq_of_r_eq_some", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "obtain", "rw", "congr", "simpa", "simp"], "tactic_count": 6}
{"name": "ComplexShape.embeddingUp'Add", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.instIsRelIffEmbeddingUp'Add", "kind": "instance", "module": "Mathlib.Algebra.Homology.Embedding.Basic", "is_tactic_proof": true, "tactics": ["dsimp"], "tactic_count": 1}
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{"name": "ComplexShape.embeddingDown'Add", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.instIsRelIffEmbeddingDown'Add", "kind": "instance", "module": "Mathlib.Algebra.Homology.Embedding.Basic", "is_tactic_proof": true, "tactics": ["dsimp"], "tactic_count": 1}
{"name": "ComplexShape.instIsTruncLEEmbeddingDown'Add", "kind": "instance", "module": "Mathlib.Algebra.Homology.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.embeddingUpNat", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.instIsRelIffNatIntEmbeddingUpNat", "kind": "instance", "module": "Mathlib.Algebra.Homology.Embedding.Basic", "is_tactic_proof": true, "tactics": ["dsimp"], "tactic_count": 1}
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{"name": "ComplexShape.embeddingDownNat", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.instIsRelIffNatIntEmbeddingDownNat", "kind": "instance", "module": "Mathlib.Algebra.Homology.Embedding.Basic", "is_tactic_proof": true, "tactics": ["dsimp"], "tactic_count": 1}
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{"name": "ComplexShape.embeddingUpIntGE", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.instIsRelIffNatIntEmbeddingUpIntGE", "kind": "instance", "module": "Mathlib.Algebra.Homology.Embedding.Basic", "is_tactic_proof": true, "tactics": ["dsimp"], "tactic_count": 1}
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{"name": "ComplexShape.embeddingUpIntLE", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.instIsRelIffNatIntEmbeddingUpIntLE", "kind": "instance", "module": "Mathlib.Algebra.Homology.Embedding.Basic", "is_tactic_proof": true, "tactics": ["dsimp"], "tactic_count": 1}
{"name": "ComplexShape.instIsTruncLENatIntEmbeddingUpIntLE", "kind": "instance", "module": "Mathlib.Algebra.Homology.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ComplexShape.Embedding.BoundaryGE", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.Boundary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.Embedding.boundaryGE", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.Boundary", "is_tactic_proof": true, "tactics": ["constructor", "simpa", "intro", "apply", "rw"], "tactic_count": 5}
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{"name": "ComplexShape.Embedding.prev_f_of_not_boundaryGE", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.Boundary", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "obtain", "apply", "intro", "simp", "obtain", "rw", "rw", "exact"], "tactic_count": 10}
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{"name": "ComplexShape.Embedding.BoundaryLE", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.Boundary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.Embedding.boundaryLE", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.Boundary", "is_tactic_proof": true, "tactics": ["constructor", "simpa", "intro", "apply", "rw"], "tactic_count": 5}
{"name": "ComplexShape.Embedding.not_boundaryLE_prev", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.Boundary", "is_tactic_proof": true, "tactics": ["dsimp", "simp", "intro", "exact"], "tactic_count": 4}
{"name": "ComplexShape.Embedding.not_boundaryLE_prev'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.Boundary", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "subst", "simpa"], "tactic_count": 4}
{"name": "ComplexShape.Embedding.BoundaryLE.notMem", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.Boundary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.Embedding.next_f_of_not_boundaryLE", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.Boundary", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "obtain", "apply", "intro", "simp", "obtain", "rw", "rw", "exact"], "tactic_count": 10}
{"name": "ComplexShape.Embedding.next_f", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.Boundary", "is_tactic_proof": true, "tactics": ["by_cases", "obtain", "rw", "rw", "rw", "intro", "apply", "rw", "simpa"], "tactic_count": 9}
{"name": "ComplexShape.Embedding.prev_f", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.Boundary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.Embedding.BoundaryLE.false_of_isTruncGE", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.Boundary", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "ComplexShape.Embedding.op_boundaryLE_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.Boundary", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "ComplexShape.Embedding.op_boundaryGE_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.Boundary", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "ComplexShape.boundaryGE_embeddingUpIntGE_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.Boundary", "is_tactic_proof": true, "tactics": ["constructor", "intro", "obtain", "rfl", "have", "dsimp", "lia", "rintro", "constructor", "simp", "intro", "dsimp", "lia"], "tactic_count": 13}
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{"name": "CochainComplex.truncLE", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.Embedding.CochainComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.truncGE", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.Embedding.CochainComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.ιTruncLE", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.CochainComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.πTruncGE", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.CochainComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.truncLEMap", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.Embedding.CochainComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.truncGEMap", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.Embedding.CochainComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.ιTruncLE_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.CochainComplex", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CochainComplex.πTruncGE_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.CochainComplex", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CochainComplex.IsStrictlyGE", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.Embedding.CochainComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.IsStrictlyLE", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.Embedding.CochainComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.IsGE", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.Embedding.CochainComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.IsLE", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.Embedding.CochainComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.isStrictlyGE_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.CochainComplex", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "intro", "refine", "rw", "exact"], "tactic_count": 7}
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{"name": "CochainComplex.isLE_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.CochainComplex", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "intro", "refine", "rw", "exact"], "tactic_count": 7}
{"name": "CochainComplex.isStrictlyLE_of_le", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.CochainComplex", "is_tactic_proof": true, "tactics": ["rw", "intro", "exact"], "tactic_count": 3}
{"name": "CochainComplex.isStrictlyGE_of_ge", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.CochainComplex", "is_tactic_proof": true, "tactics": ["rw", "intro", "exact"], "tactic_count": 3}
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{"name": "CochainComplex.isGE_of_ge", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.CochainComplex", "is_tactic_proof": true, "tactics": ["rw", "intro", "exact"], "tactic_count": 3}
{"name": "CochainComplex.isStrictlyLE_of_iso", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.CochainComplex", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CochainComplex.isStrictlyGE_of_iso", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.CochainComplex", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CochainComplex.isLE_of_iso", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.CochainComplex", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CochainComplex.isGE_of_iso", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.CochainComplex", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CochainComplex.instIsStrictlyGEExtendNatIntEmbeddingUpNatOfNat", "kind": "instance", "module": "Mathlib.Algebra.Homology.Embedding.CochainComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.instIsStrictlyLEExtendNatIntEmbeddingDownNatOfNat", "kind": "instance", "module": "Mathlib.Algebra.Homology.Embedding.CochainComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.exists_iso_single", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.CochainComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.instIsStrictlyGEObjHomologicalComplexIntUpSingle", "kind": "instance", "module": "Mathlib.Algebra.Homology.Embedding.CochainComplex", "is_tactic_proof": true, "tactics": ["rw", "intro", "exact"], "tactic_count": 3}
{"name": "CochainComplex.instIsStrictlyLEObjHomologicalComplexIntUpSingle", "kind": "instance", "module": "Mathlib.Algebra.Homology.Embedding.CochainComplex", "is_tactic_proof": true, "tactics": ["rw", "intro", "exact"], "tactic_count": 3}
{"name": "CochainComplex.instIsIsoIntπTruncGEOfIsStrictlyGE", "kind": "instance", "module": "Mathlib.Algebra.Homology.Embedding.CochainComplex", "is_tactic_proof": true, "tactics": ["dsimp"], "tactic_count": 1}
{"name": "CochainComplex.instIsIsoIntιTruncLEOfIsStrictlyLE", "kind": "instance", "module": "Mathlib.Algebra.Homology.Embedding.CochainComplex", "is_tactic_proof": true, "tactics": ["dsimp"], "tactic_count": 1}
{"name": "CochainComplex.isIso_πTruncGE_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.CochainComplex", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CochainComplex.isIso_ιTruncLE_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.CochainComplex", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CochainComplex.quasiIso_πTruncGE_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.CochainComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.quasiIso_ιTruncLE_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.CochainComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.instQuasiIsoIntπTruncGEOfIsGE", "kind": "instance", "module": "Mathlib.Algebra.Homology.Embedding.CochainComplex", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CochainComplex.instQuasiIsoIntιTruncLEOfIsLE", "kind": "instance", "module": "Mathlib.Algebra.Homology.Embedding.CochainComplex", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CochainComplex.quasiIso_truncGEMap_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.CochainComplex", "is_tactic_proof": true, "tactics": ["rw", "constructor", "intro", "obtain", "exact", "rintro", "exact"], "tactic_count": 7}
{"name": "CochainComplex.quasiIso_truncLEMap_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.CochainComplex", "is_tactic_proof": true, "tactics": ["rw", "constructor", "intro", "obtain", "exact", "rintro", "exact"], "tactic_count": 7}
{"name": "CochainComplex.instIsStrictlyGEObjIntSingleFunctor", "kind": "instance", "module": "Mathlib.Algebra.Homology.Embedding.CochainComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.instIsStrictlyLEObjIntSingleFunctor", "kind": "instance", "module": "Mathlib.Algebra.Homology.Embedding.CochainComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.isStrictlyLE_shift", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.CochainComplex", "is_tactic_proof": true, "tactics": ["rw", "intro", "exact"], "tactic_count": 3}
{"name": "CochainComplex.isStrictlyGE_shift", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.CochainComplex", "is_tactic_proof": true, "tactics": ["rw", "intro", "exact"], "tactic_count": 3}
{"name": "CochainComplex.isLE_shift", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.CochainComplex", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "exact"], "tactic_count": 4}
{"name": "CochainComplex.isGE_shift", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.CochainComplex", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "exact"], "tactic_count": 4}
{"name": "CochainComplex.shortComplexTruncLE", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.Embedding.CochainComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.shortComplexTruncLE_shortExact", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.CochainComplex", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CochainComplex.shortComplexTruncLEX₃ToTruncGE", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.Embedding.CochainComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.g_shortComplexTruncLEX₃ToTruncGE", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.CochainComplex", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CochainComplex.ConnectData.X", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.Connect", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.ConnectData.X_ofNat", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.Connect", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.ConnectData.X_negSucc", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.Connect", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.ConnectData.X_zero", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.Connect", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.ConnectData.X_negOne", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.Connect", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.ConnectData.d", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.Connect", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.ConnectData.d_ofNat", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.Connect", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.ConnectData.d_negSucc", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.Connect", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CochainComplex.ConnectData.d_sub_one_zero", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.Connect", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.ConnectData.d_zero_one", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.Connect", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.ConnectData.d_sub_two_sub_one", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.Connect", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.ConnectData.shape", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.Connect", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.ConnectData.d_comp_d", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.Connect", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "by_cases", "rw", "obtain", "obtain", "obtain", "simp", "obtain", "obtain", "simp", "obtain", "obtain", "simp", "obtain", "obtain", "simp"], "tactic_count": 17}
{"name": "CochainComplex.ConnectData.cochainComplex", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.Connect", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.ConnectData.restrictionGEIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.Connect", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.ConnectData.restrictionLEIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.Connect", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.ConnectData.homologyIsoPos", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.Connect", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.ConnectData.homologyIsoNeg", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.Connect", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.ConnectData.map", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.Connect", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.ConnectData.map_id", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.Connect", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CochainComplex.ConnectData.map_comp_map", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.Connect", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CochainComplex.ConnectData.homologyMap_map_of_eq_succ", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.Connect", "is_tactic_proof": true, "tactics": ["rw", "dsimp", "simp", "restrictionHomologyIso_inv_homologyι_assoc]", "congr", "rw", "subst", "simp"], "tactic_count": 8}
{"name": "CochainComplex.ConnectData.homologyMap_map_of_eq_neg_succ", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.Connect", "is_tactic_proof": true, "tactics": ["rw", "dsimp", "simp", "restrictionHomologyIso_inv_homologyι_assoc]", "congr", "rw", "obtain", "simp"], "tactic_count": 8}
{"name": "HomologicalComplex.extend.X", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.extend.XIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.extend.isZero_X", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.Extend", "is_tactic_proof": true, "tactics": ["subst", "exact"], "tactic_count": 2}
{"name": "HomologicalComplex.extend.XOpIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.extend.d", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.extend.d_none_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.Extend", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "HomologicalComplex.extend.d_none_eq_zero'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.Extend", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "HomologicalComplex.extend.d_eq", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.Extend", "is_tactic_proof": true, "tactics": ["subst", "simp"], "tactic_count": 2}
{"name": "HomologicalComplex.extend.XOpIso_hom_d_op", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.extend.mapX", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.extend.mapX_some", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.Extend", "is_tactic_proof": true, "tactics": ["subst", "dsimp", "rw", "rfl"], "tactic_count": 4}
{"name": "HomologicalComplex.extend.mapX_none", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.Extend", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "HomologicalComplex.extend", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.extendXIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.isZero_extend_X'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.isZero_extend_X", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.instIsStrictlySupportedExtend", "kind": "instance", "module": "Mathlib.Algebra.Homology.Embedding.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.extend_d_eq", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.Extend", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "HomologicalComplex.extend_d_from_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.Extend", "is_tactic_proof": true, "tactics": ["obtain", "exact", "rw", "intro", "obtain", "exact"], "tactic_count": 6}
{"name": "HomologicalComplex.extend_d_to_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.Extend", "is_tactic_proof": true, "tactics": ["obtain", "exact", "rw", "intro", "obtain", "exact"], "tactic_count": 6}
{"name": "HomologicalComplex.extendMap", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.extendMap_f", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.Extend", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "rfl"], "tactic_count": 3}
{"name": "HomologicalComplex.extendMap_f_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.Extend", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "HomologicalComplex.extendMap_comp", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.Extend", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "obtain", "simp", "simp"], "tactic_count": 5}
{"name": "HomologicalComplex.extendMap_id_f", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.Extend", "is_tactic_proof": true, "tactics": ["by_cases", "obtain", "simp", "apply"], "tactic_count": 4}
{"name": "HomologicalComplex.extendMap_id", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.Extend", "is_tactic_proof": true, "tactics": ["ext", "simpa"], "tactic_count": 2}
{"name": "HomologicalComplex.extendMap_zero", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.Extend", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "obtain", "simp", "apply"], "tactic_count": 5}
{"name": "HomologicalComplex.extendOpIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.extend_op_d", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.Extend", "is_tactic_proof": true, "tactics": ["have", "dsimp", "rw"], "tactic_count": 3}
{"name": "HomologicalComplex.extendMap_add", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.Extend", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "obtain", "simp", "apply"], "tactic_count": 5}
{"name": "HomologicalComplex.extend_single_d", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.Extend", "is_tactic_proof": true, "tactics": ["by_cases", "obtain", "by_cases", "obtain", "simp", "exact", "exact"], "tactic_count": 7}
{"name": "HomologicalComplex.extendSingleIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.extendSingleIso_hom_f", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.Extend", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HomologicalComplex.extendSingleIso_inv_f", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.Extend", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ComplexShape.Embedding.extendFunctor", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.Embedding.instPreservesZeroMorphismsHomologicalComplexExtendFunctor", "kind": "instance", "module": "Mathlib.Algebra.Homology.Embedding.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.Embedding.instAdditiveHomologicalComplexExtendFunctor", "kind": "instance", "module": "Mathlib.Algebra.Homology.Embedding.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.Embedding.fullyFaithfulExtendFunctor", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.Embedding.instFaithfulHomologicalComplexExtendFunctor", "kind": "instance", "module": "Mathlib.Algebra.Homology.Embedding.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.Embedding.instFullHomologicalComplexExtendFunctor", "kind": "instance", "module": "Mathlib.Algebra.Homology.Embedding.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.extend.comp_d_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.ExtendHomology", "is_tactic_proof": true, "tactics": ["by_cases", "have", "rw", "simp", "rw", "rw", "exact"], "tactic_count": 7}
{"name": "HomologicalComplex.extend.d_comp_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.ExtendHomology", "is_tactic_proof": true, "tactics": ["by_cases", "have", "rw", "simp", "rw", "rw", "exact"], "tactic_count": 7}
{"name": "HomologicalComplex.extend.leftHomologyData.kernelFork", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.ExtendHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.extend.leftHomologyData.isLimitKernelFork", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.ExtendHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.extend.leftHomologyData.lift_d_comp_eq_zero_iff'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.ExtendHomology", "is_tactic_proof": true, "tactics": ["by_cases", "have", "have", "apply", "rw", "rw", "have", "apply", "simp", "have", "apply", "dsimp", "rw", "rw", "exact", "simp"], "tactic_count": 16}
{"name": "HomologicalComplex.extend.leftHomologyData.lift_d_comp_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.ExtendHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.extend.leftHomologyData.cokernelCofork", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.ExtendHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.extend.leftHomologyData.isColimitCokernelCofork", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.ExtendHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.extend.leftHomologyData", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.ExtendHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.extend.rightHomologyData.cokernelCofork", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.ExtendHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.extend.rightHomologyData.isColimitCokernelCofork", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.ExtendHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.extend.rightHomologyData.d_comp_desc_eq_zero_iff'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.ExtendHomology", "is_tactic_proof": true, "tactics": ["by_cases", "have", "have", "apply", "rw", "rw", "have", "apply", "simp", "have", "apply", "rw", "rw", "exact", "simp"], "tactic_count": 15}
{"name": "HomologicalComplex.extend.rightHomologyData.d_comp_desc_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.ExtendHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.extend.rightHomologyData.kernelFork", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.ExtendHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.extend.rightHomologyData.isLimitKernelFork", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.ExtendHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.extend.rightHomologyData", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.ExtendHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.extend.rightHomologyData_g'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.ExtendHomology", "is_tactic_proof": true, "tactics": ["rw", "have", "dsimp", "rw", "rw"], "tactic_count": 5}
{"name": "HomologicalComplex.extend.homologyData", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.ExtendHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.extend.homologyData'", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.ExtendHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.extend.hasHomology", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.ExtendHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.extend.instHasHomologyF", "kind": "instance", "module": "Mathlib.Algebra.Homology.Embedding.ExtendHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.extend.instHasHomology", "kind": "instance", "module": "Mathlib.Algebra.Homology.Embedding.ExtendHomology", "is_tactic_proof": true, "tactics": ["by_cases", "obtain", "infer_instance", "have", "exact"], "tactic_count": 5}
{"name": "HomologicalComplex.extend_exactAt", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.ExtendHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.extendCyclesIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.ExtendHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.extendOpcyclesIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.ExtendHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.extendHomologyIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.ExtendHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.extend_exactAt_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.ExtendHomology", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "HomologicalComplex.extendCyclesIso_hom_iCycles", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.ExtendHomology", "is_tactic_proof": true, "tactics": ["rw", "dsimp", "rw", "dsimp", "rw"], "tactic_count": 5}
{"name": "HomologicalComplex.extendCyclesIso_inv_iCycles", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.ExtendHomology", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HomologicalComplex.homologyπ_extendHomologyIso_hom", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.ExtendHomology", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "cancel_mono", "dsimp", "simp"], "tactic_count": 5}
{"name": "HomologicalComplex.homologyπ_extendHomologyIso_inv", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.ExtendHomology", "is_tactic_proof": true, "tactics": ["simp", "homologyπ_extendHomologyIso_hom,"], "tactic_count": 2}
{"name": "HomologicalComplex.pOpcycles_extendOpcyclesIso_inv", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.ExtendHomology", "is_tactic_proof": true, "tactics": ["rw", "dsimp", "rw", "dsimp", "rw", "rfl"], "tactic_count": 6}
{"name": "HomologicalComplex.pOpcycles_extendOpcyclesIso_hom", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.ExtendHomology", "is_tactic_proof": true, "tactics": ["simp", "pOpcycles_extendOpcyclesIso_inv,"], "tactic_count": 2}
{"name": "HomologicalComplex.extendHomologyIso_hom_homologyι", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.ExtendHomology", "is_tactic_proof": true, "tactics": ["simp", "extendCyclesIso_hom_iCycles_assoc,"], "tactic_count": 2}
{"name": "HomologicalComplex.extendHomologyIso_inv_homologyι", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.ExtendHomology", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HomologicalComplex.extendCyclesIso_hom_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.ExtendHomology", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HomologicalComplex.extendHomologyIso_hom_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.ExtendHomology", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HomologicalComplex.quasiIsoAt_extendMap_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.ExtendHomology", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "HomologicalComplex.quasiIso_extendMap_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.ExtendHomology", "is_tactic_proof": true, "tactics": ["simp", "constructor", "tauto", "intro", "by_cases", "obtain", "exact", "rw", "all_goals"], "tactic_count": 9}
{"name": "HomologicalComplex.instQuasiIsoExtendMap", "kind": "instance", "module": "Mathlib.Algebra.Homology.Embedding.ExtendHomology", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Homotopy.extend.homAux", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.ExtendHomotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homotopy.extend.homAux_eq", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.ExtendHomotopy", "is_tactic_proof": true, "tactics": ["subst", "simp"], "tactic_count": 2}
{"name": "Homotopy.extend.hom", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.ExtendHomotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homotopy.extend.hom_eq_zero₁", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.ExtendHomotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homotopy.extend.hom_eq_zero₂", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.ExtendHomotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homotopy.extend.hom_eq", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.ExtendHomotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homotopy.extend", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.ExtendHomotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homotopy.extend_hom_eq", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.ExtendHomotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homotopy.ofExtend", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.ExtendHomotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homotopy.extend_ofExtend", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.ExtendHomotopy", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "obtain", "by_cases", "obtain", "simp", "exact", "exact"], "tactic_count": 8}
{"name": "Homotopy.ofExtend_extend", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.ExtendHomotopy", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Homotopy.extendEquiv", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.ExtendHomotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.Embedding.extendHomotopyFunctor", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.ExtendHomotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.Embedding.extendHomotopyFunctorFactors", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.ExtendHomotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.Embedding.instFullHomotopyCategoryExtendHomotopyFunctor", "kind": "instance", "module": "Mathlib.Algebra.Homology.Embedding.ExtendHomotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.Embedding.instFaithfulHomotopyCategoryExtendHomotopyFunctor", "kind": "instance", "module": "Mathlib.Algebra.Homology.Embedding.ExtendHomotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.Embedding.HasLift", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.HomEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.Embedding.liftExtend.f", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.HomEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.Embedding.liftExtend.f_eq", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.HomEquiv", "is_tactic_proof": true, "tactics": ["have", "have", "grind"], "tactic_count": 3}
{"name": "ComplexShape.Embedding.liftExtend.comm", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.HomEquiv", "is_tactic_proof": true, "tactics": ["by_cases", "by_cases", "obtain", "rw", "by_cases", "obtain", "rw", "subst", "simp", "apply", "have", "rw", "by_cases", "obtain", "rw", "dsimp", "rw", "have", "rw", "simp"], "tactic_count": 20}
{"name": "ComplexShape.Embedding.liftExtend", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.HomEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.Embedding.liftExtend_f", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.HomEquiv", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "ComplexShape.Embedding.liftExtendfArrowIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.HomEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.Embedding.isIso_liftExtend_f_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.HomEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.Embedding.mono_liftExtend_f_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.HomEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.Embedding.epi_liftExtend_f_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.HomEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.Embedding.homRestrict.f", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.HomEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.Embedding.homRestrict.f_eq", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.HomEquiv", "is_tactic_proof": true, "tactics": ["subst", "simp"], "tactic_count": 2}
{"name": "ComplexShape.Embedding.homRestrict.comm", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.HomEquiv", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "ComplexShape.Embedding.homRestrict", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.HomEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.Embedding.homRestrict_f", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.HomEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.Embedding.homRestrict_hasLift", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.HomEquiv", "is_tactic_proof": true, "tactics": ["intro", "have", "dsimp", "rw", "comp_zero]"], "tactic_count": 5}
{"name": "ComplexShape.Embedding.liftExtend_homRestrict", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.HomEquiv", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "obtain", "simp", "apply"], "tactic_count": 5}
{"name": "ComplexShape.Embedding.homRestrict_liftExtend", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.HomEquiv", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "ComplexShape.Embedding.homRestrict_precomp", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.HomEquiv", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "ComplexShape.Embedding.homRestrict_comp_extendMap", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.HomEquiv", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "ComplexShape.Embedding.homEquiv", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.HomEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.isZero_X_of_isStrictlySupported", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.IsSupported", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.isStrictlySupported_of_iso", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.IsSupported", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.isStrictlySupported_op_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.IsSupported", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.instIsStrictlySupportedOppositeOpOp", "kind": "instance", "module": "Mathlib.Algebra.Homology.Embedding.IsSupported", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "HomologicalComplex.exactAt_of_isSupported", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.IsSupported", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.isSupported_of_iso", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.IsSupported", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.isSupported_iff_of_quasiIso", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.IsSupported", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HomologicalComplex.instIsSupportedOfIsStrictlySupported", "kind": "instance", "module": "Mathlib.Algebra.Homology.Embedding.IsSupported", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.isSupported_op_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.IsSupported", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.isStrictlySupportedOutside_op_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.IsSupported", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.isSupportedOutside_op_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.IsSupported", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.IsStrictlySupportedOutside.isSupportedOutside", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.IsSupported", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.instIsStrictlySupportedOfNat", "kind": "instance", "module": "Mathlib.Algebra.Homology.Embedding.IsSupported", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.isZero_iff_isStrictlySupported_and_isStrictlySupportedOutside", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.IsSupported", "is_tactic_proof": true, "tactics": ["constructor", "intro", "constructor", "all_goals", "constructor", "intros", "exact", "rintro", "rw", "ext", "apply", "by_cases", "obtain", "exact", "exact"], "tactic_count": 15}
{"name": "HomologicalComplex.map_isStrictlySupported", "kind": "instance", "module": "Mathlib.Algebra.Homology.Embedding.IsSupported", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.restriction", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.Restriction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.restrictionXIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.Restriction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.restriction_d_eq", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.Restriction", "is_tactic_proof": true, "tactics": ["subst", "simp"], "tactic_count": 2}
{"name": "HomologicalComplex.restrictionMap", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.Restriction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.restrictionMap_f'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.Restriction", "is_tactic_proof": true, "tactics": ["subst", "simp"], "tactic_count": 2}
{"name": "HomologicalComplex.restrictionMap_id", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.Restriction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.restrictionMap_comp", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.Restriction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.Embedding.restrictionFunctor", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.Restriction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.Embedding.instPreservesZeroMorphismsHomologicalComplexRestrictionFunctor", "kind": "instance", "module": "Mathlib.Algebra.Homology.Embedding.Restriction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.Embedding.instAdditiveHomologicalComplexRestrictionFunctor", "kind": "instance", "module": "Mathlib.Algebra.Homology.Embedding.Restriction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.restriction.sc'Iso", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.RestrictionHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.restriction.hasHomology", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.RestrictionHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.restrictionCyclesIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.RestrictionHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.restrictionCyclesIso_hom_iCycles", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.RestrictionHomology", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HomologicalComplex.restrictionCyclesIso_inv_iCycles", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.RestrictionHomology", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HomologicalComplex.restrictionOpcyclesIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.RestrictionHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.pOpcycles_restrictionOpcyclesIso_hom", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.RestrictionHomology", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HomologicalComplex.pOpcycles_restrictionOpcyclesIso_inv", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.RestrictionHomology", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HomologicalComplex.restrictionHomologyIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.RestrictionHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.homologyπ_restrictionHomologyIso_hom", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.RestrictionHomology", "is_tactic_proof": true, "tactics": ["have", "have", "dsimp", "rw", "apply", "dsimp", "rw", "apply", "congr", "symm", "apply"], "tactic_count": 11}
{"name": "HomologicalComplex.homologyπ_restrictionHomologyIso_inv", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.RestrictionHomology", "is_tactic_proof": true, "tactics": ["rw", "homologyπ_restrictionHomologyIso_hom,"], "tactic_count": 2}
{"name": "HomologicalComplex.restrictionHomologyIso_inv_homologyι", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.RestrictionHomology", "is_tactic_proof": true, "tactics": ["have", "have", "dsimp", "rw", "apply", "dsimp", "rw", "refine", "congr", "apply"], "tactic_count": 10}
{"name": "HomologicalComplex.restrictionHomologyIso_hom_homologyι", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.RestrictionHomology", "is_tactic_proof": true, "tactics": ["rw", "restrictionHomologyIso_inv_homologyι_assoc,"], "tactic_count": 2}
{"name": "HomologicalComplex.stupidTrunc", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.StupidTrunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.instIsStrictlySupportedStupidTrunc", "kind": "instance", "module": "Mathlib.Algebra.Homology.Embedding.StupidTrunc", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "HomologicalComplex.stupidTruncXIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.StupidTrunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.isZero_stupidTrunc_X", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.StupidTrunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.instIsStrictlySupportedStupidTrunc_1", "kind": "instance", "module": "Mathlib.Algebra.Homology.Embedding.StupidTrunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.isZero_stupidTrunc_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.StupidTrunc", "is_tactic_proof": true, "tactics": ["constructor", "exact", "intro", "rw", "constructor", "infer_instance", "exact"], "tactic_count": 7}
{"name": "HomologicalComplex.stupidTruncMap", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.StupidTrunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.stupidTruncMap_id", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.StupidTrunc", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HomologicalComplex.stupidTruncMap_comp", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.StupidTrunc", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HomologicalComplex.stupidTruncMap_stupidTruncXIso_hom", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.StupidTrunc", "is_tactic_proof": true, "tactics": ["subst", "simp"], "tactic_count": 2}
{"name": "ComplexShape.Embedding.stupidTruncFunctor", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.StupidTrunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.truncGE'.X", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.TruncGE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.truncGE'.XIsoOpcycles", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.TruncGE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.truncGE'.XIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.TruncGE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.truncGE'.d", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.TruncGE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.truncGE'.d_comp_d", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.TruncGE", "is_tactic_proof": true, "tactics": ["dsimp", "by_cases", "by_cases", "rw", "split_ifs", "rw", "rw"], "tactic_count": 7}
{"name": "HomologicalComplex.truncGE'", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.TruncGE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.truncGE'XIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.TruncGE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.truncGE'XIsoOpcycles", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.TruncGE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.truncGE'_d_eq", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.TruncGE", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "subst", "simp"], "tactic_count": 4}
{"name": "HomologicalComplex.truncGE'_d_eq_fromOpcycles", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.TruncGE", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "subst", "simp"], "tactic_count": 4}
{"name": "HomologicalComplex.truncGE", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.TruncGE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.truncGEXIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.TruncGE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.truncGEXIsoOpcycles", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.TruncGE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.truncGE'Map", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.TruncGE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.truncGE'Map_f_eq_opcyclesMap", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.TruncGE", "is_tactic_proof": true, "tactics": ["subst", "exact"], "tactic_count": 2}
{"name": "HomologicalComplex.truncGE'Map_f_eq", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.TruncGE", "is_tactic_proof": true, "tactics": ["subst", "exact"], "tactic_count": 2}
{"name": "HomologicalComplex.truncGE'Map_id", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.TruncGE", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "simp", "simp"], "tactic_count": 4}
{"name": "HomologicalComplex.truncGE'Map_comp", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.TruncGE", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "simp", "simp"], "tactic_count": 4}
{"name": "HomologicalComplex.truncGEMap", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.TruncGE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.truncGEMap_id", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.TruncGE", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HomologicalComplex.truncGEMap_comp", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.TruncGE", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "HomologicalComplex.restrictionToTruncGE'.f_eq_iso_hom_pOpcycles_iso_inv", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.TruncGE", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "subst", "simp"], "tactic_count": 4}
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{"name": "HomologicalComplex.restrictionToTruncGE'_hasLift", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.TruncGE", "is_tactic_proof": true, "tactics": ["intro", "dsimp", "rw", "simp"], "tactic_count": 4}
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{"name": "ComplexShape.Embedding.restrictionToTruncGE'NatTrans", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.TruncGE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ComplexShape.Embedding.πTruncGENatTrans", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.TruncGE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.truncGE'.hasHomology_sc'_of_not_mem_boundary", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.TruncGEHomology", "is_tactic_proof": false, "tactics": ["have", "restriction.hasHomology", "have", "let", "have", "have", "have", "exact"], "tactic_count": 8}
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{"name": "HomologicalComplex.truncGE'.quasiIsoAt_restrictionToTruncGE'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.TruncGEHomology", "is_tactic_proof": true, "tactics": ["rw", "let", "have", "have", "have", "exact"], "tactic_count": 6}
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{"name": "HomologicalComplex.truncGE'.homologyData_right_g'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.TruncGEHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "HomologicalComplex.truncLE'XIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.TruncLE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "HomologicalComplex.truncLE'_d_eq", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.TruncLE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.truncLE'_d_eq_toCycles", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.TruncLE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "HomologicalComplex.truncLEMap_id", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.TruncLE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "HomologicalComplex.instIsStrictlySupportedTruncLE_1", "kind": "instance", "module": "Mathlib.Algebra.Homology.Embedding.TruncLE", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
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{"name": "ComplexShape.Embedding.truncLE'ToRestrictionNatTrans", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.TruncLE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ComplexShape.Embedding.ιTruncLENatTrans", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.TruncLE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.truncLE'.quasiIsoAt_truncLE'ToRestriction", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.TruncLEHomology", "is_tactic_proof": true, "tactics": ["dsimp", "have", "rw", "exact"], "tactic_count": 4}
{"name": "HomologicalComplex.truncLE'.truncLE'_hasHomology", "kind": "instance", "module": "Mathlib.Algebra.Homology.Embedding.TruncLEHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.instHasHomologyTruncLE", "kind": "instance", "module": "Mathlib.Algebra.Homology.Embedding.TruncLEHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.quasiIsoAt_ιTruncLE", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.TruncLEHomology", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
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{"name": "HomologicalComplex.quasiIso_ιTruncLE_iff_isSupported", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.TruncLEHomology", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "HomologicalComplex.acyclic_truncLE_iff_isSupportedOutside", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.TruncLEHomology", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "HomologicalComplex.quasiIso_truncLEMap_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.TruncLEHomology", "is_tactic_proof": true, "tactics": ["rw", "simp", "apply"], "tactic_count": 3}
{"name": "HomologicalComplex.shortComplexTruncLE", "kind": "definition", "module": "Mathlib.Algebra.Homology.Embedding.TruncLEHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.instMonoFShortComplexTruncLE", "kind": "instance", "module": "Mathlib.Algebra.Homology.Embedding.TruncLEHomology", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "HomologicalComplex.instEpiGShortComplexTruncLE", "kind": "instance", "module": "Mathlib.Algebra.Homology.Embedding.TruncLEHomology", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "HomologicalComplex.shortComplexTruncLE_shortExact", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.TruncLEHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.mono_homologyMap_shortComplexTruncLE_g", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.TruncLEHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.shortComplexTruncLE_shortExact_δ_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.TruncLEHomology", "is_tactic_proof": true, "tactics": ["by_cases", "obtain", "rw", "exact", "apply"], "tactic_count": 5}
{"name": "HomologicalComplex.epi_homologyMap_shortComplexTruncLE_g", "kind": "instance", "module": "Mathlib.Algebra.Homology.Embedding.TruncLEHomology", "is_tactic_proof": true, "tactics": ["by_cases", "obtain", "exact", "exact"], "tactic_count": 4}
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{"name": "HomologicalComplex.quasiIsoAt_shortComplexTruncLE_g", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.TruncLEHomology", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "HomologicalComplex.shortComplexTruncLE_X₃_isSupportedOutside", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Embedding.TruncLEHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.ShortComplex.mapToComposableArrows", "kind": "definition", "module": "Mathlib.Algebra.Homology.ExactSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.mapToComposableArrows_app_0", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ExactSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.mapToComposableArrows_app_1", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ExactSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.mapToComposableArrows_app_2", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ExactSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.mapToComposableArrows_id", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ExactSequence", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
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{"name": "CategoryTheory.ComposableArrows.isComplex_iff_of_iso", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ExactSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.ComposableArrows.isComplex₁", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ExactSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.exact_of_iso", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ExactSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.exact_iff_of_iso", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ExactSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.ComposableArrows.exact₁", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ExactSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.isComplex₂_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ExactSequence", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "intro", "refine", "obtain", "exact"], "tactic_count": 7}
{"name": "CategoryTheory.ComposableArrows.isComplex₂_mk", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ExactSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.isComplex_toComposableArrows", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ExactSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.exact₂_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ExactSequence", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "intro", "refine", "obtain", "exact"], "tactic_count": 7}
{"name": "CategoryTheory.ComposableArrows.exact₂_mk", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ExactSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.Exact.exact_toComposableArrows", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ExactSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.exact_iff_exact_toComposableArrows", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ExactSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.exact_iff_δ₀", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ExactSequence", "is_tactic_proof": true, "tactics": ["constructor", "intro", "constructor", "rw", "rw", "exact", "exact", "exact", "rintro", "refine", "obtain", "exact", "exact", "obtain", "exact", "exact"], "tactic_count": 16}
{"name": "CategoryTheory.ComposableArrows.Exact.δ₀", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ExactSequence", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.ComposableArrows.exact_of_δ₀", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ExactSequence", "is_tactic_proof": true, "tactics": ["rw", "constructor"], "tactic_count": 2}
{"name": "CategoryTheory.ComposableArrows.exact_iff_δlast", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ExactSequence", "is_tactic_proof": true, "tactics": ["constructor", "intro", "constructor", "exact", "rw", "rw", "exact", "exact", "rintro", "refine", "simp", "obtain", "exact", "exact", "simp", "obtain", "exact", "exact"], "tactic_count": 18}
{"name": "CategoryTheory.ComposableArrows.Exact.δlast", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ExactSequence", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.ComposableArrows.exact_of_δlast", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ExactSequence", "is_tactic_proof": true, "tactics": ["rw", "constructor"], "tactic_count": 2}
{"name": "CategoryTheory.ComposableArrows.Exact.isIso_map'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ExactSequence", "is_tactic_proof": true, "tactics": ["have", "have", "apply"], "tactic_count": 3}
{"name": "CategoryTheory.ComposableArrows.IsComplex.cokerToKer'", "kind": "definition", "module": "Mathlib.Algebra.Homology.ExactSequenceFour", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.IsComplex.cokerToKer'_fac", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ExactSequenceFour", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.ComposableArrows.IsComplex.epi_cokerToKer'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ExactSequenceFour", "is_tactic_proof": true, "tactics": ["have", "have", "have", "let", "have", "have", "rw", "exact"], "tactic_count": 8}
{"name": "CategoryTheory.ComposableArrows.IsComplex.mono_cokerToKer'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ExactSequenceFour", "is_tactic_proof": true, "tactics": ["have", "have", "have", "let", "have", "have", "rw", "exact"], "tactic_count": 8}
{"name": "CategoryTheory.ComposableArrows.Exact.cokerToKer'", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.ExactSequenceFour", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.Exact.isIso_cokerToKer'", "kind": "instance", "module": "Mathlib.Algebra.Homology.ExactSequenceFour", "is_tactic_proof": false, "tactics": ["have", "have", "apply"], "tactic_count": 3}
{"name": "CategoryTheory.ComposableArrows.Exact.cokerIsoKer'", "kind": "definition", "module": "Mathlib.Algebra.Homology.ExactSequenceFour", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.Exact.cokerIsoKer'_hom_inv_id", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ExactSequenceFour", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.Exact.cokerIsoKer'_inv_hom_id", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ExactSequenceFour", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.degreewiseEpiWithInjectiveKernel", "kind": "definition", "module": "Mathlib.Algebra.Homology.Factorizations.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.instIsMultiplicativeIntDegreewiseEpiWithInjectiveKernel", "kind": "instance", "module": "Mathlib.Algebra.Homology.Factorizations.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.cm5b.I", "kind": "definition", "module": "Mathlib.Algebra.Homology.Factorizations.CM5b", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.cm5b.instInjectiveXIntI", "kind": "instance", "module": "Mathlib.Algebra.Homology.Factorizations.CM5b", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CochainComplex.cm5b.instIsStrictlyGEI", "kind": "instance", "module": "Mathlib.Algebra.Homology.Factorizations.CM5b", "is_tactic_proof": true, "tactics": ["rw", "intro", "exact"], "tactic_count": 3}
{"name": "CochainComplex.cm5b.instIsStrictlyGEBiprodIntMappingConeIdIOfHAddOfNat", "kind": "instance", "module": "Mathlib.Algebra.Homology.Factorizations.CM5b", "is_tactic_proof": true, "tactics": ["rw", "intro", "refine", "simp", "refine", "all_goals"], "tactic_count": 6}
{"name": "CochainComplex.cm5b.p", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.Factorizations.CM5b", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.cm5b.i", "kind": "definition", "module": "Mathlib.Algebra.Homology.Factorizations.CM5b", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.cm5b.i_f_comp", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Factorizations.CM5b", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CochainComplex.cm5b.instMonoFIntI", "kind": "instance", "module": "Mathlib.Algebra.Homology.Factorizations.CM5b", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.cm5b.instMonoIntI", "kind": "instance", "module": "Mathlib.Algebra.Homology.Factorizations.CM5b", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.cm5b.fac", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Factorizations.CM5b", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CochainComplex.cm5b.instInjectiveXIntMappingConeIdI", "kind": "instance", "module": "Mathlib.Algebra.Homology.Factorizations.CM5b", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.cm5b.degreewiseEpiWithInjectiveKernel_p", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Factorizations.CM5b", "is_tactic_proof": true, "tactics": ["intro", "rw", "refine", "all_goals"], "tactic_count": 4}
{"name": "CochainComplex.cm5b.homotopyEquiv", "kind": "definition", "module": "Mathlib.Algebra.Homology.Factorizations.CM5b", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.cm5b.instQuasiIsoIntP", "kind": "instance", "module": "Mathlib.Algebra.Homology.Factorizations.CM5b", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.cm5b", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Factorizations.CM5b", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.asFunctor", "kind": "definition", "module": "Mathlib.Algebra.Homology.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.complexOfFunctorsToFunctorToComplex", "kind": "definition", "module": "Mathlib.Algebra.Homology.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.locallySmall", "kind": "instance", "module": "Mathlib.Algebra.Homology.GrothendieckAbelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.instHasFilteredColimitsOfSize", "kind": "instance", "module": "Mathlib.Algebra.Homology.GrothendieckAbelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.hasExactColimitsOfShape", "kind": "instance", "module": "Mathlib.Algebra.Homology.GrothendieckAbelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.ab5OfSize", "kind": "instance", "module": "Mathlib.Algebra.Homology.GrothendieckAbelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.isGrothendieckAbelian", "kind": "instance", "module": "Mathlib.Algebra.Homology.GrothendieckAbelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.not_rel_self", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HasNoLoop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.not_rel_of_eq", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HasNoLoop", "is_tactic_proof": true, "tactics": ["subst", "exact"], "tactic_count": 2}
{"name": "ComplexShape.instHasNoLoopSymm", "kind": "instance", "module": "Mathlib.Algebra.Homology.HasNoLoop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.exists_distinct_prev_or", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HasNoLoop", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "ComplexShape.exists_distinct_next_or", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HasNoLoop", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "ComplexShape.hasNoLoop_up'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HasNoLoop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.hasNoLoop_down'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HasNoLoop", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "ComplexShape.hasNoLoop_up", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HasNoLoop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.hasNoLoop_down", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HasNoLoop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.instHasNoLoopIntUp", "kind": "instance", "module": "Mathlib.Algebra.Homology.HasNoLoop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.instHasNoLoopNatUp", "kind": "instance", "module": "Mathlib.Algebra.Homology.HasNoLoop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.instHasNoLoopIntDown", "kind": "instance", "module": "Mathlib.Algebra.Homology.HasNoLoop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.instHasNoLoopNatDown", "kind": "instance", "module": "Mathlib.Algebra.Homology.HasNoLoop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex₂", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.HomologicalBicomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex₂.toGradedObject", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomologicalBicomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex₂.toGradedObjectMap", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomologicalBicomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex₂.toGradedObjectMap_apply", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalBicomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex₂.toGradedObjectFunctor", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomologicalBicomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex₂.instFaithfulGradedObjectProdToGradedObjectFunctor", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomologicalBicomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex₂.ofGradedObject", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomologicalBicomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex₂.ofGradedObject_toGradedObject", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalBicomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex₂.homMk", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomologicalBicomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex₂.shape_f", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalBicomplex", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HomologicalComplex₂.d_f_comp_d_f", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalBicomplex", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HomologicalComplex₂.d_comm", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalBicomplex", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HomologicalComplex₂.comm_f", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalBicomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex₂.flip", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomologicalBicomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex₂.flip_flip", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalBicomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex₂.flipFunctor", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomologicalBicomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex₂.flipEquivalenceUnitIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomologicalBicomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex₂.flipEquivalenceCounitIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomologicalBicomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex₂.flipEquivalence", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomologicalBicomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex₂.XXIsoOfEq", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomologicalBicomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex₂.XXIsoOfEq_rfl", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalBicomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.d_comp_d", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": true, "tactics": ["by_cases", "by_cases", "exact", "rw", "rw"], "tactic_count": 5}
{"name": "HomologicalComplex.ext", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "dsimp", "subst", "simp", "ext", "by_cases", "simpa", "rw"], "tactic_count": 9}
{"name": "HomologicalComplex.XIsoOfEq", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.XIsoOfEq_rfl", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.XIsoOfEq_hom_comp_XIsoOfEq_hom", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "HomologicalComplex.XIsoOfEq_hom_comp_XIsoOfEq_inv", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "HomologicalComplex.XIsoOfEq_inv_comp_XIsoOfEq_hom", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "HomologicalComplex.XIsoOfEq_inv_comp_XIsoOfEq_inv", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "HomologicalComplex.XIsoOfEq_hom_comp_d", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "HomologicalComplex.XIsoOfEq_inv_comp_d", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "HomologicalComplex.d_comp_XIsoOfEq_hom", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "HomologicalComplex.d_comp_XIsoOfEq_inv", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "ChainComplex", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ChainComplex.prev", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ChainComplex.next", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ChainComplex.next_nat_zero", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": true, "tactics": ["classical", "refine", "push_neg", "intro", "apply"], "tactic_count": 5}
{"name": "ChainComplex.next_nat_succ", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.prev", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.next", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.prev_nat_zero", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": true, "tactics": ["classical", "refine", "push_neg", "intro", "apply"], "tactic_count": 5}
{"name": "CochainComplex.prev_nat_succ", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.Hom.comm", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "rw"], "tactic_count": 3}
{"name": "HomologicalComplex.instInhabitedHom", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.id", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.comp", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.instCategory", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.hom_ext", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": true, "tactics": ["apply", "funext", "apply"], "tactic_count": 3}
{"name": "HomologicalComplex.id_f", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.comp_f", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.eqToHom_f", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": true, "tactics": ["subst", "rfl"], "tactic_count": 2}
{"name": "HomologicalComplex.hom_f_injective", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "HomologicalComplex.instZeroHom", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.zero_f", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.instHasZeroMorphisms", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.zero", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.isZero_zero", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": true, "tactics": ["refine", "all_goals", "ext", "dsimp", "subsingleton"], "tactic_count": 5}
{"name": "HomologicalComplex.instHasZeroObject", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.instInhabitedOfHasZeroObject", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.congr_hom", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.mono_of_mono_f", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.epi_of_epi_f", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.eval", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.instPreservesZeroMorphismsEval", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.forget", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.instFaithfulGradedObjectForget", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.forgetEval", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.XIsoOfEq_hom_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "HomologicalComplex.XIsoOfEq_inv_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "HomologicalComplex.d_comp_eqToHom", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": true, "tactics": ["obtain", "simp"], "tactic_count": 2}
{"name": "HomologicalComplex.eqToHom_comp_d", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": true, "tactics": ["obtain", "simp"], "tactic_count": 2}
{"name": "HomologicalComplex.kernel_eq_kernel", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "HomologicalComplex.image_eq_image", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "HomologicalComplex.xPrev", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.xPrevIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.xPrevIsoSelf", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.xNext", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.xNextIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.xNextIsoSelf", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.dTo", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.dFrom", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.dTo_eq", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "HomologicalComplex.dTo_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HomologicalComplex.dFrom_eq", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "HomologicalComplex.dFrom_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HomologicalComplex.xPrevIso_comp_dTo", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HomologicalComplex.xPrevIsoSelf_comp_dTo", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HomologicalComplex.dFrom_comp_xNextIso", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HomologicalComplex.dFrom_comp_xNextIsoSelf", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HomologicalComplex.dTo_comp_dFrom", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.kernel_from_eq_kernel", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "HomologicalComplex.image_to_eq_image", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "HomologicalComplex.Hom.isoApp", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.Hom.isoOfComponents_app", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "HomologicalComplex.Hom.isIso_of_components", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.Hom.prev", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.Hom.prev_eq", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": true, "tactics": ["obtain", "simp"], "tactic_count": 2}
{"name": "HomologicalComplex.Hom.next", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.Hom.next_eq", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": true, "tactics": ["obtain", "simp"], "tactic_count": 2}
{"name": "HomologicalComplex.Hom.comm_from", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.Hom.comm_to", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.Hom.sqFrom", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.Hom.sqFrom_left", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.Hom.sqFrom_right", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.Hom.sqFrom_id", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.Hom.sqFrom_comp", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.Hom.sqTo", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.Hom.sqTo_left", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.Hom.sqTo_right", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ChainComplex.of", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ChainComplex.of_x", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ChainComplex.of_d", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "ChainComplex.of_d_ne", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "ChainComplex.ofHom", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ChainComplex.mkAux", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ChainComplex.mk", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ChainComplex.mk_X_0", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ChainComplex.mk_X_1", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ChainComplex.mk_X_2", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ChainComplex.mk_d_1_0", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": true, "tactics": ["change", "rw"], "tactic_count": 2}
{"name": "ChainComplex.mk_d_2_1", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": true, "tactics": ["change", "rw"], "tactic_count": 2}
{"name": "ChainComplex.mk_congr_succ_X₃", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ChainComplex.mk_congr_succ_d₂", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": true, "tactics": ["subst", "simp"], "tactic_count": 2}
{"name": "ChainComplex.mkAux_eq_shortComplex_mk_d_comp_d", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": true, "tactics": ["change", "dsimp", "congr", "rw", "simp"], "tactic_count": 5}
{"name": "ChainComplex.mkXIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ChainComplex.mk_d", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": true, "tactics": ["have", "rw", "refine", "dsimp", "rw", "rfl"], "tactic_count": 6}
{"name": "ChainComplex.mk'", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ChainComplex.mk'_X_0", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ChainComplex.mk'_X_1", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ChainComplex.mk'_d_1_0", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": true, "tactics": ["change", "rw"], "tactic_count": 2}
{"name": "ChainComplex.mk'XIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": true, "tactics": ["obtain", "apply", "dsimp", "rw", "exact"], "tactic_count": 5}
{"name": "ChainComplex.mk'_congr_succ'_d", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": true, "tactics": ["subst", "simp"], "tactic_count": 2}
{"name": "ChainComplex.mk'_d", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": true, "tactics": ["obtain", "dsimp", "rw", "apply", "rw", "apply"], "tactic_count": 6}
{"name": "ChainComplex.mkHomAux", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ChainComplex.mkHom", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ChainComplex.mkHom_f_0", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ChainComplex.mkHom_f_1", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ChainComplex.mkHom_f_succ_succ", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": true, "tactics": ["dsimp"], "tactic_count": 1}
{"name": "CochainComplex.of", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.of_x", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.of_d", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "CochainComplex.of_d_ne", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "CochainComplex.ofHom", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.mkAux", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.mk", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.mk_X_0", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.mk_X_1", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.mk_X_2", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.mk_d_1_0", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": true, "tactics": ["change", "rw"], "tactic_count": 2}
{"name": "CochainComplex.mk_d_2_0", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": true, "tactics": ["change", "rw"], "tactic_count": 2}
{"name": "CochainComplex.mk'", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.mk'_X_0", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.mk'_X_1", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.mk'_d_1_0", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": true, "tactics": ["change", "rw"], "tactic_count": 2}
{"name": "CochainComplex.mkHomAux", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.mkHom", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.mkHom_f_0", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.mkHom_f_1", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.mkHom_f_succ_succ", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplex", "is_tactic_proof": true, "tactics": ["dsimp"], "tactic_count": 1}
{"name": "HomologicalComplex.instIsNormalEpiCategory", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomologicalComplexAbelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.instIsNormalMonoCategory", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomologicalComplexAbelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.instAbelian", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomologicalComplexAbelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.exact_of_degreewise_exact", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplexAbelian", "is_tactic_proof": true, "tactics": ["simp", "rw", "ext", "apply"], "tactic_count": 4}
{"name": "HomologicalComplex.shortExact_of_degreewise_shortExact", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplexAbelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.exact_iff_degreewise_exact", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplexAbelian", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "exact"], "tactic_count": 4}
{"name": "HomologicalComplex.shortExact_iff_degreewise_shortExact", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplexAbelian", "is_tactic_proof": true, "tactics": ["constructor", "intro", "have", "have", "exact", "exact"], "tactic_count": 6}
{"name": "HomologicalComplex.instHasBinaryBiproductObjEval", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomologicalComplexBiprod", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "HomologicalComplex.instHasLimitDiscreteWalkingPairCompPairEval", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomologicalComplexBiprod", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "HomologicalComplex.instHasColimitDiscreteWalkingPairCompPairEval", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomologicalComplexBiprod", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "HomologicalComplex.instHasBinaryBiproduct", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomologicalComplexBiprod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.instPreservesBinaryBiproductEval", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomologicalComplexBiprod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.biprodXIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomologicalComplexBiprod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.inl_biprodXIso_inv", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplexBiprod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HomologicalComplex.inr_biprodXIso_inv", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplexBiprod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HomologicalComplex.biprodXIso_hom_fst", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplexBiprod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HomologicalComplex.biprodXIso_hom_snd", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplexBiprod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HomologicalComplex.biprod_inl_fst_f", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplexBiprod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HomologicalComplex.biprod_inl_snd_f", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplexBiprod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HomologicalComplex.biprod_inr_fst_f", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplexBiprod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HomologicalComplex.biprod_inr_snd_f", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplexBiprod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HomologicalComplex.biprod_inl_desc_f", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplexBiprod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HomologicalComplex.biprod_inr_desc_f", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplexBiprod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HomologicalComplex.biprod_lift_fst_f", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplexBiprod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HomologicalComplex.biprod_lift_snd_f", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplexBiprod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HomologicalComplex.isLimitOfEval", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomologicalComplexLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.coneOfHasLimitEval", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomologicalComplexLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.isLimitConeOfHasLimitEval", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomologicalComplexLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.instHasLimit", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomologicalComplexLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.instPreservesLimitEval", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomologicalComplexLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.instHasLimitsOfShape", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomologicalComplexLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.instPreservesLimitsOfShapeEvalOfHasLimitsOfShape", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomologicalComplexLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.instHasFiniteLimits", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomologicalComplexLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.instPreservesFiniteLimitsEvalOfHasFiniteLimits", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomologicalComplexLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.instMonoFOfHasFiniteLimits", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomologicalComplexLimits", "is_tactic_proof": true, "tactics": ["change", "infer_instance"], "tactic_count": 2}
{"name": "HomologicalComplex.isColimitOfEval", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomologicalComplexLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.coconeOfHasColimitEval", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomologicalComplexLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.isColimitCoconeOfHasColimitEval", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomologicalComplexLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.instHasColimit", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomologicalComplexLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.instPreservesColimitEval", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomologicalComplexLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.instHasColimitsOfShape", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomologicalComplexLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.instPreservesColimitsOfShapeEvalOfHasColimitsOfShape", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomologicalComplexLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.instHasFiniteColimits", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomologicalComplexLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.instPreservesFiniteColimitsEvalOfHasFiniteColimits", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomologicalComplexLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.instEpiFOfHasFiniteColimits", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomologicalComplexLimits", "is_tactic_proof": true, "tactics": ["change", "infer_instance"], "tactic_count": 2}
{"name": "HomologicalComplex.preservesLimitsOfShape_of_eval", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplexLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.preservesColimitsOfShape_of_eval", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologicalComplexLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.instPreservesLimitsOfShapeSingle", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomologicalComplexLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.instPreservesColimitsOfShapeSingle", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomologicalComplexLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.instPreservesFiniteLimitsSingle", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomologicalComplexLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.instPreservesFiniteColimitsSingle", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomologicalComplexLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.opcyclesToCycles", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomologySequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.opcyclesToCycles_iCycles", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologySequence", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "HomologicalComplex.pOpcycles_opcyclesToCycles_iCycles", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologySequence", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HomologicalComplex.pOpcycles_opcyclesToCycles", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologySequence", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HomologicalComplex.homologyι_opcyclesToCycles", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologySequence", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HomologicalComplex.opcyclesToCycles_homologyπ", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologySequence", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HomologicalComplex.opcyclesToCycles_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologySequence", "is_tactic_proof": true, "tactics": ["simp", "pOpcycles_opcyclesToCycles_iCycles,"], "tactic_count": 2}
{"name": "HomologicalComplex.natTransOpCyclesToCycles", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomologySequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.HomologySequence.composableArrows₃", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomologySequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.HomologySequence.instMonoMap'ComposableArrows₃OfNatNat", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomologySequence", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "HomologicalComplex.HomologySequence.instEpiMap'ComposableArrows₃OfNatNat", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomologySequence", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "HomologicalComplex.HomologySequence.composableArrows₃_exact", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologySequence", "is_tactic_proof": true, "tactics": ["let", "let", "let", "τ₂", "τ₃", "have", "rw", "exact", "let", "let", "let", "τ₂", "τ₃", "have", "rw", "exact", "apply", "exact", "exact"], "tactic_count": 19}
{"name": "HomologicalComplex.HomologySequence.composableArrows₃Functor", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomologySequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.opcycles_right_exact", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologySequence", "is_tactic_proof": true, "tactics": ["have", "have", "apply", "refine", "dsimp", "have", "dsimp", "rw", "dsimp", "refine", "rw", "rw"], "tactic_count": 12}
{"name": "HomologicalComplex.cycles_left_exact", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologySequence", "is_tactic_proof": true, "tactics": ["have", "have", "apply", "exact", "dsimp", "have", "dsimp", "rw", "dsimp", "refine", "rw", "rw"], "tactic_count": 12}
{"name": "HomologicalComplex.HomologySequence.snakeInput", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomologySequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.ShortExact.δ", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomologySequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.ShortExact.δ_comp", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologySequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.ShortExact.comp_δ", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologySequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.ShortExact.homology_exact₁", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologySequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.ShortExact.homology_exact₂", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologySequence", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "have", "have", "have", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.ShortComplex.ShortExact.homology_exact₃", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologySequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.ShortExact.δ_eq'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologySequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.ShortExact.δ_eq", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologySequence", "is_tactic_proof": true, "tactics": ["simpa", "hS.δ_eq", "simp", "rw", "hx₁])"], "tactic_count": 5}
{"name": "CategoryTheory.ShortComplex.ShortExact.mono_δ", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologySequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.ShortExact.epi_δ", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologySequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.ShortExact.isIso_δ", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologySequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.ShortExact.δIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomologySequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.HomologySequence.mapSnakeInput", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomologySequenceLemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.HomologySequence.δ_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologySequenceLemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.HomologySequence.composableArrows₂", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomologySequenceLemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.HomologySequence.composableArrows₂_exact", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologySequenceLemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.HomologySequence.composableArrows₅", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomologySequenceLemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.HomologySequence.composableArrows₅_exact", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologySequenceLemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.HomologySequence.mapComposableArrows₂", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomologySequenceLemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.HomologySequence.mapComposableArrows₅", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomologySequenceLemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.HomologySequence.mono_homologyMap_τ₃", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologySequenceLemmas", "is_tactic_proof": true, "tactics": ["by_cases", "obtain", "apply", "exact", "exact", "exact", "exact", "exact", "refine", "mono_of_epi_of_epi_of_mono", "have", "apply", "simpa"], "tactic_count": 13}
{"name": "HomologicalComplex.HomologySequence.epi_homologyMap_τ₃", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologySequenceLemmas", "is_tactic_proof": true, "tactics": ["by_cases", "obtain", "apply", "exact", "exact", "exact", "exact", "exact", "have", "have", "dsimp", "simp", "have", "exact"], "tactic_count": 14}
{"name": "HomologicalComplex.HomologySequence.isIso_homologyMap_τ₃", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologySequenceLemmas", "is_tactic_proof": false, "tactics": ["have", "mono_homologyMap_τ₃", "have", "infer_instance)", "have", "epi_homologyMap_τ₃", "have", "infer_instance)", "h₄", "apply"], "tactic_count": 10}
{"name": "HomologicalComplex.HomologySequence.quasiIso_τ₃", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomologySequenceLemmas", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "apply", "all_goals"], "tactic_count": 5}
{"name": "dNext", "kind": "definition", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fromNext", "kind": "definition", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dNext_eq_dFrom_fromNext", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dNext_eq", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": true, "tactics": ["obtain", "rfl"], "tactic_count": 2}
{"name": "dNext_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "dNext_comp_left", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dNext_comp_right", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "prevD", "kind": "definition", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "prevD_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "toPrev", "kind": "definition", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "prevD_eq_toPrev_dTo", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "prevD_eq", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": true, "tactics": ["obtain", "rfl"], "tactic_count": 2}
{"name": "prevD_comp_left", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "prevD_comp_right", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "dNext_nat", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": true, "tactics": ["dsimp", "cases", "simp", "congr"], "tactic_count": 4}
{"name": "prevD_nat", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": true, "tactics": ["dsimp", "cases", "simp", "congr"], "tactic_count": 4}
{"name": "Homotopy.equivSubZero", "kind": "definition", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homotopy.ofEq", "kind": "definition", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homotopy.refl", "kind": "definition", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homotopy.symm", "kind": "definition", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homotopy.trans", "kind": "definition", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homotopy.add", "kind": "definition", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homotopy.smul", "kind": "definition", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homotopy.compRight", "kind": "definition", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homotopy.compLeft", "kind": "definition", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homotopy.comp", "kind": "definition", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homotopy.compRightId", "kind": "definition", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homotopy.compLeftId", "kind": "definition", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homotopy.nullHomotopicMap", "kind": "definition", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homotopy.nullHomotopicMap'", "kind": "definition", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homotopy.nullHomotopicMap_comp", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "simp"], "tactic_count": 3}
{"name": "Homotopy.nullHomotopicMap'_comp", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": true, "tactics": ["rw", "congr", "ext", "split_ifs", "rfl", "rw"], "tactic_count": 6}
{"name": "Homotopy.comp_nullHomotopicMap", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "simp"], "tactic_count": 3}
{"name": "Homotopy.comp_nullHomotopicMap'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": true, "tactics": ["rw", "congr", "ext", "split_ifs", "rfl", "rw"], "tactic_count": 6}
{"name": "Homotopy.map_nullHomotopicMap", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "simp"], "tactic_count": 3}
{"name": "Homotopy.map_nullHomotopicMap'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": true, "tactics": ["rw", "congr", "ext", "split_ifs", "rfl", "rw"], "tactic_count": 6}
{"name": "Homotopy.nullHomotopy", "kind": "definition", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homotopy.nullHomotopy'", "kind": "definition", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": true, "tactics": ["apply", "grind"], "tactic_count": 2}
{"name": "Homotopy.nullHomotopicMap_f", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "Homotopy.nullHomotopicMap'_f", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": true, "tactics": ["simp", "rw", "split_ifs", "rfl"], "tactic_count": 4}
{"name": "Homotopy.nullHomotopicMap_f_of_not_rel_left", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "exact", "hk₀"], "tactic_count": 4}
{"name": "Homotopy.nullHomotopicMap'_f_of_not_rel_left", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": true, "tactics": ["simp", "rw", "split_ifs", "rfl"], "tactic_count": 4}
{"name": "Homotopy.nullHomotopicMap_f_of_not_rel_right", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "exact", "hk₁"], "tactic_count": 4}
{"name": "Homotopy.nullHomotopicMap'_f_of_not_rel_right", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": true, "tactics": ["simp", "rw", "split_ifs", "rfl"], "tactic_count": 4}
{"name": "Homotopy.nullHomotopicMap_f_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "Homotopy.nullHomotopicMap'_f_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": true, "tactics": ["simp", "apply"], "tactic_count": 2}
{"name": "Homotopy.prevD_chainComplex", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": true, "tactics": ["dsimp", "have", "congr"], "tactic_count": 3}
{"name": "Homotopy.dNext_succ_chainComplex", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": true, "tactics": ["dsimp", "have", "congr"], "tactic_count": 3}
{"name": "Homotopy.dNext_zero_chainComplex", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "rw"], "tactic_count": 3}
{"name": "Homotopy.mkInductiveAux₁", "kind": "definition", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homotopy.mkInductiveAux₂", "kind": "definition", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homotopy.mkInductiveAux₂_zero", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homotopy.mkInductiveAux₂_add_one", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homotopy.mkInductiveAux₃", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": true, "tactics": ["subst", "rcases"], "tactic_count": 2}
{"name": "Homotopy.mkInductive", "kind": "definition", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homotopy.dNext_cochainComplex", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": true, "tactics": ["dsimp", "have", "congr"], "tactic_count": 3}
{"name": "Homotopy.prevD_succ_cochainComplex", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": true, "tactics": ["dsimp", "have", "congr"], "tactic_count": 3}
{"name": "Homotopy.prevD_zero_cochainComplex", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "rw"], "tactic_count": 3}
{"name": "Homotopy.mkCoinductiveAux₁", "kind": "definition", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homotopy.mkCoinductiveAux₂", "kind": "definition", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homotopy.mkCoinductiveAux₂_zero", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homotopy.mkCoinductiveAux₂_add_one", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homotopy.mkCoinductiveAux₃", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": true, "tactics": ["subst", "rcases"], "tactic_count": 2}
{"name": "Homotopy.mkCoinductive", "kind": "definition", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.homotopyEquivalences", "kind": "definition", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopyEquiv.refl", "kind": "definition", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopyEquiv.instInhabited", "kind": "instance", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopyEquiv.symm", "kind": "definition", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopyEquiv.trans", "kind": "definition", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopyEquiv.ofIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapHomotopy", "kind": "definition", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapHomotopyEquiv", "kind": "definition", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homotopy.toShortComplex", "kind": "definition", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homotopy.homologyMap_eq", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopyEquiv.toHomologyIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.Homotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "homotopic", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "homotopy_congruence", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomotopyCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopyCategory", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCategoryHomotopyCategory", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomotopyCategory", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "HomotopyCategory.instPreadditive", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomotopyCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopyCategory.quotient", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopyCategory.instFullHomologicalComplexQuotient", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomotopyCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopyCategory.instEssSurjHomologicalComplexQuotient", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomotopyCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopyCategory.instAdditiveHomologicalComplexQuotient", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomotopyCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopyCategory.instPreadditiveQuotientHomologicalComplexHomotopic", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomotopyCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopyCategory.instAdditiveHomologicalComplexQuotientHomotopicFunctor", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomotopyCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopyCategory.instLinear", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomotopyCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopyCategory.instLinearHomologicalComplexQuotient", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomotopyCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopyCategory.instInhabitedOfHasZeroObject", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomotopyCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopyCategory.instHasZeroObject", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomotopyCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopyCategory.instFullFunctorHomologicalComplexObjWhiskeringLeftQuotient", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomotopyCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopyCategory.instFaithfulFunctorHomologicalComplexObjWhiskeringLeftQuotient", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomotopyCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopyCategory.quotient_obj_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopyCategory.quotient_obj_as", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopyCategory.quotient_map_out", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopyCategory.quot_mk_eq_quotient_map", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopyCategory.eq_of_homotopy", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopyCategory.homotopyOfEq", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopyCategory.quotient_map_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopyCategory.homotopyOutMap", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "HomotopyCategory.quotient_map_out_comp_out", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HomotopyCategory.isoOfHomotopyEquiv", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopyCategory.homotopyEquivOfIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopyCategory.quotient_inverts_homotopyEquivalences", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory", "is_tactic_proof": true, "tactics": ["rintro", "change", "infer_instance"], "tactic_count": 3}
{"name": "HomotopyCategory.isZero_quotient_obj_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory", "is_tactic_proof": true, "tactics": ["rw", "constructor", "intro", "exact", "rintro", "simpa"], "tactic_count": 6}
{"name": "HomotopyCategory.homologyFunctor", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopyCategory.homologyFunctorFactors", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopyCategory.instAdditiveHomologyFunctor", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomotopyCategory", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.mapHomotopyCategory", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapHomotopyCategory_map", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapHomotopyCategoryFactors", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.mapHomotopyCategory", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.mapHomotopyCategory_id", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.NatTrans.mapHomotopyCategory_comp", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.instAdditiveHomotopyCategoryMapHomotopyCategory", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomotopyCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instLinearHomotopyCategoryMapHomotopyCategory", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomotopyCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopyCategory.subcategoryAcyclic", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Acyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopyCategory.instIsTriangulatedIntUpSubcategoryAcyclic", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Acyclic", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "HomotopyCategory.instIsClosedUnderIsomorphismsIntUpSubcategoryAcyclic", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Acyclic", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "HomotopyCategory.mem_subcategoryAcyclic_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Acyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopyCategory.quotient_obj_mem_subcategoryAcyclic_iff_exactAt", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Acyclic", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp", "exact"], "tactic_count": 4}
{"name": "HomotopyCategory.quotient_obj_mem_subcategoryAcyclic_iff_acyclic", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Acyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopyCategory.quasiIso_eq_subcategoryAcyclic_W", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Acyclic", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "CochainComplex.cocycleOfDegreewiseSplit", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory.DegreewiseSplit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.homOfDegreewiseSplit", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory.DegreewiseSplit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.homOfDegreewiseSplit_f", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.DegreewiseSplit", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CochainComplex.triangleOfDegreewiseSplit", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory.DegreewiseSplit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.trianglehOfDegreewiseSplit", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.HomotopyCategory.DegreewiseSplit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.mappingConeHomOfDegreewiseSplitXIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory.DegreewiseSplit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.mappingConeHomOfDegreewiseSplitIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory.DegreewiseSplit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.shift_f_comp_mappingConeHomOfDegreewiseSplitIso_inv", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.DegreewiseSplit", "is_tactic_proof": true, "tactics": ["ext", "have", "dsimp", "dsimp", "rw"], "tactic_count": 5}
{"name": "CochainComplex.mappingConeHomOfDegreewiseSplitIso_inv_comp_triangle_mor₃", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.DegreewiseSplit", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "simp", "shiftFunctorObjXIso,", "sub_zero]"], "tactic_count": 5}
{"name": "CochainComplex.triangleOfDegreewiseSplitRotateRotateIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory.DegreewiseSplit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.trianglehOfDegreewiseSplitRotateRotateIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory.DegreewiseSplit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.mappingCone.triangleRotateShortComplex", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory.DegreewiseSplit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.mappingCone.triangleRotateShortComplexSplitting", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory.DegreewiseSplit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.mappingCone.cocycleOfDegreewiseSplit_triangleRotateShortComplexSplitting_v", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.DegreewiseSplit", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CochainComplex.mappingCone.triangleRotateIsoTriangleOfDegreewiseSplit", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory.DegreewiseSplit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.mappingCone.trianglehRotateIsoTrianglehOfDegreewiseSplit", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory.DegreewiseSplit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopyCategory.distinguished_iff_iso_trianglehOfDegreewiseSplit", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.DegreewiseSplit", "is_tactic_proof": true, "tactics": ["constructor", "intro", "obtain", "exact", "rintro", "rw", "refine", "isomorphic_distinguished", "exact"], "tactic_count": 9}
{"name": "CochainComplex.HomComplex.Cochain", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CochainComplex.HomComplex.Cochain.leftShift_comp", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexShift", "is_tactic_proof": true, "tactics": ["ext", "have", "dsimp", "simp", "congr", "rw"], "tactic_count": 6}
{"name": "CochainComplex.HomComplex.Cochain.leftShift_comp_zero_cochain", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexShift", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CochainComplex.HomComplex.Cochain.δ_rightShift", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexShift", "is_tactic_proof": true, "tactics": ["by_cases", "have", "ext", "dsimp", "rw", "δ_v", "γ.rightShift_v", "simp", "smul_add,", "simp", "have", "rw"], "tactic_count": 12}
{"name": "CochainComplex.HomComplex.Cochain.δ_rightUnshift", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexShift", "is_tactic_proof": true, "tactics": ["obtain", "dsimp", "simp"], "tactic_count": 3}
{"name": "CochainComplex.HomComplex.Cochain.δ_leftShift", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexShift", "is_tactic_proof": true, "tactics": ["by_cases", "have", "ext", "dsimp", "rw", "δ_v", "δ_v", "γ.leftShift_v", "simp", "congr", "rw", "simp", "simp", "congr", "linarith", "have", "rw"], "tactic_count": 17}
{"name": "CochainComplex.HomComplex.Cochain.δ_leftUnshift", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexShift", "is_tactic_proof": true, "tactics": ["obtain", "dsimp", "simp"], "tactic_count": 3}
{"name": "CochainComplex.HomComplex.Cochain.δ_shift", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexShift", "is_tactic_proof": true, "tactics": ["by_cases", "ext", "dsimp", "simp", "δ_v", "rw", "rw"], "tactic_count": 7}
{"name": "CochainComplex.HomComplex.Cochain.leftShift_rightShift", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexShift", "is_tactic_proof": true, "tactics": ["ext", "simp", "rightShift_v", "dsimp", "rw"], "tactic_count": 5}
{"name": "CochainComplex.HomComplex.Cochain.rightShift_leftShift", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexShift", "is_tactic_proof": true, "tactics": ["ext", "simp", "leftShift_v", "dsimp", "rw"], "tactic_count": 5}
{"name": "CochainComplex.HomComplex.Cochain.leftShift_rightShift_eq_negOnePow_rightShift_leftShift", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexShift", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CochainComplex.HomComplex.Cocycle.rightShift", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexShift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.HomComplex.Cocycle.rightUnshift", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexShift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.HomComplex.Cocycle.leftShift", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexShift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.HomComplex.Cocycle.leftUnshift", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexShift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.HomComplex.Cocycle.shift", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexShift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.HomComplex.Cocycle.rightShiftAddEquiv", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexShift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.HomComplex.Cocycle.equivHomShift", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexShift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.HomComplex.Cocycle.equivHomShift_comp", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexShift", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CochainComplex.HomComplex.Cocycle.equivHomShift_symm_precomp", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexShift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.HomComplex.Cocycle.equivHomShift_comp_shift", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexShift", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CochainComplex.HomComplex.Cocycle.equivHomShift_symm_postcomp", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexShift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.HomComplex.Cocycle.leftShiftAddEquiv", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexShift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.HomComplex.Cocycle.equivHomShift'", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexShift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.HomComplex.Cochain.fromSingleMk", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexSingle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.HomComplex.Cochain.fromSingleMk_zero", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexSingle", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CochainComplex.HomComplex.Cochain.fromSingleMk_v", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexSingle", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CochainComplex.HomComplex.Cochain.fromSingleMk_v_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexSingle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.HomComplex.Cochain.δ_fromSingleMk", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexSingle", "is_tactic_proof": true, "tactics": ["by_cases", "dsimp", "rw", "simp", "simp"], "tactic_count": 5}
{"name": "CochainComplex.HomComplex.Cochain.fromSingleEquiv", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexSingle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.HomComplex.Cochain.fromSingleEquiv_fromSingleMk", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexSingle", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CochainComplex.HomComplex.Cochain.fromSingleMk_add", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexSingle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.HomComplex.Cochain.fromSingleMk_sub", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexSingle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.HomComplex.Cochain.fromSingleMk_neg", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexSingle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.HomComplex.Cochain.fromSingleMk_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexSingle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.HomComplex.Cochain.fromSingleMk_precomp", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexSingle", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "CochainComplex.HomComplex.Cochain.fromSingleMk_postcomp", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexSingle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.HomComplex.Cochain.toSingleMk", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexSingle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.HomComplex.Cochain.toSingleMk_zero", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexSingle", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CochainComplex.HomComplex.Cochain.toSingleMk_v", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexSingle", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CochainComplex.HomComplex.Cochain.toSingleMk_v_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexSingle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.HomComplex.Cochain.δ_toSingleMk", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexSingle", "is_tactic_proof": true, "tactics": ["by_cases", "dsimp", "rw", "simp", "simp"], "tactic_count": 5}
{"name": "CochainComplex.HomComplex.Cochain.toSingleEquiv", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexSingle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.HomComplex.Cochain.toSingleEquiv_toSingleMk", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexSingle", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CochainComplex.HomComplex.Cochain.toSingleMk_add", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexSingle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.HomComplex.Cochain.toSingleMk_sub", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexSingle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.HomComplex.Cochain.toSingleMk_neg", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexSingle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.HomComplex.Cochain.toSingleMk_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexSingle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.HomComplex.Cochain.toSingleMk_postcomp", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexSingle", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "CochainComplex.HomComplex.Cochain.toSingleMk_precomp", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexSingle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.HomComplex.Cocycle.fromSingleMk", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexSingle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.HomComplex.Cocycle.fromSingleMk_precomp", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexSingle", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "CochainComplex.HomComplex.Cocycle.fromSingleMk_postcomp", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexSingle", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "CochainComplex.HomComplex.Cocycle.fromSingleMk_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexSingle", "is_tactic_proof": true, "tactics": ["obtain", "have", "rw", "replace", "exact"], "tactic_count": 5}
{"name": "CochainComplex.HomComplex.Cocycle.fromSingleMk_add", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexSingle", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CochainComplex.HomComplex.Cocycle.fromSingleMk_sub", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexSingle", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CochainComplex.HomComplex.Cocycle.fromSingleMk_neg", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexSingle", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CochainComplex.HomComplex.Cocycle.fromSingleMk_zero", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexSingle", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CochainComplex.HomComplex.Cocycle.fromSingleMk_mem_coboundaries_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexSingle", "is_tactic_proof": true, "tactics": ["rw", "constructor", "rintro", "obtain", "refine", "rw", "exact", "rintro", "exact"], "tactic_count": 9}
{"name": "CochainComplex.HomComplex.Cocycle.toSingleMk", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexSingle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.HomComplex.Cocycle.toSingleMk_postcomp", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexSingle", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "CochainComplex.HomComplex.Cocycle.toSingleMk_precomp", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexSingle", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "CochainComplex.HomComplex.Cocycle.toSingleMk_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexSingle", "is_tactic_proof": true, "tactics": ["obtain", "have", "rw", "one_smul]", "refine", "simpa", "ext"], "tactic_count": 7}
{"name": "CochainComplex.HomComplex.Cocycle.toSingleMk_add", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexSingle", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CochainComplex.HomComplex.Cocycle.toSingleMk_sub", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexSingle", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CochainComplex.HomComplex.Cocycle.toSingleMk_neg", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexSingle", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CochainComplex.HomComplex.Cocycle.toSingleMk_zero", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexSingle", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CochainComplex.HomComplex.Cocycle.toSingleMk_mem_coboundaries_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexSingle", "is_tactic_proof": true, "tactics": ["rw", "constructor", "rintro", "obtain", "refine", "rw", "exact", "rintro", "exact"], "tactic_count": 9}
{"name": "HomotopyCategory.instIsHomologicalIntUpHomologyFunctor", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomologicalFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.definition._@.Mathlib.Algebra.Homology.HomotopyCategory.KInjective.2101789899._hygCtx._hyg.2", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory.KInjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.wrapped._@.Mathlib.Algebra.Homology.HomotopyCategory.KInjective.2101789899._hygCtx._hyg.2", "kind": "opaque", "module": "Mathlib.Algebra.Homology.HomotopyCategory.KInjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.IsKInjective.homotopyZero", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory.KInjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.IsKInjective.homotopyZero_def", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.KInjective", "is_tactic_proof": true, "tactics": ["intros", "delta", "rw", "rfl"], "tactic_count": 4}
{"name": "HomotopyEquiv.isKInjective", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.KInjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.isKInjective_of_iso", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.KInjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.isKInjective_iff_of_iso", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.KInjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.isKInjective_iff_rightOrthogonal", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.KInjective", "is_tactic_proof": true, "tactics": ["refine", "obtain", "obtain", "rw", "rw", "rw", "rw"], "tactic_count": 7}
{"name": "CochainComplex.IsKInjective.rightOrthogonal", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.KInjective", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "CochainComplex.instIsKInjectiveObjIntShiftFunctor", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomotopyCategory.KInjective", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CochainComplex.isKInjective_shift_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.KInjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.isKInjective_of_injective_aux", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.KInjective", "is_tactic_proof": true, "tactics": ["subst", "let", "have", "have", "simp", "one_smul,", "simp", "rw", "obtain", "refine", "intro", "obtain", "obtain", "rw", "δ_v", "simp", "rw", "simp"], "tactic_count": 18}
{"name": "CochainComplex.isKInjective_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.KInjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.definition._@.Mathlib.Algebra.Homology.HomotopyCategory.KProjective.595972877._hygCtx._hyg.2", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory.KProjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.wrapped._@.Mathlib.Algebra.Homology.HomotopyCategory.KProjective.595972877._hygCtx._hyg.2", "kind": "opaque", "module": "Mathlib.Algebra.Homology.HomotopyCategory.KProjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.IsKProjective.homotopyZero", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory.KProjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.IsKProjective.homotopyZero_def", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.KProjective", "is_tactic_proof": true, "tactics": ["intros", "delta", "rw", "rfl"], "tactic_count": 4}
{"name": "HomotopyEquiv.isKProjective", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.KProjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.isKProjective_of_iso", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.KProjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.isKProjective_iff_of_iso", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.KProjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.isKProjective_iff_leftOrthogonal", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.KProjective", "is_tactic_proof": true, "tactics": ["refine", "obtain", "obtain", "rw", "rw", "rw", "rw"], "tactic_count": 7}
{"name": "CochainComplex.IsKProjective.leftOrthogonal", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.KProjective", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "CochainComplex.instIsKProjectiveObjIntShiftFunctor", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomotopyCategory.KProjective", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CochainComplex.isKProjective_shift_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.KProjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.isKProjective_of_op", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.KProjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.isKProjective_of_projective", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.KProjective", "is_tactic_proof": true, "tactics": ["let", "have", "dsimp", "infer_instance", "have", "rw", "intro", "exact", "exact"], "tactic_count": 9}
{"name": "CochainComplex.instHasHomotopyCofiberOfHasBinaryBiproductXHAddOfNat", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomotopyCategory.MappingCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.mappingCone", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory.MappingCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CochainComplex.mappingCone.inl_v_triangle_mor₃_f", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Pretriangulated", "is_tactic_proof": false, "tactics": ["dsimp", "simp"], "tactic_count": 2}
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{"name": "CochainComplex.mappingCone.inr_triangleδ", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Pretriangulated", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CochainComplex.mappingCone.triangleh", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Pretriangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.mappingCone.homotopyToZeroOfId", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Pretriangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CochainComplex.mappingCone.map_eq_mapOfHomotopy", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Pretriangulated", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CochainComplex.mappingCone.map_id", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Pretriangulated", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
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{"name": "CochainComplex.mappingCone.triangleMap", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Pretriangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.mappingCone.rotateHomotopyEquiv", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Pretriangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.mappingCone.rotateHomotopyEquivComm₂Homotopy", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Pretriangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.mappingCone.rotateHomotopyEquiv_comm₂", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Pretriangulated", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CochainComplex.mappingCone.rotateHomotopyEquiv_comm₃", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Pretriangulated", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "simp", "shiftFunctor_obj_X,", "comp_id,"], "tactic_count": 5}
{"name": "CochainComplex.mappingCone.rotateTrianglehIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Pretriangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.mappingCone.shiftIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Pretriangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CochainComplex.mappingCone.map_δ", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Pretriangulated", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "rw", "simp", "shiftFunctorObjXIso,", "comp_zero,", "dsimp", "rw", "simp", "comp_id,"], "tactic_count": 10}
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{"name": "CochainComplex.mappingCone.mapTrianglehIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Pretriangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopyCategory.Pretriangulated.distinguishedTriangles", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Pretriangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopyCategory.Pretriangulated.isomorphic_distinguished", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Pretriangulated", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "HomotopyCategory.Pretriangulated.contractible_distinguished", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Pretriangulated", "is_tactic_proof": true, "tactics": ["obtain", "refine", "have", "exact"], "tactic_count": 4}
{"name": "HomotopyCategory.Pretriangulated.distinguished_cocone_triangle", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Pretriangulated", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "HomotopyCategory.Pretriangulated.rotate_distinguished_triangle'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Pretriangulated", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "HomotopyCategory.Pretriangulated.shift_distinguished_triangle", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Pretriangulated", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "HomotopyCategory.Pretriangulated.invRotate_distinguished_triangle'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Pretriangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopyCategory.Pretriangulated.rotate_distinguished_triangle", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Pretriangulated", "is_tactic_proof": true, "tactics": ["constructor", "exact", "intro", "exact", "isomorphic_distinguished"], "tactic_count": 5}
{"name": "HomotopyCategory.Pretriangulated.complete_distinguished_triangle_morphism", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Pretriangulated", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "obtain", "obtain", "obtain", "obtain", "have", "homotopyOfEq", "have", "have", "dsimp", "simp", "let", "have", "have", "dsimp", "simp", "refine", "simpa", "triangle_mor₁,", "simpa", "triangle_mor₁,"], "tactic_count": 22}
{"name": "HomotopyCategory.instPretriangulatedIntUp", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Pretriangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopyCategory.mappingCone_triangleh_distinguished", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Pretriangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopyCategory.instIsTriangulatedIntUpMapHomotopyCategory", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Pretriangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.shiftFunctor", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Shift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.instAdditiveIntShiftFunctor", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Shift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.instLinearIntShiftFunctor", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Shift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.shiftFunctorObjXIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Shift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.shiftFunctorZero'", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Shift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.shiftFunctorAdd'", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Shift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.instHasShiftInt", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Shift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.instAdditiveHomologicalComplexIntUpShiftFunctor", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Shift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.instLinearHomologicalComplexIntUpShiftFunctor", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Shift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.shiftFunctor_obj_X'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Shift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.shiftFunctor_map_f'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Shift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.shiftFunctor_obj_d'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Shift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.shiftFunctorAdd_inv_app_f", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Shift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.shiftFunctorAdd_hom_app_f", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Shift", "is_tactic_proof": true, "tactics": ["tauto"], "tactic_count": 1}
{"name": "CochainComplex.shiftFunctorAdd'_inv_app_f'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Shift", "is_tactic_proof": true, "tactics": ["subst", "rw"], "tactic_count": 2}
{"name": "CochainComplex.shiftFunctorAdd'_hom_app_f'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Shift", "is_tactic_proof": true, "tactics": ["subst", "rw"], "tactic_count": 2}
{"name": "CochainComplex.shiftFunctorZero_inv_app_f", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Shift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.shiftFunctorZero_hom_app_f", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Shift", "is_tactic_proof": true, "tactics": ["tauto"], "tactic_count": 1}
{"name": "CochainComplex.XIsoOfEq_shift", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Shift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.shiftFunctorAdd'_eq", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Shift", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CochainComplex.shiftFunctorAdd_eq", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Shift", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CochainComplex.shiftFunctorZero_eq", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Shift", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "CochainComplex.shiftFunctorComm_hom_app_f", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Shift", "is_tactic_proof": true, "tactics": ["rw", "dsimp", "rw", "simp"], "tactic_count": 4}
{"name": "CochainComplex.shiftEval", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Shift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapCochainComplexShiftIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Shift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.commShiftMapCochainComplex", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Shift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapHomologicalComplex_commShiftIso_eq", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Shift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapHomologicalComplex_commShiftIso_hom_app_f", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Shift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapHomologicalComplex_commShiftIso_inv_app_f", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Shift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homotopy.shift", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Shift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopyCategory.instIsCompatibleWithShiftHomologicalComplexIntUpHomotopic", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Shift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopyCategory.hasShift", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Shift", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "HomotopyCategory.commShiftQuotient", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Shift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopyCategory.instAdditiveIntUpShiftFunctor", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Shift", "is_tactic_proof": false, "tactics": ["have", "apply"], "tactic_count": 2}
{"name": "HomotopyCategory.instLinearIntUpShiftFunctor", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Shift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopyCategory.instCommShiftIntUpMapHomotopyCategory", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Shift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopyCategory.instCommShiftHomologicalComplexIntUpHomFunctorMapHomotopyCategoryFactors", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Shift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.shiftShortComplexFunctor'", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory.ShiftSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.shiftShortComplexFunctorIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory.ShiftSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.shiftShortComplexFunctorIso_zero_add_hom_app", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.ShiftSequence", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CochainComplex.shiftShortComplexFunctorIso_add'_hom_app", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.ShiftSequence", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CochainComplex.ShiftSequence.shiftIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory.ShiftSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.ShiftSequence.shiftIso_hom_app", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.ShiftSequence", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CochainComplex.ShiftSequence.shiftIso_inv_app", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.ShiftSequence", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CochainComplex.instShiftSequenceHomologicalComplexIntUpHomologyFunctorOfNat", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomotopyCategory.ShiftSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.quasiIsoAt_shift_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.ShiftSequence", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "CochainComplex.quasiIso_shift_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.ShiftSequence", "is_tactic_proof": true, "tactics": ["simp", "constructor", "intro", "obtain", "exact", "intro", "exact"], "tactic_count": 7}
{"name": "CochainComplex.instQuasiIsoIntMapHomologicalComplexUpShiftFunctor", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomotopyCategory.ShiftSequence", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CochainComplex.instIsCompatibleWithShiftHomologicalComplexIntUpQuasiIso", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomotopyCategory.ShiftSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.homologyFunctor_shift", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.ShiftSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.liftCycles_shift_homologyπ", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.ShiftSequence", "is_tactic_proof": false, "tactics": ["simp", "shiftShortComplexFunctorIso_inv_app_τ₂,", "rfl"], "tactic_count": 3}
{"name": "HomotopyCategory.instShiftSequenceIntUpHomologyFunctorOfNat", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomotopyCategory.ShiftSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopyCategory.homologyShiftIso_hom_app", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.ShiftSequence", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "HomotopyCategory.homologyFunctor_shiftMap", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.ShiftSequence", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CochainComplex.homologySequenceδ_quotient_mapTriangle_obj", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.ShortExact", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CochainComplex.mappingCone.descShortComplex", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory.ShortExact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.mappingCone.inr_descShortComplex", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.ShortExact", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CochainComplex.mappingCone.inr_f_descShortComplex_f", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.ShortExact", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CochainComplex.mappingCone.inl_v_descShortComplex_f", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.ShortExact", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CochainComplex.mappingCone.homologySequenceδ_triangleh", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.ShortExact", "is_tactic_proof": true, "tactics": ["cocycles", "dsimp", "rw", "cancel_epi", "apply", "ext", "obtain", "erw", "dsimp", "rw", "erw", "rw", "and", "obtain", "rw", "inr_f_fst_v,", "neg_eq_zero,", "inl_v_fst_v_assoc,", "conv_rhs", "rw", "dsimp", "rw", "dsimp", "simp", "comp_id,"], "tactic_count": 25}
{"name": "CochainComplex.mappingCone.quasiIso_descShortComplex", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.ShortExact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.singleFunctors", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory.SingleFunctors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.instAdditiveIntFunctorSingleFunctors", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomotopyCategory.SingleFunctors", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CochainComplex.instLinearIntFunctorSingleFunctors", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomotopyCategory.SingleFunctors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.singleFunctor", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.HomotopyCategory.SingleFunctors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.singleFunctor_obj_d", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.SingleFunctors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.instFullIntSingleFunctor", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomotopyCategory.SingleFunctors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.instFaithfulIntSingleFunctor", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomotopyCategory.SingleFunctors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapCochainComplexSingleFunctor", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory.SingleFunctors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopyCategory.singleFunctors", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory.SingleFunctors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopyCategory.singleFunctor", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.HomotopyCategory.SingleFunctors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopyCategory.instAdditiveIntUpSingleFunctor", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomotopyCategory.SingleFunctors", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "HomotopyCategory.quotient_obj_singleFunctors_obj", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.SingleFunctors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopyCategory.instLinearIntUpSingleFunctor", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomotopyCategory.SingleFunctors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopyCategory.singleFunctorsPostcompQuotientIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory.SingleFunctors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopyCategory.singleFunctorPostcompQuotientIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory.SingleFunctors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopyCategory.composableArrowsFunctor", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory.SpectralObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopyCategory.spectralObjectMappingCone", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory.SpectralObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.mappingConeCompTriangle", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Triangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.mappingConeCompTriangleh", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Triangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.mappingConeCompTriangle_mor₃_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Triangulated", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "simp", "inl_v_desc_f_assoc,", "shiftFunctor_obj_X',", "comp_zero,"], "tactic_count": 6}
{"name": "CochainComplex.MappingConeCompHomotopyEquiv.hom", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Triangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.MappingConeCompHomotopyEquiv.inv", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Triangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.MappingConeCompHomotopyEquiv.hom_inv_id", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Triangulated", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CochainComplex.MappingConeCompHomotopyEquiv.homotopyInvHomId", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Triangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.mappingConeCompHomotopyEquiv", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Triangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.mappingConeCompHomotopyEquiv_hom_inv_id", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Triangulated", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CochainComplex.mappingConeCompHomotopyEquiv_comm₁", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Triangulated", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CochainComplex.mappingConeCompHomotopyEquiv_comm₂", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Triangulated", "is_tactic_proof": true, "tactics": ["ext", "simp", "ext_from_iff"], "tactic_count": 3}
{"name": "CochainComplex.mappingConeCompTriangleh_comm₁", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Triangulated", "is_tactic_proof": true, "tactics": ["rw", "dsimp", "rw", "mappingConeCompHomotopyEquiv_comm₁"], "tactic_count": 4}
{"name": "HomotopyCategory.mappingConeCompTriangleh_distinguished", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Triangulated", "is_tactic_proof": true, "tactics": ["refine", "refine", "dsimp", "rw", "congr", "exact"], "tactic_count": 6}
{"name": "HomotopyCategory.instIsTriangulatedIntUp", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Triangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.instHasHomotopyCofiberOfHasBinaryBiproducts", "kind": "instance", "module": "Mathlib.Algebra.Homology.HomotopyCofiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.homotopyCofiber.X", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCofiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.homotopyCofiber.XIsoBiprod", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCofiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.homotopyCofiber.XIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCofiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.homotopyCofiber.sndX", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCofiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.homotopyCofiber.inrX", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCofiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.homotopyCofiber.inrX_sndX", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCofiber", "is_tactic_proof": true, "tactics": ["dsimp", "split_ifs"], "tactic_count": 2}
{"name": "HomologicalComplex.homotopyCofiber.sndX_inrX", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCofiber", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "HomologicalComplex.homotopyCofiber.fstX", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCofiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.homotopyCofiber.inlX", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCofiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.homotopyCofiber.inlX_fstX", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCofiber", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HomologicalComplex.homotopyCofiber.inlX_sndX", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCofiber", "is_tactic_proof": true, "tactics": ["obtain", "simp"], "tactic_count": 2}
{"name": "HomologicalComplex.homotopyCofiber.inrX_fstX", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCofiber", "is_tactic_proof": true, "tactics": ["obtain", "simp"], "tactic_count": 2}
{"name": "HomologicalComplex.homotopyCofiber.d", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCofiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.homotopyCofiber.ext_to_X", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCofiber", "is_tactic_proof": true, "tactics": ["haveI", "rw", "apply", "simpa", "obtain", "simpa"], "tactic_count": 6}
{"name": "HomologicalComplex.homotopyCofiber.ext_to_X'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCofiber", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "HomologicalComplex.homotopyCofiber.ext_from_X", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCofiber", "is_tactic_proof": true, "tactics": ["haveI", "rw", "apply", "simpa", "obtain", "simpa"], "tactic_count": 6}
{"name": "HomologicalComplex.homotopyCofiber.ext_from_X'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCofiber", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "HomologicalComplex.homotopyCofiber.d_fstX", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCofiber", "is_tactic_proof": true, "tactics": ["obtain", "simp"], "tactic_count": 2}
{"name": "HomologicalComplex.homotopyCofiber.d_sndX", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCofiber", "is_tactic_proof": true, "tactics": ["dsimp", "split_ifs"], "tactic_count": 2}
{"name": "HomologicalComplex.homotopyCofiber.inlX_d", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCofiber", "is_tactic_proof": true, "tactics": ["apply", "simp", "simp"], "tactic_count": 3}
{"name": "HomologicalComplex.homotopyCofiber.inlX_d'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCofiber", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "HomologicalComplex.homotopyCofiber.shape", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCofiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.homotopyCofiber.inrX_d", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCofiber", "is_tactic_proof": true, "tactics": ["by_cases", "by_cases", "apply", "simp", "simp", "apply", "simp", "rw"], "tactic_count": 8}
{"name": "HomologicalComplex.homotopyCofiber", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCofiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.homotopyCofiber.inr", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCofiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.homotopyCofiber.inrCompHomotopy", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCofiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.homotopyCofiber.inrCompHomotopy_hom", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCofiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.homotopyCofiber.inrCompHomotopy_hom_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCofiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.homotopyCofiber.desc", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCofiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.homotopyCofiber.desc_f", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCofiber", "is_tactic_proof": true, "tactics": ["obtain", "apply"], "tactic_count": 2}
{"name": "HomologicalComplex.homotopyCofiber.desc_f'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCofiber", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "HomologicalComplex.homotopyCofiber.inlX_desc_f", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCofiber", "is_tactic_proof": true, "tactics": ["obtain", "dsimp", "rw"], "tactic_count": 3}
{"name": "HomologicalComplex.homotopyCofiber.inrX_desc_f", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCofiber", "is_tactic_proof": true, "tactics": ["dsimp", "split_ifs"], "tactic_count": 2}
{"name": "HomologicalComplex.homotopyCofiber.inr_desc", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCofiber", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "HomologicalComplex.homotopyCofiber.inrCompHomotopy_hom_desc_hom", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCofiber", "is_tactic_proof": true, "tactics": ["by_cases", "dsimp", "simp", "zero_comp,", "simp"], "tactic_count": 5}
{"name": "HomologicalComplex.homotopyCofiber.eq_desc", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCofiber", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "apply", "simp", "simp", "apply", "simp"], "tactic_count": 7}
{"name": "HomologicalComplex.homotopyCofiber.descSigma_ext_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCofiber", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "tauto", "obtain", "obtain", "rintro", "simp", "ext", "by_cases", "exact", "simp"], "tactic_count": 11}
{"name": "HomologicalComplex.homotopyCofiber.descEquiv", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCofiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.cylinder", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.HomotopyCofiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.cylinder.ι₀", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCofiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.cylinder.ι₁", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCofiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.cylinder.desc", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCofiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.cylinder.ι₀_desc", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCofiber", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HomologicalComplex.cylinder.ι₁_desc", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCofiber", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HomologicalComplex.cylinder.π", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCofiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.cylinder.ι₀_π", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCofiber", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HomologicalComplex.cylinder.ι₁_π", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCofiber", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HomologicalComplex.cylinder.inlX", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.HomotopyCofiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.cylinder.inrX", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.HomotopyCofiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.cylinder.inlX_π", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCofiber", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HomologicalComplex.cylinder.inrX_π", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCofiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.cylinder.πCompι₀Homotopy.nullHomotopicMap", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCofiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.cylinder.πCompι₀Homotopy.nullHomotopy", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCofiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.cylinder.πCompι₀Homotopy.inlX_nullHomotopy_f", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCofiber", "is_tactic_proof": true, "tactics": ["dsimp", "by_cases", "obtain", "simp", "homotopyCofiber.d_sndX_assoc", "homotopyCofiber.inlX_sndX_assoc,", "simp", "comp_sub,", "homotopyCofiber.inlX_fstX_assoc,", "biprod.lift_snd,"], "tactic_count": 10}
{"name": "HomologicalComplex.cylinder.πCompι₀Homotopy.inrX_nullHomotopy_f", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCofiber", "is_tactic_proof": true, "tactics": ["have", "obtain", "dsimp", "by_cases", "obtain", "simp", "homotopyCofiber.inrX_d_assoc,", "homotopyCofiber.inlX_d", "rw", "ext", "simp", "dsimp", "simp", "comp_f,", "simp", "simp", "homotopyCofiber.inlX_d", "comp_f,", "rw", "ext", "simp", "simp"], "tactic_count": 22}
{"name": "HomologicalComplex.cylinder.πCompι₀Homotopy.nullHomotopicMap_eq", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCofiber", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "exact", "homotopyCofiber.ext_from_X", "exact"], "tactic_count": 5}
{"name": "HomologicalComplex.cylinder.πCompι₀Homotopy", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCofiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.cylinder.homotopyEquiv", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCofiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.cylinder.homotopy₀₁", "kind": "definition", "module": "Mathlib.Algebra.Homology.HomotopyCofiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.cylinder.map_ι₀_eq_map_ι₁", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCofiber", "is_tactic_proof": true, "tactics": ["have", "simp"], "tactic_count": 2}
{"name": "Homotopy.map_eq_of_inverts_homotopyEquivalences", "kind": "theorem", "module": "Mathlib.Algebra.Homology.HomotopyCofiber", "is_tactic_proof": true, "tactics": ["classical", "simp"], "tactic_count": 2}
{"name": "image_le_kernel", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ImageToKernel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "imageToKernel", "kind": "definition", "module": "Mathlib.Algebra.Homology.ImageToKernel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instMonoImageToKernel", "kind": "instance", "module": "Mathlib.Algebra.Homology.ImageToKernel", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "subobject_ofLE_as_imageToKernel", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ImageToKernel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "imageToKernel_arrow", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ImageToKernel", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "factorThruImageSubobject_comp_imageToKernel", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ImageToKernel", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "imageToKernel_zero_left", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ImageToKernel", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "imageToKernel_zero_right", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ImageToKernel", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "imageToKernel_comp_right", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ImageToKernel", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "imageToKernel_comp_left", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ImageToKernel", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "imageToKernel_comp_mono", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ImageToKernel", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "imageToKernel_epi_comp", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ImageToKernel", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "imageToKernel_comp_hom_inv_comp", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ImageToKernel", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "imageToKernel_epi_of_zero_of_mono", "kind": "instance", "module": "Mathlib.Algebra.Homology.ImageToKernel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "imageToKernel_epi_of_epi_of_zero", "kind": "instance", "module": "Mathlib.Algebra.Homology.ImageToKernel", "is_tactic_proof": true, "tactics": ["simp", "haveI", "rw", "infer_instance"], "tactic_count": 4}
{"name": "imageToKernel'", "kind": "definition", "module": "Mathlib.Algebra.Homology.ImageToKernel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "imageSubobjectIso_imageToKernel'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ImageToKernel", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "imageToKernel'_kernelSubobjectIso", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ImageToKernel", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Abelian.LeftResolution.π_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Homology.LeftResolution.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.LeftResolution.chainComplex", "kind": "definition", "module": "Mathlib.Algebra.Homology.LeftResolution.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.LeftResolution.chainComplexXZeroIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.LeftResolution.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.LeftResolution.chainComplexXOneIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.LeftResolution.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.LeftResolution.map_chainComplex_d_1_0", "kind": "theorem", "module": "Mathlib.Algebra.Homology.LeftResolution.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Abelian.LeftResolution.chainComplexXIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.LeftResolution.Basic", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Abelian.LeftResolution.map_chainComplex_d", "kind": "theorem", "module": "Mathlib.Algebra.Homology.LeftResolution.Basic", "is_tactic_proof": true, "tactics": ["have", "dsimp", "rw", "congr", "apply"], "tactic_count": 5}
{"name": "CategoryTheory.Abelian.LeftResolution.exactAt_map_chainComplex_succ", "kind": "theorem", "module": "Mathlib.Algebra.Homology.LeftResolution.Basic", "is_tactic_proof": false, "tactics": ["rw", "convert", "rw", "simp"], "tactic_count": 4}
{"name": "CategoryTheory.Abelian.LeftResolution.chainComplexMap", "kind": "definition", "module": "Mathlib.Algebra.Homology.LeftResolution.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.LeftResolution.chainComplexMap_f_0", "kind": "theorem", "module": "Mathlib.Algebra.Homology.LeftResolution.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.LeftResolution.chainComplexMap_f_1", "kind": "theorem", "module": "Mathlib.Algebra.Homology.LeftResolution.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.LeftResolution.chainComplexMap_f_succ_succ", "kind": "theorem", "module": "Mathlib.Algebra.Homology.LeftResolution.Basic", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Abelian.LeftResolution.chainComplexMap_id", "kind": "theorem", "module": "Mathlib.Algebra.Homology.LeftResolution.Basic", "is_tactic_proof": true, "tactics": ["ext", "induction", "zero", "succ"], "tactic_count": 4}
{"name": "CategoryTheory.Abelian.LeftResolution.chainComplexMap_zero", "kind": "theorem", "module": "Mathlib.Algebra.Homology.LeftResolution.Basic", "is_tactic_proof": true, "tactics": ["ext", "induction", "zero", "succ"], "tactic_count": 4}
{"name": "CategoryTheory.Abelian.LeftResolution.chainComplexMap_comp", "kind": "theorem", "module": "Mathlib.Algebra.Homology.LeftResolution.Basic", "is_tactic_proof": true, "tactics": ["ext", "induction", "zero", "succ", "obtain", "all_goals", "dsimp", "simp", "congr", "cat_disch"], "tactic_count": 10}
{"name": "CategoryTheory.Abelian.LeftResolution.chainComplexFunctor", "kind": "definition", "module": "Mathlib.Algebra.Homology.LeftResolution.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.LeftResolution.karoubi.F'", "kind": "definition", "module": "Mathlib.Algebra.Homology.LeftResolution.Reduced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.LeftResolution.karoubi.F", "kind": "definition", "module": "Mathlib.Algebra.Homology.LeftResolution.Reduced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.LeftResolution.instPreservesZeroMorphismsKaroubiF", "kind": "instance", "module": "Mathlib.Algebra.Homology.LeftResolution.Reduced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.LeftResolution.karoubi.π'", "kind": "definition", "module": "Mathlib.Algebra.Homology.LeftResolution.Reduced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.LeftResolution.karoubi.retractArrow", "kind": "definition", "module": "Mathlib.Algebra.Homology.LeftResolution.Reduced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.LeftResolution.instEpiKaroubiAppπ'", "kind": "instance", "module": "Mathlib.Algebra.Homology.LeftResolution.Reduced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.LeftResolution.karoubi.π", "kind": "definition", "module": "Mathlib.Algebra.Homology.LeftResolution.Reduced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.LeftResolution.karoubi.π_app_toKaroubi_obj", "kind": "theorem", "module": "Mathlib.Algebra.Homology.LeftResolution.Reduced", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Abelian.LeftResolution.instEpiKaroubiAppπObjToKaroubi", "kind": "instance", "module": "Mathlib.Algebra.Homology.LeftResolution.Reduced", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Abelian.LeftResolution.instEpiKaroubiAppπ", "kind": "instance", "module": "Mathlib.Algebra.Homology.LeftResolution.Reduced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.LeftResolution.karoubi", "kind": "definition", "module": "Mathlib.Algebra.Homology.LeftResolution.Reduced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.LeftResolution.instPreservesZeroMorphismsKaroubiFKaroubi", "kind": "instance", "module": "Mathlib.Algebra.Homology.LeftResolution.Reduced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.LeftResolution.reduced", "kind": "definition", "module": "Mathlib.Algebra.Homology.LeftResolution.Reduced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.LeftResolution.instPreservesZeroMorphismsFReduced", "kind": "instance", "module": "Mathlib.Algebra.Homology.LeftResolution.Reduced", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Abelian.LeftResolution.transport", "kind": "definition", "module": "Mathlib.Algebra.Homology.LeftResolution.Transport", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.LeftResolution.ofCompIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.LeftResolution.Transport", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.instSMulHom", "kind": "instance", "module": "Mathlib.Algebra.Homology.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.smul_f_apply", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.units_smul_f_apply", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.instModuleHom", "kind": "instance", "module": "Mathlib.Algebra.Homology.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.instLinear", "kind": "instance", "module": "Mathlib.Algebra.Homology.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapHomologicalComplex_linear", "kind": "instance", "module": "Mathlib.Algebra.Homology.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "localCohomology.ringModIdeals", "kind": "definition", "module": "Mathlib.Algebra.Homology.LocalCohomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "localCohomology.diagram", "kind": "definition", "module": "Mathlib.Algebra.Homology.LocalCohomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "localCohomology.hasColimitDiagram", "kind": "theorem", "module": "Mathlib.Algebra.Homology.LocalCohomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "localCohomology.ofDiagram", "kind": "definition", "module": "Mathlib.Algebra.Homology.LocalCohomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "localCohomology.diagramComp", "kind": "definition", "module": "Mathlib.Algebra.Homology.LocalCohomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "localCohomology.isoOfFinal", "kind": "definition", "module": "Mathlib.Algebra.Homology.LocalCohomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "localCohomology.idealPowersDiagram", "kind": "definition", "module": "Mathlib.Algebra.Homology.LocalCohomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "localCohomology.SelfLERadical", "kind": "definition", "module": "Mathlib.Algebra.Homology.LocalCohomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "localCohomology.SelfLERadical.inhabited", "kind": "instance", "module": "Mathlib.Algebra.Homology.LocalCohomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "localCohomology.selfLERadicalDiagram", "kind": "definition", "module": "Mathlib.Algebra.Homology.LocalCohomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "localCohomology", "kind": "definition", "module": "Mathlib.Algebra.Homology.LocalCohomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "localCohomology.ofSelfLERadical", "kind": "definition", "module": "Mathlib.Algebra.Homology.LocalCohomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "localCohomology.idealPowersToSelfLERadical", "kind": "definition", "module": "Mathlib.Algebra.Homology.LocalCohomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "localCohomology.ideal_powers_initial", "kind": "instance", "module": "Mathlib.Algebra.Homology.LocalCohomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "localCohomology._example", "kind": "example", "module": "Mathlib.Algebra.Homology.LocalCohomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "localCohomology.isoSelfLERadical", "kind": "definition", "module": "Mathlib.Algebra.Homology.LocalCohomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "localCohomology.SelfLERadical.cast", "kind": "definition", "module": "Mathlib.Algebra.Homology.LocalCohomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "localCohomology.SelfLERadical.castEquivalence", "kind": "definition", "module": "Mathlib.Algebra.Homology.LocalCohomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "localCohomology.SelfLERadical.cast_isEquivalence", "kind": "instance", "module": "Mathlib.Algebra.Homology.LocalCohomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "localCohomology.SelfLERadical.isoOfSameRadical", "kind": "definition", "module": "Mathlib.Algebra.Homology.LocalCohomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "localCohomology.isoOfSameRadical", "kind": "definition", "module": "Mathlib.Algebra.Homology.LocalCohomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.homologyFunctor_inverts_quasiIso", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplexUpToQuasiIso", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplexUpToQuasiIso.Q", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplexUpToQuasiIso.homologyFunctor", "kind": "definition", "module": "Mathlib.Algebra.Homology.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplexUpToQuasiIso.homologyFunctorFactors", "kind": "definition", "module": "Mathlib.Algebra.Homology.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplexUpToQuasiIso.isIso_Q_map_iff_mem_quasiIso", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Localization", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "intro", "rw", "refine", "dsimp", "infer_instance", "intro", "exact"], "tactic_count": 10}
{"name": "HomologicalComplexUpToQuasiIso.Q_inverts_homotopyEquivalences", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopyCategory.quasiIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopyCategory.mem_quasiIso_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Localization", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "HomotopyCategory.quotient_map_mem_quasiIso_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Localization", "is_tactic_proof": true, "tactics": ["have", "dsimp", "simp"], "tactic_count": 3}
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{"name": "HomotopyCategory.homologyFunctor_inverts_quasiIso", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopyCategory.quasiIso_eq_quasiIso_map_quotient", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Localization", "is_tactic_proof": true, "tactics": ["ext", "obtain", "constructor", "intro", "rw", "exact", "rintro", "rw", "exact"], "tactic_count": 9}
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{"name": "HomologicalComplexUpToQuasiIso.Qh", "kind": "definition", "module": "Mathlib.Algebra.Homology.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplexUpToQuasiIso.quotientCompQhIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.Localization", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "HomologicalComplexUpToQuasiIso.Qh_inverts_quasiIso", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Localization", "is_tactic_proof": true, "tactics": ["rintro", "obtain", "rw", "exact"], "tactic_count": 4}
{"name": "HomologicalComplexUpToQuasiIso.instIsLocalizationHomologicalComplexCompHomotopyCategoryQuotientQhQuasiIso", "kind": "instance", "module": "Mathlib.Algebra.Homology.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplexUpToQuasiIso.homologyFunctorFactorsh", "kind": "definition", "module": "Mathlib.Algebra.Homology.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplexUpToQuasiIso.instIsLocalizationHomotopyCategoryQhQuasiIso", "kind": "instance", "module": "Mathlib.Algebra.Homology.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.strictUniversalPropertyFixedTargetQuotient", "kind": "definition", "module": "Mathlib.Algebra.Homology.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexShape.quotient_isLocalization", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Localization", "is_tactic_proof": true, "tactics": ["apply", "all_goals"], "tactic_count": 2}
{"name": "ComplexShape.QFactorsThroughHomotopy_of_exists_prev", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsLocalizationHomologicalComplexDownHomotopyCategoryQuotientHomotopyEquivalences", "kind": "instance", "module": "Mathlib.Algebra.Homology.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instQFactorsThroughHomotopyDown", "kind": "instance", "module": "Mathlib.Algebra.Homology.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_example", "kind": "example", "module": "Mathlib.Algebra.Homology.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsLocalizationHomologicalComplexIntUpHomotopyCategoryQuotientHomotopyEquivalences", "kind": "instance", "module": "Mathlib.Algebra.Homology.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instQFactorsThroughHomotopyIntUp", "kind": "instance", "module": "Mathlib.Algebra.Homology.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Functor.mapHomologicalComplexUpToQuasiIsoLocalizerMorphism", "kind": "definition", "module": "Mathlib.Algebra.Homology.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapHomologicalComplex_upToQuasiIso_Q_inverts_quasiIso", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Localization", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.mapHomologicalComplexUpToQuasiIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instLiftingHomologicalComplexHomologicalComplexUpToQuasiIsoQQuasiIsoCompMapHomologicalComplexMapHomologicalComplexUpToQuasiIso", "kind": "instance", "module": "Mathlib.Algebra.Homology.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapHomologicalComplexUpToQuasiIsoFactors", "kind": "definition", "module": "Mathlib.Algebra.Homology.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapHomologicalComplexUpToQuasiIsoFactorsh", "kind": "definition", "module": "Mathlib.Algebra.Homology.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instLiftingHomotopyCategoryHomologicalComplexUpToQuasiIsoQhQuasiIsoCompMapHomotopyCategoryMapHomologicalComplexUpToQuasiIso", "kind": "instance", "module": "Mathlib.Algebra.Homology.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapHomologicalComplexUpToQuasiIsoFactorsh_hom_app", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Localization", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "dsimp", "simp", "change", "simp"], "tactic_count": 6}
{"name": "HomologicalComplex.HasTensor", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.tensorObj", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.ιTensorObj", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.tensorHom", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.HasGoodTensor₁₂", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.HasGoodTensor₂₃", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.associator", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.tensorUnit", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.tensorUnitIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.instHasTensorOfHasTensorX", "kind": "instance", "module": "Mathlib.Algebra.Homology.Monoidal", "is_tactic_proof": true, "tactics": ["assumption"], "tactic_count": 1}
{"name": "HomologicalComplex.instHasGoodTensor₁₂OfHasGoodTensor₁₂TensorX", "kind": "instance", "module": "Mathlib.Algebra.Homology.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.instHasGoodTensor₂₃OfHasGoodTensorTensor₂₃X", "kind": "instance", "module": "Mathlib.Algebra.Homology.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.instHasTensorXTensorUnit", "kind": "instance", "module": "Mathlib.Algebra.Homology.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.instHasTensorTensorUnit", "kind": "instance", "module": "Mathlib.Algebra.Homology.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.unit_tensor_d₁", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Monoidal", "is_tactic_proof": true, "tactics": ["by_cases", "by_cases", "rw", "rw", "rw"], "tactic_count": 5}
{"name": "HomologicalComplex.instHasTensorXTensorUnit_1", "kind": "instance", "module": "Mathlib.Algebra.Homology.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.instHasTensorTensorUnit_1", "kind": "instance", "module": "Mathlib.Algebra.Homology.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.tensor_unit_d₂", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Monoidal", "is_tactic_proof": true, "tactics": ["by_cases", "by_cases", "rw", "rw", "rw"], "tactic_count": 5}
{"name": "HomologicalComplex.leftUnitor'", "kind": "definition", "module": "Mathlib.Algebra.Homology.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.leftUnitor'_inv", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Monoidal", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "dsimp", "rw", "congr", "rw", "dsimp", "rw", "rfl"], "tactic_count": 9}
{"name": "HomologicalComplex.leftUnitor'_inv_comm", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Monoidal", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "unit_tensor_d₁,", "rw", "dsimp", "simp", "simp"], "tactic_count": 7}
{"name": "HomologicalComplex.leftUnitor", "kind": "definition", "module": "Mathlib.Algebra.Homology.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.rightUnitor'", "kind": "definition", "module": "Mathlib.Algebra.Homology.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.rightUnitor'_inv", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Monoidal", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "dsimp", "rw", "congr", "rw", "dsimp", "rw", "rfl"], "tactic_count": 9}
{"name": "HomologicalComplex.rightUnitor'_inv_comm", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Monoidal", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "tensor_unit_d₂,", "rw", "dsimp", "simp", "simp"], "tactic_count": 7}
{"name": "HomologicalComplex.rightUnitor", "kind": "definition", "module": "Mathlib.Algebra.Homology.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.monoidalCategoryStruct", "kind": "instance", "module": "Mathlib.Algebra.Homology.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.Monoidal.inducingFunctorData", "kind": "definition", "module": "Mathlib.Algebra.Homology.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.monoidalCategory", "kind": "instance", "module": "Mathlib.Algebra.Homology.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex._example", "kind": "example", "module": "Mathlib.Algebra.Homology.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "imageToKernel_op", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Opposite", "is_tactic_proof": true, "tactics": ["ext", "simp", "kernelSubobject_arrow',", "rfl"], "tactic_count": 4}
{"name": "imageToKernel_unop", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Opposite", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "simp", "kernelSubobject_arrow',", "factorThruImage_comp_imageUnopOp_inv,"], "tactic_count": 5}
{"name": "HomologicalComplex.op", "kind": "definition", "module": "Mathlib.Algebra.Homology.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.opSymm", "kind": "definition", "module": "Mathlib.Algebra.Homology.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.unop", "kind": "definition", "module": "Mathlib.Algebra.Homology.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.unopSymm", "kind": "definition", "module": "Mathlib.Algebra.Homology.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.opFunctor", "kind": "definition", "module": "Mathlib.Algebra.Homology.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.opInverse", "kind": "definition", "module": "Mathlib.Algebra.Homology.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.opUnitIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.opCounitIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.opEquivalence", "kind": "definition", "module": "Mathlib.Algebra.Homology.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.unopFunctor", "kind": "definition", "module": "Mathlib.Algebra.Homology.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.unopInverse", "kind": "definition", "module": "Mathlib.Algebra.Homology.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.unopUnitIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.unopCounitIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.unopEquivalence", "kind": "definition", "module": "Mathlib.Algebra.Homology.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.instHasHomologyOppositeOp", "kind": "instance", "module": "Mathlib.Algebra.Homology.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.instHasHomologyUnopOfOpposite", "kind": "instance", "module": "Mathlib.Algebra.Homology.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.instHasHomologyOppositeObjSymmOpFunctorOp", "kind": "instance", "module": "Mathlib.Algebra.Homology.Opposite", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "HomologicalComplex.instHasHomologyObjOppositeSymmUnopFunctorOp", "kind": "instance", "module": "Mathlib.Algebra.Homology.Opposite", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "HomologicalComplex.quasiIsoAt_opFunctor_map_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Opposite", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "HomologicalComplex.quasiIsoAt_unopFunctor_map_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Opposite", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "HomologicalComplex.instQuasiIsoAtOppositeMapSymmOpFunctorOp", "kind": "instance", "module": "Mathlib.Algebra.Homology.Opposite", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "HomologicalComplex.instQuasiIsoAtMapOppositeSymmUnopFunctorOp", "kind": "instance", "module": "Mathlib.Algebra.Homology.Opposite", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "HomologicalComplex.quasiIso_opFunctor_map_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Opposite", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HomologicalComplex.quasiIso_unopFunctor_map_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Opposite", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HomologicalComplex.instQuasiIsoOppositeMapSymmOpFunctorOp", "kind": "instance", "module": "Mathlib.Algebra.Homology.Opposite", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "HomologicalComplex.instQuasiIsoMapOppositeSymmUnopFunctorOp", "kind": "instance", "module": "Mathlib.Algebra.Homology.Opposite", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "HomologicalComplex.ExactAt.op", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.ExactAt.unop", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.exactAt_op_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.Acyclic.op", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.Acyclic.unop", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.acyclic_op_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.homologyOp", "kind": "definition", "module": "Mathlib.Algebra.Homology.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.homologyUnop", "kind": "definition", "module": "Mathlib.Algebra.Homology.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.cyclesOpIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.opcyclesOpIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.opcyclesOpIso_hom_toCycles_op", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Opposite", "is_tactic_proof": true, "tactics": ["by_cases", "obtain", "exact", "rw"], "tactic_count": 4}
{"name": "HomologicalComplex.fromOpcycles_op_cyclesOpIso_inv", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Opposite", "is_tactic_proof": true, "tactics": ["by_cases", "obtain", "exact", "rw"], "tactic_count": 4}
{"name": "HomologicalComplex.homologyOp_hom_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.opcyclesOpIso_hom_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.opcyclesOpIso_inv_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.cyclesOpIso_hom_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.cyclesOpIso_inv_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.cyclesOpNatIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.opcyclesOpNatIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.homologyOpNatIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.opFunctor_additive", "kind": "instance", "module": "Mathlib.Algebra.Homology.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.unopFunctor_additive", "kind": "instance", "module": "Mathlib.Algebra.Homology.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "quasiIsoAt_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.QuasiIso", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "intro", "exact"], "tactic_count": 5}
{"name": "quasiIsoAt_of_isIso", "kind": "instance", "module": "Mathlib.Algebra.Homology.QuasiIso", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "quasiIsoAt_iff'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.QuasiIso", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "quasiIsoAt_of_retract", "kind": "theorem", "module": "Mathlib.Algebra.Homology.QuasiIso", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "quasiIsoAt_iff_isIso_homologyMap", "kind": "theorem", "module": "Mathlib.Algebra.Homology.QuasiIso", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "quasiIsoAt_iff_exactAt", "kind": "theorem", "module": "Mathlib.Algebra.Homology.QuasiIso", "is_tactic_proof": false, "tactics": ["simp", "constructor", "intro", "exact", "intro", "exact"], "tactic_count": 6}
{"name": "quasiIsoAt_iff_exactAt'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.QuasiIso", "is_tactic_proof": false, "tactics": ["simp", "constructor", "intro", "exact", "intro", "exact"], "tactic_count": 6}
{"name": "exactAt_iff_of_quasiIsoAt", "kind": "theorem", "module": "Mathlib.Algebra.Homology.QuasiIso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsIsoHomologyMapOfQuasiIsoAt", "kind": "instance", "module": "Mathlib.Algebra.Homology.QuasiIso", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "isoOfQuasiIsoAt", "kind": "definition", "module": "Mathlib.Algebra.Homology.QuasiIso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isoOfQuasiIsoAt_hom_inv_id", "kind": "theorem", "module": "Mathlib.Algebra.Homology.QuasiIso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isoOfQuasiIsoAt_inv_hom_id", "kind": "theorem", "module": "Mathlib.Algebra.Homology.QuasiIso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.quasiIsoAt₀_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.QuasiIso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ChainComplex.quasiIsoAt₀_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.QuasiIso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "quasiIso_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.QuasiIso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "quasiIso_of_isIso", "kind": "instance", "module": "Mathlib.Algebra.Homology.QuasiIso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "quasiIsoAt_comp", "kind": "instance", "module": "Mathlib.Algebra.Homology.QuasiIso", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "quasiIso_comp", "kind": "instance", "module": "Mathlib.Algebra.Homology.QuasiIso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "quasiIsoAt_of_comp_left", "kind": "theorem", "module": "Mathlib.Algebra.Homology.QuasiIso", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "quasiIsoAt_iff_comp_left", "kind": "theorem", "module": "Mathlib.Algebra.Homology.QuasiIso", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "intro", "infer_instance"], "tactic_count": 5}
{"name": "quasiIso_iff_comp_left", "kind": "theorem", "module": "Mathlib.Algebra.Homology.QuasiIso", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "quasiIso_of_comp_left", "kind": "theorem", "module": "Mathlib.Algebra.Homology.QuasiIso", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "quasiIsoAt_of_comp_right", "kind": "theorem", "module": "Mathlib.Algebra.Homology.QuasiIso", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "quasiIsoAt_iff_comp_right", "kind": "theorem", "module": "Mathlib.Algebra.Homology.QuasiIso", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "intro", "infer_instance"], "tactic_count": 5}
{"name": "quasiIso_iff_comp_right", "kind": "theorem", "module": "Mathlib.Algebra.Homology.QuasiIso", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "quasiIso_of_comp_right", "kind": "theorem", "module": "Mathlib.Algebra.Homology.QuasiIso", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "quasiIso_iff_of_arrow_mk_iso", "kind": "theorem", "module": "Mathlib.Algebra.Homology.QuasiIso", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "quasiIso_of_arrow_mk_iso", "kind": "theorem", "module": "Mathlib.Algebra.Homology.QuasiIso", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "quasiIso_of_retractArrow", "kind": "theorem", "module": "Mathlib.Algebra.Homology.QuasiIso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.quasiIsoAt_map_of_preservesHomology", "kind": "instance", "module": "Mathlib.Algebra.Homology.QuasiIso", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "HomologicalComplex.quasiIsoAt_map_iff_of_preservesHomology", "kind": "theorem", "module": "Mathlib.Algebra.Homology.QuasiIso", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "HomologicalComplex.quasiIso_map_of_preservesHomology", "kind": "instance", "module": "Mathlib.Algebra.Homology.QuasiIso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.quasiIso_map_iff_of_preservesHomology", "kind": "theorem", "module": "Mathlib.Algebra.Homology.QuasiIso", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HomologicalComplex.quasiIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.QuasiIso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.mem_quasiIso_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.QuasiIso", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "HomologicalComplex.instIsMultiplicativeQuasiIso", "kind": "instance", "module": "Mathlib.Algebra.Homology.QuasiIso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.instHasTwoOutOfThreePropertyQuasiIso", "kind": "instance", "module": "Mathlib.Algebra.Homology.QuasiIso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.instIsStableUnderRetractsQuasiIso", "kind": "instance", "module": "Mathlib.Algebra.Homology.QuasiIso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.instRespectsIsoQuasiIso", "kind": "instance", "module": "Mathlib.Algebra.Homology.QuasiIso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopyEquiv.quasiIsoAt_hom", "kind": "instance", "module": "Mathlib.Algebra.Homology.QuasiIso", "is_tactic_proof": true, "tactics": ["classical", "rw", "exact"], "tactic_count": 3}
{"name": "HomotopyEquiv.quasiIsoAt_inv", "kind": "instance", "module": "Mathlib.Algebra.Homology.QuasiIso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopyEquiv.quasiIso_hom", "kind": "instance", "module": "Mathlib.Algebra.Homology.QuasiIso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopyEquiv.quasiIso_inv", "kind": "instance", "module": "Mathlib.Algebra.Homology.QuasiIso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "homotopyEquivalences_le_quasiIso", "kind": "theorem", "module": "Mathlib.Algebra.Homology.QuasiIso", "is_tactic_proof": true, "tactics": ["rintro", "simp", "infer_instance"], "tactic_count": 3}
{"name": "HomologicalComplex.eq_liftCycles_homologyπ_up_to_refinements", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Refinements", "is_tactic_proof": true, "tactics": ["subst", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.ab_zero_apply", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Ab", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.abToCycles", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Ab", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.abLeftHomologyData", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Ab", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.abLeftHomologyData_f'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Ab", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.abCyclesIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Ab", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.abCyclesIso_inv_apply_iCycles", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Ab", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "rfl"], "tactic_count": 3}
{"name": "CategoryTheory.ShortComplex.abHomologyIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Ab", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.exact_iff_surjective_abToCycles", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Ab", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.ab_exact_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Ab", "is_tactic_proof": true, "tactics": ["rw", "constructor", "intro", "obtain", "exact", "rintro", "obtain", "exact"], "tactic_count": 8}
{"name": "CategoryTheory.ShortComplex.ab_exact_iff_function_exact", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Ab", "is_tactic_proof": true, "tactics": ["rw", "apply", "intro", "constructor", "intro", "refine", "rintro", "simp", "tauto"], "tactic_count": 9}
{"name": "CategoryTheory.ShortComplex.ab_exact_iff_ker_le_range", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Ab", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.ab_exact_iff_range_eq_ker", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Ab", "is_tactic_proof": true, "tactics": ["rw", "constructor", "intro", "refine", "rintro", "rw", "rfl", "intro", "rw"], "tactic_count": 9}
{"name": "CategoryTheory.ShortComplex.Exact.ab_finite", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Ab", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "exact", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.ShortComplex.ShortExact.ab_injective_f", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Ab", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.ShortExact.ab_surjective_g", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Ab", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.ShortExact.ab_finite_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Ab", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.abelianImageToKernel", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.abelianImageToKernel_comp_kernel_ι", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.instMonoAbelianImageToKernel", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.abelianImageToKernel_comp_kernel_ι_comp_cokernel_π", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Abelian", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.abelianImageToKernelIsKernel", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.LeftHomologyData.ofAbelian", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Abelian", "is_tactic_proof": true, "tactics": ["let", "let", "have", "have", "rw", "simp", "let", "have", "have", "rw", "simp", "have", "cokernel.desc", "simpa", "hx))", "exact", "i", "wi", "hi", "wπ", "hπ"], "tactic_count": 21}
{"name": "CategoryTheory.ShortComplex.cokernelToAbelianCoimage", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.cokernel_π_comp_cokernelToAbelianCoimage", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.instEpiCokernelToAbelianCoimage", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.kernel_ι_comp_cokernel_π_comp_cokernelToAbelianCoimage", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Abelian", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.cokernelToAbelianCoimageIsCokernel", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.RightHomologyData.ofAbelian", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Abelian", "is_tactic_proof": true, "tactics": ["let", "let", "have", "have", "let", "have", "have", "rw", "simp", "have", "kernel.lift", "simpa", "hx))", "exact", "p", "ι", "wp", "hp", "wι", "hι"], "tactic_count": 20}
{"name": "CategoryTheory.ShortComplex.HomologyData.ofAbelian", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.categoryWithHomology_of_abelian", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.instIsNormalMonoCategory", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.instIsNormalEpiCategory", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.instAbelian", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.homologyIsoImageICyclesCompPOpcycles", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.homologyIsoImageICyclesCompPOpcycles_ι", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.isoImage", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Abelian", "is_tactic_proof": false, "tactics": ["have", "simp", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.isoImage_ι", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Abelian", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.isoHomology", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.π_comp_isoHomology_hom", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Abelian", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.isoHomology_hom_comp_ι", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Abelian", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.f'_eq", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Abelian", "is_tactic_proof": true, "tactics": ["have", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.g'_eq", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Abelian", "is_tactic_proof": true, "tactics": ["have", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.homologyπ_isoHomology_inv", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Abelian", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.isoHomology_inv_homologyι", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Abelian", "is_tactic_proof": true, "tactics": ["rw", "isoHomology_hom_comp_ι"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.leftHomologyData", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.rightHomologyData", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.Hom.id", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.Hom.comp", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.instCategory", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.hom_ext", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.homMk", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.id_τ₁", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.id_τ₂", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.id_τ₃", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.comp_τ₁", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.comp_τ₂", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.comp_τ₃", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.instZeroHom", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.zero_τ₁", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.zero_τ₂", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.zero_τ₃", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.instHasZeroMorphisms", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.π₁", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.π₂", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.π₃", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.preservesZeroMorphisms_π₁", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.preservesZeroMorphisms_π₂", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.preservesZeroMorphisms_π₃", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.instIsIsoτ₁", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.instIsIsoτ₂", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.instIsIsoτ₃", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.π₁Toπ₂", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.π₂Toπ₃", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.π₁Toπ₂_comp_π₂Toπ₃", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Basic", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.map", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.map_id", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.map_comp", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.mapNatTrans", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.mapNatIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapShortComplex", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.isIso_of_isIso", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.isIso_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Basic", "is_tactic_proof": true, "tactics": ["refine", "rintro", "apply"], "tactic_count": 3}
{"name": "CategoryTheory.ShortComplex.fFunctor", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.gFunctor", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.op", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.opMap", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.opMap_id", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.unop", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.unopMap", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.unopMap_id", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.opFunctor", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.unopFunctor", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.opEquiv", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.unopOp", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.ShortComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.opUnop", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.ShortComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.zero_apply", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.ConcreteCategory", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "CategoryTheory.Preadditive.mono_iff_injective", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.ConcreteCategory", "is_tactic_proof": true, "tactics": ["rw", "constructor", "intro", "infer_instance", "apply"], "tactic_count": 5}
{"name": "CategoryTheory.Preadditive.mono_iff_injective'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.ConcreteCategory", "is_tactic_proof": true, "tactics": ["simp", "apply", "have", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.Preadditive.epi_iff_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.ConcreteCategory", "is_tactic_proof": true, "tactics": ["rw", "constructor", "intro", "infer_instance", "apply"], "tactic_count": 5}
{"name": "CategoryTheory.Preadditive.epi_iff_surjective'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.ConcreteCategory", "is_tactic_proof": true, "tactics": ["simp", "apply", "have", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.ShortComplex.exact_iff_exact_map_forget₂", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.ConcreteCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.exact_iff_of_hasForget", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.ConcreteCategory", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.ShortExact.injective_f", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.ConcreteCategory", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.ShortExact.surjective_g", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.ConcreteCategory", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.cyclesMk", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.ConcreteCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.i_cyclesMk", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.ConcreteCategory", "is_tactic_proof": false, "tactics": ["dsimp", "have", "simp", "rw"], "tactic_count": 4}
{"name": "CategoryTheory.ShortComplex.SnakeInput.δ_apply", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.ConcreteCategory", "is_tactic_proof": true, "tactics": ["have", "have", "have", "simpa", "have", "have", "have", "rw", "rw", "refine", "apply", "rw", "dsimp", "rw", "exact"], "tactic_count": 15}
{"name": "CategoryTheory.ShortComplex.SnakeInput.δ_apply'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.ConcreteCategory", "is_tactic_proof": true, "tactics": ["have", "apply", "refine", "refine", "dsimp", "rw", "refine", "dsimp", "rw"], "tactic_count": 9}
{"name": "CategoryTheory.ShortComplex.Exact.hasHomology", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.Exact.hasZeroObject", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.exact_iff_isZero_homology", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "exact", "intro", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.ShortComplex.LeftHomologyData.exact_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.RightHomologyData.exact_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.exact_iff_isZero_leftHomology", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.exact_iff_isZero_rightHomology", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.HomologyData.exact_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": true, "tactics": ["haveI", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.HomologyData.exact_iff'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": true, "tactics": ["haveI", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.exact_iff_homology_iso_zero", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": true, "tactics": ["rw", "constructor", "intro", "exact", "rintro", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.ShortComplex.exact_of_iso", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.exact_iff_of_iso", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.exact_and_mono_f_iff_of_iso", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": false, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.exact_and_epi_g_iff_of_iso", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": false, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.exact_of_isZero_X₂", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.exact_iff_of_epi_of_isIso_of_mono", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.ShortComplex.HomologyData.exact_iff_i_p_zero", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": true, "tactics": ["haveI", "rw", "constructor", "intro", "rw", "intro", "simp", "eq,"], "tactic_count": 8}
{"name": "CategoryTheory.ShortComplex.exact_iff_i_p_zero", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.exact_iff_iCycles_pOpcycles_zero", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.exact_iff_kernel_ι_comp_cokernel_π_zero", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": true, "tactics": ["haveI", "haveI", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.ShortComplex.Exact.op", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.Exact.unop", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.exact_op_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.exact_unop_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.LeftHomologyData.exact_map_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.RightHomologyData.exact_map_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.Exact.map_of_preservesLeftHomologyOf", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": true, "tactics": ["have", "rw", "rw"], "tactic_count": 3}
{"name": "CategoryTheory.ShortComplex.Exact.map_of_preservesRightHomologyOf", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": true, "tactics": ["have", "rw", "rw"], "tactic_count": 3}
{"name": "CategoryTheory.ShortComplex.Exact.map", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.exact_map_iff_of_faithful", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "rw", "apply", "rw", "intro", "exact"], "tactic_count": 8}
{"name": "CategoryTheory.ShortComplex.Exact.comp_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "rw"], "tactic_count": 4}
{"name": "CategoryTheory.ShortComplex.Exact.isZero_of_both_zeros", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.exact_iff_mono", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": true, "tactics": ["constructor", "intro", "have", "simp", "have", "have", "rw", "apply", "intro", "rw", "exact"], "tactic_count": 11}
{"name": "CategoryTheory.ShortComplex.exact_iff_epi", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": true, "tactics": ["constructor", "intro", "have", "simp", "haveI", "haveI", "rw", "apply", "intro", "rw", "exact"], "tactic_count": 11}
{"name": "CategoryTheory.ShortComplex.Exact.epi_f'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.Exact.mono_g'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.Exact.epi_toCycles", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.Exact.mono_fromOpcycles", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.LeftHomologyData.exact_iff_epi_f'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "intro", "simp"], "tactic_count": 5}
{"name": "CategoryTheory.ShortComplex.RightHomologyData.exact_iff_mono_g'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "intro", "simp"], "tactic_count": 5}
{"name": "CategoryTheory.ShortComplex.Exact.leftHomologyDataOfIsLimitKernelFork", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.Exact.rightHomologyDataOfIsColimitCokernelCofork", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.exact_iff_epi_toCycles", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.exact_iff_mono_fromOpcycles", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.exact_iff_epi_kernel_lift", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": true, "tactics": ["rw", "apply", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.ShortComplex.exact_iff_mono_cokernel_desc", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": true, "tactics": ["rw", "refine", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.ShortComplex.Exact.mono_cokernelDesc", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.Exact.epi_kernelLift", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.QuasiIso.exact_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.exact_of_f_is_kernel", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": true, "tactics": ["rw", "have", "id", "rw", "exact", "infer_instance"], "tactic_count": 6}
{"name": "CategoryTheory.ShortComplex.exact_of_g_is_cokernel", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": true, "tactics": ["rw", "have", "id", "rw", "exact", "infer_instance"], "tactic_count": 6}
{"name": "CategoryTheory.ShortComplex.Exact.mono_g", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": true, "tactics": ["have", "have", "have", "apply", "intro", "rw"], "tactic_count": 6}
{"name": "CategoryTheory.ShortComplex.Exact.epi_f", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": true, "tactics": ["have", "have", "have", "apply", "intro", "rw"], "tactic_count": 6}
{"name": "CategoryTheory.ShortComplex.Exact.mono_g_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.ShortComplex.Exact.epi_f_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.ShortComplex.Exact.isZero_X₂", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.Exact.isZero_X₂_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "rintro", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.ShortComplex.Splitting.r_f", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.Splitting.g_s", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.Splitting.splitMono_f", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.Splitting.isSplitMono_f", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.Splitting.mono_f", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": true, "tactics": ["have", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.Splitting.splitEpi_g", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.Splitting.isSplitEpi_g", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.Splitting.epi_g", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": true, "tactics": ["have", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.Splitting.s_r", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": true, "tactics": ["have", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.Splitting.ext_r", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "cases", "congr"], "tactic_count": 5}
{"name": "CategoryTheory.ShortComplex.Splitting.ext_s", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "cases", "congr"], "tactic_count": 5}
{"name": "CategoryTheory.ShortComplex.Splitting.leftHomologyData", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": false, "tactics": ["have", "let", "have", "have", "have", "exact", "i", "wi", "hi", "π", "wπ", "hπ"], "tactic_count": 12}
{"name": "CategoryTheory.ShortComplex.Splitting.rightHomologyData", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": false, "tactics": ["have", "let", "have", "have", "have", "exact", "p", "wp", "hp", "ι", "wι", "hι"], "tactic_count": 12}
{"name": "CategoryTheory.ShortComplex.Splitting.homologyData", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.Splitting.exact", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.Splitting.fIsKernel", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.Splitting.gIsCokernel", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.Splitting.map", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.Splitting.ofIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.Splitting.ofHasBinaryBiproduct", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.Splitting.ofIsZeroOfIsIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.Splitting.ofIsIsoOfIsZero", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.Splitting.op", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.Splitting.unop", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.Splitting.isoBinaryBiproduct", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.Exact.isIso_f'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": true, "tactics": ["have", "have", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.ShortComplex.Exact.isIso_toCycles", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.Exact.isIso_g'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": true, "tactics": ["have", "have", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.ShortComplex.Exact.isIso_fromOpcycles", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.Exact.fIsKernel", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": true, "tactics": ["have", "have", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.ShortComplex.Exact.map_of_mono_of_preservesKernel", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.Exact.gIsCokernel", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": true, "tactics": ["have", "have", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.ShortComplex.Exact.map_of_epi_of_preservesCokernel", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.Exact.lift", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.Exact.lift_f", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.Exact.lift'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.Exact.desc", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.Exact.g_desc", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.Exact.desc'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.mono_τ₂_of_exact_of_mono", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": true, "tactics": ["rw", "intro", "obtain", "suffices", "simp"], "tactic_count": 5}
{"name": "CategoryTheory.ShortComplex.epi_τ₂_of_exact_of_epi", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": true, "tactics": ["have", "have", "have", "have", "have", "exact"], "tactic_count": 6}
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{"name": "CategoryTheory.ShortComplex.exact_and_epi_g_iff_g_is_cokernel", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "intro", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.ShortComplex.kernelSequence", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.cokernelSequence", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.instMonoFKernelSequence", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.instEpiGCokernelSequence", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.kernelSequence_exact", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.cokernelSequence_exact", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.quasiIso_iff_of_zeros", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": true, "tactics": ["have", "rw", "constructor", "intro", "have", "rw", "apply", "refine", "apply", "exact", "rintro", "refine", "rw", "rw"], "tactic_count": 14}
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{"name": "CategoryTheory.ShortComplex.Exact.descToInjective", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.Exact.comp_descToInjective", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.Exact.liftFromProjective", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.Exact.liftFromProjective_comp", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.instPreservesMonomorphisms", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instPreservesEpimorphisms", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.Splitting.ofExactOfSection", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.Splitting.ofExactOfRetraction", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.preservesFiniteLimits_of_preservesHomology", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.ExactFunctor", "is_tactic_proof": true, "tactics": ["have", "have", "have", "have", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.Functor.preservesFiniteColimits_of_preservesHomology", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.ExactFunctor", "is_tactic_proof": true, "tactics": ["have", "have", "have", "have", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.Functor.preservesMonomorphisms_of_preserves_shortExact_left", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.ExactFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.preservesFiniteLimits_tfae", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.ExactFunctor", "is_tactic_proof": false, "tactics": ["tfae_have", "hF,", "have", "refine", "let", "let", "τ₂", "τ₃", "comm₂₃", "show", "exact", "tfae_have", "hF,", "refine", "apply", "let", "let", "have", "exact", "tfae_have", "hF", "tfae_have", "tfae_finish"], "tactic_count": 23}
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{"name": "CategoryTheory.Functor.preservesEpimorphisms_of_preserves_shortExact_right", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.ExactFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.preservesFiniteColimits_tfae", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.ExactFunctor", "is_tactic_proof": false, "tactics": ["tfae_have", "hF,", "have", "refine", "let", "let", "τ₂", "τ₃", "comm₁₂", "show", "exact", "tfae_have", "hF,", "refine", "apply", "let", "let", "have", "exact", "tfae_have", "hF", "tfae_have", "tfae_finish"], "tactic_count": 23}
{"name": "CategoryTheory.Functor.exact_tfae", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.ExactFunctor", "is_tactic_proof": false, "tactics": ["tfae_have", "hF", "refine", "have", "exact", "have", "exact", "tfae_have", "hF,", "have", "exact_iff_mono", "hF", "have", "exact_iff_epi", "hF", "exact", "tfae_have", "h", "tfae_have", "tfae_finish"], "tactic_count": 20}
{"name": "CategoryTheory.Functor.preservesFiniteColimits_iff_forall_exact_map_and_epi", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.ExactFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.FunctorEquivalence.functor", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.FunctorEquivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.FunctorEquivalence.inverse", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.FunctorEquivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.FunctorEquivalence.unitIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.FunctorEquivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.FunctorEquivalence.counitIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.FunctorEquivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.functorEquivalence", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.FunctorEquivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.shortComplexFunctor'", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.shortComplexFunctor", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.natIsoSc'", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.sc'", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.sc", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.isoSc'", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.HasHomology", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.hasHomology_of_iso", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.homology", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.cycles", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.iCycles", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.homologyπ", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.liftCycles", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.liftCycles'", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.liftCycles_i", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "HomologicalComplex.toCycles", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.iCycles_d", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": true, "tactics": ["by_cases", "obtain", "exact", "rw"], "tactic_count": 4}
{"name": "HomologicalComplex.cyclesIsKernel", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "HomologicalComplex.toCycles_i", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.instMonoICycles", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "HomologicalComplex.instEpiHomologyπ", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "HomologicalComplex.d_toCycles", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HomologicalComplex.toCycles_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HomologicalComplex.comp_liftCycles", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HomologicalComplex.liftCycles_homologyπ_eq_zero_of_boundary", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": true, "tactics": ["by_cases", "obtain", "exact", "have", "rw", "rw", "rw"], "tactic_count": 7}
{"name": "HomologicalComplex.toCycles_comp_homologyπ", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.homologyIsCokernel", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": true, "tactics": ["subst", "exact"], "tactic_count": 2}
{"name": "HomologicalComplex.opcycles", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.pOpcycles", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.homologyι", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.descOpcycles", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.descOpcycles'", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.p_descOpcycles", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "HomologicalComplex.fromOpcycles", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.d_pOpcycles", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": true, "tactics": ["by_cases", "obtain", "exact", "rw"], "tactic_count": 4}
{"name": "HomologicalComplex.opcyclesIsCokernel", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "HomologicalComplex.p_fromOpcycles", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.instEpiPOpcycles", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "HomologicalComplex.instMonoHomologyι", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "HomologicalComplex.fromOpcycles_d", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HomologicalComplex.fromOpcycles_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HomologicalComplex.descOpcycles_comp", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HomologicalComplex.homologyι_descOpcycles_eq_zero_of_boundary", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": true, "tactics": ["by_cases", "obtain", "exact", "have", "rw", "rw", "rw"], "tactic_count": 7}
{"name": "HomologicalComplex.homologyι_comp_fromOpcycles", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.homologyIsKernel", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": true, "tactics": ["subst", "exact"], "tactic_count": 2}
{"name": "HomologicalComplex.homologyMap", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.cyclesMap", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.opcyclesMap", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.cyclesMap_i", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.p_opcyclesMap", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.instMonoCyclesMapOfF", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.instEpiOpcyclesMapOfF", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.homologyMap_id", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.cyclesMap_id", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.opcyclesMap_id", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.homologyMap_comp", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "HomologicalComplex.cyclesMap_comp", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "HomologicalComplex.opcyclesMap_comp", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "HomologicalComplex.homologyMap_zero", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.cyclesMap_zero", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.opcyclesMap_zero", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.homologyπ_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.homologyι_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.homology_π_ι", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.homologyMapIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.cyclesMapIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.opcyclesMapIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.opcyclesMap_comp_descOpcycles", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HomologicalComplex.liftCycles_comp_cyclesMap", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HomologicalComplex.homologyFunctor", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.gradedHomologyFunctor", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.cyclesFunctor", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.opcyclesFunctor", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.natTransHomologyπ", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.natTransHomologyι", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.homologyFunctorIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.homologyFunctorIso'", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.instPreservesZeroMorphismsHomologyFunctor", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.instPreservesZeroMorphismsOpcyclesFunctor", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.instPreservesZeroMorphismsCyclesFunctor", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.isIso_iCycles", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": true, "tactics": ["subst", "exact"], "tactic_count": 2}
{"name": "HomologicalComplex.iCyclesIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.iCyclesIso_hom_inv_id", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.iCyclesIso_inv_hom_id", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.isIso_homologyι", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.isoHomologyι", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.isoHomologyι_hom_inv_id", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.isoHomologyι_inv_hom_id", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.isIso_pOpcycles", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "HomologicalComplex.pOpcyclesIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.pOpcyclesIso_hom_inv_id", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.pOpcyclesIso_inv_hom_id", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.isIso_homologyπ", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.isoHomologyπ", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.isoHomologyπ_hom_inv_id", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.isoHomologyπ_inv_hom_id", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.epi_homologyMap_of_epi_of_not_rel", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.mono_homologyMap_of_mono_of_not_rel", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.ExactAt", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.exactAt_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "HomologicalComplex.ExactAt.of_iso", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "HomologicalComplex.exactAt_iff'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.exactAt_iff_isZero_homology", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "HomologicalComplex.ExactAt.isZero_homology", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "HomologicalComplex.Acyclic", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.acyclic_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "HomologicalComplex.acyclic_of_isZero", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": true, "tactics": ["rw", "intro", "apply", "exact"], "tactic_count": 4}
{"name": "ChainComplex.isIso_homologyι₀", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ChainComplex.isoHomologyι₀", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ChainComplex.isoHomologyι₀_inv_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CochainComplex.isIso_homologyπ₀", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.isoHomologyπ₀", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.isoHomologyπ₀_inv_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HomologicalComplex.homologyMap_neg", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "rfl"], "tactic_count": 3}
{"name": "HomologicalComplex.homologyMap_add", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "rfl"], "tactic_count": 3}
{"name": "HomologicalComplex.homologyMap_sub", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "rfl"], "tactic_count": 3}
{"name": "HomologicalComplex.instAdditiveHomologyFunctor", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.isIso_liftCycles_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": ["suffices", "from", "rintro", "let", "τ₂", "τ₃", "exact"], "tactic_count": 7}
{"name": "ChainComplex.isIso_descOpcycles_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": ["suffices", "from", "rintro", "let", "τ₂", "τ₃", "exact"], "tactic_count": 7}
{"name": "HomologicalComplex.cyclesIsoSc'", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.cyclesIsoSc'_hom_iCycles", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": true, "tactics": ["dsimp", "simp", "comp_id]", "rfl"], "tactic_count": 4}
{"name": "HomologicalComplex.cyclesIsoSc'_inv_iCycles", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HomologicalComplex.toCycles_cyclesIsoSc'_hom", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": true, "tactics": ["simp", "shortComplexFunctor'_obj_f]"], "tactic_count": 2}
{"name": "HomologicalComplex.opcyclesIsoSc'", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.pOpcycles_opcyclesIsoSc'_inv", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": true, "tactics": ["dsimp", "simp", "id_comp]", "rfl"], "tactic_count": 4}
{"name": "HomologicalComplex.pOpcycles_opcyclesIsoSc'_hom", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HomologicalComplex.opcyclesIsoSc'_inv_fromOpcycles", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HomologicalComplex.homologyIsoSc'", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.π_homologyIsoSc'_hom", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "HomologicalComplex.π_homologyIsoSc'_inv", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "HomologicalComplex.homologyIsoSc'_hom_ι", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "HomologicalComplex.homologyIsoSc'_inv_ι", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.HomologyMapData.comm", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.HomologyMapData.instSubsingleton", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.HomologyMapData.instInhabited", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.HomologyMapData.instUnique", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.HomologyMapData.homologyMapData", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.HomologyMapData.congr_left_φH", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.HomologyData.ofIsLimitKernelFork", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.HomologyData.ofHasKernel", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.HomologyData.ofIsColimitCokernelCofork", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.HomologyData.ofHasCokernel", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.HomologyData.ofZeros", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.HomologyData.ofEpiOfIsIsoOfMono", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.HomologyData.ofEpiOfIsIsoOfMono'", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.HomologyData.ofIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.ShortComplex.HomologyData.unop", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.ShortComplex.HasHomology.mk'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.instHasHomologyOppositeOp", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.instHasHomologyUnopOfOpposite", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.hasLeftHomology_of_hasHomology", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.hasRightHomology_of_hasHomology", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.hasHomology_of_hasCokernel", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.hasHomology_of_hasKernel", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.hasHomology_of_zeros", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.hasHomology_of_epi_of_isIso_of_mono", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.hasHomology_of_epi_of_isIso_of_mono'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.hasHomology_of_iso", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.HomologyMapData.id", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.HomologyMapData.zero", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.ShortComplex.HomologyMapData.unop", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.HomologyMapData.ofZeros", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.HomologyMapData.ofIsColimitCokernelCofork", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.HomologyMapData.ofIsLimitKernelFork", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.HomologyMapData.compatibilityOfZerosOfIsColimitCokernelCofork", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.HomologyMapData.compatibilityOfZerosOfIsLimitKernelFork", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.HomologyMapData.ofEpiOfIsIsoOfMono", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.HomologyMapData.ofEpiOfIsIsoOfMono'", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.homology", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.leftHomologyIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.rightHomologyIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.LeftHomologyData.homologyIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.RightHomologyData.homologyIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.LeftHomologyData.homologyIso_leftHomologyData", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "rw"], "tactic_count": 3}
{"name": "CategoryTheory.ShortComplex.RightHomologyData.homologyIso_rightHomologyData", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.homologyMap'", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.homologyMap", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.HomologyMapData.homologyMap'_eq", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.HomologyMapData.cyclesMap'_eq", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.HomologyMapData.opcyclesMap'_eq", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.LeftHomologyMapData.homologyMap_eq", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.LeftHomologyMapData.homologyMap_comm", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.RightHomologyMapData.homologyMap_eq", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": ["dsimp", "have", "simp", "γ'.left.leftHomologyMap'_eq,"], "tactic_count": 4}
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{"name": "CategoryTheory.ShortComplex.homologyMap'_id", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.homologyMap_id", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.homologyMap'_zero", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.homologyMap_zero", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.homologyMap'_comp", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.homologyMap_comp", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.homologyMapIso'", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.isIso_homologyMap'_of_isIso", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.homologyMapIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.isIso_homologyMap_of_iso", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.leftRightHomologyComparison'", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.leftRightHomologyComparison'_eq_liftH", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.π_leftRightHomologyComparison'_ι", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.leftRightHomologyComparison'_eq_descH", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.leftRightHomologyComparison", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.π_leftRightHomologyComparison_ι", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.leftRightHomologyComparison'_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": true, "tactics": ["simp", "π_leftRightHomologyComparison'_ι,"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.leftRightHomologyComparison'_compatibility", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": true, "tactics": ["rw", "rightHomologyMap'_id,"], "tactic_count": 2}
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{"name": "CategoryTheory.ShortComplex.HomologyData.leftRightHomologyComparison'_eq", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.isIso_leftRightHomologyComparison'_of_homologyData", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.isIso_leftRightHomologyComparison'", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.isIso_leftRightHomologyComparison", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.HomologyData.ofIsIsoLeftRightHomologyComparison'", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.leftRightHomologyComparison'_eq_leftHomologpMap'_comp_iso_hom_comp_rightHomologyMap'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.leftRightHomologyComparison'_fac", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": true, "tactics": ["rw", "dsimp", "leftHomologyMapIso',", "rightHomologyMapIso',", "simp"], "tactic_count": 5}
{"name": "CategoryTheory.ShortComplex.leftRightHomologyComparison_fac", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": true, "tactics": ["simpa", "leftRightHomologyComparison'_fac"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.HomologyData.right_homologyIso_eq_left_homologyIso_trans_iso", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": true, "tactics": ["suffices", "ext", "dsimp", "rw"], "tactic_count": 4}
{"name": "CategoryTheory.ShortComplex.HomologyData.left_homologyIso_eq_right_homologyIso_trans_iso_symm", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": true, "tactics": ["rw", "cat_disch"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.hasHomology_of_isIso_leftRightHomologyComparison'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.hasHomology_of_isIsoLeftRightHomologyComparison", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": true, "tactics": ["haveI", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.LeftHomologyData.leftHomologyIso_hom_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
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{"name": "CategoryTheory.ShortComplex.leftHomologyIso_hom_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.leftHomologyIso_inv_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.RightHomologyData.rightHomologyIso_hom_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": true, "tactics": ["rw", "cancel_epi", "leftRightHomologyComparison'_naturality", "cancel_epi", "leftRightHomologyComparison'_fac,"], "tactic_count": 5}
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{"name": "CategoryTheory.ShortComplex.rightHomologyIso_hom_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.rightHomologyIso_inv_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.instCategoryWithHomologyOpposite", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.homologyFunctor", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.isIso_homologyMap'_of_epi_of_isIso_of_mono", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.isIso_homologyMap_of_epi_of_isIso_of_mono'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.isIso_homologyMap_of_epi_of_isIso_of_mono", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.isIso_homologyFunctor_map_of_epi_of_isIso_of_mono", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.isIso_homologyMap_of_isIso", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.homologyπ", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.homologyι", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.homologyπ_comp_leftHomologyIso_inv", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.rightHomologyIso_hom_comp_homologyι", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.toCycles_comp_homologyπ", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.homologyι_comp_fromOpcycles", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.homologyIsCokernel", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.homologyIsKernel", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.instEpiHomologyπ", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.instMonoHomologyι", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.descHomology", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.liftHomology", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.π_descHomology", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.liftHomology_ι", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.ShortComplex.homologyIsoKernelDesc", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.homologyIsoCokernelLift", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.LeftHomologyData.homologyπ_comp_homologyIso_hom", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
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{"name": "CategoryTheory.ShortComplex.RightHomologyData.homologyIso_hom_comp_ι", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.LeftHomologyData.homologyIso_hom_comp_leftHomologyIso_inv", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.LeftHomologyData.leftHomologyIso_hom_comp_homologyIso_inv", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.RightHomologyData.homologyIso_hom_comp_rightHomologyIso_inv", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
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{"name": "CategoryTheory.ShortComplex.homologyOpIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.ShortComplex.homologyFunctorOpNatIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.ShortComplex.isIso_homologyMap_of_isIso_cyclesMap_of_epi", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": false, "tactics": ["have", "simp", "comp_zero]", "have", "dsimp", "refine", "rw", "rw"], "tactic_count": 8}
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{"name": "CategoryTheory.ShortComplex.isIso_homologyπ", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Homology", "is_tactic_proof": true, "tactics": ["have", "dsimp", "infer_instance"], "tactic_count": 3}
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{"name": "CategoryTheory.ShortComplex.LeftHomologyData.ofHasKernelOfHasCokernel", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.LeftHomologyData.instMonoI", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.LeftHomologyData.instEpiπ", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.ShortComplex.LeftHomologyData.liftK_i", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.ShortComplex.LeftHomologyData.f'_π", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.LeftHomologyData.liftK_π_eq_zero_of_boundary", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": true, "tactics": ["rw", "congr", "simp"], "tactic_count": 3}
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{"name": "CategoryTheory.ShortComplex.LeftHomologyData.ofIsColimitCokernelCofork_f'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
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{"name": "CategoryTheory.ShortComplex.LeftHomologyData.ofIsLimitKernelFork", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.LeftHomologyData.ofIsLimitKernelFork_f'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "CategoryTheory.ShortComplex.LeftHomologyData.ofZeros", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.LeftHomologyData.ofZeros_f'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.LeftHomologyData.copy", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.leftHomologyData", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.HasLeftHomology.mk'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.HasLeftHomology.of_hasKernel_of_hasCokernel", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.HasLeftHomology.of_hasCokernel", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.HasLeftHomology.of_hasKernel", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.HasLeftHomology.of_zeros", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.LeftHomologyMapData.zero", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.LeftHomologyMapData.id", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.LeftHomologyMapData.comp", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.LeftHomologyMapData.instSubsingleton", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.LeftHomologyMapData.instInhabited", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.LeftHomologyMapData.instUnique", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.LeftHomologyMapData.congr_φH", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.LeftHomologyMapData.congr_φK", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.LeftHomologyMapData.ofZeros", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.LeftHomologyMapData.ofIsColimitCokernelCofork", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.LeftHomologyMapData.ofIsLimitKernelFork", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.LeftHomologyMapData.compatibilityOfZerosOfIsColimitCokernelCofork", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.LeftHomologyMapData.compatibilityOfZerosOfIsLimitKernelFork", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.leftHomology", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.leftHomologyData_H", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.cycles", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.leftHomologyπ", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.iCycles", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.toCycles", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.iCycles_g", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.toCycles_i", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.instMonoICycles", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.instEpiLeftHomologyπ", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.leftHomology_ext_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.leftHomology_ext", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.cycles_ext_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.cycles_ext", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.isIso_iCycles", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.cyclesIsoX₂", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.cyclesIsoX₂_hom_inv_id", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.cyclesIsoX₂_inv_hom_id", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.isIso_leftHomologyπ", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.cyclesIsoLeftHomology", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.cyclesIsoLeftHomology_hom_inv_id", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.cyclesIsoLeftHomology_inv_hom_id", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.leftHomologyMapData", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.leftHomologyMap'", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.cyclesMap'", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.cyclesMap'_i", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.f'_cyclesMap'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.leftHomologyπ_naturality'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.leftHomologyMap", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.cyclesMap", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.cyclesMap_i", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.toCycles_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.leftHomologyπ_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.LeftHomologyMapData.leftHomologyMap'_eq", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.LeftHomologyMapData.cyclesMap'_eq", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.leftHomologyMap'_id", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.cyclesMap'_id", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.leftHomologyMap_id", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.ShortComplex.leftHomologyMap'_zero", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.cyclesMap'_zero", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.leftHomologyMap_zero", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.cyclesMap_zero", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.leftHomologyMap'_comp", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": true, "tactics": ["let", "let", "rw"], "tactic_count": 3}
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{"name": "CategoryTheory.ShortComplex.leftHomologyMap_comp", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.cyclesMap_comp", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.leftHomologyMapIso'", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.isIso_leftHomologyMap'_of_isIso", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.cyclesMapIso'", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.isIso_cyclesMap'_of_isIso", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.leftHomologyMapIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.isIso_leftHomologyMap_of_iso", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.cyclesMapIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.isIso_cyclesMap_of_iso", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.LeftHomologyData.leftHomologyIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.LeftHomologyData.cyclesIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.LeftHomologyData.cyclesIso_hom_comp_i", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.LeftHomologyData.cyclesIso_inv_comp_iCycles", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.LeftHomologyData.leftHomologyπ_comp_leftHomologyIso_hom", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.LeftHomologyData.π_comp_leftHomologyIso_inv", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.LeftHomologyMapData.leftHomologyMap_eq", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "rfl"], "tactic_count": 3}
{"name": "CategoryTheory.ShortComplex.LeftHomologyMapData.cyclesMap_eq", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "rfl"], "tactic_count": 3}
{"name": "CategoryTheory.ShortComplex.LeftHomologyMapData.leftHomologyMap_comm", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.LeftHomologyMapData.cyclesMap_comm", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.leftHomologyFunctor", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.cyclesFunctor", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.leftHomologyπNatTrans", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.iCyclesNatTrans", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.toCyclesNatTrans", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.LeftHomologyData.ofEpiOfIsIsoOfMono", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": true, "tactics": ["let", "have", "have", "h.liftK", "dsimp", "rw", "let", "have", "have", "simp", "rw", "have", "have", "exact"], "tactic_count": 14}
{"name": "CategoryTheory.ShortComplex.LeftHomologyData.τ₁_ofEpiOfIsIsoOfMono_f'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.LeftHomologyData.ofEpiOfIsIsoOfMono'", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": true, "tactics": ["let", "have", "rw", "have", "rw", "comp_id])", "let", "have", "have", "rw", "have", "have", "exact"], "tactic_count": 13}
{"name": "CategoryTheory.ShortComplex.LeftHomologyData.ofEpiOfIsIsoOfMono'_f'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.LeftHomologyData.ofIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.hasLeftHomology_of_epi_of_isIso_of_mono", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.hasLeftHomology_of_epi_of_isIso_of_mono'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.hasLeftHomology_of_iso", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.LeftHomologyMapData.ofEpiOfIsIsoOfMono", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.LeftHomologyMapData.ofEpiOfIsIsoOfMono'", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.instIsIsoLeftHomologyMap'OfEpiτ₁Ofτ₂OfMonoτ₃", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": true, "tactics": ["let", "have", "rw", "dsimp", "infer_instance", "have", "rw", "rw", "infer_instance"], "tactic_count": 9}
{"name": "CategoryTheory.ShortComplex.instIsIsoLeftHomologyMapOfEpiτ₁Ofτ₂OfMonoτ₃", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.liftCycles", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.liftCycles_i", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.comp_liftCycles", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.cyclesIsKernel", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.cyclesIsoKernel", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.isoCyclesOfIsLimit", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.isoCyclesOfIsLimit_inv_ι", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.isoCyclesOfIsLimit_hom_iCycles", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.liftLeftHomology", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.liftCycles_leftHomologyπ_eq_zero_of_boundary", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.toCycles_comp_leftHomologyπ", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.leftHomologyIsCokernel", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.liftCycles_comp_cyclesMap", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.LeftHomologyData.liftCycles_comp_cyclesIso_hom", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.LeftHomologyData.lift_K_comp_cyclesIso_inv", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.HasLeftHomology.hasKernel", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.HasLeftHomology.hasCokernel", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": true, "tactics": ["let", "haveI", "let", "parallelPair.ext", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.ShortComplex.leftHomologyIsoCokernelLift", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.isIso_cyclesMap'_of_isIso_of_mono", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": true, "tactics": ["refine", "simp", "simp", "simp"], "tactic_count": 4}
{"name": "CategoryTheory.ShortComplex.isIso_cyclesMap_of_isIso_of_mono'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.isIso_cyclesMap_of_isIso_of_mono", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.LeftHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.isLimitOfIsLimitπ", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.limitCone", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.isLimitπ₁MapConeLimitCone", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.isLimitπ₂MapConeLimitCone", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.isLimitπ₃MapConeLimitCone", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.isLimitLimitCone", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.hasLimit_of_hasLimitπ", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.instPreservesLimitπ₁", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.instPreservesLimitπ₂", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.instPreservesLimitπ₃", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.hasLimitsOfShape", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.instPreservesLimitsOfShapeπ₁", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.instPreservesLimitsOfShapeπ₂", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.instPreservesLimitsOfShapeπ₃", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.hasFiniteLimits", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.instPreservesFiniteLimitsπ₁", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.instPreservesFiniteLimitsπ₂", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.instPreservesFiniteLimitsπ₃", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.preservesMonomorphisms_π₁", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.preservesMonomorphisms_π₂", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.preservesMonomorphisms_π₃", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.isColimitOfIsColimitπ", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.colimitCocone", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.isColimitπ₁MapCoconeColimitCocone", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.isColimitπ₂MapCoconeColimitCocone", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.isColimitπ₃MapCoconeColimitCocone", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.isColimitColimitCocone", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.hasColimit_of_hasColimitπ", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.instPreservesColimitπ₁", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.instPreservesColimitπ₂", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.instPreservesColimitπ₃", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.hasColimitsOfShape", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.instPreservesColimitsOfShapeπ₁", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.instPreservesColimitsOfShapeπ₂", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.instPreservesColimitsOfShapeπ₃", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.hasFiniteColimits", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.instPreservesFiniteColimitsπ₁", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.instPreservesFiniteColimitsπ₂", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.instPreservesFiniteColimitsπ₃", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.preservesEpimorphisms_π₁", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.preservesEpimorphisms_π₂", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.preservesEpimorphisms_π₃", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.instSMulHom", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.smul_τ₁", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.smul_τ₂", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.smul_τ₃", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.instModuleHom", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.instLinear", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.LeftHomologyMapData.smul", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.leftHomologyMap'_smul", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Linear", "is_tactic_proof": true, "tactics": ["have", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.cyclesMap'_smul", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Linear", "is_tactic_proof": true, "tactics": ["have", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.leftHomologyMap_smul", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.cyclesMap_smul", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.leftHomologyFunctor_linear", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.cyclesFunctor_linear", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.RightHomologyMapData.smul", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.rightHomologyMap'_smul", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Linear", "is_tactic_proof": true, "tactics": ["have", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.opcyclesMap'_smul", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Linear", "is_tactic_proof": true, "tactics": ["have", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.rightHomologyMap_smul", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.opcyclesMap_smul", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.rightHomologyFunctor_linear", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.opcyclesFunctor_linear", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.HomologyMapData.smul", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.homologyMap'_smul", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.homologyMap_smul", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.homologyFunctor_linear", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.Homotopy.smul", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.instPreservesHomologyModuleCatAbForget₂", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.ModuleCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.moduleCatMk", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.ModuleCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.moduleCat_zero_apply", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.ModuleCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.moduleCat_exact_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.ModuleCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.moduleCat_exact_iff_ker_sub_range", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.ModuleCat", "is_tactic_proof": true, "tactics": ["rw", "aesop"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.moduleCat_exact_iff_range_eq_ker", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.ModuleCat", "is_tactic_proof": true, "tactics": ["rw", "aesop"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.Exact.moduleCat_range_eq_ker", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.ModuleCat", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.ShortExact.moduleCat_injective_f", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.ModuleCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.ShortExact.moduleCat_surjective_g", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.ModuleCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.ShortExact.moduleCat_exact_iff_function_exact", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.ModuleCat", "is_tactic_proof": true, "tactics": ["rw", "tauto"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.moduleCatMkOfKerLERange", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.ModuleCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.Exact.moduleCat_of_range_eq_ker", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.ModuleCat", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.moduleCatToCycles", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.ShortComplex.ModuleCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.moduleCatLeftHomologyData", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.ModuleCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.moduleCatLeftHomologyData_f'_hom", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.ModuleCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.moduleCatLeftHomologyData_descH_hom", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.ModuleCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.moduleCatLeftHomologyData_liftK_hom", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.ModuleCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.moduleCatCyclesIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.ModuleCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.moduleCatCyclesIso_hom_i", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.ModuleCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_iCycles", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.ModuleCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.toCycles_moduleCatCyclesIso_hom", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.ModuleCat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.moduleCatOpcyclesIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.ModuleCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.pOpcycles_comp_moduleCatOpcyclesIso_hom", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.ModuleCat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.moduleCat_pOpcycles_eq_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.ModuleCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.moduleCat_pOpcycles_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.ModuleCat", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.moduleCatHomologyIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.ModuleCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.π_moduleCatCyclesIso_hom", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.ModuleCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_π", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.ModuleCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.exact_iff_surjective_moduleCatToCycles", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.ModuleCat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LinearMap.shortComplexKer", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.ShortComplex.ModuleCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.shortExact_shortComplexKer", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.ModuleCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.instAddHom", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.instSubHom", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.instNegHom", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.instAddCommGroupHom", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.add_τ₁", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.add_τ₂", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.add_τ₃", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.sub_τ₁", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.sub_τ₂", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.sub_τ₃", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.neg_τ₁", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.neg_τ₂", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.neg_τ₃", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.instPreadditive", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.LeftHomologyMapData.neg", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.LeftHomologyMapData.add", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.leftHomologyMap'_neg", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": true, "tactics": ["have", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.cyclesMap'_neg", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": true, "tactics": ["have", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.leftHomologyMap'_add", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": true, "tactics": ["have", "have", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.ShortComplex.cyclesMap'_add", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": true, "tactics": ["have", "have", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.ShortComplex.leftHomologyMap'_sub", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.cyclesMap'_sub", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.leftHomologyMap_neg", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.cyclesMap_neg", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.leftHomologyMap_add", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.cyclesMap_add", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.leftHomologyMap_sub", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.cyclesMap_sub", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.leftHomologyFunctor_additive", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.cyclesFunctor_additive", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.RightHomologyMapData.neg", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.RightHomologyMapData.add", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.rightHomologyMap'_neg", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": true, "tactics": ["have", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.opcyclesMap'_neg", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": true, "tactics": ["have", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.rightHomologyMap'_add", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": true, "tactics": ["have", "have", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.ShortComplex.opcyclesMap'_add", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": true, "tactics": ["have", "have", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.ShortComplex.rightHomologyMap'_sub", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.opcyclesMap'_sub", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.rightHomologyMap_neg", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.opcyclesMap_neg", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.rightHomologyMap_add", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.opcyclesMap_add", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.rightHomologyMap_sub", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.opcyclesMap_sub", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.rightHomologyFunctor_additive", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.opcyclesFunctor_additive", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.HomologyMapData.neg", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.HomologyMapData.add", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.homologyMap'_neg", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.homologyMap'_add", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.homologyMap'_sub", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.homologyMap_neg", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.homologyMap_add", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.homologyMap_sub", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.homologyFunctor_additive", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.nullHomotopic", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.Homotopy.ofEq", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.Homotopy.refl", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.Homotopy.symm", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.Homotopy.neg", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.Homotopy.trans", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.Homotopy.add", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.Homotopy.sub", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.Homotopy.compLeft", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.Homotopy.compRight", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.Homotopy.comp", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.Homotopy.op", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.Homotopy.unop", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.Homotopy.equivSubZero", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.Homotopy.eq_add_nullHomotopic", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "dsimp", "dsimp"], "tactic_count": 4}
{"name": "CategoryTheory.ShortComplex.Homotopy.ofNullHomotopic", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.LeftHomologyMapData.ofNullHomotopic", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.RightHomologyMapData.ofNullHomotopic", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.leftHomologyMap'_nullHomotopic", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.rightHomologyMap'_nullHomotopic", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.homologyMap'_nullHomotopic", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.leftHomologyMap_nullHomotopic", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.rightHomologyMap_nullHomotopic", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.homologyMap_nullHomotopic", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.Homotopy.leftHomologyMap'_congr", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.Homotopy.rightHomologyMap'_congr", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.Homotopy.homologyMap'_congr", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.Homotopy.leftHomologyMap_congr", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.Homotopy.rightHomologyMap_congr", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.Homotopy.homologyMap_congr", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.HomotopyEquiv.refl", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.HomotopyEquiv.symm", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.HomotopyEquiv.trans", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.PreservesHomology.preservesKernel", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.PreservesHomology.preservesCokernel", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.preservesHomologyOfExact", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.LeftHomologyData.isPreservedBy_of_preservesHomology", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.LeftHomologyData.IsPreservedBy.hg", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.LeftHomologyData.IsPreservedBy.hf'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.ShortComplex.LeftHomologyData.map_f'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.LeftHomologyMapData.map", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.RightHomologyData.isPreservedBy_of_preservesHomology", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.RightHomologyData.IsPreservedBy.hf", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.RightHomologyData.IsPreservedBy.hg'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.ShortComplex.RightHomologyData.map_g'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.RightHomologyMapData.map", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.HomologyData.map", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.HomologyMapData.map", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.map_leftRightHomologyComparison'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": true, "tactics": ["apply", "apply", "trans", "simp", "trans", "rw", "simp"], "tactic_count": 7}
{"name": "CategoryTheory.Functor.PreservesHomology.preservesLeftHomologyOf", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.PreservesHomology.preservesRightHomologyOf", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.PreservesLeftHomologyOf.mk'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.PreservesRightHomologyOf.mk'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.LeftHomologyData.isPreservedBy_of_preserves", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.RightHomologyData.isPreservedBy_of_preserves", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.hasLeftHomology_of_preserves", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.hasLeftHomology_of_preserves'", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": true, "tactics": ["dsimp"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.hasRightHomology_of_preserves", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.hasRightHomology_of_preserves'", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": true, "tactics": ["dsimp"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.hasHomology_of_preserves", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.hasHomology_of_preserves'", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": true, "tactics": ["dsimp"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.LeftHomologyData.map_cyclesMap'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.LeftHomologyData.map_leftHomologyMap'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.RightHomologyData.map_opcyclesMap'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.RightHomologyData.map_rightHomologyMap'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.HomologyData.map_homologyMap'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.mapCyclesIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.mapCyclesIso_hom_iCycles", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.mapLeftHomologyIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.mapOpcyclesIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.mapRightHomologyIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.mapHomologyIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.mapHomologyIso'", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.LeftHomologyData.mapCyclesIso_eq", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.ShortComplex.LeftHomologyData.mapLeftHomologyIso_eq", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.ShortComplex.RightHomologyData.mapOpcyclesIso_eq", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.ShortComplex.RightHomologyData.mapRightHomologyIso_eq", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.ShortComplex.LeftHomologyData.mapHomologyIso_eq", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.ShortComplex.RightHomologyData.mapHomologyIso'_eq", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "rightHomologyMapIso',", "simp"], "tactic_count": 4}
{"name": "CategoryTheory.ShortComplex.mapCyclesIso_hom_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.mapCyclesIso_inv_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.mapLeftHomologyIso_hom_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": false, "tactics": ["dsimp", "simp", "id_comp]"], "tactic_count": 3}
{"name": "CategoryTheory.ShortComplex.mapLeftHomologyIso_inv_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.mapOpcyclesIso_hom_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.mapOpcyclesIso_inv_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.mapRightHomologyIso_hom_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": false, "tactics": ["dsimp", "simp", "id_comp]"], "tactic_count": 3}
{"name": "CategoryTheory.ShortComplex.mapRightHomologyIso_inv_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.mapHomologyIso_hom_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": false, "tactics": ["dsimp", "leftHomologyMapIso',", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.ShortComplex.mapHomologyIso_inv_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.mapHomologyIso'_hom_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": true, "tactics": ["dsimp", "simp", "assoc,"], "tactic_count": 3}
{"name": "CategoryTheory.ShortComplex.mapHomologyIso'_inv_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.mapHomologyIso'_eq_mapHomologyIso", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": true, "tactics": ["ext", "rw", "dsimp", "simp", "leftHomologyMapIso'_inv,", "have", "have", "rw", "dsimp", "simp"], "tactic_count": 10}
{"name": "CategoryTheory.ShortComplex.LeftHomologyMapData.natTransApp", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.RightHomologyMapData.natTransApp", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.HomologyMapData.natTransApp", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.homologyMap_mapNatTrans", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.cyclesFunctorIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.leftHomologyFunctorIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.opcyclesFunctorIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.rightHomologyFunctorIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.homologyFunctorIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.LeftHomologyMapData.quasiIso_map_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.RightHomologyMapData.quasiIso_map_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.quasiIso_map_of_preservesLeftHomology", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "infer_instance", "rw", "infer_instance"], "tactic_count": 6}
{"name": "CategoryTheory.ShortComplex.quasiIso_map_iff_of_preservesLeftHomology", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": true, "tactics": ["have", "rw", "constructor", "intro", "exact", "intro", "infer_instance"], "tactic_count": 7}
{"name": "CategoryTheory.ShortComplex.quasiIso_map_of_preservesRightHomology", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "infer_instance", "rw", "infer_instance"], "tactic_count": 6}
{"name": "CategoryTheory.ShortComplex.quasiIso_map_iff_of_preservesRightHomology", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": true, "tactics": ["have", "rw", "constructor", "intro", "exact", "intro", "infer_instance"], "tactic_count": 7}
{"name": "CategoryTheory.Functor.preservesLeftHomology_of_zero_f", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.preservesRightHomology_of_zero_g", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.preservesLeftHomology_of_zero_g", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.preservesRightHomology_of_zero_f", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.app_homology", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.QuasiIso.isIso", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.QuasiIso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.quasiIso_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.QuasiIso", "is_tactic_proof": true, "tactics": ["constructor", "intro", "infer_instance", "intro", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.ShortComplex.quasiIso_of_isIso", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.QuasiIso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.quasiIso_comp", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.QuasiIso", "is_tactic_proof": true, "tactics": ["rw", "rw", "infer_instance"], "tactic_count": 3}
{"name": "CategoryTheory.ShortComplex.quasiIso_of_comp_left", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.QuasiIso", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.ShortComplex.quasiIso_iff_comp_left", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.QuasiIso", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "intro", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.ShortComplex.quasiIso_of_comp_right", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.QuasiIso", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.ShortComplex.quasiIso_iff_comp_right", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.QuasiIso", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "intro", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.ShortComplex.quasiIso_of_arrow_mk_iso", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.QuasiIso", "is_tactic_proof": true, "tactics": ["let", "let", "suffices", "rw", "infer_instance", "simp", "e.inv_hom_id,"], "tactic_count": 7}
{"name": "CategoryTheory.ShortComplex.quasiIso_iff_of_arrow_mk_iso", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.QuasiIso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.LeftHomologyMapData.quasiIso_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.QuasiIso", "is_tactic_proof": true, "tactics": ["rw", "constructor", "intro", "haveI", "exact", "intro", "infer_instance"], "tactic_count": 7}
{"name": "CategoryTheory.ShortComplex.RightHomologyMapData.quasiIso_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.QuasiIso", "is_tactic_proof": true, "tactics": ["rw", "constructor", "intro", "haveI", "exact", "intro", "infer_instance"], "tactic_count": 7}
{"name": "CategoryTheory.ShortComplex.quasiIso_iff_isIso_leftHomologyMap'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.QuasiIso", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.quasiIso_iff_isIso_rightHomologyMap'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.QuasiIso", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.quasiIso_iff_isIso_homologyMap'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.QuasiIso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.quasiIso_of_epi_of_isIso_of_mono", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.QuasiIso", "is_tactic_proof": true, "tactics": ["rw", "dsimp", "infer_instance"], "tactic_count": 3}
{"name": "CategoryTheory.ShortComplex.quasiIso_opMap_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.QuasiIso", "is_tactic_proof": true, "tactics": ["have", "rw", "dsimp", "constructor", "intro", "apply", "intro", "infer_instance"], "tactic_count": 8}
{"name": "CategoryTheory.ShortComplex.quasiIso_opMap", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.QuasiIso", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.quasiIso_unopMap", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.QuasiIso", "is_tactic_proof": true, "tactics": ["rw", "change", "infer_instance"], "tactic_count": 3}
{"name": "CategoryTheory.ShortComplex.quasiIso_iff_isIso_liftCycles", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.QuasiIso", "is_tactic_proof": false, "tactics": ["let", "φH", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.ShortComplex.quasiIso_iff_isIso_descOpcycles", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.QuasiIso", "is_tactic_proof": false, "tactics": ["let", "φH", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.ShortComplex.quasiIso_of_retract", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.Retract", "is_tactic_proof": true, "tactics": ["rw", "have", "r", "retract", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.ShortComplex.RightHomologyData.ofHasCokernelOfHasKernel", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.RightHomologyData.instEpiP", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.RightHomologyData.instMonoι", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.RightHomologyData.descQ", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.RightHomologyData.p_descQ", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.RightHomologyData.descH", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.RightHomologyData.g'", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.RightHomologyData.p_g'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.RightHomologyData.ι_g'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.RightHomologyData.ι_descQ_eq_zero_of_boundary", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": true, "tactics": ["rw", "congr", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.ShortComplex.RightHomologyData.hι'", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.ShortComplex.rightHomologyFunctor", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.opcyclesFunctor", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.rightHomologyιNatTrans", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.pOpcyclesNatTrans", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.fromOpcyclesNatTrans", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.LeftHomologyMapData.op", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.LeftHomologyMapData.unop", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.RightHomologyMapData.op", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.RightHomologyMapData.unop", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.rightHomologyOpIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.leftHomologyOpIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.opcyclesOpIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.cyclesOpIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.opcyclesOpIso_hom_toCycles_op", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.fromOpcycles_op_cyclesOpIso_inv", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.op_pOpcycles_opcyclesOpIso_hom", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "rfl"], "tactic_count": 3}
{"name": "CategoryTheory.ShortComplex.cyclesOpIso_inv_op_iCycles", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "rfl"], "tactic_count": 3}
{"name": "CategoryTheory.ShortComplex.opcyclesOpIso_hom_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": true, "tactics": ["rw", "op_pOpcycles_opcyclesOpIso_hom_assoc,"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.opcyclesOpIso_inv_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": true, "tactics": ["rw", "comp_id]"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.cyclesOpIso_inv_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": true, "tactics": ["rw", "cyclesOpIso_inv_op_iCycles_assoc,"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.cyclesOpIso_hom_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.leftHomologyMap'_op", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": true, "tactics": ["let", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.leftHomologyMap_op", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.rightHomologyMap'_op", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": true, "tactics": ["let", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.rightHomologyMap_op", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.RightHomologyData.ofEpiOfIsIsoOfMono", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": true, "tactics": ["haveI", "haveI", "haveI", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.ShortComplex.RightHomologyData.ofEpiOfIsIsoOfMono_Q", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.RightHomologyData.ofEpiOfIsIsoOfMono_H", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.RightHomologyData.ofEpiOfIsIsoOfMono_p", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.RightHomologyData.ofEpiOfIsIsoOfMono_ι", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.RightHomologyData.ofEpiOfIsIsoOfMono_g'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.RightHomologyData.ofEpiOfIsIsoOfMono'", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": true, "tactics": ["haveI", "haveI", "haveI", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.ShortComplex.RightHomologyData.ofEpiOfIsIsoOfMono'_Q", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.RightHomologyData.ofEpiOfIsIsoOfMono'_H", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.RightHomologyData.ofEpiOfIsIsoOfMono'_p", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.RightHomologyData.ofEpiOfIsIsoOfMono'_ι", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.RightHomologyData.ofEpiOfIsIsoOfMono'_g'_τ₃", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.RightHomologyData.ofIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.hasRightHomology_of_epi_of_isIso_of_mono", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.hasRightHomology_of_epi_of_isIso_of_mono'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.hasRightHomology_of_iso", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.RightHomologyMapData.ofEpiOfIsIsoOfMono", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.RightHomologyMapData.ofEpiOfIsIsoOfMono'", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.instIsIsoRightHomologyMap'OfEpiτ₁Ofτ₂OfMonoτ₃", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": true, "tactics": ["let", "haveI", "rw", "dsimp", "infer_instance", "have", "rw", "rw", "infer_instance"], "tactic_count": 9}
{"name": "CategoryTheory.ShortComplex.instIsIsoRightHomologyMapOfEpiτ₁Ofτ₂OfMonoτ₃", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.rightHomologyFunctorOpNatIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.leftHomologyFunctorOpNatIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.descOpcycles", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.p_descOpcycles", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.descOpcycles_comp", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.opcyclesIsCokernel", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.opcyclesIsoCokernel", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.isoOpcyclesOfIsColimit", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.π_isoOpcyclesOfIsColimit_hom", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.pOpcycles_π_isoOpcyclesOfIsColimit_inv", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.descRightHomology", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.rightHomologyι_descOpcycles_π_eq_zero_of_boundary", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.rightHomologyι_comp_fromOpcycles", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.rightHomologyIsKernel", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.opcyclesMap_comp_descOpcycles", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.RightHomologyData.opcyclesIso_inv_comp_descOpcycles", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.RightHomologyData.opcyclesIso_hom_comp_descQ", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.HasRightHomology.hasCokernel", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.HasRightHomology.hasKernel", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": true, "tactics": ["let", "haveI", "let", "parallelPair.ext", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.ShortComplex.rightHomologyIsoKernelDesc", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.isIso_opcyclesMap'_of_isIso_of_epi", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": true, "tactics": ["refine", "simp", "simp", "simp"], "tactic_count": 4}
{"name": "CategoryTheory.ShortComplex.isIso_opcyclesMap_of_isIso_of_epi'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.isIso_opcyclesMap_of_isIso_of_epi", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.ShortExact.mk'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.ShortExact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.shortExact_of_iso", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.ShortExact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.shortExact_iff_of_iso", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.ShortExact", "is_tactic_proof": true, "tactics": ["constructor", "exact", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.ShortComplex.ShortExact.op", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.ShortExact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.ShortExact.unop", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.ShortExact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.shortExact_iff_op", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.ShortExact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.shortExact_iff_unop", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.ShortExact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.ShortExact.map", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.ShortExact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.ShortExact.map_of_exact", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.ShortExact", "is_tactic_proof": true, "tactics": ["have", "have", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.ShortComplex.ShortExact.isIso_f_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.ShortExact", "is_tactic_proof": true, "tactics": ["have", "have", "have", "constructor", "intro", "simp", "intro", "have", "apply"], "tactic_count": 9}
{"name": "CategoryTheory.ShortComplex.ShortExact.isIso_g_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.ShortExact", "is_tactic_proof": true, "tactics": ["have", "have", "have", "constructor", "intro", "simp", "intro", "have", "apply"], "tactic_count": 9}
{"name": "CategoryTheory.ShortComplex.isIso₂_of_shortExact_of_isIso₁₃", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.ShortExact", "is_tactic_proof": true, "tactics": ["have", "have", "have", "have", "have", "have", "apply"], "tactic_count": 7}
{"name": "CategoryTheory.ShortComplex.isIso₂_of_shortExact_of_isIso₁₃'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.ShortExact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.ShortExact.fIsKernel", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.ShortExact", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.ShortExact.gIsCokernel", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.ShortExact", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.Exact.shortExact", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.ShortExact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.Splitting.shortExact", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.ShortExact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.ShortExact.splittingOfInjective", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.ShortExact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.ShortExact.splittingOfProjective", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.ShortExact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.SnakeInput.op", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.SnakeLemma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.SnakeInput.w₀₂_τ₁", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.SnakeLemma", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.SnakeInput.w₀₂_τ₂", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.SnakeLemma", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.SnakeInput.w₀₂_τ₃", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.SnakeLemma", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.SnakeInput.w₁₃_τ₁", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.SnakeLemma", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.SnakeInput.w₁₃_τ₂", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.SnakeLemma", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.SnakeInput.w₁₃_τ₃", "kind": "theorem", "module": "Mathlib.Algebra.Homology.ShortComplex.SnakeLemma", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.ShortComplex.SnakeInput.h₀τ₁", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.SnakeLemma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.SnakeInput.h₀τ₂", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.SnakeLemma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.SnakeInput.h₀τ₃", "kind": "definition", "module": "Mathlib.Algebra.Homology.ShortComplex.SnakeLemma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.SnakeInput.mono_v₀₁_τ₁", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.SnakeLemma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.SnakeInput.mono_v₀₁_τ₂", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.SnakeLemma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.SnakeInput.mono_v₀₁_τ₃", "kind": "instance", "module": "Mathlib.Algebra.Homology.ShortComplex.SnakeLemma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "HomologicalComplex.single_obj_X_self", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Single", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "HomologicalComplex.mkHomToSingle_f", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Single", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "rfl"], "tactic_count": 3}
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{"name": "HomologicalComplex.mkHomFromSingle_f", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Single", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "rfl"], "tactic_count": 3}
{"name": "HomologicalComplex.instPreservesZeroMorphismsSingle", "kind": "instance", "module": "Mathlib.Algebra.Homology.Single", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ChainComplex.single₀", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.Single", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ChainComplex.single₀_obj_zero", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Single", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ChainComplex.single₀ObjXSelf", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Single", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ChainComplex.fromSingle₀Equiv_symm_apply_f_zero", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Single", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "CochainComplex.single₀", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.Single", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.single₀_obj_zero", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Single", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.single₀_map_f_zero", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Single", "is_tactic_proof": true, "tactics": ["rw", "dsimp", "rw"], "tactic_count": 3}
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{"name": "CochainComplex.fromSingle₀Equiv_symm_apply_f_zero", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Single", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "CochainComplex.toSingle₀Equiv_symm_apply_f_zero", "kind": "theorem", "module": "Mathlib.Algebra.Homology.Single", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "HomologicalComplex.isZero_single_obj_homology", "kind": "theorem", "module": "Mathlib.Algebra.Homology.SingleHomology", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HomologicalComplex.singleObjCyclesSelfIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.SingleHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.singleObjCyclesSelfIso_hom", "kind": "theorem", "module": "Mathlib.Algebra.Homology.SingleHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.singleObjOpcyclesSelfIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.SingleHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.singleObjOpcyclesSelfIso_hom", "kind": "theorem", "module": "Mathlib.Algebra.Homology.SingleHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.singleObjHomologySelfIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.SingleHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.singleObjCyclesSelfIso_inv_iCycles", "kind": "theorem", "module": "Mathlib.Algebra.Homology.SingleHomology", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HomologicalComplex.homologyπ_singleObjHomologySelfIso_hom", "kind": "theorem", "module": "Mathlib.Algebra.Homology.SingleHomology", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HomologicalComplex.singleObjHomologySelfIso_hom_singleObjHomologySelfIso_inv", "kind": "theorem", "module": "Mathlib.Algebra.Homology.SingleHomology", "is_tactic_proof": true, "tactics": ["simp", "homologyπ_singleObjHomologySelfIso_hom]"], "tactic_count": 2}
{"name": "HomologicalComplex.singleObjCyclesSelfIso_hom_singleObjOpcyclesSelfIso_hom", "kind": "theorem", "module": "Mathlib.Algebra.Homology.SingleHomology", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HomologicalComplex.singleObjCyclesSelfIso_inv_homologyπ", "kind": "theorem", "module": "Mathlib.Algebra.Homology.SingleHomology", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HomologicalComplex.singleObjHomologySelfIso_inv_homologyι", "kind": "theorem", "module": "Mathlib.Algebra.Homology.SingleHomology", "is_tactic_proof": true, "tactics": ["rw", "homology_π_ι,"], "tactic_count": 2}
{"name": "HomologicalComplex.homologyι_singleObjOpcyclesSelfIso_inv", "kind": "theorem", "module": "Mathlib.Algebra.Homology.SingleHomology", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HomologicalComplex.singleObjHomologySelfIso_hom_singleObjOpcyclesSelfIso_hom", "kind": "theorem", "module": "Mathlib.Algebra.Homology.SingleHomology", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HomologicalComplex.pOpcycles_singleObjOpcyclesSelfIso_inv", "kind": "theorem", "module": "Mathlib.Algebra.Homology.SingleHomology", "is_tactic_proof": true, "tactics": ["have", "rw", "homologyι_singleObjOpcyclesSelfIso_inv,"], "tactic_count": 3}
{"name": "HomologicalComplex.singleObjCyclesSelfIso_hom_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Homology.SingleHomology", "is_tactic_proof": false, "tactics": ["rw", "cancel_mono", "simp", "iCyclesIso_inv_hom_id,"], "tactic_count": 4}
{"name": "HomologicalComplex.singleObjCyclesSelfIso_inv_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Homology.SingleHomology", "is_tactic_proof": true, "tactics": ["rw", "singleObjCyclesSelfIso_hom_naturality_assoc,"], "tactic_count": 2}
{"name": "HomologicalComplex.singleObjHomologySelfIso_hom_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Homology.SingleHomology", "is_tactic_proof": true, "tactics": ["rw", "homologyπ_singleObjHomologySelfIso_hom,", "homologyπ_singleObjHomologySelfIso_hom_assoc]"], "tactic_count": 3}
{"name": "HomologicalComplex.singleObjHomologySelfIso_inv_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Homology.SingleHomology", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HomologicalComplex.singleObjOpcyclesSelfIso_hom_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Homology.SingleHomology", "is_tactic_proof": true, "tactics": ["rw", "p_opcyclesMap,"], "tactic_count": 2}
{"name": "HomologicalComplex.singleObjOpcyclesSelfIso_inv_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Homology.SingleHomology", "is_tactic_proof": true, "tactics": ["rw", "singleObjOpcyclesSelfIso_hom_naturality,"], "tactic_count": 2}
{"name": "HomologicalComplex.homologyFunctorSingleIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.SingleHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ChainComplex.exactAt_succ_single_obj", "kind": "theorem", "module": "Mathlib.Algebra.Homology.SingleHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CochainComplex.exactAt_succ_single_obj", "kind": "theorem", "module": "Mathlib.Algebra.Homology.SingleHomology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Square.cokernelCofork", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.Square", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Square.isPushoutEquivIsColimitCokernelCofork", "kind": "definition", "module": "Mathlib.Algebra.Homology.Square", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Square.IsPushout.isColimitCokernelCofork", "kind": "definition", "module": "Mathlib.Algebra.Homology.Square", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Square.kernelFork", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.Square", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Square.isPullbackEquivIsLimitKernelFork", "kind": "definition", "module": "Mathlib.Algebra.Homology.Square", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Square.IsPullback.isLimitKernelFork", "kind": "definition", "module": "Mathlib.Algebra.Homology.Square", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex₂.HasTotal", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.TotalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex₂.hasTotal_of_iso", "kind": "theorem", "module": "Mathlib.Algebra.Homology.TotalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex₂.d₁", "kind": "definition", "module": "Mathlib.Algebra.Homology.TotalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex₂.d₂", "kind": "definition", "module": "Mathlib.Algebra.Homology.TotalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex₂.d₁_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Homology.TotalComplex", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "HomologicalComplex₂.d₂_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Homology.TotalComplex", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "HomologicalComplex₂.totalAux.d₁_eq'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.TotalComplex", "is_tactic_proof": true, "tactics": ["obtain", "rfl"], "tactic_count": 2}
{"name": "HomologicalComplex₂.totalAux.d₁_eq", "kind": "theorem", "module": "Mathlib.Algebra.Homology.TotalComplex", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HomologicalComplex₂.totalAux.d₂_eq'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.TotalComplex", "is_tactic_proof": true, "tactics": ["obtain", "rfl"], "tactic_count": 2}
{"name": "HomologicalComplex₂.totalAux.d₂_eq", "kind": "theorem", "module": "Mathlib.Algebra.Homology.TotalComplex", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HomologicalComplex₂.d₁_eq_zero'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.TotalComplex", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "HomologicalComplex₂.d₂_eq_zero'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.TotalComplex", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "HomologicalComplex₂.D₁", "kind": "definition", "module": "Mathlib.Algebra.Homology.TotalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex₂.D₂", "kind": "definition", "module": "Mathlib.Algebra.Homology.TotalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex₂.totalAux.ιMapObj_D₁", "kind": "theorem", "module": "Mathlib.Algebra.Homology.TotalComplex", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HomologicalComplex₂.totalAux.ιMapObj_D₂", "kind": "theorem", "module": "Mathlib.Algebra.Homology.TotalComplex", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HomologicalComplex₂.D₁_shape", "kind": "theorem", "module": "Mathlib.Algebra.Homology.TotalComplex", "is_tactic_proof": true, "tactics": ["ext", "simp", "by_cases", "rw", "intro", "exact", "exact"], "tactic_count": 7}
{"name": "HomologicalComplex₂.D₂_shape", "kind": "theorem", "module": "Mathlib.Algebra.Homology.TotalComplex", "is_tactic_proof": true, "tactics": ["ext", "simp", "by_cases", "rw", "intro", "exact", "exact"], "tactic_count": 7}
{"name": "HomologicalComplex₂.D₁_D₁", "kind": "theorem", "module": "Mathlib.Algebra.Homology.TotalComplex", "is_tactic_proof": true, "tactics": ["by_cases", "by_cases", "ext", "simp", "by_cases", "rw", "rw", "simp", "by_cases", "rw", "smul_zero]", "rw", "rw", "rw", "rw", "rw"], "tactic_count": 16}
{"name": "HomologicalComplex₂.D₂_D₂", "kind": "theorem", "module": "Mathlib.Algebra.Homology.TotalComplex", "is_tactic_proof": true, "tactics": ["by_cases", "by_cases", "ext", "simp", "by_cases", "rw", "rw", "simp", "by_cases", "rw", "smul_zero,", "rw", "c₁₂.next_eq", "rw", "rw", "rw", "rw"], "tactic_count": 17}
{"name": "HomologicalComplex₂.D₂_D₁", "kind": "theorem", "module": "Mathlib.Algebra.Homology.TotalComplex", "is_tactic_proof": true, "tactics": ["by_cases", "by_cases", "ext", "simp", "by_cases", "rw", "rw", "simp", "by_cases", "have", "rw", "have", "rw", "simp", "totalAux.ιMapObj_D₁,", "simp", "rw", "by_cases", "rw", "rw", "simp", "rw", "rw", "rw", "rw"], "tactic_count": 25}
{"name": "HomologicalComplex₂.D₁_D₂", "kind": "theorem", "module": "Mathlib.Algebra.Homology.TotalComplex", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HomologicalComplex₂.total", "kind": "definition", "module": "Mathlib.Algebra.Homology.TotalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex₂.ιTotal", "kind": "definition", "module": "Mathlib.Algebra.Homology.TotalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex₂.XXIsoOfEq_hom_ιTotal", "kind": "theorem", "module": "Mathlib.Algebra.Homology.TotalComplex", "is_tactic_proof": true, "tactics": ["subst", "simp"], "tactic_count": 2}
{"name": "HomologicalComplex₂.XXIsoOfEq_inv_ιTotal", "kind": "theorem", "module": "Mathlib.Algebra.Homology.TotalComplex", "is_tactic_proof": true, "tactics": ["subst", "simp"], "tactic_count": 2}
{"name": "HomologicalComplex₂.ιTotalOrZero", "kind": "definition", "module": "Mathlib.Algebra.Homology.TotalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex₂.ιTotalOrZero_eq", "kind": "theorem", "module": "Mathlib.Algebra.Homology.TotalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex₂.ιTotalOrZero_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Homology.TotalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex₂.ι_D₁", "kind": "theorem", "module": "Mathlib.Algebra.Homology.TotalComplex", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "HomologicalComplex₂.ι_D₂", "kind": "theorem", "module": "Mathlib.Algebra.Homology.TotalComplex", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "HomologicalComplex₂.d₁_eq'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.TotalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex₂.d₁_eq", "kind": "theorem", "module": "Mathlib.Algebra.Homology.TotalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex₂.d₂_eq'", "kind": "theorem", "module": "Mathlib.Algebra.Homology.TotalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex₂.d₂_eq", "kind": "theorem", "module": "Mathlib.Algebra.Homology.TotalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex₂.totalDesc", "kind": "definition", "module": "Mathlib.Algebra.Homology.TotalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex₂.ι_totalDesc", "kind": "theorem", "module": "Mathlib.Algebra.Homology.TotalComplex", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HomologicalComplex₂.total.hom_ext", "kind": "theorem", "module": "Mathlib.Algebra.Homology.TotalComplex", "is_tactic_proof": true, "tactics": ["apply", "rintro", "exact"], "tactic_count": 3}
{"name": "HomologicalComplex₂.total.mapAux.d₁_mapMap", "kind": "theorem", "module": "Mathlib.Algebra.Homology.TotalComplex", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "simp"], "tactic_count": 3}
{"name": "HomologicalComplex₂.total.mapAux.d₂_mapMap", "kind": "theorem", "module": "Mathlib.Algebra.Homology.TotalComplex", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "simp"], "tactic_count": 3}
{"name": "HomologicalComplex₂.total.mapAux.mapMap_D₁", "kind": "theorem", "module": "Mathlib.Algebra.Homology.TotalComplex", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "HomologicalComplex₂.total.mapAux.mapMap_D₂", "kind": "theorem", "module": "Mathlib.Algebra.Homology.TotalComplex", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "HomologicalComplex₂.total.map", "kind": "definition", "module": "Mathlib.Algebra.Homology.TotalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex₂.total.forget_map", "kind": "theorem", "module": "Mathlib.Algebra.Homology.TotalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex₂.total.map_id", "kind": "theorem", "module": "Mathlib.Algebra.Homology.TotalComplex", "is_tactic_proof": true, "tactics": ["apply", "apply"], "tactic_count": 2}
{"name": "HomologicalComplex₂.total.map_comp", "kind": "theorem", "module": "Mathlib.Algebra.Homology.TotalComplex", "is_tactic_proof": true, "tactics": ["apply", "exact"], "tactic_count": 2}
{"name": "HomologicalComplex₂.total.mapIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.TotalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex₂.ιTotal_map", "kind": "theorem", "module": "Mathlib.Algebra.Homology.TotalComplex", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HomologicalComplex₂.ιTotalOrZero_map", "kind": "theorem", "module": "Mathlib.Algebra.Homology.TotalComplex", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HomologicalComplex₂.totalFunctor", "kind": "definition", "module": "Mathlib.Algebra.Homology.TotalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex₂.shiftFunctor₁", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.TotalComplexShift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex₂.shiftFunctor₂", "kind": "abbrev", "module": "Mathlib.Algebra.Homology.TotalComplexShift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex₂.shiftFunctor₁XXIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.TotalComplexShift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex₂.shiftFunctor₂XXIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.TotalComplexShift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex₂.shiftFunctor₁XXIso_refl", "kind": "theorem", "module": "Mathlib.Algebra.Homology.TotalComplexShift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex₂.shiftFunctor₂XXIso_refl", "kind": "theorem", "module": "Mathlib.Algebra.Homology.TotalComplexShift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex₂.instHasTotalIntObjUpShiftFunctor₁", "kind": "instance", "module": "Mathlib.Algebra.Homology.TotalComplexShift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex₂.instHasTotalIntObjUpShiftFunctor₂", "kind": "instance", "module": "Mathlib.Algebra.Homology.TotalComplexShift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex₂.instHasTotalIntObjUpCompShiftFunctor₂ShiftFunctor₁", "kind": "instance", "module": "Mathlib.Algebra.Homology.TotalComplexShift", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "HomologicalComplex₂.instHasTotalIntObjUpCompShiftFunctor₁ShiftFunctor₂", "kind": "instance", "module": "Mathlib.Algebra.Homology.TotalComplexShift", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "HomologicalComplex₂.totalShift₁XIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.TotalComplexShift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex₂.D₁_totalShift₁XIso_hom", "kind": "theorem", "module": "Mathlib.Algebra.Homology.TotalComplexShift", "is_tactic_proof": true, "tactics": ["by_cases", "apply", "intro", "dsimp", "dsimp", "rw", "dsimp", "rw", "rw", "grind"], "tactic_count": 10}
{"name": "HomologicalComplex₂.D₂_totalShift₁XIso_hom", "kind": "theorem", "module": "Mathlib.Algebra.Homology.TotalComplexShift", "is_tactic_proof": true, "tactics": ["by_cases", "apply", "intro", "dsimp", "dsimp", "rw", "dsimp", "congr", "rw", "rw", "grind"], "tactic_count": 11}
{"name": "HomologicalComplex₂.totalShift₁Iso", "kind": "definition", "module": "Mathlib.Algebra.Homology.TotalComplexShift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex₂.ι_totalShift₁Iso_hom_f", "kind": "theorem", "module": "Mathlib.Algebra.Homology.TotalComplexShift", "is_tactic_proof": true, "tactics": ["subst", "dsimp", "simp"], "tactic_count": 3}
{"name": "HomologicalComplex₂.ι_totalShift₁Iso_inv_f", "kind": "theorem", "module": "Mathlib.Algebra.Homology.TotalComplexShift", "is_tactic_proof": true, "tactics": ["subst", "obtain", "dsimp", "simp"], "tactic_count": 4}
{"name": "HomologicalComplex₂.totalShift₁Iso_hom_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Homology.TotalComplexShift", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "rw", "dsimp", "rw"], "tactic_count": 5}
{"name": "HomologicalComplex₂.totalShift₂XIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.TotalComplexShift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex₂.D₁_totalShift₂XIso_hom", "kind": "theorem", "module": "Mathlib.Algebra.Homology.TotalComplexShift", "is_tactic_proof": true, "tactics": ["by_cases", "apply", "intro", "dsimp", "dsimp", "rw", "dsimp", "rw", "congr", "linarith", "rw", "grind"], "tactic_count": 12}
{"name": "HomologicalComplex₂.D₂_totalShift₂XIso_hom", "kind": "theorem", "module": "Mathlib.Algebra.Homology.TotalComplexShift", "is_tactic_proof": true, "tactics": ["by_cases", "apply", "intro", "dsimp", "dsimp", "rw", "smul_smul,", "dsimp", "rw", "congr", "lia", "rw", "simp_all", "grind"], "tactic_count": 14}
{"name": "HomologicalComplex₂.totalShift₂Iso", "kind": "definition", "module": "Mathlib.Algebra.Homology.TotalComplexShift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex₂.ι_totalShift₂Iso_hom_f", "kind": "theorem", "module": "Mathlib.Algebra.Homology.TotalComplexShift", "is_tactic_proof": true, "tactics": ["subst", "dsimp", "simp"], "tactic_count": 3}
{"name": "HomologicalComplex₂.ι_totalShift₂Iso_inv_f", "kind": "theorem", "module": "Mathlib.Algebra.Homology.TotalComplexShift", "is_tactic_proof": true, "tactics": ["subst", "obtain", "dsimp", "simp"], "tactic_count": 4}
{"name": "HomologicalComplex₂.totalShift₂Iso_hom_naturality", "kind": "theorem", "module": "Mathlib.Algebra.Homology.TotalComplexShift", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "rw", "dsimp", "rw"], "tactic_count": 5}
{"name": "HomologicalComplex₂.shiftFunctor₁₂CommIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.TotalComplexShift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex₂.totalShift₁Iso_trans_totalShift₂Iso", "kind": "theorem", "module": "Mathlib.Algebra.Homology.TotalComplexShift", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "rw", "ι_totalShift₂Iso_hom_f_assoc", "dsimp", "rw", "smul_smul,", "dsimp", "rw", "dsimp", "rw"], "tactic_count": 11}
{"name": "HomologicalComplex₂.totalShift₁Iso_hom_totalShift₂Iso_hom", "kind": "theorem", "module": "Mathlib.Algebra.Homology.TotalComplexShift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex₂.instHasTotalFlip", "kind": "instance", "module": "Mathlib.Algebra.Homology.TotalComplexSymmetry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex₂.flip_hasTotal_iff", "kind": "theorem", "module": "Mathlib.Algebra.Homology.TotalComplexSymmetry", "is_tactic_proof": true, "tactics": ["constructor", "intro", "change", "have", "infer_instance", "intro", "infer_instance"], "tactic_count": 7}
{"name": "HomologicalComplex₂.totalFlipIsoX", "kind": "definition", "module": "Mathlib.Algebra.Homology.TotalComplexSymmetry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex₂.totalFlipIsoX_hom_D₁", "kind": "theorem", "module": "Mathlib.Algebra.Homology.TotalComplexSymmetry", "is_tactic_proof": true, "tactics": ["by_cases", "ext", "dsimp", "rw", "dsimp", "by_cases", "have", "rw", "have", "rw", "dsimp", "rw", "rw"], "tactic_count": 13}
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{"name": "HomologicalComplex₂.totalFlipIso", "kind": "definition", "module": "Mathlib.Algebra.Homology.TotalComplexSymmetry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex₂.totalFlipIso_hom_f_D₁", "kind": "theorem", "module": "Mathlib.Algebra.Homology.TotalComplexSymmetry", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "HomologicalComplex₂.totalFlipIso_hom_f_D₂", "kind": "theorem", "module": "Mathlib.Algebra.Homology.TotalComplexSymmetry", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "HomologicalComplex₂.ιTotal_totalFlipIso_f_hom", "kind": "theorem", "module": "Mathlib.Algebra.Homology.TotalComplexSymmetry", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HomologicalComplex₂.ιTotal_totalFlipIso_f_inv", "kind": "theorem", "module": "Mathlib.Algebra.Homology.TotalComplexSymmetry", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HomologicalComplex₂.instHasTotalFlip_1", "kind": "instance", "module": "Mathlib.Algebra.Homology.TotalComplexSymmetry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex₂.flip_totalFlipIso", "kind": "theorem", "module": "Mathlib.Algebra.Homology.TotalComplexSymmetry", "is_tactic_proof": true, "tactics": ["ext", "rw", "dsimp", "rw"], "tactic_count": 4}
{"name": "IsPrimePow", "kind": "definition", "module": "Mathlib.Algebra.IsPrimePow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isPrimePow_def", "kind": "theorem", "module": "Mathlib.Algebra.IsPrimePow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isPrimePow_iff_pow_succ", "kind": "theorem", "module": "Mathlib.Algebra.IsPrimePow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_isPrimePow_zero", "kind": "theorem", "module": "Mathlib.Algebra.IsPrimePow", "is_tactic_proof": true, "tactics": ["simp", "intro", "rw", "simp"], "tactic_count": 4}
{"name": "IsPrimePow.not_unit", "kind": "theorem", "module": "Mathlib.Algebra.IsPrimePow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUnit.not_isPrimePow", "kind": "theorem", "module": "Mathlib.Algebra.IsPrimePow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_isPrimePow_one", "kind": "theorem", "module": "Mathlib.Algebra.IsPrimePow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prime.isPrimePow", "kind": "theorem", "module": "Mathlib.Algebra.IsPrimePow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimePow.pow", "kind": "theorem", "module": "Mathlib.Algebra.IsPrimePow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimePow.ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.IsPrimePow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimePow.ne_one", "kind": "theorem", "module": "Mathlib.Algebra.IsPrimePow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isPrimePow_nat_iff", "kind": "theorem", "module": "Mathlib.Algebra.IsPrimePow", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.Prime.isPrimePow", "kind": "theorem", "module": "Mathlib.Algebra.IsPrimePow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isPrimePow_nat_iff_bounded", "kind": "theorem", "module": "Mathlib.Algebra.IsPrimePow", "is_tactic_proof": true, "tactics": ["rw", "refine", "rintro", "refine", "conv", "exact"], "tactic_count": 6}
{"name": "isPrimePow_nat_iff_bounded_log", "kind": "theorem", "module": "Mathlib.Algebra.IsPrimePow", "is_tactic_proof": true, "tactics": ["rw", "constructor", "rintro", "refine", "calc", "k", "rintro", "exact"], "tactic_count": 8}
{"name": "isPrimePow_nat_iff_bounded_log_minFac", "kind": "theorem", "module": "Mathlib.Algebra.IsPrimePow", "is_tactic_proof": true, "tactics": ["rw", "obtain", "simp", "constructor", "rintro", "refine", "rw", "rintro", "refine", "grind", "grind"], "tactic_count": 11}
{"name": "instDecidableIsPrimePowNat", "kind": "instance", "module": "Mathlib.Algebra.IsPrimePow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimePow.dvd", "kind": "theorem", "module": "Mathlib.Algebra.IsPrimePow", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "IsPrimePow.two_le", "kind": "theorem", "module": "Mathlib.Algebra.IsPrimePow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimePow.pos", "kind": "theorem", "module": "Mathlib.Algebra.IsPrimePow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimePow.one_lt", "kind": "theorem", "module": "Mathlib.Algebra.IsPrimePow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCommJordan.toIsJordan", "kind": "instance", "module": "Mathlib.Algebra.Jordan.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Semigroup.isJordan", "kind": "instance", "module": "Mathlib.Algebra.Jordan.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommSemigroup.isCommJordan", "kind": "instance", "module": "Mathlib.Algebra.Jordan.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Jordan.Basic.0.termL", "kind": "definition", "module": "Mathlib.Algebra.Jordan.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Jordan.Basic.0._aux_Mathlib_Algebra_Jordan_Basic___macroRules__private_Mathlib_Algebra_Jordan_Basic_0_termL_1", "kind": "definition", "module": "Mathlib.Algebra.Jordan.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Jordan.Basic.0._aux_Mathlib_Algebra_Jordan_Basic___unexpand_AddMonoid_End_mulLeft_1", "kind": "definition", "module": "Mathlib.Algebra.Jordan.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Jordan.Basic.0.termR", "kind": "definition", "module": "Mathlib.Algebra.Jordan.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Jordan.Basic.0._aux_Mathlib_Algebra_Jordan_Basic___macroRules__private_Mathlib_Algebra_Jordan_Basic_0_termR_1", "kind": "definition", "module": "Mathlib.Algebra.Jordan.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Jordan.Basic.0._aux_Mathlib_Algebra_Jordan_Basic___unexpand_AddMonoid_End_mulRight_1", "kind": "definition", "module": "Mathlib.Algebra.Jordan.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "commute_lmul_rmul", "kind": "theorem", "module": "Mathlib.Algebra.Jordan.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "commute_lmul_lmul_sq", "kind": "theorem", "module": "Mathlib.Algebra.Jordan.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "commute_lmul_rmul_sq", "kind": "theorem", "module": "Mathlib.Algebra.Jordan.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "commute_lmul_sq_rmul", "kind": "theorem", "module": "Mathlib.Algebra.Jordan.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "commute_rmul_rmul_sq", "kind": "theorem", "module": "Mathlib.Algebra.Jordan.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "two_nsmul_lie_lmul_lmul_add_eq_lie_lmul_lmul_add", "kind": "theorem", "module": "Mathlib.Algebra.Jordan.Basic", "is_tactic_proof": false, "tactics": ["suffices", "rwa", "convert", "simp", "abel"], "tactic_count": 5}
{"name": "_private.Mathlib.Algebra.Jordan.Basic.0.aux0", "kind": "theorem", "module": "Mathlib.Algebra.Jordan.Basic", "is_tactic_proof": true, "tactics": ["rw", "iterate", "iterate", "rw", "iterate", "simp", "abel"], "tactic_count": 7}
{"name": "_private.Mathlib.Algebra.Jordan.Basic.0.aux1", "kind": "theorem", "module": "Mathlib.Algebra.Jordan.Basic", "is_tactic_proof": true, "tactics": ["rw", "iterate"], "tactic_count": 2}
{"name": "_private.Mathlib.Algebra.Jordan.Basic.0.aux2", "kind": "theorem", "module": "Mathlib.Algebra.Jordan.Basic", "is_tactic_proof": false, "tactics": ["rw", "add_zero,", "simp", "abel"], "tactic_count": 4}
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{"name": "LieRinehartAlgebra.instLieRinehartRingDerivation", "kind": "instance", "module": "Mathlib.Algebra.LieRinehartAlgebra.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieRinehartAlgebra.instDerivation", "kind": "instance", "module": "Mathlib.Algebra.LieRinehartAlgebra.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieRinehartAlgebra.Hom.term_→ₗ⁅_⁆_", "kind": "definition", "module": "Mathlib.Algebra.LieRinehartAlgebra.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieRinehartAlgebra.Hom._aux_Mathlib_Algebra_LieRinehartAlgebra_Defs___macroRules_LieRinehartAlgebra_Hom_term_→ₗ⁅_⁆__1", "kind": "definition", "module": "Mathlib.Algebra.LieRinehartAlgebra.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieRinehartAlgebra.Hom._aux_Mathlib_Algebra_LieRinehartAlgebra_Defs___unexpand_LieRinehartAlgebra_Hom_1", "kind": "definition", "module": "Mathlib.Algebra.LieRinehartAlgebra.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieRinehartAlgebra.Hom.instCoeFunForall", "kind": "instance", "module": "Mathlib.Algebra.LieRinehartAlgebra.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieRinehartAlgebra.Hom.map_smul_apply", "kind": "theorem", "module": "Mathlib.Algebra.LieRinehartAlgebra.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieRinehartAlgebra.Hom.apply_lie", "kind": "theorem", "module": "Mathlib.Algebra.LieRinehartAlgebra.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieRinehartAlgebra.Hom.toLinearMap'", "kind": "definition", "module": "Mathlib.Algebra.LieRinehartAlgebra.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieRinehartAlgebra.Hom.toLinearMap'_apply", "kind": "theorem", "module": "Mathlib.Algebra.LieRinehartAlgebra.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieRinehartAlgebra.Hom.comp", "kind": "definition", "module": "Mathlib.Algebra.LieRinehartAlgebra.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieRinehartAlgebra.Hom.id", "kind": "definition", "module": "Mathlib.Algebra.LieRinehartAlgebra.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieRinehartAlgebra.Hom.anchor", "kind": "definition", "module": "Mathlib.Algebra.LieRinehartAlgebra.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieRinehartAlgebra.Hom.anchor_derivation", "kind": "theorem", "module": "Mathlib.Algebra.LieRinehartAlgebra.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "trivial_lie_zero", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.instIsTrivialOfSubsingleton", "kind": "instance", "module": "Mathlib.Algebra.Lie.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.instIsTrivialOfSubsingleton'", "kind": "instance", "module": "Mathlib.Algebra.Lie.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLieAbelian", "kind": "abbrev", "module": "Mathlib.Algebra.Lie.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieIdeal.isLieAbelian_of_trivial", "kind": "instance", "module": "Mathlib.Algebra.Lie.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.isLieAbelian", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.isLieAbelian", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lie_abelian_iff_equiv_lie_abelian", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "commutative_ring_iff_abelian_lie_ring", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Abelian", "is_tactic_proof": true, "tactics": ["have", "have", "simp"], "tactic_count": 3}
{"name": "LieSubalgebra.isLieAbelian_lieSpan_iff", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Abelian", "is_tactic_proof": true, "tactics": ["refine", "let", "let", "suffices", "simp", "induction", "mem", "induction", "mem", "zero", "add", "hv", "simp", "simp", "smul", "simp", "simp", "lie", "hv", "simp", "rw", "simp", "zero", "add", "hv", "simp", "simp", "smul", "simp", "simp", "lie", "simp", "simp"], "tactic_count": 33}
{"name": "LieModule.ker", "kind": "definition", "module": "Mathlib.Algebra.Lie.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.mem_ker", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Abelian", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LieIdeal.isLieAbelian_iff", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Abelian", "is_tactic_proof": true, "tactics": ["refine", "ext", "have", "rw", "simp", "simpa"], "tactic_count": 6}
{"name": "LieModule.isFaithful_iff_ker_eq_bot", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Abelian", "is_tactic_proof": true, "tactics": ["rw", "aesop"], "tactic_count": 2}
{"name": "LieModule.ker_eq_bot", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.maxTrivSubmodule", "kind": "definition", "module": "Mathlib.Algebra.Lie.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.mem_maxTrivSubmodule", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.instIsTrivialSubtypeMemLieSubmoduleMaxTrivSubmodule", "kind": "instance", "module": "Mathlib.Algebra.Lie.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.ideal_oper_maxTrivSubmodule_eq_bot", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Abelian", "is_tactic_proof": false, "tactics": ["rw", "rintro", "exact"], "tactic_count": 3}
{"name": "LieModule.le_max_triv_iff_bracket_eq_bot", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Abelian", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact", "rw", "rw", "exact"], "tactic_count": 6}
{"name": "LieModule.trivial_iff_le_maximal_trivial", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.isTrivial_iff_max_triv_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Abelian", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "intro", "rw"], "tactic_count": 4}
{"name": "LieModule.maxTrivHom", "kind": "definition", "module": "Mathlib.Algebra.Lie.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.coe_maxTrivHom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.maxTrivEquiv", "kind": "definition", "module": "Mathlib.Algebra.Lie.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.coe_maxTrivEquiv_apply", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.maxTrivEquiv_of_refl_eq_refl", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Abelian", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "LieModule.maxTrivEquiv_of_equiv_symm_eq_symm", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.maxTrivLinearMapEquivLieModuleHom", "kind": "definition", "module": "Mathlib.Algebra.Lie.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.coe_maxTrivLinearMapEquivLieModuleHom", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Abelian", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "LieModule.coe_maxTrivLinearMapEquivLieModuleHom_symm", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.toLinearMap_maxTrivLinearMapEquivLieModuleHom", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Abelian", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "LieModule.toLinearMap_maxTrivLinearMapEquivLieModuleHom_symm", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieAlgebra.center", "kind": "abbrev", "module": "Mathlib.Algebra.Lie.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieAlgebra.instIsLieAbelianSubtypeMemLieSubmoduleCenter", "kind": "instance", "module": "Mathlib.Algebra.Lie.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieAlgebra.ad_ker_eq_self_module_ker", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieAlgebra.self_module_ker_eq_center", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Abelian", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "LieAlgebra.abelian_of_le_center", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieAlgebra.isLieAbelian_iff_center_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieAlgebra.isFaithful_self_iff", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Abelian", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LieAlgebra.center_eq_bot", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.commute_toEnd_of_mem_center_left", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Abelian", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "LieSubmodule.trivial_lie_oper_zero", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Abelian", "is_tactic_proof": true, "tactics": ["suffices", "rw", "rintro"], "tactic_count": 3}
{"name": "LieSubmodule.lie_abelian_iff_lie_self_eq_bot", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Abelian", "is_tactic_proof": false, "tactics": ["simp", "refine", "hz.symm.trans"], "tactic_count": 3}
{"name": "lie_eq_self_of_isAtom_of_ne_bot", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lie_eq_self_of_isAtom_of_nonabelian", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TrivialLieModule", "kind": "definition", "module": "Mathlib.Algebra.Lie.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TrivialLieModule.instAddCommGroup", "kind": "instance", "module": "Mathlib.Algebra.Lie.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TrivialLieModule.instModule", "kind": "instance", "module": "Mathlib.Algebra.Lie.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TrivialLieModule.equiv", "kind": "definition", "module": "Mathlib.Algebra.Lie.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TrivialLieModule.instLieRingModule", "kind": "instance", "module": "Mathlib.Algebra.Lie.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TrivialLieModule.instIsTrivial", "kind": "instance", "module": "Mathlib.Algebra.Lie.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TrivialLieModule.instLieModule", "kind": "instance", "module": "Mathlib.Algebra.Lie.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Lie.BaseChange.0.LieAlgebra.ExtendScalars.bracket'", "kind": "definition", "module": "Mathlib.Algebra.Lie.BaseChange", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Lie.BaseChange.0.LieAlgebra.ExtendScalars.bracket'_tmul", "kind": "theorem", "module": "Mathlib.Algebra.Lie.BaseChange", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieAlgebra.ExtendScalars.instBracketTensorProduct", "kind": "instance", "module": "Mathlib.Algebra.Lie.BaseChange", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Lie.BaseChange.0.LieAlgebra.ExtendScalars.bracket_def", "kind": "theorem", "module": "Mathlib.Algebra.Lie.BaseChange", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieAlgebra.ExtendScalars.bracket_tmul", "kind": "theorem", "module": "Mathlib.Algebra.Lie.BaseChange", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Lie.BaseChange.0.LieAlgebra.ExtendScalars.bracket_lie_self", "kind": "theorem", "module": "Mathlib.Algebra.Lie.BaseChange", "is_tactic_proof": true, "tactics": ["simp", "refine", "simp", "intro", "simp", "intro", "suffices", "rw", "refine", "simp", "intro", "simp", "intro", "simp", "intro", "simp", "intro", "simp"], "tactic_count": 18}
{"name": "_private.Mathlib.Algebra.Lie.BaseChange.0.LieAlgebra.ExtendScalars.bracket_leibniz_lie", "kind": "theorem", "module": "Mathlib.Algebra.Lie.BaseChange", "is_tactic_proof": true, "tactics": ["simp", "refine", "simp", "intro", "refine", "simp", "intro", "refine", "simp", "intro", "rw", "grind", "grind", "grind"], "tactic_count": 14}
{"name": "LieAlgebra.ExtendScalars.instLieRing", "kind": "instance", "module": "Mathlib.Algebra.Lie.BaseChange", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieAlgebra.ExtendScalars.instLieAlgebra", "kind": "instance", "module": "Mathlib.Algebra.Lie.BaseChange", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieAlgebra.ExtendScalars.instLieRingModule", "kind": "instance", "module": "Mathlib.Algebra.Lie.BaseChange", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieAlgebra.ExtendScalars.instLieModule", "kind": "instance", "module": "Mathlib.Algebra.Lie.BaseChange", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieAlgebra.RestrictScalars.instLieRingRestrictScalars", "kind": "instance", "module": "Mathlib.Algebra.Lie.BaseChange", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieAlgebra.RestrictScalars.lieAlgebra", "kind": "instance", "module": "Mathlib.Algebra.Lie.BaseChange", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.toEnd_baseChange", "kind": "theorem", "module": "Mathlib.Algebra.Lie.BaseChange", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "LieSubmodule.baseChange", "kind": "definition", "module": "Mathlib.Algebra.Lie.BaseChange", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.coe_baseChange", "kind": "theorem", "module": "Mathlib.Algebra.Lie.BaseChange", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.tmul_mem_baseChange_of_mem", "kind": "theorem", "module": "Mathlib.Algebra.Lie.BaseChange", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.mem_baseChange_iff", "kind": "theorem", "module": "Mathlib.Algebra.Lie.BaseChange", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LieSubmodule.baseChange_bot", "kind": "theorem", "module": "Mathlib.Algebra.Lie.BaseChange", "is_tactic_proof": true, "tactics": ["simp", "rfl"], "tactic_count": 2}
{"name": "LieSubmodule.baseChange_top", "kind": "theorem", "module": "Mathlib.Algebra.Lie.BaseChange", "is_tactic_proof": true, "tactics": ["simp", "rfl"], "tactic_count": 2}
{"name": "LieSubmodule.lie_baseChange", "kind": "theorem", "module": "Mathlib.Algebra.Lie.BaseChange", "is_tactic_proof": true, "tactics": ["set", "have", "rw", "lieIdeal_oper_eq_linear_span']", "refine", "rintro", "exact", "rintro", "rw", "refine", "hm", "rintro", "all_goals"], "tactic_count": 13}
{"name": "leibniz_lie", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lie_swap_lie", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieAlgebra.toModule_injective", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": true, "tactics": ["rintro", "congr"], "tactic_count": 2}
{"name": "instSubsingletonLieAlgebraRat", "kind": "instance", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "add_lie", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lie_add", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smul_lie", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lie_smul", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsLieTower", "kind": "instance", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lie_zero", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zero_lie", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lie_self", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lieRingSelfModule", "kind": "instance", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lie_skew", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "lieAlgebraSelfModule", "kind": "instance", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "neg_lie", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "lie_neg", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "sub_lie", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "lie_sub", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "nsmul_lie", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lie_nsmul", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zsmul_lie", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lie_zsmul", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "lie_jacobi", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": true, "tactics": ["rw", "abel"], "tactic_count": 2}
{"name": "LieRingModule.toEnd", "kind": "definition", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieRing.instLieAlgebra", "kind": "instance", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instLieModuleInt", "kind": "instance", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.instLieRingModule", "kind": "instance", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieHom.lie_apply", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.instLieModule", "kind": "instance", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Dual.instLieRingModule", "kind": "instance", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Dual.lie_apply", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Dual.instLieModule", "kind": "instance", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieRing.toNonUnitalNonAssocRing", "kind": "definition", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sum_lie", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lie_sum", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sum_lie_sum", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "term_→ₗ⁅_⁆_", "kind": "definition", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Algebra_Lie_Basic___macroRules_term_→ₗ⁅_⁆__1", "kind": "definition", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Algebra_Lie_Basic___unexpand_LieHom_1", "kind": "definition", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LieHom.coe_toLinearMap", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieHom.toFun_eq_coe", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieHom.instLinearMapClass", "kind": "instance", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieHom.map_lie", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieHom.id", "kind": "definition", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LieHom.id_apply", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieHom.instZero", "kind": "instance", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieHom.coe_zero", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieHom.zero_apply", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieHom.instOne", "kind": "instance", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieHom.coe_one", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieHom.one_apply", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieHom.instInhabited", "kind": "instance", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieHom.coe_injective", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": true, "tactics": ["rintro", "congr"], "tactic_count": 2}
{"name": "LieHom.ext", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieHom.congr_fun", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieHom.mk_coe", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
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{"name": "LieHom.comp_apply", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieHom.coe_comp", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieHom.toLinearMap_comp", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieHom.comp_id", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieHom.id_comp", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieHom.inverse", "kind": "definition", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieRingModule.compLieHom", "kind": "definition", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieRingModule.compLieHom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.compLieHom", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "term_≃ₗ⁅_⁆_", "kind": "definition", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Algebra_Lie_Basic___macroRules_term_≃ₗ⁅_⁆__1", "kind": "definition", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Algebra_Lie_Basic___unexpand_LieEquiv_1", "kind": "definition", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieEquiv.toLinearEquiv", "kind": "definition", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieEquiv.hasCoeToLieHom", "kind": "instance", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieEquiv.hasCoeToLinearEquiv", "kind": "instance", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieEquiv.instEquivLike", "kind": "instance", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieEquiv.coe_toLieHom", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieEquiv.coe_toLinearEquiv", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieEquiv.coe_coe", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieEquiv.toLinearEquiv_mk", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieEquiv.toLinearEquiv_injective", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": true, "tactics": ["rintro", "simp"], "tactic_count": 2}
{"name": "LieEquiv.coe_injective", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieEquiv.instLinearEquivClass", "kind": "instance", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LieEquiv.instOne", "kind": "instance", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieEquiv.one_apply", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LieEquiv.refl", "kind": "definition", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieEquiv.refl_apply", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieEquiv.symm", "kind": "definition", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieEquiv.symm_symm", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieEquiv.symm_bijective", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LieAlgebra.matrix_trace_commutator_zero", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Classical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieAlgebra.SpecialLinear.sl", "kind": "definition", "module": "Mathlib.Algebra.Lie.Classical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieAlgebra.SpecialLinear.sl_bracket", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Classical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieAlgebra.SpecialLinear.single", "kind": "definition", "module": "Mathlib.Algebra.Lie.Classical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieAlgebra.SpecialLinear.val_single", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Classical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieAlgebra.SpecialLinear.singleSubSingle", "kind": "definition", "module": "Mathlib.Algebra.Lie.Classical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieAlgebra.SpecialLinear.val_singleSubSingle", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Classical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieAlgebra.SpecialLinear.singleSubSingle_add_singleSubSingle", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Classical", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "LieAlgebra.SpecialLinear.singleSubSingle_sub_singleSubSingle", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Classical", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "LieAlgebra.SpecialLinear.singleSubSingle_sub_singleSubSingle'", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Classical", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
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{"name": "LieAlgebra.Orthogonal.so", "kind": "definition", "module": "Mathlib.Algebra.Lie.Classical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieAlgebra.Orthogonal.mem_so", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Classical", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "LieAlgebra.Orthogonal.indefiniteDiagonal", "kind": "definition", "module": "Mathlib.Algebra.Lie.Classical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieAlgebra.Orthogonal.so'", "kind": "definition", "module": "Mathlib.Algebra.Lie.Classical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LieAlgebra.Orthogonal.pso_inv", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Classical", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "simp", "simp", "by_cases"], "tactic_count": 5}
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{"name": "LieAlgebra.Orthogonal.indefiniteDiagonal_transform", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Classical", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "simp", "simp", "by_cases"], "tactic_count": 5}
{"name": "LieAlgebra.Orthogonal.soIndefiniteEquiv", "kind": "definition", "module": "Mathlib.Algebra.Lie.Classical", "is_tactic_proof": false, "tactics": ["apply", "apply", "ext"], "tactic_count": 3}
{"name": "LieAlgebra.Orthogonal.soIndefiniteEquiv_apply", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Classical", "is_tactic_proof": true, "tactics": ["rw", "grind"], "tactic_count": 2}
{"name": "LieAlgebra.Orthogonal.JD", "kind": "definition", "module": "Mathlib.Algebra.Lie.Classical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieAlgebra.Orthogonal.typeD", "kind": "definition", "module": "Mathlib.Algebra.Lie.Classical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieAlgebra.Orthogonal.PD", "kind": "definition", "module": "Mathlib.Algebra.Lie.Classical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LieAlgebra.Orthogonal.s_as_blocks", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Classical", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
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{"name": "LieAlgebra.Orthogonal.typeDEquivSo'", "kind": "definition", "module": "Mathlib.Algebra.Lie.Classical", "is_tactic_proof": true, "tactics": ["apply", "apply", "ext", "rw", "mem_skewAdjointMatricesLieSubalgebra_unit_smul]", "rfl"], "tactic_count": 6}
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{"name": "LieAlgebra.Orthogonal.typeB", "kind": "definition", "module": "Mathlib.Algebra.Lie.Classical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieAlgebra.Orthogonal.PB", "kind": "definition", "module": "Mathlib.Algebra.Lie.Classical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieAlgebra.Orthogonal.pb_inv", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Classical", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
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{"name": "LieAlgebra.Orthogonal.jb_transform", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Classical", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LieAlgebra.Orthogonal.indefiniteDiagonal_assoc", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Classical", "is_tactic_proof": true, "tactics": ["ext", "simp", "congr"], "tactic_count": 3}
{"name": "LieAlgebra.Orthogonal.typeBEquivSo'", "kind": "definition", "module": "Mathlib.Algebra.Lie.Classical", "is_tactic_proof": true, "tactics": ["apply", "symm", "apply", "apply", "ext", "rw", "mem_skewAdjointMatricesLieSubalgebra_unit_smul]", "simp"], "tactic_count": 8}
{"name": "LieModule.Cohomology.oneCochain", "kind": "abbrev", "module": "Mathlib.Algebra.Lie.Cochain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.Cohomology.twoCochain", "kind": "definition", "module": "Mathlib.Algebra.Lie.Cochain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.Cohomology.instFunLikeSubtypeLinearMapIdMemSubmoduleTwoCochain", "kind": "instance", "module": "Mathlib.Algebra.Lie.Cochain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.Cohomology.instLinearMapClassSubtypeLinearMapIdMemSubmoduleTwoCochain", "kind": "instance", "module": "Mathlib.Algebra.Lie.Cochain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.Cohomology.mem_twoCochain_iff", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Cochain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.Cohomology.twoCochain_alt", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Cochain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.Cohomology.twoCochain_skew", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Cochain", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "LieModule.Cohomology.twoCochain_val_apply", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Cochain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.Cohomology.add_apply_apply", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Cochain", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "LieModule.Cohomology.smul_apply_apply", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Cochain", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "LieModule.Cohomology.d₁₂", "kind": "definition", "module": "Mathlib.Algebra.Lie.Cochain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LieModule.Cohomology.d₁₂_apply_apply_ofTrivial", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Cochain", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "LieModule.Cohomology.mem_twoCocycle_iff", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Cochain", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "LieDerivation.coe_ad_apply_eq_ad_apply", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Derivation.AdjointAction", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
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{"name": "LieDerivation.instLinearMapClass", "kind": "instance", "module": "Mathlib.Algebra.Lie.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LieDerivation.apply_lie_eq_sub", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LieDerivation.instInhabited", "kind": "instance", "module": "Mathlib.Algebra.Lie.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieDerivation.instAdd", "kind": "instance", "module": "Mathlib.Algebra.Lie.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LieDerivation.instNeg", "kind": "instance", "module": "Mathlib.Algebra.Lie.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LieDerivation.coe_neg_linearMap", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieDerivation.neg_apply", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieDerivation.instSub", "kind": "instance", "module": "Mathlib.Algebra.Lie.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LieDerivation.coe_sub_linearMap", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LieDerivation.coeFnAddMonoidHom", "kind": "definition", "module": "Mathlib.Algebra.Lie.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieDerivation.coeFnAddMonoidHom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LieSubmodule.lcs_le_self", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "simp", "exact"], "tactic_count": 5}
{"name": "LieSubmodule.lowerCentralSeries_eq_lcs_comap", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "simp", "have", "rw", "apply", "rw"], "tactic_count": 8}
{"name": "LieSubmodule.lowerCentralSeries_map_eq_lcs", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "LieSubmodule.lowerCentralSeries_eq_bot_iff_lcs_eq_bot", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": true, "tactics": ["refine", "rw", "simpa", "rw", "simp"], "tactic_count": 5}
{"name": "LieModule.antitone_lowerCentralSeries", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": true, "tactics": ["intro", "induction", "zero", "succ", "intro", "rcases", "rw", "exact", "exact"], "tactic_count": 9}
{"name": "LieModule.eventually_iInf_lowerCentralSeries_eq", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": true, "tactics": ["have", "obtain", "h_wf.monotone_chain_condition", "refine", "rcases", "rw", "exact"], "tactic_count": 7}
{"name": "LieModule.trivial_iff_lower_central_eq_bot", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": true, "tactics": ["constructor", "simp", "rw", "apply", "simp", "exact"], "tactic_count": 6}
{"name": "LieModule.iterate_toEnd_mem_lowerCentralSeries", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "ih", "simp", "exact"], "tactic_count": 6}
{"name": "LieModule.iterate_toEnd_mem_lowerCentralSeries₂", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "have", "simp", "refine", "exact"], "tactic_count": 7}
{"name": "LieModule.map_lowerCentralSeries_le", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "simp", "exact"], "tactic_count": 5}
{"name": "LieModule.map_lowerCentralSeries_eq", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": true, "tactics": ["apply", "induction", "zero", "succ", "simp", "apply", "assumption"], "tactic_count": 7}
{"name": "LieModule.derivedSeries_le_lowerCentralSeries", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "have", "rw", "exact"], "tactic_count": 6}
{"name": "LieModule.isNilpotent_iff", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LieModule.IsNilpotent.nilpotent", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.IsNilpotent.mk", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.iInf_lowerCentralSeries_eq_bot_of_isNilpotent", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact"], "tactic_count": 3}
{"name": "LieSubmodule.isNilpotent_iff_exists_lcs_eq_bot", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw"], "tactic_count": 3}
{"name": "LieModule.trivialIsNilpotent", "kind": "instance", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.instIsNilpotentSup", "kind": "instance", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "let", "lowerCentralSeries", "have", "have", "refine", "simp"], "tactic_count": 8}
{"name": "LieModule.exists_forall_pow_toEnd_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": true, "tactics": ["obtain", "use", "intro", "rw", "exact"], "tactic_count": 5}
{"name": "LieModule.isNilpotent_toEnd_of_isNilpotent", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": true, "tactics": ["change", "have", "tauto"], "tactic_count": 3}
{"name": "LieModule.isNilpotent_toEnd_of_isNilpotent₂", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": true, "tactics": ["obtain", "replace", "exact", "use", "ext", "rw", "exact"], "tactic_count": 7}
{"name": "LieModule.maxGenEigenSpace_toEnd_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": true, "tactics": ["ext", "simp", "obtain", "exact"], "tactic_count": 4}
{"name": "LieModule.nilpotentOfNilpotentQuotient", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": true, "tactics": ["rw", "obtain", "use", "simp", "suffices", "replace", "rwa", "rw", "exact"], "tactic_count": 9}
{"name": "LieModule.isNilpotent_quotient_iff", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw"], "tactic_count": 3}
{"name": "LieModule.iInf_lcs_le_of_isNilpotent_quot", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "LieModule.nilpotencyLength", "kind": "definition", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.nilpotencyLength_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": true, "tactics": ["let", "have", "obtain", "exact", "change", "rw", "refine", "rw", "exact"], "tactic_count": 9}
{"name": "LieModule.nilpotencyLength_eq_succ_iff", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": false, "tactics": ["have", "simp", "let", "rw", "change", "have", "rintro", "exact", "exact"], "tactic_count": 9}
{"name": "LieModule.nilpotencyLength_eq_one_iff", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "LieModule.isTrivial_of_nilpotencyLength_le_one", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": true, "tactics": ["nontriviality", "rcases", "rw", "rwa"], "tactic_count": 4}
{"name": "LieModule.lowerCentralSeriesLast", "kind": "definition", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.lowerCentralSeriesLast_le_max_triv", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": true, "tactics": ["rw", "rcases", "exact", "rw", "rw", "exact"], "tactic_count": 6}
{"name": "LieModule.nontrivial_lowerCentralSeriesLast", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": true, "tactics": ["rw", "cases", "rw", "contradiction", "rw", "exact"], "tactic_count": 6}
{"name": "LieModule.lowerCentralSeriesLast_le_of_not_isTrivial", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": true, "tactics": ["rw", "replace", "by_contra", "have", "contradiction", "rcases", "contradiction", "exact"], "tactic_count": 8}
{"name": "LieModule.disjoint_lowerCentralSeries_maxTrivSubmodule_iff", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": true, "tactics": ["refine", "nontriviality", "by_contra", "have", "le_inf_iff.mpr", "suffices", "rw", "exact"], "tactic_count": 8}
{"name": "LieModule.nontrivial_max_triv_of_isNilpotent", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.coe_lcs_range_toEnd_eq", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "ih", "simp", "simp"], "tactic_count": 6}
{"name": "LieModule.isNilpotent_range_toEnd_iff", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": true, "tactics": ["simp", "constructor"], "tactic_count": 2}
{"name": "LieSubmodule.ucs", "kind": "definition", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.ucs_zero", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.ucs_succ", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.ucs_add", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.ucs_mono", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "simp", "gcongr"], "tactic_count": 5}
{"name": "LieSubmodule.ucs_eq_self_of_normalizer_eq_self", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "LieSubmodule.ucs_le_of_normalizer_eq_self", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": true, "tactics": ["rw", "gcongr", "simp"], "tactic_count": 3}
{"name": "LieSubmodule.lcs_add_le_iff", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "LieSubmodule.lcs_le_iff", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "LieSubmodule.gc_lcs_ucs", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.ucs_eq_top_iff", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LieModule.isNilpotent_iff_exists_ucs_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LieSubmodule.ucs_comap_incl", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "LieSubmodule.isNilpotent_iff_exists_self_le_ucs", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "LieSubmodule.ucs_bot_one", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "lieModule_lcs_map_le", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "ih", "rw", "rintro", "simp", "have", "use", "simp", "obtain", "rw", "apply", "simp", "exact"], "tactic_count": 15}
{"name": "Function.Injective.lieModuleIsNilpotent", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": true, "tactics": ["obtain", "rw", "use", "rw", "apply", "simpa"], "tactic_count": 6}
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{"name": "Function.Surjective.lieModuleIsNilpotent", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": true, "tactics": ["obtain", "rw", "use", "rw", "simp"], "tactic_count": 5}
{"name": "Equiv.lieModule_isNilpotent_iff", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": true, "tactics": ["constructor", "have", "exact", "have", "refine", "rw", "f.apply_symm_apply,"], "tactic_count": 7}
{"name": "LieModule.isNilpotent_of_top_iff", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.isNilpotent_of_top_iff'", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.isNilpotent_of_le", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": true, "tactics": ["let", "let", "have", "exact"], "tactic_count": 4}
{"name": "LieModule.maxNilpotentSubmodule", "kind": "definition", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.instMaxNilpotentSubmoduleIsNilpotent", "kind": "instance", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": true, "tactics": ["have", "refine"], "tactic_count": 2}
{"name": "LieModule.isNilpotent_iff_le_maxNilpotentSubmodule", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.maxNilpotentSubmodule_eq_top_of_isNilpotent", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": true, "tactics": ["rw", "apply", "simpa"], "tactic_count": 3}
{"name": "LieAlgebra.isSolvable_of_isNilpotent", "kind": "instance", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": true, "tactics": ["obtain", "use", "exact"], "tactic_count": 3}
{"name": "LieRing.IsNilpotent", "kind": "abbrev", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieAlgebra.nilpotent_ad_of_nilpotent_algebra", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "coe_lowerCentralSeries_ideal_quot_eq", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "simp", "congr", "ext", "constructor", "rintro", "rw", "exact", "rintro", "rw", "exact"], "tactic_count": 13}
{"name": "LieModule.coe_lowerCentralSeries_ideal_le", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "simp", "apply", "rintro", "exact"], "tactic_count": 7}
{"name": "LieAlgebra.nilpotent_of_nilpotent_quotient", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": true, "tactics": ["suffices", "simp", "peel", "simp"], "tactic_count": 4}
{"name": "LieAlgebra.non_trivial_center_of_isNilpotent", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieIdeal.map_lowerCentralSeries_le", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "simp", "exact"], "tactic_count": 5}
{"name": "LieIdeal.lowerCentralSeries_map_eq", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": false, "tactics": ["have", "rw", "exact", "induction", "zero", "succ"], "tactic_count": 6}
{"name": "Function.Injective.lieAlgebra_isNilpotent", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": true, "tactics": ["rw", "peel", "apply", "apply"], "tactic_count": 4}
{"name": "Function.Surjective.lieAlgebra_isNilpotent", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": true, "tactics": ["rw", "peel", "rw", "simp"], "tactic_count": 4}
{"name": "LieEquiv.nilpotent_iff_equiv_nilpotent", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": true, "tactics": ["constructor", "exact", "exact"], "tactic_count": 3}
{"name": "LieHom.isNilpotent_range", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieAlgebra.isNilpotent_range_ad_iff", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": true, "tactics": ["refine", "have", "exact", "intro", "exact"], "tactic_count": 5}
{"name": "instIsNilpotentSubtypeMemLieSubalgebraTop", "kind": "instance", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieIdeal.lcs", "kind": "definition", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieIdeal.lcs_zero", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieIdeal.lcs_succ", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieIdeal.lcs_top", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieIdeal.coe_lcs_eq", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "ih", "simp_rw", "simp"], "tactic_count": 6}
{"name": "LieIdeal.instIsNilpotentSubtypeMemLieSubmoduleOfIsNilpotent", "kind": "instance", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": true, "tactics": ["let", "let", "have", "exact"], "tactic_count": 4}
{"name": "LieAlgebra.ad_nilpotent_of_nilpotent", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": true, "tactics": ["rw", "have", "have", "have", "exact"], "tactic_count": 5}
{"name": "LieSubalgebra.isNilpotent_ad_of_isNilpotent_ad", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": true, "tactics": ["obtain", "use", "exact"], "tactic_count": 3}
{"name": "LieAlgebra.isNilpotent_ad_of_isNilpotent", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.lowerCentralSeries_tensor_eq_baseChange", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "LieModule.instIsNilpotentTensor", "kind": "instance", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact"], "tactic_count": 3}
{"name": "LieAlgebra.maxNilpotentIdeal", "kind": "definition", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieAlgebra.maxNilpotentIdealIsNilpotent", "kind": "instance", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieAlgebra.LieIdeal.isNilpotent_iff_le_maxNilpotentIdeal", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieAlgebra.center_le_maxNilpotentIdeal", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieAlgebra.maxNilpotentIdeal_le_radical", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieAlgebra.maxNilpotentIdeal_eq_top_of_isNilpotent", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Nilpotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommutatorRing", "kind": "definition", "module": "Mathlib.Algebra.Lie.NonUnitalNonAssocAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instNonUnitalNonAssocRingCommutatorRing", "kind": "instance", "module": "Mathlib.Algebra.Lie.NonUnitalNonAssocAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieAlgebra.instNonemptyCommutatorRing", "kind": "instance", "module": "Mathlib.Algebra.Lie.NonUnitalNonAssocAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieAlgebra.instInhabitedCommutatorRing", "kind": "instance", "module": "Mathlib.Algebra.Lie.NonUnitalNonAssocAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieAlgebra.instLieRingCommutatorRing", "kind": "instance", "module": "Mathlib.Algebra.Lie.NonUnitalNonAssocAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LieAlgebra.isScalarTower", "kind": "instance", "module": "Mathlib.Algebra.Lie.NonUnitalNonAssocAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieAlgebra.smulCommClass", "kind": "instance", "module": "Mathlib.Algebra.Lie.NonUnitalNonAssocAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LieSubmodule.mem_normalizer", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Normalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LieSubmodule.monotone_normalizer", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Normalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.comap_normalizer", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Normalizer", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
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{"name": "LieSubalgebra.coe_normalizer_eq_normalizer", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Normalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LieRing.lie_apply", "kind": "theorem", "module": "Mathlib.Algebra.Lie.OfAssociative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieRingModule.ofAssociativeModule", "kind": "abbrev", "module": "Mathlib.Algebra.Lie.OfAssociative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lie_eq_smul", "kind": "theorem", "module": "Mathlib.Algebra.Lie.OfAssociative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieAlgebra.ofAssociativeAlgebra", "kind": "instance", "module": "Mathlib.Algebra.Lie.OfAssociative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.ofAssociativeModule", "kind": "theorem", "module": "Mathlib.Algebra.Lie.OfAssociative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.instLieRingModule", "kind": "instance", "module": "Mathlib.Algebra.Lie.OfAssociative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.instLieModule", "kind": "instance", "module": "Mathlib.Algebra.Lie.OfAssociative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.lie_apply", "kind": "theorem", "module": "Mathlib.Algebra.Lie.OfAssociative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.toLieHom", "kind": "definition", "module": "Mathlib.Algebra.Lie.OfAssociative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.instCoeLieHom", "kind": "instance", "module": "Mathlib.Algebra.Lie.OfAssociative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.coe_toLieHom", "kind": "theorem", "module": "Mathlib.Algebra.Lie.OfAssociative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.toLieHom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Lie.OfAssociative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.toLieHom_id", "kind": "theorem", "module": "Mathlib.Algebra.Lie.OfAssociative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.toLieHom_comp", "kind": "theorem", "module": "Mathlib.Algebra.Lie.OfAssociative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LieModule.toEnd", "kind": "definition", "module": "Mathlib.Algebra.Lie.OfAssociative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieAlgebra.ad", "kind": "definition", "module": "Mathlib.Algebra.Lie.OfAssociative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieAlgebra.ad_apply", "kind": "theorem", "module": "Mathlib.Algebra.Lie.OfAssociative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.toEnd_module_end", "kind": "theorem", "module": "Mathlib.Algebra.Lie.OfAssociative", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "LieSubalgebra.toEnd_eq", "kind": "theorem", "module": "Mathlib.Algebra.Lie.OfAssociative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubalgebra.toEnd_mk", "kind": "theorem", "module": "Mathlib.Algebra.Lie.OfAssociative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.toEnd_eq_iff", "kind": "theorem", "module": "Mathlib.Algebra.Lie.OfAssociative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.ext_of_isFaithful", "kind": "theorem", "module": "Mathlib.Algebra.Lie.OfAssociative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.toEnd_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Lie.OfAssociative", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
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{"name": "LieModule.instIsFaithfulEnd", "kind": "instance", "module": "Mathlib.Algebra.Lie.OfAssociative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.coe_toEnd", "kind": "theorem", "module": "Mathlib.Algebra.Lie.OfAssociative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LieSubmodule.Quotient.lieQuotientLieAlgebra", "kind": "instance", "module": "Mathlib.Algebra.Lie.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LieSubmodule.Quotient.mk_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LieHom.rangeRestrict", "kind": "definition", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieHom.rangeRestrict_apply", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieHom.surjective_rangeRestrict", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": true, "tactics": ["rintro", "rw", "use", "simp"], "tactic_count": 4}
{"name": "LieHom.equivRangeOfInjective", "kind": "definition", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieHom.equivRangeOfInjective_apply", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.exists_lieSubalgebra_coe_eq_iff", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "exact", "intro", "use"], "tactic_count": 5}
{"name": "LieSubalgebra.incl_range", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "LieSubalgebra.map", "kind": "definition", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubalgebra.mem_map", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubalgebra.mem_map_submodule", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubalgebra.comap", "kind": "definition", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubalgebra.mem_comap", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubalgebra.instPartialOrder_1", "kind": "instance", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubalgebra.le_def", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubalgebra.toSubmodule_le_toSubmodule", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubalgebra.instBot", "kind": "instance", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubalgebra.bot_coe", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubalgebra.bot_toSubmodule", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubalgebra.toSubmodule_eq_bot", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LieSubalgebra.mem_bot", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubalgebra.instTop", "kind": "instance", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubalgebra.top_coe", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubalgebra.top_toSubmodule", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubalgebra.toSubmodule_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LieSubalgebra.mem_top", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieHom.range_eq_map", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "LieSubalgebra.instMin", "kind": "instance", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubalgebra.instInfSet", "kind": "instance", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubalgebra.coe_inf", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubalgebra.sInf_toSubmodule", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubalgebra.coe_sInf", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": true, "tactics": ["rw", "ext", "simp"], "tactic_count": 3}
{"name": "LieSubalgebra.sInf_glb", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": false, "tactics": ["have", "intros", "exact", "apply", "simp", "exact"], "tactic_count": 6}
{"name": "LieSubalgebra.completeLattice", "kind": "instance", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubalgebra.instAdd", "kind": "instance", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubalgebra.instZero", "kind": "instance", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubalgebra.addCommMonoid", "kind": "instance", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubalgebra.instIsOrderedAddMonoid", "kind": "instance", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubalgebra.instCanonicallyOrderedAdd", "kind": "instance", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubalgebra.add_eq_sup", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubalgebra.inf_toSubmodule", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubalgebra.mem_inf", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LieSubalgebra.eq_bot_iff", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "LieSubalgebra.subsingleton_of_bot", "kind": "instance", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": true, "tactics": ["apply", "ext", "simp", "rfl"], "tactic_count": 4}
{"name": "LieSubalgebra.subsingleton_bot", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubalgebra.wellFoundedGT_of_noetherian", "kind": "instance", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubalgebra.inclusion", "kind": "definition", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubalgebra.coe_inclusion", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubalgebra.inclusion_apply", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubalgebra.inclusion_injective", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubalgebra.ofLe", "kind": "definition", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubalgebra.mem_ofLe", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": true, "tactics": ["simp", "constructor", "rintro", "exact", "intro", "use"], "tactic_count": 6}
{"name": "LieSubalgebra.ofLe_eq_comap_incl", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": true, "tactics": ["ext", "rw", "rfl"], "tactic_count": 3}
{"name": "LieSubalgebra.coe_ofLe", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubalgebra.equivOfLe", "kind": "definition", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubalgebra.equivOfLe_apply", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubalgebra.map_le_iff_le_comap", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubalgebra.gc_map_comap", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubalgebra.lieSpan", "kind": "definition", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubalgebra.mem_lieSpan", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "LieSubalgebra.subset_lieSpan", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": true, "tactics": ["intro", "rw", "intro", "exact"], "tactic_count": 4}
{"name": "LieSubalgebra.submodule_span_le_lieSpan", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "LieSubalgebra.lieSpan_le", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": true, "tactics": ["constructor", "exact", "intro", "rw", "exact"], "tactic_count": 5}
{"name": "LieSubalgebra.lieSpan_mono", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "LieSubalgebra.lieSpan_eq", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubalgebra.coe_lieSpan_submodule_eq_iff", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "exact", "rw"], "tactic_count": 5}
{"name": "LieSubalgebra.coe_lieSpan_eq_span_of_forall_lie_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": false, "tactics": ["suffices", "refine", "change", "rw", "exact", "intro", "induction", "mem_mem", "zero_left", "zero_right", "add_left", "add_right", "smul_left", "smul_right"], "tactic_count": 14}
{"name": "LieSubalgebra.gi", "kind": "definition", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubalgebra.span_empty", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubalgebra.span_univ", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubalgebra.span_union", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubalgebra.span_iUnion", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubalgebra.lieSpan_induction", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": false, "tactics": ["let", "add_mem", "zero_mem", "smul_mem", "lie_mem", "exact"], "tactic_count": 6}
{"name": "LieEquiv.ofInjective", "kind": "definition", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieEquiv.ofInjective_apply", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieEquiv.ofEq", "kind": "definition", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieEquiv.ofEq_apply", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieEquiv.lieSubalgebraMap", "kind": "definition", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieEquiv.lieSubalgebraMap_apply", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieEquiv.ofSubalgebras", "kind": "definition", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieEquiv.ofSubalgebras_apply", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieEquiv.ofSubalgebras_symm_apply", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.instSetLike", "kind": "instance", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.instPartialOrder", "kind": "instance", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.instAddSubgroupClass", "kind": "instance", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.instSMulMemClass", "kind": "instance", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.instZero", "kind": "instance", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.instInhabited", "kind": "instance", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.coeSort", "kind": "instance", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.coeSubmodule", "kind": "instance", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.instCanLiftSubmoduleToSubmoduleForallForallForallMemBracket", "kind": "instance", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.coe_toSubmodule", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.mem_carrier", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.mem_mk_iff", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.mem_mk_iff'", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.mem_toSubmodule", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.mem_coe", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.zero_mem", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.mk_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.coe_toSet_mk", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.toSubmodule_mk", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "LieSubmodule.toSubmodule_injective", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.ext", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.toSubmodule_inj", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.copy", "kind": "definition", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.coe_copy", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.copy_eq", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.instLieRingModuleSubtypeMem", "kind": "instance", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.coe_zero", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.coe_add", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.coe_neg", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.coe_sub", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.coe_smul", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.coe_bracket", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.instIsNoetherianSubtypeMem", "kind": "instance", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.instIsArtinianSubtypeMem", "kind": "instance", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.instIsTorsionFreeSubtypeMem", "kind": "instance", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.instLieModule", "kind": "instance", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.instUniqueOfSubsingleton", "kind": "instance", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.exists_lieSubmodule_coe_eq_iff", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "intro"], "tactic_count": 3}
{"name": "LieSubalgebra.toLieSubmodule", "kind": "definition", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubalgebra.coe_toLieSubmodule", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubalgebra.mem_toLieSubmodule", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.coe_injective", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.toSubmodule_le_toSubmodule", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.instBot", "kind": "instance", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.instUniqueBot", "kind": "instance", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.bot_coe", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.bot_toSubmodule", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.toSubmodule_eq_bot", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LieSubmodule.mk_eq_bot_iff", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LieSubmodule.mem_bot", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.instTop", "kind": "instance", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.top_coe", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.top_toSubmodule", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.toSubmodule_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LieSubmodule.mk_eq_top_iff", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LieSubmodule.mem_top", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.instMin", "kind": "instance", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.instInfSet", "kind": "instance", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.coe_inf", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.inf_toSubmodule", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.sInf_toSubmodule", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.sInf_toSubmodule_eq_iInf", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LieSubmodule.iInf_toSubmodule", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LieSubmodule.coe_sInf", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": true, "tactics": ["rw", "ext", "simp"], "tactic_count": 3}
{"name": "LieSubmodule.coe_iInf", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LieSubmodule.mem_iInf", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LieSubmodule.instMax", "kind": "instance", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.instSupSet", "kind": "instance", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.sup_toSubmodule", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "LieSubmodule.sSup_toSubmodule", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.sSup_toSubmodule_eq_iSup", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LieSubmodule.iSup_toSubmodule", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LieSubmodule.instCompleteLattice", "kind": "instance", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.mem_iSup_of_mem", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.iSup_induction", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "LieSubmodule.iSup_induction'", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": true, "tactics": ["refine", "refine", "iSup_induction", "exact", "exact", "rintro", "exact"], "tactic_count": 7}
{"name": "LieSubmodule.disjoint_toSubmodule", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LieSubmodule.codisjoint_toSubmodule", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LieSubmodule.isCompl_toSubmodule", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LieSubmodule.iSupIndep_toSubmodule", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LieSubmodule.iSup_toSubmodule_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LieSubmodule.instAdd", "kind": "instance", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.instAddCommMonoid", "kind": "instance", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.add_eq_sup", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.mem_inf", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LieSubmodule.mem_sup", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LieSubmodule.eq_bot_iff", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LieSubmodule.subsingleton_of_bot", "kind": "instance", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": true, "tactics": ["apply", "subsingleton"], "tactic_count": 2}
{"name": "LieSubmodule.instIsModularLattice", "kind": "instance", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.toSubmodule_orderEmbedding", "kind": "definition", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.wellFoundedGT_of_noetherian", "kind": "instance", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.wellFoundedLT_of_isArtinian", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.instIsAtomicOfIsArtinian", "kind": "instance", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.subsingleton_iff", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.nontrivial_iff", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.instNontrivial", "kind": "instance", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.nontrivial_iff_ne_bot", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "simp", "contrapose", "rw", "rintro", "simpa"], "tactic_count": 7}
{"name": "LieSubmodule.incl", "kind": "definition", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.incl_coe", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.incl_apply", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.incl_eq_val", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.injective_incl", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.inclusion", "kind": "definition", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.coe_inclusion", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.inclusion_apply", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.inclusion_injective", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.lieSpan", "kind": "definition", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.mem_lieSpan", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "LieSubmodule.subset_lieSpan", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": true, "tactics": ["intro", "rw", "intro", "exact"], "tactic_count": 4}
{"name": "LieSubmodule.submodule_span_le_lieSpan", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "LieSubmodule.lieSpan_le", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": true, "tactics": ["constructor", "exact", "intro"], "tactic_count": 3}
{"name": "LieSubmodule.lieSpan_mono", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "LieSubmodule.lieSpan_eq", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.coe_lieSpan_submodule_eq_iff", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw"], "tactic_count": 3}
{"name": "LieSubmodule.gi", "kind": "definition", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.span_empty", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.span_univ", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.lieSpan_eq_bot_iff", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LieSubmodule.span_union", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.span_iUnion", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.lieSpan_induction", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": ["let", "add_mem", "zero_mem", "smul_mem", "lie_mem", "exact"], "tactic_count": 6}
{"name": "LieSubmodule.isCompactElement_lieSpan_singleton", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": true, "tactics": ["rw", "intro", "replace", "suffices", "replace", "have", "simp_rw", "rw"], "tactic_count": 8}
{"name": "LieSubmodule.sSup_image_lieSpan_singleton", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": true, "tactics": ["refine", "simp_rw", "refine", "replace", "exact"], "tactic_count": 5}
{"name": "LieSubmodule.instIsCompactlyGenerated", "kind": "instance", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.map", "kind": "definition", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.coe_map", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.toSubmodule_map", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.comap", "kind": "definition", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.toSubmodule_comap", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.map_le_iff_le_comap", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.gc_map_comap", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.map_inf_le", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.map_inf", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.map_sup", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.comap_inf", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.map_iSup", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.mem_map", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.mem_map_of_mem", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.mem_comap", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.comap_incl_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LieSubmodule.comap_incl_eq_bot", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": true, "tactics": ["simp", "rw"], "tactic_count": 2}
{"name": "LieSubmodule.map_mono", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.map_comp", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.map_id", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "LieSubmodule.map_bot", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "LieSubmodule.map_le_map_iff", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.map_injective_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.mapOrderEmbedding", "kind": "definition", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.equivMapOfInjective", "kind": "definition", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.orderIsoMapComap", "kind": "definition", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModuleHom.ker", "kind": "definition", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModuleHom.ker_toSubmodule", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModuleHom.ker_eq_bot", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": true, "tactics": ["rw", "coe_toLinearMap]"], "tactic_count": 2}
{"name": "LieModuleHom.mem_ker", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModuleHom.ker_id", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModuleHom.comp_ker_incl", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "LieModuleHom.le_ker_iff_map", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LieModuleHom.range", "kind": "definition", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModuleHom.coe_range", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModuleHom.toSubmodule_range", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModuleHom.mem_range", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModuleHom.map_top", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "LieModuleHom.range_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LieModuleHom.codRestrict", "kind": "definition", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModuleHom.codRestrict_apply", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.ker_incl", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieSubmodule.range_incl", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": true, "tactics": ["simp", "rw"], "tactic_count": 2}
{"name": "LieSubmodule.comap_incl_self", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": true, "tactics": ["simp", "rw"], "tactic_count": 2}
{"name": "LieSubmodule.map_incl_top", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LieSubmodule.map_le_range", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "LieSubmodule.map_incl_lt_iff_lt_top", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "LieSubmodule.map_incl_le", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": true, "tactics": ["conv_rhs", "exact"], "tactic_count": 2}
{"name": "LieModuleEquiv.ofTop", "kind": "definition", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModuleEquiv.ofTop_apply", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LieModule.Weight.apply_eq_zero_of_isNilpotent", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.zero_genWeightSpace_eq_top_of_nilpotent'", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "LieModule.isNilpotent_toEnd_genWeightSpace_zero", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
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{"name": "LieModule.genWeightSpace_zero_normalizer_eq_self", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.Basic", "is_tactic_proof": true, "tactics": ["refine", "intro", "rw", "simp", "intro", "obtain", "use", "simpa"], "tactic_count": 8}
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{"name": "LieModule.mem_posFittingCompOf", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LieModule.posFittingCompOf_le_lowerCentralSeries", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.Basic", "is_tactic_proof": false, "tactics": ["suffices", "intro", "obtain", "exact", "intro", "induction", "zero", "succ", "simp", "exact"], "tactic_count": 10}
{"name": "LieModule.posFittingCompOf_eq_bot_of_isNilpotent", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "posFittingCompOf_le_lowerCentralSeries,"], "tactic_count": 2}
{"name": "LieModule.posFittingComp", "kind": "definition", "module": "Mathlib.Algebra.Lie.Weights.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.mem_posFittingComp", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.Basic", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "LieModule.posFittingCompOf_le_posFittingComp", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LieModule.posFittingComp_le_iInf_lowerCentralSeries", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LieModule.iInf_lowerCentralSeries_eq_posFittingComp", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.Basic", "is_tactic_proof": true, "tactics": ["refine", "apply", "rw", "intro", "obtain", "use", "ext", "set", "replace", "apply", "simp_rw", "apply", "suffices", "have", "simpa"], "tactic_count": 15}
{"name": "LieModule.posFittingComp_eq_bot_of_isNilpotent", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LieModule.map_posFittingComp_le", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp", "simp", "intro", "obtain", "use", "rw"], "tactic_count": 8}
{"name": "LieModule.map_genWeightSpace_le", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.Basic", "is_tactic_proof": true, "tactics": ["rw", "intro", "simp", "intro", "have", "obtain", "refine", "simpa"], "tactic_count": 8}
{"name": "LieModule.comap_genWeightSpace_eq_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.Basic", "is_tactic_proof": true, "tactics": ["refine", "simp", "simp", "intro", "have", "obtain", "use", "suffices", "simpa", "rw", "exact"], "tactic_count": 11}
{"name": "LieModule.map_genWeightSpace_eq_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.Basic", "is_tactic_proof": true, "tactics": ["refine", "rintro", "simp", "exact"], "tactic_count": 4}
{"name": "LieModule.map_genWeightSpace_eq", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LieModule.map_posFittingComp_eq", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.Basic", "is_tactic_proof": true, "tactics": ["refine", "suffices", "rw", "exact", "rw", "convert", "ext", "simp"], "tactic_count": 8}
{"name": "LieModule.posFittingComp_map_incl_sup_of_codisjoint", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.Basic", "is_tactic_proof": false, "tactics": ["obtain", "obtain", "simp_rw"], "tactic_count": 3}
{"name": "LieModule.genWeightSpace_genWeightSpaceOf_map_incl", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.Basic", "is_tactic_proof": true, "tactics": ["simpa", "genWeightSpace_le_genWeightSpaceOf"], "tactic_count": 2}
{"name": "LieModule.isCompl_genWeightSpaceOf_zero_posFittingCompOf", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.Basic", "is_tactic_proof": true, "tactics": ["simpa", "coe_genWeightSpaceOf_zero]"], "tactic_count": 2}
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{"name": "LieModule.disjoint_genWeightSpaceOf", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.Basic", "is_tactic_proof": true, "tactics": ["rw", "dsimp", "exact"], "tactic_count": 3}
{"name": "LieModule.disjoint_genWeightSpace", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.Basic", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "LieModule.injOn_genWeightSpace", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.Basic", "is_tactic_proof": true, "tactics": ["rintro", "contrapose", "simpa"], "tactic_count": 3}
{"name": "LieModule.iSupIndep_genWeightSpace", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.Basic", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
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{"name": "LieModule.iSupIndep_genWeightSpaceOf", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.Basic", "is_tactic_proof": true, "tactics": ["rw", "dsimp", "exact"], "tactic_count": 3}
{"name": "LieModule.finite_genWeightSpaceOf_ne_bot", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.finite_genWeightSpace_ne_bot", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LieModule.Weight.instFintype", "kind": "instance", "module": "Mathlib.Algebra.Lie.Weights.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.instIsTriangularizableSubtypeMemLieSubalgebra", "kind": "instance", "module": "Mathlib.Algebra.Lie.Weights.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.instIsTriangularizableSubtypeMemLieSubmodule", "kind": "instance", "module": "Mathlib.Algebra.Lie.Weights.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.instIsTriangularizableSubtypeEndMemLieSubalgebraRangeToEnd", "kind": "instance", "module": "Mathlib.Algebra.Lie.Weights.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.iSup_genWeightSpaceOf_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.Basic", "is_tactic_proof": true, "tactics": ["rw", "dsimp", "exact"], "tactic_count": 3}
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{"name": "LieModule.instIsTriangularizableSubtypeMemLieSubmodule_1", "kind": "instance", "module": "Mathlib.Algebra.Lie.Weights.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "LieModule.iSup_genWeightSpace_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.Basic", "is_tactic_proof": false, "tactics": ["simp", "refine", "apply"], "tactic_count": 3}
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{"name": "LieAlgebra.rootSpace", "kind": "abbrev", "module": "Mathlib.Algebra.Lie.Weights.Cartan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieAlgebra.zero_rootSpace_eq_top_of_nilpotent", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.Cartan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieAlgebra.rootSpace_comap_eq_genWeightSpace", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.Cartan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LieAlgebra.rootSpaceWeightSpaceProduct", "kind": "definition", "module": "Mathlib.Algebra.Lie.Weights.Cartan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieAlgebra.coe_rootSpaceWeightSpaceProduct_tmul", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.Cartan", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LieAlgebra.mapsTo_toEnd_genWeightSpace_add_of_mem_rootSpace", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.Cartan", "is_tactic_proof": true, "tactics": ["intro", "let", "let", "exact"], "tactic_count": 4}
{"name": "LieAlgebra.rootSpaceProduct", "kind": "definition", "module": "Mathlib.Algebra.Lie.Weights.Cartan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieAlgebra.rootSpaceProduct_def", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.Cartan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieAlgebra.rootSpaceProduct_tmul", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.Cartan", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LieAlgebra.zeroRootSubalgebra", "kind": "definition", "module": "Mathlib.Algebra.Lie.Weights.Cartan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieAlgebra.coe_zeroRootSubalgebra", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.Cartan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieAlgebra.mem_zeroRootSubalgebra", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.Cartan", "is_tactic_proof": true, "tactics": ["change", "simp"], "tactic_count": 2}
{"name": "LieAlgebra.toLieSubmodule_le_rootSpace_zero", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.Cartan", "is_tactic_proof": true, "tactics": ["intro", "simp", "simp", "intro", "obtain", "use", "let", "let", "have", "change", "rw", "have", "rw", "simp", "exact"], "tactic_count": 15}
{"name": "LieAlgebra.instNontrivialSubtypeMemLieSubmoduleLieSubalgebraGenWeightSpaceOfNatForall", "kind": "instance", "module": "Mathlib.Algebra.Lie.Weights.Cartan", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "LieAlgebra.le_zeroRootSubalgebra", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.Cartan", "is_tactic_proof": false, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "LieAlgebra.zeroRootSubalgebra_normalizer_eq_self", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.Cartan", "is_tactic_proof": true, "tactics": ["refine", "intro", "rw", "rw", "rintro", "specialize", "rw", "obtain", "rw", "use", "rw"], "tactic_count": 11}
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{"name": "LieAlgebra.zeroRootSubalgebra_eq_of_is_cartan", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.Cartan", "is_tactic_proof": true, "tactics": ["refine", "suffices", "obtain", "exact"], "tactic_count": 4}
{"name": "LieAlgebra.zeroRootSubalgebra_eq_iff_is_cartan", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.Cartan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieAlgebra.rootSpace_zero_eq", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.Cartan", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LieAlgebra.corootSpace", "kind": "definition", "module": "Mathlib.Algebra.Lie.Weights.Cartan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieAlgebra.mem_corootSpace", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.Cartan", "is_tactic_proof": false, "tactics": ["have", "rw", "simp", "rfl", "simp_rw", "exists_exists_exists_and_eq]", "change", "simp"], "tactic_count": 8}
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{"name": "LieAlgebra.cartan_sup_iSup_rootSpace_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.Cartan", "is_tactic_proof": true, "tactics": ["rw", "intro", "by_cases", "simp", "exact"], "tactic_count": 5}
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{"name": "LieModule.genWeightSpaceChain_def", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.genWeightSpaceChain_def'", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.Chain", "is_tactic_proof": true, "tactics": ["have", "simp_rw"], "tactic_count": 2}
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{"name": "LieModule.genWeightSpace_le_genWeightSpaceChain", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LieModule.chainTopCoeff", "kind": "definition", "module": "Mathlib.Algebra.Lie.Weights.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.chainBotCoeff", "kind": "definition", "module": "Mathlib.Algebra.Lie.Weights.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.chainTopCoeff_neg", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.chainBotCoeff_neg", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.Chain", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LieModule.chainTopCoeff_zero", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.chainBotCoeff_zero", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LieModule.Weight.toLinear_neg", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.Killing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LieSubalgebra.root", "kind": "abbrev", "module": "Mathlib.Algebra.Lie.Weights.Killing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieAlgebra.IsKilling.restrict_killingForm_eq_sum", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.Killing", "is_tactic_proof": true, "tactics": ["rw", "refine", "replace", "simp"], "tactic_count": 4}
{"name": "LieModule.Weight.toLinear", "kind": "definition", "module": "Mathlib.Algebra.Lie.Weights.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.Weight.instCoeLinearMap", "kind": "instance", "module": "Mathlib.Algebra.Lie.Weights.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.Weight.instLinearMapClass", "kind": "instance", "module": "Mathlib.Algebra.Lie.Weights.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.Weight.apply_lie", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.Weight.coe_coe", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.Weight.coe_toLinear_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.Weight.coe_toLinear_ne_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.Linear", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LieModule.Weight.ker", "kind": "abbrev", "module": "Mathlib.Algebra.Lie.Weights.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.instLinearWeightsOfIsLieAbelian", "kind": "instance", "module": "Mathlib.Algebra.Lie.Weights.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.trace_comp_toEnd_genWeightSpace_eq", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.Linear", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "LieModule.zero_lt_finrank_genWeightSpace", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.Linear", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "LieModule.instLinearWeightsOfCharZero", "kind": "instance", "module": "Mathlib.Algebra.Lie.Weights.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.shiftedGenWeightSpace", "kind": "definition", "module": "Mathlib.Algebra.Lie.Weights.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Lie.Weights.Linear.0.LieModule.shiftedGenWeightSpace.aux", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.shiftedGenWeightSpace.instLieRingModuleSubtypeMemLieSubmodule", "kind": "instance", "module": "Mathlib.Algebra.Lie.Weights.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.shiftedGenWeightSpace.coe_lie_shiftedGenWeightSpace_apply", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.shiftedGenWeightSpace.instSubtypeMemLieSubmodule", "kind": "instance", "module": "Mathlib.Algebra.Lie.Weights.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.shiftedGenWeightSpace.shift", "kind": "definition", "module": "Mathlib.Algebra.Lie.Weights.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.shiftedGenWeightSpace.toEnd_eq", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.Linear", "is_tactic_proof": true, "tactics": ["tauto"], "tactic_count": 1}
{"name": "LieModule.shiftedGenWeightSpace.instIsNilpotentSubtypeMemLieSubmoduleOfIsNoetherian", "kind": "instance", "module": "Mathlib.Algebra.Lie.Weights.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieModule.exists_forall_lie_eq_smul", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.Linear", "is_tactic_proof": false, "tactics": ["replace", "obtain", "simp_rw", "refine", "intro", "have", "rwa"], "tactic_count": 7}
{"name": "LieModule.exists_nontrivial_weightSpace_of_isNilpotent", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.Linear", "is_tactic_proof": false, "tactics": ["obtain", "by_contra", "simpa", "obtain", "simp", "exact"], "tactic_count": 6}
{"name": "_private.Mathlib.Algebra.Lie.Weights.RootSystem.0.LieAlgebra.IsKilling.chainLength_aux", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.RootSystem", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "obtain", "obtain", "have", "have", "obtain", "exact"], "tactic_count": 8}
{"name": "LieAlgebra.IsKilling.chainLength", "kind": "definition", "module": "Mathlib.Algebra.Lie.Weights.RootSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieAlgebra.IsKilling.chainLength_of_isZero", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.RootSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieAlgebra.IsKilling.chainLength_nsmul", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.RootSystem", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "let", "have", "obtain", "simpa", "rw"], "tactic_count": 7}
{"name": "LieAlgebra.IsKilling.chainLength_smul", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.RootSystem", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LieAlgebra.IsKilling.apply_coroot_eq_cast'", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.RootSystem", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "mul_zero,", "obtain", "have", "rw", "coe_chainTop',", "simp"], "tactic_count": 8}
{"name": "LieAlgebra.IsKilling.rootSpace_neg_nsmul_add_chainTop_of_le", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.RootSystem", "is_tactic_proof": true, "tactics": ["by_cases", "simpa", "obtain", "obtain", "obtain", "have", "have", "simp", "exact"], "tactic_count": 9}
{"name": "LieAlgebra.IsKilling.rootSpace_neg_nsmul_add_chainTop_of_lt", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.RootSystem", "is_tactic_proof": true, "tactics": ["by_contra", "let", "have", "have", "have", "simp", "lia", "have", "simp", "congr", "ring", "have", "rw", "exact"], "tactic_count": 14}
{"name": "LieAlgebra.IsKilling.chainTopCoeff_le_chainLength", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.RootSystem", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "rw", "intro", "apply", "rw", "exact"], "tactic_count": 7}
{"name": "LieAlgebra.IsKilling.chainBotCoeff_add_chainTopCoeff", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.RootSystem", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "apply", "rw", "intro", "apply", "rw", "add_smul,", "exact", "rw", "intro", "apply", "rw", "neg_add,", "exact"], "tactic_count": 15}
{"name": "LieAlgebra.IsKilling.chainTopCoeff_add_chainBotCoeff", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.RootSystem", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LieAlgebra.IsKilling.chainBotCoeff_le_chainLength", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.RootSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieAlgebra.IsKilling.chainLength_neg", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.RootSystem", "is_tactic_proof": true, "tactics": ["rw", "chainBotCoeff_neg]"], "tactic_count": 2}
{"name": "LieAlgebra.IsKilling.chainLength_zero", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.RootSystem", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LieAlgebra.IsKilling.apply_coroot_eq_cast", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.RootSystem", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LieAlgebra.IsKilling.le_chainBotCoeff_of_rootSpace_ne_top", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.RootSystem", "is_tactic_proof": true, "tactics": ["contrapose", "lift", "rw", "have", "rwa", "neg_add_cancel,"], "tactic_count": 6}
{"name": "LieAlgebra.IsKilling.rootSpace_zsmul_add_ne_bot_iff", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.RootSystem", "is_tactic_proof": true, "tactics": ["constructor", "refine", "rw", "apply", "rwa", "rintro", "set", "lift", "rw", "subst", "simp", "have", "rwa"], "tactic_count": 13}
{"name": "LieAlgebra.IsKilling.rootSpace_zsmul_add_ne_bot_iff_mem", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.RootSystem", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LieAlgebra.IsKilling.chainTopCoeff_of_eq_zsmul_add", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.RootSystem", "is_tactic_proof": true, "tactics": ["apply", "refine", "rw", "exact", "refine", "rw", "exact"], "tactic_count": 7}
{"name": "LieAlgebra.IsKilling.chainBotCoeff_of_eq_zsmul_add", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.RootSystem", "is_tactic_proof": true, "tactics": ["have", "rw", "sub_neg_eq_add]"], "tactic_count": 3}
{"name": "LieAlgebra.IsKilling.chainLength_of_eq_zsmul_add", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.RootSystem", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "apply", "rw", "chainTopCoeff_of_eq_zsmul_add", "add_add_add_comm,"], "tactic_count": 6}
{"name": "LieAlgebra.IsKilling.chainTopCoeff_zero_right", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.RootSystem", "is_tactic_proof": true, "tactics": ["symm", "apply", "rw", "intro", "exact", "α.2", "obtain", "obtain", "obtain", "have", "have", "obtain", "have", "convert", "rw", "simpa", "apply_fun", "simp", "intro", "refine", "have", "simp", "rwa"], "tactic_count": 23}
{"name": "LieAlgebra.IsKilling.chainBotCoeff_zero_right", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.RootSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieAlgebra.IsKilling.chainLength_zero_right", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.RootSystem", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LieAlgebra.IsKilling.rootSpace_two_smul", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.RootSystem", "is_tactic_proof": true, "tactics": ["cases", "exact", "simpa"], "tactic_count": 3}
{"name": "LieAlgebra.IsKilling.rootSpace_one_div_two_smul", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.RootSystem", "is_tactic_proof": true, "tactics": ["by_contra", "let", "have", "change", "rw", "apply", "have", "rwa"], "tactic_count": 8}
{"name": "LieAlgebra.IsKilling.eq_neg_one_or_eq_zero_or_eq_one_of_eq_smul", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.RootSystem", "is_tactic_proof": true, "tactics": ["cases", "exact", "have", "rw", "simp", "rcases", "rw", "simp", "rw", "have", "rw", "set", "subst", "have", "change", "exact", "simpa", "apply_fun", "rw", "have", "have", "swap", "simp", "rw", "lia", "rw", "simp", "cases"], "tactic_count": 28}
{"name": "LieAlgebra.IsKilling.eq_neg_or_eq_of_eq_smul", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.RootSystem", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "rcases", "exact", "cases", "exact"], "tactic_count": 6}
{"name": "LieAlgebra.IsKilling.reflectRoot", "kind": "definition", "module": "Mathlib.Algebra.Lie.Weights.RootSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieAlgebra.IsKilling.reflectRoot_isNonZero", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.RootSystem", "is_tactic_proof": true, "tactics": ["intro", "have", "by_cases", "simp", "simpa", "have", "exact"], "tactic_count": 7}
{"name": "LieAlgebra.IsKilling.rootSystem", "kind": "definition", "module": "Mathlib.Algebra.Lie.Weights.RootSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieAlgebra.IsKilling.instIsRootSystemSubtypeWeightMemLieSubalgebraFinsetRootDualRootSystem", "kind": "instance", "module": "Mathlib.Algebra.Lie.Weights.RootSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieAlgebra.IsKilling.corootForm_rootSystem_eq_killing", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.RootSystem", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "LieAlgebra.IsKilling.rootSystem_toLinearMap_apply", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.RootSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieAlgebra.IsKilling.rootSystem_pairing_apply", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.RootSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieAlgebra.IsKilling.rootSystem_root_apply", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.RootSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieAlgebra.IsKilling.rootSystem_coroot_apply", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.RootSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieAlgebra.IsKilling.biSup_corootSpace_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.RootSystem", "is_tactic_proof": false, "tactics": ["simp", "congr", "ext", "simp"], "tactic_count": 4}
{"name": "LieAlgebra.IsKilling.biSup_corootSubmodule_eq_cartan", "kind": "theorem", "module": "Mathlib.Algebra.Lie.Weights.RootSystem", "is_tactic_proof": false, "tactics": ["suffices", "le_antisymm", "simp"], "tactic_count": 3}
{"name": "LieAlgebra.IsKilling.instIsCrystallographicSubtypeWeightMemLieSubalgebraFinsetRootDualRootSystem", "kind": "instance", "module": "Mathlib.Algebra.Lie.Weights.RootSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieAlgebra.IsKilling.instIsReducedSubtypeWeightMemLieSubalgebraFinsetRootDualRootSystem", "kind": "instance", "module": "Mathlib.Algebra.Lie.Weights.RootSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInhabitedLinearRecurrence", "kind": "instance", "module": "Mathlib.Algebra.LinearRecurrence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearRecurrence.IsSolution", "kind": "definition", "module": "Mathlib.Algebra.LinearRecurrence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearRecurrence.mkSol", "kind": "definition", "module": "Mathlib.Algebra.LinearRecurrence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearRecurrence.is_sol_mkSol", "kind": "theorem", "module": "Mathlib.Algebra.LinearRecurrence", "is_tactic_proof": true, "tactics": ["intro", "rw", "simp"], "tactic_count": 3}
{"name": "LinearRecurrence.mkSol_eq_init", "kind": "theorem", "module": "Mathlib.Algebra.LinearRecurrence", "is_tactic_proof": true, "tactics": ["intro", "rw", "simp"], "tactic_count": 3}
{"name": "LinearRecurrence.eq_mk_of_is_sol_of_eq_init", "kind": "theorem", "module": "Mathlib.Algebra.LinearRecurrence", "is_tactic_proof": true, "tactics": ["intro", "rw", "split_ifs", "exact", "dsimp", "rw", "congr", "rw", "simp"], "tactic_count": 9}
{"name": "LinearRecurrence.eq_mk_of_is_sol_of_eq_init'", "kind": "theorem", "module": "Mathlib.Algebra.LinearRecurrence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearRecurrence.solSpace", "kind": "definition", "module": "Mathlib.Algebra.LinearRecurrence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearRecurrence.is_sol_iff_mem_solSpace", "kind": "theorem", "module": "Mathlib.Algebra.LinearRecurrence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearRecurrence.toInit", "kind": "definition", "module": "Mathlib.Algebra.LinearRecurrence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearRecurrence.sol_eq_of_eq_init", "kind": "theorem", "module": "Mathlib.Algebra.LinearRecurrence", "is_tactic_proof": true, "tactics": ["refine", "intro", "set", "set", "change", "suffices", "rw", "ext", "exact"], "tactic_count": 9}
{"name": "LinearRecurrence.tupleSucc", "kind": "definition", "module": "Mathlib.Algebra.LinearRecurrence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearRecurrence.solSpace_rank", "kind": "theorem", "module": "Mathlib.Algebra.LinearRecurrence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearRecurrence.charPoly", "kind": "definition", "module": "Mathlib.Algebra.LinearRecurrence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearRecurrence.geom_sol_iff_root_charPoly", "kind": "theorem", "module": "Mathlib.Algebra.LinearRecurrence", "is_tactic_proof": true, "tactics": ["rw", "simp", "constructor", "intro", "simpa", "intro", "simp", "exact"], "tactic_count": 8}
{"name": "Units.neg_smul", "kind": "theorem", "module": "Mathlib.Algebra.Module.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "invOf_two_smul_add_invOf_two_smul", "kind": "theorem", "module": "Mathlib.Algebra.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "map_inv_natCast_smul", "kind": "theorem", "module": "Mathlib.Algebra.Module.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "suffices", "clear", "intro", "rw", "simp", "suffices", "clear", "intro", "rw", "rw"], "tactic_count": 12}
{"name": "map_inv_intCast_smul", "kind": "theorem", "module": "Mathlib.Algebra.Module.Basic", "is_tactic_proof": true, "tactics": ["obtain", "rw", "simp_rw"], "tactic_count": 3}
{"name": "inv_natCast_smul_eq", "kind": "theorem", "module": "Mathlib.Algebra.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_intCast_smul_eq", "kind": "theorem", "module": "Mathlib.Algebra.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_natCast_smul_comm", "kind": "theorem", "module": "Mathlib.Algebra.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_intCast_smul_comm", "kind": "theorem", "module": "Mathlib.Algebra.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.support_smul_subset_left", "kind": "theorem", "module": "Mathlib.Algebra.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.support_smul_subset_right", "kind": "theorem", "module": "Mathlib.Algebra.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.support_const_smul_of_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.support_smul", "kind": "theorem", "module": "Mathlib.Algebra.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.support_const_smul_subset", "kind": "theorem", "module": "Mathlib.Algebra.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.indicator_smul_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "split_ifs", "exacts"], "tactic_count": 3}
{"name": "Set.indicator_smul", "kind": "theorem", "module": "Mathlib.Algebra.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.indicator_const_smul_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.indicator_const_smul", "kind": "theorem", "module": "Mathlib.Algebra.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.indicator_smul_apply_left", "kind": "theorem", "module": "Mathlib.Algebra.Module.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "split_ifs", "exacts"], "tactic_count": 3}
{"name": "Set.indicator_smul_left", "kind": "theorem", "module": "Mathlib.Algebra.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.indicator_smul_const_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.indicator_smul_const", "kind": "theorem", "module": "Mathlib.Algebra.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smul_indicator_one_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "List.sum_smul", "kind": "theorem", "module": "Mathlib.Algebra.Module.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.sum_smul", "kind": "theorem", "module": "Mathlib.Algebra.Module.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.sum_smul_sum", "kind": "theorem", "module": "Mathlib.Algebra.Module.BigOperators", "is_tactic_proof": true, "tactics": ["induction", "empty", "cons"], "tactic_count": 3}
{"name": "Finset.sum_smul", "kind": "theorem", "module": "Mathlib.Algebra.Module.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sum_smul_sum", "kind": "theorem", "module": "Mathlib.Algebra.Module.BigOperators", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Fintype.sum_smul_sum", "kind": "theorem", "module": "Mathlib.Algebra.Module.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.cast_card", "kind": "theorem", "module": "Mathlib.Algebra.Module.BigOperators", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fintype.sum_piFinset_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.BigOperators", "is_tactic_proof": true, "tactics": ["classical", "rw", "simp", "inter_self]"], "tactic_count": 4}
{"name": "Fintype.sum_single_smul", "kind": "theorem", "module": "Mathlib.Algebra.Module.BigOperators", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subbimodule.mk", "kind": "definition", "module": "Mathlib.Algebra.Module.Bimodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subbimodule.smul_mem", "kind": "theorem", "module": "Mathlib.Algebra.Module.Bimodule", "is_tactic_proof": true, "tactics": ["suffices", "simp"], "tactic_count": 2}
{"name": "Subbimodule.smul_mem'", "kind": "theorem", "module": "Mathlib.Algebra.Module.Bimodule", "is_tactic_proof": true, "tactics": ["suffices", "simp"], "tactic_count": 2}
{"name": "Subbimodule.baseChange", "kind": "definition", "module": "Mathlib.Algebra.Module.Bimodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subbimodule.toSubmodule", "kind": "definition", "module": "Mathlib.Algebra.Module.Bimodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subbimodule.toSubmodule'", "kind": "definition", "module": "Mathlib.Algebra.Module.Bimodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subbimodule.toSubbimoduleInt", "kind": "definition", "module": "Mathlib.Algebra.Module.Bimodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subbimodule.toSubbimoduleNat", "kind": "definition", "module": "Mathlib.Algebra.Module.Bimodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_le_of_module", "kind": "theorem", "module": "Mathlib.Algebra.Module.Card", "is_tactic_proof": true, "tactics": ["obtain", "have", "exact"], "tactic_count": 3}
{"name": "CharacterModule", "kind": "definition", "module": "Mathlib.Algebra.Module.CharacterModule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CharacterModule.instFunLikeAddCircleRatOfNat", "kind": "instance", "module": "Mathlib.Algebra.Module.CharacterModule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CharacterModule.instLinearMapClassIntAddCircleRatOfNat", "kind": "instance", "module": "Mathlib.Algebra.Module.CharacterModule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CharacterModule.instAddCommGroup", "kind": "instance", "module": "Mathlib.Algebra.Module.CharacterModule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CharacterModule.ext", "kind": "theorem", "module": "Mathlib.Algebra.Module.CharacterModule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CharacterModule.instModule", "kind": "instance", "module": "Mathlib.Algebra.Module.CharacterModule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CharacterModule.smul_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.CharacterModule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CharacterModule.dual", "kind": "definition", "module": "Mathlib.Algebra.Module.CharacterModule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CharacterModule.dual_zero", "kind": "theorem", "module": "Mathlib.Algebra.Module.CharacterModule", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "CharacterModule.dual_comp", "kind": "theorem", "module": "Mathlib.Algebra.Module.CharacterModule", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "CharacterModule.dual_injective_of_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Module.CharacterModule", "is_tactic_proof": true, "tactics": ["intro", "ext", "obtain", "change", "rw"], "tactic_count": 5}
{"name": "CharacterModule.dual_surjective_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Module.CharacterModule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CharacterModule.congr", "kind": "definition", "module": "Mathlib.Algebra.Module.CharacterModule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CharacterModule.uncurry", "kind": "definition", "module": "Mathlib.Algebra.Module.CharacterModule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CharacterModule.curry", "kind": "definition", "module": "Mathlib.Algebra.Module.CharacterModule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CharacterModule.homEquiv", "kind": "definition", "module": "Mathlib.Algebra.Module.CharacterModule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CharacterModule.dual_rTensor_conj_homEquiv", "kind": "theorem", "module": "Mathlib.Algebra.Module.CharacterModule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CharacterModule.int", "kind": "abbrev", "module": "Mathlib.Algebra.Module.CharacterModule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CharacterModule.int.divByNat", "kind": "abbrev", "module": "Mathlib.Algebra.Module.CharacterModule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CharacterModule.int.divByNat_self", "kind": "theorem", "module": "Mathlib.Algebra.Module.CharacterModule", "is_tactic_proof": true, "tactics": ["obtain", "apply", "exact"], "tactic_count": 3}
{"name": "CharacterModule.intSpanEquivQuotAddOrderOf", "kind": "definition", "module": "Mathlib.Algebra.Module.CharacterModule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CharacterModule.intSpanEquivQuotAddOrderOf_apply_self", "kind": "theorem", "module": "Mathlib.Algebra.Module.CharacterModule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CharacterModule.ofSpanSingleton", "kind": "definition", "module": "Mathlib.Algebra.Module.CharacterModule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CharacterModule.eq_zero_of_ofSpanSingleton_apply_self", "kind": "theorem", "module": "Mathlib.Algebra.Module.CharacterModule", "is_tactic_proof": false, "tactics": ["erw", "rcases", "apply_fun", "rw", "split_ifs", "cases", "rwa", "grind"], "tactic_count": 8}
{"name": "CharacterModule.exists_character_apply_ne_zero_of_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Module.CharacterModule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CharacterModule.eq_zero_of_character_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.CharacterModule", "is_tactic_proof": true, "tactics": ["contrapose"], "tactic_count": 1}
{"name": "CharacterModule.dual_surjective_iff_injective", "kind": "theorem", "module": "Mathlib.Algebra.Module.CharacterModule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "rTensor_injective_iff_lcomp_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Module.CharacterModule", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CharacterModule.surjective_of_dual_injective", "kind": "theorem", "module": "Mathlib.Algebra.Module.CharacterModule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CharacterModule.dual_injective_iff_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Module.CharacterModule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CharacterModule.dual_bijective_iff_bijective", "kind": "theorem", "module": "Mathlib.Algebra.Module.CharacterModule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SMulCon.Quotient", "kind": "definition", "module": "Mathlib.Algebra.Module.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SMulCon.instSMulQuotient", "kind": "instance", "module": "Mathlib.Algebra.Module.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SMulCon.instZeroQuotient", "kind": "instance", "module": "Mathlib.Algebra.Module.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SMulCon.instSMulZeroClassQuotient", "kind": "instance", "module": "Mathlib.Algebra.Module.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SMulCon.instSMulWithZeroQuotient", "kind": "instance", "module": "Mathlib.Algebra.Module.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SMulCon.instMulActionQuotient", "kind": "instance", "module": "Mathlib.Algebra.Module.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SMulCon.addConGen'", "kind": "definition", "module": "Mathlib.Algebra.Module.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SMulCon.addConGen", "kind": "abbrev", "module": "Mathlib.Algebra.Module.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCon.Quotient", "kind": "definition", "module": "Mathlib.Algebra.Module.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCon.instSMulQuotient", "kind": "instance", "module": "Mathlib.Algebra.Module.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCon.instZeroQuotient", "kind": "instance", "module": "Mathlib.Algebra.Module.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCon.instAddQuotient", "kind": "instance", "module": "Mathlib.Algebra.Module.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCon.instAddZeroClassQuotient", "kind": "instance", "module": "Mathlib.Algebra.Module.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCon.instAddCommMagmaQuotient", "kind": "instance", "module": "Mathlib.Algebra.Module.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCon.instAddSemigroupQuotient", "kind": "instance", "module": "Mathlib.Algebra.Module.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCon.instAddCommSemigroupQuotient", "kind": "instance", "module": "Mathlib.Algebra.Module.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCon.instAddMonoidQuotient", "kind": "instance", "module": "Mathlib.Algebra.Module.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCon.instAddCommMonoidQuotient", "kind": "instance", "module": "Mathlib.Algebra.Module.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCon.instAddGroupQuotient", "kind": "instance", "module": "Mathlib.Algebra.Module.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCon.instAddCommGroupQuotient", "kind": "instance", "module": "Mathlib.Algebra.Module.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCon.instSMulZeroClassQuotient", "kind": "instance", "module": "Mathlib.Algebra.Module.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCon.instSMulWithZeroQuotient", "kind": "instance", "module": "Mathlib.Algebra.Module.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCon.instMulActionQuotient", "kind": "instance", "module": "Mathlib.Algebra.Module.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCon.instDistribSMulQuotient", "kind": "instance", "module": "Mathlib.Algebra.Module.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCon.instDistribMulActionQuotient", "kind": "instance", "module": "Mathlib.Algebra.Module.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCon.instModuleQuotient", "kind": "instance", "module": "Mathlib.Algebra.Module.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SMulCon.ker", "kind": "definition", "module": "Mathlib.Algebra.Module.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCon.ker", "kind": "definition", "module": "Mathlib.Algebra.Module.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCon.quotientKerEquivOfSurjective", "kind": "definition", "module": "Mathlib.Algebra.Module.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.isInternal_prime_power_torsion_of_is_torsion_by_ideal", "kind": "theorem", "module": "Mathlib.Algebra.Module.DedekindDomain", "is_tactic_proof": true, "tactics": ["let", "have", "apply", "convert", "rw", "exact", "exact", "exact", "intro", "rw", "suffices", "rw", "exact", "rw", "exact"], "tactic_count": 15}
{"name": "Submodule.isInternal_prime_power_torsion", "kind": "theorem", "module": "Mathlib.Algebra.Module.DedekindDomain", "is_tactic_proof": true, "tactics": ["have", "have", "refine", "rw", "obtain"], "tactic_count": 5}
{"name": "Submodule.exists_isInternal_prime_power_torsion", "kind": "theorem", "module": "Mathlib.Algebra.Module.DedekindDomain", "is_tactic_proof": true, "tactics": ["classical", "exact"], "tactic_count": 2}
{"name": "Module.toMulActionWithZero", "kind": "instance", "module": "Mathlib.Algebra.Module.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "add_smul", "kind": "theorem", "module": "Mathlib.Algebra.Module.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Convex.combo_self", "kind": "theorem", "module": "Mathlib.Algebra.Module.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "two_smul", "kind": "theorem", "module": "Mathlib.Algebra.Module.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Function.Injective.module", "kind": "abbrev", "module": "Mathlib.Algebra.Module.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.module", "kind": "abbrev", "module": "Mathlib.Algebra.Module.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.eq_zero_of_zero_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Module.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "smul_add_one_sub_smul", "kind": "theorem", "module": "Mathlib.Algebra.Module.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Convex.combo_eq_smul_sub_add", "kind": "theorem", "module": "Mathlib.Algebra.Module.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.ext'", "kind": "theorem", "module": "Mathlib.Algebra.Module.Defs", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "neg_smul", "kind": "theorem", "module": "Mathlib.Algebra.Module.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "neg_smul_neg", "kind": "theorem", "module": "Mathlib.Algebra.Module.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "neg_one_smul", "kind": "theorem", "module": "Mathlib.Algebra.Module.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "sub_smul", "kind": "theorem", "module": "Mathlib.Algebra.Module.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Module.subsingleton", "kind": "theorem", "module": "Mathlib.Algebra.Module.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.nontrivial", "kind": "theorem", "module": "Mathlib.Algebra.Module.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Semiring.toModule", "kind": "instance", "module": "Mathlib.Algebra.Module.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDistribSMul", "kind": "instance", "module": "Mathlib.Algebra.Module.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoid.End.natCast_def", "kind": "theorem", "module": "Mathlib.Algebra.Module.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.toAddMonoidEnd", "kind": "definition", "module": "Mathlib.Algebra.Module.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smulAddHom", "kind": "definition", "module": "Mathlib.Algebra.Module.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smulAddHom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAddUnit.smul_left", "kind": "theorem", "module": "Mathlib.Algebra.Module.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAddUnit.smul_right", "kind": "theorem", "module": "Mathlib.Algebra.Module.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoid.End.intCast_def", "kind": "theorem", "module": "Mathlib.Algebra.Module.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.restrictScalars", "kind": "definition", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.restrictScalars_injective", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.restrictScalars_inj", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.isUnit_iff", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.automorphismGroup", "kind": "instance", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.one_eq_refl", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.mul_eq_trans", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.coe_one", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.coe_inv", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.coe_toLinearMap_one", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.coe_toLinearMap_mul", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.coe_pow", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.pow_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.mul_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.automorphismGroup.toLinearMapMonoidHom", "kind": "definition", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.applyDistribMulAction", "kind": "instance", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.smul_def", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.apply_faithfulSMul", "kind": "instance", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.apply_smulCommClass", "kind": "instance", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.apply_smulCommClass'", "kind": "instance", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.ofSubsingleton", "kind": "definition", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.ofSubsingleton_self", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Module.compHom.toLinearEquiv", "kind": "definition", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DistribMulAction.toLinearEquiv", "kind": "definition", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DistribMulAction.toModuleAut", "kind": "definition", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddEquiv.toLinearEquiv", "kind": "definition", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddEquiv.coe_toLinearEquiv", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddEquiv.coe_toLinearEquiv_symm", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddEquiv.toNatLinearEquiv", "kind": "definition", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddEquiv.coe_toNatLinearEquiv", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddEquiv.coe_symm_toNatLinearEquiv", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddEquiv.toNatLinearEquiv_toAddEquiv", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.toAddEquiv_toNatLinearEquiv", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddEquiv.toNatLinearEquiv_symm", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddEquiv.toNatLinearEquiv_refl", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddEquiv.toNatLinearEquiv_trans", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddEquiv.toIntLinearEquiv", "kind": "definition", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": true, "tactics": ["refine", "convert", "exact", "exact"], "tactic_count": 4}
{"name": "AddEquiv.coe_toIntLinearEquiv", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddEquiv.coe_symm_toIntLinearEquiv", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddEquiv.toIntLinearEquiv_toAddEquiv", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "LinearEquiv.toAddEquiv_toIntLinearEquiv", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddEquiv.toIntLinearEquiv_symm", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddEquiv.toIntLinearEquiv_refl", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddEquiv.toIntLinearEquiv_trans", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.ringLmapEquivSelf", "kind": "definition", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "addMonoidHomLequivNat", "kind": "definition", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "addMonoidHomLequivInt", "kind": "definition", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "addMonoidEndRingEquivInt", "kind": "definition", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.instZero", "kind": "instance", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.zero_symm", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.coe_zero", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.zero_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.instUnique", "kind": "instance", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.uniqueOfSubsingleton", "kind": "instance", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": true, "tactics": ["haveI", "haveI", "infer_instance"], "tactic_count": 3}
{"name": "LinearEquiv.curry", "kind": "definition", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.coe_curry", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.coe_curry_symm", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.ofLinear", "kind": "definition", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.ofLinear_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.ofLinear_symm_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.ofLinear_toLinearMap", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.ofLinear_symm_toLinearMap", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.neg", "kind": "definition", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.coe_neg", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.neg_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LinearEquiv.symm_neg", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.arrowCongrAddEquiv", "kind": "definition", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.conjRingEquiv", "kind": "definition", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.domMulActCongrRight", "kind": "definition", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.smulOfUnit", "kind": "definition", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.arrowCongr", "kind": "definition", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.arrowCongr_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LinearEquiv.arrowCongr_trans", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LinearEquiv.smulOfNeZero", "kind": "definition", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.toLinearEquiv", "kind": "definition", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.funLeft", "kind": "definition", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LinearMap.funLeft_id", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LinearMap.funLeft_surjective_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.funLeft_injective_of_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.funCongrLeft", "kind": "definition", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.funCongrLeft_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.funCongrLeft_id", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.funCongrLeft_comp", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.funCongrLeft_symm", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.sumPiEquivProdPi", "kind": "definition", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.piUnique", "kind": "definition", "module": "Mathlib.Algebra.Module.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "term_≃ₛₗ[_]_", "kind": "definition", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Algebra_Module_Equiv_Defs___macroRules_term_≃ₛₗ[_]__1", "kind": "definition", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Algebra_Module_Equiv_Defs___unexpand_LinearEquiv_1", "kind": "definition", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "term_≃ₗ[_]_", "kind": "definition", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Algebra_Module_Equiv_Defs___macroRules_term_≃ₗ[_]__1", "kind": "definition", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Algebra_Module_Equiv_Defs___unexpand_LinearEquiv_2", "kind": "definition", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquivClass", "kind": "abbrev", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemilinearEquivClass.instSemilinearMapClass", "kind": "instance", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemilinearEquivClass.semilinearEquiv", "kind": "definition", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemilinearEquivClass.instCoeToSemilinearEquiv", "kind": "instance", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.instCoeLinearMap", "kind": "instance", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.toEquiv", "kind": "definition", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.toEquiv_injective", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.toEquiv_inj", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.toLinearMap_injective", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.toLinearMap_inj", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.instEquivLike", "kind": "instance", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.instSemilinearEquivClass", "kind": "instance", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.toLinearMap_eq_coe", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.coe_mk", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SemilinearEquivClass.semilinearEquiv_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.coe_coe", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.coe_toEquiv", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.coe_toLinearMap", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.toFun_eq_coe", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": true, "tactics": ["dsimp"], "tactic_count": 1}
{"name": "LinearEquiv.ext", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.congr_arg", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.congr_fun", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.refl", "kind": "definition", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.refl_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.symm", "kind": "definition", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.Simps.apply", "kind": "definition", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.Simps.symm_apply", "kind": "definition", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.invFun_eq_symm", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.coe_toEquiv_symm", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.toEquiv_symm", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.coe_symm_toEquiv", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.trans", "kind": "definition", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.transNotation", "kind": "definition", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv._aux_Mathlib_Algebra_Module_Equiv_Defs___macroRules_LinearEquiv_transNotation_1", "kind": "definition", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv._aux_Mathlib_Algebra_Module_Equiv_Defs___delab_app_LinearEquiv_transNotation_1", "kind": "definition", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.symmEquiv", "kind": "definition", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.coe_toAddEquiv", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.coe_addEquiv_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.toAddMonoidHom_commutes", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.coe_toAddEquiv_symm", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.trans_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.coe_trans", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.apply_symm_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.symm_apply_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.comp_symm", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.symm_comp", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.comp_symm_assoc", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "LinearEquiv.symm_comp_assoc", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "LinearEquiv.trans_symm", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.symm_trans_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.trans_refl", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.refl_trans", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.symm_apply_eq", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.eq_symm_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.eq_comp_symm", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.comp_symm_eq", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.eq_symm_comp", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.symm_comp_eq", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.comp_coe", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.trans_assoc", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.eq_comp_toLinearMap_symm", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": true, "tactics": ["constructor", "simp", "simp"], "tactic_count": 3}
{"name": "LinearEquiv.comp_toLinearMap_symm_eq", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": true, "tactics": ["constructor", "simp", "simp"], "tactic_count": 3}
{"name": "LinearEquiv.eq_toLinearMap_symm_comp", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": true, "tactics": ["constructor", "simp", "simp"], "tactic_count": 3}
{"name": "LinearEquiv.toLinearMap_symm_comp_eq", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": true, "tactics": ["constructor", "simp", "simp"], "tactic_count": 3}
{"name": "LinearEquiv.comp_toLinearMap_eq_iff", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "LinearEquiv.eq_comp_toLinearMap_iff", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "LinearEquiv.comp_symm_cancel_left", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "LinearEquiv.symm_comp_cancel_left", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "LinearEquiv.comp_symm_cancel_right", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "LinearEquiv.symm_comp_cancel_right", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "LinearEquiv.trans_symm_cancel_left", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "LinearEquiv.symm_trans_cancel_left", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "LinearEquiv.trans_symm_cancel_right", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "LinearEquiv.symm_trans_cancel_right", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "LinearEquiv.refl_symm", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.self_trans_symm", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "LinearEquiv.symm_trans_self", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "LinearEquiv.refl_toLinearMap", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.mk_coe", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.map_add", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.map_zero", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.map_smulₛₗ", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.map_smul", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.map_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.map_ne_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.symm_symm", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.symm_bijective", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.mk_coe'", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.symm_mk.aux", "kind": "definition", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.symm_mk", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.coe_symm_mk", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.coe_symm_mk'", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.bijective", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.injective", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.surjective", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.image_eq_preimage_symm", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.image_symm_eq_preimage", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.cast", "kind": "definition", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.toSemilinearEquiv", "kind": "definition", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.ofInvolutive", "kind": "definition", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.coe_ofInvolutive", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.ext_ring_op", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.opLinearEquiv", "kind": "definition", "module": "Mathlib.Algebra.Module.Equiv.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.coe_opLinearEquiv", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.coe_opLinearEquiv_symm", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.coe_opLinearEquiv_toLinearMap", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.coe_opLinearEquiv_symm_toLinearMap", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.opLinearEquiv_toAddEquiv", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.coe_opLinearEquiv_addEquiv", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.opLinearEquiv_symm_toAddEquiv", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.coe_opLinearEquiv_symm_addEquiv", "kind": "theorem", "module": "Mathlib.Algebra.Module.Equiv.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Module.finitePresentation_of_finite", "kind": "theorem", "module": "Mathlib.Algebra.Module.FinitePresentation", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Module.finitePresentation_iff_finite", "kind": "theorem", "module": "Mathlib.Algebra.Module.FinitePresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.finitePresentation_of_free_of_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Module.FinitePresentation", "is_tactic_proof": true, "tactics": ["classical", "let", "let", "have", "obtain", "exact", "choose", "have", "have", "have", "refine", "let", "convert", "ext", "constructor", "intro", "refine", "simp", "simp", "rw", "rintro", "simp"], "tactic_count": 22}
{"name": "Module.finitePresentation_of_projective", "kind": "theorem", "module": "Mathlib.Algebra.Module.FinitePresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFinitePresentation", "kind": "instance", "module": "Mathlib.Algebra.Module.FinitePresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFinitePresentationFinsupp", "kind": "instance", "module": "Mathlib.Algebra.Module.FinitePresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFinitePresentationForall", "kind": "instance", "module": "Mathlib.Algebra.Module.FinitePresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.finitePresentation_of_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Module.FinitePresentation", "is_tactic_proof": true, "tactics": ["classical", "obtain", "obtain", "have", "apply", "choose", "have", "rw", "exact"], "tactic_count": 9}
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{"name": "Module.FinitePresentation.fg_ker_iff", "kind": "theorem", "module": "Mathlib.Algebra.Module.FinitePresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.finitePresentation_of_ker", "kind": "theorem", "module": "Mathlib.Algebra.Module.FinitePresentation", "is_tactic_proof": false, "tactics": ["obtain", "apply", "rw", "rw", "refine", "let", "have", "have", "let", "have", "have", "rw", "apply", "rw", "change", "have", "rw", "exact"], "tactic_count": 18}
{"name": "Module.finitePresentation_of_split_exact", "kind": "theorem", "module": "Mathlib.Algebra.Module.FinitePresentation", "is_tactic_proof": true, "tactics": ["have", "have", "obtain", "refine", "rw", "exact"], "tactic_count": 6}
{"name": "Module.finitePresentation_of_projective_of_exact", "kind": "theorem", "module": "Mathlib.Algebra.Module.FinitePresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.FinitePresentation.of_equiv", "kind": "theorem", "module": "Mathlib.Algebra.Module.FinitePresentation", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LinearEquiv.finitePresentation_iff", "kind": "theorem", "module": "Mathlib.Algebra.Module.FinitePresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.FinitePresentation.of_subsingleton", "kind": "instance", "module": "Mathlib.Algebra.Module.FinitePresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.FinitePresentation.prod", "kind": "instance", "module": "Mathlib.Algebra.Module.FinitePresentation", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "exact", "apply"], "tactic_count": 5}
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{"name": "Module.FinitePresentation.trans", "kind": "theorem", "module": "Mathlib.Algebra.Module.FinitePresentation", "is_tactic_proof": true, "tactics": ["obtain", "let", "refine", "obtain", "exact", "have", "simp", "exact"], "tactic_count": 8}
{"name": "instFinitePresentationTensorProduct", "kind": "instance", "module": "Mathlib.Algebra.Module.FinitePresentation", "is_tactic_proof": true, "tactics": ["classical", "obtain", "have", "apply", "have", "lTensor_exact", "rw", "rw", "have", "exact"], "tactic_count": 10}
{"name": "FinitePresentation.of_isBaseChange", "kind": "theorem", "module": "Mathlib.Algebra.Module.FinitePresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFinitePresentationLocalizationLocalizedModule", "kind": "instance", "module": "Mathlib.Algebra.Module.FinitePresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.FinitePresentation.exists_lift_of_isLocalizedModule", "kind": "theorem", "module": "Mathlib.Algebra.Module.FinitePresentation", "is_tactic_proof": true, "tactics": ["obtain", "let", "have", "classical", "choose", "let", "let", "have", "ext", "simp", "rw", "exact", "have", "intro", "convert_to", "simp", "apply", "rw", "convert", "rw", "exact", "choose", "let", "have", "rw", "intro", "simp", "rw", "convert", "exact", "refine", "ext", "obtain", "rw", "congr", "convert", "ext", "apply", "simp"], "tactic_count": 39}
{"name": "Module.Finite.exists_smul_of_comp_eq_of_isLocalizedModule", "kind": "theorem", "module": "Mathlib.Algebra.Module.FinitePresentation", "is_tactic_proof": true, "tactics": ["classical", "have", "choose", "obtain", "use", "rw", "intro", "simp"], "tactic_count": 8}
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{"name": "Module.FinitePresentation.exists_notMem_bijective", "kind": "theorem", "module": "Mathlib.Algebra.Module.FinitePresentation", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Module.FinitePresentation.exists_lift_equiv_of_isLocalizedModule", "kind": "theorem", "module": "Mathlib.Algebra.Module.FinitePresentation", "is_tactic_proof": true, "tactics": ["obtain", "have", "have", "apply", "apply", "simp", "rw", "simp", "rw", "exact", "obtain", "let", "let", "have", "isUnit_of_dvd_unit", "have", "refine", "apply", "map_units", "ext", "apply", "have", "simp", "algebraMap_end_apply]", "rw", "simp"], "tactic_count": 26}
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{"name": "Module.FinitePresentation.isLocalizedModule_mapExtendScalars", "kind": "instance", "module": "Mathlib.Algebra.Module.FinitePresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsLocalizedModuleLinearMapIdLocalizationLocalizedModuleMapOfFinitePresentation", "kind": "instance", "module": "Mathlib.Algebra.Module.FinitePresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalizedModule.exists_isLocalizedModule_powers_of_finitePresentation", "kind": "theorem", "module": "Mathlib.Algebra.Module.FinitePresentation", "is_tactic_proof": false, "tactics": ["have", "obtain", "exists_bijective_map_powers", "convert", "apply", "exact", "simp", "have", "refine", "intro", "obtain", "obtain", "obtain", "simpa", "exact", "exact"], "tactic_count": 16}
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{"name": "LinearMapClass.instCoeToLinearMap", "kind": "instance", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.instFunLike", "kind": "instance", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.semilinearMapClass", "kind": "instance", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.coe_coe", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.toDistribMulActionHom", "kind": "definition", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.coe_toAddHom", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.toFun_eq_coe", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.ext", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LinearMap.copy_eq", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.coe_mk", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.coe_addHom_mk", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.coe_semilinearMap", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.toLinearMap_injective", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": true, "tactics": ["apply", "intro", "exact"], "tactic_count": 3}
{"name": "LinearMap.id", "kind": "definition", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.id_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.id_coe", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.id'", "kind": "definition", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.id'_coe", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.isLinear", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.coe_injective", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.congr_arg", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.congr_fun", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.mk_coe", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.mk_coe'", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.map_add", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.map_zero", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.map_smulₛₗ", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.map_smul", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.map_smul_inv", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LinearMap.map_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsScalarTower.compatibleSMul", "kind": "instance", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsScalarTower.compatibleSMul'", "kind": "instance", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.map_smul_of_tower", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMapClass.map_smul_of_tower", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.isScalarTower_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "map_zsmul_unit", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LinearMap.isLinearMap_of_compatibleSMul", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.toAddMonoidHom", "kind": "definition", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.toAddMonoidHom_coe", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.restrictScalars", "kind": "definition", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.coeIsScalarTower", "kind": "instance", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.coe_restrictScalars", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.restrictScalars_self", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.restrictScalars_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.restrictScalars_injective", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.restrictScalars_inj", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.restrictScalars_id", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.toAddMonoidHom_injective", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.ext_ring", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.toSemilinearMap", "kind": "definition", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.coe_toSemilinearMap", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.comp", "kind": "definition", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.compNotation", "kind": "definition", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap._aux_Mathlib_Algebra_Module_LinearMap_Defs___macroRules_LinearMap_compNotation_1", "kind": "definition", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap._aux_Mathlib_Algebra_Module_LinearMap_Defs___delab_app_LinearMap_compNotation_1", "kind": "definition", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.term_∘ₛₗ_", "kind": "definition", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LinearMap._aux_Mathlib_Algebra_Module_LinearMap_Defs___unexpand_LinearMap_comp_1", "kind": "definition", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.comp_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Function.Surjective.injective_linearMapComp_right", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.cancel_right", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.injective_linearMapComp_left", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.surjective_comp_left_of_exists_rightInverse", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": true, "tactics": ["intro", "obtain", "refine", "simp_rw"], "tactic_count": 4}
{"name": "LinearMap.cancel_left", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.inverse", "kind": "definition", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": true, "tactics": ["dsimp", "exact", "map_add", "map_smul", "rw", "simp"], "tactic_count": 6}
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{"name": "LinearMap.surjective_of_comp_eq_id", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LinearMap.map_sub", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.CompatibleSMul.intModule", "kind": "instance", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.CompatibleSMul.units", "kind": "instance", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.compHom.toLinearMap", "kind": "definition", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DistribMulActionHom.instSemilinearMapClass", "kind": "instance", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DistribMulActionHom.instLinearMapClassId", "kind": "instance", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DistribMulActionHom.coe_toLinearMap", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DistribMulActionHom.toLinearMap_injective", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "IsLinearMap.mk'", "kind": "definition", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLinearMap.mk'_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLinearMap.isLinearMap_smul", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": true, "tactics": ["refine", "intro", "simp"], "tactic_count": 3}
{"name": "IsLinearMap.isLinearMap_smul'", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLinearMap.map_zero", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLinearMap.isLinearMap_neg", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLinearMap.map_neg", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLinearMap.map_sub", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.toNatLinearMap", "kind": "definition", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.toNatLinearMap_injective", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": true, "tactics": ["intro", "ext", "exact"], "tactic_count": 3}
{"name": "AddMonoidHom.coe_toNatLinearMap", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.toIntLinearMap", "kind": "definition", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.toIntLinearMap_injective", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": true, "tactics": ["intro", "ext", "exact"], "tactic_count": 3}
{"name": "AddMonoidHom.coe_toIntLinearMap", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.instSMul", "kind": "instance", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.smul_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.coe_smul", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.instSMulCommClass", "kind": "instance", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.instIsScalarTower", "kind": "instance", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.instIsCentralScalar", "kind": "instance", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.instZero", "kind": "instance", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.zero_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.comp_zero", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.zero_comp", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.instInhabited", "kind": "instance", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.default_def", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.uniqueOfLeft", "kind": "instance", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.uniqueOfRight", "kind": "instance", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.ne_zero_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.ne_zero_of_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.instAdd", "kind": "instance", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.add_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.add_comp", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.comp_add", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.addCommMonoid", "kind": "instance", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.instNeg", "kind": "instance", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.neg_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.neg_comp", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.comp_neg", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.instSub", "kind": "instance", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.sub_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LinearMap.evalAddMonoidHom", "kind": "definition", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.toAddMonoidHom'", "kind": "definition", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.identityMapOfZeroModuleIsZero", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.instDistribMulAction", "kind": "instance", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.smul_comp", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LinearMap.module", "kind": "instance", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.restrictScalars_zero", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.restrictScalars_add", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.restrictScalars_neg", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.restrictScalars_smul", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.restrictScalars_comp", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.restrictScalars_trans", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.restrictScalarsₗ", "kind": "definition", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LinearMap.mulLeft_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.toAddMonoidHom_mulLeft", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LinearMap.mulRight_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.toAddMonoidHom_mulRight", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LinearMap.mulLeftRight_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.surjective_iff_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.DivisionRing", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact"], "tactic_count": 3}
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{"name": "Module.End.natCast_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Module.End.instSMulCommClass", "kind": "instance", "module": "Mathlib.Algebra.Module.LinearMap.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.instSMulCommClass'", "kind": "instance", "module": "Mathlib.Algebra.Module.LinearMap.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "DistribSMul.toLinearMap", "kind": "definition", "module": "Mathlib.Algebra.Module.LinearMap.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Module.toModuleEnd", "kind": "definition", "module": "Mathlib.Algebra.Module.LinearMap.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.moduleEndSelf", "kind": "definition", "module": "Mathlib.Algebra.Module.LinearMap.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.moduleEndSelfOp", "kind": "definition", "module": "Mathlib.Algebra.Module.LinearMap.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LinearMap.zero_smulRight", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.End", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "LinearMap.smulRight_apply_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.End", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "LinearMap.compRight_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LinearMap.smulRightₗ", "kind": "definition", "module": "Mathlib.Algebra.Module.LinearMap.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.smulRightₗ_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.smulRightₗ_apply_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Matrix.toMvPolynomial", "kind": "definition", "module": "Mathlib.Algebra.Module.LinearMap.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.toMvPolynomial_eval_eq_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Polynomial", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.toMvPolynomial_map", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Polynomial", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.toMvPolynomial_isHomogeneous", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Polynomial", "is_tactic_proof": true, "tactics": ["apply", "rintro", "apply", "simp"], "tactic_count": 4}
{"name": "Matrix.toMvPolynomial_totalDegree_le", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Polynomial", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "Matrix.toMvPolynomial_constantCoeff", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Polynomial", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.toMvPolynomial_zero", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Polynomial", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Matrix.toMvPolynomial_one", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Polynomial", "is_tactic_proof": true, "tactics": ["ext", "rw", "simp", "rintro", "simp", "grind"], "tactic_count": 6}
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{"name": "Matrix.toMvPolynomial_mul", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Polynomial", "is_tactic_proof": true, "tactics": ["simp", "eval₂_monomial,"], "tactic_count": 2}
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{"name": "LinearMap.toMvPolynomial_eval_eq_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Polynomial", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LinearMap.toMvPolynomial_baseChange", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Polynomial", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LinearMap.toMvPolynomial_isHomogeneous", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.toMvPolynomial_totalDegree_le", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LinearMap.toMvPolynomial_zero", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Polynomial", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "LinearMap.toMvPolynomial_id", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Polynomial", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "LinearMap.toMvPolynomial_add", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Polynomial", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "LinearMap.toMvPolynomial_comp", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Polynomial", "is_tactic_proof": true, "tactics": ["simp", "rfl"], "tactic_count": 2}
{"name": "LinearMap.polyCharpolyAux", "kind": "definition", "module": "Mathlib.Algebra.Module.LinearMap.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.polyCharpolyAux_baseChange", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Polynomial", "is_tactic_proof": true, "tactics": ["simp", "rw", "simp", "congr", "apply", "intro", "simp", "rintro", "simp", "classical", "rw", "suffices", "toMvPolynomial", "simp", "suffices", "rw", "rw", "rintro", "rw", "grind", "intro", "rw", "dsimp", "rw"], "tactic_count": 24}
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{"name": "LinearMap.polyCharpolyAux_map_aeval", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Polynomial", "is_tactic_proof": false, "tactics": ["rw", "congr", "exact"], "tactic_count": 3}
{"name": "LinearMap.polyCharpolyAux_basisIndep", "kind": "theorem", "module": "Mathlib.Algebra.Module.LinearMap.Polynomial", "is_tactic_proof": false, "tactics": ["let", "have", "simp", "exact", "apply", "let", "let", "simp"], "tactic_count": 8}
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{"name": "LocalizedModule.lift_unique", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": true, "tactics": ["ext", "induction", "rw", "rw", "congr", "refine"], "tactic_count": 6}
{"name": "localizedModuleIsLocalizedModule", "kind": "instance", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalizedModule.of_restrictScalars", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalizedModule.of_exists_mul_mem", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalizedModule.fromLocalizedModule'", "kind": "definition", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalizedModule.fromLocalizedModule'_mk", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalizedModule.fromLocalizedModule'_add", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalizedModule.fromLocalizedModule'_smul", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalizedModule.fromLocalizedModule", "kind": "definition", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalizedModule.fromLocalizedModule_mk", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalizedModule.fromLocalizedModule.inj", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalizedModule.fromLocalizedModule.surj", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalizedModule.fromLocalizedModule.bij", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalizedModule.iso", "kind": "definition", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalizedModule.iso_apply_mk", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalizedModule.iso_mk_one", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsLocalizedModule.iso_symm_apply_aux", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": true, "tactics": ["apply_fun", "rw", "simp"], "tactic_count": 3}
{"name": "IsLocalizedModule.iso_symm_apply'", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalizedModule.iso_symm_comp", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": true, "tactics": ["ext", "rw", "exact"], "tactic_count": 3}
{"name": "IsLocalizedModule.iso_symm_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalizedModule.lift", "kind": "definition", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalizedModule.lift_comp", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "IsLocalizedModule.lift_iso", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsLocalizedModule.lift_comp_iso", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalizedModule.lift_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalizedModule.lift_unique", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "rw", "ext", "simp"], "tactic_count": 5}
{"name": "IsLocalizedModule.is_universal", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalizedModule.linearMap_ext", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalizedModule.ext", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "IsLocalizedModule.linearEquiv", "kind": "definition", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalizedModule.linearEquiv_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsLocalizedModule.linearEquiv_symm_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsLocalizedModule.smul_injective", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalizedModule.smul_inj", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalizedModule.isRegular_of_smul_left_injective", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalizedModule.mk'", "kind": "definition", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalizedModule.mk'_smul", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": true, "tactics": ["delta", "rw"], "tactic_count": 2}
{"name": "IsLocalizedModule.mk'_add_mk'", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": true, "tactics": ["delta", "rw"], "tactic_count": 2}
{"name": "IsLocalizedModule.mk'_zero", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsLocalizedModule.mk'_one", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": true, "tactics": ["delta", "rw"], "tactic_count": 2}
{"name": "IsLocalizedModule.mk'_cancel", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": true, "tactics": ["delta", "rw"], "tactic_count": 2}
{"name": "IsLocalizedModule.mk'_cancel'", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsLocalizedModule.mk'_cancel_left", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": true, "tactics": ["delta", "rw"], "tactic_count": 2}
{"name": "IsLocalizedModule.mk'_cancel_right", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": true, "tactics": ["delta", "rw"], "tactic_count": 2}
{"name": "IsLocalizedModule.mk'_add", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsLocalizedModule.mk'_eq_mk'_iff", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": true, "tactics": ["delta", "rw", "simp_rw"], "tactic_count": 3}
{"name": "IsLocalizedModule.mk'_neg", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": true, "tactics": ["delta", "rw"], "tactic_count": 2}
{"name": "IsLocalizedModule.mk'_sub", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsLocalizedModule.mk'_sub_mk'", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsLocalizedModule.mk'_mul_mk'_of_map_mul", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": true, "tactics": ["symm", "apply", "simp_rw", "rw", "simp_rw"], "tactic_count": 5}
{"name": "IsLocalizedModule.mk'_mul_mk'", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalizedModule.mk'_eq_iff", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsLocalizedModule.mk'_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsLocalizedModule.mk'_eq_zero'", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "IsLocalizedModule.mk_eq_mk'", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsLocalizedModule.mk'_smul_mk'", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": true, "tactics": ["apply", "conv_lhs", "simp", "rw"], "tactic_count": 4}
{"name": "IsLocalizedModule.eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalizedModule.mk'_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": true, "tactics": ["intro", "obtain", "exact"], "tactic_count": 3}
{"name": "IsLocalizedModule.liftOfLE", "kind": "definition", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocalizedModule.liftOfLE", "kind": "abbrev", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalizedModule.liftOfLE_comp", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalizedModule.liftOfLE_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalizedModule.liftOfLE_mk'", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": true, "tactics": ["apply", "simp", "rw", "exact"], "tactic_count": 4}
{"name": "IsLocalizedModule.instLiftOfLE", "kind": "instance", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalizedModule.injective_of_map_eq", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": true, "tactics": ["intro", "obtain", "obtain", "suffices", "apply", "rw", "rwa", "simp"], "tactic_count": 8}
{"name": "IsLocalizedModule.injective_of_map_zero", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "apply", "simpa"], "tactic_count": 4}
{"name": "IsLocalizedModule.map", "kind": "definition", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalizedModule.map_comp", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalizedModule.map_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalizedModule.map_mk'", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": false, "tactics": ["simp", "rw", "rfl"], "tactic_count": 3}
{"name": "IsLocalizedModule.map_id", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": true, "tactics": ["ext", "obtain", "simp"], "tactic_count": 3}
{"name": "IsLocalizedModule.map_injective", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": true, "tactics": ["intro", "obtain", "obtain", "simp", "forall_exists_index,", "intro", "exact"], "tactic_count": 7}
{"name": "IsLocalizedModule.map_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": true, "tactics": ["intro", "obtain", "obtain", "exact"], "tactic_count": 4}
{"name": "IsLocalizedModule.iso_localizedModule_eq_refl", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": true, "tactics": ["let", "obtain", "rw", "exact"], "tactic_count": 4}
{"name": "IsLocalizedModule.map_LocalizedModules", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": true, "tactics": ["have", "rw", "simpa"], "tactic_count": 3}
{"name": "IsLocalizedModule.map_iso_commute", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": true, "tactics": ["ext", "induction", "refine", "rw", "smul'_mk,", "simp"], "tactic_count": 6}
{"name": "IsLocalizedModule.map_comp'", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": true, "tactics": ["ext", "obtain", "simp"], "tactic_count": 3}
{"name": "IsLocalizedModule.mkOfAlgebra", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": false, "tactics": ["replace", "rw", "simpa", "constructor", "intro", "rw", "constructor", "rintro", "simp_rw", "exact", "intro", "refine", "rw", "exact", "intro", "dsimp", "rw", "simp_rw", "exact"], "tactic_count": 19}
{"name": "IsLocalizedModule.module", "kind": "definition", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalizedModule.isScalarTower_module", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalizedModule.mem_ker_iff", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsLocalizedModule.subsingleton_iff_ker_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "obtain", "simpa"], "tactic_count": 4}
{"name": "IsLocalizedModule.subsingleton_iff", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "true_implies]"], "tactic_count": 2}
{"name": "IsLocalizedModule.subsingleton_of_subsingleton", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": true, "tactics": ["rw", "intro", "use", "simp"], "tactic_count": 4}
{"name": "LocalizedModule.mem_ker_mkLinearMap_iff", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocalizedModule.subsingleton_iff_ker_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocalizedModule.subsingleton_iff", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocalizedModule.instSubsingleton", "kind": "instance", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": true, "tactics": ["rw", "intro", "use"], "tactic_count": 3}
{"name": "IsLocalizedModule.isTorsionFree_of_forall_isRegular", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalizedModule.isTorsionFree", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalizedModule.instIsTorsionFreeLocalizationLocalizedModuleOfIsDomain", "kind": "instance", "module": "Mathlib.Algebra.Module.LocalizedModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocalizedModule.map_exact", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalizedModule.map_exact", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalizedModule.IsInteger", "kind": "definition", "module": "Mathlib.Algebra.Module.LocalizedModule.Int", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalizedModule.isInteger_zero", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Int", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalizedModule.isInteger_add", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Int", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalizedModule.isInteger_smul", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Int", "is_tactic_proof": true, "tactics": ["rcases", "use", "rw"], "tactic_count": 3}
{"name": "IsLocalizedModule.exists_integer_multiple", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Int", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalizedModule.exist_integer_multiples", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Int", "is_tactic_proof": true, "tactics": ["classical", "choose", "refine", "exact", "simp", "rw", "congr", "simp", "rw"], "tactic_count": 9}
{"name": "IsLocalizedModule.exist_integer_multiples_of_finite", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Int", "is_tactic_proof": true, "tactics": ["cases", "obtain", "exact"], "tactic_count": 3}
{"name": "IsLocalizedModule.exist_integer_multiples_of_finset", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Int", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalizedModule.commonDenom", "kind": "definition", "module": "Mathlib.Algebra.Module.LocalizedModule.Int", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalizedModule.integerMultiple", "kind": "definition", "module": "Mathlib.Algebra.Module.LocalizedModule.Int", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalizedModule.map_integerMultiple", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Int", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalizedModule.commonDenomOfFinset", "kind": "definition", "module": "Mathlib.Algebra.Module.LocalizedModule.Int", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalizedModule.finsetIntegerMultiple", "kind": "definition", "module": "Mathlib.Algebra.Module.LocalizedModule.Int", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalizedModule.finsetIntegerMultiple_image", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Int", "is_tactic_proof": true, "tactics": ["delta", "rw", "ext", "constructor", "rintro", "rw", "exact", "rintro", "exact"], "tactic_count": 9}
{"name": "IsLocalizedModule.smul_mem_finsetIntegerMultiple_span", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Int", "is_tactic_proof": true, "tactics": ["let", "have", "apply", "rw", "replace", "rw", "obtain", "obtain", "use", "convert", "convert", "simp"], "tactic_count": 12}
{"name": "isLocalizedModule_iff_isLocalization", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.IsLocalization", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp_rw", "simp_rw", "simp", "congr"], "tactic_count": 6}
{"name": "instIsLocalizedModuleToLinearMapToAlgHomOfIsLocalizationAlgebraMapSubmonoid", "kind": "instance", "module": "Mathlib.Algebra.Module.LocalizedModule.IsLocalization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLocalizedModule_iff_isLocalization'", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.IsLocalization", "is_tactic_proof": true, "tactics": ["convert", "exact"], "tactic_count": 2}
{"name": "instIsLocalizedModuleLinearMapOfIsLocalization", "kind": "instance", "module": "Mathlib.Algebra.Module.LocalizedModule.IsLocalization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.mk'_algebraMap_eq_mk'", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.IsLocalization", "is_tactic_proof": false, "tactics": ["rw", "exact"], "tactic_count": 2}
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{"name": "Submodule.localized'", "kind": "definition", "module": "Mathlib.Algebra.Module.LocalizedModule.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mem_localized₀", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mem_localized'", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Submodule.localized'gi", "kind": "definition", "module": "Mathlib.Algebra.Module.LocalizedModule.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Submodule.localized₀_bot", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Submodule", "is_tactic_proof": true, "tactics": ["rw", "rintro", "simp"], "tactic_count": 3}
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{"name": "Submodule.localized₀_top", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Submodule", "is_tactic_proof": true, "tactics": ["rw", "rintro", "obtain", "exact"], "tactic_count": 4}
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{"name": "Submodule.localized₀_inf", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Submodule", "is_tactic_proof": true, "tactics": ["simp", "refine", "rintro", "have", "rw", "obtain", "refine", "rw", "exact", "rwa"], "tactic_count": 10}
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{"name": "Submodule.localized'_iSup", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Submodule", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "Submodule.localized₀_iSup", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Submodule", "is_tactic_proof": true, "tactics": ["let", "have", "simpa"], "tactic_count": 3}
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{"name": "Submodule.IsLocalizedModule.localized₀FrameHom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.localized'FrameHom", "kind": "definition", "module": "Mathlib.Algebra.Module.LocalizedModule.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.IsLocalizedModule.localized'FrameHom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.LocalizedModule.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Submodule.toLocalized₀", "kind": "definition", "module": "Mathlib.Algebra.Module.LocalizedModule.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.toLocalized'", "kind": "definition", "module": "Mathlib.Algebra.Module.LocalizedModule.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Module.Relations.Quotient.linearMap_ext", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Relations.surjective_toQuotient", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Relations.ker_toQuotient", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Relations.toQuotient_relation", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "exact"], "tactic_count": 3}
{"name": "Module.Relations.map", "kind": "definition", "module": "Mathlib.Algebra.Module.Presentation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Relations.map_single", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Module.Relations.range_map", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Relations.toQuotient_map", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.Basic", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Module.Relations.toQuotient_map_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Relations.Solution.π", "kind": "definition", "module": "Mathlib.Algebra.Module.Presentation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Relations.Solution.π_single", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Module.Relations.Solution.π_relation", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Relations.Solution.π_comp_map", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.Basic", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Module.Relations.Solution.π_comp_map_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.Basic", "is_tactic_proof": true, "tactics": ["change", "rw"], "tactic_count": 2}
{"name": "Module.Relations.Solution.range_π", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Relations.Solution.span_relation_le_ker_π", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.Basic", "is_tactic_proof": true, "tactics": ["rw", "rintro", "simp"], "tactic_count": 3}
{"name": "Module.Relations.Solution.fromQuotient", "kind": "definition", "module": "Mathlib.Algebra.Module.Presentation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Relations.Solution.fromQuotient_comp_toQuotient", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Relations.Solution.fromQuotient_toQuotient", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Relations.Solution.postcomp", "kind": "definition", "module": "Mathlib.Algebra.Module.Presentation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Relations.Solution.postcomp_comp", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Relations.Solution.postcomp_id", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Relations.Solution.congr_var", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Module.Relations.Solution.congr_postcomp", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Module.Relations.Solution.ofπ", "kind": "definition", "module": "Mathlib.Algebra.Module.Presentation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Relations.Solution.ofπ_π", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Module.Relations.Solution.ofπ'", "kind": "definition", "module": "Mathlib.Algebra.Module.Presentation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Relations.Solution.ofπ'_π", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Module.Relations.Solution.injective_fromQuotient_iff_ker_π_eq_span", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.Basic", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "intro", "rw", "intro", "obtain", "replace", "rw", "obtain", "simp"], "tactic_count": 11}
{"name": "Module.Relations.Solution.surjective_fromQuotient_iff_surjective_π", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Module.Relations.Solution.surjective_π_iff_span_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Module.Relations.Solution.IsPresentation.linearEquiv", "kind": "definition", "module": "Mathlib.Algebra.Module.Presentation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Relations.Solution.IsPresentation.linearEquiv_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Relations.Solution.IsPresentation.linearEquiv_symm_var", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Relations.Solution.IsPresentation.surjective_π", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Module.Relations.Solution.IsPresentation.ker_π", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Module.Relations.Solution.IsPresentation.exact", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Module.Relations.Solution.IsPresentation.desc", "kind": "definition", "module": "Mathlib.Algebra.Module.Presentation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Relations.Solution.IsPresentation.desc_var", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "Module.Relations.Solution.IsPresentation.desc_comp_π", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.Basic", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Module.Relations.Solution.IsPresentation.π_desc_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Relations.Solution.IsPresentation.postcomp_desc", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.Basic", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Module.Relations.Solution.IsPresentation.postcomp_injective", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.Basic", "is_tactic_proof": false, "tactics": ["suffices", "ext", "obtain", "exact", "ext", "simpa"], "tactic_count": 6}
{"name": "Module.Relations.Solution.IsPresentation.linearMapEquiv", "kind": "definition", "module": "Mathlib.Algebra.Module.Presentation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Relations.Solution.IsPresentation.uniq", "kind": "definition", "module": "Mathlib.Algebra.Module.Presentation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Relations.Solution.IsPresentation.postcomp_uniq", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Module.Relations.Solution.IsPresentation.postcomp_uniq_symm", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Module.Relations.Solution.IsPresentation.uniq_var", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Module.Relations.Solution.IsPresentation.uniq_symm_var", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Module.Relations.Solution.IsPresentation.of_linearEquiv", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Relations.Solution.ofQuotient", "kind": "definition", "module": "Mathlib.Algebra.Module.Presentation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Relations.Solution.ofQuotient_π", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Relations.Solution.ofQuotient_fromQuotient", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.Basic", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Module.Relations.Solution.ofQuotient_isPresentation", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Relations.Solution.IsPresentationCore.desc_var", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Relations.Solution.IsPresentationCore.down", "kind": "definition", "module": "Mathlib.Algebra.Module.Presentation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Relations.Solution.IsPresentationCore.isPresentation", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Relations.Solution.isPresentation_iff", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.Basic", "is_tactic_proof": false, "tactics": ["rw", "surjective_fromQuotient_iff_surjective_π,", "exact"], "tactic_count": 3}
{"name": "Module.Relations.Solution.isPresentation_mk", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Module.Presentation.ofIsPresentation", "kind": "definition", "module": "Mathlib.Algebra.Module.Presentation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Presentation.ofLinearEquiv", "kind": "definition", "module": "Mathlib.Algebra.Module.Presentation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Presentation.CokernelData.ofSection", "kind": "definition", "module": "Mathlib.Algebra.Module.Presentation.Cokernel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Presentation.nonempty_cokernelData", "kind": "instance", "module": "Mathlib.Algebra.Module.Presentation.Cokernel", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Module.Presentation.cokernelRelations", "kind": "definition", "module": "Mathlib.Algebra.Module.Presentation.Cokernel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Presentation.cokernelSolution", "kind": "definition", "module": "Mathlib.Algebra.Module.Presentation.Cokernel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Presentation.cokernelSolution.isPresentationCore", "kind": "definition", "module": "Mathlib.Algebra.Module.Presentation.Cokernel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Presentation.cokernelSolution.isPresentation", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.Cokernel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Presentation.cokernel", "kind": "definition", "module": "Mathlib.Algebra.Module.Presentation.Cokernel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Presentation.ofExact", "kind": "definition", "module": "Mathlib.Algebra.Module.Presentation.Cokernel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Presentation.differentialsRelations", "kind": "definition", "module": "Mathlib.Algebra.Module.Presentation.Differentials", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Presentation.differentials.comm₂₃'", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.Differentials", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Algebra.Presentation.differentials.hom₁", "kind": "definition", "module": "Mathlib.Algebra.Module.Presentation.Differentials", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Presentation.differentials.hom₁_single", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.Differentials", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Algebra.Presentation.differentials.surjective_hom₁", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.Differentials", "is_tactic_proof": false, "tactics": ["let", "map_add", "map_smul", "change", "have", "have", "refine", "rw", "simp", "congr", "aesop", "rw", "rw", "dsimp", "rw", "rintro", "simp", "refine", "simp", "rfl"], "tactic_count": 20}
{"name": "Algebra.Presentation.differentials.comm₁₂_single", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.Differentials", "is_tactic_proof": false, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Algebra.Presentation.differentials.comm₁₂", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.Differentials", "is_tactic_proof": true, "tactics": ["ext", "have", "dsimp", "rw"], "tactic_count": 4}
{"name": "Algebra.Presentation.differentialsSolution", "kind": "definition", "module": "Mathlib.Algebra.Module.Presentation.Differentials", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Presentation.differentials.comm₂₃", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.Differentials", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Presentation.differentialsSolution_isPresentation", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.Differentials", "is_tactic_proof": true, "tactics": ["rw", "constructor", "rw", "exact", "rw", "exact", "pres.cotangentSpaceBasis.repr.symm.toLinearMap", "pres.toExtension.exact_cotangentComplex_toKaehler)"], "tactic_count": 8}
{"name": "Algebra.Presentation.differentials", "kind": "definition", "module": "Mathlib.Algebra.Module.Presentation.Differentials", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Relations.directSum", "kind": "definition", "module": "Mathlib.Algebra.Module.Presentation.DirectSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Relations.Solution.directSumEquiv", "kind": "definition", "module": "Mathlib.Algebra.Module.Presentation.DirectSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Relations.Solution.directSum", "kind": "definition", "module": "Mathlib.Algebra.Module.Presentation.DirectSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Relations.Solution.directSum_var", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.DirectSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Relations.Solution.IsPresentation.directSum.isRepresentationCore", "kind": "definition", "module": "Mathlib.Algebra.Module.Presentation.DirectSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Relations.Solution.IsPresentation.directSum", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.DirectSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Presentation.directSum", "kind": "definition", "module": "Mathlib.Algebra.Module.Presentation.DirectSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Presentation.directSum_var", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.DirectSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Presentation.finsupp", "kind": "definition", "module": "Mathlib.Algebra.Module.Presentation.DirectSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Presentation.finsupp_var", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.DirectSum", "is_tactic_proof": true, "tactics": ["apply", "erw", "rw", "rfl"], "tactic_count": 4}
{"name": "Module.Presentation.finite", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Presentation.finitePresentation", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.finitePresentation_iff_exists_presentation", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.Finite", "is_tactic_proof": true, "tactics": ["constructor", "intro", "obtain", "obtain", "exact", "relation", "var", "linearCombination_var_relation", "rw", "exact", "toIsPresentation", "rw", "exact", "inferInstance,", "rintro", "exact"], "tactic_count": 16}
{"name": "Module.Relations.solutionFinsupp", "kind": "definition", "module": "Mathlib.Algebra.Module.Presentation.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Relations.solutionFinsupp.isPresentationCore", "kind": "definition", "module": "Mathlib.Algebra.Module.Presentation.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Relations.solutionFinsupp_isPresentation", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Relations.Solution.IsPresentation.free", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.presentationFinsupp", "kind": "definition", "module": "Mathlib.Algebra.Module.Presentation.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.free_iff_exists_presentation", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.Free", "is_tactic_proof": true, "tactics": ["constructor", "rw", "rintro", "exact", "rintro", "exact"], "tactic_count": 6}
{"name": "Module.Presentation.RestrictScalarsData", "kind": "abbrev", "module": "Mathlib.Algebra.Module.Presentation.RestrictScalars", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Presentation.restrictScalars", "kind": "definition", "module": "Mathlib.Algebra.Module.Presentation.RestrictScalars", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Presentation.tautological.R", "kind": "inductive", "module": "Mathlib.Algebra.Module.Presentation.Tautological", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Presentation.tautologicalRelations", "kind": "definition", "module": "Mathlib.Algebra.Module.Presentation.Tautological", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Presentation.tautologicalRelationsSolutionEquiv", "kind": "definition", "module": "Mathlib.Algebra.Module.Presentation.Tautological", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Presentation.tautologicalSolution", "kind": "definition", "module": "Mathlib.Algebra.Module.Presentation.Tautological", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Presentation.tautologicalSolutionIsPresentationCore", "kind": "definition", "module": "Mathlib.Algebra.Module.Presentation.Tautological", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Presentation.tautologicalSolution_isPresentation", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.Tautological", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Presentation.tautological", "kind": "definition", "module": "Mathlib.Algebra.Module.Presentation.Tautological", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Relations.tensor", "kind": "definition", "module": "Mathlib.Algebra.Module.Presentation.Tensor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Relations.Solution.tensor", "kind": "definition", "module": "Mathlib.Algebra.Module.Presentation.Tensor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Relations.Solution.isPresentationCoreTensor", "kind": "definition", "module": "Mathlib.Algebra.Module.Presentation.Tensor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Relations.Solution.IsPresentation.tensor", "kind": "theorem", "module": "Mathlib.Algebra.Module.Presentation.Tensor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Presentation.tensor", "kind": "definition", "module": "Mathlib.Algebra.Module.Presentation.Tensor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instModule", "kind": "instance", "module": "Mathlib.Algebra.Module.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.projective_def", "kind": "theorem", "module": "Mathlib.Algebra.Module.Projective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.projective_def'", "kind": "theorem", "module": "Mathlib.Algebra.Module.Projective", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Module.projective_lifting_property", "kind": "theorem", "module": "Mathlib.Algebra.Module.Projective", "is_tactic_proof": true, "tactics": ["on", "a", "let", "obtain", "use", "ext", "conv_rhs", "simp"], "tactic_count": 8}
{"name": "LinearMap.exists_rightInverse_of_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Module.Projective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.surjective_linearMapComp_left", "kind": "theorem", "module": "Mathlib.Algebra.Module.Projective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Projective.of_lifting_property''", "kind": "theorem", "module": "Mathlib.Algebra.Module.Projective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.instProjectiveProd", "kind": "instance", "module": "Mathlib.Algebra.Module.Projective", "is_tactic_proof": true, "tactics": ["refine", "rcases", "rcases", "refine", "rw"], "tactic_count": 5}
{"name": "Module.instProjectiveDFinsupp", "kind": "instance", "module": "Mathlib.Algebra.Module.Projective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Projective.of_basis", "kind": "theorem", "module": "Mathlib.Algebra.Module.Projective", "is_tactic_proof": true, "tactics": ["use", "intro", "simp", "exact"], "tactic_count": 4}
{"name": "Module.Projective.of_free", "kind": "instance", "module": "Mathlib.Algebra.Module.Projective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Projective.of_split", "kind": "theorem", "module": "Mathlib.Algebra.Module.Projective", "is_tactic_proof": false, "tactics": ["obtain", "projective_lifting_property", "refine", "rw"], "tactic_count": 4}
{"name": "Module.Projective.of_equiv", "kind": "theorem", "module": "Mathlib.Algebra.Module.Projective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Projective.iff_split_of_projective", "kind": "theorem", "module": "Mathlib.Algebra.Module.Projective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Projective.of_ringEquiv", "kind": "theorem", "module": "Mathlib.Algebra.Module.Projective", "is_tactic_proof": true, "tactics": ["obtain", "let", "map_add", "map_smul", "refine", "replace", "simpa"], "tactic_count": 7}
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{"name": "Module.Projective.iff_split", "kind": "theorem", "module": "Mathlib.Algebra.Module.Projective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Projective.tensorProduct", "kind": "instance", "module": "Mathlib.Algebra.Module.Projective", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "have", "fapply", "exact", "exact", "ext", "fapply", "exact", "exact", "ext"], "tactic_count": 11}
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{"name": "map_nnratCast_smul", "kind": "theorem", "module": "Mathlib.Algebra.Module.Rat", "is_tactic_proof": true, "tactics": ["rw", "map_inv_natCast_smul"], "tactic_count": 2}
{"name": "map_ratCast_smul", "kind": "theorem", "module": "Mathlib.Algebra.Module.Rat", "is_tactic_proof": true, "tactics": ["rw", "map_inv_natCast_smul"], "tactic_count": 2}
{"name": "map_nnrat_smul", "kind": "theorem", "module": "Mathlib.Algebra.Module.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "map_rat_smul", "kind": "theorem", "module": "Mathlib.Algebra.Module.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "subsingleton_nnrat_module", "kind": "instance", "module": "Mathlib.Algebra.Module.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "subsingleton_rat_module", "kind": "instance", "module": "Mathlib.Algebra.Module.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nnratCast_smul_eq", "kind": "theorem", "module": "Mathlib.Algebra.Module.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ratCast_smul_eq", "kind": "theorem", "module": "Mathlib.Algebra.Module.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsScalarTower.nnrat", "kind": "instance", "module": "Mathlib.Algebra.Module.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsScalarTower.rat", "kind": "instance", "module": "Mathlib.Algebra.Module.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.cast_smul_eq_nnqsmul", "kind": "theorem", "module": "Mathlib.Algebra.Module.Rat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Rat.cast_smul_eq_qsmul", "kind": "theorem", "module": "Mathlib.Algebra.Module.Rat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SMulCommClass.nnrat", "kind": "instance", "module": "Mathlib.Algebra.Module.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SMulCommClass.rat", "kind": "instance", "module": "Mathlib.Algebra.Module.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SMulCommClass.nnrat'", "kind": "instance", "module": "Mathlib.Algebra.Module.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SMulCommClass.rat'", "kind": "instance", "module": "Mathlib.Algebra.Module.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAddTorsionFree.of_module_nnrat", "kind": "theorem", "module": "Mathlib.Algebra.Module.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAddTorsionFree.of_module_rat", "kind": "theorem", "module": "Mathlib.Algebra.Module.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.moduleLeft", "kind": "abbrev", "module": "Mathlib.Algebra.Module.RingHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.compHom", "kind": "abbrev", "module": "Mathlib.Algebra.Module.RingHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.toModule", "kind": "abbrev", "module": "Mathlib.Algebra.Module.RingHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.smulOneHom", "kind": "definition", "module": "Mathlib.Algebra.Module.RingHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ringHomEquivModuleIsScalarTower", "kind": "definition", "module": "Mathlib.Algebra.Module.RingHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Shrink.instModule", "kind": "instance", "module": "Mathlib.Algebra.Module.Shrink", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Shrink.linearEquiv", "kind": "definition", "module": "Mathlib.Algebra.Module.Shrink", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SnakeLemma.δ_aux", "kind": "theorem", "module": "Mathlib.Algebra.Module.SnakeLemma", "is_tactic_proof": false, "tactics": ["obtain", "rw", "rw"], "tactic_count": 3}
{"name": "SnakeLemma.eq_of_eq", "kind": "theorem", "module": "Mathlib.Algebra.Module.SnakeLemma", "is_tactic_proof": true, "tactics": ["have", "rw", "obtain", "rw", "rw", "exact"], "tactic_count": 6}
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{"name": "SnakeLemma.δ_eq", "kind": "theorem", "module": "Mathlib.Algebra.Module.SnakeLemma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SnakeLemma.exact_δ_right", "kind": "theorem", "module": "Mathlib.Algebra.Module.SnakeLemma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SnakeLemma.exact_δ_left", "kind": "theorem", "module": "Mathlib.Algebra.Module.SnakeLemma", "is_tactic_proof": true, "tactics": ["haveI", "intro", "constructor", "intro", "obtain", "obtain", "obtain", "exact", "rintro", "simp", "rw"], "tactic_count": 11}
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{"name": "SnakeLemma.δ'_eq", "kind": "theorem", "module": "Mathlib.Algebra.Module.SnakeLemma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SnakeLemma.exact_δ'_right", "kind": "theorem", "module": "Mathlib.Algebra.Module.SnakeLemma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SnakeLemma.exact_δ'_left", "kind": "theorem", "module": "Mathlib.Algebra.Module.SnakeLemma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.spanRank", "kind": "definition", "module": "Mathlib.Algebra.Module.SpanRank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.spanFinrank", "kind": "definition", "module": "Mathlib.Algebra.Module.SpanRank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.instNonemptySubtypeSetEqSpan", "kind": "instance", "module": "Mathlib.Algebra.Module.SpanRank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.spanRank_toENat_eq_iInf_encard", "kind": "theorem", "module": "Mathlib.Algebra.Module.SpanRank", "is_tactic_proof": true, "tactics": ["rw", "apply", "refine", "rw", "exact", "have", "rw", "refine", "have", "ofENatHom.monotone", "apply", "rw", "exact"], "tactic_count": 13}
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{"name": "Submodule.spanRank_finite_iff_fg", "kind": "theorem", "module": "Mathlib.Algebra.Module.SpanRank", "is_tactic_proof": true, "tactics": ["rw", "constructor", "rintro", "obtain", "csInf_mem", "refine", "simpa", "rintro", "exact"], "tactic_count": 9}
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{"name": "Submodule.fg_iff_spanRank_eq_spanFinrank", "kind": "theorem", "module": "Mathlib.Algebra.Module.SpanRank", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Submodule.spanRank_span_le_card", "kind": "theorem", "module": "Mathlib.Algebra.Module.SpanRank", "is_tactic_proof": true, "tactics": ["rw", "let", "exact"], "tactic_count": 3}
{"name": "Submodule.spanRank_span_range_of_linearIndependent", "kind": "theorem", "module": "Mathlib.Algebra.Module.SpanRank", "is_tactic_proof": true, "tactics": ["refine", "have", "rw", "refine", "rw", "exact", "apply", "simp"], "tactic_count": 8}
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{"name": "Submodule.spanFinrank_span_le_encard", "kind": "theorem", "module": "Mathlib.Algebra.Module.SpanRank", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
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{"name": "Submodule.exists_span_set_card_eq_spanRank", "kind": "theorem", "module": "Mathlib.Algebra.Module.SpanRank", "is_tactic_proof": true, "tactics": ["rw", "obtain", "csInf_mem", "exact"], "tactic_count": 4}
{"name": "Submodule.FG.exists_span_set_encard_eq_spanFinrank", "kind": "theorem", "module": "Mathlib.Algebra.Module.SpanRank", "is_tactic_proof": true, "tactics": ["obtain", "refine", "have", "rw", "simp"], "tactic_count": 5}
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{"name": "Submodule.spanFinrank_bot", "kind": "theorem", "module": "Mathlib.Algebra.Module.SpanRank", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Submodule.generators", "kind": "definition", "module": "Mathlib.Algebra.Module.SpanRank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.generators_card", "kind": "theorem", "module": "Mathlib.Algebra.Module.SpanRank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.FG.generators_ncard", "kind": "theorem", "module": "Mathlib.Algebra.Module.SpanRank", "is_tactic_proof": false, "tactics": ["rw", "generators_card,", "exact"], "tactic_count": 3}
{"name": "Submodule.FG.finite_generators", "kind": "theorem", "module": "Mathlib.Algebra.Module.SpanRank", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Submodule.span_generators", "kind": "theorem", "module": "Mathlib.Algebra.Module.SpanRank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.FG.generators_mem", "kind": "theorem", "module": "Mathlib.Algebra.Module.SpanRank", "is_tactic_proof": true, "tactics": ["nth_rw", "exact"], "tactic_count": 2}
{"name": "Submodule.spanRank_sup_le_sum_spanRank", "kind": "theorem", "module": "Mathlib.Algebra.Module.SpanRank", "is_tactic_proof": true, "tactics": ["apply", "obtain", "obtain", "exact"], "tactic_count": 4}
{"name": "Submodule.spanFinrank_eq_zero_iff_eq_bot", "kind": "theorem", "module": "Mathlib.Algebra.Module.SpanRank", "is_tactic_proof": true, "tactics": ["refine", "rw", "rw"], "tactic_count": 3}
{"name": "Submodule.spanFinrank_singleton", "kind": "theorem", "module": "Mathlib.Algebra.Module.SpanRank", "is_tactic_proof": true, "tactics": ["apply", "exact", "by_contra", "simp"], "tactic_count": 4}
{"name": "Submodule.spanRank_map_le", "kind": "theorem", "module": "Mathlib.Algebra.Module.SpanRank", "is_tactic_proof": true, "tactics": ["rw", "exact", "le_antisymm"], "tactic_count": 3}
{"name": "Submodule.spanFinrank_map_le_of_fg", "kind": "theorem", "module": "Mathlib.Algebra.Module.SpanRank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.spanRank_map_eq_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Module.SpanRank", "is_tactic_proof": true, "tactics": ["refine", "obtain", "obtain", "obtain", "grw"], "tactic_count": 5}
{"name": "Submodule.spanRank_range_le", "kind": "theorem", "module": "Mathlib.Algebra.Module.SpanRank", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Submodule.spanRank_top", "kind": "theorem", "module": "Mathlib.Algebra.Module.SpanRank", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Submodule.spanRank_eq_of_equiv", "kind": "theorem", "module": "Mathlib.Algebra.Module.SpanRank", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submodule.le_spanRank_restrictScalars", "kind": "theorem", "module": "Mathlib.Algebra.Module.SpanRank", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "le_antisymm", "grw"], "tactic_count": 4}
{"name": "Submodule.spanRank_restrictScalars_eq", "kind": "theorem", "module": "Mathlib.Algebra.Module.SpanRank", "is_tactic_proof": true, "tactics": ["refine", "obtain", "grw"], "tactic_count": 3}
{"name": "Ideal.spanRank_map_le", "kind": "theorem", "module": "Mathlib.Algebra.Module.SpanRank", "is_tactic_proof": true, "tactics": ["rw", "refine", "le_antisymm", "refine", "simp", "rw", "exact"], "tactic_count": 7}
{"name": "Ideal.spanFinrank_map_le_of_fg", "kind": "theorem", "module": "Mathlib.Algebra.Module.SpanRank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.mk_eq_spanRank", "kind": "theorem", "module": "Mathlib.Algebra.Module.SpanRank", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Submodule.rank_eq_spanRank_of_free", "kind": "theorem", "module": "Mathlib.Algebra.Module.SpanRank", "is_tactic_proof": true, "tactics": ["haveI", "obtain", "rw"], "tactic_count": 3}
{"name": "Submodule.rank_le_spanRank", "kind": "theorem", "module": "Mathlib.Algebra.Module.SpanRank", "is_tactic_proof": true, "tactics": ["rw", "refine", "have", "simpa"], "tactic_count": 4}
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{"name": "Submodule.toAddSubmonoid_le", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.toAddSubmonoid_mono", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.toSubMulAction_strictMono", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.toSubMulAction_mono", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.sum_mem", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.sum_smul_mem", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.isCentralScalar", "kind": "instance", "module": "Mathlib.Algebra.Module.Submodule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.instIsTorsionFree", "kind": "instance", "module": "Mathlib.Algebra.Module.Submodule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.instVAddSubtypeMem", "kind": "instance", "module": "Mathlib.Algebra.Module.Submodule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.vaddCommClass", "kind": "instance", "module": "Mathlib.Algebra.Module.Submodule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.instFaithfulVAddSubtypeMem", "kind": "instance", "module": "Mathlib.Algebra.Module.Submodule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.vadd_def", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.toAddSubgroup_strictMono", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.toAddSubgroup_le", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.toAddSubgroup_mono", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.toAddSubgroup_toAddSubmonoid", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.neg_coe", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.notMem_of_ortho", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Basic", "is_tactic_proof": true, "tactics": ["intro", "simpa"], "tactic_count": 2}
{"name": "Submodule.ne_zero_of_ortho", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Subspace", "kind": "abbrev", "module": "Mathlib.Algebra.Module.Submodule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Submodule.instPartialOrder", "kind": "instance", "module": "Mathlib.Algebra.Module.Submodule.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.carrier_eq_coe", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.ofClass", "kind": "definition", "module": "Mathlib.Algebra.Module.Submodule.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Submodule.instCanLiftSetCoeAndMemOfNatForallForallForallForallHAddForallForallForallHSMul", "kind": "instance", "module": "Mathlib.Algebra.Module.Submodule.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.addSubmonoidClass", "kind": "instance", "module": "Mathlib.Algebra.Module.Submodule.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.smulMemClass", "kind": "instance", "module": "Mathlib.Algebra.Module.Submodule.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mem_toAddSubmonoid", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Submodule.eta", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Submodule.toAddSubmonoid_injective", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LinearMap.eqLocus_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.EqLocus", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "LinearEquiv.ofBijective_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.ofBijective_symm_apply_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Equiv", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LinearEquiv.apply_ofBijective_symm_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Equiv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submodule.equivSubtypeMap", "kind": "definition", "module": "Mathlib.Algebra.Module.Submodule.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.equivSubtypeMap_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.equivSubtypeMap_symm_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.comap_equiv_self_of_inj_of_le", "kind": "definition", "module": "Mathlib.Algebra.Module.Submodule.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.codRestrictOfInjective", "kind": "definition", "module": "Mathlib.Algebra.Module.Submodule.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.codRestrictOfInjective_comp_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Equiv", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LinearMap.codRestrictOfInjective_comp", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Equiv", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "LinearMap.codRestrict₂", "kind": "definition", "module": "Mathlib.Algebra.Module.Submodule.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.codRestrict₂_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Equiv", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Module.End.invtSubmodule", "kind": "definition", "module": "Mathlib.Algebra.Module.Submodule.Invariant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.mem_invtSubmodule", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Invariant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.mem_invtSubmodule_iff_map_le", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Invariant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.mem_invtSubmodule_iff_mapsTo", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Invariant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.mem_invtSubmodule_iff_forall_mem_of_mem", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Invariant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.mem_invtSubmodule_symm_iff_le_map", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Invariant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.invtSubmodule.inf_mem", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Invariant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.invtSubmodule.sup_mem", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Invariant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.invtSubmodule.top_mem", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Invariant", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Module.End.invtSubmodule.bot_mem", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Invariant", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Module.End.invtSubmodule.instBoundedOrderSubtypeSubmoduleMemSublattice", "kind": "instance", "module": "Mathlib.Algebra.Module.Submodule.Invariant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.invtSubmodule.zero", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Invariant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.invtSubmodule.id", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Invariant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.invtSubmodule.one", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Invariant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.invtSubmodule.mk_eq_bot_iff", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Invariant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.invtSubmodule.mk_eq_top_iff", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Invariant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.invtSubmodule.disjoint_mk_iff", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Invariant", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Module.End.invtSubmodule.disjoint_iff", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Invariant", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "simp"], "tactic_count": 3}
{"name": "Module.End.invtSubmodule.codisjoint_mk_iff", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Invariant", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Module.End.invtSubmodule.codisjoint_iff", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Invariant", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "simp"], "tactic_count": 3}
{"name": "Module.End.invtSubmodule.isCompl_mk_iff", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Invariant", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Module.End.invtSubmodule.isCompl_iff", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Invariant", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "simp"], "tactic_count": 3}
{"name": "Module.End.invtSubmodule.map_subtype_mem_of_mem_invtSubmodule", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Invariant", "is_tactic_proof": true, "tactics": ["rintro", "specialize", "rw", "simpa"], "tactic_count": 4}
{"name": "Module.End.invtSubmodule.comp", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Invariant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.map_mem_invtSubmodule_conj_iff", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Invariant", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "LinearEquiv.map_mem_invtSubmodule_iff", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Invariant", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Module.End.span_orbit_mem_invtSubmodule", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Invariant", "is_tactic_proof": true, "tactics": ["rw", "intro", "simp", "exact"], "tactic_count": 4}
{"name": "LinearMap.iterateMapComap", "kind": "definition", "module": "Mathlib.Algebra.Module.Submodule.IterateMapComap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.iterateMapComap_le_succ", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.IterateMapComap", "is_tactic_proof": true, "tactics": ["nth_rw", "rw", "induction", "zero", "succ", "simp_rw", "calc"], "tactic_count": 7}
{"name": "LinearMap.iterateMapComap_eq_succ", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.IterateMapComap", "is_tactic_proof": true, "tactics": ["induction", "zero", "contrapose", "induction", "zero", "succ", "rw", "exact", "succ", "rw", "iterateMapComap,"], "tactic_count": 11}
{"name": "LinearMap.ker_le_of_iterateMapComap_eq_succ", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.IterateMapComap", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "LinearMap.ker", "kind": "definition", "module": "Mathlib.Algebra.Module.Submodule.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.mem_ker", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.ker_id", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.map_coe_ker", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.ker_toAddSubmonoid", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.le_ker_iff_comp_subtype_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Ker", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LinearMap.comp_ker_subtype", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.ker_comp", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.ker_le_ker_comp", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Ker", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LinearMap.ker_sup_ker_le_ker_comp_of_commute", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Ker", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "LinearMap.ker_le_comap", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.disjoint_ker", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Ker", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LinearMap.ker_eq_bot'", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Ker", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "LinearMap.ker_eq_bot_of_inverse", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.le_ker_iff_map", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Ker", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LinearMap.ker_codRestrict", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Ker", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LinearMap.ker_domRestrict", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.ker_restrict", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Ker", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LinearMap.ker_zero", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.ker_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.exists_ne_zero_of_sSup_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Ker", "is_tactic_proof": true, "tactics": ["contrapose", "simp_rw", "exact"], "tactic_count": 3}
{"name": "AddMonoidHom.coe_toIntLinearMap_ker", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.ker_eq_bot_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Ker", "is_tactic_proof": true, "tactics": ["rw", "intro", "simpa"], "tactic_count": 3}
{"name": "LinearMap.iterateKer", "kind": "definition", "module": "Mathlib.Algebra.Module.Submodule.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.ker_toAddSubgroup", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.sub_mem_ker_iff", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Ker", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LinearMap.disjoint_ker_iff_injOn", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Ker", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LinearMap.disjoint_ker'", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Ker", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LinearMap.injOn_of_disjoint_ker", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.ker_eq_bot", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Ker", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "LinearMap.injective_domRestrict_iff", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Ker", "is_tactic_proof": true, "tactics": ["rw", "refine", "intro", "have", "rw", "simpa", "rintro", "have", "rw", "simpa"], "tactic_count": 10}
{"name": "LinearMap.injective_restrict_iff_disjoint", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Ker", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LinearMap.ker_smul", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.ker_smul'", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.comap_bot", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.ker_subtype", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.ker_inclusion", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Ker", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LinearMap.ker_comp_of_ker_eq_bot", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Ker", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LinearMap.ker_restrictScalars", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.ker", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.ker_comp", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.instBot", "kind": "instance", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.inhabited'", "kind": "instance", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.bot_coe", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.bot_toAddSubmonoid", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.bot_toAddSubgroup", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mem_bot", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mk_eq_bot", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Submodule.uniqueBot", "kind": "instance", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.instOrderBot", "kind": "instance", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.eq_bot_iff", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.bot_ext", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": true, "tactics": ["subsingleton"], "tactic_count": 1}
{"name": "Submodule.ne_bot_iff", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Submodule.nonzero_mem_of_bot_lt", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.exists_mem_ne_zero_of_ne_bot", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.botEquivPUnit", "kind": "definition", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.subsingleton_iff_eq_bot", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": true, "tactics": ["rw", "refine"], "tactic_count": 2}
{"name": "Submodule.eq_bot_of_subsingleton", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.nontrivial_iff_ne_bot", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submodule.instTop", "kind": "instance", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.top_coe", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.coe_eq_univ", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submodule.mem_top", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.top_toAddSubmonoid", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.top_toAddSubgroup", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.toAddSubgroup_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Submodule.mk_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Submodule.instOrderTop", "kind": "instance", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.eq_top_iff'", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.topEquiv", "kind": "definition", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.instInfSet", "kind": "instance", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Module.Submodule.Lattice.0.Submodule.sInf_le'", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Module.Submodule.Lattice.0.Submodule.le_sInf'", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.instMin", "kind": "instance", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.completeLattice", "kind": "instance", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.coe_inf", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mem_inf", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.coe_sInf", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.coe_finsetInf", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": true, "tactics": ["letI", "refine", "simp", "rw", "simp"], "tactic_count": 5}
{"name": "Submodule.coe_iInf", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submodule.mem_sInf", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mem_iInf", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submodule.mem_finsetInf", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Submodule.inf_iInf", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mem_sup_left", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "Submodule.mem_sup_right", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "Submodule.add_mem_sup", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.sub_mem_sup", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Submodule.mem_iSup_of_mem", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.sum_mem_iSup", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.sum_mem_biSup", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mem_sSup_of_mem", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "Submodule.toAddSubmonoid_sSup", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": false, "tactics": ["let", "smul_mem", "simp_rw", "induction", "mem", "obtain", "suffices", "apply", "rw", "exact", "zero", "add", "refine", "exact", "exact"], "tactic_count": 15}
{"name": "Submodule.subsingleton_iff", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.nontrivial_iff", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.instUniqueOfSubsingleton", "kind": "instance", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.unique'", "kind": "instance", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": true, "tactics": ["haveI"], "tactic_count": 1}
{"name": "Submodule.instNontrivial", "kind": "instance", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.disjoint_def", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.disjoint_def'", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.eq_zero_of_coe_mem_of_disjoint", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mem_right_iff_eq_zero_of_disjoint", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mem_left_iff_eq_zero_of_disjoint", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.toNatSubmodule", "kind": "definition", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.toNatSubmodule_symm", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.coe_toNatSubmodule", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.toNatSubmodule_toAddSubmonoid", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.toAddSubmonoid_toNatSubmodule", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroup.toIntSubmodule", "kind": "definition", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroup.toIntSubmodule_symm", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroup.coe_toIntSubmodule", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroup.toIntSubmodule_toAddSubgroup", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.toAddSubgroup_toIntSubmodule", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SMulMemClass.subtype", "kind": "definition", "module": "Mathlib.Algebra.Module.Submodule.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SMulMemClass.subtype_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SMulMemClass.subtype_injective", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SMulMemClass.coe_subtype", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.subtype", "kind": "definition", "module": "Mathlib.Algebra.Module.Submodule.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.subtype_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.subtype_injective", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.coe_subtype", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.injective_subtype", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.coe_sum", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.instAddActionSubtypeMem", "kind": "instance", "module": "Mathlib.Algebra.Module.Submodule.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.domRestrict", "kind": "definition", "module": "Mathlib.Algebra.Module.Submodule.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.domRestrict_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.coe_domRestrict", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.codRestrict", "kind": "definition", "module": "Mathlib.Algebra.Module.Submodule.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.codRestrict_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.comp_codRestrict", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.subtype_comp_codRestrict", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.codLift", "kind": "definition", "module": "Mathlib.Algebra.Module.Submodule.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.codLift_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.comp_codLift", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.LinearMap", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "LinearMap.restrict", "kind": "definition", "module": "Mathlib.Algebra.Module.Submodule.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.restrict_coe_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.restrict_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.restrict_commute", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.LinearMap", "is_tactic_proof": true, "tactics": ["change", "congr"], "tactic_count": 2}
{"name": "LinearMap.subtype_comp_restrict", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.restrict_eq_codRestrict_domRestrict", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.restrict_eq_domRestrict_codRestrict", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.sum_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.coe_sum", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.submodule_pow_eq_zero_of_pow_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.LinearMap", "is_tactic_proof": true, "tactics": ["ext", "have", "rw", "simpa"], "tactic_count": 4}
{"name": "Module.End.pow_apply_mem_of_forall_mem", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.LinearMap", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "LinearMap.domRestrict'", "kind": "definition", "module": "Mathlib.Algebra.Module.Submodule.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.domRestrict'_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.inclusion", "kind": "definition", "module": "Mathlib.Algebra.Module.Submodule.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.coe_inclusion", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.inclusion_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.inclusion_injective", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.subtype_comp_inclusion", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.map", "kind": "definition", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.map_coe", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.map_toAddSubmonoid", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.map_toAddSubmonoid'", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.coe_toIntLinearMap_map", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.coe_toAdditive_map", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.coe_toMultiplicative_map", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mem_map", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mem_map_of_mem", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.apply_coe_mem_map", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.map_id", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.map_comp", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.map_mono", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.map_zero", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.map_add_le", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "Submodule.map_inf_le", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.map_inf", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.map_iInf", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.range_map_nonempty", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.equivMapOfInjective", "kind": "definition", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.coe_equivMapOfInjective_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.map_equivMapOfInjective_symm_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submodule.comap", "kind": "definition", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.comap_coe", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.AddMonoidHom.coe_toIntLinearMap_comap", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mem_comap", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.comap_id", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.comap_comp", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.comap_mono", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.le_comap_pow_of_le_comap", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Submodule.map_le_iff_le_comap", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.gc_map_comap", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.map_bot", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.map_sup", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.map_iSup", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.disjoint_map", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submodule.comap_top", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.comap_inf", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.comap_iInf", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.comap_finsetInf", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Submodule.comap_zero", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.map_comap_le", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.le_comap_map", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.submoduleOf", "kind": "definition", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.submoduleOfEquivOfLe", "kind": "definition", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.giMapComap", "kind": "definition", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.map_comap_eq_of_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.map_surjective_of_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.comap_injective_of_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.map_sup_comap_of_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.map_iSup_comap_of_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.map_inf_comap_of_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.map_iInf_comap_of_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.comap_le_comap_iff_of_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.comap_lt_comap_iff_of_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "Submodule.comap_strictMono_of_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.le_map_of_comap_le_of_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.lt_map_of_comap_lt_of_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Submodule.gciMapComap", "kind": "definition", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.comap_map_eq_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.comap_surjective_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.map_injective_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.comap_inf_map_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.comap_iInf_map_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.comap_sup_map_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.comap_iSup_map_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.map_le_map_iff_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.map_strictMono_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.map_lt_map_iff_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submodule.comap_lt_of_lt_map_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Submodule.map_covBy_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": true, "tactics": ["refine", "intro", "refine", "rw", "refine", "exact"], "tactic_count": 6}
{"name": "Submodule.orderIsoMapComapOfBijective", "kind": "definition", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.orderIsoMapComap", "kind": "definition", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.orderIsoMapComap_symm_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.map_eq_bot_iff", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.map_eq_top_iff", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.map_ne_bot_iff", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Submodule.map_ne_top_iff", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Submodule.map_inf_eq_map_inf_comap", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.map_comap_subtype", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.eq_zero_of_bot_submodule", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.iInf_invariant", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Submodule.disjoint_iff_comap_eq_bot", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": true, "tactics": ["rw", "map_bot,"], "tactic_count": 2}
{"name": "Submodule.map_neg", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.comap_neg", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Submodule.map_toAddSubgroup", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.comap_smul", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Submodule.map_smul", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.comap_smul'", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Submodule.map_smul'", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Submodule.comapSubtypeEquivOfLe", "kind": "definition", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mem_map_equiv", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": true, "tactics": ["rw", "rintro", "simp", "intro", "exact"], "tactic_count": 5}
{"name": "Submodule.map_equiv_eq_comap_symm", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.comap_equiv_eq_map_symm", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.map_symm_eq_iff", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Submodule.orderIsoMapComap_apply'", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.orderIsoMapComap_symm_apply'", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.inf_comap_le_comap_add", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Submodule.surjOn_iff_le_map", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.comap_le_comap_smul", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Submodule.compatibleMaps", "kind": "definition", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.submoduleComap", "kind": "definition", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.submoduleComap_surjective_of_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.submoduleMap", "kind": "definition", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.submoduleMap_coe_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.submoduleMap_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.map_codRestrict", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.comap_codRestrict", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.submoduleMap", "kind": "definition", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.submoduleMap_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.submoduleMap_symm_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.toIsOrderedAddMonoid", "kind": "instance", "module": "Mathlib.Algebra.Module.Submodule.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.toIsOrderedCancelAddMonoid", "kind": "instance", "module": "Mathlib.Algebra.Module.Submodule.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.pointwiseNeg", "kind": "definition", "module": "Mathlib.Algebra.Module.Submodule.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.coe_set_neg", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.neg_toAddSubmonoid", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mem_neg", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.involutivePointwiseNeg", "kind": "definition", "module": "Mathlib.Algebra.Module.Submodule.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.neg_le_neg", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.neg_le", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.negOrderIso", "kind": "definition", "module": "Mathlib.Algebra.Module.Submodule.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.span_neg_eq_neg", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Pointwise", "is_tactic_proof": true, "tactics": ["apply", "rw", "exact", "rw", "exact"], "tactic_count": 5}
{"name": "Submodule.neg_inf", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.neg_sup", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.neg_bot", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.neg_top", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.neg_iInf", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.neg_iSup", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.neg_eq_self", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.pointwiseZero", "kind": "instance", "module": "Mathlib.Algebra.Module.Submodule.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.pointwiseAdd", "kind": "instance", "module": "Mathlib.Algebra.Module.Submodule.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.pointwiseAddCommMonoid", "kind": "instance", "module": "Mathlib.Algebra.Module.Submodule.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.add_eq_sup", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.zero_eq_bot", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.instIsOrderedAddMonoid", "kind": "instance", "module": "Mathlib.Algebra.Module.Submodule.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.instCanonicallyOrderedAdd", "kind": "instance", "module": "Mathlib.Algebra.Module.Submodule.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.pointwiseDistribMulAction", "kind": "definition", "module": "Mathlib.Algebra.Module.Submodule.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.coe_pointwise_smul", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.pointwise_smul_toAddSubmonoid", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.pointwise_smul_toAddSubgroup", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mem_smul_pointwise_iff_exists", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.smul_mem_pointwise_smul", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.instCovariantClassHSMulLe", "kind": "instance", "module": "Mathlib.Algebra.Module.Submodule.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.smul_bot'", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.smul_sup'", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.smul_iSup'", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.smul_span", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.smul_def", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Pointwise", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Submodule.span_smul", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.pointwiseCentralScalar", "kind": "instance", "module": "Mathlib.Algebra.Module.Submodule.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.smul_le_self_of_tower", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Pointwise", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "Submodule.pointwiseMulActionWithZero", "kind": "definition", "module": "Mathlib.Algebra.Module.Submodule.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.pointwiseSetSMul", "kind": "definition", "module": "Mathlib.Algebra.Module.Submodule.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mem_set_smul_def", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mem_set_smul_of_mem_mem", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Pointwise", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Submodule.set_smul_le", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.set_smul_le_iff", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Pointwise", "is_tactic_proof": true, "tactics": ["fconstructor", "intro", "exact", "apply"], "tactic_count": 4}
{"name": "Submodule.set_smul_eq_of_le", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.instCovariantClassSetHSMulLe", "kind": "instance", "module": "Mathlib.Algebra.Module.Submodule.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.set_smul_mono_left", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.set_smul_le_of_le_le", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.set_smul_eq_iSup", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Pointwise", "is_tactic_proof": true, "tactics": ["refine", "simp_rw", "exact"], "tactic_count": 3}
{"name": "Submodule.set_smul_span", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Pointwise", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Submodule.span_set_smul", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.set_smul_inductionOn", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.set_smul_eq_map", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Pointwise", "is_tactic_proof": true, "tactics": ["classical", "apply", "intro", "exact", "intro", "obtain", "simp", "rw", "refine", "rintro", "rw", "rintro", "exact", "ext", "simp", "fconstructor", "refine", "rw", "exact", "simp_all"], "tactic_count": 20}
{"name": "Submodule.mem_set_smul", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Pointwise", "is_tactic_proof": true, "tactics": ["fconstructor", "intro", "rw", "obtain", "exact", "rw", "rintro", "rw", "exact"], "tactic_count": 9}
{"name": "Submodule.empty_set_smul", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Pointwise", "is_tactic_proof": true, "tactics": ["ext", "fconstructor", "intro", "rw", "exact", "rintro"], "tactic_count": 6}
{"name": "Submodule.set_smul_bot", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.singleton_set_smul", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Pointwise", "is_tactic_proof": true, "tactics": ["apply", "rintro", "rintro", "rw", "intro"], "tactic_count": 5}
{"name": "Submodule.mem_singleton_set_smul", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Pointwise", "is_tactic_proof": true, "tactics": ["fconstructor", "intro", "induction", "smul₀", "rcases", "exact", "add", "rcases", "rcases", "exact", "zero", "aesop"], "tactic_count": 12}
{"name": "Submodule.smul_inductionOn_pointwise", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Pointwise", "is_tactic_proof": true, "tactics": ["simp_all", "let", "refine", "push", "subst", "exact"], "tactic_count": 6}
{"name": "Submodule.pointwiseSetMulAction", "kind": "definition", "module": "Mathlib.Algebra.Module.Submodule.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.pointwiseSetDistribMulAction", "kind": "definition", "module": "Mathlib.Algebra.Module.Submodule.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.sup_set_smul", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.range", "kind": "definition", "module": "Mathlib.Algebra.Module.Submodule.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.coe_range", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.range_toAddSubmonoid", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.mem_range", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.range_eq_map", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Range", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "LinearMap.mem_range_self", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.range_id", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.range_comp", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.range_comp_le_range", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.range_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Range", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LinearMap.range_eq_top_of_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.range_add_le", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Range", "is_tactic_proof": true, "tactics": ["rintro", "apply", "all_goals"], "tactic_count": 3}
{"name": "LinearMap.range_le_iff_comap", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Range", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LinearMap.map_le_range", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.range_neg", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Range", "is_tactic_proof": true, "tactics": ["change", "rw"], "tactic_count": 2}
{"name": "LinearMap.range_domRestrict", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Range", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "LinearMap.range_domRestrict_le_range", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Range", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "AddMonoidHom.coe_toIntLinearMap_range", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.map_comap_eq_of_le", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.range_restrictScalars", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.iterateRange", "kind": "definition", "module": "Mathlib.Algebra.Module.Submodule.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.rangeRestrict", "kind": "abbrev", "module": "Mathlib.Algebra.Module.Submodule.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.fintypeRange", "kind": "instance", "module": "Mathlib.Algebra.Module.Submodule.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.range_codRestrict", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Range", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Submodule.map_comap_eq", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.map_comap_eq_self", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Range", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "LinearMap.range_zero", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Range", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "LinearMap.range_le_bot_iff", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Range", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LinearMap.range_eq_bot", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Range", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LinearMap.range_le_ker_iff", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.comap_le_comap_iff", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.comap_injective", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.ker_eq_range_of_comp_eq_id", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.range_toAddSubgroup", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.ker_le_iff", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Range", "is_tactic_proof": true, "tactics": ["constructor", "intro", "use", "rw", "exact", "rintro", "rw", "intro", "simp", "rw", "obtain", "have", "have", "apply", "simp", "suffices", "exact"], "tactic_count": 17}
{"name": "LinearMap.range_smul", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Range", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "LinearMap.range_smul'", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Range", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Submodule.map_top", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.range_subtype", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Range", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Submodule.map_subtype_le", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Range", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Submodule.map_subtype_top", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Range", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Submodule.comap_subtype_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.submoduleOf_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Range", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Submodule.comap_subtype_self", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.submoduleOf_self", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.submoduleOf_sup_of_le", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Range", "is_tactic_proof": true, "tactics": ["apply", "simp", "simp_all"], "tactic_count": 3}
{"name": "Submodule.comap_subtype_le_iff", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.range_inclusion", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Range", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submodule.map_subtype_range_inclusion", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Range", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Submodule.restrictScalars_map", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.MapSubtype.orderIso", "kind": "definition", "module": "Mathlib.Algebra.Module.Submodule.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.MapSubtype.orderEmbedding", "kind": "definition", "module": "Mathlib.Algebra.Module.Submodule.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.map_subtype_embedding_eq", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mapIic", "kind": "definition", "module": "Mathlib.Algebra.Module.Submodule.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.coe_mapIic_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.codisjoint_map", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Range", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LinearMap.ker_eq_bot_of_cancel", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Range", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "LinearMap.range_comp_of_range_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Range", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LinearMap.submoduleImage", "kind": "definition", "module": "Mathlib.Algebra.Module.Submodule.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.mem_submoduleImage", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Range", "is_tactic_proof": true, "tactics": ["refine", "rintro", "exact", "rintro", "exact"], "tactic_count": 5}
{"name": "LinearMap.mem_submoduleImage_of_le", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Range", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "LinearMap.submoduleImage_apply_of_le", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Range", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LinearMap.range_rangeRestrict", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Range", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LinearMap.surjective_rangeRestrict", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Range", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LinearMap.ker_rangeRestrict", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.injective_rangeRestrict_iff", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.restrictScalars", "kind": "definition", "module": "Mathlib.Algebra.Module.Submodule.RestrictScalars", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.coe_restrictScalars", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.RestrictScalars", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.toAddSubmonoid_restrictScalars", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.RestrictScalars", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.restrictScalars_mem", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.RestrictScalars", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.restrictScalars_self", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.RestrictScalars", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.restrictScalars_injective", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.RestrictScalars", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.restrictScalars_inj", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.RestrictScalars", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.restrictScalars.origModule", "kind": "instance", "module": "Mathlib.Algebra.Module.Submodule.RestrictScalars", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.restrictScalars.isScalarTower", "kind": "instance", "module": "Mathlib.Algebra.Module.Submodule.RestrictScalars", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.restrictScalars_le", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.RestrictScalars", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.restrictScalars_lt", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.RestrictScalars", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.restrictScalarsEmbedding", "kind": "definition", "module": "Mathlib.Algebra.Module.Submodule.RestrictScalars", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.restrictScalars_monotone", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.RestrictScalars", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.restrictScalars_mono", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.RestrictScalars", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.restrictScalarsEquiv", "kind": "definition", "module": "Mathlib.Algebra.Module.Submodule.RestrictScalars", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.restrictScalars_bot", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.RestrictScalars", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.restrictScalars_eq_bot_iff", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.RestrictScalars", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Submodule.restrictScalars_top", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.RestrictScalars", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.restrictScalars_eq_top_iff", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.RestrictScalars", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Submodule.restrictScalars_sInf", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.RestrictScalars", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Submodule.restrictScalars_sSup", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.RestrictScalars", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Submodule.restrictScalarsLatticeHom", "kind": "definition", "module": "Mathlib.Algebra.Module.Submodule.RestrictScalars", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.restrictScalars_iInf", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.RestrictScalars", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Submodule.restrictScalars_iSup", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.RestrictScalars", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.restrictScalars_inf", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.RestrictScalars", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Submodule.restrictScalars_sup", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.RestrictScalars", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Submodule.toIntSubmodule_toAddSubgroup", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.RestrictScalars", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.iUnion_ssubset_of_forall_ne_top_of_card_lt", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Union", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "insert", "simp", "rcases", "simpa", "replace", "specialize", "contrapose", "replace", "simpa", "suffices", "intro", "rcases", "simpa", "obtain", "have", "let", "have", "suffices", "rw", "rintro", "rw", "contradiction", "obtain", "suffices", "obtain", "exact", "choose", "have", "suffices", "obtain", "exact", "simp_all,", "have", "refine", "have", "have", "rw", "obtain", "exact", "replace", "have", "refine", "rwa", "replace", "simpa"], "tactic_count": 48}
{"name": "Submodule.exists_forall_notMem_of_forall_ne_top", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Union", "is_tactic_proof": true, "tactics": ["let", "suffices", "simpa"], "tactic_count": 3}
{"name": "Module.Dual.exists_forall_ne_zero_of_forall_exists", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Union", "is_tactic_proof": true, "tactics": ["let", "replace", "obtain", "exact"], "tactic_count": 4}
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{"name": "Module.exists_dual_forall_apply_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Module.Submodule.Union", "is_tactic_proof": true, "tactics": ["refine", "by_contra", "simp_rw", "exact"], "tactic_count": 4}
{"name": "Ideal.torsionOf", "kind": "definition", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.torsionOf_zero", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Ideal.mem_torsionOf_iff", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.torsionOf_eq_top_iff", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "Ideal.torsionOf_eq_bot_iff_of_noZeroSMulDivisors", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact", "rw", "tauto"], "tactic_count": 5}
{"name": "Ideal.iSupIndep.linearIndependent'", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": true, "tactics": ["refine", "replace", "simp", "have", "rw", "refine", "convert", "ext", "simp", "rw", "simpa"], "tactic_count": 11}
{"name": "Ideal.quotTorsionOfEquivSpanSingleton", "kind": "definition", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.quotTorsionOfEquivSpanSingleton_apply_mk", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.torsionBy", "kind": "definition", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.torsionBySet", "kind": "definition", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.torsion'", "kind": "definition", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.torsion", "kind": "abbrev", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.IsTorsionBy", "kind": "abbrev", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.IsTorsionBySet", "kind": "abbrev", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.IsTorsion'", "kind": "abbrev", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.IsTorsion", "kind": "abbrev", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.isTorsionBySet_annihilator", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.isTorsionBy_iff_mem_annihilator", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Module.isTorsionBySet_iff_subset_annihilator", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "rw"], "tactic_count": 2}
{"name": "isSMulRegular_iff_torsionBy_eq_bot", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.smul_torsionBy", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.smul_coe_torsionBy", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mem_torsionBy_iff", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mem_torsionBySet_iff", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": true, "tactics": ["refine", "rintro"], "tactic_count": 2}
{"name": "Submodule.torsionBySet_singleton_eq", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Submodule.torsionBySet_le_torsionBySet_of_subset", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.torsionBySet_eq_torsionBySet_span", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "suffices", "rintro", "exact", "rw", "exact"], "tactic_count": 7}
{"name": "Submodule.torsionBySet_span_singleton_eq", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.torsionBy_le_torsionBy_of_dvd", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply", "rintro"], "tactic_count": 3}
{"name": "Submodule.torsionBy_one", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.torsionBySet_univ", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Module.isTorsionBySet_of_subset", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.isTorsionBySet_singleton_iff", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": true, "tactics": ["refine", "rintro"], "tactic_count": 2}
{"name": "Module.isTorsionBySet_iff_is_torsion_by_span", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Module.isTorsionBySet_span_singleton_iff", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.isTorsionBySet_iff_torsionBySet_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.isTorsionBy_iff_torsionBy_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Module.isTorsionBySet_iff_subseteq_ker_lsmul", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.isTorsionBy_iff_mem_ker_lsmul", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.torsionBySet_isTorsionBySet", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.torsionBy_isTorsionBy", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.torsionBy_torsionBy_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.torsionBySet_torsionBySet_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.torsion_gc", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.iSup_torsionBySet_ideal_eq_torsionBySet_iInf", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simp", "apply", "apply", "intro", "apply", "intro", "apply", "exact", "intro", "rw", "obtain", "refine", "rw", "rintro", "rw", "suffices", "rw", "intro", "rw", "intro", "by_cases", "rw", "exact", "have", "simp", "exact", "rw"], "tactic_count": 28}
{"name": "Submodule.supIndep_torsionBySet_ideal", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.iSup_torsionBy_eq_torsionBy_prod", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": ["rw", "congr", "ext", "congr", "ext", "exact", "exact"], "tactic_count": 7}
{"name": "Submodule.supIndep_torsionBy", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": ["convert", "supIndep_torsionBySet_ideal", "exact"], "tactic_count": 3}
{"name": "Submodule.torsionBySet_isInternal", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.torsionBy_isInternal", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": ["rw", "convert", "exact"], "tactic_count": 3}
{"name": "Module.IsTorsionBySet.hasSMul", "kind": "definition", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.IsTorsionBy.hasSMul", "kind": "abbrev", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.IsTorsionBySet.mk_smul", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.IsTorsionBy.mk_smul", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.IsTorsionBySet.module", "kind": "definition", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.IsTorsionBySet.isScalarTower", "kind": "instance", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.IsTorsionBySet.semilinearMap", "kind": "definition", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.IsTorsionBySet.isSemisimpleModule_iff", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.IsTorsionBy.module", "kind": "abbrev", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Module.quotientAnnihilator", "kind": "definition", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.isTorsionBy_quotient_iff", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.IsTorsionBy.quotient", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.isTorsionBySet_quotient_iff", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.IsTorsionBySet.quotient", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.isTorsionBySet_quotient_set_smul", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.isTorsionBySet_quotient_ideal_smul", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.instQuotientIdealSubmoduleHSMulTop", "kind": "instance", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Quotient.mk_smul_mk", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.isTorsionBy_quotient_element_smul", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.instQuotientIdealSpanSubmoduleHSMulSetTop", "kind": "instance", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.instQuotientIdealSpanSingletonSetSubmoduleHSMulTop", "kind": "instance", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.instModuleQuotientIdealSubtypeMemTorsionBySetCoe", "kind": "instance", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.torsionBySet.mk_smul", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.instIsScalarTowerQuotientIdealSubtypeMemTorsionBySetCoe", "kind": "instance", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.instModuleQuotientTorsionBy", "kind": "instance", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.instModuleQuotientIdealSpanSingletonSetSubtypeMemTorsionBy", "kind": "instance", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.torsionBy.mk_ideal_smul", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.torsionBy.mk_smul", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.instIsScalarTowerQuotientSpanSingletonSetSubtypeMemTorsionBy", "kind": "instance", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.submodule_torsionBy_orderIso", "kind": "definition", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mem_torsion'_iff", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mem_torsion_iff", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.instSMulSubtypeMemTorsion'", "kind": "instance", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.instDistribMulActionSubtypeMemTorsion'", "kind": "instance", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.instSMulCommClassSubtypeMemTorsion'", "kind": "instance", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.isTorsion'_iff_torsion'_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.torsion'_isTorsion'", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.torsion'_torsion'_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.torsion_torsion_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.torsion_isTorsion", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.isTorsionBySet_annihilator_top", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.annihilator_top_inter_nonZeroDivisors", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": true, "tactics": ["obtain", "refine", "rw", "intro", "letI", "rw"], "tactic_count": 6}
{"name": "Submodule.coe_torsion_eq_annihilator_ne_bot", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": true, "tactics": ["ext", "exact", "nonZeroDivisors.coe_ne_zero"], "tactic_count": 3}
{"name": "Submodule.torsion_int", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": true, "tactics": ["ext", "refine", "simp"], "tactic_count": 3}
{"name": "Submodule.isTorsionFree_iff_torsion_eq_bot", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": true, "tactics": ["simp", "grind"], "tactic_count": 2}
{"name": "Submodule.QuotientTorsion.torsion_eq_bot", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.QuotientTorsion.instIsTorsionFree", "kind": "instance", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.isTorsion'_powers_iff", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": true, "tactics": ["constructor", "intro", "let", "dsimp", "use", "rw", "apply", "intro", "let", "exact"], "tactic_count": 10}
{"name": "Submodule.pOrder", "kind": "definition", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.pow_pOrder_smul", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.exists_isTorsionBy", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": true, "tactics": ["let", "have", "use", "rw", "intro", "have", "rw"], "tactic_count": 7}
{"name": "Ideal.Quotient.torsionBy_eq_span_singleton", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": true, "tactics": ["ext", "obtain", "rw", "obtain", "rw", "use", "rw", "obtain", "rw", "smul_zero]"], "tactic_count": 10}
{"name": "AddMonoid.isTorsion_iff_isTorsion_nat", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact", "rw", "obtain", "exact"], "tactic_count": 6}
{"name": "AddMonoid.isTorsion_iff_isTorsion_int", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact", "rw", "obtain", "exact"], "tactic_count": 6}
{"name": "AddSubgroup.torsionBy", "kind": "definition", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroup.torsionByStx", "kind": "definition", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroup._aux_Mathlib_Algebra_Module_Torsion_Basic___macroRules_AddSubgroup_torsionByStx_1", "kind": "definition", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroup.torsionByUnexpander", "kind": "definition", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroup.torsionBy.neg", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "AddSubgroup.torsionBy.nsmul", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroup.torsionBy.nsmul_iff", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroup.torsionBy.mod_self_nsmul", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroup.torsionBy.mod_self_nsmul'", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroup.torsionBy.zmodModule", "kind": "definition", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "infinite_range_add_smul_iff", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "infinite_range_add_nsmul_iff", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "simpa"], "tactic_count": 3}
{"name": "DivisionSemiring.to_moduleIsTorsionFree", "kind": "instance", "module": "Mathlib.Algebra.Module.Torsion.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsTorsionFree", "kind": "instance", "module": "Mathlib.Algebra.Module.Torsion.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Function.Injective.moduleIsTorsionFree", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.IsTorsionFree.comap", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAddTorsionFree.to_isTorsionFree_nat", "kind": "instance", "module": "Mathlib.Algebra.Module.Torsion.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsingleton.to_moduleIsTorsionFree", "kind": "instance", "module": "Mathlib.Algebra.Module.Torsion.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "IsRegular.smul_right_inj", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Module.IsTorsionFree.trans", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSMulRegular.of_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smul_right_injective", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "smul_eq_zero_iff_left", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Free", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "IsAddTorsionFree.of_isTorsionFree", "kind": "theorem", "module": "Mathlib.Algebra.Module.Torsion.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "instIsTorsionFreeIntOfIsAddTorsionFree", "kind": "instance", "module": "Mathlib.Algebra.Module.Torsion.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Prod.moduleIsTorsionFree", "kind": "instance", "module": "Mathlib.Algebra.Module.Torsion.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Equiv.linearEquiv", "kind": "definition", "module": "Mathlib.Algebra.Module.TransferInstance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AddEquiv.module", "kind": "abbrev", "module": "Mathlib.Algebra.Module.TransferInstance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.isScalarTower", "kind": "theorem", "module": "Mathlib.Algebra.Module.TransferInstance", "is_tactic_proof": true, "tactics": ["letI", "constructor", "intro", "simp", "apply"], "tactic_count": 5}
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{"name": "ULift.isScalarTower", "kind": "instance", "module": "Mathlib.Algebra.Module.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.isScalarTower'", "kind": "instance", "module": "Mathlib.Algebra.Module.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.isScalarTower''", "kind": "instance", "module": "Mathlib.Algebra.Module.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.instIsCentralScalar", "kind": "instance", "module": "Mathlib.Algebra.Module.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.mulAction", "kind": "instance", "module": "Mathlib.Algebra.Module.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ULift.distribSMul", "kind": "instance", "module": "Mathlib.Algebra.Module.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.distribSMul'", "kind": "instance", "module": "Mathlib.Algebra.Module.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ULift.smulWithZero", "kind": "instance", "module": "Mathlib.Algebra.Module.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ULift.mulActionWithZero", "kind": "instance", "module": "Mathlib.Algebra.Module.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ZSpan.span_top", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "ZSpan.map_fundamentalDomain", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": true, "tactics": ["ext", "rw", "show", "rfl"], "tactic_count": 4}
{"name": "ZSpan.fundamentalDomain_reindex", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "ZSpan.fundamentalDomain_pi_basisFun", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
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{"name": "ZSpan.repr_ceil_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": true, "tactics": ["classical", "simp", "coe_smul_of_tower,"], "tactic_count": 3}
{"name": "ZSpan.floor_eq_self_of_mem", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": true, "tactics": ["apply", "simp_rw", "intro", "obtain", "rw", "exact"], "tactic_count": 6}
{"name": "ZSpan.ceil_eq_self_of_mem", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": true, "tactics": ["apply", "simp_rw", "intro", "obtain", "rw", "exact"], "tactic_count": 6}
{"name": "ZSpan.fract", "kind": "definition", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZSpan.fract_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZSpan.repr_fract_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ZSpan.fract_fract", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZSpan.fract_zSpan_add", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": true, "tactics": ["classical", "refine", "simp_rw", "use", "rw"], "tactic_count": 5}
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{"name": "ZSpan.fract_eq_self", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "ZSpan.fract_mem_fundamentalDomain", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZSpan.fractRestrict", "kind": "definition", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZSpan.fractRestrict_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZSpan.fractRestrict_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZSpan.fract_eq_fract", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": true, "tactics": ["classical", "rw", "simp_rw"], "tactic_count": 3}
{"name": "ZSpan.norm_fract_le", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": true, "tactics": ["classical", "calc", "suffices", "convert", "exact", "rw", "apply", "rw", "exact"], "tactic_count": 9}
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{"name": "ZSpan.coe_fract_self", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZSpan.fundamentalDomain_isBounded", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": true, "tactics": ["cases", "refine", "rw", "apply"], "tactic_count": 4}
{"name": "ZSpan.vadd_mem_fundamentalDomain", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": true, "tactics": ["rw", "fract_zSpan_add"], "tactic_count": 2}
{"name": "ZSpan.exist_unique_vadd_mem_fundamentalDomain", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": true, "tactics": ["cases", "refine", "exact", "exact"], "tactic_count": 4}
{"name": "ZSpan.quotientEquiv", "kind": "definition", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": true, "tactics": ["refine", "refine", "rw", "exact", "refine", "rw", "apply", "rwa", "obtain", "exact"], "tactic_count": 10}
{"name": "ZSpan.quotientEquiv_apply_mk", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZSpan.quotientEquiv.symm_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ZSpan.discreteTopology_pi_basisFun", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": true, "tactics": ["cases", "refine", "ext", "rw", "simp_rw", "refine", "rsuffices", "rw", "exact"], "tactic_count": 9}
{"name": "ZSpan.fundamentalDomain_subset_parallelepiped", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ZSpan.instDiscreteTopologySubtypeMemSubmoduleIntSpanRangeCoeBasisRealOfFinite", "kind": "instance", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": false, "tactics": ["have", "intro", "rwa", "convert", "exact", "refine"], "tactic_count": 6}
{"name": "ZSpan.instDiscreteTopologySubtypeMemAddSubgroupToAddSubgroupIntSpanRangeCoeBasisRealOfFinite", "kind": "instance", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZSpan.setFinite_inter", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": true, "tactics": ["have", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "ZSpan.fundamentalDomain_measurableSet", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": true, "tactics": ["cases", "haveI", "let", "rw", "refine", "exact", "ext", "simp"], "tactic_count": 8}
{"name": "ZSpan.isAddFundamentalDomain", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": true, "tactics": ["cases", "exact", "exist_unique_vadd_mem_fundamentalDomain"], "tactic_count": 3}
{"name": "ZSpan.isAddFundamentalDomain'", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZSpan.measure_fundamentalDomain_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": true, "tactics": ["convert", "exact"], "tactic_count": 2}
{"name": "ZSpan.measure_fundamentalDomain", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": true, "tactics": ["have", "convert", "rw", "simp"], "tactic_count": 4}
{"name": "ZSpan.measureReal_fundamentalDomain", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ZSpan.volume_fundamentalDomain", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": false, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "ZSpan.volume_real_fundamentalDomain", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ZSpan.fundamentalDomain_ae_parallelepiped", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": true, "tactics": ["classical", "have", "rw", "suffices", "refine", "refine", "simp_rw", "exact", "intro", "simp_rw", "not_forall,", "obtain", "have", "rw", "refine", "exact"], "tactic_count": 16}
{"name": "instIsZLatticeRealSpan", "kind": "instance", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZLattice.FG", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": false, "tactics": ["obtain", "exists_linearIndependent", "refine", "refine", "let", "rw", "exact", "rw", "have", "refine", "have", "change", "have", "exact", "refine", "rintro", "rw", "refine", "exact", "rw", "refine", "rw", "exact", "rw", "exact"], "tactic_count": 25}
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{"name": "instModuleFinite_of_discrete_submodule", "kind": "instance", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": true, "tactics": ["let", "let", "have", "rw", "exact", "suffices", "have", "convert", "have", "refine", "exact", "have", "rw", "range_subtype,", "exact"], "tactic_count": 15}
{"name": "ZLattice.module_free", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": true, "tactics": ["have", "have", "have", "infer_instance"], "tactic_count": 4}
{"name": "instModuleFree_of_discrete_submodule", "kind": "instance", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": true, "tactics": ["have", "have", "infer_instance"], "tactic_count": 3}
{"name": "ZLattice.rank", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": true, "tactics": ["classical", "have", "have", "have", "let", "let", "have", "have", "convert", "rw", "rfl", "exact", "have", "rw", "exact", "have", "rw", "rfl", "exact", "rw", "refine", "obtain", "exists_linearIndependent", "let", "have", "have", "rwa", "contrapose", "obtain", "rw", "contrapose", "rw", "replace", "rwa", "suffices", "contrapose", "refine", "exact", "rw", "linearIndepOn_id_insert", "intro", "have", "rw", "refine", "rw", "refine", "exact", "exact", "have", "change", "have", "exact", "obtain", "have", "apply", "refine", "rwa", "rw", "convert"], "tactic_count": 59}
{"name": "Module.Basis.ofZLatticeBasis", "kind": "definition", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": true, "tactics": ["have", "have", "let", "have", "refine", "rw", "hs.span_top]", "rw"], "tactic_count": 8}
{"name": "Module.Basis.ofZLatticeBasis_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Module.Basis.ofZLatticeBasis_repr_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": false, "tactics": ["suffices", "refine", "simp_rw", "b.ofZLatticeBasis_apply"], "tactic_count": 4}
{"name": "Module.Basis.ofZLatticeBasis_span", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": true, "tactics": ["calc", "span"], "tactic_count": 2}
{"name": "ZLattice.isAddFundamentalDomain", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": true, "tactics": ["convert", "all_goals"], "tactic_count": 2}
{"name": "instCountable_of_discrete_submodule", "kind": "instance", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "infer_instance"], "tactic_count": 2}
{"name": "Real.finrank_eq_int_finrank_of_discrete", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": true, "tactics": ["let", "let", "let", "have", "let", "exact", "have", "rw", "exact"], "tactic_count": 9}
{"name": "IsZLattice.basis", "kind": "definition", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZLattice.comap", "kind": "definition", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZLattice.coe_comap", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZLattice.comap_refl", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZLattice.comap_discreteTopology", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "instDiscreteTopologySubtypeMemSubmoduleIntComap", "kind": "instance", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZLattice.comap_span_top", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "instIsZLatticeComap", "kind": "instance", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZLattice.comap_toAddSubgroup", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZLattice.comap_comp", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZLattice.comap_equiv", "kind": "definition", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZLattice.comap_equiv_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.ofZLatticeComap", "kind": "definition", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.ofZLatticeComap_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Module.Basis.ofZLatticeComap_repr_apply", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Module.Basis.ofZLatticeBasis_comap", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "IsZLattice.isCompact_range_of_periodic", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Basic", "is_tactic_proof": true, "tactics": ["have", "let", "convert", "refine", "rintro", "let", "refine", "simp"], "tactic_count": 8}
{"name": "ZLattice.covolume_eq_measure_fundamentalDomain", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Covolume", "is_tactic_proof": true, "tactics": ["have", "have", "exact"], "tactic_count": 3}
{"name": "ZLattice.covolume_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Covolume", "is_tactic_proof": false, "tactics": ["rw", "measureReal_ne_zero_iff", "exact", "exact"], "tactic_count": 4}
{"name": "ZLattice.covolume_pos", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Covolume", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZLattice.covolume_eq_det_mul_measureReal", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Covolume", "is_tactic_proof": false, "tactics": ["rw", "measureReal_congr", "congr", "ext", "exact"], "tactic_count": 5}
{"name": "ZLattice.covolume_eq_det", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Covolume", "is_tactic_proof": false, "tactics": ["rw", "congr", "ext1", "exact"], "tactic_count": 4}
{"name": "ZLattice.covolume_eq_det_inv", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Covolume", "is_tactic_proof": true, "tactics": ["classical", "rw", "rfl"], "tactic_count": 3}
{"name": "ZLattice.covolume_div_covolume_eq_relIndex", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Covolume", "is_tactic_proof": true, "tactics": ["classical", "let", "let", "rw", "trans", "rw", "mul_comm,", "congr", "rw", "congr", "rw", "exact"], "tactic_count": 12}
{"name": "ZLattice.covolume_div_covolume_eq_relIndex'", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Covolume", "is_tactic_proof": true, "tactics": ["let", "have", "rw", "covolume_div_covolume_eq_relIndex"], "tactic_count": 4}
{"name": "ZLattice.volume_image_eq_volume_div_covolume", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Covolume", "is_tactic_proof": true, "tactics": ["rw", "covolume_eq_det_inv", "inv_inv,"], "tactic_count": 3}
{"name": "ZLattice.volume_image_eq_volume_div_covolume'", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Covolume", "is_tactic_proof": true, "tactics": ["classical", "let", "let", "have", "rw", "volume_image_eq_volume_div_covolume", "simp"], "tactic_count": 7}
{"name": "ZLattice.covolume.tendsto_card_div_pow''", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Covolume", "is_tactic_proof": true, "tactics": ["refine", "filter_upwards", "congr", "refine", "simp_rw", "rw", "exact", "exact"], "tactic_count": 8}
{"name": "_private.Mathlib.Algebra.Module.ZLattice.Covolume.0.ZLattice.covolume.tendsto_card_le_div''_aux", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Covolume", "is_tactic_proof": true, "tactics": ["ext", "simp_rw", "inv_mul_le_iff₀", "exact"], "tactic_count": 4}
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{"name": "_private.Mathlib.Algebra.Module.ZLattice.Covolume.0.ZLattice.covolume.frontier_equivFun", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Covolume", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ZLattice.covolume.tendsto_card_div_pow", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Covolume", "is_tactic_proof": true, "tactics": ["classical", "convert", "simp", "rw", "rw"], "tactic_count": 5}
{"name": "ZLattice.covolume.tendsto_card_le_div", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Covolume", "is_tactic_proof": true, "tactics": ["classical", "let", "refine", "rw", "let", "convert", "simp", "rw", "rw"], "tactic_count": 9}
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{"name": "ZLattice.covolume.tendsto_card_le_div'", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Covolume", "is_tactic_proof": true, "tactics": ["let", "convert", "simp", "rw", "have", "infer_instance", "rwa", "rw", "exact"], "tactic_count": 9}
{"name": "ZLattice.exists_forall_abs_repr_le_norm", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Summable", "is_tactic_proof": true, "tactics": ["wlog", "let", "let", "have", "let", "have", "obtain", "exact", "have", "let", "let", "have", "obtain", "refine", "by_cases", "simp", "have", "have", "simpa", "rw", "abs_eq_self.mpr", "exact"], "tactic_count": 22}
{"name": "ZLattice.normBound", "kind": "definition", "module": "Mathlib.Algebra.Module.ZLattice.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZLattice.normBound_pos", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZLattice.normBound_spec", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZLattice.abs_repr_le", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Summable", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ZLattice.abs_repr_lt_of_norm_lt", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Summable", "is_tactic_proof": true, "tactics": ["refine", "rwa"], "tactic_count": 2}
{"name": "ZLattice.le_norm_of_le_abs_repr", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Summable", "is_tactic_proof": true, "tactics": ["contrapose", "exact"], "tactic_count": 2}
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{"name": "ZLattice.exists_finsetSum_norm_rpow_le_tsum", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Summable", "is_tactic_proof": true, "tactics": ["classical", "cases", "refine", "have", "simpa", "classical", "let", "have", "let", "simp_rw", "set", "have", "let", "obtain", "refine", "let", "obtain", "dsimp", "simp", "obtain", "obtain", "refine", "have", "have", "simp", "simpa", "refine", "dsimp", "simp", "convert", "simp", "by_cases", "refine", "rw", "exact", "refine", "rw", "refine", "rw", "refine", "simp", "refine", "simpa"], "tactic_count": 43}
{"name": "ZLattice.tsumNormRPowBound", "kind": "definition", "module": "Mathlib.Algebra.Module.ZLattice.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZLattice.tsumNormRPowBound_pos", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZLattice.tsumNormRPowBound_spec", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZLattice.summable_norm_rpow", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZLattice.tsum_norm_rpow_le", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZLattice.summable_norm_sub_rpow", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Summable", "is_tactic_proof": true, "tactics": ["cases", "exact", "refine", "have", "refine", "intro", "by_cases", "simp", "by_cases", "simpa", "have", "have", "rw", "simpa", "have", "rw", "simpa"], "tactic_count": 17}
{"name": "ZLattice.summable_norm_sub_zpow", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZLattice.summable_norm_zpow", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Summable", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ZLattice.summable_norm_sub_inv_pow", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Summable", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ZLattice.summable_norm_pow_inv", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZLattice.Summable", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "AddCommMonoid.zmodModule", "kind": "abbrev", "module": "Mathlib.Algebra.Module.ZMod", "is_tactic_proof": false, "tactics": ["have", "suffices", "rw", "have", "n", "exact", "smul_zero", "zero_smul", "smul_add", "one_smul", "add_smul", "mul_smul"], "tactic_count": 12}
{"name": "AddCommGroup.zmodModule", "kind": "abbrev", "module": "Mathlib.Algebra.Module.ZMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientAddGroup.zmodModule", "kind": "abbrev", "module": "Mathlib.Algebra.Module.ZMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.map_smul", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZMod", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ZMod.smul_mem", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZMod", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "AddMonoidHom.toZModLinearMap", "kind": "definition", "module": "Mathlib.Algebra.Module.ZMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.toZModLinearMap_injective", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.coe_toZModLinearMap", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.toZModLinearMapEquiv", "kind": "definition", "module": "Mathlib.Algebra.Module.ZMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroup.toZModSubmodule", "kind": "definition", "module": "Mathlib.Algebra.Module.ZMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroup.toZModSubmodule_symm", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroup.coe_toZModSubmodule", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroup.mem_toZModSubmodule", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroup.toZModSubmodule_toAddSubgroup", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.toAddSubgroup_toZModSubmodule", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZModModule.exists_submodule_subset_card_le", "kind": "theorem", "module": "Mathlib.Algebra.Module.ZMod", "is_tactic_proof": false, "tactics": ["obtain", "isPGroup_multiplicative", "exact"], "tactic_count": 3}
{"name": "MonoidAlgebra.nonUnitalAlgHom_ext", "kind": "theorem", "module": "Mathlib.Algebra.MonoidAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidAlgebra.nonUnitalAlgHom_ext'", "kind": "theorem", "module": "Mathlib.Algebra.MonoidAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidAlgebra.liftMagma", "kind": "definition", "module": "Mathlib.Algebra.MonoidAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidAlgebra.algebra", "kind": "instance", "module": "Mathlib.Algebra.MonoidAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidAlgebra.singleOneAlgHom", "kind": "definition", "module": "Mathlib.Algebra.MonoidAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidAlgebra.coe_algebraMap", "kind": "theorem", "module": "Mathlib.Algebra.MonoidAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidAlgebra.single_eq_algebraMap_mul_of", "kind": "theorem", "module": "Mathlib.Algebra.MonoidAlgebra.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MonoidAlgebra.single_algebraMap_eq_algebraMap_mul_of", "kind": "theorem", "module": "Mathlib.Algebra.MonoidAlgebra.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MonoidAlgebra.isLocalHom_singleOneAlgHom", "kind": "instance", "module": "Mathlib.Algebra.MonoidAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidAlgebra.isLocalHom_algebraMap", "kind": "instance", "module": "Mathlib.Algebra.MonoidAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MonoidAlgebra.curryAlgEquiv", "kind": "definition", "module": "Mathlib.Algebra.MonoidAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidAlgebra.curryAlgEquiv_single", "kind": "theorem", "module": "Mathlib.Algebra.MonoidAlgebra.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MonoidAlgebra.curryAlgEquiv_symm_single", "kind": "theorem", "module": "Mathlib.Algebra.MonoidAlgebra.Basic", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
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{"name": "MonoidAlgebra.lift_apply'", "kind": "theorem", "module": "Mathlib.Algebra.MonoidAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MonoidAlgebra.mapDomain_algebraMap", "kind": "theorem", "module": "Mathlib.Algebra.MonoidAlgebra.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "MonoidAlgebra.mapDomainAlgHom_id", "kind": "theorem", "module": "Mathlib.Algebra.MonoidAlgebra.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
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{"name": "MonoidAlgebra.domCongr_apply", "kind": "theorem", "module": "Mathlib.Algebra.MonoidAlgebra.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "MonoidAlgebra.commAlgEquiv", "kind": "definition", "module": "Mathlib.Algebra.MonoidAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidAlgebra.symm_commAlgEquiv", "kind": "theorem", "module": "Mathlib.Algebra.MonoidAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MonoidAlgebra.commRingEquiv", "kind": "definition", "module": "Mathlib.Algebra.MonoidAlgebra.MapDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidAlgebra.symm_commRingEquiv", "kind": "theorem", "module": "Mathlib.Algebra.MonoidAlgebra.MapDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidAlgebra.commRingEquiv_single_single", "kind": "theorem", "module": "Mathlib.Algebra.MonoidAlgebra.MapDomain", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AddMonoidAlgebra.toMultiplicative", "kind": "definition", "module": "Mathlib.Algebra.MonoidAlgebra.MapDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidAlgebra.toAdditive", "kind": "definition", "module": "Mathlib.Algebra.MonoidAlgebra.MapDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidAlgebra.distribMulAction", "kind": "instance", "module": "Mathlib.Algebra.MonoidAlgebra.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidAlgebra.module", "kind": "instance", "module": "Mathlib.Algebra.MonoidAlgebra.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidAlgebra.instIsTorsionFree", "kind": "instance", "module": "Mathlib.Algebra.MonoidAlgebra.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidAlgebra.faithfulSMul", "kind": "instance", "module": "Mathlib.Algebra.MonoidAlgebra.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidAlgebra.comapDistribMulActionSelf", "kind": "definition", "module": "Mathlib.Algebra.MonoidAlgebra.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidAlgebra.singleDistribMulActionHom", "kind": "definition", "module": "Mathlib.Algebra.MonoidAlgebra.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidAlgebra.distribMulActionHom_ext'", "kind": "theorem", "module": "Mathlib.Algebra.MonoidAlgebra.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidAlgebra.lsingle", "kind": "abbrev", "module": "Mathlib.Algebra.MonoidAlgebra.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidAlgebra.lsingle_apply", "kind": "theorem", "module": "Mathlib.Algebra.MonoidAlgebra.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidAlgebra.lhom_ext'", "kind": "theorem", "module": "Mathlib.Algebra.MonoidAlgebra.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidAlgebra.smul_of", "kind": "theorem", "module": "Mathlib.Algebra.MonoidAlgebra.Module", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MonoidAlgebra.of_mem_span_of_iff", "kind": "theorem", "module": "Mathlib.Algebra.MonoidAlgebra.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidAlgebra.mem_closure_of_mem_span_closure", "kind": "theorem", "module": "Mathlib.Algebra.MonoidAlgebra.Module", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MonoidAlgebra.liftNC_smul", "kind": "theorem", "module": "Mathlib.Algebra.MonoidAlgebra.Module", "is_tactic_proof": false, "tactics": ["suffices", "ext", "simp_rw", "liftNC_single,"], "tactic_count": 4}
{"name": "MonoidAlgebra.isScalarTower_self", "kind": "instance", "module": "Mathlib.Algebra.MonoidAlgebra.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidAlgebra.smulCommClass_self", "kind": "instance", "module": "Mathlib.Algebra.MonoidAlgebra.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidAlgebra.smulCommClass_symm_self", "kind": "instance", "module": "Mathlib.Algebra.MonoidAlgebra.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidAlgebra.submoduleOfSMulMem", "kind": "definition", "module": "Mathlib.Algebra.MonoidAlgebra.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidAlgebra.of'_mem_span", "kind": "theorem", "module": "Mathlib.Algebra.MonoidAlgebra.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidAlgebra.mem_closure_of_mem_span_closure", "kind": "theorem", "module": "Mathlib.Algebra.MonoidAlgebra.Module", "is_tactic_proof": false, "tactics": ["suffices", "simpa", "let", "have", "rw", "simpa"], "tactic_count": 6}
{"name": "AddMonoidAlgebra.liftNC_smul", "kind": "theorem", "module": "Mathlib.Algebra.MonoidAlgebra.Module", "is_tactic_proof": false, "tactics": ["suffices", "ext", "simp_rw", "liftNC_single,"], "tactic_count": 4}
{"name": "MonoidAlgebra.mul_apply_mul_eq_mul_of_uniqueMul", "kind": "theorem", "module": "Mathlib.Algebra.MonoidAlgebra.NoZeroDivisors", "is_tactic_proof": true, "tactics": ["classical", "simp_rw", "refine", "refine", "exacts", "refine", "rcases", "rw", "rw"], "tactic_count": 9}
{"name": "MonoidAlgebra.instNoZeroDivisorsOfUniqueProds", "kind": "instance", "module": "Mathlib.Algebra.MonoidAlgebra.NoZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidAlgebra.instIsLeftCancelMulZeroOfIsCancelAddOfUniqueProds", "kind": "instance", "module": "Mathlib.Algebra.MonoidAlgebra.NoZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidAlgebra.instIsRightCancelMulZeroOfIsCancelAddOfUniqueProds", "kind": "instance", "module": "Mathlib.Algebra.MonoidAlgebra.NoZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidAlgebra.instIsCancelMulZeroOfIsCancelAddOfUniqueProds", "kind": "instance", "module": "Mathlib.Algebra.MonoidAlgebra.NoZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidAlgebra.instIsDomainOfIsCancelAddOfUniqueProds", "kind": "instance", "module": "Mathlib.Algebra.MonoidAlgebra.NoZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidAlgebra.opRingEquiv", "kind": "definition", "module": "Mathlib.Algebra.MonoidAlgebra.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidAlgebra.opRingEquiv_single", "kind": "theorem", "module": "Mathlib.Algebra.MonoidAlgebra.Opposite", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MonoidAlgebra.opRingEquiv_symm_single", "kind": "theorem", "module": "Mathlib.Algebra.MonoidAlgebra.Opposite", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "MonoidAlgebra.support_single_mul_eq_image", "kind": "theorem", "module": "Mathlib.Algebra.MonoidAlgebra.Support", "is_tactic_proof": true, "tactics": ["refine", "obtain", "simp"], "tactic_count": 3}
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{"name": "MonoidAlgebra.support_one", "kind": "theorem", "module": "Mathlib.Algebra.MonoidAlgebra.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidAlgebra.mem_span_support", "kind": "theorem", "module": "Mathlib.Algebra.MonoidAlgebra.Support", "is_tactic_proof": true, "tactics": ["simp", "rw"], "tactic_count": 2}
{"name": "AddMonoidAlgebra.mem_span_support", "kind": "theorem", "module": "Mathlib.Algebra.MonoidAlgebra.Support", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AddMonoidAlgebra.toDirectSum", "kind": "definition", "module": "Mathlib.Algebra.MonoidAlgebra.ToDirectSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidAlgebra.toDirectSum_single", "kind": "theorem", "module": "Mathlib.Algebra.MonoidAlgebra.ToDirectSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.toAddMonoidAlgebra", "kind": "definition", "module": "Mathlib.Algebra.MonoidAlgebra.ToDirectSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.toAddMonoidAlgebra_of", "kind": "theorem", "module": "Mathlib.Algebra.MonoidAlgebra.ToDirectSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidAlgebra.toDirectSum_toAddMonoidAlgebra", "kind": "theorem", "module": "Mathlib.Algebra.MonoidAlgebra.ToDirectSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.toAddMonoidAlgebra_toDirectSum", "kind": "theorem", "module": "Mathlib.Algebra.MonoidAlgebra.ToDirectSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidAlgebra.toDirectSum_zero", "kind": "theorem", "module": "Mathlib.Algebra.MonoidAlgebra.ToDirectSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidAlgebra.toDirectSum_add", "kind": "theorem", "module": "Mathlib.Algebra.MonoidAlgebra.ToDirectSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidAlgebra.toDirectSum_natCast", "kind": "theorem", "module": "Mathlib.Algebra.MonoidAlgebra.ToDirectSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidAlgebra.toDirectSum_ofNat", "kind": "theorem", "module": "Mathlib.Algebra.MonoidAlgebra.ToDirectSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidAlgebra.toDirectSum_sub", "kind": "theorem", "module": "Mathlib.Algebra.MonoidAlgebra.ToDirectSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AddMonoidAlgebra.toDirectSum_one", "kind": "theorem", "module": "Mathlib.Algebra.MonoidAlgebra.ToDirectSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidAlgebra.toDirectSum_mul", "kind": "theorem", "module": "Mathlib.Algebra.MonoidAlgebra.ToDirectSum", "is_tactic_proof": false, "tactics": ["let", "map_zero", "map_add", "change", "revert", "rw", "ext", "simp"], "tactic_count": 8}
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{"name": "DirectSum.toAddMonoidAlgebra_add", "kind": "theorem", "module": "Mathlib.Algebra.MonoidAlgebra.ToDirectSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "DirectSum.toAddMonoidAlgebra_ofNat", "kind": "theorem", "module": "Mathlib.Algebra.MonoidAlgebra.ToDirectSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "DirectSum.toAddMonoidAlgebra_mul", "kind": "theorem", "module": "Mathlib.Algebra.MonoidAlgebra.ToDirectSum", "is_tactic_proof": true, "tactics": ["apply_fun", "simp", "apply", "apply"], "tactic_count": 4}
{"name": "addMonoidAlgebraEquivDirectSum", "kind": "definition", "module": "Mathlib.Algebra.MonoidAlgebra.ToDirectSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "addMonoidAlgebraAddEquivDirectSum", "kind": "definition", "module": "Mathlib.Algebra.MonoidAlgebra.ToDirectSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "addMonoidAlgebraRingEquivDirectSum", "kind": "definition", "module": "Mathlib.Algebra.MonoidAlgebra.ToDirectSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "addMonoidAlgebraAlgEquivDirectSum", "kind": "definition", "module": "Mathlib.Algebra.MonoidAlgebra.ToDirectSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidAlgebra.toDirectSum_pow", "kind": "theorem", "module": "Mathlib.Algebra.MonoidAlgebra.ToDirectSum", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
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{"name": "MvPolynomial", "kind": "definition", "module": "Mathlib.Algebra.MvPolynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.decidableEqMvPolynomial", "kind": "instance", "module": "Mathlib.Algebra.MvPolynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.commSemiring", "kind": "instance", "module": "Mathlib.Algebra.MvPolynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.inhabited", "kind": "instance", "module": "Mathlib.Algebra.MvPolynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.distribuMulAction", "kind": "instance", "module": "Mathlib.Algebra.MvPolynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.smulZeroClass", "kind": "instance", "module": "Mathlib.Algebra.MvPolynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.faithfulSMul", "kind": "instance", "module": "Mathlib.Algebra.MvPolynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.module", "kind": "instance", "module": "Mathlib.Algebra.MvPolynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.isScalarTower", "kind": "instance", "module": "Mathlib.Algebra.MvPolynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.smulCommClass", "kind": "instance", "module": "Mathlib.Algebra.MvPolynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.isCentralScalar", "kind": "instance", "module": "Mathlib.Algebra.MvPolynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.algebra", "kind": "instance", "module": "Mathlib.Algebra.MvPolynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.isScalarTower_right", "kind": "instance", "module": "Mathlib.Algebra.MvPolynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.smulCommClass_right", "kind": "instance", "module": "Mathlib.Algebra.MvPolynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.unique", "kind": "instance", "module": "Mathlib.Algebra.MvPolynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.monomial", "kind": "definition", "module": "Mathlib.Algebra.MvPolynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.one_def", "kind": "theorem", "module": "Mathlib.Algebra.MvPolynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.single_eq_monomial", "kind": "theorem", "module": "Mathlib.Algebra.MvPolynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.mul_def", "kind": "theorem", "module": "Mathlib.Algebra.MvPolynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.C", "kind": "definition", "module": "Mathlib.Algebra.MvPolynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MvPolynomial.C_mul_monomial", "kind": "theorem", "module": "Mathlib.Algebra.MvPolynomial.Basic", "is_tactic_proof": true, "tactics": ["change", "simp"], "tactic_count": 2}
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{"name": "MvPolynomial.aeval_comp_toMvPolynomial", "kind": "theorem", "module": "Mathlib.Algebra.MvPolynomial.Equiv", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
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{"name": "MvPolynomial.eval₂", "kind": "definition", "module": "Mathlib.Algebra.MvPolynomial.Eval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.eval₂_eq", "kind": "theorem", "module": "Mathlib.Algebra.MvPolynomial.Eval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MvPolynomial.eval₂_dvd", "kind": "theorem", "module": "Mathlib.Algebra.MvPolynomial.Eval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MvPolynomial.eval₂Hom_congr", "kind": "theorem", "module": "Mathlib.Algebra.MvPolynomial.Eval", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "MvPolynomial.eval₂Hom_C", "kind": "theorem", "module": "Mathlib.Algebra.MvPolynomial.Eval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MvPolynomial.eval₂Hom_monomial", "kind": "theorem", "module": "Mathlib.Algebra.MvPolynomial.Eval", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MvPolynomial.eval₂_comp_left", "kind": "theorem", "module": "Mathlib.Algebra.MvPolynomial.Eval", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "MvPolynomial.eval₂_eta", "kind": "theorem", "module": "Mathlib.Algebra.MvPolynomial.Eval", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
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{"name": "MvPolynomial.eval_eval₂", "kind": "theorem", "module": "Mathlib.Algebra.MvPolynomial.Eval", "is_tactic_proof": true, "tactics": ["apply", "simp", "intro", "simp", "intro", "simp"], "tactic_count": 6}
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{"name": "MvPolynomial.map_monomial", "kind": "theorem", "module": "Mathlib.Algebra.MvPolynomial.Eval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.map_C", "kind": "theorem", "module": "Mathlib.Algebra.MvPolynomial.Eval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.map_ofNat", "kind": "theorem", "module": "Mathlib.Algebra.MvPolynomial.Eval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.map_X", "kind": "theorem", "module": "Mathlib.Algebra.MvPolynomial.Eval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.map_id", "kind": "theorem", "module": "Mathlib.Algebra.MvPolynomial.Eval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.map_map", "kind": "theorem", "module": "Mathlib.Algebra.MvPolynomial.Eval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.eval₂_eq_eval_map", "kind": "theorem", "module": "Mathlib.Algebra.MvPolynomial.Eval", "is_tactic_proof": true, "tactics": ["unfold", "have", "dsimp", "rw", "congr", "ext1", "simp", "ext1", "simp"], "tactic_count": 9}
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{"name": "MvPolynomial.map_surjective", "kind": "theorem", "module": "Mathlib.Algebra.MvPolynomial.Eval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.map_surjective_iff", "kind": "theorem", "module": "Mathlib.Algebra.MvPolynomial.Eval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.map_leftInverse", "kind": "theorem", "module": "Mathlib.Algebra.MvPolynomial.Eval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.map_rightInverse", "kind": "theorem", "module": "Mathlib.Algebra.MvPolynomial.Eval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.eval_map", "kind": "theorem", "module": "Mathlib.Algebra.MvPolynomial.Eval", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "MvPolynomial.eval₂_comp", "kind": "theorem", "module": "Mathlib.Algebra.MvPolynomial.Eval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MvPolynomial.eval₂_map", "kind": "theorem", "module": "Mathlib.Algebra.MvPolynomial.Eval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MvPolynomial.eval₂Hom_map_hom", "kind": "theorem", "module": "Mathlib.Algebra.MvPolynomial.Eval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.constantCoeff_map", "kind": "theorem", "module": "Mathlib.Algebra.MvPolynomial.Eval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.constantCoeff_comp_map", "kind": "theorem", "module": "Mathlib.Algebra.MvPolynomial.Eval", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "MvPolynomial.support_map_subset", "kind": "theorem", "module": "Mathlib.Algebra.MvPolynomial.Eval", "is_tactic_proof": true, "tactics": ["simp", "intro", "contrapose", "rw"], "tactic_count": 4}
{"name": "MvPolynomial.support_map_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.MvPolynomial.Eval", "is_tactic_proof": true, "tactics": ["apply", "exact", "simp", "intro", "contrapose", "rw", "exact"], "tactic_count": 7}
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{"name": "MvPolynomial.map_mapRange_eq_iff", "kind": "theorem", "module": "Mathlib.Algebra.MvPolynomial.Eval", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MvPolynomial.coeffs_map", "kind": "theorem", "module": "Mathlib.Algebra.MvPolynomial.Eval", "is_tactic_proof": true, "tactics": ["classical", "induction", "mul_X", "monomial_add", "ih", "rw", "rw", "exact", "exact"], "tactic_count": 9}
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{"name": "MvPolynomial.mem_range_map_iff_coeffs_subset", "kind": "theorem", "module": "Mathlib.Algebra.MvPolynomial.Eval", "is_tactic_proof": true, "tactics": ["classical", "refine", "obtain", "exact", "induction", "by_cases", "subst", "exact", "simp", "obtain", "exact", "mul_X", "rw", "obtain", "exact", "monomial_add", "ih", "rw", "simp", "obtain", "obtain", "exact"], "tactic_count": 22}
{"name": "MvPolynomial.mapAlgHom", "kind": "definition", "module": "Mathlib.Algebra.MvPolynomial.Eval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.mapAlgHom_id", "kind": "theorem", "module": "Mathlib.Algebra.MvPolynomial.Eval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.mapAlgHom_coe_ringHom", "kind": "theorem", "module": "Mathlib.Algebra.MvPolynomial.Eval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.range_mapAlgHom", "kind": "theorem", "module": "Mathlib.Algebra.MvPolynomial.Eval", "is_tactic_proof": true, "tactics": ["ext", "rw", "mem_range_map_iff_coeffs_subset,", "simp"], "tactic_count": 4}
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{"name": "MvPolynomial.aeval_def", "kind": "theorem", "module": "Mathlib.Algebra.MvPolynomial.Eval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.aeval_eq_eval₂Hom", "kind": "theorem", "module": "Mathlib.Algebra.MvPolynomial.Eval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MulOpposite.op_sub", "kind": "theorem", "module": "Mathlib.Algebra.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.unop_sub", "kind": "theorem", "module": "Mathlib.Algebra.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.op_smul", "kind": "theorem", "module": "Mathlib.Algebra.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.unop_smul", "kind": "theorem", "module": "Mathlib.Algebra.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.unop_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.op_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.unop_ne_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.op_ne_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.unop_eq_one_iff", "kind": "theorem", "module": "Mathlib.Algebra.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.op_eq_one_iff", "kind": "theorem", "module": "Mathlib.Algebra.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddOpposite.instOne", "kind": "instance", "module": "Mathlib.Algebra.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddOpposite.op_one", "kind": "theorem", "module": "Mathlib.Algebra.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddOpposite.unop_one", "kind": "theorem", "module": "Mathlib.Algebra.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddOpposite.op_eq_one_iff", "kind": "theorem", "module": "Mathlib.Algebra.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddOpposite.unop_eq_one_iff", "kind": "theorem", "module": "Mathlib.Algebra.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddOpposite.instMul", "kind": "instance", "module": "Mathlib.Algebra.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddOpposite.op_mul", "kind": "theorem", "module": "Mathlib.Algebra.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddOpposite.unop_mul", "kind": "theorem", "module": "Mathlib.Algebra.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddOpposite.instInv", "kind": "instance", "module": "Mathlib.Algebra.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddOpposite.instInvolutiveInv", "kind": "instance", "module": "Mathlib.Algebra.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddOpposite.op_inv", "kind": "theorem", "module": "Mathlib.Algebra.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddOpposite.unop_inv", "kind": "theorem", "module": "Mathlib.Algebra.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddOpposite.instDiv", "kind": "instance", "module": "Mathlib.Algebra.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddOpposite.op_div", "kind": "theorem", "module": "Mathlib.Algebra.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddOpposite.unop_div", "kind": "theorem", "module": "Mathlib.Algebra.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AbsoluteValue.funLike", "kind": "instance", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AbsoluteValue.zeroHomClass", "kind": "instance", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AbsoluteValue.mulHomClass", "kind": "instance", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AbsoluteValue.nonnegHomClass", "kind": "instance", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AbsoluteValue.subadditiveHomClass", "kind": "instance", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AbsoluteValue.coe_mk", "kind": "theorem", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AbsoluteValue.ext", "kind": "theorem", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AbsoluteValue.Simps.apply", "kind": "definition", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AbsoluteValue.coe_toMulHom", "kind": "theorem", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AbsoluteValue.nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AbsoluteValue.eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AbsoluteValue.add_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AbsoluteValue.listSum_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "AbsoluteValue.map_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AbsoluteValue.ne_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AbsoluteValue.pos_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AbsoluteValue.nonpos_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AbsoluteValue.map_one_of_isLeftRegular", "kind": "theorem", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AbsoluteValue.map_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AbsoluteValue.sub_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "AbsoluteValue.map_sub_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AbsoluteValue.map_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AbsoluteValue.monoidWithZeroHomClass", "kind": "instance", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AbsoluteValue.toMonoidWithZeroHom", "kind": "definition", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AbsoluteValue.coe_toMonoidWithZeroHom", "kind": "theorem", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AbsoluteValue.toMonoidHom", "kind": "definition", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AbsoluteValue.coe_toMonoidHom", "kind": "theorem", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AbsoluteValue.map_pow", "kind": "theorem", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AbsoluteValue.apply_nat_le_self", "kind": "theorem", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": true, "tactics": ["cases", "simp", "induction", "zero", "succ"], "tactic_count": 5}
{"name": "AbsoluteValue.le_sub", "kind": "theorem", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AbsoluteValue.map_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "refine", "exact"], "tactic_count": 3}
{"name": "AbsoluteValue.map_sub", "kind": "theorem", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AbsoluteValue.le_add", "kind": "theorem", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "AbsoluteValue.sub_le_add", "kind": "theorem", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "AbsoluteValue.instMulRingNormClassOfNontrivialOfIsDomain", "kind": "instance", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AbsoluteValue.apply_natAbs_eq", "kind": "theorem", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "AbsoluteValue.eq_on_nat_iff_eq_on_int", "kind": "theorem", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": true, "tactics": ["refine", "obtain"], "tactic_count": 2}
{"name": "AbsoluteValue.abs", "kind": "definition", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AbsoluteValue.instInhabited", "kind": "instance", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AbsoluteValue.abs_abv_sub_le_abv_sub", "kind": "theorem", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AbsoluteValue.trivial", "kind": "definition", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AbsoluteValue.trivial_apply", "kind": "theorem", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AbsoluteValue.IsNontrivial", "kind": "definition", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AbsoluteValue.isNontrivial_iff_ne_trivial", "kind": "theorem", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": true, "tactics": ["refine", "simp", "contrapose", "ext1", "rcases", "simp", "simp"], "tactic_count": 7}
{"name": "AbsoluteValue.not_isNontrivial_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": true, "tactics": ["simp", "push_neg", "rfl"], "tactic_count": 3}
{"name": "AbsoluteValue.not_isNontrivial_apply", "kind": "theorem", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AbsoluteValue.IsNontrivial.exists_abv_gt_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": true, "tactics": ["obtain", "rcases", "refine", "rw", "exact", "exact"], "tactic_count": 6}
{"name": "AbsoluteValue.IsNontrivial.exists_abv_lt_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": true, "tactics": ["obtain", "have", "refine", "rw", "exact"], "tactic_count": 5}
{"name": "IsAbsoluteValue.abv_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAbsoluteValue.Mathlib.Meta.Positivity.evalAbv", "kind": "definition", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAbsoluteValue.abv_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAbsoluteValue.abv_add", "kind": "theorem", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AbsoluteValue.isAbsoluteValue", "kind": "instance", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAbsoluteValue.toAbsoluteValue", "kind": "definition", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAbsoluteValue.abv_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAbsoluteValue.abv_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAbsoluteValue.abs_isAbsoluteValue", "kind": "instance", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAbsoluteValue.abv_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAbsoluteValue.abvHom", "kind": "definition", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAbsoluteValue.abv_pow", "kind": "theorem", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAbsoluteValue.abv_sub_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsAbsoluteValue.sub_abv_le_abv_sub", "kind": "theorem", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAbsoluteValue.abv_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAbsoluteValue.abv_sub", "kind": "theorem", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAbsoluteValue.abs_abv_sub_le_abv_sub", "kind": "theorem", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAbsoluteValue.abv_one'", "kind": "theorem", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAbsoluteValue.abvHom'", "kind": "definition", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAbsoluteValue.abv_inv", "kind": "theorem", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAbsoluteValue.abv_div", "kind": "theorem", "module": "Mathlib.Algebra.Order.AbsoluteValue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Order.AbsoluteValue.Euclidean.0.term_≺_", "kind": "definition", "module": "Mathlib.Algebra.Order.AbsoluteValue.Euclidean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Order.AbsoluteValue.Euclidean.0._aux_Mathlib_Algebra_Order_AbsoluteValue_Euclidean___macroRules__private_Mathlib_Algebra_Order_AbsoluteValue_Euclidean_0_term_≺__1", "kind": "definition", "module": "Mathlib.Algebra.Order.AbsoluteValue.Euclidean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Order.AbsoluteValue.Euclidean.0._aux_Mathlib_Algebra_Order_AbsoluteValue_Euclidean___unexpand_EuclideanDomain_r_1", "kind": "definition", "module": "Mathlib.Algebra.Order.AbsoluteValue.Euclidean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AbsoluteValue.IsEuclidean.map_lt_map_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.AbsoluteValue.Euclidean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AbsoluteValue.IsEuclidean.sub_mod_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.AbsoluteValue.Euclidean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AbsoluteValue.abs_isEuclidean", "kind": "theorem", "module": "Mathlib.Algebra.Order.AbsoluteValue.Euclidean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "top_add", "kind": "theorem", "module": "Mathlib.Algebra.Order.AddGroupWithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "add_top", "kind": "theorem", "module": "Mathlib.Algebra.Order.AddGroupWithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAddRegular.of_ne_top", "kind": "theorem", "module": "Mathlib.Algebra.Order.AddGroupWithTop", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "add_left_injective_of_ne_top", "kind": "theorem", "module": "Mathlib.Algebra.Order.AddGroupWithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "add_right_injective_of_ne_top", "kind": "theorem", "module": "Mathlib.Algebra.Order.AddGroupWithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "add_left_inj_of_ne_top", "kind": "theorem", "module": "Mathlib.Algebra.Order.AddGroupWithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "add_right_strictMono_of_ne_top", "kind": "theorem", "module": "Mathlib.Algebra.Order.AddGroupWithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "add_le_add_iff_right_of_ne_top", "kind": "theorem", "module": "Mathlib.Algebra.Order.AddGroupWithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "add_lt_add_iff_left_of_ne_top", "kind": "theorem", "module": "Mathlib.Algebra.Order.AddGroupWithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "add_lt_add_iff_right_of_ne_top", "kind": "theorem", "module": "Mathlib.Algebra.Order.AddGroupWithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LinearOrderedAddCommGroupWithTop.neg_add_cancel_left_of_ne_top", "kind": "theorem", "module": "Mathlib.Algebra.Order.AddGroupWithTop", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LinearOrderedAddCommGroupWithTop.add_neg_cancel_right_of_ne_top", "kind": "theorem", "module": "Mathlib.Algebra.Order.AddGroupWithTop", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LinearOrderedAddCommGroupWithTop.neg_add_cancel_right_of_ne_top", "kind": "theorem", "module": "Mathlib.Algebra.Order.AddGroupWithTop", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LinearOrderedAddCommGroupWithTop.top_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.AddGroupWithTop", "is_tactic_proof": true, "tactics": ["intro", "obtain", "rw", "simp"], "tactic_count": 4}
{"name": "LinearOrderedAddCommGroupWithTop.zero_ne_top", "kind": "theorem", "module": "Mathlib.Algebra.Order.AddGroupWithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LinearOrderedAddCommGroupWithTop.isAddUnit_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.AddGroupWithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LinearOrderedAddCommGroupWithTop.add_ne_top", "kind": "theorem", "module": "Mathlib.Algebra.Order.AddGroupWithTop", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "LinearOrderedAddCommGroupWithTop.add_lt_top", "kind": "theorem", "module": "Mathlib.Algebra.Order.AddGroupWithTop", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "LinearOrderedAddCommGroupWithTop.sub_le_sub_iff_left_of_ne_top", "kind": "theorem", "module": "Mathlib.Algebra.Order.AddGroupWithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearOrderedAddCommGroupWithTop.sub_lt_sub_iff_left_of_ne_top", "kind": "theorem", "module": "Mathlib.Algebra.Order.AddGroupWithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LinearOrderedAddCommGroupWithTop.sub_self_eq_zero_iff_ne_top", "kind": "theorem", "module": "Mathlib.Algebra.Order.AddGroupWithTop", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LinearOrderedAddCommGroupWithTop.sub_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.AddGroupWithTop", "is_tactic_proof": true, "tactics": ["obtain", "simp", "simp"], "tactic_count": 3}
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{"name": "LinearOrderedAddCommGroupWithTop.sub_self_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.AddGroupWithTop", "is_tactic_proof": true, "tactics": ["obtain", "simp", "rw"], "tactic_count": 3}
{"name": "LinearOrderedAddCommGroupWithTop.sub_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.AddGroupWithTop", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "WithTop.LinearOrderedAddCommGroup.instSub", "kind": "instance", "module": "Mathlib.Algebra.Order.AddGroupWithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.LinearOrderedAddCommGroup.coe_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.AddGroupWithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "WithTop.LinearOrderedAddCommGroup.top_sub", "kind": "theorem", "module": "Mathlib.Algebra.Order.AddGroupWithTop", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
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{"name": "WithTop.LinearOrderedAddCommGroup.sub_eq_top_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.AddGroupWithTop", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "WithTop.LinearOrderedAddCommGroup.instLinearOrderedAddCommGroupWithTopOfIsOrderedAddMonoid", "kind": "instance", "module": "Mathlib.Algebra.Order.AddGroupWithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCovariantClassHSMulLeOfIsOrderedSMul", "kind": "instance", "module": "Mathlib.Algebra.Order.AddTorsor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "instIsCancelSMulOfIsOrderedCancelSMul", "kind": "instance", "module": "Mathlib.Algebra.Order.AddTorsor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsOrderedCancelSMulOfIsOrderedCancelMonoid", "kind": "instance", "module": "Mathlib.Algebra.Order.AddTorsor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instContravariantClassHSMulLeOfIsOrderedCancelSMul", "kind": "instance", "module": "Mathlib.Algebra.Order.AddTorsor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Nat.dvd_of_mem_finMulAntidiag", "kind": "theorem", "module": "Mathlib.Algebra.Order.Antidiag.Nat", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
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{"name": "Nat.finMulAntidiag_eq_piFinset_divisors_filter", "kind": "theorem", "module": "Mathlib.Algebra.Order.Antidiag.Nat", "is_tactic_proof": true, "tactics": ["ext", "simp", "constructor", "intro", "refine", "exact", "rw", "exact"], "tactic_count": 8}
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{"name": "_private.Mathlib.Algebra.Order.Antidiag.Nat.0.Nat.primeFactorsPiBij_img", "kind": "theorem", "module": "Mathlib.Algebra.Order.Antidiag.Nat", "is_tactic_proof": true, "tactics": ["rw", "refine", "unfold", "rw", "apply", "apply"], "tactic_count": 6}
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{"name": "_private.Mathlib.Algebra.Order.Antidiag.Nat.0.Nat.primeFactorsPiBij_surj", "kind": "theorem", "module": "Mathlib.Algebra.Order.Antidiag.Nat", "is_tactic_proof": false, "tactics": ["have", "choose", "refine", "simp", "funext", "have", "trans", "rw", "congr", "grind", "rw", "rw", "exact"], "tactic_count": 13}
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{"name": "Nat.card_finMulAntidiag_of_squarefree", "kind": "theorem", "module": "Mathlib.Algebra.Order.Antidiag.Nat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.finMulAntidiag_three", "kind": "theorem", "module": "Mathlib.Algebra.Order.Antidiag.Nat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "_private.Mathlib.Algebra.Order.Antidiag.Nat.0.Nat.card_pair_lcm_eq.f", "kind": "definition", "module": "Mathlib.Algebra.Order.Antidiag.Nat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Finset.finAntidiagonal", "kind": "definition", "module": "Mathlib.Algebra.Order.Antidiag.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_finAntidiagonal", "kind": "theorem", "module": "Mathlib.Algebra.Order.Antidiag.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Finset.piAntidiag_empty_of_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.Antidiag.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Finset.finsetCongr_piAntidiag_eq_antidiag", "kind": "theorem", "module": "Mathlib.Algebra.Order.Antidiag.Pi", "is_tactic_proof": true, "tactics": ["ext", "simp_rw", "simp"], "tactic_count": 3}
{"name": "Finset.pairwiseDisjoint_piAntidiag_map_addRightEmbedding", "kind": "theorem", "module": "Mathlib.Algebra.Order.Antidiag.Pi", "is_tactic_proof": true, "tactics": ["rintro", "simp", "not_exists,", "rintro", "exact"], "tactic_count": 5}
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{"name": "_private.Mathlib.Algebra.Order.Antidiag.Pi.0.Finset._aux_Mathlib_Algebra_Order_Antidiag_Pi___macroRules__private_Mathlib_Algebra_Order_Antidiag_Pi_0_Finset_term_•ℕ__1", "kind": "definition", "module": "Mathlib.Algebra.Order.Antidiag.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Finset.nsmul_piAntidiag", "kind": "theorem", "module": "Mathlib.Algebra.Order.Antidiag.Pi", "is_tactic_proof": true, "tactics": ["ext", "refine", "simp", "constructor", "rintro", "simpa", "rintro", "have", "by_cases", "exact", "rw", "exact", "refine", "simp", "grind"], "tactic_count": 15}
{"name": "Finset.map_nsmul_piAntidiag", "kind": "theorem", "module": "Mathlib.Algebra.Order.Antidiag.Pi", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finset.nsmul_piAntidiag_univ", "kind": "theorem", "module": "Mathlib.Algebra.Order.Antidiag.Pi", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.map_nsmul_piAntidiag_univ", "kind": "theorem", "module": "Mathlib.Algebra.Order.Antidiag.Pi", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.map_sym_eq_piAntidiag", "kind": "theorem", "module": "Mathlib.Algebra.Order.Antidiag.Pi", "is_tactic_proof": true, "tactics": ["ext", "simp", "exists_and_left,", "constructor", "rintro", "simpa", "rintro", "refine", "simp", "simpa"], "tactic_count": 10}
{"name": "Finset.instSubsingletonHasAntidiagonal", "kind": "instance", "module": "Mathlib.Algebra.Order.Antidiag.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.hasAntidiagonal_congr", "kind": "theorem", "module": "Mathlib.Algebra.Order.Antidiag.Prod", "is_tactic_proof": true, "tactics": ["congr"], "tactic_count": 1}
{"name": "Finset.swap_mem_antidiagonal", "kind": "theorem", "module": "Mathlib.Algebra.Order.Antidiag.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.map_prodComm_antidiagonal", "kind": "theorem", "module": "Mathlib.Algebra.Order.Antidiag.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.map_swap_antidiagonal", "kind": "theorem", "module": "Mathlib.Algebra.Order.Antidiag.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.antidiagonal_congr", "kind": "theorem", "module": "Mathlib.Algebra.Order.Antidiag.Prod", "is_tactic_proof": true, "tactics": ["refine", "rw", "rw"], "tactic_count": 3}
{"name": "Finset.antidiagonal_subtype_ext", "kind": "theorem", "module": "Mathlib.Algebra.Order.Antidiag.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.antidiagonal_congr'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Antidiag.Prod", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finset.antidiagonal_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.Antidiag.Prod", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Finset.antidiagonal.fst_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Antidiag.Prod", "is_tactic_proof": true, "tactics": ["rw", "use", "rwa"], "tactic_count": 3}
{"name": "Finset.antidiagonal.snd_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Antidiag.Prod", "is_tactic_proof": true, "tactics": ["rw", "use", "rwa"], "tactic_count": 3}
{"name": "Finset.filter_fst_eq_antidiagonal", "kind": "theorem", "module": "Mathlib.Algebra.Order.Antidiag.Prod", "is_tactic_proof": true, "tactics": ["ext", "suffices", "rw", "simpa", "rintro", "constructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 10}
{"name": "Finset.filter_snd_eq_antidiagonal", "kind": "theorem", "module": "Mathlib.Algebra.Order.Antidiag.Prod", "is_tactic_proof": true, "tactics": ["have", "rw", "simp"], "tactic_count": 3}
{"name": "Finset.sigmaAntidiagonalEquivProd", "kind": "definition", "module": "Mathlib.Algebra.Order.Antidiag.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.antidiagonalOfLocallyFinite", "kind": "abbrev", "module": "Mathlib.Algebra.Order.Antidiag.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulArchimedean.comap", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instMulArchimedean", "kind": "instance", "module": "Mathlib.Algebra.Order.Archimedean.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Additive.instArchimedean", "kind": "instance", "module": "Mathlib.Algebra.Order.Archimedean.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiplicative.instMulArchimedean", "kind": "instance", "module": "Mathlib.Algebra.Order.Archimedean.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_lt_pow", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "existsUnique_zpow_near_of_one_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Basic", "is_tactic_proof": true, "tactics": ["let", "obtain", "have", "obtain", "have", "intro", "apply", "rw", "exact", "obtain", "have", "contrapose", "exact", "refine", "rw", "exact"], "tactic_count": 16}
{"name": "existsUnique_zpow_near_of_one_lt'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "existsUnique_div_zpow_mem_Ico", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Basic", "is_tactic_proof": true, "tactics": ["simpa", "existsUnique_zpow_near_of_one_lt"], "tactic_count": 2}
{"name": "existsUnique_mul_zpow_mem_Ico", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "existsUnique_add_zpow_mem_Ioc", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "existsUnique_sub_zpow_mem_Ioc", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_pow_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_nat_ge", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Basic", "is_tactic_proof": true, "tactics": ["nontriviality", "exact"], "tactic_count": 2}
{"name": "instIsDirectedOrder", "kind": "instance", "module": "Mathlib.Algebra.Order.Archimedean.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_nat_gt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "add_one_pow_unbounded_of_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pow_unbounded_of_one_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Basic", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact"], "tactic_count": 3}
{"name": "exists_int_ge", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_int_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsCodirectedOrder", "kind": "instance", "module": "Mathlib.Algebra.Order.Archimedean.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_int_gt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_int_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_floor", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Basic", "is_tactic_proof": true, "tactics": ["apply", "obtain", "exact", "obtain", "exact"], "tactic_count": 5}
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{"name": "exists_nat_one_div_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Basic", "is_tactic_proof": true, "tactics": ["obtain", "use", "rw", "apply", "simp", "exact"], "tactic_count": 6}
{"name": "exists_mem_Ico_zpow", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Basic", "is_tactic_proof": true, "tactics": ["classical", "have", "obtain", "use", "rw", "exact", "have", "obtain", "refine", "contrapose", "rw", "exact", "obtain", "exact"], "tactic_count": 14}
{"name": "exists_mem_Ioc_zpow", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_pow_lt_of_lt_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "use", "simp", "exact", "rcases", "exact"], "tactic_count": 6}
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{"name": "exists_pow_btwn_of_lt_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Basic", "is_tactic_proof": true, "tactics": ["have", "refine", "by_contra", "have", "intro", "simp", "exact", "rw", "exact"], "tactic_count": 9}
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{"name": "archimedean_iff_nat_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "archimedean_iff_int_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "archimedean_iff_int_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "archimedean_iff_rat_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "instArchimedeanRat", "kind": "instance", "module": "Mathlib.Algebra.Order.Archimedean.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_rat_gt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_rat_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "exists_rat_mem_uIoo", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "le_of_forall_rat_lt_imp_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "le_iff_forall_rat_lt_imp_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_iff_forall_lt_rat_imp_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_of_forall_rat_lt_iff_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_of_forall_lt_rat_iff_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "exists_rat_near", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instArchimedeanNat", "kind": "instance", "module": "Mathlib.Algebra.Order.Archimedean.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instArchimedeanInt", "kind": "instance", "module": "Mathlib.Algebra.Order.Archimedean.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.instArchimedean", "kind": "instance", "module": "Mathlib.Algebra.Order.Archimedean.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.instMulArchimedean", "kind": "instance", "module": "Mathlib.Algebra.Order.Archimedean.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instArchimedeanNNRat", "kind": "instance", "module": "Mathlib.Algebra.Order.Archimedean.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instMulArchimedeanNNRat", "kind": "instance", "module": "Mathlib.Algebra.Order.Archimedean.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Archimedean.floorRing", "kind": "definition", "module": "Mathlib.Algebra.Order.Archimedean.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FloorRing.archimedean", "kind": "instance", "module": "Mathlib.Algebra.Order.Archimedean.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Units.instMulArchimedean", "kind": "instance", "module": "Mathlib.Algebra.Order.Archimedean.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.instArchimedean", "kind": "instance", "module": "Mathlib.Algebra.Order.Archimedean.Basic", "is_tactic_proof": true, "tactics": ["constructor", "intro", "cases", "bot", "coe", "cases", "bot", "coe"], "tactic_count": 8}
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{"name": "MulArchimedeanOrder", "kind": "definition", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulArchimedeanOrder.of", "kind": "definition", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MulArchimedeanOrder.of_symm_eq", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulArchimedeanOrder.val_symm_eq", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MulArchimedeanOrder.instInhabited", "kind": "instance", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulArchimedeanOrder.instSubsingleton", "kind": "instance", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MulArchimedeanClass.lift", "kind": "definition", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulArchimedeanClass.lift_mk", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": true, "tactics": ["unfold", "exact"], "tactic_count": 2}
{"name": "MulArchimedeanClass.lift₂", "kind": "definition", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulArchimedeanClass.lift₂_mk", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": true, "tactics": ["unfold", "exact"], "tactic_count": 2}
{"name": "MulArchimedeanClass.out", "kind": "definition", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulArchimedeanClass.mk_out", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulArchimedeanClass.mk_inv", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulArchimedeanClass.mk_div_comm", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MulArchimedeanClass.mk_mabs", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulArchimedeanClass.instSubsingleton", "kind": "instance", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulArchimedeanClass.instLinearOrder", "kind": "instance", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": true, "tactics": ["classical", "unfold", "infer_instance"], "tactic_count": 3}
{"name": "MulArchimedeanClass.mk_le_mk", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulArchimedeanClass.mk_lt_mk", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulArchimedeanClass.mk_le_mk_iff_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact", "exact"], "tactic_count": 4}
{"name": "MulArchimedeanClass.instOrderTop", "kind": "instance", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulArchimedeanClass.instInhabited", "kind": "instance", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulArchimedeanClass.mk_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulArchimedeanClass.mk_eq_top_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulArchimedeanClass.top_eq_mk_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MulArchimedeanClass.out_top", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MulArchimedeanClass.instNontrivial", "kind": "instance", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulArchimedeanClass.mk_antitoneOn", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": true, "tactics": ["intro", "contrapose", "rw", "obtain", "rw", "simpa"], "tactic_count": 6}
{"name": "MulArchimedeanClass.mk_monotoneOn", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": true, "tactics": ["intro", "contrapose", "rw", "obtain", "rw", "simpa"], "tactic_count": 6}
{"name": "MulArchimedeanClass.mk_le_mk_of_mabs", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": true, "tactics": ["rw", "have", "exact"], "tactic_count": 3}
{"name": "MulArchimedeanClass.min_le_mk_of_le_of_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": true, "tactics": ["have", "rw", "apply", "obtain", "rw", "exact", "rw", "exact"], "tactic_count": 8}
{"name": "MulArchimedeanClass.min_le_mk_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": true, "tactics": ["by_contra", "rw", "have", "have", "simp", "exact"], "tactic_count": 6}
{"name": "MulArchimedeanClass.min_le_mk_div", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MulArchimedeanClass.mk_left_le_mk_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MulArchimedeanClass.mk_right_le_mk_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MulArchimedeanClass.mk_left_le_mk_div", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MulArchimedeanClass.mk_right_le_mk_div", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MulArchimedeanClass.mk_left_le_mk_mul_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulArchimedeanClass.mk_right_le_mk_mul_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MulArchimedeanClass.mk_left_le_mk_div_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulArchimedeanClass.mk_right_le_mk_div_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MulArchimedeanClass.mk_mul_lt_mk_left_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulArchimedeanClass.mk_mul_lt_mk_right_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulArchimedeanClass.mk_div_lt_mk_left_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulArchimedeanClass.mk_div_lt_mk_right_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulArchimedeanClass.mk_mul_eq_mk_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": true, "tactics": ["refine", "rw", "apply", "rw", "apply", "rw", "exact"], "tactic_count": 7}
{"name": "MulArchimedeanClass.mk_mul_eq_mk_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulArchimedeanClass.mk_div_eq_mk_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MulArchimedeanClass.mk_div_eq_mk_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MulArchimedeanClass.mk_prod", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": true, "tactics": ["induction", "singleton", "cons", "intro", "obtain", "rw", "have", "have", "by_contra", "obtain", "rw", "exact", "rw", "obtain", "rw", "congr", "apply", "intro", "obtain", "rfl", "refine", "apply", "rw", "exact", "rw", "congr", "refine", "intro", "obtain", "apply", "rw", "exact", "exact"], "tactic_count": 33}
{"name": "MulArchimedeanClass.lt_of_mk_lt_mk_of_one_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact"], "tactic_count": 3}
{"name": "MulArchimedeanClass.lt_of_mk_lt_mk_of_le_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact"], "tactic_count": 3}
{"name": "MulArchimedeanClass.one_lt_of_one_lt_of_mk_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": true, "tactics": ["suffices", "apply", "simpa", "simpa"], "tactic_count": 4}
{"name": "MulArchimedeanClass.mulArchimedean_of_mk_eq_mk", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulArchimedeanClass.mk_eq_mk_of_mulArchimedean", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "exact"], "tactic_count": 3}
{"name": "MulArchimedeanClass.orderHom", "kind": "definition", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulArchimedeanClass.orderHom_mk", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulArchimedeanClass.map_mk_eq", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MulArchimedeanClass.map_mk_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MulArchimedeanClass.orderHom_injective", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": true, "tactics": ["intro", "induction", "mk", "induction", "mk", "simp_rw", "obtain", "intro", "exact"], "tactic_count": 9}
{"name": "MulArchimedeanClass.orderHom_top", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MulArchimedeanClass.liftOrderHom", "kind": "definition", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulArchimedeanClass.liftOrderHom_mk", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulArchimedeanClass.subsemigroup", "kind": "definition", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulArchimedeanClass.subsemigroup_strictAnti", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": true, "tactics": ["intro", "rw", "refine", "contrapose", "apply", "simpa"], "tactic_count": 6}
{"name": "MulArchimedeanClass.subgroup", "kind": "definition", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulArchimedeanClass.subsemigroup_eq_subgroup_of_ne_top", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MulArchimedeanClass.subgroup_eq_bot", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MulArchimedeanClass.mem_subgroup_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MulArchimedeanClass.subgroup_strictAntiOn", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": true, "tactics": ["intro", "rw", "rw", "rw", "refine", "contrapose", "apply", "simpa"], "tactic_count": 8}
{"name": "MulArchimedeanClass.subgroup_antitone", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": true, "tactics": ["intro", "obtain", "rw", "obtain", "simp", "rwa"], "tactic_count": 6}
{"name": "MulArchimedeanClass.ballSubgroup", "kind": "abbrev", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulArchimedeanClass.closedBallSubgroup", "kind": "abbrev", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulArchimedeanClass.mem_ballSubgroup_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MulArchimedeanClass.mem_closedBallSubgroup_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MulArchimedeanClass.ballSubgroup_top", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "MulArchimedeanClass.closedBallSubgroup_top", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "MulArchimedeanClass.ballSubgroup_antitone", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": true, "tactics": ["intro", "exact"], "tactic_count": 2}
{"name": "FiniteMulArchimedeanClass", "kind": "abbrev", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteMulArchimedeanClass.mk", "kind": "definition", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteMulArchimedeanClass.val_mk", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteMulArchimedeanClass.mk_le_mk", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteMulArchimedeanClass.mk_lt_mk", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteMulArchimedeanClass.min_le_mk_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteMulArchimedeanClass.mk_inv", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteMulArchimedeanClass.ind", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "FiniteMulArchimedeanClass.instSubsingletonOfMulArchimedean", "kind": "instance", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteMulArchimedeanClass.instNonemptyOfNontrivial", "kind": "instance", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "FiniteMulArchimedeanClass.lift", "kind": "definition", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteMulArchimedeanClass.lift_mk", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FiniteMulArchimedeanClass.liftOrderHom", "kind": "definition", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteMulArchimedeanClass.liftOrderHom_mk", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteMulArchimedeanClass.withTopOrderIso", "kind": "definition", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteMulArchimedeanClass.withTopOrderIso_apply_coe", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteMulArchimedeanClass.withTopOrderIso_symm_apply", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteMulArchimedeanClass.congrOrderIso", "kind": "definition", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteMulArchimedeanClass.coe_congrOrderIso_apply", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteMulArchimedeanClass.congrOrderIso_symm", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteMulArchimedeanClass.toUpperSetMulArchimedeanClass", "kind": "definition", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteMulArchimedeanClass.subgroup", "kind": "definition", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteMulArchimedeanClass.subsemigroup_eq_subgroup", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteMulArchimedeanClass.subgroup_eq_bot", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "FiniteMulArchimedeanClass.mem_subgroup_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "FiniteMulArchimedeanClass.subgroup_strictAnti", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteMulArchimedeanClass.ballSubgroup", "kind": "abbrev", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteMulArchimedeanClass.closedBallSubgroup", "kind": "abbrev", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteMulArchimedeanClass.mem_ballSubgroup_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FiniteMulArchimedeanClass.mem_closedBallSubgroup_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FiniteMulArchimedeanClass.ballSubgroup_strictAnti", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingHom.subsingleton", "kind": "instance", "module": "Mathlib.Algebra.Order.Archimedean.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingIso.subsingleton_right", "kind": "instance", "module": "Mathlib.Algebra.Order.Archimedean.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingIso.subsingleton_left", "kind": "instance", "module": "Mathlib.Algebra.Order.Archimedean.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingHom.eq_id", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingIso.eq_refl", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingHom.apply_eq_self", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.Hom", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "Set.sum_indicator_eventually_eq_card", "kind": "theorem", "module": "Mathlib.Algebra.Order.Archimedean.IndicatorCard", "is_tactic_proof": false, "tactics": ["have", "intro", "rw", "rw", "obtain", "refine", "rw", "exact", "exact"], "tactic_count": 9}
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{"name": "_private.Mathlib.Algebra.Order.BigOperators.Expect.0._aux_Mathlib_Algebra_Order_BigOperators_Expect___macroRules__private_Mathlib_Algebra_Order_BigOperators_Expect_0_term_/ℚ__1", "kind": "definition", "module": "Mathlib.Algebra.Order.BigOperators.Expect", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Finset.exists_lt_of_lt_expect", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Expect", "is_tactic_proof": true, "tactics": ["contrapose"], "tactic_count": 1}
{"name": "Finset.exists_lt_of_expect_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Expect", "is_tactic_proof": true, "tactics": ["contrapose"], "tactic_count": 1}
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{"name": "Finset.expect_mul_sq_le_sq_mul_sq", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Expect", "is_tactic_proof": true, "tactics": ["simp", "gcongr", "exact"], "tactic_count": 3}
{"name": "Fintype.expect_eq_zero_iff_of_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Expect", "is_tactic_proof": true, "tactics": ["rw", "aesop"], "tactic_count": 2}
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{"name": "Mathlib.Meta.Positivity._example", "kind": "example", "module": "Mathlib.Algebra.Order.BigOperators.Expect", "is_tactic_proof": true, "tactics": ["positivity"], "tactic_count": 1}
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{"name": "List.prod_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.GroupWithZero.List", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "simp", "simp", "exact"], "tactic_count": 6}
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{"name": "List.prod_map_le_prod_map₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.GroupWithZero.List", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "simp", "have", "apply", "apply", "simp", "grind", "grind", "apply"], "tactic_count": 11}
{"name": "List.prod_map_le_pow_length₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.GroupWithZero.List", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
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{"name": "List.prod_map_lt_prod_map", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.GroupWithZero.List", "is_tactic_proof": true, "tactics": ["a", "simp", "have", "apply", "apply", "simp", "apply", "intro", "apply", "apply", "simp", "intro", "apply", "apply", "simp", "apply", "grind", "apply"], "tactic_count": 18}
{"name": "Multiset.prod_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.GroupWithZero.Multiset", "is_tactic_proof": true, "tactics": ["cases", "simp", "apply"], "tactic_count": 3}
{"name": "Multiset.one_le_prod", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.GroupWithZero.Multiset", "is_tactic_proof": true, "tactics": ["cases", "simp", "apply"], "tactic_count": 3}
{"name": "Multiset.prod_map_le_prod_map₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.GroupWithZero.Multiset", "is_tactic_proof": true, "tactics": ["cases", "simp", "apply"], "tactic_count": 3}
{"name": "Multiset.prod_map_le_pow_card", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.GroupWithZero.Multiset", "is_tactic_proof": true, "tactics": ["induction", "simp_all"], "tactic_count": 2}
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{"name": "Multiset.prod_map_lt_prod_map", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.GroupWithZero.Multiset", "is_tactic_proof": true, "tactics": ["cases", "simp", "apply"], "tactic_count": 3}
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{"name": "Finset.le_prod_nonempty_of_submultiplicative", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Finset.one_le_prod'", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Finset.prod_le_prod_of_subset_of_one_le'", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.Finset", "is_tactic_proof": true, "tactics": ["classical", "calc", "le_mul_of_one_le_left"], "tactic_count": 3}
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{"name": "Finset.prod_mono_set_of_one_le'", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_anti_set_of_le_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_le_univ_prod_of_one_le'", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_eq_one_iff_of_one_le'", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.Finset", "is_tactic_proof": true, "tactics": ["classical", "refine", "intro", "have", "rw", "ih"], "tactic_count": 6}
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{"name": "Finset.prod_le_prod_fiberwise_of_prod_fiber_le_one'", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Finset.mulLECancellable_prod", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.Finset", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "Finset.card_le_mul_card_image_of_maps_to", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Finset.prod_eq_prod_iff_of_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.Finset", "is_tactic_proof": true, "tactics": ["classical", "revert", "refine", "specialize", "rw", "exact", "mul_eq_mul_iff_eq_and_eq"], "tactic_count": 7}
{"name": "Finset.prod_sdiff_le_prod_sdiff", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.Finset", "is_tactic_proof": false, "tactics": ["rw", "sdiff_union_inter]", "simpa"], "tactic_count": 3}
{"name": "Finset.prod_sdiff_lt_prod_sdiff", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.Finset", "is_tactic_proof": false, "tactics": ["rw", "sdiff_union_inter]", "simpa"], "tactic_count": 3}
{"name": "Finset.exists_lt_of_prod_lt'", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.Finset", "is_tactic_proof": true, "tactics": ["contrapose", "exact"], "tactic_count": 2}
{"name": "Finset.exists_le_of_prod_le'", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.Finset", "is_tactic_proof": true, "tactics": ["contrapose", "exact"], "tactic_count": 2}
{"name": "Finset.exists_one_lt_of_prod_one_of_exists_ne_one'", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.Finset", "is_tactic_proof": true, "tactics": ["contrapose", "obtain", "apply", "calc"], "tactic_count": 4}
{"name": "Finset.apply_sup_le_sum", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.Finset", "is_tactic_proof": true, "tactics": ["classical", "refine", "simpa"], "tactic_count": 3}
{"name": "Finset.apply_union_le_sum", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sum_le_one_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.Finset", "is_tactic_proof": true, "tactics": ["classical", "refine", "replace", "grind", "by_cases", "obtain", "have", "simp", "simp"], "tactic_count": 9}
{"name": "Fintype.prod_mono'", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.one_le_prod", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.prod_le_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.prod_eq_one_iff_of_one_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.prod_eq_one_iff_of_le_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.prod_strictMono'", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.one_lt_prod", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.prod_lt_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.one_lt_prod_iff_of_one_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.Finset", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "Fintype.prod_lt_one_iff_of_le_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.Finset", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "Multiset.finset_sum_eq_sup_iff_disjoint", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.Finset", "is_tactic_proof": true, "tactics": ["induction", "empty", "simp", "cons", "hr", "simp_rw", "not_true_eq_false,", "have", "simp", "simp_rw", "exact"], "tactic_count": 11}
{"name": "Multiset.sup_powerset_len", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.Finset", "is_tactic_proof": true, "tactics": ["convert", "rw", "exact"], "tactic_count": 3}
{"name": "Multiset.card_le_card_toFinset_add_one_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.Finset", "is_tactic_proof": false, "tactics": ["rw", "simp", "exact"], "tactic_count": 3}
{"name": "List.Forall₂.prod_le_prod'", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.List", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "List.Sublist.prod_le_prod'", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.List", "is_tactic_proof": true, "tactics": ["induction", "slnil", "cons", "simp", "exact", "cons₂", "simp", "grw"], "tactic_count": 8}
{"name": "List.SublistForall₂.prod_le_prod'", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.prod_le_prod'", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.prod_lt_prod'", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.List", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "simp", "simp", "cases", "exact", "exact"], "tactic_count": 8}
{"name": "List.prod_lt_prod_of_ne_nil", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.prod_le_pow_card", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.List", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "List.pow_card_le_prod", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.exists_lt_of_prod_lt'", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.List", "is_tactic_proof": true, "tactics": ["contrapose", "exact"], "tactic_count": 2}
{"name": "List.exists_le_of_prod_le'", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.List", "is_tactic_proof": true, "tactics": ["contrapose", "exact"], "tactic_count": 2}
{"name": "List.one_le_prod_of_one_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.List", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "rw", "exact"], "tactic_count": 5}
{"name": "List.max_prod_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.List", "is_tactic_proof": true, "tactics": ["rw", "constructor", "apply", "apply"], "tactic_count": 4}
{"name": "List.prod_min_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.List", "is_tactic_proof": true, "tactics": ["rw", "constructor", "apply", "apply"], "tactic_count": 4}
{"name": "List.monotone_prod_take", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.List", "is_tactic_proof": true, "tactics": ["refine", "rcases", "rw", "exact", "simp"], "tactic_count": 5}
{"name": "List.le_prod_of_mem", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.List", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "simp", "rcases", "simp", "specialize", "simp", "exact"], "tactic_count": 9}
{"name": "List.le_prod_of_submultiplicative_on_pred", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.List", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "have", "have", "grw"], "tactic_count": 6}
{"name": "List.le_prod_of_submultiplicative", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.le_prod_nonempty_of_submultiplicative_on_pred", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.List", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "rw", "by_cases", "simp", "have", "have", "have", "grw"], "tactic_count": 10}
{"name": "List.le_prod_nonempty_of_submultiplicative", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sum_le_foldr_max", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.List", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "simp", "exact"], "tactic_count": 5}
{"name": "List.one_lt_prod_of_one_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.single_le_prod", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.List", "is_tactic_proof": true, "tactics": ["induction", "simp", "simp_rw", "constructor", "exact", "exact"], "tactic_count": 6}
{"name": "List.all_one_of_le_one_le_of_prod_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.prod_eq_one_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.apply_prod_le_sum_map", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.List", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "List.sum_map_le_apply_prod", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mul_prod_Ico_eq_prod_Icc", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.LocallyFinite", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.prod_Ico_mul_eq_prod_Icc", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.LocallyFinite", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.mul_prod_Ioc_eq_prod_Icc", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.LocallyFinite", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.prod_Ioc_mul_eq_prod_Icc", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.LocallyFinite", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.mul_prod_Ioo_eq_prod_Ico", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.LocallyFinite", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.prod_Ioo_mul_eq_prod_Ico", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.LocallyFinite", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.mul_prod_Ioo_eq_prod_Ioc", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.LocallyFinite", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.prod_Ioo_mul_eq_prod_Ioc", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.LocallyFinite", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.prod_eq_prod_Ico_succ_bot", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.LocallyFinite", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "Finset.mul_prod_Ioi_eq_prod_Ici", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.LocallyFinite", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.prod_Ioi_mul_eq_prod_Ici", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.LocallyFinite", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.mul_prod_Iio_eq_prod_Iic", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.LocallyFinite", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.prod_Iio_mul_eq_prod_Iic", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.LocallyFinite", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.prod_Ico_mul_eq_prod_Ico_add_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.LocallyFinite", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.prod_prod_Ioi_mul_eq_prod_prod_off_diag", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.LocallyFinite", "is_tactic_proof": true, "tactics": ["simp_rw", "congr", "rw", "refine"], "tactic_count": 4}
{"name": "Finset.prod_eq_prod_range_sdiff", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.LocallyFinite", "is_tactic_proof": false, "tactics": ["conv_lhs", "rw", "congrm", "simp", "change", "rw"], "tactic_count": 6}
{"name": "Multiset.one_le_prod_of_one_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.single_le_prod", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.prod_le_pow_card", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.Multiset", "is_tactic_proof": true, "tactics": ["induction", "simpa"], "tactic_count": 2}
{"name": "Multiset.all_one_of_le_one_le_of_prod_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.prod_le_prod_of_rel_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.Multiset", "is_tactic_proof": true, "tactics": ["induction", "zero", "cons", "rw", "exact"], "tactic_count": 5}
{"name": "Multiset.prod_map_le_prod_map", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.prod_map_le_prod", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.prod_le_prod_map", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.pow_card_le_prod", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.Multiset", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Multiset.le_prod_of_submultiplicative_on_pred", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.Multiset", "is_tactic_proof": true, "tactics": ["induction", "h"], "tactic_count": 2}
{"name": "Multiset.le_prod_of_submultiplicative", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.Multiset", "is_tactic_proof": true, "tactics": ["induction", "h"], "tactic_count": 2}
{"name": "Multiset.le_prod_nonempty_of_submultiplicative_on_pred", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.Multiset", "is_tactic_proof": true, "tactics": ["induction", "h", "simp"], "tactic_count": 3}
{"name": "Multiset.le_prod_nonempty_of_submultiplicative", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.Multiset", "is_tactic_proof": true, "tactics": ["induction", "h"], "tactic_count": 2}
{"name": "Multiset.prod_lt_prod'", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.Multiset", "is_tactic_proof": true, "tactics": ["obtain", "simp", "exact"], "tactic_count": 3}
{"name": "Multiset.prod_lt_prod_of_nonempty'", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.Multiset", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Multiset.prod_eq_one_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.le_prod_of_mem", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.Multiset", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact"], "tactic_count": 3}
{"name": "Multiset.max_le_of_forall_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.Multiset", "is_tactic_proof": true, "tactics": ["induction", "simpa"], "tactic_count": 2}
{"name": "Multiset.max_prod_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.Multiset", "is_tactic_proof": true, "tactics": ["obtain", "simp_rw", "apply"], "tactic_count": 3}
{"name": "Multiset.prod_min_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.Multiset", "is_tactic_proof": true, "tactics": ["obtain", "simp_rw", "apply"], "tactic_count": 3}
{"name": "Multiset.abs_sum_le_sum_abs", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.apply_prod_le_sum_map", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.Multiset", "is_tactic_proof": true, "tactics": ["induction", "h"], "tactic_count": 2}
{"name": "Multiset.sum_map_le_apply_prod", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Group.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Ring.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_le_prod", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Ring.Finset", "is_tactic_proof": true, "tactics": ["induction", "empty", "cons", "simp", "have", "gcongr", "exacts"], "tactic_count": 7}
{"name": "Finset.prod_le_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Ring.Finset", "is_tactic_proof": true, "tactics": ["convert", "exact"], "tactic_count": 2}
{"name": "Finset.prod_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Ring.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_lt_prod", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Ring.Finset", "is_tactic_proof": true, "tactics": ["classical", "obtain", "rw", "have", "refine", "exact", "exact", "exact"], "tactic_count": 8}
{"name": "Finset.prod_lt_prod_of_nonempty", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Ring.Finset", "is_tactic_proof": true, "tactics": ["apply", "obtain", "exact"], "tactic_count": 3}
{"name": "Finset.sum_sq_le_sq_sum_of_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Ring.Finset", "is_tactic_proof": true, "tactics": ["simp", "refine", "rw", "gcongr", "exact", "exact"], "tactic_count": 6}
{"name": "Finset.prod_add_prod_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Ring.Finset", "is_tactic_proof": true, "tactics": ["classical", "simp_rw", "refine", "rw", "gcongr", "apply", "simp", "exact"], "tactic_count": 8}
{"name": "Finset.le_prod_of_submultiplicative_on_pred_of_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Ring.Finset", "is_tactic_proof": false, "tactics": ["apply", "le_trans", "intro", "obtain", "exact"], "tactic_count": 5}
{"name": "Finset.le_prod_of_submultiplicative_of_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Ring.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sum_mul_self_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Ring.Finset", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Finset.abs_prod", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Ring.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.PNat.coe_prod", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Ring.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CanonicallyOrderedAdd.prod_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Ring.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_add_prod_le'", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Ring.Finset", "is_tactic_proof": true, "tactics": ["classical", "simp_rw", "grw", "gcongr"], "tactic_count": 4}
{"name": "Finset.sum_sq_le_sum_mul_sum_of_sq_eq_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Ring.Finset", "is_tactic_proof": true, "tactics": ["obtain", "have", "sum_eq_zero", "rw", "simp", "refine", "calc", "gcongr", "have", "grind", "refine", "le_of_eq_of_le", "repeat"], "tactic_count": 13}
{"name": "Finset.sum_mul_sq_le_sq_mul_sq", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Ring.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sq_sum_div_le_sum_sq_div", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Ring.Finset", "is_tactic_proof": true, "tactics": ["have", "have", "refine", "rw", "exact"], "tactic_count": 5}
{"name": "AbsoluteValue.sum_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Ring.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAbsoluteValue.abv_sum", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Ring.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AbsoluteValue.map_prod", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Ring.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAbsoluteValue.map_prod", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Ring.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalFinsetProd", "kind": "definition", "module": "Mathlib.Algebra.Order.BigOperators.Ring.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CanonicallyOrderedAdd.list_prod_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Ring.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CanonicallyOrderedAdd.multiset_prod_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Ring.Multiset", "is_tactic_proof": true, "tactics": ["rcases", "rw", "exact"], "tactic_count": 3}
{"name": "Multiset.le_prod_of_submultiplicative_on_pred_of_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Ring.Multiset", "is_tactic_proof": true, "tactics": ["revert", "refine", "intro", "by_cases", "simp", "have", "have", "rw", "exact"], "tactic_count": 9}
{"name": "Multiset.le_prod_of_submultiplicative_of_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Ring.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.mem_le_prod_of_one_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.BigOperators.Ring.Multiset", "is_tactic_proof": true, "tactics": ["obtain", "rw", "calc", "f", "gcongr", "exact", "simp_all"], "tactic_count": 7}
{"name": "rat_add_continuous_lemma", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "rat_mul_continuous_lemma", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": true, "tactics": ["have", "have", "refine", "replace", "replace", "set", "have", "rw", "simpa"], "tactic_count": 9}
{"name": "rat_inv_continuous_lemma", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": true, "tactics": ["refine", "have", "have", "rw", "abv_sub", "refine", "rw", "refine", "gcongr", "exact"], "tactic_count": 10}
{"name": "IsCauSeq", "kind": "definition", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCauSeq.cauchy₂", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "refine", "rw"], "tactic_count": 4}
{"name": "IsCauSeq.cauchy₃", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCauSeq.bounded", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": true, "tactics": ["obtain", "set", "have", "refine", "rintro", "simp", "exact", "refine", "obtain", "exact", "simpa"], "tactic_count": 11}
{"name": "IsCauSeq.bounded'", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCauSeq.const", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCauSeq.add", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCauSeq.mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCauSeq_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CauSeq", "kind": "definition", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.instCoeFunForallNat", "kind": "instance", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.ext", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.isCauSeq", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.cauchy", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.ofEq", "kind": "definition", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.cauchy₂", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.cauchy₃", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.bounded", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.bounded'", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.instAdd", "kind": "instance", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.coe_add", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.add_apply", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.const", "kind": "definition", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Order.CauSeq.Basic.0.CauSeq.termConst", "kind": "definition", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Order.CauSeq.Basic.0.CauSeq._aux_Mathlib_Algebra_Order_CauSeq_Basic___macroRules__private_Mathlib_Algebra_Order_CauSeq_Basic_0_CauSeq_termConst_1", "kind": "definition", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Order.CauSeq.Basic.0.CauSeq._aux_Mathlib_Algebra_Order_CauSeq_Basic___unexpand_CauSeq_const_1", "kind": "definition", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.coe_const", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.const_apply", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.const_inj", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.instZero", "kind": "instance", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.instOne", "kind": "instance", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.instInhabited", "kind": "instance", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.coe_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.coe_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.zero_apply", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.one_apply", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.const_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.const_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.const_add", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.instMul", "kind": "instance", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.coe_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.mul_apply", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.const_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.instNeg", "kind": "instance", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.coe_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.neg_apply", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.const_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.instSub", "kind": "instance", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.coe_sub", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.sub_apply", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.const_sub", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.instSMul", "kind": "instance", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.coe_smul", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.smul_apply", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.const_smul", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.instIsScalarTower", "kind": "instance", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.addGroup", "kind": "instance", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.instNatCast", "kind": "instance", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.instIntCast", "kind": "instance", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.addGroupWithOne", "kind": "instance", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.instPowNat", "kind": "instance", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.coe_pow", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.pow_apply", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.const_pow", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.ring", "kind": "instance", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.instCommRingOfIsAbsoluteValue", "kind": "instance", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.LimZero", "kind": "definition", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.add_limZero", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.mul_limZero_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.mul_limZero_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.neg_limZero", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CauSeq.sub_limZero", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CauSeq.limZero_sub_rev", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CauSeq.zero_limZero", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.const_limZero", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.equiv", "kind": "instance", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.add_equiv_add", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CauSeq.neg_equiv_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CauSeq.sub_equiv_sub", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CauSeq.equiv_def₃", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.limZero_congr", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.abv_pos_of_not_limZero", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": true, "tactics": ["by_contra", "refine", "simp", "obtain", "rcases", "refine", "have", "rwa"], "tactic_count": 8}
{"name": "CauSeq.of_near", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.not_limZero_of_not_congr_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": true, "tactics": ["intro", "have", "exact"], "tactic_count": 3}
{"name": "CauSeq.mul_equiv_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.mul_equiv_zero'", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.mul_not_equiv_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.const_equiv", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.mul_equiv_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CauSeq.smul_equiv_smul", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CauSeq.pow_equiv_pow", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "CauSeq.one_not_equiv_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.inv_aux", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.inv", "kind": "definition", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.coe_inv", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.inv_apply", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.inv_mul_cancel", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.mul_inv_cancel", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.const_inv", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Order.CauSeq.Basic.0.CauSeq.termConst_1", "kind": "definition", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Order.CauSeq.Basic.0.CauSeq._aux_Mathlib_Algebra_Order_CauSeq_Basic___macroRules__private_Mathlib_Algebra_Order_CauSeq_Basic_0_CauSeq_termConst_1_1", "kind": "definition", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Order.CauSeq.Basic.0.CauSeq._aux_Mathlib_Algebra_Order_CauSeq_Basic___unexpand_CauSeq_const_2", "kind": "definition", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.Pos", "kind": "definition", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.not_limZero_of_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.const_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.add_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.pos_add_limZero", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.mul_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.trichotomy", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simp", "rcases", "rcases", "refine", "obtain", "rwa", "rw", "exact", "rwa", "rw", "rw", "exact"], "tactic_count": 14}
{"name": "CauSeq.instLTAbs", "kind": "instance", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.instLEAbs", "kind": "instance", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.lt_of_lt_of_eq", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.lt_of_eq_of_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "CauSeq.lt_trans", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.lt_irrefl", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.le_of_eq_of_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.le_of_le_of_eq", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.instPreorderAbs", "kind": "instance", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.le_antisymm", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.lt_total", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.le_total", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.const_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.const_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CauSeq.le_of_exists", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.exists_gt", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.exists_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.rat_sup_continuous_lemma", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.rat_inf_continuous_lemma", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.instMaxAbs", "kind": "instance", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.instMinAbs", "kind": "instance", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.coe_sup", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.coe_inf", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.sup_limZero", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.inf_limZero", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.sup_equiv_sup", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": true, "tactics": ["intro", "obtain", "obtain", "exact"], "tactic_count": 4}
{"name": "CauSeq.inf_equiv_inf", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": true, "tactics": ["intro", "obtain", "obtain", "exact"], "tactic_count": 4}
{"name": "CauSeq.sup_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": true, "tactics": ["obtain", "refine", "have", "exact"], "tactic_count": 4}
{"name": "CauSeq.lt_inf", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": true, "tactics": ["obtain", "refine", "have", "exact"], "tactic_count": 4}
{"name": "CauSeq.sup_idem", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.inf_idem", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.sup_comm", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.inf_comm", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.sup_eq_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": true, "tactics": ["obtain", "intro", "refine", "dsimp", "rw", "rwa", "rw", "exact", "refine", "rw"], "tactic_count": 10}
{"name": "CauSeq.inf_eq_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": true, "tactics": ["obtain", "intro", "refine", "dsimp", "rw", "rwa", "exact", "refine", "rw"], "tactic_count": 9}
{"name": "CauSeq.sup_eq_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CauSeq.inf_eq_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CauSeq.le_sup_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.inf_le_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.le_sup_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.inf_le_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.sup_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "exact", "replace", "refine", "exact", "replace", "refine", "exact"], "tactic_count": 9}
{"name": "CauSeq.le_inf", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "exact", "replace", "refine", "exact", "replace", "refine", "exact"], "tactic_count": 9}
{"name": "CauSeq.sup_inf_distrib_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.sup_inf_distrib_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCauSeq.of_abv_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.BigOperators", "is_tactic_proof": true, "tactics": ["intro", "obtain", "exists", "intro", "have", "have", "have", "have", "rw", "refine", "generalize", "clear", "rw", "rw", "dsimp", "clear", "induction", "zero", "succ", "simp", "simp", "simp", "grw"], "tactic_count": 23}
{"name": "IsCauSeq.of_abv", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cauchy_product", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.BigOperators", "is_tactic_proof": true, "tactics": ["let", "let", "have", "have", "let", "have", "div_pos", "let", "refine", "have", "simpa", "have", "simp", "have", "have", "have", "have", "have", "rw", "div_mul_cancel₀", "have", "have", "calc", "have", "gcongr", "refine", "rw", "gcongr", "exact", "exact", "have", "calc", "rw", "refine", "suffices", "ε", "rw", "simpa", "gcongr", "exact", "rw", "calc", "gcongr", "rw", "grw", "rw", "gcongr", "rw", "have", "gcongr", "exact", "hM"], "tactic_count": 52}
{"name": "IsCauSeq.of_decreasing_bounded", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCauSeq.of_mono_bounded", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCauSeq.geo_series", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.BigOperators", "is_tactic_proof": true, "tactics": ["have", "refine", "simp", "conv", "have", "refine", "intro", "rw", "gcongr", "exact", "refine", "exact", "intro", "rw", "gcongr"], "tactic_count": 15}
{"name": "IsCauSeq.geo_series_const", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.BigOperators", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsCauSeq.series_ratio_test", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.BigOperators", "is_tactic_proof": true, "tactics": ["have", "refine", "obtain", "have", "have", "simpa", "generalize", "replace", "induction", "zero", "rw", "positivity", "succ", "ih", "have", "rw", "refine", "exact"], "tactic_count": 18}
{"name": "CauSeq.Completion.Cauchy", "kind": "definition", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.Completion.mk", "kind": "definition", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.Completion.mk_eq_mk", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.Completion.mk_eq", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.Completion.ofRat", "kind": "definition", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.Completion.instZeroCauchy", "kind": "instance", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.Completion.instOneCauchy", "kind": "instance", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.Completion.instInhabitedCauchy", "kind": "instance", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.Completion.ofRat_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.Completion.ofRat_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.Completion.mk_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "CauSeq.Completion.instAddCauchy", "kind": "instance", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.Completion.mk_add", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.Completion.instNegCauchy", "kind": "instance", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.Completion.mk_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.Completion.instMulCauchy", "kind": "instance", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.Completion.mk_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.Completion.instSubCauchy", "kind": "instance", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.Completion.mk_sub", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.Completion.instSMulCauchyOfIsScalarTower", "kind": "instance", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.Completion.mk_smul", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.Completion.instPowCauchyNat", "kind": "instance", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.Completion.mk_pow", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.Completion.instNatCastCauchy", "kind": "instance", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.Completion.instIntCastCauchy", "kind": "instance", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.Completion.ofRat_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.Completion.ofRat_intCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.Completion.ofRat_add", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.Completion.ofRat_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.Completion.ofRat_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.Completion.ofRat_injective", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.Completion.Cauchy.ring", "kind": "instance", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.Completion.ofRatRingHom", "kind": "definition", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.Completion.ofRat_sub", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.Completion.Cauchy.instNonTrivial", "kind": "instance", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.Completion.Cauchy.commRing", "kind": "instance", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.Completion.instNNRatCast", "kind": "instance", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.Completion.instRatCast", "kind": "instance", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.Completion.ofRat_nnratCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.Completion.ofRat_ratCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.Completion.instInvCauchy", "kind": "instance", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.Completion.inv_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.Completion.inv_mk", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.Completion.cau_seq_zero_ne_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.Completion.zero_ne_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.Completion.inv_mul_cancel", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.Completion.mul_inv_cancel", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.Completion.ofRat_inv", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.Completion.instDivInvMonoid", "kind": "instance", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.Completion.ofRat_div", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CauSeq.Completion.Cauchy.divisionRing", "kind": "instance", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.Completion.instReprCauchy", "kind": "instance", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.Completion.Cauchy.field", "kind": "instance", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.complete", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.lim", "kind": "definition", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.equiv_lim", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.eq_lim_of_const_equiv", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.lim_eq_of_equiv_const", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.lim_eq_lim_of_equiv", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.lim_const", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.lim_add", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.lim_mul_lim", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.lim_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CauSeq.lim_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.lim_sub", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CauSeq.lim_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.lim_inv", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.lim_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.le_lim", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.lt_lim", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.lim_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.CauSeq.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonovaryOn.sum_smul_sum_le_card_smul_sum", "kind": "theorem", "module": "Mathlib.Algebra.Order.Chebyshev", "is_tactic_proof": true, "tactics": ["classical", "obtain", "rw", "exact", "sum_le_card_nsmul", "hfg.sum_smul_comp_perm_le_sum_smul"], "tactic_count": 6}
{"name": "AntivaryOn.card_smul_sum_le_sum_smul_sum", "kind": "theorem", "module": "Mathlib.Algebra.Order.Chebyshev", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monovary.sum_smul_sum_le_card_smul_sum", "kind": "theorem", "module": "Mathlib.Algebra.Order.Chebyshev", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antivary.card_smul_sum_le_sum_smul_sum", "kind": "theorem", "module": "Mathlib.Algebra.Order.Chebyshev", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonovaryOn.sum_mul_sum_le_card_mul_sum", "kind": "theorem", "module": "Mathlib.Algebra.Order.Chebyshev", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "AntivaryOn.card_mul_sum_le_sum_mul_sum", "kind": "theorem", "module": "Mathlib.Algebra.Order.Chebyshev", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "pow_sum_le_card_mul_sum_pow", "kind": "theorem", "module": "Mathlib.Algebra.Order.Chebyshev", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sq_sum_le_card_mul_sum_sq", "kind": "theorem", "module": "Mathlib.Algebra.Order.Chebyshev", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Monovary.sum_mul_sum_le_card_mul_sum", "kind": "theorem", "module": "Mathlib.Algebra.Order.Chebyshev", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antivary.card_mul_sum_le_sum_mul_sum", "kind": "theorem", "module": "Mathlib.Algebra.Order.Chebyshev", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pow_sum_div_card_le_sum_pow", "kind": "theorem", "module": "Mathlib.Algebra.Order.Chebyshev", "is_tactic_proof": true, "tactics": ["obtain", "simp", "rw", "exact"], "tactic_count": 4}
{"name": "sum_div_card_sq_le_sum_sq_div_card", "kind": "theorem", "module": "Mathlib.Algebra.Order.Chebyshev", "is_tactic_proof": true, "tactics": ["obtain", "simp", "rw", "exact"], "tactic_count": 4}
{"name": "ConditionallyCompleteLinearOrderedField.to_archimedean", "kind": "instance", "module": "Mathlib.Algebra.Order.CompleteField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearOrderedField.cutMap", "kind": "definition", "module": "Mathlib.Algebra.Order.CompleteField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearOrderedField.cutMap_mono", "kind": "theorem", "module": "Mathlib.Algebra.Order.CompleteField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearOrderedField.mem_cutMap_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.CompleteField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearOrderedField.coe_mem_cutMap_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.CompleteField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearOrderedField.cutMap_self", "kind": "theorem", "module": "Mathlib.Algebra.Order.CompleteField", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "LinearOrderedField.cutMap_coe", "kind": "theorem", "module": "Mathlib.Algebra.Order.CompleteField", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "LinearOrderedField.cutMap_nonempty", "kind": "theorem", "module": "Mathlib.Algebra.Order.CompleteField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearOrderedField.cutMap_bddAbove", "kind": "theorem", "module": "Mathlib.Algebra.Order.CompleteField", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "LinearOrderedField.cutMap_add", "kind": "theorem", "module": "Mathlib.Algebra.Order.CompleteField", "is_tactic_proof": true, "tactics": ["refine", "rw", "obtain", "refine", "norm_cast", "rw", "exact", "rintro", "refine", "rw", "exact"], "tactic_count": 11}
{"name": "LinearOrderedField.inducedMap", "kind": "definition", "module": "Mathlib.Algebra.Order.CompleteField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearOrderedField.inducedMap_mono", "kind": "theorem", "module": "Mathlib.Algebra.Order.CompleteField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearOrderedField.inducedMap_rat", "kind": "theorem", "module": "Mathlib.Algebra.Order.CompleteField", "is_tactic_proof": true, "tactics": ["refine", "rw", "obtain", "exact", "obtain", "rw", "exact"], "tactic_count": 7}
{"name": "LinearOrderedField.inducedMap_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.CompleteField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearOrderedField.inducedMap_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.CompleteField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearOrderedField.inducedMap_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.CompleteField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearOrderedField.coe_lt_inducedMap_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.CompleteField", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact", "obtain", "apply", "exact"], "tactic_count": 6}
{"name": "LinearOrderedField.lt_inducedMap_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.CompleteField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearOrderedField.inducedMap_self", "kind": "theorem", "module": "Mathlib.Algebra.Order.CompleteField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearOrderedField.inducedMap_inducedMap", "kind": "theorem", "module": "Mathlib.Algebra.Order.CompleteField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearOrderedField.inducedMap_inv_self", "kind": "theorem", "module": "Mathlib.Algebra.Order.CompleteField", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LinearOrderedField.inducedMap_add", "kind": "theorem", "module": "Mathlib.Algebra.Order.CompleteField", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "LinearOrderedField.le_inducedMap_mul_self_of_mem_cutMap", "kind": "theorem", "module": "Mathlib.Algebra.Order.CompleteField", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "trans", "exact", "rw", "exact", "mul_self_le_mul_self"], "tactic_count": 7}
{"name": "LinearOrderedField.exists_mem_cutMap_mul_self_of_lt_inducedMap_mul_self", "kind": "theorem", "module": "Mathlib.Algebra.Order.CompleteField", "is_tactic_proof": true, "tactics": ["obtain", "refine", "rw", "exact", "obtain", "rw", "refine", "rw", "push_cast", "obtain", "exact"], "tactic_count": 11}
{"name": "LinearOrderedField.inducedAddHom", "kind": "definition", "module": "Mathlib.Algebra.Order.CompleteField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearOrderedField.inducedOrderRingHom", "kind": "definition", "module": "Mathlib.Algebra.Order.CompleteField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearOrderedField.inducedOrderRingIso", "kind": "definition", "module": "Mathlib.Algebra.Order.CompleteField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearOrderedField.coe_inducedOrderRingIso", "kind": "theorem", "module": "Mathlib.Algebra.Order.CompleteField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearOrderedField.inducedOrderRingIso_symm", "kind": "theorem", "module": "Mathlib.Algebra.Order.CompleteField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearOrderedField.inducedOrderRingIso_self", "kind": "theorem", "module": "Mathlib.Algebra.Order.CompleteField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearOrderedField.uniqueOrderRingHom", "kind": "instance", "module": "Mathlib.Algebra.Order.CompleteField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearOrderedField.uniqueOrderRingIso", "kind": "instance", "module": "Mathlib.Algebra.Order.CompleteField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ringHom_monotone", "kind": "theorem", "module": "Mathlib.Algebra.Order.CompleteField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "disjointed_add_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Disjointed", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "partialSups_add_one_eq_sup_disjointed", "kind": "theorem", "module": "Mathlib.Algebra.Order.Disjointed", "is_tactic_proof": true, "tactics": ["by_cases", "have", "have", "rw", "apply", "exact", "simp", "apply", "rw", "simp"], "tactic_count": 10}
{"name": "Monotone.disjointed_add_one_sup", "kind": "theorem", "module": "Mathlib.Algebra.Order.Disjointed", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Monotone.disjointed_add_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Disjointed", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Nat.disjointedRec", "kind": "definition", "module": "Mathlib.Algebra.Order.Disjointed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "disjointedRec_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.Disjointed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_div_self", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "one_le_div", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "div_le_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "one_lt_div", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "div_lt_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "one_div_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "one_div_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "le_one_div", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "lt_one_div", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Bound.one_lt_div_of_pos_of_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bound.div_lt_one_of_pos_of_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_div_le_one_div_of_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "one_div_lt_one_div_of_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "le_of_one_div_le_one_div", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "lt_of_one_div_lt_one_div", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "div_le_self", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "div_lt_self", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "one_div_le_one_div", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_div_lt_one_div", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_lt_one_div", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "one_le_one_div", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "half_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_half_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "half_le_self_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "half_lt_self_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "one_half_lt_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "two_inv_lt_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "left_lt_add_div_two", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "add_div_two_lt_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "add_thirds", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "div_pos_iff_of_pos_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "div_pos_iff_of_pos_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "div_mul_le_div_mul_of_div_le_div", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "mul_le_mul_of_mul_div_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["rw", "rwa"], "tactic_count": 2}
{"name": "monotone_div_right_of_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictMono_div_right_of_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.div_const", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.div_const", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["simpa", "hf.mul_const"], "tactic_count": 2}
{"name": "LinearOrderedSemiField.toDenselyOrdered", "kind": "instance", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_div_strictAntiOn", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_div_pow_le_one_div_pow_of_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["refine"], "tactic_count": 1}
{"name": "one_div_pow_lt_one_div_pow_of_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["refine"], "tactic_count": 1}
{"name": "one_div_pow_anti", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_div_pow_strictAnti", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_strictAntiOn", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_pow_le_inv_pow_of_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "inv_pow_lt_inv_pow_of_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "inv_pow_anti", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_pow_strictAnti", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_iff_forall_one_lt_le_mul₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["refine", "obtain", "simp_rw", "exact", "refine", "convert", "rw"], "tactic_count": 7}
{"name": "div_nat_le_self_of_nonnneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "div_nat_lt_self_of_pos_of_two_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGLB.mul_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["rcases", "exact", "simp_rw", "rw", "exact"], "tactic_count": 5}
{"name": "IsGLB.mul_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsLUB.mul_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["obtain", "exact", "simp_rw", "obtain", "simp", "have", "rw", "exact", "rw", "exact"], "tactic_count": 10}
{"name": "IsLUB.mul_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "exists_pos_mul_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["have", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "exists_pos_lt_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "min_div_div_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "max_div_div_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_lt_zero'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "inv_nonpos'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "div_nonneg_of_nonpos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "div_pos_of_neg_of_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "div_neg_of_neg_of_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "div_neg_of_pos_of_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "div_le_iff_of_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "div_le_iff_of_neg'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "le_div_iff_of_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "le_div_iff_of_neg'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "div_lt_iff_of_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "div_lt_iff_of_neg'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "lt_div_iff_of_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "lt_div_iff_of_neg'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "div_le_one_of_ge", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "inv_le_inv_of_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "inv_le_of_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "le_inv_of_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "inv_lt_inv_of_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "inv_lt_of_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "lt_inv_of_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "sub_inv_antitoneOn_Ioi", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sub_inv_antitoneOn_Iio", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sub_inv_antitoneOn_Icc_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "simp"], "tactic_count": 3}
{"name": "sub_inv_antitoneOn_Icc_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "simp"], "tactic_count": 3}
{"name": "inv_antitoneOn_Ioi", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["convert", "exact"], "tactic_count": 2}
{"name": "inv_antitoneOn_Iio", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["convert", "exact"], "tactic_count": 2}
{"name": "inv_antitoneOn_Icc_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["convert", "exact"], "tactic_count": 2}
{"name": "inv_antitoneOn_Icc_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["convert", "exact"], "tactic_count": 2}
{"name": "div_le_div_of_nonpos_of_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "div_lt_div_of_neg_of_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "div_le_div_right_of_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "div_lt_div_right_of_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "one_le_div_of_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "div_le_one_of_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "one_lt_div_of_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "div_lt_one_of_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "one_div_le_of_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "one_div_lt_of_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "le_one_div_of_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "lt_one_div_of_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "one_div_le_one_div_of_neg_of_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "one_div_lt_one_div_of_neg_of_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "le_of_neg_of_one_div_le_one_div", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "lt_of_neg_of_one_div_lt_one_div", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "one_div_le_one_div_of_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "one_div_lt_one_div_of_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "one_div_lt_neg_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_div_le_neg_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sub_self_div_two", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "div_two_sub_self", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "add_sub_div_two_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["rwa", "sub_self_div_two,"], "tactic_count": 2}
{"name": "sub_one_div_inv_le_two", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "convert", "rw"], "tactic_count": 4}
{"name": "mul_sub_mul_div_mul_neg_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mul_sub_mul_div_mul_nonpos_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "exists_add_lt_and_pos_of_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "div_pos_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "div_neg_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "div_nonneg_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "div_nonpos_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "one_lt_div_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simp", "simp"], "tactic_count": 4}
{"name": "one_le_div_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simp", "simp"], "tactic_count": 4}
{"name": "div_lt_one_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simp", "simp"], "tactic_count": 4}
{"name": "div_le_one_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simp", "simp"], "tactic_count": 4}
{"name": "le_of_forall_sub_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["contrapose", "simpa"], "tactic_count": 2}
{"name": "_private.Mathlib.Algebra.Order.Field.Basic.0.exists_lt_mul_left_of_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["have", "obtain", "exact"], "tactic_count": 3}
{"name": "_private.Mathlib.Algebra.Order.Field.Basic.0.exists_lt_mul_right_of_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["have", "simp_rw", "exact"], "tactic_count": 3}
{"name": "_private.Mathlib.Algebra.Order.Field.Basic.0.exists_mul_left_lt₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["rcases", "obtain", "exact", "obtain", "exact"], "tactic_count": 5}
{"name": "_private.Mathlib.Algebra.Order.Field.Basic.0.exists_mul_right_lt₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "le_mul_of_forall_lt₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["refine", "obtain", "obtain", "exact"], "tactic_count": 4}
{"name": "mul_le_of_forall_lt_of_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["refine", "rcases", "exact", "obtain", "obtain", "exact", "d_ab.le.trans"], "tactic_count": 7}
{"name": "mul_self_inj_of_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["have", "grind"], "tactic_count": 2}
{"name": "min_div_div_right_of_nonpos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "max_div_div_right_of_nonpos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "abs_inv", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "abs_div", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "abs_one_div", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "uniform_continuous_npow_on_bounded", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["wlog", "have", "exact", "have", "zero_lt_one.trans_le", "le_add_of_nonneg_right", "mul_nonneg", "refine", "rw", "obtain", "simpa", "refine", "refine", "mul_le_mul_of_nonneg_left", "refine", "exact"], "tactic_count": 16}
{"name": "two_mul_le_add_mul_sq", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": true, "tactics": ["have", "calc", "rw"], "tactic_count": 3}
{"name": "Mathlib.Meta.Positivity.div_nonneg_of_pos_of_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.div_nonneg_of_nonneg_of_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.div_ne_zero_of_pos_of_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.div_ne_zero_of_ne_zero_of_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.zpow_zero_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalDiv", "kind": "definition", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalInv", "kind": "definition", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalPowZeroInt", "kind": "definition", "module": "Mathlib.Algebra.Order.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CanonicallyOrderedAdd.toLinearOrderedCommGroupWithZero", "kind": "abbrev", "module": "Mathlib.Algebra.Order.Field.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tsub_div", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Canonical", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "geom₂_sum_of_gt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.GeomSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "geom₂_sum_of_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.GeomSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "geom_sum_of_one_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.GeomSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "geom_sum_of_lt_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.GeomSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "geom_sum_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.GeomSum", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact", "rwa", "rwa"], "tactic_count": 5}
{"name": "geom_sum_Ico_le_of_lt_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.GeomSum", "is_tactic_proof": true, "tactics": ["rcases", "rw", "apply", "simpa", "rw", "apply", "simpa", "simpa"], "tactic_count": 8}
{"name": "Pi.exists_forall_pos_add_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Pi", "is_tactic_proof": true, "tactics": ["cases", "cases", "obtain", "obtain", "choose", "obtain", "have", "obtain", "exact"], "tactic_count": 9}
{"name": "LinearOrderedField.smul_Ioo", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearOrderedField.smul_Icc", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearOrderedField.smul_Ico", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearOrderedField.smul_Ioc", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearOrderedField.smul_Ioi", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearOrderedField.smul_Iio", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearOrderedField.smul_Ici", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearOrderedField.smul_Iic", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "zpow_two_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Field.Power", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "instFloorRingInt", "kind": "instance", "module": "Mathlib.Algebra.Order.Floor.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FloorRing.ofFloor", "kind": "definition", "module": "Mathlib.Algebra.Order.Floor.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ENat.term⌊_⌋ₑ", "kind": "definition", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat._aux_Mathlib_Algebra_Order_Floor_Extended___macroRules_ENat_term⌊_⌋ₑ_1", "kind": "definition", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat._aux_Mathlib_Algebra_Order_Floor_Extended___unexpand_ENat_floor_1", "kind": "definition", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ENat._aux_Mathlib_Algebra_Order_Floor_Extended___macroRules_ENat_term⌈_⌉ₑ_1", "kind": "definition", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat._aux_Mathlib_Algebra_Order_Floor_Extended___unexpand_ENat_ceil_1", "kind": "definition", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.floor_top", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.ceil_top", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.floor_coe", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.ceil_coe", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.floor_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "ENat.ceil_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "ENat.floor_lt_top", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "ENat.ceil_lt_top", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "ENat.le_floor", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "ENat.ceil_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "ENat.floor_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.lt_ceil", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.gc_toENNReal_floor", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.gc_ceil_toENNReal", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.floor_le_self", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.le_ceil_self", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.floor_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENat.le_ceil", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": true, "tactics": ["lift", "cases", "simp", "norm_cast", "exact", "simp", "norm_cast", "rw", "lia"], "tactic_count": 9}
{"name": "ENat.lt_floor", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENat.ceil_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ENat.floor_mono", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.ceil_mono", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.floor_le_floor", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.ceil_le_ceil", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.floor_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.ceil_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.floor_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ENat.ceil_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ENat.floor_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ENat.ceil_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ENat.floor_ofNat", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.ceil_ofNat", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.floor_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENat.ceil_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENat.floor_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENat.ceil_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ENat.floor_le_ceil", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.ceil_le_floor_add_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.floor_lt_ceil", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.floor_congr", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.ceil_congr", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.floor_add_toENNReal", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.ceil_add_toENNReal", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.floor_toENNReal_add", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENat.ceil_toENNReal_add", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENat.floor_add_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.ceil_add_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.floor_natCast_add", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.ceil_natCast_add", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.floor_add_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.ceil_add_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.floor_add_ofNat", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.ceil_add_ofNat", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.floor_sub_toENNReal", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.ceil_sub_toENNReal", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.floor_sub_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ENat.floor_sub_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.ceil_sub_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.floor_sub_ofNat", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.ceil_sub_ofNat", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.ceil_lt_add_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": true, "tactics": ["lift"], "tactic_count": 1}
{"name": "ENat.ceil_add_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.toENNReal_iSup", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.toENNReal_iInf", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalENatCeil", "kind": "definition", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity._example", "kind": "example", "module": "Mathlib.Algebra.Order.Floor.Extended", "is_tactic_proof": true, "tactics": ["positivity"], "tactic_count": 1}
{"name": "Mathlib.Meta.Positivity.int_floor_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.int_floor_nonneg_of_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalIntFloor", "kind": "definition", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.nat_ceil_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalNatCeil", "kind": "definition", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.int_ceil_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalIntCeil", "kind": "definition", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.floor_le_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.lt_floor_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.floor_le_sub_one_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.floor_le_neg_one_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Int.lt_succ_floor", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.lt_floor_add_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Int.floor_mono", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.floor_le_floor", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.floor_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.floor_eq_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.floor_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Int.floor_eq_on_Ico", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.floor_eq_on_Ico'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.preimage_floor_singleton", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.sub_one_lt_floor", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.floor_intCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.floor_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.floor_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.floor_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.floor_ofNat", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.floor_add_intCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.floor_add_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.le_floor_add", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["rw", "gcongr"], "tactic_count": 2}
{"name": "Int.le_floor_add_floor", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "Int.floor_intCast_add", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Int.floor_add_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.floor_add_ofNat", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.floor_natCast_add", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.floor_ofNat_add", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.floor_sub_intCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.floor_sub_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.floor_sub_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.floor_sub_ofNat", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.abs_sub_lt_one_of_floor_eq_floor", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["have", "have", "have", "have", "have", "exact"], "tactic_count": 6}
{"name": "Int.floor_eq_self_iff_mem", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Int.floor_lt_self_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.mul_cast_floor_div_cancel_of_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "Int.mul_natCast_floor_div_cancel", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Int.mul_fract_eq_one_iff_exists_int", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["rw", "refine", "rintro", "convert", "have", "rw", "simp"], "tactic_count": 7}
{"name": "Int.cast_mul_floor_div_cancel_of_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.natCast_mul_floor_div_cancel", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.floor_div_cast_of_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["obtain", "simp", "nth_rw", "rw"], "tactic_count": 4}
{"name": "Int.floor_div_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Int.self_sub_floor", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.floor_add_fract", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.fract_add_floor", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.self_sub_fract", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.fract_sub_self", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.fract_add", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.fract_add_intCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Int.fract_add_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Int.fract_add_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.fract_add_ofNat", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.fract_intCast_add", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.fract_natCast_add", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.fract_one_add", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.fract_ofNat_add", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.fract_sub_intCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Int.fract_sub_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Int.fract_sub_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.fract_sub_ofNat", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.fract_add_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Int.fract_add_fract_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Int.fract_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.fract_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.fract_lt_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.fract_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.fract_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Int.abs_fract", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.abs_one_sub_fract", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.fract_intCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["unfold", "rw", "exact"], "tactic_count": 3}
{"name": "Int.fract_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Int.fract_ofNat", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.fract_floor", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.floor_fract", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.fract_eq_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.fract_eq_fract", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.fract_eq_self", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.fract_fract", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.fract_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Int.fract_ne_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.fract_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["rw", "constructor", "rw", "exact", "refine", "simp", "conv", "simp"], "tactic_count": 8}
{"name": "Int.fract_neg_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["simp", "constructor"], "tactic_count": 2}
{"name": "Int.fract_mul_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rcases", "rw", "rcases", "use", "rw", "abel"], "tactic_count": 9}
{"name": "Int.preimage_fract", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["ext", "simp", "refine", "rintro", "obtain", "exact"], "tactic_count": 6}
{"name": "Int.image_fract", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["ext", "simp", "rintro", "exact", "rintro", "obtain", "exact"], "tactic_count": 7}
{"name": "Int.fract_div_mul_self_mem_Ico", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.fract_div_mul_self_add_zsmul_eq", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.sub_floor_div_mul_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.sub_floor_div_mul_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.fract_div_natCast_eq_div_natCast_mod", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["rcases", "simp", "have", "refine", "positivity", "simpa", "rw", "norm_cast", "rw"], "tactic_count": 9}
{"name": "Int.fract_div_intCast_eq_div_intCast_mod", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["rcases", "simp", "replace", "have", "intro", "obtain", "rw", "rw", "simp", "obtain", "exact", "let", "let", "have", "calc", "fract", "rw", "simp", "congr", "simp", "rw"], "tactic_count": 21}
{"name": "Int.le_ceil_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.ceil_lt_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.add_one_le_ceil_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.one_le_ceil_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Int.ceil_le_floor_add_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Int.ceil_mono", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.ceil_le_ceil", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.ceil_nonneg_of_neg_one_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Int.ceil_eq_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.ceil_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Int.ceil_eq_on_Ioc", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.preimage_ceil_singleton", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.floor_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.ceil_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.ceil_intCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.ceil_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.ceil_ofNat", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.ceil_add_intCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.ceil_intCast_add", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.ceil_add_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.ceil_natCast_add", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.ceil_add_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.ceil_one_add", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.ceil_add_ofNat", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.ceil_ofNat_add", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.ceil_sub_intCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.ceil_sub_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "Int.ceil_sub_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.ceil_sub_ofNat", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.ceil_lt_add_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "Int.ceil_add_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["rw", "gcongr"], "tactic_count": 2}
{"name": "Int.ceil_add_ceil_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "Int.ceil_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.ceil_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.ceil_eq_on_Ioc'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.ceil_eq_self_iff_mem", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Int.floor_le_ceil", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.floor_lt_ceil_of_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.ceil_eq_floor_add_one_iff_notMem", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["refine", "have", "linarith", "apply", "rw", "exact"], "tactic_count": 6}
{"name": "Int.fract_eq_zero_or_add_one_sub_ceil", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["rcases", "exact", "right", "suffices", "rw", "abel", "norm_cast", "rw", "refine", "rw", "exact"], "tactic_count": 11}
{"name": "Int.ceil_eq_add_one_sub_fract", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["rw", "abel"], "tactic_count": 2}
{"name": "Int.ceil_sub_self_eq", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["rw", "abel"], "tactic_count": 2}
{"name": "Int.mul_lt_floor", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["calc", "b", "rwa"], "tactic_count": 3}
{"name": "Int.ceil_div_ceil_inv_sub_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["obtain", "simp", "have", "refine", "rw", "convert", "field"], "tactic_count": 7}
{"name": "Int.ceil_lt_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["obtain", "calc", "rw", "calc"], "tactic_count": 4}
{"name": "Int.ceil_le_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["obtain", "rw", "positivity", "exact"], "tactic_count": 4}
{"name": "Int.div_two_lt_floor", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.ceil_lt_two_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.ceil_le_two_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.preimage_Ioo", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Int.preimage_Ico", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Int.preimage_Ioc", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Int.preimage_Icc", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Int.preimage_Ioi", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Int.preimage_Ici", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Int.preimage_Iio", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Int.preimage_Iic", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Int.floor_congr", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.ceil_congr", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.map_floor", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.map_ceil", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.map_fract", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Nat.ceil_lt_add_one_of_gt_neg_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "rw", "exact"], "tactic_count": 4}
{"name": "Int.natCast_floor_eq_floor", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.natCast_ceil_eq_ceil", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.natCast_ceil_eq_ceil_of_neg_one_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "natCast_floor_eq_intCast_floor", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "natCast_ceil_eq_intCast_ceil", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "natCast_ceil_eq_intCast_ceil_of_neg_one_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "subsingleton_floorRing", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Ring", "is_tactic_proof": true, "tactics": ["refine", "have", "have", "cases"], "tactic_count": 4}
{"name": "Nat.floor_div_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semifield", "is_tactic_proof": true, "tactics": ["obtain", "simp", "nth_rw", "rw"], "tactic_count": 4}
{"name": "Nat.floor_div_ofNat", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semifield", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.floor_div_eq_div", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semifield", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "Nat.mul_lt_floor", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semifield", "is_tactic_proof": true, "tactics": ["calc", "b", "rw", "exact"], "tactic_count": 4}
{"name": "Nat.ceil_lt_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semifield", "is_tactic_proof": true, "tactics": ["obtain", "calc", "rw", "calc"], "tactic_count": 4}
{"name": "Nat.ceil_le_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semifield", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact", "positivity", "exact"], "tactic_count": 5}
{"name": "Nat.div_two_lt_floor", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semifield", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.ceil_lt_two_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semifield", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.ceil_le_two_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semifield", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.IsNat.natFloor", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semifield", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "Mathlib.Meta.NormNum.IsInt.natFloor", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semifield", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "Mathlib.Meta.NormNum.IsNNRat.natFloor", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semifield", "is_tactic_proof": true, "tactics": ["constructor", "rw"], "tactic_count": 2}
{"name": "Mathlib.Meta.NormNum.IsRat.natFloor", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semifield", "is_tactic_proof": true, "tactics": ["rcases", "constructor", "rw", "exact"], "tactic_count": 4}
{"name": "Mathlib.Meta.NormNum.evalNatFloor", "kind": "definition", "module": "Mathlib.Algebra.Order.Floor.Semifield", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.floor_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.floor_lt_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.floor_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.floor_eq_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.lt_of_floor_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.lt_one_of_floor_lt_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.lt_succ_floor", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.lt_floor_add_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Nat.floor_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.floor_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.floor_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.floor_ofNat", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.floor_of_nonpos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.floor_mono", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.floor_le_floor", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.le_floor_iff'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact", "iff_of_false", "exact"], "tactic_count": 5}
{"name": "Nat.one_le_floor_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.floor_lt'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.floor_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.pos_of_floor_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.lt_of_lt_floor", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.floor_le_of_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.floor_le_one_of_le_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.floor_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Nat.floor_eq_iff'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": true, "tactics": ["rw", "le_antisymm_iff,"], "tactic_count": 2}
{"name": "Nat.floor_eq_on_Ico", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.floor_eq_on_Ico'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.preimage_floor_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.preimage_floor_of_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.mul_cast_floor_div_cancel", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": true, "tactics": ["rcases", "rw", "simp", "apply", "refine", "rw", "cast_mul,"], "tactic_count": 7}
{"name": "Nat.cast_mul_floor_div_cancel", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.add_one_le_ceil_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.one_le_ceil_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.le_ceil", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.ceil_mono", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.ceil_le_ceil", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.ceil_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.ceil_eq_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.preimage_ceil_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.preimage_ceil_of_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.ceil_le_floor_add_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Nat.ceil_intCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.ceil_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.ceil_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.ceil_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.ceil_ofNat", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.lt_of_ceil_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.le_of_ceil_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.floor_le_ceil", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact", "exact"], "tactic_count": 4}
{"name": "Nat.floor_lt_ceil_of_lt_of_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": true, "tactics": ["rcases", "rw", "exact", "rwa"], "tactic_count": 4}
{"name": "Nat.preimage_Ioo", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Nat.preimage_Ico", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Nat.preimage_Ioc", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Nat.preimage_Icc", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Nat.preimage_Ioi", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Nat.preimage_Ici", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Nat.preimage_Iio", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Nat.preimage_Iic", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Nat.floor_add_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.floor_add_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.floor_add_ofNat", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.floor_sub_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": true, "tactics": ["obtain", "rw", "rcases", "rw", "exact", "rw", "exact"], "tactic_count": 7}
{"name": "Nat.floor_sub_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.floor_sub_ofNat", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.ceil_add_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.ceil_add_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.ceil_add_ofNat", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.ceil_lt_add_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.ceil_add_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": true, "tactics": ["rw", "gcongr"], "tactic_count": 2}
{"name": "Nat.ceil_sub_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": true, "tactics": ["obtain", "rwa", "refine", "rw", "exact"], "tactic_count": 5}
{"name": "Nat.ceil_sub_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Nat.ceil_sub_ofNat", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.sub_one_lt_floor", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.abs_sub_floor_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": true, "tactics": ["refine", "simpa", "simpa"], "tactic_count": 3}
{"name": "Nat.abs_floor_sub_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.abs_sub_ceil_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": true, "tactics": ["refine", "simpa", "simpa"], "tactic_count": 3}
{"name": "Nat.abs_ceil_sub_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.floor_congr", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": true, "tactics": ["have", "obtain", "rw", "exact"], "tactic_count": 4}
{"name": "Nat.ceil_congr", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.map_floor", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.map_ceil", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "subsingleton_floorSemiring", "kind": "theorem", "module": "Mathlib.Algebra.Order.Floor.Semiring", "is_tactic_proof": true, "tactics": ["refine", "have", "have", "ext", "rcases", "rw", "refine", "rw", "cases", "cases", "congr"], "tactic_count": 11}
{"name": "OrderDual.instSMulWithZero", "kind": "instance", "module": "Mathlib.Algebra.Order.GroupWithZero.Action.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instSMulWithZero'", "kind": "instance", "module": "Mathlib.Algebra.Order.GroupWithZero.Action.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instDistribSMul", "kind": "instance", "module": "Mathlib.Algebra.Order.GroupWithZero.Action.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instDistribSMul'", "kind": "instance", "module": "Mathlib.Algebra.Order.GroupWithZero.Action.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instDistribMulAction", "kind": "instance", "module": "Mathlib.Algebra.Order.GroupWithZero.Action.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instDistribMulAction'", "kind": "instance", "module": "Mathlib.Algebra.Order.GroupWithZero.Action.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instMulActionWithZero", "kind": "instance", "module": "Mathlib.Algebra.Order.GroupWithZero.Action.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instMulActionWithZero'", "kind": "instance", "module": "Mathlib.Algebra.Order.GroupWithZero.Action.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lex.instSMulWithZero", "kind": "instance", "module": "Mathlib.Algebra.Order.GroupWithZero.Action.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lex.instSMulWithZero'", "kind": "instance", "module": "Mathlib.Algebra.Order.GroupWithZero.Action.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lex.instDistribSMul", "kind": "instance", "module": "Mathlib.Algebra.Order.GroupWithZero.Action.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lex.instDistribSMul'", "kind": "instance", "module": "Mathlib.Algebra.Order.GroupWithZero.Action.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lex.instDistribMulAction", "kind": "instance", "module": "Mathlib.Algebra.Order.GroupWithZero.Action.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lex.instDistribMulAction'", "kind": "instance", "module": "Mathlib.Algebra.Order.GroupWithZero.Action.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lex.instMulActionWithZero", "kind": "instance", "module": "Mathlib.Algebra.Order.GroupWithZero.Action.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lex.instMulActionWithZero'", "kind": "instance", "module": "Mathlib.Algebra.Order.GroupWithZero.Action.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddAbove.range_comp_of_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Bounds", "is_tactic_proof": true, "tactics": ["suffices", "apply", "obtain", "use", "simp", "exact"], "tactic_count": 6}
{"name": "bddAbove_range_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Bounds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zero_le'", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_lt_zero'", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "zero_lt_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ne_zero_of_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bot_eq_zero''", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearOrderedCommMonoidWithZero.toZeroLeOneClass", "kind": "instance", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearOrderedCommMonoidWithZero.toMulPosStrictMono", "kind": "instance", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearOrderedCommMonoidWithZero.toIsOrderedMonoid", "kind": "instance", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsCancelMulZero_1", "kind": "instance", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.linearOrderedCommMonoidWithZero", "kind": "abbrev", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearOrderedCommMonoidWithZero.toIsMulTorsionFree", "kind": "instance", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instLinearOrderedAddCommMonoidWithTopAdditiveOrderDual", "kind": "instance", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instLinearOrderedAddCommMonoidWithTopOrderDualAdditive", "kind": "instance", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pow_pos_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Units.zero_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_inv_lt_of_lt_mul₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": true, "tactics": ["contrapose", "simpa"], "tactic_count": 2}
{"name": "inv_mul_lt_of_lt_mul₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "lt_of_mul_lt_mul_of_le₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": true, "tactics": ["have", "rw", "simpa", "mul_lt_mul_of_le_of_lt_of_nonneg_of_pos"], "tactic_count": 4}
{"name": "instLinearOrderedAddCommGroupWithTopAdditiveOrderDual", "kind": "instance", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instLinearOrderedAddCommGroupWithTopOrderDualAdditive", "kind": "instance", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "denselyOrdered_iff_denselyOrdered_units_and_nontrivial_units", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact", "refine", "obtain", "refine", "refine", "lift", "obtain", "obtain", "exact", "lift", "obtain", "exact"], "tactic_count": 14}
{"name": "instNontrivialUnitsOfDenselyOrdered", "kind": "instance", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDenselyOrderedUnits", "kind": "instance", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "denselyOrdered_units_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instLinearOrderedCommMonoidWithZeroMultiplicativeOrderDual", "kind": "instance", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofAdd_toDual_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofDual_toAdd_eq_top_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofAdd_bot", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofDual_toAdd_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instLinearOrderedCommGroupWithZeroMultiplicativeOrderDualOfLinearOrderedAddCommGroupWithTop", "kind": "instance", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.instBot", "kind": "instance", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.zero_eq_bot", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.le", "kind": "instance", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.le_def", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.coe_le_coe", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.not_coe_le_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.instOrderBot", "kind": "instance", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.instBoundedOrder", "kind": "instance", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.zero_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.nonpos_iff_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.coe_le_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.le_coe_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMax.withZero", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.le_unzero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.unbot_le_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.one_le_coe", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.coe_le_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.unzero_le_unzero", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.instLT", "kind": "instance", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.lt_def", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.lt_iff_exists", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.coe_lt_coe", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WithZero.zero_lt_coe", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WithZero.not_lt_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WithZero.lt_iff_exists_coe", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.lt_coe_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.pos_iff_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.lt_unzero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.unzero_lt_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.one_lt_coe", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.coe_lt_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.instPreorder", "kind": "instance", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.instMulLeftMono", "kind": "instance", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": true, "tactics": ["refine", "induction", "induction", "rcases", "rw", "exact"], "tactic_count": 6}
{"name": "WithZero.addLeftMono", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": true, "tactics": ["refine", "induction", "rwa", "induction", "rw", "induction", "rw", "rw", "exact", "rcases", "rw", "gcongr"], "tactic_count": 12}
{"name": "WithZero.instExistsAddOfLE", "kind": "instance", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.map'_mono", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "WithZero.map'_strictMono", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "WithZero.exists_ne_zero_and_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact"], "tactic_count": 3}
{"name": "WithZero.toAdd_unzero_lt_of_lt_ofAdd", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "WithZero.lt_ofAdd_of_toAdd_unzero_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "WithZero.lt_ofAdd_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.toAdd_unzero_le_of_lt_ofAdd", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "WithZero.le_ofAdd_of_toAdd_unzero_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "WithZero.le_ofAdd_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.instPartialOrder", "kind": "instance", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.instMulLeftReflectLT", "kind": "instance", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": true, "tactics": ["refine", "have", "induction", "simp", "induction", "simp", "induction", "exacts"], "tactic_count": 8}
{"name": "WithZero.semilatticeSup", "kind": "instance", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.coe_sup", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.semilatticeInf", "kind": "instance", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.coe_inf", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.instLattice", "kind": "instance", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.decidableEq", "kind": "instance", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.decidableLE", "kind": "instance", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.decidableLT", "kind": "instance", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.total_le", "kind": "instance", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.instLinearOrder", "kind": "instance", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.le_max_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WithZero.min_le_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WithZero.exists_ne_zero_and_le_and_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.exists_ne_zero_and_lt_and_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "use", "constructor"], "tactic_count": 4}
{"name": "WithZero.isOrderedMonoid", "kind": "instance", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.isOrderedAddMonoid", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "WithZero.instCanonicallyOrderedAdd", "kind": "instance", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.instLinearOrderedCommMonoidWithZero", "kind": "instance", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.instLinearOrderedCommGroupWithZero", "kind": "instance", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.exp_le_exp", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WithZero.exp_lt_exp", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WithZero.exp_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WithZero.log_le_log", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": true, "tactics": ["lift"], "tactic_count": 1}
{"name": "WithZero.log_lt_log", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": true, "tactics": ["lift"], "tactic_count": 1}
{"name": "WithZero.log_le_iff_le_exp", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": true, "tactics": ["lift"], "tactic_count": 1}
{"name": "WithZero.log_lt_iff_lt_exp", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": true, "tactics": ["lift"], "tactic_count": 1}
{"name": "WithZero.le_log_iff_exp_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": true, "tactics": ["lift"], "tactic_count": 1}
{"name": "WithZero.lt_log_iff_exp_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": true, "tactics": ["lift"], "tactic_count": 1}
{"name": "WithZero.le_exp_of_log_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "WithZero.lt_exp_of_log_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "WithZero.le_log_of_exp_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.lt_log_of_exp_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.expOrderIso", "kind": "definition", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.logOrderIso", "kind": "definition", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.lt_mul_exp_iff_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": true, "tactics": ["lift", "obtain", "simp", "lift", "rw"], "tactic_count": 5}
{"name": "WithZero.le_exp_log", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Canonical", "is_tactic_proof": true, "tactics": ["cases", "simp", "rfl"], "tactic_count": 3}
{"name": "Finset.sup_mul_le_mul_sup_of_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mul_inf_le_inf_mul_of_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sup'_mul_le_mul_sup'_of_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inf'_mul_le_mul_inf'_of_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sup'_mul₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mul₀_sup'", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sup'_div₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sup_div₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Finset", "is_tactic_proof": true, "tactics": ["obtain", "simp", "rw"], "tactic_count": 3}
{"name": "MonoidWithZeroHom.inl_mono", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Lex", "is_tactic_proof": true, "tactics": ["refine", "intro", "obtain", "obtain", "simp"], "tactic_count": 5}
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{"name": "pow_lt_one₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pow_right_mono₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_le_pow₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_lt_pow₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bound.pow_le_pow_right_of_le_one_or_one_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["obtain", "exact", "exact"], "tactic_count": 3}
{"name": "pow_le_pow_right₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_self_pow₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Bound.le_self_pow_of_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pow_le_pow_left₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pow_left_monotoneOn", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monotone_mul_left_of_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monotone_mul_right_of_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.mul_const", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.const_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.mul_const", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.const_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_self_lt_mul_self", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictMonoOn_mul_self", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Decidable.mul_lt_mul''", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lt_mul_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "lt_mul_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "lt_mul_self", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sq_pos_of_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "pow_succ_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pow_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pow_lt_pow_left₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pow_left_strictMonoOn₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pow_right_strictMono₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pow_lt_pow_right₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pow_lt_pow_iff_right₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pow_le_pow_iff_right₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lt_self_pow₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "pow_right_strictAnti₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pow_le_pow_iff_right_of_lt_one₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pow_lt_pow_iff_right_of_lt_one₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pow_lt_pow_right_of_lt_one₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pow_lt_self_of_lt_one₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "strictMono_mul_left_of_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictMono_mul_right_of_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.mul_const", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.const_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictAnti.mul_const", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictAnti.const_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.mul_monotone", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.mul_strictMono", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pow_le_pow_iff_left₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pow_lt_pow_iff_left₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pow_left_inj₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pow_right_injective₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["obtain", "exact", "exact"], "tactic_count": 3}
{"name": "pow_right_inj₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pow_le_one_iff_of_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["refine", "contrapose", "exact"], "tactic_count": 3}
{"name": "one_le_pow_iff_of_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["refine", "contrapose", "exact"], "tactic_count": 3}
{"name": "pow_lt_one_iff_of_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_lt_pow_iff_of_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "pow_eq_one_iff_of_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "sq_le_one_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sq_lt_one_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_le_sq_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_lt_sq_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lt_of_pow_lt_pow_left₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_of_pow_le_pow_left₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sq_eq_sq₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "lt_of_mul_self_lt_mul_self₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "sq_lt_sq₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sq_le_sq₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosMulMono.toPosMulStrictMono", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "posMulMono_iff_posMulStrictMono", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulPosMono.toMulPosStrictMono", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mulPosMono_iff_mulPosStrictMono", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosMulReflectLT.toPosMulReflectLE", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "posMulReflectLE_iff_posMulReflectLT", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulPosReflectLT.toMulPosReflectLE", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mulPosReflectLE_iff_mulPosReflectLT", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_inv_left_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "le_mul_inv_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "inv_mul_left_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "le_inv_mul_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "mul_inv_right_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "le_mul_inv_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "inv_mul_right_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "le_inv_mul_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "mul_div_mul_right_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["obtain", "simpa", "rw"], "tactic_count": 3}
{"name": "le_mul_div_mul_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["obtain", "simpa", "rw"], "tactic_count": 3}
{"name": "div_self_le_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "mul_inv_le_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "inv_mul_le_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "inv_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["suffices", "intro", "apply", "apply", "simpa"], "tactic_count": 5}
{"name": "inv_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "one_div_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_div_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosMulReflectLT.toPosMulStrictMono", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulPosReflectLE.of_posMulReflectLT_of_mulPosMono", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "div_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "div_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "le_inv_mul_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "inv_mul_le_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "one_le_inv_mul₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "inv_mul_le_one₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "inv_le_iff_one_le_mul₀'", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "one_le_inv₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "inv_le_one₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "mul_le_of_le_inv_mul₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["obtain", "simpa", "rwa"], "tactic_count": 3}
{"name": "inv_mul_le_of_le_mul₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["obtain", "simp", "rwa"], "tactic_count": 3}
{"name": "lt_inv_mul_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "inv_mul_lt_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "inv_lt_iff_one_lt_mul₀'", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "one_lt_inv_mul₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "inv_mul_lt_one₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "one_lt_inv₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "inv_lt_one₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "inv_lt_one_of_one_lt₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_lt_inv_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_le_one_of_one_le₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_le_inv_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_mul_le_one_of_le₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zpow_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zpow_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zpow_right_mono₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "zpow_right_anti₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "zpow_right_strictMono₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "zpow_right_strictAnti₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "zpow_le_zpow_right₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zpow_le_zpow_right_of_le_one₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_le_zpow₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "zpow_le_one₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "zpow_le_one_of_nonpos₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "one_le_zpow_of_nonpos₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "zpow_lt_zpow_right₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zpow_lt_zpow_right_of_lt_one₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_lt_zpow₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "zpow_lt_one₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "zpow_lt_one_of_neg₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "one_lt_zpow_of_neg₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "zpow_le_zpow_iff_right₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zpow_lt_zpow_iff_right₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zpow_le_zpow_iff_right_of_lt_one₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zpow_lt_zpow_iff_right_of_lt_one₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_le_zpow_iff_right₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "one_lt_zpow_iff_right₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "one_le_zpow_iff_right_of_lt_one₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "one_lt_zpow_iff_right_of_lt_one₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "zpow_le_one_iff_right₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "zpow_lt_one_iff_right₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "zpow_le_one_iff_right_of_lt_one₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "zpow_lt_one_iff_right_of_lt_one₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "zpow_left_monoOn₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["lift"], "tactic_count": 1}
{"name": "zpow_left_strictMonoOn₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["lift"], "tactic_count": 1}
{"name": "zpow_le_zpow_left₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zpow_lt_zpow_left₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Right.inv_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["suffices", "intro", "apply", "apply", "simpa"], "tactic_count": 5}
{"name": "MulPosReflectLT.toMulPosStrictMono", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Right.inv_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "div_nonpos_of_nonpos_of_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "le_mul_inv_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mul_inv_le_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "lt_mul_inv_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mul_inv_lt_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "le_div_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "div_le_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "lt_div_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "div_lt_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "div_le_div_iff_of_pos_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "div_lt_div_iff_of_pos_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "inv_le_iff_one_le_mul₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "inv_lt_iff_one_lt_mul₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "one_le_div₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "one_lt_div₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "div_le_one₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "div_lt_one₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mul_le_of_le_mul_inv₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["obtain", "simpa", "rwa"], "tactic_count": 3}
{"name": "mul_inv_le_of_le_mul₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["obtain", "simp", "rwa"], "tactic_count": 3}
{"name": "mul_le_of_le_div₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "div_le_of_le_mul₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_inv_le_one_of_le₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "div_le_one_of_le₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "div_le_div_of_nonneg_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "div_lt_div_of_pos_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "inv_le_inv₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "inv_lt_inv₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "inv_anti₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_strictAnti₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_le_comm₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "inv_lt_comm₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "inv_le_of_inv_le₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_lt_of_inv_lt₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_inv_comm₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "lt_inv_comm₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "le_inv_of_le_inv₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lt_inv_of_lt_inv₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "div_le_div_iff_of_pos_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "div_lt_div_iff_of_pos_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "div_le_div_of_nonneg_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw", "gcongr", "exacts"], "tactic_count": 3}
{"name": "div_lt_div_of_pos_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "div_le_div₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "div_lt_div₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply", "exact"], "tactic_count": 3}
{"name": "div_lt_div₀'", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "inv_neg''", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["have"], "tactic_count": 1}
{"name": "inv_nonpos", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["have"], "tactic_count": 1}
{"name": "one_div_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_div_nonpos", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "div_nonpos_of_nonneg_of_nonpos", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "neg_of_div_neg_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "neg_of_div_neg_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_lt_one_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "inv_le_one_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "zpow_right_injective₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["obtain", "exact", "exact"], "tactic_count": 3}
{"name": "zpow_right_inj₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zpow_eq_one_iff_right₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["obtain", "exact", "simpa"], "tactic_count": 3}
{"name": "zpow_le_zpow_iff_left₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zpow_lt_zpow_iff_left₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zpow_left_injOn₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zpow_left_inj₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_div_mul_left_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["obtain", "simpa", "rw"], "tactic_count": 3}
{"name": "le_mul_div_mul_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["obtain", "simpa", "rw"], "tactic_count": 3}
{"name": "le_inv_mul_iff₀'", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "inv_mul_le_iff₀'", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "le_mul_inv_iff₀'", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mul_inv_le_iff₀'", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "div_le_div_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "le_div_iff₀'", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "div_le_iff₀'", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "le_div_comm₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "div_le_comm₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "mabs_div", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Abs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "mabs_div_le_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Abs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mabs_div_lt_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Abs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "div_le_of_mabs_div_le_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "div_le_of_mabs_div_le_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "div_lt_of_mabs_div_lt_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "div_lt_of_mabs_div_lt_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mabs_div_mabs_le_mabs_div", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mabs_div_mabs_le_mabs_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mabs_mabs_div_mabs_le_mabs_div", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mabs_div_le_of_one_le_of_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Abs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "mabs_div_lt_of_one_le_of_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Abs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "mabs_eq", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Abs", "is_tactic_proof": true, "tactics": ["refine", "rintro"], "tactic_count": 2}
{"name": "mabs_le_max_mabs_mabs", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "min_mabs_mabs_le_mabs_max", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "min_mabs_mabs_le_mabs_min", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mabs_max_le_max_mabs_mabs", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mabs_min_le_max_mabs_mabs", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_of_mabs_div_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mabs_div_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mabs_div_le_max_div", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Abs", "is_tactic_proof": true, "tactics": ["rcases", "rw", "exact", "rw", "exact"], "tactic_count": 5}
{"name": "mabs_mul_three", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Abs", "is_tactic_proof": true, "tactics": ["grw"], "tactic_count": 1}
{"name": "mabs_div_le_of_le_of_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_of_mabs_div_le_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_of_mabs_div_lt_all", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_of_mabs_div_le_all", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mabs_div_le_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mabs_div_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mabs_eq_self", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Abs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mabs_eq_inv_self", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Abs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mabs_cases", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Abs", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "max_one_mul_max_inv_one_eq_mabs_self", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Abs", "is_tactic_proof": true, "tactics": ["symm", "rcases"], "tactic_count": 2}
{"name": "apply_abs_le_mul_of_one_le'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "apply_abs_le_mul_of_one_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smul_mono_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smul_le_smul_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smul_inf_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smul_iInf_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smul_strictMono_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_pow_smul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Action", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "exact"], "tactic_count": 5}
{"name": "pow_smul_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Action", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "exact"], "tactic_count": 5}
{"name": "RelHom.applyMulAction", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Action.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelHom.smul_def", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Action.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelHom.apply_faithfulSMul", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Action.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelEmbedding.applyMulAction", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Action.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelEmbedding.smul_def", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Action.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelEmbedding.apply_faithfulSMul", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Action.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelIso.applyMulAction", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Action.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelIso.smul_def", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Action.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelIso.apply_faithfulSMul", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Action.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Flag.instSMulOrderIso", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Action.Flag", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Flag.coe_smul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Action.Flag", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Flag.instMulActionOrderIso", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Action.Flag", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instMulAction", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Action.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instMulAction'", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Action.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instSMulCommClass", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Action.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instSMulCommClass'", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Action.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instSMulCommClass''", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Action.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instIsScalarTower", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Action.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instIsScalarTower'", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Action.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instIsScalarTower''", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Action.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lex.instMulAction", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Action.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lex.instMulAction'", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Action.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lex.instSMulCommClass", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Action.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lex.instSMulCommClass'", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Action.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lex.instSMulCommClass''", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Action.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lex.instIsScalarTower", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Action.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lex.instIsScalarTower'", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Action.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lex.instIsScalarTower''", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Action.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zpow_right_strictMono", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "zpow_right_strictAnti", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "zpow_right_inj", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zpow_right_mono", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "zpow_le_zpow_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zpow_lt_zpow_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zpow_le_zpow_iff_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zpow_lt_zpow_iff_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zpow_left_strictMono", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zpow_left_mono", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zpow_le_zpow_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zpow_lt_zpow_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zpow_le_zpow_iff_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zpow_lt_zpow_iff_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_isCyclic_of_denselyOrdered", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Basic", "is_tactic_proof": true, "tactics": ["intro", "rcases", "rcases", "rcases", "rcases", "suffices", "rw", "simp_rw", "simp_all", "rcases", "simpa", "rcases", "rcases", "suffices", "simp_rw", "simp_all"], "tactic_count": 16}
{"name": "IsGLB.exists_between_self_add", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Bounds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGLB.exists_between_self_add'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Bounds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLUB.exists_between_sub_self", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Bounds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLUB.exists_between_sub_self'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Bounds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ciSup_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ciSup_div", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.CompleteLattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ciInf_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ciInf_div", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.CompleteLattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "mul_ciSup", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_ciInf", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupCone.instSetLike", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Cone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instPartialOrderGroupCone", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Cone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupCone.instGroupConeClass", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Cone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupCone.oneLE", "kind": "definition", "module": "Mathlib.Algebra.Order.Group.Cone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupCone.oneLE_toSubmonoid", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Cone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupCone.mem_oneLE", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Cone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupCone.coe_oneLE", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Cone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupCone.oneLE.hasMemOrInvMem", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Cone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialOrder.mkOfGroupCone", "kind": "abbrev", "module": "Mathlib.Algebra.Order.Group.Cone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialOrder.mkOfGroupCone_le_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Cone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearOrder.mkOfGroupCone", "kind": "abbrev", "module": "Mathlib.Algebra.Order.Group.Cone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOrderedMonoid.mkOfCone", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Cone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearOrderedCommGroup.Subgroup.exists_generator_lt_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Cyclic", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "exact", "rw", "exact", "use", "rw"], "tactic_count": 7}
{"name": "LinearOrderedCommGroup.Subgroup.genLTOne", "kind": "definition", "module": "Mathlib.Algebra.Order.Group.Cyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearOrderedCommGroup.Subgroup.genLTOne_lt_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Cyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearOrderedCommGroup.Subgroup.genLTOne_zpowers_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Cyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearOrderedCommGroup.Subgroup.genLTOne_mem", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Cyclic", "is_tactic_proof": true, "tactics": ["nth_rewrite", "exact"], "tactic_count": 2}
{"name": "LinearOrderedCommGroup.Subgroup.genLTOne_unique", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Cyclic", "is_tactic_proof": true, "tactics": ["have", "rw", "rcases", "assumption", "rw", "exact"], "tactic_count": 6}
{"name": "LinearOrderedCommGroup.Subgroup.genLTOne_unique_of_zpowers_eq", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Cyclic", "is_tactic_proof": true, "tactics": ["rcases", "rw", "simp_all", "have", "have", "have", "simp", "simp", "simp"], "tactic_count": 9}
{"name": "LinearOrderedCommGroup.genLTOne", "kind": "definition", "module": "Mathlib.Algebra.Order.Group.Cyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearOrderedCommGroup.genLTOne_eq_of_top", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Cyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearOrderedCommGroup.genLTOne_unique", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Cyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOrderedMonoid.toIsOrderedCancelMonoid", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_one_of_inv_eq'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_one_lt'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Defs", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "exact", "exact"], "tactic_count": 4}
{"name": "LinearOrderedCommGroup.to_noMaxOrder", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearOrderedCommGroup.to_noMinOrder", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_le_self_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "inv_lt_self_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "le_inv_self_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Defs", "is_tactic_proof": true, "tactics": ["contrapose"], "tactic_count": 1}
{"name": "lt_inv_self_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Defs", "is_tactic_proof": true, "tactics": ["contrapose"], "tactic_count": 1}
{"name": "inv_le_inv'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_lt_inv'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_lt_one_of_one_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_le_one_of_one_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_le_inv_of_le_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_of_forall_lt_one_mul_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.DenselyOrdered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_of_forall_one_lt_div_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.DenselyOrdered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_iff_forall_lt_one_mul_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.DenselyOrdered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Order.Group.DenselyOrdered.0.exists_lt_mul_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.DenselyOrdered", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
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{"name": "RelHom.instMonoid", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelHom.one_def", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelHom.mul_def", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelHom.coe_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelHom.coe_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelHom.one_apply", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelHom.mul_apply", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelEmbedding.instMonoid", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelEmbedding.one_def", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelEmbedding.mul_def", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelEmbedding.coe_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelEmbedding.coe_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelEmbedding.one_apply", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelEmbedding.mul_apply", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelIso.instGroup", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelIso.one_def", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelIso.mul_def", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelIso.coe_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelIso.coe_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelIso.one_apply", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelIso.mul_apply", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelIso.inv_apply_self", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelIso.apply_inv_self", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toLexMulEquiv", "kind": "definition", "module": "Mathlib.Algebra.Order.Group.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofLexMulEquiv", "kind": "definition", "module": "Mathlib.Algebra.Order.Group.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "coe_toLexMulEquiv", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "coe_ofLexMulEquiv", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "symm_toLexMulEquiv", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "symm_ofLexMulEquiv", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toEquiv_toLexMulEquiv", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toEquiv_ofLexMulEquiv", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.toFinset_nsmul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.toFinset_eq_singleton_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.toFinset_card_eq_one_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Finset", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Finset.fold_max_add", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Finset", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finset.inf'_pow", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sup'_pow", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sup'_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mul_sup'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sup'_add'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Finset", "is_tactic_proof": true, "tactics": ["apply", "apply", "exact", "exact", "exact"], "tactic_count": 5}
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{"name": "Finset.add_sup", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Finset", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.sup_add_sup", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Finset", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SemigroupIdeal.fg_of_wellQuasiOrderedLE", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Ideal", "is_tactic_proof": true, "tactics": ["have", "refine", "ext", "simp", "constructor", "intro", "rcases", "rw", "rcases", "exact", "rintro", "apply", "exact"], "tactic_count": 13}
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{"name": "Function.mulSupport_sup", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.mulSupport_inf", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.mulSupport_max", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.mulSupport_min", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.mulSupport_iSup", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Indicator", "is_tactic_proof": true, "tactics": ["simp", "intro", "simp"], "tactic_count": 3}
{"name": "Function.mulSupport_iInf", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mulIndicator_apply_le'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Indicator", "is_tactic_proof": true, "tactics": ["by_cases", "simpa", "simpa"], "tactic_count": 3}
{"name": "Set.mulIndicator_le'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.le_mulIndicator_apply", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.le_mulIndicator", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.one_le_mulIndicator_apply", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.one_le_mulIndicator", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mulIndicator_apply_le_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mulIndicator_le_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mulIndicator_le_mulIndicator'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mulIndicator_le_mulIndicator", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mulIndicator_mono", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mulIndicator_le_mulIndicator_apply_of_subset", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mulIndicator_le_mulIndicator_of_subset", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mulIndicator_le_self'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.indicator_le_indicator_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Indicator", "is_tactic_proof": true, "tactics": ["intro", "classical", "simp_rw", "split_ifs", "exacts"], "tactic_count": 5}
{"name": "Set.indicator_nonpos_le_indicator", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mulIndicator_iUnion_apply", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Indicator", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "rw", "refine", "rcases", "exact", "rw", "simp", "simp"], "tactic_count": 9}
{"name": "Set.mulIndicator_iInter_apply", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Indicator", "is_tactic_proof": true, "tactics": ["by_cases", "simp_all", "rw", "simp", "rcases", "refine", "simpa"], "tactic_count": 7}
{"name": "Set.iSup_mulIndicator", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Indicator", "is_tactic_proof": true, "tactics": ["simp", "refine", "grw", "intro", "by_cases", "obtain", "rw", "refine", "obtain", "refine", "rw", "rw", "exact"], "tactic_count": 13}
{"name": "Set.mulIndicator_le_self", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mulIndicator_apply_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mulIndicator_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mabs_mulIndicator_symmDiff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.instIsOrderedAddMonoid", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Int", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sum_le_sum_Ioc", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Int.Sum", "is_tactic_proof": true, "tactics": ["set", "calc", "rw", "gcongr", "refine", "rw", "have", "rw", "rw", "rw", "gcongr", "refine", "rw"], "tactic_count": 13}
{"name": "Finset.sum_le_sum_range", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Int.Sum", "is_tactic_proof": true, "tactics": ["convert", "refine", "intro", "intro", "intro", "rw", "use"], "tactic_count": 7}
{"name": "Finset.sum_Ico_le_sum", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Int.Sum", "is_tactic_proof": true, "tactics": ["set", "calc", "grw", "rw", "rw", "rw", "grw", "rw", "have"], "tactic_count": 9}
{"name": "Finset.sum_range_le_sum", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Int.Sum", "is_tactic_proof": true, "tactics": ["convert", "refine", "intro", "intro", "intro", "rw", "use"], "tactic_count": 7}
{"name": "mul_sup", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sup_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_inf", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inf_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sup_div", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inf_div", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_sup", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_inf", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "div_sup", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "div_inf", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pow_two_semiclosed", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Lattice", "is_tactic_proof": true, "tactics": ["suffices", "rw"], "tactic_count": 2}
{"name": "inf_mul_sup", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGroup.toDistribLattice", "kind": "definition", "module": "Mathlib.Algebra.Order.Group.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "max_one_div_max_inv_one_eq_self", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.MinMax", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "max_inv_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.MinMax", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "min_inv_inv'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "max_inv_inv'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "min_div_div_right'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.MinMax", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "max_div_div_right'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.MinMax", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "min_div_div_left'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.MinMax", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "max_div_div_left'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.MinMax", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "max_sub_max_le_max", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.MinMax", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "abs_max_sub_max_le_max", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.MinMax", "is_tactic_proof": true, "tactics": ["refine", "exact", "rw", "exact"], "tactic_count": 4}
{"name": "abs_min_sub_min_le_max", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.MinMax", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "abs_max_sub_max_le_abs", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.MinMax", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Multiset.instAddLeftMono", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.instAddLeftReflectLE", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.instAddCancelCommMonoid", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.mem_of_mem_nsmul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Multiset", "is_tactic_proof": true, "tactics": ["induction", "zero", "rw", "exact", "succ", "rw", "exact"], "tactic_count": 7}
{"name": "Multiset.mem_nsmul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Multiset", "is_tactic_proof": true, "tactics": ["refine", "rintro", "simp", "obtain", "rw", "exact"], "tactic_count": 6}
{"name": "Multiset.mem_nsmul_of_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Multiset", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.nsmul_cons", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Multiset", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.cardHom", "kind": "definition", "module": "Mathlib.Algebra.Order.Group.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.card_nsmul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.replicateAddMonoidHom", "kind": "definition", "module": "Mathlib.Algebra.Order.Group.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.nsmul_replicate", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.nsmul_singleton", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Multiset", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.mapAddMonoidHom", "kind": "definition", "module": "Mathlib.Algebra.Order.Group.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.coe_mapAddMonoidHom", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.map_nsmul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.instOrderedSub", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.instExistsAddOfLE", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.filter_nsmul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Multiset", "is_tactic_proof": true, "tactics": ["refine", "simp", "intro", "rw", "congr", "split_ifs", "simp", "intro", "rwa"], "tactic_count": 9}
{"name": "Multiset.countP_nsmul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Multiset", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "Multiset.countPAddMonoidHom", "kind": "definition", "module": "Mathlib.Algebra.Order.Group.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.coe_countPAddMonoidHom", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.dedup_nsmul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Multiset", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Multiset.Nodup.le_nsmul_iff_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Multiset", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Multiset.countAddMonoidHom", "kind": "definition", "module": "Mathlib.Algebra.Order.Group.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.coe_countAddMonoidHom", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.count_nsmul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Multiset", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "Multiset.addHom_ext", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Multiset", "is_tactic_proof": true, "tactics": ["ext", "induction", "empty", "cons"], "tactic_count": 4}
{"name": "Multiset.le_smul_dedup", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.instIsOrderedAddMonoid", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Nat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.instIsOrderedCancelAddMonoid", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Nat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.instCanonicallyOrderedAdd", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Nat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.instOrderedSub", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Nat", "is_tactic_proof": true, "tactics": ["refine", "induction", "zero", "succ"], "tactic_count": 4}
{"name": "Nat.pow_left_strictMono", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Nat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.nat_pow", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Nat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instPreorder", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.unop_le_unop", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.op_le_op", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instPartialOrder", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instIsOrderedMonoid", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.unop_le_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.one_le_unop", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.op_le_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.one_le_op", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instIsOrderedAddMonoid", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.unop_nonpos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.unop_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.op_nonpos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.op_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddOpposite.instIsOrderedMonoid", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddOpposite.unop_le_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddOpposite.one_le_unop", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddOpposite.op_le_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddOpposite.one_le_op", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.inv", "kind": "definition", "module": "Mathlib.Algebra.Order.Group.OrderIso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_le'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.OrderIso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_inv'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.OrderIso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.divLeft", "kind": "definition", "module": "Mathlib.Algebra.Order.Group.OrderIso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.mulRight", "kind": "definition", "module": "Mathlib.Algebra.Order.Group.OrderIso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.mulRight_symm", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.OrderIso", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "OrderIso.divRight", "kind": "definition", "module": "Mathlib.Algebra.Order.Group.OrderIso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.mulLeft", "kind": "definition", "module": "Mathlib.Algebra.Order.Group.OrderIso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.mulLeft_symm", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.OrderIso", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "partialSups_const_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.PartialSups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "partialSups_mul_const", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.PartialSups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.Lex.isOrderedCancelMonoid", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.PiLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_mem_upperBounds_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Bounds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "subset_upperBounds_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Bounds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_mem_lowerBounds_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Bounds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "subset_lowerBounds_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Bounds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddAbove.mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Bounds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddBelow.mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Bounds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddAbove.range_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Bounds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddBelow.range_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Bounds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bddAbove_inv", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Bounds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bddBelow_inv", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Bounds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddAbove.inv", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Bounds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddBelow.inv", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Bounds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLUB_inv", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Bounds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLUB_inv'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Bounds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGLB.inv", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Bounds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isGLB_inv", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Bounds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isGLB_inv'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Bounds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLUB.inv", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Bounds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddBelow.range_inv", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Bounds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddAbove.range_inv", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Bounds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLUB.mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Bounds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGLB.mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Bounds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLUB.div", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Bounds", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsGLB.div", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Bounds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csSup_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csInf_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csSup_inv", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.CompleteLattice", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "csInf_inv", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.CompleteLattice", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "csSup_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csInf_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csSup_div", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.CompleteLattice", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "csInf_div", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.CompleteLattice", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "sSup_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sInf_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sSup_inv", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.CompleteLattice", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "sInf_inv", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.CompleteLattice", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "sSup_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sInf_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sSup_div", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.CompleteLattice", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "sInf_div", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.CompleteLattice", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.Icc_mul_Icc_subset'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Interval", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "Set.Iic_mul_Iic_subset'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Interval", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "Set.Ici_mul_Ici_subset'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Interval", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "Set.Icc_mul_Ico_subset'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Interval", "is_tactic_proof": true, "tactics": ["have", "have", "rintro", "exact"], "tactic_count": 4}
{"name": "Set.Ico_mul_Icc_subset'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Interval", "is_tactic_proof": true, "tactics": ["have", "have", "rintro", "exact"], "tactic_count": 4}
{"name": "Set.Ioc_mul_Ico_subset'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Interval", "is_tactic_proof": true, "tactics": ["have", "have", "rintro", "exact"], "tactic_count": 4}
{"name": "Set.Ico_mul_Ioc_subset'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Interval", "is_tactic_proof": true, "tactics": ["have", "have", "rintro", "exact"], "tactic_count": 4}
{"name": "Set.Iic_mul_Iio_subset'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Interval", "is_tactic_proof": true, "tactics": ["have", "rintro", "exact"], "tactic_count": 3}
{"name": "Set.Iio_mul_Iic_subset'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Interval", "is_tactic_proof": true, "tactics": ["have", "rintro", "exact"], "tactic_count": 3}
{"name": "Set.Ioi_mul_Ici_subset'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Interval", "is_tactic_proof": true, "tactics": ["have", "rintro", "exact"], "tactic_count": 3}
{"name": "Set.Ici_mul_Ioi_subset'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Interval", "is_tactic_proof": true, "tactics": ["have", "rintro", "exact"], "tactic_count": 3}
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{"name": "Set.preimage_const_mul_Ioc₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Interval", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.preimage_const_mul_Ico₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Interval", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.image_affine_Icc'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Interval", "is_tactic_proof": true, "tactics": ["suffices", "rw"], "tactic_count": 2}
{"name": "Set.image_affine_Ico", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Interval", "is_tactic_proof": true, "tactics": ["suffices", "rw"], "tactic_count": 2}
{"name": "Set.image_affine_Ioc", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Interval", "is_tactic_proof": true, "tactics": ["suffices", "rw"], "tactic_count": 2}
{"name": "Set.image_affine_Ioo", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Interval", "is_tactic_proof": true, "tactics": ["suffices", "rw"], "tactic_count": 2}
{"name": "Set.preimage_mul_const_Iio_of_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.preimage_mul_const_Ioi_of_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.preimage_mul_const_Iic_of_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.preimage_mul_const_Ici_of_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.preimage_mul_const_Ioo_of_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Interval", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.preimage_mul_const_Ioc_of_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Interval", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.preimage_mul_const_Ico_of_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Interval", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.preimage_mul_const_Icc_of_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Interval", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.preimage_const_mul_Iio_of_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Interval", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.preimage_const_mul_Ioi_of_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Interval", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.preimage_const_mul_Iic_of_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Interval", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.preimage_const_mul_Ici_of_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Interval", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.preimage_const_mul_Ioo_of_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Interval", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.preimage_const_mul_Ioc_of_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Interval", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.preimage_const_mul_Ico_of_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Interval", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.preimage_const_mul_Icc_of_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Interval", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.preimage_mul_const_uIcc", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.preimage_const_mul_uIcc", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Interval", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.preimage_div_const_uIcc", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Interval", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.preimage_const_mul_Ioi_or_Iio", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Interval", "is_tactic_proof": false, "tactics": ["obtain", "rcases", "right", "left", "left", "right"], "tactic_count": 6}
{"name": "Set.image_mul_const_uIcc", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_const_mul_uIcc", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Interval", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.image_div_const_uIcc", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Interval", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.inv_Ioo_0_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Interval", "is_tactic_proof": true, "tactics": ["ext", "refine", "have", "exact"], "tactic_count": 4}
{"name": "Set.inv_Iio₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Interval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.Ici_mul_Ici_eq", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Interval", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact"], "tactic_count": 3}
{"name": "Set.Ici_pow_eq", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ici_one_eq_univ", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Pointwise.Interval", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "instOneLePart", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.PosPart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instLeOnePart", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.PosPart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "leOnePart_def", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.PosPart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "oneLePart_def", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.PosPart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "oneLePart_mono", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.PosPart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "oneLePart_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.PosPart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "leOnePart_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.PosPart", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "one_le_oneLePart", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.PosPart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_le_leOnePart", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.PosPart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_oneLePart", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.PosPart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_le_leOnePart", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.PosPart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "oneLePart_eq_self", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.PosPart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "oneLePart_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.PosPart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "leOnePart_eq_inv'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.PosPart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "leOnePart_eq_one'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.PosPart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "oneLePart_le_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.PosPart", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "leOnePart_le_one'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.PosPart", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "one_lt_oneLePart", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.PosPart", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "oneLePart_inv", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.PosPart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "leOnePart_inv", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.PosPart", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "oneLePart_max", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.PosPart", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "leOnePart_eq_inv", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.PosPart", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "leOnePart_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.PosPart", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "leOnePart_le_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.PosPart", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "one_lt_leOnePart", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.PosPart", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "oneLePart_div_leOnePart", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.PosPart", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "leOnePart_div_oneLePart", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.PosPart", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "oneLePart_leOnePart_injective", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.PosPart", "is_tactic_proof": true, "tactics": ["simp", "rintro", "rw"], "tactic_count": 3}
{"name": "oneLePart_leOnePart_inj", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.PosPart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "leOnePart_anti", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.PosPart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "leOnePart_eq_inv_inf_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.PosPart", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "oneLePart_mul_leOnePart", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.PosPart", "is_tactic_proof": false, "tactics": ["rw", "sup_eq_right.2", "exact"], "tactic_count": 3}
{"name": "leOnePart_mul_oneLePart", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.PosPart", "is_tactic_proof": false, "tactics": ["rw", "sup_eq_right.2", "exact"], "tactic_count": 3}
{"name": "oneLePart_inf_leOnePart_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.PosPart", "is_tactic_proof": true, "tactics": ["rw", "leOnePart_eq_inv_inf_one,"], "tactic_count": 2}
{"name": "leOnePart_min", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.PosPart", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "sup_eq_mul_oneLePart_div", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.PosPart", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "inf_eq_div_oneLePart_div", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.PosPart", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "le_iff_oneLePart_leOnePart", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.PosPart", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "mabs_mul_eq_oneLePart_sq", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.PosPart", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mul_mabs_eq_oneLePart_sq", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.PosPart", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mabs_div_eq_leOnePart_sq", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.PosPart", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "div_mabs_eq_inv_leOnePart_sq", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.PosPart", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "oneLePart_min", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.PosPart", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "leOnePart_max", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.PosPart", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "oneLePart_eq_ite", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.PosPart", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "oneLePart_eq_ite_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.PosPart", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "one_lt_oneLePart_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.PosPart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "oneLePart_of_one_lt_oneLePart", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.PosPart", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "oneLePart_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.PosPart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "leOnePart_eq_ite", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.PosPart", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "leOnePart_eq_ite_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.PosPart", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "one_lt_leOnePart_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.PosPart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "leOnePart_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.PosPart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.oneLePart_apply", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.PosPart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.leOnePart_apply", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.PosPart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.oneLePart_def", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.PosPart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.leOnePart_def", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.PosPart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instOneOrderDual", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instMulOrderDual", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInvOrderDual", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDivOrderDual", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instPow", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instPow'", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instSemigroupOrderDual", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCommSemigroupOrderDual", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsLeftCancelMulOrderDual", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsRightCancelMulOrderDual", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsCancelMulOrderDual", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instLeftCancelSemigroupOrderDual", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instRightCancelSemigroupOrderDual", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instMulOneClassOrderDual", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instMonoidOrderDual", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instCommMonoid", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instLeftCancelMonoidOrderDual", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instRightCancelMonoidOrderDual", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCancelMonoidOrderDual", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instCancelCommMonoid", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInvolutiveInvOrderDual", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDivInvMonoidOrderDual", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDivisionMonoidOrderDual", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDivisionCommMonoidOrderDual", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instGroup", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCommGroupOrderDual", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toDual_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofDual_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toDual_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "sup_div_inf_eq_mabs_div", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Abs", "is_tactic_proof": true, "tactics": ["simp_rw", "rw", "exact"], "tactic_count": 3}
{"name": "sup_sq_eq_mul_mul_mabs_div", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Abs", "is_tactic_proof": true, "tactics": ["rw", "inv_mul_cancel_left]"], "tactic_count": 2}
{"name": "inf_sq_eq_mul_div_mabs_div", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Abs", "is_tactic_proof": true, "tactics": ["rw", "mul_inv_cancel_comm_assoc,"], "tactic_count": 2}
{"name": "mabs_div_sup_mul_mabs_div_inf", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Abs", "is_tactic_proof": true, "tactics": ["letI", "calc", "rw", "rw", "rw", "inf_comm"], "tactic_count": 6}
{"name": "mabs_sup_div_sup_le_mabs", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Abs", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "mabs_inf_div_inf_le_mabs", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Abs", "is_tactic_proof": true, "tactics": ["apply", "rw"], "tactic_count": 2}
{"name": "m_Birkhoff_inequalities", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mabs_choice", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_mabs", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mabs_eq_max_inv", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lt_mabs", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mabs_by_cases", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_or_eq_inv_of_mabs_eq", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Abs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "mabs_eq_mabs", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Abs", "is_tactic_proof": true, "tactics": ["refine", "obtain", "simpa"], "tactic_count": 3}
{"name": "isSquare_mabs", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lt_of_mabs_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "map_mabs", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Abs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "one_lt_mabs", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Abs", "is_tactic_proof": true, "tactics": ["obtain", "simp", "simp", "simp"], "tactic_count": 4}
{"name": "one_lt_mabs_pos_of_one_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_lt_mabs_of_lt_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_mabs_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Abs", "is_tactic_proof": true, "tactics": ["obtain", "simpa", "simp"], "tactic_count": 3}
{"name": "one_le_mul_mabs", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Abs", "is_tactic_proof": true, "tactics": ["grw"], "tactic_count": 1}
{"name": "inv_mabs_le_inv", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Abs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "mabs_ne_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mabs_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mabs_le_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mabs_le_mabs_of_le_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Abs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mabs_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_lt_of_mabs_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "max_div_min_eq_mabs'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Abs", "is_tactic_proof": true, "tactics": ["rcases", "rw", "rwa", "rw", "rwa"], "tactic_count": 5}
{"name": "max_div_min_eq_mabs", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Abs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LatticeOrderedAddCommGroup.IsSolid", "kind": "definition", "module": "Mathlib.Algebra.Order.Group.Unbundled.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LatticeOrderedAddCommGroup.solidClosure", "kind": "definition", "module": "Mathlib.Algebra.Order.Group.Unbundled.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LatticeOrderedAddCommGroup.isSolid_solidClosure", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LatticeOrderedAddCommGroup.solidClosure_min", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.abs_apply", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.abs_def", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Left.inv_le_one_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Left.one_le_inv_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "le_inv_mul_iff_mul_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "inv_mul_le_iff_le_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "inv_le_iff_one_le_mul'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_inv_iff_mul_le_one_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_inv_mul_iff_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "inv_mul_le_one_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Left.one_lt_inv_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Left.inv_lt_one_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "lt_inv_mul_iff_mul_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "inv_mul_lt_iff_lt_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "inv_lt_iff_one_lt_mul'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lt_inv_iff_mul_lt_one'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lt_inv_mul_iff_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "inv_mul_lt_one_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Right.inv_le_one_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Right.one_le_inv_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "inv_le_iff_one_le_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_inv_iff_mul_le_one_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_inv_le_iff_le_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_mul_inv_iff_mul_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_inv_le_one_iff_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_mul_inv_iff_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mul_inv_le_one_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Right.inv_lt_one_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Right.one_lt_inv_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "inv_lt_iff_one_lt_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lt_inv_iff_mul_lt_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_inv_lt_iff_lt_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "lt_mul_inv_iff_mul_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_mul_lt_one_iff_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "lt_mul_inv_iff_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mul_inv_lt_one_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "div_le_self_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "le_div_self_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "inv_le_inv_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "mul_inv_le_inv_mul_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "div_lt_self_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "inv_lt_inv_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "inv_lt'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "lt_inv'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mul_inv_lt_inv_mul_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Left.inv_le_self", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Left.self_le_inv", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Left.inv_lt_self", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Left.self_lt_inv", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Right.inv_le_self", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Right.self_le_inv", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Right.inv_lt_self", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Right.self_lt_inv", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_mul_le_iff_le_mul'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mul_inv_le_iff_le_mul'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mul_inv_le_mul_inv_iff'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "inv_mul_lt_iff_lt_mul'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mul_inv_lt_iff_le_mul'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mul_inv_lt_mul_inv_iff'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "div_le_div_iff_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "div_le_div_right'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_le_div'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "div_le_one'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "le_div_iff_mul_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "div_le_iff_le_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AddGroup.toOrderedSub", "kind": "instance", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "div_le_div_iff_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw", "inv_le_inv_iff]"], "tactic_count": 2}
{"name": "div_le_div_left'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "div_le_div_iff'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "le_div_iff_mul_le'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "div_le_iff_le_mul'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "inv_le_div_iff_le_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_le_div_iff_le_mul'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "div_le_comm", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_div_comm", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "div_le_div''", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "div_lt_div_iff_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "div_lt_div_right'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_lt_div'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "div_lt_one'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Group.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "OrderMonoidHom.coe_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidHom.one_apply", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidHom.one_comp", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidHom.comp_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidHom.instMulOfIsOrderedMonoid", "kind": "instance", "module": "Mathlib.Algebra.Order.Hom.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidHom.coe_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidHom.mul_apply", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidHom.mul_comp", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidHom.comp_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidHom.toMonoidHom_eq_coe", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidHom.toOrderHom_eq_coe", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidHom.mk'", "kind": "definition", "module": "Mathlib.Algebra.Order.Hom.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidIso.instEquivLike", "kind": "instance", "module": "Mathlib.Algebra.Order.Hom.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidIso.instOrderIsoClass", "kind": "instance", "module": "Mathlib.Algebra.Order.Hom.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidIso.instMulEquivClass", "kind": "instance", "module": "Mathlib.Algebra.Order.Hom.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidIso.ext", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidIso.toFun_eq_coe", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidIso.coe_mk", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidIso.mk_coe", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidIso.toOrderIso", "kind": "definition", "module": "Mathlib.Algebra.Order.Hom.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidIso.coe_mulEquiv", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidIso.coe_orderIso", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidIso.toMulEquiv_injective", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidIso.toOrderIso_injective", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidIso.refl", "kind": "definition", "module": "Mathlib.Algebra.Order.Hom.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidIso.coe_refl", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidIso.instInhabited", "kind": "instance", "module": "Mathlib.Algebra.Order.Hom.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidIso.trans", "kind": "definition", "module": "Mathlib.Algebra.Order.Hom.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidIso.coe_trans", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidIso.trans_apply", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidIso.coe_trans_mulEquiv", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidIso.coe_trans_orderIso", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidIso.trans_assoc", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidIso.trans_refl", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidIso.refl_trans", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidIso.cancel_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidIso.cancel_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidIso.toMulEquiv_eq_coe", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidIso.toOrderIso_eq_coe", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidIso.symm", "kind": "definition", "module": "Mathlib.Algebra.Order.Hom.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidIso.Simps.apply", "kind": "definition", "module": "Mathlib.Algebra.Order.Hom.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidIso.Simps.symm_apply", "kind": "definition", "module": "Mathlib.Algebra.Order.Hom.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidIso.invFun_eq_symm", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidIso.coe_toEquiv_symm", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidIso.equivLike_inv_eq_symm", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidIso.toEquiv_symm", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidIso.symm_symm", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidIso.symm_bijective", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidIso.refl_symm", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidIso.apply_symm_apply", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidIso.symm_apply_apply", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidIso.symm_comp_self", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidIso.self_comp_symm", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidIso.apply_eq_iff_symm_apply", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidIso.symm_apply_eq", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidIso.eq_symm_apply", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidIso.eq_comp_symm", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidIso.comp_symm_eq", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidIso.eq_symm_comp", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidIso.symm_comp_eq", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidIso.strictMono", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidIso.strictMono_symm", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidIso.mk'", "kind": "definition", "module": "Mathlib.Algebra.Order.Hom.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "term_→*₀o_", "kind": "definition", "module": "Mathlib.Algebra.Order.Hom.MonoidWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Algebra_Order_Hom_MonoidWithZero___macroRules_term_→*₀o__1", "kind": "definition", "module": "Mathlib.Algebra.Order.Hom.MonoidWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Algebra_Order_Hom_MonoidWithZero___unexpand_OrderMonoidWithZeroHom_1", "kind": "definition", "module": "Mathlib.Algebra.Order.Hom.MonoidWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidWithZeroHomClass.toOrderMonoidWithZeroHom", "kind": "definition", "module": "Mathlib.Algebra.Order.Hom.MonoidWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCoeTCOrderMonoidWithZeroHomOfOrderHomClassOfMonoidWithZeroHomClass", "kind": "instance", "module": "Mathlib.Algebra.Order.Hom.MonoidWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidWithZeroHom.instFunLike", "kind": "instance", "module": "Mathlib.Algebra.Order.Hom.MonoidWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidWithZeroHom.instMonoidWithZeroHomClass", "kind": "instance", "module": "Mathlib.Algebra.Order.Hom.MonoidWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidWithZeroHom.instOrderHomClass", "kind": "instance", "module": "Mathlib.Algebra.Order.Hom.MonoidWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidWithZeroHom.ext", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.MonoidWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidWithZeroHom.toFun_eq_coe", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.MonoidWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidWithZeroHom.coe_mk", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.MonoidWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidWithZeroHom.mk_coe", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.MonoidWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidWithZeroHom.toOrderMonoidHom", "kind": "definition", "module": "Mathlib.Algebra.Order.Hom.MonoidWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidWithZeroHom.coe_monoidWithZeroHom", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.MonoidWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidWithZeroHom.coe_orderMonoidHom", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.MonoidWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidWithZeroHom.toOrderMonoidHom_injective", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.MonoidWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidWithZeroHom.toMonoidWithZeroHom_injective", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.MonoidWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidWithZeroHom.copy", "kind": "definition", "module": "Mathlib.Algebra.Order.Hom.MonoidWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidWithZeroHom.coe_copy", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.MonoidWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidWithZeroHom.copy_eq", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.MonoidWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidWithZeroHom.id", "kind": "definition", "module": "Mathlib.Algebra.Order.Hom.MonoidWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidWithZeroHom.coe_id", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.MonoidWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidWithZeroHom.instInhabited", "kind": "instance", "module": "Mathlib.Algebra.Order.Hom.MonoidWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidWithZeroHom.comp", "kind": "definition", "module": "Mathlib.Algebra.Order.Hom.MonoidWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidWithZeroHom.coe_comp", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.MonoidWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidWithZeroHom.comp_apply", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.MonoidWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidWithZeroHom.coe_comp_monoidWithZeroHom", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.MonoidWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidWithZeroHom.coe_comp_orderMonoidHom", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.MonoidWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidWithZeroHom.comp_assoc", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.MonoidWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidWithZeroHom.comp_id", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.MonoidWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidWithZeroHom.id_comp", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.MonoidWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidWithZeroHom.cancel_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.MonoidWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidWithZeroHom.cancel_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.MonoidWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidWithZeroHom.instMul", "kind": "instance", "module": "Mathlib.Algebra.Order.Hom.MonoidWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidWithZeroHom.coe_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.MonoidWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidWithZeroHom.mul_apply", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.MonoidWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidWithZeroHom.mul_comp", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.MonoidWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidWithZeroHom.comp_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.MonoidWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidWithZeroHom.toMonoidWithZeroHom_eq_coe", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.MonoidWithZero", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "OrderMonoidWithZeroHom.toMonoidWithZeroHom_mk", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.MonoidWithZero", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "OrderMonoidWithZeroHom.toMonoidWithZeroHom_coe", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.MonoidWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidWithZeroHom.toOrderMonoidHom_eq_coe", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.MonoidWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidWithZeroHom.toOrderMonoidHom_comp", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.MonoidWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidIso.unitsWithZero", "kind": "definition", "module": "Mathlib.Algebra.Order.Hom.MonoidWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidIso.withZero", "kind": "definition", "module": "Mathlib.Algebra.Order.Hom.MonoidWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidIso.withZeroUnits", "kind": "definition", "module": "Mathlib.Algebra.Order.Hom.MonoidWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "term_→+*o_", "kind": "definition", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Algebra_Order_Hom_Ring___macroRules_term_→+*o__1", "kind": "definition", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Algebra_Order_Hom_Ring___unexpand_OrderRingHom_1", "kind": "definition", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "term_≃+*o_", "kind": "definition", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Algebra_Order_Hom_Ring___macroRules_term_≃+*o__1", "kind": "definition", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Algebra_Order_Hom_Ring___unexpand_OrderRingIso_1", "kind": "definition", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingHomClass.toOrderRingHom", "kind": "definition", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCoeTCOrderRingHomOfOrderHomClassOfRingHomClass", "kind": "instance", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingIsoClass.toOrderRingIso", "kind": "definition", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCoeTCOrderRingIsoOfOrderIsoClassOfRingEquivClass", "kind": "instance", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingHom.toOrderAddMonoidHom", "kind": "definition", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingHom.toOrderMonoidWithZeroHom", "kind": "definition", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingHom.instFunLike", "kind": "instance", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingHom.instOrderHomClass", "kind": "instance", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingHom.instRingHomClass", "kind": "instance", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingHom.toFun_eq_coe", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingHom.ext", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingHom.toRingHom_eq_coe", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingHom.toOrderAddMonoidHom_eq_coe", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingHom.toOrderMonoidWithZeroHom_eq_coe", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingHom.coe_coe_ringHom", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingHom.coe_coe_orderAddMonoidHom", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingHom.coe_coe_orderMonoidWithZeroHom", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingHom.coe_ringHom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingHom.coe_orderAddMonoidHom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingHom.coe_orderMonoidWithZeroHom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingHom.copy", "kind": "definition", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingHom.coe_copy", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingHom.copy_eq", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingHom.id", "kind": "definition", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingHom.instInhabited", "kind": "instance", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingHom.coe_id", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingHom.id_apply", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingHom.coe_ringHom_id", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingHom.coe_orderAddMonoidHom_id", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingHom.coe_orderMonoidWithZeroHom_id", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingHom.comp", "kind": "definition", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingHom.coe_comp", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingHom.comp_apply", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingHom.comp_assoc", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingHom.comp_id", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingHom.id_comp", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingHom.cancel_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingHom.cancel_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingHom.instPreorder", "kind": "instance", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingHom.instPartialOrder", "kind": "instance", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingIso.toOrderIso", "kind": "definition", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingIso.instEquivLike", "kind": "instance", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingIso.instOrderIsoClass", "kind": "instance", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingIso.instRingEquivClass", "kind": "instance", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingIso.toFun_eq_coe", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingIso.ext", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingIso.coe_mk", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingIso.mk_coe", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingIso.toRingEquiv_eq_coe", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingIso.toOrderIso_eq_coe", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingIso.coe_toRingEquiv", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingIso.coe_toOrderIso", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingIso.refl", "kind": "definition", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingIso.instInhabited", "kind": "instance", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingIso.refl_apply", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "OrderRingIso.coe_ringEquiv_refl", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingIso.coe_orderIso_refl", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingIso.symm", "kind": "definition", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingIso.Simps.symm_apply", "kind": "definition", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingIso.symm_symm", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingIso.symm_bijective", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingIso.symm_apply_apply", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingIso.apply_symm_apply", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingIso.trans", "kind": "definition", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingIso.trans_toRingEquiv", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingIso.trans_toRingEquiv_aux", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingIso.trans_apply", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingIso.self_trans_symm", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingIso.symm_trans_self", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingIso.lt_symm_apply", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "OrderRingIso.symm_apply_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "OrderRingIso.toOrderRingHom", "kind": "definition", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingIso.toOrderRingHom_eq_coe", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingIso.coe_toOrderRingHom", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingIso.coe_toOrderRingHom_refl", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderRingIso.toOrderRingHom_injective", "kind": "theorem", "module": "Mathlib.Algebra.Order.Hom.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.topOrderMonoidIso", "kind": "definition", "module": "Mathlib.Algebra.Order.Hom.Submonoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidIso.toAdditive", "kind": "definition", "module": "Mathlib.Algebra.Order.Hom.TypeTags", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderAddMonoidIso.toMultiplicative", "kind": "definition", "module": "Mathlib.Algebra.Order.Hom.TypeTags", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderAddMonoidIso.toMultiplicativeRight", "kind": "definition", "module": "Mathlib.Algebra.Order.Hom.TypeTags", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidIso.toAdditiveLeft", "kind": "abbrev", "module": "Mathlib.Algebra.Order.Hom.TypeTags", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderAddMonoidIso.toMultiplicativeLeft", "kind": "definition", "module": "Mathlib.Algebra.Order.Hom.TypeTags", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidIso.toAdditiveRight", "kind": "abbrev", "module": "Mathlib.Algebra.Order.Hom.TypeTags", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidIso.toMultiplicative_toAdditive", "kind": "definition", "module": "Mathlib.Algebra.Order.Hom.TypeTags", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderAddMonoidIso.toAdditive_toMultiplicative", "kind": "definition", "module": "Mathlib.Algebra.Order.Hom.TypeTags", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Additive.instUniqueOrderAddMonoidIso", "kind": "instance", "module": "Mathlib.Algebra.Order.Hom.TypeTags", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiplicative.instUniqueOrderdMonoidIso", "kind": "instance", "module": "Mathlib.Algebra.Order.Hom.TypeTags", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidIso.unitsCongr", "kind": "definition", "module": "Mathlib.Algebra.Order.Hom.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instOneNonemptyInterval", "kind": "instance", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.toProd_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.fst_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.snd_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.coe_one_interval", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.pure_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.pure_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.one_ne_bot", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.bot_ne_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.coe_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.one_mem_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.coe_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.one_mem_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instMulNonemptyInterval", "kind": "instance", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instMulInterval", "kind": "instance", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.toProd_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.fst_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.snd_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.coe_mul_interval", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.pure_mul_pure", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.bot_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.mul_bot", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.hasNSMul", "kind": "instance", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.hasPow", "kind": "instance", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.toProd_pow", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.fst_pow", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.snd_pow", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.pure_pow", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.commMonoid", "kind": "instance", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.mulOneClass", "kind": "instance", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.commMonoid", "kind": "instance", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.coe_pow_interval", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.bot_pow", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.instNatCast", "kind": "instance", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.fst_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.snd_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.pure_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.instCommSemiringOfCanonicallyOrderedAdd", "kind": "instance", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instSubNonemptyInterval", "kind": "instance", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instSubInterval", "kind": "instance", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.fst_sub", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.snd_sub", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.coe_sub_interval", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.sub_mem_sub", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.pure_sub_pure", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.bot_sub", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.sub_bot", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDivNonemptyInterval", "kind": "instance", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDivInterval", "kind": "instance", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.fst_div", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.snd_div", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.coe_div_interval", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.div_mem_div", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.pure_div_pure", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.bot_div", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.div_bot", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInvNonemptyInterval", "kind": "instance", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInvInterval", "kind": "instance", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.fst_inv", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.snd_inv", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.coe_inv_interval", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.inv_mem_inv", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.inv_pure", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.inv_bot", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.mul_eq_one_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "have", "refine", "nth_rw", "nth_rw", "rintro", "rw"], "tactic_count": 8}
{"name": "NonemptyInterval.subtractionCommMonoid", "kind": "instance", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.divisionCommMonoid", "kind": "instance", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.mul_eq_one_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": true, "tactics": ["cases", "simp", "cases", "simp", "simp_rw", "exact"], "tactic_count": 6}
{"name": "Interval.subtractionCommMonoid", "kind": "instance", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.divisionCommMonoid", "kind": "instance", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.length", "kind": "definition", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.length_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.length_pure", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.length_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.length_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.length_add", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.length_sub", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NonemptyInterval.length_sum", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.length", "kind": "definition", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.length_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.length_pure", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.length_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.length_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.length_add_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.length_sub_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Interval.length_sum_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalNonemptyIntervalLength", "kind": "definition", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalIntervalLength", "kind": "definition", "module": "Mathlib.Algebra.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.map_add_left_Icc", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finset.map_add_right_Icc", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finset.map_add_left_Ico", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finset.map_add_right_Ico", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finset.map_add_left_Ioc", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finset.map_add_right_Ioc", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finset.map_add_left_Ioo", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finset.map_add_right_Ioo", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finset.image_add_left_Icc", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.image_add_left_Ico", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.image_add_left_Ioc", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.image_add_left_Ioo", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.image_add_right_Icc", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.image_add_right_Ico", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.image_add_right_Ioc", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.image_add_right_Ioo", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.Ico_add_one_left_eq_Ioo", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Finset.SuccPred", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.Icc_add_one_left_eq_Ioc_of_not_isMax", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Finset.SuccPred", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.Ico_add_one_right_eq_Icc_of_not_isMax", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Finset.SuccPred", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.Ioo_add_one_right_eq_Ioc_of_not_isMax", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Finset.SuccPred", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.Ico_add_one_add_one_eq_Ioc_of_not_isMax", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Finset.SuccPred", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.insert_Icc_add_one_left_eq_Icc", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Finset.SuccPred", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.insert_Icc_right_eq_Icc_add_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Finset.SuccPred", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.insert_Ico_right_eq_Ico_add_one_of_not_isMax", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Finset.SuccPred", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.insert_Ico_add_one_left_eq_Ico", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Finset.SuccPred", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.insert_Ioc_right_eq_Ioc_add_one_of_not_isMax", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Finset.SuccPred", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.insert_Ioc_add_one_left_eq_Ioc", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Finset.SuccPred", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.Icc_add_one_left_eq_Ioc", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Finset.SuccPred", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.Ico_add_one_right_eq_Icc", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Finset.SuccPred", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.Ioo_add_one_right_eq_Ioc", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Finset.SuccPred", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.Ico_add_one_add_one_eq_Ioc", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Finset.SuccPred", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.insert_Ico_right_eq_Ico_add_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Finset.SuccPred", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.insert_Ioc_right_eq_Ioc_add_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Finset.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ioc_sub_one_right_eq_Ioo", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Finset.SuccPred", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.Icc_sub_one_right_eq_Ico_of_not_isMin", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Finset.SuccPred", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.Ioc_sub_one_left_eq_Icc_of_not_isMin", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Finset.SuccPred", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.Ioo_sub_one_left_eq_Ioc_of_not_isMin", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Finset.SuccPred", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.Ioc_sub_one_sub_one_eq_Ico_of_not_isMin", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Finset.SuccPred", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.insert_Icc_sub_one_right_eq_Icc", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Finset.SuccPred", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.insert_Icc_left_eq_Icc_sub_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Finset.SuccPred", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.insert_Ioc_left_eq_Ioc_sub_one_of_not_isMin", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Finset.SuccPred", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.insert_Ioc_sub_one_right_eq_Ioc", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Finset.SuccPred", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.insert_Ico_left_eq_Ico_sub_one_of_not_isMin", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Finset.SuccPred", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.insert_Ico_sub_one_right_eq_Ico", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Finset.SuccPred", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.Icc_sub_one_right_eq_Ico", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Finset.SuccPred", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.Ioc_sub_one_left_eq_Icc", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Finset.SuccPred", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.Ioo_sub_one_left_eq_Ioc", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Finset.SuccPred", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.Ioc_sub_one_sub_one_eq_Ico", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Finset.SuccPred", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.insert_Ioc_left_eq_Ioc_sub_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Finset.SuccPred", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.insert_Ico_left_eq_Ico_sub_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Finset.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Icc_add_one_sub_one_eq_Ioo", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Finset.SuccPred", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.Iio_add_one_eq_Iic_of_not_isMax", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Finset.SuccPred", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.Iio_add_one_eq_Iic", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Finset.SuccPred", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.Iic_sub_one_eq_Iio_of_not_isMin", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Finset.SuccPred", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.Iic_sub_one_eq_Iio", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Finset.SuccPred", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.Ici_add_one_eq_Ioi_of_not_isMax", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Finset.SuccPred", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.Ici_add_one_eq_Ioi", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Finset.SuccPred", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.Ioi_sub_one_eq_Ici_of_not_isMin", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Finset.SuccPred", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.Ioi_sub_one_eq_Ici", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Finset.SuccPred", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Multiset.map_add_left_Icc", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Multiset", "is_tactic_proof": true, "tactics": ["classical", "rw"], "tactic_count": 2}
{"name": "Multiset.map_add_left_Ico", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Multiset", "is_tactic_proof": true, "tactics": ["classical", "rw"], "tactic_count": 2}
{"name": "Multiset.map_add_left_Ioc", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Multiset", "is_tactic_proof": true, "tactics": ["classical", "rw"], "tactic_count": 2}
{"name": "Multiset.map_add_left_Ioo", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Multiset", "is_tactic_proof": true, "tactics": ["classical", "rw"], "tactic_count": 2}
{"name": "Multiset.map_add_right_Icc", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Multiset", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Multiset.map_add_right_Ico", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Multiset", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Multiset.map_add_right_Ioc", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Multiset", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Multiset.map_add_right_Ioo", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Multiset", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Set.inv_mem_Icc_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inv_mem_Ico_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inv_mem_Ioc_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inv_mem_Ioo_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.add_mem_Icc_iff_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.add_mem_Ico_iff_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.add_mem_Ioc_iff_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.add_mem_Ioo_iff_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.add_mem_Icc_iff_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.add_mem_Ico_iff_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.add_mem_Ioc_iff_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.add_mem_Ioo_iff_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sub_mem_Icc_iff_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sub_mem_Ico_iff_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sub_mem_Ioc_iff_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sub_mem_Ioo_iff_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sub_mem_Icc_iff_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sub_mem_Ico_iff_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sub_mem_Ioc_iff_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sub_mem_Ioo_iff_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_Icc_iff_abs_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sub_mem_Icc_zero_iff_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Group", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.sub_mem_Ico_zero_iff_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Group", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.sub_mem_Ioc_zero_iff_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Group", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.sub_mem_Ioo_zero_iff_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Group", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.nonempty_Ico_sdiff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Group", "is_tactic_proof": true, "tactics": ["rcases", "use", "simp", "use", "simp"], "tactic_count": 5}
{"name": "Set.pairwise_disjoint_Ioc_mul_zpow", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Group", "is_tactic_proof": true, "tactics": ["simp", "simp_rw", "intro", "apply", "have", "have", "rwa", "have", "have", "rw", "exact"], "tactic_count": 11}
{"name": "Set.pairwise_disjoint_Ico_mul_zpow", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Group", "is_tactic_proof": true, "tactics": ["simp", "simp_rw", "intro", "apply", "have", "have", "rwa", "have", "have", "rw", "exact"], "tactic_count": 11}
{"name": "Set.pairwise_disjoint_Ioo_mul_zpow", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.pairwise_disjoint_Ioc_zpow", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Group", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.pairwise_disjoint_Ico_zpow", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Group", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.pairwise_disjoint_Ioo_zpow", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Group", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.pairwise_disjoint_Ioc_add_intCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Group", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.pairwise_disjoint_Ico_add_intCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Group", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.pairwise_disjoint_Ioo_add_intCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Group", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.pairwise_disjoint_Ico_intCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Group", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.pairwise_disjoint_Ioo_intCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Group", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.pairwise_disjoint_Ioc_intCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Group", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.Icc.instZero", "kind": "instance", "module": "Mathlib.Algebra.Order.Interval.Set.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc.instOne", "kind": "instance", "module": "Mathlib.Algebra.Order.Interval.Set.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc.instZeroLEOneClass", "kind": "instance", "module": "Mathlib.Algebra.Order.Interval.Set.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc.coe_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc.coe_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc.mk_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc.mk_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc.coe_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Instances", "is_tactic_proof": true, "tactics": ["symm", "exact"], "tactic_count": 2}
{"name": "Set.Icc.coe_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc.coe_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Instances", "is_tactic_proof": true, "tactics": ["symm", "exact"], "tactic_count": 2}
{"name": "Set.Icc.coe_ne_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc.coe_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc.coe_le_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc.nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc.le_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc.instMul", "kind": "instance", "module": "Mathlib.Algebra.Order.Interval.Set.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc.instPow", "kind": "instance", "module": "Mathlib.Algebra.Order.Interval.Set.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc.coe_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc.coe_pow", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc.mul_le_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc.mul_le_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc.instMonoidWithZero", "kind": "instance", "module": "Mathlib.Algebra.Order.Interval.Set.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc.instCommMonoidWithZero", "kind": "instance", "module": "Mathlib.Algebra.Order.Interval.Set.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc.instIsCancelMulZero", "kind": "instance", "module": "Mathlib.Algebra.Order.Interval.Set.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc.one_sub_mem", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Instances", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.Icc.mem_iff_one_sub_mem", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc.one_sub_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Instances", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.Icc.one_sub_le_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Instances", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.Ico.instZero", "kind": "instance", "module": "Mathlib.Algebra.Order.Interval.Set.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ico.coe_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Set.Ico.coe_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Instances", "is_tactic_proof": true, "tactics": ["symm", "exact"], "tactic_count": 2}
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{"name": "Set.Ico.instMul", "kind": "instance", "module": "Mathlib.Algebra.Order.Interval.Set.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ico.coe_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Set.Ico.instCommSemigroup", "kind": "instance", "module": "Mathlib.Algebra.Order.Interval.Set.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioc.instOne", "kind": "instance", "module": "Mathlib.Algebra.Order.Interval.Set.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Set.Ioc.mk_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioc.coe_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Instances", "is_tactic_proof": true, "tactics": ["symm", "exact"], "tactic_count": 2}
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{"name": "Set.Ioc.coe_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioc.coe_le_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioc.le_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioc.instMul", "kind": "instance", "module": "Mathlib.Algebra.Order.Interval.Set.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioc.instPow", "kind": "instance", "module": "Mathlib.Algebra.Order.Interval.Set.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioc.coe_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioc.coe_pow", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioc.instSemigroup", "kind": "instance", "module": "Mathlib.Algebra.Order.Interval.Set.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioc.instMonoid", "kind": "instance", "module": "Mathlib.Algebra.Order.Interval.Set.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioc.instCommSemigroup", "kind": "instance", "module": "Mathlib.Algebra.Order.Interval.Set.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioc.instCommMonoid", "kind": "instance", "module": "Mathlib.Algebra.Order.Interval.Set.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioc.instCancelMonoid", "kind": "instance", "module": "Mathlib.Algebra.Order.Interval.Set.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioc.instCancelCommMonoid", "kind": "instance", "module": "Mathlib.Algebra.Order.Interval.Set.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioo.pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioo.lt_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioo.instMul", "kind": "instance", "module": "Mathlib.Algebra.Order.Interval.Set.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioo.coe_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioo.instSemigroup", "kind": "instance", "module": "Mathlib.Algebra.Order.Interval.Set.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioo.instCommSemigroup", "kind": "instance", "module": "Mathlib.Algebra.Order.Interval.Set.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioo.one_sub_mem", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Instances", "is_tactic_proof": true, "tactics": ["simp_all"], "tactic_count": 1}
{"name": "Set.Ioo.mem_iff_one_sub_mem", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioo.one_minus_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Instances", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.Ioo.one_minus_lt_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Instances", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.Ici_add_bij", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Monoid", "is_tactic_proof": true, "tactics": ["refine", "obtain", "rw", "exact"], "tactic_count": 4}
{"name": "Set.Ioi_add_bij", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Monoid", "is_tactic_proof": true, "tactics": ["refine", "obtain", "rw", "exact"], "tactic_count": 4}
{"name": "Set.Icc_add_bij", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Monoid", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.Ioo_add_bij", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Monoid", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.Ioc_add_bij", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Monoid", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.Ico_add_bij", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Monoid", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.image_add_const_Ici", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_add_const_Ioi", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_add_const_Icc", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_add_const_Ico", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_add_const_Ioc", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_add_const_Ioo", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_const_add_Ici", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Monoid", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.image_const_add_Ioi", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Monoid", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.image_const_add_Icc", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Monoid", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.image_const_add_Ico", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Monoid", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.image_const_add_Ioc", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Monoid", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.image_const_add_Ioo", "kind": "theorem", "module": "Mathlib.Algebra.Order.Interval.Set.Monoid", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "invOf_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Invertible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "invOf_lt_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.Invertible", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "invOf_le_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Invertible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pos_invOf_of_invertible_cast", "kind": "theorem", "module": "Mathlib.Algebra.Order.Invertible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computability.term_∗", "kind": "definition", "module": "Mathlib.Algebra.Order.Kleene", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computability._aux_Mathlib_Algebra_Order_Kleene___macroRules_Computability_term_∗_1", "kind": "definition", "module": "Mathlib.Algebra.Order.Kleene", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computability._aux_Mathlib_Algebra_Order_Kleene___unexpand_KStar_kstar_1", "kind": "definition", "module": "Mathlib.Algebra.Order.Kleene", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IdemSemiring.toOrderBot", "kind": "instance", "module": "Mathlib.Algebra.Order.Kleene", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IdemSemiring.ofSemiring", "kind": "abbrev", "module": "Mathlib.Algebra.Order.Kleene", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "add_eq_sup", "kind": "theorem", "module": "Mathlib.Algebra.Order.Kleene", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "natCast_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Kleene", "is_tactic_proof": true, "tactics": ["rw", "induction", "base", "succ"], "tactic_count": 4}
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{"name": "nsmul_eq_self", "kind": "theorem", "module": "Mathlib.Algebra.Order.Kleene", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "add_eq_left_iff_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Kleene", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "IdemSemiring.toCanonicallyOrderedAdd", "kind": "instance", "module": "Mathlib.Algebra.Order.Kleene", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IdemSemiring.toMulLeftMono", "kind": "instance", "module": "Mathlib.Algebra.Order.Kleene", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IdemSemiring.toMulRightMono", "kind": "instance", "module": "Mathlib.Algebra.Order.Kleene", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_le_kstar", "kind": "theorem", "module": "Mathlib.Algebra.Order.Kleene", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_kstar_le_kstar", "kind": "theorem", "module": "Mathlib.Algebra.Order.Kleene", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "kstar_mul_le_kstar", "kind": "theorem", "module": "Mathlib.Algebra.Order.Kleene", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_kstar_le_self", "kind": "theorem", "module": "Mathlib.Algebra.Order.Kleene", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "kstar_mul_le_self", "kind": "theorem", "module": "Mathlib.Algebra.Order.Kleene", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_kstar_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Kleene", "is_tactic_proof": true, "tactics": ["grw"], "tactic_count": 1}
{"name": "kstar_mul_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Kleene", "is_tactic_proof": true, "tactics": ["grw"], "tactic_count": 1}
{"name": "kstar_le_of_mul_le_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Kleene", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "kstar_le_of_mul_le_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Kleene", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "le_kstar", "kind": "theorem", "module": "Mathlib.Algebra.Order.Kleene", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "kstar_mono", "kind": "theorem", "module": "Mathlib.Algebra.Order.Kleene", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "kstar_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Kleene", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "kstar_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.Kleene", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "kstar_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Kleene", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "kstar_mul_kstar", "kind": "theorem", "module": "Mathlib.Algebra.Order.Kleene", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "kstar_eq_self", "kind": "theorem", "module": "Mathlib.Algebra.Order.Kleene", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "kstar_idem", "kind": "theorem", "module": "Mathlib.Algebra.Order.Kleene", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pow_le_kstar", "kind": "theorem", "module": "Mathlib.Algebra.Order.Kleene", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instIdemSemiring", "kind": "instance", "module": "Mathlib.Algebra.Order.Kleene", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instIdemCommSemiring", "kind": "instance", "module": "Mathlib.Algebra.Order.Kleene", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instKleeneAlgebra", "kind": "instance", "module": "Mathlib.Algebra.Order.Kleene", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.kstar_def", "kind": "theorem", "module": "Mathlib.Algebra.Order.Kleene", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.fst_kstar", "kind": "theorem", "module": "Mathlib.Algebra.Order.Kleene", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.snd_kstar", "kind": "theorem", "module": "Mathlib.Algebra.Order.Kleene", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instIdemSemiring", "kind": "instance", "module": "Mathlib.Algebra.Order.Kleene", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instIdemCommSemiringForall", "kind": "instance", "module": "Mathlib.Algebra.Order.Kleene", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instKleeneAlgebraForall", "kind": "instance", "module": "Mathlib.Algebra.Order.Kleene", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.kstar_def", "kind": "theorem", "module": "Mathlib.Algebra.Order.Kleene", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.kstar_apply", "kind": "theorem", "module": "Mathlib.Algebra.Order.Kleene", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.idemSemiring", "kind": "abbrev", "module": "Mathlib.Algebra.Order.Kleene", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.idemCommSemiring", "kind": "abbrev", "module": "Mathlib.Algebra.Order.Kleene", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.kleeneAlgebra", "kind": "abbrev", "module": "Mathlib.Algebra.Order.Kleene", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ArchimedeanClass.submodule", "kind": "definition", "module": "Mathlib.Algebra.Order.Module.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArchimedeanClass.ball", "kind": "abbrev", "module": "Mathlib.Algebra.Order.Module.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArchimedeanClass.closedBall", "kind": "abbrev", "module": "Mathlib.Algebra.Order.Module.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArchimedeanClass.toAddSubgroup_ball", "kind": "theorem", "module": "Mathlib.Algebra.Order.Module.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArchimedeanClass.toAddSubgroup_closedBall", "kind": "theorem", "module": "Mathlib.Algebra.Order.Module.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ArchimedeanClass.mem_closedBall_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Module.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "FiniteArchimedeanClass.closedBall", "kind": "abbrev", "module": "Mathlib.Algebra.Order.Module.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteArchimedeanClass.toAddSubgroup_ball", "kind": "theorem", "module": "Mathlib.Algebra.Order.Module.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteArchimedeanClass.toAddSubgroup_closedBall", "kind": "theorem", "module": "Mathlib.Algebra.Order.Module.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteArchimedeanClass.mem_ball_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Module.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteArchimedeanClass.mem_closedBall_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Module.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteArchimedeanClass.ball_strictAnti", "kind": "theorem", "module": "Mathlib.Algebra.Order.Module.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteArchimedeanClass.ball_lt_closedBall", "kind": "theorem", "module": "Mathlib.Algebra.Order.Module.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inf_eq_half_smul_add_sub_abs_sub", "kind": "theorem", "module": "Mathlib.Algebra.Order.Module.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "PosMulStrictMono.toPosSMulStrictMono", "kind": "instance", "module": "Mathlib.Algebra.Order.Module.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "PosMulReflectLE.toPosSMulReflectLE", "kind": "instance", "module": "Mathlib.Algebra.Order.Module.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MulPosStrictMono.toSMulPosStrictMono", "kind": "instance", "module": "Mathlib.Algebra.Order.Module.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MulPosReflectLE.toSMulPosReflectLE", "kind": "instance", "module": "Mathlib.Algebra.Order.Module.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instPosSMulMonoNatOfIsOrderedAddMonoid", "kind": "instance", "module": "Mathlib.Algebra.Order.Module.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instSMulPosMonoNatOfIsOrderedAddMonoid", "kind": "instance", "module": "Mathlib.Algebra.Order.Module.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instPosSMulStrictMonoNatOfIsOrderedAddMonoid", "kind": "instance", "module": "Mathlib.Algebra.Order.Module.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instSMulPosStrictMonoNatOfIsOrderedCancelAddMonoid", "kind": "instance", "module": "Mathlib.Algebra.Order.Module.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instPosSMulStrictMonoIntOfIsOrderedAddMonoid", "kind": "instance", "module": "Mathlib.Algebra.Order.Module.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instSMulPosStrictMonoIntOfIsOrderedAddMonoid", "kind": "instance", "module": "Mathlib.Algebra.Order.Module.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monotone_smul_left_of_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Module.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictMono_smul_left_of_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Module.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smul_le_smul_of_nonneg_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Module.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "lt_of_smul_lt_smul_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Module.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_of_smul_le_smul_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Module.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "smul_lt_smul_of_lt_of_le'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Module.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smul_lt_smul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Module.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "smul_le_smul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Module.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smul_le_smul'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Module.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOrderedRing.toIsOrderedModule", "kind": "instance", "module": "Mathlib.Algebra.Order.Module.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsStrictOrderedRing.toIsStrictOrderedModule", "kind": "instance", "module": "Mathlib.Algebra.Order.Module.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "posSMulStrictMono_iff_PosSMulReflectLE", "kind": "theorem", "module": "Mathlib.Algebra.Order.Module.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "posSMulMono_iff_posSMulReflectLT", "kind": "theorem", "module": "Mathlib.Algebra.Order.Module.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "smul_nonpos_of_nonneg_of_nonpos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Module.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
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{"name": "SMulPosReflectLT.of_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Module.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "PosSMulReflectLE.toPosSMulReflectLT", "kind": "instance", "module": "Mathlib.Algebra.Order.Module.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SMulPosReflectLE.toSMulPosReflectLT", "kind": "instance", "module": "Mathlib.Algebra.Order.Module.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsStrictOrderedModule.toIsOrderedModule", "kind": "instance", "module": "Mathlib.Algebra.Order.Module.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smul_eq_smul_iff_eq_and_eq_of_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Module.Defs", "is_tactic_proof": true, "tactics": ["refine", "simp", "refine", "exact", "exact"], "tactic_count": 5}
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{"name": "neg_of_smul_pos_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Module.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "neg_iff_neg_of_smul_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Module.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "neg_of_smul_neg_left'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Module.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "neg_of_smul_neg_right'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Module.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "lt_smul_iff_one_lt_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Module.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smul_le_iff_le_one_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Module.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smul_lt_iff_lt_one_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Module.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smul_le_of_le_one_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Module.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "le_smul_of_one_le_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Module.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
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{"name": "PosSMulMono.toPosSMulStrictMono", "kind": "theorem", "module": "Mathlib.Algebra.Order.Module.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosSMulReflectLT.toPosSMulReflectLE", "kind": "instance", "module": "Mathlib.Algebra.Order.Module.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "PosSMulReflectLE_iff_posSMulReflectLT", "kind": "theorem", "module": "Mathlib.Algebra.Order.Module.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SMulPosMono.toSMulPosStrictMono", "kind": "theorem", "module": "Mathlib.Algebra.Order.Module.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smulPosMono_iff_smulPosStrictMono", "kind": "theorem", "module": "Mathlib.Algebra.Order.Module.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SMulPosReflectLE_iff_smulPosReflectLT", "kind": "theorem", "module": "Mathlib.Algebra.Order.Module.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "HahnEmbedding.Partial.mem_domain", "kind": "theorem", "module": "Mathlib.Algebra.Order.Module.HahnEmbedding", "is_tactic_proof": true, "tactics": ["apply", "apply"], "tactic_count": 2}
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{"name": "HahnEmbedding.Partial.orderTop_eq_finiteArchimedeanClassMk", "kind": "theorem", "module": "Mathlib.Algebra.Order.Module.HahnEmbedding", "is_tactic_proof": true, "tactics": ["apply_fun", "simp"], "tactic_count": 2}
{"name": "HahnEmbedding.Partial.coeff_eq_zero_of_mem", "kind": "theorem", "module": "Mathlib.Algebra.Order.Module.HahnEmbedding", "is_tactic_proof": true, "tactics": ["obtain", "simp", "apply", "apply_fun", "rw", "apply", "simpa"], "tactic_count": 7}
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{"name": "HahnEmbedding.Partial.evalCoeff_eq", "kind": "theorem", "module": "Mathlib.Algebra.Order.Module.HahnEmbedding", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
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{"name": "HahnEmbedding.Partial.eval_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.Module.HahnEmbedding", "is_tactic_proof": true, "tactics": ["unfold", "convert", "ext", "rw", "simp"], "tactic_count": 5}
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{"name": "HahnEmbedding.Partial.eval_eq_truncLT", "kind": "theorem", "module": "Mathlib.Algebra.Order.Module.HahnEmbedding", "is_tactic_proof": true, "tactics": ["unfold", "rw", "ext", "simp", "obtain", "rw", "exact", "rw", "apply", "contrapose", "obtain", "exact"], "tactic_count": 12}
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{"name": "forall_lt_add_iff_lt_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.Canonical.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "aesop"], "tactic_count": 2}
{"name": "exists_lt_add_iff_lt_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.Canonical.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "aesop"], "tactic_count": 2}
{"name": "le_add_iff_lt_left_or_exists_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.Canonical.Basic", "is_tactic_proof": true, "tactics": ["obtain", "have", "tauto", "obtain", "simp"], "tactic_count": 5}
{"name": "forall_le_add_iff_le_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.Canonical.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "aesop"], "tactic_count": 2}
{"name": "exists_le_add_iff_le_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.Canonical.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "aesop"], "tactic_count": 2}
{"name": "lt_add_iff_lt_right_or_exists_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.Canonical.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp_rw"], "tactic_count": 2}
{"name": "forall_lt_add_iff_lt_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.Canonical.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "aesop"], "tactic_count": 2}
{"name": "exists_lt_add_iff_lt_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.Canonical.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "aesop"], "tactic_count": 2}
{"name": "le_add_iff_lt_right_or_exists_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.Canonical.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp_rw"], "tactic_count": 2}
{"name": "forall_le_add_iff_le_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.Canonical.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "aesop"], "tactic_count": 2}
{"name": "exists_le_add_iff_le_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.Canonical.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "aesop"], "tactic_count": 2}
{"name": "le_mul_self", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.Canonical.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_self_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.Canonical.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "self_le_mul_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.Canonical.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "self_le_mul_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.Canonical.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_iff_exists_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.Canonical.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_of_mul_le_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.Canonical.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_mul_of_le_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.Canonical.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_of_mul_le_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.Canonical.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_mul_of_le_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.Canonical.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_iff_exists_mul'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.Canonical.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "one_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.Canonical.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isBot_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.Canonical.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_lt_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.Canonical.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_lt_of_gt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.Canonical.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bot_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.Canonical.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_one_iff_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.Canonical.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_lt_iff_ne_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.Canonical.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_lt_of_ne_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.Canonical.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_one_or_one_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.Canonical.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_notMem_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.Canonical.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_one_lt_mul_of_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.Canonical.Defs", "is_tactic_proof": true, "tactics": ["obtain", "refine", "rintro", "simp"], "tactic_count": 4}
{"name": "lt_iff_exists_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.Canonical.Defs", "is_tactic_proof": true, "tactics": ["rw", "apply", "intro", "rw", "rintro", "constructor", "rw", "apply", "rintro", "rw", "rw", "apply"], "tactic_count": 12}
{"name": "CanonicallyOrderedMul.toMulLeftMono", "kind": "instance", "module": "Mathlib.Algebra.Order.Monoid.Canonical.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CanonicallyOrderedMul.toIsOrderedMonoid", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.Canonical.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CanonicallyOrderedCommMonoid.toUniqueUnits", "kind": "instance", "module": "Mathlib.Algebra.Order.Monoid.Canonical.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_lt_mul_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.Canonical.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NeZero.pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.Canonical.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NeZero.of_gt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.Canonical.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NeZero.of_gt'", "kind": "instance", "module": "Mathlib.Algebra.Order.Monoid.Canonical.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NeZero.of_ge", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.Canonical.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "min_mul_distrib", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.Canonical.Defs", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rcases", "simp", "simp"], "tactic_count": 5}
{"name": "min_mul_distrib'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.Canonical.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "one_min", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.Canonical.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "min_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.Canonical.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bot_eq_one'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.Canonical.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOrderedMonoid.toMulLeftMono", "kind": "instance", "module": "Mathlib.Algebra.Order.Monoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOrderedMonoid.toMulRightMono", "kind": "instance", "module": "Mathlib.Algebra.Order.Monoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOrderedCancelMonoid.toMulLeftReflectLE", "kind": "instance", "module": "Mathlib.Algebra.Order.Monoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOrderedCancelMonoid.toMulLeftReflectLT", "kind": "instance", "module": "Mathlib.Algebra.Order.Monoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOrderedCancelMonoid.toMulRightReflectLT", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOrderedCancelMonoid.toIsCancelMul", "kind": "instance", "module": "Mathlib.Algebra.Order.Monoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOrderedCancelMonoid.of_mul_lt_mul_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_le_mul_self_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_lt_mul_self_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_self_le_one_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.Defs", "is_tactic_proof": true, "tactics": ["contrapose"], "tactic_count": 1}
{"name": "mul_self_lt_one_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.Defs", "is_tactic_proof": true, "tactics": ["contrapose"], "tactic_count": 1}
{"name": "MonoidHom.inl_mono", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.inl_strictMono", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.inr_mono", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.inr_strictMono", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.fst_mono", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.snd_mono", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidHom.inl", "kind": "definition", "module": "Mathlib.Algebra.Order.Monoid.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidHom.inr", "kind": "definition", "module": "Mathlib.Algebra.Order.Monoid.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidHom.fst", "kind": "definition", "module": "Mathlib.Algebra.Order.Monoid.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidHom.snd", "kind": "definition", "module": "Mathlib.Algebra.Order.Monoid.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidHom.inlₗ", "kind": "definition", "module": "Mathlib.Algebra.Order.Monoid.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidHom.inrₗ", "kind": "definition", "module": "Mathlib.Algebra.Order.Monoid.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidHom.fstₗ", "kind": "definition", "module": "Mathlib.Algebra.Order.Monoid.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidHom.fst_comp_inl", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidHom.fstₗ_comp_inlₗ", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidHom.snd_comp_inl", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidHom.fst_comp_inr", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidHom.snd_comp_inr", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidHom.inl_mul_inr_eq_mk", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.Lex", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "OrderMonoidHom.inlₗ_mul_inrₗ_eq_toLex", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.Lex", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "OrderMonoidHom.commute_inl_inr", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidHom.commute_inlₗ_inrₗ", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_Ico_mul_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.LocallyFiniteOrder", "is_tactic_proof": false, "tactics": ["have", "ext", "simp", "constructor", "rintro", "obtain", "exact", "aesop", "simp"], "tactic_count": 9}
{"name": "card_Ico_one_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.LocallyFiniteOrder", "is_tactic_proof": true, "tactics": ["have", "rw", "simp"], "tactic_count": 3}
{"name": "LocallyFiniteOrder.addMonoidHom", "kind": "definition", "module": "Mathlib.Algebra.Order.Monoid.LocallyFiniteOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyFiniteOrder.orderAddMonoidHom", "kind": "definition", "module": "Mathlib.Algebra.Order.Monoid.LocallyFiniteOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyFiniteOrder.orderAddMonoidHom_toAddMonoidHom", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.LocallyFiniteOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyFiniteOrder.orderAddMonoidHom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.LocallyFiniteOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyFiniteOrder.orderAddMonoidHom_strictMono", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.LocallyFiniteOrder", "is_tactic_proof": true, "tactics": ["rw", "intro", "simpa"], "tactic_count": 3}
{"name": "LocallyFiniteOrder.orderAddMonoidHom_bijective", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.LocallyFiniteOrder", "is_tactic_proof": true, "tactics": ["refine", "suffices", "obtain", "exact", "have", "obtain", "exists_covBy_of_wellFoundedLT", "use", "have", "suffices", "ext", "simp", "constructor", "rintro", "by_contra", "have", "simp", "exact", "rintro", "simpa"], "tactic_count": 20}
{"name": "LocallyFiniteOrder.orderAddMonoidEquiv", "kind": "definition", "module": "Mathlib.Algebra.Order.Monoid.LocallyFiniteOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyFiniteOrder.orderAddMonoidEquiv_apply", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.LocallyFiniteOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyFiniteOrder.orderMonoidEquiv", "kind": "definition", "module": "Mathlib.Algebra.Order.Monoid.LocallyFiniteOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyFiniteOrder.orderMonoidHom", "kind": "definition", "module": "Mathlib.Algebra.Order.Monoid.LocallyFiniteOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyFiniteOrder.orderMonoidHom_strictMono", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.LocallyFiniteOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyFiniteOrder.orderMonoidWithZeroEquiv", "kind": "definition", "module": "Mathlib.Algebra.Order.Monoid.LocallyFiniteOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyFiniteOrder.orderMonoidWithZeroHom", "kind": "definition", "module": "Mathlib.Algebra.Order.Monoid.LocallyFiniteOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyFiniteOrder.orderMonoidWithZeroHom_strictMono", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.LocallyFiniteOrder", "is_tactic_proof": true, "tactics": ["have", "intro", "aesop"], "tactic_count": 3}
{"name": "lt_add_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.NatCast", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lt_one_add", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.NatCast", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zero_le_two", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.NatCast", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "zero_le_three", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.NatCast", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "zero_le_four", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.NatCast", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "one_le_two", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.NatCast", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_le_two'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.NatCast", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zero_lt_two", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.NatCast", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zero_lt_three", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.NatCast", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "zero_lt_four", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.NatCast", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "zero_lt_two'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.NatCast", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zero_lt_three'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.NatCast", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zero_lt_four'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.NatCast", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroLEOneClass.neZero.two", "kind": "instance", "module": "Mathlib.Algebra.Order.Monoid.NatCast", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroLEOneClass.neZero.three", "kind": "instance", "module": "Mathlib.Algebra.Order.Monoid.NatCast", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroLEOneClass.neZero.four", "kind": "instance", "module": "Mathlib.Algebra.Order.Monoid.NatCast", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_lt_two", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.NatCast", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "OrderDual.isOrderedMonoid", "kind": "instance", "module": "Mathlib.Algebra.Order.Monoid.OrderDual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.isOrderedCancelMonoid", "kind": "instance", "module": "Mathlib.Algebra.Order.Monoid.OrderDual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Units.orderEmbeddingVal", "kind": "definition", "module": "Mathlib.Algebra.Order.Monoid.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.isOrderedAddMonoid", "kind": "instance", "module": "Mathlib.Algebra.Order.Monoid.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.canonicallyOrderedAdd", "kind": "instance", "module": "Mathlib.Algebra.Order.Monoid.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.isOrderedAddMonoid", "kind": "instance", "module": "Mathlib.Algebra.Order.Monoid.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.le_self_add", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.WithTop", "is_tactic_proof": true, "tactics": ["induction", "simp", "induction", "simp", "rw", "exact"], "tactic_count": 6}
{"name": "WithBot.le_add_self", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monoid.WithTop", "is_tactic_proof": true, "tactics": ["induction", "simp", "induction", "simp", "rw", "exact"], "tactic_count": 6}
{"name": "monovaryOn_inv_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "antivaryOn_inv_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "monovary_inv_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "antivary_inv_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MonovaryOn.mul_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntivaryOn.mul_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonovaryOn.div_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntivaryOn.div_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonovaryOn.pow_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntivaryOn.pow_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monovary.mul_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antivary.mul_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monovary.div_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antivary.div_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monovary.pow_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antivary.pow_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monovaryOn_inv_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "antivaryOn_inv_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "monovary_inv_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "antivary_inv_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "monovaryOn_inv", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "antivaryOn_inv", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "monovary_inv", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "antivary_inv", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MonovaryOn.mul_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntivaryOn.mul_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonovaryOn.div_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntivaryOn.div_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonovaryOn.pow_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntivaryOn.pow_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monovary.mul_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antivary.mul_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monovary.div_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antivary.div_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monovary.pow_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antivary.pow_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonovaryOn.mul_left₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntivaryOn.mul_left₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonovaryOn.pow_left₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntivaryOn.pow_left₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monovary.mul_left₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antivary.mul_left₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monovary.pow_left₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antivary.pow_left₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonovaryOn.mul_right₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntivaryOn.mul_right₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonovaryOn.pow_right₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntivaryOn.pow_right₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monovary.mul_right₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antivary.mul_right₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monovary.pow_right₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antivary.pow_right₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monovaryOn_inv_left₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "antivaryOn_inv_left₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monovary_inv_left₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "antivary_inv_left₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonovaryOn.div_left₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntivaryOn.div_left₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monovary.div_left₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antivary.div_left₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monovaryOn_inv_right₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "antivaryOn_inv_right₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monovary_inv_right₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "antivary_inv_right₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonovaryOn.div_right₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntivaryOn.div_right₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monovary.div_right₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antivary.div_right₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monovaryOn_inv₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "antivaryOn_inv₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "monovary_inv₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "antivary_inv₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "monovaryOn_iff_forall_smul_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "antivaryOn_iff_forall_smul_nonpos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monovary_iff_forall_smul_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "antivary_iff_forall_smul_nonpos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monovaryOn_iff_smul_rearrangement", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "antivaryOn_iff_smul_rearrangement", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monovary_iff_smul_rearrangement", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "antivary_iff_smul_rearrangement", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monovaryOn_iff_forall_mul_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "antivaryOn_iff_forall_mul_nonpos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "monovary_iff_forall_mul_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "antivary_iff_forall_mul_nonpos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "monovaryOn_iff_mul_rearrangement", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "antivaryOn_iff_mul_rearrangement", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "monovary_iff_mul_rearrangement", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "antivary_iff_mul_rearrangement", "kind": "theorem", "module": "Mathlib.Algebra.Order.Monovary", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nonneg.inhabited", "kind": "instance", "module": "Mathlib.Algebra.Order.Nonneg.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.zero", "kind": "instance", "module": "Mathlib.Algebra.Order.Nonneg.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.coe_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.Nonneg.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.mk_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.Nonneg.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.add", "kind": "instance", "module": "Mathlib.Algebra.Order.Nonneg.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Nonneg.coe_add", "kind": "theorem", "module": "Mathlib.Algebra.Order.Nonneg.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.instIsLeftCancelAddSubtypeLeOfNat", "kind": "instance", "module": "Mathlib.Algebra.Order.Nonneg.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.instIsRightCancelAddSubtypeLeOfNat", "kind": "instance", "module": "Mathlib.Algebra.Order.Nonneg.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.instIsCancelAddSubtypeLeOfNat", "kind": "instance", "module": "Mathlib.Algebra.Order.Nonneg.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.nsmul", "kind": "instance", "module": "Mathlib.Algebra.Order.Nonneg.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.nsmul_mk", "kind": "theorem", "module": "Mathlib.Algebra.Order.Nonneg.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.coe_nsmul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Nonneg.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.one", "kind": "instance", "module": "Mathlib.Algebra.Order.Nonneg.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.coe_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Nonneg.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.mk_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Nonneg.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.mul", "kind": "instance", "module": "Mathlib.Algebra.Order.Nonneg.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.coe_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Nonneg.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.mk_mul_mk", "kind": "theorem", "module": "Mathlib.Algebra.Order.Nonneg.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.addMonoid", "kind": "instance", "module": "Mathlib.Algebra.Order.Nonneg.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.coeAddMonoidHom", "kind": "definition", "module": "Mathlib.Algebra.Order.Nonneg.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.nsmul_coe", "kind": "theorem", "module": "Mathlib.Algebra.Order.Nonneg.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.addCommMonoid", "kind": "instance", "module": "Mathlib.Algebra.Order.Nonneg.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Nonneg.natCast", "kind": "instance", "module": "Mathlib.Algebra.Order.Nonneg.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.coe_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.Nonneg.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Nonneg.addMonoidWithOne", "kind": "instance", "module": "Mathlib.Algebra.Order.Nonneg.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.pow", "kind": "instance", "module": "Mathlib.Algebra.Order.Nonneg.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.coe_pow", "kind": "theorem", "module": "Mathlib.Algebra.Order.Nonneg.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Nonneg.monoidWithZero", "kind": "instance", "module": "Mathlib.Algebra.Order.Nonneg.Basic", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Nonneg.coeRingHom", "kind": "definition", "module": "Mathlib.Algebra.Order.Nonneg.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.commSemiring", "kind": "instance", "module": "Mathlib.Algebra.Order.Nonneg.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.commMonoidWithZero", "kind": "instance", "module": "Mathlib.Algebra.Order.Nonneg.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.toNonneg", "kind": "definition", "module": "Mathlib.Algebra.Order.Nonneg.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.coe_toNonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Nonneg.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.toNonneg_of_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Nonneg.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nonneg.toNonneg_coe", "kind": "theorem", "module": "Mathlib.Algebra.Order.Nonneg.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.toNonneg_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Nonneg.Basic", "is_tactic_proof": true, "tactics": ["obtain", "simp"], "tactic_count": 2}
{"name": "Nonneg.sub", "kind": "instance", "module": "Mathlib.Algebra.Order.Nonneg.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.mk_sub_mk", "kind": "theorem", "module": "Mathlib.Algebra.Order.Nonneg.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.toNonneg_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Nonneg.Basic", "is_tactic_proof": true, "tactics": ["obtain", "simp"], "tactic_count": 2}
{"name": "NNRat.cast_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Nonneg.Field", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "nnqsmul_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Nonneg.Field", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nonneg.unitsEquivPos", "kind": "definition", "module": "Mathlib.Algebra.Order.Nonneg.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.inv", "kind": "instance", "module": "Mathlib.Algebra.Order.Nonneg.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.coe_inv", "kind": "theorem", "module": "Mathlib.Algebra.Order.Nonneg.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.inv_mk", "kind": "theorem", "module": "Mathlib.Algebra.Order.Nonneg.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.div", "kind": "instance", "module": "Mathlib.Algebra.Order.Nonneg.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.coe_div", "kind": "theorem", "module": "Mathlib.Algebra.Order.Nonneg.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.mk_div_mk", "kind": "theorem", "module": "Mathlib.Algebra.Order.Nonneg.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.zpow", "kind": "instance", "module": "Mathlib.Algebra.Order.Nonneg.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.coe_zpow", "kind": "theorem", "module": "Mathlib.Algebra.Order.Nonneg.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.mk_zpow", "kind": "theorem", "module": "Mathlib.Algebra.Order.Nonneg.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.instNNRatCast", "kind": "instance", "module": "Mathlib.Algebra.Order.Nonneg.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.instNNRatSMul", "kind": "instance", "module": "Mathlib.Algebra.Order.Nonneg.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.coe_nnratCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.Nonneg.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.mk_nnratCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.Nonneg.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.coe_nnqsmul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Nonneg.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.mk_nnqsmul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Nonneg.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.semifield", "kind": "instance", "module": "Mathlib.Algebra.Order.Nonneg.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.linearOrderedCommGroupWithZero", "kind": "instance", "module": "Mathlib.Algebra.Order.Nonneg.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.floorSemiring", "kind": "instance", "module": "Mathlib.Algebra.Order.Nonneg.Floor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.nat_floor_coe", "kind": "theorem", "module": "Mathlib.Algebra.Order.Nonneg.Floor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.nat_ceil_coe", "kind": "theorem", "module": "Mathlib.Algebra.Order.Nonneg.Floor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.orderBot", "kind": "instance", "module": "Mathlib.Algebra.Order.Nonneg.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.bot_eq", "kind": "theorem", "module": "Mathlib.Algebra.Order.Nonneg.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.noMaxOrder", "kind": "instance", "module": "Mathlib.Algebra.Order.Nonneg.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.semilatticeSup", "kind": "instance", "module": "Mathlib.Algebra.Order.Nonneg.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.semilatticeInf", "kind": "instance", "module": "Mathlib.Algebra.Order.Nonneg.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.distribLattice", "kind": "instance", "module": "Mathlib.Algebra.Order.Nonneg.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.instDenselyOrdered", "kind": "instance", "module": "Mathlib.Algebra.Order.Nonneg.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.conditionallyCompleteLinearOrder", "kind": "abbrev", "module": "Mathlib.Algebra.Order.Nonneg.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.conditionallyCompleteLinearOrderBot", "kind": "abbrev", "module": "Mathlib.Algebra.Order.Nonneg.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Order.Nonneg.Module.0.termR≥0", "kind": "definition", "module": "Mathlib.Algebra.Order.Nonneg.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Order.Nonneg.Module.0._aux_Mathlib_Algebra_Order_Nonneg_Module___macroRules__private_Mathlib_Algebra_Order_Nonneg_Module_0_termR≥0_1", "kind": "definition", "module": "Mathlib.Algebra.Order.Nonneg.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Order.Nonneg.Module.0._aux_Mathlib_Algebra_Order_Nonneg_Module___delab_app__private_Mathlib_Algebra_Order_Nonneg_Module_0_termR≥0_1", "kind": "definition", "module": "Mathlib.Algebra.Order.Nonneg.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.instSMul", "kind": "instance", "module": "Mathlib.Algebra.Order.Nonneg.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.coe_smul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Nonneg.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.mk_smul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Nonneg.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.instIsScalarTower", "kind": "instance", "module": "Mathlib.Algebra.Order.Nonneg.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.instSMulWithZero", "kind": "instance", "module": "Mathlib.Algebra.Order.Nonneg.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.instIsOrderedModule", "kind": "instance", "module": "Mathlib.Algebra.Order.Nonneg.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.instIsStrictOrderedModule", "kind": "instance", "module": "Mathlib.Algebra.Order.Nonneg.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.instModule", "kind": "instance", "module": "Mathlib.Algebra.Order.Nonneg.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.isOrderedAddMonoid", "kind": "instance", "module": "Mathlib.Algebra.Order.Nonneg.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.isOrderedCancelAddMonoid", "kind": "instance", "module": "Mathlib.Algebra.Order.Nonneg.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.isOrderedRing", "kind": "instance", "module": "Mathlib.Algebra.Order.Nonneg.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.isStrictOrderedRing", "kind": "instance", "module": "Mathlib.Algebra.Order.Nonneg.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.existsAddOfLE", "kind": "instance", "module": "Mathlib.Algebra.Order.Nonneg.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.nontrivial", "kind": "instance", "module": "Mathlib.Algebra.Order.Nonneg.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.instNontrivialSubtypeLeOfNatOfAddLeftMono", "kind": "instance", "module": "Mathlib.Algebra.Order.Nonneg.Ring", "is_tactic_proof": true, "tactics": ["have", "obtain", "exact", "exact"], "tactic_count": 4}
{"name": "Nonneg.linearOrderedCommMonoidWithZero", "kind": "instance", "module": "Mathlib.Algebra.Order.Nonneg.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.canonicallyOrderedAdd", "kind": "instance", "module": "Mathlib.Algebra.Order.Nonneg.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.noZeroDivisors", "kind": "instance", "module": "Mathlib.Algebra.Order.Nonneg.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.orderedSub", "kind": "instance", "module": "Mathlib.Algebra.Order.Nonneg.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PUnit.canonicallyOrderedAdd", "kind": "instance", "module": "Mathlib.Algebra.Order.PUnit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PUnit.isOrderedCancelAddMonoid", "kind": "instance", "module": "Mathlib.Algebra.Order.PUnit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PUnit.instLinearOrderedAddCommMonoidWithTop", "kind": "instance", "module": "Mathlib.Algebra.Order.PUnit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.isOrderedMonoid", "kind": "instance", "module": "Mathlib.Algebra.Order.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.existsMulOfLe", "kind": "instance", "module": "Mathlib.Algebra.Order.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instCanonicallyOrderedMulForall", "kind": "instance", "module": "Mathlib.Algebra.Order.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.isOrderedCancelMonoid", "kind": "instance", "module": "Mathlib.Algebra.Order.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.isOrderedRing", "kind": "instance", "module": "Mathlib.Algebra.Order.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.one_le_const_of_one_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.const_le_one_of_le_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.one_le_const", "kind": "theorem", "module": "Mathlib.Algebra.Order.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.one_lt_const", "kind": "theorem", "module": "Mathlib.Algebra.Order.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.const_le_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.const_lt_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.one_le_extend", "kind": "theorem", "module": "Mathlib.Algebra.Order.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.extend_le_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.mulSingle_le_mulSingle", "kind": "theorem", "module": "Mathlib.Algebra.Order.Pi", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Pi.one_le_mulSingle", "kind": "theorem", "module": "Mathlib.Algebra.Order.Pi", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Pi.mulSingle_le_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Pi", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Positive.Subtype.inv", "kind": "instance", "module": "Mathlib.Algebra.Order.Positive.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Positive.coe_inv", "kind": "theorem", "module": "Mathlib.Algebra.Order.Positive.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Positive.instPowSubtypeLtOfNatInt_mathlib", "kind": "instance", "module": "Mathlib.Algebra.Order.Positive.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Positive.coe_zpow", "kind": "theorem", "module": "Mathlib.Algebra.Order.Positive.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Positive.instCommGroupSubtypeLtOfNat", "kind": "instance", "module": "Mathlib.Algebra.Order.Positive.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Positive.instAddSubtypeLtOfNat_mathlib", "kind": "instance", "module": "Mathlib.Algebra.Order.Positive.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Positive.coe_add", "kind": "theorem", "module": "Mathlib.Algebra.Order.Positive.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Positive.addSemigroup", "kind": "instance", "module": "Mathlib.Algebra.Order.Positive.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Positive.addCommSemigroup", "kind": "instance", "module": "Mathlib.Algebra.Order.Positive.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Positive.addLeftCancelSemigroup", "kind": "instance", "module": "Mathlib.Algebra.Order.Positive.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Positive.addRightCancelSemigroup", "kind": "instance", "module": "Mathlib.Algebra.Order.Positive.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Positive.addLeftStrictMono", "kind": "instance", "module": "Mathlib.Algebra.Order.Positive.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Positive.addRightStrictMono", "kind": "instance", "module": "Mathlib.Algebra.Order.Positive.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Positive.addLeftReflectLT", "kind": "instance", "module": "Mathlib.Algebra.Order.Positive.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Positive.addRightReflectLT", "kind": "instance", "module": "Mathlib.Algebra.Order.Positive.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Positive.addLeftReflectLE", "kind": "instance", "module": "Mathlib.Algebra.Order.Positive.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Positive.addRightReflectLE", "kind": "instance", "module": "Mathlib.Algebra.Order.Positive.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Positive.addLeftMono", "kind": "instance", "module": "Mathlib.Algebra.Order.Positive.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Positive.instMulSubtypeLtOfNat_mathlib", "kind": "instance", "module": "Mathlib.Algebra.Order.Positive.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Positive.val_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Positive.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Positive.instPowSubtypeLtOfNatNat_mathlib", "kind": "instance", "module": "Mathlib.Algebra.Order.Positive.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Positive.val_pow", "kind": "theorem", "module": "Mathlib.Algebra.Order.Positive.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Positive.instSemigroupSubtypeLtOfNat", "kind": "instance", "module": "Mathlib.Algebra.Order.Positive.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Positive.instDistribSubtypeLtOfNat", "kind": "instance", "module": "Mathlib.Algebra.Order.Positive.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Positive.instOneSubtypeLtOfNat_mathlib", "kind": "instance", "module": "Mathlib.Algebra.Order.Positive.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Positive.val_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Positive.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Positive.instMonoidSubtypeLtOfNat", "kind": "instance", "module": "Mathlib.Algebra.Order.Positive.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Positive.commMonoid", "kind": "instance", "module": "Mathlib.Algebra.Order.Positive.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Positive.isOrderedMonoid", "kind": "instance", "module": "Mathlib.Algebra.Order.Positive.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Positive.isOrderedCancelMonoid", "kind": "instance", "module": "Mathlib.Algebra.Order.Positive.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_sSup_distrib", "kind": "theorem", "module": "Mathlib.Algebra.Order.Quantale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sSup_mul_distrib", "kind": "theorem", "module": "Mathlib.Algebra.Order.Quantale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddQuantale.leftAddResiduation", "kind": "definition", "module": "Mathlib.Algebra.Order.Quantale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddQuantale.rightAddResiduation", "kind": "definition", "module": "Mathlib.Algebra.Order.Quantale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddQuantale.term_⇨ₗ_", "kind": "definition", "module": "Mathlib.Algebra.Order.Quantale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddQuantale._aux_Mathlib_Algebra_Order_Quantale___macroRules_AddQuantale_term_⇨ₗ__1", "kind": "definition", "module": "Mathlib.Algebra.Order.Quantale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddQuantale._aux_Mathlib_Algebra_Order_Quantale___unexpand_AddQuantale_leftAddResiduation_1", "kind": "definition", "module": "Mathlib.Algebra.Order.Quantale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddQuantale.term_⇨ᵣ_", "kind": "definition", "module": "Mathlib.Algebra.Order.Quantale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddQuantale._aux_Mathlib_Algebra_Order_Quantale___macroRules_AddQuantale_term_⇨ᵣ__1", "kind": "definition", "module": "Mathlib.Algebra.Order.Quantale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddQuantale._aux_Mathlib_Algebra_Order_Quantale___unexpand_AddQuantale_rightAddResiduation_1", "kind": "definition", "module": "Mathlib.Algebra.Order.Quantale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quantale.leftMulResiduation", "kind": "definition", "module": "Mathlib.Algebra.Order.Quantale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quantale.rightMulResiduation", "kind": "definition", "module": "Mathlib.Algebra.Order.Quantale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "pow_eq_neg_one_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Abs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Odd.mod_even_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Even.mod_even_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Odd.mod_even", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Even.mod_even", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Odd.of_dvd_nat", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Odd.ne_two_of_dvd_nat", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Abs", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "Int.le_abs_of_dvd", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArchimedeanClass.instZero", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArchimedeanClass.mk_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArchimedeanClass.top_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Archimedean", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ArchimedeanClass.zero_ne_top", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Order.Ring.Archimedean.0.ArchimedeanClass.mk_mul_le_of_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Archimedean", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "use", "convert", "simp_rw", "ring"], "tactic_count": 6}
{"name": "ArchimedeanClass.instAdd", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArchimedeanClass.mk_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArchimedeanClass.instSMulNat", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArchimedeanClass.mk_pow", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArchimedeanClass.instAddCommMagma", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Order.Ring.Archimedean.0.ArchimedeanClass.zero_add'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Archimedean", "is_tactic_proof": false, "tactics": ["induction", "mk", "rw"], "tactic_count": 3}
{"name": "_private.Mathlib.Algebra.Order.Ring.Archimedean.0.ArchimedeanClass.add_assoc'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Archimedean", "is_tactic_proof": false, "tactics": ["induction", "mk", "induction", "mk", "induction", "mk", "simp_rw"], "tactic_count": 7}
{"name": "ArchimedeanClass.instAddCommMonoid", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArchimedeanClass.instIsOrderedAddMonoid", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArchimedeanClass.isAddRegular_mk", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Archimedean", "is_tactic_proof": true, "tactics": ["rw", "rintro", "induction", "mk", "induction", "mk"], "tactic_count": 6}
{"name": "ArchimedeanClass.instLinearOrderedAddCommMonoidWithTop", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArchimedeanClass.addValuation", "kind": "definition", "module": "Mathlib.Algebra.Order.Ring.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArchimedeanClass.addValuation_apply", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArchimedeanClass.orderHom_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Archimedean", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ArchimedeanClass.mk_eq_zero_of_archimedean", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArchimedeanClass.eq_zero_or_top_of_archimedean", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Archimedean", "is_tactic_proof": false, "tactics": ["induction", "mk", "obtain"], "tactic_count": 3}
{"name": "ArchimedeanClass.mk_map_of_archimedean", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Archimedean", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ArchimedeanClass.mk_map_of_archimedean'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Archimedean", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ArchimedeanClass.mk_le_mk_add_of_archimedean", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Archimedean", "is_tactic_proof": true, "tactics": ["obtain", "simp", "rw"], "tactic_count": 3}
{"name": "ArchimedeanClass.mk_le_add_mk_of_archimedean", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Archimedean", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ArchimedeanClass.mk_map_nonneg_of_archimedean", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Archimedean", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ArchimedeanClass.lt_of_pos_of_archimedean", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Archimedean", "is_tactic_proof": true, "tactics": ["apply", "rwa", "simpa"], "tactic_count": 3}
{"name": "ArchimedeanClass.lt_of_neg_of_archimedean", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Archimedean", "is_tactic_proof": true, "tactics": ["apply", "rwa", "simpa"], "tactic_count": 3}
{"name": "ArchimedeanClass.mk_intCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Archimedean", "is_tactic_proof": true, "tactics": ["obtain", "exact", "exact"], "tactic_count": 3}
{"name": "ArchimedeanClass.mk_intCast_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Archimedean", "is_tactic_proof": true, "tactics": ["obtain", "simp", "rw"], "tactic_count": 3}
{"name": "ArchimedeanClass.mk_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArchimedeanClass.mk_ofNat", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArchimedeanClass.mk_natCast_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArchimedeanClass.exists_nat_ge_of_mk_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Archimedean", "is_tactic_proof": true, "tactics": ["obtain", "refine", "simpa"], "tactic_count": 3}
{"name": "ArchimedeanClass.exists_nat_gt_of_mk_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Archimedean", "is_tactic_proof": true, "tactics": ["obtain", "refine", "simp"], "tactic_count": 3}
{"name": "ArchimedeanClass.exists_int_ge_of_mk_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Archimedean", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "ArchimedeanClass.exists_int_gt_of_mk_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Archimedean", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "ArchimedeanClass.exists_int_le_of_mk_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Archimedean", "is_tactic_proof": true, "tactics": ["obtain", "use", "simpa"], "tactic_count": 3}
{"name": "ArchimedeanClass.exists_int_lt_of_mk_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Archimedean", "is_tactic_proof": true, "tactics": ["obtain", "use", "simpa"], "tactic_count": 3}
{"name": "ArchimedeanClass.mk_nonneg_of_le_of_le_of_archimedean", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Archimedean", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "ArchimedeanClass.add_left_cancel_of_ne_top", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Archimedean", "is_tactic_proof": false, "tactics": ["induction", "mk", "induction", "mk", "induction", "mk", "simp_rw", "obtain", "simp_rw", "refine"], "tactic_count": 10}
{"name": "ArchimedeanClass.add_right_cancel_of_ne_top", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Archimedean", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "ArchimedeanClass.mk_le_mk_iff_denselyOrdered", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Archimedean", "is_tactic_proof": true, "tactics": ["have", "constructor", "rintro", "simp_all", "obtain", "refine", "simpa", "rintro", "have", "obtain", "refine", "have", "rw", "exact", "simpa"], "tactic_count": 15}
{"name": "ArchimedeanClass.instNeg", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArchimedeanClass.mk_inv", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArchimedeanClass.instSMulInt", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArchimedeanClass.mk_zpow", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Order.Ring.Archimedean.0.ArchimedeanClass.zsmul_succ'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Archimedean", "is_tactic_proof": false, "tactics": ["induction", "mk", "rw", "obtain", "simp", "rw"], "tactic_count": 6}
{"name": "ArchimedeanClass.instLinearOrderedAddCommGroupWithTop", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArchimedeanClass.mk_div", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Archimedean", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ArchimedeanClass.mk_ratCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Archimedean", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ArchimedeanClass.mk_ratCast_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Archimedean", "is_tactic_proof": true, "tactics": ["obtain", "simp", "rw"], "tactic_count": 3}
{"name": "ArchimedeanClass.mk_le_mk_iff_ratCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Archimedean", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsSquare.nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Basic", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "not_isSquare_of_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pow_add_pow_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Basic", "is_tactic_proof": true, "tactics": ["rcases", "induction", "zero", "succ", "let", "have", "have", "calc", "x", "rw", "exact", "rw", "add_assoc", "rw", "exact"], "tactic_count": 15}
{"name": "pow_add_pow_le'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Basic", "is_tactic_proof": true, "tactics": ["rw", "gcongr", "exacts"], "tactic_count": 3}
{"name": "sq_pos_of_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Even.pow_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Basic", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "pow_four_le_pow_two_of_pow_two_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsNonarchimedean", "kind": "definition", "module": "Mathlib.Algebra.Order.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "add_sq_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Basic", "is_tactic_proof": false, "tactics": ["calc", "simp_rw", "cases", "exact", "exact", "mul_add_mul_le_mul_add_mul"], "tactic_count": 6}
{"name": "add_pow_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Even.add_pow_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Basic", "is_tactic_proof": true, "tactics": ["obtain", "rw", "calc", "rw", "simp", "cases", "rfl", "simp"], "tactic_count": 8}
{"name": "Even.pow_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Even.pow_pos_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Basic", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "Odd.pow_neg_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Basic", "is_tactic_proof": true, "tactics": ["refine", "obtain", "rw", "exact"], "tactic_count": 4}
{"name": "Odd.pow_nonneg_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Odd.pow_nonpos_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Basic", "is_tactic_proof": true, "tactics": ["rw", "rintro"], "tactic_count": 2}
{"name": "Odd.pow_pos_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Odd.strictMono_pow", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Basic", "is_tactic_proof": true, "tactics": ["have", "intro", "obtain", "exact", "obtain", "exact", "obtain", "obtain", "have", "refine", "dsimp", "calc", "a", "refine", "rwa"], "tactic_count": 15}
{"name": "Odd.pow_injective", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Odd.pow_lt_pow", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Odd.pow_le_pow", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Odd.pow_inj", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sq_pos_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CanonicallyOrderedAdd.toZeroLEOneClass", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Odd.pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Canonical", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "CanonicallyOrderedAdd.toMulLeftMono", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Canonical", "is_tactic_proof": true, "tactics": ["refine", "dsimp", "rcases", "rw", "apply"], "tactic_count": 5}
{"name": "CanonicallyOrderedAdd.toMulRightMono", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Canonical", "is_tactic_proof": true, "tactics": ["refine", "dsimp", "rcases", "rw", "apply"], "tactic_count": 5}
{"name": "CanonicallyOrderedAdd.toIsOrderedMonoid", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CanonicallyOrderedAdd.toIsOrderedRing", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CanonicallyOrderedAdd.mul_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Canonical", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CanonicallyOrderedAdd.pow_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CanonicallyOrderedAdd.mul_lt_mul_of_lt_of_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Canonical", "is_tactic_proof": true, "tactics": ["have", "obtain", "rw", "exact", "exact"], "tactic_count": 5}
{"name": "AddLECancellable.mul_tsub", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Canonical", "is_tactic_proof": true, "tactics": ["obtain", "rw", "apply", "rw"], "tactic_count": 4}
{"name": "AddLECancellable.tsub_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Canonical", "is_tactic_proof": true, "tactics": ["obtain", "rw", "apply", "rw"], "tactic_count": 4}
{"name": "mul_tsub", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tsub_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_tsub_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Canonical", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "tsub_one_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Canonical", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mul_self_tsub_mul_self", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Canonical", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "sq_tsub_sq", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Canonical", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mul_self_tsub_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Canonical", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.cast_mono", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Cast", "is_tactic_proof": true, "tactics": ["intro", "rw", "lift", "rw", "exact"], "tactic_count": 5}
{"name": "Int.cast_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Cast", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.cast_nonneg_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Cast", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.cast_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Cast", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.cast_strictMono", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Cast", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.cast_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Cast", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.cast_nonpos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Cast", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.cast_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Cast", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.cast_lt_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Cast", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.cast_min", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Cast", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.cast_max", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Cast", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.cast_abs", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Cast", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Int.cast_one_le_of_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Cast", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.cast_le_neg_one_of_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Cast", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Int.cast_le_neg_one_or_one_le_cast_of_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Cast", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.nneg_mul_add_sq_of_abs_le_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Cast", "is_tactic_proof": false, "tactics": ["have", "have", "rwa", "have", "have", "rwa", "rw", "rcases", "exact", "simp", "exact"], "tactic_count": 11}
{"name": "OrderDual.instIntCast", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Cast", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instAddGroupWithOne", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Cast", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instAddCommGroupWithOne", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Cast", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toDual_intCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Cast", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofDual_intCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Cast", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lex.instIntCast", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Cast", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lex.instAddGroupWithOne", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Cast", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lex.instAddCommGroupWithOne", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Cast", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toLex_intCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Cast", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofLex_intCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Cast", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCone.instSetLike", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Cone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instPartialOrderRingCone", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Cone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCone.instRingConeClass", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Cone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCone.mem_mk", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Cone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCone.coe_set_mk", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Cone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCone.nonneg", "kind": "definition", "module": "Mathlib.Algebra.Order.Ring.Cone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCone.nonneg_toSubsemiring", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Cone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCone.nonneg_toAddGroupCone", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Cone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCone.mem_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Cone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCone.coe_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Cone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCone.nonneg.hasMemOrNegMem", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Cone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOrderedRing.mkOfCone", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Cone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instOrderedRingOfIsStrictOrderedRing", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOrderedRing.of_mul_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsStrictOrderedRing.of_mul_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOrderedRing.toIsStrictOrderedRing", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsStrictOrderedRing.toIsOrderedRing", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidWithOne.toCharZero", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsStrictOrderedRing.toCharZero", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsStrictOrderedRing.toNoMaxOrder", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsStrictOrderedRing.noZeroDivisors", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsStrictOrderedRing.isDomain", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_add_le_one_sub_mul_one_add", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Defs", "is_tactic_proof": true, "tactics": ["rw", "gcongr"], "tactic_count": 2}
{"name": "one_add_le_one_add_mul_one_sub", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Defs", "is_tactic_proof": true, "tactics": ["rw", "gcongr"], "tactic_count": 2}
{"name": "one_sub_le_one_sub_mul_one_add", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Defs", "is_tactic_proof": true, "tactics": ["rw", "gcongr"], "tactic_count": 2}
{"name": "one_sub_le_one_add_mul_one_sub", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Defs", "is_tactic_proof": true, "tactics": ["rw", "gcongr"], "tactic_count": 2}
{"name": "instNoMaxOrderOfNontrivial", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instNoMinOrderOfNontrivial", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.cast_finsetSup'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.cast_finsetInf'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.cast_finsetSup", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mul_sup₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Finset", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "insert"], "tactic_count": 4}
{"name": "Finset.sup_mul₀", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Finset", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "insert"], "tactic_count": 4}
{"name": "geom_sum_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.GeomSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "geom_sum_alternating_of_le_neg_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.GeomSum", "is_tactic_proof": true, "tactics": ["have", "induction", "zero", "succ", "simp", "split_ifs", "rw", "exact", "grw", "gcongr", "simpa"], "tactic_count": 11}
{"name": "geom_sum_pos_and_lt_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.GeomSum", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact", "clear", "intro", "rw", "exact", "mul_neg_of_neg_of_pos"], "tactic_count": 8}
{"name": "geom_sum_alternating_of_lt_neg_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.GeomSum", "is_tactic_proof": true, "tactics": ["have", "refine", "simp", "clear", "intro", "simp", "split_ifs", "rw", "exact", "grw", "gcongr", "simpa"], "tactic_count": 12}
{"name": "geom_sum_pos'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.GeomSum", "is_tactic_proof": true, "tactics": ["obtain", "cases", "simp", "obtain", "exact", "exact"], "tactic_count": 6}
{"name": "Odd.geom_sum_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.GeomSum", "is_tactic_proof": true, "tactics": ["rcases", "exact", "simp", "rw", "rcases", "have", "simp", "exact", "simp", "exact"], "tactic_count": 10}
{"name": "geom_sum_pos_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.GeomSum", "is_tactic_proof": true, "tactics": ["refine", "rw", "refine", "simpa", "rintro", "exact", "exact"], "tactic_count": 7}
{"name": "geom_sum_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.GeomSum", "is_tactic_proof": true, "tactics": ["obtain", "cases", "simp", "rw", "obtain", "have", "split_ifs", "exact", "exact", "exact"], "tactic_count": 10}
{"name": "geom_sum_eq_zero_iff_neg_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.GeomSum", "is_tactic_proof": true, "tactics": ["refine", "contrapose", "have", "rcases", "rw", "simp", "exact"], "tactic_count": 7}
{"name": "geom_sum_neg_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.GeomSum", "is_tactic_proof": true, "tactics": ["rw", "or_comm,"], "tactic_count": 2}
{"name": "Nat.pred_mul_geom_sum_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.GeomSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.geom_sum_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.GeomSum", "is_tactic_proof": true, "tactics": ["refine", "rcases", "rw", "exact", "rw", "exact"], "tactic_count": 6}
{"name": "Nat.geom_sum_Ico_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.GeomSum", "is_tactic_proof": true, "tactics": ["rcases", "rw", "exact", "rw", "calc", "rw"], "tactic_count": 6}
{"name": "Nat.geomSum_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.GeomSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instComplSubtypeProdAndEqHMulFstSndOfNatHAdd", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Idempotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_of_mul_eq_add_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Idempotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_eq_zero_add_eq_one_ext_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Idempotent", "is_tactic_proof": true, "tactics": ["refine", "rw", "rw"], "tactic_count": 3}
{"name": "mul_eq_zero_add_eq_one_ext_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Idempotent", "is_tactic_proof": true, "tactics": ["refine", "rw", "rw", "rw"], "tactic_count": 4}
{"name": "instPartialOrderSubtypeProdAndEqHMulFstSndOfNatHAdd", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Idempotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instSemilatticeSupSubtypeProdAndEqHMulFstSndOfNatHAdd", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Idempotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instBooleanAlgebraSubtypeProdAndEqHMulFstSndOfNatHAdd", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Idempotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instSemilatticeInfSubtypeIsIdempotentElem", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Idempotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instOrderTopSubtypeIsIdempotentElem", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Idempotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instOrderBotSubtypeIsIdempotentElem", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Idempotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instLatticeSubtypeIsIdempotentElem", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Idempotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instBooleanAlgebraSubtypeIsIdempotentElem", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Idempotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.isIdempotentElemMulZeroAddOne", "kind": "definition", "module": "Mathlib.Algebra.Order.Ring.Idempotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.isOrderedRing", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.isStrictOrderedRing", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.instIsStrictOrderedRing", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Int", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.isCompl_even_odd", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Int", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.cast_natAbs", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Int", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.two_le_iff_pos_of_even", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Int", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.add_two_le_iff_lt_of_even_sub", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Int", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Nat.exists_add_mul_eq_of_gcd_dvd_of_mul_pred_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Int", "is_tactic_proof": true, "tactics": ["obtain", "have", "exact", "obtain", "have", "exact", "rw", "have", "let", "let", "refine", "have", "rw", "mul_comm", "rw", "by_contra", "replace", "apply", "have", "rw", "calc", "n"], "tactic_count": 22}
{"name": "IsStrictOrderedRing.int_mem_Icc_of_mul_mem_Ioo", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Interval", "is_tactic_proof": true, "tactics": ["simp", "grind"], "tactic_count": 2}
{"name": "IsStrictOrderedRing.int_eq_of_mul_mem_Ioo", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Interval", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsNonarchimedean.add_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.IsNonarchimedean", "is_tactic_proof": true, "tactics": ["apply", "rw", "exact"], "tactic_count": 3}
{"name": "IsNonarchimedean.nsmul_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.IsNonarchimedean", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "apply", "simpa"], "tactic_count": 6}
{"name": "IsNonarchimedean.nmul_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.IsNonarchimedean", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsNonarchimedean.apply_natCast_le_one_of_isNonarchimedean", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.IsNonarchimedean", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsNonarchimedean.apply_intCast_le_one_of_isNonarchimedean", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.IsNonarchimedean", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "IsNonarchimedean.add_eq_right_of_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.IsNonarchimedean", "is_tactic_proof": true, "tactics": ["by_contra", "have", "apply", "calc", "f", "rw", "exact"], "tactic_count": 7}
{"name": "IsNonarchimedean.add_eq_left_of_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.IsNonarchimedean", "is_tactic_proof": true, "tactics": ["by_contra", "have", "apply", "calc", "f", "rw", "apply"], "tactic_count": 7}
{"name": "IsNonarchimedean.add_eq_max_of_ne", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.IsNonarchimedean", "is_tactic_proof": true, "tactics": ["rcases", "rw", "exact", "rw", "exact"], "tactic_count": 5}
{"name": "IsNonarchimedean.multiset_image_add_of_nonempty", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.IsNonarchimedean", "is_tactic_proof": true, "tactics": ["induction", "empty", "cons", "simp", "by_cases", "simp", "obtain", "rcases", "exact", "exact"], "tactic_count": 10}
{"name": "IsNonarchimedean.finset_image_add_of_nonempty", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.IsNonarchimedean", "is_tactic_proof": true, "tactics": ["apply", "simp_all"], "tactic_count": 2}
{"name": "IsNonarchimedean.multiset_image_add", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.IsNonarchimedean", "is_tactic_proof": true, "tactics": ["induction", "empty", "cons", "h", "obtain", "exact"], "tactic_count": 6}
{"name": "IsNonarchimedean.finset_image_add", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.IsNonarchimedean", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "IsNonarchimedean.multiset_powerset_image_add", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.IsNonarchimedean", "is_tactic_proof": true, "tactics": ["set", "obtain", "have", "rw", "exact", "exact"], "tactic_count": 6}
{"name": "IsNonarchimedean.finset_powerset_image_add", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.IsNonarchimedean", "is_tactic_proof": true, "tactics": ["set", "obtain", "exact"], "tactic_count": 3}
{"name": "IsNonarchimedean.apply_sum_le_sup_of_isNonarchimedean", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.IsNonarchimedean", "is_tactic_proof": true, "tactics": ["induction", "singleton", "cons", "simp", "rw", "rcases", "exact", "exact"], "tactic_count": 8}
{"name": "IsNonarchimedean.add_pow_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.IsNonarchimedean", "is_tactic_proof": false, "tactics": ["obtain", "simp", "forall_true_left]", "refine", "simp", "rw", "exact"], "tactic_count": 7}
{"name": "Nat.instIsStrictOrderedRing", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Nat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.instLinearOrderedCommMonoidWithZero", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Nat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.isCompl_even_odd", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Nat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MulOpposite.instIsOrderedRing", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddOpposite.instIsOrderedRing", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingPreordering.toSubsemiring_le_toSubsemiring", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Ordering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingPreordering.toSubsemiring_lt_toSubsemiring", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Ordering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingPreordering.toSubsemiring_mono", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Ordering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingPreordering.toSubsemiring_strictMono", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Ordering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingPreordering.unitsInv_mem", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Ordering.Basic", "is_tactic_proof": true, "tactics": ["have", "simp_all"], "tactic_count": 2}
{"name": "RingPreordering.inv_mem", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Ordering.Basic", "is_tactic_proof": true, "tactics": ["have", "field_simp", "simp_all"], "tactic_count": 3}
{"name": "RingPreordering.mem_of_isSumSq", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Ordering.Basic", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "RingPreordering.mk'", "kind": "definition", "module": "Mathlib.Algebra.Order.Ring.Ordering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingPreordering.mem_mk'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Ordering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingPreordering.coe_mk'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Ordering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingPreordering.one_notMem_supportAddSubgroup", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Ordering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingPreordering.one_notMem_support", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Ordering.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "RingPreordering.supportAddSubgroup_ne_top", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Ordering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingPreordering.support_ne_top", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Ordering.Basic", "is_tactic_proof": true, "tactics": ["apply_fun", "simpa"], "tactic_count": 2}
{"name": "RingPreordering.IsOrdering.mk'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Ordering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingPreordering.HasIdealSupport.smul_mem", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Ordering.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "RingPreordering.HasIdealSupport.neg_smul_mem", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Ordering.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "RingPreordering.hasIdealSupport_of_isUnit_two", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Ordering.Basic", "is_tactic_proof": true, "tactics": ["rw", "intro", "rcases", "set", "set", "rw", "ring_nf", "aesop"], "tactic_count": 8}
{"name": "RingPreordering.instHasIdealSupportOfFactIsUnitOfNat", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Ordering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingPreordering.eq_zero_of_mem_of_neg_mem", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Ordering.Basic", "is_tactic_proof": true, "tactics": ["by_contra", "have", "field_simp", "exact"], "tactic_count": 4}
{"name": "RingPreordering.supportAddSubgroup_eq_bot", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Ordering.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "RingPreordering.instHasIdealSupport", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Ordering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingPreordering.support_eq_bot", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Ordering.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "RingPreordering.instIsPrimeSupport", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Ordering.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "RingPreordering.isOrdering_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Ordering.Basic", "is_tactic_proof": true, "tactics": ["refine", "by_contra", "have", "have", "simp_all", "have", "refine", "by_contra", "have", "have", "have", "have", "cases"], "tactic_count": 13}
{"name": "RingPreordering.instSetLike", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Ordering.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingPreordering.instPartialOrder", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Ordering.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingPreordering.instSubsemiringClass", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Ordering.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingPreordering.mem_of_isSquare", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Ordering.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingPreordering.mul_self_mem", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Ordering.Defs", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "RingPreordering.pow_two_mem", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Ordering.Defs", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "RingPreordering.neg_one_notMem", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Ordering.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingPreordering.toSubsemiring_injective", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Ordering.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingPreordering.toSubsemiring_inj", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Ordering.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingPreordering.mem_toSubsemiring", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Ordering.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingPreordering.coe_toSubsemiring", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Ordering.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingPreordering.mem_mk", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Ordering.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingPreordering.coe_set_mk", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Ordering.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingPreordering.copy", "kind": "definition", "module": "Mathlib.Algebra.Order.Ring.Ordering.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingPreordering.mem_copy", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Ordering.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingPreordering.copy_eq", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Ordering.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingPreordering.supportAddSubgroup", "kind": "definition", "module": "Mathlib.Algebra.Order.Ring.Ordering.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingPreordering.mem_supportAddSubgroup", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Ordering.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingPreordering.coe_supportAddSubgroup", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Ordering.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingPreordering.hasIdealSupport_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Ordering.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingPreordering.instHasIdealSupportOfHasMemOrNegMem", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Ordering.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingPreordering.support", "kind": "definition", "module": "Mathlib.Algebra.Order.Ring.Ordering.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingPreordering.mem_support", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Ordering.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingPreordering.coe_support", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Ordering.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingPreordering.supportAddSubgroup_eq", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Ordering.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.pow_add_mul_le_add_pow_of_sq_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_add_mul_le_pow_of_sq_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Pow", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "one_add_mul_le_pow'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pow_add_mul_le_add_pow_of_sq_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.pow_add_mul_le_add_pow", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pow_add_mul_le_add_pow", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_add_le_pow_of_two_add_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_add_mul_le_pow", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_add_mul_sub_le_pow", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Pow", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "instIsOrderedRingProd", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.instIsOrderedAddMonoid", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.instIsStrictOrderedRing", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArchimedeanClass.FiniteElement", "kind": "definition", "module": "Mathlib.Algebra.Order.Ring.StandardPart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArchimedeanClass.FiniteElement.instCommRing", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.StandardPart", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "ArchimedeanClass.FiniteElement.instIsDomain", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.StandardPart", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "ArchimedeanClass.FiniteElement.instValuationRing", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.StandardPart", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "ArchimedeanClass.FiniteElement.instLinearOrder", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.StandardPart", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "ArchimedeanClass.FiniteElement.instIsStrictOrderedRing", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.StandardPart", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "ArchimedeanClass.FiniteElement.val_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.StandardPart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArchimedeanClass.FiniteElement.val_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.StandardPart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArchimedeanClass.FiniteElement.val_add", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.StandardPart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArchimedeanClass.FiniteElement.val_sub", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.StandardPart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArchimedeanClass.FiniteElement.val_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.StandardPart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArchimedeanClass.FiniteElement.ext", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.StandardPart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArchimedeanClass.FiniteElement.mk", "kind": "definition", "module": "Mathlib.Algebra.Order.Ring.StandardPart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArchimedeanClass.FiniteElement.mk_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.StandardPart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArchimedeanClass.FiniteElement.mk_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.StandardPart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArchimedeanClass.FiniteElement.mk_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.StandardPart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArchimedeanClass.FiniteElement.mk_intCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.StandardPart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArchimedeanClass.FiniteElement.neg_mk", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.StandardPart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArchimedeanClass.FiniteElement.mk_add_mk", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.StandardPart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArchimedeanClass.FiniteElement.mk_sub_mk", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.StandardPart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArchimedeanClass.FiniteElement.mk_mul_mk", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.StandardPart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArchimedeanClass.FiniteElement.mk_le_mk", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.StandardPart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArchimedeanClass.FiniteElement.mk_lt_mk", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.StandardPart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArchimedeanClass.FiniteElement.not_isUnit_iff_mk_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.StandardPart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArchimedeanClass.FiniteElement.isUnit_iff_mk_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.StandardPart", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ArchimedeanClass.FiniteElement.instRatCast", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.StandardPart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArchimedeanClass.FiniteElement.mk_ratCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.StandardPart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArchimedeanClass.FiniteElement.instFloorRing", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.StandardPart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArchimedeanClass.FiniteResidueField", "kind": "definition", "module": "Mathlib.Algebra.Order.Ring.StandardPart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArchimedeanClass.FiniteResidueField.instField", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.StandardPart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Order.Ring.StandardPart.0.ArchimedeanClass.FiniteResidueField.ordConnected_preimage_mk'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.StandardPart", "is_tactic_proof": true, "tactics": ["refine", "rintro", "have", "rw", "mem_nonunits_iff,", "apply"], "tactic_count": 6}
{"name": "ArchimedeanClass.FiniteResidueField.instLinearOrder", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.StandardPart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArchimedeanClass.FiniteResidueField.mk", "kind": "definition", "module": "Mathlib.Algebra.Order.Ring.StandardPart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArchimedeanClass.FiniteResidueField.ind", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.StandardPart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArchimedeanClass.FiniteResidueField.ordConnected_preimage_mk", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.StandardPart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArchimedeanClass.FiniteResidueField.mk_eq_mk", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.StandardPart", "is_tactic_proof": true, "tactics": ["apply", "rw"], "tactic_count": 2}
{"name": "ArchimedeanClass.FiniteResidueField.mk_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.StandardPart", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "ArchimedeanClass.FiniteResidueField.mk_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.StandardPart", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ArchimedeanClass.FiniteResidueField.mk_le_mk", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.StandardPart", "is_tactic_proof": true, "tactics": ["refine", "rw", "rfl"], "tactic_count": 3}
{"name": "ArchimedeanClass.FiniteResidueField.mk_lt_mk", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.StandardPart", "is_tactic_proof": true, "tactics": ["refine", "rw", "rfl"], "tactic_count": 3}
{"name": "ArchimedeanClass.FiniteResidueField.lt_of_mk_lt_mk", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.StandardPart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Order.Ring.StandardPart.0.ArchimedeanClass.FiniteResidueField.mul_le_mul_of_nonneg_left'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.StandardPart", "is_tactic_proof": false, "tactics": ["induction", "mk", "induction", "mk", "induction", "mk", "rw", "rw", "rw", "grind"], "tactic_count": 10}
{"name": "ArchimedeanClass.FiniteResidueField.instIsOrderedRing", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.StandardPart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArchimedeanClass.FiniteResidueField.instArchimedean", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.StandardPart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArchimedeanClass.FiniteResidueField.mk_ratCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.StandardPart", "is_tactic_proof": true, "tactics": ["change", "cases", "div", "rw", "simp_all"], "tactic_count": 5}
{"name": "ArchimedeanClass.FiniteResidueField.ofArchimedean", "kind": "definition", "module": "Mathlib.Algebra.Order.Ring.StandardPart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArchimedeanClass.FiniteResidueField.ofArchimedean_apply", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.StandardPart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArchimedeanClass.FiniteResidueField.ofArchimedean_injective", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.StandardPart", "is_tactic_proof": true, "tactics": ["rw", "intro", "contrapose", "rw", "exact"], "tactic_count": 5}
{"name": "ArchimedeanClass.FiniteResidueField.ofArchimedean_inj", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.StandardPart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArchimedeanClass.stdPart", "kind": "definition", "module": "Mathlib.Algebra.Order.Ring.StandardPart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArchimedeanClass.stdPart_of_mk_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.StandardPart", "is_tactic_proof": true, "tactics": ["rw", "congr", "exact"], "tactic_count": 3}
{"name": "ArchimedeanClass.stdPart_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.StandardPart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArchimedeanClass.stdPart_monotoneOn", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.StandardPart", "is_tactic_proof": true, "tactics": ["intro", "unfold", "rw", "apply", "rwa"], "tactic_count": 5}
{"name": "ArchimedeanClass.stdPart_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.StandardPart", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "add_le_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "add_le_mul'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_nonneg_iff_right_nonneg_of_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_nonneg_iff_left_nonneg_of_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nonpos_of_mul_nonneg_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nonpos_of_mul_nonneg_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.inv_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.inv_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cmp_mul_pos_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cmp_mul_pos_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_max_of_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_min_of_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "max_mul_of_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "min_mul_of_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_of_mul_le_of_one_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nonneg_le_nonneg_of_sq_le_sq", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_self_le_mul_self_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_self_lt_mul_self_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_self_inj", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sign_cases_of_C_mul_pow_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["have", "refine", "simpa"], "tactic_count": 3}
{"name": "mul_pos_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_nonneg_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_nonneg_of_three", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["iterate", "have", "have", "have", "aesop"], "tactic_count": 5}
{"name": "mul_nonneg_iff_pos_imp_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["refine", "simp_rw", "have", "have", "tauto"], "tactic_count": 5}
{"name": "mul_le_mul_left_of_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_le_mul_right_of_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_lt_mul_left_of_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_lt_mul_right_of_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lt_of_mul_lt_mul_of_nonpos_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lt_of_mul_lt_mul_of_nonpos_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cmp_mul_neg_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cmp_mul_neg_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_self_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "rw", "exact", "intro", "rcases", "exacts"], "tactic_count": 7}
{"name": "nonneg_of_mul_nonpos_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nonneg_of_mul_nonpos_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pos_of_mul_neg_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pos_of_mul_neg_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "neg_iff_pos_of_mul_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pos_iff_neg_of_mul_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sq_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["obtain", "exact", "obtain", "have", "calc"], "tactic_count": 5}
{"name": "sq_nonpos_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["trans", "rw", "exact"], "tactic_count": 3}
{"name": "mul_self_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "mul_self_add_mul_self_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "eq_zero_of_mul_self_add_mul_self_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "max_mul_mul_le_max_mul_max", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "two_mul_le_add_sq", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["simpa", "mul_add_mul_le_mul_add_mul"], "tactic_count": 2}
{"name": "four_mul_le_sq_add", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["calc"], "tactic_count": 1}
{"name": "two_mul_le_add_of_sq_eq_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["apply", "conv_rhs", "convert", "rw"], "tactic_count": 4}
{"name": "mul_neg_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mul_nonpos_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mul_nonneg_iff_neg_imp_nonpos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mul_nonpos_iff_pos_imp_nonpos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "mul_nonpos_iff_neg_imp_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "neg_one_lt_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sub_one_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_self_le_mul_self_of_le_of_neg_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sub_mul_sub_nonneg_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw", "and_iff_left_of_imp"], "tactic_count": 2}
{"name": "sub_mul_sub_nonpos_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "sub_mul_sub_pos_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw", "or_comm]"], "tactic_count": 2}
{"name": "sub_mul_sub_neg_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Rat.mkRat_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Rat", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Rat.ofScientific_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Rat", "is_tactic_proof": true, "tactics": ["rw", "cases", "rw", "exact", "grind"], "tactic_count": 5}
{"name": "NNRatCast.toOfScientific", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRatCast.toOfScientific_def", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.cast_ofScientific", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.divInt_le_divInt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Rat", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Rat.lt_iff_le_not_ge", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.linearOrder", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.mkRat_nonneg_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.mkRat_pos_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Rat", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Rat.mkRat_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.mkRat_nonpos_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Rat", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Rat.mkRat_nonpos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Rat", "is_tactic_proof": true, "tactics": ["obtain", "simp", "exact"], "tactic_count": 3}
{"name": "Rat.mkRat_neg_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Rat", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Rat.mkRat_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.instDistribLattice", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.instLattice", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.instSemilatticeInf", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.instSemilatticeSup", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.instInf", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.instSup", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.instPartialOrder", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.instPreorder", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.instAddLeftMono", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.num_nonpos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Rat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Rat.num_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.num_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.div_lt_div_iff_mul_lt_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Rat", "is_tactic_proof": true, "tactics": ["simp", "apply", "simp", "simp"], "tactic_count": 4}
{"name": "Rat.lt_one_iff_num_lt_denom", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Rat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Rat.abs_def", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Rat", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Rat.abs_def'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Rat", "is_tactic_proof": true, "tactics": ["refine", "simp"], "tactic_count": 2}
{"name": "Rat.num_abs_eq_abs_num", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Rat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Rat.den_abs_eq_den", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Unbundled.Rat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Units.index_posSubgroup", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.Units", "is_tactic_proof": true, "tactics": ["rw", "refine", "obtain", "simp", "simp"], "tactic_count": 5}
{"name": "WithTop.instMulZeroClass", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.coe_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.mul_top'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.mul_top", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "WithTop.top_mul'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.top_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "WithTop.top_mul_top", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.mul_def", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "WithTop.mul_eq_top_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "WithTop.mul_coe_eq_bind", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.coe_mul_eq_bind", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.untopD_zero_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": true, "tactics": ["by_cases", "by_cases", "cases", "cases", "rw"], "tactic_count": 5}
{"name": "WithTop.mul_ne_top", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WithTop.mul_lt_top", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "WithTop.instNoZeroDivisors", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": true, "tactics": ["refine", "rw", "rcases", "exact"], "tactic_count": 4}
{"name": "WithTop.mul_right_strictMono", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": true, "tactics": ["lift", "rintro", "lift", "simp", "exact"], "tactic_count": 5}
{"name": "WithTop.mul_left_strictMono", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": true, "tactics": ["lift", "rintro", "lift", "simp", "exact"], "tactic_count": 5}
{"name": "WithTop.instMulZeroOneClass", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.withTopMap", "kind": "definition", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.instSemigroupWithZero", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.instMonoidWithZero", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.coe_pow", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.top_pow", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.pow_eq_top_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "WithTop.pow_ne_top_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WithTop.pow_lt_top_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "WithTop.eq_top_of_pow", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.pow_ne_top", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.pow_lt_top", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.instCommMonoidWithZero", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.instNonUnitalNonAssocSemiring", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.instNonAssocSemiring", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.instNonUnitalSemiring", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.instSemiring", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.instCommSemiring", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.instIsOrderedRing", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.withTopMap", "kind": "definition", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.mul_lt_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": true, "tactics": ["have", "lift", "lift", "obtain", "rw", "exact", "obtain", "rw", "exact", "lift", "lift", "norm_cast", "obtain", "rw", "exact", "exact"], "tactic_count": 16}
{"name": "WithTop.pow_right_strictMono", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.pow_lt_pow_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.instMulZeroClass", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.coe_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.mul_bot'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.mul_bot", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "WithBot.bot_mul'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.bot_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "WithBot.bot_mul_bot", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.mul_def", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "WithBot.mul_eq_bot_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "WithBot.mul_coe_eq_bind", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.coe_mul_eq_bind", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.unbotD_zero_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": true, "tactics": ["by_cases", "by_cases", "cases", "cases", "rw"], "tactic_count": 5}
{"name": "WithBot.mul_ne_bot", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.bot_lt_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.instNoZeroDivisors", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.instMulZeroOneClass", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.instSemigroupWithZero", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.instMonoidWithZero", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.coe_pow", "kind": "theorem", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.instCommMonoidWithZero", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.instCommSemiring", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.instPosMulMono", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.instMulPosMono", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.instPosMulStrictMono", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.instMulPosStrictMono", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.instPosMulReflectLT", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.instMulPosReflectLT", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.instPosMulReflectLE", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.instMulPosReflectLE", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.instIsOrderedRing", "kind": "instance", "module": "Mathlib.Algebra.Order.Ring.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "round", "kind": "definition", "module": "Mathlib.Algebra.Order.Round", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "round_eq_div", "kind": "theorem", "module": "Mathlib.Algebra.Order.Round", "is_tactic_proof": false, "tactics": ["rw", "split_ifs", "rw", "simp", "simp", "suffices", "refine", "apply", "have", "suffices", "contrapose", "grw", "simp"], "tactic_count": 13}
{"name": "round_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.Round", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "round_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Round", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "round_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.Round", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "round_ofNat", "kind": "theorem", "module": "Mathlib.Algebra.Order.Round", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "round_intCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.Round", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "round_eq_half_ceil_two_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Round", "is_tactic_proof": true, "tactics": ["rcases", "rw", "rcases", "obtain", "rw", "refine", "exact", "rw"], "tactic_count": 8}
{"name": "round_add_intCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.Round", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "round_add_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Round", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "round_sub_intCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.Round", "is_tactic_proof": true, "tactics": ["rw", "norm_cast", "rw"], "tactic_count": 3}
{"name": "round_sub_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Round", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "round_add_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.Round", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "round_add_ofNat", "kind": "theorem", "module": "Mathlib.Algebra.Order.Round", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "round_sub_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Order.Round", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "round_sub_ofNat", "kind": "theorem", "module": "Mathlib.Algebra.Order.Round", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "round_intCast_add", "kind": "theorem", "module": "Mathlib.Algebra.Order.Round", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "round_natCast_add", "kind": "theorem", "module": "Mathlib.Algebra.Order.Round", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "round_ofNat_add", "kind": "theorem", "module": "Mathlib.Algebra.Order.Round", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "abs_sub_round_eq_min", "kind": "theorem", "module": "Mathlib.Algebra.Order.Round", "is_tactic_proof": true, "tactics": ["simp_rw", "rcases", "rw", "have", "replace", "simpa", "rw"], "tactic_count": 7}
{"name": "round_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Round", "is_tactic_proof": true, "tactics": ["rw", "rcases", "conv_rhs", "simpa", "rw", "conv_rhs", "rw", "norm_cast", "rwa"], "tactic_count": 9}
{"name": "round_eq", "kind": "theorem", "module": "Mathlib.Algebra.Order.Round", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "round_eq_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Round", "is_tactic_proof": true, "tactics": ["norm_num"], "tactic_count": 1}
{"name": "round_two_inv", "kind": "theorem", "module": "Mathlib.Algebra.Order.Round", "is_tactic_proof": true, "tactics": ["norm_num"], "tactic_count": 1}
{"name": "round_neg_two_inv", "kind": "theorem", "module": "Mathlib.Algebra.Order.Round", "is_tactic_proof": true, "tactics": ["norm_num"], "tactic_count": 1}
{"name": "round_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Round", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "abs_sub_round", "kind": "theorem", "module": "Mathlib.Algebra.Order.Round", "is_tactic_proof": true, "tactics": ["rw", "have", "have", "constructor"], "tactic_count": 4}
{"name": "abs_sub_round_div_natCast_eq", "kind": "theorem", "module": "Mathlib.Algebra.Order.Round", "is_tactic_proof": true, "tactics": ["rcases", "simp", "have", "rw"], "tactic_count": 4}
{"name": "sub_half_lt_round", "kind": "theorem", "module": "Mathlib.Algebra.Order.Round", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "round_le_add_half", "kind": "theorem", "module": "Mathlib.Algebra.Order.Round", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Int.map_round", "kind": "theorem", "module": "Mathlib.Algebra.Order.Round", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "smul_mem_closure_star_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.Star.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "add", "mem", "induction", "zero", "add", "mem", "obtain", "obtain", "exact"], "tactic_count": 11}
{"name": "StarOrderedRing.of_le_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarOrderedRing.toIsOrderedAddMonoid", "kind": "instance", "module": "Mathlib.Algebra.Order.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarOrderedRing.toExistsAddOfLE", "kind": "instance", "module": "Mathlib.Algebra.Order.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarOrderedRing.nonneg_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Star.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "StarOrderedRing.pos_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Star.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "StarOrderedRing.lt_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Star.Basic", "is_tactic_proof": true, "tactics": ["rw", "congr", "simp"], "tactic_count": 3}
{"name": "StarOrderedRing.of_nonneg_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarOrderedRing.of_nonneg_iff'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSelfAdjoint.mono", "kind": "theorem", "module": "Mathlib.Algebra.Order.Star.Basic", "is_tactic_proof": true, "tactics": ["rw", "obtain", "rw", "congr", "refine", "rintro", "simp"], "tactic_count": 7}
{"name": "IsSelfAdjoint.of_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LE.le.star_eq", "kind": "theorem", "module": "Mathlib.Algebra.Order.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "star_mul_self_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_star_self_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Star.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsSelfAdjoint.mul_self_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Star.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsStarProjection.nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "star_left_conjugate_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Star.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "obtain", "convert", "rw", "calc"], "tactic_count": 6}
{"name": "star_right_conjugate_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Star.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsSelfAdjoint.conjugate_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Star.Basic", "is_tactic_proof": true, "tactics": ["nth_rewrite"], "tactic_count": 1}
{"name": "conjugate_nonneg_of_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "star_left_conjugate_le_conjugate", "kind": "theorem", "module": "Mathlib.Algebra.Order.Star.Basic", "is_tactic_proof": true, "tactics": ["rw", "obtain", "simp_rw", "exact"], "tactic_count": 4}
{"name": "star_right_conjugate_le_conjugate", "kind": "theorem", "module": "Mathlib.Algebra.Order.Star.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsSelfAdjoint.conjugate_le_conjugate", "kind": "theorem", "module": "Mathlib.Algebra.Order.Star.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "conjugate_le_conjugate_of_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "star_le_star_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Star.Basic", "is_tactic_proof": true, "tactics": ["suffices", "intro", "rw", "obtain", "refine", "refine", "rintro", "exact"], "tactic_count": 8}
{"name": "star_lt_star_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Star.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "simpa"], "tactic_count": 3}
{"name": "star_le_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Star.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "star_lt_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Star.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "star_nonneg_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Star.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "star_nonpos_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Star.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "star_pos_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Star.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "star_neg_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Star.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "star_left_conjugate_lt_conjugate", "kind": "theorem", "module": "Mathlib.Algebra.Order.Star.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "star_right_conjugate_lt_conjugate", "kind": "theorem", "module": "Mathlib.Algebra.Order.Star.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "star_left_conjugate_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Star.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "star_right_conjugate_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Star.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "star_mul_self_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Star.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "mul_star_self_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Star.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "instZeroLEOneClass", "kind": "instance", "module": "Mathlib.Algebra.Order.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_le_star_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Star.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "star_le_one_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Star.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "one_lt_star_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Star.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "star_lt_one_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Star.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsSelfAdjoint.sq_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Star.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsUnit.star_right_conjugate_nonneg_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Star.Basic", "is_tactic_proof": true, "tactics": ["refine", "obtain", "have", "rwa"], "tactic_count": 4}
{"name": "IsUnit.star_left_conjugate_nonneg_iff", "kind": "theorem", "module": "Mathlib.Algebra.Order.Star.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MulOpposite.instStarOrderedRing", "kind": "instance", "module": "Mathlib.Algebra.Order.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsOrderedModule", "kind": "instance", "module": "Mathlib.Algebra.Order.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instPosSMulStrictMono", "kind": "instance", "module": "Mathlib.Algebra.Order.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsStrictOrderedModuleOfIsCancelAdd", "kind": "instance", "module": "Mathlib.Algebra.Order.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarModule.smul_lt_smul_of_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarRingHom.map_le_map_of_map_star", "kind": "theorem", "module": "Mathlib.Algebra.Order.Star.Basic", "is_tactic_proof": true, "tactics": ["rw", "obtain", "refine", "have", "induction", "all_goals"], "tactic_count": 6}
{"name": "StarRingHomClass.instOrderHomClass", "kind": "instance", "module": "Mathlib.Algebra.Order.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarRingEquivClass.instOrderIsoClass", "kind": "instance", "module": "Mathlib.Algebra.Order.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.instStarOrderedRing", "kind": "instance", "module": "Mathlib.Algebra.Order.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsStarProjection.one_sub_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsStarProjection.le_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsStarProjection.mem_Icc", "kind": "theorem", "module": "Mathlib.Algebra.Order.Star.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsStarProjection.le_of_mul_eq_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsStarProjection.le_of_mul_eq_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "conjneg_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Order.Star.Conjneg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "conjneg_pos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Star.Conjneg", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "conjneg_nonpos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Star.Conjneg", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "conjneg_neg'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Star.Conjneg", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Pi.instStarOrderedRing", "kind": "instance", "module": "Mathlib.Algebra.Order.Star.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instStarOrderedRing", "kind": "instance", "module": "Mathlib.Algebra.Order.Star.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "add_tsub_cancel_iff_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Sub.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tsub_add_cancel_iff_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Sub.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "tsub_eq_zero_iff_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Sub.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "tsub_self", "kind": "theorem", "module": "Mathlib.Algebra.Order.Sub.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tsub_le_self", "kind": "theorem", "module": "Mathlib.Algebra.Order.Sub.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zero_tsub", "kind": "theorem", "module": "Mathlib.Algebra.Order.Sub.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tsub_self_add", "kind": "theorem", "module": "Mathlib.Algebra.Order.Sub.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tsub_pos_iff_not_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Sub.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "tsub_pos_of_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Sub.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tsub_lt_of_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Sub.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddLECancellable.tsub_le_tsub_iff_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Sub.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "apply"], "tactic_count": 3}
{"name": "AddLECancellable.tsub_right_inj", "kind": "theorem", "module": "Mathlib.Algebra.Order.Sub.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "tsub_le_tsub_iff_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Sub.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tsub_right_inj", "kind": "theorem", "module": "Mathlib.Algebra.Order.Sub.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CanonicallyOrderedAddCommMonoid.toAddCancelCommMonoid", "kind": "abbrev", "module": "Mathlib.Algebra.Order.Sub.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tsub_pos_iff_lt", "kind": "theorem", "module": "Mathlib.Algebra.Order.Sub.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "tsub_eq_tsub_min", "kind": "theorem", "module": "Mathlib.Algebra.Order.Sub.Basic", "is_tactic_proof": true, "tactics": ["rcases", "rw", "rw"], "tactic_count": 3}
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{"name": "AddLECancellable.lt_tsub_iff_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Sub.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "tsub_lt_tsub_iff_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Sub.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "tsub_lt_tsub_iff_left_of_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Sub.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tsub_tsub_eq_min", "kind": "theorem", "module": "Mathlib.Algebra.Order.Sub.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "tsub_add_eq_max", "kind": "theorem", "module": "Mathlib.Algebra.Order.Sub.Basic", "is_tactic_proof": true, "tactics": ["rcases", "rw", "rw"], "tactic_count": 3}
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{"name": "tsub_min", "kind": "theorem", "module": "Mathlib.Algebra.Order.Sub.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tsub_add_min", "kind": "theorem", "module": "Mathlib.Algebra.Order.Sub.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
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{"name": "CanonicallyOrderedAdd.toOrderedSub", "kind": "theorem", "module": "Mathlib.Algebra.Order.Sub.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "add_tsub_le_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Sub.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "tsub_le_iff_tsub_le", "kind": "theorem", "module": "Mathlib.Algebra.Order.Sub.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "antitone_const_tsub", "kind": "theorem", "module": "Mathlib.Algebra.Order.Sub.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "add_tsub_le_assoc", "kind": "theorem", "module": "Mathlib.Algebra.Order.Sub.Defs", "is_tactic_proof": true, "tactics": ["grw"], "tactic_count": 1}
{"name": "add_tsub_le_tsub_add", "kind": "theorem", "module": "Mathlib.Algebra.Order.Sub.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
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{"name": "le_tsub_of_add_le_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Sub.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "tsub_nonpos", "kind": "theorem", "module": "Mathlib.Algebra.Order.Sub.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "tsub_tsub", "kind": "theorem", "module": "Mathlib.Algebra.Order.Sub.Defs", "is_tactic_proof": true, "tactics": ["apply", "rw", "rw"], "tactic_count": 3}
{"name": "tsub_add_eq_tsub_tsub", "kind": "theorem", "module": "Mathlib.Algebra.Order.Sub.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tsub_add_eq_tsub_tsub_swap", "kind": "theorem", "module": "Mathlib.Algebra.Order.Sub.Defs", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
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{"name": "AddLECancellable.tsub_eq_of_eq_add", "kind": "theorem", "module": "Mathlib.Algebra.Order.Sub.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddLECancellable.tsub_eq_of_eq_add'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Sub.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddLECancellable.eq_tsub_of_add_eq", "kind": "theorem", "module": "Mathlib.Algebra.Order.Sub.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddLECancellable.eq_tsub_of_add_eq'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Sub.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddLECancellable.tsub_eq_of_eq_add_rev", "kind": "theorem", "module": "Mathlib.Algebra.Order.Sub.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddLECancellable.tsub_eq_of_eq_add_rev'", "kind": "theorem", "module": "Mathlib.Algebra.Order.Sub.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AddLECancellable.add_tsub_cancel_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Sub.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddLECancellable.lt_add_of_tsub_lt_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Sub.Defs", "is_tactic_proof": true, "tactics": ["rw", "refine", "rintro", "simp"], "tactic_count": 4}
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{"name": "eq_tsub_of_add_eq", "kind": "theorem", "module": "Mathlib.Algebra.Order.Sub.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "add_tsub_cancel_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.Sub.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "add_tsub_cancel_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Sub.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tsub_eq_tsub_of_add_eq_add", "kind": "theorem", "module": "Mathlib.Algebra.Order.Sub.Defs", "is_tactic_proof": true, "tactics": ["calc", "a"], "tactic_count": 2}
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{"name": "lt_tsub_of_add_lt_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.Sub.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "instIsSuccArchimedeanMultiplicative", "kind": "instance", "module": "Mathlib.Algebra.Order.SuccPred.TypeTags", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "toIcoDiv_add_left'", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "toIocDiv_sub'", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "toIcoDiv_sub_eq_toIcoDiv_add", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": true, "tactics": ["apply", "rw", "exact"], "tactic_count": 3}
{"name": "toIocDiv_sub_eq_toIocDiv_add", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": true, "tactics": ["apply", "rw", "exact"], "tactic_count": 3}
{"name": "toIcoDiv_sub_eq_toIcoDiv_add'", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "toIocDiv_sub_eq_toIocDiv_add'", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "toIcoMod_nsmul_add'", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "toIocMod_zsmul_add'", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "toIocMod_nsmul_add'", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "toIcoMod_sub_nsmul", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toIcoMod_sub_zsmul'", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "toIcoMod_sub_nsmul'", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toIocMod_sub_zsmul", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "toIocMod_sub_nsmul", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toIocMod_sub_zsmul'", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
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{"name": "toIcoMod_add_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "toIcoMod_add_right'", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "toIocMod_add_right", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "toIocMod_add_right'", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
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{"name": "toIcoMod_add_left'", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "toIocMod_add_left", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "toIocMod_add_left'", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "toIcoMod_sub", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "toIcoMod_sub'", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "toIocMod_sub", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "toIocMod_sub'", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "toIcoMod_sub_eq_sub", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "toIocMod_sub_eq_sub", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "toIcoMod_add_right_eq_add", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "toIocMod_add_right_eq_add", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
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{"name": "toIcoMod_neg'", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "toIocMod_neg", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": true, "tactics": ["simp_rw", "abel"], "tactic_count": 2}
{"name": "toIocMod_neg'", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "toIcoMod_eq_toIcoMod", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": true, "tactics": ["refine", "conv_lhs", "rw", "abel", "rcases", "rw", "rw"], "tactic_count": 7}
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{"name": "AddCommGroup.modEq_iff_toIcoMod_ne_toIocMod", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGroup.modEq_iff_toIcoMod_add_period_eq_toIocMod", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGroup.not_modEq_iff_toIcoMod_eq_toIocMod", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGroup.not_modEq_iff_toIcoDiv_eq_toIocDiv", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AddCommGroup.modEq_iff_toIcoDiv_eq_toIocDiv_add_one", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": true, "tactics": ["rw", "add_one_zsmul,"], "tactic_count": 2}
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{"name": "toIcoMod_le_toIocMod", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "toIocMod_le_toIcoMod_add", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": false, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "toIcoMod_eq_self", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
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{"name": "toIcoMod_toIcoMod", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toIcoMod_toIocMod", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toIocMod_toIocMod", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toIocMod_toIcoMod", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toIcoMod_periodic", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toIocMod_periodic", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toIcoMod_zero_sub_comm", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "toIocMod_zero_sub_comm", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "toIcoDiv_eq_sub", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "toIocDiv_eq_sub", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "toIcoMod_eq_sub", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "toIocMod_eq_sub", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "toIcoMod_add_toIocMod_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "toIocMod_add_toIcoMod_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "QuotientAddGroup.equivIcoMod", "kind": "definition", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientAddGroup.equivIcoMod_coe", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientAddGroup.equivIcoMod_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientAddGroup.equivIocMod", "kind": "definition", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientAddGroup.equivIocMod_coe", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientAddGroup.equivIocMod_zero", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "_private.Mathlib.Algebra.Order.ToIntervalMod.0.toIxxMod_total'", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": true, "tactics": ["have", "simp", "rw", "replace", "rw", "rw", "grw", "exact"], "tactic_count": 8}
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{"name": "QuotientAddGroup.instBtwQuotientAddSubgroupZmultiples", "kind": "instance", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientAddGroup.btw_coe_iff'", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "QuotientAddGroup.circularPreorder", "kind": "instance", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientAddGroup.circularOrder", "kind": "instance", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "self_sub_toIcoDiv_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "self_sub_toIocDiv_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "toIcoDiv_mul_sub_self", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "toIocDiv_mul_sub_self", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "toIcoMod_sub_self_eq_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "toIocMod_sub_self_eq_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "self_sub_toIcoMod_eq_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "self_sub_toIocMod_eq_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "toIcoMod_add_toIcoDiv_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "toIocMod_add_toIocDiv_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "toIcoDiv_mul_sub_toIcoMod", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "toIocDiv_mul_sub_toIocMod", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "toIcoDiv_add_intCast_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "toIcoDiv_add_natCast_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toIcoDiv_add_ofNat_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toIcoDiv_add_intCast_mul'", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "toIcoDiv_add_natCast_mul'", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toIcoDiv_add_ofNat_mul'", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toIocDiv_add_intCast_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
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{"name": "toIocDiv_add_ofNat_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toIocDiv_add_intCast_mul'", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "toIocDiv_add_natCast_mul'", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toIocDiv_add_ofNat_mul'", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toIcoDiv_intCast_mul_add", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "toIcoDiv_natCast_mul_add", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toIcoDiv_ofNat_mul_add", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toIocDiv_intCast_mul_add", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "toIocDiv_natCast_mul_add", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toIocDiv_ofNat_mul_add", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "toIcoDiv_sub_natCast_mul", "kind": "theorem", "module": "Mathlib.Algebra.Order.ToIntervalMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Int.instZeroLEOneClass", "kind": "instance", "module": "Mathlib.Algebra.Order.ZeroLEOne", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SemigroupPEmpty", "kind": "instance", "module": "Mathlib.Algebra.PEmptyInstances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.stabilizer_empty", "kind": "theorem", "module": "Mathlib.Algebra.Pointwise.Stabilizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.stabilizer_univ", "kind": "theorem", "module": "Mathlib.Algebra.Pointwise.Stabilizer", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
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{"name": "MulAction.mem_stabilizer_set", "kind": "theorem", "module": "Mathlib.Algebra.Pointwise.Stabilizer", "is_tactic_proof": true, "tactics": ["refine", "rw", "simp_rw", "exact"], "tactic_count": 4}
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{"name": "MulAction.stabilizer_inf_stabilizer_le_stabilizer_union", "kind": "theorem", "module": "Mathlib.Algebra.Pointwise.Stabilizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.stabilizer_inf_stabilizer_le_stabilizer_inter", "kind": "theorem", "module": "Mathlib.Algebra.Pointwise.Stabilizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.stabilizer_inf_stabilizer_le_stabilizer_sdiff", "kind": "theorem", "module": "Mathlib.Algebra.Pointwise.Stabilizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.stabilizer_union_eq_left", "kind": "theorem", "module": "Mathlib.Algebra.Pointwise.Stabilizer", "is_tactic_proof": true, "tactics": ["refine", "calc", "stabilizer", "calc", "stabilizer"], "tactic_count": 5}
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{"name": "MulAction.op_smul_set_stabilizer_subset", "kind": "theorem", "module": "Mathlib.Algebra.Pointwise.Stabilizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.stabilizer_subset_div_right", "kind": "theorem", "module": "Mathlib.Algebra.Pointwise.Stabilizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MulAction.stabilizer_finset_empty", "kind": "theorem", "module": "Mathlib.Algebra.Pointwise.Stabilizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MulAction.stabilizer_finset_singleton", "kind": "theorem", "module": "Mathlib.Algebra.Pointwise.Stabilizer", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "MulAction.mem_stabilizer_finset", "kind": "theorem", "module": "Mathlib.Algebra.Pointwise.Stabilizer", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MulAction.mem_stabilizer_finset_iff_subset_smul_finset", "kind": "theorem", "module": "Mathlib.Algebra.Pointwise.Stabilizer", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MulAction.mem_stabilizer_finset_iff_smul_finset_subset", "kind": "theorem", "module": "Mathlib.Algebra.Pointwise.Stabilizer", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MulAction.mem_stabilizer_finset'", "kind": "theorem", "module": "Mathlib.Algebra.Pointwise.Stabilizer", "is_tactic_proof": true, "tactics": ["rw", "simp_rw"], "tactic_count": 2}
{"name": "MulAction.mem_stabilizer_set_iff_subset_smul_set", "kind": "theorem", "module": "Mathlib.Algebra.Pointwise.Stabilizer", "is_tactic_proof": true, "tactics": ["lift", "classical", "rw"], "tactic_count": 3}
{"name": "MulAction.mem_stabilizer_set_iff_smul_set_subset", "kind": "theorem", "module": "Mathlib.Algebra.Pointwise.Stabilizer", "is_tactic_proof": true, "tactics": ["lift", "classical", "rw"], "tactic_count": 3}
{"name": "MulAction.mem_stabilizer_set'", "kind": "theorem", "module": "Mathlib.Algebra.Pointwise.Stabilizer", "is_tactic_proof": true, "tactics": ["lift", "classical"], "tactic_count": 2}
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{"name": "_private.Mathlib.Algebra.Pointwise.Stabilizer.0.MulAction.termQ", "kind": "definition", "module": "Mathlib.Algebra.Pointwise.Stabilizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Pointwise.Stabilizer.0.MulAction._aux_Mathlib_Algebra_Pointwise_Stabilizer___macroRules__private_Mathlib_Algebra_Pointwise_Stabilizer_0_MulAction_termQ_1", "kind": "definition", "module": "Mathlib.Algebra.Pointwise.Stabilizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Polynomial.algebraMap_apply", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Polynomial.ofFinsupp_algebraMap", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Polynomial.algHom_ext'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Polynomial.subalgebraNontrivial", "kind": "instance", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.algHom_eval₂_algebraMap", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": true, "tactics": ["simp", "simp"], "tactic_count": 2}
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{"name": "Polynomial.mapAlgHom_eq_eval₂AlgHom'_CAlgHom", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "Polynomial.coeff_mapAlgHom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "Polynomial.mapAlgHom_monomial", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "Polynomial.coe_mapAlgEquiv", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Polynomial.mapAlgEquiv_coe_ringHom", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Polynomial.algHom_ext", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.aeval_def", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eval_map_algebraMap", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.mapAlg_eq_map", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
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{"name": "Polynomial.aeval_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.aeval_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.aeval_monomial", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.aeval_X_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Polynomial.aeval_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.aeval_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Polynomial.aeval_comp", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Polynomial.algEquivCMulXAddC_symm_eq", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": true, "tactics": ["ext", "simp", "congr", "simp"], "tactic_count": 4}
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{"name": "Polynomial.aeval_X_left", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.aeval_X_left_apply", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.aeval_X_left_eq_map", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eval_unique", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.aeval_algHom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": false, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "Polynomial.aeval_smul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.coe_aeval_mk_apply", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.aeval_algEquiv", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.aeval_algebraMap_apply_eq_algebraMap_eval", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.aeval_prod", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.aeval_prod_apply", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.aeval_pi", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.aeval_pi_apply₂", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.aeval_pi_apply", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coe_aeval_eq_eval", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coe_aeval_eq_evalRingHom", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.aeval_fn_apply", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.aeval_subalgebra_coe", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coeff_zero_eq_aeval_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.coeff_zero_eq_aeval_zero'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.map_aeval_eq_aeval_map", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": true, "tactics": ["conv_rhs", "rw"], "tactic_count": 2}
{"name": "Polynomial.aeval_eq_zero_of_dvd_aeval_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Polynomial.aeval_eq_sum_range", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Polynomial.aeval_eq_sum_range'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Polynomial.isRoot_of_eval₂_map_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": true, "tactics": ["intro", "apply", "rw"], "tactic_count": 3}
{"name": "Polynomial.isRoot_of_aeval_algebraMap_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.aevalTower", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.aevalTower_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.aevalTower_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.aevalTower_comp_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.aevalTower_algebraMap", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.aevalTower_comp_algebraMap", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.aevalTower_toAlgHom", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.aevalTower_comp_toAlgHom", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.aevalTower_id", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Polynomial.aevalTower_ofId", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Polynomial.X_pow_smul_rTensor_monomial", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": true, "tactics": ["induction", "zero", "add", "tmul", "simp", "rw"], "tactic_count": 6}
{"name": "Polynomial.dvd_term_of_dvd_eval_of_dvd_terms", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "rw", "refine", "apply", "intro", "exact", "convert", "rw", "simp"], "tactic_count": 10}
{"name": "Polynomial.dvd_term_of_isRoot_of_dvd_terms", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eval_mul_X_sub_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": true, "tactics": ["simp", "have", "calc", "rw", "swap", "simp", "rw", "conv_lhs", "congr", "arg", "simp", "rw", "simp"], "tactic_count": 13}
{"name": "Polynomial.not_isUnit_X_sub_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.aeval_neg", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.aeval_sub", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.aeval_endomorphism", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Polynomial.X_sub_C_pow_dvd_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "Polynomial.comp_X_add_C_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.comp_X_add_C_ne_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.dvd_comp_C_mul_X_add_C_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "Polynomial.dvd_comp_X_sub_C_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": true, "tactics": ["let", "simpa"], "tactic_count": 2}
{"name": "Polynomial.dvd_comp_X_add_C_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Polynomial.dvd_comp_neg_X_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": true, "tactics": ["let", "let", "simpa"], "tactic_count": 3}
{"name": "Polynomial.units_coeff_zero_smul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.aeval_apply_smul_mem_of_le_comap'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": true, "tactics": ["induction", "add", "simp_rw", "exact", "monomial", "dsimp", "rw", "solve_by_elim"], "tactic_count": 8}
{"name": "Polynomial.aeval_apply_smul_mem_of_le_comap", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eq_zero_of_mul_eq_zero_of_smul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": false, "tactics": ["suffices", "rw", "apply", "simpa", "apply", "use", "intro", "rw", "intro", "obtain", "apply", "rw", "suffices", "rwa", "let", "suffices", "rw", "apply", "simp", "intro", "obtain", "have", "rw", "lia", "rw", "termination_by"], "tactic_count": 26}
{"name": "Polynomial.notMem_nonZeroDivisors_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": true, "tactics": ["refine", "by_contra", "obtain", "refine", "contrapose", "exact"], "tactic_count": 6}
{"name": "Polynomial.mem_nonZeroDivisors_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Polynomial.mem_nonzeroDivisors_of_coeff_mem", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.X_mem_nonzeroDivisors", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.AlgebraMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.term_[X]", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial._aux_Mathlib_Algebra_Polynomial_Basic___macroRules_Polynomial_term_[X]_1", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial._aux_Mathlib_Algebra_Polynomial_Basic___unexpand_Polynomial_1", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.forall_iff_forall_finsupp", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.exists_iff_exists_finsupp", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eta", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["constructor"], "tactic_count": 1}
{"name": "Polynomial.instZero", "kind": "instance", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.instOne", "kind": "instance", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.instAdd", "kind": "instance", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.instNeg", "kind": "instance", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.instSub", "kind": "instance", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.instMul", "kind": "instance", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.instNSMul", "kind": "instance", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.smulZeroClass", "kind": "instance", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.pow", "kind": "instance", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.ofFinsupp_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.ofFinsupp_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.ofFinsupp_add", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.ofFinsupp_neg", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.ofFinsupp_sub", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Polynomial.ofFinsupp_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.ofFinsupp_nsmul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.ofFinsupp_smul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.ofFinsupp_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["change", "induction", "zero", "succ"], "tactic_count": 4}
{"name": "Polynomial.toFinsupp_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.toFinsupp_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.toFinsupp_add", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.toFinsupp_neg", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.toFinsupp_sub", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Polynomial.toFinsupp_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.toFinsupp_nsmul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.toFinsupp_smul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.toFinsupp_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsSMulRegular.polynomial", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.toFinsupp_injective", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.toFinsupp_inj", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.toFinsupp_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.toFinsupp_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.ofFinsupp_inj", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.ofFinsupp_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.ofFinsupp_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.inhabited", "kind": "instance", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.instNatCast", "kind": "instance", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.ofFinsupp_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.toFinsupp_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.ofFinsupp_ofNat", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.toFinsupp_ofNat", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.semiring", "kind": "instance", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.distribSMul", "kind": "instance", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.distribMulAction", "kind": "instance", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.faithfulSMul", "kind": "instance", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.module", "kind": "instance", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.smulCommClass", "kind": "instance", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.isScalarTower", "kind": "instance", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.isScalarTower_right", "kind": "instance", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.isCentralScalar", "kind": "instance", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.instIsTorsionFree", "kind": "instance", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.unique", "kind": "instance", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.toFinsuppIso", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.instDecidableEq", "kind": "instance", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.toFinsuppIsoLinear", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.ofFinsupp_sum", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.toFinsupp_sum", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.support", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.support_ofFinsupp", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.support_toFinsupp", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.support_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.support_eq_empty", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simp"], "tactic_count": 2}
{"name": "Polynomial.support_nonempty", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.card_support_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.monomial", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.toFinsupp_monomial", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.ofFinsupp_single", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.monomial_zero_right", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.monomial_zero_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.monomial_add", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.monomial_mul_monomial", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.monomial_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Polynomial.smul_monomial", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.monomial_injective", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.monomial_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.monomial_eq_monomial_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.support_add", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Polynomial.C", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.monomial_zero_left", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.toFinsupp_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.C_0", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.C_1", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.C_ofNat", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.C_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.C_add", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.smul_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.C_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.C_eq_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.C_mul_monomial", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.monomial_mul_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.X", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.monomial_one_one_eq_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.monomial_one_right_eq_X_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Polynomial.toFinsupp_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.X_ne_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["intro", "simpa"], "tactic_count": 2}
{"name": "Polynomial.X_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simp", "ext", "simp"], "tactic_count": 4}
{"name": "Polynomial.X_pow_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "conv_lhs", "rw"], "tactic_count": 5}
{"name": "Polynomial.X_mul_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.X_pow_mul_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.X_pow_mul_assoc", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.X_pow_mul_assoc_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.commute_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.commute_X_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.monomial_mul_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.monomial_mul_X_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Polynomial.X_mul_monomial", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.X_pow_mul_monomial", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.coeff", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coeff_ofFinsupp", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.coeff_injective", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["rintro", "simp"], "tactic_count": 2}
{"name": "Polynomial.coeff_inj", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.toFinsupp_apply", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Polynomial.finite_range_coeff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coeff_monomial", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.coeff_monomial_same", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coeff_monomial_of_ne", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coeff_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coeff_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Polynomial.coeff_one_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.coeff_X_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coeff_X_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coeff_monomial_succ", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.coeff_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coeff_X_of_ne_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.mem_support_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simp"], "tactic_count": 2}
{"name": "Polynomial.notMem_support_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.coeff_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "Polynomial.coeff_C_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coeff_C_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.coeff_C_succ", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.coeff_natCast_ite", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.coeff_ofNat_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coeff_ofNat_succ", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Polynomial.C_mul_X_pow_eq_monomial", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.toFinsupp_C_mul_X_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.C_mul_X_eq_monomial", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.toFinsupp_C_mul_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.C_injective", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.C_inj", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.C_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.C_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.subsingleton_iff_subsingleton", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Nontrivial.of_polynomial_ne", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.forall_eq_iff_forall_eq", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Polynomial.ext_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "simpa"], "tactic_count": 3}
{"name": "Polynomial.ext", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.addSubmonoid_closure_setOf_eq_monomial", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["apply", "rw", "refine", "rintro", "exact"], "tactic_count": 5}
{"name": "Polynomial.addHom_ext", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.addHom_ext'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.lhom_ext'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eq_zero_of_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.support_monomial", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.support_monomial'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Polynomial.support_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.support_C_subset", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.support_C_mul_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.support_C_mul_X'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Polynomial.support_C_mul_X_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.support_C_mul_X_pow'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Polynomial.support_binomial'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.support_trinomial'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.X_pow_eq_monomial", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.toFinsupp_X_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.smul_X_eq_monomial", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.support_X_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["convert", "exact"], "tactic_count": 2}
{"name": "Polynomial.support_X_empty", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.support_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.monomial_left_inj", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.binomial_eq_binomial", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Polynomial.natCast_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.sum", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.sum_def", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.sum_eq_of_subset", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.mul_eq_sum_sum", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["apply", "simp_rw"], "tactic_count": 2}
{"name": "Polynomial.sum_zero_index", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.sum_monomial_index", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.sum_C_index", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.sum_X_index", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.sum_add_index", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Polynomial.sum_add'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.sum_add", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.sum_smul_index", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.sum_smul_index'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.smul_sum", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.sum_monomial_eq", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.sum_C_mul_X_pow_eq", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Polynomial.induction_on", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": ["have", "intro", "induction", "zero", "succ", "have", "apply", "convert", "exact", "intro", "rw", "exact", "rw", "exact"], "tactic_count": 14}
{"name": "Polynomial.induction_on'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.definition._@.Mathlib.Algebra.Polynomial.Basic.2141038364._hygCtx._hyg.2", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.wrapped._@.Mathlib.Algebra.Polynomial.Basic.2141038364._hygCtx._hyg.2", "kind": "opaque", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.erase", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.erase_def", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["intros", "delta", "rw", "rfl"], "tactic_count": 4}
{"name": "Polynomial.toFinsupp_erase", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.ofFinsupp_erase", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.support_erase", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.monomial_add_erase", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coeff_erase", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simp", "exact"], "tactic_count": 3}
{"name": "Polynomial.erase_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.erase_monomial", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.erase_same", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.erase_ne", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.update", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coeff_update", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Polynomial.coeff_update_apply", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.coeff_update_same", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.coeff_update_ne", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.update_zero_eq_erase", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "Polynomial.support_update", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["classical", "simp", "congr"], "tactic_count": 3}
{"name": "Polynomial.support_update_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.support_update_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Polynomial.coeffs", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coeffs_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.mem_coeffs_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.coeffs_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["classical", "simp_rw", "simp_all"], "tactic_count": 3}
{"name": "Polynomial.coeff_mem_coeffs", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["classical", "simp", "exact"], "tactic_count": 3}
{"name": "Polynomial.coeffs_empty_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["refine", "contrapose", "intro", "rw", "obtain", "rw", "exact"], "tactic_count": 7}
{"name": "Polynomial.coeffs_nonempty_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.coeffs_monomial", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Polynomial.commSemiring", "kind": "instance", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.instZSMul", "kind": "instance", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.ofFinsupp_zsmul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.toFinsupp_zsmul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.instIntCast", "kind": "instance", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.ofFinsupp_intCast", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.toFinsupp_intCast", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.ring", "kind": "instance", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coeff_neg", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["rcases", "rw"], "tactic_count": 2}
{"name": "Polynomial.coeff_sub", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "rw"], "tactic_count": 3}
{"name": "Polynomial.monomial_neg", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.monomial_sub", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.support_neg", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["rcases", "rw"], "tactic_count": 2}
{"name": "Polynomial.C_eq_intCast", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.C_neg", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.C_sub", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.commRing", "kind": "instance", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.nontrivial", "kind": "instance", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["have", "rcases", "refine", "simp"], "tactic_count": 4}
{"name": "Polynomial.X_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.instNoZeroDivisors", "kind": "instance", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.instIsLeftCancelMulZeroOfIsCancelAdd", "kind": "instance", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.instIsRightCancelMulZeroOfIsCancelAdd", "kind": "instance", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.instIsCancelMulZeroOfIsCancelAdd", "kind": "instance", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.instIsDomainOfIsCancelAdd", "kind": "instance", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.noZeroDivisors_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.nnqsmul_eq_C_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.qsmul_eq_C_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.nontrivial_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.ofMultiset", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.repr", "kind": "instance", "module": "Mathlib.Algebra.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.basisMonomials", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coe_basisMonomials", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natDegree_list_sum_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.BigOperators", "is_tactic_proof": true, "tactics": ["apply", "simp", "exact"], "tactic_count": 3}
{"name": "Polynomial.natDegree_multiset_sum_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natDegree_sum_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.BigOperators", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Polynomial.natDegree_sum_le_of_forall_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.leadingCoeff_sum_of_degree_eq", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.BigOperators", "is_tactic_proof": true, "tactics": ["obtain", "simp_all", "replace", "suffices", "apply", "aesop", "simp_all"], "tactic_count": 7}
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{"name": "Polynomial.degree_list_sum_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.BigOperators", "is_tactic_proof": true, "tactics": ["apply", "intro", "by_cases", "subst", "simp", "rw", "apply", "rw", "use", "simp"], "tactic_count": 10}
{"name": "Polynomial.natDegree_list_prod_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_list_prod_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coeff_list_prod_of_natDegree_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.BigOperators", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "have", "simp", "rw", "have", "refine", "rw", "refine", "simpa", "exact"], "tactic_count": 12}
{"name": "Polynomial.natDegree_multiset_prod_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natDegree_prod_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.BigOperators", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Polynomial.degree_multiset_prod_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_prod_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.BigOperators", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Polynomial.leadingCoeff_multiset_prod'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.BigOperators", "is_tactic_proof": false, "tactics": ["induction", "empty", "cons", "simp", "rw", "rw", "simp", "apply", "rw", "exact", "simp", "apply"], "tactic_count": 12}
{"name": "Polynomial.leadingCoeff_prod'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.BigOperators", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Polynomial.natDegree_multiset_prod'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.BigOperators", "is_tactic_proof": true, "tactics": ["revert", "refine", "rw", "rw", "apply", "rwa", "apply"], "tactic_count": 7}
{"name": "Polynomial.natDegree_prod'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.BigOperators", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Polynomial.natDegree_multiset_prod_of_monic", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.BigOperators", "is_tactic_proof": true, "tactics": ["nontriviality", "apply", "simp_all"], "tactic_count": 3}
{"name": "Polynomial.degree_multiset_prod_of_monic", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.BigOperators", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "Polynomial.natDegree_prod_of_monic", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.BigOperators", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Polynomial.degree_prod_of_monic", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.BigOperators", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Polynomial.coeff_multiset_prod_of_natDegree_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.BigOperators", "is_tactic_proof": true, "tactics": ["induction", "simpa"], "tactic_count": 2}
{"name": "Polynomial.coeff_prod_of_natDegree_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.BigOperators", "is_tactic_proof": true, "tactics": ["obtain", "convert", "simp", "simp", "simpa"], "tactic_count": 5}
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{"name": "Polynomial.coeff_zero_prod", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.BigOperators", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Polynomial.multiset_prod_X_sub_C_nextCoeff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.BigOperators", "is_tactic_proof": true, "tactics": ["rw", "simp", "exact", "intros", "apply"], "tactic_count": 5}
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{"name": "Polynomial.multiset_prod_X_sub_C_coeff_card_pred", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.BigOperators", "is_tactic_proof": true, "tactics": ["nontriviality", "convert", "rw", "swap", "rw", "swap", "simp", "rintro", "apply", "simp_rw", "obtain", "exact", "congr"], "tactic_count": 13}
{"name": "Polynomial.prod_X_sub_C_coeff_card_pred", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.BigOperators", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Polynomial.natDegree_multiset_prod_X_sub_C_eq_card", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.BigOperators", "is_tactic_proof": true, "tactics": ["rw", "simp", "exact"], "tactic_count": 3}
{"name": "Polynomial.natDegree_finset_prod_X_sub_C_eq_card", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.BigOperators", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.degree_list_prod", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natDegree_prod", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.BigOperators", "is_tactic_proof": true, "tactics": ["nontriviality", "apply", "rw", "intro"], "tactic_count": 4}
{"name": "Polynomial.natDegree_multiset_prod", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.BigOperators", "is_tactic_proof": true, "tactics": ["nontriviality", "rw", "simp_rw", "rintro", "contradiction"], "tactic_count": 5}
{"name": "Polynomial.degree_multiset_prod", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_prod", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.leadingCoeff_multiset_prod", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.BigOperators", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
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{"name": "Polynomial.Bivariate.termY", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Bivariate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Bivariate._aux_Mathlib_Algebra_Polynomial_Bivariate___macroRules_Polynomial_Bivariate_termY_1", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Bivariate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Polynomial.CC", "kind": "abbrev", "module": "Mathlib.Algebra.Polynomial.Bivariate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Polynomial.evalEval_CC", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Bivariate", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "Polynomial.coe_algebraMap_eq_CC", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Bivariate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Polynomial.coe_evalEvalRingHom", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Bivariate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.evalEvalRingHom_eq", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Bivariate", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
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{"name": "Polynomial.map_evalRingHom_eval", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Bivariate", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.map_mapRingHom_eval_map", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Bivariate", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.map_mapRingHom_eval_map_eval", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Bivariate", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.map_mapRingHom_evalEval", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Bivariate", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.eval₂RingHom_eval₂RingHom", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Bivariate", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Polynomial.eval₂_eval₂RingHom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Bivariate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Polynomial.eval_C_X_eval₂_map_C_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Bivariate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.aevalAeval", "kind": "abbrev", "module": "Mathlib.Algebra.Polynomial.Bivariate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coe_aevalAeval_eq_evalEval", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Bivariate", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Polynomial.Bivariate.swap", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Bivariate", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "Polynomial.Bivariate.swap_apply", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Bivariate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Bivariate.swap_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Bivariate", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.Bivariate.swap_Y", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Bivariate", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.Bivariate.swap_monomial_monomial", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Bivariate", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.Bivariate.aevalAeval_swap", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Bivariate", "is_tactic_proof": true, "tactics": ["induction", "add", "monomial", "simp", "induction"], "tactic_count": 5}
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{"name": "Polynomial.Bivariate.equivMvPolynomial_C_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Bivariate", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.Bivariate.equivMvPolynomial_C_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Bivariate", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.Bivariate.equivMvPolynomial_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Bivariate", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.Bivariate.equivMvPolynomial_symm_X_0", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Bivariate", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "Polynomial.mul_X_pow_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Coeff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.isRegular_X_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Coeff", "is_tactic_proof": true, "tactics": ["suffices", "intro", "ext", "rw"], "tactic_count": 4}
{"name": "Polynomial.isRegular_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Coeff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coeff_X_add_C_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Coeff", "is_tactic_proof": true, "tactics": ["rw", "simp", "rw", "intro", "simp", "simp", "intro", "rw"], "tactic_count": 8}
{"name": "Polynomial.coeff_X_add_one_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Coeff", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.coeff_one_add_X_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Coeff", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.one_add_X_pow_sub_X_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Coeff", "is_tactic_proof": true, "tactics": ["ext", "simp", "split_ifs"], "tactic_count": 3}
{"name": "Polynomial.C_dvd_iff_dvd_coeff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Coeff", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "rw", "apply", "intro", "choose", "classical", "let", "let", "use", "ext", "simp", "split_ifs", "rw", "rw", "rwa"], "tactic_count": 16}
{"name": "Polynomial.smul_eq_C_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Coeff", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.update_eq_add_sub_coeff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Coeff", "is_tactic_proof": true, "tactics": ["ext", "rw", "split_ifs"], "tactic_count": 3}
{"name": "Polynomial.natCast_coeff_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Coeff", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.natCast_inj", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Coeff", "is_tactic_proof": true, "tactics": ["constructor", "intro", "apply_fun", "simpa", "rintro", "rfl"], "tactic_count": 6}
{"name": "Polynomial.intCast_coeff_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Coeff", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Polynomial.intCast_inj", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Coeff", "is_tactic_proof": true, "tactics": ["constructor", "intro", "apply_fun", "simpa", "rintro", "rfl"], "tactic_count": 6}
{"name": "Polynomial.charZero", "kind": "instance", "module": "Mathlib.Algebra.Polynomial.Coeff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.charP", "kind": "instance", "module": "Mathlib.Algebra.Polynomial.Coeff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coeffList", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.CoeffList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coeffList_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.CoeffList", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.coeffList_eq_nil", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.CoeffList", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.coeffList_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.CoeffList", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.coeffList_eq_cons_leadingCoeff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.CoeffList", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.head?_coeffList", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.CoeffList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.head_coeffList", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.CoeffList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.length_coeffList_eq_withBotSucc_degree", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.CoeffList", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.length_coeffList_eq_ite", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.CoeffList", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "Polynomial.leadingCoeff_cons_eraseLead", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.CoeffList", "is_tactic_proof": true, "tactics": ["have", "have", "simpa", "withBotSucc_degree_eq_natDegree_add_one"], "tactic_count": 4}
{"name": "Polynomial.coeffList_monomial", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.CoeffList", "is_tactic_proof": true, "tactics": ["have", "apply", "rintro", "exact", "rw", "have", "simpa"], "tactic_count": 7}
{"name": "Polynomial.coeffList_eraseLead", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.CoeffList", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "simp", "by_cases", "have", "simpa", "nth_rewrite", "simp", "have", "have", "obtain", "use", "have", "lia", "rw", "apply", "rintro", "obtain", "simp_all", "simp", "by_cases", "rw", "obtain", "rw", "conv_lhs", "equals", "rw", "congr", "lia", "by_cases", "simpa", "rw", "rw", "congr", "lia", "simpa"], "tactic_count": 36}
{"name": "Polynomial.coeffList_neg", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.CoeffList", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "simp"], "tactic_count": 3}
{"name": "Polynomial.coeffList_C_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.CoeffList", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "simp"], "tactic_count": 3}
{"name": "_private.Mathlib.Algebra.Polynomial.CoeffMem.0.Polynomial.termDeg(_)", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.CoeffMem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Polynomial.CoeffMem.0.Polynomial._aux_Mathlib_Algebra_Polynomial_CoeffMem___macroRules__private_Mathlib_Algebra_Polynomial_CoeffMem_0_Polynomial_termDeg(_)_1", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.CoeffMem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Polynomial.CoeffMem.0.Polynomial._aux_Mathlib_Algebra_Polynomial_CoeffMem___delab_app__private_Mathlib_Algebra_Polynomial_CoeffMem_0_Polynomial_termDeg(_)_1", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.CoeffMem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Polynomial.CoeffMem.0.Polynomial.termCoeffs(_)", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.CoeffMem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Polynomial.CoeffMem.0.Polynomial._aux_Mathlib_Algebra_Polynomial_CoeffMem___macroRules__private_Mathlib_Algebra_Polynomial_CoeffMem_0_Polynomial_termCoeffs(_)_1", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.CoeffMem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Polynomial.CoeffMem.0.Polynomial._aux_Mathlib_Algebra_Polynomial_CoeffMem___delab_app__private_Mathlib_Algebra_Polynomial_CoeffMem_0_Polynomial_termCoeffs(_)_1", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.CoeffMem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Polynomial.CoeffMem.0.Polynomial.termSpanCoeffs(_)", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.CoeffMem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Polynomial.CoeffMem.0.Polynomial._aux_Mathlib_Algebra_Polynomial_CoeffMem___macroRules__private_Mathlib_Algebra_Polynomial_CoeffMem_0_Polynomial_termSpanCoeffs(_)_1", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.CoeffMem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Polynomial.CoeffMem.0.Polynomial._aux_Mathlib_Algebra_Polynomial_CoeffMem___delab_app__private_Mathlib_Algebra_Polynomial_CoeffMem_0_Polynomial_termSpanCoeffs(_)_1", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.CoeffMem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coeff_divModByMonicAux_mem_span_pow_mul_span", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.CoeffMem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coeff_modByMonic_mem_pow_natDegree_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.CoeffMem", "is_tactic_proof": true, "tactics": ["delta", "split_ifs", "refine", "gcongr", "rw", "exact"], "tactic_count": 6}
{"name": "Polynomial.coeff_divByMonic_mem_pow_natDegree_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.CoeffMem", "is_tactic_proof": true, "tactics": ["delta", "split_ifs", "refine", "gcongr", "simp"], "tactic_count": 5}
{"name": "Polynomial.idealSpan_range_update_divByMonic", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.CoeffMem", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.cardPowDegree", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Degree.CardPowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.cardPowDegree_apply", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.CardPowDegree", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.cardPowDegree_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.CardPowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.cardPowDegree_nonzero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.CardPowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.cardPowDegree_isEuclidean", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.CardPowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natDegree", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.leadingCoeff", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Monic", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Monic.def", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Monic.decidable", "kind": "instance", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "Polynomial.Monic.leadingCoeff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Monic.coeff_natDegree", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natDegree_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coeff_natDegree", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_eq_bot", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_ne_bot", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_eq_natDegree", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": true, "tactics": ["let", "have", "rw"], "tactic_count": 3}
{"name": "Polynomial.degree_eq_iff_natDegree_eq", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.degree_eq_iff_natDegree_eq_of_pos", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": true, "tactics": ["obtain", "simp", "exact"], "tactic_count": 3}
{"name": "Polynomial.natDegree_eq_of_degree_eq_some", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.degree_ne_of_natDegree_ne", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_le_natDegree", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natDegree_eq_of_degree_eq", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "Polynomial.le_degree_of_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Polynomial.degree_mono", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_le_degree", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "exact", "rw", "exact"], "tactic_count": 5}
{"name": "Polynomial.natDegree_le_iff_degree_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natDegree_lt_iff_degree_lt", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natDegree_le_natDegree", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.degree_C_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "exact", "rw"], "tactic_count": 4}
{"name": "Polynomial.degree_C_lt", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_one_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.natDegree_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": true, "tactics": ["by_cases", "have", "rw", "rw"], "tactic_count": 4}
{"name": "Polynomial.natDegree_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natDegree_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.natDegree_ofNat", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_natCast_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_monomial", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.degree_C_mul_X_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.degree_C_mul_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Polynomial.degree_monomial_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_C_mul_X_pow_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "Polynomial.degree_C_mul_X_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Polynomial.natDegree_C_mul_X_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natDegree_C_mul_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Polynomial.natDegree_monomial", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": true, "tactics": ["split_ifs", "simp", "rw"], "tactic_count": 3}
{"name": "Polynomial.natDegree_monomial_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": true, "tactics": ["classical", "rw", "split_ifs", "exacts"], "tactic_count": 4}
{"name": "Polynomial.natDegree_monomial_eq", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coeff_ne_zero_of_eq_degree", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_X_pow_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Polynomial.degree_X_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natDegree_X_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.withBotSucc_degree_eq_natDegree_add_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Polynomial.degree_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natDegree_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_neg", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "Polynomial.degree_neg_le_of_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natDegree_neg", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.natDegree_neg_le_of_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natDegree_intCast", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.degree_intCast_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.leadingCoeff_neg", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.nextCoeff", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.nextCoeff_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.nextCoeff_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.nextCoeff_C_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Polynomial.nextCoeff_of_natDegree_pos", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": true, "tactics": ["rw", "contrapose", "simpa"], "tactic_count": 3}
{"name": "Polynomial.degree_add_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Polynomial.degree_add_le_of_degree_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_add_le_of_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natDegree_add_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "Polynomial.natDegree_add_le_of_degree_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natDegree_add_le_of_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.leadingCoeff_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.leadingCoeff_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.leadingCoeff_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.leadingCoeff_eq_zero_iff_deg_eq_bot", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.natDegree_C_mul_X_pow_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_erase_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": true, "tactics": ["simp", "apply", "simpa"], "tactic_count": 3}
{"name": "Polynomial.degree_erase_lt", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": true, "tactics": ["apply", "rw", "exact"], "tactic_count": 3}
{"name": "Polynomial.degree_update_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": true, "tactics": ["classical", "rw", "split_ifs", "exact", "rw", "exact"], "tactic_count": 6}
{"name": "Polynomial.degree_sum_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_mul_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Polynomial.degree_mul_le_of_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": true, "tactics": ["grw"], "tactic_count": 1}
{"name": "Polynomial.degree_pow_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_pow_le_of_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "exact"], "tactic_count": 5}
{"name": "Polynomial.leadingCoeff_monomial", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": true, "tactics": ["classical", "by_cases", "simp", "rw", "simp"], "tactic_count": 5}
{"name": "Polynomial.leadingCoeff_C_mul_X_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.leadingCoeff_C_mul_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Polynomial.leadingCoeff_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.leadingCoeff_X_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Polynomial.leadingCoeff_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Polynomial.monic_X_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.monic_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.leadingCoeff_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.monic_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Monic.ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": true, "tactics": ["rintro", "simp"], "tactic_count": 2}
{"name": "Polynomial.Monic.ne_zero_of_ne", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": true, "tactics": ["nontriviality", "exact"], "tactic_count": 2}
{"name": "Polynomial.Monic.ne_zero_of_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": true, "tactics": ["rintro", "simp"], "tactic_count": 2}
{"name": "Polynomial.Monic.ne_zero_of_polynomial_ne", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natDegree_mul_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": true, "tactics": ["apply", "apply", "rw", "apply"], "tactic_count": 4}
{"name": "Polynomial.natDegree_mul_le_of_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natDegree_pow_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Polynomial.natDegree_pow_le_of_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natDegree_eq_zero_iff_degree_le_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.degree_zero_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_le_iff_coeff_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.degree_lt_iff_coeff_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": true, "tactics": ["simp", "max_eq_sup_coe,"], "tactic_count": 2}
{"name": "Polynomial.natDegree_pos_iff_degree_pos", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_X_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.natDegree_X_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_sub_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Polynomial.degree_sub_le_of_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natDegree_sub_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Polynomial.natDegree_sub_le_of_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_sub_lt", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_X_sub_C_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natDegree_X_sub_C_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natDegree_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Domain", "is_tactic_proof": true, "tactics": ["rw", "degree_eq_natDegree"], "tactic_count": 2}
{"name": "Polynomial.natDegree_smul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Domain", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "apply", "exact", "simp", "apply", "simp"], "tactic_count": 7}
{"name": "Polynomial.natDegree_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Domain", "is_tactic_proof": true, "tactics": ["classical", "obtain", "obtain", "exact"], "tactic_count": 4}
{"name": "Polynomial.natDegree_le_of_dvd", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Domain", "is_tactic_proof": true, "tactics": ["obtain", "rw", "rw"], "tactic_count": 3}
{"name": "Polynomial.degree_le_of_dvd", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Domain", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "Polynomial.eq_zero_of_dvd_of_degree_lt", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Domain", "is_tactic_proof": true, "tactics": ["by_contra", "exact"], "tactic_count": 2}
{"name": "Polynomial.eq_zero_of_dvd_of_natDegree_lt", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Domain", "is_tactic_proof": true, "tactics": ["by_contra", "exact"], "tactic_count": 2}
{"name": "Polynomial.not_dvd_of_degree_lt", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Domain", "is_tactic_proof": true, "tactics": ["by_contra", "exact"], "tactic_count": 2}
{"name": "Polynomial.not_dvd_of_natDegree_lt", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Domain", "is_tactic_proof": true, "tactics": ["by_contra", "exact"], "tactic_count": 2}
{"name": "Polynomial.natDegree_sub_eq_of_prod_eq", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Domain", "is_tactic_proof": true, "tactics": ["rw", "norm_cast", "rw"], "tactic_count": 3}
{"name": "Polynomial.isMonicOfDegree_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.IsMonicOfDegree", "is_tactic_proof": true, "tactics": ["simp", "refine", "subst", "simp"], "tactic_count": 4}
{"name": "Polynomial.IsMonicOfDegree.leadingCoeff_eq", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.IsMonicOfDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.isMonicOfDegree_iff_of_subsingleton", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.IsMonicOfDegree", "is_tactic_proof": true, "tactics": ["rw", "refine", "rwa", "rw"], "tactic_count": 4}
{"name": "Polynomial.isMonicOfDegree_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.IsMonicOfDegree", "is_tactic_proof": true, "tactics": ["simp", "refine", "exact", "exact"], "tactic_count": 4}
{"name": "Polynomial.IsMonicOfDegree.exists_natDegree_lt", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.IsMonicOfDegree", "is_tactic_proof": true, "tactics": ["refine", "nth_rewrite", "rw", "refine", "rw", "lia"], "tactic_count": 6}
{"name": "Polynomial.IsMonicOfDegree.mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.IsMonicOfDegree", "is_tactic_proof": true, "tactics": ["rcases", "simp", "exact", "refine", "have", "rw", "exact", "rw"], "tactic_count": 8}
{"name": "Polynomial.IsMonicOfDegree.pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.IsMonicOfDegree", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "exact"], "tactic_count": 5}
{"name": "Polynomial.IsMonicOfDegree.coeff_eq", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.IsMonicOfDegree", "is_tactic_proof": true, "tactics": ["nontriviality", "rw", "rcases", "rw", "replace", "replace", "rw"], "tactic_count": 7}
{"name": "Polynomial.IsMonicOfDegree.of_mul_left", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.IsMonicOfDegree", "is_tactic_proof": true, "tactics": ["rcases", "simp", "exact", "have", "refine", "have", "have", "rw", "exact", "rw", "exact"], "tactic_count": 11}
{"name": "Polynomial.IsMonicOfDegree.of_mul_right", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.IsMonicOfDegree", "is_tactic_proof": true, "tactics": ["rcases", "simp", "exact", "have", "refine", "have", "have", "rw", "exact", "rw", "exact"], "tactic_count": 11}
{"name": "Polynomial.IsMonicOfDegree.add_right", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.IsMonicOfDegree", "is_tactic_proof": true, "tactics": ["rcases", "simpa", "refine", "exact", "rw", "exact"], "tactic_count": 6}
{"name": "Polynomial.IsMonicOfDegree.add_left", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.IsMonicOfDegree", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Polynomial.IsMonicOfDegree.comp", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.IsMonicOfDegree", "is_tactic_proof": true, "tactics": ["rcases", "simp", "exact", "rw", "refine", "rw"], "tactic_count": 6}
{"name": "Polynomial.IsMonicOfDegree.ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.IsMonicOfDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.isMonicOfDegree_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.IsMonicOfDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.isMonicOfDegree_X_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.IsMonicOfDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.isMonicOfDegree_monomial_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.IsMonicOfDegree", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Polynomial.isMonicOfDegree_X_add_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.IsMonicOfDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.isMonicOfDegree_one_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.IsMonicOfDegree", "is_tactic_proof": true, "tactics": ["refine", "refine", "ext1", "rcases", "simp", "exact"], "tactic_count": 6}
{"name": "Polynomial.isMonicOfDegree_add_add_two", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.IsMonicOfDegree", "is_tactic_proof": true, "tactics": ["rw", "exact", "calc"], "tactic_count": 3}
{"name": "Polynomial.isMonicOfDegree_two_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.IsMonicOfDegree", "is_tactic_proof": true, "tactics": ["refine", "refine", "rcases", "obtain", "simp", "simp", "exact"], "tactic_count": 7}
{"name": "Polynomial.IsMonicOfDegree.natDegree_sub_X_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.IsMonicOfDegree", "is_tactic_proof": true, "tactics": ["obtain", "simpa"], "tactic_count": 2}
{"name": "Polynomial.IsMonicOfDegree.natDegree_sub_lt", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.IsMonicOfDegree", "is_tactic_proof": true, "tactics": ["rw", "replace", "replace", "rw", "exact"], "tactic_count": 5}
{"name": "Polynomial.IsMonicOfDegree.sub", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.IsMonicOfDegree", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Polynomial.isMonicOfDegree_X_sub_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.IsMonicOfDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.isMonicOfDegree_sub_add_two", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.IsMonicOfDegree", "is_tactic_proof": true, "tactics": ["rw", "exact", "rw", "calc"], "tactic_count": 4}
{"name": "Polynomial.isMonicOfDegree_two_iff'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.IsMonicOfDegree", "is_tactic_proof": true, "tactics": ["refine", "simp", "obtain", "exact"], "tactic_count": 4}
{"name": "Polynomial.IsMonicOfDegree.of_dvd_add", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.IsMonicOfDegree", "is_tactic_proof": true, "tactics": ["obtain", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "Polynomial.IsMonicOfDegree.of_dvd_sub", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.IsMonicOfDegree", "is_tactic_proof": true, "tactics": ["convert", "rw", "rwa"], "tactic_count": 3}
{"name": "Polynomial.IsMonicOfDegree.aeval_add", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.IsMonicOfDegree", "is_tactic_proof": true, "tactics": ["rcases", "simpa", "rw", "exact"], "tactic_count": 4}
{"name": "Polynomial.IsMonicOfDegree.aeval_sub", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.IsMonicOfDegree", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Polynomial.natDegree_comp_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natDegree_comp_eq_of_mul_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Lemmas", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "apply", "rwa"], "tactic_count": 4}
{"name": "Polynomial.degree_pos_of_root", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natDegree_le_iff_coeff_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Lemmas", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Polynomial.natDegree_add_le_iff_left", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Lemmas", "is_tactic_proof": true, "tactics": ["refine", "refine", "convert", "rw"], "tactic_count": 4}
{"name": "Polynomial.natDegree_add_le_iff_right", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Polynomial.natDegree_C_mul_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Lemmas", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Polynomial.natDegree_mul_C_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Lemmas", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Polynomial.eq_natDegree_of_le_mem_support", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natDegree_C_mul_eq_of_mul_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natDegree_mul_C_eq_of_mul_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natDegree_mul_C_eq_of_mul_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Lemmas", "is_tactic_proof": true, "tactics": ["refine", "refine", "rwa"], "tactic_count": 3}
{"name": "Polynomial.natDegree_C_mul_of_mul_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Lemmas", "is_tactic_proof": true, "tactics": ["refine", "refine", "rwa"], "tactic_count": 3}
{"name": "Polynomial.degree_C_mul_of_mul_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.natDegree_add_coeff_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.natDegree_lt_coeff_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coeff_pow_of_natDegree_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Lemmas", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "refine", "exact"], "tactic_count": 6}
{"name": "Polynomial.coeff_pow_eq_ite_of_natDegree_le_of_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Lemmas", "is_tactic_proof": true, "tactics": ["rcases", "simpa", "simpa", "coeff_eq_zero_of_natDegree_lt"], "tactic_count": 4}
{"name": "Polynomial.coeff_add_eq_left_of_lt", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coeff_add_eq_right_of_lt", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Polynomial.degree_sum_eq_of_disjoint", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Lemmas", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "insert", "simp", "specialize", "rcases", "rw", "rcases", "simp", "obtain", "rw", "by_cases", "simp", "have", "contrapose", "simpa", "refine", "simp", "simp", "exact", "rw"], "tactic_count": 22}
{"name": "Polynomial.natDegree_sum_eq_of_disjoint", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Lemmas", "is_tactic_proof": true, "tactics": ["by_cases", "obtain", "have", "refine", "rw", "rw", "refine", "rw", "intro", "by_cases", "simpa", "rw", "exact", "rw", "intro", "simp", "by_cases", "refine", "contrapose", "simpa", "exact", "exact", "rw", "intro", "simp"], "tactic_count": 25}
{"name": "Polynomial.natDegree_pos_of_eval₂_root", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_pos_of_eval₂_root", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coe_lt_degree", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Lemmas", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "simp"], "tactic_count": 3}
{"name": "Polynomial.degree_map_eq_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Lemmas", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simp", "refine", "have", "have", "rwa"], "tactic_count": 7}
{"name": "Polynomial.natDegree_map_eq_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Lemmas", "is_tactic_proof": true, "tactics": ["rcases", "simp_rw", "simp_all"], "tactic_count": 3}
{"name": "Polynomial.degree_map_eq_of_isUnit_leadingCoeff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natDegree_map_eq_of_isUnit_leadingCoeff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.leadingCoeff_map_eq_of_isUnit_leadingCoeff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.nextCoeff_map_eq_of_isUnit_leadingCoeff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_map_eq_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.natDegree_map_eq_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.leadingCoeff_map_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.nextCoeff_map", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Lemmas", "is_tactic_proof": true, "tactics": ["simp", "split_ifs"], "tactic_count": 2}
{"name": "Polynomial.natDegree_pos_of_nextCoeff_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Lemmas", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Polynomial.natDegree_sub", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.natDegree_sub_le_iff_left", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "rw"], "tactic_count": 2}
{"name": "Polynomial.natDegree_sub_le_iff_right", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Lemmas", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Polynomial.coeff_sub_eq_left_of_lt", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "rw"], "tactic_count": 2}
{"name": "Polynomial.coeff_sub_eq_neg_right_of_lt", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Lemmas", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Polynomial.nextCoeff_C_mul_X_add_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.natDegree_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Lemmas", "is_tactic_proof": true, "tactics": ["refine", "rw", "simp_all", "ext", "obtain", "simp", "simp", "simp", "rw", "simp", "rintro", "simp"], "tactic_count": 12}
{"name": "Polynomial.subsingleton_isRoot_of_natDegree_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Lemmas", "is_tactic_proof": true, "tactics": ["intro", "obtain", "have", "grind"], "tactic_count": 4}
{"name": "Polynomial.degree_mul_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.degree_C_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.natDegree_mul_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.natDegree_C_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.natDegree_comp", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Lemmas", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "by_cases", "simp", "simp", "ne_zero_of_natDegree_gt"], "tactic_count": 6}
{"name": "Polynomial.natDegree_iterate_comp", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Lemmas", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Polynomial.leadingCoeff_comp", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.nextCoeff_C_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Lemmas", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "Polynomial.nextCoeff_mul_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Lemmas", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "Polynomial.comp_neg_X_leadingCoeff_eq", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Lemmas", "is_tactic_proof": true, "tactics": ["nontriviality", "by_cases", "simp", "rw", "simp"], "tactic_count": 5}
{"name": "Polynomial.comp_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Lemmas", "is_tactic_proof": true, "tactics": ["refine", "have", "obtain", "rw", "exact", "rw", "exact"], "tactic_count": 7}
{"name": "Polynomial.irreducible_mul_leadingCoeff_inv", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Lemmas", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "exact"], "tactic_count": 3}
{"name": "Polynomial.dvd_mul_leadingCoeff_inv", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.monic_mul_leadingCoeff_inv", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "mul_inv_cancel₀"], "tactic_count": 2}
{"name": "Polynomial.degree_leadingCoeff_inv", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.degree_mul_leadingCoeff_inv", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Lemmas", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "Polynomial.natDegree_mul_leadingCoeff_inv", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_mul_leadingCoeff_self_inv", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Lemmas", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "exact"], "tactic_count": 3}
{"name": "Polynomial.natDegree_mul_leadingCoeff_self_inv", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_add_degree_leadingCoeff_inv", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.natDegree_le_pred", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Monomial", "is_tactic_proof": true, "tactics": ["obtain", "exact", "refine", "rw", "simp_all"], "tactic_count": 5}
{"name": "Polynomial.monomial_natDegree_leadingCoeff_eq_self", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Monomial", "is_tactic_proof": true, "tactics": ["classical", "rcases", "by_cases"], "tactic_count": 3}
{"name": "Polynomial.C_mul_X_pow_eq_self", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Monomial", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.supDegree_eq_degree", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_lt_wf", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.instWellFoundedRelation", "kind": "instance", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.monic_of_subsingleton", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_of_subsingleton", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.natDegree_of_subsingleton", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.le_natDegree_of_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": true, "tactics": ["rw", "exact", "rintro", "exact"], "tactic_count": 4}
{"name": "Polynomial.degree_eq_of_le_of_coeff_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natDegree_eq_of_le_of_coeff_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natDegree_lt_natDegree", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "rwa"], "tactic_count": 3}
{"name": "Polynomial.natDegree_eq_natDegree", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.coeff_eq_zero_of_degree_lt", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coeff_eq_zero_of_natDegree_lt", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": true, "tactics": ["apply", "by_cases", "subst", "exact", "rwa"], "tactic_count": 5}
{"name": "Polynomial.ext_iff_natDegree_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": true, "tactics": ["refine", "refine", "refine", "exact"], "tactic_count": 4}
{"name": "Polynomial.ext_iff_degree_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coeff_natDegree_succ_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.ite_le_natDegree_coeff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": true, "tactics": ["split_ifs", "rfl", "exact"], "tactic_count": 3}
{"name": "Polynomial.coeff_mul_X_sub_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.coeff_X_sub_C_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.coeff_natDegree_eq_zero_of_degree_lt", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.ne_zero_of_degree_gt", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.ne_zero_of_degree_ge_degree", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.ne_zero_of_natDegree_gt", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_lt_degree", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "rw", "intro", "simp", "rwa"], "tactic_count": 6}
{"name": "Polynomial.natDegree_lt_natDegree_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eq_C_of_degree_le_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": true, "tactics": ["ext", "simp", "rw", "exact"], "tactic_count": 4}
{"name": "Polynomial.eq_C_of_degree_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_le_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_add_eq_left_of_degree_lt", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_add_eq_right_of_degree_lt", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.natDegree_add_eq_left_of_degree_lt", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natDegree_add_eq_left_of_natDegree_lt", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natDegree_add_eq_right_of_degree_lt", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natDegree_add_eq_right_of_natDegree_lt", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_add_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natDegree_add_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": true, "tactics": ["rcases", "simp", "by_cases", "rw", "rw", "exact"], "tactic_count": 6}
{"name": "Polynomial.natDegree_C_add", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.degree_add_eq_of_leadingCoeff_add_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natDegree_eq_of_natDegree_add_lt_left", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": true, "tactics": ["by_contra", "cases", "inl", "inr", "rw", "exact"], "tactic_count": 6}
{"name": "Polynomial.natDegree_eq_of_natDegree_add_lt_right", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natDegree_eq_of_natDegree_add_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "apply", "apply"], "tactic_count": 4}
{"name": "Polynomial.monic_of_natDegree_le_of_coeff_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": true, "tactics": ["unfold", "nontriviality", "refine", "exact"], "tactic_count": 4}
{"name": "Polynomial.monic_of_degree_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.leadingCoeff_add_of_degree_lt", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": true, "tactics": ["have", "simp"], "tactic_count": 2}
{"name": "Polynomial.leadingCoeff_add_of_degree_lt'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Polynomial.leadingCoeff_add_of_degree_eq", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": false, "tactics": ["have", "apply", "rw", "simp"], "tactic_count": 4}
{"name": "Polynomial.coeff_mul_degree_add_degree", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_mul'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Monic.degree_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natDegree_mul'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.leadingCoeff_mul'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.leadingCoeff_pow'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_pow'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natDegree_pow'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.leadingCoeff_monic_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rw", "rwa"], "tactic_count": 4}
{"name": "Polynomial.leadingCoeff_mul_monic", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_C_mul_of_isUnit", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": true, "tactics": ["obtain", "simp", "nontriviality", "rw", "simp", "simpa"], "tactic_count": 6}
{"name": "Polynomial.degree_mul_C_of_isUnit", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": true, "tactics": ["obtain", "simp", "nontriviality", "rw", "simp", "simpa"], "tactic_count": 6}
{"name": "Polynomial.natDegree_C_mul_of_isUnit", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.natDegree_mul_C_of_isUnit", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.leadingCoeff_C_mul_of_isUnit", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Polynomial.leadingCoeff_mul_C_of_isUnit", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Polynomial.leadingCoeff_mul_X_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.leadingCoeff_mul_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coeff_pow_mul_natDegree", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "by_cases", "rw", "by_cases", "rw", "apply", "have", "refine", "rw", "exact", "calc", "rw", "exact"], "tactic_count": 16}
{"name": "Polynomial.coeff_mul_add_eq_of_natDegree_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": true, "tactics": ["rw", "rw", "rintro", "obtain", "rw", "obtain", "rw", "obtain", "exact"], "tactic_count": 9}
{"name": "Polynomial.degree_smul_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": true, "tactics": ["refine", "rw", "simp"], "tactic_count": 3}
{"name": "Polynomial.natDegree_smul_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_smul_of_isRightRegular_leadingCoeff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "Polynomial.degree_lt_degree_mul_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": true, "tactics": ["haveI", "have", "rw", "norm_cast", "exact"], "tactic_count": 5}
{"name": "Polynomial.eq_C_of_natDegree_le_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eq_C_of_natDegree_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natDegree_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eq_C_coeff_zero_iff_natDegree_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eq_one_of_monic_natDegree_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": true, "tactics": ["rw", "rw"], "tactic_count": 2}
{"name": "Polynomial.Monic.natDegree_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_sum_fin_lt", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_C_lt_degree_C_mul_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Polynomial.natDegree_mul_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.natDegree_X_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.natDegree_mul_X_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.natDegree_X_pow_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.natDegree_X_pow_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": true, "tactics": ["nontriviality", "rw"], "tactic_count": 2}
{"name": "Polynomial.not_isUnit_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_mul_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.degree_mul_X_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.degree_sub_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.natDegree_sub_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.leadingCoeff_sub_of_degree_lt", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": true, "tactics": ["rw", "rw"], "tactic_count": 2}
{"name": "Polynomial.leadingCoeff_sub_of_degree_lt'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": true, "tactics": ["rw", "rw"], "tactic_count": 2}
{"name": "Polynomial.leadingCoeff_sub_of_degree_eq", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": true, "tactics": ["replace", "replace", "rwa", "rw"], "tactic_count": 4}
{"name": "Polynomial.degree_sub_eq_left_of_degree_lt", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": true, "tactics": ["rw", "rw"], "tactic_count": 2}
{"name": "Polynomial.degree_sub_eq_right_of_degree_lt", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": true, "tactics": ["rw", "rw"], "tactic_count": 2}
{"name": "Polynomial.natDegree_sub_eq_left_of_natDegree_lt", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natDegree_sub_eq_right_of_natDegree_lt", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_X_add_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": false, "tactics": ["have", "calc", "degree", "rw"], "tactic_count": 4}
{"name": "Polynomial.natDegree_X_add_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.nextCoeff_X_add_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": true, "tactics": ["nontriviality", "simp"], "tactic_count": 2}
{"name": "Polynomial.degree_X_pow_add_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "Polynomial.X_pow_add_C_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.X_add_C_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.zero_notMem_multiset_map_X_add_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natDegree_X_pow_add_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.X_pow_add_C_ne_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.X_add_C_ne_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.leadingCoeff_X_pow_add_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": true, "tactics": ["nontriviality", "rw", "add_zero]"], "tactic_count": 3}
{"name": "Polynomial.leadingCoeff_X_add_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.leadingCoeff_X_pow_add_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.leadingCoeff_pow_X_add_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": true, "tactics": ["nontriviality", "rw"], "tactic_count": 2}
{"name": "Polynomial.degree_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degreeMonoidHom", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.leadingCoeff_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "by_cases", "simp", "rw", "exact"], "tactic_count": 6}
{"name": "Polynomial.leadingCoeffHom", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.leadingCoeffHom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.leadingCoeff_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.leadingCoeff_dvd_leadingCoeff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_le_mul_left", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": true, "tactics": ["classical", "obtain", "simp", "rw", "exact"], "tactic_count": 5}
{"name": "Polynomial.Monic.natDegree_pos", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Monic.degree_pos", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.leadingCoeff_X_pow_sub_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.leadingCoeff_X_pow_sub_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_X_sub_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.natDegree_X_sub_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.nextCoeff_X_sub_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.degree_X_pow_sub_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.X_pow_sub_C_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Polynomial.X_sub_C_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.zero_notMem_multiset_map_X_sub_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natDegree_X_pow_sub_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.leadingCoeff_X_sub_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.eq_X_add_C_of_degree_le_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.SmallDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eq_X_add_C_of_degree_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.SmallDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eq_X_add_C_of_natDegree_le_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.SmallDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Monic.eq_X_add_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.SmallDegree", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.exists_eq_X_add_C_of_natDegree_le_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.SmallDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.zero_le_degree_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.SmallDegree", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.ne_zero_of_coe_le_degree", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.SmallDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.le_natDegree_of_coe_le_degree", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.SmallDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_linear_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.SmallDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_linear_lt", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.SmallDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_linear", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.SmallDegree", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.natDegree_linear_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.SmallDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natDegree_linear", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.SmallDegree", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.leadingCoeff_linear", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.SmallDegree", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.degree_quadratic_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.SmallDegree", "is_tactic_proof": true, "tactics": ["simpa", "degree_add_le_of_degree_le"], "tactic_count": 2}
{"name": "Polynomial.degree_quadratic_lt", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.SmallDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_linear_lt_degree_C_mul_X_sq", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.SmallDegree", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Polynomial.degree_quadratic", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.SmallDegree", "is_tactic_proof": false, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Polynomial.natDegree_quadratic_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.SmallDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natDegree_quadratic", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.SmallDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.leadingCoeff_quadratic", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.SmallDegree", "is_tactic_proof": true, "tactics": ["rw", "leadingCoeff_C_mul_X_pow]"], "tactic_count": 2}
{"name": "Polynomial.degree_cubic_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.SmallDegree", "is_tactic_proof": true, "tactics": ["simpa", "degree_add_le_of_degree_le"], "tactic_count": 2}
{"name": "Polynomial.degree_cubic_lt", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.SmallDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_quadratic_lt_degree_C_mul_X_cb", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.SmallDegree", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Polynomial.degree_cubic", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.SmallDegree", "is_tactic_proof": false, "tactics": ["rw", "degree_add_eq_left_of_degree_lt", "rfl"], "tactic_count": 3}
{"name": "Polynomial.natDegree_cubic_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.SmallDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natDegree_cubic", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.SmallDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.leadingCoeff_cubic", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.SmallDegree", "is_tactic_proof": true, "tactics": ["rw", "leadingCoeff_add_of_degree_lt"], "tactic_count": 2}
{"name": "Polynomial.supDegree_eq_natDegree", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Support", "is_tactic_proof": true, "tactics": ["obtain", "simp", "apply", "rw", "rwa"], "tactic_count": 5}
{"name": "Polynomial.le_natDegree_of_mem_supp", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.supp_subset_range", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.supp_subset_range_natDegree_succ", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.as_sum_support", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.as_sum_support_C_mul_X_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.sum_over_range'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Support", "is_tactic_proof": true, "tactics": ["have", "simp", "exact"], "tactic_count": 3}
{"name": "Polynomial.sum_over_range", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.sum_fin", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Support", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "intro", "exact", "rw"], "tactic_count": 5}
{"name": "Polynomial.as_sum_range'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.as_sum_range", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.as_sum_range_C_mul_X_pow'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.as_sum_range_C_mul_X_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.mem_support_C_mul_X_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.card_support_C_mul_X_pow_le_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Support", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "Polynomial.card_supp_le_succ_natDegree", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Support", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Polynomial.le_degree_of_mem_supp", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.nonempty_support_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Support", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.natDegree_mem_support_of_nonzero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Support", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Polynomial.natDegree_eq_support_max'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.trailingDegree", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.trailingDegree_lt_wf", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natTrailingDegree", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.trailingCoeff", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.TrailingMonic", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.TrailingMonic.def", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.TrailingMonic.decidable", "kind": "instance", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.TrailingMonic.trailingCoeff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.trailingDegree_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.trailingCoeff_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natTrailingDegree_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.trailingDegree_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.trailingDegree_eq_natTrailingDegree", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.trailingDegree_eq_iff_natTrailingDegree_eq", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.trailingDegree_eq_iff_natTrailingDegree_eq_of_pos", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.natTrailingDegree_eq_of_trailingDegree_eq_some", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.natTrailingDegree_le_trailingDegree", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natTrailingDegree_eq_of_trailingDegree_eq", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": true, "tactics": ["unfold", "rw"], "tactic_count": 2}
{"name": "Polynomial.trailingDegree_le_of_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natTrailingDegree_le_of_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coeff_natTrailingDegree_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "by_contra", "obtain", "obtain", "exact", "rintro", "simp"], "tactic_count": 8}
{"name": "Polynomial.coeff_natTrailingDegree_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.trailingDegree_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natTrailingDegree_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.natTrailingDegree_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.trailingDegree_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.trailingDegree_le_trailingDegree", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.trailingCoeff_eq_coeff_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.trailingDegree_ne_of_natTrailingDegree_ne", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natTrailingDegree_le_of_trailingDegree_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Polynomial.natTrailingDegree_le_natTrailingDegree", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.trailingDegree_monomial", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Polynomial.natTrailingDegree_monomial", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Polynomial.natTrailingDegree_monomial_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.le_trailingDegree_monomial", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.trailingDegree_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.le_trailingDegree_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.trailingDegree_one_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Polynomial.natTrailingDegree_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natTrailingDegree_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natTrailingDegree_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.trailingDegree_C_mul_X_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.le_trailingDegree_C_mul_X_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Polynomial.coeff_eq_zero_of_lt_trailingDegree", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coeff_eq_zero_of_lt_natTrailingDegree", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": true, "tactics": ["apply", "by_cases", "rw", "exact", "rw", "exact"], "tactic_count": 6}
{"name": "Polynomial.coeff_natTrailingDegree_pred_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.le_trailingDegree_X_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Polynomial.le_trailingDegree_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natTrailingDegree_X_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.trailingCoeff_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.trailingCoeff_nonzero_iff_nonzero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natTrailingDegree_mem_support_of_nonzero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natTrailingDegree_le_of_mem_supp", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natTrailingDegree_eq_support_min'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.le_natTrailingDegree", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Polynomial.natTrailingDegree_le_natDegree", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "exact"], "tactic_count": 3}
{"name": "Polynomial.natTrailingDegree_mul_X_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": true, "tactics": ["apply", "refine", "rwa", "rw", "intro", "have", "rw", "exact", "rw", "exact"], "tactic_count": 10}
{"name": "Polynomial.le_trailingDegree_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": true, "tactics": ["refine", "rw", "obtain", "refine", "rwa"], "tactic_count": 5}
{"name": "Polynomial.le_natTrailingDegree_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "trailingDegree_eq_natTrailingDegree", "trailingDegree_eq_natTrailingDegree", "exact"], "tactic_count": 6}
{"name": "Polynomial.coeff_mul_natTrailingDegree_add_natTrailingDegree", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": true, "tactics": ["rw", "refine", "rintro", "rw", "by_cases", "rw", "by_cases", "rw", "refine", "exact"], "tactic_count": 10}
{"name": "Polynomial.trailingDegree_mul'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": true, "tactics": ["have", "have", "refine", "rw", "apply", "rwa"], "tactic_count": 6}
{"name": "Polynomial.natTrailingDegree_mul'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": true, "tactics": ["have", "have", "apply", "rw", "trailingDegree_eq_natTrailingDegree"], "tactic_count": 5}
{"name": "Polynomial.natTrailingDegree_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.trailingDegree_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.trailingDegree_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natTrailingDegree_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.trailingDegree_X_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.natTrailingDegree_X_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.trailingDegree_neg", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": true, "tactics": ["unfold", "rw"], "tactic_count": 2}
{"name": "Polynomial.natTrailingDegree_neg", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.natTrailingDegree_intCast", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.nextCoeffUp", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.nextCoeffUp_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.nextCoeffUp_C_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Polynomial.nextCoeffUp_of_constantCoeff_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": true, "tactics": ["obtain", "simp", "rw"], "tactic_count": 3}
{"name": "Polynomial.coeff_natTrailingDegree_eq_zero_of_trailingDegree_lt", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.ne_zero_of_trailingDegree_lt", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natTrailingDegree_eq_zero_of_constantCoeff_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Monic.eq_X_pow_iff_natDegree_le_natTrailingDegree", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": true, "tactics": ["refine", "nontriviality", "rw", "ext", "rw", "obtain", "rw", "simpa", "rw"], "tactic_count": 9}
{"name": "Polynomial.Monic.eq_X_pow_iff_natTrailingDegree_eq_natDegree", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.TrailingDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natDegree_eq_zero_of_isUnit", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Units", "is_tactic_proof": true, "tactics": ["nontriviality", "obtain", "have", "rw", "exact"], "tactic_count": 5}
{"name": "Polynomial.degree_eq_zero_of_isUnit", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_coe_units", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.isUnit_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.not_isUnit_of_degree_pos", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Units", "is_tactic_proof": true, "tactics": ["cases", "simp", "intro", "simp"], "tactic_count": 4}
{"name": "Polynomial.not_isUnit_of_natDegree_pos", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natDegree_coe_units", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Units", "is_tactic_proof": true, "tactics": ["nontriviality", "exact"], "tactic_count": 2}
{"name": "Polynomial.coeff_coe_units_zero_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Units", "is_tactic_proof": true, "tactics": ["conv", "rw", "exact"], "tactic_count": 3}
{"name": "Polynomial.Monic.C_dvd_iff_isUnit", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Monic.degree_pos_of_not_isUnit", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Monic.natDegree_pos_of_not_isUnit", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_pos_of_not_isUnit_of_dvd_monic", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Units", "is_tactic_proof": true, "tactics": ["contrapose", "rw", "simpa"], "tactic_count": 3}
{"name": "Polynomial.natDegree_pos_of_not_isUnit_of_dvd_monic", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Degree.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DenomsClearable", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.DenomsClearable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "denomsClearable_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.DenomsClearable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "denomsClearable_C_mul_X_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.DenomsClearable", "is_tactic_proof": true, "tactics": ["refine", "rw", "rw", "rw", "conv_lhs", "simp"], "tactic_count": 6}
{"name": "DenomsClearable.add", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.DenomsClearable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "denomsClearable_of_natDegree_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.DenomsClearable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "denomsClearable_natDegree", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.DenomsClearable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_le_pow_mul_abs_eval_div", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.DenomsClearable", "is_tactic_proof": false, "tactics": ["obtain", "denomsClearable_natDegree", "rw", "rw", "exact", "obtain", "rw", "rw", "rw", "refine", "rw", "rcases", "exact", "rwa"], "tactic_count": 14}
{"name": "Polynomial.derivative'", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Derivation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.derivation_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.C_smul_derivation_apply", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivation", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "Polynomial.derivation_ext", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.mkDerivation", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Derivation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.mkDerivation_apply", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivation", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "Polynomial.mkDerivation_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivation", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.mkDerivation_one_eq_derivative'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivation", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Polynomial.mkDerivation_one_eq_derivative", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivation", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Polynomial.mkDerivationEquiv", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Derivation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.mkDerivationEquiv_apply", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivation", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "Polynomial.mkDerivationEquiv_symm_apply", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.compAEval", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Derivation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.compAEval_eq", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivation", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Derivation.comp_aeval_eq", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.derivative", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.derivative_apply", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coeff_derivative", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": true, "tactics": ["rw", "simp", "rw", "simp", "intro", "cases", "intros", "rw", "intro", "rw", "simp_all"], "tactic_count": 11}
{"name": "Polynomial.derivative_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.iterate_derivative_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.derivative_monomial", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Polynomial.derivative_monomial_succ", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.derivative_C_mul_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.derivative_C_mul_X_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.derivative_C_mul_X_sq", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.derivative_X_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "Polynomial.derivative_X_pow_succ", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.derivative_X_sq", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.derivative_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.derivative_of_natDegree_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.derivative_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.derivative_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.derivative_add", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.derivative_X_add_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.derivative_sum", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.iterate_derivative_sum", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Polynomial.derivative_smul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.iterate_derivative_smul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Polynomial.iterate_derivative_C_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Polynomial.derivative_C_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.of_mem_support_derivative", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_derivative_lt", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_derivative_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natDegree_derivative_lt", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": true, "tactics": ["rcases", "rw", "exact", "rw", "exact"], "tactic_count": 5}
{"name": "Polynomial.natDegree_derivative_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "exact"], "tactic_count": 3}
{"name": "Polynomial.natDegree_iterate_derivative", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "exact"], "tactic_count": 5}
{"name": "Polynomial.derivative_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Polynomial.derivative_ofNat", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.iterate_derivative_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": false, "tactics": ["induction", "subst", "obtain", "rw", "by_cases", "rw", "have", "exact"], "tactic_count": 8}
{"name": "Polynomial.iterate_derivative_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.iterate_derivative_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.iterate_derivative_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natDegree_eq_zero_of_derivative_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": true, "tactics": ["rcases", "exact", "rw", "by_contra", "rw", "let", "have", "have", "rw", "rw", "replace", "rw", "exact"], "tactic_count": 13}
{"name": "Polynomial.eq_C_of_derivative_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.derivative_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": false, "tactics": ["induction", "add", "monomial", "induction", "add", "monomial", "simp", "simp", "cases", "zero", "succ", "cases", "zero", "succ"], "tactic_count": 14}
{"name": "Polynomial.derivative_eval", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Polynomial.derivative_map", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": true, "tactics": ["let", "rw", "rw", "on_goal", "simp", "all_goals"], "tactic_count": 6}
{"name": "Polynomial.iterate_derivative_map", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Polynomial.derivative_natCast_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.iterate_derivative_natCast_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "Polynomial.mem_support_derivative", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": false, "tactics": ["suffices", "simpa", "rw", "simp"], "tactic_count": 4}
{"name": "Polynomial.degree_derivative_eq", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": true, "tactics": ["apply", "rw", "apply", "intro", "apply", "apply", "refine", "rw", "rw", "intro", "rw", "exact", "exact"], "tactic_count": 13}
{"name": "Polynomial.coeff_iterate_derivative", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "calc", "rw", "rw", "rw"], "tactic_count": 7}
{"name": "Polynomial.iterate_derivative_eq_sum", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": true, "tactics": ["conv_lhs", "refine", "rw"], "tactic_count": 3}
{"name": "Polynomial.iterate_derivative_eq_factorial_smul_sum", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": true, "tactics": ["conv_lhs", "rw", "refine", "rw"], "tactic_count": 4}
{"name": "Polynomial.iterate_derivative_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "calc", "derivative^", "derivative", "simp_rw", "sum_add_distrib]", "rw", "congr", "refine", "rw", "refine", "rw", "congr", "lia", "rw"], "tactic_count": 17}
{"name": "Polynomial.derivativeFinsupp", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.support_derivativeFinsupp_subset_range", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": true, "tactics": ["dsimp", "exact"], "tactic_count": 2}
{"name": "Polynomial.derivativeFinsupp_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": true, "tactics": ["ext", "i"], "tactic_count": 2}
{"name": "Polynomial.derivativeFinsupp_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Polynomial.derivativeFinsupp_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Polynomial.derivativeFinsupp_map", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Polynomial.derivativeFinsupp_derivative", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Polynomial.derivative_pow_succ", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.derivative_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.derivative_sq", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.pow_sub_one_dvd_derivative_of_pow_dvd", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact"], "tactic_count": 3}
{"name": "Polynomial.pow_sub_dvd_iterate_derivative_of_pow_dvd", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "exact"], "tactic_count": 5}
{"name": "Polynomial.pow_sub_dvd_iterate_derivative_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.dvd_iterate_derivative_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": true, "tactics": ["obtain", "rw", "eval_natCast]", "exact"], "tactic_count": 4}
{"name": "Polynomial.iterate_derivative_X_pow_eq_natCast_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "ih", "rw", "simp"], "tactic_count": 6}
{"name": "Polynomial.iterate_derivative_X_pow_eq_C_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.iterate_derivative_X_pow_eq_smul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.derivative_X_add_C_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.derivative_X_add_C_sq", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.iterate_derivative_X_add_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "ring"], "tactic_count": 5}
{"name": "Polynomial.iterate_derivative_mul_X_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": false, "tactics": ["have", "derivative^", "simp_rw", "congr", "norm_cast", "ring", "rw", "refine", "rcases", "replace", "simp", "simp"], "tactic_count": 12}
{"name": "Polynomial.iterate_derivative_mul_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": true, "tactics": ["convert", "rcases"], "tactic_count": 2}
{"name": "Polynomial.iterate_derivative_derivative_mul_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": true, "tactics": ["convert", "rcases"], "tactic_count": 2}
{"name": "Polynomial.iterate_derivative_derivative_mul_X_sq", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": true, "tactics": ["convert", "rcases", "rcases", "suffices", "simp", "ring", "rw", "exact"], "tactic_count": 8}
{"name": "Polynomial.derivative_comp", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": true, "tactics": ["induction", "simp", "simp", "zero_add,", "ring"], "tactic_count": 5}
{"name": "Polynomial.derivative_eval₂_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.derivative_prod", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": true, "tactics": ["refine", "rw", "congr", "rw", "simp", "refine", "rw", "by_cases", "simp", "simp"], "tactic_count": 10}
{"name": "Polynomial.derivative_prod_finset", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Polynomial.derivative_neg", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.iterate_derivative_neg", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.derivative_sub", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.derivative_X_sub_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.iterate_derivative_sub", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.derivative_intCast", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Polynomial.derivative_intCast_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.iterate_derivative_intCast_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "Polynomial.derivative_comp_one_sub_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.iterate_derivative_comp_one_sub_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Polynomial.eval_multiset_prod_X_sub_C_derivative", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": true, "tactics": ["nth_rw", "have", "simpa"], "tactic_count": 3}
{"name": "Polynomial.derivative_X_sub_C_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.derivative_X_sub_C_sq", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.iterate_derivative_X_sub_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.iterate_derivative_X_sub_pow_self", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.iterate_derivative_eq_zero_of_degree_lt", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": true, "tactics": ["induction", "exact", "by_cases", "simp", "rw", "by_cases", "simp", "hP", "have", "contrapose", "exact", "refine", "linarith"], "tactic_count": 13}
{"name": "Polynomial.iterate_derivative_prod_X_sub_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": true, "tactics": ["classical", "induction", "simp", "specialize", "nth_rewrite", "rw", "derivative_sum,", "congr", "calc", "congr", "simp_rw", "rw", "grind", "apply", "intro", "intro", "all_goals", "rw", "grind", "rw", "congr", "simp"], "tactic_count": 22}
{"name": "Polynomial.dvd_derivative_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.derivative_pow_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Derivative", "is_tactic_proof": true, "tactics": ["nontriviality", "rw", "simp"], "tactic_count": 3}
{"name": "Polynomial.X_dvd_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.X_pow_dvd_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.finiteMultiplicity_of_degree_pos_of_monic", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eq_mul_leadingCoeff_of_monic_of_dvd_of_natDegree_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "simp", "have", "rw", "simp"], "tactic_count": 6}
{"name": "Polynomial.eq_of_monic_of_dvd_of_natDegree_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Polynomial.div_wf_lemma", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.divModByMonicAux", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.divByMonic", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.modByMonic", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.term_/ₘ_", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial._aux_Mathlib_Algebra_Polynomial_Div___macroRules_Polynomial_term_/ₘ__1", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial._aux_Mathlib_Algebra_Polynomial_Div___unexpand_Polynomial_divByMonic_1", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.term_%ₘ_", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial._aux_Mathlib_Algebra_Polynomial_Div___macroRules_Polynomial_term_%ₘ__1", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial._aux_Mathlib_Algebra_Polynomial_Div___unexpand_Polynomial_modByMonic_1", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_modByMonic_lt", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natDegree_modByMonic_lt", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "contrapose", "exact", "haveI", "exact"], "tactic_count": 6}
{"name": "Polynomial.zero_modByMonic", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Polynomial.zero_divByMonic", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Polynomial.modByMonic_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.divByMonic_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.divByMonic_eq_of_not_monic", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.modByMonic_eq_of_not_monic", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.modByMonic_eq_self_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_modByMonic_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": true, "tactics": ["nontriviality", "exact"], "tactic_count": 2}
{"name": "Polynomial.degree_modByMonic_le_left", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": true, "tactics": ["nontriviality", "by_cases", "cases", "rw", "exact", "rw"], "tactic_count": 6}
{"name": "Polynomial.natDegree_modByMonic_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natDegree_modByMonic_le_left", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.X_dvd_sub_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.modByMonic_eq_sub_mul_div", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.modByMonic_add_div", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.divByMonic_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_add_divByMonic", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": true, "tactics": ["nontriviality", "have", "have", "have", "calc", "degree", "rw", "exact", "calc", "degree"], "tactic_count": 10}
{"name": "Polynomial.degree_divByMonic_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_divByMonic_lt", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natDegree_divByMonic", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": true, "tactics": ["nontriviality", "by_cases", "rw", "rw", "rw", "have", "rw", "push_neg", "have", "have", "intro", "apply", "rw", "rw", "rw"], "tactic_count": 15}
{"name": "Polynomial.div_modByMonic_unique", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": true, "tactics": ["nontriviality", "have", "eq_of_sub_eq_zero", "rw", "simp", "have", "have", "calc", "degree", "have", "not_le_of_gt", "calc", "degree", "rw", "norm_cast", "exact", "exact"], "tactic_count": 17}
{"name": "Polynomial.map_mod_divByMonic", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": true, "tactics": ["nontriviality", "haveI", "have", "div_modByMonic_unique", "calc", "exact"], "tactic_count": 6}
{"name": "Polynomial.map_divByMonic", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.map_modByMonic", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.modByMonic_eq_zero_iff_dvd", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.self_mul_modByMonic", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Polynomial.map_dvd_map", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Polynomial.modByMonic_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.divByMonic_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": true, "tactics": ["conv_rhs"], "tactic_count": 1}
{"name": "Polynomial.sum_modByMonic_coeff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": true, "tactics": ["nontriviality", "exact"], "tactic_count": 2}
{"name": "Polynomial.mul_divByMonic_cancel_left", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": true, "tactics": ["nontriviality", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "Polynomial.coeff_divByMonic_X_sub_C_rec", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": true, "tactics": ["nontriviality", "have", "set", "rw", "have", "degree_X_sub_C", "simp"], "tactic_count": 7}
{"name": "Polynomial.coeff_divByMonic_X_sub_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": true, "tactics": ["wlog", "refine", "rw", "pow_zero,", "congr", "ext", "rw", "apply", "rw", "exact", "rw", "nontriviality", "by_cases", "rw", "apply", "apply", "rw", "exact"], "tactic_count": 18}
{"name": "Polynomial.not_isField", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": true, "tactics": ["nontriviality", "intro", "letI", "simpa"], "tactic_count": 4}
{"name": "Polynomial.decidableDvdMonic", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.finiteMultiplicity_X_sub_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": true, "tactics": ["haveI", "refine", "rw", "decide", "make"], "tactic_count": 5}
{"name": "Polynomial.rootMultiplicity", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.rootMultiplicity_eq_nat_find_of_nonzero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": true, "tactics": ["dsimp", "cases", "rw"], "tactic_count": 3}
{"name": "Polynomial.rootMultiplicity_eq_multiplicity", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": true, "tactics": ["simp", "split", "rfl", "rename_i", "simp", "rw", "congr"], "tactic_count": 7}
{"name": "Polynomial.rootMultiplicity_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.rootMultiplicity_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": true, "tactics": ["cases", "rw", "classical", "rw", "split_ifs", "rfl", "have", "simp_rw"], "tactic_count": 8}
{"name": "Polynomial.pow_rootMultiplicity_dvd", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.pow_mul_divByMonic_rootMultiplicity_eq", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": true, "tactics": ["have", "conv_rhs", "simp"], "tactic_count": 3}
{"name": "Polynomial.exists_eq_pow_rootMultiplicity_mul_and_not_dvd", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": true, "tactics": ["classical", "rw", "apply"], "tactic_count": 3}
{"name": "Polynomial.modByMonic_X_sub_C_eq_C_eval", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": true, "tactics": ["nontriviality", "have", "rw", "sub_zero]", "have", "have", "revert", "cases", "exact", "exact", "rw", "rw"], "tactic_count": 12}
{"name": "Polynomial.mul_divByMonic_eq_iff_isRoot", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.dvd_iff_isRoot", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.X_sub_C_dvd_sub_C_eval", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.modByMonic_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.eval₂_modByMonic_eq_self_of_root", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.sub_dvd_eval_sub", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": false, "tactics": ["suffices", "simpa", "simp"], "tactic_count": 3}
{"name": "Polynomial.IsRoot.dvd_coeff_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Polynomial.rootMultiplicity_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": true, "tactics": ["classical", "simp"], "tactic_count": 2}
{"name": "Polynomial.rootMultiplicity_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.rootMultiplicity_pos'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.rootMultiplicity_pos", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eval_divByMonic_pow_rootMultiplicity_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": true, "tactics": ["classical", "haveI", "rw", "rintro", "have", "rw", "exact"], "tactic_count": 7}
{"name": "Polynomial.mul_self_modByMonic", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Polynomial.modByMonic_eq_of_dvd_sub", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": true, "tactics": ["nontriviality", "obtain", "refine", "rw"], "tactic_count": 4}
{"name": "Polynomial.add_modByMonic", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": true, "tactics": ["by_cases", "rcases", "simp", "exact", "rw", "modByMonic_add_div", "simp_rw"], "tactic_count": 7}
{"name": "Polynomial.neg_modByMonic", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.sub_modByMonic", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.mul_modByMonic", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "apply", "have", "rw", "apply", "all_goals", "apply", "simp"], "tactic_count": 9}
{"name": "Polynomial.eval_divByMonic_eq_trailingCoeff_comp", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": true, "tactics": ["obtain", "rw", "have", "set", "set", "have", "rw", "rw", "reverse_leadingCoeff,"], "tactic_count": 9}
{"name": "Polynomial.le_rootMultiplicity_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": true, "tactics": ["classical", "simp_rw", "refine", "rcases", "rw", "apply", "exact"], "tactic_count": 7}
{"name": "Polynomial.rootMultiplicity_le_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.rootMultiplicity_add", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Polynomial.le_rootMultiplicity_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": true, "tactics": ["rw", "gcongr"], "tactic_count": 2}
{"name": "Polynomial.rootMultiplicity_le_rootMultiplicity_of_dvd", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Polynomial.pow_rootMultiplicity_not_dvd", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.rootMultiplicity_eq_natTrailingDegree'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "refine", "rw", "exact", "rw", "exact"], "tactic_count": 7}
{"name": "Polynomial.leadingCoeff_divByMonic_of_monic", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": true, "tactics": ["nontriviality", "have", "simpa", "nth_rw", "rw", "rw", "exact"], "tactic_count": 7}
{"name": "Polynomial.degree_eq_one_of_irreducible_of_root", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Irreducible.not_isRoot_of_natDegree_ne_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Irreducible.isRoot_eq_bot_of_natDegree_ne_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Irreducible.subsingleton_isRoot", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.leadingCoeff_divByMonic_X_sub_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": true, "tactics": ["nontriviality", "rcases", "rw", "refine", "rwa"], "tactic_count": 5}
{"name": "Polynomial.eq_of_dvd_of_natDegree_le_of_leadingCoeff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": true, "tactics": ["rcases", "simpa", "replace", "obtain", "rw", "rw", "rw", "mul_eq_left₀", "rw"], "tactic_count": 9}
{"name": "Polynomial.associated_of_dvd_of_natDegree_le_of_leadingCoeff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.associated_of_dvd_of_natDegree_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.associated_of_dvd_of_degree_eq", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eq_leadingCoeff_mul_of_monic_of_dvd_of_natDegree_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Div", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.eraseLead", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.EraseLead", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eraseLead_support", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.EraseLead", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.eraseLead_coeff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.EraseLead", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.eraseLead_coeff_natDegree", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.EraseLead", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.eraseLead_coeff_of_ne", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.EraseLead", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.eraseLead_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.EraseLead", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.eraseLead_add_monomial_natDegree_leadingCoeff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.EraseLead", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eraseLead_add_C_mul_X_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.EraseLead", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.self_sub_monomial_natDegree_leadingCoeff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.EraseLead", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.self_sub_C_mul_X_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.EraseLead", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.eraseLead_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.EraseLead", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Polynomial.lt_natDegree_of_mem_eraseLead_support", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.EraseLead", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Polynomial.ne_natDegree_of_mem_eraseLead_support", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.EraseLead", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natDegree_notMem_eraseLead_support", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.EraseLead", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eraseLead_support_card_lt", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.EraseLead", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Polynomial.card_support_eraseLead_add_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.EraseLead", "is_tactic_proof": true, "tactics": ["set", "cases", "by_contra", "exact", "rw", "rfl"], "tactic_count": 6}
{"name": "Polynomial.card_support_eraseLead", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.EraseLead", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "rw"], "tactic_count": 3}
{"name": "Polynomial.card_support_eraseLead'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.EraseLead", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.card_support_eq_one_of_eraseLead_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.EraseLead", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.card_support_le_one_of_eraseLead_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.EraseLead", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "exact"], "tactic_count": 3}
{"name": "Polynomial.eraseLead_monomial", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.EraseLead", "is_tactic_proof": true, "tactics": ["classical", "by_cases", "subst", "simp", "rw"], "tactic_count": 5}
{"name": "Polynomial.eraseLead_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.EraseLead", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eraseLead_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.EraseLead", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eraseLead_X_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.EraseLead", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.eraseLead_C_mul_X_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.EraseLead", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.eraseLead_C_mul_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.EraseLead", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Polynomial.eraseLead_add_of_degree_lt_left", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.EraseLead", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "rw", "simpa", "rw", "rintro", "exact"], "tactic_count": 7}
{"name": "Polynomial.eraseLead_add_of_natDegree_lt_left", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.EraseLead", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eraseLead_add_of_degree_lt_right", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.EraseLead", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "rw", "simpa", "rw", "rintro", "exact"], "tactic_count": 7}
{"name": "Polynomial.eraseLead_add_of_natDegree_lt_right", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.EraseLead", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eraseLead_degree_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.EraseLead", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_eraseLead_lt", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.EraseLead", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eraseLead_natDegree_le_aux", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.EraseLead", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eraseLead_natDegree_lt", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.EraseLead", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natDegree_pos_of_eraseLead_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.EraseLead", "is_tactic_proof": true, "tactics": ["by_contra", "rw", "simp"], "tactic_count": 3}
{"name": "Polynomial.eraseLead_natDegree_lt_or_eraseLead_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.EraseLead", "is_tactic_proof": true, "tactics": ["by_cases", "right", "rw", "simp", "left", "apply"], "tactic_count": 6}
{"name": "Polynomial.eraseLead_natDegree_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.EraseLead", "is_tactic_proof": true, "tactics": ["rcases", "exact", "simp"], "tactic_count": 3}
{"name": "Polynomial.natDegree_eraseLead", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.EraseLead", "is_tactic_proof": true, "tactics": ["have", "refine", "rwa", "all_goals"], "tactic_count": 4}
{"name": "Polynomial.natDegree_eraseLead_add_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.EraseLead", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Polynomial.natDegree_eraseLead_le_of_nextCoeff_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.EraseLead", "is_tactic_proof": true, "tactics": ["refine", "rw", "obtain", "simp", "rw", "simp"], "tactic_count": 6}
{"name": "Polynomial.two_le_natDegree_of_nextCoeff_eraseLead", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.EraseLead", "is_tactic_proof": true, "tactics": ["contrapose", "rw", "obtain", "simp", "rw", "subst", "simp"], "tactic_count": 7}
{"name": "Polynomial.leadingCoeff_eraseLead_eq_nextCoeff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.EraseLead", "is_tactic_proof": true, "tactics": ["have", "rw", "all_goals"], "tactic_count": 3}
{"name": "Polynomial.nextCoeff_eq_zero_of_eraseLead_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.EraseLead", "is_tactic_proof": true, "tactics": ["by_contra", "exact"], "tactic_count": 2}
{"name": "Polynomial.eraseLead_mul_eq_mul_eraseLead_of_nextCoeff_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.EraseLead", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "by_cases", "rw", "by_cases", "simp", "suffices", "rw", "linarith", "have", "simpa", "have", "rw", "linarith", "have", "rw", "obtain", "have", "simp", "rw", "simp", "ext", "rcases", "have", "rw", "rw", "rw", "add_eq_left]", "rcases", "simpa", "rw", "trans", "grw", "simpa", "grw", "simpa"], "tactic_count": 36}
{"name": "Polynomial.induction_with_natDegree_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.EraseLead", "is_tactic_proof": true, "tactics": ["induction", "zero", "convert", "simpa", "succ", "rw", "cases", "convert", "convert", "rw", "rw", "exact", "refine", "refine", "exact", "rw", "rintro", "simp", "exact", "exact", "refine", "rw", "exact"], "tactic_count": 23}
{"name": "Polynomial.mono_map_natDegree_eq", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.EraseLead", "is_tactic_proof": false, "tactics": ["refine", "induction_with_natDegree_le", "intro", "rw", "intro", "rw", "by_cases", "rw", "rw", "exact", "cases", "nomatch", "rwa"], "tactic_count": 13}
{"name": "Polynomial.map_natDegree_eq_sub", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.EraseLead", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.map_natDegree_eq_natDegree", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.EraseLead", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.card_support_eq'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.EraseLead", "is_tactic_proof": false, "tactics": ["suffices", "simp_rw", "refine", "obtain", "exact", "rintro", "rw", "exact", "exact"], "tactic_count": 9}
{"name": "Polynomial.card_support_eq", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.EraseLead", "is_tactic_proof": true, "tactics": ["refine", "induction", "zero", "succ", "intro", "obtain", "have", "rintro", "exact", "refine", "intro", "have", "simp", "exact", "obtain", "rw", "by_cases", "obtain", "rwa", "rw", "apply", "rw", "rw", "exact", "intro", "rw", "exact", "intro", "by_cases", "obtain", "rw", "exact", "rw", "exact", "rw", "simp", "rw", "all_goals"], "tactic_count": 38}
{"name": "Polynomial.card_support_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.EraseLead", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact", "rintro", "rw"], "tactic_count": 5}
{"name": "Polynomial.card_support_eq_two", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.EraseLead", "is_tactic_proof": true, "tactics": ["refine", "obtain", "refine", "rw", "rfl", "rintro", "exact"], "tactic_count": 7}
{"name": "Polynomial.card_support_eq_three", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.EraseLead", "is_tactic_proof": true, "tactics": ["refine", "obtain", "refine", "rw", "rfl", "rintro", "exact"], "tactic_count": 7}
{"name": "Polynomial.eval₂_mul'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Algebra", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "Polynomial.eval₂_pow'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Algebra", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Polynomial.eval₂_comp'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Algebra", "is_tactic_proof": true, "tactics": ["induction", "add", "monomial"], "tactic_count": 3}
{"name": "Polynomial.eval₂_at_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Coeff", "is_tactic_proof": true, "tactics": ["simp", "sum_ite_eq',"], "tactic_count": 2}
{"name": "Polynomial.eval₂_C_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Coeff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coeff_zero_eq_eval_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Coeff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.zero_isRoot_iff_coeff_zero_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Coeff", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.coeff_map", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Coeff", "is_tactic_proof": true, "tactics": ["rw", "simp_all"], "tactic_count": 2}
{"name": "Polynomial.coeff_map_eq_comp", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Coeff", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Polynomial.map_map", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Coeff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.map_id", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Coeff", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.piEquiv", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Eval.Coeff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.map_injective", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Coeff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.map_injective_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Coeff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.map_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Coeff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.map_surjective_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Coeff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.map_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Coeff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.map_ne_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Coeff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.mapRingHom_id", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Coeff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.mapRingHom_comp", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Coeff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eval₂_map", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Coeff", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.eval_zero_map", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Coeff", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.eval_one_map", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Coeff", "is_tactic_proof": true, "tactics": ["induction", "add", "monomial"], "tactic_count": 3}
{"name": "Polynomial.eval_natCast_map", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Coeff", "is_tactic_proof": true, "tactics": ["induction", "add", "monomial"], "tactic_count": 3}
{"name": "Polynomial.eval_intCast_map", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Coeff", "is_tactic_proof": true, "tactics": ["induction", "add", "monomial"], "tactic_count": 3}
{"name": "Polynomial.hom_eval₂", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Coeff", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.eval₂_hom", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Coeff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.evalRingHom_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Coeff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.support_map_subset", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Coeff", "is_tactic_proof": true, "tactics": ["intro", "contrapose", "simp"], "tactic_count": 3}
{"name": "Polynomial.support_map_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Coeff", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Polynomial.IsRoot.map", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Coeff", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.IsRoot.of_map", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Coeff", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Polynomial.isRoot_map_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Coeff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.definition._@.Mathlib.Algebra.Polynomial.Eval.Defs.2849575019._hygCtx._hyg.2", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.wrapped._@.Mathlib.Algebra.Polynomial.Eval.Defs.2849575019._hygCtx._hyg.2", "kind": "opaque", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eval₂", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eval₂_def", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": true, "tactics": ["intros", "delta", "rw", "rfl"], "tactic_count": 4}
{"name": "Polynomial.eval₂_eq_sum", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.eval₂_congr", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "Polynomial.eval₂_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.eval₂_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.eval₂_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.eval₂_monomial", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.eval₂_X_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": true, "tactics": ["rw", "convert", "simp"], "tactic_count": 3}
{"name": "Polynomial.eval₂_add", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": true, "tactics": ["simp", "apply"], "tactic_count": 2}
{"name": "Polynomial.eval₂_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.eval₂AddMonoidHom", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eval₂_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Polynomial.eval₂_ofNat", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.eval₂_sum", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": ["let", "map_zero", "map_add", "have", "simp", "rw"], "tactic_count": 6}
{"name": "Polynomial.eval₂_list_sum", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eval₂_multiset_sum", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eval₂_finset_sum", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eval₂_ofFinsupp", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": true, "tactics": ["simp", "rfl"], "tactic_count": 2}
{"name": "Polynomial.eval₂_mul_noncomm", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simp", "exact"], "tactic_count": 4}
{"name": "Polynomial.eval₂_mul_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": true, "tactics": ["refine", "rcases", "simp", "simp"], "tactic_count": 4}
{"name": "Polynomial.eval₂_X_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.eval₂_mul_C'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": true, "tactics": ["rw", "intro", "by_cases", "simp", "simp"], "tactic_count": 5}
{"name": "Polynomial.eval₂_list_prod_noncomm", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": true, "tactics": ["induction", "nil", "append_singleton", "ihp", "simp", "simp"], "tactic_count": 6}
{"name": "Polynomial.eval₂RingHom'", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eval₂_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eval₂_mul_eq_zero_of_left", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Polynomial.eval₂_mul_eq_zero_of_right", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Polynomial.eval₂RingHom", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coe_eval₂RingHom", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eval₂_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eval₂_dvd", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eval₂_eq_zero_of_dvd_of_eval₂_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eval₂_list_prod", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eval", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eval₂_id", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eval_eq_sum", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Polynomial.eval₂_at_apply", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Polynomial.eval₂_at_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "Polynomial.eval₂_at_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "Polynomial.eval₂_at_ofNat", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.eval_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eval_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.eval_ofNat", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.eval_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eval_monomial", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eval_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eval_add", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eval_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eval_C_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": true, "tactics": ["induction", "add", "monomial"], "tactic_count": 3}
{"name": "Polynomial.eval_natCast_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.eval_mul_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eval_mul_X_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Polynomial.eval_listSum", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eval_multisetSum", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eval_sum", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eval_finset_sum", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.IsRoot", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.IsRoot.decidable", "kind": "instance", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "Polynomial.IsRoot.def", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.IsRoot.eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.IsRoot.dvd", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Polynomial.not_isRoot_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Polynomial.eval_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.comp", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.comp_eq_sum_left", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.comp_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Polynomial.X_comp", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.comp_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.C_comp", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natCast_comp", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.ofNat_comp", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.comp_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.zero_comp", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.comp_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.one_comp", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.add_comp", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.monomial_comp", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.mul_X_comp", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": true, "tactics": ["induction", "add", "monomial"], "tactic_count": 3}
{"name": "Polynomial.X_pow_comp", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Polynomial.mul_X_pow_comp", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Polynomial.C_mul_comp", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": true, "tactics": ["induction", "add", "monomial"], "tactic_count": 3}
{"name": "Polynomial.natCast_mul_comp", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.mul_X_add_natCast_comp", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.mul_comp", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.mul_comp_neg_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.pow_comp", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.comp_assoc", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": true, "tactics": ["refine", "intros", "simp_all"], "tactic_count": 3}
{"name": "Polynomial.sum_comp", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.map", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.map_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.map_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.map_monomial", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "Polynomial.map_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.map_add", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.map_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.map_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Polynomial.mapRingHom", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coe_mapRingHom", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.map_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.map_ofNat", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.map_dvd", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.associated_map_map", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.mapRingHom_comp_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Polynomial.eval₂_eq_eval_map", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": true, "tactics": ["induction", "add", "monomial"], "tactic_count": 3}
{"name": "Polynomial.map_list_prod", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.map_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eval_map", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eval_map_apply", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.map_sum", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.map_comp", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eval_X_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.eval_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.evalRingHom", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coe_evalRingHom", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eval_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eval_comp", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": true, "tactics": ["induction", "add", "monomial"], "tactic_count": 3}
{"name": "Polynomial.isRoot_comp", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Polynomial.compRingHom", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coe_compRingHom", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coe_compRingHom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.root_mul_left_of_isRoot", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.root_mul_right_of_isRoot", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eval₂_multiset_prod", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eval₂_finset_prod", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eval_list_prod", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eval_multiset_prod", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eval_prod", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.list_prod_comp", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.multiset_prod_comp", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.prod_comp", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.isRoot_prod", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.eval_dvd", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eval_eq_zero_of_dvd_of_eval_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eval_geom_sum", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.root_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Polynomial.root_or_root_of_root_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.map_multiset_prod", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.map_prod", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.map_sub", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.map_neg", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.map_intCast", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eval_intCast", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.eval₂_neg", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.eval₂_sub", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.eval_neg", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eval_sub", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.root_X_sub_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.neg_comp", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.sub_comp", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.intCast_comp", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Polynomial.eval₂_at_intCast", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "Polynomial.mul_X_sub_intCast_comp", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.eval₂_eq_sum_range", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Degree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eval₂_eq_sum_range'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Degree", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw"], "tactic_count": 3}
{"name": "Polynomial.eval_eq_sum_range", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Degree", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.eval_eq_sum_range'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Degree", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.eval_monomial_one_add_sub", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Degree", "is_tactic_proof": true, "tactics": ["have", "rw", "simp", "rw", "refine", "rw"], "tactic_count": 6}
{"name": "Polynomial.coeff_comp_degree_mul_degree", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Degree", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp", "intro", "refine", "rw", "refine", "gcongr", "exact", "simp"], "tactic_count": 10}
{"name": "Polynomial.comp_C_mul_X_coeff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Degree", "is_tactic_proof": false, "tactics": ["simp_rw", "rw", "intro", "rw", "rwa"], "tactic_count": 5}
{"name": "Polynomial.comp_C_mul_X_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Degree", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "rw"], "tactic_count": 3}
{"name": "Polynomial.mapEquiv", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Eval.Degree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.map_monic_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Degree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.map_monic_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Degree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_map_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Degree", "is_tactic_proof": true, "tactics": ["refine", "rw", "simp"], "tactic_count": 3}
{"name": "Polynomial.natDegree_map_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Degree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_map_lt", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Degree", "is_tactic_proof": true, "tactics": ["refine", "rw", "rw"], "tactic_count": 3}
{"name": "Polynomial.natDegree_map_lt", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Degree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natDegree_map_lt'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Degree", "is_tactic_proof": true, "tactics": ["by_cases", "rwa", "exact"], "tactic_count": 3}
{"name": "Polynomial.degree_map_eq_of_leadingCoeff_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Degree", "is_tactic_proof": true, "tactics": ["refine", "have", "rw", "refine", "rw", "exact"], "tactic_count": 6}
{"name": "Polynomial.natDegree_map_of_leadingCoeff_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Degree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.leadingCoeff_map_of_leadingCoeff_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Degree", "is_tactic_proof": true, "tactics": ["unfold", "rw"], "tactic_count": 2}
{"name": "Polynomial.nextCoeff_map_of_leadingCoeff_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Degree", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Polynomial.eval₂_comp", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Degree", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.iterate_comp_eval₂", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Degree", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Polynomial.iterate_comp_eval", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Degree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.isUnit_of_isUnit_leadingCoeff_of_isUnit_map", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Degree", "is_tactic_proof": true, "tactics": ["have", "rw", "rw", "refine", "convert", "change", "rw", "rfl", "rintro", "simp", "intro", "have", "rw", "simp"], "tactic_count": 14}
{"name": "Polynomial.Monic.irreducible_of_irreducible_map", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Irreducible", "is_tactic_proof": true, "tactics": ["refine", "dsimp", "have", "rw", "refine", "apply", "apply", "exact", "rw", "exact"], "tactic_count": 10}
{"name": "Polynomial.eval₂_smul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.SMul", "is_tactic_proof": true, "tactics": ["have", "have", "rw"], "tactic_count": 3}
{"name": "Polynomial.eval_smul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.SMul", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.leval", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Eval.SMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.smul_comp", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.SMul", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.map_smul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.SMul", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.mem_map_rangeS", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Subring", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "rw", "exact", "intro", "rw", "refine", "intro", "rcases", "use", "rw"], "tactic_count": 11}
{"name": "Polynomial.mem_map_range", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Eval.Subring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.expand", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Expand", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coe_expand", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Expand", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.expand_eq_comp_X_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Expand", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.expand_eq_sum", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Expand", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.expand_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Expand", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.expand_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Expand", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.expand_monomial", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Expand", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Polynomial.expand_expand", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Expand", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.expand_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Expand", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.expand_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Expand", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.expand_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Expand", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.expand_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Expand", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.derivative_expand", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Expand", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.coeff_expand", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Expand", "is_tactic_proof": true, "tactics": ["simp", "simp_rw", "split_ifs", "rw", "intro", "rw", "intro", "apply", "rw", "intro", "rw", "split_ifs", "rw", "intro", "rw", "exact"], "tactic_count": 16}
{"name": "Polynomial.coeff_expand_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Expand", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.coeff_expand_mul'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Expand", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.expand_injective", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Expand", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.expand_inj", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Expand", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.expand_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Expand", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.expand_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Expand", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.expand_eq_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Expand", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.natDegree_expand", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Expand", "is_tactic_proof": true, "tactics": ["rcases", "rw", "by_cases", "rw", "have", "rw", "refine", "rw", "split_ifs", "rw", "contrapose", "norm_cast", "rw", "exact", "rfl", "refine", "rw", "exact"], "tactic_count": 18}
{"name": "Polynomial.leadingCoeff_expand", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Expand", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Polynomial.monic_expand_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Expand", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.map_expand", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Expand", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "ext", "rw", "split_ifs"], "tactic_count": 5}
{"name": "Polynomial.expand_eval", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Expand", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "Polynomial.expand_aeval", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Expand", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "Polynomial.contract", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Expand", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coeff_contract", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Expand", "is_tactic_proof": true, "tactics": ["simp", "intro", "apply", "calc", "f.natDegree"], "tactic_count": 5}
{"name": "Polynomial.map_contract", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Expand", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.contract_expand", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Expand", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Polynomial.contract_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Expand", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.contract_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Expand", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.contract_add", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Expand", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Polynomial.contract_mul_expand", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Expand", "is_tactic_proof": true, "tactics": ["ext", "rw", "sum_image]", "simp_rw", "intro", "simp_rw", "simp_rw", "intro", "by_cases", "obtain", "obtain", "refine", "rw", "rw"], "tactic_count": 14}
{"name": "Polynomial.isCoprime_expand", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Expand", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.expand_contract", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Expand", "is_tactic_proof": true, "tactics": ["ext", "rw", "split_ifs", "rw", "rcases", "exact", "have", "rw", "rcases", "rw", "rename_i", "rw", "exact"], "tactic_count": 13}
{"name": "Polynomial.expand_contract'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Expand", "is_tactic_proof": true, "tactics": ["obtain", "rw", "haveI"], "tactic_count": 3}
{"name": "Polynomial.map_frobenius_expand", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Expand", "is_tactic_proof": true, "tactics": ["refine", "rw", "rw", "frobenius_def]", "ring"], "tactic_count": 5}
{"name": "Polynomial.map_iterateFrobenius_expand", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Expand", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "symm", "conv_lhs", "simp_rw", "expand_mul,"], "tactic_count": 7}
{"name": "Polynomial.rootMultiplicity_expand_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Expand", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "rw", "conv_lhs", "rw", "rootMultiplicity_mul_X_sub_C_pow", "rootMultiplicity_eq_zero"], "tactic_count": 7}
{"name": "Polynomial.rootMultiplicity_expand", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Expand", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.isLocalHom_expand", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Expand", "is_tactic_proof": true, "tactics": ["refine", "have", "rw", "rw"], "tactic_count": 4}
{"name": "Polynomial.of_irreducible_expand", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Expand", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.of_irreducible_expand_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Expand", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.rootMultiplicity_sub_one_le_derivative_rootMultiplicity_of_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.derivative_rootMultiplicity_of_root_of_mem_nonZeroDivisors", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "obtain", "set", "have", "have", "rw", "mul_comm", "rw", "rwa", "have", "exact", "le_antisymm"], "tactic_count": 13}
{"name": "Polynomial.isRoot_iterate_derivative_of_lt_rootMultiplicity", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eval_iterate_derivative_rootMultiplicity", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": true, "tactics": ["set", "conv_lhs", "rw", "rw", "nsmul_eq_mul]", "rfl", "intro", "rw", "zero_mul,"], "tactic_count": 9}
{"name": "Polynomial.lt_rootMultiplicity_of_isRoot_iterate_derivative_of_mem_nonZeroDivisors", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": true, "tactics": ["by_contra", "replace", "simp", "obtain", "rw", "rw", "exact"], "tactic_count": 7}
{"name": "Polynomial.lt_rootMultiplicity_of_isRoot_iterate_derivative_of_mem_nonZeroDivisors'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": true, "tactics": ["apply", "clear", "induction", "zero", "simp", "exact", "succ", "rw", "exact"], "tactic_count": 9}
{"name": "Polynomial.lt_rootMultiplicity_iff_isRoot_iterate_derivative_of_mem_nonZeroDivisors", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.lt_rootMultiplicity_iff_isRoot_iterate_derivative_of_mem_nonZeroDivisors'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.one_lt_rootMultiplicity_iff_isRoot_iterate_derivative", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.one_lt_rootMultiplicity_iff_isRoot", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": true, "tactics": ["rw", "refine", "obtain", "exacts"], "tactic_count": 4}
{"name": "Polynomial.one_lt_rootMultiplicity_iff_isRoot_gcd", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Polynomial.derivative_rootMultiplicity_of_root", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "exact", "derivative_rootMultiplicity_of_root_of_mem_nonZeroDivisors", "mem_nonZeroDivisors_of_ne_zero"], "tactic_count": 5}
{"name": "Polynomial.rootMultiplicity_sub_one_le_derivative_rootMultiplicity", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "rw", "exact"], "tactic_count": 4}
{"name": "Polynomial.lt_rootMultiplicity_of_isRoot_iterate_derivative", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.lt_rootMultiplicity_iff_isRoot_iterate_derivative", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.isRoot_of_isRoot_of_dvd_derivative_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": true, "tactics": ["rcases", "have", "contrapose", "rw", "exact", "by_contra", "have", "have", "have", "rw", "rootMultiplicity_mul", "lia"], "tactic_count": 12}
{"name": "Polynomial.instNormalizationMonoid", "kind": "instance", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coe_normUnit", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.leadingCoeff_normalize", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.Monic.normalize_eq_self", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.roots_normalize", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.normUnit_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "Polynomial.X_eq_normalize", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.degree_pos_of_ne_zero_of_nonunit", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.map_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.map_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_map", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natDegree_map", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.leadingCoeff_map", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.nextCoeff_map_eq", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.monic_map_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.isUnit_iff_degree_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.div", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.mod", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Polynomial.FieldDivision.0.Polynomial.quotient_mul_add_remainder_eq_aux", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "conv", "rhs", "rw", "rw"], "tactic_count": 6}
{"name": "_private.Mathlib.Algebra.Polynomial.FieldDivision.0.Polynomial.remainder_lt_aux", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Polynomial.instDiv", "kind": "instance", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.instMod", "kind": "instance", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.div_def", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.mod_def", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.modByMonic_eq_mod", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.divByMonic_eq_div", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.mod_X_sub_C_eq_C_eval", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.mul_div_eq_iff_isRoot", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.instEuclideanDomain", "kind": "instance", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.mod_eq_self_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.div_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_add_div", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": false, "tactics": ["have", "calc", "degree", "conv_rhs"], "tactic_count": 4}
{"name": "Polynomial.degree_div_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "rw"], "tactic_count": 3}
{"name": "Polynomial.degree_div_lt", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "Polynomial.isUnit_map", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Polynomial.map_div", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": true, "tactics": ["rw", "map_C,"], "tactic_count": 2}
{"name": "Polynomial.map_mod", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "rw", "map_modByMonic"], "tactic_count": 4}
{"name": "Polynomial.natDegree_mod_lt", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": false, "tactics": ["have", "rw", "contrapose", "simp", "rw", "refine", "refine", "rw", "contrapose", "rw", "simp", "exact"], "tactic_count": 12}
{"name": "Polynomial.degree_mod_lt", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp"], "tactic_count": 3}
{"name": "Polynomial.add_mod", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.sub_mod", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.mul_mod", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": true, "tactics": ["simp_rw", "apply"], "tactic_count": 2}
{"name": "Polynomial.gcd_map", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eval₂_gcd_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": true, "tactics": ["rw", "zero_mul,"], "tactic_count": 2}
{"name": "Polynomial.eval_gcd_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.root_left_of_root_gcd", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": true, "tactics": ["obtain", "rw"], "tactic_count": 2}
{"name": "Polynomial.root_right_of_root_gcd", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": true, "tactics": ["obtain", "rw"], "tactic_count": 2}
{"name": "Polynomial.root_gcd_iff_root_left_right", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.isRoot_gcd_iff_isRoot_left_right", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.isCoprime_map", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Polynomial.mem_roots_map", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.rootSet_monomial", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": true, "tactics": ["classical", "rw"], "tactic_count": 2}
{"name": "Polynomial.rootSet_C_mul_X_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.rootSet_X_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Polynomial.rootSet_prod", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": true, "tactics": ["classical", "simp", "rw", "rwa"], "tactic_count": 4}
{"name": "Polynomial.roots_C_mul_X_sub_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.roots_C_mul_X_add_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.roots_degree_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": true, "tactics": ["rw", "have", "simp"], "tactic_count": 3}
{"name": "Polynomial.exists_root_of_degree_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coeff_inv_units", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": false, "tactics": ["rw", "inv_eq_one_div]", "split_ifs", "rw", "eval_mul,", "simp", "simp"], "tactic_count": 7}
{"name": "Polynomial.monic_normalize", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": true, "tactics": ["rw", "rw", "apply"], "tactic_count": 3}
{"name": "Polynomial.normalize_eq_self_iff_monic", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.leadingCoeff_div", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "rw", "mul_comm,", "rwa"], "tactic_count": 5}
{"name": "Polynomial.div_C_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "simp", "congr", "rw"], "tactic_count": 5}
{"name": "Polynomial.div_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Polynomial.C_div", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.C_mul_dvd", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.dvd_C_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coe_normUnit_of_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": true, "tactics": ["have", "simp"], "tactic_count": 2}
{"name": "Polynomial.map_dvd_map'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "classical", "rw", "coe_normUnit_of_ne_zero"], "tactic_count": 5}
{"name": "Polynomial.degree_normalize", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.prime_of_degree_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": true, "tactics": ["classical", "have", "exact"], "tactic_count": 3}
{"name": "Polynomial.irreducible_of_degree_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.not_irreducible_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "exact", "exact"], "tactic_count": 4}
{"name": "Polynomial.degree_pos_of_irreducible", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.X_sub_C_mul_divByMonic_eq_sub_modByMonic", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Polynomial.divByMonic_add_X_sub_C_mul_derivative_divByMonic_eq_derivative", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": true, "tactics": ["have", "simpa", "modByMonic_X_sub_C_eq_C_eval]"], "tactic_count": 3}
{"name": "Polynomial.X_sub_C_dvd_derivative_of_X_sub_C_dvd_divByMonic", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "use"], "tactic_count": 4}
{"name": "Polynomial.isCoprime_of_is_root_of_eval_derivative_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": true, "tactics": ["classical", "refine", "contrapose", "have", "rw", "rwa"], "tactic_count": 6}
{"name": "Polynomial.irreducible_iff_degree_lt", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": true, "tactics": ["rw", "simp", "contrapose", "exact"], "tactic_count": 4}
{"name": "Polynomial.irreducible_iff_lt_natDegree_lt", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": false, "tactics": ["have", "contrapose", "exact", "rw", "natDegree_mul_leadingCoeff_inv", "simp"], "tactic_count": 6}
{"name": "Polynomial.leadingCoeff_mul_prod_normalizedFactors", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "rw", "map_mul,", "simp_all"], "tactic_count": 5}
{"name": "Polynomial.mem_normalizedFactors_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": true, "tactics": ["by_cases", "simpa", "rw"], "tactic_count": 3}
{"name": "Polynomial.map_normalize", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "simp"], "tactic_count": 3}
{"name": "Polynomial.monic_mapAlg_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.mod_eq_of_dvd_sub", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": true, "tactics": ["obtain", "simpa", "simp_rw", "apply", "rw", "exact"], "tactic_count": 6}
{"name": "Irreducible.natDegree_pos", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Irreducible.degree_pos", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.FieldDivision", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Polynomial.smul_eq_map", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.GroupRingAction", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Polynomial.instMulSemiringAction", "kind": "instance", "module": "Mathlib.Algebra.Polynomial.GroupRingAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.smul_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.GroupRingAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.smul_eval_smul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.GroupRingAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eval_smul'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.GroupRingAction", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.smul_eval", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.GroupRingAction", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "prodXSubSMul", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.GroupRingAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "prodXSubSMul.monic", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.GroupRingAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "prodXSubSMul.eval", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.GroupRingAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "prodXSubSMul.smul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.GroupRingAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "prodXSubSMul.coeff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.GroupRingAction", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MulSemiringActionHom.polynomial", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.GroupRingAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulSemiringActionHom.coe_polynomial", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.GroupRingAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.hasseDeriv", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.HasseDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.hasseDeriv_apply", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.HasseDeriv", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "Polynomial.hasseDeriv_coeff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.HasseDeriv", "is_tactic_proof": true, "tactics": ["rw", "simp", "intro", "rw", "by_cases", "simp", "grind", "intro", "simp"], "tactic_count": 9}
{"name": "Polynomial.hasseDeriv_zero'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.HasseDeriv", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.hasseDeriv_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.HasseDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.hasseDeriv_eq_zero_of_lt_natDegree", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.HasseDeriv", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp"], "tactic_count": 3}
{"name": "Polynomial.hasseDeriv_one'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.HasseDeriv", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.hasseDeriv_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.HasseDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.hasseDeriv_monomial", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.HasseDeriv", "is_tactic_proof": true, "tactics": ["ext", "simp", "by_cases", "grind", "rw", "by_cases", "rw", "rw", "rw"], "tactic_count": 9}
{"name": "Polynomial.hasseDeriv_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.HasseDeriv", "is_tactic_proof": true, "tactics": ["rw", "monomial_zero_right]"], "tactic_count": 2}
{"name": "Polynomial.hasseDeriv_apply_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.HasseDeriv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.hasseDeriv_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.HasseDeriv", "is_tactic_proof": true, "tactics": ["rw", "monomial_zero_right]"], "tactic_count": 2}
{"name": "Polynomial.factorial_smul_hasseDeriv", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.HasseDeriv", "is_tactic_proof": false, "tactics": ["induction", "zero", "succ", "ext", "rw", "simp", "simp", "rw", "simp", "norm_cast", "congr", "rw", "congr", "have", "rw", "congr", "rw"], "tactic_count": 17}
{"name": "Polynomial.hasseDeriv_comp", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.HasseDeriv", "is_tactic_proof": true, "tactics": ["ext", "simp", "monomial_eq_zero_iff,", "rw_mod_cast", "rw", "congr", "by_cases", "rw", "by_cases", "rw", "rw", "rw", "apply", "have", "have", "have", "push_cast", "rw", "rw", "simp", "field"], "tactic_count": 21}
{"name": "Polynomial.natDegree_hasseDeriv_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.HasseDeriv", "is_tactic_proof": true, "tactics": ["classical", "rw", "refine", "simp_rw", "rw", "simp", "mem_support_iff,", "intro", "have", "grind", "simp"], "tactic_count": 11}
{"name": "Polynomial.hasseDeriv_natDegree_eq_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.HasseDeriv", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "Polynomial.natDegree_hasseDeriv", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.HasseDeriv", "is_tactic_proof": true, "tactics": ["classical", "refine", "simp", "simp"], "tactic_count": 4}
{"name": "Polynomial.hasseDeriv_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.HasseDeriv", "is_tactic_proof": true, "tactics": ["let", "let", "change", "simp", "congr", "clear", "ext", "simp", "have", "x", "monomial", "monomial", "intro", "rw", "subst", "by_cases", "simp", "by_cases", "simp", "rw", "mul_assoc", "rw", "rw", "congr", "rw_mod_cast"], "tactic_count": 25}
{"name": "Polynomial.homogenize", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Homogenize", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.homogenize_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Homogenize", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.homogenize_add", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Homogenize", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.homogenize_smul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Homogenize", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.homogenizeLM", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Homogenize", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.homogenize_finsetSum", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Homogenize", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.homogenize_map", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Homogenize", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.homogenize_C_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Homogenize", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.homogenize_monomial", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Homogenize", "is_tactic_proof": true, "tactics": ["rw", "simp", "aesop", "simp"], "tactic_count": 4}
{"name": "Polynomial.homogenize_monomial_of_lt", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Homogenize", "is_tactic_proof": true, "tactics": ["rw", "apply", "aesop"], "tactic_count": 3}
{"name": "Polynomial.homogenize_X_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Homogenize", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.homogenize_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Homogenize", "is_tactic_proof": true, "tactics": ["rw", "rwa"], "tactic_count": 2}
{"name": "Polynomial.homogenize_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Homogenize", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Polynomial.homogenize_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Homogenize", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Polynomial.coeff_homogenize", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Homogenize", "is_tactic_proof": true, "tactics": ["induction", "add", "monomial", "rcases", "rw", "have", "aesop", "aesop"], "tactic_count": 8}
{"name": "Polynomial.eval₂_homogenize_of_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Homogenize", "is_tactic_proof": false, "tactics": ["apply", "simp", "simp", "simp", "assumption"], "tactic_count": 5}
{"name": "Polynomial.aeval_homogenize_of_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Homogenize", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "Polynomial.aeval_homogenize_X_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Homogenize", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.isHomogeneous_homogenize", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Homogenize", "is_tactic_proof": true, "tactics": ["refine", "simp", "rintro", "apply", "simp"], "tactic_count": 5}
{"name": "Polynomial.homogenize_eq_of_isHomogeneous", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Homogenize", "is_tactic_proof": true, "tactics": ["subst", "rw", "simp", "homogenize_C_mul]", "refine", "rw", "congr", "obtain", "simp"], "tactic_count": 9}
{"name": "Polynomial.homogenize_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Homogenize", "is_tactic_proof": true, "tactics": ["apply", "apply_rules", "simp"], "tactic_count": 3}
{"name": "Polynomial.homogenize_finsetProd", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Homogenize", "is_tactic_proof": true, "tactics": ["induction", "empty", "cons", "simp", "rw", "exact"], "tactic_count": 6}
{"name": "Polynomial.homogenize_dvd", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Homogenize", "is_tactic_proof": true, "tactics": ["rcases", "obtain", "simp", "simp", "rw", "apply"], "tactic_count": 6}
{"name": "Polynomial.homogenize_neg", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Homogenize", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.homogenize_sub", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Homogenize", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eval_homogenize", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Homogenize", "is_tactic_proof": false, "tactics": ["simp", "refine", "rw", "ring", "all_goals"], "tactic_count": 5}
{"name": "Polynomial.powAddExpansion", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Identities", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Polynomial.Identities.0.Polynomial.polyBinomAux1", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Identities", "is_tactic_proof": true, "tactics": ["exists", "congr", "apply"], "tactic_count": 3}
{"name": "_private.Mathlib.Algebra.Polynomial.Identities.0.Polynomial.poly_binom_aux2", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Identities", "is_tactic_proof": true, "tactics": ["unfold", "apply"], "tactic_count": 2}
{"name": "_private.Mathlib.Algebra.Polynomial.Identities.0.Polynomial.poly_binom_aux3", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Identities", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Polynomial.binomExpansion", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Identities", "is_tactic_proof": true, "tactics": ["exists", "rw", "congr", "rw", "rw", "exact", "exact"], "tactic_count": 7}
{"name": "Polynomial.powSubPowFactor", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Identities", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.evalSubFactor", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Identities", "is_tactic_proof": true, "tactics": ["refine", "delta", "simp", "dsimp", "congr", "rw"], "tactic_count": 6}
{"name": "Polynomial.divX", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Inductions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coeff_divX", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Inductions", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.divX_mul_X_add", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Inductions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.X_mul_divX_add", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Inductions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.divX_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Inductions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.divX_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Inductions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.divX_add", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Inductions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.divX_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Inductions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.divX_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Inductions", "is_tactic_proof": true, "tactics": ["ext", "simpa"], "tactic_count": 2}
{"name": "Polynomial.divX_C_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Inductions", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Polynomial.divX_X_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Inductions", "is_tactic_proof": true, "tactics": ["cases", "simp", "ext", "simp"], "tactic_count": 4}
{"name": "Polynomial.divX_hom", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Inductions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.divX_hom_toFun", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Inductions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natDegree_divX_eq_natDegree_tsub_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Inductions", "is_tactic_proof": true, "tactics": ["apply", "intro", "simpa", "intro", "rw", "split_ifs", "simp", "exact"], "tactic_count": 8}
{"name": "Polynomial.natDegree_divX_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Inductions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.divX_C_mul_X_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Inductions", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.degree_divX_lt", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Inductions", "is_tactic_proof": true, "tactics": ["haveI", "calc", "degree", "have", "rw", "exact", "have", "have", "have", "calc", "degree", "rw", "exact", "add_le_add", "rw", "exact", "le_rfl", "rw"], "tactic_count": 18}
{"name": "Polynomial.recOnHorner", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Inductions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_pos_induction_on", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Inductions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natDegree_ne_zero_induction_on", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Inductions", "is_tactic_proof": true, "tactics": ["suffices", "refine", "exact", "rintro", "refine", "rw", "refine", "rw", "exact", "refine", "rw", "exact", "exact", "intro", "by_cases", "exact", "refine", "rw", "exact"], "tactic_count": 19}
{"name": "LaurentPolynomial", "kind": "abbrev", "module": "Mathlib.Algebra.Polynomial.Laurent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Polynomial.mem_lifts_and_degree_eq", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Lifts", "is_tactic_proof": true, "tactics": ["rw", "let", "have", "let", "have", "have", "simp_rw", "mem_support_iff,", "exact", "exact"], "tactic_count": 10}
{"name": "Polynomial.lifts_and_degree_eq_and_monic", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Lifts", "is_tactic_proof": true, "tactics": ["rw", "let", "have", "let", "have", "simp_rw", "hp.as_sum]", "have", "exact"], "tactic_count": 9}
{"name": "Polynomial.lifts_and_natDegree_eq_and_monic", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Lifts", "is_tactic_proof": true, "tactics": ["rcases", "obtain", "exact", "obtain", "exact"], "tactic_count": 5}
{"name": "Polynomial.liftsRing", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Lifts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.lifts_iff_liftsRing", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Lifts", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.mem_lifts_iff_mem_alg", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Lifts", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.smul_mem_lifts", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Lifts", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Polynomial.monic_of_monic_mapAlg", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Lifts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.mirror", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Mirror", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.mirror_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Mirror", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.mirror_monomial", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Mirror", "is_tactic_proof": true, "tactics": ["classical", "by_cases", "rw", "rw", "reflect_C_mul_X_pow,"], "tactic_count": 5}
{"name": "Polynomial.mirror_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Mirror", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.mirror_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Mirror", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.mirror_natDegree", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Mirror", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "nontriviality", "rw", "tsub_add_cancel_of_le", "rwa"], "tactic_count": 6}
{"name": "Polynomial.mirror_natTrailingDegree", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Mirror", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "rw"], "tactic_count": 3}
{"name": "Polynomial.coeff_mirror", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Mirror", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "by_cases", "rw", "exact", "rw", "rw", "rw", "by_cases", "rw", "revAt_le", "rw", "rw", "exact", "coeff_eq_zero_of_lt_natTrailingDegree"], "tactic_count": 15}
{"name": "Polynomial.mirror_eval_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Mirror", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "exact", "intro", "rw", "rw", "rw", "exact", "exact", "intro", "use", "refine", "rw", "rw", "rw", "exact", "change", "rwa", "exact"], "tactic_count": 19}
{"name": "Polynomial.mirror_mirror", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Mirror", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.mirror_involutive", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Mirror", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.mirror_eq_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Mirror", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.mirror_inj", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Mirror", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.mirror_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Mirror", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.mirror_trailingCoeff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Mirror", "is_tactic_proof": true, "tactics": ["rw", "add_tsub_cancel_right]"], "tactic_count": 2}
{"name": "Polynomial.mirror_leadingCoeff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Mirror", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.coeff_mul_mirror", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Mirror", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw"], "tactic_count": 3}
{"name": "Polynomial.natDegree_mul_mirror", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Mirror", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "rw"], "tactic_count": 3}
{"name": "Polynomial.natTrailingDegree_mul_mirror", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Mirror", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "rw"], "tactic_count": 3}
{"name": "Polynomial.mirror_neg", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Mirror", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.mirror_mul_of_domain", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Mirror", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "by_cases", "rw", "rw", "rw", "repeat"], "tactic_count": 7}
{"name": "Polynomial.mirror_smul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Mirror", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "Module.AEval", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Module.AEval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.AEval.instAddCommGroup", "kind": "instance", "module": "Mathlib.Algebra.Polynomial.Module.AEval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.AEval.instAddCommMonoid", "kind": "instance", "module": "Mathlib.Algebra.Polynomial.Module.AEval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.AEval.instModuleOrig", "kind": "instance", "module": "Mathlib.Algebra.Polynomial.Module.AEval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.AEval.instFiniteOrig", "kind": "instance", "module": "Mathlib.Algebra.Polynomial.Module.AEval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.AEval.instModulePolynomial", "kind": "instance", "module": "Mathlib.Algebra.Polynomial.Module.AEval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.AEval.of", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Module.AEval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.AEval.of_aeval_smul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Module.AEval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.AEval.of_symm_smul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Module.AEval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.AEval.C_smul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Module.AEval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.AEval.X_smul_of", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Module.AEval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Module.AEval.X_pow_smul_of", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Module.AEval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Module.AEval.of_symm_X_smul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Module.AEval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Module.AEval.instIsScalarTowerOrigPolynomial", "kind": "instance", "module": "Mathlib.Algebra.Polynomial.Module.AEval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.AEval.instFinitePolynomial", "kind": "instance", "module": "Mathlib.Algebra.Polynomial.Module.AEval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.ofAEval", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Module.AEval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.ofAEval", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Module.AEval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.AEval.annihilator_eq_ker_aeval", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Module.AEval", "is_tactic_proof": true, "tactics": ["ext", "simp_rw", "change", "exact"], "tactic_count": 4}
{"name": "Module.AEval.annihilator_top_eq_ker_aeval", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Module.AEval", "is_tactic_proof": true, "tactics": ["ext", "simp", "change", "exact"], "tactic_count": 4}
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{"name": "Module.AEval.mem_mapSubmodule_apply", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Module.AEval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.AEval.mem_mapSubmodule_symm_apply", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Module.AEval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.AEval.equiv_mapSubmodule", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Module.AEval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.AEval.restrict_equiv_mapSubmodule", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Module.AEval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.AEval'", "kind": "abbrev", "module": "Mathlib.Algebra.Polynomial.Module.AEval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.AEval'.of", "kind": "abbrev", "module": "Mathlib.Algebra.Polynomial.Module.AEval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.AEval'_def", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Module.AEval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.AEval'.X_smul_of", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Module.AEval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.AEval'.X_pow_smul_of", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Module.AEval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Module.instFinitePolynomialAEval'", "kind": "instance", "module": "Mathlib.Algebra.Polynomial.Module.AEval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "PolynomialModule.instModule", "kind": "instance", "module": "Mathlib.Algebra.Polynomial.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PolynomialModule.zero_apply", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PolynomialModule.add_apply", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PolynomialModule.single", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PolynomialModule.single_apply", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PolynomialModule.lsingle", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PolynomialModule.lsingle_apply", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PolynomialModule.single_smul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PolynomialModule.induction_linear", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PolynomialModule.polynomialModule", "kind": "instance", "module": "Mathlib.Algebra.Polynomial.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PolynomialModule.smul_def", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Module.Basic", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "PolynomialModule.instIsScalarTower", "kind": "instance", "module": "Mathlib.Algebra.Polynomial.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "PolynomialModule.monomial_smul_apply", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Module.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "add", "simp", "split_ifs", "exacts", "single", "rw", "grind"], "tactic_count": 9}
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{"name": "PolynomialModule.equivPolynomial", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PolynomialModule.equivPolynomialSelf_apply_eq", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PolynomialModule.equivPolynomial_single", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PolynomialModule.hom_ext", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PolynomialModule.map", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PolynomialModule.map_single", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PolynomialModule.map_lsingle", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "PolynomialModule.aeval_equivPolynomial", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Module.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "add", "single", "rw"], "tactic_count": 5}
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{"name": "Polynomial.monic_C_mul_of_mul_leadingCoeff_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": true, "tactics": ["unfold", "nontriviality", "rw"], "tactic_count": 3}
{"name": "Polynomial.monic_mul_C_of_leadingCoeff_mul_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": true, "tactics": ["unfold", "nontriviality", "rw"], "tactic_count": 3}
{"name": "Polynomial.monic_X_pow_add", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.monic_X_pow_add_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.monic_X_add_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Monic.mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Monic.pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Monic.add_of_left", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Polynomial.Monic.add_of_right", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Polynomial.Monic.of_mul_monic_left", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": true, "tactics": ["contrapose", "rw", "rwa"], "tactic_count": 3}
{"name": "Polynomial.Monic.of_mul_monic_right", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": true, "tactics": ["contrapose", "rw", "rwa"], "tactic_count": 3}
{"name": "Polynomial.Monic.comp", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": true, "tactics": ["nontriviality", "have", "natDegree_comp_eq_of_mul_ne_zero", "rw", "one_pow,"], "tactic_count": 5}
{"name": "Polynomial.Monic.comp_X_add_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": true, "tactics": ["nontriviality", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "Polynomial.Monic.degree_le_zero_iff_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.Monic.natDegree_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": true, "tactics": ["nontriviality", "apply", "simp"], "tactic_count": 3}
{"name": "Polynomial.Monic.degree_mul_comm", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "rw", "exact", "rwa"], "tactic_count": 5}
{"name": "Polynomial.Monic.natDegree_mul'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "Polynomial.Monic.natDegree_mul_comm", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "rw", "simpa"], "tactic_count": 4}
{"name": "Polynomial.not_isUnit_X_add_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": true, "tactics": ["rintro", "have", "rw", "grind"], "tactic_count": 4}
{"name": "Polynomial.Monic.not_dvd_of_natDegree_lt", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": true, "tactics": ["rintro", "rw", "exact"], "tactic_count": 3}
{"name": "Polynomial.Monic.not_dvd_of_degree_lt", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Monic.nextCoeff_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": true, "tactics": ["nontriviality", "simp", "rw"], "tactic_count": 3}
{"name": "Polynomial.Monic.nextCoeff_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Polynomial.Monic.eq_one_of_map_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": true, "tactics": ["nontriviality", "have", "rw", "rw", "exact", "have", "convert", "rw"], "tactic_count": 8}
{"name": "Polynomial.Monic.natDegree_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Polynomial.natDegree_pow_X_add_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.Monic.eq_one_of_isUnit", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": true, "tactics": ["nontriviality", "obtain", "have", "rw", "exact"], "tactic_count": 5}
{"name": "Polynomial.Monic.isUnit_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eq_of_monic_of_associated", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": true, "tactics": ["obtain", "rw"], "tactic_count": 2}
{"name": "Polynomial.MonicDegreeEq", "kind": "abbrev", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.MonicDegreeEq.natDegree", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.MonicDegreeEq.degree", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.MonicDegreeEq.monic", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": true, "tactics": ["nontriviality", "rw"], "tactic_count": 2}
{"name": "Polynomial.MonicDegreeEq.coeff_of_ge", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": true, "tactics": ["split_ifs"], "tactic_count": 1}
{"name": "Polynomial.MonicDegreeEq.mk", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.MonicDegreeEq.map", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.monic_multiset_prod_of_monic", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": true, "tactics": ["revert", "refine", "intro", "rw", "exact"], "tactic_count": 5}
{"name": "Polynomial.monic_prod_of_monic", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.monic_finprod_of_monic", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": true, "tactics": ["classical", "rw", "split_ifs", "exact", "exact"], "tactic_count": 5}
{"name": "Polynomial.Monic.nextCoeff_multiset_prod", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": true, "tactics": ["revert", "refine", "simp", "rw", "rw", "rw", "exacts", "monic_multiset_prod_of_monic"], "tactic_count": 8}
{"name": "Polynomial.Monic.nextCoeff_prod", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.irreducible_of_monic", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": false, "tactics": ["refine", "rwa", "rwa", "rw"], "tactic_count": 4}
{"name": "Polynomial.Monic.irreducible_iff_natDegree", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "refine", "rw"], "tactic_count": 4}
{"name": "Polynomial.Monic.irreducible_iff_natDegree'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": true, "tactics": ["simp_rw", "apply", "constructor", "rw", "exact", "simp_rw", "contrapose", "obtain", "exact", "exact"], "tactic_count": 10}
{"name": "Polynomial.Monic.irreducible_iff_lt_natDegree_lt", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": true, "tactics": ["rw", "constructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 6}
{"name": "Polynomial.Monic.not_irreducible_iff_exists_add_mul_eq_coeff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": true, "tactics": ["cases", "simp", "rw", "push_neg", "constructor", "rintro", "simp", "have", "rw", "use", "simpa", "rintro", "refine", "rw", "hm.coeff_natDegree,", "ring", "simp", "rintro", "simp"], "tactic_count": 19}
{"name": "Polynomial.Monic.natDegree_map", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "Polynomial.Monic.degree_map", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": true, "tactics": ["simp_all"], "tactic_count": 1}
{"name": "Polynomial.monic_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": true, "tactics": ["apply", "rw"], "tactic_count": 2}
{"name": "Function.Injective.monic_map_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.monic_X_sub_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Polynomial.monic_X_pow_sub", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Polynomial.monic_X_pow_sub_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Polynomial.not_isUnit_X_pow_sub_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": true, "tactics": ["intro", "rcases", "simp", "apply", "rw"], "tactic_count": 5}
{"name": "Polynomial.Monic.comp_X_sub_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Polynomial.Monic.sub_of_left", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": true, "tactics": ["rw", "apply", "rwa"], "tactic_count": 3}
{"name": "Polynomial.Monic.sub_of_right", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": false, "tactics": ["have", "rw", "rw", "apply", "rwa"], "tactic_count": 5}
{"name": "Polynomial.not_monic_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Monic.mul_left_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": true, "tactics": ["by_cases", "simpa", "rw", "refine", "rw", "refine", "simp"], "tactic_count": 7}
{"name": "Polynomial.Monic.mul_right_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": true, "tactics": ["by_cases", "simpa", "rw", "refine", "rw", "refine", "simp"], "tactic_count": 7}
{"name": "Polynomial.Monic.mul_natDegree_lt_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": true, "tactics": ["by_cases", "suffices", "exact", "simp"], "tactic_count": 4}
{"name": "Polynomial.Monic.mul_right_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "Polynomial.Monic.mul_left_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "Polynomial.Monic.isRegular", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": true, "tactics": ["constructor", "intro", "dsimp", "rw", "intro", "simp", "rw"], "tactic_count": 7}
{"name": "Polynomial.degree_smul_of_smul_regular", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": true, "tactics": ["refine", "rw", "intro", "rw", "simp", "rw", "intro", "rw", "refine", "simpa"], "tactic_count": 10}
{"name": "Polynomial.natDegree_smul_of_smul_regular", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "rw", "contrapose", "rw", "exact"], "tactic_count": 6}
{"name": "Polynomial.leadingCoeff_smul_of_smul_regular", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.monic_of_isUnit_leadingCoeff_inv_smul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Polynomial.isUnit_leadingCoeff_mul_right_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "have", "ext", "simp", "refine", "rw", "rwa", "exact", "rintro", "simp"], "tactic_count": 12}
{"name": "Polynomial.isUnit_leadingCoeff_mul_left_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monic", "is_tactic_proof": true, "tactics": ["constructor", "intro", "replace", "simp", "rwa", "refine", "simp", "rintro", "rw"], "tactic_count": 9}
{"name": "Polynomial.monomial_one_eq_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monomial", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Polynomial.infinite", "kind": "instance", "module": "Mathlib.Algebra.Polynomial.Monomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.card_support_le_one_iff_monomial", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monomial", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "rcases", "refine", "ext", "by_cases", "simp", "have", "rw", "exact", "simp", "rintro", "rw", "apply", "exact"], "tactic_count": 16}
{"name": "Polynomial.ringHom_ext", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monomial", "is_tactic_proof": true, "tactics": ["set", "set", "have", "ext", "simp", "simpa", "have", "rw", "ext", "simp", "have", "rw", "ext", "simp", "rw"], "tactic_count": 15}
{"name": "Polynomial.ringHom_ext'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Monomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.toFn", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.OfFn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.toFn_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.OfFn", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.ofFn", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.OfFn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.ofFn_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.OfFn", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.ofFn_zero'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.OfFn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.ne_zero_of_ofFn_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.OfFn", "is_tactic_proof": true, "tactics": ["contrapose", "subst", "simp"], "tactic_count": 3}
{"name": "Polynomial.ofFn_coeff_eq_val_of_lt", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.OfFn", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.ofFn_coeff_eq_zero_of_ge", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.OfFn", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.ofFn_natDegree_lt", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.OfFn", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Polynomial.ofFn_degree_lt", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.OfFn", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "exact", "exact"], "tactic_count": 4}
{"name": "Polynomial.ofFn_eq_sum_monomial", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.OfFn", "is_tactic_proof": true, "tactics": ["by_cases", "subst", "simp", "rw", "simp"], "tactic_count": 5}
{"name": "Polynomial.toFn_comp_ofFn_eq_id", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.OfFn", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.injective_ofFn", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.OfFn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.surjective_toFn", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.OfFn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.ofFn_comp_toFn_eq_id_of_natDegree_lt", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.OfFn", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "simp", "have", "simp"], "tactic_count": 5}
{"name": "div_eq_quo_add_rem_div_add_rem_div", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.PartialFractions", "is_tactic_proof": true, "tactics": ["rcases", "refine", "have", "norm_cast", "exact", "have", "norm_cast", "exact", "have", "have", "field_simp", "norm_cast", "linear_combination"], "tactic_count": 13}
{"name": "div_eq_quo_add_sum_rem_div", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.PartialFractions", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "refine", "rintro", "insert", "obtain", "div_eq_quo_add_rem_div_add_rem_div", "hcop", "obtain", "refine", "intro", "dsimp", "split_ifs", "cases", "intro", "exact", "intro", "exact", "norm_cast", "rw", "trans", "push_cast", "ring", "congr", "refine", "grind"], "tactic_count": 27}
{"name": "Polynomial.revAtFun", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Reverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.revAtFun_invol", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Reverse", "is_tactic_proof": true, "tactics": ["unfold", "grind"], "tactic_count": 2}
{"name": "Polynomial.revAtFun_inj", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Reverse", "is_tactic_proof": true, "tactics": ["intro", "rw"], "tactic_count": 2}
{"name": "Polynomial.revAt", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Reverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.revAtFun_eq", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Reverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.revAt_invol", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Reverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.revAt_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Reverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.revAt_eq_self_of_lt", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Reverse", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.revAt_add", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Reverse", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "repeat", "rw", "repeat"], "tactic_count": 5}
{"name": "Polynomial.revAt_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Reverse", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.reflect", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Reverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.reflect_support", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Reverse", "is_tactic_proof": true, "tactics": ["rcases", "ext1", "simp"], "tactic_count": 3}
{"name": "Polynomial.coeff_reflect", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Reverse", "is_tactic_proof": true, "tactics": ["rcases", "simp", "calc"], "tactic_count": 3}
{"name": "Polynomial.reflect_reflect", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Reverse", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Polynomial.reflect_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Reverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.reflect_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Reverse", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.reflect_add", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Reverse", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Polynomial.reflect_C_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Reverse", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Polynomial.reflect_C_mul_X_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Reverse", "is_tactic_proof": true, "tactics": ["ext", "grind"], "tactic_count": 2}
{"name": "Polynomial.reflect_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Reverse", "is_tactic_proof": true, "tactics": ["conv_lhs"], "tactic_count": 1}
{"name": "Polynomial.reflect_monomial", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Reverse", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.reflect_one_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Reverse", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Polynomial.reflect_map", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Reverse", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Polynomial.reflect_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Reverse", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.reflect_mul_induction", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Reverse", "is_tactic_proof": true, "tactics": ["induction", "zero", "induction", "zero", "rw", "simp_rw", "revAt_add", "succ", "by_cases", "rw", "rw", "exact", "exact", "exact", "exact", "succ", "by_cases", "rw", "rw", "exact", "exact", "exact", "exact"], "tactic_count": 23}
{"name": "Polynomial.reflect_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Reverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natDegree_reflect_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Reverse", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.eval₂_reflect_mul_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Reverse", "is_tactic_proof": true, "tactics": ["refine", "simp", "intro", "simp", "conv", "rw", "intros", "simp"], "tactic_count": 8}
{"name": "Polynomial.eval₂_reflect_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Reverse", "is_tactic_proof": true, "tactics": ["conv_rhs", "constructor", "intro", "rw", "intro", "rw"], "tactic_count": 6}
{"name": "Polynomial.reverse", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Reverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coeff_reverse", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Reverse", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.coeff_zero_reverse", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Reverse", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.reverse_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Reverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.reverse_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Reverse", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.reverse_natDegree_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Reverse", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "rw"], "tactic_count": 4}
{"name": "Polynomial.natDegree_eq_reverse_natDegree_add_natTrailingDegree", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Reverse", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "apply", "refine", "apply", "rw", "exact", "rw", "apply", "have", "rwa"], "tactic_count": 11}
{"name": "Polynomial.reverse_natDegree", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Reverse", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.reverse_leadingCoeff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Reverse", "is_tactic_proof": true, "tactics": ["rw", "trailingCoeff]"], "tactic_count": 2}
{"name": "Polynomial.natTrailingDegree_reverse", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Reverse", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Polynomial.reverse_trailingCoeff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Reverse", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.reverse_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Reverse", "is_tactic_proof": true, "tactics": ["unfold", "rw"], "tactic_count": 2}
{"name": "Polynomial.reverse_mul_of_domain", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Reverse", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "by_cases", "rw", "simp"], "tactic_count": 5}
{"name": "Polynomial.trailingCoeff_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Reverse", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.coeff_one_reverse", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Reverse", "is_tactic_proof": true, "tactics": ["rw", "split_ifs", "have", "simp", "rw", "exact"], "tactic_count": 6}
{"name": "Polynomial.reverse_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Reverse", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.reverse_mul_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Reverse", "is_tactic_proof": true, "tactics": ["nontriviality", "rcases", "simp", "simp"], "tactic_count": 4}
{"name": "Polynomial.reverse_X_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Reverse", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.reverse_mul_X_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Reverse", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Polynomial.reverse_X_pow_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Reverse", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.reverse_add_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Reverse", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.reverse_C_add", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Reverse", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.eval₂_reverse_mul_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Reverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eval₂_reverse_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Reverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.reflect_neg", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Reverse", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.reflect_sub", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Reverse", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.reverse_neg", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Reverse", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.natDegree_pos_of_aeval_root", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.RingDivision", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_pos_of_aeval_root", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.RingDivision", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.smul_modByMonic", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.RingDivision", "is_tactic_proof": true, "tactics": ["by_cases", "rcases", "simp", "exact", "simp_rw"], "tactic_count": 5}
{"name": "Polynomial.modByMonicHom", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.RingDivision", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.mem_ker_modByMonic", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.RingDivision", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.aeval_modByMonic_eq_self_of_root", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.RingDivision", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.trailingDegree_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.RingDivision", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "by_cases", "rw", "rw", "trailingDegree_eq_natTrailingDegree", "apply"], "tactic_count": 7}
{"name": "Polynomial.rootMultiplicity_eq_rootMultiplicity", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.RingDivision", "is_tactic_proof": true, "tactics": ["classical", "simp_rw", "congr", "rw", "convert", "simp"], "tactic_count": 6}
{"name": "Polynomial.rootMultiplicity_eq_natTrailingDegree", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.RingDivision", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Monic.mem_nonZeroDivisors", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.RingDivision", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.mem_nonZeroDivisors_of_leadingCoeff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.RingDivision", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.mem_nonZeroDivisors_of_trailingCoeff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.RingDivision", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Irreducible.aeval_ne_zero_of_natDegree_ne_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.RingDivision", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact", "hp.not_isRoot_of_natDegree_ne_one"], "tactic_count": 4}
{"name": "Polynomial.natDegree_pos_of_monic_of_aeval_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.RingDivision", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.rootMultiplicity_mul_X_sub_C_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.RingDivision", "is_tactic_proof": true, "tactics": ["have", "refine", "rw", "dvd_cancel_right_mem_nonZeroDivisors", "exact", "rw", "exact"], "tactic_count": 7}
{"name": "Polynomial.rootMultiplicity_X_sub_C_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.RingDivision", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "Polynomial.rootMultiplicity_X_sub_C_self", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.RingDivision", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.rootMultiplicity_X_sub_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.RingDivision", "is_tactic_proof": true, "tactics": ["split_ifs", "rw", "exact", "exact"], "tactic_count": 4}
{"name": "Polynomial.rootMultiplicity_mul'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.RingDivision", "is_tactic_proof": true, "tactics": ["simp_rw", "simp_rw"], "tactic_count": 2}
{"name": "Polynomial.Monic.neg_one_pow_natDegree_mul_comp_neg_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.RingDivision", "is_tactic_proof": true, "tactics": ["simp", "calc", "simp", "apply", "simp"], "tactic_count": 5}
{"name": "Polynomial.degree_eq_degree_of_associated", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.RingDivision", "is_tactic_proof": true, "tactics": ["let", "simp"], "tactic_count": 2}
{"name": "Polynomial.prime_X_sub_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.RingDivision", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.prime_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.RingDivision", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "Polynomial.Monic.prime_of_degree_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.RingDivision", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.irreducible_X_sub_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.RingDivision", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.irreducible_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.RingDivision", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Monic.irreducible_of_degree_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.RingDivision", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.irreducible_of_degree_eq_one_of_isRelPrime_coeff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.RingDivision", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.irreducible_C_mul_X_add_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.RingDivision", "is_tactic_proof": true, "tactics": ["apply", "compute_degree", "simpa"], "tactic_count": 3}
{"name": "Polynomial.aeval_ne_zero_of_isCoprime", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.RingDivision", "is_tactic_proof": true, "tactics": ["by_contra", "rcases", "apply_fun", "simp"], "tactic_count": 4}
{"name": "Polynomial.isCoprime_X_sub_C_of_isUnit_sub", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.RingDivision", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.pairwise_coprime_X_sub_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.RingDivision", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.rootMultiplicity_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.RingDivision", "is_tactic_proof": true, "tactics": ["classical", "have", "have", "rw", "rootMultiplicity_eq_multiplicity", "multiplicity_mul"], "tactic_count": 6}
{"name": "Polynomial.exists_multiset_roots", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.RingDivision", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.roots", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.roots_def", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["rename_i", "obtain", "obtain", "rfl"], "tactic_count": 4}
{"name": "Polynomial.roots_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.card_roots", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["classical", "unfold", "rw", "exact"], "tactic_count": 4}
{"name": "Polynomial.card_roots'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "exact"], "tactic_count": 3}
{"name": "Polynomial.card_roots_sub_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.card_roots_sub_C'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.count_roots", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["classical", "by_cases", "simp", "rw", "exact"], "tactic_count": 5}
{"name": "Polynomial.mem_roots'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Polynomial.mem_roots", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.ne_zero_of_mem_roots", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.isRoot_of_mem_roots", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.roots_eq_zero_iff_isRoot_eq_bot", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["refine", "ext", "simp"], "tactic_count": 3}
{"name": "Polynomial.roots_eq_zero_iff_eq_zero_or_isRoot_eq_bot", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["rcases", "simp"], "tactic_count": 2}
{"name": "Polynomial.mem_roots_map_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.mem_roots_iff_aeval_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["rw", "map_id]"], "tactic_count": 2}
{"name": "Polynomial.card_le_degree_of_subset_roots", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.finite_setOf_isRoot", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Polynomial.eq_zero_of_infinite_isRoot", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.exists_max_root", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.exists_min_root", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eq_of_infinite_eval_eq", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["rw", "apply", "simpa"], "tactic_count": 3}
{"name": "Polynomial.roots_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["classical", "exact"], "tactic_count": 2}
{"name": "Polynomial.roots.le_of_dvd", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "Polynomial.mem_roots_sub_C'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.mem_roots_sub_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.roots_X_sub_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["classical", "ext", "rw"], "tactic_count": 3}
{"name": "Polynomial.roots_X_add_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Polynomial.roots_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.roots_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["classical", "exact"], "tactic_count": 2}
{"name": "Polynomial.roots_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.roots_C_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["by_cases", "simp"], "tactic_count": 2}
{"name": "Associated.roots_eq", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["obtain", "rw"], "tactic_count": 2}
{"name": "Polynomial.roots_smul_nonzero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.roots_neg", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.roots_C_mul_X_sub_C_of_IsUnit", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Polynomial.roots_C_mul_X_add_C_of_IsUnit", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.roots_list_prod", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.roots_multiset_prod", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["rcases", "simpa"], "tactic_count": 2}
{"name": "Polynomial.roots_prod", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["rcases", "simpa"], "tactic_count": 2}
{"name": "Polynomial.roots_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rcases", "rw", "rw"], "tactic_count": 6}
{"name": "Polynomial.roots_X_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.roots_C_mul_X_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.roots_monomial", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.roots_prod_X_sub_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["apply", "simp_rw", "rw", "refine"], "tactic_count": 4}
{"name": "Polynomial.roots_multiset_prod_X_sub_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "rw", "rw", "rintro", "exact"], "tactic_count": 6}
{"name": "Polynomial.roots_ofMultiset", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.rightInverse_ofMultiset_roots", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.ofMultiset_injective", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.card_roots_X_pow_sub_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.roots_eq_of_degree_le_card_of_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["refine", "exact", "simpa"], "tactic_count": 3}
{"name": "Polynomial.roots_eq_of_degree_eq_card", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.roots_eq_of_natDegree_le_card_of_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.nthRoots", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.mem_nthRoots", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.nthRoots_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.nthRoots_zero_right", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.card_nthRoots", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["classical", "exact", "rw", "exact", "rw", "rw", "exact"], "tactic_count": 7}
{"name": "Polynomial.nthRoots_two_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Polynomial.nthRootsFinset", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.nthRootsFinset_def", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["unfold", "convert"], "tactic_count": 2}
{"name": "Polynomial.mem_nthRootsFinset", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Polynomial.nthRootsFinset_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Polynomial.map_mem_nthRootsFinset", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "rw"], "tactic_count": 3}
{"name": "Polynomial.map_mem_nthRootsFinset_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Polynomial.mul_mem_nthRootsFinset", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["cases", "zero", "succ", "rw", "rw"], "tactic_count": 5}
{"name": "Polynomial.ne_zero_of_mem_nthRootsFinset", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["rintro", "cases", "zero", "succ", "rw", "exact"], "tactic_count": 6}
{"name": "Polynomial.one_mem_nthRootsFinset", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.nthRoots_two_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["have", "have", "rw"], "tactic_count": 3}
{"name": "Polynomial.zero_of_eval_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["classical", "by_contra", "refine", "exact"], "tactic_count": 4}
{"name": "Polynomial.funext", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["rw", "apply", "intro", "rw"], "tactic_count": 4}
{"name": "Polynomial.aroots", "kind": "abbrev", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.aroots_def", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.mem_aroots'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.mem_aroots", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Polynomial.aroots_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": false, "tactics": ["suffices", "rwa"], "tactic_count": 2}
{"name": "Polynomial.aroots_X_sub_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.aroots_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.aroots_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.aroots_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.aroots_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.aroots_neg", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.aroots_C_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["rw", "rwa", "exact"], "tactic_count": 3}
{"name": "Polynomial.aroots_smul_nonzero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.aroots_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.aroots_X_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.aroots_C_mul_X_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.aroots_monomial", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.aroots_map", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.rootSet", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.rootSet_def", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["rw", "convert"], "tactic_count": 2}
{"name": "Polynomial.rootSet_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Polynomial.rootSet_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.rootSet_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.rootSet_neg", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.rootSetFintype", "kind": "instance", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.rootSet_finite", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.bUnion_roots_finite", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.mem_rootSet'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Polynomial.mem_rootSet", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.mem_rootSet_of_ne", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.preimage_eval_singleton", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Polynomial.Monic.mem_rootSet", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.rootSet_maps_to'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.ne_zero_of_mem_rootSet", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.aeval_eq_zero_of_mem_rootSet", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.rootSet_mapsTo", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact"], "tactic_count": 3}
{"name": "Polynomial.mem_rootSet_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Polynomial.nthRootsFinset_toSet", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["ext", "simp_all"], "tactic_count": 2}
{"name": "Polynomial.smul_mem_rootSet", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.smul_mem_rootSet_iff_of_isUnit", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact"], "tactic_count": 3}
{"name": "Polynomial.smul_mem_rootSet_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.instMulActionElemRootSetOfSMulCommClass", "kind": "instance", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.rootSet.coe_smul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.instSMulCommClassElemRootSet", "kind": "instance", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.instIsScalarTowerElemRootSet", "kind": "instance", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eq_zero_of_natDegree_lt_card_of_eval_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["classical", "by_contra", "refine", "calc", "intro", "simp", "forall_exists_index,", "rintro", "exact"], "tactic_count": 9}
{"name": "Polynomial.eq_of_natDegree_lt_card_of_eval_eq", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["rw", "apply", "simpa", "grind"], "tactic_count": 4}
{"name": "Polynomial.eq_zero_of_natDegree_lt_card_of_eval_eq_zero'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eq_of_natDegree_lt_card_of_eval_eq'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eq_zero_of_forall_eval_zero_of_natDegree_lt_card", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["obtain", "have", "apply", "simpa", "exact"], "tactic_count": 5}
{"name": "Polynomial.exists_eval_ne_zero_of_natDegree_lt_card", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["contrapose", "exact"], "tactic_count": 2}
{"name": "Polynomial.monic_multisetProd_X_sub_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.monic_prod_X_sub_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.monic_finprod_X_sub_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.prod_multiset_root_eq_finset_root", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.prod_multiset_X_sub_C_dvd", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["classical", "rw", "rw", "refine", "simp_rw", "exact", "exact"], "tactic_count": 7}
{"name": "Multiset.prod_X_sub_C_dvd_iff_le_roots", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["classical", "exact", "rw", "exact"], "tactic_count": 4}
{"name": "Polynomial.exists_prod_multiset_X_sub_C_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["obtain", "use", "obtain", "rw", "subst", "simp", "constructor", "conv_rhs", "rw", "replace", "rw", "exacts"], "tactic_count": 12}
{"name": "Polynomial.C_leadingCoeff_mul_prod_multiset_X_sub_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.prod_multiset_X_sub_C_of_monic_of_roots_card_eq", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "Polynomial.Monic.isUnit_leadingCoeff_of_dvd", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.card_roots_le_one_of_irreducible", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["obtain", "simp", "convert", "exact"], "tactic_count": 4}
{"name": "Polynomial.roots_eq_zero_of_irreducible_of_natDegree_ne_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["by_contra", "have", "exact"], "tactic_count": 3}
{"name": "Polynomial.Monic.irreducible_iff_degree_lt", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": false, "tactics": ["simp", "natDegree_le_iff_degree_le]", "constructor", "rintro", "by_contra", "have", "have", "refine", "rwa", "rwa", "rw", "rintro", "exact"], "tactic_count": 13}
{"name": "Polynomial.le_rootMultiplicity_map", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw"], "tactic_count": 3}
{"name": "Polynomial.eq_rootMultiplicity_map", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["by_cases", "apply", "rw", "map_X,", "apply"], "tactic_count": 5}
{"name": "Polynomial.count_map_roots", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["rw", "rw", "refine", "convert", "simp"], "tactic_count": 5}
{"name": "Polynomial.count_map_roots_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "le_refl]", "exact"], "tactic_count": 4}
{"name": "Polynomial.map_roots_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["classical", "exact", "rw", "apply"], "tactic_count": 4}
{"name": "Polynomial.map_roots_le_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "exact"], "tactic_count": 3}
{"name": "Polynomial.card_roots_map_le_degree", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "exact"], "tactic_count": 3}
{"name": "Polynomial.card_roots_map_le_natDegree", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.ncard_rootSet_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["classical", "grw", "exact"], "tactic_count": 3}
{"name": "Polynomial.filter_roots_map_range_eq_map_roots", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["classical", "ext", "rw", "split_ifs", "obtain", "simp", "refine", "exact"], "tactic_count": 8}
{"name": "Polynomial.card_roots_le_map", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Polynomial.card_roots_le_map_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "exact"], "tactic_count": 3}
{"name": "Polynomial.roots_map_of_injective_of_card_eq_natDegree", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": true, "tactics": ["apply", "simpa"], "tactic_count": 2}
{"name": "Polynomial.roots_map_of_map_ne_zero_of_card_eq_natDegree", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Monic.roots_map_of_card_eq_natDegree", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Roots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.signVariations", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.RuleOfSigns", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.signVariations_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.RuleOfSigns", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.signVariations_monomial", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.RuleOfSigns", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "simp"], "tactic_count": 3}
{"name": "Polynomial.signVariations_eraseLead", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.RuleOfSigns", "is_tactic_proof": true, "tactics": ["by_cases", "simp_all", "have", "obtain", "simp"], "tactic_count": 5}
{"name": "Polynomial.signVariations_eq_eraseLead_add_ite", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.RuleOfSigns", "is_tactic_proof": true, "tactics": ["by_cases", "simp_all", "have", "rw", "rw", "rcases", "simp", "simp", "have", "by_contra", "suffices", "by_contra", "have", "grind", "simp", "obtain", "have", "obtain", "grind", "by_cases", "grind", "rw", "grind", "cases", "grind"], "tactic_count": 25}
{"name": "Polynomial.signVariations_eraseLead_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.RuleOfSigns", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "grind"], "tactic_count": 3}
{"name": "Polynomial.signVariations_le_eraseLead_succ", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.RuleOfSigns", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "grind"], "tactic_count": 3}
{"name": "Polynomial.signVariations_neg", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.RuleOfSigns", "is_tactic_proof": true, "tactics": ["rw", "simp", "have", "have", "grind", "rw", "congr", "funext", "simp"], "tactic_count": 9}
{"name": "Polynomial.signVariations_C_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.RuleOfSigns", "is_tactic_proof": true, "tactics": ["wlog", "simpa", "rw", "rw", "congr", "funext", "simp"], "tactic_count": 7}
{"name": "Polynomial.signVariations_eraseLead_mul_X_sub_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.RuleOfSigns", "is_tactic_proof": true, "tactics": ["obtain", "have", "have", "rw", "have", "have", "rw", "exact", "have", "grind", "have", "rw", "trans", "grind", "exact", "have", "apply", "rw", "suffices", "suffices", "have", "grind", "coeffList_eraseLead,", "rw", "rw", "rw", "rw", "rw", "rw", "rw", "abel"], "tactic_count": 31}
{"name": "Polynomial.succ_signVariations_X_sub_C_mul_monomial", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.RuleOfSigns", "is_tactic_proof": false, "tactics": ["have", "convert", "simp", "simp", "have", "apply", "simp", "have", "simpa", "coeffList_eraseLead,"], "tactic_count": 10}
{"name": "_private.Mathlib.Algebra.Polynomial.RuleOfSigns.0.Polynomial.exists_cons_of_leadingCoeff_pos", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.RuleOfSigns", "is_tactic_proof": true, "tactics": ["have", "have", "have", "have", "obtain", "apply", "have", "generalize", "use", "constructor", "have", "have", "simp", "have", "simp", "have", "have", "by_cases", "suffices", "have", "we", "have", "grind", "suffices", "grind", "grind", "suffices", "have", "have", "grind", "suffices", "monomial", "monomial", "grind", "leadingCoeff_eraseLead_eq_nextCoeff]", "grind", "rw"], "tactic_count": 37}
{"name": "Polynomial.signVariations_X_sub_C_mul_eraseLead_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.RuleOfSigns", "is_tactic_proof": true, "tactics": ["obtain", "simp", "tsub_le_iff_right,", "rw", "split", "swap", "rfl", "rw", "split", "swap", "rfl", "rcases", "simp", "rw", "grind"], "tactic_count": 15}
{"name": "Polynomial.succ_signVariations_le_X_sub_C_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.RuleOfSigns", "is_tactic_proof": true, "tactics": ["generalize", "induction", "wlog", "simpa", "have", "have", "rw", "rcases", "have", "have", "dsimp", "rw", "simp", "generalize", "generalize", "have", "have", "have", "rcases", "obtain", "have", "simp", "hypothesis", "and", "true", "by_cases", "grind", "decreases", "most", "have", "simp", "leadingCoeff_eraseLead_eq_nextCoeff,", "have", "have", "rwa", "grind", "grind", "all_goals", "specialize", "have", "simp", "exact", "becomes", "grind", "becomes", "one,", "trans", "grind", "suffices", "simp", "grind"], "tactic_count": 51}
{"name": "Polynomial.roots_countP_pos_le_signVariations", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.RuleOfSigns", "is_tactic_proof": true, "tactics": ["generalize", "induction", "exact", "rename_i", "have", "grind", "obtain", "grind", "obtain", "dvd_iff_isRoot.mpr", "grw", "exact", "simp"], "tactic_count": 13}
{"name": "Polynomial.Sequence.coeFun", "kind": "instance", "module": "Mathlib.Algebra.Polynomial.Sequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Sequence.degree_eq", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Sequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Sequence.natDegree_eq", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Sequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Sequence.ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Sequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Sequence.degree_strictMono", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Sequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Sequence.natDegree_strictMono", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Sequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Sequence.span", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Sequence", "is_tactic_proof": true, "tactics": ["rw", "intro", "nontriviality", "generalize", "induction", "h", "by_cases", "simp", "obtain", "let", "let", "have", "have", "have", "rwa", "by_cases", "simp", "refine", "sub_mem_iff_left", "ih", "have", "simpa", "have", "degree_smul_of_isRightRegular_leadingCoeff", "have", "degree_smul_of_isRightRegular_leadingCoeff", "rw", "have", "degree_eq_natDegree", "grind", "have", "rw", "nth_rw", "rw_mod_cast", "dsimp", "nth_rw", "rw", "have", "rwa"], "tactic_count": 39}
{"name": "Polynomial.Sequence.linearIndependent", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Sequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Sequence.basis", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Sequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Sequence.basis_eq_self", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Sequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Sequence.basis_degree_strictMono", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Sequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Sequence.basis_natDegree_strictMono", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Sequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.smul_pow", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Smeval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.definition._@.Mathlib.Algebra.Polynomial.Smeval.3997496041._hygCtx._hyg.2", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Smeval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.wrapped._@.Mathlib.Algebra.Polynomial.Smeval.3997496041._hygCtx._hyg.2", "kind": "opaque", "module": "Mathlib.Algebra.Polynomial.Smeval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.smeval", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Smeval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.smeval_def", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Smeval", "is_tactic_proof": true, "tactics": ["intros", "delta", "rw", "rfl"], "tactic_count": 4}
{"name": "Polynomial.smeval_eq_sum", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Smeval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.smeval_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Smeval", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.smeval_monomial", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Smeval", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.eval_eq_smeval", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Smeval", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Polynomial.eval₂_smulOneHom_eq_smeval", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Smeval", "is_tactic_proof": true, "tactics": ["rw", "congr", "simp"], "tactic_count": 3}
{"name": "Polynomial.smeval_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Smeval", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.smeval_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Smeval", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Polynomial.smeval_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Smeval", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.smeval_X_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Smeval", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.smeval_add", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Smeval", "is_tactic_proof": true, "tactics": ["simp", "refine", "rw", "rw"], "tactic_count": 4}
{"name": "Polynomial.smeval_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Smeval", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Polynomial.smeval_smul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Smeval", "is_tactic_proof": true, "tactics": ["induction", "add", "monomial"], "tactic_count": 3}
{"name": "Polynomial.smeval.linearMap", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Smeval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.smeval.linearMap_apply", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Smeval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.leval_coe_eq_smeval", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Smeval", "is_tactic_proof": true, "tactics": ["ext", "simpa"], "tactic_count": 2}
{"name": "Polynomial.leval_eq_smeval.linearMap", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Smeval", "is_tactic_proof": true, "tactics": ["refine", "intro", "rw"], "tactic_count": 3}
{"name": "Polynomial.smeval_neg", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Smeval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.smeval_sub", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Smeval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.smeval_neg_nat", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Smeval", "is_tactic_proof": true, "tactics": ["rw", "simp", "simp"], "tactic_count": 3}
{"name": "Polynomial.smeval_C_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Smeval", "is_tactic_proof": true, "tactics": ["induction", "add", "monomial"], "tactic_count": 3}
{"name": "Polynomial.smeval_at_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Smeval", "is_tactic_proof": true, "tactics": ["induction", "add", "intro", "simp", "monomial", "intro", "rw"], "tactic_count": 7}
{"name": "Polynomial.smeval_at_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Smeval", "is_tactic_proof": true, "tactics": ["induction", "add", "monomial", "cases", "zero", "succ"], "tactic_count": 6}
{"name": "Polynomial.smeval_X_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Smeval", "is_tactic_proof": true, "tactics": ["induction", "add", "monomial", "rw", "smeval_monomial]"], "tactic_count": 5}
{"name": "Polynomial.smeval_X_pow_assoc", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Smeval", "is_tactic_proof": true, "tactics": ["induction", "add", "monomial"], "tactic_count": 3}
{"name": "Polynomial.smeval_X_pow_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Smeval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.smeval_monomial_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Smeval", "is_tactic_proof": true, "tactics": ["induction", "add", "simp", "rw", "monomial"], "tactic_count": 5}
{"name": "Polynomial.smeval_mul_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Smeval", "is_tactic_proof": true, "tactics": ["induction", "add", "monomial", "simp", "npow_one]"], "tactic_count": 5}
{"name": "Polynomial.smeval_assoc_X_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Smeval", "is_tactic_proof": true, "tactics": ["induction", "add", "monomial"], "tactic_count": 3}
{"name": "Polynomial.smeval_mul_X_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Smeval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.smeval_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Smeval", "is_tactic_proof": true, "tactics": ["induction", "add", "monomial"], "tactic_count": 3}
{"name": "Polynomial.smeval_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Smeval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.smeval_comp", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Smeval", "is_tactic_proof": true, "tactics": ["induction", "add", "monomial"], "tactic_count": 3}
{"name": "Polynomial.smeval_commute_left", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Smeval", "is_tactic_proof": true, "tactics": ["induction", "add", "monomial", "simp", "refine", "induction", "zero", "succ", "refine", "rw", "rw", "exact"], "tactic_count": 12}
{"name": "Polynomial.smeval_commute", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Smeval", "is_tactic_proof": true, "tactics": ["induction", "add", "monomial", "simp", "refine", "induction", "zero", "succ", "refine", "rw", "have", "refine", "exact", "rw"], "tactic_count": 14}
{"name": "Polynomial.aeval_eq_smeval", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Smeval", "is_tactic_proof": true, "tactics": ["rw", "simp", "exact"], "tactic_count": 3}
{"name": "Polynomial.aeval_coe_eq_smeval", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Smeval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Monic.irreducible_iff_roots_eq_zero_of_degree_le_three", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.SpecificDegree", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "simp_rw", "show", "dvd_iff_isRoot]", "refine", "rw", "apply"], "tactic_count": 9}
{"name": "Polynomial.irreducible_iff_roots_eq_zero_of_degree_le_three", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.SpecificDegree", "is_tactic_proof": true, "tactics": ["have", "rw", "exact", "rwa", "rwa"], "tactic_count": 5}
{"name": "Polynomial.irreducible_of_degree_le_three_of_not_isRoot", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.SpecificDegree", "is_tactic_proof": true, "tactics": ["rw", "by_cases", "rw", "apply", "simp_all", "apply", "rw", "exact"], "tactic_count": 8}
{"name": "Polynomial.Splits", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Splits.C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Splits.zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Polynomial.Splits.one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Splits.X_add_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Splits.X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Polynomial.Splits.mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Splits.C_mul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Splits.listProd", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Splits.pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Splits.X_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Splits.C_mul_X_pow", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Splits.monomial", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.Splits.map", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "Polynomial.splits_of_natDegree_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.splits_of_degree_le_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUnit.splits", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.splits_of_natDegree_le_one_of_invertible", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": true, "tactics": ["obtain", "rcases", "simp", "replace", "rw", "exact"], "tactic_count": 6}
{"name": "Polynomial.splits_of_degree_le_one_of_invertible", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.splits_of_natDegree_le_one_of_monic", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.splits_of_degree_le_one_of_monic", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Splits.multisetProd", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Splits.prod", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Splits.taylor", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": true, "tactics": ["have", "induction"], "tactic_count": 2}
{"name": "Polynomial.splits_iff_exists_multiset'", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": true, "tactics": ["refine", "let", "have", "rw", "obtain", "obtain", "choose", "have", "rw", "use", "rw", "apply", "simp", "rintro", "exact"], "tactic_count": 15}
{"name": "Polynomial.Splits.natDegree_le_one_of_irreducible", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": true, "tactics": ["nontriviality", "obtain", "rcases", "rw", "simp", "obtain", "rw", "rw", "simp", "have", "grw", "simp"], "tactic_count": 12}
{"name": "Polynomial.Splits.degree_le_one_of_irreducible", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Splits.comp_of_natDegree_le_one_of_invertible", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": true, "tactics": ["rcases", "rw", "simp", "obtain", "rw", "refine", "simp", "rintro", "apply", "rw", "simpa"], "tactic_count": 11}
{"name": "Polynomial.Splits.comp_of_degree_le_one_of_invertible", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Splits.comp_of_natDegree_le_one_of_monic", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Splits.comp_of_degree_le_one_of_monic", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Splits.comp_X_add_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Splits.of_algHom", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "Polynomial.Splits.of_isScalarTower", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Splits.X_sub_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Polynomial.Splits.neg", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Polynomial.splits_neg_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Splits.comp_neg_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": true, "tactics": ["refine", "rintro", "simp", "rw", "exact"], "tactic_count": 5}
{"name": "Polynomial.splits_iff_exists_multiset", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": true, "tactics": ["refine"], "tactic_count": 1}
{"name": "Polynomial.Splits.exists_eval_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": true, "tactics": ["obtain", "by_cases", "simp", "obtain", "rw", "contradiction", "obtain", "exact"], "tactic_count": 8}
{"name": "Polynomial.rootOfSplits", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eval_rootOfSplits", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Splits.comp_X_sub_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Splits.eq_prod_roots", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "obtain", "suffices", "rw"], "tactic_count": 5}
{"name": "Polynomial.Splits.eq_prod_roots_of_monic", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": true, "tactics": ["conv_lhs"], "tactic_count": 1}
{"name": "Polynomial.Splits.eval_eq_prod_roots", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": true, "tactics": ["conv_lhs", "simp"], "tactic_count": 2}
{"name": "Polynomial.Splits.eval_eq_prod_roots_of_monic", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.Splits.aeval_eq_prod_aroots", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.Splits.aeval_eq_prod_aroots_of_monic", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.Splits.eval_derivative", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": true, "tactics": ["conv_lhs", "simp"], "tactic_count": 2}
{"name": "Polynomial.Splits.eval_root_derivative", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.Splits.of_splits_map_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": true, "tactics": ["choose", "rw", "refine", "conv_lhs", "simp"], "tactic_count": 5}
{"name": "Polynomial.Splits.of_splits_map", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Splits.mem_lift_of_roots_mem_range", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": true, "tactics": ["rw", "refine", "obtain", "exact"], "tactic_count": 4}
{"name": "Polynomial.Splits.eq_X_sub_C_of_single_root", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Polynomial.Splits.natDegree_eq_card_roots", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "conv_lhs"], "tactic_count": 3}
{"name": "Polynomial.Splits.degree_eq_card_roots", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.splits_iff_card_roots", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Splits.roots_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Polynomial.Splits.roots_map_of_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": true, "tactics": ["induction", "mem", "one", "mul"], "tactic_count": 4}
{"name": "Polynomial.Splits.roots_map_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Splits.roots_map", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Splits.mem_range_of_isRoot", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": true, "tactics": ["rw", "obtain", "exact"], "tactic_count": 3}
{"name": "Polynomial.Splits.image_rootSet", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": true, "tactics": ["classical", "rw", "g.comp_algebraMap,"], "tactic_count": 3}
{"name": "Polynomial.Splits.adjoin_rootSet_eq_range", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Polynomial.Splits.image_rootSet_of_map_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": true, "tactics": ["classical", "replace", "replace", "rw", "simp"], "tactic_count": 5}
{"name": "Polynomial.Splits.coeff_zero_eq_leadingCoeff_mul_prod_roots", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": true, "tactics": ["conv_lhs", "simp"], "tactic_count": 2}
{"name": "Polynomial.Splits.coeff_zero_eq_prod_roots_of_monic", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.Splits.nextCoeff_eq_neg_sum_roots_mul_leadingCoeff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": true, "tactics": ["conv_lhs", "simp"], "tactic_count": 2}
{"name": "Polynomial.Splits.nextCoeff_eq_neg_sum_roots_of_monic", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.splits_X_sub_C_mul_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": true, "tactics": ["refine", "by_cases", "aesop", "have", "rw", "rw", "aesop"], "tactic_count": 7}
{"name": "Polynomial.splits_mul_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": true, "tactics": ["refine", "generalize", "generalize", "induction", "zero", "rw", "exact", "succ", "obtain", "have", "rw", "wlog", "exact", "obtain", "rw", "rw", "have", "aesop"], "tactic_count": 18}
{"name": "Polynomial.Splits.of_dvd", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Polynomial.splits_prod_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Splits.splits", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.map_sub_sprod_roots_eq_prod_map_eval", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": true, "tactics": ["have", "rw", "conv_rhs", "simp_rw", "congr", "ext"], "tactic_count": 6}
{"name": "Polynomial.map_sub_roots_sprod_eq_prod_map_eval", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": true, "tactics": ["trans", "rw", "rw"], "tactic_count": 3}
{"name": "Polynomial.Splits.of_natDegree_le_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": true, "tactics": ["obtain", "by_cases", "aesop", "rw", "exact"], "tactic_count": 5}
{"name": "Polynomial.Splits.of_natDegree_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Splits.of_degree_le_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Splits.of_degree_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Splits.dvd_of_roots_le_roots", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Polynomial.Splits.dvd_iff_roots_le_roots", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Splits.comp_of_natDegree_le_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": true, "tactics": ["rcases", "simp", "exact"], "tactic_count": 3}
{"name": "Polynomial.Splits.comp_of_degree_le_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.splits_iff_comp_splits_of_natDegree_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": true, "tactics": ["refine", "obtain", "have", "have", "simp", "rw", "rw", "refine", "rw"], "tactic_count": 9}
{"name": "Polynomial.splits_iff_comp_splits_of_degree_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Splits.degree_eq_one_of_irreducible", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Splits.natDegree_eq_one_of_irreducible", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Splits.eval_derivative_eq_eval_mul_sum", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": true, "tactics": ["classical", "simp", "refine", "rw", "aesop"], "tactic_count": 5}
{"name": "Polynomial.Splits.eval_derivative_div_eval_of_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.Splits.mem_subfield_of_isRoot", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Polynomial.Splits.of_natDegree_eq_two", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": false, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "Polynomial.Splits.of_degree_eq_two", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.splits_iff_splits", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": false, "tactics": ["refine", "rintro", "aesop", "classical", "by_cases", "simp", "obtain", "rw", "refine", "exact"], "tactic_count": 10}
{"name": "Polynomial.splits_of_map_eq_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.splits_map_iff", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.splits_id_iff_splits", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.splits_of_splits_gcd_left", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.splits_of_splits_gcd_right", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.rootOfSplits'_eq_rootOfSplits", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Polynomial.Splits.0.Polynomial.term_~ᵤ_", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Polynomial.Splits.0.Polynomial._aux_Mathlib_Algebra_Polynomial_Splits___macroRules__private_Mathlib_Algebra_Polynomial_Splits_0_Polynomial_term_~ᵤ__1", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Polynomial.Splits.0.Polynomial._aux_Mathlib_Algebra_Polynomial_Splits___unexpand_Associated_1", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.Splits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.sumIDeriv", "kind": "definition", "module": "Mathlib.Algebra.Polynomial.SumIteratedDerivative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.sumIDeriv_apply", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.SumIteratedDerivative", "is_tactic_proof": true, "tactics": ["dsimp", "exact"], "tactic_count": 2}
{"name": "Polynomial.sumIDeriv_apply_of_lt", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.SumIteratedDerivative", "is_tactic_proof": true, "tactics": ["dsimp", "exact"], "tactic_count": 2}
{"name": "Polynomial.sumIDeriv_apply_of_le", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.SumIteratedDerivative", "is_tactic_proof": true, "tactics": ["dsimp", "exact"], "tactic_count": 2}
{"name": "Polynomial.sumIDeriv_C", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.SumIteratedDerivative", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.sumIDeriv_X", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.SumIteratedDerivative", "is_tactic_proof": true, "tactics": ["rw", "derivative_X,"], "tactic_count": 2}
{"name": "Polynomial.sumIDeriv_map", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.SumIteratedDerivative", "is_tactic_proof": true, "tactics": ["let", "rw", "rw", "simp_rw"], "tactic_count": 4}
{"name": "Polynomial.sumIDeriv_derivative", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.SumIteratedDerivative", "is_tactic_proof": true, "tactics": ["rw", "simp_rw"], "tactic_count": 2}
{"name": "Polynomial.sumIDeriv_eq_self_add", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.SumIteratedDerivative", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "iterate_derivative_eq_zero"], "tactic_count": 3}
{"name": "Polynomial.exists_iterate_derivative_eq_factorial_smul", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.SumIteratedDerivative", "is_tactic_proof": true, "tactics": ["refine", "rw", "refine", "dsimp", "exact"], "tactic_count": 5}
{"name": "Polynomial.aeval_iterate_derivative_of_lt", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.SumIteratedDerivative", "is_tactic_proof": false, "tactics": ["have", "rw", "rw", "exact", "rw", "simp_rw", "mul_assoc,"], "tactic_count": 7}
{"name": "Polynomial.aeval_iterate_derivative_self", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.SumIteratedDerivative", "is_tactic_proof": false, "tactics": ["have", "rw", "rwa", "rw", "simp_rw", "rw", "smul_mul_assoc,", "convert", "rw", "apply", "intro", "rw", "eval_sub,"], "tactic_count": 13}
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{"name": "Polynomial.IsUnitTrinomial.irreducible_of_isCoprime", "kind": "theorem", "module": "Mathlib.Algebra.Polynomial.UnitTrinomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresentedMonoid", "kind": "definition", "module": "Mathlib.Algebra.PresentedMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresentedMonoid.instMonoid", "kind": "instance", "module": "Mathlib.Algebra.PresentedMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "_private.Mathlib.Algebra.PresentedMonoid.Basic.0.PresentedMonoid.termP₁", "kind": "definition", "module": "Mathlib.Algebra.PresentedMonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "QuaternionAlgebra.smul_coe", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "QuaternionAlgebra.instStarQuaternionAlgebra", "kind": "instance", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuaternionAlgebra.re_star", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuaternionAlgebra.imI_star", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuaternionAlgebra.imJ_star", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuaternionAlgebra.imK_star", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuaternionAlgebra.im_star", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuaternionAlgebra.star_mk", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuaternionAlgebra.instStarRing", "kind": "instance", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuaternionAlgebra.self_add_star'", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "QuaternionAlgebra.self_add_star", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "QuaternionAlgebra.star_add_self'", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "QuaternionAlgebra.star_add_self", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "QuaternionAlgebra.star_eq_two_re_sub", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuaternionAlgebra.comm", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "QuaternionAlgebra.instIsStarNormal", "kind": "instance", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuaternionAlgebra.star_coe", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "QuaternionAlgebra.star_im", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "QuaternionAlgebra.star_smul", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuaternionAlgebra.star_smul'", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuaternionAlgebra.eq_re_of_eq_coe", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "QuaternionAlgebra.eq_re_iff_mem_range_coe", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuaternionAlgebra.star_eq_self", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": true, "tactics": ["simp_all"], "tactic_count": 1}
{"name": "QuaternionAlgebra.star_eq_neg", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "QuaternionAlgebra.star_mul_eq_coe", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "QuaternionAlgebra.mul_star_eq_coe", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "QuaternionAlgebra.starAe", "kind": "definition", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuaternionAlgebra.coe_starAe", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion", "kind": "definition", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.termℍ[_]", "kind": "definition", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion._aux_Mathlib_Algebra_Quaternion___macroRules_Quaternion_termℍ[_]_1", "kind": "definition", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion._aux_Mathlib_Algebra_Quaternion___unexpand_Quaternion_1", "kind": "definition", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.equivProd", "kind": "definition", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.equivTuple", "kind": "definition", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.equivTuple_apply", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instSubsingletonQuaternion", "kind": "instance", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instNontrivialQuaternion", "kind": "instance", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.coe", "kind": "definition", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.instCoeTC", "kind": "instance", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.instRing", "kind": "instance", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.instInhabited", "kind": "instance", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.instSMul", "kind": "instance", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.instIsScalarTower", "kind": "instance", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.instSMulCommClass", "kind": "instance", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.instMulAction", "kind": "instance", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.instDistribMulAction", "kind": "instance", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.instModule", "kind": "instance", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.algebra", "kind": "instance", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.instStar", "kind": "instance", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.instStarRing", "kind": "instance", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.instIsStarNormal", "kind": "instance", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.ext", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.im", "kind": "definition", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.re_im", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.imI_im", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.imJ_im", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.imK_im", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.im_idem", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.re_add_im", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.sub_im_self", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.sub_re_self", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.re_coe", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.imI_coe", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.imJ_coe", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Quaternion.im_coe", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.re_zero", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.imI_zero", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.imJ_zero", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.imK_zero", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.im_zero", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.coe_zero", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.re_one", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.imI_one", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Quaternion.coe_one", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.re_add", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.imI_add", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.imJ_add", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.imK_add", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.im_add", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Quaternion.re_neg", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.imI_neg", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.imJ_neg", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.imK_neg", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Quaternion.coe_neg", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.re_sub", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Quaternion.re_mul", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Quaternion.imJ_mul", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.imK_mul", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.coe_mul", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.coe_pow", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.re_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.imI_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Quaternion.imK_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Quaternion.coe_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.re_intCast", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Quaternion.coe_intCast", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.coe_injective", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.coe_inj", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.re_smul", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.imI_smul", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Quaternion.coe_mul_eq_smul", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.mul_coe_eq_smul", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Quaternion.algebraMap_injective", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.smul_coe", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Quaternion.instFree", "kind": "instance", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.rank_eq_four", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.finrank_eq_four", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.re_star", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Quaternion.imI_star", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.imJ_star", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.imK_star", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.im_star", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.self_add_star'", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Quaternion.self_add_star", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Quaternion.star_add_self'", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Quaternion.star_add_self", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Quaternion.star_eq_two_re_sub", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Quaternion.star_coe", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.star_im", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Quaternion.star_smul", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.eq_re_of_eq_coe", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.eq_re_iff_mem_range_coe", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.star_eq_self", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.star_eq_neg", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.star_mul_eq_coe", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.mul_star_eq_coe", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.starAe", "kind": "definition", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.coe_starAe", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.normSq", "kind": "definition", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.normSq_def", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.normSq_def'", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Quaternion.normSq_coe", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Quaternion.normSq_star", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Quaternion.normSq_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Quaternion.normSq_intCast", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Quaternion.normSq_neg", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Quaternion.self_mul_star", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Quaternion.star_mul_self", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Quaternion.im_sq", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Quaternion.coe_normSq_add", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Quaternion.normSq_smul", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Quaternion.normSq_add", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.normSq_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": true, "tactics": ["refine", "rw", "apply", "exacts", "all_goals"], "tactic_count": 5}
{"name": "Quaternion.normSq_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.normSq_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": true, "tactics": ["rw", "apply_rules"], "tactic_count": 2}
{"name": "Quaternion.normSq_le_zero", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.instNontrivial", "kind": "instance", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.instNoZeroDivisors", "kind": "instance", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.instIsDomain", "kind": "instance", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.sq_eq_normSq", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Quaternion.sq_eq_neg_normSq", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": true, "tactics": ["simp_rw", "obtain", "simp", "rw"], "tactic_count": 4}
{"name": "Quaternion.instNNRatCast", "kind": "instance", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.instRatCast", "kind": "instance", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.re_nnratCast", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.im_nnratCast", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.imI_nnratCast", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.imJ_nnratCast", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.imK_nnratCast", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.re_ratCast", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.im_ratCast", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.imI_ratCast", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.imJ_ratCast", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.imK_ratCast", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.coe_nnratCast", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.coe_ratCast", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.instInv", "kind": "instance", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.instGroupWithZero", "kind": "instance", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.coe_inv", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.coe_div", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.coe_zpow", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.instDivisionRing", "kind": "instance", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.normSq_inv", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.normSq_div", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.normSq_zpow", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.normSq_ratCast", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "_private.Mathlib.Algebra.Quaternion.0.Cardinal.pow_four", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_quaternionAlgebra", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": true, "tactics": ["rw", "simp", "ring"], "tactic_count": 3}
{"name": "Cardinal.mk_quaternionAlgebra_of_infinite", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.mk_univ_quaternionAlgebra", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.mk_univ_quaternionAlgebra_of_infinite", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.instReprQuaternionAlgebra", "kind": "instance", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_quaternion", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_quaternion_of_infinite", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_univ_quaternion", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_univ_quaternion_of_infinite", "kind": "theorem", "module": "Mathlib.Algebra.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuaternionAlgebra.Basis.ext", "kind": "theorem", "module": "Mathlib.Algebra.QuaternionBasis", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "QuaternionAlgebra.Basis.self", "kind": "definition", "module": "Mathlib.Algebra.QuaternionBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuaternionAlgebra.Basis.instInhabited", "kind": "instance", "module": "Mathlib.Algebra.QuaternionBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuaternionAlgebra.Basis.i_mul_k", "kind": "theorem", "module": "Mathlib.Algebra.QuaternionBasis", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "QuaternionAlgebra.Basis.k_mul_i", "kind": "theorem", "module": "Mathlib.Algebra.QuaternionBasis", "is_tactic_proof": true, "tactics": ["rw", "linear_combination"], "tactic_count": 2}
{"name": "QuaternionAlgebra.Basis.k_mul_j", "kind": "theorem", "module": "Mathlib.Algebra.QuaternionBasis", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "QuaternionAlgebra.Basis.j_mul_k", "kind": "theorem", "module": "Mathlib.Algebra.QuaternionBasis", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "QuaternionAlgebra.Basis.k_mul_k", "kind": "theorem", "module": "Mathlib.Algebra.QuaternionBasis", "is_tactic_proof": false, "tactics": ["rw", "add_mul,", "add_mul,", "linear_combination"], "tactic_count": 4}
{"name": "QuaternionAlgebra.Basis.lift", "kind": "definition", "module": "Mathlib.Algebra.QuaternionBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuaternionAlgebra.Basis.lift_zero", "kind": "theorem", "module": "Mathlib.Algebra.QuaternionBasis", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "QuaternionAlgebra.Basis.lift_one", "kind": "theorem", "module": "Mathlib.Algebra.QuaternionBasis", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "QuaternionAlgebra.Basis.lift_add", "kind": "theorem", "module": "Mathlib.Algebra.QuaternionBasis", "is_tactic_proof": true, "tactics": ["simp", "abel"], "tactic_count": 2}
{"name": "QuaternionAlgebra.Basis.lift_mul", "kind": "theorem", "module": "Mathlib.Algebra.QuaternionBasis", "is_tactic_proof": true, "tactics": ["simp", "simp_rw", "simp", "simp", "simp", "simp", "simp", "simp", "simp", "linear_combination"], "tactic_count": 10}
{"name": "QuaternionAlgebra.Basis.lift_smul", "kind": "theorem", "module": "Mathlib.Algebra.QuaternionBasis", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "QuaternionAlgebra.Basis.liftHom", "kind": "definition", "module": "Mathlib.Algebra.QuaternionBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuaternionAlgebra.Basis.range_liftHom", "kind": "theorem", "module": "Mathlib.Algebra.QuaternionBasis", "is_tactic_proof": true, "tactics": ["apply", "rintro", "refine", "exact", "all_goals", "rw", "rintro", "all_goals"], "tactic_count": 8}
{"name": "QuaternionAlgebra.Basis.compHom", "kind": "definition", "module": "Mathlib.Algebra.QuaternionBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuaternionAlgebra.lift", "kind": "definition", "module": "Mathlib.Algebra.QuaternionBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuaternionAlgebra.hom_ext", "kind": "theorem", "module": "Mathlib.Algebra.QuaternionBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.hom_ext", "kind": "theorem", "module": "Mathlib.Algebra.QuaternionBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasQuotient.quotient'", "kind": "abbrev", "module": "Mathlib.Algebra.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "term_⧸_", "kind": "definition", "module": "Mathlib.Algebra.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Algebra_Quotient___macroRules_term_⧸__1", "kind": "definition", "module": "Mathlib.Algebra.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Algebra_Quotient___unexpand_HasQuotient_Quotient_1", "kind": "definition", "module": "Mathlib.Algebra.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLeftRegular.right_of_commute", "kind": "theorem", "module": "Mathlib.Algebra.Regular.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRightRegular.left_of_commute", "kind": "theorem", "module": "Mathlib.Algebra.Regular.Basic", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Commute.isRightRegular_iff", "kind": "theorem", "module": "Mathlib.Algebra.Regular.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.isRegular_iff", "kind": "theorem", "module": "Mathlib.Algebra.Regular.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLeftRegular.mul", "kind": "theorem", "module": "Mathlib.Algebra.Regular.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRightRegular.mul", "kind": "theorem", "module": "Mathlib.Algebra.Regular.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRegular.mul", "kind": "theorem", "module": "Mathlib.Algebra.Regular.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLeftRegular.of_mul", "kind": "theorem", "module": "Mathlib.Algebra.Regular.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_isLeftRegular_iff", "kind": "theorem", "module": "Mathlib.Algebra.Regular.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRightRegular.of_mul", "kind": "theorem", "module": "Mathlib.Algebra.Regular.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "mul_isRightRegular_iff", "kind": "theorem", "module": "Mathlib.Algebra.Regular.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isRegular_mul_and_mul_iff", "kind": "theorem", "module": "Mathlib.Algebra.Regular.Basic", "is_tactic_proof": true, "tactics": ["refine", "rintro", "exact", "rintro", "exact"], "tactic_count": 5}
{"name": "IsRegular.and_of_mul_of_mul", "kind": "theorem", "module": "Mathlib.Algebra.Regular.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isRegular_one", "kind": "theorem", "module": "Mathlib.Algebra.Regular.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isRegular_mul_iff", "kind": "theorem", "module": "Mathlib.Algebra.Regular.Basic", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "isLeftRegular_of_mul_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Regular.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isRightRegular_of_mul_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Regular.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.isRegular", "kind": "theorem", "module": "Mathlib.Algebra.Regular.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUnit.isRegular", "kind": "theorem", "module": "Mathlib.Algebra.Regular.Basic", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "IsLeftRegular.pow", "kind": "theorem", "module": "Mathlib.Algebra.Regular.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsRightRegular.pow", "kind": "theorem", "module": "Mathlib.Algebra.Regular.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsRegular.pow", "kind": "theorem", "module": "Mathlib.Algebra.Regular.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLeftRegular.pow_iff", "kind": "theorem", "module": "Mathlib.Algebra.Regular.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRightRegular.pow_iff", "kind": "theorem", "module": "Mathlib.Algebra.Regular.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRegular.pow_iff", "kind": "theorem", "module": "Mathlib.Algebra.Regular.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLeftRegular.mul_left_eq_self_iff", "kind": "theorem", "module": "Mathlib.Algebra.Regular.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRightRegular.mul_right_eq_self_iff", "kind": "theorem", "module": "Mathlib.Algebra.Regular.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindFiniteMonoid.iff_isLeftRegular_of_mul_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Regular.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindFiniteMonoid.iff_isRightRegular_of_mul_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Regular.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLeftRegular", "kind": "definition", "module": "Mathlib.Algebra.Regular.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRightRegular", "kind": "definition", "module": "Mathlib.Algebra.Regular.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isRegular_iff", "kind": "theorem", "module": "Mathlib.Algebra.Regular.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLeftRegular_op", "kind": "theorem", "module": "Mathlib.Algebra.Regular.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isRightRegular_op", "kind": "theorem", "module": "Mathlib.Algebra.Regular.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isRegular_op", "kind": "theorem", "module": "Mathlib.Algebra.Regular.Opposite", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "isLeftRegular_unop", "kind": "theorem", "module": "Mathlib.Algebra.Regular.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isRightRegular_unop", "kind": "theorem", "module": "Mathlib.Algebra.Regular.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isRegular_unop", "kind": "theorem", "module": "Mathlib.Algebra.Regular.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.isLeftRegular_iff", "kind": "theorem", "module": "Mathlib.Algebra.Regular.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.isRightRegular_iff", "kind": "theorem", "module": "Mathlib.Algebra.Regular.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.isRegular_iff", "kind": "theorem", "module": "Mathlib.Algebra.Regular.Pi", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Pi.isSMulRegular_iff", "kind": "theorem", "module": "Mathlib.Algebra.Regular.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLeftRegular.prod", "kind": "theorem", "module": "Mathlib.Algebra.Regular.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRightRegular.prod", "kind": "theorem", "module": "Mathlib.Algebra.Regular.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRegular.prod", "kind": "theorem", "module": "Mathlib.Algebra.Regular.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.isLeftRegular_mk", "kind": "theorem", "module": "Mathlib.Algebra.Regular.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.isRightRegular_mk", "kind": "theorem", "module": "Mathlib.Algebra.Regular.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.isRegular_mk", "kind": "theorem", "module": "Mathlib.Algebra.Regular.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsLeftRegular.prodMk", "kind": "theorem", "module": "Mathlib.Algebra.Regular.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRightRegular.prodMk", "kind": "theorem", "module": "Mathlib.Algebra.Regular.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRegular.prodMk", "kind": "theorem", "module": "Mathlib.Algebra.Regular.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.isSMulRegular_iff", "kind": "theorem", "module": "Mathlib.Algebra.Regular.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSMulRegular", "kind": "definition", "module": "Mathlib.Algebra.Regular.SMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLeftRegular.isSMulRegular", "kind": "theorem", "module": "Mathlib.Algebra.Regular.SMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLeftRegular_iff", "kind": "theorem", "module": "Mathlib.Algebra.Regular.SMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRightRegular.isSMulRegular", "kind": "theorem", "module": "Mathlib.Algebra.Regular.SMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isRightRegular_iff", "kind": "theorem", "module": "Mathlib.Algebra.Regular.SMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isSMulRegular_map", "kind": "theorem", "module": "Mathlib.Algebra.Regular.SMul", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsSMulRegular.natAbs_iff", "kind": "theorem", "module": "Mathlib.Algebra.Regular.SMul", "is_tactic_proof": true, "tactics": ["simp_rw", "conv_rhs", "obtain", "simp", "simp", "simp"], "tactic_count": 6}
{"name": "IsSMulRegular.smul", "kind": "theorem", "module": "Mathlib.Algebra.Regular.SMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSMulRegular.of_smul", "kind": "theorem", "module": "Mathlib.Algebra.Regular.SMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSMulRegular.smul_iff", "kind": "theorem", "module": "Mathlib.Algebra.Regular.SMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSMulRegular.isLeftRegular", "kind": "theorem", "module": "Mathlib.Algebra.Regular.SMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSMulRegular.isRightRegular", "kind": "theorem", "module": "Mathlib.Algebra.Regular.SMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSMulRegular.mul", "kind": "theorem", "module": "Mathlib.Algebra.Regular.SMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSMulRegular.of_mul", "kind": "theorem", "module": "Mathlib.Algebra.Regular.SMul", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsSMulRegular.mul_iff_right", "kind": "theorem", "module": "Mathlib.Algebra.Regular.SMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSMulRegular.mul_and_mul_iff", "kind": "theorem", "module": "Mathlib.Algebra.Regular.SMul", "is_tactic_proof": true, "tactics": ["refine", "rintro", "exact", "rintro", "exact"], "tactic_count": 5}
{"name": "IsSMulRegular.one", "kind": "theorem", "module": "Mathlib.Algebra.Regular.SMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSMulRegular.of_mul_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Regular.SMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSMulRegular.pow", "kind": "theorem", "module": "Mathlib.Algebra.Regular.SMul", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "exact"], "tactic_count": 5}
{"name": "IsSMulRegular.pow_iff", "kind": "theorem", "module": "Mathlib.Algebra.Regular.SMul", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "IsSMulRegular.of_smul_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Regular.SMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSMulRegular.subsingleton", "kind": "theorem", "module": "Mathlib.Algebra.Regular.SMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSMulRegular.zero_iff_subsingleton", "kind": "theorem", "module": "Mathlib.Algebra.Regular.SMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSMulRegular.not_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Regular.SMul", "is_tactic_proof": true, "tactics": ["rw", "push_neg", "exact"], "tactic_count": 3}
{"name": "IsSMulRegular.zero", "kind": "theorem", "module": "Mathlib.Algebra.Regular.SMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSMulRegular.not_zero", "kind": "theorem", "module": "Mathlib.Algebra.Regular.SMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSMulRegular.mul_iff", "kind": "theorem", "module": "Mathlib.Algebra.Regular.SMul", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "isSMulRegular_of_group", "kind": "theorem", "module": "Mathlib.Algebra.Regular.SMul", "is_tactic_proof": true, "tactics": ["intro", "convert"], "tactic_count": 2}
{"name": "Units.isSMulRegular", "kind": "theorem", "module": "Mathlib.Algebra.Regular.SMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUnit.isSMulRegular", "kind": "theorem", "module": "Mathlib.Algebra.Regular.SMul", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "IsSMulRegular.right_eq_zero_of_smul", "kind": "theorem", "module": "Mathlib.Algebra.Regular.SMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isSMulRegular_iff_right_eq_zero_of_smul", "kind": "theorem", "module": "Mathlib.Algebra.Regular.SMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.isSMulRegular_congr", "kind": "theorem", "module": "Mathlib.Algebra.Regular.SMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.isLeftRegular_up", "kind": "theorem", "module": "Mathlib.Algebra.Regular.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.isRightRegular_up", "kind": "theorem", "module": "Mathlib.Algebra.Regular.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.isRegular_up", "kind": "theorem", "module": "Mathlib.Algebra.Regular.ULift", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ULift.isLeftRegular_down", "kind": "theorem", "module": "Mathlib.Algebra.Regular.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.isRightRegular_down", "kind": "theorem", "module": "Mathlib.Algebra.Regular.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.isRegular_down", "kind": "theorem", "module": "Mathlib.Algebra.Regular.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.isSMulRegular_iff", "kind": "theorem", "module": "Mathlib.Algebra.Regular.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.instAlgebraQuotient", "kind": "instance", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.mkₐ", "kind": "definition", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.mkₐ_surjective", "kind": "theorem", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.coe_algebraMap", "kind": "theorem", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingQuot.Rel", "kind": "inductive", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingQuot.Rel.add_right", "kind": "theorem", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "RingQuot.Rel.neg", "kind": "theorem", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RingQuot.Rel.sub_left", "kind": "theorem", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RingQuot.Rel.sub_right", "kind": "theorem", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RingQuot.Rel.smul", "kind": "theorem", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RingQuot.ringCon", "kind": "definition", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingQuot.eqvGen_rel_eq", "kind": "theorem", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": true, "tactics": ["ext", "constructor", "intro", "induction", "rel", "induction", "of", "add_left", "mul_left", "mul_right", "refl", "symm", "trans", "intro", "induction", "of", "refl", "symm", "trans", "add", "mul"], "tactic_count": 21}
{"name": "RingQuot.natCast", "kind": "definition", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingQuot.instNatCast", "kind": "instance", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingQuot.instZero", "kind": "instance", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingQuot.instOne", "kind": "instance", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingQuot.instAdd", "kind": "instance", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingQuot.instMul", "kind": "instance", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingQuot.instNatPow", "kind": "instance", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingQuot.instNeg", "kind": "instance", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingQuot.instSub", "kind": "instance", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingQuot.smul", "kind": "definition", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingQuot.instSMulOfAlgebra", "kind": "instance", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingQuot.zero_quot", "kind": "theorem", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingQuot.one_quot", "kind": "theorem", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingQuot.add_quot", "kind": "theorem", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingQuot.mul_quot", "kind": "theorem", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingQuot.pow_quot", "kind": "theorem", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingQuot.neg_quot", "kind": "theorem", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingQuot.sub_quot", "kind": "theorem", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingQuot.smul_quot", "kind": "theorem", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingQuot.instIsScalarTower", "kind": "instance", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingQuot.instSMulCommClass", "kind": "instance", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingQuot.instAddCommMonoid", "kind": "instance", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingQuot.instMonoidWithZero", "kind": "instance", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingQuot.instSemiring", "kind": "instance", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingQuot.intCast", "kind": "definition", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingQuot.instRing", "kind": "instance", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingQuot.instCommSemiring", "kind": "instance", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingQuot.instCommRing", "kind": "instance", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingQuot.instInhabited", "kind": "instance", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingQuot.instAlgebra", "kind": "instance", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingQuot.definition._@.Mathlib.Algebra.RingQuot.3469094938._hygCtx._hyg.2", "kind": "definition", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingQuot.wrapped._@.Mathlib.Algebra.RingQuot.3469094938._hygCtx._hyg.2", "kind": "opaque", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingQuot.mkRingHom", "kind": "definition", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingQuot.mkRingHom_def", "kind": "theorem", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": true, "tactics": ["intros", "delta", "rw", "rfl"], "tactic_count": 4}
{"name": "RingQuot.mkRingHom_rel", "kind": "theorem", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RingQuot.mkRingHom_surjective", "kind": "theorem", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": true, "tactics": ["simp", "rintro", "simp"], "tactic_count": 3}
{"name": "RingQuot.ringQuot_ext", "kind": "theorem", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": true, "tactics": ["ext", "rcases", "exact"], "tactic_count": 3}
{"name": "RingQuot.definition._@.Mathlib.Algebra.RingQuot.1093876312._hygCtx._hyg.2", "kind": "definition", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "RingQuot.preLift", "kind": "definition", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingQuot.preLift_def", "kind": "theorem", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": true, "tactics": ["intros", "delta", "rw", "rfl"], "tactic_count": 4}
{"name": "RingQuot.definition._@.Mathlib.Algebra.RingQuot.1987113737._hygCtx._hyg.2", "kind": "definition", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingQuot.wrapped._@.Mathlib.Algebra.RingQuot.1987113737._hygCtx._hyg.2", "kind": "opaque", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingQuot.lift", "kind": "definition", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingQuot.lift_def", "kind": "theorem", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": true, "tactics": ["intros", "delta", "rw", "rfl"], "tactic_count": 4}
{"name": "RingQuot.lift_mkRingHom_apply", "kind": "theorem", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": true, "tactics": ["simp_rw", "rfl"], "tactic_count": 2}
{"name": "RingQuot.lift_unique", "kind": "theorem", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "RingQuot.eq_lift_comp_mkRingHom", "kind": "theorem", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingQuot.ringQuotToIdealQuotient", "kind": "definition", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingQuot.ringQuotToIdealQuotient_apply", "kind": "theorem", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": true, "tactics": ["simp_rw", "rfl"], "tactic_count": 2}
{"name": "RingQuot.idealQuotientToRingQuot", "kind": "definition", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingQuot.idealQuotientToRingQuot_apply", "kind": "theorem", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingQuot.ringQuotEquivIdealQuotient", "kind": "definition", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingQuot.definition._@.Mathlib.Algebra.RingQuot.3673095128._hygCtx._hyg.2", "kind": "definition", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingQuot.wrapped._@.Mathlib.Algebra.RingQuot.3673095128._hygCtx._hyg.2", "kind": "opaque", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingQuot.mkAlgHom", "kind": "definition", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingQuot.mkAlgHom_def", "kind": "theorem", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": true, "tactics": ["intros", "delta", "rw", "rfl"], "tactic_count": 4}
{"name": "RingQuot.mkAlgHom_coe", "kind": "theorem", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": true, "tactics": ["simp_rw", "rfl"], "tactic_count": 2}
{"name": "RingQuot.mkAlgHom_rel", "kind": "theorem", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RingQuot.mkAlgHom_surjective", "kind": "theorem", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": true, "tactics": ["suffices", "rintro", "use"], "tactic_count": 3}
{"name": "RingQuot.ringQuot_ext'", "kind": "theorem", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": true, "tactics": ["ext", "rcases", "exact"], "tactic_count": 3}
{"name": "RingQuot.definition._@.Mathlib.Algebra.RingQuot.1554258878._hygCtx._hyg.2", "kind": "definition", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingQuot.wrapped._@.Mathlib.Algebra.RingQuot.1554258878._hygCtx._hyg.2", "kind": "opaque", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingQuot.preLiftAlgHom", "kind": "definition", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingQuot.preLiftAlgHom_def", "kind": "theorem", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": true, "tactics": ["intros", "delta", "rw", "rfl"], "tactic_count": 4}
{"name": "RingQuot.definition._@.Mathlib.Algebra.RingQuot.2555519587._hygCtx._hyg.2", "kind": "definition", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingQuot.wrapped._@.Mathlib.Algebra.RingQuot.2555519587._hygCtx._hyg.2", "kind": "opaque", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingQuot.liftAlgHom", "kind": "definition", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingQuot.liftAlgHom_def", "kind": "theorem", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": true, "tactics": ["intros", "delta", "rw", "rfl"], "tactic_count": 4}
{"name": "RingQuot.liftAlgHom_mkAlgHom_apply", "kind": "theorem", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": true, "tactics": ["simp_rw", "rfl"], "tactic_count": 2}
{"name": "RingQuot.liftAlgHom_unique", "kind": "theorem", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "RingQuot.eq_liftAlgHom_comp_mkAlgHom", "kind": "theorem", "module": "Mathlib.Algebra.RingQuot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulSemiringAction.toMulDistribMulAction", "kind": "instance", "module": "Mathlib.Algebra.Ring.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulSemiringAction.toRingHom", "kind": "definition", "module": "Mathlib.Algebra.Ring.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toRingHom_injective", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.applyMulSemiringAction", "kind": "instance", "module": "Mathlib.Algebra.Ring.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.smul_def", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.applyFaithfulSMul", "kind": "instance", "module": "Mathlib.Algebra.Ring.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulSemiringAction.compHom", "kind": "abbrev", "module": "Mathlib.Algebra.Ring.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjAct.unitsMulSemiringAction", "kind": "instance", "module": "Mathlib.Algebra.Ring.Action.ConjAct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingAut.applyMulSemiringAction", "kind": "instance", "module": "Mathlib.Algebra.Ring.Action.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingAut.smul_def", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Action.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingAut.apply_faithfulSMul", "kind": "instance", "module": "Mathlib.Algebra.Ring.Action.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulSemiringAction.toRingAut", "kind": "definition", "module": "Mathlib.Algebra.Ring.Action.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smul_inv''", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Action.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulSemiringAction.toRingEquiv", "kind": "definition", "module": "Mathlib.Algebra.Ring.Action.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsInvariantSubring.toMulSemiringAction", "kind": "instance", "module": "Mathlib.Algebra.Ring.Action.Invariant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsInvariantSubring.subtypeHom", "kind": "definition", "module": "Mathlib.Algebra.Ring.Action.Invariant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsInvariantSubring.coe_subtypeHom", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Action.Invariant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsInvariantSubring.coe_subtypeHom'", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Action.Invariant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.zero_mem_smul_finset_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Action.Pointwise.Finset", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.zero_mem_smul_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Action.Pointwise.Finset", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.neg_smul_finset", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Action.Pointwise.Finset", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.neg_smul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Action.Pointwise.Finset", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Set.smul_set_neg", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Action.Pointwise.Set", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.smul_neg", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Action.Pointwise.Set", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Set.add_smul_subset", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Action.Pointwise.Set", "is_tactic_proof": true, "tactics": ["rintro", "simpa"], "tactic_count": 2}
{"name": "Set.zero_mem_smul_set_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Action.Pointwise.Set", "is_tactic_proof": true, "tactics": ["refine", "rintro", "rwa"], "tactic_count": 3}
{"name": "Set.zero_mem_smul_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Action.Pointwise.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.neg_smul_set", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Action.Pointwise.Set", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.neg_smul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Action.Pointwise.Set", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "NNRat.instDistribSMul", "kind": "instance", "module": "Mathlib.Algebra.Ring.Action.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.instIsScalarTowerRight", "kind": "instance", "module": "Mathlib.Algebra.Ring.Action.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.instDistribSMul", "kind": "instance", "module": "Mathlib.Algebra.Ring.Action.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.instIsScalarTowerRight", "kind": "instance", "module": "Mathlib.Algebra.Ring.Action.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FixedPoints.addSubmonoid", "kind": "definition", "module": "Mathlib.Algebra.Ring.Action.Submonoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FixedPoints.mem_addSubmonoid", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Action.Submonoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FixedPoints.addSubgroup", "kind": "definition", "module": "Mathlib.Algebra.Ring.Action.Submonoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "term_^+_", "kind": "definition", "module": "Mathlib.Algebra.Ring.Action.Submonoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Algebra_Ring_Action_Submonoid___macroRules_term_^+__1", "kind": "definition", "module": "Mathlib.Algebra.Ring.Action.Submonoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Algebra_Ring_Action_Submonoid___unexpand_FixedPoints_addSubgroup_1", "kind": "definition", "module": "Mathlib.Algebra.Ring.Action.Submonoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FixedPoints.mem_addSubgroup", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Action.Submonoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FixedPoints.addSubgroup_toAddSubmonoid", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Action.Submonoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instMulSemiringActionSubtypeMem", "kind": "instance", "module": "Mathlib.Algebra.Ring.Action.Subobjects", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.mulSemiringAction", "kind": "instance", "module": "Mathlib.Algebra.Ring.Action.Subobjects", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.mulSemiringAction", "kind": "instance", "module": "Mathlib.Algebra.Ring.Action.Subobjects", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddAut.mulLeft", "kind": "definition", "module": "Mathlib.Algebra.Ring.AddAut", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddAut.mulRight", "kind": "definition", "module": "Mathlib.Algebra.Ring.AddAut", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddAut.mulRight_apply", "kind": "theorem", "module": "Mathlib.Algebra.Ring.AddAut", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddAut.mulRight_symm_apply", "kind": "theorem", "module": "Mathlib.Algebra.Ring.AddAut", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associated.neg_left", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associated.neg_right", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associated.neg_neg", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associated.neg_left_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associated.neg_right_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Associated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "associator", "kind": "definition", "module": "Mathlib.Algebra.Ring.Associator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "associator_apply", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Associator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "associator_eq_zero_iff_associative", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Associator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "associator_cocycle", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Associator", "is_tactic_proof": true, "tactics": ["simp", "abel1"], "tactic_count": 2}
{"name": "associator_op", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Associator", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "associator_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Associator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.mulLeft₃", "kind": "definition", "module": "Mathlib.Algebra.Ring.Associator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.mulLeft₃_apply", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Associator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.mulRight₃", "kind": "definition", "module": "Mathlib.Algebra.Ring.Associator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.mulRight₃_apply", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Associator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.mulLeft₃_eq_mulRight₃_iff_associative", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Associator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.mulLeft₃_eq_mulRight₃", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Associator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.associator", "kind": "definition", "module": "Mathlib.Algebra.Ring.Associator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.associator_apply", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Associator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.associator_eq_zero_iff_associative", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Associator", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AddMonoidHom.associator_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Associator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingAut", "kind": "abbrev", "module": "Mathlib.Algebra.Ring.Aut", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingAut.instGroup", "kind": "instance", "module": "Mathlib.Algebra.Ring.Aut", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingAut.instInhabited", "kind": "instance", "module": "Mathlib.Algebra.Ring.Aut", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingAut.toAddAut", "kind": "definition", "module": "Mathlib.Algebra.Ring.Aut", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingAut.toMulAut", "kind": "definition", "module": "Mathlib.Algebra.Ring.Aut", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingAut.toPerm", "kind": "definition", "module": "Mathlib.Algebra.Ring.Aut", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingAut.one_eq_refl", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Aut", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingAut.one_apply", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Aut", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingAut.coe_one", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Aut", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingAut.mul_apply", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Aut", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingAut.inv_apply", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Aut", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingAut.coe_pow", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Aut", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "ext", "simp"], "tactic_count": 5}
{"name": "AddHom.mulLeft", "kind": "definition", "module": "Mathlib.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddHom.mulRight", "kind": "definition", "module": "Mathlib.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.mulLeft", "kind": "definition", "module": "Mathlib.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.coe_mulLeft", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.mulRight", "kind": "definition", "module": "Mathlib.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.coe_mulRight", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.mulRight_apply", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.mul", "kind": "definition", "module": "Mathlib.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.mul_apply", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.coe_mul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.coe_flip_mul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.map_mul_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.mulLeft_eq_mulRight_iff_forall_commute", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.mulRight_eq_mulLeft_iff_forall_commute", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoid.End.mulLeft", "kind": "definition", "module": "Mathlib.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoid.End.mulRight", "kind": "definition", "module": "Mathlib.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoid.End.mulRight_eq_mulLeft", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instHasDistribNeg", "kind": "instance", "module": "Mathlib.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "vieta_formula_quadratic", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Basic", "is_tactic_proof": true, "tactics": ["have", "refine", "rw"], "tactic_count": 3}
{"name": "succ_ne_self", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pred_ne_self", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLeftRegular_iff_right_eq_zero_of_mul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isRightRegular_iff_left_eq_zero_of_mul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isRegular_iff_eq_zero_of_mul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "noZeroDivisors_tfae", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": ["simp_rw", "isLeftRegular_iff_right_eq_zero_of_mul,", "tfae_have", "tfae_have", "tfae_have", "tfae_finish"], "tactic_count": 6}
{"name": "isCancelMulZero_iff_noZeroDivisors", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NoZeroDivisors.to_isCancelMulZero", "kind": "instance", "module": "Mathlib.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NoZeroDivisors.to_isDomain", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDomain.to_noZeroDivisors", "kind": "instance", "module": "Mathlib.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsingleton.to_isCancelMulZero", "kind": "instance", "module": "Mathlib.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsingleton.to_noZeroDivisors", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isDomain_iff_cancelMulZero_and_nontrivial", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCancelMulZero_iff_isDomain_or_subsingleton", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "isDomain_iff_noZeroDivisors_and_nontrivial", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "noZeroDivisors_iff_isDomain_or_subsingleton", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "one_div_neg_one_eq_neg_one", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_div_neg_eq_neg_one_div", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "div_neg_eq_neg_div", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "neg_div", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "neg_div'", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "neg_div_neg_eq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "neg_inv", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "div_neg", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "div_neg_eq_neg_div'", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_neg", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "inv_neg_one", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "BooleanRing.mul_self", "kind": "theorem", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanRing.instIdempotentOpHMul", "kind": "instance", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanRing.add_self", "kind": "theorem", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": ["have", "calc", "a", "rwa"], "tactic_count": 4}
{"name": "BooleanRing.neg_eq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanRing.add_eq_zero'", "kind": "theorem", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanRing.mul_add_mul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": ["have", "calc", "a", "rwa"], "tactic_count": 4}
{"name": "BooleanRing.sub_eq_add", "kind": "theorem", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "BooleanRing.mul_one_add_self", "kind": "theorem", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "BooleanRing.toCommRing", "kind": "instance", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instBooleanRingPUnit", "kind": "instance", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AsBoolAlg", "kind": "definition", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toBoolAlg", "kind": "definition", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofBoolAlg", "kind": "definition", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toBoolAlg_symm_eq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofBoolAlg_symm_eq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toBoolAlg_ofBoolAlg", "kind": "theorem", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofBoolAlg_toBoolAlg", "kind": "theorem", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toBoolAlg_inj", "kind": "theorem", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofBoolAlg_inj", "kind": "theorem", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInhabitedAsBoolAlg", "kind": "instance", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanRing.sup", "kind": "definition", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanRing.inf", "kind": "definition", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanRing.sup_comm", "kind": "theorem", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": true, "tactics": ["dsimp", "ring"], "tactic_count": 2}
{"name": "BooleanRing.inf_comm", "kind": "theorem", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": true, "tactics": ["dsimp", "ring"], "tactic_count": 2}
{"name": "BooleanRing.sup_assoc", "kind": "theorem", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": true, "tactics": ["dsimp", "ring"], "tactic_count": 2}
{"name": "BooleanRing.inf_assoc", "kind": "theorem", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": true, "tactics": ["dsimp", "ring"], "tactic_count": 2}
{"name": "BooleanRing.sup_inf_self", "kind": "theorem", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "BooleanRing.inf_sup_self", "kind": "theorem", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "BooleanRing.le_sup_inf_aux", "kind": "theorem", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanRing.le_sup_inf", "kind": "theorem", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "BooleanRing.toBooleanAlgebra", "kind": "definition", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instBooleanAlgebraAsBoolAlg", "kind": "instance", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofBoolAlg_top", "kind": "theorem", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofBoolAlg_bot", "kind": "theorem", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofBoolAlg_sup", "kind": "theorem", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofBoolAlg_inf", "kind": "theorem", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofBoolAlg_compl", "kind": "theorem", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofBoolAlg_sdiff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Ring.BooleanRing.0.of_boolalg_symmDiff_aux", "kind": "theorem", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofBoolAlg_symmDiff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ofBoolAlg_mul_ofBoolAlg_eq_left_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toBoolAlg_zero", "kind": "theorem", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toBoolAlg_one", "kind": "theorem", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toBoolAlg_mul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toBoolAlg_add_add_mul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toBoolAlg_add", "kind": "theorem", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.asBoolAlg", "kind": "definition", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.asBoolAlg_id", "kind": "theorem", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.asBoolAlg_comp", "kind": "theorem", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AsBoolRing", "kind": "definition", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toBoolRing", "kind": "definition", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofBoolRing", "kind": "definition", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toBoolRing_symm_eq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofBoolRing_symm_eq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toBoolRing_ofBoolRing", "kind": "theorem", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofBoolRing_toBoolRing", "kind": "theorem", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toBoolRing_inj", "kind": "theorem", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofBoolRing_inj", "kind": "theorem", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInhabitedAsBoolRing", "kind": "instance", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GeneralizedBooleanAlgebra.toNonUnitalCommRing", "kind": "abbrev", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instNonUnitalCommRingAsBoolRingOfGeneralizedBooleanAlgebra", "kind": "instance", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanAlgebra.toBooleanRing", "kind": "abbrev", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instBooleanRingAsBoolRing", "kind": "instance", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofBoolRing_zero", "kind": "theorem", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofBoolRing_one", "kind": "theorem", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofBoolRing_neg", "kind": "theorem", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofBoolRing_add", "kind": "theorem", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofBoolRing_sub", "kind": "theorem", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofBoolRing_mul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofBoolRing_le_ofBoolRing_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toBoolRing_bot", "kind": "theorem", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toBoolRing_top", "kind": "theorem", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toBoolRing_inf", "kind": "theorem", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toBoolRing_symmDiff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedLatticeHom.asBoolRing", "kind": "definition", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedLatticeHom.asBoolRing_id", "kind": "theorem", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedLatticeHom.asBoolRing_comp", "kind": "theorem", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.asBoolAlgAsBoolRing", "kind": "definition", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.asBoolRingAsBoolAlg", "kind": "definition", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instZeroBool_mathlib", "kind": "instance", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instOneBool_mathlib", "kind": "instance", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instAddBool_mathlib", "kind": "instance", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instNegBool_mathlib", "kind": "instance", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instSubBool_mathlib", "kind": "instance", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instMulBool_mathlib", "kind": "instance", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instBooleanRingBool", "kind": "instance", "module": "Mathlib.Algebra.Ring.BooleanRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.natCast_mem_center", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ofNat_mem_center", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.intCast_mem_center", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.add_mem_center", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.neg_mem_center", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.add_mem_centralizer", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Centralizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.neg_mem_centralizer", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Centralizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCoeTCCentroidHomOfCentroidHomClass", "kind": "instance", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.instFunLike", "kind": "instance", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.instCentroidHomClass", "kind": "instance", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.toFun_eq_coe", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.ext", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.coe_toAddMonoidHom", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.toAddMonoidHom_eq_coe", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.coe_toAddMonoidHom_injective", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.toEnd", "kind": "definition", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.toEnd_injective", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.copy", "kind": "definition", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.coe_copy", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.copy_eq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.id", "kind": "definition", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.instInhabited", "kind": "instance", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.coe_id", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.toAddMonoidHom_id", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.id_apply", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.comp", "kind": "definition", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.coe_comp", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.comp_apply", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.coe_comp_addMonoidHom", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.comp_assoc", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.comp_id", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.id_comp", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.cancel_right", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.cancel_left", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.instZero", "kind": "instance", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.instOne", "kind": "instance", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.instAdd", "kind": "instance", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.instMul", "kind": "instance", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.instSMul", "kind": "instance", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.instIsScalarTower", "kind": "instance", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.instSMulCommClass", "kind": "instance", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.instIsCentralScalar", "kind": "instance", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.isScalarTowerRight", "kind": "instance", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.hasNPowNat", "kind": "instance", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.coe_zero", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.coe_one", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.coe_add", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.coe_mul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.coe_smul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.zero_apply", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.one_apply", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.add_apply", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.mul_apply", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.smul_apply", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom._example", "kind": "example", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.toEnd_zero", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.toEnd_add", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.toEnd_smul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.instAddCommMonoid", "kind": "instance", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.instNatCast", "kind": "instance", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.coe_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.natCast_apply", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.toEnd_one", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.toEnd_mul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.toEnd_pow", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.toEnd_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.instSemiring", "kind": "instance", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.toEndRingHom", "kind": "definition", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.comp_mul_comm", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": true, "tactics": ["simp", "rw"], "tactic_count": 2}
{"name": "CentroidHom.instDistribMulAction", "kind": "instance", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.instModule", "kind": "instance", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.applyModule", "kind": "instance", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.smul_def", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.instSMulCommClass_1", "kind": "instance", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.instSMulCommClass_2", "kind": "instance", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.instIsScalarTower_1", "kind": "instance", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.toCentroidHom", "kind": "definition", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom._example", "kind": "example", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Ring.CentroidHom.0.CentroidHom.termL", "kind": "definition", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Ring.CentroidHom.0.CentroidHom._aux_Mathlib_Algebra_Ring_CentroidHom___macroRules__private_Mathlib_Algebra_Ring_CentroidHom_0_CentroidHom_termL_1", "kind": "definition", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Ring.CentroidHom.0.CentroidHom._aux_Mathlib_Algebra_Ring_CentroidHom___unexpand_AddMonoid_End_mulLeft_1", "kind": "definition", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Ring.CentroidHom.0.CentroidHom.termR", "kind": "definition", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Ring.CentroidHom.0.CentroidHom._aux_Mathlib_Algebra_Ring_CentroidHom___macroRules__private_Mathlib_Algebra_Ring_CentroidHom_0_CentroidHom_termR_1", "kind": "definition", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Ring.CentroidHom.0.CentroidHom._aux_Mathlib_Algebra_Ring_CentroidHom___unexpand_AddMonoid_End_mulRight_1", "kind": "definition", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.centroid_eq_centralizer_mulLeftRight", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.centerToCentroidCenter", "kind": "definition", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.instFunLikeSubtypeMemSubsemiringCenter", "kind": "instance", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.centerToCentroidCenter_apply", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.centerToCentroid", "kind": "definition", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.centerToCentroid_apply", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalNonAssocSemiring.mem_center_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Ring.CentroidHom.0.CentroidHom.termL_1", "kind": "definition", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Ring.CentroidHom.0.CentroidHom._aux_Mathlib_Algebra_Ring_CentroidHom___macroRules__private_Mathlib_Algebra_Ring_CentroidHom_0_CentroidHom_termL_1_1", "kind": "definition", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Ring.CentroidHom.0.CentroidHom._aux_Mathlib_Algebra_Ring_CentroidHom___unexpand_AddMonoid_End_mulLeft_2", "kind": "definition", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalNonAssocCommSemiring.mem_center_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": ["rw", "aesop"], "tactic_count": 2}
{"name": "CentroidHom.centerIsoCentroid", "kind": "definition", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.instNeg", "kind": "instance", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.instSub", "kind": "instance", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.instIntCast", "kind": "instance", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.coe_intCast", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.intCast_apply", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.toEnd_neg", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.toEnd_sub", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.instAddCommGroup", "kind": "instance", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.coe_neg", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.coe_sub", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.neg_apply", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.sub_apply", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.toEnd_intCast", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.instRing", "kind": "instance", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.commRing", "kind": "abbrev", "module": "Mathlib.Algebra.Ring.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.castEmbedding", "kind": "definition", "module": "Mathlib.Algebra.Ring.CharZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CharZero.NeZero.two", "kind": "instance", "module": "Mathlib.Algebra.Ring.CharZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.support_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CharZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.mulSupport_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CharZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.charZero", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CharZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.charZero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CharZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.injective_nat", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CharZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "add_self_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CharZero", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.cast_pow_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CharZero", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsAddTorsionFree.of_isCancelMulZero_charZero", "kind": "instance", "module": "Mathlib.Algebra.Ring.CharZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CharZero.neg_eq_self_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CharZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CharZero.eq_neg_self_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CharZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nat_mul_inj", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CharZero", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "nat_mul_inj'", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CharZero", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "units_ne_neg_self", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CharZero", "is_tactic_proof": true, "tactics": ["simp_rw", "not_false_iff]"], "tactic_count": 2}
{"name": "neg_units_ne_self", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CharZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.add_right", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Commute", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.add_left", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Commute", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.mul_self_sub_mul_self_eq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Commute", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Commute.mul_self_sub_mul_self_eq'", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Commute", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Commute.mul_self_eq_mul_self_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Commute", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Commute.neg_right", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Commute", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.neg_right_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Commute", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.neg_left", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Commute", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.neg_left_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Commute", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.neg_one_right", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Commute", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.neg_one_left", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Commute", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.sub_right", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Commute", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.sub_left", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Commute", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.add_sq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Commute", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Commute.sq_sub_sq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Commute", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Commute.sub_sq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Commute", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Commute.sq_eq_sq_iff_eq_or_eq_neg", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Commute", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "neg_one_pow_eq_or", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Commute", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "neg_pow", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Commute", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "neg_pow'", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Commute", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "neg_sq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Commute", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "neg_one_sq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Commute", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "neg_one_pow_mul_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Commute", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "mul_neg_one_pow_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Commute", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "neg_one_pow_eq_pow_mod_two", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Commute", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "sq_eq_one_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Commute", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "sq_ne_one_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Commute", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_self_sub_mul_self", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Commute", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_self_sub_one", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Commute", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mul_self_eq_mul_self_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Commute", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_self_eq_one_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Commute", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "sq_sub_sq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Commute", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sub_sq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Commute", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "sub_sq'", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Commute", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "sub_sq_comm", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Commute", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "sq_eq_sq_iff_eq_or_eq_neg", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Commute", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_or_eq_neg_of_sq_eq_sq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Commute", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.sq_eq_sq_iff_eq_or_eq_neg", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Commute", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Units.eq_or_eq_neg_of_sq_eq_sq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Commute", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.inv_eq_self_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Commute", "is_tactic_proof": true, "tactics": ["rw", "simp", "push_cast", "exact"], "tactic_count": 4}
{"name": "Ring.instBracket", "kind": "instance", "module": "Mathlib.Algebra.Ring.Commute", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ring.lie_def", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Commute", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "commute_iff_lie_eq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Commute", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.lie_eq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Commute", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instRingHomIdId", "kind": "instance", "module": "Mathlib.Algebra.Ring.CompTypeclasses", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHomCompTriple.comp_apply", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CompTypeclasses", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHomInvPair.comp_apply_eq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CompTypeclasses", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "RingHomInvPair.comp_apply_eq₂", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CompTypeclasses", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "RingHomInvPair.ids", "kind": "instance", "module": "Mathlib.Algebra.Ring.CompTypeclasses", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHomInvPair.triples", "kind": "instance", "module": "Mathlib.Algebra.Ring.CompTypeclasses", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHomInvPair.triples₂", "kind": "instance", "module": "Mathlib.Algebra.Ring.CompTypeclasses", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHomInvPair.of_ringEquiv", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CompTypeclasses", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHomInvPair.symm", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CompTypeclasses", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHomCompTriple.ids", "kind": "instance", "module": "Mathlib.Algebra.Ring.CompTypeclasses", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHomCompTriple.right_ids", "kind": "instance", "module": "Mathlib.Algebra.Ring.CompTypeclasses", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.surjective", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CompTypeclasses", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHomSurjective.invPair", "kind": "instance", "module": "Mathlib.Algebra.Ring.CompTypeclasses", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHomSurjective.ids", "kind": "instance", "module": "Mathlib.Algebra.Ring.CompTypeclasses", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHomSurjective.comp", "kind": "theorem", "module": "Mathlib.Algebra.Ring.CompTypeclasses", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHomSurjective.instToRingHomRingEquiv", "kind": "instance", "module": "Mathlib.Algebra.Ring.CompTypeclasses", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Distrib.leftDistribClass", "kind": "instance", "module": "Mathlib.Algebra.Ring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Distrib.rightDistribClass", "kind": "instance", "module": "Mathlib.Algebra.Ring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "left_distrib", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "right_distrib", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "distrib_three_right", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "add_one_mul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mul_add_one", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "one_add_mul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mul_one_add", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "two_mul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_two", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nsmul_eq_mul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Defs", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "ite_zero_mul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "mul_ite_zero", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ite_zero_mul_ite_zero", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "mul_boole", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "boole_mul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NonUnitalCommSemiring.toNonUnitalNonAssocCommSemiring", "kind": "instance", "module": "Mathlib.Algebra.Ring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommSemiring.toNonAssocCommSemiring", "kind": "instance", "module": "Mathlib.Algebra.Ring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommSemiring.toNonUnitalCommSemiring", "kind": "instance", "module": "Mathlib.Algebra.Ring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommSemiring.toCommMonoidWithZero", "kind": "instance", "module": "Mathlib.Algebra.Ring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "add_mul_self_eq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "add_sq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "add_sq'", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "neg_mul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_neg", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "neg_mul_neg", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "neg_mul_eq_neg_mul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "neg_mul_eq_mul_neg", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "neg_mul_comm", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "neg_eq_neg_one_mul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "mul_neg_one", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "neg_one_mul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MulZeroClass.negZeroClass", "kind": "instance", "module": "Mathlib.Algebra.Ring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalNonAssocRing.toHasDistribNeg", "kind": "instance", "module": "Mathlib.Algebra.Ring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_sub_left_distrib", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "mul_sub_right_distrib", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "sub_one_mul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mul_sub_one", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "one_sub_mul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mul_one_sub", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ring.toNonUnitalRing", "kind": "instance", "module": "Mathlib.Algebra.Ring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ring.toNonAssocRing", "kind": "instance", "module": "Mathlib.Algebra.Ring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalCommRing.toNonUnitalCommSemiring", "kind": "instance", "module": "Mathlib.Algebra.Ring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRing.toNonAssocCommRing", "kind": "instance", "module": "Mathlib.Algebra.Ring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRing.toCommSemiring", "kind": "instance", "module": "Mathlib.Algebra.Ring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRing.toNonUnitalCommRing", "kind": "instance", "module": "Mathlib.Algebra.Ring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRing.toAddCommGroupWithOne", "kind": "instance", "module": "Mathlib.Algebra.Ring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "map_dvd_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Divisibility.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "map_dvd_iff_dvd_symm", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Divisibility.Basic", "is_tactic_proof": true, "tactics": ["obtain", "simp"], "tactic_count": 2}
{"name": "MulEquiv.decompositionMonoid", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Divisibility.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.dvd", "kind": "definition", "module": "Mathlib.Algebra.Ring.Divisibility.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.dvd_apply", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Divisibility.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dvd_add", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Divisibility.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "min_pow_dvd_add", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Divisibility.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dvd.dvd.linear_comb", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Divisibility.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dvd_neg", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Divisibility.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "neg_dvd", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Divisibility.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dvd_sub", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Divisibility.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "dvd_add_left", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Divisibility.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dvd_add_right", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Divisibility.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "dvd_sub_left", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Divisibility.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "dvd_sub_right", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Divisibility.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "dvd_iff_dvd_of_dvd_sub", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Divisibility.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "dvd_sub_comm", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Divisibility.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "dvd_add_self_left", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Divisibility.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dvd_add_self_right", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Divisibility.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dvd_sub_self_left", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Divisibility.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dvd_sub_self_right", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Divisibility.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dvd_mul_sub_mul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Divisibility.Basic", "is_tactic_proof": true, "tactics": ["convert", "rw", "simp"], "tactic_count": 3}
{"name": "dvd_smul_of_dvd", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Divisibility.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dvd_nsmul_of_dvd", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Divisibility.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dvd_zsmul_of_dvd", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Divisibility.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.pow_dvd_add_pow_of_pow_eq_zero_right", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Divisibility.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "refine", "replace", "apply", "rcases", "exact", "simp"], "tactic_count": 7}
{"name": "Commute.pow_dvd_add_pow_of_pow_eq_zero_left", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Divisibility.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.pow_dvd_pow_of_sub_pow_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Divisibility.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "apply", "rw"], "tactic_count": 3}
{"name": "Commute.pow_dvd_pow_of_add_pow_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Divisibility.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "apply", "apply", "simpa"], "tactic_count": 4}
{"name": "Commute.pow_dvd_sub_pow_of_pow_eq_zero_right", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Divisibility.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.pow_dvd_sub_pow_of_pow_eq_zero_left", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Divisibility.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "apply", "exact"], "tactic_count": 3}
{"name": "Commute.add_pow_dvd_pow_of_pow_eq_zero_right", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Divisibility.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.add_pow_dvd_pow_of_pow_eq_zero_left", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Divisibility.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dvd_mul_sub_mul_mul_left_of_dvd", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Divisibility.Lemmas", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "refine", "grind"], "tactic_count": 4}
{"name": "dvd_mul_sub_mul_mul_right_of_dvd", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Divisibility.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dvd_mul_sub_mul_mul_gcd_of_dvd", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Divisibility.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "associated_abs_left_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Divisibility.Lemmas", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "associated_abs_right_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Divisibility.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NonUnitalRingHom.inverse", "kind": "definition", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.inverse", "kind": "definition", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "term_≃+*_", "kind": "definition", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Algebra_Ring_Equiv___macroRules_term_≃+*__1", "kind": "definition", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Algebra_Ring_Equiv___unexpand_RingEquiv_1", "kind": "definition", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquivClass.toAddEquivClass", "kind": "instance", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquivClass.toRingHomClass", "kind": "instance", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquivClass.toNonUnitalRingHomClass", "kind": "instance", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquivClass.toRingEquiv", "kind": "definition", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCoeTCRingEquivOfRingEquivClass", "kind": "instance", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.instEquivLike", "kind": "instance", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.instRingEquivClass", "kind": "instance", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.ext", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.congr_arg", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.congr_fun", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.coe_mk", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.mk_coe", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.toEquiv_eq_coe", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.coe_toEquiv", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.toAddEquiv_eq_coe", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.toMulEquiv_eq_coe", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.coe_toMulEquiv", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.coe_toAddEquiv", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.map_mul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.map_add", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.bijective", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.injective", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.surjective", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.refl", "kind": "definition", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.instInhabited", "kind": "instance", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.refl_apply", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.coe_refl", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.coe_addEquiv_refl", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.coe_mulEquiv_refl", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.symm", "kind": "definition", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.invFun_eq_symm", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.symm_symm", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.symm_bijective", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.mk_coe'", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.symm_mk.aux", "kind": "definition", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.symm_mk", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.symm_refl", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.coe_toEquiv_symm", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.coe_toMulEquiv_symm", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.coe_toAddEquiv_symm", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.apply_symm_apply", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.symm_apply_apply", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.image_symm_eq_preimage", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.image_eq_preimage_symm", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.symm_apply_eq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.eq_symm_apply", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.Simps.symm_apply", "kind": "definition", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.trans", "kind": "definition", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.coe_trans", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.trans_apply", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.symm_trans_apply", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.symm_trans", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.coe_mulEquiv_trans", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.coe_addEquiv_trans", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.ofUnique", "kind": "definition", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.instUnique", "kind": "instance", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.op", "kind": "definition", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.unop", "kind": "definition", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.opOp", "kind": "definition", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.toOpposite", "kind": "definition", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.toOpposite_apply", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.toOpposite_symm_apply", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.map_zero", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.map_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.map_ne_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.ofBijective", "kind": "definition", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.coe_ofBijective", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.ofBijective_apply", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.ofBijective_symm_comp", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "RingEquiv.comp_ofBijective_symm", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "RingEquiv.piUnique", "kind": "definition", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.cast", "kind": "definition", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.piCongrRight", "kind": "definition", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.piCongrRight_refl", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.piCongrRight_symm", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.piCongrRight_trans", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.piCongrLeft'", "kind": "definition", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.piCongrLeft'_symm", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RingEquiv.piCongrLeft", "kind": "definition", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.piEquivPiSubtypeProd", "kind": "definition", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.piMulOpposite", "kind": "definition", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.prodCongr", "kind": "definition", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.coe_prodCongr", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.piOptionEquivProd", "kind": "definition", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.map_one", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.map_eq_one_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.map_ne_one_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.coe_monoidHom_refl", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.coe_addMonoidHom_refl", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.coe_ringHom_refl", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.coe_monoidHom_trans", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.coe_addMonoidHom_trans", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.coe_ringHom_trans", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.comp_symm", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.symm_comp", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.map_neg", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.map_sub", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.map_neg_one", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.map_eq_neg_one_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RingEquiv.toNonUnitalRingHom", "kind": "definition", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.toNonUnitalRingHom_injective", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.toNonUnitalRingHom_eq_coe", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.coe_toNonUnitalRingHom", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.coe_nonUnitalRingHom_inj_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.toNonUnitalRingHom_refl", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.toNonUnitalRingHom_apply_symm_toNonUnitalRingHom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.symm_toNonUnitalRingHom_apply_toNonUnitalRingHom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.toNonUnitalRingHom_trans", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.toNonUnitalRingHomm_comp_symm_toNonUnitalRingHom", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "RingEquiv.symm_toNonUnitalRingHom_comp_toNonUnitalRingHom", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "RingEquiv.toRingHom", "kind": "definition", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.toRingHom_injective", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.toRingHom_eq_coe", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.coe_toRingHom", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.coe_ringHom_inj_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.toNonUnitalRingHom_commutes", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.toMonoidHom", "kind": "abbrev", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.toAddMonoidHom", "kind": "abbrev", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.toAddMonoidMom_commutes", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.toMonoidHom_commutes", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.toEquiv_commutes", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.toRingHom_refl", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.toMonoidHom_refl", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.toAddMonoidHom_refl", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.toRingHom_apply_symm_toRingHom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.symm_toRingHom_apply_toRingHom_apply", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.toRingHom_trans", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.toRingHom_comp_symm_toRingHom", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RingEquiv.symm_toRingHom_comp_toRingHom", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RingEquiv.map_pow", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.toRingEquiv", "kind": "definition", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddEquiv.toRingEquiv", "kind": "definition", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.self_trans_symm", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.symm_trans_self", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.ofNonUnitalRingHom", "kind": "definition", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.symm_ofNonUnitalRingHom", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.ofRingHom", "kind": "definition", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.coe_ringHom_ofRingHom", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.ofRingHom_coe_ringHom", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.ofRingHom_symm", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.sumArrowEquivProdArrow", "kind": "definition", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.sumArrowEquivProdArrow_apply", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.sumArrowEquivProdArrow_symm_apply", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.noZeroDivisors", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.isDomain", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.isDomain_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.noZeroDivisors_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.isLeftCancelMulZero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.isRightCancelMulZero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.isCancelMulZero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Ring.Ext.0.termLocal_hAdd[_,_]", "kind": "definition", "module": "Mathlib.Algebra.Ring.Ext", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Ring.Ext.0._aux_Mathlib_Algebra_Ring_Ext___macroRules__private_Mathlib_Algebra_Ring_Ext_0_termLocal_hAdd[_,_]_1", "kind": "definition", "module": "Mathlib.Algebra.Ring.Ext", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Ring.Ext.0.termLocal_hMul[_,_]", "kind": "definition", "module": "Mathlib.Algebra.Ring.Ext", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Ring.Ext.0._aux_Mathlib_Algebra_Ring_Ext___macroRules__private_Mathlib_Algebra_Ring_Ext_0_termLocal_hMul[_,_]_1", "kind": "definition", "module": "Mathlib.Algebra.Ring.Ext", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Distrib.ext", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Ext", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "congr"], "tactic_count": 3}
{"name": "NonUnitalNonAssocSemiring.ext", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Ext", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "congr"], "tactic_count": 3}
{"name": "NonUnitalNonAssocSemiring.toDistrib_injective", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Ext", "is_tactic_proof": true, "tactics": ["intro", "ext", "exact", "exact"], "tactic_count": 4}
{"name": "NonUnitalSemiring.toNonUnitalNonAssocSemiring_injective", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Ext", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "NonUnitalSemiring.ext", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Ext", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidWithOne.ext", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Ext", "is_tactic_proof": true, "tactics": ["have", "have", "have", "have", "induction", "zero", "rewrite", "exact", "succ", "rw", "exact", "rcases", "congr"], "tactic_count": 13}
{"name": "AddCommMonoidWithOne.toAddMonoidWithOne_injective", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Ext", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "AddCommMonoidWithOne.ext", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Ext", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonAssocSemiring.ext", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Ext", "is_tactic_proof": true, "tactics": ["have", "have", "congrArg", "have", "congr", "have", "congrArg", "have", "have", "cases", "congr"], "tactic_count": 11}
{"name": "NonAssocSemiring.toNonUnitalNonAssocSemiring_injective", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Ext", "is_tactic_proof": true, "tactics": ["intro", "ext"], "tactic_count": 2}
{"name": "NonUnitalNonAssocRing.ext", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Ext", "is_tactic_proof": true, "tactics": ["rcases", "congr"], "tactic_count": 2}
{"name": "NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring_injective", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Ext", "is_tactic_proof": true, "tactics": ["intro", "ext", "exact", "exact"], "tactic_count": 4}
{"name": "NonUnitalRing.ext", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Ext", "is_tactic_proof": false, "tactics": ["have", "ext", "assumption", "cases", "congr"], "tactic_count": 5}
{"name": "NonUnitalRing.toNonUnitalSemiring_injective", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Ext", "is_tactic_proof": true, "tactics": ["intro", "ext", "exact", "exact"], "tactic_count": 4}
{"name": "NonUnitalRing.toNonUnitalNonAssocring_injective", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Ext", "is_tactic_proof": true, "tactics": ["intro", "ext"], "tactic_count": 2}
{"name": "AddGroupWithOne.ext", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Ext", "is_tactic_proof": true, "tactics": ["have", "have", "have", "injection", "have", "cases", "ofNat", "negSucc", "rcases", "congr"], "tactic_count": 10}
{"name": "AddCommGroupWithOne.ext", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Ext", "is_tactic_proof": true, "tactics": ["have", "have", "injection", "cases", "congr"], "tactic_count": 5}
{"name": "NonAssocRing.ext", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Ext", "is_tactic_proof": true, "tactics": ["have", "have", "ext", "assumption", "have", "cases", "congr", "solve", "injection", "injection", "injection"], "tactic_count": 11}
{"name": "NonAssocRing.toNonAssocSemiring_injective", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Ext", "is_tactic_proof": true, "tactics": ["intro", "ext", "exact", "exact"], "tactic_count": 4}
{"name": "NonAssocRing.toNonUnitalNonAssocring_injective", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Ext", "is_tactic_proof": true, "tactics": ["intro", "ext"], "tactic_count": 2}
{"name": "Semiring.ext", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Ext", "is_tactic_proof": true, "tactics": ["have", "have", "have", "cases", "congr", "solve", "injection", "injection", "injection"], "tactic_count": 9}
{"name": "Semiring.toNonUnitalSemiring_injective", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Ext", "is_tactic_proof": true, "tactics": ["intro", "ext", "exact", "exact"], "tactic_count": 4}
{"name": "Semiring.toNonAssocSemiring_injective", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Ext", "is_tactic_proof": true, "tactics": ["intro", "ext", "exact", "exact"], "tactic_count": 4}
{"name": "Ring.ext", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Ext", "is_tactic_proof": true, "tactics": ["have", "have", "ext", "assumption", "field", "have", "congrArg", "cases", "congr", "solve", "injection", "injection"], "tactic_count": 12}
{"name": "Ring.toNonUnitalRing_injective", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Ext", "is_tactic_proof": true, "tactics": ["intro", "ext", "exact", "exact"], "tactic_count": 4}
{"name": "Ring.toNonAssocRing_injective", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Ext", "is_tactic_proof": true, "tactics": ["intro", "ext"], "tactic_count": 2}
{"name": "Ring.toSemiring_injective", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Ext", "is_tactic_proof": true, "tactics": ["intro", "ext", "exact", "exact"], "tactic_count": 4}
{"name": "NonUnitalNonAssocCommSemiring.toNonUnitalNonAssocSemiring_injective", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Ext", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "NonUnitalNonAssocCommSemiring.ext", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Ext", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalCommSemiring.toNonUnitalSemiring_injective", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Ext", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "NonUnitalCommSemiring.ext", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Ext", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing_injective", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Ext", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "NonUnitalNonAssocCommRing.ext", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Ext", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalCommRing.toNonUnitalRing_injective", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Ext", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "NonUnitalCommRing.ext", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Ext", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommSemiring.toSemiring_injective", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Ext", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "CommSemiring.ext", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Ext", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRing.toRing_injective", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Ext", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "CommRing.ext", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Ext", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.piFinTwo", "kind": "definition", "module": "Mathlib.Algebra.Ring.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "geom_sum_succ", "kind": "theorem", "module": "Mathlib.Algebra.Ring.GeomSum", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "geom_sum_succ'", "kind": "theorem", "module": "Mathlib.Algebra.Ring.GeomSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "geom_sum_zero", "kind": "theorem", "module": "Mathlib.Algebra.Ring.GeomSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "geom_sum_one", "kind": "theorem", "module": "Mathlib.Algebra.Ring.GeomSum", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "geom_sum_two", "kind": "theorem", "module": "Mathlib.Algebra.Ring.GeomSum", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "zero_geom_sum", "kind": "theorem", "module": "Mathlib.Algebra.Ring.GeomSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_geom_sum", "kind": "theorem", "module": "Mathlib.Algebra.Ring.GeomSum", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "op_geom_sum", "kind": "theorem", "module": "Mathlib.Algebra.Ring.GeomSum", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "op_geom_sum₂", "kind": "theorem", "module": "Mathlib.Algebra.Ring.GeomSum", "is_tactic_proof": true, "tactics": ["rw", "refine", "grind"], "tactic_count": 3}
{"name": "geom_sum₂_with_one", "kind": "theorem", "module": "Mathlib.Algebra.Ring.GeomSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.geom_sum₂_mul_add", "kind": "theorem", "module": "Mathlib.Algebra.Ring.GeomSum", "is_tactic_proof": true, "tactics": ["let", "change", "induction", "zero", "succ", "ih", "have", "dsimp", "rw", "have", "dsimp", "have", "rw", "add_comm", "have", "rw", "rw", "rw", "mul_add"], "tactic_count": 19}
{"name": "geom_sum₂_self", "kind": "theorem", "module": "Mathlib.Algebra.Ring.GeomSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "geom_sum_mul_add", "kind": "theorem", "module": "Mathlib.Algebra.Ring.GeomSum", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "Commute.geom_sum₂_comm", "kind": "theorem", "module": "Mathlib.Algebra.Ring.GeomSum", "is_tactic_proof": true, "tactics": ["cases", "simp", "rw", "refine", "simpa", "h.pow_pow"], "tactic_count": 6}
{"name": "RingHom.map_geom_sum", "kind": "theorem", "module": "Mathlib.Algebra.Ring.GeomSum", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RingHom.map_geom_sum₂", "kind": "theorem", "module": "Mathlib.Algebra.Ring.GeomSum", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "geom_sum₂_mul_add", "kind": "theorem", "module": "Mathlib.Algebra.Ring.GeomSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "geom_sum₂_comm", "kind": "theorem", "module": "Mathlib.Algebra.Ring.GeomSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "geom_sum₂_mul_of_ge", "kind": "theorem", "module": "Mathlib.Algebra.Ring.GeomSum", "is_tactic_proof": true, "tactics": ["apply", "simpa"], "tactic_count": 2}
{"name": "geom_sum₂_mul_of_le", "kind": "theorem", "module": "Mathlib.Algebra.Ring.GeomSum", "is_tactic_proof": true, "tactics": ["rw", "convert", "simp_all", "rw", "congr", "lia"], "tactic_count": 6}
{"name": "geom_sum_mul_of_one_le", "kind": "theorem", "module": "Mathlib.Algebra.Ring.GeomSum", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "geom_sum_mul_of_le_one", "kind": "theorem", "module": "Mathlib.Algebra.Ring.GeomSum", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "neg_one_geom_sum", "kind": "theorem", "module": "Mathlib.Algebra.Ring.GeomSum", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "simp", "split_ifs", "rw", "rw"], "tactic_count": 7}
{"name": "Commute.geom_sum₂_mul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.GeomSum", "is_tactic_proof": true, "tactics": ["have", "rw", "rw"], "tactic_count": 3}
{"name": "Commute.mul_neg_geom_sum₂", "kind": "theorem", "module": "Mathlib.Algebra.Ring.GeomSum", "is_tactic_proof": true, "tactics": ["apply", "simp", "simp"], "tactic_count": 3}
{"name": "Commute.mul_geom_sum₂", "kind": "theorem", "module": "Mathlib.Algebra.Ring.GeomSum", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Commute.sub_dvd_pow_sub_pow", "kind": "theorem", "module": "Mathlib.Algebra.Ring.GeomSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_sub_dvd_one_sub_pow", "kind": "theorem", "module": "Mathlib.Algebra.Ring.GeomSum", "is_tactic_proof": true, "tactics": ["conv_rhs", "exact"], "tactic_count": 2}
{"name": "sub_one_dvd_pow_sub_one", "kind": "theorem", "module": "Mathlib.Algebra.Ring.GeomSum", "is_tactic_proof": true, "tactics": ["conv_rhs", "exact"], "tactic_count": 2}
{"name": "pow_one_sub_dvd_pow_mul_sub_one", "kind": "theorem", "module": "Mathlib.Algebra.Ring.GeomSum", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "dvd_pow_sub_one_of_dvd", "kind": "theorem", "module": "Mathlib.Algebra.Ring.GeomSum", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "dvd_pow_pow_sub_self_of_dvd", "kind": "theorem", "module": "Mathlib.Algebra.Ring.GeomSum", "is_tactic_proof": true, "tactics": ["by_cases", "by_cases", "rw", "exact", "have", "rw", "have", "rw", "refine", "rw", "exact"], "tactic_count": 11}
{"name": "geom_sum_mul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.GeomSum", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "mul_geom_sum", "kind": "theorem", "module": "Mathlib.Algebra.Ring.GeomSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "geom_sum_mul_neg", "kind": "theorem", "module": "Mathlib.Algebra.Ring.GeomSum", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "mul_neg_geom_sum", "kind": "theorem", "module": "Mathlib.Algebra.Ring.GeomSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.mul_geom_sum₂_Ico", "kind": "theorem", "module": "Mathlib.Algebra.Ring.GeomSum", "is_tactic_proof": true, "tactics": ["rw", "have", "refine", "rw", "congr", "rw", "lia", "rw", "simp_rw", "simp_rw", "rw", "sub_sub_sub_cancel_right"], "tactic_count": 12}
{"name": "Commute.geom_sum₂_succ_eq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.GeomSum", "is_tactic_proof": false, "tactics": ["simp_rw", "refine", "suffices", "rw", "lia"], "tactic_count": 5}
{"name": "Commute.geom_sum₂_Ico_mul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.GeomSum", "is_tactic_proof": true, "tactics": ["apply", "simp", "have", "refine", "have", "simpa", "simp", "convert"], "tactic_count": 8}
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{"name": "geom_sum_Ico_mul_neg", "kind": "theorem", "module": "Mathlib.Algebra.Ring.GeomSum", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "pow_sub_one_mul_geom_sum_eq_pow_sub_one_mul_geom_sum", "kind": "theorem", "module": "Mathlib.Algebra.Ring.GeomSum", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
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{"name": "sub_dvd_pow_sub_pow", "kind": "theorem", "module": "Mathlib.Algebra.Ring.GeomSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Odd.add_dvd_pow_add_pow", "kind": "theorem", "module": "Mathlib.Algebra.Ring.GeomSum", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "geom_sum₂_succ_eq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.GeomSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_geom_sum₂_Ico", "kind": "theorem", "module": "Mathlib.Algebra.Ring.GeomSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.sub_dvd_pow_sub_pow", "kind": "theorem", "module": "Mathlib.Algebra.Ring.GeomSum", "is_tactic_proof": true, "tactics": ["rcases", "have", "exact", "have", "exact"], "tactic_count": 5}
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{"name": "Nat.pow_sub_pow_dvd_pow_sub_pow", "kind": "theorem", "module": "Mathlib.Algebra.Ring.GeomSum", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
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{"name": "Odd.nat_add_dvd_pow_add_pow", "kind": "theorem", "module": "Mathlib.Algebra.Ring.GeomSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.geomSum_eq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.GeomSum", "is_tactic_proof": true, "tactics": ["refine", "simpa"], "tactic_count": 2}
{"name": "Semiring.toGrindSemiring", "kind": "instance", "module": "Mathlib.Algebra.Ring.GrindInstances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommSemiring.toGrindCommSemiring", "kind": "instance", "module": "Mathlib.Algebra.Ring.GrindInstances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ring.toGrindRing", "kind": "instance", "module": "Mathlib.Algebra.Ring.GrindInstances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRing.toGrindCommRing", "kind": "instance", "module": "Mathlib.Algebra.Ring.GrindInstances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Semiring.toGrindSemiring_ofNat", "kind": "theorem", "module": "Mathlib.Algebra.Ring.GrindInstances", "is_tactic_proof": true, "tactics": ["n"], "tactic_count": 1}
{"name": "_example", "kind": "example", "module": "Mathlib.Algebra.Ring.GrindInstances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_example", "kind": "example", "module": "Mathlib.Algebra.Ring.GrindInstances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_example", "kind": "example", "module": "Mathlib.Algebra.Ring.GrindInstances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "term_→ₙ+*_", "kind": "definition", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Algebra_Ring_Hom_Defs___macroRules_term_→ₙ+*__1", "kind": "definition", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Algebra_Ring_Hom_Defs___unexpand_NonUnitalRingHom_1", "kind": "definition", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHomClass.toNonUnitalRingHom", "kind": "definition", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCoeTCNonUnitalRingHom", "kind": "instance", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.instFunLike", "kind": "instance", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.instNonUnitalRingHomClass", "kind": "instance", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.coe_toMulHom", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.coe_mulHom_mk", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.coe_toAddMonoidHom", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.coe_addMonoidHom_mk", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.copy", "kind": "definition", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.coe_copy", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.copy_eq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.ext", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.mk_coe", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.coe_addMonoidHom_injective", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.coe_mulHom_injective", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.id", "kind": "definition", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.instZero", "kind": "instance", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.instInhabited", "kind": "instance", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.coe_zero", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.zero_apply", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.id_apply", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.coe_addMonoidHom_id", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.coe_mulHom_id", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.comp", "kind": "definition", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.comp_assoc", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.coe_comp", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.comp_apply", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.coe_comp_addMonoidHom", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.coe_comp_mulHom", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.comp_zero", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "NonUnitalRingHom.zero_comp", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "NonUnitalRingHom.comp_id", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.id_comp", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.instMonoidWithZero", "kind": "instance", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.one_def", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.coe_one", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.mul_def", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.coe_mul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.cancel_right", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.cancel_left", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "term_→+*_", "kind": "definition", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Algebra_Ring_Hom_Defs___macroRules_term_→+*__1", "kind": "definition", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Algebra_Ring_Hom_Defs___unexpand_RingHom_1", "kind": "definition", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHomClass.toRingHom", "kind": "definition", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCoeTCRingHom", "kind": "instance", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHomClass.toNonUnitalRingHomClass", "kind": "instance", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.instFunLike", "kind": "instance", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.instRingHomClass", "kind": "instance", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.toFun_eq_coe", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.coe_mk", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.coe_coe", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.coeToMonoidHom", "kind": "instance", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.toMonoidHom_eq_coe", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.toMonoidWithZeroHom_eq_coe", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "RingHom.coe_monoidHom_mk", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.toAddMonoidHom_eq_coe", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.coe_addMonoidHom_mk", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.copy", "kind": "definition", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.coe_copy", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.copy_eq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.congr_fun", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.congr_arg", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.coe_inj", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.ext", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.mk_coe", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.coe_addMonoidHom_injective", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.coe_monoidHom_injective", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.map_zero", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.map_one", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.map_add", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.map_mul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.codomain_trivial_iff_map_one_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RingHom.codomain_trivial_iff_range_trivial", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.map_one_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.domain_nontrivial", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.codomain_trivial", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.map_neg", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.map_sub", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.mk'", "kind": "definition", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.id", "kind": "definition", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.instInhabited", "kind": "instance", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.coe_id", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.id_apply", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.coe_addMonoidHom_id", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.coe_monoidHom_id", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.comp", "kind": "definition", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.comp_assoc", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.coe_comp", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.comp_apply", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.comp_id", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.id_comp", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.instOne", "kind": "instance", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.instMul", "kind": "instance", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.one_def", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.mul_def", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.coe_one", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.coe_mul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.instMonoid", "kind": "instance", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.coe_pow", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.cancel_right", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.cancel_left", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.map_pow", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.mkRingHomOfMulSelfOfTwoNeZero", "kind": "definition", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.coe_fn_mkRingHomOfMulSelfOfTwoNeZero", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.coe_addMonoidHom_mkRingHomOfMulSelfOfTwoNeZero", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.Defs", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "Function.Injective.isDomain", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Hom.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIdempotentElem.one_sub", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Idempotent", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsIdempotentElem.one_sub_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Idempotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIdempotentElem.mul_one_sub_self", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Idempotent", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsIdempotentElem.one_sub_mul_self", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Idempotent", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "isIdempotentElem_iff_mul_one_sub_self", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Idempotent", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "isIdempotentElem_iff_one_sub_mul_self", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Idempotent", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsIdempotentElem.instComplSubtype", "kind": "instance", "module": "Mathlib.Algebra.Ring.Idempotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIdempotentElem.coe_compl", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Idempotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIdempotentElem.compl_compl", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Idempotent", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "IsIdempotentElem.zero_compl", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Idempotent", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "IsIdempotentElem.one_compl", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Idempotent", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "IsIdempotentElem.of_mul_add", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Idempotent", "is_tactic_proof": true, "tactics": ["simp_rw", "conv_rhs", "conv_rhs"], "tactic_count": 3}
{"name": "IsIdempotentElem.add_sub_mul_of_commute", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Idempotent", "is_tactic_proof": false, "tactics": ["simp", "hb.mul_self_mul,", "rw"], "tactic_count": 3}
{"name": "IsIdempotentElem.add_sub_mul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Idempotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIdempotentElem.add", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Idempotent", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "IsIdempotentElem.add_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Idempotent", "is_tactic_proof": true, "tactics": ["refine", "rw", "simpa"], "tactic_count": 3}
{"name": "IsIdempotentElem.sub", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Idempotent", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "IsIdempotentElem.mul_eq_zero_of_anticommute", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Idempotent", "is_tactic_proof": false, "tactics": ["have", "rw", "have", "simp_rw", "exact", "suffices", "rw"], "tactic_count": 7}
{"name": "IsIdempotentElem.commute_of_anticommute", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Idempotent", "is_tactic_proof": true, "tactics": ["have", "rw", "rw"], "tactic_count": 3}
{"name": "IsIdempotentElem.sub_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Idempotent", "is_tactic_proof": true, "tactics": ["refine", "have", "have", "simp_rw", "have", "have", "simp_rw", "simp_rw", "exact", "rw", "convert", "simp"], "tactic_count": 12}
{"name": "sq_add_sq_mul_sq_add_sq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Identities", "is_tactic_proof": true, "tactics": ["ring"], "tactic_count": 1}
{"name": "sq_add_mul_sq_mul_sq_add_mul_sq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Identities", "is_tactic_proof": true, "tactics": ["ring"], "tactic_count": 1}
{"name": "pow_four_add_four_mul_pow_four", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Identities", "is_tactic_proof": true, "tactics": ["ring"], "tactic_count": 1}
{"name": "pow_four_add_four_mul_pow_four'", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Identities", "is_tactic_proof": true, "tactics": ["ring"], "tactic_count": 1}
{"name": "sum_four_sq_mul_sum_four_sq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Identities", "is_tactic_proof": true, "tactics": ["ring"], "tactic_count": 1}
{"name": "sum_eight_sq_mul_sum_eight_sq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Identities", "is_tactic_proof": true, "tactics": ["ring"], "tactic_count": 1}
{"name": "Function.Injective.leftDistribClass", "kind": "theorem", "module": "Mathlib.Algebra.Ring.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.rightDistribClass", "kind": "theorem", "module": "Mathlib.Algebra.Ring.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.distrib", "kind": "abbrev", "module": "Mathlib.Algebra.Ring.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.hasDistribNeg", "kind": "abbrev", "module": "Mathlib.Algebra.Ring.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.addMonoidWithOne", "kind": "abbrev", "module": "Mathlib.Algebra.Ring.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.addCommMonoidWithOne", "kind": "abbrev", "module": "Mathlib.Algebra.Ring.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.addGroupWithOne", "kind": "abbrev", "module": "Mathlib.Algebra.Ring.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.addCommGroupWithOne", "kind": "abbrev", "module": "Mathlib.Algebra.Ring.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.nonUnitalNonAssocSemiring", "kind": "abbrev", "module": "Mathlib.Algebra.Ring.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.nonUnitalSemiring", "kind": "abbrev", "module": "Mathlib.Algebra.Ring.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.nonAssocSemiring", "kind": "abbrev", "module": "Mathlib.Algebra.Ring.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.semiring", "kind": "abbrev", "module": "Mathlib.Algebra.Ring.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.nonUnitalNonAssocRing", "kind": "abbrev", "module": "Mathlib.Algebra.Ring.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.nonUnitalRing", "kind": "abbrev", "module": "Mathlib.Algebra.Ring.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.nonAssocRing", "kind": "abbrev", "module": "Mathlib.Algebra.Ring.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.ring", "kind": "abbrev", "module": "Mathlib.Algebra.Ring.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.nonUnitalNonAssocCommSemiring", "kind": "abbrev", "module": "Mathlib.Algebra.Ring.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.nonUnitalCommSemiring", "kind": "abbrev", "module": "Mathlib.Algebra.Ring.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.commSemiring", "kind": "abbrev", "module": "Mathlib.Algebra.Ring.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.nonUnitalNonAssocCommRing", "kind": "abbrev", "module": "Mathlib.Algebra.Ring.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.nonUnitalCommRing", "kind": "abbrev", "module": "Mathlib.Algebra.Ring.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.commRing", "kind": "abbrev", "module": "Mathlib.Algebra.Ring.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.leftDistribClass", "kind": "theorem", "module": "Mathlib.Algebra.Ring.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.rightDistribClass", "kind": "theorem", "module": "Mathlib.Algebra.Ring.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.distrib", "kind": "abbrev", "module": "Mathlib.Algebra.Ring.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.hasDistribNeg", "kind": "abbrev", "module": "Mathlib.Algebra.Ring.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.addMonoidWithOne", "kind": "abbrev", "module": "Mathlib.Algebra.Ring.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.addCommMonoidWithOne", "kind": "abbrev", "module": "Mathlib.Algebra.Ring.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.addGroupWithOne", "kind": "abbrev", "module": "Mathlib.Algebra.Ring.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.addCommGroupWithOne", "kind": "abbrev", "module": "Mathlib.Algebra.Ring.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.nonUnitalNonAssocSemiring", "kind": "abbrev", "module": "Mathlib.Algebra.Ring.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.nonUnitalSemiring", "kind": "abbrev", "module": "Mathlib.Algebra.Ring.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.nonAssocSemiring", "kind": "abbrev", "module": "Mathlib.Algebra.Ring.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.semiring", "kind": "abbrev", "module": "Mathlib.Algebra.Ring.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.nonUnitalNonAssocRing", "kind": "abbrev", "module": "Mathlib.Algebra.Ring.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.nonUnitalRing", "kind": "abbrev", "module": "Mathlib.Algebra.Ring.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.nonAssocRing", "kind": "abbrev", "module": "Mathlib.Algebra.Ring.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.ring", "kind": "abbrev", "module": "Mathlib.Algebra.Ring.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.nonUnitalNonAssocCommSemiring", "kind": "abbrev", "module": "Mathlib.Algebra.Ring.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.nonUnitalCommSemiring", "kind": "abbrev", "module": "Mathlib.Algebra.Ring.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.commSemiring", "kind": "abbrev", "module": "Mathlib.Algebra.Ring.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.nonUnitalNonAssocCommRing", "kind": "abbrev", "module": "Mathlib.Algebra.Ring.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.nonUnitalCommRing", "kind": "abbrev", "module": "Mathlib.Algebra.Ring.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.commRing", "kind": "abbrev", "module": "Mathlib.Algebra.Ring.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddOpposite.instHasDistribNeg", "kind": "instance", "module": "Mathlib.Algebra.Ring.InjSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.instCommRing", "kind": "instance", "module": "Mathlib.Algebra.Ring.Int.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.instIsCancelMulZero", "kind": "instance", "module": "Mathlib.Algebra.Ring.Int.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.instIsDomain", "kind": "instance", "module": "Mathlib.Algebra.Ring.Int.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.instCharZero", "kind": "instance", "module": "Mathlib.Algebra.Ring.Int.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.instMulDivCancelClass", "kind": "instance", "module": "Mathlib.Algebra.Ring.Int.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.cast_mul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Int.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.cast_mul_eq_zsmul_cast", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Int.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.cast_pow", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Int.Defs", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "Int.instCommSemiring", "kind": "instance", "module": "Mathlib.Algebra.Ring.Int.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.instSemiring", "kind": "instance", "module": "Mathlib.Algebra.Ring.Int.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.instRing", "kind": "instance", "module": "Mathlib.Algebra.Ring.Int.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.instDistrib", "kind": "instance", "module": "Mathlib.Algebra.Ring.Int.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.odd_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Int.Parity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.not_odd_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Int.Parity", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Int.not_odd_zero", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Int.Parity", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Int.not_odd_iff_even", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Int.Parity", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Int.not_even_iff_odd", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Int.Parity", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Int.even_or_odd", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Int.Parity", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Int.even_or_odd'", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Int.Parity", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Int.even_xor'_odd", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Int.Parity", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Int.even_xor'_odd'", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Int.Parity", "is_tactic_proof": true, "tactics": ["rcases", "use", "grind"], "tactic_count": 3}
{"name": "Int.instDecidablePredOdd", "kind": "instance", "module": "Mathlib.Algebra.Ring.Int.Parity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.even_add'", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Int.Parity", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Int.not_even_two_mul_add_one", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Int.Parity", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Int.even_sub'", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Int.Parity", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Int.odd_mul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Int.Parity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Int.Odd.of_mul_left", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Int.Parity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.Odd.of_mul_right", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Int.Parity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.odd_pow", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Int.Parity", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Int.odd_pow'", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Int.Parity", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Int.odd_add", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Int.Parity", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Int.odd_add'", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Int.Parity", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Int.ne_of_odd_add", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Int.Parity", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Int.odd_sub", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Int.Parity", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Int.odd_sub'", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Int.Parity", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Int.even_mul_succ_self", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Int.Parity", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Int.even_mul_pred_self", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Int.Parity", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Int.odd_coe_nat", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Int.Parity", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Int.natAbs_even", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Int.Parity", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Int.natAbs_odd", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Int.Parity", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Int.four_dvd_add_or_sub_of_odd", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Int.Parity", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Int.two_dvd_mul_add_one", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Int.Parity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.two_mul_ediv_two_add_one_of_odd", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Int.Parity", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Int.ediv_two_mul_two_add_one_of_odd", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Int.Parity", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Int.add_one_ediv_two_mul_two_of_odd", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Int.Parity", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Int.two_mul_ediv_two_of_odd", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Int.Parity", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Int.even_sign_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Int.Parity", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Int.odd_sign_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Int.Parity", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Int.isSquare_natCast_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Int.Parity", "is_tactic_proof": true, "tactics": ["constructor", "exact", "exact"], "tactic_count": 3}
{"name": "Int.isSquare_ofNat_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Int.Parity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.natCast_pow_pred", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Int.Parity", "is_tactic_proof": true, "tactics": ["have", "norm_cast"], "tactic_count": 2}
{"name": "Int.coe_nat_two_pow_pred", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Int.Parity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.units_eq_one_or", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Int.Units", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Int.units_ne_iff_eq_neg", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Int.Units", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "AddUnits.mulLeft", "kind": "definition", "module": "Mathlib.Algebra.Ring.Invertible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddUnits.mulRight", "kind": "definition", "module": "Mathlib.Algebra.Ring.Invertible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddUnits.neg_mulLeft", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Invertible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddUnits.neg_mulRight", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Invertible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddUnits.neg_mul_eq_mul_neg", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Invertible", "is_tactic_proof": true, "tactics": ["rw", "apply", "simp"], "tactic_count": 3}
{"name": "AddUnits.neg_mul_neg", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Invertible", "is_tactic_proof": true, "tactics": ["rw", "apply", "simp"], "tactic_count": 3}
{"name": "IsAddUnit.mul_left", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Invertible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAddUnit.mul_right", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Invertible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "invertibleNeg", "kind": "definition", "module": "Mathlib.Algebra.Ring.Invertible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "invOf_neg", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Invertible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_sub_invOf_two", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Invertible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "invOf_two_add_invOf_two", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Invertible", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "pos_of_invertible_cast", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Invertible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "invOf_add_invOf", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Invertible", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "invOf_sub_invOf", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Invertible", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "neg_add_eq_mul_invOf_mul_same_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Invertible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "neg_one_eq_invOf_mul_add_invOf_mul_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Invertible", "is_tactic_proof": true, "tactics": ["calc"], "tactic_count": 1}
{"name": "eq_of_invOf_add_eq_invOf_add_invOf", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Invertible", "is_tactic_proof": true, "tactics": ["have", "have", "have", "rw", "exact", "rw"], "tactic_count": 6}
{"name": "Ring.inverse_add_inverse", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Invertible", "is_tactic_proof": true, "tactics": ["by_cases", "have", "obtain", "obtain", "simp_rw", "have", "simp"], "tactic_count": 7}
{"name": "Ring.inverse_sub_inverse", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Invertible", "is_tactic_proof": true, "tactics": ["by_cases", "have", "obtain", "obtain", "simp_rw", "have", "simp"], "tactic_count": 7}
{"name": "Ring.ofMinimalAxioms", "kind": "abbrev", "module": "Mathlib.Algebra.Ring.MinimalAxioms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRing.ofMinimalAxioms", "kind": "abbrev", "module": "Mathlib.Algebra.Ring.MinimalAxioms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.instAddMonoidWithOne", "kind": "instance", "module": "Mathlib.Algebra.Ring.Nat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.instAddCommMonoidWithOne", "kind": "instance", "module": "Mathlib.Algebra.Ring.Nat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.instDistrib", "kind": "instance", "module": "Mathlib.Algebra.Ring.Nat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.instNonUnitalNonAssocSemiring", "kind": "instance", "module": "Mathlib.Algebra.Ring.Nat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.instNonUnitalSemiring", "kind": "instance", "module": "Mathlib.Algebra.Ring.Nat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.instNonAssocSemiring", "kind": "instance", "module": "Mathlib.Algebra.Ring.Nat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.instSemiring", "kind": "instance", "module": "Mathlib.Algebra.Ring.Nat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.instCommSemiring", "kind": "instance", "module": "Mathlib.Algebra.Ring.Nat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.instCharZero", "kind": "instance", "module": "Mathlib.Algebra.Ring.Nat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.instIsDomain", "kind": "instance", "module": "Mathlib.Algebra.Ring.Nat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.negOnePow", "kind": "definition", "module": "Mathlib.Algebra.Ring.NegOnePow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.negOnePow_def", "kind": "theorem", "module": "Mathlib.Algebra.Ring.NegOnePow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.negOnePow_add", "kind": "theorem", "module": "Mathlib.Algebra.Ring.NegOnePow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.negOnePow_zero", "kind": "theorem", "module": "Mathlib.Algebra.Ring.NegOnePow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.negOnePow_one", "kind": "theorem", "module": "Mathlib.Algebra.Ring.NegOnePow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.negOnePow_succ", "kind": "theorem", "module": "Mathlib.Algebra.Ring.NegOnePow", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.negOnePow_even", "kind": "theorem", "module": "Mathlib.Algebra.Ring.NegOnePow", "is_tactic_proof": true, "tactics": ["obtain", "rw"], "tactic_count": 2}
{"name": "Int.negOnePow_two_mul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.NegOnePow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.negOnePow_odd", "kind": "theorem", "module": "Mathlib.Algebra.Ring.NegOnePow", "is_tactic_proof": true, "tactics": ["obtain", "simp"], "tactic_count": 2}
{"name": "Int.negOnePow_two_mul_add_one", "kind": "theorem", "module": "Mathlib.Algebra.Ring.NegOnePow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.negOnePow_eq_one_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.NegOnePow", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "intro", "simp", "contradiction", "exact"], "tactic_count": 7}
{"name": "Int.negOnePow_eq_neg_one_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.NegOnePow", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "intro", "rw", "contradiction", "exact"], "tactic_count": 7}
{"name": "Int.abs_negOnePow", "kind": "theorem", "module": "Mathlib.Algebra.Ring.NegOnePow", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.negOnePow_neg", "kind": "theorem", "module": "Mathlib.Algebra.Ring.NegOnePow", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "Int.negOnePow_abs", "kind": "theorem", "module": "Mathlib.Algebra.Ring.NegOnePow", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "Int.negOnePow_sub", "kind": "theorem", "module": "Mathlib.Algebra.Ring.NegOnePow", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Int.negOnePow_eq_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.NegOnePow", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "tauto", "rw", "rw", "tauto"], "tactic_count": 6}
{"name": "Int.negOnePow_mul_self", "kind": "theorem", "module": "Mathlib.Algebra.Ring.NegOnePow", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Int.cast_negOnePow_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Ring.NegOnePow", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "Int.coe_negOnePow_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Ring.NegOnePow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLeftRegular.pow_injective", "kind": "theorem", "module": "Mathlib.Algebra.Ring.NonZeroDivisors", "is_tactic_proof": true, "tactics": ["intro", "have", "obtain", "rw", "rw", "obtain", "exact", "exact"], "tactic_count": 8}
{"name": "IsRightRegular.pow_injective", "kind": "theorem", "module": "Mathlib.Algebra.Ring.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMulTorsionFree.pow_right_injective", "kind": "theorem", "module": "Mathlib.Algebra.Ring.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMulTorsionFree.pow_right_inj", "kind": "theorem", "module": "Mathlib.Algebra.Ring.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMulTorsionFree.pow_right_injective₀", "kind": "theorem", "module": "Mathlib.Algebra.Ring.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMulTorsionFree.pow_right_inj₀", "kind": "theorem", "module": "Mathlib.Algebra.Ring.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLeftRegular.isUnit_of_finite", "kind": "theorem", "module": "Mathlib.Algebra.Ring.NonZeroDivisors", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "IsRightRegular.isUnit_of_finite", "kind": "theorem", "module": "Mathlib.Algebra.Ring.NonZeroDivisors", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "isRegular_iff_isUnit_of_finite", "kind": "theorem", "module": "Mathlib.Algebra.Ring.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLeftRegular_iff_mem_nonZeroDivisorsLeft", "kind": "theorem", "module": "Mathlib.Algebra.Ring.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isRightRegular_iff_mem_nonZeroDivisorsRight", "kind": "theorem", "module": "Mathlib.Algebra.Ring.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isRegular_iff_mem_nonZeroDivisors", "kind": "theorem", "module": "Mathlib.Algebra.Ring.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_nonZeroDivisorsLeft_iff_isLeftRegular", "kind": "theorem", "module": "Mathlib.Algebra.Ring.NonZeroDivisors", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "le_nonZeroDivisorsRight_iff_isRightRegular", "kind": "theorem", "module": "Mathlib.Algebra.Ring.NonZeroDivisors", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "le_nonZeroDivisors_iff_isRegular", "kind": "theorem", "module": "Mathlib.Algebra.Ring.NonZeroDivisors", "is_tactic_proof": true, "tactics": ["simp_rw", "le_nonZeroDivisorsRight_iff_isRightRegular,"], "tactic_count": 2}
{"name": "mul_cancel_left_mem_nonZeroDivisorsLeft", "kind": "theorem", "module": "Mathlib.Algebra.Ring.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_cancel_right_mem_nonZeroDivisorsRight", "kind": "theorem", "module": "Mathlib.Algebra.Ring.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_cancel_left_mem_nonZeroDivisors", "kind": "theorem", "module": "Mathlib.Algebra.Ring.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_cancel_left_coe_nonZeroDivisors", "kind": "theorem", "module": "Mathlib.Algebra.Ring.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_cancel_right_mem_nonZeroDivisors", "kind": "theorem", "module": "Mathlib.Algebra.Ring.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_cancel_right_coe_nonZeroDivisors", "kind": "theorem", "module": "Mathlib.Algebra.Ring.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isUnit_iff_mem_nonZeroDivisors_of_finite", "kind": "theorem", "module": "Mathlib.Algebra.Ring.NonZeroDivisors", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "dvd_cancel_left_mem_nonZeroDivisors", "kind": "theorem", "module": "Mathlib.Algebra.Ring.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dvd_cancel_left_coe_nonZeroDivisors", "kind": "theorem", "module": "Mathlib.Algebra.Ring.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dvd_cancel_right_mem_nonZeroDivisors", "kind": "theorem", "module": "Mathlib.Algebra.Ring.NonZeroDivisors", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "dvd_cancel_right_coe_nonZeroDivisors", "kind": "theorem", "module": "Mathlib.Algebra.Ring.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instDistrib", "kind": "instance", "module": "Mathlib.Algebra.Ring.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instNatCast", "kind": "instance", "module": "Mathlib.Algebra.Ring.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instIntCast", "kind": "instance", "module": "Mathlib.Algebra.Ring.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.op_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.op_ofNat", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.op_intCast", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.unop_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.unop_ofNat", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.unop_intCast", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instAddMonoidWithOne", "kind": "instance", "module": "Mathlib.Algebra.Ring.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instAddCommMonoidWithOne", "kind": "instance", "module": "Mathlib.Algebra.Ring.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instAddGroupWithOne", "kind": "instance", "module": "Mathlib.Algebra.Ring.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instAddCommGroupWithOne", "kind": "instance", "module": "Mathlib.Algebra.Ring.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instNonUnitalNonAssocSemiring", "kind": "instance", "module": "Mathlib.Algebra.Ring.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instNonUnitalSemiring", "kind": "instance", "module": "Mathlib.Algebra.Ring.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instNonAssocSemiring", "kind": "instance", "module": "Mathlib.Algebra.Ring.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instSemiring", "kind": "instance", "module": "Mathlib.Algebra.Ring.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instNonUnitalCommSemiring", "kind": "instance", "module": "Mathlib.Algebra.Ring.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instCommSemiring", "kind": "instance", "module": "Mathlib.Algebra.Ring.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instNonUnitalNonAssocRing", "kind": "instance", "module": "Mathlib.Algebra.Ring.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instNonUnitalRing", "kind": "instance", "module": "Mathlib.Algebra.Ring.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instNonAssocRing", "kind": "instance", "module": "Mathlib.Algebra.Ring.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instRing", "kind": "instance", "module": "Mathlib.Algebra.Ring.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instNonUnitalCommRing", "kind": "instance", "module": "Mathlib.Algebra.Ring.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instCommRing", "kind": "instance", "module": "Mathlib.Algebra.Ring.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instIsDomain", "kind": "instance", "module": "Mathlib.Algebra.Ring.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddOpposite.instDistrib", "kind": "instance", "module": "Mathlib.Algebra.Ring.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddOpposite.instAddCommMonoidWithOne", "kind": "instance", "module": "Mathlib.Algebra.Ring.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddOpposite.instAddCommGroupWithOne", "kind": "instance", "module": "Mathlib.Algebra.Ring.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddOpposite.instNonUnitalNonAssocSemiring", "kind": "instance", "module": "Mathlib.Algebra.Ring.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddOpposite.instNonUnitalSemiring", "kind": "instance", "module": "Mathlib.Algebra.Ring.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddOpposite.instNonAssocSemiring", "kind": "instance", "module": "Mathlib.Algebra.Ring.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AddOpposite.instNonUnitalCommSemiring", "kind": "instance", "module": "Mathlib.Algebra.Ring.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddOpposite.instCommSemiring", "kind": "instance", "module": "Mathlib.Algebra.Ring.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddOpposite.instNonUnitalNonAssocRing", "kind": "instance", "module": "Mathlib.Algebra.Ring.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddOpposite.instNonUnitalRing", "kind": "instance", "module": "Mathlib.Algebra.Ring.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddOpposite.instNonAssocRing", "kind": "instance", "module": "Mathlib.Algebra.Ring.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddOpposite.instRing", "kind": "instance", "module": "Mathlib.Algebra.Ring.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddOpposite.instNonUnitalCommRing", "kind": "instance", "module": "Mathlib.Algebra.Ring.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AddOpposite.instIsDomain", "kind": "instance", "module": "Mathlib.Algebra.Ring.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.toOpposite", "kind": "definition", "module": "Mathlib.Algebra.Ring.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.fromOpposite", "kind": "definition", "module": "Mathlib.Algebra.Ring.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.op", "kind": "definition", "module": "Mathlib.Algebra.Ring.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.unop", "kind": "definition", "module": "Mathlib.Algebra.Ring.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.toOpposite", "kind": "definition", "module": "Mathlib.Algebra.Ring.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.fromOpposite", "kind": "definition", "module": "Mathlib.Algebra.Ring.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.op", "kind": "definition", "module": "Mathlib.Algebra.Ring.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.unop", "kind": "definition", "module": "Mathlib.Algebra.Ring.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PUnit.commRing", "kind": "instance", "module": "Mathlib.Algebra.Ring.PUnit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PUnit.instIsCancelMulZero", "kind": "instance", "module": "Mathlib.Algebra.Ring.PUnit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Even.neg_pow", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["rintro", "simp_rw"], "tactic_count": 2}
{"name": "Even.neg_one_pow", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsSquare.zero", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "even_two", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Even.mul_left", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["rcases", "use", "rw"], "tactic_count": 3}
{"name": "Even.mul_right", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["rcases", "use", "rw"], "tactic_count": 3}
{"name": "even_iff_exists_two_mul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "even_iff_two_dvd", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Even.trans_dvd", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dvd.dvd.even", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "range_two_mul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "even_two_mul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Even.pow_of_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Odd", "kind": "definition", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "odd_iff_exists_bit1", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "range_two_mul_add_one", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Even.add_odd", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "Even.odd_add", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Odd.add_even", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Odd.add_odd", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["rintro", "refine", "rw", "ac_rfl"], "tactic_count": 4}
{"name": "odd_one", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Even.add_one", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Even.one_add", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Odd.add_one", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Odd.one_add", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "odd_two_mul_add_one", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "odd_add_self_one'", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "odd_add_one_self", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "odd_add_one_self'", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Odd.map", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "Odd.natCast", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Odd.mul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["rintro", "refine", "rw"], "tactic_count": 3}
{"name": "Odd.pow", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Odd.pow_add_pow_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["obtain", "induction", "zero", "succ", "have", "add_right_cancel", "calc", "a", "refine", "calc"], "tactic_count": 10}
{"name": "Even.of_isUnit_two", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isUnit_two_iff_forall_even", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["refine", "obtain", "rw", "exact"], "tactic_count": 4}
{"name": "Odd.of_isUnit_two", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Odd.neg_pow", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "Odd.neg_one_pow", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "even_neg_two", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Odd.neg", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["obtain", "use", "rw"], "tactic_count": 3}
{"name": "odd_neg", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "odd_neg_one", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Odd.sub_even", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Even.sub_odd", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Odd.sub_odd", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "even_add_one", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "even_sub_one", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "even_add_two", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "even_sub_two", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "odd_add_one", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "odd_sub_one", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "odd_add_two", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "odd_sub_two", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.odd_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.instDecidablePredOdd", "kind": "instance", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.not_odd_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Nat.not_odd_iff_even", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Nat.not_even_iff_odd", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Nat.not_odd_zero", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Odd.not_two_dvd_nat", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Nat.even_xor_odd", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Nat.even_or_odd", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.even_or_odd'", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Nat.even_xor_odd'", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["obtain", "use", "grind"], "tactic_count": 3}
{"name": "Nat.odd_add_one", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Nat.mod_two_add_add_odd_mod_two", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Nat.mod_two_add_succ_mod_two", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["lia"], "tactic_count": 1}
{"name": "Nat.succ_mod_two_add_mod_two", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["lia"], "tactic_count": 1}
{"name": "Nat.even_add'", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Nat.not_even_bit1", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.not_even_two_mul_add_one", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Nat.even_sub'", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Nat.Odd.sub_odd", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Nat.odd_mul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Nat.Odd.of_mul_left", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Odd.of_mul_right", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.odd_pow_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Nat.even_div", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.odd_add", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Nat.odd_add'", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Nat.ne_of_odd_add", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Nat.odd_sub", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Nat.Odd.sub_even", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Nat.odd_sub'", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Nat.Even.sub_odd", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Nat.two_mul_div_two_add_one_of_odd", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Nat.div_two_mul_two_add_one_of_odd", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Nat.one_add_div_two_mul_two_of_odd", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Nat.two_dvd_mul_add_one", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.two_dvd_mul_sub_one", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["rcases", "simpa"], "tactic_count": 2}
{"name": "Nat._example", "kind": "example", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat._example", "kind": "example", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "Function.Involutive.iterate_two_mul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Function.Involutive.iterate_two_mul_add_one", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Function.Involutive.iterate_even", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["obtain", "rw"], "tactic_count": 2}
{"name": "Function.Involutive.iterate_odd", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["obtain", "rw"], "tactic_count": 2}
{"name": "Function.Involutive.iterate_eq_self", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Involutive.iterate_eq_id", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "neg_one_pow_eq_ite", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["cases", "inl", "inr"], "tactic_count": 3}
{"name": "neg_one_pow_congr", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "neg_one_pow_eq_one_iff_even", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "neg_one_pow_eq_neg_one_iff_odd", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Even.neg_zpow", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "Even.neg_one_zpow", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "neg_one_zpow_eq_ite", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["obtain", "aesop"], "tactic_count": 2}
{"name": "_private.Mathlib.Algebra.Ring.Parity.0.natCast_eq_zero_or_one_of_two_eq_zero'", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["induction", "zero", "one", "more"], "tactic_count": 4}
{"name": "natCast_eq_zero_of_even_of_two_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "natCast_eq_one_of_odd_of_two_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "natCast_eq_zero_or_one_of_two_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Parity", "is_tactic_proof": true, "tactics": ["obtain", "exact", "exact"], "tactic_count": 3}
{"name": "Function.Periodic", "kind": "definition", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Periodic.funext", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Periodic.comp", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": true, "tactics": ["simp_all"], "tactic_count": 1}
{"name": "Function.Periodic.comp_addHom", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Periodic.mul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": true, "tactics": ["simp_all"], "tactic_count": 1}
{"name": "Function.Periodic.div", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": true, "tactics": ["simp_all"], "tactic_count": 1}
{"name": "List.periodic_prod", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "rw", "simpa"], "tactic_count": 5}
{"name": "Multiset.periodic_prod", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.periodic_prod", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Periodic.smul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": true, "tactics": ["simp_all"], "tactic_count": 1}
{"name": "Function.Periodic.const_smul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Periodic.const_inv_smul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Function.Periodic.add_period", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": true, "tactics": ["simp_all"], "tactic_count": 1}
{"name": "Function.Periodic.sub_eq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Function.Periodic.sub_eq'", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Function.Periodic.neg", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Function.Periodic.sub_period", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Periodic.const_add", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Periodic.add_const", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Periodic.const_sub", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Periodic.sub_const", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Function.Periodic.nsmul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "Function.Periodic.nat_mul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Function.Periodic.neg_nsmul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Periodic.neg_nat_mul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Periodic.sub_nsmul_eq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Function.Periodic.sub_nat_mul_eq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Function.Periodic.nsmul_sub_eq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Periodic.nat_mul_sub_eq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Function.Periodic.zsmul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": true, "tactics": ["rcases", "simpa", "simpa"], "tactic_count": 3}
{"name": "Function.Periodic.int_mul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Function.Periodic.sub_zsmul_eq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Periodic.sub_int_mul_eq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Periodic.zsmul_sub_eq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Periodic.int_mul_sub_eq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Periodic.eq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Function.Periodic.neg_eq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Periodic.nsmul_eq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Periodic.nat_mul_eq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Periodic.zsmul_eq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Periodic.int_mul_eq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.periodic_with_period_zero", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.periodic_iterate_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": true, "tactics": ["refine", "simp"], "tactic_count": 2}
{"name": "Function.Periodic.map_vadd_zmultiples", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": true, "tactics": ["rcases", "simp"], "tactic_count": 2}
{"name": "Function.Periodic.map_vadd_multiples", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": true, "tactics": ["rcases", "simp"], "tactic_count": 2}
{"name": "Function.Periodic.lift", "kind": "definition", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Periodic.lift_coe", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Periodic.not_injective", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Antiperiodic", "kind": "definition", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Antiperiodic.funext", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Antiperiodic.funext'", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Antiperiodic.periodic", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Function.Antiperiodic.periodic_two_mul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Antiperiodic.eq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Function.Antiperiodic.even_nsmul_periodic", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Antiperiodic.nat_even_mul_periodic", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Antiperiodic.odd_nsmul_antiperiodic", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Antiperiodic.nat_odd_mul_antiperiodic", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Antiperiodic.even_zsmul_periodic", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Function.Antiperiodic.int_even_mul_periodic", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Antiperiodic.odd_zsmul_antiperiodic", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": true, "tactics": ["intro", "rw"], "tactic_count": 2}
{"name": "Function.Antiperiodic.int_odd_mul_antiperiodic", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Antiperiodic.sub_eq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Function.Antiperiodic.sub_eq'", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Function.Antiperiodic.neg", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Function.Antiperiodic.neg_eq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Function.Antiperiodic.nat_mul_eq_of_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Antiperiodic.int_mul_eq_of_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Antiperiodic.add_zsmul_eq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": true, "tactics": ["rcases", "rw", "rw"], "tactic_count": 3}
{"name": "Function.Antiperiodic.sub_zsmul_eq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Function.Antiperiodic.zsmul_sub_eq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Function.Antiperiodic.add_int_mul_eq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Function.Antiperiodic.sub_int_mul_eq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Function.Antiperiodic.int_mul_sub_eq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Function.Antiperiodic.add_nsmul_eq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": true, "tactics": ["rcases", "rw", "simp", "rw", "simp"], "tactic_count": 5}
{"name": "Function.Antiperiodic.sub_nsmul_eq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Function.Antiperiodic.nsmul_sub_eq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Function.Antiperiodic.const_add", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Antiperiodic.add_const", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Antiperiodic.const_sub", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Antiperiodic.sub_const", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Function.Antiperiodic.smul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": true, "tactics": ["simp_all"], "tactic_count": 1}
{"name": "Function.Antiperiodic.const_smul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Antiperiodic.const_inv_smul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Function.Antiperiodic.add", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": true, "tactics": ["simp_all"], "tactic_count": 1}
{"name": "Function.Antiperiodic.sub", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Function.Periodic.add_antiperiod", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": true, "tactics": ["simp_all"], "tactic_count": 1}
{"name": "Function.Periodic.sub_antiperiod", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Function.Periodic.add_antiperiod_eq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Periodic.sub_antiperiod_eq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Antiperiodic.mul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": true, "tactics": ["simp_all"], "tactic_count": 1}
{"name": "Function.Antiperiodic.div", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Periodic", "is_tactic_proof": true, "tactics": ["simp_all"], "tactic_count": 1}
{"name": "Pi.distrib", "kind": "instance", "module": "Mathlib.Algebra.Ring.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.hasDistribNeg", "kind": "instance", "module": "Mathlib.Algebra.Ring.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.addMonoidWithOne", "kind": "instance", "module": "Mathlib.Algebra.Ring.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.addGroupWithOne", "kind": "instance", "module": "Mathlib.Algebra.Ring.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.nonUnitalNonAssocSemiring", "kind": "instance", "module": "Mathlib.Algebra.Ring.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.nonUnitalSemiring", "kind": "instance", "module": "Mathlib.Algebra.Ring.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.nonAssocSemiring", "kind": "instance", "module": "Mathlib.Algebra.Ring.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.semiring", "kind": "instance", "module": "Mathlib.Algebra.Ring.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.nonUnitalCommSemiring", "kind": "instance", "module": "Mathlib.Algebra.Ring.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.commSemiring", "kind": "instance", "module": "Mathlib.Algebra.Ring.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.nonUnitalNonAssocRing", "kind": "instance", "module": "Mathlib.Algebra.Ring.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.nonUnitalRing", "kind": "instance", "module": "Mathlib.Algebra.Ring.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.nonAssocRing", "kind": "instance", "module": "Mathlib.Algebra.Ring.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.ring", "kind": "instance", "module": "Mathlib.Algebra.Ring.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.nonUnitalCommRing", "kind": "instance", "module": "Mathlib.Algebra.Ring.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.commRing", "kind": "instance", "module": "Mathlib.Algebra.Ring.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.nonUnitalRingHom", "kind": "definition", "module": "Mathlib.Algebra.Ring.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.nonUnitalRingHom_injective", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.ringHom", "kind": "definition", "module": "Mathlib.Algebra.Ring.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.ringHom_injective", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.evalNonUnitalRingHom", "kind": "definition", "module": "Mathlib.Algebra.Ring.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.constNonUnitalRingHom", "kind": "definition", "module": "Mathlib.Algebra.Ring.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.compLeft", "kind": "definition", "module": "Mathlib.Algebra.Ring.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.evalRingHom", "kind": "definition", "module": "Mathlib.Algebra.Ring.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instRingHomSurjectiveForallEvalRingHom", "kind": "instance", "module": "Mathlib.Algebra.Ring.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.constRingHom", "kind": "definition", "module": "Mathlib.Algebra.Ring.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.compLeft", "kind": "definition", "module": "Mathlib.Algebra.Ring.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.distribNeg", "kind": "definition", "module": "Mathlib.Algebra.Ring.Pointwise.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mul_add_subset", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Pointwise.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.add_mul_subset", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Pointwise.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.hasDistribNeg", "kind": "definition", "module": "Mathlib.Algebra.Ring.Pointwise.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mul_add_subset", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Pointwise.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.add_mul_subset", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Pointwise.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instDistrib", "kind": "instance", "module": "Mathlib.Algebra.Ring.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instNonUnitalNonAssocSemiring", "kind": "instance", "module": "Mathlib.Algebra.Ring.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instNonUnitalSemiring", "kind": "instance", "module": "Mathlib.Algebra.Ring.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instNonAssocSemiring", "kind": "instance", "module": "Mathlib.Algebra.Ring.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instSemiring", "kind": "instance", "module": "Mathlib.Algebra.Ring.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instNonUnitalCommSemiring", "kind": "instance", "module": "Mathlib.Algebra.Ring.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instCommSemiring", "kind": "instance", "module": "Mathlib.Algebra.Ring.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instNonUnitalNonAssocRing", "kind": "instance", "module": "Mathlib.Algebra.Ring.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instNonUnitalRing", "kind": "instance", "module": "Mathlib.Algebra.Ring.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instNonAssocRing", "kind": "instance", "module": "Mathlib.Algebra.Ring.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instRing", "kind": "instance", "module": "Mathlib.Algebra.Ring.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instNonUnitalCommRing", "kind": "instance", "module": "Mathlib.Algebra.Ring.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instCommRing", "kind": "instance", "module": "Mathlib.Algebra.Ring.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.fst", "kind": "definition", "module": "Mathlib.Algebra.Ring.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.snd", "kind": "definition", "module": "Mathlib.Algebra.Ring.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.coe_fst", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.coe_snd", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.prod", "kind": "definition", "module": "Mathlib.Algebra.Ring.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.prod_apply", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.fst_comp_prod", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.snd_comp_prod", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.prod_unique", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.prodMap", "kind": "definition", "module": "Mathlib.Algebra.Ring.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.prodMap_def", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.coe_prodMap", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.prod_comp_prodMap", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.fst", "kind": "definition", "module": "Mathlib.Algebra.Ring.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.snd", "kind": "definition", "module": "Mathlib.Algebra.Ring.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.instRingHomSurjectiveProdFst", "kind": "instance", "module": "Mathlib.Algebra.Ring.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.instRingHomSurjectiveProdSnd", "kind": "instance", "module": "Mathlib.Algebra.Ring.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.coe_fst", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.coe_snd", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.prod", "kind": "definition", "module": "Mathlib.Algebra.Ring.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.prod_apply", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.fst_comp_prod", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.snd_comp_prod", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.prod_unique", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.prodMap", "kind": "definition", "module": "Mathlib.Algebra.Ring.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.prodMap_def", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.coe_prodMap", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.prod_comp_prodMap", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.prodComm", "kind": "definition", "module": "Mathlib.Algebra.Ring.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.coe_prodComm", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.coe_prodComm_symm", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.fst_comp_coe_prodComm", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.snd_comp_coe_prodComm", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.prodProdProdComm", "kind": "definition", "module": "Mathlib.Algebra.Ring.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.prodProdProdComm_symm", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.prodProdProdComm_toAddEquiv", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.prodProdProdComm_toMulEquiv", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.prodProdProdComm_toEquiv", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.prodZeroRing", "kind": "definition", "module": "Mathlib.Algebra.Ring.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.zeroRingProd", "kind": "definition", "module": "Mathlib.Algebra.Ring.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "false_of_nontrivial_of_product_domain", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Prod", "is_tactic_proof": true, "tactics": ["have", "rw", "rcases", "exact", "exact"], "tactic_count": 5}
{"name": "Rat.commRing", "kind": "instance", "module": "Mathlib.Algebra.Ring.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.commGroupWithZero", "kind": "instance", "module": "Mathlib.Algebra.Ring.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.isDomain", "kind": "instance", "module": "Mathlib.Algebra.Ring.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.instCharZero", "kind": "instance", "module": "Mathlib.Algebra.Ring.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.commSemiring", "kind": "instance", "module": "Mathlib.Algebra.Ring.Rat", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Rat.semiring", "kind": "instance", "module": "Mathlib.Algebra.Ring.Rat", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Rat.divInt_div_divInt_cancel_left", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Rat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Rat.divInt_div_divInt_cancel_right", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Rat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Rat.num_div_den", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Rat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Rat.divInt_pow", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Rat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Rat.mkRat_pow", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Rat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Rat.natCast_eq_divInt", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Rat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Rat.mul_den_eq_num", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Rat", "is_tactic_proof": true, "tactics": ["suffices", "have", "rw"], "tactic_count": 3}
{"name": "Rat.den_mul_eq_num", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Rat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "isLeftRegular_of_non_zero_divisor", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Regular", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "isRightRegular_of_non_zero_divisor", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Regular", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "IsRegular.of_ne_zero'", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isRegular_iff_ne_zero'", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NoZeroDivisors.toIsCancelMulZero", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindFiniteMonoid.iff_eq_of_mul_left_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Regular", "is_tactic_proof": true, "tactics": ["refine", "simpa", "have", "rwa"], "tactic_count": 4}
{"name": "IsDedekindFiniteMonoid.iff_eq_of_mul_right_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Regular", "is_tactic_proof": true, "tactics": ["refine", "simpa", "have", "rwa"], "tactic_count": 4}
{"name": "SemiconjBy.add_right", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Semiconj", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SemiconjBy.add_left", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Semiconj", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SemiconjBy.neg_right", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Semiconj", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SemiconjBy.neg_right_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Semiconj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiconjBy.neg_left", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Semiconj", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SemiconjBy.neg_left_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Semiconj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiconjBy.neg_one_right", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Semiconj", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SemiconjBy.neg_one_left", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Semiconj", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SemiconjBy.sub_right", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Semiconj", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "SemiconjBy.sub_left", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Semiconj", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsSemireal.not_isSumSq_neg_one", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Semireal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isSemireal_iff_not_isSumSq_neg_one", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Semireal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsSemirealOfIsStrictOrderedRingOfExistsAddOfLE", "kind": "instance", "module": "Mathlib.Algebra.Ring.Semireal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCharZeroOfIsSemireal", "kind": "instance", "module": "Mathlib.Algebra.Ring.Semireal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Shrink.ringEquiv", "kind": "definition", "module": "Mathlib.Algebra.Ring.Shrink", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Shrink.instNonUnitalNonAssocSemiring", "kind": "instance", "module": "Mathlib.Algebra.Ring.Shrink", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Shrink.instNonUnitalSemiring", "kind": "instance", "module": "Mathlib.Algebra.Ring.Shrink", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Shrink.instAddMonoidWithOne", "kind": "instance", "module": "Mathlib.Algebra.Ring.Shrink", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Shrink.instAddGroupWithOne", "kind": "instance", "module": "Mathlib.Algebra.Ring.Shrink", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Shrink.instNonAssocSemiring", "kind": "instance", "module": "Mathlib.Algebra.Ring.Shrink", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Shrink.instSemiring", "kind": "instance", "module": "Mathlib.Algebra.Ring.Shrink", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Shrink.instNonUnitalCommSemiring", "kind": "instance", "module": "Mathlib.Algebra.Ring.Shrink", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Shrink.instCommSemiring", "kind": "instance", "module": "Mathlib.Algebra.Ring.Shrink", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Shrink.instNonUnitalNonAssocRing", "kind": "instance", "module": "Mathlib.Algebra.Ring.Shrink", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Shrink.instNonUnitalRing", "kind": "instance", "module": "Mathlib.Algebra.Ring.Shrink", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Shrink.instNonAssocRing", "kind": "instance", "module": "Mathlib.Algebra.Ring.Shrink", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Shrink.instRing", "kind": "instance", "module": "Mathlib.Algebra.Ring.Shrink", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Shrink.instNonUnitalCommRing", "kind": "instance", "module": "Mathlib.Algebra.Ring.Shrink", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Shrink.instCommRing", "kind": "instance", "module": "Mathlib.Algebra.Ring.Shrink", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Shrink.instIsDomain", "kind": "instance", "module": "Mathlib.Algebra.Ring.Shrink", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroup.mul", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroup.mul_toAddSubmonoid", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroup.zero_smul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subgroup", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MulMemClass.mul_right_mem_add_closure", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Submonoid.Basic", "is_tactic_proof": true, "tactics": ["induction", "mem", "zero", "add"], "tactic_count": 4}
{"name": "MulMemClass.mul_mem_add_closure", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Submonoid.Basic", "is_tactic_proof": true, "tactics": ["induction", "mem", "zero", "add"], "tactic_count": 4}
{"name": "MulMemClass.mul_left_mem_add_closure", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Submonoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.one", "kind": "definition", "module": "Mathlib.Algebra.Ring.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.one_eq_mrange", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.natCast_mem_one", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.mem_one", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.one_eq_closure", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Submonoid.Pointwise", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AddSubmonoid.one_eq_closure_one_set", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.smul", "kind": "definition", "module": "Mathlib.Algebra.Ring.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.smul_mem_smul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.smul_le", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.smul_induction_on", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.addSubmonoid_smul_bot", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.smul_le_smul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.smul_le_smul_left", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.smul_le_smul_right", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.smul_subset_smul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.addSubmonoid_smul_sup", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.smul_iSup", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.mul", "kind": "definition", "module": "Mathlib.Algebra.Ring.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.mul_mem_mul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.mul_le", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.mul_induction_on", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.closure_mul_closure", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Submonoid.Pointwise", "is_tactic_proof": true, "tactics": ["apply", "refine", "rw", "refine", "change", "refine", "change", "exact", "rw", "rintro", "exact"], "tactic_count": 11}
{"name": "AddSubmonoid.mul_eq_closure_mul_set", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Submonoid.Pointwise", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AddSubmonoid.mul_bot", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.bot_mul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.mul_le_mul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.mul_le_mul_left", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.mul_le_mul_right", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.mul_subset_mul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.mul_sup", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.sup_mul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.iSup_mul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.mul_iSup", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.mul_comm_of_commute", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.hasDistribNeg", "kind": "definition", "module": "Mathlib.Algebra.Ring.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.mulOneClass", "kind": "definition", "module": "Mathlib.Algebra.Ring.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.semigroup", "kind": "definition", "module": "Mathlib.Algebra.Ring.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.monoid", "kind": "definition", "module": "Mathlib.Algebra.Ring.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.closure_pow", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.pow_eq_closure_pow_set", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Submonoid.Pointwise", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AddSubmonoid.pow_subset_pow", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Submonoid.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.toSubsemiring_strictMono", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.toSubsemiring_mono", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.toSubsemiring_lt_toSubsemiring", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.toSubsemiring_le_toSubsemiring", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.toAddSubgroup_strictMono", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.toAddSubgroup_mono", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.toAddSubgroup_lt_toAddSubgroup", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.toAddSubgroup_le_toAddSubgroup", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.toSubmonoid_strictMono", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.toSubmonoid_mono", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.list_prod_mem", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.list_sum_mem", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.multiset_prod_mem", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.multiset_sum_mem", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.prod_mem", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.sum_mem", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.instTop", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.mem_top", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.coe_top", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.toSubsemiring_top", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.toAddSubgroup_top", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.toSubsemiring_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Subring.toAddSubgroup_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Subring.topEquiv", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.instFintypeSubtypeMemTop", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.card_top", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.comap", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.coe_comap", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.mem_comap", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.comap_comap", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.map", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.coe_map", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.mem_map", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.map_id", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.map_map", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.map_le_iff_le_comap", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.gc_map_comap", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.equivMapOfInjective", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.coe_equivMapOfInjective_apply", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.range", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.coe_range", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.mem_range", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.range_eq_map", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "RingHom.mem_range_self", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.map_range", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "RingHom.fintypeRange", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.instBot", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.instInhabited", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.coe_bot", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.mem_bot", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.instMin", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.coe_inf", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.mem_inf", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.instInfSet", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.coe_sInf", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.mem_sInf", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.coe_iInf", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Subring.mem_iInf", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Subring.sInf_toSubmonoid", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.sInf_toAddSubgroup", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.instCompleteLattice", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.eq_top_iff'", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.center", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.coe_center", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.center_toSubsemiring", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.mem_center_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.decidableMemCenter", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.center_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.instCommRingSubtypeMemCenter", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.centerCongr", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.centerToMulOpposite", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.instField", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.center.coe_inv", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.center.coe_div", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.centralizer", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.coe_centralizer", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.centralizer_toSubmonoid", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.centralizer_toSubsemiring", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.mem_centralizer_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.center_le_centralizer", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.centralizer_le", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.centralizer_eq_top_iff_subset", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.centralizer_univ", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.closure", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.mem_closure", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.subset_closure", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.mem_closure_of_mem", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.notMem_of_notMem_closure", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.closure_le", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.closure_mono", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.closure_eq_of_le", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.closure_induction", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.closure_induction₂", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": true, "tactics": ["induction", "mem", "induction", "mem", "zero", "one", "mul", "add", "neg", "zero", "one", "mul", "add", "neg"], "tactic_count": 14}
{"name": "Subring.mem_closure_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.closure_le_centralizer_centralizer", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.closureCommRingOfComm", "kind": "abbrev", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.exists_list_of_mem_closure", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": true, "tactics": ["rw", "induction", "mem", "obtain", "exact", "zero", "add", "obtain", "exact", "neg", "obtain", "exact", "hL.2"], "tactic_count": 13}
{"name": "Subring.gi", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.closure_eq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.closure_empty", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.closure_univ", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.closure_union", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.closure_iUnion", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.closure_sUnion", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.closure_singleton_intCast", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.closure_singleton_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.closure_singleton_zero", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.closure_singleton_one", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.closure_insert_intCast", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Subring.closure_insert_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.closure_insert_zero", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.closure_insert_one", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.map_sup", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.map_iSup", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.map_inf", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.map_iInf", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": true, "tactics": ["apply", "simpa"], "tactic_count": 2}
{"name": "Subring.comap_inf", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.comap_iInf", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.map_bot", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.comap_top", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.prod", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.coe_prod", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.mem_prod", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.prod_mono", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.prod_mono_right", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.prod_mono_left", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.prod_top", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.top_prod", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.top_prod_top", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.prodEquiv", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.mem_iSup_of_directed", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": true, "tactics": ["refine", "let", "suffices", "exact"], "tactic_count": 4}
{"name": "Subring.coe_iSup_of_directed", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.mem_sSup_of_directedOn", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": true, "tactics": ["haveI", "simp"], "tactic_count": 2}
{"name": "Subring.coe_sSup_of_directedOn", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.mem_map_equiv", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.map_equiv_eq_comap_symm", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.comap_equiv_eq_map_symm", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.rangeRestrict", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.coe_rangeRestrict", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.rangeRestrict_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.range_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.range_eq_top_of_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.eqLocus", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.mem_eqLocus", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.eqLocus_same", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.eqOn_set_closure", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.eq_of_eqOn_set_top", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.eq_of_eqOn_set_dense", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.closure_preimage_le", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.map_closure", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.mem_closure_image_of", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Subring.inclusion", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.coe_inclusion", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Subring.range_subtype", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.range_fst", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.range_snd", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.prod_bot_sup_bot_prod", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.subringCongr", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.ofLeftInverse", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.ofLeftInverse_apply", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.ofLeftInverse_symm_apply", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.subringMap", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.restrict", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.InClosure.recOn", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": true, "tactics": ["have", "rcases", "clear", "induction", "nil", "cons", "rw", "suffices", "rw", "exact", "replace", "clear", "rsuffices", "rw", "clear", "induction", "nil", "cons", "rw", "rw", "exact", "rw", "clear", "induction", "nil", "cons", "rw", "rw", "exact", "induction", "nil", "cons", "rw", "rcases", "exact", "exact", "exact", "exact"], "tactic_count": 38}
{"name": "Subring.closure_preimage_le", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.instSMulSubtypeMem", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.smul_def", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.smulCommClass_left", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.smulCommClass_right", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.instIsScalarTowerSubtypeMem", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.instFaithfulSMulSubtypeMem", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.instMulActionSubtypeMem", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.instDistribMulActionSubtypeMem", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.instMulDistribMulActionSubtypeMem", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.instSMulWithZeroSubtypeMem", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.instMulActionWithZeroSubtypeMem", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.instModuleSubtypeMem", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.instMulSemiringActionSubtypeMem", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.center.smulCommClass_left", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.center.smulCommClass_right", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.instSMulCommClassSubtypeMemCenter", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.instSMulCommClassSubtypeMemCenter_1", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.map_comap_eq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.map_comap_eq_self", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Subring.map_comap_eq_self_of_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.comap_map_eq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": true, "tactics": ["apply", "intro", "rw", "obtain", "replace", "rw", "exact", "rw", "apply", "rw", "exact"], "tactic_count": 11}
{"name": "Subring.comap_map_eq_self", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": true, "tactics": ["convert", "rwa"], "tactic_count": 2}
{"name": "Subring.comap_map_eq_self_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroup.int_mul_mem", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Basic", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "SubringClass.addSubgroupClass", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubringClass.nonUnitalSubringClass", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intCast_mem", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SubringClass.toHasIntCast", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubringClass.toRing", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubringClass.toCommRing", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubringClass.instIsDomainSubtypeMem", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubringClass.subtype", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubringClass.subtype_apply", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubringClass.subtype_injective", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubringClass.coe_subtype", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubringClass.coe_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubringClass.coe_intCast", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.toSubsemiring_injective", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.toSubsemiring_inj", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.instSetLike", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.toAddSubgroup_injective", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.toSubmonoid_injective", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.instPartialOrder", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.ofClass", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.instCanLiftSetCoeAndMemOfNatForallForallForallForallHAddForallForallForallForallHMulForallForallNeg", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.instSubringClass", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.toNonUnitalSubring", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.mem_toSubsemiring", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.mem_carrier", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.mem_mk", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.coe_set_mk", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.mk_le_mk", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.one_mem_toNonUnitalSubring", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.ext", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.copy", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.copy_eq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.mk'", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.mem_mk'", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.mk'_toSubmonoid", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.mk'_toAddSubgroup", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.toSubring", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.one_mem", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.zero_mem", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.mul_mem", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.add_mem", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.neg_mem", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.sub_mem", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.toRing", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.zsmul_mem", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.pow_mem", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.coe_add", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.coe_neg", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.coe_mul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.coe_zero", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.coe_one", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.coe_pow", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.coe_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.mk_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.toCommRing", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.instNontrivialSubtypeMem", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.instNoZeroDivisorsSubtypeMem", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.instIsDomainSubtypeMem", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.subtype", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.subtype_apply", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.subtype_injective", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.coe_subtype", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.coe_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.coe_intCast", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.coe_toSubsemiring", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.mem_toSubmonoid", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.coe_toSubmonoid", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.mem_toAddSubgroup", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.coe_toAddSubgroup", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.toSubring", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.toNonUnitalSubring_toSubring", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "NonUnitalSubring.toSubring_toNonUnitalSubring", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Defs", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Polynomial.int", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subring.IntPolynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.int_coeff_eq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.IntPolynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.int_leadingCoeff_eq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.IntPolynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.int_monic_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.IntPolynomial", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.int_natDegree", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.IntPolynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.int_eval₂_eq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.IntPolynomial", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Subring.op", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.mem_op", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.unop", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.mem_unop", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.unop_op", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.op_unop", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.op_le_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.le_op_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.op_le_op_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.unop_le_unop_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.opEquiv", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.op_injective", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.unop_injective", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.op_inj", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.unop_inj", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.op_bot", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.op_eq_bot", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.unop_bot", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.unop_eq_bot", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.op_top", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.op_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.unop_top", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.unop_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.op_sup", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.unop_sup", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.op_inf", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.unop_inf", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.op_sSup", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.unop_sSup", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.op_sInf", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.unop_sInf", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.op_iSup", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.unop_iSup", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.op_iInf", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.unop_iInf", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.op_closure", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.MulOpposite", "is_tactic_proof": true, "tactics": ["simp_rw", "congr", "exact"], "tactic_count": 3}
{"name": "Subring.unop_closure", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.MulOpposite", "is_tactic_proof": true, "tactics": ["rw", "simp_rw"], "tactic_count": 2}
{"name": "Subring.addEquivOp", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.ringEquivOpMop", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.mopRingEquivOp", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.toIsOrderedRing", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subring.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.toIsStrictOrderedRing", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subring.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.orderedSubtype", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subring.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.orderedSubtype_coe", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.pointwiseMulAction", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subring.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.pointwise_smul_def", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.coe_pointwise_smul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.pointwise_smul_toAddSubgroup", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.pointwise_smul_toSubsemiring", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.smul_mem_pointwise_smul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.instCovariantClassHSMulLe", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subring.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.mem_smul_pointwise_iff_exists", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.smul_bot", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.smul_sup", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.smul_closure", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.pointwise_central_scalar", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subring.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.smul_mem_pointwise_smul_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.mem_pointwise_smul_iff_inv_smul_mem", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.mem_inv_pointwise_smul_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.pointwise_smul_le_pointwise_smul_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.pointwise_smul_subset_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.subset_pointwise_smul_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.smul_mem_pointwise_smul_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.mem_pointwise_smul_iff_inv_smul_mem₀", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.mem_inv_pointwise_smul_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.pointwise_smul_le_pointwise_smul_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.pointwise_smul_le_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.le_pointwise_smul_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.posSubgroup", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subring.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.mem_posSubgroup", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subring.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubsemiringClass.instCharZero", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.toSubmonoid_strictMono", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.toSubmonoid_mono", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.toAddSubmonoid_strictMono", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.toAddSubmonoid_mono", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.list_prod_mem", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.list_sum_mem", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.multiset_prod_mem", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.multiset_sum_mem", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.prod_mem", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.sum_mem", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.topEquiv", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.comap", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.mem_comap", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.comap_comap", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.map", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.mem_map", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.map_id", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.map_map", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.map_le_iff_le_comap", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.gc_map_comap", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.equivMapOfInjective", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.coe_equivMapOfInjective_apply", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.rangeS", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.mem_rangeS", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.rangeS_eq_map", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "RingHom.mem_rangeS_self", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.map_rangeS", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "RingHom.rangeS_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RingHom.fintypeRangeS", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.instBot", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.instInhabited", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.coe_bot", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.mem_bot", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.instInfSet", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.coe_sInf", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.mem_sInf", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.coe_iInf", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Subsemiring.mem_iInf", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Subsemiring.sInf_toSubmonoid", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.sInf_toAddSubmonoid", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.instCompleteLattice", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.eq_top_iff'", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.center", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.center.commSemiring'", "kind": "abbrev", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.centerCongr", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.centerToMulOpposite", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.center.commSemiring", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring._example", "kind": "example", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": true, "tactics": ["with_reducible_and_instances"], "tactic_count": 1}
{"name": "Subsemiring.mem_center_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.decidableMemCenter", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.center_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.centralizer", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.coe_centralizer", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.centralizer_toSubmonoid", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.mem_centralizer_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.center_le_centralizer", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.centralizer_le", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.centralizer_eq_top_iff_subset", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.centralizer_univ", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.le_centralizer_centralizer", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.centralizer_centralizer_centralizer", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "Subsemiring.closure", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.mem_closure", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.subset_closure", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.mem_closure_of_mem", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.notMem_of_notMem_closure", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.closure_le", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.closure_mono", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.closure_eq_of_le", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.mem_map_equiv", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "Subsemiring.map_equiv_eq_comap_symm", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.comap_equiv_eq_map_symm", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.subsemiringClosure", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.subsemiringClosure_coe", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.subsemiringClosure_mem", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.subsemiringClosure_toAddSubmonoid", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.subsemiringClosure_toNonUnitalSubsemiring", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": true, "tactics": ["refine", "simp", "simp", "induction"], "tactic_count": 4}
{"name": "Submonoid.subsemiringClosure_eq_closure", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": true, "tactics": ["ext", "refine", "rintro", "rintro", "exact", "exact"], "tactic_count": 6}
{"name": "Subsemiring.closure_submonoid_closure", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.coe_closure_eq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Subsemiring.mem_closure_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.closure_addSubmonoid_closure", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": true, "tactics": ["ext", "refine", "rintro", "rintro", "refine", "refine", "exact"], "tactic_count": 7}
{"name": "Subsemiring.closure_induction", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.closure_induction₂", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": true, "tactics": ["induction", "mem", "induction", "mem", "zero", "one", "mul", "add", "zero", "one", "mul", "add"], "tactic_count": 12}
{"name": "Subsemiring.mem_closure_iff_exists_list", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "induction", "mem", "hx", "suffices", "let", "induction", "mem", "one", "mul", "obtain", "exact", "zero", "add", "obtain", "exact", "rintro", "exact", "list_sum_mem", "let", "ht2"], "tactic_count": 23}
{"name": "Subsemiring.gi", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.closure_eq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.closure_empty", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.closure_univ", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.closure_union", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.closure_iUnion", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.closure_sUnion", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.closure_singleton_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.closure_singleton_zero", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.closure_singleton_one", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.closure_insert_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Subsemiring.closure_insert_zero", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.closure_insert_one", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.map_sup", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.map_iSup", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.map_inf", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.map_iInf", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": true, "tactics": ["apply", "simpa"], "tactic_count": 2}
{"name": "Subsemiring.comap_inf", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.comap_iInf", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.map_bot", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.comap_top", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.prod", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.coe_prod", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.mem_prod", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.prod_mono", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.prod_mono_right", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.prod_mono_left", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.prod_top", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.top_prod", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.top_prod_top", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.prodEquiv", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.mem_iSup_of_directed", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": true, "tactics": ["refine", "let", "suffices", "exact"], "tactic_count": 4}
{"name": "Subsemiring.coe_iSup_of_directed", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.mem_sSup_of_directedOn", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": true, "tactics": ["haveI", "simp"], "tactic_count": 2}
{"name": "Subsemiring.coe_sSup_of_directedOn", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.codRestrict", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.codRestrict_apply", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.injective_codRestrict", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.rangeS_codRestrict", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.surjective_codRestrict", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.restrict", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.coe_restrict_apply", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.comp_restrict", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.rangeSRestrict", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.coe_rangeSRestrict", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.rangeSRestrict_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.rangeS_top_iff_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.rangeS_top_of_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.eqOn_sclosure", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.eq_of_eqOn_stop", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.eq_of_eqOn_sdense", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.sclosure_preimage_le", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.map_closureS", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.inclusion", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.inclusion_injective", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.rangeS_subtype", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.range_fst", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.range_snd", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.prod_bot_sup_bot_prod", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.subsemiringCongr", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.ofLeftInverseS", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.ofLeftInverseS_apply", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.ofLeftInverseS_symm_apply", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.subsemiringMap", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.subsemiringMap_apply_coe", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.subsemiringMap_symm_apply_coe", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.smul", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.smul_def", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.smulCommClass_left", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.smulCommClass_right", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.instSMulCommClassSubtypeMemCenter", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.instSMulCommClassSubtypeMemCenter_1", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.isScalarTower", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.instFaithfulSMulSubtypeMem", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.faithfulSMul", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.instSMulWithZeroSubtypeMem", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.instSMulWithZeroSubtypeMem_1", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.mulAction", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.distribMulAction", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.mulDistribMulAction", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.instMulActionWithZeroSubtypeMem", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.mulActionWithZero", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.instModuleSubtypeMem", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.module", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.instMulSemiringActionSubtypeMem", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.center.smulCommClass_left", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.center.smulCommClass_right", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.closure_le_centralizer_centralizer", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.closureCommSemiringOfComm", "kind": "abbrev", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.map_comap_eq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.map_comap_eq_self", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Subsemiring.map_comap_eq_self_of_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.comap_map_eq_self_of_injective", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "natCast_mem", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "ofNat_mem", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AddSubmonoidWithOneClass.toAddMonoidWithOne", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubsemiringClass.addSubmonoidWithOneClass", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubsemiringClass.nonUnitalSubsemiringClass", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubsemiringClass.toNonAssocSemiring", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubsemiringClass.nontrivial", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubsemiringClass.noZeroDivisors", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubsemiringClass.subtype", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubsemiringClass.coe_subtype", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubsemiringClass.subtype_apply", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubsemiringClass.subtype_injective", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubsemiringClass.toSemiring", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubsemiringClass.toCommSemiring", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.instSetLike", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.instPartialOrder", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.ofClass", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.instCanLiftSetCoeAndMemOfNatForallForallForallForallHAddForallForallForallForallHMul", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.instSubsemiringClass", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.toNonUnitalSubsemiring", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.mem_toSubmonoid", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.mem_toNonUnitalSubsemiring", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.mem_carrier", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.coe_toNonUnitalSubsemiring", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.mem_mk", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.coe_set_mk", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.ext", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.copy", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.copy_eq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.toSubmonoid_injective", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.toAddSubmonoid_injective", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.toNonUnitalSubsemiring_injective", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.toNonUnitalSubsemiring_inj", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.one_mem_toNonUnitalSubsemiring", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.mk'", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.mem_mk'", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.mk'_toSubmonoid", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.mk'_toAddSubmonoid", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.one_mem", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.zero_mem", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.mul_mem", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.add_mem", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.toNonAssocSemiring", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.coe_one", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.coe_zero", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.coe_add", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.coe_mul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.nontrivial", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.pow_mem", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.noZeroDivisors", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.toSemiring", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.coe_pow", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.toCommSemiring", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.subtype", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.subtype_apply", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.subtype_injective", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.coe_subtype", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.nsmul_mem", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.coe_toSubmonoid", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.coe_carrier_toSubmonoid", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.mem_toAddSubmonoid", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.coe_toAddSubmonoid", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.instTop", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.mem_top", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.coe_top", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.instMin", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.coe_inf", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.mem_inf", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.domRestrict", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.restrict_apply", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.eqLocusS", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.mem_eqLocusS", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.eqLocusS_same", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.toSubsemiring", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.toNonUnitalSubsemiring_toSubsemiring", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.toSubsemiring_toNonUnitalSubsemiring", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.op", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subsemiring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.mem_op", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.unop", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subsemiring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.mem_unop", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.unop_op", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.op_unop", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.op_le_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.le_op_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.op_le_op_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.unop_le_unop_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.opEquiv", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subsemiring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.op_injective", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.unop_injective", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.op_inj", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.unop_inj", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.op_bot", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.op_eq_bot", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.unop_bot", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.unop_eq_bot", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.op_top", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.op_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.unop_top", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.unop_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.op_sup", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.unop_sup", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.op_inf", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.unop_inf", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.op_sSup", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.unop_sSup", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.op_sInf", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.unop_sInf", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.op_iSup", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.unop_iSup", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.op_iInf", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.unop_iInf", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.op_closure", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.MulOpposite", "is_tactic_proof": true, "tactics": ["simp_rw", "congr", "exact"], "tactic_count": 3}
{"name": "Subsemiring.unop_closure", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.MulOpposite", "is_tactic_proof": true, "tactics": ["rw", "simp_rw"], "tactic_count": 2}
{"name": "Subsemiring.addEquivOp", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subsemiring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.ringEquivOpMop", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subsemiring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.mopRingEquivOp", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subsemiring.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubsemiringClass.toIsOrderedRing", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subsemiring.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubsemiringClass.toIsStrictOrderedRing", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subsemiring.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.toIsOrderedRing", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subsemiring.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.toIsStrictOrderedRing", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subsemiring.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.nonneg", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subsemiring.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.mem_nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.nonneg_toAddSubmonoid", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.pointwiseMulAction", "kind": "definition", "module": "Mathlib.Algebra.Ring.Subsemiring.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.pointwise_smul_def", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.coe_pointwise_smul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.pointwise_smul_toAddSubmonoid", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.smul_mem_pointwise_smul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.instCovariantClassHSMulLe", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subsemiring.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.mem_smul_pointwise_iff_exists", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.smul_bot", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.smul_sup", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.smul_closure", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.pointwise_central_scalar", "kind": "instance", "module": "Mathlib.Algebra.Ring.Subsemiring.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.smul_mem_pointwise_smul_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.mem_pointwise_smul_iff_inv_smul_mem", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.mem_inv_pointwise_smul_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.pointwise_smul_le_pointwise_smul_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.pointwise_smul_subset_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.subset_pointwise_smul_iff", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.smul_mem_pointwise_smul_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.mem_pointwise_smul_iff_inv_smul_mem₀", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.mem_inv_pointwise_smul_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.pointwise_smul_le_pointwise_smul_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.pointwise_smul_le_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.le_pointwise_smul_iff₀", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Subsemiring.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSumSq", "kind": "inductive", "module": "Mathlib.Algebra.Ring.SumsOfSquares", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSumSq.rec'", "kind": "theorem", "module": "Mathlib.Algebra.Ring.SumsOfSquares", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSumSq.add", "kind": "theorem", "module": "Mathlib.Algebra.Ring.SumsOfSquares", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "AddSubmonoid.sumSq", "kind": "definition", "module": "Mathlib.Algebra.Ring.SumsOfSquares", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.mem_sumSq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.SumsOfSquares", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSumSq.mul_self", "kind": "theorem", "module": "Mathlib.Algebra.Ring.SumsOfSquares", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsSquare.isSumSq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.SumsOfSquares", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "IsSumSq.one", "kind": "theorem", "module": "Mathlib.Algebra.Ring.SumsOfSquares", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "AddSubmonoid.closure_isSquare", "kind": "theorem", "module": "Mathlib.Algebra.Ring.SumsOfSquares", "is_tactic_proof": true, "tactics": ["refine", "induction"], "tactic_count": 2}
{"name": "IsSumSq.sum", "kind": "theorem", "module": "Mathlib.Algebra.Ring.SumsOfSquares", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsSumSq.sum_isSquare", "kind": "theorem", "module": "Mathlib.Algebra.Ring.SumsOfSquares", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "IsSumSq.sum_mul_self", "kind": "theorem", "module": "Mathlib.Algebra.Ring.SumsOfSquares", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "IsSumSq.sum_sq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.SumsOfSquares", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "NonUnitalSubsemiring.sumSq", "kind": "definition", "module": "Mathlib.Algebra.Ring.SumsOfSquares", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.sumSq_toAddSubmonoid", "kind": "theorem", "module": "Mathlib.Algebra.Ring.SumsOfSquares", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NonUnitalSubsemiring.mem_sumSq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.SumsOfSquares", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NonUnitalSubsemiring.coe_sumSq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.SumsOfSquares", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "NonUnitalSubsemiring.closure_isSquare", "kind": "theorem", "module": "Mathlib.Algebra.Ring.SumsOfSquares", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsSumSq.natCast", "kind": "theorem", "module": "Mathlib.Algebra.Ring.SumsOfSquares", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "Nat.isSumSq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.SumsOfSquares", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSumSq.mul", "kind": "theorem", "module": "Mathlib.Algebra.Ring.SumsOfSquares", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "_private.Mathlib.Algebra.Ring.SumsOfSquares.0.Submonoid.square_subsemiringClosure", "kind": "theorem", "module": "Mathlib.Algebra.Ring.SumsOfSquares", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Subsemiring.sumSq", "kind": "definition", "module": "Mathlib.Algebra.Ring.SumsOfSquares", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.sumSq_toNonUnitalSubsemiring", "kind": "theorem", "module": "Mathlib.Algebra.Ring.SumsOfSquares", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.mem_sumSq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.SumsOfSquares", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Subsemiring.coe_sumSq", "kind": "theorem", "module": "Mathlib.Algebra.Ring.SumsOfSquares", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Subsemiring.closure_isSquare", "kind": "theorem", "module": "Mathlib.Algebra.Ring.SumsOfSquares", "is_tactic_proof": true, "tactics": ["apply_fun", "simp"], "tactic_count": 2}
{"name": "IsSumSq.prod", "kind": "theorem", "module": "Mathlib.Algebra.Ring.SumsOfSquares", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsSumSq.nonneg", "kind": "theorem", "module": "Mathlib.Algebra.Ring.SumsOfSquares", "is_tactic_proof": true, "tactics": ["induction", "zero", "sq_add"], "tactic_count": 3}
{"name": "IsDomain.instIsAddTorsionFreeOfCharZero", "kind": "instance", "module": "Mathlib.Algebra.Ring.Torsion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.map_neg_one", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Torsion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.map_neg", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Torsion", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MonoidHom.map_sub_swap", "kind": "theorem", "module": "Mathlib.Algebra.Ring.Torsion", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Equiv.ringEquiv", "kind": "definition", "module": "Mathlib.Algebra.Ring.TransferInstance", "is_tactic_proof": true, "tactics": ["intros", "exact", "map_add", "map_mul"], "tactic_count": 4}
{"name": "Equiv.ringEquiv_apply", "kind": "theorem", "module": "Mathlib.Algebra.Ring.TransferInstance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.ringEquiv_symm_apply", "kind": "theorem", "module": "Mathlib.Algebra.Ring.TransferInstance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.nonUnitalNonAssocSemiring", "kind": "abbrev", "module": "Mathlib.Algebra.Ring.TransferInstance", "is_tactic_proof": true, "tactics": ["let", "let", "let", "let", "apply"], "tactic_count": 5}
{"name": "Equiv.nonUnitalSemiring", "kind": "abbrev", "module": "Mathlib.Algebra.Ring.TransferInstance", "is_tactic_proof": true, "tactics": ["let", "let", "let", "let", "apply"], "tactic_count": 5}
{"name": "Equiv.addMonoidWithOne", "kind": "abbrev", "module": "Mathlib.Algebra.Ring.TransferInstance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.addGroupWithOne", "kind": "abbrev", "module": "Mathlib.Algebra.Ring.TransferInstance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.nonAssocSemiring", "kind": "abbrev", "module": "Mathlib.Algebra.Ring.TransferInstance", "is_tactic_proof": true, "tactics": ["let", "let", "apply"], "tactic_count": 3}
{"name": "Equiv.semiring", "kind": "abbrev", "module": "Mathlib.Algebra.Ring.TransferInstance", "is_tactic_proof": true, "tactics": ["let", "let", "let", "apply"], "tactic_count": 4}
{"name": "Equiv.nonUnitalCommSemiring", "kind": "abbrev", "module": "Mathlib.Algebra.Ring.TransferInstance", "is_tactic_proof": true, "tactics": ["let", "let", "let", "let", "apply"], "tactic_count": 5}
{"name": "Equiv.commSemiring", "kind": "abbrev", "module": "Mathlib.Algebra.Ring.TransferInstance", "is_tactic_proof": true, "tactics": ["let", "let", "let", "apply"], "tactic_count": 4}
{"name": "Equiv.nonUnitalNonAssocRing", "kind": "abbrev", "module": "Mathlib.Algebra.Ring.TransferInstance", "is_tactic_proof": true, "tactics": ["let", "let", "let", "let", "let", "let", "let", "apply"], "tactic_count": 8}
{"name": "Equiv.nonUnitalRing", "kind": "abbrev", "module": "Mathlib.Algebra.Ring.TransferInstance", "is_tactic_proof": true, "tactics": ["let", "let", "let", "let", "let", "let", "let", "apply"], "tactic_count": 8}
{"name": "Equiv.nonAssocRing", "kind": "abbrev", "module": "Mathlib.Algebra.Ring.TransferInstance", "is_tactic_proof": true, "tactics": ["let", "let", "apply"], "tactic_count": 3}
{"name": "Equiv.ring", "kind": "abbrev", "module": "Mathlib.Algebra.Ring.TransferInstance", "is_tactic_proof": true, "tactics": ["let", "let", "let", "apply"], "tactic_count": 4}
{"name": "Equiv.nonUnitalCommRing", "kind": "abbrev", "module": "Mathlib.Algebra.Ring.TransferInstance", "is_tactic_proof": true, "tactics": ["let", "let", "let", "let", "let", "let", "let", "apply"], "tactic_count": 8}
{"name": "Equiv.commRing", "kind": "abbrev", "module": "Mathlib.Algebra.Ring.TransferInstance", "is_tactic_proof": true, "tactics": ["let", "let", "let", "apply"], "tactic_count": 4}
{"name": "Equiv.isDomain", "kind": "theorem", "module": "Mathlib.Algebra.Ring.TransferInstance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.mulZeroClass", "kind": "instance", "module": "Mathlib.Algebra.Ring.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.distrib", "kind": "instance", "module": "Mathlib.Algebra.Ring.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.instNatCast", "kind": "instance", "module": "Mathlib.Algebra.Ring.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.instIntCast", "kind": "instance", "module": "Mathlib.Algebra.Ring.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.up_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Ring.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.up_ofNat", "kind": "theorem", "module": "Mathlib.Algebra.Ring.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.up_intCast", "kind": "theorem", "module": "Mathlib.Algebra.Ring.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.down_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Ring.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.down_ofNat", "kind": "theorem", "module": "Mathlib.Algebra.Ring.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.down_intCast", "kind": "theorem", "module": "Mathlib.Algebra.Ring.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ULift.addCommMonoidWithOne", "kind": "instance", "module": "Mathlib.Algebra.Ring.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Finset.squarefree_prod_of_pairwise_isCoprime", "kind": "theorem", "module": "Mathlib.Algebra.Squarefree.Basic", "is_tactic_proof": true, "tactics": ["induction", "empty", "cons", "rw", "rw", "refine", "exact", "exact"], "tactic_count": 8}
{"name": "isRadical_iff_squarefree_or_zero", "kind": "theorem", "module": "Mathlib.Algebra.Squarefree.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isRadical_iff_squarefree_of_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Squarefree.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_squarefree_dvd_pow_of_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Squarefree.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "unit", "mul", "obtain", "rcases", "exact", "by_cases", "exact", "suffices", "exact"], "tactic_count": 11}
{"name": "UniqueFactorizationMonoid.squarefree_iff_nodup_normalizedFactors", "kind": "theorem", "module": "Mathlib.Algebra.Squarefree.Basic", "is_tactic_proof": true, "tactics": ["classical", "rw", "haveI", "constructor", "by_cases", "have", "rcases", "rw", "rw", "assumption_mod_cast", "have", "contradiction", "simp", "rw", "intro", "rcases", "simp", "rcases", "apply", "rw", "exact_mod_cast"], "tactic_count": 21}
{"name": "Int.squarefree_natAbs", "kind": "theorem", "module": "Mathlib.Algebra.Squarefree.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Int.squarefree_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Squarefree.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "StarMemClass.instStar", "kind": "instance", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarMemClass.coe_star", "kind": "theorem", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "star_star", "kind": "theorem", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "star_mem_iff", "kind": "theorem", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "star_injective", "kind": "theorem", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_of_star_mem", "kind": "theorem", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "star_inj", "kind": "theorem", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.star", "kind": "definition", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_star_of_eq_star", "kind": "theorem", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "eq_star_iff_eq_star", "kind": "theorem", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "star_eq_iff_star_eq", "kind": "theorem", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "star_star_mul", "kind": "theorem", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "star_mul_star", "kind": "theorem", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "semiconjBy_star_star_star", "kind": "theorem", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "commute_star_star", "kind": "theorem", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "commute_star_comm", "kind": "theorem", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "star_mul'", "kind": "theorem", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "starMulEquiv", "kind": "definition", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "starMulAut", "kind": "definition", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "star_one", "kind": "theorem", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.star_mulSingle", "kind": "theorem", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "star_pow", "kind": "theorem", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "star_inv", "kind": "theorem", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "star_zpow", "kind": "theorem", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "star_div", "kind": "theorem", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "starMulOfComm", "kind": "abbrev", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "star_id_of_comm", "kind": "theorem", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "starAddEquiv", "kind": "definition", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "star_zero", "kind": "theorem", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.star_single", "kind": "theorem", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "star_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "star_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "star_neg", "kind": "theorem", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "star_sub", "kind": "theorem", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "star_nsmul", "kind": "theorem", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "star_zsmul", "kind": "theorem", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarRing.toStarAddMonoid", "kind": "instance", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "starRingEquiv", "kind": "definition", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "star_natCast", "kind": "theorem", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "star_ofNat", "kind": "theorem", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "star_intCast", "kind": "theorem", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "starRingAut", "kind": "definition", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "starRingEnd", "kind": "definition", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexConjugate.termConj", "kind": "definition", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexConjugate._aux_Mathlib_Algebra_Star_Basic___macroRules_ComplexConjugate_termConj_1", "kind": "definition", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplexConjugate._aux_Mathlib_Algebra_Star_Basic___unexpand_starRingEnd_1", "kind": "definition", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "starRingEnd_apply", "kind": "theorem", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "starRingEnd_self_apply", "kind": "theorem", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.involutiveStar", "kind": "instance", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.star_def", "kind": "theorem", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.star_apply", "kind": "theorem", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "conj_trivial", "kind": "theorem", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "star_inv₀", "kind": "theorem", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "star_zpow₀", "kind": "theorem", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "star_div₀", "kind": "theorem", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": true, "tactics": ["apply", "rw"], "tactic_count": 2}
{"name": "starRingOfComm", "kind": "abbrev", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.instStarRing", "kind": "instance", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.instStarRing", "kind": "instance", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.instTrivialStar", "kind": "instance", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.instTrivialStar", "kind": "instance", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarMul.toStarModule", "kind": "instance", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarAddMonoid.toStarModuleNat", "kind": "instance", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarAddMonoid.toStarModuleInt", "kind": "instance", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHomInvPair.instStarRingEnd", "kind": "instance", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.instStarMul", "kind": "instance", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.coe_star", "kind": "theorem", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.coe_star_inv", "kind": "theorem", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.instStarModule", "kind": "instance", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUnit.star", "kind": "theorem", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isUnit_star", "kind": "theorem", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Invertible.star", "kind": "instance", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "star_invOf", "kind": "theorem", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": true, "tactics": ["have", "rw", "have", "rw"], "tactic_count": 4}
{"name": "IsLeftRegular.star", "kind": "theorem", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRightRegular.star", "kind": "theorem", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRegular.star", "kind": "theorem", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isRightRegular_star_iff", "kind": "theorem", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "isRegular_star_iff", "kind": "theorem", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MulOpposite.instStar", "kind": "instance", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.unop_star", "kind": "theorem", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.op_star", "kind": "theorem", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instInvolutiveStar", "kind": "instance", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instStarMul", "kind": "instance", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instStarAddMonoid", "kind": "instance", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instStarRing", "kind": "instance", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instStarModule", "kind": "instance", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSemigroup.toOpposite_starModule", "kind": "instance", "module": "Mathlib.Algebra.Star.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "star_prod", "kind": "theorem", "module": "Mathlib.Algebra.Star.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "star_sum", "kind": "theorem", "module": "Mathlib.Algebra.Star.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isSelfAdjoint_sum", "kind": "theorem", "module": "Mathlib.Algebra.Star.BigOperators", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "star_finsuppSum", "kind": "theorem", "module": "Mathlib.Algebra.Star.BigOperators", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "star_finsuppProd", "kind": "theorem", "module": "Mathlib.Algebra.Star.BigOperators", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CHSH_id", "kind": "theorem", "module": "Mathlib.Algebra.Star.CHSH", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "CHSH_inequality_of_comm", "kind": "theorem", "module": "Mathlib.Algebra.Star.CHSH", "is_tactic_proof": true, "tactics": ["let", "have", "have", "have", "have", "rw", "simp", "have", "dsimp", "simp", "simpa", "apply", "simpa"], "tactic_count": 13}
{"name": "TsirelsonInequality.sqrt_two_inv_mul_self", "kind": "theorem", "module": "Mathlib.Algebra.Star.CHSH", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "tsirelson_inequality", "kind": "theorem", "module": "Mathlib.Algebra.Star.CHSH", "is_tactic_proof": true, "tactics": ["have", "rw", "let", "let", "have", "dsimp", "simp", "simp", "simp", "simp", "abel_nf", "simp", "simp", "neg_smul,", "grind", "have", "have", "simp", "have", "simp", "have", "have", "positivity", "apply", "simpa"], "tactic_count": 25}
{"name": "Set.star_mem_center", "kind": "theorem", "module": "Mathlib.Algebra.Star.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.star_centralizer", "kind": "theorem", "module": "Mathlib.Algebra.Star.Center", "is_tactic_proof": true, "tactics": ["simp_rw", "conv_lhs", "conv_rhs"], "tactic_count": 3}
{"name": "Set.union_star_self_comm", "kind": "theorem", "module": "Mathlib.Algebra.Star.Center", "is_tactic_proof": true, "tactics": ["change", "simp_rw", "exact"], "tactic_count": 3}
{"name": "Set.star_mem_centralizer'", "kind": "theorem", "module": "Mathlib.Algebra.Star.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.star_mem_centralizer", "kind": "theorem", "module": "Mathlib.Algebra.Star.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.instStar", "kind": "instance", "module": "Mathlib.Algebra.Star.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.star_apply", "kind": "theorem", "module": "Mathlib.Algebra.Star.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.instStarAddMonoid", "kind": "instance", "module": "Mathlib.Algebra.Star.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.instStarSubtypeMemSubsemiringCenter", "kind": "instance", "module": "Mathlib.Algebra.Star.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.instStarAddMonoidCenter", "kind": "instance", "module": "Mathlib.Algebra.Star.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.instStarRingSubtypeMemSubsemiringCenter", "kind": "instance", "module": "Mathlib.Algebra.Star.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.centerStarEmbedding", "kind": "definition", "module": "Mathlib.Algebra.Star.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.star_centerToCentroidCenter", "kind": "theorem", "module": "Mathlib.Algebra.Star.CentroidHom", "is_tactic_proof": true, "tactics": ["ext", "calc"], "tactic_count": 2}
{"name": "CentroidHom.starCenterToCentroidCenter", "kind": "definition", "module": "Mathlib.Algebra.Star.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.starCenterToCentroid", "kind": "definition", "module": "Mathlib.Algebra.Star.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.starCenterToCentroid_apply", "kind": "theorem", "module": "Mathlib.Algebra.Star.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.starRingOfCommCentroidHom", "kind": "definition", "module": "Mathlib.Algebra.Star.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.starCenterIsoCentroid", "kind": "definition", "module": "Mathlib.Algebra.Star.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.starCenterIsoCentroid_apply", "kind": "theorem", "module": "Mathlib.Algebra.Star.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CentroidHom.starCenterIsoCentroid_symm_apply_coe", "kind": "theorem", "module": "Mathlib.Algebra.Star.CentroidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "conjneg", "kind": "definition", "module": "Mathlib.Algebra.Star.Conjneg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "conjneg_apply", "kind": "theorem", "module": "Mathlib.Algebra.Star.Conjneg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "conjneg_conjneg", "kind": "theorem", "module": "Mathlib.Algebra.Star.Conjneg", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "conjneg_involutive", "kind": "theorem", "module": "Mathlib.Algebra.Star.Conjneg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "conjneg_bijective", "kind": "theorem", "module": "Mathlib.Algebra.Star.Conjneg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "conjneg_injective", "kind": "theorem", "module": "Mathlib.Algebra.Star.Conjneg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "conjneg_surjective", "kind": "theorem", "module": "Mathlib.Algebra.Star.Conjneg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "conjneg_inj", "kind": "theorem", "module": "Mathlib.Algebra.Star.Conjneg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "conjneg_ne_conjneg", "kind": "theorem", "module": "Mathlib.Algebra.Star.Conjneg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "conjneg_conj", "kind": "theorem", "module": "Mathlib.Algebra.Star.Conjneg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "conjneg_zero", "kind": "theorem", "module": "Mathlib.Algebra.Star.Conjneg", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "conjneg_one", "kind": "theorem", "module": "Mathlib.Algebra.Star.Conjneg", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "conjneg_add", "kind": "theorem", "module": "Mathlib.Algebra.Star.Conjneg", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "conjneg_mul", "kind": "theorem", "module": "Mathlib.Algebra.Star.Conjneg", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "conjneg_sum", "kind": "theorem", "module": "Mathlib.Algebra.Star.Conjneg", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "conjneg_prod", "kind": "theorem", "module": "Mathlib.Algebra.Star.Conjneg", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "conjneg_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Star.Conjneg", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "conjneg_eq_one", "kind": "theorem", "module": "Mathlib.Algebra.Star.Conjneg", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "conjneg_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Star.Conjneg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "conjneg_ne_one", "kind": "theorem", "module": "Mathlib.Algebra.Star.Conjneg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sum_conjneg", "kind": "theorem", "module": "Mathlib.Algebra.Star.Conjneg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "support_conjneg", "kind": "theorem", "module": "Mathlib.Algebra.Star.Conjneg", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "conjnegRingHom", "kind": "definition", "module": "Mathlib.Algebra.Star.Conjneg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "conjneg_sub", "kind": "theorem", "module": "Mathlib.Algebra.Star.Conjneg", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "conjneg_neg", "kind": "theorem", "module": "Mathlib.Algebra.Star.Conjneg", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "FreeMonoid.instStarMul", "kind": "instance", "module": "Mathlib.Algebra.Star.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeMonoid.star_of", "kind": "theorem", "module": "Mathlib.Algebra.Star.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeMonoid.star_one", "kind": "theorem", "module": "Mathlib.Algebra.Star.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeAlgebra.instStarRing", "kind": "instance", "module": "Mathlib.Algebra.Star.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeAlgebra.star_ι", "kind": "theorem", "module": "Mathlib.Algebra.Star.Free", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FreeAlgebra.star_algebraMap", "kind": "theorem", "module": "Mathlib.Algebra.Star.Free", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FreeAlgebra.starHom", "kind": "definition", "module": "Mathlib.Algebra.Star.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.intrinsicStar", "kind": "definition", "module": "Mathlib.Algebra.Star.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.intrinsicStar_apply", "kind": "theorem", "module": "Mathlib.Algebra.Star.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.intrinsicInvolutiveStar", "kind": "definition", "module": "Mathlib.Algebra.Star.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.intrinsicStarAddMonoid", "kind": "definition", "module": "Mathlib.Algebra.Star.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IntrinsicStar.isSelfAdjoint_iff_map_star", "kind": "theorem", "module": "Mathlib.Algebra.Star.LinearMap", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "IntrinsicStar.StarHomClass.isSelfAdjoint", "kind": "theorem", "module": "Mathlib.Algebra.Star.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.intrinsicStar_comp", "kind": "theorem", "module": "Mathlib.Algebra.Star.LinearMap", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "LinearMap.intrinsicStar_id", "kind": "theorem", "module": "Mathlib.Algebra.Star.LinearMap", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "LinearMap.intrinsicStar_zero", "kind": "theorem", "module": "Mathlib.Algebra.Star.LinearMap", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "LinearMap.intrinsicStar_mulLeft", "kind": "theorem", "module": "Mathlib.Algebra.Star.LinearMap", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "LinearMap.intrinsicStar_mulRight", "kind": "theorem", "module": "Mathlib.Algebra.Star.LinearMap", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LinearMap.intrinsicStar_mul'", "kind": "theorem", "module": "Mathlib.Algebra.Star.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.intrinsicStarModule", "kind": "theorem", "module": "Mathlib.Algebra.Star.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.intrinsicStar_map", "kind": "theorem", "module": "Mathlib.Algebra.Star.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.intrinsicStar_lTensor", "kind": "theorem", "module": "Mathlib.Algebra.Star.LinearMap", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LinearMap.intrinsicStar_rTensor", "kind": "theorem", "module": "Mathlib.Algebra.Star.LinearMap", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LinearMap.intrinsicStar_eq_comp", "kind": "theorem", "module": "Mathlib.Algebra.Star.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IntrinsicStar.starLinearEquiv_eq_arrowCongr", "kind": "theorem", "module": "Mathlib.Algebra.Star.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.intrinsicStar_toSpanSingleton", "kind": "theorem", "module": "Mathlib.Algebra.Star.LinearMap", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "LinearMap.intrinsicStar_smulRight", "kind": "theorem", "module": "Mathlib.Algebra.Star.LinearMap", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "LinearMap.toMatrix'_intrinsicStar", "kind": "theorem", "module": "Mathlib.Algebra.Star.LinearMap", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "LinearMap.IntrinsicStar.isSelfAdjoint_iff_toMatrix'", "kind": "theorem", "module": "Mathlib.Algebra.Star.LinearMap", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.intrinsicStar_toLin'", "kind": "theorem", "module": "Mathlib.Algebra.Star.LinearMap", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.IntrinsicStar.isSelfAdjoint_toLin'_iff", "kind": "theorem", "module": "Mathlib.Algebra.Star.LinearMap", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Module.End.Units.intrinsicStar", "kind": "definition", "module": "Mathlib.Algebra.Star.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.IsUnit.intrinsicStar", "kind": "theorem", "module": "Mathlib.Algebra.Star.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.isUnit_intrinsicStar_iff", "kind": "theorem", "module": "Mathlib.Algebra.Star.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.mem_eigenspace_intrinsicStar_iff", "kind": "theorem", "module": "Mathlib.Algebra.Star.LinearMap", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Module.End.spectrum_intrinsicStar", "kind": "theorem", "module": "Mathlib.Algebra.Star.LinearMap", "is_tactic_proof": true, "tactics": ["ext", "simp_rw", "rw"], "tactic_count": 3}
{"name": "star_natCast_smul", "kind": "theorem", "module": "Mathlib.Algebra.Star.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "star_intCast_smul", "kind": "theorem", "module": "Mathlib.Algebra.Star.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "star_inv_natCast_smul", "kind": "theorem", "module": "Mathlib.Algebra.Star.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "star_inv_intCast_smul", "kind": "theorem", "module": "Mathlib.Algebra.Star.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "star_ratCast_smul", "kind": "theorem", "module": "Mathlib.Algebra.Star.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "star_nnrat_smul", "kind": "theorem", "module": "Mathlib.Algebra.Star.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "star_rat_smul", "kind": "theorem", "module": "Mathlib.Algebra.Star.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarAddMonoid.toStarModuleNNRat", "kind": "instance", "module": "Mathlib.Algebra.Star.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarAddMonoid.toStarModuleRat", "kind": "instance", "module": "Mathlib.Algebra.Star.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "starLinearEquiv", "kind": "definition", "module": "Mathlib.Algebra.Star.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "selfAdjoint.submodule", "kind": "definition", "module": "Mathlib.Algebra.Star.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "skewAdjoint.submodule", "kind": "definition", "module": "Mathlib.Algebra.Star.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "selfAdjointPart", "kind": "definition", "module": "Mathlib.Algebra.Star.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "skewAdjointPart", "kind": "definition", "module": "Mathlib.Algebra.Star.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarModule.selfAdjointPart_add_skewAdjointPart", "kind": "theorem", "module": "Mathlib.Algebra.Star.Module", "is_tactic_proof": true, "tactics": ["simp", "invOf_two_smul_add_invOf_two_smul]"], "tactic_count": 2}
{"name": "IsSelfAdjoint.coe_selfAdjointPart_apply", "kind": "theorem", "module": "Mathlib.Algebra.Star.Module", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsSelfAdjoint.selfAdjointPart_apply", "kind": "theorem", "module": "Mathlib.Algebra.Star.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "selfAdjointPart_comp_subtype_selfAdjoint", "kind": "theorem", "module": "Mathlib.Algebra.Star.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSelfAdjoint.skewAdjointPart_apply", "kind": "theorem", "module": "Mathlib.Algebra.Star.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "skewAdjointPart_comp_subtype_selfAdjoint", "kind": "theorem", "module": "Mathlib.Algebra.Star.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "selfAdjointPart_comp_subtype_skewAdjoint", "kind": "theorem", "module": "Mathlib.Algebra.Star.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "skewAdjointPart_comp_subtype_skewAdjoint", "kind": "theorem", "module": "Mathlib.Algebra.Star.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarModule.decomposeProdAdjoint", "kind": "definition", "module": "Mathlib.Algebra.Star.Module", "is_tactic_proof": false, "tactics": ["refine", "ext"], "tactic_count": 2}
{"name": "algebraMap_star_comm", "kind": "theorem", "module": "Mathlib.Algebra.Star.Module", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsSelfAdjoint.algebraMap", "kind": "theorem", "module": "Mathlib.Algebra.Star.Module", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "isSelfAdjoint_algebraMap_iff", "kind": "theorem", "module": "Mathlib.Algebra.Star.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIdempotentElem.star_iff", "kind": "theorem", "module": "Mathlib.Algebra.Star.Module", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "term_→⋆*_", "kind": "definition", "module": "Mathlib.Algebra.Star.MonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Algebra_Star_MonoidHom___macroRules_term_→⋆*__1", "kind": "definition", "module": "Mathlib.Algebra.Star.MonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Algebra_Star_MonoidHom___unexpand_StarMonoidHom_1", "kind": "definition", "module": "Mathlib.Algebra.Star.MonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarMonoidHom.instFunLike", "kind": "instance", "module": "Mathlib.Algebra.Star.MonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarMonoidHom.instMonoidHomClass", "kind": "instance", "module": "Mathlib.Algebra.Star.MonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarMonoidHom.instStarHomClass", "kind": "instance", "module": "Mathlib.Algebra.Star.MonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarMonoidHom.Simps.coe", "kind": "definition", "module": "Mathlib.Algebra.Star.MonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarMonoidHom.ofClass", "kind": "definition", "module": "Mathlib.Algebra.Star.MonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarMonoidHom.coe_toMonoidHom", "kind": "theorem", "module": "Mathlib.Algebra.Star.MonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarMonoidHom.ext", "kind": "theorem", "module": "Mathlib.Algebra.Star.MonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarMonoidHom.copy", "kind": "definition", "module": "Mathlib.Algebra.Star.MonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarMonoidHom.coe_copy", "kind": "theorem", "module": "Mathlib.Algebra.Star.MonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarMonoidHom.copy_eq", "kind": "theorem", "module": "Mathlib.Algebra.Star.MonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarMonoidHom.coe_mk", "kind": "theorem", "module": "Mathlib.Algebra.Star.MonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarMonoidHom.id", "kind": "definition", "module": "Mathlib.Algebra.Star.MonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarMonoidHom.coe_id", "kind": "theorem", "module": "Mathlib.Algebra.Star.MonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarMonoidHom.comp", "kind": "definition", "module": "Mathlib.Algebra.Star.MonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarMonoidHom.coe_comp", "kind": "theorem", "module": "Mathlib.Algebra.Star.MonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarMonoidHom.comp_apply", "kind": "theorem", "module": "Mathlib.Algebra.Star.MonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarMonoidHom.comp_assoc", "kind": "theorem", "module": "Mathlib.Algebra.Star.MonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarMonoidHom.id_comp", "kind": "theorem", "module": "Mathlib.Algebra.Star.MonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarMonoidHom.comp_id", "kind": "theorem", "module": "Mathlib.Algebra.Star.MonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarMonoidHom.instMonoid", "kind": "instance", "module": "Mathlib.Algebra.Star.MonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarMonoidHom.coe_one", "kind": "theorem", "module": "Mathlib.Algebra.Star.MonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarMonoidHom.one_apply", "kind": "theorem", "module": "Mathlib.Algebra.Star.MonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "term_≃⋆*_", "kind": "definition", "module": "Mathlib.Algebra.Star.MonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Algebra_Star_MonoidHom___macroRules_term_≃⋆*__1", "kind": "definition", "module": "Mathlib.Algebra.Star.MonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Algebra_Star_MonoidHom___unexpand_StarMulEquiv_1", "kind": "definition", "module": "Mathlib.Algebra.Star.MonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarMulEquiv.instEquivLike", "kind": "instance", "module": "Mathlib.Algebra.Star.MonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarMulEquiv.instMulEquivClass", "kind": "instance", "module": "Mathlib.Algebra.Star.MonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarMulEquiv.instStarHomClass", "kind": "instance", "module": "Mathlib.Algebra.Star.MonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarMulEquiv.ext", "kind": "theorem", "module": "Mathlib.Algebra.Star.MonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarMulEquiv.refl", "kind": "definition", "module": "Mathlib.Algebra.Star.MonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarMulEquiv.instInhabited", "kind": "instance", "module": "Mathlib.Algebra.Star.MonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarMulEquiv.coe_refl", "kind": "theorem", "module": "Mathlib.Algebra.Star.MonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarMulEquiv.symm", "kind": "definition", "module": "Mathlib.Algebra.Star.MonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarMulEquiv.Simps.apply", "kind": "definition", "module": "Mathlib.Algebra.Star.MonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarMulEquiv.Simps.symm_apply", "kind": "definition", "module": "Mathlib.Algebra.Star.MonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarMulEquiv.invFun_eq_symm", "kind": "theorem", "module": "Mathlib.Algebra.Star.MonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarMulEquiv.symm_symm", "kind": "theorem", "module": "Mathlib.Algebra.Star.MonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarMulEquiv.symm_bijective", "kind": "theorem", "module": "Mathlib.Algebra.Star.MonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarMulEquiv.coe_mk", "kind": "theorem", "module": "Mathlib.Algebra.Star.MonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "StarMulEquiv.coe_toMulEquiv", "kind": "theorem", "module": "Mathlib.Algebra.Star.MonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarMulEquiv.toMulEquiv_symm", "kind": "theorem", "module": "Mathlib.Algebra.Star.MonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarMulEquiv.refl_symm", "kind": "theorem", "module": "Mathlib.Algebra.Star.MonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarMulEquiv.trans", "kind": "definition", "module": "Mathlib.Algebra.Star.MonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarMulEquiv.apply_symm_apply", "kind": "theorem", "module": "Mathlib.Algebra.Star.MonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarMulEquiv.symm_apply_apply", "kind": "theorem", "module": "Mathlib.Algebra.Star.MonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarMulEquiv.symm_trans_apply", "kind": "theorem", "module": "Mathlib.Algebra.Star.MonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarMulEquiv.coe_trans", "kind": "theorem", "module": "Mathlib.Algebra.Star.MonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarMulEquiv.trans_apply", "kind": "theorem", "module": "Mathlib.Algebra.Star.MonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarMulEquiv.toMulEquiv_trans", "kind": "theorem", "module": "Mathlib.Algebra.Star.MonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarMulEquiv.leftInverse_symm", "kind": "theorem", "module": "Mathlib.Algebra.Star.MonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarMulEquiv.rightInverse_symm", "kind": "theorem", "module": "Mathlib.Algebra.Star.MonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarMulEquiv.toStarMonoidHom", "kind": "definition", "module": "Mathlib.Algebra.Star.MonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarMulEquiv.ofStarMonoidHom", "kind": "definition", "module": "Mathlib.Algebra.Star.MonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarMulEquiv.ofBijective", "kind": "definition", "module": "Mathlib.Algebra.Star.MonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarMulEquiv.coe_ofBijective", "kind": "theorem", "module": "Mathlib.Algebra.Star.MonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarMulEquiv.ofBijective_apply", "kind": "theorem", "module": "Mathlib.Algebra.Star.MonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarMemClass.instInvolutiveStar", "kind": "instance", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarMemClass.instStarMul", "kind": "instance", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarMemClass.instStarAddMonoid", "kind": "instance", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarMemClass.instStarRing", "kind": "instance", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarMemClass.instStarModule", "kind": "instance", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebraClass.subtype", "kind": "definition", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebraClass.subtype_apply", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebraClass.subtype_injective", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebraClass.coe_subtype", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.instSetLike", "kind": "instance", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.instPartialOrder", "kind": "instance", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.ofClass", "kind": "definition", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.instCanLiftSetCoeAndMemOfNatForallForallForallForallHAddForallForallForallForallHMulForallForallForallHSMulForallForallStar", "kind": "instance", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.instNonUnitalSubsemiringClass", "kind": "instance", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.instSMulMemClass", "kind": "instance", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.instStarMemClass", "kind": "instance", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.instNonUnitalSubringClass", "kind": "instance", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.mem_carrier", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.ext", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.mem_toNonUnitalSubalgebra", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.coe_toNonUnitalSubalgebra", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.toNonUnitalSubalgebra_injective", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.toNonUnitalSubalgebra_inj", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.toNonUnitalSubalgebra_le_iff", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.copy", "kind": "definition", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.coe_copy", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.copy_eq", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.toNonUnitalSubring", "kind": "definition", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.mem_toNonUnitalSubring", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.coe_toNonUnitalSubring", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.toNonUnitalSubring_injective", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.toNonUnitalSubring_inj", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.instInhabited", "kind": "instance", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.toNonUnitalSemiring", "kind": "instance", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.toNonUnitalCommSemiring", "kind": "instance", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.toNonUnitalRing", "kind": "instance", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.toNonUnitalCommRing", "kind": "instance", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.toNonUnitalSubalgebra'", "kind": "definition", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.module'", "kind": "instance", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.instModule", "kind": "instance", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.instIsScalarTower'", "kind": "instance", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.instIsScalarTower", "kind": "instance", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.instSMulCommClass'", "kind": "instance", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.instSMulCommClass", "kind": "instance", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.instIsTorsionFree", "kind": "instance", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.coe_add", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.coe_mul", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.coe_zero", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.coe_neg", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.coe_sub", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.coe_smul", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.coe_eq_zero", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.toNonUnitalSubalgebra_subtype", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.toSubring_subtype", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.map", "kind": "definition", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.map_mono", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.map_injective", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.map_id", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.map_map", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.mem_map", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.map_toNonUnitalSubalgebra", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.coe_map", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.comap", "kind": "definition", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.map_le", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.gc_map_comap", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.mem_comap", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "NonUnitalStarSubalgebra.instNoZeroDivisors", "kind": "instance", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.toNonUnitalStarSubalgebra", "kind": "definition", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.mem_toNonUnitalStarSubalgebra", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "NonUnitalSubalgebra.toNonUnitalStarSubalgebra_toNonUnitalSubalgebra", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.toNonUnitalSubalgebra_toNonUnitalStarSubalgebra", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarAlgHom.range", "kind": "definition", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarAlgHom.mem_range", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarAlgHom.mem_range_self", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarAlgHom.coe_range", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "NonUnitalStarAlgHom.range_comp", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarAlgHom.range_comp_le_range", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarAlgHom.codRestrict", "kind": "definition", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarAlgHom.subtype_comp_codRestrict", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "NonUnitalStarAlgHom.rangeRestrict", "kind": "abbrev", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarAlgHom.equalizer", "kind": "definition", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "StarAlgEquiv.ofInjective'_apply", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "NonUnitalSubalgebra.mem_star_iff", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.star_mem_star_iff", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NonUnitalSubalgebra.coe_star", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.star_mono", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.star_adjoin_comm", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.starClosure", "kind": "definition", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.coe_starClosure", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "NonUnitalSubalgebra.starClosure_toNonUnitalSubalgebra", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "NonUnitalSubalgebra.starClosure_le_iff", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "NonUnitalStarAlgebra.adjoin", "kind": "definition", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarAlgebra.adjoin_eq_starClosure_adjoin", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarAlgebra.adjoin_toNonUnitalSubalgebra", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarAlgebra.subset_adjoin", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarAlgebra.star_subset_adjoin", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarAlgebra.mem_adjoin_of_mem", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarAlgebra.self_mem_adjoin_singleton", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarAlgebra.star_self_mem_adjoin_singleton", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarAlgebra.adjoin_induction", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": true, "tactics": ["refine", "push", "obtain", "exact", "simpa"], "tactic_count": 5}
{"name": "NonUnitalStarAlgebra.gc", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": true, "tactics": ["intro", "rw", "coe_toNonUnitalSubalgebra]", "exact"], "tactic_count": 4}
{"name": "NonUnitalStarAlgebra.gi", "kind": "definition", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarAlgebra.adjoin_le", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarAlgebra.adjoin_le_iff", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarAlgebra.adjoin_mono", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarAlgebra.adjoin_eq", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarAlgebra.adjoin_eq_span", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NonUnitalStarAlgebra.span_eq_toSubmodule", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NonUnitalSubalgebra.starClosure_eq_adjoin", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarAlgebra.instCompleteLatticeNonUnitalStarSubalgebra", "kind": "instance", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarAlgebra.coe_top", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarAlgebra.mem_top", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarAlgebra.top_toNonUnitalSubalgebra", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "NonUnitalStarAlgebra.toNonUnitalSubalgebra_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarAlgebra.mem_sup_left", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "NonUnitalStarAlgebra.mem_sup_right", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "NonUnitalStarAlgebra.mul_mem_sup", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarAlgebra.map_sup", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarAlgebra.map_inf", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarAlgebra.coe_inf", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarAlgebra.mem_inf", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarAlgebra.inf_toNonUnitalSubalgebra", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarAlgebra.coe_sInf", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarAlgebra.mem_sInf", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NonUnitalStarAlgebra.sInf_toNonUnitalSubalgebra", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarAlgebra.coe_iInf", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NonUnitalStarAlgebra.mem_iInf", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NonUnitalStarAlgebra.map_iInf", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": true, "tactics": ["apply", "simpa"], "tactic_count": 2}
{"name": "NonUnitalStarAlgebra.iInf_toNonUnitalSubalgebra", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarAlgebra.instInhabitedNonUnitalStarSubalgebra", "kind": "instance", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarAlgebra.mem_bot", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarAlgebra.toNonUnitalSubalgebra_bot", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "NonUnitalStarAlgebra.coe_bot", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NonUnitalStarAlgebra.eq_top_iff", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarAlgebra.range_id", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarAlgebra.map_bot", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarAlgebra.comap_top", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarAlgebra.toTop", "kind": "definition", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarAlgebra.range_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarAlgebra.map_top", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.inclusion", "kind": "definition", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.inclusion_injective", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.inclusion_self", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.inclusion_mk", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.inclusion_right", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.inclusion_inclusion", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.val_inclusion", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarAlgHom.map_adjoin", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarAlgHom.map_adjoin_singleton", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NonUnitalStarSubalgebra.subsingleton_of_subsingleton", "kind": "instance", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarAlgHom.subsingleton", "kind": "instance", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.range_val", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.prod", "kind": "definition", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.coe_prod", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.prod_toNonUnitalSubalgebra", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.mem_prod", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.prod_mono", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.prod_top", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "NonUnitalStarSubalgebra.prod_inf_prod", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.coe_iSup_of_directed", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.iSupLift", "kind": "definition", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": true, "tactics": ["subst", "exact", "let", "simp", "rw", "rfl)", "map_zero", "dsimp", "eq_mpr_eq_cast]", "exact", "map_mul", "dsimp", "eq_mpr_eq_cast,", "apply", "all_goals", "map_add", "dsimp", "eq_mpr_eq_cast]", "apply", "all_goals", "map_smul", "dsimp", "eq_mpr_eq_cast]", "apply", "all_goals", "map_star", "dsimp", "apply", "all_goals"], "tactic_count": 29}
{"name": "NonUnitalStarSubalgebra.iSupLift_inclusion", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": true, "tactics": ["subst", "dsimp", "apply", "exact"], "tactic_count": 4}
{"name": "NonUnitalStarSubalgebra.iSupLift_comp_inclusion", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "NonUnitalStarSubalgebra.iSupLift_mk", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": true, "tactics": ["subst", "dsimp", "apply"], "tactic_count": 3}
{"name": "NonUnitalStarSubalgebra.iSupLift_of_mem", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": true, "tactics": ["subst", "dsimp", "apply"], "tactic_count": 3}
{"name": "NonUnitalStarSubalgebra.center", "kind": "definition", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.coe_center", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.center_toNonUnitalSubalgebra", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.center_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.instNonUnitalCommSemiring", "kind": "instance", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.instNonUnitalCommRing", "kind": "instance", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.mem_center_iff", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.centralizer", "kind": "definition", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.coe_centralizer", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.mem_centralizer_iff", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": true, "tactics": ["change", "simp", "exact"], "tactic_count": 3}
{"name": "NonUnitalStarSubalgebra.centralizer_le", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.centralizer_univ", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.centralizer_toNonUnitalSubalgebra", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.coe_centralizer_centralizer", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NonUnitalStarAlgebra.adjoin_le_centralizer_centralizer", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": true, "tactics": ["rw", "convert", "rw", "simp"], "tactic_count": 4}
{"name": "NonUnitalStarAlgebra.commute_of_mem_adjoin_of_forall_mem_commute", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarAlgebra.commute_of_mem_adjoin_singleton_of_commute", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarAlgebra.commute_of_mem_adjoin_self", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarAlgebra.adjoinNonUnitalCommSemiringOfComm", "kind": "abbrev", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarAlgebra.adjoinNonUnitalCommRingOfComm", "kind": "abbrev", "module": "Mathlib.Algebra.Star.NonUnitalSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubsemiring.instSetLike", "kind": "instance", "module": "Mathlib.Algebra.Star.NonUnitalSubsemiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubsemiring.ofClass", "kind": "definition", "module": "Mathlib.Algebra.Star.NonUnitalSubsemiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubsemiring.instCanLiftSetCoeAndMemOfNatForallForallForallForallHAddForallForallForallForallHMulForallForallStar", "kind": "instance", "module": "Mathlib.Algebra.Star.NonUnitalSubsemiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubsemiring.instNonUnitalSubsemiringClass", "kind": "instance", "module": "Mathlib.Algebra.Star.NonUnitalSubsemiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubsemiring.instStarMemClass", "kind": "instance", "module": "Mathlib.Algebra.Star.NonUnitalSubsemiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubsemiring.mem_carrier", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubsemiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubsemiring.copy", "kind": "definition", "module": "Mathlib.Algebra.Star.NonUnitalSubsemiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubsemiring.coe_copy", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubsemiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubsemiring.copy_eq", "kind": "theorem", "module": "Mathlib.Algebra.Star.NonUnitalSubsemiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubsemiring.center", "kind": "definition", "module": "Mathlib.Algebra.Star.NonUnitalSubsemiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instTrivialStarForall", "kind": "instance", "module": "Mathlib.Algebra.Star.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instInvolutiveStarForall", "kind": "instance", "module": "Mathlib.Algebra.Star.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instStarMulForall", "kind": "instance", "module": "Mathlib.Algebra.Star.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instStarAddMonoidForall", "kind": "instance", "module": "Mathlib.Algebra.Star.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instStarRingForall", "kind": "instance", "module": "Mathlib.Algebra.Star.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instStarModuleForall", "kind": "instance", "module": "Mathlib.Algebra.Star.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.single_star", "kind": "theorem", "module": "Mathlib.Algebra.Star.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.conj_apply", "kind": "theorem", "module": "Mathlib.Algebra.Star.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.update_star", "kind": "theorem", "module": "Mathlib.Algebra.Star.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.star_sumElim", "kind": "theorem", "module": "Mathlib.Algebra.Star.Pi", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "_private.Mathlib.Algebra.Star.Pointwise.0.Set.term_⋆", "kind": "definition", "module": "Mathlib.Algebra.Star.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Star.Pointwise.0.Set._aux_Mathlib_Algebra_Star_Pointwise___macroRules__private_Mathlib_Algebra_Star_Pointwise_0_Set_term_⋆_1", "kind": "definition", "module": "Mathlib.Algebra.Star.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Star.Pointwise.0.Set._aux_Mathlib_Algebra_Star_Pointwise___unexpand_Star_star_1", "kind": "definition", "module": "Mathlib.Algebra.Star.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.star", "kind": "definition", "module": "Mathlib.Algebra.Star.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.star_empty", "kind": "theorem", "module": "Mathlib.Algebra.Star.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.star_univ", "kind": "theorem", "module": "Mathlib.Algebra.Star.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.nonempty_star", "kind": "theorem", "module": "Mathlib.Algebra.Star.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nonempty.star", "kind": "theorem", "module": "Mathlib.Algebra.Star.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_star", "kind": "theorem", "module": "Mathlib.Algebra.Star.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.star_mem_star", "kind": "theorem", "module": "Mathlib.Algebra.Star.Pointwise", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.star_preimage", "kind": "theorem", "module": "Mathlib.Algebra.Star.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_star", "kind": "theorem", "module": "Mathlib.Algebra.Star.Pointwise", "is_tactic_proof": true, "tactics": ["simp", "rw"], "tactic_count": 2}
{"name": "Set.inter_star", "kind": "theorem", "module": "Mathlib.Algebra.Star.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.union_star", "kind": "theorem", "module": "Mathlib.Algebra.Star.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iInter_star", "kind": "theorem", "module": "Mathlib.Algebra.Star.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_star", "kind": "theorem", "module": "Mathlib.Algebra.Star.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.compl_star", "kind": "theorem", "module": "Mathlib.Algebra.Star.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instInvolutiveStar", "kind": "instance", "module": "Mathlib.Algebra.Star.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.star_subset_star", "kind": "theorem", "module": "Mathlib.Algebra.Star.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.star_subset", "kind": "theorem", "module": "Mathlib.Algebra.Star.Pointwise", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.Finite.star", "kind": "theorem", "module": "Mathlib.Algebra.Star.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.star_singleton", "kind": "theorem", "module": "Mathlib.Algebra.Star.Pointwise", "is_tactic_proof": true, "tactics": ["ext1", "rw"], "tactic_count": 2}
{"name": "Set.star_mul", "kind": "theorem", "module": "Mathlib.Algebra.Star.Pointwise", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.star_add", "kind": "theorem", "module": "Mathlib.Algebra.Star.Pointwise", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.instTrivialStar", "kind": "instance", "module": "Mathlib.Algebra.Star.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.star_inv", "kind": "theorem", "module": "Mathlib.Algebra.Star.Pointwise", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Set.star_inv'", "kind": "theorem", "module": "Mathlib.Algebra.Star.Pointwise", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "StarMemClass.star_coe_eq", "kind": "theorem", "module": "Mathlib.Algebra.Star.Pointwise", "is_tactic_proof": true, "tactics": ["ext", "simpa"], "tactic_count": 2}
{"name": "Prod.instTrivialStar", "kind": "instance", "module": "Mathlib.Algebra.Star.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instInvolutiveStar", "kind": "instance", "module": "Mathlib.Algebra.Star.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instStarMul", "kind": "instance", "module": "Mathlib.Algebra.Star.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instStarAddMonoid", "kind": "instance", "module": "Mathlib.Algebra.Star.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instStarRing", "kind": "instance", "module": "Mathlib.Algebra.Star.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instStarModule", "kind": "instance", "module": "Mathlib.Algebra.Star.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.embed_product_star", "kind": "theorem", "module": "Mathlib.Algebra.Star.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.instStarRing", "kind": "instance", "module": "Mathlib.Algebra.Star.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.instStarRing", "kind": "instance", "module": "Mathlib.Algebra.Star.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.instTrivialStar", "kind": "instance", "module": "Mathlib.Algebra.Star.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.instTrivialStar", "kind": "instance", "module": "Mathlib.Algebra.Star.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "star_nnratCast", "kind": "theorem", "module": "Mathlib.Algebra.Star.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "star_ratCast", "kind": "theorem", "module": "Mathlib.Algebra.Star.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingQuot.Rel.star", "kind": "theorem", "module": "Mathlib.Algebra.Star.RingQuot", "is_tactic_proof": true, "tactics": ["induction", "of", "add_left", "rw", "exact", "mul_left", "rw", "exact", "mul_right", "rw", "exact"], "tactic_count": 11}
{"name": "_private.Mathlib.Algebra.Star.RingQuot.0.RingQuot.star'", "kind": "definition", "module": "Mathlib.Algebra.Star.RingQuot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Algebra.Star.RingQuot.0.RingQuot.star'_quot", "kind": "theorem", "module": "Mathlib.Algebra.Star.RingQuot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingQuot.starRing", "kind": "definition", "module": "Mathlib.Algebra.Star.RingQuot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSelfAdjoint", "kind": "definition", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "star_comm_self'", "kind": "theorem", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSelfAdjoint.all", "kind": "theorem", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSelfAdjoint.star_eq", "kind": "theorem", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isSelfAdjoint_iff", "kind": "theorem", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSelfAdjoint.star_iff", "kind": "theorem", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsSelfAdjoint.star_mul_self", "kind": "theorem", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsSelfAdjoint.mul_star_self", "kind": "theorem", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsSelfAdjoint.commute_iff", "kind": "theorem", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": true, "tactics": ["refine", "rw", "simpa"], "tactic_count": 3}
{"name": "IsSelfAdjoint.map", "kind": "theorem", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isSelfAdjoint_map", "kind": "theorem", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSelfAdjoint.isStarNormal", "kind": "theorem", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSelfAdjoint.zero", "kind": "theorem", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSelfAdjoint.add", "kind": "theorem", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsSelfAdjoint.neg", "kind": "theorem", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsSelfAdjoint.sub", "kind": "theorem", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsSelfAdjoint.add_star_self", "kind": "theorem", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsSelfAdjoint.star_add_self", "kind": "theorem", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsSelfAdjoint.conjugate", "kind": "theorem", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsSelfAdjoint.conjugate'", "kind": "theorem", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsSelfAdjoint.conjugate_self", "kind": "theorem", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": true, "tactics": ["nth_rewrite"], "tactic_count": 1}
{"name": "IsSelfAdjoint.one", "kind": "theorem", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSelfAdjoint.pow", "kind": "theorem", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsUnit.isSelfAdjoint_conjugate_iff", "kind": "theorem", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsUnit.isSelfAdjoint_conjugate_iff'", "kind": "theorem", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsSelfAdjoint.natCast", "kind": "theorem", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSelfAdjoint.ofNat", "kind": "theorem", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSelfAdjoint.mul", "kind": "theorem", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsSelfAdjoint.conj_eq", "kind": "theorem", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSelfAdjoint.intCast", "kind": "theorem", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSelfAdjoint.inv", "kind": "theorem", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsSelfAdjoint.zpow", "kind": "theorem", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsSelfAdjoint.inv₀", "kind": "theorem", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsSelfAdjoint.zpow₀", "kind": "theorem", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsSelfAdjoint.nnratCast", "kind": "theorem", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSelfAdjoint.ratCast", "kind": "theorem", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSelfAdjoint.div", "kind": "theorem", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsSelfAdjoint.smul", "kind": "theorem", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsSelfAdjoint.smul_iff", "kind": "theorem", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": true, "tactics": ["refine", "lift", "rw", "replace", "exact"], "tactic_count": 5}
{"name": "selfAdjoint", "kind": "definition", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "skewAdjoint", "kind": "definition", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "selfAdjoint.mem_iff", "kind": "theorem", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "selfAdjoint.star_val_eq", "kind": "theorem", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "selfAdjoint.instInhabitedSubtypeMemAddSubgroup", "kind": "instance", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "selfAdjoint.isSelfAdjoint", "kind": "theorem", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "selfAdjoint.isStarNormal", "kind": "instance", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "selfAdjoint.instOneSubtypeMemAddSubgroup", "kind": "instance", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "selfAdjoint.val_one", "kind": "theorem", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "selfAdjoint.instNontrivialSubtypeMemAddSubgroup", "kind": "instance", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "selfAdjoint.instNatCastSubtypeMemAddSubgroup", "kind": "instance", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "selfAdjoint.instIntCastSubtypeMemAddSubgroup", "kind": "instance", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "selfAdjoint.instPowSubtypeMemAddSubgroupNat", "kind": "instance", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "selfAdjoint.val_pow", "kind": "theorem", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "selfAdjoint.instMulSubtypeMemAddSubgroup", "kind": "instance", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "selfAdjoint.val_mul", "kind": "theorem", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "selfAdjoint.instCommRingSubtypeMemAddSubgroup", "kind": "instance", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "selfAdjoint.instInvSubtypeMemAddSubgroup", "kind": "instance", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "selfAdjoint.val_inv", "kind": "theorem", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "selfAdjoint.instDivSubtypeMemAddSubgroup", "kind": "instance", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "selfAdjoint.val_div", "kind": "theorem", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "selfAdjoint.instPowSubtypeMemAddSubgroupInt", "kind": "instance", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "selfAdjoint.val_zpow", "kind": "theorem", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "selfAdjoint.instNNRatCast", "kind": "instance", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "selfAdjoint.instRatCast", "kind": "instance", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "selfAdjoint.val_nnratCast", "kind": "theorem", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "selfAdjoint.val_ratCast", "kind": "theorem", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "selfAdjoint.instSMulNNRat", "kind": "instance", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "selfAdjoint.instSMulRat", "kind": "instance", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "selfAdjoint.val_nnqsmul", "kind": "theorem", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "selfAdjoint.val_qsmul", "kind": "theorem", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "selfAdjoint.instField", "kind": "instance", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "selfAdjoint.instSMulSubtypeMemAddSubgroupOfStarModule", "kind": "instance", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "selfAdjoint.val_smul", "kind": "theorem", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "selfAdjoint.instMulActionSubtypeMemAddSubgroupOfStarModule", "kind": "instance", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "selfAdjoint.instDistribMulActionSubtypeMemAddSubgroupOfStarModule", "kind": "instance", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "selfAdjoint.instModuleSubtypeMemAddSubgroupOfStarModule", "kind": "instance", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "skewAdjoint.mem_iff", "kind": "theorem", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "skewAdjoint.star_val_eq", "kind": "theorem", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "skewAdjoint.instInhabitedSubtypeMemAddSubgroup", "kind": "instance", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "skewAdjoint.conjugate", "kind": "theorem", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "skewAdjoint.conjugate'", "kind": "theorem", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "skewAdjoint.isStarNormal_of_mem", "kind": "theorem", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "skewAdjoint.instIsStarNormalValMemAddSubgroup", "kind": "instance", "module": "Mathlib.Algebra.Star.SelfAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "StarRingEquiv.Simps.apply", "kind": "definition", "module": "Mathlib.Algebra.Star.StarRingHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarRingEquiv.Simps.symm_apply", "kind": "definition", "module": "Mathlib.Algebra.Star.StarRingHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarRingEquiv.invFun_eq_symm", "kind": "theorem", "module": "Mathlib.Algebra.Star.StarRingHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarRingEquiv.symm_symm", "kind": "theorem", "module": "Mathlib.Algebra.Star.StarRingHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarRingEquiv.symm_bijective", "kind": "theorem", "module": "Mathlib.Algebra.Star.StarRingHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarRingEquiv.coe_mk", "kind": "theorem", "module": "Mathlib.Algebra.Star.StarRingHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarRingEquiv.mk_coe", "kind": "theorem", "module": "Mathlib.Algebra.Star.StarRingHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarRingEquiv.symm_mk.aux", "kind": "definition", "module": "Mathlib.Algebra.Star.StarRingHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarRingEquiv.symm_mk", "kind": "theorem", "module": "Mathlib.Algebra.Star.StarRingHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarRingEquiv.refl_symm", "kind": "theorem", "module": "Mathlib.Algebra.Star.StarRingHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarRingEquiv.trans", "kind": "definition", "module": "Mathlib.Algebra.Star.StarRingHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarRingEquiv.apply_symm_apply", "kind": "theorem", "module": "Mathlib.Algebra.Star.StarRingHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarRingEquiv.symm_apply_apply", "kind": "theorem", "module": "Mathlib.Algebra.Star.StarRingHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarRingEquiv.symm_trans_apply", "kind": "theorem", "module": "Mathlib.Algebra.Star.StarRingHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarRingEquiv.coe_trans", "kind": "theorem", "module": "Mathlib.Algebra.Star.StarRingHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarRingEquiv.trans_apply", "kind": "theorem", "module": "Mathlib.Algebra.Star.StarRingHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarRingEquiv.leftInverse_symm", "kind": "theorem", "module": "Mathlib.Algebra.Star.StarRingHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarRingEquiv.rightInverse_symm", "kind": "theorem", "module": "Mathlib.Algebra.Star.StarRingHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarRingEquiv.ofStarRingHom", "kind": "definition", "module": "Mathlib.Algebra.Star.StarRingHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarRingEquiv.ofBijective", "kind": "definition", "module": "Mathlib.Algebra.Star.StarRingHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarRingEquiv.coe_ofBijective", "kind": "theorem", "module": "Mathlib.Algebra.Star.StarRingHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarRingEquiv.ofBijective_apply", "kind": "theorem", "module": "Mathlib.Algebra.Star.StarRingHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.setLike", "kind": "instance", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.instPartialOrder", "kind": "instance", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.ofClass", "kind": "definition", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.instCanLiftSetCoeAndForallForallForallMemForallHAddForallForallForallForallHMulForallCoeRingHomAlgebraMapForallForallStar", "kind": "instance", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.starMemClass", "kind": "instance", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.subsemiringClass", "kind": "instance", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.smulMemClass", "kind": "instance", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.subringClass", "kind": "instance", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.starRing", "kind": "instance", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.algebra", "kind": "instance", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.starModule", "kind": "instance", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.toNonUnitalStarSubalgebra", "kind": "definition", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.one_mem_toNonUnitalStarSubalgebra", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.mem_carrier", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.ext", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.coe_mk", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.mem_toSubalgebra", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.coe_toSubalgebra", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.toSubalgebra_injective", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.toSubalgebra_inj", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.toSubalgebra_le_iff", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.copy", "kind": "definition", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.coe_copy", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.copy_eq", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.algebraMap_mem", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.rangeS_le", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.range_subset", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.range_le", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.smul_mem", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.subtype", "kind": "definition", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.coe_subtype", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.subtype_apply", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.toSubalgebra_subtype", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.inclusion", "kind": "definition", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.inclusion_injective", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.subtype_comp_inclusion", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.map", "kind": "definition", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.map_mono", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.map_injective", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.map_id", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.map_map", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.mem_map", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.map_toSubalgebra", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.coe_map", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.comap", "kind": "definition", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.map_le_iff_le_comap", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.gc_map_comap", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.comap_mono", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.comap_injective", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.comap_id", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.comap_comap", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.mem_comap", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.coe_comap", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.centralizer", "kind": "definition", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.coe_centralizer", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.mem_centralizer_iff", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "StarSubalgebra.centralizer_le", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.centralizer_toSubalgebra", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.coe_centralizer_centralizer", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subalgebra.involutiveStar", "kind": "instance", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.mem_star_iff", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.star_mem_star_iff", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Subalgebra.coe_star", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.star_mono", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.star_adjoin_comm", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.starClosure", "kind": "definition", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.coe_starClosure", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.mem_starClosure", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.starClosure_toSubalgebra", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.starClosure_le", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.starClosure_le_iff", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarAlgebra.adjoin", "kind": "definition", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarAlgebra.adjoin_eq_starClosure_adjoin", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarAlgebra.adjoin_toSubalgebra", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarAlgebra.subset_adjoin", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarAlgebra.star_subset_adjoin", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarAlgebra.mem_adjoin_of_mem", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarAlgebra.self_mem_adjoin_singleton", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarAlgebra.star_self_mem_adjoin_singleton", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarAlgebra.gc", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": true, "tactics": ["intro", "rw", "exact"], "tactic_count": 3}
{"name": "StarAlgebra.gi", "kind": "definition", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarAlgebra.adjoin_le", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarAlgebra.adjoin_le_iff", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarAlgebra.adjoin_mono", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarAlgebra.adjoin_eq", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarAlgebra.adjoin_eq_span", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "StarAlgebra.adjoin_nonUnitalStarSubalgebra_eq_span", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subalgebra.starClosure_eq_adjoin", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarAlgebra.adjoin_induction", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": true, "tactics": ["refine", "push", "obtain", "exact", "simpa"], "tactic_count": 5}
{"name": "StarAlgebra.adjoin_induction₂", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": true, "tactics": ["induction", "mem", "induction", "mem", "algebraMap", "mul", "add", "star", "algebraMap", "induction", "mem", "algebraMap", "mul", "add", "star", "mul", "add", "star"], "tactic_count": 18}
{"name": "StarAlgebra.adjoin_induction_subtype", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarAlgebra.adjoin_le_centralizer_centralizer", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": true, "tactics": ["rw", "convert", "rw", "simp"], "tactic_count": 4}
{"name": "StarAlgebra.adjoinCommSemiringOfComm", "kind": "abbrev", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarAlgebra.adjoinCommRingOfComm", "kind": "abbrev", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarAlgebra.adjoinCommSemiringOfIsStarNormal", "kind": "instance", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarAlgebra.adjoinCommRingOfIsStarNormal", "kind": "instance", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.completeLattice", "kind": "instance", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.inhabited", "kind": "instance", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.coe_top", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.mem_top", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.top_toSubalgebra", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "StarSubalgebra.toSubalgebra_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.mem_sup_left", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.mem_sup_right", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.mul_mem_sup", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.map_sup", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.map_inf", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.coe_inf", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.mem_inf", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.inf_toSubalgebra", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "StarSubalgebra.coe_sInf", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.mem_sInf", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "StarSubalgebra.sInf_toSubalgebra", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.coe_iInf", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "StarSubalgebra.mem_iInf", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "StarSubalgebra.map_iInf", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": true, "tactics": ["apply", "simpa"], "tactic_count": 2}
{"name": "StarSubalgebra.iInf_toSubalgebra", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.bot_toSubalgebra", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.mem_bot", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.coe_bot", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.eq_top_iff", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarAlgHom.ext_adjoin", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": ["refine", "adjoin_induction_subtype", "exact", "simp", "simp", "simp", "simp"], "tactic_count": 7}
{"name": "StarAlgHom.ext_adjoin_singleton", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarAlgHom.equalizer", "kind": "definition", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarAlgHom.mem_equalizer", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarAlgHom.adjoin_le_equalizer", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarAlgHom.ext_of_adjoin_eq_top", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarAlgHom.map_adjoin", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarAlgHom.range", "kind": "definition", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarAlgHom.range_eq_map_top", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarAlgHom.codRestrict", "kind": "definition", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarAlgHom.coe_codRestrict", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarAlgHom.subtype_comp_codRestrict", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarAlgHom.injective_codRestrict", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarAlgHom.rangeRestrict", "kind": "definition", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarAlgEquiv.ofInjective", "kind": "definition", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarAlgHom.restrictScalars", "kind": "definition", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarAlgHom.restrictScalars_injective", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarAlgEquiv.restrictScalars", "kind": "definition", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarAlgEquiv.restrictScalars_injective", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.toStarSubalgebra", "kind": "definition", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.toNonUnitalStarSubalgebra_toStarSubalgebra", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "NonUnitalStarSubalgebra.toStarSubalgebra_toNonUnitalStarSubalgebra", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "NonUnitalStarAlgebra.adjoin_le_starAlgebra_adjoin", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarAlgebra.adjoin_nonUnitalStarSubalgebra", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubsemiring.setLike", "kind": "instance", "module": "Mathlib.Algebra.Star.Subsemiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubsemiring.instPartialOrder", "kind": "instance", "module": "Mathlib.Algebra.Star.Subsemiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubsemiring.ofClass", "kind": "definition", "module": "Mathlib.Algebra.Star.Subsemiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubsemiring.instCanLiftSetCoeAndMemOfNatForallForallForallForallHAddForallForallForallForallHMulForallForallStar", "kind": "instance", "module": "Mathlib.Algebra.Star.Subsemiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubsemiring.starMemClass", "kind": "instance", "module": "Mathlib.Algebra.Star.Subsemiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubsemiring.subsemiringClass", "kind": "instance", "module": "Mathlib.Algebra.Star.Subsemiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubsemiring.starRing", "kind": "instance", "module": "Mathlib.Algebra.Star.Subsemiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubsemiring.semiring", "kind": "instance", "module": "Mathlib.Algebra.Star.Subsemiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubsemiring.mem_carrier", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subsemiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubsemiring.ext", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subsemiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubsemiring.coe_mk", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subsemiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubsemiring.mem_toSubsemiring", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subsemiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubsemiring.coe_toSubsemiring", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subsemiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubsemiring.toSubsemiring_injective", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subsemiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubsemiring.toSubsemiring_inj", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subsemiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubsemiring.toSubsemiring_le_iff", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subsemiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubsemiring.copy", "kind": "definition", "module": "Mathlib.Algebra.Star.Subsemiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubsemiring.coe_copy", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subsemiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubsemiring.copy_eq", "kind": "theorem", "module": "Mathlib.Algebra.Star.Subsemiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubsemiring.center", "kind": "definition", "module": "Mathlib.Algebra.Star.Subsemiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubStarSemigroup.center", "kind": "definition", "module": "Mathlib.Algebra.Star.Subsemiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.instStar", "kind": "instance", "module": "Mathlib.Algebra.Star.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.star_tmul", "kind": "theorem", "module": "Mathlib.Algebra.Star.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.instInvolutiveStar", "kind": "instance", "module": "Mathlib.Algebra.Star.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.instStarAddMonoid", "kind": "instance", "module": "Mathlib.Algebra.Star.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.instStarModule", "kind": "instance", "module": "Mathlib.Algebra.Star.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "starLinearEquiv_tensor", "kind": "theorem", "module": "Mathlib.Algebra.Star.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitary", "kind": "definition", "module": "Mathlib.Algebra.Star.Unitary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitary.mem_iff", "kind": "theorem", "module": "Mathlib.Algebra.Star.Unitary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitary.star_mul_self_of_mem", "kind": "theorem", "module": "Mathlib.Algebra.Star.Unitary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitary.mul_star_self_of_mem", "kind": "theorem", "module": "Mathlib.Algebra.Star.Unitary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitary.star_mem", "kind": "theorem", "module": "Mathlib.Algebra.Star.Unitary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitary.star_mem_iff", "kind": "theorem", "module": "Mathlib.Algebra.Star.Unitary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitary.instStarSubtypeMemSubmonoidUnitary", "kind": "instance", "module": "Mathlib.Algebra.Star.Unitary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitary.coe_star", "kind": "theorem", "module": "Mathlib.Algebra.Star.Unitary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitary.coe_star_mul_self", "kind": "theorem", "module": "Mathlib.Algebra.Star.Unitary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitary.coe_mul_star_self", "kind": "theorem", "module": "Mathlib.Algebra.Star.Unitary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitary.star_mul_self", "kind": "theorem", "module": "Mathlib.Algebra.Star.Unitary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitary.mul_star_self", "kind": "theorem", "module": "Mathlib.Algebra.Star.Unitary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitary.instGroupSubtypeMemSubmonoidUnitary", "kind": "instance", "module": "Mathlib.Algebra.Star.Unitary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitary.instInvolutiveStarSubtypeMemSubmonoidUnitary", "kind": "instance", "module": "Mathlib.Algebra.Star.Unitary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitary.instStarMulSubtypeMemSubmonoidUnitary", "kind": "instance", "module": "Mathlib.Algebra.Star.Unitary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitary.instInhabitedSubtypeMemSubmonoidUnitary", "kind": "instance", "module": "Mathlib.Algebra.Star.Unitary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitary.star_eq_inv", "kind": "theorem", "module": "Mathlib.Algebra.Star.Unitary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitary.star_eq_inv'", "kind": "theorem", "module": "Mathlib.Algebra.Star.Unitary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitary.toUnits", "kind": "definition", "module": "Mathlib.Algebra.Star.Unitary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitary.toUnits_injective", "kind": "theorem", "module": "Mathlib.Algebra.Star.Unitary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUnit.mem_unitary_iff_star_mul_self", "kind": "theorem", "module": "Mathlib.Algebra.Star.Unitary", "is_tactic_proof": true, "tactics": ["rw", "lift", "exact"], "tactic_count": 3}
{"name": "IsUnit.mem_unitary_iff_mul_star_self", "kind": "theorem", "module": "Mathlib.Algebra.Star.Unitary", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Unitary.isUnit_coe", "kind": "theorem", "module": "Mathlib.Algebra.Star.Unitary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitary.mul_left_inj", "kind": "theorem", "module": "Mathlib.Algebra.Star.Unitary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitary.mul_right_inj", "kind": "theorem", "module": "Mathlib.Algebra.Star.Unitary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitary.mul_inv_mem_iff", "kind": "theorem", "module": "Mathlib.Algebra.Star.Unitary", "is_tactic_proof": true, "tactics": ["rw", "mul_assoc,"], "tactic_count": 2}
{"name": "Unitary.inv_mul_mem_iff", "kind": "theorem", "module": "Mathlib.Algebra.Star.Unitary", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Units.unitary_eq", "kind": "theorem", "module": "Mathlib.Algebra.Star.Unitary", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Units.mul_inv_mem_unitary", "kind": "theorem", "module": "Mathlib.Algebra.Star.Unitary", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Units.inv_mul_mem_unitary", "kind": "theorem", "module": "Mathlib.Algebra.Star.Unitary", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Unitary.instIsStarNormal", "kind": "instance", "module": "Mathlib.Algebra.Star.Unitary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitary.coe_isStarNormal", "kind": "instance", "module": "Mathlib.Algebra.Star.Unitary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isStarNormal_of_mem_unitary", "kind": "theorem", "module": "Mathlib.Algebra.Star.Unitary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitary.inv_mem", "kind": "theorem", "module": "Mathlib.Algebra.Star.Unitary", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "unitarySubgroup", "kind": "definition", "module": "Mathlib.Algebra.Star.Unitary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitarySubgroup_toSubmonoid", "kind": "theorem", "module": "Mathlib.Algebra.Star.Unitary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_unitarySubgroup_iff", "kind": "theorem", "module": "Mathlib.Algebra.Star.Unitary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitary.inv_mem_iff", "kind": "theorem", "module": "Mathlib.Algebra.Star.Unitary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitary.smul_mem_of_mem", "kind": "theorem", "module": "Mathlib.Algebra.Star.Unitary", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Unitary.smul_mem", "kind": "theorem", "module": "Mathlib.Algebra.Star.Unitary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitary.instSMulSubtypeMemSubmonoidUnitary", "kind": "instance", "module": "Mathlib.Algebra.Star.Unitary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitary.coe_smul", "kind": "theorem", "module": "Mathlib.Algebra.Star.Unitary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitary.instMulActionSubtypeMemSubmonoidUnitary", "kind": "instance", "module": "Mathlib.Algebra.Star.Unitary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitary.instStarModuleSubtypeMemSubmonoidUnitary", "kind": "instance", "module": "Mathlib.Algebra.Star.Unitary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitary.instSMulCommClassSubtypeMemSubmonoidUnitary", "kind": "instance", "module": "Mathlib.Algebra.Star.Unitary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitary.instIsScalarTowerSubtypeMemSubmonoidUnitary", "kind": "instance", "module": "Mathlib.Algebra.Star.Unitary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitary.map_mem", "kind": "theorem", "module": "Mathlib.Algebra.Star.Unitary", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "Unitary.map", "kind": "definition", "module": "Mathlib.Algebra.Star.Unitary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitary.coe_map", "kind": "theorem", "module": "Mathlib.Algebra.Star.Unitary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitary.coe_map_star", "kind": "theorem", "module": "Mathlib.Algebra.Star.Unitary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitary.map_id", "kind": "theorem", "module": "Mathlib.Algebra.Star.Unitary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitary.map_comp", "kind": "theorem", "module": "Mathlib.Algebra.Star.Unitary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitary.map_injective", "kind": "theorem", "module": "Mathlib.Algebra.Star.Unitary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitary.toUnits_comp_map", "kind": "theorem", "module": "Mathlib.Algebra.Star.Unitary", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Unitary.mapEquiv", "kind": "definition", "module": "Mathlib.Algebra.Star.Unitary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitary.mapEquiv_refl", "kind": "theorem", "module": "Mathlib.Algebra.Star.Unitary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitary.mapEquiv_symm", "kind": "theorem", "module": "Mathlib.Algebra.Star.Unitary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitary.mapEquiv_trans", "kind": "theorem", "module": "Mathlib.Algebra.Star.Unitary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitary.toMonoidHom_mapEquiv", "kind": "theorem", "module": "Mathlib.Algebra.Star.Unitary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitarySubgroupUnitsEquiv", "kind": "definition", "module": "Mathlib.Algebra.Star.Unitary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitary.instCommGroupSubtypeMemSubmonoidUnitary", "kind": "instance", "module": "Mathlib.Algebra.Star.Unitary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitary.mem_iff_star_mul_self", "kind": "theorem", "module": "Mathlib.Algebra.Star.Unitary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitary.mem_iff_self_mul_star", "kind": "theorem", "module": "Mathlib.Algebra.Star.Unitary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitary.coe_inv", "kind": "theorem", "module": "Mathlib.Algebra.Star.Unitary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "TrivSqZeroExt.map_inr", "kind": "theorem", "module": "Mathlib.Algebra.TrivSqZeroExt", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "TrivSqZeroExt.fst_map", "kind": "theorem", "module": "Mathlib.Algebra.TrivSqZeroExt", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "TrivSqZeroExt.snd_map", "kind": "theorem", "module": "Mathlib.Algebra.TrivSqZeroExt", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "TrivSqZeroExt.map_comp_inlAlgHom", "kind": "theorem", "module": "Mathlib.Algebra.TrivSqZeroExt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TrivSqZeroExt.map_comp_inrHom", "kind": "theorem", "module": "Mathlib.Algebra.TrivSqZeroExt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TrivSqZeroExt.fstHom_comp_map", "kind": "theorem", "module": "Mathlib.Algebra.TrivSqZeroExt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TrivSqZeroExt.sndHom_comp_map", "kind": "theorem", "module": "Mathlib.Algebra.TrivSqZeroExt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TrivSqZeroExt.map_id", "kind": "theorem", "module": "Mathlib.Algebra.TrivSqZeroExt", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "TrivSqZeroExt.map_comp_map", "kind": "theorem", "module": "Mathlib.Algebra.TrivSqZeroExt", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "Tropical", "kind": "definition", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Tropical.trop_injective", "kind": "theorem", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.untrop_injective", "kind": "theorem", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.trop_inj_iff", "kind": "theorem", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.untrop_inj_iff", "kind": "theorem", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.trop_untrop", "kind": "theorem", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.untrop_trop", "kind": "theorem", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.leftInverse_trop", "kind": "theorem", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.rightInverse_trop", "kind": "theorem", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.tropEquiv", "kind": "definition", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.tropEquiv_coe_fn", "kind": "theorem", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.tropEquiv_symm_coe_fn", "kind": "theorem", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.trop_eq_iff_eq_untrop", "kind": "theorem", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.untrop_eq_iff_eq_trop", "kind": "theorem", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.injective_trop", "kind": "theorem", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.injective_untrop", "kind": "theorem", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.surjective_trop", "kind": "theorem", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.surjective_untrop", "kind": "theorem", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.instInhabited", "kind": "instance", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.tropRec", "kind": "definition", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.instDecidableEq", "kind": "instance", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.instLETropical", "kind": "instance", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.untrop_le_iff", "kind": "theorem", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.decidableLE", "kind": "instance", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.instLTTropical", "kind": "instance", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.untrop_lt_iff", "kind": "theorem", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.decidableLT", "kind": "instance", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.instPreorderTropical", "kind": "instance", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.tropOrderIso", "kind": "definition", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.tropOrderIso_coe_fn", "kind": "theorem", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.tropOrderIso_symm_coe_fn", "kind": "theorem", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.trop_monotone", "kind": "theorem", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.untrop_monotone", "kind": "theorem", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.instPartialOrderTropical", "kind": "instance", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.instZeroTropical", "kind": "instance", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.instTopTropical", "kind": "instance", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.untrop_zero", "kind": "theorem", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.trop_top", "kind": "theorem", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.trop_coe_ne_zero", "kind": "theorem", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.zero_ne_trop_coe", "kind": "theorem", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.le_zero", "kind": "theorem", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.instOrderTop", "kind": "instance", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.instAdd", "kind": "instance", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.instAddCommSemigroupTropical", "kind": "instance", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.untrop_add", "kind": "theorem", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.trop_min", "kind": "theorem", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.trop_inf", "kind": "theorem", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.trop_add_def", "kind": "theorem", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.instLinearOrderTropical", "kind": "instance", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.untrop_sup", "kind": "theorem", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.untrop_max", "kind": "theorem", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.min_eq_add", "kind": "theorem", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.inf_eq_add", "kind": "theorem", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.trop_max_def", "kind": "theorem", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.trop_sup_def", "kind": "theorem", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.add_eq_left", "kind": "theorem", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.add_eq_right", "kind": "theorem", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.add_eq_left_iff", "kind": "theorem", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Tropical.add_eq_right_iff", "kind": "theorem", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Tropical.add_self", "kind": "theorem", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Tropical.instMulOfAdd", "kind": "instance", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Tropical.untrop_mul", "kind": "theorem", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.trop_mul_def", "kind": "theorem", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.instOneTropical", "kind": "instance", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.trop_zero", "kind": "theorem", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.untrop_one", "kind": "theorem", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.instAddMonoidWithOneTropical", "kind": "instance", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.instNontrivialWithTopOfZero", "kind": "instance", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.instInvOfNeg", "kind": "instance", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.untrop_inv", "kind": "theorem", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.instDivOfSub", "kind": "instance", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.untrop_div", "kind": "theorem", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.instSemigroupTropical", "kind": "instance", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Tropical.instPowOfSMul", "kind": "instance", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.untrop_pow", "kind": "theorem", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.trop_smul", "kind": "theorem", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.instMulOneClassTropical", "kind": "instance", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.instMonoidTropical", "kind": "instance", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.trop_nsmul", "kind": "theorem", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.instCommMonoidTropical", "kind": "instance", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Tropical.instCommGroupOfAddCommGroup", "kind": "instance", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.untrop_zpow", "kind": "theorem", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.trop_zsmul", "kind": "theorem", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.mulLeftMono", "kind": "instance", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.mulRightMono", "kind": "instance", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.addLeftMono", "kind": "instance", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.mulLeftStrictMono", "kind": "instance", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.mulRightStrictMono", "kind": "instance", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.instDistribTropical", "kind": "instance", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Tropical.instCommSemiring", "kind": "instance", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tropical.succ_nsmul", "kind": "theorem", "module": "Mathlib.Algebra.Tropical.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw"], "tactic_count": 4}
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{"name": "List.trop_sum", "kind": "theorem", "module": "Mathlib.Algebra.Tropical.BigOperators", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
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{"name": "instSupSetTropical", "kind": "instance", "module": "Mathlib.Algebra.Tropical.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "instConditionallyCompleteLatticeTropical", "kind": "instance", "module": "Mathlib.Algebra.Tropical.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instConditionallyCompleteLinearOrderTropical", "kind": "instance", "module": "Mathlib.Algebra.Tropical.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AlgebraicGeometry.AffineScheme", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instIsIsoSchemeAppUnitOppositeCommRingCatAdjunctionOfIsAffine", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AlgebraicGeometry.Scheme.isoSpec_hom_naturality", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "AlgebraicGeometry.AffineScheme.ofHom", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.essImage_Spec", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AlgebraicGeometry.IsAffineOpen.preimage_of_isOpenImmersion", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "AlgebraicGeometry.IsOpenImmersion.affineOpensEquiv", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.affineOpensRestrict", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.affineOpensRestrict_symm_apply_coe", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.compactSpace_of_isAffine", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsAffineOpen.fromSpec_preimage_self", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "AlgebraicGeometry.IsAffineOpen.ΓSpecIso_hom_fromSpec_app", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": true, "tactics": ["change", "simp"], "tactic_count": 2}
{"name": "AlgebraicGeometry.IsAffineOpen.fromSpec_app_self", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgebraicGeometry.IsAffineOpen.fromSpec_preimage_basicOpen'", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "AlgebraicGeometry.IsAffineOpen.fromSpec_preimage_basicOpen", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgebraicGeometry.IsAffineOpen.fromSpec_image_basicOpen", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": true, "tactics": ["rw", "ext1", "change", "rw", "exact"], "tactic_count": 5}
{"name": "AlgebraicGeometry.IsAffineOpen.basicOpen_fromSpec_app", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgebraicGeometry.IsAffineOpen.basicOpen", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": true, "tactics": ["rw", "convert", "exact"], "tactic_count": 3}
{"name": "AlgebraicGeometry.IsAffineOpen.Spec_basicOpen", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsAffineOpen.instIsAffineToSchemeBasicOpen", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsAffineOpen.ι_basicOpen_preimage", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": true, "tactics": ["apply", "rw", "exact"], "tactic_count": 3}
{"name": "AlgebraicGeometry.IsAffineOpen.exists_basicOpen_le", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": true, "tactics": ["have", "obtain", "replace", "replace", "simpa", "exact"], "tactic_count": 6}
{"name": "AlgebraicGeometry.IsAffineOpen.instAlgebraCarrierObjOppositeOpensCarrierCarrierCommRingCatSpecPresheafOpOpens", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsAffineOpen.algebraMap_Spec_obj", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsAffineOpen.instAwayCarrierObjOppositeOpensCarrierCarrierCommRingCatSpecPresheafOpOpensBasicOpen", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsAffineOpen.basicOpenSectionsToAffine", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsAffineOpen.basicOpenSectionsToAffine_isIso", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsAffineOpen.isLocalization_basicOpen", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": false, "tactics": ["apply", "convert", "congr", "dsimp", "rw", "simp", "exact"], "tactic_count": 7}
{"name": "AlgebraicGeometry.isLocalization_away_of_isAffine", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsAffineOpen.appLE_eq_away_map", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": true, "tactics": ["letI", "letI", "ext", "apply", "rw"], "tactic_count": 5}
{"name": "AlgebraicGeometry.IsAffineOpen.app_basicOpen_eq_away_map", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": true, "tactics": ["haveI", "haveI", "ext", "apply", "rw", "simp"], "tactic_count": 6}
{"name": "AlgebraicGeometry.IsAffineOpen.appBasicOpenIsoAwayMap", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsAffineOpen.isLocalization_of_eq_basicOpen", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Γ_restrict_isLocalization", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsAffineOpen.basicOpen_basicOpen_is_basicOpen", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": true, "tactics": ["have", "obtain", "use", "rw", "refine", "exact"], "tactic_count": 6}
{"name": "AlgebraicGeometry.exists_basicOpen_le_affine_inter", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "obtain", "replace", "exact"], "tactic_count": 5}
{"name": "AlgebraicGeometry.IsAffineOpen.primeIdealOf", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsAffineOpen.fromSpec_primeIdealOf", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "rfl"], "tactic_count": 3}
{"name": "AlgebraicGeometry.IsAffineOpen.primeIdealOf_eq_map_closedPoint", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsAffineOpen.primeIdealOf_isMaximal_of_isClosed", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": false, "tactics": ["have", "simpa", "hx.preimage", "apply", "rw", "refine", "apply", "infer_instance"], "tactic_count": 8}
{"name": "AlgebraicGeometry.IsAffineOpen.isLocalization_stalk'", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": false, "tactics": ["apply", "y.asIdeal.primeCompl", "convert", "delta", "congr", "simp", "rfl"], "tactic_count": 7}
{"name": "AlgebraicGeometry.IsAffineOpen.isLocalization_stalk", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": true, "tactics": ["rcases", "set", "have", "clear_value", "subst", "exact"], "tactic_count": 6}
{"name": "AlgebraicGeometry.IsAffineOpen.stalkMap_injective", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": true, "tactics": ["letI", "apply", "exact"], "tactic_count": 3}
{"name": "AlgebraicGeometry.IsAffineOpen.mem_ideal_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": true, "tactics": ["refine", "letI", "have", "hU.isLocalization_stalk", "refine", "intro", "rw", "exact"], "tactic_count": 8}
{"name": "AlgebraicGeometry.IsAffineOpen.ideal_le_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsAffineOpen.ideal_ext_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.affineBasicOpen", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.affineBasicOpen_le", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsAffineOpen.iSup_basicOpen_eq_self_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": true, "tactics": ["trans", "trans", "refine", "intro", "apply_fun", "rw", "simp", "ext1", "refine", "simp", "intro", "exact", "simp", "congr", "refine", "ext1", "exact", "exact", "simp", "rw", "simp"], "tactic_count": 21}
{"name": "AlgebraicGeometry.IsAffineOpen.self_le_iSup_basicOpen_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp", "intro", "exact"], "tactic_count": 5}
{"name": "AlgebraicGeometry.SpecMapRestrictBasicOpenIso", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": true, "tactics": ["letI", "letI", "refine", "exact", "exact", "have", "rw", "simp", "conv", "congr", "enter", "tactic", "change", "ext", "simp", "enter", "tactic", "change", "ext", "simp", "simp", "morphismRestrict_ι_assoc]", "simp", "rfl"], "tactic_count": 24}
{"name": "AlgebraicGeometry.stalkMap_injective_of_isAffine", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.iSup_basicOpen_of_span_eq_top", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": true, "tactics": ["apply", "rw", "exact", "intro", "obtain", "refine", "rw", "simp", "exact"], "tactic_count": 9}
{"name": "AlgebraicGeometry.of_affine_open_cover", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": true, "tactics": ["classical", "have", "intro", "obtain", "obtain", "refine", "convert", "ext1", "exact", "choose", "suffices", "obtain", "apply", "rintro", "obtain", "exact", "rw", "intro", "rw", "exact"], "tactic_count": 20}
{"name": "AlgebraicGeometry.eq_of_SpecMap_comp_eq_of_isAffineOpen", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": true, "tactics": ["have", "rw", "congr", "rw", "simp"], "tactic_count": 5}
{"name": "AlgebraicGeometry.Scheme.toSpecΓ_preimage_zeroLocus", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.isoSpec_image_zeroLocus", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.toSpecΓ_image_zeroLocus", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.isoSpec_inv_preimage_zeroLocus", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": false, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.isoSpec_inv_image_zeroLocus", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.eq_zeroLocus_of_isClosed_of_isAffine", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": true, "tactics": ["refine", "let", "have", "obtain", "use", "simp", "symm", "exact", "rintro", "exact"], "tactic_count": 10}
{"name": "AlgebraicGeometry.Scheme.Opens.toSpecΓ_preimage_basicOpen", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": true, "tactics": ["dsimp", "simp", "rw", "congr", "simp", "rfl"], "tactic_count": 6}
{"name": "AlgebraicGeometry.Scheme.Opens.toSpecΓ_preimage_zeroLocus", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": true, "tactics": ["ext", "refine", "exact"], "tactic_count": 3}
{"name": "AlgebraicGeometry.IsAffineOpen.fromSpec_preimage_zeroLocus", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": true, "tactics": ["ext", "suffices", "simp_rw", "rfl"], "tactic_count": 4}
{"name": "AlgebraicGeometry.IsAffineOpen.fromSpec_image_zeroLocus", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.zeroLocus_inf", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": false, "tactics": ["suffices", "ext", "by_cases", "simpa", "simp", "codisjoint_iff_compl_le_left.mp", "codisjoint_iff_compl_le_left.mp", "simp"], "tactic_count": 8}
{"name": "AlgebraicGeometry.Scheme.zeroLocus_biInf", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": true, "tactics": ["refine", "simp", "congr", "simp"], "tactic_count": 4}
{"name": "AlgebraicGeometry.Scheme.zeroLocus_biInf_of_nonempty", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": true, "tactics": ["rw", "obtain", "exact"], "tactic_count": 3}
{"name": "AlgebraicGeometry.Scheme.zeroLocus_iInf", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.zeroLocus_iInf_of_nonempty", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Hom.liftQuotient", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.liftQuotient_comp", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": false, "tactics": ["rw", "simp", "simp"], "tactic_count": 3}
{"name": "AlgebraicGeometry.specTargetImageIdeal", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.specTargetImage", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.specTargetImageFactorization", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.specTargetImageRingHom", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.specTargetImageRingHom_surjective", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.specTargetImageFactorization_app_injective", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": true, "tactics": ["let", "let", "change", "rw", "apply", "exact"], "tactic_count": 6}
{"name": "AlgebraicGeometry.specTargetImageFactorization_comp", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.localRingHom_comp_stalkIso", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.arrowStalkMapSpecIso", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.AffineScheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.AlgebraicGeometry.AffineSpace.0.AlgebraicGeometry.termℤ[_]", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.AffineSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.AlgebraicGeometry.AffineSpace.0.AlgebraicGeometry._aux_Mathlib_AlgebraicGeometry_AffineSpace___macroRules__private_Mathlib_AlgebraicGeometry_AffineSpace_0_AlgebraicGeometry_termℤ[_]_1", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.AffineSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.AlgebraicGeometry.AffineSpace.0.AlgebraicGeometry._aux_Mathlib_AlgebraicGeometry_AffineSpace___delab_app__private_Mathlib_AlgebraicGeometry_AffineSpace_0_AlgebraicGeometry_termℤ[_]_1", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.AffineSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.AlgebraicGeometry.AffineSpace.0.AlgebraicGeometry.termℤ[_].{_,_}", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.AffineSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.AlgebraicGeometry.AffineSpace.0.AlgebraicGeometry._aux_Mathlib_AlgebraicGeometry_AffineSpace___macroRules__private_Mathlib_AlgebraicGeometry_AffineSpace_0_AlgebraicGeometry_termℤ[_].{_,_}_1", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.AffineSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.AlgebraicGeometry.AffineSpace.0.AlgebraicGeometry._aux_Mathlib_AlgebraicGeometry_AffineSpace___delab_app__private_Mathlib_AlgebraicGeometry_AffineSpace_0_AlgebraicGeometry_termℤ[_].{_,_}_1", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.AffineSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.AffineSpace", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.AffineSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.term𝔸(_;_)", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.AffineSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AlgebraicGeometry._aux_Mathlib_AlgebraicGeometry_AffineSpace___unexpand_AlgebraicGeometry_AffineSpace_1", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.AffineSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.AffineSpace.of_mvPolynomial_int_ext", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineSpace", "is_tactic_proof": false, "tactics": ["suffices", "f.hom.comp", "g.hom.comp", "ext", "obtain", "simpa", "simpa", "ext1", "exact", "simpa"], "tactic_count": 10}
{"name": "AlgebraicGeometry.AffineSpace.over", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.AffineSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.AffineSpace.toSpecMvPoly", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.AffineSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.AffineSpace.toSpecMvPolyIntEquiv", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.AffineSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.AffineSpace.toSpecMvPolyIntEquiv_comp", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.AffineSpace.coord", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.AffineSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.AffineSpace.homOfVector", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.AffineSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.AffineSpace.homOfVector_over", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.AffineSpace.homOfVector_toSpecMvPoly", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.AffineSpace.homOfVector_appTop_coord", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineSpace", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgebraicGeometry.AffineSpace.hom_ext", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineSpace", "is_tactic_proof": true, "tactics": ["apply", "change", "apply", "ext", "rw", "exact"], "tactic_count": 6}
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{"name": "AlgebraicGeometry.AffineSpace.instIsOverHomOfVectorOverSchemeInferInstanceOverClass", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.AffineSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AlgebraicGeometry.AffineSpace.map_appTop_coord", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.AffineSpace.map_toSpecMvPoly", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineSpace", "is_tactic_proof": true, "tactics": ["apply", "ext", "rw"], "tactic_count": 3}
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{"name": "AlgebraicGeometry.AffineSpace.map_SpecMap", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineSpace", "is_tactic_proof": true, "tactics": ["rw", "ext1", "simp", "rw", "simp", "conv_lhs", "conv_rhs", "rw"], "tactic_count": 8}
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{"name": "AlgebraicGeometry.AffineSpace.isPullback_map", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineSpace", "is_tactic_proof": true, "tactics": ["refine", "simp", "convert", "rw"], "tactic_count": 4}
{"name": "AlgebraicGeometry.AffineSpace.reindex", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.AffineSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.AffineSpace.reindex_over", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.AffineSpace.reindex_appTop_coord", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.AffineSpace.reindex_id", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineSpace", "is_tactic_proof": true, "tactics": ["ext1"], "tactic_count": 1}
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{"name": "AlgebraicGeometry.AffineSpace.functor", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.AffineSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.AffineSpace.instIsAffineHomOverSchemeInferInstanceOverClass", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.AffineSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.AffineSpace.instSurjectiveOverSchemeInferInstanceOverClass", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.AffineSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.AffineSpace.instLocallyOfFinitePresentationOverSchemeInferInstanceOverClassOfFinite", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.AffineSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.AffineSpace.isOpenMap_over", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineSpace", "is_tactic_proof": true, "tactics": ["change", "wlog", "refine", "intro", "have", "rwa", "obtain", "rw", "exact"], "tactic_count": 9}
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{"name": "AlgebraicGeometry.AffineSpace.not_isIntegralHom", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineSpace", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.AffineSpace.spec_le_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineSpace", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "AlgebraicGeometry.AffineSpace._example", "kind": "example", "module": "Mathlib.AlgebraicGeometry.AffineSpace", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.nonempty_of_isLimit", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineTransitionLimit", "is_tactic_proof": true, "tactics": ["classical", "cases", "have", "exact", "have", "have", "let", "have", "obtain", "by_contra", "choose", "let", "have", "let", "pullback.map", "rw", "simp", "simp", "exact", "exact", "obtain", "exact", "let", "have", "have", "isAffine_of_isAffineHom", "have", "let", "have", "have", "let", "have", "apply", "have", "apply", "simp", "exact", "let", "exact", "this.map"], "tactic_count": 40}
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{"name": "AlgebraicGeometry.exists_mem_of_isClosed_of_nonempty'", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineTransitionLimit", "is_tactic_proof": true, "tactics": ["have", "simpa", "exists_mem_of_isClosed_of_nonempty"], "tactic_count": 3}
{"name": "AlgebraicGeometry.exists_map_eq_top", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineTransitionLimit", "is_tactic_proof": true, "tactics": ["by_contra", "obtain", "exists_mem_of_isClosed_of_nonempty", "simp", "exact", "exact"], "tactic_count": 6}
{"name": "AlgebraicGeometry.opensDiagram", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.AffineTransitionLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.opensDiagramι", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.AffineTransitionLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instIsOpenImmersionAppOverSchemeOpensDiagramι", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.AffineTransitionLimit", "is_tactic_proof": true, "tactics": ["delta"], "tactic_count": 1}
{"name": "AlgebraicGeometry.opensCone", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.AffineTransitionLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.isLimitOpensCone", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.AffineTransitionLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instIsAffineHomMapOverSchemeOpensDiagram", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.AffineTransitionLimit", "is_tactic_proof": true, "tactics": ["refine", "convert", "ext", "change", "refine", "change", "rw", "exact", "convert", "exact", "rintro", "convert", "exact", "simp", "rintro", "obtain", "dsimp", "rw", "rwa"], "tactic_count": 19}
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{"name": "AlgebraicGeometry.isBasis_preimage_isAffineOpen", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineTransitionLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AlgebraicGeometry.Scheme.compactSpace_of_isLimit", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineTransitionLimit", "is_tactic_proof": true, "tactics": ["obtain", "have", "exact"], "tactic_count": 3}
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{"name": "AlgebraicGeometry.ExistsHomHomCompEqCompAux.hii'", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.AffineTransitionLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AlgebraicGeometry.ExistsHomHomCompEqCompAux.range_g_subset", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.AffineTransitionLimit", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "AlgebraicGeometry.ExistsHomHomCompEqCompAux.𝒰D₀", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.AffineTransitionLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AlgebraicGeometry.IsLocallyArtinian.of_isLocallyNoetherian_of_discreteTopology", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Artinian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AlgebraicGeometry.instIsLocallyArtinianXScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Artinian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsLocallyArtinian.discreteTopology", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Artinian", "is_tactic_proof": true, "tactics": ["apply", "intro", "obtain", "have", "have", "have", "simpa"], "tactic_count": 7}
{"name": "AlgebraicGeometry.IsLocallyArtinian.iff_isLocallyNoetherian_and_discreteTopology", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Artinian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsLocallyArtinian.of_isImmersion", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Artinian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.isLocallyArtinianScheme_Spec", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Artinian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.isLocallyArtinian_iff_openCover", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Artinian", "is_tactic_proof": true, "tactics": ["refine", "refine", "exact", "refine", "obtain", "simpa"], "tactic_count": 6}
{"name": "AlgebraicGeometry.isLocallyArtinian_iff_of_isOpenCover", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Artinian", "is_tactic_proof": true, "tactics": ["refine", "rw", "have", "exact"], "tactic_count": 4}
{"name": "AlgebraicGeometry.IsArtinianScheme.finite", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Artinian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsArtinianScheme.isNoetherianScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Artinian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsArtinianScheme.iff_isNoetherian_and_discreteTopology", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Artinian", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "AlgebraicGeometry.instIsArtinianSchemeSpecOfIsArtinianRingCarrier", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Artinian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.isArtinianScheme_Spec", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Artinian", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Cover.ColimitGluingData.trans", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.ColimitsOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Cover.ColimitGluingData.transitionCocone", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.ColimitsOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Cover.ColimitGluingData.transitionMap", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.ColimitsOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Cover.ColimitGluingData.cocone_ι_transitionMap", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ColimitsOver", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Cover.ColimitGluingData.transitionMap_id", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ColimitsOver", "is_tactic_proof": true, "tactics": ["apply", "intro", "ext", "simp"], "tactic_count": 4}
{"name": "AlgebraicGeometry.Scheme.Cover.ColimitGluingData.transitionMap_comp", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ColimitsOver", "is_tactic_proof": true, "tactics": ["apply", "intro", "ext", "simp"], "tactic_count": 4}
{"name": "AlgebraicGeometry.Scheme.Cover.ColimitGluingData.functor", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.ColimitsOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Cover.ColimitGluingData.isPullback", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ColimitsOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Cover.ColimitGluingData.relativeGluingData", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.ColimitsOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Cover.ColimitGluingData.glued", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.ColimitsOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Cover.ColimitGluingData.pullbackGluedIso", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.ColimitsOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Cover.ColimitGluingData.pullbackGluedIso_inv_fst", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ColimitsOver", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Cover.ColimitGluingData.pullbackGluedIso_inv_snd", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ColimitsOver", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Cover.ColimitGluingData.gluedCocone", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.ColimitsOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Cover.ColimitGluingData.fst_gluedCocone_ι", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ColimitsOver", "is_tactic_proof": true, "tactics": ["simp", "generalize_proofs", "let", "apply"], "tactic_count": 4}
{"name": "AlgebraicGeometry.Scheme.Cover.ColimitGluingData.isColimitGluedCocone", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.ColimitsOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Cover.hasColimit_of_locallyDirected", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ColimitsOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Cover.trans", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Cover.Directed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Cover.trans_map", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Cover.Directed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Cover.trans_id", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Cover.Directed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Cover.trans_comp", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Cover.Directed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Cover.exists_lift_trans_eq", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Cover.Directed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Cover.exists_of_f_eq_f", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Cover.Directed", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "use", "simp"], "tactic_count": 4}
{"name": "AlgebraicGeometry.Scheme.Cover.exists_of_trans_eq_trans", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Cover.Directed", "is_tactic_proof": false, "tactics": ["have", "rw", "obtain", "obtain", "refine"], "tactic_count": 5}
{"name": "AlgebraicGeometry.Scheme.Cover.property_trans", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Cover.Directed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Cover.intersectionOfLocallyDirected", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Cover.Directed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Cover.functorOfLocallyDirected", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Cover.Directed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Cover.instIsLocallyDirectedI₀CompFunctorOfLocallyDirectedForget", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Cover.Directed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Cover.functorOfLocallyDirectedHomBase", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Cover.Directed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Cover.coconeOfLocallyDirected", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Cover.Directed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Cover.instCategoryI₀Pullback₁", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Cover.Directed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Cover.locallyDirectedPullbackCover", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Cover.Directed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.OpenCover.instIsOpenImmersionTrans", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Cover.Directed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.OpenCover.instIsOpenImmersionMapI₀FunctorOfLocallyDirected", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Cover.Directed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.OpenCover.glueMorphismsOfLocallyDirected", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Cover.Directed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.OpenCover.map_glueMorphismsOfLocallyDirected", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Cover.Directed", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.OpenCover.isColimitCoconeOfLocallyDirected", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Cover.Directed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.OpenCover.glueMorphismsOverOfLocallyDirected", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Cover.Directed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.OpenCover.map_glueMorphismsOverOfLocallyDirected_left", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Cover.Directed", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Cover.LocallyDirected.ofIsBasisOpensRange", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Cover.Directed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Cover.LocallyDirected.ofIsBasisOpensRange_le_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Cover.Directed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Cover.LocallyDirected.ofIsBasisOpensRange_trans", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Cover.Directed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.directedAffineCover", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Cover.Directed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.instPreorderI₀DirectedAffineCover", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Cover.Directed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.instLocallyDirectedIsOpenImmersionDirectedAffineCover", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Cover.Directed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.directedAffineCover_trans", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Cover.Directed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Cover", "kind": "abbrev", "module": "Mathlib.AlgebraicGeometry.Cover.MorphismProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Cover.exists_eq", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Cover.MorphismProperty", "is_tactic_proof": true, "tactics": ["obtain", "use"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.Cover.idx", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Cover.MorphismProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Cover.covers", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Cover.MorphismProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Cover.iUnion_range", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Cover.MorphismProperty", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "exact"], "tactic_count": 4}
{"name": "AlgebraicGeometry.Scheme.Cover.nonempty_of_nonempty", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Cover.MorphismProperty", "is_tactic_proof": true, "tactics": ["obtain", "use"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.presieve₀_mem_precoverage_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Cover.MorphismProperty", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Cover.map_prop", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Cover.MorphismProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.coverOfIsIso", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Cover.MorphismProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.instJointlySurjectivePrecoverage", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Cover.MorphismProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Cover.changeProp", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Cover.MorphismProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Cover.copy", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Cover.MorphismProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Cover.pushforwardIso", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Cover.MorphismProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Cover.pullbackHom", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Cover.MorphismProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Cover.pullbackHom_map", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Cover.MorphismProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.AffineCover.cover", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Cover.MorphismProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Cover.ulift", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Cover.MorphismProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.instSmallPrecoverage", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Cover.MorphismProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Cover.Hom", "kind": "abbrev", "module": "Mathlib.AlgebraicGeometry.Cover.MorphismProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.instHasPullbacksIsOpenImmersion", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Cover.Open", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.OpenCover", "kind": "abbrev", "module": "Mathlib.AlgebraicGeometry.Cover.Open", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.instIsOpenImmersionF", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Cover.Open", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.affineCover", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Cover.Open", "is_tactic_proof": true, "tactics": ["choose", "let", "exact", "f", "mem₀", "rw", "refine", "change", "cat_disch"], "tactic_count": 9}
{"name": "AlgebraicGeometry.Scheme.instInhabitedOpenCover", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Cover.Open", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.OpenCover.iSup_opensRange", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Cover.Open", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.OpenCover.isOpenCover_opensRange", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Cover.Open", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.OpenCover.finiteSubcover", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Cover.Open", "is_tactic_proof": false, "tactics": ["have", "let", "have", "intro", "have", "rw", "rcases", "exact", "exact", "f", "mem₀", "rw", "exact"], "tactic_count": 13}
{"name": "AlgebraicGeometry.Scheme.instFintypeI₀FiniteSubcover", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Cover.Open", "is_tactic_proof": true, "tactics": ["delta"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.OpenCover.compactSpace", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Cover.Open", "is_tactic_proof": true, "tactics": ["cases", "rw", "apply", "intro", "rw", "exact"], "tactic_count": 6}
{"name": "AlgebraicGeometry.Scheme.AffineOpenCover", "kind": "abbrev", "module": "Mathlib.AlgebraicGeometry.Cover.Open", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.AffineOpenCover.instIsOpenImmersionF", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Cover.Open", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.AffineOpenCover.openCover", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Cover.Open", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.affineOpenCover", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Cover.Open", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.openCover_affineOpenCover", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Cover.Open", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.OpenCover.affineRefinement", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Cover.Open", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.OpenCover.pullbackCoverAffineRefinementObjIso", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Cover.Open", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.OpenCover.pullbackCoverAffineRefinementObjIso_inv_map", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Cover.Open", "is_tactic_proof": false, "tactics": ["simp", "asIso_inv,", "pullbackSymmetry_hom_comp_fst]", "convert", "exact"], "tactic_count": 5}
{"name": "AlgebraicGeometry.Scheme.OpenCover.pullbackCoverAffineRefinementObjIso_inv_pullbackHom", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Cover.Open", "is_tactic_proof": false, "tactics": ["simp", "asIso_inv,", "convert", "exact"], "tactic_count": 4}
{"name": "AlgebraicGeometry.Scheme.affineOpenCoverOfSpanRangeEqTop", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Cover.Open", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.OpenCover.fromAffineRefinement", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Cover.Open", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.OpenCover.ext_elem", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Cover.Open", "is_tactic_proof": false, "tactics": ["fapply", "intro", "simp", "refine", "simpa", "intro", "replace", "rw", "exact"], "tactic_count": 9}
{"name": "AlgebraicGeometry.Scheme.zero_of_zero_cover", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Cover.Open", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.isNilpotent_of_isNilpotent_cover", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Cover.Open", "is_tactic_proof": true, "tactics": ["choose", "have", "let", "have", "use", "apply", "on_goal", "simp", "exact"], "tactic_count": 9}
{"name": "AlgebraicGeometry.Scheme.affineBasisCoverOfAffine", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Cover.Open", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.affineBasisCover", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Cover.Open", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.affineBasisCoverRing", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Cover.Open", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.affineBasisCover_obj", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Cover.Open", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.affineBasisCover_map_range", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Cover.Open", "is_tactic_proof": false, "tactics": ["simp", "congr", "exact"], "tactic_count": 3}
{"name": "AlgebraicGeometry.Scheme.affineBasisCover_is_basis", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Cover.Open", "is_tactic_proof": true, "tactics": ["apply", "rintro", "exact", "rintro", "rcases", "let", "have", "rcases", "refine", "exact", "rw"], "tactic_count": 11}
{"name": "AlgebraicGeometry.Scheme.asOverProp", "kind": "abbrev", "module": "Mathlib.AlgebraicGeometry.Cover.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.asOverProp", "kind": "abbrev", "module": "Mathlib.AlgebraicGeometry.Cover.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.instOverCoverOfIsIsoOfIsOver", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Cover.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Cover.pullbackCoverOver", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Cover.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.instOverXPullbackCoverOver", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Cover.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AlgebraicGeometry.QuasiCompactCover.homCover", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Cover.QuasiCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AlgebraicGeometry.QuasiCompactCover.instCoverOfIsIso", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Cover.QuasiCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.QuasiCompactCover.instSumScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Cover.QuasiCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.QuasiCompactCover.instSumScheme_1", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Cover.QuasiCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AlgebraicGeometry.Scheme.quasiCompactCover_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Cover.QuasiCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "WeierstrassCurve.Affine.equation_neg", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Formula", "is_tactic_proof": true, "tactics": ["rw", "congr", "ring1"], "tactic_count": 3}
{"name": "WeierstrassCurve.Affine.nonsingular_neg", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Formula", "is_tactic_proof": true, "tactics": ["rw", "exact", "and_congr_right"], "tactic_count": 3}
{"name": "WeierstrassCurve.Affine.linePolynomial", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Formula", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeierstrassCurve.Affine.slope", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Formula", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeierstrassCurve.Affine.slope_of_Y_eq", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Formula", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "WeierstrassCurve.Affine.slope_of_Y_ne'", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Formula", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WeierstrassCurve.Affine.slope_of_Y_ne", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Formula", "is_tactic_proof": true, "tactics": ["simp_all"], "tactic_count": 1}
{"name": "WeierstrassCurve.Affine.slope_of_X_ne", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Formula", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "WeierstrassCurve.Affine.slope_of_Y_ne_eq_evalEval", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Formula", "is_tactic_proof": true, "tactics": ["rw", "congr", "rw", "ring1"], "tactic_count": 4}
{"name": "WeierstrassCurve.Affine.addPolynomial", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Formula", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeierstrassCurve.Affine.C_addPolynomial", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Formula", "is_tactic_proof": true, "tactics": ["rw", "eval_simp", "ring1"], "tactic_count": 3}
{"name": "WeierstrassCurve.Affine.addPolynomial_eq", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Formula", "is_tactic_proof": true, "tactics": ["rw", "eval_simp", "ring1"], "tactic_count": 3}
{"name": "WeierstrassCurve.Affine.addX", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Formula", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeierstrassCurve.Affine.negAddY", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Formula", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeierstrassCurve.Affine.addY", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Formula", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeierstrassCurve.Affine.addPolynomial_slope", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Formula", "is_tactic_proof": true, "tactics": ["rw", "by_cases", "have", "rcases", "rw", "rw", "rw", "replace", "ext", "rfl", "simp", "ring1", "simp", "ring1", "linear_combination", "rw", "rw", "simp", "grind"], "tactic_count": 19}
{"name": "WeierstrassCurve.Affine.C_addPolynomial_slope", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Formula", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "WeierstrassCurve.Affine.derivative_addPolynomial_slope", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Formula", "is_tactic_proof": true, "tactics": ["rw", "derivative_simp", "ring1"], "tactic_count": 3}
{"name": "WeierstrassCurve.Affine.nonsingular_negAdd_of_eval_derivative_ne_zero", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Formula", "is_tactic_proof": true, "tactics": ["rw", "eval_simp", "contrapose", "rw", "eval_simp", "derivative_simp", "simp", "eval_simp", "linear_combination"], "tactic_count": 9}
{"name": "WeierstrassCurve.Affine.equation_add_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Formula", "is_tactic_proof": true, "tactics": ["rw", "eval_simp"], "tactic_count": 2}
{"name": "WeierstrassCurve.Affine.equation_negAdd", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Formula", "is_tactic_proof": true, "tactics": ["rw", "eval_simp", "rw"], "tactic_count": 3}
{"name": "WeierstrassCurve.Affine.equation_add", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Formula", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeierstrassCurve.Affine.nonsingular_negAdd", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Formula", "is_tactic_proof": true, "tactics": ["by_cases", "rwa", "by_cases", "by_cases", "subst", "contradiction", "rwa", "sub_add_cancel]", "apply", "rw", "eval_simp", "simp", "exact"], "tactic_count": 13}
{"name": "WeierstrassCurve.Affine.nonsingular_add", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Formula", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeierstrassCurve.Affine.addX_eq_addX_negY_sub", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Formula", "is_tactic_proof": true, "tactics": ["simp_rw", "simp", "ring1"], "tactic_count": 3}
{"name": "WeierstrassCurve.Affine.cyclic_sum_Y_mul_X_sub_X", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Formula", "is_tactic_proof": true, "tactics": ["simp_rw", "simp", "ring1"], "tactic_count": 3}
{"name": "WeierstrassCurve.Affine.addY_sub_negY_addY", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Formula", "is_tactic_proof": true, "tactics": ["simp_rw", "linear_combination"], "tactic_count": 2}
{"name": "WeierstrassCurve.Affine.map_negPolynomial", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Formula", "is_tactic_proof": true, "tactics": ["simp", "map_simp"], "tactic_count": 2}
{"name": "WeierstrassCurve.Affine.map_negY", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Formula", "is_tactic_proof": true, "tactics": ["simp", "map_simp"], "tactic_count": 2}
{"name": "WeierstrassCurve.Affine.map_linePolynomial", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Formula", "is_tactic_proof": true, "tactics": ["simp", "map_simp"], "tactic_count": 2}
{"name": "WeierstrassCurve.Affine.map_addPolynomial", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Formula", "is_tactic_proof": false, "tactics": ["rw", "linePolynomial]", "simp"], "tactic_count": 3}
{"name": "WeierstrassCurve.Affine.map_addX", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Formula", "is_tactic_proof": true, "tactics": ["simp", "map_simp"], "tactic_count": 2}
{"name": "WeierstrassCurve.Affine.map_negAddY", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Formula", "is_tactic_proof": true, "tactics": ["simp", "map_simp"], "tactic_count": 2}
{"name": "WeierstrassCurve.Affine.map_addY", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Formula", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WeierstrassCurve.Affine.map_slope", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Formula", "is_tactic_proof": true, "tactics": ["by_cases", "by_cases", "rw", "rw", "slope_of_Y_ne", "map_simp", "rw", "map_simp"], "tactic_count": 8}
{"name": "WeierstrassCurve.Affine.baseChange_negPolynomial", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Formula", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "WeierstrassCurve.Affine.baseChange_negY", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Formula", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "WeierstrassCurve.Affine.baseChange_addPolynomial", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Formula", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "WeierstrassCurve.Affine.baseChange_addX", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Formula", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "WeierstrassCurve.Affine.baseChange_negAddY", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Formula", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "WeierstrassCurve.Affine.baseChange_addY", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Formula", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "WeierstrassCurve.Affine.baseChange_slope", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Formula", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "_private.Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point.0.tacticC_simp", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point.0._aux_Mathlib_AlgebraicGeometry_EllipticCurve_Affine_Point___macroRules__private_Mathlib_AlgebraicGeometry_EllipticCurve_Affine_Point_0_tacticC_simp_1", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeierstrassCurve.Affine.CoordinateRing", "kind": "abbrev", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeierstrassCurve.Affine.FunctionField", "kind": "abbrev", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeierstrassCurve.Affine.CoordinateRing.instAlgebra", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeierstrassCurve.Affine.CoordinateRing.instAlgebraPolynomial", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeierstrassCurve.Affine.CoordinateRing.instIsScalarTowerPolynomial", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeierstrassCurve.Affine.CoordinateRing.instSubsingleton", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeierstrassCurve.Affine.CoordinateRing.mk", "kind": "abbrev", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeierstrassCurve.Affine.CoordinateRing.basis", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeierstrassCurve.Affine.CoordinateRing.basis_apply", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point", "is_tactic_proof": true, "tactics": ["classical", "nontriviality", "rw", "finCongr_symm_apply,"], "tactic_count": 4}
{"name": "WeierstrassCurve.Affine.CoordinateRing.basis_zero", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "WeierstrassCurve.Affine.CoordinateRing.basis_one", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "WeierstrassCurve.Affine.CoordinateRing.coe_basis", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point", "is_tactic_proof": true, "tactics": ["ext", "fin_cases", "exacts"], "tactic_count": 3}
{"name": "WeierstrassCurve.Affine.CoordinateRing.smul", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeierstrassCurve.Affine.CoordinateRing.smul_basis_eq_zero", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "WeierstrassCurve.Affine.CoordinateRing.exists_smul_basis_eq", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "WeierstrassCurve.Affine.CoordinateRing.smul_basis_mul_C", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point", "is_tactic_proof": true, "tactics": ["simp", "ring1"], "tactic_count": 2}
{"name": "WeierstrassCurve.Affine.CoordinateRing.smul_basis_mul_Y", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point", "is_tactic_proof": false, "tactics": ["have", "mk", "simp", "ring1"], "tactic_count": 4}
{"name": "WeierstrassCurve.Affine.CoordinateRing.map", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeierstrassCurve.Affine.CoordinateRing.map_mk", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "WeierstrassCurve.Affine.CoordinateRing.map_smul", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "WeierstrassCurve.Affine.CoordinateRing.map_injective", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeierstrassCurve.Affine.CoordinateRing.instIsDomain", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeierstrassCurve.Affine.CoordinateRing.XClass", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeierstrassCurve.Affine.CoordinateRing.XClass_ne_zero", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeierstrassCurve.Affine.CoordinateRing.YClass", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeierstrassCurve.Affine.CoordinateRing.YClass_ne_zero", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeierstrassCurve.Affine.CoordinateRing.C_addPolynomial", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeierstrassCurve.Affine.CoordinateRing.C_addPolynomial_slope", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeierstrassCurve.Affine.CoordinateRing.XIdeal", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeierstrassCurve.Affine.CoordinateRing.YIdeal", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeierstrassCurve.Affine.CoordinateRing.XYIdeal", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeierstrassCurve.Affine.CoordinateRing.quotientXYIdealEquiv", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeierstrassCurve.Affine.CoordinateRing.XYIdeal_add_eq", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point", "is_tactic_proof": true, "tactics": ["simp", "rw", "span_pair_add_mul_right", "apply", "ring1"], "tactic_count": 5}
{"name": "WeierstrassCurve.Affine.CoordinateRing.XYIdeal_eq₁", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point", "is_tactic_proof": true, "tactics": ["simp", "rw", "apply", "ring1"], "tactic_count": 4}
{"name": "WeierstrassCurve.Affine.CoordinateRing.XYIdeal_eq₂", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point", "is_tactic_proof": false, "tactics": ["have", "by_cases", "have", "rcases", "simp", "simp", "ring1", "nth_rw", "simp", "rw", "apply", "simp", "ring1"], "tactic_count": 13}
{"name": "WeierstrassCurve.Affine.CoordinateRing.XYIdeal_neg_mul", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point", "is_tactic_proof": false, "tactics": ["have", "linear_combination", "congr_arg", "simp_rw", "map_mul,", "convert", "on_goal", "simp_rw", "convert", "apply", "simp_rw", "rcases", "let", "refine", "rw", "simp", "ring1", "let", "refine", "rw", "simp", "ring1"], "tactic_count": 22}
{"name": "WeierstrassCurve.Affine.CoordinateRing.XYIdeal_mul_XYIdeal", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point", "is_tactic_proof": false, "tactics": ["have", "rw", "rw", "simp_rw", "rw", "simp_rw", "rw", "span_pair_add_mul_right", "apply", "convert", "simp_rw", "mem_map_iff_of_surjective", "by_cases", "have", "rcases", "let", "replace", "refine", "rw", "simp", "linear_combination", "replace", "refine", "rw", "simp", "ring1"], "tactic_count": 26}
{"name": "WeierstrassCurve.Affine.CoordinateRing.XYIdeal'", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeierstrassCurve.Affine.CoordinateRing.XYIdeal'_eq", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeierstrassCurve.Affine.CoordinateRing.mk_XYIdeal'_neg_mul", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "WeierstrassCurve.Affine.CoordinateRing.mk_XYIdeal'_mul_mk_XYIdeal'", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "WeierstrassCurve.Affine.CoordinateRing.norm_smul_basis", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point", "is_tactic_proof": false, "tactics": ["simp_rw", "basis_zero,", "basis_zero,", "ring1"], "tactic_count": 4}
{"name": "WeierstrassCurve.Affine.CoordinateRing.coe_norm_smul_basis", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "WeierstrassCurve.Affine.Point.instAddCommGroup", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeierstrassCurve.Affine.Point.map", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeierstrassCurve.Affine.Point.map_zero", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "WeierstrassCurve.Affine.Point.map_id", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
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{"name": "WeierstrassCurve.Jacobian.add_of_Z_eq_zero_right", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Jacobian.Point", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "WeierstrassCurve.Projective.negMap_eq", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Point", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeierstrassCurve.Projective.negMap_of_Z_eq_zero", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Point", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "WeierstrassCurve.Projective.add_of_Z_eq_zero_left", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Point", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "WeierstrassCurve.Projective.add_of_Z_eq_zero_right", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Point", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "WeierstrassCurve.Projective.add_of_Y_eq", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Point", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "WeierstrassCurve.Projective.add_of_Y_ne", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Point", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "WeierstrassCurve.Projective.addMap_eq", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Point", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "WeierstrassCurve.Projective.Point.zero_point", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Point", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "WeierstrassCurve.Projective.Point.fromAffine_zero", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Point", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "WeierstrassCurve.Projective.Point.fromAffine_some_ne_zero", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Point", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "WeierstrassCurve.Projective.Point.neg_def", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Point", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeierstrassCurve.Projective.Point.neg_point", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Point", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeierstrassCurve.Projective.Point.add", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Point", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeierstrassCurve.Projective.Point.instAdd", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Point", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeierstrassCurve.Projective.Point.add_def", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Point", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeierstrassCurve.Projective.Point.add_point", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Point", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "WeierstrassCurve.Projective.Point.toAffine_of_singular", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Point", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "WeierstrassCurve.Projective.Point.toAffine_of_Z_eq_zero", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Point", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "WeierstrassCurve.Projective.Point.toAffine_zero", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Point", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeierstrassCurve.Projective.Point.toAffine_of_Z_ne_zero", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Point", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "WeierstrassCurve.Projective.Point.toAffine_some", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Point", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WeierstrassCurve.Projective.Point.toAffine_smul", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Point", "is_tactic_proof": true, "tactics": ["by_cases", "by_cases", "rw", "rw", "toAffine_of_Z_ne_zero", "simp", "rw"], "tactic_count": 7}
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{"name": "WeierstrassCurve.Projective.Point.toAffineLift_eq", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Point", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "WeierstrassCurve.Projective.Point.toAffineLift_some", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Point", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "WeierstrassCurve.Projective.Point.toAffineAddEquiv", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Point", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeierstrassCurve.Projective.Point.instAddCommGroup", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Point", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeierstrassCurve.Projective.map_neg", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Point", "is_tactic_proof": true, "tactics": ["simp", "map_simp"], "tactic_count": 2}
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{"name": "WeierstrassCurve.Projective.baseChange_neg", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Point", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "WeierstrassCurve.Projective.baseChange_add", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Point", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "WeierstrassCurve.Affine.Point.toProjective", "kind": "abbrev", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Point", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "WeierstrassCurve.baseChange_integralModel_eq", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Reduction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeierstrassCurve.isIntegral_of_exists_lift", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Reduction", "is_tactic_proof": true, "tactics": ["use", "ext", "all_goals", "apply", "apply", "apply", "apply", "apply"], "tactic_count": 8}
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{"name": "WeierstrassCurve.integralModel_Δ_eq", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Reduction", "is_tactic_proof": true, "tactics": ["conv_rhs", "simp"], "tactic_count": 2}
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{"name": "WeierstrassCurve.valuation_Δ_aux", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Reduction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeierstrassCurve.valuation_Δ_aux_eq_of_isIntegral", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Reduction", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WeierstrassCurve.instIsIntegralOfIsMinimal", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Reduction", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "WeierstrassCurve.exists_isMinimal", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Reduction", "is_tactic_proof": false, "tactics": ["obtain", "exists_maximalFor_of_wellFoundedGT", "refine", "intro", "let", "simp_all", "rw", "exact"], "tactic_count": 8}
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{"name": "WeierstrassCurve.reduction", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.Reduction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "WeierstrassCurve.VariableChange.mul_def", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.EllipticCurve.VariableChange", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AlgebraicGeometry.Scheme.Hom.fiber", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Fiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.fiberι", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Fiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instCanonicallyOverFiber", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Fiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.fiberToSpecResidueField", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Fiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.fiberOverSpecResidueField", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Fiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.fiberToSpecResidueField_apply", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Fiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.range_fiberι", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Fiber", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.instIsPreimmersionFiberι", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Fiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.fiberHomeo", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Fiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.fiberHomeo_apply", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Fiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.fiberι_fiberHomeo_symm", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Fiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.asFiber", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Fiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.fiberι_asFiber", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Fiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instCompactSpaceCarrierCarrierCommRingCatFiberOfQuasiCompact", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Fiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.QuasiCompact.isCompact_preimage_singleton", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Fiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instIsAffineFiberOfIsAffineHom", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Fiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instJacobsonSpaceCarrierCarrierCommRingCatFiberOfLocallyOfFiniteType", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Fiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instFiniteCarrierCarrierCommRingCatFiberOfIsFinite", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Fiber", "is_tactic_proof": true, "tactics": ["have", "have", "exact"], "tactic_count": 3}
{"name": "AlgebraicGeometry.IsFinite.finite_preimage_singleton", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Fiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.finite_preimage", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Fiber", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.Hom.discrete_fiber", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Fiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.functionField", "kind": "abbrev", "module": "Mathlib.AlgebraicGeometry.FunctionField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.germToFunctionField", "kind": "abbrev", "module": "Mathlib.AlgebraicGeometry.FunctionField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instAlgebraCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensFunctionFieldOfNonemptyToScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.FunctionField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instFieldCarrierFunctionField", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.FunctionField", "is_tactic_proof": true, "tactics": ["refine", "obtain", "rw", "intro", "replace", "have", "rw", "erw", "exact", "exact", "have", "rwa"], "tactic_count": 12}
{"name": "AlgebraicGeometry.germ_injective_of_isIntegral", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.FunctionField", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "obtain", "cases", "haveI", "exact"], "tactic_count": 7}
{"name": "AlgebraicGeometry.Scheme.germToFunctionField_injective", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.FunctionField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.genericPoint_eq_of_isOpenImmersion", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.FunctionField", "is_tactic_proof": true, "tactics": ["apply", "convert", "symm", "rw", "convert", "rw", "apply", "exact"], "tactic_count": 8}
{"name": "AlgebraicGeometry.stalkFunctionFieldAlgebra", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.FunctionField", "is_tactic_proof": true, "tactics": ["apply", "exact"], "tactic_count": 2}
{"name": "AlgebraicGeometry.functionField_isScalarTower", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.FunctionField", "is_tactic_proof": true, "tactics": ["apply", "simp_rw", "change", "rw"], "tactic_count": 4}
{"name": "AlgebraicGeometry.instAlgebraCarrierFunctionFieldSpec", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.FunctionField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.genericPoint_eq_bot_of_affine", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.FunctionField", "is_tactic_proof": true, "tactics": ["apply", "rw", "rw", "rw", "rfl"], "tactic_count": 5}
{"name": "AlgebraicGeometry.functionField_isFractionRing_of_affine", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.FunctionField", "is_tactic_proof": true, "tactics": ["convert", "delta", "apply", "congr", "rw", "ext", "exact"], "tactic_count": 7}
{"name": "AlgebraicGeometry.instIsIntegralToSchemeOfNonemptyCarrierCarrierCommRingCat", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.FunctionField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsAffineOpen.primeIdealOf_genericPoint", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.FunctionField", "is_tactic_proof": true, "tactics": ["haveI", "delta", "convert", "genericPoint_eq_of_isOpenImmersion", "apply", "exact"], "tactic_count": 6}
{"name": "AlgebraicGeometry.functionField_isFractionRing_of_isAffineOpen", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.FunctionField", "is_tactic_proof": true, "tactics": ["haveI", "haveI", "delta", "convert", "hU.isLocalization_stalk", "rw", "ext"], "tactic_count": 7}
{"name": "AlgebraicGeometry.instIsAffineXSchemeAffineCover", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.FunctionField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instIsFractionRingCarrierStalkCommRingCatPresheafFunctionField", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.FunctionField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instIsDomainCarrierStalkCommRingCatPresheafOfIsIntegral", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.FunctionField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.LocallyRingedSpace.toΓSpecFun", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.LocallyRingedSpace.notMem_prime_iff_unit_in_stalk", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.LocallyRingedSpace.toΓSpec_preimage_basicOpen_eq", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "simp", "rw", "exact"], "tactic_count": 5}
{"name": "AlgebraicGeometry.LocallyRingedSpace.toΓSpec_continuous", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": true, "tactics": ["rw", "rintro", "rw", "exact"], "tactic_count": 4}
{"name": "AlgebraicGeometry.LocallyRingedSpace.toΓSpecBase", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.LocallyRingedSpace.toΓSpecMapBasicOpen", "kind": "abbrev", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.LocallyRingedSpace.toΓSpecMapBasicOpen_eq", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.LocallyRingedSpace.toToΓSpecMapBasicOpen", "kind": "abbrev", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.LocallyRingedSpace.isUnit_res_toΓSpecMapBasicOpen", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": false, "tactics": ["convert", "rw", "congr"], "tactic_count": 3}
{"name": "AlgebraicGeometry.LocallyRingedSpace.toΓSpecCApp", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.LocallyRingedSpace.toΓSpecCApp_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": true, "tactics": ["have", "refine", "rw", "constructor", "intro", "ext", "exact", "apply"], "tactic_count": 8}
{"name": "AlgebraicGeometry.LocallyRingedSpace.toΓSpecCApp_spec", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.LocallyRingedSpace.toΓSpecCBasicOpens", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.LocallyRingedSpace.toΓSpecSheafedSpace", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.LocallyRingedSpace.toΓSpecSheafedSpace_app_eq", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "AlgebraicGeometry.LocallyRingedSpace.toΓSpecSheafedSpace_app_spec", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.LocallyRingedSpace.toStalk_stalkMap_toΓSpec", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": false, "tactics": ["rw", "erw", "congr", "exact"], "tactic_count": 4}
{"name": "AlgebraicGeometry.LocallyRingedSpace.toΓSpec", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.LocallyRingedSpace.toΓSpec_preimage_zeroLocus_eq", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": true, "tactics": ["simp", "have", "symm", "rw", "erw", "erw", "simp_rw", "rw", "simp"], "tactic_count": 9}
{"name": "AlgebraicGeometry.LocallyRingedSpace.comp_ring_hom_ext", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": true, "tactics": ["refine", "intro", "erw", "dsimp", "rw", "erw", "exact"], "tactic_count": 7}
{"name": "AlgebraicGeometry.LocallyRingedSpace.Γ_Spec_left_triangle", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": true, "tactics": ["unfold", "rw", "erw", "convert"], "tactic_count": 4}
{"name": "AlgebraicGeometry.identityToΓSpec", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.ΓSpec.left_triangle", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.ΓSpec.right_triangle", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": true, "tactics": ["apply", "ext", "dsimp", "refine", "rw", "rfl", "intro"], "tactic_count": 7}
{"name": "AlgebraicGeometry.ΓSpec.locallyRingedSpaceAdjunction", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.ΓSpec.toSpecΓ_unop", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.ΓSpec.toSpecΓ_of", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.ΓSpec.locallyRingedSpaceAdjunction_counit_app", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.ΓSpec.locallyRingedSpaceAdjunction_counit_app'", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.ΓSpec.locallyRingedSpaceAdjunction_homEquiv_apply", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.ΓSpec.locallyRingedSpaceAdjunction_homEquiv_apply'", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.ΓSpec.toOpen_comp_locallyRingedSpaceAdjunction_homEquiv_app", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": false, "tactics": ["rw", "locallyRingedSpaceAdjunction_counit_app']", "simp_rw", "rw", "rfl"], "tactic_count": 5}
{"name": "AlgebraicGeometry.ΓSpec.adjunction", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.ΓSpec.adjunction_homEquiv_apply", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.ΓSpec.adjunction_homEquiv_symm_apply", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.ΓSpec.adjunction_counit_app'", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.ΓSpec.adjunction_counit_app", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.toSpecΓ", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.ΓSpec.adjunction_unit_app", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.ΓSpec.isIso_locallyRingedSpaceAdjunction_counit", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.ΓSpec.isIso_adjunction_counit", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": true, "tactics": ["apply", "intro", "rw", "infer_instance"], "tactic_count": 4}
{"name": "AlgebraicGeometry.Scheme.toSpecΓ_apply", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.toSpecΓ_naturality", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.toSpecΓ_appTop", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": true, "tactics": ["have", "dsimp", "rw", "simp", "rw"], "tactic_count": 5}
{"name": "AlgebraicGeometry.SpecMap_ΓSpecIso_hom", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": true, "tactics": ["have", "dsimp", "rwa"], "tactic_count": 3}
{"name": "AlgebraicGeometry.SpecMap_ΓSpecIso_inv_toSpecΓ", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgebraicGeometry.toSpecΓ_SpecMap_ΓSpecIso_inv", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.toSpecΓ_preimage_basicOpen", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": true, "tactics": ["rw", "congr", "rw", "exact"], "tactic_count": 4}
{"name": "AlgebraicGeometry.toOpen_toSpecΓ_app", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": false, "tactics": ["rw", "change", "rw", "dsimp", "exact"], "tactic_count": 5}
{"name": "AlgebraicGeometry.ΓSpecIso_inv_ΓSpec_adjunction_homEquiv", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": true, "tactics": ["simp", "simp"], "tactic_count": 2}
{"name": "AlgebraicGeometry.ΓSpec_adjunction_homEquiv_eq", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgebraicGeometry.ΓSpecIso_obj_hom", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Spec.fullyFaithfulToLocallyRingedSpace", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instFullOppositeCommRingCatLocallyRingedSpaceToLocallyRingedSpace", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instFaithfulOppositeCommRingCatLocallyRingedSpaceToLocallyRingedSpace", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Spec.fullyFaithful", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Spec.full", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Spec.faithful", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Spec.map_inj", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Spec.map_injective", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Spec.map_eq_id", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Spec.preimage", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Spec.map_preimage", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Spec.map_preimage_unop", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Spec.preimage_map", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Spec.map_surjective", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": true, "tactics": ["intro", "use", "simp"], "tactic_count": 3}
{"name": "AlgebraicGeometry.Spec.homEquiv", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Spec.preimage_id", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Spec.preimage_comp", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instReflectiveLocallyRingedSpaceOppositeCommRingCatToLocallyRingedSpace", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Spec.reflective", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instIsRightAdjointCommRingCatOppositeLocallyRingedSpaceΓ", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instIsRightAdjointCommRingCatOppositeSchemeΓ", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.GammaSpecAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AlgebraicGeometry.Scheme.GlueData.toLocallyRingedSpaceGlueData", "kind": "abbrev", "module": "Mathlib.AlgebraicGeometry.Gluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.GlueData.instIsOpenImmersionFLocallyRingedSpaceToLocallyRingedSpaceGlueData", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Gluing", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.GlueData.instIsOpenImmersionCommRingCatFSheafedSpaceToSheafedSpaceGlueDataToLocallyRingedSpaceGlueData", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Gluing", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
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{"name": "AlgebraicGeometry.Scheme.GlueData.gluedScheme", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Gluing", "is_tactic_proof": true, "tactics": ["apply", "intro", "obtain", "obtain", "refine", "constructor", "simp", "exact", "infer_instance"], "tactic_count": 9}
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{"name": "AlgebraicGeometry.Scheme.GlueData.instPreservesColimitTopCatWalkingMultispanProdJMultispanDiagramForgetToTop", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Gluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.GlueData.instPreservesColimitWalkingMultispanProdJMultispanDiagramForget", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Gluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.GlueData.instHasMulticoequalizerDiagram", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Gluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.GlueData.glued", "kind": "abbrev", "module": "Mathlib.AlgebraicGeometry.Gluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.GlueData.ι", "kind": "abbrev", "module": "Mathlib.AlgebraicGeometry.Gluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.GlueData.isoLocallyRingedSpace", "kind": "abbrev", "module": "Mathlib.AlgebraicGeometry.Gluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.GlueData.ι_isoLocallyRingedSpace_inv", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Gluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.GlueData.ι_isOpenImmersion", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Gluing", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.GlueData.ι_jointly_surjective", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Gluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.GlueData.glue_condition", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Gluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.GlueData.vPullbackCone", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Gluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.GlueData.vPullbackConeIsLimit", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Gluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.AlgebraicGeometry.Gluing.0.AlgebraicGeometry.Scheme.GlueData.termD_", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Gluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AlgebraicGeometry.Scheme.GlueData.isoCarrier", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Gluing", "is_tactic_proof": true, "tactics": ["refine", "refine", "refine", "exact"], "tactic_count": 4}
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{"name": "AlgebraicGeometry.Scheme.GlueData.Rel", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Gluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.GlueData.ι_eq_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Gluing", "is_tactic_proof": false, "tactics": ["refine", "rw", "simp_rw", "rfl", "infer_instance"], "tactic_count": 5}
{"name": "AlgebraicGeometry.Scheme.GlueData.isOpen_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Gluing", "is_tactic_proof": true, "tactics": ["rw", "apply", "intro", "rw", "rfl"], "tactic_count": 5}
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{"name": "AlgebraicGeometry.Scheme.Cover.gluedCoverT'", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Gluing", "is_tactic_proof": true, "tactics": ["refine", "refine", "refine", "refine", "simp", "simp"], "tactic_count": 6}
{"name": "AlgebraicGeometry.Scheme.Cover.gluedCoverT'_fst_fst", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Gluing", "is_tactic_proof": true, "tactics": ["delta"], "tactic_count": 1}
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{"name": "AlgebraicGeometry.Scheme.IsLocallyDirected.V_self", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Gluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.IsLocallyDirected.exists_of_pullback_V_V", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Gluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.IsLocallyDirected.fst_inv_eq_snd_inv", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Gluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AlgebraicGeometry.Scheme.IsLocallyDirected.homOfLE_tAux", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Gluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AlgebraicGeometry.Scheme.IdealSheafData.ideal_top", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.ideal_bot", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.ideal_sup", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.ideal_sSup", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.ideal_iSup", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.ideal_inf", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.ideal_biInf", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": true, "tactics": ["refine", "simp"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.ideal_iInf", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "_private.Mathlib.AlgebraicGeometry.IdealSheaf.Basic.0.AlgebraicGeometry.Scheme.IdealSheafData.map_ideal_basicOpen_of_eq", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.map_ideal", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": true, "tactics": ["rw", "intro", "obtain", "have", "rw", "apply_fun", "simp", "simp"], "tactic_count": 8}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.map_ideal'", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.ideal_le_comap_ideal", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.le_of_iSup_eq_top", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": true, "tactics": ["intro", "have", "intro", "obtain", "exact", "choose", "have", "rw", "exact", "have", "refine", "rintro", "dsimp", "simp", "erw", "delta", "rw", "rw", "exact"], "tactic_count": 19}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.ext_of_iSup_eq_top", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.mem_supportSet_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.supportSet_subset_zeroLocus", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.zeroLocus_inter_subset_supportSet", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "apply", "rintro", "simp", "intro", "obtain", "have", "have", "rw", "obtain", "apply_fun", "refine", "cases"], "tactic_count": 14}
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{"name": "AlgebraicGeometry.Scheme.IdealSheafData.supportSet_inter", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "simp", "simp"], "tactic_count": 4}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.isClosed_supportSet", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": true, "tactics": ["rw", "intro", "refine", "simp", "apply", "simp"], "tactic_count": 6}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.support", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.coe_support_eq_eq_iInter_zeroLocus", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.mem_support_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.mem_support_iff_of_mem", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.coe_support_inter", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.Simps.coe_support", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.mkOfMemSupportIff", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.support_top", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.support_bot", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.support_antitone", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": true, "tactics": ["intro", "rw", "exact"], "tactic_count": 3}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.support_eq_bot_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": true, "tactics": ["refine", "have", "simp", "simp"], "tactic_count": 4}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.ofIdealTop", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.le_of_isAffine", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": true, "tactics": ["intro", "rw", "map_ideal", "exact"], "tactic_count": 4}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.ext_of_isAffine", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.equivOfIsAffine", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.radical", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.support_radical", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.nilradical", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.support_nilradical", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.le_radical", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.radical_top", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.radical_bot", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.radical_sup", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.radical_inf", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.vanishingIdeal", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.le_support_iff_le_vanishingIdeal", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": true, "tactics": ["simp", "trans", "refine", "obtain", "exact", "refine", "rw"], "tactic_count": 7}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.gc", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.vanishingIdeal_antimono", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.vanishingIdeal_support", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "rw", "congr", "apply", "rw", "coe_support_inter]"], "tactic_count": 7}
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{"name": "AlgebraicGeometry.Scheme.IdealSheafData.vanishingIdeal_top", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.vanishingIdeal_iSup", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.vanishingIdeal_sSup", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.vanishingIdeal_sup", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.support_sup", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.support_iSup", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.support_sSup", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.nilradical_eq_bot", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.support_eq_top_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Hom.ker", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.ideal_ker_le", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.ker_apply", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.le_ker_comp", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "AlgebraicGeometry.Scheme.ker_eq_top_of_isEmpty", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.ker_eq_bot_of_isIso", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.Hom.ker_comp_of_isIso", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.ker_of_isAffine", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": true, "tactics": ["refine", "simp", "f.naturality]", "intro", "simp"], "tactic_count": 5}
{"name": "AlgebraicGeometry.Scheme.Hom.range_subset_ker_support", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": true, "tactics": ["rintro", "obtain", "refine", "simp", "intro", "have", "rwa"], "tactic_count": 7}
{"name": "AlgebraicGeometry.Scheme.Hom.ker_eq_top_iff_isEmpty", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.iInf_ker_openCover_map_comp_apply", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": true, "tactics": ["refine", "intro", "simp", "apply", "rintro", "obtain", "simp", "refine", "apply", "rw", "simp", "simpa"], "tactic_count": 12}
{"name": "AlgebraicGeometry.Scheme.Hom.iInf_ker_openCover_map_comp", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": true, "tactics": ["refine", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "AlgebraicGeometry.Scheme.Hom.iUnion_support_ker_openCover_map_comp", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": true, "tactics": ["cases", "have", "simp", "suffices", "ext", "obtain", "simpa", "intro", "simp"], "tactic_count": 9}
{"name": "AlgebraicGeometry.Scheme.ker_morphismRestrict_ideal", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": false, "tactics": ["have", "ext", "simpa", "map_eq_zero_iff"], "tactic_count": 4}
{"name": "AlgebraicGeometry.Scheme.ker_ideal_of_isPullback_of_isOpenImmersion", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": true, "tactics": ["have", "have", "ext", "have", "let", "have", "rw", "simp", "simp", "simpa"], "tactic_count": 10}
{"name": "AlgebraicGeometry.Scheme.Hom.support_ker", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": true, "tactics": ["apply", "wlog", "intro", "let", "obtain", "have", "have", "this", "have", "rw", "exact", "rw", "ker_ideal_of_isPullback_of_isOpenImmersion", "exact", "exact", "exact", "obtain", "wlog", "intro", "have", "let", "obtain", "have", "exact", "obtain", "obtain", "rw", "simp", "exact", "rw", "exact"], "tactic_count": 31}
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{"name": "AlgebraicGeometry.Scheme.ker_toSpecΓ", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Basic", "is_tactic_proof": true, "tactics": ["apply", "simpa"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.comap", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Functorial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.comapIso", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Functorial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.comapIso_inv_subschemeι", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Functorial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.comapIso_hom_fst", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Functorial", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.comap_comp", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Functorial", "is_tactic_proof": false, "tactics": ["let", "asIso", "rw", "simp"], "tactic_count": 4}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.comap_id", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Functorial", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.support_comap", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Functorial", "is_tactic_proof": true, "tactics": ["ext1", "rw"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.ker_fst_of_isClosedImmersion", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Functorial", "is_tactic_proof": true, "tactics": ["delta", "rw", "pullback.lift_fst,"], "tactic_count": 3}
{"name": "AlgebraicGeometry.isPullback_of_isClosedImmersion", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Functorial", "is_tactic_proof": false, "tactics": ["suffices", "simpa", "refine", "rw"], "tactic_count": 4}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.map", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Functorial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.le_map_iff_comap_le", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Functorial", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "pullback.lift_fst", "exact", "intro", "have", "simp", "rw", "exact"], "tactic_count": 10}
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{"name": "AlgebraicGeometry.Scheme.IdealSheafData.map_mono", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Functorial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.comap_mono", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Functorial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AlgebraicGeometry.Scheme.IdealSheafData.comap_map_le", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Functorial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.map_top", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Functorial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.comap_bot", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Functorial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.map_inf", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Functorial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.comap_sup", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Functorial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AlgebraicGeometry.Scheme.IdealSheafData.map_vanishingIdeal", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Functorial", "is_tactic_proof": true, "tactics": ["apply", "rw", "refine", "rw", "simp"], "tactic_count": 5}
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{"name": "AlgebraicGeometry.Scheme.IdealSheafData.glueDataObjMap", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Subscheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.isLocalization_away", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Subscheme", "is_tactic_proof": true, "tactics": ["letI", "let", "letI", "have", "simp", "refine", "simp", "simp"], "tactic_count": 8}
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{"name": "AlgebraicGeometry.Scheme.IdealSheafData.subSchemeCover_map_inclusion", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Subscheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.IdealSheafData.inclusion_subschemeι", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Subscheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AlgebraicGeometry.Scheme.Hom.stalkFunctor_toImage_injective", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Subscheme", "is_tactic_proof": false, "tactics": ["apply", "rintro", "exact"], "tactic_count": 3}
{"name": "AlgebraicGeometry.Scheme.kerAdjunction", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Subscheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.instFullOppositeIdealSheafDataOverSubschemeFunctor", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.IdealSheaf.Subscheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.empty_ext", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.eq_emptyTo", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.emptyIsInitial_to", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.isInitial_iff_isEmpty", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.isAffineOpen_bot", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsAffineOpen.of_subsingleton", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.sigmaι_eq_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Limits", "is_tactic_proof": true, "tactics": ["refine", "rintro", "simp", "rintro", "obtain", "exact"], "tactic_count": 6}
{"name": "AlgebraicGeometry.disjoint_opensRange_sigmaι", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Limits", "is_tactic_proof": true, "tactics": ["intro", "obtain", "obtain", "obtain", "cases"], "tactic_count": 5}
{"name": "AlgebraicGeometry.isEmpty_of_commSq_sigmaι_of_ne", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Limits", "is_tactic_proof": true, "tactics": ["refine", "fapply", "exact", "exact"], "tactic_count": 4}
{"name": "AlgebraicGeometry.isEmpty_pullback_sigmaι_of_ne", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.sigmaMk_mk", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Limits", "is_tactic_proof": false, "tactics": ["change", "x", "congr", "refine", "exact"], "tactic_count": 5}
{"name": "_private.Mathlib.AlgebraicGeometry.Limits.0.AlgebraicGeometry.isOpenImmersion_sigmaDesc_aux", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Limits", "is_tactic_proof": true, "tactics": ["rw", "constructor", "suffices", "ext", "refine", "fun_prop", "rintro", "have", "obtain", "by_contra", "exact", "rw", "rw", "intro", "simpa", "intro", "have", "rw", "refine", "simp", "simp"], "tactic_count": 21}
{"name": "AlgebraicGeometry.isOpenImmersion_sigmaDesc", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Limits", "is_tactic_proof": true, "tactics": ["obtain", "convert", "refine", "obtain", "simp", "apply", "intro", "exact"], "tactic_count": 8}
{"name": "AlgebraicGeometry.nonempty_isColimit_cofanMk_of", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Limits", "is_tactic_proof": false, "tactics": ["have", "refine", "simpa", "simp", "apply", "rw", "intro", "have", "obtain", "use", "simp"], "tactic_count": 11}
{"name": "AlgebraicGeometry.ι_left_coprodIsoSigma_inv", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.ι_right_coprodIsoSigma_inv", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.isCompl_range_inl_inr", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.isCompl_opensRange_inl_inr", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Limits", "is_tactic_proof": true, "tactics": ["convert", "simp", "rfl"], "tactic_count": 3}
{"name": "AlgebraicGeometry.inl_ne_inr", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.inr_ne_inl", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.coprodMk_inl", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Limits", "is_tactic_proof": false, "tactics": ["change", "congr", "refine", "exact"], "tactic_count": 4}
{"name": "AlgebraicGeometry.coprodMk_inr", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Limits", "is_tactic_proof": false, "tactics": ["change", "congr", "refine", "exact"], "tactic_count": 4}
{"name": "AlgebraicGeometry.nonempty_isColimit_binaryCofanMk_of_isCompl", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Limits", "is_tactic_proof": true, "tactics": ["let", "let", "refine", "let", "convert", "intro", "cases", "simpa", "intro"], "tactic_count": 9}
{"name": "AlgebraicGeometry.isPullback_inl_inl_coprodMap", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Limits", "is_tactic_proof": true, "tactics": ["refine", "apply", "rintro", "obtain", "rw", "simp", "simp", "cases", "rintro", "exact"], "tactic_count": 10}
{"name": "AlgebraicGeometry.isPullback_inr_inr_coprodMap", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.coprodPresheafObjIso_hom_fst", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Limits", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.coprodPresheafObjIso_hom_snd", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Limits", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.coprodSpec_inl", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.coprodSpec_inr", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.coprodSpec_coprodMk", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Limits", "is_tactic_proof": true, "tactics": ["apply", "obtain", "simp", "change", "ext", "change", "ext"], "tactic_count": 7}
{"name": "AlgebraicGeometry.coprodSpec_apply", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Limits", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgebraicGeometry.isIso_stalkMap_coprodSpec", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Limits", "is_tactic_proof": true, "tactics": ["obtain", "have", "rw", "rw", "letI", "have", "infer_instance", "have", "rw", "rw", "letI", "have", "infer_instance"], "tactic_count": 13}
{"name": "AlgebraicGeometry.ι_sigmaSpec", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.AlgebraicGeometry.Limits.0.AlgebraicGeometry.IsAffineOpen.iSup_of_disjoint_aux", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Limits", "is_tactic_proof": false, "tactics": ["have", "isOpenImmersion_sigmaDesc", "convert", "ext", "simp", "have", "infer_instance"], "tactic_count": 7}
{"name": "AlgebraicGeometry.IsAffineOpen.iSup_of_disjoint", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Limits", "is_tactic_proof": true, "tactics": ["obtain", "have", "rw", "exact"], "tactic_count": 4}
{"name": "AlgebraicGeometry.IsAffineOpen.biSup_of_disjoint", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Limits", "is_tactic_proof": true, "tactics": ["rw", "have", "exact"], "tactic_count": 3}
{"name": "AlgebraicGeometry.IsAffineOpen.sup_of_disjoint", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Limits", "is_tactic_proof": false, "tactics": ["convert", "iSup_of_disjoint", "aesop"], "tactic_count": 3}
{"name": "AlgebraicGeometry.Scheme.isAffine_of_isLimit", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Limits", "is_tactic_proof": true, "tactics": ["let", "have", "have", "have", "hc.conePointUniqueUpToIso", "exact"], "tactic_count": 6}
{"name": "AlgebraicGeometry.instHasColimitOverScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.LimitsOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instMonoObjWalkingSpanCompOverSchemeTopMorphismPropertySpanOverForgetForgetForgetNoneWalkingPairSomeMapInitOfIsOpenImmersionLeftDiscretePUnit", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.LimitsOver", "is_tactic_proof": true, "tactics": ["rw", "cases", "simpa", "simpa"], "tactic_count": 4}
{"name": "AlgebraicGeometry.instIsOpenImmersionLeftSchemeDiscretePUnitMapWalkingSpanOverTopMorphismPropertySpan", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.LimitsOver", "is_tactic_proof": true, "tactics": ["obtain", "simp", "infer_instance", "simpa", "simpa"], "tactic_count": 5}
{"name": "AlgebraicGeometry.instIsLocallyDirectedCompSchemeOverOverTopMorphismPropertyForgetForgetForget", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.LimitsOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instIsOpenImmersionMapSchemeCompOverOverTopMorphismPropertyForgetForget", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.LimitsOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instCreatesColimitOverSchemeTopMorphismPropertyOverForget", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.LimitsOver", "is_tactic_proof": true, "tactics": ["have", "refine", "createsColimitOfFullyFaithfulOfIso", "prop", "let", "colimit", "preservesColimitIso", "let", "rw", "intro", "simpa"], "tactic_count": 11}
{"name": "AlgebraicGeometry.instHasColimitOverSchemeTopMorphismProperty", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.LimitsOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instPreservesColimitOverSchemeTopMorphismPropertyOverForget", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.LimitsOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instIsOpenImmersionLeftSchemeDiscretePUnitιOverTopMorphismProperty", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.LimitsOver", "is_tactic_proof": true, "tactics": ["rw", "let", "preservesColimitIso", "rw", "simp", "exact"], "tactic_count": 6}
{"name": "AlgebraicGeometry.instHasCoproductsOfShapeOverSchemeTopMorphismPropertyOfSmall", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.LimitsOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instHasFiniteCoproductsOverSchemeTopMorphismProperty", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.LimitsOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instCreatesColimitsOfShapeOverSchemeTopMorphismPropertyOverDiscreteForgetOfSmall", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.LimitsOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.ringCatSheaf", "kind": "abbrev", "module": "Mathlib.AlgebraicGeometry.Modules.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.PresheafOfModules", "kind": "abbrev", "module": "Mathlib.AlgebraicGeometry.Modules.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.toRingCatSheafHom", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Modules.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.Hom", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.instCategory", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.instAbelian", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.instHasLimits", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.instHasColimits", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.toPresheafOfModules", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.fullyFaithfulToPresheafOfModules", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.instFullPresheafOfModulesToPresheafOfModules", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.instFaithfulPresheafOfModulesToPresheafOfModules", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.instIsRightAdjointPresheafOfModulesToPresheafOfModules", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.toPresheaf", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.instFaithfulPresheafAbCarrierCommRingCatToPresheaf", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.instPreservesLimitsPresheafAbCarrierCommRingCatToPresheaf", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.instReflectsIsomorphismsPresheafAbCarrierCommRingCatToPresheaf", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.presheaf", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.termΓ(_,_)_1", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry._aux_Mathlib_AlgebraicGeometry_Modules_Sheaf___macroRules_AlgebraicGeometry_termΓ(_,_)_1_1", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry._aux_Mathlib_AlgebraicGeometry_Modules_Sheaf___delab_app_AlgebraicGeometry_termΓ(_,_)_1_1", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensCarrierAbPresheaf", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.map_smul", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.Hom.mapPresheaf", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.Hom.app", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.mapPresheaf_app", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.Hom.app_smul", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.Hom.add_app", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.Hom.sub_app", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.Hom.zero_app", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.Hom.id_app", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.Hom.comp_app", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.hom_ext", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.isSheaf", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.toPresheaf_obj", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.toPresheaf_map", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.Hom.isIso_iff_isIso_app", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.Modules.instIsIsoAbApp", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.inv_app", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.Modules.pushforward", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.pushforward_obj_obj", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.pushforward_obj_presheaf_map", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.pushforward_map_app", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.pullback", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.pullbackPushforwardAdjunction", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.instIsLeftAdjointPullback", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.instIsRightAdjointPushforward", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.instAdditivePushforward", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.instAdditivePullback", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.pushforwardId", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.pushforwardId_hom_app_app", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.pushforwardId_inv_app_app", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.pullbackId", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.conjugateEquiv_pullbackId_hom", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.pushforwardComp", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.pushforwardComp_hom_app_app", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.pushforwardComp_inv_app_app", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.pullbackComp", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.pushforwardCongr", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.pushforwardCongr_hom_app_app", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.pushforwardCongr_inv_app_app", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.pullbackCongr", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.conjugateEquiv_pullbackComp_inv", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.pseudofunctor_associativity", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": true, "tactics": ["let", "let", "let", "let", "change", "have", "congr_arg", "simp"], "tactic_count": 8}
{"name": "AlgebraicGeometry.Scheme.Modules.pseudofunctor_left_unitality", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": true, "tactics": ["let", "let", "let", "change", "have", "simp"], "tactic_count": 6}
{"name": "AlgebraicGeometry.Scheme.Modules.pseudofunctor_right_unitality", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": true, "tactics": ["let", "let", "let", "change", "have", "simp"], "tactic_count": 6}
{"name": "AlgebraicGeometry.Scheme.Modules.pseudofunctor", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.restrictFunctor", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.restrict", "kind": "abbrev", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.restrict_obj", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.restrict_map", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.restrictFunctorAdjCounitIso", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.restrictAdjunction", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.instIsIsoFunctorCounitRestrictAdjunction", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.instIsLeftAdjointRestrictFunctor", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.instFullPushforward", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.instFaithfulPushforward", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.restrictAdjunction_unit_app_app", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.restrictAdjunction_counit_app_app", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.restrictFunctorIsoPullback", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.restrictFunctorId", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.restrictFunctorId_hom_app_app", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.restrictFunctorId_inv_app_app", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.restrictFunctorComp", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.restrictFunctorComp_hom_app_app", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.restrictFunctorComp_inv_app_app", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.restrictFunctorCongr", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.restrictFunctorCongr_hom_app_app", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.restrictFunctorCongr_inv_app_app", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.restrictStalkNatIso", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.germ_restrictStalkNatIso_hom_app", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Modules.germ_restrictStalkNatIso_inv_app", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Modules.Sheaf", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "ModuleCat.Tilde.Localizations", "kind": "abbrev", "module": "Mathlib.AlgebraicGeometry.Modules.Tilde", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.Tilde.isFraction", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Modules.Tilde", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.Tilde.isFractionPrelocal", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Modules.Tilde", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.Tilde.isLocallyFraction", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Modules.Tilde", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.Tilde.isLocallyFraction_pred", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Modules.Tilde", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.Tilde.instModuleCarrierObjOppositeOpensCarrierTopCommRingCatValStructureSheafLocalizationsValMemUnop", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Modules.Tilde", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.Tilde.instIsScalarTowerAtPrimeAsIdealValCarrierTopMemOpensUnopLocalizations", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Modules.Tilde", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.Tilde.instIsScalarTowerCarrierObjOppositeOpensCarrierTopCommRingCatValStructureSheafLocalizationsValMemUnop", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Modules.Tilde", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.Tilde.sections_smul_localizations_def", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Modules.Tilde", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.Tilde.sectionsSubmodule", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Modules.Tilde", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.tildeInType", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Modules.Tilde", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.instAddCommGroupObjOppositeOpensCarrierTopValTildeInType", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Modules.Tilde", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatSpecOfRingCatValRingCatSheafTopTildeInType", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Modules.Tilde", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.tilde", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Modules.Tilde", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.tildeInModuleCat", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Modules.Tilde", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.Tilde.res_apply", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Modules.Tilde", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.Tilde.smul_section_apply", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Modules.Tilde", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.Tilde.smul_stalk_no_nonzero_divisor", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Modules.Tilde", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.Tilde.toOpen", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Modules.Tilde", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.Tilde.toOpen_res", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Modules.Tilde", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.Tilde.toStalk", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Modules.Tilde", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.Tilde.isUnit_toStalk", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Modules.Tilde", "is_tactic_proof": true, "tactics": ["rw", "refine", "obtain", "let", "refine", "simpa", "germ_ext", "obtain", "refine", "obtain", "refine", "simp", "smul_eq_iff_of_mem", "simpa"], "tactic_count": 14}
{"name": "ModuleCat.Tilde.localizationToStalk", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Modules.Tilde", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.Tilde.openToLocalization", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Modules.Tilde", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.Tilde.stalkToFiberLinearMap", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Modules.Tilde", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.Tilde.germ_comp_stalkToFiberLinearMap", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Modules.Tilde", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.Tilde.stalkToFiberLinearMap_germ", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Modules.Tilde", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.Tilde.toOpen_germ", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Modules.Tilde", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ModuleCat.Tilde.toStalk_comp_stalkToFiberLinearMap", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Modules.Tilde", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ModuleCat.Tilde.stalkToFiberLinearMap_toStalk", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Modules.Tilde", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.Tilde.const", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Modules.Tilde", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.Tilde.const_apply", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Modules.Tilde", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.Tilde.exists_const", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Modules.Tilde", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.Tilde.res_const", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Modules.Tilde", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.Tilde.localizationToStalk_mk", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Modules.Tilde", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.Tilde.stalkIso", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Modules.Tilde", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.Tilde.instIsLocalizedModuleCarrierOfStalkTildeInModuleCatPrimeComplAsIdealHomToStalk", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Modules.Tilde", "is_tactic_proof": false, "tactics": ["convert", "ext", "simp", "erw"], "tactic_count": 4}
{"name": "AlgebraicGeometry.IsAffineOpen.preimage", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instIsAffineHomOfIsIsoScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instQuasiCompactOfIsAffineHom", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instIsAffineHomCompScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Affine", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "apply", "apply", "exact"], "tactic_count": 6}
{"name": "AlgebraicGeometry.instIsMultiplicativeSchemeIsAffineHom", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instIsAffineHomιBasicOpen", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Affine", "is_tactic_proof": true, "tactics": ["constructor", "intro", "fapply", "convert", "rw", "ext1", "refine", "simp"], "tactic_count": 8}
{"name": "AlgebraicGeometry.isRetrocompact_basicOpen", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.AlgebraicGeometry.Morphisms.Affine.0.AlgebraicGeometry.isAffine_of_isAffineOpen_basicOpen_aux", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Affine", "is_tactic_proof": true, "tactics": ["rw", "intro", "obtain", "rw", "apply", "intro", "rw", "refine", "rw", "exact", "rw", "exact"], "tactic_count": 12}
{"name": "AlgebraicGeometry.isAffine_of_isAffineOpen_basicOpen", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Affine", "is_tactic_proof": true, "tactics": ["have", "have", "obtain", "rw", "simp", "apply", "exact", "constructor", "refine", "change", "simp", "exact", "rw", "rw", "exact", "simp", "refine", "convert", "exact"], "tactic_count": 19}
{"name": "AlgebraicGeometry.isAffineOpen_of_isAffineOpen_basicOpen", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Affine", "is_tactic_proof": true, "tactics": ["apply", "rw", "rintro", "rw", "simpa"], "tactic_count": 5}
{"name": "AlgebraicGeometry.instHasAffinePropertyIsAffineHomIsAffine", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.isAffineHom_isStableUnderBaseChange", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Affine", "is_tactic_proof": true, "tactics": ["apply", "letI", "apply", "introv", "infer_instance"], "tactic_count": 5}
{"name": "AlgebraicGeometry.isAffineHom_of_isAffine", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.isAffine_of_isAffineHom", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.isAffineHom_of_forall_exists_isAffineOpen", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Affine", "is_tactic_proof": true, "tactics": ["choose", "rw", "exact", "exact"], "tactic_count": 4}
{"name": "AlgebraicGeometry.instIsAffinePullbackSchemeOfIsAffineHom", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instIsAffinePullbackSchemeOfIsAffineHom_1", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instIsAffineHomDescScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Affine", "is_tactic_proof": true, "tactics": ["refine", "have", "have", "let", "convert", "apply", "intro", "obtain", "replace", "exact", "replace", "exact", "rintro", "obtain", "simpa", "simpa"], "tactic_count": 16}
{"name": "AlgebraicGeometry.isAffineHom_of_isInducing", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Affine", "is_tactic_proof": true, "tactics": ["apply", "intro", "by_cases", "obtain", "obtain", "obtain", "obtain", "obtain", "exact", "obtain", "refine", "convert", "simp", "simpa", "obtain", "rw", "refine", "convert", "exact"], "tactic_count": 19}
{"name": "AlgebraicGeometry.IsAffineOpen.isCompact_pullback_inf", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Affine", "is_tactic_proof": true, "tactics": ["have", "have", "have", "let", "let", "let", "convert", "simp"], "tactic_count": 8}
{"name": "AlgebraicGeometry.affineAnd", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Morphisms.AffineAnd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.affineAnd_apply", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.AffineAnd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.affineAnd_respectsIso", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.AffineAnd", "is_tactic_proof": true, "tactics": ["refine", "intro", "simpa", "intro", "simpa"], "tactic_count": 5}
{"name": "AlgebraicGeometry.affineAnd_isLocal", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.AffineAnd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.affineAnd_isLocal_of_propertyIsLocal", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.AffineAnd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.affineAnd_isStableUnderBaseChange", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.AffineAnd", "is_tactic_proof": true, "tactics": ["haveI", "apply", "intro", "exact"], "tactic_count": 4}
{"name": "AlgebraicGeometry.targetAffineLocally_affineAnd_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.AffineAnd", "is_tactic_proof": false, "tactics": ["simp", "refine", "obtain", "use", "have", "rwa", "refine", "change", "rw", "exact"], "tactic_count": 10}
{"name": "AlgebraicGeometry.targetAffineLocally_affineAnd_iff'", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.AffineAnd", "is_tactic_proof": true, "tactics": ["rw", "aesop"], "tactic_count": 2}
{"name": "AlgebraicGeometry.targetAffineLocally_affineAnd_iff_affineLocally", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.AffineAnd", "is_tactic_proof": true, "tactics": ["haveI", "rw", "simp", "intro", "constructor", "wlog", "intro", "rw", "intro", "have", "rw", "hQ.respectsIso.cancel_right_isIso]", "apply", "rw", "exact", "intro", "have", "rw", "exact", "intro", "rw", "rw", "exact"], "tactic_count": 23}
{"name": "AlgebraicGeometry.targetAffineLocally_affineAnd_eq_affineLocally", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.AffineAnd", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "AlgebraicGeometry.targetAffineLocally_affineAnd_le", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.AffineAnd", "is_tactic_proof": true, "tactics": ["intro", "exact"], "tactic_count": 2}
{"name": "AlgebraicGeometry.HasAffineProperty.affineAnd_isStableUnderComposition", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.AffineAnd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.HasAffineProperty.affineAnd_isStableUnderBaseChange", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.AffineAnd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.HasAffineProperty.affineAnd_containsIdentities", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.AffineAnd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.HasAffineProperty.affineAnd_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.AffineAnd", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "rw", "aesop", "ext", "rw", "aesop"], "tactic_count": 7}
{"name": "AlgebraicGeometry.HasAffineProperty.affineAnd_le_isAffineHom", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.AffineAnd", "is_tactic_proof": true, "tactics": ["intro", "wlog", "rw", "intro", "exact", "rw", "rw", "exact"], "tactic_count": 8}
{"name": "AlgebraicGeometry.HasAffineProperty.affineAnd_eq_of_propertyIsLocal", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.AffineAnd", "is_tactic_proof": false, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "AlgebraicGeometry.HasAffineProperty.SpecMap_iff_of_affineAnd", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.AffineAnd", "is_tactic_proof": true, "tactics": ["have", "rw", "exacts", "inferInstance]"], "tactic_count": 4}
{"name": "AlgebraicGeometry.HasAffineProperty.affineAnd_le_affineAnd", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.AffineAnd", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "AlgebraicGeometry.HasAffineProperty.coprodDesc_affineAnd", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.AffineAnd", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "refine", "let", "rw", "hQi.cancel_right_isIso", "have", "refine", "have", "simp", "convert", "exact", "have", "simp", "convert", "exact"], "tactic_count": 17}
{"name": "AlgebraicGeometry.IsZariskiLocalAtTarget", "kind": "abbrev", "module": "Mathlib.AlgebraicGeometry.Morphisms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsZariskiLocalAtTarget.mk'", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsZariskiLocalAtTarget.of_isPullback", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsZariskiLocalAtTarget.restrict", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsZariskiLocalAtTarget.of_iSup_eq_top", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Basic", "is_tactic_proof": false, "tactics": ["refine", "obtain", "refine", "change", "rw", "exact"], "tactic_count": 6}
{"name": "AlgebraicGeometry.IsZariskiLocalAtTarget.iff_of_iSup_eq_top", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsZariskiLocalAtTarget.of_openCover", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Basic", "is_tactic_proof": true, "tactics": ["apply", "exact"], "tactic_count": 2}
{"name": "AlgebraicGeometry.IsZariskiLocalAtTarget.iff_of_openCover", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsZariskiLocalAtTarget.of_range_subset_iSup", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Basic", "is_tactic_proof": true, "tactics": ["let", "rw", "apply", "rw", "intro", "have", "change", "simp", "let", "simp", "rw", "exact", "apply", "dsimp", "rw", "simp"], "tactic_count": 16}
{"name": "AlgebraicGeometry.IsZariskiLocalAtTarget.of_forall_source_exists_preimage", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Basic", "is_tactic_proof": true, "tactics": ["choose", "apply", "rintro", "simp", "exact", "intro", "exact"], "tactic_count": 7}
{"name": "AlgebraicGeometry.IsZariskiLocalAtTarget.coprodMap", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Basic", "is_tactic_proof": true, "tactics": ["refine", "rintro", "rw", "convert", "simp", "rw", "convert", "simp"], "tactic_count": 8}
{"name": "AlgebraicGeometry.IsZariskiLocalAtSource", "kind": "abbrev", "module": "Mathlib.AlgebraicGeometry.Morphisms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsZariskiLocalAtSource.mk'", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsZariskiLocalAtSource.comp", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsZariskiLocalAtSource.respectsLeft_isOpenImmersion", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsZariskiLocalAtSource.of_iSup_eq_top", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Basic", "is_tactic_proof": false, "tactics": ["refine", "obtain", "exact"], "tactic_count": 3}
{"name": "AlgebraicGeometry.IsZariskiLocalAtSource.iff_of_iSup_eq_top", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsZariskiLocalAtSource.of_openCover", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "AlgebraicGeometry.IsZariskiLocalAtSource.iff_of_openCover", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsZariskiLocalAtSource.of_isOpenImmersion", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsZariskiLocalAtSource.isZariskiLocalAtTarget", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsZariskiLocalAtSource.sigmaDesc", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "AlgebraicGeometry.IsZariskiLocalAtSource.resLE", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsZariskiLocalAtSource.iff_exists_resLE", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Basic", "is_tactic_proof": true, "tactics": ["refine", "choose", "rw", "intro", "rw", "exact", "rw", "rintro", "simp", "use"], "tactic_count": 10}
{"name": "AlgebraicGeometry.AffineTargetMorphismProperty", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Morphisms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.AffineTargetMorphismProperty.ext", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Basic", "is_tactic_proof": true, "tactics": ["delta"], "tactic_count": 1}
{"name": "AlgebraicGeometry.AffineTargetMorphismProperty.of", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Morphisms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.AffineTargetMorphismProperty.toProperty", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Morphisms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.AffineTargetMorphismProperty.toProperty_apply", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Basic", "is_tactic_proof": true, "tactics": ["delta"], "tactic_count": 1}
{"name": "AlgebraicGeometry.AffineTargetMorphismProperty.cancel_left_of_respectsIso", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgebraicGeometry.AffineTargetMorphismProperty.cancel_right_of_respectsIso", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgebraicGeometry.AffineTargetMorphismProperty.arrow_mk_iso_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgebraicGeometry.AffineTargetMorphismProperty.respectsIso_mk", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Basic", "is_tactic_proof": true, "tactics": ["apply", "rintro", "rintro"], "tactic_count": 3}
{"name": "AlgebraicGeometry.AffineTargetMorphismProperty.respectsIso_of", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Basic", "is_tactic_proof": true, "tactics": ["apply", "intro", "intro"], "tactic_count": 3}
{"name": "AlgebraicGeometry.AffineTargetMorphismProperty.instIsLocalOfOfIsZariskiLocalAtTarget", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.AffineTargetMorphismProperty.IsStableUnderBaseChange", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Morphisms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.AffineTargetMorphismProperty.IsStableUnderBaseChange.mk", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Basic", "is_tactic_proof": true, "tactics": ["intro", "rw", "exact"], "tactic_count": 3}
{"name": "AlgebraicGeometry.targetAffineLocally", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Morphisms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.of_targetAffineLocally_of_isPullback", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "AlgebraicGeometry.instRespectsIsoSchemeTargetAffineLocallyOfToProperty", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Basic", "is_tactic_proof": true, "tactics": ["apply", "introv", "rw", "exact", "introv", "rintro", "haveI", "rw", "exact"], "tactic_count": 9}
{"name": "AlgebraicGeometry.HasAffineProperty.instTargetAffineLocallyOfIsLocal", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.HasAffineProperty.eq_targetAffineLocally", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.HasAffineProperty.of_isZariskiLocalAtTarget", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.HasAffineProperty.copy", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.HasAffineProperty.of_isPullback", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.HasAffineProperty.restrict", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.HasAffineProperty.instRespectsIsoScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Basic", "is_tactic_proof": true, "tactics": ["letI", "rw", "infer_instance"], "tactic_count": 3}
{"name": "AlgebraicGeometry.HasAffineProperty.of_iSup_eq_top", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Basic", "is_tactic_proof": true, "tactics": ["letI", "rw", "classical", "intro", "induction", "basicOpen", "haveI", "have", "exact", "openCover", "apply", "intro", "obtain", "exact", "hU"], "tactic_count": 15}
{"name": "AlgebraicGeometry.HasAffineProperty.iff_of_iSup_eq_top", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.HasAffineProperty.of_openCover", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.HasAffineProperty.iff_of_openCover", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Basic", "is_tactic_proof": true, "tactics": ["letI", "rw", "exact"], "tactic_count": 3}
{"name": "AlgebraicGeometry.HasAffineProperty.iff_of_isAffine", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Basic", "is_tactic_proof": true, "tactics": ["letI", "haveI", "rw", "trans", "exact", "rw"], "tactic_count": 6}
{"name": "AlgebraicGeometry.HasAffineProperty.instIsZariskiLocalAtTarget", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Basic", "is_tactic_proof": true, "tactics": ["letI", "apply", "rw", "intro", "rw", "exact", "rintro", "let", "apply", "rintro", "have", "refine", "exact", "rw", "exact"], "tactic_count": 15}
{"name": "AlgebraicGeometry.HasAffineProperty.iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.AlgebraicGeometry.Morphisms.Basic.0.AlgebraicGeometry.HasAffineProperty.pullback_fst_of_right", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Basic", "is_tactic_proof": true, "tactics": ["letI", "rw", "intro", "let", "have", "simp", "rw", "apply", "exact"], "tactic_count": 9}
{"name": "AlgebraicGeometry.HasAffineProperty.isStableUnderBaseChange", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.HasAffineProperty.isZariskiLocalAtSource", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Basic", "is_tactic_proof": true, "tactics": ["refine", "intro", "simp_rw", "rw", "refine", "simp_rw", "exact"], "tactic_count": 7}
{"name": "AlgebraicGeometry.hasOfPostcompProperty_isOpenImmersion_of_morphismRestrict", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instHasOfPostcompPropertySchemeIsOpenImmersionOfIsStableUnderBaseChange", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsClosedImmersion.eq_inf", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.ClosedImmersion", "is_tactic_proof": true, "tactics": ["ext", "rw", "rfl"], "tactic_count": 3}
{"name": "AlgebraicGeometry.IsClosedImmersion.iff_isPreimmersion", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.ClosedImmersion", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgebraicGeometry.IsClosedImmersion.of_isPreimmersion", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.ClosedImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsClosedImmersion.instIsPreimmersion", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.ClosedImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsClosedImmersion.instOfIsIsoScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.ClosedImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsClosedImmersion.instOfIsEmptyCarrierCarrierCommRingCat", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.ClosedImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsClosedImmersion.instIsMultiplicativeScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.ClosedImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsClosedImmersion.comp", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.ClosedImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsClosedImmersion.respectsIso", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.ClosedImmersion", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "AlgebraicGeometry.IsClosedImmersion.instSubschemeι", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.ClosedImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsClosedImmersion.spec_of_surjective", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.ClosedImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsClosedImmersion.spec_of_quotient_mk", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.ClosedImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsClosedImmersion.of_surjective_of_isAffine", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.ClosedImmersion", "is_tactic_proof": true, "tactics": ["rw", "apply", "exact"], "tactic_count": 3}
{"name": "AlgebraicGeometry.IsClosedImmersion.of_comp_isClosedImmersion", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.ClosedImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsClosedImmersion.SpecMap_residue", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.ClosedImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsClosedImmersion.instIsAffineHom", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.ClosedImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsClosedImmersion.instIsIsoSchemeToImage", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.ClosedImmersion", "is_tactic_proof": false, "tactics": ["have", "have", "isHomeomorph_iff_isEmbedding_surjective.mpr", "rw", "exact", "refine", "exact", "intro", "refine", "change", "simp", "refine", "have", "f.toImage.isEmbedding.isInducing", "exact"], "tactic_count": 15}
{"name": "AlgebraicGeometry.IsClosedImmersion.overEquivIdealSheafData", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Morphisms.ClosedImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsClosedImmersion.isIso_iff_ker_eq_bot", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.ClosedImmersion", "is_tactic_proof": true, "tactics": ["refine", "have", "exact"], "tactic_count": 3}
{"name": "AlgebraicGeometry.IsClosedImmersion.lift", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Morphisms.ClosedImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsClosedImmersion.lift_fac", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.ClosedImmersion", "is_tactic_proof": true, "tactics": ["nth_rw", "simp"], "tactic_count": 2}
{"name": "AlgebraicGeometry.IsClosedImmersion.isIso_of_ker_eq", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.ClosedImmersion", "is_tactic_proof": true, "tactics": ["let", "suffices", "rwa", "isIso_iff_of_reflects_iso", "rw", "simpa"], "tactic_count": 6}
{"name": "AlgebraicGeometry.IsClosedImmersion.isIso_lift", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.ClosedImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.isDominant_of_of_appTop_injective", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.ClosedImmersion", "is_tactic_proof": true, "tactics": ["have", "have", "exact", "simpa"], "tactic_count": 4}
{"name": "AlgebraicGeometry.instIsDominantToSpecΓOfCompactSpaceCarrierCarrierCommRingCat", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.ClosedImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.stalkMap_injective_of_isOpenMap_of_injective", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.ClosedImmersion", "is_tactic_proof": true, "tactics": ["let", "let", "let", "refine", "rw", "obtain", "obtain", "let", "have", "change", "rw", "refine", "simp", "have", "rw", "simp", "rw", "simp", "have", "obtain", "exact", "have", "choose", "refine", "rw", "simp", "apply", "obtain", "apply", "rw", "exact"], "tactic_count": 31}
{"name": "AlgebraicGeometry.IsClosedImmersion.isIso_of_injective_of_isAffine", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.ClosedImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsClosedImmersion.isAffine_surjective_of_isAffine", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.ClosedImmersion", "is_tactic_proof": true, "tactics": ["refine", "simp", "rw", "exact"], "tactic_count": 4}
{"name": "AlgebraicGeometry.IsClosedImmersion.Spec_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.ClosedImmersion", "is_tactic_proof": true, "tactics": ["constructor", "intro", "obtain", "let", "refine", "exact", "simp", "change", "simp", "simp", "rintro", "infer_instance"], "tactic_count": 12}
{"name": "AlgebraicGeometry.IsClosedImmersion.isZariskiLocalAtTarget", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.ClosedImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsClosedImmersion.hasAffineProperty", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.ClosedImmersion", "is_tactic_proof": true, "tactics": ["convert", "refine"], "tactic_count": 2}
{"name": "AlgebraicGeometry.isClosedImmersion_iff_isAffineHom", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.ClosedImmersion", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.Hom.app_surjective", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.ClosedImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsClosedImmersion.isStableUnderBaseChange", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.ClosedImmersion", "is_tactic_proof": true, "tactics": ["apply", "haveI", "apply", "intro", "exact"], "tactic_count": 5}
{"name": "AlgebraicGeometry.instIsClosedImmersionFstScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.ClosedImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instIsClosedImmersionSndScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.ClosedImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instIsClosedImmersionMorphismRestrict", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.ClosedImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instLocallyOfFiniteTypeOfIsClosedImmersion", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.ClosedImmersion", "is_tactic_proof": false, "tactics": ["rw", "and_iff_right", "targetAffineLocally_affineAnd_iff_affineLocally", "rw", "exact"], "tactic_count": 5}
{"name": "AlgebraicGeometry.isIso_of_isClosedImmersion_of_surjective", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.ClosedImmersion", "is_tactic_proof": false, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "AlgebraicGeometry.isClosed_singleton_iff_isClosedImmersion", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.ClosedImmersion", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "AlgebraicGeometry.isClosedImmersion_of_comp_eq_id", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.ClosedImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instIsClosedImmersionISchemeOfSubsingletonCarrierCarrierCommRingCat", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.ClosedImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instIsClosedImmersionOfSubsingletonCarrierCarrierCommRingCatOfIsOver", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.ClosedImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.AffineTargetMorphismProperty.diagonal", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Morphisms.Constructors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.AffineTargetMorphismProperty.diagonal_respectsIso", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Constructors", "is_tactic_proof": true, "tactics": ["delta", "apply", "introv", "rw", "apply", "introv", "rw", "apply"], "tactic_count": 8}
{"name": "AlgebraicGeometry.HasAffineProperty.diagonal_of_openCover", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Constructors", "is_tactic_proof": true, "tactics": ["letI", "let", "have", "apply", "rintro", "dsimp", "convert", "simp", "ext1", "simp", "convert", "ext1"], "tactic_count": 12}
{"name": "AlgebraicGeometry.HasAffineProperty.diagonal_of_openCover_diagonal", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Constructors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.HasAffineProperty.diagonal_of_diagonal_of_isPullback", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Constructors", "is_tactic_proof": true, "tactics": ["letI", "rw", "rintro", "rw", "convert", "apply", "infer_instance", "infer_instance"], "tactic_count": 8}
{"name": "AlgebraicGeometry.HasAffineProperty.diagonal_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Constructors", "is_tactic_proof": true, "tactics": ["letI", "refine", "rw", "let", "have", "exact"], "tactic_count": 6}
{"name": "AlgebraicGeometry.AffineTargetMorphismProperty.diagonal_of_openCover_source", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Constructors", "is_tactic_proof": true, "tactics": ["rw", "let", "have", "refine", "dsimp", "have", "rw", "exact"], "tactic_count": 8}
{"name": "AlgebraicGeometry.HasAffineProperty.diagonal_affineProperty_isLocal", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Constructors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instHasAffinePropertyDiagonalSchemeDiagonal", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Constructors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instIsZariskiLocalAtTargetDiagonalScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Constructors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instIsZariskiLocalAtSourceDiagonalSchemeOfHasOfPostcompPropertyOfRespectsRightIsOpenImmersion", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Constructors", "is_tactic_proof": false, "tactics": ["let", "pullback.map", "refine", "change", "apply", "rw", "apply", "exact", "change", "refine", "rw", "exact"], "tactic_count": 12}
{"name": "AlgebraicGeometry.universally_isZariskiLocalAtTarget", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Constructors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.universally_isZariskiLocalAtSource", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Constructors", "is_tactic_proof": true, "tactics": ["refine", "intro", "refine", "apply", "intro", "rw", "exact", "apply", "intro", "rw", "intro", "dsimp", "rw", "exact"], "tactic_count": 14}
{"name": "AlgebraicGeometry.topologically", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Morphisms.Constructors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.topologically_isStableUnderComposition", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Constructors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.topologically_iso_le", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Constructors", "is_tactic_proof": true, "tactics": ["intro", "exact"], "tactic_count": 2}
{"name": "AlgebraicGeometry.topologically_respectsIso", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Constructors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.topologically_isZariskiLocalAtTarget", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Constructors", "is_tactic_proof": true, "tactics": ["apply", "intro", "simp_rw", "exact", "intro", "apply", "rw", "exact"], "tactic_count": 8}
{"name": "AlgebraicGeometry.topologically_isZariskiLocalAtTarget'", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Constructors", "is_tactic_proof": true, "tactics": ["refine", "introv", "refine", "rw", "exact"], "tactic_count": 5}
{"name": "AlgebraicGeometry.topologically_isZariskiLocalAtSource", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Constructors", "is_tactic_proof": true, "tactics": ["apply", "introv", "exact", "introv", "exact"], "tactic_count": 5}
{"name": "AlgebraicGeometry.topologically_isZariskiLocalAtSource'", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Constructors", "is_tactic_proof": true, "tactics": ["refine", "introv", "refine", "rw", "exact"], "tactic_count": 5}
{"name": "AlgebraicGeometry.stalkwise", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Morphisms.Constructors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.stalkwise_respectsIso", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Constructors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.stalkwiseIsZariskiLocalAtTarget_of_respectsIso", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Constructors", "is_tactic_proof": true, "tactics": ["have", "letI", "apply", "intro", "apply", "intro", "have", "obtain", "exact"], "tactic_count": 9}
{"name": "AlgebraicGeometry.stalkwise_isZariskiLocalAtSource_of_respectsIso", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Constructors", "is_tactic_proof": true, "tactics": ["letI", "apply", "intro", "rw", "exact", "intro", "have", "obtain", "rw", "simpa"], "tactic_count": 10}
{"name": "AlgebraicGeometry.stalkwise_SpecMap_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Constructors", "is_tactic_proof": true, "tactics": ["have", "trans", "exact", "exact"], "tactic_count": 4}
{"name": "AlgebraicGeometry.AffineTargetMorphismProperty.isStableUnderBaseChange_of_isStableUnderBaseChangeOnAffine_of_isZariskiLocalAtTarget", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Constructors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.exists_hom_isAffine_of_isZariskiLocalAtSource", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Descent", "is_tactic_proof": true, "tactics": ["let", "let", "refine", "obtain", "use", "rw", "rw", "exact"], "tactic_count": 8}
{"name": "AlgebraicGeometry.IsZariskiLocalAtTarget.descendsAlong", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Descent", "is_tactic_proof": true, "tactics": ["apply", "introv", "wlog", "rw", "intro", "let", "let", "pullbackLeftPullbackSndIso", "pullback.congrHom", "pullback.congrHom", "have", "e.hom", "refine", "exact", "change", "rw", "exact", "obtain", "exact"], "tactic_count": 19}
{"name": "AlgebraicGeometry.of_pullback_fst_Spec_of_codescendsAlong", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Descent", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "algebraize", "replace", "hf", "rw", "refine", "rwa"], "tactic_count": 8}
{"name": "AlgebraicGeometry.IsStableUnderBaseChange.of_pullback_fst_of_isAffine", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Descent", "is_tactic_proof": true, "tactics": ["apply", "rw", "exact", "rw", "exact"], "tactic_count": 5}
{"name": "AlgebraicGeometry.IsZariskiLocalAtTarget.descendsAlong_inf_quasiCompact", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Descent", "is_tactic_proof": true, "tactics": ["apply", "intro", "wlog", "have", "obtain", "refine", "rw", "exact", "rw", "exact", "obtain", "obtain", "exact"], "tactic_count": 13}
{"name": "AlgebraicGeometry.HasRingHomProperty.descendsAlong", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Descent", "is_tactic_proof": true, "tactics": ["apply", "introv", "wlog", "rw", "intro", "have", "pullback.fst", "pullback.map", "exact", "obtain", "apply", "simp"], "tactic_count": 12}
{"name": "AlgebraicGeometry.HasAffineProperty.descendsAlong_of_affineAnd", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Descent", "is_tactic_proof": true, "tactics": ["apply", "introv", "have", "convert", "exact", "wlog", "rw", "have", "pullback.fst", "pullback.map", "refine", "rwa", "obtain", "apply", "simp"], "tactic_count": 15}
{"name": "AlgebraicGeometry.IsEtale", "kind": "abbrev", "module": "Mathlib.AlgebraicGeometry.Morphisms.Etale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsEtale.instIsSmooth", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Etale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsEtale.instIsStableUnderBaseChangeScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Etale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsEtale.instFormallyUnramified", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Etale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsEtale.instHasOfPostcompPropertySchemeMinMorphismPropertyLocallyOfFiniteTypeFormallyUnramified", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Etale", "is_tactic_proof": true, "tactics": ["rw", "intro", "exact"], "tactic_count": 3}
{"name": "AlgebraicGeometry.IsEtale.of_comp", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Etale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsEtale.instHasOfPostcompPropertyScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Etale", "is_tactic_proof": false, "tactics": ["apply", "intro", "constructor"], "tactic_count": 3}
{"name": "AlgebraicGeometry.Scheme.Etale", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Morphisms.Etale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.instCategoryEtale", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Etale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Etale.forget", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Morphisms.Etale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Etale.forgetFullyFaithful", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Morphisms.Etale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.instFullEtaleOverForget", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Etale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.instFaithfulEtaleOverForget", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Etale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.instHasPullbacksEtale", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Etale", "is_tactic_proof": true, "tactics": ["unfold", "infer_instance"], "tactic_count": 2}
{"name": "AlgebraicGeometry.IsFinite.instHasAffinePropertyAndIsAffineFiniteCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTopHomAppTop", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Finite", "is_tactic_proof": true, "tactics": ["change", "rw", "simp"], "tactic_count": 3}
{"name": "AlgebraicGeometry.IsFinite.instIsStableUnderCompositionScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsFinite.instIsStableUnderBaseChangeScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsFinite.instContainsIdentitiesScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsFinite.instIsMultiplicativeScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsFinite.SpecMap_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Finite", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgebraicGeometry.IsFinite.instOfIsIsoScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsFinite.instCompScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsFinite.instFstScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsFinite.instSndScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsFinite.instMorphismRestrict", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsFinite.iff_isIntegralHom_and_locallyOfFiniteType", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Finite", "is_tactic_proof": true, "tactics": ["wlog", "rw", "simp_rw", "rw", "refine"], "tactic_count": 5}
{"name": "AlgebraicGeometry.IsFinite.eq_inf", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Finite", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "AlgebraicGeometry.IsFinite.instIsIntegralHom", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsFinite.instLocallyOfFiniteType", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsClosedImmersion.iff_isFinite_and_mono", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Finite", "is_tactic_proof": true, "tactics": ["wlog", "change", "rw", "simp_rw", "rw", "refine", "trans", "exact", "exact"], "tactic_count": 9}
{"name": "AlgebraicGeometry.IsClosedImmersion.eq_isFinite_inf_mono", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Finite", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "AlgebraicGeometry.IsFinite.instOfIsClosedImmersion", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsFinite.instHasOfPostcompPropertySchemeIsSeparated", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsFinite.of_comp", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsFinite.comp_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsFinite.instDescScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Finite", "is_tactic_proof": true, "tactics": ["refine", "intros", "algebraize", "refine"], "tactic_count": 4}
{"name": "AlgebraicGeometry.isFinite_iff_locallyOfFiniteType_of_jacobsonSpace", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Finite", "is_tactic_proof": true, "tactics": ["wlog", "rw", "have", "have", "have", "exact", "obtain", "wlog", "rw", "have", "refine", "cases", "exact", "have", "obtain", "have", "obtain", "rw", "have", "letI", "letI", "have", "change", "exact"], "tactic_count": 24}
{"name": "AlgebraicGeometry.Scheme.Hom.closePoints_subset_preimage_closedPoints", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Finite", "is_tactic_proof": true, "tactics": ["intro", "have", "have", "simpa"], "tactic_count": 4}
{"name": "AlgebraicGeometry.isClosed_singleton_iff_locallyOfFiniteType", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Finite", "is_tactic_proof": true, "tactics": ["constructor", "exact", "have", "inferInstance", "intro", "simpa"], "tactic_count": 6}
{"name": "AlgebraicGeometry.instHasRingHomPropertyLocallyOfFinitePresentationFinitePresentation", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.FinitePresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.locallyOfFinitePresentation_of_isOpenImmersion", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.FinitePresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instIsStableUnderCompositionSchemeLocallyOfFinitePresentation", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.FinitePresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.locallyOfFinitePresentation_comp", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.FinitePresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.locallyOfFinitePresentation_isStableUnderBaseChange", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.FinitePresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instLocallyOfFinitePresentationFstScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.FinitePresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instLocallyOfFinitePresentationSndScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.FinitePresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instLocallyOfFinitePresentationMorphismRestrict", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.FinitePresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instLocallyOfFinitePresentationResLE", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.FinitePresentation", "is_tactic_proof": true, "tactics": ["delta"], "tactic_count": 1}
{"name": "AlgebraicGeometry.instLocallyOfFiniteTypeOfLocallyOfFinitePresentation", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.FinitePresentation", "is_tactic_proof": true, "tactics": ["rw", "rw", "refine", "exact"], "tactic_count": 4}
{"name": "AlgebraicGeometry.Scheme.Hom.isLocallyConstructible_image", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.FinitePresentation", "is_tactic_proof": true, "tactics": ["wlog", "refine", "have", "have", "convert", "refine", "apply", "rw", "change", "rw", "simp", "obtain", "wlog", "have", "let", "rw", "refine", "have", "convert", "rw", "obtain", "obtain", "rw", "exact"], "tactic_count": 24}
{"name": "AlgebraicGeometry.Scheme.Hom.isConstructible_image", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.FinitePresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.isConstructible_preimage", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.FinitePresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instHasRingHomPropertyLocallyOfFiniteTypeFiniteType", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.FiniteType", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.locallyOfFiniteType_of_isOpenImmersion", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.FiniteType", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instIsStableUnderCompositionSchemeLocallyOfFiniteType", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.FiniteType", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.locallyOfFiniteType_comp", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.FiniteType", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.locallyOfFiniteType_of_comp", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.FiniteType", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instIsMultiplicativeSchemeLocallyOfFiniteType", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.FiniteType", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.locallyOfFiniteType_isStableUnderBaseChange", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.FiniteType", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instLocallyOfFiniteTypeFstScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.FiniteType", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instLocallyOfFiniteTypeSndScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.FiniteType", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instLocallyOfFiniteTypeMorphismRestrict", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.FiniteType", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instLocallyOfFiniteTypeResLE", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.FiniteType", "is_tactic_proof": true, "tactics": ["delta"], "tactic_count": 1}
{"name": "AlgebraicGeometry.LocallyOfFiniteType.stalkMap", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.FiniteType", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instJacobsonSpaceCarrierCarrierCommRingCatSpecOfOfIsJacobsonRing", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.FiniteType", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instJacobsonSpaceCarrierCarrierCommRingCatSpecOfIsJacobsonRingCarrier", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.FiniteType", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.LocallyOfFiniteType.jacobsonSpace", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.FiniteType", "is_tactic_proof": true, "tactics": ["wlog", "rw", "intro", "have", "have", "have", "let", "have", "exact", "obtain", "wlog", "have", "rw", "intro", "have", "let", "exact", "obtain", "obtain", "have", "algebraize", "have", "exact"], "tactic_count": 23}
{"name": "AlgebraicGeometry.Flat.instHasRingHomPropertyFlat", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Flat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Flat.instOfIsOpenImmersion", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Flat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Flat.instIsStableUnderCompositionScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Flat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Flat.comp", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Flat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Flat.instIsMultiplicativeScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Flat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Flat.isStableUnderBaseChange", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Flat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Flat.instFstScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Flat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Flat.instSndScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Flat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Flat.instMorphismRestrict", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Flat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Flat.instResLE", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Flat", "is_tactic_proof": true, "tactics": ["delta"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Flat.of_stalkMap", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Flat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Flat.stalkMap", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Flat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Flat.iff_flat_stalkMap", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Flat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Flat.instDescScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Flat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Flat.isQuotientMap_of_surjective", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Flat", "is_tactic_proof": true, "tactics": ["rw", "refine", "wlog", "let", "rw", "intro", "rw", "apply", "refine", "rw", "exact", "obtain", "wlog", "have", "let", "let", "refine", "rw", "exact", "obtain", "obtain", "refine", "exact", "apply", "rwa"], "tactic_count": 25}
{"name": "AlgebraicGeometry.Flat.epi_of_flat_of_surjective", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Flat", "is_tactic_proof": true, "tactics": ["apply", "apply", "apply", "intro", "apply", "algebraize", "have", "exact"], "tactic_count": 8}
{"name": "AlgebraicGeometry.Flat.flat_and_surjective_iff_faithfullyFlat_of_isAffine", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Flat", "is_tactic_proof": false, "tactics": ["rw", "surjective_iff]", "rfl"], "tactic_count": 3}
{"name": "AlgebraicGeometry.flat_and_surjective_SpecMap_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Flat", "is_tactic_proof": false, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Flat.surjective_descendsAlong_surjective_inf_flat_inf_quasicompact", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.FlatDescent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.descendsAlong_universallyClosed_surjective_inf_flat_inf_quasicompact", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.FlatDescent", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact", "refine", "let", "let", "pullback.map", "have", "rw", "exact", "rwa"], "tactic_count": 11}
{"name": "AlgebraicGeometry.descendsAlong_universallyOpen_surjective_inf_flat_inf_quasicompact", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.FlatDescent", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact", "refine", "let", "let", "pullback.map", "have", "rw", "exact", "rwa"], "tactic_count": 11}
{"name": "AlgebraicGeometry.descendsAlong_universallyInjective_surjective_inf_flat_inf_quasicompact", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.FlatDescent", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "AlgebraicGeometry.descendsAlong_isomorphisms_surjective_inf_flat_inf_quasicompact", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.FlatDescent", "is_tactic_proof": true, "tactics": ["apply", "rw", "exact", "intro", "have", "have", "of_pullback_fst_of_descendsAlong", "have", "of_pullback_fst_of_descendsAlong", "have", "of_pullback_fst_of_descendsAlong", "have", "have", "isAffine_of_isAffineHom", "wlog", "rw", "have", "pullback.fst", "pullback.map", "refine", "change", "rwa", "obtain", "obtain", "refine", "of_pullback_fst_Spec_of_codescendsAlong", "intro", "rwa", "simp_rw"], "tactic_count": 29}
{"name": "AlgebraicGeometry.descendsAlong_isOpenImmersion_surjective_inf_flat_inf_quasicompact'", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.FlatDescent", "is_tactic_proof": true, "tactics": ["apply", "intro", "have", "let", "let", "let", "have", "have", "rw", "refine", "have", "have", "rw", "infer_instance", "exact", "have", "apply", "exact", "rw", "infer_instance"], "tactic_count": 20}
{"name": "AlgebraicGeometry.instDescendsAlongSchemeMinMorphismPropertySurjectiveFlatLocallyOfFinitePresentationOfQuasiCompactOfIsZariskiLocalAtTarget", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.FlatDescent", "is_tactic_proof": true, "tactics": ["apply", "rintro", "obtain", "f.isOpenMap.exists_opens_image_eq_of_prespectralSpace", "refine", "exact", "have", "dsimp", "exact"], "tactic_count": 9}
{"name": "AlgebraicGeometry.Flat.isIso_of_surjective_of_mono", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.FlatMono", "is_tactic_proof": false, "tactics": ["apply", "tauto", "exact"], "tactic_count": 3}
{"name": "AlgebraicGeometry.IsOpenImmersion.of_flat_of_mono", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.FlatMono", "is_tactic_proof": true, "tactics": ["wlog", "let", "have", "let", "have", "have", "have", "of_postcomp", "have", "rw", "have", "infer_instance", "have", "have", "have", "exact"], "tactic_count": 16}
{"name": "Algebra.FormallyUnramified.isOpenImmersion_SpecMap_lmul", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.FormallyUnramified", "is_tactic_proof": true, "tactics": ["rw", "apply", "apply", "exact"], "tactic_count": 4}
{"name": "AlgebraicGeometry.FormallyUnramified.instHasRingHomPropertyFormallyUnramified", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.FormallyUnramified", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.FormallyUnramified.instIsStableUnderCompositionScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.FormallyUnramified", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.FormallyUnramified.instOfIsOpenImmersionDiagonalScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.FormallyUnramified", "is_tactic_proof": true, "tactics": ["wlog", "rw", "intro", "have", "exact", "obtain", "wlog", "rw", "intro", "have", "exact", "obtain", "obtain", "rw", "algebraize", "let", "have", "have", "rwa", "obtain", "refine", "obtain", "obtain", "refine", "rw", "exact"], "tactic_count": 26}
{"name": "AlgebraicGeometry.FormallyUnramified.of_comp", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.FormallyUnramified", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.FormallyUnramified.instIsMultiplicativeScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.FormallyUnramified", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.FormallyUnramified.instIsStableUnderBaseChangeScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.FormallyUnramified", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.FormallyUnramified.isOpenImmersion_diagonal", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.FormallyUnramified", "is_tactic_proof": true, "tactics": ["wlog", "let", "let", "apply", "intro", "rw", "have", "comp_mem", "have", "comp_mem", "exact", "obtain", "obtain", "rw", "algebraize", "rw", "cancel_right_of_respectsIso", "infer_instance"], "tactic_count": 18}
{"name": "AlgebraicGeometry.Scheme.Hom.isLocallyClosed_range", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Immersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.coborderRange", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Morphisms.Immersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.liftCoborder", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Morphisms.Immersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.liftCoborder_ι", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Immersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.liftCoborder_preimage", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Immersion", "is_tactic_proof": true, "tactics": ["conv_rhs", "rw"], "tactic_count": 2}
{"name": "AlgebraicGeometry.liftCoborder_app", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Immersion", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "AlgebraicGeometry.instIsClosedImmersionLiftCoborder", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Immersion", "is_tactic_proof": false, "tactics": ["have", "have", "refine", "convert", "apply", "rw", "exact"], "tactic_count": 7}
{"name": "AlgebraicGeometry.instIsDominantιCoborderRange", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Immersion", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "AlgebraicGeometry.isImmersion_eq_inf", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Immersion", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "AlgebraicGeometry.IsImmersion.instIsZariskiLocalAtTarget", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Immersion", "is_tactic_proof": false, "tactics": ["suffices", "isImmersion_eq_inf", "apply", "refine", "intro", "change", "change", "simpa", "intro", "change", "change", "simp", "refine", "rw", "exact", "simp_rw", "exact"], "tactic_count": 17}
{"name": "AlgebraicGeometry.IsImmersion.instOfIsOpenImmersion", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Immersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsImmersion.instOfIsClosedImmersion", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Immersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsImmersion.instIsMultiplicativeScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Immersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsImmersion.comp", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Immersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsImmersion.isImmersion_iff_exists", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Immersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsImmersion.isStableUnderBaseChange", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Immersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsImmersion.instFstScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Immersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsImmersion.instSndScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Immersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsImmersion.instMorphismRestrict", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Immersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsImmersion.instResLE", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Immersion", "is_tactic_proof": true, "tactics": ["delta"], "tactic_count": 1}
{"name": "AlgebraicGeometry.IsImmersion.instLocallyOfFiniteType", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Immersion", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "AlgebraicGeometry.IsImmersion.instDiagonalScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Immersion", "is_tactic_proof": true, "tactics": ["let", "let", "have", "top_le_iff.mp", "have", "have", "rwa"], "tactic_count": 7}
{"name": "AlgebraicGeometry.IsImmersion.instMapDescScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Immersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsImmersion.instHasOfPostcompPropertySchemeTopMorphismProperty", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Immersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsImmersion.of_comp", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Immersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsImmersion.comp_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Immersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsImmersion.instLiftSchemeId", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Immersion", "is_tactic_proof": true, "tactics": ["rw", "convert", "ext"], "tactic_count": 3}
{"name": "AlgebraicGeometry.IsImmersion.instιScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Immersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsImmersion.instToImage", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Immersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsImmersion.isPullback_toImage_liftCoborder", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Immersion", "is_tactic_proof": true, "tactics": ["refine", "rw", "ext", "simp", "dsimp", "rw", "rw", "infer_instance"], "tactic_count": 8}
{"name": "AlgebraicGeometry.IsImmersion.instIsOpenImmersionToImageOfQuasiCompact", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Immersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsImmersion.isImmersion_iff_exists_of_quasiCompact", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Immersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsIntegralHom.hasAffineProperty", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Integral", "is_tactic_proof": true, "tactics": ["change", "rw", "simp"], "tactic_count": 3}
{"name": "AlgebraicGeometry.IsIntegralHom.instIsStableUnderCompositionScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsIntegralHom.instIsStableUnderBaseChangeScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsIntegralHom.instOfIsClosedImmersion", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsIntegralHom.instIsMultiplicativeScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsIntegralHom.instCompScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsIntegralHom.instFstScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsIntegralHom.instSndScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsIntegralHom.instMorphismRestrict", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsIntegralHom.instHasOfPostcompPropertySchemeIsSeparated", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsIntegralHom.of_comp", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsIntegralHom.comp_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsIntegralHom.SpecMap_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Integral", "is_tactic_proof": true, "tactics": ["have", "rw", "exacts", "inferInstance]"], "tactic_count": 4}
{"name": "AlgebraicGeometry.IsIntegralHom.instIsMultiplicativeScheme_1", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsIntegralHom.instDescScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Integral", "is_tactic_proof": true, "tactics": ["refine", "intros", "algebraize", "refine"], "tactic_count": 4}
{"name": "AlgebraicGeometry.IsIntegralHom.instUniversallyClosed", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Integral", "is_tactic_proof": true, "tactics": ["revert", "rw", "apply", "intro", "wlog", "rw", "exact", "obtain", "wlog", "intro", "have", "rw", "rw", "exact", "obtain", "obtain", "rw", "exact"], "tactic_count": 18}
{"name": "AlgebraicGeometry.IsIntegralHom.iff_universallyClosed_and_isAffineHom", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Integral", "is_tactic_proof": true, "tactics": ["refine", "clear", "wlog", "rw", "rw", "rw", "exact", "obtain", "wlog", "have", "rw", "exact", "obtain", "obtain", "rw", "apply", "algebraize", "exact"], "tactic_count": 18}
{"name": "AlgebraicGeometry.IsIntegralHom.eq_universallyClosed_inf_isAffineHom", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Integral", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "AlgebraicGeometry.isIso_iff_isOpenImmersion_and_surjective", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.IsIso", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgebraicGeometry.isomorphisms_eq_isOpenImmersion_inf_surjective", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.IsIso", "is_tactic_proof": true, "tactics": ["ext", "rw", "rfl"], "tactic_count": 3}
{"name": "AlgebraicGeometry.isomorphisms_eq_stalkwise", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.IsIso", "is_tactic_proof": false, "tactics": ["rw", "inf_right_comm]", "congr", "ext", "exact", "let"], "tactic_count": 6}
{"name": "AlgebraicGeometry._example", "kind": "example", "module": "Mathlib.AlgebraicGeometry.Morphisms.IsIso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instHasAffinePropertyIsomorphismsSchemeAndIsAffineIsIsoCommRingCatAppTop", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.IsIso", "is_tactic_proof": true, "tactics": ["convert", "exact"], "tactic_count": 2}
{"name": "AlgebraicGeometry.instIsZariskiLocalAtTargetMonomorphismsScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.IsIso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.isIso_SpecMap_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.IsIso", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "infer_instance"], "tactic_count": 4}
{"name": "AlgebraicGeometry.sourceLocalClosure", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Morphisms.LocalClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.sourceLocalClosure.cover", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Morphisms.LocalClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.sourceLocalClosure.property_coverMap_comp", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.LocalClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.sourceLocalClosure.le", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.LocalClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.sourceLocalClosure.iff_forall_exists", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.LocalClosure", "is_tactic_proof": true, "tactics": ["refine", "refine", "rw", "apply", "choose", "exact"], "tactic_count": 6}
{"name": "AlgebraicGeometry.sourceLocalClosure.instRespectsLeftSchemeOfIsStableUnderBaseChange", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.LocalClosure", "is_tactic_proof": true, "tactics": ["refine", "simpa"], "tactic_count": 2}
{"name": "AlgebraicGeometry.sourceLocalClosure.instRespectsRightScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.LocalClosure", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "AlgebraicGeometry.sourceLocalClosure.instRespectsIsoScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.LocalClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.sourceLocalClosure.instIsZariskiLocalAtSourceIsOpenImmersionOfRespectsIsoOfRespectsLeftScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.LocalClosure", "is_tactic_proof": true, "tactics": ["refine", "refine", "simpa", "choose", "exact"], "tactic_count": 5}
{"name": "AlgebraicGeometry.sourceLocalClosure.instIsStableUnderBaseChangeScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.LocalClosure", "is_tactic_proof": true, "tactics": ["refine", "simpa"], "tactic_count": 2}
{"name": "AlgebraicGeometry.sourceLocalClosure.instContainsIdentitiesScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.LocalClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.sourceLocalClosure.instIsStableUnderCompositionSchemeOfIsStableUnderBaseChange", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.LocalClosure", "is_tactic_proof": true, "tactics": ["refine", "refine", "simpa"], "tactic_count": 3}
{"name": "AlgebraicGeometry.sourceLocalClosure.instIsMultiplicativeSchemeOfIsStableUnderBaseChange", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.LocalClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsLocalIso.eq_sourceLocalClosure_isOpenImmersion", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.LocalIso", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "AlgebraicGeometry.IsLocalIso.instIsZariskiLocalAtSource", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.LocalIso", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "AlgebraicGeometry.IsLocalIso.instIsMultiplicativeScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.LocalIso", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "AlgebraicGeometry.IsLocalIso.instIsStableUnderBaseChangeScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.LocalIso", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "AlgebraicGeometry.IsLocalIso.le_of_isZariskiLocalAtSource", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.LocalIso", "is_tactic_proof": true, "tactics": ["intro", "obtain", "rw", "exact"], "tactic_count": 4}
{"name": "AlgebraicGeometry.IsLocalIso.eq_iInf", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.LocalIso", "is_tactic_proof": true, "tactics": ["refine", "simp", "apply", "refine", "infer_instance"], "tactic_count": 5}
{"name": "AlgebraicGeometry.isOpenImmersion_SpecMap_iff_of_surjective", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.OpenImmersion", "is_tactic_proof": true, "tactics": ["constructor", "intro", "obtain", "refine", "let", "have", "have", "have", "let", "have", "have", "rw", "simp", "rintro", "letI", "have", "exact"], "tactic_count": 17}
{"name": "AlgebraicGeometry.IsOpenImmersion.of_openCover_source", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.OpenImmersion", "is_tactic_proof": true, "tactics": ["refine", "intro", "convert", "ext", "exact", "intro", "obtain", "rw", "infer_instance"], "tactic_count": 9}
{"name": "AlgebraicGeometry.IsOpenImmersion.of_forall_source_exists", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.OpenImmersion", "is_tactic_proof": true, "tactics": ["choose", "let", "exact"], "tactic_count": 3}
{"name": "AlgebraicGeometry.isOpenImmersion_eq_inf", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.OpenImmersion", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "AlgebraicGeometry.instIsZariskiLocalAtTargetStalkwiseBijectiveCoeRingHom", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.OpenImmersion", "is_tactic_proof": true, "tactics": ["apply", "rw", "convert", "ext", "exact"], "tactic_count": 5}
{"name": "AlgebraicGeometry.isOpenImmersion_isZariskiLocalAtTarget", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instIsOpenImmersionMapScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.isPreimmersion_eq_inf", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Preimmersion", "is_tactic_proof": true, "tactics": ["ext", "rw", "rfl"], "tactic_count": 3}
{"name": "AlgebraicGeometry.IsPreimmersion.instIsZariskiLocalAtTarget", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Preimmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsPreimmersion.instOfIsOpenImmersion", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Preimmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsPreimmersion.instIsMultiplicativeScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Preimmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsPreimmersion.comp", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Preimmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsPreimmersion.instMonoScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Preimmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsPreimmersion.of_comp", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Preimmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsPreimmersion.comp_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Preimmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsPreimmersion.SpecMap_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Preimmersion", "is_tactic_proof": false, "tactics": ["haveI", "rw", "exact", "rw", "rfl"], "tactic_count": 5}
{"name": "AlgebraicGeometry.IsPreimmersion.mk_SpecMap", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Preimmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsPreimmersion.of_isLocalization", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Preimmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsPreimmersion.instIsStableUnderBaseChangeScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Preimmersion", "is_tactic_proof": true, "tactics": ["refine", "have", "constructor", "let", "simp", "have", "exact"], "tactic_count": 7}
{"name": "AlgebraicGeometry.isProper_eq", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Proper", "is_tactic_proof": true, "tactics": ["ext", "rw", "rfl"], "tactic_count": 3}
{"name": "AlgebraicGeometry.IsProper.instRespectsIsoScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Proper", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "AlgebraicGeometry.IsProper.stableUnderComposition", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Proper", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "AlgebraicGeometry.IsProper.instIsMultiplicativeScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Proper", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "AlgebraicGeometry.IsProper.instCompScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Proper", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsProper.instOfIsFinite", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Proper", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsProper.isStableUnderBaseChange", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Proper", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "AlgebraicGeometry.IsProper.instIsZariskiLocalAtTarget", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Proper", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "AlgebraicGeometry.IsProper.instFstScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Proper", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsProper.instSndScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Proper", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsProper.instMorphismRestrict", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Proper", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsFinite.eq_isProper_inf_isAffineHom", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Proper", "is_tactic_proof": false, "tactics": ["have", "inf_eq_left.mpr", "rw", "inf_assoc,"], "tactic_count": 4}
{"name": "AlgebraicGeometry.IsFinite.iff_isProper_and_isAffineHom", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Proper", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "AlgebraicGeometry.instIsProperOfIsFinite", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Proper", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instHasOfPostcompPropertySchemeUniversallyClosedIsSeparated", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Proper", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.UniversallyClosed.of_comp_of_isSeparated", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Proper", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instHasOfPostcompPropertySchemeIsProperIsSeparated", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Proper", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsProper.of_comp", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Proper", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsProper.comp_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Proper", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.isIntegral_appTop_of_universallyClosed", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Proper", "is_tactic_proof": true, "tactics": ["have", "have", "rwa", "have", "rw", "exact"], "tactic_count": 6}
{"name": "AlgebraicGeometry.isField_of_universallyClosed", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Proper", "is_tactic_proof": true, "tactics": ["let", "have", "apply", "exact", "algebraize", "exact"], "tactic_count": 6}
{"name": "AlgebraicGeometry.finite_appTop_of_universallyClosed", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Proper", "is_tactic_proof": true, "tactics": ["have", "obtain", "letI", "letI", "have", "apply", "exact"], "tactic_count": 7}
{"name": "AlgebraicGeometry.quasiCompact_iff_isSpectralMap", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.isSpectralMap", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiCompact", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Hom.isCompact_preimage", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.quasiCompact_of_isIso", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiCompact", "is_tactic_proof": true, "tactics": ["constructor", "intro", "convert", "rw", "delta", "exact", "exact"], "tactic_count": 7}
{"name": "AlgebraicGeometry.quasiCompact_comp", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiCompact", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "apply", "exact", "apply"], "tactic_count": 6}
{"name": "AlgebraicGeometry.isCompact_and_isOpen_iff_finite_and_eq_biUnion_affineOpens", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiCompact", "is_tactic_proof": true, "tactics": ["apply", "rw", "exact"], "tactic_count": 3}
{"name": "AlgebraicGeometry.isCompact_iff_finite_and_eq_biUnion_affineOpens", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiCompact", "is_tactic_proof": true, "tactics": ["convert", "simp", "convert"], "tactic_count": 3}
{"name": "AlgebraicGeometry.isCompact_and_isOpen_iff_finite_and_eq_biUnion_basicOpen", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.quasiCompact_iff_forall_isAffineOpen", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiCompact", "is_tactic_proof": true, "tactics": ["rw", "refine", "intro", "obtain", "simp", "exact"], "tactic_count": 6}
{"name": "AlgebraicGeometry.isCompact_basicOpen", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiCompact", "is_tactic_proof": true, "tactics": ["classical", "refine", "obtain", "let", "rw", "exact", "haveI", "refine", "rw"], "tactic_count": 9}
{"name": "AlgebraicGeometry.instHasAffinePropertyQuasiCompactCompactSpaceCarrierCarrierCommRingCat", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.compactSpace_iff_quasiCompact", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiCompact", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgebraicGeometry.instQuasiCompactToSpecΓOfCompactSpaceCarrierCarrierCommRingCat", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.QuasiCompact.compactSpace_of_compactSpace", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiCompact", "is_tactic_proof": true, "tactics": ["constructor", "rw", "exact"], "tactic_count": 3}
{"name": "AlgebraicGeometry.quasiCompact_isStableUnderComposition", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instIsMultiplicativeSchemeQuasiCompact", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.quasiCompact_isStableUnderBaseChange", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiCompact", "is_tactic_proof": true, "tactics": ["letI", "apply", "apply", "intro", "let", "have", "have", "exact"], "tactic_count": 8}
{"name": "AlgebraicGeometry.instQuasiCompactFstScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instQuasiCompactSndScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instQuasiCompactMorphismRestrict", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instCompactSpaceCarrierCarrierCommRingCatPullbackSchemeOfQuasiCompact", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instCompactSpaceCarrierCarrierCommRingCatPullbackSchemeOfQuasiCompact_1", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.compactSpace_iff_exists", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiCompact", "is_tactic_proof": true, "tactics": ["refine", "let", "refine", "refine", "obtain", "exact"], "tactic_count": 6}
{"name": "AlgebraicGeometry.isCompact_iff_exists", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiCompact", "is_tactic_proof": true, "tactics": ["refine", "refine", "refine", "rw", "apply", "simp", "rwa"], "tactic_count": 7}
{"name": "AlgebraicGeometry.isClosedMap_iff_specializingMap", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiCompact", "is_tactic_proof": true, "tactics": ["refine", "wlog", "change", "rw", "intro", "have", "refine", "exact", "obtain", "clear", "intro", "replace", "wlog", "obtain", "have", "have", "simp_rw", "exact", "obtain", "obtain", "exact"], "tactic_count": 21}
{"name": "AlgebraicGeometry.compact_open_induction_on", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiCompact", "is_tactic_proof": true, "tactics": ["obtain", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "AlgebraicGeometry.exists_pow_mul_eq_zero_of_res_basicOpen_eq_zero_of_isAffineOpen", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiCompact", "is_tactic_proof": true, "tactics": ["rw", "obtain", "exact"], "tactic_count": 3}
{"name": "AlgebraicGeometry.exists_pow_mul_eq_zero_of_res_basicOpen_eq_zero_of_isCompact", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiCompact", "is_tactic_proof": true, "tactics": ["obtain", "replace", "have", "rw", "exact", "have", "exists_pow_mul_eq_zero_of_res_basicOpen_eq_zero_of_isAffineOpen", "swap", "change", "have", "convert", "simp", "rfl", "rw", "simp", "choose", "haveI", "cases", "use", "suffices", "subst", "apply", "intro", "change", "rw", "apply", "intro", "replace", "dsimp", "simp", "rwa", "apply"], "tactic_count": 32}
{"name": "AlgebraicGeometry.Scheme.isNilpotent_iff_basicOpen_eq_bot_of_isCompact", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiCompact", "is_tactic_proof": true, "tactics": ["refine", "have", "have", "rw", "rw", "change", "rw", "obtain", "rw", "use"], "tactic_count": 10}
{"name": "AlgebraicGeometry.Scheme.isNilpotent_iff_basicOpen_eq_bot", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.zeroLocus_eq_univ_iff_subset_nilradical_of_isCompact", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiCompact", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.zeroLocus_eq_univ_iff_subset_nilradical", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instHasRingHomPropertyLocallyQuasiFiniteQuasiFinite", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instIsStableUnderCompositionSchemeLocallyQuasiFinite", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instLocallyQuasiFiniteCompScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instLocallyQuasiFiniteOfIsFinite", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiFinite", "is_tactic_proof": true, "tactics": ["rw", "rw", "refine", "exact"], "tactic_count": 4}
{"name": "AlgebraicGeometry.instLocallyQuasiFiniteOfIsImmersion", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiFinite", "is_tactic_proof": true, "tactics": ["rw", "have", "infer_instance"], "tactic_count": 3}
{"name": "AlgebraicGeometry.LocallyQuasiFinite.of_comp", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instIsMultiplicativeSchemeLocallyQuasiFinite", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instIsStableUnderBaseChangeSchemeLocallyQuasiFinite", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instLocallyQuasiFiniteFstScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instLocallyQuasiFiniteSndScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instLocallyQuasiFiniteMorphismRestrict", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instLocallyQuasiFiniteResLE", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiFinite", "is_tactic_proof": true, "tactics": ["delta"], "tactic_count": 1}
{"name": "AlgebraicGeometry.quasiSeparatedSpace_iff_forall_affineOpens", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiSeparated", "is_tactic_proof": true, "tactics": ["rw", "constructor", "intro", "intro", "suffices", "intro", "intro", "refine", "simp", "intro", "change", "rw", "apply", "clear", "refine", "simp", "intro", "change", "rw", "apply", "apply"], "tactic_count": 21}
{"name": "AlgebraicGeometry.quasiCompact_affineProperty_iff_quasiSeparatedSpace", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiSeparated", "is_tactic_proof": true, "tactics": ["delta", "rw", "constructor", "intro", "haveI", "haveI", "let", "have", "rw", "erw", "rw", "exact", "introv", "let", "have", "rw", "simp_rw", "exact"], "tactic_count": 18}
{"name": "AlgebraicGeometry.quasiSeparated_eq_diagonal_is_quasiCompact", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiSeparated", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "AlgebraicGeometry.instHasAffinePropertyQuasiSeparatedQuasiSeparatedSpaceCarrierCarrierCommRingCat", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiSeparated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instQuasiSeparatedOfMonoScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiSeparated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.quasiSeparated_isStableUnderComposition", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiSeparated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instIsMultiplicativeSchemeQuasiSeparated", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiSeparated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.quasiSeparated_isStableUnderBaseChange", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiSeparated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.quasiSeparated_comp", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiSeparated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.quasiSeparatedSpace_iff_quasiSeparated", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiSeparated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instQuasiSeparatedFstScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiSeparated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instQuasiSeparatedSndScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiSeparated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instQuasiSeparatedMorphismRestrict", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiSeparated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instQuasiSeparatedResLE", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiSeparated", "is_tactic_proof": true, "tactics": ["delta"], "tactic_count": 1}
{"name": "AlgebraicGeometry.quasiSeparatedSpace_of_quasiSeparated", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiSeparated", "is_tactic_proof": true, "tactics": ["rw", "rw", "infer_instance"], "tactic_count": 3}
{"name": "AlgebraicGeometry.Scheme.Hom.isQuasiSeparated_preimage", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiSeparated", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "AlgebraicGeometry.quasiSeparatedSpace_of_isAffine", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiSeparated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsAffineOpen.isQuasiSeparated", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiSeparated", "is_tactic_proof": true, "tactics": ["rw", "exacts"], "tactic_count": 2}
{"name": "AlgebraicGeometry.instQuasiSeparatedToSpecΓOfQuasiSeparatedSpaceCarrierCarrierCommRingCat", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiSeparated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.quasiSeparatedSpace_of_isOpenCover", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiSeparated", "is_tactic_proof": true, "tactics": ["letI", "rw", "have", "refine", "rw", "simpa"], "tactic_count": 6}
{"name": "AlgebraicGeometry.quasiSeparatedSpace_iff_quasiCompact_prod_lift", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiSeparated", "is_tactic_proof": false, "tactics": ["rw", "congr", "ext"], "tactic_count": 3}
{"name": "AlgebraicGeometry.instQuasiCompactLiftSchemeIdOfQuasiSeparatedSpaceCarrierCarrierCommRingCat", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiSeparated", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "AlgebraicGeometry.instQuasiCompactιSchemeOfQuasiSeparatedSpaceCarrierCarrierCommRingCat", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiSeparated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instCompactSpaceCarrierCarrierCommRingCatEqualizerSchemeOfQuasiSeparatedSpace", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiSeparated", "is_tactic_proof": true, "tactics": ["constructor", "simpa"], "tactic_count": 2}
{"name": "AlgebraicGeometry.QuasiSeparated.of_comp", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiSeparated", "is_tactic_proof": true, "tactics": ["let", "have", "apply", "rintro", "refine", "exact", "pullback.map", "exact"], "tactic_count": 8}
{"name": "AlgebraicGeometry.QuasiSeparated.of_quasiSeparatedSpace", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiSeparated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.quasiSeparated_iff_quasiSeparatedSpace", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiSeparated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instHasOfPostcompPropertySchemeQuasiSeparatedTopMorphismProperty", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiSeparated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instHasOfPostcompPropertySchemeQuasiCompactQuasiSeparated", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiSeparated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.QuasiCompact.of_comp", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiSeparated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.quasiCompact_of_compactSpace", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiSeparated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.quasiCompact_iff_compactSpace", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiSeparated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.exists_eq_pow_mul_of_isAffineOpen", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiSeparated", "is_tactic_proof": true, "tactics": ["have", "obtain", "use", "simpa"], "tactic_count": 4}
{"name": "AlgebraicGeometry.exists_eq_pow_mul_of_is_compact_of_quasi_separated_space_aux_aux", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiSeparated", "is_tactic_proof": true, "tactics": ["apply_fun", "apply_fun", "dsimp", "simp", "rw"], "tactic_count": 5}
{"name": "AlgebraicGeometry.exists_eq_pow_mul_of_is_compact_of_quasi_separated_space_aux", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiSeparated", "is_tactic_proof": false, "tactics": ["obtain", "apply", "change", "simp", "exact", "change", "simp", "exact", "use", "intro", "rw", "simp", "rw"], "tactic_count": 13}
{"name": "AlgebraicGeometry.exists_eq_pow_mul_of_isCompact_of_isQuasiSeparated", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiSeparated", "is_tactic_proof": true, "tactics": ["dsimp", "revert", "refine", "intro", "use", "refine", "rw", "exact", "intro", "obtain", "hU", "obtain", "exists_eq_pow_mul_of_isAffineOpen", "dsimp", "obtain", "isCompact_and_isOpen_iff_finite_and_eq_biUnion_affineOpens.mp", "haveI", "cases", "replace", "have", "refine", "rw", "exact", "have", "refine", "rw", "exact", "have", "choose", "have", "fapply", "refine", "exact", "exact", "intro", "change", "simp", "apply", "exact", "use", "use", "refine", "change", "rw", "simp", "homOfLE_comp]", "change", "simp", "homOfLE_comp]"], "tactic_count": 49}
{"name": "AlgebraicGeometry.isLocalization_basicOpen_of_qcqs", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiSeparated", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "simp", "exact", "intro", "obtain", "refine", "simpa", "intro", "rw", "simp_rw", "generalize", "intro", "obtain", "refine", "simpa"], "tactic_count": 16}
{"name": "AlgebraicGeometry.exists_of_res_eq_of_qcqs", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiSeparated", "is_tactic_proof": true, "tactics": ["obtain", "use"], "tactic_count": 2}
{"name": "AlgebraicGeometry.exists_of_res_eq_of_qcqs_of_top", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiSeparated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.exists_of_res_zero_of_qcqs", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiSeparated", "is_tactic_proof": true, "tactics": ["suffices", "apply", "simpa"], "tactic_count": 3}
{"name": "AlgebraicGeometry.exists_of_res_zero_of_qcqs_of_top", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiSeparated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.isIso_ΓSpec_adjunction_unit_app_basicOpen", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.QuasiSeparated", "is_tactic_proof": false, "tactics": ["refine", "rw", "apply", "exact", "refine", "exact", "exact", "simp"], "tactic_count": 8}
{"name": "RingHom.IsStableUnderBaseChange.pullback_fst_appTop", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties", "is_tactic_proof": true, "tactics": ["erw", "rw", "have", "congr_arg", "simp", "rw", "hP'.cancel_right_isIso]", "exact"], "tactic_count": 8}
{"name": "AlgebraicGeometry.sourceAffineLocally", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.affineLocally", "kind": "abbrev", "module": "Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.sourceAffineLocally_respectsIso", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties", "is_tactic_proof": true, "tactics": ["apply", "introv", "have", "inferInstanceAs", "rw", "exact", "introv", "rw", "exact"], "tactic_count": 9}
{"name": "AlgebraicGeometry.affineLocally_respectsIso", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.sourceAffineLocally_morphismRestrict", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.affineLocally_iff_affineOpens_le", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.affineLocally_iff_forall_isAffineOpen", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.sourceAffineLocally_isLocal", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties", "is_tactic_proof": true, "tactics": ["constructor", "exact", "intro", "rw", "intro", "have", "simp", "rw", "simpa", "rw", "simp", "apply", "exact", "introv", "apply", "intro", "simp_rw", "have", "hs", "rwa", "h₁.isLocalization_away_iff]"], "tactic_count": 21}
{"name": "AlgebraicGeometry.affineLocally_le", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.exists_basicOpen_le_appLE_of_appLE_of_isAffine", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties", "is_tactic_proof": true, "tactics": ["obtain", "have", "have", "simpa", "obtain", "haveI", "haveI", "haveI", "have", "rw", "apply", "simp", "have", "f.appLE", "f.appLE", "simp", "congr", "apply", "refine", "rw", "apply", "rw", "exact"], "tactic_count": 23}
{"name": "AlgebraicGeometry.exists_affineOpens_le_appLE_of_appLE", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "obtain", "exists_basicOpen_le_appLE_of_appLE_of_isAffine", "exact", "le_trans"], "tactic_count": 6}
{"name": "AlgebraicGeometry.HasRingHomProperty.copy", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties", "is_tactic_proof": true, "tactics": ["subst", "have", "ext", "exact", "rw", "infer_instance"], "tactic_count": 6}
{"name": "AlgebraicGeometry.HasRingHomProperty.eq_affineLocally", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.HasRingHomProperty.HasAffineProperty", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.HasRingHomProperty.instIsZariskiLocalAtTarget", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.HasRingHomProperty.appLE", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "AlgebraicGeometry.HasRingHomProperty.appTop", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "AlgebraicGeometry.HasRingHomProperty.comp_of_isOpenImmersion", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties", "is_tactic_proof": true, "tactics": ["rw", "intro", "have", "inferInstanceAs", "rw", "exact"], "tactic_count": 6}
{"name": "AlgebraicGeometry.HasRingHomProperty.iff_appLE", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgebraicGeometry.HasRingHomProperty.of_source_openCover", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties", "is_tactic_proof": true, "tactics": ["rw", "intro", "let", "induction", "basicOpen", "simp_rw", "have", "exact", "openCover", "apply", "hs", "rintro", "refine", "rw", "exact", "hU", "specialize", "rw", "exact"], "tactic_count": 19}
{"name": "AlgebraicGeometry.HasRingHomProperty.iff_of_source_openCover", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.HasRingHomProperty.iff_of_isAffine", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "AlgebraicGeometry.HasRingHomProperty.Spec_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "AlgebraicGeometry.HasRingHomProperty.of_iSup_eq_top", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties", "is_tactic_proof": true, "tactics": ["have", "refine", "simpa"], "tactic_count": 3}
{"name": "AlgebraicGeometry.HasRingHomProperty.iff_of_iSup_eq_top", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.HasRingHomProperty.instIsZariskiLocalAtSource", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties", "is_tactic_proof": true, "tactics": ["apply", "intro", "simp_rw", "iff_of_source_openCover", "simp"], "tactic_count": 5}
{"name": "AlgebraicGeometry.HasRingHomProperty.containsIdentities", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.HasRingHomProperty.isLocal_ringHomProperty_of_isZariskiLocalAtSource_of_isZariskiLocalAtTarget", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties", "is_tactic_proof": false, "tactics": ["have", "constructor", "intro", "refine", "exact", "intro", "apply", "intro", "simp", "exact", "intro", "apply", "intro", "exact", "intro", "have", "change", "rw", "exact"], "tactic_count": 19}
{"name": "AlgebraicGeometry.HasRingHomProperty.of_isZariskiLocalAtSource_of_isZariskiLocalAtTarget", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.HasRingHomProperty.stalkwise", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties", "is_tactic_proof": true, "tactics": ["have", "have", "convert", "exact"], "tactic_count": 4}
{"name": "AlgebraicGeometry.HasRingHomProperty.stableUnderComposition", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.HasRingHomProperty.of_comp", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties", "is_tactic_proof": true, "tactics": ["wlog", "rw", "intro", "have", "rw", "exact", "wlog", "rw", "intro", "have", "rw", "exact", "wlog", "rw", "intro", "have", "rw", "exact", "rw", "exact"], "tactic_count": 20}
{"name": "AlgebraicGeometry.HasRingHomProperty.isMultiplicative", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.HasRingHomProperty.of_isOpenImmersion", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.HasRingHomProperty.isStableUnderBaseChange", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties", "is_tactic_proof": true, "tactics": ["apply", "letI", "apply", "intro", "rw", "wlog", "rw", "intro", "simp", "apply", "rw", "exact"], "tactic_count": 12}
{"name": "_private.Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties.0.AlgebraicGeometry.HasRingHomProperty.respects_isOpenImmersion_aux", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties", "is_tactic_proof": true, "tactics": ["wlog", "obtain", "let", "rw", "intro", "let", "have", "let", "simpa", "have", "simp", "rw", "refine", "rwa", "obtain", "use", "apply", "apply", "simp", "conv_rhs", "ext", "have", "simp", "obtain", "wlog", "rw", "intro", "rw", "exact", "rw", "exact"], "tactic_count": 31}
{"name": "AlgebraicGeometry.HasRingHomProperty.respects_isOpenImmersion", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.HasRingHomProperty.iff_exists_appLE_locally", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties", "is_tactic_proof": true, "tactics": ["have", "refine", "obtain", "obtain", "simp_rw", "obtain", "apply", "have", "have", "obtain", "refine", "rw", "haveI", "exact", "obtain", "use", "simp", "haveI", "toMorphismProperty_respectsIso_iff.mp", "exact"], "tactic_count": 20}
{"name": "AlgebraicGeometry.HasRingHomProperty.iff_exists_appLE", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties", "is_tactic_proof": true, "tactics": ["haveI", "haveI", "apply", "infer_instance", "rfl", "intro", "exact", "rw", "haveI", "apply"], "tactic_count": 10}
{"name": "AlgebraicGeometry.HasRingHomProperty.locally_of_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.HasRingHomProperty.of_stalkMap", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties", "is_tactic_proof": true, "tactics": ["have", "wlog", "rw", "intro", "refine", "exact", "wlog", "rw", "intro", "refine", "intro", "rw", "exact", "wlog", "rw", "rw", "refine", "rw", "apply", "use", "obtain", "obtain", "rw", "apply", "intro", "specialize", "rwa"], "tactic_count": 27}
{"name": "AlgebraicGeometry.HasRingHomProperty.stalkMap_of_respectsIso", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties", "is_tactic_proof": true, "tactics": ["wlog", "obtain", "obtain", "rw", "exact", "obtain", "wlog", "have", "refine", "rwa", "use", "rw", "have", "rwa", "obtain", "obtain", "rw", "rw", "apply"], "tactic_count": 19}
{"name": "AlgebraicGeometry.HasRingHomProperty.stalkMap", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsSeparated.isSeparated_eq_diagonal_isClosedImmersion", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Separated", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "AlgebraicGeometry.IsSeparated.isSeparated_of_mono", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Separated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsSeparated.instRespectsIsoScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Separated", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "AlgebraicGeometry.IsSeparated.instQuasiSeparated", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Separated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsSeparated.stableUnderComposition", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Separated", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "AlgebraicGeometry.IsSeparated.instCompScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Separated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsSeparated.instIsMultiplicativeScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Separated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsSeparated.isStableUnderBaseChange", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Separated", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "AlgebraicGeometry.IsSeparated.instIsZariskiLocalAtTarget", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Separated", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "AlgebraicGeometry.IsSeparated.instFstScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Separated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsSeparated.instSndScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Separated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsSeparated.instMorphismRestrict", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Separated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsSeparated.instResLE", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Separated", "is_tactic_proof": true, "tactics": ["delta"], "tactic_count": 1}
{"name": "AlgebraicGeometry.IsSeparated.instMap", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Separated", "is_tactic_proof": true, "tactics": ["constructor", "letI", "change", "rw", "exact"], "tactic_count": 5}
{"name": "AlgebraicGeometry.IsSeparated.of_isAffineHom", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Separated", "is_tactic_proof": true, "tactics": ["wlog", "rw", "intro", "have", "exact", "have", "rw", "infer_instance"], "tactic_count": 8}
{"name": "AlgebraicGeometry.IsSeparated.instIsClosedImmersionMapDescScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Separated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsSeparated.instIsClosedImmersionLiftSchemeId", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Separated", "is_tactic_proof": true, "tactics": ["rw", "rw", "convert", "ext"], "tactic_count": 4}
{"name": "AlgebraicGeometry.Scheme.Pullback.diagonalCoverDiagonalRange_eq_top_of_injective", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Separated", "is_tactic_proof": true, "tactics": ["rw", "rintro", "simp", "have", "hf", "let", "obtain", "obtain", "let", "obtain", "refine", "simp_rw", "change", "simp", "rw", "simp"], "tactic_count": 16}
{"name": "AlgebraicGeometry.Scheme.Pullback.range_diagonal_subset_diagonalCoverDiagonalRange", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Separated", "is_tactic_proof": true, "tactics": ["rintro", "simp", "let", "obtain", "obtain", "let", "obtain", "refine", "rw", "simp", "openCoverOfBase_X,", "simp_rw", "congr", "apply"], "tactic_count": 14}
{"name": "AlgebraicGeometry.isClosedImmersion_diagonal_restrict_diagonalCoverDiagonalRange", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Separated", "is_tactic_proof": false, "tactics": ["let", "have", "rw", "exact", "have", "rw", "intro", "rw", "infer_instance"], "tactic_count": 9}
{"name": "AlgebraicGeometry.isSeparated_of_injective", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Separated", "is_tactic_proof": true, "tactics": ["constructor", "let", "let", "refine", "rw", "exact"], "tactic_count": 6}
{"name": "AlgebraicGeometry.instHasOfPostcompPropertySchemeIsClosedImmersionIsSeparated", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Separated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsClosedImmersion.of_comp", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Separated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsClosedImmersion.comp_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Separated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instIsClosedImmersionInclusion", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Separated", "is_tactic_proof": false, "tactics": ["have", "simp", "infer_instance", "exact"], "tactic_count": 4}
{"name": "AlgebraicGeometry.IsSeparated.of_comp", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Separated", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "AlgebraicGeometry.IsSeparated.comp_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Separated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instHasOfPostcompPropertySchemeIsSeparatedTopMorphismProperty", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Separated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instHasOfPostcompPropertySchemeIsAffineHomIsSeparated", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Separated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsAffineHom.of_comp", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Separated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsAffineHom.comp_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Separated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.isClosedImmersion_equalizer_ι_left", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Separated", "is_tactic_proof": true, "tactics": ["refine", "rw", "convert", "ext1"], "tactic_count": 4}
{"name": "AlgebraicGeometry.ext_of_isDominant_of_isSeparated", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Separated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.ext_of_isDominant_of_isSeparated'", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Separated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.isSeparated_iff_isClosedImmersion_prod_lift", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Separated", "is_tactic_proof": false, "tactics": ["rw", "congr", "ext"], "tactic_count": 3}
{"name": "AlgebraicGeometry.Scheme.instIsClosedImmersionLiftIdOfIsSeparated", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Separated", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.instIsSeparatedOfIsAffine", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Separated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.instQuasiSeparatedSpaceCarrierCarrierCommRingCatOfIsSeparated", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Separated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.instIsSeparatedOfIsSeparated", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Separated", "is_tactic_proof": true, "tactics": ["apply", "rw", "infer_instance"], "tactic_count": 3}
{"name": "AlgebraicGeometry.Scheme.instIsClosedImmersionιOfIsSeparated", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Separated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsSeparated.hasAffineProperty", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Separated", "is_tactic_proof": true, "tactics": ["convert", "rw", "rfl"], "tactic_count": 3}
{"name": "AlgebraicGeometry.ext_of_isDominant", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Separated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instHasRingHomPropertyIsSmoothLocallyIsStandardSmooth", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Smooth", "is_tactic_proof": true, "tactics": ["apply", "exact", "exact", "intro", "rw"], "tactic_count": 5}
{"name": "AlgebraicGeometry.instIsStableUnderCompositionSchemeIsSmooth", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Smooth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.isSmooth_comp", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Smooth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.isSmooth_isStableUnderBaseChange", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Smooth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsSmoothOfRelativeDimension.isSmooth", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Smooth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instHasRingHomPropertyIsSmoothOfRelativeDimensionLocallyIsStandardSmoothOfRelativeDimension", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Smooth", "is_tactic_proof": true, "tactics": ["apply", "exact", "exact", "intro", "rw"], "tactic_count": 5}
{"name": "AlgebraicGeometry.isSmoothOfRelativeDimension_isStableUnderBaseChange", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.Smooth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instIsSmoothOfRelativeDimensionOfNatNatOfIsOpenImmersion", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Smooth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instIsSmoothOfIsOpenImmersion", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Smooth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.isSmoothOfRelativeDimension_comp", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Smooth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instIsSmoothOfRelativeDimensionOfNatNatCompScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Smooth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instIsMultiplicativeSchemeIsSmoothOfRelativeDimensionOfNatNat", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Smooth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instLocallyOfFinitePresentationOfIsSmooth", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.Smooth", "is_tactic_proof": true, "tactics": ["rw", "rw", "refine", "apply", "rwa", "finitePresentation_ofLocalizationSpanTarget]", "introv", "algebraize", "haveI", "exact"], "tactic_count": 10}
{"name": "AlgebraicGeometry.SurjectiveOnStalks.instOfIsOpenImmersion", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.SurjectiveOnStalks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.SurjectiveOnStalks.instIsMultiplicativeScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.SurjectiveOnStalks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.SurjectiveOnStalks.comp", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.SurjectiveOnStalks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.SurjectiveOnStalks.eq_stalkwise", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.SurjectiveOnStalks", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "AlgebraicGeometry.SurjectiveOnStalks.instIsZariskiLocalAtTarget", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.SurjectiveOnStalks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.SurjectiveOnStalks.instIsZariskiLocalAtSource", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.SurjectiveOnStalks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.SurjectiveOnStalks.Spec_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.SurjectiveOnStalks", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgebraicGeometry.SurjectiveOnStalks.instHasRingHomPropertySurjectiveOnStalks", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.SurjectiveOnStalks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.SurjectiveOnStalks.iff_of_isAffine", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.SurjectiveOnStalks", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgebraicGeometry.SurjectiveOnStalks.of_comp", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.SurjectiveOnStalks", "is_tactic_proof": true, "tactics": ["refine", "have", "rw", "exact"], "tactic_count": 4}
{"name": "AlgebraicGeometry.SurjectiveOnStalks.stableUnderBaseChange", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.SurjectiveOnStalks", "is_tactic_proof": true, "tactics": ["apply", "apply", "exact", "intro", "exact"], "tactic_count": 5}
{"name": "AlgebraicGeometry.SurjectiveOnStalks.mono_of_injective", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.SurjectiveOnStalks", "is_tactic_proof": true, "tactics": ["refine", "apply", "exact", "exact"], "tactic_count": 4}
{"name": "AlgebraicGeometry.SurjectiveOnStalks.isEmbedding_pullback", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.SurjectiveOnStalks", "is_tactic_proof": true, "tactics": ["let", "have", "intro", "have", "have", "obtain", "obtain", "algebraize", "rw", "convert", "ext1", "obtain", "simp", "ext", "simp", "erw", "rfl", "simp", "erw", "rfl", "let", "let", "let", "let", "have", "simp", "intro", "simp", "obtain", "have", "rwa", "obtain", "hsx.symm", "obtain", "hsy.symm", "obtain", "obtain", "refine", "let", "refine", "fun_prop", "rintro", "obtain", "hx₁.symm", "obtain", "hx₂.symm", "obtain", "refine", "simp", "simp", "dsimp", "rw", "erw", "congr", "apply", "intro", "have", "convert", "apply"], "tactic_count": 59}
{"name": "AlgebraicGeometry.instRespectsIsoSchemeTopologicallyInjective", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.UnderlyingMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.injective_isZariskiLocalAtTarget", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.UnderlyingMap", "is_tactic_proof": false, "tactics": ["refine", "obtain", "exact"], "tactic_count": 3}
{"name": "AlgebraicGeometry.surjective_eq_topologically", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.UnderlyingMap", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Hom.surjective", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.UnderlyingMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instSurjectiveOfIsIsoScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.UnderlyingMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instSurjectiveCompScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.UnderlyingMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Surjective.of_comp", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.UnderlyingMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Surjective.comp_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.UnderlyingMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instIsStableUnderCompositionSchemeSurjective", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.UnderlyingMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instRespectsIsoSchemeSurjective", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.UnderlyingMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instHasOfPrecompPropertySchemeSurjective", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.UnderlyingMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.surjective_isZariskiLocalAtTarget", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.UnderlyingMap", "is_tactic_proof": true, "tactics": ["have", "rw", "refine", "intro", "obtain", "obtain", "exact"], "tactic_count": 7}
{"name": "AlgebraicGeometry.range_eq_univ", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.UnderlyingMap", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "AlgebraicGeometry.range_eq_range_of_surjective", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.UnderlyingMap", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "AlgebraicGeometry.mem_range_iff_of_surjective", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.UnderlyingMap", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Surjective.sigmaDesc_of_union_range_eq_univ", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.UnderlyingMap", "is_tactic_proof": true, "tactics": ["refine", "simp_rw", "obtain", "use", "rw"], "tactic_count": 5}
{"name": "AlgebraicGeometry.instSurjectiveDescI₀SchemeF", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.UnderlyingMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.cover", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Morphisms.UnderlyingMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instUniqueI₀SchemeCover", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.UnderlyingMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.injective_isStableUnderComposition", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.UnderlyingMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instRespectsIsoSchemeTopologicallyIsOpenMap", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.UnderlyingMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.isOpenMap_isZariskiLocalAtTarget", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.UnderlyingMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instIsZariskiLocalAtSourceTopologicallyIsOpenMap", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.UnderlyingMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instRespectsIsoSchemeTopologicallyIsClosedMap", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.UnderlyingMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.isClosedMap_isZariskiLocalAtTarget", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.UnderlyingMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instRespectsIsoSchemeTopologicallyIsEmbedding", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.UnderlyingMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.isEmbedding_isZariskiLocalAtTarget", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.UnderlyingMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instRespectsIsoSchemeTopologicallyIsOpenEmbedding", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.UnderlyingMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.isOpenEmbedding_isZariskiLocalAtTarget", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.UnderlyingMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instRespectsIsoSchemeTopologicallyIsClosedEmbedding", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.UnderlyingMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.isClosedEmbedding_isZariskiLocalAtTarget", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.UnderlyingMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.dominant_eq_topologically", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.UnderlyingMap", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Hom.denseRange", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.UnderlyingMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instIsDominantOfSurjective", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.UnderlyingMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instIsDominantCompScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.UnderlyingMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instIsMultiplicativeSchemeIsDominant", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.UnderlyingMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsDominant.of_comp", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.UnderlyingMap", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "AlgebraicGeometry.IsDominant.comp_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.UnderlyingMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsDominant.respectsIso", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.UnderlyingMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsDominant.isZariskiLocalAtTarget", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.UnderlyingMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.surjective_of_isDominant_of_isClosed_range", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.UnderlyingMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsDominant.of_comp_of_isOpenImmersion", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.UnderlyingMap", "is_tactic_proof": true, "tactics": ["rw", "simp", "convert", "rw"], "tactic_count": 4}
{"name": "AlgebraicGeometry.specializingMap_respectsIso", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.UnderlyingMap", "is_tactic_proof": true, "tactics": ["apply", "introv", "exact", "introv", "exact"], "tactic_count": 5}
{"name": "AlgebraicGeometry.specializingMap_isZariskiLocalAtTarget", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.UnderlyingMap", "is_tactic_proof": true, "tactics": ["apply", "introv", "rw", "intro", "simp", "obtain", "rw", "exact", "introv", "simp_rw", "intro", "have", "obtain", "rw", "have", "have", "simp", "rwa", "obtain", "rw", "simp", "apply_fun", "simp", "use"], "tactic_count": 24}
{"name": "AlgebraicGeometry.instRespectsIsoSchemeTopologicallyGeneralizingMap", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.UnderlyingMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instIsZariskiLocalAtSourceTopologicallyGeneralizingMap", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.UnderlyingMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instIsZariskiLocalAtTargetTopologicallyGeneralizingMap", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.UnderlyingMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.isClosedMap", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.UniversallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.universallyClosed_eq", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.UniversallyClosed", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "AlgebraicGeometry.instUniversallyClosedOfIsClosedImmersion", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.UniversallyClosed", "is_tactic_proof": true, "tactics": ["rw", "intro", "have", "exact"], "tactic_count": 4}
{"name": "AlgebraicGeometry.universallyClosed_respectsIso", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.UniversallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.universallyClosed_isStableUnderBaseChange", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.UniversallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.isClosedMap_isStableUnderComposition", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.UniversallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.universallyClosed_isStableUnderComposition", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.UniversallyClosed", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "AlgebraicGeometry.UniversallyClosed.of_comp_surjective", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.UniversallyClosed", "is_tactic_proof": true, "tactics": ["constructor", "intro", "have", "exact"], "tactic_count": 4}
{"name": "AlgebraicGeometry.universallyClosedTypeComp", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.UniversallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instIsMultiplicativeSchemeUniversallyClosed", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.UniversallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.universallyClosed_fst", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.UniversallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.universallyClosed_snd", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.UniversallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.universallyClosed_isZariskiLocalAtTarget", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.UniversallyClosed", "is_tactic_proof": true, "tactics": ["rw", "apply", "intro", "simp_rw", "exact"], "tactic_count": 5}
{"name": "AlgebraicGeometry.instUniversallyClosedMorphismRestrict", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.UniversallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.compactSpace_of_universallyClosed", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.UniversallyClosed", "is_tactic_proof": true, "tactics": ["classical", "let", "let", "let", "let", "let", "let", "let", "let", "have", "simp", "exact", "let", "let", "let", "have", "have", "intro", "suffices", "exact", "obtain", "let", "let", "let", "have", "show", "have", "suffices", "rw", "contrapose", "obtain", "obtain", "suffices", "intro", "rw", "cases"], "tactic_count": 36}
{"name": "AlgebraicGeometry.Scheme.Hom.isProperMap", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.UniversallyClosed", "is_tactic_proof": true, "tactics": ["rw", "refine", "have", "rw", "exact"], "tactic_count": 5}
{"name": "AlgebraicGeometry.instQuasiCompactOfUniversallyClosed", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.UniversallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.universallyClosed_eq_universallySpecializing", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.UniversallyClosed", "is_tactic_proof": true, "tactics": ["rw", "apply", "rw", "exact", "rw", "exact"], "tactic_count": 6}
{"name": "AlgebraicGeometry.Surjective.of_universallyClosed_of_isDominant", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.UniversallyClosed", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Hom.injective", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.UniversallyInjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.universallyInjective_eq", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.UniversallyInjective", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "AlgebraicGeometry.universallyInjective_eq_diagonal", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.UniversallyInjective", "is_tactic_proof": true, "tactics": ["apply", "intro", "refine", "rw", "rfl", "rw", "universallyInjective_eq]", "apply", "intro", "obtain", "obtain", "rw"], "tactic_count": 12}
{"name": "AlgebraicGeometry.UniversallyInjective.iff_diagonal", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.UniversallyInjective", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgebraicGeometry.instUniversallyInjectiveOfMonoScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.UniversallyInjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.UniversallyInjective.respectsIso", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.UniversallyInjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.UniversallyInjective.isStableUnderBaseChange", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.UniversallyInjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.universallyInjective_isStableUnderComposition", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.UniversallyInjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instIsMultiplicativeSchemeUniversallyInjective", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.UniversallyInjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.universallyInjective_isZariskiLocalAtTarget", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.UniversallyInjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.isOpenMap", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.UniversallyOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.UniversallyOpen.eq", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.UniversallyOpen", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "AlgebraicGeometry.UniversallyOpen.instOfIsOpenImmersion", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.UniversallyOpen", "is_tactic_proof": true, "tactics": ["rw", "intro", "have", "exact"], "tactic_count": 4}
{"name": "AlgebraicGeometry.UniversallyOpen.instRespectsIsoScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.UniversallyOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.UniversallyOpen.instIsStableUnderBaseChangeScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.UniversallyOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.UniversallyOpen.instIsStableUnderCompositionSchemeTopologicallyIsOpenMap", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.UniversallyOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.UniversallyOpen.instIsStableUnderCompositionScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.UniversallyOpen", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "AlgebraicGeometry.UniversallyOpen.instCompScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.UniversallyOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.UniversallyOpen.instIsMultiplicativeScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.UniversallyOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.UniversallyOpen.fst", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.UniversallyOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.UniversallyOpen.snd", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.UniversallyOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.UniversallyOpen.instIsZariskiLocalAtTarget", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.UniversallyOpen", "is_tactic_proof": true, "tactics": ["rw", "apply", "intro", "simp_rw", "exact"], "tactic_count": 5}
{"name": "AlgebraicGeometry.UniversallyOpen.instIsZariskiLocalAtSource", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.UniversallyOpen", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "AlgebraicGeometry.isOpenMap_of_generalizingMap", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.UniversallyOpen", "is_tactic_proof": true, "tactics": ["change", "wlog", "rw", "intro", "dsimp", "refine", "exact", "obtain", "wlog", "rw", "intro", "refine", "exact", "obtain", "obtain", "algebraize", "convert", "rwa", "apply"], "tactic_count": 19}
{"name": "AlgebraicGeometry.Flat.generalizingMap", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Morphisms.UniversallyOpen", "is_tactic_proof": false, "tactics": ["have", "change", "rw", "intro", "algebraize", "apply", "convert", "exact"], "tactic_count": 8}
{"name": "AlgebraicGeometry.UniversallyOpen.of_flat", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Morphisms.UniversallyOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.isNoetherianRing_of_away", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Noetherian", "is_tactic_proof": true, "tactics": ["apply", "intro", "let", "let", "let", "have", "intro", "apply", "let", "exact", "let", "use", "have", "intro", "rw", "iInf_subtype',", "apply", "intro", "congr", "rw", "exact"], "tactic_count": 21}
{"name": "AlgebraicGeometry.isLocallyNoetherian_of_affine_cover", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Noetherian", "is_tactic_proof": true, "tactics": ["refine", "induction", "basicOpen", "have", "exact", "openCover", "apply", "intro", "have", "have", "have", "exact", "hU"], "tactic_count": 13}
{"name": "AlgebraicGeometry.isLocallyNoetherian_iff_of_iSup_eq_top", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Noetherian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.isLocallyNoetherian_iff_of_affine_openCover", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Noetherian", "is_tactic_proof": true, "tactics": ["constructor", "intro", "let", "have", "apply", "apply", "exact", "intro", "let", "apply", "rw", "intro", "apply", "apply", "exact"], "tactic_count": 15}
{"name": "AlgebraicGeometry.isLocallyNoetherian_of_isOpenImmersion", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Noetherian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instIsLocallyNoetherianToScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Noetherian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instIsLocallyNoetherianXScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Noetherian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.isLocallyNoetherian_iff_openCover", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Noetherian", "is_tactic_proof": true, "tactics": ["refine", "rw", "intro", "exact"], "tactic_count": 4}
{"name": "AlgebraicGeometry.instNoetherianSpaceCarrierCarrierCommRingCatSpecOfIsNoetherianRingCarrier", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Noetherian", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "AlgebraicGeometry.noetherianSpace_of_isAffine", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Noetherian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.noetherianSpace_of_isAffineOpen", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Noetherian", "is_tactic_proof": false, "tactics": ["have", "isNoetherianRing_of_ringEquiv", "exact"], "tactic_count": 3}
{"name": "AlgebraicGeometry.instIsLocallyNoetherianSpecOfIsNoetherianRingCarrier", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Noetherian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.isLocallyNoetherian_Spec", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Noetherian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instQuasiCompactOfIsLocallyNoetherianOfIsOpenImmersion", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Noetherian", "is_tactic_proof": true, "tactics": ["apply", "intro", "rw", "apply", "apply", "convert", "apply", "exact", "exact"], "tactic_count": 9}
{"name": "AlgebraicGeometry.IsLocallyNoetherian.quasiSeparatedSpace", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Noetherian", "is_tactic_proof": true, "tactics": ["apply", "intro", "have", "apply", "rw", "apply", "apply", "convert", "apply", "exact", "rw", "exact", "rw", "exact"], "tactic_count": 14}
{"name": "AlgebraicGeometry.LocallyOfFiniteType.isLocallyNoetherian", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Noetherian", "is_tactic_proof": false, "tactics": ["change", "id", "wlog", "exact", "this", "wlog", "exact", "obtain", "obtain", "obtain", "have", "algebraize", "simp_all"], "tactic_count": 13}
{"name": "AlgebraicGeometry.isNoetherian_iff_of_finite_iSup_eq_top", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Noetherian", "is_tactic_proof": true, "tactics": ["constructor", "intro", "apply", "exact", "intro", "convert", "exact", "constructor", "rw", "apply", "intro", "apply", "convert", "have", "apply"], "tactic_count": 15}
{"name": "AlgebraicGeometry.isNoetherian_iff_of_finite_affine_openCover", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Noetherian", "is_tactic_proof": true, "tactics": ["constructor", "intro", "apply", "exact", "intro", "convert", "exact", "exact"], "tactic_count": 8}
{"name": "AlgebraicGeometry.IsNoetherian.noetherianSpace", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Noetherian", "is_tactic_proof": true, "tactics": ["apply", "let", "rw", "suffices", "intro", "have", "rw", "apply", "let", "convert", "apply"], "tactic_count": 11}
{"name": "AlgebraicGeometry.quasiCompact_of_noetherianSpace_source", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Noetherian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instIsNoetherianSpecOfIsNoetherianRingCarrier", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Noetherian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instIsNoetherianSpecOfOfIsNoetherianRing", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Noetherian", "is_tactic_proof": true, "tactics": ["suffices", "assumption"], "tactic_count": 2}
{"name": "AlgebraicGeometry.instIsNoetherianRingCarrierStalkCommRingCatPresheafOfIsLocallyNoetherian", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Noetherian", "is_tactic_proof": true, "tactics": ["obtain", "have", "exact"], "tactic_count": 3}
{"name": "AlgebraicGeometry.isNoetherian_Spec", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Noetherian", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.finite_irreducibleComponents_of_isNoetherian", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Noetherian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.normalizationDiagram", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Normalization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.normalizationDiagramMap", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Normalization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.preservesLocalization_normalizationDiagramMap", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Normalization", "is_tactic_proof": true, "tactics": ["intro", "let", "let", "let", "let", "have", "have", "let", "dsimp", "rw", "exact", "isLocalization_basicOpen_of_qcqs", "change", "letI", "have", "have", "simp", "have", "have", "exact"], "tactic_count": 20}
{"name": "AlgebraicGeometry.Scheme.Hom.instIsLocallyDirectedAffineZariskiSiteCompOppositeCommRingCatRightOpOpensOpToOpensFunctorNormalizationDiagramSpecForget", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Normalization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.instIsOpenImmersionMapAffineZariskiSiteCompOppositeCommRingCatRightOpOpensOpToOpensFunctorNormalizationDiagramSpec", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Normalization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.normalization", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Normalization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.normalizationOpenCover", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Normalization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.toNormalization", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Normalization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.ι_toNormalization", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Normalization", "is_tactic_proof": true, "tactics": ["rw", "trans", "congr", "delta", "generalize_proofs", "exact"], "tactic_count": 6}
{"name": "AlgebraicGeometry.Scheme.Hom.fromNormalization", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Normalization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.ι_fromNormalization", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Normalization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.fromNormalization_preimage", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Normalization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.toNormalization_fromNormalization", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Normalization", "is_tactic_proof": false, "tactics": ["refine", "refine", "rw", "change", "simp"], "tactic_count": 5}
{"name": "AlgebraicGeometry.Scheme.Hom.instIsIntegralHomFromNormalization", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Normalization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.toNormalization_app_preimage", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Normalization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.instIsIsoToNormalizationOfIsIntegralHom", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Normalization", "is_tactic_proof": true, "tactics": ["refine", "let", "simp", "rw", "letI", "convert_to", "rw", "simp", "have", "rw", "exact", "rw", "exact", "inferInstanceAs"], "tactic_count": 14}
{"name": "AlgebraicGeometry.Scheme.Hom.instIsAffineHomToNormalization", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Normalization", "is_tactic_proof": true, "tactics": ["apply", "infer_instance", "rw", "infer_instance"], "tactic_count": 4}
{"name": "AlgebraicGeometry.Scheme.Hom.instQuasiCompactToNormalization", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Normalization", "is_tactic_proof": true, "tactics": ["apply", "infer_instance", "rw", "infer_instance"], "tactic_count": 4}
{"name": "AlgebraicGeometry.Scheme.Hom.instQuasiSeparatedToNormalization", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Normalization", "is_tactic_proof": true, "tactics": ["suffices", "rw", "infer_instance"], "tactic_count": 3}
{"name": "AlgebraicGeometry.Scheme.Hom.ker_toNormalization", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Normalization", "is_tactic_proof": false, "tactics": ["refine", "simp", "rw", "simp", "rw", "exact"], "tactic_count": 6}
{"name": "AlgebraicGeometry.Scheme.Hom.instIsDominantToNormalization", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Normalization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.instIsReducedNormalization", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Normalization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.instIsIntegralNormalization", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Normalization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.normalizationDesc", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Normalization", "is_tactic_proof": false, "tactics": ["refine", "colimit.desc", "ι.app", "ι.naturality", "algebraize", "have", "simp", "exact", "intros", "dsimp", "rw", "congr", "ext", "apply", "dsimp", "simp"], "tactic_count": 16}
{"name": "AlgebraicGeometry.Scheme.Hom.toNormalization_normalizationDesc", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Normalization", "is_tactic_proof": false, "tactics": ["refine", "letI", "refine", "dsimp", "simp", "change", "simp"], "tactic_count": 7}
{"name": "AlgebraicGeometry.Scheme.Hom.normalizationDesc_comp", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Normalization", "is_tactic_proof": true, "tactics": ["refine", "dsimp", "rw", "congr", "ext", "dsimp", "rw", "simp_rw"], "tactic_count": 8}
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{"name": "AlgebraicGeometry.Scheme.Hom.normalization.hom_ext", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Normalization", "is_tactic_proof": true, "tactics": ["apply", "let", "have", "have", "have", "have", "let", "have", "refine", "eq_of_SpecMap_comp_eq_of_isAffineOpen", "simp", "simp", "have", "simp", "have", "simp", "have", "have", "have", "trans", "simp", "rw", "have", "f.normalization.presheaf.map", "rw", "simp", "simp", "rw", "have", "f.normalization.presheaf.map", "rw", "simp"], "tactic_count": 32}
{"name": "AlgebraicGeometry.Scheme.Hom.normalizationCoprodIso", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Normalization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.toNormalization_inl_normalizationCoprodIso_hom", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Normalization", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Hom.toNormalization_inr_normalizationCoprodIso_hom", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Normalization", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Hom.inl_toNormalization_normalizationCoprodIso_inv", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Normalization", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Hom.inr_toNormalization_normalizationCoprodIso_inv", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Normalization", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Hom.inl_normalizationCoprodIso_hom_fromNormalization", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Normalization", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Hom.inr_normalizationCoprodIso_hom_fromNormalization", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Normalization", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Hom.normalizationCoprodIso_inv_coprodDesc_fromNormalization", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Normalization", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.IsOpenImmersion", "kind": "abbrev", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsOpenImmersion.comp", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.scheme", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsOpenImmersion.isOpen_range", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.isOpenEmbedding", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.opensRange", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.mem_opensRange", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.opensFunctor", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.term_''ᵁ_", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry._aux_Mathlib_AlgebraicGeometry_OpenImmersion___macroRules_AlgebraicGeometry_term_''ᵁ__1", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry._aux_Mathlib_AlgebraicGeometry_OpenImmersion___delab_app_AlgebraicGeometry_term_''ᵁ__1", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.coe_image", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.image_mono", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.opensFunctor_map_homOfLE", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.instIsContinuousOpensOpensFunctorGrothendieckTopologyCarrierCarrierCommRingCat", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.image_top_eq_opensRange", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.Hom.opensRange_comp", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.opensRange_of_isIso", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.opensRange_comp_of_isIso", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Hom.image_le_opensRange", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Hom.preimage_image_eq", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.Hom.image_le_image_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": true, "tactics": ["refine", "rw", "apply"], "tactic_count": 3}
{"name": "AlgebraicGeometry.Scheme.Hom.image_preimage_eq_opensRange_inf", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.Hom.image_preimage_le", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.image_injective", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": true, "tactics": ["intro", "simpa"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.Hom.image_iSup", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.Hom.image_iSup₂", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.Hom.comp_image", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.id_image", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.inv_image", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.apply_mem_image_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.preimage_opensRange", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Hom.instIsIsoCommRingCatAppObjOpensOpensFunctor", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": true, "tactics": ["delta"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Hom.isIso_app", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.Hom.appIso", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.appIso_inv_naturality", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.appIso_hom", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.appIso_hom'", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.app_appIso_inv", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.app_invApp'", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.appIso_inv_app", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.appLE_appIso_inv", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": ["simp", "opensFunctor_map_homOfLE,", "rw", "rfl"], "tactic_count": 4}
{"name": "AlgebraicGeometry.Scheme.Hom.appIso_inv_appLE", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": true, "tactics": ["simp", "rw", "rfl"], "tactic_count": 3}
{"name": "AlgebraicGeometry.Scheme.Hom.appIso_inv_app_presheafMap", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Hom.id_appIso", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Hom.comp_appIso", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "AlgebraicGeometry.IsOpenImmersion.opensEquiv", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.isOpenImmersion_SpecMap_localizationAway", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": true, "tactics": ["apply", "exact", "intro", "exact"], "tactic_count": 4}
{"name": "AlgebraicGeometry.Scheme.instIsOpenImmersionMapOfHomAwayAlgebraMap", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsOpenImmersion.of_isLocalization", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": true, "tactics": ["have", "rw", "have", "exact", "inferInstanceAs", "simp", "infer_instance"], "tactic_count": 7}
{"name": "AlgebraicGeometry.Scheme.exists_affine_mem_range_and_range_subset", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.toScheme", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": true, "tactics": ["apply", "intro", "obtain", "refine", "rw", "delta"], "tactic_count": 6}
{"name": "AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.toScheme_toLocallyRingedSpace", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.toSchemeHom", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.toSchemeHom_toPshHom", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.toSchemeHom_isOpenImmersion", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.scheme_eq_of_locallyRingedSpace_eq", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.scheme_toScheme", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": true, "tactics": ["apply", "exact"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.restrict", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.restrict_toPresheafedSpace", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.ofRestrict", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.ofRestrict_app", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsOpenImmersion.ofRestrict", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.ofRestrict_appLE", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": true, "tactics": ["dsimp", "exact"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.ofRestrict_appIso", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": true, "tactics": ["ext1", "simp"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.restrict_presheaf_map", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsOpenImmersion.of_isIso", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsOpenImmersion.isIso", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsOpenImmersion.of_isIso_stalkMap", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsOpenImmersion.instIsIsoCommRingCatStalkMap", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsOpenImmersion.of_comp", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsOpenImmersion.instHasOfPostcompPropertyScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsOpenImmersion.iff_isIso_stalkMap", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.isIso_iff_isOpenImmersion_and_epi_base", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.isIso_iff_isIso_stalkMap", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": true, "tactics": ["rw", "refine", "rintro", "convert_to", "h₂.continuous", "infer_instance", "intro"], "tactic_count": 7}
{"name": "AlgebraicGeometry.IsOpenImmersion.isoRestrict", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.AlgebraicGeometry.OpenImmersion.0.AlgebraicGeometry.IsOpenImmersion.termForget", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.AlgebraicGeometry.OpenImmersion.0.AlgebraicGeometry.IsOpenImmersion._aux_Mathlib_AlgebraicGeometry_OpenImmersion___macroRules__private_Mathlib_AlgebraicGeometry_OpenImmersion_0_AlgebraicGeometry_IsOpenImmersion_termForget_1", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.AlgebraicGeometry.OpenImmersion.0.AlgebraicGeometry.IsOpenImmersion._aux_Mathlib_AlgebraicGeometry_OpenImmersion___unexpand_AlgebraicGeometry_Scheme_forgetToLocallyRingedSpace_1", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsOpenImmersion.mono", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsOpenImmersion.le_monomorphisms", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsOpenImmersion.instIsOpenImmersionMapSchemeLocallyRingedSpaceForgetToLocallyRingedSpace", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsOpenImmersion.hasLimit_cospan_forget_of_left", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "AlgebraicGeometry.IsOpenImmersion.hasLimit_cospan_forget_of_left'", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsOpenImmersion.hasLimit_cospan_forget_of_right", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "AlgebraicGeometry.IsOpenImmersion.hasLimit_cospan_forget_of_right'", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsOpenImmersion.forgetCreatesPullbackOfLeft", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsOpenImmersion.forgetCreatesPullbackOfRight", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsOpenImmersion.instPreservesLimitSchemeLocallyRingedSpaceWalkingCospanCospanForgetToLocallyRingedSpace", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsOpenImmersion.instPreservesLimitSchemeLocallyRingedSpaceWalkingCospanCospanForgetToLocallyRingedSpace_1", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AlgebraicGeometry.IsOpenImmersion.instSndScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": true, "tactics": ["have", "dsimp", "change", "rw", "infer_instance"], "tactic_count": 5}
{"name": "AlgebraicGeometry.IsOpenImmersion.instFstScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "AlgebraicGeometry.IsOpenImmersion.instπWalkingCospanSchemeCospanOne", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": true, "tactics": ["rw", "change", "infer_instance"], "tactic_count": 3}
{"name": "AlgebraicGeometry.IsOpenImmersion.instPreservesLimitSchemeTopCatWalkingCospanCospanForgetToTop", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": true, "tactics": ["delta", "refine", "infer_instance", "refine", "dsimp", "infer_instance"], "tactic_count": 6}
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{"name": "AlgebraicGeometry.IsOpenImmersion.instPreservesLimitSchemeWalkingCospanCospanForget", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": true, "tactics": ["delta"], "tactic_count": 1}
{"name": "AlgebraicGeometry.IsOpenImmersion.instPreservesLimitSchemeWalkingCospanCospanForget_1", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": true, "tactics": ["delta"], "tactic_count": 1}
{"name": "AlgebraicGeometry.IsOpenImmersion.range_pullbackSnd", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": ["rw", "erw", "rw", "rfl", "rw", "infer_instance"], "tactic_count": 6}
{"name": "AlgebraicGeometry.Scheme.Hom.opensRange_pullbackSnd", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsOpenImmersion.range_pullbackFst", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": ["rw", "erw", "rw", "rfl", "rw", "infer_instance"], "tactic_count": 6}
{"name": "AlgebraicGeometry.Scheme.Hom.opensRange_pullbackFst", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsOpenImmersion.range_pullback_to_base_of_left", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgebraicGeometry.IsOpenImmersion.range_pullback_to_base_of_right", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgebraicGeometry.IsOpenImmersion.image_preimage_eq_preimage_image_of_isPullback", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "obtain", "simp", "simp", "constructor", "rintro", "rintro", "obtain", "rw", "cases"], "tactic_count": 11}
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{"name": "AlgebraicGeometry.IsOpenImmersion.lift_fac", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsOpenImmersion.lift_uniq", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsOpenImmersion.comp_lift", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.IsOpenImmersion.isPullback_lift_id", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": true, "tactics": ["convert", "exact", "simp"], "tactic_count": 3}
{"name": "AlgebraicGeometry.IsOpenImmersion.isoOfRangeEq", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsOpenImmersion.isoOfRangeEq_hom_fac", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsOpenImmersion.isoOfRangeEq_inv_fac", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsOpenImmersion.app_eq_invApp_app_of_comp_eq_aux", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": true, "tactics": ["simp_all"], "tactic_count": 1}
{"name": "AlgebraicGeometry.IsOpenImmersion.app_eq_appIso_inv_app_of_comp_eq", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": true, "tactics": ["subst", "rw", "op_comp,"], "tactic_count": 3}
{"name": "AlgebraicGeometry.IsOpenImmersion.lift_app", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsOpenImmersion.isPullback", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": ["let", "convert", "simp"], "tactic_count": 3}
{"name": "AlgebraicGeometry.IsOpenImmersion.ΓIso", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsOpenImmersion.ΓIso_inv", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.IsOpenImmersion.map_ΓIso_inv", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.IsOpenImmersion.app_ΓIso_hom", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "AlgebraicGeometry.IsOpenImmersion.ΓIsoTop", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsOpenImmersion.instLift", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.isIso_of_isOpenImmersion_of_opensRange_eq_top", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "AlgebraicGeometry.isOpenImmersion_isStableUnderComposition", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.isOpenImmersion_respectsIso", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": true, "tactics": ["apply", "intro", "have", "infer_instance"], "tactic_count": 4}
{"name": "AlgebraicGeometry.isOpenImmersion_isMultiplicative", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.isOpenImmersion_stableUnderBaseChange", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.image_basicOpen", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": true, "tactics": ["have", "rw", "rw", "refine", "exact"], "tactic_count": 5}
{"name": "AlgebraicGeometry.Scheme.image_zeroLocus", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.OpenImmersion", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "obtain", "simp", "simp", "exact"], "tactic_count": 6}
{"name": "AlgebraicGeometry.Scheme.Over", "kind": "abbrev", "module": "Mathlib.AlgebraicGeometry.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.CanonicallyOver", "kind": "abbrev", "module": "Mathlib.AlgebraicGeometry.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.IsOver", "kind": "abbrev", "module": "Mathlib.AlgebraicGeometry.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.isOver_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.asOver", "kind": "abbrev", "module": "Mathlib.AlgebraicGeometry.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.asOver", "kind": "abbrev", "module": "Mathlib.AlgebraicGeometry.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Ideal.span_eq_top_of_span_image_evalRingHom", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.PointsPi", "is_tactic_proof": false, "tactics": ["simp", "choose", "have", "refine", "ext", "simpa"], "tactic_count": 6}
{"name": "AlgebraicGeometry.eq_top_of_sigmaSpec_subset_of_isCompact", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.PointsPi", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "obtain", "hV'.elim_finite_subcover", "exact", "replace", "have", "rw", "trans", "simp", "rw", "exact", "have", "top_le_iff.mp", "simpa"], "tactic_count": 15}
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{"name": "AlgebraicGeometry.pointsPi", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.PointsPi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.pointsPi_injective", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.PointsPi", "is_tactic_proof": true, "tactics": ["rintro", "have", "isIso_of_comp_eq_sigmaSpec", "rw"], "tactic_count": 4}
{"name": "AlgebraicGeometry.pointsPi_surjective_of_isAffine", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.PointsPi", "is_tactic_proof": true, "tactics": ["rintro", "refine", "ext", "simp", "exact"], "tactic_count": 5}
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{"name": "AlgebraicGeometry.Proj.mem_basicOpen", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Proj.basicOpen_one", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Proj.basicOpen_zero", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Proj.basicOpen_pow", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Proj.basicOpen_mul", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Proj.basicOpen_mono", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Proj.basicOpen_eq_iSup_proj", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Proj.isBasis_basicOpen", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Basic", "is_tactic_proof": true, "tactics": ["delta", "convert", "exact"], "tactic_count": 3}
{"name": "AlgebraicGeometry.Proj.iSup_basicOpen_eq_top", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Basic", "is_tactic_proof": true, "tactics": ["classical", "refine", "by_contra", "simp", "refine", "rwa"], "tactic_count": 6}
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{"name": "AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.carrier.add_mem", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme", "is_tactic_proof": true, "tactics": ["refine", "change", "simp_rw", "let", "rotate_left", "rw", "apply", "rw", "rw", "apply", "rw", "convert_to", "refine", "exacts", "rw", "change", "dsimp", "apply", "intro", "change", "rw", "split_ifs", "exact", "all_goals", "congr", "dsimp", "simp_rw", "dsimp", "simp_rw"], "tactic_count": 29}
{"name": "AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.carrier.zero_mem", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.carrier.smul_mem", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme", "is_tactic_proof": true, "tactics": ["revert", "refine", "rw", "rintro", "simp_rw", "let", "split_ifs", "convert_to", "dsimp", "rw", "simp_rw", "congr", "apply", "rw", "mem_tac", "simp", "simpa", "rw", "mem_tac", "simp", "simp_rw"], "tactic_count": 21}
{"name": "AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.carrier.asIdeal", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.carrier.asIdeal.homogeneous", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.carrier.asHomogeneousIdeal", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.carrier.denom_notMem", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.carrier.relevant", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.carrier.asIdeal.ne_top", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.carrier.asIdeal.prime", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.toFun", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec_fromSpec", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme", "is_tactic_proof": true, "tactics": ["apply", "ext", "obtain", "rw", "exact"], "tactic_count": 5}
{"name": "AlgebraicGeometry.ProjIsoSpecTopComponent.fromSpec_toSpec", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme", "is_tactic_proof": true, "tactics": ["refine", "intro", "refine", "exact"], "tactic_count": 4}
{"name": "AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec_injective", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme", "is_tactic_proof": true, "tactics": ["intro", "have", "rwa"], "tactic_count": 3}
{"name": "AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec_surjective", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec_bijective", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec.image_basicOpen_eq_basicOpen", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.ProjIsoSpecTopComponent.fromSpec", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.projIsoSpecTopComponent", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.ProjectiveSpectrum.Proj.awayToSection", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.ProjectiveSpectrum.Proj.awayToSection_germ", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme", "is_tactic_proof": true, "tactics": ["ext", "apply", "apply"], "tactic_count": 3}
{"name": "AlgebraicGeometry.ProjectiveSpectrum.Proj.awayToSection_apply", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme", "is_tactic_proof": true, "tactics": ["obtain", "change", "dsimp", "rw", "rfl"], "tactic_count": 5}
{"name": "AlgebraicGeometry.ProjectiveSpectrum.Proj.awayToΓ", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.ProjectiveSpectrum.Proj.awayToΓ_ΓToStalk", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme", "is_tactic_proof": false, "tactics": ["rw", "rw", "simp", "rw", "rfl"], "tactic_count": 5}
{"name": "AlgebraicGeometry.ProjectiveSpectrum.Proj.toSpec", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.ProjectiveSpectrum.Proj.toSpec_base_apply_eq_comap", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme", "is_tactic_proof": false, "tactics": ["change", "rw", "exact", "congr"], "tactic_count": 4}
{"name": "AlgebraicGeometry.ProjectiveSpectrum.Proj.toSpec_base_apply_eq", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.ProjectiveSpectrum.Proj.toSpec_base_isIso", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme", "is_tactic_proof": true, "tactics": ["convert", "exact"], "tactic_count": 2}
{"name": "AlgebraicGeometry.ProjectiveSpectrum.Proj.mk_mem_toSpec_base_apply", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.ProjectiveSpectrum.Proj.toSpec_preimage_basicOpen", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.ProjectiveSpectrum.Proj.toOpen_toSpec_val_c_app", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.ProjectiveSpectrum.Proj.toStalk_stalkMap_toSpec", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "rw", "rfl"], "tactic_count": 4}
{"name": "AlgebraicGeometry.ProjectiveSpectrum.Proj.isLocalization_atPrime", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme", "is_tactic_proof": false, "tactics": ["letI", "constructor", "rintro", "obtain", "refine", "simp", "intro", "obtain", "refine", "val_injective", "convert", "rw", "simp", "rw", "intro", "obtain", "obtain", "obtain", "apply_fun", "simp", "obtain", "obtain", "refine", "apply_fun", "conv_rhs", "rwa", "coe_decompose_mul_add_of_right_mem,", "exacts", "refine", "val_injective", "simp", "mul_assoc]", "congr", "rw", "mul_assoc,"], "tactic_count": 35}
{"name": "AlgebraicGeometry.ProjectiveSpectrum.Proj.specStalkEquiv", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.ProjectiveSpectrum.Proj.toStalk_specStalkEquiv", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.ProjectiveSpectrum.Proj.stalkMap_toSpec", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.ProjectiveSpectrum.Proj.isIso_toSpec", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme", "is_tactic_proof": true, "tactics": ["haveI", "haveI", "haveI", "exact"], "tactic_count": 4}
{"name": "AlgebraicGeometry.projIsoSpec", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Proj", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf.0.AlgebraicGeometry.termAt_", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf.0.AlgebraicGeometry._aux_Mathlib_AlgebraicGeometry_ProjectiveSpectrum_StructureSheaf___macroRules__private_Mathlib_AlgebraicGeometry_ProjectiveSpectrum_StructureSheaf_0_AlgebraicGeometry_termAt__1", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf.0.AlgebraicGeometry._aux_Mathlib_AlgebraicGeometry_ProjectiveSpectrum_StructureSheaf___delab_app__private_Mathlib_AlgebraicGeometry_ProjectiveSpectrum_StructureSheaf_0_AlgebraicGeometry_termAt__1", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf.IsFraction", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf.isFractionPrelocal", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf.isLocallyFraction", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf.SectionSubring.zero_mem'", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf.SectionSubring.one_mem'", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf.SectionSubring.add_mem'", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf.SectionSubring.neg_mem'", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf.SectionSubring.mul_mem'", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf.sectionsSubring", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf.structureSheafInType", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf.commRingStructureSheafInTypeObj", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf.structurePresheafInCommRing", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf.structurePresheafCompForget", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.ProjectiveSpectrum.Proj.structureSheaf", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Proj.res_apply", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Proj.ext", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Proj.add_apply", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Proj.mul_apply", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Proj.sub_apply", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Proj.pow_apply", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Proj.zero_apply", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Proj.one_apply", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Proj.toSheafedSpace", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.openToLocalization", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.stalkToFiberRingHom", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.germ_comp_stalkToFiberRingHom", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.stalkToFiberRingHom_germ", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.mem_basicOpen_den", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "AlgebraicGeometry.sectionInBasicOpen", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.homogeneousLocalizationToStalk", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.homogeneousLocalizationToStalk_stalkToFiberRingHom", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf", "is_tactic_proof": true, "tactics": ["obtain", "change", "homogeneousLocalizationToStalk", "obtain", "simp", "rw", "refine", "change", "apply", "ext", "rw", "simp"], "tactic_count": 12}
{"name": "AlgebraicGeometry.stalkToFiberRingHom_homogeneousLocalizationToStalk", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf", "is_tactic_proof": true, "tactics": ["obtain", "rw"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Proj.stalkIso'", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Proj.stalkIso'_germ", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Proj.stalkIso'_symm_mk", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Proj.toLocallyRingedSpace", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProjectiveSpectrum.instIsPrimeToIdealNatAsHomogeneousIdeal", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProjectiveSpectrum.zeroLocus", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProjectiveSpectrum.mem_zeroLocus", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProjectiveSpectrum.zeroLocus_span", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "ProjectiveSpectrum.vanishingIdeal", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProjectiveSpectrum.coe_vanishingIdeal", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": true, "tactics": ["ext", "rw", "refine", "rw"], "tactic_count": 4}
{"name": "ProjectiveSpectrum.mem_vanishingIdeal", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ProjectiveSpectrum.vanishingIdeal_singleton", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ProjectiveSpectrum.subset_zeroLocus_iff_le_vanishingIdeal", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProjectiveSpectrum.gc_ideal", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProjectiveSpectrum.gc_set", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "ProjectiveSpectrum.gc_homogeneousIdeal", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProjectiveSpectrum.subset_zeroLocus_iff_subset_vanishingIdeal", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProjectiveSpectrum.subset_vanishingIdeal_zeroLocus", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProjectiveSpectrum.ideal_le_vanishingIdeal_zeroLocus", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProjectiveSpectrum.homogeneousIdeal_le_vanishingIdeal_zeroLocus", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProjectiveSpectrum.subset_zeroLocus_vanishingIdeal", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProjectiveSpectrum.zeroLocus_anti_mono", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProjectiveSpectrum.zeroLocus_anti_mono_ideal", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProjectiveSpectrum.zeroLocus_anti_mono_homogeneousIdeal", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProjectiveSpectrum.vanishingIdeal_anti_mono", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProjectiveSpectrum.zeroLocus_bot", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProjectiveSpectrum.zeroLocus_singleton_zero", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProjectiveSpectrum.zeroLocus_empty", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProjectiveSpectrum.vanishingIdeal_univ", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ProjectiveSpectrum.zeroLocus_empty_of_one_mem", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProjectiveSpectrum.zeroLocus_singleton_one", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProjectiveSpectrum.zeroLocus_univ", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProjectiveSpectrum.zeroLocus_sup_ideal", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProjectiveSpectrum.zeroLocus_sup_homogeneousIdeal", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProjectiveSpectrum.zeroLocus_union", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProjectiveSpectrum.vanishingIdeal_union", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": true, "tactics": ["ext1"], "tactic_count": 1}
{"name": "ProjectiveSpectrum.zeroLocus_iSup_ideal", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProjectiveSpectrum.zeroLocus_iSup_homogeneousIdeal", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProjectiveSpectrum.zeroLocus_iUnion", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProjectiveSpectrum.zeroLocus_bUnion", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ProjectiveSpectrum.vanishingIdeal_iUnion", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProjectiveSpectrum.zeroLocus_inf", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProjectiveSpectrum.union_zeroLocus", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "ProjectiveSpectrum.zeroLocus_mul_ideal", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProjectiveSpectrum.zeroLocus_mul_homogeneousIdeal", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProjectiveSpectrum.zeroLocus_singleton_mul", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProjectiveSpectrum.zeroLocus_singleton_pow", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProjectiveSpectrum.sup_vanishingIdeal_le", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": true, "tactics": ["intro", "rw", "rintro", "rw", "apply"], "tactic_count": 5}
{"name": "ProjectiveSpectrum.mem_compl_zeroLocus_iff_notMem", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ProjectiveSpectrum.zariskiTopology", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProjectiveSpectrum.top", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProjectiveSpectrum.isOpen_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ProjectiveSpectrum.isClosed_iff_zeroLocus", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ProjectiveSpectrum.isClosed_zeroLocus", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ProjectiveSpectrum.zeroLocus_vanishingIdeal_eq_closure", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": true, "tactics": ["apply", "rintro", "obtain", "rw", "exact", "rw", "exact"], "tactic_count": 7}
{"name": "ProjectiveSpectrum.vanishingIdeal_closure", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": true, "tactics": ["have", "ext1", "rw", "exact"], "tactic_count": 4}
{"name": "ProjectiveSpectrum.basicOpen", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProjectiveSpectrum.mem_basicOpen", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProjectiveSpectrum.mem_coe_basicOpen", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProjectiveSpectrum.isOpen_basicOpen", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProjectiveSpectrum.basicOpen_eq_zeroLocus_compl", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProjectiveSpectrum.basicOpen_one", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProjectiveSpectrum.basicOpen_zero", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProjectiveSpectrum.basicOpen_mul", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProjectiveSpectrum.basicOpen_mul_le_left", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ProjectiveSpectrum.basicOpen_mul_le_right", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ProjectiveSpectrum.basicOpen_pow", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProjectiveSpectrum.basicOpen_eq_union_of_projection", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProjectiveSpectrum.isTopologicalBasis_basic_opens", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": true, "tactics": ["apply", "rintro", "exact", "rintro", "rw", "obtain", "refine", "rw", "exact"], "tactic_count": 9}
{"name": "ProjectiveSpectrum.instPartialOrder", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProjectiveSpectrum.as_ideal_le_as_ideal", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProjectiveSpectrum.as_ideal_lt_as_ideal", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProjectiveSpectrum.le_iff_mem_closure", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "AlgebraicGeometry.instT0SpaceCarrierCarrierCommRingCat", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instQuasiSoberCarrierCarrierCommRingCat", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Properties", "is_tactic_proof": true, "tactics": ["apply", "rintro", "rintro", "exact", "rw", "intro"], "tactic_count": 6}
{"name": "AlgebraicGeometry.instPrespectralSpaceCarrierCarrierCommRingCat", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.isReduced_of_isReduced_stalk", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Properties", "is_tactic_proof": true, "tactics": ["refine", "apply", "intro", "change", "rw", "change", "exact"], "tactic_count": 7}
{"name": "AlgebraicGeometry.isReduced_stalk_of_isReduced", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Properties", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "obtain", "rw", "obtain", "rw", "replace", "rw"], "tactic_count": 8}
{"name": "AlgebraicGeometry.isReduced_of_isOpenImmersion", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Properties", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "exact", "isReduced_of_injective"], "tactic_count": 5}
{"name": "AlgebraicGeometry.instIsReducedSpecOfIsReducedCarrier", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Properties", "is_tactic_proof": true, "tactics": ["apply", "intro", "have", "exact", "isReduced_of_injective"], "tactic_count": 5}
{"name": "AlgebraicGeometry.affine_isReduced_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Properties", "is_tactic_proof": true, "tactics": ["refine", "intro", "exact"], "tactic_count": 3}
{"name": "AlgebraicGeometry.isReduced_of_isAffine_isReduced", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsReduced.of_openCover", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Properties", "is_tactic_proof": false, "tactics": ["have", "obtain", "exact", "exact"], "tactic_count": 4}
{"name": "AlgebraicGeometry.reduce_to_affine_global", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Properties", "is_tactic_proof": true, "tactics": ["apply", "intro", "obtain", "let", "let", "refine", "obtain", "apply", "apply"], "tactic_count": 9}
{"name": "AlgebraicGeometry.reduce_to_affine_nbhd", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Properties", "is_tactic_proof": true, "tactics": ["intro", "obtain", "convert", "rw", "apply"], "tactic_count": 5}
{"name": "AlgebraicGeometry.eq_zero_of_basicOpen_eq_bot", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Properties", "is_tactic_proof": true, "tactics": ["apply", "intro", "change", "rw", "induction", "h₁", "obtain", "specialize", "rw", "specialize", "rw", "exact", "h₂", "refine", "rintro", "haveI", "specialize", "rw", "have", "rw", "apply_fun", "rw", "exact", "h₃", "rw", "replace", "rw", "rw"], "tactic_count": 28}
{"name": "AlgebraicGeometry.basicOpen_eq_bot_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Properties", "is_tactic_proof": true, "tactics": ["refine", "rintro", "simp"], "tactic_count": 3}
{"name": "AlgebraicGeometry.instIsDomainCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTopOfIsIntegral", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.isReduced_of_isIntegral", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Properties", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rcases", "have", "haveI", "infer_instance", "haveI", "infer_instance"], "tactic_count": 8}
{"name": "AlgebraicGeometry.Scheme.component_nontrivial", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.irreducibleSpace_of_isIntegral", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Properties", "is_tactic_proof": true, "tactics": ["by_contra", "replace", "toNonempty", "simp_rw", "rcases", "rw", "haveI", "haveI", "haveI", "let", "have", "exact", "ext", "constructor", "rintro", "rcases", "exacts", "simp"], "tactic_count": 18}
{"name": "AlgebraicGeometry.isIntegral_of_irreducibleSpace_of_isReduced", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Properties", "is_tactic_proof": true, "tactics": ["constructor", "intro", "haveI", "have", "refine", "simp_rw", "by_contra", "obtain", "replace", "rw", "refine", "convert", "exact", "exact"], "tactic_count": 14}
{"name": "AlgebraicGeometry.isIntegral_iff_irreducibleSpace_and_isReduced", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.isIntegral_of_isOpenImmersion", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Properties", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "have", "apply", "exact", "exact"], "tactic_count": 7}
{"name": "AlgebraicGeometry.instIrreducibleSpaceCarrierCarrierCommRingCatSpecOfIsDomainCarrier", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Properties", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "AlgebraicGeometry.instIsIntegralSpecOfIsDomainCarrier", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.affine_isIntegral_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.isIntegral_of_isAffine_of_isDomain", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.map_injective_of_isIntegral", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Properties", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "rw", "revert", "contrapose", "simp_rw", "apply", "simpa"], "tactic_count": 9}
{"name": "AlgebraicGeometry.instOrderTopCarrierCarrierCommRingCatOfIsIntegral", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Pullback.Triplet.ext", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.PullbackCarrier", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Pullback.Triplet.mk'", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.PullbackCarrier", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Pullback.Triplet.tensor", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.PullbackCarrier", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Pullback.Triplet.instNontrivialCarrierTensor", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.PullbackCarrier", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Pullback.Triplet.tensorInl", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.PullbackCarrier", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Pullback.Triplet.tensorInr", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.PullbackCarrier", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Pullback.Triplet.isPullback_SpecMap_tensor", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.PullbackCarrier", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Pullback.Triplet.tensorCongr", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.PullbackCarrier", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Pullback.Triplet.tensorCongr_refl", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.PullbackCarrier", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Pullback.Triplet.tensorCongr_symm", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.PullbackCarrier", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Pullback.Triplet.tensorCongr_inv", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.PullbackCarrier", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Pullback.Triplet.tensorCongr_trans", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.PullbackCarrier", "is_tactic_proof": true, "tactics": ["subst", "rfl"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.Pullback.Triplet.tensorCongr_trans_hom", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.PullbackCarrier", "is_tactic_proof": true, "tactics": ["subst", "rfl"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.Pullback.Triplet.SpecMap_tensorInl_fromSpecResidueField", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.PullbackCarrier", "is_tactic_proof": false, "tactics": ["simp", "rw", "simp"], "tactic_count": 3}
{"name": "AlgebraicGeometry.Scheme.Pullback.Triplet.SpecTensorTo", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.PullbackCarrier", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Pullback.Triplet.fst_SpecTensorTo_apply", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.PullbackCarrier", "is_tactic_proof": true, "tactics": ["simp", "rw", "simp"], "tactic_count": 3}
{"name": "AlgebraicGeometry.Scheme.Pullback.Triplet.snd_SpecTensorTo_apply", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.PullbackCarrier", "is_tactic_proof": true, "tactics": ["simp", "rw", "simp"], "tactic_count": 3}
{"name": "AlgebraicGeometry.Scheme.Pullback.Triplet.specTensorTo_fst", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.PullbackCarrier", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Pullback.Triplet.specTensorTo_snd", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.PullbackCarrier", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Pullback.Triplet.ofPoint", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.PullbackCarrier", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Pullback.Triplet.ofPoint_SpecTensorTo", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.PullbackCarrier", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Pullback.residueFieldCongr_inv_residueFieldMap_ofPoint", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.PullbackCarrier", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Pullback.ofPointTensor", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.PullbackCarrier", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Pullback.ofPointTensor_SpecTensorTo", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.PullbackCarrier", "is_tactic_proof": true, "tactics": ["apply", "rw", "simp", "rw", "rfl", "rw", "simp", "rw", "rfl"], "tactic_count": 9}
{"name": "AlgebraicGeometry.Scheme.Pullback.SpecOfPoint", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.PullbackCarrier", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Pullback.SpecTensorTo_SpecOfPoint", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.PullbackCarrier", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Pullback.tensorCongr_SpecTensorTo", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.PullbackCarrier", "is_tactic_proof": true, "tactics": ["subst", "simp"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.Pullback.Triplet.Spec_ofPointTensor_SpecTensorTo", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.PullbackCarrier", "is_tactic_proof": true, "tactics": ["apply", "rw", "simp_rw", "rw", "rw", "simp_rw", "rw"], "tactic_count": 7}
{"name": "AlgebraicGeometry.Scheme.Pullback.carrierEquiv_eq_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.PullbackCarrier", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "simp", "obtain", "obtain", "rintro", "simpa"], "tactic_count": 7}
{"name": "AlgebraicGeometry.Scheme.Pullback.carrierEquiv", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.PullbackCarrier", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Pullback.carrierEquiv_symm_fst", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.PullbackCarrier", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Pullback.carrierEquiv_symm_snd", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.PullbackCarrier", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Pullback.Triplet.exists_preimage", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.PullbackCarrier", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Pullback.exists_preimage_pullback", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.PullbackCarrier", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.isEmpty_pullback_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.PullbackCarrier", "is_tactic_proof": true, "tactics": ["refine", "rw", "contrapose", "rintro", "obtain", "exact"], "tactic_count": 6}
{"name": "AlgebraicGeometry.Scheme.Pullback.range_fst", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.PullbackCarrier", "is_tactic_proof": true, "tactics": ["ext", "refine", "rintro", "simp", "simp", "obtain", "use"], "tactic_count": 7}
{"name": "AlgebraicGeometry.Scheme.Pullback.range_snd", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.PullbackCarrier", "is_tactic_proof": true, "tactics": ["ext", "refine", "rintro", "simp", "simp", "obtain", "use"], "tactic_count": 7}
{"name": "AlgebraicGeometry.Scheme.Pullback.range_fst_comp", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.PullbackCarrier", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Pullback.range_snd_comp", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.PullbackCarrier", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Pullback.range_map", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.PullbackCarrier", "is_tactic_proof": true, "tactics": ["ext", "constructor", "rintro", "constructor", "use", "rw", "simp", "use", "rw", "simp", "intro", "let", "obtain", "let", "obtain", "let", "obtain", "use", "rw", "simp"], "tactic_count": 20}
{"name": "AlgebraicGeometry.Scheme.isJointlySurjectivePreserving", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.PullbackCarrier", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.pullbackComparison_forget_surjective", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.PullbackCarrier", "is_tactic_proof": false, "tactics": ["refine", "obtain", "use", "ext", "simp", "rwa", "simp", "rwa"], "tactic_count": 8}
{"name": "AlgebraicGeometry.Scheme.exists_preimage_of_isPullback", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.PullbackCarrier", "is_tactic_proof": true, "tactics": ["let", "obtain", "use", "simp"], "tactic_count": 4}
{"name": "AlgebraicGeometry.Scheme.image_preimage_eq_of_isPullback", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.PullbackCarrier", "is_tactic_proof": true, "tactics": ["refine", "rw", "rw", "exact", "obtain", "obtain", "use", "simpa"], "tactic_count": 8}
{"name": "AlgebraicGeometry.Surjective.instIsStableUnderBaseChangeScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.PullbackCarrier", "is_tactic_proof": true, "tactics": ["refine", "introv", "simp", "rw"], "tactic_count": 4}
{"name": "AlgebraicGeometry.Surjective.instFstScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.PullbackCarrier", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Surjective.instSndScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.PullbackCarrier", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Pullback.v", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Pullback.t", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": true, "tactics": ["have", "have", "refine", "refine", "refine", "rw", "rw"], "tactic_count": 7}
{"name": "AlgebraicGeometry.Scheme.Pullback.t_fst_fst", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": true, "tactics": ["simp", "pullbackSymmetry_hom_comp_snd,"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.Pullback.t_fst_snd", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Pullback.t_snd", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": true, "tactics": ["simp", "pullbackSymmetry_hom_comp_fst,"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.Pullback.t_id", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": true, "tactics": ["apply", "apply", "rw", "simp", "rw"], "tactic_count": 5}
{"name": "AlgebraicGeometry.Scheme.Pullback.fV", "kind": "abbrev", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Pullback.t'", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": true, "tactics": ["refine", "refine", "refine", "refine", "simp_rw", "rw"], "tactic_count": 6}
{"name": "AlgebraicGeometry.Scheme.Pullback.t'_fst_fst_fst", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": true, "tactics": ["simp", "pullback.lift_fst_assoc,"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.Pullback.t'_fst_fst_snd", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": true, "tactics": ["simp", "pullback.lift_fst_assoc,"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.Pullback.t'_fst_snd", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": true, "tactics": ["simp", "pullback.lift_snd,"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.Pullback.t'_snd_fst_fst", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": true, "tactics": ["simp", "pullback.lift_fst_assoc,"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.Pullback.t'_snd_fst_snd", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": true, "tactics": ["simp", "pullback.lift_fst_assoc,"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.Pullback.t'_snd_snd", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": true, "tactics": ["simp", "pullback.lift_fst_assoc,"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.Pullback.cocycle_fst_fst_fst", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Pullback.cocycle_fst_fst_snd", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Pullback.cocycle_fst_snd", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Pullback.cocycle_snd_fst_fst", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Pullback.cocycle_snd_fst_snd", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Pullback.cocycle_snd_snd", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Pullback.cocycle", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": true, "tactics": ["apply", "apply", "apply", "simp_rw", "simp_rw", "simp_rw", "apply", "apply", "simp_rw", "simp_rw", "simp_rw"], "tactic_count": 11}
{"name": "AlgebraicGeometry.Scheme.Pullback.gluing", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Pullback.gluing_ι", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Pullback.p1", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.Pullback.p2", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.Pullback.p_comm", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.Pullback.gluedLiftPullbackMap", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": true, "tactics": ["refine", "refine", "exact", "simpa", "simp"], "tactic_count": 5}
{"name": "AlgebraicGeometry.Scheme.Pullback.gluedLiftPullbackMap_fst", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Pullback.gluedLiftPullbackMap_snd", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Pullback.gluedLift", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": true, "tactics": ["fapply", "exact", "pullback.map", "intro", "rw", "simp_rw", "congr", "apply", "rw", "congr", "rw", "rw", "simp_rw", "exact"], "tactic_count": 14}
{"name": "AlgebraicGeometry.Scheme.Pullback.gluedLift_p1", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": true, "tactics": ["rw", "apply", "intro", "simp_rw", "simp_rw", "simp"], "tactic_count": 6}
{"name": "AlgebraicGeometry.Scheme.Pullback.gluedLift_p2", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": true, "tactics": ["rw", "apply", "intro", "simp_rw", "simp_rw", "simp"], "tactic_count": 6}
{"name": "AlgebraicGeometry.Scheme.Pullback.pullbackFstιToV", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Pullback.pullbackFstιToV_fst", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Pullback.pullbackFstιToV_snd", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Pullback.lift_comp_ι", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": true, "tactics": ["apply", "intro", "dsimp", "trans", "rw", "simp_rw", "congr", "rw", "apply", "simp_rw", "simp_rw", "p2]", "simp", "rw", "simp_rw"], "tactic_count": 15}
{"name": "AlgebraicGeometry.Scheme.Pullback.pullbackP1Iso", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": true, "tactics": ["fconstructor", "exact", "pullback.lift", "exact", "apply", "simpa", "simp_rw", "apply", "simp_rw", "simp"], "tactic_count": 10}
{"name": "AlgebraicGeometry.Scheme.Pullback.pullbackP1Iso_hom_fst", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Pullback.pullbackP1Iso_hom_snd", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Pullback.pullbackP1Iso_inv_fst", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Pullback.pullbackP1Iso_inv_snd", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Pullback.pullbackP1Iso_hom_ι", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Pullback.gluedIsLimit", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": true, "tactics": ["apply", "intro", "refine", "intro", "simp_rw", "apply", "intro", "rw", "dsimp", "rw", "pullbackRightPullbackFstIso_hom_fst_assoc,", "conv_lhs", "simp_rw", "congr", "apply", "simp_rw", "pullback.lift_snd,", "simp_rw", "pullback.lift_fst_assoc,", "h₂]"], "tactic_count": 20}
{"name": "AlgebraicGeometry.Scheme.Pullback.hasPullback_of_cover", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Pullback.affine_hasPullback", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.Pullback.affine_affine_hasPullback", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Pullback.base_affine_hasPullback", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Pullback.left_affine_comp_pullback_hasPullback", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Pullback.instHasPullback", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Pullback.instHasPullbacks", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Pullback.isAffine_of_isAffine_isAffine_isAffine", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.isEmpty_pullback", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Pullback.openCoverOfLeft", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Pullback.openCoverOfRight", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": false, "tactics": ["fapply", "pullbackSymmetry", "intro", "dsimp", "apply"], "tactic_count": 5}
{"name": "AlgebraicGeometry.Scheme.Pullback.openCoverOfLeftRight", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": false, "tactics": ["fapply", "rintro", "apply"], "tactic_count": 3}
{"name": "AlgebraicGeometry.Scheme.Pullback.openCoverOfBase'", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": true, "tactics": ["apply", "intro", "haveI", "refine", "inferInstance", "simp", "simp"], "tactic_count": 7}
{"name": "AlgebraicGeometry.Scheme.Pullback.openCoverOfBase", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": false, "tactics": ["apply", "pullback.map", "pullback.condition.symm)", "intro", "rw", "ext", "simp", "rfl"], "tactic_count": 8}
{"name": "AlgebraicGeometry.Scheme.isPullback_of_openCover", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": true, "tactics": ["have", "suffices", "have", "let", "have", "simpa", "have", "rw", "simpa", "convert", "aesop", "exact"], "tactic_count": 12}
{"name": "AlgebraicGeometry.Scheme.Pullback.diagonalCover", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Pullback.diagonalCoverDiagonalRange", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Pullback.diagonalCover_map", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": true, "tactics": ["cases", "ext1"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.Pullback.diagonalRestrictIsoDiagonal", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": true, "tactics": ["refine", "refine", "exact", "pullback.congrHom", "pullbackDiagonalMapIso", "have", "pullback.snd", "pullback.snd", "rw", "apply", "trans", "pullback.snd", "simp", "symm", "trans", "pullback.snd", "simp", "rw", "simp", "simp", "dsimp", "apply", "simp", "simp", "apply", "simp", "simp", "apply"], "tactic_count": 28}
{"name": "AlgebraicGeometry.Scheme.pullback_map_isOpenImmersion", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "AlgebraicGeometry.instCartesianMonoidalCategoryOverScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instBraidedCategoryOverScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.pullbackSpecIso", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.pullbackSpecIso_inv_fst", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.pullbackSpecIso_inv_fst'", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.pullbackSpecIso_inv_snd", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.pullbackSpecIso_hom_fst", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgebraicGeometry.pullbackSpecIso_hom_fst'", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.pullbackSpecIso_hom_snd", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgebraicGeometry.pullbackSpecIso_hom_base", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.isPullback_SpecMap_of_isPushout", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.isPullback_SpecMap_pushout", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": true, "tactics": ["apply", "exact"], "tactic_count": 2}
{"name": "AlgebraicGeometry.diagonal_SpecMap", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": false, "tactics": ["ext1", "simp", "congr", "congr"], "tactic_count": 4}
{"name": "AlgebraicGeometry.Scheme.canonicallyOverPullback", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.monObjAsOverPullback", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.isCommMonObj_asOver_pullback", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.GrpObjAsOverPullback", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.instIsOverFstOverInferInstanceOverClassId", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.isMonHom_fst_id_right", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Pullbacks", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.instIsQuasiAffineOfIsAffine", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.QuasiAffine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.instIsSeparatedOfIsQuasiAffine", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.QuasiAffine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.instIsOpenImmersionToSpecΓOfIsQuasiAffine", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.QuasiAffine", "is_tactic_proof": true, "tactics": ["have", "rw", "infer_instance"], "tactic_count": 3}
{"name": "AlgebraicGeometry.Scheme.IsQuasiAffine.of_isImmersion", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.QuasiAffine", "is_tactic_proof": true, "tactics": ["have", "have", "constructor"], "tactic_count": 3}
{"name": "AlgebraicGeometry.Scheme.IsQuasiAffine.isBasis_basicOpen", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.QuasiAffine", "is_tactic_proof": true, "tactics": ["refine", "obtain", "simp_rw", "refine", "rw", "convert", "exact"], "tactic_count": 7}
{"name": "AlgebraicGeometry.Scheme.IsQuasiAffine.of_forall_exists_mem_basicOpen", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.QuasiAffine", "is_tactic_proof": true, "tactics": ["suffices", "have", "choose", "exact", "refine", "obtain", "refine", "suffices", "rw", "have", "exact"], "tactic_count": 11}
{"name": "AlgebraicGeometry.Scheme.IsQuasiAffine.of_isAffineHom", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.QuasiAffine", "is_tactic_proof": true, "tactics": ["have", "refine", "obtain", "refine", "rw", "exact"], "tactic_count": 6}
{"name": "AlgebraicGeometry.Scheme.openCoverBasicOpenTop", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.QuasiAffine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.isPullback_toSpecΓ_toSpecΓ", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.QuasiAffine", "is_tactic_proof": true, "tactics": ["have", "have", "have", "have", "have", "refine", "change", "rw", "refine", "let", "pullbackRestrictIsoRestrict", "refine", "simp", "dsimp", "simp", "simp_rw", "congr", "rw", "simp", "simp", "simp"], "tactic_count": 21}
{"name": "AlgebraicGeometry.Scheme.preimage_opensRange_toSpecΓ", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.QuasiAffine", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.PartialMap.IsOver", "kind": "abbrev", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.PartialMap.ext_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "simp", "obtain", "obtain", "rintro", "congr", "simpa"], "tactic_count": 8}
{"name": "AlgebraicGeometry.Scheme.PartialMap.ext", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.PartialMap.restrict", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.PartialMap.restrict_id", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": true, "tactics": ["ext1"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.PartialMap.restrict_id_hom", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.PartialMap.restrict_restrict", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": true, "tactics": ["ext1"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.PartialMap.restrict_restrict_hom", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.PartialMap.instIsOverRestrict", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.PartialMap.compHom", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.PartialMap.instIsOverCompHomOfIsOver", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.toPartialMap", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.PartialMap.instIsOverToPartialMapOfIsOver", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.PartialMap.isOver_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.PartialMap.isOver_iff_eq_restrict", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.PartialMap.fromSpecStalkOfMem", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.PartialMap.fromFunctionField", "kind": "abbrev", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.PartialMap.fromSpecStalkOfMem_restrict", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": true, "tactics": ["dsimp", "have", "rw", "rfl", "rw", "simp", "congr", "rw", "simp", "rw"], "tactic_count": 10}
{"name": "AlgebraicGeometry.Scheme.PartialMap.fromFunctionField_restrict", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.PartialMap.ofFromSpecStalk", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.PartialMap.ofFromSpecStalk_comp", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.PartialMap.mem_domain_ofFromSpecStalk", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.PartialMap.fromSpecStalkOfMem_ofFromSpecStalk", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.PartialMap.fromSpecStalkOfMem_compHom", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.PartialMap.fromSpecStalkOfMem_toPartialMap", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.PartialMap.equiv", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.PartialMap.equivalence_rel", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.PartialMap.instSetoid", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.PartialMap.restrict_equiv", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.PartialMap.equiv_of_fromSpecStalkOfMem_eq", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": false, "tactics": ["have", "have", "have", "spread_out_unique_of_isGermInjective", "obtain", "refine", "rw", "simp", "convert", "rw", "g.fromSpecStalkOfMem_restrict", "simpa"], "tactic_count": 12}
{"name": "AlgebraicGeometry.Scheme.PartialMap.instIsReducedToScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.PartialMap.Opens.isDominant_ι", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.PartialMap.Opens.isDominant_homOfLE", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.PartialMap.equiv_iff_of_isSeparated_of_le", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": true, "tactics": ["refine", "have", "apply", "simpa"], "tactic_count": 4}
{"name": "AlgebraicGeometry.Scheme.PartialMap.equiv_iff_of_isSeparated", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.PartialMap.equiv_iff_of_domain_eq_of_isSeparated", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": true, "tactics": ["rw", "obtain", "obtain", "obtain", "simp"], "tactic_count": 5}
{"name": "AlgebraicGeometry.Scheme.PartialMap.equiv_toPartialMap_iff_of_isSeparated", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": true, "tactics": ["rw", "simp", "rfl"], "tactic_count": 3}
{"name": "AlgebraicGeometry.Scheme.RationalMap", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.term_⤏_", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry._aux_Mathlib_AlgebraicGeometry_RationalMap___macroRules_AlgebraicGeometry_term_⤏__1", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry._aux_Mathlib_AlgebraicGeometry_RationalMap___unexpand_AlgebraicGeometry_Scheme_RationalMap_1", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.PartialMap.toRationalMap", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.toRationalMap", "kind": "abbrev", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.PartialMap.toRationalMap_surjective", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.RationalMap.exists_rep", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.PartialMap.toRationalMap_eq_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.PartialMap.restrict_toRationalMap", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.instIsOverToRationalMapOfIsOver", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.RationalMap.exists_partialMap_over", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.RationalMap.compHom", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": true, "tactics": ["refine", "intro", "refine", "simp", "rw"], "tactic_count": 5}
{"name": "AlgebraicGeometry.Scheme.RationalMap.compHom_toRationalMap", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.instIsOverCompHomOfIsOver", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.PartialMap.exists_restrict_isOver", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "exact"], "tactic_count": 3}
{"name": "AlgebraicGeometry.Scheme.RationalMap.isOver_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": true, "tactics": ["constructor", "intro", "obtain", "rw", "intro", "obtain", "obtain", "exact"], "tactic_count": 8}
{"name": "AlgebraicGeometry.Scheme.PartialMap.isOver_toRationalMap_iff_of_isSeparated", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": true, "tactics": ["refine", "obtain", "rw", "have", "exact"], "tactic_count": 5}
{"name": "AlgebraicGeometry.Scheme.RationalMap.fromFunctionField", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": true, "tactics": ["refine", "intro", "have", "ext1", "rfl", "rw", "rw"], "tactic_count": 7}
{"name": "AlgebraicGeometry.Scheme.RationalMap.fromFunctionField_toRationalMap", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.RationalMap.ofFunctionField", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.RationalMap.fromFunctionField_ofFunctionField", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.RationalMap.eq_of_fromFunctionField_eq", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "refine", "exact"], "tactic_count": 4}
{"name": "AlgebraicGeometry.Scheme.RationalMap.equivFunctionField", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.RationalMap.equivFunctionFieldOver", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.RationalMap.domain", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.PartialMap.le_domain_toRationalMap", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.RationalMap.mem_domain", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.RationalMap.dense_domain", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.RationalMap.openCoverDomain", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.RationalMap.toPartialMap", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.PartialMap.toPartialMap_toRationalMap_restrict", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": true, "tactics": ["dsimp", "refine", "generalize_proofs", "have", "exact"], "tactic_count": 5}
{"name": "AlgebraicGeometry.Scheme.RationalMap.toRationalMap_toPartialMap", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": true, "tactics": ["obtain", "trans", "simp", "congr", "exact"], "tactic_count": 5}
{"name": "AlgebraicGeometry.Scheme.instIsOverToPartialMapOfIsSeparatedOfIsOver", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.RationalMap", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.isLocallyDirected_of_equifibered_of_injective", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.RelativeGluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Cover.RelativeGluingData.instIsOpenImmersionMapI₀Functor", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.RelativeGluing", "is_tactic_proof": true, "tactics": ["apply", "infer_instance"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.Cover.RelativeGluingData.instIsLocallyDirectedI₀CompFunctorForgetOfIsThin", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.RelativeGluing", "is_tactic_proof": true, "tactics": ["apply", "intro", "exact"], "tactic_count": 3}
{"name": "AlgebraicGeometry.Scheme.Cover.RelativeGluingData.glued", "kind": "abbrev", "module": "Mathlib.AlgebraicGeometry.RelativeGluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Cover.RelativeGluingData.cover", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.RelativeGluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Cover.RelativeGluingData.instCategoryI₀Cover", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.RelativeGluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Cover.RelativeGluingData.toBase", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.RelativeGluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Cover.RelativeGluingData.ι_toBase", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.RelativeGluing", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Cover.RelativeGluingData.instLocallyDirectedIsOpenImmersionCover", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.RelativeGluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Cover.RelativeGluingData.preimage_toBase_eq_range_ι", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.RelativeGluing", "is_tactic_proof": true, "tactics": ["ext", "refine", "obtain", "obtain", "simp", "obtain", "exists_preimage_of_isPullback", "apply", "simp", "rw", "simp", "use", "simp", "rintro", "use", "rw", "simp"], "tactic_count": 17}
{"name": "AlgebraicGeometry.Scheme.Cover.RelativeGluingData.isPullback_natTrans_ι_toBase", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.RelativeGluing", "is_tactic_proof": true, "tactics": ["refine", "intro", "apply", "rw", "rintro", "use", "rw", "simp", "intro", "rw", "simp", "intro", "simpa"], "tactic_count": 13}
{"name": "AlgebraicGeometry.Scheme.residueField", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.ResidueField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.instFieldCarrierResidueField", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.ResidueField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.instUniqueCarrierCarrierCommRingCatSpecResidueField", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.ResidueField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.residue", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.ResidueField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.instIsPreimmersionMapResidue", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.ResidueField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.SpecMap_residue_apply", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ResidueField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.residue_surjective", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ResidueField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.instEpiCommRingCatResidue", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.ResidueField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.descResidueField", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.ResidueField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.residue_descResidueField", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ResidueField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.evaluation", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.ResidueField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.germ_residue", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ResidueField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Γevaluation", "kind": "abbrev", "module": "Mathlib.AlgebraicGeometry.ResidueField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.evaluation_eq_zero_iff_notMem_basicOpen", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ResidueField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.evaluation_ne_zero_iff_mem_basicOpen", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ResidueField", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.basicOpen_eq_bot_iff_forall_evaluation_eq_zero", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ResidueField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.residueFieldMap", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.ResidueField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.residue_residueFieldMap", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ResidueField", "is_tactic_proof": true, "tactics": ["simp", "rfl"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.residueFieldMap_id", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ResidueField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.residueFieldMap_comp", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ResidueField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.evaluation_naturality", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ResidueField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.evaluation_naturality_apply", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ResidueField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Γevaluation_naturality", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ResidueField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Γevaluation_naturality_apply", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ResidueField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.instIsIsoCommRingCatResidueFieldMapOfIsOpenImmersion", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.ResidueField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.residueFieldCongr", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.ResidueField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.residueFieldCongr_refl", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ResidueField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.residueFieldCongr_symm", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ResidueField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.residueFieldCongr_inv", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ResidueField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.residueFieldCongr_trans", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ResidueField", "is_tactic_proof": true, "tactics": ["subst", "rfl"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.residueFieldCongr_trans_hom", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ResidueField", "is_tactic_proof": true, "tactics": ["subst", "rfl"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.residue_residueFieldCongr", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ResidueField", "is_tactic_proof": true, "tactics": ["subst", "simp"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.Hom.residueFieldMap_congr", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ResidueField", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.fromSpecResidueField", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.ResidueField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.instIsPreimmersionFromSpecResidueField", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.ResidueField", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "infer_instance"], "tactic_count": 3}
{"name": "AlgebraicGeometry.Scheme.instOverSpecResidueField", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.ResidueField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.instCanonicallyOverSpecResidueField", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.ResidueField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.residueFieldCongr_fromSpecResidueField", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ResidueField", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.instIsOverMapHomCommRingCatResidueFieldCongr", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.ResidueField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.SpecMap_residueFieldMap_fromSpecResidueField", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ResidueField", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "rfl"], "tactic_count": 3}
{"name": "AlgebraicGeometry.Scheme.instIsOverMapResidueFieldMapOverInferInstanceOverClass", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.ResidueField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.fromSpecResidueField_apply", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ResidueField", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.range_fromSpecResidueField", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ResidueField", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.descResidueField_fromSpecResidueField", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ResidueField", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.descResidueField_stalkClosedPointTo_fromSpecResidueField", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ResidueField", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.SpecToEquivOfField_eq_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.ResidueField", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "simp", "obtain", "obtain", "rintro", "simpa"], "tactic_count": 7}
{"name": "AlgebraicGeometry.Scheme.SpecToEquivOfField", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.ResidueField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Opens.toScheme", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Opens.instCoeOut", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Opens.ι", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Opens.ι_apply", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Opens.instIsOpenImmersionι", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Opens.instCanonicallyOverToScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Opens.instIsOverι", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Opens.toScheme_carrier", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Opens.toScheme_presheaf_obj", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Opens.forall_toScheme", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Opens.exists_toScheme", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Opens.toScheme_presheaf_map", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Opens.ι_app", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Opens.ι_appTop", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Opens.ι_appLE", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": ["simp", "rfl"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.Opens.ι_appIso", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Opens.opensRange_ι", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Opens.range_ι", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Opens.ι_image_top", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Opens.ι_image_le", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.Opens.ι_preimage_self", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Opens.mem_ι_image_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Opens.instIsIsoCommRingCatAppLEιTopToScheme", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": true, "tactics": ["simp", "change", "infer_instance"], "tactic_count": 3}
{"name": "AlgebraicGeometry.Scheme.Opens.ι_app_self", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Opens.eq_presheaf_map_eqToHom", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Opens.nonempty_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": true, "tactics": ["simp", "rfl"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.Opens.topIso", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Opens.stalkIso", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Opens.germ_stalkIso_hom", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Opens.germ_stalkIso_inv", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Opens.stalkIso_inv", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": true, "tactics": ["rw", "apply", "intro", "simp", "convert", "refine", "exact"], "tactic_count": 7}
{"name": "AlgebraicGeometry.Scheme.openCoverOfIsOpenCover", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.opensRestrict", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.ΓRestrictAlgebra", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Opens.ι_image_basicOpen'", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": true, "tactics": ["refine", "rw", "rw", "congr", "exact"], "tactic_count": 5}
{"name": "AlgebraicGeometry.Scheme.Opens.ι_image_basicOpen", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Opens.ι_image_basicOpen_topIso_inv", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": true, "tactics": ["simp", "rw"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.Opens.mem_basicOpen_toScheme", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.homOfLE", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.homOfLE_ι", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instIsOverHomOfLE", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.homOfLE_rfl", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.homOfLE_homOfLE", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.homOfLE_base", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.homOfLE_apply", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.ι_image_homOfLE_le_ι_image", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": ["simp", "rintro", "exact"], "tactic_count": 3}
{"name": "AlgebraicGeometry.Scheme.homOfLE_app", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": true, "tactics": ["have", "have", "have", "have", "dsimp", "rw", "rw", "congr"], "tactic_count": 8}
{"name": "AlgebraicGeometry.Scheme.homOfLE_appLE", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.homOfLE_appTop", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instIsOpenImmersionHomOfLE", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": true, "tactics": ["delta", "infer_instance"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.opensRange_homOfLE", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Opens.iSupOpenCover", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.restrictFunctor", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.restrictFunctorΓ", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.restrictRestrictComm", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.isoImage", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.isoImage_hom_ι", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.isoImage_inv_ι", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.isoOpensRange", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.isoOpensRange_hom_ι", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Hom.isoOpensRange_inv_comp", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.topIso", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.toIso_inv_ι", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.ι_toIso_inv", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.isoOfEq", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.isoOfEq_hom_ι", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.isoOfEq_inv_ι", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.isoOfEq_hom", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.isoOfEq_inv", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.isoOfEq_rfl", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": true, "tactics": ["ext1", "rw"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.Hom.preimageIso", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": true, "tactics": ["apply", "dsimp", "rw", "refine"], "tactic_count": 4}
{"name": "AlgebraicGeometry.Scheme.Hom.preimageIso_hom_ι", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.preimageIso_inv_ι", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Opens.isoOfLE", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Opens.isoOfLE_hom_ι", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Opens.isoOfLE_inv_ι", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.basicOpenIsoSpecAway", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.basicOpenIsoSpecAway_inv_homOfLE", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": true, "tactics": ["subst", "rw", "simp", "simp", "congr", "ext", "exact"], "tactic_count": 7}
{"name": "AlgebraicGeometry.pullbackRestrictIsoRestrict", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": true, "tactics": ["refine", "simp"], "tactic_count": 2}
{"name": "AlgebraicGeometry.pullbackRestrictIsoRestrict_inv_fst", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": true, "tactics": ["delta"], "tactic_count": 1}
{"name": "AlgebraicGeometry.pullbackRestrictIsoRestrict_hom_ι", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": true, "tactics": ["delta"], "tactic_count": 1}
{"name": "AlgebraicGeometry.morphismRestrict", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.term_∣__", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry._aux_Mathlib_AlgebraicGeometry_Restrict___macroRules_AlgebraicGeometry_term_∣___1", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry._aux_Mathlib_AlgebraicGeometry_Restrict___unexpand_AlgebraicGeometry_morphismRestrict_1", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.pullbackRestrictIsoRestrict_hom_morphismRestrict", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.morphismRestrict_ι", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": true, "tactics": ["delta", "rw"], "tactic_count": 2}
{"name": "AlgebraicGeometry.isPullback_morphismRestrict", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": true, "tactics": ["delta", "rw", "refine", "erw", "rw"], "tactic_count": 5}
{"name": "AlgebraicGeometry.isPullback_opens_inf_le", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": ["refine", "rw", "exact", "exact", "all_goals"], "tactic_count": 5}
{"name": "AlgebraicGeometry.isPullback_opens_inf", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.morphismRestrict_id", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "AlgebraicGeometry.morphismRestrict_comp", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": true, "tactics": ["delta", "rw", "simp_rw", "congr", "rw", "simp_rw", "rw", "pullbackRestrictIsoRestrict_inv_fst_assoc,", "rfl"], "tactic_count": 9}
{"name": "AlgebraicGeometry.instIsIsoSchemeMorphismRestrict", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": true, "tactics": ["delta"], "tactic_count": 1}
{"name": "AlgebraicGeometry.morphismRestrict_base_coe", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.morphismRestrict_base", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.image_morphismRestrict_preimage", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.morphismRestrict_app", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": true, "tactics": ["obtain", "simpa", "congr"], "tactic_count": 3}
{"name": "AlgebraicGeometry.morphismRestrict_appTop", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.morphismRestrict_app'", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.morphismRestrict_appLE", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgebraicGeometry.morphismRestrictOpensRange", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": true, "tactics": ["let", "let", "let", "pullback.map", "symm", "refine", "rw", "pullbackRestrictIsoRestrict_hom_ι_assoc,"], "tactic_count": 8}
{"name": "AlgebraicGeometry.morphismRestrictEq", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.morphismRestrictRestrict", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": ["refine", "exact", "rw", "morphismRestrict_ι,", "morphismRestrict_ι_assoc,"], "tactic_count": 5}
{"name": "AlgebraicGeometry.morphismRestrictRestrictBasicOpen", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": true, "tactics": ["refine", "have", "rw", "rw", "erw", "rw", "erw", "ext1", "dsimp", "rw", "exact"], "tactic_count": 11}
{"name": "AlgebraicGeometry.morphismRestrictStalkMap", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instIsOpenImmersionMorphismRestrict", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": true, "tactics": ["delta", "exact"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.Hom.resLE", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.resLE_eq_morphismRestrict", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Hom.resLE_id", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": true, "tactics": ["simp", "rfl"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.Hom.resLE_comp_ι", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Hom.resLE_comp_resLE", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Hom.map_resLE", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
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{"name": "AlgebraicGeometry.Scheme.Hom.resLE_congr", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Hom.resLE_preimage", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Hom.le_resLE_preimage_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Hom.resLE_appLE", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": true, "tactics": ["dsimp", "simp", "rw", "rfl"], "tactic_count": 4}
{"name": "AlgebraicGeometry.Scheme.Hom.coe_resLE_apply", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Hom.resLEStalkMap", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.arrowResLEAppIso", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.OpenCover.restrict", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Restrict", "is_tactic_proof": false, "tactics": ["refine", "dsimp", "rw", "exact", "intro", "rw", "simp"], "tactic_count": 7}
{"name": "AlgebraicGeometry.Scheme.instCoeSortType", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.delabAdjoinNotation", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Opens", "kind": "abbrev", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.toLRSHom", "kind": "abbrev", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.Simps.toLRSHom", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.instCategory", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.term_⁻¹ᵁ_", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry._aux_Mathlib_AlgebraicGeometry_Scheme___macroRules_AlgebraicGeometry_term_⁻¹ᵁ__1", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry._aux_Mathlib_AlgebraicGeometry_Scheme___delab_app_AlgebraicGeometry_term_⁻¹ᵁ__1", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.termΓ(_,_)", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry._aux_Mathlib_AlgebraicGeometry_Scheme___macroRules_AlgebraicGeometry_termΓ(_,_)_1", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry._aux_Mathlib_AlgebraicGeometry_Scheme___delab_app_AlgebraicGeometry_termΓ(_,_)_1", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.instCoeFunHomForallCarrierCarrierCommRingCat", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.instSubsingletonCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensBot", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.continuous", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.sheaf", "kind": "abbrev", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.instPreorderCarrierCarrierCommRingCat", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.le_iff_specializes", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.height_of_isClosed", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": true, "tactics": ["simp", "intro", "obtain", "assumption", "have", "contradiction"], "tactic_count": 6}
{"name": "AlgebraicGeometry.Scheme.Hom.app", "kind": "abbrev", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.appTop", "kind": "abbrev", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.naturality", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.appLE", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.appLE_map", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.Hom.appLE_map'", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.map_appLE", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.Hom.map_appLE'", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.app_eq_appLE", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Hom.appLE_eq_app", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.appLE_congr", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Hom.stalkMap", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.ext", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": true, "tactics": ["cases", "apply", "ext", "exact", "exact"], "tactic_count": 5}
{"name": "AlgebraicGeometry.Scheme.Hom.ext'", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Hom.mem_preimage", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.coe_preimage", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.preimage_sup", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.preimage_inf", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.preimage_top", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.preimage_bot", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.preimage_iSup", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.iSup_preimage_eq_top", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.preimage_mono", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.id_preimage", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.comp_preimage", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.forgetToLocallyRingedSpace", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.fullyFaithfulForgetToLocallyRingedSpace", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.instFullLocallyRingedSpaceForgetToLocallyRingedSpace", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.instFaithfulLocallyRingedSpaceForgetToLocallyRingedSpace", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.forgetToTop", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.homeoOfIso", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.coe_homeoOfIso", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.coe_homeoOfIso_symm", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.homeoOfIso_symm", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.homeoOfIso_apply", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.homeomorph", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.homeomorph_apply", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.hasCoeToTopCat", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.forgetToTop_obj_eq_coe", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.forget", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.forget_obj_eq_coe", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.forget_obj", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.forget_map", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.id_base", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.id_app", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.id_appTop", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.comp_toLRSHom", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.comp_base", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.comp_apply", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Hom.comp_app", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.comp_appTop", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.appLE_comp_appLE", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "rfl"], "tactic_count": 3}
{"name": "AlgebraicGeometry.Scheme.Hom.comp_appLE", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Hom.congr_app", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Hom.app_eq", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Hom.eqToHom_app", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Hom.isIso_toLRSHom", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.isIso_toPshHom", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.isIso_base", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.instIsIsoCommRingCatApp", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.inv_app", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Hom.inv_appTop", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Hom.copyBase", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.copyBase_eq", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": true, "tactics": ["subst", "obtain", "simp", "congr", "cat_disch"], "tactic_count": 5}
{"name": "AlgebraicGeometry.Spec", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SpecOfNotation.termSpec(_)", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SpecOfNotation._aux_Mathlib_AlgebraicGeometry_Scheme___macroRules_SpecOfNotation_termSpec(_)_1", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SpecOfNotation._aux_Mathlib_AlgebraicGeometry_Scheme___delab_app_SpecOfNotation_termSpec(_)_1", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Spec_toLocallyRingedSpace", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Spec.map", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Spec.map_id", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Spec.map_comp", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Spec", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Spec.map_eqToHom", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "AlgebraicGeometry.instIsIsoSchemeMapOfCommRingCat", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Spec.map_inv", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": true, "tactics": ["change", "rw"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Spec_carrier", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Spec_sheaf", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Spec_presheaf", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Spec.map_base", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Spec.map_apply", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Spec.map_app", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Spec.map_appLE", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instNonemptyCarrierCarrierCommRingCatSpecOfNontrivialCarrier", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.isEmpty_of_commSq", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.empty", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.instEmptyCollection", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Γ", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Γ_def", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Γ_obj", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Γ_obj_op", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Γ_map", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Γ_map_op", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.SpecΓIdentity", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.ΓSpecIso", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.SpecΓIdentity_app", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.SpecΓIdentity_hom_app", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.SpecΓIdentity_inv_app", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.ΓSpecIso_naturality", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.ΓSpecIso_inv_naturality", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.ΓSpecIso_inv", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.toOpen_eq", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.instUniqueCarrierCarrierCommRingCatSpecOf", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.default_asIdeal", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.basicOpen", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.mem_basicOpen", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.mem_basicOpen'", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.mem_basicOpen''", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.mem_basicOpen_top", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.basicOpen_res", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.basicOpen_res_eq", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.basicOpen_le", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.basicOpen_restrict", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.preimage_basicOpen", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.preimage_basicOpen_top", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.basicOpen_appLE", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": true, "tactics": ["simp", "rw"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.basicOpen_zero", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.basicOpen_mul", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.basicOpen_pow", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.basicOpen_add_le", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": true, "tactics": ["intro", "have", "simp_rw", "simp", "exact"], "tactic_count": 5}
{"name": "AlgebraicGeometry.Scheme.basicOpen_of_isUnit", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.basicOpen_one", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.algebra_section_section_basicOpen", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.SpecMap_preimage_basicOpen", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.zeroLocus", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.zeroLocus_def", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.zeroLocus_isClosed", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.zeroLocus_singleton", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.zeroLocus_empty_eq_univ", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.mem_zeroLocus_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.codisjoint_zeroLocus", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.zeroLocus_span", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": true, "tactics": ["ext", "simp", "refine", "simp", "exact", "simp"], "tactic_count": 6}
{"name": "AlgebraicGeometry.Scheme.zeroLocus_map", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": true, "tactics": ["ext", "suffices", "grind"], "tactic_count": 3}
{"name": "AlgebraicGeometry.Scheme.zeroLocus_map_of_eq", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.zeroLocus_mono", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.preimage_zeroLocus", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.zeroLocus_univ", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": true, "tactics": ["ext", "simp", "not_iff_not]", "exact"], "tactic_count": 4}
{"name": "AlgebraicGeometry.Scheme.zeroLocus_iUnion", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.zeroLocus_radical", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": true, "tactics": ["refine", "simp", "rintro", "rcases", "exact", "exact"], "tactic_count": 6}
{"name": "AlgebraicGeometry.basicOpen_eq_of_affine", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": true, "tactics": ["ext", "simp", "suffices", "rw", "exact"], "tactic_count": 5}
{"name": "AlgebraicGeometry.basicOpen_eq_of_affine'", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": true, "tactics": ["convert", "exact"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.SpecMap_presheaf_map_eqToHom", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": ["have", "cases", "refine", "simp"], "tactic_count": 4}
{"name": "AlgebraicGeometry.germ_eq_zero_of_pow_mul_eq_zero", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": true, "tactics": ["rw", "have", "rw", "exact", "rw"], "tactic_count": 5}
{"name": "AlgebraicGeometry.Scheme.hom_base_inv_base", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.hom_inv_apply", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": true, "tactics": ["change", "simp"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.inv_base_hom_base", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.inv_hom_apply", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": true, "tactics": ["change", "simp"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Spec_zeroLocus_eq_zeroLocus", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": true, "tactics": ["ext", "suffices", "simp"], "tactic_count": 3}
{"name": "AlgebraicGeometry.Spec_zeroLocus", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": true, "tactics": ["convert", "rw", "exact"], "tactic_count": 3}
{"name": "AlgebraicGeometry.Scheme.Hom.instIsLocalHomCarrierStalkCommRingCatPresheafCoeContinuousMapCarrierCarrierHomTopCatBaseRingHomHomStalkMap", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.stalkMap_id", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.stalkMap_comp", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.stalkSpecializes_stalkMap", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.stalkSpecializes_stalkMap_apply", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.stalkMap_congr", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.stalkMap_congr_hom", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.stalkMap_congr_point", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.stalkMap_hom_inv", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.stalkMap_hom_inv_apply", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.stalkMap_inv_hom", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.stalkMap_inv_hom_apply", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.germ_stalkMap", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.germ_stalkMap_apply", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Hom.arrowStalkMapIsoOfEq", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Spec_closedPoint", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Scheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.zariskiPretopology", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Sites.BigZariski", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.zariskiTopology", "kind": "abbrev", "module": "Mathlib.AlgebraicGeometry.Sites.BigZariski", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.zariskiTopology_eq", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Sites.BigZariski", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.subcanonical_zariskiTopology", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Sites.BigZariski", "is_tactic_proof": true, "tactics": ["apply", "intro", "rw", "rintro", "obtain", "let", "intro", "apply", "exact", "refine", "rintro", "dsimp", "rw", "intro", "apply", "intro", "rw", "exact"], "tactic_count": 18}
{"name": "AlgebraicGeometry.Scheme.etalePretopology", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Sites.Etale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.etaleTopology", "kind": "abbrev", "module": "Mathlib.AlgebraicGeometry.Sites.Etale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.zariskiTopology_le_etaleTopology", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Sites.Etale", "is_tactic_proof": true, "tactics": ["apply", "intro", "infer_instance"], "tactic_count": 3}
{"name": "AlgebraicGeometry.Scheme.smallEtaleTopology", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Sites.Etale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.smallEtalePretopology", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Sites.Etale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.IsJointlySurjectivePreserving.exists_preimage_snd_triplet_of_prop", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Sites.MorphismProperty", "is_tactic_proof": true, "tactics": ["let", "haveI", "obtain", "use", "rwa"], "tactic_count": 5}
{"name": "AlgebraicGeometry.Scheme.instIsJointlySurjectivePreservingIsOpenImmersion", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Sites.MorphismProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.jointlySurjectivePrecoverage", "kind": "abbrev", "module": "Mathlib.AlgebraicGeometry.Sites.MorphismProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.precoverage", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Sites.MorphismProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.ofArrows_mem_precoverage_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Sites.MorphismProperty", "is_tactic_proof": false, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.singleton_mem_precoverage_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Sites.MorphismProperty", "is_tactic_proof": true, "tactics": ["rw", "aesop"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.instIsStableUnderCompositionPrecoverageOfIsStableUnderComposition", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Sites.MorphismProperty", "is_tactic_proof": true, "tactics": ["dsimp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.instHasIsosPrecoverageOfContainsIdentitiesOfRespectsIso", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Sites.MorphismProperty", "is_tactic_proof": true, "tactics": ["dsimp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.instHasPullbacksPrecoverageOfHasPullbacks", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Sites.MorphismProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.instIsStableUnderBaseChangePrecoverageOfIsJointlySurjectivePreservingOfIsStableUnderBaseChange", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Sites.MorphismProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.zariskiPrecoverage", "kind": "abbrev", "module": "Mathlib.AlgebraicGeometry.Sites.MorphismProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.pretopology", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Sites.Pretopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.grothendieckTopology", "kind": "abbrev", "module": "Mathlib.AlgebraicGeometry.Sites.Pretopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.instIsStableUnderBaseChangeJointlySurjectivePrecoverage", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Sites.Pretopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.jointlySurjectivePretopology", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Sites.Pretopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Cover.mem_pretopology", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Sites.Pretopology", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.mem_pretopology_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Sites.Pretopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.mem_grothendieckTopology_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Sites.Pretopology", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "rw", "obtain", "use"], "tactic_count": 5}
{"name": "AlgebraicGeometry.Scheme.Cover.mem_grothendieckTopology", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Sites.Pretopology", "is_tactic_proof": true, "tactics": ["rw", "use", "exact"], "tactic_count": 3}
{"name": "AlgebraicGeometry.Scheme.jointlySurjectiveTopology", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Sites.Pretopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.mem_jointlySurjectiveTopology_iff_jointlySurjectivePretopology", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Sites.Pretopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.jointlySurjectiveTopology_eq_toGrothendieck_jointlySurjectivePretopology", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Sites.Pretopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.pretopology_eq_inf", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Sites.Pretopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.grothendieckTopology_eq_inf", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Sites.Pretopology", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.pretopology_monotone", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Sites.Pretopology", "is_tactic_proof": true, "tactics": ["rintro", "obtain", "rw", "use", "rfl"], "tactic_count": 5}
{"name": "AlgebraicGeometry.Scheme.grothendieckTopology_monotone", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Sites.Pretopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.quasiCompactCover_shrink_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Sites.QuasiCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.qcCoverFamily", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Sites.QuasiCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.qcPrecoverage", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Sites.QuasiCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.presieve₀_mem_qcPrecoverage_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Sites.QuasiCompact", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.instHasIsosQcPrecoverage", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Sites.QuasiCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.instIsStableUnderBaseChangeQcPrecoverage", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Sites.QuasiCompact", "is_tactic_proof": true, "tactics": ["refine", "intro", "exact", "intro", "simp", "infer_instance"], "tactic_count": 6}
{"name": "AlgebraicGeometry.Scheme.instIsStableUnderCompositionQcPrecoverage", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Sites.QuasiCompact", "is_tactic_proof": true, "tactics": ["refine", "simp", "infer_instance"], "tactic_count": 3}
{"name": "AlgebraicGeometry.Scheme.instIsStableUnderSupQcPrecoverage", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Sites.QuasiCompact", "is_tactic_proof": true, "tactics": ["refine", "simp", "infer_instance"], "tactic_count": 3}
{"name": "AlgebraicGeometry.Scheme.precoverage_le_qcPrecoverage_of_isOpenMap", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Sites.QuasiCompact", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "AlgebraicGeometry.Scheme.zariskiPrecoverage_le_qcPrecoverage", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Sites.QuasiCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.LocalRepresentability.glueData", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Sites.Representability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.LocalRepresentability.toGlued", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Sites.Representability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.LocalRepresentability.instIsOpenImmersionToGlued", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Sites.Representability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.LocalRepresentability.yonedaGluedToSheaf", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Sites.Representability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.LocalRepresentability.yoneda_toGlued_yonedaGluedToSheaf", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Sites.Representability", "is_tactic_proof": true, "tactics": ["apply", "rw", "yonedaEquiv_symm_app_apply]", "apply"], "tactic_count": 4}
{"name": "AlgebraicGeometry.Scheme.LocalRepresentability.yonedaGluedToSheaf_app_toGlued", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Sites.Representability", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.LocalRepresentability.yonedaGluedToSheaf_app_comp", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Sites.Representability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.LocalRepresentability.instIsLocallySurjectiveHomObjForgetTypeYonedaGluedToSheafOfIsLocallySurjectiveZariskiTopologyDescFunctorOpposite", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Sites.Representability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.LocalRepresentability.comp_toGlued_eq", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Sites.Representability", "is_tactic_proof": true, "tactics": ["rw", "conv_rhs", "congr", "exact"], "tactic_count": 4}
{"name": "AlgebraicGeometry.Scheme.LocalRepresentability.glueData_openCover_map", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Sites.Representability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.LocalRepresentability.instIsLocallyInjectiveHomObjForgetTypeYonedaGluedToSheaf", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Sites.Representability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.LocalRepresentability.instIsIsoSheafZariskiTopologyTypeYonedaGluedToSheaf", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Sites.Representability", "is_tactic_proof": true, "tactics": ["rw", "constructor"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.LocalRepresentability.yonedaIsoSheaf", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Sites.Representability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.LocalRepresentability.representableBy", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Sites.Representability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.LocalRepresentability.isRepresentable", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Sites.Representability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Cover.toPresieveOver", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Sites.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Cover.toPresieveOverProp", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Sites.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Cover.overEquiv_generate_toPresieveOver_eq_ofArrows", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Sites.Small", "is_tactic_proof": true, "tactics": ["ext", "simp", "constructor", "rintro", "exact", "rintro", "have", "refine", "ext", "simpa"], "tactic_count": 10}
{"name": "AlgebraicGeometry.Scheme.Cover.toPresieveOver_le_arrows_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Sites.Small", "is_tactic_proof": true, "tactics": ["simp_rw", "rw"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.overPretopology", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Sites.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.overGrothendieckTopology", "kind": "abbrev", "module": "Mathlib.AlgebraicGeometry.Sites.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.overGrothendieckTopology_eq_toGrothendieck_overPretopology", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Sites.Small", "is_tactic_proof": true, "tactics": ["ext", "rw", "constructor", "intro", "obtain", "rw", "letI", "letI", "isOver_map", "use", "rwa", "rintro", "use", "rwa"], "tactic_count": 14}
{"name": "AlgebraicGeometry.Scheme.mem_overGrothendieckTopology", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Sites.Small", "is_tactic_proof": true, "tactics": ["rw", "constructor", "rintro", "use", "rintro", "exact"], "tactic_count": 6}
{"name": "AlgebraicGeometry.Scheme.locallyCoverDense_of_le", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Sites.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.instLocallyCoverDenseOverTopMorphismPropertyOverForgetOverGrothendieckTopology", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Sites.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.smallGrothendieckTopologyOfLE", "kind": "abbrev", "module": "Mathlib.AlgebraicGeometry.Sites.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.smallGrothendieckTopology", "kind": "abbrev", "module": "Mathlib.AlgebraicGeometry.Sites.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.smallPretopology", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Sites.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.smallGrothendieckTopologyOfLE_eq_toGrothendieck_smallPretopology", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Sites.Small", "is_tactic_proof": true, "tactics": ["ext", "simp", "mem_overGrothendieckTopology]", "constructor", "intro", "have", "rw", "exact", "refine", "use", "rintro", "let", "have", "rwa", "rintro", "use", "rintro", "exact"], "tactic_count": 18}
{"name": "AlgebraicGeometry.Scheme.smallGrothendieckTopology_eq_toGrothendieck_smallPretopology", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Sites.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.mem_toGrothendieck_smallPretopology", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Sites.Small", "is_tactic_proof": true, "tactics": ["rw", "refine", "rintro", "intro", "obtain", "refine", "use", "choose", "let", "f", "mem₀", "rw", "refine", "letI", "isOver_map", "refine", "use", "rintro", "exact"], "tactic_count": 19}
{"name": "AlgebraicGeometry.Scheme.mem_smallGrothendieckTopology", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Sites.Small", "is_tactic_proof": true, "tactics": ["rw", "constructor", "rintro", "use", "rintro", "exact"], "tactic_count": 6}
{"name": "AlgebraicGeometry.Scheme.AffineZariskiSite", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Sites.SmallAffineZariski", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.AffineZariskiSite.toOpens", "kind": "abbrev", "module": "Mathlib.AlgebraicGeometry.Sites.SmallAffineZariski", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.AffineZariskiSite.instPreorder", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Sites.SmallAffineZariski", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.AffineZariskiSite.toOpens_mono", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Sites.SmallAffineZariski", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.AffineZariskiSite.toOpens_injective", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Sites.SmallAffineZariski", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.AffineZariskiSite.instPartialOrder", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Sites.SmallAffineZariski", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.AffineZariskiSite.basicOpen", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Sites.SmallAffineZariski", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.AffineZariskiSite.basicOpen_le", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Sites.SmallAffineZariski", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.AffineZariskiSite.toOpensFunctor", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Sites.SmallAffineZariski", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.AffineZariskiSite.instFaithfulOpensToOpensFunctor", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Sites.SmallAffineZariski", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.AffineZariskiSite.instIsLocallyFullOpensToOpensFunctorGrothendieckTopologyCarrierCarrierCommRingCat", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Sites.SmallAffineZariski", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.AffineZariskiSite.instIsCoverDenseOpensToOpensFunctorGrothendieckTopologyCarrierCarrierCommRingCat", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Sites.SmallAffineZariski", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.AffineZariskiSite.grothendieckTopology", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Sites.SmallAffineZariski", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.AffineZariskiSite.mem_grothendieckTopology", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Sites.SmallAffineZariski", "is_tactic_proof": true, "tactics": ["apply", "rintro", "exact", "rintro", "exact"], "tactic_count": 5}
{"name": "AlgebraicGeometry.Scheme.AffineZariskiSite.instIsDenseSubsiteOpensCarrierCarrierCommRingCatGrothendieckTopologyGrothendieckTopologyToOpensFunctor", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Sites.SmallAffineZariski", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.AffineZariskiSite.presieveOfSections", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Sites.SmallAffineZariski", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.AffineZariskiSite.sectionsOfPresieve", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Sites.SmallAffineZariski", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.AffineZariskiSite.presieveOfSections_sectionsOfPresieve", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Sites.SmallAffineZariski", "is_tactic_proof": true, "tactics": ["refine", "rintro", "exact", "intro", "obtain", "exact"], "tactic_count": 6}
{"name": "AlgebraicGeometry.Scheme.AffineZariskiSite.presieveOfSections_surjective", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Sites.SmallAffineZariski", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.AffineZariskiSite.presieveOfSections_eq_ofArrows", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Sites.SmallAffineZariski", "is_tactic_proof": true, "tactics": ["refine", "rintro", "exact", "rintro", "exact"], "tactic_count": 5}
{"name": "AlgebraicGeometry.Scheme.AffineZariskiSite.generate_presieveOfSections", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Sites.SmallAffineZariski", "is_tactic_proof": true, "tactics": ["obtain", "constructor", "rintro", "subst", "obtain", "refine", "rw", "exact", "rintro", "refine", "exact"], "tactic_count": 11}
{"name": "AlgebraicGeometry.Scheme.AffineZariskiSite.generate_presieveOfSections_mem_grothendieckTopology", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Sites.SmallAffineZariski", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp", "constructor", "simp", "rintro", "exact", "rintro", "refine"], "tactic_count": 9}
{"name": "AlgebraicGeometry.Scheme.AffineZariskiSite.mem_grothendieckTopology_iff_sectionsOfPresieve", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Sites.SmallAffineZariski", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.AffineZariskiSite.sheafEquiv", "kind": "abbrev", "module": "Mathlib.AlgebraicGeometry.Sites.SmallAffineZariski", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.AffineZariskiSite.directedCover", "kind": "abbrev", "module": "Mathlib.AlgebraicGeometry.Sites.SmallAffineZariski", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.AffineZariskiSite.instLocallyDirectedIsOpenImmersionDirectedCover", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Sites.SmallAffineZariski", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.AffineZariskiSite.cocone", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Sites.SmallAffineZariski", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.AffineZariskiSite.PreservesLocalization", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Sites.SmallAffineZariski", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.AffineZariskiSite.PreservesLocalization.isLocallyDirected", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Sites.SmallAffineZariski", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "let", "have", "let", "have", "rw", "exact", "obtain", "refine", "simp", "simp", "refine", "change", "rw", "exact", "refine", "change", "rw", "exact"], "tactic_count": 20}
{"name": "AlgebraicGeometry.Scheme.AffineZariskiSite.PreservesLocalization.isOpenImmersion", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Sites.SmallAffineZariski", "is_tactic_proof": true, "tactics": ["rintro", "have", "let", "exact"], "tactic_count": 4}
{"name": "AlgebraicGeometry.Scheme.AffineZariskiSite.PreservesLocalization.opensRange_map", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Sites.SmallAffineZariski", "is_tactic_proof": true, "tactics": ["have", "let", "apply", "refine"], "tactic_count": 4}
{"name": "AlgebraicGeometry.Scheme.AffineZariskiSite.PreservesLocalization.colimitDesc_preimage", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Sites.SmallAffineZariski", "is_tactic_proof": true, "tactics": ["haveI", "haveI", "let", "let", "change", "apply", "rintro", "obtain", "dsimp", "replace", "have", "obtain", "obtain", "suffices", "rw", "rw", "exact", "refine", "congr", "change", "congr", "simp", "refine", "rintro", "simpa"], "tactic_count": 25}
{"name": "AlgebraicGeometry.Scheme.preservesLocalization_toOpensFunctor", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Sites.SmallAffineZariski", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.AffineZariskiSite.isColimitCocone", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Sites.SmallAffineZariski", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Spec.topObj", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Spec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Spec.topObj_forget", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Spec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Spec.topMap", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Spec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Spec.topMap_id", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Spec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Spec.topMap_comp", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Spec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Spec.toTop", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Spec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Spec.sheafedSpaceObj", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Spec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Spec.sheafedSpaceMap", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Spec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Spec.sheafedSpaceMap_id", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Spec", "is_tactic_proof": true, "tactics": ["ext", "exact", "ext", "dsimp", "rw", "simp", "rfl"], "tactic_count": 7}
{"name": "AlgebraicGeometry.Spec.sheafedSpaceMap_comp", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Spec", "is_tactic_proof": true, "tactics": ["ext", "exact", "ext", "rw", "erw", "dsimp", "rw", "rfl"], "tactic_count": 8}
{"name": "AlgebraicGeometry.Spec.toSheafedSpace", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Spec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Spec.toPresheafedSpace", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Spec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Spec.toPresheafedSpace_obj", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Spec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Spec.toPresheafedSpace_obj_op", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Spec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Spec.toPresheafedSpace_map", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Spec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Spec.toPresheafedSpace_map_op", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Spec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Spec.basicOpen_hom_ext", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Spec", "is_tactic_proof": true, "tactics": ["ext", "exact", "apply", "intro", "apply", "simpa"], "tactic_count": 6}
{"name": "AlgebraicGeometry.Spec.locallyRingedSpaceObj", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Spec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Spec.locallyRingedSpaceObj_sheaf", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Spec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Spec.locallyRingedSpaceObj_sheaf'", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Spec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Spec.locallyRingedSpaceObj_presheaf_map", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Spec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Spec.locallyRingedSpaceObj_presheaf'", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Spec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Spec.locallyRingedSpaceObj_presheaf_map'", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Spec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.stalkMap_toStalk", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Spec", "is_tactic_proof": true, "tactics": ["rw", "erw", "rw", "erw", "rfl"], "tactic_count": 5}
{"name": "AlgebraicGeometry.localRingHom_comp_stalkIso", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Spec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.localRingHom_comp_stalkIso_apply'", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Spec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Spec.locallyRingedSpaceMap", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Spec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Spec.locallyRingedSpaceMap_id", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Spec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Spec.locallyRingedSpaceMap_comp", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Spec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Spec.toLocallyRingedSpace", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Spec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.toSpecΓ", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Spec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.isIso_toSpecΓ", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Spec", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Spec_Γ_naturality", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Spec", "is_tactic_proof": true, "tactics": ["ext", "refine", "apply"], "tactic_count": 3}
{"name": "AlgebraicGeometry.LocallyRingedSpace.SpecΓIdentity", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Spec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.isIso_SpecMap_stakMap_localization", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Spec", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "refine", "change", "infer_instance"], "tactic_count": 5}
{"name": "AlgebraicGeometry.StructureSheaf.toPushforwardStalk", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Spec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.StructureSheaf.toPushforwardStalk_comp", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Spec", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "AlgebraicGeometry.StructureSheaf.instAlgebraCarrierStalkCommRingCatObjPresheafTopObjPushforwardTopMapValOpensCarrierTopStructureSheaf", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Spec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.StructureSheaf.algebraMap_pushforward_stalk", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Spec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.StructureSheaf.toPushforwardStalkAlgHom", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Spec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.StructureSheaf.isLocalizedModule_toPushforwardStalkAlgHom_aux", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Spec", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "change", "replace", "e", "set", "replace", "rw", "clear_value", "obtain", "refine", "rw", "iterate", "erw", "rw", "let", "rw", "dsimp", "rw", "congr"], "tactic_count": 20}
{"name": "AlgebraicGeometry.StructureSheaf.isLocalizedModule_toPushforwardStalkAlgHom", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Spec", "is_tactic_proof": true, "tactics": ["apply", "intro", "change", "exact", "apply", "intro", "rw", "toPushforwardStalk]", "rw", "obtain", "obtain", "apply_fun", "simp", "have", "have", "this", "obtain", "refine", "rw", "exact"], "tactic_count": 20}
{"name": "AlgebraicGeometry.injective_germ_basicOpen", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.SpreadingOut", "is_tactic_proof": true, "tactics": ["rw", "intro", "have", "obtain", "rw", "swap", "rw"], "tactic_count": 7}
{"name": "AlgebraicGeometry.Scheme.exists_germ_injective", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.SpreadingOut", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.exists_le_and_germ_injective", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.SpreadingOut", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "exact"], "tactic_count": 3}
{"name": "AlgebraicGeometry.instIsGermInjectiveAtCoeContinuousMapCarrierCarrierCommRingCatHomTopCatBaseOfIsOpenImmersion", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.SpreadingOut", "is_tactic_proof": true, "tactics": ["obtain", "refine", "refine", "refine", "simpa"], "tactic_count": 5}
{"name": "AlgebraicGeometry.isGermInjectiveAt_iff_of_isOpenImmersion", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.SpreadingOut", "is_tactic_proof": true, "tactics": ["refine", "obtain", "obtain", "obtain", "obtain", "obtain", "refine", "replace", "replace", "simpa"], "tactic_count": 10}
{"name": "AlgebraicGeometry.Scheme.IsGermInjective", "kind": "abbrev", "module": "Mathlib.AlgebraicGeometry.SpreadingOut", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.IsGermInjective.of_openCover", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.SpreadingOut", "is_tactic_proof": true, "tactics": ["intro", "rw", "infer_instance"], "tactic_count": 3}
{"name": "AlgebraicGeometry.Scheme.IsGermInjective.Spec", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.SpreadingOut", "is_tactic_proof": true, "tactics": ["refine", "obtain", "refine", "rw", "exact", "rw", "intro", "obtain", "x", "rw", "swap", "exact", "erw", "obtain", "obtain", "refine", "exact"], "tactic_count": 17}
{"name": "AlgebraicGeometry.instIsGermInjectiveOfIsIntegral", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.SpreadingOut", "is_tactic_proof": false, "tactics": ["refine", "have", "have", "exact"], "tactic_count": 4}
{"name": "AlgebraicGeometry.instIsGermInjectiveOfIsLocallyNoetherian", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.SpreadingOut", "is_tactic_proof": false, "tactics": ["suffices", "refine", "exact", "refine", "let", "have", "choose", "obtain", "have", "refine", "rw", "refine", "rw", "intro", "rw", "refine", "rw", "exact"], "tactic_count": 18}
{"name": "AlgebraicGeometry.spread_out_unique_of_isGermInjective", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.SpreadingOut", "is_tactic_proof": false, "tactics": ["obtain", "have", "obtain", "refine", "rw", "congr", "have", "suffices", "f.appLE", "rw", "simp", "congr", "apply", "rintro", "have", "rw", "simp", "simp"], "tactic_count": 18}
{"name": "AlgebraicGeometry.spread_out_unique_of_isGermInjective'", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.SpreadingOut", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.exists_lift_of_germInjective_aux", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.SpreadingOut", "is_tactic_proof": true, "tactics": ["letI", "obtain", "choose", "have", "rw", "exact", "refine", "letI", "letI", "letI", "let", "let", "change", "rw", "rintro", "refine", "exact"], "tactic_count": 17}
{"name": "AlgebraicGeometry.exists_lift_of_germInjective", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.SpreadingOut", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "let", "have", "rw", "exact", "let", "refine", "iV'V.trans", "ext", "change", "simp", "rfl", "ext", "apply", "change", "rw", "ext", "change", "rw", "rfl"], "tactic_count": 21}
{"name": "AlgebraicGeometry.spread_out_of_isGermInjective", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.SpreadingOut", "is_tactic_proof": false, "tactics": ["obtain", "have", "obtain", "have", "rw", "simp", "obtain", "exists_lift_of_germInjective", "refine", "rw", "simp", "rw", "hW.isoSpec_hom,"], "tactic_count": 13}
{"name": "AlgebraicGeometry.spread_out_of_isGermInjective'", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.SpreadingOut", "is_tactic_proof": true, "tactics": ["have", "simpa", "rw", "apply", "rw", "simpa"], "tactic_count": 6}
{"name": "AlgebraicGeometry.IsAffineOpen.fromSpecStalk", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Stalk", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsAffineOpen.fromSpecStalk_eq", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Stalk", "is_tactic_proof": false, "tactics": ["obtain", "transitivity", "delta", "rw", "erw", "rw", "delta", "rw", "erw", "rw"], "tactic_count": 10}
{"name": "AlgebraicGeometry.Scheme.fromSpecStalk", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Stalk", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instOverSpecStalkCommRingCatPresheaf", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Stalk", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.instCanonicallyOverSpecStalkCommRingCatPresheaf", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Stalk", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsAffineOpen.fromSpecStalk_eq_fromSpecStalk", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Stalk", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsAffineOpen.fromSpecStalk_isPreimmersion", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Stalk", "is_tactic_proof": true, "tactics": ["dsimp", "haveI", "letI", "haveI", "apply"], "tactic_count": 5}
{"name": "AlgebraicGeometry.instIsPreimmersionFromSpecStalk", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Stalk", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.IsAffineOpen.fromSpecStalk_closedPoint", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Stalk", "is_tactic_proof": true, "tactics": ["rw", "rw"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.fromSpecStalk_closedPoint", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Stalk", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.fromSpecStalk_app", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Stalk", "is_tactic_proof": true, "tactics": ["obtain", "rw", "hV.fromSpec_app_of_le", "simp"], "tactic_count": 4}
{"name": "AlgebraicGeometry.Scheme.fromSpecStalk_appTop", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Stalk", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.SpecMap_stalkSpecializes_fromSpecStalk", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Stalk", "is_tactic_proof": false, "tactics": ["obtain", "have", "rw"], "tactic_count": 3}
{"name": "AlgebraicGeometry.Scheme.instIsOverMapStalkSpecializesCommRingCatPresheaf", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Stalk", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.SpecMap_stalkMap_fromSpecStalk", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Stalk", "is_tactic_proof": false, "tactics": ["obtain", "obtain", "rw"], "tactic_count": 3}
{"name": "AlgebraicGeometry.Scheme.instIsOverMapStalkMapOverInferInstanceOverClass", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Stalk", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Spec_fromSpecStalk", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Stalk", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.Spec_fromSpecStalk'", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Stalk", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.range_fromSpecStalk", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Stalk", "is_tactic_proof": true, "tactics": ["ext", "constructor", "rintro", "exact", "rintro", "have", "rw", "exact"], "tactic_count": 8}
{"name": "AlgebraicGeometry.Scheme.Opens.fromSpecStalkOfMem", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Stalk", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.Opens.fromSpecStalkOfMem_ι", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Stalk", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.instIsOverFromSpecStalkOfMem", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Stalk", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.fromSpecStalk_toSpecΓ", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Stalk", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.Opens.fromSpecStalkOfMem_toSpecΓ", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Stalk", "is_tactic_proof": false, "tactics": ["rw", "congr", "rw", "erw", "rw", "exact"], "tactic_count": 6}
{"name": "AlgebraicGeometry.stalkClosedPointIso", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Stalk", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.stalkClosedPointIso_inv", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Stalk", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "AlgebraicGeometry.ΓSpecIso_hom_stalkClosedPointIso_inv", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Stalk", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "AlgebraicGeometry.germ_stalkClosedPointIso_hom", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Stalk", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Spec_stalkClosedPointIso", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Stalk", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgebraicGeometry.Scheme.stalkClosedPointTo", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Stalk", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.isLocalHom_stalkClosedPointTo", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Stalk", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.isLocalHom_stalkClosedPointTo'", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.Stalk", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.preimage_eq_top_of_closedPoint_mem", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Stalk", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Scheme.stalkClosedPointTo_comp", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Stalk", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Scheme.germ_stalkClosedPointTo_Spec", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Stalk", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "rw"], "tactic_count": 3}
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{"name": "AlgebraicGeometry.Scheme.germ_stalkClosedPointTo_Spec_fromSpecStalk", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Stalk", "is_tactic_proof": false, "tactics": ["have", "rw", "have", "simp", "simp_rw", "rw"], "tactic_count": 6}
{"name": "AlgebraicGeometry.Scheme.stalkClosedPointTo_fromSpecStalk", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Stalk", "is_tactic_proof": true, "tactics": ["refine", "simp", "have", "convert"], "tactic_count": 4}
{"name": "AlgebraicGeometry.Scheme.Spec_stalkClosedPointTo_fromSpecStalk", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Stalk", "is_tactic_proof": false, "tactics": ["obtain", "have", "rw", "rw", "germ_stalkClosedPointTo]", "simpa"], "tactic_count": 6}
{"name": "AlgebraicGeometry.SpecToEquivOfLocalRing_eq_iff", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.Stalk", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "obtain", "obtain", "rintro", "simp"], "tactic_count": 6}
{"name": "AlgebraicGeometry.SpecToEquivOfLocalRing", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.Stalk", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.PrimeSpectrum.Top", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.StructureSheaf.Localizations", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.StructureSheaf.commRingLocalizations", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.StructureSheaf.localRingLocalizations", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.StructureSheaf.instInhabitedLocalizations", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.StructureSheaf.instAlgebraLocalizationsValCarrierTopMemOpens", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.StructureSheaf.instAtPrimeLocalizationsValCarrierTopMemOpensAsIdeal", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.StructureSheaf.IsFraction", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.StructureSheaf.IsFraction.eq_mk'", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": true, "tactics": ["rcases", "refine", "exact"], "tactic_count": 3}
{"name": "AlgebraicGeometry.StructureSheaf.isFractionPrelocal", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.StructureSheaf.isLocallyFraction", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.StructureSheaf.isLocallyFraction_pred", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.StructureSheaf.sectionsSubring", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.structureSheafInType", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.commRingStructureSheafInTypeObj", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.structurePresheafInCommRing", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.structurePresheafCompForget", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Spec.structureSheaf", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.StructureSheaf.res_apply", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.StructureSheaf.const", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.StructureSheaf.const_apply", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.StructureSheaf.const_apply'", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.StructureSheaf.exists_const", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.StructureSheaf.res_const", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.StructureSheaf.res_const'", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.StructureSheaf.const_zero", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.StructureSheaf.const_self", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.StructureSheaf.const_one", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.StructureSheaf.const_add", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.StructureSheaf.const_mul", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.StructureSheaf.const_ext", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.StructureSheaf.const_congr", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": true, "tactics": ["substs"], "tactic_count": 1}
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{"name": "AlgebraicGeometry.StructureSheaf.const_mul_cancel", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "AlgebraicGeometry.StructureSheaf.toOpen", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.StructureSheaf.toOpen_res", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.StructureSheaf.toOpen_apply", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.StructureSheaf.toOpen_eq_const", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.StructureSheaf.toStalk", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.StructureSheaf.toOpen_germ", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "AlgebraicGeometry.StructureSheaf.isUnit_to_basicOpen_self", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.StructureSheaf.isUnit_toStalk", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
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{"name": "AlgebraicGeometry.StructureSheaf.localizationToStalk_of", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.StructureSheaf.localizationToStalk_mk'", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.StructureSheaf.openToLocalization", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.StructureSheaf.coe_openToLocalization", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.StructureSheaf.openToLocalization_apply", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.StructureSheaf.stalkToFiberRingHom", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.StructureSheaf.germ_comp_stalkToFiberRingHom", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.StructureSheaf.stalkToFiberRingHom_germ", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.StructureSheaf.toStalk_comp_stalkToFiberRingHom", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgebraicGeometry.StructureSheaf.stalkToFiberRingHom_toStalk", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.StructureSheaf.stalkIso", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.StructureSheaf.instIsIsoCommRingCatStalkToFiberRingHom", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.StructureSheaf.instIsLocalHomCarrierStalkCommRingCatPresheafStructureSheafOfAtPrimeAsIdealRingHomHomStalkToFiberRingHom", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.StructureSheaf.instIsIsoCommRingCatLocalizationToStalk", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.StructureSheaf.instIsLocalHomCarrierOfAtPrimeAsIdealStalkCommRingCatPresheafStructureSheafRingHomHomLocalizationToStalk", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.StructureSheaf.stalkToFiberRingHom_localizationToStalk", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.StructureSheaf.localizationToStalk_stalkToFiberRingHom", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AlgebraicGeometry.StructureSheaf.toBasicOpen_mk'", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.StructureSheaf.localization_toBasicOpen", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.StructureSheaf.toBasicOpen_to_map", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.StructureSheaf.toBasicOpen_injective", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": true, "tactics": ["intro", "obtain", "obtain", "simp", "rw", "let", "zero_mem", "add_mem", "smul_mem", "suffices", "obtain", "exact", "rw", "intro", "contrapose", "rw", "have", "dsimp", "rw", "obtain", "exact"], "tactic_count": 21}
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{"name": "AlgebraicGeometry.StructureSheaf.basicOpenIso", "kind": "definition", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.StructureSheaf.stalkAlgebra", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.StructureSheaf.stalkAlgebra_map", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.StructureSheaf.IsLocalization.to_stalk", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": false, "tactics": ["convert", "apply", "intro", "rw", "congr", "change", "rw", "exact"], "tactic_count": 8}
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{"name": "AlgebraicGeometry.StructureSheaf.openAlgebra_map", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.StructureSheaf.IsLocalization.to_basicOpen", "kind": "instance", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": false, "tactics": ["convert", "apply", "intro", "congr", "exact"], "tactic_count": 5}
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{"name": "AlgebraicGeometry.StructureSheaf.to_global_factors", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": true, "tactics": ["rw", "change", "toOpen", "rw"], "tactic_count": 4}
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{"name": "AlgebraicGeometry.StructureSheaf.globalSectionsIso_hom", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.StructureSheaf.toStalk_stalkSpecializes", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": true, "tactics": ["dsimp"], "tactic_count": 1}
{"name": "AlgebraicGeometry.StructureSheaf.localizationToStalk_stalkSpecializes", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": true, "tactics": ["ext", "apply", "rw", "dsimp", "rw", "exact"], "tactic_count": 6}
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{"name": "AlgebraicGeometry.StructureSheaf.comapFunIsLocallyFraction", "kind": "theorem", "module": "Mathlib.AlgebraicGeometry.StructureSheaf", "is_tactic_proof": false, "tactics": ["rintro", "rcases", "refine", "rintro", "specialize", "refine", "dsimp", "erw", "rfl"], "tactic_count": 9}
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{"name": "AlgebraicTopology.DoldKan.MorphComponents.postComp_φ", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.Decomposition", "is_tactic_proof": true, "tactics": ["unfold", "simp"], "tactic_count": 2}
{"name": "AlgebraicTopology.DoldKan.MorphComponents.preComp", "kind": "definition", "module": "Mathlib.AlgebraicTopology.DoldKan.Decomposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.MorphComponents.preComp_φ", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.Decomposition", "is_tactic_proof": true, "tactics": ["unfold", "simp", "congr", "simp", "simp"], "tactic_count": 5}
{"name": "AlgebraicTopology.DoldKan.HigherFacesVanish.comp_σ", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.Degeneracies", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.σ_comp_P_eq_zero", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.Degeneracies", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "by_cases", "rw", "replace", "rcases", "fin_cases", "dsimp", "rw", "change", "simp", "rw", "dsimp", "rw", "simp", "one_mul,", "rw", "simp", "rw", "have", "dsimp", "rw", "add_zero,", "intro", "simp", "obtain", "rw", "have", "ext", "simp", "have", "hq", "simp", "lia)", "rw", "comp_zero]", "simp", "lia"], "tactic_count": 39}
{"name": "AlgebraicTopology.DoldKan.σ_comp_PInfty", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.Degeneracies", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "AlgebraicTopology.DoldKan.degeneracy_comp_PInfty", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.Degeneracies", "is_tactic_proof": true, "tactics": ["rw", "cases", "exfalso", "apply", "intro", "fin_cases", "fin_cases", "rfl", "obtain", "rw"], "tactic_count": 10}
{"name": "CategoryTheory.Abelian.DoldKan.N", "kind": "definition", "module": "Mathlib.AlgebraicTopology.DoldKan.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.DoldKan.Γ", "kind": "definition", "module": "Mathlib.AlgebraicTopology.DoldKan.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.DoldKan.comparisonN", "kind": "definition", "module": "Mathlib.AlgebraicTopology.DoldKan.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.DoldKan.equivalence", "kind": "definition", "module": "Mathlib.AlgebraicTopology.DoldKan.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.DoldKan.equivalence_inverse", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.DoldKan.N", "kind": "definition", "module": "Mathlib.AlgebraicTopology.DoldKan.EquivalenceAdditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.DoldKan.Γ", "kind": "definition", "module": "Mathlib.AlgebraicTopology.DoldKan.EquivalenceAdditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.DoldKan.equivalence", "kind": "definition", "module": "Mathlib.AlgebraicTopology.DoldKan.EquivalenceAdditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.DoldKan.isoN₁_hom_app_f", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.EquivalencePseudoabelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.DoldKan.N₂_map_isoΓ₀_hom_app_f", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.EquivalencePseudoabelian", "is_tactic_proof": true, "tactics": ["ext", "apply"], "tactic_count": 2}
{"name": "CategoryTheory.Idempotents.DoldKan.equivalence_functor", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.EquivalencePseudoabelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.DoldKan.equivalence_inverse", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.EquivalencePseudoabelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.DoldKan.hη", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.EquivalencePseudoabelian", "is_tactic_proof": true, "tactics": ["ext", "simp", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Idempotents.DoldKan.equivalence_counitIso", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.EquivalencePseudoabelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.DoldKan.hε", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.EquivalencePseudoabelian", "is_tactic_proof": true, "tactics": ["dsimp", "ext1", "rw", "ext", "rw", "dsimp", "toKaroubiEquivalence,", "rw"], "tactic_count": 8}
{"name": "CategoryTheory.Idempotents.DoldKan.equivalence_unitIso", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.EquivalencePseudoabelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.HigherFacesVanish", "kind": "definition", "module": "Mathlib.AlgebraicTopology.DoldKan.Faces", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.HigherFacesVanish.comp_δ_eq_zero", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.Faces", "is_tactic_proof": true, "tactics": ["obtain", "apply", "simp", "lia"], "tactic_count": 4}
{"name": "AlgebraicTopology.DoldKan.HigherFacesVanish.of_succ", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.Faces", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.HigherFacesVanish.of_comp", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.Faces", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.HigherFacesVanish.comp_Hσ_eq", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.Faces", "is_tactic_proof": true, "tactics": ["have", "rw", "hσ'_eq", "simp", "simp", "rw", "swap", "rintro", "suffices", "simp", "convert", "dsimp", "lia", "rw", "swap", "rintro", "rw", "intro", "replace", "lia", "dsimp", "rw", "lia", "simp", "dsimp", "lia", "simp", "conv_lhs", "congr", "rw", "rw", "dsimp", "to", "have", "intro", "rw", "apply", "rw", "exact", "rw", "simp", "rw", "apply", "rintro", "simp", "have", "rw", "dsimp", "lia", "generalize_proofs", "rw", "neg_zsmul]", "congr", "ring"], "tactic_count": 54}
{"name": "AlgebraicTopology.DoldKan.HigherFacesVanish.comp_Hσ_eq_zero", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.Faces", "is_tactic_proof": true, "tactics": ["simp", "rw", "by_cases", "rw", "simp", "eqToHom_refl,", "rw", "simp", "comp_neg,", "intro", "rw", "simp", "dsimp", "lia", "simp"], "tactic_count": 15}
{"name": "AlgebraicTopology.DoldKan.HigherFacesVanish.induction", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.Faces", "is_tactic_proof": true, "tactics": ["intro", "dsimp", "simp", "by_cases", "rw", "obtain", "rw", "rcases", "simp", "rfl", "by_cases", "simp", "rfl", "have", "have", "rw", "swap", "rw", "simpa", "obtain", "rw", "swap", "rw", "dsimp", "lia", "simp", "rw", "swap", "ext", "cases", "dsimp", "dsimp", "lia", "simp"], "tactic_count": 34}
{"name": "AlgebraicTopology.DoldKan.Isδ₀", "kind": "definition", "module": "Mathlib.AlgebraicTopology.DoldKan.FunctorGamma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.Isδ₀.iff", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.FunctorGamma", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "by_contra", "exact", "rintro", "exact"], "tactic_count": 6}
{"name": "AlgebraicTopology.DoldKan.Isδ₀.eq_δ₀", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.FunctorGamma", "is_tactic_proof": true, "tactics": ["obtain", "rw", "rw"], "tactic_count": 3}
{"name": "AlgebraicTopology.DoldKan.Γ₀.Obj.summand", "kind": "definition", "module": "Mathlib.AlgebraicTopology.DoldKan.FunctorGamma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.Γ₀.Obj.obj₂", "kind": "definition", "module": "Mathlib.AlgebraicTopology.DoldKan.FunctorGamma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono", "kind": "definition", "module": "Mathlib.AlgebraicTopology.DoldKan.FunctorGamma", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "by_cases", "exact", "exact"], "tactic_count": 5}
{"name": "AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_id", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.FunctorGamma", "is_tactic_proof": true, "tactics": ["unfold", "simp"], "tactic_count": 2}
{"name": "AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_δ₀'", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.FunctorGamma", "is_tactic_proof": true, "tactics": ["unfold", "suffices", "rintro", "simpa"], "tactic_count": 4}
{"name": "AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_δ₀", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.FunctorGamma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_eq_zero", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.FunctorGamma", "is_tactic_proof": true, "tactics": ["unfold", "rw", "split_ifs", "rfl"], "tactic_count": 4}
{"name": "AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_naturality", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.FunctorGamma", "is_tactic_proof": true, "tactics": ["unfold", "split_ifs", "subst", "simp", "rw", "rw"], "tactic_count": 6}
{"name": "AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_comp", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.FunctorGamma", "is_tactic_proof": true, "tactics": ["by_cases", "subst", "simp", "by_cases", "subst", "simp", "obtain", "obtain", "have", "rw", "by_contra", "simp", "by_contra", "simp", "lia", "by_cases", "by_cases", "rw", "simp", "simp"], "tactic_count": 20}
{"name": "AlgebraicTopology.DoldKan.Γ₀.Obj.map", "kind": "definition", "module": "Mathlib.AlgebraicTopology.DoldKan.FunctorGamma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand₀", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.FunctorGamma", "is_tactic_proof": true, "tactics": ["simp", "have", "subst", "congr", "exact", "dsimp", "congr", "exact"], "tactic_count": 8}
{"name": "AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand₀'", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.FunctorGamma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.Γ₀.obj", "kind": "definition", "module": "Mathlib.AlgebraicTopology.DoldKan.FunctorGamma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.Γ₀.splitting", "kind": "definition", "module": "Mathlib.AlgebraicTopology.DoldKan.FunctorGamma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.FunctorGamma", "is_tactic_proof": true, "tactics": ["dsimp", "change", "rw", "dsimp", "rw", "dsimp", "rw", "dsimp", "rw", "rfl"], "tactic_count": 10}
{"name": "AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand'", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.FunctorGamma", "is_tactic_proof": true, "tactics": ["apply", "apply"], "tactic_count": 2}
{"name": "AlgebraicTopology.DoldKan.Γ₀.Obj.mapMono_on_summand_id", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.FunctorGamma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.Γ₀.Obj.map_epi_on_summand_id", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.FunctorGamma", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "AlgebraicTopology.DoldKan.Γ₀.map", "kind": "definition", "module": "Mathlib.AlgebraicTopology.DoldKan.FunctorGamma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.Γ₀'", "kind": "definition", "module": "Mathlib.AlgebraicTopology.DoldKan.FunctorGamma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.Γ₀", "kind": "definition", "module": "Mathlib.AlgebraicTopology.DoldKan.FunctorGamma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.Γ₂", "kind": "definition", "module": "Mathlib.AlgebraicTopology.DoldKan.FunctorGamma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.HigherFacesVanish.on_Γ₀_summand_id", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.FunctorGamma", "is_tactic_proof": true, "tactics": ["intro", "have", "rw", "intro", "exact", "exact", "exact"], "tactic_count": 7}
{"name": "AlgebraicTopology.DoldKan.PInfty_on_Γ₀_splitting_summand_eq_self", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.FunctorGamma", "is_tactic_proof": true, "tactics": ["rw", "rcases", "simpa", "exact"], "tactic_count": 4}
{"name": "AlgebraicTopology.DoldKan.N₁", "kind": "definition", "module": "Mathlib.AlgebraicTopology.DoldKan.FunctorN", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.N₂", "kind": "definition", "module": "Mathlib.AlgebraicTopology.DoldKan.FunctorN", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.toKaroubiCompN₂IsoN₁", "kind": "definition", "module": "Mathlib.AlgebraicTopology.DoldKan.FunctorN", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.toKaroubiCompN₂IsoN₁_hom_app", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.FunctorN", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.toKaroubiCompN₂IsoN₁_inv_app", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.FunctorN", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.N₁Γ₀_app", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.GammaCompN", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "AlgebraicTopology.DoldKan.N₁Γ₀_hom_app", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.GammaCompN", "is_tactic_proof": true, "tactics": ["change", "simp", "rfl"], "tactic_count": 3}
{"name": "AlgebraicTopology.DoldKan.N₁Γ₀_inv_app", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.GammaCompN", "is_tactic_proof": true, "tactics": ["change", "simp", "rfl"], "tactic_count": 3}
{"name": "AlgebraicTopology.DoldKan.N₁Γ₀_hom_app_f_f", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.GammaCompN", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "AlgebraicTopology.DoldKan.N₁Γ₀_inv_app_f_f", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.GammaCompN", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "AlgebraicTopology.DoldKan.N₂Γ₂ToKaroubiIso_hom_app", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.GammaCompN", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "simp", "conv_rhs", "congr", "apply", "intro", "rw", "apply"], "tactic_count": 9}
{"name": "AlgebraicTopology.DoldKan.N₂Γ₂ToKaroubiIso_inv_app", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.GammaCompN", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "simp", "convert", "apply", "intro", "rw", "erw"], "tactic_count": 8}
{"name": "AlgebraicTopology.DoldKan.N₂Γ₂_inv_app_f_f", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.GammaCompN", "is_tactic_proof": true, "tactics": ["dsimp", "simp", "unop_op,", "apply"], "tactic_count": 4}
{"name": "AlgebraicTopology.DoldKan.whiskerLeft_toKaroubi_N₂Γ₂_hom", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.GammaCompN", "is_tactic_proof": true, "tactics": ["let", "have", "dsimp", "exact"], "tactic_count": 4}
{"name": "AlgebraicTopology.DoldKan.N₂Γ₂_compatible_with_N₁Γ₀", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.GammaCompN", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.c", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.DoldKan.Homotopies", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.c_mk", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.Homotopies", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.cs_down_0_not_rel_left", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.Homotopies", "is_tactic_proof": true, "tactics": ["intro", "dsimp", "apply", "rw"], "tactic_count": 4}
{"name": "AlgebraicTopology.DoldKan.hσ", "kind": "definition", "module": "Mathlib.AlgebraicTopology.DoldKan.Homotopies", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.hσ'", "kind": "definition", "module": "Mathlib.AlgebraicTopology.DoldKan.Homotopies", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.hσ'_eq_zero", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.Homotopies", "is_tactic_proof": true, "tactics": ["simp", "split_ifs", "exact"], "tactic_count": 3}
{"name": "AlgebraicTopology.DoldKan.hσ'_eq", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.Homotopies", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "AlgebraicTopology.DoldKan.hσ'_eq'", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.Homotopies", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgebraicTopology.DoldKan.Hσ", "kind": "definition", "module": "Mathlib.AlgebraicTopology.DoldKan.Homotopies", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.homotopyHσToZero", "kind": "definition", "module": "Mathlib.AlgebraicTopology.DoldKan.Homotopies", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.Hσ_eq_zero", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.Homotopies", "is_tactic_proof": true, "tactics": ["unfold", "rw", "rcases", "rw", "simp", "erw", "rw", "neg_smul,", "δ_comp_σ_self", "rw"], "tactic_count": 10}
{"name": "AlgebraicTopology.DoldKan.hσ'_naturality", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.Homotopies", "is_tactic_proof": true, "tactics": ["have", "subst", "simp", "unfold", "split_ifs", "rw", "simp"], "tactic_count": 7}
{"name": "AlgebraicTopology.DoldKan.natTransHσ", "kind": "definition", "module": "Mathlib.AlgebraicTopology.DoldKan.Homotopies", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.map_hσ'", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.Homotopies", "is_tactic_proof": true, "tactics": ["unfold", "split_ifs", "simp", "simp", "rfl"], "tactic_count": 5}
{"name": "AlgebraicTopology.DoldKan.map_Hσ", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.Homotopies", "is_tactic_proof": true, "tactics": ["unfold", "have", "simp", "rw", "let", "congr"], "tactic_count": 6}
{"name": "AlgebraicTopology.DoldKan.homotopyPToId", "kind": "definition", "module": "Mathlib.AlgebraicTopology.DoldKan.HomotopyEquivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.homotopyQToZero", "kind": "definition", "module": "Mathlib.AlgebraicTopology.DoldKan.HomotopyEquivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.homotopyPToId_eventually_constant", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.HomotopyEquivalence", "is_tactic_proof": true, "tactics": ["simp", "hσ'_eq_zero"], "tactic_count": 2}
{"name": "AlgebraicTopology.DoldKan.homotopyPInftyToId", "kind": "definition", "module": "Mathlib.AlgebraicTopology.DoldKan.HomotopyEquivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.homotopyEquivNormalizedMooreComplexAlternatingFaceMapComplex", "kind": "definition", "module": "Mathlib.AlgebraicTopology.DoldKan.HomotopyEquivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.PInfty_comp_map_mono_eq_zero", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.NCompGamma", "is_tactic_proof": false, "tactics": ["induction", "obtain", "rw", "exact", "simp", "rcases", "change", "subst", "obtain", "rw", "have", "by_contra", "exact", "exact", "simp", "clear", "subst", "obtain", "eq_comp_δ_of_not_surjective", "rw", "grind", "obtain", "eq_comp_δ_of_not_surjective", "rw", "grind", "by_cases", "subst", "rw", "simp", "erw", "simp", "lia", "simp", "erw", "by_contra", "exact"], "tactic_count": 36}
{"name": "AlgebraicTopology.DoldKan.Γ₀_obj_termwise_mapMono_comp_PInfty", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.NCompGamma", "is_tactic_proof": false, "tactics": ["induction", "induction", "dsimp", "by_cases", "subst", "simp", "dsimp", "simp", "by_cases", "have", "subst", "simp", "dsimp", "rw", "simp", "rw", "rotate_left", "intro", "rw", "rw", "exact", "zsmul_zero]", "simp", "simp", "rfl", "rw", "swap", "by_contra", "exact", "rw", "exact", "assumption"], "tactic_count": 32}
{"name": "AlgebraicTopology.DoldKan.Γ₂N₁.natTrans", "kind": "definition", "module": "Mathlib.AlgebraicTopology.DoldKan.NCompGamma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.Γ₂N₂ToKaroubiIso", "kind": "definition", "module": "Mathlib.AlgebraicTopology.DoldKan.NCompGamma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.Γ₂N₂.natTrans", "kind": "definition", "module": "Mathlib.AlgebraicTopology.DoldKan.NCompGamma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.Γ₂N₂.natTrans_app_f_app", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.NCompGamma", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "AlgebraicTopology.DoldKan.compatibility_Γ₂N₁_Γ₂N₂_natTrans", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.NCompGamma", "is_tactic_proof": true, "tactics": ["rw", "dsimp", "rw", "dsimp", "erw", "rw"], "tactic_count": 6}
{"name": "AlgebraicTopology.DoldKan.identity_N₂_objectwise", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.NCompGamma", "is_tactic_proof": true, "tactics": ["ext", "have", "have", "dsimp", "rw", "dsimp", "rw", "dsimp", "rw", "simp", "simp"], "tactic_count": 11}
{"name": "AlgebraicTopology.DoldKan.identity_N₂", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.NCompGamma", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "rw"], "tactic_count": 3}
{"name": "AlgebraicTopology.DoldKan.instIsIsoFunctorKaroubiSimplicialObjectNatTrans", "kind": "instance", "module": "Mathlib.AlgebraicTopology.DoldKan.NCompGamma", "is_tactic_proof": false, "tactics": ["have", "intro", "have", "have", "dsimp", "rw", "rw", "infer_instance", "exact", "apply"], "tactic_count": 10}
{"name": "AlgebraicTopology.DoldKan.instIsIsoFunctorSimplicialObjectKaroubiNatTrans", "kind": "instance", "module": "Mathlib.AlgebraicTopology.DoldKan.NCompGamma", "is_tactic_proof": false, "tactics": ["have", "intro", "rw", "infer_instance", "apply"], "tactic_count": 5}
{"name": "AlgebraicTopology.DoldKan.Γ₂N₂", "kind": "definition", "module": "Mathlib.AlgebraicTopology.DoldKan.NCompGamma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.Γ₂N₁", "kind": "definition", "module": "Mathlib.AlgebraicTopology.DoldKan.NCompGamma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.instReflectsIsomorphismsSimplicialObjectKaroubiChainComplexNatN₁", "kind": "instance", "module": "Mathlib.AlgebraicTopology.DoldKan.NReflectsIso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.compatibility_N₂_N₁_karoubi", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.NReflectsIso", "is_tactic_proof": true, "tactics": ["refine", "refine", "ext", "rfl", "dsimp", "simp", "rintro", "ext", "have", "dsimp", "simp", "ext", "dsimp", "simp", "app_p_comp,", "app_comp_p,"], "tactic_count": 16}
{"name": "AlgebraicTopology.DoldKan.instReflectsIsomorphismsKaroubiSimplicialObjectChainComplexNatN₂", "kind": "instance", "module": "Mathlib.AlgebraicTopology.DoldKan.NReflectsIso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.HigherFacesVanish.inclusionOfMooreComplexMap", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.Normalized", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.factors_normalizedMooreComplex_PInfty", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.Normalized", "is_tactic_proof": true, "tactics": ["rcases", "apply", "rw", "intro", "apply", "exact"], "tactic_count": 6}
{"name": "AlgebraicTopology.DoldKan.PInftyToNormalizedMooreComplex", "kind": "definition", "module": "Mathlib.AlgebraicTopology.DoldKan.Normalized", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.PInftyToNormalizedMooreComplex_comp_inclusionOfMooreComplexMap", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.Normalized", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "AlgebraicTopology.DoldKan.PInftyToNormalizedMooreComplex_naturality", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.Normalized", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "AlgebraicTopology.DoldKan.PInfty_comp_PInftyToNormalizedMooreComplex", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.Normalized", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "AlgebraicTopology.DoldKan.inclusionOfMooreComplexMap_comp_PInfty", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.Normalized", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "simp", "exact"], "tactic_count": 4}
{"name": "AlgebraicTopology.DoldKan.instMonoChainComplexNatInclusionOfMooreComplexMap", "kind": "instance", "module": "Mathlib.AlgebraicTopology.DoldKan.Normalized", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.splitMonoInclusionOfMooreComplexMap", "kind": "definition", "module": "Mathlib.AlgebraicTopology.DoldKan.Normalized", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.N₁_iso_normalizedMooreComplex_comp_toKaroubi", "kind": "definition", "module": "Mathlib.AlgebraicTopology.DoldKan.Normalized", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DoldKan.termK[_]", "kind": "definition", "module": "Mathlib.AlgebraicTopology.DoldKan.Notations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DoldKan._aux_Mathlib_AlgebraicTopology_DoldKan_Notations___macroRules_DoldKan_termK[_]_1", "kind": "definition", "module": "Mathlib.AlgebraicTopology.DoldKan.Notations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DoldKan._aux_Mathlib_AlgebraicTopology_DoldKan_Notations___unexpand_AlgebraicTopology_AlternatingFaceMapComplex_obj_1", "kind": "definition", "module": "Mathlib.AlgebraicTopology.DoldKan.Notations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DoldKan.termN[_]", "kind": "definition", "module": "Mathlib.AlgebraicTopology.DoldKan.Notations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DoldKan._aux_Mathlib_AlgebraicTopology_DoldKan_Notations___macroRules_DoldKan_termN[_]_1", "kind": "definition", "module": "Mathlib.AlgebraicTopology.DoldKan.Notations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DoldKan._aux_Mathlib_AlgebraicTopology_DoldKan_Notations___unexpand_AlgebraicTopology_NormalizedMooreComplex_obj_1", "kind": "definition", "module": "Mathlib.AlgebraicTopology.DoldKan.Notations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.P_is_eventually_constant", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.PInfty", "is_tactic_proof": true, "tactics": ["cases", "zero", "succ", "n", "simp", "exact"], "tactic_count": 6}
{"name": "AlgebraicTopology.DoldKan.Q_is_eventually_constant", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.PInfty", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicTopology.DoldKan.PInfty", "kind": "definition", "module": "Mathlib.AlgebraicTopology.DoldKan.PInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.QInfty", "kind": "definition", "module": "Mathlib.AlgebraicTopology.DoldKan.PInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.PInfty_f_0", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.PInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.PInfty_f", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.PInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.QInfty_f_0", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.PInfty", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "AlgebraicTopology.DoldKan.QInfty_f", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.PInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.PInfty_f_naturality", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.PInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.QInfty_f_naturality", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.PInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.PInfty_f_idem", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.PInfty", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicTopology.DoldKan.PInfty_idem", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.PInfty", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "AlgebraicTopology.DoldKan.QInfty_f_idem", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.PInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.QInfty_idem", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.PInfty", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "AlgebraicTopology.DoldKan.PInfty_f_comp_QInfty_f", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.PInfty", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "AlgebraicTopology.DoldKan.PInfty_comp_QInfty", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.PInfty", "is_tactic_proof": true, "tactics": ["ext", "apply"], "tactic_count": 2}
{"name": "AlgebraicTopology.DoldKan.QInfty_f_comp_PInfty_f", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.PInfty", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "AlgebraicTopology.DoldKan.QInfty_comp_PInfty", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.PInfty", "is_tactic_proof": true, "tactics": ["ext", "apply"], "tactic_count": 2}
{"name": "AlgebraicTopology.DoldKan.PInfty_add_QInfty", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.PInfty", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "AlgebraicTopology.DoldKan.PInfty_f_add_QInfty_f", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.PInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.natTransPInfty", "kind": "definition", "module": "Mathlib.AlgebraicTopology.DoldKan.PInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.natTransPInfty_f", "kind": "definition", "module": "Mathlib.AlgebraicTopology.DoldKan.PInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.map_PInfty_f", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.PInfty", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicTopology.DoldKan.karoubi_PInfty_f", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.PInfty", "is_tactic_proof": true, "tactics": ["let", "let", "let", "let", "let", "let", "let", "let", "change", "have", "have", "have", "simp", "congr", "have", "dsimp", "rw", "rw", "simp", "let", "have", "simp", "dsimp", "rw"], "tactic_count": 24}
{"name": "AlgebraicTopology.DoldKan.P", "kind": "definition", "module": "Mathlib.AlgebraicTopology.DoldKan.Projections", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.P_zero", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.Projections", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.P_succ", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.Projections", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.P_f_0_eq", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.Projections", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "simp"], "tactic_count": 4}
{"name": "AlgebraicTopology.DoldKan.Q", "kind": "definition", "module": "Mathlib.AlgebraicTopology.DoldKan.Projections", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.P_add_Q", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.Projections", "is_tactic_proof": true, "tactics": ["rw", "abel"], "tactic_count": 2}
{"name": "AlgebraicTopology.DoldKan.P_add_Q_f", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.Projections", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.Q_zero", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.Projections", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.Q_succ", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.Projections", "is_tactic_proof": true, "tactics": ["simp", "abel"], "tactic_count": 2}
{"name": "AlgebraicTopology.DoldKan.Q_f_0_eq", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.Projections", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicTopology.DoldKan.HigherFacesVanish.of_P", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.Projections", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.HigherFacesVanish.comp_P_eq_self", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.Projections", "is_tactic_proof": true, "tactics": ["induction", "zero", "simp", "apply", "succ", "hq", "simp", "hq", "by_cases", "exact", "obtain", "have", "simp", "have", "v", "simp", "rfl)", "simp", "simp"], "tactic_count": 19}
{"name": "AlgebraicTopology.DoldKan.comp_P_eq_self_iff", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.Projections", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "apply", "apply", "exact"], "tactic_count": 6}
{"name": "AlgebraicTopology.DoldKan.P_f_idem", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.Projections", "is_tactic_proof": true, "tactics": ["rcases", "rw", "exact"], "tactic_count": 3}
{"name": "AlgebraicTopology.DoldKan.Q_f_idem", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.Projections", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.P_idem", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.Projections", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "AlgebraicTopology.DoldKan.Q_idem", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.Projections", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "AlgebraicTopology.DoldKan.natTransP", "kind": "definition", "module": "Mathlib.AlgebraicTopology.DoldKan.Projections", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.P_f_naturality", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.Projections", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.Q_f_naturality", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.Projections", "is_tactic_proof": false, "tactics": ["simp", "sub_left_inj]", "dsimp", "simp"], "tactic_count": 4}
{"name": "AlgebraicTopology.DoldKan.natTransQ", "kind": "definition", "module": "Mathlib.AlgebraicTopology.DoldKan.Projections", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.DoldKan.map_P", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.Projections", "is_tactic_proof": true, "tactics": ["induction", "zero", "simp", "apply", "succ", "simp"], "tactic_count": 6}
{"name": "AlgebraicTopology.DoldKan.map_Q", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.Projections", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "SimplicialObject.Splitting.πSummand", "kind": "definition", "module": "Mathlib.AlgebraicTopology.DoldKan.SplitSimplicialObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplicialObject.Splitting.cofan_inj_πSummand_eq_id", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.SplitSimplicialObject", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimplicialObject.Splitting.cofan_inj_πSummand_eq_zero", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.SplitSimplicialObject", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "SimplicialObject.Splitting.decomposition_id", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.SplitSimplicialObject", "is_tactic_proof": true, "tactics": ["apply", "intro", "dsimp", "erw", "intro", "rw", "simp"], "tactic_count": 7}
{"name": "SimplicialObject.Splitting.σ_comp_πSummand_id_eq_zero", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.SplitSimplicialObject", "is_tactic_proof": true, "tactics": ["apply", "intro", "dsimp", "rw", "rw", "change", "rw", "have", "dsimp", "lia"], "tactic_count": 10}
{"name": "SimplicialObject.Splitting.cofan_inj_comp_PInfty_eq_zero", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.SplitSimplicialObject", "is_tactic_proof": true, "tactics": ["rw", "rw"], "tactic_count": 2}
{"name": "SimplicialObject.Splitting.comp_PInfty_eq_zero_iff", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.SplitSimplicialObject", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rcases", "dsimp", "rw", "rw", "have", "dsimp", "rw", "rw", "intro", "simp", "intro", "rw", "intro", "by_cases", "dsimp", "subst", "rw", "simp"], "tactic_count": 20}
{"name": "SimplicialObject.Splitting.PInfty_comp_πSummand_id", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.SplitSimplicialObject", "is_tactic_proof": true, "tactics": ["conv_rhs", "symm", "rw"], "tactic_count": 3}
{"name": "SimplicialObject.Splitting.πSummand_comp_cofan_inj_id_comp_PInfty_eq_PInfty", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.SplitSimplicialObject", "is_tactic_proof": true, "tactics": ["conv_rhs", "dsimp", "rw", "rw", "rintro", "rw"], "tactic_count": 6}
{"name": "SimplicialObject.Splitting.d", "kind": "definition", "module": "Mathlib.AlgebraicTopology.DoldKan.SplitSimplicialObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplicialObject.Splitting.ιSummand_comp_d_comp_πSummand_eq_zero", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.DoldKan.SplitSimplicialObject", "is_tactic_proof": true, "tactics": ["rw", "rw", "degeneracy_comp_PInfty_assoc"], "tactic_count": 3}
{"name": "SimplicialObject.Splitting.nondegComplex", "kind": "definition", "module": "Mathlib.AlgebraicTopology.DoldKan.SplitSimplicialObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplicialObject.Splitting.toKaroubiNondegComplexIsoN₁", "kind": "definition", "module": "Mathlib.AlgebraicTopology.DoldKan.SplitSimplicialObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplicialObject.Split.nondegComplexFunctor", "kind": "definition", "module": "Mathlib.AlgebraicTopology.DoldKan.SplitSimplicialObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplicialObject.Split.toKaroubiNondegComplexFunctorIsoN₁", "kind": "definition", "module": "Mathlib.AlgebraicTopology.DoldKan.SplitSimplicialObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.map", "kind": "definition", "module": "Mathlib.AlgebraicTopology.ExtraDegeneracy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.ofIso", "kind": "definition", "module": "Mathlib.AlgebraicTopology.ExtraDegeneracy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Augmented.StandardSimplex.shiftFun", "kind": "definition", "module": "Mathlib.AlgebraicTopology.ExtraDegeneracy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Augmented.StandardSimplex.shiftFun_zero", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.ExtraDegeneracy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Augmented.StandardSimplex.shiftFun_succ", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.ExtraDegeneracy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Augmented.StandardSimplex.shift", "kind": "definition", "module": "Mathlib.AlgebraicTopology.ExtraDegeneracy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Augmented.StandardSimplex.extraDegeneracy", "kind": "definition", "module": "Mathlib.AlgebraicTopology.ExtraDegeneracy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Augmented.StandardSimplex.nonempty_extraDegeneracy_stdSimplex", "kind": "instance", "module": "Mathlib.AlgebraicTopology.ExtraDegeneracy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Arrow.AugmentedCechNerve.ExtraDegeneracy.s", "kind": "definition", "module": "Mathlib.AlgebraicTopology.ExtraDegeneracy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Arrow.AugmentedCechNerve.ExtraDegeneracy.s_comp_π_0", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.ExtraDegeneracy", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Arrow.AugmentedCechNerve.ExtraDegeneracy.s_comp_π_succ", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.ExtraDegeneracy", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Arrow.AugmentedCechNerve.ExtraDegeneracy.s_comp_base", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.ExtraDegeneracy", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Arrow.AugmentedCechNerve.extraDegeneracy", "kind": "definition", "module": "Mathlib.AlgebraicTopology.ExtraDegeneracy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.const", "kind": "definition", "module": "Mathlib.AlgebraicTopology.ExtraDegeneracy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.homotopyEquiv", "kind": "definition", "module": "Mathlib.AlgebraicTopology.ExtraDegeneracy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopy.reflTransSymmAux", "kind": "definition", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopy.continuous_reflTransSymmAux", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopy.reflTransSymmAux_mem_I", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "split_ifs", "constructor", "apply", "rw", "apply", "constructor", "apply", "apply"], "tactic_count": 9}
{"name": "Path.Homotopy.reflTransSymm", "kind": "definition", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopy.reflSymmTrans", "kind": "definition", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopy.transReflReparamAux", "kind": "definition", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopy.continuous_transReflReparamAux", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopy.transReflReparamAux_mem_I", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic", "is_tactic_proof": true, "tactics": ["unfold", "split_ifs"], "tactic_count": 2}
{"name": "Path.Homotopy.transReflReparamAux_zero", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic", "is_tactic_proof": true, "tactics": ["norm_num"], "tactic_count": 1}
{"name": "Path.Homotopy.transReflReparamAux_one", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic", "is_tactic_proof": true, "tactics": ["norm_num"], "tactic_count": 1}
{"name": "Path.Homotopy.trans_refl_reparam", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic", "is_tactic_proof": true, "tactics": ["ext", "unfold", "simp", "grind"], "tactic_count": 4}
{"name": "Path.Homotopy.transRefl", "kind": "definition", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopy.reflTrans", "kind": "definition", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopy.transAssocReparamAux", "kind": "definition", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopy.continuous_transAssocReparamAux", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopy.transAssocReparamAux_mem_I", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic", "is_tactic_proof": true, "tactics": ["unfold", "split_ifs"], "tactic_count": 2}
{"name": "Path.Homotopy.transAssocReparamAux_zero", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic", "is_tactic_proof": true, "tactics": ["norm_num"], "tactic_count": 1}
{"name": "Path.Homotopy.transAssocReparamAux_one", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic", "is_tactic_proof": true, "tactics": ["norm_num"], "tactic_count": 1}
{"name": "Path.Homotopy.trans_assoc_reparam", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp", "split_ifs", "iterate", "linarith", "linarith", "grind"], "tactic_count": 7}
{"name": "Path.Homotopy.transAssoc", "kind": "definition", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopic.refl_trans", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopic.trans_refl", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopic.trans_symm", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopic.symm_trans", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopic.trans_assoc", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopic.Quotient.refl_trans", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic", "is_tactic_proof": true, "tactics": ["induction", "mk"], "tactic_count": 2}
{"name": "Path.Homotopic.Quotient.trans_refl", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic", "is_tactic_proof": true, "tactics": ["induction", "mk"], "tactic_count": 2}
{"name": "Path.Homotopic.Quotient.trans_symm", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic", "is_tactic_proof": true, "tactics": ["induction", "mk"], "tactic_count": 2}
{"name": "Path.Homotopic.Quotient.symm_trans", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic", "is_tactic_proof": true, "tactics": ["induction", "mk"], "tactic_count": 2}
{"name": "Path.Homotopic.Quotient.trans_assoc", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic", "is_tactic_proof": true, "tactics": ["induction", "mk", "induction", "mk", "induction", "mk"], "tactic_count": 6}
{"name": "FundamentalGroupoid.equiv", "kind": "definition", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FundamentalGroupoid.isEmpty_iff", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FundamentalGroupoid.instIsEmpty", "kind": "instance", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FundamentalGroupoid.nonempty_iff", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FundamentalGroupoid.instNonempty", "kind": "instance", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FundamentalGroupoid.subsingleton_iff", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FundamentalGroupoid.instSubsingleton", "kind": "instance", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FundamentalGroupoid.instInhabited", "kind": "instance", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FundamentalGroupoid.instGroupoid", "kind": "instance", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FundamentalGroupoid.comp_eq", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FundamentalGroupoid.id_eq_path_refl", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FundamentalGroupoid.map", "kind": "definition", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FundamentalGroupoid.map_id", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FundamentalGroupoid.map_comp", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FundamentalGroupoid.fundamentalGroupoidFunctor", "kind": "definition", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FundamentalGroupoid.termπ", "kind": "definition", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FundamentalGroupoid._aux_Mathlib_AlgebraicTopology_FundamentalGroupoid_Basic___macroRules_FundamentalGroupoid_termπ_1", "kind": "definition", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FundamentalGroupoid._aux_Mathlib_AlgebraicTopology_FundamentalGroupoid_Basic___unexpand_FundamentalGroupoid_fundamentalGroupoidFunctor_1", "kind": "definition", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FundamentalGroupoid.termπₓ", "kind": "definition", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FundamentalGroupoid._aux_Mathlib_AlgebraicTopology_FundamentalGroupoid_Basic___macroRules_FundamentalGroupoid_termπₓ_1", "kind": "definition", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FundamentalGroupoid.termπₘ", "kind": "definition", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FundamentalGroupoid._aux_Mathlib_AlgebraicTopology_FundamentalGroupoid_Basic___macroRules_FundamentalGroupoid_termπₘ_1", "kind": "definition", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FundamentalGroupoid.map_eq", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FundamentalGroupoid.toTop", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FundamentalGroupoid.fromTop", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FundamentalGroupoid.toPath", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FundamentalGroupoid.fromPath", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FundamentalGroupoid.fromPath_eq_iff_homotopic", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FundamentalGroupoid.eqToHom_eq", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "FundamentalGroupoid.conj_eqToHom", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "FundamentalGroup", "kind": "definition", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.FundamentalGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instGroupFundamentalGroup", "kind": "instance", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.FundamentalGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInhabitedFundamentalGroup", "kind": "instance", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.FundamentalGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FundamentalGroup.fundamentalGroupMulEquivOfPath", "kind": "definition", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.FundamentalGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FundamentalGroup.fundamentalGroupMulEquivOfPathConnected", "kind": "definition", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.FundamentalGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FundamentalGroup.toArrow", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.FundamentalGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FundamentalGroup.toPath", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.FundamentalGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FundamentalGroup.fromArrow", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.FundamentalGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FundamentalGroup.fromPath", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.FundamentalGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FundamentalGroup.map", "kind": "definition", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.FundamentalGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FundamentalGroup.mapOfEq", "kind": "definition", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.FundamentalGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FundamentalGroup.mapOfEq_apply", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.FundamentalGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopic.map_trans_evalAt", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.InducedMaps", "is_tactic_proof": true, "tactics": ["between", "set", "set", "set", "set", "refine", "all_goals"], "tactic_count": 7}
{"name": "FundamentalGroupoidFunctor.homotopicMapsNatIso", "kind": "definition", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.InducedMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FundamentalGroupoidFunctor.instIsIsoFunctorFundamentalGroupoidHomotopicMapsNatIso", "kind": "instance", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.InducedMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FundamentalGroupoidFunctor.equivOfHomotopyEquiv", "kind": "definition", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.InducedMaps", "is_tactic_proof": true, "tactics": ["apply", "simpa", "simpa", "asIso"], "tactic_count": 4}
{"name": "unitInterval.path01", "kind": "definition", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.InducedMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.upath01", "kind": "definition", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.InducedMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.uhpath01", "kind": "definition", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.InducedMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.Homotopy.hcast", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.InducedMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.Homotopy.hcast_def", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.InducedMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.Homotopy.heq_path_of_eq_image", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.InducedMaps", "is_tactic_proof": true, "tactics": ["simp", "apply", "exact"], "tactic_count": 3}
{"name": "_private.Mathlib.AlgebraicTopology.FundamentalGroupoid.InducedMaps.0.ContinuousMap.Homotopy.start_path", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.InducedMaps", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "_private.Mathlib.AlgebraicTopology.FundamentalGroupoid.InducedMaps.0.ContinuousMap.Homotopy.end_path", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.InducedMaps", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "ContinuousMap.Homotopy.eq_path_of_eq_image", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.InducedMaps", "is_tactic_proof": false, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ContinuousMap.Homotopy.uliftMap", "kind": "definition", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.InducedMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.Homotopy.ulift_apply", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.InducedMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.Homotopy.prodToProdTopI", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.InducedMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.Homotopy.diagonalPath", "kind": "definition", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.InducedMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.Homotopy.diagonalPath'", "kind": "definition", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.InducedMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.Homotopy.apply_zero_path", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.InducedMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.Homotopy.apply_one_path", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.InducedMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.Homotopy.evalAt_eq", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.InducedMaps", "is_tactic_proof": true, "tactics": ["dsimp", "refine", "simp", "apply", "rfl"], "tactic_count": 5}
{"name": "ContinuousMap.Homotopy.eq_diag_path", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.InducedMaps", "is_tactic_proof": true, "tactics": ["rw", "erw", "dsimp", "constructor", "slice_lhs", "rw", "slice_lhs", "rfl", "slice_lhs", "rw", "slice_lhs", "rfl"], "tactic_count": 12}
{"name": "Path.instSubsingletonPUnitUnit", "kind": "instance", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.PUnit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FundamentalGroupoid.instSubsingletonHomPUnit", "kind": "instance", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.PUnit", "is_tactic_proof": true, "tactics": ["convert_to", "apply"], "tactic_count": 2}
{"name": "FundamentalGroupoid.punitEquivDiscretePUnit", "kind": "definition", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.PUnit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FundamentalGroupoidFunctor.proj", "kind": "definition", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Product", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FundamentalGroupoidFunctor.proj_map", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Product", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FundamentalGroupoidFunctor.piToPiTop", "kind": "definition", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Product", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FundamentalGroupoidFunctor.piIso", "kind": "definition", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Product", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FundamentalGroupoidFunctor.coneDiscreteComp", "kind": "definition", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Product", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FundamentalGroupoidFunctor.coneDiscreteComp_obj_mapCone", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Product", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FundamentalGroupoidFunctor.piTopToPiCone", "kind": "definition", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Product", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FundamentalGroupoidFunctor.instIsIsoFanGrpdObjTopCatFundamentalGroupoidFunctorPiTopToPiCone", "kind": "instance", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Product", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FundamentalGroupoidFunctor.preservesProduct", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Product", "is_tactic_proof": true, "tactics": ["apply", "apply", "simp", "apply", "exact"], "tactic_count": 5}
{"name": "FundamentalGroupoidFunctor.projLeft", "kind": "definition", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Product", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FundamentalGroupoidFunctor.projRight", "kind": "definition", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Product", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FundamentalGroupoidFunctor.projLeft_map", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Product", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FundamentalGroupoidFunctor.projRight_map", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Product", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FundamentalGroupoidFunctor.prodToProdTop", "kind": "definition", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Product", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FundamentalGroupoidFunctor.prodToProdTop_map", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Product", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FundamentalGroupoidFunctor.prodIso", "kind": "definition", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.Product", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "simply_connected_iff_unique_homotopic", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.SimplyConnected", "is_tactic_proof": false, "tactics": ["simp", "intros", "exact"], "tactic_count": 3}
{"name": "ContinuousMap.HomotopyEquiv.simplyConnectedSpace", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.SimplyConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.HomotopyEquiv.simplyConnectedSpace_iff", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.SimplyConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplyConnectedSpace.instSubsingletonQuotient", "kind": "instance", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.SimplyConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplyConnectedSpace.instPathConnectedSpace", "kind": "instance", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.SimplyConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplyConnectedSpace.paths_homotopic", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.SimplyConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplyConnectedSpace.ofContractible", "kind": "instance", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.SimplyConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "simply_connected_iff_paths_homotopic", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.SimplyConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "simply_connected_iff_paths_homotopic'", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.SimplyConnected", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "simply_connected_iff_loops_nullhomotopic", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.SimplyConnected", "is_tactic_proof": true, "tactics": ["rw", "constructor", "intro", "exact", "intro", "refine", "rw", "replace", "have", "calc"], "tactic_count": 10}
{"name": "IsSimplyConnected", "kind": "definition", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.SimplyConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSimplyConnected.simplyConnectedSpace", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.SimplyConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSimplyConnected.isPathConnected", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.SimplyConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSimplyConnected.nonempty", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.SimplyConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsEmbedding.isSimplyConnected_image", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.SimplyConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.isSimplyConnected_image", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.SimplyConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.isSimplyConnected_preimage", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.SimplyConnected", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "isSimplyConnected_iff_exists_homotopy_refl_forall_mem", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.SimplyConnected", "is_tactic_proof": true, "tactics": ["rw", "refine", "lift", "rcases", "h", "toFun", "source", "target", "exact", "rcases", "exact", "map_zero_left", "map_one_left", "prop"], "tactic_count": 14}
{"name": "isSimplyConnected_smul_set_iff", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.SimplyConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isSimplyConnected_smul_set₀_iff", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.FundamentalGroupoid.SimplyConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.ModelCategory.instIsWeakFactorizationSystemTrivialCofibrationsFibrations", "kind": "instance", "module": "Mathlib.AlgebraicTopology.ModelCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.ModelCategory.instIsWeakFactorizationSystemCofibrationsTrivialFibrations", "kind": "instance", "module": "Mathlib.AlgebraicTopology.ModelCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "HomotopicalAlgebra.cofibrantObjects", "kind": "definition", "module": "Mathlib.AlgebraicTopology.ModelCategory.Bifibrant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.CofibrantObject", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.ModelCategory.Bifibrant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.CofibrantObject.mk", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.ModelCategory.Bifibrant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.CofibrantObject.mk_surjective", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.ModelCategory.Bifibrant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.CofibrantObject.homMk", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.ModelCategory.Bifibrant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.CofibrantObject.homMk_surjective", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.ModelCategory.Bifibrant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.CofibrantObject.weakEquivalence_homMk_iff", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.ModelCategory.Bifibrant", "is_tactic_proof": true, "tactics": ["simp", "rfl"], "tactic_count": 2}
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{"name": "HomotopicalAlgebra.CofibrantObject.ι", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.ModelCategory.Bifibrant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "HomotopicalAlgebra.FibrantBrownFactorization.instWeakEquivalencePTrivialCofibrationsFibrations", "kind": "instance", "module": "Mathlib.AlgebraicTopology.ModelCategory.BrownLemma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "HomotopicalAlgebra.weakEquivalences", "kind": "definition", "module": "Mathlib.AlgebraicTopology.ModelCategory.CategoryWithCofibrations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.mem_weakEquivalences", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.ModelCategory.CategoryWithCofibrations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.trivialFibrations", "kind": "definition", "module": "Mathlib.AlgebraicTopology.ModelCategory.CategoryWithCofibrations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.trivialFibrations_sub_fibrations", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.ModelCategory.CategoryWithCofibrations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.trivialFibrations_sub_weakEquivalences", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.ModelCategory.CategoryWithCofibrations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "HomotopicalAlgebra.mem_trivialFibrations_iff", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.ModelCategory.CategoryWithCofibrations", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "HomotopicalAlgebra.trivialCofibrations", "kind": "definition", "module": "Mathlib.AlgebraicTopology.ModelCategory.CategoryWithCofibrations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.trivialCofibrations_sub_cofibrations", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.ModelCategory.CategoryWithCofibrations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.trivialCofibrations_sub_weakEquivalences", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.ModelCategory.CategoryWithCofibrations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.mem_trivialCofibrations", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.ModelCategory.CategoryWithCofibrations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.mem_trivialCofibrations_iff", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.ModelCategory.CategoryWithCofibrations", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "HomotopicalAlgebra.instCategoryWithFibrationsOpposite", "kind": "instance", "module": "Mathlib.AlgebraicTopology.ModelCategory.CategoryWithCofibrations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.fibrations_op", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.ModelCategory.CategoryWithCofibrations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.cofibrations_eq_unop", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.ModelCategory.CategoryWithCofibrations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.fibration_op_iff", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.ModelCategory.CategoryWithCofibrations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HomotopicalAlgebra.cofibration_unop_iff", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.ModelCategory.CategoryWithCofibrations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HomotopicalAlgebra.instFibrationOppositeOpOfCofibration", "kind": "instance", "module": "Mathlib.AlgebraicTopology.ModelCategory.CategoryWithCofibrations", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "HomotopicalAlgebra.instCofibrationUnopOfFibrationOpposite", "kind": "instance", "module": "Mathlib.AlgebraicTopology.ModelCategory.CategoryWithCofibrations", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "HomotopicalAlgebra.instCategoryWithCofibrationsOpposite", "kind": "instance", "module": "Mathlib.AlgebraicTopology.ModelCategory.CategoryWithCofibrations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.cofibrations_op", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.ModelCategory.CategoryWithCofibrations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.fibrations_eq_unop", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.ModelCategory.CategoryWithCofibrations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.cofibration_op_iff", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.ModelCategory.CategoryWithCofibrations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "HomotopicalAlgebra.instCofibrationOppositeOpOfFibration", "kind": "instance", "module": "Mathlib.AlgebraicTopology.ModelCategory.CategoryWithCofibrations", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "HomotopicalAlgebra.instFibrationUnopOfCofibrationOpposite", "kind": "instance", "module": "Mathlib.AlgebraicTopology.ModelCategory.CategoryWithCofibrations", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "HomotopicalAlgebra.instCategoryWithWeakEquivalencesOpposite", "kind": "instance", "module": "Mathlib.AlgebraicTopology.ModelCategory.CategoryWithCofibrations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.weakEquivalences_op", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.ModelCategory.CategoryWithCofibrations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.weakEquivalences_eq_unop", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.ModelCategory.CategoryWithCofibrations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.weakEquivalences_op_iff", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.ModelCategory.CategoryWithCofibrations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "HomotopicalAlgebra.instWeakEquivalenceOppositeOp", "kind": "instance", "module": "Mathlib.AlgebraicTopology.ModelCategory.CategoryWithCofibrations", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "HomotopicalAlgebra.instWeakEquivalenceUnopOfOpposite", "kind": "instance", "module": "Mathlib.AlgebraicTopology.ModelCategory.CategoryWithCofibrations", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "HomotopicalAlgebra.trivialFibrations_op", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.ModelCategory.CategoryWithCofibrations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.trivialCofibrations_eq_unop", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.ModelCategory.CategoryWithCofibrations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.trivialCofibrations_op", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.ModelCategory.CategoryWithCofibrations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "HomotopicalAlgebra.instIsMultiplicativeFullSubcategoryWeakEquivalences", "kind": "instance", "module": "Mathlib.AlgebraicTopology.ModelCategory.CategoryWithCofibrations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "HomotopicalAlgebra.instWeakEquivalenceMapFullSubcategoryι", "kind": "instance", "module": "Mathlib.AlgebraicTopology.ModelCategory.CategoryWithCofibrations", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
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{"name": "HomotopicalAlgebra.CofibrantObject.homRel_iff_rightHomotopyRel", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.ModelCategory.CofibrantObjectHomotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.CofibrantObject.instIsStableUnderPostcompHomRel", "kind": "instance", "module": "Mathlib.AlgebraicTopology.ModelCategory.CofibrantObjectHomotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.CofibrantObject.instIsStableUnderPrecompHomRel", "kind": "instance", "module": "Mathlib.AlgebraicTopology.ModelCategory.CofibrantObjectHomotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.CofibrantObject.homRel_equivalence_of_isFibrant_tgt", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.ModelCategory.CofibrantObjectHomotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "HomotopicalAlgebra.CofibrantObject.toHoCat_obj_surjective", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.ModelCategory.CofibrantObjectHomotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "HomotopicalAlgebra.CofibrantObject.instCategoryWithWeakEquivalencesHoCat", "kind": "instance", "module": "Mathlib.AlgebraicTopology.ModelCategory.CofibrantObjectHomotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "HomotopicalAlgebra.CofibrantObject.HoCat.ιCompResolutionNatTrans", "kind": "definition", "module": "Mathlib.AlgebraicTopology.ModelCategory.CofibrantObjectHomotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "HomotopicalAlgebra.Cylinder.instIsGoodSymmOfRespectsIsoCofibrations", "kind": "instance", "module": "Mathlib.AlgebraicTopology.ModelCategory.Cylinder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.Cylinder.instIsFibrantIOfIsVeryGood", "kind": "instance", "module": "Mathlib.AlgebraicTopology.ModelCategory.Cylinder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.Cylinder.instIsVeryGoodSymmOfRespectsIsoCofibrations", "kind": "instance", "module": "Mathlib.AlgebraicTopology.ModelCategory.Cylinder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.Cylinder.ofFactorizationData", "kind": "definition", "module": "Mathlib.AlgebraicTopology.ModelCategory.Cylinder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.Cylinder.ofFactorizationData_i", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.ModelCategory.Cylinder", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "HomotopicalAlgebra.Cylinder.instIsVeryGoodOfFactorizationData", "kind": "instance", "module": "Mathlib.AlgebraicTopology.ModelCategory.Cylinder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.Cylinder.instIsFibrantIOfFactorizationDataOfIsStableUnderCompositionFibrations", "kind": "instance", "module": "Mathlib.AlgebraicTopology.ModelCategory.Cylinder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.Cylinder.exists_very_good", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.ModelCategory.Cylinder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.Cylinder.instNonempty", "kind": "instance", "module": "Mathlib.AlgebraicTopology.ModelCategory.Cylinder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.Cylinder.trans", "kind": "definition", "module": "Mathlib.AlgebraicTopology.ModelCategory.Cylinder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.Cylinder.instIsGoodTrans", "kind": "instance", "module": "Mathlib.AlgebraicTopology.ModelCategory.Cylinder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.CofibrantObject.instWeakEquivalenceWWeakEquivalences", "kind": "instance", "module": "Mathlib.AlgebraicTopology.ModelCategory.DerivabilityStructureCofibrant", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HomotopicalAlgebra.CofibrantObject.instIsConnectedLeftResolutionWeakEquivalencesLocalizerMorphism", "kind": "instance", "module": "Mathlib.AlgebraicTopology.ModelCategory.DerivabilityStructureCofibrant", "is_tactic_proof": false, "tactics": ["let", "w", "hw", "have", "have", "exact", "have", "exact"], "tactic_count": 8}
{"name": "HomotopicalAlgebra.CofibrantObject.instHasLeftResolutionsArrowArrowWeakEquivalencesArrowLocalizerMorphism", "kind": "instance", "module": "Mathlib.AlgebraicTopology.ModelCategory.DerivabilityStructureCofibrant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.CofibrantObject.instIsLeftDerivabilityStructureWeakEquivalencesLocalizerMorphism", "kind": "instance", "module": "Mathlib.AlgebraicTopology.ModelCategory.DerivabilityStructureCofibrant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.FibrantObject.instWeakEquivalenceWWeakEquivalences", "kind": "instance", "module": "Mathlib.AlgebraicTopology.ModelCategory.DerivabilityStructureFibrant", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HomotopicalAlgebra.FibrantObject.instIsConnectedRightResolutionWeakEquivalencesLocalizerMorphism", "kind": "instance", "module": "Mathlib.AlgebraicTopology.ModelCategory.DerivabilityStructureFibrant", "is_tactic_proof": false, "tactics": ["let", "w", "hw", "have", "have", "exact", "have", "exact"], "tactic_count": 8}
{"name": "HomotopicalAlgebra.FibrantObject.instHasRightResolutionsArrowArrowWeakEquivalencesArrowLocalizerMorphism", "kind": "instance", "module": "Mathlib.AlgebraicTopology.ModelCategory.DerivabilityStructureFibrant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.FibrantObject.instIsRightDerivabilityStructureWeakEquivalencesLocalizerMorphism", "kind": "instance", "module": "Mathlib.AlgebraicTopology.ModelCategory.DerivabilityStructureFibrant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.FibrantObject.homRel", "kind": "definition", "module": "Mathlib.AlgebraicTopology.ModelCategory.FibrantObjectHomotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.FibrantObject.homRel_iff_leftHomotopyRel", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.ModelCategory.FibrantObjectHomotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.FibrantObject.instIsStableUnderPostcompHomRel", "kind": "instance", "module": "Mathlib.AlgebraicTopology.ModelCategory.FibrantObjectHomotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.FibrantObject.instIsStableUnderPrecompHomRel", "kind": "instance", "module": "Mathlib.AlgebraicTopology.ModelCategory.FibrantObjectHomotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.FibrantObject.homRel_equivalence_of_isCofibrant_src", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.ModelCategory.FibrantObjectHomotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.FibrantObject.HoCat", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.ModelCategory.FibrantObjectHomotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.FibrantObject.toHoCat", "kind": "definition", "module": "Mathlib.AlgebraicTopology.ModelCategory.FibrantObjectHomotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.FibrantObject.toHoCat_obj_surjective", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.ModelCategory.FibrantObjectHomotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.FibrantObject.instFullHoCatToHoCat", "kind": "instance", "module": "Mathlib.AlgebraicTopology.ModelCategory.FibrantObjectHomotopy", "is_tactic_proof": true, "tactics": ["dsimp"], "tactic_count": 1}
{"name": "HomotopicalAlgebra.FibrantObject.toHoCat_map_eq", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.ModelCategory.FibrantObjectHomotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.FibrantObject.toHoCat_map_eq_iff", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.ModelCategory.FibrantObjectHomotopy", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "homRel_equivalence_of_isCofibrant_src.eqvGen_eq]"], "tactic_count": 3}
{"name": "HomotopicalAlgebra.FibrantObject.instHasQuotientWeakEquivalencesHomRel", "kind": "instance", "module": "Mathlib.AlgebraicTopology.ModelCategory.FibrantObjectHomotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.FibrantObject.instCategoryWithWeakEquivalencesHoCat", "kind": "instance", "module": "Mathlib.AlgebraicTopology.ModelCategory.FibrantObjectHomotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.FibrantObject.weakEquivalence_toHoCat_map_iff", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.ModelCategory.FibrantObjectHomotopy", "is_tactic_proof": true, "tactics": ["simp", "apply"], "tactic_count": 2}
{"name": "HomotopicalAlgebra.FibrantObject.toHoCatLocalizerMorphism", "kind": "definition", "module": "Mathlib.AlgebraicTopology.ModelCategory.FibrantObjectHomotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.FibrantObject.factorsThroughLocalization", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.ModelCategory.FibrantObjectHomotopy", "is_tactic_proof": true, "tactics": ["rintro", "obtain", "let", "rw", "suffices", "simp", "have", "simp", "infer_instance)", "simp"], "tactic_count": 10}
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{"name": "HomotopicalAlgebra.FibrantObject.instIsLocalizationCompHoCatToHoCatWeakEquivalences", "kind": "instance", "module": "Mathlib.AlgebraicTopology.ModelCategory.FibrantObjectHomotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.FibrantObject.HoCat.exists_resolution", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.ModelCategory.FibrantObjectHomotopy", "is_tactic_proof": true, "tactics": ["have", "refine", "rw", "infer_instance"], "tactic_count": 4}
{"name": "HomotopicalAlgebra.FibrantObject.HoCat.resolutionObj", "kind": "definition", "module": "Mathlib.AlgebraicTopology.ModelCategory.FibrantObjectHomotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.FibrantObject.instIsFibrantResolutionObj", "kind": "instance", "module": "Mathlib.AlgebraicTopology.ModelCategory.FibrantObjectHomotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.FibrantObject.HoCat.iResolutionObj", "kind": "definition", "module": "Mathlib.AlgebraicTopology.ModelCategory.FibrantObjectHomotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.FibrantObject.instCofibrationIResolutionObj", "kind": "instance", "module": "Mathlib.AlgebraicTopology.ModelCategory.FibrantObjectHomotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.FibrantObject.instWeakEquivalenceIResolutionObj", "kind": "instance", "module": "Mathlib.AlgebraicTopology.ModelCategory.FibrantObjectHomotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.FibrantObject.HoCat.exists_resolution_map", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.ModelCategory.FibrantObjectHomotopy", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
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{"name": "HomotopicalAlgebra.FibrantObject.HoCat.resolutionMap_fac", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.ModelCategory.FibrantObjectHomotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.FibrantObject.HoCat.weakEquivalence_resolutionMap_iff", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.ModelCategory.FibrantObjectHomotopy", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HomotopicalAlgebra.FibrantObject.HoCat.resolutionObj_hom_ext", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.ModelCategory.FibrantObjectHomotopy", "is_tactic_proof": true, "tactics": ["apply", "rw", "apply", "rw", "exact"], "tactic_count": 5}
{"name": "HomotopicalAlgebra.FibrantObject.HoCat.resolution", "kind": "definition", "module": "Mathlib.AlgebraicTopology.ModelCategory.FibrantObjectHomotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.FibrantObject.HoCat.localizerMorphismResolution", "kind": "definition", "module": "Mathlib.AlgebraicTopology.ModelCategory.FibrantObjectHomotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.FibrantObject.HoCat.ιCompResolutionNatTrans", "kind": "definition", "module": "Mathlib.AlgebraicTopology.ModelCategory.FibrantObjectHomotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.FibrantObject.instWeakEquivalenceHoCatAppιCompResolutionNatTrans", "kind": "instance", "module": "Mathlib.AlgebraicTopology.ModelCategory.FibrantObjectHomotopy", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "infer_instance"], "tactic_count": 3}
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{"name": "HomotopicalAlgebra.FibrantObject.HoCat.toLocalization", "kind": "definition", "module": "Mathlib.AlgebraicTopology.ModelCategory.FibrantObjectHomotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.FibrantObject.HoCat.toHoCatCompToLocalizationIso", "kind": "definition", "module": "Mathlib.AlgebraicTopology.ModelCategory.FibrantObjectHomotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.FibrantObject.HoCat.resolutionCompToLocalizationNatTrans", "kind": "definition", "module": "Mathlib.AlgebraicTopology.ModelCategory.FibrantObjectHomotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.FibrantObject.instIsIsoFunctorResolutionCompToLocalizationNatTrans", "kind": "instance", "module": "Mathlib.AlgebraicTopology.ModelCategory.FibrantObjectHomotopy", "is_tactic_proof": true, "tactics": ["rw", "intro", "apply", "rw", "infer_instance"], "tactic_count": 5}
{"name": "HomotopicalAlgebra.FibrantObject.localizerMorphism", "kind": "definition", "module": "Mathlib.AlgebraicTopology.ModelCategory.FibrantObjectHomotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.FibrantObject.instIsLocalizedEquivalenceWeakEquivalencesLocalizerMorphism", "kind": "instance", "module": "Mathlib.AlgebraicTopology.ModelCategory.FibrantObjectHomotopy", "is_tactic_proof": true, "tactics": ["let", "let", "let", "let", "let", "let", "let", "let", "let", "let", "have", "have", "let", "have", "exact"], "tactic_count": 15}
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{"name": "HomotopicalAlgebra.FibrantObject.instIsLocalizationCompιWeakEquivalences", "kind": "instance", "module": "Mathlib.AlgebraicTopology.ModelCategory.FibrantObjectHomotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "HomotopicalAlgebra.leftHomotopyClassEquivRightHomotopyClass_mk", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.ModelCategory.Homotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.leftHomotopyClassEquivRightHomotopyClass_symm_mk", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.ModelCategory.Homotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.instIsStableUnderRetractsTrivialCofibrationsOfCofibrationsOfWeakEquivalences", "kind": "instance", "module": "Mathlib.AlgebraicTopology.ModelCategory.Instances", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "HomotopicalAlgebra.instIsStableUnderRetractsTrivialFibrationsOfFibrationsOfWeakEquivalences", "kind": "instance", "module": "Mathlib.AlgebraicTopology.ModelCategory.Instances", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "HomotopicalAlgebra.instCofibrationCompOfIsStableUnderCompositionCofibrations", "kind": "instance", "module": "Mathlib.AlgebraicTopology.ModelCategory.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.instFibrationCompOfIsStableUnderCompositionFibrations", "kind": "instance", "module": "Mathlib.AlgebraicTopology.ModelCategory.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.instWeakEquivalenceCompOfIsStableUnderCompositionWeakEquivalences", "kind": "instance", "module": "Mathlib.AlgebraicTopology.ModelCategory.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.weakEquivalence_of_postcomp", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.ModelCategory.Instances", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
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{"name": "HomotopicalAlgebra.weakEquivalence_postcomp_iff", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.ModelCategory.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.weakEquivalence_precomp_iff", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.ModelCategory.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.weakEquivalence_of_postcomp_of_fac", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.ModelCategory.Instances", "is_tactic_proof": true, "tactics": ["subst", "exact"], "tactic_count": 2}
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{"name": "HomotopicalAlgebra.trivialCofibrations_rlp", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.ModelCategory.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.instIsStableUnderCobaseChangeTrivialCofibrations", "kind": "instance", "module": "Mathlib.AlgebraicTopology.ModelCategory.Instances", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
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{"name": "HomotopicalAlgebra.instCofibrationMapOfIsWeakFactorizationSystemCofibrationsTrivialFibrations_1", "kind": "instance", "module": "Mathlib.AlgebraicTopology.ModelCategory.Instances", "is_tactic_proof": true, "tactics": ["rw", "apply", "rintro"], "tactic_count": 3}
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{"name": "HomotopicalAlgebra.instCofibrationOfIsWeakFactorizationSystemTrivialCofibrationsFibrationsOfIsIso", "kind": "instance", "module": "Mathlib.AlgebraicTopology.ModelCategory.Instances", "is_tactic_proof": true, "tactics": ["have", "rw", "simpa"], "tactic_count": 3}
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{"name": "HomotopicalAlgebra.instRespectsIsoWeakEquivalencesOfIsWeakFactorizationSystemTrivialCofibrationsFibrationsOfIsStableUnderRetractsOfIsStableUnderComposition", "kind": "instance", "module": "Mathlib.AlgebraicTopology.ModelCategory.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.instWeakEquivalenceIdOfContainsIdentitiesWeakEquivalences", "kind": "instance", "module": "Mathlib.AlgebraicTopology.ModelCategory.Instances", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
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{"name": "HomotopicalAlgebra.LeftHomotopyClass.sound", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.ModelCategory.LeftHomotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "HomotopicalAlgebra.instIsStableUnderRetractsOppositeFibrationsOfCofibrations", "kind": "instance", "module": "Mathlib.AlgebraicTopology.ModelCategory.Opposite", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
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{"name": "HomotopicalAlgebra.instHasFactorizationOppositeCofibrationsTrivialFibrationsOfTrivialCofibrationsFibrations", "kind": "instance", "module": "Mathlib.AlgebraicTopology.ModelCategory.Opposite", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
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{"name": "HomotopicalAlgebra.instCategoryWithCofibrationsOver", "kind": "instance", "module": "Mathlib.AlgebraicTopology.ModelCategory.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.cofibrations_over_def", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.ModelCategory.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SSet.Truncated.HomotopyCategory₂.homMk_surjective", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.Quasicategory.TwoTruncated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.HomotopyCategory₂.homMk_id", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.Quasicategory.TwoTruncated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.HomotopicL.congr_homotopyCategory₂HomMk", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.Quasicategory.TwoTruncated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.HomotopicR.congr_homotopyCategory₂HomMk", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.Quasicategory.TwoTruncated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.Edge.CompStruct.homotopyCategory₂_fac", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.Quasicategory.TwoTruncated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.Edge.CompStruct.ofHomotopyCategory₂Fac", "kind": "definition", "module": "Mathlib.AlgebraicTopology.Quasicategory.TwoTruncated", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "exact"], "tactic_count": 3}
{"name": "SSet.Truncated.Edge.CompStruct.nonempty_iff", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.Quasicategory.TwoTruncated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.instCategoryHomotopyCategory₂", "kind": "instance", "module": "Mathlib.AlgebraicTopology.Quasicategory.TwoTruncated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.AttachCells.pushouts_coproducts", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.RelativeCellComplex.AttachCells", "is_tactic_proof": true, "tactics": ["refine", "have", "c.isColimit₁.hom_ext", "rw", "exact"], "tactic_count": 5}
{"name": "HomotopicalAlgebra.AttachCells.cell", "kind": "definition", "module": "Mathlib.AlgebraicTopology.RelativeCellComplex.AttachCells", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.AttachCells.cell_def", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.RelativeCellComplex.AttachCells", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.AttachCells.hom_ext", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.RelativeCellComplex.AttachCells", "is_tactic_proof": true, "tactics": ["apply", "apply", "simpa"], "tactic_count": 3}
{"name": "HomotopicalAlgebra.AttachCells.ofArrowIso", "kind": "definition", "module": "Mathlib.AlgebraicTopology.RelativeCellComplex.AttachCells", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.AttachCells.reindex", "kind": "definition", "module": "Mathlib.AlgebraicTopology.RelativeCellComplex.AttachCells", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.AttachCells.reindexCellTypes", "kind": "definition", "module": "Mathlib.AlgebraicTopology.RelativeCellComplex.AttachCells", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.nonempty_attachCells_iff", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.RelativeCellComplex.AttachCells", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "exact", "rintro", "rw", "obtain", "let", "let", "let", "let", "exact", "π", "cofan₁", "cofan₂", "isColimit₁", "isColimit₂", "hm", "isPushout"], "tactic_count": 18}
{"name": "HomotopicalAlgebra.RelativeCellComplex.Cells.i", "kind": "definition", "module": "Mathlib.AlgebraicTopology.RelativeCellComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.RelativeCellComplex.Cells.ι", "kind": "definition", "module": "Mathlib.AlgebraicTopology.RelativeCellComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomotopicalAlgebra.RelativeCellComplex.hom_ext", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.RelativeCellComplex.Basic", "is_tactic_proof": true, "tactics": ["refine", "dsimp", "induction", "isMin", "obtain", "simpa", "succ", "apply", "simpa", "intro", "simpa", "isSuccLimit", "exact"], "tactic_count": 13}
{"name": "HomotopicalAlgebra.RelativeCellComplex.transfiniteCompositionOfShape", "kind": "definition", "module": "Mathlib.AlgebraicTopology.RelativeCellComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AugmentedSimplexCategory", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Augmented.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AugmentedSimplexCategory.inclusion", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Augmented.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AugmentedSimplexCategory.instFullSimplexCategoryInclusion", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Augmented.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AugmentedSimplexCategory.instFaithfulSimplexCategoryInclusion", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Augmented.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AugmentedSimplexCategory.instHasInitial", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Augmented.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AugmentedSimplexCategory.equivAugmentedCosimplicialObject", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Augmented.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompDropIso", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Augmented.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompPointIso", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Augmented.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompToArrowIso", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Augmented.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AugmentedSimplexCategory.equivAugmentedSimplicialObject", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Augmented.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompDropIso", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Augmented.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompPointIso", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Augmented.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompToArrowIso", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Augmented.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AugmentedSimplexCategory.eqToHom_toOrderHom", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Augmented.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AugmentedSimplexCategory.tensorObjOf", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Augmented.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AugmentedSimplexCategory.tensorObj", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Augmented.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AugmentedSimplexCategory.tensorHomOf", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Augmented.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AugmentedSimplexCategory.tensorHom", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Augmented.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AugmentedSimplexCategory.tensorUnit", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Augmented.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AugmentedSimplexCategory.associator", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Augmented.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AugmentedSimplexCategory.leftUnitor", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Augmented.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AugmentedSimplexCategory.rightUnitor", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Augmented.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AugmentedSimplexCategory.instMonoidalCategoryStruct", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Augmented.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AugmentedSimplexCategory.id_tensorHom", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Augmented.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AugmentedSimplexCategory.tensorHom_id", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Augmented.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AugmentedSimplexCategory.whiskerLeft_id_star", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Augmented.Monoidal", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "AugmentedSimplexCategory.id_star_whiskerRight", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Augmented.Monoidal", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "AugmentedSimplexCategory.inl", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Augmented.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AugmentedSimplexCategory.inr", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Augmented.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AugmentedSimplexCategory.inl'", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Augmented.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AugmentedSimplexCategory.inr'", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Augmented.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AugmentedSimplexCategory.inl'_eval", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Augmented.Monoidal", "is_tactic_proof": false, "tactics": ["dsimp", "rightUnitor,", "ext", "simp"], "tactic_count": 4}
{"name": "AugmentedSimplexCategory.inr'_eval", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Augmented.Monoidal", "is_tactic_proof": false, "tactics": ["dsimp", "leftUnitor,", "ext", "simp"], "tactic_count": 4}
{"name": "AugmentedSimplexCategory.tensorObj_hom_ext", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Augmented.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AugmentedSimplexCategory.inl_comp_tensorHom", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Augmented.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AugmentedSimplexCategory.inr_comp_tensorHom", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Augmented.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AugmentedSimplexCategory.inr_comp_associator", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Augmented.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AugmentedSimplexCategory.inl_comp_inl_comp_associator", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Augmented.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AugmentedSimplexCategory.inr_comp_inl_comp_associator", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Augmented.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AugmentedSimplexCategory.tensorHom_comp_tensorHom", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Augmented.Monoidal", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "AugmentedSimplexCategory.tensor_id", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Augmented.Monoidal", "is_tactic_proof": true, "tactics": ["ext", "simpa", "simpa"], "tactic_count": 3}
{"name": "AugmentedSimplexCategory.instMonoidalCategory", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Augmented.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.instFiniteHom", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.instDecidableEqHom", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.congr_toOrderHom_apply", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimplexCategory.const", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.const_eq_id", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SimplexCategory.const_apply", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.const_comp", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.const_fac_thru_zero", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimplexCategory.eq_const_of_zero", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "SimplexCategory.exists_eq_const_of_zero", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.eq_const_to_zero", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": true, "tactics": ["ext", "apply"], "tactic_count": 2}
{"name": "SimplexCategory.eq_of_one_to_one", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": true, "tactics": ["refine", "ext", "right", "ext", "have", "rw", "exact"], "tactic_count": 7}
{"name": "SimplexCategory.mkHom", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.mkOfLe", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.mkOfLe_refl", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.diag", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.intervalEdge", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.mkOfSucc", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.mkOfSucc_homToOrderHom_zero", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.mkOfSucc_homToOrderHom_one", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.mkOfSucc_eq_id", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "SimplexCategory.mkOfLeComp", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.subinterval", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.const_subinterval_eq", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": true, "tactics": ["rw", "congr", "ext", "dsimp", "rw"], "tactic_count": 5}
{"name": "SimplexCategory.mkOfSucc_subinterval_eq", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": true, "tactics": ["unfold", "ext"], "tactic_count": 2}
{"name": "SimplexCategory.diag_subinterval_eq", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": true, "tactics": ["unfold", "ext"], "tactic_count": 2}
{"name": "SimplexCategory.instSubsingletonHomMkOfNatNat", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.hom_zero_zero", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "SimplexCategory.eqToHom_toOrderHom", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": true, "tactics": ["subst", "rfl"], "tactic_count": 2}
{"name": "SimplexCategory.δ", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.σ", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.δ_comp_δ", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "rcases", "rcases", "rcases", "split_ifs"], "tactic_count": 6}
{"name": "SimplexCategory.δ_comp_δ'", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": true, "tactics": ["rw", "rw", "simpa"], "tactic_count": 3}
{"name": "SimplexCategory.δ_comp_δ''", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": true, "tactics": ["rw", "rfl", "exact"], "tactic_count": 3}
{"name": "SimplexCategory.δ_comp_δ_self", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.δ_comp_δ_self'", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": true, "tactics": ["subst", "rw"], "tactic_count": 2}
{"name": "SimplexCategory.δ_comp_σ_of_le", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "rcases", "rw", "rcases", "rwa", "rw", "exact", "rw", "have", "rw", "rwa"], "tactic_count": 12}
{"name": "SimplexCategory.δ_comp_σ_self", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": true, "tactics": ["rcases", "ext", "simp", "dsimp", "simp", "split_ifs", "any_goals", "all_goals"], "tactic_count": 8}
{"name": "SimplexCategory.δ_comp_σ_self'", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": true, "tactics": ["subst", "rw"], "tactic_count": 2}
{"name": "SimplexCategory.δ_comp_σ_succ", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": true, "tactics": ["ext", "rcases", "rcases", "dsimp", "split_ifs"], "tactic_count": 5}
{"name": "SimplexCategory.δ_comp_σ_succ'", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": true, "tactics": ["subst", "rw"], "tactic_count": 2}
{"name": "SimplexCategory.δ_comp_σ_of_gt", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "rcases", "rw", "rcases", "rw", "rw", "exact", "rw", "rwa", "rw", "have", "rw", "rwa"], "tactic_count": 14}
{"name": "SimplexCategory.δ_comp_σ_of_gt'", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp", "rw", "exact"], "tactic_count": 4}
{"name": "SimplexCategory.σ_comp_σ", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "cases", "last", "cast", "cases", "zero", "succ", "rcases", "simp_rw", "rw", "rcases", "rwa", "rw", "exact", "simp_rw", "rw"], "tactic_count": 17}
{"name": "SimplexCategory.δ_zero_eq_const", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "SimplexCategory.δ_one_eq_const", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "SimplexCategory.factor_δ", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.factor_δ_spec", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": true, "tactics": ["ext", "cases"], "tactic_count": 2}
{"name": "SimplexCategory.δ_zero_mkOfSucc", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": true, "tactics": ["ext", "fin_cases", "rfl"], "tactic_count": 3}
{"name": "SimplexCategory.δ_one_mkOfSucc", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": true, "tactics": ["ext", "fin_cases", "rfl"], "tactic_count": 3}
{"name": "SimplexCategory.mkOfSucc_δ_lt", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": true, "tactics": ["ext", "fin_cases", "simp", "simp"], "tactic_count": 4}
{"name": "SimplexCategory.mkOfSucc_δ_gt", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp", "fin_cases", "rfl", "exact", "rfl", "exact"], "tactic_count": 7}
{"name": "SimplexCategory.mkOfSucc_δ_eq", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": true, "tactics": ["ext", "fin_cases", "subst", "simp", "rfl", "simp", "subst", "rw", "rfl"], "tactic_count": 9}
{"name": "SimplexCategory.mkOfSucc_one_eq_δ", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "SimplexCategory.mkOfSucc_zero_eq_δ", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "SimplexCategory.eq_of_one_to_two", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": true, "tactics": ["have", "refine", "ext", "refine", "ext", "refine", "ext", "refine", "ext", "rw", "exact"], "tactic_count": 11}
{"name": "SimplexCategory.eq_of_one_to_two'", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.skeletalFunctor", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.skeletalFunctor.coe_map", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.skeletal", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.SkeletalFunctor.instFullNonemptyFinLinOrdSkeletalFunctor", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.SkeletalFunctor.instFaithfulNonemptyFinLinOrdSkeletalFunctor", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.SkeletalFunctor.instEssSurjNonemptyFinLinOrdSkeletalFunctor", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.SkeletalFunctor.isEquivalence", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.skeletalEquivalence", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.isSkeletonOf", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.instConcreteCategoryOrderHomFinHAddNatLenOfNat", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.instFintypeToTypeOrderHomFinHAddNatLenOfNat", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.instOfNatToTypeOrderHomFinHAddNatLenOfNat", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.toType_apply", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.concreteCategoryHom_id", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.mono_iff_injective", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": true, "tactics": ["rw", "dsimp", "simp"], "tactic_count": 3}
{"name": "SimplexCategory.epi_iff_surjective", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": true, "tactics": ["rw", "dsimp", "simp"], "tactic_count": 3}
{"name": "SimplexCategory.len_le_of_mono", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "SimplexCategory.le_of_mono", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.len_le_of_epi", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "SimplexCategory.le_of_epi", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.len_eq_of_isIso", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.eq_of_isIso", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.instEpiσ", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "SimplexCategory.instReflectsIsomorphismsForget", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.isIso_of_bijective", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.isIso_iff_of_mono", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": true, "tactics": ["refine", "obtain", "rw", "exact"], "tactic_count": 4}
{"name": "SimplexCategory.instMonoδ", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SimplexCategory.isIso_iff_of_epi", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": true, "tactics": ["refine", "obtain", "rw", "exact"], "tactic_count": 4}
{"name": "SimplexCategory.instBalanced", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.orderIsoOfIso", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.iso_eq_iso_refl", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": true, "tactics": ["have", "have", "have", "ext", "convert", "ext", "rfl"], "tactic_count": 7}
{"name": "SimplexCategory.eq_id_of_isIso", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.eq_σ_comp_of_not_injective'", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": true, "tactics": ["use", "ext", "simp", "by_cases", "rw", "dsimp", "rw", "rw", "exact", "simp", "let", "have", "rw", "rw", "by_cases", "rw", "refine", "congr", "dsimp", "rw", "exact", "dsimp", "rw", "simp", "lia"], "tactic_count": 25}
{"name": "SimplexCategory.eq_σ_comp_of_not_injective", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": true, "tactics": ["simp", "have", "rcases", "by_cases", "exact", "refine", "lia", "rcases", "use", "apply", "apply", "exact", "rw", "exact"], "tactic_count": 14}
{"name": "SimplexCategory.eq_comp_δ_of_not_surjective'", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": true, "tactics": ["use", "ext", "suffices", "dsimp", "exact", "intro", "cases"], "tactic_count": 7}
{"name": "SimplexCategory.eq_comp_δ_of_not_surjective", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": true, "tactics": ["obtain", "use", "exact"], "tactic_count": 3}
{"name": "SimplexCategory.eq_id_of_mono", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": true, "tactics": ["suffices", "apply", "dsimp", "rw", "infer_instance"], "tactic_count": 5}
{"name": "SimplexCategory.eq_id_of_epi", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": true, "tactics": ["suffices", "apply", "dsimp", "rw", "infer_instance"], "tactic_count": 5}
{"name": "SimplexCategory.eq_σ_of_epi", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": false, "tactics": ["obtain", "eq_σ_comp_of_not_injective", "rw", "grind", "use", "haveI", "rw", "infer_instance", "haveI", "rw"], "tactic_count": 10}
{"name": "SimplexCategory.eq_δ_of_mono", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": false, "tactics": ["obtain", "eq_comp_δ_of_not_surjective", "rw", "grind", "use", "haveI", "rw", "infer_instance", "haveI", "rw"], "tactic_count": 10}
{"name": "SimplexCategory.len_lt_of_mono", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "SimplexCategory.instSplitEpiCategory", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.instHasStrongEpiMonoFactorisations", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.instHasStrongEpiImages", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.instEpiFactorThruImage", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.image_eq", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": true, "tactics": ["haveI", "let", "ext", "exact"], "tactic_count": 4}
{"name": "SimplexCategory.image_ι_eq", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": true, "tactics": ["haveI", "rw"], "tactic_count": 2}
{"name": "SimplexCategory.factorThruImage_eq", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimplexCategory.toCat", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.toCat.obj_eq_Fin", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.uniqueHomToZero", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.isTerminalZero", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.instHasTerminal", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.topIsoZero", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.δ_injective", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.σ_injective", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.mk", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Simplicial.term⦋_⦌", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Simplicial._aux_Mathlib_AlgebraicTopology_SimplexCategory_Defs___macroRules_Simplicial_term⦋_⦌_1", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Simplicial._aux_Mathlib_AlgebraicTopology_SimplexCategory_Defs___unexpand_SimplexCategory_mk_1", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.len", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.ext", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.len_mk", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.mk_len", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.rec", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.Hom", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.Hom.mk", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.Hom.toOrderHom", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.Hom.ext'", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.Hom.mk_toOrderHom", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.Hom.toOrderHom_mk", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.Hom.mk_toOrderHom_apply", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.Hom.id", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.Hom.comp", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.smallCategory", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.id_toOrderHom", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.comp_toOrderHom", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.Hom.ext", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.homEquivOrderHom", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.homEquivFunctor", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.Truncated", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.Truncated.instInhabited", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.Truncated.inclusion", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.Truncated.inclusion.fullyFaithful", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.Truncated.Hom.ext", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.Truncated.tacticTrunc", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.Truncated._aux_Mathlib_AlgebraicTopology_SimplexCategory_Defs___macroRules_SimplexCategory_Truncated_tacticTrunc_1", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.Truncated.mkNotation", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.Truncated._aux_Mathlib_AlgebraicTopology_SimplexCategory_Defs___macroRules_SimplexCategory_Truncated_mkNotation_1", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.Truncated.inclCompInclusion", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeSimplexQuiver", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeSimplexQuiver.mk", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeSimplexQuiver.len", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeSimplexQuiver.Hom", "kind": "inductive", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeSimplexQuiver.quiv", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeSimplexQuiver.δ", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeSimplexQuiver.σ", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeSimplexQuiver.homRel", "kind": "inductive", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategoryGenRel", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategoryGenRel.mk", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategoryGenRel.δ", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategoryGenRel.σ", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategoryGenRel.len", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.Basic", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "SimplexCategoryGenRel.mk_len", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategoryGenRel.faces", "kind": "inductive", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategoryGenRel.degeneracies", "kind": "inductive", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategoryGenRel.generators", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategoryGenRel.generators.δ", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategoryGenRel.generators.σ", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategoryGenRel.multiplicativeClosure_isGenerator_eq_top", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.Basic", "is_tactic_proof": true, "tactics": ["apply", "intro", "apply", "apply", "exact", "rintro", "exact", "exact"], "tactic_count": 8}
{"name": "SimplexCategoryGenRel.hom_induction", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.Basic", "is_tactic_proof": false, "tactics": ["suffices", "rw", "rw", "apply", "intro", "induction", "of", "rcases", "simpa", "simpa", "id", "comp_of", "rcases", "simpa", "simpa"], "tactic_count": 15}
{"name": "SimplexCategoryGenRel.hom_induction'", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.Basic", "is_tactic_proof": false, "tactics": ["suffices", "rw", "top_le_iff]", "rw", "apply", "intro", "induction", "of", "rcases", "simpa", "simpa", "id", "of_comp", "rcases", "simpa", "simpa"], "tactic_count": 16}
{"name": "SimplexCategoryGenRel.rec", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.Basic", "is_tactic_proof": true, "tactics": ["intro", "exact"], "tactic_count": 2}
{"name": "SimplexCategoryGenRel.ext", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.Basic", "is_tactic_proof": true, "tactics": ["cases", "cases", "simp", "congr"], "tactic_count": 4}
{"name": "SimplexCategoryGenRel.δ_comp_δ", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.Basic", "is_tactic_proof": true, "tactics": ["apply", "exact"], "tactic_count": 2}
{"name": "SimplexCategoryGenRel.δ_comp_σ_of_le", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.Basic", "is_tactic_proof": true, "tactics": ["apply", "exact"], "tactic_count": 2}
{"name": "SimplexCategoryGenRel.δ_comp_σ_self", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.Basic", "is_tactic_proof": true, "tactics": ["apply", "exact"], "tactic_count": 2}
{"name": "SimplexCategoryGenRel.δ_comp_σ_succ", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.Basic", "is_tactic_proof": true, "tactics": ["apply", "exact"], "tactic_count": 2}
{"name": "SimplexCategoryGenRel.δ_comp_σ_of_gt", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.Basic", "is_tactic_proof": true, "tactics": ["apply", "exact"], "tactic_count": 2}
{"name": "SimplexCategoryGenRel.σ_comp_σ", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.Basic", "is_tactic_proof": true, "tactics": ["apply", "exact"], "tactic_count": 2}
{"name": "SimplexCategoryGenRel.δ_comp_δ_nat", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategoryGenRel.σ_comp_σ_nat", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategoryGenRel.toSimplexCategory", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategoryGenRel.toSimplexCategory_obj_mk", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategoryGenRel.toSimplexCategory_map_δ", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategoryGenRel.toSimplexCategory_map_σ", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategoryGenRel.toSimplexCategory_len", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategoryGenRel.splitMonoδ", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategoryGenRel.instIsSplitMonoδ", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategoryGenRel.splitEpiσ", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategoryGenRel.instIsSplitEpiσ", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategoryGenRel.P_σ", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategoryGenRel.P_δ", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategoryGenRel.P_σ.σ", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategoryGenRel.P_δ.δ", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategoryGenRel.isSplitEpi_P_σ", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.EpiMono", "is_tactic_proof": true, "tactics": ["induction", "of", "id", "comp_of"], "tactic_count": 4}
{"name": "SimplexCategoryGenRel.isSplitMono_P_δ", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.EpiMono", "is_tactic_proof": true, "tactics": ["induction", "of", "id", "comp_of"], "tactic_count": 4}
{"name": "SimplexCategoryGenRel.isSplitEpi_toSimplexCategory_map_of_P_σ", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.EpiMono", "is_tactic_proof": true, "tactics": ["constructor", "constructor", "apply", "exact"], "tactic_count": 4}
{"name": "SimplexCategoryGenRel.isSplitMono_toSimplexCategory_map_of_P_δ", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.EpiMono", "is_tactic_proof": true, "tactics": ["constructor", "constructor", "apply", "exact"], "tactic_count": 4}
{"name": "SimplexCategoryGenRel.eq_or_len_le_of_P_δ", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.EpiMono", "is_tactic_proof": true, "tactics": ["induction", "of", "id", "comp_of", "rcases", "rw", "exact", "exact"], "tactic_count": 8}
{"name": "_private.Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.EpiMono.0.SimplexCategoryGenRel.switch_δ_σ", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.EpiMono", "is_tactic_proof": true, "tactics": ["obtain", "rw", "obtain", "obtain", "rw", "obtain", "exact", "exact", "exact", "obtain", "rw", "obtain", "rw", "exact"], "tactic_count": 14}
{"name": "_private.Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.EpiMono.0.SimplexCategoryGenRel.switch_δ_σ₀", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.EpiMono", "is_tactic_proof": true, "tactics": ["fin_cases", "exact", "exact"], "tactic_count": 3}
{"name": "_private.Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.EpiMono.0.SimplexCategoryGenRel.factor_δ_σ", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.EpiMono", "is_tactic_proof": true, "tactics": ["cases", "zero", "succ", "obtain", "exact", "exact"], "tactic_count": 6}
{"name": "_private.Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.EpiMono.0.SimplexCategoryGenRel.factor_P_δ_σ", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.EpiMono", "is_tactic_proof": true, "tactics": ["induction", "zero", "cases", "of", "id", "comp_of", "obtain", "obtain", "simpa", "simp", "succ", "cases", "of", "id", "comp_of", "obtain", "obtain", "simpa", "obtain", "exact", "obtain", "exact"], "tactic_count": 22}
{"name": "SimplexCategoryGenRel.exists_P_σ_P_δ_factorization", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.EpiMono", "is_tactic_proof": true, "tactics": ["induction", "obtain", "exact", "obtain", "cases", "of", "rcases", "obtain", "exact", "comp_of", "cases", "zero", "cases", "exact", "succ", "rcases", "obtain", "exact", "obtain", "exact"], "tactic_count": 20}
{"name": "SimplexCategoryGenRel.instHasFactorizationP_σP_δ", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategoryGenRel.IsAdmissible", "kind": "inductive", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.NormalForms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategoryGenRel.isAdmissible_singleton_iff", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.NormalForms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategoryGenRel.isAdmissible_cons_cons_iff", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.NormalForms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategoryGenRel.isAdmissible_cons_iff", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.NormalForms", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "SimplexCategoryGenRel.isAdmissible_iff_isChain_and_le", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.NormalForms", "is_tactic_proof": true, "tactics": ["induction", "nil", "singleton", "cons_cons", "simp_rw", "and_congr_right_iff,", "exact"], "tactic_count": 7}
{"name": "SimplexCategoryGenRel.isAdmissible_iff_pairwise_and_le", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.NormalForms", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimplexCategoryGenRel.isAdmissible_of_isChain_of_forall_getElem_le", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.NormalForms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategoryGenRel.IsAdmissible.isChain", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.NormalForms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategoryGenRel.IsAdmissible.le", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.NormalForms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategoryGenRel.IsAdmissible.of_cons", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.NormalForms", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "SimplexCategoryGenRel.IsAdmissible.cons", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.NormalForms", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "SimplexCategoryGenRel.IsAdmissible.sortedLT", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.NormalForms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategoryGenRel.IsAdmissible.head_lt", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.NormalForms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategoryGenRel.IsAdmissible.getElem_lt", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.NormalForms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategoryGenRel.IsAdmissible.getElemAsFin", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.NormalForms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategoryGenRel.IsAdmissible.head", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.NormalForms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategoryGenRel.IsAdmissible.mono", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.NormalForms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategoryGenRel.simplicialInsert", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.NormalForms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategoryGenRel.simplicialInsert_length", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.NormalForms", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "SimplexCategoryGenRel.simplicialInsert_isAdmissible", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.NormalForms", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "SimplexCategoryGenRel.standardσ", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.NormalForms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategoryGenRel.standardσ_nil", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.NormalForms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategoryGenRel.standardσ_cons", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.NormalForms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategoryGenRel.standardσ_comp_standardσ", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.NormalForms", "is_tactic_proof": true, "tactics": ["induction", "nil", "obtain", "simp", "cons", "dsimp", "obtain", "simp"], "tactic_count": 8}
{"name": "SimplexCategoryGenRel.simplicialEvalσ", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.NormalForms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategoryGenRel.simplicialEvalσ_of_le_mem", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.NormalForms", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "SimplexCategoryGenRel.simplicialEvalσ_monotone", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.NormalForms", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "SimplexCategoryGenRel.simplicialEvalσ_of_isAdmissible", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.NormalForms", "is_tactic_proof": true, "tactics": ["induction", "nil", "obtain", "simp", "cons", "simp", "subst", "set", "have", "simp", "split_ifs", "rfl", "simp", "simp", "rfl", "have", "have", "simpa", "toSimplexCategory_map_σ,", "simplicialEvalσ,"], "tactic_count": 20}
{"name": "SimplexCategoryGenRel.standardσ_simplicialInsert", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.NormalForms", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "simp", "split_ifs", "simp", "have", "simp", "have", "grind", "have", "convert", "grind"], "tactic_count": 13}
{"name": "SimplexCategoryGenRel.exists_normal_form_P_σ", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.NormalForms", "is_tactic_proof": true, "tactics": ["induction", "id", "use", "rfl", "of", "cases", "use", "simp", "cases", "obtain", "obtain", "use", "subst_vars", "have", "standardσ", "simp_all"], "tactic_count": 16}
{"name": "SimplexCategoryGenRel.IsAdmissible.simplicialEvalσ_succ_getElem", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.NormalForms", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "SimplexCategoryGenRel.mem_isAdmissible_of_lt_and_eval_eq_eval_add_one", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.NormalForms", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "have", "rcases"], "tactic_count": 5}
{"name": "SimplexCategoryGenRel.lt_and_eval_eq_eval_add_one_of_mem_isAdmissible", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.NormalForms", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "SimplexCategoryGenRel.mem_isAdmissible_iff", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.NormalForms", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "SimplexCategory.Truncated.morphismProperty_eq_top", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.MorphismProperty", "is_tactic_proof": true, "tactics": ["ext", "simp", "induction", "induction", "dsimp", "generalize", "induction", "zero", "obtain", "obtain", "obtain", "ext", "apply", "apply", "succ", "by_cases", "obtain", "exact", "obtain", "replace", "rw", "exact", "by_cases", "obtain", "exact", "obtain", "replace", "rw", "exact", "rw", "rw", "obtain", "obtain", "apply"], "tactic_count": 34}
{"name": "SimplexCategory.morphismProperty_eq_top", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.MorphismProperty", "is_tactic_proof": false, "tactics": ["have", "ext", "simp", "change", "simp"], "tactic_count": 5}
{"name": "SimplexCategory.rev", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Rev", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.rev_map_apply", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Rev", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "SimplexCategory.rev_map_δ", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Rev", "is_tactic_proof": true, "tactics": ["ext", "rw", "dsimp", "rw"], "tactic_count": 4}
{"name": "SimplexCategory.rev_map_σ", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Rev", "is_tactic_proof": true, "tactics": ["ext", "rw", "dsimp", "rw"], "tactic_count": 4}
{"name": "SimplexCategory.revCompRevIso", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Rev", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.rev_map_rev_map", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Rev", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SimplexCategory.revEquivalence", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Rev", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.Truncated.instDecidableEqHom", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Truncated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SimplexCategory.Truncated.δ₂_two_comp_σ₂_one", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplexCategory.Truncated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.SimplicialObject.instEnrichedCategorySSet", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialCategory.SimplicialObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.SimplicialThickening.instCategoryPath", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialNerve", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SimplicialThickening.instCategoryStruct", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialNerve", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.SimplicialThickening.compFunctor", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialNerve", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.SimplicialThickening.SimplicialCategory.id", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.SimplicialNerve", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.SimplicialThickening.SimplicialCategory.id_comp", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialNerve", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
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{"name": "CategoryTheory.SimplicialThickening.SimplicialCategory.assoc", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialNerve", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.SimplicialThickening.instSimplicialCategory", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialNerve", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SimplicialThickening.functorMap", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.SimplicialNerve", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SimplicialThickening.functor", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialNerve", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SimplicialThickening.functor_id", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialNerve", "is_tactic_proof": true, "tactics": ["refine", "ext", "exact"], "tactic_count": 3}
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{"name": "CategoryTheory.SimplicialObject", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instCategorySimplicialObject", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
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{"name": "CategoryTheory.SimplicialObject.instHasColimitsOfShape", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
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{"name": "CategoryTheory.SimplicialObject.δ", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SimplicialObject.δ_def", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.SimplicialObject.eqToIso_refl", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "CategoryTheory.SimplicialObject.Truncated.cosk", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.SimplicialObject.Augmented.point", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SimplicialObject.Augmented.toArrow", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SimplicialObject.Augmented.w₀", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
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{"name": "CategoryTheory.SimplicialObject.augment", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SimplicialObject.augment_hom_zero", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.CosimplicialObject", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CosimplicialObject.instCategory", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "Simplicial.term_^⦋_⦌", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Simplicial._aux_Mathlib_AlgebraicTopology_SimplicialObject_Basic___macroRules_Simplicial_term_^⦋_⦌_1", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Simplicial._aux_Mathlib_AlgebraicTopology_SimplicialObject_Basic___delab_app_Simplicial_term_^⦋_⦌_1", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CosimplicialObject.instHasLimitsOfShape", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.CosimplicialObject.instHasLimits", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CosimplicialObject.instHasColimitsOfShape", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.CosimplicialObject.instHasColimits", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CosimplicialObject.hom_ext", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CosimplicialObject.δ", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CosimplicialObject.σ", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CosimplicialObject.eqToIso", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CosimplicialObject.eqToIso_refl", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.CosimplicialObject.δ_comp_δ", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.CosimplicialObject.δ_comp_δ'", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.CosimplicialObject.δ_comp_δ''", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.CosimplicialObject.δ_comp_δ_self", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.CosimplicialObject.δ_comp_δ_self'", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": true, "tactics": ["subst", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.CosimplicialObject.δ_comp_σ_of_le", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.CosimplicialObject.δ_comp_σ_self", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.CosimplicialObject.δ_comp_σ_self'", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": true, "tactics": ["subst", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.CosimplicialObject.δ_comp_σ_succ", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.CosimplicialObject.δ_comp_σ_succ'", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": true, "tactics": ["subst", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.CosimplicialObject.δ_comp_σ_of_gt", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.CosimplicialObject.δ_comp_σ_of_gt'", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.CosimplicialObject.σ_comp_σ", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.CosimplicialObject.δ_naturality", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CosimplicialObject.σ_naturality", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CosimplicialObject.whiskering", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CosimplicialObject.Truncated", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CosimplicialObject.instCategoryTruncated", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.CosimplicialObject.Truncated.instHasLimitsOfShape", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.CosimplicialObject.Truncated.instHasLimits", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CosimplicialObject.Truncated.instHasColimitsOfShape", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.CosimplicialObject.Truncated.instHasColimits", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CosimplicialObject.Truncated.whiskering", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CosimplicialObject.Truncated.mkNotation", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CosimplicialObject.Truncated._aux_Mathlib_AlgebraicTopology_SimplicialObject_Basic___macroRules_CategoryTheory_CosimplicialObject_Truncated_mkNotation_1", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CosimplicialObject.truncation", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CosimplicialObject.truncationCompTrunc", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CosimplicialObject.const", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CosimplicialObject.Augmented", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CosimplicialObject.instCategoryAugmented", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.CosimplicialObject.Augmented.hom_ext", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CosimplicialObject.Augmented.drop", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CosimplicialObject.Augmented.point", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CosimplicialObject.Augmented.toArrow", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CosimplicialObject.Augmented.whiskeringObj", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CosimplicialObject.Augmented.whiskering", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CosimplicialObject.Augmented.const", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CosimplicialObject.augment", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CosimplicialObject.augment_hom_zero", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.simplicialCosimplicialEquiv", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.cosimplicialSimplicialEquiv", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SimplicialObject.Augmented.rightOp", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CosimplicialObject.Augmented.leftOp", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SimplicialObject.Augmented.rightOpLeftOpIso", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CosimplicialObject.Augmented.leftOpRightOpIso", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.simplicialToCosimplicialAugmented", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.cosimplicialToSimplicialAugmented", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.simplicialCosimplicialAugmentedEquiv", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SimplicialObject.Truncated.rightExtensionInclusion", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Coskeletal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SimplicialObject.IsCoskeletal.isUniversalOfIsRightKanExtension", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Coskeletal", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.SimplicialObject.isCoskeletal_iff_isIso", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Coskeletal", "is_tactic_proof": true, "tactics": ["rw", "exact", "isRightKanExtension_iff_isIso"], "tactic_count": 3}
{"name": "CategoryTheory.SimplicialObject.instIsIsoAppUnitTruncatedCoskAdj", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Coskeletal", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.SimplicialObject.isoCoskOfIsCoskeletal", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Coskeletal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.II.finset", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialObject.II", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.II.mem_finset_iff", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.II", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimplexCategory.II.last_mem_finset", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.II", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimplexCategory.II.castSucc_mem_finset_iff", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.II", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimplexCategory.II.nonempty_finset", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.II", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.II.map'", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialObject.II", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.II.map'_eq_last_iff", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.II", "is_tactic_proof": true, "tactics": ["simp", "constructor", "intro", "by_contra", "exact", "intro", "by_contra", "obtain", "simp", "exact"], "tactic_count": 10}
{"name": "SimplexCategory.II.map'_eq_castSucc_iff", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.II", "is_tactic_proof": true, "tactics": ["simp", "intro", "constructor", "intro", "by_contra", "exact", "intro", "obtain", "simp", "by_contra", "exact", "apply"], "tactic_count": 12}
{"name": "SimplexCategory.II.map'_last", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.II", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimplexCategory.II.map'_zero", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.II", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimplexCategory.II.map'_id", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.II", "is_tactic_proof": true, "tactics": ["obtain", "rw", "aesop", "simp"], "tactic_count": 4}
{"name": "SimplexCategory.II.map'_map'", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.II", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "rw", "rw", "obtain", "rw", "rw", "constructor", "refine", "simp", "exact", "intro", "exact", "rw", "rw", "intro", "exact", "rw", "rw", "intro", "apply", "simp"], "tactic_count": 22}
{"name": "SimplexCategory.II.map'_succAboveOrderEmb", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.II", "is_tactic_proof": true, "tactics": ["obtain", "by_cases", "rw", "obtain", "simp", "constructor", "obtain", "rwa", "simpa", "intro", "rwa", "obtain", "simp", "obtain", "rw", "map'_eq_castSucc_iff]", "simp", "intro", "by_cases", "simpa", "rwa", "simp"], "tactic_count": 22}
{"name": "SimplexCategory.II.map'_predAbove", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.II", "is_tactic_proof": true, "tactics": ["obtain", "by_cases", "rw", "simp", "constructor", "rw", "intro", "by_cases", "rwa", "rw", "exact", "rw", "simp", "constructor", "simp", "intro", "by_cases", "rw", "exact", "rwa", "simp"], "tactic_count": 21}
{"name": "SimplexCategory.II.monotone_map'", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.II", "is_tactic_proof": true, "tactics": ["intro", "exact", "obtain", "simp", "exact", "simp)"], "tactic_count": 6}
{"name": "SimplexCategory.II", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialObject.II", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.II_δ", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.II", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplexCategory.II_σ", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.II", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplicialObject.opFunctor", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Op", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplicialObject.opObjIso", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Op", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplicialObject.opFunctor_map_app", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Op", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimplicialObject.opFunctor_obj_map", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Op", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimplicialObject.opFunctor_obj_δ", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Op", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimplicialObject.opFunctor_obj_σ", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Op", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimplicialObject.opFunctorCompOpFunctorIso", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Op", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplicialObject.opFunctorCompOpFunctorIso_hom_app_app", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Op", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimplicialObject.opFunctorCompOpFunctorIso_inv_app_app", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Op", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimplicialObject.opEquivalence", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Op", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplicialObject.Splitting.IndexSet", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Split", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplicialObject.Splitting.IndexSet.mk", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Split", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplicialObject.Splitting.IndexSet.e", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Split", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplicialObject.Splitting.IndexSet.instEpiSimplexCategoryE", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Split", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplicialObject.Splitting.IndexSet.ext'", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Split", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplicialObject.Splitting.IndexSet.ext", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Split", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "simp", "subst", "simp", "simp"], "tactic_count": 6}
{"name": "SimplicialObject.Splitting.IndexSet.instFintype", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Split", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplicialObject.Splitting.IndexSet.id", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Split", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplicialObject.Splitting.IndexSet.instInhabited", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Split", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplicialObject.Splitting.IndexSet.EqId", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Split", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplicialObject.Splitting.IndexSet.eqId_iff_eq", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Split", "is_tactic_proof": true, "tactics": ["constructor", "intro", "dsimp", "rw", "rfl", "intro", "rcases", "simp", "subst", "refine", "simp", "exact"], "tactic_count": 12}
{"name": "SimplicialObject.Splitting.IndexSet.eqId_iff_len_eq", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Split", "is_tactic_proof": true, "tactics": ["rw", "constructor", "intro", "rw", "intro", "rw", "ext", "exact"], "tactic_count": 8}
{"name": "SimplicialObject.Splitting.IndexSet.eqId_iff_len_le", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Split", "is_tactic_proof": true, "tactics": ["rw", "constructor", "intro", "rw", "exact"], "tactic_count": 5}
{"name": "SimplicialObject.Splitting.IndexSet.eqId_iff_mono", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Split", "is_tactic_proof": true, "tactics": ["constructor", "intro", "dsimp", "subst", "dsimp", "infer_instance", "intro", "rw", "exact"], "tactic_count": 9}
{"name": "SimplicialObject.Splitting.IndexSet.epiComp", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Split", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplicialObject.Splitting.IndexSet.pull", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Split", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplicialObject.Splitting.IndexSet.fac_pull", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Split", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplicialObject.Splitting.summand", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Split", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplicialObject.Splitting.cofan'", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Split", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplicialObject.Splitting.cofan", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Split", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplicialObject.Splitting.isColimit", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Split", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplicialObject.Splitting.cofan_inj_eq", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Split", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplicialObject.Splitting.cofan_inj_id", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Split", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimplicialObject.Splitting.φ", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Split", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplicialObject.Splitting.cofan_inj_comp_app", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Split", "is_tactic_proof": true, "tactics": ["simp", "rw"], "tactic_count": 2}
{"name": "SimplicialObject.Splitting.hom_ext'", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Split", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplicialObject.Splitting.hom_ext", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Split", "is_tactic_proof": true, "tactics": ["ext", "apply", "intro", "induction", "dsimp", "simp"], "tactic_count": 6}
{"name": "SimplicialObject.Splitting.desc", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Split", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplicialObject.Splitting.ι_desc", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Split", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "SimplicialObject.Splitting.ofIso", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Split", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplicialObject.Splitting.cofan_inj_epi_naturality", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Split", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "rfl"], "tactic_count": 3}
{"name": "SimplicialObject.Split.mk'", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Split", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplicialObject.Split.Hom.ext", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Split", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "have", "ext", "apply", "subst", "simp", "apply", "intro", "dsimp", "rw"], "tactic_count": 11}
{"name": "SimplicialObject.instCategorySplit", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Split", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplicialObject.Split.hom_ext", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Split", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplicialObject.Split.congr_F", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Split", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimplicialObject.Split.congr_f", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Split", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimplicialObject.Split.id_F", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Split", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplicialObject.Split.id_f", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Split", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplicialObject.Split.comp_F", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Split", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplicialObject.Split.comp_f", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Split", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplicialObject.Split.cofan_inj_naturality_symm", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Split", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimplicialObject.Split.forget", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Split", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplicialObject.Split.evalN", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Split", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimplicialObject.Split.natTransCofanInj", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialObject.Split", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.S.IsUniquelyCodimOneFace", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.IsUniquelyCodimOneFace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.S.IsUniquelyCodimOneFace.iff", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.IsUniquelyCodimOneFace", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "obtain", "exact", "rintro", "refine", "obtain", "obtain", "rfl"], "tactic_count": 9}
{"name": "SSet.S.IsUniquelyCodimOneFace.dim_eq", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.IsUniquelyCodimOneFace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.S.IsUniquelyCodimOneFace.cast", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.IsUniquelyCodimOneFace", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "SSet.S.IsUniquelyCodimOneFace.existsUnique_δ_cast_simplex", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.IsUniquelyCodimOneFace", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "SSet.S.IsUniquelyCodimOneFace.index", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.IsUniquelyCodimOneFace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.S.IsUniquelyCodimOneFace.δ_index", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.IsUniquelyCodimOneFace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.S.IsUniquelyCodimOneFace.δ_eq_iff", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.IsUniquelyCodimOneFace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.Pairing.isUniquelyCodimOneFace", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.Pairing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.Pairing.dim_p", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.Pairing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.Pairing.AncestralRel", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.Pairing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.Pairing.AncestralRel.dim_le", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.Pairing", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "SSet.Subcomplex.Pairing.wf", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.Pairing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.Pairing.instIsWellFoundedElemNIIAncestralRel", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.Pairing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.Pairing.exists_or", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.Pairing", "is_tactic_proof": true, "tactics": ["have", "rw", "obtain", "obtain", "exact", "exact"], "tactic_count": 6}
{"name": "SSet.Subcomplex.Pairing.ne", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.Pairing", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "rintro", "have", "simp"], "tactic_count": 5}
{"name": "SSet.Subcomplex.Pairing.pairingCore", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.PairingCore", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.PairingCore.type₁", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.PairingCore", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.PairingCore.type₂", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.PairingCore", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.PairingCore.injective_type₁", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.PairingCore", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.PairingCore.injective_type₂", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.PairingCore", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.PairingCore.type₁_ne_type₂", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.PairingCore", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "SSet.Subcomplex.PairingCore.surjective", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.PairingCore", "is_tactic_proof": true, "tactics": ["obtain", "exact", "exact"], "tactic_count": 3}
{"name": "SSet.Subcomplex.PairingCore.I", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.PairingCore", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.PairingCore.II", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.PairingCore", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.PairingCore.equivI", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.PairingCore", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.PairingCore.equivII", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.PairingCore", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.PairingCore.pairing", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.PairingCore", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.PairingCore.pairing_p_equivII", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.PairingCore", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SSet.Subcomplex.PairingCore.pairing_p_symm_equivI", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.PairingCore", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SSet.Subcomplex.PairingCore.isUniquelyCodimOneFace", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.PairingCore", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.PairingCore.instIsProperPairingOfIsProper", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.PairingCore", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.PairingCore.isUniquelyCodimOneFace_index", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.PairingCore", "is_tactic_proof": true, "tactics": ["symm", "simp"], "tactic_count": 2}
{"name": "SSet.Subcomplex.PairingCore.isUniquelyCodimOneFace_index_coe", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.PairingCore", "is_tactic_proof": true, "tactics": ["subst", "simp"], "tactic_count": 2}
{"name": "SSet.Subcomplex.PairingCore.instIsInnerPairingOfIsInner", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.PairingCore", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.PairingCore.AncestralRel", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.PairingCore", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.PairingCore.ancestralRel_iff", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.PairingCore", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SSet.Subcomplex.PairingCore.instIsRegularPairingOfIsRegular", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.PairingCore", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.Pairing.RankFunction.wf_ancestralRel", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.Rank", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SSet.Subcomplex.Pairing.RankFunction.isRegular", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.Rank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.Pairing.WeakRankFunction.wf_ancestralRel", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.Rank", "is_tactic_proof": true, "tactics": ["rw", "refine", "obtain", "dsimp", "refine", "rw", "exact"], "tactic_count": 7}
{"name": "SSet.Subcomplex.Pairing.WeakRankFunction.isRegular", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.Rank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.Pairing.RankFunction.toWeakRankFunction", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.Rank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.PairingCore.rankFunctionEquiv", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.Rank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.PairingCore.weakRankFunctionEquiv", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.Rank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.Pairing.instFiniteSubtypeElemNIIAncestralRel", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RankNat", "is_tactic_proof": true, "tactics": ["let", "let", "let", "have", "obtain", "refine", "simpa", "rwa", "choose", "apply", "intro", "rw"], "tactic_count": 12}
{"name": "SSet.Subcomplex.Pairing.rank'", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RankNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.Pairing.rank'_eq", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RankNat", "is_tactic_proof": true, "tactics": ["change", "rfl"], "tactic_count": 2}
{"name": "SSet.Subcomplex.Pairing.rank'_lt", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RankNat", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SSet.Subcomplex.Pairing.rank", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RankNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.Pairing.rank_lt", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RankNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.Pairing.rankFunction", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RankNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.Pairing.instNonemptyRankFunctionNat", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RankNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.Pairing.instNonemptyWeakRankFunctionNat", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RankNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.Pairing.isRegular_iff_nonempty_rankFunction", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RankNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.Pairing.isRegular_iff_nonempty_weakRankFunction", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RankNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.largeCategory", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "SSet.hasLimits", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "SSet.hasColimits", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "SSet.hom_ext", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.id_app", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.comp_app", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.const", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.comp_const", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.const_comp", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "SSet.uliftFunctor", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.largeCategory", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "SSet.Truncated.hasLimits", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "SSet.Truncated.hasColimits", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "SSet.Truncated.uliftFunctor", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.hom_ext", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.id_app", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.comp_app", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.truncation", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.truncationCompTrunc", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.sk", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.cosk", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.sk", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.cosk", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.skAdj", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.coskAdj", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.cosk_reflective", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.sk_coreflective", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.cosk.fullyFaithful", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.cosk.full", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.cosk.faithful", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.coskAdj.reflective", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.sk.fullyFaithful", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SSet.Truncated.skAdj.coreflective", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Augmented", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.δ_comp_δ_apply", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.δ_comp_δ'_apply", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.δ_comp_δ''_apply", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.δ_comp_δ_self_apply", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.δ_comp_δ_self'_apply", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.δ_comp_σ_of_le_apply", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.δ_comp_σ_self_apply", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.δ_comp_σ_self'_apply", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.δ_comp_σ_succ_apply", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.δ_comp_σ_succ'_apply", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.δ_comp_σ_of_gt_apply", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.δ_comp_σ_of_gt'_apply", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.σ_comp_σ_apply", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SSet.boundary", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Boundary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Simplicial.term∂Δ[_]", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Boundary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Simplicial._aux_Mathlib_AlgebraicTopology_SimplicialSet_Boundary___macroRules_Simplicial_term∂Δ[_]_1", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Boundary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Simplicial._aux_Mathlib_AlgebraicTopology_SimplicialSet_Boundary___delab_app_Simplicial_term∂Δ[_]_1", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Boundary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.boundary_eq_iSup", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Boundary", "is_tactic_proof": true, "tactics": ["ext", "simp", "tauto"], "tactic_count": 3}
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{"name": "SSet.modelCategoryQuillen.boundary_ι_mem_I", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.CategoryWithFibrations", "is_tactic_proof": true, "tactics": ["constructor"], "tactic_count": 1}
{"name": "SSet.modelCategoryQuillen.J", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.CategoryWithFibrations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.modelCategoryQuillen.horn_ι_mem_J", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.CategoryWithFibrations", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "SSet.modelCategoryQuillen.I_le_monomorphisms", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.CategoryWithFibrations", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "SSet.modelCategoryQuillen.J_le_monomorphisms", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.CategoryWithFibrations", "is_tactic_proof": true, "tactics": ["rintro", "simp", "obtain", "exact"], "tactic_count": 4}
{"name": "SSet.modelCategoryQuillen.instCategoryWithCofibrations", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.CategoryWithFibrations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.modelCategoryQuillen.instCategoryWithFibrations", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.CategoryWithFibrations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.modelCategoryQuillen.cofibrations_eq", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.CategoryWithFibrations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.modelCategoryQuillen.fibrations_eq", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.CategoryWithFibrations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.modelCategoryQuillen.cofibration_iff", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.CategoryWithFibrations", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "SSet.modelCategoryQuillen.fibration_iff", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.CategoryWithFibrations", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "SSet.modelCategoryQuillen.mono_of_cofibration", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.CategoryWithFibrations", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "SSet.modelCategoryQuillen.cofibration_of_mono", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.CategoryWithFibrations", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "SSet.modelCategoryQuillen.instHasLiftingPropertyιHornHAddNatOfNatOfFibration", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.CategoryWithFibrations", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SSet.Edge", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.CompStruct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SSet.Edge.ofTruncated_edge", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.CompStruct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Edge.toTruncated_edge", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.CompStruct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SSet.Edge.tgt_eq", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.CompStruct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SSet.Edge.mk", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.CompStruct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Edge.mk_edge", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.CompStruct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Edge.id", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.CompStruct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SSet.Edge.map_edge", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.CompStruct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SSet.Edge.CompStruct.d₀", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.CompStruct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Edge.CompStruct.d₁", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.CompStruct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SSet.Edge.CompStruct.mk_simplex", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.CompStruct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SSet.Edge.CompStruct.idComp_simplex", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.CompStruct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SSet.Edge.CompStruct.compId_simplex", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.CompStruct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SSet.Truncated.Edge.exists_of_simplex", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.CompStructTruncated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SSet.Truncated.Edge.map_id", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.CompStructTruncated", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
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{"name": "SSet.Truncated.Edge.CompStruct.exists_of_simplex", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.CompStructTruncated", "is_tactic_proof": false, "tactics": ["refine", "all_goals", "rw", "apply", "decide"], "tactic_count": 5}
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{"name": "SSet.Truncated.Edge.CompStruct.compId", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.CompStructTruncated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.Edge.CompStruct.idCompId", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.CompStructTruncated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.Edge.CompStruct.map", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.CompStructTruncated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.rightExtensionInclusion", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Coskeletal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.StrictSegal.isPointwiseRightKanExtensionAt.lift", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Coskeletal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.StrictSegal.isPointwiseRightKanExtensionAt.fac_aux₁", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Coskeletal", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "rfl"], "tactic_count": 3}
{"name": "SSet.StrictSegal.isPointwiseRightKanExtensionAt.fac_aux₂", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Coskeletal", "is_tactic_proof": true, "tactics": ["obtain", "revert", "induction", "zero", "rintro", "obtain", "have", "mkOfLe", "rw", "let", "have", "dsimp", "rw", "simp", "refine", "unfold", "rw", "congr", "succ", "intro", "let", "strArrowMk₂", "let", "let", "let", "let", "let", "let", "have", "subst", "exact", "have", "change", "have", "apply", "apply", "intro", "dsimp", "rw", "have", "rw", "rfl", "have", "rw", "rfl", "rw", "dsimp"], "tactic_count": 47}
{"name": "SSet.StrictSegal.isPointwiseRightKanExtensionAt.fac_aux₃", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Coskeletal", "is_tactic_proof": false, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "SSet.StrictSegal.isPointwiseRightKanExtensionAt", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Coskeletal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.StrictSegal.isPointwiseRightKanExtension", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Coskeletal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.StrictSegal.isRightKanExtension", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Coskeletal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.StrictSegal.isCoskeletal", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Coskeletal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.StrictSegal.isCoskeletal'", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Coskeletal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Nerve.instIsCoskeletalNerveOfNatNat", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Coskeletal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Nerve.nerveFunctor₂", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Coskeletal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Nerve.instIsStrictSegalObjCatTruncatedOfNatNatNerveFunctor₂", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Coskeletal", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Nerve.cosk₂Iso", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Coskeletal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.degenerate", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Degenerate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.nonDegenerate", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Degenerate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.degenerate_zero", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Degenerate", "is_tactic_proof": true, "tactics": ["ext", "simp", "rintro", "simp"], "tactic_count": 4}
{"name": "SSet.nondegenerate_zero", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Degenerate", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SSet.mem_nonDegenerate_iff_notMem_degenerate", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Degenerate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.mem_degenerate_iff_notMem_nonDegenerate", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Degenerate", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SSet.σ_mem_degenerate", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Degenerate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.mem_degenerate_iff", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Degenerate", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "rw", "have", "exact", "rintro", "exact"], "tactic_count": 7}
{"name": "SSet.degenerate_eq_iUnion_range_σ", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Degenerate", "is_tactic_proof": true, "tactics": ["ext", "constructor", "intro", "rw", "obtain", "obtain", "rw", "have", "lia)", "aesop", "intro", "simp", "obtain", "apply"], "tactic_count": 14}
{"name": "SSet.exists_nonDegenerate", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Degenerate", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "by_cases", "exact", "simp", "obtain", "obtain", "exact"], "tactic_count": 9}
{"name": "SSet.isIso_of_nonDegenerate", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Degenerate", "is_tactic_proof": true, "tactics": ["obtain", "induction", "rw", "by_contra", "refine", "rw", "exact"], "tactic_count": 7}
{"name": "SSet.mono_of_nonDegenerate", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Degenerate", "is_tactic_proof": false, "tactics": ["have", "rw", "infer_instance"], "tactic_count": 3}
{"name": "_private.Mathlib.AlgebraicTopology.SimplicialSet.Degenerate.0.SSet.unique_nonDegenerate.g", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Degenerate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.AlgebraicTopology.SimplicialSet.Degenerate.0.SSet.unique_nonDegenerate.map_g_op_y₂", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Degenerate", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "_private.Mathlib.AlgebraicTopology.SimplicialSet.Degenerate.0.SSet.unique_nonDegenerate.isIso_factorThruImage_g", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Degenerate", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "_private.Mathlib.AlgebraicTopology.SimplicialSet.Degenerate.0.SSet.unique_nonDegenerate.mono_g", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Degenerate", "is_tactic_proof": true, "tactics": ["have", "rw", "infer_instance"], "tactic_count": 3}
{"name": "_private.Mathlib.AlgebraicTopology.SimplicialSet.Degenerate.0.SSet.unique_nonDegenerate.le", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Degenerate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.AlgebraicTopology.SimplicialSet.Degenerate.0.SSet.unique_nonDegenerate.g_eq_id", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Degenerate", "is_tactic_proof": true, "tactics": ["have", "apply"], "tactic_count": 2}
{"name": "SSet.unique_nonDegenerate_dim", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Degenerate", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "exact"], "tactic_count": 3}
{"name": "SSet.unique_nonDegenerate_simplex", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Degenerate", "is_tactic_proof": true, "tactics": ["obtain", "ext", "simpa"], "tactic_count": 3}
{"name": "SSet.unique_nonDegenerate_map", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Degenerate", "is_tactic_proof": true, "tactics": ["ext", "suffices", "obtain", "dsimp", "simpa", "obtain", "let", "have", "dsimp", "split_ifs", "rw", "apply", "have", "rintro", "by_contra", "suffices", "simpa", "exact"], "tactic_count": 18}
{"name": "SSet.Subcomplex.mem_degenerate_iff", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Degenerate", "is_tactic_proof": true, "tactics": ["rw", "constructor", "rintro", "exact", "obtain", "rintro", "refine", "have", "simpa"], "tactic_count": 9}
{"name": "SSet.Subcomplex.mem_nonDegenerate_iff", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Degenerate", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SSet.Subcomplex.le_iff_contains_nonDegenerate", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Degenerate", "is_tactic_proof": true, "tactics": ["constructor", "aesop", "rintro", "induction", "obtain", "simp", "subst", "rw", "exact"], "tactic_count": 9}
{"name": "SSet.Subcomplex.eq_top_iff_contains_nonDegenerate", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Degenerate", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "SSet.Subcomplex.degenerate_eq_top_iff", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Degenerate", "is_tactic_proof": true, "tactics": ["constructor", "intro", "ext", "simp", "intro", "simp", "intro", "simp", "ext", "simpa"], "tactic_count": 10}
{"name": "SSet.Subcomplex.iSup_ofSimplex_nonDegenerate_eq_top", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Degenerate", "is_tactic_proof": true, "tactics": ["rw", "intro", "simp", "exact"], "tactic_count": 4}
{"name": "SSet.degenerate_app_apply", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Degenerate", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "SSet.degenerate_le_preimage", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Degenerate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.image_degenerate_le", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Degenerate", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "SSet.degenerate_iff_of_isIso", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Degenerate", "is_tactic_proof": true, "tactics": ["constructor", "intro", "simpa", "exact"], "tactic_count": 4}
{"name": "SSet.nonDegenerate_iff_of_isIso", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Degenerate", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SSet.nonDegenerateEquivOfIso", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Degenerate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.degenerate_iff_of_mono", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Degenerate", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "SSet.nonDegenerate_iff_of_mono", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Degenerate", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SSet.HasDimensionLE", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Dimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.degenerate_eq_top_of_hasDimensionLT", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Dimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.nonDegenerate_eq_bot_of_hasDimensionLT", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Dimension", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SSet.dim_lt_of_nonDegenerate", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Dimension", "is_tactic_proof": true, "tactics": ["by_contra", "obtain", "simp"], "tactic_count": 3}
{"name": "SSet.dim_le_of_nonDegenerate", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Dimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.instHasDimensionLTHAddNat", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Dimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.instHasDimensionLTToSSet", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Dimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.le_iff_of_hasDimensionLT", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Dimension", "is_tactic_proof": true, "tactics": ["refine", "rw", "rintro", "exact"], "tactic_count": 4}
{"name": "SSet.Subcomplex.eq_top_iff_of_hasDimensionLT", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Dimension", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SSet.hasDimensionLT_of_mono", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Dimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.hasDimensionLT_of_le", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Dimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.hasDimensionLT_of_epi", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Dimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.hasDimensionLT_iff_of_iso", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Dimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.instHasDimensionLTToSSetRange", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Dimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.hasDimensionLT_iSup_iff", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Dimension", "is_tactic_proof": true, "tactics": ["simp", "aesop"], "tactic_count": 2}
{"name": "SSet.hasDimensionLT_subcomplex_top_iff", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Dimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.instHasDimensionLTToSSetBotSubcomplex", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Dimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.instFiniteElemObjOppositeSimplexCategoryOpMkNonDegenerateOfFinite", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.finite_of_hasDimensionLT", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.hasDimensionLT_of_finite", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Finite", "is_tactic_proof": true, "tactics": ["have", "let", "obtain", "by_cases", "obtain", "exact", "rw", "simp", "exact", "refine", "ext", "simp", "intro", "have", "dsimp", "lia"], "tactic_count": 16}
{"name": "SSet.instFiniteObjOppositeSimplexCategoryOfFinite", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Finite", "is_tactic_proof": true, "tactics": ["obtain", "induction", "let", "have", "obtain", "have", "exact", "exact"], "tactic_count": 8}
{"name": "SSet.instFiniteToSSet", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Finite", "is_tactic_proof": true, "tactics": ["obtain", "refine", "apply", "rintro", "rfl"], "tactic_count": 5}
{"name": "SSet.finite_of_mono", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Finite", "is_tactic_proof": true, "tactics": ["obtain", "have", "exact", "finite_of_hasDimensionLT"], "tactic_count": 4}
{"name": "SSet.finite_of_epi", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Finite", "is_tactic_proof": true, "tactics": ["obtain", "have", "refine", "have", "rw", "simp", "exact", "infer_instance"], "tactic_count": 8}
{"name": "SSet.finite_of_iso", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.finite_iff_of_iso", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.finite_subcomplex_top_iff", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.finite_range", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.finite_iSup_iff", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Finite", "is_tactic_proof": true, "tactics": ["refine", "refine", "intro", "obtain", "simp", "obtain", "rw", "exact"], "tactic_count": 8}
{"name": "SSet.iSup_range_eq_top_of_isColimit", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.FiniteColimits", "is_tactic_proof": true, "tactics": ["ext", "simp", "exact"], "tactic_count": 3}
{"name": "SSet.range_eq_iSup_of_isColimit", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.FiniteColimits", "is_tactic_proof": true, "tactics": ["conv_lhs", "simp_rw"], "tactic_count": 2}
{"name": "SSet.hasDimensionLT_of_isColimit", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.FiniteColimits", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "SSet.finite_of_isColimit", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.FiniteColimits", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "SSet.instFiniteInitial", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.FiniteColimits", "is_tactic_proof": true, "tactics": ["apply", "rintro"], "tactic_count": 2}
{"name": "SSet.instFiniteCoprod", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.FiniteColimits", "is_tactic_proof": true, "tactics": ["apply", "rintro"], "tactic_count": 2}
{"name": "SSet.instFiniteSigmaObjOfFinite", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.FiniteColimits", "is_tactic_proof": false, "tactics": ["have", "obtain", "exact", "exact"], "tactic_count": 4}
{"name": "SSet.range_eq_iSup_sigma_ι", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.FiniteColimits", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp", "intro", "exact", "simp", "intro", "exact"], "tactic_count": 8}
{"name": "SSet.iSup_subcomplexOfSimplex_prod_eq_top", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.FiniteProd", "is_tactic_proof": true, "tactics": ["ext", "simp", "have", "have", "simp", "obtain", "obtain", "exact"], "tactic_count": 8}
{"name": "SSet.Subcomplex.ofSimplexProd_eq_range", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.FiniteProd", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SSet.instHasDimensionLTTensorObjHAddNat", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.FiniteProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.instHasDimensionLETensorObjHAddNat", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.FiniteProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.instFiniteTensorObj", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.FiniteProd", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "exact"], "tactic_count": 3}
{"name": "SSet.finite_of_isPullback", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.FiniteProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.instFinitePullback", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.FiniteProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.Edge.tensor", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HoFunctorMonoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.Edge.tensor_surjective", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HoFunctorMonoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.Edge.id_tensor_id", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HoFunctorMonoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.Edge.map_tensorHom", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HoFunctorMonoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.Edge.map_whiskerRight", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HoFunctorMonoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.Edge.map_whiskerLeft", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HoFunctorMonoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.Edge.map_associator_hom", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HoFunctorMonoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.Edge.map_fst", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HoFunctorMonoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.Edge.map_snd", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HoFunctorMonoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.Edge.CompStruct.tensor", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HoFunctorMonoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.HomotopyCategory.instUniqueObjOppositeTruncatedTensorUnit", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HoFunctorMonoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.HomotopyCategory.isoTerminal", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HoFunctorMonoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.HomotopyCategory.BinaryProduct.square", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HoFunctorMonoidal", "is_tactic_proof": true, "tactics": ["rw", "homMk_comp_homMk"], "tactic_count": 2}
{"name": "SSet.Truncated.HomotopyCategory.BinaryProduct.functor", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HoFunctorMonoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.HomotopyCategory.BinaryProduct.functor_obj", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HoFunctorMonoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.HomotopyCategory.BinaryProduct.functor_map", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HoFunctorMonoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.HomotopyCategory.BinaryProduct.curriedInverse", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HoFunctorMonoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.HomotopyCategory.BinaryProduct.inverse", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HoFunctorMonoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.HomotopyCategory.BinaryProduct.inverse_obj", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HoFunctorMonoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.HomotopyCategory.BinaryProduct.inverse_map_mkHom_homMk_id", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HoFunctorMonoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.HomotopyCategory.BinaryProduct.inverse_map_mkHom_id_homMk", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HoFunctorMonoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.HomotopyCategory.BinaryProduct.inverse_map_mkHom_homMk_homMk", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HoFunctorMonoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.HomotopyCategory.BinaryProduct.functorCompInverseIso", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HoFunctorMonoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.HomotopyCategory.BinaryProduct.functorCompInverseIso_hom_app", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HoFunctorMonoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.HomotopyCategory.BinaryProduct.functorCompInverseIso_inv_app", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HoFunctorMonoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.HomotopyCategory.BinaryProduct.inverseCompFunctorIso", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HoFunctorMonoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.HomotopyCategory.BinaryProduct.inverseCompFunctorIso_hom_app", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HoFunctorMonoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.HomotopyCategory.BinaryProduct.inverseCompFunctorIso_inv_app", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HoFunctorMonoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.HomotopyCategory.BinaryProduct.functor_comp_inverse", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HoFunctorMonoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.HomotopyCategory.BinaryProduct.inverse_comp_functor", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HoFunctorMonoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.HomotopyCategory.BinaryProduct.equivalence", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HoFunctorMonoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.HomotopyCategory.BinaryProduct.iso", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HoFunctorMonoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.HomotopyCategory.BinaryProduct.mapHomotopyCategoryProdIdCompInverseIso", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HoFunctorMonoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.HomotopyCategory.BinaryProduct.idProdMapHomotopyCategoryCompInverseIso", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HoFunctorMonoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.HomotopyCategory.BinaryProduct.mapHomotopyCategory_prod_id_comp_inverse", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HoFunctorMonoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.HomotopyCategory.BinaryProduct.id_prod_mapHomotopyCategory_comp_inverse", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HoFunctorMonoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.HomotopyCategory.BinaryProduct.inverseCompMapHomotopyCategoryFstIso", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HoFunctorMonoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.HomotopyCategory.BinaryProduct.inverseCompMapHomotopyCategorySndIso", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HoFunctorMonoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.HomotopyCategory.BinaryProduct.inverse_comp_mapHomotopyCategory_fst", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HoFunctorMonoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.HomotopyCategory.BinaryProduct.inverse_comp_mapHomotopyCategory_snd", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HoFunctorMonoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.HomotopyCategory.BinaryProduct.left_unitality", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HoFunctorMonoidal", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "SSet.Truncated.HomotopyCategory.BinaryProduct.right_unitality", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HoFunctorMonoidal", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "SSet.Truncated.HomotopyCategory.BinaryProduct.associativity'Iso", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HoFunctorMonoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.HomotopyCategory.BinaryProduct.associativity'Iso_hom_app", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HoFunctorMonoidal", "is_tactic_proof": true, "tactics": ["change", "rw", "rfl"], "tactic_count": 3}
{"name": "SSet.Truncated.HomotopyCategory.BinaryProduct.associativityIso", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HoFunctorMonoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.HomotopyCategory.BinaryProduct.associativityIso_hom_app", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HoFunctorMonoidal", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "dsimp", "rw"], "tactic_count": 4}
{"name": "SSet.Truncated.HomotopyCategory.BinaryProduct.associativity", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HoFunctorMonoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.instMonoidalOfNatNatCatHoFunctor₂", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HoFunctorMonoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.hoFunctor.monoidal", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HoFunctorMonoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.hoFunctor.unitHomEquiv", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HoFunctorMonoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.hoFunctor.unitHomEquiv_eq", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HoFunctorMonoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.OneTruncation₂", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.OneTruncation₂.reflQuiver", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.OneTruncation₂.hom_ext", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.OneTruncation₂.id_edge", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "SSet.OneTruncation₂.map", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.oneTruncation₂", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.OneTruncation₂.homOfEq_edge", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": true, "tactics": ["subst", "rfl"], "tactic_count": 2}
{"name": "SSet.OneTruncation₂.nerveEquiv", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.OneTruncation₂.nerveHomEquiv", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.OneTruncation₂.nerveHomEquiv_apply", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.OneTruncation₂.nerveHomEquiv_id", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.OneTruncation₂.ofNerve₂", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.OneTruncation₂.nerve_hom_ext", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.OneTruncation₂.ofNerve₂.natIso", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat.0.SSet.map_map_of_eq", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": true, "tactics": ["rintro", "simp"], "tactic_count": 2}
{"name": "SSet.Truncated.ι0₂", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.ι1₂", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.ι2₂", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.ev0₂", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.ev1₂", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.ev2₂", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.δ0₂", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.δ1₂", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.δ2₂", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.ev12₂", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.ev02₂", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.ev01₂", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.OneTruncation₂.HoRel₂", "kind": "inductive", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.OneTruncation₂.HoRel₂.mk", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.HomotopyCategory", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.HomotopyCategory.quotientFunctor", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.HomotopyCategory.instFullFreeReflOneTruncation₂QuotientFunctor", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.HomotopyCategory.mk", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.HomotopyCategory.mk_surjective", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "SSet.Truncated.HomotopyCategory.ext", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "obtain", "rfl"], "tactic_count": 4}
{"name": "SSet.Truncated.HomotopyCategory.cases_on", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "SSet.Truncated.HomotopyCategory.homMk", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.HomotopyCategory.congr_arrowMk_homMk", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "obtain", "rfl"], "tactic_count": 4}
{"name": "SSet.Truncated.HomotopyCategory.homMk_id", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "SSet.Truncated.HomotopyCategory.homMk_comp_homMk", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "SSet.Truncated.HomotopyCategory.morphismPropertyHomMk", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.HomotopyCategory.morphismPropertyHomMk_of_edge", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "exact"], "tactic_count": 3}
{"name": "SSet.Truncated.HomotopyCategory.morphismPropertyHomMk_eq_strictMap", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": true, "tactics": ["ext", "constructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 6}
{"name": "SSet.Truncated.HomotopyCategory.multiplicativeClosure_morphismPropertyHomMk", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.HomotopyCategory.morphismProperty_eq_top", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.HomotopyCategory.lift", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.HomotopyCategory.lift_obj_mk", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.HomotopyCategory.lift_map_homMk", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.HomotopyCategory.mkNatTrans", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.HomotopyCategory.mkNatTrans_app_mk", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.HomotopyCategory.mkNatIso", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.HomotopyCategory.mkNatIso_hom_app_mk", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.HomotopyCategory.mkNatIso_inv_app_mk", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.HomotopyCategory.functor_ext", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.HomotopyCategory.instSubsingletonOfObjOppositeTruncatedOfNatNatOpMkSimplexCategoryLeLenMk", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.HomotopyCategory.subsingleton_hom", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.HomotopyCategory.instUniqueOfObjOppositeTruncatedOfNatNatOpMkSimplexCategoryLeLenMk", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.HomotopyCategory.isTerminal", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.mapHomotopyCategory", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.mapHomotopyCategory_obj", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.mapHomotopyCategory_homMk", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.hoFunctor₂", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.hoFunctor₂_naturality", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.HomotopyCategory.lift_unique'", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.hoFunctor", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.hoFunctor.obj.equiv", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.instUniqueOneTruncation₂DeltaZero", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.instUniqueHomOneTruncation₂ObjTruncatedOfNatNatTruncationSimplexCategoryStdSimplexMk", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.instUniqueHomotopyCategoryObjTruncatedOfNatNatTruncationSimplexCategoryStdSimplexMk", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.instIsDiscreteHomotopyCategoryObjTruncatedOfNatNatTruncationSimplexCategoryStdSimplexMk", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.isTerminalHoFunctorDeltaZero", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.hoFunctor.terminalIso", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.hoFunctor.preservesTerminal", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.hoFunctor.preservesTerminal'", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.horn", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Horn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Simplicial.termΛ[_,_]", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Horn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Simplicial._aux_Mathlib_AlgebraicTopology_SimplicialSet_Horn___macroRules_Simplicial_termΛ[_,_]_1", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Horn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Simplicial._aux_Mathlib_AlgebraicTopology_SimplicialSet_Horn___delab_app_Simplicial_termΛ[_,_]_1", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Horn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.horn_eq_iSup", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Horn", "is_tactic_proof": true, "tactics": ["ext", "simp", "rfl"], "tactic_count": 3}
{"name": "SSet.face_le_horn", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Horn", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SSet.horn_obj_zero", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Horn", "is_tactic_proof": true, "tactics": ["ext", "simp", "let", "have", "have", "simp", "have", "lia", "rw", "obtain", "simp", "refine", "fin_cases", "exact"], "tactic_count": 14}
{"name": "SSet.horn.const", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Horn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.horn.const_val_apply", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Horn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.horn.edge", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Horn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.horn.edge₃", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Horn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.horn.primitiveEdge", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Horn", "is_tactic_proof": true, "tactics": ["refine", "simp", "simp", "obtain", "revert", "exact"], "tactic_count": 6}
{"name": "SSet.horn.primitiveTriangle", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Horn", "is_tactic_proof": true, "tactics": ["refine", "simp", "simp", "simp", "have", "obtain", "by_cases", "subst", "have", "rw", "simp", "or_self,", "simp", "lia", "have", "rw", "simp", "and_false,", "obtain", "rw", "obtain", "simp", "refine", "fin_cases", "exact", "exact", "exact"], "tactic_count": 27}
{"name": "SSet.horn.face", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Horn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.horn.hom_ext", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Horn", "is_tactic_proof": true, "tactics": ["rw", "apply", "simp", "intro", "exact"], "tactic_count": 5}
{"name": "SSet.horn.faceι", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Horn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.horn.faceι_ι", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Horn", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SSet.horn.ι", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Horn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.horn.yonedaEquiv_ι", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Horn", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SSet.horn.ι_ι", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Horn", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SSet.horn.faceSingletonComplIso_inv_ι", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Horn", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "SSet.horn₂₀.sq", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HornColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.horn₂₀.ι₀₁", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HornColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.horn₂₀.ι₀₂", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HornColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.horn₂₀.isPushout", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HornColimits", "is_tactic_proof": false, "tactics": ["fapply", "sq.", "all_goals"], "tactic_count": 3}
{"name": "SSet.horn₂₁.sq", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HornColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.horn₂₁.ι₀₁", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HornColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.horn₂₁.ι₁₂", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HornColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.horn₂₁.isPushout", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HornColimits", "is_tactic_proof": false, "tactics": ["apply", "sq.", "all_goals"], "tactic_count": 3}
{"name": "SSet.horn₂₂.sq", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HornColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.horn₂₂.ι₀₂", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HornColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.horn₂₂.ι₁₂", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HornColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.horn₂₂.isPushout", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HornColimits", "is_tactic_proof": false, "tactics": ["fapply", "sq.", "all_goals"], "tactic_count": 3}
{"name": "SSet.horn.multicoequalizerDiagram", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HornColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.horn.isColimit", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HornColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.horn₃₁.ι₀", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HornColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.horn₃₁.ι₂", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HornColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.horn₃₁.ι₃", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HornColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.horn₃₁.desc.multicofork", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HornColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.horn₃₁.desc.multicofork_π_zero", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HornColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.horn₃₁.desc.multicofork_π_two", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HornColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.horn₃₁.desc.multicofork_π_three", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HornColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.horn₃₁.desc", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HornColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.horn₃₁.ι₀_desc", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HornColimits", "is_tactic_proof": false, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SSet.horn₃₁.ι₂_desc", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HornColimits", "is_tactic_proof": false, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SSet.horn₃₁.ι₃_desc", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HornColimits", "is_tactic_proof": false, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SSet.horn₃₁.exists_desc", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HornColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.horn₃₂.ι₀", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HornColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.horn₃₂.ι₁", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HornColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.horn₃₂.ι₃", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HornColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.horn₃₂.desc.multicofork", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HornColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.horn₃₂.desc.multicofork_π_zero", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HornColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.horn₃₂.desc.multicofork_π_one", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HornColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.horn₃₂.desc.multicofork_π_three", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HornColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.horn₃₂.desc", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HornColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.horn₃₂.ι₀_desc", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HornColimits", "is_tactic_proof": false, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SSet.horn₃₂.ι₁_desc", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HornColimits", "is_tactic_proof": false, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SSet.horn₃₂.ι₃_desc", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HornColimits", "is_tactic_proof": false, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SSet.horn₃₂.exists_desc", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.HornColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.KanComplex", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.SimplicialSet.KanComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.KanComplex.hornFilling", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.KanComplex", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "SSet.PtSimplex", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.SimplicialSet.KanComplex.MulStruct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.instCartesianMonoidalCategory", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.instMonoidalClosed", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.leftUnitor_hom_app_apply", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.leftUnitor_inv_app_apply", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.rightUnitor_hom_app_apply", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.rightUnitor_inv_app_apply", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.tensorHom_app_apply", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.whiskerLeft_app_apply", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.whiskerRight_app_apply", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.associator_hom_app_apply", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.associator_inv_app_apply", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.unitHomEquiv", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.stdSimplex.isTerminalObj₀", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.stdSimplex.ext₀", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.instFiniteObjOppositeSimplexCategoryTensorObj", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.instFiniteTensorUnit", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.instHasDimensionLETensorUnitOfNatNat", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.prod", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.prod_monotone", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.range_tensorHom", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Monoidal", "is_tactic_proof": true, "tactics": ["ext", "constructor", "rintro", "rw", "exact", "rintro", "exact"], "tactic_count": 7}
{"name": "SSet.ι₀", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.ι₀_comp", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.ι₀_fst", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.ι₀_snd", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.ι₀_app_fst", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.ι₁", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.ι₁_fst", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.ι₁_snd", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.ι₁_comp", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.ι₁_app_fst", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.instCartesianMonoidalCategory", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.instMonoidalClosed", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.instMonoidalTruncation", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.tensor_map_apply_fst", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.tensor_map_apply_snd", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.instIsStableUnderCoproductsMonomorphismsOfHasCoproductsType", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Monomorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.instIsStableUnderCobaseChangeMonomorphisms", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Monomorphisms", "is_tactic_proof": true, "tactics": ["change", "rw", "infer_instance"], "tactic_count": 3}
{"name": "SSet.instIsStableUnderFilteredColimitsMonomorphisms", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Monomorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet._example", "kind": "example", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Monomorphisms", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "CategoryTheory.nerve", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Nerve", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instCategoryObjOppositeSimplexCategoryNerve", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Nerve", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.nerveMap", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Nerve", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.nerveMap_app_mk₀", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Nerve", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.nerveMap_app_mk₁", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Nerve", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.nerveFunctor", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Nerve", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.nerveEquiv", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Nerve", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.nerve.representableBy", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Nerve", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.nerve.δ_obj", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Nerve", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.nerve.σ_obj", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Nerve", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.nerve.δ₀_eq", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Nerve", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.nerve.σ₀_mk₀_eq", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Nerve", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.nerve.δ₂_mk₂_eq", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Nerve", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.nerve.δ₀_mk₂_eq", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Nerve", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.nerve.δ₁_mk₂_eq", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Nerve", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.nerve.ext_of_isThin", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Nerve", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.nerve.left_edge", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Nerve", "is_tactic_proof": true, "tactics": ["simp", "rfl"], "tactic_count": 2}
{"name": "CategoryTheory.nerve.right_edge", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Nerve", "is_tactic_proof": true, "tactics": ["simp", "rfl"], "tactic_count": 2}
{"name": "CategoryTheory.nerve.δ₂_two", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Nerve", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.nerve.δ₂_zero", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Nerve", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.nerve.homEquiv", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Nerve", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.nerve.mk₁_homEquiv_apply", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Nerve", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.nerve.edgeMk", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Nerve", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.nerve.edgeMk_edge", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Nerve", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.nerve.edgeMk_id", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Nerve", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.nerve.edgeMk_surjective", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Nerve", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.nerve.homEquiv_edgeMk", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Nerve", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.nerve.homEquiv_id", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Nerve", "is_tactic_proof": true, "tactics": ["obtain", "dsimp", "cat_disch"], "tactic_count": 3}
{"name": "CategoryTheory.nerve.nonempty_compStruct_iff", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Nerve", "is_tactic_proof": false, "tactics": ["let", "refine", "rw", "apply", "convert_to", "exact", "exact", "have", "have", "have", "have", "simp", "exact", "congr_arg"], "tactic_count": 14}
{"name": "CategoryTheory.nerve.homEquiv_comp", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Nerve", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "obtain", "obtain", "obtain", "obtain", "convert"], "tactic_count": 7}
{"name": "CategoryTheory.nerve.σ_zero_nerveEquiv_symm", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Nerve", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.nerve.homEquiv_edgeMk_map_nerveMap", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Nerve", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SSet.Truncated.liftOfStrictSegal.f₂", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.liftOfStrictSegal.spineEquiv_f₂_arrow_zero", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SSet.Truncated.liftOfStrictSegal.spineEquiv_f₂_arrow_one", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SSet.Truncated.liftOfStrictSegal.hδ'₀", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SSet.Truncated.liftOfStrictSegal.hδ'₂", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SSet.Truncated.liftOfStrictSegal.hδ'₁", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.liftOfStrictSegal.hσ'₀", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction", "is_tactic_proof": true, "tactics": ["apply", "ext", "fin_cases", "dsimp", "rw", "dsimp", "rw", "dsimp", "rw", "simp"], "tactic_count": 10}
{"name": "SSet.Truncated.liftOfStrictSegal.hσ'₁", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction", "is_tactic_proof": true, "tactics": ["apply", "ext", "fin_cases", "dsimp", "rw", "simp", "dsimp", "rw", "dsimp", "rw"], "tactic_count": 10}
{"name": "SSet.Truncated.liftOfStrictSegal.app", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction", "is_tactic_proof": true, "tactics": ["obtain", "induction"], "tactic_count": 2}
{"name": "SSet.Truncated.liftOfStrictSegal.naturalityProperty", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.liftOfStrictSegal.naturalityProperty_eq_top", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction", "is_tactic_proof": true, "tactics": ["refine", "obtain", "fin_cases", "ext", "ext", "fin_cases", "ext", "ext", "ext", "lia", "obtain", "fin_cases", "ext", "fin_cases", "ext", "ext", "lia"], "tactic_count": 17}
{"name": "SSet.Truncated.liftOfStrictSegal", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.liftOfStrictSegal_app_0", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.liftOfStrictSegal_app_1", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.HomotopyCategory.descOfTruncation", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.HomotopyCategory.descOfTruncation_obj_mk", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.HomotopyCategory.descOfTruncation_map_homMk", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.HomotopyCategory.descOfTruncation_comp", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.HomotopyCategory.homToNerveMk", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.HomotopyCategory.homToNerveMk_app_zero", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.HomotopyCategory.homToNerveMk_app_one", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.HomotopyCategory.homToNerveMk_app_edge", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SSet.Truncated.HomotopyCategory.functorEquiv", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.HomotopyCategory.homToNerveMk_comp", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.nerve₂Adj", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.nerve.functorOfNerveMap", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.nerve.nerveFunctor₂_map_functorOfNerveMap", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.nerve.functorOfNerveMap_nerveFunctor₂_map", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.nerve.fullyFaithfulNerveFunctor₂", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.nerve.instFaithfulCatTruncatedOfNatNatNerveFunctor₂", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.nerve.instFullCatTruncatedOfNatNatNerveFunctor₂", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.nerve.instReflectiveTruncatedOfNatNatCatNerveFunctor₂", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.nerveAdjunction", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.nerveFunctor.faithful", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.nerveFunctor.full", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.nerveFunctor.fullyfaithful", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.nerveAdjunction.isIso_counit", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.nerveFunctorCompHoFunctorIso", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instReflectiveSSetCatNerveFunctor", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instIsIsoSSetProdComparisonCatCompNerveFunctorHoFunctorOf", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction", "is_tactic_proof": false, "tactics": ["let", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.hoFunctor.instIsLeftAdjointSSetCatHoFunctor", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.hoFunctor.instIsIsoCatProdComparisonSSetHoFunctorNerve", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction", "is_tactic_proof": false, "tactics": ["have", "have", "exact", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.hoFunctor.isIso_prodComparison_stdSimplex", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.hoFunctor.isIso_prodComparison_of_stdSimplex", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction", "is_tactic_proof": false, "tactics": ["have", "rw", "exact", "exact", "isIso_app_coconePt_of_preservesColimit"], "tactic_count": 5}
{"name": "CategoryTheory.hoFunctor.isIso_prodComparison", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.hoFunctor.preservesBinaryProduct", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.hoFunctor.preservesBinaryProducts", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.hoFunctor.preservesFiniteProducts", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialOrder.mem_range_nerve_σ_iff", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NerveNondegenerate", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "simp", "intro", "refine", "ext", "rw", "by_cases", "obtain", "rw", "simp", "grind"], "tactic_count": 12}
{"name": "PartialOrder.mem_nerve_degenerate_of_eq", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NerveNondegenerate", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "PartialOrder.mem_nerve_nonDegenerate_iff_strictMono", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NerveNondegenerate", "is_tactic_proof": true, "tactics": ["obtain", "simpa", "rw", "simp", "apply", "intro", "have", "grind"], "tactic_count": 8}
{"name": "PartialOrder.mem_nerve_nonDegenerate_iff_injective", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NerveNondegenerate", "is_tactic_proof": true, "tactics": ["rw", "refine", "obtain", "exact", "exact"], "tactic_count": 5}
{"name": "SSet.N.mk'_surjective", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NonDegenerateSimplices", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.N.mk", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NonDegenerateSimplices", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.N.mk_surjective", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NonDegenerateSimplices", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.N.ext_iff", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NonDegenerateSimplices", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "SSet.N.instPreorder", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NonDegenerateSimplices", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.N.le_iff", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NonDegenerateSimplices", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.N.le_iff_exists_mono", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NonDegenerateSimplices", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "SSet.N.dim_le_of_le", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NonDegenerateSimplices", "is_tactic_proof": true, "tactics": ["rw", "obtain", "exact"], "tactic_count": 3}
{"name": "SSet.N.dim_lt_of_lt", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NonDegenerateSimplices", "is_tactic_proof": true, "tactics": ["obtain", "exact", "obtain", "obtain", "obtain", "obtain", "obtain", "obtain", "simp"], "tactic_count": 9}
{"name": "SSet.N.instPartialOrder", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NonDegenerateSimplices", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.N.subcomplex_injective", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NonDegenerateSimplices", "is_tactic_proof": true, "tactics": ["apply", "all_goals"], "tactic_count": 2}
{"name": "SSet.N.subcomplex_injective_iff", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NonDegenerateSimplices", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.N.eq_iff", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NonDegenerateSimplices", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.N.cast", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NonDegenerateSimplices", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.N.cast_eq_self", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NonDegenerateSimplices", "is_tactic_proof": true, "tactics": ["subst", "rfl"], "tactic_count": 2}
{"name": "SSet.N.iSup_subcomplex_eq_top", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NonDegenerateSimplices", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.orderEmbeddingN", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NonDegenerateSimplices", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.S.existsUnique_n", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NonDegenerateSimplices", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.S.toN", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NonDegenerateSimplices", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.S.subcomplex_toN", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NonDegenerateSimplices", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.S.toN_eq_iff", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NonDegenerateSimplices", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.N.mk'_surjective", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NonDegenerateSimplicesSubcomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.N.mk", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NonDegenerateSimplicesSubcomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.N.mk_surjective", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NonDegenerateSimplicesSubcomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.N.ext_iff", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NonDegenerateSimplicesSubcomplex", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "SSet.Subcomplex.N.instPartialOrder", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NonDegenerateSimplicesSubcomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.N.le_iff", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NonDegenerateSimplicesSubcomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.N.cast", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NonDegenerateSimplicesSubcomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.N.cast_eq_self", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.NonDegenerateSimplicesSubcomplex", "is_tactic_proof": true, "tactics": ["subst", "rfl"], "tactic_count": 2}
{"name": "SSet.opFunctor", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Op", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.op", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Op", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.opObjEquiv", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Op", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.opFunctor_map", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Op", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.op_map", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Op", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.op_δ", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Op", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SSet.op_σ", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Op", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SSet.opFunctorCompOpFunctorIso", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Op", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.opEquivalence", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Op", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.Path", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.Path.vertex", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.Path.arrow", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.Path.arrow_src", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.Path.arrow_tgt", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.Path.ext", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.Path.ext'", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Path", "is_tactic_proof": true, "tactics": ["ext", "rcases", "rw", "simp", "rw", "exact"], "tactic_count": 6}
{"name": "SSet.Truncated.Path.mk₂", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.Path.map", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.Path.map_vertex", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.Path.map_arrow", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.Path.map_interval", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.trunc_spine", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.spine_vertex", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.spine_arrow", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.spine_map_vertex", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Path", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "SSet.Truncated.spine_map_subinterval", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Path", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "rw", "dsimp", "rw"], "tactic_count": 5}
{"name": "SSet.Path", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Path.vertex", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Path.arrow", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Path.congr_vertex", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Path", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SSet.Path.congr_arrow", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Path", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SSet.Path.arrow_src", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Path.arrow_tgt", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Path.ext", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Path.ext'", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Path.ext₀", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Path", "is_tactic_proof": true, "tactics": ["ext", "fin_cases", "fin_cases"], "tactic_count": 3}
{"name": "SSet.Path.map", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Path.map_vertex", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Path.map_arrow", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Path.map_interval", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.spine", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.spine_vertex", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.spine_arrow", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.spine_δ₀", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Path", "is_tactic_proof": true, "tactics": ["obtain", "ext", "simp", "ext", "dsimp", "rw", "symm", "exact"], "tactic_count": 8}
{"name": "SSet.truncation_spine", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.spine_map_vertex", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.spine_map_subinterval", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.stdSimplex.spineId", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.stdSimplex.spineId_vertex", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.stdSimplex.spineId_arrow_apply_zero", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.stdSimplex.spineId_arrow_apply_one", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.liftPath", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.map_ι_liftPath", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.horn.spineId", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.horn.spineId_map_hornInclusion", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Finite.instIsFinitelyPresentableObjSimplexCategoryStdSimplex", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Presentable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Finite.exists_epi_from_isCardinalPresentable", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Presentable", "is_tactic_proof": true, "tactics": ["refine", "apply", "exact", "rintro", "dsimp", "infer_instance", "simp"], "tactic_count": 7}
{"name": "SSet.Finite.instIsFinitelyPresentable", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Presentable", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "have", "have", "apply", "isCardinalPresentable_of_isColimit", "exact", "rintro"], "tactic_count": 8}
{"name": "SSet.prodStdSimplex.objEquiv", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.ProdStdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.prodStdSimplex.objEquiv_apply_fst", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.ProdStdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.prodStdSimplex.objEquiv_apply_snd", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.ProdStdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.prodStdSimplex.objEquiv_naturality", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.ProdStdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.prodStdSimplex.objEquiv_map_apply", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.ProdStdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.prodStdSimplex.objEquiv_δ_apply", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.ProdStdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.prodStdSimplex.isoNerve", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.ProdStdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.prodStdSimplex.nonDegenerate_iff_injective_objEquiv", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.ProdStdSimplex", "is_tactic_proof": false, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "SSet.prodStdSimplex.nonDegenerate_iff_strictMono_objEquiv", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.ProdStdSimplex", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "SSet.prodStdSimplex.orderHomOfSimplex", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.ProdStdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.prodStdSimplex.strictMono_orderHomOfSimplex_iff", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.ProdStdSimplex", "is_tactic_proof": false, "tactics": ["have", "obtain", "rw", "lia", "simp", "exact"], "tactic_count": 6}
{"name": "SSet.prodStdSimplex.instHasDimensionLETensorObjObjSimplexCategoryStdSimplexMkHAddNat", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.ProdStdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.prodStdSimplex.instFiniteTensorObjObjSimplexCategoryStdSimplexMk", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.ProdStdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.instIsRegularEpiCategory", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.RegularEpi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.RelativeMorphism.const", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.RelativeMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.RelativeMorphism.ofSimplex₀", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.RelativeMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.RelativeMorphism.map_eq_of_mem", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.RelativeMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.RelativeMorphism.map_coe", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.RelativeMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.RelativeMorphism.image_le", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.RelativeMorphism", "is_tactic_proof": true, "tactics": ["rintro", "have", "aesop"], "tactic_count": 3}
{"name": "SSet.RelativeMorphism.le_preimage", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.RelativeMorphism", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "SSet.RelativeMorphism.Homotopy.ofEq", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.RelativeMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.RelativeMorphism.Homotopy.refl", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.RelativeMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.RelativeMorphism.HomotopyClass", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.RelativeMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.RelativeMorphism.homotopyClass", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.RelativeMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.RelativeMorphism.Homotopy.eq", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.RelativeMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.RelativeMorphism.HomotopyClass.eq_homotopyClass", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.RelativeMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.RelativeMorphism.comp", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.RelativeMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.RelativeMorphism.Homotopy.postcomp", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.RelativeMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.RelativeMorphism.Homotopy.precomp", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.RelativeMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.RelativeMorphism.HomotopyClass.postcomp", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.RelativeMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.RelativeMorphism.postcomp_homotopyClass", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.RelativeMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.RelativeMorphism.HomotopyClass.precomp", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.RelativeMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.RelativeMorphism.precomp_homotopyClass", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.RelativeMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.S.mk_surjective", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Simplices", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.S.map", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Simplices", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.S.dim_eq_of_eq", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Simplices", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.S.dim_eq_of_mk_eq", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Simplices", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.S.cast", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Simplices", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.S.cast_eq_self", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Simplices", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "rfl"], "tactic_count": 3}
{"name": "SSet.S.cast_simplex_rfl", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Simplices", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.S.ext_iff'", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Simplices", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.S.ext_iff", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Simplices", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SSet.S.subcomplex", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Simplices", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.S.instPreorder", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Simplices", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.S.le_def", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Simplices", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.S.le_iff", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Simplices", "is_tactic_proof": true, "tactics": ["rw", "tauto"], "tactic_count": 2}
{"name": "SSet.S.mk_map_le", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Simplices", "is_tactic_proof": true, "tactics": ["rw", "tauto"], "tactic_count": 2}
{"name": "SSet.S.mk_map_eq_iff_of_mono", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Simplices", "is_tactic_proof": true, "tactics": ["constructor", "intro", "obtain", "obtain", "infer_instance", "intro", "obtain", "obtain", "simp"], "tactic_count": 9}
{"name": "SSet.S.equivElements", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Simplices", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.S.le_iff_nonempty_hom", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Simplices", "is_tactic_proof": true, "tactics": ["rw", "constructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 6}
{"name": "SSet.skeleton", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Skeleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.skeleton_obj_eq_top", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Skeleton", "is_tactic_proof": true, "tactics": ["rw", "intro", "exact"], "tactic_count": 3}
{"name": "SSet.ofSimplex_le_skeleton", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Skeleton", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "SSet.mem_skeleton_obj_iff_of_nonDegenerate", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Skeleton", "is_tactic_proof": true, "tactics": ["refine", "obtain", "simp", "obtain", "have", "have", "lia"], "tactic_count": 7}
{"name": "SSet.skeleton_zero", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Skeleton", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SSet.iSup_skeleton", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Skeleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.skeleton_succ", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Skeleton", "is_tactic_proof": true, "tactics": ["apply", "conv_lhs", "simp", "rintro", "rw", "obtain", "exact", "exact", "simp", "constructor", "exact", "intro", "apply"], "tactic_count": 13}
{"name": "SSet.skeletonOfMono", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Skeleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.skeleton_le_skeletonOfMono", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Skeleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.skeletonOfMono_zero", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Skeleton", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SSet.iSup_skeletonOfMono", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Skeleton", "is_tactic_proof": true, "tactics": ["apply", "rw", "intro", "exact"], "tactic_count": 4}
{"name": "SSet.mem_skeletonOfMono_obj_iff_of_nonDegenerate", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Skeleton", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SSet.skeletonOfMono_obj_eq_top", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Skeleton", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SSet.skeletonOfMono_succ", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Skeleton", "is_tactic_proof": true, "tactics": ["dsimp", "apply", "simp", "refine", "by_cases", "exact", "exact", "simp", "exact"], "tactic_count": 9}
{"name": "SSet.stdSimplex", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Simplicial.termΔ[_]", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Simplicial._aux_Mathlib_AlgebraicTopology_SimplicialSet_StdSimplex___macroRules_Simplicial_termΔ[_]_1", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Simplicial._aux_Mathlib_AlgebraicTopology_SimplicialSet_StdSimplex___delab_app_Simplicial_termΔ[_]_1", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.instInhabited", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.instInhabitedTruncated", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.stdSimplex.map_id", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.stdSimplex.objEquiv", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.stdSimplex.instDecidableEqObjOppositeSimplexCategory", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.stdSimplex.instFunLikeObjOppositeSimplexCategoryMkOpFinHAddNatOfNat", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.stdSimplex.monotone_apply", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.stdSimplex.ext", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.stdSimplex.objEquiv_toOrderHom_apply", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.stdSimplex.objEquiv_symm_comp", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.stdSimplex.objEquiv_symm_apply", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.stdSimplex.objMk", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.stdSimplex.objMk_apply", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.stdSimplex.asOrderHom", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.stdSimplex.map_apply", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "SSet.yonedaEquiv", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.stdSimplex.instDecidableEqHomObjSimplexCategoryOfOppositeOp", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.stdSimplex.yonedaEquiv_map", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.stdSimplex.const", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.stdSimplex.const_down_toOrderHom", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.stdSimplex.obj₀Equiv", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.stdSimplex.edge", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex", "is_tactic_proof": true, "tactics": ["refine", "rw", "simp", "apply"], "tactic_count": 4}
{"name": "SSet.stdSimplex.coe_edge_down_toOrderHom", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.stdSimplex.triangle", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex", "is_tactic_proof": true, "tactics": ["refine", "rw", "simp", "dsimp", "simp"], "tactic_count": 5}
{"name": "SSet.stdSimplex.coe_triangle_down_toOrderHom", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.stdSimplex.face", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.stdSimplex.mem_face_iff", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SSet.stdSimplex.face_inter_face", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SSet.yonedaEquiv_comp", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.range_eq_ofSimplex", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.yonedaEquiv_coe", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "SSet.stdSimplex.obj₀Equiv_symm_mem_face_iff", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.stdSimplex.face_le_face_iff", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex", "is_tactic_proof": true, "tactics": ["refine", "simp", "exact"], "tactic_count": 3}
{"name": "SSet.stdSimplex.face_eq_ofSimplex", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex", "is_tactic_proof": true, "tactics": ["apply", "rintro", "induction", "rw", "let", "monotone", "refine", "ext", "simpa", "simp"], "tactic_count": 10}
{"name": "SSet.stdSimplex.faceRepresentableBy", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.stdSimplex.isoOfRepresentableBy", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.stdSimplex.ofSimplex_yonedaEquiv_δ", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.stdSimplex.range_δ", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SSet.stdSimplex.isoNerve", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.stdSimplex.isoNerve_hom_app_apply", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.stdSimplex.isoNerve_inv_app_apply", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.stdSimplex.mem_nonDegenerate_iff_strictMono", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "SSet.stdSimplex.mem_nonDegenerate_iff_mono", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "intro", "obtain", "exact", "simpa"], "tactic_count": 7}
{"name": "SSet.stdSimplex.objEquiv_symm_mem_nonDegenerate_iff_mono", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SSet.stdSimplex.nonDegenerateEquiv", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.stdSimplex.instHasDimensionLEObjSimplexCategoryMk", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.stdSimplex.finSuccAboveOrderIsoFinset", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.stdSimplex.face_singleton_compl", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.stdSimplex.faceSingletonComplIso", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.stdSimplex.faceSingletonComplIso_hom_ι", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.stdSimplex.faceSingletonIso", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.stdSimplex.faceSingletonIso_zero_hom_comp_ι_eq_δ", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "SSet.stdSimplex.faceSingletonIso_one_hom_comp_ι_eq_δ", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "SSet.stdSimplex.facePairIso", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.stdSimplex.instFiniteObjOppositeSimplexCategory", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "SSet.stdSimplex.instFiniteObjSimplexCategory", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex", "is_tactic_proof": false, "tactics": ["induction", "exact"], "tactic_count": 2}
{"name": "SSet.stdSimplex.instFiniteToSSetOfSimplex", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex", "is_tactic_proof": true, "tactics": ["obtain", "rw", "infer_instance"], "tactic_count": 3}
{"name": "SSet.S1", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Augmented.stdSimplex", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.spine_injective", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.IsStrictSegal.ext", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.IsStrictSegal.hom_ext", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal", "is_tactic_proof": true, "tactics": ["ext", "induction", "obtain", "have", "dsimp", "simpa", "congr_arg", "exact"], "tactic_count": 8}
{"name": "SSet.Truncated.StrictSegal.ofIsStrictSegal", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.StrictSegal.spine_spineToSimplex_apply", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.StrictSegal.spineToSimplex_spine_apply", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.StrictSegal.spineEquiv", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.StrictSegal.spineInjective", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.StrictSegal.spineToDiagonal", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.StrictSegal.isStrictSegal", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Truncated.StrictSegal.spineToSimplex_vertex", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SSet.Truncated.StrictSegal.spineToSimplex_arrow", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SSet.Truncated.StrictSegal.spineToSimplex_interval", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal", "is_tactic_proof": true, "tactics": ["apply", "dsimp", "rw", "convert", "exact"], "tactic_count": 5}
{"name": "SSet.Truncated.StrictSegal.spineToSimplex_edge", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "SSet.Truncated.StrictSegal.spineToSimplex_map", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal", "is_tactic_proof": true, "tactics": ["apply", "ext", "dsimp", "rw", "simp"], "tactic_count": 5}
{"name": "SSet.Truncated.StrictSegal.spine_δ_vertex_lt", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal", "is_tactic_proof": false, "tactics": ["rw", "spineToSimplex_vertex]", "dsimp", "rw"], "tactic_count": 4}
{"name": "SSet.Truncated.StrictSegal.spine_δ_vertex_ge", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal", "is_tactic_proof": false, "tactics": ["rw", "spineToSimplex_vertex]", "dsimp", "rw"], "tactic_count": 4}
{"name": "SSet.Truncated.StrictSegal.spine_δ_arrow_lt", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SSet.Truncated.StrictSegal.spine_δ_arrow_gt", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SSet.Truncated.StrictSegal.spine_δ_arrow_eq", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SSet.StrictSegal.ofIsStrictSegal", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.StrictSegal.truncation", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.StrictSegal.instIsStrictSegalObjTruncatedHAddNatOfNatTruncationOfIsStrictSegal", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.StrictSegal.spine_spineToSimplex_apply", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.StrictSegal.spineToSimplex_spine_apply", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.StrictSegal.spineEquiv", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.StrictSegal.spineInjective", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.StrictSegal.isStrictSegal", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.StrictSegal.spineToSimplex_vertex", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SSet.StrictSegal.spineToSimplex_arrow", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SSet.StrictSegal.spineToDiagonal", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.StrictSegal.spineToSimplex_interval", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal", "is_tactic_proof": true, "tactics": ["apply", "dsimp", "rw"], "tactic_count": 3}
{"name": "SSet.StrictSegal.spineToSimplex_edge", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "SSet.StrictSegal.spineToSimplex_map", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal", "is_tactic_proof": true, "tactics": ["apply", "ext", "dsimp", "rw", "spineToSimplex_arrow,"], "tactic_count": 5}
{"name": "SSet.StrictSegal.spine_δ_vertex_lt", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal", "is_tactic_proof": true, "tactics": ["simp", "rw", "simp", "rw"], "tactic_count": 4}
{"name": "SSet.StrictSegal.spine_δ_vertex_ge", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal", "is_tactic_proof": true, "tactics": ["simp", "rw", "simp", "rw"], "tactic_count": 4}
{"name": "SSet.StrictSegal.spine_δ_arrow_lt", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal", "is_tactic_proof": true, "tactics": ["simp", "rw", "rw"], "tactic_count": 3}
{"name": "SSet.StrictSegal.spine_δ_arrow_gt", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal", "is_tactic_proof": true, "tactics": ["simp", "rw", "rw"], "tactic_count": 3}
{"name": "SSet.StrictSegal.spine_δ_arrow_eq", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal", "is_tactic_proof": true, "tactics": ["simp", "rw", "rw"], "tactic_count": 3}
{"name": "SSet.StrictSegalCore.spineToSimplexAux", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "refine", "rw", "exact", "ext", "obtain", "dsimp", "rw", "simpa"], "tactic_count": 11}
{"name": "SSet.StrictSegalCore.spineToSimplex", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.StrictSegalCore.spine_spineToSimplex", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.StrictSegalCore.spineToSimplex_zero", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.StrictSegalCore.spineToSimplex_succ", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.StrictSegalCore.map_mkOfSucc_zero_spineToSimplex", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SSet.StrictSegalCore.δ₀_spineToSimplex", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SSet.StrictSegalCore.spineToSimplex_spine", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "exact"], "tactic_count": 4}
{"name": "SSet.StrictSegal.ofCore", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Nerve.strictSegal", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Nerve.isStrictSegal", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.instBalanced", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.toSSet", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.instCoeOut", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.instDecidableEqObjOppositeSimplexCategoryToSSet", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.ι", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.instMonoι", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.homOfLE", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.homOfLE_comp", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.homOfLE_refl", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.homOfLE_app_val", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.homOfLE_ι", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.mono_homOfLE", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.eqToIso", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.toSSetFunctor", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.topIso", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.topIso_hom", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.topIso_inv_ι", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.instSubsingletonHomToSSetBot", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.instUniqueHomToSSetBot", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.isInitialBot", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.ofSimplex", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.ofSimplex_ι", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex", "is_tactic_proof": true, "tactics": ["ext", "obtain", "rfl"], "tactic_count": 3}
{"name": "SSet.Subcomplex.mem_ofSimplex_obj", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.ofSimplex_le_iff", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.mem_ofSimplex_obj_iff", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex", "is_tactic_proof": true, "tactics": ["dsimp", "aesop"], "tactic_count": 2}
{"name": "SSet.Subcomplex.range", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.toRange", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.toRange_ι", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.toRange_app_val", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.instEpiToRange", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.instMonoToRange", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.instIsIsoToRangeOfMono", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.range_eq_top_iff", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "SSet.Subcomplex.range_eq_top", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "SSet.Subcomplex.lift", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.lift_ι", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.lift_app_coe", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.preimage", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.preimage_max", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.preimage_min", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.preimage_iSup", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SSet.Subcomplex.preimage_iInf", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SSet.Subcomplex.image", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.image_le_iff", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SSet.Subcomplex.image_top", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SSet.Subcomplex.image_id", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SSet.Subcomplex.image_comp", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SSet.Subcomplex.range_comp", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SSet.Subcomplex.image_eq_range", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SSet.Subcomplex.image_iSup", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SSet.Subcomplex.preimage_range", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.image_le_range", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SSet.Subcomplex.image_ofSimplex", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex", "is_tactic_proof": true, "tactics": ["apply", "rw", "apply", "rw", "exact"], "tactic_count": 5}
{"name": "SSet.Subcomplex.toImage", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.toImage_ι", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.instEpiToImage", "kind": "instance", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex", "is_tactic_proof": true, "tactics": ["rw", "apply", "rintro", "exact"], "tactic_count": 4}
{"name": "SSet.Subcomplex.image_monotone", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex", "is_tactic_proof": true, "tactics": ["intro", "rw", "exact"], "tactic_count": 3}
{"name": "SSet.Subcomplex.preimage_eq_top_iff", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SSet.Subcomplex.image_preimage_le", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SSet.Subcomplex.fromPreimage", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.fromPreimage_ι", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.MulticoequalizerDiagram", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.SimplicialSet.SubcomplexColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.MulticoequalizerDiagram.isColimit", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.SubcomplexColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.MulticoequalizerDiagram.isColimit'", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SimplicialSet.SubcomplexColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.BicartSq", "kind": "abbrev", "module": "Mathlib.AlgebraicTopology.SimplicialSet.SubcomplexColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.Subcomplex.BicartSq.isPushout", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SimplicialSet.SubcomplexColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.SSet.singularChainComplexFunctor", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SingularHomology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.singularChainComplexFunctor", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SingularHomology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.singularHomologyFunctor", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SingularHomology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.singularChainComplexFunctorIsoOfTotallyDisconnectedSpace", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SingularHomology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.singularChainComplexFunctor_exactAt_of_totallyDisconnectedSpace", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SingularHomology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.isZero_singularHomologyFunctor_of_totallyDisconnectedSpace", "kind": "theorem", "module": "Mathlib.AlgebraicTopology.SingularHomology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicTopology.singularHomologyFunctorZeroOfTotallyDisconnectedSpace", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SingularHomology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.toSSet", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SingularSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.toSSetObjEquiv", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SingularSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SSet.toTop", "kind": "definition", "module": "Mathlib.AlgebraicTopology.SingularSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AbsoluteValue.IsEquiv", "kind": "definition", "module": "Mathlib.Analysis.AbsoluteValue.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AbsoluteValue.IsEquiv.lt_iff_lt", "kind": "theorem", "module": "Mathlib.Analysis.AbsoluteValue.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AbsoluteValue.IsEquiv.isNontrivial_congr", "kind": "theorem", "module": "Mathlib.Analysis.AbsoluteValue.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AbsoluteValue.isEquiv_trivial_iff_eq_trivial", "kind": "theorem", "module": "Mathlib.Analysis.AbsoluteValue.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AbsoluteValue.isEquiv_iff_lt_one_iff", "kind": "theorem", "module": "Mathlib.Analysis.AbsoluteValue.Equivalence", "is_tactic_proof": true, "tactics": ["refine", "rcases", "simp_all", "rw", "mul_inv_lt_iff₀", "exact"], "tactic_count": 6}
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{"name": "_private.Mathlib.Analysis.AbsoluteValue.Equivalence.0.AbsoluteValue.exists_one_lt_lt_one_pi_of_eq_one", "kind": "theorem", "module": "Mathlib.Analysis.AbsoluteValue.Equivalence", "is_tactic_proof": true, "tactics": ["classical", "let", "have", "simpa", "have", "simpa", "simp_rw", "choose", "choose", "have", "let", "refine", "exact", "simpa"], "tactic_count": 14}
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{"name": "HasFPowerSeriesOnBall.radius_pos", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "HasFPowerSeriesWithinOnBall.of_le", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "HasFPowerSeriesWithinOnBall.unique", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFPowerSeriesOnBall.unique", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFPowerSeriesWithinAt.eventually", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFPowerSeriesAt.eventually", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFPowerSeriesOnBall.eventually_hasSum", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Basic", "is_tactic_proof": true, "tactics": ["filter_upwards"], "tactic_count": 1}
{"name": "HasFPowerSeriesAt.eventually_hasSum", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFPowerSeriesOnBall.eventually_hasSum_sub", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Basic", "is_tactic_proof": true, "tactics": ["filter_upwards"], "tactic_count": 1}
{"name": "HasFPowerSeriesAt.eventually_hasSum_sub", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFPowerSeriesOnBall.eventually_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Basic", "is_tactic_proof": true, "tactics": ["filter_upwards"], "tactic_count": 1}
{"name": "HasFPowerSeriesAt.eventually_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasFPowerSeriesWithinOnBall_univ", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Basic", "is_tactic_proof": true, "tactics": ["constructor", "intro", "refine", "intro", "exact"], "tactic_count": 5}
{"name": "hasFPowerSeriesWithinAt_univ", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HasFPowerSeriesWithinOnBall.mono", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFPowerSeriesOnBall.hasFPowerSeriesWithinOnBall", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
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{"name": "HasFPowerSeriesAt.hasFPowerSeriesWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
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{"name": "analyticOnNhd_empty", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Basic", "is_tactic_proof": true, "tactics": ["intro"], "tactic_count": 1}
{"name": "analyticWithinAt_univ", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "AnalyticOnNhd.analyticOn", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AnalyticWithinAt.congr_of_eventuallyEq_insert", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Basic", "is_tactic_proof": true, "tactics": ["apply", "apply"], "tactic_count": 2}
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{"name": "analyticWithinAt_insert", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousLinearMap.comp_hasFPowerSeriesWithinOnBall", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.comp_hasFPowerSeriesOnBall", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ContinuousLinearMap.comp_analyticOn", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Basic", "is_tactic_proof": true, "tactics": ["rintro", "rcases", "exact"], "tactic_count": 3}
{"name": "ContinuousLinearMap.comp_analyticOnNhd", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Basic", "is_tactic_proof": true, "tactics": ["rintro", "rcases", "exact"], "tactic_count": 3}
{"name": "HasFPowerSeriesWithinOnBall.tendsto_partialSum", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "HasFPowerSeriesWithinAt.isBigO_sub_partialSum_pow", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Basic", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "obtain", "hf.uniform_geometric_approx", "refine", "replace", "filter_upwards", "simpa"], "tactic_count": 8}
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{"name": "HasFPowerSeriesWithinOnBall.tendstoUniformlyOn'", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Basic", "is_tactic_proof": true, "tactics": ["convert", "simp", "ext", "simp"], "tactic_count": 4}
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{"name": "HasFPowerSeriesWithinOnBall.continuousOn", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFPowerSeriesOnBall.continuousOn", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Basic", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
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{"name": "HasFPowerSeriesWithinOnBall.continuousWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFPowerSeriesWithinAt.continuousWithinAt_insert", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Basic", "is_tactic_proof": true, "tactics": ["rcases", "apply"], "tactic_count": 2}
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{"name": "AnalyticWithinAt.continuousWithinAt_insert", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticWithinAt.continuousWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AnalyticAt.eventually_continuousAt", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Basic", "is_tactic_proof": true, "tactics": ["rcases", "have", "filter_upwards", "apply", "exact"], "tactic_count": 5}
{"name": "AnalyticOnNhd.continuousOn", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticOn.continuousOn", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticOnNhd.continuous", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "FormalMultilinearSeries.hasFPowerSeriesOnBall", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFPowerSeriesWithinOnBall.sum", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFPowerSeriesOnBall.sum", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "hasFPowerSeriesAt_iff", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Basic", "is_tactic_proof": false, "tactics": ["refine", "simp", "rintro", "refine", "simp", "obtain", "have", "simp", "apply", "convert", "simp", "refine", "simp", "exact", "simp", "refine", "simpa"], "tactic_count": 17}
{"name": "hasFPowerSeriesAt_iff'", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp_rw"], "tactic_count": 2}
{"name": "Complex.ofReal_choose", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Binomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "binomialSeries", "kind": "definition", "module": "Mathlib.Analysis.Analytic.Binomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "binomialSeries_apply", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Binomial", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "binomialSeries_eq_ordinaryHypergeometricSeries", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Binomial", "is_tactic_proof": true, "tactics": ["simp", "congr", "rw", "simp", "ascPochhammer_eval_neg_eq_descPochhammer,", "ring_nf", "simp"], "tactic_count": 7}
{"name": "binomialSeries_radius_eq_top_of_nat", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Binomial", "is_tactic_proof": true, "tactics": ["simp", "ordinaryHypergeometric_radius_top_of_neg_nat₁]"], "tactic_count": 2}
{"name": "binomialSeries_radius_eq_one", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Binomial", "is_tactic_proof": false, "tactics": ["simp", "conv", "exact"], "tactic_count": 3}
{"name": "binomialSeries_radius_ge_one", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Binomial", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "push_neg", "rcases", "simp"], "tactic_count": 5}
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{"name": "Real.hasFPowerSeriesOnBall_ofScalars_mul_add_zero", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Binomial", "is_tactic_proof": false, "tactics": ["convert", "simp", "ext"], "tactic_count": 3}
{"name": "hasFiniteFPowerSeriesOnBall_const", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.CPolynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasFiniteFPowerSeriesAt_const", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.CPolynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CPolynomialAt_const", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.CPolynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CPolynomialOn_const", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.CPolynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFiniteFPowerSeriesOnBall.add", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.CPolynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFiniteFPowerSeriesAt.add", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.CPolynomial", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "CPolynomialAt.add", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.CPolynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFiniteFPowerSeriesOnBall.neg", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.CPolynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFiniteFPowerSeriesAt.neg", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.CPolynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CPolynomialAt.neg", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.CPolynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFiniteFPowerSeriesOnBall.sub", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.CPolynomial", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasFiniteFPowerSeriesAt.sub", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.CPolynomial", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CPolynomialAt.sub", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.CPolynomial", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CPolynomialOn.add", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.CPolynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CPolynomialOn.sub", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.CPolynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.hasFiniteFPowerSeriesOnBall", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.CPolynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.cpolynomialAt", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.CPolynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.cpolynomialOn", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.CPolynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.analyticOnNhd", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.CPolynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.analyticOn", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.CPolynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.analyticAt", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.CPolynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.analyticWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.CPolynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AnalyticAt.exists_ball_analyticOnNhd", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.ChangeOrigin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.analyticOnNhd", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.ChangeOrigin", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "exact"], "tactic_count": 3}
{"name": "FormalMultilinearSeries.applyComposition", "kind": "definition", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.applyComposition_ones", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": true, "tactics": ["funext", "apply", "intro", "obtain", "refine", "rw"], "tactic_count": 6}
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{"name": "FormalMultilinearSeries.removeZero_applyComposition", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "FormalMultilinearSeries.applyComposition_update", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "rw", "let", "simp", "change", "let", "suffices", "suffices", "exact", "exact", "simp", "let", "change", "suffices", "apply", "rwa"], "tactic_count": 17}
{"name": "FormalMultilinearSeries.compContinuousLinearMap_applyComposition", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "ContinuousMultilinearMap.compAlongComposition", "kind": "definition", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.compAlongComposition_apply", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.compAlongComposition", "kind": "definition", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.compAlongComposition_apply", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.comp", "kind": "definition", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.comp_coeff_zero", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": true, "tactics": ["let", "dsimp", "have", "apply", "rw", "symm"], "tactic_count": 6}
{"name": "FormalMultilinearSeries.comp_coeff_zero'", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.comp_coeff_zero''", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "FormalMultilinearSeries.comp_coeff_one", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": false, "tactics": ["have", "simp", "refine", "simp", "exact"], "tactic_count": 5}
{"name": "FormalMultilinearSeries.removeZero_comp_of_pos", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": true, "tactics": ["ext", "simp", "refine", "rw"], "tactic_count": 4}
{"name": "FormalMultilinearSeries.comp_removeZero", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "FormalMultilinearSeries.compAlongComposition_bound", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.compAlongComposition_norm", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.compAlongComposition_nnnorm", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "FormalMultilinearSeries.id", "kind": "definition", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.id_apply_zero", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.id_apply_one", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.id_apply_one'", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": true, "tactics": ["subst", "apply"], "tactic_count": 2}
{"name": "FormalMultilinearSeries.id_apply_of_one_lt", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": true, "tactics": ["n"], "tactic_count": 1}
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{"name": "FormalMultilinearSeries.id_comp'", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FormalMultilinearSeries.comp_summable_nnreal", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": true, "tactics": ["giving", "fact", "rcases", "rcases", "simp", "obtain", "obtain", "rcases", "exact", "let", "have", "set", "have", "have", "rintro", "have", "calc", "mul_le_mul", "have", "calc", "simp", "calc", "grw", "simp", "simp", "refine", "simp_rw", "refine", "have", "intro", "convert", "simp", "refine", "convert", "ext1", "rw", "simp"], "tactic_count": 37}
{"name": "FormalMultilinearSeries.le_comp_radius_of_summable", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": false, "tactics": ["refine", "le_radius_of_bound_nnreal", "calc", "rw", "exact"], "tactic_count": 5}
{"name": "FormalMultilinearSeries.compPartialSumSource", "kind": "definition", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.mem_compPartialSumSource_iff", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FormalMultilinearSeries.compChangeOfVariables", "kind": "definition", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": true, "tactics": ["rcases", "rw", "refine", "obtain", "exact"], "tactic_count": 5}
{"name": "FormalMultilinearSeries.compChangeOfVariables_length", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": true, "tactics": ["rcases", "dsimp", "simp"], "tactic_count": 3}
{"name": "FormalMultilinearSeries.compChangeOfVariables_blocksFun", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": true, "tactics": ["rcases", "dsimp", "simp"], "tactic_count": 3}
{"name": "FormalMultilinearSeries.compPartialSumTargetSet", "kind": "definition", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.compPartialSumTargetSet_image_compPartialSumSource", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": true, "tactics": ["rcases", "refine", "simp", "simp", "exact", "dsimp", "rw", "simp", "conv_rhs"], "tactic_count": 9}
{"name": "FormalMultilinearSeries.compPartialSumTarget", "kind": "definition", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.mem_compPartialSumTarget_iff", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FormalMultilinearSeries.compChangeOfVariables_sum", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": false, "tactics": ["apply", "rintro", "rw", "simp", "intro", "simp", "rintro", "obtain", "have", "rwa", "congr", "funext", "calc", "blocks_fun", "intro", "apply", "simpa", "assumption"], "tactic_count": 18}
{"name": "FormalMultilinearSeries.compPartialSumTarget_tendsto_prod_atTop", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": true, "tactics": ["apply", "intro", "have", "have", "simp_all", "rintro", "simp", "obtain", "refine", "lt_of_le_of_lt", "apply", "simp"], "tactic_count": 12}
{"name": "FormalMultilinearSeries.compPartialSumTarget_tendsto_atTop", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "FormalMultilinearSeries.comp_partialSum", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": true, "tactics": ["suffices", "rw", "apply", "rintro", "apply", "intros", "rw"], "tactic_count": 7}
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{"name": "AnalyticWithinAt.comp", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": true, "tactics": ["let", "let", "exact"], "tactic_count": 3}
{"name": "AnalyticWithinAt.comp_of_eq", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "AnalyticOn.comp", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticAt.comp", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "AnalyticAt.comp'", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticAt.comp_of_eq", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "AnalyticAt.comp_of_eq'", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "AnalyticAt.comp_analyticWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "AnalyticAt.comp_analyticWithinAt_of_eq", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "AnalyticOnNhd.comp'", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticOnNhd.comp", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticOnNhd.comp_analyticOn", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFiniteFPowerSeriesAt.comp", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": true, "tactics": ["rcases", "refine", "apply", "rintro", "ext", "simp", "rcases", "simp", "obtain", "contrapose", "rw", "rcases", "have", "apply", "have", "grind", "rw", "exact", "calc", "apply", "exact", "apply", "simp"], "tactic_count": 23}
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{"name": "CPolynomialAt.fun_comp", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CPolynomialAt.comp_of_eq", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CPolynomialAt.fun_comp_of_eq", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CPolynomialOn.comp'", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CPolynomialOn.comp", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Composition.sigma_composition_eq_iff", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": true, "tactics": ["refine", "rcases", "rcases", "rintro", "obtain", "obtain", "rfl"], "tactic_count": 7}
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{"name": "Composition.gather", "kind": "definition", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Composition.length_gather", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Composition.sigmaCompositionAux", "kind": "definition", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Composition.length_sigmaCompositionAux", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Composition.blocksFun_sigmaCompositionAux", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": true, "tactics": ["unfold", "rw"], "tactic_count": 2}
{"name": "Composition.sizeUpTo_sizeUpTo_add", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": true, "tactics": ["induction", "zero", "change", "induction", "zero", "succ", "have", "have", "have", "rw", "have", "take", "take", "rw", "apply", "rw", "take_append_drop", "congr", "rw", "succ", "have", "have", "rw", "have", "simp", "exact", "have", "have", "rw", "simp", "rw"], "tactic_count": 31}
{"name": "Composition.sigmaEquivSigmaPi", "kind": "definition", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.comp_assoc", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Composition", "is_tactic_proof": true, "tactics": ["ext", "let", "r", "let", "r", "suffices", "simpa", "compAlongComposition_apply,", "variables", "rw", "one", "apply", "rintro", "dsimp", "apply", "intro", "apply", "intro", "apply", "intro", "refine", "dsimp", "rw"], "tactic_count": 23}
{"name": "hasFPowerSeriesOnBall_const", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": true, "tactics": ["refine", "simp"], "tactic_count": 2}
{"name": "hasFPowerSeriesAt_const", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "analyticAt_const", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "analyticOnNhd_const", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "analyticWithinAt_const", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "analyticOn_const", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFPowerSeriesWithinOnBall.add", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFPowerSeriesOnBall.add", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFPowerSeriesWithinAt.add", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "HasFPowerSeriesAt.add", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "AnalyticWithinAt.add", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticAt.add", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticOn.add", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticOnNhd.add", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFPowerSeriesWithinOnBall.neg", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFPowerSeriesOnBall.neg", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFPowerSeriesWithinAt.neg", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFPowerSeriesAt.neg", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticWithinAt.neg", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticAt.neg", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "analyticAt_neg", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AnalyticOnNhd.neg", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFPowerSeriesWithinOnBall.sub", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasFPowerSeriesOnBall.sub", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasFPowerSeriesWithinAt.sub", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasFPowerSeriesAt.sub", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "AnalyticWithinAt.sub", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "AnalyticAt.sub", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "AnalyticOn.sub", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticOnNhd.sub", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFPowerSeriesWithinOnBall.const_smul", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFPowerSeriesOnBall.const_smul", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFPowerSeriesWithinAt.const_smul", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFPowerSeriesAt.const_smul", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticWithinAt.const_smul", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticAt.const_smul", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticOn.const_smul", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticOnNhd.const_smul", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticWithinAt.div_const", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "AnalyticAt.div_const", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "AnalyticOn.div_const", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "AnalyticOnNhd.div_const", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "FormalMultilinearSeries.radius_prod_eq_min", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": true, "tactics": ["apply", "refine", "rw", "have", "constructor", "all_goals", "apply", "refine", "rw", "refine", "rw", "apply", "apply", "refine", "rw", "have", "refine", "rw", "refine", "rw", "refine", "apply"], "tactic_count": 22}
{"name": "HasFPowerSeriesWithinOnBall.prod", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFPowerSeriesOnBall.prod", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "HasFPowerSeriesWithinAt.prod", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "exact"], "tactic_count": 3}
{"name": "HasFPowerSeriesAt.prod", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "exact"], "tactic_count": 3}
{"name": "AnalyticWithinAt.prod", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "exact"], "tactic_count": 3}
{"name": "AnalyticAt.prod", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "exact"], "tactic_count": 3}
{"name": "AnalyticOn.prod", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticOnNhd.prod", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticAt.comp₂", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticWithinAt.comp₂", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticAt.comp₂_analyticWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticOnNhd.comp₂", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticOn.comp₂", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticAt.curry_left", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticWithinAt.curry_left", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticAt.curry_right", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticWithinAt.curry_right", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticOnNhd.curry_left", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticOn.curry_left", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticOnNhd.curry_right", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticOn.curry_right", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.radius_pi_le", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": true, "tactics": ["apply", "obtain", "apply", "apply", "gcongr", "rw", "exact"], "tactic_count": 7}
{"name": "FormalMultilinearSeries.le_radius_pi", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": true, "tactics": ["apply", "have", "choose", "obtain", "apply", "rcases", "exact", "simp", "rw", "intro", "exact"], "tactic_count": 11}
{"name": "FormalMultilinearSeries.radius_pi_eq_iInf", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": true, "tactics": ["refine", "apply", "exact"], "tactic_count": 3}
{"name": "HasFPowerSeriesWithinOnBall.pi", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasFPowerSeriesWithinOnBall_pi_iff", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFPowerSeriesOnBall.pi", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "hasFPowerSeriesOnBall_pi_iff", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "HasFPowerSeriesWithinAt.pi", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": ["have", "eventually_all.mpr", "obtain", "exact"], "tactic_count": 4}
{"name": "hasFPowerSeriesWithinAt_pi_iff", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact"], "tactic_count": 3}
{"name": "HasFPowerSeriesAt.pi", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "hasFPowerSeriesAt_pi_iff", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "AnalyticWithinAt.pi", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": true, "tactics": ["choose", "exact"], "tactic_count": 2}
{"name": "analyticWithinAt_pi_iff", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "AnalyticAt.pi", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "analyticAt_pi_iff", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "AnalyticOn.pi", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "analyticOn_pi_iff", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticOnNhd.pi", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "analyticOnNhd_pi_iff", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "analyticAt_smul", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "analyticAt_mul", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticWithinAt.smul", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticAt.smul", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticOn.smul", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticOnNhd.smul", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticWithinAt.mul", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticAt.mul", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticOn.mul", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticOnNhd.mul", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticWithinAt.pow", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": true, "tactics": ["induction", "zero", "simp", "apply", "succ", "simp", "exact"], "tactic_count": 7}
{"name": "AnalyticAt.pow", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "AnalyticOn.pow", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticOnNhd.pow", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticWithinAt.zpow_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "AnalyticAt.zpow_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "AnalyticOn.zpow_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "AnalyticOnNhd.zpow_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": true, "tactics": ["simp_rw", "apply"], "tactic_count": 2}
{"name": "HasFPowerSeriesWithinOnBall.restrictScalars", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFPowerSeriesOnBall.restrictScalars", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFPowerSeriesWithinAt.restrictScalars", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "HasFPowerSeriesAt.restrictScalars", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "AnalyticWithinAt.restrictScalars", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "AnalyticAt.restrictScalars", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "AnalyticOn.restrictScalars", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticOnNhd.restrictScalars", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "formalMultilinearSeries_geometric", "kind": "definition", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "formalMultilinearSeries_geometric_eq_ofScalars", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": true, "tactics": ["simp_rw", "one_smul,"], "tactic_count": 2}
{"name": "formalMultilinearSeries_geometric_apply_norm_le", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "formalMultilinearSeries_geometric_apply_norm", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_le_formalMultilinearSeries_geometric_radius", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": ["convert", "formalMultilinearSeries_geometric_eq_ofScalars", "simp"], "tactic_count": 3}
{"name": "formalMultilinearSeries_geometric_radius", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasFPowerSeriesOnBall_inverse_one_sub", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": true, "tactics": ["constructor", "exact", "exact", "intro", "simp", "simp", "exact"], "tactic_count": 7}
{"name": "analyticAt_inverse_one_sub", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "analyticAt_inverse", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": true, "tactics": ["rcases", "convert", "let", "let", "let", "have", "have", "apply", "simp", "filter_upwards", "simp", "have", "rw", "simp", "simp", "rw", "congr", "simp", "apply", "apply", "apply", "simp", "exact", "exact"], "tactic_count": 24}
{"name": "analyticOnNhd_inverse", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasFPowerSeriesOnBall_inv_one_sub", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": true, "tactics": ["convert", "exact"], "tactic_count": 2}
{"name": "analyticAt_inv_one_sub", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "analyticAt_inv", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": true, "tactics": ["convert", "exact"], "tactic_count": 2}
{"name": "analyticOnNhd_inv", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": true, "tactics": ["intro"], "tactic_count": 1}
{"name": "analyticOn_inv", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticWithinAt.inv", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticAt.inv", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticOn.inv", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticOnNhd.inv", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticWithinAt.zpow", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "rw", "conv", "exact"], "tactic_count": 5}
{"name": "AnalyticAt.zpow", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "rw", "conv", "exact"], "tactic_count": 5}
{"name": "AnalyticOn.zpow", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticOnNhd.zpow", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "analyticAt_iff_analytic_fun_smul", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": true, "tactics": ["constructor", "exact", "intro", "rw", "exact", "filter_upwards", "intro", "rw", "simp", "multiplication"], "tactic_count": 10}
{"name": "analyticAt_iff_analytic_smul", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "analyticAt_iff_analytic_fun_mul", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "analyticAt_iff_analytic_mul", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticWithinAt.div", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "AnalyticAt.div", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "AnalyticOn.div", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticOnNhd.div", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.analyticWithinAt_fun_sum", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "simp", "exact", "insert", "simp_rw", "simp", "exact"], "tactic_count": 9}
{"name": "Finset.analyticWithinAt_sum", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "Finset.analyticAt_fun_sum", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Finset.analyticAt_sum", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "Finset.analyticOn_fun_sum", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.analyticOn_sum", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.analyticOnNhd_fun_sum", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.analyticOnNhd_sum", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.analyticWithinAt_fun_prod", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "simp", "exact", "insert", "simp_rw", "simp", "exact"], "tactic_count": 9}
{"name": "Finset.analyticWithinAt_prod", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "Finset.analyticAt_fun_prod", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Finset.analyticAt_prod", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "Finset.analyticOn_fun_prod", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.analyticOn_prod", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.analyticOnNhd_fun_prod", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.analyticOnNhd_prod", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "analyticAt_finprod", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": true, "tactics": ["by_cases", "simp_all", "rw", "apply"], "tactic_count": 4}
{"name": "HasFPowerSeriesWithinOnBall.unshift", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFPowerSeriesOnBall.unshift", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFPowerSeriesWithinAt.unshift", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFPowerSeriesWithinOnBall.compContinuousLinearMap", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFPowerSeriesOnBall.compContinuousLinearMap", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "HasFPowerSeriesAt.compContinuousLinearMap", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFPowerSeriesWithinAt.compContinuousLinearMap", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticAt.compContinuousLinearMap", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticAtWithin.compContinuousLinearMap", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticOn.compContinuousLinearMap", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticOnNhd.compContinuousLinearMap", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.sum", "kind": "definition", "module": "Mathlib.Analysis.Analytic.ConvergenceRadius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.partialSum", "kind": "definition", "module": "Mathlib.Analysis.Analytic.ConvergenceRadius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.partialSum_continuous", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.ConvergenceRadius", "is_tactic_proof": true, "tactics": ["unfold", "fun_prop"], "tactic_count": 2}
{"name": "FormalMultilinearSeries.radius", "kind": "definition", "module": "Mathlib.Analysis.Analytic.ConvergenceRadius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.le_radius_of_bound", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.ConvergenceRadius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.le_radius_of_bound_nnreal", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.ConvergenceRadius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.le_radius_of_isBigO", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.ConvergenceRadius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.le_radius_of_eventually_le", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.ConvergenceRadius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.le_radius_of_summable_nnnorm", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.ConvergenceRadius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.le_radius_of_summable", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.ConvergenceRadius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.radius_eq_top_of_forall_nnreal_isBigO", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.ConvergenceRadius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.radius_eq_top_of_eventually_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.ConvergenceRadius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.radius_eq_top_of_forall_image_add_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.ConvergenceRadius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.constFormalMultilinearSeries_radius", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.ConvergenceRadius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.zero_radius", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.ConvergenceRadius", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "FormalMultilinearSeries.isLittleO_of_lt_radius", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.ConvergenceRadius", "is_tactic_proof": true, "tactics": ["have", "rw", "simp", "rcases", "rw", "have", "rw", "refine", "calc"], "tactic_count": 9}
{"name": "FormalMultilinearSeries.isLittleO_one_of_lt_radius", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.ConvergenceRadius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.norm_mul_pow_le_mul_pow_of_lt_radius", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.ConvergenceRadius", "is_tactic_proof": false, "tactics": ["have", "rcases", "exact"], "tactic_count": 3}
{"name": "FormalMultilinearSeries.lt_radius_of_isBigO", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.ConvergenceRadius", "is_tactic_proof": true, "tactics": ["have", "rcases", "rw", "lift", "have", "norm_cast", "rw", "refine", "rw", "exact"], "tactic_count": 10}
{"name": "FormalMultilinearSeries.norm_mul_pow_le_of_lt_radius", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.ConvergenceRadius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.norm_le_div_pow_of_pos_of_lt_radius", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.ConvergenceRadius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.nnnorm_mul_pow_le_of_lt_radius", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.ConvergenceRadius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.le_radius_of_tendsto", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.ConvergenceRadius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.le_radius_of_summable_norm", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.ConvergenceRadius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.not_summable_norm_of_radius_lt_nnnorm", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.ConvergenceRadius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.summable_norm_mul_pow", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.ConvergenceRadius", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "FormalMultilinearSeries.summable_norm_apply", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.ConvergenceRadius", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp"], "tactic_count": 3}
{"name": "FormalMultilinearSeries.summable_nnnorm_mul_pow", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.ConvergenceRadius", "is_tactic_proof": true, "tactics": ["rw", "push_cast", "exact"], "tactic_count": 3}
{"name": "FormalMultilinearSeries.summable", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.ConvergenceRadius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.radius_eq_top_of_summable_norm", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.ConvergenceRadius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.radius_eq_top_iff_summable_norm", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.ConvergenceRadius", "is_tactic_proof": true, "tactics": ["constructor", "intro", "obtain", "p.norm_mul_pow_le_mul_pow_of_lt_radius", "refine", "specialize", "rwa", "exact"], "tactic_count": 8}
{"name": "FormalMultilinearSeries.le_mul_pow_of_radius_pos", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.ConvergenceRadius", "is_tactic_proof": true, "tactics": ["rcases", "have", "rcases", "refine", "rw", "exact"], "tactic_count": 6}
{"name": "FormalMultilinearSeries.radius_le_of_le", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.ConvergenceRadius", "is_tactic_proof": true, "tactics": ["apply", "rcases", "apply", "apply", "gcongr", "exact"], "tactic_count": 6}
{"name": "FormalMultilinearSeries.min_radius_le_radius_add", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.ConvergenceRadius", "is_tactic_proof": true, "tactics": ["refine", "rw", "have", "refine", "rw", "gcongr", "exact"], "tactic_count": 7}
{"name": "FormalMultilinearSeries.radius_neg", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.ConvergenceRadius", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FormalMultilinearSeries.radius_le_smul", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.ConvergenceRadius", "is_tactic_proof": true, "tactics": ["simp", "refine", "simp", "intro", "grw"], "tactic_count": 5}
{"name": "FormalMultilinearSeries.radius_smul_eq", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.ConvergenceRadius", "is_tactic_proof": true, "tactics": ["apply", "exact"], "tactic_count": 2}
{"name": "FormalMultilinearSeries.norm_compContinuousLinearMap_le", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.ConvergenceRadius", "is_tactic_proof": true, "tactics": ["simp", "apply", "simp"], "tactic_count": 3}
{"name": "FormalMultilinearSeries.enorm_compContinuousLinearMap_le", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.ConvergenceRadius", "is_tactic_proof": false, "tactics": ["rw", "gcongr", "apply"], "tactic_count": 3}
{"name": "FormalMultilinearSeries.nnnorm_compContinuousLinearMap_le", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.ConvergenceRadius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.div_le_radius_compContinuousLinearMap", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.ConvergenceRadius", "is_tactic_proof": true, "tactics": ["obtain", "simp", "rw", "refine", "rw", "obtain", "refine", "calc", "gcongr", "exact", "simp", "rw", "rw", "positivity"], "tactic_count": 14}
{"name": "FormalMultilinearSeries.le_radius_compContinuousLinearMap", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.ConvergenceRadius", "is_tactic_proof": true, "tactics": ["obtain", "simp", "simpa"], "tactic_count": 3}
{"name": "FormalMultilinearSeries.radius_compContinuousLinearMap_le", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.ConvergenceRadius", "is_tactic_proof": false, "tactics": ["have", "u.symm.toContinuousLinearMap", "simp", "rwa"], "tactic_count": 4}
{"name": "FormalMultilinearSeries.radius_compContinuousLinearMap_linearIsometryEquiv_eq", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.ConvergenceRadius", "is_tactic_proof": true, "tactics": ["refine", "have", "convert", "have", "simp"], "tactic_count": 5}
{"name": "FormalMultilinearSeries.radius_compContinuousLinearMap_eq", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.ConvergenceRadius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.radius_compNeg", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.ConvergenceRadius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.radius_shift", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.ConvergenceRadius", "is_tactic_proof": true, "tactics": ["simp", "congr", "ext", "apply", "apply", "intro", "use", "apply", "intro", "simp", "intro", "rcases", "simp", "right", "rw", "gcongr", "apply", "intro", "use", "apply", "intro", "simp", "intro", "cases", "inl", "rw", "cases", "inr", "right", "rw", "specialize", "rw", "rwa"], "tactic_count": 33}
{"name": "FormalMultilinearSeries.radius_unshift", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.ConvergenceRadius", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "FormalMultilinearSeries.hasSum", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.ConvergenceRadius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.radius_le_radius_continuousLinearMap_comp", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.ConvergenceRadius", "is_tactic_proof": true, "tactics": ["refine", "apply", "apply", "refine", "refine", "simpa"], "tactic_count": 6}
{"name": "FormalMultilinearSeries.leftInv", "kind": "definition", "module": "Mathlib.Analysis.Analytic.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.leftInv_coeff_zero", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Inverse", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "FormalMultilinearSeries.leftInv_coeff_one", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Inverse", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "FormalMultilinearSeries.leftInv_removeZero", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Inverse", "is_tactic_proof": true, "tactics": ["ext1", "induction", "simp", "simp", "n", "simp", "refine", "rcases", "ext", "simp"], "tactic_count": 10}
{"name": "FormalMultilinearSeries.leftInv_comp", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Inverse", "is_tactic_proof": true, "tactics": ["ext", "classical", "simp", "n", "have", "refine", "by_cases", "simp", "simp", "have", "have", "p", "p.leftInv", "apply", "exact", "have", "simp", "convert", "simp", "congr", "ext", "congr", "ext", "simp", "simp"], "tactic_count": 25}
{"name": "FormalMultilinearSeries.rightInv", "kind": "definition", "module": "Mathlib.Analysis.Analytic.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.rightInv_coeff_zero", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Inverse", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "FormalMultilinearSeries.rightInv_coeff_one", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Inverse", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "FormalMultilinearSeries.rightInv_removeZero", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Inverse", "is_tactic_proof": true, "tactics": ["ext1", "induction", "n", "simp", "rw", "congr", "by_cases"], "tactic_count": 7}
{"name": "FormalMultilinearSeries.comp_rightInv_aux1", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Inverse", "is_tactic_proof": true, "tactics": ["classical", "have", "refine", "by_cases", "simp", "have", "rw", "simp", "have", "have", "p", "apply", "simp", "simp"], "tactic_count": 14}
{"name": "FormalMultilinearSeries.comp_rightInv_aux2", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Inverse", "is_tactic_proof": true, "tactics": ["have", "refine", "have", "simp", "simp", "simp"], "tactic_count": 6}
{"name": "FormalMultilinearSeries.comp_rightInv", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Inverse", "is_tactic_proof": true, "tactics": ["ext", "simp", "congr", "ext", "exact", "simp", "n", "have", "simp"], "tactic_count": 9}
{"name": "FormalMultilinearSeries.rightInv_coeff", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Inverse", "is_tactic_proof": true, "tactics": ["n", "simp", "congr", "ext", "have", "have", "simp"], "tactic_count": 7}
{"name": "FormalMultilinearSeries.leftInv_eq_rightInv", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.radius_right_inv_pos_of_radius_pos_aux1", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.radius_rightInv_pos_of_radius_pos_aux2", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.radius_rightInv_pos_of_radius_pos", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Inverse", "is_tactic_proof": false, "tactics": ["obtain", "le_mul_pow_of_radius_pos", "let", "obtain", "have", "tendsto_const_nhds.mul", "have", "simp", "have", "have", "have", "rcases", "exact", "let", "have", "apply", "simp", "rw", "exact", "intro", "have", "have", "calc", "r", "calc", "radius_rightInv_pos_of_radius_pos_aux2", "exact", "gcongr", "simp", "positivity", "linarith", "gcongr", "let", "suffices", "apply", "simpa", "apply", "filter_upwards", "calc", "single_le_sum"], "tactic_count": 40}
{"name": "FormalMultilinearSeries.radius_leftInv_pos_of_radius_pos", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Inverse", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "HasFPowerSeriesAt.tendsto_partialSum_prod_of_comp", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Inverse", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "let", "have", "filter_upwards", "have", "have", "have", "apply", "simp", "rintro", "calc", "apply", "apply", "rw", "gcongr", "rw", "have", "rwa", "apply", "simpa", "have", "have", "simpa", "apply", "filter_upwards", "rintro", "congr", "rw", "congr", "exact"], "tactic_count": 31}
{"name": "HasFPowerSeriesAt.eventually_hasSum_of_comp", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Inverse", "is_tactic_proof": false, "tactics": ["have", "have", "apply", "exact", "have", "exact", "filter_upwards", "h''y", "have", "apply", "rintro", "simp", "rcases", "obtain", "simpa", "refine", "have", "have", "apply", "apply", "convert", "exact", "apply", "filter_upwards", "have", "have", "exact", "exact"], "tactic_count": 28}
{"name": "OpenPartialHomeomorph.hasFPowerSeriesAt_symm", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Inverse", "is_tactic_proof": false, "tactics": ["have", "have", "rw", "exact", "apply", "filter_upwards", "have", "simpa", "have", "rw", "have", "simpa", "have", "simp", "filter_upwards", "simpa", "have", "have", "exact", "have", "filter_upwards", "simpa", "rcases", "refine", "have", "simp", "exact", "simpa"], "tactic_count": 28}
{"name": "HasSum.hasSum_at_zero", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.IsolatedZeros", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "HasSum.exists_hasSum_smul_of_apply_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.IsolatedZeros", "is_tactic_proof": true, "tactics": ["obtain", "simpa", "by_cases", "have", "exact", "refine", "have", "have", "convert", "match_scalars", "simp", "simp"], "tactic_count": 12}
{"name": "HasFPowerSeriesAt.has_fpower_series_dslope_fslope", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.IsolatedZeros", "is_tactic_proof": true, "tactics": ["have", "have", "simp", "refine", "by_cases", "convert", "have", "suffices", "simpa", "simpa"], "tactic_count": 10}
{"name": "HasFPowerSeriesAt.has_fpower_series_iterate_dslope_fslope", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.IsolatedZeros", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "HasFPowerSeriesAt.iterate_dslope_fslope_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.IsolatedZeros", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "HasFPowerSeriesAt.eq_pow_order_mul_iterate_dslope", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.IsolatedZeros", "is_tactic_proof": true, "tactics": ["have", "filter_upwards", "have", "obtain", "convert", "simp", "exact"], "tactic_count": 7}
{"name": "HasFPowerSeriesAt.locally_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.IsolatedZeros", "is_tactic_proof": true, "tactics": ["rw", "have", "have", "filter_upwards", "simpa"], "tactic_count": 5}
{"name": "HasFPowerSeriesAt.locally_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.IsolatedZeros", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticAt.eventually_eq_zero_or_eventually_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.IsolatedZeros", "is_tactic_proof": true, "tactics": ["rcases", "by_cases", "exact", "exact"], "tactic_count": 4}
{"name": "AnalyticAt.eventually_eq_or_eventually_ne", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.IsolatedZeros", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
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{"name": "AnalyticAt.frequently_eq_iff_eventually_eq", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.IsolatedZeros", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
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{"name": "AnalyticAt.preimage_of_nhdsNE", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.IsolatedZeros", "is_tactic_proof": false, "tactics": ["have", "filter_upwards", "tauto", "contrapose", "rw", "use", "rw", "apply", "intro", "rw", "tauto"], "tactic_count": 11}
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{"name": "AnalyticOnNhd.preimage_mem_codiscreteWithin", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.IsolatedZeros", "is_tactic_proof": true, "tactics": ["simp_rw", "intro", "apply", "rw", "apply", "intro", "push", "push_neg", "tauto"], "tactic_count": 9}
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{"name": "FormalMultilinearSeries.iteratedFDerivSeries", "kind": "definition", "module": "Mathlib.Analysis.Analytic.IteratedFDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFPowerSeriesWithinOnBall.iteratedFDerivWithin", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.IteratedFDeriv", "is_tactic_proof": true, "tactics": ["induction", "zero", "exact", "h", "succ", "rw", "apply"], "tactic_count": 7}
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{"name": "ContinuousLinearMap.fpowerSeries_radius", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.hasFiniteFPowerSeriesOnBall", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.hasFPowerSeriesOnBall", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.hasFPowerSeriesAt", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.cpolynomialAt", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.analyticAt", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.cpolynomialOn", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.analyticOnNhd", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.analyticWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ContinuousLinearMap.uncurryBilinear", "kind": "definition", "module": "Mathlib.Analysis.Analytic.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.uncurryBilinear_apply", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.fpowerSeriesBilinear", "kind": "definition", "module": "Mathlib.Analysis.Analytic.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.fpowerSeriesBilinear_apply_zero", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.fpowerSeriesBilinear_apply_one", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.fpowerSeriesBilinear_apply_two", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.fpowerSeriesBilinear_apply_add_three", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.fpowerSeriesBilinear_radius", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.hasFPowerSeriesOnBall_bilinear", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.hasFPowerSeriesAt_bilinear", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.analyticAt_bilinear", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.analyticWithinAt_bilinear", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.analyticOnNhd_bilinear", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.analyticOn_bilinear", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "analyticWithinAt_id", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "analyticOnNhd_id", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "analyticOn_id", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "analyticAt_fst", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "analyticAt_snd", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "analyticWithinAt_snd", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "analyticOnNhd_fst", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "analyticOnNhd_snd", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ContinuousLinearEquiv.analyticAt", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.analyticOnNhd", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LinearIsometryEquiv.analyticOnNhd", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.analyticWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.analyticOn", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.ofScalars", "kind": "definition", "module": "Mathlib.Analysis.Analytic.OfScalars", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.ofScalars_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.OfScalars", "is_tactic_proof": true, "tactics": ["rw", "refine", "use", "simp"], "tactic_count": 4}
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{"name": "FormalMultilinearSeries.ofScalars_series_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.OfScalars", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "FormalMultilinearSeries.ofScalars_apply_zero", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.OfScalars", "is_tactic_proof": true, "tactics": ["rw", "cases"], "tactic_count": 2}
{"name": "FormalMultilinearSeries.coeff_ofScalars", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.OfScalars", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FormalMultilinearSeries.ofScalars_add", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.OfScalars", "is_tactic_proof": true, "tactics": ["unfold", "simp_rw", "exact"], "tactic_count": 3}
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{"name": "FormalMultilinearSeries.ofScalars_comp_neg", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.OfScalars", "is_tactic_proof": true, "tactics": ["conv", "rw"], "tactic_count": 2}
{"name": "FormalMultilinearSeries.ofScalarsSubmodule", "kind": "definition", "module": "Mathlib.Analysis.Analytic.OfScalars", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.ofScalars_apply_eq", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.OfScalars", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "FormalMultilinearSeries.ofScalarsSum", "kind": "definition", "module": "Mathlib.Analysis.Analytic.OfScalars", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.ofScalars_sum_eq", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.OfScalars", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.ofScalarsSum_eq_tsum", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.OfScalars", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.ofScalarsSum_zero", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.OfScalars", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FormalMultilinearSeries.ofScalarsSum_of_subsingleton", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.OfScalars", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FormalMultilinearSeries.ofScalarsSum_op", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.OfScalars", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FormalMultilinearSeries.ofScalarsSum_unop", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.OfScalars", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FormalMultilinearSeries.ofScalars_norm_eq_mul", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.OfScalars", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "analyticOrderAt", "kind": "definition", "module": "Mathlib.Analysis.Analytic.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "analyticOrderAt_of_not_analyticAt", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "analyticOrderNatAt_of_not_analyticAt", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Order", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "analyticOrderAt_eq_top", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eventuallyConst_iff_analyticOrderAt_sub_eq_top", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Order", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
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{"name": "AnalyticAt.analyticOrderAt_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Order", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AnalyticAt.analyticOrderAt_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "apply_eq_zero_of_analyticOrderAt_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Order", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "apply_eq_zero_of_analyticOrderNatAt_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Order", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
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{"name": "analyticOrderAt_neg", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Order", "is_tactic_proof": true, "tactics": ["by_cases", "refine", "simp", "exact", "rw"], "tactic_count": 5}
{"name": "le_analyticOrderAt_add", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Order", "is_tactic_proof": true, "tactics": ["by_cases", "by_cases", "refine", "simp", "refine", "filter_upwards", "simp", "simp"], "tactic_count": 8}
{"name": "le_analyticOrderAt_sub", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Order", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "analyticOrderAt_add_eq_left_of_lt", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "analyticOrderAt_add_eq_right_of_lt", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Order", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "analyticOrderAt_add_of_ne", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Order", "is_tactic_proof": true, "tactics": ["obtain", "simpa", "simpa"], "tactic_count": 3}
{"name": "analyticOrderAt_smul_eq_top_of_left", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Order", "is_tactic_proof": true, "tactics": ["rw", "obtain", "exact"], "tactic_count": 3}
{"name": "analyticOrderAt_smul_eq_top_of_right", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Order", "is_tactic_proof": true, "tactics": ["rw", "obtain", "exact"], "tactic_count": 3}
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{"name": "analyticOrderAt_centeredMonomial", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Order", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "analyticOrderAt_mul_eq_top_of_left", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "analyticOrderAt_mul_eq_top_of_right", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "analyticOrderAt_pow", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "analyticOrderNatAt_pow", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Order", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "AnalyticOnNhd.analyticOrderAt_ne_top_of_isPreconnected", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticOnNhd.codiscrete_setOf_analyticOrderAt_eq_zero_or_top", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Order", "is_tactic_proof": true, "tactics": ["simp_rw", "intro", "rcases", "filter_upwards", "simp", "filter_upwards", "simp"], "tactic_count": 7}
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{"name": "AnalyticOnNhd.eval_polynomial", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticOn.eval_polynomial", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticAt.aeval_mvPolynomial", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Polynomial", "is_tactic_proof": false, "tactics": ["apply", "p.induction_on", "simp_rw", "simp_rw", "simp_rw"], "tactic_count": 5}
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{"name": "AnalyticOnNhd.eval_continuousLinearMap", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticOnNhd.eval_continuousLinearMap'", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticOnNhd.eval_linearMap", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticOnNhd.eval_linearMap'", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticOnNhd.eval_mvPolynomial", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.radius_eq_liminf", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.RadiusLiminf", "is_tactic_proof": false, "tactics": ["have", "intro", "have", "conv_lhs", "rw", "mul_inv_cancel₀", "apply", "have", "obtain", "apply", "infer_param", "rw", "refine", "push_cast", "exact", "refine", "filter_upwards", "simpa"], "tactic_count": 18}
{"name": "FormalMultilinearSeries.radius_inv_eq_limsup", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.RadiusLiminf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsBigO.continuousMultilinearMap_apply_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Uniqueness", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "obtain", "clear", "rcases", "exact", "norm_eq_zero.mp", "simpa", "ht", "refine", "replace", "refine", "have", "obtain", "have", "rw", "exact", "have", "calc", "simpa", "simp", "ring", "have", "inv_mul_cancel_right₀", "calc", "simpa", "congr_arg", "rw", "simp", "rw", "simpa"], "tactic_count": 31}
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{"name": "HasFPowerSeriesAt.eq_formalMultilinearSeries", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Uniqueness", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFPowerSeriesAt.eq_formalMultilinearSeries_of_eventually", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Uniqueness", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFPowerSeriesAt.eq_zero_of_eventually", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Uniqueness", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFPowerSeriesOnBall.exchange_radius", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Uniqueness", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFPowerSeriesOnBall.r_eq_top_of_exists", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Uniqueness", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticOnNhd.eqOn_zero_of_preconnected_of_eventuallyEq_zero_aux", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Uniqueness", "is_tactic_proof": true, "tactics": ["that", "let", "suffices", "have", "intro", "simpa", "mem_of_mem_nhds", "contained", "on", "it", "rintro", "rcases", "obtain", "let", "have", "have", "have", "simp", "apply", "apply", "apply", "exact", "have", "filter_upwards", "have", "have", "have", "convert", "ext", "exact", "exact"], "tactic_count": 31}
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{"name": "AnalyticOnNhd.eq_of_eventuallyEq", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Uniqueness", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "WithLp.analyticOn_toLp", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.WithLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiLp.analyticOn_ofLp", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.WithLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiLp.analyticOn_toLp", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.WithLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "analyticWithinAt_of_singleton_mem", "kind": "theorem", "module": "Mathlib.Analysis.Analytic.Within", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "exact", "r_pos", "hasSum", "intro", "simp", "simp", "have", "rcases", "simp", "exact", "simp", "apply", "simp"], "tactic_count": 15}
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{"name": "Asymptotics.IsLittleO.def'", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsLittleO.eventuallyLE", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Asymptotics.IsBigOWith.isBigO", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Asymptotics.IsLittleO.isBigOWith", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsLittleO.isBigO", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsBigO.isBigOWith", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsBigOWith.weaken", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsBigOWith.exists_pos", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsBigO.exists_pos", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsBigOWith.exists_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsBigO.exists_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isBigO_iff_eventually_isBigOWith", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isBigO_iff_eventually", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsBigO.exists_mem_basis", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isBigOWith_inv", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Asymptotics.isLittleO_iff_nat_mul_le_aux", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "refine", "rw", "refine", "rwa", "have", "exact", "refine", "rcases", "have", "refine", "refine", "refine", "exact"], "tactic_count": 15}
{"name": "Asymptotics.isLittleO_iff_nat_mul_le", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isLittleO_iff_nat_mul_le'", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isLittleO_of_subsingleton", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isBigO_of_subsingleton", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isBigOWith_congr", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": true, "tactics": ["simp", "subst", "apply", "filter_upwards", "rw"], "tactic_count": 5}
{"name": "Asymptotics.IsBigOWith.congr'", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsBigOWith.congr", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsBigOWith.congr_left", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsBigOWith.congr_right", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsBigOWith.congr_const", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isBigO_congr", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Asymptotics.IsBigO.congr'", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsBigO.congr", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsBigO.congr_left", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsBigO.congr_right", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isLittleO_congr", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Asymptotics.IsLittleO.congr'", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsLittleO.congr", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsLittleO.congr_left", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsLittleO.congr_right", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.trans_isBigO", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.transEventuallyEqIsBigO", "kind": "instance", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.trans_isLittleO", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.transEventuallyEqIsLittleO", "kind": "instance", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsBigO.trans_eventuallyEq", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.transIsBigOEventuallyEq", "kind": "instance", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsLittleO.trans_eventuallyEq", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.transIsLittleOEventuallyEq", "kind": "instance", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsBigOWith.comp_tendsto", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsBigO.comp_tendsto", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsBigO.comp_neg_int", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Asymptotics.IsLittleO.comp_tendsto", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isBigOWith_map", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Asymptotics.isBigO_map", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Asymptotics.isLittleO_map", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Asymptotics.IsBigOWith.mono", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsBigO.mono", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsLittleO.mono", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsBigOWith.trans", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": true, "tactics": ["simp", "filter_upwards", "calc"], "tactic_count": 3}
{"name": "Asymptotics.IsBigO.trans", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.transIsBigOIsBigO", "kind": "instance", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsLittleO.trans_isBigOWith", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": true, "tactics": ["simp", "intro", "have", "exact"], "tactic_count": 4}
{"name": "Asymptotics.IsLittleO.trans_isBigO", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.transIsLittleOIsBigO", "kind": "instance", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsBigOWith.trans_isLittleO", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": true, "tactics": ["simp", "intro", "have", "exact"], "tactic_count": 4}
{"name": "Asymptotics.IsBigO.trans_isLittleO", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.transIsBigOIsLittleO", "kind": "instance", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsLittleO.trans", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.transIsLittleOIsLittleO", "kind": "instance", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Eventually.trans_isBigO", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Eventually.isBigO", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isBigOWith_of_le'", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isBigOWith_of_le", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isBigO_of_le'", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isBigO_of_le", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isBigOWith_refl", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isBigO_refl", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.isBigO", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsBigOWith.trans_le", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsBigO.trans_le", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsLittleO.trans_le", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isLittleO_irrefl'", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": true, "tactics": ["intro", "rcases", "rw", "exact"], "tactic_count": 4}
{"name": "Asymptotics.isLittleO_irrefl", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsBigO.not_isLittleO", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsLittleO.not_isBigO", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isBigOWith_bot", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isBigO_bot", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isLittleO_bot", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isBigOWith_pure", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsBigOWith.sup", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsBigOWith.sup'", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsBigO.sup", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsLittleO.sup", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isBigO_sup", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isLittleO_sup", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isBigOWith_insert", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Asymptotics.IsBigOWith.insert", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isLittleO_insert", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "rw", "rw", "exact"], "tactic_count": 5}
{"name": "Asymptotics.IsLittleO.insert", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isBigOWith_norm_right", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Asymptotics.isBigOWith_abs_right", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isBigO_norm_right", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Asymptotics.isBigO_abs_right", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isLittleO_norm_right", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Asymptotics.isLittleO_abs_right", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isBigOWith_norm_left", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Asymptotics.isBigOWith_abs_left", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isBigO_norm_left", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Asymptotics.isBigO_abs_left", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isLittleO_norm_left", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Asymptotics.isLittleO_abs_left", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isBigOWith_norm_norm", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isBigOWith_abs_abs", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isBigO_norm_norm", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isBigO_abs_abs", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isLittleO_norm_norm", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isLittleO_abs_abs", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isBigOWith_neg_right", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Asymptotics.isBigO_neg_right", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Asymptotics.isLittleO_neg_right", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Asymptotics.isBigOWith_neg_left", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Asymptotics.isBigO_neg_left", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Asymptotics.isLittleO_neg_left", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
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{"name": "Asymptotics.IsBigOWith.eventually_mul_div_cancel", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsBigO.eventually_mul_div_cancel", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsLittleO.eventually_mul_div_cancel", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ExpGrowth.expGrowthInf", "kind": "definition", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ExpGrowth.expGrowthSup", "kind": "definition", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ExpGrowth.expGrowthInf_def", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "ExpGrowth.expGrowthSup_def", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "ExpGrowth.expGrowthInf_congr", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ExpGrowth.expGrowthSup_congr", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ExpGrowth.expGrowthInf_eventually_monotone", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ExpGrowth.expGrowthInf_monotone", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ExpGrowth.expGrowthSup_eventually_monotone", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ExpGrowth.expGrowthSup_monotone", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ExpGrowth.expGrowthInf_le_expGrowthSup", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ExpGrowth.expGrowthInf_le_expGrowthSup_of_frequently_le", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ExpGrowth.expGrowthInf_le_iff", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "ExpGrowth.le_expGrowthInf_iff", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": true, "tactics": ["rw", "refine", "nth_rw", "exact"], "tactic_count": 4}
{"name": "ExpGrowth.expGrowthSup_le_iff", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "ExpGrowth.le_expGrowthSup_iff", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": true, "tactics": ["rw", "refine", "nth_rw", "exact"], "tactic_count": 4}
{"name": "ExpGrowth.frequently_le_exp", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ExpGrowth.eventually_exp_le", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ExpGrowth.eventually_le_exp", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ExpGrowth.frequently_exp_le", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Frequently.expGrowthInf_le", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": true, "tactics": ["apply", "gcongr"], "tactic_count": 2}
{"name": "Eventually.le_expGrowthInf", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Eventually.expGrowthSup_le", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Frequently.le_expGrowthSup", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ExpGrowth.expGrowthSup_zero", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": true, "tactics": ["rw", "congr", "ext", "rw"], "tactic_count": 4}
{"name": "ExpGrowth.expGrowthInf_zero", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": true, "tactics": ["apply", "rw", "exact"], "tactic_count": 3}
{"name": "ExpGrowth.expGrowthInf_top", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "ExpGrowth.expGrowthSup_top", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": true, "tactics": ["apply", "rw", "exact"], "tactic_count": 3}
{"name": "ExpGrowth.expGrowthInf_const", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ExpGrowth.expGrowthSup_const", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ExpGrowth.expGrowthInf_pow", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "log_pow,"], "tactic_count": 4}
{"name": "ExpGrowth.expGrowthSup_pow", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "log_pow,"], "tactic_count": 4}
{"name": "ExpGrowth.expGrowthInf_exp", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ExpGrowth.expGrowthSup_exp", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ExpGrowth.le_expGrowthInf_mul", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "ExpGrowth.expGrowthInf_mul_le", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "ExpGrowth.expGrowthInf_mul_le'", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ExpGrowth.le_expGrowthSup_mul", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "ExpGrowth.le_expGrowthSup_mul'", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ExpGrowth.expGrowthSup_mul_le", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "ExpGrowth.expGrowthInf_inv", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw"], "tactic_count": 3}
{"name": "ExpGrowth.expGrowthSup_inv", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw"], "tactic_count": 3}
{"name": "ExpGrowth.expGrowthInf_le_of_eventually_le", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": true, "tactics": ["apply", "rcases", "simp", "apply", "exact", "exact", "exact"], "tactic_count": 7}
{"name": "ExpGrowth.expGrowthSup_le_of_eventually_le", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": true, "tactics": ["apply", "rcases", "simp", "apply", "exact", "exact", "exact"], "tactic_count": 7}
{"name": "ExpGrowth.expGrowthInf_of_eventually_ge", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": true, "tactics": ["apply", "rcases", "rw", "exact", "rw"], "tactic_count": 5}
{"name": "ExpGrowth.expGrowthSup_of_eventually_ge", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": true, "tactics": ["apply", "rcases", "exact", "rw"], "tactic_count": 4}
{"name": "ExpGrowth.expGrowthInf_inf", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "ExpGrowth.expGrowthInfTopHom", "kind": "definition", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ExpGrowth.expGrowthInf_biInf", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "ExpGrowth.expGrowthInf_iInf", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ExpGrowth.expGrowthSup_sup", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "ExpGrowth.expGrowthSupBotHom", "kind": "definition", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ExpGrowth.expGrowthSup_biSup", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "ExpGrowth.expGrowthSup_iSup", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ExpGrowth.le_expGrowthInf_add", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ExpGrowth.expGrowthSup_add", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": true, "tactics": ["rw", "apply", "refine", "rw", "exact", "refine", "exact", "sup_le"], "tactic_count": 8}
{"name": "ExpGrowth.expGrowthSup_sum", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "insert", "rw", "ha]"], "tactic_count": 6}
{"name": "ExpGrowth.le_expGrowthInf_comp", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": true, "tactics": ["apply", "rw", "rwa"], "tactic_count": 3}
{"name": "ExpGrowth.expGrowthSup_comp_le", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": true, "tactics": ["apply", "rwa"], "tactic_count": 2}
{"name": "Monotone.expGrowthInf_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": true, "tactics": ["apply", "simp", "exact"], "tactic_count": 3}
{"name": "Monotone.expGrowthSup_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ExpGrowth.expGrowthInf_comp_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": true, "tactics": ["apply", "simp", "exact"], "tactic_count": 3}
{"name": "ExpGrowth.expGrowthSup_comp_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.expGrowthInf_comp_le", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.le_expGrowthSup_comp", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.expGrowthInf_comp", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.expGrowthSup_comp", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.expGrowthInf_comp_mul", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.expGrowthSup_comp_mul", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.ExpGrowth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isBigOWith_principal", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Asymptotics.isBigO_principal", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Asymptotics.isLittleO_principal", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": true, "tactics": ["refine", "simp", "have", "apply", "apply", "exact", "apply", "exact"], "tactic_count": 8}
{"name": "Asymptotics.isBigOWith_top", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Asymptotics.isBigO_top", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Asymptotics.isLittleO_top", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Asymptotics.isBigOWith_const_one", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Asymptotics.isBigO_const_one", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isLittleO_const_iff_isLittleO_one", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isLittleO_one_iff", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": true, "tactics": ["simp", "dist_zero_right]"], "tactic_count": 2}
{"name": "Asymptotics.isBigO_one_iff", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Asymptotics.isLittleO_one_left_iff", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.isBigO_one", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsBigO.trans_tendsto_nhds", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isBigO_one_nhds_ne_iff", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": true, "tactics": ["refine", "simp", "obtain", "use", "filter_upwards", "rcases", "apply", "exact"], "tactic_count": 8}
{"name": "Asymptotics.isLittleO_const_iff", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isLittleO_id_const", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.IsBoundedUnder.isBigO_const", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isBigO_const_of_tendsto", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsBigO.isBoundedUnder_le", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isBigO_const_of_ne", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isBigO_const_iff", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": true, "tactics": ["refine", "rintro", "rcases", "exacts"], "tactic_count": 4}
{"name": "Asymptotics.isBigO_iff_isBoundedUnder_le_div", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Asymptotics.isBigO_const_left_iff_pos_le_norm", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rcases", "refine", "exact", "rintro", "refine", "rw", "exact"], "tactic_count": 9}
{"name": "Asymptotics.IsBigO.trans_tendsto", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsLittleO.trans_tendsto", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isLittleO_id_one", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.continuousAt_iff_isLittleO", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Asymptotics.IsBigO.of_pow", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": true, "tactics": ["rcases", "obtain", "exact"], "tactic_count": 3}
{"name": "Asymptotics.IsBigO.pow_of_le_right", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "Asymptotics.IsBigOWith.const_smul_self", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsBigO.const_smul_self", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsBigOWith.const_smul_left", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsBigO.const_smul_left", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsLittleO.const_smul_left", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isBigO_const_smul_left", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": true, "tactics": ["have", "rw", "simp", "rw"], "tactic_count": 4}
{"name": "Asymptotics.isLittleO_const_smul_left", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": true, "tactics": ["have", "rw", "simp", "rw"], "tactic_count": 4}
{"name": "Asymptotics.isBigO_const_smul_right", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": true, "tactics": ["have", "rw", "simp", "rw"], "tactic_count": 4}
{"name": "Asymptotics.isLittleO_const_smul_right", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": true, "tactics": ["have", "rw", "simp", "rw"], "tactic_count": 4}
{"name": "Asymptotics.IsBigOWith.smul", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": true, "tactics": ["simp", "filter_upwards", "apply", "convert", "rw"], "tactic_count": 5}
{"name": "Asymptotics.IsBigO.smul", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "exact"], "tactic_count": 3}
{"name": "Asymptotics.IsBigO.smul_isLittleO", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": true, "tactics": ["simp", "intro", "rcases", "exact"], "tactic_count": 4}
{"name": "Asymptotics.IsLittleO.smul_isBigO", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": true, "tactics": ["simp", "intro", "rcases", "exact"], "tactic_count": 4}
{"name": "Asymptotics.IsLittleO.smul", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsBigO.listProd", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "simp", "exact"], "tactic_count": 5}
{"name": "Asymptotics.IsBigO.multisetProd", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Asymptotics.IsBigO.finsetProd", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsLittleO.listProd", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "ihL", "simp", "cases", "inl", "inr"], "tactic_count": 8}
{"name": "Asymptotics.IsLittleO.multisetProd", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Asymptotics.IsLittleO.finsetProd", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsLittleO.tendsto_div_nhds_zero", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsLittleO.tendsto_inv_smul_nhds_zero", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": true, "tactics": ["simpa", "h.norm_norm.tendsto_div_nhds_zero"], "tactic_count": 2}
{"name": "Asymptotics.isLittleO_iff_tendsto'", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isLittleO_iff_tendsto", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isLittleO_const_left_of_ne", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Asymptotics.isLittleO_const_left", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simp"], "tactic_count": 3}
{"name": "Asymptotics.isLittleO_const_const_iff", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": true, "tactics": ["have", "simp", "exact"], "tactic_count": 3}
{"name": "Asymptotics.isLittleO_pure", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isLittleO_const_id_cobounded", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isLittleO_const_id_atTop", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isLittleO_const_id_atBot", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isBigOWith_of_eq_mul", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": true, "tactics": ["simp", "refine", "simp", "refine", "gcongr"], "tactic_count": 5}
{"name": "Asymptotics.isBigOWith_iff_exists_eq_mul", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": true, "tactics": ["constructor", "intro", "use", "refine", "simpa", "rintro", "exact"], "tactic_count": 7}
{"name": "Asymptotics.IsBigOWith.exists_eq_mul", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isBigO_iff_exists_eq_mul", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "rcases", "rcases", "exact", "rintro", "exact"], "tactic_count": 7}
{"name": "Asymptotics.isLittleO_iff_exists_eq_mul", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": true, "tactics": ["constructor", "exact", "simp", "rintro", "rw", "exact"], "tactic_count": 6}
{"name": "Asymptotics.div_isBoundedUnder_of_isBigO", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": true, "tactics": ["obtain", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "Asymptotics.isBigO_iff_div_isBoundedUnder", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": true, "tactics": ["refine", "obtain", "simp", "refine", "by_cases", "simp", "exact"], "tactic_count": 7}
{"name": "Asymptotics.isBigO_of_div_tendsto_nhds", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsLittleO.tendsto_zero_of_tendsto", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": true, "tactics": ["suffices", "exact"], "tactic_count": 2}
{"name": "Asymptotics.isLittleO_pow_pow", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": true, "tactics": ["rcases", "suffices", "exact"], "tactic_count": 3}
{"name": "Asymptotics.isLittleO_norm_pow_norm_pow", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isLittleO_pow_id", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "Asymptotics.isLittleO_norm_pow_id", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": true, "tactics": ["have", "simp", "exact"], "tactic_count": 3}
{"name": "Asymptotics.IsBigO.eq_zero_of_norm_pow_within", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsBigO.eq_zero_of_norm_pow", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Asymptotics.isLittleO_pow_sub_pow_sub", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isLittleO_pow_sub_sub", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Asymptotics.IsBigOWith.right_le_sub_of_lt_one", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsBigOWith.right_le_add_of_lt_one", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsLittleO.right_isBigO_sub", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsLittleO.right_isBigO_add", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsLittleO.right_isBigO_add'", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.bound_of_isBigO_cofinite", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": true, "tactics": ["rcases", "rw", "rcases", "have", "refine", "rw", "exact"], "tactic_count": 7}
{"name": "Asymptotics.isBigO_cofinite_iff", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": true, "tactics": ["classical", "exact", "let"], "tactic_count": 3}
{"name": "Asymptotics.bound_of_isBigO_nat_atTop", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isBigO_nat_atTop_iff", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Asymptotics.isBigO_one_nat_atTop_iff", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsBigO.nat_of_atTop", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": true, "tactics": ["obtain", "refine", "filter_upwards", "by_cases", "simp", "exact"], "tactic_count": 6}
{"name": "Asymptotics.isBigOWith_pi", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": true, "tactics": ["have", "simp"], "tactic_count": 2}
{"name": "Asymptotics.isBigO_pi", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Asymptotics.isLittleO_pi", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Asymptotics.IsBigO.natCast_atTop", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsLittleO.natCast_atTop", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isBigO_atTop_iff_eventually_exists", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Asymptotics.isBigO_atTop_iff_eventually_exists_pos", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Asymptotics.isBigOWith_mul_iff_isBigOWith_div", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "refine", "refine", "rw"], "tactic_count": 4}
{"name": "Asymptotics.isBigO_mul_iff_isBigO_div", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Asymptotics.isLittleO_mul_iff_isLittleO_div", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Asymptotics.isBigO_nat_atTop_induction", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "obtain", "obtain", "rw", "rw", "obtain", "let", "let", "have", "rw", "intro", "calc", "gcongr", "exact", "refine", "filter_upwards", "induction", "ind", "refine", "by_cases", "have", "grw", "grind", "grind"], "tactic_count": 24}
{"name": "Asymptotics.isBigO_nat_atTop_induction_of_eventually_pos", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": true, "tactics": ["refine", "filter_upwards", "hrec", "filter_upwards", "obtain", "refine", "filter_upwards", "grind"], "tactic_count": 8}
{"name": "summable_of_isBigO", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "summable_of_isBigO_nat", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsBigO.comp_summable_norm", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Summable.mul_tendsto_const", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": true, "tactics": ["apply", "simpa"], "tactic_count": 2}
{"name": "OpenPartialHomeomorph.isBigOWith_congr", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.isBigO_congr", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "OpenPartialHomeomorph.isLittleO_congr", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Homeomorph.isBigOWith_congr", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.isBigO_congr", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Homeomorph.isLittleO_congr", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "ContinuousOn.isBigOWith_principal", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "exact", "hs.image_of_continuousOn"], "tactic_count": 3}
{"name": "ContinuousOn.isBigO_principal", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.isBigOWith_rev_principal", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": true, "tactics": ["refine", "rw", "replace", "have", "refine", "le_mul_of_one_le_right", "obtain", "rw", "exact"], "tactic_count": 9}
{"name": "ContinuousOn.isBigO_rev_principal", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedField.tendsto_zero_smul_of_tendsto_zero_of_bounded", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "LinearGrowth.linearGrowthInf", "kind": "definition", "module": "Mathlib.Analysis.Asymptotics.LinearGrowth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearGrowth.linearGrowthSup", "kind": "definition", "module": "Mathlib.Analysis.Asymptotics.LinearGrowth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearGrowth.linearGrowthInf_congr", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.LinearGrowth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearGrowth.linearGrowthSup_congr", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.LinearGrowth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearGrowth.linearGrowthInf_eventually_monotone", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.LinearGrowth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearGrowth.linearGrowthInf_monotone", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.LinearGrowth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearGrowth.linearGrowthSup_eventually_monotone", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.LinearGrowth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearGrowth.linearGrowthSup_monotone", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.LinearGrowth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearGrowth.linearGrowthInf_le_linearGrowthSup_of_frequently_le", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.LinearGrowth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearGrowth.linearGrowthInf_le_iff", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.LinearGrowth", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw"], "tactic_count": 3}
{"name": "LinearGrowth.le_linearGrowthInf_iff", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.LinearGrowth", "is_tactic_proof": true, "tactics": ["rw", "refine", "nth_rw"], "tactic_count": 3}
{"name": "LinearGrowth.linearGrowthSup_le_iff", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.LinearGrowth", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw"], "tactic_count": 3}
{"name": "LinearGrowth.le_linearGrowthSup_iff", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.LinearGrowth", "is_tactic_proof": true, "tactics": ["rw", "refine", "nth_rw"], "tactic_count": 3}
{"name": "LinearGrowth.frequently_le_mul", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.LinearGrowth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearGrowth.eventually_mul_le", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.LinearGrowth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearGrowth.eventually_le_mul", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.LinearGrowth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearGrowth.frequently_mul_le", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.LinearGrowth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Frequently.linearGrowthInf_le", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.LinearGrowth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Eventually.le_linearGrowthInf", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.LinearGrowth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Eventually.linearGrowthSup_le", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.LinearGrowth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Frequently.le_linearGrowthSup", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.LinearGrowth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearGrowth.linearGrowthSup_bot", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.LinearGrowth", "is_tactic_proof": true, "tactics": ["nth_rw", "refine", "exact"], "tactic_count": 3}
{"name": "LinearGrowth.linearGrowthInf_bot", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.LinearGrowth", "is_tactic_proof": true, "tactics": ["apply", "rw", "exact"], "tactic_count": 3}
{"name": "LinearGrowth.linearGrowthInf_top", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.LinearGrowth", "is_tactic_proof": true, "tactics": ["nth_rw", "refine", "exact"], "tactic_count": 3}
{"name": "LinearGrowth.linearGrowthSup_top", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.LinearGrowth", "is_tactic_proof": true, "tactics": ["apply", "rw", "exact"], "tactic_count": 3}
{"name": "LinearGrowth.linearGrowthInf_const", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.LinearGrowth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearGrowth.linearGrowthSup_const", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.LinearGrowth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearGrowth.linearGrowthInf_zero", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.LinearGrowth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearGrowth.linearGrowthSup_zero", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.LinearGrowth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearGrowth.linearGrowthInf_const_mul_self", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.LinearGrowth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearGrowth.linearGrowthSup_const_mul_self", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.LinearGrowth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearGrowth.linearGrowthInf_natCast_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.LinearGrowth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearGrowth.tendsto_atTop_of_linearGrowthInf_pos", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.LinearGrowth", "is_tactic_proof": true, "tactics": ["obtain", "apply", "refine", "lift", "rw", "obtain", "refine", "rw", "exact"], "tactic_count": 9}
{"name": "LinearGrowth.le_linearGrowthInf_add", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.LinearGrowth", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "LinearGrowth.linearGrowthInf_add_le", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.LinearGrowth", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "LinearGrowth.linearGrowthInf_add_le'", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.LinearGrowth", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "LinearGrowth.le_linearGrowthSup_add", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.LinearGrowth", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "LinearGrowth.le_linearGrowthSup_add'", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.LinearGrowth", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "LinearGrowth.linearGrowthSup_add_le", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.LinearGrowth", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "LinearGrowth.linearGrowthInf_neg", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.LinearGrowth", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw"], "tactic_count": 3}
{"name": "LinearGrowth.linearGrowthSup_inv", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.LinearGrowth", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw"], "tactic_count": 3}
{"name": "LinearGrowth.linearGrowthInf_le_of_eventually_le", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.LinearGrowth", "is_tactic_proof": true, "tactics": ["apply", "rcases", "simp", "apply", "exact", "exact", "exact"], "tactic_count": 7}
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{"name": "LinearGrowth.linearGrowthInf_inf", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.LinearGrowth", "is_tactic_proof": true, "tactics": ["rw", "refine", "exact"], "tactic_count": 3}
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{"name": "LinearGrowth.linearGrowthInf_biInf", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.LinearGrowth", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
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{"name": "LinearGrowth.Real.eventually_atTop_exists_nat_between", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.LinearGrowth", "is_tactic_proof": true, "tactics": ["filter_upwards", "refine", "apply", "norm_cast", "exact"], "tactic_count": 5}
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{"name": "LinearGrowth.tendsto_atTop_of_linearGrowthInf_natCast_pos", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.LinearGrowth", "is_tactic_proof": true, "tactics": ["refine", "have", "refine", "rw", "exact"], "tactic_count": 5}
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{"name": "LinearGrowth.linearGrowthInf_comp_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.LinearGrowth", "is_tactic_proof": true, "tactics": ["simp", "obtain", "have", "apply", "rcases", "rw", "rw"], "tactic_count": 7}
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{"name": "Monotone.linearGrowthInf_comp_mul", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.LinearGrowth", "is_tactic_proof": false, "tactics": ["have", "refine", "rw", "exact", "exact"], "tactic_count": 5}
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{"name": "pow_div_pow_eventuallyEq_atTop", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.SpecificAsymptotics", "is_tactic_proof": true, "tactics": ["apply", "intro", "simp"], "tactic_count": 3}
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{"name": "tendsto_pow_div_pow_atTop_atTop", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.SpecificAsymptotics", "is_tactic_proof": true, "tactics": ["rw", "apply", "lia"], "tactic_count": 3}
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{"name": "Asymptotics.IsEquivalent.rpow", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.SpecificAsymptotics", "is_tactic_proof": true, "tactics": ["obtain", "rw", "have", "rw", "exact", "use", "conv", "filter_upwards", "simp"], "tactic_count": 9}
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{"name": "Asymptotics.SuperpolynomialDecay.congr'", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.SuperpolynomialDecay", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Asymptotics.SuperpolynomialDecay.mul_const", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.SuperpolynomialDecay", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Asymptotics.superpolynomialDecay_const_mul_iff", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.SuperpolynomialDecay", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Asymptotics.SuperpolynomialDecay.param_inv_mul", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.SuperpolynomialDecay", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Asymptotics.superpolynomialDecay_mul_param_pow_iff", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.SuperpolynomialDecay", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Asymptotics.superpolynomialDecay_iff_norm_tendsto_zero", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.SuperpolynomialDecay", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.superpolynomialDecay_iff_superpolynomialDecay_norm", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.SuperpolynomialDecay", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Asymptotics.IsLittleOTVS.congr_right", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isBigOTVS_congr", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": true, "tactics": ["simp", "peel", "exact"], "tactic_count": 3}
{"name": "Asymptotics.IsBigOTVS.congr'", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsBigOTVS.congr", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsBigOTVS.congr_left", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsBigOTVS.congr_right", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsBigOTVS.refl", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Asymptotics.IsBigOTVS.rfl", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsThetaTVS.refl", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsThetaTVS.rfl", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsLittleOTVS.isBigOTVS", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": true, "tactics": ["refine", "rcases", "use", "simpa"], "tactic_count": 4}
{"name": "Asymptotics.IsThetaTVS.isBigOTVS", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsThetaTVS.symm", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isThetaTVS_comm", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsBigOTVS.trans", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": true, "tactics": ["refine", "obtain", "obtain", "refine", "filter_upwards"], "tactic_count": 5}
{"name": "Asymptotics.instTransIsBigOTVSIsBigOTVS", "kind": "instance", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsBigOTVS.trans_isThetaTVS", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.instTransIsBigOTVSIsThetaTVS", "kind": "instance", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsThetaTVS.trans_isBigOTVS", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.instTransIsThetaOTVSIsBigOTVS", "kind": "instance", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsThetaTVS.trans", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.instTransIsThetaOTVS", "kind": "instance", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsLittleOTVS.trans_isBigOTVS", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": true, "tactics": ["refine", "obtain", "obtain", "refine", "filter_upwards"], "tactic_count": 5}
{"name": "Asymptotics.instTransIsLittleOTVSIsBigOTVS", "kind": "instance", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsLittleOTVS.trans_isThetaTVS", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.instTransIsLittleOTVSIsThetaTVS", "kind": "instance", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsBigOTVS.trans_isLittleOTVS", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": true, "tactics": ["refine", "obtain", "obtain", "refine", "filter_upwards"], "tactic_count": 5}
{"name": "Asymptotics.instTransIsBigOTVSIsLittleOTVS", "kind": "instance", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsThetaTVS.trans_isLittleOTVS", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.instTransIsThetaTVSIsLittleOTVS", "kind": "instance", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsLittleOTVS.trans", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.instTransIsLittleOTVSIsLittleOTVS", "kind": "instance", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.isLittleOTVS_iff", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": true, "tactics": ["rw", "refine", "rintro", "exact", "refine", "simp", "gcongr"], "tactic_count": 7}
{"name": "Filter.HasBasis.isBigOTVS_iff", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": true, "tactics": ["rw", "refine", "rintro", "exact", "exact"], "tactic_count": 5}
{"name": "Asymptotics.IsBigOTVS.of_egauge_le_mul", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": true, "tactics": ["rw", "intro", "rcases", "rcases", "have", "refine", "refine", "simp", "grw", "simp"], "tactic_count": 10}
{"name": "Asymptotics.isLittleOTVS_iff_smallSets", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isBigOTVS_iff_smallSets", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isLittleOTVS_map", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Asymptotics.isBigOTVS_map", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Asymptotics.IsLittleOTVS.mono", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsBigOTVS.mono", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsLittleOTVS.comp_tendsto", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsBigOTVS.comp_tendsto", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isLittleOTVS_sup", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Asymptotics.IsLittleOTVS.sup", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.isBigOTVS_id", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.isBigOTVS_comp", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.isBigOTVS_fun_comp", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.isBigOTVS_rev_comp", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rcases", "use", "filter_upwards", "refine", "apply", "grw", "exact"], "tactic_count": 9}
{"name": "ContinuousLinearMap.isThetaTVS_comp", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsLittleOTVS.zero", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": true, "tactics": ["refine", "use", "simp"], "tactic_count": 3}
{"name": "Asymptotics.isLittleOTVS_insert", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Asymptotics.IsLittleOTVS.insert", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsLittleOTVS.bot", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsLittleOTVS.prodMk", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": true, "tactics": ["rw", "rintro", "rcases", "refine", "filter_upwards", "simp"], "tactic_count": 6}
{"name": "Asymptotics.IsLittleOTVS.fst", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsLittleOTVS.snd", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isLittleOTVS_prodMk_left", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsBigOTVS.prodMk", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": true, "tactics": ["rw", "rintro", "rcases", "refine", "filter_upwards", "simp"], "tactic_count": 6}
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{"name": "Asymptotics.IsBigOTVS.snd", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isBigOTVS_prodMk_left", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsLittleOTVS.add", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsBigOTVS.add", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsLittleOTVS.triangle", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Asymptotics.IsBigOTVS.triangle", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Asymptotics.IsBigOTVS.neg_left", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isBigOTVS_neg_left", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isBigOTVS_fun_neg_left", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsLittleOTVS.neg_left", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isLittleOTVS_neg_left", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isLittleOTVS_fun_neg_left", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsLittleOTVS.symm", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Asymptotics.isLittleOTVS_comm", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isLittleOTVS_fun_comm", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsBigOTVS.symm", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Asymptotics.isBigOTVS_comm", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isBigOTVS_fun_comm", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsBigOTVS.neg_right", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isBigOTVS_neg_right", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isBigOTVS_fun_neg_right", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsLittleOTVS.neg_right", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isLittleOTVS_neg_right", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isLittleOTVS_fun_neg_right", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsLittleOTVS.pi", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": true, "tactics": ["have", "rw", "simp", "rintro", "have", "rcases", "refine", "refine", "simpa"], "tactic_count": 9}
{"name": "Asymptotics.IsLittleOTVS.proj", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isLittleOTVS_pi", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsBigOTVS.pi", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": true, "tactics": ["have", "rw", "simp", "rintro", "have", "rcases", "use", "refine", "simpa"], "tactic_count": 9}
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{"name": "Asymptotics.isBigOTVS_pi", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsLittleOTVS.smul_left", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": true, "tactics": ["simp", "peel", "simp", "rw", "gcongr", "all_goals"], "tactic_count": 6}
{"name": "Asymptotics.isLittleOTVS_one", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "rw", "rintro", "rcases", "lift", "norm_cast", "rcases", "obtain", "apply", "refine", "fun_prop", "first", "apply", "positivity)", "filter_upwards", "refine", "calc", "rw", "gcongr", "simpa", "simp", "intro", "refine", "rcases", "replace", "filter_upwards", "calc", "egauge", "apply", "simpa"], "tactic_count": 32}
{"name": "Asymptotics.IsLittleOTVS.tendsto_inv_smul", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": true, "tactics": ["rw", "intro", "rcases", "refine", "by_cases"], "tactic_count": 5}
{"name": "Asymptotics.isLittleOTVS_iff_tendsto_inv_smul", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": true, "tactics": ["refine", "refine", "by_cases"], "tactic_count": 3}
{"name": "Asymptotics.Filter.Tendsto.isBigOTVS_one", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": true, "tactics": ["replace", "rw", "rintro", "obtain", "apply", "refine", "refine", "suffices", "simpa", "use", "filter_upwards", "calc", "egauge", "simpa", "apply", "refine", "simp", "rwa"], "tactic_count": 18}
{"name": "Asymptotics.isLittleOTVS_iff_isLittleO", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": true, "tactics": ["rcases", "have", "simp", "refine", "rcases", "lift", "filter_upwards", "suffices", "rw", "rw", "exact_mod_cast", "calc", "gcongr", "exacts", "filter_upwards", "lift", "calc", "egauge", "simp"], "tactic_count": 19}
{"name": "Asymptotics.isBigOTVS_iff_isBigO", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.TVS", "is_tactic_proof": true, "tactics": ["rcases", "constructor", "rw", "intro", "rcases", "lift", "norm_cast", "refine", "suffices", "simp", "exact", "calc", "rw", "have", "rintro", "lift", "lift", "refine", "calc", "egauge", "gcongr", "simp", "exact", "simp_all", "ac_rfl"], "tactic_count": 25}
{"name": "Asymptotics.IsTheta", "kind": "definition", "module": "Mathlib.Analysis.Asymptotics.Theta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.term_=Θ[_]_", "kind": "definition", "module": "Mathlib.Analysis.Asymptotics.Theta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics._aux_Mathlib_Analysis_Asymptotics_Theta___macroRules_Asymptotics_term_=Θ[_]__1", "kind": "definition", "module": "Mathlib.Analysis.Asymptotics.Theta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics._aux_Mathlib_Analysis_Asymptotics_Theta___unexpand_Asymptotics_IsTheta_1", "kind": "definition", "module": "Mathlib.Analysis.Asymptotics.Theta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsBigO.antisymm", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Theta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsTheta.isBigO", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Theta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsTheta.isBigO_symm", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Theta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isTheta_refl", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Theta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isTheta_rfl", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Theta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsTheta.symm", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Theta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isTheta_comm", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Theta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsTheta.trans", "kind": "theorem", "module": "Mathlib.Analysis.Asymptotics.Theta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.instTransForallIsTheta", "kind": "instance", "module": "Mathlib.Analysis.Asymptotics.Theta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "BoxIntegral.Integrable.tendsto_integralSum_toFilter_prod_self_inf_iUnion_eq_uniformity", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Basic", "is_tactic_proof": false, "tactics": ["refine", "replace", "use", "rw", "exact"], "tactic_count": 5}
{"name": "BoxIntegral.Integrable.cauchy_map_integralSum_toFilteriUnion", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact", "h.tendsto_integralSum_toFilter_prod_self_inf_iUnion_eq_uniformity.mono_left"], "tactic_count": 4}
{"name": "BoxIntegral.Integrable.to_subbox_aux", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Basic", "is_tactic_proof": false, "tactics": ["refine", "convert", "hy.comp"], "tactic_count": 3}
{"name": "BoxIntegral.Integrable.to_subbox", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Integrable.tendsto_integralSum_toFilteriUnion_single", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Integrable.dist_integralSum_sum_integral_le_of_memBaseSet_of_iUnion_eq", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Basic", "is_tactic_proof": true, "tactics": ["refine", "le_of_forall_pos_le_add", "set", "have", "have", "set", "have", "πi.IsPartition", "dist", "intro", "have", "have", "set", "have", "rcases", "have", "exact", "have", "exact", "exact", "same", "choose", "have", "biUnionTagged_memBaseSet", "have", "have", "rw", "calc", "dist", "dist", "dist", "dist_triangle"], "tactic_count": 32}
{"name": "BoxIntegral.Integrable.dist_integralSum_sum_integral_le_of_memBaseSet", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Integrable.tendsto_integralSum_sum_integral", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Basic", "is_tactic_proof": true, "tactics": ["refine", "refine", "simp", "rintro", "exact"], "tactic_count": 5}
{"name": "BoxIntegral.Integrable.sum_integral_congr", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "BoxIntegral.Integrable.toBoxAdditive", "kind": "definition", "module": "Mathlib.Analysis.BoxIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.integrable_of_bounded_and_ae_continuousWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Basic", "is_tactic_proof": true, "tactics": ["two", "sufficiently", "refine", "rcases", "rcases", "have", "obtain", "exact", "rcases", "have", "let", "let", "have", "rcases", "exact", "obtain", "rw", "have", "have", "intro", "suffices", "simpa", "rcases", "an", "fully", "refine", "simp", "have", "let", "let", "let", "classical", "let", "have", "have", "lt_top_iff_ne_top.1", "have", "iUnion_subset_iff.2", "rw", "apply", "le_trans", "the", "have", "intro", "rw", "rw", "gcongr", "obtain", "have", "have", "apply", "refine", "exact", "exact", "h₂.isSubordinate.infPrepartition", "rw", "simpa", "refine", "rw", "trans", "linarith", "simp_rw", "refine", "simp_rw", "rw", "refine", "refine", "exact", "have", "intro", "rw", "gcongr", "apply", "apply", "simp_rw", "suffices", "linarith", "rw", "refine", "trans", "simp", "exact", "le_of_eq", "measure_biUnion_finset", "apply", "simp_rw", "exact"], "tactic_count": 87}
{"name": "BoxIntegral.integrable_of_bounded_and_ae_continuous", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.integrable_of_continuousOn", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Basic", "is_tactic_proof": true, "tactics": ["apply", "obtain", "use", "simpa", "refine", "rw"], "tactic_count": 6}
{"name": "BoxIntegral.HasIntegral.of_bRiemann_eq_false_of_forall_isLittleO", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Basic", "is_tactic_proof": true, "tactics": ["that", "that", "need", "box", "refine", "intro", "simp", "choose", "choose", "have", "rcases", "simp", "rcases", "classical", "set", "refine", "simp", "rintro", "rw", "sum_filter_add_sum_filter_not", "sum_filter_add_sum_filter_not", "refine", "rcases", "simp", "same", "specialize", "have", "rw", "refine", "convert", "refine", "rw", "refine", "rintro", "rw", "refine", "refine", "exact", "rw", "exact", "calc", "dist", "dist_sum_sum_le_of_le", "rw", "refine", "convert", "gcongr", "exact", "apply"], "tactic_count": 49}
{"name": "BoxIntegral.HasIntegral.of_le_Henstock_of_forall_isLittleO", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.HasIntegral.mcShane_of_forall_isLittleO", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Box.instInhabited", "kind": "instance", "module": "Mathlib.Analysis.BoxIntegral.Box.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Box.lower_le_upper", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Box.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Box.lower_ne_upper", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Box.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Box.instMembershipForallReal", "kind": "instance", "module": "Mathlib.Analysis.BoxIntegral.Box.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Box.toSet", "kind": "definition", "module": "Mathlib.Analysis.BoxIntegral.Box.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Box.instCoeTCSetForallReal", "kind": "instance", "module": "Mathlib.Analysis.BoxIntegral.Box.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Box.mem_mk", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Box.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Box.mem_coe", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Box.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Box.mem_def", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Box.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Box.mem_univ_Ioc", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Box.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Box.coe_eq_pi", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Box.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Box.upper_mem", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Box.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Box.exists_mem", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Box.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Box.nonempty_coe", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Box.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Box.coe_ne_empty", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Box.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Box.empty_ne_coe", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Box.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Box.instLE", "kind": "instance", "module": "Mathlib.Analysis.BoxIntegral.Box.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Box.le_def", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Box.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Box.le_TFAE", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Box.Basic", "is_tactic_proof": true, "tactics": ["tfae_have", "tfae_have", "h", "tfae_have", "tfae_have", "h,", "tfae_finish"], "tactic_count": 7}
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{"name": "BoxIntegral.Box.le_iff_bounds", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Box.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Box.injective_coe", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Box.Basic", "is_tactic_proof": true, "tactics": ["rintro", "simp", "congr", "exacts"], "tactic_count": 4}
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{"name": "BoxIntegral.Box.ext", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Box.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Box.ne_of_disjoint_coe", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Box.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Box.instPartialOrder", "kind": "instance", "module": "Mathlib.Analysis.BoxIntegral.Box.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Box.Icc", "kind": "definition", "module": "Mathlib.Analysis.BoxIntegral.Box.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Box.Icc_def", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Box.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Box.upper_mem_Icc", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Box.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Box.lower_mem_Icc", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Box.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Box.isCompact_Icc", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Box.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Box.Icc_eq_pi", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Box.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "BoxIntegral.Box.antitone_lower", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Box.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Box.monotone_upper", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Box.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Box.coe_subset_Icc", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Box.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Box.isBounded_Icc", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Box.Basic", "is_tactic_proof": true, "tactics": ["cases", "exact"], "tactic_count": 2}
{"name": "BoxIntegral.Box.isBounded", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Box.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Box.instSemilatticeSup", "kind": "instance", "module": "Mathlib.Analysis.BoxIntegral.Box.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Box.withBotToSet", "kind": "definition", "module": "Mathlib.Analysis.BoxIntegral.Box.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Box.withBotCoe", "kind": "instance", "module": "Mathlib.Analysis.BoxIntegral.Box.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Box.coe_bot", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Box.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "BoxIntegral.Box.isSome_iff", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Box.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Box.biUnion_coe_eq_coe", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Box.Basic", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "BoxIntegral.Box.withBotCoe_subset_iff", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Box.Basic", "is_tactic_proof": true, "tactics": ["induction", "induction", "simp"], "tactic_count": 3}
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{"name": "BoxIntegral.Box.mk'_eq_bot", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Box.Basic", "is_tactic_proof": true, "tactics": ["rw", "split_ifs"], "tactic_count": 2}
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{"name": "BoxIntegral.Box.WithBot.inf", "kind": "instance", "module": "Mathlib.Analysis.BoxIntegral.Box.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Box.coe_inf", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Box.Basic", "is_tactic_proof": true, "tactics": ["induction", "change", "simp", "induction", "change", "simp", "change", "simp"], "tactic_count": 8}
{"name": "BoxIntegral.Box.instLatticeWithBot", "kind": "instance", "module": "Mathlib.Analysis.BoxIntegral.Box.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Box.disjoint_withBotCoe", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Box.Basic", "is_tactic_proof": true, "tactics": ["simp", "rfl"], "tactic_count": 2}
{"name": "BoxIntegral.Box.disjoint_coe", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Box.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Box.not_disjoint_coe_iff_nonempty_inter", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Box.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "BoxIntegral.Box.face", "kind": "definition", "module": "Mathlib.Analysis.BoxIntegral.Box.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Box.face_mk", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Box.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Box.face_mono", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Box.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Box.monotone_face", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Box.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Box.mapsTo_insertNth_face_Icc", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Box.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Box.mapsTo_insertNth_face", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Box.Basic", "is_tactic_proof": true, "tactics": ["intro", "simp_rw", "exact"], "tactic_count": 3}
{"name": "BoxIntegral.Box.continuousOn_face_Icc", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Box.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Box.Ioo", "kind": "definition", "module": "Mathlib.Analysis.BoxIntegral.Box.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Box.Ioo_subset_coe", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Box.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Box.Ioo_subset_Icc", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Box.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Box.iUnion_Ioo_of_tendsto", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Box.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "BoxIntegral.Box.distortion_eq_of_sub_eq_div", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Box.Basic", "is_tactic_proof": true, "tactics": ["simp", "congr", "have", "by_contra", "have", "rw", "exact", "have", "simp_rw"], "tactic_count": 9}
{"name": "BoxIntegral.Box.nndist_le_distortion_mul", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Box.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Box.dist_le_distortion_mul", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Box.Basic", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "BoxIntegral.Box.diam_Icc_le_of_distortion_le", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Box.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "BoxIntegral.Box.mem_splitCenterBox", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Box.SubboxInduction", "is_tactic_proof": true, "tactics": ["simp", "refine", "dsimp", "split_ifs", "exacts"], "tactic_count": 5}
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{"name": "BoxIntegral.norm_volume_sub_integral_face_upper_sub_lower_smul_le", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.DivergenceTheorem", "is_tactic_proof": true, "tactics": ["set", "i.insertNth", "volume", "integrate", "required", "have", "have", "have", "have", "set", "change", "clear_value", "convert_to", "congr", "have", "simp", "have", "replace", "intro", "refine", "rw", "exact", "rw", "exact", "calc", "integral", "f", "rw", "integral_sub", "simp", "refine", "rw", "gcongr", "exact", "rw", "ac_rfl"], "tactic_count": 36}
{"name": "BoxIntegral.hasIntegral_GP_pderiv", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.DivergenceTheorem", "is_tactic_proof": true, "tactics": ["box-additive", "have", "by_cases", "exacts", "set", "integral.", "set", "set", "change", "refine", "exact", "exact", "intro", "have", "δ", "refine", "rcases", "filter_upwards", "have", "rw", "calc", "dist", "have", "refine", "simpa", "rcases", "refine", "have", "have", "have", "have", "have", "simp", "rw", "refine", "simp_rw", "refine", "have", "calc", "dist", "calc", "prod_le_prod", "refine", "refine", "rw", "refine", "calc", "le_abs_self", "intro", "rcases", "rcases", "refine", "simp", "refine", "exact", "rw", "exact"], "tactic_count": 57}
{"name": "BoxIntegral.hasIntegral_GP_divergence_of_forall_hasDerivWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.DivergenceTheorem", "is_tactic_proof": true, "tactics": ["refine", "simp", "exact"], "tactic_count": 3}
{"name": "BoxIntegral.hasIntegralIndicatorConst", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Integrability", "is_tactic_proof": true, "tactics": ["refine", "lift", "have", "have", "obtain", "obtain", "have", "rcases", "exact", "choose", "have", "obtain", "exact", "choose", "classical", "set", "refine", "rw", "hence", "dsimp", "simp", "gcongr", "set", "change", "have", "simp", "refine", "simpa", "refine", "refine", "refine", "refine", "exact", "have", "refine", "refine", "rintro", "refine", "simp", "rcases", "refine", "contrapose", "refine", "simpa"], "tactic_count": 44}
{"name": "BoxIntegral.HasIntegral.of_aeEq_zero", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Integrability", "is_tactic_proof": true, "tactics": ["measure", "refine", "lift", "rcases", "haveI", "change", "set", "have", "have", "refine", "rcases", "simp", "refine", "exact", "simp", "choose", "have", "obtain", "exact", "choose", "refine", "rw", "grw", "apply", "rintro", "dsimp", "have", "rw", "rw", "gcongr", "exact", "refine", "rw", "let", "change", "have", "simp", "refine", "simp", "rintro", "exact", "clear_value", "lift", "grw"], "tactic_count": 44}
{"name": "BoxIntegral.HasIntegral.congr_ae", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Integrability", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "MeasureTheory.SimpleFunc.hasBoxIntegral", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Integrability", "is_tactic_proof": true, "tactics": ["induction", "borelize", "rw", "exacts"], "tactic_count": 4}
{"name": "MeasureTheory.SimpleFunc.box_integral_eq_integral", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Integrability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IntegrableOn.hasBoxIntegral", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Integrability", "is_tactic_proof": true, "tactics": ["borelize", "rcases", "haveI", "rw", "refine", "clear", "set", "have", "have", "have", "intro", "rw", "edist_nndist,", "exact", "refine", "lift", "obtain", "have", "refine", "exact", "have", "have", "exact", "choose", "rcases", "the", "of", "at", "set", "refine", "integral", "integral", "refine", "rw", "refine", "the", "rw", "refine", "rw", "gcongr", "rw", "to", "to", "rw", "grw", "refine", "have", "have", "obtain", "rfl", "have", "convert", "refine", "simp", "refine", "rw", "exact", "than", "refine", "have", "have", "have", "rw", "integral_biUnion_finset", "integral_biUnion_finset", "refine", "rw", "refine", "exact"], "tactic_count": 69}
{"name": "MeasureTheory.ContinuousOn.hasBoxIntegral", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Integrability", "is_tactic_proof": true, "tactics": ["obtain", "convert", "have", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.AEContinuous.hasBoxIntegral", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Integrability", "is_tactic_proof": true, "tactics": ["obtain", "convert", "refine", "constructor", "let", "have", "refine", "repeat", "apply", "refine", "rw", "refine", "exact", "have", "have", "isFiniteMeasure_of_le", "obtain", "refine", "use"], "tactic_count": 19}
{"name": "BoxIntegral.term_→ᵇᵃ_", "kind": "definition", "module": "Mathlib.Analysis.BoxIntegral.Partition.Additive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral._aux_Mathlib_Analysis_BoxIntegral_Partition_Additive___macroRules_BoxIntegral_term_→ᵇᵃ__1", "kind": "definition", "module": "Mathlib.Analysis.BoxIntegral.Partition.Additive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral._aux_Mathlib_Analysis_BoxIntegral_Partition_Additive___unexpand_BoxIntegral_BoxAdditiveMap_1", "kind": "definition", "module": "Mathlib.Analysis.BoxIntegral.Partition.Additive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.term_→ᵇᵃ[_]_", "kind": "definition", "module": "Mathlib.Analysis.BoxIntegral.Partition.Additive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral._aux_Mathlib_Analysis_BoxIntegral_Partition_Additive___macroRules_BoxIntegral_term_→ᵇᵃ[_]__1", "kind": "definition", "module": "Mathlib.Analysis.BoxIntegral.Partition.Additive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral._aux_Mathlib_Analysis_BoxIntegral_Partition_Additive___unexpand_BoxIntegral_BoxAdditiveMap_2", "kind": "definition", "module": "Mathlib.Analysis.BoxIntegral.Partition.Additive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.BoxAdditiveMap.instFunLikeBox", "kind": "instance", "module": "Mathlib.Analysis.BoxIntegral.Partition.Additive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.BoxAdditiveMap.coe_mk", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Additive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.BoxAdditiveMap.coe_injective", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Additive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.BoxAdditiveMap.coe_inj", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Additive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.BoxAdditiveMap.sum_partition_boxes", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Additive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.BoxAdditiveMap.instZero", "kind": "instance", "module": "Mathlib.Analysis.BoxIntegral.Partition.Additive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.BoxAdditiveMap.instInhabited", "kind": "instance", "module": "Mathlib.Analysis.BoxIntegral.Partition.Additive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.BoxAdditiveMap.instAdd", "kind": "instance", "module": "Mathlib.Analysis.BoxIntegral.Partition.Additive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.BoxAdditiveMap.instSMulOfDistribMulAction", "kind": "instance", "module": "Mathlib.Analysis.BoxIntegral.Partition.Additive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.BoxAdditiveMap.instAddCommMonoid", "kind": "instance", "module": "Mathlib.Analysis.BoxIntegral.Partition.Additive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.BoxAdditiveMap.map_split_add", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Additive", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "BoxIntegral.BoxAdditiveMap.restrict", "kind": "definition", "module": "Mathlib.Analysis.BoxIntegral.Partition.Additive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.BoxAdditiveMap.ofMapSplitAdd", "kind": "definition", "module": "Mathlib.Analysis.BoxIntegral.Partition.Additive", "is_tactic_proof": true, "tactics": ["classical", "refine", "replace", "induction", "empty", "insert", "rw", "refine", "by_cases", "rw", "exact", "rw", "intro", "have", "rcases", "rw", "exact"], "tactic_count": 17}
{"name": "BoxIntegral.BoxAdditiveMap.map", "kind": "definition", "module": "Mathlib.Analysis.BoxIntegral.Partition.Additive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.BoxAdditiveMap.sum_boxes_congr", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Additive", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rcases", "rw", "calc", "exacts"], "tactic_count": 6}
{"name": "BoxIntegral.BoxAdditiveMap.toSMul", "kind": "definition", "module": "Mathlib.Analysis.BoxIntegral.Partition.Additive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.BoxAdditiveMap.toSMul_apply", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Additive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.BoxAdditiveMap.upperSubLower", "kind": "definition", "module": "Mathlib.Analysis.BoxIntegral.Partition.Additive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.instMembershipBox", "kind": "instance", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.mem_boxes", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.mem_mk", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.disjoint_coe_of_mem", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.eq_of_mem_of_mem", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.eq_of_le_of_le", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.eq_of_le", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.le_of_mem", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.lower_le_lower", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.upper_le_upper", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.injective_boxes", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": true, "tactics": ["rintro", "rfl"], "tactic_count": 2}
{"name": "BoxIntegral.Prepartition.ext", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.single", "kind": "definition", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.mem_single", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.instLE", "kind": "instance", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.partialOrder", "kind": "instance", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.instOrderTop", "kind": "instance", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.instOrderBot", "kind": "instance", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.instInhabited", "kind": "instance", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.le_def", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.mem_top", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.top_boxes", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.notMem_bot", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.bot_boxes", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.injOn_setOf_mem_Icc_setOf_lower_eq", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": true, "tactics": ["rintro", "suffices", "choose", "exact", "intro", "simp", "rcases", "have", "have", "have", "rw", "exact", "have", "exact"], "tactic_count": 14}
{"name": "BoxIntegral.Prepartition.card_filter_mem_Icc_le", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "simpa"], "tactic_count": 3}
{"name": "BoxIntegral.Prepartition.iUnion", "kind": "definition", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.iUnion_def", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.iUnion_def'", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.mem_iUnion", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "BoxIntegral.Prepartition.iUnion_single", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "BoxIntegral.Prepartition.iUnion_top", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "BoxIntegral.Prepartition.iUnion_eq_empty", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "BoxIntegral.Prepartition.iUnion_bot", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.subset_iUnion", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.iUnion_subset", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.iUnion_mono", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.disjoint_boxes_of_disjoint_iUnion", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.le_iff_nonempty_imp_le_and_iUnion_subset", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": true, "tactics": ["constructor", "refine", "rcases", "rcases", "rwa", "rintro", "simp", "rcases", "exact"], "tactic_count": 9}
{"name": "BoxIntegral.Prepartition.eq_of_boxes_subset_iUnion_superset", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.biUnion", "kind": "definition", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.mem_biUnion", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "BoxIntegral.Prepartition.biUnion_le", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.biUnion_top", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "BoxIntegral.Prepartition.biUnion_congr", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": true, "tactics": ["subst", "ext", "simp", "constructor"], "tactic_count": 4}
{"name": "BoxIntegral.Prepartition.biUnion_congr_of_le", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.iUnion_biUnion", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "BoxIntegral.Prepartition.sum_biUnion_boxes", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "BoxIntegral.Prepartition.biUnionIndex", "kind": "definition", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.biUnionIndex_mem", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "BoxIntegral.Prepartition.biUnionIndex_le", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "rw"], "tactic_count": 3}
{"name": "BoxIntegral.Prepartition.mem_biUnionIndex", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "BoxIntegral.Prepartition.le_biUnionIndex", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.biUnionIndex_of_mem", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.biUnion_assoc", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp", "constructor", "rintro", "refine", "rwa", "rintro", "refine", "rwa"], "tactic_count": 9}
{"name": "BoxIntegral.Prepartition.ofWithBot", "kind": "definition", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.mem_ofWithBot", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.iUnion_ofWithBot", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": ["suffices", "simp"], "tactic_count": 2}
{"name": "BoxIntegral.Prepartition.ofWithBot_le", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": ["have", "simpa", "simpa"], "tactic_count": 3}
{"name": "BoxIntegral.Prepartition.le_ofWithBot", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": true, "tactics": ["intro", "rcases", "lift", "exact"], "tactic_count": 4}
{"name": "BoxIntegral.Prepartition.ofWithBot_mono", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.sum_ofWithBot", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.restrict", "kind": "definition", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.mem_restrict", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "BoxIntegral.Prepartition.mem_restrict'", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "BoxIntegral.Prepartition.restrict_mono", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": true, "tactics": ["classical", "refine", "rw", "rcases", "exact"], "tactic_count": 5}
{"name": "BoxIntegral.Prepartition.monotone_restrict", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.restrict_boxes_of_le", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": true, "tactics": ["classical", "simp", "refine", "refine", "intro", "rw", "exact"], "tactic_count": 7}
{"name": "BoxIntegral.Prepartition.restrict_self", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.iUnion_restrict", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "BoxIntegral.Prepartition.restrict_biUnion", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": true, "tactics": ["refine", "refine", "exact", "simp", "rintro", "obtain", "exact"], "tactic_count": 7}
{"name": "BoxIntegral.Prepartition.biUnion_le_iff", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": true, "tactics": ["constructor", "rw", "exact", "rw", "rcases", "rcases", "rcases", "exact"], "tactic_count": 8}
{"name": "BoxIntegral.Prepartition.le_biUnion_iff", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact", "rintro", "rcases", "have", "rcases", "exact"], "tactic_count": 8}
{"name": "BoxIntegral.Prepartition.instSemilatticeInf", "kind": "instance", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.inf_def", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.mem_inf", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "BoxIntegral.Prepartition.iUnion_inf", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "BoxIntegral.Prepartition.filter", "kind": "definition", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.mem_filter", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "BoxIntegral.Prepartition.filter_le", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.filter_of_true", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": true, "tactics": ["ext", "simpa"], "tactic_count": 2}
{"name": "BoxIntegral.Prepartition.filter_true", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.iUnion_filter_not", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": true, "tactics": ["simp", "convert", "simp", "rw", "convert", "rw", "exact"], "tactic_count": 7}
{"name": "BoxIntegral.Prepartition.sum_fiberwise", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "BoxIntegral.Prepartition.disjUnion", "kind": "definition", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.mem_disjUnion", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "BoxIntegral.Prepartition.iUnion_disjUnion", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "BoxIntegral.Prepartition.sum_disj_union_boxes", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.distortion", "kind": "definition", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.distortion_le_of_mem", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.distortion_le_iff", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.distortion_biUnion", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "BoxIntegral.Prepartition.distortion_disjUnion", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "BoxIntegral.Prepartition.distortion_of_const", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.distortion_top", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.distortion_bot", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.IsPartition", "kind": "definition", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.isPartition_iff_iUnion_eq", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "BoxIntegral.Prepartition.isPartition_single_iff", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "BoxIntegral.Prepartition.isPartitionTop", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.IsPartition.iUnion_eq", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.IsPartition.iUnion_subset", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.IsPartition.existsUnique", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "BoxIntegral.Prepartition.IsPartition.nonempty_boxes", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.IsPartition.eq_of_boxes_subset", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.IsPartition.le_iff", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.IsPartition.biUnion", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.IsPartition.restrict", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.IsPartition.inf", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.iUnion_biUnion_partition", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.isPartitionDisjUnionOfEqDiff", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.IntegrationParams.equivProd", "kind": "definition", "module": "Mathlib.Analysis.BoxIntegral.Partition.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.IntegrationParams.instPartialOrder", "kind": "instance", "module": "Mathlib.Analysis.BoxIntegral.Partition.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.IntegrationParams.isoProd", "kind": "definition", "module": "Mathlib.Analysis.BoxIntegral.Partition.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.IntegrationParams.instBoundedOrder", "kind": "instance", "module": "Mathlib.Analysis.BoxIntegral.Partition.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.IntegrationParams.instInhabited", "kind": "instance", "module": "Mathlib.Analysis.BoxIntegral.Partition.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.IntegrationParams.instDecidableLE", "kind": "instance", "module": "Mathlib.Analysis.BoxIntegral.Partition.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.IntegrationParams.instDecidableEq", "kind": "instance", "module": "Mathlib.Analysis.BoxIntegral.Partition.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.IntegrationParams.Riemann", "kind": "definition", "module": "Mathlib.Analysis.BoxIntegral.Partition.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.IntegrationParams.Henstock", "kind": "definition", "module": "Mathlib.Analysis.BoxIntegral.Partition.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.IntegrationParams.McShane", "kind": "definition", "module": "Mathlib.Analysis.BoxIntegral.Partition.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.IntegrationParams.GP", "kind": "definition", "module": "Mathlib.Analysis.BoxIntegral.Partition.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.IntegrationParams.henstock_le_riemann", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Filter", "is_tactic_proof": true, "tactics": ["trivial"], "tactic_count": 1}
{"name": "BoxIntegral.IntegrationParams.henstock_le_mcShane", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Filter", "is_tactic_proof": true, "tactics": ["trivial"], "tactic_count": 1}
{"name": "BoxIntegral.IntegrationParams.gp_le", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.IntegrationParams.RCond", "kind": "definition", "module": "Mathlib.Analysis.BoxIntegral.Partition.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.IntegrationParams.toFilterDistortion", "kind": "definition", "module": "Mathlib.Analysis.BoxIntegral.Partition.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.IntegrationParams.toFilter", "kind": "definition", "module": "Mathlib.Analysis.BoxIntegral.Partition.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.IntegrationParams.toFilterDistortioniUnion", "kind": "definition", "module": "Mathlib.Analysis.BoxIntegral.Partition.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.IntegrationParams.toFilteriUnion", "kind": "definition", "module": "Mathlib.Analysis.BoxIntegral.Partition.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.IntegrationParams.rCond_of_bRiemann_eq_false", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Filter", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "BoxIntegral.IntegrationParams.toFilter_inf_iUnion_eq", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.IntegrationParams.MemBaseSet.mono'", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.IntegrationParams.MemBaseSet.mono", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.IntegrationParams.MemBaseSet.exists_common_compl", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Filter", "is_tactic_proof": true, "tactics": ["wlog", "simpa", "by_cases", "rcases", "exact", "exact"], "tactic_count": 6}
{"name": "BoxIntegral.IntegrationParams.MemBaseSet.unionComplToSubordinate", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.IntegrationParams.MemBaseSet.filter", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Filter", "is_tactic_proof": true, "tactics": ["classical", "refine", "rcases", "set", "have", "refine", "suffices", "have", "ext", "fconstructor", "rintro", "exacts", "rintro", "by_cases", "exacts", "have", "simpa"], "tactic_count": 17}
{"name": "BoxIntegral.IntegrationParams.biUnionTagged_memBaseSet", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Filter", "is_tactic_proof": false, "tactics": ["refine", "rw", "exact", "refine", "rw", "rfl"], "tactic_count": 6}
{"name": "BoxIntegral.IntegrationParams.RCond.mono", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.IntegrationParams.RCond.min", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.IntegrationParams.toFilterDistortion_mono", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.IntegrationParams.toFilter_mono", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.IntegrationParams.toFilteriUnion_mono", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.IntegrationParams.toFilteriUnion_congr", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Filter", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "BoxIntegral.IntegrationParams.hasBasis_toFilterDistortion", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.IntegrationParams.hasBasis_toFilterDistortioniUnion", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.IntegrationParams.hasBasis_toFilteriUnion", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Filter", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "BoxIntegral.IntegrationParams.hasBasis_toFilteriUnion_top", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Filter", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "BoxIntegral.IntegrationParams.hasBasis_toFilter", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Filter", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "BoxIntegral.IntegrationParams.tendsto_embedBox_toFilteriUnion_top", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Filter", "is_tactic_proof": true, "tactics": ["simp", "set", "refine", "refine", "refine", "rw", "refine", "refine", "congr", "exact", "exact"], "tactic_count": 11}
{"name": "BoxIntegral.IntegrationParams.exists_memBaseSet_le_iUnion_eq", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Filter", "is_tactic_proof": true, "tactics": ["rcases", "refine", "exact"], "tactic_count": 3}
{"name": "BoxIntegral.IntegrationParams.exists_memBaseSet_isPartition", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Filter", "is_tactic_proof": true, "tactics": ["rw", "have", "simpa"], "tactic_count": 3}
{"name": "BoxIntegral.IntegrationParams.toFilterDistortioniUnion_neBot", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.IntegrationParams.toFilterDistortioniUnion_neBot'", "kind": "instance", "module": "Mathlib.Analysis.BoxIntegral.Partition.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.IntegrationParams.toFilterDistortion_neBot", "kind": "instance", "module": "Mathlib.Analysis.BoxIntegral.Partition.Filter", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "BoxIntegral.IntegrationParams.toFilter_neBot", "kind": "instance", "module": "Mathlib.Analysis.BoxIntegral.Partition.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.IntegrationParams.toFilteriUnion_neBot", "kind": "instance", "module": "Mathlib.Analysis.BoxIntegral.Partition.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.IntegrationParams.eventually_isPartition", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Box.measure_Icc_lt_top", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Box.measure_coe_lt_top", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Box.measurableSet_coe", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Measure", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "BoxIntegral.Box.measurableSet_Icc", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Box.measurableSet_Ioo", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Box.coe_ae_eq_Icc", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Measure", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "BoxIntegral.Box.Ioo_ae_eq_Icc", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.measure_iUnion_toReal", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Measure", "is_tactic_proof": true, "tactics": ["simp", "rw", "simp", "rw", "exact"], "tactic_count": 5}
{"name": "MeasureTheory.Measure.toBoxAdditive", "kind": "definition", "module": "Mathlib.Analysis.BoxIntegral.Partition.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Box.volume_apply", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Measure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "BoxIntegral.Box.volume_apply'", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Measure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "BoxIntegral.Box.volume_face_mul", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Measure", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "BoxIntegral.BoxAdditiveMap.volume", "kind": "definition", "module": "Mathlib.Analysis.BoxIntegral.Partition.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.BoxAdditiveMap.volume_apply", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Measure", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "BoxIntegral.Box.splitLower", "kind": "definition", "module": "Mathlib.Analysis.BoxIntegral.Partition.Split", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Box.coe_splitLower", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Split", "is_tactic_proof": true, "tactics": ["rw", "ext", "simp", "le_min_iff,", "rw"], "tactic_count": 5}
{"name": "BoxIntegral.Box.splitLower_le", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Split", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Box.splitLower_eq_bot", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Split", "is_tactic_proof": true, "tactics": ["classical", "rw", "simp"], "tactic_count": 3}
{"name": "BoxIntegral.Box.splitLower_eq_self", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Split", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "BoxIntegral.Box.splitUpper", "kind": "definition", "module": "Mathlib.Analysis.BoxIntegral.Partition.Split", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Box.coe_splitUpper", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Split", "is_tactic_proof": true, "tactics": ["classical", "rw", "ext", "simp", "forall_update_iff", "and_forall_ne", "exact"], "tactic_count": 7}
{"name": "BoxIntegral.Box.splitUpper_le", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Split", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Box.splitUpper_eq_bot", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Split", "is_tactic_proof": true, "tactics": ["classical", "rw", "simp"], "tactic_count": 3}
{"name": "BoxIntegral.Box.splitUpper_eq_self", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Split", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "BoxIntegral.Box.disjoint_splitLower_splitUpper", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Split", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "BoxIntegral.Box.splitLower_ne_splitUpper", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Split", "is_tactic_proof": true, "tactics": ["rcases", "rw", "exact", "refine", "rwa"], "tactic_count": 5}
{"name": "BoxIntegral.Prepartition.split", "kind": "definition", "module": "Mathlib.Analysis.BoxIntegral.Partition.Split", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.mem_split_iff", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Split", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "BoxIntegral.Prepartition.mem_split_iff'", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Split", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "BoxIntegral.Prepartition.iUnion_split", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Split", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "BoxIntegral.Prepartition.isPartitionSplit", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Split", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.sum_split_boxes", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Split", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "BoxIntegral.Prepartition.split_of_notMem_Ioo", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Split", "is_tactic_proof": true, "tactics": ["refine", "rcases", "rw", "rw", "cases", "rwa", "rwa"], "tactic_count": 7}
{"name": "BoxIntegral.Prepartition.coe_eq_of_mem_split_of_mem_le", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Split", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "BoxIntegral.Prepartition.coe_eq_of_mem_split_of_lt_mem", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Split", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "BoxIntegral.Prepartition.restrict_split", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Split", "is_tactic_proof": true, "tactics": ["refine", "simp", "have", "rintro"], "tactic_count": 4}
{"name": "BoxIntegral.Prepartition.inf_split", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Split", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.splitMany", "kind": "definition", "module": "Mathlib.Analysis.BoxIntegral.Partition.Split", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.splitMany_empty", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Split", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.splitMany_insert", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Split", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "BoxIntegral.Prepartition.splitMany_le_split", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Split", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.isPartition_splitMany", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Split", "is_tactic_proof": true, "tactics": ["classical", "exact", "simpa"], "tactic_count": 3}
{"name": "BoxIntegral.Prepartition.iUnion_splitMany", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Split", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.inf_splitMany", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Split", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "insert"], "tactic_count": 4}
{"name": "BoxIntegral.Prepartition.not_disjoint_imp_le_of_subset_of_mem_splitMany", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Split", "is_tactic_proof": true, "tactics": ["simp", "rcases", "refine", "rcases", "have", "rw", "exact", "rcases", "have", "rw", "exact"], "tactic_count": 11}
{"name": "BoxIntegral.Prepartition.eventually_not_disjoint_imp_le_of_mem_splitMany", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Split", "is_tactic_proof": true, "tactics": ["classical", "cases", "refine", "eventually_atTop.2", "not_disjoint_imp_le_of_subset_of_mem_splitMany", "exact"], "tactic_count": 6}
{"name": "BoxIntegral.Prepartition.eventually_splitMany_inf_eq_filter", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Split", "is_tactic_proof": true, "tactics": ["refine", "refine", "refine", "simp", "rintro", "refine", "exact", "rw", "rcases", "refine", "exact"], "tactic_count": 11}
{"name": "BoxIntegral.Prepartition.exists_splitMany_inf_eq_filter_of_finite", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Split", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.IsPartition.exists_splitMany_le", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Split", "is_tactic_proof": true, "tactics": ["refine", "rwa", "exact"], "tactic_count": 3}
{"name": "BoxIntegral.Prepartition.exists_iUnion_eq_diff", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Split", "is_tactic_proof": true, "tactics": ["rcases", "use", "simp"], "tactic_count": 3}
{"name": "BoxIntegral.Prepartition.compl", "kind": "definition", "module": "Mathlib.Analysis.BoxIntegral.Partition.Split", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.iUnion_compl", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Split", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.compl_congr", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Split", "is_tactic_proof": true, "tactics": ["dsimp", "congr", "rw"], "tactic_count": 3}
{"name": "BoxIntegral.Prepartition.IsPartition.compl_eq_bot", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Split", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "BoxIntegral.Prepartition.compl_top", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Split", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.splitCenter", "kind": "definition", "module": "Mathlib.Analysis.BoxIntegral.Partition.SubboxInduction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.mem_splitCenter", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.SubboxInduction", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "BoxIntegral.Prepartition.isPartition_splitCenter", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.SubboxInduction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.upper_sub_lower_of_mem_splitCenter", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.SubboxInduction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Box.subbox_induction_on", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.SubboxInduction", "is_tactic_proof": true, "tactics": ["refine", "rcases", "exact"], "tactic_count": 3}
{"name": "BoxIntegral.Box.exists_taggedPartition_isHenstock_isSubordinate_homothetic", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.SubboxInduction", "is_tactic_proof": true, "tactics": ["refine", "choose", "choose", "have", "have", "intro", "rcases", "refine", "simp", "refine", "refine", "rcases", "exact", "refine", "intro", "rw", "refine", "distortion_single", "simp", "refine", "simp"], "tactic_count": 21}
{"name": "BoxIntegral.Prepartition.exists_tagged_le_isHenstock_isSubordinate_iUnion_eq", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.SubboxInduction", "is_tactic_proof": true, "tactics": ["have", "choose", "refine", "isSubordinate_biUnionTagged.2", "rw", "exact"], "tactic_count": 6}
{"name": "BoxIntegral.Prepartition.toSubordinate", "kind": "definition", "module": "Mathlib.Analysis.BoxIntegral.Partition.SubboxInduction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.toSubordinate_toPrepartition_le", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.SubboxInduction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.isHenstock_toSubordinate", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.SubboxInduction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.isSubordinate_toSubordinate", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.SubboxInduction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.distortion_toSubordinate", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.SubboxInduction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.iUnion_toSubordinate", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.SubboxInduction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.TaggedPrepartition.unionComplToSubordinate", "kind": "definition", "module": "Mathlib.Analysis.BoxIntegral.Partition.SubboxInduction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.TaggedPrepartition.isPartition_unionComplToSubordinate", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.SubboxInduction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.TaggedPrepartition.unionComplToSubordinate_boxes", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.SubboxInduction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.TaggedPrepartition.iUnion_unionComplToSubordinate_boxes", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.SubboxInduction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.TaggedPrepartition.distortion_unionComplToSubordinate", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.SubboxInduction", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "BoxIntegral.TaggedPrepartition.instMembershipBox", "kind": "instance", "module": "Mathlib.Analysis.BoxIntegral.Partition.Tagged", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.TaggedPrepartition.mem_toPrepartition", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Tagged", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.TaggedPrepartition.mem_mk", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Tagged", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.TaggedPrepartition.iUnion", "kind": "definition", "module": "Mathlib.Analysis.BoxIntegral.Partition.Tagged", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.TaggedPrepartition.iUnion_def", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Tagged", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.TaggedPrepartition.iUnion_mk", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Tagged", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.TaggedPrepartition.iUnion_toPrepartition", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Tagged", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.TaggedPrepartition.mem_iUnion", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Tagged", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "BoxIntegral.TaggedPrepartition.subset_iUnion", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Tagged", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.TaggedPrepartition.iUnion_subset", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Tagged", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.TaggedPrepartition.IsPartition", "kind": "definition", "module": "Mathlib.Analysis.BoxIntegral.Partition.Tagged", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.TaggedPrepartition.isPartition_iff_iUnion_eq", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Tagged", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.TaggedPrepartition.filter", "kind": "definition", "module": "Mathlib.Analysis.BoxIntegral.Partition.Tagged", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.TaggedPrepartition.mem_filter", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Tagged", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "BoxIntegral.TaggedPrepartition.iUnion_filter_not", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Tagged", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.biUnionTagged", "kind": "definition", "module": "Mathlib.Analysis.BoxIntegral.Partition.Tagged", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.mem_biUnionTagged", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Tagged", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.tag_biUnionTagged", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Tagged", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "BoxIntegral.Prepartition.iUnion_biUnionTagged", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Tagged", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.forall_biUnionTagged", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Tagged", "is_tactic_proof": true, "tactics": ["simp", "refine", "rw", "exact", "rw", "exact"], "tactic_count": 6}
{"name": "BoxIntegral.Prepartition.IsPartition.biUnionTagged", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Tagged", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.TaggedPrepartition.biUnionPrepartition", "kind": "definition", "module": "Mathlib.Analysis.BoxIntegral.Partition.Tagged", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.TaggedPrepartition.IsPartition.biUnionPrepartition", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Tagged", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.TaggedPrepartition.infPrepartition", "kind": "definition", "module": "Mathlib.Analysis.BoxIntegral.Partition.Tagged", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.TaggedPrepartition.infPrepartition_toPrepartition", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Tagged", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.TaggedPrepartition.mem_infPrepartition_comm", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Tagged", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "BoxIntegral.TaggedPrepartition.IsPartition.infPrepartition", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Tagged", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.TaggedPrepartition.IsHenstock", "kind": "definition", "module": "Mathlib.Analysis.BoxIntegral.Partition.Tagged", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.TaggedPrepartition.isHenstock_biUnionTagged", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Tagged", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.TaggedPrepartition.IsHenstock.card_filter_tag_eq_le", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Tagged", "is_tactic_proof": true, "tactics": ["classical", "calc", "refine", "rw", "exact"], "tactic_count": 5}
{"name": "BoxIntegral.TaggedPrepartition.IsSubordinate", "kind": "definition", "module": "Mathlib.Analysis.BoxIntegral.Partition.Tagged", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.TaggedPrepartition.isSubordinate_biUnionTagged", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Tagged", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.TaggedPrepartition.IsSubordinate.biUnionPrepartition", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Tagged", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.TaggedPrepartition.IsSubordinate.infPrepartition", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Tagged", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.TaggedPrepartition.IsSubordinate.mono'", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Tagged", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.TaggedPrepartition.IsSubordinate.mono", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Tagged", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.TaggedPrepartition.IsSubordinate.diam_le", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Tagged", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.TaggedPrepartition.single", "kind": "definition", "module": "Mathlib.Analysis.BoxIntegral.Partition.Tagged", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.TaggedPrepartition.mem_single", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Tagged", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.TaggedPrepartition.instInhabited", "kind": "instance", "module": "Mathlib.Analysis.BoxIntegral.Partition.Tagged", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.TaggedPrepartition.isPartition_single_iff", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Tagged", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.TaggedPrepartition.isPartition_single", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Tagged", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.TaggedPrepartition.forall_mem_single", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Tagged", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "BoxIntegral.TaggedPrepartition.isHenstock_single_iff", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Tagged", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.TaggedPrepartition.isHenstock_single", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Tagged", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.TaggedPrepartition.isSubordinate_single", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Tagged", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.TaggedPrepartition.iUnion_single", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Tagged", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.TaggedPrepartition.disjUnion", "kind": "definition", "module": "Mathlib.Analysis.BoxIntegral.Partition.Tagged", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.TaggedPrepartition.disjUnion_boxes", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Tagged", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.TaggedPrepartition.mem_disjUnion", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Tagged", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "BoxIntegral.TaggedPrepartition.iUnion_disjUnion", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Tagged", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.TaggedPrepartition.disjUnion_tag_of_mem_left", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Tagged", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.TaggedPrepartition.disjUnion_tag_of_mem_right", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Tagged", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.TaggedPrepartition.IsSubordinate.disjUnion", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Tagged", "is_tactic_proof": true, "tactics": ["classical", "refine", "rw", "exact", "rw", "exact"], "tactic_count": 6}
{"name": "BoxIntegral.TaggedPrepartition.IsHenstock.disjUnion", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Tagged", "is_tactic_proof": true, "tactics": ["classical", "refine", "rw", "exact", "rw", "exact"], "tactic_count": 6}
{"name": "BoxIntegral.TaggedPrepartition.embedBox", "kind": "definition", "module": "Mathlib.Analysis.BoxIntegral.Partition.Tagged", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.TaggedPrepartition.distortion", "kind": "definition", "module": "Mathlib.Analysis.BoxIntegral.Partition.Tagged", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.TaggedPrepartition.distortion_le_of_mem", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Tagged", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.TaggedPrepartition.distortion_le_iff", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Tagged", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.Prepartition.distortion_biUnionTagged", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Tagged", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "BoxIntegral.TaggedPrepartition.distortion_biUnionPrepartition", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Tagged", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "BoxIntegral.TaggedPrepartition.distortion_disjUnion", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Tagged", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "BoxIntegral.TaggedPrepartition.distortion_of_const", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Tagged", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.TaggedPrepartition.distortion_single", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Tagged", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.TaggedPrepartition.distortion_filter_le", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.Partition.Tagged", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "BoxIntegral.hasIntegralVertices", "kind": "definition", "module": "Mathlib.Analysis.BoxIntegral.UnitPartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.le_hasIntegralVertices_of_isBounded", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.UnitPartition", "is_tactic_proof": true, "tactics": ["have", "obtain", "let", "have", "let", "refine", "suffices", "intro", "simp_rw", "exact"], "tactic_count": 10}
{"name": "BoxIntegral.unitPartition.box", "kind": "definition", "module": "Mathlib.Analysis.BoxIntegral.UnitPartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.unitPartition.box_lower", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.UnitPartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.unitPartition.box_upper", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.UnitPartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.unitPartition.mem_box_iff", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.UnitPartition", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "BoxIntegral.unitPartition.mem_box_iff'", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.UnitPartition", "is_tactic_proof": true, "tactics": ["have", "simp_rw"], "tactic_count": 2}
{"name": "BoxIntegral.unitPartition.tag", "kind": "abbrev", "module": "Mathlib.Analysis.BoxIntegral.UnitPartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.unitPartition.tag_apply", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.UnitPartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.unitPartition.tag_injective", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.UnitPartition", "is_tactic_proof": true, "tactics": ["refine", "have", "simp_rw", "exact"], "tactic_count": 4}
{"name": "BoxIntegral.unitPartition.tag_mem", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.UnitPartition", "is_tactic_proof": true, "tactics": ["refine", "rw", "have", "exact"], "tactic_count": 4}
{"name": "BoxIntegral.unitPartition.index", "kind": "definition", "module": "Mathlib.Analysis.BoxIntegral.UnitPartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.unitPartition.index_apply", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.UnitPartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.unitPartition.mem_box_iff_index", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.UnitPartition", "is_tactic_proof": true, "tactics": ["simp_rw", "add_sub_cancel_right]"], "tactic_count": 2}
{"name": "BoxIntegral.unitPartition.index_tag", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.UnitPartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.unitPartition.disjoint", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.UnitPartition", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw"], "tactic_count": 3}
{"name": "BoxIntegral.unitPartition.box_injective", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.UnitPartition", "is_tactic_proof": true, "tactics": ["intro", "contrapose", "exact"], "tactic_count": 3}
{"name": "BoxIntegral.unitPartition.box.upper_sub_lower", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.UnitPartition", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "BoxIntegral.unitPartition.diam_boxIcc", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.UnitPartition", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp_rw"], "tactic_count": 3}
{"name": "BoxIntegral.unitPartition.volume_box", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.UnitPartition", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "BoxIntegral.unitPartition.setFinite_index", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.UnitPartition", "is_tactic_proof": false, "tactics": ["refine", "refine", "exact", "exact", "exact", "lt_top_iff_ne_top.mp", "measure_lt_top_of_subset", "rw"], "tactic_count": 8}
{"name": "BoxIntegral.unitPartition.admissibleIndex", "kind": "definition", "module": "Mathlib.Analysis.BoxIntegral.UnitPartition", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "BoxIntegral.unitPartition.mem_admissibleIndex_iff", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.UnitPartition", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "BoxIntegral.unitPartition.prepartition", "kind": "definition", "module": "Mathlib.Analysis.BoxIntegral.UnitPartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.unitPartition.mem_prepartition_iff", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.UnitPartition", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "BoxIntegral.unitPartition.mem_prepartition_boxes_iff", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.UnitPartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoxIntegral.unitPartition.prepartition_tag", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.UnitPartition", "is_tactic_proof": true, "tactics": ["dsimp", "have", "rw", "exact"], "tactic_count": 4}
{"name": "BoxIntegral.unitPartition.box_index_tag_eq_self", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.UnitPartition", "is_tactic_proof": true, "tactics": ["obtain", "rw"], "tactic_count": 2}
{"name": "BoxIntegral.unitPartition.prepartition_isHenstock", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.UnitPartition", "is_tactic_proof": true, "tactics": ["intro", "obtain", "rw", "exact"], "tactic_count": 4}
{"name": "BoxIntegral.unitPartition.prepartition_isSubordinate", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.UnitPartition", "is_tactic_proof": true, "tactics": ["intro", "obtain", "refine", "rw", "exact", "exact"], "tactic_count": 6}
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{"name": "BoxIntegral.unitPartition.mem_admissibleIndex_of_mem_box", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.UnitPartition", "is_tactic_proof": true, "tactics": ["obtain", "simp_rw", "forall_and]", "push_cast", "refine", "exact", "exact"], "tactic_count": 7}
{"name": "BoxIntegral.unitPartition.prepartition_isPartition", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.UnitPartition", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
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{"name": "BoxIntegral.unitPartition.integralSum_eq_tsum_div", "kind": "theorem", "module": "Mathlib.Analysis.BoxIntegral.UnitPartition", "is_tactic_proof": true, "tactics": ["classical", "unfold", "have", "apply", "rw", "exact", "rw", "simp_rw", "mul_zero,", "refine", "rw", "refine", "simp_rw", "tag_index_eq_self_of_mem_smul_span", "rw", "exact", "rw", "refine", "rw", "exact", "rw", "rw", "tag_index_eq_self_of_mem_smul_span"], "tactic_count": 23}
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{"name": "starNormedAddGroupHom", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "star_isometry", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedStarGroup.to_continuousStar", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instNormedSpaceSubtypeMemAddSubgroupSelfAdjointOfTrivialStarOfStarModule", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHomIsometric.starRingEnd", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCStarRingReal", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarRing.of_le_norm_mul_star_self", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarRing.to_normedStarGroup", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarRing.norm_star_mul_self", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarRing.norm_self_mul_star", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Basic", "is_tactic_proof": true, "tactics": ["nth_rw", "simp"], "tactic_count": 2}
{"name": "CStarRing.norm_star_mul_self'", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CStarRing.nnnorm_self_mul_star", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarRing.nnnorm_star_mul_self", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSelfAdjoint.norm_mul_self", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsSelfAdjoint.nnnorm_mul_self", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarRing.star_mul_self_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CStarRing.star_mul_self_ne_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CStarRing.mul_star_self_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CStarRing.mul_star_self_ne_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Pi.starRing'", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.cstarRing", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.cstarRing", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.cstarRing'", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarRing.MulOpposite.instMulOpposite", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarRing.norm_one", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Basic", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "CStarRing.instNormOneClassOfNontrivial", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarRing.norm_coe_unitary", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CStarRing.norm_of_mem_unitary", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarRing.norm_coe_unitary_mul", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Basic", "is_tactic_proof": true, "tactics": ["nontriviality", "refine", "calc", "calc", "rw", "exact"], "tactic_count": 6}
{"name": "CStarRing.norm_unitary_smul", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarRing.norm_mem_unitary_mul", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarRing.norm_mul_coe_unitary", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarRing.norm_mul_mem_unitary", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSelfAdjoint.nnnorm_pow_two_pow", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "IsSelfAdjoint.norm_pow_two_pow", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "starₗᵢ", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "coe_starₗᵢ", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "starₗᵢ_apply", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "starₗᵢ_toContinuousLinearEquiv", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.toNormedAlgebra", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.to_cstarRing", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarMatrix", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.CStarMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarMatrix.ofMatrix", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.CStarMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarMatrix.ofMatrix_apply", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.CStarMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarMatrix.ofMatrix_symm_apply", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.CStarMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarMatrix.ext_iff", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.CStarMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarMatrix.ext", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.CStarMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarMatrix.map", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.CStarMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarMatrix.map_apply", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.CStarMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarMatrix.map_id", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.CStarMatrix", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
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{"name": "CStarMatrix.map_map", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.CStarMatrix", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CStarMatrix.map_injective", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.CStarMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarMatrix.transpose", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.CStarMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CStarMatrix.conjTranspose", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.CStarMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarMatrix.conjTranspose_apply", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.CStarMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarMatrix.instStar", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.CStarMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarMatrix.star_eq_conjTranspose", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.CStarMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarMatrix.instInvolutiveStar", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.CStarMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarMatrix.instInhabited", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.CStarMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarMatrix.instDecidableEq", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.CStarMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarMatrix.instFintypeOfDecidableEq", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.CStarMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarMatrix.instFinite", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.CStarMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarMatrix.instAdd", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.CStarMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarMatrix.instAddSemigroup", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.CStarMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarMatrix.instAddCommSemigroup", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.CStarMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarMatrix.instZero", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.CStarMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarMatrix.instAddZeroClass", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.CStarMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarMatrix.instAddMonoid", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.CStarMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarMatrix.instAddCommMonoid", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.CStarMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarMatrix.instNeg", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.CStarMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CStarMatrix.instAddGroup", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.CStarMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarMatrix.instAddCommGroup", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.CStarMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarMatrix.instUnique", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.CStarMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarMatrix.instSubsingleton", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.CStarMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarMatrix.instNontrivial", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.CStarMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarMatrix.instSMul", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.CStarMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarMatrix.instSMulCommClass", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.CStarMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarMatrix.instIsScalarTower", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.CStarMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarMatrix.instIsCentralScalar", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.CStarMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarMatrix.instMulAction", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.CStarMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarMatrix.instDistribMulAction", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.CStarMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarMatrix.instModule", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.CStarMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarMatrix.zero_apply", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.CStarMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarMatrix.add_apply", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.CStarMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarMatrix.smul_apply", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.CStarMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarMatrix.sub_apply", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.CStarMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CStarMatrix.conjTranspose_zero", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.CStarMatrix", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CStarMatrix.of_zero", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.CStarMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarMatrix.of_add_of", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.CStarMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarMatrix.of_sub_of", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.CStarMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CStarMatrix.smul_of", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.CStarMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarMatrix.star_apply", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.CStarMatrix", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CStarMatrix.star_apply_of_isSelfAdjoint", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.CStarMatrix", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CStarMatrix.instStarAddMonoid", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.CStarMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarMatrix.instStarModule", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.CStarMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarMatrix.ofMatrixₗ", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.CStarMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarMatrix.mapₗ", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.CStarMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarMatrix.instOne", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.CStarMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarMatrix.one_apply", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.CStarMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarMatrix.one_apply_eq", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.CStarMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarMatrix.one_apply_ne", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.CStarMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarMatrix.one_apply_ne'", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.CStarMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CStarMatrix.instAddGroupWithOne", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.CStarMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CStarMatrix.instHMulOfFintypeOfMulOfAddCommMonoid", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.CStarMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "inr_comp_cfcₙHom_eq_cfcₙAux", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Basic", "is_tactic_proof": true, "tactics": ["have", "refine", "change", "exact", "trans", "congrm", "exact"], "tactic_count": 7}
{"name": "SpectrumRestricts.nnreal_iff_nnnorm", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Basic", "is_tactic_proof": true, "tactics": ["have", "rw", "exact", "all_goals", "try", "assumption"], "tactic_count": 6}
{"name": "SpectrumRestricts.nnreal_add", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Basic", "is_tactic_proof": false, "tactics": ["rw", "refine", "gcongr", "all_goals", "rw", "first", "rfl", "assumption"], "tactic_count": 8}
{"name": "IsSelfAdjoint.sq_spectrumRestricts", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Basic", "is_tactic_proof": true, "tactics": ["rw", "rintro", "exact"], "tactic_count": 3}
{"name": "SpectrumRestricts.eq_zero_of_neg", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply", "rw", "simp", "peel", "linarith"], "tactic_count": 6}
{"name": "SpectrumRestricts.smul_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Basic", "is_tactic_proof": true, "tactics": ["rw", "nontriviality", "intro", "by_cases", "simp", "exact", "lift", "rw", "refine", "simpa"], "tactic_count": 10}
{"name": "spectrum_star_mul_self_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Basic", "is_tactic_proof": true, "tactics": ["set", "have", "simp", "set", "have", "calc", "simp", "simp", "have", "simp", "rw", "rintro", "positivity", "have", "rw", "refine", "exact", "exact", "rw", "refine", "simp", "rw", "cfcₙ_eq_cfc", "have", "exact"], "tactic_count": 25}
{"name": "CStarAlgebra.instNonnegSpectrumClass", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarAlgebra.instNonnegSpectrumClassComplexUnital", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarAlgebra.spectralOrder", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarAlgebra.spectralOrderedRing", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarAlgebra.instNonnegSpectrumClass'", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsStarNormal.instIsometricContinuousFunctionalCalculus", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSelfAdjoint.instIsometricContinuousFunctionalCalculus", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsStarNormal.instNonUnitalIsometricContinuousFunctionalCalculus", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSelfAdjoint.instNonUnitalIsometricContinuousFunctionalCalculus", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.cfcHom", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Commute", "is_tactic_proof": true, "tactics": ["open", "induction", "const", "r", "conv", "enter", "equals", "rw", "exact", "id", "star_id", "add", "mul", "frequently", "hf", "rw", "apply", "exact"], "tactic_count": 18}
{"name": "IsSelfAdjoint.commute_cfcHom", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Commute", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.cfc", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Commute", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSelfAdjoint.commute_cfc", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Commute", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.cfc_real", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Commute", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.cfc_nnreal", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Commute", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "exact", "simp"], "tactic_count": 4}
{"name": "Commute.cfcₙHom", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Commute", "is_tactic_proof": true, "tactics": ["open", "induction", "zero", "smul", "id", "star_id", "add", "mul", "frequently", "hf", "rw", "apply", "exact"], "tactic_count": 13}
{"name": "IsSelfAdjoint.commute_cfcₙHom", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Commute", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.cfcₙ", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Commute", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSelfAdjoint.commute_cfcₙ", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Commute", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.cfcₙ_real", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Commute", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.cfcₙ_nnreal", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Commute", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "exact", "simp"], "tactic_count": 4}
{"name": "tendsto_cfc_fun", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Continuity", "is_tactic_proof": true, "tactics": ["open", "obtain", "simp", "have", "by_cases", "let", "rw", "conv", "enter", "rw", "rw", "apply", "rw", "intro", "simp", "peel", "simp_all", "simpa"], "tactic_count": 18}
{"name": "continuousAt_cfc_fun", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Continuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousWithinAt_cfc_fun", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Continuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lipschitzOnWith_cfc_fun", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Continuity", "is_tactic_proof": true, "tactics": ["by_cases", "intro", "simp", "rw", "simp", "rw", "simpa"], "tactic_count": 7}
{"name": "lipschitzOnWith_cfc_fun_of_subset", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Continuity", "is_tactic_proof": true, "tactics": ["have", "have", "have", "simpa"], "tactic_count": 4}
{"name": "continuousOn_cfc_setProd", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Continuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousOn_cfc_nnreal_setProd", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Continuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_cfcₙ_fun", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Continuity", "is_tactic_proof": true, "tactics": ["open", "obtain", "simp", "have", "have", "tendsto_nhds_unique", "h_tendsto.tendsto_at", "by_cases", "let", "have", "rw", "conv", "enter", "rw", "rw", "apply", "rw", "change", "rw", "intro", "simp", "peel", "simp_all", "simpa"], "tactic_count": 24}
{"name": "continuousAt_cfcₙ_fun", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Continuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.cfcₙ_fun", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Continuity", "is_tactic_proof": true, "tactics": ["rw", "simp", "toFun_ofFun,", "refine", "all_goals", "exacts"], "tactic_count": 6}
{"name": "lipschitzOnWith_cfcₙ_fun", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Continuity", "is_tactic_proof": true, "tactics": ["by_cases", "rintro", "simp", "rw", "simp", "rw", "simpa"], "tactic_count": 7}
{"name": "lipschitzOnWith_cfcₙ_fun_of_subset", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Continuity", "is_tactic_proof": true, "tactics": ["have", "have", "simpa"], "tactic_count": 3}
{"name": "continuousOn_cfcₙ_setProd", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Continuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousOn_cfcₙ_nnreal_setProd", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Continuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Instances.0.termσₙ", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Instances.0._aux_Mathlib_Analysis_CStarAlgebra_ContinuousFunctionalCalculus_Instances___macroRules__private_Mathlib_Analysis_CStarAlgebra_ContinuousFunctionalCalculus_Instances_0_termσₙ_1", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Instances.0._aux_Mathlib_Analysis_CStarAlgebra_ContinuousFunctionalCalculus_Instances___unexpand_quasispectrum_1", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Instances.0.termσ", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Instances.0._aux_Mathlib_Analysis_CStarAlgebra_ContinuousFunctionalCalculus_Instances___macroRules__private_Mathlib_Analysis_CStarAlgebra_ContinuousFunctionalCalculus_Instances_0_termσ_1", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Instances.0._aux_Mathlib_Analysis_CStarAlgebra_ContinuousFunctionalCalculus_Instances___unexpand_spectrum_1", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Instances.0.term_⁺¹", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Instances.0._aux_Mathlib_Analysis_CStarAlgebra_ContinuousFunctionalCalculus_Instances___macroRules__private_Mathlib_Analysis_CStarAlgebra_ContinuousFunctionalCalculus_Instances_0_term_⁺¹_1", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cfcₙAux", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cfcₙAux_id", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosedEmbedding_cfcₙAux", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Instances", "is_tactic_proof": true, "tactics": ["simp", "refine", "let", "exact"], "tactic_count": 4}
{"name": "spec_cfcₙAux", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Instances", "is_tactic_proof": true, "tactics": ["rw", "simp", "rw", "simp"], "tactic_count": 4}
{"name": "cfcₙAux_mem_range_inr", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Instances", "is_tactic_proof": false, "tactics": ["have", "rw", "refine", "rw", "apply", "apply", "rw", "exact", "have", "simp", "convert", "aesop"], "tactic_count": 12}
{"name": "RCLike.nonUnitalContinuousFunctionalCalculus", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isSelfAdjoint_iff_isStarNormal_and_quasispectrumRestricts", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Instances", "is_tactic_proof": true, "tactics": ["refine", "have", "exact", "rintro", "rw", "nth_rw", "rw", "refine", "obtain", "exact"], "tactic_count": 10}
{"name": "IsSelfAdjoint.quasispectrumRestricts", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuasispectrumRestricts.isSelfAdjoint", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSelfAdjoint.instNonUnitalContinuousFunctionalCalculus", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSelfAdjoint.spectrumRestricts", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSelfAdjoint.instContinuousFunctionalCalculus", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSelfAdjoint.spectrum_nonempty", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CFC.exists_sqrt_of_isSelfAdjoint_of_quasispectrumRestricts", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Instances", "is_tactic_proof": true, "tactics": ["use", "constructor", "simpa", "and_imp,", "rw", "nth_rw", "apply", "rw", "apply", "simp"], "tactic_count": 10}
{"name": "nonneg_iff_isSelfAdjoint_and_quasispectrumRestricts", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Instances", "is_tactic_proof": true, "tactics": ["refine", "rintro", "obtain", "simpa"], "tactic_count": 4}
{"name": "Nonneg.instNonUnitalContinuousFunctionalCalculus", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.mul_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Instances", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "obtain", "have", "rw", "exact"], "tactic_count": 7}
{"name": "commute_iff_mul_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.spectrum_nonempty", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.instContinuousFunctionalCalculus", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsStrictlyPositive.commute_iff", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Instances", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "cfcHom_real_eq_restrict", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cfcₙHom_real_eq_restrict", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cfcHom_nnreal_eq_restrict", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Instances", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "cfcₙHom_nnreal_eq_restrict", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Instances", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "_private.Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Isometric.0.termσ", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Isometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "_private.Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Isometric.0._aux_Mathlib_Analysis_CStarAlgebra_ContinuousFunctionalCalculus_Isometric___macroRules__private_Mathlib_Analysis_CStarAlgebra_ContinuousFunctionalCalculus_Isometric_0_termσₙ_1", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Isometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Isometric.0._aux_Mathlib_Analysis_CStarAlgebra_ContinuousFunctionalCalculus_Isometric___unexpand_quasispectrum_1", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Isometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "nnnorm_cfc_lt", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Isometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SpectrumRestricts.isometric_cfc", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Isometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "norm_cfcₙ_le", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Isometric", "is_tactic_proof": true, "tactics": ["refine", "simpa", "simp", "rintro", "exact"], "tactic_count": 5}
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{"name": "nnnorm_cfcₙ_lt", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Isometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuasispectrumRestricts.isometric_cfc", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Isometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.instIsometricContinuousFunctionalCalculus", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Isometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.instNonUnitalIsometricContinuousFunctionalCalculus", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Isometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nnnorm_cfc_nnreal_le", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Isometric", "is_tactic_proof": true, "tactics": ["obtain", "rw", "simp", "refine", "simp", "rintro", "exact"], "tactic_count": 7}
{"name": "nnnorm_cfc_nnreal_lt", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Isometric", "is_tactic_proof": true, "tactics": ["obtain", "rw", "simpa", "refine", "simp", "rintro", "exact"], "tactic_count": 7}
{"name": "nnnorm_cfcₙ_nnreal_le", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Isometric", "is_tactic_proof": true, "tactics": ["refine", "simp", "rintro", "exact"], "tactic_count": 4}
{"name": "nnnorm_cfcₙ_nnreal_lt", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Isometric", "is_tactic_proof": true, "tactics": ["refine", "simpa", "simp", "rintro", "exact"], "tactic_count": 5}
{"name": "IsometricContinuousFunctionalCalculus.toNonUnital", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Isometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital.0.termσₙ", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital.0._aux_Mathlib_Analysis_CStarAlgebra_ContinuousFunctionalCalculus_NonUnital___macroRules__private_Mathlib_Analysis_CStarAlgebra_ContinuousFunctionalCalculus_NonUnital_0_termσₙ_1", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital.0._aux_Mathlib_Analysis_CStarAlgebra_ContinuousFunctionalCalculus_NonUnital___unexpand_quasispectrum_1", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFactMemSetQuasispectrumOfNat", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalContinuousFunctionalCalculus.isCompact_quasispectrum", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarAlgHom.ext_continuousMap", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cfcₙHom", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cfcₙHom_isClosedEmbedding", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cfcₙHom_continuous", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cfcₙHom_id", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cfcₙHom_map_quasispectrum", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cfcₙHom_predicate", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cfcₙHom_eq_of_continuous_of_map_id", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cfcₙHom_comp", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital", "is_tactic_proof": false, "tactics": ["let", "map_smul", "map_add", "map_mul", "map_zero", "map_star", "let", "suffices", "refine", "refine", "exact", "simp", "congr", "ext", "simp"], "tactic_count": 15}
{"name": "cfcₙL", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "definition._@.Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital.138735502._hygCtx._hyg.8", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "wrapped._@.Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital.138735502._hygCtx._hyg.8", "kind": "opaque", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cfcₙ", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cfcₙ_def", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital", "is_tactic_proof": true, "tactics": ["intros", "delta", "rw", "rfl"], "tactic_count": 4}
{"name": "cfcₙ_apply", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "cfcₙ_apply_of_not_and_and", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "cfcₙ_apply_of_not_predicate", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "cfcₙ_apply_of_not_continuousOn", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "cfcₙ_apply_of_not_map_zero", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "cfcₙHom_eq_cfcₙ_extend", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital", "is_tactic_proof": true, "tactics": ["have", "have", "continuousOn_iff_continuous_restrict.mpr", "have", "rw", "exact", "generalize", "rw", "congr"], "tactic_count": 9}
{"name": "cfcₙ_eq_cfcₙL", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "cfcₙ_apply_mkD", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital", "is_tactic_proof": true, "tactics": ["by_cases", "by_cases", "rw", "rw", "exact", "rw"], "tactic_count": 6}
{"name": "cfcₙ_eq_cfcₙL_mkD", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cfcₙ_cases", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "exact", "simp", "obtain", "rwa", "rwa", "rwa"], "tactic_count": 8}
{"name": "cfcₙ_commute_cfcₙ", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital", "is_tactic_proof": true, "tactics": ["refine", "refine", "exact"], "tactic_count": 3}
{"name": "cfcₙ_id", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cfcₙ_id'", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cfcₙ_map_quasispectrum", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "cfcₙ_predicate_zero", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cfcₙ_predicate", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cfcₙ_congr", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "congr", "exact", "simp", "obtain", "simp", "rw", "exact", "rw", "exact"], "tactic_count": 11}
{"name": "cfcₙ_zero", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "rw"], "tactic_count": 3}
{"name": "cfcₙ_const_zero", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cfcₙ_mul", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "congr", "simp"], "tactic_count": 4}
{"name": "cfcₙ_add", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "simp_rw", "congr", "simp"], "tactic_count": 5}
{"name": "cfcₙ_star", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital", "is_tactic_proof": true, "tactics": ["by_cases", "obtain", "rw", "congr", "simp", "obtain", "simp", "rw", "exact", "rw", "exact"], "tactic_count": 11}
{"name": "cfcₙ_star_id", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "range_cfcₙ_eq_range_cfcₙHom", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital", "is_tactic_proof": true, "tactics": ["ext", "constructor", "all_goals", "exact", "exact"], "tactic_count": 5}
{"name": "CFC.quasispectrum_zero_eq", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital", "is_tactic_proof": true, "tactics": ["refine", "rw", "cfcₙ_map_quasispectrum", "simp_all"], "tactic_count": 4}
{"name": "cfcₙ_apply_zero", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital", "is_tactic_proof": true, "tactics": ["by_cases", "nth_rw", "apply", "simpa", "exact"], "tactic_count": 5}
{"name": "IsStarNormal.cfcₙ_map", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSelfAdjoint.cfcₙ", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cfcₙ_nonneg_of_predicate", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cfcₙ_sub", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "congr", "simp"], "tactic_count": 4}
{"name": "cfcₙ_neg", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital", "is_tactic_proof": true, "tactics": ["by_cases", "obtain", "rw", "congr", "simp", "obtain", "simp", "rw", "exact", "rw", "exact"], "tactic_count": 11}
{"name": "cfcₙHom_mono", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cfcₙHom_nonneg_iff", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital", "is_tactic_proof": true, "tactics": ["constructor", "exact", "simpa"], "tactic_count": 3}
{"name": "cfcₙ_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital", "is_tactic_proof": true, "tactics": ["by_cases", "obtain", "simpa", "simp", "obtain", "simp", "simp"], "tactic_count": 7}
{"name": "cfcₙ_nonpos", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital", "is_tactic_proof": true, "tactics": ["by_cases", "obtain", "simpa", "simp", "obtain", "simp", "simp"], "tactic_count": 7}
{"name": "cfcₙHom_le_iff", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "cfcₙHomSuperset", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cfcₙHomSuperset_continuous", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cfcₙHomSuperset_id", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cfcₙHom_of_cfcHom", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cfcₙHom_of_cfcHom_map_quasispectrum", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital", "is_tactic_proof": true, "tactics": ["intro", "simp", "rw", "simp", "rw", "ext", "constructor", "rintro", "exact", "exact", "rintro", "have", "simp_rw", "obtain", "exact", "apply", "push", "rw"], "tactic_count": 18}
{"name": "isClosedEmbedding_cfcₙHom_of_cfcHom", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital", "is_tactic_proof": true, "tactics": ["let", "refine", "have", "uniformSpace_eq_inf_precomp_of_cover", "simp", "range_zero,", "simp_rw", "uniformity_comap,", "refine", "have", "convert"], "tactic_count": 11}
{"name": "ContinuousFunctionalCalculus.toNonUnital", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cfcₙHom_eq_cfcₙHom_of_cfcHom", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital", "is_tactic_proof": true, "tactics": ["refine", "exact", "exact", "simpa"], "tactic_count": 4}
{"name": "LibraryNote.continuous_functional_calculus", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Note", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Order.0.termσₙ", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Order.0._aux_Mathlib_Analysis_CStarAlgebra_ContinuousFunctionalCalculus_Order___macroRules__private_Mathlib_Analysis_CStarAlgebra_ContinuousFunctionalCalculus_Order_0_termσₙ_1", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Order.0._aux_Mathlib_Analysis_CStarAlgebra_ContinuousFunctionalCalculus_Order___unexpand_quasispectrum_1", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitization.instPartialOrder", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitization.instStarOrderedRing", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitization.inr_nonneg_iff", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Order", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "refine", "all_goals", "exact", "exact"], "tactic_count": 6}
{"name": "CStarAlgebra.mul_star_le_algebraMap_norm_sq", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Order", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "CStarAlgebra.star_mul_le_algebraMap_norm_sq", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Order", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "IsSelfAdjoint.toReal_spectralRadius_eq_norm", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Order", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CStarAlgebra.mem_Icc_algebraMap_iff_norm_le", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Order", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CStarAlgebra.mem_Icc_algebraMap_iff_nnnorm_le", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarAlgebra.mem_Icc_iff_norm_le_one", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Order", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CStarAlgebra.mem_Icc_iff_nnnorm_le_one", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_iff_norm_sqrt_mul_sqrt_inv", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Order", "is_tactic_proof": false, "tactics": ["rw", "le_iff_norm_sqrt_mul_rpow", "simp"], "tactic_count": 3}
{"name": "CStarAlgebra.inv_le_inv", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Order", "is_tactic_proof": true, "tactics": ["have", "have", "have", "rw", "rw", "rwa"], "tactic_count": 6}
{"name": "CStarAlgebra.inv_le_inv_iff", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarAlgebra.inv_le_iff", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Order", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CStarAlgebra.le_inv_iff", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Order", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CStarAlgebra.one_le_inv_iff_le_one", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Order", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CStarAlgebra.inv_le_one_iff_one_le", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Order", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CStarAlgebra.inv_le_one", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarAlgebra.le_one_of_one_le_inv", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Order", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CStarAlgebra.rpow_neg_one_le_one", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Order", "is_tactic_proof": true, "tactics": ["lift", "rw", "exact"], "tactic_count": 3}
{"name": "IsStrictlyPositive.of_le", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsStrictlyPositive.add_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsStrictlyPositive.nonneg_add", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CStarAlgebra.instNonnegSpectrumClassComplexNonUnital", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarAlgebra.isClosed_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Order", "is_tactic_proof": false, "tactics": ["suffices", "rw", "convert", "ext", "simp", "congr", "exact", "simp", "and_congr_right", "refine", "all_goals"], "tactic_count": 11}
{"name": "CStarAlgebra.instOrderClosedTopology", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarAlgebra.inr_mem_Icc_iff_norm_le", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Order", "is_tactic_proof": true, "tactics": ["simp", "rw", "exact"], "tactic_count": 3}
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{"name": "CStarAlgebra.preimage_inr_Icc_zero_one", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Order", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CStarAlgebra.pow_monotone", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Order", "is_tactic_proof": true, "tactics": ["have", "intro", "simp", "rw", "rw", "peel", "exact"], "tactic_count": 7}
{"name": "range_cfcHom", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Range", "is_tactic_proof": false, "tactics": ["rw", "congr", "simpa"], "tactic_count": 3}
{"name": "range_cfc", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Range", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "cfcHom_apply_mem_elemental", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cfc_apply_mem_elemental", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "range_cfc_nnreal_eq_image_cfc_real", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Range", "is_tactic_proof": true, "tactics": ["ext", "constructor", "rintro", "simp", "exact", "rintro", "simp", "exact"], "tactic_count": 8}
{"name": "range_cfc_nnreal", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Range", "is_tactic_proof": false, "tactics": ["rw", "refine", "rintro", "simp", "obtain", "refine", "rwa", "exact", "exact"], "tactic_count": 9}
{"name": "range_cfcₙHom", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Range", "is_tactic_proof": false, "tactics": ["rw", "congr", "simpa"], "tactic_count": 3}
{"name": "range_cfcₙ", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Range", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "cfcₙHom_apply_mem_elemental", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cfcₙ_apply_mem_elemental", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "range_cfcₙ_nnreal_eq_image_cfcₙ_real", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Range", "is_tactic_proof": true, "tactics": ["ext", "constructor", "rintro", "simp", "exact", "rintro", "simp", "exact"], "tactic_count": 8}
{"name": "range_cfcₙ_nnreal", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Range", "is_tactic_proof": false, "tactics": ["rw", "refine", "rintro", "simp", "obtain", "simpa", "refine", "rwa", "exact", "exact", "exact"], "tactic_count": 11}
{"name": "SpectrumRestricts.homeomorph", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SpectrumRestricts.compactSpace", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Restrict", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SpectrumRestricts.starAlgHom", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SpectrumRestricts.starAlgHom_id", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Restrict", "is_tactic_proof": true, "tactics": ["simp", "convert", "ext", "exact"], "tactic_count": 4}
{"name": "SpectrumRestricts.isClosedEmbedding_starAlgHom", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SpectrumRestricts.cfc", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SpectrumRestricts.cfcHom_eq_restrict", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Restrict", "is_tactic_proof": true, "tactics": ["apply", "exact", "exact"], "tactic_count": 3}
{"name": "SpectrumRestricts.cfc_eq_restrict", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Restrict", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "apply", "lift", "simp", "have", "refine", "rw", "simpa", "hg'.comp", "rw"], "tactic_count": 11}
{"name": "_private.Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Restrict.0.QuasispectrumRestricts.termσₙ", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Restrict.0.QuasispectrumRestricts._aux_Mathlib_Analysis_CStarAlgebra_ContinuousFunctionalCalculus_Restrict___macroRules__private_Mathlib_Analysis_CStarAlgebra_ContinuousFunctionalCalculus_Restrict_0_QuasispectrumRestricts_termσₙ_1", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Restrict.0.QuasispectrumRestricts._aux_Mathlib_Analysis_CStarAlgebra_ContinuousFunctionalCalculus_Restrict___unexpand_quasispectrum_1", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuasispectrumRestricts.homeomorph", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuasispectrumRestricts.nonUnitalStarAlgHom", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuasispectrumRestricts.nonUnitalStarAlgHom_id", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Restrict", "is_tactic_proof": true, "tactics": ["simp", "convert", "ext", "exact"], "tactic_count": 4}
{"name": "QuasispectrumRestricts.isClosedEmbedding_nonUnitalStarAlgHom", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Restrict", "is_tactic_proof": true, "tactics": ["have", "refine", "hφ.comp"], "tactic_count": 3}
{"name": "QuasispectrumRestricts.cfc", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuasispectrumRestricts.cfcₙHom_eq_restrict", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Restrict", "is_tactic_proof": true, "tactics": ["apply", "exact", "exact"], "tactic_count": 3}
{"name": "QuasispectrumRestricts.cfcₙ_eq_restrict", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Restrict", "is_tactic_proof": true, "tactics": ["by_cases", "obtain", "rw", "apply", "lift", "simp", "simp", "obtain", "have", "refine", "rw", "simpa", "hg'.comp", "rw", "rw"], "tactic_count": 15}
{"name": "RCLike.instContinuousMapUniqueHom", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.instContinuousMapUniqueHom", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.instContinuousMapUniqueHom", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.toNNReal", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.continuous_toNNReal", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.toNNReal_apply", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.toNNReal_add_add_neg_add_neg_eq", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unique", "is_tactic_proof": true, "tactics": ["ext", "simp", "abel"], "tactic_count": 3}
{"name": "ContinuousMap.toNNReal_mul_add_neg_mul_add_mul_neg_eq", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unique", "is_tactic_proof": true, "tactics": ["ext", "simp", "abel"], "tactic_count": 3}
{"name": "ContinuousMap.toNNReal_algebraMap", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unique", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "ContinuousMap.toNNReal_neg_algebraMap", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unique", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "ContinuousMap.toNNReal_one", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "StarAlgHom.realContinuousMapOfNNReal", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarAlgHom.continuous_realContinuousMapOfNNReal", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unique", "is_tactic_proof": true, "tactics": ["dsimp", "fun_prop"], "tactic_count": 2}
{"name": "StarAlgHom.realContinuousMapOfNNReal_apply_comp_toReal", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unique", "is_tactic_proof": true, "tactics": ["simp", "convert_to", "on_goal", "all_goals", "congr", "ext", "simp"], "tactic_count": 7}
{"name": "StarAlgHom.realContinuousMapOfNNReal_injective", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.instContinuousMap.UniqueHom", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.uniqueNonUnitalContinuousFunctionalCalculus", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.toNNReal", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.toNNReal_apply", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.continuous_toNNReal", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unique", "is_tactic_proof": true, "tactics": ["rw", "convert_to", "exact"], "tactic_count": 3}
{"name": "ContinuousMapZero.toContinuousMapHom_toNNReal", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.toNNReal_smul", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unique", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "simpa", "simpa"], "tactic_count": 4}
{"name": "ContinuousMapZero.toNNReal_neg_smul", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unique", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ContinuousMapZero.toNNReal_mul_add_neg_mul_add_mul_neg_eq", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unique", "is_tactic_proof": true, "tactics": ["apply", "simpa"], "tactic_count": 2}
{"name": "ContinuousMapZero.toNNReal_add_add_neg_add_neg_eq", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unique", "is_tactic_proof": true, "tactics": ["apply", "simpa"], "tactic_count": 2}
{"name": "NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarAlgHom.continuous_realContinuousMapZeroOfNNReal", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unique", "is_tactic_proof": true, "tactics": ["dsimp", "fun_prop"], "tactic_count": 2}
{"name": "NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_apply_comp_toReal", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unique", "is_tactic_proof": true, "tactics": ["simp", "convert_to", "on_goal", "all_goals", "congr", "ext", "simp"], "tactic_count": 7}
{"name": "NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_injective", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.instContinuousMapZero.UniqueHom", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousFunctionalCalculus.isCompact_spectrum", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarAlgHom.ext_continuousMap", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cfcHom", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cfcHom_isClosedEmbedding", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cfcHom_continuous", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cfcHom_id", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cfcHom_map_spectrum", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cfcHom_predicate", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cfcHom_eq_of_continuous_of_map_id", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cfcHom_comp", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital", "is_tactic_proof": true, "tactics": ["let", "suffices", "refine", "exact", "simp", "congr", "ext", "simp"], "tactic_count": 8}
{"name": "cfcL", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "definition._@.Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital.1784184353._hygCtx._hyg.8", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "cfc", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "cfc_apply", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "cfc_apply_of_not_and", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "cfc_apply_of_not_predicate", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "cfc_apply_of_not_continuousOn", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "cfcHom_eq_cfc_extend", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital", "is_tactic_proof": true, "tactics": ["have", "have", "continuousOn_iff_continuous_restrict.mpr", "rw", "congr"], "tactic_count": 5}
{"name": "cfc_eq_cfcL", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "cfc_apply_mkD", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "rw"], "tactic_count": 3}
{"name": "cfc_eq_cfcL_mkD", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "cfc_predicate_algebraMap", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cfc_predicate_one", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cfc_congr", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "congr", "exact", "obtain", "simp", "rw", "exact"], "tactic_count": 8}
{"name": "cfc_eq_cfc_iff_eqOn", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cfc_one", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cfc_const_one", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cfc_zero", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "rw"], "tactic_count": 3}
{"name": "cfc_const_zero", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cfc_star", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital", "is_tactic_proof": true, "tactics": ["by_cases", "obtain", "rw", "congr", "obtain", "simp", "rw", "exact"], "tactic_count": 8}
{"name": "cfc_star_id", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "range_cfc_eq_range_cfcHom", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital", "is_tactic_proof": true, "tactics": ["ext", "constructor", "all_goals", "exact", "exact"], "tactic_count": 5}
{"name": "CFC.spectrum_algebraMap_subset", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital", "is_tactic_proof": true, "tactics": ["rw", "rintro", "simp"], "tactic_count": 3}
{"name": "CFC.spectrum_algebraMap_eq", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "CFC.spectrum_zero_eq", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "CFC.spectrum_one_eq", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "cfc_algebraMap", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital", "is_tactic_proof": false, "tactics": ["have", "continuousOn_singleton", "rw", "congr", "ext", "apply", "simp_all"], "tactic_count": 7}
{"name": "cfc_apply_zero", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "cfc_apply_one", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsStarNormal.cfc_map", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSelfAdjoint.cfc", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cfc_nonneg_of_predicate", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.continuousOn_inv₀_spectrum", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.continuousOn_zpow₀_spectrum", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cfc_sub", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "congr", "simp"], "tactic_count": 4}
{"name": "cfc_neg", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital", "is_tactic_proof": true, "tactics": ["by_cases", "obtain", "rw", "congr", "obtain", "simp", "rw", "exact"], "tactic_count": 8}
{"name": "cfcHom_mono", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cfcHom_nonneg_iff", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital", "is_tactic_proof": true, "tactics": ["constructor", "exact", "simpa"], "tactic_count": 3}
{"name": "cfcHom_isStrictlyPositive_iff", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital", "is_tactic_proof": false, "tactics": ["refine", "apply", "grind"], "tactic_count": 3}
{"name": "cfc_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital", "is_tactic_proof": true, "tactics": ["by_cases", "simpa", "simp"], "tactic_count": 3}
{"name": "cfc_nonpos", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital", "is_tactic_proof": true, "tactics": ["by_cases", "simpa", "simp"], "tactic_count": 3}
{"name": "cfc_le_one", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital", "is_tactic_proof": true, "tactics": ["apply", "rw", "apply", "simpa"], "tactic_count": 4}
{"name": "CFC.inv_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cfcHom_le_iff", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "cfcHomSuperset", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cfcHomSuperset_continuous", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cfcHomSuperset_id", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitary_iff_isStarNormal_and_spectrum_subset_unitary", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unitary", "is_tactic_proof": true, "tactics": ["rw", "refine", "nth_rw", "rw", "simp"], "tactic_count": 5}
{"name": "mem_unitary_of_spectrum_subset_unitary", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unitary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "spectrum_subset_unitary_of_mem_unitary", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unitary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCStarAlgebraContinuousLinearMapComplexIdOfCompleteSpace", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousLinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.instNonUnitalCStarAlgebra", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.instNonUnitalCommCStarAlgebra", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.instCStarAlgebra", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.instCommCStarAlgebra", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instNonUnitalCStarAlgebra", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instNonUnitalCommCStarAlgebra", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instCStarAlgebra", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instCommCStarAlgebra", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.instNonUnitalCStarAlgebra", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.instNonUnitalCommCStarAlgebra", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.ContinuousMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "selfAdjoint.expUnitary", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "selfAdjoint.expUnitary_zero", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Exponential", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "selfAdjoint.continuous_expUnitary", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Exponential", "is_tactic_proof": true, "tactics": ["simp", "let", "fun_prop"], "tactic_count": 3}
{"name": "Commute.expUnitary_add", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Exponential", "is_tactic_proof": true, "tactics": ["let", "ext", "have", "unfold", "simp", "simpa"], "tactic_count": 6}
{"name": "Commute.expUnitary", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.toCharacterSpace", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.GelfandDuality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.toCharacterSpace_apply_eq_zero_of_mem", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.GelfandDuality", "is_tactic_proof": true, "tactics": ["unfold", "simp", "simp_rw", "exact"], "tactic_count": 4}
{"name": "WeakDual.CharacterSpace.exists_apply_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.GelfandDuality", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "WeakDual.CharacterSpace.mem_spectrum_iff_exists", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.GelfandDuality", "is_tactic_proof": true, "tactics": ["refine", "obtain", "simp", "exact", "rintro", "exact"], "tactic_count": 6}
{"name": "spectrum.gelfandTransform_eq", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.GelfandDuality", "is_tactic_proof": true, "tactics": ["ext", "rw", "exact"], "tactic_count": 3}
{"name": "instNonemptyElemWeakDualComplexCharacterSpaceOfNontrivial", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.GelfandDuality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "gelfandTransform_map_star", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.GelfandDuality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "gelfandTransform_isometry", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.GelfandDuality", "is_tactic_proof": false, "tactics": ["refine", "self-adjoint,", "roots", "have", "unfold", "rw", "simp", "simpa"], "tactic_count": 8}
{"name": "gelfandTransform_bijective", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.GelfandDuality", "is_tactic_proof": false, "tactics": ["refine", "hard", "nontrivial", "let", "star_mem", "rintro", "use", "ext1", "dsimp", "simp", "suffices", "have", "le_antisymm", "refine", "h", "of", "contrapose", "exact"], "tactic_count": 18}
{"name": "gelfandStarTransform", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.GelfandDuality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakDual.CharacterSpace.compContinuousMap", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.GelfandDuality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakDual.CharacterSpace.compContinuousMap_id", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.GelfandDuality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakDual.CharacterSpace.compContinuousMap_comp", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.GelfandDuality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "gelfandStarTransform_naturality", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.GelfandDuality", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "WeakDual.CharacterSpace.homeoEval_naturality", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.GelfandDuality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PositiveLinearMap.PreGNS", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.GelfandNaimarkSegal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PositiveLinearMap.instAddCommGroupPreGNS", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.GelfandNaimarkSegal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PositiveLinearMap.instModuleComplexPreGNS", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.GelfandNaimarkSegal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PositiveLinearMap.toPreGNS", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.GelfandNaimarkSegal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PositiveLinearMap.ofPreGNS", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.GelfandNaimarkSegal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PositiveLinearMap.toPreGNS_ofPreGNS", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.GelfandNaimarkSegal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PositiveLinearMap.ofPreGNS_toPreGNS", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.GelfandNaimarkSegal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PositiveLinearMap.preGNSpreInnerProdSpace", "kind": "abbrev", "module": "Mathlib.Analysis.CStarAlgebra.GelfandNaimarkSegal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PositiveLinearMap.instSeminormedAddCommGroupPreGNS", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.GelfandNaimarkSegal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PositiveLinearMap.instInnerProductSpaceComplexPreGNS", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.GelfandNaimarkSegal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PositiveLinearMap.preGNS_inner_def", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.GelfandNaimarkSegal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PositiveLinearMap.preGNS_norm_def", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.GelfandNaimarkSegal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PositiveLinearMap.preGNS_norm_sq", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.GelfandNaimarkSegal", "is_tactic_proof": true, "tactics": ["have", "rw", "rw", "rwa"], "tactic_count": 4}
{"name": "PositiveLinearMap.GNS", "kind": "abbrev", "module": "Mathlib.Analysis.CStarAlgebra.GelfandNaimarkSegal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PositiveLinearMap.leftMulMapPreGNS", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.GelfandNaimarkSegal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PositiveLinearMap.leftMulMapPreGNS_mul_eq_comp", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.GelfandNaimarkSegal", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "PositiveLinearMap.gnsNonUnitalStarAlgHom", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.GelfandNaimarkSegal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PositiveLinearMap.gnsNonUnitalStarAlgHom_apply", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.GelfandNaimarkSegal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PositiveLinearMap.gnsNonUnitalStarAlgHom_apply_coe", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.GelfandNaimarkSegal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "_private.Mathlib.Analysis.CStarAlgebra.GelfandNaimarkSegal.0.PositiveLinearMap.gnsNonUnitalStarAlgHom_map_one", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.GelfandNaimarkSegal", "is_tactic_proof": true, "tactics": ["ext", "induction", "hp", "ih"], "tactic_count": 4}
{"name": "PositiveLinearMap.gnsStarAlgHom", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.GelfandNaimarkSegal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSelfAdjoint.map_spectrum_real", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Hom", "is_tactic_proof": true, "tactics": ["have", "refine", "by_contra", "obtain", "exists_continuous_zero_one_of_isClosed", "simpa", "hence", "suffices", "rw", "exact", "zero_ne_one", "calc", "calc", "φ"], "tactic_count": 14}
{"name": "NonUnitalStarAlgHom.norm_map", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Hom", "is_tactic_proof": true, "tactics": ["that", "suffices", "intro", "rw", "simp", "have", "calc"], "tactic_count": 7}
{"name": "NonUnitalStarAlgHom.nnnorm_map", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarAlgHom.isometry", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "entry_norm_bound_of_unitary", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Matrix", "is_tactic_proof": true, "tactics": ["have", "apply", "intro", "rw", "obtain", "rw", "apply", "rw", "use", "simp", "have", "simp", "norm_cast", "have", "rw", "rw", "norm_cast", "have", "have", "simp", "rw", "exact"], "tactic_count": 22}
{"name": "entrywise_sup_norm_bound_of_unitary", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Matrix", "is_tactic_proof": true, "tactics": ["simp_rw", "intros", "exact"], "tactic_count": 3}
{"name": "Matrix.toEuclideanCLM", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.coe_toEuclideanCLM_eq_toEuclideanLin", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.toEuclideanCLM_toLp", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.ofLp_toEuclideanCLM", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.l2OpNormedAddCommGroupAux", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.l2OpNormedRingAux", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.instL2OpMetricSpace", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.Matrix", "is_tactic_proof": true, "tactics": ["letI", "l2OpNormedAddCommGroupAux.replaceTopology", "toContinuousLinearMap", "norm", "dist_eq", "exact", "normed_add_comm_group.replaceUniformity", "congr", "rw", "rw"], "tactic_count": 10}
{"name": "Matrix.instL2OpNormedAddCommGroup", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.l2_opNorm_def", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.l2_opNNNorm_def", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "DoubleCentralizer.instNormedAlgebra", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.Multiplier", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DoubleCentralizer.isUniformEmbedding_toProdMulOpposite", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Multiplier", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DoubleCentralizer.instCompleteSpace", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.Multiplier", "is_tactic_proof": true, "tactics": ["rw", "apply", "simp", "exact"], "tactic_count": 4}
{"name": "DoubleCentralizer.norm_fst_eq_snd", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Multiplier", "is_tactic_proof": true, "tactics": ["have", "intro", "have", "have", "f.opNNNorm_le_bound", "convert", "simp", "simp", "simp", "have", "intro", "calc", "have", "intro", "calc", "exact"], "tactic_count": 16}
{"name": "DoubleCentralizer.nnnorm_fst_eq_snd", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Multiplier", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DoubleCentralizer.norm_fst", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Multiplier", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DoubleCentralizer.norm_snd", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Multiplier", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "DoubleCentralizer.nnnorm_fst", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Multiplier", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DoubleCentralizer.nnnorm_snd", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Multiplier", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DoubleCentralizer.instCStarRing", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.Multiplier", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DoubleCentralizer.instCStarAlgebraComplex", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.Multiplier", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "map_isSelfAdjoint", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.PositiveLinearMap", "is_tactic_proof": true, "tactics": ["rw", "cfc_tac"], "tactic_count": 2}
{"name": "PositiveLinearMap.apply_le_of_isSelfAdjoint", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.PositiveLinearMap", "is_tactic_proof": true, "tactics": ["gcongr", "exact"], "tactic_count": 2}
{"name": "PositiveLinearMap.norm_apply_le_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.PositiveLinearMap", "is_tactic_proof": true, "tactics": ["have", "rw", "clear", "refine", "rw", "gcongr", "rw", "exact"], "tactic_count": 8}
{"name": "PositiveLinearMap.exists_norm_apply_le", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.PositiveLinearMap", "is_tactic_proof": true, "tactics": ["parts", "suffices", "obtain", "refine", "obtain", "conv_lhs", "simp", "apply", "simp", "apply", "apply", "simp", "gcongr", "exact", "by_contra", "have", "obtain", "set", "have", "refine", "simp", "simpa", "choose", "simp", "obtain", "have", "refine", "have", "simp", "obtain", "tendsto_pow_atTop_atTop_of_one_lt", "apply", "trans", "have", "rw", "simpa", "have", "refine", "gcongr", "exact"], "tactic_count": 40}
{"name": "PositiveLinearMap.instContinuousLinearMapClassComplexOfLinearMapClassOfOrderHomClass", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.PositiveLinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PositiveLinearMap.instStarHomClassOfLinearMapClassComplexOfOrderHomClass", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.PositiveLinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIdempotentElem.isSelfAdjoint_iff_isStarNormal", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Projection", "is_tactic_proof": false, "tactics": ["simp", "and_iff_left_iff_imp]", "intro", "rcases"], "tactic_count": 4}
{"name": "isStarProjection_iff_isIdempotentElem_and_isStarNormal", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Projection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarAlgebra.span_nonneg_inter_closedBall", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.SpecialFunctions.PosPart", "is_tactic_proof": true, "tactics": ["rw", "intro", "obtain", "exact", "suffices", "rw", "refine", "norm_cast", "exact", "simp", "apply", "norm_cast", "positivity"], "tactic_count": 13}
{"name": "CStarAlgebra.span_nonneg_inter_ball", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.SpecialFunctions.PosPart", "is_tactic_proof": true, "tactics": ["rw", "gcongr", "exact"], "tactic_count": 3}
{"name": "CStarAlgebra.span_nonneg_inter_unitClosedBall", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.SpecialFunctions.PosPart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarAlgebra.span_nonneg_inter_unitBall", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.SpecialFunctions.PosPart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarAlgebra.exists_sum_four_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.SpecialFunctions.PosPart", "is_tactic_proof": true, "tactics": ["use", "rw", "constructor", "intro", "fin_cases", "all_goals", "constructor", "simp", "cfc_tac", "exact", "exact", "exact", "exact", "nth_rw", "simp", "module"], "tactic_count": 16}
{"name": "_private.Mathlib.Analysis.CStarAlgebra.Spectrum.0.termσ", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.Spectrum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.CStarAlgebra.Spectrum.0._aux_Mathlib_Analysis_CStarAlgebra_Spectrum___macroRules__private_Mathlib_Analysis_CStarAlgebra_Spectrum_0_termσ_1", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.Spectrum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.CStarAlgebra.Spectrum.0._aux_Mathlib_Analysis_CStarAlgebra_Spectrum___unexpand_spectrum_1", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.Spectrum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.CStarAlgebra.Spectrum.0.term_⋆", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.Spectrum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.CStarAlgebra.Spectrum.0._aux_Mathlib_Analysis_CStarAlgebra_Spectrum___macroRules__private_Mathlib_Analysis_CStarAlgebra_Spectrum_0_term_⋆_1", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.Spectrum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.CStarAlgebra.Spectrum.0._aux_Mathlib_Analysis_CStarAlgebra_Spectrum___unexpand_Star_star_1", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.Spectrum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitary.spectrum_subset_circle", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Spectrum", "is_tactic_proof": true, "tactics": ["nontriviality", "refine", "simpa", "rw", "have", "rw", "have", "simpa"], "tactic_count": 8}
{"name": "spectrum.subset_circle_of_unitary", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Spectrum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "spectrum.norm_eq_one_of_unitary", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Spectrum", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CStarAlgebra.le_nnnorm_of_mem_quasispectrum", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Spectrum", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "_private.Mathlib.Analysis.CStarAlgebra.Spectrum.0.term↑ₐ", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.Spectrum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.CStarAlgebra.Spectrum.0._aux_Mathlib_Analysis_CStarAlgebra_Spectrum___macroRules__private_Mathlib_Analysis_CStarAlgebra_Spectrum_0_term↑ₐ_1", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.Spectrum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.CStarAlgebra.Spectrum.0._aux_Mathlib_Analysis_CStarAlgebra_Spectrum___unexpand_algebraMap_1", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.Spectrum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSelfAdjoint.spectralRadius_eq_nnnorm", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Spectrum", "is_tactic_proof": true, "tactics": ["have", "refine", "convert", "refine", "rw", "simp"], "tactic_count": 6}
{"name": "IsSelfAdjoint.toReal_spectralRadius_complex_eq_norm", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Spectrum", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsStarNormal.spectralRadius_eq_nnnorm", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Spectrum", "is_tactic_proof": true, "tactics": ["refine", "have", "funext", "rw", "nnnorm_star_mul_self,", "have", "rw", "convert", "rw"], "tactic_count": 9}
{"name": "IsSelfAdjoint.mem_spectrum_eq_re", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Spectrum", "is_tactic_proof": true, "tactics": ["let", "have", "let", "have", "simpa", "exact", "simpa", "neg_eq_zero]"], "tactic_count": 8}
{"name": "selfAdjoint.mem_spectrum_eq_re", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Spectrum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSelfAdjoint.im_eq_zero_of_mem_spectrum", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Spectrum", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsSelfAdjoint.val_re_map_spectrum", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Spectrum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "selfAdjoint.val_re_map_spectrum", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Spectrum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSelfAdjoint.isConnected_spectrum_compl", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Spectrum", "is_tactic_proof": false, "tactics": ["suffices", "rw", "rw", "convert", "exact", "refine", "nonempty", "have", "exact", "apply", "apply", "all_goals", "refine", "rw", "simp_all"], "tactic_count": 15}
{"name": "StarSubalgebra.coe_isUnit", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Spectrum", "is_tactic_proof": true, "tactics": ["refine", "have", "have", "have", "rw", "spectrum.zero_notMem_iff]", "have", "have", "exact", "exact", "exact"], "tactic_count": 11}
{"name": "StarSubalgebra.mem_spectrum_iff", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Spectrum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.spectrum_eq", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Spectrum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarAlgHom.nnnorm_apply_le", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Spectrum", "is_tactic_proof": false, "tactics": ["have", "suffices", "refine", "simp_rw", "exact", "intro", "suffices", "rwa", "exact", "simpa"], "tactic_count": 10}
{"name": "NonUnitalStarAlgHom.norm_apply_le", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Spectrum", "is_tactic_proof": true, "tactics": ["exact_mod_cast"], "tactic_count": 1}
{"name": "NonUnitalStarAlgHom.instContinuousLinearMapClassComplex", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Spectrum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarAlgEquiv.nnnorm_map", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Spectrum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarAlgEquiv.norm_map", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Spectrum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarAlgEquiv.isometry", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Spectrum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakDual.Complex.instStarHomClass", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.Spectrum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHomClass.instStarHomClass", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Spectrum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakDual.CharacterSpace.instStarHomClass", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.Spectrum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitary.two_mul_one_sub_le_norm_sub_one_sq", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Unitary.Connected", "is_tactic_proof": true, "tactics": ["rw", "have", "simp", "rw", "convert", "simpa"], "tactic_count": 6}
{"name": "Unitary.norm_sub_one_sq_eq", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Unitary.Connected", "is_tactic_proof": true, "tactics": ["obtain", "exfalso", "rw", "have", "have", "have", "simpa", "have", "have", "simpa", "exact"], "tactic_count": 11}
{"name": "Unitary.norm_sub_one_lt_two_iff", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Unitary.Connected", "is_tactic_proof": true, "tactics": ["nontriviality", "rw", "constructor", "intro", "have", "norm_num", "contrapose", "obtain", "spectrum.isCompact", "rw", "obtain", "intro", "replace", "have", "rw", "exact"], "tactic_count": 16}
{"name": "Unitary.spectrum_subset_slitPlane_iff_norm_lt_two", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Unitary.Connected", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsSelfAdjoint.cfc_arg", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Unitary.Connected", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Unitary.argSelfAdjoint", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.Unitary.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "selfAdjoint.norm_sq_expUnitary_sub_one", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Unitary.Connected", "is_tactic_proof": true, "tactics": ["nontriviality", "apply", "simp", "rw", "x.2.spectrumRestricts.algebraMap_image]", "simp", "refine", "cases", "inl", "inr", "rintro", "exact"], "tactic_count": 12}
{"name": "argSelfAdjoint_expUnitary", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Unitary.Connected", "is_tactic_proof": true, "tactics": ["nontriviality", "ext", "have", "rw", "norm_sq_expUnitary_sub_one", "calc", "gcongr", "exact", "simp", "rw", "refine", "rwa", "conv_rhs", "refine", "rw", "obtain", "simp", "replace", "simp", "rw"], "tactic_count": 20}
{"name": "expUnitary_argSelfAdjoint", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Unitary.Connected", "is_tactic_proof": true, "tactics": ["ext", "have", "continuousOn_arg.mono", "rw", "conv_rhs", "refine", "have", "have", "simpa"], "tactic_count": 9}
{"name": "Unitary.norm_argSelfAdjoint_le_pi", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Unitary.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitary.two_mul_one_sub_cos_norm_argSelfAdjoint", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Unitary.Connected", "is_tactic_proof": true, "tactics": ["conv_rhs", "exact"], "tactic_count": 2}
{"name": "Unitary.norm_argSelfAdjoint", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Unitary.Connected", "is_tactic_proof": true, "tactics": ["refine", "linarith"], "tactic_count": 2}
{"name": "Unitary.norm_expUnitary_smul_argSelfAdjoint_sub_one_le", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Unitary.Connected", "is_tactic_proof": false, "tactics": ["have", "rw", "simp_rw", "gcongr", "exact", "rw", "rw", "trans", "gcongr", "exact", "exact"], "tactic_count": 11}
{"name": "Unitary.continuousOn_argSelfAdjoint", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Unitary.Connected", "is_tactic_proof": true, "tactics": ["rw", "simp", "rw", "intro", "obtain", "have", "have", "apply", "apply", "apply", "rintro", "simp", "refine", "intro", "simp", "trans", "exact", "refine", "simpa", "exact", "refine", "apply", "norm_num", "exact"], "tactic_count": 24}
{"name": "Unitary.openPartialHomeomorph", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.Unitary.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitary.norm_sub_eq", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Unitary.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitary.expUnitary_eq_mul_inv", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Unitary.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "selfAdjoint.expUnitaryPathToOne", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.Unitary.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "selfAdjoint.joined_one_expUnitary", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Unitary.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitary.path", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.Unitary.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitary.joined", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Unitary.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitary.isPathConnected_ball", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Unitary.Connected", "is_tactic_proof": false, "tactics": ["suffices", "convert", "ext", "rw", "simp", "refine", "have", "refine", "simpa", "norm_expUnitary_smul_argSelfAdjoint_sub_one_le"], "tactic_count": 10}
{"name": "Unitary.instLocPathConnectedSpace", "kind": "instance", "module": "Mathlib.Analysis.CStarAlgebra.Unitary.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitary.mem_pathComponentOne_iff", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Unitary.Connected", "is_tactic_proof": true, "tactics": ["constructor", "revert", "simp_rw", "refine", "refine", "intro", "rw", "obtain", "refine", "simp", "rintro", "induction", "nil", "cons"], "tactic_count": 14}
{"name": "IsSelfAdjoint.self_add_I_smul_cfcSqrt_sub_sq_mem_unitary", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Unitary.Span", "is_tactic_proof": true, "tactics": ["obtain", "simp", "have", "rw", "rwa", "sq_le_one_iff₀", "rw", "cfc_real_eq_complex", "cfc_const_one", "rw", "intro", "rw", "exact"], "tactic_count": 13}
{"name": "selfAdjoint.unitarySelfAddISMul", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.Unitary.Span", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "selfAdjoint.star_coe_unitarySelfAddISMul", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Unitary.Span", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "selfAdjoint.realPart_unitarySelfAddISMul", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Unitary.Span", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CStarAlgebra.norm_smul_two_inv_smul_add_four_unitary", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Unitary.Span", "is_tactic_proof": true, "tactics": ["intro", "rw", "realPart_apply_coe", "simpa"], "tactic_count": 4}
{"name": "CStarAlgebra.exists_sum_four_unitary", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Unitary.Span", "is_tactic_proof": true, "tactics": ["let", "let", "obtain", "exact", "have", "extract_lets", "use", "constructor", "conv_lhs", "simp", "module", "intro", "fin_cases", "all_goals"], "tactic_count": 14}
{"name": "CStarAlgebra.span_unitary", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Unitary.Span", "is_tactic_proof": true, "tactics": ["rw", "rintro", "obtain", "exact"], "tactic_count": 4}
{"name": "_private.Mathlib.Analysis.CStarAlgebra.Unitization.0.term_⋆", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.Unitization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.CStarAlgebra.Unitization.0._aux_Mathlib_Analysis_CStarAlgebra_Unitization___macroRules__private_Mathlib_Analysis_CStarAlgebra_Unitization_0_term_⋆_1", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.Unitization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.CStarAlgebra.Unitization.0._aux_Mathlib_Analysis_CStarAlgebra_Unitization___unexpand_Star_star_1", "kind": "definition", "module": "Mathlib.Analysis.CStarAlgebra.Unitization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.opNorm_mul_flip_apply", "kind": "theorem", "module": "Mathlib.Analysis.CStarAlgebra.Unitization", "is_tactic_proof": false, "tactics": ["refine", "suffices", "refine", "calc", "simpa", "simpa"], "tactic_count": 6}
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{"name": "ContDiffBump.normed_def", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.BumpFunction.Normed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ContDiffBump.contDiff_normed", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.BumpFunction.Normed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ContDiffBump.normed_neg", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.BumpFunction.Normed", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "ContDiffBump.integrable", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.BumpFunction.Normed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffBump.integrable_normed", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.BumpFunction.Normed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ContDiffBump.support_normed_eq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.BumpFunction.Normed", "is_tactic_proof": true, "tactics": ["unfold", "rw"], "tactic_count": 2}
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{"name": "ContDiffBump.hasCompactSupport_normed", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.BumpFunction.Normed", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContDiffBump.tendsto_support_normed_smallSets", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.BumpFunction.Normed", "is_tactic_proof": true, "tactics": ["simp_rw", "rw", "refine", "rw", "exact"], "tactic_count": 5}
{"name": "ContDiffBump.integral_normed_smul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.BumpFunction.Normed", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "ContDiffBump.measure_closedBall_le_integral", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.BumpFunction.Normed", "is_tactic_proof": true, "tactics": ["calc", "μ.real"], "tactic_count": 2}
{"name": "ContDiffBump.normed_le_div_measure_closedBall_rIn", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.BumpFunction.Normed", "is_tactic_proof": true, "tactics": ["rw", "gcongr", "exact", "exact", "exact"], "tactic_count": 5}
{"name": "ContDiffBump.integral_le_measure_closedBall", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.BumpFunction.Normed", "is_tactic_proof": true, "tactics": ["calc", "apply", "apply", "simpa", "apply", "simp"], "tactic_count": 6}
{"name": "ContDiffBump.measure_closedBall_div_le_integral", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.BumpFunction.Normed", "is_tactic_proof": true, "tactics": ["have", "apply", "rw", "addHaar_real_closedBall", "gcongr", "exact"], "tactic_count": 6}
{"name": "ContDiffBump.normed_le_div_measure_closedBall_rOut", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.BumpFunction.Normed", "is_tactic_proof": true, "tactics": ["have", "have", "gcongr", "exact", "exact", "apply", "rw", "exact", "exact"], "tactic_count": 9}
{"name": "MeasureTheory.LocallyIntegrable.exists_contDiff_dist_le_of_forall_mem_ball_dist_le", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.BumpFunction.SmoothApprox", "is_tactic_proof": true, "tactics": ["set", "refine", "exact"], "tactic_count": 3}
{"name": "Continuous.exists_contDiff_dist_le_of_forall_mem_ball_dist_le", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.BumpFunction.SmoothApprox", "is_tactic_proof": true, "tactics": ["borelize", "exact"], "tactic_count": 2}
{"name": "UniformContinuous.exists_contDiff_dist_le", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.BumpFunction.SmoothApprox", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "exact"], "tactic_count": 3}
{"name": "ContinuousMap.dense_setOf_contDiff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.BumpFunction.SmoothApprox", "is_tactic_proof": true, "tactics": ["intro", "rw", "simp", "intro", "have", "rcases", "rcases", "refine", "rw", "exact"], "tactic_count": 10}
{"name": "conformalAt_iff'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Conformal.InnerProduct", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "conformalAt_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Conformal.InnerProduct", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "conformalFactorAt", "kind": "definition", "module": "Mathlib.Analysis.Calculus.Conformal.InnerProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "conformalFactorAt_pos", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Conformal.InnerProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "conformalFactorAt_inner_eq_mul_inner'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Conformal.InnerProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "conformalFactorAt_inner_eq_mul_inner", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Conformal.InnerProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConformalAt", "kind": "definition", "module": "Mathlib.Analysis.Calculus.Conformal.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "conformalAt_id", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Conformal.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "conformalAt_const_smul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Conformal.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsingleton.conformalAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Conformal.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "conformalAt_iff_isConformalMap_fderiv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Conformal.NormedSpace", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "rwa", "intro", "by_cases", "exact", "nontriviality", "exact"], "tactic_count": 8}
{"name": "ConformalAt.differentiableAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Conformal.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConformalAt.congr", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Conformal.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConformalAt.comp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Conformal.NormedSpace", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "exact"], "tactic_count": 3}
{"name": "ConformalAt.const_smul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Conformal.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Conformal", "kind": "definition", "module": "Mathlib.Analysis.Calculus.Conformal.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "conformal_id", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Conformal.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "conformal_const_smul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Conformal.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Conformal.conformalAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Conformal.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Conformal.differentiable", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Conformal.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Conformal.comp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Conformal.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Conformal.const_smul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Conformal.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffAt.contDiffPointwiseHolderAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiffHolder.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffPointwiseHolderAt.continuousAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiffHolder.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffPointwiseHolderAt.differentiableAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiffHolder.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffPointwiseHolderAt.zero_exponent_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiffHolder.Pointwise", "is_tactic_proof": true, "tactics": ["refine", "simpa"], "tactic_count": 2}
{"name": "ContDiffPointwiseHolderAt.zero_order_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiffHolder.Pointwise", "is_tactic_proof": true, "tactics": ["simp", "intro", "simp", "rw", "simp_rw"], "tactic_count": 5}
{"name": "ContDiffPointwiseHolderAt.of_exponent_le", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiffHolder.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffPointwiseHolderAt.of_order_lt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiffHolder.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffPointwiseHolderAt.of_toLex_le", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiffHolder.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffPointwiseHolderAt.of_order_le", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiffHolder.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffPointwiseHolderAt.of_contDiffOn_holderOnWith", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiffHolder.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffPointwiseHolderAt.fst", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiffHolder.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffPointwiseHolderAt.snd", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiffHolder.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffPointwiseHolderAt.prodMk", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiffHolder.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffPointwiseHolderAt.comp_of_differentiableAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiffHolder.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffPointwiseHolderAt.comp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiffHolder.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffPointwiseHolderAt.comp₂_of_differentiableAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiffHolder.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.contDiffPointwiseHolderAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiffHolder.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.contDiffPointwiseHolderAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiffHolder.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffPointwiseHolderAt.continuousLinearMap_comp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiffHolder.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.contDiffPointwiseHolderAt_left_comp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiffHolder.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.contDiffPointwiseHolderAt_left_comp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiffHolder.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffPointwiseHolderAt.id", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiffHolder.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffPointwiseHolderAt.const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiffHolder.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffPointwiseHolderAt.fderiv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiffHolder.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffPointwiseHolderAt.iteratedFDeriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiffHolder.Pointwise", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "simpa"], "tactic_count": 5}
{"name": "ContDiffPointwiseHolderAt.congr_of_eventuallyEq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiffHolder.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffPointwiseHolderAt.clm_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiffHolder.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iteratedFDerivWithin_succ_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "ext1", "simp", "succ", "rw", "simp"], "tactic_count": 7}
{"name": "iteratedFDerivWithin_zero_fun", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": true, "tactics": ["cases", "zero", "succ"], "tactic_count": 3}
{"name": "iteratedFDeriv_zero_fun", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiff_zero_fun", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiff_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiffOn_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiffAt_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiffWithinAt_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiff_of_subsingleton", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "contDiffAt_of_subsingleton", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "contDiffWithinAt_of_subsingleton", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "contDiffOn_of_subsingleton", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "iteratedFDerivWithin_const_of_ne", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": true, "tactics": ["cases", "zero", "succ"], "tactic_count": 3}
{"name": "iteratedFDeriv_const_of_ne", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "iteratedFDeriv_succ_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiffWithinAt_singleton", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBoundedLinearMap.contDiff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.contDiff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.contDiff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.contDiff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.contDiff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiff_id", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiff_fun_id", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiffWithinAt_id", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiffWithinAt_fun_id", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiffAt_id", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiffAt_fun_id", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiffOn_id", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiffOn_fun_id", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBoundedBilinearMap.contDiff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFTaylorSeriesUpToOn.continuousLinearMap_comp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffWithinAt.continuousLinearMap_comp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": true, "tactics": ["ω", "obtain", "refine", "change", "apply", "exact", "intro", "rcases", "exact"], "tactic_count": 9}
{"name": "ContDiffAt.continuousLinearMap_comp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffOn.continuousLinearMap_comp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.continuousLinearMap_comp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.iteratedFDerivWithin_comp_left", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": true, "tactics": ["rcases", "rw", "rw", "exact", "le_rfl"], "tactic_count": 5}
{"name": "ContinuousLinearMap.iteratedFDeriv_comp_left", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "ContinuousLinearEquiv.iteratedFDerivWithin_comp_left", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "simp", "coe_coe]", "succ", "rw", "have", "fderivWithin", "fderivWithin", "fderivWithin_congr", "simp_rw", "rw", "simp", "rw"], "tactic_count": 14}
{"name": "ContinuousLinearEquiv.iteratedFDeriv_comp_left", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": true, "tactics": ["simp", "apply"], "tactic_count": 2}
{"name": "LinearIsometry.norm_iteratedFDerivWithin_comp_left", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": ["have", "iteratedFDerivWithin", "g.toContinuousLinearMap.compContinuousMultilinearMap", "g.toContinuousLinearMap.iteratedFDerivWithin_comp_left", "rw", "apply"], "tactic_count": 6}
{"name": "LinearIsometry.norm_iteratedFDeriv_comp_left", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "LinearIsometryEquiv.norm_iteratedFDerivWithin_comp_left", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": ["have", "iteratedFDerivWithin", "g.toContinuousLinearEquiv.iteratedFDerivWithin_comp_left", "rw", "apply"], "tactic_count": 5}
{"name": "LinearIsometryEquiv.norm_iteratedFDeriv_comp_left", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "ContinuousLinearEquiv.comp_contDiffWithinAt_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.comp_contDiffAt_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousLinearEquiv.comp_contDiffOn_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousLinearEquiv.comp_contDiff_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HasFTaylorSeriesUpToOn.comp_continuousAffineMap", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": true, "tactics": ["let", "have", "isBoundedLinearMap_continuousMultilinearMap_comp_linear", "constructor", "intro", "simp", "change", "rw", "rfl", "intro", "convert", "ext", "change", "rw", "intro", "exact"], "tactic_count": 16}
{"name": "HasFTaylorSeriesUpToOn.compContinuousLinearMap", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffWithinAt.comp_continuousLinearMap", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": true, "tactics": ["ω", "obtain", "refine", "refine", "exact", "intro", "change", "apply", "exact", "exact", "intro", "rcases", "refine", "refine", "exact"], "tactic_count": 15}
{"name": "ContDiffOn.comp_continuousLinearMap", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.comp_continuousLinearMap", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.iteratedFDerivWithin_comp_right", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.iteratedFDerivWithin_comp_right", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "simp", "succ", "simp", "iteratedFDerivWithin_succ_apply_left]", "have", "fderivWithin", "fderivWithin", "fderivWithin_congr", "rw", "simp", "rw"], "tactic_count": 13}
{"name": "ContinuousLinearMap.iteratedFDeriv_comp_right", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "LinearIsometryEquiv.norm_iteratedFDerivWithin_comp_right", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": ["have", "iteratedFDerivWithin", "g.toContinuousLinearEquiv.iteratedFDerivWithin_comp_right", "rw"], "tactic_count": 4}
{"name": "LinearIsometryEquiv.norm_iteratedFDeriv_comp_right", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": true, "tactics": ["simp", "apply"], "tactic_count": 2}
{"name": "ContinuousLinearEquiv.contDiffWithinAt_comp_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": true, "tactics": ["constructor", "intro", "simpa", "intro", "rw", "exact"], "tactic_count": 6}
{"name": "ContinuousLinearEquiv.contDiffAt_comp_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ContinuousLinearEquiv.contDiffOn_comp_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.contDiff_comp_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "HasFTaylorSeriesUpToOn.prodMk", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": true, "tactics": ["set", "constructor", "intro", "intro", "convert", "intro", "exact"], "tactic_count": 7}
{"name": "ContDiffWithinAt.prodMk", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": true, "tactics": ["ω", "obtain", "obtain", "refine", "change", "apply", "exact", "intro", "rcases", "rcases", "exact"], "tactic_count": 11}
{"name": "ContDiffOn.prodMk", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffAt.prodMk", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.prodMk", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iteratedFDerivWithin_prodMk", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": true, "tactics": ["ext", "rw", "simp"], "tactic_count": 3}
{"name": "iteratedFDeriv_prodMk", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "ContDiffOn.union_of_isOpen", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": true, "tactics": ["rintro", "exact", "exact"], "tactic_count": 3}
{"name": "contDiffOn_union_iff_of_isOpen", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiff_of_contDiffOn_union_of_isOpen", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ContDiffOn.iUnion_of_isOpen", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "contDiffOn_iUnion_iff_of_isOpen", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiff_of_contDiffOn_iUnion_of_isOpen", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ContDiffWithinAt.comp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": true, "tactics": ["ω", "have", "obtain", "obtain", "let", "have", "have", "refine", "apply", "apply", "apply", "simp", "apply", "exact", "have", "have", "have", "simpa", "exact", "intro", "rcases", "rcases", "let", "have", "have", "refine", "apply", "apply", "apply", "simp", "apply", "exact"], "tactic_count": 32}
{"name": "ContDiffOn.comp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffOn.comp_inter", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.comp_contDiffOn", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.fun_comp_contDiffOn", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffOn.comp_contDiff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ContDiffOn.image_comp_contDiff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.comp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.fun_comp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffWithinAt.comp_of_eq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "ContDiffWithinAt.comp_of_mem_nhdsWithin_image", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffWithinAt.comp_of_mem_nhdsWithin_image_of_eq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "ContDiffWithinAt.comp_inter", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffWithinAt.comp_inter_of_eq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "ContDiffWithinAt.comp_of_preimage_mem_nhdsWithin", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffWithinAt.comp_of_preimage_mem_nhdsWithin_of_eq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "ContDiffAt.comp_contDiffWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffAt.comp_contDiffWithinAt_of_eq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "ContDiffAt.comp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffAt.fun_comp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.comp_contDiffWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.comp_contDiffAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iteratedFDerivWithin_comp_of_eventually_mem", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": ["obtain", "x", "have", "have", "have", "hf.eventually_hasFTaylorSeriesUpToOn", "have", "hf_tendsto.image_smallSets.eventually", "rcases", "exact", "exact", "iteratedFDerivWithin_inter_open"], "tactic_count": 12}
{"name": "iteratedFDerivWithin_comp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iteratedFDeriv_comp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": true, "tactics": ["simp", "exact", "iteratedFDerivWithin_comp"], "tactic_count": 3}
{"name": "contDiff_fst", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.fst", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.fst'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiffOn_fst", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffOn.fst", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiffAt_fst", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffAt.fst", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffAt.fst'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffAt.fst''", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiffWithinAt_fst", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiff_snd", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.snd", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.snd'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiffOn_snd", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffOn.snd", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiffAt_snd", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffAt.snd", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffAt.snd'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffAt.snd''", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiffWithinAt_snd", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.comp₂", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffAt.comp₂", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffAt.comp₂_contDiffWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.comp₂_contDiffAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.comp₂_contDiffWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.comp₂_contDiffOn", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.comp₃", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.comp₃_contDiffOn", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.clm_comp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffOn.clm_comp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffAt.clm_comp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffWithinAt.clm_comp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.clm_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffOn.clm_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffAt.clm_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffWithinAt.clm_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.smulRight", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffOn.smulRight", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffAt.smulRight", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffWithinAt.smulRight", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iteratedFDerivWithin_clm_apply_const_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "replace", "have", "have", "simp", "rw", "rw", "rw", "rw", "simp", "rw"], "tactic_count": 13}
{"name": "iteratedFDeriv_clm_apply_const_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "contDiff_prodAssoc", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiff_prodAssoc_symm", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffWithinAt.hasFDerivWithinAt_nhds", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": ["have", "refine", "simp_rw", "subset_preimage_image]", "obtain", "refine", "refine", "have", "refine", "refine", "rw", "exact", "intro", "have", "refine", "exact", "exact", "x₀"], "tactic_count": 18}
{"name": "ContDiffWithinAt.fderivWithin''", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": ["have", "intro", "obtain", "refine", "filter_upwards", "exact", "ω", "obtain", "obtain", "refine", "filter_upwards", "exact", "rw", "exact"], "tactic_count": 14}
{"name": "ContDiffWithinAt.fderivWithin'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffWithinAt.fderivWithin", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "ContDiffWithinAt.fderivWithin_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffWithinAt.fderivWithin_right", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffWithinAt.fderivWithin_right_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffWithinAt.iteratedFDerivWithin_right", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "simp", "exact", "succ", "rw", "exact"], "tactic_count": 7}
{"name": "ContDiffAt.fderiv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "univ_mem", "rw"], "tactic_count": 4}
{"name": "ContDiffAt.fderiv_succ", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffAt.fderiv_right", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffAt.fderiv_right_succ", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffAt.iteratedFDeriv_right", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ContDiff.fderiv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.fderiv_succ", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.fderiv_right", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.iteratedFDeriv_right", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.iteratedFDeriv_right'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.fderiv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.fderiv_one", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Differentiable.fderiv_two", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.fderiv_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiffOn_fderivWithin_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffOn.continuousOn_fderivWithin_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.contDiff_fderiv_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "ContDiffWithinAt.continuousWithinAt_fderivWithin", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "contDiffOn_iff_forall_nat_le", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiffOn_infty", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiffOn_all_iff_nat", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": true, "tactics": ["refine", "rintro", "exacts"], "tactic_count": 3}
{"name": "ContDiffOn.continuousOn", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffOn.continuousOn_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffOn.congr", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiffOn_congr", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffOn.mono", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffOn.congr_mono", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffOn.differentiableOn", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffOn.differentiableOn_one", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiffOn_of_locally_contDiffOn", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": true, "tactics": ["intro", "rcases", "apply", "exact"], "tactic_count": 4}
{"name": "contDiffOn_succ_iff_hasFDerivWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rcases", "rcases", "rw", "have", "rw", "exact", "intro", "rw", "rcases", "have", "exact"], "tactic_count": 13}
{"name": "contDiffOn_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": true, "tactics": ["refine", "have", "rw", "refine", "rw", "exact"], "tactic_count": 6}
{"name": "contDiffWithinAt_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": true, "tactics": ["constructor", "intro", "obtain", "refine", "simpa", "simp", "exact", "rintro", "rw", "have", "exact"], "tactic_count": 11}
{"name": "ContDiffOn.ftaylorSeriesWithin", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": true, "tactics": ["constructor", "intro", "simp", "intro", "have", "rcases", "rw", "rcases", "rw", "have", "change", "rw", "exact", "rw", "have", "rintro", "change", "rw", "exact", "exact", "intro", "apply", "intro", "rcases", "rcases", "rw", "rw", "refine", "have", "rintro", "change", "rw", "exact", "exact"], "tactic_count": 34}
{"name": "iteratedFDerivWithin_subset", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffWithinAt.eventually_hasFTaylorSeriesUpToOn", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": true, "tactics": ["rcases", "have", "rw", "exact", "refine", "rw", "refine", "exact"], "tactic_count": 8}
{"name": "AnalyticOn.contDiffOn", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": true, "tactics": ["suffices", "rcases", "intro", "refine", "rw", "exact"], "tactic_count": 6}
{"name": "AnalyticOnNhd.contDiffOn", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticOn.contDiffOn_of_completeSpace", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticOnNhd.contDiffOn_of_completeSpace", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiffOn_of_continuousOn_differentiableOn", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": true, "tactics": ["intro", "rw", "refine", "constructor", "intro", "simp", "intro", "convert", "intro", "exact"], "tactic_count": 10}
{"name": "contDiffOn_of_differentiableOn", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiffOn_of_analyticOn_iteratedFDerivWithin", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": true, "tactics": ["suffices", "intro", "refine", "rw", "constructor", "intro", "simp", "intro", "exact", "intro", "exact", "intro", "rw", "exact"], "tactic_count": 14}
{"name": "contDiffOn_omega_iff_analyticOn", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffOn.continuousOn_iteratedFDerivWithin", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffOn.differentiableOn_iteratedFDerivWithin", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": true, "tactics": ["intro", "have", "apply", "exact_mod_cast"], "tactic_count": 4}
{"name": "ContDiffWithinAt.differentiableWithinAt_iteratedFDerivWithin", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": true, "tactics": ["have", "rcases", "set", "have", "simp", "rw", "exacts", "have", "iteratedFDerivWithin_eventually_congr_set", "have", "hu.differentiableOn_iteratedFDerivWithin", "rw", "exact"], "tactic_count": 13}
{"name": "contDiffOn_iff_continuousOn_differentiableOn", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiffOn_nat_iff_continuousOn_differentiableOn", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "contDiffOn_succ_of_fderivWithin", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": true, "tactics": ["rcases", "rw", "intro", "apply", "rw", "exact", "intro", "rw", "exact"], "tactic_count": 9}
{"name": "contDiffOn_of_analyticOn_of_fderivWithin", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": true, "tactics": ["suffices", "exact"], "tactic_count": 2}
{"name": "contDiffOn_succ_iff_fderivWithin", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": true, "tactics": ["refine", "refine", "rintro", "exact", "have", "rcases", "rcases", "rw", "have", "rw", "apply", "have", "rw", "refine", "have", "rwa", "ω"], "tactic_count": 17}
{"name": "contDiffOn_succ_iff_hasFDerivWithinAt_of_uniqueDiffOn", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": true, "tactics": ["rw", "refine", "rcases", "refine", "exact"], "tactic_count": 5}
{"name": "contDiffOn_infty_iff_fderivWithin", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "contDiffOn_succ_iff_fderiv_of_isOpen", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "contDiffOn_infty_iff_fderiv_of_isOpen", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "ContDiffOn.fderivWithin", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffOn.fderiv_of_isOpen", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffOn.continuousOn_fderivWithin", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffOn.continuousOn_fderiv_of_isOpen", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffAt", "kind": "definition", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiffWithinAt_univ", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiffAt_infty", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContDiffAt.contDiffWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffWithinAt.contDiffAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "contDiffWithinAt_iff_contDiffAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsOpen.contDiffOn_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffOn.contDiffAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffAt.congr_of_eventuallyEq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffAt.of_le", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffAt.continuousAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ContDiffAt.analyticAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "AnalyticAt.contDiffAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "contDiffWithinAt_compl_self", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ContDiffAt.differentiableAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ContDiffAt.differentiableAt_iteratedFDeriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": true, "tactics": ["rw", "convert", "exact"], "tactic_count": 3}
{"name": "ContDiffAt.differentiableAt_one", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ContDiffAt.contDiffOn", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "contDiffAt_succ_iff_hasFDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": true, "tactics": ["rw", "simp", "constructor", "rintro", "rcases", "refine", "refine", "intro", "refine", "exact", "rintro", "refine", "exact"], "tactic_count": 13}
{"name": "ContDiffAt.eventually", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "iteratedFDerivWithin_eq_iteratedFDeriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": true, "tactics": ["rw", "rcases", "rw", "apply", "exact", "exact", "apply", "simpa", "exact"], "tactic_count": 9}
{"name": "ContDiff", "kind": "definition", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFTaylorSeriesUpTo.contDiff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiffOn_empty", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiffOn_univ", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": true, "tactics": ["ω", "constructor", "intro", "use", "rw", "refine", "rw", "exact", "rintro", "exact", "constructor", "intro", "use", "rw", "exact", "rintro", "exact"], "tactic_count": 17}
{"name": "contDiff_iff_contDiffAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContDiff.contDiffAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.contDiffWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiff_infty", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "contDiff_all_iff_nat", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContDiff.contDiffOn", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiff_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "contDiffAt_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "contDiffAt_one_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "exists_mem_and_iff"], "tactic_count": 3}
{"name": "ContDiff.of_le", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.of_succ", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.one_of_succ", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "ContDiff.continuous", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.continuous_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.differentiable", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.differentiable_one", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiff_iff_forall_nat_le", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "contDiff_succ_iff_hasFDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": true, "tactics": ["simp", "contDiffOn_succ_iff_hasFDerivWithinAt_of_uniqueDiffOn", "false_implies,"], "tactic_count": 3}
{"name": "contDiff_one_iff_hasFDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "AnalyticOn.contDiff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "AnalyticOnNhd.contDiff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.analyticOnNhd", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": true, "tactics": ["rw", "have", "rw", "exact"], "tactic_count": 4}
{"name": "contDiff_omega_iff_analyticOnNhd", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.ftaylorSeries", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "contDiff_iff_ftaylorSeries", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": true, "tactics": ["constructor", "rw", "exact", "exact"], "tactic_count": 4}
{"name": "contDiff_iff_continuous_differentiable", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": true, "tactics": ["simp", "contDiffOn_iff_continuousOn_differentiableOn"], "tactic_count": 2}
{"name": "contDiff_nat_iff_continuous_differentiable", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "ContDiff.continuous_iteratedFDeriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.continuous_iteratedFDeriv'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.differentiable_iteratedFDeriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiff_of_differentiable_iteratedFDeriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiff_succ_iff_fderiv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": true, "tactics": ["simp", "contDiffOn_succ_iff_fderivWithin"], "tactic_count": 2}
{"name": "contDiff_one_iff_fderiv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "contDiff_infty_iff_fderiv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "ContDiff.continuous_fderiv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.continuous_fderiv_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.termω", "kind": "definition", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff._aux_Mathlib_Analysis_Calculus_ContDiff_FTaylorSeries___macroRules_ContDiff_termω_1", "kind": "definition", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff._aux_Mathlib_Analysis_Calculus_ContDiff_FTaylorSeries___delab_app_ContDiff_termω_1", "kind": "definition", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.term∞", "kind": "definition", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff._aux_Mathlib_Analysis_Calculus_ContDiff_FTaylorSeries___macroRules_ContDiff_term∞_1", "kind": "definition", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff._aux_Mathlib_Analysis_Calculus_ContDiff_FTaylorSeries___delab_app_ContDiff_term∞_1", "kind": "definition", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFTaylorSeriesUpToOn.zero_eq'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "hasFTaylorSeriesUpToOn_empty", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": true, "tactics": ["constructor"], "tactic_count": 1}
{"name": "HasFTaylorSeriesUpToOn.congr", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
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{"name": "HasFTaylorSeriesUpToOn.mono", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFTaylorSeriesUpToOn.of_le", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFTaylorSeriesUpToOn.continuousOn", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "hasFTaylorSeriesUpToOn_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": false, "tactics": ["refine", "obtain", "have", "rw", "exact"], "tactic_count": 5}
{"name": "hasFTaylorSeriesUpToOn_top_iff_add", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": true, "tactics": ["constructor", "intro", "apply", "intro", "constructor", "exact", "intro", "apply", "intro", "apply"], "tactic_count": 10}
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{"name": "hasFTaylorSeriesUpToOn_top_iff'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": true, "tactics": ["refine"], "tactic_count": 1}
{"name": "HasFTaylorSeriesUpToOn.hasFDerivWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": true, "tactics": ["have", "suffices", "x", "from", "rw", "have", "convert", "ext", "change", "congr", "rw", "rfl"], "tactic_count": 12}
{"name": "HasFTaylorSeriesUpToOn.differentiableOn", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFTaylorSeriesUpToOn.hasFDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFTaylorSeriesUpToOn.eventually_hasFDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFTaylorSeriesUpToOn.differentiableAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasFTaylorSeriesUpToOn_succ_iff_left", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": true, "tactics": ["constructor", "exact", "intro", "constructor", "exact", "intro", "by_cases", "exact", "have", "rw", "exact", "intro", "by_cases", "apply", "have", "rw", "exact"], "tactic_count": 17}
{"name": "HasFTaylorSeriesUpToOn.shift_of_succ", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rfl", "intro", "have", "rw", "exact", "change", "rw", "convert", "ext", "change", "rw", "intro", "suffices", "refine", "rw", "exact"], "tactic_count": 18}
{"name": "hasFTaylorSeriesUpToOn_succ_nat_iff_right", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": true, "tactics": ["constructor", "intro", "refine", "exact", "rintro", "constructor", "exact", "intro", "rcases", "exact", "have", "rw", "exact", "have", "rw", "convert", "ext", "change", "rw", "intro", "rcases", "have", "exact", "refine", "refine", "rw", "exact"], "tactic_count": 27}
{"name": "hasFTaylorSeriesUpToOn_top_iff_right", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": true, "tactics": ["refine", "rw", "rw", "exact", "apply", "rw", "exact"], "tactic_count": 7}
{"name": "hasFTaylorSeriesUpToOn_succ_iff_right", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": true, "tactics": [], "tactic_count": 0}
{"name": "iteratedFDerivWithin", "kind": "definition", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ftaylorSeriesWithin", "kind": "definition", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iteratedFDerivWithin_zero_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iteratedFDerivWithin_zero_eq_comp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dist_iteratedFDerivWithin_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "norm_iteratedFDerivWithin_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "iteratedFDerivWithin_succ_apply_left", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iteratedFDerivWithin_succ_eq_comp_left", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderivWithin_iteratedFDerivWithin", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "norm_fderivWithin_iteratedFDerivWithin", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "dist_iteratedFDerivWithin_one", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": false, "tactics": ["simp", "iteratedFDerivWithin_zero_eq_comp,", "apply"], "tactic_count": 3}
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{"name": "iteratedFDerivWithin_succ_eq_comp_right", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "norm_iteratedFDerivWithin_fderivWithin", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "iteratedFDerivWithin_one_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "iteratedFDerivWithin_two_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": true, "tactics": ["simp", "rfl"], "tactic_count": 2}
{"name": "iteratedFDerivWithin_two_apply'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.iteratedFDerivWithin'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "have", "refine", "simp"], "tactic_count": 6}
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{"name": "Filter.EventuallyEq.iteratedFDerivWithin_eq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iteratedFDerivWithin_congr", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.EqOn.iteratedFDerivWithin", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iteratedFDerivWithin_eventually_congr_set'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "refine", "simp", "rw"], "tactic_count": 6}
{"name": "iteratedFDerivWithin_eventually_congr_set", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iteratedFDerivWithin_congr_set'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iteratedFDerivWithin_insert", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iteratedFDerivWithin_congr_set", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ftaylorSeriesWithin_insert", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": true, "tactics": ["ext", "apply"], "tactic_count": 2}
{"name": "iteratedFDerivWithin_inter'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iteratedFDerivWithin_inter", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iteratedFDerivWithin_inter_open", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFTaylorSeriesUpToOn.eq_iteratedFDerivWithin_of_uniqueDiffOn", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "have", "have", "rw", "exact"], "tactic_count": 7}
{"name": "iteratedFDerivWithin_comp_add_left'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "ext", "rw", "simp", "congr", "rw"], "tactic_count": 8}
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{"name": "iteratedFDerivWithin_comp_add_right'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
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{"name": "iteratedFDerivWithin_comp_sub", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HasFTaylorSeriesUpTo.zero_eq'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "hasFTaylorSeriesUpToOn_univ_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": true, "tactics": ["constructor", "intro", "constructor", "exact", "intro", "rw", "exact", "intro", "rw", "exact", "intro", "constructor", "exact", "intro", "rw", "exact", "intro", "rw", "exact"], "tactic_count": 19}
{"name": "HasFTaylorSeriesUpTo.hasFTaylorSeriesUpToOn", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFTaylorSeriesUpTo.of_le", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HasFTaylorSeriesUpTo.continuous", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "hasFTaylorSeriesUpTo_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "hasFTaylorSeriesUpTo_top_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "hasFTaylorSeriesUpTo_top_iff'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": true, "tactics": ["simp", "hasFDerivWithinAt_univ]"], "tactic_count": 2}
{"name": "HasFTaylorSeriesUpTo.hasFDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "HasFTaylorSeriesUpTo.differentiable", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasFTaylorSeriesUpTo_succ_nat_iff_right", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": true, "tactics": ["simp", "hasFDerivWithinAt_univ]"], "tactic_count": 2}
{"name": "iteratedFDeriv", "kind": "definition", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ftaylorSeries", "kind": "definition", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iteratedFDeriv_zero_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iteratedFDeriv_zero_eq_comp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "norm_iteratedFDeriv_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "iteratedFDerivWithin_zero_eq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iteratedFDeriv_succ_apply_left", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iteratedFDeriv_succ_eq_comp_left", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderiv_iteratedFDeriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tsupport_iteratedFDeriv_subset", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": true, "tactics": ["induction", "zero", "rw", "exact", "succ", "rw", "exact", "closure_minimal"], "tactic_count": 8}
{"name": "support_iteratedFDeriv_subset", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasCompactSupport.iteratedFDeriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "norm_fderiv_iteratedFDeriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "iteratedFDerivWithin_univ", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "ext", "rw"], "tactic_count": 5}
{"name": "Filter.EventuallyEq.iteratedFDeriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": true, "tactics": ["simp_all"], "tactic_count": 1}
{"name": "HasFTaylorSeriesUpTo.eq_iteratedFDeriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "iteratedFDerivWithin_of_isOpen", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": true, "tactics": ["induction", "zero", "intro", "ext1", "simp", "succ", "intro", "rw", "dsimp", "congr", "rw", "apply", "filter_upwards", "exact"], "tactic_count": 14}
{"name": "ftaylorSeriesWithin_univ", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": true, "tactics": ["ext1", "change", "rw"], "tactic_count": 3}
{"name": "iteratedFDeriv_succ_apply_right", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "iteratedFDeriv_succ_eq_comp_right", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "norm_iteratedFDeriv_fderiv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "iteratedFDeriv_one_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "norm_iteratedFDeriv_one", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "iteratedFDeriv_two_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "iteratedFDeriv_comp_add_left'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "iteratedFDeriv_comp_add_left", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "iteratedFDeriv_comp_add_right'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "iteratedFDeriv_comp_add_right", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "iteratedFDeriv_comp_sub'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "iteratedFDeriv_comp_sub", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "instDecidableEqOrderedFinpartition", "kind": "instance", "module": "Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderedFinpartition.atomic", "kind": "definition", "module": "Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderedFinpartition.instInhabited", "kind": "instance", "module": "Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderedFinpartition.default_eq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderedFinpartition.length_le", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "OrderedFinpartition.partSize_le", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "OrderedFinpartition.embSigma", "kind": "definition", "module": "Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderedFinpartition.injective_embSigma", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno", "is_tactic_proof": true, "tactics": ["rintro", "intro", "simp_all", "have", "subst", "simp_all", "ext", "exact", "mk.inj_iff.mp", "for"], "tactic_count": 10}
{"name": "OrderedFinpartition.instFintype", "kind": "instance", "module": "Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderedFinpartition.instUniqueZero", "kind": "instance", "module": "Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno", "is_tactic_proof": false, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "OrderedFinpartition.exists_inverse", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "OrderedFinpartition.emb_injective", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno", "is_tactic_proof": true, "tactics": ["rintro", "have", "contrapose", "have", "apply", "subst", "simpa"], "tactic_count": 7}
{"name": "OrderedFinpartition.emb_ne_emb_of_ne", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderedFinpartition.index", "kind": "definition", "module": "Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderedFinpartition.invEmbedding", "kind": "definition", "module": "Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderedFinpartition.emb_invEmbedding", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderedFinpartition.equivSigma", "kind": "definition", "module": "Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderedFinpartition.prod_sigma_eq_prod", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "OrderedFinpartition.length_pos", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderedFinpartition.neZero_length", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderedFinpartition.neZero_partSize", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderedFinpartition.instUniqueOne", "kind": "instance", "module": "Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderedFinpartition.emb_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno", "is_tactic_proof": true, "tactics": ["apply", "conv_rhs", "apply"], "tactic_count": 3}
{"name": "OrderedFinpartition.partSize_eq_one_of_range_emb_eq_singleton", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno", "is_tactic_proof": false, "tactics": ["have", "card_range_of_injective", "simpa"], "tactic_count": 3}
{"name": "OrderedFinpartition.one_lt_partSize_index_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno", "is_tactic_proof": false, "tactics": ["have", "rw", "rw", "rcases", "rw", "have", "apply", "simpa", "simpa", "apply", "have", "range", "simp", "convert", "simp", "apply", "exact"], "tactic_count": 17}
{"name": "OrderedFinpartition.extendLeft", "kind": "definition", "module": "Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderedFinpartition.range_extendLeft_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno", "is_tactic_proof": true, "tactics": ["simp", "apply"], "tactic_count": 2}
{"name": "OrderedFinpartition.extendMiddle", "kind": "definition", "module": "Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderedFinpartition.index_extendMiddle_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno", "is_tactic_proof": true, "tactics": ["have", "conv_rhs", "contrapose", "exact"], "tactic_count": 4}
{"name": "OrderedFinpartition.range_emb_extendMiddle_ne_singleton_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno", "is_tactic_proof": true, "tactics": ["intro", "rcases", "have", "rw", "simp", "have", "refine", "simp", "simp", "exact", "have", "rw", "simp", "exact"], "tactic_count": 14}
{"name": "OrderedFinpartition.extend", "kind": "definition", "module": "Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderedFinpartition.extend_none", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderedFinpartition.extend_some", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderedFinpartition.eraseLeft", "kind": "definition", "module": "Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderedFinpartition.eraseMiddle", "kind": "definition", "module": "Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderedFinpartition.extendEquiv", "kind": "definition", "module": "Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderedFinpartition.applyOrderedFinpartition", "kind": "definition", "module": "Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderedFinpartition.applyOrderedFinpartition_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderedFinpartition.norm_applyOrderedFinpartition_le", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderedFinpartition.applyOrderedFinpartition_update_right", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "rw", "simp", "congr", "rw", "simp", "exact", "simp", "congr", "apply", "have", "have", "exact"], "tactic_count": 14}
{"name": "OrderedFinpartition.applyOrderedFinpartition_update_left", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "rw", "simp", "simp"], "tactic_count": 5}
{"name": "OrderedFinpartition.compAlongOrderedFinpartition", "kind": "definition", "module": "Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderedFinpartition.compAlongOrderFinpartition_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderedFinpartition.norm_compAlongOrderedFinpartition_le", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "OrderedFinpartition.compAlongOrderedFinpartitionₗ", "kind": "definition", "module": "Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderedFinpartition.compAlongOrderedFinpartitionL", "kind": "definition", "module": "Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno", "is_tactic_proof": true, "tactics": ["refine", "simp", "apply"], "tactic_count": 3}
{"name": "OrderedFinpartition.compAlongOrderedFinpartitionL_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderedFinpartition.norm_compAlongOrderedFinpartitionL_le", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderedFinpartition.norm_compAlongOrderedFinpartitionL_apply_le", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderedFinpartition.norm_compAlongOrderedFinpartition_sub_compAlongOrderedFinpartition_le", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.compAlongOrderedFinpartition", "kind": "definition", "module": "Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.compAlongOrderedFinpartition_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.taylorComp", "kind": "definition", "module": "Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.taylorComp_sub_taylorComp_isBigO", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno", "is_tactic_proof": true, "tactics": ["simp", "refine", "refine", "refine", "have", "have", "have", "have", "rw", "have", "simpa", "have", "have", "simpa"], "tactic_count": 14}
{"name": "FormalMultilinearSeries.taylorComp_sub_taylorComp_isLittleO", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "analyticOn_taylorComp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno", "is_tactic_proof": true, "tactics": ["apply", "let", "change", "apply", "apply", "exact", "exact"], "tactic_count": 7}
{"name": "_private.Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno.0.faaDiBruno_aux1", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno", "is_tactic_proof": true, "tactics": ["ext", "simp", "compAlongOrderFinpartition_apply]", "congr", "ext", "exact"], "tactic_count": 6}
{"name": "_private.Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno.0.faaDiBruno_aux2", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno", "is_tactic_proof": true, "tactics": ["ext", "simp", "simp", "compAlongOrderedFinpartitionL_apply,", "congr", "ext", "rcases", "simp", "apply", "intro", "a", "simp", "apply", "simp"], "tactic_count": 14}
{"name": "HasFTaylorSeriesUpToOn.comp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno", "is_tactic_proof": true, "tactics": ["is", "multilinear", "thanks", "needs", "classical", "constructor", "intro", "simp", "intro", "have", "let", "change", "have", "have", "have", "hf.fderivWithin", "have", "hg.fderivWithin", "have", "hf.hasFDerivWithinAt", "convert", "simp", "have", "s", "suffices", "rw", "convert", "ext", "simp", "rw", "exact", "intro", "apply", "let", "change", "apply", "have", "exact", "apply", "have", "exact"], "tactic_count": 41}
{"name": "contDiffOn_clm_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FiniteDimension", "is_tactic_proof": true, "tactics": ["refine", "let", "have", "let", "let", "rw", "exact"], "tactic_count": 7}
{"name": "contDiff_clm_apply_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FiniteDimension", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "contDiff_succ_iff_fderiv_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FiniteDimension", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "contDiffOn_succ_of_fderiv_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiffOn_succ_iff_fderiv_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.FiniteDimension", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "hasFTaylorSeriesUpToOn_pi", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": true, "tactics": ["set", "set", "refine", "exact", "ext1", "exact", "intro", "exact", "intro", "exact"], "tactic_count": 10}
{"name": "hasFTaylorSeriesUpToOn_pi'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "contDiffWithinAt_pi", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": true, "tactics": ["set", "refine", "ω", "choose", "refine", "set", "change", "apply", "exact", "intro", "choose", "exact"], "tactic_count": 12}
{"name": "contDiffOn_pi", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiffAt_pi", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiff_pi", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "contDiff_pi'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiffOn_pi'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiffAt_pi'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiff_update", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": true, "tactics": ["rw", "intro", "dsimp", "split_ifs", "subst", "exact", "exact"], "tactic_count": 7}
{"name": "contDiff_single", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiff_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiffAt_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiffOn_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiff_apply_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFTaylorSeriesUpToOn.add", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "contDiff_add", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffWithinAt.add", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffAt.add", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ContDiff.add", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffOn.add", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iteratedFDerivWithin_add_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": true, "tactics": ["have", "obtain", "have", "have", "have", "have", "rw", "exact", "hut"], "tactic_count": 9}
{"name": "iteratedFDerivWithin_add_apply'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iteratedFDeriv_add_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "iteratedFDeriv_add_apply'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iteratedFDeriv_add", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiff_neg", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffWithinAt.neg", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffAt.neg", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ContDiff.neg", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffOn.neg", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iteratedFDerivWithin_neg_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "calc", "iteratedFDerivWithin", "fderivWithin", "iteratedFDerivWithin_succ_apply_left", "rw", "rw"], "tactic_count": 9}
{"name": "iteratedFDeriv_neg_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "iteratedFDeriv_neg", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffWithinAt.sub", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ContDiffAt.sub", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ContDiffOn.sub", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ContDiff.sub", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ContDiffWithinAt.sum", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "insert", "simp", "exact"], "tactic_count": 6}
{"name": "ContDiffAt.sum", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ContDiffOn.sum", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.sum", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "iteratedFDerivWithin_sum_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": true, "tactics": ["induction", "empty", "cons", "simp", "simp", "rw"], "tactic_count": 6}
{"name": "iteratedFDeriv_sum", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiff_mul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffWithinAt.mul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffAt.mul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffOn.mul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.mul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiffWithinAt_prod'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiffWithinAt_prod", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "contDiffAt_prod'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiffAt_prod", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiffOn_prod'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiffOn_prod", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiff_prod'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiff_prod", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.pow", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffWithinAt.pow", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffAt.pow", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffOn.pow", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffWithinAt.div_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ContDiffAt.div_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffOn.div_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.div_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "contDiff_smul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffWithinAt.smul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffAt.smul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ContDiff.smul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffOn.smul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiff_const_smul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiff_smul_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffWithinAt.const_smul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffWithinAt.smul_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffAt.const_smul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ContDiffAt.smul_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ContDiff.const_smul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.smul_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffOn.const_smul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffOn.smul_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iteratedFDerivWithin_const_smul_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iteratedFDerivWithin_smul_const_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iteratedFDeriv_const_smul_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iteratedFDeriv_const_smul_apply'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iteratedFDeriv_smul_const_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffWithinAt.prodMap'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffWithinAt.prodMap", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffOn.prodMap", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffAt.prodMap", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "ContDiffAt.prodMap'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.prodMap", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "contDiff_prodMk_left", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiff_prodMk_right", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiffAt_ringInverse", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "contDiffAt_inv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "contDiffOn_inv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffWithinAt.inv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffOn.inv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffAt.inv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.inv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": true, "tactics": ["rw", "exact", "hf.contDiffAt.inv"], "tactic_count": 3}
{"name": "ContDiffWithinAt.div", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ContDiffOn.div", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffOn.fun_div", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffAt.div", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.div", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "contDiffAt_map_inverse", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": true, "tactics": ["nontriviality", "let", "let", "have", "rw", "have", "have", "refine", "convert", "simp"], "tactic_count": 10}
{"name": "ContinuousLinearMap.IsInvertible.contDiffAt_map_inverse", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "OpenPartialHomeomorph.contDiffAt_symm", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": true, "tactics": ["ω", "apply", "exact", "induction", "zero", "apply", "exact", "succ", "obtain", "apply", "contDiffAt_succ_iff_hasFDerivAt.2", "have", "refine", "have", "have", "rw", "exact", "obtain", "use", "refine", "exact", "exact", "intro", "obtain", "have", "rw", "exact", "convert", "simp", "have", "rw", "exact", "have", "refine", "norm_cast", "exact", "exact", "top"], "tactic_count": 38}
{"name": "Homeomorph.contDiff_symm", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.contDiffAt_symm_deriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.contDiff_symm_deriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.restrContDiff", "kind": "definition", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.contDiffOn_restrContDiff_source", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.contDiffOn_restrContDiff_target", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFTaylorSeriesUpToOn.restrictScalars", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffWithinAt.restrict_scalars", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": true, "tactics": ["ω", "obtain", "refine", "change", "apply", "exact", "intro", "rcases", "exact"], "tactic_count": 9}
{"name": "ContDiffOn.restrict_scalars", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffAt.restrict_scalars", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.restrict_scalars", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.contDiff_aeval", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.Polynomial", "is_tactic_proof": true, "tactics": ["induction", "add", "monomial"], "tactic_count": 3}
{"name": "HasFTaylorSeriesUpToOn.hasStrictFDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.RCLike", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffAt.hasStrictFDerivAt'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.RCLike", "is_tactic_proof": true, "tactics": ["rcases", "simp", "have", "rwa"], "tactic_count": 4}
{"name": "ContDiffAt.hasStrictDerivAt'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.RCLike", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffAt.hasStrictFDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.RCLike", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffAt.hasStrictDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.RCLike", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.hasStrictFDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.RCLike", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.hasStrictDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.RCLike", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFTaylorSeriesUpToOn.exists_lipschitzOnWith_of_nnnorm_lt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.RCLike", "is_tactic_proof": true, "tactics": ["set", "have", "have", "replace", "exact", "hs.exists_nhdsWithin_lipschitzOnWith_of_hasFDerivWithinAt_of_nnnorm_lt"], "tactic_count": 6}
{"name": "HasFTaylorSeriesUpToOn.exists_lipschitzOnWith", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.RCLike", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffWithinAt.exists_lipschitzOnWith", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.RCLike", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "replace", "clear", "rw", "rcases", "rw", "exact"], "tactic_count": 8}
{"name": "ContDiffAt.exists_lipschitzOnWith_of_nnnorm_lt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.RCLike", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffAt.exists_lipschitzOnWith", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.RCLike", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffOn.locallyLipschitzOn", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.RCLike", "is_tactic_proof": true, "tactics": ["intro", "obtain", "use"], "tactic_count": 3}
{"name": "ContDiff.locallyLipschitz", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.RCLike", "is_tactic_proof": true, "tactics": ["intro", "rcases", "use"], "tactic_count": 3}
{"name": "ContDiffOn.exists_lipschitzOnWith", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.RCLike", "is_tactic_proof": true, "tactics": ["apply", "exact"], "tactic_count": 2}
{"name": "ContDiff.lipschitzWith_of_hasCompactSupport", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.RCLike", "is_tactic_proof": true, "tactics": ["obtain", "refine", "apply", "simp"], "tactic_count": 4}
{"name": "fderivWithin_restrictScalars_comp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.RestrictScalars", "is_tactic_proof": true, "tactics": ["simp", "rw", "ext", "simp"], "tactic_count": 4}
{"name": "ContDiffWithinAt.restrictScalars_iteratedFDerivWithin_eventuallyEq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.RestrictScalars", "is_tactic_proof": true, "tactics": ["induction", "zero", "filter_upwards", "ext", "simp", "succ", "have", "have", "nth_rw", "apply", "filter_upwards", "h₁a", "rw", "ext", "simp", "rw", "simp", "apply", "rw", "simp", "have", "simpa", "apply"], "tactic_count": 23}
{"name": "ContDiffAt.restrictScalars_iteratedFDeriv_eventuallyEq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.RestrictScalars", "is_tactic_proof": true, "tactics": ["have", "convert", "simp"], "tactic_count": 3}
{"name": "ContDiffAt.restrictScalars_iteratedFDeriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.RestrictScalars", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiffWithinAt_piLp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.WithLp", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "contDiffWithinAt_piLp'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.WithLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiffWithinAt_piLp_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.WithLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiffAt_piLp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.WithLp", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "contDiffAt_piLp'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.WithLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiffAt_piLp_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.WithLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiffOn_piLp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.WithLp", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "contDiffOn_piLp'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.WithLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiffOn_piLp_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.WithLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiff_piLp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.WithLp", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "contDiff_piLp'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.WithLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiff_piLp_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.WithLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiLp.contDiff_ofLp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.WithLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiLp.contDiff_toLp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.WithLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.contDiff_ofLp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.WithLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.contDiff_toLp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.ContDiff.WithLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dslope", "kind": "definition", "module": "Mathlib.Analysis.Calculus.DSlope", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dslope_same", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DSlope", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "dslope_of_ne", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DSlope", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "ContinuousLinearMap.dslope_comp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DSlope", "is_tactic_proof": true, "tactics": ["rcases", "simp", "exact", "simpa"], "tactic_count": 4}
{"name": "eqOn_dslope_slope", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DSlope", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dslope_eventuallyEq_slope_of_ne", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DSlope", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dslope_eventuallyEq_slope_nhdsNE", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DSlope", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sub_smul_dslope", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DSlope", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "dslope_sub_smul_of_ne", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DSlope", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "eqOn_dslope_sub_smul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DSlope", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dslope_sub_smul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DSlope", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousAt_dslope_same", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DSlope", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousWithinAt.of_dslope", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DSlope", "is_tactic_proof": false, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "ContinuousAt.of_dslope", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DSlope", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.of_dslope", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DSlope", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousWithinAt_dslope_of_ne", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DSlope", "is_tactic_proof": true, "tactics": ["refine", "classical", "simp", "exact"], "tactic_count": 4}
{"name": "continuousAt_dslope_of_ne", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DSlope", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "continuousOn_dslope", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DSlope", "is_tactic_proof": true, "tactics": ["refine", "rintro", "rcases", "exacts"], "tactic_count": 4}
{"name": "DifferentiableWithinAt.of_dslope", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DSlope", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "DifferentiableAt.of_dslope", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DSlope", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableOn.of_dslope", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DSlope", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableWithinAt_dslope_of_ne", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DSlope", "is_tactic_proof": true, "tactics": ["refine", "refine", "refine", "exact"], "tactic_count": 4}
{"name": "differentiableOn_dslope_of_notMem", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DSlope", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableAt_dslope_of_ne", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DSlope", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "exists_hasDerivWithinAt_eq_of_gt_of_lt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Darboux", "is_tactic_proof": true, "tactics": ["rcases", "exact", "set", "have", "intro", "simpa", "obtain", "isCompact_Icc.exists_isMinOn", "have", "rcases", "refine", "have", "sub_mem_posTangentConeAt_of_segment_subset", "simpa", "hc.localize.hasFDerivWithinAt_nonneg", "rcases", "refine", "have", "sub_mem_posTangentConeAt_of_segment_subset", "simpa", "hc.localize.hasFDerivWithinAt_nonneg", "exact", "use", "rw", "have", "exact"], "tactic_count": 26}
{"name": "exists_hasDerivWithinAt_eq_of_lt_of_gt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Darboux", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.OrdConnected.image_hasDerivWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Darboux", "is_tactic_proof": true, "tactics": ["apply", "rintro", "rcases", "have", "rcases", "exact", "have", "rcases", "exact"], "tactic_count": 9}
{"name": "Set.OrdConnected.image_derivWithin", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Darboux", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.OrdConnected.image_deriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Darboux", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Convex.image_hasDerivWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Darboux", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Convex.image_derivWithin", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Darboux", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Convex.image_deriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Darboux", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_hasDerivWithinAt_eq_of_ge_of_le", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Darboux", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_hasDerivWithinAt_eq_of_le_of_ge", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Darboux", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivWithinAt_forall_lt_or_forall_gt_of_forall_ne", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Darboux", "is_tactic_proof": true, "tactics": ["contrapose", "rcases", "exact"], "tactic_count": 3}
{"name": "contDiffAt_abs", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffAt.abs", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiffWithinAt_abs", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffWithinAt.abs", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiffOn_abs", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffOn.abs", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.abs", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasStrictDerivAt_abs_neg", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivAt_abs_neg", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasStrictDerivAt_abs_pos", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivAt_abs_pos", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasStrictDerivAt_abs", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Abs", "is_tactic_proof": true, "tactics": ["obtain", "simpa", "simpa"], "tactic_count": 3}
{"name": "hasDerivAt_abs", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictFDerivAt.abs_of_neg", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Abs", "is_tactic_proof": true, "tactics": ["convert", "ext", "simp"], "tactic_count": 3}
{"name": "HasFDerivAt.abs_of_neg", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Abs", "is_tactic_proof": true, "tactics": ["convert", "ext", "simp"], "tactic_count": 3}
{"name": "HasStrictFDerivAt.abs_of_pos", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Abs", "is_tactic_proof": true, "tactics": ["convert", "ext", "simp"], "tactic_count": 3}
{"name": "HasFDerivAt.abs_of_pos", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Abs", "is_tactic_proof": true, "tactics": ["convert", "ext", "simp"], "tactic_count": 3}
{"name": "HasStrictFDerivAt.abs", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Abs", "is_tactic_proof": true, "tactics": ["convert", "ext", "simp"], "tactic_count": 3}
{"name": "HasFDerivAt.abs", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Abs", "is_tactic_proof": true, "tactics": ["convert", "ext", "simp"], "tactic_count": 3}
{"name": "hasDerivWithinAt_abs_neg", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivWithinAt_abs_pos", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivWithinAt_abs", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivWithinAt.abs_of_neg", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Abs", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "HasFDerivWithinAt.abs_of_pos", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Abs", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "HasFDerivWithinAt.abs", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableAt_abs_neg", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableAt_abs_pos", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableAt_abs", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableAt.abs_of_neg", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableAt.abs_of_pos", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableAt.abs", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableWithinAt_abs_neg", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableWithinAt_abs_pos", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableWithinAt_abs", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableWithinAt.abs_of_neg", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableWithinAt.abs_of_pos", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableWithinAt.abs", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableOn_abs", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableOn.abs", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Differentiable.abs", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_differentiableAt_abs_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Abs", "is_tactic_proof": true, "tactics": ["intro", "have", "have", "linarith"], "tactic_count": 4}
{"name": "deriv_abs_neg", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv_abs_pos", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv_abs_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv_abs", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Abs", "is_tactic_proof": true, "tactics": ["obtain", "simpa", "simpa"], "tactic_count": 3}
{"name": "HasDerivAtFilter.add", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasStrictDerivAt.add", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasDerivWithinAt.add", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivAt.add", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "derivWithin_fun_add", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "simp"], "tactic_count": 3}
{"name": "derivWithin_add", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv_fun_add", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv_add", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivAtFilter_add_const_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasStrictDerivAt_add_const_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivWithinAt_add_const_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivAt_add_const_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "derivWithin_add_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "deriv_add_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "deriv_add_const'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivAtFilter_const_add_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasStrictDerivAt_const_add_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivWithinAt_const_add_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivAt_const_add_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "derivWithin_const_add", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "derivWithin_const_add_fun", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": true, "tactics": ["ext", "apply"], "tactic_count": 2}
{"name": "deriv_const_add", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "deriv_const_add'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableAt_comp_add_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "differentiableAt_iff_comp_const_add", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "differentiableAt_iff_comp_add_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HasDerivAtFilter.fun_sum", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasDerivAtFilter.sum", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "HasStrictDerivAt.fun_sum", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasStrictDerivAt.sum", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasDerivWithinAt.fun_sum", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivWithinAt.sum", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivAt.fun_sum", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivAt.sum", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "derivWithin_fun_sum", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "simp"], "tactic_count": 3}
{"name": "derivWithin_sum", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "simp"], "tactic_count": 3}
{"name": "deriv_fun_sum", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv_sum", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivAtFilter.neg", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasDerivWithinAt.neg", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivAt.neg", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictDerivAt.neg", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "derivWithin.neg", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "simp"], "tactic_count": 3}
{"name": "deriv.neg", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "deriv.neg'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivAtFilter_neg", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivWithinAt_neg", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivAt_neg", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivAt_neg'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasStrictDerivAt_neg", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv_neg", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv_neg'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv_neg''", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "derivWithin_neg", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiable_neg", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableOn_neg", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableAt_comp_neg", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": true, "tactics": ["refine", "convert", "ext", "simp"], "tactic_count": 4}
{"name": "differentiableAt_iff_comp_neg", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "HasDerivAtFilter.sub", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasDerivWithinAt.sub", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivAt.sub", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictDerivAt.sub", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "derivWithin_fun_sub", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "derivWithin_sub", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv_fun_sub", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv_sub", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivAtFilter_sub_const_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivWithinAt_sub_const_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivAt_sub_const_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "derivWithin_sub_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "derivWithin_sub_const_fun", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": true, "tactics": ["ext", "apply"], "tactic_count": 2}
{"name": "deriv_sub_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "deriv_sub_const_fun", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": true, "tactics": ["ext", "apply"], "tactic_count": 2}
{"name": "HasDerivAtFilter.const_sub", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasDerivWithinAt.const_sub", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictDerivAt.const_sub", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasDerivAt.const_sub", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "derivWithin_const_sub", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "deriv_const_sub", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "differentiableAt_comp_sub_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "differentiableAt_comp_const_sub", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": true, "tactics": ["refine", "convert", "ext", "simp"], "tactic_count": 4}
{"name": "differentiableAt_iff_comp_sub_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "differentiableAt_iff_comp_const_sub", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Add", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AffineMap.hasStrictDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.AffineMap", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "AffineMap.hasDerivAtFilter", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.AffineMap", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "AffineMap.hasDerivWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.hasDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.derivWithin", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.deriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.differentiableAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.differentiable", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.differentiableWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.differentiableOn", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.hasStrictDerivAt_lineMap", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.AffineMap", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "AffineMap.hasDerivAt_lineMap", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.hasDerivWithinAt_lineMap", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivAtFilter", "kind": "definition", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivWithinAt", "kind": "definition", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivAt", "kind": "definition", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictDerivAt", "kind": "definition", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "derivWithin", "kind": "definition", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv", "kind": "definition", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasFDerivAtFilter_iff_hasDerivAtFilter", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HasFDerivAtFilter.hasDerivAtFilter", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasFDerivWithinAt_iff_hasDerivWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivWithinAt_iff_hasFDerivWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivWithinAt.hasDerivWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivWithinAt.hasFDerivWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasFDerivAt_iff_hasDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivAt.hasDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasStrictFDerivAt_iff_hasStrictDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HasStrictFDerivAt.hasStrictDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasStrictDerivAt_iff_hasStrictFDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivAt_iff_hasFDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "derivWithin_zero_of_not_differentiableWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": true, "tactics": ["unfold", "rw", "simp"], "tactic_count": 3}
{"name": "differentiableWithinAt_of_derivWithin_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "derivWithin_zero_of_not_accPt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "derivWithin_zero_of_not_uniqueDiffWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "derivWithin_zero_of_notMem_closure", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "deriv_zero_of_not_differentiableAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": true, "tactics": ["unfold", "rw", "simp"], "tactic_count": 3}
{"name": "differentiableAt_of_deriv_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniqueDiffWithinAt.eq_deriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivAtFilter_iff_isLittleO", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivAtFilter_iff_tendsto", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivWithinAt_iff_isLittleO", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivWithinAt_iff_tendsto", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivAt_iff_isLittleO", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivAt_iff_tendsto", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivAtFilter.isBigO_sub", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivAtFilter.isBigO_sub_rev", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictDerivAt.hasDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivWithinAt_congr_set'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivWithinAt_congr_set", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivWithinAt_diff_singleton", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivWithinAt_Ioi_iff_Ici", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "hasDerivWithinAt_Iio_iff_Iic", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HasDerivWithinAt.Ioi_iff_Ioo", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivAt_iff_isLittleO_nhds_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivAtFilter.mono", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivWithinAt.mono", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivWithinAt.mono_of_mem_nhdsWithin", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivAt.hasDerivAtFilter", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivAt.hasDerivWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivWithinAt.differentiableWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivAt.differentiableAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivWithinAt_univ", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivAt.unique", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivWithinAt_inter'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivWithinAt_inter", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivWithinAt.union", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivWithinAt.hasDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableWithinAt.hasDerivWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableAt.hasDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivAt_deriv_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivWithinAt_derivWithin_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableOn.hasDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivAt.deriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv_eq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivWithinAt.derivWithin", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderivWithin_derivWithin", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toSpanSingleton_derivWithin", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "norm_derivWithin_eq_norm_fderivWithin", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "fderiv_apply_one_eq_deriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderiv_eq_smul_deriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "toSpanSingleton_deriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "fderiv_eq_deriv_mul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "norm_deriv_eq_norm_fderiv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DifferentiableAt.derivWithin", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": true, "tactics": ["unfold", "rw"], "tactic_count": 2}
{"name": "HasDerivWithinAt.deriv_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "derivWithin_of_mem_nhdsWithin", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "derivWithin_subset", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "derivWithin_congr_set'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "derivWithin_congr_set", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "derivWithin_univ", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": true, "tactics": ["ext", "unfold", "rw"], "tactic_count": 3}
{"name": "derivWithin_inter", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": true, "tactics": ["unfold", "rw"], "tactic_count": 2}
{"name": "derivWithin_of_mem_nhds", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "derivWithin_of_isOpen", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv_eqOn", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv_mem_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "derivWithin_mem_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "differentiableWithinAt_Ioi_iff_Ici", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "derivWithin_Ioi_eq_Ici", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "have", "have", "simpa", "rw", "rwa"], "tactic_count": 6}
{"name": "Filter.EventuallyEq.hasDerivAtFilter_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivAtFilter.congr_of_eventuallyEq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "HasDerivWithinAt.congr_mono", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivWithinAt.congr", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivWithinAt.congr_of_mem", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivWithinAt.congr_of_eventuallyEq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.hasDerivWithinAt_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivWithinAt.congr_of_eventuallyEq_of_mem", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.hasDerivWithinAt_iff_of_mem", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictDerivAt.congr_deriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivAt.congr_deriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivWithinAt.congr_deriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivAt.congr_of_eventuallyEq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.hasDerivAt_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.derivWithin_eq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": true, "tactics": ["unfold", "rw"], "tactic_count": 2}
{"name": "Filter.EventuallyEq.derivWithin_eq_of_mem", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.derivWithin_eq_of_nhds", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "derivWithin_congr", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": true, "tactics": ["unfold", "rw"], "tactic_count": 2}
{"name": "Set.EqOn.deriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": true, "tactics": ["intro", "rw", "exact"], "tactic_count": 3}
{"name": "Filter.EventuallyEq.deriv_eq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": true, "tactics": ["unfold", "rwa"], "tactic_count": 2}
{"name": "Filter.EventuallyEq.deriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.nhdsNE_deriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": true, "tactics": ["rw", "filter_upwards", "apply"], "tactic_count": 3}
{"name": "hasDerivAtFilter_id", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivWithinAt_id", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivAt_id", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivAt_id'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasStrictDerivAt_id", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv_id", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv_id'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv_id''", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "derivWithin_id", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "derivWithin_id'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivAtFilter_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivAtFilter_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivAtFilter_one", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivAtFilter_natCast", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivAtFilter_intCast", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivAtFilter_ofNat", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasStrictDerivAt_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasStrictDerivAt_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasStrictDerivAt_one", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasStrictDerivAt_natCast", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasStrictDerivAt_intCast", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictDerivAt_ofNat", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivWithinAt_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivWithinAt_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivWithinAt_one", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivWithinAt_natCast", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivWithinAt_intCast", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivWithinAt_ofNat", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivAt_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivAt_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivAt_one", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivAt_natCast", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivAt_intCast", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivAt_ofNat", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv_const'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv_one", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv_natCast", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv_intCast", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv_ofNat", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "derivWithin_fun_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "derivWithin_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "derivWithin_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "derivWithin_one", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "derivWithin_natCast", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "derivWithin_intCast", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "derivWithin_ofNat", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivAtFilter.tendsto_nhds", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivWithinAt.continuousWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivAt.continuousAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivWithinAt.continuousOn", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivAt.continuousOn", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivAt.le_of_lip'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasDerivAt.le_of_lipschitzOn", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasDerivAt.le_of_lipschitz", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "norm_deriv_le_of_lip'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "norm_deriv_le_of_lipschitzOn", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "norm_deriv_le_of_lipschitz", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasDerivAt.comp_semilinear", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": true, "tactics": ["have", "let", "have", "rw", "convert", "ext", "simp", "rwa"], "tactic_count": 8}
{"name": "DifferentiableAt.comp_semilinear₁", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivAt.comp_ringHom", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableAt.comp_ringHom", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivAtFilter.scomp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Comp", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasDerivAtFilter.scomp_of_eq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Comp", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HasDerivWithinAt.scomp_hasDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Comp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivWithinAt.scomp_hasDerivAt_of_eq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Comp", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HasDerivWithinAt.scomp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Comp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivWithinAt.scomp_of_eq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Comp", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HasDerivAt.scomp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Comp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivAt.scomp_of_eq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Comp", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HasStrictDerivAt.scomp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Comp", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasStrictDerivAt.scomp_of_eq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Comp", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HasDerivAt.scomp_hasDerivWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Comp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivAt.scomp_hasDerivWithinAt_of_eq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Comp", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "derivWithin.scomp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Comp", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "simp"], "tactic_count": 3}
{"name": "derivWithin.scomp_of_eq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Comp", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "deriv.scomp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Comp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv.scomp_of_eq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Comp", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HasDerivAtFilter.comp_hasFDerivAtFilter", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Comp", "is_tactic_proof": true, "tactics": ["convert", "ext", "simp"], "tactic_count": 3}
{"name": "HasDerivAtFilter.comp_hasFDerivAtFilter_of_eq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Comp", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HasStrictDerivAt.comp_hasStrictFDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Comp", "is_tactic_proof": true, "tactics": ["rw", "convert", "ext", "simp"], "tactic_count": 4}
{"name": "HasStrictDerivAt.comp_hasStrictFDerivAt_of_eq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Comp", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HasDerivAt.comp_hasFDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Comp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivAt.comp_hasFDerivAt_of_eq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Comp", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HasDerivAt.comp_hasFDerivWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Comp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivAt.comp_hasFDerivWithinAt_of_eq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Comp", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HasDerivWithinAt.comp_hasFDerivWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Comp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivWithinAt.comp_hasFDerivWithinAt_of_eq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Comp", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HasDerivWithinAt.comp_hasFDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Comp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivWithinAt.comp_hasFDerivAt_of_eq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Comp", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "HasDerivAtFilter.comp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Comp", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "HasDerivAtFilter.comp_of_eq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Comp", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HasDerivWithinAt.comp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Comp", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "HasDerivWithinAt.comp_of_eq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Comp", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HasDerivAt.comp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Comp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivAt.comp_of_eq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Comp", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HasStrictDerivAt.comp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Comp", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "HasStrictDerivAt.comp_of_eq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Comp", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HasDerivAt.comp_hasDerivWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Comp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivAt.comp_hasDerivWithinAt_of_eq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Comp", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HasDerivWithinAt.comp_hasDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Comp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivWithinAt.comp_hasDerivAt_of_eq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Comp", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "derivWithin_comp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Comp", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "simp"], "tactic_count": 3}
{"name": "derivWithin_comp_of_eq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Comp", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "deriv_comp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Comp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv_comp_of_eq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Comp", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "HasDerivAtFilter.iterate", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Comp", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "HasDerivAt.iterate", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Comp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivWithinAt.iterate", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Comp", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "HasStrictDerivAt.iterate", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Comp", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "HasFDerivWithinAt.comp_hasDerivWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Comp", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasFDerivWithinAt.comp_hasDerivWithinAt_of_eq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Comp", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HasFDerivWithinAt.comp_hasDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Comp", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasFDerivWithinAt.comp_hasDerivAt_of_eq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Comp", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "HasFDerivAt.comp_hasDerivWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Comp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivAt.comp_hasDerivWithinAt_of_eq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Comp", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HasFDerivAt.comp_hasDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Comp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivAt.comp_hasDerivAt_of_eq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Comp", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HasStrictFDerivAt.comp_hasStrictDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Comp", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasStrictFDerivAt.comp_hasStrictDerivAt_of_eq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Comp", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "fderivWithin_comp_derivWithin", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Comp", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "simp"], "tactic_count": 3}
{"name": "fderivWithin_comp_derivWithin_of_eq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Comp", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "fderiv_comp_deriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Comp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderiv_comp_deriv_of_eq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Comp", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "hasDerivWithinAt_comp_mul_left_smul_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.CompMul", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "derivWithin_comp_mul_left", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.CompMul", "is_tactic_proof": true, "tactics": ["simp", "rw"], "tactic_count": 2}
{"name": "deriv_comp_mul_left", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.CompMul", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "hasStrictDerivAt_inv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Inv", "is_tactic_proof": false, "tactics": ["suffices", "refine", "refine", "rintro", "simp", "simp", "ring", "refine", "rw", "exact"], "tactic_count": 10}
{"name": "hasDerivAt_inv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivWithinAt_inv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableAt_inv_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv_inv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Inv", "is_tactic_proof": true, "tactics": ["rcases", "simp", "exact"], "tactic_count": 3}
{"name": "deriv_inv'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "derivWithin_inv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Inv", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "hasFDerivAt_inv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasStrictFDerivAt_inv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasFDerivWithinAt_inv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderiv_inv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Inv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "fderivWithin_inv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Inv", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "HasDerivWithinAt.inv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Inv", "is_tactic_proof": true, "tactics": ["convert", "ring"], "tactic_count": 2}
{"name": "HasDerivAt.inv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Inv", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "derivWithin_fun_inv'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Inv", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "simp"], "tactic_count": 3}
{"name": "derivWithin_inv'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv_fun_inv''", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv_inv''", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivWithinAt.fun_div", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Inv", "is_tactic_proof": true, "tactics": ["convert", "simp", "simp", "ring"], "tactic_count": 4}
{"name": "HasDerivWithinAt.div", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictDerivAt.fun_div", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Inv", "is_tactic_proof": true, "tactics": ["convert", "simp", "simp", "ring"], "tactic_count": 4}
{"name": "HasStrictDerivAt.div", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivAt.fun_div", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Inv", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "HasDerivAt.div", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableWithinAt.fun_div", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableWithinAt.div", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableAt.fun_div", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableAt.div", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableOn.fun_div", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableOn.div", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Differentiable.fun_div", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Differentiable.div", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "derivWithin_fun_div", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Inv", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "simp"], "tactic_count": 3}
{"name": "derivWithin_div", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv_fun_div", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv_div", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictDerivAt.hasStrictFDerivAt_equiv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivAt.hasFDerivAt_equiv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictDerivAt.of_local_left_inverse", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.hasStrictDerivAt_symm", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivAt.of_local_left_inverse", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.hasDerivAt_symm", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivWithinAt.eventually_ne", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivAt.eventually_ne", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Inverse", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasDerivAt.tendsto_nhdsNE", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "derivWithin_zero_of_frequently_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Inverse", "is_tactic_proof": true, "tactics": ["by_cases", "contrapose", "exact", "exact"], "tactic_count": 4}
{"name": "deriv_zero_of_frequently_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Inverse", "is_tactic_proof": true, "tactics": ["rw", "rwa"], "tactic_count": 2}
{"name": "not_differentiableWithinAt_of_local_left_inverse_hasDerivWithinAt_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Inverse", "is_tactic_proof": true, "tactics": ["intro", "have", "simpa"], "tactic_count": 3}
{"name": "not_differentiableAt_of_local_left_inverse_hasDerivAt_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Inverse", "is_tactic_proof": true, "tactics": ["intro", "have", "simpa"], "tactic_count": 3}
{"name": "ContinuousLinearMap.hasDerivAtFilter", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.hasStrictDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.hasDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.hasDerivWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.deriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.derivWithin", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.hasDerivAtFilter", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.hasStrictDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.hasDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.hasDerivWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.deriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.derivWithin", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_ratio_hasDerivAt_eq_ratio_slope", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.MeanValue", "is_tactic_proof": true, "tactics": ["let", "have", "let", "have", "have", "rcases", "exact"], "tactic_count": 7}
{"name": "exists_ratio_hasDerivAt_eq_ratio_slope'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.MeanValue", "is_tactic_proof": true, "tactics": ["let", "have", "have", "convert", "ring", "have", "have", "convert", "ring", "let", "have", "intro", "exact", "rcases", "exact"], "tactic_count": 15}
{"name": "exists_hasDerivAt_eq_slope", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.MeanValue", "is_tactic_proof": false, "tactics": ["obtain", "exists_ratio_hasDerivAt_eq_ratio_slope", "use", "rwa"], "tactic_count": 4}
{"name": "exists_ratio_deriv_eq_ratio_slope", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.MeanValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_ratio_deriv_eq_ratio_slope'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.MeanValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_deriv_eq_slope", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.MeanValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_deriv_eq_slope'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.MeanValue", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "not_differentiableWithinAt_of_deriv_tendsto_atTop_Ioi", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.MeanValue", "is_tactic_proof": false, "tactics": ["replace", "refine", "filter_upwards", "have", "exact", "by_cases", "intro", "have", "rw", "simp", "intro", "replace", "rw", "have", "rw", "rw", "obtain", "refine", "simp", "exact", "have", "rw", "specialize", "filter_upwards", "have", "filter_upwards", "have", "refine", "have", "exact", "have", "intro", "refine", "have", "refine", "simp", "ext", "exact", "rw", "exact", "have", "intro", "by_cases", "rw", "exact", "exact", "obtain", "specialize", "replace", "have", "rwa", "rw", "linarith", "simp"], "tactic_count": 54}
{"name": "not_differentiableWithinAt_of_deriv_tendsto_atBot_Ioi", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.MeanValue", "is_tactic_proof": true, "tactics": ["intro", "have", "rw", "exact", "exact"], "tactic_count": 5}
{"name": "not_differentiableWithinAt_of_deriv_tendsto_atBot_Iio", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.MeanValue", "is_tactic_proof": true, "tactics": ["let", "have", "rw", "specialize", "rw", "rw", "obtain", "refine", "simp", "suffices", "refine", "rw", "have", "have", "exact", "have", "refine", "refine", "exact", "intro", "have", "refine", "simp", "fun_prop", "intro", "simp", "exact"], "tactic_count": 27}
{"name": "not_differentiableWithinAt_of_deriv_tendsto_atTop_Iio", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.MeanValue", "is_tactic_proof": true, "tactics": ["intro", "have", "rw", "exact", "exact"], "tactic_count": 5}
{"name": "Convex.mul_sub_lt_image_sub_of_lt_deriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.MeanValue", "is_tactic_proof": true, "tactics": ["intro", "have", "have", "obtain", "exists_deriv_eq_slope", "have", "exact"], "tactic_count": 7}
{"name": "mul_sub_lt_image_sub_of_lt_deriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.MeanValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Convex.mul_sub_le_image_sub_of_le_deriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.MeanValue", "is_tactic_proof": true, "tactics": ["intro", "rcases", "rw", "have", "have", "obtain", "exists_deriv_eq_slope", "have", "exact"], "tactic_count": 9}
{"name": "mul_sub_le_image_sub_of_le_deriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.MeanValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Convex.image_sub_lt_mul_sub_of_deriv_lt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.MeanValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "image_sub_lt_mul_sub_of_deriv_lt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.MeanValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Convex.image_sub_le_mul_sub_of_deriv_le", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.MeanValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "image_sub_le_mul_sub_of_deriv_le", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.MeanValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictMonoOn_of_deriv_pos", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.MeanValue", "is_tactic_proof": true, "tactics": ["intro", "have", "simpa"], "tactic_count": 3}
{"name": "strictMono_of_deriv_pos", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.MeanValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictMonoOn_of_hasDerivWithinAt_pos", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.MeanValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictMono_of_hasDerivAt_pos", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.MeanValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monotoneOn_of_deriv_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.MeanValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monotone_of_deriv_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.MeanValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monotoneOn_of_hasDerivWithinAt_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.MeanValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monotone_of_hasDerivAt_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.MeanValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictAntiOn_of_deriv_neg", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.MeanValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictAnti_of_deriv_neg", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.MeanValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictAntiOn_of_hasDerivWithinAt_neg", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.MeanValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictAnti_of_hasDerivAt_neg", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.MeanValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "antitoneOn_of_deriv_nonpos", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.MeanValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "antitone_of_deriv_nonpos", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.MeanValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "antitoneOn_of_hasDerivWithinAt_nonpos", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.MeanValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "antitone_of_hasDerivAt_nonpos", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.MeanValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "domain_mvt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.MeanValue", "is_tactic_proof": true, "tactics": ["set", "set", "have", "have", "have", "have", "refine", "exact", "exact", "rcases", "rw", "refine", "simpa"], "tactic_count": 13}
{"name": "ContinuousLinearMap.hasDerivWithinAt_of_bilinear", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ContinuousLinearMap.hasDerivAt_of_bilinear", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ContinuousLinearMap.hasStrictDerivAt_of_bilinear", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ContinuousLinearMap.derivWithin_of_bilinear", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "simp"], "tactic_count": 3}
{"name": "ContinuousLinearMap.deriv_of_bilinear", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivWithinAt.smul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasDerivAt.smul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "HasStrictDerivAt.smul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "derivWithin_fun_smul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "simp"], "tactic_count": 3}
{"name": "derivWithin_smul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv_fun_smul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv_smul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictDerivAt.smul_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "HasDerivWithinAt.smul_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "HasDerivAt.smul_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "derivWithin_smul_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "simp"], "tactic_count": 3}
{"name": "deriv_smul_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictDerivAt.const_smul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasDerivAtFilter.const_smul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasDerivWithinAt.const_smul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivAt.const_smul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "derivWithin_fun_const_smul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "simp"], "tactic_count": 3}
{"name": "derivWithin_const_smul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "derivWithin_fun_const_smul_field", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "simp"], "tactic_count": 3}
{"name": "derivWithin_const_smul_field", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv_fun_const_smul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv_const_smul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv_fun_const_smul_field", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "deriv_const_smul_field", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HasDerivWithinAt.mul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasDerivAt.mul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "HasStrictDerivAt.mul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "derivWithin_fun_mul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "simp"], "tactic_count": 3}
{"name": "derivWithin_mul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv_fun_mul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv_mul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivWithinAt.mul_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "HasDerivAt.mul_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "hasDerivAt_mul_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasStrictDerivAt.mul_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "derivWithin_mul_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "simp"], "tactic_count": 3}
{"name": "derivWithin_mul_const_field", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "by_cases", "simp", "rw", "have", "exact"], "tactic_count": 7}
{"name": "deriv_mul_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv_mul_const_field", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "rw", "rcases", "simp", "refine", "simpa"], "tactic_count": 7}
{"name": "deriv_mul_const_field'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivWithinAt.const_mul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "HasDerivAt.const_mul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "hasDerivAt_const_mul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasStrictDerivAt.const_mul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "derivWithin_const_mul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "simp"], "tactic_count": 3}
{"name": "derivWithin_const_mul_field", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "deriv_const_mul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv_const_mul_field", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "deriv_const_mul_field'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivAt.fun_finset_prod", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasDerivAt.finset_prod", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "HasDerivWithinAt.fun_finset_prod", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasDerivWithinAt.finset_prod", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "HasStrictDerivAt.fun_finset_prod", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasStrictDerivAt.finset_prod", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "deriv_fun_finset_prod", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv_finset_prod", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "derivWithin_fun_finset_prod", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "simp"], "tactic_count": 3}
{"name": "derivWithin_finset_prod", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "DifferentiableAt.fun_finset_prod", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "DifferentiableAt.finset_prod", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "DifferentiableWithinAt.fun_finset_prod", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": true, "tactics": ["classical", "exact"], "tactic_count": 2}
{"name": "DifferentiableWithinAt.finset_prod", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "DifferentiableOn.fun_finset_prod", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableOn.finset_prod", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Differentiable.fun_finset_prod", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Differentiable.finset_prod", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivAt.div_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasDerivWithinAt.div_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasStrictDerivAt.div_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "DifferentiableWithinAt.div_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableAt.div_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableOn.div_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Differentiable.div_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "derivWithin_div_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "deriv_div_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HasStrictDerivAt.clm_comp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasDerivWithinAt.clm_comp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasDerivAt.clm_comp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "derivWithin_clm_comp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "simp"], "tactic_count": 3}
{"name": "deriv_clm_comp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictDerivAt.clm_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasDerivWithinAt.clm_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasDerivAt.clm_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "derivWithin_clm_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "simp"], "tactic_count": 3}
{"name": "deriv_clm_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivAt_update", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Pi", "is_tactic_proof": true, "tactics": ["have", "convert", "ext", "rw", "split_ifs", "simp", "simp"], "tactic_count": 7}
{"name": "hasDerivAt_single", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv_update", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv_single", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.hasStrictDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Polynomial", "is_tactic_proof": true, "tactics": ["induction", "add", "monomial"], "tactic_count": 3}
{"name": "Polynomial.hasStrictDerivAt_aeval", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Polynomial", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Polynomial.hasDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.hasDerivAt_aeval", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.hasDerivWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.hasDerivWithinAt_aeval", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.differentiableAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.differentiableAt_aeval", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.differentiableWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.differentiableWithinAt_aeval", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.differentiable", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.differentiable_aeval", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.differentiableOn", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.differentiableOn_aeval", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.deriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.deriv_aeval", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.derivWithin", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Polynomial", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Polynomial.derivWithin_aeval", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Polynomial", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Polynomial.hasFDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.hasFDerivAt_aeval", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.hasFDerivWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.hasFDerivWithinAt_aeval", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.fderiv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.fderiv_aeval", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.fderivWithin", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.fderivWithin_aeval", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictDerivAt.fun_pow'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Pow", "is_tactic_proof": true, "tactics": ["unfold", "convert", "ext", "simp"], "tactic_count": 4}
{"name": "HasStrictDerivAt.pow'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivWithinAt.fun_pow'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Pow", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasDerivWithinAt.pow'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivAt.fun_pow'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Pow", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasDerivAt.pow'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "derivWithin_fun_pow'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Pow", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "simp"], "tactic_count": 3}
{"name": "derivWithin_pow'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv_fun_pow'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv_pow'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictDerivAt.fun_pow", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Pow", "is_tactic_proof": true, "tactics": ["unfold", "convert", "ext", "simp"], "tactic_count": 4}
{"name": "HasStrictDerivAt.pow", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivWithinAt.fun_pow", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Pow", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasDerivWithinAt.pow", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivAt.fun_pow", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Pow", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasDerivAt.pow", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "derivWithin_fun_pow", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Pow", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "simp"], "tactic_count": 3}
{"name": "derivWithin_pow", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv_fun_pow", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv_pow", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv_fun_pow''", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv_pow''", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasStrictDerivAt_pow", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Pow", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "hasDerivWithinAt_pow", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Pow", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "hasDerivAt_pow", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Pow", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "derivWithin_pow_field", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Pow", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "deriv_pow_field", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Pow", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HasDerivAtFilter.prodMk", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivWithinAt.prodMk", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivAt.prodMk", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictDerivAt.prodMk", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasStrictDerivAt_pi", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivAtFilter_pi", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivAt_pi", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivWithinAt_pi", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "derivWithin_pi", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Prod", "is_tactic_proof": true, "tactics": ["have", "by_cases", "exact", "simp"], "tactic_count": 4}
{"name": "deriv_pi", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasStrictDerivAt_finCons", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasStrictDerivAt_finCons'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictDerivAt.finCons", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivAtFilter_finCons", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivAtFilter_finCons'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivAtFilter.finCons", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivAt_finCons", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivAt_finCons'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivAt.finCons", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivWithinAt_finCons", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivWithinAt_finCons'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivWithinAt.finCons", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivAt.comp_const_add", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Shift", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasDerivAt.comp_add_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Shift", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasDerivAt.comp_const_sub", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Shift", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasDerivAt.comp_sub_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Shift", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "derivWithin_comp_neg", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Shift", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "deriv_comp_neg", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Shift", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "derivWithin_comp_const_add", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Shift", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "deriv_comp_const_add", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Shift", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "derivWithin_comp_add_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Shift", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "deriv_comp_add_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Shift", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "derivWithin_comp_const_sub", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Shift", "is_tactic_proof": true, "tactics": ["simp", "rw"], "tactic_count": 2}
{"name": "deriv_comp_const_sub", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Shift", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "derivWithin_comp_sub_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Shift", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "deriv_comp_sub_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Shift", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "hasDerivAtFilter_iff_tendsto_slope", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Slope", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivWithinAt_iff_tendsto_slope", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Slope", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "hasDerivWithinAt_iff_tendsto_slope'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Slope", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "hasDerivAt_iff_tendsto_slope", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Slope", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivAt_iff_tendsto_slope_left_right", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Slope", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "hasDerivAt_iff_tendsto_slope_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Slope", "is_tactic_proof": false, "tactics": ["have", "simp", "simp"], "tactic_count": 3}
{"name": "HasDerivAt.tendsto_slope_zero_right", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Slope", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivAt.tendsto_slope_zero_left", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Slope", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "range_derivWithin_subset_closure_span_image", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Slope", "is_tactic_proof": true, "tactics": ["rintro", "by_cases", "simpa", "by_cases", "rw", "exact", "have", "rw", "exact", "have", "apply", "rw", "exact", "rw", "apply", "filter_upwards", "simp", "refine", "apply", "apply", "exact", "apply", "suffices", "apply", "apply", "rw", "exact"], "tactic_count": 27}
{"name": "range_deriv_subset_closure_span_image", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Slope", "is_tactic_proof": true, "tactics": ["rw", "apply", "simp"], "tactic_count": 3}
{"name": "isSeparable_range_derivWithin", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Slope", "is_tactic_proof": false, "tactics": ["obtain", "have", "apply", "exact"], "tactic_count": 4}
{"name": "isSeparable_range_deriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Slope", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "HasDerivAt.continuousAt_div", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Slope", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "HasDerivWithinAt.nonneg_of_monotoneOn", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Slope", "is_tactic_proof": true, "tactics": ["have", "have", "have", "apply", "filter_upwards", "simp", "exact"], "tactic_count": 7}
{"name": "MonotoneOn.derivWithin_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Slope", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "by_cases", "simp", "exact"], "tactic_count": 5}
{"name": "HasDerivAt.nonneg_of_monotone", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Slope", "is_tactic_proof": true, "tactics": ["rw", "apply", "exact"], "tactic_count": 3}
{"name": "Monotone.deriv_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Slope", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "HasDerivWithinAt.nonpos_of_antitoneOn", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Slope", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "AntitoneOn.derivWithin_nonpos", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Slope", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasDerivAt.nonpos_of_antitone", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Slope", "is_tactic_proof": true, "tactics": ["rw", "apply", "exact"], "tactic_count": 3}
{"name": "Antitone.deriv_nonpos", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Slope", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "HasDerivWithinAt.limsup_slope_le", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Slope", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivWithinAt.limsup_slope_le'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Slope", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivWithinAt.liminf_right_slope_le", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Slope", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivWithinAt.limsup_norm_slope_le", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Slope", "is_tactic_proof": true, "tactics": ["have", "have", "have", "mem_of_superset", "have", "rw", "filter_upwards", "simp", "exact"], "tactic_count": 9}
{"name": "HasDerivWithinAt.limsup_slope_norm_le", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Slope", "is_tactic_proof": true, "tactics": ["apply", "intro", "refine", "exact"], "tactic_count": 4}
{"name": "HasDerivWithinAt.liminf_right_norm_slope_le", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Slope", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivWithinAt.liminf_right_slope_norm_le", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Slope", "is_tactic_proof": true, "tactics": ["have", "refine", "rwa"], "tactic_count": 3}
{"name": "HasDerivAtFilter.star", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Star", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasDerivWithinAt.star", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivAt.star", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictDerivAt.star", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Star", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "derivWithin.star", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Star", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "simp"], "tactic_count": 3}
{"name": "deriv.star", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv.star'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivAt.star_conj", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Star", "is_tactic_proof": true, "tactics": ["rw", "convert", "ext", "simp"], "tactic_count": 4}
{"name": "HasDerivAt.conj_conj", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableAt.conj_conj", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "support_deriv_subset", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Support", "is_tactic_proof": true, "tactics": ["intro", "rw", "intro", "rw", "exact"], "tactic_count": 5}
{"name": "HasCompactSupport.deriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasStrictDerivAt_zpow", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.ZPow", "is_tactic_proof": false, "tactics": ["have", "lift", "simp", "convert", "rw", "norm_cast", "rcases", "have", "have", "simp", "convert", "rw", "congr", "abel", "simp", "exact"], "tactic_count": 16}
{"name": "hasDerivAt_zpow", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.ZPow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivWithinAt_zpow", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.ZPow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableAt_zpow", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.ZPow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableWithinAt_zpow", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.ZPow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableOn_zpow", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.ZPow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv_zpow", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.ZPow", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "rw", "push_neg", "rcases", "rw"], "tactic_count": 6}
{"name": "deriv_zpow'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.ZPow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "derivWithin_zpow", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.ZPow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iter_deriv_zpow'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.ZPow", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "simp"], "tactic_count": 4}
{"name": "iter_deriv_zpow", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.ZPow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iter_deriv_pow", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.ZPow", "is_tactic_proof": true, "tactics": ["simp", "rcases", "rw", "have", "simp"], "tactic_count": 5}
{"name": "iter_deriv_pow'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.ZPow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iter_deriv_inv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.ZPow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iter_deriv_inv'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.ZPow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iter_deriv_inv_linear", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.ZPow", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "ext", "simp", "by_cases", "simp", "have", "have", "ext", "field_simp", "rw", "simp", "field_simp", "ring_nf"], "tactic_count": 16}
{"name": "iter_deriv_inv_linear_sub", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.ZPow", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "DifferentiableWithinAt.zpow", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.ZPow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableAt.zpow", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.ZPow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableOn.zpow", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.ZPow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Differentiable.zpow", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Deriv.ZPow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLocalMax_of_deriv_Ioo", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DerivativeTest", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLocalMin_of_deriv_Ioo", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DerivativeTest", "is_tactic_proof": false, "tactics": ["have", "isLocalMax_of_deriv_Ioo", "exact"], "tactic_count": 3}
{"name": "isLocalMax_of_deriv'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DerivativeTest", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "exact", "isLocalMax_of_deriv_Ioo"], "tactic_count": 4}
{"name": "isLocalMin_of_deriv'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DerivativeTest", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "exact", "isLocalMin_of_deriv_Ioo"], "tactic_count": 4}
{"name": "isLocalMax_of_deriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DerivativeTest", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLocalMin_of_deriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DerivativeTest", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eventually_nhdsWithin_sign_eq_of_deriv_pos", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DerivativeTest", "is_tactic_proof": true, "tactics": ["rw", "refine", "have", "filter_upwards", "rw", "obtain", "rw", "rw"], "tactic_count": 8}
{"name": "eventually_nhdsWithin_sign_eq_of_deriv_neg", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DerivativeTest", "is_tactic_proof": true, "tactics": ["simpa", "eventually_nhdsWithin_sign_eq_of_deriv_pos"], "tactic_count": 2}
{"name": "deriv_neg_left_of_sign_deriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DerivativeTest", "is_tactic_proof": true, "tactics": ["filter_upwards", "rwa"], "tactic_count": 2}
{"name": "deriv_neg_right_of_sign_deriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DerivativeTest", "is_tactic_proof": true, "tactics": ["filter_upwards", "rwa"], "tactic_count": 2}
{"name": "deriv_pos_right_of_sign_deriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DerivativeTest", "is_tactic_proof": true, "tactics": ["filter_upwards", "rwa"], "tactic_count": 2}
{"name": "deriv_pos_left_of_sign_deriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DerivativeTest", "is_tactic_proof": true, "tactics": ["filter_upwards", "rwa"], "tactic_count": 2}
{"name": "isLocalMax_of_sign_deriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DerivativeTest", "is_tactic_proof": true, "tactics": ["have", "have", "replace", "exact", "isLocalMax_of_deriv"], "tactic_count": 5}
{"name": "isLocalMin_of_sign_deriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DerivativeTest", "is_tactic_proof": true, "tactics": ["refine", "simpa"], "tactic_count": 2}
{"name": "isLocalMin_of_deriv_deriv_pos", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DerivativeTest", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLocalMax_of_deriv_deriv_neg", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DerivativeTest", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "DifferentiableOn.diffContOnCl", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DiffContOnCl", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Differentiable.diffContOnCl", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DiffContOnCl", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.diffContOnCl_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DiffContOnCl", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "diffContOnCl_univ", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DiffContOnCl", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "diffContOnCl_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DiffContOnCl", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiffContOnCl.comp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DiffContOnCl", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiffContOnCl.continuousOn_ball", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DiffContOnCl", "is_tactic_proof": true, "tactics": ["rcases", "rw", "exact", "rw", "exact"], "tactic_count": 5}
{"name": "DiffContOnCl.mk_ball", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DiffContOnCl", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiffContOnCl.differentiableAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DiffContOnCl", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiffContOnCl.differentiableAt'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DiffContOnCl", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiffContOnCl.mono", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DiffContOnCl", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiffContOnCl.add", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DiffContOnCl", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiffContOnCl.add_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DiffContOnCl", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiffContOnCl.const_add", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DiffContOnCl", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiffContOnCl.neg", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DiffContOnCl", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiffContOnCl.sub", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DiffContOnCl", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiffContOnCl.sub_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DiffContOnCl", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiffContOnCl.const_sub", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DiffContOnCl", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiffContOnCl.const_smul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DiffContOnCl", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiffContOnCl.smul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DiffContOnCl", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiffContOnCl.smul_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DiffContOnCl", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiffContOnCl.inv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DiffContOnCl", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Differentiable.comp_diffContOnCl", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DiffContOnCl", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableOn.diffContOnCl_ball", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DiffContOnCl", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "extDeriv", "kind": "definition", "module": "Mathlib.Analysis.Calculus.DifferentialForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "extDerivWithin", "kind": "definition", "module": "Mathlib.Analysis.Calculus.DifferentialForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "extDerivWithin_univ", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DifferentialForm.Basic", "is_tactic_proof": true, "tactics": ["ext1", "rw"], "tactic_count": 2}
{"name": "extDerivWithin_add", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DifferentialForm.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "extDerivWithin_fun_add", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DifferentialForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "extDeriv_add", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DifferentialForm.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "extDeriv_fun_add", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DifferentialForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "extDerivWithin_smul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DifferentialForm.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "extDerivWithin_fun_smul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DifferentialForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "extDeriv_smul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DifferentialForm.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "extDeriv_fun_smul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DifferentialForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "extDerivWithin_constOfIsEmpty", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DifferentialForm.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "extDeriv_constOfIsEmpty", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DifferentialForm.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.EventuallyEq.extDerivWithin_eq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DifferentialForm.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.EventuallyEq.extDerivWithin_eq_of_mem", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DifferentialForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.extDerivWithin_eq_of_insert", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DifferentialForm.Basic", "is_tactic_proof": true, "tactics": ["apply", "exact"], "tactic_count": 2}
{"name": "Filter.EventuallyEq.extDerivWithin'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DifferentialForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.extDerivWithin", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DifferentialForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.extDerivWithin_eq_nhds", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DifferentialForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "extDerivWithin_congr", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DifferentialForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "extDerivWithin_congr'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DifferentialForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.extDeriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DifferentialForm.Basic", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Filter.EventuallyEq.extDeriv_eq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DifferentialForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "extDerivWithin_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DifferentialForm.Basic", "is_tactic_proof": true, "tactics": ["simp", "fderivWithin_continuousAlternatingMap_apply_const_apply,"], "tactic_count": 2}
{"name": "extDeriv_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DifferentialForm.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "extDerivWithin_extDerivWithin_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DifferentialForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "extDerivWithin_extDerivWithin_eqOn", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DifferentialForm.Basic", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "extDeriv_extDeriv_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DifferentialForm.Basic", "is_tactic_proof": true, "tactics": ["simp", "apply"], "tactic_count": 2}
{"name": "extDeriv_extDeriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DifferentialForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "extDerivWithin_pullback", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DifferentialForm.Basic", "is_tactic_proof": false, "tactics": ["have", "hf.differentiableWithinAt", "have", "rw", "fderivWithin_continuousAlternatingMapCompContinuousLinearMap", "alternatizeUncurryFin_add,", "alternatizeUncurryFin_fderivCompContinuousLinearMap_eq_zero,", "ext", "simp", "apply"], "tactic_count": 10}
{"name": "extDeriv_pullback", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DifferentialForm.Basic", "is_tactic_proof": false, "tactics": ["simp", "apply"], "tactic_count": 2}
{"name": "extDerivWithin_apply_vectorField", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DifferentialForm.VectorField", "is_tactic_proof": false, "tactics": ["have", "symm", "simp", "fderivWithin_continuousAlternatingMap_apply_apply", "add_eq_left,", "rw", "refine", "rw", "simp", "rw", "have", "have", "have", "simp"], "tactic_count": 14}
{"name": "extDeriv_apply_vectorField", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DifferentialForm.VectorField", "is_tactic_proof": false, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "extDerivWithin_apply_vectorField_of_pairwise_commute", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DifferentialForm.VectorField", "is_tactic_proof": true, "tactics": ["cases", "zero", "simp", "fderivWithin_continuousAlternatingMap_apply_apply,", "succ", "rw", "refine", "rw"], "tactic_count": 8}
{"name": "extDeriv_apply_vectorField_of_pairwise_commute", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.DifferentialForm.VectorField", "is_tactic_proof": false, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "HasStrictFDerivAt.const_smul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivAtFilter.const_smul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivWithinAt.const_smul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivAt.const_smul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableWithinAt.const_smul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableAt.const_smul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableOn.const_smul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Differentiable.const_smul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderivWithin_fun_const_smul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderivWithin_const_smul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableWithinAt_smul_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": true, "tactics": ["refine", "apply", "filter_upwards"], "tactic_count": 3}
{"name": "fderivWithin_const_smul_of_invertible", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "have", "contrapose", "exact", "simp"], "tactic_count": 6}
{"name": "fderiv_fun_const_smul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderiv_const_smul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableAt_smul_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "fderiv_const_smul_of_invertible", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "fderivWithin_const_smul_field", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": true, "tactics": ["obtain", "simp", "have", "ext", "simp"], "tactic_count": 5}
{"name": "fderiv_const_smul_field", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": true, "tactics": ["simp_rw", "ext", "simp"], "tactic_count": 3}
{"name": "HasStrictFDerivAt.add", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivAtFilter.add", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivWithinAt.add", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivAt.add", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableWithinAt.add", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableAt.add", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableOn.add", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Differentiable.add", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderivWithin_add", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "fderiv_fun_add", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasFDerivAtFilter_add_const_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "hasStrictFDerivAt_add_const_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "hasFDerivWithinAt_add_const_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasFDerivAt_add_const_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableWithinAt_add_const_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableAt_add_const_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableOn_add_const_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiable_add_const_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderivWithin_add_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "fderiv_add_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "hasFDerivAtFilter_const_add_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "hasStrictFDerivAt_const_add_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
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{"name": "differentiableWithinAt_const_add_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableAt_const_add_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableOn_const_add_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiable_const_add_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderivWithin_const_add", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "fderiv_const_add", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HasStrictFDerivAt.fun_sum", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": true, "tactics": ["simp", "convert", "simp"], "tactic_count": 3}
{"name": "HasStrictFDerivAt.sum", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "HasFDerivAtFilter.fun_sum", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": true, "tactics": ["simp", "convert", "simp"], "tactic_count": 3}
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{"name": "HasFDerivWithinAt.fun_sum", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "DifferentiableAt.sum", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableOn.fun_sum", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableOn.sum", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "fderivWithin_fun_sum", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderivWithin_sum", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "fderiv_sum", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictFDerivAt.neg", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivAtFilter.neg", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivWithinAt.neg", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivAt.neg", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableWithinAt.neg", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableWithinAt_fun_neg_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableWithinAt_neg_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableAt.neg", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "differentiableOn_fun_neg_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "differentiable_fun_neg_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "fderiv_fun_neg", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "HasStrictFDerivAt.sub", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasFDerivAtFilter.sub", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasFDerivWithinAt.sub", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivAt.sub", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "DifferentiableAt.sub", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableAt.add_iff_left", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": true, "tactics": ["refine", "simpa"], "tactic_count": 2}
{"name": "DifferentiableAt.add_iff_right", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DifferentiableAt.sub_iff_left", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DifferentiableAt.sub_iff_right", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DifferentiableOn.sub", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableOn.add_iff_left", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": true, "tactics": ["refine", "simpa"], "tactic_count": 2}
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{"name": "DifferentiableOn.sub_iff_left", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DifferentiableOn.sub_iff_right", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Differentiable.sub", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Differentiable.add_iff_left", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": true, "tactics": ["refine", "simpa"], "tactic_count": 2}
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{"name": "Differentiable.sub_iff_left", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "fderivWithin_fun_sub", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "hasFDerivAtFilter_sub_const_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "hasStrictFDerivAt_sub_const_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "hasFDerivWithinAt_sub_const_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasFDerivAt_sub_const_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasStrictFDerivAt_sub_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasFDerivAt_sub_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableWithinAt.sub_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableWithinAt_sub_const_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DifferentiableAt.sub_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableOn.sub_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Differentiable.sub_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderivWithin_sub_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "fderiv_sub_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HasFDerivAtFilter.const_sub", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasStrictFDerivAt.const_sub", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasFDerivWithinAt.const_sub", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivAt.const_sub", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableWithinAt.const_sub", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableWithinAt_const_sub_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DifferentiableAt.const_sub", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableOn.const_sub", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Differentiable.const_sub", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "fderiv_const_sub", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "hasFDerivWithinAt_comp_add_left", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": false, "tactics": ["have", "simp", "simp", "simp"], "tactic_count": 4}
{"name": "differentiableWithinAt_comp_add_left", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "fderivWithin_comp_add_left", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "hasFDerivWithinAt_comp_add_right", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "differentiableWithinAt_comp_add_right", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "fderivWithin_comp_add_right", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "hasFDerivAt_comp_add_right", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "fderiv_comp_add_right", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "hasFDerivAt_comp_add_left", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
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{"name": "hasFDerivAt_comp_sub", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Add", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "ContinuousAffineMap.hasStrictFDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Affine", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
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{"name": "ContinuousAffineMap.differentiableOn", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AnalyticAt.differentiableWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Analytic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFPowerSeriesWithinAt.fderivWithin_eq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Analytic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFPowerSeriesAt.fderiv_eq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Analytic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "HasFPowerSeriesWithinOnBall.differentiableOn", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Analytic", "is_tactic_proof": true, "tactics": ["intro", "have", "rcases", "exact", "apply", "suffices", "rw", "exact"], "tactic_count": 8}
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{"name": "AnalyticOnNhd.differentiableOn", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Analytic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ContinuousMultilinearMap.changeOrigin_toFormalMultilinearSeries", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Analytic", "is_tactic_proof": true, "tactics": ["ext", "rw", "cases", "have", "simp_rw", "rw", "intro", "rw", "rw", "rw", "simp_rw", "refine", "exact", "use", "intro", "have", "obtain", "exact", "rw", "dif_pos", "simp_rw", "congr", "grind"], "tactic_count": 23}
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{"name": "ContinuousMultilinearMap.hasStrictFDerivAt_uncurry", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Analytic", "is_tactic_proof": true, "tactics": ["let", "have", "convert", "ext", "suffices", "congr", "congr", "rcases", "suffices", "congr", "congr", "rcases"], "tactic_count": 12}
{"name": "HasStrictFDerivAt.continuousMultilinearMap_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Analytic", "is_tactic_proof": false, "tactics": ["convert", "ext", "simp"], "tactic_count": 3}
{"name": "HasFDerivWithinAt.continuousMultilinearMap_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Analytic", "is_tactic_proof": false, "tactics": ["convert", "ext", "simp"], "tactic_count": 3}
{"name": "HasFDerivAt.continuousMultilinearMap_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Analytic", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "HasFDerivWithinAt.multilinear_comp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Analytic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasFDerivAt.multilinear_comp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Analytic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "_private.Mathlib.Analysis.Calculus.FDeriv.Analytic.0.Equiv.succ_embeddingFinSucc_fst_symm_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Analytic", "is_tactic_proof": true, "tactics": ["rcases", "have", "rintro", "simp", "simp", "have", "simp_rw", "simp"], "tactic_count": 8}
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{"name": "ContinuousMultilinearMap.norm_iteratedFDeriv_le", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Analytic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
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{"name": "HasFPowerSeriesOnBall.iteratedFDeriv_zero_apply_diag", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Analytic", "is_tactic_proof": true, "tactics": ["ext", "simpa"], "tactic_count": 2}
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{"name": "ContinuousLinearMap.hasFDerivAt_uncurry_of_multilinear", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Analytic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "HasFDerivWithinAt.lim", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": ["have", "rw", "exact", "have", "calc", "simpa", "rw", "simpa"], "tactic_count": 8}
{"name": "HasFDerivWithinAt.unique_on", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": true, "tactics": ["intro", "rcases", "exact"], "tactic_count": 3}
{"name": "UniqueDiffWithinAt.eq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniqueDiffOn.eq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivAt.unique", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "HasFDerivAtFilter.mono", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivWithinAt.mono_of_mem_nhdsWithin", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivWithinAt.mono", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivAt.hasFDerivAtFilter", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivAt.hasFDerivWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivWithinAt.differentiableWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivAt.differentiableAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasFDerivWithinAt_univ", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "differentiableWithinAt_univ", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "fderiv_zero_of_not_differentiableAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": true, "tactics": ["rw", "rwa"], "tactic_count": 2}
{"name": "hasFDerivWithinAt_of_mem_nhds", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "hasFDerivWithinAt_of_isOpen", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasFDerivWithinAt_insert", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simp_rw", "apply", "simp", "refine", "simp_rw"], "tactic_count": 6}
{"name": "HasFDerivWithinAt.insert", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasFDerivWithinAt_diff_singleton", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HasFDerivWithinAt.empty", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DifferentiableWithinAt.empty", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivWithinAt.of_finite", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": true, "tactics": ["induction", "empty", "insert"], "tactic_count": 3}
{"name": "DifferentiableWithinAt.of_finite", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivWithinAt.singleton", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableWithinAt.singleton", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivWithinAt.of_subsingleton", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableWithinAt.of_subsingleton", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictFDerivAt.hasFDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictFDerivAt.differentiableAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivAt.lim", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "simpa", "refine", "refine", "simp"], "tactic_count": 6}
{"name": "hasFDerivWithinAt_inter'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "hasFDerivWithinAt_inter", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HasFDerivWithinAt.union", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "HasFDerivWithinAt.hasFDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "DifferentiableWithinAt.differentiableAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivWithinAt.of_not_accPt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "HasFDerivWithinAt.of_notMem_closure", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderivWithin_zero_of_not_accPt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "fderivWithin_zero_of_notMem_closure", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableWithinAt.hasFDerivWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": true, "tactics": ["simp", "split_ifs", "exacts"], "tactic_count": 3}
{"name": "DifferentiableAt.hasFDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "DifferentiableOn.hasFDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableOn.differentiableAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableOn.eventually_differentiableAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivAt.fderiv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "fderiv_eq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivWithinAt.fderivWithin", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableWithinAt.mono", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "DifferentiableWithinAt.mono_of_mem_nhdsWithin", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableWithinAt.congr_nhds", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableWithinAt_congr_nhds", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableWithinAt_inter", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "differentiableWithinAt_inter'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "differentiableWithinAt_insert_self", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableWithinAt_insert", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": true, "tactics": ["rcases", "exact", "apply", "exact"], "tactic_count": 4}
{"name": "DifferentiableWithinAt.insert", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableAt.differentiableWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Differentiable.differentiableAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableAt.fderivWithin", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableOn.mono", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableOn_univ", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Differentiable.differentiableOn", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableOn_of_locally_differentiableOn", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": true, "tactics": ["intro", "rcases", "exact"], "tactic_count": 3}
{"name": "fderivWithin_of_mem_nhdsWithin", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderivWithin_subset", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderivWithin_inter", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "fderivWithin_of_mem_nhds", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "fderivWithin_of_isOpen", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderivWithin_eq_fderiv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "fderiv_mem_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "fderivWithin_mem_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "DifferentiableOn.union_of_isOpen", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": true, "tactics": ["intro", "obtain", "exact", "exact"], "tactic_count": 4}
{"name": "differentiableOn_union_iff_of_isOpen", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiable_of_differentiableOn_union_of_isOpen", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "DifferentiableOn.iUnion_of_isOpen", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "differentiableOn_iUnion_iff_of_isOpen", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiable_of_differentiableOn_iUnion_of_isOpen", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "HasFDerivAtFilter.tendsto_nhds", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": true, "tactics": ["suffices", "have", "have", "rw", "exact", "simpa"], "tactic_count": 6}
{"name": "HasFDerivWithinAt.continuousWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivAt.continuousAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableWithinAt.continuousWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableAt.continuousAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableOn.continuousOn", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Differentiable.continuous", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictFDerivAt.continuousAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasStrictFDerivAt_id", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasFDerivAtFilter_id", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasFDerivWithinAt_id", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasFDerivAt_id", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableAt_id", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableAt_fun_id", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableWithinAt_id", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableWithinAt_id'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiable_id", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiable_fun_id", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableOn_id", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderiv_id", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderiv_id'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderivWithin_id", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "fderivWithin_id'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasFDerivAtFilter_iff_tendsto", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": ["have", "rw", "simp", "rw", "exact"], "tactic_count": 5}
{"name": "hasFDerivWithinAt_iff_tendsto", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasFDerivAt_iff_tendsto", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasFDerivAt_iff_isLittleO_nhds_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "HasStrictFDerivAt.isBigO_sub", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivAtFilter.isBigO_sub", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictFDerivAt.exists_lipschitzOnWith_of_nnnorm_lt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": true, "tactics": ["have", "simp", "rcases", "exact"], "tactic_count": 4}
{"name": "HasStrictFDerivAt.exists_lipschitzOnWith", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivWithinAt.isBigO_sub", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableWithinAt.isBigO_sub", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivAt.isBigO_sub", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableAt.isBigO_sub", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsBigO.hasFDerivWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "sub_zero,"], "tactic_count": 2}
{"name": "Asymptotics.IsBigO.hasFDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "HasStrictFDerivAt.isBigO_sub_rev", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivAtFilter.isBigO_sub_rev", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivAt.le_of_lip'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": true, "tactics": ["refine", "exact", "rw", "filter_upwards", "rw", "calc"], "tactic_count": 6}
{"name": "HasFDerivAt.le_of_lipschitzOn", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": true, "tactics": ["refine", "filter_upwards"], "tactic_count": 2}
{"name": "HasFDerivAt.le_of_lipschitz", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "norm_fderiv_le_of_lip'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "rw", "simp"], "tactic_count": 4}
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{"name": "HasFDerivAt.comp_semilinear", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Basic", "is_tactic_proof": true, "tactics": ["have", "rw", "have", "simpa"], "tactic_count": 4}
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{"name": "IsBoundedBilinearMap.hasFDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBoundedBilinearMap.hasFDerivWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBoundedBilinearMap.differentiableAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBoundedBilinearMap.differentiableWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBoundedBilinearMap.fderiv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBoundedBilinearMap.fderivWithin", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Bilinear", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsBoundedBilinearMap.differentiable", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBoundedBilinearMap.differentiableOn", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.hasFDerivWithinAt_of_bilinear", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Bilinear", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "ContinuousLinearMap.hasFDerivAt_of_bilinear", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Bilinear", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "ContinuousLinearMap.hasStrictFDerivAt_of_bilinear", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.fderivWithin_of_bilinear", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.fderiv_of_bilinear", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "HasFDerivWithinAt.comp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Comp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivAt.comp_hasFDerivWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Comp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "HasFDerivWithinAt.comp_hasFDerivAt_of_eq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Comp", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
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{"name": "DifferentiableAt.comp_differentiableWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Comp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Differentiable.iterate", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Comp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "HasFDerivAtFilter.iterate", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Comp", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "rw", "exact"], "tactic_count": 6}
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{"name": "HasStrictFDerivAt.continuousMultilinear_apply_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.CompCLM", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivWithinAt.continuousMultilinear_apply_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.CompCLM", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "fderivWithin_continuousMultilinear_apply_const_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.CompCLM", "is_tactic_proof": true, "tactics": ["have", "simp"], "tactic_count": 2}
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{"name": "hasFDerivWithinAt_congr_set'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Congr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "fderivWithin_eventually_congr_set'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Congr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "HasFDerivWithinAt.congr_mono", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Congr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivWithinAt.congr", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Congr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivWithinAt.congr'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Congr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivWithinAt.congr_of_eventuallyEq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Congr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivAt.congr_of_eventuallyEq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Congr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableWithinAt.congr_mono", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Congr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableWithinAt.congr", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Congr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableWithinAt.congr_of_eventuallyEq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Congr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableWithinAt.congr_of_eventuallyEq_of_mem", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Congr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableWithinAt.congr_of_eventuallyEq_insert", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Congr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableOn.congr_mono", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Congr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableOn.congr", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Congr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableOn_congr", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Congr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableAt.congr_of_eventuallyEq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Congr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableWithinAt.fderivWithin_congr_mono", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Congr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.fderivWithin_eq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Congr", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Filter.EventuallyEq.fderivWithin_eq_of_mem", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Congr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.fderivWithin_eq_of_insert", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Congr", "is_tactic_proof": true, "tactics": ["apply", "exact"], "tactic_count": 2}
{"name": "Filter.EventuallyEq.fderivWithin'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Congr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.fderivWithin", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Congr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.fderivWithin_eq_of_nhds", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Congr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderivWithin_congr", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Congr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderivWithin_congr'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Congr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.fderiv_eq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Congr", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.EventuallyEq.fderiv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Congr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasStrictFDerivAt_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasStrictFDerivAt_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasStrictFDerivAt_one", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasStrictFDerivAt_natCast", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasStrictFDerivAt_intCast", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasStrictFDerivAt_ofNat", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasFDerivAtFilter_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasFDerivAtFilter_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasFDerivAtFilter_one", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasFDerivAtFilter_natCast", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasFDerivAtFilter_intCast", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasFDerivAtFilter_ofNat", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasFDerivWithinAt_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasFDerivWithinAt_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasFDerivWithinAt_one", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasFDerivWithinAt_natCast", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasFDerivWithinAt_intCast", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasFDerivWithinAt_ofNat", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasFDerivAt_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasFDerivAt_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasFDerivAt_one", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasFDerivAt_natCast", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasFDerivAt_intCast", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasFDerivAt_ofNat", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableAt_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableAt_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableAt_one", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableAt_natCast", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableAt_intCast", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableAt_ofNat", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableWithinAt_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableWithinAt_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableWithinAt_one", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableWithinAt_natCast", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableWithinAt_intCast", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableWithinAt_ofNat", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderivWithin_const_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "fderivWithin_fun_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "fderivWithin_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderivWithin_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderivWithin_one", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderivWithin_natCast", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderivWithin_intCast", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderivWithin_ofNat", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderiv_const_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderiv_fun_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "fderiv_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderiv_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderiv_one", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderiv_natCast", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderiv_intCast", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderiv_ofNat", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiable_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiable_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiable_one", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiable_natCast", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiable_intCast", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiable_ofNat", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableOn_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableOn_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableOn_one", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableOn_natCast", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableOn_intCast", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableOn_ofNat", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasFDerivWithinAt_singleton", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "hasFDerivAt_of_subsingleton", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "differentiableOn_empty", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableOn_singleton", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Subsingleton.differentiableOn", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasFDerivAt_zero_of_eventually_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableWithinAt_of_isInvertible_fderivWithin", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": true, "tactics": ["contrapose", "rw", "contrapose", "rcases", "exact"], "tactic_count": 5}
{"name": "differentiableAt_of_isInvertible_fderiv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "HasStrictFDerivAt.of_notMem_tsupport", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "HasFDerivAt.of_notMem_tsupport", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivWithinAt.of_notMem_tsupport", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderiv_of_notMem_tsupport", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "support_fderiv_subset", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tsupport_fderiv_subset", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tsupport_fderiv_apply_subset", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasCompactSupport.fderiv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasCompactSupport.fderiv_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Const", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.hasStrictFDerivAt_toContinuousMultilinearMap_comp_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.ContinuousAlternatingMap", "is_tactic_proof": true, "tactics": ["cases", "constructor", "rw", "refine", "simp", "apply", "simp", "exact"], "tactic_count": 8}
{"name": "ContinuousAlternatingMap.hasStrictFDerivAt_compContinuousLinearMap", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.ContinuousAlternatingMap", "is_tactic_proof": true, "tactics": ["rw", "have", "have", "have", "exact"], "tactic_count": 5}
{"name": "HasStrictFDerivAt.continuousAlternatingMapCompContinuousLinearMap", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.ContinuousAlternatingMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivAt.continuousAlternatingMapCompContinuousLinearMap", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.ContinuousAlternatingMap", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "HasFDerivWithinAt.continuousAlternatingMapCompContinuousLinearMap", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.ContinuousAlternatingMap", "is_tactic_proof": true, "tactics": ["convert", "hasStrictFDerivAt_compContinuousLinearMap"], "tactic_count": 2}
{"name": "fderivWithin_continuousAlternatingMapCompContinuousLinearMap", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.ContinuousAlternatingMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderiv_continuousAlternatingMapCompContinuousLinearMap", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.ContinuousAlternatingMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableWithinAt.continuousAlternatingMapCompContinuousLinearMap", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.ContinuousAlternatingMap", "is_tactic_proof": true, "tactics": ["cases", "classical", "exact", "hf.hasFDerivWithinAt.continuousAlternatingMapCompContinuousLinearMap"], "tactic_count": 4}
{"name": "DifferentiableAt.continuousAlternatingMapCompContinuousLinearMap", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.ContinuousAlternatingMap", "is_tactic_proof": true, "tactics": ["cases", "classical"], "tactic_count": 2}
{"name": "ContinuousAlternatingMap.hasStrictFDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.ContinuousAlternatingMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.hasFDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.ContinuousAlternatingMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.hasFDerivWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.ContinuousAlternatingMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictFDerivAt.continuousAlternatingMap_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.ContinuousAlternatingMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivAt.continuousAlternatingMap_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.ContinuousAlternatingMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivWithinAt.continuousAlternatingMap_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.ContinuousAlternatingMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderivWithin_continuousAlternatingMap_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.ContinuousAlternatingMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderivWithin_continuousAlternatingMap_apply_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.ContinuousAlternatingMap", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "fderiv_continuousAlternatingMap_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.ContinuousAlternatingMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderiv_continuousAlternatingMap_apply_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.ContinuousAlternatingMap", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DifferentiableWithinAt.continuousAlternatingMap_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.ContinuousAlternatingMap", "is_tactic_proof": true, "tactics": ["cases", "classical", "exact", "hf.hasFDerivWithinAt.continuousAlternatingMap_apply"], "tactic_count": 4}
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{"name": "DifferentiableOn.continuousAlternatingMap_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.ContinuousAlternatingMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Differentiable.continuousAlternatingMap_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.ContinuousAlternatingMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.differentiable", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.ContinuousAlternatingMap", "is_tactic_proof": true, "tactics": ["cases", "apply"], "tactic_count": 2}
{"name": "ContinuousMultilinearMap.hasStrictFDerivAt_compContinuousLinearMap", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.ContinuousMultilinearMap", "is_tactic_proof": true, "tactics": ["have", "convert", "ext"], "tactic_count": 3}
{"name": "HasStrictFDerivAt.continuousMultilinearMapCompContinuousLinearMap", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.ContinuousMultilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivAt.continuousMultilinearMapCompContinuousLinearMap", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.ContinuousMultilinearMap", "is_tactic_proof": true, "tactics": ["convert", "hasStrictFDerivAt_compContinuousLinearMap"], "tactic_count": 2}
{"name": "HasFDerivWithinAt.continuousMultilinearMapCompContinuousLinearMap", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.ContinuousMultilinearMap", "is_tactic_proof": true, "tactics": ["convert", "hasStrictFDerivAt_compContinuousLinearMap"], "tactic_count": 2}
{"name": "fderivWithin_continuousMultilinearMapCompContinuousLinearMap", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.ContinuousMultilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderiv_continuousMultilinearMapCompContinuousLinearMap", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.ContinuousMultilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableWithinAt.continuousMultilinearMapCompContinuousLinearMap", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.ContinuousMultilinearMap", "is_tactic_proof": true, "tactics": ["cases", "classical", "exact", "hf.hasFDerivWithinAt.continuousMultilinearMapCompContinuousLinearMap"], "tactic_count": 4}
{"name": "DifferentiableAt.continuousMultilinearMapCompContinuousLinearMap", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.ContinuousMultilinearMap", "is_tactic_proof": true, "tactics": ["cases", "classical", "exact", "hf.hasFDerivAt.continuousMultilinearMapCompContinuousLinearMap"], "tactic_count": 4}
{"name": "DifferentiableOn.continuousMultilinearMapCompContinuousLinearMap", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.ContinuousMultilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Differentiable.continuousMultilinearMapCompContinuousLinearMap", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.ContinuousMultilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivWithinAt", "kind": "definition", "module": "Mathlib.Analysis.Calculus.FDeriv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivAt", "kind": "definition", "module": "Mathlib.Analysis.Calculus.FDeriv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableWithinAt", "kind": "definition", "module": "Mathlib.Analysis.Calculus.FDeriv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableAt", "kind": "definition", "module": "Mathlib.Analysis.Calculus.FDeriv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "definition._@.Mathlib.Analysis.Calculus.FDeriv.Defs.639413672._hygCtx._hyg.8", "kind": "definition", "module": "Mathlib.Analysis.Calculus.FDeriv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "wrapped._@.Mathlib.Analysis.Calculus.FDeriv.Defs.639413672._hygCtx._hyg.8", "kind": "opaque", "module": "Mathlib.Analysis.Calculus.FDeriv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderivWithin", "kind": "definition", "module": "Mathlib.Analysis.Calculus.FDeriv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderivWithin_def", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Defs", "is_tactic_proof": true, "tactics": ["intros", "delta", "rw", "rfl"], "tactic_count": 4}
{"name": "definition._@.Mathlib.Analysis.Calculus.FDeriv.Defs.1964793704._hygCtx._hyg.2", "kind": "definition", "module": "Mathlib.Analysis.Calculus.FDeriv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "fderiv", "kind": "definition", "module": "Mathlib.Analysis.Calculus.FDeriv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderiv_def", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Defs", "is_tactic_proof": true, "tactics": ["intros", "delta", "rw", "rfl"], "tactic_count": 4}
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{"name": "Differentiable", "kind": "definition", "module": "Mathlib.Analysis.Calculus.FDeriv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderivWithin_zero_of_not_differentiableWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "fderivWithin_univ", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Defs", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "hasFDerivAtFilter_iff_isLittleO", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasStrictFDerivAt_iff_isLittleO", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.hasStrictFDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.hasFDerivWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.hasFDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.differentiableAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ContinuousLinearEquiv.fderiv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ContinuousLinearEquiv.differentiable", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.differentiableOn", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.comp_differentiableWithinAt_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Equiv", "is_tactic_proof": true, "tactics": ["refine", "have", "iso.symm.differentiable.differentiableAt.comp_differentiableWithinAt", "rwa"], "tactic_count": 4}
{"name": "ContinuousLinearEquiv.comp_differentiableAt_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Equiv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ContinuousLinearEquiv.comp_differentiableOn_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Equiv", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
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{"name": "ContinuousLinearEquiv.comp_hasStrictFDerivAt_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Equiv", "is_tactic_proof": true, "tactics": ["refine", "convert"], "tactic_count": 2}
{"name": "ContinuousLinearEquiv.comp_hasFDerivAt_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Equiv", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "ContinuousLinearEquiv.comp_hasFDerivWithinAt_iff'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Equiv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ContinuousLinearEquiv.comp_hasFDerivAt_iff'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Equiv", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "ContinuousLinearEquiv.comp_fderivWithin", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Equiv", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "have", "rw"], "tactic_count": 4}
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{"name": "fderivWithin_continuousLinearEquiv_comp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Equiv", "is_tactic_proof": true, "tactics": ["change", "rw"], "tactic_count": 2}
{"name": "fderiv_continuousLinearEquiv_comp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Equiv", "is_tactic_proof": true, "tactics": ["change", "rw"], "tactic_count": 2}
{"name": "fderiv_continuousLinearEquiv_comp'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Equiv", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "ContinuousLinearEquiv.comp_right_differentiableWithinAt_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Equiv", "is_tactic_proof": true, "tactics": ["refine", "have", "rw", "apply", "intro", "simpa", "rwa"], "tactic_count": 7}
{"name": "ContinuousLinearEquiv.comp_right_differentiableAt_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Equiv", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousLinearEquiv.comp_right_differentiableOn_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Equiv", "is_tactic_proof": true, "tactics": ["refine", "rw", "apply", "simpa"], "tactic_count": 4}
{"name": "ContinuousLinearEquiv.comp_right_differentiable_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Equiv", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "ContinuousLinearEquiv.comp_right_hasFDerivAt_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Equiv", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousLinearEquiv.comp_right_hasFDerivWithinAt_iff'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Equiv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ContinuousLinearEquiv.comp_right_hasFDerivAt_iff'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Equiv", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousLinearEquiv.comp_right_fderivWithin", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Equiv", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "have", "intro", "exact", "rw"], "tactic_count": 6}
{"name": "ContinuousLinearEquiv.comp_right_fderiv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Equiv", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "LinearIsometryEquiv.hasStrictFDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.hasFDerivWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.hasFDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.differentiableAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.differentiableWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.fderiv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.fderivWithin", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.differentiable", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.differentiableOn", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.comp_differentiableWithinAt_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.comp_differentiableAt_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LinearIsometryEquiv.comp_differentiable_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.comp_hasFDerivWithinAt_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.comp_hasStrictFDerivAt_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.comp_hasFDerivAt_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.comp_hasFDerivWithinAt_iff'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.comp_hasFDerivAt_iff'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.comp_fderivWithin", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.comp_fderiv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.comp_fderiv'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Equiv", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "HasFDerivWithinAt.of_local_left_inverse", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Equiv", "is_tactic_proof": false, "tactics": ["have", "refine", "clear", "refine", "intro", "simp", "refine", "rintro", "simp"], "tactic_count": 9}
{"name": "HasStrictFDerivAt.of_local_left_inverse", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Equiv", "is_tactic_proof": true, "tactics": ["replace", "replace", "have", "f", "refine", "simp", "refine", "clear", "refine", "rintro", "simp", "refine", "rintro", "simp"], "tactic_count": 14}
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{"name": "OpenPartialHomeomorph.hasStrictFDerivAt_symm", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.hasFDerivAt_symm", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivWithinAt.eventually_ne", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Equiv", "is_tactic_proof": true, "tactics": ["rcases", "rw", "have", "isBigO_iff.2", "have", "simpa", "exact"], "tactic_count": 7}
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{"name": "has_fderiv_at_filter_real_equiv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Equiv", "is_tactic_proof": true, "tactics": ["symm", "rw", "refine", "simp"], "tactic_count": 4}
{"name": "HasFDerivAt.lim_real", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Equiv", "is_tactic_proof": true, "tactics": ["apply", "rw", "exact"], "tactic_count": 3}
{"name": "HasFDerivWithinAt.mapsTo_tangent_cone", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Equiv", "is_tactic_proof": true, "tactics": ["intro", "rcases", "apply", "rw", "refine", "simpa", "exact", "exact"], "tactic_count": 8}
{"name": "HasFDerivWithinAt.uniqueDiffWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Equiv", "is_tactic_proof": true, "tactics": ["refine", "change", "rw", "exact"], "tactic_count": 4}
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{"name": "HasFDerivWithinAt.uniqueDiffWithinAt_of_continuousLinearEquiv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "fderivWithin_comp_smul_eq_fderivWithin_smul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Equiv", "is_tactic_proof": true, "tactics": ["rcases", "simp", "classical"], "tactic_count": 3}
{"name": "fderivWithin_comp_smul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Equiv", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rw", "exact"], "tactic_count": 4}
{"name": "fderiv_comp_smul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Equiv", "is_tactic_proof": true, "tactics": ["rw", "rcases"], "tactic_count": 2}
{"name": "hasFDerivWithinAt_closure_of_tendsto_fderiv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Extend", "is_tactic_proof": true, "tactics": ["classical", "by_cases", "rw", "rw", "suffices", "of", "proof.", "intro", "obtain", "simpa", "set", "suffices", "mem_nhdsWithin_iff.2", "suffices", "rw", "intro", "apply", "have", "exact", "have", "rintro", "have", "have", "have", "intro", "have", "have", "have", "rw", "exact", "rw", "exact", "simpa", "rintro", "have", "intro", "exact", "refine", "all_goals", "have", "obtain", "apply", "simp", "rw", "have", "simp", "exact", "apply", "rw", "exact"], "tactic_count": 50}
{"name": "hasDerivWithinAt_Ici_of_tendsto_deriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Extend", "is_tactic_proof": true, "tactics": ["setting", "we", "obtain", "let", "have", "have", "have", "have", "have", "have", "rw", "intro", "by_cases", "rw", "have", "exact", "have", "simp", "exact", "have", "rw", "exact", "exact"], "tactic_count": 23}
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{"name": "hasDerivAt_of_hasDerivAt_of_ne", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Extend", "is_tactic_proof": false, "tactics": ["have", "have", "apply", "have", "apply", "apply", "intro", "exact", "have", "have", "apply", "have", "apply", "apply", "intro", "exact", "simpa"], "tactic_count": 17}
{"name": "hasDerivAt_of_hasDerivAt_of_ne'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Extend", "is_tactic_proof": true, "tactics": ["rcases", "exact", "exact"], "tactic_count": 3}
{"name": "ContinuousLinearMap.hasStrictFDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.hasFDerivAtFilter", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.hasFDerivWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.hasFDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.differentiableAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.differentiableWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.fderiv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.fderivWithin", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Linear", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ContinuousLinearMap.differentiable", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.differentiableOn", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBoundedLinearMap.hasFDerivAtFilter", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBoundedLinearMap.hasFDerivWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBoundedLinearMap.hasFDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBoundedLinearMap.differentiableAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBoundedLinearMap.differentiableWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBoundedLinearMap.fderiv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBoundedLinearMap.fderivWithin", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Linear", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsBoundedLinearMap.differentiable", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBoundedLinearMap.differentiableOn", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.measurable_apply₂", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Measurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FDerivMeasurableAux.A", "kind": "definition", "module": "Mathlib.Analysis.Calculus.FDeriv.Measurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FDerivMeasurableAux.B", "kind": "definition", "module": "Mathlib.Analysis.Calculus.FDeriv.Measurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FDerivMeasurableAux.D", "kind": "definition", "module": "Mathlib.Analysis.Calculus.FDeriv.Measurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FDerivMeasurableAux.isOpen_A", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Measurable", "is_tactic_proof": true, "tactics": ["rw", "rintro", "obtain", "have", "refine", "have", "intro", "exact"], "tactic_count": 8}
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{"name": "FDerivMeasurableAux.A_mono", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Measurable", "is_tactic_proof": true, "tactics": ["rintro", "refine", "linarith"], "tactic_count": 3}
{"name": "FDerivMeasurableAux.le_of_mem_A", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Measurable", "is_tactic_proof": true, "tactics": ["rcases", "apply", "exact"], "tactic_count": 3}
{"name": "FDerivMeasurableAux.mem_A_of_differentiable", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Measurable", "is_tactic_proof": true, "tactics": ["let", "obtain", "eventually_nhds_iff_ball.1", "refine", "have", "refine", "calc"], "tactic_count": 7}
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{"name": "FDerivMeasurableAux.differentiable_set_subset_D", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Measurable", "is_tactic_proof": true, "tactics": ["intro", "rw", "intro", "have", "rcases", "obtain", "simp", "refine", "refine", "exact"], "tactic_count": 10}
{"name": "FDerivMeasurableAux.D_subset_differentiable_set", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Measurable", "is_tactic_proof": true, "tactics": ["have", "rcases", "intro", "have", "intro", "have", "rcases", "refine", "simp", "rcases", "exact", "such", "choose", "have", "n", "intro", "let", "have", "have", "have", "have", "exact", "have", "have", "have", "exact", "have", "have", "have", "exact", "calc", "abel", "ring", "is", "let", "have", "rw", "intro", "obtain", "refine", "rw", "calc", "field", "obtain", "cauchySeq_tendsto_of_isComplete", "have", "intro", "apply", "rw", "exact", "have", "simp", "some", "this", "the", "intro", "have", "obtain", "exists_pow_lt_of_lt_one", "rw", "refine", "by_cases", "simp", "have", "have", "have", "le_trans", "obtain", "exists_nat_pow_near_of_lt_one", "have", "have", "rw", "lia", "set", "have", "have", "rw", "have", "apply", "simp", "positivity", "simpa", "have", "calc", "gcongr", "calc", "rw", "exact"], "tactic_count": 88}
{"name": "FDerivMeasurableAux.differentiable_set_eq_D", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Measurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "measurable_fderiv_apply_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Measurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_deriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Measurable", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "stronglyMeasurable_deriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Measurable", "is_tactic_proof": true, "tactics": ["borelize", "rcases", "exact", "exact"], "tactic_count": 4}
{"name": "aemeasurable_deriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Measurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "aestronglyMeasurable_deriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Measurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RightDerivMeasurableAux.A", "kind": "definition", "module": "Mathlib.Analysis.Calculus.FDeriv.Measurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RightDerivMeasurableAux.B", "kind": "definition", "module": "Mathlib.Analysis.Calculus.FDeriv.Measurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RightDerivMeasurableAux.D", "kind": "definition", "module": "Mathlib.Analysis.Calculus.FDeriv.Measurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RightDerivMeasurableAux.A_mem_nhdsGT", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Measurable", "is_tactic_proof": true, "tactics": ["rcases", "obtain", "have", "filter_upwards", "use", "have", "apply", "linarith", "intro", "exact"], "tactic_count": 10}
{"name": "RightDerivMeasurableAux.B_mem_nhdsGT", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Measurable", "is_tactic_proof": false, "tactics": ["obtain", "simpa", "filter_upwards", "simp", "exact"], "tactic_count": 5}
{"name": "RightDerivMeasurableAux.measurableSet_B", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Measurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RightDerivMeasurableAux.A_mono", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Measurable", "is_tactic_proof": true, "tactics": ["rintro", "refine", "linarith"], "tactic_count": 3}
{"name": "RightDerivMeasurableAux.le_of_mem_A", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Measurable", "is_tactic_proof": true, "tactics": ["rcases", "have", "exact"], "tactic_count": 3}
{"name": "RightDerivMeasurableAux.mem_A_of_differentiable", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Measurable", "is_tactic_proof": true, "tactics": ["have", "simp_rw", "rcases", "refine", "have", "refine", "calc", "gcongr", "rw", "rw"], "tactic_count": 10}
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{"name": "RightDerivMeasurableAux.differentiable_set_subset_D", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Measurable", "is_tactic_proof": true, "tactics": ["intro", "rw", "intro", "have", "rcases", "obtain", "simp", "refine", "refine", "exact"], "tactic_count": 10}
{"name": "RightDerivMeasurableAux.D_subset_differentiable_set", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Measurable", "is_tactic_proof": true, "tactics": ["have", "intro", "have", "intro", "have", "rcases", "refine", "simp", "rcases", "exact", "such", "choose", "have", "intro", "let", "have", "have", "have", "have", "exact", "have", "have", "have", "exact", "have", "have", "have", "exact", "calc", "abel", "ring", "is", "let", "have", "rw", "intro", "obtain", "refine", "rw", "calc", "ring", "obtain", "cauchySeq_tendsto_of_isComplete", "have", "intro", "apply", "rw", "exact", "have", "simp", "some", "this", "the", "intro", "obtain", "filter_upwards", "rcases", "simp", "have", "have", "have", "le_trans", "obtain", "exists_nat_pow_near_of_lt_one", "have", "have", "rw", "lia", "set", "have", "have", "rw", "have", "calc", "apply", "simp", "positivity", "simp", "simpa", "calc", "simp", "ring", "rw", "exact"], "tactic_count": 84}
{"name": "RightDerivMeasurableAux.differentiable_set_eq_D", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Measurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurableSet_of_differentiableWithinAt_Ici_of_isComplete", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Measurable", "is_tactic_proof": true, "tactics": ["simp", "repeat", "exact"], "tactic_count": 3}
{"name": "measurableSet_of_differentiableWithinAt_Ici", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Measurable", "is_tactic_proof": true, "tactics": ["have", "convert", "simp"], "tactic_count": 3}
{"name": "measurable_derivWithin_Ici", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Measurable", "is_tactic_proof": true, "tactics": ["refine", "have", "rw", "exact"], "tactic_count": 4}
{"name": "stronglyMeasurable_derivWithin_Ici", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Measurable", "is_tactic_proof": true, "tactics": ["borelize", "apply", "obtain", "suffices", "rintro", "suffices", "apply", "calc", "apply", "simpa", "rw", "exact"], "tactic_count": 12}
{"name": "aemeasurable_derivWithin_Ici", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Measurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "aestronglyMeasurable_derivWithin_Ici", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Measurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurableSet_of_differentiableWithinAt_Ioi", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Measurable", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "measurable_derivWithin_Ioi", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Measurable", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "stronglyMeasurable_derivWithin_Ioi", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Measurable", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "aemeasurable_derivWithin_Ioi", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Measurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "aestronglyMeasurable_derivWithin_Ioi", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Measurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FDerivMeasurableAux.isOpen_A_with_param", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Measurable", "is_tactic_proof": true, "tactics": ["have", "simp", "apply", "rintro", "rcases", "rcases", "obtain", "have", "have", "rcases", "simp", "refine", "have", "exact", "obtain", "obtain", "have", "have", "rintro", "simp", "simp", "obtain", "obtain", "generalized_tube_lemma", "refine", "rintro", "exact", "have", "filter_upwards", "rintro", "simp", "refine", "have", "have", "calc", "abel", "gcongr", "rw", "change", "apply", "exact", "simp", "rw", "change", "apply", "exact", "simp", "simp"], "tactic_count": 48}
{"name": "FDerivMeasurableAux.isOpen_B_with_param", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Measurable", "is_tactic_proof": false, "tactics": ["suffices", "simp", "refine", "exact"], "tactic_count": 4}
{"name": "measurableSet_of_differentiableAt_of_isComplete_with_param", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Measurable", "is_tactic_proof": false, "tactics": ["have", "simp", "rw", "simp", "simp", "refine", "refine", "refine", "refine", "refine", "refine", "have", "exact"], "tactic_count": 13}
{"name": "measurableSet_of_differentiableAt_with_param", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Measurable", "is_tactic_proof": true, "tactics": ["have", "convert", "simp"], "tactic_count": 3}
{"name": "measurable_fderiv_with_param", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Measurable", "is_tactic_proof": true, "tactics": ["refine", "have", "rw", "exact"], "tactic_count": 4}
{"name": "measurable_fderiv_apply_const_with_param", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Measurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_deriv_with_param", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Measurable", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "stronglyMeasurable_deriv_with_param", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Measurable", "is_tactic_proof": true, "tactics": ["borelize", "rcases", "have", "apply", "have", "rintro", "have", "rw", "apply", "have", "rintro", "exact", "exact", "exact", "exact"], "tactic_count": 15}
{"name": "aemeasurable_deriv_with_param", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Measurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "aestronglyMeasurable_deriv_with_param", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Measurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictFDerivAt.smul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivWithinAt.smul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Mul", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "HasFDerivAt.smul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Mul", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "DifferentiableWithinAt.smul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableAt.smul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableOn.smul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Differentiable.smul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "norm_fderiv_norm", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Norm", "is_tactic_proof": true, "tactics": ["have", "refine", "apply", "calc"], "tactic_count": 4}
{"name": "hasFDerivAt_update", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Pi", "is_tactic_proof": true, "tactics": ["set", "have", "ext", "dsimp", "split_ifs", "subst", "simp", "simp", "rw", "have", "convert", "rw"], "tactic_count": 12}
{"name": "hasFDerivAt_single", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderiv_update", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderiv_single", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.Calculus.FDeriv.Pow.0.aux", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Pow", "is_tactic_proof": true, "tactics": ["rw", "simp", "simp_rw", "congr", "simp", "rw"], "tactic_count": 6}
{"name": "HasStrictFDerivAt.fun_pow'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictFDerivAt.pow'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasStrictFDerivAt_pow'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivWithinAt.fun_pow'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivWithinAt.pow'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasFDerivWithinAt_pow'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivAt.fun_pow'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivAt.pow'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasFDerivAt_pow'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableWithinAt.fun_pow", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableWithinAt.pow", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableWithinAt_pow", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableAt.fun_pow", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableAt.pow", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableAt_pow", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableOn.fun_pow", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableOn.pow", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableOn_pow", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Differentiable.fun_pow", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Differentiable.pow", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiable_pow", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderiv_fun_pow'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderiv_pow'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderiv_pow_ring'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Pow", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "fderivWithin_fun_pow'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderivWithin_pow'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderivWithin_pow_ring'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Pow", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "_private.Mathlib.Analysis.Calculus.FDeriv.Pow.0.aux_sum_eq_pow", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Pow", "is_tactic_proof": true, "tactics": ["simp_rw", "rw", "intro", "congr", "exact"], "tactic_count": 5}
{"name": "HasStrictFDerivAt.pow", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasStrictFDerivAt_pow", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivWithinAt.pow", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasFDerivWithinAt_pow", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivAt.pow", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasFDerivAt_pow", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderiv_fun_pow", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderiv_pow", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderiv_pow_ring", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Pow", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "fderivWithin_fun_pow", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderivWithin_pow", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderivWithin_pow_ring", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Pow", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HasStrictFDerivAt.prodMk", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivAtFilter.prodMk", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivWithinAt.prodMk", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivAt.prodMk", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasFDerivAt_prodMk_left", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasFDerivAt_prodMk_right", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableWithinAt.prodMk", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableAt.prodMk", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableOn.prodMk", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Differentiable.prodMk", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableAt.fderiv_prodMk", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableWithinAt.fderivWithin_prodMk", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasStrictFDerivAt_fst", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "hasFDerivAtFilter_fst", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "HasFDerivAt.fst", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasFDerivWithinAt_fst", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "DifferentiableAt.fst", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiable_fst", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Differentiable.fst", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableWithinAt_fst", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableWithinAt.fst", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableOn_fst", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableOn.fst", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderiv_fst", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderiv.fst", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderivWithin_fst", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderivWithin.fst", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasStrictFDerivAt_snd", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictFDerivAt.snd", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasFDerivAtFilter_snd", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivAtFilter.snd", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasFDerivAt_snd", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivAt.snd", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasFDerivWithinAt_snd", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivWithinAt.snd", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableAt_snd", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableAt.snd", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiable_snd", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Differentiable.snd", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableWithinAt_snd", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableWithinAt.snd", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableOn_snd", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableOn.snd", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderiv_snd", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderiv.snd", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderivWithin_snd", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderivWithin.snd", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictFDerivAt.prodMap", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivWithinAt.prodMap", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivAt.prodMap", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableAt.prodMap", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasStrictFDerivAt_pi'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": true, "tactics": ["have", "simp", "exact"], "tactic_count": 3}
{"name": "hasStrictFDerivAt_pi''", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasStrictFDerivAt_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": true, "tactics": ["have", "let", "have", "have", "rw"], "tactic_count": 5}
{"name": "hasStrictFDerivAt_pi", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasFDerivAtFilter_pi'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": true, "tactics": ["have", "simp", "exact"], "tactic_count": 3}
{"name": "hasFDerivAtFilter_pi", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasFDerivAt_pi'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasFDerivAt_pi''", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasFDerivAt_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": true, "tactics": ["have", "apply", "apply"], "tactic_count": 3}
{"name": "hasFDerivAt_pi", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasFDerivWithinAt_pi'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "hasFDerivWithinAt_pi", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableWithinAt_pi", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableWithinAt_pi''", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableWithinAt_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": true, "tactics": ["have", "apply", "fun_prop"], "tactic_count": 3}
{"name": "differentiableAt_pi", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "differentiableOn_pi", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "PiLp.hasStrictFDerivAt_toLp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.WithLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiLp.hasStrictFDerivAt_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.WithLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiLp.hasFDerivAt_ofLp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.WithLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiLp.hasFDerivAt_toLp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.WithLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiLp.hasFDerivAt_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FDeriv.WithLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries", "kind": "definition", "module": "Mathlib.Analysis.Calculus.FormalMultilinearSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instModuleFormalMultilinearSeriesOfContinuousConstSMulOfSMulCommClass", "kind": "instance", "module": "Mathlib.Analysis.Calculus.FormalMultilinearSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.zero_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FormalMultilinearSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.add_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FormalMultilinearSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.smul_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FormalMultilinearSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.ext", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FormalMultilinearSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.ne_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FormalMultilinearSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.prod", "kind": "definition", "module": "Mathlib.Analysis.Calculus.FormalMultilinearSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.pi", "kind": "definition", "module": "Mathlib.Analysis.Calculus.FormalMultilinearSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.removeZero", "kind": "definition", "module": "Mathlib.Analysis.Calculus.FormalMultilinearSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.removeZero_coeff_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FormalMultilinearSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.removeZero_coeff_succ", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FormalMultilinearSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.removeZero_of_pos", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FormalMultilinearSeries", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "FormalMultilinearSeries.congr", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FormalMultilinearSeries", "is_tactic_proof": true, "tactics": ["subst", "congr", "exact"], "tactic_count": 3}
{"name": "FormalMultilinearSeries.congr_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FormalMultilinearSeries", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "FormalMultilinearSeries.compContinuousLinearMap", "kind": "definition", "module": "Mathlib.Analysis.Calculus.FormalMultilinearSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.compContinuousLinearMap_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FormalMultilinearSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.compContinuousLinearMap_id", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FormalMultilinearSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.compContinuousLinearMap_comp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FormalMultilinearSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.restrictScalars", "kind": "definition", "module": "Mathlib.Analysis.Calculus.FormalMultilinearSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.instAddCommGroup", "kind": "instance", "module": "Mathlib.Analysis.Calculus.FormalMultilinearSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.neg_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FormalMultilinearSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.sub_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FormalMultilinearSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.shift", "kind": "definition", "module": "Mathlib.Analysis.Calculus.FormalMultilinearSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.unshift", "kind": "definition", "module": "Mathlib.Analysis.Calculus.FormalMultilinearSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.unshift_shift", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FormalMultilinearSeries", "is_tactic_proof": true, "tactics": ["ext1", "simp", "exact"], "tactic_count": 3}
{"name": "ContinuousLinearMap.compFormalMultilinearSeries", "kind": "definition", "module": "Mathlib.Analysis.Calculus.FormalMultilinearSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.compFormalMultilinearSeries_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FormalMultilinearSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.compFormalMultilinearSeries_apply'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FormalMultilinearSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.toFormalMultilinearSeries", "kind": "definition", "module": "Mathlib.Analysis.Calculus.FormalMultilinearSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.order", "kind": "definition", "module": "Mathlib.Analysis.Calculus.FormalMultilinearSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.order_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FormalMultilinearSeries", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FormalMultilinearSeries.ne_zero_of_order_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FormalMultilinearSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.order_eq_find", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FormalMultilinearSeries", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "FormalMultilinearSeries.order_eq_find'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FormalMultilinearSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.order_eq_zero_iff'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FormalMultilinearSeries", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "FormalMultilinearSeries.order_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FormalMultilinearSeries", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FormalMultilinearSeries.apply_order_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FormalMultilinearSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.apply_order_ne_zero'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FormalMultilinearSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.apply_eq_zero_of_lt_order", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FormalMultilinearSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.coeff", "kind": "definition", "module": "Mathlib.Analysis.Calculus.FormalMultilinearSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.mkPiRing_coeff_eq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FormalMultilinearSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.apply_eq_prod_smul_coeff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FormalMultilinearSeries", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "FormalMultilinearSeries.coeff_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FormalMultilinearSeries", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "FormalMultilinearSeries.apply_eq_pow_smul_coeff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FormalMultilinearSeries", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FormalMultilinearSeries.norm_apply_eq_norm_coef", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FormalMultilinearSeries", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "FormalMultilinearSeries.fslope", "kind": "definition", "module": "Mathlib.Analysis.Calculus.FormalMultilinearSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FormalMultilinearSeries.coeff_fslope", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FormalMultilinearSeries", "is_tactic_proof": true, "tactics": ["simp", "congr", "exact"], "tactic_count": 3}
{"name": "FormalMultilinearSeries.coeff_iterate_fslope", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FormalMultilinearSeries", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "constFormalMultilinearSeries", "kind": "definition", "module": "Mathlib.Analysis.Calculus.FormalMultilinearSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "constFormalMultilinearSeries_apply_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FormalMultilinearSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "constFormalMultilinearSeries_apply_succ", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FormalMultilinearSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "constFormalMultilinearSeries_apply_of_nonzero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FormalMultilinearSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "constFormalMultilinearSeries_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FormalMultilinearSeries", "is_tactic_proof": true, "tactics": ["ext", "simp", "induction", "simp", "simp"], "tactic_count": 5}
{"name": "compContinuousLinearMap_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FormalMultilinearSeries", "is_tactic_proof": true, "tactics": ["ext", "cases", "zero", "simp", "constFormalMultilinearSeries_apply_zero,", "congr", "apply", "succ"], "tactic_count": 8}
{"name": "ContinuousLinearMap.fpowerSeries", "kind": "definition", "module": "Mathlib.Analysis.Calculus.FormalMultilinearSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.fpowerSeries_apply_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FormalMultilinearSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.fpowerSeries_apply_one", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FormalMultilinearSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.fpowerSeries_apply_add_two", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.FormalMultilinearSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasGradientAtFilter", "kind": "definition", "module": "Mathlib.Analysis.Calculus.Gradient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasGradientWithinAt", "kind": "definition", "module": "Mathlib.Analysis.Calculus.Gradient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasGradientAt", "kind": "definition", "module": "Mathlib.Analysis.Calculus.Gradient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "gradientWithin", "kind": "definition", "module": "Mathlib.Analysis.Calculus.Gradient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "gradient", "kind": "definition", "module": "Mathlib.Analysis.Calculus.Gradient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Gradient.term∇", "kind": "definition", "module": "Mathlib.Analysis.Calculus.Gradient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Gradient._aux_Mathlib_Analysis_Calculus_Gradient_Basic___macroRules_Gradient_term∇_1", "kind": "definition", "module": "Mathlib.Analysis.Calculus.Gradient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Gradient._aux_Mathlib_Analysis_Calculus_Gradient_Basic___unexpand_gradient_1", "kind": "definition", "module": "Mathlib.Analysis.Calculus.Gradient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.Calculus.Gradient.Basic.0.term⟪_,_⟫", "kind": "definition", "module": "Mathlib.Analysis.Calculus.Gradient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.Calculus.Gradient.Basic.0._aux_Mathlib_Analysis_Calculus_Gradient_Basic___macroRules__private_Mathlib_Analysis_Calculus_Gradient_Basic_0_term⟪_,_⟫_1", "kind": "definition", "module": "Mathlib.Analysis.Calculus.Gradient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.Calculus.Gradient.Basic.0._aux_Mathlib_Analysis_Calculus_Gradient_Basic___unexpand_Inner_inner_1", "kind": "definition", "module": "Mathlib.Analysis.Calculus.Gradient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasGradientWithinAt_iff_hasFDerivWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Gradient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasFDerivWithinAt_iff_hasGradientWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Gradient.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "hasGradientAt_iff_hasFDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Gradient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasFDerivAt_iff_hasGradientAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Gradient.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "gradient_eq_zero_of_not_differentiableAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Gradient.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HasGradientAt.unique", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Gradient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableAt.hasGradientAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Gradient.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "HasGradientAt.differentiableAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Gradient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableWithinAt.hasGradientWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Gradient.Basic", "is_tactic_proof": false, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "HasGradientWithinAt.differentiableWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Gradient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasGradientWithinAt_univ", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Gradient.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "DifferentiableOn.hasGradientAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Gradient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasGradientAt.gradient", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Gradient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "gradient_eq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Gradient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasGradientAtFilter.hasDerivAtFilter", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Gradient.Basic", "is_tactic_proof": true, "tactics": ["tauto"], "tactic_count": 1}
{"name": "HasDerivAtFilter.hasGradientAtFilter", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Gradient.Basic", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "HasGradientAt.hasDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Gradient.Basic", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "HasDerivAt.hasGradientAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Gradient.Basic", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "gradient_eq_deriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Gradient.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "rw"], "tactic_count": 3}
{"name": "HasGradientAtFilter.hasDerivAtFilter'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Gradient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivAtFilter.hasGradientAtFilter'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Gradient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasGradientAt.hasDerivAt'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Gradient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivAt.hasGradientAt'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Gradient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "gradient_eq_deriv'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Gradient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasGradientAtFilter_iff_isLittleO", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Gradient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasGradientWithinAt_iff_isLittleO", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Gradient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasGradientWithinAt_iff_tendsto", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Gradient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasGradientAt_iff_isLittleO", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Gradient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasGradientAt_iff_tendsto", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Gradient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasGradientAtFilter.isBigO_sub", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Gradient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasGradientWithinAt_congr_set'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Gradient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasGradientWithinAt_congr_set", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Gradient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasGradientAt_iff_isLittleO_nhds_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Gradient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasGradientWithinAt.fderivWithin_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Gradient.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HasGradientAt.fderiv_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Gradient.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "inner_gradientWithin_left", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Gradient.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "inner_gradient_left", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Gradient.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "inner_gradientWithin_right", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Gradient.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "inner_gradient_right", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Gradient.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.EventuallyEq.hasGradientAtFilter_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Gradient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasGradientAtFilter.congr_of_eventuallyEq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Gradient.Basic", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "HasGradientWithinAt.congr_mono", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Gradient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasGradientWithinAt.congr", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Gradient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ApproximatesLinearOn.toOpenPartialHomeomorph_source", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.InverseFunctionTheorem.ApproximatesLinearOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ApproximatesLinearOn.toOpenPartialHomeomorph_target", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.InverseFunctionTheorem.ApproximatesLinearOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ApproximatesLinearOn.toHomeomorph", "kind": "definition", "module": "Mathlib.Analysis.Calculus.InverseFunctionTheorem.ApproximatesLinearOn", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "ApproximatesLinearOn.closedBall_subset_target", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.InverseFunctionTheorem.ApproximatesLinearOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffAt.toOpenPartialHomeomorph", "kind": "definition", "module": "Mathlib.Analysis.Calculus.InverseFunctionTheorem.ContDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffAt.toOpenPartialHomeomorph_coe", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.InverseFunctionTheorem.ContDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffAt.mem_toOpenPartialHomeomorph_source", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.InverseFunctionTheorem.ContDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffAt.image_mem_toOpenPartialHomeomorph_target", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.InverseFunctionTheorem.ContDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffAt.localInverse", "kind": "definition", "module": "Mathlib.Analysis.Calculus.InverseFunctionTheorem.ContDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffAt.localInverse_apply_image", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.InverseFunctionTheorem.ContDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffAt.to_localInverse", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.InverseFunctionTheorem.ContDiff", "is_tactic_proof": true, "tactics": ["have", "apply", "convert", "convert"], "tactic_count": 4}
{"name": "HasStrictDerivAt.localInverse", "kind": "abbrev", "module": "Mathlib.Analysis.Calculus.InverseFunctionTheorem.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictDerivAt.eventually_left_inverse", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.InverseFunctionTheorem.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictDerivAt.eventually_right_inverse", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.InverseFunctionTheorem.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictDerivAt.map_nhds_eq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.InverseFunctionTheorem.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictDerivAt.to_localInverse", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.InverseFunctionTheorem.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictDerivAt.to_local_left_inverse", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.InverseFunctionTheorem.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpenMap_of_hasStrictDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.InverseFunctionTheorem.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictFDerivAt.approximates_deriv_on_nhds", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.InverseFunctionTheorem.FDeriv", "is_tactic_proof": true, "tactics": ["rcases", "refine", "simp", "have", "rw", "rcases", "exact"], "tactic_count": 7}
{"name": "HasStrictFDerivAt.map_nhds_eq_of_surj", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.InverseFunctionTheorem.FDeriv", "is_tactic_proof": true, "tactics": ["let", "set", "have", "have", "obtain", "apply", "simp"], "tactic_count": 7}
{"name": "HasStrictFDerivAt.approximates_deriv_on_open_nhds", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.InverseFunctionTheorem.FDeriv", "is_tactic_proof": true, "tactics": ["simp", "refine", "exact"], "tactic_count": 3}
{"name": "HasStrictFDerivAt.toOpenPartialHomeomorph", "kind": "definition", "module": "Mathlib.Analysis.Calculus.InverseFunctionTheorem.FDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictFDerivAt.toOpenPartialHomeomorph_coe", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.InverseFunctionTheorem.FDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictFDerivAt.mem_toOpenPartialHomeomorph_source", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.InverseFunctionTheorem.FDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictFDerivAt.image_mem_toOpenPartialHomeomorph_target", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.InverseFunctionTheorem.FDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictFDerivAt.map_nhds_eq_of_equiv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.InverseFunctionTheorem.FDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictFDerivAt.localInverse", "kind": "definition", "module": "Mathlib.Analysis.Calculus.InverseFunctionTheorem.FDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictFDerivAt.localInverse_def", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.InverseFunctionTheorem.FDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictFDerivAt.eventually_left_inverse", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.InverseFunctionTheorem.FDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictFDerivAt.localInverse_apply_image", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.InverseFunctionTheorem.FDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictFDerivAt.eventually_right_inverse", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.InverseFunctionTheorem.FDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictFDerivAt.localInverse_continuousAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.InverseFunctionTheorem.FDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictFDerivAt.localInverse_tendsto", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.InverseFunctionTheorem.FDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictFDerivAt.localInverse_unique", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.InverseFunctionTheorem.FDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictFDerivAt.to_localInverse", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.InverseFunctionTheorem.FDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictFDerivAt.to_local_left_inverse", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.InverseFunctionTheorem.FDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpenMap_of_hasStrictFDerivAt_equiv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.InverseFunctionTheorem.FDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ApproximatesLinearOn.exists_homeomorph_extension", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.InverseFunctionTheorem.FiniteDimensional", "is_tactic_proof": true, "tactics": ["obtain", "hf.lipschitzOnWith.extend_finite_dimension", "let", "have", "have", "apply", "rw", "convert", "ext", "simp", "haveI", "exact"], "tactic_count": 12}
{"name": "AnalyticOn.hasFPowerSeriesOnSubball", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.ConvergenceOnBall", "is_tactic_proof": true, "tactics": ["rw", "intro", "set", "let", "have", "have", "replace", "apply", "apply", "symm", "apply", "have", "apply", "unfold", "rw", "obtain", "exact"], "tactic_count": 17}
{"name": "AnalyticOn.hasFPowerSeriesOnBall", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.ConvergenceOnBall", "is_tactic_proof": true, "tactics": ["intro", "exact"], "tactic_count": 2}
{"name": "iteratedDeriv", "kind": "definition", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iteratedDerivWithin", "kind": "definition", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iteratedDerivWithin_univ", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.Defs", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "iteratedDerivWithin_eq_iteratedDeriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "iteratedDerivWithin_eq_iteratedFDerivWithin", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iteratedDerivWithin_eq_equiv_comp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.Defs", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "iteratedFDerivWithin_eq_equiv_comp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "iteratedFDerivWithin_apply_eq_iteratedDerivWithin_mul_prod", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.Defs", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "norm_iteratedFDerivWithin_eq_norm_iteratedDerivWithin", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "iteratedDerivWithin_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.Defs", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "iteratedDerivWithin_one", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.Defs", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "simp", "simp", "fderivWithin_zero_of_not_accPt"], "tactic_count": 5}
{"name": "contDiffOn_of_continuousOn_differentiableOn_deriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.Defs", "is_tactic_proof": true, "tactics": ["apply", "simpa", "simpa"], "tactic_count": 3}
{"name": "contDiffOn_of_differentiableOn_deriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.Defs", "is_tactic_proof": true, "tactics": ["apply", "simpa"], "tactic_count": 2}
{"name": "ContDiffOn.continuousOn_iteratedDerivWithin", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.Defs", "is_tactic_proof": true, "tactics": ["simpa", "h.continuousOn_iteratedFDerivWithin"], "tactic_count": 2}
{"name": "ContDiffWithinAt.differentiableWithinAt_iteratedDerivWithin", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.Defs", "is_tactic_proof": true, "tactics": ["simpa", "h.differentiableWithinAt_iteratedFDerivWithin"], "tactic_count": 2}
{"name": "ContDiffOn.differentiableOn_iteratedDerivWithin", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiffOn_iff_continuousOn_differentiableOn_deriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "contDiffOn_nat_iff_continuousOn_differentiableOn_deriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.Defs", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "iteratedDerivWithin_succ", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.Defs", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "iteratedFDerivWithin_eq_equiv_comp,", "change", "simp", "simp", "fderivWithin_zero_of_not_accPt"], "tactic_count": 7}
{"name": "iteratedDerivWithin_eq_iterate", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.Defs", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "exact"], "tactic_count": 5}
{"name": "iteratedDerivWithin_succ'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "iteratedDeriv_eq_iteratedFDeriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iteratedDeriv_eq_equiv_comp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.Defs", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "iteratedFDeriv_eq_equiv_comp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "iteratedFDeriv_apply_eq_iteratedDeriv_mul_prod", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "norm_iteratedFDeriv_eq_norm_iteratedDeriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "iteratedDeriv_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.Defs", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "iteratedDeriv_one", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.Defs", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "contDiff_iff_iteratedDeriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "contDiff_nat_iff_iteratedDeriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.Defs", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "contDiff_of_differentiable_iteratedDeriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.continuous_iteratedDeriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.continuous_iteratedDeriv'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.differentiable_iteratedDeriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.differentiable_iteratedDeriv'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iteratedDeriv_succ", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.Defs", "is_tactic_proof": true, "tactics": ["ext", "rw", "exact"], "tactic_count": 3}
{"name": "iteratedDeriv_eq_iterate", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.Defs", "is_tactic_proof": true, "tactics": ["ext", "rw", "convert", "simp"], "tactic_count": 4}
{"name": "iteratedDerivWithin_of_isOpen", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.Defs", "is_tactic_proof": true, "tactics": ["intro", "simp_rw"], "tactic_count": 2}
{"name": "iteratedDerivWithin_congr_right_of_isOpen", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.Defs", "is_tactic_proof": true, "tactics": ["intro", "rw"], "tactic_count": 2}
{"name": "iteratedDerivWithin_of_isOpen_eq_iterate", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.Defs", "is_tactic_proof": true, "tactics": ["apply", "rw", "exact"], "tactic_count": 3}
{"name": "iteratedDeriv_succ'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AnalyticAt.hasFPowerSeriesAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.Defs", "is_tactic_proof": true, "tactics": ["obtain", "convert", "obtain", "ext", "have", "simp", "smul_eq_mul,", "simp", "mul_eq_mul_left_iff]", "left", "rw", "norm_cast", "positivity"], "tactic_count": 13}
{"name": "iteratedDeriv_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.Defs", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "iteratedDerivWithin_const", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.Defs", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "iteratedDeriv_fun_const_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "iteratedDeriv_const_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "iteratedDerivWithin_fun_const_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "iteratedDerivWithin_const_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "iteratedDerivWithin_vcomp_eq_sum_orderedFinpartition", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.FaaDiBruno", "is_tactic_proof": true, "tactics": ["simp", "simp", "comp_def]"], "tactic_count": 3}
{"name": "iteratedDeriv_vcomp_eq_sum_orderedFinpartition", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.FaaDiBruno", "is_tactic_proof": true, "tactics": ["simp", "exact", "iteratedDerivWithin_vcomp_eq_sum_orderedFinpartition"], "tactic_count": 3}
{"name": "iteratedDerivWithin_vcomp_two", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.FaaDiBruno", "is_tactic_proof": true, "tactics": ["rw", "simp", "have", "simp"], "tactic_count": 4}
{"name": "iteratedDeriv_vcomp_two", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.FaaDiBruno", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "iteratedDerivWithin_vcomp_three", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.FaaDiBruno", "is_tactic_proof": true, "tactics": ["rw", "simp", "simp", "simp", "iteratedFDerivWithin_one_apply", "have", "congr"], "tactic_count": 7}
{"name": "iteratedDeriv_vcomp_three", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.FaaDiBruno", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "iteratedDerivWithin_scomp_eq_sum_orderedFinpartition", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.FaaDiBruno", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "iteratedDeriv_scomp_eq_sum_orderedFinpartition", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.FaaDiBruno", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "iteratedDerivWithin_scomp_two", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.FaaDiBruno", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "iteratedDeriv_scomp_two", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.FaaDiBruno", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "iteratedDerivWithin_scomp_three", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.FaaDiBruno", "is_tactic_proof": true, "tactics": ["rw", "simp", "iteratedFDerivWithin_apply_eq_iteratedDerivWithin_mul_prod]", "abel"], "tactic_count": 4}
{"name": "iteratedDeriv_scomp_three", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.FaaDiBruno", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "iteratedDerivWithin_comp_eq_sum_orderedFinpartition", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.FaaDiBruno", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "iteratedDeriv_comp_eq_sum_orderedFinpartition", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.FaaDiBruno", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "iteratedDerivWithin_comp_two", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.FaaDiBruno", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "iteratedDeriv_comp_two", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.FaaDiBruno", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "iteratedDerivWithin_comp_three", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.IteratedDeriv.FaaDiBruno", "is_tactic_proof": true, "tactics": ["rw", "simp", "ring"], "tactic_count": 3}
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{"name": "HasLineDerivAt", "kind": "definition", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LineDifferentiableWithinAt", "kind": "definition", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LineDifferentiableAt", "kind": "definition", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lineDerivWithin", "kind": "definition", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lineDeriv", "kind": "definition", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasLineDerivWithinAt.mono", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasLineDerivAt.hasLineDerivWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasLineDerivWithinAt.lineDifferentiableWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasLineDerivAt.lineDifferentiableAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LineDifferentiableWithinAt.hasLineDerivWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LineDifferentiableAt.hasLineDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasLineDerivWithinAt_univ", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "lineDerivWithin_zero_of_not_lineDifferentiableWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lineDeriv_zero_of_not_lineDifferentiableAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasLineDerivAt_iff_isLittleO_nhds_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HasLineDerivAt.unique", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasLineDerivAt.lineDeriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "lineDifferentiableWithinAt_univ", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LineDifferentiableAt.lineDifferentiableWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lineDerivWithin_univ", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LineDifferentiableWithinAt.mono", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasLineDerivWithinAt.congr_mono", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasLineDerivWithinAt.congr", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasLineDerivWithinAt.congr'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LineDifferentiableWithinAt.congr_mono", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LineDifferentiableWithinAt.congr", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lineDerivWithin_congr", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lineDerivWithin_congr'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasLineDerivAt_iff_tendsto_slope_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HasLineDerivAt.tendsto_slope_zero_right", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasLineDerivAt.tendsto_slope_zero_left", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasLineDerivWithinAt.hasLineDerivAt'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasLineDerivWithinAt.mono_of_mem_nhdsWithin", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": true, "tactics": ["apply", "apply", "apply"], "tactic_count": 3}
{"name": "HasLineDerivWithinAt.hasLineDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LineDifferentiableWithinAt.lineDifferentiableAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivWithinAt.hasLineDerivWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": true, "tactics": ["let", "rw", "have", "simp", "exact"], "tactic_count": 5}
{"name": "DifferentiableWithinAt.lineDifferentiableWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivAt.hasLineDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "DifferentiableAt.lineDifferentiableAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableAt.lineDeriv_eq_fderiv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LineDifferentiableWithinAt.mono_of_mem_nhdsWithin", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lineDerivWithin_of_mem_nhds", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": true, "tactics": ["apply", "apply", "fun_prop"], "tactic_count": 3}
{"name": "lineDerivWithin_of_isOpen", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasLineDerivWithinAt_congr_set", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": true, "tactics": ["apply", "let", "have", "have", "exact"], "tactic_count": 5}
{"name": "lineDifferentiableWithinAt_congr_set", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lineDerivWithin_congr_set", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": true, "tactics": ["apply", "let", "have", "have", "exact"], "tactic_count": 5}
{"name": "Filter.EventuallyEq.hasLineDerivAt_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": true, "tactics": ["apply", "let", "have", "have", "exact"], "tactic_count": 5}
{"name": "Filter.EventuallyEq.lineDifferentiableAt_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.hasLineDerivWithinAt_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": true, "tactics": ["apply", "have", "exact", "simpa"], "tactic_count": 4}
{"name": "Filter.EventuallyEq.hasLineDerivWithinAt_iff_of_mem", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.lineDifferentiableWithinAt_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.lineDifferentiableWithinAt_iff_of_mem", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasLineDerivWithinAt.congr_of_eventuallyEq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasLineDerivAt.congr_of_eventuallyEq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LineDifferentiableWithinAt.congr_of_eventuallyEq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LineDifferentiableAt.congr_of_eventuallyEq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.lineDerivWithin_eq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": true, "tactics": ["apply", "have", "exact"], "tactic_count": 3}
{"name": "Filter.EventuallyEq.lineDerivWithin_eq_nhds", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.lineDeriv_eq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HasLineDerivAt.le_of_lip'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": true, "tactics": ["apply", "have", "have", "filter_upwards", "simp", "simpa"], "tactic_count": 6}
{"name": "HasLineDerivAt.le_of_lipschitzOn", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": true, "tactics": ["refine", "filter_upwards"], "tactic_count": 2}
{"name": "HasLineDerivAt.le_of_lipschitz", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "norm_lineDeriv_le_of_lip'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": true, "tactics": ["apply", "have", "have", "filter_upwards", "simp", "simpa"], "tactic_count": 6}
{"name": "norm_lineDeriv_le_of_lipschitzOn", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": true, "tactics": ["refine", "filter_upwards"], "tactic_count": 2}
{"name": "norm_lineDeriv_le_of_lipschitz", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasLineDerivWithinAt_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "hasLineDerivAt_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "lineDifferentiableWithinAt_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lineDifferentiableAt_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lineDeriv_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasLineDerivAt.of_comp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "LineDifferentiableAt.of_comp", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasLineDerivWithinAt.smul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": true, "tactics": ["simp", "let", "let", "have", "have", "have", "simp", "convert", "ext", "simp"], "tactic_count": 10}
{"name": "hasLineDerivWithinAt_smul_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasLineDerivAt.smul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "hasLineDerivAt_smul_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LineDifferentiableWithinAt.smul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lineDifferentiableWithinAt_smul_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LineDifferentiableAt.smul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lineDifferentiableAt_smul_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lineDeriv_smul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simp", "by_cases", "exact", "have", "simp"], "tactic_count": 6}
{"name": "lineDeriv_neg", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "integral_bilinear_hasLineDerivAt_right_eq_neg_left_of_integrable_aux1", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.IntegrationByParts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "integral_bilinear_hasLineDerivAt_right_eq_neg_left_of_integrable_aux2", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.IntegrationByParts", "is_tactic_proof": true, "tactics": ["let", "have", "have", "have", "have", "rw", "simp"], "tactic_count": 7}
{"name": "integral_bilinear_hasLineDerivAt_right_eq_neg_left_of_integrable", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.IntegrationByParts", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "rcases", "have", "have", "simp", "have", "let", "let", "obtain", "have", "have", "obtain", "apply", "simpa", "simp", "exact", "let", "suffices", "have", "have", "simpa", "have", "apply", "simpa", "simpa", "simpa", "intro", "have", "specialize", "rw", "convert", "simp", "simp", "intro", "have", "specialize", "rw", "convert", "simp", "simp"], "tactic_count": 41}
{"name": "integral_bilinear_hasFDerivAt_right_eq_neg_left_of_integrable", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.IntegrationByParts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "integral_bilinear_fderiv_right_eq_neg_left_of_integrable", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.IntegrationByParts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "integral_smul_fderiv_eq_neg_fderiv_smul_of_integrable", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.IntegrationByParts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "integral_mul_fderiv_eq_neg_fderiv_mul_of_integrable", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.IntegrationByParts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurableSet_lineDifferentiableAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Measurable", "is_tactic_proof": true, "tactics": ["borelize", "let", "have", "exact"], "tactic_count": 4}
{"name": "measurable_lineDeriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Measurable", "is_tactic_proof": true, "tactics": ["borelize", "let", "have", "exact"], "tactic_count": 4}
{"name": "stronglyMeasurable_lineDeriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Measurable", "is_tactic_proof": true, "tactics": ["borelize", "let", "have", "exact"], "tactic_count": 4}
{"name": "aemeasurable_lineDeriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Measurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "aestronglyMeasurable_lineDeriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Measurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurableSet_lineDifferentiableAt_uncurry", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Measurable", "is_tactic_proof": true, "tactics": ["borelize", "let", "have", "hf.comp", "have", "measurableSet_of_differentiableAt_with_param", "exact"], "tactic_count": 7}
{"name": "measurable_lineDeriv_uncurry", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Measurable", "is_tactic_proof": true, "tactics": ["borelize", "let", "have", "hf.comp", "exact"], "tactic_count": 5}
{"name": "stronglyMeasurable_lineDeriv_uncurry", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Measurable", "is_tactic_proof": true, "tactics": ["borelize", "let", "have", "hf.comp", "exact"], "tactic_count": 5}
{"name": "aemeasurable_lineDeriv_uncurry", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Measurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "aestronglyMeasurable_lineDeriv_uncurry", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.Measurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.hasLineDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.QuadraticMap", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "QuadraticMap.lineDifferentiableAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.QuadraticMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.lineDeriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LineDeriv.QuadraticMap", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "posTangentConeAt_mono", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LocalExtr.Basic", "is_tactic_proof": true, "tactics": ["intro", "exact"], "tactic_count": 2}
{"name": "mem_posTangentConeAt_of_frequently_mem", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LocalExtr.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply", "exact", "simp"], "tactic_count": 4}
{"name": "sub_mem_posTangentConeAt_of_segment_subset", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LocalExtr.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_posTangentConeAt_of_segment_subset", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LocalExtr.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "posTangentConeAt_univ", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LocalExtr.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMaxOn.hasFDerivWithinAt_nonpos", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LocalExtr.Basic", "is_tactic_proof": true, "tactics": ["rcases", "suffices", "replace", "rw", "refine", "exact"], "tactic_count": 6}
{"name": "IsLocalMaxOn.fderivWithin_nonpos", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LocalExtr.Basic", "is_tactic_proof": true, "tactics": ["classical", "exact"], "tactic_count": 2}
{"name": "IsLocalMaxOn.hasFDerivWithinAt_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LocalExtr.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMaxOn.fderivWithin_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.LocalExtr.Basic", "is_tactic_proof": true, "tactics": ["classical", "exact"], "tactic_count": 2}
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{"name": "UniqueDiffWithinAt.mono", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.Basic", "is_tactic_proof": true, "tactics": ["rw", "grw", "exact"], "tactic_count": 3}
{"name": "UniqueDiffWithinAt.closure", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniqueDiffWithinAt.mono_nhds", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.Basic", "is_tactic_proof": true, "tactics": ["simp", "rw", "exact"], "tactic_count": 3}
{"name": "uniqueDiffWithinAt_congr", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniqueDiffWithinAt_inter", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniqueDiffWithinAt.inter", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniqueDiffOn.inter", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniqueDiffWithinAt_inter'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniqueDiffWithinAt.inter'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zero_mem_tangentConeAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply", "exact", "simpa", "simp", "exact"], "tactic_count": 6}
{"name": "zero_mem_tangentConeAt_iff", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tangentConeAt_subset_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.Basic", "is_tactic_proof": true, "tactics": ["intro", "rcases", "have", "have", "simp", "simpa", "have", "simpa"], "tactic_count": 8}
{"name": "AccPt.of_mem_tangentConeAt_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.Basic", "is_tactic_proof": true, "tactics": ["contrapose", "exact"], "tactic_count": 2}
{"name": "UniqueDiffWithinAt.accPt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.Basic", "is_tactic_proof": true, "tactics": ["by_contra", "have", "simp"], "tactic_count": 3}
{"name": "mem_tangentConeAt_of_add_smul_mem", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "simpa", "refine", "simp_all"], "tactic_count": 5}
{"name": "tangentConeAt_univ", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "tangentConeAt_of_mem_nhds", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "uniqueDiffOn_empty", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniqueDiffWithinAt.congr_pt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniqueDiffWithinAt.mono_field", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.Basic", "is_tactic_proof": true, "tactics": ["simp_all", "apply", "trans"], "tactic_count": 3}
{"name": "UniqueDiffOn.mono_field", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniqueDiffWithinAt_closure", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "UniqueDiffWithinAt.mono_closure", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniqueDiffWithinAt_univ", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "uniqueDiffOn_univ", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniqueDiffWithinAt_of_mem_nhds", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsOpen.uniqueDiffWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.uniqueDiffOn", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "definition._@.Mathlib.Analysis.Calculus.TangentCone.Defs.1253705803._hygCtx._hyg.2", "kind": "definition", "module": "Mathlib.Analysis.Calculus.TangentCone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "wrapped._@.Mathlib.Analysis.Calculus.TangentCone.Defs.1253705803._hygCtx._hyg.2", "kind": "opaque", "module": "Mathlib.Analysis.Calculus.TangentCone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tangentConeAt", "kind": "definition", "module": "Mathlib.Analysis.Calculus.TangentCone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tangentConeAt_def", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.Defs", "is_tactic_proof": true, "tactics": ["intros", "delta", "rw", "rfl"], "tactic_count": 4}
{"name": "mem_tangentConeAt_of_frequently", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.Defs", "is_tactic_proof": false, "tactics": ["suffices", "rw", "rw", "exact", "rw", "refine", "exact", "simp"], "tactic_count": 8}
{"name": "mem_tangentConeAt_of_seq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_fun_of_mem_tangentConeAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.Defs", "is_tactic_proof": true, "tactics": ["rw", "refine", "refine", "gcongr", "apply", "refine", "rw", "filter_upwards", "simp", "exact"], "tactic_count": 10}
{"name": "posTangentConeAt", "kind": "abbrev", "module": "Mathlib.Analysis.Calculus.TangentCone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniqueDiffOn", "kind": "definition", "module": "Mathlib.Analysis.Calculus.TangentCone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniqueDiffOn.uniqueDiffWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tangentConeAt_eq_univ", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.DimOne", "is_tactic_proof": true, "tactics": ["refine", "apply", "exact", "simpa", "apply", "refine", "have", "simp"], "tactic_count": 8}
{"name": "uniqueDiffWithinAt_iff_accPt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.DimOne", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mapsTo_tangentConeAt_pi", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.Pi", "is_tactic_proof": true, "tactics": ["rw", "intro", "rcases", "apply", "rw", "intro", "rcases", "refine", "rw", "intro", "rcases", "rw", "intro", "rcases"], "tactic_count": 14}
{"name": "UniqueDiffWithinAt.univ_pi", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.Pi", "is_tactic_proof": true, "tactics": ["classical", "simp", "refine", "simp", "gcongr", "refine", "gcongr", "exact"], "tactic_count": 8}
{"name": "UniqueDiffOn.univ_pi", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniqueDiffWithinAt.pi", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.Pi", "is_tactic_proof": true, "tactics": ["classical", "rw", "refine", "by_cases"], "tactic_count": 4}
{"name": "UniqueDiffOn.pi", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "subset_tangentConeAt_prod_left", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.Prod", "is_tactic_proof": true, "tactics": ["rw", "rintro", "rcases", "refine", "mem_tangentConeAt_of_seq", "simpa"], "tactic_count": 6}
{"name": "subset_tangentConeAt_prod_right", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.Prod", "is_tactic_proof": true, "tactics": ["rw", "rintro", "rcases", "refine", "mem_tangentConeAt_of_seq", "simpa"], "tactic_count": 6}
{"name": "UniqueDiffWithinAt.prod", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.Prod", "is_tactic_proof": true, "tactics": ["rw", "rw", "refine", "have", "rw", "exact"], "tactic_count": 6}
{"name": "UniqueDiffOn.prod", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tangentConeAt_nonempty_of_properSpace", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.ProperSpace", "is_tactic_proof": true, "tactics": ["of", "a", "the", "obtain", "exists_seq_strictAnti_tendsto", "have", "choose", "choose", "let", "have", "let", "have", "choose", "obtain", "apply", "exact", "simp", "refine", "push", "contrapose", "simp", "norm_pos_iff,", "contrapose", "simp", "apply", "refine", "exact", "exact", "exact"], "tactic_count": 29}
{"name": "sub_mem_posTangentConeAt_of_openSegment_subset", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.Real", "is_tactic_proof": true, "tactics": ["refine", "filter_upwards", "apply", "rw", "use", "simp"], "tactic_count": 6}
{"name": "mem_tangentConeAt_of_openSegment_subset", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_tangentConeAt_of_segment_subset", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Convex.span_tangentConeAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.Real", "is_tactic_proof": true, "tactics": ["rcases", "suffices", "apply", "exact", "rw", "replace", "apply", "rintro", "refine", "exact"], "tactic_count": 10}
{"name": "uniqueDiffWithinAt_convex", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.Real", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "uniqueDiffOn_convex", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniqueDiffOn_Ici", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniqueDiffOn_Iic", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniqueDiffOn_Ioi", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniqueDiffOn_Iio", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniqueDiffOn_Icc", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniqueDiffOn_Ico", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniqueDiffOn_Ioc", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniqueDiffOn_Ioo", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniqueDiffOn_Icc_zero_one", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniqueDiffWithinAt_Ioo", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniqueDiffWithinAt_Ioi", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniqueDiffWithinAt_Iio", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniqueDiffWithinAt_Ici", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniqueDiffWithinAt_Iic", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_tangentConeAt_iff_exists_seq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.Seq", "is_tactic_proof": true, "tactics": ["constructor", "intro", "simp", "rcases", "simp", "exact", "rintro", "exact"], "tactic_count": 8}
{"name": "tangentConeAt.lim_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.Seq", "is_tactic_proof": false, "tactics": ["have", "rw", "simpa"], "tactic_count": 3}
{"name": "mem_tangentConeAt_of_pow_smul", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.Seq", "is_tactic_proof": false, "tactics": ["refine", "mem_tangentConeAt_of_add_smul_mem", "hs", "simp"], "tactic_count": 4}
{"name": "mem_tangentConeAt_iff_exists_seq_norm_tendsto_atTop", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.TangentCone.Seq", "is_tactic_proof": true, "tactics": ["constructor", "rcases", "rw", "intro", "obtain", "have", "rw", "rcases", "use", "simp_all", "choose", "refine", "simp", "exact", "tendsto_cd", "rw", "refine", "rw", "suffices", "rw", "refine", "grw", "simp", "norm_num1", "rw", "rintro", "refine", "replace", "have", "replace", "simp", "refine", "rw", "simpa", "rintro", "exact"], "tactic_count": 36}
{"name": "taylorCoeffWithin", "kind": "definition", "module": "Mathlib.Analysis.Calculus.Taylor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "taylorWithin", "kind": "definition", "module": "Mathlib.Analysis.Calculus.Taylor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "taylorWithinEval", "kind": "definition", "module": "Mathlib.Analysis.Calculus.Taylor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "taylorWithin_succ", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Taylor", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "taylorWithinEval_succ", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Taylor", "is_tactic_proof": true, "tactics": ["simp_rw", "congr", "simp", "dsimp", "rw"], "tactic_count": 5}
{"name": "taylor_within_zero_eval", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Taylor", "is_tactic_proof": true, "tactics": ["dsimp", "dsimp", "dsimp", "simp"], "tactic_count": 4}
{"name": "taylorWithinEval_self", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Taylor", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "taylor_within_apply", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Taylor", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "simp"], "tactic_count": 5}
{"name": "continuousOn_taylorWithinEval", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Taylor", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "refine", "rw", "simp", "refine", "simp"], "tactic_count": 7}
{"name": "monomial_has_deriv_aux", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Taylor", "is_tactic_proof": true, "tactics": ["simp_rw", "rw", "convert", "simp"], "tactic_count": 4}
{"name": "hasDerivWithinAt_taylor_coeff_within", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Taylor", "is_tactic_proof": false, "tactics": ["replace", "convert", "rw", "exact", "have", "have", "rw", "exact", "convert", "field_simp", "module"], "tactic_count": 11}
{"name": "hasDerivWithinAt_taylorWithinEval", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Taylor", "is_tactic_proof": false, "tactics": ["have", "induction", "zero", "simp", "one_smul]", "simp", "rw", "exact", "succ", "simp_rw", "simp", "have", "have", "specialize", "convert", "exact"], "tactic_count": 16}
{"name": "taylorWithinEval_hasDerivAt_Ioo", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Taylor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivWithinAt_taylorWithinEval_at_Icc", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Taylor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivAt_taylorWithinEval_succ", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Taylor", "is_tactic_proof": true, "tactics": ["change", "simp_rw", "have", "apply", "rw", "apply", "intro", "rw", "congr", "simp"], "tactic_count": 10}
{"name": "taylor_isLittleO", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Taylor", "is_tactic_proof": true, "tactics": ["induction", "zero", "simp", "rw", "exact", "succ", "rcases", "simp", "replace", "simp", "convert", "f", "simp", "intro", "refine", "exact"], "tactic_count": 16}
{"name": "taylor_tendsto", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Taylor", "is_tactic_proof": true, "tactics": ["have", "rw", "rw", "simpa", "simp", "intro", "rw", "simp"], "tactic_count": 8}
{"name": "Real.taylor_tendsto", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Taylor", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "taylor_mean_remainder", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Taylor", "is_tactic_proof": true, "tactics": ["rcases", "exists_ratio_hasDerivAt_eq_ratio_slope", "use", "simp", "rw", "rw", "simp"], "tactic_count": 7}
{"name": "taylor_mean_remainder_lagrange", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Taylor", "is_tactic_proof": true, "tactics": ["have", "have", "intro", "refine", "rw", "rw", "exact", "have", "mul_ne_zero", "rcases", "use", "simp", "rw", "simp"], "tactic_count": 14}
{"name": "taylor_mean_remainder_lagrange_iteratedDeriv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Taylor", "is_tactic_proof": true, "tactics": ["have", "have", "refine", "norm_cast", "simp", "obtain", "use", "rw", "iteratedFDerivWithin_eq_iteratedFDeriv", "exact"], "tactic_count": 10}
{"name": "taylor_mean_remainder_cauchy", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Taylor", "is_tactic_proof": true, "tactics": ["have", "have", "hasDerivAt_id", "rcases", "use", "rw", "simp"], "tactic_count": 7}
{"name": "taylor_mean_remainder_bound", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Taylor", "is_tactic_proof": true, "tactics": ["rcases", "rw", "simp", "have", "hf.differentiableOn_iteratedDerivWithin", "have", "rintro", "rw", "gcongr", "rw", "gcongr", "exact", "exact", "hC", "have", "intro", "have", "exact", "have", "simp", "refine", "this.trans_eq", "rw", "ring"], "tactic_count": 24}
{"name": "exists_taylor_mean_remainder_bound", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.Taylor", "is_tactic_proof": true, "tactics": ["rcases", "refine", "have", "simp", "let", "use", "intro", "rw", "refine", "exact"], "tactic_count": 10}
{"name": "uniformCauchySeqOnFilter_of_fderiv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.UniformLimitsDeriv", "is_tactic_proof": true, "tactics": ["letI", "letI", "rw", "suffices", "have", "rw", "exact", "constructor", "rw", "intro", "have", "obtain", "obtain", "let", "have", "have", "hR", "have", "intro", "rw", "exact", "have", "intro", "exact", "refine", "eventually_prod_iff.mpr", "simp", "refine", "exact", "refine", "obtain", "exact", "eventually_prod_iff.mpr", "eventually_prod_iff.mpr"], "tactic_count": 34}
{"name": "uniformCauchySeqOn_ball_of_fderiv", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.UniformLimitsDeriv", "is_tactic_proof": true, "tactics": ["letI", "letI", "have", "rcases", "simp", "eventually_const,", "rw", "suffices", "have", "rw", "refine", "filter_upwards", "constructor", "rw", "intro", "obtain", "simp_rw", "exact", "apply", "intro", "simp_rw", "have", "refine", "have", "mul_lt_mul", "exact", "refine", "obtain", "rw", "refine", "intro", "rw", "exact"], "tactic_count": 33}
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{"name": "UniformCauchySeqOnFilter.one_smulRight", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.UniformLimitsDeriv", "is_tactic_proof": true, "tactics": ["rw", "intro", "obtain", "apply", "intro", "refine", "simp", "refine", "intro", "simp", "rw", "gcongr"], "tactic_count": 12}
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{"name": "VectorField.lieBracket", "kind": "definition", "module": "Mathlib.Analysis.Calculus.VectorField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorField.lieBracketWithin", "kind": "definition", "module": "Mathlib.Analysis.Calculus.VectorField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorField.lieBracket_eq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.VectorField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorField.lieBracketWithin_eq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.VectorField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorField.lieBracketWithin_univ", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.VectorField", "is_tactic_proof": true, "tactics": ["ext1", "simp"], "tactic_count": 2}
{"name": "VectorField.lieBracketWithin_eq_zero_of_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.VectorField", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "VectorField.lieBracket_eq_zero_of_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.VectorField", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "VectorField.lieBracketWithin_swap", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.VectorField", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "VectorField.lieBracket_swap", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.VectorField", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "VectorField.lieBracketWithin_self", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.VectorField", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "VectorField.lieBracket_self", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.VectorField", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "VectorField.lieBracketWithin_const_smul_left", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.VectorField", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "VectorField.lieBracket_const_smul_left", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.VectorField", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "VectorField.lieBracketWithin_const_smul_right", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.VectorField", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "VectorField.lieBracketWithin_add_left", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.VectorField", "is_tactic_proof": true, "tactics": ["simp", "rw", "abel"], "tactic_count": 3}
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{"name": "VectorField.lieBracketWithin_zero_left", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.VectorField", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "VectorField.lieBracketWithin_zero_right", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.VectorField", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
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{"name": "VectorField.fderivWithin_apply_lieBracket_of_isSymmSndFDerivWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.VectorField", "is_tactic_proof": false, "tactics": ["have", "have", "rw", "simp"], "tactic_count": 4}
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{"name": "VectorField.fderivWithin_apply_lieBracket", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.VectorField", "is_tactic_proof": true, "tactics": ["apply", "exacts"], "tactic_count": 2}
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{"name": "ContDiffWithinAt.lieBracketWithin_vectorField", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.VectorField", "is_tactic_proof": true, "tactics": ["apply", "exact", "exact"], "tactic_count": 3}
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{"name": "ContDiffOn.lieBracketWithin_vectorField", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.VectorField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.lieBracket_vectorField", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.VectorField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorField.lieBracketWithin_of_mem_nhdsWithin", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.VectorField", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "VectorField.lieBracketWithin_subset", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.VectorField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorField.lieBracketWithin_inter", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.VectorField", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "VectorField.lieBracketWithin_of_mem_nhds", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.VectorField", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "VectorField.lieBracketWithin_of_isOpen", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.VectorField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorField.lieBracketWithin_eq_lieBracket", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.VectorField", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "VectorField.lieBracketWithin_congr_set'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.VectorField", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "VectorField.lieBracketWithin_congr_set", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.VectorField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorField.lieBracketWithin_eventually_congr_set'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.VectorField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorField.lieBracketWithin_eventually_congr_set", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.VectorField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableWithinAt.lieBracketWithin_congr_mono", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.VectorField", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.EventuallyEq.lieBracketWithin_vectorField_eq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.VectorField", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.EventuallyEq.lieBracketWithin_vectorField_eq_of_mem", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.VectorField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.lieBracketWithin_vectorField'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.VectorField", "is_tactic_proof": true, "tactics": ["filter_upwards", "simp"], "tactic_count": 2}
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{"name": "Filter.EventuallyEq.lieBracketWithin_vectorField_eq_of_insert", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.VectorField", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "Filter.EventuallyEq.lieBracketWithin_vectorField_eq_nhds", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.VectorField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorField.lieBracketWithin_congr", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.VectorField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorField.lieBracketWithin_congr'", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.VectorField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.lieBracket_vectorField_eq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.VectorField", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.EventuallyEq.lieBracket_vectorField", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.VectorField", "is_tactic_proof": true, "tactics": ["filter_upwards", "exact"], "tactic_count": 2}
{"name": "VectorField.leibniz_identity_lieBracketWithin_of_isSymmSndFDerivWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.VectorField", "is_tactic_proof": true, "tactics": ["simp", "have", "have", "this.differentiableWithinAt", "have", "fderivWithin", "refine", "exact", "rw", "rw", "rw", "rw", "simp", "abel"], "tactic_count": 14}
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{"name": "VectorField.pullback", "kind": "definition", "module": "Mathlib.Analysis.Calculus.VectorField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorField.pullbackWithin", "kind": "definition", "module": "Mathlib.Analysis.Calculus.VectorField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorField.pullbackWithin_eq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.VectorField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorField.pullback_eq_of_fderiv_eq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.VectorField", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "VectorField.pullback_eq_of_not_isInvertible", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.VectorField", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "VectorField.pullbackWithin_eq_of_not_isInvertible", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.VectorField", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "VectorField.pullbackWithin_eq_of_fderivWithin_eq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.VectorField", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "VectorField.pullbackWithin_univ", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.VectorField", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "VectorField.fderiv_pullback", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.VectorField", "is_tactic_proof": true, "tactics": ["rcases", "simp"], "tactic_count": 2}
{"name": "VectorField.fderivWithin_pullbackWithin", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.VectorField", "is_tactic_proof": true, "tactics": ["rcases", "simp"], "tactic_count": 2}
{"name": "exists_continuousLinearEquiv_fderivWithin_symm_eq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.VectorField", "is_tactic_proof": true, "tactics": ["classical", "rcases", "let", "have", "have", "rw", "exact", "have", "exact", "let", "have", "filter_upwards", "simpa", "have", "have", "have", "apply", "have", "have", "convert", "simp", "refine", "have", "simp", "have", "fderivWithin", "have", "rw", "simpa", "have", "rw", "simp"], "tactic_count": 32}
{"name": "VectorField.DifferentiableWithinAt.pullbackWithin", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.VectorField", "is_tactic_proof": true, "tactics": ["rcases", "simp", "have", "apply", "exact", "exact", "apply", "filter_upwards", "have", "simp"], "tactic_count": 10}
{"name": "exists_continuousLinearEquiv_fderiv_symm_eq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.VectorField", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
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{"name": "VectorField.pullbackWithin_lieBracketWithin_of_isSymmSndFDerivWithinAt_of_eventuallyEq", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.VectorField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorField.pullback_lieBracket_of_isSymmSndFDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.VectorField", "is_tactic_proof": false, "tactics": ["simp", "exact", "pullbackWithin_lieBracketWithin_of_isSymmSndFDerivWithinAt"], "tactic_count": 3}
{"name": "VectorField.pullbackWithin_lieBracketWithin", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.VectorField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorField.pullback_lieBracket", "kind": "theorem", "module": "Mathlib.Analysis.Calculus.VectorField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.stolzSet", "kind": "definition", "module": "Mathlib.Analysis.Complex.AbelLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.stolzCone", "kind": "definition", "module": "Mathlib.Analysis.Complex.AbelLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.stolzSet_empty", "kind": "theorem", "module": "Mathlib.Analysis.Complex.AbelLimit", "is_tactic_proof": true, "tactics": ["ext", "rw", "intro", "calc"], "tactic_count": 4}
{"name": "Complex.nhdsWithin_lt_le_nhdsWithin_stolzSet", "kind": "theorem", "module": "Mathlib.Analysis.Complex.AbelLimit", "is_tactic_proof": true, "tactics": ["rw", "refine", "tendsto_map", "tendsto_nhdsWithin_of_tendsto_nhds_of_eventually_within", "simp", "refine", "push", "simp", "norm_of_nonneg", "exact"], "tactic_count": 10}
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{"name": "Complex.nhdsWithin_stolzCone_le_nhdsWithin_stolzSet", "kind": "theorem", "module": "Mathlib.Analysis.Complex.AbelLimit", "is_tactic_proof": true, "tactics": ["obtain", "use", "rw", "refine", "simp"], "tactic_count": 5}
{"name": "Complex.abel_aux", "kind": "theorem", "module": "Mathlib.Analysis.Complex.AbelLimit", "is_tactic_proof": true, "tactics": ["let", "have", "simp_rw", "range_eq_Ico,", "conv", "enter", "rw", "suffices", "simp_rw", "replace", "conv", "enter", "rw", "enter", "rw", "rwa", "rw", "apply", "simpa", "conv", "enter", "rw", "rw", "apply", "simp"], "tactic_count": 25}
{"name": "Complex.tendsto_tsum_powerSeries_nhdsWithin_stolzSet", "kind": "theorem", "module": "Mathlib.Analysis.Complex.AbelLimit", "is_tactic_proof": true, "tactics": ["rcases", "simp_rw", "let", "let", "have", "rw", "simp", "intro", "obtain", "hm", "let", "use", "intro", "have", "simp_rw", "obtain", "clear", "replace", "suffices", "calc", "calc", "gcongr", "simp_rw", "have", "calc", "gcongr", "gcongr", "have", "calc", "gcongr", "have", "rw", "exact", "gcongr", "exact", "rw", "convert", "linarith"], "tactic_count": 38}
{"name": "Complex.tendsto_tsum_powerSeries_nhdsWithin_stolzCone", "kind": "theorem", "module": "Mathlib.Analysis.Complex.AbelLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.tendsto_tsum_powerSeries_nhdsWithin_lt", "kind": "theorem", "module": "Mathlib.Analysis.Complex.AbelLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.tendsto_tsum_powerSeries_nhdsWithin_lt", "kind": "theorem", "module": "Mathlib.Analysis.Complex.AbelLimit", "is_tactic_proof": true, "tactics": ["have", "replace", "rw", "push_cast", "replace", "rw", "rw", "convert", "simp_rw", "norm_cast"], "tactic_count": 10}
{"name": "_private.Mathlib.Analysis.Complex.AbsMax.0.term_̂", "kind": "definition", "module": "Mathlib.Analysis.Complex.AbsMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.Complex.AbsMax.0._aux_Mathlib_Analysis_Complex_AbsMax___macroRules__private_Mathlib_Analysis_Complex_AbsMax_0_term_̂_1", "kind": "definition", "module": "Mathlib.Analysis.Complex.AbsMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.Complex.AbsMax.0._aux_Mathlib_Analysis_Complex_AbsMax___unexpand_UniformSpace_Completion_1", "kind": "definition", "module": "Mathlib.Analysis.Complex.AbsMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.norm_max_aux₁", "kind": "theorem", "module": "Mathlib.Analysis.Complex.AbsMax", "is_tactic_proof": true, "tactics": ["set", "have", "refine", "rintro", "have", "dist_pos.2", "suffices", "refine", "have", "hd.circleIntegral_sub_inv_smul", "simp", "suffices", "rwa", "have", "refine", "show", "refine", "exact", "show", "rintro", "rw", "exact", "show", "rw", "exact"], "tactic_count": 25}
{"name": "Complex.norm_max_aux₂", "kind": "theorem", "module": "Mathlib.Analysis.Complex.AbsMax", "is_tactic_proof": true, "tactics": ["set", "have", "replace", "simpa", "simpa"], "tactic_count": 5}
{"name": "Complex.norm_max_aux₃", "kind": "theorem", "module": "Mathlib.Analysis.Complex.AbsMax", "is_tactic_proof": true, "tactics": ["subst", "rcases", "rw", "exact"], "tactic_count": 4}
{"name": "Complex.norm_eqOn_closedBall_of_isMaxOn", "kind": "theorem", "module": "Mathlib.Analysis.Complex.AbsMax", "is_tactic_proof": true, "tactics": ["intro", "rw", "rcases", "set", "have", "suffices", "have", "have", "refine", "simpa", "exact"], "tactic_count": 11}
{"name": "Complex.norm_eq_norm_of_isMaxOn_of_ball_subset", "kind": "theorem", "module": "Mathlib.Analysis.Complex.AbsMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.norm_eventually_eq_of_isLocalMax", "kind": "theorem", "module": "Mathlib.Analysis.Complex.AbsMax", "is_tactic_proof": true, "tactics": ["rcases", "exact", "nhds_basis_closedBall.eventually_iff.2", "norm_eqOn_closedBall_of_isMaxOn"], "tactic_count": 4}
{"name": "Complex.isOpen_setOf_mem_nhds_and_isMaxOn_norm", "kind": "theorem", "module": "Mathlib.Analysis.Complex.AbsMax", "is_tactic_proof": true, "tactics": ["refine", "replace", "exact"], "tactic_count": 3}
{"name": "Complex.norm_eqOn_of_isPreconnected_of_isMaxOn", "kind": "theorem", "module": "Mathlib.Analysis.Complex.AbsMax", "is_tactic_proof": true, "tactics": ["set", "have", "suffices", "have", "simpa", "have", "set", "have", "have", "have", "exact"], "tactic_count": 11}
{"name": "Complex.norm_eqOn_closure_of_isPreconnected_of_isMaxOn", "kind": "theorem", "module": "Mathlib.Analysis.Complex.AbsMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.eqOn_of_isPreconnected_of_isMaxOn_norm", "kind": "theorem", "module": "Mathlib.Analysis.Complex.AbsMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.eqOn_closure_of_isPreconnected_of_isMaxOn_norm", "kind": "theorem", "module": "Mathlib.Analysis.Complex.AbsMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.eq_of_isMaxOn_of_ball_subset", "kind": "theorem", "module": "Mathlib.Analysis.Complex.AbsMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.eqOn_closedBall_of_isMaxOn_norm", "kind": "theorem", "module": "Mathlib.Analysis.Complex.AbsMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.eq_const_of_exists_max", "kind": "theorem", "module": "Mathlib.Analysis.Complex.AbsMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.eq_const_of_exists_le", "kind": "theorem", "module": "Mathlib.Analysis.Complex.AbsMax", "is_tactic_proof": false, "tactics": ["obtain", "isCompact_closedBall", "suffices", "apply", "obtain", "exact"], "tactic_count": 6}
{"name": "Complex.eventually_eq_of_isLocalMax_norm", "kind": "theorem", "module": "Mathlib.Analysis.Complex.AbsMax", "is_tactic_proof": true, "tactics": ["rcases", "exact", "nhds_basis_closedBall.eventually_iff.2", "eqOn_closedBall_of_isMaxOn_norm"], "tactic_count": 4}
{"name": "Complex.eventually_eq_or_eq_zero_of_isLocalMin_norm", "kind": "theorem", "module": "Mathlib.Analysis.Complex.AbsMax", "is_tactic_proof": true, "tactics": ["refine", "have", "have", "have", "have", "filter_upwards"], "tactic_count": 6}
{"name": "Complex.exists_mem_frontier_isMaxOn_norm", "kind": "theorem", "module": "Mathlib.Analysis.Complex.AbsMax", "is_tactic_proof": true, "tactics": ["have", "obtain", "hc.exists_isMaxOn", "rw", "rcases", "have", "rcases", "refine", "refine", "rw", "exact"], "tactic_count": 11}
{"name": "Complex.norm_le_of_forall_mem_frontier_norm_le", "kind": "theorem", "module": "Mathlib.Analysis.Complex.AbsMax", "is_tactic_proof": true, "tactics": ["rw", "rcases", "rcases", "set", "have", "have", "replace", "have", "rcases", "calc"], "tactic_count": 10}
{"name": "Complex.eqOn_closure_of_eqOn_frontier", "kind": "theorem", "module": "Mathlib.Analysis.Complex.AbsMax", "is_tactic_proof": true, "tactics": ["suffices", "refine", "simp"], "tactic_count": 3}
{"name": "Complex.eqOn_of_eqOn_frontier", "kind": "theorem", "module": "Mathlib.Analysis.Complex.AbsMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.angle_eq_abs_arg", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Angle", "is_tactic_proof": true, "tactics": ["refine", "rw", "simp", "field"], "tactic_count": 4}
{"name": "Complex.angle_one_left", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Angle", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.angle_one_right", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Angle", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.angle_mul_left", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Angle", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "Complex.angle_mul_right", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Angle", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.angle_div_left_eq_angle_mul_right", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Angle", "is_tactic_proof": true, "tactics": ["obtain", "simp", "rw"], "tactic_count": 3}
{"name": "Complex.angle_div_right_eq_angle_mul_left", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Angle", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.angle_exp_exp", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Angle", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Complex.angle_exp_one", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Angle", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Complex.norm_sub_mem_Icc_angle", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Angle", "is_tactic_proof": true, "tactics": ["wlog", "have", "rwa", "rintro", "simp", "subst", "rw", "obtain", "rw", "norm_cast", "rw", "refine", "rw", "calc", "rw", "calc", "convert", "ring"], "tactic_count": 18}
{"name": "Complex.norm_sub_le_angle", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Angle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.mul_angle_le_norm_sub", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Angle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.angle_le_mul_norm_sub", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Angle", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.sameRay_iff", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Arg", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rcases", "simp", "simp", "simp", "rw"], "tactic_count": 7}
{"name": "Complex.sameRay_iff_arg_div_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Arg", "is_tactic_proof": true, "tactics": ["rw", "by_cases", "by_cases", "simp"], "tactic_count": 4}
{"name": "Complex.norm_add_eq_iff", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Arg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.norm_sub_eq_iff", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Arg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.sameRay_of_arg_eq", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Arg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.norm_add_eq", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Arg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.norm_sub_eq", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Arg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.isTheta_ofReal", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Asymptotics", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.isLittleO_ofReal_left", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Asymptotics", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.isLittleO_ofReal_right", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Asymptotics", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.isBigO_ofReal_left", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Asymptotics", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.isBigO_ofReal_right", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Asymptotics", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.isTheta_ofReal_left", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Asymptotics", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.isTheta_ofReal_right", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Asymptotics", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.isBigO_comp_ofReal_nhds", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Asymptotics", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.isBigO_comp_ofReal_nhds_ne", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Asymptotics", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.isBigO_re_sub_re", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Asymptotics", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.isBigO_im_sub_im", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Asymptotics", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.cast_complex_isTheta_cast_real", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Asymptotics", "is_tactic_proof": true, "tactics": ["apply", "filter_upwards"], "tactic_count": 2}
{"name": "Complex.instModuleSelf", "kind": "instance", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.instNormedField", "kind": "instance", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.instDenselyNormedField", "kind": "instance", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.instNormedAlgebraOfReal", "kind": "instance", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedSpace.complexToReal", "kind": "instance", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAlgebra.complexToReal", "kind": "instance", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.nnnorm_intCast", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Complex.continuous_normSq", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Complex.nnnorm_eq_one_of_pow_eq_one", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.norm_eq_one_of_pow_eq_one", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.le_of_eq_sum_of_eq_sum_norm", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": true, "tactics": ["norm_cast"], "tactic_count": 1}
{"name": "Complex.equivRealProd_apply_le", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.equivRealProd_apply_le'", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Complex.lipschitz_equivRealProd", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Complex.antilipschitz_equivRealProd", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.isUniformEmbedding_equivRealProd", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.instCompleteSpace", "kind": "instance", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.instT2Space", "kind": "instance", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.equivRealProdCLM", "kind": "definition", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.equivRealProdCLM_symm_apply", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.instProperSpace", "kind": "instance", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.tendsto_normSq_cocompact_atTop", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": true, "tactics": ["simpa", "tendsto_norm_cocompact_atTop.atTop_mul_atTop₀"], "tactic_count": 2}
{"name": "Complex.reCLM", "kind": "definition", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.continuous_re", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.uniformlyContinuous_re", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.reCLM_coe", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.reCLM_apply", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.imCLM", "kind": "definition", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.continuous_im", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.uniformlyContinuous_im", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.imCLM_coe", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.imCLM_apply", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.restrictScalars_toSpanSingleton'", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Complex.restrictScalars_toSpanSingleton", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": true, "tactics": ["ext1", "dsimp", "apply"], "tactic_count": 3}
{"name": "Complex.conjLIE", "kind": "definition", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.conjLIE_apply", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.conjLIE_symm", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.isometry_conj", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.dist_conj_conj", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.nndist_conj_conj", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.dist_conj_comm", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.nndist_conj_comm", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.instContinuousStar", "kind": "instance", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.continuous_conj", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.ringHom_eq_id_or_conj_of_continuous", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Complex.conjCLE", "kind": "definition", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.conjCLE_coe", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.conjCLE_apply", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.ofRealLI", "kind": "definition", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.ofRealLI_apply", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.isometry_ofReal", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.continuous_ofReal", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.isUniformEmbedding_ofReal", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.isUniformEmbedding_ofReal", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_ofReal_iff", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_ofReal_iff'", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.ofReal", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.ringHom_eq_ofReal_of_continuous", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "Complex.ofRealCLM", "kind": "definition", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.ofRealCLM_coe", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.ofRealCLM_apply", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.instRCLike", "kind": "instance", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.re_eq_complex_re", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.im_eq_complex_im", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.ofReal_eq_complex_ofReal", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.mul_conj'", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.conj_mul'", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.inv_eq_conj", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.exists_norm_eq_mul_self", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.exists_norm_mul_eq_self", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.im_eq_zero_iff_isSelfAdjoint", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Complex.re_eq_ofReal_of_isSelfAdjoint", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Complex.ofReal_eq_re_of_isSelfAdjoint", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "RCLike.complexRingEquiv", "kind": "definition", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.map_nonneg_iff", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "RCLike.to_complex_nonneg_iff", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.complexLinearIsometryEquiv", "kind": "definition", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.toContinuousLinearMap_complexLinearIsometryEquiv", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.norm_to_complex", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": true, "tactics": ["obtain", "rw", "simp", "exact"], "tactic_count": 4}
{"name": "Complex.isometry_intCast", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.closedEmbedding_intCast", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.isClosed_range_intCast", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.isOpen_compl_range_intCast", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.eq_coe_norm_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": true, "tactics": ["lift", "rw"], "tactic_count": 2}
{"name": "Complex.orderClosedTopology", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.norm_of_nonneg'", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Complex.re_nonneg_iff_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Complex.re_le_re", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "_private.Mathlib.Analysis.Complex.Basic.0.RCLike.termReC", "kind": "definition", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.Complex.Basic.0.RCLike._aux_Mathlib_Analysis_Complex_Basic___macroRules__private_Mathlib_Analysis_Complex_Basic_0_RCLike_termReC_1", "kind": "definition", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.Complex.Basic.0.RCLike.termImC", "kind": "definition", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.Complex.Basic.0.RCLike._aux_Mathlib_Analysis_Complex_Basic___macroRules__private_Mathlib_Analysis_Complex_Basic_0_RCLike_termImC_1", "kind": "definition", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.Complex.Basic.0.RCLike.termIC", "kind": "definition", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.Complex.Basic.0.RCLike._aux_Mathlib_Analysis_Complex_Basic___macroRules__private_Mathlib_Analysis_Complex_Basic_0_RCLike_termIC_1", "kind": "definition", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.Complex.Basic.0.RCLike.termNorm_sqC", "kind": "definition", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.Complex.Basic.0.RCLike._aux_Mathlib_Analysis_Complex_Basic___macroRules__private_Mathlib_Analysis_Complex_Basic_0_RCLike_termNorm_sqC_1", "kind": "definition", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.re_to_complex", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.im_to_complex", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.I_to_complex", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.normSq_to_complex", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.hasSum_conj", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.hasSum_conj'", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.summable_conj", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.conj_tsum", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.hasSum_ofReal", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.summable_ofReal", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.ofReal_tsum", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.hasSum_re", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.hasSum_im", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.re_tsum", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.im_tsum", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.hasSum_iff", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": true, "tactics": ["refine", "rintro", "simpa"], "tactic_count": 3}
{"name": "Complex.hasSum_conj", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.hasSum_conj'", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.summable_conj", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.conj_tsum", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.hasSum_ofReal", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.summable_ofReal", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.ofReal_tsum", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.hasSum_re", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.hasSum_im", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.re_tsum", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.im_tsum", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.hasSum_iff", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.slitPlane", "kind": "definition", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.mem_slitPlane_iff", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.mem_slitPlane_or_neg_mem_slitPlane", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": true, "tactics": ["rw", "rw", "push_neg", "simp_all", "by_contra", "exact"], "tactic_count": 6}
{"name": "Complex.slitPlane_eq_union", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.isOpen_slitPlane", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.ofReal_mem_slitPlane", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.neg_ofReal_mem_slitPlane", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Complex.one_mem_slitPlane", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.zero_notMem_slitPlane", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.natCast_mem_slitPlane", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Complex.ofNat_mem_slitPlane", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.mem_slitPlane_iff_not_le_zero", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.compl_Iic_zero", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.slitPlane_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.ball_one_subset_slitPlane", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.mem_slitPlane_of_norm_lt_one", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.subset_slitPlane_iff_of_subset_sphere", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "contrapose", "refine", "rintro", "have", "simpa"], "tactic_count": 6}
{"name": "IsCompact.reProdIm", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "realPart.norm_le", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": false, "tactics": ["rw", "gcongr", "exact"], "tactic_count": 3}
{"name": "imaginaryPart.norm_le", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Basic", "is_tactic_proof": true, "tactics": ["calc", "simpa"], "tactic_count": 2}
{"name": "Complex.eq_mul_div_one_add_of_eq_div_sub", "kind": "theorem", "module": "Mathlib.Analysis.Complex.BorelCaratheodory", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.norm_two_mul_div_one_add_le", "kind": "theorem", "module": "Mathlib.Analysis.Complex.BorelCaratheodory", "is_tactic_proof": true, "tactics": ["simp", "gcongr", "rw"], "tactic_count": 3}
{"name": "Complex.norm_lt_norm_two_mul_sub", "kind": "theorem", "module": "Mathlib.Analysis.Complex.BorelCaratheodory", "is_tactic_proof": true, "tactics": ["rw", "suffices", "nlinarith"], "tactic_count": 3}
{"name": "Complex.schwarz_applied", "kind": "theorem", "module": "Mathlib.Analysis.Complex.BorelCaratheodory", "is_tactic_proof": true, "tactics": ["rw", "nth_rw", "apply", "apply", "have", "aesop", "simpa"], "tactic_count": 7}
{"name": "Complex.borelCaratheodory_zero", "kind": "theorem", "module": "Mathlib.Analysis.Complex.BorelCaratheodory", "is_tactic_proof": true, "tactics": ["set", "have", "have", "simpa", "have", "calc", "simp", "gcongr", "linarith", "simpa"], "tactic_count": 10}
{"name": "Complex.borelCaratheodory", "kind": "theorem", "module": "Mathlib.Analysis.Complex.BorelCaratheodory", "is_tactic_proof": false, "tactics": ["have", "apply", "intro", "simp", "calc", "have", "calc"], "tactic_count": 7}
{"name": "Cardinal.mk_complex", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Cardinality", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.mk_univ_complex", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Cardinality", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "not_countable_complex", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Cardinality", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "Complex.integral_boundary_rect_of_hasFDerivAt_real_off_countable", "kind": "theorem", "module": "Mathlib.Analysis.Complex.CauchyIntegral", "is_tactic_proof": true, "tactics": ["set", "have", "have", "simp", "set", "set", "have", "rintro", "simp", "set", "set", "rw", "have", "have", "have", "simp_rw", "refine", "w.re", "rw", "simpa"], "tactic_count": 20}
{"name": "Complex.integral_boundary_rect_of_continuousOn_of_hasFDerivAt_real", "kind": "theorem", "module": "Mathlib.Analysis.Complex.CauchyIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.integral_boundary_rect_of_differentiableOn_real", "kind": "theorem", "module": "Mathlib.Analysis.Complex.CauchyIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Complex.circleIntegral_sub_center_inv_smul_eq_of_differentiable_on_annulus_off_countable", "kind": "theorem", "module": "Mathlib.Analysis.Complex.CauchyIntegral", "is_tactic_proof": true, "tactics": ["set", "obtain", "obtain", "rw", "suffices", "simpa", "mul_div_cancel_left₀", "set", "set", "have", "replace", "have", "replace", "replace", "refine", "simpa", "simpa", "integral_boundary_rect_eq_zero_of_differentiable_on_off_countable"], "tactic_count": 18}
{"name": "Complex.circleIntegral_eq_of_differentiable_on_annulus_off_countable", "kind": "theorem", "module": "Mathlib.Analysis.Complex.CauchyIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Complex.circleIntegral_sub_center_inv_smul_of_differentiable_on_off_countable", "kind": "theorem", "module": "Mathlib.Analysis.Complex.CauchyIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.circleIntegral_eq_zero_of_differentiable_on_off_countable", "kind": "theorem", "module": "Mathlib.Analysis.Complex.CauchyIntegral", "is_tactic_proof": true, "tactics": ["wlog", "simp", "rcases", "calc"], "tactic_count": 4}
{"name": "DiffContOnCl.circleIntegral_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.Complex.CauchyIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.circleIntegral_sub_inv_smul_of_differentiable_on_off_countable_aux", "kind": "theorem", "module": "Mathlib.Analysis.Complex.CauchyIntegral", "is_tactic_proof": true, "tactics": ["have", "set", "have", "have", "have", "have", "have", "have", "calc", "have", "rw", "circleIntegral.integral_sub,", "exacts"], "tactic_count": 13}
{"name": "Complex.two_pi_I_inv_smul_circleIntegral_sub_inv_smul_of_differentiable_on_off_countable", "kind": "theorem", "module": "Mathlib.Analysis.Complex.CauchyIntegral", "is_tactic_proof": true, "tactics": ["have", "suffices", "lift", "have", "have", "refine", "rwa", "have", "refine", "intro", "rw", "simp", "refine", "mem_closure_iff_nhds.2", "set", "have", "rcases", "obtain", "refine", "have", "rw", "exact", "exact"], "tactic_count": 23}
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{"name": "DiffContOnCl.circleIntegral_sub_inv_smul", "kind": "theorem", "module": "Mathlib.Analysis.Complex.CauchyIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiffContOnCl.two_pi_i_inv_smul_circleIntegral_sub_inv_smul", "kind": "theorem", "module": "Mathlib.Analysis.Complex.CauchyIntegral", "is_tactic_proof": true, "tactics": ["have", "refine", "simpa", "simpa"], "tactic_count": 4}
{"name": "DifferentiableOn.circleIntegral_sub_inv_smul", "kind": "theorem", "module": "Mathlib.Analysis.Complex.CauchyIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.circleIntegral_div_sub_of_differentiable_on_off_countable", "kind": "theorem", "module": "Mathlib.Analysis.Complex.CauchyIntegral", "is_tactic_proof": true, "tactics": ["simpa", "circleIntegral_sub_inv_smul_of_differentiable_on_off_countable"], "tactic_count": 2}
{"name": "Complex.hasFPowerSeriesOnBall_of_differentiable_off_countable", "kind": "theorem", "module": "Mathlib.Analysis.Complex.CauchyIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiffContOnCl.hasFPowerSeriesOnBall", "kind": "theorem", "module": "Mathlib.Analysis.Complex.CauchyIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableOn.hasFPowerSeriesOnBall", "kind": "theorem", "module": "Mathlib.Analysis.Complex.CauchyIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableOn.analyticAt", "kind": "theorem", "module": "Mathlib.Analysis.Complex.CauchyIntegral", "is_tactic_proof": true, "tactics": ["rcases", "lift", "exact"], "tactic_count": 3}
{"name": "DifferentiableOn.analyticOnNhd", "kind": "theorem", "module": "Mathlib.Analysis.Complex.CauchyIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableOn.analyticOn", "kind": "theorem", "module": "Mathlib.Analysis.Complex.CauchyIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableOn.contDiffOn", "kind": "theorem", "module": "Mathlib.Analysis.Complex.CauchyIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableOn.deriv", "kind": "theorem", "module": "Mathlib.Analysis.Complex.CauchyIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Differentiable.analyticAt", "kind": "theorem", "module": "Mathlib.Analysis.Complex.CauchyIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Differentiable.contDiff", "kind": "theorem", "module": "Mathlib.Analysis.Complex.CauchyIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Differentiable.hasFPowerSeriesOnBall", "kind": "theorem", "module": "Mathlib.Analysis.Complex.CauchyIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.analyticOnNhd_iff_differentiableOn", "kind": "theorem", "module": "Mathlib.Analysis.Complex.CauchyIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.analyticOn_iff_differentiableOn", "kind": "theorem", "module": "Mathlib.Analysis.Complex.CauchyIntegral", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Complex.analyticOnNhd_univ_iff_differentiable", "kind": "theorem", "module": "Mathlib.Analysis.Complex.CauchyIntegral", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Complex.analyticOn_univ_iff_differentiable", "kind": "theorem", "module": "Mathlib.Analysis.Complex.CauchyIntegral", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Complex.analyticAt_iff_eventually_differentiableAt", "kind": "theorem", "module": "Mathlib.Analysis.Complex.CauchyIntegral", "is_tactic_proof": true, "tactics": ["constructor", "intro", "filter_upwards", "apply", "intro", "rcases", "have", "refine", "intro", "exact", "exact"], "tactic_count": 11}
{"name": "Complex.circleIntegral_one_div_sub_center_pow_smul_of_differentiable_on_off_countable", "kind": "theorem", "module": "Mathlib.Analysis.Complex.CauchyIntegral", "is_tactic_proof": false, "tactics": ["have", "rw", "rw", "div_mul_cancel₀", "simp"], "tactic_count": 5}
{"name": "Complex.differentiable_on_off_countable_deriv_eq_smul_circleIntegral", "kind": "theorem", "module": "Mathlib.Analysis.Complex.CauchyIntegral", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "DiffContOnCl.circleIntegral_one_div_sub_center_pow_smul", "kind": "theorem", "module": "Mathlib.Analysis.Complex.CauchyIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiffContOnCl.deriv_eq_smul_circleIntegral", "kind": "theorem", "module": "Mathlib.Analysis.Complex.CauchyIntegral", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "DifferentiableOn.circleIntegral_one_div_sub_center_pow_smul", "kind": "theorem", "module": "Mathlib.Analysis.Complex.CauchyIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableOn.deriv_eq_smul_circleIntegral", "kind": "theorem", "module": "Mathlib.Analysis.Complex.CauchyIntegral", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Circle", "kind": "definition", "module": "Mathlib.Analysis.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Circle.instCoeOut", "kind": "instance", "module": "Mathlib.Analysis.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Circle.instCommGroup", "kind": "instance", "module": "Mathlib.Analysis.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Circle.instMetricSpace", "kind": "instance", "module": "Mathlib.Analysis.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Circle.ext", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Circle.coe_injective", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Circle.coe_inj", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Circle.norm_coe", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Circle.normSq_coe", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Circle", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Circle.coe_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Circle.coe_one", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Circle.coe_eq_one", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Circle", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Circle.coe_mul", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Circle.coe_inv", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Circle.coe_inv_eq_conj", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Circle", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Circle.coe_div", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Circle.coeHom", "kind": "definition", "module": "Mathlib.Analysis.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Circle.toUnits", "kind": "definition", "module": "Mathlib.Analysis.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Circle.toUnits_apply", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Circle.instCompactSpace", "kind": "instance", "module": "Mathlib.Analysis.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Circle.instIsTopologicalGroup", "kind": "instance", "module": "Mathlib.Analysis.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Circle.instUniformSpace", "kind": "instance", "module": "Mathlib.Analysis.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Circle.instIsUniformGroup", "kind": "instance", "module": "Mathlib.Analysis.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Circle.ofConjDivSelf", "kind": "definition", "module": "Mathlib.Analysis.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Circle.exp", "kind": "definition", "module": "Mathlib.Analysis.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Circle.coe_exp", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Circle.exp_zero", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Circle.exp_add", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Circle.expHom", "kind": "definition", "module": "Mathlib.Analysis.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Circle.exp_sub", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Circle.exp_neg", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Circle.exp_pi_ne_one", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Circle", "is_tactic_proof": true, "tactics": ["intro", "have", "rw", "norm_num"], "tactic_count": 4}
{"name": "Circle.star_addChar", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Circle", "is_tactic_proof": true, "tactics": ["have", "simp", "simp"], "tactic_count": 3}
{"name": "Circle.starRingEnd_addChar", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Circle.instSMul", "kind": "instance", "module": "Mathlib.Analysis.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Circle.instSMulCommClass_left", "kind": "instance", "module": "Mathlib.Analysis.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Circle.instSMulCommClass_right", "kind": "instance", "module": "Mathlib.Analysis.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Circle.instIsScalarTower", "kind": "instance", "module": "Mathlib.Analysis.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Circle.instMulAction", "kind": "instance", "module": "Mathlib.Analysis.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Circle.instDistribMulAction", "kind": "instance", "module": "Mathlib.Analysis.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Circle.smul_def", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Circle.instContinuousSMul", "kind": "instance", "module": "Mathlib.Analysis.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Circle.norm_smul", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Circle", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.fourierChar", "kind": "definition", "module": "Mathlib.Analysis.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FourierTransform.term𝐞", "kind": "definition", "module": "Mathlib.Analysis.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FourierTransform._aux_Mathlib_Analysis_Complex_Circle___macroRules_FourierTransform_term𝐞_1", "kind": "definition", "module": "Mathlib.Analysis.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FourierTransform._aux_Mathlib_Analysis_Complex_Circle___unexpand_Real_fourierChar_1", "kind": "definition", "module": "Mathlib.Analysis.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.fourierChar_apply'", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.fourierChar_apply", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.continuous_fourierChar", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.fourierChar_ne_one", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Circle", "is_tactic_proof": true, "tactics": ["rw", "use", "simp", "rw", "exact"], "tactic_count": 5}
{"name": "Real.probChar", "kind": "definition", "module": "Mathlib.Analysis.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.probChar_apply'", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.probChar_apply", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.continuous_probChar", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.probChar_ne_one", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Circle", "is_tactic_proof": true, "tactics": ["rw", "use", "simpa"], "tactic_count": 3}
{"name": "isConformalMap_conj", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Conformal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isConformalMap_complex_linear", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Conformal", "is_tactic_proof": true, "tactics": ["have", "refine", "intro", "simp", "have", "nth_rw", "rw", "simp", "field", "ext1", "simp"], "tactic_count": 11}
{"name": "isConformalMap_complex_linear_conj", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Conformal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsConformalMap.is_complex_or_conj_linear", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Conformal", "is_tactic_proof": true, "tactics": ["rcases", "obtain", "rcases", "refine", "ext1", "simp", "refine", "ext1", "simp"], "tactic_count": 9}
{"name": "isConformalMap_iff_is_complex_or_conj_linear", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Conformal", "is_tactic_proof": true, "tactics": ["constructor", "exact", "rintro", "refine", "contrapose", "simp", "have", "ext1", "simp", "starRingEnd_self_apply]", "rw", "refine", "contrapose", "simp"], "tactic_count": 14}
{"name": "DifferentiableAt.conformalAt", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Conformal", "is_tactic_proof": true, "tactics": ["rw", "apply", "simpa"], "tactic_count": 3}
{"name": "conformalAt_iff_differentiableAt_or_differentiableAt_comp_conj", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Conformal", "is_tactic_proof": true, "tactics": ["rw", "rw", "apply", "intro", "have", "apply", "rw", "rw", "rw", "refine", "have", "simp"], "tactic_count": 12}
{"name": "real_linearMap_map_smul_complex", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Conformal", "is_tactic_proof": true, "tactics": ["rw", "have", "simp", "have", "simp", "repeat", "have", "simp", "match_scalars", "simp", "ring"], "tactic_count": 11}
{"name": "LinearMap.complexOfReal", "kind": "definition", "module": "Mathlib.Analysis.Complex.Conformal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.coe_complexOfReal", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Conformal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.complexOfReal", "kind": "definition", "module": "Mathlib.Analysis.Complex.Conformal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.coe_complexOfReal", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Conformal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableWithinAt_complex_iff_differentiableWithinAt_real", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Conformal", "is_tactic_proof": true, "tactics": ["refine", "simp", "rw", "simp", "apply", "use", "rfl"], "tactic_count": 7}
{"name": "HasFDerivWithinAt.complexOfReal", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Conformal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "complexOfReal_fderivWithin", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Conformal", "is_tactic_proof": false, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "complexOfReal_hasDerivWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Conformal", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "complexOfReal_derivWithin", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Conformal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableAt_complex_iff_differentiableAt_real", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Conformal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivAt.complexOfReal_hasFDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Conformal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "complexOfReal_hasDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Conformal", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "complexOfReal_deriv", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Conformal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "complexOfReal_fderiv", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Conformal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.convexHull_reProdIm", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Convex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.starConvex_slitPlane", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Convex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.starConvex_ofReal_slitPlane", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Convex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.starConvex_one_slitPlane", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Convex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "convex_halfSpace_re_lt", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Convex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "convex_halfSpace_re_le", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Convex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "convex_halfSpace_re_gt", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Convex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "convex_halfSpace_re_ge", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Convex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "convex_halfSpace_im_lt", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Convex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "convex_halfSpace_im_le", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Convex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "convex_halfSpace_im_gt", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Convex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "convex_halfSpace_im_ge", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Convex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.isConnected_of_upperHalfPlane", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Convex", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "Complex.isConnected_of_lowerHalfPlane", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Convex", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "Complex.rectangle_eq_convexHull", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Convex", "is_tactic_proof": true, "tactics": ["simp_rw", "insert_prod,", "image_singleton,"], "tactic_count": 3}
{"name": "Complex.Convex.rectangle_subset", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Convex", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Complex.instPathConnectedSpaceUnits", "kind": "instance", "module": "Mathlib.Analysis.Complex.Convex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.isAddQuotientCoveringMap_exp", "kind": "theorem", "module": "Mathlib.Analysis.Complex.CoveringMap", "is_tactic_proof": false, "tactics": ["refine", "refine", "exact", "simp_rw", "eq_add_neg_iff_add_eq,"], "tactic_count": 5}
{"name": "Complex.isCoveringMap_exp", "kind": "theorem", "module": "Mathlib.Analysis.Complex.CoveringMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.isCoveringMapOn_exp", "kind": "theorem", "module": "Mathlib.Analysis.Complex.CoveringMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.isCoveringMapOn_eval", "kind": "theorem", "module": "Mathlib.Analysis.Complex.CoveringMap", "is_tactic_proof": false, "tactics": ["refine", "p.isClosedMap_eval.isCoveringMapOn_of_openPartialHomeomorph", "simp⟩", "obtain", "simp", "simpa"], "tactic_count": 6}
{"name": "isCoveringMapOn_npow", "kind": "theorem", "module": "Mathlib.Analysis.Complex.CoveringMap", "is_tactic_proof": true, "tactics": ["convert", "simp", "assumption", "simpa"], "tactic_count": 4}
{"name": "isCoveringMap_npow", "kind": "theorem", "module": "Mathlib.Analysis.Complex.CoveringMap", "is_tactic_proof": true, "tactics": ["convert", "ext"], "tactic_count": 2}
{"name": "isCoveringMap_zpow", "kind": "theorem", "module": "Mathlib.Analysis.Complex.CoveringMap", "is_tactic_proof": true, "tactics": ["obtain", "convert", "convert", "simp", "simpa"], "tactic_count": 5}
{"name": "isCoveringMapOn_zpow", "kind": "theorem", "module": "Mathlib.Analysis.Complex.CoveringMap", "is_tactic_proof": true, "tactics": ["have", "refine", "convert", "ext", "convert", "ext"], "tactic_count": 6}
{"name": "isQuotientCoveringMap_npow", "kind": "theorem", "module": "Mathlib.Analysis.Complex.CoveringMap", "is_tactic_proof": true, "tactics": ["rw", "have", "have", "have", "let", "convert", "exact", "ext", "refine", "this.isQuotientCoveringMap_of_subgroup", "simp"], "tactic_count": 11}
{"name": "Complex.isQuotientCoveringMap_npow", "kind": "theorem", "module": "Mathlib.Analysis.Complex.CoveringMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isQuotientCoveringMap_zpow", "kind": "theorem", "module": "Mathlib.Analysis.Complex.CoveringMap", "is_tactic_proof": true, "tactics": ["obtain", "exact", "rw", "convert", "ext", "convert"], "tactic_count": 6}
{"name": "Complex.isCauSeq_norm_exp", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.isCauSeq_exp", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.exp'", "kind": "definition", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.definition._@.Mathlib.Analysis.Complex.Exponential.867311647._hygCtx._hyg.2", "kind": "definition", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.867311647._hygCtx._hyg.2", "kind": "opaque", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.exp", "kind": "definition", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.exp_def", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": true, "tactics": ["intros", "delta", "rw", "rfl"], "tactic_count": 4}
{"name": "Complex.termCexp", "kind": "definition", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex._aux_Mathlib_Analysis_Complex_Exponential___macroRules_Complex_termCexp_1", "kind": "definition", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex._aux_Mathlib_Analysis_Complex_Exponential___unexpand_Complex_exp_1", "kind": "definition", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.exp", "kind": "definition", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.termRexp", "kind": "definition", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real._aux_Mathlib_Analysis_Complex_Exponential___macroRules_Real_termRexp_1", "kind": "definition", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real._aux_Mathlib_Analysis_Complex_Exponential___unexpand_Real_exp_1", "kind": "definition", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.exp_zero", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": true, "tactics": ["rw", "refine", "convert", "rcases", "exact", "dsimp", "induction", "zero", "succ", "rw", "simp", "simp"], "tactic_count": 12}
{"name": "Complex.exp_add", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": false, "tactics": ["have", "intro", "refine", "rw", "refine", "have", "have", "rw", "simp", "rw", "simp", "simp_rw", "apply", "simp", "exact"], "tactic_count": 15}
{"name": "Complex.expMonoidHom", "kind": "definition", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.exp_list_sum", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.exp_multiset_sum", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.exp_sum", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.exp_nsmul", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.exp_nsmul'", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": true, "tactics": ["rw", "ring_nf"], "tactic_count": 2}
{"name": "Complex.exp_nat_mul", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.exp_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.exp_neg", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.exp_sub", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.exp_int_mul", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": true, "tactics": ["cases", "simp", "simp"], "tactic_count": 3}
{"name": "Complex.exp_conj", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": true, "tactics": ["simp", "rw", "refine", "dsimp", "rw", "refine", "rw"], "tactic_count": 7}
{"name": "Complex.ofReal_exp_ofReal_re", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.ofReal_exp", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.exp_ofReal_im", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.exp_ofReal_re", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.exp_zero", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.exp_add", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.expMonoidHom", "kind": "definition", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.exp_list_sum", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.exp_multiset_sum", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.exp_sum", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.exp_nsmul", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.exp_nat_mul", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.exp_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.exp_neg", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.exp_sub", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.sum_le_exp_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.pow_div_factorial_le_exp", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.quadratic_le_exp_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.Complex.Exponential.0.Real.add_one_lt_exp_of_pos", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.Complex.Exponential.0.Real.add_one_le_exp_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": true, "tactics": ["rcases", "simp", "exact"], "tactic_count": 3}
{"name": "Real.one_le_exp", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": true, "tactics": ["linarith"], "tactic_count": 1}
{"name": "Real.exp_pos", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.exp_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.abs_exp", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.exp_abs_le", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Real.exp_strictMono", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.exp_lt_exp_of_lt", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.exp_monotone", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.exp_le_exp_of_le", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.exp_lt_exp", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.exp_le_exp", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.exp_injective", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.exp_eq_exp", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.exp_eq_one_iff", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.one_lt_exp_iff", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.exp_lt_one_iff", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.exp_le_one_iff", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.one_le_exp_iff", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.sum_div_factorial_le", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.exp_bound", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp_rw", "change", "rw", "calc", "refine", "rw", "rw", "simp_rw", "gcongr", "rw", "exact", "gcongr", "exact"], "tactic_count": 15}
{"name": "Complex.exp_bound'", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp_rw", "change", "let", "have", "rw", "calc", "gcongr", "exact", "simp", "rw", "gcongr", "simp_rw", "rw", "trans", "linarith", "simp", "positivity", "linarith", "linarith"], "tactic_count": 21}
{"name": "Complex.norm_exp_sub_one_le", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.norm_exp_sub_one_sub_id_le", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.norm_exp_sub_one_sub_id_le", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.norm_exp_sub_sum_le_exp_norm_sub_sum", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": false, "tactics": ["rw", "refine", "simp_rw", "calc", "rw", "refine", "congr", "simp", "gcongr", "exact"], "tactic_count": 10}
{"name": "Complex.norm_exp_le_exp_norm", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "Complex.norm_exp_sub_sum_le_norm_mul_exp", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": false, "tactics": ["rw", "refine", "simp_rw", "change", "rw", "calc", "refine", "rw", "rw", "simp_rw", "gcongr", "rw", "simp", "congr", "refine", "grind", "intro", "simpa", "intro", "simp", "simp", "refine", "rw", "exact", "rw", "simp", "gcongr", "refine", "exact"], "tactic_count": 29}
{"name": "Real.exp_bound", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": true, "tactics": ["have", "convert"], "tactic_count": 2}
{"name": "Real.exp_bound'", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": true, "tactics": ["have", "have", "have", "rw", "have", "have", "simpa"], "tactic_count": 7}
{"name": "Real.abs_exp_sub_one_le", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": true, "tactics": ["have", "exact_mod_cast"], "tactic_count": 2}
{"name": "Real.abs_exp_sub_one_sub_id_le", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": true, "tactics": ["rw", "have", "exact_mod_cast"], "tactic_count": 3}
{"name": "Real.expNear", "kind": "definition", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.expNear_zero", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.expNear_succ", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": true, "tactics": ["simp", "ac_rfl"], "tactic_count": 2}
{"name": "Real.expNear_sub", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.exp_approx_end", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": true, "tactics": ["simp", "convert", "simp", "lia"], "tactic_count": 4}
{"name": "Real.exp_approx_succ", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": true, "tactics": ["grw", "subst", "convert", "simp", "ac_rfl", "simp"], "tactic_count": 6}
{"name": "Real.exp_approx_end'", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": true, "tactics": ["subst", "exact"], "tactic_count": 2}
{"name": "Real.exp_1_approx_succ_eq", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": true, "tactics": ["subst", "refine", "simp", "field_simp", "simp"], "tactic_count": 5}
{"name": "Real.exp_approx_start", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.exp_bound_div_one_sub_of_interval'", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": false, "tactics": ["have", "calc", "calc", "exp", "rw", "repeat", "norm_num", "nlinarith"], "tactic_count": 8}
{"name": "Real.exp_bound_div_one_sub_of_interval", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": true, "tactics": ["rcases", "simp", "exact"], "tactic_count": 3}
{"name": "Real.add_one_lt_exp", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": true, "tactics": ["obtain", "exact", "obtain", "linarith", "have", "simpa"], "tactic_count": 6}
{"name": "Real.add_one_le_exp", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": true, "tactics": ["obtain", "simp", "exact"], "tactic_count": 3}
{"name": "Real.one_sub_lt_exp_neg", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.one_sub_le_exp_neg", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.one_sub_div_pow_le_exp_neg", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rwa", "calc", "gcongr", "exact", "exact"], "tactic_count": 7}
{"name": "Real.le_inv_mul_exp", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": true, "tactics": ["rw", "calc", "c"], "tactic_count": 3}
{"name": "Mathlib.Meta.Positivity.evalExp", "kind": "definition", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.norm_exp_ofReal", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Exponential", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Real.exp_one_near_10", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ExponentialBounds", "is_tactic_proof": true, "tactics": ["apply", "iterate", "refine", "norm_num1"], "tactic_count": 4}
{"name": "Real.exp_one_near_20", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ExponentialBounds", "is_tactic_proof": true, "tactics": ["apply", "iterate", "refine", "norm_num1"], "tactic_count": 4}
{"name": "Real.exp_one_gt_d9", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ExponentialBounds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.exp_one_lt_d9", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ExponentialBounds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.exp_one_gt_two", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ExponentialBounds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.exp_one_lt_three", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ExponentialBounds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.floor_exp_one_eq_two", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ExponentialBounds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.ceil_exp_one_eq_three", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ExponentialBounds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.round_exp_one_eq_three", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ExponentialBounds", "is_tactic_proof": true, "tactics": ["refine", "grw", "norm_num"], "tactic_count": 3}
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{"name": "_private.Mathlib.Analysis.Complex.MeanValue.0.circleAverage_of_differentiable_on_off_countable_posRadius", "kind": "theorem", "module": "Mathlib.Analysis.Complex.MeanValue", "is_tactic_proof": true, "tactics": ["calc", "circleAverage", "rw", "match_scalars", "simp"], "tactic_count": 5}
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{"name": "Complex.instNorm", "kind": "instance", "module": "Mathlib.Analysis.Complex.Norm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Complex.norm_mul_self_eq_normSq", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Norm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Complex.abs_re_le_norm", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Norm", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
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{"name": "_private.Mathlib.Analysis.Complex.Norm.0.Complex.norm_map_zero'", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Norm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.Complex.Norm.0.Complex.norm_neg'", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Norm", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.instNormedAddCommGroup", "kind": "instance", "module": "Mathlib.Analysis.Complex.Norm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.norm_mul", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Norm", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.norm_div", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Norm", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.isAbsoluteValueNorm", "kind": "instance", "module": "Mathlib.Analysis.Complex.Norm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.norm_pow", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Norm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.norm_zpow", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Norm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.norm_prod", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Norm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.norm_conj", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Norm", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.norm_I", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Norm", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.nnnorm_I", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Norm", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.norm_real", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Norm", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "Complex.norm_natCast", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Norm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Complex.norm_intCast", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Norm", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.norm_int_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Norm", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.norm_ratCast", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Norm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Complex.normSq_eq_norm_sq", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Norm", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.sq_norm", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Norm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.sq_norm_sub_sq_re", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Norm", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.sq_norm_sub_sq_im", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Norm", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.norm_add_mul_I", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Norm", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.norm_eq_sqrt_sq_add_sq", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Norm", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.range_norm", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Norm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.range_normSq", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Norm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.norm_le_abs_re_add_abs_im", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Norm", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Complex.abs_im_le_norm", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Norm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.im_le_norm", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Norm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.abs_re_lt_norm", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Norm", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.abs_im_lt_norm", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Norm", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Complex.abs_re_eq_norm", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Norm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.abs_im_eq_norm", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Norm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.norm_le_sqrt_two_mul_max", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Norm", "is_tactic_proof": true, "tactics": ["obtain", "simp", "set", "have", "calc", "gcongr", "exacts"], "tactic_count": 7}
{"name": "Complex.abs_re_div_norm_le_one", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Norm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.abs_im_div_norm_le_one", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Norm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.dist_eq", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Norm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.dist_eq_re_im", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Norm", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Complex.dist_mk", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Norm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.dist_of_re_eq", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Norm", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.nndist_of_re_eq", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Norm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.edist_of_re_eq", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Norm", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.dist_of_im_eq", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Norm", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "Complex.instIsComplete", "kind": "instance", "module": "Mathlib.Analysis.Complex.Norm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.lim_eq_lim_im_add_lim_re", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Norm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Complex.ofRealCLM_norm", "kind": "theorem", "module": "Mathlib.Analysis.Complex.OperatorNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Complex.nonneg_iff", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Complex.real_le_real", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Order", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "Complex.eq_re_of_ofReal_le", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Order", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "Complex.re_eq_neg_norm", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Order", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.monotone_ofReal", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Order", "is_tactic_proof": true, "tactics": ["intro", "simp"], "tactic_count": 2}
{"name": "Mathlib.Meta.Positivity.evalComplexOfReal", "kind": "definition", "module": "Mathlib.Analysis.Complex.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "HasDerivAt.comp_ofReal", "kind": "theorem", "module": "Mathlib.Analysis.Complex.RealDeriv", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasDerivAt.ofReal_comp", "kind": "theorem", "module": "Mathlib.Analysis.Complex.RealDeriv", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Complex.analyticAt_of_differentiable_on_punctured_nhds_of_continuousAt", "kind": "theorem", "module": "Mathlib.Analysis.Complex.RemovableSingularity", "is_tactic_proof": true, "tactics": ["rcases", "lift", "replace", "refine", "rcases", "exacts", "exact"], "tactic_count": 7}
{"name": "Complex.differentiableOn_compl_singleton_and_continuousAt_iff", "kind": "theorem", "module": "Mathlib.Analysis.Complex.RemovableSingularity", "is_tactic_proof": true, "tactics": ["refine", "rintro", "rcases", "refine", "refine", "exact", "simpa"], "tactic_count": 7}
{"name": "Complex.differentiableOn_dslope", "kind": "theorem", "module": "Mathlib.Analysis.Complex.RemovableSingularity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.differentiableOn_update_limUnder_of_isLittleO", "kind": "theorem", "module": "Mathlib.Analysis.Complex.RemovableSingularity", "is_tactic_proof": true, "tactics": ["set", "suffices", "rw", "have", "rwa", "refine", "rw", "have", "have", "simpa"], "tactic_count": 10}
{"name": "Complex.differentiableOn_update_limUnder_insert_of_isLittleO", "kind": "theorem", "module": "Mathlib.Analysis.Complex.RemovableSingularity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.differentiableOn_update_limUnder_of_bddAbove", "kind": "theorem", "module": "Mathlib.Analysis.Complex.RemovableSingularity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.tendsto_limUnder_of_differentiable_on_punctured_nhds_of_isLittleO", "kind": "theorem", "module": "Mathlib.Analysis.Complex.RemovableSingularity", "is_tactic_proof": true, "tactics": ["rw", "have", "have", "exact"], "tactic_count": 4}
{"name": "Complex.tendsto_limUnder_of_differentiable_on_punctured_nhds_of_bounded_under", "kind": "theorem", "module": "Mathlib.Analysis.Complex.RemovableSingularity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.two_pi_I_inv_smul_circleIntegral_sub_sq_inv_smul_of_differentiable", "kind": "theorem", "module": "Mathlib.Analysis.Complex.RemovableSingularity", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "congr", "trans", "have", "refine", "exact", "have", "refine", "exact", "have", "have", "simpa", "simp", "refine", "simp", "not_false_iff,"], "tactic_count": 18}
{"name": "Complex.schwarz_aux", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Schwarz", "is_tactic_proof": true, "tactics": ["have", "wlog", "suffices", "refine", "refine", "fun_prop", "rw", "filter_upwards", "apply", "exact", "exact", "rwa", "exact", "exact", "clear", "rcases", "rcases", "simp", "set", "set", "have", "refine", "apply", "exact", "refine", "fun_prop", "refine", "simp", "refine", "rw", "simp", "suffices", "have", "simpa", "refine", "grw", "intro", "have", "have", "rw", "simpa", "exact"], "tactic_count": 42}
{"name": "Complex.dist_le_mul_div_pow_of_mapsTo_ball_of_isLittleO", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Schwarz", "is_tactic_proof": true, "tactics": ["have", "have", "rcases", "trans", "have", "rcases", "set", "have", "intro", "simpa", "have", "refine", "simpa", "have", "g.differentiable.comp_differentiableOn", "have", "simp", "refine", "rw", "refine", "exact", "simpa", "have", "rw", "simpa"], "tactic_count": 25}
{"name": "Complex.dist_le_div_mul_dist_of_mapsTo_ball", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Schwarz", "is_tactic_proof": true, "tactics": ["refine", "simpa", "simp"], "tactic_count": 3}
{"name": "Complex.norm_fderiv_le_div_of_mapsTo_ball", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Schwarz", "is_tactic_proof": true, "tactics": ["have", "refine", "filter_upwards", "simpa"], "tactic_count": 4}
{"name": "Complex.dist_le_dist_of_mapsTo_ball", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Schwarz", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Complex.norm_fderiv_le_one_of_mapsTo_ball", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Schwarz", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Complex.norm_le_norm_of_mapsTo_ball", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Schwarz", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Complex.norm_deriv_le_div_of_mapsTo_ball", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Schwarz", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Complex.norm_deriv_le_one_of_mapsTo_ball", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Schwarz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.norm_dslope_le_div_of_mapsTo_ball", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Schwarz", "is_tactic_proof": true, "tactics": ["rcases", "simpa", "rw", "div_eq_inv_mul,", "exact", "simpa"], "tactic_count": 6}
{"name": "Complex.affine_of_mapsTo_ball_of_norm_dslope_eq_div", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Schwarz", "is_tactic_proof": true, "tactics": ["set", "set", "rintro", "have", "have", "ext", "simp", "rw", "rintro", "exact", "have", "norm_dslope_le_div_of_mapsTo_ball", "have", "isMaxOn_iff.mpr", "have", "have", "simpa", "norm_eqOn_of_isPreconnected_of_isMaxOn", "have", "simpa", "norm_eqOn_of_isPreconnected_of_isMaxOn", "h_z₀", "have", "eq_of_norm_eq_of_norm_add_eq", "simp"], "tactic_count": 25}
{"name": "Complex.affine_of_mapsTo_ball_of_exists_norm_dslope_eq_div'", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Schwarz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SpectrumRestricts.real_iff", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Spectrum", "is_tactic_proof": true, "tactics": ["refine", "obtain", "simp", "exact"], "tactic_count": 4}
{"name": "_private.Mathlib.Analysis.Complex.Spectrum.0.QuasispectrumRestricts.termσₙ", "kind": "definition", "module": "Mathlib.Analysis.Complex.Spectrum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.Complex.Spectrum.0.QuasispectrumRestricts._aux_Mathlib_Analysis_Complex_Spectrum___macroRules__private_Mathlib_Analysis_Complex_Spectrum_0_QuasispectrumRestricts_termσₙ_1", "kind": "definition", "module": "Mathlib.Analysis.Complex.Spectrum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.Complex.Spectrum.0.QuasispectrumRestricts._aux_Mathlib_Analysis_Complex_Spectrum___unexpand_quasispectrum_1", "kind": "definition", "module": "Mathlib.Analysis.Complex.Spectrum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuasispectrumRestricts.real_iff", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Spectrum", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SummableLocallyUniformlyOn.differentiableOn", "kind": "theorem", "module": "Mathlib.Analysis.Complex.SummableUniformlyOn", "is_tactic_proof": true, "tactics": ["obtain", "have", "apply", "apply", "filter_upwards"], "tactic_count": 5}
{"name": "Complex.hasSum_taylorSeries_on_ball", "kind": "theorem", "module": "Mathlib.Analysis.Complex.TaylorSeries", "is_tactic_proof": false, "tactics": ["obtain", "obtain", "exact", "lift", "have", "rw", "exact", "have", "simp", "convert", "simpa"], "tactic_count": 11}
{"name": "Complex.taylorSeries_eq_on_ball", "kind": "theorem", "module": "Mathlib.Analysis.Complex.TaylorSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.taylorSeries_eq_on_ball'", "kind": "theorem", "module": "Mathlib.Analysis.Complex.TaylorSeries", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "Complex.hasSum_taylorSeries_on_eball", "kind": "theorem", "module": "Mathlib.Analysis.Complex.TaylorSeries", "is_tactic_proof": true, "tactics": ["obtain", "lift", "rw", "refine", "rw", "exact"], "tactic_count": 6}
{"name": "Complex.taylorSeries_eq_on_eball", "kind": "theorem", "module": "Mathlib.Analysis.Complex.TaylorSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.taylorSeries_eq_on_eball'", "kind": "theorem", "module": "Mathlib.Analysis.Complex.TaylorSeries", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "Complex.hasSum_taylorSeries_of_entire", "kind": "theorem", "module": "Mathlib.Analysis.Complex.TaylorSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.taylorSeries_eq_of_entire", "kind": "theorem", "module": "Mathlib.Analysis.Complex.TaylorSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.taylorSeries_eq_of_entire'", "kind": "theorem", "module": "Mathlib.Analysis.Complex.TaylorSeries", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "TietzeExtension.of_tvs", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Tietze", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.instTietzeExtension", "kind": "instance", "module": "Mathlib.Analysis.Complex.Tietze", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.instTietzeExtension", "kind": "instance", "module": "Mathlib.Analysis.Complex.Tietze", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.instTietzeExtensionTVS", "kind": "instance", "module": "Mathlib.Analysis.Complex.Tietze", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instTietzeExtensionUnitBall", "kind": "instance", "module": "Mathlib.Analysis.Complex.Tietze", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instTietzeExtensionUnitClosedBall", "kind": "instance", "module": "Mathlib.Analysis.Complex.Tietze", "is_tactic_proof": true, "tactics": ["have", "have", "let", "classical", "suffices", "refine", "by_cases", "simpa", "simp", "by_cases", "ext", "simp", "refine", "replace", "simp", "refine", "simp", "not_lt,", "exact"], "tactic_count": 19}
{"name": "Metric.instTietzeExtensionBall", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Tietze", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.instTietzeExtensionClosedBall", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Tietze", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.instTietzeExtension", "kind": "instance", "module": "Mathlib.Analysis.Complex.Tietze", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "BoundedContinuousFunction.exists_norm_eq_restrict_eq", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Tietze", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.sin", "kind": "definition", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.cos", "kind": "definition", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.tan", "kind": "definition", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.cot", "kind": "definition", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.sinh", "kind": "definition", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.cosh", "kind": "definition", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.tanh", "kind": "definition", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sin", "kind": "definition", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cos", "kind": "definition", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.tan", "kind": "definition", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cot", "kind": "definition", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sinh", "kind": "definition", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cosh", "kind": "definition", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.tanh", "kind": "definition", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.two_sinh", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.two_cosh", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.sinh_zero", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.sinh_neg", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "_private.Mathlib.Analysis.Complex.Trigonometric.0.Complex.sinh_add_aux", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["ring"], "tactic_count": 1}
{"name": "Complex.sinh_add", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": ["rw", "mul_left_comm,", "exact"], "tactic_count": 3}
{"name": "Complex.cosh_zero", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.cosh_neg", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "_private.Mathlib.Analysis.Complex.Trigonometric.0.Complex.cosh_add_aux", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["ring"], "tactic_count": 1}
{"name": "Complex.cosh_add", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": ["rw", "mul_assoc,", "exact"], "tactic_count": 3}
{"name": "Complex.sinh_sub", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.cosh_sub", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.sinh_conj", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.ofReal_sinh_ofReal_re", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.ofReal_sinh", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.sinh_ofReal_im", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.sinh_ofReal_re", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.cosh_conj", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.ofReal_cosh_ofReal_re", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.ofReal_cosh", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.cosh_ofReal_im", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.cosh_ofReal_re", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.tanh_eq_sinh_div_cosh", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.tanh_zero", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.tanh_neg", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.tanh_conj", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.ofReal_tanh_ofReal_re", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.ofReal_tanh", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.tanh_ofReal_im", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.tanh_ofReal_re", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.cosh_add_sinh", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.sinh_add_cosh", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.exp_sub_cosh", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.exp_sub_sinh", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.cosh_sub_sinh", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.sinh_sub_cosh", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.cosh_sq_sub_sinh_sq", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.cosh_sq", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw", "ring"], "tactic_count": 2}
{"name": "Complex.sinh_sq", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw", "ring"], "tactic_count": 2}
{"name": "Complex.cosh_two_mul", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.sinh_two_mul", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw", "ring"], "tactic_count": 2}
{"name": "Complex.cosh_three_mul", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["have", "rw", "simp", "have", "rw", "ring"], "tactic_count": 6}
{"name": "Complex.sinh_three_mul", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["have", "rw", "simp", "have", "rw", "ring"], "tactic_count": 6}
{"name": "Complex.sin_zero", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.sin_neg", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.two_sin", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.two_cos", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.sinh_mul_I", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw", "neg_mul_eq_neg_mul]"], "tactic_count": 2}
{"name": "Complex.cosh_mul_I", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.tanh_mul_I", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.cos_mul_I", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.sin_mul_I", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": ["have", "rw", "ring_nf", "simp", "rw", "apply"], "tactic_count": 6}
{"name": "Complex.tan_mul_I", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.sin_add", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.cos_zero", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.cos_neg", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.cos_add", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw", "mul_neg_one,"], "tactic_count": 2}
{"name": "Complex.sin_sub", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.cos_sub", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.sin_add_mul_I", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.sin_eq", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "Complex.cos_add_mul_I", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.cos_eq", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "Complex.sin_sub_sin", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "rw", "rw", "ring"], "tactic_count": 6}
{"name": "Complex.cos_sub_cos", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "rw", "rw", "ring"], "tactic_count": 6}
{"name": "Complex.sin_add_sin", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Complex.cos_add_cos", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": ["calc", "cos", "cos", "congr", "rw", "ring"], "tactic_count": 6}
{"name": "Complex.sin_conj", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw", "sinh_mul_I,"], "tactic_count": 2}
{"name": "Complex.ofReal_sin_ofReal_re", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.ofReal_sin", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.sin_ofReal_im", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.sin_ofReal_re", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.cos_conj", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.ofReal_cos_ofReal_re", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.ofReal_cos", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.cos_ofReal_im", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.cos_ofReal_re", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.tan_zero", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.tan_eq_sin_div_cos", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.cot_eq_cos_div_sin", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.tan_mul_cos", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.tan_inv_eq_cot", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.cot_inv_eq_tan", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.tan_neg", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.tan_conj", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.cot_conj", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.ofReal_tan_ofReal_re", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.ofReal_cot_ofReal_re", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.ofReal_tan", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.ofReal_cot", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.tan_ofReal_im", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.tan_ofReal_re", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.cos_add_sin_I", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.cos_sub_sin_I", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.sin_sq_add_cos_sq", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.cos_sq_add_sin_sq", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.cos_two_mul'", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.cos_two_mul", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.sin_two_mul", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.cos_sq", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.cos_sq'", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.sin_sq", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.one_add_tan_sq_mul_cos_sq_eq_one", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["conv_rhs", "ring"], "tactic_count": 2}
{"name": "Complex.inv_one_add_tan_sq", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Complex.tan_sq_div_one_add_tan_sq", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.cos_three_mul", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["have", "rw", "simp", "have", "rw", "ring"], "tactic_count": 6}
{"name": "Complex.sin_three_mul", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["have", "rw", "simp", "have", "rw", "ring"], "tactic_count": 6}
{"name": "Complex.exp_mul_I", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.exp_add_mul_I", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.exp_eq_exp_re_mul_sin_add_cos", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.exp_re", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Complex.exp_im", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Complex.exp_ofReal_mul_I_re", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.exp_ofReal_mul_I_im", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.cos_add_sin_mul_I_pow", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.cos_bound", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.sin_bound", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sin_zero", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.sin_neg", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.sin_add", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cos_zero", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.cos_neg", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.cos_abs", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Real.cos_add", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sin_sub", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.cos_sub", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.sin_add_sin", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sin_sub_sin", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cos_add_cos", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cos_sub_cos", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.two_mul_sin_mul_sin", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["simp", "ring"], "tactic_count": 2}
{"name": "Real.two_mul_cos_mul_cos", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["simp", "ring"], "tactic_count": 2}
{"name": "Real.two_mul_sin_mul_cos", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["simp", "ring"], "tactic_count": 2}
{"name": "Real.tan_eq_sin_div_cos", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cot_eq_cos_div_sin", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.tan_mul_cos", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.tan_inv_eq_cot", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cot_inv_eq_tan", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.tan_zero", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.tan_neg", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.sin_sq_add_cos_sq", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cos_sq_add_sin_sq", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.sin_sq_le_one", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.cos_sq_le_one", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.abs_sin_le_one", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.abs_cos_le_one", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sin_le_one", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cos_le_one", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.neg_one_le_sin", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.neg_one_le_cos", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cos_two_mul", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cos_two_mul'", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sin_two_mul", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cos_sq", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cos_sq'", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.sin_sq", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sin_sq_eq_half_sub", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.abs_sin_eq_sqrt_one_sub_cos_sq", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.abs_cos_eq_sqrt_one_sub_sin_sq", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.one_add_tan_sq_mul_cos_sq_eq_one", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.inv_one_add_tan_sq", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.tan_sq_div_one_add_tan_sq", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.inv_sqrt_one_add_tan_sq", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.tan_div_sqrt_one_add_tan_sq", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.cos_three_mul", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.sin_three_mul", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.sinh_eq", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sinh_zero", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.sinh_neg", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.sinh_add", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.cosh_eq", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cosh_zero", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.cosh_neg", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cosh_abs", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Real.cosh_add", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.sinh_sub", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.cosh_sub", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.tanh_eq_sinh_div_cosh", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.tanh_eq", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.tanh_zero", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.tanh_neg", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.cosh_add_sinh", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.sinh_add_cosh", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.exp_sub_cosh", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.exp_sub_sinh", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cosh_sub_sinh", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Real.sinh_sub_cosh", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.cosh_sq_sub_sinh_sq", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.cosh_sq", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.cosh_sq'", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sinh_sq", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.cosh_two_mul", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.sinh_two_mul", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.cosh_three_mul", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.sinh_three_mul", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.cosh_pos", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sinh_lt_cosh", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.tanh_lt_one", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw", "field_simp", "grind"], "tactic_count": 3}
{"name": "Real.neg_one_lt_tanh", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw", "field_simp", "grind"], "tactic_count": 3}
{"name": "Real.abs_tanh_lt_one", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.tanh_sq_lt_one", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cos_bound", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.sin_bound", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.cos_pos_of_le_one", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sin_pos_of_pos_of_le_one", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sin_pos_of_pos_of_le_two", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cos_one_le", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cos_one_pos", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cos_two_neg", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalCosh", "kind": "definition", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity._example", "kind": "example", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["positivity"], "tactic_count": 1}
{"name": "Complex.norm_cos_add_sin_mul_I", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["have", "simp_all"], "tactic_count": 2}
{"name": "Complex.norm_exp_ofReal_mul_I", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.norm_exp_I_mul_ofReal", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.nnnorm_exp_ofReal_mul_I", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.nnnorm_exp_I_mul_ofReal", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.enorm_exp_ofReal_mul_I", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.enorm_exp_I_mul_ofReal", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.norm_exp_I_mul_ofReal_sub_one", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw", "nth_rw", "rw", "add_mul]", "norm_cast", "rw", "one_mul,"], "tactic_count": 7}
{"name": "Complex.norm_exp", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.norm_exp_eq_iff_re_eq", "kind": "theorem", "module": "Mathlib.Analysis.Complex.Trigonometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.UnitDisc", "kind": "definition", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.UnitDisc.term𝔻", "kind": "definition", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.UnitDisc._aux_Mathlib_Analysis_Complex_UnitDisc_Basic___macroRules_Complex_UnitDisc_term𝔻_1", "kind": "definition", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.UnitDisc._aux_Mathlib_Analysis_Complex_UnitDisc_Basic___unexpand_Complex_UnitDisc_1", "kind": "definition", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.UnitDisc.coe", "kind": "definition", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.UnitDisc.instCommSemigroup", "kind": "instance", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "Complex.UnitDisc.instSemigroupWithZero", "kind": "instance", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "Complex.UnitDisc.instIsCancelMulZero", "kind": "instance", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "Complex.UnitDisc.instHasDistribNeg", "kind": "instance", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "Complex.UnitDisc.instCoe", "kind": "instance", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.UnitDisc.coe_injective", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.UnitDisc.coe_inj", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.UnitDisc.isEmbedding_coe", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.UnitDisc.continuous_coe", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.UnitDisc.norm_lt_one", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.UnitDisc.norm_ne_one", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.UnitDisc.sq_norm_lt_one", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Complex.UnitDisc.normSq_lt_one", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Complex.UnitDisc.coe_ne_one", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.UnitDisc.coe_ne_neg_one", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.UnitDisc.one_add_coe_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.UnitDisc.coe_mul", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.UnitDisc.coe_neg", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.UnitDisc.mk", "kind": "definition", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.UnitDisc.instCanLiftCoeLtRealNormOfNat", "kind": "instance", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.UnitDisc.casesOn", "kind": "definition", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.UnitDisc.casesOn_mk", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.UnitDisc.coe_mk", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.UnitDisc.mk_inj", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.UnitDisc.forall", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.UnitDisc.exists", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.UnitDisc.mk_neg", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.UnitDisc.coe_zero", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.UnitDisc.coe_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.UnitDisc.mk_zero", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.UnitDisc.mk_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.UnitDisc.instInhabited", "kind": "instance", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.UnitDisc.instMulActionCircle", "kind": "instance", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.UnitDisc.instIsScalarTower_circle_circle", "kind": "instance", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.UnitDisc.instIsScalarTower_circle", "kind": "instance", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.UnitDisc.instSMulCommClass_circle_left", "kind": "instance", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.UnitDisc.instSMulCommClass_circle_right", "kind": "instance", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.UnitDisc.coe_circle_smul", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.UnitDisc.instMulActionClosedBall", "kind": "instance", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.UnitDisc.instIsScalarTower_closedBall_closedBall", "kind": "instance", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.UnitDisc.instIsScalarTower_closedBall", "kind": "instance", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.UnitDisc.instSMulCommClass_closedBall_left", "kind": "instance", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.UnitDisc.instSMulCommClass_closedBall_right", "kind": "instance", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.UnitDisc.instSMulCommClass_circle_closedBall", "kind": "instance", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.UnitDisc.instSMulCommClass_closedBall_circle", "kind": "instance", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.UnitDisc.coe_closedBall_smul", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.UnitDisc.instPowPNat", "kind": "instance", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.UnitDisc.coe_pow", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.UnitDisc.continuous_pow", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": true, "tactics": ["simp", "fun_prop"], "tactic_count": 2}
{"name": "Complex.UnitDisc.pow_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Complex.UnitDisc.instPNatPowAssoc", "kind": "instance", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.UnitDisc.tendsto_pow_atTop_nhds_zero", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Complex.UnitDisc.re", "kind": "definition", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.UnitDisc.im", "kind": "definition", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.UnitDisc.re_coe", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.UnitDisc.im_coe", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.UnitDisc.re_neg", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.UnitDisc.im_neg", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.UnitDisc.re_zero", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.UnitDisc.im_zero", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.UnitDisc.instStar", "kind": "instance", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.UnitDisc.conj", "kind": "definition", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.UnitDisc.coe_star", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.UnitDisc.star_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.UnitDisc.star_zero", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.UnitDisc.instInvolutiveStar", "kind": "instance", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.UnitDisc.conj_conj", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.UnitDisc.star_neg", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.UnitDisc.re_star", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.UnitDisc.im_star", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.UnitDisc.instStarMul", "kind": "instance", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.UnitDisc.conj_mul", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UnitDisc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane", "kind": "definition", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.termℍ", "kind": "definition", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane._aux_Mathlib_Analysis_Complex_UpperHalfPlane_Basic___macroRules_UpperHalfPlane_termℍ_1", "kind": "definition", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane._aux_Mathlib_Analysis_Complex_UpperHalfPlane_Basic___unexpand_UpperHalfPlane_1", "kind": "definition", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.coe", "kind": "definition", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.instCoeOutComplex", "kind": "instance", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.instInhabited", "kind": "instance", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.ext", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.ext_iff'", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.canLift", "kind": "instance", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.im", "kind": "definition", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.re", "kind": "definition", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.ext'", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.mk", "kind": "definition", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.coe_im", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.coe_re", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.mk_re", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.mk_im", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.coe_mk", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.coe_mk_subtype", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Basic", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "UpperHalfPlane.instNontrivial", "kind": "instance", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Basic", "is_tactic_proof": true, "tactics": ["constructor", "use", "simp"], "tactic_count": 3}
{"name": "UpperHalfPlane.re_add_im", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.im_pos", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.im_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.I", "kind": "definition", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.I_im", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.I_re", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.coe_I", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalUpperHalfPlaneIm", "kind": "definition", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalUpperHalfPlaneCoe", "kind": "definition", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.normSq_pos", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "UpperHalfPlane.normSq_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.im_inv_neg_coe_pos", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "UpperHalfPlane.im_pnat_div_pos", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Basic", "is_tactic_proof": true, "tactics": ["suffices", "positivity"], "tactic_count": 2}
{"name": "UpperHalfPlane.ne_nat", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Basic", "is_tactic_proof": true, "tactics": ["intro", "have", "aesop"], "tactic_count": 3}
{"name": "UpperHalfPlane.ne_int", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Basic", "is_tactic_proof": true, "tactics": ["intro", "have", "aesop"], "tactic_count": 3}
{"name": "UpperHalfPlane.posRealAction", "kind": "instance", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.coe_pos_real_smul", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.pos_real_im", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.pos_real_re", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.instAddActionReal", "kind": "instance", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.coe_vadd", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.vadd_re", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.vadd_im", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.upperHalfPlaneSet", "kind": "abbrev", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.Complex.UpperHalfPlane.Basic.0.UpperHalfPlane.termℍₒ", "kind": "definition", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.Complex.UpperHalfPlane.Basic.0.UpperHalfPlane._aux_Mathlib_Analysis_Complex_UpperHalfPlane_Basic___macroRules__private_Mathlib_Analysis_Complex_UpperHalfPlane_Basic_0_UpperHalfPlane_termℍₒ_1", "kind": "definition", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.Complex.UpperHalfPlane.Basic.0.UpperHalfPlane._aux_Mathlib_Analysis_Complex_UpperHalfPlane_Basic___unexpand_UpperHalfPlane_upperHalfPlaneSet_1", "kind": "definition", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.isOpen_upperHalfPlaneSet", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.Complex.UpperHalfPlane.Exp.0.term𝕢", "kind": "definition", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Exp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.Complex.UpperHalfPlane.Exp.0._aux_Mathlib_Analysis_Complex_UpperHalfPlane_Exp___macroRules__private_Mathlib_Analysis_Complex_UpperHalfPlane_Exp_0_term𝕢_1", "kind": "definition", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Exp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.Complex.UpperHalfPlane.Exp.0._aux_Mathlib_Analysis_Complex_UpperHalfPlane_Exp___unexpand_Function_Periodic_qParam_1", "kind": "definition", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Exp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Periodic.im_invQParam_pos_of_norm_lt_one", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Exp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Periodic.norm_qParam_le_of_one_half_le_im", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Exp", "is_tactic_proof": true, "tactics": ["rwa", "neg_le_neg_iff,", "le_mul_iff_one_le_right"], "tactic_count": 3}
{"name": "UpperHalfPlane.norm_qParam_lt_one", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Exp", "is_tactic_proof": false, "tactics": ["rw", "div_pos_iff_of_pos_right", "positivity"], "tactic_count": 3}
{"name": "UpperHalfPlane.norm_exp_two_pi_I_lt_one", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Exp", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "UpperHalfPlane.atImInfty", "kind": "definition", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.FunctionsBoundedAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.instNeBotAtImInfty", "kind": "instance", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.FunctionsBoundedAtInfty", "is_tactic_proof": true, "tactics": ["refine", "filter_upwards"], "tactic_count": 2}
{"name": "UpperHalfPlane.atImInfty_basis", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.FunctionsBoundedAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.atImInfty_mem", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.FunctionsBoundedAtInfty", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "UpperHalfPlane.IsBoundedAtImInfty", "kind": "definition", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.FunctionsBoundedAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.IsZeroAtImInfty", "kind": "definition", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.FunctionsBoundedAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.zero_form_isBoundedAtImInfty", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.FunctionsBoundedAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.zeroAtImInftySubmodule", "kind": "definition", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.FunctionsBoundedAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.boundedAtImInftySubalgebra", "kind": "definition", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.FunctionsBoundedAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.isBoundedAtImInfty_iff", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.FunctionsBoundedAtInfty", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "UpperHalfPlane.isZeroAtImInfty_iff", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.FunctionsBoundedAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.IsZeroAtImInfty.isBoundedAtImInfty", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.FunctionsBoundedAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.tendsto_comap_im_ofComplex", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.FunctionsBoundedAtInfty", "is_tactic_proof": true, "tactics": ["simp", "refine", "filter_upwards", "simp"], "tactic_count": 4}
{"name": "UpperHalfPlane.tendsto_coe_atImInfty", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.FunctionsBoundedAtInfty", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "UpperHalfPlane.tendsto_smul_atImInfty", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.FunctionsBoundedAtInfty", "is_tactic_proof": false, "tactics": ["suffices", "simpa", "abs_of_pos", "apply", "simpa"], "tactic_count": 5}
{"name": "UpperHalfPlane.instChartedSpaceComplex", "kind": "instance", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Manifold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.instIsManifoldComplexModelWithCornersSelfTopWithTopENat", "kind": "instance", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Manifold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.contMDiff_coe", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Manifold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.mdifferentiable_coe", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Manifold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.contMDiffAt_ofComplex", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Manifold", "is_tactic_proof": true, "tactics": ["rw", "constructor", "rw", "refine", "simpa", "simpa"], "tactic_count": 6}
{"name": "UpperHalfPlane.mdifferentiableAt_ofComplex", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Manifold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.contMDiffAt_iff", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Manifold", "is_tactic_proof": true, "tactics": ["rw", "refine", "exact", "simpa"], "tactic_count": 4}
{"name": "UpperHalfPlane.mdifferentiableAt_iff", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Manifold", "is_tactic_proof": true, "tactics": ["rw", "refine", "exact", "simpa"], "tactic_count": 4}
{"name": "UpperHalfPlane.mdifferentiable_iff", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Manifold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.contMDiff_num", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Manifold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.contMDiff_denom", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Manifold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.contMDiff_denom_zpow", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Manifold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.contMDiff_inv_denom", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Manifold", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "UpperHalfPlane.contMDiff_smul", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Manifold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.mdifferentiable_num", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Manifold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.mdifferentiable_denom", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Manifold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.mdifferentiable_denom_zpow", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Manifold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.mdifferentiable_inv_denom", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Manifold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.mdifferentiable_smul", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Manifold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.eq_zero_of_frequently", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Manifold", "is_tactic_proof": true, "tactics": ["rw", "have", "ext", "convert", "rw", "rfl", "exact", "contrapose", "rw", "rw", "filter_upwards", "simpa"], "tactic_count": 12}
{"name": "UpperHalfPlane.mul_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Manifold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.prod_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Manifold", "is_tactic_proof": true, "tactics": ["refine", "have", "simp", "exact"], "tactic_count": 4}
{"name": "UpperHalfPlane.instDist", "kind": "instance", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.dist_eq", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.sinh_half_dist", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Metric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "UpperHalfPlane.cosh_half_dist", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Metric", "is_tactic_proof": true, "tactics": ["rw", "congr", "simp", "ring", "all_goals"], "tactic_count": 5}
{"name": "UpperHalfPlane.tanh_half_dist", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Metric", "is_tactic_proof": true, "tactics": ["rw", "positivity"], "tactic_count": 2}
{"name": "UpperHalfPlane.exp_half_dist", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Metric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "UpperHalfPlane.cosh_dist", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Metric", "is_tactic_proof": true, "tactics": ["rw", "mul_assoc,", "positivity"], "tactic_count": 3}
{"name": "UpperHalfPlane.sinh_half_dist_add_dist", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Metric", "is_tactic_proof": true, "tactics": ["simp", "rw", "congr", "rw"], "tactic_count": 4}
{"name": "UpperHalfPlane.dist_comm", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Metric", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "UpperHalfPlane.dist_le_iff_le_sinh", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Metric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "UpperHalfPlane.dist_eq_iff_eq_sinh", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Metric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "UpperHalfPlane.dist_eq_iff_eq_sq_sinh", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Metric", "is_tactic_proof": true, "tactics": ["rw", "norm_num", "all_goals"], "tactic_count": 3}
{"name": "UpperHalfPlane.dist_triangle", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Metric", "is_tactic_proof": false, "tactics": ["rw", "gcongr", "exact", "rw", "exact"], "tactic_count": 5}
{"name": "UpperHalfPlane.dist_le_dist_coe_div_sqrt", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Metric", "is_tactic_proof": true, "tactics": ["rw", "positivity"], "tactic_count": 2}
{"name": "UpperHalfPlane.metricSpaceAux", "kind": "definition", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.cosh_dist'", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Metric", "is_tactic_proof": true, "tactics": ["simp", "ring"], "tactic_count": 2}
{"name": "UpperHalfPlane.center", "kind": "definition", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.center_re", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.center_im", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.center_zero", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.dist_coe_center_sq", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Metric", "is_tactic_proof": true, "tactics": ["have", "simp", "mul_div_cancel₀", "ring"], "tactic_count": 4}
{"name": "UpperHalfPlane.dist_coe_center", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Metric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "UpperHalfPlane.cmp_dist_eq_cmp_dist_coe_center", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Metric", "is_tactic_proof": true, "tactics": ["letI", "rcases", "trans", "exacts", "have", "have", "simp", "rw"], "tactic_count": 8}
{"name": "UpperHalfPlane.dist_eq_iff_dist_coe_center_eq", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.dist_self_center", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Metric", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "UpperHalfPlane.dist_center_dist", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.dist_lt_iff_dist_coe_center_lt", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.lt_dist_iff_lt_dist_coe_center", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.dist_le_iff_dist_coe_center_le", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.le_dist_iff_le_dist_coe_center", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.dist_of_re_eq", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Metric", "is_tactic_proof": true, "tactics": ["have", "rw", "dist_of_re_eq,", "nth_rw", "simp", "congr", "field"], "tactic_count": 7}
{"name": "UpperHalfPlane.dist_log_im_le", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.im_le_im_mul_exp_dist", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Metric", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "UpperHalfPlane.im_div_exp_dist_le", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.dist_coe_le", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.le_dist_coe", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.instMetricSpace", "kind": "instance", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.im_pos_of_dist_center_le", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.image_coe_closedBall", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Metric", "is_tactic_proof": true, "tactics": ["ext", "rintro", "exact", "intro", "lift", "exact"], "tactic_count": 6}
{"name": "UpperHalfPlane.image_coe_ball", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Metric", "is_tactic_proof": true, "tactics": ["ext", "rintro", "exact", "intro", "lift", "exact"], "tactic_count": 6}
{"name": "UpperHalfPlane.image_coe_sphere", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Metric", "is_tactic_proof": true, "tactics": ["ext", "rintro", "exact", "intro", "lift", "exact"], "tactic_count": 6}
{"name": "UpperHalfPlane.instProperSpace", "kind": "instance", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Metric", "is_tactic_proof": true, "tactics": ["refine", "rw", "apply"], "tactic_count": 3}
{"name": "UpperHalfPlane.isometry_vertical_line", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Metric", "is_tactic_proof": true, "tactics": ["refine", "rw", "exacts"], "tactic_count": 3}
{"name": "UpperHalfPlane.isometry_real_vadd", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.isometry_pos_mul", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Metric", "is_tactic_proof": true, "tactics": ["refine", "simp", "rw", "mul_left_comm]", "exact"], "tactic_count": 5}
{"name": "UpperHalfPlane.instIsIsometricSMulSpecialLinearGroupFinOfNatNatReal", "kind": "instance", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.term↑ₘ_", "kind": "definition", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane._aux_Mathlib_Analysis_Complex_UpperHalfPlane_MoebiusAction___macroRules_UpperHalfPlane_term↑ₘ__1", "kind": "definition", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.instCoeFun", "kind": "instance", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.term↑ₘ[_]_", "kind": "definition", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane._aux_Mathlib_Analysis_Complex_UpperHalfPlane_MoebiusAction___macroRules_UpperHalfPlane_term↑ₘ[_]__1", "kind": "definition", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.num", "kind": "definition", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.denom", "kind": "definition", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.num_neg", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "UpperHalfPlane.denom_neg", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "UpperHalfPlane.linear_ne_zero_of_im", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": true, "tactics": ["contrapose", "have", "apply_fun", "simpa", "or_false]", "simp", "ext", "fin_cases"], "tactic_count": 8}
{"name": "UpperHalfPlane.linear_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.denom_ne_zero_of_im", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": true, "tactics": ["refine", "simp"], "tactic_count": 2}
{"name": "UpperHalfPlane.denom_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.normSq_denom_pos", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.normSq_denom_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.denom_cocycle", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": true, "tactics": ["change", "field_simp", "simp", "ring"], "tactic_count": 4}
{"name": "UpperHalfPlane.moebius_im", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": false, "tactics": ["simp", "add_zero,", "ring"], "tactic_count": 3}
{"name": "UpperHalfPlane.σ", "kind": "definition", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.σ_conj", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": true, "tactics": ["simp", "split_ifs"], "tactic_count": 2}
{"name": "UpperHalfPlane.σ_ofReal", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": true, "tactics": ["simp", "split_ifs"], "tactic_count": 2}
{"name": "UpperHalfPlane.σ_num", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "UpperHalfPlane.σ_denom", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "UpperHalfPlane.σ_neg", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "UpperHalfPlane.σ_sq", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": true, "tactics": ["simp", "split_ifs"], "tactic_count": 2}
{"name": "UpperHalfPlane.σ_im_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": true, "tactics": ["simp", "split_ifs"], "tactic_count": 2}
{"name": "UpperHalfPlane.σ_mul", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": true, "tactics": ["simp", "rcases", "simp", "simp", "simp", "simp"], "tactic_count": 6}
{"name": "UpperHalfPlane.σ_mul_comm", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": true, "tactics": ["simp", "split_ifs"], "tactic_count": 2}
{"name": "UpperHalfPlane.norm_σ", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": true, "tactics": ["simp", "split_ifs"], "tactic_count": 2}
{"name": "UpperHalfPlane.smulAux'", "kind": "definition", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.smulAux'_im", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": true, "tactics": ["simp", "split_ifs", "simpa"], "tactic_count": 3}
{"name": "UpperHalfPlane.smulAux", "kind": "definition", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.denom_cocycle'", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": true, "tactics": ["simp", "change", "field_simp", "simp", "ring"], "tactic_count": 5}
{"name": "UpperHalfPlane.mul_smul'", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": true, "tactics": ["ext", "simp", "generalize", "have", "have", "rw", "exact", "rw", "div_add", "conv_rhs", "rw", "congr", "simp", "ring"], "tactic_count": 14}
{"name": "UpperHalfPlane.glAction", "kind": "instance", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.coe_smul", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.coe_smul_of_det_pos", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": true, "tactics": ["change", "rw"], "tactic_count": 2}
{"name": "UpperHalfPlane.denom_cocycle_σ", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.glPos_smul_def", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "UpperHalfPlane.re_smul", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": true, "tactics": ["change", "simp"], "tactic_count": 2}
{"name": "UpperHalfPlane.im_smul", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": true, "tactics": ["change", "simp", "abs_of_nonneg", "split_ifs"], "tactic_count": 4}
{"name": "UpperHalfPlane.im_smul_eq_div_normSq", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.c_mul_im_sq_le_normSq_denom", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": true, "tactics": ["set", "set", "calc"], "tactic_count": 3}
{"name": "UpperHalfPlane.neg_smul", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": true, "tactics": ["ext1", "simp"], "tactic_count": 2}
{"name": "UpperHalfPlane.denom_one", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "UpperHalfPlane.SLAction", "kind": "instance", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.coe_specialLinearGroup_apply", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "UpperHalfPlane.specialLinearGroup_apply", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": true, "tactics": ["ext", "simp", "instead"], "tactic_count": 3}
{"name": "UpperHalfPlane.modular_S_smul", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "UpperHalfPlane.modular_T_zpow_smul", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": true, "tactics": ["rw", "simp", "div_one]"], "tactic_count": 3}
{"name": "UpperHalfPlane.modular_T_smul", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "UpperHalfPlane.exists_SL2_smul_eq_of_apply_zero_one_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": true, "tactics": ["obtain", "refine", "ext1", "suffices", "ring"], "tactic_count": 5}
{"name": "UpperHalfPlane.exists_SL2_smul_eq_of_apply_zero_one_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": true, "tactics": ["have", "induction", "replace", "refine", "ext1", "suffices", "simpa", "replace", "replace", "replace", "grind"], "tactic_count": 11}
{"name": "ModularGroup.coe", "kind": "definition", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModularGroup.coe_inj", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": true, "tactics": ["refine", "simp", "simpa"], "tactic_count": 3}
{"name": "ModularGroup.instCoeSpecialLinearGroupFinOfNatNatIntSubtypeGeneralLinearGroupRealMemSubgroupGLPos", "kind": "instance", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModularGroup.coeHom", "kind": "definition", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModularGroup.coeHom_apply", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModularGroup.coe_apply_complex", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModularGroup.det_coe", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ModularGroup.coe_one", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ModularGroup.SLOnGLPos", "kind": "instance", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModularGroup.SLOnGLPos_smul_apply", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModularGroup.SL_to_GL_tower", "kind": "instance", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModularGroup.sl_moeb", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModularGroup.SL_neg_smul", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": true, "tactics": ["rw", "congr", "simp"], "tactic_count": 3}
{"name": "ModularGroup.im_smul_eq_div_normSq", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ModularGroup.denom_apply", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModularGroup.denom_S", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "UpperHalfPlane.instTopologicalSpace", "kind": "instance", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.isOpenEmbedding_coe", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.isEmbedding_coe", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.continuous_coe", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.continuous_re", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.continuous_im", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.instSecondCountableTopology", "kind": "instance", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.instT3Space", "kind": "instance", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.instT4Space", "kind": "instance", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.instContractibleSpace", "kind": "instance", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.instLocPathConnectedSpace", "kind": "instance", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.instNoncompactSpace", "kind": "instance", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Topology", "is_tactic_proof": true, "tactics": ["refine", "have", "simpa"], "tactic_count": 3}
{"name": "UpperHalfPlane.instLocallyCompactSpace", "kind": "instance", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.instContinuousGLSMul", "kind": "instance", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.verticalStrip", "kind": "definition", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.mem_verticalStrip_iff", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.verticalStrip_mono", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Topology", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "UpperHalfPlane.verticalStrip_mono_left", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.verticalStrip_anti_right", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.subset_verticalStrip_of_isCompact", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Topology", "is_tactic_proof": true, "tactics": ["rcases", "exact", "obtain", "obtain", "exact"], "tactic_count": 5}
{"name": "UpperHalfPlane.ModularGroup_T_zpow_mem_verticalStrip", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Topology", "is_tactic_proof": true, "tactics": ["let", "use", "rw", "refine", "have", "norm_cast", "rw", "simp", "have", "have", "rw", "apply"], "tactic_count": 12}
{"name": "UpperHalfPlane.ofComplex", "kind": "definition", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.term↑ₕ_", "kind": "definition", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane._aux_Mathlib_Analysis_Complex_UpperHalfPlane_Topology___macroRules_UpperHalfPlane_term↑ₕ__1", "kind": "definition", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.ofComplex_apply", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.ofComplex_apply_eq_ite", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Topology", "is_tactic_proof": true, "tactics": ["split_ifs", "exact", "change", "simp", "rintro", "exact"], "tactic_count": 6}
{"name": "UpperHalfPlane.ofComplex_apply_of_im_pos", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Topology", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "UpperHalfPlane.ofComplex_apply_of_im_nonpos", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Topology", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "UpperHalfPlane.ofComplex_apply_eq_of_im_nonpos", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Topology", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "UpperHalfPlane.comp_ofComplex", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.comp_ofComplex_of_im_pos", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHalfPlane.comp_ofComplex_of_im_le_zero", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Topology", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "UpperHalfPlane.eventuallyEq_coe_comp_ofComplex", "kind": "theorem", "module": "Mathlib.Analysis.Complex.UpperHalfPlane.Topology", "is_tactic_proof": true, "tactics": ["filter_upwards", "simp"], "tactic_count": 2}
{"name": "ValueDistribution.characteristic", "kind": "definition", "module": "Mathlib.Analysis.Complex.ValueDistribution.CharacteristicFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValueDistribution.characteristic_congr_codiscrete", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.CharacteristicFunction", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ValueDistribution.characteristic_sub_characteristic_eq_proximity_sub_proximity", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.CharacteristicFunction", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ValueDistribution.characteristic_even", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.CharacteristicFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValueDistribution.characteristic_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.CharacteristicFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValueDistribution.characteristic_eventually_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.CharacteristicFunction", "is_tactic_proof": true, "tactics": ["filter_upwards"], "tactic_count": 1}
{"name": "ValueDistribution.characteristic_add_top_le", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.CharacteristicFunction", "is_tactic_proof": true, "tactics": ["simp", "calc", "proximity", "gcongr", "apply", "exact"], "tactic_count": 6}
{"name": "ValueDistribution.characteristic_add_top_eventuallyLE", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.CharacteristicFunction", "is_tactic_proof": true, "tactics": ["filter_upwards"], "tactic_count": 1}
{"name": "ValueDistribution.characteristic_sum_top_le", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.CharacteristicFunction", "is_tactic_proof": true, "tactics": ["simp", "calc", "proximity", "gcongr", "apply", "apply"], "tactic_count": 6}
{"name": "ValueDistribution.characteristic_sum_top_eventuallyLE", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.CharacteristicFunction", "is_tactic_proof": true, "tactics": ["filter_upwards"], "tactic_count": 1}
{"name": "ValueDistribution.characteristic_mul_zero_le", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.CharacteristicFunction", "is_tactic_proof": true, "tactics": ["simp", "rw", "apply"], "tactic_count": 3}
{"name": "ValueDistribution.characteristic_mul_zero_eventuallyLE", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.CharacteristicFunction", "is_tactic_proof": true, "tactics": ["filter_upwards"], "tactic_count": 1}
{"name": "ValueDistribution.characteristic_mul_top_le", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.CharacteristicFunction", "is_tactic_proof": true, "tactics": ["simp", "rw", "apply"], "tactic_count": 3}
{"name": "ValueDistribution.characteristic_mul_top_eventuallyLE", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.CharacteristicFunction", "is_tactic_proof": true, "tactics": ["filter_upwards"], "tactic_count": 1}
{"name": "ValueDistribution.characteristic_pow_zero", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.CharacteristicFunction", "is_tactic_proof": true, "tactics": ["simp_all"], "tactic_count": 1}
{"name": "ValueDistribution.characteristic_pow_top", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.CharacteristicFunction", "is_tactic_proof": true, "tactics": ["simp_all"], "tactic_count": 1}
{"name": "ValueDistribution.characteristic_sub_characteristic_inv", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.FirstMainTheorem", "is_tactic_proof": true, "tactics": ["calc", "characteristic", "unfold", "ring", "rw", "rw"], "tactic_count": 6}
{"name": "ValueDistribution.characteristic_sub_characteristic_inv_of_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.FirstMainTheorem", "is_tactic_proof": true, "tactics": ["calc", "characteristic", "rw", "rw", "unfold", "have", "simp"], "tactic_count": 7}
{"name": "ValueDistribution.characteristic_sub_characteristic_inv_at_zero", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.FirstMainTheorem", "is_tactic_proof": true, "tactics": ["calc", "characteristic", "rw"], "tactic_count": 3}
{"name": "ValueDistribution.characteristic_sub_characteristic_inv_le", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.FirstMainTheorem", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "simp"], "tactic_count": 3}
{"name": "ValueDistribution.isBigO_characteristic_sub_characteristic_inv", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.FirstMainTheorem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValueDistribution.abs_characteristic_sub_characteristic_shift_le", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.FirstMainTheorem", "is_tactic_proof": false, "tactics": ["have", "have", "apply", "apply", "rw", "simp", "apply", "apply", "apply", "intro", "simp", "by_cases", "simpa", "simp", "convert", "rw", "abel_nf", "simp"], "tactic_count": 18}
{"name": "ValueDistribution.isBigO_characteristic_sub_characteristic_shift", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.FirstMainTheorem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.locallyFinsuppWithin.toClosedBall", "kind": "definition", "module": "Mathlib.Analysis.Complex.ValueDistribution.LogCounting.Basic", "is_tactic_proof": true, "tactics": ["apply", "tauto"], "tactic_count": 2}
{"name": "Function.locallyFinsuppWithin.toClosedBall_eval_within", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.LogCounting.Basic", "is_tactic_proof": true, "tactics": ["unfold", "simp_all"], "tactic_count": 2}
{"name": "Function.locallyFinsuppWithin.toClosedBall_divisor", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.LogCounting.Basic", "is_tactic_proof": true, "tactics": ["simp_all"], "tactic_count": 1}
{"name": "Function.locallyFinsuppWithin.toClosedBall_support_subset_closedBall", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.LogCounting.Basic", "is_tactic_proof": true, "tactics": ["simp_all"], "tactic_count": 1}
{"name": "Function.locallyFinsuppWithin.logCounting", "kind": "definition", "module": "Mathlib.Analysis.Complex.ValueDistribution.LogCounting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.locallyFinsuppWithin.logCounting_eval_zero", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.LogCounting.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Function.locallyFinsuppWithin.logCounting_even", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.LogCounting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.locallyFinsuppWithin.logCounting_mono", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.LogCounting.Basic", "is_tactic_proof": true, "tactics": ["intro", "simp_all", "gcongr", "let", "have", "repeat", "gcongr", "by_cases", "simp", "have", "rw", "by_cases", "rw", "gcongr", "exact", "simp", "apply", "apply", "simp_all", "intro", "aesop", "intro", "simp", "inv_eq_zero,", "intro", "have", "rw", "rwa", "simp_all", "linarith", "exact"], "tactic_count": 31}
{"name": "Function.locallyFinsuppWithin.logCounting_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.LogCounting.Basic", "is_tactic_proof": true, "tactics": ["have", "suffices", "add_nonneg", "intro", "by_cases", "simp_all", "by_cases", "refine", "simpa", "simpa", "simp"], "tactic_count": 11}
{"name": "Function.locallyFinsuppWithin.logCounting_le", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.LogCounting.Basic", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "Function.locallyFinsuppWithin.logCounting_eventuallyLE", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.LogCounting.Basic", "is_tactic_proof": true, "tactics": ["filter_upwards", "exact"], "tactic_count": 2}
{"name": "ValueDistribution.logCounting", "kind": "definition", "module": "Mathlib.Analysis.Complex.ValueDistribution.LogCounting.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "exact"], "tactic_count": 3}
{"name": "locallyFinsuppWithin.logCounting_divisor", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.LogCounting.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ValueDistribution.logCounting_coe", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.LogCounting.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ValueDistribution.logCounting_coe_eq_logCounting_sub_const_zero", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.LogCounting.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ValueDistribution.logCounting_zero", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.LogCounting.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ValueDistribution.logCounting_top", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.LogCounting.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ValueDistribution.logCounting_eval_zero", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.LogCounting.Basic", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "ValueDistribution.log_counting_zero_sub_logCounting_top", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.LogCounting.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ValueDistribution.logCounting_const", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.LogCounting.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ValueDistribution.logCounting_const_zero", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.LogCounting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValueDistribution.logCounting_even", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.LogCounting.Basic", "is_tactic_proof": true, "tactics": ["intro", "by_cases"], "tactic_count": 2}
{"name": "ValueDistribution.logCounting_monotoneOn", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.LogCounting.Basic", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "ValueDistribution.logCounting_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.LogCounting.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "simp", "locallyFinsuppWithin.logCounting_nonneg"], "tactic_count": 4}
{"name": "ValueDistribution.logCounting_eventually_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.LogCounting.Basic", "is_tactic_proof": true, "tactics": ["filter_upwards"], "tactic_count": 1}
{"name": "ValueDistribution.logCounting_congr_codiscrete", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.LogCounting.Basic", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "simp", "congr", "exact", "simp", "congr", "apply", "filter_upwards"], "tactic_count": 9}
{"name": "ValueDistribution.logCounting_inv", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.LogCounting.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ValueDistribution.logCounting_add_analyticOn", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.LogCounting.Basic", "is_tactic_proof": true, "tactics": ["simp", "rw"], "tactic_count": 2}
{"name": "ValueDistribution.logCounting_add_const", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.LogCounting.Basic", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "ValueDistribution.logCounting_sub_const", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.LogCounting.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ValueDistribution.logCounting_add_top_le", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.LogCounting.Basic", "is_tactic_proof": true, "tactics": ["simp", "rw", "exact"], "tactic_count": 3}
{"name": "ValueDistribution.logCounting_add_top_eventuallyLE", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.LogCounting.Basic", "is_tactic_proof": true, "tactics": ["filter_upwards", "exact"], "tactic_count": 2}
{"name": "ValueDistribution.logCounting_sum_top_le", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.LogCounting.Basic", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "insert", "rw", "calc", "logCounting"], "tactic_count": 7}
{"name": "ValueDistribution.logCounting_sum_top_eventuallyLE", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.LogCounting.Basic", "is_tactic_proof": true, "tactics": ["filter_upwards", "exact"], "tactic_count": 2}
{"name": "ValueDistribution.logCounting_mul_zero_le", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.LogCounting.Basic", "is_tactic_proof": true, "tactics": ["simp", "rw", "locallyFinsuppWithin.logCounting.map_add]", "apply", "apply"], "tactic_count": 5}
{"name": "ValueDistribution.logCounting_mul_zero_eventuallyLE", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.LogCounting.Basic", "is_tactic_proof": true, "tactics": ["filter_upwards", "exact"], "tactic_count": 2}
{"name": "ValueDistribution.logCounting_mul_top_le", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.LogCounting.Basic", "is_tactic_proof": true, "tactics": ["simp", "rw", "locallyFinsuppWithin.logCounting.map_add]", "apply", "apply"], "tactic_count": 5}
{"name": "ValueDistribution.logCounting_mul_top_eventuallyLE", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.LogCounting.Basic", "is_tactic_proof": true, "tactics": ["filter_upwards", "exact"], "tactic_count": 2}
{"name": "ValueDistribution.logCounting_pow_zero", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.LogCounting.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ValueDistribution.logCounting_pow_top", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.LogCounting.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Function.locallyFinsuppWithin.logCounting_divisor_eq_circleAverage_sub_const", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.LogCounting.Basic", "is_tactic_proof": true, "tactics": ["have", "simp", "congr", "simp_all", "rw", "all_goals"], "tactic_count": 6}
{"name": "ValueDistribution.logCounting_zero_sub_logCounting_top_eq_circleAverage_sub_const", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.LogCounting.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ValueDistribution.proximity", "kind": "definition", "module": "Mathlib.Analysis.Complex.ValueDistribution.Proximity.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "exact"], "tactic_count": 3}
{"name": "ValueDistribution.proximity_coe", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.Proximity.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ValueDistribution.proximity_zero", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.Proximity.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ValueDistribution.proximity_zero_of_complexValued", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.Proximity.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ValueDistribution.proximity_top", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.Proximity.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ValueDistribution.proximity_congr_codiscreteWithin", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.Proximity.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "all_goals", "simp", "apply", "filter_upwards"], "tactic_count": 5}
{"name": "ValueDistribution.proximity_congr_codiscrete", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.Proximity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValueDistribution.proximity_coe_eq_proximity_sub_const_zero", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.Proximity.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ValueDistribution.proximity_inv", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.Proximity.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ValueDistribution.proximity_sub_proximity_inv_eq_circleAverage", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.Proximity.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp", "rw", "simp_rw", "apply", "simp_rw", "apply"], "tactic_count": 7}
{"name": "ValueDistribution.proximity_even", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.Proximity.Basic", "is_tactic_proof": true, "tactics": ["intro", "by_cases"], "tactic_count": 2}
{"name": "ValueDistribution.proximity_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.Proximity.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "intro", "simpa"], "tactic_count": 3}
{"name": "ValueDistribution.proximity_const", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.Proximity.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ValueDistribution.proximity_sum_top_le", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.Proximity.Basic", "is_tactic_proof": true, "tactics": ["simp", "intro", "have", "circleIntegrable_posLog_norm_meromorphicOn", "simp", "calc", "circleAverage", "apply", "apply", "apply", "fun_prop", "apply", "intro", "rw", "apply", "nth_rw", "rw", "circleAverage_add", "congr", "ext", "simp"], "tactic_count": 21}
{"name": "ValueDistribution.proximity_add_top_le", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.Proximity.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ValueDistribution.proximity_mul_top_le", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.Proximity.Basic", "is_tactic_proof": true, "tactics": ["calc", "proximity", "intro", "apply", "simp_rw", "apply", "apply", "fun_prop", "apply", "exact", "ext", "apply", "exact", "exact"], "tactic_count": 14}
{"name": "ValueDistribution.proximity_mul_zero_le", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.Proximity.Basic", "is_tactic_proof": true, "tactics": ["calc", "proximity", "rw", "apply"], "tactic_count": 4}
{"name": "ValueDistribution.proximity_pow_top", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.Proximity.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "ValueDistribution.proximity_pow_zero", "kind": "theorem", "module": "Mathlib.Analysis.Complex.ValueDistribution.Proximity.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HasConstantSpeedOnWith", "kind": "definition", "module": "Mathlib.Analysis.ConstantSpeed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasConstantSpeedOnWith.hasLocallyBoundedVariationOn", "kind": "theorem", "module": "Mathlib.Analysis.ConstantSpeed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasConstantSpeedOnWith_of_subsingleton", "kind": "theorem", "module": "Mathlib.Analysis.ConstantSpeed", "is_tactic_proof": true, "tactics": ["rintro", "rw", "simp"], "tactic_count": 3}
{"name": "hasConstantSpeedOnWith_iff_ordered", "kind": "theorem", "module": "Mathlib.Analysis.ConstantSpeed", "is_tactic_proof": true, "tactics": ["refine", "rcases", "exact", "rw", "exact", "rintro", "cases", "cases", "rfl"], "tactic_count": 9}
{"name": "hasConstantSpeedOnWith_iff_variationOnFromTo_eq", "kind": "theorem", "module": "Mathlib.Analysis.ConstantSpeed", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "rw", "rcases", "rw", "exact", "rw", "have", "simp_all", "rw", "rintro", "rw"], "tactic_count": 12}
{"name": "HasConstantSpeedOnWith.union", "kind": "theorem", "module": "Mathlib.Analysis.ConstantSpeed", "is_tactic_proof": true, "tactics": ["rw", "rintro", "have", "ext", "rintro", "exact", "exact", "rintro", "rw", "have", "ext", "rintro", "exacts", "rintro", "exacts", "rw", "have", "simp", "rw", "ring_nf", "exacts", "cases", "simp", "exact", "have", "ext", "rintro", "exact", "exact", "rintro", "rw"], "tactic_count": 31}
{"name": "HasConstantSpeedOnWith.Icc_Icc", "kind": "theorem", "module": "Mathlib.Analysis.ConstantSpeed", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "rw", "exact", "rintro", "rw", "rintro", "rw", "sup_of_le_right"], "tactic_count": 9}
{"name": "hasConstantSpeedOnWith_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.ConstantSpeed", "is_tactic_proof": true, "tactics": ["dsimp", "simp", "constructor", "by_contra", "simp_rw", "push_neg", "obtain", "rcases", "exact", "rw", "exact", "rintro", "simpa"], "tactic_count": 13}
{"name": "HasConstantSpeedOnWith.ratio", "kind": "theorem", "module": "Mathlib.Analysis.ConstantSpeed", "is_tactic_proof": true, "tactics": ["rintro", "rw", "rw", "rw", "symm", "calc"], "tactic_count": 6}
{"name": "HasUnitSpeedOn", "kind": "definition", "module": "Mathlib.Analysis.ConstantSpeed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasUnitSpeedOn.union", "kind": "theorem", "module": "Mathlib.Analysis.ConstantSpeed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasUnitSpeedOn.Icc_Icc", "kind": "theorem", "module": "Mathlib.Analysis.ConstantSpeed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unique_unit_speed", "kind": "theorem", "module": "Mathlib.Analysis.ConstantSpeed", "is_tactic_proof": true, "tactics": ["dsimp", "convert", "simp"], "tactic_count": 3}
{"name": "unique_unit_speed_on_Icc_zero", "kind": "theorem", "module": "Mathlib.Analysis.ConstantSpeed", "is_tactic_proof": true, "tactics": ["rw", "convert", "have", "have", "obtain", "apply", "have", "exact", "simp", "rfl"], "tactic_count": 10}
{"name": "naturalParameterization", "kind": "definition", "module": "Mathlib.Analysis.ConstantSpeed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "edist_naturalParameterization_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.ConstantSpeed", "is_tactic_proof": true, "tactics": ["dsimp", "haveI", "obtain", "rw", "apply"], "tactic_count": 5}
{"name": "has_unit_speed_naturalParameterization", "kind": "theorem", "module": "Mathlib.Analysis.ConstantSpeed", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "rintro", "rcases", "rw", "exact", "rw", "variationOnFromTo.add", "rw", "eVariationOn.comp_inter_Icc_eq_of_monotoneOn", "rw", "rw", "rintro", "exact"], "tactic_count": 14}
{"name": "AmpleSet", "kind": "definition", "module": "Mathlib.Analysis.Convex.AmpleSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ampleSet_univ", "kind": "theorem", "module": "Mathlib.Analysis.Convex.AmpleSet", "is_tactic_proof": true, "tactics": ["intro", "rw"], "tactic_count": 2}
{"name": "ampleSet_empty", "kind": "theorem", "module": "Mathlib.Analysis.Convex.AmpleSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AmpleSet.union", "kind": "theorem", "module": "Mathlib.Analysis.Convex.AmpleSet", "is_tactic_proof": true, "tactics": ["intro", "rcases", "rw", "apply", "apply"], "tactic_count": 5}
{"name": "AmpleSet.image", "kind": "theorem", "module": "Mathlib.Analysis.Convex.AmpleSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AmpleSet.image_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.AmpleSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AmpleSet.preimage", "kind": "theorem", "module": "Mathlib.Analysis.Convex.AmpleSet", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "AmpleSet.preimage_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.AmpleSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AmpleSet.vadd", "kind": "theorem", "module": "Mathlib.Analysis.Convex.AmpleSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AmpleSet.vadd_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.AmpleSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AmpleSet.of_one_lt_codim", "kind": "theorem", "module": "Mathlib.Analysis.Convex.AmpleSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Convex", "kind": "definition", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Convex.starConvex", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "convex_iff_segment_subset", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Convex.segment_subset", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Convex.openSegment_subset", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "convex_iff_add_mem", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "convex_iff_pointwise_add_subset", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "convex_empty", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "convex_univ", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Convex.inter", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "convex_sInter", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "convex_iInter", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "convex_iInter₂", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Convex.prod", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "convex_pi", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Directed.convex_iUnion", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": true, "tactics": ["rintro", "rw", "obtain", "obtain", "obtain", "exact"], "tactic_count": 6}
{"name": "DirectedOn.convex_sUnion", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Convex.setOf_const_imp", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "convex_iff_openSegment_subset", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "convex_iff_forall_pos", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "convex_iff_pairwise_pos", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": true, "tactics": ["refine", "intro", "obtain", "rwa", "exact"], "tactic_count": 5}
{"name": "Convex.starConvex_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Subsingleton.convex", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "convex_singleton", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "convex_zero", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "convex_segment", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": true, "tactics": ["rintro", "refine", "add_nonneg", "rw", "match_scalars"], "tactic_count": 5}
{"name": "Convex.linear_image", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "Convex.is_linear_image", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Convex.linear_preimage", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Convex.is_linear_preimage", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Convex.add", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "convexAddSubmonoid", "kind": "definition", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "coe_convexAddSubmonoid", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_convexAddSubmonoid", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "convex_list_sum", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "convex_multiset_sum", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "convex_sum", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Convex.vadd", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Convex.translate", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Convex.translate_preimage_right", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": true, "tactics": ["intro", "have", "rwa"], "tactic_count": 3}
{"name": "Convex.translate_preimage_left", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "convex_Iic", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "convex_Ici", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "convex_Icc", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "convex_halfSpace_le", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "convex_halfSpace_ge", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "convex_hyperplane", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "convex_Iio", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": true, "tactics": ["intro", "obtain", "rw", "rwa", "rw", "calc", "a", "add_lt_add_of_lt_of_le"], "tactic_count": 8}
{"name": "convex_Ioi", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "convex_Ioo", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "convex_Ico", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "convex_Ioc", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "convex_halfSpace_lt", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "convex_halfSpace_gt", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "convex_uIcc", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Convex.lift", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonotoneOn.convex_le", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonotoneOn.convex_lt", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonotoneOn.convex_ge", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonotoneOn.convex_gt", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntitoneOn.convex_le", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntitoneOn.convex_lt", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntitoneOn.convex_ge", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntitoneOn.convex_gt", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.convex_le", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.convex_lt", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.convex_ge", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.convex_gt", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.convex_le", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.convex_lt", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.convex_ge", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.convex_gt", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Convex.smul", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Convex.smul_preimage", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Convex.affinity", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "convex_openSegment", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": true, "tactics": ["rw", "rintro", "refine", "linear_combination", "module"], "tactic_count": 5}
{"name": "convex_vadd", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.convex", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Convex.affine_preimage", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Convex.affine_image", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "Convex.neg", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Convex.sub", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Convex.add_smul_mem", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "Convex.smul_mem_of_zero_mem", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Convex.mapsTo_lineMap", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Convex.lineMap_mem", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Convex.add_smul_sub_mem", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Convex.semilinear_image", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": true, "tactics": ["rintro", "obtain", "obtain", "refine", "apply_fun", "simpa"], "tactic_count": 6}
{"name": "Convex_subadditive_le", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": true, "tactics": ["rw", "rintro", "calc"], "tactic_count": 3}
{"name": "Convex.midpoint_mem", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "convex_iff_div", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Convex.mem_smul_of_zero_mem", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Convex.exists_mem_add_smul_eq", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": true, "tactics": ["rcases", "use", "simp", "replace", "refine", "match_scalars"], "tactic_count": 6}
{"name": "Convex.add_smul", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.OrdConnected.convex_of_chain", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact", "rw", "exact"], "tactic_count": 5}
{"name": "Set.OrdConnected.convex", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "convex_iff_ordConnected", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Submodule.convex", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": true, "tactics": ["repeat", "refine"], "tactic_count": 2}
{"name": "Submodule.starConvex", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.Convex.semilinear_range", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "convex_of_nonneg_surjective_algebraMap", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Basic", "is_tactic_proof": true, "tactics": ["simp", "intro", "obtain", "obtain", "convert", "rw", "rw", "rw", "exact"], "tactic_count": 9}
{"name": "affineSegment", "kind": "definition", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "affineSegment_subset_affineSpan", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["rw", "rintro", "exact"], "tactic_count": 3}
{"name": "affineSegment_image", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "affineSegment_const_vadd_image", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "affineSegment_vadd_const_image", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "affineSegment_const_vsub_image", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "affineSegment_vsub_const_image", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_const_vadd_affineSegment", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mem_vadd_const_affineSegment", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mem_const_vsub_affineSegment", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mem_vsub_const_affineSegment", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "affineSegment_eq_segment", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "affineSegment_comm", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["refine", "constructor", "rintro", "refine", "rwa", "rwa"], "tactic_count": 6}
{"name": "left_mem_affineSegment", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "right_mem_affineSegment", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "affineSegment_same", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Wbtw", "kind": "definition", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sbtw", "kind": "definition", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_segment_iff_wbtw", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Convex.mem_of_wbtw", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "wbtw_comm", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "sbtw_comm", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AffineSubspace.mem_of_wbtw", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "Wbtw.map", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Function.Injective.wbtw_map_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["refine", "rwa"], "tactic_count": 2}
{"name": "Function.Injective.sbtw_map_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.InjOn.wbtw_map_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["refine", "rwa", "hf.mem_image_iff"], "tactic_count": 3}
{"name": "Set.InjOn.sbtw_map_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "AffineEquiv.wbtw_map_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["have", "apply"], "tactic_count": 2}
{"name": "AffineEquiv.sbtw_map_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["have", "apply"], "tactic_count": 2}
{"name": "wbtw_const_vadd_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "wbtw_const_add_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "wbtw_vadd_const_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "wbtw_add_const_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "wbtw_const_vsub_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "wbtw_const_sub_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "wbtw_neg_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "wbtw_vsub_const_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "wbtw_sub_const_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sbtw_const_vadd_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "sbtw_const_add_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sbtw_vadd_const_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "sbtw_add_const_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sbtw_const_vsub_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "sbtw_const_sub_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sbtw_neg_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "sbtw_vsub_const_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "sbtw_sub_const_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sbtw.wbtw", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sbtw.ne_left", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sbtw.left_ne", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sbtw.ne_right", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sbtw.right_ne", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sbtw.mem_image_Ioo", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "exfalso", "exact", "exfalso", "exact", "exact"], "tactic_count": 7}
{"name": "Wbtw.mem_affineSpan", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "wbtw_self_left", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "wbtw_self_right", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "wbtw_self_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["refine", "simpa", "rw", "exact"], "tactic_count": 4}
{"name": "affineSegment.lift", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["rintro", "refine", "rw", "exact", "nth_rw", "exact"], "tactic_count": 6}
{"name": "Wbtw.lift", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sbtw.lift", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_sbtw_self_left", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_sbtw_self_right", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Wbtw.left_ne_right_of_ne_left", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["rintro", "rw", "exact"], "tactic_count": 3}
{"name": "Wbtw.left_ne_right_of_ne_right", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["rintro", "rw", "exact"], "tactic_count": 3}
{"name": "Sbtw.left_ne_right", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_sbtw_self", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "wbtw_zero_one_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "simp"], "tactic_count": 3}
{"name": "wbtw_one_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "sbtw_zero_one_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "sbtw_one_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Wbtw.trans_left", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "refine", "rw"], "tactic_count": 4}
{"name": "Wbtw.trans_right", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "sbtw_iff_mem_image_Ioo_and_ne", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["refine", "rcases", "refine", "rw", "neg_vsub_eq_vsub_rev", "simp"], "tactic_count": 6}
{"name": "wbtw_swap_left_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "rcases", "rcases", "rw", "rw", "smul_eq_zero]", "rcases", "nth_rw", "rw", "have", "refine", "rw", "exact", "simp", "rw", "rw", "rintro", "exact"], "tactic_count": 19}
{"name": "wbtw_swap_right_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "wbtw_rotate_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Wbtw.swap_left_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Wbtw.swap_right_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Wbtw.rotate_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Sbtw.not_swap_left", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sbtw.not_swap_right", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sbtw.not_rotate", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "wbtw_lineMap_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "simp", "rw"], "tactic_count": 4}
{"name": "sbtw_lineMap_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw"], "tactic_count": 3}
{"name": "wbtw_mul_sub_add_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sbtw_mul_sub_add_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Wbtw.trans_sbtw_left", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["refine", "rintro", "exact"], "tactic_count": 3}
{"name": "Wbtw.trans_sbtw_right", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "Sbtw.trans_left", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sbtw.trans_right", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Wbtw.trans_left_ne", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "Wbtw.trans_right_ne", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "Sbtw.trans_wbtw_left_ne", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sbtw.trans_wbtw_right_ne", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sbtw.affineCombination_of_mem_affineSpan_pair", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["rw", "rcases", "rw", "change", "rw", "rw", "sbtw_lineMap_iff,", "intro", "have", "refine", "have", "rwa"], "tactic_count": 12}
{"name": "Affine.Simplex.closedInterior_eq_affineSegment", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["ext", "constructor", "rintro", "have", "rw", "ext", "fin_cases", "rw", "exact", "rintro", "rw", "affineCombination_mem_closedInterior_iff", "intro", "fin_cases"], "tactic_count": 14}
{"name": "Affine.Simplex.mem_closedInterior_iff_wbtw", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Affine.Simplex.closedInterior_face_eq_affineSegment", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": false, "tactics": ["have", "rcases", "simp", "nth_rw", "simp", "rw", "congr", "convert", "exact", "lia", "convert", "exact", "lia"], "tactic_count": 13}
{"name": "Affine.Simplex.mem_closedInterior_face_iff_wbtw", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Affine.Simplex.interior_eq_image_Ioo", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["ext", "constructor", "rintro", "have", "rw", "ext", "fin_cases", "rw", "exact", "rintro", "rw", "affineCombination_mem_interior_iff", "intro", "fin_cases"], "tactic_count": 14}
{"name": "Affine.Simplex.mem_interior_iff_sbtw", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Affine.Simplex.mem_interior_face_iff_sbtw", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": false, "tactics": ["have", "rcases", "simp", "nth_rw", "simp", "rw", "congr", "convert", "exact", "lia", "convert", "exact", "lia"], "tactic_count": 13}
{"name": "Wbtw.sameRay_vsub", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["rcases", "simp_rw", "rcases", "rcases", "refine", "simp", "ring_nf"], "tactic_count": 7}
{"name": "Wbtw.sameRay_vsub_left", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["rcases", "simpa"], "tactic_count": 2}
{"name": "Wbtw.sameRay_vsub_right", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["rcases", "simpa"], "tactic_count": 2}
{"name": "sbtw_of_sbtw_of_sbtw_of_mem_affineSpan_pair", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": false, "tactics": ["have", "rintro", "simp", "have", "rintro", "simp", "have", "have", "clear", "decide", "have", "have", "refine", "have", "refine", "simp", "rw", "exact", "rw", "exact", "have", "have", "rw", "rcases", "rcases", "rcases", "have", "sign_eq_of_affineCombination_mem_affineSpan_single_lineMap", "have", "sign_eq_of_affineCombination_mem_affineSpan_single_lineMap", "rw", "refine", "rw", "sbtw_one_zero_iff]", "have", "intro", "rcases", "exact", "exact", "rfl", "have", "have", "rw", "simp_rw", "refine", "rw", "rw", "by_contra", "rw", "exact", "simpa", "simpa"], "tactic_count": 52}
{"name": "wbtw_iff_of_le", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["cases", "inl", "subst", "rw", "inr", "have", "let", "have", "simp", "hxz.ne]"], "tactic_count": 10}
{"name": "Wbtw.of_le_of_le", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sbtw.of_lt_of_lt", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "wbtw_iff_left_eq_or_right_mem_image_Ici", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["refine", "rcases", "rcases", "rw", "refine", "simp", "rw", "simp", "rcases", "exact", "rw", "refine", "simp", "rw"], "tactic_count": 14}
{"name": "Wbtw.right_mem_image_Ici_of_left_ne", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Wbtw.right_mem_affineSpan_of_left_ne", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "sbtw_iff_left_ne_and_right_mem_image_Ioi", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["refine", "obtain", "rw", "rcases", "exact", "simp", "rcases", "rw", "refine", "hne.symm,", "rw", "nth_rw", "rw", "exact"], "tactic_count": 14}
{"name": "Sbtw.right_mem_image_Ioi", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sbtw.right_mem_affineSpan", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "wbtw_iff_right_eq_or_left_mem_image_Ici", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Wbtw.left_mem_image_Ici_of_right_ne", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Wbtw.left_mem_affineSpan_of_right_ne", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sbtw_iff_right_ne_and_left_mem_image_Ioi", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Sbtw.left_mem_image_Ioi", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sbtw.left_mem_affineSpan", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.right_mem_of_wbtw", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["obtain", "have", "simpa"], "tactic_count": 3}
{"name": "wbtw_smul_vadd_smul_vadd_of_nonneg_of_le", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["refine", "by_cases", "simp"], "tactic_count": 3}
{"name": "wbtw_or_wbtw_smul_vadd_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["rcases", "exact", "exact"], "tactic_count": 3}
{"name": "wbtw_smul_vadd_smul_vadd_of_nonpos_of_le", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "wbtw_or_wbtw_smul_vadd_of_nonpos", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["rcases", "exact", "exact"], "tactic_count": 3}
{"name": "wbtw_smul_vadd_smul_vadd_of_nonpos_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["convert", "wbtw_smul_vadd_smul_vadd_of_nonneg_of_le", "simp"], "tactic_count": 3}
{"name": "wbtw_smul_vadd_smul_vadd_of_nonneg_of_nonpos", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Wbtw.trans_left_right", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "refine", "div_le_one_of_le₀", "simp", "vadd_right_cancel_iff,", "nth_rw", "rw", "by_cases", "rw", "rw", "suffices", "exact", "rw", "ring_nf"], "tactic_count": 15}
{"name": "Wbtw.trans_right_left", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Sbtw.trans_left_right", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sbtw.trans_right_left", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Wbtw.collinear", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["rw", "refine", "intro", "simp_rw", "rcases", "refine", "simp", "rcases", "exact", "refine", "simp"], "tactic_count": 11}
{"name": "Collinear.wbtw_or_wbtw_or_wbtw", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["rw", "rcases", "simp_rw", "have", "have", "rcases", "rcases", "rcases", "rcases", "rw", "rw", "exact", "simp", "exact", "simp", "rcases", "refine", "simp", "rw", "rw", "exact"], "tactic_count": 21}
{"name": "wbtw_iff_sameRay_vsub", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["refine", "rcases", "rw", "simp", "rw", "simp", "refine", "div_le_one_of_le₀", "have", "rw", "simp", "convert", "field"], "tactic_count": 13}
{"name": "AffineIndependent.not_wbtw_of_injective", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["replace", "rw", "contrapose", "simp"], "tactic_count": 4}
{"name": "wbtw_pointReflection", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["refine", "rw", "simp"], "tactic_count": 3}
{"name": "sbtw_pointReflection_of_ne", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["refine", "nth_rw", "exact"], "tactic_count": 3}
{"name": "wbtw_midpoint", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "sbtw_midpoint_of_ne", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Between", "is_tactic_proof": true, "tactics": ["have", "convert", "rw"], "tactic_count": 3}
{"name": "List.Wbtw", "kind": "definition", "module": "Mathlib.Analysis.Convex.BetweenList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.wbtw_cons", "kind": "theorem", "module": "Mathlib.Analysis.Convex.BetweenList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Sbtw", "kind": "definition", "module": "Mathlib.Analysis.Convex.BetweenList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.wbtw_nil", "kind": "theorem", "module": "Mathlib.Analysis.Convex.BetweenList", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.sbtw_nil", "kind": "theorem", "module": "Mathlib.Analysis.Convex.BetweenList", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.wbtw_singleton", "kind": "theorem", "module": "Mathlib.Analysis.Convex.BetweenList", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.sbtw_singleton", "kind": "theorem", "module": "Mathlib.Analysis.Convex.BetweenList", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.wbtw_pair", "kind": "theorem", "module": "Mathlib.Analysis.Convex.BetweenList", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.sbtw_pair", "kind": "theorem", "module": "Mathlib.Analysis.Convex.BetweenList", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.wbtw_triple", "kind": "theorem", "module": "Mathlib.Analysis.Convex.BetweenList", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.sbtw_triple", "kind": "theorem", "module": "Mathlib.Analysis.Convex.BetweenList", "is_tactic_proof": false, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "List.wbtw_four", "kind": "theorem", "module": "Mathlib.Analysis.Convex.BetweenList", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.sbtw_four", "kind": "theorem", "module": "Mathlib.Analysis.Convex.BetweenList", "is_tactic_proof": true, "tactics": ["simp", "aesop"], "tactic_count": 2}
{"name": "List.Sbtw.wbtw", "kind": "theorem", "module": "Mathlib.Analysis.Convex.BetweenList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Sbtw.pairwise_ne", "kind": "theorem", "module": "Mathlib.Analysis.Convex.BetweenList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sbtw_iff_triplewise_and_ne_pair", "kind": "theorem", "module": "Mathlib.Analysis.Convex.BetweenList", "is_tactic_proof": true, "tactics": ["rw", "induction", "nil", "cons", "rw", "refine", "rcases", "refine", "clear", "induction", "nil", "cons", "rw", "refine", "refine", "simp", "rw", "grind", "rw", "exact", "grind", "have", "simp", "rw", "refine", "rintro", "cases", "nil", "cons", "rw", "rcases", "cases", "nil", "cons", "simpa", "rintro", "simp"], "tactic_count": 37}
{"name": "List.sbtw_cons", "kind": "theorem", "module": "Mathlib.Analysis.Convex.BetweenList", "is_tactic_proof": true, "tactics": ["rw", "simp", "intro", "rw", "rintro", "simp"], "tactic_count": 6}
{"name": "List.Wbtw.map", "kind": "theorem", "module": "Mathlib.Analysis.Convex.BetweenList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.list_wbtw_map_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.BetweenList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.list_sbtw_map_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.BetweenList", "is_tactic_proof": true, "tactics": ["rw", "refine"], "tactic_count": 2}
{"name": "AffineEquiv.list_wbtw_map_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.BetweenList", "is_tactic_proof": true, "tactics": ["have", "apply"], "tactic_count": 2}
{"name": "AffineEquiv.list_sbtw_map_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.BetweenList", "is_tactic_proof": true, "tactics": ["have", "apply"], "tactic_count": 2}
{"name": "List.SortedLE.wbtw", "kind": "theorem", "module": "Mathlib.Analysis.Convex.BetweenList", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "rw", "refine", "clear", "induction", "nil", "cons", "rw", "refine", "simp_rw", "exact", "simp"], "tactic_count": 14}
{"name": "List.SortedLT.sbtw", "kind": "theorem", "module": "Mathlib.Analysis.Convex.BetweenList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.exists_map_eq_of_sorted_nonempty_iff_wbtw", "kind": "theorem", "module": "Mathlib.Analysis.Convex.BetweenList", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact", "suffices", "rcases", "exact", "induction", "nil", "cons", "by_cases", "refine", "simp", "rw", "replace", "rcases", "simp", "cases", "nil", "cons", "by_cases", "exact", "simp", "rw", "have", "rcases", "refine", "simp", "forall_apply_eq_imp_iff₂,", "intro", "have", "nlinarith", "simp", "forall_apply_eq_imp_iff₂]", "refine", "intro", "have", "nlinarith", "refine", "gcongr", "linarith", "simp", "lineMap_lineMap_left,", "ring_nf", "simp"], "tactic_count": 44}
{"name": "List.exists_map_eq_of_sorted_iff_wbtw", "kind": "theorem", "module": "Mathlib.Analysis.Convex.BetweenList", "is_tactic_proof": true, "tactics": ["refine", "subst", "exact", "by_cases", "exact", "exact"], "tactic_count": 6}
{"name": "List.exists_map_eq_of_sorted_nonempty_iff_sbtw", "kind": "theorem", "module": "Mathlib.Analysis.Convex.BetweenList", "is_tactic_proof": false, "tactics": ["refine", "rw", "rcases", "grind", "exact", "rw", "rcases", "refine", "rw", "have", "exact", "cases", "nil", "cons", "simp", "cases", "nil", "cons", "simp", "rw", "refine", "simp"], "tactic_count": 22}
{"name": "List.exists_map_eq_of_sorted_iff_sbtw", "kind": "theorem", "module": "Mathlib.Analysis.Convex.BetweenList", "is_tactic_proof": true, "tactics": ["refine", "subst", "rw", "exact", "by_cases", "rcases", "exact", "by_cases", "rw", "rcases", "rcases", "exact", "refine", "rw", "simp", "rcases", "exact"], "tactic_count": 17}
{"name": "_private.Mathlib.Analysis.Convex.Birkhoff.0.exists_perm_eq_zero_implies_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Birkhoff", "is_tactic_proof": true, "tactics": ["rw", "let", "have", "have", "have", "have", "suffices", "rw", "trans", "refine", "exact", "exact", "obtain", "rw", "refine", "simp", "rintro", "simpa"], "tactic_count": 18}
{"name": "_private.Mathlib.Analysis.Convex.Birkhoff.0.doublyStochastic_sum_perm_aux", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Birkhoff", "is_tactic_proof": true, "tactics": ["rcases", "exact", "set", "clear_value", "induction", "rcases", "use", "simp", "simp", "obtain", "obtain", "rw", "let", "have", "let", "have", "simp", "exact", "have", "rw", "simp", "smul_eq_mul,", "refine", "split", "exact", "exact", "have", "rw", "gcongr", "rw", "simp_rw", "refine", "simp", "rintro", "dsimp", "simp", "obtain", "linarith", "obtain", "refine", "simp", "sub_add_cancel,", "intro", "split"], "tactic_count": 44}
{"name": "exists_eq_sum_perm_of_mem_doublyStochastic", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Birkhoff", "is_tactic_proof": true, "tactics": ["rcases", "exact", "obtain", "refine", "inhabit", "have", "simp", "rw", "simpa"], "tactic_count": 9}
{"name": "doublyStochastic_eq_convexHull_permMatrix", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Birkhoff", "is_tactic_proof": true, "tactics": ["refine", "rintro", "exact", "obtain", "exact"], "tactic_count": 5}
{"name": "extremePoints_doublyStochastic", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Birkhoff", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact", "rintro", "refine", "suffices", "obtain", "simp_all", "intro", "have", "image_openSegment", "by_contra", "have", "rw", "apply", "specialize", "aesop"], "tactic_count": 17}
{"name": "Matrix.l2_opNorm_le_one_of_mem_doublyStochastic", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Birkhoff", "is_tactic_proof": true, "tactics": ["rw", "have", "exact"], "tactic_count": 3}
{"name": "ConvexBody.instSetLike", "kind": "instance", "module": "Mathlib.Analysis.Convex.Body", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexBody.instPartialOrder", "kind": "instance", "module": "Mathlib.Analysis.Convex.Body", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexBody.convex", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Body", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexBody.isCompact", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Body", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexBody.isClosed", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Body", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexBody.nonempty", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Body", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexBody.ext", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Body", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexBody.coe_mk", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Body", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexBody.zero_mem_of_symmetric", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Body", "is_tactic_proof": true, "tactics": ["obtain", "rw", "apply", "all_goals"], "tactic_count": 4}
{"name": "ConvexBody.instZero", "kind": "instance", "module": "Mathlib.Analysis.Convex.Body", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexBody.coe_zero", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Body", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexBody.instInhabited", "kind": "instance", "module": "Mathlib.Analysis.Convex.Body", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexBody.instAdd", "kind": "instance", "module": "Mathlib.Analysis.Convex.Body", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexBody.instSMulNat", "kind": "instance", "module": "Mathlib.Analysis.Convex.Body", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexBody.coe_nsmul", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Body", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexBody.instAddMonoid", "kind": "instance", "module": "Mathlib.Analysis.Convex.Body", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexBody.coe_add", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Body", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexBody.instAddCommMonoid", "kind": "instance", "module": "Mathlib.Analysis.Convex.Body", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexBody.instSMulReal", "kind": "instance", "module": "Mathlib.Analysis.Convex.Body", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexBody.coe_smul", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Body", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexBody.instDistribMulActionReal", "kind": "instance", "module": "Mathlib.Analysis.Convex.Body", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexBody.coe_smul'", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Body", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexBody.instModuleNNReal", "kind": "instance", "module": "Mathlib.Analysis.Convex.Body", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexBody.smul_le_of_le", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Body", "is_tactic_proof": true, "tactics": ["rw", "obtain", "rw", "exact", "intro", "obtain", "rw", "refine", "rwa"], "tactic_count": 9}
{"name": "ConvexBody.isBounded", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Body", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexBody.hausdorffEDist_ne_top", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Body", "is_tactic_proof": true, "tactics": ["apply_rules"], "tactic_count": 1}
{"name": "ConvexBody.instPseudoMetricSpace", "kind": "instance", "module": "Mathlib.Analysis.Convex.Body", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexBody.hausdorffDist_coe", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Body", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexBody.hausdorffEDist_coe", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Body", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ConvexBody.iInter_smul_eq_self", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Body", "is_tactic_proof": true, "tactics": ["ext", "refine", "obtain", "rw", "rw", "intro", "obtain", "obtain", "refine", "rw", "specialize", "rw", "refine", "exact", "refine", "exact"], "tactic_count": 16}
{"name": "ConvexBody.instMetricSpace", "kind": "instance", "module": "Mathlib.Analysis.Convex.Body", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Caratheodory.mem_convexHull_erase", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Caratheodory", "is_tactic_proof": true, "tactics": ["simp", "obtain", "obtain", "replace", "clear", "let", "obtain", "apply", "obtain", "exact", "have", "rw", "exact", "have", "let", "have", "have", "calc", "conv_rhs", "refine", "simp", "intro", "by_cases", "have", "rw", "exact", "rw", "exact", "calc", "apply", "apply", "simpa", "rw", "calc", "simp", "inv_one,"], "tactic_count": 36}
{"name": "Caratheodory.minCardFinsetOfMemConvexHull", "kind": "definition", "module": "Mathlib.Analysis.Convex.Caratheodory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Caratheodory.minCardFinsetOfMemConvexHull_subseteq", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Caratheodory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Caratheodory.mem_minCardFinsetOfMemConvexHull", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Caratheodory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Caratheodory.minCardFinsetOfMemConvexHull_nonempty", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Caratheodory", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Caratheodory.minCardFinsetOfMemConvexHull_card_le_card", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Caratheodory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Caratheodory.affineIndependent_minCardFinsetOfMemConvexHull", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Caratheodory", "is_tactic_proof": true, "tactics": ["let", "have", "classical", "by_contra", "obtain", "have", "minCardFinsetOfMemConvexHull_card_le_card", "hp", "rw", "apply", "rw", "exact"], "tactic_count": 12}
{"name": "convexHull_eq_union", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Caratheodory", "is_tactic_proof": true, "tactics": ["apply", "intro", "simp", "exact", "iterate", "exact"], "tactic_count": 6}
{"name": "eq_pos_convex_span_of_mem_convexHull", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Caratheodory", "is_tactic_proof": true, "tactics": ["rw", "simp", "obtain", "simp", "obtain", "let", "refine", "rw", "exact", "exact", "exact", "simp", "rw", "change", "rw", "rw", "exact", "intro", "apply", "rw"], "tactic_count": 20}
{"name": "Finset.centerMass", "kind": "definition", "module": "Mathlib.Analysis.Convex.Combination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.centerMass_empty", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Combination", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.centerMass_pair", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Combination", "is_tactic_proof": true, "tactics": ["simp", "module"], "tactic_count": 2}
{"name": "Finset.centerMass_insert", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Combination", "is_tactic_proof": true, "tactics": ["simp", "congr", "rw"], "tactic_count": 3}
{"name": "Finset.centerMass_singleton", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Combination", "is_tactic_proof": true, "tactics": ["rw", "match_scalars", "field"], "tactic_count": 3}
{"name": "Finset.centerMass_neg_left", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Combination", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.centerMass_smul_left", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Combination", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.centerMass_eq_of_sum_1", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Combination", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.centerMass_smul", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Combination", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.centerMass_segment'", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Combination", "is_tactic_proof": false, "tactics": ["rw", "congr", "rw"], "tactic_count": 3}
{"name": "Finset.centerMass_segment", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Combination", "is_tactic_proof": true, "tactics": ["have", "simp"], "tactic_count": 2}
{"name": "Finset.centerMass_ite_eq", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Combination", "is_tactic_proof": true, "tactics": ["rw", "trans", "congr", "split_ifs", "exacts", "rw", "rw"], "tactic_count": 7}
{"name": "Finset.centerMass_subset", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Combination", "is_tactic_proof": true, "tactics": ["rw", "apply", "intro", "rw"], "tactic_count": 4}
{"name": "Finset.centerMass_filter_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Combination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.centerMass_le_sup", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Combination", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finset.inf_le_centerMass", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Combination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.centerMass_const", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Combination", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.centerMass_congr", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Combination", "is_tactic_proof": true, "tactics": ["classical", "rw", "congr", "congr", "exact", "exact"], "tactic_count": 6}
{"name": "Finset.centerMass_congr_finset", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Combination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.centerMass_congr_weights", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Combination", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finset.centerMass_congr_fun", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Combination", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finset.centerMass_of_sum_add_sum_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Combination", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Convex.centerMass_mem", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Combination", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "insert", "intro", "have", "have", "rw", "by_cases", "have", "have", "simp", "simp", "rw", "exact", "rw", "refine", "exact", "intro", "exact", "exact"], "tactic_count": 21}
{"name": "Convex.sum_mem", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Combination", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Convex.finsum_mem", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Combination", "is_tactic_proof": false, "tactics": ["have", "by_contra", "rw", "exact", "have", "rw", "refine", "rwa", "rwa"], "tactic_count": 9}
{"name": "convex_iff_sum_mem", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Combination", "is_tactic_proof": true, "tactics": ["classical", "refine", "intro", "by_cases", "rw", "exact", "convert", "simp", "grind", "simp", "intro", "simp", "cases"], "tactic_count": 13}
{"name": "Finset.centerMass_mem_convexHull", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Combination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.centerMass_mem_convexHull_of_nonpos", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Combination", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finset.centerMass_id_mem_convexHull", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Combination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.centerMass_id_mem_convexHull_of_nonpos", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Combination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "affineCombination_eq_centerMass", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Combination", "is_tactic_proof": false, "tactics": ["rw", "vadd_eq_add,", "simp_rw"], "tactic_count": 3}
{"name": "affineCombination_mem_convexHull", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Combination", "is_tactic_proof": true, "tactics": ["rw", "apply", "simp", "simp"], "tactic_count": 4}
{"name": "Finset.centroid_eq_centerMass", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Combination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.centroid_mem_convexHull", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Combination", "is_tactic_proof": true, "tactics": ["rw", "apply", "simp", "have", "simp"], "tactic_count": 5}
{"name": "convexHull_range_eq_exists_affineCombination", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Combination", "is_tactic_proof": true, "tactics": ["classical", "refine", "intro", "obtain", "exact", "rintro", "let", "have", "rw", "sum_ite_of_true,", "intros", "simp_all", "refine", "rintro", "by_cases", "simp", "simp_rw", "affineCombination_eq_linear_combination", "add_smul,", "rw", "simp", "intro", "simp", "intro", "simp", "rintro", "exact"], "tactic_count": 27}
{"name": "convexHull_eq", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Combination", "is_tactic_proof": true, "tactics": ["refine", "intro", "use", "simp", "rintro", "rw", "refine", "rintro", "rw", "rcases", "apply_rules", "simp", "intro", "rw", "rcases", "rintro", "exact"], "tactic_count": 17}
{"name": "mem_convexHull_of_exists_fintype", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Combination", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "mem_convexHull_iff_exists_fintype", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Combination", "is_tactic_proof": true, "tactics": ["constructor", "simp", "rintro", "refine", "simpa", "rintro", "exact"], "tactic_count": 7}
{"name": "Finset.convexHull_eq", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Combination", "is_tactic_proof": true, "tactics": ["classical", "refine", "intro", "rw", "refine", "intros", "split_ifs", "exacts", "rw", "rintro", "rw", "refine", "rintro", "apply_rules", "simp", "rintro", "exact"], "tactic_count": 17}
{"name": "Finset.mem_convexHull", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Combination", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.mem_convexHull'", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Combination", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp_rw"], "tactic_count": 3}
{"name": "Set.Finite.convexHull_eq", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Combination", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "convexHull_eq_union_convexHull_finite_subsets", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Combination", "is_tactic_proof": true, "tactics": ["classical", "refine", "rw", "rintro", "simp", "refine", "rw", "exact", "apply", "simp", "exact", "exact"], "tactic_count": 12}
{"name": "mk_mem_convexHull_prod", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Combination", "is_tactic_proof": true, "tactics": ["rw", "obtain", "obtain", "have", "refine", "ext", "simp_rw", "simp_rw"], "tactic_count": 8}
{"name": "convexHull_prod", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Combination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "convexHull_add", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Combination", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "convexHullAddMonoidHom", "kind": "definition", "module": "Mathlib.Analysis.Convex.Combination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "convexHull_sub", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Combination", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "convexHull_list_sum", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Combination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "convexHull_multiset_sum", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Combination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "convexHull_sum", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Combination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineBasis.convexHull_eq_nonneg_coord", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Combination", "is_tactic_proof": true, "tactics": ["rw", "ext", "refine", "rintro", "by_cases", "rw", "exact", "rw", "have", "rw", "exact", "obtain", "refine", "intro", "specialize", "rw", "exact"], "tactic_count": 17}
{"name": "AffineIndependent.convexHull_inter", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Combination", "is_tactic_proof": true, "tactics": ["classical", "refine", "simp_rw", "rintro", "let", "have", "replace", "hs.eq_zero_of_sum_eq_zero_subtype", "simp", "have", "refine", "simp", "exact", "all_goals", "rwa", "rintro", "simp_intro", "simp"], "tactic_count": 18}
{"name": "AffineIndependent.convexHull_inter'", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Combination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_convexHull_pi", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Combination", "is_tactic_proof": true, "tactics": ["classical", "cases", "wlog", "rw", "refine", "split_ifs", "exact", "simp", "subst", "simp", "choose", "refine", "mem_convexHull_of_exists_fintype", "rw", "exact", "ext", "calc", "rw", "simp_rw", "congr", "exact", "congr", "calc", "rw", "mul_one]", "simp"], "tactic_count": 26}
{"name": "convexHull_pi", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Combination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.Convex.Cone.Basic.0.termR≥0", "kind": "definition", "module": "Mathlib.Analysis.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.Convex.Cone.Basic.0._aux_Mathlib_Analysis_Convex_Cone_Basic___macroRules__private_Mathlib_Analysis_Convex_Cone_Basic_0_termR≥0_1", "kind": "definition", "module": "Mathlib.Analysis.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProperCone", "kind": "abbrev", "module": "Mathlib.Analysis.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProperCone.toPointedCone", "kind": "abbrev", "module": "Mathlib.Analysis.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProperCone.instCoePointedCone", "kind": "instance", "module": "Mathlib.Analysis.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProperCone.toPointedCone_injective", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProperCone.instSetLike", "kind": "instance", "module": "Mathlib.Analysis.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProperCone.instPartialOrder", "kind": "instance", "module": "Mathlib.Analysis.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProperCone.ext", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProperCone.mem_toPointedCone", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProperCone.pointed_toConvexCone", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProperCone.nonempty", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProperCone.isClosed", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProperCone.convex", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProperCone.smul_mem", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProperCone.mem_bot", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProperCone.coe_bot", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProperCone.toPointedCone_bot", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProperCone.comap", "kind": "abbrev", "module": "Mathlib.Analysis.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProperCone.comap_id", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProperCone.coe_comap", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProperCone.comap_comap", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProperCone.mem_comap", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProperCone.map", "kind": "abbrev", "module": "Mathlib.Analysis.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProperCone.map_id", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProperCone.coe_map", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProperCone.mem_map", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProperCone.positive", "kind": "definition", "module": "Mathlib.Analysis.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProperCone.mem_positive", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProperCone.toPointedCone_positive", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.isOpen_hull", "kind": "proofWanted", "module": "Mathlib.Analysis.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.Pointed.of_nonempty_of_isClosed", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Cone.Basic", "is_tactic_proof": true, "tactics": ["obtain", "let", "have", "hSclos.closure_subset_iff.2", "have", "fun_prop", "simpa"], "tactic_count": 7}
{"name": "ConvexCone.canLift", "kind": "instance", "module": "Mathlib.Analysis.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.closure", "kind": "definition", "module": "Mathlib.Analysis.Convex.Cone.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.coe_closure", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Cone.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.mem_closure", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Cone.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.closure_eq", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Cone.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PointedCone.toConvexCone_closure_pointed", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Cone.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PointedCone.closure", "kind": "definition", "module": "Mathlib.Analysis.Convex.Cone.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PointedCone.coe_closure", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Cone.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PointedCone.mem_closure", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Cone.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PointedCone.closure_eq", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Cone.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PointedCone.isClosed_dual", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Cone.Dual", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "exact"], "tactic_count": 3}
{"name": "ProperCone.dual", "kind": "definition", "module": "Mathlib.Analysis.Convex.Cone.Dual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProperCone.mem_dual", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Cone.Dual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProperCone.dual_empty", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Cone.Dual", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "ProperCone.dual_zero", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Cone.Dual", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "ProperCone.dual_univ", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Cone.Dual", "is_tactic_proof": true, "tactics": ["refine", "ext", "exact"], "tactic_count": 3}
{"name": "ProperCone.dual_le_dual", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Cone.Dual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProperCone.dual_singleton", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Cone.Dual", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "ProperCone.dual_union", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Cone.Dual", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "ProperCone.dual_insert", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Cone.Dual", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ProperCone.dual_iUnion", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Cone.Dual", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "ProperCone.dual_sUnion", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Cone.Dual", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "ProperCone.subset_dual_dual", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Cone.Dual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProperCone.hyperplane_separation", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Cone.Dual", "is_tactic_proof": true, "tactics": ["obtain", "exact", "obtain", "have", "refine", "by_contra", "simpa", "hv"], "tactic_count": 8}
{"name": "ProperCone.hyperplane_separation_point", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Cone.Dual", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ProperCone.dual_flip_dual", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Cone.Dual", "is_tactic_proof": true, "tactics": ["refine", "simp", "contrapose", "simpa"], "tactic_count": 4}
{"name": "ProperCone.dual_dual_flip", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Cone.Dual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RieszExtension.step", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Cone.Extension", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "set", "set", "suffices", "simpa", "refine", "rcases", "rw", "exact", "rintro", "have", "rw", "replace", "rwa", "refine", "refine", "replace", "rw", "exact", "rintro", "rcases", "rcases", "simp", "rw", "rcases", "have", "rwa", "one_smul,", "replace", "rwa", "mul_assoc,", "subst", "simp", "apply", "exact", "have", "replace", "rwa"], "tactic_count": 39}
{"name": "RieszExtension.exists_top", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Cone.Extension", "is_tactic_proof": true, "tactics": ["set", "have", "intro", "clear", "have", "have", "refine", "rintro", "have", "directedOn_image.2", "rcases", "have", "convert", "exact", "obtain", "refine", "contrapose", "have", "let", "rcases", "exact"], "tactic_count": 21}
{"name": "riesz_extension", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Cone.Extension", "is_tactic_proof": true, "tactics": ["rcases", "refine", "exact", "exact"], "tactic_count": 4}
{"name": "exists_extension_of_le_sublinear", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Cone.Extension", "is_tactic_proof": false, "tactics": ["let", "smul_mem", "calc", "add_mem", "set", "have", "simpa", "have", "rintro", "refine", "simp", "obtain", "replace", "refine", "simp", "calc"], "tactic_count": 16}
{"name": "ProperCone.innerDual", "kind": "definition", "module": "Mathlib.Analysis.Convex.Cone.InnerDual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProperCone.mem_innerDual", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Cone.InnerDual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProperCone.innerDual_empty", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Cone.InnerDual", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "ProperCone.innerDual_zero", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Cone.InnerDual", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "ProperCone.innerDual_univ", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Cone.InnerDual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProperCone.innerDual_le_innerDual", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Cone.InnerDual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProperCone.innerDual_singleton", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Cone.InnerDual", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "ProperCone.innerDual_union", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Cone.InnerDual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProperCone.innerDual_insert", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Cone.InnerDual", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ProperCone.innerDual_iUnion", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Cone.InnerDual", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "ProperCone.innerDual_sUnion", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Cone.InnerDual", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "ProperCone.hyperplane_separation'", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Cone.InnerDual", "is_tactic_proof": true, "tactics": ["obtain", "refine", "simpa"], "tactic_count": 3}
{"name": "ProperCone.innerDual_innerDual", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Cone.InnerDual", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ProperCone.relative_hyperplane_separation", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Cone.InnerDual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProperCone.hyperplane_separation_of_notMem", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Cone.InnerDual", "is_tactic_proof": true, "tactics": ["contrapose"], "tactic_count": 1}
{"name": "ConvexCone.hyperplane_separation_of_nonempty_of_isClosed_of_notMem", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Cone.InnerDual", "is_tactic_proof": true, "tactics": ["obtain", "have", "use", "constructor", "rintro", "specialize", "rwa", "one_smul,", "have", "hinner", "rw", "have", "rw", "contrapose", "rwa", "rw", "one_smul]", "calc"], "tactic_count": 18}
{"name": "ConvexOn.lipschitzOnWith_of_abs_le", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Continuous", "is_tactic_proof": true, "tactics": ["set", "have", "obtain", "simp", "have", "have", "have", "let", "replace", "have", "mem_ball_iff_norm.2", "calc", "let", "let", "have", "have", "calc", "x", "rw", "calc", "ε", "have", "simp", "field_simp", "linear_combination", "rw", "gcongr", "exact", "exact", "refine", "simp_rw", "exact"], "tactic_count": 32}
{"name": "ConcaveOn.lipschitzOnWith_of_abs_le", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Continuous", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ConvexOn.exists_lipschitzOnWith_of_isBounded", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Continuous", "is_tactic_proof": true, "tactics": ["rw", "simp", "forall_apply_eq_imp_iff₂]", "obtain", "rw", "exact"], "tactic_count": 6}
{"name": "ConcaveOn.exists_lipschitzOnWith_of_isBounded", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Continuous", "is_tactic_proof": true, "tactics": ["replace", "simpa"], "tactic_count": 2}
{"name": "ConvexOn.isBoundedUnder_abs", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Continuous", "is_tactic_proof": true, "tactics": ["refine", "rintro", "refine", "have", "simp", "filter_upwards", "refine", "rw", "calc", "have", "simp", "not_false_eq_true,", "cancel_denoms", "rwa"], "tactic_count": 14}
{"name": "ConcaveOn.isBoundedUnder_abs", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Continuous", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ConvexOn.continuousOn_tfae", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Continuous", "is_tactic_proof": true, "tactics": ["tfae_have", "tfae_have", "obtain", "exact", "tfae_have", "tfae_have", "have", "have", "exact", "obtain", "set", "refine", "simp", "obtain", "refine", "have", "simp", "sub_smul]", "let", "have", "have", "calc", "f", "hf.le_max_of_mem_segment", "tfae_have", "tfae_have", "h,", "obtain", "obtain", "simp", "obtain", "exists_lipschitzOnWith_of_isBounded", "isBounded_iff_forall_norm_le.2", "exact", "tfae_finish"], "tactic_count": 35}
{"name": "ConcaveOn.continuousOn_tfae", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Continuous", "is_tactic_proof": true, "tactics": ["have", "simp", "convert"], "tactic_count": 3}
{"name": "ConvexOn.locallyLipschitzOn_iff_continuousOn", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Continuous", "is_tactic_proof": true, "tactics": ["obtain", "simp", "exact"], "tactic_count": 3}
{"name": "ConcaveOn.locallyLipschitzOn_iff_continuousOn", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Continuous", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ConvexOn.locallyLipschitzOn", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Continuous", "is_tactic_proof": true, "tactics": ["obtain", "simp", "obtain", "refine", "refine", "exact"], "tactic_count": 6}
{"name": "ConcaveOn.locallyLipschitzOn", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Continuous", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ConvexOn.continuousOn", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConcaveOn.continuousOn", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexOn.locallyLipschitzOn_interior", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConcaveOn.locallyLipschitzOn_interior", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexOn.continuousOn_interior", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConcaveOn.continuousOn_interior", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexOn.locallyLipschitz", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Continuous", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ConcaveOn.locallyLipschitz", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Continuous", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ContinuousLinearEquiv.strictConvex_preimage", "kind": "theorem", "module": "Mathlib.Analysis.Convex.ContinuousLinearEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.strictConvex_image", "kind": "theorem", "module": "Mathlib.Analysis.Convex.ContinuousLinearEquiv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "StarConvex.contractibleSpace", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Contractible", "is_tactic_proof": false, "tactics": ["refine", "exact", "exact"], "tactic_count": 3}
{"name": "Convex.contractibleSpace", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Contractible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RealTopologicalVectorSpace.contractibleSpace", "kind": "instance", "module": "Mathlib.Analysis.Convex.Contractible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonotoneOn.convexOn_of_deriv", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntitoneOn.concaveOn_of_deriv", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMonoOn.exists_slope_lt_deriv_aux", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": false, "tactics": ["have", "obtain", "rcases", "refine", "rw", "exact"], "tactic_count": 6}
{"name": "StrictMonoOn.exists_slope_lt_deriv", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": true, "tactics": ["by_cases", "apply", "rcases", "obtain", "apply", "exact", "exact", "intro", "rw", "apply", "exact", "obtain", "apply", "refine", "exact", "intro", "rw", "apply", "exact", "refine", "simp", "have", "apply", "exact", "rw", "exact", "linarith"], "tactic_count": 27}
{"name": "StrictMonoOn.exists_deriv_lt_slope_aux", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": false, "tactics": ["have", "obtain", "rcases", "refine", "rw", "exact"], "tactic_count": 6}
{"name": "StrictMonoOn.exists_deriv_lt_slope", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": true, "tactics": ["by_cases", "apply", "rcases", "obtain", "apply", "exact", "exact", "intro", "rw", "apply", "exact", "obtain", "apply", "refine", "exact", "intro", "rw", "apply", "exact", "refine", "simp", "have", "apply", "exact", "rw", "exact", "linarith"], "tactic_count": 27}
{"name": "StrictMonoOn.strictConvexOn_of_deriv", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictAntiOn.strictConcaveOn_of_deriv", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.convexOn_univ_of_deriv", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.concaveOn_univ_of_deriv", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.strictConvexOn_univ_of_deriv", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictAnti.strictConcaveOn_univ_of_deriv", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "convexOn_of_deriv2_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "concaveOn_of_deriv2_nonpos", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "convexOn_of_hasDerivWithinAt2_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": true, "tactics": ["have", "refine", "rw", "exact", "rintro", "convert", "dsimp", "rw", "exact"], "tactic_count": 9}
{"name": "concaveOn_of_hasDerivWithinAt2_nonpos", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": true, "tactics": ["have", "refine", "rw", "exact", "rintro", "convert", "dsimp", "rw", "exact"], "tactic_count": 9}
{"name": "strictConvexOn_of_deriv2_pos", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictConcaveOn_of_deriv2_neg", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "convexOn_of_deriv2_nonneg'", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "concaveOn_of_deriv2_nonpos'", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictConvexOn_of_deriv2_pos'", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictConcaveOn_of_deriv2_neg'", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "convexOn_univ_of_deriv2_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "concaveOn_univ_of_deriv2_nonpos", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictConvexOn_univ_of_deriv2_pos", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictConcaveOn_univ_of_deriv2_neg", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexOn.slope_mono", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexOn.monotoneOn_slope_gt", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexOn.monotoneOn_slope_lt", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConcaveOn.slope_anti", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ConcaveOn.antitoneOn_slope_gt", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConcaveOn.antitoneOn_slope_lt", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bddBelow_slope_lt_of_mem_interior", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": true, "tactics": ["obtain", "refine", "simp_rw", "refine", "simp", "simp"], "tactic_count": 6}
{"name": "bddAbove_slope_gt_of_mem_interior", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": true, "tactics": ["obtain", "refine", "simp_rw", "refine", "simp", "simp"], "tactic_count": 6}
{"name": "ConvexOn.hasDerivWithinAt_sInf_slope_of_mem_interior", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": true, "tactics": ["have", "rw", "obtain", "simp_rw", "simp", "have", "have", "suffices", "apply", "rintro", "obtain", "exact"], "tactic_count": 12}
{"name": "ConvexOn.hasDerivWithinAt_sSup_slope_of_mem_interior", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": true, "tactics": ["have", "rw", "obtain", "simp_rw", "simp", "have", "have", "suffices", "apply", "rintro", "obtain", "exact"], "tactic_count": 12}
{"name": "ConvexOn.differentiableWithinAt_Ioi_of_mem_interior", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexOn.differentiableWithinAt_Iio_of_mem_interior", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexOn.hasDerivWithinAt_rightDeriv_of_mem_interior", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexOn.hasDerivWithinAt_leftDeriv_of_mem_interior", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexOn.rightDeriv_eq_sInf_slope_of_mem_interior", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexOn.leftDeriv_eq_sSup_slope_of_mem_interior", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexOn.monotoneOn_rightDeriv", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": true, "tactics": ["intro", "rcases", "simp_rw", "refine", "csInf_le_of_le", "have", "rw", "obtain", "rw", "obtain", "exact", "rintro", "rw", "exact"], "tactic_count": 14}
{"name": "ConvexOn.monotoneOn_leftDeriv", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": true, "tactics": ["intro", "rcases", "simp_rw", "refine", "le_csSup_of_le", "have", "rw", "obtain", "rw", "obtain", "exact", "rintro", "exact"], "tactic_count": 13}
{"name": "ConvexOn.leftDeriv_le_rightDeriv_of_mem_interior", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": true, "tactics": ["have", "rw", "obtain", "rw", "refine", "rw", "obtain", "exact", "rintro", "refine", "rw", "obtain", "exact", "rintro", "exact"], "tactic_count": 15}
{"name": "ConvexOn.le_slope_of_hasDerivWithinAt_Ioi", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": true, "tactics": ["apply", "simp_rw", "filter_upwards", "refine", "exact"], "tactic_count": 5}
{"name": "ConvexOn.rightDeriv_le_slope", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexOn.rightDeriv_le_slope_of_mem_interior", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexOn.le_slope_of_hasDerivWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexOn.derivWithin_le_slope", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexOn.le_slope_of_hasDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexOn.deriv_le_slope", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexOn.slope_le_of_hasDerivWithinAt_Iio", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": true, "tactics": ["apply", "simp_rw", "filter_upwards", "refine", "exact"], "tactic_count": 5}
{"name": "ConvexOn.slope_le_leftDeriv", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexOn.slope_le_leftDeriv_of_mem_interior", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ConvexOn.slope_le_derivWithin", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexOn.slope_le_of_hasDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexOn.slope_le_deriv", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexOn.monotoneOn_derivWithin", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": true, "tactics": ["intro", "rcases", "rfl", "exact"], "tactic_count": 4}
{"name": "ConvexOn.monotoneOn_deriv", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": true, "tactics": ["intro", "rcases", "rfl", "exact"], "tactic_count": 4}
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{"name": "ConvexOn.isMinOn_of_leftDeriv_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "StrictConvexOn.lt_slope_of_hasDerivWithinAt_Ioi", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": true, "tactics": ["obtain", "have", "have", "simp", "exact"], "tactic_count": 5}
{"name": "StrictConvexOn.rightDeriv_lt_slope", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "StrictConvexOn.derivWithin_lt_slope", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "StrictConvexOn.deriv_lt_slope", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictConvexOn.slope_lt_of_hasDerivWithinAt_Iio", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": true, "tactics": ["obtain", "have", "have", "simp_rw", "exact"], "tactic_count": 5}
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{"name": "StrictConvexOn.slope_lt_deriv", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictConvexOn.strictMonoOn_derivWithin", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": true, "tactics": ["intro", "exact"], "tactic_count": 2}
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{"name": "ConcaveOn.slope_le_derivWithin", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ConcaveOn.leftDeriv_le_slope", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ConcaveOn.derivWithin_le_slope", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ConcaveOn.deriv_le_slope", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConcaveOn.antitoneOn_derivWithin", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": true, "tactics": ["intro", "rcases", "rfl", "exact"], "tactic_count": 4}
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{"name": "StrictConcaveOn.leftDeriv_lt_slope", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "StrictConcaveOn.strictAntiOn_deriv", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Deriv", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "doublyStochastic", "kind": "definition", "module": "Mathlib.Analysis.Convex.DoublyStochasticMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_doublyStochastic", "kind": "theorem", "module": "Mathlib.Analysis.Convex.DoublyStochasticMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_doublyStochastic_iff_sum", "kind": "theorem", "module": "Mathlib.Analysis.Convex.DoublyStochasticMatrix", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "doublyStochastic_eq_rowStochastic_inf_colStochastic", "kind": "theorem", "module": "Mathlib.Analysis.Convex.DoublyStochasticMatrix", "is_tactic_proof": true, "tactics": ["ext", "simp", "doublyStochastic]", "grind"], "tactic_count": 4}
{"name": "mem_doublyStochastic_iff_mem_rowStochastic_and_mem_colStochastic", "kind": "theorem", "module": "Mathlib.Analysis.Convex.DoublyStochasticMatrix", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "sum_row_of_mem_doublyStochastic", "kind": "theorem", "module": "Mathlib.Analysis.Convex.DoublyStochasticMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sum_col_of_mem_doublyStochastic", "kind": "theorem", "module": "Mathlib.Analysis.Convex.DoublyStochasticMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mulVec_one_of_mem_doublyStochastic", "kind": "theorem", "module": "Mathlib.Analysis.Convex.DoublyStochasticMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_vecMul_of_mem_doublyStochastic", "kind": "theorem", "module": "Mathlib.Analysis.Convex.DoublyStochasticMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_one_of_mem_doublyStochastic", "kind": "theorem", "module": "Mathlib.Analysis.Convex.DoublyStochasticMatrix", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "convex_doublyStochastic", "kind": "theorem", "module": "Mathlib.Analysis.Convex.DoublyStochasticMatrix", "is_tactic_proof": true, "tactics": ["intro", "simp", "simp"], "tactic_count": 3}
{"name": "permMatrix_mem_doublyStochastic", "kind": "theorem", "module": "Mathlib.Analysis.Convex.DoublyStochasticMatrix", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "transpose_mem_doublyStochastif_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.DoublyStochasticMatrix", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "exists_mem_doublyStochastic_eq_smul_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.DoublyStochasticMatrix", "is_tactic_proof": true, "tactics": ["classical", "constructor", "rintro", "rw", "simp", "exact", "rcases", "simp", "intro", "refine", "ext", "specialize", "rw", "exact", "rintro", "exact"], "tactic_count": 16}
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{"name": "Set.MapsTo.egauge_le", "kind": "theorem", "module": "Mathlib.Analysis.Convex.EGauge", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "egauge_anti", "kind": "theorem", "module": "Mathlib.Analysis.Convex.EGauge", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "egauge_empty", "kind": "theorem", "module": "Mathlib.Analysis.Convex.EGauge", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "egauge_le_of_mem_smul", "kind": "theorem", "module": "Mathlib.Analysis.Convex.EGauge", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_egauge_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.EGauge", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "egauge_eq_top", "kind": "theorem", "module": "Mathlib.Analysis.Convex.EGauge", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "egauge_lt_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.EGauge", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "egauge_union", "kind": "theorem", "module": "Mathlib.Analysis.Convex.EGauge", "is_tactic_proof": true, "tactics": ["unfold", "simp"], "tactic_count": 2}
{"name": "le_egauge_inter", "kind": "theorem", "module": "Mathlib.Analysis.Convex.EGauge", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_egauge_pi", "kind": "theorem", "module": "Mathlib.Analysis.Convex.EGauge", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_egauge_prod", "kind": "theorem", "module": "Mathlib.Analysis.Convex.EGauge", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "egauge_zero_left_eq_top", "kind": "theorem", "module": "Mathlib.Analysis.Convex.EGauge", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "egauge_le_of_smul_mem_of_ne", "kind": "theorem", "module": "Mathlib.Analysis.Convex.EGauge", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "egauge_le_of_smul_mem", "kind": "theorem", "module": "Mathlib.Analysis.Convex.EGauge", "is_tactic_proof": true, "tactics": ["rcases", "simp", "exact"], "tactic_count": 3}
{"name": "mem_smul_of_egauge_lt", "kind": "theorem", "module": "Mathlib.Analysis.Convex.EGauge", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_of_egauge_lt_one", "kind": "theorem", "module": "Mathlib.Analysis.Convex.EGauge", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "egauge_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.EGauge", "is_tactic_proof": true, "tactics": ["refine", "rw", "simp"], "tactic_count": 3}
{"name": "egauge_univ", "kind": "theorem", "module": "Mathlib.Analysis.Convex.EGauge", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp_all"], "tactic_count": 3}
{"name": "egauge_zero_right", "kind": "theorem", "module": "Mathlib.Analysis.Convex.EGauge", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "egauge_zero_zero", "kind": "theorem", "module": "Mathlib.Analysis.Convex.EGauge", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "egauge_le_one", "kind": "theorem", "module": "Mathlib.Analysis.Convex.EGauge", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "le_egauge_of_forall_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.Convex.EGauge", "is_tactic_proof": true, "tactics": ["rw", "intro", "rcases", "exact", "obtain", "grw", "exact", "apply", "intro", "rcases", "exact"], "tactic_count": 11}
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{"name": "egauge_smul_left", "kind": "theorem", "module": "Mathlib.Analysis.Convex.EGauge", "is_tactic_proof": true, "tactics": ["refine", "rw", "calc", "egauge"], "tactic_count": 4}
{"name": "le_egauge_smul_right", "kind": "theorem", "module": "Mathlib.Analysis.Convex.EGauge", "is_tactic_proof": true, "tactics": ["rw", "rintro", "rcases", "simp", "refine", "rw", "refine", "simp"], "tactic_count": 8}
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{"name": "egauge_prod_mk", "kind": "theorem", "module": "Mathlib.Analysis.Convex.EGauge", "is_tactic_proof": true, "tactics": ["refine", "simp", "rcases", "cases", "inl", "inr"], "tactic_count": 6}
{"name": "egauge_add_add_le", "kind": "theorem", "module": "Mathlib.Analysis.Convex.EGauge", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "egauge_pi'", "kind": "theorem", "module": "Mathlib.Analysis.Convex.EGauge", "is_tactic_proof": true, "tactics": ["refine", "refine", "have", "choose", "obtain", "have", "rcases", "obtain", "use", "simp", "rcases", "exact", "obtain", "by_cases", "exact", "have", "have", "have", "rcases", "refine", "simp", "refine", "rw", "intro", "exact"], "tactic_count": 25}
{"name": "egauge_univ_pi", "kind": "theorem", "module": "Mathlib.Analysis.Convex.EGauge", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "egauge_pi", "kind": "theorem", "module": "Mathlib.Analysis.Convex.EGauge", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "div_le_egauge_closedBall", "kind": "theorem", "module": "Mathlib.Analysis.Convex.EGauge", "is_tactic_proof": true, "tactics": ["rw", "rintro", "rw", "rw", "apply", "gcongr", "rwa"], "tactic_count": 7}
{"name": "le_egauge_closedBall_one", "kind": "theorem", "module": "Mathlib.Analysis.Convex.EGauge", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "div_le_egauge_ball", "kind": "theorem", "module": "Mathlib.Analysis.Convex.EGauge", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_egauge_ball_one", "kind": "theorem", "module": "Mathlib.Analysis.Convex.EGauge", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "egauge_ball_le_of_one_lt_norm", "kind": "theorem", "module": "Mathlib.Analysis.Convex.EGauge", "is_tactic_proof": true, "tactics": ["letI", "rcases", "rw", "apply", "simpa", "simpa", "rcases", "have", "simp", "refine", "simp", "rcases", "calc", "egauge"], "tactic_count": 14}
{"name": "egauge_ball_one_le_of_one_lt_norm", "kind": "theorem", "module": "Mathlib.Analysis.Convex.EGauge", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsExposed", "kind": "definition", "module": "Mathlib.Analysis.Convex.Exposed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.toExposed", "kind": "definition", "module": "Mathlib.Analysis.Convex.Exposed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.toExposed.isExposed", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Exposed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isExposed_empty", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Exposed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsExposed.subset", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Exposed", "is_tactic_proof": true, "tactics": ["rintro", "obtain", "exact"], "tactic_count": 3}
{"name": "IsExposed.refl", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Exposed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsExposed.antisymm", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Exposed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsExposed.mono", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Exposed", "is_tactic_proof": true, "tactics": ["rintro", "obtain", "exact"], "tactic_count": 3}
{"name": "IsExposed.eq_inter_halfSpace'", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Exposed", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "exact"], "tactic_count": 3}
{"name": "IsExposed.eq_inter_halfSpace", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Exposed", "is_tactic_proof": true, "tactics": ["obtain", "refine", "rw", "rintro", "rw", "have", "contradiction", "exact"], "tactic_count": 8}
{"name": "IsExposed.inter", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Exposed", "is_tactic_proof": true, "tactics": ["rintro", "obtain", "obtain", "refine", "rintro", "exact", "rintro", "refine", "exact", "exact"], "tactic_count": 10}
{"name": "IsExposed.sInter", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Exposed", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "insert", "rw", "obtain", "rw", "exact", "exact"], "tactic_count": 9}
{"name": "IsExposed.inter_left", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Exposed", "is_tactic_proof": true, "tactics": ["rintro", "obtain", "exact"], "tactic_count": 3}
{"name": "IsExposed.inter_right", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Exposed", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsExposed.isClosed", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Exposed", "is_tactic_proof": true, "tactics": ["obtain", "simp", "obtain", "exact"], "tactic_count": 4}
{"name": "IsExposed.isCompact", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Exposed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.exposedPoints", "kind": "definition", "module": "Mathlib.Analysis.Convex.Exposed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exposed_point_def", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Exposed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exposedPoints_subset", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Exposed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exposedPoints_empty", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Exposed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_exposedPoints_iff_exposed_singleton", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Exposed", "is_tactic_proof": false, "tactics": ["use", "rintro", "obtain", "rw", "exact"], "tactic_count": 5}
{"name": "IsExposed.convex", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Exposed", "is_tactic_proof": true, "tactics": ["obtain", "exact", "obtain", "exact"], "tactic_count": 4}
{"name": "IsExposed.isExtreme", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Exposed", "is_tactic_proof": true, "tactics": ["refine", "obtain", "have", "have", "have", "refine", "rw", "exact"], "tactic_count": 8}
{"name": "exposedPoints_subset_extremePoints", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Exposed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMinOn.of_isLocalMinOn_of_convexOn_Icc", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Extrema", "is_tactic_proof": true, "tactics": ["rintro", "dsimp", "rw", "rcases", "exact", "have", "have", "rcases", "rcases", "suffices", "calc", "ya"], "tactic_count": 12}
{"name": "IsMinOn.of_isLocalMinOn_of_convexOn", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Extrema", "is_tactic_proof": true, "tactics": ["intro", "let", "have", "have", "have", "have", "simpa", "have", "rw", "exact", "have", "refine", "exact", "simpa"], "tactic_count": 14}
{"name": "IsMaxOn.of_isLocalMaxOn_of_concaveOn", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Extrema", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMinOn.of_isLocalMin_of_convex_univ", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Extrema", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMaxOn.of_isLocalMax_of_convex_univ", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Extrema", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.extremePoints", "kind": "definition", "module": "Mathlib.Analysis.Convex.Extreme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsExtreme.refl", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Extreme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsExtreme.rfl", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Extreme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsExtreme.right_mem_of_mem_openSegment", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Extreme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsExtreme.trans", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Extreme", "is_tactic_proof": true, "tactics": ["refine", "exact", "hBC.left_mem_of_mem_openSegment"], "tactic_count": 3}
{"name": "IsExtreme.antisymm", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Extreme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsPartialOrderSetIsExtreme", "kind": "instance", "module": "Mathlib.Analysis.Convex.Extreme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsExtreme.inter", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Extreme", "is_tactic_proof": true, "tactics": ["use", "rintro", "exact"], "tactic_count": 3}
{"name": "IsExtreme.mono", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Extreme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isExtreme_iInter", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Extreme", "is_tactic_proof": true, "tactics": ["inhabit", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "isExtreme_biInter", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Extreme", "is_tactic_proof": true, "tactics": ["haveI", "simpa"], "tactic_count": 2}
{"name": "isExtreme_sInter", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Extreme", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "mem_extremePoints", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Extreme", "is_tactic_proof": false, "tactics": ["refine", "apply", "rwa"], "tactic_count": 3}
{"name": "mem_extremePoints_iff_left", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Extreme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isExtreme_singleton", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Extreme", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "extremePoints_subset", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Extreme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "extremePoints_empty", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Extreme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "extremePoints_singleton", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Extreme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inter_extremePoints_subset_extremePoints_of_subset", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Extreme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsExtreme.extremePoints_subset_extremePoints", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Extreme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsExtreme.extremePoints_eq", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Extreme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsExtreme.convex_diff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Extreme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "extremePoints_prod", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Extreme", "is_tactic_proof": true, "tactics": ["ext", "refine", "rintro", "ext", "exact", "exact", "rintro", "refine", "rw", "exact", "rintro", "refine", "rw", "exact"], "tactic_count": 14}
{"name": "extremePoints_pi", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Extreme", "is_tactic_proof": true, "tactics": ["classical", "ext", "simp", "refine", "rintro", "rw", "rintro", "obtain", "rw", "exact", "rintro", "obtain", "rintro", "ext", "exact"], "tactic_count": 15}
{"name": "image_extremePoints", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Extreme", "is_tactic_proof": true, "tactics": ["ext", "obtain", "have", "image_openSegment", "simp"], "tactic_count": 5}
{"name": "mem_extremePoints_iff_forall_segment", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Extreme", "is_tactic_proof": true, "tactics": ["rw", "refine", "constructor", "rw", "rintro", "exacts", "intro", "rcases", "exacts"], "tactic_count": 9}
{"name": "Convex.mem_extremePoints_iff_convex_diff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Extreme", "is_tactic_proof": true, "tactics": ["use", "rintro", "refine", "rw", "by_contra", "exact"], "tactic_count": 6}
{"name": "Convex.mem_extremePoints_iff_mem_diff_convexHull_diff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Extreme", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "extremePoints_convexHull_subset", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Extreme", "is_tactic_proof": true, "tactics": ["rintro", "rw", "by_contra", "exact"], "tactic_count": 4}
{"name": "ConvexOn", "kind": "definition", "module": "Mathlib.Analysis.Convex.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConcaveOn", "kind": "definition", "module": "Mathlib.Analysis.Convex.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictConvexOn", "kind": "definition", "module": "Mathlib.Analysis.Convex.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictConcaveOn", "kind": "definition", "module": "Mathlib.Analysis.Convex.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexOn.dual", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConcaveOn.dual", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictConvexOn.dual", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictConcaveOn.dual", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "convexOn_id", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "concaveOn_id", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexOn.congr", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConcaveOn.congr", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictConvexOn.congr", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictConcaveOn.congr", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexOn.subset", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConcaveOn.subset", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictConvexOn.subset", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictConcaveOn.subset", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexOn.comp", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConcaveOn.comp", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexOn.comp_concaveOn", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConcaveOn.comp_convexOn", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictConvexOn.comp", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictConcaveOn.comp", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictConvexOn.comp_strictConcaveOn", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictConcaveOn.comp_strictConvexOn", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexOn.add", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConcaveOn.add", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "convexOn_const", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "concaveOn_const", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexOn.add_const", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConcaveOn.add_const", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "convexOn_of_convex_epigraph", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "concaveOn_of_convex_hypograph", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexOn.convex_le", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConcaveOn.convex_ge", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexOn.convex_epigraph", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Function", "is_tactic_proof": true, "tactics": ["rintro", "refine", "calc", "f"], "tactic_count": 4}
{"name": "ConcaveOn.convex_hypograph", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "convexOn_iff_convex_epigraph", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "concaveOn_iff_convex_hypograph", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexOn.translate_right", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConcaveOn.translate_right", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexOn.translate_left", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Function", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ConcaveOn.translate_left", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "convexOn_iff_forall_pos", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Function", "is_tactic_proof": false, "tactics": ["refine", "and_congr_right", "obtain", "rw", "subst", "simp_rw", "obtain", "rw", "subst", "simp_rw", "exact"], "tactic_count": 11}
{"name": "concaveOn_iff_forall_pos", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "convexOn_iff_pairwise_pos", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Function", "is_tactic_proof": true, "tactics": ["rw", "refine", "obtain", "rw", "exact"], "tactic_count": 5}
{"name": "concaveOn_iff_pairwise_pos", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.convexOn", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.concaveOn", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictConvexOn.convexOn", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictConcaveOn.concaveOn", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictConvexOn.convex_lt", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictConcaveOn.convex_gt", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearOrder.convexOn_of_lt", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Function", "is_tactic_proof": true, "tactics": ["refine", "wlog", "rw", "rw", "exact", "exact"], "tactic_count": 6}
{"name": "LinearOrder.concaveOn_of_lt", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearOrder.strictConvexOn_of_lt", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Function", "is_tactic_proof": true, "tactics": ["refine", "wlog", "rw", "rw", "exact", "exact"], "tactic_count": 6}
{"name": "LinearOrder.strictConcaveOn_of_lt", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexOn.comp_linearMap", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConcaveOn.comp_linearMap", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictConvexOn.add_convexOn", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "intrinsicFrontier_subset", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Intrinsic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intrinsicFrontier_subset_intrinsicClosure", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Intrinsic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "subset_intrinsicClosure", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Intrinsic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intrinsicInterior_empty", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Intrinsic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "intrinsicFrontier_empty", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Intrinsic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "intrinsicClosure_empty", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Intrinsic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "intrinsicClosure_nonempty", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Intrinsic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intrinsicInterior_singleton", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Intrinsic", "is_tactic_proof": true, "tactics": ["simp", "mem_affineSpan_singleton,"], "tactic_count": 2}
{"name": "intrinsicFrontier_singleton", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Intrinsic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "intrinsicClosure_singleton", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Intrinsic", "is_tactic_proof": true, "tactics": ["simp", "mem_affineSpan_singleton,"], "tactic_count": 2}
{"name": "intrinsicClosure_mono", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Intrinsic", "is_tactic_proof": true, "tactics": ["refine", "refine", "refine", "exact"], "tactic_count": 4}
{"name": "interior_subset_intrinsicInterior", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Intrinsic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intrinsicClosure_subset_closure", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Intrinsic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intrinsicFrontier_subset_frontier", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Intrinsic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intrinsicClosure_subset_affineSpan", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Intrinsic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intrinsicClosure_diff_intrinsicFrontier", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Intrinsic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intrinsicClosure_diff_intrinsicInterior", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Intrinsic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intrinsicInterior_union_intrinsicFrontier", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Intrinsic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "intrinsicFrontier_union_intrinsicInterior", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Intrinsic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "isClosed_intrinsicClosure", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Intrinsic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosed_intrinsicFrontier", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Intrinsic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "affineSpan_intrinsicClosure", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Intrinsic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.intrinsicClosure", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Intrinsic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "intrinsicClosure_idem", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Intrinsic", "is_tactic_proof": true, "tactics": ["refine", "set", "clear_value", "obtain", "rw", "exact"], "tactic_count": 6}
{"name": "intrinsicClosure_eq_closure_inter_affineSpan", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Intrinsic", "is_tactic_proof": true, "tactics": ["have", "rw", "rw", "apply"], "tactic_count": 4}
{"name": "AffineIsometry.image_intrinsicInterior", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Intrinsic", "is_tactic_proof": true, "tactics": ["obtain", "simp", "haveI", "let", "have", "rw", "φ.injective.preimage_image]"], "tactic_count": 7}
{"name": "AffineIsometry.image_intrinsicFrontier", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Intrinsic", "is_tactic_proof": true, "tactics": ["obtain", "simp", "haveI", "let", "have", "rw", "φ.injective.preimage_image]"], "tactic_count": 7}
{"name": "AffineIsometry.image_intrinsicClosure", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Intrinsic", "is_tactic_proof": true, "tactics": ["obtain", "simp", "haveI", "let", "have", "rw", "φ.injective.preimage_image]"], "tactic_count": 7}
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{"name": "closure_diff_intrinsicInterior", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Intrinsic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "closure_diff_intrinsicFrontier", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Intrinsic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Convex.intrinsicClosure", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Intrinsic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "_private.Mathlib.Analysis.Convex.Intrinsic.0.aux", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Intrinsic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.Nonempty.intrinsicInterior", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Intrinsic", "is_tactic_proof": true, "tactics": ["haveI", "obtain", "let", "rw", "exact", "hscv.affine_preimage"], "tactic_count": 6}
{"name": "intrinsicInterior_nonempty", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Intrinsic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ConcaveOn.le_map_centerMass", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Jensen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexOn.map_sum_le", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Jensen", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ConcaveOn.le_map_sum", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Jensen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexOn.map_add_sum_le", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Jensen", "is_tactic_proof": true, "tactics": ["let", "let", "have", "hf.map_sum_le", "simpa"], "tactic_count": 5}
{"name": "ConcaveOn.map_add_sum_le", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Jensen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "StrictConcaveOn.lt_map_sum", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Jensen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictConvexOn.eq_of_le_map_sum", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Jensen", "is_tactic_proof": true, "tactics": ["by_contra"], "tactic_count": 1}
{"name": "StrictConcaveOn.eq_of_map_sum_eq", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Jensen", "is_tactic_proof": true, "tactics": ["by_contra"], "tactic_count": 1}
{"name": "StrictConvexOn.map_sum_eq_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Jensen", "is_tactic_proof": true, "tactics": ["constructor", "obtain", "simp", "intro", "have", "intro", "apply", "calc", "p", "intro", "have", "intro", "simp", "rw"], "tactic_count": 14}
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{"name": "ConvexOn.exists_ge_of_centerMass", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Jensen", "is_tactic_proof": true, "tactics": ["set", "obtain", "have", "refine", "rw", "centerMass_filter_ne_zero]", "exact", "rw", "exact"], "tactic_count": 9}
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{"name": "ConvexOn.bddAbove_convexHull", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Jensen", "is_tactic_proof": true, "tactics": ["rintro", "refine", "rintro", "obtain", "exact"], "tactic_count": 5}
{"name": "ConcaveOn.bddBelow_convexHull", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Jensen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "mem_convexJoin", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Join", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "convexJoin_comm", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Join", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "convexJoin_mono", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Join", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "convexJoin_singleton_left", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Join", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "convexJoin_singletons", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Join", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "convexJoin_union_left", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Join", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
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{"name": "convexJoin_iUnion_right", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Join", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "segment_subset_convexJoin", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Join", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "subset_convexJoin_left", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Join", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "subset_convexJoin_right", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Join", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "convexJoin_subset", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Join", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "convexJoin_subset_convexHull", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Join", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "convexJoin_assoc_aux", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Join", "is_tactic_proof": true, "tactics": ["simp_rw", "rintro", "obtain", "refine", "linear_combination", "refine", "positivity,", "linear_combination", "match_scalars"], "tactic_count": 9}
{"name": "convexJoin_assoc", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Join", "is_tactic_proof": true, "tactics": ["refine", "simp_rw", "exact"], "tactic_count": 3}
{"name": "convexJoin_left_comm", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Join", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
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{"name": "Convex.convexHull_union", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Join", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "convexJoin_segment_singleton", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Join", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "convexJoin_singleton_segment", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Join", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsCompact.extremePoints_nonempty", "kind": "theorem", "module": "Mathlib.Analysis.Convex.KreinMilman", "is_tactic_proof": true, "tactics": ["let", "rsuffices", "obtain", "refine", "rwa", "by_contra", "obtain", "obtain", "have", "rw", "exact", "refine", "obtain", "exact", "refine", "sInter_subset_of_mem", "haveI", "rw", "refine", "obtain", "exacts"], "tactic_count": 21}
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{"name": "LinearIsometryEquiv.strictConvex_preimage", "kind": "theorem", "module": "Mathlib.Analysis.Convex.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.strictConvex_image", "kind": "theorem", "module": "Mathlib.Analysis.Convex.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictConvex.linearIsometry_preimage", "kind": "theorem", "module": "Mathlib.Analysis.Convex.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.strictConvexSpace_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.LinearIsometry", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LinearIsometry.strictConvexSpace_range_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.strictConvexSpace_range", "kind": "instance", "module": "Mathlib.Analysis.Convex.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.strictConvexSpace", "kind": "theorem", "module": "Mathlib.Analysis.Convex.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.instStrictConvexSpace", "kind": "instance", "module": "Mathlib.Analysis.Convex.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ConvexOn.smul_concaveOn'", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Mul", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ConcaveOn.smul_convexOn'", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Mul", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ConvexOn.mul", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConcaveOn.mul", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexOn.mul'", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConcaveOn.mul'", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexOn.mul_concaveOn", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConcaveOn.mul_convexOn", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexOn.mul_concaveOn'", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConcaveOn.mul_convexOn'", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexOn.pow", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "convexOn_pow", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Even.convexOn_pow", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Mul", "is_tactic_proof": true, "tactics": ["obtain", "simp_rw", "refine", "calc"], "tactic_count": 4}
{"name": "convexOn_zpow", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.Icc_subset_segment", "kind": "theorem", "module": "Mathlib.Analysis.Convex.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.segment_eq_Icc", "kind": "theorem", "module": "Mathlib.Analysis.Convex.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.segment_eq_uIcc", "kind": "theorem", "module": "Mathlib.Analysis.Convex.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.convex_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.NNReal", "is_tactic_proof": true, "tactics": ["refine", "intro", "exact"], "tactic_count": 3}
{"name": "PartitionOfUnity.finsum_smul_mem_convex", "kind": "theorem", "module": "Mathlib.Analysis.Convex.PartitionOfUnity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_continuous_forall_mem_convex_of_local", "kind": "theorem", "module": "Mathlib.Analysis.Convex.PartitionOfUnity", "is_tactic_proof": true, "tactics": ["choose", "obtain", "mem_iUnion.2", "refine", "hf.continuous_finsum_smul", "exact"], "tactic_count": 6}
{"name": "exists_continuous_forall_mem_convex_of_local_const", "kind": "theorem", "module": "Mathlib.Analysis.Convex.PartitionOfUnity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.segment", "kind": "definition", "module": "Mathlib.Analysis.Convex.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.range_segment", "kind": "theorem", "module": "Mathlib.Analysis.Convex.PathConnected", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Path.segment_same", "kind": "theorem", "module": "Mathlib.Analysis.Convex.PathConnected", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Path.segment_symm", "kind": "theorem", "module": "Mathlib.Analysis.Convex.PathConnected", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Path.segment_add_segment", "kind": "theorem", "module": "Mathlib.Analysis.Convex.PathConnected", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Path.cast_segment", "kind": "theorem", "module": "Mathlib.Analysis.Convex.PathConnected", "is_tactic_proof": true, "tactics": ["subst_vars"], "tactic_count": 1}
{"name": "Path.eqOn_extend_segment", "kind": "theorem", "module": "Mathlib.Analysis.Convex.PathConnected", "is_tactic_proof": true, "tactics": ["intro", "simp"], "tactic_count": 2}
{"name": "JoinedIn.of_segment_subset", "kind": "theorem", "module": "Mathlib.Analysis.Convex.PathConnected", "is_tactic_proof": true, "tactics": ["use", "rwa"], "tactic_count": 2}
{"name": "StarConvex.isPathConnected", "kind": "theorem", "module": "Mathlib.Analysis.Convex.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Convex.isPathConnected", "kind": "theorem", "module": "Mathlib.Analysis.Convex.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Convex.isConnected", "kind": "theorem", "module": "Mathlib.Analysis.Convex.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Convex.isPreconnected", "kind": "theorem", "module": "Mathlib.Analysis.Convex.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.isPathConnected", "kind": "theorem", "module": "Mathlib.Analysis.Convex.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsTopologicalAddGroup.pathConnectedSpace", "kind": "theorem", "module": "Mathlib.Analysis.Convex.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isPathConnected_compl_of_isPathConnected_compl_zero", "kind": "theorem", "module": "Mathlib.Analysis.Convex.PathConnected", "is_tactic_proof": true, "tactics": ["convert", "trans", "rw", "ext", "simp", "ext", "simp"], "tactic_count": 7}
{"name": "convexOn_univ_piecewise_Iic_of_antitoneOn_Iic_monotoneOn_Ici", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Piecewise", "is_tactic_proof": true, "tactics": ["refine", "obtain", "have", "rw", "exact", "rw", "obtain", "rw", "have", "trans", "exact", "rw", "gcongr", "exact", "rw", "have", "trans", "exact", "rw", "gcongr", "exact", "rw", "obtain", "rw", "have", "trans", "exact", "rw", "gcongr", "exact", "rw", "have", "trans", "exact", "rw", "gcongr", "exact", "have", "rw", "exact"], "tactic_count": 40}
{"name": "convexOn_univ_piecewise_Ici_of_monotoneOn_Ici_antitoneOn_Iic", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Piecewise", "is_tactic_proof": false, "tactics": ["have", "by_cases", "rw", "exact"], "tactic_count": 4}
{"name": "concaveOn_univ_piecewise_Iic_of_monotoneOn_Iic_antitoneOn_Ici", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Piecewise", "is_tactic_proof": true, "tactics": ["rw", "exact", "convexOn_univ_piecewise_Iic_of_antitoneOn_Iic_monotoneOn_Ici"], "tactic_count": 3}
{"name": "concaveOn_univ_piecewise_Ici_of_antitoneOn_Ici_monotoneOn_Iic", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Piecewise", "is_tactic_proof": true, "tactics": ["rw", "exact", "convexOn_univ_piecewise_Ici_of_monotoneOn_Ici_antitoneOn_Iic"], "tactic_count": 3}
{"name": "QuasiconvexOn", "kind": "definition", "module": "Mathlib.Analysis.Convex.Quasiconvex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuasiconcaveOn", "kind": "definition", "module": "Mathlib.Analysis.Convex.Quasiconvex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuasilinearOn", "kind": "definition", "module": "Mathlib.Analysis.Convex.Quasiconvex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuasiconvexOn.dual", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Quasiconvex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuasiconcaveOn.dual", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Quasiconvex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuasilinearOn.dual", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Quasiconvex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Convex.quasiconvexOn_of_convex_le", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Quasiconvex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Convex.quasiconcaveOn_of_convex_ge", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Quasiconvex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuasiconvexOn.convex", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Quasiconvex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuasiconcaveOn.convex", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Quasiconvex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuasiconvexOn.monotone_comp", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Quasiconvex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuasiconvexOn.antitone_comp", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Quasiconvex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuasiconcaveOn.monotone_comp", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Quasiconvex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuasiconcaveOn.antitone_comp", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Quasiconvex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuasilinearOn.monotone_comp", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Quasiconvex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuasilinearOn.antitone_comp", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Quasiconvex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Convex.quasiconvexOn_restrict", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Quasiconvex", "is_tactic_proof": true, "tactics": ["intro", "rw", "exact"], "tactic_count": 3}
{"name": "Convex.quasiconcaveOn_restrict", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Quasiconvex", "is_tactic_proof": true, "tactics": ["intro", "rw", "exact"], "tactic_count": 3}
{"name": "QuasiconcaveOn.isPreconnected_preimage_subtype", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Quasiconvex", "is_tactic_proof": false, "tactics": ["rw", "inter_comm]", "exact"], "tactic_count": 3}
{"name": "QuasiconvexOn.isPreconnected_preimage_subtype", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Quasiconvex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuasilinearOn.isPreconnected_preimage_subtype", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Quasiconvex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuasiconvexOn.sup", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Quasiconvex", "is_tactic_proof": true, "tactics": ["intro", "simp_rw", "exact"], "tactic_count": 3}
{"name": "QuasiconcaveOn.inf", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Quasiconvex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "quasiconvexOn_iff_le_max", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Quasiconvex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "quasiconcaveOn_iff_min_le", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Quasiconvex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "quasilinearOn_iff_mem_uIcc", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Quasiconvex", "is_tactic_proof": true, "tactics": ["rw", "apply", "simp_rw"], "tactic_count": 3}
{"name": "QuasiconvexOn.convex_lt", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Quasiconvex", "is_tactic_proof": true, "tactics": ["refine", "have", "exact"], "tactic_count": 3}
{"name": "QuasiconcaveOn.convex_gt", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Quasiconvex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexOn.quasiconvexOn", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Quasiconvex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConcaveOn.quasiconcaveOn", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Quasiconvex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonotoneOn.quasiconvexOn", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Quasiconvex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonotoneOn.quasiconcaveOn", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Quasiconvex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonotoneOn.quasilinearOn", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Quasiconvex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntitoneOn.quasiconvexOn", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Quasiconvex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntitoneOn.quasiconcaveOn", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Quasiconvex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntitoneOn.quasilinearOn", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Quasiconvex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.quasiconvexOn", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Quasiconvex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.quasiconcaveOn", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Quasiconvex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.quasilinearOn", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Quasiconvex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.quasiconvexOn", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Quasiconvex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.quasiconcaveOn", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Quasiconvex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.quasilinearOn", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Quasiconvex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuasilinearOn.monotoneOn_or_antitoneOn", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Quasiconvex", "is_tactic_proof": true, "tactics": ["simp_rw", "rintro", "refine"], "tactic_count": 3}
{"name": "quasilinearOn_iff_monotoneOn_or_antitoneOn", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Quasiconvex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Convex.radon_partition", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Radon", "is_tactic_proof": true, "tactics": ["rw", "push_neg", "obtain", "let", "let", "let", "have", "simpa", "have", "rcases", "exact", "sum_pos", "have", "centerMass_of_sum_add_sum_eq_zero", "simpa", "refine", "exact", "rw", "refine", "centerMass_mem_convexHull_of_nonpos", "linarith", "exact"], "tactic_count": 22}
{"name": "_private.Mathlib.Analysis.Convex.Radon.0.Convex.helly_theorem_corner", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Radon", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Convex.helly_theorem'", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Radon", "is_tactic_proof": true, "tactics": ["classical", "obtain", "exact", "generalize", "rw", "induction", "base", "succ", "hk", "let", "apply", "exact", "intro", "exact", "simp", "lia", "dimension", "have", "rw", "exact", "simp", "lia", "lies", "obtain", "use", "apply", "intro", "let", "hull", "suffices", "by_cases", "exact", "apply", "rwa", "show", "intro", "rw", "rintro", "rw", "apply", "apply", "simp", "suffices", "simp", "constructor", "exact", "assumption", "apply"], "tactic_count": 48}
{"name": "Convex.helly_theorem", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Radon", "is_tactic_proof": true, "tactics": ["apply", "intro", "obtain", "apply", "exact"], "tactic_count": 5}
{"name": "Convex.helly_theorem_set'", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Radon", "is_tactic_proof": true, "tactics": ["classical", "rw", "apply", "intro", "rw", "exact"], "tactic_count": 6}
{"name": "Convex.helly_theorem_set", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Radon", "is_tactic_proof": true, "tactics": ["apply", "intro", "obtain", "have", "apply", "exact"], "tactic_count": 6}
{"name": "Convex.helly_theorem_compact'", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Radon", "is_tactic_proof": true, "tactics": ["classical", "rcases", "simp", "have", "apply", "exact", "have", "rw", "apply", "exact", "intro", "exact", "intro", "simpa"], "tactic_count": 14}
{"name": "Convex.helly_theorem_compact", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Radon", "is_tactic_proof": true, "tactics": ["apply", "intro", "have", "by_cases", "exact", "have", "have", "apply", "simp", "rwa", "obtain", "apply", "exact"], "tactic_count": 13}
{"name": "Convex.helly_theorem_set_compact'", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Radon", "is_tactic_proof": true, "tactics": ["classical", "rw", "refine", "helly_theorem_compact", "intro", "let", "rw", "apply", "simp", "apply", "assumption"], "tactic_count": 11}
{"name": "Convex.helly_theorem_set_compact", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Radon", "is_tactic_proof": true, "tactics": ["apply", "intro", "obtain", "exists_superset_subset_encard_eq", "apply", "have", "let", "rw", "apply", "simpa", "rwa"], "tactic_count": 11}
{"name": "segment", "kind": "definition", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "openSegment", "kind": "definition", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Convex.term[_-[_]_]", "kind": "definition", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Convex._aux_Mathlib_Analysis_Convex_Segment___macroRules_Convex_term[_-[_]_]_1", "kind": "definition", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Convex._aux_Mathlib_Analysis_Convex_Segment___unexpand_segment_1", "kind": "definition", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "segment_eq_image₂", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "openSegment_eq_image₂", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "segment_symm", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "openSegment_symm", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "openSegment_subset_segment", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "segment_subset_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "openSegment_subset_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "left_mem_segment", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "right_mem_segment", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "segment_same", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "insert_endpoints_openSegment", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": false, "tactics": ["simp", "true_and]", "rintro", "refine", "rintro", "rw", "rintro", "rw", "exact"], "tactic_count": 9}
{"name": "mem_openSegment_of_ne_left_right", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "openSegment_subset_iff_segment_subset", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "segment.lift", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "openSegment.lift", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "openSegment_same", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "segment_eq_image", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "openSegment_eq_image", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "segment_eq_image'", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": true, "tactics": ["convert", "simp", "abel"], "tactic_count": 3}
{"name": "openSegment_eq_image'", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": true, "tactics": ["convert", "simp", "abel"], "tactic_count": 3}
{"name": "segment_eq_image_lineMap", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": true, "tactics": ["convert", "exact"], "tactic_count": 2}
{"name": "openSegment_eq_image_lineMap", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": true, "tactics": ["convert", "exact"], "tactic_count": 2}
{"name": "lineMap_mem_openSegment", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "image_segment", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "image_openSegment", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "vadd_segment", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "vadd_openSegment", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_segment_translate", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "mem_openSegment_translate", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "segment_translate_preimage", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "openSegment_translate_preimage", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "segment_translate_image", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "openSegment_translate_image", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "segment_inter_subset_endpoint_of_linearIndependent_sub", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": true, "tactics": ["intro", "rw", "rcases", "rcases", "have", "have", "rw", "have", "obtain", "simp"], "tactic_count": 10}
{"name": "segment_inter_eq_endpoint_of_linearIndependent_sub", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": true, "tactics": ["refine", "simp"], "tactic_count": 2}
{"name": "sameRay_of_mem_segment", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": true, "tactics": ["rw", "rcases", "simpa"], "tactic_count": 3}
{"name": "segment_inter_eq_endpoint_of_linearIndependent_of_ne", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": true, "tactics": ["apply", "simp", "suffices", "simp", "nontriviality", "rw", "aesop"], "tactic_count": 7}
{"name": "midpoint_mem_segment", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "mem_segment_sub_add", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "mem_segment_add_sub", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "left_mem_openSegment_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "refine", "rw", "rintro", "rw", "exact"], "tactic_count": 7}
{"name": "right_mem_openSegment_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mem_segment_iff_div", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "use", "simp", "rintro", "refine", "rw"], "tactic_count": 7}
{"name": "mem_openSegment_iff_div", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "use", "rw", "rintro", "have", "refine", "rw"], "tactic_count": 8}
{"name": "mem_segment_iff_sameRay", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": true, "tactics": ["refine", "rcases", "rw", "rw", "refine", "rw"], "tactic_count": 6}
{"name": "openSegment_subset_union", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rintro", "rcases", "right", "left", "have", "refine", "simp", "left", "rfl", "right", "right", "have", "simp", "refine", "simp", "sub_sub_sub_cancel_right]"], "tactic_count": 18}
{"name": "segment_subset_Icc", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": true, "tactics": ["rintro", "constructor", "calc", "x", "calc", "a"], "tactic_count": 6}
{"name": "openSegment_subset_Ioo", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": true, "tactics": ["rintro", "constructor", "calc", "x", "calc", "a"], "tactic_count": 6}
{"name": "segment_subset_uIcc", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": true, "tactics": ["rcases", "rw", "exact", "rw", "exact"], "tactic_count": 5}
{"name": "Convex.min_le_combo", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Convex.combo_le_max", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Icc_subset_segment", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": true, "tactics": ["rintro", "obtain", "rw", "exact", "rw", "rw", "refine", "rw", "rw", "sub_mul,"], "tactic_count": 10}
{"name": "segment_eq_Icc", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ioo_subset_openSegment", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "openSegment_eq_Ioo", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "segment_eq_Icc'", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": true, "tactics": ["rcases", "rw", "rw"], "tactic_count": 3}
{"name": "openSegment_eq_Ioo'", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": true, "tactics": ["rcases", "rw", "rw"], "tactic_count": 3}
{"name": "segment_eq_uIcc", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Convex.mem_Icc", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Convex.mem_Ioo", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Convex.mem_Ioc", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": true, "tactics": ["refine", "obtain", "obtain", "rw", "rw", "exact", "exact", "rintro", "obtain", "rw", "rwa", "exact"], "tactic_count": 12}
{"name": "Convex.mem_Ico", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": true, "tactics": ["refine", "obtain", "obtain", "rw", "rw", "exact", "exact", "rintro", "obtain", "rw", "rwa", "exact"], "tactic_count": 12}
{"name": "Nonneg.Icc_subset_segment", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": true, "tactics": ["intro", "rw", "rcases", "refine"], "tactic_count": 4}
{"name": "Nonneg.segment_eq_Icc", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": true, "tactics": ["refine"], "tactic_count": 1}
{"name": "Nonneg.segment_eq_uIcc", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simp"], "tactic_count": 3}
{"name": "Prod.segment_subset", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "Prod.openSegment_subset", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "Prod.image_mk_segment_left", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp"], "tactic_count": 3}
{"name": "Prod.image_mk_segment_right", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp"], "tactic_count": 3}
{"name": "Prod.image_mk_openSegment_left", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp"], "tactic_count": 3}
{"name": "Prod.image_mk_openSegment_right", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp"], "tactic_count": 3}
{"name": "Pi.segment_subset", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "Pi.openSegment_subset", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "Pi.image_update_segment", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp"], "tactic_count": 3}
{"name": "Pi.image_update_openSegment", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Segment", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp"], "tactic_count": 3}
{"name": "AffineSubspace.WSameSide", "kind": "definition", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.SSameSide", "kind": "definition", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.WOppSide", "kind": "definition", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.SOppSide", "kind": "definition", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.WSameSide.map", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["rcases", "refine", "simp_rw", "exact"], "tactic_count": 4}
{"name": "Function.Injective.wSameSide_map_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["refine", "rcases", "rw", "rcases", "rcases", "refine", "simp_rw", "exact"], "tactic_count": 8}
{"name": "Function.Injective.sSameSide_map_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "AffineEquiv.wSameSide_map_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineEquiv.sSameSide_map_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.WOppSide.map", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["rcases", "refine", "simp_rw", "exact"], "tactic_count": 4}
{"name": "Function.Injective.wOppSide_map_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["refine", "rcases", "rw", "rcases", "rcases", "refine", "simp_rw", "exact"], "tactic_count": 8}
{"name": "Function.Injective.sOppSide_map_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "AffineEquiv.wOppSide_map_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineEquiv.sOppSide_map_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.WSameSide.nonempty", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.SSameSide.nonempty", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.WOppSide.nonempty", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.SOppSide.nonempty", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.SSameSide.wSameSide", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.SSameSide.left_notMem", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.SSameSide.right_notMem", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.SOppSide.wOppSide", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.SOppSide.left_notMem", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.SOppSide.right_notMem", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.wSameSide_comm", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.sSameSide_comm", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AffineSubspace.wOppSide_comm", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "refine", "rwa", "rintro", "refine", "rwa"], "tactic_count": 7}
{"name": "AffineSubspace.sOppSide_comm", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AffineSubspace.not_wSameSide_bot", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.not_sSameSide_bot", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.not_wOppSide_bot", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.not_sOppSide_bot", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.wSameSide_self_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.sSameSide_self_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.wSameSide_of_left_mem", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["refine", "rw", "apply"], "tactic_count": 3}
{"name": "AffineSubspace.wSameSide_of_right_mem", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.wOppSide_of_left_mem", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["refine", "rw", "apply"], "tactic_count": 3}
{"name": "AffineSubspace.wOppSide_of_right_mem", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.wSameSide_vadd_left_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "refine", "rwa", "rintro", "refine", "rwa"], "tactic_count": 7}
{"name": "AffineSubspace.wSameSide_vadd_right_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AffineSubspace.sSameSide_vadd_left_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AffineSubspace.sSameSide_vadd_right_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AffineSubspace.wOppSide_vadd_left_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "refine", "rwa", "rintro", "refine", "rwa"], "tactic_count": 7}
{"name": "AffineSubspace.wOppSide_vadd_right_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AffineSubspace.sOppSide_vadd_left_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AffineSubspace.sOppSide_vadd_right_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AffineSubspace.wSameSide_smul_vsub_vadd_left", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "AffineSubspace.wSameSide_smul_vsub_vadd_right", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.wSameSide_lineMap_left", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.wSameSide_lineMap_right", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.wOppSide_smul_vsub_vadd_left", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "AffineSubspace.wOppSide_smul_vsub_vadd_right", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.wOppSide_lineMap_left", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.wOppSide_lineMap_right", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Wbtw.wSameSide₂₃", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "Wbtw.wSameSide₃₂", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Wbtw.wSameSide₁₂", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Wbtw.wSameSide₂₁", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Wbtw.wOppSide₁₃", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["rcases", "refine", "rcases", "simp", "rcases", "simp", "refine", "rw", "module"], "tactic_count": 9}
{"name": "Wbtw.wOppSide₃₁", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.wOppSide_self_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "obtain", "rw", "rw", "exact", "exact"], "tactic_count": 7}
{"name": "AffineSubspace.not_sOppSide_self", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "AffineSubspace.wSameSide_iff_exists_left", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "rw", "rw", "exact", "refine", "rw", "exact", "refine", "rw", "vsub_sub_vsub_cancel_right]", "rintro", "exact", "exact"], "tactic_count": 14}
{"name": "AffineSubspace.wSameSide_iff_exists_right", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["rw", "simp_rw"], "tactic_count": 2}
{"name": "AffineSubspace.sSameSide_iff_exists_left", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw"], "tactic_count": 3}
{"name": "AffineSubspace.sSameSide_iff_exists_right", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["rw", "simp_rw"], "tactic_count": 2}
{"name": "AffineSubspace.wOppSide_iff_exists_left", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "rw", "rw", "exact", "refine", "rw", "exact", "refine", "rw", "linear_combination", "rintro", "exact", "exact"], "tactic_count": 14}
{"name": "AffineSubspace.wOppSide_iff_exists_right", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["rw", "constructor", "rintro", "exact", "refine", "rwa", "rintro", "exact", "refine", "rwa"], "tactic_count": 10}
{"name": "AffineSubspace.sOppSide_iff_exists_left", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw"], "tactic_count": 3}
{"name": "AffineSubspace.sOppSide_iff_exists_right", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["rw", "rintro", "rw"], "tactic_count": 3}
{"name": "AffineSubspace.WSameSide.trans", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["rcases", "rw", "rcases", "refine", "refine", "rw", "exact"], "tactic_count": 7}
{"name": "AffineSubspace.WSameSide.trans_sSameSide", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.WSameSide.trans_wOppSide", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["rcases", "rw", "rcases", "refine", "refine", "rw", "exact"], "tactic_count": 7}
{"name": "AffineSubspace.WSameSide.trans_sOppSide", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.SSameSide.trans_wSameSide", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.SSameSide.trans", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.SSameSide.trans_wOppSide", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.SSameSide.trans_sOppSide", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.WOppSide.trans_wSameSide", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.WOppSide.trans_sSameSide", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.WOppSide.trans", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["rcases", "rw", "rcases", "rw", "refine", "refine", "rw", "exact"], "tactic_count": 8}
{"name": "AffineSubspace.WOppSide.trans_sOppSide", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.SOppSide.trans_wSameSide", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.SOppSide.trans_sSameSide", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.SOppSide.trans_wOppSide", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.SOppSide.trans", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.wSameSide_and_wOppSide_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "rw", "by_contra", "rw", "exact", "rintro", "exact", "exact"], "tactic_count": 9}
{"name": "AffineSubspace.WSameSide.not_sOppSide", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["intro", "have", "rcases", "exact", "exact"], "tactic_count": 5}
{"name": "AffineSubspace.SSameSide.not_wOppSide", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["intro", "have", "rcases", "exact", "exact"], "tactic_count": 5}
{"name": "AffineSubspace.SSameSide.not_sOppSide", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.WOppSide.not_sSameSide", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.SOppSide.not_wSameSide", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.SOppSide.not_sSameSide", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.wOppSide_iff_exists_wbtw", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["refine", "rcases", "rw", "rw", "exact", "rw", "rw", "exact", "refine", "have", "rw", "linear_combination", "rw", "vadd_eq_add,", "exact", "exact"], "tactic_count": 16}
{"name": "AffineSubspace.SOppSide.exists_sbtw", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["obtain", "refine", "rintro", "exact", "rintro", "exact"], "tactic_count": 6}
{"name": "Sbtw.sOppSide_of_notMem_of_mem", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["refine", "rcases", "rw", "have", "rintro", "simp", "have", "rw", "s.direction.smul_mem_iff", "rwa"], "tactic_count": 10}
{"name": "AffineSubspace.sSameSide_smul_vsub_vadd_left", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["refine", "rwa"], "tactic_count": 2}
{"name": "AffineSubspace.sSameSide_smul_vsub_vadd_right", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.sSameSide_lineMap_left", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.sSameSide_lineMap_right", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.sOppSide_smul_vsub_vadd_left", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["refine", "rwa"], "tactic_count": 2}
{"name": "AffineSubspace.sOppSide_smul_vsub_vadd_right", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.sOppSide_lineMap_left", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.sOppSide_lineMap_right", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.setOf_wSameSide_eq_image2", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["ext", "simp_rw", "constructor", "rw", "rintro", "rw", "exact", "rw", "refine", "simp", "refine", "rw", "rintro", "exact"], "tactic_count": 14}
{"name": "AffineSubspace.setOf_sSameSide_eq_image2", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["ext", "simp_rw", "constructor", "rw", "rintro", "rw", "exact", "rw", "exact", "refine", "rw", "rintro", "exact"], "tactic_count": 13}
{"name": "AffineSubspace.setOf_wOppSide_eq_image2", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["ext", "simp_rw", "constructor", "rw", "rintro", "rw", "exact", "rw", "refine", "simp", "refine", "rw", "neg_vsub_eq_vsub_rev,", "rintro", "exact"], "tactic_count": 15}
{"name": "AffineSubspace.setOf_sOppSide_eq_image2", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["ext", "simp_rw", "constructor", "rw", "rintro", "rw", "exact", "rw", "exact", "refine", "rw", "neg_vsub_eq_vsub_rev,", "rintro", "exact"], "tactic_count": 14}
{"name": "AffineSubspace.wOppSide_pointReflection", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.sOppSide_pointReflection", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["refine", "rwa"], "tactic_count": 2}
{"name": "AffineSubspace.isConnected_setOf_wSameSide", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["obtain", "haveI", "by_cases", "simp", "have", "exact", "rw", "refine", "convert"], "tactic_count": 9}
{"name": "AffineSubspace.isPreconnected_setOf_wSameSide", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["rcases", "rw", "simp", "exact", "exact"], "tactic_count": 5}
{"name": "AffineSubspace.isConnected_setOf_sSameSide", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["obtain", "haveI", "rw", "refine", "convert"], "tactic_count": 5}
{"name": "AffineSubspace.isPreconnected_setOf_sSameSide", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["rcases", "rw", "simp", "exact", "by_cases", "simp", "exact", "exact"], "tactic_count": 8}
{"name": "AffineSubspace.isConnected_setOf_wOppSide", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["obtain", "haveI", "by_cases", "simp", "have", "exact", "rw", "refine", "convert"], "tactic_count": 9}
{"name": "AffineSubspace.isPreconnected_setOf_wOppSide", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["rcases", "rw", "simp", "exact", "exact"], "tactic_count": 5}
{"name": "AffineSubspace.isConnected_setOf_sOppSide", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["obtain", "haveI", "rw", "refine", "convert"], "tactic_count": 5}
{"name": "AffineSubspace.isPreconnected_setOf_sOppSide", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["rcases", "rw", "simp", "exact", "by_cases", "simp", "exact", "exact"], "tactic_count": 8}
{"name": "Affine.Simplex.sSameSide_affineSpan_faceOpposite_of_sign_eq", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["have", "refine", "obtain", "have", "refine", "rw", "let", "have", "have", "refine", "simp", "left", "rcases", "rw", "exact", "rw", "positivity"], "tactic_count": 17}
{"name": "Affine.Simplex.sOppSide_affineSpan_faceOpposite_of_pos_of_neg", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["let", "have", "have", "have", "have", "rwa", "refine", "h'.sOppSide_of_notMem_of_mem", "simp", "rw", "simp"], "tactic_count": 11}
{"name": "Affine.Simplex.sSameSide_affineSpan_faceOpposite_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["refine", "have", "refine", "have", "rcases", "exact", "exfalso", "rcases", "rw", "exact", "rw", "exact"], "tactic_count": 12}
{"name": "Affine.Simplex.sOppSide_affineSpan_faceOpposite_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["refine", "have", "refine", "have", "rcases", "exfalso", "exact", "exact", "rcases", "rw", "exact", "rw", "exact"], "tactic_count": 13}
{"name": "Affine.Simplex.wSameSide_affineSpan_faceOpposite_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["refine", "by_cases", "simp", "by_cases", "simp", "exact", "by_cases", "exact", "by_cases", "exact", "simp", "exact"], "tactic_count": 12}
{"name": "Affine.Simplex.wOppSide_affineSpan_faceOpposite_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["refine", "by_cases", "simp", "by_cases", "simp", "exact", "by_cases", "exact", "by_cases", "exact", "simp", "rcases", "rw", "exact", "rw", "exact"], "tactic_count": 16}
{"name": "Affine.Simplex.sSameSide_affineSpan_faceOpposite_point_left_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": false, "tactics": ["rw", "s.sSameSide_affineSpan_faceOpposite_iff", "eq_comm]", "simp"], "tactic_count": 4}
{"name": "Affine.Simplex.sSameSide_affineSpan_faceOpposite_point_right_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Affine.Simplex.sOppSide_affineSpan_faceOpposite_point_left_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": false, "tactics": ["rw", "s.sOppSide_affineSpan_faceOpposite_iff", "eq_comm,", "simp"], "tactic_count": 4}
{"name": "Affine.Simplex.sOppSide_affineSpan_faceOpposite_point_right_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Affine.Simplex.wSameSide_affineSpan_faceOpposite_point_left_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": false, "tactics": ["rw", "s.wSameSide_affineSpan_faceOpposite_iff", "eq_comm]", "simp"], "tactic_count": 4}
{"name": "Affine.Simplex.wSameSide_affineSpan_faceOpposite_point_right_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Affine.Simplex.wOppSide_affineSpan_faceOpposite_point_left_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": false, "tactics": ["rw", "s.wOppSide_affineSpan_faceOpposite_iff", "eq_comm,", "simp"], "tactic_count": 4}
{"name": "Affine.Simplex.wOppSide_affineSpan_faceOpposite_point_right_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Side", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Geometry.SimplicialComplex.instMembershipFinset", "kind": "instance", "module": "Mathlib.Analysis.Convex.SimplicialComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Geometry.SimplicialComplex.nonempty_of_mem_faces", "kind": "theorem", "module": "Mathlib.Analysis.Convex.SimplicialComplex.Basic", "is_tactic_proof": true, "tactics": ["by_contra"], "tactic_count": 1}
{"name": "Geometry.SimplicialComplex.space", "kind": "definition", "module": "Mathlib.Analysis.Convex.SimplicialComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Geometry.SimplicialComplex.mem_space_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.SimplicialComplex.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Geometry.SimplicialComplex.convexHull_subset_space", "kind": "theorem", "module": "Mathlib.Analysis.Convex.SimplicialComplex.Basic", "is_tactic_proof": true, "tactics": ["convert", "rfl"], "tactic_count": 2}
{"name": "Geometry.SimplicialComplex.subset_space", "kind": "theorem", "module": "Mathlib.Analysis.Convex.SimplicialComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Geometry.SimplicialComplex.convexHull_inter_convexHull", "kind": "theorem", "module": "Mathlib.Analysis.Convex.SimplicialComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Geometry.SimplicialComplex.disjoint_or_exists_inter_eq_convexHull", "kind": "theorem", "module": "Mathlib.Analysis.Convex.SimplicialComplex.Basic", "is_tactic_proof": true, "tactics": ["classical", "by_contra", "rw", "refine", "simpa", "rw"], "tactic_count": 6}
{"name": "Geometry.SimplicialComplex.ofErase", "kind": "definition", "module": "Mathlib.Analysis.Convex.SimplicialComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Geometry.SimplicialComplex.ofSubcomplex", "kind": "definition", "module": "Mathlib.Analysis.Convex.SimplicialComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Geometry.SimplicialComplex.vertices", "kind": "definition", "module": "Mathlib.Analysis.Convex.SimplicialComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Geometry.SimplicialComplex.mem_vertices", "kind": "theorem", "module": "Mathlib.Analysis.Convex.SimplicialComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Geometry.SimplicialComplex.vertices_eq", "kind": "theorem", "module": "Mathlib.Analysis.Convex.SimplicialComplex.Basic", "is_tactic_proof": true, "tactics": ["ext", "refine", "obtain", "exact"], "tactic_count": 4}
{"name": "Geometry.SimplicialComplex.vertices_subset_space", "kind": "theorem", "module": "Mathlib.Analysis.Convex.SimplicialComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Geometry.SimplicialComplex.vertex_mem_convexHull_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.SimplicialComplex.Basic", "is_tactic_proof": true, "tactics": ["refine", "classical", "have", "by_contra", "rwa", "convexHull_empty]"], "tactic_count": 6}
{"name": "Geometry.SimplicialComplex.face_subset_face_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.SimplicialComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Geometry.SimplicialComplex.facets", "kind": "definition", "module": "Mathlib.Analysis.Convex.SimplicialComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Geometry.SimplicialComplex.mem_facets", "kind": "theorem", "module": "Mathlib.Analysis.Convex.SimplicialComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Geometry.SimplicialComplex.facets_subset", "kind": "theorem", "module": "Mathlib.Analysis.Convex.SimplicialComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Geometry.SimplicialComplex.not_facet_iff_subface", "kind": "theorem", "module": "Mathlib.Analysis.Convex.SimplicialComplex.Basic", "is_tactic_proof": true, "tactics": ["refine", "push_neg", "obtain", "exact", "rintro", "have", "rw", "exact"], "tactic_count": 8}
{"name": "Geometry.SimplicialComplex.instMin", "kind": "instance", "module": "Mathlib.Analysis.Convex.SimplicialComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Geometry.SimplicialComplex.instSemilatticeInf", "kind": "instance", "module": "Mathlib.Analysis.Convex.SimplicialComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Geometry.SimplicialComplex.hasBot", "kind": "instance", "module": "Mathlib.Analysis.Convex.SimplicialComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Geometry.SimplicialComplex.instOrderBot", "kind": "instance", "module": "Mathlib.Analysis.Convex.SimplicialComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Geometry.SimplicialComplex.instInhabited", "kind": "instance", "module": "Mathlib.Analysis.Convex.SimplicialComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Geometry.SimplicialComplex.faces_bot", "kind": "theorem", "module": "Mathlib.Analysis.Convex.SimplicialComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Geometry.SimplicialComplex.space_bot", "kind": "theorem", "module": "Mathlib.Analysis.Convex.SimplicialComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Geometry.SimplicialComplex.facets_bot", "kind": "theorem", "module": "Mathlib.Analysis.Convex.SimplicialComplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexOn.slope_mono_adjacent", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Slope", "is_tactic_proof": true, "tactics": ["have", "rw", "have", "have", "have", "simp", "ring_nf", "field_simp", "linarith"], "tactic_count": 9}
{"name": "ConcaveOn.slope_anti_adjacent", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Slope", "is_tactic_proof": true, "tactics": ["have", "simp", "linear_combination"], "tactic_count": 3}
{"name": "StrictConvexOn.slope_strict_mono_adjacent", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Slope", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "have", "have", "have", "simp", "ring_nf", "field_simp", "linarith"], "tactic_count": 10}
{"name": "StrictConcaveOn.slope_anti_adjacent", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Slope", "is_tactic_proof": true, "tactics": ["have", "simp", "linear_combination"], "tactic_count": 3}
{"name": "convexOn_of_slope_mono_adjacent", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Slope", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "concaveOn_of_slope_anti_adjacent", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Slope", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp", "linear_combination"], "tactic_count": 4}
{"name": "strictConvexOn_of_slope_strict_mono_adjacent", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Slope", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictConcaveOn_of_slope_strict_anti_adjacent", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Slope", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp", "linear_combination"], "tactic_count": 4}
{"name": "convexOn_iff_slope_mono_adjacent", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Slope", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "concaveOn_iff_slope_anti_adjacent", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Slope", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictConvexOn_iff_slope_strict_mono_adjacent", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Slope", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictConcaveOn_iff_slope_strict_anti_adjacent", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Slope", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexOn.secant_mono_aux1", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Slope", "is_tactic_proof": true, "tactics": ["have", "have", "have", "have", "have", "have", "simp", "ring_nf", "field_simp", "linear_combination", "field"], "tactic_count": 11}
{"name": "ConvexOn.secant_mono_aux2", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Slope", "is_tactic_proof": true, "tactics": ["have", "have", "field_simp", "linarith"], "tactic_count": 4}
{"name": "ConvexOn.secant_mono_aux3", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Slope", "is_tactic_proof": true, "tactics": ["have", "have", "field_simp", "linarith"], "tactic_count": 4}
{"name": "ConvexOn.secant_mono", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Slope", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rcases", "rcases", "convert", "convert", "rw", "exact"], "tactic_count": 8}
{"name": "StrictConvexOn.secant_strict_mono_aux1", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Slope", "is_tactic_proof": true, "tactics": ["have", "have", "have", "have", "have", "have", "simp", "ring_nf", "field_simp", "linear_combination", "field"], "tactic_count": 11}
{"name": "StrictConvexOn.secant_strict_mono_aux2", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Slope", "is_tactic_proof": true, "tactics": ["have", "have", "field_simp", "linarith"], "tactic_count": 4}
{"name": "StrictConvexOn.secant_strict_mono_aux3", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Slope", "is_tactic_proof": true, "tactics": ["have", "have", "field_simp", "linarith"], "tactic_count": 4}
{"name": "StrictConvexOn.secant_strict_mono", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Slope", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "convert", "convert", "rw", "exact"], "tactic_count": 6}
{"name": "StrictConcaveOn.secant_strict_mono", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Slope", "is_tactic_proof": true, "tactics": ["have", "simp", "linear_combination"], "tactic_count": 3}
{"name": "ConvexOn.strictMonoOn", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Slope", "is_tactic_proof": true, "tactics": ["intro", "have", "intro", "refine", "rw", "exact", "rcases", "exact", "refine", "apply", "rw", "exact", "rw", "exact"], "tactic_count": 14}
{"name": "ConvexOn.strictAntiOn", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Slope", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "ConcaveOn.strictMonoOn", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Slope", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ConcaveOn.strictAntiOn", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Slope", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "strictConvexOn_exp", "kind": "theorem", "module": "Mathlib.Analysis.Convex.SpecificFunctions.Basic", "is_tactic_proof": true, "tactics": ["apply", "rintro", "trans", "have", "have", "rw", "calc", "exp", "have", "rw", "calc", "exp", "gcongr", "linarith"], "tactic_count": 14}
{"name": "convexOn_exp", "kind": "theorem", "module": "Mathlib.Analysis.Convex.SpecificFunctions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictConcaveOn_log_Ioi", "kind": "theorem", "module": "Mathlib.Analysis.Convex.SpecificFunctions.Basic", "is_tactic_proof": true, "tactics": ["apply", "intro", "have", "trans", "have", "rw", "have", "have", "contrapose", "rw", "simp", "calc", "log", "have", "rw", "have", "have", "contrapose", "rw", "simp", "calc", "y⁻¹"], "tactic_count": 22}
{"name": "one_add_mul_self_lt_rpow_one_add", "kind": "theorem", "module": "Mathlib.Analysis.Convex.SpecificFunctions.Basic", "is_tactic_proof": true, "tactics": ["have", "rcases", "rwa", "have", "rcases", "exact", "have", "have", "rwa", "rw", "apply", "rcases", "rw", "convert", "rw", "rw", "gcongr", "exact", "rw", "convert", "rw", "rw", "gcongr", "exact"], "tactic_count": 24}
{"name": "one_add_mul_self_le_rpow_one_add", "kind": "theorem", "module": "Mathlib.Analysis.Convex.SpecificFunctions.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simp", "by_cases", "simp", "exact"], "tactic_count": 5}
{"name": "rpow_one_add_lt_one_add_mul_self", "kind": "theorem", "module": "Mathlib.Analysis.Convex.SpecificFunctions.Basic", "is_tactic_proof": true, "tactics": ["rcases", "rwa", "have", "have", "rw", "rcases", "exact", "exact", "have", "have", "rwa", "rw", "apply", "rcases", "rw", "convert", "rw", "rw", "gcongr", "exact", "rw", "convert", "rw", "rw", "gcongr", "exact"], "tactic_count": 26}
{"name": "rpow_one_add_le_one_add_mul_self", "kind": "theorem", "module": "Mathlib.Analysis.Convex.SpecificFunctions.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rcases", "simp", "by_cases", "simp", "exact"], "tactic_count": 7}
{"name": "strictConvexOn_rpow", "kind": "theorem", "module": "Mathlib.Analysis.Convex.SpecificFunctions.Basic", "is_tactic_proof": true, "tactics": ["apply", "intro", "have", "have", "trans", "have", "rw", "sub_lt_comm,", "rpow_sub", "neg_sub,", "apply", "rw", "exact", "rw", "exact", "have", "rw", "lt_sub_iff_add_lt',", "mul_div_assoc,", "div_self", "apply", "rw", "exact", "rw", "exact"], "tactic_count": 25}
{"name": "convexOn_rpow", "kind": "theorem", "module": "Mathlib.Analysis.Convex.SpecificFunctions.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simpa", "exact"], "tactic_count": 3}
{"name": "convexOn_rpow_left", "kind": "theorem", "module": "Mathlib.Analysis.Convex.SpecificFunctions.Basic", "is_tactic_proof": true, "tactics": ["convert", "ext", "simp"], "tactic_count": 3}
{"name": "strictConcaveOn_log_Iio", "kind": "theorem", "module": "Mathlib.Analysis.Convex.SpecificFunctions.Basic", "is_tactic_proof": true, "tactics": ["refine", "intro", "have", "have", "have", "calc", "a"], "tactic_count": 7}
{"name": "Real.exp_mul_le_cosh_add_mul_sinh", "kind": "theorem", "module": "Mathlib.Analysis.Convex.SpecificFunctions.Basic", "is_tactic_proof": true, "tactics": ["rw", "calc"], "tactic_count": 2}
{"name": "strictConvexOn_pow", "kind": "theorem", "module": "Mathlib.Analysis.Convex.SpecificFunctions.Deriv", "is_tactic_proof": true, "tactics": ["apply", "eta_expand", "simp_rw", "exact", "mul_lt_mul_of_pos_left"], "tactic_count": 5}
{"name": "Even.strictConvexOn_pow", "kind": "theorem", "module": "Mathlib.Analysis.Convex.SpecificFunctions.Deriv", "is_tactic_proof": true, "tactics": ["apply", "eta_expand", "simp_rw", "replace", "exact"], "tactic_count": 5}
{"name": "Finset.prod_nonneg_of_card_nonpos_even", "kind": "theorem", "module": "Mathlib.Analysis.Convex.SpecificFunctions.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "int_prod_range_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Convex.SpecificFunctions.Deriv", "is_tactic_proof": true, "tactics": ["rcases", "induction", "zero", "succ", "rw", "rw", "mul_assoc]", "refine", "rcases", "have", "convert", "convert", "exact"], "tactic_count": 13}
{"name": "int_prod_range_pos", "kind": "theorem", "module": "Mathlib.Analysis.Convex.SpecificFunctions.Deriv", "is_tactic_proof": true, "tactics": ["refine", "rw", "obtain", "rw", "exact"], "tactic_count": 5}
{"name": "strictConvexOn_zpow", "kind": "theorem", "module": "Mathlib.Analysis.Convex.SpecificFunctions.Deriv", "is_tactic_proof": true, "tactics": ["apply", "exact", "intro", "rw", "rw", "refine", "norm_cast", "refine", "rw", "norm_cast", "fin_cases"], "tactic_count": 11}
{"name": "hasDerivAt_sqrt_mul_log", "kind": "theorem", "module": "Mathlib.Analysis.Convex.SpecificFunctions.Deriv", "is_tactic_proof": true, "tactics": ["convert", "rw", "div_eq_inv_mul]"], "tactic_count": 3}
{"name": "deriv_sqrt_mul_log", "kind": "theorem", "module": "Mathlib.Analysis.Convex.SpecificFunctions.Deriv", "is_tactic_proof": true, "tactics": ["rcases", "exact", "rw", "refine", "refine", "rw"], "tactic_count": 6}
{"name": "deriv_sqrt_mul_log'", "kind": "theorem", "module": "Mathlib.Analysis.Convex.SpecificFunctions.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv2_sqrt_mul_log", "kind": "theorem", "module": "Mathlib.Analysis.Convex.SpecificFunctions.Deriv", "is_tactic_proof": true, "tactics": ["simp", "rcases", "rw", "refine", "refine", "rw", "have", "convert", "mul_ne_zero", "nth_rw", "field"], "tactic_count": 11}
{"name": "strictConcaveOn_sqrt_mul_log_Ioi", "kind": "theorem", "module": "Mathlib.Analysis.Convex.SpecificFunctions.Deriv", "is_tactic_proof": true, "tactics": ["apply", "exact", "rw", "exact", "div_neg_of_neg_of_pos"], "tactic_count": 5}
{"name": "strictConcaveOn_sin_Icc", "kind": "theorem", "module": "Mathlib.Analysis.Convex.SpecificFunctions.Deriv", "is_tactic_proof": true, "tactics": ["apply", "rw", "simp"], "tactic_count": 3}
{"name": "strictConcaveOn_cos_Icc", "kind": "theorem", "module": "Mathlib.Analysis.Convex.SpecificFunctions.Deriv", "is_tactic_proof": true, "tactics": ["apply", "rw", "simp"], "tactic_count": 3}
{"name": "NNReal.strictConcaveOn_rpow", "kind": "theorem", "module": "Mathlib.Analysis.Convex.SpecificFunctions.Pow", "is_tactic_proof": true, "tactics": ["have", "have", "let", "have", "refine", "exact", "have", "refine", "simp", "exact"], "tactic_count": 10}
{"name": "NNReal.concaveOn_rpow", "kind": "theorem", "module": "Mathlib.Analysis.Convex.SpecificFunctions.Pow", "is_tactic_proof": true, "tactics": ["rcases", "simpa", "rcases", "simpa", "exact"], "tactic_count": 5}
{"name": "NNReal.strictConcaveOn_sqrt", "kind": "theorem", "module": "Mathlib.Analysis.Convex.SpecificFunctions.Pow", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "Real.strictConcaveOn_rpow", "kind": "theorem", "module": "Mathlib.Analysis.Convex.SpecificFunctions.Pow", "is_tactic_proof": true, "tactics": ["refine", "let", "let", "let", "let", "have", "have", "exact_mod_cast"], "tactic_count": 8}
{"name": "Real.concaveOn_rpow", "kind": "theorem", "module": "Mathlib.Analysis.Convex.SpecificFunctions.Pow", "is_tactic_proof": true, "tactics": ["rcases", "simpa", "rcases", "simpa", "exact"], "tactic_count": 5}
{"name": "Real.strictConcaveOn_sqrt", "kind": "theorem", "module": "Mathlib.Analysis.Convex.SpecificFunctions.Pow", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "StarConvex", "kind": "definition", "module": "Mathlib.Analysis.Convex.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "starConvex_iff_segment_subset", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Star", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 5}
{"name": "StarConvex.segment_subset", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarConvex.openSegment_subset", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "starConvex_iff_pointwise_add_subset", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Star", "is_tactic_proof": false, "tactics": ["refine", "rintro", "exact"], "tactic_count": 3}
{"name": "starConvex_empty", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "starConvex_univ", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarConvex.inter", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "starConvex_sInter", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "starConvex_iInter", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "starConvex_iInter₂", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarConvex.union", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Star", "is_tactic_proof": true, "tactics": ["rintro", "exact", "exact"], "tactic_count": 3}
{"name": "starConvex_iUnion", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Star", "is_tactic_proof": true, "tactics": ["rintro", "rw", "obtain", "exact"], "tactic_count": 4}
{"name": "starConvex_iUnion₂", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "starConvex_sUnion", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Star", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "StarConvex.prod", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "starConvex_pi", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarConvex.mem", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Star", "is_tactic_proof": true, "tactics": ["obtain", "convert", "rw"], "tactic_count": 3}
{"name": "starConvex_iff_forall_pos", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Star", "is_tactic_proof": true, "tactics": ["refine", "intro", "obtain", "rw", "rwa", "obtain", "rw", "rwa", "exact"], "tactic_count": 9}
{"name": "starConvex_iff_forall_ne_pos", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Star", "is_tactic_proof": true, "tactics": ["refine", "intro", "obtain", "rw", "rwa", "obtain", "rw", "rwa", "obtain", "rwa", "exact"], "tactic_count": 11}
{"name": "starConvex_iff_openSegment_subset", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "starConvex_singleton", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Star", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "StarConvex.linear_image", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Star", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "StarConvex.is_linear_image", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarConvex.linear_preimage", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Star", "is_tactic_proof": true, "tactics": ["intro", "rw", "exact"], "tactic_count": 3}
{"name": "StarConvex.is_linear_preimage", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarConvex.add", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Star", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "StarConvex.add_left", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Star", "is_tactic_proof": true, "tactics": ["intro", "obtain", "refine", "match_scalars"], "tactic_count": 4}
{"name": "StarConvex.add_right", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Star", "is_tactic_proof": true, "tactics": ["intro", "obtain", "refine", "match_scalars"], "tactic_count": 4}
{"name": "StarConvex.preimage_add_right", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Star", "is_tactic_proof": true, "tactics": ["intro", "have", "rwa"], "tactic_count": 3}
{"name": "StarConvex.preimage_add_left", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Star", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "StarConvex.sub'", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarConvex.smul", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarConvex.zero_smul", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Star", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "StarConvex.preimage_smul", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarConvex.affinity", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Star", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "starConvex_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Star", "is_tactic_proof": true, "tactics": ["refine", "simpa", "h", "rw", "exact"], "tactic_count": 5}
{"name": "StarConvex.add_smul_mem", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Star", "is_tactic_proof": false, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "StarConvex.smul_mem", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Star", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "StarConvex.add_smul_sub_mem", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Star", "is_tactic_proof": true, "tactics": ["apply", "rw", "exact"], "tactic_count": 3}
{"name": "StarConvex.affine_preimage", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Star", "is_tactic_proof": true, "tactics": ["intro", "rw", "exact"], "tactic_count": 3}
{"name": "StarConvex.affine_image", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Star", "is_tactic_proof": true, "tactics": ["rintro", "refine", "rw"], "tactic_count": 3}
{"name": "StarConvex.neg", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Star", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "StarConvex.sub", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Star", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "starConvex_compl_Iic", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Star", "is_tactic_proof": true, "tactics": ["refine", "rw", "contrapose", "refine", "calc", "b", "rw", "gcongr"], "tactic_count": 8}
{"name": "starConvex_compl_Ici", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "starConvex_iff_div", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarConvex.mem_smul", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Star", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.OrdConnected.starConvex", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Star", "is_tactic_proof": true, "tactics": ["intro", "obtain", "refine", "calc", "x", "calc", "a", "refine", "calc", "y", "calc", "a"], "tactic_count": 12}
{"name": "starConvex_iff_ordConnected", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Star", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "stdSimplex", "kind": "definition", "module": "Mathlib.Analysis.Convex.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "stdSimplex_eq_inter", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StdSimplex", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "convex_stdSimplex", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StdSimplex", "is_tactic_proof": true, "tactics": ["refine", "apply_rules", "simp_rw", "rwa", "mul_one]"], "tactic_count": 5}
{"name": "stdSimplex_of_subsingleton", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "stdSimplex_of_isEmpty_index", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "stdSimplex_unique", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StdSimplex", "is_tactic_proof": true, "tactics": ["cases", "refine", "rintro", "rw", "exact"], "tactic_count": 5}
{"name": "mem_Icc_of_mem_stdSimplex", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "single_mem_stdSimplex", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ite_eq_mem_stdSimplex", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StdSimplex", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "segment_single_subset_stdSimplex", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "stdSimplex_fin_two", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StdSimplex", "is_tactic_proof": true, "tactics": ["refine", "rintro", "rw", "refine", "simp"], "tactic_count": 5}
{"name": "stdSimplexEquivIcc", "kind": "definition", "module": "Mathlib.Analysis.Convex.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "stdSimplexEquivIcc_zero", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "stdSimplexEquivIcc_one", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "convexHull_basis_eq_stdSimplex", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StdSimplex", "is_tactic_proof": true, "tactics": ["refine", "rintro", "exact", "rintro", "rw", "rw", "exact"], "tactic_count": 7}
{"name": "convexHull_rangle_single_eq_stdSimplex", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StdSimplex", "is_tactic_proof": true, "tactics": ["convert", "aesop"], "tactic_count": 2}
{"name": "Set.Finite.convexHull_eq_image", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StdSimplex", "is_tactic_proof": true, "tactics": ["classical", "letI", "rw", "apply", "aesop"], "tactic_count": 5}
{"name": "stdSimplex_subset_closedBall", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bounded_stdSimplex", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosed_stdSimplex", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCompact_stdSimplex", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "stdSimplex.instCompactSpace_coe", "kind": "instance", "module": "Mathlib.Analysis.Convex.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isPathConnected_stdSimplex", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instPathConnectedSpaceElemForallRealStdSimplexOfNonempty", "kind": "instance", "module": "Mathlib.Analysis.Convex.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "stdSimplexHomeomorphUnitInterval", "kind": "definition", "module": "Mathlib.Analysis.Convex.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "stdSimplexHomeomorphUnitInterval_zero", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "stdSimplexHomeomorphUnitInterval_one", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "diam_stdSimplex_le", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "diam_stdSimplex_of_subsingleton", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StdSimplex", "is_tactic_proof": true, "tactics": ["cases", "inl", "inr"], "tactic_count": 3}
{"name": "diam_stdSimplex", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StdSimplex", "is_tactic_proof": true, "tactics": ["refine", "obtain", "classical", "rw", "simp", "exact"], "tactic_count": 6}
{"name": "stdSimplex.instFunLikeElemForall", "kind": "instance", "module": "Mathlib.Analysis.Convex.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "stdSimplex.ext", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StdSimplex", "is_tactic_proof": true, "tactics": ["ext", "assumption"], "tactic_count": 2}
{"name": "stdSimplex.zero_le", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "stdSimplex.sum_eq_one", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "stdSimplex.add_eq_one", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StdSimplex", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "stdSimplex.le_one", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StdSimplex", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "stdSimplex.image_linearMap", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StdSimplex", "is_tactic_proof": true, "tactics": ["classical", "rintro", "refine", "rw", "exact", "simp", "exact"], "tactic_count": 7}
{"name": "stdSimplex.map", "kind": "definition", "module": "Mathlib.Analysis.Convex.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "stdSimplex.map_coe", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "stdSimplex.map_id_apply", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StdSimplex", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "stdSimplex.map_comp_apply", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StdSimplex", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "stdSimplex.vertex", "kind": "abbrev", "module": "Mathlib.Analysis.Convex.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "stdSimplex.vertex_coe", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "stdSimplex.map_vertex", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StdSimplex", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "stdSimplex.continuous_map", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "stdSimplex.vertex_injective", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StdSimplex", "is_tactic_proof": true, "tactics": ["intro", "replace", "by_contra", "simp"], "tactic_count": 4}
{"name": "stdSimplex.instNonemptyElemForall", "kind": "instance", "module": "Mathlib.Analysis.Convex.StdSimplex", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "stdSimplex.instNontrivialElemForall", "kind": "instance", "module": "Mathlib.Analysis.Convex.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "stdSimplex.instSubsingletonElemForall", "kind": "instance", "module": "Mathlib.Analysis.Convex.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "stdSimplex.instUniqueElemForall", "kind": "instance", "module": "Mathlib.Analysis.Convex.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "stdSimplex.eq_one_of_unique", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StdSimplex", "is_tactic_proof": true, "tactics": ["obtain", "rfl"], "tactic_count": 2}
{"name": "stdSimplex.barycenter", "kind": "definition", "module": "Mathlib.Analysis.Convex.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "stdSimplex.barycenter_apply", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StdSimplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "stdSimplex.barycenter_eq_centerMass", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StdSimplex", "is_tactic_proof": true, "tactics": ["simp", "ext", "simp"], "tactic_count": 3}
{"name": "not_disjoint_segment_convexHull_triple", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StoneSeparation", "is_tactic_proof": true, "tactics": ["rw", "obtain", "obtain", "rw", "rw", "refine", "obtain", "obtain", "rw", "rw", "exact", "obtain", "have", "refine", "positivity", "positivity", "rw", "classical", "let", "let", "have", "rintro", "fin_cases", "exact", "exact", "exact", "have", "trans", "simp", "linear_combination", "have", "convert", "rw", "trans", "module", "congr", "simp"], "tactic_count": 37}
{"name": "exists_convex_convex_compl_subset", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StoneSeparation", "is_tactic_proof": true, "tactics": ["let", "obtain", "zorn_subset_nonempty", "s", "obtain", "refine", "suffices", "obtain", "obtain", "refine", "not_disjoint_segment_convexHull_triple", "simp", "rintro", "by_contra", "suffices", "rw", "exact", "rw", "refine", "rwa"], "tactic_count": 20}
{"name": "StrictConvex", "kind": "definition", "module": "Mathlib.Analysis.Convex.Strict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictConvex_iff_openSegment_subset", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictConvex.openSegment_subset", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictConvex_empty", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictConvex_univ", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strict", "is_tactic_proof": true, "tactics": ["intro", "rw", "exact"], "tactic_count": 3}
{"name": "StrictConvex.eq", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictConvex.inter", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strict", "is_tactic_proof": true, "tactics": ["intro", "rw", "exact"], "tactic_count": 3}
{"name": "Directed.strictConvex_iUnion", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strict", "is_tactic_proof": true, "tactics": ["rintro", "rw", "obtain", "obtain", "obtain", "exact"], "tactic_count": 6}
{"name": "DirectedOn.strictConvex_sUnion", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strict", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "StrictConvex.convex", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Convex.strictConvex_of_isOpen", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.strictConvex_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictConvex_singleton", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Subsingleton.strictConvex", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictConvex.linear_image", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strict", "is_tactic_proof": true, "tactics": ["rintro", "refine", "rw"], "tactic_count": 3}
{"name": "StrictConvex.is_linear_image", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictConvex.linear_preimage", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strict", "is_tactic_proof": true, "tactics": ["intro", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "StrictConvex.is_linear_preimage", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.OrdConnected.strictConvex", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strict", "is_tactic_proof": true, "tactics": ["refine", "rcases", "exact"], "tactic_count": 3}
{"name": "strictConvex_Iic", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictConvex_Ici", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictConvex_Iio", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictConvex_Ioi", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictConvex_Icc", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictConvex_Ioo", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictConvex_Ico", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictConvex_Ioc", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictConvex_uIcc", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictConvex_uIoc", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictConvex.preimage_add_right", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strict", "is_tactic_proof": true, "tactics": ["intro", "refine", "have", "rwa"], "tactic_count": 4}
{"name": "StrictConvex.preimage_add_left", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strict", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "StrictConvex.add", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strict", "is_tactic_proof": true, "tactics": ["rintro", "rw", "obtain", "refine", "rw", "exact", "exact"], "tactic_count": 7}
{"name": "StrictConvex.add_left", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strict", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "StrictConvex.add_right", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strict", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "StrictConvex.vadd", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictConvex.smul", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strict", "is_tactic_proof": true, "tactics": ["obtain", "exact", "exact"], "tactic_count": 3}
{"name": "StrictConvex.affinity", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictConvex.preimage_smul", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strict", "is_tactic_proof": true, "tactics": ["classical", "obtain", "simp_rw", "split_ifs", "exact", "exact", "refine", "unfold", "exact"], "tactic_count": 9}
{"name": "StrictConvex.eq_of_openSegment_subset_frontier", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strict", "is_tactic_proof": true, "tactics": ["obtain", "classical", "by_contra", "exact"], "tactic_count": 4}
{"name": "StrictConvex.add_smul_mem", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strict", "is_tactic_proof": true, "tactics": ["have", "rw", "exact", "hs"], "tactic_count": 4}
{"name": "StrictConvex.smul_mem_of_zero_mem", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strict", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "StrictConvex.add_smul_sub_mem", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strict", "is_tactic_proof": true, "tactics": ["apply", "rw", "exact"], "tactic_count": 3}
{"name": "StrictConvex.affine_preimage", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strict", "is_tactic_proof": true, "tactics": ["intro", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "StrictConvex.affine_image", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strict", "is_tactic_proof": true, "tactics": ["rintro", "exact", "hf.image_interior_subset"], "tactic_count": 3}
{"name": "StrictConvex.neg", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictConvex.sub", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictConvex_iff_div", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictConvex.mem_smul_of_zero_mem", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strict", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "strictConvex_iff_convex", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictConvex_iff_ordConnected", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictConvex.centerMass_mem_interior", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StrictCombination", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "insert", "intro", "have", "have", "by_cases", "have", "have", "exfalso", "rcases", "exact", "exact", "rw", "by_cases", "simp", "grind", "by_cases", "have", "refine", "have", "grw", "simp", "exact", "simp", "by_cases", "grind", "exfalso", "obtain", "have", "have", "have", "grind", "exact", "strictConvex_iff_div.1", "hzi"], "tactic_count": 37}
{"name": "StrictConvex.sum_mem_interior", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StrictCombination", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "centerMass_mem_ball_of_strictConvexSpace", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StrictCombination", "is_tactic_proof": true, "tactics": ["rcases", "simp_all", "rw", "exact"], "tactic_count": 4}
{"name": "sum_mem_ball_of_strictConvexSpace", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StrictCombination", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "norm_sum_lt_of_strictConvexSpace", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StrictCombination", "is_tactic_proof": true, "tactics": ["simp_rw", "rw", "exact"], "tactic_count": 3}
{"name": "dist_affineCombination_lt_of_strictConvexSpace", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StrictCombination", "is_tactic_proof": false, "tactics": ["rw", "dist_vadd_left]", "simp_rw", "exact"], "tactic_count": 4}
{"name": "Affine.Simplex.dist_lt_of_mem_closedInterior_of_strictConvexSpace", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StrictCombination", "is_tactic_proof": true, "tactics": ["rcases", "obtain", "by_contra", "simp_all", "obtain", "by_contra", "apply", "rw", "congr", "ext", "by_cases", "simp", "rw", "exact", "rw", "exact", "exact", "dist_affineCombination_lt_of_strictConvexSpace"], "tactic_count": 18}
{"name": "Affine.Simplex.dist_lt_of_mem_interior_of_strictConvexSpace", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StrictCombination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sbtw.dist_lt_max_dist", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StrictConvexBetween", "is_tactic_proof": true, "tactics": ["have", "rw", "rcases", "rw", "exact", "rw", "exact", "rw", "rcases", "simp_rw", "exact"], "tactic_count": 11}
{"name": "Wbtw.dist_le_max_dist", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StrictConvexBetween", "is_tactic_proof": true, "tactics": ["by_cases", "by_cases", "have", "exact"], "tactic_count": 4}
{"name": "Collinear.wbtw_of_dist_eq_of_dist_le", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StrictConvexBetween", "is_tactic_proof": true, "tactics": ["rcases", "exact", "by_cases", "simp", "have", "have", "rw", "exact", "by_cases", "simp", "have", "have", "rw", "exact"], "tactic_count": 14}
{"name": "Collinear.sbtw_of_dist_eq_of_dist_lt", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StrictConvexBetween", "is_tactic_proof": true, "tactics": ["refine", "rintro", "exact", "rintro", "exact"], "tactic_count": 5}
{"name": "dist_add_dist_eq_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StrictConvexBetween", "is_tactic_proof": false, "tactics": ["have", "dist", "simp_rw", "rwa"], "tactic_count": 4}
{"name": "dist_lt_dist_add_dist_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StrictConvexBetween", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "eq_lineMap_of_dist_eq_mul_of_dist_eq_mul", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StrictConvexBetween", "is_tactic_proof": false, "tactics": ["have", "rw", "dist_eq_norm_vsub',", "obtain", "obtain", "simp", "rw", "obtain", "rw", "have", "rw", "rw"], "tactic_count": 12}
{"name": "eq_midpoint_of_dist_eq_half", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StrictConvexBetween", "is_tactic_proof": true, "tactics": ["apply", "rwa", "rwa"], "tactic_count": 3}
{"name": "Isometry.affineIsometryOfStrictConvexSpace", "kind": "definition", "module": "Mathlib.Analysis.Convex.StrictConvexBetween", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Isometry.coe_affineIsometryOfStrictConvexSpace", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StrictConvexBetween", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Isometry.affineIsometryOfStrictConvexSpace_apply", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StrictConvexBetween", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictConvex_closedBall", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StrictConvexSpace", "is_tactic_proof": true, "tactics": ["rcases", "exact", "rw", "exact"], "tactic_count": 4}
{"name": "StrictConvexSpace.of_strictConvex_unitClosedBall", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StrictConvexSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictConvexSpace.of_norm_combo_lt_one", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StrictConvexSpace", "is_tactic_proof": false, "tactics": ["refine", "rw", "rcases", "use", "rwa", "sub_eq_iff_eq_add.2"], "tactic_count": 6}
{"name": "StrictConvexSpace.of_norm_combo_ne_one", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StrictConvexSpace", "is_tactic_proof": true, "tactics": ["refine", "simp", "mem_sphere_zero_iff_norm]", "intro", "rcases", "exact"], "tactic_count": 6}
{"name": "StrictConvexSpace.of_norm_add_ne_two", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StrictConvexSpace", "is_tactic_proof": false, "tactics": ["refine", "rw", "div_eq_one_iff_eq", "exact"], "tactic_count": 4}
{"name": "StrictConvexSpace.of_pairwise_sphere_norm_ne_two", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StrictConvexSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictConvexSpace.of_norm_add", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StrictConvexSpace", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "combo_mem_ball_of_ne", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StrictConvexSpace", "is_tactic_proof": true, "tactics": ["rcases", "rw", "exact", "simp", "exact"], "tactic_count": 5}
{"name": "openSegment_subset_ball_of_ne", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StrictConvexSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "norm_combo_lt_of_ne", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StrictConvexSpace", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "norm_add_lt_of_not_sameRay", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StrictConvexSpace", "is_tactic_proof": true, "tactics": ["simp", "rcases", "rw", "have", "have", "combo_mem_ball_of_ne", "rwa", "smul_inv_smul₀", "div_lt_one"], "tactic_count": 9}
{"name": "lt_norm_sub_of_not_sameRay", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StrictConvexSpace", "is_tactic_proof": true, "tactics": ["nth_rw", "exact"], "tactic_count": 2}
{"name": "abs_lt_norm_sub_of_not_sameRay", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StrictConvexSpace", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "sameRay_iff_norm_add", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StrictConvexSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_of_norm_eq_of_norm_add_eq", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StrictConvexSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_sameRay_iff_norm_add_lt", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StrictConvexSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sameRay_iff_norm_sub", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StrictConvexSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_sameRay_iff_abs_lt_norm_sub", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StrictConvexSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "norm_midpoint_lt_iff", "kind": "theorem", "module": "Mathlib.Analysis.Convex.StrictConvexSpace", "is_tactic_proof": true, "tactics": ["rw", "div_lt_iff₀"], "tactic_count": 2}
{"name": "UniformConvexOn", "kind": "definition", "module": "Mathlib.Analysis.Convex.Strong", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformConcaveOn", "kind": "definition", "module": "Mathlib.Analysis.Convex.Strong", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformConvexOn_zero", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strong", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "uniformConcaveOn_zero", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strong", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "UniformConvexOn.mono", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strong", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformConcaveOn.mono", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strong", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformConvexOn.convexOn", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strong", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "UniformConcaveOn.concaveOn", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strong", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "UniformConvexOn.strictConvexOn", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strong", "is_tactic_proof": true, "tactics": ["refine", "rw", "positivity"], "tactic_count": 3}
{"name": "UniformConcaveOn.strictConcaveOn", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strong", "is_tactic_proof": false, "tactics": ["refine", "rw", "positivity"], "tactic_count": 3}
{"name": "UniformConvexOn.add", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strong", "is_tactic_proof": true, "tactics": ["refine", "simpa"], "tactic_count": 2}
{"name": "UniformConcaveOn.add", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strong", "is_tactic_proof": true, "tactics": ["refine", "simpa"], "tactic_count": 2}
{"name": "UniformConvexOn.neg", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strong", "is_tactic_proof": true, "tactics": ["refine", "simpa"], "tactic_count": 2}
{"name": "UniformConcaveOn.neg", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strong", "is_tactic_proof": true, "tactics": ["refine", "simpa"], "tactic_count": 2}
{"name": "UniformConvexOn.sub", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strong", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "UniformConcaveOn.sub", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strong", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "StrongConvexOn", "kind": "definition", "module": "Mathlib.Analysis.Convex.Strong", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrongConcaveOn", "kind": "definition", "module": "Mathlib.Analysis.Convex.Strong", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrongConvexOn.mono", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strong", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrongConcaveOn.mono", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strong", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strongConvexOn_zero", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strong", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "strongConcaveOn_zero", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strong", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "StrongConvexOn.strictConvexOn", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strong", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrongConcaveOn.strictConcaveOn", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strong", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.Convex.Strong.0.aux_sub", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strong", "is_tactic_proof": false, "tactics": ["rw", "norm_of_nonneg", "obtain", "ring_nf"], "tactic_count": 4}
{"name": "_private.Mathlib.Analysis.Convex.Strong.0.aux_add", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strong", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "strongConvexOn_iff_convex", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strong", "is_tactic_proof": true, "tactics": ["refine", "simp_rw"], "tactic_count": 2}
{"name": "strongConcaveOn_iff_convex", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Strong", "is_tactic_proof": true, "tactics": ["refine", "simp_rw"], "tactic_count": 2}
{"name": "Real.closedBall_eq_segment", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Topology", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.ball_eq_openSegment", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Topology", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.convex_iff_isPreconnected", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "segment_subset_closure_openSegment", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Topology", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "closure_openSegment", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Topology", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Convex.combo_interior_closure_subset_interior", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Convex.combo_interior_self_subset_interior", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Convex.combo_closure_interior_subset_interior", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Topology", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Convex.combo_self_interior_subset_interior", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Topology", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Convex.combo_interior_closure_mem_interior", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Convex.combo_interior_self_mem_interior", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Convex.combo_closure_interior_mem_interior", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Convex.combo_self_interior_mem_interior", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Convex.openSegment_interior_closure_subset_interior", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Topology", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "Convex.openSegment_interior_self_subset_interior", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Convex.openSegment_closure_interior_subset_interior", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Topology", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "Convex.openSegment_self_interior_subset_interior", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Convex.add_smul_sub_mem_interior'", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Topology", "is_tactic_proof": true, "tactics": ["simpa", "hs.combo_interior_closure_mem_interior"], "tactic_count": 2}
{"name": "Convex.add_smul_sub_mem_interior", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Convex.add_smul_mem_interior'", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Topology", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Convex.add_smul_mem_interior", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Convex.interior", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Convex.closure", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Convex.strictConvex'", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Topology", "is_tactic_proof": true, "tactics": ["refine", "intro", "by_cases", "exact", "by_cases", "exact", "rcases", "refine", "exacts"], "tactic_count": 9}
{"name": "Convex.strictConvex", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Topology", "is_tactic_proof": true, "tactics": ["refine", "simp", "rintro", "refine", "exact"], "tactic_count": 5}
{"name": "Convex.closure_interior_eq_closure_of_nonempty_interior", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Convex.interior_closure_eq_interior_of_nonempty_interior", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Topology", "is_tactic_proof": true, "tactics": ["refine", "intro", "rcases", "have", "obtain", "apply", "nth_rw", "exact"], "tactic_count": 8}
{"name": "convex_closed_sInter", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "closedConvexHull", "kind": "definition", "module": "Mathlib.Analysis.Convex.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "convex_closedConvexHull", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosed_closedConvexHull", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "subset_closedConvexHull", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "closure_subset_closedConvexHull", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "closedConvexHull_min", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "convexHull_subset_closedConvexHull", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "closedConvexHull_closure_eq_closedConvexHull", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "closedConvexHull_eq_closure_convexHull", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.isCompact_convexHull", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Topology", "is_tactic_proof": true, "tactics": ["rw", "apply", "haveI", "apply"], "tactic_count": 4}
{"name": "Set.Finite.isClosed_convexHull", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Convex.closure_subset_image_homothety_interior_of_one_lt", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Topology", "is_tactic_proof": true, "tactics": ["intro", "have", "refine", "rw", "homothety_eq_lineMap]", "exact"], "tactic_count": 6}
{"name": "Convex.closure_subset_interior_image_homothety_of_one_lt", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Convex.subset_interior_image_homothety_of_one_lt", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Convex.nontrivial_iff_nonempty_interior", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Topology", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "have", "rw", "exact", "rintro", "rcases", "rw", "exact", "exact"], "tactic_count": 10}
{"name": "Convex.Ioo_subset_of_mem_closure", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Topology", "is_tactic_proof": true, "tactics": ["cases", "inl", "simp", "simp", "inr", "simp", "calc"], "tactic_count": 7}
{"name": "Convex.nhdsWithin_inter_Iio_eq_nhdsLT", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Topology", "is_tactic_proof": true, "tactics": ["obtain", "refine", "exact"], "tactic_count": 3}
{"name": "Convex.nhdsWithin_inter_Ioi_eq_nhdsGT", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Topology", "is_tactic_proof": true, "tactics": ["obtain", "refine", "exact"], "tactic_count": 3}
{"name": "Convex.nhdsWithin_diff_eq_nhdsNE", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Topology", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Convex.nhdsWithin_diff_eq_nhdsLT", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Topology", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Convex.nhdsWithin_diff_eq_nhdsGT", "kind": "theorem", "module": "Mathlib.Analysis.Convex.Topology", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
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{"name": "HasCompactSupport.convolutionExists_right", "kind": "theorem", "module": "Mathlib.Analysis.Convolution", "is_tactic_proof": true, "tactics": ["intro", "refine", "refine", "refine", "simp_rw"], "tactic_count": 5}
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{"name": "MeasureTheory.convolutionExistsAt_flip", "kind": "theorem", "module": "Mathlib.Analysis.Convolution", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
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{"name": "MeasureTheory.convolutionExistsAt_iff_integrable_swap", "kind": "theorem", "module": "Mathlib.Analysis.Convolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasCompactSupport.convolutionExists_left", "kind": "theorem", "module": "Mathlib.Analysis.Convolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasCompactSupport.convolutionExists_right_of_continuous_left", "kind": "theorem", "module": "Mathlib.Analysis.Convolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasureTheory.convolution_def", "kind": "theorem", "module": "Mathlib.Analysis.Convolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.convolution_lsmul", "kind": "theorem", "module": "Mathlib.Analysis.Convolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasureTheory.convolution_eq_swap", "kind": "theorem", "module": "Mathlib.Analysis.Convolution", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "SchwartzMap.seminorm_le_bound", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.seminorm_le_bound'", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": true, "tactics": ["refine", "simpa"], "tactic_count": 2}
{"name": "SchwartzMap.le_seminorm", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.le_seminorm'", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "SchwartzMap.norm_iteratedFDeriv_le_seminorm", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "SchwartzMap.norm_pow_mul_le_seminorm", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "SchwartzMap.norm_le_seminorm", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "schwartzSeminormFamily", "kind": "definition", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.schwartzSeminormFamily_apply", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.schwartzSeminormFamily_apply_zero", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.one_add_le_sup_seminorm_apply", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp", "norm_cast", "rw", "push_cast", "rw", "have", "grw", "gcongr", "move_mul", "gcongr", "grw", "apply", "exact"], "tactic_count": 14}
{"name": "SchwartzMap.instTopologicalSpace", "kind": "instance", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "schwartz_withSeminorms", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": true, "tactics": ["have", "rw", "rw", "rfl"], "tactic_count": 4}
{"name": "SchwartzMap.instContinuousSMul", "kind": "instance", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SchwartzMap.instIsTopologicalAddGroup", "kind": "instance", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.instUniformSpace", "kind": "instance", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.instIsUniformAddGroup", "kind": "instance", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.instLocallyConvexSpace", "kind": "instance", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.instFirstCountableTopology", "kind": "instance", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.hasTemperateGrowth", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": true, "tactics": ["refine", "rcases", "exact"], "tactic_count": 3}
{"name": "HasCompactSupport.toSchwartzMap", "kind": "definition", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.mkLM", "kind": "definition", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.mkCLM", "kind": "definition", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.mkCLMtoNormedSpace", "kind": "definition", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.evalCLM", "kind": "definition", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.evalCLM_apply_apply", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.bilinLeftCLM", "kind": "definition", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": false, "tactics": ["refine", "mkCLM", "rintro", "rcases", "use", "intro", "have", "simp_rw", "have", "grw", "rw", "move_mul", "simp_rw", "gcongr", "rw", "have", "simp_rw", "rw", "refine", "simp", "move_mul", "gcongr", "swap", "norm_cast", "exact", "specialize", "grw", "move_mul", "gcongr", "rw", "change", "refine", "rw", "move_mul", "gcongr", "simp"], "tactic_count": 36}
{"name": "SchwartzMap.bilinLeftCLM_apply", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.smulLeftCLM", "kind": "definition", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.smulLeftCLM_apply", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SchwartzMap.smulLeftCLM_apply_apply", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SchwartzMap.smulLeftCLM_const", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": true, "tactics": ["ext", "have", "simp"], "tactic_count": 3}
{"name": "SchwartzMap.smulLeftCLM_smulLeftCLM_apply", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "SchwartzMap.smulLeftCLM_compL_smulLeftCLM", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": true, "tactics": ["ext1", "exact"], "tactic_count": 2}
{"name": "SchwartzMap.smulLeftCLM_smul", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": true, "tactics": ["have", "convert", "simp"], "tactic_count": 3}
{"name": "SchwartzMap.smulLeftCLM_add", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "SchwartzMap.smulLeftCLM_sub", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "SchwartzMap.smulLeftCLM_neg", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "SchwartzMap.smulLeftCLM_fun_neg", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.smulLeftCLM_sum", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "SchwartzMap.smulLeftCLM_ofReal", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "SchwartzMap.smulLeftCLM_real_smul", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SchwartzMap.tsupport_smulLeftCLM_subset", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simpa", "simp"], "tactic_count": 3}
{"name": "SchwartzMap.pairing", "kind": "definition", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.pairing_apply", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.pairing_apply_apply", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.pairing_continuous_left", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.smulRightCLM", "kind": "definition", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.smulRightCLM_apply_apply", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SchwartzMap.compCLM_apply", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.compCLMOfAntilipschitz", "kind": "definition", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": true, "tactics": ["refine", "calc", "rw", "apply", "gcongr", "exact", "gcongr", "exact", "simp", "gcongr", "exact"], "tactic_count": 11}
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{"name": "SchwartzMap.compCLMOfContinuousLinearEquiv", "kind": "definition", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.compCLMOfContinuousLinearEquiv_apply", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.smulLeftCLM_compCLMOfContinuousLinearEquiv", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": true, "tactics": ["ext", "have", "simp"], "tactic_count": 3}
{"name": "SchwartzMap.integral_pow_mul_iteratedFDeriv_le", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.integrable_pow_mul_iteratedFDeriv", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SchwartzMap.integrable", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SchwartzMap.integralCLM_apply", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "SchwartzMap.instBoundedContinuousMapClass", "kind": "instance", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.toBoundedContinuousFunction", "kind": "definition", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.toBoundedContinuousFunction_apply", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.toContinuousMap", "kind": "definition", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.toBoundedContinuousFunctionCLM", "kind": "definition", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.toBoundedContinuousFunctionCLM_apply", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.instZeroAtInftyContinuousMapClass", "kind": "instance", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.toZeroAtInfty", "kind": "definition", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.toZeroAtInfty_apply", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.toZeroAtInfty_toBCF", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.toZeroAtInftyCLM", "kind": "definition", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.toZeroAtInftyCLM_apply", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.norm_toLp", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SchwartzMap.toLpCLM_apply", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.continuous_toLp", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.denseRange_toLpCLM", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Basic", "is_tactic_proof": true, "tactics": ["intro", "refine", "obtain", "use", "have", "filter_upwards", "simp", "simp", "eLpNorm_congr_ae", "grw", "simp"], "tactic_count": 11}
{"name": "SchwartzMap.derivCLM", "kind": "definition", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.derivCLM_apply", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.hasDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.fderivCLM", "kind": "definition", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.fderivCLM_apply", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.hasFDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.instLineDeriv", "kind": "instance", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.lineDerivOp_apply_eq_fderiv", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.instLineDerivAdd", "kind": "instance", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.instLineDerivSMul", "kind": "instance", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.instLineDerivLeftSMulReal", "kind": "instance", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.instContinuousLineDeriv", "kind": "instance", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.lineDerivOpCLM_eq", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.lineDerivOp_apply", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.lineDerivOp_compCLMOfContinuousLinearEquiv", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Deriv", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "SchwartzMap.iteratedLineDerivOp_eq_iteratedFDeriv", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Deriv", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "ih", "rw", "simp", "exact"], "tactic_count": 7}
{"name": "SchwartzMap.instLaplacian", "kind": "instance", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.laplacianCLM_eq'", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.laplacian_eq_sum", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.laplacianCLM_eq", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Deriv", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SchwartzMap.laplacian_apply", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Deriv", "is_tactic_proof": true, "tactics": ["rw", "simp", "congr", "ext", "rw", "rfl"], "tactic_count": 6}
{"name": "SchwartzMap.integral_bilinear_deriv_right_eq_neg_left", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.integral_mul_deriv_eq_neg_deriv_mul", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.integral_smul_deriv_right_eq_neg_left", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.integral_clm_comp_deriv_right_eq_neg_left", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.integral_bilinear_lineDerivOp_right_eq_neg_left", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Deriv", "is_tactic_proof": false, "tactics": ["apply", "integral_bilinear_hasLineDerivAt_right_eq_neg_left_of_integrable", "all_goals", "intro", "exact"], "tactic_count": 5}
{"name": "SchwartzMap.integral_mul_lineDerivOp_right_eq_neg_left", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.integral_smul_lineDerivOp_right_eq_neg_left", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.integral_clm_comp_lineDerivOp_right_eq_neg_left", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.integral_bilinear_laplacian_right_eq_left", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.SchwartzSpace.Deriv", "is_tactic_proof": false, "tactics": ["simp_rw", "rw", "simp", "exact", "exact"], "tactic_count": 5}
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{"name": "TemperedDistribution", "kind": "abbrev", "module": "Mathlib.Analysis.Distribution.TemperedDistribution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.term𝓢'(_,_)", "kind": "definition", "module": "Mathlib.Analysis.Distribution.TemperedDistribution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasureTheory.Lp.toTemperedDistribution", "kind": "definition", "module": "Mathlib.Analysis.Distribution.TemperedDistribution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasureTheory.Lp.toTemperedDistribution_toLp_eq", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.TemperedDistribution", "is_tactic_proof": true, "tactics": ["ext", "simp", "apply", "filter_upwards", "rw"], "tactic_count": 5}
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{"name": "TemperedDistribution.smulLeftCLM_apply_apply", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.TemperedDistribution", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
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{"name": "TemperedDistribution.derivCLM", "kind": "definition", "module": "Mathlib.Analysis.Distribution.TemperedDistribution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TemperedDistribution.derivCLM_apply_apply", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.TemperedDistribution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TemperedDistribution.derivCLM_toTemperedDistributionCLM_eq", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.TemperedDistribution", "is_tactic_proof": true, "tactics": ["ext1", "simp"], "tactic_count": 2}
{"name": "TemperedDistribution.instLineDeriv", "kind": "instance", "module": "Mathlib.Analysis.Distribution.TemperedDistribution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TemperedDistribution.lineDerivOp_apply_apply", "kind": "theorem", "module": "Mathlib.Analysis.Distribution.TemperedDistribution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "TemperedDistribution.instFourierAdd", "kind": "instance", "module": "Mathlib.Analysis.Distribution.TemperedDistribution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AddCircle.instIsProbabilityMeasureRealHaarAddCircle", "kind": "instance", "module": "Mathlib.Analysis.Fourier.AddCircle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCircle.volume_eq_smul_haarAddCircle", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.AddCircle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasureTheory.memLp_haarAddCircle_iff", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.AddCircle", "is_tactic_proof": true, "tactics": ["rw", "have", "refine", "have", "rwa"], "tactic_count": 5}
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{"name": "fourier_coe_apply'", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.AddCircle", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "fourier_zero", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.AddCircle", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "fourier_add_half_inv_index", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.AddCircle", "is_tactic_proof": true, "tactics": ["rw", "have", "rw", "convert", "field_simp", "rw"], "tactic_count": 6}
{"name": "fourierSubalgebra", "kind": "definition", "module": "Mathlib.Analysis.Fourier.AddCircle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fourierSubalgebra_coe", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.AddCircle", "is_tactic_proof": true, "tactics": ["apply", "refine", "intro", "refine", "ext1", "rintro", "refine", "ext1", "exact"], "tactic_count": 9}
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{"name": "fourierSubalgebra_closure_eq_top", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.AddCircle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "fourierLp", "kind": "abbrev", "module": "Mathlib.Analysis.Fourier.AddCircle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "coeFn_fourierLp", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.AddCircle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "span_fourierLp_closure_eq_top", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.AddCircle", "is_tactic_proof": false, "tactics": ["convert", "span_fourier_closure_eq_top", "rw", "unfold", "rw", "simp"], "tactic_count": 6}
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{"name": "fourierCoeff_eq_intervalIntegral", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.AddCircle", "is_tactic_proof": true, "tactics": ["have", "simp_rw", "rw", "integral_smul_measure,", "one_smul]"], "tactic_count": 5}
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{"name": "fourierCoeffOn.const_mul", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.AddCircle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "coe_fourierBasis", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.AddCircle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fourierBasis_repr", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.AddCircle", "is_tactic_proof": true, "tactics": ["trans", "rw", "simp", "apply", "filter_upwards", "rw"], "tactic_count": 6}
{"name": "hasSum_fourier_series_L2", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.AddCircle", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "hasSum_sq_fourierCoeff", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.AddCircle", "is_tactic_proof": true, "tactics": ["simp_rw", "have", "apply_mod_cast", "simp", "have", "have", "rw", "simp", "rwa", "exact"], "tactic_count": 10}
{"name": "tsum_sq_fourierCoeff", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.AddCircle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasSum_sq_fourierCoeffOn", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.AddCircle", "is_tactic_proof": true, "tactics": ["haveI", "rw", "have", "convert", "simp", "nth_rw", "rw", "simp", "apply", "filter_upwards", "simp"], "tactic_count": 11}
{"name": "tsum_sq_fourierCoeffOn", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.AddCircle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fourierCoeff_toLp", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.AddCircle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasSum_fourier_series_of_summable", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.AddCircle", "is_tactic_proof": true, "tactics": ["have", "simp_rw", "refine", "simp_rw", "exact"], "tactic_count": 5}
{"name": "has_pointwise_sum_fourier_series_of_summable", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.AddCircle", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "hasDerivAt_fourier", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.AddCircle", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "rw", "refine", "convert", "ext1"], "tactic_count": 6}
{"name": "hasDerivAt_fourier_neg", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.AddCircle", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "has_antideriv_at_fourier_neg", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.AddCircle", "is_tactic_proof": true, "tactics": ["convert", "ext1", "simp"], "tactic_count": 3}
{"name": "fourierCoeffOn_of_hasDeriv_right", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.AddCircle", "is_tactic_proof": true, "tactics": ["rw", "have", "simp_rw", "conv", "rw", "have", "conv", "rw", "have", "rw", "congr", "conv_lhs", "rw", "ring", "ring"], "tactic_count": 15}
{"name": "fourierCoeffOn_of_hasDerivAt_Ioo", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.AddCircle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fourierCoeffOn_of_hasDerivAt", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.AddCircle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instMeasureSpaceUnitAddCircle", "kind": "instance", "module": "Mathlib.Analysis.Fourier.AddCircleMulti", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsAddHaarMeasureUnitAddCircleVolume", "kind": "instance", "module": "Mathlib.Analysis.Fourier.AddCircleMulti", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsProbabilityMeasureUnitAddCircleVolume", "kind": "instance", "module": "Mathlib.Analysis.Fourier.AddCircleMulti", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UnitAddTorus", "kind": "abbrev", "module": "Mathlib.Analysis.Fourier.AddCircleMulti", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UnitAddTorus.mFourier", "kind": "definition", "module": "Mathlib.Analysis.Fourier.AddCircleMulti", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UnitAddTorus.mFourier_neg", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.AddCircleMulti", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "UnitAddTorus.mFourier_add", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.AddCircleMulti", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "UnitAddTorus.mFourier_zero", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.AddCircleMulti", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "UnitAddTorus.mFourier_norm", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.AddCircleMulti", "is_tactic_proof": true, "tactics": ["apply", "refine", "simp", "refine", "simp"], "tactic_count": 5}
{"name": "UnitAddTorus.mFourier_single", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.AddCircleMulti", "is_tactic_proof": true, "tactics": ["simp_rw", "have", "rw", "rw", "rw", "simp"], "tactic_count": 6}
{"name": "UnitAddTorus.mFourierSubalgebra", "kind": "definition", "module": "Mathlib.Analysis.Fourier.AddCircleMulti", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UnitAddTorus.mFourierSubalgebra_coe", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.AddCircleMulti", "is_tactic_proof": true, "tactics": ["apply", "refine", "ext", "simp", "rintro", "refine", "ext", "simp"], "tactic_count": 8}
{"name": "UnitAddTorus.mFourierSubalgebra_separatesPoints", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.AddCircleMulti", "is_tactic_proof": true, "tactics": ["classical", "intro", "rw", "obtain", "refine", "dsimp", "rw", "contrapose", "exact"], "tactic_count": 9}
{"name": "UnitAddTorus.mFourierSubalgebra_closure_eq_top", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.AddCircleMulti", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UnitAddTorus.span_mFourier_closure_eq_top", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.AddCircleMulti", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "UnitAddTorus.mFourierLp", "kind": "abbrev", "module": "Mathlib.Analysis.Fourier.AddCircleMulti", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UnitAddTorus.coeFn_mFourierLp", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.AddCircleMulti", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UnitAddTorus.instContinuousSMulComplexSubtypeAEEqFunVolumeMemAddSubgroupLp", "kind": "instance", "module": "Mathlib.Analysis.Fourier.AddCircleMulti", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UnitAddTorus.span_mFourierLp_closure_eq_top", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.AddCircleMulti", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "UnitAddTorus.orthonormal_mFourier", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.AddCircleMulti", "is_tactic_proof": true, "tactics": ["rw", "intro", "simp", "split_ifs", "simpa", "integral_const", "rw", "obtain", "apply", "simpa"], "tactic_count": 10}
{"name": "UnitAddTorus.mFourierCoeff", "kind": "definition", "module": "Mathlib.Analysis.Fourier.AddCircleMulti", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.Fourier.AddCircleMulti.0.UnitAddTorus.termL²(_)", "kind": "definition", "module": "Mathlib.Analysis.Fourier.AddCircleMulti", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.Fourier.AddCircleMulti.0.UnitAddTorus._aux_Mathlib_Analysis_Fourier_AddCircleMulti___macroRules__private_Mathlib_Analysis_Fourier_AddCircleMulti_0_UnitAddTorus_termL²(_)_1", "kind": "definition", "module": "Mathlib.Analysis.Fourier.AddCircleMulti", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.Fourier.AddCircleMulti.0.UnitAddTorus._aux_Mathlib_Analysis_Fourier_AddCircleMulti___unexpand_MeasureTheory_Lp_1", "kind": "definition", "module": "Mathlib.Analysis.Fourier.AddCircleMulti", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UnitAddTorus.mFourierBasis", "kind": "definition", "module": "Mathlib.Analysis.Fourier.AddCircleMulti", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UnitAddTorus.coe_mFourierBasis", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.AddCircleMulti", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UnitAddTorus.mFourierBasis_repr", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.AddCircleMulti", "is_tactic_proof": true, "tactics": ["trans", "rw", "simp", "apply", "filter_upwards", "rw"], "tactic_count": 6}
{"name": "UnitAddTorus.hasSum_mFourier_series_L2", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.AddCircleMulti", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "UnitAddTorus.hasSum_prod_mFourierCoeff", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.AddCircleMulti", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "simp"], "tactic_count": 3}
{"name": "UnitAddTorus.hasSum_sq_mFourierCoeff", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.AddCircleMulti", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "UnitAddTorus.mFourierCoeff_toLp", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.AddCircleMulti", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UnitAddTorus.hasSum_mFourier_series_of_summable", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.AddCircleMulti", "is_tactic_proof": true, "tactics": ["have", "simp", "refine", "simpa"], "tactic_count": 4}
{"name": "UnitAddTorus.hasSum_mFourier_series_apply_of_summable", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.AddCircleMulti", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "BoundedContinuousFunction.char", "kind": "definition", "module": "Mathlib.Analysis.Fourier.BoundedContinuousFunctionChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.char_apply", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.BoundedContinuousFunctionChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.char_zero_eq_one", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.BoundedContinuousFunctionChar", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "BoundedContinuousFunction.char_add_eq_mul", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.BoundedContinuousFunctionChar", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "BoundedContinuousFunction.char_neg", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.BoundedContinuousFunctionChar", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "BoundedContinuousFunction.ext_of_char_eq", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.BoundedContinuousFunctionChar", "is_tactic_proof": true, "tactics": ["contrapose", "obtain", "obtain", "use", "simp", "rw", "simp", "grind"], "tactic_count": 8}
{"name": "BoundedContinuousFunction.charMonoidHom", "kind": "definition", "module": "Mathlib.Analysis.Fourier.BoundedContinuousFunctionChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.charMonoidHom_apply", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.BoundedContinuousFunctionChar", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "BoundedContinuousFunction.charAlgHom", "kind": "definition", "module": "Mathlib.Analysis.Fourier.BoundedContinuousFunctionChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.charAlgHom_apply", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.BoundedContinuousFunctionChar", "is_tactic_proof": true, "tactics": ["simp", "rw", "simp", "rfl", "simp"], "tactic_count": 5}
{"name": "BoundedContinuousFunction.star_mem_range_charAlgHom", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.BoundedContinuousFunctionChar", "is_tactic_proof": true, "tactics": ["simp", "obtain", "let", "let", "refine", "ext1", "simp", "star_sum,", "rw", "simp"], "tactic_count": 10}
{"name": "BoundedContinuousFunction.charPoly", "kind": "definition", "module": "Mathlib.Analysis.Fourier.BoundedContinuousFunctionChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.mem_charPoly", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.BoundedContinuousFunctionChar", "is_tactic_proof": true, "tactics": ["change", "simp"], "tactic_count": 2}
{"name": "BoundedContinuousFunction.char_mem_charPoly", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.BoundedContinuousFunctionChar", "is_tactic_proof": true, "tactics": ["rw", "refine", "ext", "simp", "rw", "simp", "simp", "simp"], "tactic_count": 8}
{"name": "BoundedContinuousFunction.separatesPoints_charPoly", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.BoundedContinuousFunctionChar", "is_tactic_proof": true, "tactics": ["intro", "obtain", "contrapose", "exact", "use", "simp", "exists_exists_and_eq_and,", "exact"], "tactic_count": 8}
{"name": "Real.integrable_prod_sub", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.Convolution", "is_tactic_proof": true, "tactics": ["apply", "rw", "constructor", "filter_upwards", "exact", "have", "apply", "filter_upwards", "convert", "ext", "simp_rw", "rw", "congr", "convert", "rfl"], "tactic_count": 15}
{"name": "Real.fourier_bilin_convolution_eq_integral", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.Convolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.fourier_bilin_convolution_eq", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.Convolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.fourier_smul_convolution_eq", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.Convolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.fourier_mul_convolution_eq", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.Convolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.convolution", "kind": "definition", "module": "Mathlib.Analysis.Fourier.Convolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.convolution_flip", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.Convolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.convolution_continuous_left", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.Convolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SchwartzMap.fourier_convolution", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.Convolution", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SchwartzMap.fourier_convolution_apply", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.Convolution", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SchwartzMap.convolution_apply", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.Convolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.expect_eq_ite", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.FiniteAbelian.Orthogonality", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AddChar.expect_eq_zero_iff_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.FiniteAbelian.Orthogonality", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AddChar.expect_ne_zero_iff_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.FiniteAbelian.Orthogonality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.wInner_cWeight_self", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.FiniteAbelian.Orthogonality", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AddChar.wInner_cWeight_eq_boole", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.FiniteAbelian.Orthogonality", "is_tactic_proof": true, "tactics": ["split_ifs", "rw", "have", "simp_rw", "simpa"], "tactic_count": 5}
{"name": "AddChar.wInner_cWeight_eq_zero_iff_ne", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.FiniteAbelian.Orthogonality", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AddChar.wInner_cWeight_eq_one_iff_eq", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.FiniteAbelian.Orthogonality", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AddChar.linearIndependent", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.FiniteAbelian.Orthogonality", "is_tactic_proof": true, "tactics": ["cases", "exact"], "tactic_count": 2}
{"name": "AddChar.instFintype", "kind": "instance", "module": "Mathlib.Analysis.Fourier.FiniteAbelian.Orthogonality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.card_addChar_le", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.FiniteAbelian.Orthogonality", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "AddChar.zmod", "kind": "definition", "module": "Mathlib.Analysis.Fourier.FiniteAbelian.PontryaginDuality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.zmod_intCast", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.FiniteAbelian.PontryaginDuality", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AddChar.zmod_zero", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.FiniteAbelian.PontryaginDuality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.zmod_add", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.FiniteAbelian.PontryaginDuality", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AddChar.zmod_injective", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.FiniteAbelian.PontryaginDuality", "is_tactic_proof": true, "tactics": ["simp_rw", "rintro", "have", "simpa"], "tactic_count": 4}
{"name": "AddChar.zmod_inj", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.FiniteAbelian.PontryaginDuality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.zmodHom", "kind": "definition", "module": "Mathlib.Analysis.Fourier.FiniteAbelian.PontryaginDuality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.Fourier.FiniteAbelian.PontryaginDuality.0.AddChar.mkZModAux", "kind": "definition", "module": "Mathlib.Analysis.Fourier.FiniteAbelian.PontryaginDuality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.Fourier.FiniteAbelian.PontryaginDuality.0.AddChar.mkZModAux_injective", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.FiniteAbelian.PontryaginDuality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.circleEquivComplex", "kind": "definition", "module": "Mathlib.Analysis.Fourier.FiniteAbelian.PontryaginDuality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.card_eq", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.FiniteAbelian.PontryaginDuality", "is_tactic_proof": true, "tactics": ["obtain", "classical", "have", "let", "have", "circleEquivComplex.injective.comp", "mkZModAux_injective.comp", "exact"], "tactic_count": 8}
{"name": "AddChar.zmodAddEquiv", "kind": "definition", "module": "Mathlib.Analysis.Fourier.FiniteAbelian.PontryaginDuality", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "AddChar.zmodAddEquiv_apply", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.FiniteAbelian.PontryaginDuality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.complexBasis", "kind": "definition", "module": "Mathlib.Analysis.Fourier.FiniteAbelian.PontryaginDuality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.coe_complexBasis", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.FiniteAbelian.PontryaginDuality", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AddChar.complexBasis_apply", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.FiniteAbelian.PontryaginDuality", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AddChar.exists_apply_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.FiniteAbelian.PontryaginDuality", "is_tactic_proof": true, "tactics": ["refine", "rintro", "exact", "classical", "by_contra", "let", "have", "have", "simp", "if_neg", "exact"], "tactic_count": 11}
{"name": "AddChar.forall_apply_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.FiniteAbelian.PontryaginDuality", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "AddChar.doubleDualEmb_injective", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.FiniteAbelian.PontryaginDuality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.doubleDualEmb_bijective", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.FiniteAbelian.PontryaginDuality", "is_tactic_proof": true, "tactics": ["cases", "exact"], "tactic_count": 2}
{"name": "AddChar.doubleDualEmb_inj", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.FiniteAbelian.PontryaginDuality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.doubleDualEmb_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.FiniteAbelian.PontryaginDuality", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "Real.instFourierTransformInv", "kind": "instance", "module": "Mathlib.Analysis.Fourier.FourierTransform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.fourier_eq", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.FourierTransform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Real.fourierInv_eq_fourier_comp_neg", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.FourierTransform", "is_tactic_proof": true, "tactics": ["ext", "rw", "change", "exact"], "tactic_count": 4}
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{"name": "Real.fourier_continuousMultilinearMap_apply", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.FourierTransform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Real.differentiable_fourierChar", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.FourierTransformDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "VectorFourier.fourierSMulRight_apply", "kind": "theorem", "module": "Mathlib.Analysis.Fourier.FourierTransformDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ContinuousLinearMap.innerSL_apply_comp", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Adjoint", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "ContinuousLinearMap.innerSL_apply_comp_of_isSymmetric", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Adjoint", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "InnerProductSpace.adjoint_rankOne", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Adjoint", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "InnerProductSpace.rankOne_comp", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Adjoint", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "IsSelfAdjoint.adjoint_eq", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Adjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSelfAdjoint.isSymmetric", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Adjoint", "is_tactic_proof": true, "tactics": ["intro", "rw_mod_cast"], "tactic_count": 2}
{"name": "IsSelfAdjoint.conj_adjoint", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Adjoint", "is_tactic_proof": true, "tactics": ["rw", "simp", "exact"], "tactic_count": 3}
{"name": "IsSelfAdjoint.adjoint_conj", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Adjoint", "is_tactic_proof": true, "tactics": ["rw", "simp", "exact"], "tactic_count": 3}
{"name": "ContinuousLinearMap.isSelfAdjoint_iff_isSymmetric", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Adjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsSymmetric.isSelfAdjoint", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Adjoint", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "isSelfAdjoint_starProjection", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Adjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSelfAdjoint.conj_starProjection", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Adjoint", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ContinuousLinearMap.isStarNormal_iff_norm_eq_adjoint", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Adjoint", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "have", "star_eq_adjoint", "coe_sub", "simp_rw", "coe_coe,", "inner_self_eq_norm_sq_to_K,", "norm_cast"], "tactic_count": 9}
{"name": "ContinuousLinearMap.IsStarNormal.adjoint_apply_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Adjoint", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "ContinuousLinearMap.IsStarNormal.ker_adjoint_eq_ker", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Adjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.IsStarNormal.orthogonal_range", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Adjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.IsIdempotentElem.isSelfAdjoint_iff_isStarNormal", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Adjoint", "is_tactic_proof": true, "tactics": ["refine", "suffices", "rw", "simp_rw", "have", "calc", "exact"], "tactic_count": 7}
{"name": "ContinuousLinearMap.isStarProjection_iff_isIdempotentElem_and_isStarNormal", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Adjoint", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ContinuousLinearMap.isStarProjection_iff_isSymmetricProjection", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Adjoint", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousLinearMap.IsStarProjection.ext_iff", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Adjoint", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "InnerProductSpace.isStarProjection_rankOne_self", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Adjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isStarProjection_starProjection", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Adjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isStarProjection_iff_eq_starProjection_range", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Adjoint", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "isStarProjection_iff_eq_starProjection", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Adjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsSymmetric.toSelfAdjoint", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.Adjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsSymmetric.coe_toSelfAdjoint", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Adjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsSymmetric.toSelfAdjoint_apply", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Adjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.adjoint", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.Adjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.adjoint_toContinuousLinearMap", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Adjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.adjoint_eq_toCLM_adjoint", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Adjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.adjoint_inner_left", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Adjoint", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "exact"], "tactic_count": 4}
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{"name": "LinearMap.adjoint_comp", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Adjoint", "is_tactic_proof": true, "tactics": ["ext", "refine", "simp"], "tactic_count": 3}
{"name": "LinearMap.eq_adjoint_iff", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Adjoint", "is_tactic_proof": true, "tactics": ["refine", "ext", "exact"], "tactic_count": 3}
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{"name": "LinearMap.eq_adjoint_iff_basis", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Adjoint", "is_tactic_proof": true, "tactics": ["refine", "refine", "exact"], "tactic_count": 3}
{"name": "LinearMap.eq_adjoint_iff_basis_left", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Adjoint", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "LinearMap.eq_adjoint_iff_basis_right", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Adjoint", "is_tactic_proof": true, "tactics": ["refine", "ext", "exact"], "tactic_count": 3}
{"name": "LinearMap.instStarId", "kind": "instance", "module": "Mathlib.Analysis.InnerProductSpace.Adjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.instInvolutiveStarId", "kind": "instance", "module": "Mathlib.Analysis.InnerProductSpace.Adjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.instStarMulId", "kind": "instance", "module": "Mathlib.Analysis.InnerProductSpace.Adjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.instStarRingId", "kind": "instance", "module": "Mathlib.Analysis.InnerProductSpace.Adjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.instStarModuleId", "kind": "instance", "module": "Mathlib.Analysis.InnerProductSpace.Adjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.star_eq_adjoint", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Adjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.isSelfAdjoint_iff'", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Adjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.isSymmetric_iff_isSelfAdjoint", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Adjoint", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "LinearMap.isAdjointPair_inner", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Adjoint", "is_tactic_proof": true, "tactics": ["intro", "simp"], "tactic_count": 2}
{"name": "LinearMap.isSymmetric_adjoint_mul_self", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Adjoint", "is_tactic_proof": true, "tactics": ["intro", "simp"], "tactic_count": 2}
{"name": "LinearMap.re_inner_adjoint_mul_self_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Adjoint", "is_tactic_proof": true, "tactics": ["simp", "norm_cast", "exact"], "tactic_count": 3}
{"name": "LinearMap.im_inner_adjoint_mul_self_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Adjoint", "is_tactic_proof": true, "tactics": ["simp", "norm_cast"], "tactic_count": 2}
{"name": "LinearMap.isSelfAdjoint_toContinuousLinearMap_iff", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Adjoint", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "LinearIsometryEquiv.symm_conjStarAlgEquiv_apply_apply", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Adjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Unitary.norm_map", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Adjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LinearMap.toMatrixOrthonormal_reindex", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Adjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.toEuclideanLin_conjTranspose_eq_adjoint", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Adjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inner_vsub_left_eq_zero_symm", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Affine", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "dist_sq_lineMap_lineMap_of_inner_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Affine", "is_tactic_proof": false, "tactics": ["have", "rw", "rw", "inner_smul_left,", "simp"], "tactic_count": 5}
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{"name": "InnerProductSpace.harmonicAt_congr_nhds", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Harmonic.Basic", "is_tactic_proof": true, "tactics": ["constructor", "exact", "exact"], "tactic_count": 3}
{"name": "InnerProductSpace.HarmonicAt.eventually", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Harmonic.Basic", "is_tactic_proof": true, "tactics": ["filter_upwards", "exact"], "tactic_count": 2}
{"name": "InnerProductSpace.isOpen_setOf_harmonicAt", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Harmonic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InnerProductSpace.HarmonicOnNhd.mono", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Harmonic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InnerProductSpace.HarmonicAt.add", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Harmonic.Basic", "is_tactic_proof": true, "tactics": ["constructor", "exact", "filter_upwards", "simp_all"], "tactic_count": 4}
{"name": "InnerProductSpace.HarmonicOnNhd.add", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Harmonic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InnerProductSpace.HarmonicAt.const_smul", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Harmonic.Basic", "is_tactic_proof": true, "tactics": ["constructor", "exact", "filter_upwards", "simp_all"], "tactic_count": 4}
{"name": "InnerProductSpace.HarmonicOnNhd.const_smul", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Harmonic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InnerProductSpace.HarmonicAt.comp_CLM", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Harmonic.Basic", "is_tactic_proof": true, "tactics": ["constructor", "exact", "filter_upwards", "simp_all"], "tactic_count": 4}
{"name": "InnerProductSpace.HarmonicOnNhd.comp_CLM", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Harmonic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InnerProductSpace.harmonicAt_comp_CLE_iff", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Harmonic.Basic", "is_tactic_proof": true, "tactics": ["constructor", "simpa", "exact"], "tactic_count": 3}
{"name": "InnerProductSpace.harmonicOnNhd_comp_CLE_iff", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Harmonic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffAt.harmonicAt", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Harmonic.Constructions", "is_tactic_proof": true, "tactics": ["refine", "filter_upwards", "have", "simp_all"], "tactic_count": 4}
{"name": "AnalyticAt.harmonicAt", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Harmonic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticAt.harmonicAt_re", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Harmonic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticAt.harmonicAt_im", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Harmonic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticAt.harmonicAt_conj", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Harmonic.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.InnerProductSpace.Harmonic.Constructions.0.analyticAt_harmonicAt_log_normSq", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Harmonic.Constructions", "is_tactic_proof": true, "tactics": ["rw", "exact", "reCLM", "have", "h₁g.differentiableAt.continuousAt.preimage_mem_nhds", "calc", "filter_upwards", "simp", "rw", "exact", "filter_upwards", "simp", "congr", "rw", "simp", "simpa", "apply", "use", "intro", "simp", "congr", "rw", "simp"], "tactic_count": 23}
{"name": "AnalyticAt.harmonicAt_log_norm", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Harmonic.Constructions", "is_tactic_proof": false, "tactics": ["have", "funext", "simp", "rw", "linarith", "exact", "rw", "apply", "by_cases", "exact", "rw", "exact", "analyticAt_harmonicAt_log_normSq"], "tactic_count": 13}
{"name": "LinearMap.IsSymmetric.orthogonalFamily_eigenspace_inf_eigenspace", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.JointEigenspace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsSymmetric.orthogonalFamily_iInf_eigenspaces", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.JointEigenspace", "is_tactic_proof": true, "tactics": ["intro", "obtain", "have", "simp", "apply", "exact", "exact"], "tactic_count": 7}
{"name": "LinearMap.IsSymmetric.iSup_eigenspace_inf_eigenspace_of_commute", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.JointEigenspace", "is_tactic_proof": true, "tactics": ["conv_rhs", "simp", "congr", "simpa", "orthogonalComplement_iSup_eigenspaces_eq_bot"], "tactic_count": 5}
{"name": "LinearMap.IsSymmetric.iSup_iSup_eigenspace_inf_eigenspace_eq_top_of_commute", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.JointEigenspace", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "LinearMap.IsSymmetric.directSum_isInternal_of_commute", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.JointEigenspace", "is_tactic_proof": true, "tactics": ["apply", "rw", "exact"], "tactic_count": 3}
{"name": "LinearMap.IsSymmetric.iSup_iInf_eq_top_of_commute", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.JointEigenspace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsSymmetric.LinearMap.IsSymmetric.directSum_isInternal_of_pairwise_commute", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.JointEigenspace", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "bilinearIteratedFDerivWithinTwo", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.Laplacian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bilinearIteratedFDerivTwo", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.Laplacian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bilinearIteratedFDerivWithinTwo_eq_iteratedFDeriv", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Laplacian", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "bilinearIteratedFDerivTwo_eq_iteratedFDeriv", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Laplacian", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "tensorIteratedFDerivWithinTwo", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.Laplacian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tensorIteratedFDerivTwo", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.Laplacian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tensorIteratedFDerivWithinTwo_eq_iteratedFDerivWithin", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Laplacian", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "tensorIteratedFDerivTwo_eq_iteratedFDeriv", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Laplacian", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "InnerProductSpace.laplacianWithin", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.Laplacian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InnerProductSpace.termΔ[_]_", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.Laplacian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InnerProductSpace._aux_Mathlib_Analysis_InnerProductSpace_Laplacian___macroRules_InnerProductSpace_termΔ[_]__1", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.Laplacian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InnerProductSpace._aux_Mathlib_Analysis_InnerProductSpace_Laplacian___unexpand_InnerProductSpace_laplacianWithin_1", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.Laplacian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InnerProductSpace.instLaplacian", "kind": "instance", "module": "Mathlib.Analysis.InnerProductSpace.Laplacian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InnerProductSpace.laplacianWithin_univ", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Laplacian", "is_tactic_proof": true, "tactics": ["ext", "simp", "bilinearIteratedFDerivWithinTwo]"], "tactic_count": 3}
{"name": "InnerProductSpace.laplacianWithin_eq_iteratedFDerivWithin_orthonormalBasis", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Laplacian", "is_tactic_proof": true, "tactics": ["simp", "tensorIteratedFDerivWithinTwo_eq_iteratedFDerivWithin"], "tactic_count": 2}
{"name": "InnerProductSpace.laplacian_eq_iteratedFDeriv_orthonormalBasis", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Laplacian", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "InnerProductSpace.laplacianWithin_eq_iteratedFDerivWithin_stdOrthonormalBasis", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Laplacian", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "InnerProductSpace.laplacian_eq_iteratedFDeriv_stdOrthonormalBasis", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Laplacian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InnerProductSpace.laplacianWithin_eq_iteratedDerivWithin_real", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Laplacian", "is_tactic_proof": false, "tactics": ["simp", "congr", "fin_cases"], "tactic_count": 3}
{"name": "InnerProductSpace.laplacian_eq_iteratedDeriv_real", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Laplacian", "is_tactic_proof": true, "tactics": ["rw", "laplacianWithin_eq_iteratedDerivWithin_real"], "tactic_count": 2}
{"name": "InnerProductSpace.laplacianWithin_eq_iteratedFDerivWithin_complexPlane", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Laplacian", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "InnerProductSpace.laplacian_eq_iteratedFDeriv_complexPlane", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Laplacian", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "InnerProductSpace.laplacianWithin_congr_nhdsWithin", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Laplacian", "is_tactic_proof": true, "tactics": ["filter_upwards", "simp"], "tactic_count": 2}
{"name": "InnerProductSpace.laplacian_congr_nhds", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Laplacian", "is_tactic_proof": true, "tactics": ["filter_upwards", "simp"], "tactic_count": 2}
{"name": "ContDiffWithinAt.laplacianWithin_add", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Laplacian", "is_tactic_proof": true, "tactics": ["simp", "iteratedFDerivWithin_add_apply"], "tactic_count": 2}
{"name": "ContDiffAt.laplacian_add", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Laplacian", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContDiffAt.laplacianWithin_add_nhdsWithin", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Laplacian", "is_tactic_proof": true, "tactics": ["nth_rw", "filter_upwards", "rw", "simp"], "tactic_count": 4}
{"name": "ContDiffAt.laplacian_add_nhds", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Laplacian", "is_tactic_proof": true, "tactics": ["filter_upwards", "exact"], "tactic_count": 2}
{"name": "InnerProductSpace.laplacianWithin_smul", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Laplacian", "is_tactic_proof": true, "tactics": ["simp", "iteratedFDerivWithin_const_smul_apply"], "tactic_count": 2}
{"name": "InnerProductSpace.laplacian_smul", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Laplacian", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "InnerProductSpace.laplacianWithin_smul_nhds", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Laplacian", "is_tactic_proof": true, "tactics": ["filter_upwards", "eventually_mem_nhdsWithin]"], "tactic_count": 2}
{"name": "InnerProductSpace.laplacian_smul_nhds", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Laplacian", "is_tactic_proof": true, "tactics": ["filter_upwards", "simp"], "tactic_count": 2}
{"name": "ContDiffWithinAt.laplacianWithin_CLM_comp_left", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Laplacian", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContDiffAt.laplacian_CLM_comp_left", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Laplacian", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContDiffWithinAt.laplacianWithin_CLM_comp_left_nhds", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Laplacian", "is_tactic_proof": true, "tactics": ["filter_upwards", "eventually_mem_nhdsWithin]"], "tactic_count": 2}
{"name": "ContDiffAt.laplacian_CLM_comp_left_nhds", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Laplacian", "is_tactic_proof": true, "tactics": ["filter_upwards", "rw"], "tactic_count": 2}
{"name": "InnerProductSpace.laplacianWithin_CLE_comp_left", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Laplacian", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "InnerProductSpace.laplacian_CLE_comp_left", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Laplacian", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "_private.Mathlib.Analysis.InnerProductSpace.LaxMilgram.0.IsCoercive.term_♯", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.LaxMilgram", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.InnerProductSpace.LaxMilgram.0.IsCoercive._aux_Mathlib_Analysis_InnerProductSpace_LaxMilgram___macroRules__private_Mathlib_Analysis_InnerProductSpace_LaxMilgram_0_IsCoercive_term_♯_1", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.LaxMilgram", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCoercive.bounded_below", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.LaxMilgram", "is_tactic_proof": true, "tactics": ["rcases", "refine", "intro", "by_cases", "refine", "calc", "have", "simp"], "tactic_count": 8}
{"name": "IsCoercive.antilipschitz", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.LaxMilgram", "is_tactic_proof": true, "tactics": ["rcases", "refine", "refine", "simp_rw", "simpa"], "tactic_count": 5}
{"name": "IsCoercive.ker_eq_bot", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.LaxMilgram", "is_tactic_proof": true, "tactics": ["rw", "rcases", "exact"], "tactic_count": 3}
{"name": "IsCoercive.isClosed_range", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.LaxMilgram", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "IsCoercive.range_eq_top", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.LaxMilgram", "is_tactic_proof": true, "tactics": ["haveI", "rw", "rw", "intro", "rcases", "obtain", "rw", "apply", "calc", "positivity", "exact"], "tactic_count": 11}
{"name": "IsCoercive.continuousLinearEquivOfBilin", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.LaxMilgram", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCoercive.continuousLinearEquivOfBilin_apply", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.LaxMilgram", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCoercive.unique_continuousLinearEquivOfBilin", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.LaxMilgram", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.InnerProductSpace.LinearMap.0.term⟪_,_⟫", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.InnerProductSpace.LinearMap.0._aux_Mathlib_Analysis_InnerProductSpace_LinearMap___macroRules__private_Mathlib_Analysis_InnerProductSpace_LinearMap_0_term⟪_,_⟫_1", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.InnerProductSpace.LinearMap.0._aux_Mathlib_Analysis_InnerProductSpace_LinearMap___unexpand_Inner_inner_1", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inner_map_polarization", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.LinearMap", "is_tactic_proof": false, "tactics": ["simp", "one_mul,", "ring"], "tactic_count": 3}
{"name": "inner_map_polarization'", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.LinearMap", "is_tactic_proof": false, "tactics": ["simp", "one_mul,", "ring"], "tactic_count": 3}
{"name": "inner_map_self_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.LinearMap", "is_tactic_proof": true, "tactics": ["constructor", "intro", "ext", "rw", "simp", "simp", "rintro", "simp"], "tactic_count": 8}
{"name": "ext_inner_map", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.LinearMap", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw"], "tactic_count": 3}
{"name": "LinearIsometry.inner_map_map", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.LinearMap", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LinearIsometryEquiv.inner_map_map", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.inner_map_eq_flip", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.LinearMap", "is_tactic_proof": true, "tactics": ["conv_lhs"], "tactic_count": 1}
{"name": "LinearMap.isometryOfInner", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.coe_isometryOfInner", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.isometryOfInner_toLinearMap", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.isometryOfInner", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.coe_isometryOfInner", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.isometryOfInner_toLinearEquiv", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.norm_map_iff_inner_map_map", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "innerSL", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "coe_innerSL_apply", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "innerSL_apply_apply", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.toLinearMap_innerSL_apply", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "innerSLFlip", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "innerSLFlip_apply_apply", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "flip_innerSL_real", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.LinearMap", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "ContinuousLinearMap.toSesqForm", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.toSesqForm_apply_coe", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.toSesqForm_apply_norm_le", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.LinearMap", "is_tactic_proof": true, "tactics": ["refine", "have", "have", "calc"], "tactic_count": 4}
{"name": "innerSL_apply_norm", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.LinearMap", "is_tactic_proof": true, "tactics": ["refine", "rcases", "simp", "refine", "calc"], "tactic_count": 5}
{"name": "norm_innerSL_le", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inner_map_complex", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.LinearMap", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "nonempty_innerProductSpace", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.OfNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "OrthonormalBasis.same_orientation_iff_det_eq_det", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orientation", "is_tactic_proof": true, "tactics": ["constructor", "intro", "dsimp", "congr", "intro", "rw", "simp"], "tactic_count": 7}
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{"name": "OrthonormalBasis.orthonormal_adjustToOrientation", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orientation", "is_tactic_proof": true, "tactics": ["apply", "simpa"], "tactic_count": 2}
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{"name": "OrthonormalBasis.toBasis_adjustToOrientation", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orientation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrthonormalBasis.orientation_adjustToOrientation", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orientation", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "OrthonormalBasis.adjustToOrientation_apply_eq_or_eq_neg", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orientation", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
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{"name": "OrthonormalBasis.abs_det_adjustToOrientation", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orientation", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "Orientation.volumeForm_zero_pos", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orientation", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Orientation.volumeForm_zero_neg", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orientation", "is_tactic_proof": true, "tactics": ["simp_rw", "apply", "simp", "rw", "intro", "simpa"], "tactic_count": 6}
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{"name": "Orientation.abs_volumeForm_apply_of_pairwise_orthogonal", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orientation", "is_tactic_proof": true, "tactics": ["rcases", "refine", "haveI", "have", "let", "have", "rw", "by_cases", "obtain", "rw", "congr", "ext", "have", "simp", "rw", "field", "positivity"], "tactic_count": 17}
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{"name": "Submodule.inner_right_of_mem_orthogonal", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orthogonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Submodule.mem_orthogonal_singleton_iff_inner_right", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orthogonal", "is_tactic_proof": true, "tactics": ["refine", "intro", "rw", "obtain", "simp"], "tactic_count": 5}
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{"name": "Submodule.orthogonal_eq_inter", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orthogonal", "is_tactic_proof": true, "tactics": ["ext", "simpa"], "tactic_count": 2}
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{"name": "Submodule.top_orthogonal_eq_bot", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orthogonal", "is_tactic_proof": true, "tactics": ["ext", "rw", "exact", "rintro", "simp⟩"], "tactic_count": 5}
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{"name": "Submodule.orthogonal_eq_top_iff", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orthogonal", "is_tactic_proof": false, "tactics": ["refine", "rintro", "exact", "intro", "have", "rwa"], "tactic_count": 6}
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{"name": "Submodule.IsOrtho.symm", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orthogonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Submodule.symmetric_isOrtho", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orthogonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.IsOrtho.inner_eq", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orthogonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.isOrtho_iff_inner_eq", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orthogonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.isOrtho_bot_left", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orthogonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.isOrtho_bot_right", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orthogonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.IsOrtho.mono_left", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orthogonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.IsOrtho.mono_right", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orthogonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Submodule.isOrtho_orthogonal_right", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orthogonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Submodule.IsOrtho.disjoint", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orthogonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Submodule.isOrtho_sSup_left", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orthogonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.isOrtho_sSup_right", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orthogonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.isOrtho_iSup_left", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orthogonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.isOrtho_iSup_right", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orthogonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Submodule.IsOrtho.comap", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orthogonal", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "intro", "exact"], "tactic_count": 4}
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{"name": "OrthogonalFamily.isOrtho", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orthogonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ClosedSubmodule.toSubmodule_orthogonal_eq", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orthogonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClosedSubmodule.mem_orthogonal_toSubmodule_iff", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orthogonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ClosedSubmodule.inf_orthogonal_eq_bot", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orthogonal", "is_tactic_proof": true, "tactics": ["rw", "intro", "simpa"], "tactic_count": 3}
{"name": "ClosedSubmodule.orthogonal_disjoint", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orthogonal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "ClosedSubmodule.inf_orthogonal", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orthogonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ClosedSubmodule.sInf_orthogonal", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orthogonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClosedSubmodule.top_orthogonal_eq_bot", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orthogonal", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "ClosedSubmodule.bot_orthogonal_eq_top", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orthogonal", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "ClosedSubmodule.orthogonal_eq_top_iff", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orthogonal", "is_tactic_proof": true, "tactics": ["refine", "intro", "have", "rwa"], "tactic_count": 4}
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{"name": "Orthonormal", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.Orthonormal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orthonormal.of_isEmpty", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orthonormal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Orthonormal.norm_eq_one", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orthonormal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orthonormal.nnnorm_eq_one", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orthonormal", "is_tactic_proof": true, "tactics": ["suffices", "simp"], "tactic_count": 2}
{"name": "Orthonormal.enorm_eq_one", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orthonormal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Orthonormal.inner_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orthonormal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "orthonormal_subtype_iff_ite", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orthonormal", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Orthonormal.inner_right_finsupp", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orthonormal", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Orthonormal.inner_right_sum", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orthonormal", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Orthonormal.inner_right_fintype", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orthonormal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orthonormal.inner_left_finsupp", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orthonormal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Orthonormal.inner_left_sum", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orthonormal", "is_tactic_proof": true, "tactics": ["classical", "simp"], "tactic_count": 2}
{"name": "Orthonormal.inner_left_fintype", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orthonormal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orthonormal.inner_finsupp_eq_sum_left", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orthonormal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Orthonormal.inner_finsupp_eq_sum_right", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orthonormal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Orthonormal.inner_sum", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orthonormal", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "rw"], "tactic_count": 3}
{"name": "Orthonormal.inner_left_right_finset", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orthonormal", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Orthonormal.linearIndependent", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orthonormal", "is_tactic_proof": true, "tactics": ["rw", "intro", "ext", "have", "simpa"], "tactic_count": 5}
{"name": "Orthonormal.comp", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orthonormal", "is_tactic_proof": true, "tactics": ["classical", "rw", "intro", "convert", "simp"], "tactic_count": 5}
{"name": "orthonormal_subtype_range", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orthonormal", "is_tactic_proof": true, "tactics": ["let", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "Orthonormal.toSubtypeRange", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orthonormal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orthonormal.inner_finsupp_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orthonormal", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Orthonormal.orthonormal_of_forall_eq_or_eq_neg", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orthonormal", "is_tactic_proof": true, "tactics": ["classical", "rw", "intro", "rcases", "simpa"], "tactic_count": 5}
{"name": "orthonormal_empty", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orthonormal", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "orthonormal_iUnion_of_directed", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orthonormal", "is_tactic_proof": true, "tactics": ["classical", "rw", "rintro", "obtain", "have", "rw", "exact"], "tactic_count": 7}
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{"name": "basisOfOrthonormalOfCardEqFinrank", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.Orthonormal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "coe_basisOfOrthonormalOfCardEqFinrank", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orthonormal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Orthonormal.comp_linearIsometryEquiv", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orthonormal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orthonormal.mapLinearIsometryEquiv", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orthonormal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.isometryOfOrthonormal", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.Orthonormal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.coe_isometryOfOrthonormal", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orthonormal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.isometryOfOrthonormal_toLinearMap", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orthonormal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.isometryOfOrthonormal", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.Orthonormal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.coe_isometryOfOrthonormal", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orthonormal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.isometryOfOrthonormal_toLinearEquiv", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orthonormal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orthonormal.equiv", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.Orthonormal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orthonormal.equiv_toLinearEquiv", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Orthonormal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "_private.Mathlib.Analysis.InnerProductSpace.Orthonormal.0.term⟪_,_⟫_2", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.Orthonormal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "EuclideanSpace.projₗ", "kind": "abbrev", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanSpace.proj", "kind": "abbrev", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanSpace.single", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanSpace.ofLp_single", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanSpace.toLp_single", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanSpace.single_apply", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EuclideanSpace.single_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanSpace.inner_single_left", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "EuclideanSpace.inner_single_right", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "EuclideanSpace.norm_single", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanSpace.nnnorm_single", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanSpace.dist_single_same", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanSpace.nndist_single_same", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanSpace.edist_single_same", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanSpace.orthonormal_single", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": true, "tactics": ["simp_rw", "intros", "trivial"], "tactic_count": 3}
{"name": "EuclideanSpace.piLpCongrLeft_single", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanSpace.sumEquivProd", "kind": "abbrev", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanSpace.finAddEquivProd", "kind": "abbrev", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrthonormalBasis.repr_injective", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrthonormalBasis.instFunLike", "kind": "instance", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrthonormalBasis.coe_ofRepr", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": true, "tactics": ["dsimp", "funext", "congr"], "tactic_count": 3}
{"name": "OrthonormalBasis.repr_symm_single", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": true, "tactics": ["dsimp", "congr"], "tactic_count": 2}
{"name": "OrthonormalBasis.repr_self", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "OrthonormalBasis.repr_apply_apply", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": true, "tactics": ["classical", "rw", "simp"], "tactic_count": 3}
{"name": "OrthonormalBasis.orthonormal", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": true, "tactics": ["classical", "rw", "intro", "rw"], "tactic_count": 4}
{"name": "OrthonormalBasis.norm_eq_one", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrthonormalBasis.nnnorm_eq_one", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrthonormalBasis.enorm_eq_one", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrthonormalBasis.inner_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrthonormalBasis.inner_eq_one", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "OrthonormalBasis.inner_eq_ite", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "OrthonormalBasis.toBasis", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrthonormalBasis.coe_toBasis", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrthonormalBasis.coe_toBasis_repr", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrthonormalBasis.coe_toBasis_repr_apply", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "OrthonormalBasis.sum_repr", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "OrthonormalBasis.sum_repr'", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": true, "tactics": ["nth_rw", "simp_rw"], "tactic_count": 2}
{"name": "OrthonormalBasis.sum_repr_symm", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "OrthonormalBasis.sum_inner_mul_inner", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": true, "tactics": ["have", "rw", "convert", "rw", "simp"], "tactic_count": 5}
{"name": "OrthonormalBasis.sum_sq_norm_inner_right", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "rw", "exact"], "tactic_count": 4}
{"name": "OrthonormalBasis.sum_sq_norm_inner_left", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "OrthonormalBasis.sum_sq_inner_right", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "OrthonormalBasis.sum_sq_inner_left", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "OrthonormalBasis.norm_le_card_mul_iSup_norm_inner", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": true, "tactics": ["calc", "gcongr", "exact", "simp", "congr", "rw", "cases", "simp", "exact"], "tactic_count": 9}
{"name": "OrthonormalBasis.orthogonalProjection_apply_eq_sum", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "OrthonormalBasis.orthogonalProjection_eq_sum_rankOne", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "OrthonormalBasis.starProjection_eq_sum_rankOne", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "OrthonormalBasis.sum_rankOne_eq_id", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "OrthonormalBasis.map", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrthonormalBasis.map_apply", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrthonormalBasis.toBasis_map", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.toOrthonormalBasis", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.coe_toOrthonormalBasis_repr", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.coe_toOrthonormalBasis_repr_symm", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.toBasis_toOrthonormalBasis", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Module.Basis.coe_toOrthonormalBasis", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrthonormalBasis.singleton", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrthonormalBasis.singleton_apply", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrthonormalBasis.singleton_repr", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrthonormalBasis.coe_singleton", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "OrthonormalBasis.toBasis_singleton", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.orthonormalBasis", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.orthonormalBasis.toBasis", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Pi.orthonormalBasis_apply", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": true, "tactics": ["classical", "ext", "obtain", "simp", "obtain", "simp", "simp"], "tactic_count": 7}
{"name": "Pi.orthonormalBasis_repr", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrthonormalBasis.mk", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrthonormalBasis.coe_mk", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "OrthonormalBasis.span", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrthonormalBasis.span_apply", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "OrthonormalBasis.mkOfOrthogonalEqBot", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrthonormalBasis.coe_of_orthogonal_eq_bot_mk", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrthonormalBasis.reindex", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrthonormalBasis.reindex_apply", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": true, "tactics": ["classical", "dsimp", "rw", "dsimp", "rw"], "tactic_count": 5}
{"name": "OrthonormalBasis.reindex_toBasis", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrthonormalBasis.coe_reindex", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrthonormalBasis.repr_reindex", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "EuclideanSpace.basisFun", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanSpace.basisFun_apply", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanSpace.basisFun_repr", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanSpace.basisFun_inner", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "EuclideanSpace.inner_basisFun_real", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EuclideanSpace.basisFun_toBasis", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrthonormalBasis.instInhabited", "kind": "instance", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrthonormalBasis.equiv", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrthonormalBasis.equiv_symm", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "OrthonormalBasis.equiv_apply_basis", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": true, "tactics": ["classical", "simp", "refine", "ext", "simp"], "tactic_count": 5}
{"name": "OrthonormalBasis.equiv_self_rfl", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "OrthonormalBasis.equiv_apply", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": true, "tactics": ["nth_rw", "simp_rw"], "tactic_count": 2}
{"name": "OrthonormalBasis.equiv_apply_euclideanSpace", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "OrthonormalBasis.coe_equiv_euclideanSpace", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Complex.orthonormalBasisOneI", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.orthonormalBasisOneI_repr_apply", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.orthonormalBasisOneI_repr_symm_apply", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.toBasis_orthonormalBasisOneI", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.coe_orthonormalBasisOneI", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.isometryOfOrthonormal", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.map_isometryOfOrthonormal", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": false, "tactics": ["simp", "rw"], "tactic_count": 2}
{"name": "Complex.isometryOfOrthonormal_symm_apply", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.isometryOfOrthonormal_apply", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "OrthonormalBasis.toMatrix_orthonormalBasis_conjTranspose_mul_self", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": true, "tactics": ["ext", "convert", "simp", "congr", "rw"], "tactic_count": 5}
{"name": "OrthonormalBasis.toMatrix_orthonormalBasis_self_mul_conjTranspose", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": true, "tactics": ["classical", "rw", "a.toMatrix_orthonormalBasis_conjTranspose_mul_self"], "tactic_count": 3}
{"name": "OrthonormalBasis.toMatrix_orthonormalBasis_mem_unitary", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "OrthonormalBasis.det_to_matrix_orthonormalBasis", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": true, "tactics": ["have", "rw", "norm_cast", "rwa"], "tactic_count": 4}
{"name": "OrthonormalBasis.toMatrix_orthonormalBasis_mem_orthogonal", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrthonormalBasis.det_to_matrix_orthonormalBasis_real", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "DirectSum.IsInternal.collectedOrthonormalBasis", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.IsInternal.collectedOrthonormalBasis_mem", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Orthonormal.exists_orthonormalBasis_extension", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": true, "tactics": ["obtain", "rw", "have", "let", "let", "have", "refine", "simpa", "simpa", "simp"], "tactic_count": 10}
{"name": "Orthonormal.exists_orthonormalBasis_extension_of_card_eq", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": true, "tactics": ["have", "have", "obtain", "have", "refine", "exact", "have", "have", "rw", "exact", "obtain", "use", "intro", "simp"], "tactic_count": 14}
{"name": "exists_orthonormalBasis", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "definition._@.Mathlib.Analysis.InnerProductSpace.PiL2.2921777918._hygCtx._hyg.2", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": true, "tactics": ["let", "rw", "exact"], "tactic_count": 3}
{"name": "wrapped._@.Mathlib.Analysis.InnerProductSpace.PiL2.2921777918._hygCtx._hyg.2", "kind": "opaque", "module": "Mathlib.Analysis.InnerProductSpace.PiL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "InnerProductSpace.isPositive_rankOne_self", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Positive", "is_tactic_proof": false, "tactics": ["simp_rw", "simp"], "tactic_count": 2}
{"name": "ContinuousLinearMap.isPositive_iff_eq_sum_rankOne", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Positive", "is_tactic_proof": true, "tactics": ["refine", "let", "refine", "simp_rw", "mul_assoc,", "hT.isSymmetric.apply_eigenvectorBasis,"], "tactic_count": 6}
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{"name": "Submodule.toLinearEquiv_orthogonalDecomposition_symm", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.ProdL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.coe_orthogonalDecomposition", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.ProdL2", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
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{"name": "Submodule.fst_orthogonalDecomposition_apply", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.ProdL2", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Submodule.snd_orthogonalDecomposition_apply", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.ProdL2", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Submodule.fstL_comp_coe_orthogonalDecomposition", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.ProdL2", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
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{"name": "_private.Mathlib.Analysis.InnerProductSpace.Projection.Basic.0.term⟪_,_⟫", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.Projection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Submodule.eq_starProjection_of_mem_of_inner_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Projection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.eq_starProjection_of_mem_orthogonal", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Projection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Submodule.orthogonalProjection_mem_subspace_eq_self", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Projection.Basic", "is_tactic_proof": true, "tactics": ["ext", "apply"], "tactic_count": 2}
{"name": "Submodule.starProjection_mem_subspace_eq_self", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Projection.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "Submodule.isIdempotentElem_starProjection", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Projection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Submodule.ker_starProjection", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Projection.Basic", "is_tactic_proof": true, "tactics": ["rw", "starProjection_orthogonal,"], "tactic_count": 2}
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{"name": "LinearIsometry.map_starProjection'", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Projection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Submodule.starProjection_norm_le", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Projection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Submodule.norm_starProjection_apply", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Projection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Submodule.lipschitzWith_starProjection", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Projection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Submodule.exists_add_mem_mem_orthogonal", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Projection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Submodule.IsOrtho.orthogonalProjection_comp_subtypeL", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Projection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.IsOrtho.starProjection_comp_starProjection", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Projection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.orthogonalProjection_comp_subtypeL_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Projection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.starProjection_comp_starProjection_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Projection.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "simp", "intro", "simpa"], "tactic_count": 5}
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{"name": "Submodule.starProjection_orthogonal_apply_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Projection.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Submodule.orthogonalProjection_starProjection_of_le", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Projection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.starProjection_comp_starProjection_of_le", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Projection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.IsIdempotentElem.hasOrthogonalProjection_range", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Projection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsSymmetricProjection.hasOrthogonalProjection_range", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Projection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.orthogonalProjection_orthogonalComplement_singleton_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Projection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.starProjection_orthogonalComplement_singleton_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Projection.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Submodule.starProjection_add_starProjection_orthogonal", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Projection.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Submodule.norm_sq_eq_add_norm_sq_projection", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Projection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.norm_sq_eq_add_norm_sq_starProjection", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Projection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mem_iff_norm_starProjection", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Projection.Basic", "is_tactic_proof": true, "tactics": ["refine", "simpa"], "tactic_count": 2}
{"name": "Submodule.id_eq_sum_starProjection_self_orthogonalComplement", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Projection.Basic", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "Submodule.inner_orthogonalProjection_eq_of_mem_right", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Projection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.inner_orthogonalProjection_eq_of_mem_left", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Projection.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submodule.inner_starProjection_left_eq_right", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Projection.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "inner_orthogonalProjection_eq_of_mem_right]"], "tactic_count": 2}
{"name": "Submodule.starProjection_isSymmetric", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Projection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.isSymmetricProjection_starProjection", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Projection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.isSymmetricProjection_iff_eq_coe_starProjection_range", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Projection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.isSymmetricProjection_iff_eq_coe_starProjection", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Projection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.starProjection_apply_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Projection.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "simp"], "tactic_count": 3}
{"name": "Submodule.re_inner_starProjection_eq_normSq", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Projection.Basic", "is_tactic_proof": false, "tactics": ["rw", "div_eq_iff", "show", "exact"], "tactic_count": 4}
{"name": "Submodule.re_inner_starProjection_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Projection.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
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{"name": "LinearMap.IsSymmetric.im_inner_apply_self", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Symmetric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsSymmetric.im_inner_self_apply", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Symmetric", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LinearMap.IsSymmetric.coe_re_inner_apply_self", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Symmetric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsSymmetric.coe_re_inner_self_apply", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Symmetric", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LinearMap.isSymmetric_iff_inner_map_self_real", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Symmetric", "is_tactic_proof": true, "tactics": ["constructor", "intro", "apply", "intro", "rw", "rw", "simp", "simp", "rw", "simp", "rw", "norm_num", "ring"], "tactic_count": 13}
{"name": "LinearMap.IsSymmetric.inner_map_polarization", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Symmetric", "is_tactic_proof": true, "tactics": ["rcases", "simp_rw", "inner_sub_right,", "suffices", "rw", "ring", "rw", "simp_rw", "norm_cast", "simp_rw", "inner_smul_left,", "one_mul,", "ring"], "tactic_count": 13}
{"name": "LinearMap.isSymmetric_linearIsometryEquiv_conj_iff", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Symmetric", "is_tactic_proof": true, "tactics": ["refine", "simpa", "simp"], "tactic_count": 3}
{"name": "InnerProductSpace.isSymmetric_rankOne_self", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Symmetric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InnerProductSpace.isSymmetricProjection_rankOne_self", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Symmetric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsSymmetric.toLinearMap_symm", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Symmetric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.isSymmetric_symm_iff", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Symmetric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.InnerProductSpace.Symmetric.0.term⟪_,_⟫_1", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.Symmetric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.InnerProductSpace.Symmetric.0._aux_Mathlib_Analysis_InnerProductSpace_Symmetric___macroRules__private_Mathlib_Analysis_InnerProductSpace_Symmetric_0_term⟪_,_⟫_1_1", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.Symmetric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.InnerProductSpace.Symmetric.0._aux_Mathlib_Analysis_InnerProductSpace_Symmetric___unexpand_Inner_inner_2", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.Symmetric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsSymmetric.continuous", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Symmetric", "is_tactic_proof": true, "tactics": ["refine", "rw", "have", "intro", "rw", "refine", "simp_rw", "rw", "refine", "rw", "exact"], "tactic_count": 11}
{"name": "LinearMap.IsSymmetric.inner_map_self_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Symmetric", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "rw", "simp_rw", "ring"], "tactic_count": 5}
{"name": "LinearMap.ker_le_ker_of_range", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Symmetric", "is_tactic_proof": true, "tactics": ["intro", "rw", "obtain", "rw"], "tactic_count": 4}
{"name": "Submodule.IsCompl.projection_isSymmetric_iff", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Symmetric", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "inner_zero_left]", "nth_rw", "nth_rw", "rw", "simp"], "tactic_count": 8}
{"name": "Submodule.IsCompl.projection_isSymmetricProjection_iff", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Symmetric", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LinearMap.IsIdempotentElem.isSymmetric_iff_isOrtho_range_ker", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Symmetric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LinearMap.IsSymmetric.orthogonal_range", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Symmetric", "is_tactic_proof": true, "tactics": ["ext", "constructor", "simpa", "simp_all"], "tactic_count": 4}
{"name": "LinearMap.IsIdempotentElem.isSymmetric_iff_orthogonal_range", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Symmetric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsSymmetricProjection.ext_iff", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Symmetric", "is_tactic_proof": true, "tactics": ["refine", "rw", "hT.isIdempotentElem.isSymmetric_iff_orthogonal_range.mp", "hS.isIdempotentElem.isSymmetric_iff_orthogonal_range.mp", "simp"], "tactic_count": 5}
{"name": "LinearMap.IsSymmetricProjection.sub_of_range_le_range", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Symmetric", "is_tactic_proof": true, "tactics": ["rw", "refine", "hq.isSymmetric.sub", "simp_rw"], "tactic_count": 4}
{"name": "LinearMap.IsSymmetric.isSymmetric_smul_iff", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Symmetric", "is_tactic_proof": true, "tactics": ["refine", "simp", "simpa"], "tactic_count": 3}
{"name": "_private.Mathlib.Analysis.InnerProductSpace.TensorProduct.0.TensorProduct.inner_", "kind": "abbrev", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.instInner", "kind": "instance", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.InnerProductSpace.TensorProduct.0.TensorProduct.inner_def", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.inner_tmul", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.inner_map_map", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.inner_mapIncl_mapIncl", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.InnerProductSpace.TensorProduct.0.TensorProduct.inner_self", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": true, "tactics": ["classical", "have", "conv_lhs", "simp", "conv_lhs", "simp", "simp"], "tactic_count": 7}
{"name": "_private.Mathlib.Analysis.InnerProductSpace.TensorProduct.0.TensorProduct.inner_definite", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": true, "tactics": ["in", "obtain", "obtain", "obtain", "obtain", "have", "rw", "simpa", "have", "rw"], "tactic_count": 10}
{"name": "_private.Mathlib.Analysis.InnerProductSpace.TensorProduct.0.TensorProduct.re_inner_self_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "obtain", "obtain", "rw", "exact"], "tactic_count": 6}
{"name": "TensorProduct.instNormedAddCommGroup", "kind": "instance", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.instInnerProductSpace", "kind": "instance", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.norm_tmul", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "TensorProduct.nnnorm_tmul", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "TensorProduct.enorm_tmul", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.dist_tmul_le", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": true, "tactics": ["grw"], "tactic_count": 1}
{"name": "TensorProduct.nndist_tmul_le", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": true, "tactics": ["grw"], "tactic_count": 1}
{"name": "TensorProduct.edist_tmul_le", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": true, "tactics": ["grw"], "tactic_count": 1}
{"name": "RCLike.inner_tmul_eq", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "TensorProduct.ext_iff_inner_right", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.ext_iff_inner_left", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "TensorProduct.ext_iff_inner_right_threefold", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.ext_iff_inner_left_threefold", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": true, "tactics": ["simpa", "ext_iff_inner_right_threefold"], "tactic_count": 2}
{"name": "TensorProduct.mapIsometry", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.mapIsometry_apply", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.toLinearMap_mapIsometry", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.norm_map", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.nnnorm_map", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.enorm_map", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.mapIsometry_id_id", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "LinearIsometry.lTensor", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.rTensor", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.lTensor_def", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.rTensor_def", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.toLinearMap_lTensor", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.toLinearMap_rTensor", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.lTensor_apply", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.rTensor_apply", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.congrIsometry", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.congrIsometry_apply", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.congrIsometry_symm", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.toLinearEquiv_congrIsometry", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.congrIsometry_refl_refl", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.lTensor", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.rTensor", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.lTensor_def", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.rTensor_def", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.symm_lTensor", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.symm_rTensor", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.toLinearEquiv_lTensor", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.toLinearIsometry_lTensor", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.toLinearEquiv_rTensor", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.toLinearIsometry_rTensor", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.lTensor_apply", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.rTensor_apply", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.mapInclIsometry", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.mapInclIsometry_apply", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.toLinearMap_mapInclIsometry", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.inner_comm_comm", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.commIsometry", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.commIsometry_apply", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.commIsometry_symm", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.toLinearEquiv_commIsometry", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.norm_comm", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.nnnorm_comm", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.enorm_comm", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.inner_lid_lid", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.lidIsometry", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.lidIsometry_apply", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.lidIsometry_symm_apply", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.toLinearEquiv_lidIsometry", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.norm_lid", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.nnnorm_lid", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.enorm_lid", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.inner_assoc_assoc", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.assocIsometry", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.assocIsometry_apply", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.assocIsometry_symm_apply", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.toLinearEquiv_assocIsometry", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.norm_assoc", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.nnnorm_assoc", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.enorm_assoc", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.adjoint_map", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.adjoint_rTensor", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LinearMap.adjoint_lTensor", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "TensorProduct.ext_iff_inner_right_threefold'", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": ["simp", "simp"], "tactic_count": 2}
{"name": "TensorProduct.ext_iff_inner_left_threefold'", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": true, "tactics": ["simpa", "ext_iff_inner_right_threefold"], "tactic_count": 2}
{"name": "Orthonormal.tmul", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": true, "tactics": ["classical", "rw", "rintro", "simp"], "tactic_count": 4}
{"name": "Orthonormal.basisTensorProduct", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": true, "tactics": ["convert", "exact"], "tactic_count": 2}
{"name": "OrthonormalBasis.tensorProduct", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrthonormalBasis.tensorProduct_apply", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "OrthonormalBasis.tensorProduct_apply'", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrthonormalBasis.tensorProduct_repr_tmul_apply", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "OrthonormalBasis.tensorProduct_repr_tmul_apply'", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrthonormalBasis.toBasis_tensorProduct", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TensorProduct", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LinearMap.trace_eq_sum_inner", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Trace", "is_tactic_proof": true, "tactics": ["classical", "rw", "apply", "intro", "rw"], "tactic_count": 5}
{"name": "LinearMap.IsSymmetric.trace_eq_sum_eigenvalues", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Trace", "is_tactic_proof": true, "tactics": ["let", "rw", "apply", "intro", "rw", "simp"], "tactic_count": 6}
{"name": "LinearMap.IsSymmetric.re_trace_eq_sum_eigenvalues", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Trace", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "InnerProductSpace.trace_rankOne", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.Trace", "is_tactic_proof": false, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Orientation.definition._@.Mathlib.Analysis.InnerProductSpace.TwoDim.1773570744._hygCtx._hyg.2", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": true, "tactics": ["let", "let", "exact"], "tactic_count": 3}
{"name": "Orientation.wrapped._@.Mathlib.Analysis.InnerProductSpace.TwoDim.1773570744._hygCtx._hyg.2", "kind": "opaque", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.areaForm", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.areaForm_def", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": true, "tactics": ["intros", "delta", "rw", "rfl"], "tactic_count": 4}
{"name": "_private.Mathlib.Analysis.InnerProductSpace.TwoDim.0.Orientation.termω", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.InnerProductSpace.TwoDim.0.Orientation._aux_Mathlib_Analysis_InnerProductSpace_TwoDim___macroRules__private_Mathlib_Analysis_InnerProductSpace_TwoDim_0_Orientation_termω_1", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.areaForm_to_volumeForm", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Orientation.areaForm_apply_self", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp", "simp"], "tactic_count": 4}
{"name": "Orientation.areaForm_swap", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": true, "tactics": ["simp", "convert", "ext", "fin_cases", "simp"], "tactic_count": 5}
{"name": "Orientation.areaForm_neg_orientation", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Orientation.areaForm'", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.areaForm'_apply", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.abs_areaForm_le", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Orientation.areaForm_le", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Orientation.abs_areaForm_of_orthogonal", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": true, "tactics": ["rw", "simp", "intro", "fin_cases", "simp_all", "simpa", "simpa", "simp_all"], "tactic_count": 8}
{"name": "Orientation.areaForm_map", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": false, "tactics": ["have", "ext", "fin_cases", "simp"], "tactic_count": 4}
{"name": "Orientation.areaForm_comp_linearIsometryEquiv", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": true, "tactics": ["convert", "symm", "rwa", "rw", "simp", "simp"], "tactic_count": 6}
{"name": "Orientation.definition._@.Mathlib.Analysis.InnerProductSpace.TwoDim.2341759032._hygCtx._hyg.2", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.wrapped._@.Mathlib.Analysis.InnerProductSpace.TwoDim.2341759032._hygCtx._hyg.2", "kind": "opaque", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.rightAngleRotationAux₁", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.rightAngleRotationAux₁_def", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": true, "tactics": ["intros", "delta", "rw", "rfl"], "tactic_count": 4}
{"name": "Orientation.inner_rightAngleRotationAux₁_left", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": false, "tactics": ["simp", "rw", "norm_cast"], "tactic_count": 3}
{"name": "Orientation.inner_rightAngleRotationAux₁_right", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Orientation.rightAngleRotationAux₂", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.rightAngleRotationAux₁_rightAngleRotationAux₁", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": true, "tactics": ["apply", "intro", "have", "rw"], "tactic_count": 4}
{"name": "Orientation.definition._@.Mathlib.Analysis.InnerProductSpace.TwoDim.2712757639._hygCtx._hyg.2", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.wrapped._@.Mathlib.Analysis.InnerProductSpace.TwoDim.2712757639._hygCtx._hyg.2", "kind": "opaque", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.rightAngleRotation", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.rightAngleRotation_def", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": true, "tactics": ["intros", "delta", "rw", "rfl"], "tactic_count": 4}
{"name": "_private.Mathlib.Analysis.InnerProductSpace.TwoDim.0.Orientation.termJ", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.InnerProductSpace.TwoDim.0.Orientation._aux_Mathlib_Analysis_InnerProductSpace_TwoDim___macroRules__private_Mathlib_Analysis_InnerProductSpace_TwoDim_0_Orientation_termJ_1", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.inner_rightAngleRotation_left", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Orientation.inner_rightAngleRotation_right", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Orientation.rightAngleRotation_rightAngleRotation", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Orientation.rightAngleRotation_symm", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Orientation.inner_rightAngleRotation_self", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Orientation.inner_rightAngleRotation_swap", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Orientation.inner_rightAngleRotation_swap'", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Orientation.inner_comp_rightAngleRotation", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.areaForm_rightAngleRotation_left", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Orientation.areaForm_rightAngleRotation_right", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Orientation.areaForm_comp_rightAngleRotation", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Orientation.rightAngleRotation_trans_rightAngleRotation", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Orientation.rightAngleRotation_neg_orientation", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": true, "tactics": ["apply", "intro", "rw", "simp"], "tactic_count": 4}
{"name": "Orientation.rightAngleRotation_trans_neg_orientation", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.rightAngleRotation_map", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": true, "tactics": ["apply", "intro", "rw", "trans", "simp", "trans", "rw", "simp"], "tactic_count": 8}
{"name": "Orientation.linearIsometryEquiv_comp_rightAngleRotation", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": true, "tactics": ["convert", "simp", "symm", "rwa", "rw"], "tactic_count": 5}
{"name": "Orientation.rightAngleRotation_map'", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.linearIsometryEquiv_comp_rightAngleRotation'", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.basisRightAngleRotation", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.coe_basisRightAngleRotation", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.inner_mul_inner_add_areaForm_mul_areaForm'", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "apply", "intro", "fin_cases", "simp", "simp"], "tactic_count": 7}
{"name": "Orientation.inner_mul_inner_add_areaForm_mul_areaForm", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.inner_sq_add_areaForm_sq", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Orientation.inner_mul_areaForm_sub'", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "apply", "intro", "fin_cases", "simp", "simp"], "tactic_count": 7}
{"name": "Orientation.inner_mul_areaForm_sub", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.nonneg_inner_and_areaForm_eq_zero_iff_sameRay", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "constructor", "let", "let", "suffices", "rw", "simp", "inner_add_right,", "zero_add,", "exact", "rintro", "have", "have", "have", "exact", "intro", "obtain", "simp", "and_true]", "positivity"], "tactic_count": 21}
{"name": "Orientation.kahler", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.kahler_apply_apply", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.kahler_swap", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": true, "tactics": ["simp", "rw", "simp"], "tactic_count": 3}
{"name": "Orientation.kahler_apply_self", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Orientation.kahler_rightAngleRotation_left", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": false, "tactics": ["simp", "linear_combination"], "tactic_count": 2}
{"name": "Orientation.kahler_rightAngleRotation_right", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": false, "tactics": ["simp", "linear_combination"], "tactic_count": 2}
{"name": "Orientation.kahler_comp_rightAngleRotation", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": true, "tactics": ["simp", "linear_combination"], "tactic_count": 2}
{"name": "Orientation.kahler_comp_rightAngleRotation'", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": true, "tactics": ["linear_combination"], "tactic_count": 1}
{"name": "Orientation.kahler_neg_orientation", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Orientation.kahler_mul", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": true, "tactics": ["trans", "apply", "simp", "rw", "linear_combination", "simp", "rw", "linear_combination", "norm_cast"], "tactic_count": 9}
{"name": "Orientation.normSq_kahler", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Orientation.norm_kahler", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": true, "tactics": ["rw", "linear_combination", "positivity", "positivity"], "tactic_count": 4}
{"name": "Orientation.eq_zero_or_eq_zero_of_kahler_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": true, "tactics": ["have", "rcases", "left", "simpa", "right", "simpa"], "tactic_count": 6}
{"name": "Orientation.kahler_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": true, "tactics": ["refine", "rintro"], "tactic_count": 2}
{"name": "Orientation.kahler_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": true, "tactics": ["apply", "tauto"], "tactic_count": 2}
{"name": "Orientation.kahler_ne_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": true, "tactics": ["refine", "contrapose", "simp", "rintro"], "tactic_count": 4}
{"name": "Orientation.kahler_map", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Orientation.kahler_comp_linearIsometryEquiv", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.areaForm", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": true, "tactics": ["let", "simp", "ring"], "tactic_count": 3}
{"name": "Complex.rightAngleRotation", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": true, "tactics": ["apply", "intro", "rw", "simp", "ring"], "tactic_count": 5}
{"name": "Complex.kahler", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "_private.Mathlib.Analysis.InnerProductSpace.TwoDim.0.Orientation.termω_1", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.InnerProductSpace.TwoDim.0.Orientation._aux_Mathlib_Analysis_InnerProductSpace_TwoDim___macroRules__private_Mathlib_Analysis_InnerProductSpace_TwoDim_0_Orientation_termω_1_1", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.InnerProductSpace.TwoDim.0.Orientation.termJ_1", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.InnerProductSpace.TwoDim.0.Orientation._aux_Mathlib_Analysis_InnerProductSpace_TwoDim___macroRules__private_Mathlib_Analysis_InnerProductSpace_TwoDim_0_Orientation_termJ_1_1", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.areaForm_map_complex", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": true, "tactics": ["rw", "iterate"], "tactic_count": 2}
{"name": "Orientation.rightAngleRotation_map_complex", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Orientation.kahler_map_complex", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.TwoDim", "is_tactic_proof": true, "tactics": ["rw", "iterate"], "tactic_count": 2}
{"name": "ContinuousLinearMapWOT.ext_inner", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.WeakOperatorTopology", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ContinuousLinearMapWOT.tendsto_iff_forall_inner_apply_tendsto", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.WeakOperatorTopology", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "ContinuousLinearMapWOT.le_nhds_iff_forall_inner_apply_le_nhds", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.WeakOperatorTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.InnerProductSpace.l2Space.0.term⟪_,_⟫", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.l2Space", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.InnerProductSpace.l2Space.0._aux_Mathlib_Analysis_InnerProductSpace_l2Space___macroRules__private_Mathlib_Analysis_InnerProductSpace_l2Space_0_term⟪_,_⟫_1", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.l2Space", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.InnerProductSpace.l2Space.0._aux_Mathlib_Analysis_InnerProductSpace_l2Space___unexpand_Inner_inner_1", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.l2Space", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "termℓ²(_,_)", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.l2Space", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Analysis_InnerProductSpace_l2Space___macroRules_termℓ²(_,_)_1", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.l2Space", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Analysis_InnerProductSpace_l2Space___unexpand_lp_1", "kind": "definition", "module": "Mathlib.Analysis.InnerProductSpace.l2Space", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lp.summable_inner", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.l2Space", "is_tactic_proof": true, "tactics": ["refine", "rw", "intro", "exact"], "tactic_count": 4}
{"name": "lp.instInnerProductSpace", "kind": "instance", "module": "Mathlib.Analysis.InnerProductSpace.l2Space", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lp.inner_eq_tsum", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.l2Space", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lp.hasSum_inner", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.l2Space", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lp.inner_single_left", "kind": "theorem", "module": "Mathlib.Analysis.InnerProductSpace.l2Space", "is_tactic_proof": true, "tactics": ["refine", "simp_rw", "convert", "ext", "split_ifs", "subst", "simp"], "tactic_count": 7}
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{"name": "absConvexHull_eq_self", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.AbsConvex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "absConvex_closed_sInter", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.AbsConvex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "closedAbsConvexHull", "kind": "definition", "module": "Mathlib.Analysis.LocallyConvex.AbsConvex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "absConvex_convexClosedHull", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.AbsConvex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosed_closedAbsConvexHull", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.AbsConvex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "subset_closedAbsConvexHull", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.AbsConvex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "closure_subset_closedAbsConvexHull", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.AbsConvex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "closedAbsConvexHull_min", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.AbsConvex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "absConvexHull_subset_closedAbsConvexHull", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.AbsConvex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "closedAbsConvexHull_closure_eq_closedAbsConvexHull", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.AbsConvex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AbsConvex.closure", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.AbsConvex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "closedAbsConvexHull_eq_closure_absConvexHull", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.AbsConvex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhds_hasBasis_absConvex", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.AbsConvex", "is_tactic_proof": false, "tactics": ["refine", "refine", "refine", "refine", "exact"], "tactic_count": 5}
{"name": "nhds_hasBasis_absConvex_open", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.AbsConvex", "is_tactic_proof": true, "tactics": ["refine", "rintro", "refine", "exact", "hs_balanced.interior", "rintro", "exact"], "tactic_count": 7}
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{"name": "absConvexHull_eq_convexHull_balancedHull", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.AbsConvex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "balancedHull_convexHull_subseteq_absConvexHull", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.AbsConvex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "balancedHull_subset_convexHull_union_neg", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.AbsConvex", "is_tactic_proof": true, "tactics": ["intro", "obtain", "apply", "have", "have", "refine", "rw", "ring_nf"], "tactic_count": 8}
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{"name": "totallyBounded_absConvexHull", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.AbsConvex", "is_tactic_proof": true, "tactics": ["rw", "apply", "rw", "exact"], "tactic_count": 4}
{"name": "zero_mem_absConvexHull", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.AbsConvex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCompact_closedAbsConvexHull_of_totallyBounded", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.AbsConvex", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "AbsConvexOpenSets", "kind": "definition", "module": "Mathlib.Analysis.LocallyConvex.AbsConvexOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AbsConvexOpenSets.coe_zero_mem", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.AbsConvexOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AbsConvexOpenSets.coe_isOpen", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.AbsConvexOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Bornology.IsVonNBounded.of_sub_left", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Bornology.isVonNBounded_sub_of_nonempty", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.Bounded", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Bornology.isVonNBounded_sub", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.Bounded", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Bornology.sUnion_isVonNBounded_eq_univ", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.vonNBornology", "kind": "abbrev", "module": "Mathlib.Analysis.LocallyConvex.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.isBounded_iff_isVonNBounded", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TotallyBounded.isVonNBounded", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.Bounded", "is_tactic_proof": true, "tactics": ["letI", "rw", "intro", "have", "have", "simp_rw", "rcases", "rcases", "refine", "rw", "have", "refine", "exact", "haveI", "exact"], "tactic_count": 15}
{"name": "Filter.Tendsto.isVonNBounded_range", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.IsVonNBounded.restrict_scalars_of_nontrivial", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.Bounded", "is_tactic_proof": true, "tactics": ["intro", "refine", "refine", "rw", "mul_div_cancel_right₀"], "tactic_count": 5}
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{"name": "NormedSpace.isVonNBounded_of_isBounded", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.Bounded", "is_tactic_proof": true, "tactics": ["rcases", "rw", "rw", "exact"], "tactic_count": 4}
{"name": "NormedSpace.isVonNBounded_ball", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedSpace.isVonNBounded_closedBall", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedSpace.isVonNBounded_iff", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.Bounded", "is_tactic_proof": true, "tactics": ["refine", "rcases", "rcases", "specialize", "rw", "exact"], "tactic_count": 6}
{"name": "NormedSpace.isVonNBounded_iff'", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.Bounded", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NormedSpace.image_isVonNBounded_iff", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.Bounded", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "NormedSpace.vonNBornology_eq", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.Bounded", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "exact"], "tactic_count": 4}
{"name": "NormedSpace.isBounded_iff_subset_smul_ball", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.Bounded", "is_tactic_proof": true, "tactics": ["rw", "constructor", "intro", "rcases", "rcases", "exact", "rintro", "exact"], "tactic_count": 8}
{"name": "NormedSpace.isBounded_iff_subset_smul_closedBall", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.Bounded", "is_tactic_proof": true, "tactics": ["constructor", "rw", "exact", "rw", "rintro", "exact"], "tactic_count": 6}
{"name": "instQuasiCompleteSpaceOfCompleteSpace", "kind": "instance", "module": "Mathlib.Analysis.LocallyConvex.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCompact_closure_of_totallyBounded_quasiComplete", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.clmOfExistsBoundedImage", "kind": "definition", "module": "Mathlib.Analysis.LocallyConvex.ContinuousOfBounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.clmOfExistsBoundedImage_coe", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.ContinuousOfBounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.clmOfExistsBoundedImage_apply", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.ContinuousOfBounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.continuousAt_zero_of_locally_bounded", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.ContinuousOfBounded", "is_tactic_proof": true, "tactics": ["obtain", "have", "rcases", "simp", "have", "refine", "intro", "use", "exact", "intro", "simpa", "simp_rw", "by_contra", "rcases", "choose", "have", "apply", "intro", "simpa", "have", "specialize", "simp", "have", "have", "have", "exact", "this.congr", "simp", "refine", "filter_upwards"], "tactic_count": 30}
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{"name": "MontelSpace.isCompact_of_isClosed_of_isVonNBounded", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.Montel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MontelSpace.finiteDimensional_of_normedSpace", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.Montel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.LocallyConvex.Montel.0.LinearEquiv.toCompactConvergenceCLM", "kind": "definition", "module": "Mathlib.Analysis.LocallyConvex.Montel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.toCompactConvergenceCLM", "kind": "definition", "module": "Mathlib.Analysis.LocallyConvex.Montel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.toCompactConvergenceCLM_apply", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.Montel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.toCompactConvergenceCLM_symm_apply", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.Montel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PointwiseConvergenceCLM.seminorm", "kind": "definition", "module": "Mathlib.Analysis.LocallyConvex.PointwiseConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PointwiseConvergenceCLM.seminormFamily", "kind": "abbrev", "module": "Mathlib.Analysis.LocallyConvex.PointwiseConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PointwiseConvergenceCLM.inducingFn", "kind": "definition", "module": "Mathlib.Analysis.LocallyConvex.PointwiseConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PointwiseConvergenceCLM.isInducing_inducingFn", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.PointwiseConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PointwiseConvergenceCLM.withSeminorms", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.PointwiseConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "PointwiseConvergenceCLM.tendsto_nhds_atTop", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.PointwiseConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LinearMap.polar", "kind": "definition", "module": "Mathlib.Analysis.LocallyConvex.Polar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.polar_mem_iff", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.Polar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LinearMap.polar_eq_biInter_preimage", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.Polar", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "LinearMap.polar_isClosed", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.Polar", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "LinearMap.zero_mem_polar", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.Polar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.polar_nonempty", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.Polar", "is_tactic_proof": true, "tactics": ["use", "exact"], "tactic_count": 2}
{"name": "LinearMap.polar_eq_iInter", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.Polar", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
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{"name": "LinearMap.polar_iUnion", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.Polar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.polar_union", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.Polar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.polar_antitone", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.Polar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.polar_empty", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.Polar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.polar_singleton", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.Polar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LinearMap.polar_zero", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.Polar", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LinearMap.subset_bipolar", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.Polar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.tripolar_eq_polar", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.Polar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LinearMap.polar_subMulAction", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.Polar", "is_tactic_proof": true, "tactics": ["ext", "constructor", "intro", "obtain", "contrapose", "rw", "simpa", "intro", "simp"], "tactic_count": 9}
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{"name": "StrongDual.dualPairing_separatingLeft", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.Polar", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
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{"name": "StrongDual.mem_polar_iff", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.Polar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrongDual.polarSubmodule_eq_setOf", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.Polar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrongDual.mem_polarSubmodule", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.Polar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrongDual.zero_mem_polar", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.Polar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrongDual.polar_nonempty", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.Polar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "StrongDual.polar_univ", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.Polar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "WithSeminorms.firstCountableTopology", "kind": "theorem", "module": "Mathlib.Analysis.LocallyConvex.WithSeminorms", "is_tactic_proof": true, "tactics": ["have", "let", "have", "have", "rw", "exact", "have", "exact"], "tactic_count": 8}
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{"name": "Matrix.linfty_opNNNorm_diagonal", "kind": "theorem", "module": "Mathlib.Analysis.Matrix.Normed", "is_tactic_proof": true, "tactics": ["rw", "congr", "refine", "rw", "rw"], "tactic_count": 5}
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{"name": "Matrix.linfty_opNNNorm_mul", "kind": "theorem", "module": "Mathlib.Analysis.Matrix.Normed", "is_tactic_proof": true, "tactics": ["simp_rw", "calc", "refine", "gcongr", "exact", "simp_rw", "rfl"], "tactic_count": 7}
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{"name": "Matrix.linfty_opNNNorm_mulVec", "kind": "theorem", "module": "Mathlib.Analysis.Matrix.Normed", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Matrix.linfty_opNorm_mulVec", "kind": "theorem", "module": "Mathlib.Analysis.Matrix.Normed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.linftyOpNonUnitalSemiNormedRing", "kind": "definition", "module": "Mathlib.Analysis.Matrix.Normed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.linfty_opNormOneClass", "kind": "instance", "module": "Mathlib.Analysis.Matrix.Normed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "_private.Mathlib.Analysis.Matrix.Order.0.Matrix.PosSemidef.matrixPreInnerProductSpace", "kind": "abbrev", "module": "Mathlib.Analysis.Matrix.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Matrix.PosSemidef.re_dotProduct_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Matrix.PosDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Matrix.PosSemidef.trace_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.Matrix.PosDef", "is_tactic_proof": true, "tactics": ["classical", "conv_lhs", "rw", "simp"], "tactic_count": 4}
{"name": "Matrix.eigenvalues_conjTranspose_mul_self_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Matrix.PosDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.eigenvalues_self_mul_conjTranspose_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Matrix.PosDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Matrix.PosDef.re_dotProduct_pos", "kind": "theorem", "module": "Mathlib.Analysis.Matrix.PosDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.PosDef.eigenvalues_pos", "kind": "theorem", "module": "Mathlib.Analysis.Matrix.PosDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Matrix.toSeminormedAddCommGroup", "kind": "abbrev", "module": "Mathlib.Analysis.Matrix.PosDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.toNormedAddCommGroup", "kind": "abbrev", "module": "Mathlib.Analysis.Matrix.PosDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Matrix.finite_real_spectrum", "kind": "theorem", "module": "Mathlib.Analysis.Matrix.Spectrum", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Matrix.instFiniteElemRealSpectrum", "kind": "instance", "module": "Mathlib.Analysis.Matrix.Spectrum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.spectrum_toLpLin", "kind": "theorem", "module": "Mathlib.Analysis.Matrix.Spectrum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.spectrum_toEuclideanLin", "kind": "theorem", "module": "Mathlib.Analysis.Matrix.Spectrum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.IsHermitian.eigenvalues₀", "kind": "definition", "module": "Mathlib.Analysis.Matrix.Spectrum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.IsHermitian.eigenvalues₀_antitone", "kind": "theorem", "module": "Mathlib.Analysis.Matrix.Spectrum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.IsHermitian.eigenvalues", "kind": "definition", "module": "Mathlib.Analysis.Matrix.Spectrum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.IsHermitian.eigenvectorBasis", "kind": "definition", "module": "Mathlib.Analysis.Matrix.Spectrum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.IsHermitian.mulVec_eigenvectorBasis", "kind": "theorem", "module": "Mathlib.Analysis.Matrix.Spectrum", "is_tactic_proof": true, "tactics": ["simpa", "congr"], "tactic_count": 2}
{"name": "Matrix.IsHermitian.eigenvalues_mem_spectrum_real", "kind": "theorem", "module": "Mathlib.Analysis.Matrix.Spectrum", "is_tactic_proof": true, "tactics": ["apply", "rw", "exact"], "tactic_count": 3}
{"name": "Matrix.IsHermitian.eigenvectorUnitary", "kind": "definition", "module": "Mathlib.Analysis.Matrix.Spectrum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.IsHermitian.eigenvectorUnitary_coe", "kind": "theorem", "module": "Mathlib.Analysis.Matrix.Spectrum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.IsHermitian.eigenvectorUnitary_transpose_apply", "kind": "theorem", "module": "Mathlib.Analysis.Matrix.Spectrum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.IsHermitian.eigenvectorUnitary_col_eq", "kind": "theorem", "module": "Mathlib.Analysis.Matrix.Spectrum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.IsHermitian.eigenvectorUnitary_apply", "kind": "theorem", "module": "Mathlib.Analysis.Matrix.Spectrum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.IsHermitian.eigenvectorUnitary_mulVec", "kind": "theorem", "module": "Mathlib.Analysis.Matrix.Spectrum", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Matrix.IsHermitian.star_eigenvectorUnitary_mulVec", "kind": "theorem", "module": "Mathlib.Analysis.Matrix.Spectrum", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matrix.IsHermitian.conjStarAlgAut_star_eigenvectorUnitary", "kind": "theorem", "module": "Mathlib.Analysis.Matrix.Spectrum", "is_tactic_proof": true, "tactics": ["apply", "simp", "apply", "simp"], "tactic_count": 4}
{"name": "Matrix.IsHermitian.spectral_theorem", "kind": "theorem", "module": "Mathlib.Analysis.Matrix.Spectrum", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Matrix.IsHermitian.eigenvalues_eq", "kind": "theorem", "module": "Mathlib.Analysis.Matrix.Spectrum", "is_tactic_proof": true, "tactics": ["rw", "simp", "inner_self_eq_norm_sq_to_K,", "one_pow,"], "tactic_count": 4}
{"name": "Matrix.IsHermitian.charpoly_eq", "kind": "theorem", "module": "Mathlib.Analysis.Matrix.Spectrum", "is_tactic_proof": true, "tactics": ["conv_lhs", "simp"], "tactic_count": 2}
{"name": "Matrix.IsHermitian.roots_charpoly_eq_eigenvalues", "kind": "theorem", "module": "Mathlib.Analysis.Matrix.Spectrum", "is_tactic_proof": true, "tactics": ["rw", "simp", "simp"], "tactic_count": 3}
{"name": "Matrix.IsHermitian.roots_charpoly_eq_eigenvalues₀", "kind": "theorem", "module": "Mathlib.Analysis.Matrix.Spectrum", "is_tactic_proof": true, "tactics": ["rw", "simp", "simp"], "tactic_count": 3}
{"name": "Matrix.IsHermitian.sort_roots_charpoly_eq_eigenvalues₀", "kind": "theorem", "module": "Mathlib.Analysis.Matrix.Spectrum", "is_tactic_proof": false, "tactics": ["simp_rw", "apply", "simp_rw", "exact"], "tactic_count": 4}
{"name": "Matrix.IsHermitian.eigenvalues_eq_eigenvalues_iff", "kind": "theorem", "module": "Mathlib.Analysis.Matrix.Spectrum", "is_tactic_proof": true, "tactics": ["constructor", "rw", "suffices", "simp_rw"], "tactic_count": 4}
{"name": "Matrix.IsHermitian.splits_charpoly", "kind": "theorem", "module": "Mathlib.Analysis.Matrix.Spectrum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.IsHermitian.det_eq_prod_eigenvalues", "kind": "theorem", "module": "Mathlib.Analysis.Matrix.Spectrum", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.IsHermitian.rank_eq_rank_diagonal", "kind": "theorem", "module": "Mathlib.Analysis.Matrix.Spectrum", "is_tactic_proof": true, "tactics": ["conv_lhs", "simp"], "tactic_count": 2}
{"name": "Matrix.IsHermitian.rank_eq_card_non_zero_eigs", "kind": "theorem", "module": "Mathlib.Analysis.Matrix.Spectrum", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matrix.IsHermitian.spectrum_eq_image_range", "kind": "theorem", "module": "Mathlib.Analysis.Matrix.Spectrum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.IsHermitian.spectrum_real_eq_range_eigenvalues", "kind": "theorem", "module": "Mathlib.Analysis.Matrix.Spectrum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.IsHermitian.eigenvalues_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.Matrix.Spectrum", "is_tactic_proof": true, "tactics": ["refine", "rw", "map_zero]"], "tactic_count": 3}
{"name": "Matrix.IsHermitian.exists_eigenvector_of_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.Matrix.Spectrum", "is_tactic_proof": true, "tactics": ["classical", "have", "contrapose", "have", "rwa", "map_zero]", "obtain", "exact"], "tactic_count": 8}
{"name": "Matrix.IsHermitian.trace_eq_sum_eigenvalues", "kind": "theorem", "module": "Mathlib.Analysis.Matrix.Spectrum", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.geom_mean_le_arith_mean_weighted", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalities", "is_tactic_proof": true, "tactics": ["by_cases", "rcases", "rw", "exact", "rw", "exact", "have", "simp", "convert", "rcases", "simp", "exact", "rcases", "simp", "rw"], "tactic_count": 15}
{"name": "Real.geom_mean_le_arith_mean", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalities", "is_tactic_proof": true, "tactics": ["convert", "rw", "refine", "rw", "simp_rw", "exact", "simp_rw", "exact"], "tactic_count": 8}
{"name": "Real.geom_mean_weighted_of_constant", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalities", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.arith_mean_weighted_of_constant", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalities", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.geom_mean_eq_arith_mean_weighted_of_constant", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalities", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.geom_mean_eq_arith_mean_weighted_iff'", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalities", "is_tactic_proof": true, "tactics": ["by_cases", "rcases", "rw", "constructor", "intro", "rw", "intro", "apply", "apply", "exact", "intro", "convert", "exact", "rw", "exact", "have", "have", "simp", "convert", "apply", "simp", "constructor", "rw", "apply", "intro", "simp", "rw", "apply", "intro", "simp"], "tactic_count": 30}
{"name": "Real.geom_mean_eq_arith_mean_weighted_iff", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalities", "is_tactic_proof": true, "tactics": ["have", "have", "by_contra", "simp", "rw", "simp", "simp", "rwa", "simp_all"], "tactic_count": 9}
{"name": "Real.geom_mean_lt_arith_mean_weighted_iff_of_pos", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalities", "is_tactic_proof": true, "tactics": ["constructor", "intro", "by_contra", "rw", "exact", "intro", "rw", "apply", "rintro", "have", "by_contra", "apply", "apply", "simp"], "tactic_count": 14}
{"name": "NNReal.geom_mean_le_arith_mean_weighted", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalities", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.geom_mean_le_arith_mean2_weighted", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalities", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "NNReal.geom_mean_le_arith_mean3_weighted", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalities", "is_tactic_proof": true, "tactics": ["simpa", "geom_mean_le_arith_mean_weighted"], "tactic_count": 2}
{"name": "NNReal.geom_mean_le_arith_mean4_weighted", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalities", "is_tactic_proof": true, "tactics": ["simpa", "geom_mean_le_arith_mean_weighted"], "tactic_count": 2}
{"name": "Real.geom_mean_le_arith_mean2_weighted", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalities", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.geom_mean_le_arith_mean3_weighted", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalities", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.geom_mean_le_arith_mean4_weighted", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalities", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.harm_mean_le_geom_mean_weighted", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalities", "is_tactic_proof": false, "tactics": ["have", "geom_mean_le_arith_mean_weighted", "have", "have", "norm_num", "rw", "apply", "have", "rw", "gcongr", "exact", "rw"], "tactic_count": 12}
{"name": "Real.harm_mean_le_geom_mean", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalities", "is_tactic_proof": true, "tactics": ["have", "simp", "set", "nth_rw", "simp_rw", "convert", "rw", "refine", "rw", "exact", "simp_rw", "exact"], "tactic_count": 12}
{"name": "Real.young_inequality_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalities", "is_tactic_proof": true, "tactics": ["simpa", "geom_mean_le_arith_mean2_weighted", "hpq.inv_add_inv_eq_one"], "tactic_count": 3}
{"name": "Real.young_inequality", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalities", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.young_inequality", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalities", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.young_inequality_real", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalities", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ENNReal.young_inequality", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalities", "is_tactic_proof": true, "tactics": ["by_cases", "refine", "repeat", "rcases", "simp", "rw", "coe_rpow_of_nonneg", "coe_add,", "exact"], "tactic_count": 9}
{"name": "_private.Mathlib.Analysis.MeanInequalities.0.NNReal.inner_le_Lp_mul_Lp_of_norm_le_one", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalities", "is_tactic_proof": true, "tactics": ["have", "have", "calc", "rw", "refine"], "tactic_count": 5}
{"name": "_private.Mathlib.Analysis.MeanInequalities.0.NNReal.inner_le_Lp_mul_Lp_of_norm_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalities", "is_tactic_proof": false, "tactics": ["simp", "le_zero_iff,", "intro", "left", "rw", "exact"], "tactic_count": 6}
{"name": "NNReal.inner_le_Lp_mul_Lq", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalities", "is_tactic_proof": true, "tactics": ["obtain", "exact", "obtain", "calc", "congr", "rw", "let", "let", "suffices", "simp_rw", "rwa", "exact", "refine", "simp_rw", "simp_rw"], "tactic_count": 15}
{"name": "NNReal.inner_le_weight_mul_Lp", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalities", "is_tactic_proof": true, "tactics": ["obtain", "simp", "calc", "congr", "rw", "simp", "have", "have", "simp"], "tactic_count": 9}
{"name": "NNReal.inner_le_Lp_mul_Lq_tsum", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalities", "is_tactic_proof": false, "tactics": ["have", "intro", "refine", "rw", "exact", "rw", "exact", "have", "refine", "rintro", "exact", "have", "exact"], "tactic_count": 13}
{"name": "NNReal.summable_mul_of_Lp_Lq", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalities", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.inner_le_Lp_mul_Lq_tsum'", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalities", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.inner_le_Lp_mul_Lq_hasSum", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalities", "is_tactic_proof": true, "tactics": ["obtain", "have", "have", "refine", "simpa", "simpa"], "tactic_count": 6}
{"name": "NNReal.rpow_sum_le_const_mul_sum_rpow", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalities", "is_tactic_proof": true, "tactics": ["rcases", "simp", "let", "have", "have", "have", "rw", "ring", "simpa"], "tactic_count": 9}
{"name": "NNReal.isGreatest_Lp", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalities", "is_tactic_proof": true, "tactics": ["constructor", "use", "obtain", "simp", "have", "have", "refine", "simp", "simp", "div_le_iff₀", "rw", "simpa", "rintro", "apply", "simpa"], "tactic_count": 15}
{"name": "NNReal.Lp_add_le", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalities", "is_tactic_proof": true, "tactics": ["rcases", "simp", "have", "have", "simp", "rcases", "rw", "exact"], "tactic_count": 8}
{"name": "NNReal.Lp_add_le_tsum", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalities", "is_tactic_proof": true, "tactics": ["have", "have", "intro", "rw", "refine", "refine", "exacts", "have", "refine", "rintro", "exact", "have", "refine", "rw", "exact"], "tactic_count": 15}
{"name": "NNReal.summable_Lp_add", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalities", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.Lp_add_le_tsum'", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalities", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.Lp_add_le_hasSum", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalities", "is_tactic_proof": true, "tactics": ["have", "obtain", "have", "have", "refine", "simpa", "simpa"], "tactic_count": 7}
{"name": "Real.inner_le_Lp_mul_Lq", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalities", "is_tactic_proof": false, "tactics": ["have", "push_cast", "refine", "simp"], "tactic_count": 4}
{"name": "Real.rpow_sum_le_const_mul_sum_rpow", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalities", "is_tactic_proof": true, "tactics": ["have", "push_cast", "exact"], "tactic_count": 3}
{"name": "Real.Lp_add_le", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalities", "is_tactic_proof": false, "tactics": ["have", "push_cast", "refine", "simp"], "tactic_count": 4}
{"name": "Real.inner_le_Lp_mul_Lq_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalities", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "Real.inner_le_weight_mul_Lp_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalities", "is_tactic_proof": true, "tactics": ["lift", "lift", "beta_reduce", "norm_cast", "exact"], "tactic_count": 5}
{"name": "Real.compact_inner_le_weight_mul_Lp_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalities", "is_tactic_proof": true, "tactics": ["simp_rw", "rw", "gcongr", "exact", "any_goals", "exact", "exact"], "tactic_count": 7}
{"name": "Real.inner_le_Lp_mul_Lq_tsum_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalities", "is_tactic_proof": true, "tactics": ["lift", "lift", "beta_reduce", "norm_cast", "exact"], "tactic_count": 5}
{"name": "Real.summable_mul_of_Lp_Lq_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalities", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.inner_le_Lp_mul_Lq_tsum_of_nonneg'", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalities", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.inner_le_Lp_mul_Lq_hasSum_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalities", "is_tactic_proof": true, "tactics": ["lift", "lift", "lift", "lift", "beta_reduce", "norm_cast", "obtain", "refine", "norm_cast"], "tactic_count": 9}
{"name": "Real.rpow_sum_le_const_mul_sum_rpow_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalities", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "Real.Lp_add_le_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalities", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "Real.Lp_add_le_tsum_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalities", "is_tactic_proof": true, "tactics": ["lift", "lift", "beta_reduce", "norm_cast0", "exact"], "tactic_count": 5}
{"name": "Real.summable_Lp_add_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalities", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.Lp_add_le_tsum_of_nonneg'", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalities", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.Lp_add_le_hasSum_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalities", "is_tactic_proof": true, "tactics": ["lift", "lift", "lift", "lift", "beta_reduce", "norm_cast", "obtain", "use", "beta_reduce", "norm_cast", "exact"], "tactic_count": 11}
{"name": "ENNReal.inner_le_Lp_mul_Lq", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalities", "is_tactic_proof": true, "tactics": ["by_cases", "replace", "simpa", "sum_eq_zero_iff_of_nonneg]", "have", "simp", "by_cases", "rcases", "replace", "simpa", "not_or]", "have", "simp", "convert", "refine", "simp"], "tactic_count": 16}
{"name": "ENNReal.inner_le_weight_mul_Lp_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalities", "is_tactic_proof": true, "tactics": ["obtain", "simp", "have", "have", "by_cases", "replace", "simpa", "have", "simp", "by_cases", "rcases", "replace", "simpa", "have", "coe_le_coe.2", "rw", "simp_rw", "sum_congr", "simp", "convert", "obtain", "simp", "rw", "simpa", "convert", "exact"], "tactic_count": 26}
{"name": "ENNReal.rpow_sum_le_const_mul_sum_rpow", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalities", "is_tactic_proof": true, "tactics": ["rcases", "simp", "let", "have", "have", "have", "rw", "ring", "simpa", "rpow_one,"], "tactic_count": 10}
{"name": "ENNReal.Lp_add_le", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalities", "is_tactic_proof": true, "tactics": ["by_cases", "rcases", "have", "replace", "simpa", "have", "push_cast", "convert", "refine", "simp"], "tactic_count": 10}
{"name": "Real.pow_arith_mean_le_arith_mean_pow", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalitiesPow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.pow_arith_mean_le_arith_mean_pow_of_even", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalitiesPow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.zpow_arith_mean_le_arith_mean_zpow", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalitiesPow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.rpow_arith_mean_le_arith_mean_rpow", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalitiesPow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.arith_mean_le_rpow_mean", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalitiesPow", "is_tactic_proof": true, "tactics": ["have", "rw", "exact", "all_goals", "apply_rules", "intro", "apply_rules"], "tactic_count": 7}
{"name": "NNReal.pow_arith_mean_le_arith_mean_pow", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalitiesPow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.rpow_arith_mean_le_arith_mean_rpow", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalitiesPow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.rpow_arith_mean_le_arith_mean2_rpow", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalitiesPow", "is_tactic_proof": true, "tactics": ["have", "simpa", "simp"], "tactic_count": 3}
{"name": "NNReal.rpow_add_le_mul_rpow_add_rpow", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalitiesPow", "is_tactic_proof": true, "tactics": ["rcases", "simp", "convert", "simp", "have", "simp", "ring"], "tactic_count": 7}
{"name": "NNReal.arith_mean_le_rpow_mean", "kind": "theorem", "module": "Mathlib.Analysis.MeanInequalitiesPow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "mellinInv_eq_fourierInv", "kind": "theorem", "module": "Mathlib.Analysis.MellinInversion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MellinConvergent.const_smul", "kind": "theorem", "module": "Mathlib.Analysis.MellinTransform", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
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{"name": "MellinConvergent.div_const", "kind": "theorem", "module": "Mathlib.Analysis.MellinTransform", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
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{"name": "MeromorphicAt.meromorphicAt_add_iff_meromorphicAt₂", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeromorphicAt.meromorphicAt_sub_iff_meromorphicAt₁", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Basic", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "MeromorphicAt.meromorphicAt_sub_iff_meromorphicAt₂", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Basic", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
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{"name": "MeromorphicAt.update_iff", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeromorphicAt.update", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeromorphicAt.div", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeromorphicAt.zpow", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Basic", "is_tactic_proof": true, "tactics": ["cases", "ofNat", "negSucc"], "tactic_count": 3}
{"name": "MeromorphicAt.eventually_continuousAt", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Basic", "is_tactic_proof": true, "tactics": ["obtain", "have", "filter_upwards", "simp", "have", "apply", "filter_upwards", "simp"], "tactic_count": 8}
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{"name": "MeromorphicAt.iff_eventuallyEq_zpow_smul_analyticAt", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Basic", "is_tactic_proof": true, "tactics": ["refine", "filter_upwards", "match_scalars", "simp", "refine", "exact"], "tactic_count": 6}
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{"name": "meromorphicAt_comp_iff_of_deriv_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Basic", "is_tactic_proof": true, "tactics": ["refine", "let", "have", "have", "rw", "refine", "exact"], "tactic_count": 7}
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{"name": "AnalyticOnNhd.meromorphicOn", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeromorphicOn.congr_codiscreteWithin_of_eqOn_compl", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Basic", "is_tactic_proof": true, "tactics": ["intro", "apply", "simp_rw", "filter_upwards", "simp", "tauto"], "tactic_count": 6}
{"name": "MeromorphicOn.congr_codiscreteWithin", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Basic", "is_tactic_proof": true, "tactics": ["intro", "apply", "simp_rw", "have", "apply", "use", "filter_upwards", "simp", "tauto"], "tactic_count": 9}
{"name": "meromorphicOn_congr_codiscreteWithin", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeromorphicOn.id", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeromorphicOn.const", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeromorphicOn.mono_set", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeromorphicOn.add", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeromorphicOn.sub", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeromorphicOn.neg", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeromorphicOn.neg_iff", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeromorphicOn.smul", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeromorphicOn.mul", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeromorphicOn.prod", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeromorphicOn.fun_prod", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeromorphicOn.sum", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeromorphicOn.fun_sum", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeromorphicOn.inv", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeromorphicOn.inv_iff", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeromorphicOn.div", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeromorphicOn.pow", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeromorphicOn.zpow", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeromorphicOn.deriv", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeromorphicOn.fun_deriv", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeromorphicOn.iterated_deriv", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeromorphicOn.fun_iterated_deriv", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeromorphicOn.congr", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Basic", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "MeromorphicOn.eventually_codiscreteWithin_analyticAt", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Basic", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "apply", "intro", "simp"], "tactic_count": 6}
{"name": "MeromorphicOn.countable_compl_analyticAt_inter", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Basic", "is_tactic_proof": true, "tactics": ["apply", "simpa"], "tactic_count": 2}
{"name": "Meromorphic", "kind": "definition", "module": "Mathlib.Analysis.Meromorphic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "meromorphicOn_univ", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Basic", "is_tactic_proof": true, "tactics": ["tauto"], "tactic_count": 1}
{"name": "Meromorphic.meromorphicAt", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Meromorphic.meromorphicOn", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Meromorphic.const", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Meromorphic.neg", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Meromorphic.add", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Meromorphic.sum", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Meromorphic.sub", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Meromorphic.smul", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Meromorphic.mul", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Meromorphic.inv", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Meromorphic.prod", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Meromorphic.div", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Meromorphic.pow", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Meromorphic.zpow", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Meromorphic.deriv", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Meromorphic.iterated_deriv", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Meromorphic.congr_codiscrete", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "meromorphic_congr_codiscrete", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Meromorphic.countable_compl_analyticAt", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Meromorphic.measurable", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Basic", "is_tactic_proof": true, "tactics": ["set", "have", "have", "have", "have", "exact", "h₃.restrict.measurable"], "tactic_count": 7}
{"name": "MeromorphicNFOn.Gamma", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Meromorphic.Gamma", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeromorphicOn.Gamma", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeromorphicOn.divisor", "kind": "definition", "module": "Mathlib.Analysis.Meromorphic.Divisor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeromorphicOn.divisor_def", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Divisor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeromorphicOn.divisor_apply", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Divisor", "is_tactic_proof": true, "tactics": ["simp_all"], "tactic_count": 1}
{"name": "MeromorphicOn.divisor_congr_codiscreteWithin_of_eqOn_compl", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Divisor", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "simp", "congr", "apply", "simp_rw", "filter_upwards", "simp", "tauto", "simp"], "tactic_count": 10}
{"name": "MeromorphicOn.divisor_congr_codiscreteWithin", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Divisor", "is_tactic_proof": true, "tactics": ["by_cases", "ext", "by_cases", "simp", "congr", "apply", "simp_rw", "have", "apply", "use", "filter_upwards", "simp", "tauto", "simp", "simp"], "tactic_count": 15}
{"name": "MeromorphicOn.AnalyticOnNhd.divisor_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Divisor", "is_tactic_proof": true, "tactics": ["intro", "by_cases", "simp", "simp"], "tactic_count": 4}
{"name": "MeromorphicOn.divisor_const", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Divisor", "is_tactic_proof": true, "tactics": ["classical", "ext", "simp", "ite_eq_right_iff,", "tauto"], "tactic_count": 5}
{"name": "MeromorphicOn.divisor_intCast", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Divisor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeromorphicOn.divisor_natCast", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Divisor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeromorphicOn.divisor_ofNat", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Divisor", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "MeromorphicOn.min_divisor_le_divisor_add", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Divisor", "is_tactic_proof": true, "tactics": ["by_cases", "simp_all", "rw", "by_cases", "simp_all", "by_cases", "simp_all", "rw", "apply", "exact"], "tactic_count": 10}
{"name": "MeromorphicOn.negPart_divisor_add_le_max", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Divisor", "is_tactic_proof": true, "tactics": ["intro", "by_cases", "simp", "simp", "by_cases", "simp", "rw", "apply"], "tactic_count": 8}
{"name": "MeromorphicOn.negPart_divisor_add_le_add", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Divisor", "is_tactic_proof": true, "tactics": ["calc", "by_cases"], "tactic_count": 2}
{"name": "MeromorphicOn.divisor_smul", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Divisor", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "lift", "lift", "simp", "simp"], "tactic_count": 6}
{"name": "MeromorphicOn.divisor_fun_smul", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Divisor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeromorphicOn.divisor_mul", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Divisor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeromorphicOn.divisor_fun_mul", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Divisor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeromorphicOn.divisor_inv", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Divisor", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "simp", "simp"], "tactic_count": 4}
{"name": "MeromorphicOn.divisor_fun_inv", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Divisor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeromorphicOn.divisor_pow", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Divisor", "is_tactic_proof": true, "tactics": ["classical", "ext", "by_cases", "simp", "by_cases", "simp", "simp"], "tactic_count": 7}
{"name": "MeromorphicOn.divisor_fun_pow", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Divisor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeromorphicOn.divisor_zpow", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Divisor", "is_tactic_proof": true, "tactics": ["classical", "ext", "by_cases", "simp", "by_cases", "simp", "simp"], "tactic_count": 7}
{"name": "MeromorphicOn.divisor_fun_zpow", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Divisor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeromorphicOn.divisor_restrict", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Divisor", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "rw", "simp", "simp"], "tactic_count": 5}
{"name": "MeromorphicOn.negPart_divisor_add_of_analyticNhdOn_right", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Divisor", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "suffices", "simpa", "by_cases", "suffices", "calc", "suffices", "rwa", "calc", "meromorphicOrderAt", "simp"], "tactic_count": 12}
{"name": "MeromorphicOn.negPart_divisor_add_of_analyticNhdOn_left", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Divisor", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeromorphicOn.divisor_sub_const_of_ne", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Divisor", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "congr", "exact", "exact"], "tactic_count": 5}
{"name": "MeromorphicOn.divisor_sub_const_self", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Divisor", "is_tactic_proof": true, "tactics": ["rw", "congr", "exact"], "tactic_count": 3}
{"name": "Function.FactorizedRational.mulSupport", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.FactorizedRational", "is_tactic_proof": true, "tactics": ["ext", "constructor", "simp_all", "by_contra", "simp_all", "simp_all", "use", "simp_all"], "tactic_count": 8}
{"name": "Function.FactorizedRational.finprod_eq_fun", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.FactorizedRational", "is_tactic_proof": true, "tactics": ["ext", "rw", "simp", "intro", "contrapose", "simp_all", "simp"], "tactic_count": 7}
{"name": "Function.FactorizedRational.analyticAt", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.FactorizedRational", "is_tactic_proof": true, "tactics": ["apply", "intro", "by_cases", "apply", "rwa", "apply", "rwa"], "tactic_count": 7}
{"name": "Function.FactorizedRational.ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.FactorizedRational", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "intro", "simp", "by_cases", "simp"], "tactic_count": 6}
{"name": "Function.FactorizedRational.extractFactor", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.FactorizedRational", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "have", "rw", "have", "rw", "congr", "have", "rw", "intro", "by_cases", "simp_all"], "tactic_count": 12}
{"name": "Function.FactorizedRational.meromorphicNFOn_univ", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.FactorizedRational", "is_tactic_proof": true, "tactics": ["classical", "by_cases", "intro", "rw", "right", "use", "simp", "rw", "rw", "exact"], "tactic_count": 10}
{"name": "Function.FactorizedRational.meromorphicNFOn", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.FactorizedRational", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.FactorizedRational.meromorphicOrderAt_eq", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.FactorizedRational", "is_tactic_proof": true, "tactics": ["classical", "rw", "use", "simp", "filter_upwards", "simp"], "tactic_count": 6}
{"name": "Function.FactorizedRational.meromorphicOrderAt_ne_top", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.FactorizedRational", "is_tactic_proof": true, "tactics": ["classical", "by_cases", "simp", "rw", "simp"], "tactic_count": 5}
{"name": "Function.FactorizedRational.divisor", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.FactorizedRational", "is_tactic_proof": true, "tactics": ["ext", "by_cases"], "tactic_count": 2}
{"name": "_private.Mathlib.Analysis.Meromorphic.FactorizedRational.0.Function.FactorizedRational.mulSupport_update", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.FactorizedRational", "is_tactic_proof": true, "tactics": ["intro", "contrapose", "simp", "by_cases", "rw", "simp", "simp_all"], "tactic_count": 7}
{"name": "Function.FactorizedRational.meromorphicTrailingCoeffAt_factorizedRational", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.FactorizedRational", "is_tactic_proof": true, "tactics": ["have", "rw", "finprod_eq_prod_of_mulSupport_subset", "apply", "intro", "rw", "by_cases", "rw", "simp_all", "grind"], "tactic_count": 10}
{"name": "Function.FactorizedRational.meromorphicTrailingCoeffAt_factorizedRational_off_support", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.FactorizedRational", "is_tactic_proof": true, "tactics": ["classical", "rw", "have", "intro", "contrapose", "simp_all", "rw", "intro", "congr", "apply", "by_contra", "simp_all"], "tactic_count": 12}
{"name": "Function.FactorizedRational.log_norm_meromorphicTrailingCoeffAt", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.FactorizedRational", "is_tactic_proof": true, "tactics": ["classical", "rw", "have", "intro", "by_cases", "rw", "simp_all", "simp_all", "rw", "have", "intro", "contrapose", "simp_all", "rw", "apply", "intro", "rw", "by_cases", "simp", "rw"], "tactic_count": 20}
{"name": "MeromorphicOn.extract_zeros_poles", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.FactorizedRational", "is_tactic_proof": true, "tactics": ["let", "have", "let", "have", "refine", "rw", "divisor_smul", "neg_add_cancel]", "intro", "simpa", "intro", "rw", "meromorphicOrderAt_congr", "meromorphicOrderAt_smul", "simp", "lift", "rw", "simp", "filter_upwards", "self_mem_codiscreteWithin", "unfold", "simp", "toMeromorphicNFAt_eq_self.2", "rw", "rwa"], "tactic_count": 25}
{"name": "MeromorphicOn.extract_zeros_poles_log", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.FactorizedRational", "is_tactic_proof": true, "tactics": ["have", "ext", "rw", "simp", "constructor", "obtain", "have", "simp", "rcases", "assumption", "simp", "linarith", "simp", "simp", "linarith", "simp_all", "by_cases", "rw", "rw", "filter_upwards", "simp", "filter_upwards", "rw", "rw", "finsum_eq_sum_of_support_subset", "have", "intro", "rw", "rw", "apply", "rwa", "simp", "rw", "simp"], "tactic_count": 34}
{"name": "MeromorphicOn.meromorphicTrailingCoeffAt_extract_zeros_poles", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.FactorizedRational", "is_tactic_proof": true, "tactics": ["have", "rw", "t₀.meromorphicTrailingCoeffAt_smul", "simp"], "tactic_count": 4}
{"name": "MeromorphicOn.log_norm_meromorphicTrailingCoeffAt_extract_zeros_poles", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.FactorizedRational", "is_tactic_proof": false, "tactics": ["rw", "h₁g.meromorphicTrailingCoeffAt_of_ne_zero", "simp", "apply", "apply", "simp_all"], "tactic_count": 6}
{"name": "MeromorphicAt.frequently_zero_iff_eventuallyEq_zero", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.IsolatedZeros", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeromorphicAt.eventuallyEq_zero_nhdsNE_of_eventuallyEq_zero_codiscreteWithin", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.IsolatedZeros", "is_tactic_proof": true, "tactics": ["rw", "apply", "filter_upwards", "intro", "simp_rw", "rw", "simp_all"], "tactic_count": 7}
{"name": "MeromorphicAt.frequently_eq_iff_eventuallyEq", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.IsolatedZeros", "is_tactic_proof": true, "tactics": ["rw", "simp_rw"], "tactic_count": 2}
{"name": "MeromorphicAt.eventuallyEq_nhdsNE_of_eventuallyEq_codiscreteWithin", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.IsolatedZeros", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "MeromorphicNFAt", "kind": "definition", "module": "Mathlib.Analysis.Meromorphic.NormalForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "meromorphicNFAt_iff_analyticAt_or", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.NormalForm", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "simp", "have", "apply", "fun_prop", "have", "rw", "use", "exact", "by_cases", "left", "rw", "apply", "right", "use", "simp", "rintro", "by_cases", "rw", "tauto", "right", "use", "have", "rw", "obtain", "use", "simpa", "right", "lift", "obtain", "use", "filter_upwards", "intro", "by_cases", "simp", "rw", "apply", "by_contra", "simp", "exact"], "tactic_count": 41}
{"name": "MeromorphicNFAt.meromorphicAt", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.NormalForm", "is_tactic_proof": true, "tactics": ["rw", "rcases", "exact", "obtain", "exact"], "tactic_count": 5}
{"name": "MeromorphicNFAt.meromorphicOrderAt_nonneg_iff_analyticAt", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.NormalForm", "is_tactic_proof": true, "tactics": ["constructor", "rw", "rcases", "exact", "by_contra", "exact", "rw", "simp"], "tactic_count": 8}
{"name": "AnalyticAt.meromorphicNFAt", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.NormalForm", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeromorphicOn.meromorphicNFAt_mem_codiscreteWithin", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.NormalForm", "is_tactic_proof": true, "tactics": ["filter_upwards", "exact"], "tactic_count": 2}
{"name": "MeromorphicNFAt.meromorphicOrderAt_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.NormalForm", "is_tactic_proof": true, "tactics": ["constructor", "intro", "have", "rw", "rwa", "intro", "rcases", "have", "tauto", "have", "by_contra", "have", "simp", "tauto", "simp", "apply", "use", "simp", "exact"], "tactic_count": 19}
{"name": "MeromorphicNFAt.eventuallyEq_nhdsNE_iff_eventuallyEq_nhds", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.NormalForm", "is_tactic_proof": true, "tactics": ["constructor", "intro", "have", "by_cases", "rw", "have", "have", "exact", "apply", "let", "rw", "let", "rw", "simp", "rw", "exact"], "tactic_count": 16}
{"name": "meromorphicNFAt_congr", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.NormalForm", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "exact", "exact", "rintro", "exact", "exact"], "tactic_count": 7}
{"name": "MeromorphicNFAt.smul_analytic", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.NormalForm", "is_tactic_proof": true, "tactics": ["rcases", "left", "filter_upwards", "simp_all", "right", "use", "constructor", "simp", "filter_upwards", "intro", "simp", "rw"], "tactic_count": 12}
{"name": "meromorphicNFAt_smul_iff_right_of_analyticAt", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.NormalForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "meromorphicNFAt_mul_iff_right", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.NormalForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "meromorphicNFAt_mul_iff_left", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.NormalForm", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "toMeromorphicNFAt", "kind": "definition", "module": "Mathlib.Analysis.Meromorphic.NormalForm", "is_tactic_proof": true, "tactics": ["by_cases", "classical", "apply", "by_cases", "rw", "exact", "exact", "exact"], "tactic_count": 8}
{"name": "MeromorphicAt.eqOn_compl_singleton_toMeromorphicNFAt", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.NormalForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toMeromorphicNFAt_of_not_meromorphicAt", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.NormalForm", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeromorphicAt.eq_nhdsNE_toMeromorphicNFAt", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.NormalForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "meromorphicNFAt_toMeromorphicNFAt", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.NormalForm", "is_tactic_proof": true, "tactics": ["by_cases", "by_cases", "have", "apply", "exact", "simp", "apply", "rw", "exact", "lift", "obtain", "right", "use", "apply", "simp", "split_ifs", "obtain", "apply", "apply", "filter_upwards", "simp_all", "simp", "simp", "exact"], "tactic_count": 24}
{"name": "toMeromorphicNFAt_eq_self", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.NormalForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeromorphicNFAt.inv", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.NormalForm", "is_tactic_proof": true, "tactics": ["rcases", "left", "filter_upwards", "simp", "right", "use", "filter_upwards", "simp", "ring"], "tactic_count": 9}
{"name": "meromorphicNFAt_inv", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.NormalForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeromorphicNFOn", "kind": "definition", "module": "Mathlib.Analysis.Meromorphic.NormalForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeromorphicNFOn.meromorphicOn", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.NormalForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeromorphicNFOn.divisor_nonneg_iff_analyticOnNhd", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.NormalForm", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "have", "simp", "assumption", "by_cases", "simp", "exact", "simp"], "tactic_count": 10}
{"name": "AnalyticOnNhd.meromorphicNFOn", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.NormalForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeromorphicNFOn.zero_set_eq_divisor_support", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.NormalForm", "is_tactic_proof": true, "tactics": ["ext", "constructor", "simp_all", "simp", "constructor", "exact", "rw", "have", "simp", "simp_all"], "tactic_count": 10}
{"name": "meromorphicNFOn_smul_iff_right_of_analyticOnNhd", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.NormalForm", "is_tactic_proof": true, "tactics": ["constructor", "rw", "exact", "apply", "exact"], "tactic_count": 5}
{"name": "meromorphicNFOn_mul_iff_right_of_analyticOnNhd", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.NormalForm", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "meromorphicNFOn_mul_iff_left_of_analyticOnNhd", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.NormalForm", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "meromorphicNFOn_inv", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.NormalForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toMeromorphicNFOn", "kind": "definition", "module": "Mathlib.Analysis.Meromorphic.NormalForm", "is_tactic_proof": true, "tactics": ["by_cases", "intro", "by_cases", "exact", "exact", "exact"], "tactic_count": 6}
{"name": "toMeromorphicNFOn_of_not_meromorphicOn", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.NormalForm", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "toMeromorphicNFOn_eq_self_on_compl", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.NormalForm", "is_tactic_proof": true, "tactics": ["intro", "simp_all"], "tactic_count": 2}
{"name": "toMeromorphicNFOn_eqOn_codiscrete", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.NormalForm", "is_tactic_proof": true, "tactics": ["have", "filter_upwards", "simp"], "tactic_count": 3}
{"name": "MeromorphicOn.toMeromorphicNFOn_eq_self_on_nhdsNE", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.NormalForm", "is_tactic_proof": true, "tactics": ["filter_upwards", "rcases", "simp", "simp", "simp"], "tactic_count": 5}
{"name": "toMeromorphicNFOn_eq_toMeromorphicNFAt_on_nhds", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.NormalForm", "is_tactic_proof": true, "tactics": ["apply", "exact", "simp"], "tactic_count": 3}
{"name": "toMeromorphicNFOn_eq_toMeromorphicNFAt", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.NormalForm", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "meromorphicNFOn_toMeromorphicNFOn", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.NormalForm", "is_tactic_proof": true, "tactics": ["by_cases", "intro", "rw", "exact", "simpa"], "tactic_count": 5}
{"name": "toMeromorphicNFOn_eq_self", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.NormalForm", "is_tactic_proof": true, "tactics": ["constructor", "rw", "apply", "ext", "by_cases", "simp", "rw", "simp"], "tactic_count": 8}
{"name": "meromorphicOrderAt_toMeromorphicNFOn", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.NormalForm", "is_tactic_proof": true, "tactics": ["apply", "exact"], "tactic_count": 2}
{"name": "MeromorphicOn.divisor_of_toMeromorphicNFOn", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.NormalForm", "is_tactic_proof": true, "tactics": ["ext", "by_cases"], "tactic_count": 2}
{"name": "meromorphicOrderAt", "kind": "definition", "module": "Mathlib.Analysis.Meromorphic.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "meromorphicOrderAt_of_not_meromorphicAt", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "meromorphicAt_of_meromorphicOrderAt_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Order", "is_tactic_proof": true, "tactics": ["contrapose", "simp"], "tactic_count": 2}
{"name": "meromorphicOrderAt_eq_top_iff", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Order", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "contrapose", "exact", "simp", "by_cases", "simp", "rw", "filter_upwards", "rwa", "obtain", "simp", "contrapose", "rw", "rw", "apply", "filter_upwards", "rw"], "tactic_count": 18}
{"name": "eventuallyConst_nhdsNE_iff_meromorphicOrderAt_sub_eq_top", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Order", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "meromorphicOrderAt_eq_int_iff", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Order", "is_tactic_proof": true, "tactics": ["simp", "by_cases", "rw", "rw", "refine", "apply", "rw", "apply", "rw", "filter_upwards", "rwa", "exact", "obtain", "rw", "obtain", "replace", "rw", "filter_upwards", "rwa", "add_sub_assoc,", "exact"], "tactic_count": 21}
{"name": "meromorphicOrderAt_ne_top_iff", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "meromorphicOrderAt_ne_top_iff_eventually_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Order", "is_tactic_proof": true, "tactics": ["constructor", "intro", "obtain", "filter_upwards", "eventually_nhdsWithin_of_eventually_nhds", "simp_all", "simp_all"], "tactic_count": 7}
{"name": "tendsto_cobounded_of_meromorphicOrderAt_neg", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Order", "is_tactic_proof": true, "tactics": ["have", "simp", "obtain", "have", "rcases", "have", "simp", "apply", "have", "refine", "have", "simpa", "filter_upwards", "simpa", "exact", "apply", "filter_upwards"], "tactic_count": 17}
{"name": "tendsto_ne_zero_of_meromorphicOrderAt_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Order", "is_tactic_proof": true, "tactics": ["rcases", "refine", "apply", "filter_upwards"], "tactic_count": 4}
{"name": "tendsto_zero_of_meromorphicOrderAt_pos", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Order", "is_tactic_proof": true, "tactics": ["have", "cases", "top", "apply", "filter_upwards", "coe", "rcases", "lift", "have", "have", "simp", "rw", "have", "apply", "filter_upwards"], "tactic_count": 15}
{"name": "tendsto_nhds_of_meromorphicOrderAt_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Order", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "exact", "exact"], "tactic_count": 4}
{"name": "tendsto_cobounded_iff_meromorphicOrderAt_neg", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Order", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simp", "obtain", "exact"], "tactic_count": 5}
{"name": "tendsto_nhds_iff_meromorphicOrderAt_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Order", "is_tactic_proof": true, "tactics": ["rcases", "simp", "intro", "apply", "rw", "exact", "simp"], "tactic_count": 7}
{"name": "tendsto_ne_zero_iff_meromorphicOrderAt_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Order", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simp", "intro", "rcases", "apply", "rw", "exact", "apply", "exact"], "tactic_count": 10}
{"name": "tendsto_zero_iff_meromorphicOrderAt_pos", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Order", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simp", "intro", "rcases", "obtain", "apply", "exact", "apply", "rw", "exact"], "tactic_count": 11}
{"name": "meromorphicOrderAt_congr", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Order", "is_tactic_proof": true, "tactics": ["by_cases", "have", "contrapose", "exact", "simp", "by_cases", "rw", "rw", "exact", "obtain", "obtain", "rw", "use", "exact"], "tactic_count": 14}
{"name": "AnalyticAt.meromorphicOrderAt_eq", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Order", "is_tactic_proof": true, "tactics": ["cases", "rw", "exact", "simp_rw", "rcases", "exact"], "tactic_count": 6}
{"name": "AnalyticAt.meromorphicOrderAt_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Order", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeromorphicAt.analyticAt", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Order", "is_tactic_proof": true, "tactics": ["cases", "top", "it", "have", "apply", "rw", "filter_upwards", "coe", "would", "shows", "continuity", "rcases", "have", "apply", "exact", "lift", "have", "apply", "filter_upwards", "exact"], "tactic_count": 20}
{"name": "AnalyticAt.of_meromorphicOrderAt_pos", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Order", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "meromorphicOrderAt_const", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Order", "is_tactic_proof": true, "tactics": ["split_ifs", "simp", "exact"], "tactic_count": 3}
{"name": "meromorphicOrderAt_id", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Order", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "meromorphicOrderAt_const_intCast", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "meromorphicOrderAt_const_natCast", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "meromorphicOrderAt_const_ofNat", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Order", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "meromorphicOrderAt_smul", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Order", "is_tactic_proof": true, "tactics": ["cases", "top", "simp", "filter_upwards", "coe", "cases", "top", "simp", "filter_upwards", "coe", "rw", "obtain", "obtain", "use", "filter_upwards", "simp"], "tactic_count": 16}
{"name": "meromorphicOrderAt_mul", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "meromorphicOrderAt_pow", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Order", "is_tactic_proof": true, "tactics": ["induction", "simp", "rw", "exact", "apply", "hn", "simp", "cases", "aesop", "norm_cast", "simp", "ring"], "tactic_count": 12}
{"name": "meromorphicOrderAt_zpow", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Order", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "rw", "exact", "apply", "by_cases", "simp", "rw", "filter_upwards", "intro", "simp", "obtain", "rw", "use", "constructor", "simp_all", "filter_upwards", "intro", "rw", "congr", "rw"], "tactic_count": 21}
{"name": "meromorphicOrderAt_inv", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Order", "is_tactic_proof": true, "tactics": ["by_cases", "have", "contrapose", "simpa", "simp", "by_cases", "rw", "rw", "filter_upwards", "simp", "lift", "apply", "obtain", "use", "rw", "filter_upwards", "intro", "simp", "ring"], "tactic_count": 19}
{"name": "meromorphicOrderAt_add_of_top_left", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Order", "is_tactic_proof": true, "tactics": ["rw", "filter_upwards", "simp_all"], "tactic_count": 3}
{"name": "meromorphicOrderAt_add_of_top_right", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Order", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "meromorphicOrderAt_add", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Order", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "filter_upwards", "simp", "by_cases", "simp", "rw", "filter_upwards", "simp", "lift", "lift", "obtain", "obtain", "let", "let", "have", "apply", "apply", "apply", "have", "filter_upwards", "simp_all", "have", "have", "rw", "exact"], "tactic_count": 26}
{"name": "meromorphicOrderAt_add_eq_left_of_lt", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Order", "is_tactic_proof": true, "tactics": ["by_cases", "have", "contrapose", "simpa", "simp", "by_cases", "rw", "filter_upwards", "simp", "lift", "lift", "obtain", "obtain", "rw", "refine", "apply", "apply", "simpa", "filter_upwards", "simp_all"], "tactic_count": 20}
{"name": "meromorphicOrderAt_add_eq_right_of_lt", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Order", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "meromorphicOrderAt_add_of_ne", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Order", "is_tactic_proof": true, "tactics": ["rcases", "simpa", "simpa"], "tactic_count": 3}
{"name": "MeromorphicOn.isClopen_setOf_meromorphicOrderAt_eq_top", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Order", "is_tactic_proof": true, "tactics": ["constructor", "rw", "intro", "rcases", "rw", "tauto", "obtain", "use", "constructor", "intro", "push", "by_cases", "rwa", "rw", "apply", "rw", "use", "mem_singleton_iff.not.2", "exact", "apply", "intro", "conv", "arg", "rw", "simp", "rw", "obtain", "use", "simp", "intro", "simp", "by_cases", "rw", "tauto", "use", "constructor", "exact", "apply", "exact"], "tactic_count": 39}
{"name": "MeromorphicOn.exists_meromorphicOrderAt_ne_top_iff_forall", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Order", "is_tactic_proof": true, "tactics": ["constructor", "intro", "have", "rcases", "intro", "have", "rw", "tauto", "obtain", "have", "rw", "tauto", "intro", "obtain", "use"], "tactic_count": 15}
{"name": "MeromorphicOn.meromorphicOrderAt_ne_top_of_isPreconnected", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeromorphicOn.eventually_analyticAt", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Order", "is_tactic_proof": true, "tactics": ["and", "analytic.", "have", "have", "exact", "filter_upwards", "exact"], "tactic_count": 7}
{"name": "MeromorphicOn.eventually_analyticAt_or_mem_compl", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Order", "is_tactic_proof": true, "tactics": ["have", "rw", "simp", "refine", "filter_upwards", "filter_upwards"], "tactic_count": 6}
{"name": "MeromorphicOn.analyticAt_mem_codiscreteWithin", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Order", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "filter_upwards", "simp", "tauto"], "tactic_count": 6}
{"name": "MeromorphicOn.codiscrete_setOf_meromorphicOrderAt_eq_zero_or_top", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Order", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "rcases", "filter_upwards", "suffices", "obtain", "exact", "rw", "obtain", "use", "exact", "filter_upwards", "simp", "not_exists,", "rcases", "simp", "exact"], "tactic_count": 18}
{"name": "MeromorphicAt.meromorphicOrderAt_comp", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Order", "is_tactic_proof": true, "tactics": ["rcases", "rw", "rw", "rw", "exact", "simp", "have", "rw", "set", "rw", "obtain", "have", "have", "rw", "rw", "meromorphicOrderAt_zpow,", "fun_prop"], "tactic_count": 17}
{"name": "meromorphicOrderAt_comp_of_deriv_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Order", "is_tactic_proof": true, "tactics": ["by_cases", "have", "rw", "rw", "rwa"], "tactic_count": 5}
{"name": "meromorphicOrderAt_smul_of_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Order", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "rw", "rwa"], "tactic_count": 4}
{"name": "meromorphicOrderAt_mul_of_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "meromorphicTrailingCoeffAt", "kind": "definition", "module": "Mathlib.Analysis.Meromorphic.TrailingCoefficient", "is_tactic_proof": true, "tactics": ["by_cases", "by_cases", "exact", "exact", "exact"], "tactic_count": 5}
{"name": "meromorphicTrailingCoeffAt_of_not_MeromorphicAt", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.TrailingCoefficient", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeromorphicAt.meromorphicTrailingCoeffAt_of_order_eq_top", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.TrailingCoefficient", "is_tactic_proof": true, "tactics": ["simp_all"], "tactic_count": 1}
{"name": "AnalyticAt.meromorphicTrailingCoeffAt_of_eq_nhdsNE", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.TrailingCoefficient", "is_tactic_proof": false, "tactics": ["have", "rw", "fun_prop", "by_cases", "simp", "apply", "rw", "apply", "unfold", "simp", "obtain", "apply", "rw", "filter_upwards", "rw", "rwa", "simp_all"], "tactic_count": 17}
{"name": "AnalyticAt.meromorphicTrailingCoeffAt_of_ne_zero_of_eq_nhdsNE", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.TrailingCoefficient", "is_tactic_proof": false, "tactics": ["have", "rw", "fun_prop", "have", "simp", "use", "exact", "simp_all"], "tactic_count": 8}
{"name": "AnalyticAt.meromorphicTrailingCoeffAt_of_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.TrailingCoefficient", "is_tactic_proof": true, "tactics": ["rw", "filter_upwards", "simp"], "tactic_count": 3}
{"name": "MeromorphicAt.tendsto_nhds_meromorphicTrailingCoeffAt", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.TrailingCoefficient", "is_tactic_proof": true, "tactics": ["by_cases", "simp_all", "apply", "filter_upwards", "simp_all", "apply", "obtain", "apply", "filter_upwards", "rw", "neg_add_cancel,", "left", "simp_all", "rw", "apply"], "tactic_count": 15}
{"name": "MeromorphicAt.meromorphicTrailingCoeffAt_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.TrailingCoefficient", "is_tactic_proof": true, "tactics": ["obtain", "simpa"], "tactic_count": 2}
{"name": "meromorphicTrailingCoeffAt_const", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.TrailingCoefficient", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "apply", "rw", "simp", "exact"], "tactic_count": 6}
{"name": "meromorphicTrailingCoeffAt_id_sub_const", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.TrailingCoefficient", "is_tactic_proof": true, "tactics": ["by_cases", "simp_all", "apply", "simp", "simp_all", "apply", "simp_all"], "tactic_count": 7}
{"name": "meromorphicTrailingCoeffAt_congr_nhdsNE", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.TrailingCoefficient", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "rw", "by_cases", "simp_all", "obtain", "rw", "h₁g.meromorphicTrailingCoeffAt_of_ne_zero_of_eq_nhdsNE"], "tactic_count": 8}
{"name": "MeromorphicAt.meromorphicTrailingCoeffAt_add_eq_left_of_lt", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.TrailingCoefficient", "is_tactic_proof": true, "tactics": ["by_cases", "have", "simp_all", "by_cases", "apply", "filter_upwards", "simp", "lift", "obtain", "lift", "obtain", "rw", "have", "filter_upwards", "simp", "rw", "simp_all", "have", "h₁g₁.fun_add", "have", "rw", "τ₁.meromorphicTrailingCoeffAt_of_ne_zero_of_eq_nhdsNE", "zero_zpow", "tauto"], "tactic_count": 24}
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{"name": "MeromorphicAt.meromorphicTrailingCoeffAt_mul", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.TrailingCoefficient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "meromorphicTrailingCoeffAt_prod", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.TrailingCoefficient", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "insert", "rw"], "tactic_count": 5}
{"name": "meromorphicTrailingCoeffAt_inv", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.TrailingCoefficient", "is_tactic_proof": true, "tactics": ["by_cases", "by_cases", "simp_all", "have", "filter_upwards", "simp_all", "rw", "meromorphicTrailingCoeffAt_congr_nhdsNE", "analyticAt_const.meromorphicTrailingCoeffAt_of_ne_zero_of_eq_nhdsNE", "simp", "simp", "exact", "simp_all"], "tactic_count": 13}
{"name": "MeromorphicAt.meromorphicTrailingCoeffAt_zpow", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.TrailingCoefficient", "is_tactic_proof": true, "tactics": ["by_cases", "by_cases", "simp", "apply", "simp_all", "obtain", "rw", "simp", "filter_upwards", "simp_all"], "tactic_count": 10}
{"name": "MeromorphicAt.meromorphicTrailingCoeffAt_pow", "kind": "theorem", "module": "Mathlib.Analysis.Meromorphic.TrailingCoefficient", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "dist_center_homothety", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.AddTorsor", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "nndist_center_homothety", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.AddTorsor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dist_homothety_center", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.AddTorsor", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "nndist_homothety_center", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.AddTorsor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dist_lineMap_lineMap", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.AddTorsor", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "nndist_lineMap_lineMap", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.AddTorsor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lipschitzWith_lineMap", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.AddTorsor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dist_lineMap_left", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.AddTorsor", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "nndist_lineMap_left", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.AddTorsor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dist_left_lineMap", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.AddTorsor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nndist_left_lineMap", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.AddTorsor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dist_lineMap_right", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.AddTorsor", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "nndist_lineMap_right", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.AddTorsor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dist_right_lineMap", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.AddTorsor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nndist_right_lineMap", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.AddTorsor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dist_homothety_self", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.AddTorsor", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "nndist_homothety_self", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.AddTorsor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dist_self_homothety", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.AddTorsor", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "nndist_self_homothety", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.AddTorsor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dist_left_midpoint", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.AddTorsor", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "nndist_left_midpoint", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.AddTorsor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dist_midpoint_left", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.AddTorsor", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "nndist_midpoint_left", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.AddTorsor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dist_midpoint_right", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.AddTorsor", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "nndist_midpoint_right", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.AddTorsor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dist_right_midpoint", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.AddTorsor", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "nndist_right_midpoint", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.AddTorsor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dist_left_midpoint_eq_dist_right_midpoint", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.AddTorsor", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "dist_midpoint_midpoint_le'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.AddTorsor", "is_tactic_proof": true, "tactics": ["rw", "rw", "grw"], "tactic_count": 3}
{"name": "nndist_midpoint_midpoint_le'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.AddTorsor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dist_pointReflection_left", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.AddTorsor", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "dist_left_pointReflection", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.AddTorsor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dist_pointReflection_right", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.AddTorsor", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "dist_right_pointReflection", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.AddTorsor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "antilipschitzWith_lineMap", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.AddTorsor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dist_midpoint_midpoint_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.AddTorsor", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "nndist_midpoint_midpoint_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.AddTorsor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.ofMapMidpoint", "kind": "definition", "module": "Mathlib.Analysis.Normed.Affine.AddTorsor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DilationEquiv.smulTorsor", "kind": "definition", "module": "Mathlib.Analysis.Normed.Affine.AddTorsor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DilationEquiv.smulTorsor_ratio", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.AddTorsor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DilationEquiv.smulTorsor_preimage_ball", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.AddTorsor", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "isOpenMap_barycentric_coord", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.AddTorsorBases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_barycentric_coord", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.AddTorsorBases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineBasis.interior_convexHull", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.AddTorsorBases", "is_tactic_proof": true, "tactics": ["cases", "have", "simp", "haveI", "have", "ext", "simp", "interior_Ici,"], "tactic_count": 8}
{"name": "IsOpen.exists_between_affineIndependent_span_eq_top", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.AddTorsorBases", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "obtain", "let", "have", "refine", "simp", "rw", "abs_div,", "exact", "have", "div_ne_zero", "classical", "let", "refine", "intro", "rintro", "by_cases", "simp", "exact", "rw"], "tactic_count": 21}
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{"name": "IsOpen.affineSpan_eq_top", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.AddTorsorBases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "affineSpan_eq_top_of_nonempty_interior", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.AddTorsorBases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineBasis.centroid_mem_interior_convexHull", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.AddTorsorBases", "is_tactic_proof": true, "tactics": ["haveI", "simp"], "tactic_count": 2}
{"name": "interior_convexHull_nonempty_iff_affineSpan_eq_top", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.AddTorsorBases", "is_tactic_proof": true, "tactics": ["refine", "obtain", "suffices", "rw", "refine", "lift", "exact"], "tactic_count": 7}
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{"name": "AffineSpace.asymptoticNhds_le_cobounded", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.AsymptoticCone", "is_tactic_proof": true, "tactics": ["have", "rw", "map_prod_eq_map₂,", "change", "simp_rw", "exact"], "tactic_count": 6}
{"name": "asymptoticCone_subset_singleton_of_bounded", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.AsymptoticCone", "is_tactic_proof": true, "tactics": ["intro", "by_contra", "exact"], "tactic_count": 3}
{"name": "AffineSpace.cobounded_eq_iSup_sphere_asymptoticNhds", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.AsymptoticCone", "is_tactic_proof": false, "tactics": ["refine", "intro", "have", "simp_rw", "choose", "have", "rw", "refine", "rw", "let", "have", "rw", "have", "rw", "exact"], "tactic_count": 15}
{"name": "isBounded_iff_asymptoticCone_subset_singleton", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.AsymptoticCone", "is_tactic_proof": true, "tactics": ["refine", "simp_rw", "intro", "by_contra", "exact"], "tactic_count": 5}
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{"name": "Affine.Triangle.prod_dist_eq_prod_dist_of_mem_line_of_mem_line", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Ceva", "is_tactic_proof": true, "tactics": ["simp_rw", "choose", "simp_rw", "simp_rw", "prod_eq_prod_one_sub_of_mem_line_point_lineMap"], "tactic_count": 5}
{"name": "Affine.Triangle.prod_dist_div_dist_eq_one_of_mem_line_of_mem_line", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Ceva", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "rw", "have", "have", "have", "field_simp", "exact"], "tactic_count": 9}
{"name": "ContinuousAffineMap.hasNorm", "kind": "instance", "module": "Mathlib.Analysis.Normed.Affine.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineMap.norm_def", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineMap.norm_contLinear_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineMap.norm_image_zero_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineMap.norm_eq", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineMap.instNormedAddCommGroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Affine.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineMap.instNormedSpace", "kind": "instance", "module": "Mathlib.Analysis.Normed.Affine.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineMap.norm_comp_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.ContinuousAffineMap", "is_tactic_proof": true, "tactics": ["rw", "constructor", "calc", "calc"], "tactic_count": 4}
{"name": "ContinuousAffineMap.toConstProdContinuousLinearMap", "kind": "definition", "module": "Mathlib.Analysis.Normed.Affine.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineMap.toConstProdContinuousLinearMap_fst", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineMap.toConstProdContinuousLinearMap_snd", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Wbtw.dist_add_dist", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Convex", "is_tactic_proof": true, "tactics": ["obtain", "simp"], "tactic_count": 2}
{"name": "dist_add_dist_of_mem_segment", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Convex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_mem_interior_convexHull_affineBasis", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Convex", "is_tactic_proof": true, "tactics": ["classical", "wlog", "obtain", "use", "simpa", "subst", "obtain", "exists_affineBasis_of_finiteDimensional", "set", "have", "simpa", "b.centroid_mem_interior_convexHull", "set", "have", "simpa", "obtain", "set", "have", "have", "positivity", "have", "set", "have", "have", "simp", "simpa", "refine", "simpa", "calc", "convexHull"], "tactic_count": 30}
{"name": "Convex.exists_subset_interior_convexHull_finset_of_isCompact", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Convex", "is_tactic_proof": true, "tactics": ["classical", "rcases", "rcases", "rcases", "rcases", "hs₂.elim_finite_subcover_image", "lift", "refine", "all_goals", "grw", "intros", "gcongr", "simpa", "grw"], "tactic_count": 14}
{"name": "term_→ᵃⁱ[_]_", "kind": "definition", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Analysis_Normed_Affine_Isometry___macroRules_term_→ᵃⁱ[_]__1", "kind": "definition", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Analysis_Normed_Affine_Isometry___unexpand_AffineIsometry_1", "kind": "definition", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometry.linearIsometry", "kind": "definition", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometry.linear_eq_linearIsometry", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "AffineIsometry.instFunLike", "kind": "instance", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometry.coe_toAffineMap", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "AffineIsometry.toAffineMap_injective", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": true, "tactics": ["rintro", "rfl"], "tactic_count": 2}
{"name": "AffineIsometry.coeFn_injective", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometry.ext", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.toAffineIsometry", "kind": "definition", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.coe_toAffineIsometry", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.toAffineIsometry_linearIsometry", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "LinearIsometry.toAffineIsometry_toAffineMap", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometry.map_vadd", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometry.map_vsub", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometry.dist_map", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AffineIsometry.nndist_map", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AffineIsometry.edist_map", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AffineIsometry.isometry", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometry.injective", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometry.map_eq_iff", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometry.map_ne", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometry.lipschitz", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometry.antilipschitz", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometry.continuous", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometry.ediam_image", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometry.ediam_range", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometry.diam_image", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometry.diam_range", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometry.toContinuousAffineMap", "kind": "definition", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometry.toContinuousAffineMap_injective", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometry.toContinuousAffineMap_inj", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometry.coe_toContinuousAffineMap", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometry.comp_continuous_iff", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometry.id", "kind": "definition", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometry.coe_id", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometry.id_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometry.id_toAffineMap", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometry.toContinuousAffineMap_id", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometry.instInhabited", "kind": "instance", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometry.comp", "kind": "definition", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometry.coe_comp", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometry.id_comp", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometry.comp_id", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometry.comp_assoc", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometry.instMonoid", "kind": "instance", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometry.coe_one", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometry.coe_mul", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.subtypeₐᵢ", "kind": "definition", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.subtypeₐᵢ_linear", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.subtypeₐᵢ_linearIsometry", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.coe_subtypeₐᵢ", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.subtypeₐᵢ_toAffineMap", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.toContinuousAffineMap_subtypeₐᵢ", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "term_≃ᵃⁱ[_]_", "kind": "definition", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Analysis_Normed_Affine_Isometry___macroRules_term_≃ᵃⁱ[_]__1", "kind": "definition", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Analysis_Normed_Affine_Isometry___unexpand_AffineIsometryEquiv_1", "kind": "definition", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.linearIsometryEquiv", "kind": "definition", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.linear_eq_linear_isometry", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "AffineIsometryEquiv.instEquivLike", "kind": "instance", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.coe_mk", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.coe_toAffineEquiv", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.toAffineEquiv_injective", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.ext", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.coeFn_injective", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.toAffineIsometry", "kind": "definition", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.coe_toAffineIsometry", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.mk'", "kind": "definition", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.coe_mk'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.linearIsometryEquiv_mk'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "LinearIsometryEquiv.toAffineIsometryEquiv", "kind": "definition", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.coe_toAffineIsometryEquiv", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "LinearIsometryEquiv.toAffineIsometryEquiv_linearIsometryEquiv", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "LinearIsometryEquiv.toAffineIsometryEquiv_toAffineEquiv", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.toAffineIsometryEquiv_toAffineIsometry", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.isometry", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.toIsometryEquiv", "kind": "definition", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.coe_toIsometryEquiv", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.range_eq_univ", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "AffineIsometryEquiv.toHomeomorph", "kind": "definition", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.coe_toHomeomorph", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.continuous", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.continuousAt", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.continuousOn", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.continuousWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.toContinuousAffineEquiv", "kind": "definition", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.toContinuousAffineEquiv_injective", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.toContinuousAffineEquiv_inj", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.coe_toContinuousAffineEquiv", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.instCoeContinuousAffineEquiv", "kind": "instance", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.refl", "kind": "definition", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.instInhabited", "kind": "instance", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.coe_refl", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.toAffineEquiv_refl", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.toContinuousAffineEquiv_refl", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.toIsometryEquiv_refl", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.toHomeomorph_refl", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.symm", "kind": "definition", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.apply_symm_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.symm_apply_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.symm_symm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.symm_bijective", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.toAffineEquiv_symm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.coe_symm_toAffineEquiv", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.toContinuousAffineEquiv_symm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.coe_symm_toContinuousAffineEquiv", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.toIsometryEquiv_symm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.coe_symm_toIsometryEquiv", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.toHomeomorph_symm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.coe_symm_toHomeomorph", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.trans", "kind": "definition", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.coe_trans", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.trans_refl", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.refl_trans", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.self_trans_symm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.symm_trans_self", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.coe_symm_trans", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.trans_assoc", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.instGroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.coe_one", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.coe_mul", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.coe_inv", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.map_vadd", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.map_vsub", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.dist_map", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.edist_map", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.bijective", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.injective", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.surjective", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.map_eq_iff", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.map_ne", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.lipschitz", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.antilipschitz", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.ediam_image", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.diam_image", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.comp_continuousOn_iff", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.comp_continuous_iff", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.ofTop", "kind": "definition", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.ofTop_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.ofTop_symm_apply_coe", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.ofEq", "kind": "definition", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.coe_ofEq_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.ofEq_symm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.ofEq_rfl", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.vaddConst", "kind": "definition", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.coe_vaddConst", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.coe_vaddConst'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.coe_vaddConst_symm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.vaddConst_toAffineEquiv", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.constVSub", "kind": "definition", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.coe_constVSub", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.symm_constVSub", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "AffineIsometryEquiv.constVAdd", "kind": "definition", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.coe_constVAdd", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.constVAdd_zero", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.vadd_vsub", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": true, "tactics": ["convert", "exact"], "tactic_count": 2}
{"name": "AffineIsometryEquiv.pointReflection", "kind": "definition", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.pointReflection_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.pointReflection_toAffineEquiv", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.pointReflection_self", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.pointReflection_involutive", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.pointReflection_symm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.dist_pointReflection_fixed", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AffineIsometryEquiv.dist_pointReflection_self'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AffineIsometryEquiv.dist_pointReflection_self", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AffineIsometryEquiv.pointReflection_fixed_iff", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.dist_pointReflection_self_real", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AffineIsometryEquiv.pointReflection_midpoint_left", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometryEquiv.pointReflection_midpoint_right", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.equivMapOfInjective", "kind": "definition", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.isometryEquivMap", "kind": "definition", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.isometryEquivMap.apply_symm_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.isometryEquivMap.coe_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.isometryEquivMap.toAffineMap_eq", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.midpoint_fixed", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.MazurUlam", "is_tactic_proof": true, "tactics": ["set", "set", "haveI", "have", "refine", "rintro", "calc", "dist", "rw", "set", "set", "have", "intro", "dsimp", "rw", "have", "rintro", "constructor", "simp", "set", "have", "apply", "rintro", "simp", "exact", "replace", "refine", "exact"], "tactic_count": 28}
{"name": "IsometryEquiv.map_midpoint", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.MazurUlam", "is_tactic_proof": false, "tactics": ["set", "have", "have", "have", "simp", "rwa", "pointReflection_self,"], "tactic_count": 7}
{"name": "IsometryEquiv.toRealLinearIsometryEquivOfMapZero", "kind": "definition", "module": "Mathlib.Analysis.Normed.Affine.MazurUlam", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.coe_toRealLinearIsometryEquivOfMapZero", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.MazurUlam", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.coe_toRealLinearIsometryEquivOfMapZero_symm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.MazurUlam", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.toRealLinearIsometryEquiv", "kind": "definition", "module": "Mathlib.Analysis.Normed.Affine.MazurUlam", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.toRealLinearIsometryEquiv_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.MazurUlam", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.toRealLinearIsometryEquiv_symm_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.MazurUlam", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.toRealAffineIsometryEquiv", "kind": "definition", "module": "Mathlib.Analysis.Normed.Affine.MazurUlam", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.coeFn_toRealAffineIsometryEquiv", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.MazurUlam", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.coe_toRealAffineIsometryEquiv", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.MazurUlam", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "Affine.Simplex.Scalene", "kind": "definition", "module": "Mathlib.Analysis.Normed.Affine.Simplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.Scalene.dist_ne", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Simplex", "is_tactic_proof": true, "tactics": ["rw", "rcases", "apply", "cases", "nth_rw", "apply", "cases", "rw", "apply", "cases", "rw", "nth_rw", "apply", "cases"], "tactic_count": 14}
{"name": "Affine.Simplex.scalene_reindex_iff", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Simplex", "is_tactic_proof": false, "tactics": ["let", "simp", "intro", "split_ifs", "simp", "simp", "simp", "simp,", "simp", "intro", "split_ifs", "simp", "simp", "simp", "simp⟩", "simp_rw", "convert", "simp", "split_ifs", "simp", "simp"], "tactic_count": 21}
{"name": "Affine.Simplex.Equilateral", "kind": "definition", "module": "Mathlib.Analysis.Normed.Affine.Simplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.Equilateral.dist_eq", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Simplex", "is_tactic_proof": true, "tactics": ["rcases", "rw"], "tactic_count": 2}
{"name": "Affine.Simplex.equilateral_reindex_iff", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Simplex", "is_tactic_proof": true, "tactics": ["refine", "convert", "convert"], "tactic_count": 3}
{"name": "Affine.Simplex.Regular", "kind": "definition", "module": "Mathlib.Analysis.Normed.Affine.Simplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.regular_reindex_iff", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Simplex", "is_tactic_proof": true, "tactics": ["refine", "rcases", "refine", "ext", "simpa", "rcases", "refine", "ext", "simpa"], "tactic_count": 9}
{"name": "Affine.Simplex.Regular.equilateral", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Simplex", "is_tactic_proof": true, "tactics": ["refine", "have", "by_cases", "rw", "rcases", "nth_rw", "simp_rw", "simp", "convert", "rw", "rcases", "nth_rw", "simp_rw", "simp", "convert", "exact", "rw", "simp"], "tactic_count": 18}
{"name": "Affine.Triangle.scalene_iff_dist_ne_and_dist_ne_and_dist_ne", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Simplex", "is_tactic_proof": false, "tactics": ["refine", "h.dist_ne", "h.dist_ne", "intro", "simp", "simp", "fin_cases", "simp", "simp"], "tactic_count": 9}
{"name": "Affine.Triangle.equilateral_iff_dist_eq_and_dist_eq", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Simplex", "is_tactic_proof": true, "tactics": ["refine", "simp", "refine", "intro", "have", "clear", "decide", "rcases", "rcases", "rfl", "exact", "exact", "rw", "rw", "rw"], "tactic_count": 15}
{"name": "Affine.Triangle.equilateral_iff_dist_01_eq_02_and_dist_01_eq_12", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Affine.Simplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakDual.CharacterSpace.norm_le_norm_one", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakDual.CharacterSpace.instCompactSpaceElemCharacterSpaceOfProperSpace", "kind": "instance", "module": "Mathlib.Analysis.Normed.Algebra.Basic", "is_tactic_proof": true, "tactics": ["rw", "have", "intro", "rw", "exact", "exact"], "tactic_count": 6}
{"name": "DualNumber.exp_eps", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.DualNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DualNumber.exp_smul_eps", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.DualNumber", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NormedSpace.expSeries", "kind": "definition", "module": "Mathlib.Analysis.Normed.Algebra.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedSpace.expSeries_eq_ofScalars", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.Exponential", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "NormedSpace.definition._@.Mathlib.Analysis.Normed.Algebra.Exponential.267156490._hygCtx._hyg.8", "kind": "definition", "module": "Mathlib.Analysis.Normed.Algebra.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedSpace.wrapped._@.Mathlib.Analysis.Normed.Algebra.Exponential.267156490._hygCtx._hyg.8", "kind": "opaque", "module": "Mathlib.Analysis.Normed.Algebra.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedSpace.exp", "kind": "definition", "module": "Mathlib.Analysis.Normed.Algebra.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedSpace.exp_def", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.Exponential", "is_tactic_proof": true, "tactics": ["intros", "delta", "rw", "rfl"], "tactic_count": 4}
{"name": "NormedSpace.expSeries_apply_eq", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.Exponential", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NormedSpace.expSeries_apply_eq'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedSpace.expSeries_sum_eq", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedSpace.expSeries_sum_eq_rat", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.Exponential", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "NormedSpace.expSeries_eq_expSeries_rat", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.Exponential", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "NormedSpace.exp_eq_expSeries_sum", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.Exponential", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "NormedSpace.exp_eq_tsum", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.Exponential", "is_tactic_proof": true, "tactics": ["rw", "ext", "exact"], "tactic_count": 3}
{"name": "NormedSpace.exp_eq_tsum_rat", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedSpace.exp_eq_ofScalarsSum", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.Exponential", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NormedSpace.expSeries_apply_zero", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.Exponential", "is_tactic_proof": true, "tactics": ["rw", "rcases", "rw", "rw"], "tactic_count": 4}
{"name": "NormedSpace.exp_zero", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.Exponential", "is_tactic_proof": true, "tactics": ["rw", "split_ifs", "simp_rw", "rfl"], "tactic_count": 4}
{"name": "NormedSpace.exp_op", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.Exponential", "is_tactic_proof": true, "tactics": ["by_cases", "obtain", "rw", "simp_rw", "have", "rintro", "exact", "rw"], "tactic_count": 8}
{"name": "NormedSpace.exp_unop", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.Exponential", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "NormedSpace.star_exp", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.Exponential", "is_tactic_proof": true, "tactics": ["by_cases", "obtain", "simp_rw", "rw"], "tactic_count": 4}
{"name": "IsSelfAdjoint.exp", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.exp_right", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.Exponential", "is_tactic_proof": true, "tactics": ["by_cases", "obtain", "rw", "exact", "rw", "exact"], "tactic_count": 6}
{"name": "Commute.exp_left", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.exp", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedSpace.expSeries_apply_eq_div", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.Exponential", "is_tactic_proof": true, "tactics": ["rw", "inv_natCast_smul_eq"], "tactic_count": 2}
{"name": "NormedSpace.expSeries_apply_eq_div'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedSpace.expSeries_sum_eq_div", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedSpace.exp_eq_tsum_div", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.Exponential", "is_tactic_proof": true, "tactics": ["rw", "ext", "exact"], "tactic_count": 3}
{"name": "NormedSpace.norm_expSeries_summable_of_mem_ball", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedSpace.norm_expSeries_summable_of_mem_ball'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.Exponential", "is_tactic_proof": true, "tactics": ["change", "rw", "exact"], "tactic_count": 3}
{"name": "NormedSpace.expSeries_summable_of_mem_ball", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedSpace.expSeries_summable_of_mem_ball'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "_private.Mathlib.Analysis.Normed.Algebra.Spectrum.0.QuasispectrumRestricts.termσₙ", "kind": "definition", "module": "Mathlib.Analysis.Normed.Algebra.Spectrum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.Normed.Algebra.Spectrum.0.QuasispectrumRestricts._aux_Mathlib_Analysis_Normed_Algebra_Spectrum___macroRules__private_Mathlib_Analysis_Normed_Algebra_Spectrum_0_QuasispectrumRestricts_termσₙ_1", "kind": "definition", "module": "Mathlib.Analysis.Normed.Algebra.Spectrum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.Normed.Algebra.Spectrum.0.QuasispectrumRestricts._aux_Mathlib_Analysis_Normed_Algebra_Spectrum___unexpand_quasispectrum_1", "kind": "definition", "module": "Mathlib.Analysis.Normed.Algebra.Spectrum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuasispectrumRestricts.compactSpace", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.Spectrum", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "upperHemicontinuous_spectrum", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.Spectrum", "is_tactic_proof": true, "tactics": ["rw", "refine", "filter_upwards", "apply", "gcongr", "apply", "gcongr", "simpa", "exact", "nonunits.isClosed.mem_of_tendsto"], "tactic_count": 10}
{"name": "upperHemicontinuous_spectrum_nnreal", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.Spectrum", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "upperHemicontinuous_quasispectrum", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.Spectrum", "is_tactic_proof": true, "tactics": ["convert", "ext1", "rw", "congr"], "tactic_count": 4}
{"name": "upperHemicontinuous_quasispectrum_nnreal", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.Spectrum", "is_tactic_proof": true, "tactics": ["obtain", "simpa"], "tactic_count": 2}
{"name": "_private.Mathlib.Analysis.Normed.Algebra.TrivSqZeroExt.0.termTsze", "kind": "definition", "module": "Mathlib.Analysis.Normed.Algebra.TrivSqZeroExt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.Normed.Algebra.TrivSqZeroExt.0._aux_Mathlib_Analysis_Normed_Algebra_TrivSqZeroExt___macroRules__private_Mathlib_Analysis_Normed_Algebra_TrivSqZeroExt_0_termTsze_1", "kind": "definition", "module": "Mathlib.Analysis.Normed.Algebra.TrivSqZeroExt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.Normed.Algebra.TrivSqZeroExt.0._aux_Mathlib_Analysis_Normed_Algebra_TrivSqZeroExt___unexpand_TrivSqZeroExt_1", "kind": "definition", "module": "Mathlib.Analysis.Normed.Algebra.TrivSqZeroExt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TrivSqZeroExt.fst_expSeries", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.TrivSqZeroExt", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "TrivSqZeroExt.snd_expSeries_of_smul_comm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.TrivSqZeroExt", "is_tactic_proof": true, "tactics": ["simp_rw", "smul_assoc,", "inv_mul_cancel_right₀"], "tactic_count": 3}
{"name": "TrivSqZeroExt.hasSum_snd_expSeries_of_smul_comm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.TrivSqZeroExt", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "simp_rw", "rw", "sub_zero]", "exact"], "tactic_count": 6}
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{"name": "TrivSqZeroExt.exp_def_of_smul_comm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.TrivSqZeroExt", "is_tactic_proof": true, "tactics": ["simp_rw", "by_cases", "refine", "exact", "rw", "simp_rw", "refine", "exact"], "tactic_count": 8}
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{"name": "TrivSqZeroExt.exp_inr", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.TrivSqZeroExt", "is_tactic_proof": true, "tactics": ["rw", "rw"], "tactic_count": 2}
{"name": "TrivSqZeroExt.exp_def", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.TrivSqZeroExt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TrivSqZeroExt.fst_exp", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.TrivSqZeroExt", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "TrivSqZeroExt.snd_exp", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.TrivSqZeroExt", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "TrivSqZeroExt.eq_smul_exp_of_invertible", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.TrivSqZeroExt", "is_tactic_proof": true, "tactics": ["rw", "one_smul,"], "tactic_count": 2}
{"name": "TrivSqZeroExt.eq_smul_exp_of_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.TrivSqZeroExt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TrivSqZeroExt.instL1SeminormedAddCommGroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Algebra.TrivSqZeroExt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TrivSqZeroExt._example", "kind": "example", "module": "Mathlib.Analysis.Normed.Algebra.TrivSqZeroExt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TrivSqZeroExt.norm_def", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.TrivSqZeroExt", "is_tactic_proof": true, "tactics": ["rw", "simp", "div_self,"], "tactic_count": 3}
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{"name": "TrivSqZeroExt.norm_inl", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.TrivSqZeroExt", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "TrivSqZeroExt.norm_inr", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.TrivSqZeroExt", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "TrivSqZeroExt.nnnorm_inl", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.TrivSqZeroExt", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "TrivSqZeroExt.nnnorm_inr", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.TrivSqZeroExt", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "TrivSqZeroExt.instL1SeminormedRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Algebra.TrivSqZeroExt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TrivSqZeroExt.instL1IsBoundedSMul", "kind": "instance", "module": "Mathlib.Analysis.Normed.Algebra.TrivSqZeroExt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TrivSqZeroExt.instNormOneClass", "kind": "instance", "module": "Mathlib.Analysis.Normed.Algebra.TrivSqZeroExt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TrivSqZeroExt.instL1SeminormedCommRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Algebra.TrivSqZeroExt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TrivSqZeroExt.instL1NormedAddCommGroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Algebra.TrivSqZeroExt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TrivSqZeroExt.instL1NormedRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Algebra.TrivSqZeroExt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TrivSqZeroExt.instL1NormedCommRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Algebra.TrivSqZeroExt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TrivSqZeroExt.instL1NormedSpace", "kind": "instance", "module": "Mathlib.Analysis.Normed.Algebra.TrivSqZeroExt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TrivSqZeroExt.instL1NormedAlgebra", "kind": "instance", "module": "Mathlib.Analysis.Normed.Algebra.TrivSqZeroExt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TrivSqZeroExt._example", "kind": "example", "module": "Mathlib.Analysis.Normed.Algebra.TrivSqZeroExt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUltrametricDist.of_normedAlgebra'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.Ultra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Unitization.splitMul_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.Unitization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitization.splitMul_injective_of_clm_mul_injective", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.Unitization", "is_tactic_proof": true, "tactics": ["rw", "intro", "induction", "rw", "simp", "obtain", "simp", "rw", "rw"], "tactic_count": 9}
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{"name": "Unitization.norm_def", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.Unitization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Unitization.norm_eq_sup", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.Unitization", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Unitization.nnnorm_eq_sup", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.Unitization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitization.lipschitzWith_addEquiv", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.Unitization", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "refine", "rw", "exact", "nontriviality", "rw", "calc", "simpa", "norm_le_add_norm_add"], "tactic_count": 11}
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{"name": "Unitization.uniformity_eq_aux", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.Unitization", "is_tactic_proof": false, "tactics": ["have", "antilipschitzWith_addEquiv.isUniformInducing", "rw", "rfl"], "tactic_count": 4}
{"name": "Unitization.cobounded_eq_aux", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.Unitization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitization.isUniformEmbedding_addEquiv", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.Unitization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitization.norm_inr", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.Unitization", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Unitization.nnnorm_inr", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.Unitization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitization.isometry_inr", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.Unitization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitization.continuous_inr", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.Unitization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitization.dist_inr", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.Unitization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unitization.nndist_inr", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.Unitization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.unitization_addEquiv_prod", "kind": "definition", "module": "Mathlib.Analysis.Normed.Algebra.UnitizationL1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.instUnitizationNormedAddCommGroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Algebra.UnitizationL1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.uniformEquiv_unitization_addEquiv_prod", "kind": "definition", "module": "Mathlib.Analysis.Normed.Algebra.UnitizationL1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.instCompleteSpace", "kind": "instance", "module": "Mathlib.Analysis.Normed.Algebra.UnitizationL1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.unitization_norm_def", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.UnitizationL1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.unitization_nnnorm_def", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.UnitizationL1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.unitization_norm_inr", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.UnitizationL1", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WithLp.unitization_nnnorm_inr", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.UnitizationL1", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WithLp.unitization_isometry_inr", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.UnitizationL1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.instUnitizationRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Algebra.UnitizationL1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.unitization_mul", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.UnitizationL1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.instAlgebraOfNatENNRealUnitizationOfIsScalarTower", "kind": "instance", "module": "Mathlib.Analysis.Normed.Algebra.UnitizationL1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.unitization_algebraMap", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Algebra.UnitizationL1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.unitizationAlgEquiv", "kind": "definition", "module": "Mathlib.Analysis.Normed.Algebra.UnitizationL1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.instUnitizationNormedRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Algebra.UnitizationL1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.instUnitizationNormedAlgebra", "kind": "instance", "module": "Mathlib.Analysis.Normed.Algebra.UnitizationL1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedDivisionRing.toNormedRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedDivisionRing.toNormMulClass", "kind": "instance", "module": "Mathlib.Analysis.Normed.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedDivisionRing.to_normOneClass", "kind": "instance", "module": "Mathlib.Analysis.Normed.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "norm_div", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nnnorm_div", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "norm_inv", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nnnorm_inv", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "enorm_inv", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "norm_zpow", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nnnorm_zpow", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dist_inv_inv₀", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.Basic", "is_tactic_proof": true, "tactics": ["rw", "dist_eq_norm',"], "tactic_count": 2}
{"name": "nndist_inv_inv₀", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "norm_commutator_sub_one_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "nnnorm_commutator_sub_one_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "NormedDivisionRing.norm_eq_one_iff_ne_zero_of_discrete", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.Basic", "is_tactic_proof": true, "tactics": ["constructor", "contrapose", "simp", "have", "simp_rw", "obtain", "wlog", "rcases", "rw", "replace", "rw", "exact", "obtain", "rw", "specialize", "simp"], "tactic_count": 16}
{"name": "NormedDivisionRing.norm_le_one_of_discrete", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simp"], "tactic_count": 3}
{"name": "NormedDivisionRing.unitClosedBall_eq_univ_of_discrete", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "DenselyNormedField.toNontriviallyNormedField", "kind": "instance", "module": "Mathlib.Analysis.Normed.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedField.toNormedDivisionRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedField.toNormedCommRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedField.exists_one_lt_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedField.exists_one_lt_nnnorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedField.exists_one_lt_enorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedField.exists_lt_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedField.exists_lt_nnnorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedField.exists_lt_enorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.Basic", "is_tactic_proof": true, "tactics": ["lift", "exact"], "tactic_count": 2}
{"name": "NormedField.exists_norm_lt", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedField.exists_nnnorm_lt", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedField.exists_enorm_lt", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedField.exists_norm_lt_one", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedField.exists_nnnorm_lt_one", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedField.exists_enorm_lt_one", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedField.nhdsNE_neBot", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.Basic", "is_tactic_proof": true, "tactics": ["rw", "rintro", "rcases", "refine", "rwa"], "tactic_count": 5}
{"name": "NormedField.nhdsWithin_isUnit_neBot", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "NormedField.exists_lt_norm_lt", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedField.exists_lt_nnnorm_lt", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedField.denselyOrdered_range_norm", "kind": "instance", "module": "Mathlib.Analysis.Normed.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedField.denselyOrdered_range_nnnorm", "kind": "instance", "module": "Mathlib.Analysis.Normed.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NontriviallyNormedField.ofNormNeOne", "kind": "definition", "module": "Mathlib.Analysis.Normed.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.normedField", "kind": "instance", "module": "Mathlib.Analysis.Normed.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.denselyNormedField", "kind": "instance", "module": "Mathlib.Analysis.Normed.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.toNNReal_mul_nnnorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Real.nnnorm_mul_toNNReal", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NormedDivisionRing.induced", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedField.induced", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubfieldClass.toNormedField", "kind": "instance", "module": "Mathlib.Analysis.Normed.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AbsoluteValue.toNormedField", "kind": "definition", "module": "Mathlib.Analysis.Normed.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedField.instCompletableTopField", "kind": "instance", "module": "Mathlib.Analysis.Normed.Field.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DilationEquiv.mulLeft", "kind": "definition", "module": "Mathlib.Analysis.Normed.Field.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DilationEquiv.mulRight", "kind": "definition", "module": "Mathlib.Analysis.Normed.Field.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map_mul_left_cobounded", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map_mul_right_cobounded", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_mul_left_cobounded", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_mul_right_cobounded", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.inv_cobounded₀", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Filter.inv_nhdsNE_zero", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.tendsto_inv₀_cobounded'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_inv₀_cobounded", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_inv₀_nhdsNE_zero", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformContinuousOn_inv₀", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "intro", "rcases", "simp", "have", "refine", "calc", "dist", "rw", "gcongr"], "tactic_count": 10}
{"name": "UniformContinuousOn.inv₀", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformContinuous.inv₀", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.Lemmas", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "TendstoLocallyUniformlyOn.inv₀_of_disjoint", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "intro", "rcases", "refine", "tendsto_inf.mpr", "filter_upwards", "have", "have", "simp", "linarith", "simp_all"], "tactic_count": 11}
{"name": "TendstoLocallyUniformly.inv₀_of_disjoint", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "apply", "simpa"], "tactic_count": 3}
{"name": "TendstoLocallyUniformlyOn.inv₀", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TendstoLocallyUniformly.inv₀", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedDivisionRing.to_continuousInv₀", "kind": "instance", "module": "Mathlib.Analysis.Normed.Field.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TendstoLocallyUniformlyOn.div₀", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.Lemmas", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "TendstoLocallyUniformly.div₀", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.Lemmas", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "NormedDivisionRing.to_isTopologicalDivisionRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Field.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_norm_inv_nhdsNE_zero_atTop", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_zpow_nhdsNE_zero_cobounded", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.Lemmas", "is_tactic_proof": true, "tactics": ["obtain", "lift", "simpa"], "tactic_count": 3}
{"name": "NormedField.tendsto_norm_zpow_nhdsNE_zero_atTop", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedField.discreteTopology_or_nontriviallyNormedField", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.Lemmas", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "simp_rw", "refine", "contrapose", "refine", "simp"], "tactic_count": 7}
{"name": "NormedField.discreteTopology_of_bddAbove_range_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.Lemmas", "is_tactic_proof": true, "tactics": ["refine", "rintro", "obtain", "obtain", "exact"], "tactic_count": 5}
{"name": "NormedField.denseRange_nnnorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedField.continuousAt_zpow", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.Lemmas", "is_tactic_proof": true, "tactics": ["refine", "contrapose", "rintro", "exact"], "tactic_count": 4}
{"name": "NormedField.continuousAt_inv", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.Lemmas", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Rat.instNormedField", "kind": "instance", "module": "Mathlib.Analysis.Normed.Field.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.instDenselyNormedField", "kind": "instance", "module": "Mathlib.Analysis.Normed.Field.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedField.completeSpace_iff_isComplete_closedBall", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.Lemmas", "is_tactic_proof": true, "tactics": ["constructor", "exact", "rcases", "rwa", "refine", "obtain", "have", "obtain", "have", "have", "intro", "simp", "rw", "exact", "obtain", "refine", "have", "contrapose", "simp", "simp"], "tactic_count": 20}
{"name": "ProperSpace.of_nontriviallyNormedField_of_weaklyLocallyCompactSpace", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.ProperSpace", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "have", "have", "convert", "ext", "simp", "norm_inv,", "have", "exact"], "tactic_count": 10}
{"name": "Equiv.normedField", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Field.TransferInstance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUltrametricDist.isUltrametricDist_of_forall_norm_add_one_le_max_norm_one", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.Ultra", "is_tactic_proof": true, "tactics": ["refine", "rcases", "simpa", "have", "simpa", "div_mul_cancel₀"], "tactic_count": 6}
{"name": "IsUltrametricDist.isUltrametricDist_of_forall_norm_add_one_of_norm_le_one", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.Ultra", "is_tactic_proof": true, "tactics": ["refine", "rcases", "exact", "suffices", "rw", "apply", "simp"], "tactic_count": 7}
{"name": "IsUltrametricDist.isUltrametricDist_of_forall_norm_sub_one_of_norm_le_one", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.Ultra", "is_tactic_proof": false, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "IsUltrametricDist.isUltrametricDist_of_forall_pow_norm_le_nsmul_pow_max_one_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.Ultra", "is_tactic_proof": true, "tactics": ["refine", "isUltrametricDist_of_forall_norm_add_one_le_max_norm_one", "rw", "refine", "have", "obtain", "apply_mod_cast", "rwa", "rw", "have", "rw", "rw", "refine", "simp"], "tactic_count": 14}
{"name": "IsUltrametricDist.isUltrametricDist_of_forall_norm_natCast_le_one", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.Ultra", "is_tactic_proof": true, "tactics": ["refine", "isUltrametricDist_of_forall_pow_norm_le_nsmul_pow_max_one_norm", "replace", "rw", "rcases", "simp", "simpa", "h", "transitivity", "simpa", "rw", "rcases", "gcongr", "rcases", "simp", "show", "rw", "exact", "contrapose", "exact", "simpa"], "tactic_count": 21}
{"name": "isUltrametricDist_iff_forall_norm_natCast_le_one", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.Ultra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.unitBall", "kind": "definition", "module": "Mathlib.Analysis.Normed.Field.UnitBall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.unitBall.instSemigroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Field.UnitBall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.unitBall.instContinuousMul", "kind": "instance", "module": "Mathlib.Analysis.Normed.Field.UnitBall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.unitBall.instCommSemigroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Field.UnitBall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.unitBall.instHasDistribNeg", "kind": "instance", "module": "Mathlib.Analysis.Normed.Field.UnitBall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.unitBall.coe_mul", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.UnitBall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.unitBall.instZero", "kind": "instance", "module": "Mathlib.Analysis.Normed.Field.UnitBall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.unitBall.coe_zero", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.UnitBall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.unitBall.coe_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.UnitBall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.unitBall.instSemigroupWithZero", "kind": "instance", "module": "Mathlib.Analysis.Normed.Field.UnitBall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.unitBall.instIsLeftCancelMulZero", "kind": "instance", "module": "Mathlib.Analysis.Normed.Field.UnitBall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.unitBall.instIsRightCancelMulZero", "kind": "instance", "module": "Mathlib.Analysis.Normed.Field.UnitBall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.unitBall.instIsCancelMulZero", "kind": "instance", "module": "Mathlib.Analysis.Normed.Field.UnitBall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.unitClosedBall", "kind": "definition", "module": "Mathlib.Analysis.Normed.Field.UnitBall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.unitClosedBall.instSemigroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Field.UnitBall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.unitClosedBall.instHasDistribNeg", "kind": "instance", "module": "Mathlib.Analysis.Normed.Field.UnitBall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.unitClosedBall.instContinuousMul", "kind": "instance", "module": "Mathlib.Analysis.Normed.Field.UnitBall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.unitClosedBall.coe_mul", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.UnitBall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.unitClosedBall.instZero", "kind": "instance", "module": "Mathlib.Analysis.Normed.Field.UnitBall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.unitClosedBall.coe_zero", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.UnitBall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.unitClosedBall.coe_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.UnitBall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.unitClosedBall.instSemigroupWithZero", "kind": "instance", "module": "Mathlib.Analysis.Normed.Field.UnitBall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.unitClosedBall", "kind": "definition", "module": "Mathlib.Analysis.Normed.Field.UnitBall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.unitClosedBall.instMonoid", "kind": "instance", "module": "Mathlib.Analysis.Normed.Field.UnitBall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.unitClosedBall.instCommMonoid", "kind": "instance", "module": "Mathlib.Analysis.Normed.Field.UnitBall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.unitClosedBall.coe_one", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.UnitBall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.unitClosedBall.coe_eq_one", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.UnitBall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.unitClosedBall.coe_pow", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.UnitBall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.unitClosedBall.instMonoidWithZero", "kind": "instance", "module": "Mathlib.Analysis.Normed.Field.UnitBall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.unitClosedBall.instIsCancelMulZero", "kind": "instance", "module": "Mathlib.Analysis.Normed.Field.UnitBall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.unitSphere", "kind": "definition", "module": "Mathlib.Analysis.Normed.Field.UnitBall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.unitSphere.instInv", "kind": "instance", "module": "Mathlib.Analysis.Normed.Field.UnitBall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.unitSphere.coe_inv", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.UnitBall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.unitSphere.instDiv", "kind": "instance", "module": "Mathlib.Analysis.Normed.Field.UnitBall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.unitSphere.coe_div", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.UnitBall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.unitSphere.instZPow", "kind": "instance", "module": "Mathlib.Analysis.Normed.Field.UnitBall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.unitSphere.coe_zpow", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.UnitBall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.unitSphere.instMonoid", "kind": "instance", "module": "Mathlib.Analysis.Normed.Field.UnitBall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.unitSphere.instCommMonoid", "kind": "instance", "module": "Mathlib.Analysis.Normed.Field.UnitBall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.unitSphere.coe_one", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.UnitBall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.unitSphere.coe_mul", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.UnitBall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.unitSphere.coe_pow", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.UnitBall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitSphereToUnits", "kind": "definition", "module": "Mathlib.Analysis.Normed.Field.UnitBall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitSphereToUnits_apply_coe", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.UnitBall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitSphereToUnits_injective", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.UnitBall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.unitSphere.instGroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Field.UnitBall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.sphere.instHasDistribNeg", "kind": "instance", "module": "Mathlib.Analysis.Normed.Field.UnitBall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.sphere.instContinuousMul", "kind": "instance", "module": "Mathlib.Analysis.Normed.Field.UnitBall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.sphere.instIsTopologicalGroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Field.UnitBall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.sphere.instCommGroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Field.UnitBall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithAbs.instField", "kind": "instance", "module": "Mathlib.Analysis.Normed.Field.WithAbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithAbs.normedField", "kind": "instance", "module": "Mathlib.Analysis.Normed.Field.WithAbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithAbs.instFiniteDimensional", "kind": "instance", "module": "Mathlib.Analysis.Normed.Field.WithAbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithAbs.instIsSeparable", "kind": "instance", "module": "Mathlib.Analysis.Normed.Field.WithAbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithAbs.tendsto_one_div_one_add_pow_nhds_one", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.WithAbs", "is_tactic_proof": true, "tactics": ["simpa", "inv_one"], "tactic_count": 2}
{"name": "WithAbs.isometry_of_comp", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.WithAbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithAbs.pseudoMetricSpace_induced_of_comp", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.WithAbs", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "WithAbs.uniformSpace_comap_eq_of_comp", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.WithAbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithAbs.isUniformInducing_of_comp", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.WithAbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AbsoluteValue.Completion", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Field.WithAbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AbsoluteValue.Completion.instCoe", "kind": "instance", "module": "Mathlib.Analysis.Normed.Field.WithAbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AbsoluteValue.Completion.extensionEmbedding_of_comp", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Field.WithAbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AbsoluteValue.Completion.extensionEmbedding_of_comp_coe", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.WithAbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AbsoluteValue.Completion.extensionEmbedding_dist_eq_of_comp", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.WithAbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AbsoluteValue.Completion.isometry_extensionEmbedding_of_comp", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.WithAbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AbsoluteValue.Completion.isClosedEmbedding_extensionEmbedding_of_comp", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.WithAbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AbsoluteValue.Completion.locallyCompactSpace", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Field.WithAbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCircle.instNormedAddCommGroupReal", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.AddCircle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCircle.norm_coe_mul", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.AddCircle", "is_tactic_proof": true, "tactics": ["obtain", "simp", "simp", "congr", "simp_rw", "simp"], "tactic_count": 6}
{"name": "AddCircle.norm_neg_period", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.AddCircle", "is_tactic_proof": false, "tactics": ["suffices", "rw", "simp", "simp"], "tactic_count": 4}
{"name": "AddCircle.norm_eq_of_zero", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.AddCircle", "is_tactic_proof": true, "tactics": ["suffices", "ext", "simp"], "tactic_count": 3}
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{"name": "AddCircle.norm_le_half_period", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.AddCircle", "is_tactic_proof": true, "tactics": ["obtain", "change", "rw", "mul_div_assoc,", "exact"], "tactic_count": 5}
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{"name": "AddCircle.coe_real_preimage_closedBall_period_zero", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.AddCircle", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "AddCircle.coe_real_preimage_closedBall_eq_iUnion", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.AddCircle", "is_tactic_proof": true, "tactics": ["rcases", "simp", "ext", "simp", "refine", "rintro", "rw", "inv_mul_cancel_left₀", "exact"], "tactic_count": 9}
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{"name": "AddCircle.norm_div_natCast", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.AddCircle", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "AddCircle.exists_norm_eq_of_isOfFinAddOrder", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.AddCircle", "is_tactic_proof": true, "tactics": ["let", "change", "obtain", "refine", "rw"], "tactic_count": 5}
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{"name": "UnitAddCircle.norm_eq", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.AddCircle", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NormedAddTorsor.toAddTorsor'", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.AddTorsor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddTorsor.to_isIsIsometricVAdd", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.AddTorsor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeminormedAddCommGroup.toNormedAddTorsor", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.AddTorsor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.toNormedAddTorsor", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.AddTorsor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instNormedAddTorsorProd", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.AddTorsor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "metricSpaceOfNormedAddCommGroupOfAddTorsor", "kind": "definition", "module": "Mathlib.Analysis.Normed.Group.AddTorsor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzWith.vadd", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.AddTorsor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "instIsTopologicalAddTorsor_1", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.AddTorsor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInvolutiveNegElemSphereOfNat", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.BallSphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "coe_neg_sphere", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.BallSphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instContinuousNegElemSphereOfNat", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.BallSphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInvolutiveNegElemBallOfNat", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.BallSphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "coe_neg_ball", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.BallSphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instContinuousNegElemBallOfNat", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.BallSphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInvolutiveNegElemClosedBallOfNat", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.BallSphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "coe_neg_closedBall", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.BallSphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instContinuousNegElemClosedBallOfNat", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.BallSphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "term‖_‖", "kind": "definition", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "_aux_Mathlib_Analysis_Normed_Group_Basic___unexpand_Norm_norm_1", "kind": "definition", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "term‖_‖₊", "kind": "definition", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "_aux_Mathlib_Analysis_Normed_Group_Basic___unexpand_NNNorm_nnnorm_1", "kind": "definition", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "term‖_‖ₑ", "kind": "definition", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "NNNorm.toENorm", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "NormedGroup.toSeminormedGroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedCommGroup.toSeminormedCommGroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeminormedCommGroup.toSeminormedGroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedCommGroup.toNormedGroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "NormedCommGroup.ofSeparation", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeminormedGroup.ofMulDist", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeminormedGroup.ofMulDist'", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "NormedGroup.ofMulDist", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedGroup.ofMulDist'", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedCommGroup.ofMulDist", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedCommGroup.ofMulDist'", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "GroupSeminorm.toSeminormedCommGroup", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupNorm.toNormedGroup", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupNorm.toNormedCommGroup", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "DiscreteTopology.of_forall_le_norm'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "dist_one_left", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "dist_one", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "norm_div_rev", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "norm_inv'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "norm_zpow_abs", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "norm_pow_natAbs", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "norm_zpow_isUnit", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "norm_units_zsmul", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dist_mulIndicator", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "norm_mul_le'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "norm_mul_le_of_le'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "norm_mul₃_le'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "norm_mul₄_le'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "norm_div_le_norm_div_add_norm_div", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "norm_le_norm_div_add", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "norm_nonneg'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "abs_norm'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "norm_one'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ne_one_of_norm_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "norm_of_subsingleton'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "zero_lt_one_add_norm_sq'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["positivity"], "tactic_count": 1}
{"name": "norm_div_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "norm_div_le_of_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dist_le_norm_add_norm'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "abs_norm_sub_norm_le'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "norm_sub_norm_le'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "norm_sub_le_norm_mul", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "dist_norm_norm_le'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "norm_le_norm_add_norm_div'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw"], "tactic_count": 3}
{"name": "norm_le_norm_add_norm_div", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "norm_le_mul_norm_add", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "norm_le_mul_norm_add'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "norm_mul_eq_norm_right", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["apply", "simpa", "simpa"], "tactic_count": 3}
{"name": "norm_mul_eq_norm_left", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["apply", "simpa", "simpa"], "tactic_count": 3}
{"name": "norm_div_eq_norm_right", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["apply", "simpa", "simpa"], "tactic_count": 3}
{"name": "norm_div_eq_norm_left", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["apply", "simpa", "simpa"], "tactic_count": 3}
{"name": "ball_eq'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ball_one_eq", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_ball_iff_norm''", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mem_ball_iff_norm'''", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mem_ball_one_iff", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mem_closedBall_iff_norm''", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mem_closedBall_one_iff", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mem_closedBall_iff_norm'''", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "norm_le_of_mem_closedBall'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "norm_le_norm_add_const_of_dist_le'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "norm_lt_of_mem_ball'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "norm_div_sub_norm_div_le_norm_div", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "norm_mul_sub_norm_div_le_two_mul", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "norm_mul_sub_norm_div_le_two_mul_min", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "exact", "norm_mul_sub_norm_div_le_two_mul"], "tactic_count": 5}
{"name": "mem_sphere_iff_norm'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "mem_sphere_one_iff_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "norm_eq_of_mem_sphere'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ne_one_of_mem_sphere", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ne_one_of_mem_unit_sphere", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "normGroupSeminorm", "kind": "definition", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "coe_normGroupSeminorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedCommGroup.tendsto_nhds_one", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedCommGroup.tendsto_nhds_nhds", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "NormedCommGroup.nhds_basis_norm_lt", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "NormedCommGroup.nhds_one_basis_norm_lt", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "NormedCommGroup.uniformity_basis_dist", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "SeminormedGroup.toNNNorm", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "coe_nnnorm'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "coe_comp_nnnorm'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "norm_toNNReal'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toReal_enorm'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ofReal_norm'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "enorm'_eq_iff_norm_eq", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["simp", "refine", "exact"], "tactic_count": 3}
{"name": "enorm'_le_iff_norm_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["simp", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "nndist_eq_nnnorm_div", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nndist_one_right", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "edist_one_right", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "nnnorm_one'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ne_one_of_nnnorm_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nnnorm_mul_le'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "norm_pow_le_mul_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nnnorm_pow_le_mul_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "nnnorm_inv'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nnnorm_zpow_abs", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nnnorm_pow_natAbs", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nnnorm_zpow_isUnit", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nnnorm_units_zsmul", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nndist_one_left", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "edist_one_left", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "nndist_mulIndicator", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nnnorm_div_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "enorm_div_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "nndist_nnnorm_nnnorm_le'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nnnorm_le_nnnorm_add_nnnorm_div", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nnnorm_le_nnnorm_add_nnnorm_div'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nnnorm_le_mul_nnnorm_add", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nnnorm_le_mul_nnnorm_add'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nnnorm_mul_eq_nnnorm_right", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nnnorm_mul_eq_nnnorm_left", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nnnorm_div_eq_nnnorm_right", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nnnorm_div_eq_nnnorm_left", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toReal_coe_nnnorm'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "edist_mulIndicator", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "nontrivialTopology_iff_exists_nnnorm_ne_zero'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "indiscreteTopology_iff_forall_nnnorm_eq_zero'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "exists_nnnorm_ne_zero'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IndiscreteTopology.nnnorm_eq_zero'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nontrivialTopology_iff_exists_norm_ne_zero'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "indiscreteTopology_iff_forall_norm_eq_zero'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "exists_norm_ne_zero'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IndiscreteTopology.norm_eq_zero'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "enorm_one'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "exists_enorm_lt'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "enorm_inv'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ofReal_norm_eq_enorm'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instENormENNReal", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "enorm_eq_self", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "edist_eq_enorm_div", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "edist_one_eq_enorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "enorm_div_rev", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mem_eball_one_iff", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "continuous_enorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.enorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.enorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["fun_prop"], "tactic_count": 1}
{"name": "ContinuousWithinAt.enorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.enorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "enorm_mul_le'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "enorm_mul_le_of_le'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "enorm_mul₃_le'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "enorm_mul₄_le'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "enorm_eq_zero'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "enorm_ne_zero'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "enorm_pos'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instENormedAddCommMonoidENNReal", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeminormedGroup.disjoint_nhds", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SeminormedGroup.disjoint_nhds_one", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "SeminormedGroup.induced", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeminormedCommGroup.induced", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedGroup.induced", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedCommGroup.induced", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.norm", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.norm_eq_abs", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.normedAddCommGroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.norm_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.norm_of_nonpos", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.le_norm_self", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.norm_natCast", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.nnnorm_natCast", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.enorm_natCast", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.norm_ofNat", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.nnnorm_ofNat", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.norm_two", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.nnnorm_two", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.norm_nnratCast", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.nnnorm_nnratCast", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.nnnorm_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.enorm_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.enorm_ofReal_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.nnnorm_abs", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.enorm_abs", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.enorm_eq_ofReal", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.enorm_eq_ofReal_abs", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.toNNReal_eq_nnnorm_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["rw", "congr", "rw"], "tactic_count": 3}
{"name": "Real.ofReal_le_enorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NNReal.instNNNorm", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.nnnorm_eq_self", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dist_inv", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "norm_multiset_sum_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "enorm_multisetSum_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "norm_multiset_prod_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "enorm_multisetProd_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "enorm_sum_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "norm_sum_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "enorm_prod_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "norm_prod_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "enorm_prod_le_of_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "norm_prod_le_of_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dist_prod_prod_le_of_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "dist_prod_prod_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_mem_ball_iff_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mul_mem_closedBall_iff_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "preimage_mul_ball", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "preimage_mul_closedBall", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "preimage_mul_sphere", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "pow_mem_closedBall", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["simp", "refine", "simpa"], "tactic_count": 3}
{"name": "pow_mem_ball", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["simp", "refine", "replace", "rw", "nlinarith"], "tactic_count": 5}
{"name": "mul_mem_closedBall_mul_iff", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "mul_mem_ball_mul_iff", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "smul_closedBall''", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "smul_ball''", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "nnnorm_multiset_prod_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nnnorm_prod_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nnnorm_prod_le_of_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "norm_norm'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nnnorm_norm'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "enorm_norm'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "enorm_enorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "norm_le_zero_iff'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "norm_pos_iff'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "norm_eq_zero'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "norm_ne_zero_iff'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "norm_div_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "norm_div_pos_iff", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "eq_of_norm_div_le_zero", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "eq_one_or_norm_pos", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "eq_one_or_nnnorm_pos", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nnnorm_eq_zero'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "nnnorm_ne_zero_iff'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nnnorm_pos'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "normGroupNorm", "kind": "definition", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "coe_normGroupNorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasCompactSupport_norm_iff", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_norm_atTop_atTop", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalMulNorm", "kind": "definition", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalAddNorm", "kind": "definition", "module": "Mathlib.Analysis.Normed.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "comap_norm_atTop'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Bounded", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Filter.HasBasis.cobounded_of_norm'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.hasBasis_cobounded_norm'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_norm_atTop_iff_cobounded'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Bounded", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "tendsto_norm_cobounded_atTop'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eventually_cobounded_le_norm'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_norm_cocompact_atTop'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.inv_cobounded", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Bounded", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.tendsto_inv_cobounded", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isBounded_iff_forall_norm_le'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Bounded", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Bornology.IsBounded.exists_pos_norm_le'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.IsBounded.exists_pos_norm_lt'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedCommGroup.cauchySeq_iff", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Bounded", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsCompact.exists_bound_of_continuousOn'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasCompactMulSupport.exists_bound_of_continuous", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Bounded", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Filter.Tendsto.op_one_isBoundedUnder_le'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Bounded", "is_tactic_proof": true, "tactics": ["obtain", "rcases", "rw", "intro", "rcases", "filter_upwards", "refine", "rcases", "exact", "ε₀", "calc"], "tactic_count": 11}
{"name": "Filter.Tendsto.op_one_isBoundedUnder_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_norm_comp_cofinite_atTop_of_isClosedEmbedding'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Bounded", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "Continuous.bounded_above_of_compact_support", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Bounded", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasCompactMulSupport.exists_pos_le_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Bounded", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "refine", "contrapose", "exact"], "tactic_count": 5}
{"name": "CocompactMapClass.norm_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.CocompactMap", "is_tactic_proof": true, "tactics": ["have", "rw", "specialize", "rcases", "use", "intro", "suffices", "apply", "simp"], "tactic_count": 9}
{"name": "Filter.tendsto_cocompact_cocompact_of_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.CocompactMap", "is_tactic_proof": true, "tactics": ["rw", "intro", "rcases", "rcases", "apply", "use", "intro", "simp", "apply", "simp"], "tactic_count": 10}
{"name": "ContinuousMapClass.toCocompactMapClass_of_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.CocompactMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.exists_subseq_summable_dist_of_cauchySeq", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Completeness", "is_tactic_proof": false, "tactics": ["obtain", "refine", "refine", "exact"], "tactic_count": 4}
{"name": "NormedAddCommGroup.completeSpace_of_summable_imp_tendsto", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Completeness", "is_tactic_proof": true, "tactics": ["apply", "intro", "obtain", "simp", "let", "have", "ext", "exact", "obtain", "refine", "refine", "rw", "have", "simpa"], "tactic_count": 14}
{"name": "NormedAddCommGroup.summable_imp_tendsto_of_complete", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Completeness", "is_tactic_proof": true, "tactics": ["refine", "simp"], "tactic_count": 2}
{"name": "NormedAddCommGroup.summable_imp_tendsto_iff_completeSpace", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Completeness", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.instNorm", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.norm_coe", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.instNormedAddCommGroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.nnnorm_coe", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Completion", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "UniformSpace.Completion.enorm_coe", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Completion", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PUnit.normedAddCommGroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PUnit.norm_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.norm", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.norm_def", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.norm_up", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.norm_down", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.nnnorm", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.nnnorm_def", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.nnnorm_up", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.nnnorm_down", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.seminormedGroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.seminormedCommGroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.normedGroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.normedCommGroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Additive.toNorm", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiplicative.toNorm", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "norm_toMul", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "norm_ofMul", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "norm_toAdd", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "norm_ofAdd", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Additive.toNNNorm", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiplicative.toNNNorm", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nnnorm_toMul", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nnnorm_ofMul", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nnnorm_toAdd", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nnnorm_ofAdd", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Additive.seminormedAddGroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiplicative.seminormedGroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Additive.seminormedCommGroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiplicative.seminormedAddCommGroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Additive.normedAddGroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiplicative.normedGroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Additive.normedAddCommGroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiplicative.normedCommGroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.toNorm", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "norm_toDual", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "norm_ofDual", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.toNNNorm", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nnnorm_toDual", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nnnorm_ofDual", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.seminormedGroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.seminormedCommGroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.normedGroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.normedCommGroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.toNorm", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.norm_def", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "norm_prod_le_iff", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.seminormedGroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Prod.normedCommGroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.seminormedGroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Pi.nnnorm_def'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pi_norm_le_iff_of_nonneg'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Constructions", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "pi_nnnorm_le_iff'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pi_norm_le_iff_of_nonempty'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Constructions", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "exact", "iff_of_false", "hr"], "tactic_count": 5}
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{"name": "norm_le_pi_norm'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nnnorm_le_pi_nnnorm'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MulOpposite.instNormedAddGroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instSeminormedAddCommGroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instNormedAddCommGroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SeminormedGroup.toContinuousENorm", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Continuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedGroup.toENormedMonoid", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Continuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedCommGroup.toENormedCommMonoid", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Continuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Inseparable.nnnorm_eq_nnnorm'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Continuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ContinuousWithinAt.nnnorm'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Continuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ContinuousOn.nnnorm'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Continuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SeminormedGroup.tendstoUniformlyOn_one", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Continuity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SeminormedGroup.uniformCauchySeqOnFilter_iff_tendstoUniformlyOnFilter_one", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Continuity", "is_tactic_proof": true, "tactics": ["refine", "obtain", "refine", "simpa", "obtain", "refine", "simpa"], "tactic_count": 7}
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{"name": "comap_norm_nhdsGT_zero'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Continuity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "tendstoUniformlyOn_tsum_of_cofinite_eventually", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.FunctionSeries", "is_tactic_proof": true, "tactics": ["classical", "refine", "have", "simp", "obtain", "rw", "obtain", "refine", "have", "apply", "apply", "simp", "aesop", "rw", "apply", "apply", "apply", "simp", "apply", "have", "simp_all"], "tactic_count": 21}
{"name": "tendstoUniformlyOn_tsum_nat_eventually", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.FunctionSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendstoUniformly_tsum", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.FunctionSeries", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "tendstoUniformly_tsum_nat", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.FunctionSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendstoUniformly_tsum_of_cofinite_eventually", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.FunctionSeries", "is_tactic_proof": true, "tactics": ["rw", "apply", "simpa"], "tactic_count": 3}
{"name": "continuousOn_tsum", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.FunctionSeries", "is_tactic_proof": true, "tactics": ["classical", "refine", "intro", "exact"], "tactic_count": 4}
{"name": "continuous_tsum", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.FunctionSeries", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "AddMonoidHom.mkNormedAddGroupHom", "kind": "definition", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.mkNormedAddGroupHom'", "kind": "definition", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_pos_bound_of_bound", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.ofLipschitz", "kind": "definition", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.funLike", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.toAddMonoidHomClass", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.coe_inj", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "NormedAddGroupHom.coe_injective", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "NormedAddGroupHom.coe_inj_iff", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.ext", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.toFun_eq_coe", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.coe_mk", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.coe_mkNormedAddGroupHom", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.coe_mkNormedAddGroupHom'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.toAddMonoidHom", "kind": "definition", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.coe_toAddMonoidHom", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.toAddMonoidHom_injective", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.mk_toAddMonoidHom", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.bound", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.antilipschitz_of_norm_ge", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.SurjectiveOnWith", "kind": "definition", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.SurjectiveOnWith.mono", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": true, "tactics": ["intro", "rcases", "use", "by_cases", "simpa", "exact"], "tactic_count": 6}
{"name": "NormedAddGroupHom.SurjectiveOnWith.exists_pos", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": true, "tactics": ["refine", "linarith", "apply", "linarith"], "tactic_count": 4}
{"name": "NormedAddGroupHom.SurjectiveOnWith.surjOn", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.opNorm", "kind": "definition", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.hasOpNorm", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.norm_def", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.bounds_nonempty", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.bounds_bddBelow", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.opNorm_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.le_opNorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": true, "tactics": ["obtain", "replace", "by_cases", "rwa", "have", "exact"], "tactic_count": 6}
{"name": "NormedAddGroupHom.le_opNorm_of_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.le_of_opNorm_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.lipschitz", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.uniformContinuous", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.continuous", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.instContinuousMapClass", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.ratio_le_opNorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.opNorm_le_bound", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.opNorm_eq_of_bounds", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.opNorm_le_of_lipschitz", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.mkNormedAddGroupHom_norm_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.ofLipschitz_norm_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.mkNormedAddGroupHom_norm_le'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.add", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.opNorm_add_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.coe_add", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.add_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.zero", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.inhabited", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.opNorm_zero", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.opNorm_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.coe_zero", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.zero_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.id", "kind": "definition", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.norm_id_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.norm_id", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.norm_id_of_nontrivial_seminorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.coe_id", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.neg", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.coe_neg", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.neg_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.opNorm_neg", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NormedAddGroupHom.sub", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.coe_sub", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.sub_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.smul", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.coe_smul", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.smul_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.smulCommClass", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.isScalarTower", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.isCentralScalar", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.nsmul", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.coe_nsmul", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.nsmul_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.zsmul", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.coe_zsmul", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.zsmul_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.toAddCommGroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.toSeminormedAddCommGroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.toNormedAddCommGroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.coeAddHom", "kind": "definition", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.coe_sum", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.sum_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NormedAddGroupHom.distribMulAction", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.module", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.comp", "kind": "definition", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.norm_comp_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.norm_comp_le_of_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.norm_comp_le_of_le'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "NormedAddGroupHom.compHom", "kind": "definition", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.comp_zero", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "NormedAddGroupHom.zero_comp", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "NormedAddGroupHom.comp_assoc", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "NormedAddGroupHom.coe_comp", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.incl", "kind": "definition", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.norm_incl", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.ker", "kind": "definition", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.mem_ker", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NormedAddGroupHom.ker.lift", "kind": "definition", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.ker.incl_comp_lift", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "NormedAddGroupHom.ker_zero", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "NormedAddGroupHom.coe_ker", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.isClosed_ker", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.range", "kind": "definition", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.mem_range", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.mem_range_self", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.comp_range", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": true, "tactics": ["unfold", "rw", "rfl"], "tactic_count": 3}
{"name": "NormedAddGroupHom.incl_range", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "NormedAddGroupHom.range_comp_incl_top", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NormedAddGroupHom.NormNoninc", "kind": "definition", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.NormNoninc.normNoninc_iff_norm_le_one", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": true, "tactics": ["refine", "refine", "simpa", "simpa"], "tactic_count": 4}
{"name": "NormedAddGroupHom.NormNoninc.zero", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.NormNoninc.id", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.NormNoninc.comp", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.NormNoninc.neg_iff", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.norm_eq_of_isometry", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.isometry_id", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.isometry_comp", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.normNoninc_of_isometry", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.equalizer", "kind": "definition", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.Equalizer.ι", "kind": "definition", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.Equalizer.comp_ι_eq", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": true, "tactics": ["ext", "rw", "exact"], "tactic_count": 3}
{"name": "NormedAddGroupHom.Equalizer.lift", "kind": "definition", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.Equalizer.ι_comp_lift", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "NormedAddGroupHom.Equalizer.liftEquiv", "kind": "definition", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.Equalizer.map", "kind": "definition", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.Equalizer.ι_comp_map", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.Equalizer.map_id", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "NormedAddGroupHom.Equalizer.comm_sq₂", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NormedAddGroupHom.Equalizer.map_comp_map", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "NormedAddGroupHom.Equalizer.ι_normNoninc", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.Equalizer.lift_normNoninc", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.Equalizer.norm_lift_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.Equalizer.map_normNoninc", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.Equalizer.norm_map_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.completion", "kind": "definition", "module": "Mathlib.Analysis.Normed.Group.HomCompletion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.completion_def", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.HomCompletion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.completion_coe_to_fun", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.HomCompletion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.completion_coe", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.HomCompletion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.completion_coe'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.HomCompletion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "normedAddGroupHomCompletionHom", "kind": "definition", "module": "Mathlib.Analysis.Normed.Group.HomCompletion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.completion_id", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.HomCompletion", "is_tactic_proof": true, "tactics": ["ext", "rw", "rfl"], "tactic_count": 3}
{"name": "NormedAddGroupHom.completion_comp", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.HomCompletion", "is_tactic_proof": true, "tactics": ["ext", "rw", "rfl"], "tactic_count": 3}
{"name": "NormedAddGroupHom.completion_neg", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.HomCompletion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.completion_add", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.HomCompletion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.completion_sub", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.HomCompletion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.zero_completion", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.HomCompletion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddCommGroup.toCompl", "kind": "definition", "module": "Mathlib.Analysis.Normed.Group.HomCompletion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddCommGroup.norm_toCompl", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.HomCompletion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddCommGroup.denseRange_toCompl", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.HomCompletion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.completion_toCompl", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.HomCompletion", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "NormedAddGroupHom.norm_completion", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.HomCompletion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.ker_le_ker_completion", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.HomCompletion", "is_tactic_proof": true, "tactics": ["rintro", "simp"], "tactic_count": 2}
{"name": "NormedAddGroupHom.ker_completion", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.HomCompletion", "is_tactic_proof": true, "tactics": ["refine", "rintro", "rw", "intro", "rcases", "rcases", "obtain", "obtain", "have", "refine", "have", "calc", "calc"], "tactic_count": 13}
{"name": "NormedAddGroupHom.extension", "kind": "definition", "module": "Mathlib.Analysis.Normed.Group.HomCompletion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.extension_def", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.HomCompletion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.extension_coe", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.HomCompletion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.extension_coe_to_fun", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.HomCompletion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.extension_unique", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.HomCompletion", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "enorm_indicator_eq_indicator_enorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "enorm_indicator_le_of_subset", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Indicator", "is_tactic_proof": true, "tactics": ["simp", "grw"], "tactic_count": 2}
{"name": "indicator_enorm_le_enorm_self", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "enorm_indicator_le_enorm_self", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Indicator", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "norm_indicator_eq_indicator_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nnnorm_indicator_eq_indicator_nnnorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "norm_indicator_le_of_subset", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Indicator", "is_tactic_proof": true, "tactics": ["simp", "grw"], "tactic_count": 2}
{"name": "indicator_norm_le_norm_self", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "norm_indicator_le_norm_self", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Indicator", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "cauchySeq_finset_iff_vanishing_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.InfiniteSum", "is_tactic_proof": true, "tactics": ["rw", "simp", "rintro", "exact"], "tactic_count": 4}
{"name": "summable_iff_vanishing_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.InfiniteSum", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "cauchySeq_finset_of_norm_bounded_eventually", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.InfiniteSum", "is_tactic_proof": true, "tactics": ["refine", "rcases", "classical", "refine", "have", "intro", "simp", "exact", "calc"], "tactic_count": 9}
{"name": "cauchySeq_finset_of_norm_bounded", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.InfiniteSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cauchySeq_range_of_norm_bounded", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.InfiniteSum", "is_tactic_proof": true, "tactics": ["refine", "refine", "specialize", "rw", "calc"], "tactic_count": 5}
{"name": "cauchySeq_finset_of_summable_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.InfiniteSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasSum_of_subseq_of_summable", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.InfiniteSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasSum_iff_tendsto_nat_of_summable_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.InfiniteSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Summable.of_norm_bounded", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.InfiniteSum", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "HasSum.enorm_le_of_bounded", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.InfiniteSum", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "HasSum.norm_le_of_bounded", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.InfiniteSum", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "tsum_of_enorm_bounded", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.InfiniteSum", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "simp"], "tactic_count": 3}
{"name": "enorm_tsum_le_tsum_enorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.InfiniteSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tsum_of_norm_bounded", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.InfiniteSum", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "rw", "classical"], "tactic_count": 4}
{"name": "norm_tsum_le_tsum_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.InfiniteSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tsum_of_nnnorm_bounded", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.InfiniteSum", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "nnnorm_tsum_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.InfiniteSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Summable.of_norm_bounded_eventually", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.InfiniteSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Summable.of_norm_bounded_eventually_nat", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.InfiniteSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Summable.of_nnnorm_bounded", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.InfiniteSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Summable.of_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.InfiniteSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Summable.of_nnnorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.InfiniteSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.instNormedAddCommGroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Int", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.norm_cast_real", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Int", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.norm_eq_abs", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Int", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.norm_natCast", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Int", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NNReal.natCast_natAbs", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Int", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.abs_le_floor_nnreal_iff", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Int", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "norm_zpow_le_mul_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Int", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "nnnorm_zpow_le_mul_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Int", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "eventually_nnnorm_sub_lt", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eventually_norm_sub_lt", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nullSubgroup", "kind": "definition", "module": "Mathlib.Analysis.Normed.Group.NullSubmodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosed_nullSubgroup", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.NullSubmodule", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "mem_nullSubgroup_iff", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.NullSubmodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nullSubmodule", "kind": "definition", "module": "Mathlib.Analysis.Normed.Group.NullSubmodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosed_nullSubmodule", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.NullSubmodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_nullSubmodule_iff", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.NullSubmodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.IsBounded.mul", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Pointwise", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "refine", "rintro", "exact"], "tactic_count": 5}
{"name": "Bornology.IsBounded.of_mul", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.IsBounded.inv", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Pointwise", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Bornology.IsBounded.div", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "infEDist_inv_inv", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Pointwise", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "infEDist_inv", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Pointwise", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ediam_mul_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_thickening", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Pointwise", "is_tactic_proof": true, "tactics": ["simp_rw", "rfl"], "tactic_count": 2}
{"name": "inv_cthickening", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Pointwise", "is_tactic_proof": true, "tactics": ["simp_rw", "rfl"], "tactic_count": 2}
{"name": "inv_ball", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_closedBall", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "singleton_mul_ball", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Pointwise", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "singleton_div_ball", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Pointwise", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "ball_mul_singleton", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Pointwise", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ball_div_singleton", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Pointwise", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "singleton_mul_ball_one", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Pointwise", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "singleton_div_ball_one", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Pointwise", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ball_one_mul_singleton", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Pointwise", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ball_one_div_singleton", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Pointwise", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "smul_ball_one", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Pointwise", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "singleton_mul_closedBall", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Pointwise", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "singleton_div_closedBall", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Pointwise", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "closedBall_mul_singleton", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Pointwise", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "closedBall_div_singleton", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Pointwise", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "singleton_mul_closedBall_one", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Pointwise", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "singleton_div_closedBall_one", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Pointwise", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "closedBall_one_mul_singleton", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Pointwise", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "closedBall_one_div_singleton", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Pointwise", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "smul_closedBall_one", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Pointwise", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "mul_ball_one", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Pointwise", "is_tactic_proof": true, "tactics": ["rw", "convert", "exact", "ext", "simp_rw"], "tactic_count": 5}
{"name": "div_ball_one", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Pointwise", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ball_mul_one", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Pointwise", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ball_div_one", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Pointwise", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "mul_ball", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Pointwise", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "div_ball", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Pointwise", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ball_mul", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Pointwise", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ball_div", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Pointwise", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsCompact.mul_closedBall_one", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Pointwise", "is_tactic_proof": true, "tactics": ["rw", "ext", "simp", "exists_eq_right]"], "tactic_count": 4}
{"name": "IsCompact.div_closedBall_one", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Pointwise", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsCompact.closedBall_one_mul", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Pointwise", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsCompact.closedBall_one_div", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Pointwise", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsCompact.mul_closedBall", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Pointwise", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsCompact.div_closedBall", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Pointwise", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsCompact.closedBall_mul", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Pointwise", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsCompact.closedBall_div", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Pointwise", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "_private.Mathlib.Analysis.Normed.Group.Quotient.0.QuotientGroup.norm_aux", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.groupSeminorm", "kind": "definition", "module": "Mathlib.Analysis.Normed.Group.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.instNorm", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.norm_eq_groupSeminorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.norm_eq_infDist", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.le_norm_iff", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Quotient", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "QuotientGroup.norm_lt_iff", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Quotient", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "QuotientGroup.nhds_one_hasBasis", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Quotient", "is_tactic_proof": false, "tactics": ["have", "refine", "rw", "exact", "rw", "exact"], "tactic_count": 6}
{"name": "QuotientGroup.norm_mk", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Quotient", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "QuotientGroup.norm_mk_le_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.norm_mk_eq_zero_iff_mem_closure", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Quotient", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "QuotientGroup.norm_mk_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Quotient", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "QuotientGroup.exists_norm_mk_lt", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.exists_norm_mul_lt", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Quotient", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "QuotientGroup.instSeminormedCommGroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.instNormedCommGroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup._example", "kind": "example", "module": "Mathlib.Analysis.Normed.Group.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup._example", "kind": "example", "module": "Mathlib.Analysis.Normed.Group.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.quotientIsometryEquivOfEq", "kind": "definition", "module": "Mathlib.Analysis.Normed.Group.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.quotientBotIsometryEquiv", "kind": "definition", "module": "Mathlib.Analysis.Normed.Group.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.quotientQuotientIsometryEquivQuotient", "kind": "definition", "module": "Mathlib.Analysis.Normed.Group.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "quotient_norm_mk_eq", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Quotient", "is_tactic_proof": false, "tactics": ["rw", "infDist_eq_iInf]", "simp"], "tactic_count": 3}
{"name": "quotient_norm_add_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroup.normedMk", "kind": "definition", "module": "Mathlib.Analysis.Normed.Group.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroup.normedMk.apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroup.surjective_normedMk", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroup.ker_normedMk", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroup.norm_normedMk_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientAddGroup.norm_lift_apply_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Quotient", "is_tactic_proof": true, "tactics": ["cases", "inl", "rcases", "simpa", "inr", "rw", "rintro", "exact"], "tactic_count": 8}
{"name": "AddSubgroup.norm_normedMk", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Quotient", "is_tactic_proof": true, "tactics": ["refine", "obtain", "refine", "exact", "refine", "exact"], "tactic_count": 6}
{"name": "AddSubgroup.norm_trivial_quotient_mk", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Quotient", "is_tactic_proof": true, "tactics": ["refine", "have", "rw", "trivial", "rw", "simp"], "tactic_count": 6}
{"name": "NormedAddGroupHom.lift", "kind": "definition", "module": "Mathlib.Analysis.Normed.Group.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.lift_mk", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.lift_unique", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Quotient", "is_tactic_proof": true, "tactics": ["ext", "rcases", "change", "simp", "rfl"], "tactic_count": 5}
{"name": "NormedAddGroupHom.isQuotientQuotient", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.IsQuotient.norm_lift", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Quotient", "is_tactic_proof": true, "tactics": ["obtain", "have", "rw", "exact", "rcases", "exact"], "tactic_count": 6}
{"name": "NormedAddGroupHom.IsQuotient.norm_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Quotient", "is_tactic_proof": true, "tactics": ["rw", "apply", "use", "rintro", "apply", "exact"], "tactic_count": 6}
{"name": "NormedAddGroupHom.norm_lift_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.lift_norm_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddGroupHom.lift_normNoninc", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.Quotient.seminormedAddCommGroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.Quotient.normedAddCommGroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.Quotient.completeSpace", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.Quotient.norm_mk_lt", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.Quotient.norm_mk_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.Quotient.instIsBoundedSMul", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.Quotient.normedSpace", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.quotLIEOfEq", "kind": "definition", "module": "Mathlib.Analysis.Normed.Group.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.quotientQuotientLIEQuotient", "kind": "definition", "module": "Mathlib.Analysis.Normed.Group.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.quotientQuotientLIEQuotientSup", "kind": "definition", "module": "Mathlib.Analysis.Normed.Group.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.norm_mk_lt", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.norm_mk_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.semiNormedCommRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.normedCommRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.normedAlgebra", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.instNormedAddCommGroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.norm_cast_real", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.norm_cast_rat", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Rat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SemiNormedGrp.instCoeSortType", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.instLargeCategory", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.instConcreteCategoryNormedAddGroupHomCarrier", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.Hom.hom", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.ofHom", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.Hom.Simps.hom", "kind": "definition", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.ext", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.hom_id", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.id_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SemiNormedGrp.hom_comp", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.comp_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SemiNormedGrp.hom_ext", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.hom_ofHom", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.ofHom_hom", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.ofHom_id", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.ofHom_comp", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.ofHom_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.inv_hom_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SemiNormedGrp.hom_inv_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SemiNormedGrp.coe_of", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.coe_id", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.coe_comp", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.instInhabited", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.instZeroHom", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.hom_zero", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.zero_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.instHasZeroMorphisms", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.isZero_of_subsingleton", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": true, "tactics": ["refine", "ext", "ext"], "tactic_count": 3}
{"name": "SemiNormedGrp.hasZeroObject", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.iso_isometry_of_normNoninc", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": true, "tactics": ["apply", "intro", "apply", "calc"], "tactic_count": 4}
{"name": "SemiNormedGrp.Hom.add", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.hom_add", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.Hom.neg", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.hom_neg", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.Hom.sub", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.hom_sub", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.Hom.nsmul", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.hom_nsum", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.Hom.zsmul", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.hom_zsum", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.Hom.addCommGroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp₁.instCoeSortType", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp₁.instLargeCategory", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp₁.instFunLike", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp₁.instConcreteCategorySubtypeNormedAddGroupHomCarrierNormNoninc", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp₁.instAddMonoidHomClassSubtypeNormedAddGroupHomCarrierNormNoninc", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp₁.Hom.hom", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp₁.mkHom", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp₁.Hom.Simps.hom", "kind": "definition", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp₁.instCoeFunHomForallCarrier", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp₁.mkHom_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp₁.ext", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp₁.hom_id", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp₁.id_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SemiNormedGrp₁.hom_comp", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp₁.comp_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SemiNormedGrp₁.hom_ext", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp₁.hom_mkHom", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp₁.mkHom_hom", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp₁.mkHom_id", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp₁.mkHom_comp", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp₁.inv_hom_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "SemiNormedGrp₁.hom_inv_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "SemiNormedGrp₁.instSeminormedAddCommGroupCarrier", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp₁.mkIso", "kind": "definition", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp₁.instHasForget₂SemiNormedGrp", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp₁.coe_of", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp₁.coe_id", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp₁.coe_comp", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp₁.instInhabited", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp₁.instZeroHom", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp₁.zero_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp₁.instHasZeroMorphisms", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp₁.isZero_of_subsingleton", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": true, "tactics": ["refine", "ext", "ext"], "tactic_count": 3}
{"name": "SemiNormedGrp₁.hasZeroObject", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp₁.iso_isometry", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp", "is_tactic_proof": true, "tactics": ["change", "refine", "intro", "apply", "calc"], "tactic_count": 5}
{"name": "SemiNormedGrp.completion", "kind": "definition", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.completion_completeSpace", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.completion.incl", "kind": "definition", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.completion.norm_incl_eq", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.completion.map_normNoninc", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.completion.mapHom", "kind": "definition", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.completion.map_zero", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.instPreadditive", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.instAdditiveCompletion", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.completion.lift", "kind": "definition", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.completion.lift_comp_incl", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.completion.lift_unique", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp₁.cokernelCocone", "kind": "definition", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp₁.cokernelLift", "kind": "definition", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp.Kernels", "is_tactic_proof": false, "tactics": ["fconstructor", "apply", "rintro", "change", "simp", "exact"], "tactic_count": 6}
{"name": "SemiNormedGrp₁.instHasCokernels", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp₁._example", "kind": "example", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp.Kernels", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "SemiNormedGrp.instNormHom", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.instNNNormHom", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.fork", "kind": "definition", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.hasLimit_parallelPair", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.instHasEqualizers", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.cokernelCocone", "kind": "definition", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.cokernelLift", "kind": "definition", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.isColimitCokernelCocone", "kind": "definition", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.instHasCokernels", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp._example", "kind": "example", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp.Kernels", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "SemiNormedGrp.explicitCokernel", "kind": "definition", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.explicitCokernelDesc", "kind": "definition", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.explicitCokernelπ", "kind": "definition", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.explicitCokernelπ_surjective", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.comp_explicitCokernelπ", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp.Kernels", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "SemiNormedGrp.explicitCokernelπ_apply_dom_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.explicitCokernelπ_desc", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.explicitCokernelπ_desc_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.explicitCokernelDesc_unique", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp.Kernels", "is_tactic_proof": true, "tactics": ["apply", "rintro", "convert", "simp", "exact"], "tactic_count": 5}
{"name": "SemiNormedGrp.explicitCokernelDesc_comp_eq_desc", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp.Kernels", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "SemiNormedGrp.explicitCokernelDesc_zero", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.explicitCokernel_hom_ext", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp.Kernels", "is_tactic_proof": true, "tactics": ["let", "have", "have", "rw", "apply", "exact"], "tactic_count": 6}
{"name": "SemiNormedGrp.explicitCokernelπ.epi", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp.Kernels", "is_tactic_proof": true, "tactics": ["constructor", "intro", "ext", "rw"], "tactic_count": 4}
{"name": "SemiNormedGrp.isQuotient_explicitCokernelπ", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.normNoninc_explicitCokernelπ", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.explicitCokernelDesc_norm_le_of_norm_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.explicitCokernelDesc_normNoninc", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp.Kernels", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "SemiNormedGrp.explicitCokernelDesc_comp_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp.Kernels", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "SemiNormedGrp.explicitCokernelDesc_norm_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.explicitCokernelIso", "kind": "definition", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.explicitCokernelIso_hom_π", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp.Kernels", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SemiNormedGrp.explicitCokernelIso_inv_π", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp.Kernels", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SemiNormedGrp.explicitCokernelIso_hom_desc", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp.Kernels", "is_tactic_proof": true, "tactics": ["ext1", "simp"], "tactic_count": 2}
{"name": "SemiNormedGrp.explicitCokernel.map", "kind": "definition", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiNormedGrp.ExplicitCoker.map_desc", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.SemiNormedGrp.Kernels", "is_tactic_proof": true, "tactics": ["delta", "simp", "simp"], "tactic_count": 3}
{"name": "map_sub_le_max", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Seminorm", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "NonarchAddGroupSeminormClass.toAddGroupSeminormClass", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Seminorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonarchAddGroupNormClass.toAddGroupNormClass", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Seminorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupSeminorm.funLike", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Seminorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupSeminorm.groupSeminormClass", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Seminorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupSeminorm.toFun_eq_coe", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Seminorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupSeminorm.ext", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Seminorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupSeminorm.instPartialOrder", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Seminorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupSeminorm.le_def", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Seminorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupSeminorm.lt_def", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Seminorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupSeminorm.coe_le_coe", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Seminorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupSeminorm.coe_lt_coe", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Seminorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupSeminorm.instZeroGroupSeminorm", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Seminorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupSeminorm.coe_zero", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Seminorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupSeminorm.zero_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Seminorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupSeminorm.instInhabited", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Seminorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupSeminorm.instAdd", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Seminorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupSeminorm.coe_add", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Seminorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupSeminorm.add_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Seminorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupSeminorm.instSupSet", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Seminorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupSeminorm.sSup_of_not_bddAbove", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Seminorm", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "GroupSeminorm.coe_sSup_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Seminorm", "is_tactic_proof": true, "tactics": ["simp", "rfl"], "tactic_count": 2}
{"name": "GroupSeminorm.coe_sSup_apply'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Seminorm", "is_tactic_proof": true, "tactics": ["rw", "congr", "ext", "simp"], "tactic_count": 4}
{"name": "GroupSeminorm.coe_iSup_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Seminorm", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "GroupSeminorm.instMax", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Seminorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SubgroupClass.normedCommGroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Subgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.seminormedAddCommGroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.coe_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.norm_coe", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.normedAddCommGroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_tsum_of_dominated_convergence", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Tannery", "is_tactic_proof": true, "tactics": ["rcases", "simpa", "rcases", "simp", "have", "have", "have", "filter_upwards", "exact", "rw", "intro", "let", "obtain", "rw", "classical", "have", "calc", "simpa", "have", "rw", "filter_upwards", "rw", "refine", "simpa", "rw", "refine", "refine", "exact", "refine", "exact"], "tactic_count": 30}
{"name": "IsUltrametricDist.norm_mul_le_max", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Ultra", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsUltrametricDist.isUltrametricDist_of_forall_norm_mul_le_max_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Ultra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUltrametricDist.isUltrametricDist_of_isNonarchimedean_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Ultra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUltrametricDist.isNonarchimedean_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Ultra", "is_tactic_proof": true, "tactics": ["intro", "convert", "simp", "congr"], "tactic_count": 4}
{"name": "IsUltrametricDist.isUltrametricDist_iff_isNonarchimedean_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Ultra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUltrametricDist.nnnorm_mul_le_max", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Ultra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUltrametricDist.isUltrametricDist_of_forall_nnnorm_mul_le_max_nnnorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Ultra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUltrametricDist.isUltrametricDist_of_isNonarchimedean_nnnorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Ultra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUltrametricDist.isNonarchimedean_nnnorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Ultra", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsUltrametricDist.isUltrametricDist_iff_isNonarchimedean_nnnorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Ultra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUltrametricDist.norm_mul_eq_max_of_norm_ne_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Ultra", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "IsUltrametricDist.norm_eq_of_mul_norm_lt_max", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Ultra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUltrametricDist.nnnorm_mul_eq_max_of_nnnorm_ne_nnnorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Ultra", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsUltrametricDist.nnnorm_eq_of_mul_nnnorm_lt_max", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Ultra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUltrametricDist.norm_div_eq_max_of_norm_div_ne_norm_div", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Ultra", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsUltrametricDist.nnnorm_div_eq_max_of_nnnorm_div_ne_nnnorm_div", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Ultra", "is_tactic_proof": true, "tactics": ["simpa", "norm_div_eq_max_of_norm_div_ne_norm_div"], "tactic_count": 2}
{"name": "IsUltrametricDist.nnnorm_pow_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Ultra", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "IsUltrametricDist.norm_pow_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Ultra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUltrametricDist.nnnorm_zpow_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Ultra", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "IsUltrametricDist.norm_zpow_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Ultra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUltrametricDist.ball_openSubgroup", "kind": "definition", "module": "Mathlib.Analysis.Normed.Group.Ultra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUltrametricDist.closedBall_openSubgroup", "kind": "definition", "module": "Mathlib.Analysis.Normed.Group.Ultra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUltrametricDist.nonarchimedeanGroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Ultra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Nonempty.norm_prod_le_sup'_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Ultra", "is_tactic_proof": true, "tactics": ["simp", "induction", "singleton", "cons", "simp", "refine", "exact", "exact"], "tactic_count": 8}
{"name": "Finset.nnnorm_prod_le_sup_nnnorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Ultra", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simpa"], "tactic_count": 3}
{"name": "IsUltrametricDist.nnnorm_prod_le_of_forall_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Ultra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUltrametricDist.norm_prod_le_of_forall_le_of_nonempty", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Ultra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUltrametricDist.norm_prod_le_of_forall_le_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Ultra", "is_tactic_proof": true, "tactics": ["lift", "exact"], "tactic_count": 2}
{"name": "IsUltrametricDist.exists_norm_finset_prod_le_of_nonempty", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Ultra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUltrametricDist.exists_norm_finset_prod_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Ultra", "is_tactic_proof": true, "tactics": ["rcases", "simp", "exact"], "tactic_count": 3}
{"name": "IsUltrametricDist.exists_norm_multiset_prod_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Ultra", "is_tactic_proof": true, "tactics": ["inhabit", "induction", "empty", "cons", "obtain", "by_cases", "refine", "rw", "exact", "rcases", "exact", "refine", "simp", "rw", "exact"], "tactic_count": 15}
{"name": "IsUltrametricDist.norm_tprod_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Ultra", "is_tactic_proof": true, "tactics": ["rcases", "simp", "by_cases", "rw", "by_cases", "exact", "rw", "have", "refine", "exact", "exact"], "tactic_count": 11}
{"name": "IsUltrametricDist.nnnorm_tprod_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Ultra", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsUltrametricDist.norm_tprod_le_of_forall_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Ultra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUltrametricDist.norm_tprod_le_of_forall_le_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Ultra", "is_tactic_proof": true, "tactics": ["rcases", "simpa", "exact"], "tactic_count": 3}
{"name": "IsUltrametricDist.nnnorm_tprod_le_of_forall_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Ultra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUltrametricDist.nnnorm_prod_eq_sup_of_pairwise_ne", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Ultra", "is_tactic_proof": true, "tactics": ["induction", "empty", "cons", "rcases", "simp", "specialize", "obtain", "suffices", "rw", "apply"], "tactic_count": 10}
{"name": "IsUltrametricDist.norm_prod_eq_sup'_of_pairwise_ne", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Ultra", "is_tactic_proof": true, "tactics": ["rw", "exact", "simpa"], "tactic_count": 3}
{"name": "NormedGroup.to_isIsometricSMul_right", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Uniform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Isometry.norm_map_of_map_one", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Uniform", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "norm_map'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Uniform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nnnorm_map'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Uniform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dist_mul_self_right", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Uniform", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "dist_mul_self_left", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Uniform", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "dist_div_eq_dist_mul_left", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Uniform", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "dist_div_eq_dist_mul_right", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Uniform", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MonoidHomClass.lipschitz_of_bound", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Uniform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lipschitzOnWith_iff_norm_div_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Uniform", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LipschitzOnWith.norm_div_le_of_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Uniform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lipschitzWith_iff_norm_div_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Uniform", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LipschitzWith.norm_div_le_of_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Uniform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHomClass.continuous_of_bound", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Uniform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHomClass.uniformContinuous_of_bound", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Uniform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHomClass.isometry_iff_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Uniform", "is_tactic_proof": true, "tactics": ["simp", "refine", "simpa"], "tactic_count": 3}
{"name": "MonoidHomClass.lipschitz_of_bound_nnnorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Uniform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHomClass.antilipschitz_of_bound", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Uniform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzWith.norm_le_mul'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Uniform", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "LipschitzWith.nnorm_le_mul'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Uniform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntilipschitzWith.le_mul_norm'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Uniform", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "AntilipschitzWith.le_mul_nnnorm'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Uniform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OneHomClass.bound_of_antilipschitz", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Uniform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Isometry.nnnorm_map_of_map_one", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Uniform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lipschitzWith_one_norm'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Uniform", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "lipschitzWith_one_nnnorm'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Uniform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformContinuous_norm'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Uniform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformContinuous_nnnorm'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Uniform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedGroup.to_isIsometricSMul_left", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Uniform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dist_self_mul_right", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Uniform", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "dist_self_mul_left", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Uniform", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "dist_self_div_right", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Uniform", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "dist_self_div_left", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Uniform", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "dist_mul_mul_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Uniform", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "dist_mul_mul_le_of_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Uniform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dist_div_div_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Uniform", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "dist_div_div_le_of_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Uniform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "abs_dist_sub_le_dist_mul_mul", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Uniform", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "nndist_mul_mul_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Uniform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "edist_mul_mul_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Uniform", "is_tactic_proof": true, "tactics": ["simp", "norm_cast", "apply"], "tactic_count": 3}
{"name": "lipschitzWith_inv_iff", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Uniform", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "antilipschitzWith_inv_iff", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Uniform", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "lipschitzOnWith_inv_iff", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Uniform", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "locallyLipschitz_inv_iff", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Uniform", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "locallyLipschitzOn_inv_iff", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Uniform", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LipschitzOnWith.mul", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Uniform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzWith.mul", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Uniform", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "LocallyLipschitzOn.mul", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Uniform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyLipschitz.mul", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Uniform", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "LipschitzOnWith.div", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Uniform", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "LipschitzWith.div", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Uniform", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "LocallyLipschitzOn.div", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Uniform", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "LocallyLipschitz.div", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Uniform", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "AntilipschitzWith.mul_lipschitzWith", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Uniform", "is_tactic_proof": true, "tactics": ["letI", "refine", "rw", "rw", "rw", "calc", "sub_le_sub"], "tactic_count": 7}
{"name": "AntilipschitzWith.mul_div_lipschitzWith", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Uniform", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "AntilipschitzWith.le_mul_norm_div", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Uniform", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SeminormedCommGroup.to_lipschitzMul", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Uniform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeminormedCommGroup.to_isUniformGroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Uniform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeminormedCommGroup.toIsTopologicalGroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Uniform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.instMulNorm", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Uniform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.norm_mk'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Uniform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.instNormedCommGroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Group.Uniform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.mk_eq_one_iff", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Uniform", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SeparationQuotient.nnnorm_mk'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Uniform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cauchySeq_prod_of_eventually_eq", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Uniform", "is_tactic_proof": true, "tactics": ["let", "rw", "suffices", "intro", "dsimp", "rw", "intro", "simp"], "tactic_count": 8}
{"name": "CauchySeq.mul_norm_bddAbove", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.Uniform", "is_tactic_proof": true, "tactics": ["obtain", "simp_rw", "have", "intro", "rw", "refine", "simp", "rw", "exact"], "tactic_count": 9}
{"name": "ZeroAtInftyContinuousMapClass.norm_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.ZeroAtInfty", "is_tactic_proof": true, "tactics": ["have", "rw", "specialize", "rcases", "use", "intro", "suffices", "apply", "simp_all"], "tactic_count": 9}
{"name": "zero_at_infty_of_norm_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Group.ZeroAtInfty", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "rw", "rcases", "rcases", "use", "intro", "aesop"], "tactic_count": 9}
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{"name": "Matrix.toLpLin", "kind": "definition", "module": "Mathlib.Analysis.Normed.Lp.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.toLpLin_toLp", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Matrix.toLpLin_pow", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "PiLp", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "PiLp.projₗ", "kind": "definition", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "PiLp.instEDist", "kind": "instance", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiLp.edist_eq_card", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "PiLp.instNorm", "kind": "instance", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "PiLp.toEquiv_homeomorph", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiLp.isOpenMap_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "PiLp.secondCountableTopology", "kind": "instance", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiLp.uniformSpace", "kind": "instance", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "PiLp.normedAddCommGroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiLp.nnnorm_eq_sum", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "PiLp.nnnorm_eq_ciSup", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "PiLp.nnnorm_ofLp", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PiLp.nnnorm_toLp", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiLp.norm_ofLp", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiLp.norm_toLp", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiLp.norm_eq_of_nat", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": true, "tactics": ["have", "simp"], "tactic_count": 2}
{"name": "PiLp.norm_eq_of_L1", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PiLp.nnnorm_eq_of_L1", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiLp.dist_eq_of_L1", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "PiLp.nndist_eq_of_L1", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiLp.edist_eq_of_L1", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PiLp.norm_eq_of_L2", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": true, "tactics": ["rw", "rw", "norm_cast"], "tactic_count": 3}
{"name": "PiLp.nnnorm_eq_of_L2", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiLp.norm_sq_eq_of_L2", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": true, "tactics": ["suffices", "rw"], "tactic_count": 2}
{"name": "PiLp.dist_eq_of_L2", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "PiLp.dist_sq_eq_of_L2", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "PiLp.nndist_eq_of_L2", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiLp.edist_eq_of_L2", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PiLp.instIsBoundedSMul", "kind": "instance", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiLp.instNormSMulClass", "kind": "instance", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiLp.normedSpace", "kind": "instance", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiLp.equivₗᵢ", "kind": "definition", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.piLpCongrLeft", "kind": "definition", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.piLpCongrLeft_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.piLpCongrLeft_symm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "LinearIsometryEquiv.piLpCongrLeft_single", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "LinearIsometryEquiv.piLpCongrRight", "kind": "definition", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.piLpCongrRight_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.piLpCongrRight_refl", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.piLpCongrRight_symm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.piLpCongrRight_single", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.piLpCurry", "kind": "definition", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.piLpCurry_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.piLpCurry_symm_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiLp.sumPiLpEquivProdLpPiLp", "kind": "definition", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiLp.nnnorm_toLp_single", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": true, "tactics": ["haveI", "induction", "top", "simp_rw", "refine", "obtain", "rw", "rw", "exact", "rw", "coe", "have", "rw", "intro", "rw"], "tactic_count": 15}
{"name": "PiLp.norm_toLp_single", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiLp.nndist_toLp_single_same", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PiLp.dist_toLp_single_same", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiLp.edist_toLp_single_same", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PiLp.nnnorm_toLp_const", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": true, "tactics": ["rcases", "exact", "have", "simp_rw"], "tactic_count": 4}
{"name": "PiLp.nnnorm_toLp_const'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": true, "tactics": ["rcases", "simp", "ciSup_const]", "exact"], "tactic_count": 4}
{"name": "PiLp.norm_toLp_const", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiLp.norm_toLp_const'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiLp.nnnorm_toLp_one", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiLp.norm_toLp_one", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiLp.continuousLinearEquiv", "kind": "definition", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiLp.coe_continuousLinearEquiv", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiLp.coe_symm_continuousLinearEquiv", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiLp.proj", "kind": "definition", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiLp.basisFun", "kind": "definition", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiLp.basisFun_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "PiLp.basisFun_repr", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiLp.basisFun_equivFun", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiLp.basisFun_eq_pi_basisFun", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiLp.basisFun_map", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiLp.basis_toMatrix_basisFun_mul", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": true, "tactics": ["have", "simp_rw", "exact"], "tactic_count": 3}
{"name": "PiLp.pseudoMetricSpaceToPi", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiLp.dist_pseudoMetricSpaceToPi", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiLp.seminormedAddCommGroupToPi", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiLp.norm_seminormedAddCommGroupToPi", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiLp.nnnorm_seminormedAddCommGroupToPi", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiLp.isBoundedSMulSeminormedAddCommGroupToPi", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": true, "tactics": ["letI", "refine", "simpa", "simpa"], "tactic_count": 4}
{"name": "PiLp.normSMulClassSeminormedAddCommGroupToPi", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": true, "tactics": ["letI", "refine", "simp"], "tactic_count": 3}
{"name": "PiLp.normedSpaceSeminormedAddCommGroupToPi", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": true, "tactics": ["letI", "refine", "simp"], "tactic_count": 3}
{"name": "PiLp.normedAddCommGroupToPi", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Lp.PiLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.fst", "kind": "definition", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.snd", "kind": "definition", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.zero_fst", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.zero_snd", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.add_fst", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.add_snd", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.sub_fst", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.sub_snd", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.neg_fst", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.neg_snd", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.smul_fst", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.smul_snd", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.fstₗ", "kind": "definition", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.sndₗ", "kind": "definition", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.toLp_fst", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.toLp_snd", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.ofLp_fst", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.ofLp_snd", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.instProdEDist", "kind": "instance", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.prod_edist_eq_card", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "WithLp.prod_edist_eq_add", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.prod_edist_eq_sup", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.prod_edist_self", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": true, "tactics": ["rcases", "classical", "simp", "simp"], "tactic_count": 4}
{"name": "WithLp.prod_edist_comm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": true, "tactics": ["classical", "rcases", "simp", "simp", "simp"], "tactic_count": 5}
{"name": "WithLp.instProdDist", "kind": "instance", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.prod_dist_eq_card", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "WithLp.prod_dist_eq_add", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.prod_dist_eq_sup", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.instProdNorm", "kind": "instance", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.prod_norm_eq_card", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "WithLp.prod_norm_eq_sup", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.prod_norm_eq_add", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.prodPseudoEMetricAux", "kind": "definition", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.prod_sup_edist_ne_top_aux", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.prodPseudoMetricAux", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.Normed.Lp.ProdLp.0.WithLp.edist_proj_le_edist_aux", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": true, "tactics": ["rcases", "simp", "have", "rw", "constructor", "calc", "edist", "simp", "gcongr", "simp", "calc", "edist", "simp", "gcongr", "simp"], "tactic_count": 15}
{"name": "_private.Mathlib.Analysis.Normed.Lp.ProdLp.0.WithLp.prod_lipschitzWith_ofLp_aux", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": true, "tactics": ["intro", "change", "rw", "exact"], "tactic_count": 4}
{"name": "_private.Mathlib.Analysis.Normed.Lp.ProdLp.0.WithLp.prod_antilipschitzWith_ofLp_aux", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": true, "tactics": ["intro", "rcases", "simp", "have", "have", "have", "rw", "simp", "calc", "simp"], "tactic_count": 10}
{"name": "_private.Mathlib.Analysis.Normed.Lp.ProdLp.0.WithLp.isUniformInducing_ofLp_aux", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.Normed.Lp.ProdLp.0.WithLp.prod_uniformity_aux", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "WithLp.instProdBornology", "kind": "instance", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.Normed.Lp.ProdLp.0.WithLp.prod_cobounded_aux", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.instProdTopologicalSpace", "kind": "instance", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.prod_continuous_toLp", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.prod_continuous_ofLp", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.homeomorphProd", "kind": "definition", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.toEquiv_homeomorphProd", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.continuous_fst", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.continuous_snd", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.instProdT0Space", "kind": "instance", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.secondCountableTopology", "kind": "instance", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.instProdUniformSpace", "kind": "instance", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.prod_uniformContinuous_toLp", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.prod_uniformContinuous_ofLp", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.uniformEquivProd", "kind": "definition", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.toHomeomorph_uniformEquivProd", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.toEquiv_uniformEquivProd", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.instProdCompleteSpace", "kind": "instance", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.prodContinuousLinearEquiv", "kind": "definition", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.prodContinuousLinearEquiv_symm_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.fstL", "kind": "definition", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.sndL", "kind": "definition", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.instProdPseudoEMetricSpace", "kind": "instance", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.instProdEMetricSpace", "kind": "instance", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.instProdPseudoMetricSpace", "kind": "instance", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.instProdMetricSpace", "kind": "instance", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.prod_nndist_eq_add", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.prod_nndist_eq_sup", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.edist_fst_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.edist_snd_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.nndist_fst_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "WithLp.nndist_snd_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "WithLp.dist_fst_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.dist_snd_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.prod_lipschitzWith_ofLp", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.prod_antilipschitzWith_toLp", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.prod_antilipschitzWith_ofLp", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.prod_lipschitzWith_toLp", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.prod_isometry_ofLp_infty", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.instProdSeminormedAddCommGroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.isUniformInducing_toLp", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.enorm_fst_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "WithLp.enorm_snd_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "WithLp.nnnorm_fst_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "WithLp.nnnorm_snd_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "WithLp.norm_fst_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "WithLp.norm_snd_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "WithLp.instProdNormedAddCommGroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp._example", "kind": "example", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp._example", "kind": "example", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp._example", "kind": "example", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.prod_norm_eq_of_nat", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": true, "tactics": ["have", "simp"], "tactic_count": 2}
{"name": "WithLp.prod_nnnorm_eq_add", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "WithLp.prod_nnnorm_eq_sup", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": true, "tactics": ["ext", "norm_cast"], "tactic_count": 2}
{"name": "WithLp.prod_nnnorm_ofLp", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "WithLp.prod_nnnorm_toLp", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.prod_norm_ofLp", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.prod_norm_toLp", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.prod_norm_eq_of_L1", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WithLp.prod_nnnorm_eq_of_L1", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.prod_dist_eq_of_L1", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "WithLp.prod_nndist_eq_of_L1", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.prod_edist_eq_of_L1", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WithLp.prod_norm_eq_of_L2", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": true, "tactics": ["rw", "norm_cast"], "tactic_count": 2}
{"name": "WithLp.prod_nnnorm_eq_of_L2", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.prod_norm_sq_eq_of_L2", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": ["suffices", "rw"], "tactic_count": 2}
{"name": "WithLp.prod_dist_eq_of_L2", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "WithLp.prod_nndist_eq_of_L2", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.prod_edist_eq_of_L2", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WithLp.nnnorm_toLp_inl", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": true, "tactics": ["induction", "top", "coe", "have", "simp"], "tactic_count": 5}
{"name": "WithLp.nnnorm_toLp_inr", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": true, "tactics": ["induction", "top", "coe", "have", "simp"], "tactic_count": 5}
{"name": "WithLp.norm_toLp_fst", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.norm_toLp_snd", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.nndist_toLp_fst", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "WithLp.nndist_toLp_snd", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "WithLp.dist_toLp_fst", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.dist_toLp_snd", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.edist_toLp_fst", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WithLp.edist_toLp_snd", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WithLp.instProdIsBoundedSMul", "kind": "instance", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.prodEquivₗᵢ", "kind": "definition", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.instProdNormSMulClass", "kind": "instance", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.idemFst", "kind": "definition", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.idemSnd", "kind": "definition", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.idemFst_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.idemSnd_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.idemFst_add_idemSnd", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.idemFst_compl", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "WithLp.idemSnd_compl", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "WithLp.prod_norm_eq_idemFst_sup_idemSnd", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "WithLp.prod_norm_eq_add_idemFst", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "WithLp.prod_norm_eq_idemFst_of_L1", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "WithLp.instProdNormedSpace", "kind": "instance", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.pseudoMetricSpaceToProd", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.dist_pseudoMetricSpaceToProd", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.seminormedAddCommGroupToProd", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.norm_seminormedAddCommGroupToProd", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.nnnorm_seminormedAddCommGroupToProd", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithLp.isBoundedSMulSeminormedAddCommGroupToProd", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": true, "tactics": ["letI", "refine", "simpa", "simpa"], "tactic_count": 4}
{"name": "WithLp.normSMulClassSeminormedAddCommGroupToProd", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": true, "tactics": ["letI", "exact"], "tactic_count": 2}
{"name": "WithLp.normedSpaceSeminormedAddCommGroupToProd", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": true, "tactics": ["letI", "exact"], "tactic_count": 2}
{"name": "WithLp.normedAddCommGroupToProd", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Isometry.withLpProdMap", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": true, "tactics": ["intro", "rcases", "absurd", "simp", "simp"], "tactic_count": 5}
{"name": "IsometryEquiv.withLpProdCongr", "kind": "definition", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.withLpProdComm", "kind": "definition", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.withLpProdComm_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.withLpProdComm_symm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.withLpProdAssoc", "kind": "definition", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.withLpProdUnique", "kind": "definition", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.coe_withLpProdUnique", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.withLpUniqueProd", "kind": "definition", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.coe_withLpUniqueProd", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.withLpProdMap", "kind": "definition", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.withLpProdCongr", "kind": "definition", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.withLpProdComm", "kind": "definition", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.withLpProdComm_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.withLpProdComm_symm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.withLpProdAssoc", "kind": "definition", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LinearIsometryEquiv.coe_withLpProdUnique", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.ProdLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "lp.tsum_mul_le_mul_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.lpSpace", "is_tactic_proof": true, "tactics": ["have", "have", "have", "have", "obtain", "rw", "exact"], "tactic_count": 7}
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{"name": "lp.instIsCentralScalarPreLp", "kind": "instance", "module": "Mathlib.Analysis.Normed.Lp.lpSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lp.mem_lp_const_smul", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.lpSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lpSubmodule", "kind": "definition", "module": "Mathlib.Analysis.Normed.Lp.lpSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lp.coe_lpSubmodule", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.lpSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "lp.nonUnitalNormedRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Lp.lpSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lp.nonUnitalNormedCommRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Lp.lpSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "lp.singleContinuousAddMonoidHom", "kind": "definition", "module": "Mathlib.Analysis.Normed.Lp.lpSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lp.singleContinuousAddMonoidHom_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.lpSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "lp.singleContinuousLinearMap_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.lpSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LipschitzWith.uniformly_bounded", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Lp.lpSpace", "is_tactic_proof": true, "tactics": ["rcases", "use", "rintro", "calc", "g", "gcongr", "exact", "exact"], "tactic_count": 8}
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{"name": "AlternatingMap.norm_map_coord_zero", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.bound_of_shell_of_norm_map_coord_zero", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.bound_of_shell_of_continuous", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.exists_bound_of_continuous", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.norm_image_sub_le_of_bound'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.norm_image_sub_le_of_bound", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.continuous_of_bound", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.mkContinuous", "kind": "definition", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.coe_mkContinuous", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.bound", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.instSeminormedAddCommGroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.norm_toContinuousMultilinearMap", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.nnnorm_toContinuousMultilinearMap", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.enorm_toContinuousMultilinearMap", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.toContinuousMultilinearMapLI", "kind": "definition", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.norm_def", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.bounds_nonempty", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.bounds_bddBelow", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.isLeast_opNorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.le_opNorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.le_mul_prod_of_opNorm_le_of_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.le_opNorm_mul_prod_of_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.le_opNorm_mul_pow_card_of_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.le_opNorm_mul_pow_of_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.le_of_opNorm_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.ratio_le_opNorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.unit_le_opNorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.opNorm_le_bound", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.opNorm_le_iff", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.le_opNNNorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.le_of_opNNNorm_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.opNNNorm_le_iff", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.isLeast_opNNNorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.opNNNorm_prod", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.opNorm_prod", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.opNNNorm_pi", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.opNorm_pi", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.instNormedSpace", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.norm_ofSubsingleton", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.nnnorm_ofSubsingleton", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.ofSubsingletonLIE", "kind": "definition", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.norm_ofSubsingleton_id_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.nnnorm_ofSubsingleton_id_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.norm_constOfIsEmpty", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.nnnorm_constOfIsEmpty", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.constOfIsEmptyLIE", "kind": "definition", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.prodLIE", "kind": "definition", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.piLIE", "kind": "definition", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.norm_restrictScalars", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.restrictScalarsLI", "kind": "definition", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.norm_image_sub_le'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.norm_image_sub_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.mkContinuous_norm_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.mkContinuous_norm_le'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.norm_compContinuousAlternatingMap_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.compContinuousAlternatingMapCLM", "kind": "definition", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.continuousAlternatingMapCongrRight", "kind": "definition", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.continuousAlternatingMapCongrRight_symm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.flipAlternating", "kind": "definition", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.norm_compContinuousAlternatingMap", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.norm_compContinuousLinearMap_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.compContinuousLinearMapCLM", "kind": "definition", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.compContinuousLinearMapCLM_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.fderivCompContinuousLinearMap", "kind": "definition", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.toContinuousMultilinearMapCLM_comp_fderivCompContinuousLinearMap", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.fderivCompContinuousLinearMap_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousAlternatingMap.fderivCompContinuousLinearMap_of_isEmpty", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "ContinuousAlternatingMap.fderivCompContinuousLinearMapCLM", "kind": "definition", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.fderivCompContinuousLinearMapCLM_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.continuousAlternatingMapCongrLeft", "kind": "definition", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.continuousAlternatingMapCongr", "kind": "definition", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.mkContinuousLinear", "kind": "definition", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.mkContinuousLinear_norm_le_max", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.mkContinuousLinear_norm_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.mkContinuousAlternating", "kind": "definition", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.mkContinuousAlternating_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.mkContinuousAlternating_norm_le_max", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "exact"], "tactic_count": 2}
{"name": "AlternatingMap.mkContinuousAlternating_norm_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.instNormedAddCommGroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.norm_ofSubsingleton_id", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.nnnorm_ofSubsingleton_id", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.bound_of_shell", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.curryLeft", "kind": "definition", "module": "Mathlib.Analysis.Normed.Module.Alternating.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.toContinuousMultilinearMap_curryLeft", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.toAlternatingMap_curryLeft", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.norm_curryLeft", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.curryLeft_apply_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.curryLeft_zero", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.curryLeft_add", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.curryLeft_smul", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.curryLeftLI", "kind": "definition", "module": "Mathlib.Analysis.Normed.Module.Alternating.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.curryLeft_same", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.curryLeft_compContinuousAlternatingMap", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.curryLeft_compContinuousLinearMap", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.map_insertNth", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Uncurry.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.neg_one_pow_smul_map_insertNth", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Uncurry.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.neg_one_pow_smul_map_removeNth_add_eq_zero_of_eq", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Uncurry.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.Normed.Module.Alternating.Uncurry.Fin.0.ContinuousAlternatingMap.alternatizeUncurryFinCLM.aux", "kind": "definition", "module": "Mathlib.Analysis.Normed.Module.Alternating.Uncurry.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.Normed.Module.Alternating.Uncurry.Fin.0.ContinuousAlternatingMap.alternatizeUncurryFinCLM.aux_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Uncurry.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousAlternatingMap.alternatizeUncurryFinCLM", "kind": "definition", "module": "Mathlib.Analysis.Normed.Module.Alternating.Uncurry.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.norm_alternatizeUncurryFinCLM_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Uncurry.Fin", "is_tactic_proof": true, "tactics": ["rw", "apply", "positivity"], "tactic_count": 3}
{"name": "ContinuousAlternatingMap.alternatizeUncurryFin", "kind": "definition", "module": "Mathlib.Analysis.Normed.Module.Alternating.Uncurry.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.alternatizeUncurryFinCLM_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Uncurry.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.norm_alternatizeUncurryFin_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Uncurry.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.alternatizeUncurryFin_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Uncurry.Fin", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "ContinuousAlternatingMap.toAlternatingMap_alternatizeUncurryFin", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Uncurry.Fin", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "ContinuousAlternatingMap.alternatizeUncurryFin_add", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Uncurry.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.alternatizeUncurryFin_curryLeft", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Uncurry.Fin", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "ContinuousAlternatingMap.alternatizeUncurryFin_smul", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Uncurry.Fin", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "ContinuousAlternatingMap.alternatizeUncurryFin_constOfIsEmptyLIE_comp", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Uncurry.Fin", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "ContinuousAlternatingMap.alternatizeUncurryFin_alternatizeUncurryFinCLM_comp_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Uncurry.Fin", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ContinuousAlternatingMap.alternatizeUncurryFin_alternatizeUncurryFinCLM_comp_of_symmetric", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Uncurry.Fin", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "ContinuousAlternatingMap.fderivCompContinuousLinearMap_eq_alternatizeUncurryFin", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Uncurry.Fin", "is_tactic_proof": true, "tactics": ["ext", "have", "i.insertNth", "i.insertNth", "simp"], "tactic_count": 5}
{"name": "ContinuousAlternatingMap.alternatizeUncurryFin_fderivCompContinuousLinearMap_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Alternating.Uncurry.Fin", "is_tactic_proof": true, "tactics": ["cases", "zero", "succ", "n", "rw", "alternatizeUncurryFin_alternatizeUncurryFinCLM_comp_of_symmetric]", "intro", "ext", "simp"], "tactic_count": 9}
{"name": "mulActionClosedBallBall", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Ball.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousSMul_closedBall_ball", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Ball.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mulActionClosedBallClosedBall", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Ball.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousSMul_closedBall_closedBall", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Ball.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mulActionSphereBall", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Ball.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousSMul_sphere_ball", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Ball.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mulActionSphereClosedBall", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Ball.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousSMul_sphere_closedBall", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Ball.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mulActionSphereSphere", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Ball.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousSMul_sphere_sphere", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Ball.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isScalarTower_closedBall_closedBall_closedBall", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Ball.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isScalarTower_closedBall_closedBall_ball", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Ball.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isScalarTower_sphere_closedBall_closedBall", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Ball.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isScalarTower_sphere_closedBall_ball", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Ball.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isScalarTower_sphere_sphere_closedBall", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Ball.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isScalarTower_sphere_sphere_ball", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Ball.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isScalarTower_sphere_sphere_sphere", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Ball.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isScalarTower_sphere_ball_ball", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Ball.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isScalarTower_closedBall_ball_ball", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Ball.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instSMulCommClass_closedBall_closedBall_closedBall", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Ball.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instSMulCommClass_closedBall_closedBall_ball", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Ball.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instSMulCommClass_sphere_closedBall_closedBall", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Ball.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instSMulCommClass_sphere_closedBall_ball", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Ball.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instSMulCommClass_sphere_ball_ball", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Ball.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instSMulCommClass_sphere_sphere_closedBall", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Ball.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instSMulCommClass_sphere_sphere_ball", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Ball.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instSMulCommClass_sphere_sphere_sphere", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Ball.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ne_neg_of_mem_sphere", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ball.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ne_neg_of_mem_unit_sphere", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ball.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.univUnitBall", "kind": "definition", "module": "Mathlib.Analysis.Normed.Module.Ball.Homeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.univUnitBall_apply_zero", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ball.Homeomorph", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "OpenPartialHomeomorph.univUnitBall_symm_apply_zero", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ball.Homeomorph", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Homeomorph.unitBall", "kind": "definition", "module": "Mathlib.Analysis.Normed.Module.Ball.Homeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.coe_unitBall_apply_zero", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ball.Homeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.unitBallBall", "kind": "definition", "module": "Mathlib.Analysis.Normed.Module.Ball.Homeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.univBall", "kind": "definition", "module": "Mathlib.Analysis.Normed.Module.Ball.Homeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.univBall_source", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ball.Homeomorph", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "OpenPartialHomeomorph.univBall_target", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ball.Homeomorph", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "OpenPartialHomeomorph.ball_subset_univBall_target", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ball.Homeomorph", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "rw", "exact"], "tactic_count": 4}
{"name": "OpenPartialHomeomorph.univBall_apply_zero", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ball.Homeomorph", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "OpenPartialHomeomorph.univBall_symm_apply_center", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ball.Homeomorph", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "OpenPartialHomeomorph.continuous_univBall", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ball.Homeomorph", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "OpenPartialHomeomorph.continuousOn_univBall_symm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ball.Homeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ediam_smul_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ball.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ediam_smul₀", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ball.Pointwise", "is_tactic_proof": true, "tactics": ["refine", "obtain", "obtain", "simp", "simp", "have", "rwa", "le_inv_smul_iff_of_pos"], "tactic_count": 8}
{"name": "diam_smul₀", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ball.Pointwise", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "infEDist_smul₀", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ball.Pointwise", "is_tactic_proof": true, "tactics": ["simp_rw", "have", "trans", "refine", "simp_rw", "have", "simp_rw"], "tactic_count": 7}
{"name": "infDist_smul₀", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ball.Pointwise", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "smul_ball", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ball.Pointwise", "is_tactic_proof": true, "tactics": ["ext", "rw", "conv_lhs", "simp"], "tactic_count": 4}
{"name": "smul_unitBall", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ball.Pointwise", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "smul_sphere'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ball.Pointwise", "is_tactic_proof": true, "tactics": ["ext", "rw", "conv_lhs", "simp"], "tactic_count": 4}
{"name": "smul_closedBall'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ball.Pointwise", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "set_smul_sphere_zero", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ball.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.IsBounded.smul₀", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ball.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eventually_singleton_add_smul_subset", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ball.Pointwise", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "have", "filter_upwards", "simp", "intro", "obtain", "have", "calc", "gcongr", "exacts", "have", "apply", "simpa"], "tactic_count": 14}
{"name": "smul_unitBall_of_pos", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ball.Pointwise", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ioo_smul_sphere_zero", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ball.Pointwise", "is_tactic_proof": true, "tactics": ["have", "rw", "image_mul_right_Ioo", "ext", "simp"], "tactic_count": 5}
{"name": "exists_dist_eq", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ball.Pointwise", "is_tactic_proof": true, "tactics": ["use", "nth_rw", "nth_rw", "simp"], "tactic_count": 4}
{"name": "exists_dist_le_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ball.Pointwise", "is_tactic_proof": true, "tactics": ["obtain", "exact", "have", "refine", "rw", "rw", "rw", "exact"], "tactic_count": 8}
{"name": "exists_dist_le_lt", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ball.Pointwise", "is_tactic_proof": false, "tactics": ["refine", "rw", "rw", "rw", "exact"], "tactic_count": 5}
{"name": "exists_dist_lt_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ball.Pointwise", "is_tactic_proof": false, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "exists_dist_lt_lt", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ball.Pointwise", "is_tactic_proof": false, "tactics": ["refine", "rw", "rw", "rw", "exact"], "tactic_count": 5}
{"name": "disjoint_ball_ball_iff", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ball.Pointwise", "is_tactic_proof": true, "tactics": ["refine", "rw", "obtain", "rw", "exact", "h.le_bot"], "tactic_count": 6}
{"name": "disjoint_ball_closedBall_iff", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ball.Pointwise", "is_tactic_proof": true, "tactics": ["refine", "rw", "obtain", "rw", "exact", "h.le_bot"], "tactic_count": 6}
{"name": "disjoint_closedBall_ball_iff", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ball.Pointwise", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "disjoint_closedBall_closedBall_iff", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ball.Pointwise", "is_tactic_proof": true, "tactics": ["refine", "rw", "obtain", "rw", "exact"], "tactic_count": 5}
{"name": "infEDist_thickening", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ball.Pointwise", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact", "refine", "refine", "refine", "cases", "top", "exact", "coe", "r", "have", "refine", "have", "rw", "exact", "rw", "obtain", "refine", "infEDist_lt_iff.2", "rw"], "tactic_count": 21}
{"name": "thickening_thickening", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ball.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cthickening_thickening", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ball.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "closure_thickening", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ball.Pointwise", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "infEDist_cthickening", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ball.Pointwise", "is_tactic_proof": true, "tactics": ["obtain", "rw", "rw"], "tactic_count": 3}
{"name": "thickening_cthickening", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ball.Pointwise", "is_tactic_proof": true, "tactics": ["obtain", "rw", "rw"], "tactic_count": 3}
{"name": "cthickening_cthickening", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ball.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "thickening_ball", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ball.Pointwise", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "thickening_closedBall", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ball.Pointwise", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "cthickening_ball", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ball.Pointwise", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "cthickening_closedBall", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ball.Pointwise", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ball_add_ball", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ball.Pointwise", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ball_sub_ball", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ball.Pointwise", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "ball_add_closedBall", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ball.Pointwise", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ball_sub_closedBall", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ball.Pointwise", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "closedBall_add_ball", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ball.Pointwise", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "closedBall_sub_ball", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ball.Pointwise", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "closedBall_add_closedBall", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ball.Pointwise", "is_tactic_proof": true, "tactics": ["rw", "vadd_eq_add,"], "tactic_count": 2}
{"name": "closedBall_sub_closedBall", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ball.Pointwise", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "smul_closedBall", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ball.Pointwise", "is_tactic_proof": true, "tactics": ["rcases", "simp", "exact"], "tactic_count": 3}
{"name": "smul_unitClosedBall", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ball.Pointwise", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "smul_unitClosedBall_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ball.Pointwise", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "smul_sphere", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ball.Pointwise", "is_tactic_proof": true, "tactics": ["rcases", "simp", "exact"], "tactic_count": 3}
{"name": "affinity_unitBall", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ball.Pointwise", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "affinity_unitClosedBall", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ball.Pointwise", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "homeomorphSphereProd", "kind": "definition", "module": "Mathlib.Analysis.Normed.Module.Ball.RadialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "homeomorphUnitSphereProd", "kind": "definition", "module": "Mathlib.Analysis.Normed.Module.Ball.RadialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.smul_sphere", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ball.RadialEquiv", "is_tactic_proof": true, "tactics": ["rw", "rintro", "wlog", "replace", "rw", "exact", "specialize", "simp", "simpa", "have", "lift", "have", "replace", "rw", "homeomorphSphereProd_symm_apply_coe]", "filter_upwards", "rintro", "rw", "apply", "exacts", "exact", "simp"], "tactic_count": 22}
{"name": "NormedSpace.toNormSMulClass", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedSpace.toIsBoundedSMul", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedField.toNormedSpace", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "norm_zsmul", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "norm_intCast_eq_abs_mul_norm_one", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "norm_natCast_eq_mul_norm_one", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "norm_natCast", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "eventually_nhds_norm_smul_sub_lt", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.zero_smul_isBoundedUnder_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.IsBoundedUnder.smul_tendsto_zero", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedSpace.discreteTopology_zmultiples", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": true, "tactics": ["have", "rcases", "rw", "exact", "rw", "refine", "ext", "obtain", "rw", "mul_lt_iff_lt_one_left"], "tactic_count": 10}
{"name": "Metric.diam_sphere_eq", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": true, "tactics": ["apply", "obtain", "calc", "simp"], "tactic_count": 4}
{"name": "Metric.diam_closedBall_eq", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.diam_ball_eq", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": true, "tactics": ["but", "refine", "le_antisymm", "mul_le_of_forall_lt_of_nonneg", "calc", "a"], "tactic_count": 6}
{"name": "ULift.normedSpace", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.normedSpace", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.normedSpace", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.instNormedSpace", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instNormedSpace", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.normedSpace", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubmoduleClass.toNormedSpace", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedSpace.induced", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedSpace.exists_lt_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "use", "rwa", "rwa"], "tactic_count": 5}
{"name": "NormedSpace.unbounded_univ", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedSpace.cobounded_neBot", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "NontriviallyNormedField.cobounded_neBot", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RealNormedSpace.cobounded_neBot", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NontriviallyNormedField.infinite", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedSpace.noncompactSpace", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "letI", "exact", "rcases", "suffices", "refine", "simp", "rw", "rwa"], "tactic_count": 9}
{"name": "NormedField.noncompactSpace", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RealNormedSpace.noncompactSpace", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAlgebra.toNormedSpace", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "norm_algebraMap", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
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{"name": "norm_algebraMap'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Algebra.norm_smul_one_eq_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "nnnorm_algebraMap'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "nnnorm_algebraMap_nnreal", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_algebraMap_cobounded", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": true, "tactics": ["intro", "rw", "rw", "obtain", "exact"], "tactic_count": 5}
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{"name": "NormedAlgebra.id", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "normedAlgebraRat", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PUnit.normedAlgebra", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instNormedAlgebraULift", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.normedAlgebra", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.normedAlgebra", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.instNormedAlgebra", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instNormedAlgebra", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAlgebra.induced", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.toNormedAlgebra", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubalgebraClass.toNormedAlgebra", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instSeminormedAddCommGroupRestrictScalars", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instNormedAddCommGroupRestrictScalars", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instNonUnitalSeminormedRingRestrictScalars", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instNonUnitalNormedRingRestrictScalars", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instSeminormedRingRestrictScalars", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instNormedRingRestrictScalars", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instNonUnitalSeminormedCommRingRestrictScalars", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instNonUnitalNormedCommRingRestrictScalars", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instSeminormedCommRingRestrictScalars", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instNormedCommRingRestrictScalars", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RestrictScalars.normedSpace", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.RestrictScalars.normedSpaceOrig", "kind": "definition", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedSpace.restrictScalars", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedSpace.restrictScalars_eq", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": true, "tactics": ["ext", "apply"], "tactic_count": 2}
{"name": "RestrictScalars.normedAlgebra", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.RestrictScalars.normedAlgebraOrig", "kind": "definition", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAlgebra.restrictScalars", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoMetricSpace.ofSeminormedSpaceCore", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoEMetricSpace.ofSeminormedSpaceCore", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoMetricSpace.ofSeminormedSpaceCoreReplaceUniformity", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoMetricSpace.ofSeminormedSpaceCoreReplaceTopology", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoMetricSpace.ofSeminormedSpaceCoreReplaceAll", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeminormedAddCommGroup.ofCore", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeminormedAddCommGroup.ofCoreReplaceUniformity", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeminormedAddCommGroup.ofCoreReplaceTopology", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeminormedAddCommGroup.ofCoreReplaceAll", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddCommGroup.ofCore", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddCommGroup.ofCoreReplaceUniformity", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddCommGroup.ofCoreReplaceTopology", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddCommGroup.ofCoreReplaceAll", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedSpace.ofCore", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.continuous_of_isBounded_nhds_zero", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Basic", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "refine", "simp", "simp", "forall_apply_eq_imp_iff₂]", "have", "obtain", "have", "have", "refine", "calc", "gcongr", "simpa", "refine", "simpa"], "tactic_count": 16}
{"name": "ContinuousLinearMap.ker_closedComplemented_of_finiteDimensional_range", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Complemented", "is_tactic_proof": true, "tactics": ["set", "rcases", "simpa"], "tactic_count": 3}
{"name": "ContinuousLinearMap.equivProdOfSurjectiveOfIsCompl", "kind": "definition", "module": "Mathlib.Analysis.Normed.Module.Complemented", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.coe_equivProdOfSurjectiveOfIsCompl", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Complemented", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.equivProdOfSurjectiveOfIsCompl_toLinearEquiv", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Complemented", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Submodule.prodEquivOfClosedCompl", "kind": "definition", "module": "Mathlib.Analysis.Normed.Module.Complemented", "is_tactic_proof": true, "tactics": ["haveI", "refine", "exact"], "tactic_count": 3}
{"name": "Submodule.linearProjOfClosedCompl", "kind": "definition", "module": "Mathlib.Analysis.Normed.Module.Complemented", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.coe_prodEquivOfClosedCompl", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Complemented", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Submodule.coe_continuous_linearProjOfClosedCompl", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Complemented", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.coe_continuous_linearProjOfClosedCompl'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Complemented", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.ClosedComplemented.of_isCompl_isClosed", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Complemented", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.closedComplemented_iff_isClosed_exists_isClosed_isCompl", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Complemented", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.ClosedComplemented.of_quotient_finiteDimensional", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Complemented", "is_tactic_proof": true, "tactics": ["obtain", "haveI", "exact"], "tactic_count": 3}
{"name": "UniformSpace.Completion.instNormedSpace", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.toComplₗᵢ", "kind": "definition", "module": "Mathlib.Analysis.Normed.Module.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.coe_toComplₗᵢ", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.toComplL", "kind": "definition", "module": "Mathlib.Analysis.Normed.Module.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.coe_toComplL", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.norm_toComplL", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.instNormedRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.instNormedCommRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.instNormedAlgebra", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.instNormedFieldOfCompletableTopField", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Countable.isPathConnected_compl_of_one_lt_rank", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Connected", "is_tactic_proof": false, "tactics": ["have", "obtain", "refine", "intro", "rcases", "exact", "let", "let", "have", "simp", "module", "have", "simp", "module", "have", "obtain", "have", "apply", "intro", "apply", "have", "rw", "apply", "apply", "apply", "have", "apply", "intro", "apply", "have", "rw", "apply", "rw", "apply", "apply", "convert", "simp", "obtain", "let", "simp", "have", "apply", "rw", "convert", "exact", "have", "apply", "rw", "convert", "exact", "exact"], "tactic_count": 51}
{"name": "Set.Countable.isConnected_compl_of_one_lt_rank", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isPathConnected_compl_singleton_of_one_lt_rank", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isConnected_compl_singleton_of_one_lt_rank", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.contractibleSpace_ball", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.contractibleSpace_eball", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.contractibleSpace_closedBall", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.contractibleSpace_closedEBall", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.isPathConnected_ball", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.isPathConnected_eball", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.isPathConnected_closedBall", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.isPathConnected_closedEBall", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.isPreconnected_ball", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.isPreconnected_eball", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.isPreconnected_closedBall", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.isPreconnected_closedEBall", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.isConnected_ball", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.isConnected_eball", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.isConnected_closedBall", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.isConnected_closedEBall", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isPathConnected_sphere", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Connected", "is_tactic_proof": true, "tactics": ["is", "rcases", "simpa", "let", "have", "intro", "apply", "apply", "simpa", "have", "have", "have", "apply", "rintro", "have", "simp", "intro", "refine", "intro", "simp", "simp", "exact", "simp", "rwa"], "tactic_count": 24}
{"name": "isConnected_sphere", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isPreconnected_sphere", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Connected", "is_tactic_proof": true, "tactics": ["rcases", "exact", "simpa"], "tactic_count": 3}
{"name": "isPathConnected_compl_of_one_lt_codim", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Connected", "is_tactic_proof": true, "tactics": ["rcases", "refine", "isPathConnected_compl_of_isPathConnected_compl_zero", "rwa"], "tactic_count": 4}
{"name": "isConnected_compl_of_one_lt_codim", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.connectedComponentIn_eq_self_of_one_lt_codim", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "convexOn_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Convex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "convexOn_univ_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Convex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "convexOn_dist", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Convex", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "convexOn_univ_dist", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Convex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "convex_ball", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Convex", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "convex_eball", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Convex", "is_tactic_proof": true, "tactics": ["cases", "top", "coe"], "tactic_count": 3}
{"name": "convex_closedBall", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Convex", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "convex_closedEBall", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Convex", "is_tactic_proof": true, "tactics": ["cases", "top", "coe"], "tactic_count": 3}
{"name": "convexHull_sphere_eq_closedBall", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Convex", "is_tactic_proof": false, "tactics": ["suffices", "rw", "refine", "subset_antisymm", "have", "have", "obtain", "rw", "exact", "by_cases", "simp_all", "by_cases", "rwa", "set", "have", "simp", "grw", "have", "apply", "simp_all", "have", "rwa", "mul_one,"], "tactic_count": 23}
{"name": "convexHull_exists_dist_ge", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Convex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Convex.thickening", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Convex", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Convex.cthickening", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Convex", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact", "rw", "exact"], "tactic_count": 5}
{"name": "convexHull_exists_dist_ge2", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Convex", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "use", "exact"], "tactic_count": 4}
{"name": "convexHull_ediam", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Convex", "is_tactic_proof": true, "tactics": ["refine", "rcases", "rw", "apply", "rw", "exact"], "tactic_count": 6}
{"name": "convexHull_diam", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Convex", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "isBounded_convexHull", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Convex", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NormedSpace.instPathConnectedSpace", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Convex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isConnected_setOf_sameRay", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Convex", "is_tactic_proof": true, "tactics": ["by_cases", "simp_rw", "exact"], "tactic_count": 3}
{"name": "isConnected_setOf_sameRay_and_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Convex", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "norm_sub_le_of_mem_segment", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Convex", "is_tactic_proof": true, "tactics": ["rw", "simp", "obtain", "simp", "rw", "conv_rhs", "gcongr"], "tactic_count": 7}
{"name": "Filter.Eventually.segment_of_prod_nhds", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Convex", "is_tactic_proof": true, "tactics": ["obtain", "rw", "filter_upwards", "exact"], "tactic_count": 4}
{"name": "Filter.Eventually.segment_of_prod_nhdsWithin", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Convex", "is_tactic_proof": true, "tactics": ["refine", "apply", "simpa"], "tactic_count": 3}
{"name": "NormedSpace.inclusionInDoubleDual", "kind": "definition", "module": "Mathlib.Analysis.Normed.Module.Dual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedSpace.dual_def", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Dual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedSpace.inclusionInDoubleDual_norm_eq", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Dual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedSpace.inclusionInDoubleDual_norm_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Dual", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "NormedSpace.double_dual_bound", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Dual", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "NormedSpace.norm_le_dual_bound", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Dual", "is_tactic_proof": true, "tactics": ["classical", "by_cases", "simp", "obtain", "calc"], "tactic_count": 5}
{"name": "NormedSpace.eq_zero_of_forall_dual_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Dual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedSpace.eq_zero_iff_forall_dual_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Dual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedSpace.eq_iff_forall_dual_eq", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Dual", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "NormedSpace.inclusionInDoubleDualLi", "kind": "definition", "module": "Mathlib.Analysis.Normed.Module.Dual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedSpace.isClosed_polar", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Dual", "is_tactic_proof": true, "tactics": ["dsimp", "simp", "refine", "exact"], "tactic_count": 4}
{"name": "NormedSpace.polar_closure", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Dual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedSpace.smul_mem_polar", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Dual", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "exact", "have", "have", "intro", "rw", "apply", "have", "rwa"], "tactic_count": 10}
{"name": "NormedSpace.polar_ball_subset_closedBall_div", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Dual", "is_tactic_proof": true, "tactics": ["intro", "rw", "simp", "have", "refine", "calc"], "tactic_count": 6}
{"name": "NormedSpace.closedBall_inv_subset_polar_closedBall", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Dual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedSpace.polar_closedBall", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Dual", "is_tactic_proof": true, "tactics": ["refine", "intro", "simp", "refine", "simpa"], "tactic_count": 5}
{"name": "NormedSpace.polar_ball", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Dual", "is_tactic_proof": true, "tactics": ["apply", "intro", "rw", "apply", "intro", "rw", "rw", "apply", "rw", "exact", "rw", "exact"], "tactic_count": 12}
{"name": "NormedSpace.isBounded_polar_of_mem_nhds_zero", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Dual", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "exact", "isBounded_closedBall.subset"], "tactic_count": 4}
{"name": "NormedSpace.sInter_polar_eq_closedBall", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Dual", "is_tactic_proof": true, "tactics": ["conv_rhs", "rw"], "tactic_count": 2}
{"name": "LinearMap.polar_AbsConvex", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Dual", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsMaxFilter.norm_add_sameRay", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMaxFilter.norm_add_self", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMaxOn.norm_add_sameRay", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMaxOn.norm_add_self", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMaxOn.norm_add_sameRay", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMaxOn.norm_add_self", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMax.norm_add_sameRay", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMax.norm_add_self", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.toLinearIsometryEquiv", "kind": "definition", "module": "Mathlib.Analysis.Normed.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.coe_toLinearIsometryEquiv", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.toLinearIsometryEquiv_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometry.toAffineIsometryEquiv", "kind": "definition", "module": "Mathlib.Analysis.Normed.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometry.coe_toAffineIsometryEquiv", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIsometry.toAffineIsometryEquiv_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.continuous_of_finiteDimensional", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineEquiv.continuous_of_finiteDimensional", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineEquiv.toHomeomorphOfFiniteDimensional", "kind": "definition", "module": "Mathlib.Analysis.Normed.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineEquiv.coe_toHomeomorphOfFiniteDimensional", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineEquiv.coe_toHomeomorphOfFiniteDimensional_symm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.lipschitzWith_of_finiteDimensional", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.FiniteDimension", "is_tactic_proof": true, "tactics": ["let", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "ContinuousLinearMap.continuous_det", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.FiniteDimension", "is_tactic_proof": false, "tactics": ["change", "by_cases", "rcases", "haveI", "classical", "simp_rw", "refine", "exact", "rw", "simpa"], "tactic_count": 10}
{"name": "definition._@.Mathlib.Analysis.Normed.Module.FiniteDimension.3513382408._hygCtx._hyg.2", "kind": "definition", "module": "Mathlib.Analysis.Normed.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "lipschitzExtensionConstant", "kind": "definition", "module": "Mathlib.Analysis.Normed.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lipschitzExtensionConstant_def", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.FiniteDimension", "is_tactic_proof": true, "tactics": ["intros", "delta", "rw", "rfl"], "tactic_count": 4}
{"name": "lipschitzExtensionConstant_pos", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.FiniteDimension", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "LipschitzOnWith.extend_finite_dimension", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.FiniteDimension", "is_tactic_proof": true, "tactics": ["let", "let", "have", "have", "obtain", "refine", "have", "apply", "rw", "exact", "intro", "have", "simp"], "tactic_count": 13}
{"name": "LinearMap.exists_antilipschitzWith", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.FiniteDimension", "is_tactic_proof": true, "tactics": ["cases", "exact", "rw", "let", "exact"], "tactic_count": 5}
{"name": "LinearMap.injective_iff_antilipschitz", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.FiniteDimension", "is_tactic_proof": true, "tactics": ["constructor", "rw", "exact", "rintro", "exact"], "tactic_count": 5}
{"name": "AffineMap.antilipschitzWith_of_finiteDimensional", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.FiniteDimension", "is_tactic_proof": true, "tactics": ["obtain", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "ContinuousLinearMap.isOpen_injective", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.FiniteDimension", "is_tactic_proof": true, "tactics": ["rw", "rintro", "rcases", "have", "filter_upwards", "apply", "exact"], "tactic_count": 7}
{"name": "LinearIndependent.eventually", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.FiniteDimension", "is_tactic_proof": true, "tactics": ["cases", "classical", "simp", "rcases", "have", "tendsto_finset_sum", "simp", "refine", "replace", "rw", "push_cast", "exact", "rw", "refine", "simp", "refine", "rw", "gcongr", "exact"], "tactic_count": 19}
{"name": "isOpen_setOf_linearIndependent", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpen_setOf_nat_le_rank", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.FiniteDimension", "is_tactic_proof": true, "tactics": ["simp", "refine", "have", "continuous_pi", "exact"], "tactic_count": 5}
{"name": "isOpen_setOf_affineIndependent", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.FiniteDimension", "is_tactic_proof": true, "tactics": ["classical", "rcases", "exact", "simp_rw", "let", "cases", "haveI", "convert_to", "exact"], "tactic_count": 9}
{"name": "Module.Basis.opNNNorm_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.opNorm_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.FiniteDimension", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Module.Basis.exists_opNNNorm_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.FiniteDimension", "is_tactic_proof": true, "tactics": ["cases", "exact"], "tactic_count": 2}
{"name": "Module.Basis.exists_opNorm_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.FiniteDimension", "is_tactic_proof": true, "tactics": ["obtain", "refine", "intro", "simpa"], "tactic_count": 4}
{"name": "instSecondCountableTopologyContinuousLinearMapIdOfFiniteDimensional", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.FiniteDimension", "is_tactic_proof": true, "tactics": ["set", "suffices", "intro", "obtain", "let", "obtain", "v.exists_opNorm_le", "have", "have", "have", "intro", "have", "simp", "intro", "have", "obtain", "rw", "specialize", "simpa", "exact", "choose", "use", "replace", "have", "rw", "specialize", "rwa", "choose", "set", "change", "use", "intro", "calc", "dist"], "tactic_count": 34}
{"name": "AffineSubspace.closed_of_finiteDimensional", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_norm_le_le_norm_sub_of_finset", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.FiniteDimension", "is_tactic_proof": true, "tactics": ["let", "have", "haveI", "have", "have", "contrapose", "have", "ext", "simp", "rw", "exact", "obtain", "have", "intro", "rw", "simpa", "exact"], "tactic_count": 17}
{"name": "exists_seq_norm_le_one_le_norm_sub'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.FiniteDimension", "is_tactic_proof": false, "tactics": ["have", "constructor", "intro", "rw", "simpa", "apply", "rintro", "exact"], "tactic_count": 8}
{"name": "exists_seq_norm_le_one_le_norm_sub", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.FiniteDimension", "is_tactic_proof": true, "tactics": ["obtain", "have", "rcases", "exact"], "tactic_count": 4}
{"name": "FiniteDimensional.of_isCompact_closedBall₀", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.FiniteDimension", "is_tactic_proof": true, "tactics": ["by_contra", "obtain", "exists_seq_norm_le_one_le_norm_sub", "have", "obtain", "let", "have", "intro", "simp", "calc", "gcongr", "exact", "apply", "obtain", "h.tendsto_subseq", "have", "obtain", "apply", "calc", "conv_lhs", "simp", "gcongr", "apply", "exact"], "tactic_count": 24}
{"name": "FiniteDimensional.of_isCompact_closedBall", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteDimensional.of_locallyCompactSpace", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasCompactSupport.eq_zero_or_finiteDimensional", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasCompactMulSupport.eq_one_or_finiteDimensional", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProperSpace.of_locallyCompactSpace", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.FiniteDimension", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "have", "have", "simpa", "have", "exact"], "tactic_count": 7}
{"name": "ProperSpace.of_locallyCompact_module", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.piRing", "kind": "definition", "module": "Mathlib.Analysis.Normed.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousOn_clm_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.FiniteDimension", "is_tactic_proof": true, "tactics": ["refine", "let", "have", "let", "let", "rw", "exact"], "tactic_count": 7}
{"name": "continuous_clm_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.FiniteDimension", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "FiniteDimensional.proper", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.FiniteDimension", "is_tactic_proof": true, "tactics": ["have", "set", "exact"], "tactic_count": 3}
{"name": "FiniteDimensional.proper_real", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instProperSpaceSubtypeMemSubmoduleOfCompleteSpaceOfLocallyCompactSpace", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.FiniteDimension", "is_tactic_proof": true, "tactics": ["nontriviality", "have", "have", "exact"], "tactic_count": 4}
{"name": "exists_mem_frontier_infDist_compl_eq_dist", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.FiniteDimension", "is_tactic_proof": true, "tactics": ["rcases", "rw", "refine", "rwa"], "tactic_count": 4}
{"name": "IsCompact.exists_mem_frontier_infDist_compl_eq_dist", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.FiniteDimension", "is_tactic_proof": false, "tactics": ["obtain", "rw", "exact", "rw", "rcases", "have", "exact", "refine", "rw", "rw"], "tactic_count": 10}
{"name": "summable_norm_iff", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.FiniteDimension", "is_tactic_proof": false, "tactics": ["refine", "suffices", "obtain", "set", "have", "refine", "simpa", "clear", "intro", "have", "refine", "rw", "refine", "exact", "exact"], "tactic_count": 15}
{"name": "summable_of_sum_range_norm_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "summable_of_isBigO'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsBigO.comp_summable", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "summable_of_isBigO_nat'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "summable_norm_mul_geometric_of_norm_lt_one'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.FiniteDimension", "is_tactic_proof": true, "tactics": ["rcases", "apply", "calc", "apply", "filter_upwards", "simp", "simpa", "convert", "isBigO_norm_right.mpr", "simp"], "tactic_count": 10}
{"name": "summable_of_isEquivalent", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "summable_of_isEquivalent_nat", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsEquivalent.summable_iff", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsEquivalent.summable_iff_nat", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.continuous_coe_repr", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.continuous_toMatrix", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.exists_extension_norm_eq", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.HahnBanach", "is_tactic_proof": false, "tactics": ["rcases", "exists_extension_of_le_sublinear", "rw", "exact", "set", "refine", "apply", "refine", "dsimp", "rw", "apply"], "tactic_count": 11}
{"name": "exists_extension_norm_eq", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.HahnBanach", "is_tactic_proof": true, "tactics": ["letI", "letI", "letI", "letI", "let", "reCLM.comp", "obtain", "refine", "have", "rw", "simp", "refine", "calc", "exact"], "tactic_count": 14}
{"name": "ContinuousLinearMap.exist_extension_of_finiteDimensional_range", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.HahnBanach", "is_tactic_proof": true, "tactics": ["letI", "set", "set", "set", "choose", "use", "ext", "simp"], "tactic_count": 8}
{"name": "Submodule.ClosedComplemented.of_finiteDimensional", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.HahnBanach", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "coord_norm'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.HahnBanach", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "exists_dual_vector", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.HahnBanach", "is_tactic_proof": true, "tactics": ["let", "let", "obtain", "refine", "rw", "calc", "g"], "tactic_count": 7}
{"name": "exists_dual_vector'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.HahnBanach", "is_tactic_proof": true, "tactics": ["by_cases", "obtain", "obtain", "refine", "simp", "exact"], "tactic_count": 6}
{"name": "exists_dual_vector''", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.HahnBanach", "is_tactic_proof": true, "tactics": ["by_cases", "refine", "symm", "simp", "rcases", "exact"], "tactic_count": 6}
{"name": "IsLprojection.Lcomplement", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.MStructure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLprojection.Lcomplement_iff", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.MStructure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLprojection.commute", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.MStructure", "is_tactic_proof": false, "tactics": ["have", "refine", "rw", "have", "calc", "rw", "rw", "have", "simpa", "rw", "nth_rewrite", "rw", "rw", "refine", "rwa", "have", "have", "calc", "rwa", "change", "rw"], "tactic_count": 21}
{"name": "IsLprojection.mul", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.MStructure", "is_tactic_proof": true, "tactics": ["refine", "intro", "refine", "calc", "calc", "rw"], "tactic_count": 6}
{"name": "IsLprojection.join", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.MStructure", "is_tactic_proof": true, "tactics": ["convert", "noncomm_ring"], "tactic_count": 2}
{"name": "IsLprojection.Subtype.instCompl", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.MStructure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLprojection.coe_compl", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.MStructure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLprojection.Subtype.inf", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.MStructure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLprojection.coe_inf", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.MStructure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLprojection.Subtype.sup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.MStructure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLprojection.coe_sup", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.MStructure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLprojection.Subtype.sdiff", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.MStructure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLprojection.coe_sdiff", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.MStructure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLprojection.Subtype.partialOrder", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.MStructure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLprojection.le_def", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.MStructure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLprojection.Subtype.zero", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.MStructure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLprojection.coe_zero", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.MStructure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLprojection.Subtype.one", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.MStructure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLprojection.coe_one", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.MStructure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLprojection.Subtype.boundedOrder", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.MStructure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLprojection.coe_bot", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.MStructure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLprojection.coe_top", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.MStructure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLprojection.compl_mul", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.MStructure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsLprojection.mul_compl_self", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.MStructure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsLprojection.distrib_lattice_lemma", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.MStructure", "is_tactic_proof": true, "tactics": ["rw", "mul_assoc", "zero_add,", "all"], "tactic_count": 4}
{"name": "IsLprojection.instLatticeSubtypeOfFaithfulSMul", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.MStructure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLprojection.Subtype.distribLattice", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.MStructure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLprojection.Subtype.BooleanAlgebra", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.MStructure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.continuous_uncurry_of_multilinear", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": true, "tactics": ["fun_prop"], "tactic_count": 1}
{"name": "ContinuousLinearMap.continuousOn_uncurry_of_multilinear", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.continuousAt_uncurry_of_multilinear", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.continuousWithinAt_uncurry_of_multilinear", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.norm_map_coord_zero", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": true, "tactics": ["classical", "rw", "have", "inseparable_pi.2", "simpa"], "tactic_count": 5}
{"name": "MultilinearMap.bound_of_shell_of_norm_map_coord_zero", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "rcases", "rw", "choose", "have", "simpa"], "tactic_count": 6}
{"name": "MultilinearMap.bound_of_shell_of_continuous", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.exists_bound_of_continuous", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": true, "tactics": ["cases", "refine", "obtain", "simp", "obtain", "simp", "rcases", "have", "refine", "refine", "refine", "rw", "gcongr", "apply"], "tactic_count": 14}
{"name": "MultilinearMap.norm_image_sub_le_of_bound'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": ["have", "induction", "empty", "insert", "have", "have", "have", "rw", "apply", "gcongr", "by_cases", "rw", "simp", "by_cases", "calc", "rw", "exact", "simp", "convert", "simp"], "tactic_count": 20}
{"name": "MultilinearMap.norm_image_sub_le_of_bound", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": true, "tactics": ["classical", "have", "intro", "calc", "gcongr", "rcases", "simp", "exact", "simp", "rw", "simp", "calc", "f.norm_image_sub_le_of_bound", "rw", "ring"], "tactic_count": 15}
{"name": "MultilinearMap.continuous_of_bound", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": true, "tactics": ["let", "have", "replace", "refine", "refine", "continuousAt_of_locally_lipschitz", "rw", "have", "calc", "f.norm_image_sub_le_of_bound"], "tactic_count": 10}
{"name": "MultilinearMap.coe_mkContinuous", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.restr_norm_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": true, "tactics": ["rw", "convert", "simp", "convert"], "tactic_count": 4}
{"name": "ContinuousMultilinearMap.bound", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.norm_def", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.bounds_nonempty", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.bounds_bddBelow", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.isLeast_opNorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": true, "tactics": ["refine", "simp", "exact"], "tactic_count": 3}
{"name": "ContinuousMultilinearMap.opNorm_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.le_opNorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.le_mul_prod_of_opNorm_le_of_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.le_opNorm_mul_prod_of_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.le_opNorm_mul_pow_card_of_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ContinuousMultilinearMap.le_opNorm_mul_pow_of_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ContinuousMultilinearMap.le_of_opNorm_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.ratio_le_opNorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.unit_le_opNorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.opNorm_le_bound", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.opNorm_le_iff", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.opNorm_add_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.opNorm_zero", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.opNorm_smul_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.seminorm", "kind": "definition", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.Normed.Module.Multilinear.Basic.0.ContinuousMultilinearMap.uniformity_eq_seminorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": ["refine", "rcases", "have", "simp", "use", "suffices", "simpa", "intro", "refine", "opNorm_le_bound", "f.1.bound_of_shell_of_continuous", "calc", "rcases", "rcases", "refine", "simp", "replace", "replace", "calc"], "tactic_count": 19}
{"name": "ContinuousMultilinearMap.le_opNNNorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.le_of_opNNNorm_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.opNNNorm_le_iff", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousMultilinearMap.isLeast_opNNNorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ContinuousMultilinearMap.opNNNorm_prod", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.opNorm_prod", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.opNNNorm_pi", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.opNorm_pi", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.norm_ofSubsingleton", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": true, "tactics": ["letI", "simp"], "tactic_count": 2}
{"name": "ContinuousMultilinearMap.nnnorm_ofSubsingleton", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.norm_ofSubsingleton_id_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "ContinuousMultilinearMap.nnnorm_ofSubsingleton_id_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.norm_constOfIsEmpty", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": true, "tactics": ["apply", "refine", "rw", "simpa"], "tactic_count": 4}
{"name": "ContinuousMultilinearMap.nnnorm_constOfIsEmpty", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.norm_restrictScalars", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.norm_image_sub_le'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.norm_image_sub_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.mkContinuous_norm_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.mkContinuous_norm_le'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.norm_restr", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": true, "tactics": ["apply", "exact"], "tactic_count": 2}
{"name": "ContinuousMultilinearMap.norm_mkPiAlgebra_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": true, "tactics": ["refine", "simp", "exact"], "tactic_count": 3}
{"name": "ContinuousMultilinearMap.norm_mkPiAlgebra_of_empty", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": true, "tactics": ["apply", "apply", "convert", "simp"], "tactic_count": 4}
{"name": "ContinuousMultilinearMap.norm_mkPiAlgebra", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": true, "tactics": ["cases", "simp", "refine", "convert", "simp"], "tactic_count": 5}
{"name": "ContinuousMultilinearMap.norm_mkPiAlgebraFin_succ_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": true, "tactics": ["refine", "simp", "refine", "rw", "exact", "rw"], "tactic_count": 6}
{"name": "ContinuousMultilinearMap.norm_mkPiAlgebraFin_le_of_pos", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "ContinuousMultilinearMap.norm_mkPiAlgebraFin_zero", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": true, "tactics": ["refine", "refine", "simp", "convert", "simp"], "tactic_count": 5}
{"name": "ContinuousMultilinearMap.norm_mkPiAlgebraFin_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": true, "tactics": ["cases", "exact", "exact"], "tactic_count": 3}
{"name": "ContinuousMultilinearMap.norm_mkPiAlgebraFin", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": true, "tactics": ["cases", "rw", "simp", "refine", "refine", "simp"], "tactic_count": 6}
{"name": "ContinuousMultilinearMap.nnnorm_smulRight", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": true, "tactics": ["refine", "refine", "rw", "gcongr", "exact", "obtain", "simp", "rw", "intro", "rw", "refine", "rw"], "tactic_count": 12}
{"name": "ContinuousMultilinearMap.norm_smulRight", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.norm_mkPiRing", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ContinuousMultilinearMap.smulRightL_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.norm_smulRightL_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.piFieldEquiv", "kind": "definition", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.mkContinuousLinear_norm_le'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "exact"], "tactic_count": 2}
{"name": "MultilinearMap.mkContinuousLinear_norm_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.mkContinuousMultilinear_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.mkContinuousMultilinear_norm_le'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "exact"], "tactic_count": 2}
{"name": "MultilinearMap.mkContinuousMultilinear_norm_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.norm_compContinuousMultilinearMap_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.continuousMultilinearMapCongrRight_symm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.continuousMultilinearMapCongrRight_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.flipLinear_flipMultilinear", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.flipMultilinear_flipLinear", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.coe_flipMultilinearEquiv", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.coe_symm_flipMultilinearEquiv", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.norm_compContinuousMultilinearMap", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousMultilinearMap.norm_compContinuousLinearMap_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.norm_compContinuous_linearIsometry_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": true, "tactics": ["refine", "apply", "simp"], "tactic_count": 3}
{"name": "ContinuousMultilinearMap.norm_compContinuous_linearIsometryEquiv", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": true, "tactics": ["apply", "have", "g", "ext1", "simp", "conv_lhs", "apply"], "tactic_count": 7}
{"name": "ContinuousMultilinearMap.compContinuousLinearMapL_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.norm_compContinuousLinearMapL_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.compContinuousLinearMapLRight_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.norm_compContinuousLinearMapLRight_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.fderivCompContinuousLinearMap_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousLinearEquiv.continuousMultilinearMapCongrLeft_symm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.continuousMultilinearMapCongrLeft_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.iteratedFDerivComponent_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousMultilinearMap.norm_iteratedFDerivComponent_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.iteratedFDeriv", "kind": "definition", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.norm_iteratedFDeriv_le'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": true, "tactics": ["classical", "calc", "gcongr", "simpa"], "tactic_count": 4}
{"name": "ContinuousMultilinearMap.opNorm_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousMultilinearMap.norm_ofSubsingleton_id", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousMultilinearMap.nnnorm_ofSubsingleton_id", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.bound_of_shell", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.norm_map_removeNth_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Curry", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ContinuousLinearMap.norm_map_tail_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.norm_map_init_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Curry", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ContinuousMultilinearMap.norm_map_insertNth_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Curry", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ContinuousMultilinearMap.norm_map_cons_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Curry", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ContinuousMultilinearMap.norm_map_snoc_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Curry", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ContinuousLinearMap.uncurryLeft_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.curryLeft_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.curry_uncurryLeft", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Curry", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "ContinuousMultilinearMap.uncurry_curryLeft", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousMultilinearCurryLeftEquiv_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousMultilinearCurryLeftEquiv_symm_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.curryLeft_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.uncurryLeft_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.uncurryRight_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.curryRight_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.curry_uncurryRight", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Curry", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "ContinuousMultilinearMap.uncurry_curryRight", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Curry", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "continuousMultilinearCurryRightEquiv_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousMultilinearCurryRightEquiv_symm_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousMultilinearCurryRightEquiv_apply'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousMultilinearCurryRightEquiv_symm_apply'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.curryRight_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.uncurryRight_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.curryMid_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.curryMid_uncurryMid", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Curry", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "ContinuousMultilinearMap.uncurryMid_curryMid", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.norm_curryMid", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.norm_uncurryMid", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.uncurry0_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.curry0_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.apply_zero_uncurry0", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Curry", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "ContinuousMultilinearMap.uncurry0_curry0", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Curry", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousMultilinearMap.curry0_uncurry0", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.uncurry0_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.fin0_apply_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Curry", "is_tactic_proof": true, "tactics": ["obtain", "refine", "have", "simp", "simpa"], "tactic_count": 5}
{"name": "ContinuousMultilinearMap.curry0_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Curry", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "continuousMultilinearCurryFin0_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousMultilinearCurryFin0_symm_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousMultilinearCurryFin1_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousMultilinearCurryFin1_symm_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.norm_domDomCongr", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Curry", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousMultilinearMap.currySum_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.uncurrySum_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.curryFinFinset_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.curryFinFinset_symm_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.curryFinFinset_symm_apply_piecewise_const", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.curryFinFinset_symm_apply_const", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.curryFinFinset_apply_const", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Curry", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "ContinuousLinearMap.continuousMultilinearMapOption_apply_eq_self", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Multilinear.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TendstoUniformlyOn.comp_cexp", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.MultipliableUniformlyOn", "is_tactic_proof": true, "tactics": ["obtain", "have", "refine", "exact"], "tactic_count": 4}
{"name": "Summable.hasSumUniformlyOn_log_one_add", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.MultipliableUniformlyOn", "is_tactic_proof": true, "tactics": ["simp", "apply", "filter_upwards"], "tactic_count": 3}
{"name": "Summable.tendstoUniformlyOn_tsum_nat_log_one_add", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.MultipliableUniformlyOn", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "hasProdUniformlyOn_of_clog", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.MultipliableUniformlyOn", "is_tactic_proof": true, "tactics": ["simp", "obtain", "suffices", "refine", "exact", "refine", "simpa", "filter_upwards"], "tactic_count": 8}
{"name": "multipliableUniformlyOn_of_clog", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.MultipliableUniformlyOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Summable.hasProdUniformlyOn_one_add", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.MultipliableUniformlyOn", "is_tactic_proof": true, "tactics": ["simp", "by_cases", "simp", "haveI", "haveI", "let", "have", "simp", "filter_upwards", "have", "multipliable_one_add_of_summable", "convert", "simp", "exact"], "tactic_count": 14}
{"name": "Summable.multipliableUniformlyOn_one_add", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.MultipliableUniformlyOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Summable.hasProdUniformlyOn_nat_one_add", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.MultipliableUniformlyOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Summable.multipliableUniformlyOn_nat_one_add", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.MultipliableUniformlyOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Summable.hasProdLocallyUniformlyOn_one_add", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.MultipliableUniformlyOn", "is_tactic_proof": true, "tactics": ["apply", "refine", "filter_upwards"], "tactic_count": 3}
{"name": "Summable.multipliableLocallyUniformlyOn_one_add", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.MultipliableUniformlyOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Summable.hasProdLocallyUniformlyOn_nat_one_add", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.MultipliableUniformlyOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Summable.multipliableLocallyUniformlyOn_nat_one_add", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.MultipliableUniformlyOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedSpace.normalize", "kind": "definition", "module": "Mathlib.Analysis.Normed.Module.Normalize", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedSpace.normalize_zero_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Normalize", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NormedSpace.normalize_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Normalize", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "NormedSpace.norm_smul_normalize", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Normalize", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "NormedSpace.norm_normalize_eq_one_iff", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Normalize", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "NormedSpace.normalize_eq_self_of_norm_eq_one", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Normalize", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NormedSpace.normalize_normalize", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Normalize", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "simp"], "tactic_count": 3}
{"name": "NormedSpace.normalize_neg", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Normalize", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NormedSpace.normalize_smul_of_pos", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Normalize", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NormedSpace.normalize_smul_of_neg", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Normalize", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "NormedSpace.normalize_smul", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Normalize", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simp", "simp"], "tactic_count": 4}
{"name": "PiTensorProduct.toDualContinuousMultilinearMap", "kind": "definition", "module": "Mathlib.Analysis.Normed.Module.PiTensorProduct.InjectiveSeminorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiTensorProduct.toDualContinuousMultilinearMap_le_projectiveSeminorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.PiTensorProduct.InjectiveSeminorm", "is_tactic_proof": true, "tactics": ["simp", "apply"], "tactic_count": 2}
{"name": "PiTensorProduct.definition._@.Mathlib.Analysis.Normed.Module.PiTensorProduct.InjectiveSeminorm.2741663271._hygCtx._hyg.2", "kind": "definition", "module": "Mathlib.Analysis.Normed.Module.PiTensorProduct.InjectiveSeminorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiTensorProduct.wrapped._@.Mathlib.Analysis.Normed.Module.PiTensorProduct.InjectiveSeminorm.2741663271._hygCtx._hyg.2", "kind": "opaque", "module": "Mathlib.Analysis.Normed.Module.PiTensorProduct.InjectiveSeminorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiTensorProduct.injectiveSeminorm", "kind": "definition", "module": "Mathlib.Analysis.Normed.Module.PiTensorProduct.InjectiveSeminorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiTensorProduct.injectiveSeminorm_def", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.PiTensorProduct.InjectiveSeminorm", "is_tactic_proof": true, "tactics": ["intros", "delta", "rw", "rfl"], "tactic_count": 4}
{"name": "PiTensorProduct.dualSeminorms_bounded", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.PiTensorProduct.InjectiveSeminorm", "is_tactic_proof": true, "tactics": ["existsi", "rw", "simp", "intro", "rw", "intro", "simp", "exact"], "tactic_count": 8}
{"name": "PiTensorProduct.injectiveSeminorm_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.PiTensorProduct.InjectiveSeminorm", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "PiTensorProduct.norm_eval_le_injectiveSeminorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.PiTensorProduct.InjectiveSeminorm", "is_tactic_proof": true, "tactics": ["property", "not", "through", "the", "immediately.", "to", "it", "of", "set", "set", "set", "letI", "letI", "set", "have", "change", "simp", "exact", "set", "have", "have", "induction", "smul_tprod", "simp", "add", "suffices", "change", "rw", "exact", "have", "injectiveSeminorm", "simp", "refine", "rw", "existsi", "rfl", "refine", "simp", "rw", "exact"], "tactic_count": 40}
{"name": "PiTensorProduct.injectiveSeminorm_le_projectiveSeminorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.PiTensorProduct.InjectiveSeminorm", "is_tactic_proof": true, "tactics": ["rw", "refine", "existsi", "simp", "existsi", "ext", "simp", "rw", "intro", "simp", "obtain", "rw", "exact"], "tactic_count": 13}
{"name": "PiTensorProduct.injectiveSeminorm_tprod_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.PiTensorProduct.InjectiveSeminorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiTensorProduct.instSeminormedAddCommGroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.PiTensorProduct.InjectiveSeminorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiTensorProduct.instNormedSpace", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.PiTensorProduct.InjectiveSeminorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiTensorProduct.liftEquiv", "kind": "definition", "module": "Mathlib.Analysis.Normed.Module.PiTensorProduct.InjectiveSeminorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiTensorProduct.liftIsometry", "kind": "definition", "module": "Mathlib.Analysis.Normed.Module.PiTensorProduct.InjectiveSeminorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiTensorProduct.liftIsometry_apply_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.PiTensorProduct.InjectiveSeminorm", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PiTensorProduct.tprodL", "kind": "definition", "module": "Mathlib.Analysis.Normed.Module.PiTensorProduct.InjectiveSeminorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiTensorProduct.tprodL_coe", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.PiTensorProduct.InjectiveSeminorm", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "PiTensorProduct.liftIsometry_symm_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.PiTensorProduct.InjectiveSeminorm", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "PiTensorProduct.liftIsometry_tprodL", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.PiTensorProduct.InjectiveSeminorm", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "PiTensorProduct.mapL", "kind": "definition", "module": "Mathlib.Analysis.Normed.Module.PiTensorProduct.InjectiveSeminorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiTensorProduct.mapL_coe", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.PiTensorProduct.InjectiveSeminorm", "is_tactic_proof": true, "tactics": ["ext", "simp", "lift.tprod,", "map_tprod]"], "tactic_count": 4}
{"name": "PiTensorProduct.mapL_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.PiTensorProduct.InjectiveSeminorm", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "PiTensorProduct.mapLIncl", "kind": "definition", "module": "Mathlib.Analysis.Normed.Module.PiTensorProduct.InjectiveSeminorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiTensorProduct.mapL_comp", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.PiTensorProduct.InjectiveSeminorm", "is_tactic_proof": true, "tactics": ["apply", "ext", "simp"], "tactic_count": 3}
{"name": "PiTensorProduct.liftIsometry_comp_mapL", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.PiTensorProduct.InjectiveSeminorm", "is_tactic_proof": true, "tactics": ["apply", "ext", "simp"], "tactic_count": 3}
{"name": "PiTensorProduct.mapL_id", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.PiTensorProduct.InjectiveSeminorm", "is_tactic_proof": true, "tactics": ["apply", "ext", "simp"], "tactic_count": 3}
{"name": "PiTensorProduct.mapL_one", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.PiTensorProduct.InjectiveSeminorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiTensorProduct.mapL_mul", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.PiTensorProduct.InjectiveSeminorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiTensorProduct.mapLMonoidHom", "kind": "definition", "module": "Mathlib.Analysis.Normed.Module.PiTensorProduct.InjectiveSeminorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiTensorProduct.mapL_pow", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.PiTensorProduct.InjectiveSeminorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.Normed.Module.PiTensorProduct.InjectiveSeminorm.0.PiTensorProduct.mapL_add_smul_aux", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.PiTensorProduct.InjectiveSeminorm", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "PiTensorProduct.mapL_add", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.PiTensorProduct.InjectiveSeminorm", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "PiTensorProduct.mapL_smul", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.PiTensorProduct.InjectiveSeminorm", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "PiTensorProduct.mapL_opNorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.PiTensorProduct.InjectiveSeminorm", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "simp", "refine", "rw", "intro", "simp", "refine", "rw", "exact"], "tactic_count": 11}
{"name": "PiTensorProduct.mapLMultilinear", "kind": "definition", "module": "Mathlib.Analysis.Normed.Module.PiTensorProduct.InjectiveSeminorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiTensorProduct.mapLMultilinear_opNorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.PiTensorProduct.InjectiveSeminorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiTensorProduct.projectiveSeminormAux", "kind": "definition", "module": "Mathlib.Analysis.Normed.Module.PiTensorProduct.ProjectiveSeminorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiTensorProduct.projectiveSeminormAux_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.PiTensorProduct.ProjectiveSeminorm", "is_tactic_proof": true, "tactics": ["simp", "refine", "intro", "simp", "intro", "rw", "exact"], "tactic_count": 7}
{"name": "PiTensorProduct.projectiveSeminormAux_add_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.PiTensorProduct.ProjectiveSeminorm", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PiTensorProduct.projectiveSeminormAux_smul", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.PiTensorProduct.ProjectiveSeminorm", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PiTensorProduct.bddBelow_projectiveSemiNormAux", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.PiTensorProduct.ProjectiveSeminorm", "is_tactic_proof": true, "tactics": ["existsi", "rw", "simp", "exact"], "tactic_count": 4}
{"name": "PiTensorProduct.projectiveSeminorm", "kind": "definition", "module": "Mathlib.Analysis.Normed.Module.PiTensorProduct.ProjectiveSeminorm", "is_tactic_proof": true, "tactics": ["refine", "refine", "refine", "rfl", "letI", "exact", "intro", "letI", "exact", "le_ciInf_add_ciInf", "ciInf_le_of_le", "intro", "letI", "rw", "refine", "intro", "rw", "exact", "ciInf_le_of_le"], "tactic_count": 19}
{"name": "PiTensorProduct.projectiveSeminorm_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.PiTensorProduct.ProjectiveSeminorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiTensorProduct.projectiveSeminorm_tprod_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.PiTensorProduct.ProjectiveSeminorm", "is_tactic_proof": true, "tactics": ["rw", "convert", "simp", "rw"], "tactic_count": 4}
{"name": "PiTensorProduct.norm_eval_le_projectiveSeminorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.PiTensorProduct.ProjectiveSeminorm", "is_tactic_proof": true, "tactics": ["letI", "rw", "unfold", "refine", "intro", "rw", "conv_lhs", "refine", "simp", "rw", "refine", "simp", "map_smul,", "intro", "rw", "exact"], "tactic_count": 16}
{"name": "RCLike.norm_coe_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.RCLike.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "norm_smul_inv_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.RCLike.Basic", "is_tactic_proof": true, "tactics": ["have", "simp"], "tactic_count": 2}
{"name": "norm_smul_inv_norm'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.RCLike.Basic", "is_tactic_proof": true, "tactics": ["have", "simp"], "tactic_count": 2}
{"name": "LinearMap.bound_of_sphere_bound", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.RCLike.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "simp", "exact", "set", "have", "apply", "rw", "exact", "have", "have", "rw", "rw", "simp", "rw", "div_mul_eq_mul_div,", "apply", "exact", "apply"], "tactic_count": 19}
{"name": "LinearMap.bound_of_ball_bound'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.opNorm_bound_of_ball_bound", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.RCLike.Basic", "is_tactic_proof": true, "tactics": ["apply", "apply", "exact", "apply", "exact"], "tactic_count": 5}
{"name": "NormedSpace.sphere_nonempty_rclike", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.norm_extendTo𝕜'_bound", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.RCLike.Extend", "is_tactic_proof": true, "tactics": ["set", "by_cases", "rw", "positivity", "rw", "calc"], "tactic_count": 6}
{"name": "ContinuousLinearMap.norm_extendTo𝕜'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.RCLike.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.norm_extendTo𝕜", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.RCLike.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.punctured_nhds_module_neBot", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.RCLike.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_norm_smul_mem_unitClosedBall", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.RCLike.Real", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "norm_smul_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.RCLike.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "dist_smul_add_one_sub_smul_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.RCLike.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "closure_ball", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.RCLike.Real", "is_tactic_proof": true, "tactics": ["refine", "have", "convert", "rw", "simp", "rintro", "rw", "mul_one", "rw", "replace", "apply"], "tactic_count": 11}
{"name": "frontier_ball", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.RCLike.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "interior_closedBall", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.RCLike.Real", "is_tactic_proof": true, "tactics": ["rcases", "rw", "refine", "intro", "rcases", "exact", "set", "suffices", "have", "interior_mono", "simp", "intro", "rw", "simpa"], "tactic_count": 14}
{"name": "frontier_closedBall", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.RCLike.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "interior_sphere", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.RCLike.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "frontier_sphere", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.RCLike.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "exists_norm_eq", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.RCLike.Real", "is_tactic_proof": true, "tactics": ["rcases", "use", "simp"], "tactic_count": 3}
{"name": "range_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.RCLike.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nnnorm_surjective", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.RCLike.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "range_nnnorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.RCLike.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedSpace.sphere_nonempty", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.RCLike.Real", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact"], "tactic_count": 3}
{"name": "interior_closedBall'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.RCLike.Real", "is_tactic_proof": true, "tactics": ["rcases", "rw", "exact"], "tactic_count": 3}
{"name": "frontier_closedBall'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.RCLike.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "interior_sphere'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.RCLike.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "frontier_sphere'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.RCLike.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SameRay.norm_add", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ray", "is_tactic_proof": true, "tactics": ["rcases", "rw"], "tactic_count": 2}
{"name": "SameRay.norm_sub", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ray", "is_tactic_proof": true, "tactics": ["rcases", "wlog", "rw", "rw", "exact", "rw", "rw", "abs_of_nonneg"], "tactic_count": 8}
{"name": "SameRay.norm_smul_eq", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ray", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rw"], "tactic_count": 3}
{"name": "norm_injOn_ray_left", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ray", "is_tactic_proof": true, "tactics": ["rintro", "rcases", "rcases", "rw", "rw"], "tactic_count": 5}
{"name": "norm_injOn_ray_right", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ray", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "sameRay_iff_norm_smul_eq", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ray", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sameRay_iff_inv_norm_smul_eq_of_ne", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ray", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "sameRay_iff_inv_norm_smul_eq", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ray", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "simp"], "tactic_count": 3}
{"name": "sameRay_iff_of_norm_eq", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ray", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact", "exact"], "tactic_count": 4}
{"name": "not_sameRay_iff_of_norm_eq", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ray", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SameRay.eq_of_norm_eq", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ray", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SameRay.norm_eq_iff", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Ray", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "riesz_lemma", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.RieszLemma", "is_tactic_proof": true, "tactics": ["classical", "obtain", "let", "have", "have", "let", "have", "simp", "norm_num", "have", "have", "obtain", "have", "by_contra", "have", "simp", "exact", "refine", "have", "calc", "r", "rw", "exact"], "tactic_count": 23}
{"name": "riesz_lemma_of_norm_lt", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.RieszLemma", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "simpa", "rcases", "have", "obtain", "rescale_to_shell", "refine", "set", "have", "calc", "simp", "ring"], "tactic_count": 14}
{"name": "Metric.closedBall_infDist_compl_subset_closure", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.RieszLemma", "is_tactic_proof": true, "tactics": ["rcases", "rw", "exact", "rw", "exact"], "tactic_count": 5}
{"name": "Shrink.instSeminormedAddCommGroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Shrink", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Shrink.instNormedAddCommGroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Shrink", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Shrink.instNormedSpace", "kind": "instance", "module": "Mathlib.Analysis.Normed.Module.Shrink", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.toSpanSingleton_homothety", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Span", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "LinearEquiv.toSpanNonzeroSingleton_homothety", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Span", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.toSpanNonzeroSingleton", "kind": "definition", "module": "Mathlib.Analysis.Normed.Module.Span", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.coord", "kind": "definition", "module": "Mathlib.Analysis.Normed.Module.Span", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.coe_toSpanNonzeroSingleton_symm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Span", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.coord_toSpanNonzeroSingleton", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Span", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.toSpanNonzeroSingleton_coord", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Span", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.coord_self", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Span", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.toSpanUnitSingleton", "kind": "definition", "module": "Mathlib.Analysis.Normed.Module.Span", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.toSpanUnitSingleton_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.Span", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "Equiv.seminormedCommGroup", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Module.TransferInstance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.normedCommGroup", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Module.TransferInstance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.normedSpace", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Module.TransferInstance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrongDual.toWeakDual", "kind": "definition", "module": "Mathlib.Analysis.Normed.Module.WeakDual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrongDual.coe_toWeakDual", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.WeakDual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrongDual.toWeakDual_inj", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.WeakDual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakDual.toStrongDual", "kind": "definition", "module": "Mathlib.Analysis.Normed.Module.WeakDual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakDual.toStrongDual_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.WeakDual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakDual.coe_toStrongDual", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.WeakDual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakDual.toStrongDual_inj", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.WeakDual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakDual.polar", "kind": "definition", "module": "Mathlib.Analysis.Normed.Module.WeakDual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakDual.polar_def", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.WeakDual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakDual.isClosed_polar", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.WeakDual", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "NormedSpace.Dual.toWeakDual_continuous", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.WeakDual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedSpace.Dual.continuousLinearMapToWeakDual", "kind": "definition", "module": "Mathlib.Analysis.Normed.Module.WeakDual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedSpace.Dual.dual_norm_topology_le_weak_dual_topology", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.WeakDual", "is_tactic_proof": true, "tactics": ["convert", "exact"], "tactic_count": 2}
{"name": "WeakDual.isClosed_closedBall", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.WeakDual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakDual.isClosed_image_coe_of_bounded_of_closed", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.WeakDual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakDual.isCompact_of_bounded_of_closed", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.WeakDual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakDual.isClosed_image_polar_of_mem_nhds", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.WeakDual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedSpace.Dual.isClosed_image_polar_of_mem_nhds", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.WeakDual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakDual.isCompact_polar", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.WeakDual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakDual.isCompact_closedBall", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.WeakDual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakDual.exists_countable_separating", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.WeakDual", "is_tactic_proof": true, "tactics": ["use", "constructor", "exact", "intro", "contrapose", "exact"], "tactic_count": 6}
{"name": "WeakDual.metrizable_of_isCompact", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.WeakDual", "is_tactic_proof": true, "tactics": ["have", "obtain", "exact"], "tactic_count": 3}
{"name": "WeakDual.isSeqCompact_of_isBounded_of_isClosed", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.WeakDual", "is_tactic_proof": true, "tactics": ["have", "have", "metrizable_of_isCompact", "have", "continuous_iff_seqContinuous.mp", "simpa"], "tactic_count": 6}
{"name": "WeakDual.isSeqCompact_polar", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.WeakDual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakDual.isSeqCompact_closedBall", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Module.WeakDual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "norm_smul_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.MulAction", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "nnnorm_smul_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.MulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "enorm_smul_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.MulAction", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "dist_smul_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.MulAction", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "nndist_smul_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.MulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lipschitzWith_smul", "kind": "theorem", "module": "Mathlib.Analysis.Normed.MulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "edist_smul_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.MulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSeminormedRing.isBoundedSMul", "kind": "instance", "module": "Mathlib.Analysis.Normed.MulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSeminormedRing.isBoundedSMulOpposite", "kind": "instance", "module": "Mathlib.Analysis.Normed.MulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBoundedSMul.of_norm_smul_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.MulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBoundedSMul.of_enorm_smul_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.MulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBoundedSMul.of_nnnorm_smul_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.MulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "norm_smul", "kind": "theorem", "module": "Mathlib.Analysis.Normed.MulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormMulClass.toNormSMulClass", "kind": "instance", "module": "Mathlib.Analysis.Normed.MulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormMulClass.toNormSMulClass_op", "kind": "instance", "module": "Mathlib.Analysis.Normed.MulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "enorm_smul", "kind": "theorem", "module": "Mathlib.Analysis.Normed.MulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormSMulClass.of_nnnorm_smul", "kind": "theorem", "module": "Mathlib.Analysis.Normed.MulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nnnorm_smul", "kind": "theorem", "module": "Mathlib.Analysis.Normed.MulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instENormSMulClass", "kind": "instance", "module": "Mathlib.Analysis.Normed.MulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instNormSMulClass", "kind": "instance", "module": "Mathlib.Analysis.Normed.MulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instNormSMulClass", "kind": "instance", "module": "Mathlib.Analysis.Normed.MulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.instNormSMulClass", "kind": "instance", "module": "Mathlib.Analysis.Normed.MulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dist_smul₀", "kind": "theorem", "module": "Mathlib.Analysis.Normed.MulAction", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "nndist_smul₀", "kind": "theorem", "module": "Mathlib.Analysis.Normed.MulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "edist_smul₀", "kind": "theorem", "module": "Mathlib.Analysis.Normed.MulAction", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NormSMulClass.toIsBoundedSMul", "kind": "instance", "module": "Mathlib.Analysis.Normed.MulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedDivisionRing.toNormSMulClass", "kind": "theorem", "module": "Mathlib.Analysis.Normed.MulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.isBigOWith_id", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Asymptotics", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.isBigO_id", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Asymptotics", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.isBigOWith_comp", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Asymptotics", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.isBigO_comp", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Asymptotics", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.isBigOWith_sub", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Asymptotics", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.isBigO_sub", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Asymptotics", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.isBigO_comp", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Asymptotics", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.isBigO_sub", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Asymptotics", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.isBigO_comp_rev", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Asymptotics", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.isBigO_sub_rev", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Asymptotics", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.instCoeFunNonlinearRightInverseForall", "kind": "instance", "module": "Mathlib.Analysis.Normed.Operator.Banach", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.NonlinearRightInverse.right_inv", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Banach", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.NonlinearRightInverse.bound", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Banach", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.toNonlinearRightInverse", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.Banach", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInhabitedNonlinearRightInverseToContinuousLinearMap", "kind": "instance", "module": "Mathlib.Analysis.Normed.Operator.Banach", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.exists_approx_preimage_norm_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Banach", "is_tactic_proof": false, "tactics": ["have", "refine", "rcases", "rcases", "refine", "refine", "rwa", "have", "nonempty_interior_of_iUnion_of_closed", "simp", "rcases", "rcases", "refine", "rcases", "simp", "have", "rcases", "let", "have", "have", "rcases", "rcases", "rw", "rw", "have", "simp", "exact", "rcases", "rcases", "rw", "rw", "let", "have", "calc", "congr", "simp", "abel", "have", "calc", "rwa", "rw", "have", "calc", "gcongr", "simpa", "exact", "exact"], "tactic_count": 47}
{"name": "ContinuousLinearMap.exists_preimage_norm_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Banach", "is_tactic_proof": true, "tactics": ["obtain", "choose", "let", "have", "intro", "rw", "exact", "refine", "have", "intro", "induction", "zero", "succ", "rw", "apply", "rw", "gcongr", "let", "have", "apply", "calc", "have", "refine", "exact", "have", "let", "have", "calc", "have", "intro", "induction", "zero", "succ", "have", "have", "simp", "have", "refine", "rw", "simp", "refine", "rw", "refine", "have", "rw", "exact"], "tactic_count": 46}
{"name": "ContinuousLinearMap.isOpenMap", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Banach", "is_tactic_proof": true, "tactics": ["intro", "rcases", "refine", "rcases", "rcases", "refine", "rcases", "have", "rw", "have", "calc", "dist", "apply", "rwa", "exact"], "tactic_count": 15}
{"name": "ContinuousLinearMap.isQuotientMap", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Banach", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.isOpenMap", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Banach", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.interior_preimage", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Banach", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.closure_preimage", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Banach", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.frontier_preimage", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Banach", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.exists_nonlinearRightInverse_of_surjective", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Banach", "is_tactic_proof": true, "tactics": ["choose", "use", "toFun", "nnnorm", "bound", "right_inv", "exact"], "tactic_count": 7}
{"name": "ContinuousLinearMap.definition._@.Mathlib.Analysis.Normed.Operator.Banach.754268252._hygCtx._hyg.2", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.Banach", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.wrapped._@.Mathlib.Analysis.Normed.Operator.Banach.754268252._hygCtx._hyg.2", "kind": "opaque", "module": "Mathlib.Analysis.Normed.Operator.Banach", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.nonlinearRightInverseOfSurjective", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.Banach", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.nonlinearRightInverseOfSurjective_def", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Banach", "is_tactic_proof": true, "tactics": ["intros", "delta", "rw", "rfl"], "tactic_count": 4}
{"name": "ContinuousLinearMap.nonlinearRightInverseOfSurjective_nnnorm_pos", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Banach", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "LinearEquiv.continuous_symm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Banach", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "rw", "exact"], "tactic_count": 5}
{"name": "LinearEquiv.toContinuousLinearEquivOfContinuous", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.Banach", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.coeFn_toContinuousLinearEquivOfContinuous", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Banach", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.coeFn_toContinuousLinearEquivOfContinuous_symm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Banach", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.equivRange", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.Banach", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.coe_linearMap_equivRange", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Banach", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.coe_equivRange", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Banach", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.equivRange_symm_toLinearEquiv", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Banach", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.equivRange_symm_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Banach", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousLinearMap.antilipschitz_of_injective_of_isClosed_range", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Banach", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.isClosed_range_iff_antilipschitz_of_injective", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Banach", "is_tactic_proof": true, "tactics": ["refine", "choose", "exact"], "tactic_count": 3}
{"name": "ContinuousLinearEquiv.ofBijective", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.Banach", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.coeFn_ofBijective", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Banach", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.coe_ofBijective", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Banach", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "ContinuousLinearEquiv.ofBijective_symm_apply_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Banach", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.ofBijective_apply_symm_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Banach", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.isUnit_iff_bijective", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Banach", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "exact", "refine", "simp"], "tactic_count": 5}
{"name": "ContinuousLinearMap.coprodSubtypeLEquivOfIsCompl", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.Banach", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.range_eq_map_coprodSubtypeLEquivOfIsCompl", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Banach", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ContinuousLinearMap.closed_complemented_range_of_isCompl_of_ker_eq_bot", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Banach", "is_tactic_proof": true, "tactics": ["haveI", "let", "rw", "apply", "exact"], "tactic_count": 5}
{"name": "LinearMap.continuous_of_isClosed_graph", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Banach", "is_tactic_proof": true, "tactics": ["letI", "let", "have", "let", "let", "exact"], "tactic_count": 6}
{"name": "LinearMap.continuous_of_seq_closed_graph", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Banach", "is_tactic_proof": true, "tactics": ["refine", "rintro", "refine", "have", "ext", "exact", "rw", "exact"], "tactic_count": 8}
{"name": "ContinuousLinearMap.ofIsClosedGraph", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.Banach", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.coeFn_ofIsClosedGraph", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Banach", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.coe_ofIsClosedGraph", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Banach", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "ContinuousLinearMap.ofSeqClosedGraph", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.Banach", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.coeFn_ofSeqClosedGraph", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Banach", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.coe_ofSeqClosedGraph", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Banach", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "ContinuousLinearMap.closed_range_of_antilipschitz", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Banach", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntilipschitzWith.completeSpace_range_clm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Banach", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.bijective_iff_dense_range_and_antilipschitz", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Banach", "is_tactic_proof": true, "tactics": ["refine", "simpa", "refine", "simp", "rwa"], "tactic_count": 5}
{"name": "banach_steinhaus", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.BanachSteinhaus", "is_tactic_proof": true, "tactics": ["rw", "refine", "simpa"], "tactic_count": 3}
{"name": "banach_steinhaus_iSup_nnnorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.BanachSteinhaus", "is_tactic_proof": true, "tactics": ["rw", "refine", "simpa"], "tactic_count": 3}
{"name": "ball_zero_subset_range_iff_surjective", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ball_subset_range_iff_surjective", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "simp_rw", "intro", "rw", "apply", "simp_all"], "tactic_count": 7}
{"name": "closedBall_subset_range_iff_surjective", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sphere_subset_range_iff_surjective", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Basic", "is_tactic_proof": true, "tactics": ["refine", "grw", "exact"], "tactic_count": 3}
{"name": "norm_image_of_norm_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SemilinearMapClass.bound_of_shell_semi_normed", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemilinearMapClass.bound_of_continuous", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemilinearMapClass.nnbound_of_continuous", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemilinearMapClass.ebound_of_continuous", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.bound", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.nnbound", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.ebound", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.toSpanSingleton_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.coe_toSpanSingleton", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.norm_def", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.bounds_nonempty", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.bounds_bddBelow", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.isLeast_opNorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Basic", "is_tactic_proof": true, "tactics": ["refine", "simp", "refine"], "tactic_count": 3}
{"name": "ContinuousLinearMap.opNorm_le_bound", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.opNorm_le_bound'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.opNorm_eq_of_bounds", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.opNorm_neg", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousLinearMap.opNorm_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.opNorm_zero", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.norm_id_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.le_opNorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.dist_le_opNorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "ContinuousLinearMap.le_of_opNorm_le_of_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.le_opNorm_of_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.le_of_opNorm_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.opNorm_le_iff", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.ratio_le_opNorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.unit_le_opNorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.opNorm_le_of_shell", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.opNorm_le_of_ball", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Basic", "is_tactic_proof": true, "tactics": ["rcases", "refine", "rwa"], "tactic_count": 3}
{"name": "ContinuousLinearMap.opNorm_le_of_nhds_zero", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.opNorm_le_of_shell'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "refine", "simp", "rwa", "rw", "refine", "rwa"], "tactic_count": 7}
{"name": "ContinuousLinearMap.opNorm_le_of_unit_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Basic", "is_tactic_proof": true, "tactics": ["refine", "have", "have", "rwa", "exact"], "tactic_count": 5}
{"name": "ContinuousLinearMap.opNorm_add_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.norm_id", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.norm_id_of_nontrivial_seminorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.opNorm_smul_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.opNorm_le_iff_lipschitz", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.seminorm", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.Normed.Operator.Basic.0.ContinuousLinearMap.uniformity_eq_seminorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Basic", "is_tactic_proof": false, "tactics": ["refine", "rcases", "refine", "suffices", "simpa", "intro", "refine", "exact", "rcases", "rcases", "refine", "simp", "rw", "exact"], "tactic_count": 14}
{"name": "ContinuousLinearMap.nnnorm_id", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.opNorm_comp_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.opNorm_subsingleton", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.le_opNorm_enorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "rw", "gcongr", "exact"], "tactic_count": 4}
{"name": "ContinuousLinearMap.homothety_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Basic", "is_tactic_proof": true, "tactics": ["obtain", "replace", "have", "apply", "simpa"], "tactic_count": 5}
{"name": "ContinuousLinearMap.norm_restrictScalars", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.coe_restrictScalarsIsometry", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.restrictScalarsIsometry_toLinearMap", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.norm_pi_le_of_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Basic", "is_tactic_proof": true, "tactics": ["refine", "refine", "exact"], "tactic_count": 3}
{"name": "LinearMap.mkContinuous_norm_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.mkContinuous_norm_le'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.norm_toContinuousLinearMap_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.norm_subtypeL_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.opNorm_ext", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.opNorm_le_bound₂", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.le_opNorm₂", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.le_of_opNorm₂_le_of_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.norm_mkContinuous₂_aux", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.mkContinuous₂_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.mkContinuous₂_norm_le'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.mkContinuous₂_norm_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.Normed.Operator.Bilinear.0.ContinuousLinearMap.le_norm_flip", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.flip_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.flip_flip", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Bilinear", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "ContinuousLinearMap.opNorm_flip", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.flip_zero", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.flip_add", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.flip_smul", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.flipₗᵢ'_symm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.coe_flipₗᵢ'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.flipₗᵢ_symm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.coe_flipₗᵢ", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.apply_apply'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.apply_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.norm_compSL_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.compSL_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.const_clm_comp", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.clm_comp_const", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.norm_compL_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.compL_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.precompL_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.norm_precompR_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.norm_precompL_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Bilinear", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ContinuousLinearMap.bilinearComp_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.bilinearComp_zero", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.bilinearComp_zero_left", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Bilinear", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "ContinuousLinearMap.bilinearComp_zero_right", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Bilinear", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "ContinuousLinearMap.coe_deriv₂", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.map_add_add", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Bilinear", "is_tactic_proof": true, "tactics": ["simp", "abel"], "tactic_count": 2}
{"name": "ContinuousLinearMap.norm_smulRight_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Bilinear", "is_tactic_proof": true, "tactics": ["refine", "refine", "calc", "obtain", "simp", "rw", "refine", "rw", "calc"], "tactic_count": 9}
{"name": "ContinuousLinearMap.nnnorm_smulRight_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.norm_toSpanSingleton", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Bilinear", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousLinearMap.nnnorm_toSpanSingleton", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.norm_smulRightL_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Bilinear", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousLinearMap.bilinearRestrictScalars_eq_restrictScalarsL_comp_restrictScalars", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.bilinearRestrictScalars_eq_restrictScalars_restrictScalarsL_comp", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.bilinearRestrictScalars_apply_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.norm_bilinearRestrictScalars", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isBoundedLinearMap_iff", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.BoundedLinearMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLinearMap.with_bound", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.BoundedLinearMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBoundedLinearMap.toLinearMap", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.BoundedLinearMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBoundedLinearMap.toContinuousLinearMap", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.BoundedLinearMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBoundedLinearMap.zero", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.BoundedLinearMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBoundedLinearMap.id", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.BoundedLinearMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBoundedLinearMap.fst", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.BoundedLinearMaps", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "IsBoundedLinearMap.snd", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.BoundedLinearMaps", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "IsBoundedLinearMap.smul", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.BoundedLinearMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBoundedLinearMap.neg", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.BoundedLinearMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBoundedLinearMap.add", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.BoundedLinearMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBoundedLinearMap.sub", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.BoundedLinearMaps", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsBoundedLinearMap.comp", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.BoundedLinearMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBoundedLinearMap.tendsto", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.BoundedLinearMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBoundedLinearMap.continuous", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.BoundedLinearMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBoundedLinearMap.lim_zero_bounded_linear_map", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.BoundedLinearMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBoundedLinearMap.isBigO_id", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.BoundedLinearMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBoundedLinearMap.isBigO_comp", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.BoundedLinearMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBoundedLinearMap.isBigO_sub", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.BoundedLinearMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBoundedBilinearMap.symm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.BoundedLinearMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBoundedBilinearMap.isBoundedLinearMap_right", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.BoundedLinearMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBoundedBilinearMap.isBoundedLinearMap_left", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.BoundedLinearMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBoundedBilinearMap.map_sub_left", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.BoundedLinearMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBoundedBilinearMap.map_sub_right", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.BoundedLinearMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBoundedBilinearMap.isBigO", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.BoundedLinearMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBoundedBilinearMap.isBigO_comp", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.BoundedLinearMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBoundedBilinearMap.isBigO'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.BoundedLinearMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBoundedBilinearMap.continuous", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.BoundedLinearMaps", "is_tactic_proof": true, "tactics": ["refine", "suffices", "simpa", "apply", "rw", "refine", "refine", "exact", "exact", "rw", "refine", "apply", "rw", "exact"], "tactic_count": 14}
{"name": "IsBoundedBilinearMap.continuous_left", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.BoundedLinearMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBoundedBilinearMap.continuous_right", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.BoundedLinearMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isBoundedBilinearMap_smul", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.BoundedLinearMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isBoundedBilinearMap_mul", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.BoundedLinearMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.isBoundedLinearMap", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.BoundedLinearMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBoundedLinearMap.isLinearMap_and_continuous_iff_isBoundedLinearMap", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.BoundedLinearMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isBoundedLinearMap_prod_multilinear", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.BoundedLinearMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isBoundedLinearMap_continuousMultilinearMap_comp_linear", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.BoundedLinearMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.isBoundedBilinearMap", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.BoundedLinearMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBoundedBilinearMap.toContinuousLinearMap", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.BoundedLinearMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBoundedBilinearMap.toContinuousLinearMap_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.BoundedLinearMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.continuous₂", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.BoundedLinearMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isBoundedBilinearMap_comp", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.BoundedLinearMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.isBoundedLinearMap_comp_left", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.BoundedLinearMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.isBoundedLinearMap_comp_right", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.BoundedLinearMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isBoundedBilinearMap_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.BoundedLinearMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isBoundedBilinearMap_smulRight", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.BoundedLinearMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isBoundedBilinearMap_compMultilinear", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.BoundedLinearMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBoundedBilinearMap.linearDeriv", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.BoundedLinearMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBoundedBilinearMap.deriv", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.BoundedLinearMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBoundedBilinearMap.deriv_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.BoundedLinearMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.mulLeftRight_isBoundedBilinear", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.BoundedLinearMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBoundedBilinearMap.isBoundedLinearMap_deriv", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.BoundedLinearMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.clm_comp", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.BoundedLinearMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.clm_comp", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.BoundedLinearMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.clm_comp", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.BoundedLinearMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.clm_comp", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.BoundedLinearMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.clm_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.BoundedLinearMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.clm_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.BoundedLinearMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.clm_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.BoundedLinearMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.clm_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.BoundedLinearMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.continuousLinearMapCoprod", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.BoundedLinearMaps", "is_tactic_proof": true, "tactics": ["simp", "fun_prop"], "tactic_count": 2}
{"name": "ContinuousAt.continuousLinearMapCoprod", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.BoundedLinearMaps", "is_tactic_proof": true, "tactics": ["simp", "fun_prop"], "tactic_count": 2}
{"name": "ContinuousOn.continuousLinearMapCoprod", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.BoundedLinearMaps", "is_tactic_proof": true, "tactics": ["simp", "fun_prop"], "tactic_count": 2}
{"name": "Continuous.continuousLinearMapCoprod", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.BoundedLinearMaps", "is_tactic_proof": true, "tactics": ["apply", "fun_prop"], "tactic_count": 2}
{"name": "ContinuousLinearEquiv.isOpen", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.BoundedLinearMaps", "is_tactic_proof": true, "tactics": ["rw", "refine", "let", "have", "convert", "ext", "constructor", "rintro", "exact", "rintro", "use", "ext", "simp"], "tactic_count": 13}
{"name": "ContinuousLinearEquiv.nhds", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.BoundedLinearMaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompactOperator", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCompactOperator_zero", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCompactOperator_iff_exists_mem_nhds_image_subset_compact", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCompactOperator_iff_exists_mem_nhds_isCompact_closure_image", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Compact", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsCompactOperator.image_subset_compact_of_isVonNBounded", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompactOperator.isCompact_closure_image_of_isVonNBounded", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompactOperator.image_subset_compact_of_bounded", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompactOperator.isCompact_closure_image_of_bounded", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompactOperator.image_ball_subset_compact", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompactOperator.image_closedBall_subset_compact", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompactOperator.isCompact_closure_image_ball", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompactOperator.isCompact_closure_image_closedBall", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCompactOperator_iff_image_ball_subset_compact", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCompactOperator_iff_image_closedBall_subset_compact", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCompactOperator_iff_isCompact_closure_image_ball", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCompactOperator_iff_isCompact_closure_image_closedBall", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompactOperator.smul", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompactOperator.add", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompactOperator.neg", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompactOperator.sub", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Compact", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "compactOperator", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompactOperator.comp_clm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Compact", "is_tactic_proof": true, "tactics": ["have", "rw", "rcases", "exact"], "tactic_count": 4}
{"name": "IsCompactOperator.continuous_comp", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Compact", "is_tactic_proof": true, "tactics": ["rcases", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "IsCompactOperator.clm_comp", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompactOperator.codRestrict", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompactOperator.restrict", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompactOperator.restrict'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompactOperator.continuous", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Compact", "is_tactic_proof": true, "tactics": ["letI", "haveI", "refine", "rw", "rcases", "rcases", "rcases", "have", "suffices", "refine", "have", "rwa", "rw", "refine", "rw", "exact"], "tactic_count": 16}
{"name": "ContinuousLinearMap.mkOfIsCompactOperator", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.mkOfIsCompactOperator_to_linearMap", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.coe_mkOfIsCompactOperator", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.mkOfIsCompactOperator_mem_compactOperator", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosed_setOf_isCompactOperator", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Compact", "is_tactic_proof": true, "tactics": ["refine", "rintro", "rw", "suffices", "change", "rw", "exact", "rw", "intro", "rcases", "let", "rcases", "hu", "rcases", "totallyBounded_iff_subset_finite_iUnion_nhds_zero.mp", "hV", "have", "refine", "rw", "intro", "specialize", "rw", "rcases", "refine", "rw", "convert", "rw", "abel"], "tactic_count": 28}
{"name": "compactOperator_topologicalClosure", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCompactOperator_of_tendsto", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparatingDual.completeSpace_of_completeSpace_continuousLinearMap", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.CompleteCodomain", "is_tactic_proof": true, "tactics": ["refine", "obtain", "obtain", "let", "have", "obtain", "refine", "have", "have", "exact", "simpa"], "tactic_count": 11}
{"name": "SeparatingDual.completeSpace_continuousLinearMap_iff", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.CompleteCodomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparatingDual.completeSpace_of_completeSpace_continuousMultilinearMap", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.CompleteCodomain", "is_tactic_proof": true, "tactics": ["refine", "have", "choose", "cases", "let", "compContinuousLinearMapL", "have", "refine", "exact", "obtain", "refine", "have", "simpa"], "tactic_count": 13}
{"name": "SeparatingDual.completeSpace_continuousMultilinearMap_iff", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.CompleteCodomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.tendsto_of_tendsto_pointwise_of_cauchySeq", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Completeness", "is_tactic_proof": true, "tactics": ["rcases", "suffices", "tendsto_iff_norm_sub_tendsto_zero.2", "intro", "have", "refine", "le_of_tendsto", "exact"], "tactic_count": 8}
{"name": "ContinuousLinearMap.isCompact_closure_image_coe_of_bounded", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Completeness", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.isCompact_image_coe_of_bounded_of_closed_image", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Completeness", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.isClosed_image_coe_of_bounded_of_weak_closed", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Completeness", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.isCompact_image_coe_of_bounded_of_weak_closed", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Completeness", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.is_weak_closed_closedBall", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Completeness", "is_tactic_proof": true, "tactics": ["have", "refine", "have", "isClosed_Iic.preimage", "refine", "exact"], "tactic_count": 6}
{"name": "ContinuousLinearMap.isClosed_image_coe_closedBall", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Completeness", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.isCompact_image_coe_closedBall", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Completeness", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsConformalMap", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.Conformal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isConformalMap_id", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Conformal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsConformalMap.smul", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Conformal", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "isConformalMap_const_smul", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Conformal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.isConformalMap", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Conformal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isConformalMap_of_subsingleton", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Conformal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsConformalMap.comp", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Conformal", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "refine", "rw", "rfl"], "tactic_count": 5}
{"name": "IsConformalMap.injective", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Conformal", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "IsConformalMap.ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Conformal", "is_tactic_proof": true, "tactics": ["rintro", "rcases", "exact"], "tactic_count": 3}
{"name": "ContinuousAlgEquiv.eq_continuousLinearEquivConjContinuousAlgEquiv", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.ContinuousAlgEquiv", "is_tactic_proof": true, "tactics": ["given", "a", "by_cases", "by_cases", "exact", "simpa", "simp_rw", "eq_comp_toContinuousLinearMap_symm]", "obtain", "obtain", "obtain", "simp_rw", "smulRight_apply,", "exact", "set", "have", "have", "simp", "congr", "have", "have", "have", "have", "apply", "obtain", "simp", "simpa", "set", "set", "set", "continuous_toFun", "continuous_invFun", "change", "suffices", "simp", "exact"], "tactic_count": 36}
{"name": "auxContinuousLinearEquiv", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Operator.ContinuousAlgEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "coe_auxContinuousLinearEquiv", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.ContinuousAlgEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "auxIsometry", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Operator.ContinuousAlgEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "coe_auxIsometry", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.ContinuousAlgEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "coe_symm_auxIsometry", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.ContinuousAlgEquiv", "is_tactic_proof": true, "tactics": ["ext", "apply", "simp"], "tactic_count": 3}
{"name": "StarAlgEquiv.eq_linearIsometryEquivConjStarAlgEquiv", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.ContinuousAlgEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instOrderIsoClassContinuousLinearMapIdOfNonUnitalAlgEquivClassOfStarHomClassOfContinuousMapClass", "kind": "instance", "module": "Mathlib.Analysis.Normed.Operator.ContinuousAlgEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.mkContinuous", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.ContinuousLinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.mkContinuousOfExistsBound", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.ContinuousLinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_of_linear_of_boundₛₗ", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.ContinuousLinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_of_linear_of_bound", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.ContinuousLinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.mkContinuous_coe", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.ContinuousLinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.mkContinuous_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.ContinuousLinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.mkContinuousOfExistsBound_coe", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.ContinuousLinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.mkContinuousOfExistsBound_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.ContinuousLinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.antilipschitz_of_bound", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.ContinuousLinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.bound_of_antilipschitz", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.ContinuousLinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.toContinuousLinearEquivOfBounds", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.ContinuousLinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.toContinuousLinearMap₁", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.ContinuousLinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.toContinuousLinearMap₁_coe", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.ContinuousLinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.toContinuousLinearMap₁_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.ContinuousLinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.isUniformEmbedding_of_bound", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.ContinuousLinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.ofHomothety", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.ContinuousLinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.homothety_inverse", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.ContinuousLinearMap", "is_tactic_proof": true, "tactics": ["intro", "calc"], "tactic_count": 2}
{"name": "ContinuousLinearEquiv.ofHomothety", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.ContinuousLinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.extend_eq", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Extend", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "ContinuousLinearMap.extend_unique", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Extend", "is_tactic_proof": true, "tactics": ["simp", "exact", "uniformly_extend_unique"], "tactic_count": 3}
{"name": "ContinuousLinearMap.extend_zero", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.opNorm_extend_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Extend", "is_tactic_proof": true, "tactics": ["refine", "cases", "inl", "inr", "hN", "have", "obtain", "simp", "exact", "rw", "calc"], "tactic_count": 11}
{"name": "LinearMap.compLeftInverse_apply_of_bdd", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Extend", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LinearMap.extendOfNorm_eq", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Extend", "is_tactic_proof": false, "tactics": ["have", "isUniformEmbedding_subtype_val.isUniformInducing", "convert", "exact"], "tactic_count": 4}
{"name": "LinearMap.norm_extendOfNorm_apply_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Extend", "is_tactic_proof": false, "tactics": ["have", "intro", "simpa", "exact"], "tactic_count": 4}
{"name": "LinearMap.extendOfNorm_unique", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Extend", "is_tactic_proof": true, "tactics": ["apply", "simpa", "exact", "ext", "rw", "simp"], "tactic_count": 6}
{"name": "LinearMap.opNorm_extendOfNorm_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.extend_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.extend_symm_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.extend_eq", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.extend_symm_eq", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.norm_extend_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.norm_extend_symm_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.extendOfIsometry_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.extendOfIsometry_symm_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.extendOfIsometry_eq", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.extendOfIsometry_symm_eq", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "term_→ₛₗᵢ[_]_", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Analysis_Normed_Operator_LinearIsometry___macroRules_term_→ₛₗᵢ[_]__1", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Analysis_Normed_Operator_LinearIsometry___unexpand_LinearIsometry_1", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "term_→ₗᵢ[_]_", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Analysis_Normed_Operator_LinearIsometry___macroRules_term_→ₗᵢ[_]__1", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Analysis_Normed_Operator_LinearIsometry___unexpand_LinearIsometry_2", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "term_→ₗᵢ⋆[_]_", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Analysis_Normed_Operator_LinearIsometry___macroRules_term_→ₗᵢ⋆[_]__1", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Analysis_Normed_Operator_LinearIsometry___unexpand_LinearIsometry_3", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryClass", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemilinearIsometryClass.isometry", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemilinearIsometryClass.continuous", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemilinearIsometryClass.nnnorm_map", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemilinearIsometryClass.lipschitz", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemilinearIsometryClass.antilipschitz", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemilinearIsometryClass.ediam_image", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemilinearIsometryClass.ediam_range", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemilinearIsometryClass.diam_image", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemilinearIsometryClass.diam_range", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemilinearIsometryClass.toContinuousSemilinearMapClass", "kind": "instance", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.toLinearMap_injective", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.toLinearMap_inj", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.instFunLike", "kind": "instance", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.instSemilinearIsometryClass", "kind": "instance", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.coe_toLinearMap", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.coe_mk", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.coe_injective", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": true, "tactics": ["rintro", "simp"], "tactic_count": 2}
{"name": "LinearIsometry.Simps.apply", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.ext", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.map_zero", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.map_add", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.map_neg", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.map_sub", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.map_smulₛₗ", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.map_smul", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.norm_map", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.nnnorm_map", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.enorm_map", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LinearIsometry.isometry", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.isEmbedding", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.isComplete_image_iff", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.isComplete_image_iff'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.isComplete_map_iff", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.completeSpace_map", "kind": "instance", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.dist_map", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.edist_map", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.injective", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.map_eq_iff", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.map_ne", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.lipschitz", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.antilipschitz", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.continuous", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.preimage_ball", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.preimage_sphere", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.preimage_closedBall", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.ediam_image", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.ediam_range", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.diam_image", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.diam_range", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.toContinuousLinearMap", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.toContinuousLinearMap_injective", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.toContinuousLinearMap_inj", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.coe_toContinuousLinearMap", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.comp_continuous_iff", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.id", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.coe_id", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.id_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.id_toLinearMap", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.id_toContinuousLinearMap", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.instInhabited", "kind": "instance", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.comp", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.coe_comp", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.id_comp", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.comp_id", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.comp_assoc", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.instMonoid", "kind": "instance", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.coe_one", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.coe_mul", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.one_def", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.mul_def", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.coe_pow", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.submoduleMap", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.toLinearIsometry", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.subtypeₗᵢ", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.coe_subtypeₗᵢ", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.subtypeₗᵢ_toLinearMap", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.subtypeₗᵢ_toContinuousLinearMap", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "term_≃ₛₗᵢ[_]_", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Analysis_Normed_Operator_LinearIsometry___macroRules_term_≃ₛₗᵢ[_]__1", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Analysis_Normed_Operator_LinearIsometry___unexpand_LinearIsometryEquiv_1", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "term_≃ₗᵢ[_]_", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Analysis_Normed_Operator_LinearIsometry___macroRules_term_≃ₗᵢ[_]__1", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Analysis_Normed_Operator_LinearIsometry___unexpand_LinearIsometryEquiv_2", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "term_≃ₗᵢ⋆[_]_", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Analysis_Normed_Operator_LinearIsometry___macroRules_term_≃ₗᵢ⋆[_]__1", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Analysis_Normed_Operator_LinearIsometry___unexpand_LinearIsometryEquiv_3", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquivClass", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemilinearIsometryEquivClass.toSemilinearIsometryClass", "kind": "instance", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.toLinearEquiv_injective", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.toLinearEquiv_inj", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.instEquivLike", "kind": "instance", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.instSemilinearIsometryEquivClass", "kind": "instance", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.instCoeFun", "kind": "instance", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.coe_injective", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.coe_mk", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.coe_toLinearEquiv", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.ext", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.congr_arg", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.congr_fun", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.ofBounds", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.norm_map", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.toLinearIsometry", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.toLinearIsometry_injective", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.toLinearIsometry_inj", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.coe_toLinearIsometry", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.isometry", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.toIsometryEquiv", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.toIsometryEquiv_injective", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.toIsometryEquiv_inj", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.coe_toIsometryEquiv", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.range_eq_univ", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "LinearIsometryEquiv.toHomeomorph", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.toHomeomorph_injective", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.toHomeomorph_inj", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.coe_toHomeomorph", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.continuous", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.continuousAt", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.continuousOn", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.continuousWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.toContinuousLinearEquiv", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.toContinuousLinearEquiv_injective", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.toContinuousLinearEquiv_inj", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.coe_toContinuousLinearEquiv", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.refl", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.ulift", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.instInhabited", "kind": "instance", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.coe_refl", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.toContinuousLinearEquiv_refl", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.symm", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.apply_symm_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.symm_apply_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.map_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.symm_symm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.symm_bijective", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.toLinearEquiv_symm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.coe_symm_toLinearEquiv", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.toContinuousLinearEquiv_symm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.coe_symm_toContinuousLinearEquiv", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.toIsometryEquiv_symm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.coe_symm_toIsometryEquiv", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.toHomeomorph_symm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.coe_symm_toHomeomorph", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.Simps.apply", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.Simps.symm_apply", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.trans", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.coe_trans", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.trans_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.toLinearEquiv_trans", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.toContinuousLinearEquiv_trans", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.toIsometryEquiv_trans", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.toHomeomorph_trans", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.trans_refl", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.refl_trans", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.self_trans_symm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.symm_trans_self", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.symm_comp_self", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.self_comp_symm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.symm_trans", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.coe_symm_trans", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.trans_assoc", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.instGroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.coe_one", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.coe_mul", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.coe_inv", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.one_def", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.mul_def", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.inv_def", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.trans_one", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.one_trans", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.refl_mul", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.mul_refl", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.instCoeTCContinuousLinearEquiv", "kind": "instance", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.instCoeTCContinuousLinearMap", "kind": "instance", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.toContinuousLinearMap_toLinearIsometry", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.coe_coe", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.coe_coe''", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.map_zero", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.map_add", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.map_sub", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.map_smulₛₗ", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.map_smul", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.nnnorm_map", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.dist_map", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.edist_map", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.bijective", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.injective", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.surjective", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.map_eq_iff", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.map_ne", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.lipschitz", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.antilipschitz", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.image_eq_preimage_symm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.ediam_image", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.diam_image", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.preimage_ball", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.preimage_sphere", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.preimage_closedBall", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.image_ball", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.image_sphere", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.image_closedBall", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.comp_continuousOn_iff", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.comp_continuous_iff", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.completeSpace_map", "kind": "instance", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.ofSurjective", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.coe_ofSurjective", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "LinearIsometryEquiv.ofLinearIsometry", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.coe_ofLinearIsometry", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.coe_ofLinearIsometry_symm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.neg", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.coe_neg", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.symm_neg", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.prodComm", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.symm_prodComm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.prodAssoc", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.coe_prodAssoc", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.coe_prodAssoc_symm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.ofTop", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.ofEq", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.coe_ofEq_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.ofEq_symm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.ofEq_rfl", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.submoduleMap", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.ext_linearIsometry", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.ext_linearIsometryEquiv", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.equivRange", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.isometry_opLinearEquiv", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.opLinearIsometryEquiv", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.toLinearEquiv_opLinearIsometryEquiv", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.toContinuousLinearEquiv_opLinearIsometryEquiv", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.LinearIsometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.mul_apply'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.opNorm_mul_apply_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.opNorm_mul_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgHom.coe_Lmul", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.mulLeftRight_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.opNorm_mulLeftRight_apply_apply_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.opNorm_mulLeftRight_apply_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.opNorm_mulLeftRight_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.isometry_mul", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.opNorm_mul_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.opNNNorm_mul_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.coe_mulₗᵢ", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.flip_mul", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Mul", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "ContinuousLinearMap.lsmul_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.lsmul_flip_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.lsmul_flip_inj", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.opNorm_lsmul_apply_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.opNorm_lsmul_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Mul", "is_tactic_proof": true, "tactics": ["refine", "simp_rw", "exact"], "tactic_count": 3}
{"name": "ContinuousLinearMap.opNorm_mul", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.opNNNorm_mul", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.opNorm_lsmul", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Mul", "is_tactic_proof": true, "tactics": ["refine", "rw", "apply", "obtain", "refine", "simpa"], "tactic_count": 6}
{"name": "ContinuousLinearMap.nnnorm_def", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.NNNorm", "is_tactic_proof": true, "tactics": ["ext", "rw", "simp_rw"], "tactic_count": 3}
{"name": "ContinuousLinearMap.opNNNorm_subsingleton", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.NNNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.opNNNorm_le_bound", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.NNNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.opNNNorm_le_bound'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.NNNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.opNNNorm_le_of_unit_nnnorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.NNNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.opNNNorm_le_of_lipschitz", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.NNNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.opNNNorm_eq_of_bounds", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.NNNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.opNNNorm_le_iff", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.NNNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.isLeast_opNNNorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.NNNorm", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ContinuousLinearMap.opNNNorm_comp_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.NNNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.opENorm_comp_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.NNNorm", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ContinuousLinearMap.le_opNNNorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.NNNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.le_opENorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.NNNorm", "is_tactic_proof": true, "tactics": ["dsimp"], "tactic_count": 1}
{"name": "ContinuousLinearMap.nndist_le_opNNNorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.NNNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.lipschitz", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.NNNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.lipschitz_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.NNNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.exists_mul_lt_apply_of_lt_opNNNorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.NNNorm", "is_tactic_proof": true, "tactics": ["simpa", "notMem_of_lt_csInf"], "tactic_count": 2}
{"name": "ContinuousLinearMap.exists_mul_lt_of_lt_opNorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.NNNorm", "is_tactic_proof": true, "tactics": ["lift", "exact"], "tactic_count": 2}
{"name": "ContinuousLinearEquiv.lipschitz", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.NNNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.exists_lt_apply_of_lt_opNNNorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.NNNorm", "is_tactic_proof": true, "tactics": ["obtain", "have", "have", "rw", "obtain", "refine", "rwa"], "tactic_count": 7}
{"name": "ContinuousLinearMap.exists_lt_apply_of_lt_opNorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.NNNorm", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "lift", "exact"], "tactic_count": 4}
{"name": "ContinuousLinearMap.sSup_unit_ball_eq_nnnorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.NNNorm", "is_tactic_proof": false, "tactics": ["refine", "rintro", "simpa", "obtain", "exact"], "tactic_count": 5}
{"name": "ContinuousLinearMap.sSup_unit_ball_eq_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.NNNorm", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ContinuousLinearMap.sSup_unitClosedBall_eq_nnnorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.NNNorm", "is_tactic_proof": false, "tactics": ["have", "rintro", "exact", "refine", "rw", "gcongr", "exacts"], "tactic_count": 7}
{"name": "ContinuousLinearMap.sSup_unitClosedBall_eq_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.NNNorm", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ContinuousLinearMap.exists_nnnorm_eq_one_lt_apply_of_lt_opNNNorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.NNNorm", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "simp", "use", "suffices", "calc", "r"], "tactic_count": 7}
{"name": "ContinuousLinearMap.sSup_sphere_eq_nnnorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.NNNorm", "is_tactic_proof": true, "tactics": ["cases", "simp", "have", "refine", "csSup_eq_of_forall_le_of_forall_lt_exists_gt", "rintro", "simpa", "obtain", "exact"], "tactic_count": 9}
{"name": "ContinuousLinearMap.sSup_sphere_eq_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.NNNorm", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "LinearMap.bound_of_shell", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.NormedSpace", "is_tactic_proof": true, "tactics": ["by_cases", "exact"], "tactic_count": 2}
{"name": "LinearMap.bound_of_ball_bound", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.NormedSpace", "is_tactic_proof": true, "tactics": ["obtain", "use", "intro", "refine", "calc", "exact", "rw", "exact"], "tactic_count": 8}
{"name": "LinearMap.antilipschitz_of_comap_nhds_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.NormedSpace", "is_tactic_proof": true, "tactics": ["rcases", "simp", "lift", "rcases", "refine", "by_cases", "rw", "obtain", "exact", "have", "rw", "rcases", "simp", "calc"], "tactic_count": 14}
{"name": "ContinuousLinearMap.opNorm_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.antilipschitz_of_isEmbedding", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.norm_toContinuousLinearMap", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.nnnorm_toContinuousLinearMap", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.enorm_toContinuousLinearMap", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.norm_toContinuousLinearMap_comp", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.opNorm_comp_linearIsometryEquiv", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.NormedSpace", "is_tactic_proof": true, "tactics": ["cases", "haveI", "simp", "refine", "convert", "simp", "convert", "ext", "simp", "haveI", "simp"], "tactic_count": 11}
{"name": "ContinuousLinearMap.norm_smulRightL", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.norm_smulRightL_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.norm_subtypeL", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.antilipschitz", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.one_le_norm_mul_norm_symm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.NormedSpace", "is_tactic_proof": true, "tactics": ["rw", "convert", "rw"], "tactic_count": 3}
{"name": "ContinuousLinearEquiv.norm_pos", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.norm_symm_pos", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.nnnorm_symm_pos", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.subsingleton_or_norm_symm_pos", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.NormedSpace", "is_tactic_proof": true, "tactics": ["rcases", "left", "infer_instance", "right", "exact"], "tactic_count": 5}
{"name": "ContinuousLinearEquiv.subsingleton_or_nnnorm_symm_pos", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.coord_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.NormedSpace", "is_tactic_proof": true, "tactics": ["have", "haveI", "exact", "homothety_inverse"], "tactic_count": 4}
{"name": "NormedSpace.equicontinuous_TFAE", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.NormedSpace", "is_tactic_proof": true, "tactics": ["tfae_have", "tfae_have", "tfae_have", "tfae_have", "rw", "exact", "tfae_have", "refine", "rw", "tfae_have", "tfae_have", "tfae_have", "rw", "rfl", "tfae_have", "refine", "rw", "constructor", "intro", "rcases", "exact", "intro", "refine", "exact", "tfae_finish"], "tactic_count": 25}
{"name": "LinearIsometry.single", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.norm_single_le_one", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.norm_single", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.inl", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.inl_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.inr", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.inr_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.norm_inl_le_one", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.norm_inr_le_one", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.norm_inl", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.norm_inr", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.norm_fst_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.norm_snd_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.opNorm_prod", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.opNNNorm_prod", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.prodₗᵢ", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.prodMapL", "kind": "definition", "module": "Mathlib.Analysis.Normed.Operator.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.prodMapL_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.prod_mapL", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.prod_map_equivL", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.prod_mapL", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.prod_map_equivL", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.norm_fst", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Prod", "is_tactic_proof": true, "tactics": ["refine", "let", "have", "rw", "rwa"], "tactic_count": 5}
{"name": "ContinuousLinearMap.norm_snd", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Operator.Prod", "is_tactic_proof": true, "tactics": ["refine", "let", "have", "rw", "rwa"], "tactic_count": 5}
{"name": "GroupSeminormClass.toSeminormedGroup", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupSeminormClass.toSeminormedGroup_norm_eq", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupSeminormClass.toSeminormedCommGroup", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupSeminormClass.toSeminormedCommGroup_norm_eq", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupNormClass.toNormedGroup", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupNormClass.toNormedGroup_norm_eq", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupNormClass.toNormedCommGroup", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupNormClass.toNormedCommGroup_norm_eq", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "norm_le_norm_of_abs_le_abs", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LatticeOrderedAddCommGroup.isSolid_ball", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instHasSolidNormReal", "kind": "instance", "module": "Mathlib.Analysis.Normed.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instHasSolidNormRat", "kind": "instance", "module": "Mathlib.Analysis.Normed.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.hasSolidNorm", "kind": "instance", "module": "Mathlib.Analysis.Normed.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dual_solid", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Order.Lattice", "is_tactic_proof": true, "tactics": ["apply", "rw", "nth_rw", "rw", "rw", "nth_rw", "rwa"], "tactic_count": 7}
{"name": "OrderDual.instHasSolidNorm", "kind": "instance", "module": "Mathlib.Analysis.Normed.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "norm_abs_eq_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "norm_inf_sub_inf_le_add_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Order.Lattice", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "calc", "a", "gcongr", "exact", "rw", "exact"], "tactic_count": 9}
{"name": "norm_sup_sub_sup_le_add_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Order.Lattice", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "calc", "a", "gcongr", "exact", "rw", "exact"], "tactic_count": 9}
{"name": "norm_inf_le_add", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Order.Lattice", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "norm_sup_le_add", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Order.Lattice", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "HasSolidNorm.continuousInf", "kind": "instance", "module": "Mathlib.Analysis.Normed.Order.Lattice", "is_tactic_proof": true, "tactics": ["refine", "have", "norm_inf_sub_inf_le_add_norm", "refine", "convert", "simp"], "tactic_count": 6}
{"name": "HasSolidNorm.continuousSup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasSolidNorm.toTopologicalLattice", "kind": "instance", "module": "Mathlib.Analysis.Normed.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "norm_abs_sub_abs", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "norm_sup_sub_sup_le_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "norm_inf_sub_inf_le_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lipschitzWith_sup_right", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lipschitzWith_posPart", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lipschitzWith_negPart", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Order.Lattice", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "continuous_posPart", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_negPart", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosed_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Order.Lattice", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "isClosed_le_of_isClosed_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Order.Lattice", "is_tactic_proof": false, "tactics": ["have", "simp", "rw", "exact"], "tactic_count": 4}
{"name": "HasSolidNorm.orderClosedTopology", "kind": "instance", "module": "Mathlib.Analysis.Normed.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUpperSet.thickening'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Order.UpperLower", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsLowerSet.thickening'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Order.UpperLower", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsUpperSet.cthickening'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Order.UpperLower", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsLowerSet.cthickening'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Order.UpperLower", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "upperClosure_interior_subset'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Order.UpperLower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lowerClosure_interior_subset'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Order.UpperLower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUpperSet.mem_interior_of_forall_lt", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Order.UpperLower", "is_tactic_proof": true, "tactics": ["cases", "obtain", "obtain", "rw", "have", "refine", "rw", "exact", "obtain", "refine", "rintro", "refine", "simp_rw", "exact"], "tactic_count": 14}
{"name": "IsLowerSet.mem_interior_of_forall_lt", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Order.UpperLower", "is_tactic_proof": true, "tactics": ["cases", "obtain", "obtain", "rw", "have", "refine", "rw", "exact", "obtain", "refine", "rintro", "refine", "simp_rw", "exact"], "tactic_count": 14}
{"name": "dist_inf_sup_pi", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Order.UpperLower", "is_tactic_proof": true, "tactics": ["refine", "simp"], "tactic_count": 2}
{"name": "dist_mono_left_pi", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Order.UpperLower", "is_tactic_proof": true, "tactics": ["refine", "rw", "grw"], "tactic_count": 3}
{"name": "dist_mono_right_pi", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Order.UpperLower", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "dist_anti_left_pi", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Order.UpperLower", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "dist_anti_right_pi", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Order.UpperLower", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "dist_le_dist_of_le_pi", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Order.UpperLower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUpperSet.exists_subset_ball", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Order.UpperLower", "is_tactic_proof": true, "tactics": ["refine", "grw", "apply", "simp", "ring", "obtain", "refine", "rw", "rw", "replace", "replace", "dsimp", "rw", "linarith"], "tactic_count": 14}
{"name": "IsLowerSet.exists_subset_ball", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Order.UpperLower", "is_tactic_proof": true, "tactics": ["refine", "grw", "apply", "simp", "ring", "obtain", "refine", "rw", "rw", "replace", "replace", "dsimp", "rw", "linarith"], "tactic_count": 14}
{"name": "IsClosed.upperClosure_pi", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Order.UpperLower", "is_tactic_proof": true, "tactics": ["cases", "refine", "choose", "obtain", "obtain", "tendsto_subseq_of_bounded", "exact"], "tactic_count": 7}
{"name": "IsClosed.lowerClosure_pi", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Order.UpperLower", "is_tactic_proof": true, "tactics": ["cases", "refine", "choose", "haveI", "obtain", "obtain", "tendsto_subseq_of_bounded", "exact"], "tactic_count": 8}
{"name": "IsClopen.upperClosure_pi", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Order.UpperLower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClopen.lowerClosure_pi", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Order.UpperLower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "closure_upperClosure_comm_pi", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Order.UpperLower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "closure_lowerClosure_comm_pi", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Order.UpperLower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeminormedRing.toNonUnitalSeminormedRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalNormedRing.toNonUnitalSeminormedRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedRing.toSeminormedRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedRing.toNonUnitalNormedRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalNormedCommRing.toNonUnitalSeminormedCommRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeminormedCommRing.toNonUnitalSeminormedCommRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedCommRing.toNonUnitalNormedCommRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedCommRing.toSeminormedCommRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PUnit.normedCommRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nnnorm_one", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "enorm_one", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NormOneClass.nontrivial", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalNormedRing.toNormedAddCommGroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSeminormedRing.toSeminormedAddCommGroup", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.normOneClass", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.normOneClass", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.normOneClass", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.normOneClass", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "norm_mul_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nnnorm_mul_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "norm_mul_le_of_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nnnorm_mul_le_of_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "norm_mul₃_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nnnorm_mul₃_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_le_norm_one", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_le_nnnorm_one", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mulLeft_bound", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mulRight_bound", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.nonUnitalSeminormedRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebraClass.nonUnitalSeminormedRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.nonUnitalNormedRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebraClass.nonUnitalNormedRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.nonUnitalSeminormedRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.nonUnitalSeminormedRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instNonUnitalSeminormedRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.seminormedRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubalgebraClass.seminormedRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.normedRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubalgebraClass.normedRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.norm_cast_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.norm_prod_le'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.nnnorm_prod_le'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.norm_prod_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.nnnorm_prod_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.norm_prod_le'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": true, "tactics": ["rcases", "have", "simpa"], "tactic_count": 3}
{"name": "Finset.nnnorm_prod_le'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.norm_prod_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simpa"], "tactic_count": 2}
{"name": "Finset.nnnorm_prod_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "norm_natAbs", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": true, "tactics": ["rcases", "rw", "rw"], "tactic_count": 3}
{"name": "nnnorm_natAbs", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "norm_intCast_abs", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "nnnorm_intCast_abs", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "nnnorm_pow_le'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nnnorm_pow_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "norm_pow_le'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "norm_pow_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eventually_norm_pow_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.seminormedRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.seminormedRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instSeminormedRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "norm_sub_mul_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "norm_sub_mul_le'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "nnnorm_sub_mul_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nnnorm_sub_mul_le'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "norm_commutator_units_sub_one_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nnnorm_commutator_units_sub_one_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "RingHom.IsBounded", "kind": "definition", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.nonUnitalNormedRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.nonUnitalNormedRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instNonUnitalNormedRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.norm_pos", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.nnnorm_pos", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.normedRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.normedRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instNormedRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.nonUnitalSeminormedCommRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.nonUnitalSeminormedCommRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instNonUnitalSeminormedCommRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.nonUnitalSeminormedCommRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.nonUnitalNormedCommRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.nonUnitalNormedCommRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.nonUnitalNormedCommRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instNonUnitalNormedCommRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.seminormedCommRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.seminormedCommRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instSeminormedCommRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.seminormedCommRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.normedCommRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.normedCommRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.normedCommRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instNormedCommRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPowMul.restriction", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.normedCommRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.norm_eq", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NNReal.nnnorm_eq", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "NNReal.enorm_eq", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NormedAddCommGroup.tendsto_atTop", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedAddCommGroup.tendsto_atTop'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHomIsometric.nnnorm_map", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHomIsometric.enorm_map", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHomIsometric.ids", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "norm_mul", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nnnorm_mul", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "enorm_mul", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "normHom", "kind": "definition", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nnnormHom", "kind": "definition", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "norm_pow", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nnnorm_pow", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "enorm_pow", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.norm_prod", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.nnnorm_prod", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "norm_prod", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nnnorm_prod", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormMulClass.toNormOneClass", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormMulClass.isAbsoluteValue_norm", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormMulClass.toNoZeroDivisors", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSeminormedRing.induced", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalNormedRing.induced", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeminormedRing.induced", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedRing.induced", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSeminormedCommRing.induced", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalNormedCommRing.induced", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeminormedCommRing.induced", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedCommRing.induced", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormOneClass.induced", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormMulClass.induced", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubringClass.toSeminormedRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubringClass.toNormedRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubringClass.toSeminormedCommRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubringClass.toNormedCommRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubringClass.toNormOneClass", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubringClass.toNormMulClass", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AbsoluteValue.toNormedRing", "kind": "definition", "module": "Mathlib.Analysis.Normed.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOfFinOrder.norm_eq_one", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_example", "kind": "example", "module": "Mathlib.Analysis.Normed.Ring.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.norm_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Summable.mul_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.InfiniteSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Summable.mul_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.InfiniteSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "summable_mul_of_summable_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.InfiniteSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "summable_mul_of_summable_norm'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.InfiniteSum", "is_tactic_proof": true, "tactics": ["classical", "suffices", "let", "apply", "rw", "have", "rw", "convert", "simp"], "tactic_count": 9}
{"name": "tsum_mul_tsum_of_summable_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.InfiniteSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tsum_mul_tsum_of_summable_norm'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.InfiniteSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "summable_norm_sum_mul_antidiagonal_of_summable_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.InfiniteSum", "is_tactic_proof": false, "tactics": ["have", "summable_sum_mul_antidiagonal_of_summable_mul", "refine", "calc"], "tactic_count": 4}
{"name": "summable_sum_mul_antidiagonal_of_summable_norm'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.InfiniteSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tsum_mul_tsum_eq_tsum_sum_antidiagonal_of_summable_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.InfiniteSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tsum_mul_tsum_eq_tsum_sum_antidiagonal_of_summable_norm'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.InfiniteSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "summable_norm_sum_mul_range_of_summable_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.InfiniteSum", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "summable_sum_mul_range_of_summable_norm'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.InfiniteSum", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "tsum_mul_tsum_eq_tsum_sum_range_of_summable_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.InfiniteSum", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "hasSum_sum_range_mul_of_summable_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.InfiniteSum", "is_tactic_proof": true, "tactics": ["convert", "exact"], "tactic_count": 2}
{"name": "tsum_mul_tsum_eq_tsum_sum_range_of_summable_norm'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.InfiniteSum", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "hasSum_sum_range_mul_of_summable_norm'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.InfiniteSum", "is_tactic_proof": true, "tactics": ["convert", "exact"], "tactic_count": 2}
{"name": "summable_of_absolute_convergence_real", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.InfiniteSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.nnnorm_coe_units", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Int", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "Int.norm_coe_units", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Int", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.nnnorm_natCast", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Int", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.enorm_natCast", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Int", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.toNat_add_toNat_neg_eq_nnnorm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Int", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.toNat_add_toNat_neg_eq_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Int", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Filter.Tendsto.zero_mul_isBoundedUnder_le", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.isBoundedUnder_le_mul_tendsto_zero", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.nonUnitalSeminormedRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.seminormedRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.isometry", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHomIsometric.inv", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_pow_cobounded_cobounded", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Lemmas", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Pi.nonUnitalNormedRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.normedRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.nonUnitalSeminormedCommRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.nonUnitalNormedCommRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.seminormedCommRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.normedCommutativeRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSeminormedRing.toContinuousMul", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSeminormedRing.toIsTopologicalRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.instNonUnitalNormedRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.instNonUnitalNormedCommRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.instNormedRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.instNormedCommRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.instNormOneClass", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.lipschitzWith_sub", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "have", "convert", "norm_num"], "tactic_count": 4}
{"name": "Int.instNormedCommRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.instNormOneClass", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.instNormMulClass", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "antilipschitzWith_mul_left", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "antilipschitzWith_mul_right", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dilation.mulLeft", "kind": "definition", "module": "Mathlib.Analysis.Normed.Ring.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dilation.mulRight", "kind": "definition", "module": "Mathlib.Analysis.Normed.Ring.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.comap_mul_left_cobounded", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.comap_mul_right_cobounded", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.seminormedRing", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Ring.TransferInstance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.normedRing", "kind": "abbrev", "module": "Mathlib.Analysis.Normed.Ring.TransferInstance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUltrametricDist.norm_add_one_le_max_norm_one", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Ultra", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsUltrametricDist.nnnorm_add_one_le_max_nnnorm_one", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Ultra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUltrametricDist.nnnorm_natCast_le_one", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Ultra", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "simpa"], "tactic_count": 4}
{"name": "IsUltrametricDist.norm_natCast_le_one", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Ultra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUltrametricDist.nnnorm_intCast_le_one", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Ultra", "is_tactic_proof": true, "tactics": ["cases", "simpa", "nnnorm_natCast_le_one"], "tactic_count": 3}
{"name": "IsUltrametricDist.norm_intCast_le_one", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Ultra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.add", "kind": "definition", "module": "Mathlib.Analysis.Normed.Ring.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.ofNearby", "kind": "definition", "module": "Mathlib.Analysis.Normed.Ring.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.isOpen", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Units", "is_tactic_proof": true, "tactics": ["nontriviality", "rw", "rintro", "refine", "rw", "exact"], "tactic_count": 6}
{"name": "Units.nhds", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nonunits.subset_compl_ball", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nonunits.isClosed", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedRing.inverse_one_sub", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Units", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NormedRing.inverse_add", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Units", "is_tactic_proof": true, "tactics": ["nontriviality", "rw", "refine", "rw", "rw"], "tactic_count": 5}
{"name": "NormedRing.inverse_one_sub_nth_order'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedRing.inverse_one_sub_nth_order", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedRing.inverse_add_nth_order", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Units", "is_tactic_proof": true, "tactics": ["have", "filter_upwards", "rw", "conv_lhs", "rw"], "tactic_count": 5}
{"name": "NormedRing.inverse_one_sub_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Units", "is_tactic_proof": true, "tactics": ["simp", "refine", "rw", "have", "simp", "change", "have", "have", "linarith"], "tactic_count": 9}
{"name": "NormedRing.inverse_add_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Units", "is_tactic_proof": true, "tactics": ["refine", "simp", "have", "exact"], "tactic_count": 4}
{"name": "NormedRing.inverse_add_norm_diff_nth_order", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Units", "is_tactic_proof": true, "tactics": ["refine", "simp", "refine", "simp", "exact"], "tactic_count": 5}
{"name": "NormedRing.inverse_add_norm_diff_first_order", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Units", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "NormedRing.inverse_add_norm_diff_second_order", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Units", "is_tactic_proof": true, "tactics": ["convert", "simp", "sub_neg_eq_add]"], "tactic_count": 3}
{"name": "NormedRing.inverse_continuousAt", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Units", "is_tactic_proof": false, "tactics": ["have", "have", "refine", "exact", "rw", "simpa"], "tactic_count": 6}
{"name": "Units.isOpenEmbedding_val", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.isOpenMap_val", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.eq_top_of_norm_lt_one", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.closure_ne_top", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Units", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "Ideal.IsMaximal.closure_eq", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.IsMaximal.isClosed", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithAbs", "kind": "definition", "module": "Mathlib.Analysis.Normed.Ring.WithAbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithAbs.instNontrivial", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.WithAbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithAbs.instUnique", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.WithAbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithAbs.instSemiring", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.WithAbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithAbs.instInhabited", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.WithAbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithAbs.equiv", "kind": "definition", "module": "Mathlib.Analysis.Normed.Ring.WithAbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithAbs.equivWithAbs", "kind": "definition", "module": "Mathlib.Analysis.Normed.Ring.WithAbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithAbs.equivWithAbs_symm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.WithAbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithAbs.equiv_equivWithAbs_symm_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.WithAbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithAbs.equivWithAbs_equiv_symm_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.WithAbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithAbs.equivWithAbs_symm_equiv_symm_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.WithAbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithAbs.instCommSemiring", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.WithAbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithAbs.instRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.WithAbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithAbs.instCommRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.WithAbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithAbs.normedRing", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.WithAbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithAbs.norm_eq_abv", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.WithAbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithAbs.instModule_left", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.WithAbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithAbs.instModule_right", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.WithAbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithAbs.instAlgebra_left", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.WithAbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithAbs.algebraMap_left_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.WithAbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithAbs.instAlgebra_right", "kind": "instance", "module": "Mathlib.Analysis.Normed.Ring.WithAbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithAbs.algebraMap_right_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.WithAbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithAbs.equiv_algebraMap_apply", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.WithAbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithAbs.algEquiv", "kind": "definition", "module": "Mathlib.Analysis.Normed.Ring.WithAbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AbsoluteValue.LiesOver.comp_eq", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Ring.WithAbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInhabitedAlgebraNorm", "kind": "instance", "module": "Mathlib.Analysis.Normed.Unbundled.AlgebraNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraNorm.toRingSeminorm'", "kind": "definition", "module": "Mathlib.Analysis.Normed.Unbundled.AlgebraNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraNorm.instFunLikeReal", "kind": "instance", "module": "Mathlib.Analysis.Normed.Unbundled.AlgebraNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraNorm.algebraNormClass", "kind": "instance", "module": "Mathlib.Analysis.Normed.Unbundled.AlgebraNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraNorm.toFun_eq_coe", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Unbundled.AlgebraNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraNorm.ext", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Unbundled.AlgebraNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraNorm.extends_norm'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Unbundled.AlgebraNorm", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgebraNorm.extends_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Unbundled.AlgebraNorm", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgebraNorm.restriction", "kind": "definition", "module": "Mathlib.Analysis.Normed.Unbundled.AlgebraNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraNorm.isScalarTower_restriction", "kind": "definition", "module": "Mathlib.Analysis.Normed.Unbundled.AlgebraNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInhabitedMulAlgebraNorm", "kind": "instance", "module": "Mathlib.Analysis.Normed.Unbundled.AlgebraNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAlgebraNorm.instFunLikeReal", "kind": "instance", "module": "Mathlib.Analysis.Normed.Unbundled.AlgebraNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAlgebraNorm.mulAlgebraNormClass", "kind": "instance", "module": "Mathlib.Analysis.Normed.Unbundled.AlgebraNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAlgebraNorm.toFun_eq_coe", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Unbundled.AlgebraNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAlgebraNorm.ext", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Unbundled.AlgebraNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAlgebraNorm.extends_norm'", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Unbundled.AlgebraNorm", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MulAlgebraNorm.extends_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Unbundled.AlgebraNorm", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MulRingNorm.toRingNorm", "kind": "definition", "module": "Mathlib.Analysis.Normed.Unbundled.AlgebraNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulRingNorm.isPowMul", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Unbundled.AlgebraNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.norm", "kind": "definition", "module": "Mathlib.Analysis.Normed.Unbundled.FiniteExtension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.norm_repr_le_norm", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Unbundled.FiniteExtension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.norm_zero", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Unbundled.FiniteExtension", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Module.Basis.norm_neg", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Unbundled.FiniteExtension", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Module.Basis.norm_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Unbundled.FiniteExtension", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Module.Basis.norm_extends", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Unbundled.FiniteExtension", "is_tactic_proof": true, "tactics": ["classical", "simp", "apply", "aesop", "exact"], "tactic_count": 5}
{"name": "Module.Basis.norm_isNonarchimedean", "kind": "theorem", "module": "Mathlib.Analysis.Normed.Unbundled.FiniteExtension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Polynomial.mahlerMeasure", "kind": "definition", "module": "Mathlib.Analysis.Polynomial.MahlerMeasure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.mahlerMeasure_def_of_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.Polynomial.MahlerMeasure", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.logMahlerMeasure_eq_log_MahlerMeasure", "kind": "theorem", "module": "Mathlib.Analysis.Polynomial.MahlerMeasure", "is_tactic_proof": true, "tactics": ["rw", "split_ifs"], "tactic_count": 2}
{"name": "Polynomial.mahlerMeasure_zero", "kind": "theorem", "module": "Mathlib.Analysis.Polynomial.MahlerMeasure", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.mahlerMeasure_one", "kind": "theorem", "module": "Mathlib.Analysis.Polynomial.MahlerMeasure", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.mahlerMeasure_const", "kind": "theorem", "module": "Mathlib.Analysis.Polynomial.MahlerMeasure", "is_tactic_proof": true, "tactics": ["simp", "split_ifs", "simp", "simp"], "tactic_count": 4}
{"name": "Polynomial.mahlerMeasure_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Polynomial.MahlerMeasure", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "Polynomial.mahlerMeasure_pos_of_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.Polynomial.MahlerMeasure", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Polynomial.mahlerMeasure_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.Polynomial.MahlerMeasure", "is_tactic_proof": true, "tactics": ["refine", "contrapose", "exact"], "tactic_count": 3}
{"name": "Polynomial.intervalIntegrable_mahlerMeasure", "kind": "theorem", "module": "Mathlib.Analysis.Polynomial.MahlerMeasure", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Polynomial.mahlerMeasure_mul", "kind": "theorem", "module": "Mathlib.Analysis.Polynomial.MahlerMeasure", "is_tactic_proof": true, "tactics": ["by_cases", "simpa", "rw", "simp", "rw", "congr", "rw", "apply", "rw", "apply", "simp", "apply", "apply", "rintro", "contrapose", "simp_all"], "tactic_count": 16}
{"name": "Polynomial.prod_mahlerMeasure_eq_mahlerMeasure_prod", "kind": "theorem", "module": "Mathlib.Analysis.Polynomial.MahlerMeasure", "is_tactic_proof": true, "tactics": ["induction", "empty", "cons"], "tactic_count": 3}
{"name": "Polynomial.logMahlerMeasure_mul_eq_add_logMahlerMeasure", "kind": "theorem", "module": "Mathlib.Analysis.Polynomial.MahlerMeasure", "is_tactic_proof": true, "tactics": ["simp_all"], "tactic_count": 1}
{"name": "Polynomial.logMahlerMeasure_C_mul", "kind": "theorem", "module": "Mathlib.Analysis.Polynomial.MahlerMeasure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.logMahlerMeasure_X_sub_C", "kind": "theorem", "module": "Mathlib.Analysis.Polynomial.MahlerMeasure", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.logMahlerMeasure_X_add_C", "kind": "theorem", "module": "Mathlib.Analysis.Polynomial.MahlerMeasure", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.logMahlerMeasure_C_mul_X_add_C", "kind": "theorem", "module": "Mathlib.Analysis.Polynomial.MahlerMeasure", "is_tactic_proof": true, "tactics": ["rw", "logMahlerMeasure_C_mul"], "tactic_count": 2}
{"name": "Polynomial.logMahlerMeasure_of_degree_eq_one", "kind": "theorem", "module": "Mathlib.Analysis.Polynomial.MahlerMeasure", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Polynomial.mahlerMeasure_X_sub_C", "kind": "theorem", "module": "Mathlib.Analysis.Polynomial.MahlerMeasure", "is_tactic_proof": true, "tactics": ["have", "rw", "apply_fun", "rwa", "exp_log"], "tactic_count": 5}
{"name": "Polynomial.mahlerMeasure_X_add_C", "kind": "theorem", "module": "Mathlib.Analysis.Polynomial.MahlerMeasure", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.mahlerMeasure_C_mul_X_add_C", "kind": "theorem", "module": "Mathlib.Analysis.Polynomial.MahlerMeasure", "is_tactic_proof": false, "tactics": ["simp", "mahlerMeasure_const,", "norm_cast", "simp"], "tactic_count": 4}
{"name": "Polynomial.mahlerMeasure_of_degree_eq_one", "kind": "theorem", "module": "Mathlib.Analysis.Polynomial.MahlerMeasure", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Polynomial.logMahlerMeasure_eq_log_leadingCoeff_add_sum_log_roots", "kind": "theorem", "module": "Mathlib.Analysis.Polynomial.MahlerMeasure", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "have", "nth_rw", "rw", "simp", "log_multiset_prod"], "tactic_count": 7}
{"name": "Polynomial.mahlerMeasure_eq_leadingCoeff_mul_prod_roots", "kind": "theorem", "module": "Mathlib.Analysis.Polynomial.MahlerMeasure", "is_tactic_proof": true, "tactics": ["by_cases", "have", "rw", "apply_fun", "rw", "exp_log", "simp"], "tactic_count": 7}
{"name": "Polynomial.one_le_prod_max_one_norm_roots", "kind": "theorem", "module": "Mathlib.Analysis.Polynomial.MahlerMeasure", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Polynomial.leading_coeff_le_mahlerMeasure", "kind": "theorem", "module": "Mathlib.Analysis.Polynomial.MahlerMeasure", "is_tactic_proof": true, "tactics": ["rw", "gcongr", "exact"], "tactic_count": 3}
{"name": "Polynomial.prod_max_one_norm_roots_le_mahlerMeasure_of_one_le_leadingCoeff", "kind": "theorem", "module": "Mathlib.Analysis.Polynomial.MahlerMeasure", "is_tactic_proof": true, "tactics": ["rw", "gcongr", "exact"], "tactic_count": 3}
{"name": "Polynomial.mahlerMeasure_le_sum_norm_coeff", "kind": "theorem", "module": "Mathlib.Analysis.Polynomial.MahlerMeasure", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "have", "rw", "simp", "mahlerMeasure_def_of_ne_zero", "gcongr", "apply", "rw", "use", "constructor", "rw", "apply", "simp", "rw", "apply", "injOn_circleMap_of_abs_sub_le", "simp", "intro", "gcongr", "rw", "apply", "simp"], "tactic_count": 23}
{"name": "Polynomial.norm_coeff_le_choose_mul_mahlerMeasure", "kind": "theorem", "module": "Mathlib.Analysis.Polynomial.MahlerMeasure", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "rcases", "simp", "rw", "coeff_eq_esymm_roots_of_card", "norm_pow,", "esymm,", "apply", "simp_rw", "let", "have", "rw", "calc", "gcongr", "exact", "simp_rw", "norm_cast", "exact", "gcongr", "exact", "exact", "hx.1", "calc", "gcongr", "rw", "simp_rw", "exact", "rw", "congr", "norm_cast", "simp", "congr", "exact"], "tactic_count": 34}
{"name": "Quaternion.termℍ", "kind": "definition", "module": "Mathlib.Analysis.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion._aux_Mathlib_Analysis_Quaternion___macroRules_Quaternion_termℍ_1", "kind": "definition", "module": "Mathlib.Analysis.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion._aux_Mathlib_Analysis_Quaternion___unexpand_Quaternion_1", "kind": "definition", "module": "Mathlib.Analysis.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.instInnerReal", "kind": "instance", "module": "Mathlib.Analysis.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.inner_self", "kind": "theorem", "module": "Mathlib.Analysis.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.inner_def", "kind": "theorem", "module": "Mathlib.Analysis.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.instNormedAddCommGroupReal", "kind": "instance", "module": "Mathlib.Analysis.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.instInnerProductSpaceReal", "kind": "instance", "module": "Mathlib.Analysis.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.normSq_eq_norm_mul_self", "kind": "theorem", "module": "Mathlib.Analysis.Quaternion", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Quaternion.instNormOneClassReal", "kind": "instance", "module": "Mathlib.Analysis.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.norm_coe", "kind": "theorem", "module": "Mathlib.Analysis.Quaternion", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Quaternion.nnnorm_coe", "kind": "theorem", "module": "Mathlib.Analysis.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.norm_star", "kind": "theorem", "module": "Mathlib.Analysis.Quaternion", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Quaternion.nnnorm_star", "kind": "theorem", "module": "Mathlib.Analysis.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.instNormedDivisionRingReal", "kind": "instance", "module": "Mathlib.Analysis.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.instNormedAlgebraReal", "kind": "instance", "module": "Mathlib.Analysis.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.instCStarRingReal", "kind": "instance", "module": "Mathlib.Analysis.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.coeComplex", "kind": "definition", "module": "Mathlib.Analysis.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.instCoeComplexReal", "kind": "instance", "module": "Mathlib.Analysis.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.re_coeComplex", "kind": "theorem", "module": "Mathlib.Analysis.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.imI_coeComplex", "kind": "theorem", "module": "Mathlib.Analysis.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.imJ_coeComplex", "kind": "theorem", "module": "Mathlib.Analysis.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.imK_coeComplex", "kind": "theorem", "module": "Mathlib.Analysis.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.coeComplex_add", "kind": "theorem", "module": "Mathlib.Analysis.Quaternion", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Quaternion.coeComplex_mul", "kind": "theorem", "module": "Mathlib.Analysis.Quaternion", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Quaternion.coeComplex_zero", "kind": "theorem", "module": "Mathlib.Analysis.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.coeComplex_one", "kind": "theorem", "module": "Mathlib.Analysis.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.coe_real_complex_mul", "kind": "theorem", "module": "Mathlib.Analysis.Quaternion", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Quaternion.coeComplex_coe", "kind": "theorem", "module": "Mathlib.Analysis.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.ofComplex", "kind": "definition", "module": "Mathlib.Analysis.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.coe_ofComplex", "kind": "theorem", "module": "Mathlib.Analysis.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.norm_toLp_equivTuple", "kind": "theorem", "module": "Mathlib.Analysis.Quaternion", "is_tactic_proof": false, "tactics": ["rw", "simp_rw", "rfl"], "tactic_count": 3}
{"name": "Quaternion.linearIsometryEquivTuple", "kind": "definition", "module": "Mathlib.Analysis.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.continuous_coe", "kind": "theorem", "module": "Mathlib.Analysis.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.continuous_normSq", "kind": "theorem", "module": "Mathlib.Analysis.Quaternion", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Quaternion.continuous_re", "kind": "theorem", "module": "Mathlib.Analysis.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.continuous_imI", "kind": "theorem", "module": "Mathlib.Analysis.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.continuous_imJ", "kind": "theorem", "module": "Mathlib.Analysis.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.continuous_imK", "kind": "theorem", "module": "Mathlib.Analysis.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.continuous_im", "kind": "theorem", "module": "Mathlib.Analysis.Quaternion", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Quaternion.instCompleteSpaceReal", "kind": "instance", "module": "Mathlib.Analysis.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.hasSum_coe", "kind": "theorem", "module": "Mathlib.Analysis.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quaternion.summable_coe", "kind": "theorem", "module": "Mathlib.Analysis.Quaternion", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Quaternion.tsum_coe", "kind": "theorem", "module": "Mathlib.Analysis.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.RCLike.Basic.0.term𝓚", "kind": "definition", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.RCLike.Basic.0._aux_Mathlib_Analysis_RCLike_Basic___macroRules__private_Mathlib_Analysis_RCLike_Basic_0_term𝓚_1", "kind": "definition", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.RCLike.Basic.0._aux_Mathlib_Analysis_RCLike_Basic___unexpand_algebraMap_1", "kind": "definition", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.ofReal", "kind": "abbrev", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.algebraMapCoe", "kind": "instance", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.ofReal_alg", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.real_smul_eq_coe_mul", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.real_smul_eq_coe_smul", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RCLike.algebraMap_eq_ofReal", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.re_add_im", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.ofReal_re", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.ofReal_im", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.mul_re", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.mul_im", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.ext_iff", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.ext", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.ofReal_zero", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.zero_re", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.zero_im", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.ofReal_one", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.one_re", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RCLike.one_im", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RCLike.ofReal_injective", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.ofReal_inj", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.ofReal_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.ofReal_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.ofReal_add", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.ofReal_neg", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.ofReal_sub", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.ofReal_sum", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.ofReal_finsupp_sum", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.ofReal_mul", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.ofReal_pow", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.ofReal_prod", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.ofReal_finsuppProd", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.real_smul_ofReal", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.re_ofReal_mul", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RCLike.im_ofReal_mul", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RCLike.smul_re", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RCLike.smul_im", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RCLike.norm_ofReal", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.re_ofReal_pow", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RCLike.im_ofReal_pow", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RCLike.charZero_rclike", "kind": "instance", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.ofReal_expect", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.ofReal_balance", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.ofReal_comp_balance", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.I_re", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.I_im", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.I_im'", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RCLike.I_mul_re", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RCLike.I_mul_I", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.I_eq_zero_or_im_I_eq_one", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.conj_re", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.conj_im", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.conj_I", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.conj_ofReal", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "RCLike.conj_nat_cast", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.conj_ofNat", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.conj_neg_I", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RCLike.conj_eq_re_sub_im", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.sub_conj", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.conj_smul", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["rw", "mul_sub,"], "tactic_count": 2}
{"name": "RCLike.add_conj", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.re_eq_add_conj", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RCLike.im_eq_conj_sub", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["rw", "neg_mul,"], "tactic_count": 2}
{"name": "RCLike.is_real_TFAE", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": ["tfae_have", "h", "tfae_have", "h", "tfae_have", "tfae_have", "tfae_have", "tfae_have", "tfae_finish"], "tactic_count": 9}
{"name": "RCLike.conj_eq_iff_real", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.conj_eq_iff_re", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.conj_eq_iff_im", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.star_def", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.im_eq_zero_iff_isSelfAdjoint", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.re_eq_ofReal_of_isSelfAdjoint", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RCLike.ofReal_eq_re_of_isSelfAdjoint", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "RCLike.conjToRingEquiv", "kind": "abbrev", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.normSq", "kind": "definition", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.normSq_apply", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.norm_sq_eq_def", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.normSq_eq_def'", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.normSq_zero", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.normSq_one", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.normSq_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.normSq_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.normSq_pos", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RCLike.normSq_neg", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RCLike.normSq_conj", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RCLike.normSq_mul", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.normSq_add", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["simp", "ring"], "tactic_count": 2}
{"name": "RCLike.re_sq_le_normSq", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.im_sq_le_normSq", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.mul_conj", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "RCLike.conj_mul", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RCLike.inv_eq_conj", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.normSq_sub", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RCLike.sqrt_normSq_eq_norm", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RCLike.ofReal_inv", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.inv_def", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simp", "apply", "rw", "simpa"], "tactic_count": 5}
{"name": "RCLike.inv_re", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RCLike.inv_im", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RCLike.div_re", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RCLike.div_im", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RCLike.conj_inv", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.conj_div", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.exists_norm_eq_mul_self", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["obtain", "exact", "exact"], "tactic_count": 3}
{"name": "RCLike.exists_norm_mul_eq_self", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["obtain", "exact", "exact"], "tactic_count": 3}
{"name": "RCLike.ofReal_div", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.div_re_ofReal", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RCLike.ofReal_zpow", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.I_mul_I_of_nonzero", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.inv_I", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "field_simp", "linear_combination"], "tactic_count": 4}
{"name": "RCLike.div_I", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RCLike.normSq_inv", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.normSq_div", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.norm_conj", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RCLike.nnnorm_conj", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RCLike.enorm_conj", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RCLike.instCStarRing", "kind": "instance", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.instStarModuleReal", "kind": "instance", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.ofReal_natCast", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.ofReal_nnratCast", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.natCast_re", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RCLike.natCast_im", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RCLike.ofNat_re", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.ofNat_im", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.ofReal_ofNat", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.ofNat_mul_re", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RCLike.ofNat_mul_im", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RCLike.ofReal_intCast", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.intCast_re", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RCLike.intCast_im", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RCLike.ofReal_ratCast", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.ratCast_re", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RCLike.ratCast_im", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RCLike.norm_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.norm_natCast", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "RCLike.nnnorm_natCast", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RCLike.norm_ofNat", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.nnnorm_ofNat", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.norm_two", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.nnnorm_two", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.norm_nnratCast", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RCLike.nnnorm_nnratCast", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RCLike.norm_nsmul", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "RCLike.nnnorm_nsmul", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "RCLike.norm_nnqsmul", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "RCLike.nnnorm_nnqsmul", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "RCLike.norm_expect_le", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.mul_self_norm", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RCLike.abs_re_le_norm", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "RCLike.abs_im_le_norm", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "RCLike.norm_re_le_norm", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.norm_im_le_norm", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.re_le_norm", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.im_le_norm", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.im_eq_zero_of_le", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["simpa", "congr_arg"], "tactic_count": 2}
{"name": "RCLike.re_eq_self_of_le", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RCLike.abs_re_div_norm_le_one", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "RCLike.abs_im_div_norm_le_one", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "RCLike.norm_I_of_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["rw", "norm_one]"], "tactic_count": 2}
{"name": "RCLike.re_eq_norm_of_mul_conj", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RCLike.norm_sq_re_add_conj", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RCLike.norm_sq_re_conj_add", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RCLike.instNormSMulClassInt", "kind": "instance", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.isCauSeq_re", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.isCauSeq_im", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.cauSeqRe", "kind": "definition", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.cauSeqIm", "kind": "definition", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.isCauSeq_norm", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.instRCLike", "kind": "instance", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.lt_iff_re_im", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "constructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 6}
{"name": "RCLike.nonneg_iff", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "RCLike.pos_iff", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "RCLike.nonpos_iff", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "RCLike.neg_iff", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "RCLike.nonneg_iff_exists_ofReal", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "RCLike.pos_iff_exists_ofReal", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "RCLike.nonpos_iff_exists_ofReal", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "RCLike.neg_iff_exists_ofReal", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "RCLike.ofReal_le_ofReal", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "RCLike.ofReal_lt_ofReal", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "RCLike.ofReal_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RCLike.ofReal_nonpos", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RCLike.ofReal_pos", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RCLike.ofReal_lt_zero", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RCLike.norm_le_re_iff_eq_norm", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["refine", "have", "rw", "rw", "simp"], "tactic_count": 5}
{"name": "RCLike.re_le_neg_norm_iff_eq_neg_norm", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "RCLike.norm_of_nonneg'", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "RCLike.re_nonneg_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RCLike.re_le_re", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "RCLike.re_monotone", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.inv_pos_of_pos", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["rw", "obtain", "rw", "exact"], "tactic_count": 4}
{"name": "RCLike.inv_pos", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "RCLike.toStarOrderedRing", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.toZeroLEOneClass", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.toIsOrderedAddMonoid", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.toIsStrictOrderedRing", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.toPosMulReflectLT", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.toIsStrictOrderedModule", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.ofReal_mul_pos_iff", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["simp", "obtain", "simp", "simp", "simp"], "tactic_count": 5}
{"name": "RCLike.ofReal_mul_neg_iff", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "RCLike.instPosMulReflectLE", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.instMulPosReflectLE", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.RCLike.Basic.0.RCLike.termReR", "kind": "definition", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.RCLike.Basic.0.RCLike._aux_Mathlib_Analysis_RCLike_Basic___macroRules__private_Mathlib_Analysis_RCLike_Basic_0_RCLike_termReR_1", "kind": "definition", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.RCLike.Basic.0.RCLike.termImR", "kind": "definition", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.RCLike.Basic.0.RCLike._aux_Mathlib_Analysis_RCLike_Basic___macroRules__private_Mathlib_Analysis_RCLike_Basic_0_RCLike_termImR_1", "kind": "definition", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.RCLike.Basic.0.RCLike.termIR", "kind": "definition", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.RCLike.Basic.0.RCLike._aux_Mathlib_Analysis_RCLike_Basic___macroRules__private_Mathlib_Analysis_RCLike_Basic_0_RCLike_termIR_1", "kind": "definition", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.RCLike.Basic.0.RCLike.termNormSqR", "kind": "definition", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.RCLike.Basic.0.RCLike._aux_Mathlib_Analysis_RCLike_Basic___macroRules__private_Mathlib_Analysis_RCLike_Basic_0_RCLike_termNormSqR_1", "kind": "definition", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.re_to_real", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.im_to_real", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.conj_to_real", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.I_to_real", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.normSq_to_real", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RCLike.ofReal_real_eq_id", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.reLm", "kind": "definition", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.reLm_coe", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.reCLM", "kind": "definition", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.reCLM_coe", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.reCLM_apply", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.continuous_re", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.imLm", "kind": "definition", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.imLm_coe", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.imCLM", "kind": "definition", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.imCLM_coe", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.imCLM_apply", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.continuous_im", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.conjAe", "kind": "definition", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.conjAe_coe", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.conjLIE", "kind": "definition", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.conjLIE_apply", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.conjCLE", "kind": "definition", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.conjCLE_coe", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.conjCLE_apply", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.instContinuousStar", "kind": "instance", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.continuous_conj", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.ofRealAm", "kind": "definition", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.ofRealAm_coe", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.ofRealLI", "kind": "definition", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.ofRealLI_apply", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.ofRealCLM", "kind": "definition", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.ofRealCLM_coe", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.ofRealCLM_apply", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.continuous_ofReal", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.continuous_normSq", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.lipschitzWith_ofReal", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.lipschitzWith_re", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["intro", "simp", "calc"], "tactic_count": 3}
{"name": "RCLike.lipschitzWith_im", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["intro", "simp", "calc"], "tactic_count": 3}
{"name": "RCLike.map", "kind": "definition", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.map_same_eq_id", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "RCLike.map_to_real", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "RCLike.map_from_real", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "RCLike.im_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "RCLike.realRingEquiv", "kind": "definition", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.realLinearIsometryEquiv", "kind": "definition", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.norm_le_im_iff_eq_I_mul_norm", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["obtain", "simp", "have", "rw", "convert", "all_goals"], "tactic_count": 6}
{"name": "RCLike.im_le_neg_norm_iff_eq_neg_I_mul_norm", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "AddChar.inv_apply_eq_conj", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.map_neg_eq_conj", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "instIsRCLikeNormedField", "kind": "instance", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.copy_of_normedField", "kind": "definition", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRCLikeNormedField.rclike", "kind": "definition", "module": "Mathlib.Analysis.RCLike.Basic", "is_tactic_proof": true, "tactics": ["choose", "exact"], "tactic_count": 2}
{"name": "RCLike.restrict_toContinuousMap_eq_toContinuousMapStar_restrict", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.BoundedContinuous", "is_tactic_proof": true, "tactics": ["ext", "simp", "toContinuousMapₐ_apply,", "constructor", "intro", "use", "ext", "simp", "exact", "intro", "have", "simp", "have", "ext", "simp", "use", "refine", "ext", "simp"], "tactic_count": 19}
{"name": "LinearMap.extendTo𝕜'", "kind": "definition", "module": "Mathlib.Analysis.RCLike.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.extendTo𝕜'_apply", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.extendTo𝕜'_apply_re", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Extend", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LinearMap.norm_extendTo𝕜'_apply_sq", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.instNormedSpaceRestrictScalarsReal", "kind": "instance", "module": "Mathlib.Analysis.RCLike.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.extendTo𝕜", "kind": "definition", "module": "Mathlib.Analysis.RCLike.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.extendTo𝕜_apply", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.extendTo𝕜'", "kind": "definition", "module": "Mathlib.Analysis.RCLike.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.extendTo𝕜'_apply", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.extendTo𝕜", "kind": "definition", "module": "Mathlib.Analysis.RCLike.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.extendTo𝕜_apply", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.wInner", "kind": "definition", "module": "Mathlib.Analysis.RCLike.Inner", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.cWeight", "kind": "abbrev", "module": "Mathlib.Analysis.RCLike.Inner", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.term⟪_,_⟫_[_,_]", "kind": "definition", "module": "Mathlib.Analysis.RCLike.Inner", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike._aux_Mathlib_Analysis_RCLike_Inner___macroRules_RCLike_term⟪_,_⟫_[_,_]_1", "kind": "definition", "module": "Mathlib.Analysis.RCLike.Inner", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike._aux_Mathlib_Analysis_RCLike_Inner___unexpand_RCLike_wInner_1", "kind": "definition", "module": "Mathlib.Analysis.RCLike.Inner", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.term⟪_,_⟫_[_]", "kind": "definition", "module": "Mathlib.Analysis.RCLike.Inner", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike._aux_Mathlib_Analysis_RCLike_Inner___macroRules_RCLike_term⟪_,_⟫_[_]_1", "kind": "definition", "module": "Mathlib.Analysis.RCLike.Inner", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.term⟪_,_⟫ₙ_[_]", "kind": "definition", "module": "Mathlib.Analysis.RCLike.Inner", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike._aux_Mathlib_Analysis_RCLike_Inner___macroRules_RCLike_term⟪_,_⟫ₙ_[_]_1", "kind": "definition", "module": "Mathlib.Analysis.RCLike.Inner", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.wInner_cWeight_eq_smul_wInner_one", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Inner", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RCLike.conj_wInner_symm", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Inner", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RCLike.wInner_zero_left", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Inner", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RCLike.wInner_zero_right", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Inner", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RCLike.wInner_add_left", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Inner", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RCLike.wInner_add_right", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Inner", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RCLike.wInner_neg_left", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Inner", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RCLike.wInner_neg_right", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Inner", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RCLike.wInner_sub_left", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Inner", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "RCLike.wInner_sub_right", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Inner", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "RCLike.wInner_of_isEmpty", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Inner", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RCLike.wInner_smul_left", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Inner", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "RCLike.wInner_smul_right", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Inner", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "RCLike.mul_wInner_left", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Inner", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RCLike.wInner_one_eq_sum", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Inner", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RCLike.wInner_cWeight_eq_expect", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Inner", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RCLike.wInner_const_left", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Inner", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RCLike.wInner_const_right", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Inner", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RCLike.wInner_one_const_left", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Inner", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RCLike.wInner_one_const_right", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Inner", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RCLike.wInner_cWeight_const_left", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Inner", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RCLike.wInner_cWeight_const_right", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Inner", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RCLike.wInner_one_eq_inner", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Inner", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RCLike.inner_eq_wInner_one", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Inner", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RCLike.linearIndependent_of_ne_zero_of_wInner_one_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Inner", "is_tactic_proof": true, "tactics": ["simp_rw", "have", "exacts", "this,"], "tactic_count": 4}
{"name": "RCLike.linearIndependent_of_ne_zero_of_wInner_cWeight_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Inner", "is_tactic_proof": true, "tactics": ["cases", "have", "exact", "exact", "linearIndependent_of_ne_zero_of_wInner_one_eq_zero", "simpa"], "tactic_count": 6}
{"name": "RCLike.wInner_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Inner", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.norm_wInner_le", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Inner", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.abs_wInner_le", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Inner", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "convex_RCLike_iff_convex_real", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.ofReal_eval", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.span_one_I", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Lemmas", "is_tactic_proof": true, "tactics": ["suffices", "exact"], "tactic_count": 2}
{"name": "RCLike.rank_le_two", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.finrank_le_two", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LibraryNote.RCLike_instance", "kind": "definition", "module": "Mathlib.Analysis.RCLike.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteDimensional.rclike_to_real", "kind": "instance", "module": "Mathlib.Analysis.RCLike.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteDimensional.proper_rclike", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Lemmas", "is_tactic_proof": true, "tactics": ["have", "have", "infer_instance"], "tactic_count": 3}
{"name": "FiniteDimensional.RCLike.properSpace_submodule", "kind": "instance", "module": "Mathlib.Analysis.RCLike.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.reCLM_norm", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Lemmas", "is_tactic_proof": true, "tactics": ["apply", "convert", "simp"], "tactic_count": 3}
{"name": "RCLike.conjCLE_norm", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.ofRealCLM_norm", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.aeval_conj", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.aeval_ofReal", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.sqrt", "kind": "definition", "module": "Mathlib.Analysis.RCLike.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.sqrt_zero", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Sqrt", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.sqrt_one", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Sqrt", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.sqrt_eq_real_add_ite", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Sqrt", "is_tactic_proof": true, "tactics": ["rw", "by_cases", "simp", "simp"], "tactic_count": 4}
{"name": "RCLike.sqrt", "kind": "definition", "module": "Mathlib.Analysis.RCLike.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.sqrt_eq_ite", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Sqrt", "is_tactic_proof": true, "tactics": ["rw", "split_ifs", "simp", "have", "simp_all", "algebraMap.coe_inj,", "by_cases", "simp", "simp"], "tactic_count": 9}
{"name": "RCLike.sqrt_eq_real_add_ite", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Sqrt", "is_tactic_proof": true, "tactics": ["rw", "obtain", "rw", "simp", "aesop"], "tactic_count": 5}
{"name": "RCLike.sqrt_zero", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Sqrt", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RCLike.sqrt_one", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Sqrt", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.re_sqrt_ofReal", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Sqrt", "is_tactic_proof": true, "tactics": ["simp", "grind"], "tactic_count": 2}
{"name": "RCLike.re_sqrt_ofReal", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Sqrt", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "RCLike.sqrt_real", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Sqrt", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RCLike.sqrt_complex", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Sqrt", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.sqrt_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Sqrt", "is_tactic_proof": true, "tactics": ["obtain", "simp", "rw", "simp"], "tactic_count": 4}
{"name": "RCLike.sqrt_map", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Sqrt", "is_tactic_proof": true, "tactics": ["have", "have", "aesop"], "tactic_count": 3}
{"name": "Complex.sqrt_map", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Sqrt", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "RCLike.sqrt_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Sqrt", "is_tactic_proof": true, "tactics": ["obtain", "simp", "rw", "simp"], "tactic_count": 4}
{"name": "Complex.sqrt_neg_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Sqrt", "is_tactic_proof": true, "tactics": ["obtain", "rw", "simp", "rw", "simp"], "tactic_count": 5}
{"name": "RCLike.sqrt_neg_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Sqrt", "is_tactic_proof": true, "tactics": ["obtain", "simp", "rw", "simp"], "tactic_count": 4}
{"name": "Complex.sqrt_neg_one", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Sqrt", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RCLike.sqrt_neg_one", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Sqrt", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.sqrt_I", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Sqrt", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Complex.sqrt_neg_I", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Sqrt", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "RCLike.sqrt_I", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Sqrt", "is_tactic_proof": true, "tactics": ["rw", "split_ifs", "simp_rw", "simp", "grind"], "tactic_count": 5}
{"name": "RCLike.sqrt_neg_I", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.Sqrt", "is_tactic_proof": true, "tactics": ["rw", "split_ifs", "simp_rw", "simp", "grind"], "tactic_count": 5}
{"name": "tangentConeAt_real_subset_isRCLikeNormedField", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.TangentCone", "is_tactic_proof": true, "tactics": ["letI", "exact"], "tactic_count": 2}
{"name": "UniqueDiffWithinAt.of_real", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.TangentCone", "is_tactic_proof": true, "tactics": ["letI", "exact"], "tactic_count": 2}
{"name": "UniqueDiffOn.of_real", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.TangentCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniqueDiffWithinAt_convex_of_isRCLikeNormedField", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.TangentCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniqueDiffOn_convex_of_isRCLikeNormedField", "kind": "theorem", "module": "Mathlib.Analysis.RCLike.TangentCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.cantorFunctionAux", "kind": "definition", "module": "Mathlib.Analysis.Real.Cardinality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.cantorFunctionAux_true", "kind": "theorem", "module": "Mathlib.Analysis.Real.Cardinality", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Cardinal.cantorFunctionAux_false", "kind": "theorem", "module": "Mathlib.Analysis.Real.Cardinality", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Cardinal.cantorFunctionAux_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Real.Cardinality", "is_tactic_proof": true, "tactics": ["cases", "simp", "simpa"], "tactic_count": 3}
{"name": "Cardinal.cantorFunctionAux_eq", "kind": "theorem", "module": "Mathlib.Analysis.Real.Cardinality", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Cardinal.cantorFunctionAux_zero", "kind": "theorem", "module": "Mathlib.Analysis.Real.Cardinality", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Cardinal.cantorFunctionAux_succ", "kind": "theorem", "module": "Mathlib.Analysis.Real.Cardinality", "is_tactic_proof": true, "tactics": ["ext", "cases"], "tactic_count": 2}
{"name": "Cardinal.summable_cantor_function", "kind": "theorem", "module": "Mathlib.Analysis.Real.Cardinality", "is_tactic_proof": true, "tactics": ["apply", "intro"], "tactic_count": 2}
{"name": "Cardinal.cantorFunction", "kind": "definition", "module": "Mathlib.Analysis.Real.Cardinality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.cantorFunction_le", "kind": "theorem", "module": "Mathlib.Analysis.Real.Cardinality", "is_tactic_proof": true, "tactics": ["apply", "intro", "simp", "replace"], "tactic_count": 4}
{"name": "Cardinal.cantorFunction_succ", "kind": "theorem", "module": "Mathlib.Analysis.Real.Cardinality", "is_tactic_proof": true, "tactics": ["rw", "rw"], "tactic_count": 2}
{"name": "Cardinal.increasing_cantorFunction", "kind": "theorem", "module": "Mathlib.Analysis.Real.Cardinality", "is_tactic_proof": false, "tactics": ["have", "apply", "norm_num", "induction", "zero", "let", "have", "intro", "cases", "rw", "contradiction", "simp", "let", "have", "intro", "cases", "rw", "simp", "apply", "refine", "have", "rw", "convert", "norm_num", "rwa", "convert", "rw", "apply", "refine", "intro", "cases", "contradiction", "simp", "exact", "succ", "rw", "rw", "gcongr", "exact"], "tactic_count": 39}
{"name": "Cardinal.cantorFunction_injective", "kind": "theorem", "module": "Mathlib.Analysis.Real.Cardinality", "is_tactic_proof": true, "tactics": ["intro", "classical", "contrapose", "have", "let", "have", "intro", "apply", "exact", "cases", "apply", "refine", "apply", "rw", "apply", "exact", "apply", "refine", "apply", "rw", "apply", "exact"], "tactic_count": 22}
{"name": "Cardinal.mk_real", "kind": "theorem", "module": "Mathlib.Analysis.Real.Cardinality", "is_tactic_proof": true, "tactics": ["apply", "rw", "apply", "apply", "rw", "convert", "rw", "exact", "simp", "norm_num"], "tactic_count": 10}
{"name": "Cardinal.mk_univ_real", "kind": "theorem", "module": "Mathlib.Analysis.Real.Cardinality", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.instUncountableReal", "kind": "instance", "module": "Mathlib.Analysis.Real.Cardinality", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Cardinal.not_countable_real", "kind": "theorem", "module": "Mathlib.Analysis.Real.Cardinality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_Ioi_real", "kind": "theorem", "module": "Mathlib.Analysis.Real.Cardinality", "is_tactic_proof": true, "tactics": ["refine", "rw", "intro", "refine", "have", "convert", "exact", "rw", "grw", "have", "convert", "simp", "rw", "refine", "refine", "rw", "exact"], "tactic_count": 17}
{"name": "Cardinal.mk_Ici_real", "kind": "theorem", "module": "Mathlib.Analysis.Real.Cardinality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_Iio_real", "kind": "theorem", "module": "Mathlib.Analysis.Real.Cardinality", "is_tactic_proof": true, "tactics": ["refine", "have", "exact"], "tactic_count": 3}
{"name": "Cardinal.mk_Iic_real", "kind": "theorem", "module": "Mathlib.Analysis.Real.Cardinality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_Ioo_real", "kind": "theorem", "module": "Mathlib.Analysis.Real.Cardinality", "is_tactic_proof": true, "tactics": ["refine", "have", "refine", "rw", "replace", "have", "refine", "rw"], "tactic_count": 8}
{"name": "Cardinal.mk_Ico_real", "kind": "theorem", "module": "Mathlib.Analysis.Real.Cardinality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_Icc_real", "kind": "theorem", "module": "Mathlib.Analysis.Real.Cardinality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_Ioc_real", "kind": "theorem", "module": "Mathlib.Analysis.Real.Cardinality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.Real.Ioo_countable_iff", "kind": "theorem", "module": "Mathlib.Analysis.Real.Cardinality", "is_tactic_proof": true, "tactics": ["refine", "contrapose", "rw", "exact"], "tactic_count": 4}
{"name": "Cardinal.Real.Ico_countable_iff", "kind": "theorem", "module": "Mathlib.Analysis.Real.Cardinality", "is_tactic_proof": true, "tactics": ["refine", "contrapose", "rw", "exact"], "tactic_count": 4}
{"name": "Cardinal.Real.Ioc_countable_iff", "kind": "theorem", "module": "Mathlib.Analysis.Real.Cardinality", "is_tactic_proof": true, "tactics": ["refine", "contrapose", "rw", "exact"], "tactic_count": 4}
{"name": "Cardinal.Real.Icc_countable_iff", "kind": "theorem", "module": "Mathlib.Analysis.Real.Cardinality", "is_tactic_proof": false, "tactics": ["refine", "rcases", "simp", "simp", "contrapose", "rw", "exact"], "tactic_count": 7}
{"name": "Hyperreal", "kind": "definition", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.termℝ*", "kind": "definition", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal._aux_Mathlib_Analysis_Real_Hyperreal___macroRules_Hyperreal_termℝ*_1", "kind": "definition", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal._aux_Mathlib_Analysis_Real_Hyperreal___unexpand_Hyperreal_1", "kind": "definition", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.instField", "kind": "instance", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.instLinearOrder", "kind": "instance", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.instIsStrictOrderedRing", "kind": "instance", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.ofReal", "kind": "definition", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.instCoeTCReal", "kind": "instance", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.coe_eq_coe", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.coe_ne_coe", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.coe_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.coe_eq_one", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.coe_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.coe_ne_one", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.coe_one", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.coe_zero", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.coe_inv", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.coe_neg", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.coe_add", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.coe_ofNat", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.coe_mul", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.coe_div", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.coe_sub", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.coe_le_coe", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.coe_lt_coe", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.coe_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.coe_pos", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.coe_abs", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.coe_max", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.coe_min", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.coeRingHom", "kind": "definition", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.archimedeanClassMk_coe_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.archimdeanClassMk_coe", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.stdPart_coe", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.ofSeq", "kind": "definition", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.ofSeq_surjective", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.ofSeq_lt_ofSeq", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.omega", "kind": "definition", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.termω", "kind": "definition", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal._aux_Mathlib_Analysis_Real_Hyperreal___macroRules_Hyperreal_termω_1", "kind": "definition", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal._aux_Mathlib_Analysis_Real_Hyperreal___unexpand_Hyperreal_omega_1", "kind": "definition", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.coe_lt_omega", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": true, "tactics": ["apply", "obtain", "rw", "exact"], "tactic_count": 4}
{"name": "Hyperreal.omega_pos", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.omega_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.abs_omega", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.archimedeanClassMk_omega_neg", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.stdPart_omega", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Hyperreal.epsilon", "kind": "definition", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.termε", "kind": "definition", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal._aux_Mathlib_Analysis_Real_Hyperreal___macroRules_Hyperreal_termε_1", "kind": "definition", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal._aux_Mathlib_Analysis_Real_Hyperreal___unexpand_Hyperreal_epsilon_1", "kind": "definition", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.inv_omega", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.inv_epsilon", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.epsilon_pos", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.epsilon_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.epsilon_mul_omega", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.archimedeanClassMk_epsilon_pos", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Hyperreal.stdPart_epsilon", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.epsilon_lt_of_pos", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.epsilon_lt_of_neg", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.lt_of_tendsto_zero_of_pos", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.neg_lt_of_tendsto_zero_of_pos", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.gt_of_tendsto_zero_of_neg", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.IsSt", "kind": "definition", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.st", "kind": "definition", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.Infinitesimal", "kind": "definition", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.InfinitePos", "kind": "definition", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.InfiniteNeg", "kind": "definition", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.Infinite", "kind": "definition", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.isSt_ofSeq_iff_tendsto", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.isSt_iff_tendsto", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "Hyperreal.isSt_of_tendsto", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.IsSt.lt", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "rw", "exact"], "tactic_count": 4}
{"name": "Hyperreal.IsSt.unique", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": true, "tactics": ["rcases", "rw", "exact"], "tactic_count": 3}
{"name": "Hyperreal.IsSt.st_eq", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "Hyperreal.IsSt.not_infinite", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.not_infinite_of_exists_st", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.Infinite.st_eq", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.isSt_sSup", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": true, "tactics": ["set", "set", "have", "obtain", "exact", "have", "obtain", "exact", "intro", "constructor", "exact", "replace", "exact"], "tactic_count": 13}
{"name": "Hyperreal.exists_st_of_not_infinite", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.st_eq_sSup", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": true, "tactics": ["rcases", "rw", "cases", "inl", "convert", "exact", "inr", "convert", "exact", "exact"], "tactic_count": 10}
{"name": "Hyperreal.exists_st_iff_not_infinite", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.infinite_iff_not_exists_st", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.IsSt.isSt_st", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Hyperreal.isSt_st_of_exists_st", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.isSt_st'", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.isSt_st", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.isSt_refl_real", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.st_id_real", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.eq_of_isSt_real", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.isSt_real_iff_eq", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.isSt_symm_real", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Hyperreal.isSt_trans_real", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Hyperreal.isSt_inj_real", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.isSt_iff_abs_sub_lt_delta", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Hyperreal.IsSt.map", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "Hyperreal.IsSt.map₂", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "rw", "exact"], "tactic_count": 4}
{"name": "Hyperreal.IsSt.add", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.IsSt.neg", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.IsSt.sub", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.IsSt.le", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.st_le_of_le", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.lt_of_st_lt", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.infinitePos_def", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.infiniteNeg_def", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.InfinitePos.pos", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.InfiniteNeg.lt_zero", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.Infinite.ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.not_infinite_zero", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.InfiniteNeg.not_infinitePos", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.InfinitePos.not_infiniteNeg", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.InfinitePos.neg", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.InfiniteNeg.neg", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.infiniteNeg_neg", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.infinitePos_neg", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.infinite_neg", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.Infinitesimal.not_infinite", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.Infinite.not_infinitesimal", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.InfinitePos.not_infinitesimal", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.InfiniteNeg.not_infinitesimal", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.infinitePos_iff_infinite_and_pos", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.infiniteNeg_iff_infinite_and_neg", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.infinitePos_iff_infinite_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.infinitePos_iff_infinite_of_pos", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.infiniteNeg_iff_infinite_of_neg", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.infinitePos_abs_iff_infinite_abs", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.infinite_abs_iff", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Hyperreal.infinitePos_abs_iff_infinite", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.infinite_iff_abs_lt_abs", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.infinitePos_add_not_infiniteNeg", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": true, "tactics": ["intro", "obtain", "convert", "simp"], "tactic_count": 4}
{"name": "Hyperreal.not_infiniteNeg_add_infinitePos", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.infiniteNeg_add_not_infinitePos", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Hyperreal.not_infinitePos_add_infiniteNeg", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.infinitePos_add_infinitePos", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.infiniteNeg_add_infiniteNeg", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.infinitePos_add_not_infinite", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.infiniteNeg_add_not_infinite", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.infinitePos_of_tendsto_top", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.infiniteNeg_of_tendsto_bot", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.not_infinite_neg", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.not_infinite_add", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.not_infinite_iff_exist_lt_gt", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.not_infinite_real", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Hyperreal.Infinite.ne_real", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.IsSt.mul", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.not_infinite_mul", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.st_add", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.st_neg", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": true, "tactics": ["classical", "by_cases", "rw", "exact"], "tactic_count": 4}
{"name": "Hyperreal.st_mul", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.infinitesimal_def", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Hyperreal.lt_of_pos_of_infinitesimal", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.lt_neg_of_pos_of_infinitesimal", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.gt_of_neg_of_infinitesimal", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.abs_lt_real_iff_infinitesimal", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.infinitesimal_zero", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.Infinitesimal.eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.infinitesimal_real_iff", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.Infinitesimal.add", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Hyperreal.Infinitesimal.neg", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Hyperreal.infinitesimal_neg", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.Infinitesimal.mul", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Hyperreal.infinitesimal_of_tendsto_zero", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.infinitesimal_epsilon", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.not_real_of_infinitesimal_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.IsSt.infinitesimal_sub", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Hyperreal.infinitesimal_sub_st", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.infinitePos_iff_infinitesimal_inv_pos", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.infiniteNeg_iff_infinitesimal_inv_neg", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Hyperreal.infinitesimal_inv_of_infinite", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.infinite_of_infinitesimal_inv", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": true, "tactics": ["rcases", "exact", "exact"], "tactic_count": 3}
{"name": "Hyperreal.infinite_iff_infinitesimal_inv", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.infinitesimal_pos_iff_infinitePos_inv", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.infinitesimal_neg_iff_infiniteNeg_inv", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.infinitesimal_iff_infinite_inv", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.IsSt.inv", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.st_inv", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "by_cases", "rw", "by_cases", "rw", "exact"], "tactic_count": 7}
{"name": "Hyperreal.infinitePos_omega", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.infinite_omega", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.infinitePos_mul_of_infinitePos_not_infinitesimal_pos", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.infinitePos_mul_of_not_infinitesimal_pos_infinitePos", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.infinitePos_mul_of_infiniteNeg_not_infinitesimal_neg", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Hyperreal.infinitePos_mul_of_not_infinitesimal_neg_infiniteNeg", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.infiniteNeg_mul_of_infinitePos_not_infinitesimal_neg", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Hyperreal.infiniteNeg_mul_of_not_infinitesimal_neg_infinitePos", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.infiniteNeg_mul_of_infiniteNeg_not_infinitesimal_pos", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Hyperreal.infiniteNeg_mul_of_not_infinitesimal_pos_infiniteNeg", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.infinitePos_mul_infinitePos", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.infiniteNeg_mul_infiniteNeg", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.infinitePos_mul_infiniteNeg", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.infiniteNeg_mul_infinitePos", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.infinite_mul_of_infinite_not_infinitesimal", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.infinite_mul_of_not_infinitesimal_infinite", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hyperreal.Infinite.mul", "kind": "theorem", "module": "Mathlib.Analysis.Real.Hyperreal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.ofDigitsTerm", "kind": "definition", "module": "Mathlib.Analysis.Real.OfDigits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.ofDigitsTerm_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Real.OfDigits", "is_tactic_proof": true, "tactics": ["simp", "positivity"], "tactic_count": 2}
{"name": "_private.Mathlib.Analysis.Real.OfDigits.0.Real.b_pos", "kind": "theorem", "module": "Mathlib.Analysis.Real.OfDigits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.ofDigitsTerm_le", "kind": "theorem", "module": "Mathlib.Analysis.Real.OfDigits", "is_tactic_proof": true, "tactics": ["obtain", "unfold", "gcongr", "simp", "grind"], "tactic_count": 5}
{"name": "Real.summable_ofDigitsTerm", "kind": "theorem", "module": "Mathlib.Analysis.Real.OfDigits", "is_tactic_proof": true, "tactics": ["refine", "obtain", "simp", "simp_rw", "refine", "simp"], "tactic_count": 6}
{"name": "Real.ofDigits", "kind": "definition", "module": "Mathlib.Analysis.Real.OfDigits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.ofDigits_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.Real.OfDigits", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Real.ofDigits_le_one", "kind": "theorem", "module": "Mathlib.Analysis.Real.OfDigits", "is_tactic_proof": true, "tactics": ["obtain", "simp", "rify", "convert", "simp_rw", "rw", "have", "field", "simp_rw", "refine", "simp"], "tactic_count": 11}
{"name": "Real.ofDigits_eq_sum_add_ofDigits", "kind": "theorem", "module": "Mathlib.Analysis.Real.OfDigits", "is_tactic_proof": true, "tactics": ["simp", "rw", "congr", "ext", "simp", "ring"], "tactic_count": 6}
{"name": "Real.abs_ofDigits_sub_ofDigits_le", "kind": "theorem", "module": "Mathlib.Analysis.Real.OfDigits", "is_tactic_proof": true, "tactics": ["rw", "have", "rw", "apply", "convert", "simp"], "tactic_count": 6}
{"name": "Real.digits", "kind": "definition", "module": "Mathlib.Analysis.Real.OfDigits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.ofDigits_digits_sum_eq", "kind": "theorem", "module": "Mathlib.Analysis.Real.OfDigits", "is_tactic_proof": true, "tactics": ["have", "induction", "zero", "succ", "ih", "rw", "mul_inv_cancel₀", "set", "norm_cast", "rw"], "tactic_count": 10}
{"name": "Real.le_sum_ofDigitsTerm_digits", "kind": "theorem", "module": "Mathlib.Analysis.Real.OfDigits", "is_tactic_proof": true, "tactics": ["have", "have", "have", "rw", "rw", "linarith"], "tactic_count": 6}
{"name": "Real.sum_ofDigitsTerm_digits_le", "kind": "theorem", "module": "Mathlib.Analysis.Real.OfDigits", "is_tactic_proof": true, "tactics": ["have", "have", "have", "rw", "exact"], "tactic_count": 5}
{"name": "Real.hasSum_ofDigitsTerm_digits", "kind": "theorem", "module": "Mathlib.Analysis.Real.OfDigits", "is_tactic_proof": true, "tactics": ["rw", "refine", "tendsto_of_tendsto_of_tendsto_of_le_of_le", "convert", "simp", "simp"], "tactic_count": 6}
{"name": "Real.ofDigits_digits", "kind": "theorem", "module": "Mathlib.Analysis.Real.OfDigits", "is_tactic_proof": true, "tactics": ["simp", "rw", "exact", "exact"], "tactic_count": 4}
{"name": "Real.ofDigits_const_last_eq_one", "kind": "theorem", "module": "Mathlib.Analysis.Real.OfDigits", "is_tactic_proof": false, "tactics": ["have", "rw", "simp", "simp", "rw", "rw", "tsum_geometric_of_lt_one", "push_cast", "have", "field", "rw", "apply"], "tactic_count": 12}
{"name": "Real.ofDigits_const_last_eq_one'", "kind": "theorem", "module": "Mathlib.Analysis.Real.OfDigits", "is_tactic_proof": true, "tactics": ["convert", "grind", "constructor", "grind"], "tactic_count": 4}
{"name": "Real.ofDigits_SurjOn", "kind": "theorem", "module": "Mathlib.Analysis.Real.OfDigits", "is_tactic_proof": true, "tactics": ["have", "intro", "by_cases", "use", "simp", "simp", "exact"], "tactic_count": 7}
{"name": "Real.continuous_ofDigits", "kind": "theorem", "module": "Mathlib.Analysis.Real.OfDigits", "is_tactic_proof": true, "tactics": ["n", "obtain", "generalize", "rify", "refine", "simp", "fun_prop", "exact", "simp", "apply", "calc", "gcongr", "linarith"], "tactic_count": 13}
{"name": "Real.pi_gt_sqrtTwoAddSeries", "kind": "theorem", "module": "Mathlib.Analysis.Real.Pi.Bounds", "is_tactic_proof": false, "tactics": ["have", "rw", "focus", "apply", "apply", "all_goals", "refine", "rw"], "tactic_count": 8}
{"name": "Real.pi_lt_sqrtTwoAddSeries", "kind": "theorem", "module": "Mathlib.Analysis.Real.Pi.Bounds", "is_tactic_proof": false, "tactics": ["have", "rw", "calc", "π", "sub_lt_comm.1", "calc", "π", "refine", "ring", "simp", "rw", "rw", "all_goals"], "tactic_count": 13}
{"name": "Real.pi_lower_bound_start", "kind": "theorem", "module": "Mathlib.Analysis.Real.Pi.Bounds", "is_tactic_proof": true, "tactics": ["refine", "refine", "rwa"], "tactic_count": 3}
{"name": "Real.sqrtTwoAddSeries_step_up", "kind": "theorem", "module": "Mathlib.Analysis.Real.Pi.Bounds", "is_tactic_proof": true, "tactics": ["refine", "have", "have", "rw", "div_le_div_iff₀", "exact"], "tactic_count": 6}
{"name": "Real.pi_upper_bound_start", "kind": "theorem", "module": "Mathlib.Analysis.Real.Pi.Bounds", "is_tactic_proof": true, "tactics": ["refine", "rw", "rwa", "exact", "exact"], "tactic_count": 5}
{"name": "Real.sqrtTwoAddSeries_step_down", "kind": "theorem", "module": "Mathlib.Analysis.Real.Pi.Bounds", "is_tactic_proof": true, "tactics": ["apply", "apply", "have", "have", "rw", "exact"], "tactic_count": 6}
{"name": "Real.tacticPi_lower_bound[_,,]", "kind": "definition", "module": "Mathlib.Analysis.Real.Pi.Bounds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real._aux_Mathlib_Analysis_Real_Pi_Bounds___elabRules_Real_tacticPi_lower_bound[_,,]_1", "kind": "definition", "module": "Mathlib.Analysis.Real.Pi.Bounds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.tacticPi_upper_bound[_,,]", "kind": "definition", "module": "Mathlib.Analysis.Real.Pi.Bounds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real._aux_Mathlib_Analysis_Real_Pi_Bounds___elabRules_Real_tacticPi_upper_bound[_,,]_1", "kind": "definition", "module": "Mathlib.Analysis.Real.Pi.Bounds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.pi_gt_three", "kind": "theorem", "module": "Mathlib.Analysis.Real.Pi.Bounds", "is_tactic_proof": true, "tactics": ["pi_lower_bound"], "tactic_count": 1}
{"name": "Real.pi_lt_four", "kind": "theorem", "module": "Mathlib.Analysis.Real.Pi.Bounds", "is_tactic_proof": true, "tactics": ["pi_upper_bound"], "tactic_count": 1}
{"name": "Real.pi_gt_d2", "kind": "theorem", "module": "Mathlib.Analysis.Real.Pi.Bounds", "is_tactic_proof": true, "tactics": ["pi_lower_bound"], "tactic_count": 1}
{"name": "Real.pi_lt_d2", "kind": "theorem", "module": "Mathlib.Analysis.Real.Pi.Bounds", "is_tactic_proof": true, "tactics": ["pi_upper_bound"], "tactic_count": 1}
{"name": "Real.pi_gt_d4", "kind": "theorem", "module": "Mathlib.Analysis.Real.Pi.Bounds", "is_tactic_proof": true, "tactics": ["pi_lower_bound"], "tactic_count": 1}
{"name": "Real.pi_lt_d4", "kind": "theorem", "module": "Mathlib.Analysis.Real.Pi.Bounds", "is_tactic_proof": true, "tactics": ["pi_upper_bound"], "tactic_count": 1}
{"name": "Real.pi_gt_d6", "kind": "theorem", "module": "Mathlib.Analysis.Real.Pi.Bounds", "is_tactic_proof": true, "tactics": ["pi_lower_bound"], "tactic_count": 1}
{"name": "Real.pi_lt_d6", "kind": "theorem", "module": "Mathlib.Analysis.Real.Pi.Bounds", "is_tactic_proof": true, "tactics": ["pi_upper_bound"], "tactic_count": 1}
{"name": "Real.pi_gt_d20", "kind": "theorem", "module": "Mathlib.Analysis.Real.Pi.Bounds", "is_tactic_proof": true, "tactics": ["pi_lower_bound"], "tactic_count": 1}
{"name": "Real.pi_lt_d20", "kind": "theorem", "module": "Mathlib.Analysis.Real.Pi.Bounds", "is_tactic_proof": true, "tactics": ["pi_upper_bound"], "tactic_count": 1}
{"name": "Real.floor_pi_eq_three", "kind": "theorem", "module": "Mathlib.Analysis.Real.Pi.Bounds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.ceil_pi_eq_four", "kind": "theorem", "module": "Mathlib.Analysis.Real.Pi.Bounds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.round_pi_eq_three", "kind": "theorem", "module": "Mathlib.Analysis.Real.Pi.Bounds", "is_tactic_proof": true, "tactics": ["refine", "grw", "norm_num"], "tactic_count": 3}
{"name": "chudnovskyNum", "kind": "definition", "module": "Mathlib.Analysis.Real.Pi.Chudnovsky", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "chudnovskyDenom", "kind": "definition", "module": "Mathlib.Analysis.Real.Pi.Chudnovsky", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "chudnovskyTerm", "kind": "definition", "module": "Mathlib.Analysis.Real.Pi.Chudnovsky", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "chudnovskySum", "kind": "definition", "module": "Mathlib.Analysis.Real.Pi.Chudnovsky", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "chudnovskySum_eq_pi_inv", "kind": "proofWanted", "module": "Mathlib.Analysis.Real.Pi.Chudnovsky", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.Real.Pi.Irrational.0.I", "kind": "definition", "module": "Mathlib.Analysis.Real.Pi.Irrational", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.Real.Pi.Irrational.0.I_zero", "kind": "theorem", "module": "Mathlib.Analysis.Real.Pi.Irrational", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "_private.Mathlib.Analysis.Real.Pi.Irrational.0.recursion'", "kind": "theorem", "module": "Mathlib.Analysis.Real.Pi.Irrational", "is_tactic_proof": true, "tactics": ["rw", "let", "let", "let", "let", "let", "let", "let", "let", "let", "have", "have", "have", "have", "have", "have", "have", "have", "have", "convert", "simp", "have", "convert", "simp", "ring", "have", "have", "convert", "simp", "ring", "have", "convert_to", "simp_rw", "rw", "hu₁_eval_one,", "convert_to", "rw", "congr", "dsimp", "ring", "rw", "mul_sub,", "have", "cases", "zero", "succ", "simp_rw", "have", "rw", "congr", "simp_rw", "ring", "all_goals"], "tactic_count": 53}
{"name": "_private.Mathlib.Analysis.Real.Pi.Irrational.0.recursion", "kind": "theorem", "module": "Mathlib.Analysis.Real.Pi.Irrational", "is_tactic_proof": true, "tactics": ["rw", "push_cast", "ring"], "tactic_count": 3}
{"name": "_private.Mathlib.Analysis.Real.Pi.Irrational.0.I_one", "kind": "theorem", "module": "Mathlib.Analysis.Real.Pi.Irrational", "is_tactic_proof": true, "tactics": ["rw", "ring"], "tactic_count": 2}
{"name": "_private.Mathlib.Analysis.Real.Pi.Irrational.0.sinPoly", "kind": "definition", "module": "Mathlib.Analysis.Real.Pi.Irrational", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.Real.Pi.Irrational.0.cosPoly", "kind": "definition", "module": "Mathlib.Analysis.Real.Pi.Irrational", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.Real.Pi.Irrational.0.sinPoly_natDegree_le", "kind": "theorem", "module": "Mathlib.Analysis.Real.Pi.Irrational", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.Real.Pi.Irrational.0.cosPoly_natDegree_le", "kind": "theorem", "module": "Mathlib.Analysis.Real.Pi.Irrational", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.Real.Pi.Irrational.0.sinPoly_add_cosPoly_eval", "kind": "theorem", "module": "Mathlib.Analysis.Real.Pi.Irrational", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.Real.Pi.Irrational.0.is_integer", "kind": "theorem", "module": "Mathlib.Analysis.Real.Pi.Irrational", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "exact", "exact", "refine", "conv", "rw", "simp", "refine", "have", "rw", "exact"], "tactic_count": 12}
{"name": "_private.Mathlib.Analysis.Real.Pi.Irrational.0.I_pos", "kind": "theorem", "module": "Mathlib.Analysis.Real.Pi.Irrational", "is_tactic_proof": true, "tactics": ["refine", "refine", "rw", "exact", "refine"], "tactic_count": 5}
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{"name": "Real.arcosh_bijOn", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Arcosh", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.arcosh_injOn", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Arcosh", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.arcosh_surjOn", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Arcosh", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.sqrt_mul_le_half_add", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ArithmeticGeometricMean", "is_tactic_proof": true, "tactics": ["rw", "norm_num", "exact"], "tactic_count": 3}
{"name": "NNReal.sqrt_mul_lt_half_add_of_ne", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ArithmeticGeometricMean", "is_tactic_proof": true, "tactics": ["wlog", "specialize", "rwa", "have", "rw", "tsub_tsub,", "rw", "show", "gcongr"], "tactic_count": 9}
{"name": "NNReal.agmSequences", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.ArithmeticGeometricMean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.agmSequences_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ArithmeticGeometricMean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.agmSequences_succ", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ArithmeticGeometricMean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.agmSequences_succ'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ArithmeticGeometricMean", "is_tactic_proof": true, "tactics": ["nth_rw", "rw", "rfl"], "tactic_count": 3}
{"name": "NNReal.agmSequences_comm", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ArithmeticGeometricMean", "is_tactic_proof": true, "tactics": ["funext", "cases", "zero", "succ"], "tactic_count": 4}
{"name": "NNReal.le_gm_and_am_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ArithmeticGeometricMean", "is_tactic_proof": true, "tactics": ["constructor", "rw", "gcongr", "apply", "rw", "gcongr"], "tactic_count": 6}
{"name": "NNReal.dist_gm_am_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ArithmeticGeometricMean", "is_tactic_proof": true, "tactics": ["wlog", "simpa", "rw", "calc", "gcongr", "rw", "gcongr", "nth_rw", "rw"], "tactic_count": 9}
{"name": "NNReal.agmSequences_monotone_and_antitone", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ArithmeticGeometricMean", "is_tactic_proof": false, "tactics": ["suffices", "from", "intro", "induction", "zero", "succ"], "tactic_count": 6}
{"name": "NNReal.agmSequences_fst_monotone", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ArithmeticGeometricMean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.agmSequences_snd_antitone", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ArithmeticGeometricMean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.agmSequences_fst_le_snd", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ArithmeticGeometricMean", "is_tactic_proof": false, "tactics": ["suffices", "obtain", "exact", "exact", "intro", "induction", "zero", "succ"], "tactic_count": 8}
{"name": "NNReal.agmSequences_fst_lt_snd_of_ne", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ArithmeticGeometricMean", "is_tactic_proof": false, "tactics": ["suffices", "obtain", "exact", "exact", "intro", "induction", "zero", "succ", "rw", "exact"], "tactic_count": 10}
{"name": "NNReal.agmSequences_min_max", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ArithmeticGeometricMean", "is_tactic_proof": true, "tactics": ["obtain", "rw", "rw"], "tactic_count": 3}
{"name": "NNReal.dist_agmSequences_fst_snd", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ArithmeticGeometricMean", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "apply", "rw", "gcongr"], "tactic_count": 7}
{"name": "NNReal.tendsto_dist_agmSequences_atTop_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ArithmeticGeometricMean", "is_tactic_proof": true, "tactics": ["apply", "conv", "rw", "enter", "rw", "exact"], "tactic_count": 6}
{"name": "NNReal.agm", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.ArithmeticGeometricMean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.agm_comm", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ArithmeticGeometricMean", "is_tactic_proof": true, "tactics": ["unfold", "conv_rhs", "enter", "rw"], "tactic_count": 4}
{"name": "NNReal.agm_eq_ciInf", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ArithmeticGeometricMean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.tendsto_agmSequences_snd_agm", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ArithmeticGeometricMean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.agm_le_agmSequences_snd", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ArithmeticGeometricMean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.agm_le_max", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ArithmeticGeometricMean", "is_tactic_proof": true, "tactics": ["wlog", "simpa", "rw", "apply", "rw", "exact"], "tactic_count": 6}
{"name": "NNReal.bddAbove_range_agmSequences_fst", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ArithmeticGeometricMean", "is_tactic_proof": true, "tactics": ["rw", "use", "simp_rw", "exact"], "tactic_count": 4}
{"name": "NNReal.agm_eq_ciSup", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ArithmeticGeometricMean", "is_tactic_proof": false, "tactics": ["refine", "tendsto_nhds_unique", "conv", "enter", "rw", "exact"], "tactic_count": 6}
{"name": "NNReal.tendsto_agmSequences_fst_agm", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ArithmeticGeometricMean", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "NNReal.agmSequences_fst_le_agm", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ArithmeticGeometricMean", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "NNReal.min_le_agm", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ArithmeticGeometricMean", "is_tactic_proof": true, "tactics": ["wlog", "simpa", "rw", "refine", "rw", "exact"], "tactic_count": 6}
{"name": "NNReal.agm_self", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ArithmeticGeometricMean", "is_tactic_proof": true, "tactics": ["apply", "nth_rw", "exact", "nth_rw", "exact"], "tactic_count": 5}
{"name": "NNReal.agm_zero_left", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ArithmeticGeometricMean", "is_tactic_proof": true, "tactics": ["suffices", "intro", "induction", "zero", "succ"], "tactic_count": 5}
{"name": "NNReal.agm_zero_right", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ArithmeticGeometricMean", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NNReal.agm_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ArithmeticGeometricMean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.agm_eq_agm_agmSequences_fst_agmSequences_snd", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ArithmeticGeometricMean", "is_tactic_proof": true, "tactics": ["refine", "have", "rw", "convert", "simp_rw"], "tactic_count": 5}
{"name": "NNReal.agm_eq_agm_gm_am", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ArithmeticGeometricMean", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "NNReal.agmSequences_fst_lt_agm_of_pos_of_ne", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ArithmeticGeometricMean", "is_tactic_proof": true, "tactics": ["rw", "set", "set", "apply", "have", "have", "nth_rw", "gcongr"], "tactic_count": 8}
{"name": "NNReal.agm_lt_agmSequences_snd_of_ne", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ArithmeticGeometricMean", "is_tactic_proof": true, "tactics": ["rw", "set", "set", "apply", "have", "nth_rw", "rw", "gcongr"], "tactic_count": 8}
{"name": "NNReal.min_lt_agm_of_pos_of_ne", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ArithmeticGeometricMean", "is_tactic_proof": true, "tactics": ["wlog", "simpa", "rw", "refine", "rw", "exact"], "tactic_count": 6}
{"name": "NNReal.agm_lt_max_of_ne", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ArithmeticGeometricMean", "is_tactic_proof": true, "tactics": ["wlog", "simpa", "rw", "apply", "rw", "exact"], "tactic_count": 6}
{"name": "NNReal.agm_mul_distrib", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ArithmeticGeometricMean", "is_tactic_proof": true, "tactics": ["simp_rw", "congr", "induction", "zero", "succ", "rw"], "tactic_count": 6}
{"name": "Real.arsinh", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Arsinh", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.exp_arsinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Arsinh", "is_tactic_proof": true, "tactics": ["apply", "rw", "apply", "simp"], "tactic_count": 4}
{"name": "Real.arsinh_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Arsinh", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.arsinh_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Arsinh", "is_tactic_proof": true, "tactics": ["rw", "apply", "rw", "exact"], "tactic_count": 4}
{"name": "Real.sinh_arsinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Arsinh", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.cosh_arsinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Arsinh", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.tanh_arsinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Arsinh", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.sinh_surjective", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Arsinh", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sinh_bijective", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Arsinh", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.arsinh_sinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Arsinh", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sinhEquiv", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Arsinh", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sinhOrderIso", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Arsinh", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sinhHomeomorph", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Arsinh", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.arsinh_bijective", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Arsinh", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.arsinh_injective", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Arsinh", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.arsinh_surjective", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Arsinh", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.arsinh_strictMono", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Arsinh", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.arsinh_inj", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Arsinh", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.arsinh_le_arsinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Arsinh", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.arsinh_lt_arsinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Arsinh", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.arsinh_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Arsinh", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.arsinh_nonneg_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Arsinh", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.arsinh_nonpos_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Arsinh", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.arsinh_pos_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Arsinh", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.arsinh_neg_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Arsinh", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.hasStrictDerivAt_arsinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Arsinh", "is_tactic_proof": false, "tactics": ["convert", "sinhHomeomorph.toOpenPartialHomeomorph.hasStrictDerivAt_symm", "exact"], "tactic_count": 3}
{"name": "Real.hasDerivAt_arsinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Arsinh", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.differentiable_arsinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Arsinh", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.contDiff_arsinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Arsinh", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.continuous_arsinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Arsinh", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.analyticAt_arsinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Arsinh", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.analyticWithinAt_arsinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Arsinh", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.analyticOnNhd_arsinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Arsinh", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.analyticOn_arsinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Arsinh", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.arsinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Arsinh", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.arsinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Arsinh", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.arsinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Arsinh", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.arsinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Arsinh", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.arsinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Arsinh", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictFDerivAt.arsinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Arsinh", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivAt.arsinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Arsinh", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivWithinAt.arsinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Arsinh", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableAt.arsinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Arsinh", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableWithinAt.arsinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Arsinh", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableOn.arsinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Arsinh", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Differentiable.arsinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Arsinh", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffAt.arsinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Arsinh", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffWithinAt.arsinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Arsinh", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.arsinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Arsinh", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffOn.arsinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Arsinh", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictDerivAt.arsinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Arsinh", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivAt.arsinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Arsinh", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivWithinAt.arsinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Arsinh", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.artanh", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Artanh", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.artanh_eq_half_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Artanh", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.exp_artanh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Artanh", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.artanh_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Artanh", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.sinh_artanh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Artanh", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "Real.cosh_artanh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Artanh", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "Real.tanh_artanh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Artanh", "is_tactic_proof": true, "tactics": ["have", "grind"], "tactic_count": 2}
{"name": "Real.artanh_tanh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Artanh", "is_tactic_proof": true, "tactics": ["have", "rw", "sq_sqrt", "field"], "tactic_count": 4}
{"name": "Real.strictMonoOn_one_add_div_one_sub", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Artanh", "is_tactic_proof": true, "tactics": ["intro", "field_simp", "grind"], "tactic_count": 3}
{"name": "Real.strictMonoOn_artanh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Artanh", "is_tactic_proof": true, "tactics": ["apply", "apply", "strictMonoOn_sqrt.comp", "show"], "tactic_count": 4}
{"name": "Real.artanh_le_artanh_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Artanh", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.artanh_lt_artanh_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Artanh", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.artanh_le_artanh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Artanh", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.artanh_lt_artanh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Artanh", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.artanh_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Artanh", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Real.artanh_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Artanh", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Real.artanh_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Artanh", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Real.artanh_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Artanh", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "exact", "grind"], "tactic_count": 4}
{"name": "Real.artanh_nonpos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Artanh", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "exact", "grind"], "tactic_count": 4}
{"name": "Real.tanhPartialEquiv", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Artanh", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.tanh_bijOn", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Artanh", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.tanh_injective", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Artanh", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.tanh_surjOn", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Artanh", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.artanh_bijOn", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Artanh", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.artanh_injOn", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Artanh", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.artanh_surjOn", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Artanh", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bernstein", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Bernstein", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bernstein_apply", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Bernstein", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "bernstein_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Bernstein", "is_tactic_proof": true, "tactics": ["simp", "have", "have", "positivity"], "tactic_count": 4}
{"name": "Mathlib.Meta.Positivity.evalBernstein", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Bernstein", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bernstein.z", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Bernstein", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.SpecialFunctions.Bernstein.0.bernstein.term_/ₙ", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Bernstein", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "bernstein.z_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Bernstein", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "bernstein.z_last", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Bernstein", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "bernstein.probability", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Bernstein", "is_tactic_proof": true, "tactics": ["have", "apply_fun", "simpa"], "tactic_count": 3}
{"name": "bernstein.variance", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Bernstein", "is_tactic_proof": true, "tactics": ["convert", "simp", "field_simp", "rw", "field", "simp", "field"], "tactic_count": 7}
{"name": "_private.Mathlib.Analysis.SpecialFunctions.Bernstein.0.term_/ₙ", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Bernstein", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "bernsteinApproximation", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Bernstein", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bernsteinApproximation.apply", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Bernstein", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "bernsteinApproximation.apply_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Bernstein", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "bernsteinApproximation.apply_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Bernstein", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "Real.binEntropy", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.BinaryEntropy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.binEntropy_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.BinaryEntropy", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.binEntropy_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.BinaryEntropy", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "Real.binEntropy_eq_negMulLog_add_negMulLog_one_sub", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.BinaryEntropy", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.binEntropy_eq_negMulLog_add_negMulLog_one_sub'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.BinaryEntropy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Real.binEntropy_two_inv_add", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.BinaryEntropy", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "Real.binEntropy_nonpos_of_nonpos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.BinaryEntropy", "is_tactic_proof": true, "tactics": ["obtain", "simp", "exact"], "tactic_count": 3}
{"name": "Real.binEntropy_neg_of_one_lt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.BinaryEntropy", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.binEntropy_nonpos_of_one_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.BinaryEntropy", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.binEntropy_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.BinaryEntropy", "is_tactic_proof": true, "tactics": ["refine", "contrapose", "obtain", "exact", "obtain", "exact", "exact"], "tactic_count": 7}
{"name": "Real.binEntropy_lt_log_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.BinaryEntropy", "is_tactic_proof": true, "tactics": ["refine", "rintro", "simp", "wlog", "have", "rw", "exact", "obtain", "exact", "have", "calc", "strictConcaveOn_log_Ioi.2"], "tactic_count": 12}
{"name": "Real.binEntropy_le_log_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.BinaryEntropy", "is_tactic_proof": true, "tactics": ["obtain", "simp", "exact"], "tactic_count": 3}
{"name": "Real.binEntropy_eq_log_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.BinaryEntropy", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.binEntropy_continuous", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.BinaryEntropy", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.differentiableAt_binEntropy", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.BinaryEntropy", "is_tactic_proof": true, "tactics": ["rw", "unfold", "simp", "fun_prop"], "tactic_count": 4}
{"name": "Real.differentiableAt_binEntropy_iff_ne_zero_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.BinaryEntropy", "is_tactic_proof": false, "tactics": ["refine", "rw", "simp", "fun_prop", "rw", "simp", "fun_prop"], "tactic_count": 7}
{"name": "Real.deriv_binEntropy", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.BinaryEntropy", "is_tactic_proof": true, "tactics": ["by_cases", "obtain", "rw", "rw", "deriv_negMulLog", "ring", "all_goals", "fun_prop", "rw", "push_neg", "obtain"], "tactic_count": 11}
{"name": "Real.qaryEntropy", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.BinaryEntropy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.qaryEntropy_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.BinaryEntropy", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.qaryEntropy_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.BinaryEntropy", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.qaryEntropy_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.BinaryEntropy", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Real.qaryEntropy_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.BinaryEntropy", "is_tactic_proof": true, "tactics": ["unfold", "positivity"], "tactic_count": 2}
{"name": "Real.qaryEntropy_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.BinaryEntropy", "is_tactic_proof": true, "tactics": ["obtain", "simp", "obtain", "simpa", "exact"], "tactic_count": 5}
{"name": "Real.qaryEntropy_neg_of_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.BinaryEntropy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.qaryEntropy_nonpos_of_nonpos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.BinaryEntropy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.qaryEntropy_continuous", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.BinaryEntropy", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "Real.differentiableAt_qaryEntropy", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.BinaryEntropy", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "Real.deriv_qaryEntropy", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.BinaryEntropy", "is_tactic_proof": true, "tactics": ["unfold", "rw", "simp", "one_mul,", "all_goals"], "tactic_count": 5}
{"name": "Real.hasDerivAt_binEntropy", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.BinaryEntropy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.hasDerivAt_qaryEntropy", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.BinaryEntropy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.SpecialFunctions.BinaryEntropy.0.Real.tendsto_log_one_sub_sub_log_nhdsGT_atAtop", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.BinaryEntropy", "is_tactic_proof": true, "tactics": ["apply", "have", "filter_upwards", "gcongr", "linarith", "apply"], "tactic_count": 6}
{"name": "_private.Mathlib.Analysis.SpecialFunctions.BinaryEntropy.0.Real.tendsto_log_one_sub_sub_log_nhdsLT_one_atBot", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.BinaryEntropy", "is_tactic_proof": true, "tactics": ["apply", "have", "apply", "have", "have", "intro", "simp_all", "convert", "exact", "have", "filter_upwards", "gcongr", "exact"], "tactic_count": 13}
{"name": "Real.not_continuousAt_deriv_qaryEntropy_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.BinaryEntropy", "is_tactic_proof": false, "tactics": ["have", "have", "ext", "ring", "rw", "apply", "exact", "apply", "simp", "filter_upwards", "intros", "apply", "simp_all", "linarith", "simp_all", "linarith"], "tactic_count": 16}
{"name": "Real.not_continuousAt_deriv_qaryEntropy_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.BinaryEntropy", "is_tactic_proof": false, "tactics": ["have", "have", "rw", "exact", "apply", "simp", "filter_upwards", "intros", "apply", "simp_all", "linarith", "simp_all", "linarith"], "tactic_count": 13}
{"name": "Real.deriv2_qaryEntropy", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.BinaryEntropy", "is_tactic_proof": true, "tactics": ["simp", "by_cases", "p", "p", "obtain", "suffices", "refine", "rw", "rw", "simp", "have", "have", "simp", "ring", "apply", "simp", "exact", "filter_upwards", "have", "rw", "simp_all", "cases", "intro", "have", "cases"], "tactic_count": 25}
{"name": "Real.deriv2_binEntropy", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.BinaryEntropy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.qaryEntropy_strictMonoOn", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.BinaryEntropy", "is_tactic_proof": true, "tactics": ["intro", "apply", "exact", "intro", "have", "have", "have", "simp", "have", "linarith", "simp", "rw", "simp", "rw", "apply", "simp_all", "have", "have", "convert", "simp", "linarith", "exact"], "tactic_count": 22}
{"name": "Real.qaryEntropy_strictAntiOn", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.BinaryEntropy", "is_tactic_proof": true, "tactics": ["intro", "apply", "exact", "intro", "have", "have", "have", "simp", "rw", "simp", "rw", "apply", "simp_all", "linarith", "have", "ring_nf", "simp", "have", "have", "have", "calc", "rwa", "nlinarith", "exact"], "tactic_count": 24}
{"name": "Real.binEntropy_strictMonoOn", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.BinaryEntropy", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Real.binEntropy_strictAntiOn", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.BinaryEntropy", "is_tactic_proof": true, "tactics": ["rw", "convert", "norm_num"], "tactic_count": 3}
{"name": "Real.strictConcaveOn_qaryEntropy", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.BinaryEntropy", "is_tactic_proof": true, "tactics": ["apply", "intro", "rw", "simp_all", "apply", "norm_num", "simp_all"], "tactic_count": 7}
{"name": "Real.strictConcave_binEntropy", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.BinaryEntropy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isEquivalent_descFactorial", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Choose", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "simp_rw", "refine", "have", "rw", "simpa"], "tactic_count": 8}
{"name": "isEquivalent_choose", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Choose", "is_tactic_proof": false, "tactics": ["conv_lhs", "intro", "rw", "cast_div", "exact"], "tactic_count": 5}
{"name": "isTheta_choose", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Choose", "is_tactic_proof": true, "tactics": ["apply", "simp_rw", "exact"], "tactic_count": 3}
{"name": "Complex.IsExpCmpFilter.of_isBigO_im_re_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.CompareExp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.IsExpCmpFilter.of_isBigO_im_re_pow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.CompareExp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.IsExpCmpFilter.of_boundedUnder_abs_im", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.CompareExp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.IsExpCmpFilter.of_boundedUnder_im", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.CompareExp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.IsExpCmpFilter.eventually_ne", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.CompareExp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.IsExpCmpFilter.tendsto_abs_re", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.CompareExp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.IsExpCmpFilter.tendsto_norm", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.CompareExp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.IsExpCmpFilter.isLittleO_log_re_re", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.CompareExp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.IsExpCmpFilter.isLittleO_im_pow_exp_re", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.CompareExp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.IsExpCmpFilter.abs_im_pow_eventuallyLE_exp_re", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.CompareExp", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Complex.IsExpCmpFilter.isLittleO_log_norm_re", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.CompareExp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.IsExpCmpFilter.isTheta_cpow_exp_re_mul_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.CompareExp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.IsExpCmpFilter.isLittleO_cpow_exp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.CompareExp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.IsExpCmpFilter.isLittleO_cpow_mul_exp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.CompareExp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.IsExpCmpFilter.isLittleO_exp_cpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.CompareExp", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Complex.IsExpCmpFilter.isLittleO_pow_mul_exp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.CompareExp", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Complex.IsExpCmpFilter.isLittleO_zpow_mul_exp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.CompareExp", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "analyticAt_clog", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Analytic", "is_tactic_proof": true, "tactics": ["rw", "filter_upwards", "intro", "exact"], "tactic_count": 4}
{"name": "AnalyticAt.clog", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Analytic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticWithinAt.clog", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Analytic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticOnNhd.clog", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Analytic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticOn.clog", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Analytic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticWithinAt.cpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Analytic", "is_tactic_proof": false, "tactics": ["have", "filter_upwards", "intro", "simp", "apply", "exact"], "tactic_count": 6}
{"name": "AnalyticAt.cpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Analytic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "AnalyticOn.cpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Analytic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticOnNhd.cpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Analytic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticAt.re_ofReal", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Analytic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticAt.im_ofReal", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Analytic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticWithinAt.re_ofReal", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Analytic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticWithinAt.im_ofReal", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Analytic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticOn.re_ofReal", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Analytic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticOn.im_ofReal", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Analytic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticOnNhd.re_ofReal", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Analytic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticOnNhd.im_ofReal", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Analytic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "analyticAt_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Analytic", "is_tactic_proof": true, "tactics": ["have", "rw", "refine", "simp"], "tactic_count": 4}
{"name": "analyticOnNhd_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Analytic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "analyticOn_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Analytic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticAt.log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Analytic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticWithinAt.log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Analytic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticOnNhd.log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Analytic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticOn.log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Analytic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.arctan", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arctan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.tan_arctan", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arctan", "is_tactic_proof": true, "tactics": ["unfold", "rw", "exp_zero,", "have", "contrapose", "rw", "exact", "have", "contrapose", "rw", "exact", "have", "rw", "exact", "rw", "show"], "tactic_count": 16}
{"name": "Complex.cos_ne_zero_of_arctan_bounds", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arctan", "is_tactic_proof": true, "tactics": ["refine", "rw", "norm_cast", "rcases", "left", "rw", "rw", "norm_cast", "change", "rwa", "exact"], "tactic_count": 11}
{"name": "Complex.arctan_tan", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arctan", "is_tactic_proof": true, "tactics": ["have", "unfold", "rw", "conv_lhs", "enter", "rw", "rw", "show", "all_goals", "rwa", "rwa"], "tactic_count": 11}
{"name": "Complex.ofReal_arctan", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arctan", "is_tactic_proof": true, "tactics": ["conv_rhs", "rw", "all_goals", "rw", "exact", "exact"], "tactic_count": 6}
{"name": "Complex.arg_one_add_mem_Ioo", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arctan", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Complex.hasSum_arctan_aux", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arctan", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "rw", "have", "have", "simp_rw", "exact", "have", "have", "rw", "rw", "exact"], "tactic_count": 13}
{"name": "Complex.hasSum_arctan", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arctan", "is_tactic_proof": false, "tactics": ["have", "simp_rw", "replace", "dsimp", "simp_rw", "refine", "dsimp", "convert", "rw", "zero_mul,", "show", "congr", "rw", "neg_neg,"], "tactic_count": 14}
{"name": "Real.hasSum_arctan", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arctan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.arg", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.sin_arg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["unfold", "split_ifs", "simp", "neg_div,"], "tactic_count": 4}
{"name": "Complex.cos_arg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["rw", "split_ifs", "rw", "field_simp", "simp", "field", "rw", "field_simp", "simp", "field", "rw", "field_simp", "simp", "field"], "tactic_count": 14}
{"name": "Complex.norm_mul_exp_arg_mul_I", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["rcases", "simp", "have", "apply"], "tactic_count": 4}
{"name": "Complex.norm_mul_cos_add_sin_mul_I", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.norm_mul_cos_arg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Complex.norm_mul_sin_arg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Complex.norm_eq_one_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["refine", "calc", "exp", "rintro", "exact"], "tactic_count": 5}
{"name": "Complex.range_exp_mul_I", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Complex.arg_mul_cos_add_sin_mul_I", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["simp", "simp", "mul_div_cancel_left₀", "by_cases", "rw", "exacts", "rw", "rcases", "replace", "have", "rw", "refine", "have", "rw", "exact", "replace", "have", "have", "rw", "exact"], "tactic_count": 20}
{"name": "Complex.arg_cos_add_sin_mul_I", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.arg_exp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["convert", "rw", "push_cast", "rw", "convert", "ring"], "tactic_count": 6}
{"name": "Complex.arg_exp_mul_I", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.arg_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.ext_norm_arg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.ext_norm_arg_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.arg_mem_Ioc", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["have", "rcases", "simp", "rcases", "rw", "rw", "have", "push_cast", "rwa"], "tactic_count": 9}
{"name": "Complex.toIocMod_arg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Complex.range_arg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.arg_le_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.neg_pi_lt_arg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.abs_arg_le_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.arg_nonneg_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["rcases", "calc", "contrapose", "intro", "exact"], "tactic_count": 5}
{"name": "Complex.arg_neg_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.arg_real_mul", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["rcases", "conv_lhs", "rw", "arg_mul_cos_add_sin_mul_I"], "tactic_count": 4}
{"name": "Complex.arg_mul_real", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.arg_eq_arg_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": false, "tactics": ["simp", "true_and]", "rw", "exact"], "tactic_count": 4}
{"name": "Complex.arg_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.arg_div_self", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "Complex.arg_neg_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.arg_I", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.arg_neg_I", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.tan_arg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "rw"], "tactic_count": 3}
{"name": "Complex.arg_ofReal_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.natCast_arg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.ofNat_arg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.arg_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["refine", "rw", "simp", "obtain", "rintro", "exact"], "tactic_count": 6}
{"name": "Complex.arg_eq_zero_iff_zero_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.arg_eq_pi_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "constructor", "intro", "rw", "simp", "obtain", "rintro", "rw", "simp"], "tactic_count": 10}
{"name": "Complex.arg_eq_pi_iff_lt_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.arg_lt_pi_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.arg_ofReal_of_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.arg_eq_pi_div_two_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["by_cases", "constructor", "intro", "rw", "simp", "obtain", "rintro", "rw"], "tactic_count": 8}
{"name": "Complex.arg_eq_neg_pi_div_two_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["by_cases", "constructor", "intro", "rw", "simp", "obtain", "rintro", "rw", "simp"], "tactic_count": 9}
{"name": "Complex.arg_of_re_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.arg_of_re_neg_of_im_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.arg_of_re_neg_of_im_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.arg_of_im_nonneg_of_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.arg_of_im_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.arg_of_im_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["have", "rw", "exacts"], "tactic_count": 3}
{"name": "Complex.arg_conj", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["simp_rw", "rcases", "simp", "simp", "simp", "simp", "simp", "simp", "simp", "simp", "simp"], "tactic_count": 11}
{"name": "Complex.arg_inv", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["rw", "by_cases", "simp", "exact"], "tactic_count": 4}
{"name": "Complex.abs_arg_inv", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["rw", "split_ifs", "simp"], "tactic_count": 3}
{"name": "Complex.norm_eq_one_iff'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["rw", "constructor", "rintro", "refine", "convert", "ring", "rw", "exp_mul_I_periodic.sub_zsmul_eq]", "rintro", "exact"], "tactic_count": 10}
{"name": "Complex.image_exp_Ioc_eq_sphere", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Complex.arg_le_pi_div_two_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simp", "rcases", "simp", "rw", "exacts", "simp", "rw", "exact"], "tactic_count": 10}
{"name": "Complex.neg_pi_div_two_le_arg_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simp", "rcases", "simp", "rw", "exact", "simp", "rw", "exacts"], "tactic_count": 10}
{"name": "Complex.neg_pi_div_two_lt_arg_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["rw", "rcases", "simp", "simp", "simp"], "tactic_count": 5}
{"name": "Complex.arg_lt_pi_div_two_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["rw", "rcases", "have", "simp", "have", "simp", "simp"], "tactic_count": 7}
{"name": "Complex.abs_arg_le_pi_div_two_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.abs_arg_lt_pi_div_two_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["rw", "rcases", "simp", "simp_rw"], "tactic_count": 4}
{"name": "Complex.arg_conj_coe_angle", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "Complex.arg_inv_coe_angle", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "Complex.arg_neg_eq_arg_sub_pi_of_im_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Complex.arg_neg_eq_arg_add_pi_of_im_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Complex.arg_neg_eq_arg_sub_pi_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rw", "rcases", "rw", "simp", "simp", "rw", "simp", "simp"], "tactic_count": 10}
{"name": "Complex.arg_neg_eq_arg_add_pi_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rw", "rcases", "rw", "simp", "simp", "rw", "simp", "simp"], "tactic_count": 10}
{"name": "Complex.arg_neg_coe_angle", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["rcases", "rw", "rw", "rcases", "rw", "two_mul,", "exact", "rw", "zero_add]", "rw"], "tactic_count": 10}
{"name": "Complex.arg_mul_cos_add_sin_mul_I_eq_toIocMod", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.arg_cos_add_sin_mul_I_eq_toIocMod", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.arg_mul_cos_add_sin_mul_I_sub", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["rw", "ring_nf"], "tactic_count": 2}
{"name": "Complex.arg_cos_add_sin_mul_I_sub", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.arg_mul_cos_add_sin_mul_I_coe_angle", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": false, "tactics": ["induction", "simp"], "tactic_count": 2}
{"name": "Complex.arg_cos_add_sin_mul_I_coe_angle", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.arg_mul_coe_angle", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": false, "tactics": ["convert", "arg_mul_cos_add_sin_mul_I_coe_angle", "simp_rw", "ofReal_add,", "rw", "norm_mul_exp_arg_mul_I]"], "tactic_count": 6}
{"name": "Complex.arg_div_coe_angle", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.arg_pow_coe_angle", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["obtain", "by_cases", "induction", "zero", "succ"], "tactic_count": 5}
{"name": "Complex.arg_zpow_coe_angle", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": [], "tactic_count": 0}
{"name": "Complex.arg_coe_angle_toReal_eq_arg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Complex.arg_coe_angle_eq_iff_eq_toReal", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.arg_coe_angle_eq_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Complex.arg_mul_eq_add_arg_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.mem_slitPlane_iff_arg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.slitPlane_arg_ne_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.exp_mem_slitPlane", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.arg_eq_nhds_of_re_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.arg_eq_nhds_of_re_neg_of_im_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": false, "tactics": ["suffices", "h_forall_nhds.mono", "refine", "exact"], "tactic_count": 4}
{"name": "Complex.arg_eq_nhds_of_re_neg_of_im_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": false, "tactics": ["suffices", "h_forall_nhds.mono", "refine", "exact"], "tactic_count": 4}
{"name": "Complex.arg_eq_nhds_of_im_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.arg_eq_nhds_of_im_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.continuousAt_arg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": false, "tactics": ["have", "rw", "exact", "rw", "rcases", "exacts"], "tactic_count": 6}
{"name": "Complex.continuousOn_arg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.tendsto_arg_nhdsWithin_im_neg_of_re_neg_of_im_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": false, "tactics": ["suffices", "refine", "have", "filter_upwards", "rw", "convert", "continuous_norm.continuousWithinAt", "π", "simp", "lift", "simpa"], "tactic_count": 11}
{"name": "Complex.continuousWithinAt_arg_of_re_neg_of_im_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": false, "tactics": ["have", "have", "filter_upwards", "rw", "refine", "refine", "continuous_norm.continuousWithinAt", "tendsto_const_nhds", "lift", "simpa", "rw"], "tactic_count": 11}
{"name": "Complex.tendsto_arg_nhdsWithin_im_nonneg_of_re_neg_of_im_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Complex.continuousAt_arg_coe_angle", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Arg", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "rw", "refine", "suffices", "rwa", "have", "rw", "exact", "rw", "replace", "push_neg", "refine", "rw", "exact"], "tactic_count": 15}
{"name": "Circle.injective_arg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Circle.arg_eq_arg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Circle.arg_exp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Circle", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Circle.exp_arg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Circle.argPartialEquiv", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Circle.argEquiv", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Circle.leftInverse_exp_arg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Circle.invOn_arg_exp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Circle.surjOn_exp_neg_pi_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Circle.exp_eq_exp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Circle", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "norm_cast"], "tactic_count": 4}
{"name": "Circle.periodic_exp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Circle.exp_two_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Circle.exp_int_mul_two_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Circle.exp_two_pi_mul_int", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Circle", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Circle.exp_eq_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Circle", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Circle.exp_inj", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Circle", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Circle.exp_sub_two_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Circle.exp_add_two_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.Angle.toCircle", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.Angle.toCircle_coe", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.Angle.coe_toCircle", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Circle", "is_tactic_proof": true, "tactics": ["induction", "simp"], "tactic_count": 2}
{"name": "Real.Angle.toCircle_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Circle", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.Angle.toCircle_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Circle", "is_tactic_proof": true, "tactics": ["induction", "simp_rw"], "tactic_count": 2}
{"name": "Real.Angle.toCircle_add", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Circle", "is_tactic_proof": true, "tactics": ["induction", "induction", "exact"], "tactic_count": 3}
{"name": "Real.Angle.arg_toCircle", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Circle", "is_tactic_proof": true, "tactics": ["induction", "rw", "arg_cos_add_sin_mul_I_coe_angle]"], "tactic_count": 3}
{"name": "AddCircle.scaled_exp_map_periodic", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Circle", "is_tactic_proof": true, "tactics": ["rcases", "simp", "intro"], "tactic_count": 3}
{"name": "AddCircle.toCircle", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCircle.toCircle_apply_mk", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCircle.toCircle_add", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Circle", "is_tactic_proof": true, "tactics": ["induction", "induction", "simp_rw"], "tactic_count": 3}
{"name": "AddCircle.toCircle_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Circle", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AddCircle.toCircle_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCircle.toCircle_nsmul", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Circle", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "AddCircle.toCircle_zsmul", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Circle", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "AddCircle.continuous_toCircle", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCircle.injective_toCircle", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Circle", "is_tactic_proof": true, "tactics": ["intro", "induction", "induction", "simp_rw", "obtain", "rw", "use", "field_simp", "linarith"], "tactic_count": 9}
{"name": "AddCircle.homeomorphCircle'", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCircle.homeomorphCircle'_apply_mk", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCircle.homeomorphCircle", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCircle.homeomorphCircle_apply", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Circle", "is_tactic_proof": true, "tactics": ["cases", "rw", "toCircle_apply_mk]", "ring_nf"], "tactic_count": 4}
{"name": "Circle.isAddQuotientCoveringMap_exp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Circle", "is_tactic_proof": true, "tactics": ["convert", "on_goal", "ext"], "tactic_count": 3}
{"name": "Circle.isCoveringMap_exp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLocalHomeomorph_circleExp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Circle.isQuotientCoveringMap_zpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Circle", "is_tactic_proof": true, "tactics": ["have", "let", "refine", "refine", "convert", "e.isQuotientMap.comp", "isQuotientMap_quotient_mk", "ext", "convert", "ext", "simp"], "tactic_count": 11}
{"name": "Circle.isQuotientCoveringMap_npow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Circle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCircle.toCircle_addChar", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Complex.CircleAddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.toCircle", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Complex.CircleAddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.toCircle_intCast", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.CircleAddChar", "is_tactic_proof": false, "tactics": ["rw", "toAddCircle_intCast,", "push_cast", "ring_nf"], "tactic_count": 4}
{"name": "ZMod.toCircle_natCast", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.CircleAddChar", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ZMod.toCircle_apply", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.CircleAddChar", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ZMod.toCircle_eq_circleExp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.CircleAddChar", "is_tactic_proof": true, "tactics": ["ext", "rw", "push_cast", "congr"], "tactic_count": 4}
{"name": "ZMod.injective_toCircle", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.CircleAddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.stdAddChar", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Complex.CircleAddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.stdAddChar_coe", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.CircleAddChar", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ZMod.stdAddChar_apply", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.CircleAddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.injective_stdAddChar", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.CircleAddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.isPrimitive_stdAddChar", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.CircleAddChar", "is_tactic_proof": true, "tactics": ["refine", "rwa"], "tactic_count": 2}
{"name": "ZMod.rootsOfUnityAddChar", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Complex.CircleAddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.rootsOfUnityAddChar_val", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.CircleAddChar", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "rootsOfUnitytoCircle", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Complex.CircleAddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "rootsOfUnityCircleEquiv", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Complex.CircleAddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instHasEnoughRootsOfUnityCircle", "kind": "instance", "module": "Mathlib.Analysis.SpecialFunctions.Complex.CircleAddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "rootsOfUnityCircleEquiv_apply", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.CircleAddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "rootsOfUnityCircleEquiv_comp_rootsOfUnityAddChar_val", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.CircleAddChar", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "surjective_rootsOfUnityCircleEquiv_comp_rootsOfUnityAddChar", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.CircleAddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bijective_rootsOfUnityAddChar", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.CircleAddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "circleMap", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Complex.CircleMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "circleMap_sub_center", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.CircleMap", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "circleMap_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.CircleMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "norm_circleMap_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.CircleMap", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "circleMap_notMem_ball", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.CircleMap", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "circleMap_ne_mem_ball", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.CircleMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "circleMap_mem_sphere'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.CircleMap", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "circleMap_mem_sphere", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.CircleMap", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "circleMap_mem_closedBall", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.CircleMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "circleMap_eq_center_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.CircleMap", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "circleMap_zero_radius", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.CircleMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "circleMap_ne_center", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.CircleMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "circleMap_zero_mul", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.CircleMap", "is_tactic_proof": true, "tactics": ["simp", "ring"], "tactic_count": 2}
{"name": "circleMap_zero_div", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.CircleMap", "is_tactic_proof": true, "tactics": ["simp", "ring"], "tactic_count": 2}
{"name": "circleMap_zero_inv", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.CircleMap", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "circleMap_zero_pow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.CircleMap", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "circleMap_zero_zpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.CircleMap", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "circleMap_pi_div_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.CircleMap", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "circleMap_neg_pi_div_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.CircleMap", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "periodic_circleMap", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.CircleMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Countable.preimage_circleMap", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.CircleMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "circleMap_eq_circleMap_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.CircleMap", "is_tactic_proof": false, "tactics": ["have", "simp", "simp"], "tactic_count": 3}
{"name": "eq_of_circleMap_eq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.CircleMap", "is_tactic_proof": true, "tactics": ["rw", "obtain", "simp", "norm_cast", "simp", "abs_of_pos", "simp", "norm_cast", "simp"], "tactic_count": 9}
{"name": "injOn_circleMap_of_abs_sub_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.CircleMap", "is_tactic_proof": true, "tactics": ["rintro", "apply", "rw", "constructor"], "tactic_count": 4}
{"name": "injOn_circleMap_of_abs_sub_le'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.CircleMap", "is_tactic_proof": true, "tactics": ["rintro", "apply", "rw", "constructor"], "tactic_count": 4}
{"name": "Complex.log", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Log", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.log_re", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Log", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.log_im", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Log", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.neg_pi_lt_log_im", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Log", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.log_im_le_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Log", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.exp_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Log", "is_tactic_proof": true, "tactics": ["rw", "mul_div_cancel₀", "mul_div_cancel₀"], "tactic_count": 3}
{"name": "Complex.range_exp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Log", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.log_exp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Log", "is_tactic_proof": true, "tactics": ["rw", "arg_mul_cos_add_sin_mul_I"], "tactic_count": 2}
{"name": "Complex.log_exp_eq_re_add_toIocMod", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Log", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.log_exp_eq_sub_toIocDiv", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Log", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Complex.exp_inj_of_neg_pi_lt_of_le_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Log", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.ofReal_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Log", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.natCast_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Log", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.ofNat_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Log", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.log_ofReal_re", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Log", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.log_ofReal_mul", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Log", "is_tactic_proof": true, "tactics": ["replace", "simp_rw", "add_assoc]"], "tactic_count": 3}
{"name": "Complex.log_mul_ofReal", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Log", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.log_mul_eq_add_log_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Log", "is_tactic_proof": true, "tactics": ["refine", "simp_rw", "true_and]"], "tactic_count": 3}
{"name": "Complex.log_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Log", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.log_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Log", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.log_div_self", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Log", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.log_neg_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Log", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.log_I", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Log", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.log_neg_I", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Log", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.log_conj_eq_ite", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Log", "is_tactic_proof": true, "tactics": ["simp_rw", "split_ifs", "rw", "simp_rw"], "tactic_count": 4}
{"name": "Complex.log_conj", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Log", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.log_inv_eq_ite", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Log", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "rw", "simp_rw", "neg_add,", "norm_num", "grind", "rwa", "rwa"], "tactic_count": 9}
{"name": "Complex.log_inv", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Log", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.two_pi_I_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Log", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.exp_eq_one_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Log", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rcases", "use", "rw", "have", "rw", "rintro", "exact"], "tactic_count": 9}
{"name": "Complex.exp_eq_exp_iff_exp_sub_eq_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Log", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.exp_eq_exp_iff_exists_int", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Log", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.log_exp_exists", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Log", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Complex.countable_preimage_exp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Log", "is_tactic_proof": true, "tactics": ["refine", "refine", "rw", "exact", "rw", "refine", "by_cases", "rcases", "simp", "exact", "simp"], "tactic_count": 11}
{"name": "Complex.tendsto_log_nhdsWithin_im_neg_of_re_neg_of_im_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Log", "is_tactic_proof": false, "tactics": ["convert", "tendsto_const_nhds)", "simp", "lift", "simpa"], "tactic_count": 5}
{"name": "Complex.continuousWithinAt_log_of_re_neg_of_im_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Log", "is_tactic_proof": false, "tactics": ["convert", "continuousWithinAt_arg_of_re_neg_of_im_zero", "tendsto_const_nhds)", "lift", "simpa"], "tactic_count": 5}
{"name": "Complex.tendsto_log_nhdsWithin_im_nonneg_of_re_neg_of_im_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Log", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Complex.map_exp_comap_re_atBot", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Log", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.map_exp_comap_re_atTop", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Log", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "continuousAt_clog", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Log", "is_tactic_proof": true, "tactics": ["refine", "refine", "refine", "exact", "have", "refine", "exact"], "tactic_count": 7}
{"name": "Filter.Tendsto.clog", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Log", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.clog", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Log", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.clog", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Log", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.clog", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Log", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.clog", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Log", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.expOpenPartialHomeomorph", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Complex.Log", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.continuousOn_one_add_mul_inv", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.LogBounds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.log_eq_integral", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.LogBounds", "is_tactic_proof": false, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "Complex.log_inv_eq_integral", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.LogBounds", "is_tactic_proof": true, "tactics": ["rw", "rw", "convert", "rw"], "tactic_count": 4}
{"name": "Complex.logTaylor", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Complex.LogBounds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.logTaylor_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.LogBounds", "is_tactic_proof": true, "tactics": ["funext", "simp"], "tactic_count": 2}
{"name": "Complex.logTaylor_succ", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.LogBounds", "is_tactic_proof": true, "tactics": ["funext", "simpa"], "tactic_count": 2}
{"name": "Complex.logTaylor_at_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.LogBounds", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Complex.hasDerivAt_logTaylor", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.LogBounds", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "simp", "refine", "simp", "have", "simp_rw", "convert", "simp", "convert", "ring"], "tactic_count": 13}
{"name": "Complex.hasDerivAt_log_sub_logTaylor", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.LogBounds", "is_tactic_proof": true, "tactics": ["convert", "have", "intro", "rw", "simp", "exact", "simp_rw", "simp"], "tactic_count": 8}
{"name": "Complex.norm_one_add_mul_inv_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.LogBounds", "is_tactic_proof": true, "tactics": ["rw", "rw", "refine", "calc", "rw", "convert", "exact"], "tactic_count": 7}
{"name": "Complex.integrable_pow_mul_norm_one_add_mul_inv", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.LogBounds", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "Complex.norm_log_sub_logTaylor_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.LogBounds", "is_tactic_proof": false, "tactics": ["have", "let", "let", "have", "intro", "rw", "exact", "hasDerivAt_log_sub_logTaylor", "have", "simp", "exact", "have", "convert", "simp", "simp", "unfold", "simp", "simp_rw", "intervalIntegral.integral_const_mul,", "pow_succ',", "gcongr", "calc", "refine", "filter_upwards", "rw", "gcongr", "exact", "rw", "simp"], "tactic_count": 29}
{"name": "Complex.norm_log_one_add_sub_self_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.LogBounds", "is_tactic_proof": true, "tactics": ["convert", "simp", "norm_num"], "tactic_count": 3}
{"name": "Complex.log_sub_logTaylor_isBigO", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.LogBounds", "is_tactic_proof": true, "tactics": ["rw", "use", "filter_upwards", "rw", "have", "apply", "rw", "gcongr"], "tactic_count": 8}
{"name": "Complex.log_sub_self_isBigO", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.LogBounds", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "Complex.norm_log_one_add_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.LogBounds", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Complex.norm_log_one_add_half_le_self", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.LogBounds", "is_tactic_proof": true, "tactics": ["apply", "have", "rw", "linarith", "linarith", "have", "gcongr", "rw", "linarith", "rw", "gcongr", "simp", "linarith"], "tactic_count": 13}
{"name": "Complex.norm_log_one_sub_inv_add_logTaylor_neg_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.LogBounds", "is_tactic_proof": false, "tactics": ["rw", "sub_neg_eq_add,", "convert"], "tactic_count": 3}
{"name": "Complex.norm_log_one_sub_inv_sub_self_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.LogBounds", "is_tactic_proof": true, "tactics": ["convert", "simp", "norm_num"], "tactic_count": 3}
{"name": "Complex.hasSum_taylorSeries_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.LogBounds", "is_tactic_proof": true, "tactics": ["refine", "refine", "intro", "simp", "rcases", "simp", "conv", "gcongr", "norm_cast", "rw", "conv", "rw", "refine", "have", "have", "rw", "cases", "zero", "succ", "refine", "rw", "gcongr", "exact", "linarith", "exact", "refine", "convert", "exact"], "tactic_count": 28}
{"name": "Complex.hasSum_taylorSeries_neg_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.LogBounds", "is_tactic_proof": true, "tactics": ["conv", "refine", "convert", "rcases", "simp", "simp"], "tactic_count": 6}
{"name": "Complex.tendsto_mul_log_one_add_of_tendsto", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.LogBounds", "is_tactic_proof": true, "tactics": ["apply", "refine", "simp_rw", "calc", "have", "tendsto_zero_of_isBoundedUnder_smul_of_tendsto_cobounded", "exact", "filter_upwards", "rw", "ring"], "tactic_count": 10}
{"name": "Complex.tendsto_one_add_cpow_exp_of_tendsto", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.LogBounds", "is_tactic_proof": true, "tactics": ["apply", "have", "tendsto_zero_of_isBoundedUnder_smul_of_tendsto_cobounded", "filter_upwards", "dsimp", "rw", "intro", "rw", "norm_num"], "tactic_count": 9}
{"name": "Complex.tendsto_one_add_div_cpow_exp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.LogBounds", "is_tactic_proof": true, "tactics": ["apply", "apply", "filter_upwards", "exact"], "tactic_count": 4}
{"name": "Complex.tendsto_nat_mul_log_one_add_of_tendsto", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.LogBounds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.tendsto_one_add_pow_exp_of_tendsto", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.LogBounds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.tendsto_one_add_div_pow_exp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.LogBounds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.tendsto_mul_log_one_add_of_tendsto", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.LogBounds", "is_tactic_proof": false, "tactics": ["have", "tendsto_zero_of_isBoundedUnder_smul_of_tendsto_cobounded", "rw", "push_cast", "apply", "filter_upwards", "rw"], "tactic_count": 7}
{"name": "Real.tendsto_mul_log_one_add_div_atTop", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.LogBounds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.tendsto_one_add_rpow_exp_of_tendsto", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.LogBounds", "is_tactic_proof": false, "tactics": ["have", "tendsto_zero_of_isBoundedUnder_smul_of_tendsto_cobounded", "rw", "push_cast", "apply", "filter_upwards", "rw"], "tactic_count": 7}
{"name": "Real.tendsto_one_add_div_rpow_exp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.LogBounds", "is_tactic_proof": true, "tactics": ["apply", "apply", "filter_upwards", "exact"], "tactic_count": 4}
{"name": "Real.tendsto_nat_mul_log_one_add_of_tendsto", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.LogBounds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.tendsto_one_add_pow_exp_of_tendsto", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.LogBounds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.tendsto_one_add_div_pow_exp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.LogBounds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.isOpenMap_exp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.LogDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.hasStrictDerivAt_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.LogDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.hasDerivAt_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.LogDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.differentiableAt_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.LogDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.hasStrictFDerivAt_log_real", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.LogDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.contDiffAt_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.LogDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictFDerivAt.clog", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.LogDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictDerivAt.clog", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.LogDeriv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HasStrictDerivAt.clog_real", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.LogDeriv", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasFDerivAt.clog", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.LogDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivAt.clog", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.LogDeriv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HasDerivAt.clog_real", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.LogDeriv", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "DifferentiableAt.clog", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.LogDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivWithinAt.clog", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.LogDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivWithinAt.clog", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.LogDeriv", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "HasDerivWithinAt.clog_real", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.LogDeriv", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "DifferentiableWithinAt.clog", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.LogDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableOn.clog", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.LogDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Differentiable.clog", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.LogDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.deriv_log_comp_eq_logDeriv", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.LogDeriv", "is_tactic_proof": true, "tactics": ["have", "rw", "simp"], "tactic_count": 3}
{"name": "MeromorphicOn.logDeriv", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.LogDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Meromorphic.logDeriv", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Complex.LogDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CFC.abs", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CFC.abs_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Abs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CFC.abs_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CFC.abs_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Abs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CFC.abs_mul_abs", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.cfcAbs_left", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.cfcAbs_right", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.cfcAbs_cfcAbs", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.cfcAbs_mul_eq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Abs", "is_tactic_proof": true, "tactics": ["have", "rw", "hab.mul_mul_mul_comm,"], "tactic_count": 3}
{"name": "CFC.abs_nnrpow_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Abs", "is_tactic_proof": true, "tactics": ["simp", "apply"], "tactic_count": 2}
{"name": "CFC.abs_nnrpow_two_mul", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Abs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CFC.abs_nnrpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Abs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CFC.cfcAbs_cfcAbs", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CFC.abs_smul_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Abs", "is_tactic_proof": true, "tactics": ["suffices", "intro", "rw", "simp"], "tactic_count": 4}
{"name": "cfcₙ_norm_sq_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cfcₙ_norm_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CFC.abs_smul", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Abs", "is_tactic_proof": true, "tactics": ["trans", "simp", "simp", "lift", "simp"], "tactic_count": 5}
{"name": "CFC.abs_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Abs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CFC.abs_algebraMap_nnreal", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Abs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CFC.abs_natCast", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Abs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CFC.abs_ofNat", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Abs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CFC.abs_intCast", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Abs", "is_tactic_proof": true, "tactics": ["cases", "ofNat", "negSucc", "rw", "congr"], "tactic_count": 5}
{"name": "CFC.abs_algebraMap", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Abs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CFC.abs_sq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Abs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CFC.continuous_abs", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CFC.abs_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Abs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CFC.norm_abs", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Abs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NormedSpace.exp_continuousMap_eq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.ExpLog.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp_rw", "have", "simp_rw", "simp"], "tactic_count": 5}
{"name": "IsSelfAdjoint.exp_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.ExpLog.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CFC.log", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.ExpLog.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSelfAdjoint.log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.ExpLog.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CFC.log_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.ExpLog.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CFC.log_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.ExpLog.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CFC.log_algebraMap", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.ExpLog.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CFC.continuousOn_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.ExpLog.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CFC.log_monotoneOn", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.ExpLog.Order", "is_tactic_proof": true, "tactics": ["of", "fact", "monotone", "let", "let", "let", "have", "refine", "refine", "rw", "intro", "by_cases", "have", "exact", "simp", "eventually", "have", "filter_upwards", "have", "intro", "simp", "rw", "cfc_sub", "refine", "gcongr", "grind"], "tactic_count": 26}
{"name": "CStarAlgebra.instPosPart", "kind": "instance", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.PosPart.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarAlgebra.instNegPart", "kind": "instance", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.PosPart.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CFC.posPart_def", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.PosPart.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CFC.negPart_def", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.PosPart.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CFC.posPart_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.PosPart.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CFC.negPart_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.PosPart.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CFC.posPart_eq_zero_of_not_isSelfAdjoint", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.PosPart.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CFC.negPart_eq_zero_of_not_isSelfAdjoint", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.PosPart.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CFC.posPart_mul_negPart", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.PosPart.Basic", "is_tactic_proof": true, "tactics": ["rw", "by_cases", "rw", "refine", "simp", "simpa", "simp"], "tactic_count": 7}
{"name": "CFC.negPart_mul_posPart", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.PosPart.Basic", "is_tactic_proof": true, "tactics": ["rw", "by_cases", "rw", "refine", "simp", "simpa", "simp"], "tactic_count": 7}
{"name": "CFC.posPart_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.PosPart.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "congr", "have", "rw"], "tactic_count": 5}
{"name": "CFC.negPart_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.PosPart.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CFC.posPart_smul", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.PosPart.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "rw", "refine", "simp", "obtain", "simp", "have", "simp"], "tactic_count": 9}
{"name": "CFC.negPart_smul", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.PosPart.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CFC.posPart_smul_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.PosPart.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CFC.posPart_smul_of_nonpos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.PosPart.Basic", "is_tactic_proof": true, "tactics": ["nth_rw", "rw"], "tactic_count": 2}
{"name": "CFC.negPart_smul_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.PosPart.Basic", "is_tactic_proof": true, "tactics": ["conv_lhs"], "tactic_count": 1}
{"name": "CFC.negPart_smul_of_nonpos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.PosPart.Basic", "is_tactic_proof": true, "tactics": ["conv_lhs"], "tactic_count": 1}
{"name": "CFC.posPart_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.PosPart.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CFC.negPart_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.PosPart.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CFC.posPart_eq_self", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.PosPart.Basic", "is_tactic_proof": true, "tactics": ["refine", "conv_rhs", "rw", "refine", "simpa"], "tactic_count": 5}
{"name": "CFC.negPart_eq_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.PosPart.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "rw", "have", "conv_lhs", "refine", "rw", "rw", "simpa"], "tactic_count": 10}
{"name": "_private.Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.PosPart.Basic.0.CFC.termσₙ", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.PosPart.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.PosPart.Basic.0.CFC._aux_Mathlib_Analysis_SpecialFunctions_ContinuousFunctionalCalculus_PosPart_Basic___macroRules__private_Mathlib_Analysis_SpecialFunctions_ContinuousFunctionalCalculus_PosPart_Basic_0_CFC_termσₙ_1", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.PosPart.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.PosPart.Basic.0.CFC._aux_Mathlib_Analysis_SpecialFunctions_ContinuousFunctionalCalculus_PosPart_Basic___unexpand_quasispectrum_1", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.PosPart.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CFC.posPart_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.PosPart.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "CFC.negPart_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.PosPart.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "CFC.posPart_algebraMap", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.PosPart.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "CFC.negPart_algebraMap", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.PosPart.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "CFC.posPart_algebraMap_nnreal", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.PosPart.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "CFC.posPart_natCast", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.PosPart.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CStarAlgebra.linear_combination_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.PosPart.Basic", "is_tactic_proof": true, "tactics": ["rw", "realPart_add_I_smul_imaginaryPart"], "tactic_count": 2}
{"name": "CStarAlgebra.span_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.PosPart.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "apply_rules", "all_goals", "refine", "first", "apply", "apply"], "tactic_count": 8}
{"name": "CStarAlgebra.norm_posPart_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.PosPart.Isometric", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "refine", "obtain", "simp", "simp", "exact"], "tactic_count": 7}
{"name": "CStarAlgebra.norm_negPart_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.PosPart.Isometric", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "NNReal.nnrpow", "kind": "abbrev", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.nnrpow_def", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.continuous_nnrpow_const", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.monotone_nnrpow_const", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CFC.nnrpow", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CFC.instPowNNReal", "kind": "instance", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CFC.nnrpow_eq_pow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CFC.nnrpow_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CFC.nnrpow_def", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CFC.nnrpow_add", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic", "is_tactic_proof": true, "tactics": ["simp", "rw", "congr", "exact"], "tactic_count": 4}
{"name": "CFC.nnrpow_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CFC.zero_nnrpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CFC.nnrpow_nnrpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "obtain", "all_goals", "simp", "rw", "congr", "ext", "simp", "simp"], "tactic_count": 9}
{"name": "CFC.sqrt", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CFC.sqrt_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CFC.sqrt_eq_nnrpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic", "is_tactic_proof": true, "tactics": ["simp", "congr", "ext", "exact_mod_cast"], "tactic_count": 4}
{"name": "CFC.sqrt_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CFC.nnrpow_sqrt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CFC.sqrt_nnrpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CStarAlgebra.nonneg_TFAE", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic", "is_tactic_proof": true, "tactics": ["tfae_have", "tfae_have", "tfae_have", "tfae_have", "tfae_have", "tfae_have", "tfae_have", "tfae_have", "tfae_have", "tfae_finish"], "tactic_count": 10}
{"name": "CStarAlgebra.nonneg_iff_eq_sqrt_mul_sqrt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarAlgebra.nonneg_iff_exists_nonneg_and_eq_mul_self", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarAlgebra.nonneg_iff_exists_isSelfAdjoint_and_eq_mul_self", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarAlgebra.nonneg_iff_eq_star_mul_self", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarAlgebra.nonneg_iff_eq_mul_star_self", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarAlgebra.nonneg_iff_isSelfAdjoint_and_negPart_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CFC.rpow", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CFC.instPowReal", "kind": "instance", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CFC.rpow_eq_pow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CFC.rpow_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CFC.rpow_def", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CFC.one_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CFC.zero_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CFC.rpow_algebraMap", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CFC.rpow_add", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic", "is_tactic_proof": true, "tactics": ["have", "simp", "rw", "refine", "intro", "have", "simp"], "tactic_count": 7}
{"name": "CFC.rpow_neg_one_eq_cfc_inv", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CFC.nnrpow_eq_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CFC.sqrt_eq_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "CFC.sqrt_eq_cfc", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic", "is_tactic_proof": true, "tactics": ["unfold", "rw"], "tactic_count": 2}
{"name": "CFC.sqrt_algebraMap", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CFC.sqrt_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CFC.sqrt_eq_one_iff'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "cfc_tac"], "tactic_count": 3}
{"name": "CFC.sqrt_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "simp"], "tactic_count": 3}
{"name": "CFC.sqrt_rpow_nnreal", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "cases", "inl", "inr", "have", "have", "rw"], "tactic_count": 8}
{"name": "IsStrictlyPositive.nnrpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "IsStrictlyPositive.sqrt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "IsStrictlyPositive.rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "CStarAlgebra.isStrictlyPositive_TFAE", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic", "is_tactic_proof": true, "tactics": ["tfae_have", "tfae_have", "tfae_have", "tfae_have", "tfae_have", "tfae_have", "tfae_have", "tfae_have", "tfae_have", "tfae_finish"], "tactic_count": 10}
{"name": "CStarAlgebra.isStrictlyPositive_iff_isStrictlyPositive_sqrt_and_eq_sqrt_mul_sqrt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarAlgebra.isStrictlyPositive_iff_isUnit_sqrt_and_eq_sqrt_mul_sqrt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarAlgebra.isStrictlyPositive_iff_exists_isStrictlyPositive_and_eq_mul_self", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarAlgebra.isStrictlyPositive_iff_exists_isUnit_and_isSelfAdjoint_and_eq_mul_self", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarAlgebra.isStrictlyPositive_iff_eq_star_mul_self", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarAlgebra.isStrictlyPositive_iff_eq_mul_star_self", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CStarAlgebra.isStrictlyPositive_iff_isSelfAdjoint_and_spectrum_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.rpowIntegrand₀₁", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.IntegralRepresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.rpowIntegrand₀₁_zero_right", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.IntegralRepresentation", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.rpowIntegrand₀₁_zero_left", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.IntegralRepresentation", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.rpowIntegrand₀₁_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.IntegralRepresentation", "is_tactic_proof": true, "tactics": ["unfold", "cases", "inl", "inr", "refine", "rw", "gcongr", "linarith"], "tactic_count": 8}
{"name": "Real.rpowIntegrand₀₁_eq_pow_div", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.IntegralRepresentation", "is_tactic_proof": true, "tactics": ["by_cases", "have", "calc", "simp", "rw", "simp", "push", "have", "simp"], "tactic_count": 9}
{"name": "Real.rpowIntegrand₀₁_eqOn_pow_div", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.IntegralRepresentation", "is_tactic_proof": true, "tactics": ["intro", "simp"], "tactic_count": 2}
{"name": "Real.rpowIntegrand₀₁_apply_mul", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.IntegralRepresentation", "is_tactic_proof": true, "tactics": ["have", "rw", "by_cases", "calc", "have", "rw", "rw", "simp"], "tactic_count": 8}
{"name": "Real.rpowIntegrand₀₁_apply_mul'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.IntegralRepresentation", "is_tactic_proof": true, "tactics": ["simp", "congr", "simpa"], "tactic_count": 3}
{"name": "Real.rpowIntegrand₀₁_apply_mul_eqOn_Ici", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.IntegralRepresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.continuousOn_rpowIntegrand₀₁", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.IntegralRepresentation", "is_tactic_proof": true, "tactics": ["refine", "have", "fun_prop"], "tactic_count": 3}
{"name": "Real.aestronglyMeasurable_rpowIntegrand₀₁", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.IntegralRepresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.rpowIntegrand₀₁_monotoneOn", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.IntegralRepresentation", "is_tactic_proof": true, "tactics": ["intro", "by_cases", "simpa", "simp", "gcongr"], "tactic_count": 5}
{"name": "Real.continuousOn_rpowIntegrand₀₁_uncurry", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.IntegralRepresentation", "is_tactic_proof": true, "tactics": ["let", "refine", "simp", "refine", "refine", "exact", "exact", "intro", "simp"], "tactic_count": 9}
{"name": "Real.continuousOn_rpowIntegrand₀₁_Ici", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.IntegralRepresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.rpowIntegrand₀₁_le_rpow_sub_two_mul_self", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.IntegralRepresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.rpowIntegrand₀₁_le_rpow_sub_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.IntegralRepresentation", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "positivity", "calc"], "tactic_count": 4}
{"name": "Real.rpowIntegrand₀₁_one_ge_rpow_sub_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.IntegralRepresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.rpowIntegrand₀₁_eqOn_mul_rpowIntegrand₀₁_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.IntegralRepresentation", "is_tactic_proof": true, "tactics": ["intro", "calc", "rw", "ring", "simp"], "tactic_count": 5}
{"name": "_private.Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.IntegralRepresentation.0.Real.integrableOn_rpowIntegrand₀₁_Ioc", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.IntegralRepresentation", "is_tactic_proof": true, "tactics": ["refine", "refine", "refine", "exact", "refine", "apply", "rw", "rw", "linarith", "exact", "refine", "rw", "exact"], "tactic_count": 13}
{"name": "_private.Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.IntegralRepresentation.0.Real.integrableOn_rpowIntegrand₀₁_Ioi_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.IntegralRepresentation", "is_tactic_proof": true, "tactics": ["refine", "refine", "exact", "refine", "refine", "apply", "rw", "refine", "linarith", "refine", "rw", "exact"], "tactic_count": 12}
{"name": "Real.integrableOn_rpowIntegrand₀₁_Ioi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.IntegralRepresentation", "is_tactic_proof": true, "tactics": ["infinity.", "rw", "exact"], "tactic_count": 3}
{"name": "Real.integrableOn_rpowIntegrand₀₁_Ici", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.IntegralRepresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.integral_rpowIntegrand₀₁_eq_rpow_mul_const", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.IntegralRepresentation", "is_tactic_proof": true, "tactics": ["obtain", "simp", "suffices", "rwa", "exact", "simpa", "simpa", "simpa", "simp", "rw", "exact", "have", "simp", "integral_smul_const]", "rw"], "tactic_count": 15}
{"name": "Real.le_integral_rpowIntegrand₀₁_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.IntegralRepresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.integral_rpowIntegrand₀₁_one_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.IntegralRepresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.rpow_eq_const_mul_integral", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.IntegralRepresentation", "is_tactic_proof": true, "tactics": ["rcases", "push", "simp", "have", "rw"], "tactic_count": 5}
{"name": "Real.exists_measure_rpow_eq_integral", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.IntegralRepresentation", "is_tactic_proof": false, "tactics": ["let", "property", "rw", "exact", "refine", "unfold", "rw", "exact", "simp_rw"], "tactic_count": 9}
{"name": "CFC.cfcₙ_rpowIntegrand₀₁_eq_cfcₙ_rpowIntegrand₀₁_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.IntegralRepresentation", "is_tactic_proof": true, "tactics": ["have", "have", "intro", "simp", "positivity", "calc", "refine", "refine", "refine", "refine", "have", "fun_prop", "congr", "refine", "exact"], "tactic_count": 15}
{"name": "CFC.exists_measure_nnrpow_eq_integral_cfcₙ_rpowIntegrand₀₁", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.IntegralRepresentation", "is_tactic_proof": true, "tactics": ["obtain", "refine", "nontriviality", "have", "let", "let", "have", "let", "have", "refine", "grind", "have", "filter_upwards", "intro", "have", "unfold", "rw", "refine", "exact", "have", "rw", "exact", "have", "filter_upwards", "simp", "refine", "exact", "calc", "a", "rw", "exact"], "tactic_count": 31}
{"name": "CFC.monotoneOn_cfcₙ_rpowIntegrand₀₁", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.IntegralRepresentation", "is_tactic_proof": true, "tactics": ["intro", "calc", "rw", "gcongr", "unfold", "simp", "refine", "all_goals"], "tactic_count": 8}
{"name": "CFC.continuousOn_sqrt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Isometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CFC.continuousOn_nnrpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Isometric", "is_tactic_proof": true, "tactics": ["obtain", "simpa", "exact"], "tactic_count": 3}
{"name": "CFC.continuousOn_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Isometric", "is_tactic_proof": true, "tactics": ["refine", "simp_rw", "exact"], "tactic_count": 3}
{"name": "_private.Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Order.0.CFC.monotoneOn_nnrpow_Ioo", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Order", "is_tactic_proof": true, "tactics": ["obtain", "have", "refine", "refine", "filter_upwards", "exact"], "tactic_count": 6}
{"name": "CFC.monotone_nnrpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Order", "is_tactic_proof": true, "tactics": ["intro", "by_cases", "have", "have", "rw", "obtain", "exact", "simp_all", "simp_all", "have", "simp"], "tactic_count": 11}
{"name": "CFC.monotone_sqrt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Order", "is_tactic_proof": true, "tactics": ["intro", "rw", "refine", "constructor"], "tactic_count": 4}
{"name": "CFC.nnrpow_le_nnrpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CFC.sqrt_le_sqrt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CFC.monotone_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Order", "is_tactic_proof": true, "tactics": ["let", "change", "cases", "inl", "simp_rw", "exact", "inr", "simp", "intro", "by_cases", "have", "simp", "have", "simp"], "tactic_count": 14}
{"name": "CFC.rpow_le_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PeriodPair.basis", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PeriodPair.basis_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PeriodPair.basis_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PeriodPair.lattice", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PeriodPair.mem_lattice", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PeriodPair.ω₁_mem_lattice", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PeriodPair.ω₂_mem_lattice", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PeriodPair.mul_ω₁_add_mul_ω₂_mem_lattice", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["refine", "obtain", "have", "simp", "norm_cast", "aesop", "lift", "lift", "simp", "exact"], "tactic_count": 10}
{"name": "PeriodPair.ω₁_div_two_notMem_lattice", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "PeriodPair.ω₂_div_two_notMem_lattice", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "PeriodPair.lattice_eq_span_range_basis", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["have", "rw", "simp"], "tactic_count": 3}
{"name": "PeriodPair.instDiscreteTopologySubtypeComplexMemSubmoduleIntLattice", "kind": "instance", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PeriodPair.instIsZLatticeRealComplexLattice", "kind": "instance", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["simp_rw", "infer_instance"], "tactic_count": 2}
{"name": "PeriodPair.isClosed_lattice", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PeriodPair.isClosed_of_subset_lattice", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["convert", "convert", "simpa"], "tactic_count": 3}
{"name": "PeriodPair.isOpen_compl_lattice_diff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PeriodPair.compl_lattice_diff_singleton_mem_nhds", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PeriodPair.instProperSpaceSubtypeComplexMemSubmoduleIntLattice", "kind": "instance", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PeriodPair.latticeBasis", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PeriodPair.latticeBasis_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PeriodPair.latticeBasis_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PeriodPair.finrank_lattice", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PeriodPair.latticeEquivProd", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PeriodPair.latticeEquiv_symm_apply", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PeriodPair.hasSumLocallyUniformly_aux", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["rw", "intro", "obtain", "refine", "rw", "refine", "obtain", "refine", "intros", "obtain", "simp", "contrapose", "exact"], "tactic_count": 13}
{"name": "PeriodPair.weierstrassP_bound", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["have", "have", "calc", "rw", "simpa", "simpa", "gcongr", "rw", "exact", "congr", "rw", "ring", "gcongr", "refine", "simp", "linarith"], "tactic_count": 16}
{"name": "PeriodPair.weierstrassPExcept", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PeriodPair.term℘[_-_]", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PeriodPair._aux_Mathlib_Analysis_SpecialFunctions_Elliptic_Weierstrass___macroRules_PeriodPair_term℘[_-_]_1", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PeriodPair._aux_Mathlib_Analysis_SpecialFunctions_Elliptic_Weierstrass___delab_app_PeriodPair_term℘[_-_]_1", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PeriodPair.hasSumLocallyUniformly_weierstrassPExcept", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": false, "tactics": ["refine", "rintro", "split_ifs", "simpa", "exact"], "tactic_count": 5}
{"name": "PeriodPair.hasSum_weierstrassPExcept", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PeriodPair.differentiableOn_weierstrassPExcept", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": false, "tactics": ["refine", "split_ifs", "simp", "exact"], "tactic_count": 4}
{"name": "PeriodPair.weierstrassPExcept_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["simp", "rw", "congr", "simp", "simp", "ring"], "tactic_count": 6}
{"name": "PeriodPair.weierstrassPExcept_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PeriodPair.weierstrassP", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PeriodPair.term℘[_]", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PeriodPair._aux_Mathlib_Analysis_SpecialFunctions_Elliptic_Weierstrass___macroRules_PeriodPair_term℘[_]_1", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PeriodPair._aux_Mathlib_Analysis_SpecialFunctions_Elliptic_Weierstrass___delab_app_PeriodPair_term℘[_]_1", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PeriodPair.weierstrassPExcept_add", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["trans", "simp", "rw", "congr", "exact", "exact"], "tactic_count": 6}
{"name": "PeriodPair.weierstrassPExcept_def", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["rw", "abel"], "tactic_count": 2}
{"name": "PeriodPair.weierstrassPExcept_of_notMem", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["delta", "congr", "have", "simp"], "tactic_count": 4}
{"name": "PeriodPair.hasSumLocallyUniformly_weierstrassP", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["convert", "rw", "rw"], "tactic_count": 3}
{"name": "PeriodPair.hasSum_weierstrassP", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PeriodPair.differentiableOn_weierstrassP", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["rw", "convert", "simp"], "tactic_count": 3}
{"name": "PeriodPair.weierstrassP_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["simp", "rw", "congr", "simp", "ring"], "tactic_count": 5}
{"name": "PeriodPair.not_continuousAt_weierstrassP", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["eta_expand", "simp_rw", "intro", "apply", "simpa"], "tactic_count": 5}
{"name": "PeriodPair.derivWeierstrassPExcept", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PeriodPair.term℘'[_-_]", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PeriodPair._aux_Mathlib_Analysis_SpecialFunctions_Elliptic_Weierstrass___macroRules_PeriodPair_term℘'[_-_]_1", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PeriodPair._aux_Mathlib_Analysis_SpecialFunctions_Elliptic_Weierstrass___delab_app_PeriodPair_term℘'[_-_]_1", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PeriodPair.hasSumLocallyUniformly_derivWeierstrassPExcept", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": false, "tactics": ["refine", "rintro", "split_ifs", "simpa", "have", "have", "simp", "rw", "refine", "norm_cast", "gcongr", "refine", "norm_cast", "linarith", "exact", "exact"], "tactic_count": 16}
{"name": "PeriodPair.hasSum_derivWeierstrassPExcept", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PeriodPair.differentiableOn_derivWeierstrassPExcept", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": false, "tactics": ["refine", "split_ifs", "simp", "refine", "have", "simpa"], "tactic_count": 6}
{"name": "PeriodPair.eqOn_deriv_weierstrassPExcept_derivWeierstrassPExcept", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": false, "tactics": ["refine", "refine", "split_ifs", "simp", "refine", "have", "simpa", "refine", "intro", "simp", "rw", "congr", "split_ifs", "simp", "have", "hl₁", "obtain", "simpa", "rw", "simp_rw", "rw", "simp", "field_simp", "intros", "split_ifs", "simp", "have", "hl₁", "obtain", "simpa", "exact"], "tactic_count": 31}
{"name": "PeriodPair.deriv_weierstrassPExcept_same", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PeriodPair.derivWeierstrassPExcept_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["simp", "rw", "simp", "neg_zero]", "congr", "simp", "ring"], "tactic_count": 7}
{"name": "PeriodPair.derivWeierstrassPExcept_zero_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "PeriodPair.derivWeierstrassPExcept_add_coe", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["simp", "rw", "simp"], "tactic_count": 3}
{"name": "_private.Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass.0.PeriodPair.weierstrassPExcept_add_coe_aux", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["apply", "refine", "exact", "refine", "rintro", "exact", "refine", "intro", "simp", "rw", "simpa", "simp", "eq_sub_iff_add_eq]", "exact", "simp", "rw", "congr", "ring"], "tactic_count": 18}
{"name": "_private.Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass.0.PeriodPair.weierstrassP_add_coe_aux", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["have", "by_cases", "have", "dsimp", "rw", "simp", "ring", "have", "simp", "one_div]", "rw", "simp", "ring"], "tactic_count": 13}
{"name": "PeriodPair.weierstrassP_add_coe", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": false, "tactics": ["let", "add_mem", "zero_mem", "neg_mem", "have", "rw", "rintro", "ext", "exact", "ext", "exact", "exact"], "tactic_count": 12}
{"name": "PeriodPair.periodic_weierstrassP", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PeriodPair.weierstrassP_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PeriodPair.weierstrassP_coe", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PeriodPair.weierstrassP_sub_coe", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PeriodPair.derivWeierstrassP", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PeriodPair.term℘'[_]", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PeriodPair._aux_Mathlib_Analysis_SpecialFunctions_Elliptic_Weierstrass___macroRules_PeriodPair_term℘'[_]_1", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PeriodPair._aux_Mathlib_Analysis_SpecialFunctions_Elliptic_Weierstrass___delab_app_PeriodPair_term℘'[_]_1", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PeriodPair.derivWeierstrassPExcept_sub", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["trans", "simp", "rw", "congr", "exact", "exact"], "tactic_count": 6}
{"name": "PeriodPair.derivWeierstrassPExcept_def", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PeriodPair.derivWeierstrassPExcept_of_notMem", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["delta", "simp_rw", "congr", "have", "simp"], "tactic_count": 5}
{"name": "PeriodPair.hasSumLocallyUniformly_derivWeierstrassP", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["convert", "rw", "rw"], "tactic_count": 3}
{"name": "PeriodPair.hasSum_derivWeierstrassP", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PeriodPair.differentiableOn_derivWeierstrassP", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["rw", "convert", "simp"], "tactic_count": 3}
{"name": "PeriodPair.derivWeierstrassP_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["simp", "rw", "simp", "congr", "ring"], "tactic_count": 5}
{"name": "PeriodPair.derivWeierstrassP_add_coe", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["simp", "rw", "simp"], "tactic_count": 3}
{"name": "PeriodPair.periodic_derivWeierstrassP", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PeriodPair.derivWeierstrassP_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PeriodPair.derivWeierstrassP_coe", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PeriodPair.derivWeierstrassP_sub_coe", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PeriodPair.deriv_weierstrassP", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "rw", "exact", "rw"], "tactic_count": 5}
{"name": "PeriodPair.sumInvPow", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PeriodPair.hasSum_sumInvPow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "PeriodPair.weierstrassPExceptSummand", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PeriodPair.weierstrassPExceptSeries", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PeriodPair.coeff_weierstrassPExceptSeries", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["delta", "cases", "zero", "succ", "split_ifs", "trans", "rw", "simp", "rw", "simp_rw", "congr", "split_ifs", "simp", "dsimp", "exact", "have", "simp"], "tactic_count": 17}
{"name": "PeriodPair.summable_weierstrassPExceptSummand", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "refine", "have", "simpa", "simpa", "let", "rw", "apply", "simpa", "dsimp", "have", "have", "simpa", "have", "refine", "intro", "split_ifs", "simp", "have", "obtain", "simpa", "obtain", "simp", "calc", "simp", "gcongr", "norm_cast", "exact"], "tactic_count": 29}
{"name": "PeriodPair.weierstrassPExcept_eq_tsum", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": false, "tactics": ["trans", "delta", "congr", "split_ifs", "simp", "simpa", "trans", "simp", "simp_rw", "apply", "exact"], "tactic_count": 11}
{"name": "PeriodPair.weierstrassPExceptSeries_hasSum", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["refine", "simp_rw", "exact"], "tactic_count": 3}
{"name": "PeriodPair.hasFPowerSeriesOnBall_weierstrassPExcept", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["constructor", "apply", "convert", "simp", "simp", "intro", "simpa", "exact", "intro", "replace", "have", "simp", "convert", "rw", "smul_eq_mul]"], "tactic_count": 15}
{"name": "PeriodPair.hasFPowerSeriesAt_weierstrassPExcept", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["obtain", "lift", "simpa"], "tactic_count": 3}
{"name": "PeriodPair.analyticOnNhd_weierstrassPExcept", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PeriodPair.analyticAt_weierstrassPExcept", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PeriodPair.iteratedDeriv_weierstrassPExcept_self", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PeriodPair.derivWeierstrassPExceptSeries", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PeriodPair.hasFPowerSeriesOnBall_derivWeierstrassPExcept", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["refine", "have", "convert", "ext", "simp", "ring", "simpa"], "tactic_count": 7}
{"name": "PeriodPair.hasFPowerSeriesAt_derivWeierstrassPExcept", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["obtain", "simpa"], "tactic_count": 2}
{"name": "PeriodPair.analyticOnNhd_derivWeierstrassPExcept", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PeriodPair.analyticAt_derivWeierstrassPExcept", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PeriodPair.iteratedDeriv_derivWeierstrassPExcept_self", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PeriodPair.deriv_derivWeierstrassPExcept_self", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "PeriodPair.analyticOnNhd_derivWeierstrassP", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PeriodPair.weierstrassPSummand", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PeriodPair.weierstrassPSeries", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PeriodPair.weierstrassPExceptSeries_of_notMem", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["delta", "congr", "rw", "simp"], "tactic_count": 4}
{"name": "PeriodPair.weierstrassPExceptSummand_of_notMem", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "PeriodPair.coeff_weierstrassPSeries", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "PeriodPair.summable_weierstrassPSummand", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["simp_rw", "refine"], "tactic_count": 2}
{"name": "PeriodPair.weierstrassPSeries_hasSum", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": false, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "PeriodPair.hasFPowerSeriesOnBall_weierstrassP", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": false, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "PeriodPair.analyticOnNhd_weierstrassP", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PeriodPair.ite_eq_one_sub_sq_mul_weierstrassP", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "PeriodPair.meromorphic_weierstrassP", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["intro", "by_cases", "simp_rw", "have", "fun_prop", "exact"], "tactic_count": 6}
{"name": "PeriodPair.meromorphic_derivWeierstrassP", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["rw", "fun_prop"], "tactic_count": 2}
{"name": "PeriodPair.order_weierstrassP", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["trans", "rw", "refine", "have", "suffices", "by_cases", "simpa", "fun_prop", "simp", "filter_upwards", "have", "simp", "norm_num"], "tactic_count": 13}
{"name": "PeriodPair.G", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PeriodPair.sumInvPow_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "PeriodPair.G_eq_zero_of_odd", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["rw", "congr", "simp"], "tactic_count": 3}
{"name": "PeriodPair.g₂", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PeriodPair.g₃", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass.0.PeriodPair.relation", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass.0.PeriodPair.meromorphic_relation", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["have", "refine", "filter_upwards", "hw", "rw"], "tactic_count": 5}
{"name": "_private.Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass.0.PeriodPair.relation_mul_id_pow_six_eventuallyEq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["filter_upwards", "by_cases", "simp", "replace", "simp", "simp", "field"], "tactic_count": 7}
{"name": "_private.Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass.0.PeriodPair.analyticAt_relation_mul_id_pow_six", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["refine", "fun_prop"], "tactic_count": 2}
{"name": "_private.Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass.0.PeriodPair.relation_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "_private.Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass.0.PeriodPair.iteratedDeriv_six_relation_mul_id_pow_six", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "simp", "iteratedDeriv_const,", "iteratedDeriv_weierstrassPExcept_self]", "simp", "show", "ring"], "tactic_count": 8}
{"name": "_private.Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass.0.PeriodPair.analyticAt_relation_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["refine", "suffices", "rw", "rw", "simpa", "rw", "refine", "by_cases", "simpa", "by_cases", "simp", "by_cases", "exact", "rw", "simp_rw", "simp", "iteratedDeriv_const,", "iteratedDeriv_weierstrassPExcept_self]", "obtain", "simp", "simp"], "tactic_count": 21}
{"name": "_private.Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass.0.PeriodPair.relation_add_coe", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["simp", "congr", "simpa"], "tactic_count": 3}
{"name": "_private.Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass.0.PeriodPair.relation_sub_coe", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "_private.Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass.0.PeriodPair.analyticAt_relation", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["by_cases", "lift", "have", "rw", "convert", "ext", "simp", "have", "have", "have", "fun_prop", "apply", "filter_upwards", "simp_all"], "tactic_count": 14}
{"name": "_private.Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass.0.PeriodPair.relation_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": true, "tactics": ["ext", "have", "exact", "lift", "x"], "tactic_count": 5}
{"name": "PeriodPair.derivWeierstrassP_sq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.exp_bound_sq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.locally_lipschitz_exp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "exact", "have", "intro", "have", "rw", "exact", "calc", "ring"], "tactic_count": 11}
{"name": "Complex.continuous_exp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.continuousOn_exp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.exp_sub_sum_range_isBigO_pow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": true, "tactics": ["rcases", "simpa", "refine", "rw", "refine", "convert", "simp"], "tactic_count": 7}
{"name": "Complex.exp_sub_sum_range_succ_isLittleO_pow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.cexp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.cexp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.cexp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.cexp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.cexp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformContinuousOn.cexp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": true, "tactics": ["have", "rw", "intro", "simp", "have", "have", "rw", "obtain", "refine", "intro", "have", "rw", "have", "rw", "ring_nf", "rw", "have", "simp", "apply", "simp"], "tactic_count": 20}
{"name": "Real.continuous_exp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "Real.continuousOn_exp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": true, "tactics": ["fun_prop"], "tactic_count": 1}
{"name": "Real.exp_sub_sum_range_isBigO_pow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": true, "tactics": ["have", "simp", "norm_cast"], "tactic_count": 3}
{"name": "Real.exp_sub_sum_range_succ_isLittleO_pow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.rexp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.rexp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.rexp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.rexp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.rexp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.exp_half", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.tendsto_exp_atTop", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": true, "tactics": ["have", "have", "exact"], "tactic_count": 3}
{"name": "Real.mul_exp_neg_le_exp_neg_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": true, "tactics": ["have", "have", "simpa"], "tactic_count": 3}
{"name": "Real.tendsto_exp_neg_atTop_nhds_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.tendsto_exp_nhds_zero_nhds_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "Real.tendsto_exp_atBot", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.tendsto_exp_atBot_nhdsGT", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.isBoundedUnder_ge_exp_comp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.isBoundedUnder_le_exp_comp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.tendsto_exp_div_pow_atTop", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": true, "tactics": ["refine", "have", "have", "obtain", "eventually_atTop.1", "simp", "refine", "rw", "have", "rw", "calc", "x"], "tactic_count": 12}
{"name": "Real.tendsto_pow_mul_exp_neg_atTop_nhds_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.tendsto_mul_exp_add_div_pow_atTop", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": true, "tactics": ["rcases", "simp", "exact", "simp", "exact"], "tactic_count": 5}
{"name": "Real.tendsto_div_pow_mul_exp_add_atTop", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": false, "tactics": ["have", "intro", "convert", "ext", "simp", "rcases", "exact", "convert", "ext", "field_simp", "rw", "rw"], "tactic_count": 12}
{"name": "Real.expOrderIso", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.coe_expOrderIso_apply", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.coe_comp_expOrderIso", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.range_exp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.map_exp_atTop", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.comap_exp_atTop", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.tendsto_exp_comp_atTop", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Real.tendsto_comp_exp_atTop", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Real.map_exp_atBot", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.comap_exp_nhdsGT_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.tendsto_comp_exp_atBot", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Real.comap_exp_nhds_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.tendsto_exp_comp_nhds_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Real.isOpenEmbedding_exp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.map_exp_nhds", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.comap_exp_nhds_exp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.isLittleO_pow_exp_atTop", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": true, "tactics": ["simpa", "tendsto_div_pow_mul_exp_add_atTop"], "tactic_count": 2}
{"name": "Real.isBigO_exp_comp_exp_comp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.isTheta_exp_comp_exp_comp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.isLittleO_exp_comp_exp_comp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": true, "tactics": ["simp", "tendsto_exp_comp_nhds_zero,"], "tactic_count": 2}
{"name": "Real.isLittleO_one_exp_comp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.isBigO_one_exp_comp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.isBigO_exp_comp_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.isTheta_exp_comp_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.summable_exp_nat_mul_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.summable_exp_neg_nat", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.summable_exp_nat_mul_of_ge", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": true, "tactics": ["refine", "refine", "conv_rhs", "exact"], "tactic_count": 4}
{"name": "Real.summable_pow_mul_exp_neg_nat_mul", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": true, "tactics": ["simp_rw", "apply", "rwa"], "tactic_count": 3}
{"name": "HasSum.rexp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.comap_exp_cobounded", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.comap_exp_nhds_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.comap_exp_nhdsNE", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": true, "tactics": ["have", "simp"], "tactic_count": 2}
{"name": "Complex.tendsto_exp_nhds_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": true, "tactics": ["simp_rw", "rfl"], "tactic_count": 2}
{"name": "Complex.tendsto_exp_comap_re_atTop", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.tendsto_exp_comap_re_atBot", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.tendsto_exp_comap_re_atBot_nhdsNE", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasSum.cexp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Exp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "analyticOnNhd_cexp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ExpDeriv", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "analyticOn_cexp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ExpDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "analyticAt_cexp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ExpDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "analyticWithinAt_cexp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ExpDeriv", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "AnalyticAt.cexp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ExpDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticAt.cexp'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ExpDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticWithinAt.cexp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ExpDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticOnNhd.cexp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ExpDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticOn.cexp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ExpDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.hasDerivAt_exp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ExpDeriv", "is_tactic_proof": true, "tactics": ["rw", "have", "refine", "filter_upwards", "simp", "exact"], "tactic_count": 6}
{"name": "Complex.differentiable_exp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ExpDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.differentiableAt_exp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ExpDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.deriv_exp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ExpDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.iter_deriv_exp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ExpDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.contDiff_exp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ExpDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.hasStrictDerivAt_exp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ExpDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.hasStrictFDerivAt_exp_real", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ExpDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictDerivAt.cexp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ExpDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivAt.cexp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ExpDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivWithinAt.cexp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ExpDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "derivWithin_cexp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ExpDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv_cexp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ExpDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictFDerivAt.cexp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ExpDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivWithinAt.cexp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ExpDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivAt.cexp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ExpDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableWithinAt.cexp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ExpDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableAt.cexp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ExpDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableOn.cexp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ExpDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Differentiable.cexp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ExpDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.cexp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ExpDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffAt.cexp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ExpDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffOn.cexp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ExpDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffWithinAt.cexp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ExpDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iteratedDeriv_cexp_const_mul", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ExpDeriv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "analyticOnNhd_rexp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ExpDeriv", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "analyticOn_rexp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ExpDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "analyticAt_rexp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ExpDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "analyticWithinAt_rexp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ExpDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticAt.rexp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ExpDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticAt.rexp'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ExpDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticWithinAt.rexp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ExpDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticOnNhd.rexp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ExpDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticOn.rexp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ExpDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.hasStrictDerivAt_exp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ExpDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.hasDerivAt_exp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ExpDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.contDiff_exp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ExpDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.differentiable_exp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ExpDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.differentiableAt_exp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ExpDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.deriv_exp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ExpDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.iter_deriv_exp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ExpDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictDerivAt.exp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ExpDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivAt.exp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ExpDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivWithinAt.exp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ExpDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "derivWithin_exp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ExpDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv_exp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ExpDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.exp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ExpDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Complex.betaIntegral_eval_nat_add_one_right", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.Beta", "is_tactic_proof": true, "tactics": ["induction", "zero", "rw", "simp", "succ", "have", "swap", "rw", "swap", "rw", "swap", "rw", "div_div]", "congr", "push_cast"], "tactic_count": 15}
{"name": "Complex.GammaSeq", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.Beta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.GammaSeq_eq_betaIntegral_of_re_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.Beta", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.GammaSeq_add_one_left", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.Beta", "is_tactic_proof": true, "tactics": ["conv_lhs", "conv_rhs", "rw", "mul_comm", "congr", "rw", "refine", "push_cast", "abel"], "tactic_count": 9}
{"name": "Complex.GammaSeq_eq_approx_Gamma_integral", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.Beta", "is_tactic_proof": true, "tactics": ["have", "conv_rhs", "rw", "have", "intervalIntegral.integral_comp_div", "dsimp", "rw", "intervalIntegral.integral_const_mul]", "swap", "simp_rw", "refine", "push_cast", "have", "have", "conv_lhs", "simp", "have", "rw", "rw"], "tactic_count": 19}
{"name": "Complex.approx_Gamma_integral_tendsto_Gamma_integral", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.Beta", "is_tactic_proof": false, "tactics": ["rw", "let", "indicator", "have", "intro", "rw", "intervalIntegrable_iff_integrableOn_Ioc_of_le", "apply", "refine", "rwa", "apply", "continuity", "have", "intro", "apply", "change", "filter_upwards", "rw", "dsimp", "rw", "exact", "simp_rw", "refine", "convert", "ext1", "rw", "convert", "tendsto_integral_of_dominated_convergence", "ext1", "rw", "intervalIntegral.integral_of_le", "intro", "rw", "filter_upwards", "simp", "rcases", "rw", "exact", "rw", "norm_cpow_eq_rpow_re_of_pos", "gcongr", "exact"], "tactic_count": 42}
{"name": "Complex.GammaSeq_tendsto_Gamma", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.Beta", "is_tactic_proof": false, "tactics": ["suffices", "rw", "apply", "rw", "rcases", "exact", "refine", "rw", "intro", "induction", "zero", "rw", "rw", "refine", "refine", "exact", "rwa", "succ", "rw", "rw", "have", "pick_goal", "conv", "rwa", "simp_rw", "exact"], "tactic_count": 26}
{"name": "Complex.GammaSeq_mul", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.Beta", "is_tactic_proof": true, "tactics": ["have", "rw", "have", "rw", "rw", "add_comm", "have", "intro", "push_cast", "have", "field", "simp_rw", "rw", "mul_comm", "exact"], "tactic_count": 15}
{"name": "Complex.Gamma_mul_Gamma_one_sub", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.Beta", "is_tactic_proof": true, "tactics": ["have", "by_cases", "rw", "rw", "obtain", "rw", "rw", "cases", "rw", "rw", "refine", "have", "convert", "convert", "have", "convert", "rw", "convert", "ext1"], "tactic_count": 19}
{"name": "Complex.Gamma_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.Beta", "is_tactic_proof": true, "tactics": ["by_cases", "have", "conv_lhs", "rw", "rw", "refine", "specialize", "contrapose", "rwa", "have", "rw", "intro", "apply_fun", "rw", "exact", "have", "rw", "exact"], "tactic_count": 18}
{"name": "Complex.Gamma_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.Beta", "is_tactic_proof": true, "tactics": ["constructor", "contrapose", "rintro"], "tactic_count": 3}
{"name": "Complex.Gamma_ne_zero_of_re_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.Beta", "is_tactic_proof": true, "tactics": ["refine", "contrapose", "simpa"], "tactic_count": 3}
{"name": "Real.GammaSeq", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.Beta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.GammaSeq_tendsto_Gamma", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.Beta", "is_tactic_proof": false, "tactics": ["suffices", "exact", "convert", "ext1", "dsimp", "push_cast", "rw"], "tactic_count": 7}
{"name": "Real.Gamma_mul_Gamma_one_sub", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.Beta", "is_tactic_proof": false, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Complex.one_div_Gamma_eq_self_mul_one_div_Gamma_add_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.Beta", "is_tactic_proof": true, "tactics": ["rcases", "rw", "rw"], "tactic_count": 3}
{"name": "Complex.differentiable_one_div_Gamma", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.Beta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.betaIntegral_eq_Gamma_mul_div", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.Beta", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.Gamma_mul_Gamma_add_half", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.Beta", "is_tactic_proof": false, "tactics": ["suffices", "convert", "rw", "rw", "have", "refine", "refine", "exact", "have", "refine", "refine", "apply", "exact", "refine", "exact", "have", "rw", "exact", "exact", "refine", "refine", "refine", "rw", "cpow_neg,"], "tactic_count": 24}
{"name": "Real.Gamma_mul_Gamma_add_half", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.Beta", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "_private.Mathlib.Analysis.SpecialFunctions.Gamma.BohrMollerup.0.Real.termΓ", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.BohrMollerup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.SpecialFunctions.Gamma.BohrMollerup.0.Real._aux_Mathlib_Analysis_SpecialFunctions_Gamma_BohrMollerup___macroRules__private_Mathlib_Analysis_SpecialFunctions_Gamma_BohrMollerup_0_Real_termΓ_1", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.BohrMollerup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.SpecialFunctions.Gamma.BohrMollerup.0.Real._aux_Mathlib_Analysis_SpecialFunctions_Gamma_BohrMollerup___unexpand_Real_Gamma_1", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.BohrMollerup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.Gamma_mul_add_mul_le_rpow_Gamma_mul_rpow_Gamma", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.BohrMollerup", "is_tactic_proof": true, "tactics": ["let", "have", "have", "have", "positivity", "have", "mul_nonneg", "have", "have", "intro", "dsimp", "rw", "congr", "field", "have", "intro", "have", "have", "rw", "memLp_one_iff_integrable]", "apply", "refine", "dsimp", "rw", "congr", "exact", "refine", "refine", "exact", "continuousAt_rpow_const", "rw", "convert", "refine", "dsimp", "have", "have", "ring", "rw", "ring", "rw", "congr"], "tactic_count": 41}
{"name": "Real.convexOn_log_Gamma", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.BohrMollerup", "is_tactic_proof": true, "tactics": ["refine", "have", "subst", "simp_rw", "push", "rw", "gcongr", "exact", "all_goals"], "tactic_count": 9}
{"name": "Real.convexOn_Gamma", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.BohrMollerup", "is_tactic_proof": false, "tactics": ["refine", "exp_log", "rw", "refine", "refine", "exact"], "tactic_count": 6}
{"name": "Real.BohrMollerup.logGammaSeq", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.BohrMollerup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.BohrMollerup.f_nat_eq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.BohrMollerup", "is_tactic_proof": true, "tactics": ["refine", "have", "simp", "rw", "conv_rhs", "congr", "exact"], "tactic_count": 7}
{"name": "Real.BohrMollerup.f_add_nat_eq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.BohrMollerup", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "have", "rw", "rw", "abel", "linarith"], "tactic_count": 8}
{"name": "Real.BohrMollerup.f_add_nat_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.BohrMollerup", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "simpa", "hf_conv.2"], "tactic_count": 5}
{"name": "Real.BohrMollerup.f_add_nat_ge", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.BohrMollerup", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "have", "rwa"], "tactic_count": 5}
{"name": "Real.BohrMollerup.logGammaSeq_add_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.BohrMollerup", "is_tactic_proof": true, "tactics": ["dsimp", "conv_rhs", "rw", "rw", "rw", "have", "congr", "push_cast", "abel", "rw", "ring"], "tactic_count": 11}
{"name": "Real.BohrMollerup.le_logGammaSeq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.BohrMollerup", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "ring"], "tactic_count": 4}
{"name": "Real.BohrMollerup.ge_logGammaSeq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.BohrMollerup", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "refine", "rw", "ring", "exact", "lia"], "tactic_count": 7}
{"name": "Real.BohrMollerup.tendsto_logGammaSeq_of_le_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.BohrMollerup", "is_tactic_proof": false, "tactics": ["refine", "tendsto_of_tendsto_of_tendsto_of_le_of_le", "have", "nth_rw", "exact", "filter_upwards", "rw", "convert", "ring", "change", "filter_upwards"], "tactic_count": 11}
{"name": "Real.BohrMollerup.tendsto_logGammaSeq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.BohrMollerup", "is_tactic_proof": false, "tactics": ["suffices", "refine", "rcases", "rwa", "convert", "abel", "rw", "intro", "induction", "zero", "rw", "exact", "succ", "intro", "rw", "rw", "specialize", "have", "logGammaSeq", "refine", "have", "rw", "rw", "ring", "replace", "have", "ext1", "dsimp", "rw", "rw", "convert", "ring", "have", "rw", "rw", "ring"], "tactic_count": 36}
{"name": "Real.BohrMollerup.tendsto_log_gamma", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.BohrMollerup", "is_tactic_proof": false, "tactics": ["have", "simp_rw", "rw", "refine", "rw"], "tactic_count": 5}
{"name": "Real.eq_Gamma_of_log_convex", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.BohrMollerup", "is_tactic_proof": false, "tactics": ["suffices", "log_injOn_pos", "intro", "have", "rw", "exact", "intro", "rw", "ring"], "tactic_count": 9}
{"name": "Real.Gamma_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.BohrMollerup", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.Gamma_three_div_two_lt_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.BohrMollerup", "is_tactic_proof": true, "tactics": ["have", "have", "swap", "rw", "rw", "le_sub_iff_add_le',", "refine", "rw", "refine", "rw"], "tactic_count": 10}
{"name": "Real.Gamma_strictAntiOn_Ioc", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.BohrMollerup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.Gamma_strictMonoOn_Ici", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.BohrMollerup", "is_tactic_proof": false, "tactics": ["convert", "convexOn_Gamma.strictMonoOn", "symm", "rw", "exact"], "tactic_count": 5}
{"name": "Real.exists_isMinOn_Gamma_Ioi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.BohrMollerup", "is_tactic_proof": false, "tactics": ["have", "isCompact_Icc.exists_isMinOn", "differentiableOn_Gamma_Ioi.continuousOn.mono", "have", "simpa", "refine", "obtain", "exact", "exact", "exact"], "tactic_count": 10}
{"name": "Real.doublingGamma", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.BohrMollerup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.doublingGamma_add_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.BohrMollerup", "is_tactic_proof": false, "tactics": ["rw", "ring"], "tactic_count": 2}
{"name": "Real.doublingGamma_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.BohrMollerup", "is_tactic_proof": true, "tactics": ["simp_rw", "div_self"], "tactic_count": 2}
{"name": "Real.log_doublingGamma_eq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.BohrMollerup", "is_tactic_proof": true, "tactics": ["intro", "have", "have", "have", "have", "rw", "log_mul", "ring_nf"], "tactic_count": 8}
{"name": "Real.doublingGamma_log_convex_Ioi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.BohrMollerup", "is_tactic_proof": true, "tactics": ["refine", "convert", "simpa", "ext1", "simp", "rw", "refine", "convert", "convexOn_log_Gamma.comp_affineMap", "change", "rw", "div_self", "ext1", "change", "rw", "simpa"], "tactic_count": 16}
{"name": "Real.doublingGamma_eq_Gamma", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.BohrMollerup", "is_tactic_proof": false, "tactics": ["refine", "eq_Gamma_of_log_convex", "apply_rules", "sqrt_pos_of_pos"], "tactic_count": 4}
{"name": "Real.Gamma_mul_Gamma_add_half_of_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.BohrMollerup", "is_tactic_proof": false, "tactics": ["rw", "field"], "tactic_count": 2}
{"name": "Complex.Gammaℝ", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.Deligne", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.Gammaℝ_def", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.Deligne", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.Gammaℂ", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.Deligne", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.Gammaℂ_def", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.Deligne", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.Gammaℝ_add_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.Deligne", "is_tactic_proof": false, "tactics": ["rw", "field_simp"], "tactic_count": 2}
{"name": "Complex.Gammaℂ_add_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.Deligne", "is_tactic_proof": false, "tactics": ["rw", "cpow_add", "ring"], "tactic_count": 3}
{"name": "Complex.Gammaℝ_ne_zero_of_re_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.Deligne", "is_tactic_proof": true, "tactics": ["apply", "simp", "apply", "rw", "exact"], "tactic_count": 5}
{"name": "Complex.Gammaℝ_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.Deligne", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.Gammaℝ_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.Deligne", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Complex.Gammaℂ_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.Deligne", "is_tactic_proof": true, "tactics": ["rw", "ring"], "tactic_count": 2}
{"name": "Complex.differentiable_Gammaℝ_inv", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.Deligne", "is_tactic_proof": true, "tactics": ["conv", "refine", "refine", "exact", "exact"], "tactic_count": 5}
{"name": "Complex.Gammaℝ_residue_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.Deligne", "is_tactic_proof": false, "tactics": ["have", "refine", "rw", "exact", "eventually_of_mem", "have", "rw", "refine", "exact", "convert", "rw", "ring_nf"], "tactic_count": 12}
{"name": "Complex.Gammaℝ_mul_Gammaℝ_add_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.Deligne", "is_tactic_proof": true, "tactics": ["simp", "calc", "rw", "ofReal_cpow", "ring_nf", "rw", "ofReal_ofNat]", "ring_nf"], "tactic_count": 8}
{"name": "Complex.Gammaℝ_one_sub_mul_Gammaℝ_one_add", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.Deligne", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.Gammaℝ_div_Gammaℝ_one_sub", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.Deligne", "is_tactic_proof": false, "tactics": ["have", "simpa", "calc", "rw", "rw"], "tactic_count": 5}
{"name": "Complex.inv_Gammaℝ_one_sub", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.Deligne", "is_tactic_proof": false, "tactics": ["have", "rw", "intro", "specialize", "simp_all", "have", "intro", "specialize", "simp_all", "rw"], "tactic_count": 10}
{"name": "Complex.inv_Gammaℝ_two_sub", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.Deligne", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "div_mul_cancel₀", "rw", "have", "rcases", "rwa", "rw", "convert", "push_cast", "ring", "rw", "simp_rw", "generalize", "field"], "tactic_count": 15}
{"name": "Complex.GammaIntegral_eq_mellin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.hasDerivAt_GammaIntegral", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.Deriv", "is_tactic_proof": true, "tactics": ["rw", "convert", "refine", "exact", "rw", "simp_rw", "simpa", "simp_rw", "refine", "rw", "exact"], "tactic_count": 11}
{"name": "Complex.differentiableAt_GammaAux", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.Deriv", "is_tactic_proof": true, "tactics": ["induction", "zero", "refine", "rw", "succ", "dsimp", "specialize", "have", "have", "intro", "contrapose", "rw", "simpa", "refine", "rw", "exact", "simpa"], "tactic_count": 17}
{"name": "Complex.differentiableAt_Gamma", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.Deriv", "is_tactic_proof": true, "tactics": ["let", "have", "apply", "let", "have", "rw", "refine", "have", "exact", "rw", "exact", "apply", "intro", "apply"], "tactic_count": 14}
{"name": "Complex.differentiableAt_Gamma_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.continuousAt_Gamma", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.continuousAt_Gamma_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.tendsto_self_mul_Gamma_nhds_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.Deriv", "is_tactic_proof": true, "tactics": ["rw", "refine", "exact"], "tactic_count": 3}
{"name": "Complex.not_continuousAt_Gamma_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.not_differentiableAt_Gamma_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.not_continuousAt_Gamma_neg_nat", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.Deriv", "is_tactic_proof": true, "tactics": ["induction", "rw", "exact", "contrapose", "rw", "suffices", "suffices", "this.comp", "rw", "have", "exact"], "tactic_count": 11}
{"name": "Complex.not_differentiableAt_Gamma_neg_nat", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.deriv_Gamma_add_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.Deriv", "is_tactic_proof": true, "tactics": ["by_cases", "obtain", "rw", "deriv_zero_of_not_differentiableAt", "deriv_zero_of_not_differentiableAt", "mul_zero]", "rwa", "suffices", "rw", "exact", "refine", "simpa"], "tactic_count": 12}
{"name": "Real.differentiableAt_Gamma", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.Deriv", "is_tactic_proof": true, "tactics": ["refine", "simp_rw", "exact"], "tactic_count": 3}
{"name": "Real.differentiableOn_Gamma_Ioi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.digamma", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.Digamma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.digamma_def", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.Digamma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.digamma_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.Digamma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.digamma_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.Digamma", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.digamma_one_half", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.Digamma", "is_tactic_proof": false, "tactics": ["rw", "neg_add',", "simp"], "tactic_count": 3}
{"name": "Complex.digamma_apply_add_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.Digamma", "is_tactic_proof": true, "tactics": ["have", "rw", "div_mul_cancel_right₀"], "tactic_count": 3}
{"name": "Complex.meromorphic_digamma", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gamma.Digamma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaussianFourier.verticalIntegral", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Gaussian.FourierTransform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaussianFourier.norm_cexp_neg_mul_sq_add_mul_I", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gaussian.FourierTransform", "is_tactic_proof": true, "tactics": ["rw", "simp", "ring_nf"], "tactic_count": 3}
{"name": "GaussianFourier.norm_cexp_neg_mul_sq_add_mul_I'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gaussian.FourierTransform", "is_tactic_proof": false, "tactics": ["have", "b.re", "b.re", "rw"], "tactic_count": 4}
{"name": "GaussianFourier.verticalIntegral_norm_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gaussian.FourierTransform", "is_tactic_proof": true, "tactics": ["have", "y|", "intro", "rw", "gcongr", "gcongr", "refine", "rw", "gcongr", "rwa", "apply", "rw", "conv_lhs", "conv_rhs", "conv", "congr", "rw", "rw", "intro", "have", "rcases", "rw", "rw", "exact", "rw", "rw", "exact", "rw", "refine", "rw", "simpa"], "tactic_count": 31}
{"name": "GaussianFourier.tendsto_verticalIntegral", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gaussian.FourierTransform", "is_tactic_proof": true, "tactics": ["rw", "refine", "tendsto_of_tendsto_of_tendsto_of_le_of_le", "rw", "refine", "apply", "simp_rw", "refine", "exact"], "tactic_count": 9}
{"name": "GaussianFourier.integrable_cexp_neg_mul_sq_add_real_mul_I", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gaussian.FourierTransform", "is_tactic_proof": true, "tactics": ["refine", "rw", "simp_rw", "suffices", "exact", "simp_rw", "apply"], "tactic_count": 7}
{"name": "GaussianFourier.integral_cexp_neg_mul_sq_add_real_mul_I", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gaussian.FourierTransform", "is_tactic_proof": false, "tactics": ["refine", "tendsto_nhds_unique", "tendsto_id)", "set", "let", "let", "let", "have", "intro", "have", "integral_boundary_rect_eq_zero_of_differentiableOn", "refine", "exact", "simpa", "mul_zero,", "simp_rw", "have", "ext1", "specialize", "rw", "unfold", "rw", "simp_rw", "change", "rw", "abel", "all_goals", "rw", "refine", "exact"], "tactic_count": 30}
{"name": "integral_cexp_quadratic", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gaussian.FourierTransform", "is_tactic_proof": true, "tactics": ["have", "have", "simp_rw", "congr", "field", "simp_rw", "rw", "simp_rw", "rw", "integral_cexp_neg_mul_sq_add_real_mul_I"], "tactic_count": 10}
{"name": "integrable_cexp_quadratic'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gaussian.FourierTransform", "is_tactic_proof": true, "tactics": ["have", "by_contra", "simpa"], "tactic_count": 3}
{"name": "integrable_cexp_quadratic", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gaussian.FourierTransform", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "fourierIntegral_gaussian", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gaussian.FourierTransform", "is_tactic_proof": true, "tactics": ["conv", "rw", "neg_neg,"], "tactic_count": 3}
{"name": "fourier_gaussian_pi'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gaussian.FourierTransform", "is_tactic_proof": true, "tactics": ["haveI", "have", "ext1", "simp_rw", "have", "push_cast", "simp_rw", "congr", "rw", "rw", "exact", "field_simp", "ring_nf", "simp", "ring"], "tactic_count": 15}
{"name": "fourier_gaussian_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gaussian.FourierTransform", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "GaussianFourier.integrable_cexp_neg_sum_mul_add", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gaussian.FourierTransform", "is_tactic_proof": true, "tactics": ["simp_rw", "apply", "convert", "simp"], "tactic_count": 4}
{"name": "GaussianFourier.integrable_cexp_neg_mul_sum_add", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gaussian.FourierTransform", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "GaussianFourier.integrable_cexp_neg_mul_sq_norm_add_of_euclideanSpace", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gaussian.FourierTransform", "is_tactic_proof": true, "tactics": ["rw", "simp", "convert", "simp", "ofReal_sum,", "norm_cast", "rw", "simp", "exact"], "tactic_count": 9}
{"name": "GaussianFourier.integrable_cexp_neg_mul_sq_norm_add", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gaussian.FourierTransform", "is_tactic_proof": true, "tactics": ["let", "rw", "convert", "simp"], "tactic_count": 4}
{"name": "GaussianFourier.integral_cexp_neg_sum_mul_add", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gaussian.FourierTransform", "is_tactic_proof": true, "tactics": ["simp_rw", "rw", "congr", "have", "convert"], "tactic_count": 5}
{"name": "GaussianFourier.integral_cexp_neg_mul_sum_add", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gaussian.FourierTransform", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "GaussianFourier.integral_cexp_neg_mul_sq_norm_add_of_euclideanSpace", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gaussian.FourierTransform", "is_tactic_proof": true, "tactics": ["rw", "simp", "convert", "simp", "norm_cast", "left", "rw", "exact", "simp", "simp_rw", "simp", "congr", "norm_cast", "rw", "exact"], "tactic_count": 15}
{"name": "GaussianFourier.integral_cexp_neg_mul_sq_norm_add", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gaussian.FourierTransform", "is_tactic_proof": true, "tactics": ["let", "rw", "convert", "simp"], "tactic_count": 4}
{"name": "GaussianFourier.integral_cexp_neg_mul_sq_norm", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gaussian.FourierTransform", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "GaussianFourier.integral_rexp_neg_mul_sq_norm", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gaussian.FourierTransform", "is_tactic_proof": true, "tactics": ["rw", "convert", "change", "rw", "simp", "rw", "simp"], "tactic_count": 7}
{"name": "fourier_gaussian_innerProductSpace'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gaussian.FourierTransform", "is_tactic_proof": false, "tactics": ["simp", "real_inner_comm", "convert", "congr", "simp", "ring", "have", "simp", "ring"], "tactic_count": 9}
{"name": "fourier_gaussian_innerProductSpace", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gaussian.FourierTransform", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "exp_neg_mul_rpow_isLittleO_exp_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gaussian.GaussianIntegral", "is_tactic_proof": true, "tactics": ["rw", "suffices", "refine", "refine", "rw", "rw", "field", "apply", "refine", "exact"], "tactic_count": 10}
{"name": "exp_neg_mul_sq_isLittleO_exp_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gaussian.GaussianIntegral", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "rpow_mul_exp_neg_mul_rpow_isLittleO_exp_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gaussian.GaussianIntegral", "is_tactic_proof": true, "tactics": ["apply", "simpa"], "tactic_count": 2}
{"name": "rpow_mul_exp_neg_mul_sq_isLittleO_exp_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gaussian.GaussianIntegral", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "integrableOn_rpow_mul_exp_neg_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gaussian.GaussianIntegral", "is_tactic_proof": true, "tactics": ["obtain", "have", "rw", "constructor", "rw", "refine", "refine", "exact", "intro", "rw", "refine", "exact", "have", "intro", "refine", "exact", "refine", "integrable_of_isBigO_exp_neg", "rw", "exact", "convert", "rw", "simp_rw", "convert", "rw"], "tactic_count": 25}
{"name": "integrableOn_rpow_mul_exp_neg_mul_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gaussian.GaussianIntegral", "is_tactic_proof": true, "tactics": ["have", "suffices", "rw", "refine", "rw", "mul_inv_cancel_left₀]", "all_goals", "refine", "rw", "exact"], "tactic_count": 10}
{"name": "integrableOn_rpow_mul_exp_neg_mul_sq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gaussian.GaussianIntegral", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "integrable_rpow_mul_exp_neg_mul_sq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gaussian.GaussianIntegral", "is_tactic_proof": false, "tactics": ["rw", "refine", "rw", "simp", "apply", "apply", "exact", "have", "filter_upwards", "have", "rw", "apply", "simpa"], "tactic_count": 13}
{"name": "integrable_exp_neg_mul_sq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gaussian.GaussianIntegral", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "integrableOn_Ioi_exp_neg_mul_sq_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gaussian.GaussianIntegral", "is_tactic_proof": true, "tactics": ["refine", "by_contra", "have", "apply", "simp", "exact", "simpa"], "tactic_count": 7}
{"name": "integrable_exp_neg_mul_sq_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gaussian.GaussianIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "integrable_mul_exp_neg_mul_sq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gaussian.GaussianIntegral", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "norm_cexp_neg_mul_sq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gaussian.GaussianIntegral", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "integrable_cexp_neg_mul_sq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gaussian.GaussianIntegral", "is_tactic_proof": true, "tactics": ["refine", "rw", "simp_rw", "exact"], "tactic_count": 4}
{"name": "integrable_mul_cexp_neg_mul_sq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gaussian.GaussianIntegral", "is_tactic_proof": true, "tactics": ["refine", "fun_prop", "have", "rw", "convert", "rw"], "tactic_count": 6}
{"name": "integral_mul_cexp_neg_mul_sq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gaussian.GaussianIntegral", "is_tactic_proof": true, "tactics": ["have", "have", "intro", "convert", "field", "have", "refine", "simp_rw", "exact", "convert", "integral_Ioi_of_hasDerivAt_of_tendsto", "simp", "reduceCtorEq]"], "tactic_count": 13}
{"name": "integral_gaussian_sq_complex", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gaussian.GaussianIntegral", "is_tactic_proof": true, "tactics": ["of", "calc", "rw", "congr", "ext1", "rw", "rw", "simp", "rw", "congr", "rw", "congr", "conv_rhs", "ring", "simp", "integral_mul_cexp_neg_mul_sq", "rw", "simp", "ring"], "tactic_count": 19}
{"name": "integral_gaussian", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gaussian.GaussianIntegral", "is_tactic_proof": true, "tactics": ["rcases", "rw", "exact", "simpa", "refine", "rw", "sq_sqrt", "convert", "rw"], "tactic_count": 9}
{"name": "continuousAt_gaussian_integral", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gaussian.GaussianIntegral", "is_tactic_proof": true, "tactics": ["let", "obtain", "have", "refine", "intro", "rw", "gcongr", "exact", "exact", "continuousAt_of_dominated"], "tactic_count": 10}
{"name": "integral_gaussian_complex", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gaussian.GaussianIntegral", "is_tactic_proof": true, "tactics": ["have", "apply", "exact", "refine", "continuousOn_of_forall_continuousAt", "rw", "exact", "have", "intro", "simp", "simp_rw", "coe_algebraMap]", "conv_rhs", "congr", "rw", "rw", "rw", "convert", "rw", "rw", "dsimp", "rw", "conv_lhs", "rw", "norm_num", "rw", "exact"], "tactic_count": 27}
{"name": "integral_gaussian_complex_Ioi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gaussian.GaussianIntegral", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "suffices", "rw", "rwa", "have", "intro", "have", "simpa", "have", "have", "simp_rw", "refine", "apply", "exact"], "tactic_count": 16}
{"name": "integral_gaussian_Ioi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gaussian.GaussianIntegral", "is_tactic_proof": true, "tactics": ["rcases", "rw", "exact", "rwa", "rw", "convert", "simp", "rw", "simp", "exact"], "tactic_count": 10}
{"name": "Real.Gamma_one_half_eq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gaussian.GaussianIntegral", "is_tactic_proof": true, "tactics": ["rw", "convert", "rw", "refine", "dsimp", "have", "rw", "norm_num", "rw", "rw", "simp", "norm_num", "rw"], "tactic_count": 13}
{"name": "Complex.Gamma_one_half_eq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gaussian.GaussianIntegral", "is_tactic_proof": true, "tactics": ["convert", "simpa", "rw"], "tactic_count": 3}
{"name": "Real.Gamma_nat_add_one_add_half", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gaussian.GaussianIntegral", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "ih", "rw", "simp", "ring"], "tactic_count": 7}
{"name": "Real.Gamma_nat_add_half", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gaussian.GaussianIntegral", "is_tactic_proof": true, "tactics": ["cases", "zero", "succ"], "tactic_count": 3}
{"name": "rexp_neg_quadratic_isLittleO_rpow_atTop", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gaussian.PoissonSummation", "is_tactic_proof": false, "tactics": ["suffices", "refine", "simpa", "rw", "have", "rw", "exact"], "tactic_count": 7}
{"name": "cexp_neg_quadratic_isLittleO_rpow_atTop", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gaussian.PoissonSummation", "is_tactic_proof": true, "tactics": ["apply", "convert", "simp_rw"], "tactic_count": 3}
{"name": "cexp_neg_quadratic_isLittleO_abs_rpow_cocompact", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gaussian.PoissonSummation", "is_tactic_proof": true, "tactics": ["rw", "constructor", "refine", "simp", "refine", "simp", "refine", "refine", "simp_rw"], "tactic_count": 9}
{"name": "tendsto_rpow_abs_mul_exp_neg_mul_sq_cocompact", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gaussian.PoissonSummation", "is_tactic_proof": true, "tactics": ["conv", "rw", "erw", "exact"], "tactic_count": 4}
{"name": "isLittleO_exp_neg_mul_sq_cocompact", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gaussian.PoissonSummation", "is_tactic_proof": true, "tactics": ["convert", "simp_rw", "rwa"], "tactic_count": 3}
{"name": "Complex.tsum_exp_neg_quadratic", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gaussian.PoissonSummation", "is_tactic_proof": true, "tactics": ["let", "have", "refine", "exact", "exact", "have", "have", "rw", "exact", "have", "rw", "refine", "contrapose", "rw", "have", "convert", "rwa", "have", "rw", "have", "intro", "simp_rw", "conv", "refine", "rwa", "convert", "simp", "rw", "simp"], "tactic_count": 29}
{"name": "Complex.tsum_exp_neg_mul_int_sq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gaussian.PoissonSummation", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.tsum_exp_neg_mul_int_sq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Gaussian.PoissonSummation", "is_tactic_proof": true, "tactics": ["simpa", "ofReal_one,"], "tactic_count": 2}
{"name": "integrableOn_exp_Iic", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ImproperIntegrals", "is_tactic_proof": false, "tactics": ["refine", "integrableOn_Iic_of_intervalIntegral_norm_bounded", "simp_rw", "exact"], "tactic_count": 4}
{"name": "integrableOn_exp_neg_Ioi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ImproperIntegrals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "integral_exp_Iic", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ImproperIntegrals", "is_tactic_proof": true, "tactics": ["refine", "simp_rw", "exact"], "tactic_count": 3}
{"name": "integral_exp_Iic_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ImproperIntegrals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "integral_exp_neg_Ioi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ImproperIntegrals", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "integral_exp_neg_Ioi_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ImproperIntegrals", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "integrableOn_exp_mul_complex_Ioi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ImproperIntegrals", "is_tactic_proof": true, "tactics": ["refine", "apply", "fun_prop", "simpa", "integrableOn_exp_neg_Ioi"], "tactic_count": 5}
{"name": "integrableOn_exp_mul_complex_Iic", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ImproperIntegrals", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "integrableOn_exp_mul_Ioi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ImproperIntegrals", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "integrableOn_exp_mul_Iic", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ImproperIntegrals", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "integral_exp_mul_complex_Ioi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ImproperIntegrals", "is_tactic_proof": false, "tactics": ["refine", "tendsto_nhds_unique", "simp_rw", "suffices", "simpa"], "tactic_count": 5}
{"name": "integral_exp_mul_complex_Iic", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ImproperIntegrals", "is_tactic_proof": true, "tactics": ["simpa", "integral_exp_mul_complex_Ioi"], "tactic_count": 2}
{"name": "integral_exp_mul_Ioi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ImproperIntegrals", "is_tactic_proof": true, "tactics": ["simp_rw", "rw", "exact"], "tactic_count": 3}
{"name": "integral_exp_mul_Iic", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ImproperIntegrals", "is_tactic_proof": true, "tactics": ["simpa", "integral_exp_mul_Ioi"], "tactic_count": 2}
{"name": "integrableOn_add_rpow_Ioi_of_lt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ImproperIntegrals", "is_tactic_proof": false, "tactics": ["have", "intro", "convert", "simp", "left", "have", "rw", "exact", "exact"], "tactic_count": 9}
{"name": "integrableOn_Ioi_rpow_of_lt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ImproperIntegrals", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "integrableOn_Ioi_rpow_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ImproperIntegrals", "is_tactic_proof": true, "tactics": ["refine", "contrapose", "intro", "have", "have", "apply", "filter_upwards", "have", "simp", "rw", "exact", "exact"], "tactic_count": 12}
{"name": "integrableAtFilter_rpow_atTop_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ImproperIntegrals", "is_tactic_proof": false, "tactics": ["refine", "obtain", "refine", "exact"], "tactic_count": 4}
{"name": "not_integrableOn_Ioi_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ImproperIntegrals", "is_tactic_proof": true, "tactics": ["intro", "rcases", "have", "rw", "exact", "have", "rw", "exact"], "tactic_count": 8}
{"name": "setIntegral_Ioi_zero_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ImproperIntegrals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "integral_Ioi_rpow_of_lt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ImproperIntegrals", "is_tactic_proof": false, "tactics": ["have", "intro", "convert", "simp", "have", "apply", "simpa", "convert", "simp"], "tactic_count": 9}
{"name": "integrableOn_Ioi_norm_cpow_of_lt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ImproperIntegrals", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "integrableOn_Ioi_cpow_of_lt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ImproperIntegrals", "is_tactic_proof": true, "tactics": ["refine", "refine", "exact"], "tactic_count": 3}
{"name": "integrableOn_Ioi_norm_cpow_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ImproperIntegrals", "is_tactic_proof": true, "tactics": ["refine", "refine", "rw"], "tactic_count": 3}
{"name": "integrableOn_Ioi_cpow_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ImproperIntegrals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "integrableOn_Ioi_deriv_ofReal_cpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ImproperIntegrals", "is_tactic_proof": false, "tactics": ["have", "refine", "rwa", "refine", "rw"], "tactic_count": 5}
{"name": "integrableOn_Ioi_deriv_norm_ofReal_cpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ImproperIntegrals", "is_tactic_proof": true, "tactics": ["rw", "obtain", "simp_rw", "exact", "replace", "exact"], "tactic_count": 6}
{"name": "not_integrableOn_Ioi_cpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ImproperIntegrals", "is_tactic_proof": true, "tactics": ["intro", "rcases", "have", "rw", "exact", "have", "rw", "exact"], "tactic_count": 8}
{"name": "setIntegral_Ioi_zero_cpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ImproperIntegrals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "integral_Ioi_cpow_of_lt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ImproperIntegrals", "is_tactic_proof": false, "tactics": ["refine", "suffices", "refine", "dsimp", "rw", "refine", "apply_fun", "rw", "exact", "simp_rw", "refine", "rw", "refine", "simp_rw"], "tactic_count": 14}
{"name": "integrable_inv_one_add_sq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ImproperIntegrals", "is_tactic_proof": true, "tactics": ["suffices", "exact"], "tactic_count": 2}
{"name": "integral_Iic_inv_one_add_sq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ImproperIntegrals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "integral_univ_inv_one_add_sq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.ImproperIntegrals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.intervalIntegrable_pow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrability.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.intervalIntegrable_zpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrability.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.intervalIntegrable_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrability.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.intervalIntegrable_rpow'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrability.Basic", "is_tactic_proof": false, "tactics": ["suffices", "exact", "have", "intro", "rw", "have", "intro", "convert", "simp", "apply", "intro", "refine", "intro", "exact", "rw", "have", "rw", "refine", "rw", "simp", "rpow_def_of_neg"], "tactic_count": 21}
{"name": "intervalIntegral.integrableOn_Ioo_rpow_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrability.Basic", "is_tactic_proof": true, "tactics": ["refine", "swap", "rw", "apply", "contrapose", "intro", "have", "have", "have", "apply", "filter_upwards", "simp", "rwa", "exact", "have", "rwa", "simp"], "tactic_count": 17}
{"name": "intervalIntegral.intervalIntegrable_cpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrability.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "refine", "exact", "rw", "rcases", "exact", "refine", "refine", "exact", "continuousOn_of_forall_continuousAt", "suffices", "intro", "rcases", "have", "rw", "refine", "dsimp", "rw", "apply", "rw", "rw", "exact", "integrableOn_singleton", "isFiniteMeasureOnCompacts_of_isLocallyFiniteMeasure.lt_top_of_isCompact", "have", "intro", "rw", "refine", "rw", "right", "refine", "exact"], "tactic_count": 32}
{"name": "intervalIntegral.intervalIntegrable_cpow'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrability.Basic", "is_tactic_proof": false, "tactics": ["suffices", "exact", "have", "intro", "rw", "rw", "apply", "rw", "intro", "rw", "dsimp", "rw", "exact", "refine", "refine", "rw", "refine", "rw", "exact", "intro", "exact", "rw", "have", "rw", "refine", "dsimp", "have", "rw", "simp"], "tactic_count": 29}
{"name": "intervalIntegral.integrableOn_Ioo_cpow_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrability.Basic", "is_tactic_proof": true, "tactics": ["refine", "swap", "rw", "exact", "have", "apply", "intro", "simp", "rwa"], "tactic_count": 9}
{"name": "intervalIntegral.intervalIntegrable_id", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrability.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.intervalIntegrable_const", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrability.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.intervalIntegrable_one_div", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrability.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.intervalIntegrable_inv", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrability.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "intervalIntegral.intervalIntegrable_sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrability.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.intervalIntegrable_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrability.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.intervalIntegrable_exp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrability.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntervalIntegrable.log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrability.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.intervalIntegrable_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrability.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.intervalIntegrable_log'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrability.Basic", "is_tactic_proof": true, "tactics": ["apply", "intro", "apply", "rw", "apply", "apply", "exact", "intro", "norm_num", "simpa", "intro", "norm_num", "exact", "apply", "apply", "apply", "simpa"], "tactic_count": 17}
{"name": "intervalIntegral.intervalIntegrable_one_div_one_add_sq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrability.Basic", "is_tactic_proof": true, "tactics": ["apply", "fun_prop"], "tactic_count": 2}
{"name": "intervalIntegral.intervalIntegrable_inv_one_add_sq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrability.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "intervalIntegrable_log_norm_meromorphicOn", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrability.LogMeromorphic", "is_tactic_proof": true, "tactics": ["by_cases", "obtain", "hf.extract_zeros_poles", "have", "rw", "apply", "apply", "intro", "apply", "rw", "apply", "simp", "apply", "apply", "simp_all", "rw", "push_neg", "have", "apply", "filter_upwards", "simp", "left", "by_contra", "simp_all", "rw", "apply", "tauto"], "tactic_count": 27}
{"name": "intervalIntegrable_posLog_norm_meromorphicOn", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrability.LogMeromorphic", "is_tactic_proof": true, "tactics": ["simp_rw", "apply", "apply", "apply"], "tactic_count": 4}
{"name": "MeromorphicOn.intervalIntegrable_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrability.LogMeromorphic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "intervalIntegrable_log_sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrability.LogMeromorphic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegrable_log_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrability.LogMeromorphic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "circleIntegrable_log_norm_meromorphicOn", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrability.LogMeromorphic", "is_tactic_proof": true, "tactics": ["by_cases", "obtain", "hf.extract_zeros_poles", "have", "apply", "apply", "apply", "intro", "apply", "apply", "apply", "apply", "apply", "apply", "apply", "apply", "apply", "intro", "simp", "intro", "rw", "apply", "rw", "push_neg", "have", "filter_upwards", "simp", "left", "by_contra", "simp_all", "apply"], "tactic_count": 31}
{"name": "circleIntegrable_log_norm_meromorphicOn_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrability.LogMeromorphic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "circleIntegrable_log_norm_factorizedRational", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrability.LogMeromorphic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "circleIntegrable_posLog_norm_meromorphicOn", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrability.LogMeromorphic", "is_tactic_proof": true, "tactics": ["simp_rw", "apply", "apply", "apply"], "tactic_count": 4}
{"name": "circleIntegrable_posLog_norm_meromorphicOn_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrability.LogMeromorphic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "intervalIntegral.mul_integral_comp_mul_right", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.mul_integral_comp_mul_left", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.inv_mul_integral_comp_div", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.mul_integral_comp_mul_add", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.mul_integral_comp_add_mul", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.inv_mul_integral_comp_div_add", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.inv_mul_integral_comp_add_div", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.mul_integral_comp_mul_sub", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.mul_integral_comp_sub_mul", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.inv_mul_integral_comp_div_sub", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.inv_mul_integral_comp_sub_div", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "integral_cpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.Basic", "is_tactic_proof": true, "tactics": ["rw", "have", "rcases", "apply_fun", "rw", "exact", "rw", "by_cases", "apply", "refine", "contrapose", "replace", "suffices", "rw", "integral_symm,", "ring", "intro", "apply", "refine", "rwa", "refine", "rcases", "rw", "rw", "contrapose", "exact"], "tactic_count": 26}
{"name": "integral_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.Basic", "is_tactic_proof": false, "tactics": ["have", "cases", "left", "right", "have", "integral_cpow", "apply_fun", "simp_rw", "rw", "refine", "rcases", "exact", "exact", "rw", "simp_rw"], "tactic_count": 15}
{"name": "integral_zpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.Basic", "is_tactic_proof": true, "tactics": ["replace", "exact"], "tactic_count": 2}
{"name": "integral_pow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "integral_pow_abs_sub_uIoc", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.Basic", "is_tactic_proof": true, "tactics": ["rcases", "calc", "simp", "refine", "rw", "exact", "calc", "simp", "refine", "rw", "exact"], "tactic_count": 11}
{"name": "integral_id", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.Basic", "is_tactic_proof": true, "tactics": ["have", "norm_num", "exact"], "tactic_count": 3}
{"name": "integral_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "integral_const_on_unit_interval", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "integral_inv", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.Basic", "is_tactic_proof": true, "tactics": ["have", "rw", "log_div"], "tactic_count": 3}
{"name": "integral_inv_of_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "integral_inv_of_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "integral_one_div", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "integral_one_div_of_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "integral_one_div_of_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "integral_exp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp", "exact", "exact"], "tactic_count": 4}
{"name": "integral_exp_mul_complex", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.Basic", "is_tactic_proof": false, "tactics": ["have", "intro", "conv", "rw", "apply", "simpa", "rw", "ring", "fun_prop"], "tactic_count": 9}
{"name": "integral_exp_mul_I_eq_sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "integral_exp_mul_I_eq_sinc", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.Basic", "is_tactic_proof": true, "tactics": ["rw", "by_cases", "simp", "rw", "norm_cast", "field"], "tactic_count": 6}
{"name": "integral_log_from_zero_of_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.Basic", "is_tactic_proof": true, "tactics": ["rw", "intervalIntegrable_log')]", "abel", "exact", "intro", "simpa", "simpa", "exact"], "tactic_count": 8}
{"name": "integral_log_from_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.Basic", "is_tactic_proof": true, "tactics": ["rcases", "conv", "rw", "integral_log_from_zero_of_pos", "ring", "simp", "exact"], "tactic_count": 7}
{"name": "integral_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.Basic", "is_tactic_proof": true, "tactics": ["rw", "rw", "ring", "all_goals"], "tactic_count": 4}
{"name": "integral_sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.Basic", "is_tactic_proof": true, "tactics": ["rw", "ring", "simp", "simp", "exact"], "tactic_count": 5}
{"name": "integral_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp", "simp", "exact"], "tactic_count": 4}
{"name": "integral_cos_mul_complex", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.Basic", "is_tactic_proof": true, "tactics": ["apply", "swap", "apply", "intro", "have", "have", "have", "have", "simp", "convert", "conv_rhs", "rw"], "tactic_count": 12}
{"name": "integral_cos_sq_sub_sin_sq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.Basic", "is_tactic_proof": true, "tactics": ["simpa", "integral_deriv_mul_eq_sub", "continuousOn_cos.intervalIntegrable"], "tactic_count": 3}
{"name": "integral_one_div_one_add_sq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.Basic", "is_tactic_proof": false, "tactics": ["refine", "integral_deriv_eq_sub", "fun_prop", "nlinarith"], "tactic_count": 4}
{"name": "integral_inv_one_add_sq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "integral_inv_sq_add_sq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "integral_div_sq_add_sq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "integral_mul_cpow_one_add_sq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.Basic", "is_tactic_proof": true, "tactics": ["have", "apply", "intro", "have", "convert", "simp", "have", "intro", "convert", "simp", "convert", "ring", "exact", "apply", "refine", "apply", "intro", "norm_cast", "exact"], "tactic_count": 19}
{"name": "integral_mul_rpow_one_add_sq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.Basic", "is_tactic_proof": false, "tactics": ["have", "intro", "norm_cast", "rw", "exact", "rw", "convert", "rw", "congr", "rw", "simp_rw", "push_cast", "rw", "exact"], "tactic_count": 14}
{"name": "integral_sin_pow_aux", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.Basic", "is_tactic_proof": true, "tactics": ["let", "have", "have", "simpa", "have", "simpa", "have", "calc", "rw", "all_goals"], "tactic_count": 10}
{"name": "integral_sin_pow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.Basic", "is_tactic_proof": true, "tactics": ["field_simp", "convert", "ring"], "tactic_count": 3}
{"name": "integral_sin_sq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "integral_sin_pow_odd", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "norm_cast", "field_simp", "simp"], "tactic_count": 7}
{"name": "integral_sin_pow_even", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "norm_cast", "field_simp", "simp"], "tactic_count": 7}
{"name": "integral_sin_pow_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.Basic", "is_tactic_proof": true, "tactics": ["rcases", "refine", "norm_cast", "lia"], "tactic_count": 4}
{"name": "integral_sin_pow_succ_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.Basic", "is_tactic_proof": true, "tactics": ["let", "refine"], "tactic_count": 2}
{"name": "integral_sin_pow_antitone", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "integral_cos_pow_aux", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.Basic", "is_tactic_proof": true, "tactics": ["let", "have", "have", "simpa", "have", "have", "calc", "rw", "all_goals"], "tactic_count": 9}
{"name": "integral_cos_pow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.Basic", "is_tactic_proof": true, "tactics": ["field_simp", "convert", "ring"], "tactic_count": 3}
{"name": "integral_cos_sq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "integral_sin_pow_mul_cos_pow_odd", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "integral_sin_mul_cos₁", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "integral_sin_sq_mul_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.Basic", "is_tactic_proof": true, "tactics": ["have", "norm_num"], "tactic_count": 2}
{"name": "integral_cos_pow_three", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.Basic", "is_tactic_proof": true, "tactics": ["have", "norm_num"], "tactic_count": 2}
{"name": "integral_sin_pow_odd_mul_cos_pow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "integral_sin_mul_cos₂", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "integral_sin_mul_cos_sq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.Basic", "is_tactic_proof": true, "tactics": ["have", "norm_num"], "tactic_count": 2}
{"name": "integral_sin_pow_three", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.Basic", "is_tactic_proof": true, "tactics": ["have", "norm_num"], "tactic_count": 2}
{"name": "integral_sin_pow_even_mul_cos_pow_even", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.Basic", "is_tactic_proof": true, "tactics": ["simp", "field_simp", "norm_num"], "tactic_count": 3}
{"name": "integral_sin_sq_mul_cos_sq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.Basic", "is_tactic_proof": true, "tactics": ["convert", "have", "have", "have", "have", "simp", "ring"], "tactic_count": 7}
{"name": "integral_sqrt_one_sub_sq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.SpecialFunctions.Integrals.LogTrigonometric.0.integral_log_sin_zero_pi_eq_two_mul_integral_log_sin_zero_pi_div_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.LogTrigonometric", "is_tactic_proof": false, "tactics": ["rw", "intervalIntegral.integral_add_adjacent_intervals", "conv", "left", "intro", "rw", "rw", "ring"], "tactic_count": 8}
{"name": "integral_log_sin_zero_pi_div_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.LogTrigonometric", "is_tactic_proof": true, "tactics": ["calc", "apply", "apply", "have", "apply", "simp", "have", "apply", "simp", "filter_upwards", "simp_all", "mul_eq_zero,", "ring", "rw", "intervalIntegral.integral_const]", "simp", "simpa", "apply", "simpa", "exact", "simp", "simp", "smul_eq_mul,", "linarith"], "tactic_count": 24}
{"name": "integral_log_sin_zero_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.LogTrigonometric", "is_tactic_proof": true, "tactics": ["rw", "ring"], "tactic_count": 2}
{"name": "circleIntegrable_log_norm_sub_const", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.PosLogEqCircleAverage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "circleAverage_log_norm_sub_const₀", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.PosLogEqCircleAverage", "is_tactic_proof": true, "tactics": ["calc", "circleAverage", "apply", "intro", "simp_all", "congr", "have", "calc", "rw", "sub_zero,", "intro", "have", "calc", "apply", "rw", "by_contra", "rwa"], "tactic_count": 17}
{"name": "_private.Mathlib.Analysis.SpecialFunctions.Integrals.PosLogEqCircleAverage.0.circleAverage_log_norm_sub_const₁_integral", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.PosLogEqCircleAverage", "is_tactic_proof": true, "tactics": ["calc", "have", "rw", "simp", "apply", "apply", "have", "have", "simp", "forall_const]", "filter_upwards", "simp", "not_false_eq_true,", "rw", "rw", "intervalIntegral.integral_const_mul]", "simp", "ring"], "tactic_count": 18}
{"name": "circleAverage_log_norm_sub_const₁", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.PosLogEqCircleAverage", "is_tactic_proof": true, "tactics": ["simp", "right", "obtain", "calc", "simp", "have", "have", "simp_all", "apply", "intro", "simp", "rw", "congr", "calc", "rw", "norm_num", "rw", "simp", "rw", "ring", "nth_rw", "ring"], "tactic_count": 22}
{"name": "circleAverage_log_norm_sub_const₂", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.PosLogEqCircleAverage", "is_tactic_proof": true, "tactics": ["rw", "intro", "apply", "rw", "by_contra", "simp_all", "linarith"], "tactic_count": 7}
{"name": "circleAverage_log_norm_sub_const_eq_posLog", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.PosLogEqCircleAverage", "is_tactic_proof": true, "tactics": ["rcases", "rw", "apply", "simp_all", "rw", "simp_all", "rw", "simp_all"], "tactic_count": 8}
{"name": "circleAverage_log_norm_add_const_eq_posLog", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.PosLogEqCircleAverage", "is_tactic_proof": true, "tactics": ["have", "simp"], "tactic_count": 2}
{"name": "circleAverage_log_norm_sub_const_eq_log_radius_add_posLog", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.PosLogEqCircleAverage", "is_tactic_proof": true, "tactics": ["calc", "circleAverage", "rw", "congr", "ext", "congr", "rw", "field", "apply", "have", "apply", "intro", "use", "simp", "apply", "intro", "simp_all", "rw", "filter_upwards", "rw", "simp", "rw", "circleAverage_add", "circleAverage_const]", "simp", "congr", "rcases", "simp", "rw"], "tactic_count": 29}
{"name": "circleAverage_log_norm_sub_const_of_mem_closedBall", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Integrals.PosLogEqCircleAverage", "is_tactic_proof": true, "tactics": ["by_cases", "simp_all", "rw", "abs_of_nonneg", "rw", "apply"], "tactic_count": 6}
{"name": "sqrt_one_add_norm_sq_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.JapaneseBracket", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "one_add_norm_le_sqrt_two_mul_sqrt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.JapaneseBracket", "is_tactic_proof": true, "tactics": ["rw", "have", "apply", "linarith"], "tactic_count": 4}
{"name": "rpow_neg_one_add_norm_sq_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.JapaneseBracket", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_rpow_one_add_norm_iff_norm_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.JapaneseBracket", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "closedBall_rpow_sub_one_eq_empty_aux", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.JapaneseBracket", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "finite_integral_rpow_sub_one_pow_aux", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.JapaneseBracket", "is_tactic_proof": true, "tactics": ["have", "have", "calc", "gcongr", "rw", "exact", "simp", "refine", "refine", "rw", "apply", "rwa"], "tactic_count": 12}
{"name": "finite_integral_one_add_norm", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.JapaneseBracket", "is_tactic_proof": true, "tactics": ["have", "have", "have", "rw", "have", "congr", "ext", "simp", "exact", "rw", "set", "set", "μ", "calc", "have", "refine", "rw", "exact", "rw", "exact", "have", "simp", "rw", "exact"], "tactic_count": 24}
{"name": "integrable_one_add_norm", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.JapaneseBracket", "is_tactic_proof": true, "tactics": ["constructor", "apply", "have", "lintegral_enorm_of_nonneg", "rw", "exact"], "tactic_count": 6}
{"name": "integrable_rpow_neg_one_add_norm_sq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.JapaneseBracket", "is_tactic_proof": true, "tactics": ["have", "refine", "apply", "refine", "positivity"], "tactic_count": 5}
{"name": "Real.logb", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.log_div_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.logb_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.logb_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.logb_zero_left", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.logb_zero_left_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Real.logb_one_left", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.logb_one_left_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Real.logb_self_eq_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.logb_self_eq_one_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.logb_abs_base", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.logb_abs", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.logb_neg_base_eq_logb", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.logb_neg_eq_logb", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.logb_mul", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Real.logb_div", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Real.logb_inv", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.logb_inv_base", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.inv_logb", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Real.inv_logb_mul_base", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Real.inv_logb_div_base", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Real.logb_mul_base", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.logb_div_base", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.mul_logb", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["unfold", "rw"], "tactic_count": 2}
{"name": "Real.div_logb", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.logb_rpow_eq_mul_logb_of_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.logb_pow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.logb_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Real.rpow_logb_eq_abs", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["apply", "simp", "apply", "simp", "rw", "field"], "tactic_count": 6}
{"name": "Real.rpow_logb", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Real.rpow_logb_of_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Real.logb_eq_iff_rpow_eq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["constructor", "exact", "exact"], "tactic_count": 3}
{"name": "Real.surjOn_logb", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.logb_surjective", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.range_logb", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.surjOn_logb'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["intro", "use", "constructor", "simp", "apply", "rw"], "tactic_count": 6}
{"name": "_private.Mathlib.Analysis.SpecialFunctions.Log.Base.0.Real.b_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["linarith"], "tactic_count": 1}
{"name": "_private.Mathlib.Analysis.SpecialFunctions.Log.Base.0.Real.b_ne_one'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["linarith"], "tactic_count": 1}
{"name": "Real.logb_le_logb", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.logb_le_logb_of_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.logb_lt_logb", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Real.logb_lt_logb_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Real.logb_le_iff_le_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.logb_lt_iff_lt_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.le_logb_iff_rpow_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.lt_logb_iff_rpow_lt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.logb_pos_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["rw", "rw"], "tactic_count": 2}
{"name": "Real.logb_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Real.logb_neg_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Real.logb_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.logb_nonneg_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.logb_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.logb_nonpos_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.logb_nonpos_iff'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["rcases", "simp", "exact"], "tactic_count": 3}
{"name": "Real.logb_nonpos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.strictMonoOn_logb", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.strictAntiOn_logb", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["rintro", "rw", "refine", "rwa"], "tactic_count": 4}
{"name": "Real.logb_injOn_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.eq_one_of_pos_of_logb_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.logb_ne_zero_of_pos_of_ne_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.tendsto_logb_atTop", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.SpecialFunctions.Log.Base.0.Real.b_ne_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["linarith"], "tactic_count": 1}
{"name": "Real.logb_le_logb_of_base_lt_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.logb_lt_logb_of_base_lt_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Real.logb_lt_logb_iff_of_base_lt_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Real.logb_le_iff_le_rpow_of_base_lt_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.logb_lt_iff_lt_rpow_of_base_lt_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.le_logb_iff_rpow_le_of_base_lt_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.lt_logb_iff_rpow_lt_of_base_lt_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.logb_pos_iff_of_base_lt_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.logb_pos_of_base_lt_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Real.logb_neg_iff_of_base_lt_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.logb_neg_of_base_lt_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.logb_nonneg_iff_of_base_lt_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.logb_nonneg_of_base_lt_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Real.logb_nonpos_iff_of_base_lt_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.strictAntiOn_logb_of_base_lt_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.strictMonoOn_logb_of_base_lt_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["rintro", "rw", "refine", "rwa"], "tactic_count": 4}
{"name": "Real.logb_injOn_pos_of_base_lt_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.eq_one_of_pos_of_logb_eq_zero_of_base_lt_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.logb_ne_zero_of_pos_of_ne_one_of_base_lt_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.tendsto_logb_atTop_of_base_lt_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["rw", "intro", "use", "intro", "simp", "intro", "rw", "tauto", "exact"], "tactic_count": 9}
{"name": "Real.floor_logb_natCast", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["obtain", "rw", "by_cases", "have", "apply", "rw", "refine", "exact", "rw", "exact", "rw", "cases", "simp_all", "simp_all"], "tactic_count": 14}
{"name": "Real.ceil_logb_natCast", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["obtain", "rw", "by_cases", "have", "apply", "rw", "exact", "rw", "refine", "exact", "rw", "cases", "simp_all", "simp_all"], "tactic_count": 14}
{"name": "Real.natFloor_logb_natCast", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["obtain", "simp", "simp", "obtain", "simp", "rw", "exact"], "tactic_count": 7}
{"name": "Real.natCeil_logb_natCast", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["obtain", "simp", "simp", "obtain", "simp", "rw", "exact"], "tactic_count": 7}
{"name": "Real.natLog_le_logb", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["apply", "rw"], "tactic_count": 2}
{"name": "Real.log2_le_logb", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["calc"], "tactic_count": 1}
{"name": "Real.logb_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["simp_rw", "tauto"], "tactic_count": 2}
{"name": "Real.tendsto_logb_nhdsNE_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.tendsto_logb_nhdsNE_zero_of_base_lt_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.tendsto_logb_nhdsGT_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.tendsto_logb_nhdsGT_zero_of_base_lt_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.tendsto_abs_logb_atTop", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["wlog", "exact", "wlog", "exact", "refine", "filter_upwards", "rw", "exact"], "tactic_count": 8}
{"name": "Real.continuousOn_logb", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.continuous_logb", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.continuous_logb'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.continuousAt_logb", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.continuousAt_logb_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["refine", "rintro", "cases", "inl", "exact", "not_tendsto_nhds_of_tendsto_atTop", "inr", "exact"], "tactic_count": 8}
{"name": "Real.logb_prod", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["induction", "empty", "cons"], "tactic_count": 3}
{"name": "Finsupp.logb_prod", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.logb_nat_eq_sum_factorization", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.tendsto_pow_logb_div_mul_add_atTop", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["cases", "inl", "inr", "apply", "simp"], "tactic_count": 5}
{"name": "Real.isLittleO_pow_logb_id_atTop", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["rw", "simpa", "filter_upwards"], "tactic_count": 3}
{"name": "Real.isLittleO_logb_id_atTop", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.isLittleO_const_logb_atTop", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["rw", "intro", "exact"], "tactic_count": 3}
{"name": "Filter.Tendsto.logb", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.logb", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.logb", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.logb", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.logb", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.tendsto_logb_comp_add_sub_logb", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.tendsto_logb_nat_add_one_sub_logb", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.induction_Ico_mul", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Base", "is_tactic_proof": false, "tactics": ["suffices", "intro", "have", "refine", "rw", "exact", "intro", "induction", "zero", "succ"], "tactic_count": 10}
{"name": "Real.log", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.log_of_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.log_of_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": true, "tactics": ["rw", "congr", "exact"], "tactic_count": 3}
{"name": "Real.exp_log_eq_abs", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.exp_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Real.exp_log_of_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Real.le_exp_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "exact", "rw", "exact"], "tactic_count": 5}
{"name": "Real.log_exp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.log_comp_exp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.exp_one_mul_le_exp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "apply", "have", "rwa"], "tactic_count": 4}
{"name": "Real.two_mul_le_exp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "apply", "have", "rwa"], "tactic_count": 5}
{"name": "Real.surjOn_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.log_surjective", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.range_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.log_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.log_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.log_div_self", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "Real.log_abs", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "rw"], "tactic_count": 3}
{"name": "Real.log_neg_eq_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.sinh_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.cosh_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.surjOn_log'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.log_mul", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.log_div", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.log_inv", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "rw"], "tactic_count": 2}
{"name": "Real.log_le_log_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.log_le_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.log_lt_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Real.log_lt_log_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.log_le_iff_le_exp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.log_lt_iff_lt_exp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.le_log_iff_exp_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.lt_log_iff_exp_lt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.log_pos_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rw", "exact"], "tactic_count": 4}
{"name": "Real.log_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.log_pos_of_lt_neg_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": true, "tactics": ["rw", "have", "exact"], "tactic_count": 3}
{"name": "Real.log_neg_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Real.log_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.log_neg_of_lt_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": true, "tactics": ["rw", "have", "have", "exact"], "tactic_count": 4}
{"name": "Real.log_nonneg_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.log_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.log_nonpos_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rw"], "tactic_count": 3}
{"name": "Real.log_nonpos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.log_natCast_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "Real.log_neg_natCast_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Real.log_intCast_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": true, "tactics": ["cases", "inl", "have", "exact", "inr", "cases", "inl", "inr", "have", "rw", "exact"], "tactic_count": 11}
{"name": "Real.strictMonoOn_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.strictAntiOn_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": true, "tactics": ["rintro", "rw", "refine", "rwa"], "tactic_count": 4}
{"name": "Real.log_injOn_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.log_lt_sub_one_of_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": false, "tactics": ["have", "rwa", "exact", "linarith"], "tactic_count": 4}
{"name": "Real.eq_one_of_pos_of_log_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.log_ne_zero_of_pos_of_ne_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.log_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rcases", "refine", "rw", "exact", "exact", "exact", "rintro"], "tactic_count": 9}
{"name": "Real.log_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.log_pow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rcases", "simp", "rw"], "tactic_count": 6}
{"name": "Real.log_zpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": true, "tactics": ["cases", "rw", "rw"], "tactic_count": 3}
{"name": "Real.log_sqrt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Real.log_le_sub_one_of_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": true, "tactics": ["rw", "convert", "rw"], "tactic_count": 3}
{"name": "Real.one_sub_inv_le_log_of_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.log_le_self", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": true, "tactics": ["obtain", "simp", "exact"], "tactic_count": 3}
{"name": "Real.neg_inv_le_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.abs_log_mul_self_lt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": true, "tactics": ["have", "replace", "replace", "rw", "have", "refine", "rw", "apply", "rw", "exact", "rw", "exact"], "tactic_count": 12}
{"name": "Real.tendsto_log_atTop", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.tendsto_log_nhdsGT_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.tendsto_log_nhdsNE_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.tendsto_log_nhdsLT_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.continuousOn_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": true, "tactics": ["simp", "conv", "exact"], "tactic_count": 3}
{"name": "Real.continuous_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.continuous_log'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.continuousAt_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.continuousAt_log_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": true, "tactics": ["refine", "rintro", "exact"], "tactic_count": 3}
{"name": "Real.log_list_prod", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "ih", "simp_all", "sum_cons]", "have", "rw"], "tactic_count": 8}
{"name": "Real.log_multiset_prod", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.log_prod", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Finsupp.log_prod", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.log_nat_eq_sum_factorization", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simp", "rw", "intro", "rw"], "tactic_count": 6}
{"name": "Real.tendsto_pow_log_div_mul_add_atTop", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.isLittleO_pow_log_id_atTop", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": true, "tactics": ["rw", "simpa", "filter_upwards"], "tactic_count": 3}
{"name": "Real.isLittleO_log_id_atTop", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.isLittleO_const_log_atTop", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": true, "tactics": ["refine", "filter_upwards", "aesop"], "tactic_count": 3}
{"name": "Real.expPartialHomeomorph", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.tendsto_log_comp_add_sub_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": false, "tactics": ["have", "tendsto_const_nhds.add", "rw", "refine", "filter_upwards", "rw"], "tactic_count": 6}
{"name": "Real.tendsto_log_nat_add_one_sub_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.log_nonneg_of_isNat", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Mathlib.Meta.Positivity.log_pos_of_isNat", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply", "simpa"], "tactic_count": 3}
{"name": "Mathlib.Meta.Positivity.log_nonneg_of_isNegNat", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Mathlib.Meta.Positivity.log_pos_of_isNegNat", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": true, "tactics": ["rw", "rw", "apply", "simpa"], "tactic_count": 4}
{"name": "Mathlib.Meta.Positivity.log_pos_of_isNNRat", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.log_pos_of_isRat_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.log_nz_of_isNNRat", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.log_nz_of_isRat_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalLogNatCast", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalLogIntCast", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalLogNatLit", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Log.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.hasStrictDerivAt_log_of_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Deriv", "is_tactic_proof": false, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "Real.hasStrictDerivAt_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Deriv", "is_tactic_proof": true, "tactics": ["rcases", "convert", "ext", "ring", "exact"], "tactic_count": 5}
{"name": "Real.hasDerivAt_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.differentiableAt_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.differentiableOn_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.differentiableAt_log_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.deriv_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.deriv_log'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.contDiffAt_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Deriv", "is_tactic_proof": true, "tactics": ["refine", "have", "apply", "convert", "rw", "exact", "rcases", "have", "apply", "apply", "apply", "convert", "ext", "simp", "exact"], "tactic_count": 15}
{"name": "Real.contDiffOn_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Deriv", "is_tactic_proof": true, "tactics": ["intro", "push", "exact"], "tactic_count": 3}
{"name": "HasDerivWithinAt.log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Deriv", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "HasDerivAt.log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Deriv", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "HasStrictDerivAt.log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Deriv", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "derivWithin.log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv.log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.deriv_log_comp_eq_logDeriv", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Deriv", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HasFDerivWithinAt.log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivAt.log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictFDerivAt.log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableWithinAt.log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableAt.log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffAt.log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffWithinAt.log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffOn.log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableOn.log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Differentiable.log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderivWithin.log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderiv.log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.abs_log_sub_add_sum_range_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Deriv", "is_tactic_proof": true, "tactics": ["and", "let", "let", "have", "have", "convert", "calc", "simp", "ring", "congr", "rw", "have", "calc", "have", "have", "gcongr", "exact", "have", "refine", "exact", "simp", "simp", "simpa"], "tactic_count": 23}
{"name": "Real.hasDerivAt_half_log_one_add_div_one_sub_sub_sum_range", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Deriv", "is_tactic_proof": false, "tactics": ["refine", "simp", "have", "congr", "simp", "have", "have", "simp", "ring"], "tactic_count": 9}
{"name": "Real.sum_range_sub_log_div_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Deriv", "is_tactic_proof": true, "tactics": ["let", "let", "have", "have", "intro", "exact", "hasDerivAt_half_log_one_add_div_one_sub_sub_sum_range", "have", "have", "calc", "simp", "have", "simpa"], "tactic_count": 13}
{"name": "Real.sum_range_le_log_div", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Deriv", "is_tactic_proof": true, "tactics": ["let", "let", "have", "intro", "exact", "hasDerivAt_half_log_one_add_div_one_sub_sub_sum_range", "suffices", "refine", "monotoneOn_of_hasDerivWithinAt_nonneg", "intro", "simp", "have", "calc", "positivity"], "tactic_count": 14}
{"name": "Real.log_div_le_sum_range_add", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Deriv", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "Real.hasSum_pow_div_log_of_abs_lt_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Deriv", "is_tactic_proof": true, "tactics": ["rw", "show", "rw", "simp", "refine", "suffices", "simp", "refine", "exact", "show", "refine", "calc", "have", "rw", "gcongr", "exact"], "tactic_count": 16}
{"name": "Real.hasSum_log_sub_log_of_abs_lt_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Deriv", "is_tactic_proof": true, "tactics": ["set", "have", "ext", "dsimp", "rw", "push_cast", "ring_nf", "rw", "have", "convert", "ring_nf", "intro", "rw", "dsimp", "rw"], "tactic_count": 15}
{"name": "Real.hasSum_log_one_add_inv", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Deriv", "is_tactic_proof": false, "tactics": ["have", "rw", "linarith", "linarith", "exact", "convert", "have", "have", "rw", "congr", "simp", "ring", "field_simp", "positivity", "simp"], "tactic_count": 15}
{"name": "Real.hasSum_log_one_add", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Deriv", "is_tactic_proof": true, "tactics": ["obtain", "simp", "convert", "all_goals"], "tactic_count": 4}
{"name": "Real.le_log_one_add_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Deriv", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "Real.lt_log_one_add_of_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Deriv", "is_tactic_proof": false, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "ENNReal.log", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Log.ENNRealLog", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.log_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ENNRealLog", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.log_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ENNRealLog", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.log_top", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ENNRealLog", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.log_ofReal", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ENNRealLog", "is_tactic_proof": true, "tactics": ["simp", "split_ifs", "rfl", "rw"], "tactic_count": 4}
{"name": "ENNReal.log_ofReal_of_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ENNRealLog", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.log_pos_real", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ENNRealLog", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.log_pos_real'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ENNRealLog", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.log_of_nnreal", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ENNRealLog", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.log_strictMono", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ENNRealLog", "is_tactic_proof": true, "tactics": ["intro", "unfold", "split_ifs"], "tactic_count": 3}
{"name": "ENNReal.log_monotone", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ENNRealLog", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.log_injective", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ENNRealLog", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.log_surjective", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ENNRealLog", "is_tactic_proof": true, "tactics": ["intro", "cases", "bot", "top", "coe"], "tactic_count": 5}
{"name": "ENNReal.log_bijective", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ENNRealLog", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.log_eq_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ENNRealLog", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.log_eq_bot_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ENNRealLog", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.log_eq_one_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ENNRealLog", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.log_eq_top_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ENNRealLog", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.log_lt_log_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ENNRealLog", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.bot_lt_log_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ENNRealLog", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.log_lt_top_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ENNRealLog", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.log_lt_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ENNRealLog", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.zero_lt_log_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ENNRealLog", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.log_le_log_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ENNRealLog", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.log_le_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ENNRealLog", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.zero_le_log_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ENNRealLog", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.log_le_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ENNRealLog", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.log_lt_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ENNRealLog", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.log_mul_add", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ENNRealLog", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rw", "rcases", "rw", "simp", "rw", "simp", "exact", "rw", "rcases", "simp", "simp", "rw_mod_cast", "exact", "rw", "positivity"], "tactic_count": 17}
{"name": "ENNReal.log_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ENNRealLog", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "simp", "rw", "have", "have", "simp", "norm_cast", "exact", "simp", "rcases", "rw", "rw", "have", "have", "simp", "norm_cast", "exact"], "tactic_count": 18}
{"name": "ENNReal.log_pow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ENNRealLog", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.log_inv", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ENNRealLog", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "EReal.log_exp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ENNRealLogExp", "is_tactic_proof": true, "tactics": ["induction", "simp", "rw", "simp"], "tactic_count": 4}
{"name": "ENNReal.exp_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ENNRealLogExp", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "by_cases", "simp", "have", "rw"], "tactic_count": 6}
{"name": "EReal.exp_nmul", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ENNRealLogExp", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "EReal.exp_mul", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ENNRealLogExp", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EReal.ENNReal.rpow_eq_exp_mul_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ENNRealLogExp", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.logOrderIso", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Log.ENNRealLogExp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.logOrderIso_apply", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ENNRealLogExp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.expOrderIso", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Log.ENNRealLogExp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.expOrderIso_apply", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ENNRealLogExp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.logOrderIso_symm", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ENNRealLogExp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.expOrderIso_symm", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ENNRealLogExp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.logHomeomorph", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Log.ENNRealLogExp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.logHomeomorph_apply", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ENNRealLogExp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.expHomeomorph", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Log.ENNRealLogExp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.expHomeomorph_apply", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ENNRealLogExp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.logHomeomorph_symm", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ENNRealLogExp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.expHomeomorph_symm", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ENNRealLogExp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.continuous_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ENNRealLogExp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.continuous_exp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ENNRealLogExp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.tendsto_exp_nhds_top_nhds_top", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ENNRealLogExp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.tendsto_exp_nhds_zero_nhds_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ENNRealLogExp", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "EReal.tendsto_exp_nhds_bot_nhds_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ENNRealLogExp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.tendsto_rpow_atTop_of_one_lt_base", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ENNRealLogExp", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "convert", "rw", "all_goals"], "tactic_count": 5}
{"name": "ENNReal.tendsto_rpow_atTop_of_base_lt_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ENNRealLogExp", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "convert", "rw", "all_goals"], "tactic_count": 5}
{"name": "ENNReal.tendsto_rpow_atBot_of_one_lt_base", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ENNRealLogExp", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "convert", "rw", "all_goals"], "tactic_count": 5}
{"name": "ENNReal.tendsto_rpow_atBot_of_base_lt_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ENNRealLogExp", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "convert", "rw", "all_goals"], "tactic_count": 5}
{"name": "ENNReal.measurable_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ENNRealLogExp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.measurable_exp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ENNRealLogExp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.ennreal_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ENNRealLogExp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.ereal_exp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ENNRealLogExp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instPolishSpaceEReal", "kind": "instance", "module": "Mathlib.Analysis.SpecialFunctions.Log.ENNRealLogExp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.exp", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Log.ERealExp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.exp_bot", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ERealExp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.exp_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ERealExp", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "EReal.exp_top", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ERealExp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.exp_coe", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ERealExp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.exp_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ERealExp", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "EReal.exp_eq_top_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ERealExp", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "EReal.exp_strictMono", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ERealExp", "is_tactic_proof": true, "tactics": ["intro", "induction", "rw", "exact", "induction", "simp", "simp_rw", "exact", "simp", "exact"], "tactic_count": 10}
{"name": "EReal.exp_monotone", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ERealExp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.exp_lt_exp_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ERealExp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.zero_lt_exp_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ERealExp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.exp_lt_top_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ERealExp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.exp_lt_one_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ERealExp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.one_lt_exp_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ERealExp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.exp_le_exp_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ERealExp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.exp_le_one_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ERealExp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.one_le_exp_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ERealExp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.exp_le_exp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ERealExp", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "EReal.exp_lt_exp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ERealExp", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "EReal.exp_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ERealExp", "is_tactic_proof": true, "tactics": ["induction", "simp", "rw", "simp"], "tactic_count": 4}
{"name": "EReal.exp_add", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.ERealExp", "is_tactic_proof": true, "tactics": ["induction", "simp", "induction", "simp", "simp", "rw", "simp", "rw", "simp", "induction", "simp", "simp", "rw", "simp", "simp"], "tactic_count": 15}
{"name": "Real.not_differentiableAt_inv_log_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.InvLog", "is_tactic_proof": false, "tactics": ["simp", "smul_eq_mul,", "have", "refine", "simp", "refine", "refine", "exact"], "tactic_count": 8}
{"name": "Real.not_continuousAt_inv_log_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.InvLog", "is_tactic_proof": false, "tactics": ["suffices", "not_continuousAt_of_tendsto", "have", "exact"], "tactic_count": 4}
{"name": "Real.not_continuousAt_inv_log_neg_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.InvLog", "is_tactic_proof": true, "tactics": ["refine", "simpa"], "tactic_count": 2}
{"name": "Real.deriv_inv_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.InvLog", "is_tactic_proof": true, "tactics": ["rcases", "simpa", "rcases", "simpa", "rcases", "simpa", "simp_all"], "tactic_count": 7}
{"name": "Real.log_mul_self_monotoneOn", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Monotone", "is_tactic_proof": true, "tactics": ["simp", "intro", "have", "gcongr", "rwa"], "tactic_count": 5}
{"name": "Real.log_div_self_antitoneOn", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Monotone", "is_tactic_proof": true, "tactics": ["simp", "intro", "have", "have", "have", "have", "rw", "calc", "log"], "tactic_count": 9}
{"name": "Real.log_div_self_rpow_antitoneOn", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Monotone", "is_tactic_proof": true, "tactics": ["simp", "intro", "have", "have", "nth_rw", "nth_rw", "rw", "log_rpow", "mul_le_mul_iff_right₀", "refine", "simp", "convert", "rw", "simp", "field", "positivity", "simp", "convert", "rw", "simp", "field", "positivity", "gcongr"], "tactic_count": 23}
{"name": "Real.log_div_sqrt_antitoneOn", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Monotone", "is_tactic_proof": true, "tactics": ["simp_rw", "convert", "norm_num"], "tactic_count": 3}
{"name": "Real.continuous_mul_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.NegMulLog", "is_tactic_proof": true, "tactics": ["rw", "intro", "obtain", "exact", "rw", "simp_rw", "nth_rewrite", "have", "rw", "simp", "refine", "simpa", "convert", "simp"], "tactic_count": 14}
{"name": "Real.Continuous.mul_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.NegMulLog", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.differentiableOn_mul_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.NegMulLog", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.deriv_mul_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.NegMulLog", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.hasDerivAt_mul_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.NegMulLog", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp"], "tactic_count": 3}
{"name": "Real.rightDeriv_mul_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.NegMulLog", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.leftDeriv_mul_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.NegMulLog", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.SpecialFunctions.Log.NegMulLog.0.Real.tendsto_deriv_mul_log_nhdsWithin_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.NegMulLog", "is_tactic_proof": false, "tactics": ["have", "apply", "intro", "rw", "exact", "simp"], "tactic_count": 6}
{"name": "Real.tendsto_deriv_mul_log_atTop", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.NegMulLog", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "Real.tendsto_rightDeriv_mul_log_atTop", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.NegMulLog", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "Real.not_DifferentiableAt_log_mul_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.NegMulLog", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.deriv_mul_log_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.NegMulLog", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.not_continuousAt_deriv_mul_log_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.NegMulLog", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.deriv2_mul_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.NegMulLog", "is_tactic_proof": true, "tactics": ["simp", "by_cases", "rw", "exact", "suffices", "refine", "rw", "filter_upwards"], "tactic_count": 8}
{"name": "Real.strictConvexOn_mul_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.NegMulLog", "is_tactic_proof": true, "tactics": ["refine", "intro", "simp", "rw", "positivity"], "tactic_count": 5}
{"name": "Real.convexOn_mul_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.NegMulLog", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.mul_log_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.NegMulLog", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.mul_log_nonpos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.NegMulLog", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.negMulLog", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Log.NegMulLog", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.negMulLog_def", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.NegMulLog", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.negMulLog_eq_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.NegMulLog", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.negMulLog_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.NegMulLog", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.negMulLog_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.NegMulLog", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.negMulLog_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.NegMulLog", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.negMulLog_mul", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.NegMulLog", "is_tactic_proof": true, "tactics": ["simp", "by_cases", "simp", "by_cases", "simp", "rw", "ring"], "tactic_count": 7}
{"name": "Real.continuous_negMulLog", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.NegMulLog", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.differentiableOn_negMulLog", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.NegMulLog", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.differentiableAt_negMulLog_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.NegMulLog", "is_tactic_proof": true, "tactics": ["constructor", "unfold", "intro", "simp", "exact", "intro", "have", "have", "apply", "simp_all"], "tactic_count": 10}
{"name": "Real.deriv_negMulLog", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.NegMulLog", "is_tactic_proof": true, "tactics": ["rw", "ring"], "tactic_count": 2}
{"name": "Real.hasDerivAt_negMulLog", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.NegMulLog", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp"], "tactic_count": 3}
{"name": "Real.deriv2_negMulLog", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.NegMulLog", "is_tactic_proof": true, "tactics": ["rw", "have", "simp", "rw"], "tactic_count": 4}
{"name": "Real.strictConcaveOn_negMulLog", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.NegMulLog", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.concaveOn_negMulLog", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.NegMulLog", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.posLog", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Log.PosLog", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.termLog⁺", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Log.PosLog", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real._aux_Mathlib_Analysis_SpecialFunctions_Log_PosLog___macroRules_Real_termLog⁺_1", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Log.PosLog", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real._aux_Mathlib_Analysis_SpecialFunctions_Log_PosLog___unexpand_Real_posLog_1", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Log.PosLog", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.posLog_def", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.PosLog", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.posLog_sub_posLog_inv", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.PosLog", "is_tactic_proof": true, "tactics": ["rw", "by_cases", "simp", "simp"], "tactic_count": 4}
{"name": "Real.half_mul_log_add_log_abs", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.PosLog", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "ring", "simp"], "tactic_count": 4}
{"name": "Real.posLog_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.PosLog", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.posLog_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.PosLog", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.posLog_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.PosLog", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.posLog_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.PosLog", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.posLog_abs", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.PosLog", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.posLog_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.PosLog", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Real.posLog_eq_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.PosLog", "is_tactic_proof": true, "tactics": ["simp", "rw", "apply"], "tactic_count": 3}
{"name": "Real.log_of_nat_eq_posLog", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.PosLog", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "simp"], "tactic_count": 3}
{"name": "Real.posLog_eq_log_max_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.PosLog", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Real.monotoneOn_posLog", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.PosLog", "is_tactic_proof": true, "tactics": ["intro", "simp", "by_cases", "tauto", "right", "have", "simp", "linarith"], "tactic_count": 8}
{"name": "Real.posLog_le_posLog", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.PosLog", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.posLog_pow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.PosLog", "is_tactic_proof": true, "tactics": ["by_cases", "simp_all", "by_cases", "simp_all", "rw", "have", "simp"], "tactic_count": 7}
{"name": "Real.posLog_mul", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.PosLog", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "by_cases", "simp", "unfold", "nth_rw", "exact"], "tactic_count": 7}
{"name": "Real.posLog_nat_mul", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.PosLog", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Real.posLog_prod", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.PosLog", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "insert", "calc", "log⁺"], "tactic_count": 6}
{"name": "Real.posLog_sum", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.PosLog", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "obtain", "calc", "log⁺", "apply", "simp", "apply", "apply", "gcongr", "rw", "apply"], "tactic_count": 12}
{"name": "Real.posLog_norm_sum_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.PosLog", "is_tactic_proof": true, "tactics": ["grw"], "tactic_count": 1}
{"name": "Real.posLog_add", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.PosLog", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "Real.posLog_norm_add_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.PosLog", "is_tactic_proof": true, "tactics": ["grw"], "tactic_count": 1}
{"name": "Real.norm_inv_mul_rpow_sub_one_sub_log_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.RpowTendsto", "is_tactic_proof": true, "tactics": ["have", "calc", "simp", "congr", "rw", "gcongr", "refine", "simp", "simp", "grind"], "tactic_count": 10}
{"name": "Real.tendstoLocallyUniformlyOn_rpow_sub_one_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.RpowTendsto", "is_tactic_proof": true, "tactics": ["refine", "intro", "rw", "intro", "let", "have", "have", "refine", "grind", "have", "refine", "grind", "have", "have", "have", "have", "have", "filter_upwards", "intro", "have", "calc", "gcongr", "refine", "grind", "have", "rw", "calc", "gcongr", "refine", "grind"], "tactic_count": 30}
{"name": "tendsto_rpow_sub_one_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.RpowTendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.hasProd_of_hasSum_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.multipliable_of_summable_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Summable", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "exact"], "tactic_count": 3}
{"name": "Complex.cexp_tsum_eq_tprod", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.summable_log_one_add_of_summable", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Summable", "is_tactic_proof": true, "tactics": ["apply", "filter_upwards", "norm_log_one_add_half_le_self"], "tactic_count": 3}
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{"name": "Real.hasProd_of_hasSum_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.multipliable_of_summable_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Real.summable_log_one_add_of_summable", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Summable", "is_tactic_proof": true, "tactics": ["rw", "apply", "filter_upwards", "rw", "linarith"], "tactic_count": 5}
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{"name": "Multipliable.eventually_bounded_finset_prod", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Summable", "is_tactic_proof": true, "tactics": ["obtain", "rw", "have", "rw", "exact"], "tactic_count": 5}
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{"name": "Finset.norm_prod_one_add_sub_one_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Summable", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "insert", "rw", "show", "refine", "generalize", "rw", "transitivity", "grw", "rw", "exact"], "tactic_count": 13}
{"name": "prod_vanishing_of_summable_norm", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Summable", "is_tactic_proof": false, "tactics": ["suffices", "this.imp", "suffices", "let", "have", "exact"], "tactic_count": 6}
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{"name": "Summable.summable_log_norm_one_add", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Summable", "is_tactic_proof": true, "tactics": ["suffices", "refine", "simp", "constructor", "simpa", "simpa"], "tactic_count": 6}
{"name": "tprod_one_add_ne_zero_of_summable", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Log.Summable", "is_tactic_proof": true, "tactics": ["rw", "rw", "apply", "exact"], "tactic_count": 4}
{"name": "Real.mulExpNegMulSq", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.MulExpNegMulSq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.mulExpNegSq_apply", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.MulExpNegMulSq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.neg_mulExpNegMulSq_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.MulExpNegMulSq", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.mulExpNegMulSq_one_le_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.MulExpNegMulSq", "is_tactic_proof": true, "tactics": ["simp", "rw", "apply", "nlinarith"], "tactic_count": 4}
{"name": "Real.neg_one_le_mulExpNegMulSq_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.MulExpNegMulSq", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
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{"name": "Continuous.mulExpNegMulSq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.MulExpNegMulSq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.differentiableAt_mulExpNegMulSq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.MulExpNegMulSq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.differentiable_mulExpNegMulSq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.MulExpNegMulSq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.hasDerivAt_mulExpNegMulSq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.MulExpNegMulSq", "is_tactic_proof": true, "tactics": ["nth_rw", "apply", "apply"], "tactic_count": 3}
{"name": "Real.deriv_mulExpNegMulSq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.MulExpNegMulSq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.norm_deriv_mulExpNegMulSq_le_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.MulExpNegMulSq", "is_tactic_proof": true, "tactics": ["rw", "have", "exp", "rw", "set", "have", "rw", "exact", "apply", "simp", "refine", "exact"], "tactic_count": 12}
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{"name": "Real.lipschitzWith_one_mulExpNegMulSq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.MulExpNegMulSq", "is_tactic_proof": true, "tactics": ["apply", "exact"], "tactic_count": 2}
{"name": "Real.mulExpNegMulSq_eq_sqrt_mul_mulExpNegMulSq_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.MulExpNegMulSq", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Real.abs_mulExpNegMulSq_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.MulExpNegMulSq", "is_tactic_proof": true, "tactics": ["rw", "apply", "positivity", "exact"], "tactic_count": 4}
{"name": "Real.dist_mulExpNegMulSq_le_two_mul_sqrt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.MulExpNegMulSq", "is_tactic_proof": true, "tactics": ["apply", "simp", "exact"], "tactic_count": 3}
{"name": "Real.dist_mulExpNegMulSq_le_dist", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.MulExpNegMulSq", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "Real.tendsto_mulExpNegMulSq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.MulExpNegMulSq", "is_tactic_proof": false, "tactics": ["have", "nth_rw", "apply"], "tactic_count": 3}
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{"name": "integrable_mulExpNegMulSq_comp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.MulExpNegMulSqIntegral", "is_tactic_proof": true, "tactics": ["apply", "exact"], "tactic_count": 2}
{"name": "integrable_mulExpNegMulSq_comp_restrict_of_isCompact", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.MulExpNegMulSqIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "not_integrableOn_Ici_inv", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.NonIntegrable", "is_tactic_proof": false, "tactics": ["have", "filter_upwards", "have", "exact", "not_integrableOn_of_tendsto_norm_atTop_of_deriv_isBigO_filter"], "tactic_count": 5}
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{"name": "ordinaryHypergeometricCoefficient", "kind": "abbrev", "module": "Mathlib.Analysis.SpecialFunctions.OrdinaryHypergeometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ordinaryHypergeometricSeries", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.OrdinaryHypergeometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ordinaryHypergeometricSeries_apply_eq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.OrdinaryHypergeometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "ordinaryHypergeometric_eq_tsum", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.OrdinaryHypergeometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ordinaryHypergeometricSeries_apply_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.OrdinaryHypergeometric", "is_tactic_proof": true, "tactics": ["rw", "cases"], "tactic_count": 2}
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{"name": "ordinaryHypergeometricSeries_eq_zero_of_neg_nat", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.OrdinaryHypergeometric", "is_tactic_proof": true, "tactics": ["rw", "rcases", "all_goals", "ext", "simp"], "tactic_count": 5}
{"name": "ordinaryHypergeometric_radius_top_of_neg_nat₁", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.OrdinaryHypergeometric", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "ordinaryHypergeometric_radius_top_of_neg_nat₂", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.OrdinaryHypergeometric", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ordinaryHypergeometric_radius_top_of_neg_nat₃", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.OrdinaryHypergeometric", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
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{"name": "differentiable_descPochhammer_eval", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pochhammer", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "continuous_descPochhammer_eval", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pochhammer", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "deriv_descPochhammer_eval_eq_sum_prod_range_erase", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pochhammer", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "monotoneOn_deriv_descPochhammer_eval", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pochhammer", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "intro", "rw", "simp_rw", "apply", "apply", "intro", "rw", "apply", "exact", "intro", "rwa"], "tactic_count": 14}
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{"name": "_private.Mathlib.Analysis.SpecialFunctions.Pochhammer.0.piecewise_Ici_descPochhammer_eval_zero_eq_descFactorial", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pochhammer", "is_tactic_proof": false, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "_private.Mathlib.Analysis.SpecialFunctions.Pochhammer.0.convexOn_piecewise_Ici_descPochhammer_eval_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pochhammer", "is_tactic_proof": true, "tactics": ["rw", "apply", "convexOn_univ_piecewise_Ici_of_monotoneOn_Ici_antitoneOn_Iic", "simpa"], "tactic_count": 4}
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{"name": "polarCoord", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.PolarCoord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_polarCoord_symm", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.PolarCoord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderivPolarCoordSymm", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.PolarCoord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasFDerivAt_polarCoord_symm", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.PolarCoord", "is_tactic_proof": true, "tactics": ["unfold", "rw", "convert", "simp"], "tactic_count": 4}
{"name": "det_fderivPolarCoordSymm", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.PolarCoord", "is_tactic_proof": true, "tactics": ["conv_rhs", "unfold", "simp", "ring"], "tactic_count": 4}
{"name": "instIsAddHaarMeasureProdRealVolume", "kind": "instance", "module": "Mathlib.Analysis.SpecialFunctions.PolarCoord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "polarCoord_source_ae_eq_univ", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.PolarCoord", "is_tactic_proof": false, "tactics": ["have", "intro", "simp", "exact", "have", "apply", "rw", "intro", "have", "simp", "simp", "exact"], "tactic_count": 12}
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{"name": "lintegral_comp_polarCoord_symm", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.PolarCoord", "is_tactic_proof": true, "tactics": ["symm", "calc", "rw", "polarCoord.symm_image_target_eq_source]", "rw", "simp_rw", "exacts", "refine", "rw"], "tactic_count": 9}
{"name": "Complex.polarCoord", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.PolarCoord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.polarCoord_apply", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.PolarCoord", "is_tactic_proof": true, "tactics": ["simp_rw", "rfl"], "tactic_count": 2}
{"name": "Complex.polarCoord_source", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.PolarCoord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.polarCoord_target", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.PolarCoord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.polarCoord_symm_apply", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.PolarCoord", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.measurableEquivRealProd_symm_polarCoord_symm_apply", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.PolarCoord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.norm_polarCoord_symm", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.PolarCoord", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.integral_comp_polarCoord_symm", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.PolarCoord", "is_tactic_proof": false, "tactics": ["rw", "simp_rw"], "tactic_count": 2}
{"name": "Complex.lintegral_comp_polarCoord_symm", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.PolarCoord", "is_tactic_proof": false, "tactics": ["rw", "lintegral_comp_polarCoord_symm]", "simp_rw"], "tactic_count": 3}
{"name": "fderivPiPolarCoordSymm", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.PolarCoord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "injOn_pi_polarCoord_symm", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.PolarCoord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "abs_fst_of_mem_pi_polarCoord_target", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.PolarCoord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasFDerivAt_pi_polarCoord_symm", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.PolarCoord", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "measurableSet_pi_polarCoord_target", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.PolarCoord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "det_fderivPiPolarCoordSymm", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.PolarCoord", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "pi_polarCoord_symm_target_ae_eq_univ", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.PolarCoord", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "integral_comp_pi_polarCoord_symm", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.PolarCoord", "is_tactic_proof": true, "tactics": ["rw", "convert", "refine", "simp_rw"], "tactic_count": 4}
{"name": "Complex.integral_comp_pi_polarCoord_symm", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.PolarCoord", "is_tactic_proof": true, "tactics": ["let", "have", "rw", "exact"], "tactic_count": 4}
{"name": "lintegral_comp_pi_polarCoord_symm", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.PolarCoord", "is_tactic_proof": true, "tactics": ["rw", "convert", "refine", "simp_rw", "abs_fst_of_mem_pi_polarCoord_target"], "tactic_count": 5}
{"name": "Complex.lintegral_comp_pi_polarCoord_symm", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.PolarCoord", "is_tactic_proof": true, "tactics": ["let", "have", "rw", "exact"], "tactic_count": 4}
{"name": "Polynomial.tendsto_div_exp_atTop", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.PolynomialExp", "is_tactic_proof": true, "tactics": ["induction", "monomial", "simpa", "add"], "tactic_count": 4}
{"name": "tendsto_rpow_atTop", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Asymptotics", "is_tactic_proof": true, "tactics": ["rw", "intro", "filter_upwards", "simpa"], "tactic_count": 4}
{"name": "tendsto_rpow_neg_nhdsGT_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Asymptotics", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "tendsto_rpow_neg_atTop", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Asymptotics", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_rpow_atTop_of_base_lt_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Asymptotics", "is_tactic_proof": true, "tactics": ["rcases", "simp_rw", "rw", "refine", "rw", "refine", "rw", "linarith", "rw", "exact", "refine", "rw", "filter_upwards", "simp", "simp_rw", "refine", "exact"], "tactic_count": 17}
{"name": "tendsto_rpow_atBot_of_base_lt_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Asymptotics", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "exact"], "tactic_count": 3}
{"name": "tendsto_rpow_atBot_of_base_gt_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Asymptotics", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "exact"], "tactic_count": 3}
{"name": "tendsto_rpow_div_mul_add", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Asymptotics", "is_tactic_proof": false, "tactics": ["refine", "simpa", "tendsto_log_atTop)", "apply", "intro", "simp", "rw", "field_simp"], "tactic_count": 8}
{"name": "tendsto_rpow_div", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Asymptotics", "is_tactic_proof": true, "tactics": ["convert", "ring"], "tactic_count": 2}
{"name": "tendsto_rpow_neg_div", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Asymptotics", "is_tactic_proof": true, "tactics": ["convert", "ring"], "tactic_count": 2}
{"name": "tendsto_exp_div_rpow_atTop", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Asymptotics", "is_tactic_proof": true, "tactics": ["obtain", "refine", "filter_upwards", "gcongr", "simpa"], "tactic_count": 5}
{"name": "tendsto_exp_mul_div_rpow_atTop", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Asymptotics", "is_tactic_proof": true, "tactics": ["refine", "filter_upwards", "simp"], "tactic_count": 3}
{"name": "tendsto_rpow_mul_exp_neg_mul_atTop_nhds_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Asymptotics", "is_tactic_proof": true, "tactics": ["refine", "filter_upwards"], "tactic_count": 2}
{"name": "NNReal.tendsto_rpow_atTop", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Asymptotics", "is_tactic_proof": true, "tactics": ["rw", "intro", "obtain", "use", "intro", "exact"], "tactic_count": 6}
{"name": "ENNReal.tendsto_rpow_at_top", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Asymptotics", "is_tactic_proof": true, "tactics": ["rw", "intro", "obtain", "have", "filter_upwards", "by_cases", "simp", "lift", "simp", "rw", "exact"], "tactic_count": 11}
{"name": "Complex.isTheta_exp_arg_mul_im", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Asymptotics", "is_tactic_proof": true, "tactics": ["rcases", "refine", "rw", "refine", "rw", "exact"], "tactic_count": 6}
{"name": "Complex.isBigO_cpow_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Asymptotics", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.isTheta_cpow_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Asymptotics", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.isTheta_cpow_const_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Asymptotics", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsBigOWith.rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Asymptotics", "is_tactic_proof": true, "tactics": ["apply", "filter_upwards", "calc", "f"], "tactic_count": 4}
{"name": "Asymptotics.IsBigO.rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Asymptotics", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsTheta.rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Asymptotics", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsLittleO.rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Asymptotics", "is_tactic_proof": true, "tactics": ["refine", "rw", "refine"], "tactic_count": 3}
{"name": "Asymptotics.IsBigO.sqrt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Asymptotics", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Asymptotics.IsLittleO.sqrt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Asymptotics", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Asymptotics.IsTheta.sqrt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Asymptotics", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.isBigO_atTop_natCast_rpow_of_tendsto_div_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Asymptotics", "is_tactic_proof": true, "tactics": ["refine", "filter_upwards", "simp", "exact"], "tactic_count": 4}
{"name": "Asymptotics.IsBigO.mul_atTop_rpow_of_isBigO_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Asymptotics", "is_tactic_proof": true, "tactics": ["refine", "filter_upwards", "rw", "exact"], "tactic_count": 4}
{"name": "Asymptotics.IsBigO.mul_atTop_rpow_natCast_of_isBigO_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Asymptotics", "is_tactic_proof": true, "tactics": ["refine", "filter_upwards", "replace", "rw", "exact"], "tactic_count": 5}
{"name": "Asymptotics.IsBigO.rpow_rpow_nhdsGE_zero_of_le_of_imp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Asymptotics", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsBigO.rpow_rpow_nhdsGE_zero_of_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Asymptotics", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Asymptotics.IsBigO.id_rpow_of_le_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Asymptotics", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "isLittleO_rpow_exp_pos_mul_atTop", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Asymptotics", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLittleO_zpow_exp_pos_mul_atTop", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Asymptotics", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "isLittleO_pow_exp_pos_mul_atTop", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Asymptotics", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "isLittleO_rpow_exp_atTop", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Asymptotics", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "isLittleO_exp_neg_mul_rpow_atTop", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Asymptotics", "is_tactic_proof": true, "tactics": ["apply", "refine", "rw", "exact", "refine", "refine", "simp"], "tactic_count": 7}
{"name": "isLittleO_exp_mul_rpow_of_lt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Asymptotics", "is_tactic_proof": true, "tactics": ["refine", "simp_rw", "exact"], "tactic_count": 3}
{"name": "isLittleO_log_rpow_atTop", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Asymptotics", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLittleO_log_rpow_rpow_atTop", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Asymptotics", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLittleO_abs_log_rpow_rpow_nhdsGT_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Asymptotics", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLittleO_log_rpow_nhdsGT_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Asymptotics", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_log_div_rpow_nhdsGT_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Asymptotics", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_log_mul_rpow_nhdsGT_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Asymptotics", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_log_mul_self_nhdsLT_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Asymptotics", "is_tactic_proof": true, "tactics": ["have", "simp", "have", "simp", "intro", "simp", "refine", "nth_rewrite", "refine", "refine", "push", "simp"], "tactic_count": 12}
{"name": "Complex.cpow", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.instPow", "kind": "instance", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.cpow_eq_pow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.cpow_def", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.cpow_def_of_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.cpow_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Complex", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.cpow_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Complex", "is_tactic_proof": true, "tactics": ["simp", "split_ifs"], "tactic_count": 2}
{"name": "Complex.cpow_ne_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Complex", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.cpow_ne_zero_iff_of_exponent_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Complex", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.zero_cpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Complex", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.zero_cpow_eq_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Complex", "is_tactic_proof": true, "tactics": ["constructor", "intro", "simp", "grind", "rintro", "exact", "exact"], "tactic_count": 7}
{"name": "Complex.eq_zero_cpow_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Complex", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.cpow_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.one_cpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Complex", "is_tactic_proof": true, "tactics": ["rw", "split_ifs"], "tactic_count": 2}
{"name": "Complex.cpow_add", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Complex", "is_tactic_proof": true, "tactics": ["simp", "simp_all"], "tactic_count": 2}
{"name": "Complex.cpow_mul", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Complex", "is_tactic_proof": true, "tactics": ["simp", "split_ifs"], "tactic_count": 2}
{"name": "Complex.cpow_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Complex", "is_tactic_proof": true, "tactics": ["simp", "split_ifs"], "tactic_count": 2}
{"name": "Complex.cpow_sub", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Complex", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.cpow_neg_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Complex", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Complex.cpow_int_mul", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Complex", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "simp", "rcases", "rw"], "tactic_count": 5}
{"name": "Complex.cpow_mul_int", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Complex", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.cpow_nat_mul", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.cpow_ofNat_mul", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.cpow_mul_nat", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Complex", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.cpow_mul_ofNat", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.cpow_natCast", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Complex", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Complex.cpow_ofNat", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.cpow_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.cpow_intCast", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Complex", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Complex.cpow_nat_inv_pow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Complex", "is_tactic_proof": true, "tactics": ["rw", "assumption_mod_cast"], "tactic_count": 2}
{"name": "Complex.cpow_ofNat_inv_pow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.cpow_int_mul'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Complex", "is_tactic_proof": true, "tactics": ["rw", "rw"], "tactic_count": 2}
{"name": "Complex.cpow_nat_mul'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.cpow_ofNat_mul'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.pow_cpow_nat_inv", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Complex", "is_tactic_proof": true, "tactics": ["rw", "rwa", "rwa"], "tactic_count": 3}
{"name": "Complex.pow_cpow_ofNat_inv", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.sq_cpow_two_inv", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.isSquare", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.mul_cpow_ofReal_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Complex", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rcases", "rw", "rcases", "rw", "have", "have", "rw", "cpow_def_of_ne_zero"], "tactic_count": 10}
{"name": "Complex.natCast_mul_natCast_cpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.natCast_cpow_natCast_mul", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Complex", "is_tactic_proof": true, "tactics": ["refine", "simp", "simp"], "tactic_count": 3}
{"name": "Complex.inv_cpow_eq_ite", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Complex", "is_tactic_proof": false, "tactics": ["simp_rw", "apply_ite", "map_mul,", "split_ifs"], "tactic_count": 4}
{"name": "Complex.inv_cpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Complex", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.inv_cpow_eq_ite'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Complex", "is_tactic_proof": true, "tactics": ["rw", "split_ifs", "rfl", "rw"], "tactic_count": 4}
{"name": "Complex.conj_cpow_eq_ite", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Complex", "is_tactic_proof": false, "tactics": ["simp_rw", "split_ifs"], "tactic_count": 2}
{"name": "Complex.conj_cpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Complex", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.cpow_conj", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Complex", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.natCast_add_one_cpow_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zero_cpow_eq_nhds", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Continuity", "is_tactic_proof": false, "tactics": ["suffices", "this.mono", "dsimp", "rw", "exact"], "tactic_count": 5}
{"name": "cpow_eq_nhds", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Continuity", "is_tactic_proof": false, "tactics": ["suffices", "this.mono", "dsimp", "rw", "exact"], "tactic_count": 5}
{"name": "cpow_eq_nhds'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Continuity", "is_tactic_proof": false, "tactics": ["suffices", "this.mono", "dsimp", "rw", "refine", "change", "rw", "exact"], "tactic_count": 8}
{"name": "continuousAt_const_cpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Continuity", "is_tactic_proof": false, "tactics": ["have", "ext1", "rw", "rw", "exact"], "tactic_count": 5}
{"name": "continuousAt_const_cpow'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Continuity", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "exact", "exact"], "tactic_count": 4}
{"name": "continuousAt_cpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Continuity", "is_tactic_proof": true, "tactics": ["rw", "refine", "exact", "continuous_snd.continuousAt"], "tactic_count": 4}
{"name": "continuousAt_cpow_const", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Continuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.cpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Continuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.const_cpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Continuity", "is_tactic_proof": true, "tactics": ["cases", "inl", "inr"], "tactic_count": 3}
{"name": "ContinuousWithinAt.cpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Continuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.const_cpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Continuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.cpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Continuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.const_cpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Continuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.cpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Continuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.const_cpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Continuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.cpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Continuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.const_cpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Continuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.cpow_const", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Continuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_const_cpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Continuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.continuousAt_const_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Continuity", "is_tactic_proof": true, "tactics": ["simp", "refine", "refine", "norm_cast"], "tactic_count": 4}
{"name": "Real.continuousAt_const_rpow'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Continuity", "is_tactic_proof": true, "tactics": ["simp", "refine", "refine", "norm_cast"], "tactic_count": 4}
{"name": "Real.rpow_eq_nhds_of_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Continuity", "is_tactic_proof": false, "tactics": ["suffices", "this.mono", "dsimp", "rw", "exact"], "tactic_count": 5}
{"name": "Real.rpow_eq_nhds_of_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Continuity", "is_tactic_proof": false, "tactics": ["suffices", "this.mono", "dsimp", "rw", "exact"], "tactic_count": 5}
{"name": "Real.continuousAt_rpow_of_ne", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Continuity", "is_tactic_proof": true, "tactics": ["rw", "cases", "inl", "rw", "refine", "refine", "exact", "inr", "rw", "refine", "refine", "exact"], "tactic_count": 12}
{"name": "Real.continuousAt_rpow_of_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Continuity", "is_tactic_proof": true, "tactics": ["obtain", "dsimp", "obtain", "exact", "have", "tendsto_exp_atBot.comp", "have", "squeeze_zero_norm", "have", "rw", "exact", "simpa", "zero_rpow"], "tactic_count": 13}
{"name": "Real.continuousAt_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Continuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.continuousAt_rpow_const", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Continuity", "is_tactic_proof": true, "tactics": ["rw", "obtain", "exact", "simp_rw"], "tactic_count": 4}
{"name": "Real.continuous_rpow_const", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Continuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.continuous_const_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Continuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Continuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.rpow_const", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Continuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Continuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Continuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Continuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Continuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.rpow_const", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Continuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.rpow_const", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Continuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.rpow_const", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Continuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.rpow_const", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Continuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.continuousAt_cpow_zero_of_re_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Continuity", "is_tactic_proof": true, "tactics": ["have", "rw", "refine", "simp", "refine", "convert", "simp", "simp", "rcases", "refine", "refine", "rw", "exact"], "tactic_count": 13}
{"name": "Complex.continuousAt_cpow_of_re_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Continuity", "is_tactic_proof": true, "tactics": ["obtain", "rw", "rcases", "exacts"], "tactic_count": 4}
{"name": "Complex.continuousAt_cpow_const_of_re_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Continuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.continuousAt_ofReal_cpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Continuity", "is_tactic_proof": true, "tactics": ["rcases", "have", "refine", "rwa", "have", "rw", "apply", "tauto", "have", "exact", "suffices", "refine", "exact", "have", "apply", "refine", "rwa", "fun_prop"], "tactic_count": 18}
{"name": "Complex.continuousAt_ofReal_cpow_const", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Continuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.continuous_ofReal_cpow_const", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Continuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.continuousAt_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Continuity", "is_tactic_proof": false, "tactics": ["have", "ext", "simp", "exact_mod_cast", "rw", "refine", "apply", "simpa", "fun_prop"], "tactic_count": 9}
{"name": "NNReal.eventually_pow_one_div_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Continuity", "is_tactic_proof": true, "tactics": ["obtain", "rw", "refine", "simp", "simpa", "hm.le.trans"], "tactic_count": 6}
{"name": "Filter.Tendsto.nnrpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Continuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.continuousAt_rpow_const", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Continuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.continuous_rpow_const", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Continuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.continuousOn_rpow_const_compl_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Continuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.continuousOn_rpow_const", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Continuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.eventually_pow_one_div_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Continuity", "is_tactic_proof": true, "tactics": ["lift", "by_cases", "exact", "lift", "have", "refine", "rw"], "tactic_count": 7}
{"name": "_private.Mathlib.Analysis.SpecialFunctions.Pow.Continuity.0.ENNReal.continuousAt_rpow_const_of_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Continuity", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "convert", "simp", "lift", "rw", "convert", "ext1", "simp"], "tactic_count": 9}
{"name": "ENNReal.continuous_rpow_const", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Continuity", "is_tactic_proof": true, "tactics": ["refine", "rcases", "exact", "simp", "exact", "obtain", "have", "simp_rw", "exact"], "tactic_count": 9}
{"name": "ENNReal.tendsto_const_mul_rpow_nhds_zero_of_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Continuity", "is_tactic_proof": true, "tactics": ["convert", "simp", "exact"], "tactic_count": 3}
{"name": "Filter.Tendsto.ennrpow_const", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Continuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.hasStrictFDerivAt_cpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "refine", "simpa"], "tactic_count": 5}
{"name": "Complex.hasStrictFDerivAt_cpow'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.hasStrictDerivAt_const_cpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": true, "tactics": ["rcases", "replace", "rw", "refine", "exact", "simpa"], "tactic_count": 6}
{"name": "Complex.hasFDerivAt_cpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictFDerivAt.cpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictFDerivAt.const_cpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivAt.cpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "HasFDerivAt.const_cpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivWithinAt.cpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "HasFDerivWithinAt.const_cpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableAt.cpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableAt.const_cpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableAt.cpow_const", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableWithinAt.cpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableWithinAt.const_cpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableWithinAt.cpow_const", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableOn.cpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableOn.const_cpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableOn.cpow_const", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Differentiable.cpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Differentiable.const_cpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiable_const_cpow_of_neZero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableAt_const_cpow_of_neZero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.SpecialFunctions.Pow.Deriv.0.aux", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HasStrictDerivAt.cpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasStrictDerivAt.const_cpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.hasStrictDerivAt_cpow_const", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasStrictDerivAt.cpow_const", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivAt.cpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasDerivAt.const_cpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivAt.cpow_const", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivWithinAt.cpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasDerivWithinAt.const_cpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivWithinAt.cpow_const", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasDerivAt_ofReal_cpow_const'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": true, "tactics": ["rw", "rcases", "apply", "convert", "exact", "convert", "rw", "exact", "simp", "have", "refine", "rw", "refine", "rw", "suffices", "convert", "conv_rhs", "rw", "simp_rw", "suffices", "convert", "suffices", "convert", "rw", "suffices", "conv", "convert", "rw", "exact", "simp"], "tactic_count": 30}
{"name": "hasDerivAt_ofReal_cpow_const", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "DifferentiableAt.ofReal_cpow_const", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.deriv_cpow_const", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.deriv_ofReal_cpow_const", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv_cpow_const", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isTheta_deriv_ofReal_cpow_const_atTop", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": true, "tactics": ["calc", "filter_upwards", "filter_upwards", "rw"], "tactic_count": 4}
{"name": "isBigO_deriv_ofReal_cpow_const_atTop", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": true, "tactics": ["obtain", "simp_rw", "exact"], "tactic_count": 3}
{"name": "Real.hasStrictFDerivAt_rpow_of_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": ["have", "refine", "convert", "rw", "smul_smul,"], "tactic_count": 5}
{"name": "Real.hasStrictFDerivAt_rpow_of_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": ["have", "refine", "convert", "simp_rw", "rpow_def_of_neg", "rw"], "tactic_count": 6}
{"name": "Real.contDiffAt_rpow_of_ne", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": true, "tactics": ["rcases", "exacts"], "tactic_count": 2}
{"name": "Real.differentiableAt_rpow_of_ne", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictDerivAt.rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "Real.hasStrictDerivAt_rpow_const_of_ne", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": true, "tactics": ["rcases", "have", "convert", "simpa"], "tactic_count": 4}
{"name": "Real.hasStrictDerivAt_const_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.differentiableAt_rpow_const_of_ne", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.not_differentiableAt_rpow_const_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": true, "tactics": ["by_contra", "set", "deriv", "have", "apply", "intro", "simp", "field_simp", "nth_rw", "simp", "exact"], "tactic_count": 11}
{"name": "Real.differentiableOn_rpow_const", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.hasStrictDerivAt_const_rpow_of_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.hasDerivAt_rpow_const", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": true, "tactics": ["rcases", "exact", "replace", "apply", "exacts", "continuousAt_const.mul"], "tactic_count": 6}
{"name": "Real.differentiable_rpow_const", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.deriv_rpow_const", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "by_cases", "apply", "have", "grind"], "tactic_count": 6}
{"name": "Real.deriv_rpow_const'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.contDiffAt_rpow_const_of_ne", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.contDiff_rpow_const_of_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "have", "rw", "rw", "simp", "exact"], "tactic_count": 8}
{"name": "Real.contDiffAt_rpow_const_of_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.contDiffAt_rpow_const", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.iter_deriv_rpow_const", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": true, "tactics": ["apply", "induction", "zero", "succ", "simp", "ext", "simp", "grind"], "tactic_count": 8}
{"name": "Real.hasStrictDerivAt_rpow_const", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivWithinAt.rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "HasFDerivAt.rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "HasStrictFDerivAt.rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableWithinAt.rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "DifferentiableAt.rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "DifferentiableOn.rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Differentiable.rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivWithinAt.rpow_const", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivAt.rpow_const", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictFDerivAt.rpow_const", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableWithinAt.rpow_const", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableAt.rpow_const", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableOn.rpow_const", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Differentiable.rpow_const", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivWithinAt.const_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivAt.const_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictFDerivAt.const_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffWithinAt.rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "ContDiffAt.rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "ContDiffOn.rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffWithinAt.rpow_const_of_ne", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffAt.rpow_const_of_ne", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffOn.rpow_const_of_ne", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.rpow_const_of_ne", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffWithinAt.rpow_const_of_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffAt.rpow_const_of_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ContDiffOn.rpow_const_of_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.rpow_const_of_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivWithinAt.rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": true, "tactics": ["convert", "dsimp"], "tactic_count": 2}
{"name": "HasDerivAt.rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "HasDerivWithinAt.rpow_const", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": true, "tactics": ["convert", "ring"], "tactic_count": 2}
{"name": "HasDerivAt.rpow_const", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "derivWithin_rpow_const", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv_rpow_const", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv_norm_ofReal_cpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": true, "tactics": ["rw", "rw", "filter_upwards", "rw"], "tactic_count": 4}
{"name": "isTheta_deriv_rpow_const_atTop", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": true, "tactics": ["calc", "deriv"], "tactic_count": 2}
{"name": "isBigO_deriv_rpow_const_atTop", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": true, "tactics": ["rcases", "simp", "exact"], "tactic_count": 3}
{"name": "HasDerivWithinAt.const_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": true, "tactics": ["convert", "ring"], "tactic_count": 2}
{"name": "HasDerivAt.const_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "derivWithin_const_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv_const_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.lintegral_rpow_eq_lintegral_meas_le_mul", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Integral", "is_tactic_proof": true, "tactics": ["have", "have", "intro", "rw", "simp", "set", "have", "filter_upwards", "intro", "exact", "have", "have", "rw", "congr", "rw", "have", "exact"], "tactic_count": 17}
{"name": "MeasureTheory.lintegral_rpow_eq_lintegral_meas_lt_mul", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Integral", "is_tactic_proof": true, "tactics": ["rw", "apply", "apply", "filter_upwards", "rw"], "tactic_count": 5}
{"name": "NNReal.rpow", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.instPowReal", "kind": "instance", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.rpow_eq_pow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.coe_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.rpow_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.rpow_zero_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NNReal.rpow_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "NNReal.rpow_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NNReal.zero_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.rpow_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.rpow_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.rpow_natCast", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.rpow_intCast", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["cases", "simp", "zpow_negSucc]"], "tactic_count": 3}
{"name": "NNReal.one_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.rpow_add", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.rpow_add'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.rpow_add_intCast", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "NNReal.rpow_add_natCast", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "NNReal.rpow_sub_intCast", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "NNReal.rpow_sub_natCast", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "NNReal.rpow_add_intCast'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "NNReal.rpow_add_natCast'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "NNReal.rpow_sub_intCast'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "NNReal.rpow_sub_natCast'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "NNReal.rpow_add_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "NNReal.rpow_sub_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "NNReal.rpow_add_one'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NNReal.rpow_one_add'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NNReal.rpow_add_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "NNReal.rpow_of_add_eq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NNReal.rpow_mul", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.rpow_natCast_mul", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NNReal.rpow_mul_natCast", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NNReal.rpow_intCast_mul", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NNReal.rpow_mul_intCast", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NNReal.rpow_neg_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NNReal.rpow_sub", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.rpow_sub'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.rpow_sub_one'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NNReal.rpow_one_sub'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NNReal.rpow_inv_rpow_self", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["rw", "field_simp", "simp"], "tactic_count": 3}
{"name": "NNReal.rpow_self_rpow_inv", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["rw", "field_simp", "simp"], "tactic_count": 3}
{"name": "NNReal.inv_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.div_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.sqrt_eq_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["refine", "push_cast", "exact"], "tactic_count": 3}
{"name": "NNReal.rpow_ofNat", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.rpow_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.mul_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.rpowMonoidHom", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.list_prod_map_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.list_prod_map_rpow'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NNReal.multiset_prod_map_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.finset_prod_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.list_prod_map_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["lift", "have", "push_cast", "rw", "exact"], "tactic_count": 5}
{"name": "Real.list_prod_map_rpow'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["rw", "rfl", "simpa"], "tactic_count": 3}
{"name": "Real.multiset_prod_map_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["obtain", "simpa"], "tactic_count": 2}
{"name": "Real.finset_prod_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.rpow_le_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.rpow_lt_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.rpow_lt_rpow_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.rpow_le_rpow_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.le_rpow_inv_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NNReal.rpow_inv_le_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NNReal.lt_rpow_inv_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NNReal.rpow_inv_lt_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NNReal.rpow_lt_rpow_of_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.rpow_le_rpow_of_nonpos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.rpow_lt_rpow_iff_of_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.rpow_le_rpow_iff_of_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.le_rpow_inv_iff_of_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.rpow_inv_le_iff_of_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.lt_rpow_inv_iff_of_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.rpow_inv_lt_iff_of_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.le_rpow_inv_iff_of_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.lt_rpow_inv_iff_of_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.rpow_inv_lt_iff_of_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.rpow_inv_le_iff_of_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.rpow_lt_rpow_of_exponent_lt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.rpow_le_rpow_of_exponent_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.rpow_lt_rpow_of_exponent_gt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.rpow_le_rpow_of_exponent_ge", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.rpow_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": ["have", "intro", "rw", "exact", "rcases", "exact", "simp", "rw", "exact"], "tactic_count": 9}
{"name": "NNReal.rpow_lt_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.rpow_le_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.rpow_lt_one_of_one_lt_of_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.rpow_le_one_of_one_le_of_nonpos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.one_lt_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.one_le_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.one_lt_rpow_of_pos_of_lt_one_of_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.one_le_rpow_of_pos_of_le_one_of_nonpos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.rpow_le_self_of_le_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["rcases", "have", "simp", "nth_rw", "exact"], "tactic_count": 5}
{"name": "NNReal.rpow_left_injective", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.rpow_eq_rpow_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.rpow_left_surjective", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.rpow_left_bijective", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.eq_rpow_inv_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NNReal.rpow_inv_eq_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NNReal.rpow_rpow_inv", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NNReal.rpow_inv_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NNReal.pow_rpow_inv_natCast", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "NNReal.rpow_inv_natCast_pow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Real.toNNReal_rpow_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["nth_rw", "rw"], "tactic_count": 2}
{"name": "NNReal.strictMono_rpow_of_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.monotone_rpow_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.orderIsoRpow", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.orderIsoRpow_symm_eq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.nnnorm_rpow_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "ENNReal.rpow", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.instPowReal", "kind": "instance", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.rpow_eq_pow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.rpow_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["cases", "dsimp", "simp"], "tactic_count": 3}
{"name": "ENNReal.rpow_zero_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.top_rpow_def", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.top_rpow_of_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.top_rpow_of_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.zero_rpow_of_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["rw", "dsimp", "simp"], "tactic_count": 3}
{"name": "ENNReal.zero_rpow_of_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["rw", "dsimp", "simp"], "tactic_count": 3}
{"name": "ENNReal.zero_rpow_def", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simp", "simp"], "tactic_count": 4}
{"name": "ENNReal.zero_rpow_mul_self", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["rw", "split_ifs", "exacts"], "tactic_count": 3}
{"name": "ENNReal.coe_rpow_of_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["rw", "dsimp", "simp"], "tactic_count": 3}
{"name": "ENNReal.coe_rpow_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["by_cases", "rcases", "simp", "simp", "exact"], "tactic_count": 5}
{"name": "ENNReal.coe_rpow_def", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.rpow_ofNNReal", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.rpow_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["cases", "exact", "change", "simp", "exact"], "tactic_count": 5}
{"name": "ENNReal.one_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "ENNReal.rpow_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["cases", "top", "coe", "by_cases", "rcases", "simp"], "tactic_count": 6}
{"name": "ENNReal.rpow_eq_zero_iff_of_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.rpow_eq_top_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["cases", "top", "coe", "by_cases", "rcases", "simp"], "tactic_count": 6}
{"name": "ENNReal.rpow_eq_top_iff_of_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.rpow_lt_top_iff_of_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.rpow_eq_top_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.rpow_ne_top_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.rpow_ne_top_of_nonneg'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.rpow_lt_top_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.rpow_ne_top_of_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.rpow_add", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["cases", "top", "coe", "have", "simp"], "tactic_count": 5}
{"name": "ENNReal.rpow_add_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["induction", "rcases", "rw", "rcases", "rw", "simp", "simp"], "tactic_count": 7}
{"name": "ENNReal.rpow_add_of_add_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["obtain", "by_cases", "simp", "have", "simp", "rw"], "tactic_count": 6}
{"name": "ENNReal.rpow_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["cases", "top", "coe", "by_cases", "rcases", "have", "simp"], "tactic_count": 7}
{"name": "ENNReal.rpow_sub", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.rpow_neg_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.rpow_mul", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["cases", "top", "rcases", "simp", "mul_neg_of_neg_of_pos,", "coe", "by_cases", "rcases", "simp", "mul_neg_of_neg_of_pos,", "have", "simp"], "tactic_count": 12}
{"name": "ENNReal.rpow_natCast", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["cases", "cases", "simp"], "tactic_count": 3}
{"name": "ENNReal.rpow_ofNat", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.rpow_intCast", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["cases", "simp", "zpow_negSucc]"], "tactic_count": 3}
{"name": "ENNReal.rpow_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.mul_rpow_eq_ite", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["rcases", "replace", "wlog", "convert", "rcases", "induction", "rcases", "exact", "induction", "rcases", "induction", "rw", "rcases", "simp", "norm_cast", "rw", "norm_cast"], "tactic_count": 17}
{"name": "ENNReal.mul_rpow_of_ne_top", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.coe_mul_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.prod_coe_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "insert"], "tactic_count": 4}
{"name": "ENNReal.mul_rpow_of_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.mul_rpow_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.prod_rpow_of_ne_top", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "insert", "have", "rw", "apply"], "tactic_count": 7}
{"name": "ENNReal.prod_rpow_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "insert"], "tactic_count": 4}
{"name": "ENNReal.inv_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["rcases", "replace", "rcases", "rcases", "apply", "rw"], "tactic_count": 6}
{"name": "ENNReal.div_rpow_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.strictMono_rpow_of_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["intro", "lift", "rcases", "simp", "lift", "simp"], "tactic_count": 6}
{"name": "ENNReal.monotone_rpow_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.orderIsoRpow", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.orderIsoRpow_symm_apply", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["simp", "rfl"], "tactic_count": 2}
{"name": "ENNReal.rpow_le_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.rpow_lt_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.rpow_le_rpow_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.rpow_lt_rpow_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.max_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["rcases", "rw", "rw"], "tactic_count": 3}
{"name": "ENNReal.le_rpow_inv_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["nth_rw", "nth_rw", "rw"], "tactic_count": 3}
{"name": "ENNReal.rpow_inv_lt_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.lt_rpow_inv_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["nth_rw", "nth_rw", "rw"], "tactic_count": 3}
{"name": "ENNReal.rpow_inv_le_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["nth_rw", "nth_rw", "rw"], "tactic_count": 3}
{"name": "ENNReal.rpow_lt_rpow_of_exponent_lt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["lift", "rw", "simp"], "tactic_count": 3}
{"name": "ENNReal.rpow_le_rpow_of_exponent_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["cases", "rcases", "simp", "linarith", "simp", "simp"], "tactic_count": 6}
{"name": "ENNReal.rpow_lt_rpow_of_exponent_gt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["lift", "simp", "simp"], "tactic_count": 3}
{"name": "ENNReal.rpow_le_rpow_of_exponent_ge", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["lift", "by_cases", "rcases", "simp", "linarith", "rw", "simp"], "tactic_count": 7}
{"name": "ENNReal.rpow_le_self_of_le_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["nth_rw", "exact"], "tactic_count": 2}
{"name": "ENNReal.le_rpow_self_of_one_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["nth_rw", "exact"], "tactic_count": 2}
{"name": "ENNReal.rpow_pos_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "rw", "have", "rw", "exact"], "tactic_count": 6}
{"name": "ENNReal.rpow_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["rcases", "exact", "rw", "exact"], "tactic_count": 4}
{"name": "ENNReal.rpow_lt_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["lift", "simp", "simp"], "tactic_count": 3}
{"name": "ENNReal.rpow_le_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["lift", "simp", "simp"], "tactic_count": 3}
{"name": "ENNReal.rpow_lt_one_of_one_lt_of_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["cases", "simp", "simp", "simp"], "tactic_count": 4}
{"name": "ENNReal.rpow_le_one_of_one_le_of_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["cases", "simp", "simp", "simp"], "tactic_count": 4}
{"name": "ENNReal.one_lt_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["cases", "simp", "simp", "simp"], "tactic_count": 4}
{"name": "ENNReal.one_le_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["cases", "simp", "simp", "simp"], "tactic_count": 4}
{"name": "ENNReal.one_lt_rpow_of_pos_of_lt_one_of_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["lift", "simp", "simp"], "tactic_count": 3}
{"name": "ENNReal.one_le_rpow_of_pos_of_le_one_of_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["lift", "simp", "simp"], "tactic_count": 3}
{"name": "ENNReal.toNNReal_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["rcases", "cases", "top", "coe", "by_cases", "simp", "simp", "simp", "cases", "simp", "simp"], "tactic_count": 11}
{"name": "ENNReal.toReal_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.ofReal_rpow_of_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["simp_rw", "rw", "simp"], "tactic_count": 3}
{"name": "ENNReal.ofReal_rpow_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "by_cases", "rw", "have", "simp", "rw", "exact"], "tactic_count": 8}
{"name": "ENNReal.rpow_rpow_inv", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.rpow_inv_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.pow_rpow_inv_natCast", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.rpow_inv_natCast_pow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.rpow_natCast_mul", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.rpow_mul_natCast", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.rpow_intCast_mul", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.rpow_mul_intCast", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.rpow_left_injective", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.rpow_left_surjective", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.rpow_left_bijective", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.enorm_rpow_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.add_rpow_le_two_rpow_mul_rpow_add_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalNNRealRpow", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.SpecialFunctions.Pow.NNReal.0.Mathlib.Meta.Positivity.isFiniteM?", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalENNRealRpow", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.nthRoot_zero_left", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NthRootLemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.nthRoot_one_left", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NthRootLemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.nthRoot_zero_right", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NthRootLemmas", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "Nat.nthRoot_one_right", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NthRootLemmas", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "_private.Mathlib.Analysis.SpecialFunctions.Pow.NthRootLemmas.0.Nat.nthRoot.pow_go_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NthRootLemmas", "is_tactic_proof": true, "tactics": ["induction", "zero", "obtain", "simp", "succ", "rw", "split_ifs", "grind", "have", "replace", "grind"], "tactic_count": 11}
{"name": "Nat.pow_nthRoot_le_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NthRootLemmas", "is_tactic_proof": true, "tactics": ["rcases", "first", "grind", "simp"], "tactic_count": 4}
{"name": "_private.Mathlib.Analysis.SpecialFunctions.Pow.NthRootLemmas.0.Nat.nthRoot.lt_pow_go_succ_aux0", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NthRootLemmas", "is_tactic_proof": false, "tactics": ["rw", "have", "simp", "norm_cast", "grind"], "tactic_count": 5}
{"name": "_private.Mathlib.Analysis.SpecialFunctions.Pow.NthRootLemmas.0.Nat.nthRoot.always_exists", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NthRootLemmas", "is_tactic_proof": true, "tactics": ["have", "let", "refine", "cases", "zero", "succ"], "tactic_count": 6}
{"name": "Nat.nthRoot.lt_pow_go_succ_aux", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NthRootLemmas", "is_tactic_proof": true, "tactics": ["have", "calc", "a", "gcongr", "exact"], "tactic_count": 5}
{"name": "_private.Mathlib.Analysis.SpecialFunctions.Pow.NthRootLemmas.0.Nat.nthRoot.lt_pow_go_succ", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NthRootLemmas", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "split_ifs", "rcases", "grind", "exact", "assumption"], "tactic_count": 9}
{"name": "Nat.lt_pow_nthRoot_add_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NthRootLemmas", "is_tactic_proof": true, "tactics": ["n", "simp", "apply", "exact"], "tactic_count": 4}
{"name": "Nat.le_nthRoot_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NthRootLemmas", "is_tactic_proof": true, "tactics": ["cases", "inl", "simp", "refine", "gcongr", "inr", "simp", "refine", "gcongr", "assumption"], "tactic_count": 10}
{"name": "Nat.nthRoot_lt_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NthRootLemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.nthRoot_pow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NthRootLemmas", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "Nat.nthRoot_eq_of_le_of_lt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NthRootLemmas", "is_tactic_proof": true, "tactics": ["rcases", "grind", "simp", "grind"], "tactic_count": 4}
{"name": "Nat.exists_pow_eq_iff'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NthRootLemmas", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "rw", "grind"], "tactic_count": 4}
{"name": "Nat.exists_pow_eq_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NthRootLemmas", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "Nat.instDecidableExistsPowEq", "kind": "instance", "module": "Mathlib.Analysis.SpecialFunctions.Pow.NthRootLemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.rpow", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.instPow", "kind": "instance", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.rpow_eq_pow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.rpow_def", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.rpow_def_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["simp", "split_ifs", "simp_all"], "tactic_count": 3}
{"name": "Real.rpow_def_of_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.exp_mul", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.rpow_intCast", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.rpow_natCast", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.rpow_neg_natCast", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.rpow_ofNat", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.rpow_neg_ofNat", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.exp_one_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.exp_one_pow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.rpow_eq_zero_iff_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["simp", "split_ifs"], "tactic_count": 2}
{"name": "Real.rpow_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.rpow_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.rpow_def_of_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw", "have", "simp", "ring", "rw", "ring", "rw", "exact"], "tactic_count": 8}
{"name": "Real.rpow_def_of_nonpos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["split_ifs"], "tactic_count": 1}
{"name": "Real.rpow_pos_of_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.rpow_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.rpow_zero_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.zero_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.zero_rpow_eq_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["constructor", "intro", "simp", "by_cases", "subst", "simp", "exact", "rw", "exact", "rintro", "exact", "exact"], "tactic_count": 12}
{"name": "Real.eq_zero_rpow_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.rpow_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.one_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.zero_rpow_le_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "Real.zero_rpow_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "Real.rpow_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.abs_rpow_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "Real.abs_rpow_le_abs_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rcases", "rw", "rw", "abs_of_pos", "exact"], "tactic_count": 5}
{"name": "Real.abs_rpow_le_exp_log_mul", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["refine", "by_cases", "by_cases", "rw"], "tactic_count": 4}
{"name": "Real.rpow_inv_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Real.rpow_inv_log_le_exp_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": false, "tactics": ["calc", "rw", "obtain", "simp", "rw", "gcongr", "exact"], "tactic_count": 7}
{"name": "Real.norm_rpow_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Real.rpow_add", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.rpow_add'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rcases", "rw", "have", "exact", "exact"], "tactic_count": 5}
{"name": "Real.rpow_of_add_eq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.rpow_add_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rcases", "rw", "exact"], "tactic_count": 3}
{"name": "Real.le_rpow_add", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rcases", "by_cases", "simp", "calc", "mul_le_mul", "simp", "simp"], "tactic_count": 7}
{"name": "Real.rpow_sum_of_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.rpow_sum_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["induction", "empty", "cons", "rw", "rw"], "tactic_count": 5}
{"name": "Real.rpow_neg_eq_inv_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.rpow_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.rpow_sub", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.rpow_sub'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["simp", "simp"], "tactic_count": 2}
{"name": "HasCompactSupport.rpow_const", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.ofReal_cpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["simp", "split_ifs"], "tactic_count": 2}
{"name": "Complex.ofReal_cpow_of_nonpos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "have", "rw", "arg_ofReal_of_neg"], "tactic_count": 5}
{"name": "Complex.cpow_ofReal", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rw", "norm_cast", "rw", "rwa"], "tactic_count": 6}
{"name": "Complex.cpow_ofReal_re", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.cpow_ofReal_im", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.norm_cpow_of_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.norm_cpow_of_imp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "simp", "rw", "exact"], "tactic_count": 5}
{"name": "Complex.norm_cpow_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "simp"], "tactic_count": 3}
{"name": "Complex.norm_cpow_real", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.norm_cpow_inv_nat", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.norm_cpow_eq_rpow_re_of_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.norm_cpow_eq_rpow_re_of_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.norm_ofReal_cpow_eventually_eq_atTop", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["filter_upwards", "rw"], "tactic_count": 2}
{"name": "Complex.norm_natCast_cpow_of_re_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.norm_natCast_cpow_of_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.norm_natCast_cpow_pos_of_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.cpow_mul_ofReal_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw", "rw", "rw"], "tactic_count": 3}
{"name": "Mathlib.Meta.Positivity.evalRpowZero", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalRpow", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.rpow_mul", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw", "simp", "le_of_lt"], "tactic_count": 3}
{"name": "Real.rpow_pow_comm", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Real.rpow_zpow_comm", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Real.rpow_add_intCast", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.rpow_add_natCast", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.rpow_sub_intCast", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.rpow_sub_natCast", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.rpow_add_intCast'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.rpow_add_natCast'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.rpow_sub_intCast'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.rpow_sub_natCast'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.rpow_add_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.rpow_sub_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.rpow_add_one'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.rpow_one_add'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.rpow_sub_one'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.rpow_one_sub'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.rpow_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.rpow_neg_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.mul_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["iterate", "rw", "all_goals"], "tactic_count": 3}
{"name": "Real.inv_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.div_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.log_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["apply", "rw"], "tactic_count": 2}
{"name": "Real.mul_log_eq_log_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.rpow_rpow_inv", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.rpow_inv_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.pow_rpow_inv_natCast", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "Real.rpow_inv_natCast_pow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "Real.rpow_natCast_mul", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.rpow_mul_natCast", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.rpow_intCast_mul", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.rpow_mul_intCast", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.rpow_lt_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact", "rw", "exact"], "tactic_count": 5}
{"name": "Real.strictMonoOn_rpow_Ici_of_exponent_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.rpow_le_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "exact"], "tactic_count": 3}
{"name": "Real.monotoneOn_rpow_Ici_of_exponent_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.rpow_lt_rpow_of_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["have", "rw", "on_goal", "all_goals"], "tactic_count": 4}
{"name": "Real.rpow_le_rpow_of_nonpos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["have", "rw", "on_goal", "all_goals"], "tactic_count": 4}
{"name": "Real.rpow_lt_rpow_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.rpow_le_rpow_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.rpow_lt_rpow_iff_of_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.rpow_le_rpow_iff_of_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.le_rpow_inv_iff_of_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.rpow_inv_le_iff_of_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.lt_rpow_inv_iff_of_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.rpow_inv_lt_iff_of_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.le_rpow_inv_iff_of_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.lt_rpow_inv_iff_of_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.rpow_inv_lt_iff_of_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.rpow_inv_le_iff_of_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.rpow_lt_rpow_of_exponent_lt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["repeat", "rw"], "tactic_count": 2}
{"name": "Real.rpow_le_rpow_of_exponent_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["repeat", "rw"], "tactic_count": 2}
{"name": "Real.strictAntiOn_rpow_Ioi_of_exponent_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.antitoneOn_rpow_Ioi_of_exponent_nonpos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.rpow_le_rpow_left_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["have", "rw", "mul_le_mul_iff_left₀"], "tactic_count": 3}
{"name": "Real.rpow_lt_rpow_left_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.rpow_lt_rpow_of_exponent_gt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["repeat", "rw"], "tactic_count": 2}
{"name": "Real.rpow_le_rpow_of_exponent_ge", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["repeat", "rw"], "tactic_count": 2}
{"name": "Real.rpow_le_rpow_left_iff_of_base_lt_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw", "mul_le_mul_right_of_neg"], "tactic_count": 2}
{"name": "Real.rpow_lt_rpow_left_iff_of_base_lt_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.rpow_lt_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Real.rpow_le_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Real.rpow_lt_one_of_one_lt_of_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["convert", "exact"], "tactic_count": 2}
{"name": "Real.rpow_le_one_of_one_le_of_nonpos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["convert", "exact"], "tactic_count": 2}
{"name": "Real.one_lt_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Real.one_le_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Real.one_lt_rpow_of_pos_of_lt_one_of_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["convert", "exact"], "tactic_count": 2}
{"name": "Real.one_le_rpow_of_pos_of_le_one_of_nonpos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["convert", "exact"], "tactic_count": 2}
{"name": "Real.rpow_lt_one_iff_of_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.rpow_lt_one_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "simp"], "tactic_count": 3}
{"name": "Real.rpow_lt_one_iff'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.one_lt_rpow_iff_of_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.one_lt_rpow_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "simp"], "tactic_count": 3}
{"name": "Real.rpow_le_rpow_of_exponent_ge_of_imp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "rw", "rw", "apply", "exact"], "tactic_count": 6}
{"name": "Real.rpow_le_rpow_of_exponent_ge'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.rpow_max", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rcases", "rw", "rw"], "tactic_count": 3}
{"name": "Real.self_le_rpow_of_le_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.self_le_rpow_of_one_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.rpow_le_self_of_le_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.rpow_le_self_of_one_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.self_lt_rpow_of_lt_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.self_lt_rpow_of_one_lt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.rpow_lt_self_of_lt_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.rpow_lt_self_of_one_lt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.rpow_left_injOn", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rintro", "rw"], "tactic_count": 2}
{"name": "Real.rpow_left_inj", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.rpow_inv_eq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.eq_rpow_inv", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.le_rpow_iff_log_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.le_pow_iff_log_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.le_zpow_iff_log_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.le_rpow_of_log_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["obtain", "exact", "exact"], "tactic_count": 3}
{"name": "Real.le_pow_of_log_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.le_zpow_of_log_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.lt_rpow_iff_log_lt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.lt_pow_iff_log_lt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.lt_zpow_iff_log_lt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.lt_rpow_of_log_lt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["obtain", "exact", "exact"], "tactic_count": 3}
{"name": "Real.lt_pow_of_log_lt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.lt_zpow_of_log_lt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.rpow_le_iff_le_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.pow_le_iff_le_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.zpow_le_iff_le_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.le_log_of_rpow_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.le_log_of_pow_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.le_log_of_zpow_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.rpow_le_of_le_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["obtain", "exact", "exact"], "tactic_count": 3}
{"name": "Real.pow_le_of_le_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.zpow_le_of_le_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.rpow_lt_iff_lt_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.pow_lt_iff_lt_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.zpow_lt_iff_lt_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.lt_log_of_rpow_lt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.lt_log_of_pow_lt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.lt_log_of_zpow_lt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.rpow_lt_of_lt_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["obtain", "exact", "exact"], "tactic_count": 3}
{"name": "Real.pow_lt_of_lt_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.zpow_lt_of_lt_log", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.rpow_le_one_iff_of_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.abs_log_mul_self_rpow_lt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw", "have", "rwa"], "tactic_count": 3}
{"name": "Real.log_le_rpow_div", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rcases", "rw", "rw", "exact"], "tactic_count": 4}
{"name": "Real.log_natCast_le_rpow_div", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.strictMono_rpow_of_base_gt_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Real.monotone_rpow_of_base_ge_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rcases", "exact", "intro"], "tactic_count": 3}
{"name": "Real.strictAnti_rpow_of_base_lt_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Real.antitone_rpow_of_base_le_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rcases", "exact", "intro"], "tactic_count": 3}
{"name": "Real.rpow_right_inj", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["refine", "rcases", "exact", "exact"], "tactic_count": 4}
{"name": "Real.rpow_le_rpow_of_exponent_le_or_ge", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rcases", "exact", "exact"], "tactic_count": 3}
{"name": "Complex.norm_prime_cpow_le_one_half", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw", "refine", "linarith", "rw", "exact"], "tactic_count": 5}
{"name": "Complex.one_sub_prime_cpow_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["refine", "have", "simp", "rw", "norm_num"], "tactic_count": 5}
{"name": "Complex.norm_natCast_cpow_le_norm_natCast_cpow_of_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Complex.norm_natCast_cpow_le_norm_natCast_cpow_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Complex.norm_log_natCast_le_rpow_div", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rcases", "rw", "rw", "exact"], "tactic_count": 4}
{"name": "Real.sqrt_eq_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["obtain", "rw", "simp", "have", "rw"], "tactic_count": 5}
{"name": "Real.rpow_div_two_eq_sqrt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw", "congr", "ring"], "tactic_count": 3}
{"name": "Complex.cpow_inv_two_re", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": false, "tactics": ["rw", "sqrt_mul,", "exacts"], "tactic_count": 3}
{"name": "Complex.cpow_inv_two_im_eq_sqrt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": false, "tactics": ["rw", "rwa", "linarith"], "tactic_count": 3}
{"name": "Complex.cpow_inv_two_im_eq_neg_sqrt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": false, "tactics": ["rw", "sin_half_eq_neg_sqrt,", "linarith", "exact"], "tactic_count": 4}
{"name": "Complex.abs_cpow_inv_two_im", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw", "abs_of_nonneg", "norm_mul_cos_arg]"], "tactic_count": 3}
{"name": "Complex.inv_natCast_cpow_ofReal_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["refine", "rw", "positivity"], "tactic_count": 3}
{"name": "Mathlib.Meta.NormNum.IsNat.rpow_eq_pow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Mathlib.Meta.NormNum.IsInt.rpow_eq_inv_pow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Mathlib.Meta.NormNum.isNat_rpow_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Mathlib.Meta.NormNum.isNat_rpow_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Mathlib.Meta.NormNum.isInt_rpow_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Mathlib.Meta.NormNum.isInt_rpow_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Mathlib.Meta.NormNum.isNNRat_rpow_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Mathlib.Meta.NormNum.isRat_rpow_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Mathlib.Meta.NormNum.isNNRat_rpow_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Mathlib.Meta.NormNum.isRat_rpow_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Mathlib.Meta.NormNum.IsNat.rpow_isNNRat", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rcases", "constructor", "have", "rw", "positivity"], "tactic_count": 5}
{"name": "Mathlib.Meta.NormNum.IsNNRat.rpow_isNNRat", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["suffices", "apply", "rw", "apply", "exact"], "tactic_count": 5}
{"name": "Mathlib.Meta.NormNum.rpow_isRat_eq_inv_rpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Mathlib.Meta.NormNum.proveIsNatRPowIsNNRat", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.evalRPow", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Pow.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sigmoid", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Sigmoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sigmoid_def", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sigmoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sigmoid_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sigmoid", "is_tactic_proof": true, "tactics": ["norm_num"], "tactic_count": 1}
{"name": "Real.sigmoid_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sigmoid", "is_tactic_proof": true, "tactics": ["change", "positivity"], "tactic_count": 2}
{"name": "Real.sigmoid_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sigmoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sigmoid_lt_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sigmoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sigmoid_le_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sigmoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sigmoid_strictMono", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sigmoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sigmoid_le_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sigmoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sigmoid_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sigmoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sigmoid_lt_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sigmoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sigmoid_lt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sigmoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sigmoid_monotone", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sigmoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sigmoid_injective", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sigmoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sigmoid_inj", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sigmoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sigmoid_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sigmoid", "is_tactic_proof": true, "tactics": ["simp", "field_simp", "simp"], "tactic_count": 3}
{"name": "Real.sigmoid_mul_rexp_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sigmoid", "is_tactic_proof": true, "tactics": ["rw", "field"], "tactic_count": 2}
{"name": "Real.range_sigmoid", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sigmoid", "is_tactic_proof": true, "tactics": ["refine", "rintro", "push", "bound", "replace", "exact"], "tactic_count": 6}
{"name": "Real.tendsto_sigmoid_atTop", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sigmoid", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.tendsto_sigmoid_atBot", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sigmoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.hasDerivAt_sigmoid", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sigmoid", "is_tactic_proof": true, "tactics": ["convert", "rw", "field"], "tactic_count": 3}
{"name": "Real.deriv_sigmoid", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sigmoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "analyticAt_sigmoid", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sigmoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticAt.sigmoid", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sigmoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticAt.sigmoid'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sigmoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "analyticOnNhd_sigmoid", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sigmoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticOnNhd.sigmoid", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sigmoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "analyticOn_sigmoid", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sigmoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticOn.sigmoid", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sigmoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "analyticWithinAt_sigmoid", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sigmoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AnalyticWithinAt.sigmoid", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sigmoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiff_sigmoid", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sigmoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.sigmoid", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sigmoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiable_sigmoid", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sigmoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Differentiable.sigmoid", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sigmoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableAt_sigmoid", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sigmoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableAt.sigmoid", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sigmoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_sigmoid", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sigmoid", "is_tactic_proof": false, "tactics": ["apply", "fun_prop"], "tactic_count": 2}
{"name": "Continuous.sigmoid", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sigmoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.sigmoid", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Sigmoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.sigmoid_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sigmoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.sigmoid_lt_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sigmoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.sigmoid_strictMono", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sigmoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.sigmoid_le_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sigmoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.sigmoid_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sigmoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.sigmoid_lt_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sigmoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.sigmoid_lt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sigmoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.sigmoid_monotone", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sigmoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.sigmoid_injective", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sigmoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.sigmoid_inj", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sigmoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.continuous_sigmoid", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sigmoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.sigmoid_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sigmoid", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "unitInterval.range_sigmoid", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sigmoid", "is_tactic_proof": true, "tactics": ["rw", "ext", "simp"], "tactic_count": 3}
{"name": "unitInterval.tendsto_sigmoid_atTop", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sigmoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.tendsto_sigmoid_atBot", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sigmoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderEmbedding.sigmoid", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Sigmoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.isEmbedding_sigmoid", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sigmoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurableEmbedding_sigmoid", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sigmoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurableEmbedding_sigmoid_comp_embeddingReal", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sigmoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "expNegInvGlue", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.SmoothTransition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "expNegInvGlue.zero_of_nonpos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.SmoothTransition", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "expNegInvGlue.zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.SmoothTransition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "expNegInvGlue.pos_of_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.SmoothTransition", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "expNegInvGlue.nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.SmoothTransition", "is_tactic_proof": true, "tactics": ["cases", "inl", "inr"], "tactic_count": 3}
{"name": "expNegInvGlue.zero_iff_nonpos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.SmoothTransition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "expNegInvGlue.monotone", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.SmoothTransition", "is_tactic_proof": true, "tactics": ["intro", "rcases", "simp", "simp"], "tactic_count": 4}
{"name": "expNegInvGlue.not_analyticAt_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.SmoothTransition", "is_tactic_proof": true, "tactics": ["intro", "obtain", "suffices", "exact", "h.eqOn_zero_of_preconnected_of_mem_closure"], "tactic_count": 5}
{"name": "expNegInvGlue.tendsto_polynomial_inv_mul_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.SmoothTransition", "is_tactic_proof": true, "tactics": ["simp", "refine", "simp", "have", "refine", "simp"], "tactic_count": 6}
{"name": "expNegInvGlue.hasDerivAt_polynomial_eval_inv_mul", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.SmoothTransition", "is_tactic_proof": true, "tactics": ["rcases", "rw", "refine", "filter_upwards", "rw", "rw", "refine", "simp", "have", "convert", "simp", "ring", "filter_upwards", "simp"], "tactic_count": 14}
{"name": "expNegInvGlue.differentiable_polynomial_eval_inv_mul", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.SmoothTransition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "expNegInvGlue.continuous_polynomial_eval_inv_mul", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.SmoothTransition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "expNegInvGlue.contDiff_polynomial_eval_inv_mul", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.SmoothTransition", "is_tactic_proof": true, "tactics": ["apply", "induction", "zero", "succ", "rw", "refine", "convert", "exact"], "tactic_count": 8}
{"name": "expNegInvGlue.contDiff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.SmoothTransition", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.smoothTransition", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.SmoothTransition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.smoothTransition.pos_denom", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.SmoothTransition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.smoothTransition.one_of_one_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.SmoothTransition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.smoothTransition.zero_iff_nonpos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.SmoothTransition", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.smoothTransition.zero_of_nonpos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.SmoothTransition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.smoothTransition.zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.SmoothTransition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.smoothTransition.one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.SmoothTransition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.smoothTransition.projIcc", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.SmoothTransition", "is_tactic_proof": true, "tactics": ["refine", "rw", "rw"], "tactic_count": 3}
{"name": "Real.smoothTransition.le_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.SmoothTransition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.smoothTransition.nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.SmoothTransition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.smoothTransition.lt_one_of_lt_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.SmoothTransition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.smoothTransition.pos_of_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.SmoothTransition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.smoothTransition.eq_one_iff_one_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.SmoothTransition", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simpa"], "tactic_count": 3}
{"name": "Real.smoothTransition.contDiff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.SmoothTransition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.smoothTransition.contDiffAt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.SmoothTransition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.smoothTransition.continuous", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.SmoothTransition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.smoothTransition.continuousAt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.SmoothTransition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.smoothTransition.monotone", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.SmoothTransition", "is_tactic_proof": true, "tactics": ["intro", "simp", "rw", "simp", "gcongr", "exact", "exact", "apply", "apply"], "tactic_count": 9}
{"name": "Real.sqPartialHomeomorph", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.deriv_sqrt_aux", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sqrt", "is_tactic_proof": true, "tactics": ["rcases", "rw", "have", "exact", "contDiffAt_const.congr_of_eventuallyEq", "have", "constructor", "simpa", "exact"], "tactic_count": 9}
{"name": "Real.hasStrictDerivAt_sqrt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.contDiffAt_sqrt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.hasDerivAt_sqrt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivWithinAt.sqrt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sqrt", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasDerivAt.sqrt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sqrt", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasStrictDerivAt.sqrt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sqrt", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "derivWithin_sqrt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv_sqrt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivAt.sqrt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictFDerivAt.sqrt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivWithinAt.sqrt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableWithinAt.sqrt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableAt.sqrt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableOn.sqrt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Differentiable.sqrt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderivWithin_sqrt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderiv_sqrt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffAt.sqrt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffWithinAt.sqrt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffOn.sqrt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.sqrt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stirling.stirlingSeq", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Stirling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stirling.stirlingSeq_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Stirling", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Stirling.stirlingSeq_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Stirling", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Stirling.log_stirlingSeq_formula", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Stirling", "is_tactic_proof": true, "tactics": ["cases", "simp", "rw"], "tactic_count": 3}
{"name": "Stirling.log_stirlingSeq_diff_hasSum", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Stirling", "is_tactic_proof": true, "tactics": ["let", "change", "rw", "convert", "ext", "dsimp", "rw", "push_cast", "field", "have", "simp", "cast_succ,", "ring"], "tactic_count": 13}
{"name": "Stirling.log_stirlingSeq'_antitone", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Stirling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stirling.log_stirlingSeq_diff_le_geo_sum", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Stirling", "is_tactic_proof": true, "tactics": ["have", "have", "have", "simp_rw", "exact", "rw", "exact", "have", "refine", "rw", "exact", "exact"], "tactic_count": 12}
{"name": "Stirling.log_stirlingSeq_sub_log_stirlingSeq_succ", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Stirling", "is_tactic_proof": true, "tactics": ["have", "have", "ring_nf", "positivity", "refine", "push_cast", "field_simp", "ring_nf", "norm_cast", "lia"], "tactic_count": 10}
{"name": "Stirling.log_stirlingSeq_bounded_aux", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Stirling", "is_tactic_proof": true, "tactics": ["let", "use", "let", "intro", "have", "convert", "have", "have", "exact", "calc", "log"], "tactic_count": 11}
{"name": "Stirling.log_stirlingSeq_bounded_by_constant", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Stirling", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Stirling.stirlingSeq'_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Stirling", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "Stirling.stirlingSeq'_bounded_by_pos_constant", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Stirling", "is_tactic_proof": true, "tactics": ["obtain", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "Stirling.stirlingSeq'_antitone", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Stirling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stirling.stirlingSeq_has_pos_limit_a", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Stirling", "is_tactic_proof": true, "tactics": ["obtain", "have", "refine", "rw", "exact"], "tactic_count": 5}
{"name": "Stirling.tendsto_self_div_two_mul_self_add_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Stirling", "is_tactic_proof": false, "tactics": ["conv", "congr", "skip", "skip", "rw", "refine", "rw"], "tactic_count": 7}
{"name": "Stirling.stirlingSeq_pow_four_div_stirlingSeq_pow_two_eq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Stirling", "is_tactic_proof": true, "tactics": ["have", "rw", "simp_rw", "rw", "any_goals", "simp", "ring_nf"], "tactic_count": 7}
{"name": "Stirling.second_wallis_limit", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Stirling", "is_tactic_proof": false, "tactics": ["refine", "have", "rw", "simp", "rw", "exact", "tendsto_self_div_two_mul_self_add_one"], "tactic_count": 7}
{"name": "Stirling.tendsto_stirlingSeq_sqrt_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Stirling", "is_tactic_proof": true, "tactics": ["obtain", "have", "tendsto_nhds_unique", "rwa"], "tactic_count": 4}
{"name": "Stirling.factorial_isEquivalent_stirling", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Stirling", "is_tactic_proof": true, "tactics": ["apply", "have", "nth_rewrite", "convert", "ext", "simp"], "tactic_count": 6}
{"name": "Stirling.sqrt_pi_le_stirlingSeq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Stirling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stirling.le_factorial_stirling", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Stirling", "is_tactic_proof": true, "tactics": ["obtain", "simp", "have", "rw", "exact"], "tactic_count": 5}
{"name": "Stirling.le_log_factorial_stirling", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Stirling", "is_tactic_proof": true, "tactics": ["calc", "rw"], "tactic_count": 2}
{"name": "Real.Angle", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.Angle.coe", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.Angle.instCoe", "kind": "instance", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.Angle.instCircularOrder", "kind": "instance", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.Angle.continuous_coe", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.Angle.coeHom", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.Angle.coe_coeHom", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.Angle.induction_on", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.Angle.coe_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.Angle.coe_add", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.Angle.coe_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.Angle.coe_sub", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.Angle.coe_nsmul", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.Angle.coe_zsmul", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.Angle.coe_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.Angle.natCast_mul_eq_nsmul", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.Angle.intCast_mul_eq_zsmul", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.Angle.angle_eq_iff_two_pi_dvd_sub", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["simp", "rw", "simp"], "tactic_count": 3}
{"name": "Real.Angle.coe_two_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.Angle.neg_coe_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["rw", "use", "simp"], "tactic_count": 3}
{"name": "Real.Angle.two_nsmul_coe_div_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.Angle.two_zsmul_coe_div_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.Angle.two_nsmul_neg_pi_div_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.Angle.two_zsmul_neg_pi_div_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.Angle.sub_coe_pi_eq_add_coe_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.Angle.two_nsmul_coe_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.Angle.two_zsmul_coe_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.Angle.coe_pi_add_coe_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.Angle.zsmul_eq_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.Angle.nsmul_eq_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.Angle.two_zsmul_eq_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "Real.Angle.two_nsmul_eq_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Real.Angle.two_nsmul_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "Real.Angle.two_nsmul_ne_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.Angle.two_zsmul_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Real.Angle.two_zsmul_ne_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.Angle.eq_neg_self_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.Angle.ne_neg_self_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.Angle.neg_eq_self_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.Angle.neg_ne_self_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.Angle.two_nsmul_eq_pi_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["have", "nth_rw", "rw", "apply", "congr", "rw", "coe_two_pi]"], "tactic_count": 7}
{"name": "Real.Angle.two_zsmul_eq_pi_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.Angle.cos_eq_iff_coe_eq_or_eq_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "sin_eq_zero_iff,", "rcases", "right", "rw", "rw", "zsmul_zero]", "left", "rw", "rw", "rw", "rintro", "rw", "sin_int_mul_pi,", "rw", "mul_comm"], "tactic_count": 18}
{"name": "Real.Angle.sin_eq_iff_coe_eq_or_add_eq_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "rcases", "left", "rw", "exact", "right", "rw", "sub_eq_zero]", "exact", "rw", "rintro", "rw", "sin_int_mul_pi,", "have", "rwa", "rw", "cos_add_pi_div_two,"], "tactic_count": 19}
{"name": "Real.Angle.cos_sin_inj", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "rw", "obtain", "rw", "eq_false", "have", "rw", "exact"], "tactic_count": 9}
{"name": "Real.Angle.sin", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.Angle.sin_coe", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.Angle.continuous_sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.Angle.cos", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.Angle.cos_coe", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.Angle.continuous_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.Angle.cos_eq_real_cos_iff_eq_or_eq_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["induction", "exact"], "tactic_count": 2}
{"name": "Real.Angle.cos_eq_iff_eq_or_eq_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["induction", "exact"], "tactic_count": 2}
{"name": "Real.Angle.sin_eq_real_sin_iff_eq_or_add_eq_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["induction", "exact"], "tactic_count": 2}
{"name": "Real.Angle.sin_eq_iff_eq_or_add_eq_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["induction", "exact"], "tactic_count": 2}
{"name": "Real.Angle.sin_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.Angle.sin_coe_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.Angle.sin_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["nth_rw", "rw", "simp"], "tactic_count": 3}
{"name": "Real.Angle.sin_ne_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.Angle.sin_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["induction", "exact"], "tactic_count": 2}
{"name": "Real.Angle.sin_antiperiodic", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["intro", "induction", "exact"], "tactic_count": 3}
{"name": "Real.Angle.sin_add_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.Angle.sin_sub_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.Angle.cos_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.Angle.cos_coe_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.Angle.cos_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["induction", "exact"], "tactic_count": 2}
{"name": "Real.Angle.cos_antiperiodic", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["intro", "induction", "exact"], "tactic_count": 3}
{"name": "Real.Angle.cos_add_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.Angle.cos_sub_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.Angle.cos_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.Angle.sin_add", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["induction", "induction", "exact"], "tactic_count": 3}
{"name": "Real.Angle.cos_add", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["induction", "induction", "exact"], "tactic_count": 3}
{"name": "Real.Angle.sin_two_nsmul", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.Angle.cos_sq_add_sin_sq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["induction", "exact"], "tactic_count": 2}
{"name": "Real.Angle.sin_add_pi_div_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["induction", "exact"], "tactic_count": 2}
{"name": "Real.Angle.sin_sub_pi_div_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["induction", "exact"], "tactic_count": 2}
{"name": "Real.Angle.sin_pi_div_two_sub", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["induction", "exact"], "tactic_count": 2}
{"name": "Real.Angle.cos_add_pi_div_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["induction", "exact"], "tactic_count": 2}
{"name": "Real.Angle.cos_sub_pi_div_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["induction", "exact"], "tactic_count": 2}
{"name": "Real.Angle.cos_pi_div_two_sub", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["induction", "exact"], "tactic_count": 2}
{"name": "Real.Angle.abs_sin_eq_of_two_nsmul_eq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["rw", "rcases", "rfl", "rw"], "tactic_count": 4}
{"name": "Real.Angle.abs_sin_eq_of_two_zsmul_eq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Real.Angle.abs_cos_eq_of_two_nsmul_eq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["rw", "rcases", "rfl", "rw"], "tactic_count": 4}
{"name": "Real.Angle.abs_cos_eq_of_two_zsmul_eq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Real.Angle.coe_toIcoMod", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw"], "tactic_count": 3}
{"name": "Real.Angle.coe_toIocMod", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw"], "tactic_count": 3}
{"name": "Real.Angle.toReal", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.Angle.toReal_coe", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.Angle.toReal_coe_eq_self_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["rw", "ring_nf", "rfl"], "tactic_count": 3}
{"name": "Real.Angle.toReal_coe_eq_self_iff_mem_Ioc", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.Angle.toReal_injective", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["intro", "induction", "induction", "simpa", "eq_comm]"], "tactic_count": 5}
{"name": "Real.Angle.toReal_inj", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.Angle.coe_toReal", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["induction", "exact"], "tactic_count": 2}
{"name": "Real.Angle.neg_pi_lt_toReal", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["induction", "exact"], "tactic_count": 2}
{"name": "Real.Angle.toReal_le_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["induction", "convert", "ring"], "tactic_count": 3}
{"name": "Real.Angle.abs_toReal_le_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.Angle.toReal_mem_Ioc", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.Angle.toIocMod_toReal", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["induction", "rw", "exact"], "tactic_count": 3}
{"name": "Real.Angle.toReal_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Real.Angle.toReal_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["nth_rw", "exact"], "tactic_count": 2}
{"name": "Real.Angle.toReal_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Real.Angle.toReal_eq_pi_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.Angle.toReal_neg_eq_neg_toReal_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["nth_rw", "constructor", "rintro", "simp", "intro", "rw", "have", "exact"], "tactic_count": 8}
{"name": "Real.Angle.abs_toReal_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simp"], "tactic_count": 3}
{"name": "Real.Angle.pi_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Real.Angle.toReal_pi_div_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.Angle.toReal_eq_pi_div_two_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.Angle.toReal_neg_pi_div_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.Angle.toReal_eq_neg_pi_div_two_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.Angle.pi_div_two_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Real.Angle.neg_pi_div_two_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Real.Angle.abs_toReal_coe_eq_self_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.Angle.abs_toReal_neg_coe_eq_self_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["refine", "by_cases", "rw", "toReal_coe_eq_self_iff.2", "abs_eq_self.2"], "tactic_count": 5}
{"name": "Real.Angle.abs_toReal_eq_pi_div_two_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.Angle.nsmul_toReal_eq_mul", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["nth_rw", "have", "rw"], "tactic_count": 3}
{"name": "Real.Angle.two_nsmul_toReal_eq_two_mul", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.Angle.two_zsmul_toReal_eq_two_mul", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.Angle.toReal_coe_eq_self_sub_two_mul_int_mul_pi_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": false, "tactics": ["rw", "mul_comm", "exact"], "tactic_count": 3}
{"name": "Real.Angle.toReal_coe_eq_self_sub_two_pi_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "Real.Angle.toReal_coe_eq_self_add_two_pi_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "Real.Angle.two_nsmul_toReal_eq_two_mul_sub_two_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["nth_rw", "rw", "exact"], "tactic_count": 3}
{"name": "Real.Angle.two_zsmul_toReal_eq_two_mul_sub_two_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.Angle.two_nsmul_toReal_eq_two_mul_add_two_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["nth_rw", "rw", "refine"], "tactic_count": 3}
{"name": "Real.Angle.two_zsmul_toReal_eq_two_mul_add_two_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.Angle.sin_toReal", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["conv_rhs"], "tactic_count": 1}
{"name": "Real.Angle.cos_toReal", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["conv_rhs"], "tactic_count": 1}
{"name": "Real.Angle.cos_nonneg_iff_abs_toReal_le_pi_div_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "grind"], "tactic_count": 4}
{"name": "Real.Angle.cos_pos_iff_abs_toReal_lt_pi_div_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["rw", "rintro", "contrapose", "rw"], "tactic_count": 4}
{"name": "Real.Angle.two_nsmul_eq_iff_eq_of_abs_toReal_lt_pi_div_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["suffices", "rintro", "simp", "lia"], "tactic_count": 4}
{"name": "Real.Angle.two_zsmul_eq_iff_eq_of_abs_toReal_lt_pi_div_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Real.Angle.cos_neg_iff_pi_div_two_lt_abs_toReal", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["contrapose"], "tactic_count": 1}
{"name": "Real.Angle.abs_cos_eq_abs_sin_of_two_nsmul_add_two_nsmul_eq_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["rw", "rcases"], "tactic_count": 2}
{"name": "Real.Angle.abs_cos_eq_abs_sin_of_two_zsmul_add_two_zsmul_eq_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Real.Angle.tan", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.Angle.tan_eq_sin_div_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.Angle.tan_coe", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.Angle.tan_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.Angle.tan_coe_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.Angle.tan_periodic", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["intro", "induction", "rw", "exact"], "tactic_count": 4}
{"name": "Real.Angle.tan_add_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.Angle.tan_sub_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.Angle.tan_toReal", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["conv_rhs"], "tactic_count": 1}
{"name": "Real.Angle.tan_eq_of_two_nsmul_eq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["rw", "rcases", "rfl", "exact"], "tactic_count": 4}
{"name": "Real.Angle.tan_eq_of_two_zsmul_eq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Real.Angle.tan_eq_inv_of_two_nsmul_add_two_nsmul_eq_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["induction", "induction", "rw", "rcases", "rw", "eq_sub_iff_add_eq',", "rw", "exact"], "tactic_count": 8}
{"name": "Real.Angle.tan_eq_inv_of_two_zsmul_add_two_zsmul_eq_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Real.Angle.sign", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.Angle.sign_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.Angle.sign_coe_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.Angle.sign_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Real.Angle.sign_antiperiodic", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.Angle.sign_add_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.Angle.sign_pi_add", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.Angle.sign_sub_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.Angle.sign_pi_sub", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.Angle.sign_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.Angle.sign_ne_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.Angle.toReal_neg_iff_sign_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["rw", "grind"], "tactic_count": 2}
{"name": "Real.Angle.toReal_nonneg_iff_sign_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["simp", "grind"], "tactic_count": 2}
{"name": "Real.Angle.sign_toReal", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simp", "rw", "sign_pos"], "tactic_count": 5}
{"name": "Real.Angle.toReal_mem_Ioo_iff_sign_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simp", "exact"], "tactic_count": 4}
{"name": "Real.Angle.coe_abs_toReal_of_sign_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.Angle.neg_coe_abs_toReal_of_sign_nonpos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["rw", "rcases", "rw", "rw", "rcases"], "tactic_count": 5}
{"name": "Real.Angle.eq_iff_sign_eq_and_abs_toReal_eq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Real.Angle.eq_iff_abs_toReal_eq_of_sign_eq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.Angle.sign_coe_pi_div_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.Angle.sign_coe_neg_pi_div_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.Angle.sign_coe_nonneg_of_nonneg_of_le_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Real.Angle.sign_neg_coe_nonpos_of_nonneg_of_le_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Real.Angle.sign_two_nsmul_eq_sign_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": false, "tactics": ["simp", "mul_right_eq_self₀,", "have", "grind"], "tactic_count": 4}
{"name": "Real.Angle.sign_two_zsmul_eq_sign_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.Angle.sign_two_nsmul_eq_neg_sign_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["simpa", "sign_two_nsmul_eq_sign_iff"], "tactic_count": 2}
{"name": "Real.Angle.sign_two_zsmul_eq_neg_sign_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.Angle.eq_add_pi_of_two_zsmul_eq_of_sign_eq_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["have", "refine", "rintro", "simp", "rw", "contradiction"], "tactic_count": 6}
{"name": "Real.Angle.sub_ne_pi_of_sign_eq_of_sign_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["intro", "have", "have", "rw", "simp", "contradiction"], "tactic_count": 6}
{"name": "Real.Angle.two_zsmul_eq_iff_eq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["rw", "constructor", "intro", "rcases", "exact", "have", "rw", "have", "aesop", "intro", "aesop"], "tactic_count": 11}
{"name": "Real.Angle.abs_toReal_add_abs_toReal_eq_pi_of_two_nsmul_add_eq_zero_of_sign_eq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["rcases", "simp_all", "rw", "suffices", "rw", "rcases", "rw", "have", "fin_cases", "all_goals"], "tactic_count": 10}
{"name": "Real.Angle.abs_toReal_add_abs_toReal_eq_pi_of_two_zsmul_add_eq_zero_of_sign_eq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Real.Angle.toReal_add_of_sign_pos_sign_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["suffices", "rw", "grind"], "tactic_count": 3}
{"name": "Real.Angle.toReal_add_of_sign_eq_neg_sign", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["obtain", "all_goals"], "tactic_count": 2}
{"name": "Real.Angle.toReal_add_eq_toReal_add_toReal", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "all_goals", "rw", "have", "simpa"], "tactic_count": 6}
{"name": "_private.Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle.0.Real.Angle.abs_toReal_add_eq_two_pi_sub_abs_toReal_add_abs_toReal_aux", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["rw", "have", "obtain", "obtain", "have", "grind", "obtain", "grind", "simp_all", "abs_of_pos]", "obtain", "grind"], "tactic_count": 12}
{"name": "Real.Angle.abs_toReal_add_eq_two_pi_sub_abs_toReal_add_abs_toReal", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "have", "convert", "all_goals", "grind", "exact"], "tactic_count": 7}
{"name": "Real.Angle.continuousAt_sign", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.angle_sign_comp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact"], "tactic_count": 3}
{"name": "Real.Angle.sign_eq_of_continuousOn", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.tan_add", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.tan_add'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.tan_sub", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.tan_sub'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.tan_two_mul", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": true, "tactics": ["have", "norm_cast"], "tactic_count": 2}
{"name": "Real.tan_int_mul_pi_div_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.continuousOn_tan", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": false, "tactics": ["suffices", "have", "rwa", "exact"], "tactic_count": 4}
{"name": "Real.continuous_tan", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.continuousOn_tan_Ioo", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": true, "tactics": ["refine", "simp", "rw", "rintro", "rcases", "rw", "refine", "rw", "simp", "rw", "refine", "rw", "have", "rw", "norm_num", "assumption_mod_cast", "exact"], "tactic_count": 17}
{"name": "Real.surjOn_tan", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.tan_surjective", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.image_tan_Ioo", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.tanOrderIso", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.arctan", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.tan_arctan", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.arctan_mem_Ioo", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.range_arctan", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.arctan_tan", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cos_arctan_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sin_sq_arctan", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.cos_sq_arctan", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.sin_arctan", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.cos_arctan", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.arctan_lt_pi_div_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.neg_pi_div_two_lt_arctan", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.arctan_eq_arcsin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.arcsin_eq_arctan", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": true, "tactics": ["rw_mod_cast", "sqrt_one,", "simp", "nlinarith"], "tactic_count": 4}
{"name": "Real.arctan_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.arctan_strictMono", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.arctan_mono", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.arctan_lt_arctan", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.arctan_lt_arctan_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.arctan_le_arctan", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.arctan_le_arctan_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.arctan_injective", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.arctan_inj", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.arctan_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.tendsto_arctan_atTop", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.tendsto_arctan_atBot", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.arctan_eq_of_tan_eq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.arctan_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.arctan_sqrt_three", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": true, "tactics": ["rw", "all_goals", "field_simp", "norm_num"], "tactic_count": 4}
{"name": "Real.arctan_inv_sqrt_three", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": true, "tactics": ["rw", "all_goals", "field_simp", "norm_num"], "tactic_count": 4}
{"name": "Real.arctan_eq_pi_div_four", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.arctan_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.arctan_eq_neg_pi_div_four", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.arctan_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.arctan_lt_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.arctan_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.arctan_le_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.arctan_eq_arccos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": true, "tactics": ["rw", "congr", "rw_mod_cast", "all_goals", "positivity"], "tactic_count": 5}
{"name": "Real.arccos_eq_arctan", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw_mod_cast", "linarith", "linarith"], "tactic_count": 5}
{"name": "Real.arctan_inv_of_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": true, "tactics": ["rw", "norm_num", "exact", "rw", "exact"], "tactic_count": 5}
{"name": "Real.arctan_inv_of_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "Real.arctan_ne_mul_pi_div_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": true, "tactics": ["by_contra", "obtain", "rw", "rw", "norm_cast"], "tactic_count": 5}
{"name": "Real.arctan_add_arctan_lt_pi_div_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": true, "tactics": ["rcases", "rw", "exact", "rw", "replace", "rwa"], "tactic_count": 6}
{"name": "Real.arctan_add", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": true, "tactics": ["rw", "congr", "conv_rhs", "exact", "rw", "rw", "exact", "exact"], "tactic_count": 8}
{"name": "Real.arctan_add_eq_add_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": false, "tactics": ["have", "have", "simpa", "have", "rw", "sub_eq_iff_eq_add',", "grind"], "tactic_count": 7}
{"name": "Real.arctan_add_eq_sub_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": true, "tactics": ["rw", "have", "rw", "simp", "exact"], "tactic_count": 5}
{"name": "Real.two_mul_arctan", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.two_mul_arctan_add_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.two_mul_arctan_sub_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.arctan_inv_2_add_arctan_inv_3", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.two_mul_arctan_inv_2_sub_arctan_inv_7", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.two_mul_arctan_inv_3_add_arctan_inv_7", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.four_mul_arctan_inv_5_sub_arctan_inv_239", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": true, "tactics": ["rw", "arctan_add]", "norm_num"], "tactic_count": 3}
{"name": "Real.sin_arctan_strictMono", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sin_arctan_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.sin_arctan_lt_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.sin_arctan_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sin_arctan_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.sin_arctan_le_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.continuous_arctan", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.continuousAt_arctan", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.tanPartialHomeomorph", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.coe_tanPartialHomeomorph", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.coe_tanPartialHomeomorph_symm", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalRealArctan", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalRealCosArctan", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalRealSinArctan", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.hasStrictDerivAt_tan", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.ArctanDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.hasDerivAt_tan", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.ArctanDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.tendsto_abs_tan_of_cos_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.ArctanDeriv", "is_tactic_proof": true, "tactics": ["have", "simp", "refine", "refine", "exact"], "tactic_count": 5}
{"name": "Real.tendsto_abs_tan_atTop", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.ArctanDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.continuousAt_tan", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.ArctanDeriv", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "Real.differentiableAt_tan", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.ArctanDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.deriv_tan", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.ArctanDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.contDiffAt_tan", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.ArctanDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.hasDerivAt_tan_of_mem_Ioo", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.ArctanDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.differentiableAt_tan_of_mem_Ioo", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.ArctanDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.hasStrictDerivAt_arctan", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.ArctanDeriv", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "Real.hasDerivAt_arctan", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.ArctanDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.hasDerivAt_arctan'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.ArctanDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.differentiableAt_arctan", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.ArctanDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.differentiable_arctan", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.ArctanDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.deriv_arctan", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.ArctanDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.contDiff_arctan", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.ArctanDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictDerivAt.arctan", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.ArctanDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivAt.arctan", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.ArctanDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivWithinAt.arctan", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.ArctanDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "derivWithin_arctan", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.ArctanDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv_arctan", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.ArctanDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictFDerivAt.arctan", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.ArctanDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivAt.arctan", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.ArctanDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivWithinAt.arctan", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.ArctanDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderivWithin_arctan", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.ArctanDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderiv_arctan", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.ArctanDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableWithinAt.arctan", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.ArctanDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableAt.arctan", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.ArctanDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableOn.arctan", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.ArctanDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Differentiable.arctan", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.ArctanDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffAt.arctan", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.ArctanDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.arctan", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.ArctanDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffWithinAt.arctan", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.ArctanDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffOn.arctan", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.ArctanDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.continuous_sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["change", "fun_prop"], "tactic_count": 2}
{"name": "Complex.continuousOn_sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.continuous_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["change", "fun_prop"], "tactic_count": 2}
{"name": "Complex.continuousOn_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.continuous_sinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["change", "fun_prop"], "tactic_count": 2}
{"name": "Complex.continuous_cosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["change", "fun_prop"], "tactic_count": 2}
{"name": "Real.continuous_sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.continuousOn_sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.continuous_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.continuousOn_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.continuous_sinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.continuous_cosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.exists_cos_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.pi", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.termπ", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real._aux_Mathlib_Analysis_SpecialFunctions_Trigonometric_Basic___macroRules_Real_termπ_1", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real._aux_Mathlib_Analysis_SpecialFunctions_Trigonometric_Basic___unexpand_Real_pi_1", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cos_pi_div_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Real.one_le_pi_div_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Real.pi_div_two_le_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Real.two_le_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.pi_le_four", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.pi_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.pi_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.pi_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.pi_div_two_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.two_pi_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["linarith"], "tactic_count": 1}
{"name": "Mathlib.Meta.Positivity.evalRealPi", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.pi", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.coe_real_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.pi_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.pi_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sin_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.cos_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["rw", "norm_num"], "tactic_count": 2}
{"name": "Real.sin_two_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.cos_two_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.sin_antiperiodic", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.sin_periodic", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sin_add_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sin_add_two_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sin_sub_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sin_sub_two_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sin_pi_sub", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sin_two_pi_sub", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sin_nat_mul_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sin_int_mul_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sin_add_nat_mul_two_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sin_add_int_mul_two_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sin_sub_nat_mul_two_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sin_sub_int_mul_two_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sin_nat_mul_two_pi_sub", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sin_int_mul_two_pi_sub", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sin_add_int_mul_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sin_add_nat_mul_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sin_sub_int_mul_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sin_sub_nat_mul_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sin_int_mul_pi_sub", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.sin_nat_mul_pi_sub", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.cos_antiperiodic", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.cos_periodic", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.abs_cos_int_mul_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.cos_add_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cos_add_two_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cos_sub_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cos_sub_two_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cos_pi_sub", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cos_two_pi_sub", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cos_nat_mul_two_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cos_int_mul_two_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cos_add_nat_mul_two_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cos_add_int_mul_two_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cos_sub_nat_mul_two_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cos_sub_int_mul_two_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cos_nat_mul_two_pi_sub", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cos_int_mul_two_pi_sub", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cos_add_int_mul_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cos_int_mul_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.cos_add_nat_mul_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cos_nat_mul_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.cos_sub_int_mul_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cos_sub_nat_mul_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cos_int_mul_pi_sub", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cos_nat_mul_pi_sub", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cos_nat_mul_two_pi_add_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.cos_int_mul_two_pi_add_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.cos_nat_mul_two_pi_sub_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.cos_int_mul_two_pi_sub_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.sin_pos_of_pos_of_lt_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sin_pos_of_mem_Ioo", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sin_nonneg_of_mem_Icc", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Real.sin_nonneg_of_nonneg_of_le_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sin_neg_of_neg_of_neg_pi_lt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sin_nonpos_of_nonpos_of_neg_pi_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.abs_sin_eq_sin_abs_of_abs_le_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["rcases", "rw", "rw"], "tactic_count": 3}
{"name": "Real.sin_pi_div_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sin_add_pi_div_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.sin_sub_pi_div_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.sin_pi_div_two_sub", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.cos_add_pi_div_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.cos_sub_pi_div_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.cos_pi_div_two_sub", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.cos_pos_of_mem_Ioo", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cos_nonneg_of_mem_Icc", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cos_nonneg_of_neg_pi_div_two_le_of_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cos_neg_of_pi_div_two_lt_of_lt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cos_nonpos_of_pi_div_two_le_of_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sin_eq_sqrt_one_sub_cos_sq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.cos_eq_sqrt_one_sub_sin_sq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.cos_half", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "Real.abs_sin_half", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.sin_half_eq_sqrt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "Real.sin_half_eq_neg_sqrt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "Real.sin_eq_zero_iff_of_lt_of_lt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sin_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sin_ne_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["contrapose"], "tactic_count": 1}
{"name": "Real.sin_eq_zero_iff_cos_eq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.cos_eq_zero_iff_sin_eq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.cos_eq_one_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cos_eq_one_iff_of_lt_of_lt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sin_lt_sin_of_lt_of_le_pi_div_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["rw", "have", "have", "positivity"], "tactic_count": 4}
{"name": "Real.strictMonoOn_sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.monotoneOn_sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cos_lt_cos_of_nonneg_of_le_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "Real.cos_lt_cos_of_nonneg_of_le_pi_div_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.strictAntiOn_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.antitoneOn_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cos_le_cos_of_nonneg_of_le_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sin_le_sin_of_le_of_le_pi_div_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.injOn_sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.injOn_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.surjOn_sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["simpa", "intermediate_value_Icc"], "tactic_count": 2}
{"name": "Real.surjOn_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.sin_mem_Icc", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cos_mem_Icc", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.mapsTo_sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.mapsTo_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.bijOn_sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.bijOn_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.range_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.range_sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.range_cos_infinite", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Real.range_sin_infinite", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Real.sqrtTwoAddSeries", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sqrtTwoAddSeries_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.sqrtTwoAddSeries_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.sqrtTwoAddSeries_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.sqrtTwoAddSeries_zero_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sqrtTwoAddSeries_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sqrtTwoAddSeries_lt_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sqrtTwoAddSeries_succ", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sqrtTwoAddSeries_monotone_left", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cos_pi_over_two_pow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sin_sq_pi_over_two_pow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.sin_sq_pi_over_two_pow_succ", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["rw", "congr", "norm_num", "norm_num", "exact"], "tactic_count": 5}
{"name": "Real.sin_pi_over_two_pow_succ", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["rw", "congr", "rw", "exact", "refine", "positivity", "exact"], "tactic_count": 7}
{"name": "Real.cos_pi_div_four", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["trans", "congr", "norm_num", "simp"], "tactic_count": 4}
{"name": "Real.sin_pi_div_four", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["trans", "congr", "norm_num", "simp"], "tactic_count": 4}
{"name": "Real.cos_pi_div_eight", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["trans", "congr", "norm_num", "simp"], "tactic_count": 4}
{"name": "Real.sin_pi_div_eight", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["trans", "congr", "norm_num", "simp"], "tactic_count": 4}
{"name": "Real.cos_pi_div_sixteen", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["trans", "congr", "norm_num", "simp"], "tactic_count": 4}
{"name": "Real.sin_pi_div_sixteen", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["trans", "congr", "norm_num", "simp"], "tactic_count": 4}
{"name": "Real.cos_pi_div_thirty_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["trans", "congr", "norm_num", "simp"], "tactic_count": 4}
{"name": "Real.sin_pi_div_thirty_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["trans", "congr", "norm_num", "simp"], "tactic_count": 4}
{"name": "Real.cos_pi_div_three", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": ["have", "have", "congr", "ring", "linarith", "rcases", "linarith", "have", "linarith"], "tactic_count": 9}
{"name": "Real.cos_pi_div_six", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["rw", "div_mul_eq_div_div,", "linarith"], "tactic_count": 3}
{"name": "Real.sq_cos_pi_div_six", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.sin_pi_div_six", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["rw", "congr", "ring"], "tactic_count": 3}
{"name": "Real.sq_sin_pi_div_three", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["rw", "congr", "ring"], "tactic_count": 3}
{"name": "Real.sin_pi_div_three", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["rw", "congr", "ring"], "tactic_count": 3}
{"name": "Real.quadratic_root_cos_pi_div_five", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["set", "set", "set", "suffices", "have", "rw", "push_neg", "intro", "replace", "lia", "suffices", "calc", "s"], "tactic_count": 13}
{"name": "Real.Polynomial.isRoot_cos_pi_div_five", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.cos_pi_div_five", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["set", "have", "rw", "exact", "have", "rcases", "simp", "absurd", "rw", "exact"], "tactic_count": 10}
{"name": "Real.sinOrderIso", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.coe_sinOrderIso_apply", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sinOrderIso_apply", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.tan_pi_div_four", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["rw", "have", "exact"], "tactic_count": 3}
{"name": "Real.tan_pi_div_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.tan_pi_div_six", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["rw", "ring"], "tactic_count": 2}
{"name": "Real.tan_pi_div_three", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["rw", "ring"], "tactic_count": 2}
{"name": "Real.tan_pos_of_pos_of_lt_pi_div_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Real.tan_nonneg_of_nonneg_of_le_pi_div_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.tan_neg_of_neg_of_pi_div_two_lt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.tan_nonpos_of_nonpos_of_neg_pi_div_two_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.strictMonoOn_tan", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["rintro", "rw", "exact"], "tactic_count": 3}
{"name": "Real.tan_lt_tan_of_lt_of_lt_pi_div_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.tan_lt_tan_of_nonneg_of_lt_pi_div_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.injOn_tan", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.tan_inj_of_lt_of_lt_pi_div_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.tan_periodic", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.tan_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.tan_add_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.tan_sub_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.tan_pi_sub", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.tan_pi_div_two_sub", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.tan_nat_mul_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.tan_int_mul_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.tan_add_nat_mul_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.tan_add_int_mul_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.tan_sub_nat_mul_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.tan_sub_int_mul_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.tan_nat_mul_pi_sub", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.tan_int_mul_pi_sub", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.tendsto_sin_pi_div_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "Real.tendsto_cos_pi_div_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["apply", "convert", "simp", "filter_upwards", "exact"], "tactic_count": 5}
{"name": "Real.tendsto_tan_pi_div_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "Real.tendsto_sin_neg_pi_div_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "Real.tendsto_cos_neg_pi_div_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["apply", "convert", "simp", "filter_upwards", "exact"], "tactic_count": 5}
{"name": "Real.tendsto_tan_neg_pi_div_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "Complex.sin_eq_zero_iff_cos_eq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.cos_eq_zero_iff_sin_eq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.cos_pi_div_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.sin_pi_div_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.sin_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.cos_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.sin_two_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.cos_two_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.sin_antiperiodic", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.sin_periodic", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.sin_add_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.sin_add_two_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.sin_sub_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.sin_sub_two_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.sin_pi_sub", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.sin_two_pi_sub", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.sin_nat_mul_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.sin_int_mul_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.sin_add_nat_mul_two_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.sin_add_int_mul_two_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.sin_sub_nat_mul_two_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.sin_sub_int_mul_two_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.sin_nat_mul_two_pi_sub", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.sin_int_mul_two_pi_sub", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.cos_antiperiodic", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.cos_periodic", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.cos_add_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.cos_add_two_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.cos_sub_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.cos_sub_two_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.cos_pi_sub", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.cos_two_pi_sub", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.cos_nat_mul_two_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.cos_int_mul_two_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.cos_add_nat_mul_two_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.cos_add_int_mul_two_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.cos_sub_nat_mul_two_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.cos_sub_int_mul_two_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.cos_nat_mul_two_pi_sub", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.cos_int_mul_two_pi_sub", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.cos_nat_mul_two_pi_add_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Complex.cos_int_mul_two_pi_add_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Complex.cos_nat_mul_two_pi_sub_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Complex.cos_int_mul_two_pi_sub_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Complex.sin_add_pi_div_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.sin_sub_pi_div_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.sin_pi_div_two_sub", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.cos_add_pi_div_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.cos_sub_pi_div_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.cos_pi_div_two_sub", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.tan_periodic", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Complex.tan_add_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.tan_sub_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.tan_pi_sub", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.tan_pi_div_two_sub", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.tan_nat_mul_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.tan_int_mul_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.tan_add_nat_mul_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.tan_add_int_mul_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.tan_sub_nat_mul_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.tan_sub_int_mul_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.tan_nat_mul_pi_sub", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.tan_int_mul_pi_sub", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.exp_antiperiodic", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.exp_periodic", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.exp_mul_I_antiperiodic", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Complex.exp_mul_I_periodic", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.exp_pi_mul_I", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.exp_two_pi_mul_I", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.exp_pi_div_two_mul_I", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.exp_neg_pi_div_two_mul_I", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.exp_nat_mul_two_pi_mul_I", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.exp_int_mul_two_pi_mul_I", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.exp_add_pi_mul_I", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.exp_sub_pi_mul_I", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.norm_exp_mul_exp_add_exp_neg_le_of_abs_im_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "is_tactic_proof": false, "tactics": ["simp", "mul_comm", "have", "apply_abs_le_add_of_nonneg", "refine", "exact", "refine", "exact"], "tactic_count": 8}
{"name": "Real.sin_lt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Bounds", "is_tactic_proof": true, "tactics": ["rcases", "exact", "have", "have", "rw", "apply", "rw", "refine", "apply", "simp"], "tactic_count": 10}
{"name": "Real.sin_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Bounds", "is_tactic_proof": true, "tactics": ["obtain", "simp", "exact"], "tactic_count": 3}
{"name": "Real.lt_sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Bounds", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.le_sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Bounds", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.lt_sin_mul", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Bounds", "is_tactic_proof": true, "tactics": ["simpa", "strictConcaveOn_sin_Icc.2"], "tactic_count": 2}
{"name": "Real.le_sin_mul", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Bounds", "is_tactic_proof": true, "tactics": ["simpa", "strictConcaveOn_sin_Icc.concaveOn.2"], "tactic_count": 2}
{"name": "Real.mul_lt_sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Bounds", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "Real.mul_le_sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Bounds", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "Real.sin_le_mul", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Bounds", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.mul_abs_le_abs_sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Bounds", "is_tactic_proof": true, "tactics": ["wlog", "simpa", "rw", "exact"], "tactic_count": 4}
{"name": "Real.sin_sq_lt_sq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Bounds", "is_tactic_proof": true, "tactics": ["wlog", "simpa", "rcases", "exact", "exact"], "tactic_count": 5}
{"name": "Real.sin_sq_le_sq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Bounds", "is_tactic_proof": true, "tactics": ["rcases", "simp", "exact"], "tactic_count": 3}
{"name": "Real.abs_sin_lt_abs", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Bounds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.abs_sin_le_abs", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Bounds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.one_sub_sq_div_two_lt_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Bounds", "is_tactic_proof": true, "tactics": ["have", "ring_nf", "linarith"], "tactic_count": 3}
{"name": "Real.one_sub_sq_div_two_le_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Bounds", "is_tactic_proof": true, "tactics": ["rcases", "simp", "exact"], "tactic_count": 3}
{"name": "Real.one_sub_mul_le_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Bounds", "is_tactic_proof": true, "tactics": ["simpa", "mul_le_sin"], "tactic_count": 2}
{"name": "Real.one_add_mul_le_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Bounds", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.cos_le_one_sub_mul_cos_sq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Bounds", "is_tactic_proof": true, "tactics": ["wlog", "simpa", "rw", "have", "have", "ring_nf", "linarith"], "tactic_count": 7}
{"name": "Real.sin_gt_sub_cube", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Bounds", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "refine", "have", "rw", "refine", "apply", "simp"], "tactic_count": 9}
{"name": "Real.deriv_tan_sub_id", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Bounds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.lt_tan", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Bounds", "is_tactic_proof": true, "tactics": ["let", "have", "have", "have", "exact", "have", "rw", "exact", "have", "apply", "intro", "simp", "exact", "have", "have", "have", "simp", "norm_cast", "have", "apply", "rw", "simpa", "rwa", "exact", "simpa", "have", "have", "have", "simpa"], "tactic_count": 29}
{"name": "Real.le_tan", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Bounds", "is_tactic_proof": true, "tactics": ["rcases", "rw", "exact"], "tactic_count": 3}
{"name": "Real.cos_lt_one_div_sqrt_sq_add_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Bounds", "is_tactic_proof": false, "tactics": ["suffices", "rcases", "exact", "convert", "rw", "rw", "intro", "have", "rcases", "have", "rw", "abs_of_nonneg", "lt_one_div", "sq_lt_sq,", "exact", "refine", "exact"], "tactic_count": 17}
{"name": "Real.cos_le_one_div_sqrt_sq_add_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Bounds", "is_tactic_proof": true, "tactics": ["rcases", "simp", "exact"], "tactic_count": 3}
{"name": "Real.lipschitzWith_sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Bounds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.lipschitzWith_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Bounds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.abs_sin_sub_sin_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Bounds", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.abs_cos_sub_cos_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Bounds", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.norm_exp_I_mul_ofReal_sub_one_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Bounds", "is_tactic_proof": true, "tactics": ["rw", "calc"], "tactic_count": 2}
{"name": "Real.enorm_exp_I_mul_ofReal_sub_one_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Bounds", "is_tactic_proof": true, "tactics": ["iterate", "exact"], "tactic_count": 2}
{"name": "Real.nnnorm_exp_I_mul_ofReal_sub_one_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Bounds", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.Chebyshev.complex_ofReal_eval_T", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Chebyshev.complex_ofReal_eval_U", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Chebyshev.complex_ofReal_eval_C", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Chebyshev.complex_ofReal_eval_S", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Chebyshev.T_complex_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "one", "add_two", "ih2", "simp", "push_cast", "ring_nf", "neg_add_one", "ih2", "simp", "push_cast", "ring_nf"], "tactic_count": 13}
{"name": "Polynomial.Chebyshev.U_complex_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "one", "add_two", "ih2", "simp", "sin_add_sin]", "push_cast", "ring_nf", "neg_add_one", "ih2", "simp", "sin_add_sin]", "push_cast", "ring_nf"], "tactic_count": 15}
{"name": "Polynomial.Chebyshev.C_two_mul_complex_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.Chebyshev.S_two_mul_complex_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.Chebyshev.T_complex_cosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Chebyshev.U_complex_cosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Chebyshev.C_two_mul_complex_cosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.Chebyshev.S_two_mul_complex_cosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.Chebyshev.T_real_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Chebyshev.U_real_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Chebyshev.C_two_mul_real_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Chebyshev.S_two_mul_real_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Chebyshev.T_real_cosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Chebyshev.U_real_cosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Chebyshev.C_two_mul_real_cosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Chebyshev.S_two_mul_real_cosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Chebyshev.node", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.Extremal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Chebyshev.node_eq_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.Extremal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.Chebyshev.node_eq_neg_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.Extremal", "is_tactic_proof": true, "tactics": ["have", "simp"], "tactic_count": 2}
{"name": "Polynomial.Chebyshev.node_mem_Icc", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.Extremal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Chebyshev.eval_T_real_node", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.Extremal", "is_tactic_proof": true, "tactics": ["rcases", "simp", "have", "rw"], "tactic_count": 4}
{"name": "Polynomial.Chebyshev.strictAntiOn_node", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.Extremal", "is_tactic_proof": true, "tactics": ["rcases", "simp", "refine", "apply", "exact", "rw", "rw", "nth_rewrite", "exact"], "tactic_count": 9}
{"name": "Polynomial.Chebyshev.node_lt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.Extremal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Chebyshev.zero_lt_prod_node_sub_node", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.Extremal", "is_tactic_proof": true, "tactics": ["rcases", "simp", "have", "rw", "have", "have", "have", "rw", "exact"], "tactic_count": 9}
{"name": "_private.Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.Extremal.0.Polynomial.Chebyshev.negOnePow_mul_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.Extremal", "is_tactic_proof": true, "tactics": ["apply", "rwa"], "tactic_count": 2}
{"name": "_private.Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.Extremal.0.Polynomial.Chebyshev.negOnePow_mul_negOnePow_mul_cancel", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.Extremal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Chebyshev.sumNodes", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.Extremal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Chebyshev.sumNodes_le_sumNodes_T", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.Extremal", "is_tactic_proof": true, "tactics": ["rw", "refine", "calc", "negOnePow_mul_negOnePow_mul_cancel.symm"], "tactic_count": 4}
{"name": "Polynomial.Chebyshev.sumNodes_eq_sumNodes_T_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.Extremal", "is_tactic_proof": true, "tactics": ["refine", "rw", "apply", "apply", "rw", "rw", "replace", "contrapose", "obtain", "obtain", "replace", "suffices", "have", "refine", "rw", "exact", "refine", "have", "grind"], "tactic_count": 19}
{"name": "_private.Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.Extremal.0.Polynomial.Chebyshev.leadingCoeffC", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.Extremal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.Extremal.0.Polynomial.Chebyshev.sumNodes_eq_coeff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.Extremal", "is_tactic_proof": true, "tactics": ["simp_rw", "have", "rw", "grw", "norm_cast", "simp", "convert", "exact", "simp"], "tactic_count": 9}
{"name": "_private.Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.Extremal.0.Polynomial.Chebyshev.sumNodes_T_eq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.Extremal", "is_tactic_proof": true, "tactics": ["rw", "trans", "simp", "simp"], "tactic_count": 4}
{"name": "_private.Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.Extremal.0.Polynomial.Chebyshev.negOnePow_mul_leadingCoeffC_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.Extremal", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "Polynomial.Chebyshev.coeff_le_of_forall_abs_le_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.Extremal", "is_tactic_proof": true, "tactics": ["convert", "rw", "rw"], "tactic_count": 3}
{"name": "Polynomial.Chebyshev.leadingCoeff_le_of_forall_abs_le_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.Extremal", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "lift", "replace", "rw", "grw", "norm_num"], "tactic_count": 7}
{"name": "Polynomial.Chebyshev.coeff_eq_iff_of_forall_abs_le_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.Extremal", "is_tactic_proof": true, "tactics": ["convert", "rw", "rw"], "tactic_count": 3}
{"name": "Polynomial.Chebyshev.leadingCoeff_eq_iff_of_forall_abs_le_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.Extremal", "is_tactic_proof": true, "tactics": ["refine", "apply", "suffices", "replace", "rwa", "lift", "contrapose", "rw", "positivity", "replace", "contrapose", "have", "calc"], "tactic_count": 13}
{"name": "Polynomial.Chebyshev.measureT", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.Orthogonality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Chebyshev.integral_measureT", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.Orthogonality", "is_tactic_proof": false, "tactics": ["rw", "integral_withDensity_eq_integral_smul", "congr", "simp"], "tactic_count": 4}
{"name": "Polynomial.Chebyshev.intervalIntegrable_sqrt_one_sub_sq_inv", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.Orthogonality", "is_tactic_proof": true, "tactics": ["rw", "refine", "simpa"], "tactic_count": 3}
{"name": "Polynomial.Chebyshev.integrable_measureT", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.Orthogonality", "is_tactic_proof": true, "tactics": ["replace", "have", "rw", "rw", "unfold", "convert"], "tactic_count": 6}
{"name": "Polynomial.Chebyshev.integral_measureT_eq_integral_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.Orthogonality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Chebyshev.integral_measureT_eq_integral_cos_of_continuous", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.Orthogonality", "is_tactic_proof": false, "tactics": ["have", "refine", "simpa", "refine", "simpa"], "tactic_count": 5}
{"name": "Polynomial.Chebyshev.integral_eval_T_real_measureT_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.Orthogonality", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.Chebyshev.integral_eval_T_real_measureT_of_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.Orthogonality", "is_tactic_proof": true, "tactics": ["have", "suffices", "rw", "simp_rw", "rwa", "trans", "refine", "by_cases", "rw", "rw", "simp", "exact"], "tactic_count": 12}
{"name": "Polynomial.Chebyshev.integral_eval_T_real_mul_eval_T_real_measureT", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.Orthogonality", "is_tactic_proof": false, "tactics": ["suffices", "simp_rw", "rw", "grind", "simp_rw", "rw"], "tactic_count": 6}
{"name": "Polynomial.Chebyshev.integral_eval_T_real_mul_eval_T_real_measureT_of_ne", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.Orthogonality", "is_tactic_proof": false, "tactics": ["rw", "integral_eval_T_real_measureT_of_ne_zero", "simp"], "tactic_count": 3}
{"name": "Polynomial.Chebyshev.integral_eval_T_real_mul_self_measureT_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.Orthogonality", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Polynomial.Chebyshev.integral_T_real_mul_self_measureT_of_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.Orthogonality", "is_tactic_proof": true, "tactics": ["rw", "integral_eval_T_real_measureT_zero,"], "tactic_count": 2}
{"name": "Polynomial.Chebyshev.eval_T_real_mem_Icc", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.RootsExtrema", "is_tactic_proof": true, "tactics": ["rw", "grind"], "tactic_count": 2}
{"name": "Polynomial.Chebyshev.abs_eval_T_real_le_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.RootsExtrema", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Polynomial.Chebyshev.one_le_eval_T_real", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.RootsExtrema", "is_tactic_proof": true, "tactics": ["rw", "grind"], "tactic_count": 2}
{"name": "Polynomial.Chebyshev.one_lt_eval_T_real", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.RootsExtrema", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "Polynomial.Chebyshev.one_le_negOnePow_mul_eval_T_real", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.RootsExtrema", "is_tactic_proof": true, "tactics": ["rw", "convert", "rw", "simp"], "tactic_count": 4}
{"name": "Polynomial.Chebyshev.one_lt_negOnePow_mul_eval_T_real", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.RootsExtrema", "is_tactic_proof": true, "tactics": ["rw", "convert", "rw", "simp"], "tactic_count": 4}
{"name": "Polynomial.Chebyshev.one_le_abs_eval_T_real", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.RootsExtrema", "is_tactic_proof": true, "tactics": ["wlog", "simpa", "exact"], "tactic_count": 3}
{"name": "Polynomial.Chebyshev.one_lt_abs_eval_T_real", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.RootsExtrema", "is_tactic_proof": true, "tactics": ["wlog", "simpa", "exact"], "tactic_count": 3}
{"name": "Polynomial.Chebyshev.abs_eval_T_real_le_one_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.RootsExtrema", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Chebyshev.abs_eval_T_real_eq_one_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.RootsExtrema", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Chebyshev.eval_T_real_cos_int_mul_pi_div", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.RootsExtrema", "is_tactic_proof": true, "tactics": ["rw", "convert", "simp"], "tactic_count": 3}
{"name": "Polynomial.Chebyshev.eval_T_real_eq_one_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.RootsExtrema", "is_tactic_proof": true, "tactics": ["constructor", "intro", "obtain", "use", "refine", "rw", "exact", "rintro", "rw", "norm_cast"], "tactic_count": 10}
{"name": "Polynomial.Chebyshev.eval_T_real_eq_neg_one_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.RootsExtrema", "is_tactic_proof": true, "tactics": ["constructor", "intro", "obtain", "use", "refine", "rw", "exact", "rintro", "rw", "norm_cast"], "tactic_count": 10}
{"name": "Polynomial.Chebyshev.roots_T_real_nodup", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.RootsExtrema", "is_tactic_proof": true, "tactics": ["wlog", "simp", "refine", "refine", "field_simp", "norm_cast", "grind"], "tactic_count": 7}
{"name": "Polynomial.Chebyshev.roots_T_real", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.RootsExtrema", "is_tactic_proof": true, "tactics": ["wlog", "simp", "refine", "obtain", "rw", "use", "field_simp", "norm_cast", "rw", "exact"], "tactic_count": 10}
{"name": "Polynomial.Chebyshev.rootMultiplicity_T_real", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.RootsExtrema", "is_tactic_proof": true, "tactics": ["rw", "grind"], "tactic_count": 2}
{"name": "Polynomial.Chebyshev.roots_U_real_nodup", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.RootsExtrema", "is_tactic_proof": true, "tactics": ["refine", "apply", "intro", "field_simp", "aesop", "refine", "field_simp", "norm_cast", "grind"], "tactic_count": 9}
{"name": "Polynomial.Chebyshev.roots_U_real", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.RootsExtrema", "is_tactic_proof": true, "tactics": ["wlog", "simp", "refine", "obtain", "suffices", "refine", "field_simp", "norm_cast", "grind", "rw", "use", "field_simp", "norm_cast", "ring", "rw", "exact"], "tactic_count": 16}
{"name": "Polynomial.Chebyshev.rootMultiplicity_U_real", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.RootsExtrema", "is_tactic_proof": true, "tactics": ["rw", "grind"], "tactic_count": 2}
{"name": "Polynomial.Chebyshev.isLocalMax_T_real", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.RootsExtrema", "is_tactic_proof": true, "tactics": ["have", "have", "calc", "k", "refine", "intro", "dsimp", "rw", "exact", "rw", "exact", "rw", "exact"], "tactic_count": 13}
{"name": "Polynomial.Chebyshev.isLocalMin_T_real", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.RootsExtrema", "is_tactic_proof": true, "tactics": ["have", "have", "have", "calc", "k", "refine", "intro", "dsimp", "rw", "refine", "rw", "exact", "rw", "exact"], "tactic_count": 14}
{"name": "Polynomial.Chebyshev.isLocalExtr_T_real", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.RootsExtrema", "is_tactic_proof": true, "tactics": ["cases", "exact", "exact"], "tactic_count": 3}
{"name": "Polynomial.Chebyshev.isLocalExtr_T_real_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.RootsExtrema", "is_tactic_proof": true, "tactics": ["constructor", "intro", "replace", "rw", "mul_eq_zero_iff_left", "replace", "hx", "rw", "obtain", "refine", "rw", "congr", "exact", "rintro", "rw", "exact"], "tactic_count": 16}
{"name": "Polynomial.Chebyshev.isMaxOn_T_real", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.RootsExtrema", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Chebyshev.isMinOn_T_real", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.RootsExtrema", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Chebyshev.isExtrOn_T_real", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.RootsExtrema", "is_tactic_proof": true, "tactics": ["cases", "exact", "exact"], "tactic_count": 3}
{"name": "Polynomial.Chebyshev.isExtrOn_T_real_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.RootsExtrema", "is_tactic_proof": true, "tactics": ["constructor", "intro", "apply", "apply", "refine", "refine", "have", "rw", "assumption", "refine", "have", "rw", "assumption", "rintro", "rw", "exact"], "tactic_count": 16}
{"name": "Polynomial.Chebyshev.irrational_of_isRoot_T_real", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.RootsExtrema", "is_tactic_proof": true, "tactics": ["rw", "obtain", "have", "suffices", "field_simp", "apply", "contrapose", "have", "calc", "have", "rw_mod_cast"], "tactic_count": 11}
{"name": "Complex.cos_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex", "is_tactic_proof": false, "tactics": ["have", "rw", "neg_eq_neg_one_mul,", "ring_nf", "rw", "refine", "refine", "ring"], "tactic_count": 8}
{"name": "Complex.cos_ne_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex", "is_tactic_proof": true, "tactics": ["contrapose"], "tactic_count": 1}
{"name": "Complex.sin_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex", "is_tactic_proof": true, "tactics": ["rw", "constructor", "rintro", "use", "simp", "ring", "rintro", "use", "simp", "ring"], "tactic_count": 10}
{"name": "Complex.sin_ne_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex", "is_tactic_proof": true, "tactics": ["contrapose"], "tactic_count": 1}
{"name": "Complex.tan_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex", "is_tactic_proof": false, "tactics": ["rw", "sin_eq_zero_iff]", "simp"], "tactic_count": 3}
{"name": "Complex.tan_ne_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex", "is_tactic_proof": true, "tactics": ["contrapose"], "tactic_count": 1}
{"name": "Complex.tan_int_mul_pi_div_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.tan_eq_zero_iff'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.cos_eq_cos_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.sin_eq_sin_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex", "is_tactic_proof": true, "tactics": ["simp", "refine"], "tactic_count": 2}
{"name": "Complex.cos_eq_one_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Complex.cos_eq_neg_one_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Complex.sin_eq_one_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Complex.sin_eq_neg_one_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Complex.tan_add", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex", "is_tactic_proof": true, "tactics": ["rcases", "rw", "div_div_div_cancel_right₀", "simp", "div_self", "haveI", "obtain", "simp", "rw", "mul_div_assoc,"], "tactic_count": 10}
{"name": "Complex.tan_add'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.tan_sub", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex", "is_tactic_proof": false, "tactics": ["have", "tan_add", "rcases", "refine", "rw", "convert", "push_cast", "ring", "refine", "rcases", "use", "push_cast", "ring", "rw", "convert", "ring"], "tactic_count": 16}
{"name": "Complex.tan_sub'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.tan_two_mul", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "rw"], "tactic_count": 3}
{"name": "Complex.tan_add_mul_I", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.tan_eq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "Complex.tan_eq_zero_of_cos_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex", "is_tactic_proof": true, "tactics": ["obtain", "exact", "tan_eq_zero_iff.mpr"], "tactic_count": 3}
{"name": "Complex.cos_eq_two_mul_tan_half_div_one_sub_tan_half_sq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex", "is_tactic_proof": true, "tactics": ["conv_lhs", "have", "rw", "ring"], "tactic_count": 4}
{"name": "Complex.sin_eq_two_mul_tan_half_div_one_add_tan_half_sq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex", "is_tactic_proof": true, "tactics": ["conv_lhs", "by_cases", "simp", "rw", "ring"], "tactic_count": 5}
{"name": "Complex.tan_eq_one_sub_tan_half_sq_div_one_add_tan_half_sq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex", "is_tactic_proof": true, "tactics": ["conv_lhs"], "tactic_count": 1}
{"name": "Complex.continuousOn_tan", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.continuous_tan", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.cos_eq_iff_quadratic", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "Complex.cos_surjective", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex", "is_tactic_proof": true, "tactics": ["intro", "obtain", "rcases", "refine", "rintro", "simp", "refine", "rw", "convert", "ring"], "tactic_count": 10}
{"name": "Complex.range_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.sin_surjective", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex", "is_tactic_proof": true, "tactics": ["intro", "rcases", "exact"], "tactic_count": 3}
{"name": "Complex.range_sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cos_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cos_ne_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cos_eq_cos_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sin_eq_sin_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cos_eq_neg_one_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.abs_cos_eq_one_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex", "is_tactic_proof": true, "tactics": ["rw", "constructor", "rintro", "exact", "exact", "rintro", "obtain", "exact", "exact"], "tactic_count": 9}
{"name": "Real.sin_eq_one_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sin_eq_neg_one_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.abs_sin_eq_one_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex", "is_tactic_proof": true, "tactics": ["rw", "constructor", "rintro", "exact", "exact", "rintro", "obtain", "exact", "exact"], "tactic_count": 9}
{"name": "Real.tan_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.tan_eq_zero_iff'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex", "is_tactic_proof": true, "tactics": ["revert", "exact_mod_cast"], "tactic_count": 2}
{"name": "Real.tan_ne_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.tan_eq_zero_of_cos_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cos_eq_two_mul_tan_half_div_one_sub_tan_half_sq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sin_eq_two_mul_tan_half_div_one_add_tan_half_sq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.tan_eq_one_sub_tan_half_sq_div_one_add_tan_half_sq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.hasStrictDerivAt_tan", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.ComplexDeriv", "is_tactic_proof": true, "tactics": ["convert", "rw_mod_cast", "ring"], "tactic_count": 3}
{"name": "Complex.hasDerivAt_tan", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.ComplexDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.tendsto_norm_tan_of_cos_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.ComplexDeriv", "is_tactic_proof": true, "tactics": ["simp", "have", "have", "exact", "continuous_sin.continuousWithinAt.norm.pos_mul_atTop"], "tactic_count": 5}
{"name": "Complex.tendsto_norm_tan_atTop", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.ComplexDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.continuousAt_tan", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.ComplexDeriv", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "Complex.differentiableAt_tan", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.ComplexDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.deriv_tan", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.ComplexDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.contDiffAt_tan", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.ComplexDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent.0.termℂ_ℤ", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent.0._aux_Mathlib_Analysis_SpecialFunctions_Trigonometric_Cotangent___macroRules__private_Mathlib_Analysis_SpecialFunctions_Trigonometric_Cotangent_0_termℂ_ℤ_1", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent.0._aux_Mathlib_Analysis_SpecialFunctions_Trigonometric_Cotangent___unexpand_Complex_integerComplement_1", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent.0.termℍₒ", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent.0._aux_Mathlib_Analysis_SpecialFunctions_Trigonometric_Cotangent___macroRules__private_Mathlib_Analysis_SpecialFunctions_Trigonometric_Cotangent_0_termℍₒ_1", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent.0._aux_Mathlib_Analysis_SpecialFunctions_Trigonometric_Cotangent___unexpand_UpperHalfPlane_upperHalfPlaneSet_1", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.cot_eq_exp_ratio", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent", "is_tactic_proof": true, "tactics": ["rw", "have", "rw", "ring_nf", "have", "ring_nf", "rw", "ring_nf", "rw", "field"], "tactic_count": 10}
{"name": "Complex.cot_pi_eq_exp_ratio", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent", "is_tactic_proof": true, "tactics": ["rw", "ring_nf"], "tactic_count": 2}
{"name": "pi_mul_cot_pi_q_exp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent", "is_tactic_proof": false, "tactics": ["have", "π", "simp", "ring", "rw", "geom_series_mul_one_add", "ring"], "tactic_count": 7}
{"name": "sineTerm", "kind": "abbrev", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sineTerm_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent", "is_tactic_proof": true, "tactics": ["simp", "rw", "have", "aesop", "simp"], "tactic_count": 5}
{"name": "tendsto_euler_sin_prod'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent", "is_tactic_proof": true, "tactics": ["rw", "apply", "exact"], "tactic_count": 3}
{"name": "multipliable_sineTerm", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent", "is_tactic_proof": true, "tactics": ["apply", "have", "simpa"], "tactic_count": 3}
{"name": "euler_sineTerm_tprod", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent", "is_tactic_proof": false, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "_private.Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent.0.sineTerm_bound_aux", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent", "is_tactic_proof": true, "tactics": ["have", "obtain", "refine", "simpa", "simp", "norm_div,", "intro", "gcongr", "apply"], "tactic_count": 9}
{"name": "multipliableUniformlyOn_euler_sin_prod_on_compact", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent", "is_tactic_proof": true, "tactics": ["obtain", "refine", "filter_upwards", "fun_prop"], "tactic_count": 4}
{"name": "HasProdUniformlyOn_sineTerm_prod_on_compact", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent", "is_tactic_proof": true, "tactics": ["apply", "exact"], "tactic_count": 2}
{"name": "HasProdLocallyUniformlyOn_euler_sin_prod", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent", "is_tactic_proof": true, "tactics": ["apply", "exact"], "tactic_count": 2}
{"name": "sin_pi_mul_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent", "is_tactic_proof": true, "tactics": ["apply", "intro", "nth_rw", "exact"], "tactic_count": 4}
{"name": "cot_pi_mul_contDiffWithinAt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "tendsto_logDeriv_euler_sin_div", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent", "is_tactic_proof": false, "tactics": ["refine", "logDeriv_tendsto", "filter_upwards", "simp", "exact"], "tactic_count": 5}
{"name": "logDeriv_sin_div_eq_cot", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent", "is_tactic_proof": true, "tactics": ["have", "rw", "logDeriv_div", "logDeriv_comp", "deriv_id'',", "ring", "simp", "simp", "exact"], "tactic_count": 9}
{"name": "cotTerm", "kind": "abbrev", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "logDeriv_sineTerm_eq_cotTerm", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent", "is_tactic_proof": true, "tactics": ["have", "have", "have", "have", "rw", "aesop", "simp", "deriv_div_const,", "field"], "tactic_count": 9}
{"name": "logDeriv_prod_sineTerm_eq_sum_cotTerm", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "exact", "fun_prop"], "tactic_count": 4}
{"name": "tendsto_logDeriv_euler_cot_sub", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent", "is_tactic_proof": true, "tactics": ["simp_rw", "simpa"], "tactic_count": 2}
{"name": "cotTerm_identity", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent", "is_tactic_proof": true, "tactics": ["simp", "rw", "ring", "simpa", "simpa"], "tactic_count": 5}
{"name": "summable_cotTerm", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent", "is_tactic_proof": true, "tactics": ["rw", "apply", "suffices", "rw", "simpa", "suffices", "apply", "simp"], "tactic_count": 8}
{"name": "cot_series_rep'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "cot_series_rep", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent", "is_tactic_proof": true, "tactics": ["have", "have", "simp", "rw", "ring"], "tactic_count": 5}
{"name": "_private.Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent.0.contDiffOn_inv_linear", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "eqOn_iteratedDeriv_cotTerm", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent", "is_tactic_proof": true, "tactics": ["intro", "rw", "have", "have", "simp", "rw", "ring", "simpa", "simpa"], "tactic_count": 9}
{"name": "eqOn_iteratedDerivWithin_cotTerm_integerComplement", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent", "is_tactic_proof": true, "tactics": ["apply", "exact"], "tactic_count": 2}
{"name": "eqOn_iteratedDerivWithin_cotTerm_upperHalfPlaneSet", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent", "is_tactic_proof": false, "tactics": ["apply", "iteratedDerivWithin_congr_right_of_isOpen", "intro", "simpa"], "tactic_count": 4}
{"name": "_private.Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent.0.cotTermUpperBound", "kind": "abbrev", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent.0.summable_cotTermUpperBound", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent", "is_tactic_proof": true, "tactics": ["simp_rw", "apply", "conv", "rw", "exact"], "tactic_count": 5}
{"name": "_private.Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent.0.iteratedDerivWithin_cotTerm_bounded_uniformly", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent", "is_tactic_proof": false, "tactics": ["simp", "norm_one,", "two_mul,", "gcongr", "have", "summand_bound_of_mem_verticalStrip", "have", "abs_norm_eq_max_natAbs_neg", "simp", "refine"], "tactic_count": 10}
{"name": "summableLocallyUniformlyOn_iteratedDerivWithin_cotTerm", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent", "is_tactic_proof": true, "tactics": ["apply", "intro", "obtain", "subset_verticalStrip_of_isCompact", "exact", "iteratedDerivWithin_cotTerm_bounded_uniformly"], "tactic_count": 6}
{"name": "differentiableOn_iteratedDerivWithin_cotTerm", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent", "is_tactic_proof": false, "tactics": ["suffices", "apply", "apply", "simpa", "simpa"], "tactic_count": 5}
{"name": "_private.Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent.0.aux_summable_add", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent", "is_tactic_proof": false, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "_private.Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent.0.aux_summable_sub", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent", "is_tactic_proof": false, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "_private.Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent.0.aux_iteratedDeriv_tsum_cotTerm", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent", "is_tactic_proof": false, "tactics": ["rw", "conv", "enter", "rw", "rw", "tsum_mul_left,", "push_cast", "ring_nf"], "tactic_count": 8}
{"name": "iteratedDerivWithin_cot_sub_inv_eq_add_mul_tsum", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent", "is_tactic_proof": true, "tactics": ["simp", "refine", "simpa"], "tactic_count": 3}
{"name": "_private.Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent.0.iteratedDerivWithin_cot_pi_mul_sub_inv", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent", "is_tactic_proof": true, "tactics": ["simp_rw", "rw", "simpa", "exact", "simp", "apply", "exact"], "tactic_count": 7}
{"name": "iteratedDerivWithin_cot_pi_mul_eq_mul_tsum_zpow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent", "is_tactic_proof": true, "tactics": ["have", "rw", "rw", "ring"], "tactic_count": 4}
{"name": "iteratedDerivWithin_cot_pi_mul_eq_mul_tsum_div_pow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "Complex.hasStrictDerivAt_sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": true, "tactics": ["simp", "convert", "simp", "rw", "sub_neg_eq_add,"], "tactic_count": 5}
{"name": "Complex.hasDerivAt_sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.isEquivalent_sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Complex.contDiff_sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.differentiable_sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.differentiableAt_sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.analyticAt_sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.analyticWithinAt_sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.analyticOnNhd_sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.analyticOn_sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.deriv_sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.hasStrictDerivAt_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": true, "tactics": ["simp", "convert", "simp", "ring"], "tactic_count": 4}
{"name": "Complex.hasDerivAt_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.contDiff_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.differentiable_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.differentiableAt_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.analyticAt_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.analyticWithinAt_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.analyticOnNhd_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.analyticOn_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.deriv_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.deriv_cos'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictDerivAt.ccos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivAt.ccos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivWithinAt.ccos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "derivWithin_ccos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv_ccos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictDerivAt.csin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivAt.csin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivWithinAt.csin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "derivWithin_csin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv_csin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictFDerivAt.ccos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivAt.ccos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivWithinAt.ccos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableWithinAt.ccos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableAt.ccos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableOn.ccos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Differentiable.ccos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderivWithin_ccos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderiv_ccos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.ccos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffAt.ccos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffOn.ccos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffWithinAt.ccos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictFDerivAt.csin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivAt.csin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivWithinAt.csin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableWithinAt.csin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableAt.csin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableOn.csin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Differentiable.csin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderivWithin_csin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderiv_csin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.csin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffAt.csin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffOn.csin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffWithinAt.csin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.hasStrictDerivAt_sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.hasDerivAt_sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.isEquivalent_sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.contDiff_sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.differentiable_sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.differentiableAt_sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.analyticAt_sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.analyticWithinAt_sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.analyticOnNhd_sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.analyticOn_sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.deriv_sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.hasStrictDerivAt_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.hasDerivAt_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.contDiff_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.differentiable_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.differentiableAt_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.analyticAt_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.analyticWithinAt_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.analyticOnNhd_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.analyticOn_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.deriv_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.deriv_cos'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.iteratedDeriv_add_one_sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Complex.iteratedDeriv_add_one_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "ext", "simp"], "tactic_count": 6}
{"name": "Complex.iteratedDeriv_even_sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Complex.iteratedDeriv_even_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Complex.iteratedDeriv_odd_sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.iteratedDeriv_odd_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.differentiable_iteratedDeriv_sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.differentiable_iteratedDeriv_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.iteratedDeriv_add_one_sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Real.iteratedDeriv_add_one_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "ext", "simp"], "tactic_count": 6}
{"name": "Real.iteratedDeriv_even_sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Real.iteratedDeriv_even_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Real.iteratedDeriv_odd_sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.iteratedDeriv_odd_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.differentiable_iteratedDeriv_sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.differentiable_iteratedDeriv_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.abs_iteratedDeriv_sin_le_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.abs_iteratedDeriv_cos_le_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.iteratedDerivWithin_sin_Icc", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.iteratedDerivWithin_cos_Icc", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.iteratedDerivWithin_sin_Ioo", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.iteratedDerivWithin_cos_Ioo", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictDerivAt.cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivAt.cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivWithinAt.cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "derivWithin_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictDerivAt.sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivAt.sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivWithinAt.sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "derivWithin_sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv_sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictFDerivAt.cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivAt.cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivWithinAt.cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableWithinAt.cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableAt.cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableOn.cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Differentiable.cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderivWithin_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderiv_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffAt.cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffOn.cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffWithinAt.cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictFDerivAt.sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivAt.sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivWithinAt.sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableWithinAt.sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableAt.sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableOn.sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Differentiable.sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderivWithin_sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderiv_sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffAt.sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffOn.sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffWithinAt.sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.logDeriv_sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "Real.logDeriv_sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "Complex.logDeriv_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "Real.logDeriv_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "Complex.LogDeriv_exp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "Real.LogDeriv_exp", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "Complex.hasStrictDerivAt_sinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": true, "tactics": ["simp", "convert", "rw"], "tactic_count": 3}
{"name": "Complex.hasDerivAt_sinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.isEquivalent_sinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Complex.contDiff_sinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.differentiable_sinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.differentiableAt_sinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.analyticAt_sinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.analyticWithinAt_sinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.analyticOnNhd_sinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.analyticOn_sinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.deriv_sinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.hasStrictDerivAt_cosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": true, "tactics": ["simp", "convert", "rw"], "tactic_count": 3}
{"name": "Complex.hasDerivAt_cosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.contDiff_cosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.differentiable_cosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.differentiableAt_cosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.analyticAt_cosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.analyticWithinAt_cosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.analyticOnNhd_cosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.analyticOn_cosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.deriv_cosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictDerivAt.ccosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivAt.ccosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivWithinAt.ccosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "derivWithin_ccosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv_ccosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictDerivAt.csinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivAt.csinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivWithinAt.csinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "derivWithin_csinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv_csinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictFDerivAt.ccosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivAt.ccosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivWithinAt.ccosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableWithinAt.ccosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableAt.ccosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableOn.ccosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Differentiable.ccosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderivWithin_ccosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderiv_ccosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.ccosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffAt.ccosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffOn.ccosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffWithinAt.ccosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictFDerivAt.csinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivAt.csinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivWithinAt.csinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableWithinAt.csinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableAt.csinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableOn.csinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Differentiable.csinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderivWithin_csinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderiv_csinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.csinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffAt.csinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffOn.csinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffWithinAt.csinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.hasStrictDerivAt_sinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.hasDerivAt_sinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.isEquivalent_sinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.contDiff_sinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.differentiable_sinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.differentiableAt_sinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.analyticAt_sinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.analyticWithinAt_sinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.analyticOnNhd_sinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.analyticOn_sinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.deriv_sinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.hasStrictDerivAt_cosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.hasDerivAt_cosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.contDiff_cosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.differentiable_cosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.differentiableAt_cosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.analyticAt_cosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.analyticWithinAt_cosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.analyticOnNhd_cosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.analyticOn_cosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.deriv_cosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sinh_strictMono", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sinh_injective", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sinh_inj", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sinh_le_sinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sinh_lt_sinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sinh_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.sinh_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sinh_pos_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.sinh_nonpos_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.sinh_neg_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.sinh_nonneg_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.abs_sinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Real.cosh_strictMonoOn", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cosh_le_cosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cosh_lt_cosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.one_le_cosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.one_lt_cosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sinh_sub_id_strictMono", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": true, "tactics": ["refine", "refine", "exact", "rw", "rw", "exacts"], "tactic_count": 6}
{"name": "Real.self_le_sinh_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sinh_le_self_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.self_lt_sinh_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sinh_lt_self_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.iteratedDeriv_add_one_sinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Complex.iteratedDeriv_add_one_cosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Complex.iteratedDeriv_even_sinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Complex.iteratedDeriv_even_cosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Complex.iteratedDeriv_odd_sinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.iteratedDeriv_odd_cosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.differentiable_iteratedDeriv_sinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.differentiable_iteratedDeriv_cosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.iteratedDeriv_add_one_sinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Real.iteratedDeriv_add_one_cosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Real.iteratedDeriv_even_sinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Real.iteratedDeriv_even_cosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Real.iteratedDeriv_odd_sinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.iteratedDeriv_odd_cosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.differentiable_iteratedDeriv_sinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.differentiable_iteratedDeriv_cosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.iteratedDerivWithin_sinh_Icc", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.iteratedDerivWithin_cosh_Icc", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.iteratedDerivWithin_sinh_Ioo", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.iteratedDerivWithin_cosh_Ioo", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictDerivAt.cosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivAt.cosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivWithinAt.cosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "derivWithin_cosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv_cosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictDerivAt.sinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivAt.sinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasDerivWithinAt.sinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "derivWithin_sinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deriv_sinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictFDerivAt.cosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivAt.cosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivWithinAt.cosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableWithinAt.cosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableAt.cosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableOn.cosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Differentiable.cosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderivWithin_cosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderiv_cosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.cosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffAt.cosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffOn.cosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffWithinAt.cosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasStrictFDerivAt.sinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivAt.sinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFDerivWithinAt.sinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableWithinAt.sinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableAt.sinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableOn.sinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Differentiable.sinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderivWithin_sinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fderiv_sinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.sinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffAt.sinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffOn.sinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffWithinAt.sinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.logDeriv_cosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "Real.logDeriv_cosh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "Mathlib.Meta.Positivity.evalSinh", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity._example", "kind": "example", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": true, "tactics": ["positivity"], "tactic_count": 1}
{"name": "Mathlib.Meta.Positivity._example", "kind": "example", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": true, "tactics": ["positivity"], "tactic_count": 1}
{"name": "Mathlib.Meta.Positivity._example", "kind": "example", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp", "is_tactic_proof": true, "tactics": ["positivity"], "tactic_count": 1}
{"name": "EulerSine.antideriv_cos_comp_const_mul", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.EulerSineProd", "is_tactic_proof": true, "tactics": ["have", "have", "have", "field_simp", "exact"], "tactic_count": 5}
{"name": "EulerSine.antideriv_sin_comp_const_mul", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.EulerSineProd", "is_tactic_proof": true, "tactics": ["have", "have", "have", "simp", "exact"], "tactic_count": 5}
{"name": "EulerSine.integral_cos_mul_cos_pow_aux", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.EulerSineProd", "is_tactic_proof": false, "tactics": ["have", "intro", "have", "convert", "ring", "convert", "integral_mul_deriv_eq_deriv_mul", "ext1", "rw", "refine", "ring", "apply", "apply"], "tactic_count": 13}
{"name": "EulerSine.integral_sin_mul_sin_mul_cos_pow_eq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.EulerSineProd", "is_tactic_proof": false, "tactics": ["have", "x", "intro", "have", "convert", "simp", "simp", "rw", "congr", "rw", "have", "rw", "ring", "convert", "refine", "ring_nf", "rw", "zero_sub,", "rotate_left", "apply", "apply", "exact", "refine", "dsimp", "rw", "mul_div,", "congr", "have", "conv_lhs", "rw", "ring", "apply", "apply"], "tactic_count": 33}
{"name": "EulerSine.integral_cos_mul_cos_pow", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.EulerSineProd", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "convert"], "tactic_count": 4}
{"name": "EulerSine.integral_cos_mul_cos_pow_even", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.EulerSineProd", "is_tactic_proof": true, "tactics": ["convert", "simp", "nth_rw", "rw", "ring", "push_cast", "push_cast"], "tactic_count": 7}
{"name": "EulerSine.integral_cos_pow_eq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.EulerSineProd", "is_tactic_proof": true, "tactics": ["rw", "have", "have", "rw", "congr", "nth_rw", "nth_rw", "rw", "refine", "rw", "nth_rw", "nth_rw", "rw", "refine", "rw"], "tactic_count": 15}
{"name": "EulerSine.integral_cos_pow_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.EulerSineProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EulerSine.sin_pi_mul_eq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.EulerSineProd", "is_tactic_proof": true, "tactics": ["rcases", "simp", "induction", "zero", "simp_rw", "rw", "zero_div,", "simp", "succ", "rw", "set", "set", "set", "have", "have", "rw", "dsimp", "rw", "sub_zero,", "rw", "change", "π", "have", "π", "rw", "suffices", "rw", "have", "have", "convert", "simp", "have", "simp", "convert", "rw"], "tactic_count": 35}
{"name": "EulerSine.tendsto_integral_cos_pow_mul_div", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.EulerSineProd", "is_tactic_proof": false, "tactics": ["simp_rw", "have", "cos_lt_cos_of_nonneg_of_le_pi_div_two", "have", "cos_nonneg_of_mem_Icc", "have", "have", "rw", "exact", "exact", "tendsto_setIntegral_pow_smul_of_unique_maximum_of_isCompact_of_continuousOn", "c_nonneg"], "tactic_count": 12}
{"name": "Complex.tendsto_euler_sin_prod", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.EulerSineProd", "is_tactic_proof": false, "tactics": ["have", "atTop", "have", "simp_rw", "convert", "suffices", "atTop", "from", "have", "convert", "ext1", "rw"], "tactic_count": 12}
{"name": "Real.tendsto_euler_sin_prod", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.EulerSineProd", "is_tactic_proof": true, "tactics": ["convert", "ext1", "rw", "suffices", "rw", "rw", "refine", "norm_cast", "rw"], "tactic_count": 9}
{"name": "Real.arcsin", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.arcsin_mem_Icc", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.range_arcsin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Real.arcsin_le_pi_div_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.neg_pi_div_two_le_arcsin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.arcsin_projIcc", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.sin_arcsin'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.sin_arcsin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.arcsin_sin'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.arcsin_sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.strictMonoOn_arcsin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.arcsin_lt_arcsin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.monotone_arcsin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.arcsin_le_arcsin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.injOn_arcsin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.arcsin_inj", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.continuous_arcsin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.continuousAt_arcsin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.arcsin_eq_of_sin_eq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": true, "tactics": ["subst", "exact"], "tactic_count": 2}
{"name": "Real.arcsin_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.arcsin_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.arcsin_of_one_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.arcsin_neg_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.arcsin_of_le_neg_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.arcsin_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": true, "tactics": ["rcases", "rw", "rcases", "rw", "refine", "rw", "exact"], "tactic_count": 7}
{"name": "Real.arcsin_le_iff_le_sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.arcsin_le_iff_le_sin'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rcases", "simp", "exact"], "tactic_count": 5}
{"name": "Real.le_arcsin_iff_sin_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": true, "tactics": ["rw", "arcsin_le_iff_le_sin"], "tactic_count": 2}
{"name": "Real.le_arcsin_iff_sin_le'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.arcsin_lt_iff_lt_sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.arcsin_lt_iff_lt_sin'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.lt_arcsin_iff_sin_lt", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.lt_arcsin_iff_sin_lt'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.arcsin_eq_iff_eq_sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.arcsin_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.arcsin_nonpos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.arcsin_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.zero_eq_arcsin_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.arcsin_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.arcsin_lt_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.arcsin_lt_pi_div_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.neg_pi_div_two_lt_arcsin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.arcsin_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.pi_div_two_eq_arcsin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.pi_div_two_le_arcsin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.arcsin_eq_neg_pi_div_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.neg_pi_div_two_eq_arcsin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.arcsin_le_neg_pi_div_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.pi_div_four_le_arcsin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": true, "tactics": ["rw", "have", "constructor"], "tactic_count": 3}
{"name": "Real.cos_arcsin_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cos_arcsin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "rw", "nlinarith", "by_cases", "rw", "rw", "nlinarith", "have", "rw", "sqrt_mul_self", "rw"], "tactic_count": 12}
{"name": "Real.tan_arcsin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": true, "tactics": ["rw", "by_cases", "have", "rw", "simp", "by_cases", "have", "rw", "simp", "rw"], "tactic_count": 10}
{"name": "Real.arccos", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.arccos_eq_pi_div_two_sub_arcsin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.arcsin_eq_pi_div_two_sub_arccos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.arccos_le_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "Real.arccos_nonneg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "Real.arccos_pos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.cos_arccos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.arccos_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.arccos_eq_of_eq_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.strictAntiOn_arccos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.arccos_lt_arccos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "Real.arccos_le_arccos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "Real.antitone_arccos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.arccos_injOn", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.arccos_inj", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.arccos_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.arccos_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.arccos_neg_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.arccos_eq_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.arccos_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.arccos_eq_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.arccos_lt_pi", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Real.arccos_neg", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.arccos_of_one_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.arccos_of_le_neg_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.sin_arccos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "rw", "nlinarith", "by_cases", "rw", "rw", "nlinarith", "rw"], "tactic_count": 9}
{"name": "Real.arccos_le_pi_div_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.arccos_lt_pi_div_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.arccos_le_pi_div_four", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": true, "tactics": ["rw", "constructor", "intro", "linarith"], "tactic_count": 4}
{"name": "Real.continuous_arccos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.tan_arccos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.arccos_eq_arcsin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.arcsin_eq_arccos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Real.sinPartialHomeomorph", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sinPartialEquiv", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.mapsTo_sin_Ioo", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.arcsin_image_Icc", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.cosPartialHomeomorph", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cosPartialEquiv", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.mapsTo_cos_Ioo", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.arccos_image_Icc", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Filter.Tendsto.arcsin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.arcsin_nhdsLE", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "Filter.Tendsto.arcsin_nhdsGE", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.arccos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.arccos_nhdsLE", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.arccos_nhdsGE", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": true, "tactics": ["refine", "push", "exact"], "tactic_count": 3}
{"name": "ContinuousWithinAt.arcsin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.arccos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.arcsin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.arccos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.arcsin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.arccos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.arcsin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.arccos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.deriv_arcsin_aux", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.InverseDeriv", "is_tactic_proof": true, "tactics": ["rcases", "have", "rw", "have", "exact", "rcases", "have", "simp", "exact", "sinPartialHomeomorph.contDiffAt_symm_deriv", "have", "rw", "have", "exact"], "tactic_count": 14}
{"name": "Real.hasStrictDerivAt_arcsin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.InverseDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.hasDerivAt_arcsin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.InverseDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.contDiffAt_arcsin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.InverseDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.hasDerivWithinAt_arcsin_Ici", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.InverseDeriv", "is_tactic_proof": true, "tactics": ["rcases", "convert", "exact"], "tactic_count": 3}
{"name": "Real.hasDerivWithinAt_arcsin_Iic", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.InverseDeriv", "is_tactic_proof": true, "tactics": ["rcases", "convert", "exact"], "tactic_count": 3}
{"name": "Real.differentiableWithinAt_arcsin_Ici", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.InverseDeriv", "is_tactic_proof": true, "tactics": ["refine", "rintro", "have", "filter_upwards", "have", "simpa"], "tactic_count": 6}
{"name": "Real.differentiableWithinAt_arcsin_Iic", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.InverseDeriv", "is_tactic_proof": true, "tactics": ["refine", "rw", "have", "simpa"], "tactic_count": 4}
{"name": "Real.differentiableAt_arcsin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.InverseDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.deriv_arcsin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.InverseDeriv", "is_tactic_proof": true, "tactics": ["funext", "by_cases", "exact", "rw", "simp", "rcases"], "tactic_count": 6}
{"name": "Real.differentiableOn_arcsin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.InverseDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.contDiffOn_arcsin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.InverseDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.contDiffAt_arcsin_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.InverseDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.hasStrictDerivAt_arccos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.InverseDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.hasDerivAt_arccos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.InverseDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.contDiffAt_arccos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.InverseDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.hasDerivWithinAt_arccos_Ici", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.InverseDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.hasDerivWithinAt_arccos_Iic", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.InverseDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.differentiableWithinAt_arccos_Ici", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.InverseDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.differentiableWithinAt_arccos_Iic", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.InverseDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.differentiableAt_arccos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.InverseDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.deriv_arccos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.InverseDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.differentiableOn_arccos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.InverseDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.contDiffOn_arccos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.InverseDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.contDiffAt_arccos_iff", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.InverseDeriv", "is_tactic_proof": true, "tactics": ["refine", "simpa"], "tactic_count": 2}
{"name": "Complex.hasSum_cos'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Series", "is_tactic_proof": true, "tactics": ["rw", "have", "replace", "dsimp", "simp_rw", "refine", "dsimp", "convert", "rw", "simp_rw", "neg_div,"], "tactic_count": 11}
{"name": "Complex.hasSum_sin'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Series", "is_tactic_proof": true, "tactics": ["rw", "have", "replace", "dsimp", "simp_rw", "refine", "dsimp", "convert", "rw", "simp_rw", "zero_add,", "mul_div_cancel_left₀"], "tactic_count": 12}
{"name": "Complex.hasSum_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Series", "is_tactic_proof": true, "tactics": ["convert", "simp_rw"], "tactic_count": 2}
{"name": "Complex.hasSum_sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Series", "is_tactic_proof": true, "tactics": ["convert", "simp_rw", "div_self"], "tactic_count": 3}
{"name": "Complex.cos_eq_tsum'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Series", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.sin_eq_tsum'", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Series", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.cos_eq_tsum", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Series", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.sin_eq_tsum", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Series", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.hasSum_cos", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Series", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.hasSum_sin", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Series", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Real.sin_eq_tsum", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Series", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Complex.hasSum_sinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Series", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
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{"name": "Complex.sinh_eq_tsum", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Series", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Real.hasSum_sinh", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Series", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Real.sinh_eq_tsum", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Series", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cosh_le_exp_half_sq", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Series", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp", "gcongr", "norm_cast", "exact"], "tactic_count": 6}
{"name": "Real.sinc", "kind": "definition", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Sinc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sinc_apply", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Sinc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sinc_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Sinc", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.sinc_of_ne_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Sinc", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "Real.abs_sinc_le_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Sinc", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "rw", "refine", "rw", "exact"], "tactic_count": 6}
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{"name": "Real.neg_one_le_sinc", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Sinc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sin_div_le_inv_abs", "kind": "theorem", "module": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Sinc", "is_tactic_proof": true, "tactics": ["rcases", "rw", "ring_nf", "rw", "exact", "simpa", "simp", "rw", "exact"], "tactic_count": 9}
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{"name": "arithGeom_zero", "kind": "theorem", "module": "Mathlib.Analysis.SpecificLimits.ArithmeticGeometric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "arithGeom_zero_eq_sum", "kind": "theorem", "module": "Mathlib.Analysis.SpecificLimits.ArithmeticGeometric", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "arithGeom_eq'", "kind": "theorem", "module": "Mathlib.Analysis.SpecificLimits.ArithmeticGeometric", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "arithGeom_same_eq_mul_div'", "kind": "theorem", "module": "Mathlib.Analysis.SpecificLimits.ArithmeticGeometric", "is_tactic_proof": true, "tactics": ["rw", "field"], "tactic_count": 2}
{"name": "arithGeom_same_eq_mul_div", "kind": "theorem", "module": "Mathlib.Analysis.SpecificLimits.ArithmeticGeometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "arithGeom_zero_eq_mul_div'", "kind": "theorem", "module": "Mathlib.Analysis.SpecificLimits.ArithmeticGeometric", "is_tactic_proof": true, "tactics": ["rw", "ring"], "tactic_count": 2}
{"name": "arithGeom_zero_eq_mul_div", "kind": "theorem", "module": "Mathlib.Analysis.SpecificLimits.ArithmeticGeometric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "div_lt_arithGeom", "kind": "theorem", "module": "Mathlib.Analysis.SpecificLimits.ArithmeticGeometric", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "calc", "b"], "tactic_count": 5}
{"name": "arithGeom_strictMono", "kind": "theorem", "module": "Mathlib.Analysis.SpecificLimits.ArithmeticGeometric", "is_tactic_proof": true, "tactics": ["refine", "have", "rw", "rw", "linarith"], "tactic_count": 5}
{"name": "tendsto_arithGeom_atTop_of_one_lt", "kind": "theorem", "module": "Mathlib.Analysis.SpecificLimits.ArithmeticGeometric", "is_tactic_proof": true, "tactics": ["rw", "refine", "refine", "exact"], "tactic_count": 4}
{"name": "tendsto_arithGeom_nhds_of_lt_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecificLimits.ArithmeticGeometric", "is_tactic_proof": true, "tactics": ["rw", "conv_rhs", "refine", "conv_rhs", "exact"], "tactic_count": 5}
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{"name": "NNRat.tendsto_algebraMap_inv_atTop_nhds_zero_nat", "kind": "theorem", "module": "Mathlib.Analysis.SpecificLimits.Basic", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
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{"name": "tendsto_const_div_atTop_nhds_zero_nat", "kind": "theorem", "module": "Mathlib.Analysis.SpecificLimits.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "tendsto_one_div_atTop_nhds_zero_nat", "kind": "theorem", "module": "Mathlib.Analysis.SpecificLimits.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "tendsto_natCast_div_add_atTop", "kind": "theorem", "module": "Mathlib.Analysis.SpecificLimits.Basic", "is_tactic_proof": true, "tactics": ["convert", "exact", "simp", "have", "rw", "refine", "simp_rw", "refine", "have", "rw", "refine", "intros", "simp_all"], "tactic_count": 13}
{"name": "tendsto_add_mul_div_add_mul_atTop_nhds", "kind": "theorem", "module": "Mathlib.Analysis.SpecificLimits.Basic", "is_tactic_proof": true, "tactics": ["apply", "exact", "refine", "intro", "dsimp", "field", "apply", "all_goals", "apply", "apply", "exact"], "tactic_count": 11}
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{"name": "Filter.Tendsto.num_atTop_iff_den_atTop", "kind": "theorem", "module": "Mathlib.Analysis.SpecificLimits.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "uniformity_basis_dist_pow_of_lt_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecificLimits.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "tendsto_atTop_of_geom_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecificLimits.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.tendsto_pow_atTop_nhds_zero_of_lt_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecificLimits.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ENNReal.tendsto_pow_atTop_nhds_zero_of_lt_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecificLimits.Basic", "is_tactic_proof": true, "tactics": ["rcases", "rw", "norm_cast", "apply"], "tactic_count": 4}
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{"name": "hasSum_geometric_of_lt_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecificLimits.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "tsum_geometric_of_lt_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecificLimits.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "tsum_geometric_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecificLimits.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sum_geometric_two_le", "kind": "theorem", "module": "Mathlib.Analysis.SpecificLimits.Basic", "is_tactic_proof": false, "tactics": ["have", "intro", "apply", "norm_num", "convert", "exact"], "tactic_count": 6}
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{"name": "tsum_geometric_inv_two_ge", "kind": "theorem", "module": "Mathlib.Analysis.SpecificLimits.Basic", "is_tactic_proof": false, "tactics": ["have", "simpa", "have", "simp"], "tactic_count": 4}
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{"name": "tsum_geometric_nnreal", "kind": "theorem", "module": "Mathlib.Analysis.SpecificLimits.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.tsum_geometric", "kind": "theorem", "module": "Mathlib.Analysis.SpecificLimits.Basic", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "norm_cast", "convert", "rw", "rw", "refine", "calc"], "tactic_count": 8}
{"name": "ENNReal.tsum_geometric_add_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecificLimits.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.tsum_two_zpow_neg_add_one", "kind": "theorem", "module": "Mathlib.Analysis.SpecificLimits.Basic", "is_tactic_proof": false, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "ENNReal.tsum_geometric_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecificLimits.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.tsum_geometric_two_encode_le_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecificLimits.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tsum_geometric_lt_top", "kind": "theorem", "module": "Mathlib.Analysis.SpecificLimits.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "tsum_geometric_encode_lt_top", "kind": "theorem", "module": "Mathlib.Analysis.SpecificLimits.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cauchySeq_of_edist_le_geometric", "kind": "theorem", "module": "Mathlib.Analysis.SpecificLimits.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "finiteness"], "tactic_count": 3}
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{"name": "edist_le_of_edist_le_geometric_of_tendsto₀", "kind": "theorem", "module": "Mathlib.Analysis.SpecificLimits.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "cauchySeq_of_edist_le_geometric_two", "kind": "theorem", "module": "Mathlib.Analysis.SpecificLimits.Basic", "is_tactic_proof": true, "tactics": ["simp", "refine", "simp"], "tactic_count": 3}
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{"name": "dist_le_of_le_geometric_of_tendsto", "kind": "theorem", "module": "Mathlib.Analysis.SpecificLimits.Basic", "is_tactic_proof": true, "tactics": ["have", "convert", "simp", "rw", "exact"], "tactic_count": 5}
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{"name": "CategoryTheory.Abelian.coimageIsoImage'_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp", "coimageStrongEpiMonoFactorisation_m,"], "tactic_count": 3}
{"name": "CategoryTheory.Abelian.factorThruImage_comp_coimageIsoImage'_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Abelian.image.ι_comp_eq_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Abelian.coimage.comp_π_eq_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Abelian.im", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.coim", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.coimIsoIm", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.imageIsoImage", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Abelian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.imageIsoImage_hom_comp_image_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Abelian.imageIsoImage_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Basic", "is_tactic_proof": true, "tactics": ["ext", "rw", "kernel.lift_ι,"], "tactic_count": 3}
{"name": "CategoryTheory.Abelian.epiIsCokernelOfKernel", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.monoIsKernelOfCokernel", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.epiDesc", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.comp_epiDesc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.monoLift", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.monoLift_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.isLimitMapConeOfKernelForkOfι", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Basic", "is_tactic_proof": false, "tactics": ["let", "parallelPair.ext", "refine", "let", "refine", "change", "rw"], "tactic_count": 7}
{"name": "CategoryTheory.Abelian.isColimitMapCoconeOfCokernelCoforkOfπ", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Basic", "is_tactic_proof": false, "tactics": ["let", "parallelPair.ext", "refine", "let", "refine", "change", "rw"], "tactic_count": 7}
{"name": "CategoryTheory.Abelian.hasEqualizers", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.hasPullbacks", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.hasCoequalizers", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.hasPushouts", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.hasFiniteLimits", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.hasFiniteColimits", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.PullbackToBiproductIsKernel.pullbackToBiproduct", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Abelian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.PullbackToBiproductIsKernel.pullbackToBiproductFork", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Abelian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.PullbackToBiproductIsKernel.isLimitPullbackToBiproduct", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.BiproductToPushoutIsCokernel.biproductToPushout", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Abelian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.BiproductToPushoutIsCokernel.biproductToPushoutCofork", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Abelian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.BiproductToPushoutIsCokernel.isColimitBiproductToPushout", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.epi_pullback_of_epi_f", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.epi_pullback_of_epi_g", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.epi_snd_of_isLimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Basic", "is_tactic_proof": true, "tactics": ["haveI", "apply"], "tactic_count": 2}
{"name": "CategoryTheory.Abelian.epi_fst_of_isLimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Basic", "is_tactic_proof": true, "tactics": ["haveI", "apply"], "tactic_count": 2}
{"name": "CategoryTheory.Abelian.epi_fst_of_factor_thru_epi_mono_factorization", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Basic", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Abelian.mono_pushout_of_mono_f", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.mono_pushout_of_mono_g", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.mono_inr_of_isColimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Basic", "is_tactic_proof": false, "tactics": ["haveI", "apply"], "tactic_count": 2}
{"name": "CategoryTheory.Abelian.mono_inl_of_isColimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Basic", "is_tactic_proof": false, "tactics": ["haveI", "apply"], "tactic_count": 2}
{"name": "CategoryTheory.Abelian.mono_inl_of_factor_thru_epi_mono_factorization", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Basic", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.NonPreadditiveAbelian.abelian", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.instIsStableUnderCobaseChangeMonomorphisms", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.CommSq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.instIsStableUnderBaseChangeEpimorphisms", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.CommSq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPushout.exact_shortComplex", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.CommSq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPushout.hom_eq_add_up_to_refinements", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.CommSq", "is_tactic_proof": true, "tactics": ["have", "obtain", "refine", "simp", "congr", "cat_disch"], "tactic_count": 6}
{"name": "CategoryTheory.IsPushout.mono_of_isPullback_of_mono", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.CommSq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPullback.exact_shortComplex'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.CommSq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.mono_cokernel_map_of_isPullback", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.CommSq", "is_tactic_proof": true, "tactics": ["rw", "intro", "obtain", "have", "obtain", "this.exact_up_to_refinements", "obtain", "simp"], "tactic_count": 8}
{"name": "CategoryTheory.Abelian.epi_kernel_map_of_isPushout", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.CommSq", "is_tactic_proof": true, "tactics": ["rw", "intro", "obtain", "sq.isColimitCokernelCofork).exact_up_to_refinements", "refine", "simpa", "ext", "simpa"], "tactic_count": 8}
{"name": "CategoryTheory.Abelian.mono_of_epi_of_mono_of_mono'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.DiagramLemmas.Four", "is_tactic_proof": true, "tactics": ["apply", "intro", "have", "rw", "obtain", "dsimp", "have", "obtain", "obtain", "have", "rw", "rfl", "rw"], "tactic_count": 13}
{"name": "CategoryTheory.Abelian.mono_of_epi_of_mono_of_mono", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.DiagramLemmas.Four", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.epi_of_epi_of_epi_of_mono'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.DiagramLemmas.Four", "is_tactic_proof": true, "tactics": ["rw", "intro", "obtain", "have", "rw", "comp_zero,", "obtain", "dsimp", "have", "rw", "obtain", "dsimp", "rw", "obtain", "refine", "rw", "dsimp", "rw"], "tactic_count": 18}
{"name": "CategoryTheory.Abelian.epi_of_epi_of_epi_of_mono", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.DiagramLemmas.Four", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.isIso_of_epi_of_isIso_of_isIso_of_mono", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.DiagramLemmas.Four", "is_tactic_proof": true, "tactics": ["dsimp", "have", "apply", "dsimp", "infer_instance", "have", "apply", "infer_instance", "apply"], "tactic_count": 9}
{"name": "CategoryTheory.Abelian.mono_of_epi_of_epi_mono'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.DiagramLemmas.Four", "is_tactic_proof": false, "tactics": ["let", "homMk₃", "refine", "mono_of_epi_of_mono_of_mono", "dsimp", "rw", "exact", "rw", "exact"], "tactic_count": 9}
{"name": "CategoryTheory.Abelian.mono_of_epi_of_epi_of_mono", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.DiagramLemmas.Four", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.epi_of_mono_of_epi_of_mono'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.DiagramLemmas.Four", "is_tactic_proof": false, "tactics": ["let", "homMk₃", "refine", "epi_of_epi_of_epi_of_mono", "rw", "exact", "dsimp", "rw", "exact"], "tactic_count": 9}
{"name": "CategoryTheory.Abelian.epi_of_mono_of_epi_of_mono", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.DiagramLemmas.Four", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.mono_of_mono_of_mono_of_mono", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.DiagramLemmas.Four", "is_tactic_proof": false, "tactics": ["let", "homMk₃", "refine", "mono_of_epi_of_mono_of_mono", "rw", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.Abelian.epi_of_epi_of_epi_of_epi", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.DiagramLemmas.Four", "is_tactic_proof": false, "tactics": ["let", "homMk₃", "refine", "epi_of_epi_of_epi_of_mono", "rw", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.ShortComplex.mono_of_epi_of_epi_of_mono", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.DiagramLemmas.Four", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.epi_of_mono_of_epi_of_mono", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.DiagramLemmas.Four", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.mono_of_mono_of_mono_of_mono", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.DiagramLemmas.Four", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.epi_of_epi_of_epi_of_epi", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.DiagramLemmas.Four", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.kernelCokernelCompSequence.ι", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.DiagramLemmas.KernelCokernelComp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.kernelCokernelCompSequence.ι_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.DiagramLemmas.KernelCokernelComp", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.kernelCokernelCompSequence.ι_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.DiagramLemmas.KernelCokernelComp", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.kernelCokernelCompSequence.φ", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.DiagramLemmas.KernelCokernelComp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.kernelCokernelCompSequence.inl_φ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.DiagramLemmas.KernelCokernelComp", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.kernelCokernelCompSequence.inr_φ_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.DiagramLemmas.KernelCokernelComp", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.kernelCokernelCompSequence.φ_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.DiagramLemmas.KernelCokernelComp", "is_tactic_proof": true, "tactics": ["dsimp", "aesop"], "tactic_count": 2}
{"name": "CategoryTheory.kernelCokernelCompSequence.π", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.DiagramLemmas.KernelCokernelComp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.kernelCokernelCompSequence.inl_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.DiagramLemmas.KernelCokernelComp", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.kernelCokernelCompSequence.inr_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.DiagramLemmas.KernelCokernelComp", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.kernelCokernelCompSequence.ι_φ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.DiagramLemmas.KernelCokernelComp", "is_tactic_proof": true, "tactics": ["dsimp", "aesop"], "tactic_count": 2}
{"name": "CategoryTheory.kernelCokernelCompSequence.φ_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.DiagramLemmas.KernelCokernelComp", "is_tactic_proof": true, "tactics": ["dsimp", "ext", "rw", "simp"], "tactic_count": 4}
{"name": "CategoryTheory.kernelCokernelCompSequence.instMonoι", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.DiagramLemmas.KernelCokernelComp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.kernelCokernelCompSequence.instEpiπ", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.DiagramLemmas.KernelCokernelComp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.kernelCokernelCompSequence.isLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.DiagramLemmas.KernelCokernelComp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.kernelCokernelCompSequence.isColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.DiagramLemmas.KernelCokernelComp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.kernelCokernelCompSequence.snakeInput", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.DiagramLemmas.KernelCokernelComp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.kernelCokernelCompSequence.δ", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.DiagramLemmas.KernelCokernelComp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.kernelCokernelCompSequence.δ_fac", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.DiagramLemmas.KernelCokernelComp", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.kernelCokernelCompSequence", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Abelian.DiagramLemmas.KernelCokernelComp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instMonoMap'KernelCokernelCompSequenceOfNatNat", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.DiagramLemmas.KernelCokernelComp", "is_tactic_proof": true, "tactics": ["dsimp"], "tactic_count": 1}
{"name": "CategoryTheory.instEpiMap'KernelCokernelCompSequenceOfNatNat", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.DiagramLemmas.KernelCokernelComp", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.kernelCokernelCompSequence_exact", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.DiagramLemmas.KernelCokernelComp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.epiWithInjectiveKernel", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.EpiWithInjectiveKernel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.epiWithInjectiveKernel_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.EpiWithInjectiveKernel", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "let", "exact", "rintro", "have", "let", "exact"], "tactic_count": 8}
{"name": "CategoryTheory.Abelian.epiWithInjectiveKernel_of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.EpiWithInjectiveKernel", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Abelian.instIsMultiplicativeEpiWithInjectiveKernel", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.EpiWithInjectiveKernel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.exact_iff_epi_imageToKernel'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Exact", "is_tactic_proof": true, "tactics": ["rw", "have", "simp", "constructor", "intro", "exact", "intro", "rw", "apply"], "tactic_count": 9}
{"name": "CategoryTheory.ShortComplex.exact_iff_epi_imageToKernel", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Exact", "is_tactic_proof": true, "tactics": ["rw", "apply", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.ShortComplex.exact_iff_isIso_imageToKernel'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Exact", "is_tactic_proof": true, "tactics": ["simp", "intro", "apply"], "tactic_count": 3}
{"name": "CategoryTheory.ShortComplex.exact_iff_isIso_imageToKernel", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Exact", "is_tactic_proof": true, "tactics": ["rw", "constructor", "intro", "apply", "intro", "infer_instance"], "tactic_count": 6}
{"name": "CategoryTheory.ShortComplex.Exact.isIso_imageToKernel", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.Exact.isIso_imageToKernel'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.exact_iff_image_eq_kernel", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Exact", "is_tactic_proof": true, "tactics": ["rw", "constructor", "intro", "exact", "intro", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.ShortComplex.exact_iff_of_forks", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Exact", "is_tactic_proof": true, "tactics": ["rw", "let", "let", "have", "have", "have", "dsimp", "rw", "rw"], "tactic_count": 9}
{"name": "CategoryTheory.ShortComplex.Exact.isLimitImage", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Exact", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.Exact.isLimitImage'", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.Exact.isColimitCoimage", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Exact", "is_tactic_proof": true, "tactics": ["rw", "refine", "intro", "ext", "rw"], "tactic_count": 5}
{"name": "CategoryTheory.ShortComplex.Exact.isColimitImage", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.exact_kernel", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.exact_cokernel", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.exact_iff_exact_image_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.exact_iff_exact_coimage_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Exact", "is_tactic_proof": true, "tactics": ["symm", "exact", "τ₂", "τ₃"], "tactic_count": 4}
{"name": "CategoryTheory.Abelian.tfae_mono", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Exact", "is_tactic_proof": true, "tactics": ["tfae_have", "tfae_have", "tfae_have", "tfae_finish"], "tactic_count": 4}
{"name": "CategoryTheory.Abelian.tfae_epi", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Exact", "is_tactic_proof": true, "tactics": ["tfae_have", "tfae_have", "tfae_have", "tfae_finish"], "tactic_count": 4}
{"name": "CategoryTheory.Functor.reflects_exact_of_faithful", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Exact", "is_tactic_proof": true, "tactics": ["rw", "dsimp", "apply", "obtain", "kernel.lift", "obtain", "cokernel.desc", "rw"], "tactic_count": 8}
{"name": "CategoryTheory.Functor.preservesMonomorphisms_of_map_exact", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.preservesEpimorphisms_of_map_exact", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.preservesHomology_of_map_exact", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Exact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.preservesHomology_of_preservesMonos_and_cokernels", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Exact", "is_tactic_proof": true, "tactics": ["apply", "intro", "let", "τ₂", "τ₃", "comm₂₃", "dsimp", "rw", "apply", "apply", "exact"], "tactic_count": 11}
{"name": "CategoryTheory.Functor.preservesHomology_of_preservesEpis_and_kernels", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Exact", "is_tactic_proof": true, "tactics": ["apply", "intro", "let", "τ₂", "τ₃", "comm₁₂", "dsimp", "rw", "apply", "apply", "exact"], "tactic_count": 11}
{"name": "Ext", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Ext", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ChainComplex.linearYonedaObj", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Ext", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ProjectiveResolution.isoExt", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Ext", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isZero_Ext_succ_of_projective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Ext", "is_tactic_proof": true, "tactics": ["refine", "rw", "refine", "dsimp", "rw", "ext", "obtain", "rfl"], "tactic_count": 8}
{"name": "CategoryTheory.Abelian.FreydMitchell.instNonemptyAsSmall", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.FreydMitchell", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.FreydMitchell.EmbeddingRing", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.FreydMitchell", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.FreydMitchell.instRingEmbeddingRing", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.FreydMitchell", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.CategoryTheory.Abelian.FreydMitchell.0.CategoryTheory.Abelian.FreydMitchell.F", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.FreydMitchell", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.CategoryTheory.Abelian.FreydMitchell.0.CategoryTheory.Abelian.FreydMitchell.G", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.FreydMitchell", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.CategoryTheory.Abelian.FreydMitchell.0.CategoryTheory.Abelian.FreydMitchell.H", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.FreydMitchell", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.FreydMitchell.functor", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.FreydMitchell", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.FreydMitchell.instFaithfulModuleCatEmbeddingRingFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.FreydMitchell", "is_tactic_proof": true, "tactics": ["rw", "have", "have", "have", "infer_instance"], "tactic_count": 5}
{"name": "CategoryTheory.Abelian.FreydMitchell.instFullModuleCatEmbeddingRingFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.FreydMitchell", "is_tactic_proof": true, "tactics": ["rw", "have", "have", "have", "infer_instance"], "tactic_count": 5}
{"name": "CategoryTheory.Abelian.FreydMitchell.instPreservesFiniteLimitsModuleCatEmbeddingRingFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.FreydMitchell", "is_tactic_proof": true, "tactics": ["rw", "have", "have", "have", "infer_instance"], "tactic_count": 5}
{"name": "CategoryTheory.Abelian.FreydMitchell.instPreservesFiniteColimitsModuleCatEmbeddingRingFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.FreydMitchell", "is_tactic_proof": true, "tactics": ["rw", "have", "have", "have", "infer_instance"], "tactic_count": 5}
{"name": "CategoryTheory.Abelian.freyd_mitchell", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.FreydMitchell", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.FunctorCategory.coimageObjIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.FunctorCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.FunctorCategory.imageObjIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.FunctorCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.FunctorCategory.coimageImageComparison_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.FunctorCategory", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "dsimp", "simp", "erw", "erw", "conv_lhs", "rfl"], "tactic_count": 8}
{"name": "CategoryTheory.Abelian.FunctorCategory.coimageImageComparison_app'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.FunctorCategory", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Abelian.FunctorCategory.functor_category_isIso_coimageImageComparison", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.FunctorCategory", "is_tactic_proof": false, "tactics": ["have", "intros", "rw", "infer_instance", "apply"], "tactic_count": 5}
{"name": "CategoryTheory.Abelian.functorCategoryAbelian", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.FunctorCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasExactColimitsOfShape.domain_of_functor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasExactLimitsOfShape.domain_of_functor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasExactColimitsOfShape.of_domain_equivalence", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasExactColimitsOfShape.of_codomain_equivalence", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Basic", "is_tactic_proof": true, "tactics": ["haveI", "refine", "refine", "apply", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.HasExactLimitsOfShape.of_domain_equivalence", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasExactLimitsOfShape.of_codomain_equivalence", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Basic", "is_tactic_proof": true, "tactics": ["haveI", "refine", "refine", "apply", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.Adjunction.hasExactColimitsOfShape", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.hasExactLimitsOfShape", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.AB4", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.AB4OfSize_shrink", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instAB4OfSize", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.AB4Star", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.AB4StarOfSize_shrink", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instAB4StarOfSize", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instCountableAB4OfAB4OfSize", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instCountableAB4StarOfAB4StarOfSize", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.AB5", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.AB5OfSize_of_univLE", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Basic", "is_tactic_proof": true, "tactics": ["haveI", "constructor", "intro", "haveI", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.AB5OfSize_shrink", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.AB5Star", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.AB5StarOfSize_of_univLE", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Basic", "is_tactic_proof": true, "tactics": ["haveI", "constructor", "intro", "haveI", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.AB5StarOfSize_shrink", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.hasExactColimitsOfShape_of_final", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.hasExactLimitsOfShape_of_initial", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.preservesFiniteLimits_liftToFinset", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.hasExactColimitsOfShape_discrete_of_hasExactColimitsOfShape_finset_discrete", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.AB4.of_AB5", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CountableAB4.of_countableAB5", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.preservesFiniteColimits_liftToFinset", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.hasExactLimitsOfShape_discrete_of_hasExactLimitsOfShape_finset_discrete_op", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.AB4Star.of_AB5Star", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CountableAB4Star.of_countableAB5Star", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CountableAB4.of_hasExactColimitsOfShape_nat_and_finite", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CountableAB4Star.of_hasExactLimitsOfShape_nat_and_finite", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.hasExactColimitsOfShape_discrete_finite", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.hasExactLimitsOfShape_discrete_finite", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CountableAB4.of_hasExactColimitsOfShape_nat", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Basic", "is_tactic_proof": true, "tactics": ["apply", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.CountableAB4Star.of_hasExactLimitsOfShape_nat", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Basic", "is_tactic_proof": true, "tactics": ["apply", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.hasExactColimitsOfShape_of_preservesMono", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.hasExactLimitsOfShape_of_preservesEpi", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.colim.map_mono'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Colim", "is_tactic_proof": true, "tactics": ["refine", "exact", "dsimp", "rw"], "tactic_count": 4}
{"name": "CategoryTheory.Limits.colim.map_epi'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Colim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsColimit.mono_ι_app_of_isFiltered", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Colim", "is_tactic_proof": false, "tactics": ["let", "naturality", "g", "dsimp", "simp", "have", "exact", "colim.map_mono"], "tactic_count": 8}
{"name": "CategoryTheory.Limits.colim.mapShortComplex", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Colim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.colim.exact_mapShortComplex", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Colim", "is_tactic_proof": true, "tactics": ["refine", "refine", "dsimp", "rw", "dsimp", "rw"], "tactic_count": 6}
{"name": "CategoryTheory.MorphismProperty.isStableUnderColimitsOfShape_monomorphisms", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Colim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instIsStableUnderCoproductsMonomorphismsOfAB4OfSize", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Colim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instIsStableUnderFilteredColimitsMonomorphismsOfAB5OfSize", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Colim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsColimit.pullbackOfHasExactColimitsOfShape", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Connected", "is_tactic_proof": true, "tactics": ["suffices", "have", "dsimp", "have", "apply"], "tactic_count": 5}
{"name": "CategoryTheory.Limits.IsColimit.pullback_hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Connected", "is_tactic_proof": true, "tactics": ["refine", "rw", "simpa"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.IsColimit.pullback_zero_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Connected", "is_tactic_proof": true, "tactics": ["suffices", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.IsLimit.pushoutOfHasExactLimitsOfShape", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Connected", "is_tactic_proof": true, "tactics": ["suffices", "have", "dsimp", "have", "apply"], "tactic_count": 5}
{"name": "CategoryTheory.Limits.IsLimit.pushout_hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Connected", "is_tactic_proof": true, "tactics": ["refine", "rw", "simpa"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.IsLimit.pushout_zero_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Connected", "is_tactic_proof": true, "tactics": ["suffices", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.instHasExactColimitsOfShapeFunctorOfHasFiniteLimits", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.FunctorCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instHasExactLimitsOfShapeFunctorOfHasFiniteColimits", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.FunctorCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instHasExactColimitsOfShapeIndOfHasFiniteLimits", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Indization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instAB5IndOfHasFiniteLimits", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Indization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isGrothendieckAbelian_ind", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Indization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.instHasExactColimitsOfShapeOfHasFiniteLimitsOfPreservesColimitsOfShapeFunctorOppositeSheafToPresheaf", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.instHasExactLimitsOfShapeOfHasFiniteColimitsOfPreservesFiniteColimitsFunctorOppositeSheafToPresheaf", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.IsGrothendieckAbelian.instIsStableUnderTransfiniteCompositionMonomorphisms", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.GrothendieckCategory.Monomorphisms", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "CategoryTheory.IsGrothendieckAbelian.mono_of_isColimit_monoOver", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.GrothendieckCategory.Subobject", "is_tactic_proof": true, "tactics": ["let", "have", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.IsGrothendieckAbelian.subobjectMk_of_isColimit_eq_iSup", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.GrothendieckCategory.Subobject", "is_tactic_proof": true, "tactics": ["haveI", "apply", "rw", "intro", "induction", "let", "naturality", "f", "dsimp", "simpa", "exact", "rw", "intro", "exact"], "tactic_count": 14}
{"name": "CategoryTheory.IsGrothendieckAbelian.isColimitMapCoconeOfSubobjectMkEqISup", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.GrothendieckCategory.Subobject", "is_tactic_proof": false, "tactics": ["let", "colimit.desc", "naturality", "haveI", "have", "rw", "refine", "rw", "dsimp", "rw", "apply"], "tactic_count": 11}
{"name": "CategoryTheory.IsGrothendieckAbelian.exists_isIso_of_functor_from_monoOver", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.GrothendieckCategory.Subobject", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "let", "have", "rintro", "exact", "obtain", "have", "refine", "rw", "intro", "let", "trans", "exact", "exact"], "tactic_count": 16}
{"name": "CategoryTheory.Abelian.image", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Abelian.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.image.ι", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Abelian.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.factorThruImage", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Abelian.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.image.fac", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.mono_factorThruImage", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.coimage", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Abelian.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.coimage.π", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Abelian.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.factorThruCoimage", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Abelian.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.coimage.fac", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.epi_factorThruCoimage", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.coimageImageComparison", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.coimageImageComparison'", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.coimageImageComparison_eq_coimageImageComparison'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Images", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Abelian.coimage_image_factorisation", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Images", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Abelian.coimageImageComparisonFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instIsIsoIndCoimageImageComparison", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.Indization", "is_tactic_proof": true, "tactics": ["obtain", "let", "dsimp", "have", "rw", "infer_instance"], "tactic_count": 6}
{"name": "CategoryTheory.instAbelianInd", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.Indization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.preservesHomology_preadditiveYonedaObj_of_injective", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.Injective.Basic", "is_tactic_proof": true, "tactics": ["letI", "apply"], "tactic_count": 2}
{"name": "CategoryTheory.preservesFiniteColimits_preadditiveYonedaObj_of_injective", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.Injective.Basic", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.injective_of_preservesFiniteColimits_preadditiveYonedaObj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Injective.Basic", "is_tactic_proof": true, "tactics": ["rw", "have", "infer_instance"], "tactic_count": 3}
{"name": "CategoryTheory.HasInjectiveDimensionLE", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Abelian.Injective.Dimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasInjectiveDimensionLT.subsingleton", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Injective.Dimension", "is_tactic_proof": true, "tactics": ["letI", "have", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.HasInjectiveDimensionLT.mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Injective.Dimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.Ext.eq_zero_of_hasInjectiveDimensionLT", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Injective.Dimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.hasInjectiveDimensionLT_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Injective.Dimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsZero.hasInjectiveDimensionLT_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Injective.Dimension", "is_tactic_proof": true, "tactics": ["letI", "rw", "intro", "rw"], "tactic_count": 4}
{"name": "CategoryTheory.instHasInjectiveDimensionLTOfNatNat", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.Injective.Dimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isZero_of_hasInjectiveDimensionLT_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Injective.Dimension", "is_tactic_proof": true, "tactics": ["letI", "rw", "apply", "simpa"], "tactic_count": 4}
{"name": "CategoryTheory.hasInjectiveDimensionLT_zero_iff_isZero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Injective.Dimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.hasInjectiveDimensionLT_of_ge", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Injective.Dimension", "is_tactic_proof": true, "tactics": ["letI", "rw", "intro", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.instHasInjectiveDimensionLTHAddNat", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.Injective.Dimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instHasInjectiveDimensionLTHAddNat_1", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.Injective.Dimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instHasInjectiveDimensionLTSucc", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.Injective.Dimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instHasInjectiveDimensionLTOfNatNatOfInjective", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.Injective.Dimension", "is_tactic_proof": true, "tactics": ["letI", "rw", "intro", "obtain", "simp", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.injective_iff_subsingleton_ext_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Injective.Dimension", "is_tactic_proof": true, "tactics": ["refine", "obtain", "obtain", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.injective_iff_hasInjectiveDimensionLT_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Injective.Dimension", "is_tactic_proof": true, "tactics": ["letI", "exact", "injective_iff_subsingleton_ext_one.2"], "tactic_count": 3}
{"name": "CategoryTheory.Retract.hasInjectiveDimensionLT", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Injective.Dimension", "is_tactic_proof": true, "tactics": ["letI", "rw", "intro", "rw"], "tactic_count": 4}
{"name": "CategoryTheory.hasInjectiveDimensionLT_of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Injective.Dimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.ShortExact.hasInjectiveDimensionLT_X₂", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Injective.Dimension", "is_tactic_proof": true, "tactics": ["letI", "rw", "intro", "obtain", "rw"], "tactic_count": 5}
{"name": "CategoryTheory.ShortComplex.ShortExact.hasInjectiveDimensionLT_X₁", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Injective.Dimension", "is_tactic_proof": true, "tactics": ["letI", "rw", "rintro", "simp", "obtain", "rw"], "tactic_count": 6}
{"name": "CategoryTheory.ShortComplex.ShortExact.hasInjectiveDimensionLT_X₃", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Injective.Dimension", "is_tactic_proof": true, "tactics": ["letI", "rw", "intro", "obtain", "rw"], "tactic_count": 5}
{"name": "CategoryTheory.ShortComplex.ShortExact.hasInjectiveDimensionLT_X₃_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Injective.Dimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instHasInjectiveDimensionLTBiprod", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.Injective.Dimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.injectiveDimension", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Injective.Dimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.injectiveDimension_eq_of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Injective.Dimension", "is_tactic_proof": true, "tactics": ["simp", "congr", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Retract.injectiveDimension_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Injective.Dimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.injectiveDimension_lt_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Injective.Dimension", "is_tactic_proof": true, "tactics": ["refine", "have", "simp", "exact", "obtain", "exact", "exact"], "tactic_count": 7}
{"name": "CategoryTheory.injectiveDimension_le_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Injective.Dimension", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.injectiveDimension_ge_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Injective.Dimension", "is_tactic_proof": true, "tactics": ["contrapose"], "tactic_count": 1}
{"name": "CategoryTheory.injectiveDimension_eq_bot_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Injective.Dimension", "is_tactic_proof": true, "tactics": ["rw", "bot_eq_zero',"], "tactic_count": 2}
{"name": "CategoryTheory.injectiveDimension_ne_top_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Injective.Dimension", "is_tactic_proof": true, "tactics": ["generalize", "induction", "bot", "simp", "exact", "coe", "induction", "top", "by_contra", "simp", "obtain", "rw", "exact", "coe", "simp", "exact"], "tactic_count": 16}
{"name": "CategoryTheory.InjectiveResolution.instIsKInjectiveCochainComplex", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.Injective.Ext", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.InjectiveResolution.extEquivCohomologyClass", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Injective.Ext", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.InjectiveResolution.extEquivCohomologyClass_symm_mk_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Injective.Ext", "is_tactic_proof": true, "tactics": ["change", "simp", "isoOfHom,", "congr", "cat_disch"], "tactic_count": 5}
{"name": "CategoryTheory.InjectiveResolution.extEquivCohomologyClass_symm_add", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Injective.Ext", "is_tactic_proof": true, "tactics": ["have", "obtain", "obtain", "ext", "simp"], "tactic_count": 5}
{"name": "CategoryTheory.InjectiveResolution.extAddEquivCohomologyClass", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Injective.Ext", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.InjectiveResolution.extEquivCohomologyClass_symm_sub", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Injective.Ext", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.InjectiveResolution.extEquivCohomologyClass_symm_neg", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Injective.Ext", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.InjectiveResolution.extEquivCohomologyClass_symm_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Injective.Ext", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.InjectiveResolution.extEquivCohomologyClass_add", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Injective.Ext", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.InjectiveResolution.extEquivCohomologyClass_sub", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Injective.Ext", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.InjectiveResolution.extEquivCohomologyClass_neg", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Injective.Ext", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.InjectiveResolution.extEquivCohomologyClass_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Injective.Ext", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.InjectiveResolution.extMk", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Injective.Ext", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.InjectiveResolution.extEquivCohomologyClass_extMk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Injective.Ext", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.InjectiveResolution.add_extMk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Injective.Ext", "is_tactic_proof": true, "tactics": ["simp", "rw", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.InjectiveResolution.sub_extMk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Injective.Ext", "is_tactic_proof": true, "tactics": ["dsimp", "simp", "rw", "simp"], "tactic_count": 4}
{"name": "CategoryTheory.InjectiveResolution.neg_extMk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Injective.Ext", "is_tactic_proof": true, "tactics": ["dsimp", "simp", "rw", "simp"], "tactic_count": 4}
{"name": "CategoryTheory.InjectiveResolution.extMk_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Injective.Ext", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.InjectiveResolution.extMk_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Injective.Ext", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.InjectiveResolution.extMk_eq_zero_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Injective.Ext", "is_tactic_proof": false, "tactics": ["simp", "rw", "exact", "simp"], "tactic_count": 4}
{"name": "CategoryTheory.InjectiveResolution.extMk_surjective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Injective.Ext", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "obtain", "exact", "simpa", "simp"], "tactic_count": 6}
{"name": "CategoryTheory.InjectiveResolution.mk₀_comp_extMk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Injective.Ext", "is_tactic_proof": true, "tactics": ["have", "ext", "simp", "rw", "simp"], "tactic_count": 5}
{"name": "CategoryTheory.InjectiveResolution.extMk_comp_mk₀", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Injective.Ext", "is_tactic_proof": true, "tactics": ["have", "ext", "have", "simp", "rw", "congr", "rw", "congr", "simpa"], "tactic_count": 9}
{"name": "CategoryTheory.InjectiveResolution.cochainComplex", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Injective.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.InjectiveResolution.instIsStrictlyGECochainComplexOfNatInt", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.Injective.Extend", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.InjectiveResolution.cochainComplexXIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Injective.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.InjectiveResolution.cochainComplex_d", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Injective.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.InjectiveResolution.instIsStrictlyGECochainComplexOfNatInt_1", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.Injective.Extend", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.InjectiveResolution.instInjectiveXIntCochainComplex", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.Injective.Extend", "is_tactic_proof": true, "tactics": ["by_cases", "obtain", "exact", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.InjectiveResolution.ι'", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Injective.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.InjectiveResolution.ι'_f_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Injective.Extend", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "cat_disch"], "tactic_count": 3}
{"name": "CategoryTheory.InjectiveResolution.instQuasiIsoIntι'", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.Injective.Extend", "is_tactic_proof": true, "tactics": ["dsimp"], "tactic_count": 1}
{"name": "CategoryTheory.InjectiveResolution.instIsLECochainComplexOfNatInt", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.Injective.Extend", "is_tactic_proof": true, "tactics": ["simp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.InjectiveResolution.Hom.hom'", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Injective.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.InjectiveResolution.Hom.hom'_f", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Injective.Extend", "is_tactic_proof": true, "tactics": ["simp", "cochainComplexXIso]"], "tactic_count": 2}
{"name": "CategoryTheory.InjectiveResolution.Hom.ι'_comp_hom'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Injective.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.InjectiveResolution.descFZero", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Injective.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.InjectiveResolution.exact₀", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Injective.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.InjectiveResolution.descFOne", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Injective.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.InjectiveResolution.descFOne_zero_comm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Injective.Resolution", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.InjectiveResolution.descFSucc", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Injective.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.InjectiveResolution.desc", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Injective.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.InjectiveResolution.desc_commutes", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Injective.Resolution", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.InjectiveResolution.desc_commutes_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Injective.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.InjectiveResolution.descHomotopyZeroZero", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Injective.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.InjectiveResolution.comp_descHomotopyZeroZero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Injective.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.InjectiveResolution.descHomotopyZeroOne", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Injective.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.InjectiveResolution.comp_descHomotopyZeroOne", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Injective.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.InjectiveResolution.descHomotopyZeroSucc", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Injective.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.InjectiveResolution.comp_descHomotopyZeroSucc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Injective.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.InjectiveResolution.descHomotopyZero", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Injective.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.InjectiveResolution.descHomotopy", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Injective.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.InjectiveResolution.descIdHomotopy", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Injective.Resolution", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.InjectiveResolution.descCompHomotopy", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Injective.Resolution", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.InjectiveResolution.homotopyEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Injective.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.InjectiveResolution.homotopyEquiv_hom_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Injective.Resolution", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.InjectiveResolution.homotopyEquiv_inv_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Injective.Resolution", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.injectiveResolution", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Abelian.Injective.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.injectiveResolutions", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Injective.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.InjectiveResolution.iso", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Injective.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.InjectiveResolution.iso_hom_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Injective.Resolution", "is_tactic_proof": true, "tactics": ["apply", "apply", "all_goals"], "tactic_count": 3}
{"name": "CategoryTheory.InjectiveResolution.iso_inv_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Injective.Resolution", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.exact_f_d", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Injective.Resolution", "is_tactic_proof": false, "tactics": ["let", "τ₂", "τ₃", "rw", "apply", "apply"], "tactic_count": 6}
{"name": "CategoryTheory.InjectiveResolution.ofCocomplex", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Injective.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.InjectiveResolution.ofCocomplex_d_0_1", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Injective.Resolution", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.InjectiveResolution.ofCocomplex_exactAt_succ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Injective.Resolution", "is_tactic_proof": true, "tactics": ["rw", "dsimp", "simp", "n"], "tactic_count": 4}
{"name": "CategoryTheory.InjectiveResolution.instInjectiveXNatOfCocomplex", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.Injective.Resolution", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "CategoryTheory.InjectiveResolution.definition._@.Mathlib.CategoryTheory.Abelian.Injective.Resolution.1988488013._hygCtx._hyg.2", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Injective.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.InjectiveResolution.wrapped._@.Mathlib.CategoryTheory.Abelian.Injective.Resolution.1988488013._hygCtx._hyg.2", "kind": "opaque", "module": "Mathlib.CategoryTheory.Abelian.Injective.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.InjectiveResolution.of", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Injective.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.InjectiveResolution.of_def", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Injective.Resolution", "is_tactic_proof": true, "tactics": ["intros", "delta", "rw", "rfl"], "tactic_count": 4}
{"name": "CategoryTheory.InjectiveResolution.instHasInjectiveResolution", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.Injective.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.InjectiveResolution.instHasInjectiveResolutions", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.Injective.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.InjectivePresentation.shortComplex", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Abelian.Injective.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.InjectivePresentation.shortExact_shortComplex", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Injective.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.leftDerivedToHomotopyCategory", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.LeftDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ProjectiveResolution.isoLeftDerivedToHomotopyCategoryObj", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.LeftDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ProjectiveResolution.isoLeftDerivedToHomotopyCategoryObj_inv_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.LeftDerived", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "erw", "rfl"], "tactic_count": 4}
{"name": "CategoryTheory.ProjectiveResolution.isoLeftDerivedToHomotopyCategoryObj_hom_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.LeftDerived", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "isoLeftDerivedToHomotopyCategoryObj_inv_naturality_assoc"], "tactic_count": 3}
{"name": "CategoryTheory.Functor.leftDerived", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.LeftDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ProjectiveResolution.isoLeftDerivedObj", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.LeftDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ProjectiveResolution.isoLeftDerivedObj_hom_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.LeftDerived", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "erw", "rfl"], "tactic_count": 4}
{"name": "CategoryTheory.ProjectiveResolution.isoLeftDerivedObj_inv_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.LeftDerived", "is_tactic_proof": true, "tactics": ["rw", "comp_id]"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.isZero_leftDerived_obj_projective_succ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.LeftDerived", "is_tactic_proof": true, "tactics": ["refine", "erw", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Functor.leftDerived_map_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.LeftDerived", "is_tactic_proof": false, "tactics": ["rw", "assoc,", "rw"], "tactic_count": 3}
{"name": "CategoryTheory.NatTrans.leftDerivedToHomotopyCategory", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.LeftDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ProjectiveResolution.leftDerivedToHomotopyCategory_app_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.LeftDerived", "is_tactic_proof": true, "tactics": ["rw", "dsimp", "rw", "erw", "obtain", "rw", "dsimp", "simp", "rfl"], "tactic_count": 9}
{"name": "CategoryTheory.NatTrans.leftDerivedToHomotopyCategory_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.LeftDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.leftDerivedToHomotopyCategory_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.LeftDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.leftDerived", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.LeftDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.leftDerived_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.LeftDerived", "is_tactic_proof": true, "tactics": ["dsimp", "simp", "rfl"], "tactic_count": 3}
{"name": "CategoryTheory.NatTrans.leftDerived_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.LeftDerived", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.ProjectiveResolution.leftDerived_app_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.LeftDerived", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "erw", "simp"], "tactic_count": 4}
{"name": "CategoryTheory.ProjectiveResolution.fromLeftDerivedZero'", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.LeftDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ProjectiveResolution.pOpcycles_comp_fromLeftDerivedZero'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.LeftDerived", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.ProjectiveResolution.fromLeftDerivedZero'_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.LeftDerived", "is_tactic_proof": true, "tactics": ["simp", "pOpcycles_comp_fromLeftDerivedZero'_assoc]"], "tactic_count": 2}
{"name": "CategoryTheory.ProjectiveResolution.instIsIsoFromLeftDerivedZero'Self", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.LeftDerived", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "refine", "exact", "s", "f_r"], "tactic_count": 6}
{"name": "CategoryTheory.Functor.fromLeftDerivedZero", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.LeftDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ProjectiveResolution.fromLeftDerivedZero_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.LeftDerived", "is_tactic_proof": true, "tactics": ["dsimp", "have", "have", "id_comp", "simp", "rw", "erw", "rfl"], "tactic_count": 8}
{"name": "CategoryTheory.instIsIsoAppFromLeftDerivedZeroOfProjective", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.LeftDerived", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.instIsIsoFromLeftDerivedZero'", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.LeftDerived", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.instIsIsoAppFromLeftDerivedZero", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.LeftDerived", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.instIsIsoFunctorFromLeftDerivedZero", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.LeftDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.leftDerivedZeroIsoSelf", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.LeftDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.leftDerivedZeroIsoSelf_hom_inv_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.LeftDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.leftDerivedZeroIsoSelf_inv_hom_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.LeftDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.leftDerivedZeroIsoSelf_hom_inv_id_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.LeftDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.leftDerivedZeroIsoSelf_inv_hom_id_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.LeftDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.instIsStableUnderCobaseChangeMonomorphisms", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.Monomorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.instIsStableUnderBaseChangeEpimorphisms", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.Monomorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NonPreadditiveAbelian.instEpiFactorThruImage", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.NonPreadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NonPreadditiveAbelian.isIso_factorThruImage", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.NonPreadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NonPreadditiveAbelian.instMonoFactorThruCoimage", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.NonPreadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NonPreadditiveAbelian.isIso_factorThruCoimage", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.NonPreadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NonPreadditiveAbelian.epiIsCokernelOfKernel", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.NonPreadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NonPreadditiveAbelian.monoIsKernelOfCokernel", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.NonPreadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NonPreadditiveAbelian.r", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Abelian.NonPreadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NonPreadditiveAbelian.mono_Δ", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.NonPreadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NonPreadditiveAbelian.mono_r", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.NonPreadditive", "is_tactic_proof": false, "tactics": ["let", "monoIsKernelOfCokernel", "apply", "intro", "have", "obtain", "rw", "have", "erw", "haveI", "apply", "rw"], "tactic_count": 12}
{"name": "CategoryTheory.NonPreadditiveAbelian.epi_r", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.NonPreadditive", "is_tactic_proof": true, "tactics": ["have", "let", "refine", "intro", "apply", "intro", "haveI", "apply", "convert", "apply", "let", "apply", "intro", "have", "obtain", "rw", "have", "rw", "change", "rw", "apply", "rw"], "tactic_count": 22}
{"name": "CategoryTheory.NonPreadditiveAbelian.isIso_r", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.NonPreadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NonPreadditiveAbelian.σ", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Abelian.NonPreadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NonPreadditiveAbelian.diag_σ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.NonPreadditive", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.NonPreadditiveAbelian.lift_σ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.NonPreadditive", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.NonPreadditiveAbelian.lift_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.NonPreadditive", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.NonPreadditiveAbelian.isColimitσ", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.NonPreadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NonPreadditiveAbelian.σ_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.NonPreadditive", "is_tactic_proof": false, "tactics": ["obtain", "suffices", "calc", "f"], "tactic_count": 4}
{"name": "CategoryTheory.NonPreadditiveAbelian.hasSub", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.NonPreadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NonPreadditiveAbelian.hasNeg", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.NonPreadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NonPreadditiveAbelian.hasAdd", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.NonPreadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NonPreadditiveAbelian.sub_def", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.NonPreadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NonPreadditiveAbelian.add_def", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.NonPreadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NonPreadditiveAbelian.neg_def", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.NonPreadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NonPreadditiveAbelian.sub_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.NonPreadditive", "is_tactic_proof": true, "tactics": ["rw", "conv_lhs", "congr", "rw", "rw"], "tactic_count": 5}
{"name": "CategoryTheory.NonPreadditiveAbelian.sub_self", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.NonPreadditive", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.NonPreadditiveAbelian.lift_sub_lift", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.NonPreadditive", "is_tactic_proof": true, "tactics": ["simp", "ext", "rw", "rw"], "tactic_count": 4}
{"name": "CategoryTheory.NonPreadditiveAbelian.sub_sub_sub", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.NonPreadditive", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.NonPreadditiveAbelian.neg_sub", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.NonPreadditive", "is_tactic_proof": true, "tactics": ["conv_lhs"], "tactic_count": 1}
{"name": "CategoryTheory.NonPreadditiveAbelian.neg_neg", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.NonPreadditive", "is_tactic_proof": true, "tactics": ["rw", "conv_lhs", "rw"], "tactic_count": 3}
{"name": "CategoryTheory.NonPreadditiveAbelian.add_comm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.NonPreadditive", "is_tactic_proof": true, "tactics": ["rw", "conv_lhs", "rw", "conv_lhs", "congr", "skip", "rw", "rw"], "tactic_count": 8}
{"name": "CategoryTheory.NonPreadditiveAbelian.add_neg", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.NonPreadditive", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.NonPreadditiveAbelian.add_neg_cancel", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.NonPreadditive", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.NonPreadditiveAbelian.neg_add_cancel", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.NonPreadditive", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.NonPreadditiveAbelian.neg_sub'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.NonPreadditive", "is_tactic_proof": true, "tactics": ["rw", "conv_lhs", "rw"], "tactic_count": 3}
{"name": "CategoryTheory.NonPreadditiveAbelian.neg_add", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.NonPreadditive", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.NonPreadditiveAbelian.sub_add", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.NonPreadditive", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.NonPreadditiveAbelian.add_assoc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.NonPreadditive", "is_tactic_proof": true, "tactics": ["conv_lhs", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.NonPreadditiveAbelian.add_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.NonPreadditive", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.NonPreadditiveAbelian.comp_sub", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.NonPreadditive", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.NonPreadditiveAbelian.sub_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.NonPreadditive", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.NonPreadditiveAbelian.comp_add", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.NonPreadditive", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.NonPreadditiveAbelian.add_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.NonPreadditive", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.NonPreadditiveAbelian.preadditive", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.NonPreadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instAbelianOpposite", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.kernelOpUnop", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.cokernelOpUnop", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.kernelUnopOp", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.cokernelUnopOp", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.cokernel.π_op", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Opposite", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.kernel.ι_op", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Opposite", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.kernelOpOp", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.cokernelOpOp", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.kernelUnopUnop", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.kernel.ι_unop", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Opposite", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.cokernel.π_unop", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Opposite", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.cokernelUnopUnop", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.imageUnopOp", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.imageOpOp", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.imageOpUnop", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.imageUnopUnop", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.image_ι_op_comp_imageUnopOp_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Opposite", "is_tactic_proof": false, "tactics": ["simp", "simp", "cokernelIsoOfEq_hom_comp_desc_assoc,", "simp", "rw"], "tactic_count": 5}
{"name": "CategoryTheory.imageUnopOp_hom_comp_image_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Opposite", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.factorThruImage_comp_imageUnopOp_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Opposite", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.imageUnopOp_inv_comp_op_factorThruImage", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Opposite", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.preservesHomology_preadditiveCoyonedaObj_of_projective", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.Projective.Basic", "is_tactic_proof": true, "tactics": ["haveI", "apply"], "tactic_count": 2}
{"name": "CategoryTheory.preservesFiniteColimits_preadditiveCoyonedaObj_of_projective", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.Projective.Basic", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.projective_of_preservesFiniteColimits_preadditiveCoyonedaObj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Projective.Basic", "is_tactic_proof": true, "tactics": ["rw", "have", "infer_instance"], "tactic_count": 3}
{"name": "CategoryTheory.HasProjectiveDimensionLE", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Abelian.Projective.Dimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasProjectiveDimensionLT.subsingleton", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Projective.Dimension", "is_tactic_proof": true, "tactics": ["letI", "have", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.HasProjectiveDimensionLT.mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Projective.Dimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.Ext.eq_zero_of_hasProjectiveDimensionLT", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Projective.Dimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.hasProjectiveDimensionLT_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Projective.Dimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsZero.hasProjectiveDimensionLT_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Projective.Dimension", "is_tactic_proof": true, "tactics": ["letI", "rw", "intro", "rw"], "tactic_count": 4}
{"name": "CategoryTheory.instHasProjectiveDimensionLTOfNatNat", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.Projective.Dimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isZero_of_hasProjectiveDimensionLT_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Projective.Dimension", "is_tactic_proof": true, "tactics": ["letI", "rw", "apply", "simpa"], "tactic_count": 4}
{"name": "CategoryTheory.hasProjectiveDimensionLT_zero_iff_isZero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Projective.Dimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.hasProjectiveDimensionLT_of_ge", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Projective.Dimension", "is_tactic_proof": true, "tactics": ["letI", "rw", "intro", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.instHasProjectiveDimensionLTHAddNat", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.Projective.Dimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instHasProjectiveDimensionLTHAddNat_1", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.Projective.Dimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instHasProjectiveDimensionLTSucc", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.Projective.Dimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instHasProjectiveDimensionLTOfNatNatOfProjective", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.Projective.Dimension", "is_tactic_proof": true, "tactics": ["letI", "rw", "intro", "obtain", "simp", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.projective_iff_subsingleton_ext_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Projective.Dimension", "is_tactic_proof": true, "tactics": ["refine", "obtain", "obtain", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.projective_iff_hasProjectiveDimensionLT_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Projective.Dimension", "is_tactic_proof": true, "tactics": ["letI", "exact", "projective_iff_subsingleton_ext_one.2"], "tactic_count": 3}
{"name": "CategoryTheory.Retract.hasProjectiveDimensionLT", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Projective.Dimension", "is_tactic_proof": true, "tactics": ["letI", "rw", "intro", "rw"], "tactic_count": 4}
{"name": "CategoryTheory.hasProjectiveDimensionLT_of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Projective.Dimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.ShortExact.hasProjectiveDimensionLT_X₂", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Projective.Dimension", "is_tactic_proof": true, "tactics": ["letI", "rw", "intro", "obtain", "rw"], "tactic_count": 5}
{"name": "CategoryTheory.ShortComplex.ShortExact.hasProjectiveDimensionLT_X₃", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Projective.Dimension", "is_tactic_proof": true, "tactics": ["letI", "rw", "rintro", "simp", "obtain", "rw"], "tactic_count": 6}
{"name": "CategoryTheory.ShortComplex.ShortExact.hasProjectiveDimensionLT_X₁", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Projective.Dimension", "is_tactic_proof": true, "tactics": ["letI", "rw", "intro", "obtain", "rw"], "tactic_count": 5}
{"name": "CategoryTheory.ShortComplex.ShortExact.hasProjectiveDimensionLT_X₃_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Projective.Dimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instHasProjectiveDimensionLTBiprod", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.Projective.Dimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.projectiveDimension", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Projective.Dimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.projectiveDimension_eq_of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Projective.Dimension", "is_tactic_proof": true, "tactics": ["simp", "congr", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Retract.projectiveDimension_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Projective.Dimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.projectiveDimension_lt_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Projective.Dimension", "is_tactic_proof": true, "tactics": ["refine", "have", "simp", "exact", "obtain", "exact", "exact"], "tactic_count": 7}
{"name": "CategoryTheory.projectiveDimension_le_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Projective.Dimension", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.projectiveDimension_ge_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Projective.Dimension", "is_tactic_proof": true, "tactics": ["contrapose"], "tactic_count": 1}
{"name": "CategoryTheory.projectiveDimension_eq_bot_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Projective.Dimension", "is_tactic_proof": true, "tactics": ["rw", "bot_eq_zero',"], "tactic_count": 2}
{"name": "CategoryTheory.projectiveDimension_ne_top_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Projective.Dimension", "is_tactic_proof": true, "tactics": ["generalize", "induction", "bot", "simp", "exact", "coe", "induction", "top", "by_contra", "simp", "obtain", "rw", "exact", "coe", "simp", "exact"], "tactic_count": 16}
{"name": "CategoryTheory.ProjectiveResolution.instIsKProjectiveCochainComplex", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.Projective.Ext", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ProjectiveResolution.extEquivCohomologyClass", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Projective.Ext", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_symm_mk_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Projective.Ext", "is_tactic_proof": true, "tactics": ["change", "simp", "congr", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_symm_add", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Projective.Ext", "is_tactic_proof": true, "tactics": ["have", "obtain", "obtain", "ext", "simp"], "tactic_count": 5}
{"name": "CategoryTheory.ProjectiveResolution.extAddEquivCohomologyClass", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Projective.Ext", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_symm_sub", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Projective.Ext", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_symm_neg", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Projective.Ext", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_symm_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Projective.Ext", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_add", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Projective.Ext", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_sub", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Projective.Ext", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_neg", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Projective.Ext", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Projective.Ext", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ProjectiveResolution.extMk", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Projective.Ext", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_extMk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Projective.Ext", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.ProjectiveResolution.add_extMk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Projective.Ext", "is_tactic_proof": true, "tactics": ["simp", "rw", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.ProjectiveResolution.sub_extMk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Projective.Ext", "is_tactic_proof": true, "tactics": ["simp", "rw", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.ProjectiveResolution.neg_extMk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Projective.Ext", "is_tactic_proof": true, "tactics": ["simp", "rw", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.ProjectiveResolution.extMk_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Projective.Ext", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.ProjectiveResolution.extMk_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Projective.Ext", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ProjectiveResolution.extMk_eq_zero_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Projective.Ext", "is_tactic_proof": false, "tactics": ["simp", "rw", "refine", "rw", "simpa"], "tactic_count": 5}
{"name": "CategoryTheory.ProjectiveResolution.extMk_surjective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Projective.Ext", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "obtain", "refine", "rw", "simpa"], "tactic_count": 6}
{"name": "CategoryTheory.ProjectiveResolution.extMk_comp_mk₀", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Projective.Ext", "is_tactic_proof": true, "tactics": ["have", "ext", "simp", "simp", "rw", "dsimp"], "tactic_count": 6}
{"name": "CategoryTheory.ProjectiveResolution.mk₀_comp_extMk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Projective.Ext", "is_tactic_proof": true, "tactics": ["have", "ext", "have", "φ.hom'.f", "simp", "rw", "congr", "simp"], "tactic_count": 8}
{"name": "CategoryTheory.ProjectiveResolution.cochainComplex", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Projective.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ProjectiveResolution.instIsStrictlyLECochainComplexOfNatInt", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.Projective.Extend", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.ProjectiveResolution.instProjectiveXIntCochainComplex", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.Projective.Extend", "is_tactic_proof": true, "tactics": ["by_cases", "obtain", "exact", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.ProjectiveResolution.π'", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Projective.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ProjectiveResolution.π'_f_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Projective.Extend", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "cat_disch"], "tactic_count": 3}
{"name": "CategoryTheory.ProjectiveResolution.instQuasiIsoIntπ'", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.Projective.Extend", "is_tactic_proof": true, "tactics": ["dsimp"], "tactic_count": 1}
{"name": "CategoryTheory.ProjectiveResolution.instIsGECochainComplexOfNatInt", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.Projective.Extend", "is_tactic_proof": true, "tactics": ["simp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.ProjectiveResolution.Hom.hom'", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Projective.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ProjectiveResolution.Hom.hom'_f", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Projective.Extend", "is_tactic_proof": true, "tactics": ["simp", "cochainComplexXIso]"], "tactic_count": 2}
{"name": "CategoryTheory.ProjectiveResolution.Hom.hom'_comp_π'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Projective.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ProjectiveResolution.exact₀", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Projective.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ProjectiveResolution.liftFOne_zero_comm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Projective.Resolution", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.ProjectiveResolution.lift_commutes", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Projective.Resolution", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.ProjectiveResolution.lift_commutes_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Projective.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ProjectiveResolution.liftHomotopyZeroZero_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Projective.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ProjectiveResolution.liftHomotopyZeroOne_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Projective.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ProjectiveResolution.liftHomotopyZeroSucc_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Projective.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ProjectiveResolution.homotopyEquiv_hom_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Projective.Resolution", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.ProjectiveResolution.homotopyEquiv_inv_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Projective.Resolution", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.ProjectiveResolution.iso_inv_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Projective.Resolution", "is_tactic_proof": true, "tactics": ["apply", "apply", "all_goals"], "tactic_count": 3}
{"name": "CategoryTheory.ProjectiveResolution.iso_hom_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Projective.Resolution", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.exact_d_f", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Projective.Resolution", "is_tactic_proof": false, "tactics": ["let", "τ₂", "τ₃", "rw", "apply", "apply"], "tactic_count": 6}
{"name": "CategoryTheory.ProjectiveResolution.ofComplex_d_1_0", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Projective.Resolution", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.ProjectiveResolution.ofComplex_exactAt_succ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Projective.Resolution", "is_tactic_proof": true, "tactics": ["rw", "dsimp", "simp", "n"], "tactic_count": 4}
{"name": "CategoryTheory.ProjectiveResolution.wrapped._@.Mathlib.CategoryTheory.Abelian.Projective.Resolution.472578235._hygCtx._hyg.2", "kind": "opaque", "module": "Mathlib.CategoryTheory.Abelian.Projective.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ProjectiveResolution.of_def", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Projective.Resolution", "is_tactic_proof": true, "tactics": ["intros", "delta", "rw", "rfl"], "tactic_count": 4}
{"name": "CategoryTheory.Abelian.app", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Pseudoelements", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.app_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Pseudoelements", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.PseudoEqual", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Pseudoelements", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.pseudoEqual_refl", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Pseudoelements", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.pseudoEqual_symm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Pseudoelements", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.pseudoEqual_trans", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Pseudoelements", "is_tactic_proof": true, "tactics": ["intro", "refine", "rw"], "tactic_count": 3}
{"name": "CategoryTheory.Abelian.Pseudoelement.setoid", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Pseudoelements", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.Pseudoelement", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Pseudoelements", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.Pseudoelement.objectToSort", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Pseudoelements", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.Pseudoelement.overToSort", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Pseudoelements", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.Pseudoelement.over_coe_def", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Pseudoelements", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.Pseudoelement.pseudoApply_aux", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Pseudoelements", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.Pseudoelement.pseudoApply", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Pseudoelements", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.Pseudoelement.homToFun", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Pseudoelements", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.Pseudoelement.pseudoApply_mk'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Pseudoelements", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.Pseudoelement.comp_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Pseudoelements", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.Pseudoelement.comp_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Pseudoelements", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.Pseudoelement.pseudoZero_aux", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Pseudoelements", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.Pseudoelement.zero_eq_zero'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Pseudoelements", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.Pseudoelement.pseudoZero", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Pseudoelements", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.Pseudoelement.hasZero", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.Pseudoelements", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.Pseudoelement.instInhabited", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.Pseudoelements", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.Pseudoelement.pseudoZero_def", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Pseudoelements", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.Pseudoelement.zero_eq_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Pseudoelements", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.Pseudoelement.pseudoZero_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Pseudoelements", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Abelian.Pseudoelement.apply_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Pseudoelements", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Abelian.Pseudoelement.zero_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Pseudoelements", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.Pseudoelement.zero_morphism_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Pseudoelements", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.Pseudoelement.zero_morphism_ext'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Pseudoelements", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.Pseudoelement.eq_zero_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Pseudoelements", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.Pseudoelement.pseudo_injective_of_mono", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Pseudoelements", "is_tactic_proof": true, "tactics": ["intro", "refine", "apply", "have", "have", "exact", "simp", "exact"], "tactic_count": 8}
{"name": "CategoryTheory.Abelian.Pseudoelement.zero_of_map_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Pseudoelements", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.Pseudoelement.mono_of_zero_of_map_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Pseudoelements", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.Pseudoelement.pseudo_surjective_of_epi", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Pseudoelements", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.Pseudoelement.epi_of_pseudo_surjective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Pseudoelements", "is_tactic_proof": true, "tactics": ["intro", "have", "have", "have", "rw", "exact", "have", "apply", "dsimp", "rw", "apply"], "tactic_count": 11}
{"name": "CategoryTheory.Abelian.Pseudoelement.pseudo_exact_of_exact", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Pseudoelements", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.Pseudoelement.apply_eq_zero_of_comp_eq_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Pseudoelements", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.Pseudoelement.exact_of_pseudo_exact", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Pseudoelements", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.Pseudoelement.sub_of_eq_image", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Pseudoelements", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.Pseudoelement.pseudo_pullback", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Pseudoelements", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.Pseudoelement.ModuleCat.eq_range_of_pseudoequal", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Pseudoelements", "is_tactic_proof": true, "tactics": ["obtain", "refine", "obtain", "obtain", "refine", "dsimp", "rw", "obtain", "obtain", "refine", "dsimp", "rw"], "tactic_count": 12}
{"name": "CategoryTheory.epi_iff_surjective_up_to_refinements", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Refinements", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "intro", "obtain", "rw", "exact"], "tactic_count": 7}
{"name": "CategoryTheory.surjective_up_to_refinements_of_epi", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Refinements", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShortComplex.exact_iff_exact_up_to_refinements", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Refinements", "is_tactic_proof": true, "tactics": ["rw", "constructor", "intro", "obtain", "exact", "intro", "obtain", "exact"], "tactic_count": 8}
{"name": "CategoryTheory.ShortComplex.Exact.exact_up_to_refinements", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Refinements", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.ShortComplex.eq_liftCycles_homologyπ_up_to_refinements", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Refinements", "is_tactic_proof": true, "tactics": ["obtain", "refine", "rw", "congr", "rw"], "tactic_count": 5}
{"name": "CategoryTheory.Functor.rightDerivedToHomotopyCategory", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.RightDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.InjectiveResolution.isoRightDerivedToHomotopyCategoryObj", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.RightDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.InjectiveResolution.isoRightDerivedToHomotopyCategoryObj_hom_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.RightDerived", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "erw", "rfl"], "tactic_count": 4}
{"name": "CategoryTheory.InjectiveResolution.isoRightDerivedToHomotopyCategoryObj_inv_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.RightDerived", "is_tactic_proof": true, "tactics": ["rw", "dsimp", "rw"], "tactic_count": 3}
{"name": "CategoryTheory.Functor.rightDerived", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.RightDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.InjectiveResolution.isoRightDerivedObj", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.RightDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.InjectiveResolution.isoRightDerivedObj_hom_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.RightDerived", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "erw", "rfl"], "tactic_count": 4}
{"name": "CategoryTheory.InjectiveResolution.isoRightDerivedObj_inv_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.RightDerived", "is_tactic_proof": true, "tactics": ["rw", "comp_id]"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.isZero_rightDerived_obj_injective_succ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.RightDerived", "is_tactic_proof": true, "tactics": ["refine", "erw", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Functor.rightDerived_map_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.RightDerived", "is_tactic_proof": false, "tactics": ["rw", "assoc,", "rw"], "tactic_count": 3}
{"name": "CategoryTheory.NatTrans.rightDerivedToHomotopyCategory", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.RightDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.InjectiveResolution.rightDerivedToHomotopyCategory_app_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.RightDerived", "is_tactic_proof": true, "tactics": ["rw", "dsimp", "rw", "erw", "obtain", "rw", "dsimp", "simp", "rfl"], "tactic_count": 9}
{"name": "CategoryTheory.NatTrans.rightDerivedToHomotopyCategory_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.RightDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.rightDerivedToHomotopyCategory_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.RightDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.rightDerived", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.RightDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.rightDerived_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.RightDerived", "is_tactic_proof": true, "tactics": ["dsimp", "simp", "rfl"], "tactic_count": 3}
{"name": "CategoryTheory.NatTrans.rightDerived_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.RightDerived", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.InjectiveResolution.rightDerived_app_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.RightDerived", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "erw", "simp"], "tactic_count": 4}
{"name": "CategoryTheory.InjectiveResolution.toRightDerivedZero'", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.RightDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.InjectiveResolution.toRightDerivedZero'_comp_iCycles", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.RightDerived", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.InjectiveResolution.toRightDerivedZero'_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.RightDerived", "is_tactic_proof": true, "tactics": ["simp", "toRightDerivedZero'_comp_iCycles,"], "tactic_count": 2}
{"name": "CategoryTheory.InjectiveResolution.instIsIsoToRightDerivedZero'Self", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.RightDerived", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "refine", "exact", "s", "s_g"], "tactic_count": 6}
{"name": "CategoryTheory.Functor.toRightDerivedZero", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.RightDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.InjectiveResolution.toRightDerivedZero_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.RightDerived", "is_tactic_proof": true, "tactics": ["dsimp", "have", "simp", "have", "comp_id", "rw", "assoc,", "erw", "rfl"], "tactic_count": 9}
{"name": "CategoryTheory.instIsIsoAppToRightDerivedZeroOfInjective", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.RightDerived", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.instIsIsoToRightDerivedZero'", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.RightDerived", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.instIsIsoAppToRightDerivedZero", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.RightDerived", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.instIsIsoFunctorToRightDerivedZero", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.RightDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.rightDerivedZeroIsoSelf", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.RightDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.rightDerivedZeroIsoSelf_hom_inv_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.RightDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.rightDerivedZeroIsoSelf_inv_hom_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.RightDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.rightDerivedZeroIsoSelf_hom_inv_id_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.RightDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.rightDerivedZeroIsoSelf_inv_hom_id_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.RightDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty._example", "kind": "example", "module": "Mathlib.CategoryTheory.Abelian.SerreClass.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instIsSerreClassTop", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.SerreClass.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instIsSerreClassIsZero", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.SerreClass.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.prop_iff_of_shortExact", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.SerreClass.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.prop_X₂_of_exact", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.SerreClass.Basic", "is_tactic_proof": true, "tactics": ["let", "have", "have", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.ObjectProperty.instIsSerreClassInverseImageOfPreservesFiniteLimitsOfPreservesFiniteColimits", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.SerreClass.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.isoModSerre_kernel_eq_inverseImage_isomorphisms", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.SerreClass.Bousfield", "is_tactic_proof": true, "tactics": ["ext", "refine", "simp", "constructor", "exact", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.Abelian.isoModSerre_kernel_eq_isLocal_of_rightAdjoint", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.SerreClass.Bousfield", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Abelian.isLocalization_isoModSerre_kernel_of_leftAdjoint", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.SerreClass.Bousfield", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.ObjectProperty.monoModSerre", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.SerreClass.MorphismProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.epiModSerre", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.SerreClass.MorphismProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.isoModSerre", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.SerreClass.MorphismProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.monoModSerre_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.SerreClass.MorphismProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.monomorphisms_le_monoModSerre", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.SerreClass.MorphismProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.monoModSerre_of_mono", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.SerreClass.MorphismProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.epiModSerre_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.SerreClass.MorphismProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.epimorphisms_le_epiModSerre", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.SerreClass.MorphismProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.epiModSerre_of_epi", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.SerreClass.MorphismProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.isoModSerre_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.SerreClass.MorphismProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.isoModSerre_iff_of_mono", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.SerreClass.MorphismProperty", "is_tactic_proof": true, "tactics": ["have", "rw", "tauto"], "tactic_count": 3}
{"name": "CategoryTheory.ObjectProperty.isoModSerre_iff_of_epi", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.SerreClass.MorphismProperty", "is_tactic_proof": true, "tactics": ["have", "rw", "tauto"], "tactic_count": 3}
{"name": "CategoryTheory.ObjectProperty.isoModSerre_of_mono", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.SerreClass.MorphismProperty", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "CategoryTheory.ObjectProperty.isoModSerre_of_epi", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.SerreClass.MorphismProperty", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "CategoryTheory.ObjectProperty.isomorphisms_le_isoModSerre", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.SerreClass.MorphismProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.isoModSerre_of_isIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.SerreClass.MorphismProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instIsMultiplicativeMonoModSerre", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.SerreClass.MorphismProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instIsMultiplicativeEpiModSerre", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.SerreClass.MorphismProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instIsMultiplicativeIsoModSerre", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.SerreClass.MorphismProperty", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.ObjectProperty.instIsStableUnderRetractsMonoModSerre", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.SerreClass.MorphismProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instIsStableUnderRetractsEpiModSerre", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.SerreClass.MorphismProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instIsStableUnderRetractsIsoModSerre", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.SerreClass.MorphismProperty", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.ObjectProperty.instHasTwoOutOfThreePropertyIsoModSerre", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.SerreClass.MorphismProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.le_kernel_of_isoModSerre_isInvertedBy", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.SerreClass.MorphismProperty", "is_tactic_proof": true, "tactics": ["intro", "let", "have", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.ObjectProperty.isoModSerre_isInvertedBy_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.SerreClass.MorphismProperty", "is_tactic_proof": true, "tactics": ["refine", "have", "have", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.Abelian.subobjectIsoSubobjectOp", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Subobject", "is_tactic_proof": true, "tactics": ["refine", "change", "refine", "intro", "dsimp", "refine", "exact", "exact", "rw", "simp", "simp", "exact", "change", "refine", "intro", "dsimp", "refine", "exact", "exact", "simp", "simp", "simp"], "tactic_count": 22}
{"name": "CategoryTheory.Abelian.wellPowered_opposite", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.Subobject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.AbelianOfAdjunction.hasKernels", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Transfer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.AbelianOfAdjunction.hasCokernels", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Transfer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.abelianOfAdjunction", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Transfer", "is_tactic_proof": true, "tactics": ["haveI", "haveI", "have", "intro", "let", "have", "let", "rw", "infer_instance", "apply"], "tactic_count": 10}
{"name": "CategoryTheory.abelianOfEquivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.Abelian.Transfer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShrinkHoms.preadditive", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.Transfer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShrinkHoms.instAdditiveInverse", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.Transfer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShrinkHoms.instAdditiveFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.Transfer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShrinkHoms.hasLimitsOfShape", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.Transfer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShrinkHoms.hasFiniteLimits", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.Transfer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShrinkHoms.abelian", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.Transfer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.AsSmall.preadditive", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.Transfer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.AsSmall.instAdditiveDown", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.Transfer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.AsSmall.instAdditiveUp", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.Transfer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.AsSmall.hasLimitsOfShape", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.Transfer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.AsSmall.hasFiniteLimits", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.Transfer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.AsSmall.abelian", "kind": "instance", "module": "Mathlib.CategoryTheory.Abelian.Transfer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.preadditiveCoyonedaObj_map_surjective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Yoneda", "is_tactic_proof": false, "tactics": ["rw", "let", "have", "have", "let", "have", "apply", "exact", "simp", "infer_instance", "suffices", "exact", "simp"], "tactic_count": 13}
{"name": "CategoryTheory.Abelian.full_comp_preadditiveCoyonedaObj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Abelian.Yoneda", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.actionAsFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ActionCategory", "kind": "definition", "module": "Mathlib.CategoryTheory.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instCategoryActionCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Action", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.ActionCategory.π", "kind": "definition", "module": "Mathlib.CategoryTheory.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ActionCategory.π_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ActionCategory.π_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ActionCategory.back", "kind": "definition", "module": "Mathlib.CategoryTheory.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ActionCategory.instCoeTC", "kind": "instance", "module": "Mathlib.CategoryTheory.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ActionCategory.coe_back", "kind": "theorem", "module": "Mathlib.CategoryTheory.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ActionCategory.back_coe", "kind": "theorem", "module": "Mathlib.CategoryTheory.Action", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "CategoryTheory.ActionCategory.objEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ActionCategory.hom_as_subtype", "kind": "theorem", "module": "Mathlib.CategoryTheory.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ActionCategory.instInhabited", "kind": "instance", "module": "Mathlib.CategoryTheory.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ActionCategory.instNonempty", "kind": "instance", "module": "Mathlib.CategoryTheory.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ActionCategory.stabilizerIsoEnd", "kind": "definition", "module": "Mathlib.CategoryTheory.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ActionCategory.stabilizerIsoEnd_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ActionCategory.stabilizerIsoEnd_symm_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ActionCategory.id_val", "kind": "theorem", "module": "Mathlib.CategoryTheory.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ActionCategory.comp_val", "kind": "theorem", "module": "Mathlib.CategoryTheory.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ActionCategory.instIsConnectedOfIsPretransitiveOfNonempty", "kind": "instance", "module": "Mathlib.CategoryTheory.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ActionCategory.instGroupoid", "kind": "instance", "module": "Mathlib.CategoryTheory.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ActionCategory.endMulEquivSubgroup", "kind": "definition", "module": "Mathlib.CategoryTheory.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ActionCategory.homOfPair", "kind": "definition", "module": "Mathlib.CategoryTheory.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ActionCategory.homOfPair.val", "kind": "theorem", "module": "Mathlib.CategoryTheory.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ActionCategory.cases", "kind": "definition", "module": "Mathlib.CategoryTheory.Action", "is_tactic_proof": true, "tactics": ["refine", "rcases", "rcases", "rcases", "cases", "rfl"], "tactic_count": 6}
{"name": "CategoryTheory.ActionCategory.curry", "kind": "definition", "module": "Mathlib.CategoryTheory.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ActionCategory.uncurry", "kind": "definition", "module": "Mathlib.CategoryTheory.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.ρ_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Action.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Action.ρAut", "kind": "definition", "module": "Mathlib.CategoryTheory.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.trivial", "kind": "definition", "module": "Mathlib.CategoryTheory.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.inhabited'", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.instInhabitedAddCommGrpCat", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.Hom.id", "kind": "definition", "module": "Mathlib.CategoryTheory.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.Hom.instInhabited", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.Hom.comp", "kind": "definition", "module": "Mathlib.CategoryTheory.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.instCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.hom_injective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.id_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.comp_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.hom_inv_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Action.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Action.inv_hom_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Action.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Action.isIso_of_hom_isIso", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.isIso_hom_mk", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.instIsIsoHomHom", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.instIsIsoHomInv", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.FunctorCategoryEquivalence.functor", "kind": "definition", "module": "Mathlib.CategoryTheory.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.FunctorCategoryEquivalence.inverse", "kind": "definition", "module": "Mathlib.CategoryTheory.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.FunctorCategoryEquivalence.unitIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.FunctorCategoryEquivalence.counitIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.functorCategoryEquivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.instIsEquivalenceFunctorSingleObjFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.instIsEquivalenceFunctorSingleObjInverse", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.forget", "kind": "definition", "module": "Mathlib.CategoryTheory.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.instFaithfulForget", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.instHasForget", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.HomSubtype", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.instFunLikeHomSubtypeV", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.instConcreteCategoryHomSubtypeV", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.hasForgetToV", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.functorCategoryEquivalenceCompEvaluation", "kind": "definition", "module": "Mathlib.CategoryTheory.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.preservesLimits_forget", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.preservesColimits_forget", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.Iso.conj_ρ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Action.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Action.actionPunitEquivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.res", "kind": "definition", "module": "Mathlib.CategoryTheory.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.resId", "kind": "definition", "module": "Mathlib.CategoryTheory.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.resComp", "kind": "definition", "module": "Mathlib.CategoryTheory.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.resCongr", "kind": "definition", "module": "Mathlib.CategoryTheory.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.resEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.instFaithfulRes", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.full_res", "kind": "theorem", "module": "Mathlib.CategoryTheory.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapAction", "kind": "definition", "module": "Mathlib.CategoryTheory.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instFaithfulActionMapAction", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.FullyFaithful.mapAction", "kind": "definition", "module": "Mathlib.CategoryTheory.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instFullActionMapActionOfFaithful", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapActionComp", "kind": "definition", "module": "Mathlib.CategoryTheory.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapActionCongr", "kind": "definition", "module": "Mathlib.CategoryTheory.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.mapAction", "kind": "definition", "module": "Mathlib.CategoryTheory.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.ρ_inv_self_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Action.Concrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.ρ_self_inv_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Action.Concrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.ofMulAction", "kind": "definition", "module": "Mathlib.CategoryTheory.Action.Concrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.ofMulAction_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Action.Concrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.ofMulActionLimitCone", "kind": "definition", "module": "Mathlib.CategoryTheory.Action.Concrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.leftRegular", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Action.Concrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.diagonal", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Action.Concrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.diagonalOneIsoLeftRegular", "kind": "definition", "module": "Mathlib.CategoryTheory.Action.Concrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.FintypeCat.instMulActionCarrierOf", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Concrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.FintypeCat.ofMulAction", "kind": "definition", "module": "Mathlib.CategoryTheory.Action.Concrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.FintypeCat.ofMulAction_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Action.Concrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.FintypeCat.term_⧸ₐ_", "kind": "definition", "module": "Mathlib.CategoryTheory.Action.Concrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.FintypeCat._aux_Mathlib_CategoryTheory_Action_Concrete___macroRules_Action_FintypeCat_term_⧸ₐ__1", "kind": "definition", "module": "Mathlib.CategoryTheory.Action.Concrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.FintypeCat.toEndHom", "kind": "definition", "module": "Mathlib.CategoryTheory.Action.Concrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.FintypeCat.toEndHom_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Action.Concrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.FintypeCat.toEndHom_trivial_of_mem", "kind": "theorem", "module": "Mathlib.CategoryTheory.Action.Concrete", "is_tactic_proof": true, "tactics": ["apply", "ext", "induction", "exact"], "tactic_count": 4}
{"name": "Action.FintypeCat.quotientToEndHom", "kind": "definition", "module": "Mathlib.CategoryTheory.Action.Concrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.FintypeCat.quotientToEndHom_mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Action.Concrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.FintypeCat.quotientToQuotientOfLE", "kind": "definition", "module": "Mathlib.CategoryTheory.Action.Concrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.FintypeCat.quotientToQuotientOfLE_hom_mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Action.Concrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.instMulAction", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Concrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.instMulActionCarrierVFintypeCat", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Concrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.instHasForget₂TopCat", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.instMulActionCarrierObjTopCatForget₂", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.IsContinuous", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Action.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.isContinuous_def", "kind": "theorem", "module": "Mathlib.CategoryTheory.Action.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContAction", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Action.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContAction.instHasForget₂", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContAction.instHasForget₂TopCat", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContAction.instCoeAction", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContAction.IsDiscrete", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Action.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContAction.res", "kind": "definition", "module": "Mathlib.CategoryTheory.Action.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContAction.resComp", "kind": "definition", "module": "Mathlib.CategoryTheory.Action.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContAction.resCongr", "kind": "definition", "module": "Mathlib.CategoryTheory.Action.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContAction.resEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Action.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteContAction", "kind": "definition", "module": "Mathlib.CategoryTheory.Action.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteContAction.instCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteContAction.instHasForget", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteContAction.instConcreteCategoryHomSubtypeObjActionIsContinuousContActionIsDiscreteV", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteContAction.instHasForget₂ContAction", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteContAction.instHasForget₂TopCat", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteContAction.instDiscreteTopologyCarrierObjTopCatForget₂", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapContAction", "kind": "definition", "module": "Mathlib.CategoryTheory.Action.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapContActionComp", "kind": "definition", "module": "Mathlib.CategoryTheory.Action.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapContActionCongr", "kind": "definition", "module": "Mathlib.CategoryTheory.Action.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.mapContAction", "kind": "definition", "module": "Mathlib.CategoryTheory.Action.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.instHasFiniteProducts", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.instHasFiniteLimits", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.instHasLimits", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.hasLimitsOfShape", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.instHasFiniteCoproducts", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.instHasFiniteColimits", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.instHasColimits", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.hasColimitsOfShape", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.CategoryTheory.Action.Limits.0.Action.SingleObj.preservesLimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": true, "tactics": ["apply", "intro", "exact"], "tactic_count": 3}
{"name": "Action.preservesLimit_of_preserves", "kind": "theorem", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": true, "tactics": ["let", "have", "apply"], "tactic_count": 3}
{"name": "Action.preservesLimitsOfShape_of_preserves", "kind": "theorem", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": true, "tactics": ["constructor", "intro", "apply", "exact"], "tactic_count": 4}
{"name": "Action.preservesLimitsOfSize_of_preserves", "kind": "theorem", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": true, "tactics": ["constructor", "intro", "apply", "exact"], "tactic_count": 4}
{"name": "_private.Mathlib.CategoryTheory.Action.Limits.0.Action.SingleObj.preservesColimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": true, "tactics": ["apply", "intro", "exact"], "tactic_count": 3}
{"name": "Action.preservesColimit_of_preserves", "kind": "theorem", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": true, "tactics": ["let", "have", "apply"], "tactic_count": 3}
{"name": "Action.preservesColimitsOfShape_of_preserves", "kind": "theorem", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": true, "tactics": ["constructor", "intro", "apply", "exact"], "tactic_count": 4}
{"name": "Action.preservesColimitsOfSize_of_preserves", "kind": "theorem", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": true, "tactics": ["constructor", "intro", "apply", "exact"], "tactic_count": 4}
{"name": "Action.instPreservesLimitForgetOfHasLimitComp", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": false, "tactics": ["change", "have", "inferInstanceAs", "infer_instance"], "tactic_count": 4}
{"name": "Action.instPreservesLimitsOfShapeForgetOfHasLimitsOfShape", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.instPreservesColimitForgetOfHasColimitComp", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": false, "tactics": ["change", "have", "inferInstanceAs", "infer_instance"], "tactic_count": 4}
{"name": "Action.instPreservesColimitsOfShapeForgetOfHasColimitsOfShape", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.instPreservesFiniteLimitsForgetOfHasFiniteLimits", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": false, "tactics": ["change", "have", "constructor", "intro", "infer_instance", "apply"], "tactic_count": 6}
{"name": "Action.instPreservesFiniteColimitsForgetOfHasFiniteColimits", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": false, "tactics": ["change", "have", "constructor", "intro", "infer_instance", "apply"], "tactic_count": 6}
{"name": "Action.instReflectsLimitForget", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.instReflectsLimitsOfShapeForget", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.instReflectsLimitsForget", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.instReflectsColimitForget", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.instReflectsColimitsOfShapeForget", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.instReflectsColimitsForget", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.Functor.mapActionPreservesLimit_of_preserves", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.Functor.mapActionPreservesLimitsOfShapeOfPreserves", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.Functor.preservesLimitsOfSize_of_preserves", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.Functor.instPreservesFiniteLimitsMapActionOfHasFiniteLimits", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.Functor.mapActionPreservesColimit_of_preserves", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.Functor.mapActionPreservesColimitsOfShapeOfPreserves", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.Functor.preservesColimitsOfSize_of_preserves", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.Functor.instPreservesFiniteColimitsMapActionOfHasFiniteColimits", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.instZeroHom", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.zero_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.instHasZeroMorphisms", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.forget_preservesZeroMorphisms", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.forget₂_preservesZeroMorphisms", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.functorCategoryEquivalence_preservesZeroMorphisms", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.instAddHom", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.instNegHom", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.instSubHom", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.instSMulNatHom", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.instSMulIntHom", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.add_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.neg_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.sub_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.nsmul_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.zsmul_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.instPreadditive", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.forget_additive", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.forget₂_additive", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.functorCategoryEquivalence_additive", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.sum_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.instLinear", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.forget_linear", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.forget₂_linear", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.functorCategoryEquivalence_linear", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.smul_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.res_additive", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.res_linear", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.abelianAux", "kind": "definition", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.instAbelian", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapAction_preadditive", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapAction_linear", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.instMonoidalCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.tensorUnit_ρ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Action.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.tensor_ρ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Action.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.tensorUnitIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Action.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.instMonoidalForget", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.forget_ε", "kind": "theorem", "module": "Mathlib.CategoryTheory.Action.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.forget_η", "kind": "theorem", "module": "Mathlib.CategoryTheory.Action.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.forget_μ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Action.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.forget_δ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Action.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.instBraidedCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.β_hom_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Action.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.β_inv_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Action.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.instBraidedForget", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.instSymmetricCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.instMonoidalPreadditive", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.instMonoidalLinear", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.FunctorCategoryEquivalence.functorMonoidal", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.functorCategoryEquivalenceFunctorMonoidal", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Monoidal", "is_tactic_proof": true, "tactics": ["dsimp"], "tactic_count": 1}
{"name": "Action.FunctorCategoryEquivalence.inverseMonoidal", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.functorCategoryEquivalenceInverseMonoidal", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Monoidal", "is_tactic_proof": true, "tactics": ["dsimp"], "tactic_count": 1}
{"name": "Action.FunctorCategoryEquivalence.functor_ε", "kind": "theorem", "module": "Mathlib.CategoryTheory.Action.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Action.FunctorCategoryEquivalence.functor_μ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Action.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Action.instRightRigidCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.instLeftRigidCategoryFunctorSingleObj", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Monoidal", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Action.instLeftRigidCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.instRigidCategoryFunctorSingleObj", "kind": "instance", "module": "Mathlib.CategoryTheory.Action.Monoidal", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
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{"name": "Action.rightDual_v", "kind": "theorem", "module": "Mathlib.CategoryTheory.Action.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.leftDual_v", "kind": "theorem", "module": "Mathlib.CategoryTheory.Action.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.rightDual_ρ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Action.Monoidal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Action.leftDual_ρ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Action.Monoidal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Action.diagonalSuccIsoTensorDiagonal", "kind": "definition", "module": "Mathlib.CategoryTheory.Action.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.leftRegularTensorIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Action.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.diagonalSuccIsoTensorTrivial", "kind": "definition", "module": "Mathlib.CategoryTheory.Action.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Action.diagonalSuccIsoTensorTrivial_hom_hom_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Action.Monoidal", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "refine", "induction", "simp_all", "id_tensorHom,", "tensor_ρ,", "simp"], "tactic_count": 9}
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{"name": "CategoryTheory.IsPushout.IsVanKampen", "kind": "definition", "module": "Mathlib.CategoryTheory.Adhesive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPushout.IsVanKampen.flip", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adhesive", "is_tactic_proof": true, "tactics": ["introv", "simpa"], "tactic_count": 2}
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{"name": "CategoryTheory.adhesive_functor", "kind": "instance", "module": "Mathlib.CategoryTheory.Adhesive", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "apply", "intro", "refine", "refine", "refine", "apply"], "tactic_count": 9}
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{"name": "CategoryTheory.Adjunction.homAddEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Additive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.homAddEquiv_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Additive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.homAddEquiv_symm_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Additive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.solutionSetCondition_of_isRightAdjoint", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.AdjointFunctorTheorems", "is_tactic_proof": true, "tactics": ["intro", "refine", "intro", "refine", "rw"], "tactic_count": 5}
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{"name": "CategoryTheory.isLeftAdjoint_of_preservesColimits_of_isSeparating", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.AdjointFunctorTheorems", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Functor.leftAdjoint", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.rightAdjoint", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.ofIsLeftAdjoint", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.ofIsRightAdjoint", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.homEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Adjunction.isLeftAdjoint", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.isRightAdjoint", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Adjunction.instIsRightAdjointRightAdjoint", "kind": "instance", "module": "Mathlib.CategoryTheory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Adjunction.eq_homEquiv_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Adjunction.representableBy", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.CoreHomEquiv.homEquiv_naturality_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Adjunction.CoreHomEquiv.homEquiv_naturality_right_symm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "CategoryTheory.Adjunction.mk'_homEquiv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Basic", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.Adjunction.mkOfHomEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.mkOfHomEquiv_homEquiv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Adjunction.mkOfUnitCounit", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.id", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.instInhabitedId", "kind": "instance", "module": "Mathlib.CategoryTheory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.equivHomsetLeftOfNatIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.equivHomsetRightOfNatIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.ofNatIsoLeft", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.ofNatIsoRight", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.compYonedaIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.compCoyonedaIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.compUliftCoyonedaIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.comp", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.comp_unit_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Adjunction.comp_counit_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Adjunction.comp_homEquiv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.leftAdjointOfEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.adjunctionOfEquivLeft", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.CategoryTheory.Adjunction.Basic.0.CategoryTheory.Adjunction.he''", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Adjunction.rightAdjointOfEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.adjunctionOfEquivRight", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.toEquivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isEquivalence_of_isRightAdjoint", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.toAdjunction", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.isLeftAdjoint_functor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.isRightAdjoint_inverse", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.isLeftAdjoint_inverse", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.isRightAdjoint_functor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.refl_toAdjunction", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.trans_toAdjunction", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isLeftAdjoint_comp", "kind": "instance", "module": "Mathlib.CategoryTheory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isRightAdjoint_comp", "kind": "instance", "module": "Mathlib.CategoryTheory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isRightAdjoint_of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isLeftAdjoint_of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.adjunction", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isLeftAdjoint_of_isEquivalence", "kind": "instance", "module": "Mathlib.CategoryTheory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isRightAdjoint_of_isEquivalence", "kind": "instance", "module": "Mathlib.CategoryTheory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.leftAdjointOfStructuredArrowInitialsAux", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.leftAdjointOfStructuredArrowInitials", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.adjunctionOfStructuredArrowInitials", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isRightAdjointOfStructuredArrowInitials", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.rightAdjointOfCostructuredArrowTerminalsAux", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.rightAdjointOfCostructuredArrowTerminals", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.adjunctionOfCostructuredArrowTerminals", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isLeftAdjoint_of_costructuredArrowTerminals", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.mkInitialOfLeftAdjoint", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.mkTerminalOfRightAdjoint", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isRightAdjoint_iff_hasInitial_structuredArrow", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isLeftAdjoint_iff_hasTerminal_costructuredArrow", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.leftAdjointIdIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.CompositionIso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.conjugateEquiv_leftAdjointIdIso_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.CompositionIso", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Adjunction.leftAdjointCompNatTrans", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.CompositionIso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.leftAdjointCompIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.CompositionIso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.leftAdjointCompIso_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.CompositionIso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.conjugateEquiv_leftAdjointCompIso_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.CompositionIso", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Adjunction.leftAdjointCompIso_comp_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.CompositionIso", "is_tactic_proof": true, "tactics": ["subst", "ext", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.Adjunction.leftAdjointCompIso_id_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.CompositionIso", "is_tactic_proof": true, "tactics": ["subst", "ext", "have", "have", "simp", "simp"], "tactic_count": 6}
{"name": "CategoryTheory.Adjunction.leftAdjointCompNatTrans₀₁₃_eq_conjugateEquiv_symm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.CompositionIso", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "apply", "simp"], "tactic_count": 4}
{"name": "CategoryTheory.Adjunction.leftAdjointCompNatTrans₀₂₃_eq_conjugateEquiv_symm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.CompositionIso", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "apply", "simp", "rw", "conjugateEquiv_associator_hom"], "tactic_count": 6}
{"name": "CategoryTheory.Adjunction.leftAdjointCompNatTrans_assoc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.CompositionIso", "is_tactic_proof": true, "tactics": ["simp", "reassoc_of%"], "tactic_count": 2}
{"name": "CategoryTheory.Adjunction.leftAdjointCompIso_assoc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.CompositionIso", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.evaluationLeftAdjoint", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Evaluation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.evaluationAdjunctionRight", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Evaluation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.evaluationIsRightAdjoint", "kind": "instance", "module": "Mathlib.CategoryTheory.Adjunction.Evaluation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.mono_iff_mono_app'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Evaluation", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "intro", "apply"], "tactic_count": 5}
{"name": "CategoryTheory.evaluationRightAdjoint", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Evaluation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.evaluationAdjunctionLeft", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Evaluation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.evaluationIsLeftAdjoint", "kind": "instance", "module": "Mathlib.CategoryTheory.Adjunction.Evaluation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.epi_iff_epi_app'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Evaluation", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "intros", "apply"], "tactic_count": 5}
{"name": "CategoryTheory.Adjunction.unit_mono_of_L_faithful", "kind": "instance", "module": "Mathlib.CategoryTheory.Adjunction.FullyFaithful", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.unitSplitEpiOfLFull", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.FullyFaithful", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.unit_isSplitEpi_of_L_full", "kind": "instance", "module": "Mathlib.CategoryTheory.Adjunction.FullyFaithful", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.instIsIsoAppUnitOfFullOfFaithful", "kind": "instance", "module": "Mathlib.CategoryTheory.Adjunction.FullyFaithful", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.unit_isIso_of_L_fully_faithful", "kind": "instance", "module": "Mathlib.CategoryTheory.Adjunction.FullyFaithful", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.counit_epi_of_R_faithful", "kind": "instance", "module": "Mathlib.CategoryTheory.Adjunction.FullyFaithful", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.counitSplitMonoOfRFull", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.FullyFaithful", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.counit_isSplitMono_of_R_full", "kind": "instance", "module": "Mathlib.CategoryTheory.Adjunction.FullyFaithful", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.instIsIsoAppCounitOfFullOfFaithful", "kind": "instance", "module": "Mathlib.CategoryTheory.Adjunction.FullyFaithful", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.counit_isIso_of_R_fully_faithful", "kind": "instance", "module": "Mathlib.CategoryTheory.Adjunction.FullyFaithful", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.inv_map_unit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.FullyFaithful", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.whiskerLeftLCounitIsoOfIsIsoUnit", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.FullyFaithful", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.inv_counit_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.FullyFaithful", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.whiskerLeftRUnitIsoOfIsIsoCounit", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.FullyFaithful", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.faithful_L_of_mono_unit_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.FullyFaithful", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.full_L_of_isSplitEpi_unit_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.FullyFaithful", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.fullyFaithfulLOfIsIsoUnit", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.FullyFaithful", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.faithful_R_of_epi_counit_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.FullyFaithful", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.full_R_of_isSplitMono_counit_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.FullyFaithful", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.fullyFaithfulROfIsIsoCounit", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.FullyFaithful", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.whiskerLeft_counit_iso_of_L_fully_faithful", "kind": "instance", "module": "Mathlib.CategoryTheory.Adjunction.FullyFaithful", "is_tactic_proof": true, "tactics": ["have", "rw", "rw", "infer_instance"], "tactic_count": 4}
{"name": "CategoryTheory.Adjunction.whiskerRight_counit_iso_of_L_fully_faithful", "kind": "instance", "module": "Mathlib.CategoryTheory.Adjunction.FullyFaithful", "is_tactic_proof": true, "tactics": ["have", "rw", "rw", "infer_instance"], "tactic_count": 4}
{"name": "CategoryTheory.Adjunction.whiskerLeft_unit_iso_of_R_fully_faithful", "kind": "instance", "module": "Mathlib.CategoryTheory.Adjunction.FullyFaithful", "is_tactic_proof": true, "tactics": ["have", "rw", "rw", "infer_instance"], "tactic_count": 4}
{"name": "CategoryTheory.Adjunction.whiskerRight_unit_iso_of_R_fully_faithful", "kind": "instance", "module": "Mathlib.CategoryTheory.Adjunction.FullyFaithful", "is_tactic_proof": true, "tactics": ["have", "rw", "rw", "infer_instance"], "tactic_count": 4}
{"name": "CategoryTheory.Adjunction.instIsIsoAppCounitObjOfFaithfulOfFull", "kind": "instance", "module": "Mathlib.CategoryTheory.Adjunction.FullyFaithful", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.instIsIsoMapAppCounitOfFaithfulOfFull", "kind": "instance", "module": "Mathlib.CategoryTheory.Adjunction.FullyFaithful", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.isIso_counit_app_iff_mem_essImage", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.FullyFaithful", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "rintro", "rw", "infer_instance"], "tactic_count": 6}
{"name": "CategoryTheory.Adjunction.mem_essImage_of_counit_isIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.FullyFaithful", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.isIso_counit_app_of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.FullyFaithful", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.instIsIsoAppUnitObjOfFaithfulOfFull", "kind": "instance", "module": "Mathlib.CategoryTheory.Adjunction.FullyFaithful", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.instIsIsoMapAppUnitOfFaithfulOfFull", "kind": "instance", "module": "Mathlib.CategoryTheory.Adjunction.FullyFaithful", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.isIso_unit_app_iff_mem_essImage", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.FullyFaithful", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "rintro", "rw", "infer_instance"], "tactic_count": 6}
{"name": "CategoryTheory.Adjunction.mem_essImage_of_unit_isIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.FullyFaithful", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.isIso_unit_app_of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.FullyFaithful", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.instIsIsoFunctorUnitOfIsEquivalence", "kind": "instance", "module": "Mathlib.CategoryTheory.Adjunction.FullyFaithful", "is_tactic_proof": true, "tactics": ["have", "apply"], "tactic_count": 2}
{"name": "CategoryTheory.Adjunction.instIsIsoFunctorCounitOfIsEquivalence", "kind": "instance", "module": "Mathlib.CategoryTheory.Adjunction.FullyFaithful", "is_tactic_proof": true, "tactics": ["have", "apply"], "tactic_count": 2}
{"name": "CategoryTheory.Adjunction.isEquivalence_left_of_isEquivalence_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.FullyFaithful", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.isEquivalence_right_of_isEquivalence_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.FullyFaithful", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.instIsIsoFunctorUnitOfIsEquivalence_1", "kind": "instance", "module": "Mathlib.CategoryTheory.Adjunction.FullyFaithful", "is_tactic_proof": true, "tactics": ["have", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Adjunction.instIsIsoFunctorCounitOfIsEquivalence_1", "kind": "instance", "module": "Mathlib.CategoryTheory.Adjunction.FullyFaithful", "is_tactic_proof": true, "tactics": ["have", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.LiftLeftAdjoint.counitCoequalises", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Lifting.Left", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LiftLeftAdjoint.otherMap", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Lifting.Left", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LiftLeftAdjoint.instIsReflexivePairMapAppCounitOtherMap", "kind": "instance", "module": "Mathlib.CategoryTheory.Adjunction.Lifting.Left", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LiftLeftAdjoint.constructLeftAdjointObj", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Lifting.Left", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LiftLeftAdjoint.constructLeftAdjointEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Lifting.Left", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LiftLeftAdjoint.constructLeftAdjoint", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Lifting.Left", "is_tactic_proof": true, "tactics": ["refine", "intro", "rw", "dsimp", "erw", "erw", "simp_rw", "cat_disch"], "tactic_count": 8}
{"name": "CategoryTheory.isRightAdjoint_triangle_lift", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Lifting.Left", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isRightAdjoint_triangle_lift_monadic", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Lifting.Left", "is_tactic_proof": true, "tactics": ["let", "rsuffices", "let", "refine", "exact", "let", "refine", "exact", "let", "intro", "simp", "exact", "exact"], "tactic_count": 13}
{"name": "CategoryTheory.isRightAdjoint_square_lift", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Lifting.Left", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isRightAdjoint_square_lift_monadic", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Lifting.Left", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LiftRightAdjoint.unitEqualises", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Lifting.Right", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LiftRightAdjoint.otherMap", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Lifting.Right", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LiftRightAdjoint.instIsCoreflexivePairMapAppUnitOtherMap", "kind": "instance", "module": "Mathlib.CategoryTheory.Adjunction.Lifting.Right", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LiftRightAdjoint.constructRightAdjointObj", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Lifting.Right", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LiftRightAdjoint.constructRightAdjointEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Lifting.Right", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LiftRightAdjoint.constructRightAdjoint", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Lifting.Right", "is_tactic_proof": true, "tactics": ["refine", "intro", "rw", "dsimp", "simp", "erw", "simp", "erw", "simp"], "tactic_count": 9}
{"name": "CategoryTheory.isLeftAdjoint_triangle_lift", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Lifting.Right", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isLeftAdjoint_triangle_lift_comonadic", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Lifting.Right", "is_tactic_proof": true, "tactics": ["let", "rsuffices", "let", "refine", "exact", "let", "refine", "exact", "let", "intro", "simp", "exact", "exact"], "tactic_count": 13}
{"name": "CategoryTheory.isLeftAdjoint_square_lift", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Lifting.Right", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isLeftAdjoint_square_lift_comonadic", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Lifting.Right", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.functorialityRightAdjoint", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.functorialityUnit", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.functorialityCounit", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.functorialityAdjunction", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.leftAdjoint_preservesColimits", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.colim_preservesColimits", "kind": "instance", "module": "Mathlib.CategoryTheory.Adjunction.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.isEquivalence_preservesColimits", "kind": "instance", "module": "Mathlib.CategoryTheory.Adjunction.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.reflectsColimits_of_isEquivalence", "kind": "instance", "module": "Mathlib.CategoryTheory.Adjunction.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.createsColimitsOfIsEquivalence", "kind": "instance", "module": "Mathlib.CategoryTheory.Adjunction.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction._example", "kind": "example", "module": "Mathlib.CategoryTheory.Adjunction.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.hasColimit_comp_equivalence", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.hasColimit_of_comp_equivalence", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Limits", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Adjunction.hasColimitsOfShape_of_equivalence", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.has_colimits_of_equivalence", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.functorialityLeftAdjoint", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.functorialityUnit'", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.functorialityCounit'", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.functorialityAdjunction'", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.rightAdjoint_preservesLimits", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.lim_preservesLimits", "kind": "instance", "module": "Mathlib.CategoryTheory.Adjunction.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.isEquivalencePreservesLimits", "kind": "instance", "module": "Mathlib.CategoryTheory.Adjunction.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.reflectsLimits_of_isEquivalence", "kind": "instance", "module": "Mathlib.CategoryTheory.Adjunction.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.createsLimitsOfIsEquivalence", "kind": "instance", "module": "Mathlib.CategoryTheory.Adjunction.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction._example", "kind": "example", "module": "Mathlib.CategoryTheory.Adjunction.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.hasLimit_comp_equivalence", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.hasLimit_of_comp_equivalence", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Limits", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Adjunction.hasLimitsOfShape_of_equivalence", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.has_limits_of_equivalence", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.coconesIsoComponentHom", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.coconesIsoComponentInv", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.conesIsoComponentHom", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.conesIsoComponentInv", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.coconesIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.conesIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instPreservesColimitsOfShapeOfIsLeftAdjoint", "kind": "instance", "module": "Mathlib.CategoryTheory.Adjunction.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instPreservesColimitsOfSizeOfIsLeftAdjoint", "kind": "instance", "module": "Mathlib.CategoryTheory.Adjunction.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instPreservesLimitsOfShapeOfIsRightAdjoint", "kind": "instance", "module": "Mathlib.CategoryTheory.Adjunction.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instPreservesLimitsOfSizeOfIsRightAdjoint", "kind": "instance", "module": "Mathlib.CategoryTheory.Adjunction.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.mateEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Mates", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.mateEquiv_counit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Mates", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.mateEquiv_counit_symm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Mates", "is_tactic_proof": true, "tactics": ["conv_lhs", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.unit_mateEquiv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Mates", "is_tactic_proof": false, "tactics": ["simp", "associator_hom_app,", "id_comp]", "rw", "slice_lhs", "rw", "slice_lhs", "simp"], "tactic_count": 8}
{"name": "CategoryTheory.unit_mateEquiv_symm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Mates", "is_tactic_proof": true, "tactics": ["conv_lhs", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.mateEquiv_vcomp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Mates", "is_tactic_proof": true, "tactics": ["unfold", "ext", "simp", "id_obj,", "slice_rhs", "rw", "slice_rhs", "rw", "rw", "rw", "slice_rhs", "rw", "rw", "simp", "slice_rhs", "simp", "slice_rhs", "simp"], "tactic_count": 18}
{"name": "CategoryTheory.mateEquiv_hcomp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Mates", "is_tactic_proof": true, "tactics": ["unfold", "ext", "simp", "leftUnitor_hom_app,", "slice_rhs", "rw", "slice_rhs", "simp"], "tactic_count": 8}
{"name": "CategoryTheory.mateEquiv_square", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Mates", "is_tactic_proof": true, "tactics": ["have", "simp", "assumption"], "tactic_count": 3}
{"name": "CategoryTheory.conjugateEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Mates", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.conjugateEquiv_counit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Mates", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.conjugateEquiv_counit_symm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Mates", "is_tactic_proof": true, "tactics": ["conv_lhs", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.unit_conjugateEquiv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Mates", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "have", "dsimp", "rw", "simp"], "tactic_count": 6}
{"name": "CategoryTheory.unit_conjugateEquiv_symm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Mates", "is_tactic_proof": true, "tactics": ["conv_lhs", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.conjugateEquiv_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Mates", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.conjugateEquiv_symm_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Mates", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.conjugateEquiv_adjunction_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Mates", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.conjugateEquiv_adjunction_id_symm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Mates", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.conjugateEquiv_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Mates", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "have", "mateEquiv_vcomp", "have", "simp", "associator_hom_app,", "map_id]", "rw"], "tactic_count": 9}
{"name": "CategoryTheory.conjugateEquiv_symm_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Mates", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.conjugateEquiv_comm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Mates", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.conjugateEquiv_symm_comm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Mates", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.conjugateEquiv_iso", "kind": "instance", "module": "Mathlib.CategoryTheory.Adjunction.Mates", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.conjugateEquiv_symm_iso", "kind": "instance", "module": "Mathlib.CategoryTheory.Adjunction.Mates", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.conjugateEquiv_of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Mates", "is_tactic_proof": true, "tactics": ["suffices", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.conjugateEquiv_symm_of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Mates", "is_tactic_proof": true, "tactics": ["suffices", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.conjugateIsoEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Mates", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.iterated_mateEquiv_conjugateEquiv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Mates", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.iterated_mateEquiv_conjugateEquiv_symm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Mates", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.mateEquiv_conjugateEquiv_vcomp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Mates", "is_tactic_proof": true, "tactics": ["ext", "have", "unfold", "have", "simp", "whiskerRight_comp,", "associator_inv_app,", "whiskerRight_twice,", "simpa"], "tactic_count": 9}
{"name": "CategoryTheory.conjugateEquiv_mateEquiv_vcomp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Mates", "is_tactic_proof": true, "tactics": ["ext", "have", "unfold", "have", "simp", "leftUnitor_hom_app,", "simpa"], "tactic_count": 7}
{"name": "CategoryTheory.conjugateEquiv_associator_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Mates", "is_tactic_proof": true, "tactics": ["ext", "simp", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.conjugateEquiv_leftUnitor_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Mates", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.conjugateEquiv_rightUnitor_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Mates", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.conjugateEquiv_whiskerLeft", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Mates", "is_tactic_proof": true, "tactics": ["ext", "have", "have", "simp", "simp"], "tactic_count": 5}
{"name": "CategoryTheory.conjugateEquiv_whiskerRight", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Mates", "is_tactic_proof": true, "tactics": ["ext", "simp", "comp_counit_app,", "simp"], "tactic_count": 4}
{"name": "CategoryTheory.Adjunction.unop", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.op", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.leftOp", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.rightOp", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.leftOp_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Opposites", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Adjunction.rightOp_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Opposites", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Adjunction.leftAdjointsCoyonedaEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.natIsoOfRightAdjointNatIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.natIsoOfLeftAdjointNatIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsLeftAdjoint.op", "kind": "instance", "module": "Mathlib.CategoryTheory.Adjunction.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsRightAdjoint.op", "kind": "instance", "module": "Mathlib.CategoryTheory.Adjunction.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsLeftAdjoint.leftOp", "kind": "instance", "module": "Mathlib.CategoryTheory.Adjunction.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsRightAdjoint.leftOp", "kind": "instance", "module": "Mathlib.CategoryTheory.Adjunction.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsLeftAdjoint.rightOp", "kind": "instance", "module": "Mathlib.CategoryTheory.Adjunction.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsRightAdjoint.rightOp", "kind": "instance", "module": "Mathlib.CategoryTheory.Adjunction.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.term_⊣₂_", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Parametrized", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory._aux_Mathlib_CategoryTheory_Adjunction_Parametrized___macroRules_CategoryTheory_term_⊣₂__1", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Parametrized", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory._aux_Mathlib_CategoryTheory_Adjunction_Parametrized___unexpand_CategoryTheory_ParametrizedAdjunction_1", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Parametrized", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ParametrizedAdjunction.homEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Parametrized", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ParametrizedAdjunction.homEquiv_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Parametrized", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ParametrizedAdjunction.homEquiv_naturality_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Parametrized", "is_tactic_proof": true, "tactics": ["have", "dsimp", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.ParametrizedAdjunction.homEquiv_naturality_two", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Parametrized", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ParametrizedAdjunction.homEquiv_naturality_three", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Parametrized", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ParametrizedAdjunction.homEquiv_symm_naturality_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Parametrized", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ParametrizedAdjunction.homEquiv_symm_naturality_two", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Parametrized", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ParametrizedAdjunction.homEquiv_symm_naturality_three", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Parametrized", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ParametrizedAdjunction.whiskerLeft_map_counit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Parametrized", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "apply", "rw", "simp"], "tactic_count": 5}
{"name": "CategoryTheory.Functor.leftAdjointObjIsDefined", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.PartialAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.leftAdjointObjIsDefined_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.PartialAdjoint", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.leftAdjointObjIsDefined_of_adjunction", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.PartialAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.PartialLeftAdjointSource", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Adjunction.PartialAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instIsCorepresentableCompObjOppositeTypeCoyonedaOpObjLeftAdjointObjIsDefined", "kind": "instance", "module": "Mathlib.CategoryTheory.Adjunction.PartialAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.partialLeftAdjointObj", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.PartialAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.partialLeftAdjointHomEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.PartialAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.partialLeftAdjointHomEquiv_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.PartialAdjoint", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.partialLeftAdjointMap", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.PartialAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.partialLeftAdjointHomEquiv_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.PartialAdjoint", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.partialLeftAdjointHomEquiv_map_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.PartialAdjoint", "is_tactic_proof": true, "tactics": ["rw", "id_comp]"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.partialLeftAdjointHomEquiv_symm_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.PartialAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.partialLeftAdjointHomEquiv_comp_symm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.PartialAdjoint", "is_tactic_proof": true, "tactics": ["rw", "partialLeftAdjointHomEquiv_comp,"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.partialLeftAdjoint", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.PartialAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isRightAdjoint_of_leftAdjointObjIsDefined_eq_top", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.PartialAdjoint", "is_tactic_proof": false, "tactics": ["replace", "simp", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Functor.isRightAdjoint_iff_leftAdjointObjIsDefined_eq_top", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.PartialAdjoint", "is_tactic_proof": true, "tactics": ["refine", "ext", "simpa", "leftAdjointObjIsDefined_of_adjunction"], "tactic_count": 4}
{"name": "CategoryTheory.Functor.corepresentableByCompCoyonedaObjOfIsColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.PartialAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.leftAdjointObjIsDefined_of_isColimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.PartialAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.leftAdjointObjIsDefined_colimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.PartialAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.rightAdjointObjIsDefined", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.PartialAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.rightAdjointObjIsDefined_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.PartialAdjoint", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.rightAdjointObjIsDefined_of_adjunction", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.PartialAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.PartialRightAdjointSource", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Adjunction.PartialAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instIsRepresentableCompOppositeOpObjTypeYonedaObjRightAdjointObjIsDefined", "kind": "instance", "module": "Mathlib.CategoryTheory.Adjunction.PartialAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.partialRightAdjointObj", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.PartialAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.partialRightAdjointHomEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.PartialAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.partialRightAdjointHomEquiv_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.PartialAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.partialRightAdjointMap", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.PartialAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.partialRightAdjointHomEquiv_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.PartialAdjoint", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.partialRightAdjointHomEquiv_map_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.PartialAdjoint", "is_tactic_proof": true, "tactics": ["rw", "comp_id]"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.partialRightAdjointHomEquiv_comp_symm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.PartialAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.partialRightAdjointHomEquiv_symm_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.PartialAdjoint", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.partialRightAdjoint", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.PartialAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isLeftAdjoint_of_rightAdjointObjIsDefined_eq_top", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.PartialAdjoint", "is_tactic_proof": false, "tactics": ["replace", "simp", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Functor.isLeftAdjoint_iff_rightAdjointObjIsDefined_eq_top", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.PartialAdjoint", "is_tactic_proof": true, "tactics": ["refine", "ext", "simpa", "rightAdjointObjIsDefined_of_adjunction"], "tactic_count": 4}
{"name": "CategoryTheory.Functor.representableByCompYonedaObjOfIsLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.PartialAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.rightAdjointObjIsDefined_of_isLimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.PartialAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.rightAdjointObjIsDefined_limit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.PartialAdjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.Quadruple.leftTriple", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Quadruple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.Quadruple.rightTriple", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Quadruple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.Quadruple.op", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Quadruple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.Quadruple.op_leftTriple", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Quadruple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.Quadruple.op_rightTriple", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Quadruple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.Quadruple.epi_leftTriple_rightToLeft_app_iff_mono_rightTriple_leftToRight_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Quadruple", "is_tactic_proof": true, "tactics": ["simp_rw", "dsimp", "simp", "simp_rw", "rw", "refine", "rw", "simp_rw", "refine", "rw", "simp"], "tactic_count": 11}
{"name": "CategoryTheory.Adjunction.Quadruple.epi_leftTriple_rightToLeft_iff_mono_rightTriple_leftToRight", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Quadruple", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Adjunction.Quadruple.epi_leftTriple_leftToRight_app_iff_mono_rightTriple_rightToLeft_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Quadruple", "is_tactic_proof": true, "tactics": ["have", "rw", "rw", "simpa"], "tactic_count": 4}
{"name": "CategoryTheory.Adjunction.Quadruple.epi_leftTriple_leftToRight_iff_mono_rightTriple_rightToLeft", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Quadruple", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.reflector", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Reflective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.reflectorAdjunction", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Reflective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instIsRightAdjointOfReflective", "kind": "instance", "module": "Mathlib.CategoryTheory.Adjunction.Reflective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instIsLeftAdjointReflector", "kind": "instance", "module": "Mathlib.CategoryTheory.Adjunction.Reflective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.fullyFaithfulOfReflective", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Reflective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.unit_obj_eq_map_unit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Reflective", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "CategoryTheory._example", "kind": "example", "module": "Mathlib.CategoryTheory.Adjunction.Reflective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.essImage.unit_isIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Reflective", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "CategoryTheory.mem_essImage_of_unit_isSplitMono", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Reflective", "is_tactic_proof": true, "tactics": ["let", "haveI", "have", "refine", "rw", "apply", "haveI", "exact"], "tactic_count": 8}
{"name": "CategoryTheory.Reflective.comp", "kind": "instance", "module": "Mathlib.CategoryTheory.Adjunction.Reflective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.unitCompPartialBijectiveAux", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Reflective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.unitCompPartialBijectiveAux_symm_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Reflective", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.unitCompPartialBijective", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Reflective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.unitCompPartialBijective_symm_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Reflective", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.unitCompPartialBijective_symm_natural", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Reflective", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.unitCompPartialBijective_natural", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Reflective", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.instIsIsoAppUnitReflectorAdjunctionObjEssImage", "kind": "instance", "module": "Mathlib.CategoryTheory.Adjunction.Reflective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.equivEssImageOfReflective", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Reflective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.coreflector", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Reflective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.coreflectorAdjunction", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Reflective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instIsLeftAdjointOfCoreflective", "kind": "instance", "module": "Mathlib.CategoryTheory.Adjunction.Reflective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instIsRightAdjointCoreflector", "kind": "instance", "module": "Mathlib.CategoryTheory.Adjunction.Reflective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.fullyFaithfulOfCoreflective", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Reflective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.counit_obj_eq_map_counit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Reflective", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "CategoryTheory._example", "kind": "example", "module": "Mathlib.CategoryTheory.Adjunction.Reflective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.essImage.counit_isIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Reflective", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "CategoryTheory.mem_essImage_of_counit_isSplitEpi", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Reflective", "is_tactic_proof": true, "tactics": ["let", "haveI", "have", "refine", "rw", "apply", "haveI", "exact"], "tactic_count": 8}
{"name": "CategoryTheory.Coreflective.comp", "kind": "instance", "module": "Mathlib.CategoryTheory.Adjunction.Reflective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.restrictFullyFaithful", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.map_restrictFullyFaithful_unit_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Restrict", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Adjunction.map_restrictFullyFaithful_counit_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Restrict", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Adjunction.restrictFullyFaithful_homEquiv_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Restrict", "is_tactic_proof": true, "tactics": ["apply", "simp", "assoc,", "congr", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.Adjunction.Triple.isIso_unit_iff_isIso_counit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Triple", "is_tactic_proof": true, "tactics": ["let", "constructor", "intro", "let", "exact", "intro", "let", "exact"], "tactic_count": 8}
{"name": "CategoryTheory.Adjunction.Triple.fullyFaithfulEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Triple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.Triple.op", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Triple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.Triple.rightToLeft", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Triple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.Triple.whiskerRight_rightToLeft", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Triple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.Triple.map_rightToLeft_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Triple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.Triple.rightToLeft_eq_units", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Triple", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Adjunction.Triple.rightToLeft_eq_counits", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Triple", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Adjunction.Triple.adj₁_counit_app_rightToLeft_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Triple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.Triple.rightToLeft_app_adj₂_unit_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Triple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.Triple.op_rightToLeft", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Triple", "is_tactic_proof": true, "tactics": ["ext", "rw", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.Adjunction.Triple.epi_rightToLeft_app_iff_epi_map_adj₁_unit_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Triple", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Adjunction.Triple.epi_rightToLeft_app_iff_epi_map_adj₂_counit_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Triple", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Adjunction.Triple.epi_rightToLeft_app_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Triple", "is_tactic_proof": true, "tactics": ["have", "refine", "rw", "simpa"], "tactic_count": 4}
{"name": "CategoryTheory.Adjunction.Triple.leftToRight", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Triple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.Triple.leftToRight_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Triple", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Adjunction.Triple.leftToRight_eq_counits", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Triple", "is_tactic_proof": true, "tactics": ["ext", "rw", "refine", "rw", "simp"], "tactic_count": 5}
{"name": "CategoryTheory.Adjunction.Triple.leftToRight_app_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Triple", "is_tactic_proof": true, "tactics": ["refine", "rw", "congr", "simpa"], "tactic_count": 4}
{"name": "CategoryTheory.Adjunction.Triple.whiskerLeft_leftToRight", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Triple", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Adjunction.Triple.map_adj₂_counit_app_leftToRight_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Triple", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Adjunction.Triple.leftToRight_app_map_adj₁_unit_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Triple", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Adjunction.Triple.leftToRight_op", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Triple", "is_tactic_proof": true, "tactics": ["ext", "rw", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.Adjunction.Triple.mono_leftToRight_app_iff_mono_adj₂_unit_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Triple", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Adjunction.Triple.mono_leftToRight_app_iff_mono_adj₁_counit_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Triple", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Adjunction.Triple.mono_leftToRight_app_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Triple", "is_tactic_proof": true, "tactics": ["refine", "rw", "simpa"], "tactic_count": 3}
{"name": "CategoryTheory.Adjunction.leftAdjointUniq", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Unique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.homEquiv_leftAdjointUniq_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Unique", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Adjunction.unit_leftAdjointUniq_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Unique", "is_tactic_proof": true, "tactics": ["ext", "rw", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.Adjunction.unit_leftAdjointUniq_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Unique", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Adjunction.leftAdjointUniq_hom_counit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Unique", "is_tactic_proof": true, "tactics": ["ext", "simp", "rw", "simp"], "tactic_count": 4}
{"name": "CategoryTheory.Adjunction.leftAdjointUniq_hom_app_counit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Unique", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "CategoryTheory.Adjunction.leftAdjointUniq_inv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Unique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.leftAdjointUniq_trans", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Unique", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Adjunction.leftAdjointUniq_trans_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Unique", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "CategoryTheory.Adjunction.leftAdjointUniq_refl", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Unique", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Adjunction.rightAdjointUniq", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Unique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.homEquiv_symm_rightAdjointUniq_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Unique", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Adjunction.unit_rightAdjointUniq_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Unique", "is_tactic_proof": false, "tactics": ["simp", "conjugateEquiv_apply_app,", "rw", "simp"], "tactic_count": 4}
{"name": "CategoryTheory.Adjunction.unit_rightAdjointUniq_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Unique", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Adjunction.rightAdjointUniq_hom_app_counit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Unique", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Adjunction.rightAdjointUniq_hom_counit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Unique", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Adjunction.rightAdjointUniq_inv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Unique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.rightAdjointUniq_trans", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Unique", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Adjunction.rightAdjointUniq_trans_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Unique", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "CategoryTheory.Adjunction.rightAdjointUniq_refl", "kind": "theorem", "module": "Mathlib.CategoryTheory.Adjunction.Unique", "is_tactic_proof": true, "tactics": ["delta", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Adjunction.whiskerRight", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Whiskering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.whiskerLeft", "kind": "definition", "module": "Mathlib.CategoryTheory.Adjunction.Whiskering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isIso_of_mono_of_epi", "kind": "theorem", "module": "Mathlib.CategoryTheory.Balanced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isIso_iff_mono_and_epi", "kind": "theorem", "module": "Mathlib.CategoryTheory.Balanced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.balanced_opposite", "kind": "instance", "module": "Mathlib.CategoryTheory.Balanced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.Adj.mk_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Adj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.Adj.instCategoryStruct", "kind": "instance", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Adj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.Adj.Hom₂.conjugateEquiv_symm_τr", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Adj", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Bicategory.Adj.instCategoryStructHom", "kind": "instance", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Adj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.Adj.hom₂_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Adj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.Adj.instCategoryHom", "kind": "instance", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Adj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.Adj.Bicategory.associator", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Adj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.Adj.Bicategory.leftUnitor", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Adj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.Adj.Bicategory.rightUnitor", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Adj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.Adj.Bicategory.whiskerLeft", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Adj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.Adj.Bicategory.whiskerRight", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Adj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.Adj.inst", "kind": "instance", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Adj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.Adj.forget₁", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Adj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.Adj.lIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Adj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.Adj.rIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Adj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.leftZigzag", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.rightZigzag", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.rightZigzag_idempotent_of_left_triangle", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "calc", "bicategory", "bicategory"], "tactic_count": 4}
{"name": "CategoryTheory.Bicategory.term_⊣_", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory._aux_Mathlib_CategoryTheory_Bicategory_Adjunction_Basic___macroRules_CategoryTheory_Bicategory_term_⊣__1", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory._aux_Mathlib_CategoryTheory_Bicategory_Adjunction_Basic___unexpand_CategoryTheory_Bicategory_Adjunction_1", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.Adjunction.id", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.Adjunction.instInhabitedId", "kind": "instance", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.Adjunction.compUnit", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.Adjunction.compCounit", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.Adjunction.comp_left_triangle_aux", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Basic", "is_tactic_proof": true, "tactics": ["calc", "adj₁.unit", "f₁", "rw"], "tactic_count": 4}
{"name": "CategoryTheory.Bicategory.Adjunction.comp_right_triangle_aux", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Basic", "is_tactic_proof": true, "tactics": ["calc", "g₂", "rw"], "tactic_count": 3}
{"name": "CategoryTheory.Bicategory.Adjunction.comp", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.leftZigzagIso", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.rightZigzagIso", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.leftZigzagIso_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.rightZigzagIso_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.leftZigzagIso_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Bicategory.rightZigzagIso_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Bicategory.leftZigzagIso_symm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.rightZigzagIso_symm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.instIsIsoHomLeftZigzagHom", "kind": "instance", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.instIsIsoHomRightZigzagHom", "kind": "instance", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.right_triangle_of_left_triangle", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Basic", "is_tactic_proof": true, "tactics": ["rw", "calc"], "tactic_count": 2}
{"name": "CategoryTheory.Bicategory.adjointifyCounit", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.adjointifyCounit_left_triangle", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Basic", "is_tactic_proof": true, "tactics": ["apply", "dsimp", "calc", "rw"], "tactic_count": 4}
{"name": "CategoryTheory.Bicategory.term_≌_", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory._aux_Mathlib_CategoryTheory_Bicategory_Adjunction_Basic___macroRules_CategoryTheory_Bicategory_term_≌__1", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory._aux_Mathlib_CategoryTheory_Bicategory_Adjunction_Basic___unexpand_CategoryTheory_Bicategory_Equivalence_1", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.Equivalence.id", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.Equivalence.instInhabited", "kind": "instance", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.Equivalence.left_triangle_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.Equivalence.right_triangle", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.Equivalence.right_triangle_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.Equivalence.mkOfAdjointifyCounit", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.IsLeftAdjoint.mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.getRightAdjoint", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.rightAdjoint", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.Adjunction.ofIsLeftAdjoint", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.IsRightAdjoint.mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.getLeftAdjoint", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.leftAdjoint", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.Adjunction.ofIsRightAdjoint", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.Adjunction.ofCat_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.Adjunction.ofCat_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Cat", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Bicategory.toNatTrans_mateEquiv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Cat", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Bicategory.toNatTrans_conjugateEquiv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Cat", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "ext", "simp"], "tactic_count": 4}
{"name": "CategoryTheory.Bicategory.Adjunction.homEquiv₁", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Mate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.Adjunction.homEquiv₂", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Mate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.mateEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Mate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.mateEquiv_eq_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Mate", "is_tactic_proof": true, "tactics": ["conv_lhs", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.Bicategory.mateEquiv_apply'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Mate", "is_tactic_proof": true, "tactics": ["rw", "bicategory"], "tactic_count": 2}
{"name": "CategoryTheory.Bicategory.mateEquiv_symm_apply'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Mate", "is_tactic_proof": true, "tactics": ["rw", "bicategory"], "tactic_count": 2}
{"name": "CategoryTheory.Bicategory.mateEquiv_id_comp_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Mate", "is_tactic_proof": true, "tactics": ["simp", "dsimp", "bicategory"], "tactic_count": 3}
{"name": "CategoryTheory.Bicategory.mateEquiv_comp_id_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Mate", "is_tactic_proof": true, "tactics": ["simp", "dsimp", "bicategory"], "tactic_count": 3}
{"name": "CategoryTheory.Bicategory.leftAdjointSquare.vcomp", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Mate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.rightAdjointSquare.vcomp", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Adjunction.Mate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Bicategory.pentagon_inv_inv_hom_hom_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
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{"name": "CategoryTheory.Bicategory.triangle_assoc_comp_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Bicategory.triangle_assoc_comp_right_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Bicategory.triangle_assoc_comp_left_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Bicategory.associator_naturality_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Bicategory.associator_inv_naturality_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Bicategory.whiskerRight_comp_symm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "CategoryTheory.Bicategory.associator_inv_naturality_middle", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Bicategory.whisker_assoc_symm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Bicategory.associator_naturality_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Bicategory.associator_inv_naturality_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "CategoryTheory.Pseudofunctor.mapId'_eq_mapId", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Functor.Pseudofunctor", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Pseudofunctor.mapComp'_eq_mapComp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Functor.Pseudofunctor", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "CategoryTheory.StrictPseudofunctor.mk''", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Functor.StrictPseudofunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.StrictlyUnitaryPseudofunctor.toStrictlyUnitaryLaxFunctor_mapId", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Functor.StrictlyUnitary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StrictlyUnitaryPseudofunctor.id", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Functor.StrictlyUnitary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Bicategory.LeftExtension.IsKan.hasLeftKanExtension", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Kan.HasKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.instHasInitialLeftExtensionOfHasLeftKanExtension", "kind": "instance", "module": "Mathlib.CategoryTheory.Bicategory.Kan.HasKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.lanLeftExtension", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Kan.HasKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.lan", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Kan.HasKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.term_⁺_", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Kan.HasKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory._aux_Mathlib_CategoryTheory_Bicategory_Kan_HasKan___macroRules_CategoryTheory_Bicategory_term_⁺__1", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Kan.HasKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory._aux_Mathlib_CategoryTheory_Bicategory_Kan_HasKan___unexpand_CategoryTheory_Bicategory_lan_1", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Kan.HasKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.lanLeftExtension_extension", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Kan.HasKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.lanUnit", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Kan.HasKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.lanLeftExtension_unit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Kan.HasKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.lanIsKan", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Kan.HasKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.lanDesc", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Kan.HasKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.lanUnit_desc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Kan.HasKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.lanIsKan_desc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Kan.HasKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.Lan.existsUnique", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Kan.HasKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.Lan.CommuteWith.of_isKan_whisker", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Kan.HasKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.Lan.CommuteWith.of_lan_comp_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Kan.HasKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.Lan.CommuteWith.isKan", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Kan.HasKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.Lan.CommuteWith.instHasLeftKanExtensionComp", "kind": "instance", "module": "Mathlib.CategoryTheory.Bicategory.Kan.HasKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.Lan.CommuteWith.isKanWhisker", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Kan.HasKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.Lan.CommuteWith.lanCompIsoWhisker", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Kan.HasKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.Lan.CommuteWith.lanCompIsoWhisker_hom_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Kan.HasKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.Lan.CommuteWith.lanCompIsoWhisker_inv_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Kan.HasKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.Lan.CommuteWith.lanCompIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Kan.HasKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.instCommuteWith", "kind": "instance", "module": "Mathlib.CategoryTheory.Bicategory.Kan.HasKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.LeftExtension.IsAbsKan.hasAbsLeftKanExtension", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Kan.HasKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.LeftLift.IsKan.hasLeftKanLift", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Kan.HasKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.instHasInitialLeftLiftOfHasLeftKanLift", "kind": "instance", "module": "Mathlib.CategoryTheory.Bicategory.Kan.HasKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.lanLiftLeftLift", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Kan.HasKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.lanLift", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Kan.HasKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.term_₊_", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Kan.HasKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory._aux_Mathlib_CategoryTheory_Bicategory_Kan_HasKan___macroRules_CategoryTheory_Bicategory_term_₊__1", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Kan.HasKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory._aux_Mathlib_CategoryTheory_Bicategory_Kan_HasKan___unexpand_CategoryTheory_Bicategory_lanLift_1", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Kan.HasKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.lanLiftLeftLift_lift", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Kan.HasKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.lanLiftUnit", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Kan.HasKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.lanLiftLeftLift_unit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Kan.HasKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.lanLiftIsKan", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Kan.HasKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.lanLiftDesc", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Kan.HasKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.lanLiftUnit_desc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Kan.HasKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.lanLiftIsKan_desc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Kan.HasKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.LanLift.existsUnique", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Kan.HasKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.LanLift.CommuteWith.of_isKan_whisker", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Kan.HasKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.LanLift.CommuteWith.of_lanLift_comp_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Kan.HasKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.LanLift.CommuteWith.isKan", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Kan.HasKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.LanLift.CommuteWith.instHasLeftKanLiftComp", "kind": "instance", "module": "Mathlib.CategoryTheory.Bicategory.Kan.HasKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.LanLift.CommuteWith.isKanWhisker", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Kan.HasKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.LanLift.CommuteWith.lanLiftCompIsoWhisker", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Kan.HasKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.LanLift.CommuteWith.lanLiftCompIsoWhisker_hom_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Kan.HasKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.LanLift.CommuteWith.lanLiftCompIsoWhisker_inv_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Kan.HasKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.LanLift.CommuteWith.lanLiftCompIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Kan.HasKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.instCommuteWith_1", "kind": "instance", "module": "Mathlib.CategoryTheory.Bicategory.Kan.HasKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.LeftLift.IsAbsKan.hasAbsLeftKanLift", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Kan.HasKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.LeftExtension.IsKan", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Bicategory.Kan.IsKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.LeftExtension.IsAbsKan", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Bicategory.Kan.IsKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.LeftExtension.IsKan.mk", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Bicategory.Kan.IsKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.LeftExtension.IsKan.desc", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Bicategory.Kan.IsKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.LeftExtension.IsKan.fac", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Kan.IsKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.LeftExtension.IsKan.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Kan.IsKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.LeftExtension.IsKan.uniqueUpToIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Kan.IsKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.LeftExtension.IsKan.uniqueUpToIso_hom_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Kan.IsKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.LeftExtension.IsKan.uniqueUpToIso_inv_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Kan.IsKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.LeftExtension.IsKan.ofIsoKan", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Kan.IsKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.LeftExtension.IsKan.ofCompId", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Kan.IsKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.LeftExtension.IsKan.whiskerOfCommute", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Kan.IsKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.LeftExtension.IsAbsKan.desc", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Bicategory.Kan.IsKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.LeftExtension.IsAbsKan.isKan", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Kan.IsKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.LeftExtension.IsAbsKan.ofIsoAbsKan", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Kan.IsKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.LeftLift.IsKan", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Bicategory.Kan.IsKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.LeftLift.IsAbsKan", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Bicategory.Kan.IsKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.LeftLift.IsKan.mk", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Bicategory.Kan.IsKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.LeftLift.IsKan.desc", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Bicategory.Kan.IsKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.LeftLift.IsKan.fac", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Kan.IsKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.LeftLift.IsKan.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Kan.IsKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.LeftLift.IsKan.uniqueUpToIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Kan.IsKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.LeftLift.IsKan.uniqueUpToIso_hom_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Kan.IsKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.LeftLift.IsKan.uniqueUpToIso_inv_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Kan.IsKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.LeftLift.IsKan.ofIsoKan", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Kan.IsKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.LeftLift.IsKan.ofIdComp", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Kan.IsKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.LeftLift.IsKan.whiskerOfCommute", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Kan.IsKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.LeftLift.IsAbsKan.desc", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Bicategory.Kan.IsKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.LeftLift.IsAbsKan.isKan", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Kan.IsKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.LeftLift.IsAbsKan.ofIsoAbsKan", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.Kan.IsKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.RightExtension.IsKan", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Bicategory.Kan.IsKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.RightLift.IsKan", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Bicategory.Kan.IsKan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocallyDiscrete.mk_as", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.LocallyDiscrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocallyDiscrete.locallyDiscreteEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.LocallyDiscrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocallyDiscrete.instDecidableEq", "kind": "instance", "module": "Mathlib.CategoryTheory.Bicategory.LocallyDiscrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocallyDiscrete.instInhabited", "kind": "instance", "module": "Mathlib.CategoryTheory.Bicategory.LocallyDiscrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocallyDiscrete.categoryStruct", "kind": "instance", "module": "Mathlib.CategoryTheory.Bicategory.LocallyDiscrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocallyDiscrete.id_as", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.LocallyDiscrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocallyDiscrete.comp_as", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.LocallyDiscrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocallyDiscrete.homSmallCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Bicategory.LocallyDiscrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocallyDiscrete.subsingleton2Hom", "kind": "instance", "module": "Mathlib.CategoryTheory.Bicategory.LocallyDiscrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocallyDiscrete.eq_of_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.LocallyDiscrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.locallyDiscreteBicategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Bicategory.LocallyDiscrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.locallyDiscreteBicategory.strict", "kind": "instance", "module": "Mathlib.CategoryTheory.Bicategory.LocallyDiscrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.IsLocallyDiscrete", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Bicategory.LocallyDiscrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.instIsLocallyDiscreteLocallyDiscrete", "kind": "instance", "module": "Mathlib.CategoryTheory.Bicategory.LocallyDiscrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.instStrictOfIsLocallyDiscrete", "kind": "instance", "module": "Mathlib.CategoryTheory.Bicategory.LocallyDiscrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.Hom.toLoc", "kind": "definition", "module": "Mathlib.CategoryTheory.Bicategory.LocallyDiscrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.Hom.id_toLoc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.LocallyDiscrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.Hom.comp_toLoc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.LocallyDiscrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocallyDiscrete.eqToHom_toLoc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.LocallyDiscrete", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "CategoryTheory.CommSq.toLoc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.LocallyDiscrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.IsLocallyGroupoid", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Bicategory.LocallyGroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.Pith.mk_as", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.LocallyGroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bicategory.Pith.instInhabited", "kind": "instance", "module": "Mathlib.CategoryTheory.Bicategory.LocallyGroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Pseudofunctor.mapComp'₀₁₃_hom_comp_whiskerLeft_mapComp'_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Strict.Pseudofunctor", "is_tactic_proof": true, "tactics": ["subst", "simp"], "tactic_count": 2}
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{"name": "CategoryTheory.Pseudofunctor.mapComp'₀₂₃_hom_comp_mapComp'_hom_whiskerRight", "kind": "theorem", "module": "Mathlib.CategoryTheory.Bicategory.Strict.Pseudofunctor", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
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{"name": "pointedToBipointedSnd_comp_swap", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.Bipointed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pointedToBipointedCompBipointedToPointedFst", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.Bipointed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pointedToBipointedCompBipointedToPointedSnd", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.Bipointed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pointedToBipointedFstBipointedToPointedFstAdjunction", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.Bipointed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pointedToBipointedSndBipointedToPointedSndAdjunction", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.Bipointed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.instInhabited", "kind": "instance", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.instCoeSortType", "kind": "instance", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.str", "kind": "instance", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.of", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.instQuiver", "kind": "instance", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.toCatHom", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.equivCatHom", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.Hom.equivFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.Hom.instQuiver", "kind": "instance", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.toCatHom₂", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.Hom.instCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.toCatHom₂_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.toCatHom₂_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.Hom.toNatTrans_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.Hom.toNatTrans_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.Hom₂.ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.Hom.isoMk", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.Hom.toNatIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.Hom.isoMk_toNatIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.Hom.toNatIso_isoMk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.Hom.instIsIsoFunctorαCategoryToNatTransHomHom", "kind": "instance", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.Hom.instIsIsoFunctorαCategoryToNatTransInvHom", "kind": "instance", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.Hom.hom_inv_id_toNatTrans", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.Hom.inv_hom_id_toNatTrans", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.Hom.hom_inv_id_toNatTrans_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.Hom.inv_hom_id_toNatTrans_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.bicategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.bicategory.strict", "kind": "instance", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.category", "kind": "instance", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.Hom.id_toFunctor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.Hom.id_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Cat.Hom.id_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Cat.Hom.comp_toFunctor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.Hom.comp_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Cat.Hom.comp_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Cat.Hom₂.id_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Cat.Hom₂.comp_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.Hom₂.eqToHom_toNatTrans", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "CategoryTheory.Cat.eqToHom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Cat.whiskerLeft_toNatTrans", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.whiskerLeft_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Cat.whiskerRight_toNatTrans", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.whiskerRight_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Cat.Hom.toNatIso_leftUnitor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.leftUnitor_hom_toNatTrans", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.leftUnitor_inv_toNatTrans", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.leftUnitor_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Cat.leftUnitor_inv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Cat.Hom.toNatIso_rightUnitor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Cat.rightUnitor_hom_toNatTrans", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.rightUnitor_inv_toNatTrans", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.rightUnitor_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Cat.rightUnitor_inv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Cat.Hom.toNatIso_associator", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.associator_hom_toNatTrans", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.associator_inv_toNatTrans", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.associator_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Cat.associator_inv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Cat.id_eq_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.comp_eq_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.of_α", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.coe_of", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.objects", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.instCategoryObjObjects", "kind": "instance", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.equivOfIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.typeToCat", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instFaithfulCatTypeToCat", "kind": "instance", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instFullCatTypeToCat", "kind": "instance", "module": "Mathlib.CategoryTheory.Category.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.CategoryTheory.Category.Cat.Adjunction.0.CategoryTheory.Cat.typeToCatObjectsAdjHomEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.Cat.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.CategoryTheory.Category.Cat.Adjunction.0.CategoryTheory.Cat.typeToCatObjectsAdjCounitApp", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.Cat.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.typeToCatObjectsAdj", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.Cat.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.connectedComponents", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.Cat.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.connectedComponentsTypeToCatAdj", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.Cat.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.asSmallFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.Cat.AsSmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.exp", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.Cat.CartesianClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.curryingIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.Cat.CartesianClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.flippingIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.Cat.CartesianClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.closed", "kind": "instance", "module": "Mathlib.CategoryTheory.Category.Cat.CartesianClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.cartesianClosed", "kind": "instance", "module": "Mathlib.CategoryTheory.Category.Cat.CartesianClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.ihom_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.Cat.CartesianClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.ihom_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.Cat.CartesianClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.instHasColimits", "kind": "instance", "module": "Mathlib.CategoryTheory.Category.Cat.Colimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.HasLimits.categoryObjects", "kind": "instance", "module": "Mathlib.CategoryTheory.Category.Cat.Limit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.HasLimits.homDiagram", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.Cat.Limit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.HasLimits.instCategoryLimitCompObjects", "kind": "instance", "module": "Mathlib.CategoryTheory.Category.Cat.Limit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.HasLimits.limitConeX", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.Cat.Limit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.HasLimits.limitCone", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.Cat.Limit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.HasLimits.limitConeLift", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.Cat.Limit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.HasLimits.limit_π_homDiagram_eqToHom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.Cat.Limit", "is_tactic_proof": true, "tactics": ["subst", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Cat.HasLimits.limitConeIsLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.Cat.Limit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.instHasLimits", "kind": "instance", "module": "Mathlib.CategoryTheory.Category.Cat.Limit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.instPreservesLimitsObjects", "kind": "instance", "module": "Mathlib.CategoryTheory.Category.Cat.Limit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.opFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.Cat.Op", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.opFunctorInvolutive", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.Cat.Op", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.opEquivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.Cat.Op", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.isTerminalOfUniqueOfIsDiscrete", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.Cat.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.instHasTerminal", "kind": "instance", "module": "Mathlib.CategoryTheory.Category.Cat.Terminal", "is_tactic_proof": false, "tactics": ["have", "eq_of_hom", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Cat.terminalIsoOfUniqueOfIsDiscrete", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.Cat.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.isTerminalDiscretePUnit", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.Cat.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.isoDiscretePUnitOfIsTerminal", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.Cat.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Factorisation.Hom.id", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.Factorisation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Factorisation.Hom.comp", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.Factorisation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Factorisation.instCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Category.Factorisation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Factorisation.initial", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.Factorisation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Factorisation.initialHom", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.Factorisation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Factorisation.instUniqueHomInitial", "kind": "instance", "module": "Mathlib.CategoryTheory.Category.Factorisation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Factorisation.terminal", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.Factorisation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Factorisation.terminalHom", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.Factorisation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Factorisation.instUniqueHomTerminal", "kind": "instance", "module": "Mathlib.CategoryTheory.Category.Factorisation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Factorisation.IsInitial_initial", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.Factorisation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Factorisation.instHasInitial", "kind": "instance", "module": "Mathlib.CategoryTheory.Category.Factorisation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Factorisation.IsTerminal_terminal", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.Factorisation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Factorisation.instHasTerminal", "kind": "instance", "module": "Mathlib.CategoryTheory.Category.Factorisation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Quiv.lift", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.Quiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Quiv.pathCompositionNaturality", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.Quiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Quiv.pathComposition_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.Quiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Quiv.pathsOf_freeMap_toPrefunctor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.Quiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Quiv.freeMapPathsOfCompPathCompositionIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.Quiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Quiv.freeMap_pathsOf_pathComposition", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.Quiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Quiv.pathsOf_pathComposition_toPrefunctor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.Quiv", "is_tactic_proof": true, "tactics": ["dsimp", "congr", "funext", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.Quiv.adj", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.Quiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Quiv.pathsEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.Quiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Quiv.adj_homEquiv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.Quiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ReflQuiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ReflQuiv.instCoeSortType", "kind": "instance", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ReflQuiv.instReflQuiverα", "kind": "instance", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ReflQuiv.toQuiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ReflQuiv.of", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ReflQuiv.instInhabited", "kind": "instance", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ReflQuiv.of_val", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ReflQuiv.category", "kind": "instance", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ReflQuiv.id_eq_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ReflQuiv.comp_eq_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ReflQuiv.id_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ReflQuiv.id_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ReflQuiv.comp_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ReflQuiv.comp_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ReflQuiv.forget", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ReflQuiv.forget_faithful", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "CategoryTheory.ReflQuiv.forget.Faithful", "kind": "instance", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ReflQuiv.forgetToQuiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ReflQuiv.forgetToQuiv_faithful", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "CategoryTheory.ReflQuiv.forgetToQuiv.Faithful", "kind": "instance", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ReflQuiv.forget_forgetToQuiv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ReflQuiv.isoOfQuivIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ReflQuiv.isoOfEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ReflPrefunctor.toFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.FreeReflRel", "kind": "inductive", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.FreeRefl", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.FreeRefl.instCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.FreeRefl.mk", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.FreeRefl.induction", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.FreeRefl.quotientFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.FreeRefl.instFullPathsQuotientFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.FreeRefl.homMk", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.FreeRefl.homMk_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.FreeRefl.quotientFunctor_map_nil", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.FreeRefl.quotientFunctor_map_cons", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.FreeRefl.morphismPropertyHomMk", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.FreeRefl.morphismPropertyHomMk_homMk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Cat.FreeRefl.hom_induction", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": false, "tactics": ["induction", "induction", "obtain", "induction", "nil", "cons"], "tactic_count": 6}
{"name": "CategoryTheory.Cat.FreeRefl.multiplicativeClosure_morphismPropertyHomMk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.FreeRefl.morphismProperty_eq_top", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.FreeRefl.lift", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.FreeRefl.lift_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.FreeRefl.lift_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.FreeRefl.lift'", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.FreeRefl.lift'_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.FreeRefl.lift'_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Cat.FreeRefl.lift_unique'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.FreeRefl.functor_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.FreeRefl.quotientFunctor_map_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.FreeRefl.instUnique", "kind": "instance", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.FreeRefl.instUniqueHom", "kind": "instance", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.FreeRefl.instSubsingletonHomOfUnique", "kind": "instance", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.toFreeRefl", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.FreeRefl.lift_spec", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.freeReflMap", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.freeReflMap_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.freeReflMap_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.freeReflMap_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.freeRefl", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.freeReflNatTrans", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ReflQuiv.adj.homEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ReflQuiv.adj.homEquiv_naturality_left_symm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ReflQuiv.adj.homEquiv_naturality_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ReflQuiv.adj", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ReflQuiv.adj_unit_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ReflQuiv.adj_counit_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ReflQuiv.adj_homEquiv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": true, "tactics": ["ext", "apply"], "tactic_count": 2}
{"name": "CategoryTheory.ReflQuiv.adj.unit.map_app_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ReflQuiv.adj.counit.comp_app_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.ReflQuiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.RelCat", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.RelCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.RelCat.inhabited", "kind": "instance", "module": "Mathlib.CategoryTheory.Category.RelCat", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "CategoryTheory.RelCat.instLargeCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Category.RelCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.RelCat.Hom.ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.RelCat", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "CategoryTheory.RelCat.Hom.rel_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.RelCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.RelCat.Hom.rel_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.RelCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.RelCat.Hom.rel_id_apply₂", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.RelCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.RelCat.Hom.rel_comp_apply₂", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.RelCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.RelCat.graphFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.RelCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.RelCat.graphFunctor_faithful", "kind": "instance", "module": "Mathlib.CategoryTheory.Category.RelCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.RelCat.graphFunctor_essSurj", "kind": "instance", "module": "Mathlib.CategoryTheory.Category.RelCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.RelCat.rel_iso_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.RelCat", "is_tactic_proof": true, "tactics": ["constructor", "intro", "have", "have", "simp", "obtain", "obtain", "suffices", "use", "ext", "exact", "use", "constructor", "ext", "apply", "use", "ext", "apply", "use", "rintro", "apply"], "tactic_count": 21}
{"name": "CategoryTheory.RelCat.opFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.RelCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.RelCat.unopFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.RelCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.RelCat.opFunctor_comp_unopFunctor_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.RelCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.RelCat.unopFunctor_comp_opFunctor_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.RelCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.RelCat.opEquivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.RelCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.RelCat.instIsEquivalenceOppositeOpFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.Category.RelCat", "is_tactic_proof": true, "tactics": ["change", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.RelCat.instIsEquivalenceOppositeUnopFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.Category.RelCat", "is_tactic_proof": true, "tactics": ["change", "infer_instance"], "tactic_count": 2}
{"name": "TwoP.instCoeSortType", "kind": "instance", "module": "Mathlib.CategoryTheory.Category.TwoP", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoP.of", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Category.TwoP", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoP.coe_of", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.TwoP", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoP.instInhabited", "kind": "instance", "module": "Mathlib.CategoryTheory.Category.TwoP", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoP.toBipointed", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.TwoP", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoP.coe_toBipointed", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.TwoP", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoP.largeCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Category.TwoP", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoP.concreteCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Category.TwoP", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoP.hasForgetToBipointed", "kind": "instance", "module": "Mathlib.CategoryTheory.Category.TwoP", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoP.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.TwoP", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoP.swap", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.TwoP", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoP.swapEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.TwoP", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoP.swapEquiv_symm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.TwoP", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoP_swap_comp_forget_to_Bipointed", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.TwoP", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pointedToTwoPFst", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.TwoP", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pointedToTwoPSnd", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.TwoP", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pointedToTwoPFst_comp_swap", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.TwoP", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pointedToTwoPSnd_comp_swap", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.TwoP", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pointedToTwoPFst_comp_forget_to_bipointed", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.TwoP", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pointedToTwoPSnd_comp_forget_to_bipointed", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.TwoP", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pointedToTwoPFstForgetCompBipointedToPointedFstAdjunction", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.TwoP", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pointedToTwoPSndForgetCompBipointedToPointedSndAdjunction", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.TwoP", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ULift.upFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ULift.downFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ULift.equivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ULiftHom", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instInhabitedULiftHom", "kind": "instance", "module": "Mathlib.CategoryTheory.Category.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ULiftHom.objDown", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ULiftHom.objUp", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ULiftHom.objEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.objDown_objUp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.objUp_objDown", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ULiftHom.category", "kind": "instance", "module": "Mathlib.CategoryTheory.Category.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ULiftHom.up", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ULiftHom.down", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ULiftHom.equiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.AsSmall", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instSmallCategoryAsSmall", "kind": "instance", "module": "Mathlib.CategoryTheory.Category.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.AsSmall.up", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.AsSmall.down", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.down_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.eqToHom_down", "kind": "theorem", "module": "Mathlib.CategoryTheory.Category.ULift", "is_tactic_proof": true, "tactics": ["subst", "rfl"], "tactic_count": 2}
{"name": "CategoryTheory.AsSmall.equiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instInhabitedAsSmall", "kind": "instance", "module": "Mathlib.CategoryTheory.Category.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ULiftHomULiftCategory.objEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ULiftHomULiftCategory.equiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ULiftHomULiftCategory.equivCongrLeft", "kind": "definition", "module": "Mathlib.CategoryTheory.Category.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CatCenter", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Center.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CatCenter.app", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Center.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CatCenter.ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Center.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CatCenter.naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Center.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CatCenter.mul_app'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Center.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CatCenter.mul_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Center.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.CatCenter.instIsMulCommutative", "kind": "instance", "module": "Mathlib.CategoryTheory.Center.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CatCenter.instSMulHom", "kind": "instance", "module": "Mathlib.CategoryTheory.Center.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CatCenter.smul_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Center.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CatCenter.smul_eq'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Center.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CatCenter.instSMulUnitsIso", "kind": "instance", "module": "Mathlib.CategoryTheory.Center.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CatCenter.smul_iso_hom_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Center.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CatCenter.smul_iso_hom_eq'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Center.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CatCenter.smul_iso_inv_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Center.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CatCenter.smul_iso_inv_eq'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Center.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Linear.toCatCenter", "kind": "definition", "module": "Mathlib.CategoryTheory.Center.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Linear.smulOfRingMorphism", "kind": "definition", "module": "Mathlib.CategoryTheory.Center.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Linear.smulOfRingMorphism_smul_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Center.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Linear.smulOfRingMorphism_smul_eq'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Center.Linear", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Linear.homModuleOfRingMorphism", "kind": "definition", "module": "Mathlib.CategoryTheory.Center.Linear", "is_tactic_proof": true, "tactics": ["letI", "exact", "simp", "mul_smul", "simp", "smul_zero", "zero_smul", "smul_add", "add_smul"], "tactic_count": 9}
{"name": "CategoryTheory.Linear.ofRingMorphism", "kind": "definition", "module": "Mathlib.CategoryTheory.Center.Linear", "is_tactic_proof": true, "tactics": ["letI", "exact", "comp_smul"], "tactic_count": 3}
{"name": "CategoryTheory.CatCenter.localization", "kind": "definition", "module": "Mathlib.CategoryTheory.Center.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CatCenter.localization_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Center.Localization", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.CatCenter.ext_of_localization", "kind": "theorem", "module": "Mathlib.CategoryTheory.Center.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CatCenter.localization_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Center.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CatCenter.localization_mul", "kind": "theorem", "module": "Mathlib.CategoryTheory.Center.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CatCenter.localization_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Center.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CatCenter.localization_add", "kind": "theorem", "module": "Mathlib.CategoryTheory.Center.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CatCenter.localizationRingHom", "kind": "definition", "module": "Mathlib.CategoryTheory.Center.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CatCenter.app_neg_one_zpow", "kind": "theorem", "module": "Mathlib.CategoryTheory.Center.NegOnePow", "is_tactic_proof": true, "tactics": ["obtain", "simp", "rw", "simp"], "tactic_count": 4}
{"name": "CategoryTheory.CatCenter.app_add", "kind": "theorem", "module": "Mathlib.CategoryTheory.Center.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CatCenter.app_sub", "kind": "theorem", "module": "Mathlib.CategoryTheory.Center.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CatCenter.app_neg", "kind": "theorem", "module": "Mathlib.CategoryTheory.Center.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Codiscrete.mk_as", "kind": "theorem", "module": "Mathlib.CategoryTheory.CodiscreteCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.codiscreteEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.CodiscreteCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instDecidableEqCodiscrete", "kind": "instance", "module": "Mathlib.CategoryTheory.CodiscreteCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Codiscrete.instCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.CodiscreteCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Codiscrete.functor", "kind": "definition", "module": "Mathlib.CategoryTheory.CodiscreteCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Codiscrete.invFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.CodiscreteCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Codiscrete.natTrans", "kind": "definition", "module": "Mathlib.CategoryTheory.CodiscreteCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Codiscrete.natIso", "kind": "definition", "module": "Mathlib.CategoryTheory.CodiscreteCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Codiscrete.natIsoFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.CodiscreteCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Codiscrete.functorOfFun", "kind": "definition", "module": "Mathlib.CategoryTheory.CodiscreteCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Codiscrete.oppositeEquivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.CodiscreteCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Codiscrete.functorToCat", "kind": "definition", "module": "Mathlib.CategoryTheory.CodiscreteCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Codiscrete.equivFunctorToCodiscrete", "kind": "definition", "module": "Mathlib.CategoryTheory.CodiscreteCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Codiscrete.adj", "kind": "definition", "module": "Mathlib.CategoryTheory.CodiscreteCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Codiscrete.unitApp", "kind": "definition", "module": "Mathlib.CategoryTheory.CodiscreteCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Codiscrete.counitApp", "kind": "definition", "module": "Mathlib.CategoryTheory.CodiscreteCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Codiscrete.adj_unit_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.CodiscreteCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Codiscrete.adj_counit_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.CodiscreteCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Codiscrete.left_triangle_components", "kind": "theorem", "module": "Mathlib.CategoryTheory.CodiscreteCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Codiscrete.right_triangle_components", "kind": "theorem", "module": "Mathlib.CategoryTheory.CodiscreteCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nonempty_sections_of_finite_cofiltered_system.init", "kind": "theorem", "module": "Mathlib.CategoryTheory.CofilteredSystem", "is_tactic_proof": true, "tactics": ["let", "haveI", "haveI", "haveI", "obtain", "exact"], "tactic_count": 6}
{"name": "nonempty_sections_of_finite_cofiltered_system", "kind": "theorem", "module": "Mathlib.CategoryTheory.CofilteredSystem", "is_tactic_proof": true, "tactics": ["let", "let", "let", "haveI", "haveI", "cases", "fconstructor", "haveI", "obtain", "use", "intro", "have", "simp", "simp_rw"], "tactic_count": 14}
{"name": "nonempty_sections_of_finite_inverse_system", "kind": "theorem", "module": "Mathlib.CategoryTheory.CofilteredSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.eventualRange", "kind": "definition", "module": "Mathlib.CategoryTheory.CofilteredSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mem_eventualRange_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.CofilteredSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsMittagLeffler", "kind": "definition", "module": "Mathlib.CategoryTheory.CofilteredSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isMittagLeffler_iff_eventualRange", "kind": "theorem", "module": "Mathlib.CategoryTheory.CofilteredSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsMittagLeffler.subset_image_eventualRange", "kind": "theorem", "module": "Mathlib.CategoryTheory.CofilteredSystem", "is_tactic_proof": true, "tactics": ["obtain", "rw", "obtain", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.Functor.eventualRange_eq_range_precomp", "kind": "theorem", "module": "Mathlib.CategoryTheory.CofilteredSystem", "is_tactic_proof": true, "tactics": ["apply", "apply", "rw", "apply"], "tactic_count": 4}
{"name": "CategoryTheory.Functor.isMittagLeffler_of_surjective", "kind": "theorem", "module": "Mathlib.CategoryTheory.CofilteredSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.toPreimages", "kind": "definition", "module": "Mathlib.CategoryTheory.CofilteredSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.toPreimages_finite", "kind": "instance", "module": "Mathlib.CategoryTheory.CofilteredSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.eventualRange_mapsTo", "kind": "theorem", "module": "Mathlib.CategoryTheory.CofilteredSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsMittagLeffler.eq_image_eventualRange", "kind": "theorem", "module": "Mathlib.CategoryTheory.CofilteredSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.eventualRange_eq_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.CofilteredSystem", "is_tactic_proof": true, "tactics": ["rw", "refine", "obtain", "refine", "rw", "apply"], "tactic_count": 6}
{"name": "CategoryTheory.Functor.isMittagLeffler_iff_subset_range_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.CofilteredSystem", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.IsMittagLeffler.toPreimages", "kind": "theorem", "module": "Mathlib.CategoryTheory.CofilteredSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isMittagLeffler_of_exists_finite_range", "kind": "theorem", "module": "Mathlib.CategoryTheory.CofilteredSystem", "is_tactic_proof": true, "tactics": ["intro", "obtain", "obtain", "refine", "rintro", "refine", "have", "rwa"], "tactic_count": 8}
{"name": "CategoryTheory.Functor.toEventualRanges", "kind": "definition", "module": "Mathlib.CategoryTheory.CofilteredSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.toEventualRanges_finite", "kind": "instance", "module": "Mathlib.CategoryTheory.CofilteredSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.toEventualRangesSectionsEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.CofilteredSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.surjective_toEventualRanges", "kind": "theorem", "module": "Mathlib.CategoryTheory.CofilteredSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.toEventualRanges_nonempty", "kind": "theorem", "module": "Mathlib.CategoryTheory.CofilteredSystem", "is_tactic_proof": true, "tactics": ["let", "rw", "infer_instance"], "tactic_count": 3}
{"name": "CategoryTheory.Functor.thin_diagram_of_surjective", "kind": "theorem", "module": "Mathlib.CategoryTheory.CofilteredSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.toPreimages_nonempty_of_surjective", "kind": "theorem", "module": "Mathlib.CategoryTheory.CofilteredSystem", "is_tactic_proof": true, "tactics": ["simp", "obtain", "exact", "obtain", "obtain", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.Functor.eval_section_injective_of_eventually_injective", "kind": "theorem", "module": "Mathlib.CategoryTheory.CofilteredSystem", "is_tactic_proof": true, "tactics": ["refine", "obtain", "dsimp", "rw", "rw", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.Functor.eval_section_surjective_of_surjective", "kind": "theorem", "module": "Mathlib.CategoryTheory.CofilteredSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.eventually_injective", "kind": "theorem", "module": "Mathlib.CategoryTheory.CofilteredSystem", "is_tactic_proof": true, "tactics": ["haveI", "haveI", "have", "let", "refine", "rw", "apply"], "tactic_count": 7}
{"name": "CategoryTheory.CommSq.flip", "kind": "theorem", "module": "Mathlib.CategoryTheory.CommSq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CommSq.of_arrow", "kind": "theorem", "module": "Mathlib.CategoryTheory.CommSq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CommSq.op", "kind": "theorem", "module": "Mathlib.CategoryTheory.CommSq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CommSq.unop", "kind": "theorem", "module": "Mathlib.CategoryTheory.CommSq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CommSq.vert_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.CommSq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CommSq.horiz_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.CommSq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CommSq.horiz_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.CommSq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CommSq.vert_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.CommSq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CommSq.eq_of_mono", "kind": "theorem", "module": "Mathlib.CategoryTheory.CommSq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CommSq.eq_of_epi", "kind": "theorem", "module": "Mathlib.CategoryTheory.CommSq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.map_commSq", "kind": "theorem", "module": "Mathlib.CategoryTheory.CommSq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CommSq.LiftStruct.op", "kind": "definition", "module": "Mathlib.CategoryTheory.CommSq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CommSq.LiftStruct.unop", "kind": "definition", "module": "Mathlib.CategoryTheory.CommSq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CommSq.LiftStruct.opEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.CommSq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CommSq.LiftStruct.unopEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.CommSq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CommSq.subsingleton_liftStruct_of_epi", "kind": "instance", "module": "Mathlib.CategoryTheory.CommSq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CommSq.subsingleton_liftStruct_of_mono", "kind": "instance", "module": "Mathlib.CategoryTheory.CommSq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CommSq.HasLift.mk'", "kind": "theorem", "module": "Mathlib.CategoryTheory.CommSq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CommSq.HasLift.iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.CommSq", "is_tactic_proof": true, "tactics": ["constructor", "exacts"], "tactic_count": 2}
{"name": "CategoryTheory.CommSq.HasLift.iff_op", "kind": "theorem", "module": "Mathlib.CategoryTheory.CommSq", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.CommSq.HasLift.iff_unop", "kind": "theorem", "module": "Mathlib.CategoryTheory.CommSq", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.CommSq.lift", "kind": "definition", "module": "Mathlib.CategoryTheory.CommSq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CommSq.fac_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.CommSq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CommSq.fac_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.CommSq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Arrow", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Arrow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Arrow.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Arrow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Arrow.id_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Arrow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Arrow.id_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Arrow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Arrow.comp_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Arrow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Arrow.comp_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Arrow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Arrow.mk", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Arrow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Arrow.mk_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Arrow", "is_tactic_proof": true, "tactics": ["cases", "rfl"], "tactic_count": 2}
{"name": "CategoryTheory.Arrow.mk_surjective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Arrow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Arrow.mk_injective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Arrow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Arrow.mk_inj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Arrow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Arrow.instCoeOutHom", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Arrow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Arrow.mk_eq_mk_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Arrow", "is_tactic_proof": true, "tactics": ["constructor", "intro", "refine", "have", "dsimp", "rw", "rw", "rintro", "simp", "rw"], "tactic_count": 10}
{"name": "CategoryTheory.Arrow.ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Arrow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Arrow.arrow_mk_comp_eqToHom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Arrow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Arrow.arrow_mk_eqToHom_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Arrow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Arrow.w_mk_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Arrow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Arrow.w", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Arrow", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Arrow.isIso_of_isIso_left_of_isIso_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Arrow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Arrow.hom.congr_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Arrow", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Arrow.hom.congr_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Arrow", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "CategoryTheory.Arrow.isIso_left", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Arrow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Arrow.isIso_right", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Arrow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Arrow.isIso_of_isIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Arrow", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
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{"name": "CategoryTheory.Arrow.inv_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Arrow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Arrow.epi_right", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Arrow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Arrow.hom_inv_id_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Arrow", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "CategoryTheory.Arrow.squareToSnd", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Arrow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Arrow.leftFunc", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Arrow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Arrow.rightFunc", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Arrow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Arrow.leftToRight", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Arrow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapArrow", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Arrow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapArrowFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Arrow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapArrowEquivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Arrow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isEquivalence_mapArrow", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Arrow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Arrow.isoOfNatIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Arrow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Arrow.equivSigma", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Arrow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Arrow.discreteEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Arrow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Arrow.functor_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Arrow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.CommaMorphism.inhabited", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.commaCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Comma.snd", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comma.natTrans", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comma.eqToHom_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Basic", "is_tactic_proof": true, "tactics": ["cases", "rfl"], "tactic_count": 2}
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{"name": "CategoryTheory.Comma.instIsIsoRight", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Comma.rightIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comma.map", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comma.faithful_map", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comma.full_map", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comma.essSurj_map", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comma.isEquivalenceMap", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comma.map_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comma.mapFst", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comma.map_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comma.mapSnd", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comma.mapLeft", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comma.mapLeftId", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comma.mapLeftComp", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comma.mapLeftEq", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comma.mapLeftIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comma.mapRight", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comma.mapRightId", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comma.mapRightComp", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comma.mapRightEq", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comma.mapRightIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comma.preLeft", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comma.preLeftIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comma.instFaithfulCompPreLeft", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comma.instFullCompPreLeft", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Comma.isEquivalence_preLeft", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comma.preRight", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comma.preRightIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comma.instFaithfulCompPreRight", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Comma.isEquivalence_preRight", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comma.post", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comma.postIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comma.instFaithfulCompPost", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comma.instFullCompPostOfFaithful", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comma.instEssSurjCompPostOfFull", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comma.isEquivalence_post", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comma.fromProd", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comma.equivProd", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comma.toPUnitIdEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comma.toPUnitIdEquiv_functor_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comma.toIdPUnitEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comma.toIdPUnitEquiv_functor_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comma.opFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comma.opFunctorCompFst", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comma.opFunctorCompSnd", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comma.unopFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comma.unopFunctorCompFst", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comma.unopFunctorCompSnd", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comma.opEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Arrow.finite_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.CardinalArrow", "is_tactic_proof": true, "tactics": ["constructor", "intro", "refine", "have", "apply", "have", "change", "congr)", "apply", "rintro", "have", "infer_instance"], "tactic_count": 12}
{"name": "CategoryTheory.Arrow.finite", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.CardinalArrow", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Arrow.opEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.CardinalArrow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.hasCardinalLT_arrow_op_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.CardinalArrow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.hasCardinalLT_arrow_discrete_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.CardinalArrow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instFiniteArrowDiscrete", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.CardinalArrow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.small_of_small_arrow", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.CardinalArrow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.locallySmall_of_small_arrow", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.CardinalArrow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Arrow.shrinkHomsEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.CardinalArrow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Arrow.shrinkEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.CardinalArrow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.hasCardinalLT_arrow_shrinkHoms_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.CardinalArrow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.hasCardinalLT_arrow_shrink_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.CardinalArrow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.hasCardinalLT_of_hasCardinalLT_arrow", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.CardinalArrow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.CategoryTheory.Comma.Final.0.CategoryTheory.Comma.final_fst_small", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Final", "is_tactic_proof": true, "tactics": ["rw", "intro", "let", "colimitIsoColimitGrothendieck", "convert", "apply", "intro", "simp", "change", "simp"], "tactic_count": 10}
{"name": "CategoryTheory.Comma.final_fst", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Final", "is_tactic_proof": true, "tactics": ["let", "let", "let", "let", "let", "let", "map", "have", "apply", "exact"], "tactic_count": 10}
{"name": "CategoryTheory.Comma.initial_snd", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Final", "is_tactic_proof": false, "tactics": ["have", "final_equivalence_comp", "have", "apply"], "tactic_count": 4}
{"name": "CategoryTheory.Comma.isConnected_comma_of_final", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Final", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "CategoryTheory.Comma.isConnected_comma_of_initial", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Final", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "CategoryTheory.Comma.map_final", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Final", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comma.isFiltered_of_final", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Final", "is_tactic_proof": false, "tactics": ["haveI", "have", "let", "have", "have", "apply"], "tactic_count": 6}
{"name": "CategoryTheory.Comma.isCofiltered_of_initial", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Final", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comma.final_snd", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Final", "is_tactic_proof": true, "tactics": ["let", "let", "have", "let", "let", "apply"], "tactic_count": 6}
{"name": "CategoryTheory.Comma.initial_fst", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Final", "is_tactic_proof": true, "tactics": ["have", "have", "apply"], "tactic_count": 3}
{"name": "CategoryTheory.Comma.locallySmall", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.LocallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.locallySmall", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.LocallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.locallySmall", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.LocallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.locallySmall", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.LocallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.locallySmall", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.LocallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instCategoryOver", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.inhabited", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.OverMorphism.ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": true, "tactics": ["let", "let", "congr", "simp"], "tactic_count": 4}
{"name": "CategoryTheory.Over.over_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Over.id_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.comp_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.w", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": true, "tactics": ["have"], "tactic_count": 1}
{"name": "CategoryTheory.Over.mk", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.coeFromHom", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.coe_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.homMk_eta", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.homMk_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Over.hom_left_inv_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Over.inv_left_hom_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Over.forall_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "CategoryTheory.Over.mk_surjective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.homMk_surjective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.forget", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.forget_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.forget_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.forgetCocone", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.map", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.map_obj_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.map_obj_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.map_map_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.mapIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.mapIso_functor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.mapIso_inverse", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.instIsEquivalenceMapOfIsIso", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.mapId_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": true, "tactics": ["fapply", "intro", "dsimp", "simp", "exact", "intro", "dsimp", "simp"], "tactic_count": 8}
{"name": "CategoryTheory.Over.mapId", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.mapForget_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.mapForget", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.eqToHom_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "CategoryTheory.Over.mapComp_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": true, "tactics": ["fapply", "simp", "intro", "ext", "simp"], "tactic_count": 5}
{"name": "CategoryTheory.Over.mapComp", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.mapCongr", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.mapCongr_rfl", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.mapFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.forget_reflects_iso", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.mkIdTerminal", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.forget_faithful", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.epi_of_epi_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.epi_homMk", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.mono_of_mono_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.mono_homMk", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.mono_left_of_mono", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": true, "tactics": ["refine", "let", "homMk", "suffices", "rw", "ext", "apply"], "tactic_count": 7}
{"name": "CategoryTheory.Over.iteratedSliceForward", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.iteratedSliceBackward", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.iteratedSliceBackward_forget", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.iteratedSliceEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.iteratedSliceForward_forget", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.iteratedSliceBackward_forget_forget", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.iteratedSliceForwardNaturalityIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.iteratedSliceEquivOverMapIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.post", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.post_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.postComp", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.postMap", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.postCongr", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.instFaithfulObjPost", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.instFullObjPostOfFaithful", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.instEssSurjObjPostOfFull", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.instIsEquivalenceObjPost", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.FullyFaithful.over", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.postAdjunctionRight", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.isRightAdjoint_post", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.postEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.iteratedSliceForwardIsoPost", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.equivalenceOfIsTerminal", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.lift", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.liftCone", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.isLimitLiftCone", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cone.overPost", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.toOver", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.instFaithfulOverToOver", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.instFullOverToOver", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.instEssSurjOverToOver", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.isEquivalence_toOver", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instCategoryUnder", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.inhabited", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.UnderMorphism.ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": true, "tactics": ["let", "congr"], "tactic_count": 2}
{"name": "CategoryTheory.Under.under_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Under.id_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.comp_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.w", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": true, "tactics": ["have"], "tactic_count": 1}
{"name": "CategoryTheory.Under.mk", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.homMk_eta", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.homMk_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Under.isoMk_hom_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.isoMk_inv_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.hom_right_inv_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Under.inv_right_hom_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Under.forall_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "CategoryTheory.Under.mk_surjective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.homMk_surjective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.forget", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.forget_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.forget_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.forgetCone", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.map", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.map_obj_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.map_obj_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.map_map_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.mapIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.mapIso_functor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.mapIso_inverse", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.instIsEquivalenceMapOfIsIso", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.mapId_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": true, "tactics": ["fapply", "intro", "dsimp", "simp", "exact", "intro", "dsimp", "simp"], "tactic_count": 8}
{"name": "CategoryTheory.Under.mapId", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.mapForget_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.mapForget", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.eqToHom_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "CategoryTheory.Under.mapComp_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": true, "tactics": ["fapply", "simp", "intro", "ext", "simp"], "tactic_count": 5}
{"name": "CategoryTheory.Under.mapComp", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.mapCongr", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.mapFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.forget_reflects_iso", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.mkIdInitial", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.forget_faithful", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.mono_of_mono_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.mono_homMk", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.epi_of_epi_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.epi_homMk", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.epi_right_of_epi", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": true, "tactics": ["refine", "let", "suffices", "rw"], "tactic_count": 4}
{"name": "CategoryTheory.Under.post", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.post_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.postComp", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.postMap", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.postCongr", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.instFaithfulObjPost", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.instFullObjPostOfFaithful", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.instEssSurjObjPostOfFull", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.instIsEquivalenceObjPost", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.FullyFaithful.under", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.postAdjunctionLeft", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.isLeftAdjoint_post", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.postEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.equivalenceOfIsInitial", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.lift", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.liftCocone", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.isColimitLiftCocone", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cocone.underPost", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.toUnder", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.instFaithfulUnderToUnder", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.instFullUnderToUnder", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.instEssSurjUnderToUnder", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.isEquivalence_toUnder", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.essImage.of_overPost", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.essImage.of_underPost", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.essImage_overPost", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.essImage_underPost", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.toOver", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.toOverCompForget", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.toOver_comp_forget", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.toUnder", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.toUnderCompForget", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.toUnder_comp_forget", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.ofStructuredArrowProjEquivalence.functor", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.ofStructuredArrowProjEquivalence.inverse", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.ofStructuredArrowProjEquivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.ofDiagEquivalence.functor", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.ofDiagEquivalence.inverse", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.ofDiagEquivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.ofDiagEquivalence'", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.ofCommaSndEquivalenceFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.ofCommaSndEquivalenceInverse", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.ofCommaSndEquivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.ofCostructuredArrowProjEquivalence.functor", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.ofCostructuredArrowProjEquivalence.inverse", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.ofCostructuredArrowProjEquivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.ofDiagEquivalence.functor", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.ofDiagEquivalence.inverse", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.ofDiagEquivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.ofDiagEquivalence'", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceInverse", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.ofCommaFstEquivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.opEquivOpUnder", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.opEquivOpOver", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.term_↘_", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.OverClass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory._aux_Mathlib_CategoryTheory_Comma_Over_OverClass___macroRules_CategoryTheory_term_↘__1", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.OverClass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory._aux_Mathlib_CategoryTheory_Comma_Over_OverClass___unexpand_CategoryTheory_over_1", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.OverClass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OverClass.Simps.over", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.OverClass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CanonicallyOverClass.Simps.over", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.OverClass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instOverClass", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Over.OverClass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instIsIsoOverInferInstanceOverClass", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Over.OverClass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CanonicallyOverClass.instOverClass", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Over.OverClass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.comp_over", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.OverClass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instHomIsOverId", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Over.OverClass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instHomIsOverComp", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Over.OverClass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsOverTower", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Comma.Over.OverClass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instIsOverTower", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Over.OverClass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instIsOverTower_1", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Over.OverClass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instIsOverTower_2", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Over.OverClass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.homIsOver_of_isOverTower", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.OverClass", "is_tactic_proof": true, "tactics": ["constructor", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.instHomIsOverOfIsOverTower", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Over.OverClass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instHomIsOverOfIsOverTower_1", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Over.OverClass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OverClass.asOver", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.OverClass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OverClass.asOverHom", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.OverClass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OverClass.fromOver", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Over.OverClass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instHomIsOverLeftDiscretePUnit", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Over.OverClass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OverClass.instIsIsoOverAsOverHom", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Over.OverClass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OverClass.instHomIsOverInvOfHom", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Over.OverClass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OverClass.instHomIsOverHomOfInv", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Over.OverClass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OverClass.instHomIsOverHomAsIso", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Over.OverClass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OverClass.instHomIsOverInvAsIso", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Over.OverClass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OverClass.instHomIsOverInv", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Over.OverClass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OverClass.asOverHom_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.OverClass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OverClass.asOverHom_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.OverClass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OverClass.asOverHom_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Over.OverClass", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Iso.asOver", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.OverClass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.pullback", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Pullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.mapPullbackAdj", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Pullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.faithful_pullback", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Over.Pullback", "is_tactic_proof": false, "tactics": ["have", "simp", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Over.pullbackId", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Pullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.pullbackComp", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Pullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.pullbackIsRightAdjoint", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Over.Pullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.postAdjunctionLeft", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Pullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.isLeftAdjoint_post", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Over.Pullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.forgetMapTerminal", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Pullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.star", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Pullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.forgetAdjStar", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Pullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.instIsRightAdjointStar", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Over.Pullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.instIsLeftAdjointForget", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Over.Pullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.starPullbackIsoStar", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Pullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.pushout", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Pullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.mapPushoutAdj", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Pullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.faithful_pushout", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Over.Pullback", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Under.pushoutId", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Pullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.pushoutComp", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Pullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.pushoutIsLeftAdjoint", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Over.Pullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.postAdjunctionRight", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Pullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.isRightAdjoint_post", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Over.Pullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.forgetMapInitial", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Pullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.costar", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Pullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.costarAdjForget", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Over.Pullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.instIsLeftAdjointCostar", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Over.Pullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.instIsRightAdjointForget", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.Over.Pullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OverPresheafAux.MakesOverArrow.map₁", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OverPresheafAux.MakesOverArrow.map₂", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OverPresheafAux.MakesOverArrow.of_arrow", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OverPresheafAux.MakesOverArrow.of_yoneda_arrow", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.OverPresheafAux.OverArrows", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OverPresheafAux.OverArrows.val", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OverPresheafAux.OverArrows.val_mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OverPresheafAux.OverArrows.ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OverPresheafAux.OverArrows.app_val", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OverPresheafAux.OverArrows.map_val", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.OverPresheafAux.OverArrows.map₁", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OverPresheafAux.OverArrows.map₁_val", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OverPresheafAux.OverArrows.map₂", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OverPresheafAux.OverArrows.map₂_val", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OverPresheafAux.OverArrows.map₁_map₂", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OverPresheafAux.OverArrows.yonedaArrow", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OverPresheafAux.OverArrows.yonedaArrow_val", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OverPresheafAux.OverArrows.costructuredArrowIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OverPresheafAux.restrictedYonedaObj", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OverPresheafAux.restrictedYonedaObjMap₁", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OverPresheafAux.restrictedYoneda", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OverPresheafAux.toOverYonedaCompRestrictedYoneda", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OverPresheafAux.map_mkPrecomp_eqToHom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.OverPresheafAux.YonedaCollection", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OverPresheafAux.YonedaCollection.mk", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OverPresheafAux.YonedaCollection.fst", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OverPresheafAux.YonedaCollection.snd", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OverPresheafAux.YonedaCollection.yonedaEquivFst", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OverPresheafAux.YonedaCollection.yonedaEquivFst_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OverPresheafAux.YonedaCollection.mk_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OverPresheafAux.YonedaCollection.mk_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OverPresheafAux.YonedaCollection.ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "obtain", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.OverPresheafAux.YonedaCollection.map₁", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OverPresheafAux.YonedaCollection.map₁_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.OverPresheafAux.YonedaCollection.map₁_yonedaEquivFst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.OverPresheafAux.YonedaCollection.map₁_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.OverPresheafAux.YonedaCollection.map₂", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OverPresheafAux.YonedaCollection.map₂_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.OverPresheafAux.YonedaCollection.map₂_yonedaEquivFst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.OverPresheafAux.YonedaCollection.map₂_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.OverPresheafAux.YonedaCollection.map₁_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.OverPresheafAux.YonedaCollection.map₁_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.OverPresheafAux.YonedaCollection.map₂_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.OverPresheafAux.YonedaCollection.map₂_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.OverPresheafAux.YonedaCollection.map₁_map₂", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.OverPresheafAux.yonedaCollectionPresheaf", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OverPresheafAux.yonedaCollectionPresheafMap₁", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OverPresheafAux.yonedaCollectionFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OverPresheafAux.yonedaCollectionPresheafToA", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OverPresheafAux.costructuredArrowPresheafToOver", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OverPresheafAux.unitForward", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OverPresheafAux.unitForward_naturality₁", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.OverPresheafAux.unitForward_naturality₂", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.OverPresheafAux.app_unitForward", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.OverPresheafAux.unitBackward", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OverPresheafAux.unitForward_unitBackward", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OverPresheafAux.unitBackward_unitForward", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": true, "tactics": ["refine", "simpa", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.OverPresheafAux.unitAuxAuxAux", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OverPresheafAux.unitAuxAux", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OverPresheafAux.unitAux", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OverPresheafAux.unit", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OverPresheafAux.OverArrows.yonedaCollectionPresheafToA_val_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.OverPresheafAux.counitForward", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OverPresheafAux.counitForward_val_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.OverPresheafAux.counitForward_val_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OverPresheafAux.counitForward_naturality₁", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OverPresheafAux.counitForward_naturality₂", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": true, "tactics": ["refine", "have", "apply", "simp", "cat_disch"], "tactic_count": 5}
{"name": "CategoryTheory.OverPresheafAux.counitBackward", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OverPresheafAux.counitForward_counitBackward", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OverPresheafAux.counitBackward_counitForward", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OverPresheafAux.counitAuxAux", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OverPresheafAux.counitAux", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OverPresheafAux.counit", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.overEquivPresheafCostructuredArrow", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.toOverCompOverEquivPresheafCostructuredArrow", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.toOverCompYoneda", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.overEquivPresheafCostructuredArrow_inverse_map_toOverCompYoneda", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.CostructuredArrow.overEquivPresheafCostructuredArrow_functor_map_toOverCompYoneda", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.CostructuredArrow.toOverCompCoyoneda", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.overEquivPresheafCostructuredArrow_inverse_map_toOverCompCoyoneda", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.CostructuredArrow.overEquivPresheafCostructuredArrow_functor_map_toOverCompCoyoneda", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "_private.Mathlib.CategoryTheory.Comma.Presheaf.Colimit.0.CategoryTheory.termE", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Colimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.CategoryTheory.Comma.Presheaf.Colimit.0.CategoryTheory._aux_Mathlib_CategoryTheory_Comma_Presheaf_Colimit___macroRules__private_Mathlib_CategoryTheory_Comma_Presheaf_Colimit_0_CategoryTheory_termE_1", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Colimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.CategoryTheory.Comma.Presheaf.Colimit.0.CategoryTheory._aux_Mathlib_CategoryTheory_Comma_Presheaf_Colimit___unexpand_CategoryTheory_Equivalence_functor_1", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Colimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.CategoryTheory.Comma.Presheaf.Colimit.0.CategoryTheory.termE.obj", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Colimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.CategoryTheory.Comma.Presheaf.Colimit.0.CategoryTheory._aux_Mathlib_CategoryTheory_Comma_Presheaf_Colimit___macroRules__private_Mathlib_CategoryTheory_Comma_Presheaf_Colimit_0_CategoryTheory_termE.obj_1", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Colimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.CategoryTheory.Comma.Presheaf.Colimit.0.CategoryTheory._aux_Mathlib_CategoryTheory_Comma_Presheaf_Colimit___unexpand_CategoryTheory_Functor_obj_1", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Colimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.toOverCompYonedaColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.Presheaf.Colimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instCategoryStructuredArrow", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.proj", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.hom_eq_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.mk", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.mk_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.mk_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.mk_hom_eq_self", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.w", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": true, "tactics": ["have"], "tactic_count": 1}
{"name": "CategoryTheory.StructuredArrow.comp_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.id_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.eqToHom_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": true, "tactics": ["subst", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.StructuredArrow.left_eq_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.homMk_surjective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.homMk'", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.homMk'_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.StructuredArrow.homMk'_mk_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.StructuredArrow.homMk'_mk_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.mkPostcomp", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.mkPostcomp_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.StructuredArrow.mkPostcomp_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.StructuredArrow.obj_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": true, "tactics": ["cases", "cases", "cases", "cat_disch"], "tactic_count": 4}
{"name": "CategoryTheory.StructuredArrow.ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.ext_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.StructuredArrow.mono_of_mono_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.epi_of_epi_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.mono_homMk", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.StructuredArrow.eq_mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.eta", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.mk_surjective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.map", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.map_mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.map_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.StructuredArrow.map_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.StructuredArrow.mapIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.mapNatIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.proj_reflectsIsomorphisms", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.mkIdInitial", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.pre", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.instFaithfulCompPre", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.instFullCompPre", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.instEssSurjCompPre", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.isEquivalence_pre", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.post", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.instFaithfulObjCompPost", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.instFullObjCompPostOfFaithful", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.instEssSurjObjCompPostOfFull", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.isEquivalence_post", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.map₂", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.faithful_map₂", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
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{"name": "CategoryTheory.StructuredArrow.isEquivalenceMap₂", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.StructuredArrow.map₂CompMap₂Iso", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.postIsoMap₂", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.mapIsoMap₂", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.StructuredArrow.IsUniversal", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.IsUniversal.uniq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.IsUniversal.desc", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.IsUniversal.fac", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.IsUniversal.hom_desc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.IsUniversal.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.StructuredArrow.IsUniversal.existsUnique", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.instCategoryCostructuredArrow", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.CostructuredArrow.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.hom_eq_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.mk", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.mk_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.mk_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.mk_hom_eq_self", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.w", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.CostructuredArrow.comp_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.id_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.eqToHom_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": true, "tactics": ["subst", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.CostructuredArrow.right_eq_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.homMk_surjective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.homMk'", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.homMk'_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.CostructuredArrow.homMk'_mk_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.homMk'_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.CostructuredArrow.homMk'_mk_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.mkPrecomp", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.mkPrecomp_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.CostructuredArrow.mkPrecomp_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.CostructuredArrow.obj_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": true, "tactics": ["cases", "cases", "cases", "cat_disch"], "tactic_count": 4}
{"name": "CategoryTheory.CostructuredArrow.ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.ext_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.proj_faithful", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.mono_of_mono_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.epi_of_epi_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.mono_homMk", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.epi_homMk", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.eq_mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.eta", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.mk_surjective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.map", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.map_mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.map_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.CostructuredArrow.map_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.CostructuredArrow.mapIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.mapNatIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.proj_reflectsIsomorphisms", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.mkIdTerminal", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.pre", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.instFaithfulCompPre", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.instFullCompPre", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.instEssSurjCompPre", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.isEquivalence_pre", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.post", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.instFaithfulCompObjPost", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.instFullCompObjPostOfFaithful", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.instEssSurjCompObjPostOfFull", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.isEquivalence_post", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.map₂", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.faithful_map₂", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.CostructuredArrow.full_map₂", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.CostructuredArrow.essSurj_map₂", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.CostructuredArrow.isEquivalenceMap₂", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.CostructuredArrow.postIsoMap₂", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.IsUniversal", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.IsUniversal.uniq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.IsUniversal.lift", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.IsUniversal.fac", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.IsUniversal.hom_desc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.IsUniversal.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.CostructuredArrow.IsUniversal.existsUnique", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.toStructuredArrow", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.toStructuredArrowCompProj", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.toStructuredArrow_comp_proj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.toCostructuredArrow", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.toCostructuredArrowCompProj", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.toCostructuredArrow_comp_proj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.toCostructuredArrow", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.toCostructuredArrow'", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.toStructuredArrow", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.toStructuredArrow'", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.structuredArrowOpEquivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.costructuredArrowOpEquivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.preEquivalenceFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.preEquivalenceInverse", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.preEquivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.map₂IsoPreEquivalenceInverseCompProj", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.preEquivalence.functor", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.preEquivalence.inverse", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.preEquivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.map₂IsoPreEquivalenceInverseCompProj", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.w_prod_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.w_prod_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.prodFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.prodInverse", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.prodEquivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.w_prod_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.w_prod_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.prodFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.prodInverse", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.prodEquivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.commaMapEquivalenceFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.CommaMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.commaMapEquivalenceInverse", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.CommaMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.commaMapEquivalenceUnitIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.CommaMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.commaMapEquivalenceCounitIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.CommaMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.commaMapEquivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.CommaMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.CategoryTheory.Comma.StructuredArrow.Final.0.CategoryTheory.Functor.final_of_final_costructuredArrowToOver_small", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Final", "is_tactic_proof": true, "tactics": ["rw", "intro", "have", "inferInstanceAs", "let", "calc", "colimit", "colimit", "grothendieckPrecompFunctorToComma", "convert", "simp", "rw", "apply"], "tactic_count": 13}
{"name": "CategoryTheory.Functor.final_of_final_costructuredArrowToOver", "kind": "theorem", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Final", "is_tactic_proof": true, "tactics": ["let", "let", "let", "let", "let", "have", "dsimp", "let", "let", "map₂", "pre", "apply", "have", "exact", "have", "apply", "exact", "isoWhiskerRight"], "tactic_count": 18}
{"name": "CategoryTheory.StructuredArrow.functor", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.functor", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.grothendieckPrecompFunctorToComma", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.ιCompGrothendieckPrecompFunctorToCommaCompFst", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.commaToGrothendieckPrecompFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.grothendieckPrecompFunctorEquivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.grothendieckProj", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.ιCompGrothendieckProj", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.mapCompιCompGrothendieckProj", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.preFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.instSmallOfLocallySmall", "kind": "instance", "module": "Mathlib.CategoryTheory.Comma.StructuredArrow.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.ComposableArrows", "kind": "abbrev", "module": "Mathlib.CategoryTheory.ComposableArrows.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.tacticValid", "kind": "definition", "module": "Mathlib.CategoryTheory.ComposableArrows.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.ComposableArrows.Mk₁.map_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.ComposableArrows.isoMk", "kind": "definition", "module": "Mathlib.CategoryTheory.ComposableArrows.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.homMk₀", "kind": "definition", "module": "Mathlib.CategoryTheory.ComposableArrows.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.ComposableArrows.isIso_iff₀", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
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{"name": "CategoryTheory.ComposableArrows.hom_ext₁", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.ComposableArrows.map'_eq_hom₁", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.isIso_iff₁", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
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{"name": "CategoryTheory.ComposableArrows.mk₁_comp_eqToHom", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Basic", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
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{"name": "CategoryTheory.ComposableArrows.whiskerLeft", "kind": "definition", "module": "Mathlib.CategoryTheory.ComposableArrows.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.whiskerLeftFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.ComposableArrows.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.succFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.ComposableArrows.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.δ₀Functor", "kind": "definition", "module": "Mathlib.CategoryTheory.ComposableArrows.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.ComposableArrows.precomp_δ₀", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.castSuccFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.ComposableArrows.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.δlastFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.ComposableArrows.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.ComposableArrows.homMkSucc", "kind": "definition", "module": "Mathlib.CategoryTheory.ComposableArrows.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.homMkSucc_app_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.homMkSucc_app_succ", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.ComposableArrows.homMk₂_app_two", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.ComposableArrows.hom_ext₂", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.ComposableArrows.mk₂_surjective", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.ext₂_of_arrow", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Basic", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "obtain", "obtain", "obtain", "obtain", "obtain", "rfl"], "tactic_count": 8}
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{"name": "CategoryTheory.ComposableArrows.homMk₃_app_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.homMk₃_app_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.homMk₃_app_two", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.homMk₃_app_three", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.hom_ext₃", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.ComposableArrows.mk₃_surjective", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.homMk₄", "kind": "definition", "module": "Mathlib.CategoryTheory.ComposableArrows.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.homMk₄_app_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.homMk₄_app_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.homMk₄_app_two", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.homMk₄_app_three", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.homMk₄_app_four", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.hom_ext₄", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.map'_inv_eq_inv_map'", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.ComposableArrows.isoMk₄", "kind": "definition", "module": "Mathlib.CategoryTheory.ComposableArrows.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.ext₄", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.mk₄_surjective", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.homMk₅", "kind": "definition", "module": "Mathlib.CategoryTheory.ComposableArrows.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.homMk₅_app_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.homMk₅_app_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.homMk₅_app_two", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.homMk₅_app_three", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.homMk₅_app_four", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.homMk₅_app_five", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.hom_ext₅", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.isoMk₅", "kind": "definition", "module": "Mathlib.CategoryTheory.ComposableArrows.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.ext₅", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.mk₅_surjective", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.mkOfObjOfMapSucc_exists", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "obtain", "refine", "obtain", "simp", "exact"], "tactic_count": 8}
{"name": "CategoryTheory.ComposableArrows.mkOfObjOfMapSucc", "kind": "definition", "module": "Mathlib.CategoryTheory.ComposableArrows.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.mkOfObjOfMapSucc_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapComposableArrows", "kind": "definition", "module": "Mathlib.CategoryTheory.ComposableArrows.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapComposableArrowsObjMk₁Iso", "kind": "definition", "module": "Mathlib.CategoryTheory.ComposableArrows.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapComposableArrowsObjMk₂Iso", "kind": "definition", "module": "Mathlib.CategoryTheory.ComposableArrows.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.fourδ₄Toδ₃_app_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Four", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.fourδ₄Toδ₃_app_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Four", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.fourδ₄Toδ₃_app_two", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Four", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.fourδ₄Toδ₃_app_three", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Four", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.fourδ₃Toδ₂_app_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Four", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.fourδ₃Toδ₂_app_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Four", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.fourδ₃Toδ₂_app_two", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Four", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.fourδ₃Toδ₂_app_three", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Four", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.fourδ₂Toδ₁_app_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Four", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.fourδ₂Toδ₁_app_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Four", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.fourδ₂Toδ₁_app_two", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Four", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.fourδ₂Toδ₁_app_three", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Four", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.fourδ₁Toδ₀_app_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Four", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.fourδ₁Toδ₀_app_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Four", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.fourδ₁Toδ₀_app_two", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Four", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.fourδ₁Toδ₀_app_three", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Four", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.fourδ₄Toδ₃'", "kind": "abbrev", "module": "Mathlib.CategoryTheory.ComposableArrows.Four", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.fourδ₃Toδ₂'", "kind": "abbrev", "module": "Mathlib.CategoryTheory.ComposableArrows.Four", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.fourδ₂Toδ₁'", "kind": "abbrev", "module": "Mathlib.CategoryTheory.ComposableArrows.Four", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.fourδ₁Toδ₀'", "kind": "abbrev", "module": "Mathlib.CategoryTheory.ComposableArrows.Four", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.threeδ₃Toδ₂_app_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Three", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.threeδ₃Toδ₂_app_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Three", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.threeδ₃Toδ₂_app_two", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Three", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.threeδ₂Toδ₁_app_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Three", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.threeδ₂Toδ₁_app_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Three", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.threeδ₂Toδ₁_app_two", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Three", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.threeδ₁Toδ₀_app_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Three", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.threeδ₁Toδ₀_app_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Three", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.threeδ₁Toδ₀_app_two", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Three", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.threeδ₃Toδ₂'", "kind": "abbrev", "module": "Mathlib.CategoryTheory.ComposableArrows.Three", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.threeδ₂Toδ₁'", "kind": "abbrev", "module": "Mathlib.CategoryTheory.ComposableArrows.Three", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.threeδ₁Toδ₀'", "kind": "abbrev", "module": "Mathlib.CategoryTheory.ComposableArrows.Three", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.twoδ₂Toδ₁_app_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Two", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.twoδ₂Toδ₁_app_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Two", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.twoδ₁Toδ₀_app_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Two", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.twoδ₁Toδ₀_app_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.ComposableArrows.Two", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.instIsIsoOfNatNatTwoδ₂Toδ₁", "kind": "instance", "module": "Mathlib.CategoryTheory.ComposableArrows.Two", "is_tactic_proof": true, "tactics": ["rw", "constructor"], "tactic_count": 2}
{"name": "CategoryTheory.ComposableArrows.instIsIsoOfNatNatTwoδ₁Toδ₀", "kind": "instance", "module": "Mathlib.CategoryTheory.ComposableArrows.Two", "is_tactic_proof": true, "tactics": ["rw", "constructor"], "tactic_count": 2}
{"name": "CategoryTheory.ComposableArrows.twoδ₁Toδ₀'", "kind": "abbrev", "module": "Mathlib.CategoryTheory.ComposableArrows.Two", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ComposableArrows.twoδ₂Toδ₁'", "kind": "abbrev", "module": "Mathlib.CategoryTheory.ComposableArrows.Two", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.forget", "kind": "abbrev", "module": "Mathlib.CategoryTheory.ConcreteCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasForget.types", "kind": "abbrev", "module": "Mathlib.CategoryTheory.ConcreteCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasForget.hasCoeToSort", "kind": "definition", "module": "Mathlib.CategoryTheory.ConcreteCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasForget.instFunLike", "kind": "abbrev", "module": "Mathlib.CategoryTheory.ConcreteCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ConcreteCategory.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.ConcreteCategory.Basic", "is_tactic_proof": true, "tactics": ["apply", "dsimp", "funext", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.forget_map_eq_coe", "kind": "theorem", "module": "Mathlib.CategoryTheory.ConcreteCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.congr_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.ConcreteCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.coe_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.ConcreteCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.coe_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.ConcreteCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.id_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.ConcreteCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.comp_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.ConcreteCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.comp_apply'", "kind": "theorem", "module": "Mathlib.CategoryTheory.ConcreteCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ConcreteCategory.congr_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.ConcreteCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ConcreteCategory.congr_arg", "kind": "theorem", "module": "Mathlib.CategoryTheory.ConcreteCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ConcreteCategory.hasCoeToFun_Type", "kind": "theorem", "module": "Mathlib.CategoryTheory.ConcreteCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.forget₂", "kind": "abbrev", "module": "Mathlib.CategoryTheory.ConcreteCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.forget₂_comp_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.ConcreteCategory.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.forget₂_faithful", "kind": "instance", "module": "Mathlib.CategoryTheory.ConcreteCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.InducedCategory.hasForget", "kind": "instance", "module": "Mathlib.CategoryTheory.ConcreteCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.InducedCategory.hasForget₂", "kind": "instance", "module": "Mathlib.CategoryTheory.ConcreteCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FullSubcategory.hasForget", "kind": "instance", "module": "Mathlib.CategoryTheory.ConcreteCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FullSubcategory.hasForget₂", "kind": "instance", "module": "Mathlib.CategoryTheory.ConcreteCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasForget₂.mk'", "kind": "definition", "module": "Mathlib.CategoryTheory.ConcreteCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasForget₂.trans", "kind": "definition", "module": "Mathlib.CategoryTheory.ConcreteCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.hasForgetToType", "kind": "definition", "module": "Mathlib.CategoryTheory.ConcreteCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ToType", "kind": "abbrev", "module": "Mathlib.CategoryTheory.ConcreteCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ToHom", "kind": "abbrev", "module": "Mathlib.CategoryTheory.ConcreteCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ConcreteCategory.instCoeFunHomForallToType", "kind": "instance", "module": "Mathlib.CategoryTheory.ConcreteCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ConcreteCategory.homEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.ConcreteCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ConcreteCategory.hom_bijective", "kind": "theorem", "module": "Mathlib.CategoryTheory.ConcreteCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ConcreteCategory.hom_injective", "kind": "theorem", "module": "Mathlib.CategoryTheory.ConcreteCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ConcreteCategory.ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.ConcreteCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ConcreteCategory.coe_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.ConcreteCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ConcreteCategory.ext_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.ConcreteCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ConcreteCategory.toHasForget", "kind": "instance", "module": "Mathlib.CategoryTheory.ConcreteCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.forget_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.ConcreteCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ConcreteCategory.forget_map_eq_coe", "kind": "theorem", "module": "Mathlib.CategoryTheory.ConcreteCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.congr_fun", "kind": "theorem", "module": "Mathlib.CategoryTheory.ConcreteCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.congr_arg", "kind": "theorem", "module": "Mathlib.CategoryTheory.ConcreteCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.hom_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.ConcreteCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.hom_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.ConcreteCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.coe_toHasForget_instFunLike", "kind": "theorem", "module": "Mathlib.CategoryTheory.ConcreteCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ConcreteCategory.forget₂_comp_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.ConcreteCategory.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.hom_isIso", "kind": "instance", "module": "Mathlib.CategoryTheory.ConcreteCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.naturality_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.ConcreteCategory.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.HasForget.toFunLike", "kind": "abbrev", "module": "Mathlib.CategoryTheory.ConcreteCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasForget.toConcreteCategory", "kind": "abbrev", "module": "Mathlib.CategoryTheory.ConcreteCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory._example", "kind": "example", "module": "Mathlib.CategoryTheory.ConcreteCategory.Basic", "is_tactic_proof": true, "tactics": ["with_reducible_and_instances"], "tactic_count": 1}
{"name": "CategoryTheory.forget_eq_ConcreteCategory_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.ConcreteCategory.Basic", "is_tactic_proof": true, "tactics": ["with_reducible_and_instances"], "tactic_count": 1}
{"name": "CategoryTheory.Types.instFunLike", "kind": "abbrev", "module": "Mathlib.CategoryTheory.ConcreteCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Types.instConcreteCategory", "kind": "abbrev", "module": "Mathlib.CategoryTheory.ConcreteCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.InducedCategory.concreteCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.ConcreteCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Bundled.of", "kind": "definition", "module": "Mathlib.CategoryTheory.ConcreteCategory.Bundled", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bundled.coeSort", "kind": "instance", "module": "Mathlib.CategoryTheory.ConcreteCategory.Bundled", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bundled.coe_mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.ConcreteCategory.Bundled", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bundled.map", "kind": "abbrev", "module": "Mathlib.CategoryTheory.ConcreteCategory.Bundled", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.BundledHom.category", "kind": "instance", "module": "Mathlib.CategoryTheory.ConcreteCategory.BundledHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.BundledHom.hasForget", "kind": "instance", "module": "Mathlib.CategoryTheory.ConcreteCategory.BundledHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.BundledHom.hint._@.Mathlib.CategoryTheory.ConcreteCategory.BundledHom.3182861299._hygCtx._hyg.3", "kind": "definition", "module": "Mathlib.CategoryTheory.ConcreteCategory.BundledHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.BundledHom.mkHasForget₂", "kind": "definition", "module": "Mathlib.CategoryTheory.ConcreteCategory.BundledHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.BundledHom.MapHom", "kind": "abbrev", "module": "Mathlib.CategoryTheory.ConcreteCategory.BundledHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.BundledHom.map", "kind": "definition", "module": "Mathlib.CategoryTheory.ConcreteCategory.BundledHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.BundledHom.bundledHomOfParentProjection", "kind": "instance", "module": "Mathlib.CategoryTheory.ConcreteCategory.BundledHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.BundledHom.forget₂", "kind": "instance", "module": "Mathlib.CategoryTheory.ConcreteCategory.BundledHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.ConcreteCategory.mono_of_injective", "kind": "theorem", "module": "Mathlib.CategoryTheory.ConcreteCategory.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ConcreteCategory.forget₂_preservesMonomorphisms", "kind": "instance", "module": "Mathlib.CategoryTheory.ConcreteCategory.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ConcreteCategory.forget₂_preservesEpimorphisms", "kind": "instance", "module": "Mathlib.CategoryTheory.ConcreteCategory.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ConcreteCategory.surjective_le_epimorphisms", "kind": "theorem", "module": "Mathlib.CategoryTheory.ConcreteCategory.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ConcreteCategory.injective_le_monomorphisms", "kind": "theorem", "module": "Mathlib.CategoryTheory.ConcreteCategory.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ConcreteCategory.surjective_eq_epimorphisms_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.ConcreteCategory.EpiMono", "is_tactic_proof": true, "tactics": ["constructor", "intro", "constructor", "rintro", "rw", "rw", "exact", "intro", "apply", "intro", "have", "change", "rw", "infer_instance"], "tactic_count": 14}
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{"name": "CategoryTheory.ConcreteCategory.injective_eq_monomorphisms", "kind": "theorem", "module": "Mathlib.CategoryTheory.ConcreteCategory.EpiMono", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.ConcreteCategory.surjective_eq_epimorphisms", "kind": "theorem", "module": "Mathlib.CategoryTheory.ConcreteCategory.EpiMono", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.ConcreteCategory.functorialSurjectiveInjectiveFactorizationData", "kind": "definition", "module": "Mathlib.CategoryTheory.ConcreteCategory.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ConcreteCategory.instHasFunctorialSurjectiveInjectiveFactorization", "kind": "instance", "module": "Mathlib.CategoryTheory.ConcreteCategory.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ConcreteCategory.injective_of_mono_of_preservesPullback", "kind": "theorem", "module": "Mathlib.CategoryTheory.ConcreteCategory.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ConcreteCategory.mono_iff_injective_of_preservesPullback", "kind": "theorem", "module": "Mathlib.CategoryTheory.ConcreteCategory.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ConcreteCategory.epi_of_surjective", "kind": "theorem", "module": "Mathlib.CategoryTheory.ConcreteCategory.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ConcreteCategory.surjective_of_epi_of_preservesPushout", "kind": "theorem", "module": "Mathlib.CategoryTheory.ConcreteCategory.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ConcreteCategory.epi_iff_surjective_of_preservesPushout", "kind": "theorem", "module": "Mathlib.CategoryTheory.ConcreteCategory.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ConcreteCategory.bijective_of_isIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.ConcreteCategory.EpiMono", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.ConcreteCategory.isIso_iff_bijective", "kind": "theorem", "module": "Mathlib.CategoryTheory.ConcreteCategory.EpiMono", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.instReflectsIsomorphismsForgetType", "kind": "instance", "module": "Mathlib.CategoryTheory.ConcreteCategory.ReflectsIso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.reflectsIsomorphisms_forget₂", "kind": "theorem", "module": "Mathlib.CategoryTheory.ConcreteCategory.ReflectsIso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.UnbundledHom.bundledHom", "kind": "instance", "module": "Mathlib.CategoryTheory.ConcreteCategory.UnbundledHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.UnbundledHom.mkHasForget₂", "kind": "definition", "module": "Mathlib.CategoryTheory.ConcreteCategory.UnbundledHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.conj", "kind": "definition", "module": "Mathlib.CategoryTheory.Conj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.conj_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Conj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.conj_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Conj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.conj_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Conj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.refl_conj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Conj", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Iso.trans_conj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Conj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.symm_self_conj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Conj", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Iso.self_symm_conj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Conj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.conj_pow", "kind": "theorem", "module": "Mathlib.CategoryTheory.Conj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.conjAut", "kind": "definition", "module": "Mathlib.CategoryTheory.Conj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.conjAut_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Conj", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Iso.conjAut_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Conj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.trans_conjAut", "kind": "theorem", "module": "Mathlib.CategoryTheory.Conj", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "CategoryTheory.Iso.conjAut_trans", "kind": "theorem", "module": "Mathlib.CategoryTheory.Conj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Iso.conjAut_zpow", "kind": "theorem", "module": "Mathlib.CategoryTheory.Conj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.map_conj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Conj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.ConnectedComponents", "kind": "definition", "module": "Mathlib.CategoryTheory.ConnectedComponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapConnectedComponents", "kind": "definition", "module": "Mathlib.CategoryTheory.ConnectedComponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapConnectedComponents_mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.ConnectedComponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instInhabitedConnectedComponents", "kind": "instance", "module": "Mathlib.CategoryTheory.ConnectedComponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ConnectedComponents.functorToDiscrete", "kind": "definition", "module": "Mathlib.CategoryTheory.ConnectedComponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ConnectedComponents.liftFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.ConnectedComponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ConnectedComponents.typeToCatHomEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.ConnectedComponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ConnectedComponents.objectProperty", "kind": "definition", "module": "Mathlib.CategoryTheory.ConnectedComponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ConnectedComponents.Component", "kind": "abbrev", "module": "Mathlib.CategoryTheory.ConnectedComponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ConnectedComponents.ι", "kind": "abbrev", "module": "Mathlib.CategoryTheory.ConnectedComponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ConnectedComponents.mk", "kind": "abbrev", "module": "Mathlib.CategoryTheory.ConnectedComponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.inclusion_comp_decomposedTo", "kind": "theorem", "module": "Mathlib.CategoryTheory.ConnectedComponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.instFaithfulDecomposedDecomposedTo", "kind": "instance", "module": "Mathlib.CategoryTheory.ConnectedComponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instEssSurjDecomposedDecomposedTo", "kind": "instance", "module": "Mathlib.CategoryTheory.ConnectedComponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instIsEquivalenceDecomposedDecomposedTo", "kind": "instance", "module": "Mathlib.CategoryTheory.ConnectedComponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.decomposedEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.ConnectedComponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CartesianCopyDiscard.instComonObjOfCartesian", "kind": "abbrev", "module": "Mathlib.CategoryTheory.CopyDiscardCategory.Cartesian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CartesianCopyDiscard.instIsCommComonObjOfCartesian", "kind": "instance", "module": "Mathlib.CategoryTheory.CopyDiscardCategory.Cartesian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CartesianCopyDiscard.ofCartesianMonoidalCategory", "kind": "abbrev", "module": "Mathlib.CategoryTheory.CopyDiscardCategory.Cartesian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CartesianCopyDiscard.instDeterministic", "kind": "instance", "module": "Mathlib.CategoryTheory.CopyDiscardCategory.Cartesian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Deterministic", "kind": "abbrev", "module": "Mathlib.CategoryTheory.CopyDiscardCategory.Deterministic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Deterministic.copy_natural", "kind": "theorem", "module": "Mathlib.CategoryTheory.CopyDiscardCategory.Deterministic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Core.inclusion", "kind": "definition", "module": "Mathlib.CategoryTheory.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Core.forgetFunctorToCore", "kind": "definition", "module": "Mathlib.CategoryTheory.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Functor.coreCompInclusionIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.core_comp_inclusion", "kind": "theorem", "module": "Mathlib.CategoryTheory.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.core", "kind": "definition", "module": "Mathlib.CategoryTheory.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Iso.coreId", "kind": "theorem", "module": "Mathlib.CategoryTheory.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.coreWhiskerLeft", "kind": "theorem", "module": "Mathlib.CategoryTheory.Core", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Iso.coreWhiskerRight", "kind": "theorem", "module": "Mathlib.CategoryTheory.Core", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Iso.coreLeftUnitor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Core", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Iso.coreRightUnitor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Core", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Iso.coreAssociator", "kind": "theorem", "module": "Mathlib.CategoryTheory.Core", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Core.functorToCoreCompLeftIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Core.functorToCore_comp_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Core.functorToCoreCompRightIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Core.functorToCore_comp_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Core.inclusionCompFunctorToCoreIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Core.inclusion_comp_functorToCore", "kind": "theorem", "module": "Mathlib.CategoryTheory.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Core.functorToCoreInclusionIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Core.functorToCore_inclusion", "kind": "theorem", "module": "Mathlib.CategoryTheory.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.core", "kind": "definition", "module": "Mathlib.CategoryTheory.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.coreFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ofEquivFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.discreteCountable", "kind": "instance", "module": "Mathlib.CategoryTheory.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.countableCategoryDiscreteOfCountable", "kind": "instance", "module": "Mathlib.CategoryTheory.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Discrete.id_def'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Discrete.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Discrete.instIsIso", "kind": "instance", "module": "Mathlib.CategoryTheory.Discrete.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Discrete.functor", "kind": "definition", "module": "Mathlib.CategoryTheory.Discrete.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Discrete.functor_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Discrete.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Discrete.functor_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Discrete.Basic", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Discrete.functor_obj_eq_as", "kind": "theorem", "module": "Mathlib.CategoryTheory.Discrete.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Discrete.functor_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Discrete.Basic", "is_tactic_proof": true, "tactics": ["fapply", "intro", "intro"], "tactic_count": 3}
{"name": "CategoryTheory.Discrete.functorComp", "kind": "definition", "module": "Mathlib.CategoryTheory.Discrete.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Discrete.natTrans", "kind": "definition", "module": "Mathlib.CategoryTheory.Discrete.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Discrete.natIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Discrete.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Discrete.instIsIsoFunctorNatTrans", "kind": "instance", "module": "Mathlib.CategoryTheory.Discrete.Basic", "is_tactic_proof": true, "tactics": ["change", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Discrete.natIso_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Discrete.Basic", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Discrete.natIsoFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Discrete.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Discrete.compNatIsoDiscrete", "kind": "definition", "module": "Mathlib.CategoryTheory.Discrete.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Discrete.equivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.Discrete.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Discrete.equivOfEquivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.Discrete.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Discrete.opposite", "kind": "definition", "module": "Mathlib.CategoryTheory.Discrete.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Discrete.functor_map_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Discrete.Basic", "is_tactic_proof": true, "tactics": ["have", "rw", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.Discrete.forall", "kind": "theorem", "module": "Mathlib.CategoryTheory.Discrete.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Discrete.exists", "kind": "theorem", "module": "Mathlib.CategoryTheory.Discrete.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.piEquivalenceFunctorDiscrete", "kind": "definition", "module": "Mathlib.CategoryTheory.Discrete.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Discrete.isDiscrete", "kind": "instance", "module": "Mathlib.CategoryTheory.Discrete.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.obj_ext_of_isDiscrete", "kind": "theorem", "module": "Mathlib.CategoryTheory.Discrete.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isIso_of_isDiscrete", "kind": "instance", "module": "Mathlib.CategoryTheory.Discrete.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instIsDiscreteOpposite", "kind": "instance", "module": "Mathlib.CategoryTheory.Discrete.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Discrete.structuredArrowEquivalenceOfUnique", "kind": "definition", "module": "Mathlib.CategoryTheory.Discrete.StructuredArrow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Discrete.costructuredArrowEquivalenceOfUnique", "kind": "definition", "module": "Mathlib.CategoryTheory.Discrete.StructuredArrow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Discrete.productEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Discrete.SumsProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Discrete.sumEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Discrete.SumsProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsDiscrete.prod", "kind": "instance", "module": "Mathlib.CategoryTheory.Discrete.SumsProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsDiscrete.sum", "kind": "instance", "module": "Mathlib.CategoryTheory.Discrete.SumsProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsCartesianDistributive", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Distributive.Cartesian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsCartesianDistributive.of_isMonoidalLeftDistrib", "kind": "theorem", "module": "Mathlib.CategoryTheory.Distributive.Cartesian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsCartesianDistributive.monoCoprod", "kind": "instance", "module": "Mathlib.CategoryTheory.Distributive.Cartesian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.leftDistrib", "kind": "definition", "module": "Mathlib.CategoryTheory.Distributive.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Distributive.term∂L", "kind": "definition", "module": "Mathlib.CategoryTheory.Distributive.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Distributive._aux_Mathlib_CategoryTheory_Distributive_Monoidal___macroRules_CategoryTheory_Distributive_term∂L_1", "kind": "definition", "module": "Mathlib.CategoryTheory.Distributive.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Distributive._aux_Mathlib_CategoryTheory_Distributive_Monoidal___unexpand_CategoryTheory_leftDistrib_1", "kind": "definition", "module": "Mathlib.CategoryTheory.Distributive.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsMonoidalLeftDistrib.of_isIso_coprodComparisonTensorLeft", "kind": "theorem", "module": "Mathlib.CategoryTheory.Distributive.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.leftDistrib_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Distributive.Monoidal", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "CategoryTheory.coprod_inl_leftDistrib_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Distributive.Monoidal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.coprod_inr_leftDistrib_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Distributive.Monoidal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.whiskerLeft_coprod_inl_leftDistrib_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Distributive.Monoidal", "is_tactic_proof": true, "tactics": ["apply", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.whiskerLeft_coprod_inr_leftDistrib_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Distributive.Monoidal", "is_tactic_proof": true, "tactics": ["apply", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.rightDistrib", "kind": "definition", "module": "Mathlib.CategoryTheory.Distributive.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Distributive.term∂R", "kind": "definition", "module": "Mathlib.CategoryTheory.Distributive.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Distributive._aux_Mathlib_CategoryTheory_Distributive_Monoidal___macroRules_CategoryTheory_Distributive_term∂R_1", "kind": "definition", "module": "Mathlib.CategoryTheory.Distributive.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Distributive._aux_Mathlib_CategoryTheory_Distributive_Monoidal___unexpand_CategoryTheory_rightDistrib_1", "kind": "definition", "module": "Mathlib.CategoryTheory.Distributive.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsMonoidalRightDistrib.of_isIso_coprodComparisonTensorRight", "kind": "theorem", "module": "Mathlib.CategoryTheory.Distributive.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.rightDistrib_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Distributive.Monoidal", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "CategoryTheory.coprod_inl_rightDistrib_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Distributive.Monoidal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.coprod_inr_rightDistrib_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Distributive.Monoidal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.whiskerRight_coprod_inl_rightDistrib_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Distributive.Monoidal", "is_tactic_proof": true, "tactics": ["apply", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.whiskerRight_coprod_inr_rightDistrib_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Distributive.Monoidal", "is_tactic_proof": true, "tactics": ["apply", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.coprodComparison_tensorLeft_braiding_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Distributive.Monoidal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.coprodComparison_tensorRight_braiding_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Distributive.Monoidal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.SymmetricCategory.isMonoidalDistrib_of_isMonoidalLeftDistrib", "kind": "theorem", "module": "Mathlib.CategoryTheory.Distributive.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SymmetricCategory.rightDistrib_of_leftDistrib", "kind": "theorem", "module": "Mathlib.CategoryTheory.Distributive.Monoidal", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalClosed.isMonoidalLeftDistrib", "kind": "instance", "module": "Mathlib.CategoryTheory.Distributive.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isMonoidalDistrib.of_symmetric_monoidal_closed", "kind": "instance", "module": "Mathlib.CategoryTheory.Distributive.Monoidal", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalClosed.leftDistrib_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Distributive.Monoidal", "is_tactic_proof": true, "tactics": ["rw", "ext"], "tactic_count": 2}
{"name": "CategoryTheory.isMonoidalLeftDistrib.of_endofunctors", "kind": "instance", "module": "Mathlib.CategoryTheory.Distributive.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsMonoidalDistrib.of_MonoidalPreadditive_with_binary_coproducts", "kind": "instance", "module": "Mathlib.CategoryTheory.Distributive.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.EffectiveEpi.getStruct", "kind": "definition", "module": "Mathlib.CategoryTheory.EffectiveEpi.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.EffectiveEpi.desc", "kind": "definition", "module": "Mathlib.CategoryTheory.EffectiveEpi.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.EffectiveEpi.fac", "kind": "theorem", "module": "Mathlib.CategoryTheory.EffectiveEpi.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.EffectiveEpi.uniq", "kind": "theorem", "module": "Mathlib.CategoryTheory.EffectiveEpi.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.epi_of_effectiveEpi", "kind": "instance", "module": "Mathlib.CategoryTheory.EffectiveEpi.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.strongEpi_of_effectiveEpi", "kind": "instance", "module": "Mathlib.CategoryTheory.EffectiveEpi.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.EffectiveEpiFamily.getStruct", "kind": "definition", "module": "Mathlib.CategoryTheory.EffectiveEpi.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.EffectiveEpiFamily.desc", "kind": "definition", "module": "Mathlib.CategoryTheory.EffectiveEpi.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.EffectiveEpiFamily.fac", "kind": "theorem", "module": "Mathlib.CategoryTheory.EffectiveEpi.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.EffectiveEpiFamily.uniq", "kind": "theorem", "module": "Mathlib.CategoryTheory.EffectiveEpi.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.EffectiveEpiFamily.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.EffectiveEpi.Basic", "is_tactic_proof": false, "tactics": ["have", "apply", "rw", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.effectiveEpiFamilyStructSingletonOfEffectiveEpi", "kind": "definition", "module": "Mathlib.CategoryTheory.EffectiveEpi.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instEffectiveEpiFamily", "kind": "instance", "module": "Mathlib.CategoryTheory.EffectiveEpi.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.effectiveEpiStructOfEffectiveEpiFamilySingleton", "kind": "definition", "module": "Mathlib.CategoryTheory.EffectiveEpi.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instEffectiveEpiOfEffectiveEpiFamily", "kind": "instance", "module": "Mathlib.CategoryTheory.EffectiveEpi.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.effectiveEpi_iff_effectiveEpiFamily", "kind": "theorem", "module": "Mathlib.CategoryTheory.EffectiveEpi.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.effectiveEpiFamilyStructOfIsIsoDesc", "kind": "definition", "module": "Mathlib.CategoryTheory.EffectiveEpi.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instEffectiveEpiFamilyOfIsIsoDesc", "kind": "instance", "module": "Mathlib.CategoryTheory.EffectiveEpi.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.effectiveEpiStructOfIsIso", "kind": "definition", "module": "Mathlib.CategoryTheory.EffectiveEpi.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instEffectiveEpiOfIsIso", "kind": "instance", "module": "Mathlib.CategoryTheory.EffectiveEpi.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory._example", "kind": "example", "module": "Mathlib.CategoryTheory.EffectiveEpi.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.EffectiveEpiFamilyStruct.reindex", "kind": "definition", "module": "Mathlib.CategoryTheory.EffectiveEpi.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.EffectiveEpiFamily.reindex", "kind": "theorem", "module": "Mathlib.CategoryTheory.EffectiveEpi.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.effectiveEpiFamilyStructCompOfEffectiveEpiSplitEpi'", "kind": "definition", "module": "Mathlib.CategoryTheory.EffectiveEpi.Comp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.effectiveEpiFamilyStructCompOfEffectiveEpiSplitEpi", "kind": "definition", "module": "Mathlib.CategoryTheory.EffectiveEpi.Comp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instEffectiveEpiFamilyCompOfIsSplitEpi", "kind": "instance", "module": "Mathlib.CategoryTheory.EffectiveEpi.Comp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory._example", "kind": "example", "module": "Mathlib.CategoryTheory.EffectiveEpi.Comp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsSplitEpi.EffectiveEpi", "kind": "instance", "module": "Mathlib.CategoryTheory.EffectiveEpi.Comp", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.effectiveEpiFamilyStructOfComp", "kind": "definition", "module": "Mathlib.CategoryTheory.EffectiveEpi.Comp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.effectiveEpiFamily_of_effectiveEpi_epi_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.EffectiveEpi.Comp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.effectiveEpi_of_effectiveEpi_epi_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.EffectiveEpi.Comp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.effectiveEpiFamilyStructCompIso_aux", "kind": "theorem", "module": "Mathlib.CategoryTheory.EffectiveEpi.Comp", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "CategoryTheory.effectiveEpiFamilyStructCompIso", "kind": "definition", "module": "Mathlib.CategoryTheory.EffectiveEpi.Comp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instEffectiveEpiFamilyComp", "kind": "instance", "module": "Mathlib.CategoryTheory.EffectiveEpi.Comp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory._example", "kind": "example", "module": "Mathlib.CategoryTheory.EffectiveEpi.Comp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.effectiveEpiStructIsColimitDescOfEffectiveEpiFamily", "kind": "definition", "module": "Mathlib.CategoryTheory.EffectiveEpi.Coproduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instEffectiveEpiDescOfEffectiveEpiFamily", "kind": "instance", "module": "Mathlib.CategoryTheory.EffectiveEpi.Coproduct", "is_tactic_proof": true, "tactics": ["let", "simp", "exact"], "tactic_count": 3}
{"name": "CategoryTheory._example", "kind": "example", "module": "Mathlib.CategoryTheory.EffectiveEpi.Coproduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.effectiveEpiFamilyStructOfEffectiveEpiDesc_aux", "kind": "theorem", "module": "Mathlib.CategoryTheory.EffectiveEpi.Coproduct", "is_tactic_proof": true, "tactics": ["apply_fun", "ext", "simp", "rw", "simp", "apply_fun", "ext", "simp", "simp", "rw", "simp", "rw", "apply", "apply_fun", "rw", "simp", "apply_fun", "simp", "simp", "rw", "simpa"], "tactic_count": 21}
{"name": "CategoryTheory.effectiveEpiFamilyStructOfEffectiveEpiDesc", "kind": "definition", "module": "Mathlib.CategoryTheory.EffectiveEpi.Coproduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.effectiveEpiOverObj", "kind": "definition", "module": "Mathlib.CategoryTheory.EffectiveEpi.Enough", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.effectiveEpiOver", "kind": "definition", "module": "Mathlib.CategoryTheory.EffectiveEpi.Enough", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instEffectiveEpiEffectiveEpiOver", "kind": "instance", "module": "Mathlib.CategoryTheory.EffectiveEpi.Enough", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.equivalenceEffectivePresentation", "kind": "definition", "module": "Mathlib.CategoryTheory.EffectiveEpi.Enough", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instEffectivelyEnoughOfIsEquivalence", "kind": "instance", "module": "Mathlib.CategoryTheory.EffectiveEpi.Enough", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.effectiveEpi_desc_iff_effectiveEpiFamily", "kind": "theorem", "module": "Mathlib.CategoryTheory.EffectiveEpi.Extensive", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "CategoryTheory.instReflectsFiniteEffectiveEpiFamiliesOfReflectsEffectiveEpis", "kind": "instance", "module": "Mathlib.CategoryTheory.EffectiveEpi.Extensive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instPreservesFiniteEffectiveEpiFamiliesOfPreservesEffectiveEpis", "kind": "instance", "module": "Mathlib.CategoryTheory.EffectiveEpi.Extensive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.effectiveEpiFamilyStructOfEquivalence_aux", "kind": "theorem", "module": "Mathlib.CategoryTheory.EffectiveEpi.Preserves", "is_tactic_proof": true, "tactics": ["have", "simp", "simpa"], "tactic_count": 3}
{"name": "CategoryTheory.effectiveEpiFamilyStructOfEquivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.EffectiveEpi.Preserves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Enriched.FunctorCategory.functorEnriched_comp_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Enriched.FunctorCategory", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Enriched.FunctorCategory.functorEnriched_assoc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Enriched.FunctorCategory", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "rw"], "tactic_count": 3}
{"name": "CategoryTheory.Enriched.FunctorCategory.functorEnrichedCategory", "kind": "definition", "module": "Mathlib.CategoryTheory.Enriched.FunctorCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Enriched.FunctorCategory.functorHomEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Enriched.FunctorCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Enriched.FunctorCategory.functorHomEquiv_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Enriched.FunctorCategory", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Enriched.FunctorCategory.functorHomEquiv_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Enriched.FunctorCategory", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "ext", "rw", "simp"], "tactic_count": 5}
{"name": "CategoryTheory.Enriched.FunctorCategory.functorEnrichedOrdinaryCategory", "kind": "definition", "module": "Mathlib.CategoryTheory.Enriched.FunctorCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.eHomCongr", "kind": "definition", "module": "Mathlib.CategoryTheory.Enriched.HomCongr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.eHomCongr_refl", "kind": "theorem", "module": "Mathlib.CategoryTheory.Enriched.HomCongr", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "CategoryTheory.Iso.eHomCongr_trans", "kind": "theorem", "module": "Mathlib.CategoryTheory.Enriched.HomCongr", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Iso.eHomCongr_symm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Enriched.HomCongr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.eHomCongr_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Enriched.HomCongr", "is_tactic_proof": true, "tactics": ["simp", "rw", "hom_inv_id_assoc,", "eHom_whisker_cancel_assoc,"], "tactic_count": 4}
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{"name": "CategoryTheory.Enriched.HasConicalLimits", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Enriched.Limits.HasConicalLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Enriched.HasConicalLimit.of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Enriched.Limits.HasConicalLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Enriched.HasConicalLimit.of_equiv", "kind": "instance", "module": "Mathlib.CategoryTheory.Enriched.Limits.HasConicalLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Enriched.HasConicalLimit.of_equiv_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Enriched.Limits.HasConicalLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Enriched.HasConicalLimitsOfShape.hasLimitsOfShape", "kind": "instance", "module": "Mathlib.CategoryTheory.Enriched.Limits.HasConicalLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Enriched.HasConicalLimitsOfShape.of_equiv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Enriched.Limits.HasConicalLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Enriched.HasConicalLimitsOfSize.hasLimitsOfSize", "kind": "instance", "module": "Mathlib.CategoryTheory.Enriched.Limits.HasConicalLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Enriched._example", "kind": "example", "module": "Mathlib.CategoryTheory.Enriched.Limits.HasConicalLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Enriched.HasConicalProduct", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Enriched.Limits.HasConicalProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Enriched._example", "kind": "example", "module": "Mathlib.CategoryTheory.Enriched.Limits.HasConicalProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Enriched.HasConicalPullback", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Enriched.Limits.HasConicalPullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Enriched._example", "kind": "example", "module": "Mathlib.CategoryTheory.Enriched.Limits.HasConicalPullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Enriched.HasConicalPullbacks", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Enriched.Limits.HasConicalPullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Enriched._example", "kind": "example", "module": "Mathlib.CategoryTheory.Enriched.Limits.HasConicalPullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Enriched.HasConicalTerminal", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Enriched.Limits.HasConicalTerminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Enriched._example", "kind": "example", "module": "Mathlib.CategoryTheory.Enriched.Limits.HasConicalTerminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Enriched.HasConicalProducts.hasConicalTerminal", "kind": "instance", "module": "Mathlib.CategoryTheory.Enriched.Limits.HasConicalTerminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.EnrichedCategory.opposite", "kind": "instance", "module": "Mathlib.CategoryTheory.Enriched.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.eComp_op_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Enriched.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.tensorHom_eComp_op_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Enriched.Opposite", "is_tactic_proof": true, "tactics": ["rw", "exact", "braiding_naturality_assoc"], "tactic_count": 3}
{"name": "CategoryTheory.forgetEnrichmentOppositeEquivalence.functor", "kind": "definition", "module": "Mathlib.CategoryTheory.Enriched.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.forgetEnrichmentOppositeEquivalence.inverse", "kind": "definition", "module": "Mathlib.CategoryTheory.Enriched.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.forgetEnrichmentOppositeEquivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.Enriched.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.EnrichedOrdinaryCategory.opposite", "kind": "instance", "module": "Mathlib.CategoryTheory.Enriched.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.eHomEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Enriched.Ordinary.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.eHomEquiv_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Enriched.Ordinary.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.eHomEquiv_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Enriched.Ordinary.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.eHomWhiskerRight", "kind": "definition", "module": "Mathlib.CategoryTheory.Enriched.Ordinary.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.eHomWhiskerRight_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Enriched.Ordinary.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "CategoryTheory.eComp_eHomWhiskerRight", "kind": "theorem", "module": "Mathlib.CategoryTheory.Enriched.Ordinary.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.eHomWhiskerLeft", "kind": "definition", "module": "Mathlib.CategoryTheory.Enriched.Ordinary.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.eHomWhiskerLeft_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Enriched.Ordinary.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.eHomWhiskerLeft_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Enriched.Ordinary.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "e_assoc,", "whiskerLeft_rightUnitor_inv_assoc,", "whisker_exchange_assoc,"], "tactic_count": 5}
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{"name": "CategoryTheory.eHom_whisker_cancel", "kind": "theorem", "module": "Mathlib.CategoryTheory.Enriched.Ordinary.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "simp", "assoc]", "simp", "change", "simp"], "tactic_count": 6}
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{"name": "CategoryTheory.eHom_whisker_exchange", "kind": "theorem", "module": "Mathlib.CategoryTheory.Enriched.Ordinary.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "leftUnitor_tensor_inv_assoc,", "whisker_exchange_assoc,"], "tactic_count": 4}
{"name": "CategoryTheory.eHomFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Enriched.Ordinary.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ForgetEnrichment.enrichedOrdinaryCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Enriched.Ordinary.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ForgetEnrichment.equivInverse", "kind": "definition", "module": "Mathlib.CategoryTheory.Enriched.Ordinary.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ForgetEnrichment.equivFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Enriched.Ordinary.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ForgetEnrichment.equiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Enriched.Ordinary.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.eCoyoneda", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Enriched.Ordinary.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instCategoryTransportEnrichment", "kind": "instance", "module": "Mathlib.CategoryTheory.Enriched.Ordinary.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.TransportEnrichment.ofOrdinaryEnrichedCategoryEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Enriched.Ordinary.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.TransportEnrichment.enrichedOrdinaryCategory", "kind": "definition", "module": "Mathlib.CategoryTheory.Enriched.Ordinary.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.TransportEnrichment.forgetEnrichmentEquivFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Enriched.Ordinary.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.TransportEnrichment.forgetEnrichmentEquivInverse", "kind": "definition", "module": "Mathlib.CategoryTheory.Enriched.Ordinary.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.TransportEnrichment.forgetEnrichmentEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Enriched.Ordinary.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instEnrichedOrdinaryCategoryFullSubcategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Enriched.Ordinary.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.unop_mono_of_epi", "kind": "instance", "module": "Mathlib.CategoryTheory.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.unop_epi_of_mono", "kind": "instance", "module": "Mathlib.CategoryTheory.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.op_mono_of_epi", "kind": "instance", "module": "Mathlib.CategoryTheory.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.op_epi_of_mono", "kind": "instance", "module": "Mathlib.CategoryTheory.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.op_mono_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.op_epi_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.unop_mono_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.unop_epi_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SplitMono.comp", "kind": "definition", "module": "Mathlib.CategoryTheory.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsSplitMono.mk'", "kind": "theorem", "module": "Mathlib.CategoryTheory.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SplitEpi.comp", "kind": "definition", "module": "Mathlib.CategoryTheory.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsSplitEpi.mk'", "kind": "theorem", "module": "Mathlib.CategoryTheory.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.retraction", "kind": "definition", "module": "Mathlib.CategoryTheory.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsSplitMono.id", "kind": "theorem", "module": "Mathlib.CategoryTheory.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SplitMono.splitEpi", "kind": "definition", "module": "Mathlib.CategoryTheory.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.retraction_isSplitEpi", "kind": "instance", "module": "Mathlib.CategoryTheory.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isIso_of_epi_of_isSplitMono", "kind": "theorem", "module": "Mathlib.CategoryTheory.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.section_", "kind": "definition", "module": "Mathlib.CategoryTheory.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsSplitEpi.id", "kind": "theorem", "module": "Mathlib.CategoryTheory.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SplitEpi.splitMono", "kind": "definition", "module": "Mathlib.CategoryTheory.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.section_isSplitMono", "kind": "instance", "module": "Mathlib.CategoryTheory.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isIso_of_mono_of_isSplitEpi", "kind": "theorem", "module": "Mathlib.CategoryTheory.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsSplitMono.of_iso", "kind": "instance", "module": "Mathlib.CategoryTheory.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsSplitEpi.of_iso", "kind": "instance", "module": "Mathlib.CategoryTheory.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SplitMono.mono", "kind": "theorem", "module": "Mathlib.CategoryTheory.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsSplitMono.mono", "kind": "instance", "module": "Mathlib.CategoryTheory.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SplitEpi.epi", "kind": "theorem", "module": "Mathlib.CategoryTheory.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsSplitEpi.epi", "kind": "instance", "module": "Mathlib.CategoryTheory.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instIsSplitMonoComp", "kind": "instance", "module": "Mathlib.CategoryTheory.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instIsSplitEpiComp", "kind": "instance", "module": "Mathlib.CategoryTheory.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsIso.of_mono_retraction'", "kind": "theorem", "module": "Mathlib.CategoryTheory.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsIso.of_mono_retraction", "kind": "theorem", "module": "Mathlib.CategoryTheory.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsIso.of_epi_section'", "kind": "theorem", "module": "Mathlib.CategoryTheory.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsIso.of_epi_section", "kind": "theorem", "module": "Mathlib.CategoryTheory.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Groupoid.ofTruncSplitMono", "kind": "definition", "module": "Mathlib.CategoryTheory.EpiMono", "is_tactic_proof": true, "tactics": ["apply", "intro", "have", "have", "apply"], "tactic_count": 5}
{"name": "CategoryTheory.isSplitMono_of_mono", "kind": "theorem", "module": "Mathlib.CategoryTheory.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isSplitEpi_of_epi", "kind": "theorem", "module": "Mathlib.CategoryTheory.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SplitMono.map", "kind": "definition", "module": "Mathlib.CategoryTheory.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SplitEpi.map", "kind": "definition", "module": "Mathlib.CategoryTheory.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instIsSplitMonoMap", "kind": "instance", "module": "Mathlib.CategoryTheory.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instIsSplitEpiMap", "kind": "instance", "module": "Mathlib.CategoryTheory.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.epi_comp_iff_of_epi", "kind": "theorem", "module": "Mathlib.CategoryTheory.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.epi_comp_iff_of_isIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.EpiMono", "is_tactic_proof": true, "tactics": ["refine", "simpa"], "tactic_count": 2}
{"name": "CategoryTheory.mono_comp_iff_of_isIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.EpiMono", "is_tactic_proof": true, "tactics": ["refine", "simpa"], "tactic_count": 2}
{"name": "CategoryTheory.mono_comp_iff_of_mono", "kind": "theorem", "module": "Mathlib.CategoryTheory.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SplitMono.op", "kind": "definition", "module": "Mathlib.CategoryTheory.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SplitEpi.op", "kind": "definition", "module": "Mathlib.CategoryTheory.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instIsSplitEpiOppositeOpOfIsSplitMono", "kind": "instance", "module": "Mathlib.CategoryTheory.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instIsSplitMonoOppositeOpOfIsSplitEpi", "kind": "instance", "module": "Mathlib.CategoryTheory.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.eqToHom_refl", "kind": "theorem", "module": "Mathlib.CategoryTheory.EqToHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.eqToHom_comp_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.EqToHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.eqToHom_comp_heq", "kind": "theorem", "module": "Mathlib.CategoryTheory.EqToHom", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "CategoryTheory.heq_comp_eqToHom_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.EqToHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.heq_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.EqToHom", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "CategoryTheory.eqToHom_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.EqToHom", "is_tactic_proof": true, "tactics": ["cases", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.eqToHom_iso_hom_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.EqToHom", "is_tactic_proof": true, "tactics": ["cases", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.eqToHom_iso_inv_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.EqToHom", "is_tactic_proof": true, "tactics": ["cases", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.congrArg_cast_hom_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.EqToHom", "is_tactic_proof": true, "tactics": ["cases", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.congrArg_mpr_hom_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.EqToHom", "is_tactic_proof": true, "tactics": ["cases", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.congrArg_cast_hom_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.EqToHom", "is_tactic_proof": true, "tactics": ["cases", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.congrArg_mpr_hom_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.EqToHom", "is_tactic_proof": true, "tactics": ["cases", "simp"], "tactic_count": 2}
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{"name": "CategoryTheory.eqToIso.hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.EqToHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.eqToIso.inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.EqToHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.eqToIso_refl", "kind": "theorem", "module": "Mathlib.CategoryTheory.EqToHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.eqToIso_trans", "kind": "theorem", "module": "Mathlib.CategoryTheory.EqToHom", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
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{"name": "CategoryTheory.instIsIsoEqToHom", "kind": "instance", "module": "Mathlib.CategoryTheory.EqToHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.inv_eqToHom", "kind": "theorem", "module": "Mathlib.CategoryTheory.EqToHom", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.hext", "kind": "theorem", "module": "Mathlib.CategoryTheory.EqToHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.congr_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.EqToHom", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.congr_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.EqToHom", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
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{"name": "CategoryTheory.Functor.precomp_map_heq", "kind": "theorem", "module": "Mathlib.CategoryTheory.EqToHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.postcomp_map_heq", "kind": "theorem", "module": "Mathlib.CategoryTheory.EqToHom", "is_tactic_proof": true, "tactics": ["dsimp", "congr"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.postcomp_map_heq'", "kind": "theorem", "module": "Mathlib.CategoryTheory.EqToHom", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "CategoryTheory.NatTrans.congr", "kind": "theorem", "module": "Mathlib.CategoryTheory.EqToHom", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.eq_conj_eqToHom", "kind": "theorem", "module": "Mathlib.CategoryTheory.EqToHom", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.dcongr_arg", "kind": "theorem", "module": "Mathlib.CategoryTheory.EqToHom", "is_tactic_proof": true, "tactics": ["subst", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.InducedCategory.eqToHom_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.EqToHom", "is_tactic_proof": true, "tactics": ["subst", "rfl"], "tactic_count": 2}
{"name": "CategoryTheory.ObjectProperty.eqToHom_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.EqToHom", "is_tactic_proof": true, "tactics": ["subst", "rfl"], "tactic_count": 2}
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{"name": "CategoryTheory._aux_Mathlib_CategoryTheory_Equivalence___unexpand_CategoryTheory_Equivalence_1", "kind": "definition", "module": "Mathlib.CategoryTheory.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.unit", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Equivalence.Equivalence_mk'_unit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Equivalence.Equivalence_mk'_unitInv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Equivalence.unitInv_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Equivalence.counitInv_functor_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Equivalence", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.Equivalence.counitInv_app_functor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Equivalence", "is_tactic_proof": true, "tactics": ["symm", "simp", "rw", "rfl"], "tactic_count": 4}
{"name": "CategoryTheory.Equivalence.counit_app_functor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Equivalence", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
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{"name": "CategoryTheory.Equivalence.funInvIdAssoc_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Equivalence", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Equivalence.funInvIdAssoc_inv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Equivalence", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
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{"name": "CategoryTheory.Equivalence.invFunIdAssoc_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Equivalence", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Equivalence.invFunIdAssoc_inv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Equivalence", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
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{"name": "CategoryTheory.Equivalence.cancel_unit_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Equivalence", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Equivalence.cancel_unitInv_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Equivalence", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Equivalence.cancel_counit_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Equivalence", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Equivalence.cancel_counitInv_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Equivalence", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Equivalence.cancel_unit_right_assoc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Equivalence", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "CategoryTheory.Equivalence.cancel_unit_right_assoc'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Equivalence", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "CategoryTheory.Equivalence.pow", "kind": "definition", "module": "Mathlib.CategoryTheory.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.instPowInt", "kind": "instance", "module": "Mathlib.CategoryTheory.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.pow_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.pow_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.pow_neg_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.essSurj_functor", "kind": "instance", "module": "Mathlib.CategoryTheory.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.essSurj_inverse", "kind": "instance", "module": "Mathlib.CategoryTheory.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.fullyFaithfulFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.fullyFaithfulInverse", "kind": "definition", "module": "Mathlib.CategoryTheory.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.faithful_functor", "kind": "instance", "module": "Mathlib.CategoryTheory.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.faithful_inverse", "kind": "instance", "module": "Mathlib.CategoryTheory.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.full_functor", "kind": "instance", "module": "Mathlib.CategoryTheory.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.full_inverse", "kind": "instance", "module": "Mathlib.CategoryTheory.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.changeFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.changeFunctor_refl", "kind": "theorem", "module": "Mathlib.CategoryTheory.Equivalence", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Equivalence.changeFunctor_trans", "kind": "theorem", "module": "Mathlib.CategoryTheory.Equivalence", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Equivalence.changeInverse", "kind": "definition", "module": "Mathlib.CategoryTheory.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.isEquivalence_functor", "kind": "instance", "module": "Mathlib.CategoryTheory.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.isEquivalence_inverse", "kind": "instance", "module": "Mathlib.CategoryTheory.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsEquivalence.mk'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.inv", "kind": "definition", "module": "Mathlib.CategoryTheory.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.asEquivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isEquivalence_refl", "kind": "instance", "module": "Mathlib.CategoryTheory.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isEquivalence_inv", "kind": "instance", "module": "Mathlib.CategoryTheory.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isEquivalence_trans", "kind": "instance", "module": "Mathlib.CategoryTheory.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instIsEquivalenceObjWhiskeringLeft", "kind": "instance", "module": "Mathlib.CategoryTheory.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instIsEquivalenceObjWhiskeringRight", "kind": "instance", "module": "Mathlib.CategoryTheory.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.fun_inv_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Equivalence", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.inv_fun_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Equivalence", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.isEquivalence_of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isEquivalence_iff_of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isEquivalence_of_comp_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Equivalence", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.isEquivalence_of_comp_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Equivalence", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Equivalence.essSurjInducedFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.inducedFunctorOfEquiv", "kind": "instance", "module": "Mathlib.CategoryTheory.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.fullyFaithfulToEssImage", "kind": "instance", "module": "Mathlib.CategoryTheory.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.fullSubcategoryCongr", "kind": "definition", "module": "Mathlib.CategoryTheory.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.compInverseIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.isoCompInverse", "kind": "definition", "module": "Mathlib.CategoryTheory.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.inverseCompIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.isoInverseComp", "kind": "definition", "module": "Mathlib.CategoryTheory.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.isoInverseOfIsoFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.isoFunctorOfIsoInverse", "kind": "definition", "module": "Mathlib.CategoryTheory.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.isoFunctorOfIsoInverse_isoInverseOfIsoFunctor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Equivalence", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Iso.isoInverseOfIsoFunctor_isoFunctorOfIsoInverse", "kind": "theorem", "module": "Mathlib.CategoryTheory.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.symmEquivFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Equivalence.Symmetry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.symmEquivInverse", "kind": "definition", "module": "Mathlib.CategoryTheory.Equivalence.Symmetry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.symmEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Equivalence.Symmetry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.inverseFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Equivalence.Symmetry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.inverseFunctorObjIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Equivalence.Symmetry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.inverseFunctorMapIso_symm_eq_isoInverseOfIsoFunctor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Equivalence.Symmetry", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Equivalence.inverseFunctorObj'", "kind": "definition", "module": "Mathlib.CategoryTheory.Equivalence.Symmetry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.congrLeftFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Equivalence.Symmetry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.essImage", "kind": "definition", "module": "Mathlib.CategoryTheory.EssentialImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.essImage.witness", "kind": "definition", "module": "Mathlib.CategoryTheory.EssentialImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.essImage.getIso", "kind": "definition", "module": "Mathlib.CategoryTheory.EssentialImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.essImage.ofIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.EssentialImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instIsClosedUnderIsomorphismsEssImage", "kind": "instance", "module": "Mathlib.CategoryTheory.EssentialImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.essImage.ofNatIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.EssentialImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.essImage_eq_of_natIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.EssentialImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.obj_mem_essImage", "kind": "theorem", "module": "Mathlib.CategoryTheory.EssentialImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.EssImageSubcategory", "kind": "abbrev", "module": "Mathlib.CategoryTheory.EssentialImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.essImage_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.EssentialImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.toEssImage", "kind": "definition", "module": "Mathlib.CategoryTheory.EssentialImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.toEssImageCompι", "kind": "definition", "module": "Mathlib.CategoryTheory.EssentialImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.EssSurj.toEssImage", "kind": "instance", "module": "Mathlib.CategoryTheory.EssentialImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.essSurj_of_surj", "kind": "theorem", "module": "Mathlib.CategoryTheory.EssentialImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.objPreimage", "kind": "definition", "module": "Mathlib.CategoryTheory.EssentialImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.objObjPreimageIso", "kind": "definition", "module": "Mathlib.CategoryTheory.EssentialImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.Faithful.toEssImage", "kind": "instance", "module": "Mathlib.CategoryTheory.EssentialImage", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.Full.toEssImage", "kind": "instance", "module": "Mathlib.CategoryTheory.EssentialImage", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.instEssSurjId", "kind": "instance", "module": "Mathlib.CategoryTheory.EssentialImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.essSurj_of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.EssentialImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.essSurj_comp", "kind": "instance", "module": "Mathlib.CategoryTheory.EssentialImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.essSurj_of_comp_fully_faithful", "kind": "theorem", "module": "Mathlib.CategoryTheory.EssentialImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.essImage_comp_apply_of_essSurj", "kind": "theorem", "module": "Mathlib.CategoryTheory.EssentialImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.essImage_comp_of_essSurj", "kind": "theorem", "module": "Mathlib.CategoryTheory.EssentialImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.essImage.liftFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.EssentialImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.essImage.liftFunctorCompIso", "kind": "definition", "module": "Mathlib.CategoryTheory.EssentialImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.EssentiallySmall.mk'", "kind": "theorem", "module": "Mathlib.CategoryTheory.EssentiallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallModel", "kind": "definition", "module": "Mathlib.CategoryTheory.EssentiallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.smallCategorySmallModel", "kind": "instance", "module": "Mathlib.CategoryTheory.EssentiallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.equivSmallModel", "kind": "definition", "module": "Mathlib.CategoryTheory.EssentiallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instEssentiallySmallOpposite", "kind": "instance", "module": "Mathlib.CategoryTheory.EssentiallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.essentiallySmall_congr", "kind": "theorem", "module": "Mathlib.CategoryTheory.EssentiallySmall", "is_tactic_proof": true, "tactics": ["fconstructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.Discrete.essentiallySmallOfSmall", "kind": "theorem", "module": "Mathlib.CategoryTheory.EssentiallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.essentiallySmallSelf", "kind": "theorem", "module": "Mathlib.CategoryTheory.EssentiallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instSmallHomOfLocallySmall", "kind": "instance", "module": "Mathlib.CategoryTheory.EssentiallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instLocallySmallOpposite", "kind": "instance", "module": "Mathlib.CategoryTheory.EssentiallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.locallySmall_of_faithful", "kind": "theorem", "module": "Mathlib.CategoryTheory.EssentiallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.locallySmall_congr", "kind": "theorem", "module": "Mathlib.CategoryTheory.EssentiallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instLocallySmallSmallModel", "kind": "instance", "module": "Mathlib.CategoryTheory.EssentiallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.locallySmall_self", "kind": "instance", "module": "Mathlib.CategoryTheory.EssentiallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.locallySmall_of_univLE", "kind": "instance", "module": "Mathlib.CategoryTheory.EssentiallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.locallySmall_max", "kind": "theorem", "module": "Mathlib.CategoryTheory.EssentiallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.locallySmall_of_essentiallySmall", "kind": "instance", "module": "Mathlib.CategoryTheory.EssentiallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShrinkHoms", "kind": "definition", "module": "Mathlib.CategoryTheory.EssentiallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShrinkHoms.toShrinkHoms", "kind": "definition", "module": "Mathlib.CategoryTheory.EssentiallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShrinkHoms.fromShrinkHoms", "kind": "definition", "module": "Mathlib.CategoryTheory.EssentiallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShrinkHoms.to_from", "kind": "theorem", "module": "Mathlib.CategoryTheory.EssentiallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShrinkHoms.from_to", "kind": "theorem", "module": "Mathlib.CategoryTheory.EssentiallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShrinkHoms.instCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.EssentiallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShrinkHoms.functor", "kind": "definition", "module": "Mathlib.CategoryTheory.EssentiallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShrinkHoms.inverse", "kind": "definition", "module": "Mathlib.CategoryTheory.EssentiallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShrinkHoms.equivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.EssentiallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShrinkHoms.instIsEquivalenceFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.EssentiallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShrinkHoms.instIsEquivalenceInverse", "kind": "instance", "module": "Mathlib.CategoryTheory.EssentiallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShrinkHoms.instUnique", "kind": "instance", "module": "Mathlib.CategoryTheory.EssentiallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShrinkHoms.instIsDiscrete", "kind": "instance", "module": "Mathlib.CategoryTheory.EssentiallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Shrink.instCategoryShrink", "kind": "instance", "module": "Mathlib.CategoryTheory.EssentiallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Shrink.equivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.EssentiallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Shrink.instLocallySmallShrink", "kind": "instance", "module": "Mathlib.CategoryTheory.EssentiallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.essentiallySmall_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.EssentiallySmall", "is_tactic_proof": true, "tactics": ["fconstructor", "intro", "fconstructor", "rcases", "refine", "exact", "infer_instance", "rintro", "let", "exact"], "tactic_count": 10}
{"name": "CategoryTheory.essentiallySmall_of_small_of_locallySmall", "kind": "instance", "module": "Mathlib.CategoryTheory.EssentiallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.small_skeleton_of_essentiallySmall", "kind": "instance", "module": "Mathlib.CategoryTheory.EssentiallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.essentiallySmall_of_fully_faithful", "kind": "theorem", "module": "Mathlib.CategoryTheory.EssentiallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.locallySmall_fullSubcategory", "kind": "instance", "module": "Mathlib.CategoryTheory.EssentiallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.essentiallySmall_fullSubcategory_mem", "kind": "instance", "module": "Mathlib.CategoryTheory.EssentiallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.locallySmall_of_thin", "kind": "instance", "module": "Mathlib.CategoryTheory.EssentiallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.essentiallySmall_iff_of_thin", "kind": "theorem", "module": "Mathlib.CategoryTheory.EssentiallySmall", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.instSmallDiscrete", "kind": "instance", "module": "Mathlib.CategoryTheory.EssentiallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instSmallArrowOfLocallySmall", "kind": "instance", "module": "Mathlib.CategoryTheory.EssentiallySmall", "is_tactic_proof": true, "tactics": ["let", "refine", "rintro", "obtain", "simp", "obtain", "obtain", "rfl"], "tactic_count": 8}
{"name": "CategoryTheory.instSmallFunctorOfLocallySmall", "kind": "instance", "module": "Mathlib.CategoryTheory.EssentiallySmall", "is_tactic_proof": false, "tactics": ["refine", "small_of_injective", "exact", "have", "rw", "tauto"], "tactic_count": 6}
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{"name": "CategoryTheory.Functor.IsStronglyCartesian.map_comp_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.FiberedCategory.Cartesian", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.IsStronglyCartesian.comp", "kind": "instance", "module": "Mathlib.CategoryTheory.FiberedCategory.Cartesian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsStronglyCartesian.of_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.FiberedCategory.Cartesian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsStronglyCartesian.of_iso", "kind": "instance", "module": "Mathlib.CategoryTheory.FiberedCategory.Cartesian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsStronglyCartesian.of_isIso", "kind": "instance", "module": "Mathlib.CategoryTheory.FiberedCategory.Cartesian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsStronglyCartesian.isIso_of_base_isIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.FiberedCategory.Cartesian", "is_tactic_proof": true, "tactics": ["subst_hom_lift", "let", "use", "have", "refine", "have", "rw", "apply", "apply", "simp"], "tactic_count": 10}
{"name": "CategoryTheory.Functor.IsStronglyCartesian.domainIsoOfBaseIso", "kind": "definition", "module": "Mathlib.CategoryTheory.FiberedCategory.Cartesian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsStronglyCartesian.domainUniqueUpToIso_inv_isHomLift", "kind": "instance", "module": "Mathlib.CategoryTheory.FiberedCategory.Cartesian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsStronglyCartesian.domainUniqueUpToIso_hom_isHomLift", "kind": "instance", "module": "Mathlib.CategoryTheory.FiberedCategory.Cartesian", "is_tactic_proof": true, "tactics": ["haveI", "simpa"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.IsCocartesian.map", "kind": "definition", "module": "Mathlib.CategoryTheory.FiberedCategory.Cocartesian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsCocartesian.map_isHomLift", "kind": "instance", "module": "Mathlib.CategoryTheory.FiberedCategory.Cocartesian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsCocartesian.fac", "kind": "theorem", "module": "Mathlib.CategoryTheory.FiberedCategory.Cocartesian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsCocartesian.map_uniq", "kind": "theorem", "module": "Mathlib.CategoryTheory.FiberedCategory.Cocartesian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsCocartesian.ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.FiberedCategory.Cocartesian", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.IsCocartesian.map_self", "kind": "theorem", "module": "Mathlib.CategoryTheory.FiberedCategory.Cocartesian", "is_tactic_proof": true, "tactics": ["subst_hom_lift", "apply", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.Functor.IsCocartesian.codomainUniqueUpToIso", "kind": "definition", "module": "Mathlib.CategoryTheory.FiberedCategory.Cocartesian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsCocartesian.of_comp_iso", "kind": "instance", "module": "Mathlib.CategoryTheory.FiberedCategory.Cocartesian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsCocartesian.of_iso_comp", "kind": "instance", "module": "Mathlib.CategoryTheory.FiberedCategory.Cocartesian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsStronglyCocartesian.universal_property", "kind": "theorem", "module": "Mathlib.CategoryTheory.FiberedCategory.Cocartesian", "is_tactic_proof": true, "tactics": ["subst_hom_lift", "have", "apply"], "tactic_count": 3}
{"name": "CategoryTheory.Functor.IsStronglyCocartesian.isCocartesian_of_isStronglyCocartesian", "kind": "instance", "module": "Mathlib.CategoryTheory.FiberedCategory.Cocartesian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsStronglyCocartesian.map", "kind": "definition", "module": "Mathlib.CategoryTheory.FiberedCategory.Cocartesian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsStronglyCocartesian.map_isHomLift", "kind": "instance", "module": "Mathlib.CategoryTheory.FiberedCategory.Cocartesian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsStronglyCocartesian.fac", "kind": "theorem", "module": "Mathlib.CategoryTheory.FiberedCategory.Cocartesian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsStronglyCocartesian.map_uniq", "kind": "theorem", "module": "Mathlib.CategoryTheory.FiberedCategory.Cocartesian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsStronglyCocartesian.ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.FiberedCategory.Cocartesian", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.IsStronglyCocartesian.map_self", "kind": "theorem", "module": "Mathlib.CategoryTheory.FiberedCategory.Cocartesian", "is_tactic_proof": true, "tactics": ["subst_hom_lift", "apply", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.Functor.IsStronglyCocartesian.map_comp_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.FiberedCategory.Cocartesian", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.IsStronglyCocartesian.comp", "kind": "instance", "module": "Mathlib.CategoryTheory.FiberedCategory.Cocartesian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsStronglyCocartesian.of_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.FiberedCategory.Cocartesian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsStronglyCocartesian.of_iso", "kind": "instance", "module": "Mathlib.CategoryTheory.FiberedCategory.Cocartesian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsStronglyCocartesian.of_isIso", "kind": "instance", "module": "Mathlib.CategoryTheory.FiberedCategory.Cocartesian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsStronglyCocartesian.isIso_of_base_isIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.FiberedCategory.Cocartesian", "is_tactic_proof": true, "tactics": ["subst_hom_lift", "let", "use", "have", "refine", "have", "rw", "apply", "apply", "simp"], "tactic_count": 10}
{"name": "CategoryTheory.Functor.IsStronglyCocartesian.codomainIsoOfBaseIso", "kind": "definition", "module": "Mathlib.CategoryTheory.FiberedCategory.Cocartesian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.Fiber", "kind": "definition", "module": "Mathlib.CategoryTheory.FiberedCategory.Fiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.Fiber.fiberCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.FiberedCategory.Fiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.Fiber.fiberInclusion", "kind": "definition", "module": "Mathlib.CategoryTheory.FiberedCategory.Fiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.Fiber.instIsHomLiftIdMapFiberInclusion", "kind": "instance", "module": "Mathlib.CategoryTheory.FiberedCategory.Fiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.Fiber.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.FiberedCategory.Fiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.Fiber.instFaithfulFiberInclusion", "kind": "instance", "module": "Mathlib.CategoryTheory.FiberedCategory.Fiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.Fiber.fiberInclusion_obj_inj", "kind": "theorem", "module": "Mathlib.CategoryTheory.FiberedCategory.Fiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.Fiber.fiberInclusionCompIsoConst", "kind": "definition", "module": "Mathlib.CategoryTheory.FiberedCategory.Fiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.Fiber.fiberInclusion_comp_eq_const", "kind": "theorem", "module": "Mathlib.CategoryTheory.FiberedCategory.Fiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.Fiber.mk", "kind": "definition", "module": "Mathlib.CategoryTheory.FiberedCategory.Fiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.Fiber.fiberInclusion_mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.FiberedCategory.Fiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.Fiber.homMk", "kind": "definition", "module": "Mathlib.CategoryTheory.FiberedCategory.Fiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.Fiber.fiberInclusion_homMk", "kind": "theorem", "module": "Mathlib.CategoryTheory.FiberedCategory.Fiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.Fiber.homMk_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.FiberedCategory.Fiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.Fiber.homMk_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.FiberedCategory.Fiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.Fiber.inducedFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.FiberedCategory.Fiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.Fiber.inducedFunctorCompIsoSelf", "kind": "definition", "module": "Mathlib.CategoryTheory.FiberedCategory.Fiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.Fiber.inducedFunctor_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.FiberedCategory.Fiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.Fiber.inducedFunctor_comp_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.FiberedCategory.Fiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.Fiber.inducedFunctor_comp_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.FiberedCategory.Fiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPreFibered.exists_isCartesian", "kind": "theorem", "module": "Mathlib.CategoryTheory.FiberedCategory.Fibered", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "CategoryTheory.instIsCartesianCompOfIsFibered", "kind": "instance", "module": "Mathlib.CategoryTheory.FiberedCategory.Fibered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsPreFibered.pullbackObj", "kind": "definition", "module": "Mathlib.CategoryTheory.FiberedCategory.Fibered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsPreFibered.pullbackMap", "kind": "definition", "module": "Mathlib.CategoryTheory.FiberedCategory.Fibered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsPreFibered.pullbackMap.IsCartesian", "kind": "instance", "module": "Mathlib.CategoryTheory.FiberedCategory.Fibered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsPreFibered.pullbackObj_proj", "kind": "theorem", "module": "Mathlib.CategoryTheory.FiberedCategory.Fibered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsFibered.isStronglyCartesian_of_isCartesian", "kind": "instance", "module": "Mathlib.CategoryTheory.FiberedCategory.Fibered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsFibered.isStronglyCartesian_of_exists_isCartesian", "kind": "theorem", "module": "Mathlib.CategoryTheory.FiberedCategory.Fibered", "is_tactic_proof": true, "tactics": ["constructor", "intro", "subst_hom_lift", "obtain", "h", "let", "let", "use", "refine", "simp", "intro", "rw", "apply", "simp"], "tactic_count": 14}
{"name": "CategoryTheory.Functor.IsFibered.of_exists_isStronglyCartesian", "kind": "theorem", "module": "Mathlib.CategoryTheory.FiberedCategory.Fibered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsFibered.pullbackPullbackIso", "kind": "definition", "module": "Mathlib.CategoryTheory.FiberedCategory.Fibered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pseudofunctor.CoGrothendieck.domainCartesianLift", "kind": "abbrev", "module": "Mathlib.CategoryTheory.FiberedCategory.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pseudofunctor.CoGrothendieck.cartesianLift", "kind": "abbrev", "module": "Mathlib.CategoryTheory.FiberedCategory.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pseudofunctor.CoGrothendieck.isHomLift_cartesianLift", "kind": "instance", "module": "Mathlib.CategoryTheory.FiberedCategory.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pseudofunctor.CoGrothendieck.homCartesianLift", "kind": "abbrev", "module": "Mathlib.CategoryTheory.FiberedCategory.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pseudofunctor.CoGrothendieck.isHomLift_homCartesianLift", "kind": "instance", "module": "Mathlib.CategoryTheory.FiberedCategory.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pseudofunctor.CoGrothendieck.isStronglyCartesian_homCartesianLift", "kind": "theorem", "module": "Mathlib.CategoryTheory.FiberedCategory.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pseudofunctor.CoGrothendieck.instIsFiberedForget", "kind": "instance", "module": "Mathlib.CategoryTheory.FiberedCategory.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pseudofunctor.CoGrothendieck.ι", "kind": "definition", "module": "Mathlib.CategoryTheory.FiberedCategory.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pseudofunctor.CoGrothendieck.compIso", "kind": "definition", "module": "Mathlib.CategoryTheory.FiberedCategory.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pseudofunctor.CoGrothendieck.comp_const", "kind": "theorem", "module": "Mathlib.CategoryTheory.FiberedCategory.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pseudofunctor.CoGrothendieck.instFullαCategoryObjLocallyDiscreteOppositeCatMkOpFiberForgetInducedFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.FiberedCategory.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pseudofunctor.CoGrothendieck.instFaithfulαCategoryObjLocallyDiscreteOppositeCatMkOpFiberForgetInducedFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.FiberedCategory.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pseudofunctor.CoGrothendieck.instEssSurjαCategoryObjLocallyDiscreteOppositeCatMkOpFiberForgetInducedFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.FiberedCategory.Grothendieck", "is_tactic_proof": true, "tactics": ["apply", "intro", "have", "use", "apply", "ext"], "tactic_count": 6}
{"name": "CategoryTheory.Pseudofunctor.CoGrothendieck.instIsEquivalenceαCategoryObjLocallyDiscreteOppositeCatMkOpFiberForgetInducedFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.FiberedCategory.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pseudofunctor.CoGrothendieck.instHasFibersForget", "kind": "instance", "module": "Mathlib.CategoryTheory.FiberedCategory.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFibers.canonical", "kind": "definition", "module": "Mathlib.CategoryTheory.FiberedCategory.HasFibers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFibers.inducedFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.FiberedCategory.HasFibers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFibers.inducedFunctor.natIso", "kind": "definition", "module": "Mathlib.CategoryTheory.FiberedCategory.HasFibers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFibers.inducedFunctor_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.FiberedCategory.HasFibers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFibers.instIsEquivalenceFibFiberInducedFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.FiberedCategory.HasFibers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFibers.instFaithfulFibι", "kind": "instance", "module": "Mathlib.CategoryTheory.FiberedCategory.HasFibers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFibers.proj_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.FiberedCategory.HasFibers", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HasFibers.projMap", "kind": "definition", "module": "Mathlib.CategoryTheory.FiberedCategory.HasFibers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFibers.homLift", "kind": "instance", "module": "Mathlib.CategoryTheory.FiberedCategory.HasFibers", "is_tactic_proof": true, "tactics": ["apply", "rw", "simp"], "tactic_count": 3}
{"name": "HasFibers.Fib.homMk", "kind": "definition", "module": "Mathlib.CategoryTheory.FiberedCategory.HasFibers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFibers.Fib.map_homMk", "kind": "theorem", "module": "Mathlib.CategoryTheory.FiberedCategory.HasFibers", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HasFibers.Fib.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.FiberedCategory.HasFibers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFibers.Fib.isoMk", "kind": "definition", "module": "Mathlib.CategoryTheory.FiberedCategory.HasFibers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFibers.Fib.mk", "kind": "definition", "module": "Mathlib.CategoryTheory.FiberedCategory.HasFibers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFibers.Fib.mkIsoSelf", "kind": "definition", "module": "Mathlib.CategoryTheory.FiberedCategory.HasFibers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFibers.Fib.mkIsoSelfIsHomLift", "kind": "instance", "module": "Mathlib.CategoryTheory.FiberedCategory.HasFibers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFibers.mkPullback", "kind": "definition", "module": "Mathlib.CategoryTheory.FiberedCategory.HasFibers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFibers.pullbackMap", "kind": "definition", "module": "Mathlib.CategoryTheory.FiberedCategory.HasFibers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFibers.pullbackMap.isCartesian", "kind": "instance", "module": "Mathlib.CategoryTheory.FiberedCategory.HasFibers", "is_tactic_proof": true, "tactics": ["conv", "simp", "infer_instance"], "tactic_count": 3}
{"name": "HasFibers.inducedMap", "kind": "definition", "module": "Mathlib.CategoryTheory.FiberedCategory.HasFibers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasFibers.inducedMap_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.FiberedCategory.HasFibers", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HasFibers.fiber_factorization", "kind": "theorem", "module": "Mathlib.CategoryTheory.FiberedCategory.HasFibers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsHomLift", "kind": "classInductive", "module": "Mathlib.CategoryTheory.FiberedCategory.HomLift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.tacticSubst_hom_lift___", "kind": "definition", "module": "Mathlib.CategoryTheory.FiberedCategory.HomLift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.instIsFilteredGrothendieckOfαCategoryObjCat", "kind": "instance", "module": "Mathlib.CategoryTheory.Filtered.Grothendieck", "is_tactic_proof": false, "tactics": ["have", "obtain", "obtain", "exact", "apply"], "tactic_count": 5}
{"name": "CategoryTheory.isFiltered_of_nonempty_limit_colimit_to_colimit_limit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Filtered.OfColimitCommutesFiniteLimit", "is_tactic_proof": true, "tactics": ["refine", "suffices", "obtain", "exact", "let", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.IsFiltered.filteredClosure", "kind": "inductive", "module": "Mathlib.CategoryTheory.Filtered.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsFiltered.instIsFilteredOrEmptyFullSubcategoryFilteredClosure", "kind": "instance", "module": "Mathlib.CategoryTheory.Filtered.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.CategoryTheory.Filtered.Small.0.CategoryTheory.IsFiltered.FilteredClosureSmall.InductiveStep", "kind": "inductive", "module": "Mathlib.CategoryTheory.Filtered.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.CategoryTheory.Filtered.Small.0.CategoryTheory.IsFiltered.FilteredClosureSmall.inductiveStepRealization", "kind": "definition", "module": "Mathlib.CategoryTheory.Filtered.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.CategoryTheory.Filtered.Small.0.CategoryTheory.IsFiltered.FilteredClosureSmall.bundledAbstractFilteredClosure", "kind": "definition", "module": "Mathlib.CategoryTheory.Filtered.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.CategoryTheory.Filtered.Small.0.CategoryTheory.IsFiltered.FilteredClosureSmall.AbstractFilteredClosure", "kind": "definition", "module": "Mathlib.CategoryTheory.Filtered.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.CategoryTheory.Filtered.Small.0.CategoryTheory.IsFiltered.FilteredClosureSmall.abstractFilteredClosureRealization", "kind": "definition", "module": "Mathlib.CategoryTheory.Filtered.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsFiltered.small_fullSubcategory_filteredClosure", "kind": "theorem", "module": "Mathlib.CategoryTheory.Filtered.Small", "is_tactic_proof": false, "tactics": ["refine", "small_of_injective_of_exists", "rintro", "induction", "base", "refine", "simp", "exact", "simp", "rw", "rfl", "max", "rcases", "rcases", "refine", "simp", "refine", "all_goals", "exacts", "simp", "rw", "rfl", "coeq", "rcases", "rcases", "refine", "simp", "refine", "all_goals", "exacts", "simp", "rw", "rfl"], "tactic_count": 33}
{"name": "CategoryTheory.IsFiltered.instEssentiallySmallFullSubcategoryFilteredClosure", "kind": "instance", "module": "Mathlib.CategoryTheory.Filtered.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsFiltered.SmallFilteredIntermediate", "kind": "definition", "module": "Mathlib.CategoryTheory.Filtered.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsFiltered.instSmallCategorySmallFilteredIntermediate", "kind": "instance", "module": "Mathlib.CategoryTheory.Filtered.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsFiltered.SmallFilteredIntermediate.factoring", "kind": "definition", "module": "Mathlib.CategoryTheory.Filtered.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsFiltered.SmallFilteredIntermediate.inclusion", "kind": "definition", "module": "Mathlib.CategoryTheory.Filtered.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsFiltered.SmallFilteredIntermediate.instFaithfulInclusion", "kind": "instance", "module": "Mathlib.CategoryTheory.Filtered.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsFiltered.SmallFilteredIntermediate.instFullInclusion", "kind": "instance", "module": "Mathlib.CategoryTheory.Filtered.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsFiltered.SmallFilteredIntermediate.factoringCompInclusion", "kind": "definition", "module": "Mathlib.CategoryTheory.Filtered.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsFiltered.SmallFilteredIntermediate.instIsFilteredOrEmpty", "kind": "instance", "module": "Mathlib.CategoryTheory.Filtered.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsFiltered.SmallFilteredIntermediate.instOfNonempty", "kind": "instance", "module": "Mathlib.CategoryTheory.Filtered.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsCofiltered.cofilteredClosure", "kind": "inductive", "module": "Mathlib.CategoryTheory.Filtered.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsCofiltered.instIsCofilteredOrEmptyFullSubcategoryCofilteredClosure", "kind": "instance", "module": "Mathlib.CategoryTheory.Filtered.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.CategoryTheory.Filtered.Small.0.CategoryTheory.IsCofiltered.CofilteredClosureSmall.InductiveStep", "kind": "inductive", "module": "Mathlib.CategoryTheory.Filtered.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.CategoryTheory.Filtered.Small.0.CategoryTheory.IsCofiltered.CofilteredClosureSmall.inductiveStepRealization", "kind": "definition", "module": "Mathlib.CategoryTheory.Filtered.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.CategoryTheory.Filtered.Small.0.CategoryTheory.IsCofiltered.CofilteredClosureSmall.bundledAbstractCofilteredClosure", "kind": "definition", "module": "Mathlib.CategoryTheory.Filtered.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.IsCofiltered.small_fullSubcategory_cofilteredClosure", "kind": "theorem", "module": "Mathlib.CategoryTheory.Filtered.Small", "is_tactic_proof": false, "tactics": ["refine", "small_of_injective_of_exists", "rintro", "induction", "base", "refine", "simp", "exact", "simp", "rw", "rfl", "min", "rcases", "rcases", "refine", "simp", "refine", "all_goals", "exacts", "simp", "rw", "rfl", "eq", "rcases", "rcases", "refine", "simp", "refine", "all_goals", "exacts", "simp", "rw", "rfl"], "tactic_count": 33}
{"name": "CategoryTheory.IsCofiltered.instEssentiallySmallFullSubcategoryCofilteredClosure", "kind": "instance", "module": "Mathlib.CategoryTheory.Filtered.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsCofiltered.SmallCofilteredIntermediate", "kind": "definition", "module": "Mathlib.CategoryTheory.Filtered.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsCofiltered.instSmallCategorySmallCofilteredIntermediate", "kind": "instance", "module": "Mathlib.CategoryTheory.Filtered.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsCofiltered.SmallCofilteredIntermediate.factoring", "kind": "definition", "module": "Mathlib.CategoryTheory.Filtered.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsCofiltered.SmallCofilteredIntermediate.inclusion", "kind": "definition", "module": "Mathlib.CategoryTheory.Filtered.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.IsCofiltered.SmallCofilteredIntermediate.instIsCofilteredOrEmpty", "kind": "instance", "module": "Mathlib.CategoryTheory.Filtered.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.FinCategory.ObjAsType", "kind": "abbrev", "module": "Mathlib.CategoryTheory.FinCategory.AsType", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FinCategory.instFintypeHomObjAsType", "kind": "instance", "module": "Mathlib.CategoryTheory.FinCategory.AsType", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FinCategory.objAsTypeEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.FinCategory.AsType", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FinCategory.AsType", "kind": "abbrev", "module": "Mathlib.CategoryTheory.FinCategory.AsType", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FinCategory.categoryAsType", "kind": "instance", "module": "Mathlib.CategoryTheory.FinCategory.AsType", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FinCategory.asTypeToObjAsType", "kind": "definition", "module": "Mathlib.CategoryTheory.FinCategory.AsType", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FinCategory.objAsTypeToAsType", "kind": "definition", "module": "Mathlib.CategoryTheory.FinCategory.AsType", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FinCategory.asTypeEquivObjAsType", "kind": "definition", "module": "Mathlib.CategoryTheory.FinCategory.AsType", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FinCategory.asTypeFinCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.FinCategory.AsType", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FinCategory.equivAsType", "kind": "definition", "module": "Mathlib.CategoryTheory.FinCategory.AsType", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.discreteFintype", "kind": "instance", "module": "Mathlib.CategoryTheory.FinCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instFiniteDiscrete", "kind": "instance", "module": "Mathlib.CategoryTheory.FinCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.discreteHomFintype", "kind": "instance", "module": "Mathlib.CategoryTheory.FinCategory.Basic", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "CategoryTheory.finCategoryDiscreteOfFintype", "kind": "instance", "module": "Mathlib.CategoryTheory.FinCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instFinCategoryOfFiniteOfIsThin", "kind": "instance", "module": "Mathlib.CategoryTheory.FinCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.finCategoryOpposite", "kind": "instance", "module": "Mathlib.CategoryTheory.FinCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.finCategoryUlift", "kind": "instance", "module": "Mathlib.CategoryTheory.FinCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FintypeCat.instCoeSort", "kind": "instance", "module": "Mathlib.CategoryTheory.FintypeCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FintypeCat.instInhabited", "kind": "instance", "module": "Mathlib.CategoryTheory.FintypeCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FintypeCat.instFintypeCarrier", "kind": "instance", "module": "Mathlib.CategoryTheory.FintypeCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FintypeCat.instCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.FintypeCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FintypeCat.incl", "kind": "definition", "module": "Mathlib.CategoryTheory.FintypeCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FintypeCat.instFullIncl", "kind": "instance", "module": "Mathlib.CategoryTheory.FintypeCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "FintypeCat.instFunLikeHomCarrier", "kind": "instance", "module": "Mathlib.CategoryTheory.FintypeCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FintypeCat.concreteCategoryFintype", "kind": "instance", "module": "Mathlib.CategoryTheory.FintypeCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FintypeCat.instFullForget", "kind": "instance", "module": "Mathlib.CategoryTheory.FintypeCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "FintypeCat.hom_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.FintypeCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FintypeCat.hom_inv_id_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.FintypeCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "FintypeCat.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.FintypeCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FintypeCat.homMk", "kind": "definition", "module": "Mathlib.CategoryTheory.FintypeCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FintypeCat.homMk_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.FintypeCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FintypeCat.id_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.FintypeCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FintypeCat.comp_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.FintypeCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FintypeCat.homMk_eq_id_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.FintypeCat", "is_tactic_proof": true, "tactics": ["constructor", "intro", "ext", "exact", "rintro", "rfl"], "tactic_count": 6}
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{"name": "FintypeCat.instFiniteIso", "kind": "instance", "module": "Mathlib.CategoryTheory.FintypeCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FintypeCat.instFiniteAut", "kind": "instance", "module": "Mathlib.CategoryTheory.FintypeCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FintypeCat.Skeleton", "kind": "definition", "module": "Mathlib.CategoryTheory.FintypeCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FintypeCat.Skeleton.mk", "kind": "definition", "module": "Mathlib.CategoryTheory.FintypeCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FintypeCat.Skeleton.instInhabited", "kind": "instance", "module": "Mathlib.CategoryTheory.FintypeCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FintypeCat.Skeleton.len", "kind": "definition", "module": "Mathlib.CategoryTheory.FintypeCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FintypeCat.Skeleton.ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.FintypeCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FintypeCat.Skeleton.instSmallCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.FintypeCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FintypeCat.Skeleton.is_skeletal", "kind": "theorem", "module": "Mathlib.CategoryTheory.FintypeCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FintypeCat.Skeleton.incl", "kind": "definition", "module": "Mathlib.CategoryTheory.FintypeCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "FintypeCat.Skeleton.equivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.FintypeCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FintypeCat.Skeleton.incl_mk_nat_card", "kind": "theorem", "module": "Mathlib.CategoryTheory.FintypeCat", "is_tactic_proof": true, "tactics": ["convert", "apply"], "tactic_count": 2}
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{"name": "FintypeCat.uSwitchEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.FintypeCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FintypeCat.uSwitchEquiv_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.FintypeCat", "is_tactic_proof": true, "tactics": ["simp", "rw", "aesop"], "tactic_count": 3}
{"name": "FintypeCat.uSwitchEquiv_symm_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.FintypeCat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "FunctorToFintypeCat.naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.FintypeCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Functor.leftDerived_fac", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.Derived.LeftDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.leftDerived_fac_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.Derived.LeftDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.leftDerived_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.Derived.LeftDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.leftDerivedNatTrans", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.Derived.LeftDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.leftDerivedNatTrans_fac", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.Derived.LeftDerived", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.leftDerivedNatTrans_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.Derived.LeftDerived", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.leftDerivedNatTrans_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.Derived.LeftDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.leftDerivedNatTrans_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.Derived.LeftDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.leftDerivedNatIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.Derived.LeftDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.leftDerivedUnique", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Functor.Derived.LeftDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isLeftDerivedFunctor_iff_isIso_leftDerivedLift", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.Derived.LeftDerived", "is_tactic_proof": true, "tactics": ["rw", "have", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Functor.hasLeftDerivedFunctor_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.Derived.LeftDerived", "is_tactic_proof": false, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.hasLeftDerivedFunctor_iff_of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.Derived.LeftDerived", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.HasLeftDerivedFunctor.hasRightKanExtension", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.Derived.LeftDerived", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.HasLeftDerivedFunctor.mk'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.Derived.LeftDerived", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.totalLeftDerived", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.Derived.LeftDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.totalLeftDerivedCounit", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.Derived.LeftDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instIsLeftDerivedFunctorTotalLeftDerivedTotalLeftDerivedCounit", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.Derived.LeftDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.HasPointwiseLeftDerivedFunctor", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Functor.Derived.PointwiseLeftDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.hasPointwiseLeftDerivedFunctorAt_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.Derived.PointwiseLeftDerived", "is_tactic_proof": false, "tactics": ["rw", "hasPointwiseRightKanExtensionAt_iff_of_equivalence", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Functor.HasPointwiseLeftDerivedFunctorAt.hasLimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.Derived.PointwiseLeftDerived", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.hasPointwiseLeftDerivedFunctorAt_iff_of_mem", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.Derived.PointwiseLeftDerived", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.hasPointwiseRightKanExtension_of_hasPointwiseLeftDerivedFunctor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.Derived.PointwiseLeftDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.hasLeftDerivedFunctor_of_hasPointwiseLeftDerivedFunctor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.Derived.PointwiseLeftDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isPointwiseRightKanExtensionOfHasPointwiseLeftDerivedFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.Derived.PointwiseLeftDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isPointwiseRightKanExtensionAtOfIsoOfIsLocalization", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.Derived.PointwiseLeftDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isPointwiseRightKanExtensionOfIsoOfIsLocalization", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.Derived.PointwiseLeftDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.RightExtension.isPointwiseRightKanExtensionOfIsIsoOfIsLocalization", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.Derived.PointwiseLeftDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.hasPointwiseLeftDerivedFunctor_of_inverts", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.Derived.PointwiseLeftDerived", "is_tactic_proof": true, "tactics": ["intro", "rw", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Functor.isLeftDerivedFunctor_of_inverts", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.Derived.PointwiseLeftDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instIsLeftDerivedFunctorLiftHomFac", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.Derived.PointwiseLeftDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isIso_of_isLeftDerivedFunctor_of_inverts", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.Derived.PointwiseLeftDerived", "is_tactic_proof": false, "tactics": ["have", "α", "rw", "infer_instance"], "tactic_count": 4}
{"name": "CategoryTheory.Functor.isLeftDerivedFunctor_iff_of_inverts", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.Derived.PointwiseLeftDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.HasPointwiseRightDerivedFunctor", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Functor.Derived.PointwiseRightDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.hasPointwiseRightDerivedFunctorAt_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.Derived.PointwiseRightDerived", "is_tactic_proof": false, "tactics": ["rw", "hasPointwiseLeftKanExtensionAt_iff_of_equivalence", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Functor.HasPointwiseRightDerivedFunctorAt.hasColimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.Derived.PointwiseRightDerived", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.hasPointwiseRightDerivedFunctorAt_iff_of_mem", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.Derived.PointwiseRightDerived", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.hasPointwiseLeftKanExtension_of_hasPointwiseRightDerivedFunctor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.Derived.PointwiseRightDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.hasRightDerivedFunctor_of_hasPointwiseRightDerivedFunctor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.Derived.PointwiseRightDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isPointwiseLeftKanExtensionOfHasPointwiseRightDerivedFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.Derived.PointwiseRightDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isPointwiseLeftKanExtensionAtOfIsoOfIsLocalization", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.Derived.PointwiseRightDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isPointwiseLeftKanExtensionOfIsoOfIsLocalization", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.Derived.PointwiseRightDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.LeftExtension.isPointwiseLeftKanExtensionOfIsIsoOfIsLocalization", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.Derived.PointwiseRightDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.hasPointwiseRightDerivedFunctor_of_inverts", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.Derived.PointwiseRightDerived", "is_tactic_proof": true, "tactics": ["intro", "rw", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Functor.isRightDerivedFunctor_of_inverts", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.Derived.PointwiseRightDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instIsRightDerivedFunctorLiftInvFac", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.Derived.PointwiseRightDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isIso_of_isRightDerivedFunctor_of_inverts", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.Derived.PointwiseRightDerived", "is_tactic_proof": false, "tactics": ["have", "α", "rw", "infer_instance"], "tactic_count": 4}
{"name": "CategoryTheory.Functor.isRightDerivedFunctor_iff_of_inverts", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.Derived.PointwiseRightDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isRightDerivedFunctor_iff_isLeftKanExtension", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.Derived.RightDerived", "is_tactic_proof": true, "tactics": ["constructor", "exact", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Functor.isRightDerivedFunctor_iff_of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.Derived.RightDerived", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.rightDerivedDesc", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.Derived.RightDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.rightDerived_fac", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.Derived.RightDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.rightDerived_fac_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.Derived.RightDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.rightDerived_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.Derived.RightDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.rightDerivedNatTrans", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.Derived.RightDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.rightDerivedNatTrans_fac", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.Derived.RightDerived", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.rightDerivedNatTrans_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.Derived.RightDerived", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.rightDerivedNatTrans_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.Derived.RightDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.rightDerivedNatTrans_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.Derived.RightDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.rightDerivedNatIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.Derived.RightDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.rightDerivedUnique", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Functor.Derived.RightDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isRightDerivedFunctor_iff_isIso_rightDerivedDesc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.Derived.RightDerived", "is_tactic_proof": true, "tactics": ["rw", "have", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Functor.hasRightDerivedFunctor_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.Derived.RightDerived", "is_tactic_proof": false, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.hasRightDerivedFunctor_iff_of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.Derived.RightDerived", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.HasRightDerivedFunctor.hasLeftKanExtension", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.Derived.RightDerived", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.HasRightDerivedFunctor.mk'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.Derived.RightDerived", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.totalRightDerived", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.Derived.RightDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.totalRightDerivedUnit", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.Derived.RightDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instIsRightDerivedFunctorTotalRightDerivedTotalRightDerivedUnit", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.Derived.RightDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.map_mono", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.map_epi", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mono_of_mono_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.epi_of_epi_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.preservesMonomorphisms_comp", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.preservesEpimorphisms_comp", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.reflectsMonomorphisms_comp", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.reflectsEpimorphisms_comp", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.preservesEpimorphisms_of_preserves_of_reflects", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.preservesMonomorphisms_of_preserves_of_reflects", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.reflectsEpimorphisms_of_preserves_of_reflects", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.reflectsMonomorphisms_of_preserves_of_reflects", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.preservesMonomorphisms.of_natTrans", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.preservesMonomorphisms.of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.preservesMonomorphisms.iso_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.preservesEpimorphisms.of_natTrans", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.preservesEpimorphisms.of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.preservesEpimorphisms.iso_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.reflectsMonomorphisms.of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.reflectsMonomorphisms.iso_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.reflectsEpimorphisms.of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.reflectsEpimorphisms.iso_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.preservesEpimorphisms_of_adjunction", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.preservesEpimorphisms_of_isLeftAdjoint", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.preservesMonomorphisms_of_adjunction", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.preservesMonomorphisms_of_isRightAdjoint", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.reflectsMonomorphisms_of_faithful", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.reflectsEpimorphisms_of_faithful", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instIsSplitEpiApp", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instIsSplitMonoApp", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.preservesEpimorphisms.ofRetract", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.preservesMonomorphisms.ofRetract", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.splitEpiEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isSplitEpi_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.EpiMono", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "intro", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.Functor.splitMonoEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isSplitMono_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.EpiMono", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "intro", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.Functor.epi_map_iff_epi", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.EpiMono", "is_tactic_proof": true, "tactics": ["constructor", "exact", "intro", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.Functor.mono_map_iff_mono", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.EpiMono", "is_tactic_proof": true, "tactics": ["constructor", "exact", "intro", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.Functor.splitEpiCategoryImpOfIsEquivalence", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Functor.instIsLeftKanExtensionObjLanAppLanUnit", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Adjunction", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.isPointwiseLeftKanExtensionLeftKanExtensionUnit", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.leftKanExtensionObjIsoColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.ι_leftKanExtensionObjIsoColimit_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Adjunction", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.ι_leftKanExtensionObjIsoColimit_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.leftKanExtensionUnit_leftKanExtension_map_leftKanExtensionObjIsoColimit_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.leftKanExtensionUnit_leftKanExtensionObjIsoColimit_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Adjunction", "is_tactic_proof": true, "tactics": ["simpa", "leftKanExtensionUnit_leftKanExtension_map_leftKanExtensionObjIsoColimit_hom"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.hasColimit_map_comp_ι_comp_grothendieckProj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.leftKanExtensionIsoFiberwiseColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.lanAdjunction", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.lanAdjunction_unit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Adjunction", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.Functor.lanAdjunction_counit_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.lanUnit_app_whiskerLeft_lanAdjunction_counit_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Adjunction", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.lanUnit_app_app_lanAdjunction_counit_app_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isIso_lanAdjunction_counit_app_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isIso_lanAdjunction_homEquiv_symm_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.lanCompColimIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instHasColimitGrothendieckFunctorCompGrothendieckProj", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.colimitIsoColimitGrothendieck", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.ι_colimitIsoColimitGrothendieck_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Adjunction", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.ι_colimitIsoColimitGrothendieck_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Adjunction", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.instIsIsoAppLanUnit", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instIsIsoAppLanUnit_1", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.coreflective", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Adjunction", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.instIsIsoAppUnitLanAdjunctionOfHasPointwiseLeftKanExtension", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Adjunction", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.coreflective'", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Adjunction", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.ran", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.ranCounit", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instIsRightKanExtensionObjRanAppRanCounit", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Adjunction", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.isPointwiseRightKanExtensionRanCounit", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.ranObjObjIsoLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.ranObjObjIsoLimit_hom_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Adjunction", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.ranObjObjIsoLimit_inv_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.ranAdjunction", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.ranAdjunction_counit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Adjunction", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.Functor.ranAdjunction_unit_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.ranCounit_app_whiskerLeft_ranAdjunction_unit_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Adjunction", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.ranCounit_app_app_ranAdjunction_unit_app_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isIso_ranAdjunction_unit_app_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isIso_ranAdjunction_homEquiv_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.ranCompLimIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instIsIsoAppRanCounit", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instIsIsoAppRanCounit_1", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.reflective", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Adjunction", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.instIsIsoAppCounitRanAdjunctionOfHasPointwiseRightKanExtension", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Adjunction", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.reflective'", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Adjunction", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.RightExtension", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.LeftExtension", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.RightExtension.mk", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.LeftExtension.mk", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isUniversalOfIsRightKanExtension", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.liftOfIsRightKanExtension", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.liftOfIsRightKanExtension_fac", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.liftOfIsRightKanExtension_fac_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.hom_ext_of_isRightKanExtension", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.homEquivOfIsRightKanExtension", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isRightKanExtension_of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isRightKanExtension_iff_of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "intro", "refine", "rw"], "tactic_count": 6}
{"name": "CategoryTheory.Functor.rightKanExtensionUniqueOfIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.rightKanExtensionUnique", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isRightKanExtension_iff_isIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "infer_instance", "intro", "rw", "infer_instance"], "tactic_count": 7}
{"name": "CategoryTheory.Functor.isUniversalOfIsLeftKanExtension", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.descOfIsLeftKanExtension", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.descOfIsLeftKanExtension_fac", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.descOfIsLeftKanExtension_fac_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.hom_ext_of_isLeftKanExtension", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.homEquivOfIsLeftKanExtension", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isLeftKanExtension_of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isLeftKanExtension_iff_of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "intro", "refine", "rw"], "tactic_count": 6}
{"name": "CategoryTheory.Functor.leftKanExtensionUniqueOfIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.leftKanExtensionUnique", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isLeftKanExtension_iff_isIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "infer_instance", "intro", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.Functor.HasRightKanExtension", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.HasRightKanExtension.mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.HasLeftKanExtension", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.HasLeftKanExtension.mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.rightKanExtension", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.rightKanExtensionCounit", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instIsRightKanExtensionRightKanExtensionRightKanExtensionCounit", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.rightKanExtension_hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.leftKanExtension", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.leftKanExtensionUnit", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instIsLeftKanExtensionLeftKanExtensionLeftKanExtensionUnit", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.leftKanExtension_hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.LeftExtension.postcomp₁", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.RightExtension.postcomp₁", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instIsEquivalenceLeftExtensionPostcomp₁OfIsIso", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.instIsEquivalenceRightExtensionPostcomp₁OfIsIso", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.hasLeftExtension_iff_postcomp₁", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.hasRightExtension_iff_postcomp₁", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.LeftExtension.isUniversalPostcomp₁Equiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.RightExtension.isUniversalPostcomp₁Equiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.isLeftKanExtension_iff_postcomp₁", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": ["let", "constructor", "exact", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.Functor.isRightKanExtension_iff_postcomp₁", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": ["let", "constructor", "exact", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.Functor.LeftExtension.postcompose₂", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.RightExtension.postcompose₂", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.LeftExtension.postcompose₂ObjMkIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.RightExtension.postcompose₂ObjMkIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.LeftExtension.precomp", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.RightExtension.precomp", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instIsEquivalenceLeftExtensionCompPrecomp", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.instIsEquivalenceRightExtensionCompPrecomp", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.LeftExtension.isUniversalPrecompEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.RightExtension.isUniversalPrecompEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.isLeftKanExtension_iff_precomp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": ["let", "constructor", "exact", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.Functor.isRightKanExtension_iff_precomp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": ["let", "constructor", "exact", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.Functor.rightExtensionEquivalenceOfIso₁", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.hasRightExtension_iff_of_iso₁", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.hasLeftExtension_iff_of_iso₁", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.rightExtensionEquivalenceOfIso₂", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.hasRightExtension_iff_of_iso₂", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.leftExtensionEquivalenceOfIso₂", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.hasLeftExtension_iff_of_iso₂", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.LeftExtension.isUniversalEquivOfIso₂", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isLeftKanExtension_iff_of_iso₂", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": true, "tactics": ["let", "constructor", "exact", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.Functor.RightExtension.isUniversalEquivOfIso₂", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isRightKanExtension_iff_of_iso₂", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": true, "tactics": ["let", "constructor", "exact", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.Functor.LeftExtension.precomp₂", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.LeftExtension.isUniversalPrecomp₂", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": ["letI", "let", "refine", "ext", "haveI", "haveI", "dsimp", "simp", "dsimp", "ext1", "apply", "apply", "ext", "dsimp", "have", "have", "have", "dsimp", "simp", "const_obj_map,", "whiskerLeft_app,", "simp", "apply"], "tactic_count": 23}
{"name": "CategoryTheory.Functor.LeftExtension.isUniversalOfPrecomp₂", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": ["letI", "let", "haveI", "simp", "const_obj_map,", "refine", "apply", "ext", "have", "simp", "simp", "dsimp", "ext1", "apply", "ext", "have", "have", "simp", "simp", "apply"], "tactic_count": 20}
{"name": "CategoryTheory.Functor.LeftExtension.isUniversalPrecomp₂Equiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.coconeOfIsLeftKanExtension", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isColimitCoconeOfIsLeftKanExtension", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.colimitIsoOfIsLeftKanExtension", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.ι_colimitIsoOfIsLeftKanExtension_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.ι_colimitIsoOfIsLeftKanExtension_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.coneOfIsRightKanExtension", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isLimitConeOfIsRightKanExtension", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.limitIsoOfIsRightKanExtension", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.limitIsoOfIsRightKanExtension_inv_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.limitIsoOfIsRightKanExtension_hom_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.isLeftKanExtensionId", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isRightKanExtensionId", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isLeftKanExtensionAlongEquivalence", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": true, "tactics": ["refine", "apply", "refine", "intro", "ext", "simpa"], "tactic_count": 6}
{"name": "CategoryTheory.Functor.isLeftKanExtensionAlongEquivalence'", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isRightKanExtensionAlongEquivalence", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": true, "tactics": ["refine", "apply", "refine", "intro", "ext", "simpa"], "tactic_count": 6}
{"name": "CategoryTheory.Functor.isRightKanExtensionAlongEquivalence'", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.denseAt", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Dense", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isDense_iff_nonempty_isPointwiseLeftKanExtension", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Dense", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsDense.of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Dense", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsDense.iff_of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Dense", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instIsDenseCompOfIsEquivalence", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Dense", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsDense.comp_left_iff_of_isEquivalence", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Dense", "is_tactic_proof": true, "tactics": ["refine", "let", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Functor.instIsDenseCompOfIsEquivalence_1", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Dense", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsDense.comp_right_iff_of_isEquivalence", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Dense", "is_tactic_proof": true, "tactics": ["refine", "let", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Functor.instFaithfulOppositeTypeRestrictedULiftYonedaOfIsDense", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Dense", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instFullOppositeTypeRestrictedULiftYonedaOfIsDense", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Dense", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsDense.of_fullyFaithful_restrictedULiftYoneda", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Dense", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isDense_iff_fullyFaithful_restrictedULiftYoneda", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Dense", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isStrongGenerator_of_isDense", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Dense", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.DenseAt", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Functor.KanExtension.DenseAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.denseAtEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.DenseAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.DenseAt.ofIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.DenseAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.DenseAt.ofNatIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.DenseAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.DenseAt.precompEquivOfFinal", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.DenseAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.DenseAt.precompOfFinal", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.DenseAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.DenseAt.postcompEquivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.DenseAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isDenseAt", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.DenseAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isDenseAt_eq_isPointwiseLeftKanExtensionAt", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.DenseAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isDenseAt_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.DenseAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instIsClosedUnderIsomorphismsIsDenseAt", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.KanExtension.DenseAt", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.congr_isDenseAt", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.DenseAt", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.IsDenseAt.iff_of_final", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.DenseAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsDenseAt.of_final", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.DenseAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.HasPointwiseLeftKanExtensionAt", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.HasPointwiseLeftKanExtension", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.HasPointwiseRightKanExtensionAt", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.HasPointwiseRightKanExtension", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.hasPointwiseLeftKanExtensionAt_iff_of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": true, "tactics": ["revert", "suffices", "from", "intro", "change", "infer_instance"], "tactic_count": 6}
{"name": "CategoryTheory.Functor.hasPointwiseRightKanExtensionAt_iff_of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": true, "tactics": ["revert", "suffices", "from", "intro", "change", "infer_instance"], "tactic_count": 6}
{"name": "CategoryTheory.Functor.hasPointwiseLeftKanExtensionAt_iff_of_natIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": true, "tactics": ["revert", "suffices", "from", "intro", "let", "let", "exact"], "tactic_count": 7}
{"name": "CategoryTheory.Functor.hasPointwiseRightKanExtensionAt_iff_of_natIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": true, "tactics": ["revert", "suffices", "from", "intro", "let", "let", "exact"], "tactic_count": 7}
{"name": "CategoryTheory.Functor.hasPointwiseLeftKanExtensionAt_of_equivalence", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": true, "tactics": ["rw", "let", "have", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.Functor.hasPointwiseLeftKanExtensionAt_iff_of_equivalence", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "intro", "exact", "hasPointwiseLeftKanExtensionAt_of_equivalence"], "tactic_count": 6}
{"name": "CategoryTheory.Functor.hasPointwiseRightKanExtensionAt_of_equivalence", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": false, "tactics": ["rw", "let", "have", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.Functor.hasPointwiseRightKanExtensionAt_iff_of_equivalence", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "intro", "exact", "hasPointwiseRightKanExtensionAt_of_equivalence"], "tactic_count": 6}
{"name": "CategoryTheory.Functor.LeftExtension.coconeAt", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.LeftExtension.coconeAtFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtensionAt", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.LeftExtension.instSubsingletonIsPointwiseLeftKanExtensionAt", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.hasPointwiseLeftKanExtensionAt", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.isIso_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.LeftExtension.isPointwiseLeftKanExtensionAtOfIso'", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.LeftExtension.isPointwiseLeftKanExtensionAtEquivOfIso'", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.hom_ext'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.comp_homEquiv_symm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.isoColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.ι_isoColimit_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.ι_isoColimit_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.LeftExtension.isPointwiseLeftKanExtensionAt", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.LeftExtension.instIsClosedUnderIsomorphismsIsPointwiseLeftKanExtensionAt", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtension", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.LeftExtension.isPointwiseLeftKanExtensionAtEquivOfIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.LeftExtension.isPointwiseLeftKanExtensionEquivOfIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtension.hasPointwiseLeftKanExtension", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtension.homFrom", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtension.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": true, "tactics": ["ext", "apply", "intro", "have", "have", "dsimp", "simp", "rw"], "tactic_count": 8}
{"name": "CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtension.isUniversal", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtension.isLeftKanExtension", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtension.hasLeftKanExtension", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtension.isIso_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.RightExtension.coneAt", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.RightExtension.coneAtFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.RightExtension.IsPointwiseRightKanExtensionAt", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.RightExtension.instSubsingletonIsPointwiseRightKanExtensionAt", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.RightExtension.IsPointwiseRightKanExtensionAt.hasPointwiseRightKanExtensionAt", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.RightExtension.IsPointwiseRightKanExtensionAt.isIso_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.RightExtension.isPointwiseRightKanExtensionAtOfIso'", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.RightExtension.isPointwiseRightKanExtensionAtEquivOfIso'", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.RightExtension.IsPointwiseRightKanExtensionAt.hom_ext'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.RightExtension.IsPointwiseRightKanExtensionAt.isoLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.RightExtension.IsPointwiseRightKanExtensionAt.isoLimit_hom_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.RightExtension.IsPointwiseRightKanExtensionAt.isoLimit_inv_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.RightExtension.isPointwiseRightKanExtensionAt", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.RightExtension.instIsClosedUnderIsomorphismsIsPointwiseRightKanExtensionAt", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.RightExtension.IsPointwiseRightKanExtension", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.RightExtension.isPointwiseRightKanExtensionAtEquivOfIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.RightExtension.isPointwiseRightKanExtensionEquivOfIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.RightExtension.IsPointwiseRightKanExtension.hasPointwiseRightKanExtension", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.RightExtension.IsPointwiseRightKanExtension.homTo", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.RightExtension.IsPointwiseRightKanExtension.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": true, "tactics": ["ext", "apply", "intro", "have", "have", "dsimp", "simp"], "tactic_count": 7}
{"name": "CategoryTheory.Functor.RightExtension.IsPointwiseRightKanExtension.isUniversal", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.RightExtension.IsPointwiseRightKanExtension.isRightKanExtension", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.RightExtension.IsPointwiseRightKanExtension.hasRightKanExtension", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.RightExtension.IsPointwiseRightKanExtension.isIso_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.pointwiseLeftKanExtension", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.pointwiseLeftKanExtensionUnit", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.pointwiseLeftKanExtensionIsPointwiseLeftKanExtension", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.pointwiseLeftKanExtensionIsUniversal", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instIsLeftKanExtensionPointwiseLeftKanExtensionPointwiseLeftKanExtensionUnit", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instHasLeftKanExtension", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.costructuredArrowMapCocone", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.pointwiseLeftKanExtension_desc_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": false, "tactics": ["let", "have", "apply", "aesop", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.Functor.isPointwiseLeftKanExtensionOfIsLeftKanExtension", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.pointwiseRightKanExtension", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.pointwiseRightKanExtensionCounit", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.pointwiseRightKanExtensionIsPointwiseRightKanExtension", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.pointwiseRightKanExtensionIsUniversal", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instIsRightKanExtensionPointwiseRightKanExtensionPointwiseRightKanExtensionCounit", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instHasRightKanExtension", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.structuredArrowMapCone", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.pointwiseRightKanExtension_lift_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": false, "tactics": ["let", "have", "apply", "aesop", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.Functor.isPointwiseRightKanExtensionOfIsRightKanExtension", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.PreservesLeftKanExtension.mk'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Preserves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.PreservesLeftKanExtension.mk_of_preserves_isLeftKanExtension", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Preserves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.PreservesLeftKanExtension.mk_of_preserves_isUniversal", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Preserves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.PreservesPointwiseLeftKanExtension", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Preserves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.postcompose", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Preserves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtension.postcompose", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Preserves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.LeftExtension.coconeAtWhiskerRightIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Preserves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.PreservesPointwiseLeftKanExtensionAt.mk'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Preserves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.hasLeftKanExtension_of_preserves", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Preserves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.hasPointwiseLeftKanExtension_of_preserves", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Preserves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.leftKanExtensionCompIsoOfPreserves", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Preserves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.leftKanExtensionCompIsoOfPreserves_hom_fac", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Preserves", "is_tactic_proof": true, "tactics": ["simpa", "descOfIsLeftKanExtension_fac"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.leftKanExtensionCompIsoOfPreserves_hom_fac_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Preserves", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.leftKanExtensionCompIsoOfPreserves_inv_fac", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Preserves", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.leftKanExtensionCompIsoOfPreserves_inv_fac_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Preserves", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.preservesPointwiseLeftKanExtensionAtOfPreservesColimit", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Preserves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.preservesPointwiseLKEOfHasPointwiseAndPreservesPointwise", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Preserves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.pointwiseLeftKanExtensionCompIsoOfPreserves", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Preserves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.pointwiseLeftKanExtensionCompIsoOfPreserves_hom_fac", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Preserves", "is_tactic_proof": true, "tactics": ["simpa", "descOfIsLeftKanExtension_fac", "whiskerRight"], "tactic_count": 3}
{"name": "CategoryTheory.Functor.pointwiseLeftKanExtensionCompIsoOfPreserves_hom_fac_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Preserves", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.pointwiseLeftKanExtensionCompIsoOfPreserves_inv_fac", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Preserves", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.pointwiseLeftKanExtensionCompIsoOfPreserves_fac_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Preserves", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.PreservesLeftKanExtensions", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Preserves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.PreservesPointwiseLeftKanExtensions", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Preserves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.lanCompIsoOfPreserves", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Preserves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.PreservesRightKanExtension.mk'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Preserves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.PreservesRightKanExtension.mk_of_preserves_isRightKanExtension", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Preserves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.PreservesRightKanExtension.mk_of_preserves_isUniversal", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Preserves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.PreservesPointwiseRightKanExtension", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Preserves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.RightExtension.IsPointwiseRightKanExtensionAt.postcompose", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Preserves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.RightExtension.IsPointwiseRightKanExtension.postcompose", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Preserves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.RightExtension.coneAtWhiskerRightIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Preserves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.PreservesPointwiseRightKanExtensionAt.mk'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Preserves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.hasRightKanExtension_of_preserves", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Preserves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.hasPointwiseRightKanExtension_of_preserves", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Preserves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.rightKanExtensionCompIsoOfPreserves", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Preserves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.rightKanExtensionCompIsoOfPreserves_hom_fac", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Preserves", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.rightKanExtensionCompIsoOfPreserves_hom_fac_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Preserves", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.rightKanExtensionCompIsoOfPreserves_inv_fac", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Preserves", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.rightKanExtensionCompIsoOfPreserves_inv_fac_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Preserves", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.preservesPointwiseRightKanExtensionAtOfPreservesLimit", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Preserves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.preservesPointwiseRKEOfHasPointwiseAndPreservesPointwise", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Preserves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.pointwiseRightKanExtensionCompIsoOfPreserves", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Preserves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.pointwiseRightKanExtensionCompIsoOfPreserves_hom_fac", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Preserves", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.pointwiseRightKanExtensionCompIsoOfPreserves_hom_fac_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Preserves", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.pointwiseRightKanExtensionCompIsoOfPreserves_inv_fac", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Preserves", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.pointwiseRightKanExtensionCompIsoOfPreserves_inv_fac_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Preserves", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.PreservesRightKanExtensions", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Preserves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.PreservesPointwiseRightKanExtensions", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Preserves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.ranCompIsoOfPreserves", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.KanExtension.Preserves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.OfSequence.congr_f", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.OfSequence", "is_tactic_proof": true, "tactics": ["subst", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.OfSequence.map", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.OfSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.OfSequence.map_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.OfSequence", "is_tactic_proof": true, "tactics": ["revert", "induction", "zero", "succ", "intro", "apply"], "tactic_count": 6}
{"name": "CategoryTheory.Functor.OfSequence.map_le_succ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.OfSequence", "is_tactic_proof": true, "tactics": ["revert", "induction", "zero", "succ", "intro", "apply"], "tactic_count": 6}
{"name": "CategoryTheory.Functor.OfSequence.map_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.OfSequence", "is_tactic_proof": true, "tactics": ["induction", "zero", "induction", "zero", "succ", "obtain", "lia", "obtain", "rw", "simp", "rw", "obtain", "all_goals", "succ", "rcases", "lia", "lia", "lia", "exact", "hi"], "tactic_count": 20}
{"name": "CategoryTheory.Functor.OfSequence._example", "kind": "example", "module": "Mathlib.CategoryTheory.Functor.OfSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.OfSequence._example", "kind": "example", "module": "Mathlib.CategoryTheory.Functor.OfSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.OfSequence._example", "kind": "example", "module": "Mathlib.CategoryTheory.Functor.OfSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.ofSequence", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.OfSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.ofSequence_map_homOfLE_succ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.OfSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.ofSequence", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.OfSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.ofOpSequence", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.OfSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor._example", "kind": "example", "module": "Mathlib.CategoryTheory.Functor.OfSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor._example", "kind": "example", "module": "Mathlib.CategoryTheory.Functor.OfSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor._example", "kind": "example", "module": "Mathlib.CategoryTheory.Functor.OfSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.ofOpSequence_map_homOfLE_succ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.OfSequence", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.NatTrans.ofOpSequence", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.OfSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.reflectsIsomorphisms_of_reflectsMonomorphisms_of_reflectsEpimorphisms", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.ReflectsIso.Balanced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.balanced_of_preserves", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.ReflectsIso.Balanced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.isIso_iff_of_reflects_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.ReflectsIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.FullyFaithful.reflectsIsomorphisms", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.ReflectsIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.reflectsIsomorphisms_of_full_and_faithful", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.ReflectsIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.reflectsIsomorphisms_comp", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.ReflectsIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.reflectsIsomorphisms_of_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.ReflectsIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instReflectsIsomorphismsFunctorObjWhiskeringRight", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.ReflectsIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instIsRegularEpiCategoryOfForallEpiHasPullbackOfHasPushouts", "kind": "instance", "module": "Mathlib.CategoryTheory.Functor.RegularEpi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.bifunctorComp₁₂Obj", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.Trifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.bifunctorComp₁₂", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.Trifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.bifunctorComp₁₂FunctorObj", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.Trifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.bifunctorComp₁₂FunctorMap", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.Trifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.bifunctorComp₁₂Functor", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.Trifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.bifunctorComp₂₃Obj", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.Trifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.bifunctorComp₂₃", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.Trifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.bifunctorComp₂₃FunctorObj", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.Trifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.bifunctorComp₂₃FunctorMap", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.Trifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.bifunctorComp₂₃Functor", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.Trifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.TwoSquare", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.TwoSquare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.TwoSquare.natTrans", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Functor.TwoSquare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.TwoSquare.equivNatTrans", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.TwoSquare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.TwoSquare.op", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.TwoSquare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.TwoSquare.natTrans_op", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.TwoSquare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.TwoSquare.ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Functor.TwoSquare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.TwoSquare.hId", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.TwoSquare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.TwoSquare.term𝟙ₕ", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.TwoSquare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.TwoSquare.term𝟙ᵥ", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.TwoSquare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.TwoSquare.whiskerTop", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.TwoSquare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.TwoSquare.whiskerLeft", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.TwoSquare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.TwoSquare.whiskerRight", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.TwoSquare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.TwoSquare.whiskerBottom", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.TwoSquare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.TwoSquare.hComp", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.TwoSquare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.TwoSquare.term_≫ₕ_", "kind": "definition", "module": "Mathlib.CategoryTheory.Functor.TwoSquare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.PreGaloisCategory.functorToAction_comp_forget₂_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.PreGaloisCategory.instPreservesFiniteCoproductsActionFintypeCatAutFunctorFunctorToAction", "kind": "instance", "module": "Mathlib.CategoryTheory.Galois.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.instPreservesFiniteProductsActionFintypeCatAutFunctorFunctorToAction", "kind": "instance", "module": "Mathlib.CategoryTheory.Galois.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.PreGaloisCategory.instPreservesIsConnectedActionFintypeCatAutFunctorFunctorToAction", "kind": "instance", "module": "Mathlib.CategoryTheory.Galois.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.PreGaloisCategory.instHasBinaryProducts", "kind": "instance", "module": "Mathlib.CategoryTheory.Galois.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.instHasEqualizers", "kind": "instance", "module": "Mathlib.CategoryTheory.Galois.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.instHasColimitsOfShapeSingleObjOfFinite", "kind": "instance", "module": "Mathlib.CategoryTheory.Galois.Basic", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.PreGaloisCategory.FiberFunctor.instReflectsLimitsOfShapeFintypeCatDiscretePEmpty", "kind": "instance", "module": "Mathlib.CategoryTheory.Galois.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.PreGaloisCategory.FiberFunctor.instPreservesColimitsOfShapeFintypeCatSingleObjOfFinite", "kind": "instance", "module": "Mathlib.CategoryTheory.Galois.Basic", "is_tactic_proof": true, "tactics": ["choose", "exact"], "tactic_count": 2}
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{"name": "CategoryTheory.PreGaloisCategory.FiberFunctor.instFaithfulFintypeCat", "kind": "instance", "module": "Mathlib.CategoryTheory.Galois.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.FiberFunctor.comp_right", "kind": "instance", "module": "Mathlib.CategoryTheory.Galois.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.instMulActionAutFunctorFintypeCatCarrierObj", "kind": "instance", "module": "Mathlib.CategoryTheory.Galois.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.mulAction_def", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.mulAction_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.has_non_trivial_subobject_of_not_isConnected_of_not_initial", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.Basic", "is_tactic_proof": true, "tactics": ["contrapose", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.PreGaloisCategory.card_fiber_eq_of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.Basic", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.PreGaloisCategory.initial_iff_fiber_empty", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.Basic", "is_tactic_proof": true, "tactics": ["rw", "haveI", "change", "infer_instance", "haveI", "change", "infer_instance", "exact"], "tactic_count": 8}
{"name": "CategoryTheory.PreGaloisCategory.not_initial_iff_fiber_nonempty", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.PreGaloisCategory.not_initial_of_inhabited", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.nonempty_fiber_of_isConnected", "kind": "instance", "module": "Mathlib.CategoryTheory.Galois.Basic", "is_tactic_proof": true, "tactics": ["by_contra", "have", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.PreGaloisCategory.fiberEqualizerEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Galois.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.fiberEqualizerEquiv_symm_ι_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.Basic", "is_tactic_proof": false, "tactics": ["simp", "change", "erw"], "tactic_count": 3}
{"name": "CategoryTheory.PreGaloisCategory.fiberPullbackEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Galois.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.fiberPullbackEquiv_symm_fst_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.Basic", "is_tactic_proof": false, "tactics": ["simp", "change", "erw"], "tactic_count": 3}
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{"name": "CategoryTheory.PreGaloisCategory.fiberBinaryProductEquiv_symm_fst_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.Basic", "is_tactic_proof": false, "tactics": ["simp", "change", "erw"], "tactic_count": 3}
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{"name": "CategoryTheory.PreGaloisCategory.evaluation_injective_of_isConnected", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.Basic", "is_tactic_proof": true, "tactics": ["intro", "haveI", "apply", "exact", "exact"], "tactic_count": 5}
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{"name": "CategoryTheory.PreGaloisCategory.surjective_on_fiber_of_epi", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "_private.Mathlib.CategoryTheory.Galois.Decomposition.0.CategoryTheory.PreGaloisCategory.has_decomp_connected_components_aux_conn", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.Decomposition", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
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{"name": "_private.Mathlib.CategoryTheory.Galois.Decomposition.0.CategoryTheory.PreGaloisCategory.has_decomp_connected_components_aux", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.Decomposition", "is_tactic_proof": false, "tactics": ["induction", "intro", "by_cases", "exact", "by_cases", "obtain", "obtain", "let", "have", "rw", "exact", "have", "have", "rw", "exact", "have", "rw", "exact", "let", "let", "refine", "use", "refine", "cases", "exact", "exact", "simp", "obtain", "exact"], "tactic_count": 29}
{"name": "CategoryTheory.PreGaloisCategory.has_decomp_connected_components", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.Decomposition", "is_tactic_proof": true, "tactics": ["let", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.PreGaloisCategory.has_decomp_connected_components'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.Decomposition", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.PreGaloisCategory.fiber_in_connected_component", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.Decomposition", "is_tactic_proof": true, "tactics": ["obtain", "let", "let", "obtain", "refine", "subst", "rfl"], "tactic_count": 7}
{"name": "CategoryTheory.PreGaloisCategory.connected_component_unique", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.Decomposition", "is_tactic_proof": true, "tactics": ["subobject", "let", "let", "let", "let", "let", "let", "have", "have", "have", "use", "have", "have", "rw", "change", "simp"], "tactic_count": 16}
{"name": "_private.Mathlib.CategoryTheory.Galois.Decomposition.0.CategoryTheory.PreGaloisCategory.selfProd", "kind": "definition", "module": "Mathlib.CategoryTheory.Galois.Decomposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.CategoryTheory.Galois.Decomposition.0.CategoryTheory.PreGaloisCategory.mkSelfProdFib", "kind": "definition", "module": "Mathlib.CategoryTheory.Galois.Decomposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.CategoryTheory.Galois.Decomposition.0.CategoryTheory.PreGaloisCategory.mkSelfProdFib_map_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.Decomposition", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
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{"name": "_private.Mathlib.CategoryTheory.Galois.Decomposition.0.CategoryTheory.PreGaloisCategory.selfProdProj_fiber", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.Decomposition", "is_tactic_proof": true, "tactics": ["simp_all"], "tactic_count": 1}
{"name": "_private.Mathlib.CategoryTheory.Galois.Decomposition.0.CategoryTheory.PreGaloisCategory.fiberPerm", "kind": "definition", "module": "Mathlib.CategoryTheory.Galois.Decomposition", "is_tactic_proof": true, "tactics": ["let", "apply", "apply", "intro", "change", "have", "rw"], "tactic_count": 7}
{"name": "_private.Mathlib.CategoryTheory.Galois.Decomposition.0.CategoryTheory.PreGaloisCategory.selfProdPermIncl", "kind": "definition", "module": "Mathlib.CategoryTheory.Galois.Decomposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.CategoryTheory.Galois.Decomposition.0.CategoryTheory.PreGaloisCategory.instMonoSelfProdPermIncl", "kind": "instance", "module": "Mathlib.CategoryTheory.Galois.Decomposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.CategoryTheory.Galois.Decomposition.0.CategoryTheory.PreGaloisCategory.selfProdTermIncl_fib_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.Decomposition", "is_tactic_proof": true, "tactics": ["apply", "intro", "convert_to", "simp", "dsimp", "rw", "convert_to", "rw", "rfl"], "tactic_count": 9}
{"name": "_private.Mathlib.CategoryTheory.Galois.Decomposition.0.CategoryTheory.PreGaloisCategory.subobj_selfProd_trans", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.Decomposition", "is_tactic_proof": true, "tactics": ["apply", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.PreGaloisCategory.exists_galois_representative", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.Decomposition", "is_tactic_proof": true, "tactics": ["obtain", "use", "use", "constructor", "refine", "obtain", "obtain", "use", "change", "simp", "rw", "exact", "refine", "intro", "use", "exact"], "tactic_count": 16}
{"name": "CategoryTheory.PreGaloisCategory.exists_hom_from_galois_of_fiber", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.Decomposition", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.PreGaloisCategory.exists_hom_from_galois_of_fiber_nonempty", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.Decomposition", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.PreGaloisCategory.exists_hom_from_galois_of_connected", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.Decomposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.natTrans_ext_of_isGalois", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.Decomposition", "is_tactic_proof": true, "tactics": ["ext", "obtain", "rw"], "tactic_count": 3}
{"name": "CategoryTheory.PreGaloisCategory.functorToContAction", "kind": "definition", "module": "Mathlib.CategoryTheory.Galois.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.instFaithfulContActionFintypeCatAutFunctorFunctorToContAction", "kind": "instance", "module": "Mathlib.CategoryTheory.Galois.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.instFullContActionFintypeCatAutFunctorFunctorToContAction", "kind": "instance", "module": "Mathlib.CategoryTheory.Galois.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.instEssSurjContActionFintypeCatAutFunctorFunctorToContActionOfFiberFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.Galois.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.instEssSurjContActionFintypeCatAutFunctorFunctorToContAction", "kind": "instance", "module": "Mathlib.CategoryTheory.Galois.Equivalence", "is_tactic_proof": true, "tactics": ["let", "letI", "have", "let", "let", "rw", "change", "exact", "rw", "change", "exact", "have", "ext", "exact", "exact"], "tactic_count": 15}
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{"name": "_private.Mathlib.CategoryTheory.Galois.EssSurj.0.CategoryTheory.PreGaloisCategory.fintypeQuotient", "kind": "instance", "module": "Mathlib.CategoryTheory.Galois.EssSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.CategoryTheory.Galois.EssSurj.0.CategoryTheory.PreGaloisCategory.fintypeQuotientStabilizer", "kind": "instance", "module": "Mathlib.CategoryTheory.Galois.EssSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.PreGaloisCategory.fiberIsoQuotientStabilizer", "kind": "definition", "module": "Mathlib.CategoryTheory.Galois.EssSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.CategoryTheory.Galois.EssSurj.0.CategoryTheory.PreGaloisCategory.quotientToEndObjectHom", "kind": "definition", "module": "Mathlib.CategoryTheory.Galois.EssSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.CategoryTheory.Galois.EssSurj.0.CategoryTheory.PreGaloisCategory.functorToAction_map_quotientToEndObjectHom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.EssSurj", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "_private.Mathlib.CategoryTheory.Galois.EssSurj.0.CategoryTheory.PreGaloisCategory.quotientDiag", "kind": "definition", "module": "Mathlib.CategoryTheory.Galois.EssSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.CategoryTheory.Galois.EssSurj.0.CategoryTheory.PreGaloisCategory.coconeQuotientDiag", "kind": "definition", "module": "Mathlib.CategoryTheory.Galois.EssSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.CategoryTheory.Galois.EssSurj.0.CategoryTheory.PreGaloisCategory.coconeQuotientDiagDesc", "kind": "definition", "module": "Mathlib.CategoryTheory.Galois.EssSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.CategoryTheory.Galois.EssSurj.0.CategoryTheory.PreGaloisCategory.coconeQuotientDiagIsColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Galois.EssSurj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.exists_lift_of_quotient_openSubgroup", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.EssSurj", "is_tactic_proof": true, "tactics": ["obtain", "haveI", "haveI", "have", "obtain", "obtain", "let", "let", "have", "have", "have", "refine", "induction", "change", "apply", "apply", "simp", "exact", "simp", "have", "intro", "ext", "let", "have", "obtain", "simp", "have", "have", "exact", "colimit.isoColimitCocone"], "tactic_count": 30}
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{"name": "CategoryTheory.FintypeCat.instPreGaloisCategoryActionFintypeCat", "kind": "instance", "module": "Mathlib.CategoryTheory.Galois.Examples", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FintypeCat.instFiberFunctorActionFintypeCatForget", "kind": "instance", "module": "Mathlib.CategoryTheory.Galois.Examples", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FintypeCat.instFiberFunctorActionFintypeCatForget₂", "kind": "instance", "module": "Mathlib.CategoryTheory.Galois.Examples", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FintypeCat.instGaloisCategoryActionFintypeCat", "kind": "instance", "module": "Mathlib.CategoryTheory.Galois.Examples", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FintypeCat.Action.pretransitive_of_isConnected", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.Examples", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FintypeCat.Action.isConnected_of_transitive", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.Examples", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FintypeCat.Action.isConnected_iff_transitive", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.Examples", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FintypeCat.isoQuotientStabilizerOfIsConnected", "kind": "definition", "module": "Mathlib.CategoryTheory.Galois.Examples", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.exists_lift_of_mono_of_isConnected", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.Full", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "have", "obtain", "connected_component_unique", "refine", "apply", "evaluation_injective_of_isConnected", "suffices", "exact"], "tactic_count": 10}
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{"name": "CategoryTheory.PreGaloisCategory.functorToAction_full", "kind": "instance", "module": "Mathlib.CategoryTheory.Galois.Full", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.instPreservesColimitsOfShapeFintypeCatSingleObjInclOfFinite", "kind": "instance", "module": "Mathlib.CategoryTheory.Galois.GaloisObjects", "is_tactic_proof": true, "tactics": ["choose", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.PreGaloisCategory.autMulFiber", "kind": "instance", "module": "Mathlib.CategoryTheory.Galois.GaloisObjects", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.quotientByAutTerminalEquivUniqueQuotient", "kind": "definition", "module": "Mathlib.CategoryTheory.Galois.GaloisObjects", "is_tactic_proof": true, "tactics": ["let", "let", "preservesColimitIso", "apply", "apply", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.PreGaloisCategory.isGalois_iff_aux", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.GaloisObjects", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.isGalois_iff_pretransitive", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.GaloisObjects", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.PreGaloisCategory.isTerminalQuotientOfIsGalois", "kind": "definition", "module": "Mathlib.CategoryTheory.Galois.GaloisObjects", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.isPretransitive_of_isGalois", "kind": "instance", "module": "Mathlib.CategoryTheory.Galois.GaloisObjects", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.PreGaloisCategory.stabilizer_normal_of_isGalois", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.GaloisObjects", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.evaluation_aut_surjective_of_isGalois", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.GaloisObjects", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.evaluation_aut_bijective_of_isGalois", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.GaloisObjects", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.evaluationEquivOfIsGalois", "kind": "definition", "module": "Mathlib.CategoryTheory.Galois.GaloisObjects", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.evaluationEquivOfIsGalois_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.GaloisObjects", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.evaluationEquivOfIsGalois_symm_fiber", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.GaloisObjects", "is_tactic_proof": true, "tactics": ["change", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.PreGaloisCategory.exists_autMap", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.GaloisObjects", "is_tactic_proof": true, "tactics": ["let", "obtain", "refine", "exact", "apply", "simp", "intro", "apply", "simpa"], "tactic_count": 9}
{"name": "CategoryTheory.PreGaloisCategory.autMap", "kind": "definition", "module": "Mathlib.CategoryTheory.Galois.GaloisObjects", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.comp_autMap", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.GaloisObjects", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.comp_autMap_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.GaloisObjects", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.PreGaloisCategory.autMap_unique", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.GaloisObjects", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.autMap_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.GaloisObjects", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.autMap_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.GaloisObjects", "is_tactic_proof": true, "tactics": ["refine", "rw", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.PreGaloisCategory.autMap_surjective_of_isGalois", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.GaloisObjects", "is_tactic_proof": true, "tactics": ["intro", "let", "obtain", "obtain", "obtain", "use", "apply", "simp"], "tactic_count": 8}
{"name": "CategoryTheory.PreGaloisCategory.autMap_apply_mul", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.GaloisObjects", "is_tactic_proof": true, "tactics": ["let", "obtain", "apply", "simp"], "tactic_count": 4}
{"name": "CategoryTheory.PreGaloisCategory.autMapHom", "kind": "definition", "module": "Mathlib.CategoryTheory.Galois.GaloisObjects", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.CategoryTheory.Galois.IsFundamentalgroup.0.CategoryTheory.PreGaloisCategory.isoOnObj", "kind": "definition", "module": "Mathlib.CategoryTheory.Galois.IsFundamentalgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.toAut", "kind": "definition", "module": "Mathlib.CategoryTheory.Galois.IsFundamentalgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.toAut_hom_app_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.IsFundamentalgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.PreGaloisCategory.action_ext_of_isGalois", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.IsFundamentalgroup", "is_tactic_proof": true, "tactics": ["obtain", "have", "apply", "rw"], "tactic_count": 4}
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{"name": "CategoryTheory.PreGaloisCategory.toAut_surjective_isGalois_finite_family", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.IsFundamentalgroup", "is_tactic_proof": true, "tactics": ["let", "let", "let", "let", "let", "have", "simp", "rw", "obtain", "obtain", "refine", "rw"], "tactic_count": 12}
{"name": "CategoryTheory.PreGaloisCategory.toAut_surjective_of_isPretransitive", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.IsFundamentalgroup", "is_tactic_proof": true, "tactics": ["intro", "choose", "let", "let", "have", "rw", "apply", "intro", "apply", "exact", "intro", "rw", "obtain", "use", "simp", "intro", "rw", "inv_smul_smul]", "obtain", "refine", "ext", "simp", "have", "simp", "exact", "obtain", "rw", "exact"], "tactic_count": 28}
{"name": "CategoryTheory.PreGaloisCategory.isPretransitive_of_surjective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.IsFundamentalgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.IsFundamentalGroup.non_trivial", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.IsFundamentalgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.instIsFundamentalGroupAutFunctorFintypeCat", "kind": "instance", "module": "Mathlib.CategoryTheory.Galois.IsFundamentalgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.toAut_bijective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.IsFundamentalgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.instIsPretransitiveCarrierObjFintypeCatOfIsConnected", "kind": "instance", "module": "Mathlib.CategoryTheory.Galois.IsFundamentalgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.toAutMulEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Galois.IsFundamentalgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.toAut_isHomeomorph", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.IsFundamentalgroup", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.PreGaloisCategory.toAutMulEquiv_isHomeomorph", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.IsFundamentalgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.toAutHomeo", "kind": "definition", "module": "Mathlib.CategoryTheory.Galois.IsFundamentalgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.toAutMulEquiv_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.IsFundamentalgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.toAutHomeo_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.IsFundamentalgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.PointedGaloisObject.instCoeDep", "kind": "instance", "module": "Mathlib.CategoryTheory.Galois.Prorepresentability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.PointedGaloisObject.instCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Galois.Prorepresentability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.PointedGaloisObject.instCoeHomHomObj", "kind": "instance", "module": "Mathlib.CategoryTheory.Galois.Prorepresentability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.PointedGaloisObject.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.Prorepresentability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.PointedGaloisObject.id_val", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.Prorepresentability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.PointedGaloisObject.comp_val", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.Prorepresentability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.PointedGaloisObject.incl", "kind": "definition", "module": "Mathlib.CategoryTheory.Galois.Prorepresentability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.PointedGaloisObject.incl_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.Prorepresentability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.PointedGaloisObject.incl_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.Prorepresentability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.PointedGaloisObject.cocone", "kind": "definition", "module": "Mathlib.CategoryTheory.Galois.Prorepresentability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.PointedGaloisObject.cocone_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.Prorepresentability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.PointedGaloisObject.instIsCofilteredOrEmpty", "kind": "instance", "module": "Mathlib.CategoryTheory.Galois.Prorepresentability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.PointedGaloisObject.isColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Galois.Prorepresentability", "is_tactic_proof": true, "tactics": ["refine", "refine", "intro", "obtain", "obtain", "refine", "simp", "intro", "obtain", "refine", "apply", "change", "rw"], "tactic_count": 13}
{"name": "CategoryTheory.PreGaloisCategory.PointedGaloisObject.instHasColimitOppositeFunctorTypeCompOpInclCoyoneda", "kind": "instance", "module": "Mathlib.CategoryTheory.Galois.Prorepresentability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.autGaloisSystem", "kind": "definition", "module": "Mathlib.CategoryTheory.Galois.Prorepresentability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.AutGalois", "kind": "definition", "module": "Mathlib.CategoryTheory.Galois.Prorepresentability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.instGroupAutGalois", "kind": "instance", "module": "Mathlib.CategoryTheory.Galois.Prorepresentability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.AutGalois.π", "kind": "definition", "module": "Mathlib.CategoryTheory.Galois.Prorepresentability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.AutGalois.π_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.Prorepresentability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.autGaloisSystem_map_surjective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.Prorepresentability", "is_tactic_proof": true, "tactics": ["intro", "obtain", "use", "simp", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.PreGaloisCategory.AutGalois.ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.Prorepresentability", "is_tactic_proof": true, "tactics": ["dsimp", "ext", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.PreGaloisCategory.AutGalois.π_surjective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.Prorepresentability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.CategoryTheory.Galois.Prorepresentability.0.CategoryTheory.PreGaloisCategory.termF'", "kind": "definition", "module": "Mathlib.CategoryTheory.Galois.Prorepresentability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.CategoryTheory.Galois.Prorepresentability.0.CategoryTheory.PreGaloisCategory._aux_Mathlib_CategoryTheory_Galois_Prorepresentability___macroRules__private_Mathlib_CategoryTheory_Galois_Prorepresentability_0_CategoryTheory_PreGaloisCategory_termF'_1", "kind": "definition", "module": "Mathlib.CategoryTheory.Galois.Prorepresentability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.endEquivSectionsFibers", "kind": "definition", "module": "Mathlib.CategoryTheory.Galois.Prorepresentability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.endEquivSectionsFibers_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.Prorepresentability", "is_tactic_proof": true, "tactics": ["dsimp", "erw", "simp", "change", "f.app", "simp", "rfl"], "tactic_count": 7}
{"name": "CategoryTheory.PreGaloisCategory.autIsoFibers", "kind": "definition", "module": "Mathlib.CategoryTheory.Galois.Prorepresentability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.autIsoFibers_inv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.Prorepresentability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.endEquivAutGalois", "kind": "definition", "module": "Mathlib.CategoryTheory.Galois.Prorepresentability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.endEquivAutGalois_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.Prorepresentability", "is_tactic_proof": true, "tactics": ["dsimp", "change", "dsimp", "simp", "erw"], "tactic_count": 5}
{"name": "CategoryTheory.PreGaloisCategory.endEquivAutGalois_mul", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.Prorepresentability", "is_tactic_proof": true, "tactics": ["refine", "simp", "simp", "change", "rw"], "tactic_count": 5}
{"name": "CategoryTheory.PreGaloisCategory.endMulEquivAutGalois", "kind": "definition", "module": "Mathlib.CategoryTheory.Galois.Prorepresentability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.endMulEquivAutGalois_pi", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.Prorepresentability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.FibreFunctor.end_isUnit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.Prorepresentability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.FibreFunctor.end_isIso", "kind": "instance", "module": "Mathlib.CategoryTheory.Galois.Prorepresentability", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.PreGaloisCategory.autMulEquivAutGalois", "kind": "definition", "module": "Mathlib.CategoryTheory.Galois.Prorepresentability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.autMulEquivAutGalois_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.Prorepresentability", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "rfl"], "tactic_count": 3}
{"name": "CategoryTheory.PreGaloisCategory.autMulEquivAutGalois_symm_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.Prorepresentability", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "CategoryTheory.PreGaloisCategory.FiberFunctor.isPretransitive_of_isGalois", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.Prorepresentability", "is_tactic_proof": true, "tactics": ["refine", "obtain", "obtain", "use", "simpa"], "tactic_count": 5}
{"name": "_private.Mathlib.CategoryTheory.Galois.Prorepresentability.0.CategoryTheory.PreGaloisCategory.FiberFunctor.isPretransitive_of_isConnected'", "kind": "instance", "module": "Mathlib.CategoryTheory.Galois.Prorepresentability", "is_tactic_proof": true, "tactics": ["obtain", "have", "refine", "obtain", "obtain", "have", "obtain", "use", "rw", "change", "rw"], "tactic_count": 11}
{"name": "CategoryTheory.PreGaloisCategory.FiberFunctor.isPretransitive_of_isConnected", "kind": "instance", "module": "Mathlib.CategoryTheory.Galois.Prorepresentability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.autEmbedding", "kind": "definition", "module": "Mathlib.CategoryTheory.Galois.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.autEmbedding_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.autEmbedding_injective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.Topology", "is_tactic_proof": true, "tactics": ["intro", "ext", "have", "rw"], "tactic_count": 4}
{"name": "CategoryTheory.PreGaloisCategory.instTopologicalSpaceCarrierObjFintypeCat", "kind": "instance", "module": "Mathlib.CategoryTheory.Galois.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.obj_discreteTopology", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.instTopologicalSpaceAutFintypeCatObj", "kind": "instance", "module": "Mathlib.CategoryTheory.Galois.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.aut_discreteTopology", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.instTopologicalSpaceAutFunctorFintypeCat", "kind": "instance", "module": "Mathlib.CategoryTheory.Galois.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.autEmbedding_range", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.Topology", "is_tactic_proof": true, "tactics": ["ext", "simp", "refine", "use", "rfl"], "tactic_count": 5}
{"name": "CategoryTheory.PreGaloisCategory.autEmbedding_range_isClosed", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.Topology", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.PreGaloisCategory.autEmbedding_isClosedEmbedding", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.instCompactSpaceAutFunctorFintypeCat", "kind": "instance", "module": "Mathlib.CategoryTheory.Galois.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.instT2SpaceAutFunctorFintypeCat", "kind": "instance", "module": "Mathlib.CategoryTheory.Galois.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.instTotallyDisconnectedSpaceAutFunctorFintypeCat", "kind": "instance", "module": "Mathlib.CategoryTheory.Galois.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.instContinuousMulAutFunctorFintypeCat", "kind": "instance", "module": "Mathlib.CategoryTheory.Galois.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.instContinuousInvAutFunctorFintypeCat", "kind": "instance", "module": "Mathlib.CategoryTheory.Galois.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.instIsTopologicalGroupAutFunctorFintypeCat", "kind": "instance", "module": "Mathlib.CategoryTheory.Galois.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.instSMulAutFintypeCatObjCarrier", "kind": "instance", "module": "Mathlib.CategoryTheory.Galois.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.instContinuousSMulAutFintypeCatObjCarrier", "kind": "instance", "module": "Mathlib.CategoryTheory.Galois.Topology", "is_tactic_proof": true, "tactics": ["constructor", "fun_prop"], "tactic_count": 2}
{"name": "CategoryTheory.PreGaloisCategory.continuousSMul_aut_fiber", "kind": "instance", "module": "Mathlib.CategoryTheory.Galois.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.continuous_mapAut_whiskeringRight", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.Topology", "is_tactic_proof": true, "tactics": ["rw", "intro", "change", "fun_prop"], "tactic_count": 4}
{"name": "CategoryTheory.PreGaloisCategory.autEquivAutWhiskerRight", "kind": "definition", "module": "Mathlib.CategoryTheory.Galois.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreGaloisCategory.exists_set_ker_evaluation_subset_of_isOpen", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.Topology", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "choose", "refine", "rintro", "obtain", "exact", "refine", "suffices", "rw", "exact", "have", "have", "ext", "obtain", "rw", "simp", "exact"], "tactic_count": 18}
{"name": "CategoryTheory.PreGaloisCategory.nhds_one_has_basis_stabilizers", "kind": "theorem", "module": "Mathlib.CategoryTheory.Galois.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.has_injective_coseparator", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Abelian", "is_tactic_proof": true, "tactics": ["haveI", "haveI", "let", "refine", "refine", "suffices", "let", "let", "let", "section_", "let", "exact", "zero_of_comp_mono", "rw", "comp_zero])"], "tactic_count": 15}
{"name": "CategoryTheory.Abelian.has_projective_separator", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Abelian", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.ObjectProperty.IsSeparating", "kind": "definition", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.IsCoseparating", "kind": "definition", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.IsDetecting", "kind": "definition", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.IsCodetecting", "kind": "definition", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.IsSeparating.of_equivalence", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.IsCoseparating.of_equivalence", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.isSeparating_op_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": true, "tactics": ["refine", "refine", "simpa", "refine", "simpa"], "tactic_count": 5}
{"name": "CategoryTheory.ObjectProperty.isCoseparating_op_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": true, "tactics": ["refine", "refine", "simpa", "refine", "simpa"], "tactic_count": 5}
{"name": "CategoryTheory.ObjectProperty.isCoseparating_unop_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.isSeparating_unop_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.isDetecting_op_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": true, "tactics": ["refine", "refine", "obtain", "exact", "refine", "obtain", "refine", "exact"], "tactic_count": 8}
{"name": "CategoryTheory.ObjectProperty.isCodetecting_op_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": true, "tactics": ["refine", "refine", "obtain", "exact", "refine", "obtain", "refine", "exact"], "tactic_count": 8}
{"name": "CategoryTheory.ObjectProperty.isDetecting_unop_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.isCodetecting_unop_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.IsDetecting.isSeparating", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.IsCodetecting.isCoseparating", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.ObjectProperty.IsSeparating.mono_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.IsCoseparating.epi_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.IsSeparating.isDetecting", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": true, "tactics": ["intro", "refine", "obtain", "rw", "refine", "obtain", "rw"], "tactic_count": 7}
{"name": "CategoryTheory.ObjectProperty.IsDetecting.isIso_iff_of_mono", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "intro", "exact", "intro", "refine", "exact", "intro", "rw"], "tactic_count": 10}
{"name": "CategoryTheory.ObjectProperty.IsCodetecting.isIso_iff_of_epi", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "intro", "exact", "intro", "refine", "exact", "intro", "rw"], "tactic_count": 10}
{"name": "CategoryTheory.ObjectProperty.IsCoseparating.isCodetecting", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.ObjectProperty.isDetecting_iff_isSeparating", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.isCodetecting_iff_isCoseparating", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.IsSeparating.of_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.IsCoseparating.of_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.IsDetecting.of_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.IsCodetecting.of_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.isThin_of_isSeparating_bot", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.isSeparating_bot_of_isThin", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.isThin_of_isCoseparating_bot", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.isCoseparating_bot_of_isThin", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.isGroupoid_of_isDetecting_bot", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.isDetecting_bot_of_isGroupoid", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.isGroupoid_of_isCodetecting_bot", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.isCodetecting_bot_of_isGroupoid", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.IsSeparating.mk_of_exists_epi", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": true, "tactics": ["intro", "obtain", "rw", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.ObjectProperty.IsCoseparating.mk_of_exists_mono", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": true, "tactics": ["intro", "obtain", "rw", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.ObjectProperty.IsSeparating.mk_of_exists_colimitsOfShape", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": true, "tactics": ["intro", "obtain", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.ObjectProperty.IsCoseparating.mk_of_exists_limitsOfShape", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": true, "tactics": ["intro", "obtain", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.ObjectProperty.coproductFromFamily", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.coproductFrom", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.ιCoproductFrom", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "CategoryTheory.ObjectProperty.IsSeparating.epi_coproductFrom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.isSeparating_iff_epi", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.productToFamily", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.productTo", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.πProductTo", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "CategoryTheory.ObjectProperty.IsCoseparating.mono_productTo", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.isCoseparating_iff_mono", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.hasInitial_of_isCoseparating", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": true, "tactics": ["have", "haveI", "haveI", "letI", "suffices", "exact", "have", "refine", "let", "exact", "suffices", "intro", "suffices", "exact", "ext", "simp⟩"], "tactic_count": 16}
{"name": "CategoryTheory.hasTerminal_of_isSeparating", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": true, "tactics": ["haveI", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Subobject.eq_of_le_of_isDetecting", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": true, "tactics": ["suffices", "refine", "have", "refine", "simp", "simp", "factorThru_arrow]"], "tactic_count": 7}
{"name": "CategoryTheory.Subobject.inf_eq_of_isDetecting", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.eq_of_isDetecting", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.wellPowered_of_isDetecting", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.isCoseparating_inverseImage_proj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.CostructuredArrow.isSeparating_inverseImage_proj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.IsSeparator", "kind": "definition", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsCoseparator", "kind": "definition", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsDetector", "kind": "definition", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsCodetector", "kind": "definition", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsSeparator.of_equivalence", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.IsCoseparator.of_equivalence", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.isSeparator_op_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.isCoseparator_op_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.isCoseparator_unop_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.isSeparator_unop_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.isDetector_op_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.isCodetector_op_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.isCodetector_unop_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.isDetector_unop_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.IsDetector.isSeparator", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsCodetector.isCoseparator", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsSeparator.isDetector", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsCoseparator.isCodetector", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isSeparator_def", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsSeparator.def", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isCoseparator_def", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsCoseparator.def", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isDetector_def", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsDetector.def", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isCodetector_def", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsCodetector.def", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isSeparator_iff_faithful_coyoneda_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isCoseparator_iff_faithful_yoneda_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isSeparator_iff_epi", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "simpa", "haveI", "refine", "simpa"], "tactic_count": 6}
{"name": "CategoryTheory.isCoseparator_iff_mono", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "simpa", "haveI", "refine", "simpa"], "tactic_count": 6}
{"name": "CategoryTheory.isSeparator_of_isColimit_cofan", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "obtain", "classical"], "tactic_count": 4}
{"name": "CategoryTheory.isSeparator_iff_of_isColimit_cofan", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": true, "tactics": ["refine", "refine", "simpa"], "tactic_count": 3}
{"name": "CategoryTheory.isSeparator_sigma", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isSeparator_coprod", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": true, "tactics": ["refine", "convert", "ext", "simp", "constructor", "rintro", "rintro"], "tactic_count": 7}
{"name": "CategoryTheory.isSeparator_coprod_of_isSeparator_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isSeparator_coprod_of_isSeparator_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.IsSeparating.isSeparator_coproduct", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isSeparator_sigma_of_isSeparator", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isCoseparator_of_isLimit_fan", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "obtain", "classical"], "tactic_count": 4}
{"name": "CategoryTheory.isCoseparator_iff_of_isLimit_fan", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": true, "tactics": ["refine", "refine", "simpa"], "tactic_count": 3}
{"name": "CategoryTheory.isCoseparator_pi", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isCoseparator_prod", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": true, "tactics": ["refine", "convert", "ext", "simp", "constructor", "rintro", "rintro"], "tactic_count": 7}
{"name": "CategoryTheory.isCoseparator_prod_of_isCoseparator_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isCoseparator_prod_of_isCoseparator_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isCoseparator_pi_of_isCoseparator", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isDetector_iff_reflectsIsomorphisms_coyoneda_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact", "suffices", "rwa"], "tactic_count": 5}
{"name": "CategoryTheory.isCodetector_iff_reflectsIsomorphisms_yoneda_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": true, "tactics": ["refine", "refine", "rwa", "rw", "suffices", "rwa"], "tactic_count": 6}
{"name": "CategoryTheory.wellPowered_of_isDetector", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.wellPowered_of_isSeparator", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.separator", "kind": "definition", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.coseparator", "kind": "definition", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.detector", "kind": "definition", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.codetector", "kind": "definition", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isSeparator_separator", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isDetector_separator", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isCoseparator_coseparator", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isCodetector_coseparator", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isDetector_detector", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isSeparator_detector", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isCodetector_codetector", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isCoseparator_codetector", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasSeparator.hasDetector", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasDetector.hasSeparator", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasCoseparator.hasCodetector", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasCodetector.hasCoseparator", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasDetector.wellPowered", "kind": "instance", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasSeparator.wellPowered", "kind": "instance", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasSeparator.of_equivalence", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasCoseparator.of_equivalence", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.hasSeparator_op_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.hasCoseparator_op_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.hasDetector_op_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.hasCodetector_op_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasSeparator.hasCoseparator_op", "kind": "instance", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.HasSeparator.hasCoseparator_of_hasSeparator_op", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": true, "tactics": ["simp_all"], "tactic_count": 1}
{"name": "CategoryTheory.HasCoseparator.hasSeparator_op", "kind": "instance", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.HasCoseparator.hasSeparator_of_hasCoseparator_op", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": true, "tactics": ["simp_all"], "tactic_count": 1}
{"name": "CategoryTheory.HasDetector.hasCodetector_op", "kind": "instance", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.HasDetector.hasCodetector_of_hasDetector_op", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": true, "tactics": ["simp_all"], "tactic_count": 1}
{"name": "CategoryTheory.HasCodetector.hasDetector_op", "kind": "instance", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.HasCodetector.hasDetector_of_hasCodetector_op", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Basic", "is_tactic_proof": true, "tactics": ["simp_all"], "tactic_count": 1}
{"name": "HomologicalComplex.separatingFamily", "kind": "definition", "module": "Mathlib.CategoryTheory.Generator.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.isSeparating_separatingFamily", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.HomologicalComplex", "is_tactic_proof": true, "tactics": ["intro", "ext", "apply", "rintro", "have", "apply", "simpa"], "tactic_count": 7}
{"name": "HomologicalComplex.isSeparator_coproduct_separatingFamily", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.HomologicalComplex", "is_tactic_proof": true, "tactics": ["let", "refine", "isSeparator_of_isColimit_cofan", "exact"], "tactic_count": 4}
{"name": "HomologicalComplex.instHasSeparator", "kind": "instance", "module": "Mathlib.CategoryTheory.Generator.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Ind.isSeparating_range_yoneda", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Indization", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Ind.isSeparator_range_yoneda", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Indization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.isSeparating_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.isCoseparating_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.isSeparator_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.isCoseparator_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isSeparator_iff_faithful_preadditiveCoyoneda", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Preadditive", "is_tactic_proof": false, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.isSeparator_iff_faithful_preadditiveCoyonedaObj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Preadditive", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.isCoseparator_iff_faithful_preadditiveYoneda", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Preadditive", "is_tactic_proof": false, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.isCoseparator_iff_faithful_preadditiveYonedaObj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Preadditive", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Presheaf.freeYoneda", "kind": "definition", "module": "Mathlib.CategoryTheory.Generator.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.freeYonedaHomEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Generator.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.freeYonedaHomEquiv_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Presheaf", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Presheaf.freeYonedaHomEquiv_symm_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Presheaf", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Presheaf.isSeparating", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Presheaf", "is_tactic_proof": true, "tactics": ["intro", "ext", "refine", "rintro", "apply", "simpa"], "tactic_count": 6}
{"name": "CategoryTheory.Presheaf.isSeparator", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.hasSeparator", "kind": "instance", "module": "Mathlib.CategoryTheory.Generator.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.freeYoneda", "kind": "definition", "module": "Mathlib.CategoryTheory.Generator.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.freeYonedaHomEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Generator.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.isSeparating", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Sheaf", "is_tactic_proof": true, "tactics": ["intro", "refine", "rintro", "apply", "simpa", "hfg"], "tactic_count": 6}
{"name": "CategoryTheory.Sheaf.isSeparator", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.hasSeparator", "kind": "instance", "module": "Mathlib.CategoryTheory.Generator.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.IsStrongGenerator", "kind": "definition", "module": "Mathlib.CategoryTheory.Generator.StrongGenerator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.isStrongGenerator_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.StrongGenerator", "is_tactic_proof": true, "tactics": ["refine", "rw", "refine", "rw", "exact", "rw", "exact"], "tactic_count": 7}
{"name": "CategoryTheory.ObjectProperty.IsStrongGenerator.isSeparating", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.StrongGenerator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.IsStrongGenerator.subobject_eq_top", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.StrongGenerator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.IsStrongGenerator.isIso_of_mono", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.StrongGenerator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.IsStrongGenerator.exists_of_subobject_ne_top", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.StrongGenerator", "is_tactic_proof": true, "tactics": ["by_contra", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.ObjectProperty.IsStrongGenerator.exists_of_mono_not_isIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.StrongGenerator", "is_tactic_proof": true, "tactics": ["by_contra", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.ObjectProperty.IsStrongGenerator.mk_of_exists_extremalEpi", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.StrongGenerator", "is_tactic_proof": true, "tactics": ["rw", "refine", "obtain", "exact", "obtain", "replace", "choose", "exact"], "tactic_count": 8}
{"name": "CategoryTheory.ObjectProperty.IsStrongGenerator.extremalEpi_coproductFrom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.StrongGenerator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.isStrongGenerator_iff_exists_extremalEpi", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.StrongGenerator", "is_tactic_proof": true, "tactics": ["refine", "have", "have", "refine"], "tactic_count": 4}
{"name": "CategoryTheory.ObjectProperty.IsStrongGenerator.mk_of_exists_colimitsOfShape", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.StrongGenerator", "is_tactic_proof": true, "tactics": ["rw", "refine", "suffices", "obtain", "exact", "obtain", "choose", "let", "naturality", "refine", "dsimp", "rw"], "tactic_count": 12}
{"name": "CategoryTheory.Types.isSeparator_punit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Generator.Type", "is_tactic_proof": true, "tactics": ["intro", "ext", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.GlueData.t'_iij", "kind": "theorem", "module": "Mathlib.CategoryTheory.GlueData", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "have", "rw", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.GlueData.t'_jii", "kind": "theorem", "module": "Mathlib.CategoryTheory.GlueData", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.GlueData.t'_iji", "kind": "theorem", "module": "Mathlib.CategoryTheory.GlueData", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.GlueData.t_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.GlueData", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "simp", "rw", "simpa"], "tactic_count": 6}
{"name": "CategoryTheory.GlueData.t'_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.GlueData", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.GlueData.t_isIso", "kind": "instance", "module": "Mathlib.CategoryTheory.GlueData", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GlueData.t'_isIso", "kind": "instance", "module": "Mathlib.CategoryTheory.GlueData", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GlueData.t'_comp_eq_pullbackSymmetry", "kind": "theorem", "module": "Mathlib.CategoryTheory.GlueData", "is_tactic_proof": true, "tactics": ["trans", "exact", "rw", "simp"], "tactic_count": 4}
{"name": "CategoryTheory.GlueData.sigmaOpens", "kind": "definition", "module": "Mathlib.CategoryTheory.GlueData", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GlueData.diagram", "kind": "definition", "module": "Mathlib.CategoryTheory.GlueData", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GlueData.diagram_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.GlueData", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GlueData.diagram_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.GlueData", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GlueData.diagram_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.GlueData", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GlueData.diagram_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.GlueData", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GlueData.glued", "kind": "definition", "module": "Mathlib.CategoryTheory.GlueData", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GlueData.ι", "kind": "definition", "module": "Mathlib.CategoryTheory.GlueData", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GlueData.glue_condition", "kind": "theorem", "module": "Mathlib.CategoryTheory.GlueData", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GlueData.vPullbackCone", "kind": "definition", "module": "Mathlib.CategoryTheory.GlueData", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GlueData.π", "kind": "definition", "module": "Mathlib.CategoryTheory.GlueData", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GlueData.π_epi", "kind": "instance", "module": "Mathlib.CategoryTheory.GlueData", "is_tactic_proof": true, "tactics": ["unfold", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.GlueData.types_π_surjective", "kind": "theorem", "module": "Mathlib.CategoryTheory.GlueData", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GlueData.types_ι_jointly_surjective", "kind": "theorem", "module": "Mathlib.CategoryTheory.GlueData", "is_tactic_proof": true, "tactics": ["delta", "simp_rw", "rcases", "rw", "show", "rcases", "exact", "simp", "rfl⟩"], "tactic_count": 9}
{"name": "CategoryTheory.GlueData.instHasPullbackMapF", "kind": "instance", "module": "Mathlib.CategoryTheory.GlueData", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GlueData.mapGlueData", "kind": "definition", "module": "Mathlib.CategoryTheory.GlueData", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GlueData.diagramIso", "kind": "definition", "module": "Mathlib.CategoryTheory.GlueData", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GlueData.diagramIso_app_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.GlueData", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GlueData.diagramIso_app_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.GlueData", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GlueData.diagramIso_hom_app_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.GlueData", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GlueData.diagramIso_hom_app_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.GlueData", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GlueData.diagramIso_inv_app_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.GlueData", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GlueData.diagramIso_inv_app_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.GlueData", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GlueData.hasColimit_multispan_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.GlueData", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GlueData.hasColimit_mapGlueData_diagram", "kind": "theorem", "module": "Mathlib.CategoryTheory.GlueData", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GlueData.gluedIso", "kind": "definition", "module": "Mathlib.CategoryTheory.GlueData", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GlueData.ι_gluedIso_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.GlueData", "is_tactic_proof": true, "tactics": ["erw", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.GlueData.ι_gluedIso_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.GlueData", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.GlueData.vPullbackConeIsLimitOfMap", "kind": "definition", "module": "Mathlib.CategoryTheory.GlueData", "is_tactic_proof": true, "tactics": ["apply", "apply", "let", "cases", "exacts", "apply", "apply", "refine", "rintro", "all_goals"], "tactic_count": 10}
{"name": "CategoryTheory.GlueData.ι_jointly_surjective", "kind": "theorem", "module": "Mathlib.CategoryTheory.GlueData", "is_tactic_proof": true, "tactics": ["let", "obtain", "replace", "change", "rw", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.GlueData'.f'", "kind": "abbrev", "module": "Mathlib.CategoryTheory.GlueData", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instMonoF'", "kind": "instance", "module": "Mathlib.CategoryTheory.GlueData", "is_tactic_proof": true, "tactics": ["dsimp"], "tactic_count": 1}
{"name": "CategoryTheory.instIsIsoF'", "kind": "instance", "module": "Mathlib.CategoryTheory.GlueData", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.instHasPullbackF'", "kind": "instance", "module": "Mathlib.CategoryTheory.GlueData", "is_tactic_proof": true, "tactics": ["apply", "simp", "infer_instance", "apply", "simp", "infer_instance", "have", "convert"], "tactic_count": 8}
{"name": "CategoryTheory.GlueData'.t''", "kind": "definition", "module": "Mathlib.CategoryTheory.GlueData", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GlueData.ofGlueData'", "kind": "definition", "module": "Mathlib.CategoryTheory.GlueData", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.inhabitedGradedObject", "kind": "instance", "module": "Mathlib.CategoryTheory.GradedObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObjectWithShift", "kind": "abbrev", "module": "Mathlib.CategoryTheory.GradedObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.categoryOfGradedObjects", "kind": "instance", "module": "Mathlib.CategoryTheory.GradedObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject", "is_tactic_proof": true, "tactics": ["funext", "apply"], "tactic_count": 2}
{"name": "CategoryTheory.GradedObject.eval", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.isoMk", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.isIso_of_isIso_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject", "is_tactic_proof": true, "tactics": ["change", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.GradedObject.isIso_apply_of_isIso", "kind": "instance", "module": "Mathlib.CategoryTheory.GradedObject", "is_tactic_proof": true, "tactics": ["change", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Iso.hom_inv_id_eval", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Iso.inv_hom_id_eval", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Iso.map_hom_inv_id_eval", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Iso.map_inv_hom_id_eval", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Iso.map_hom_inv_id_eval_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Iso.map_inv_hom_id_eval_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.GradedObject.comap", "kind": "abbrev", "module": "Mathlib.CategoryTheory.GradedObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.eqToHom_proj", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject", "is_tactic_proof": true, "tactics": ["subst", "rfl"], "tactic_count": 2}
{"name": "CategoryTheory.GradedObject.comapEq", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.comapEq_symm", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.GradedObject.comapEq_trans", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.GradedObject.eqToHom_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject", "is_tactic_proof": true, "tactics": ["subst", "rfl"], "tactic_count": 2}
{"name": "CategoryTheory.GradedObject.comapEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.hasShift", "kind": "instance", "module": "Mathlib.CategoryTheory.GradedObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.shiftFunctor_obj_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.shiftFunctor_map_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.instZeroHomOfHasZeroMorphisms", "kind": "instance", "module": "Mathlib.CategoryTheory.GradedObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.zero_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.hasZeroMorphisms", "kind": "instance", "module": "Mathlib.CategoryTheory.GradedObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.hasZeroObject", "kind": "instance", "module": "Mathlib.CategoryTheory.GradedObject", "is_tactic_proof": true, "tactics": ["refine"], "tactic_count": 1}
{"name": "CategoryTheory.GradedObject.total", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.instFaithfulTotal", "kind": "instance", "module": "Mathlib.CategoryTheory.GradedObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.instHasForget", "kind": "instance", "module": "Mathlib.CategoryTheory.GradedObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.instHasForget₂", "kind": "instance", "module": "Mathlib.CategoryTheory.GradedObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.mapObjFun", "kind": "abbrev", "module": "Mathlib.CategoryTheory.GradedObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.HasMap", "kind": "abbrev", "module": "Mathlib.CategoryTheory.GradedObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.hasMap_of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.mapObj", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.ιMapObj", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.CofanMapObjFun", "kind": "abbrev", "module": "Mathlib.CategoryTheory.GradedObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.CofanMapObjFun.mk", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.cofanMapObj", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.isColimitCofanMapObj", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.mapObj_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.descMapObj", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.ι_descMapObj", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.GradedObject.CofanMapObjFun.hasMap", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.CofanMapObjFun.iso", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.CofanMapObjFun.inj_iso_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.GradedObject.CofanMapObjFun.ιMapObj_iso_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.GradedObject.mapMap", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.ι_mapMap", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.GradedObject.congr_mapMap", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject", "is_tactic_proof": true, "tactics": ["subst", "rfl"], "tactic_count": 2}
{"name": "CategoryTheory.GradedObject.mapMap_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.GradedObject.mapMap_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.GradedObject.mapIso", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.map", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.cofanMapObjComp", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.isColimitCofanMapObjComp", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.hasMap_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.ιMapObjOrZero", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.ιMapObjOrZero_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.ιMapObjOrZero_eq_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.ιMapObjOrZero_mapMap", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.GradedObject.mapBifunctorAssociator", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject.Associator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.ι_mapBifunctorAssociator_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Associator", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "mapTrifunctorMapNatTrans_app_app_app]", "erw"], "tactic_count": 4}
{"name": "CategoryTheory.GradedObject.ι_mapBifunctorAssociator_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Associator", "is_tactic_proof": true, "tactics": ["rw", "comp_id,"], "tactic_count": 2}
{"name": "CategoryTheory.GradedObject.mapBifunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject.Bifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.mapBifunctorMapObj", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject.Bifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.ιMapBifunctorMapObj", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject.Bifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.mapBifunctorMapMap", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject.Bifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.ι_mapBifunctorMapMap", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Bifunctor", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.GradedObject.mapBifunctorMapObj_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Bifunctor", "is_tactic_proof": true, "tactics": ["apply", "rintro", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.GradedObject.mapBifunctorMapObjDesc", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject.Bifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.ι_mapBifunctorMapObjDesc", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Bifunctor", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.GradedObject.mapBifunctorMapMapIso", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject.Bifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.instIsIsoMapBifunctorMapMap", "kind": "instance", "module": "Mathlib.CategoryTheory.GradedObject.Bifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.mapBifunctorMap", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject.Bifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.Monoidal.braiding", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject.Braiding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.Monoidal.braiding_naturality_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Braiding", "is_tactic_proof": true, "tactics": ["dsimp", "cat_disch"], "tactic_count": 2}
{"name": "CategoryTheory.GradedObject.Monoidal.braiding_naturality_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Braiding", "is_tactic_proof": true, "tactics": ["dsimp", "cat_disch"], "tactic_count": 2}
{"name": "CategoryTheory.GradedObject.Monoidal.hexagon_forward", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Braiding", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "conv_lhs", "rw", "ιTensorObj₃'_eq_assoc", "conv_rhs", "rw", "ιTensorObj₃'_eq_assoc", "ιTensorObj₃'_associator_hom_assoc,", "ι_tensorHom,", "ιTensorObj₃_eq"], "tactic_count": 11}
{"name": "CategoryTheory.GradedObject.Monoidal.hexagon_reverse", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Braiding", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "conv_lhs", "rw", "ιTensorObj₃_associator_inv,", "conv_rhs", "rw", "ιTensorObj₃_eq_assoc", "ιTensorObj₃_associator_inv_assoc,", "ιTensorObj₃'_eq", "categoryOfGradedObjects_id,", "ι_tensorObjDesc,", "ιTensorObj₃'_eq"], "tactic_count": 13}
{"name": "CategoryTheory.GradedObject.Monoidal.symmetry", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Braiding", "is_tactic_proof": true, "tactics": ["dsimp", "cat_disch"], "tactic_count": 2}
{"name": "CategoryTheory.GradedObject.braidedCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.GradedObject.Braiding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.symmetricCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.GradedObject.Braiding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.HasTensor", "kind": "abbrev", "module": "Mathlib.CategoryTheory.GradedObject.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.hasTensor_of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Monoidal", "is_tactic_proof": false, "tactics": ["let", "isoMk", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.GradedObject.Monoidal.tensorObj", "kind": "abbrev", "module": "Mathlib.CategoryTheory.GradedObject.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.Monoidal.ιTensorObj", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.Monoidal.tensorObj_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Monoidal", "is_tactic_proof": true, "tactics": ["apply", "rintro", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.GradedObject.Monoidal.tensorObjDesc", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.Monoidal.ι_tensorObjDesc", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Monoidal", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.GradedObject.Monoidal.tensorHom", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.Monoidal.ι_tensorHom", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Monoidal", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "CategoryTheory.GradedObject.Monoidal.whiskerLeft", "kind": "abbrev", "module": "Mathlib.CategoryTheory.GradedObject.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.Monoidal.whiskerRight", "kind": "abbrev", "module": "Mathlib.CategoryTheory.GradedObject.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.Monoidal.id_tensorHom_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Monoidal", "is_tactic_proof": true, "tactics": ["dsimp", "simp", "rfl"], "tactic_count": 3}
{"name": "CategoryTheory.GradedObject.Monoidal.tensorHom_comp_tensorHom", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Monoidal", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.GradedObject.Monoidal.tensorIso", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.Monoidal.tensorHom_def", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Monoidal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.GradedObject.Monoidal.r₁₂₃", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.Monoidal.ρ₁₂", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.Monoidal.ρ₂₃", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.Monoidal.triangleIndexData", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.HasGoodTensor₁₂Tensor", "kind": "abbrev", "module": "Mathlib.CategoryTheory.GradedObject.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.HasGoodTensorTensor₂₃", "kind": "abbrev", "module": "Mathlib.CategoryTheory.GradedObject.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.Monoidal.ιTensorObj₃", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.Monoidal.ιTensorObj₃_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Monoidal", "is_tactic_proof": true, "tactics": ["subst", "rfl"], "tactic_count": 2}
{"name": "CategoryTheory.GradedObject.Monoidal.ιTensorObj₃_tensorHom", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Monoidal", "is_tactic_proof": true, "tactics": ["rw", "id_tensorHom,"], "tactic_count": 2}
{"name": "CategoryTheory.GradedObject.Monoidal.tensorObj₃_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Monoidal", "is_tactic_proof": true, "tactics": ["apply", "intro", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.GradedObject.Monoidal.ιTensorObj₃'", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.Monoidal.ιTensorObj₃'_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Monoidal", "is_tactic_proof": true, "tactics": ["subst", "rfl"], "tactic_count": 2}
{"name": "CategoryTheory.GradedObject.Monoidal.ιTensorObj₃'_tensorHom", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Monoidal", "is_tactic_proof": true, "tactics": ["rw", "tensorHom_id,"], "tactic_count": 2}
{"name": "CategoryTheory.GradedObject.Monoidal.tensorObj₃'_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Monoidal", "is_tactic_proof": true, "tactics": ["apply", "intro", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.GradedObject.Monoidal.associator", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.Monoidal.ιTensorObj₃'_associator_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.Monoidal.ιTensorObj₃_associator_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.Monoidal.associator_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Monoidal", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.GradedObject.HasLeftTensor₃ObjExt", "kind": "abbrev", "module": "Mathlib.CategoryTheory.GradedObject.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.Monoidal.left_tensor_tensorObj₃_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Monoidal", "is_tactic_proof": false, "tactics": ["refine", "intro", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.GradedObject.Monoidal.ιTensorObj₄", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.Monoidal.ιTensorObj₄_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Monoidal", "is_tactic_proof": true, "tactics": ["subst", "rfl"], "tactic_count": 2}
{"name": "CategoryTheory.GradedObject.HasTensor₄ObjExt", "kind": "abbrev", "module": "Mathlib.CategoryTheory.GradedObject.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.Monoidal.tensorObj₄_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Monoidal", "is_tactic_proof": true, "tactics": ["apply", "intro", "apply", "intro", "have", "simpa"], "tactic_count": 6}
{"name": "CategoryTheory.GradedObject.Monoidal.pentagon_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Monoidal", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "conv_lhs", "rw", "dsimp", "rw", "ιTensorObj₃'_eq", "ιTensorObj₃_eq_assoc", "ιTensorObj₃_associator_inv_assoc,", "ιTensorObj₃'_eq_assoc", "ι_tensorHom]", "dsimp", "rw", "ιTensorObj₃_associator_inv,", "conv_rhs", "rw", "ιTensorObj₃_eq_assoc", "ιTensorObj₃_associator_inv_assoc,", "ιTensorObj₃'_eq_assoc", "whisker_exchange_assoc,", "ιTensorObj₃_associator_inv,", "ιTensorObj₃'_eq", "ιTensorObj₃'_eq"], "tactic_count": 23}
{"name": "CategoryTheory.GradedObject.Monoidal.pentagon", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Monoidal", "is_tactic_proof": false, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.GradedObject.Monoidal.tensorUnit", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.Monoidal.tensorUnit₀", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.Monoidal.isInitialTensorUnitApply", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.Monoidal.instHasTensorTensorUnit", "kind": "instance", "module": "Mathlib.CategoryTheory.GradedObject.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.Monoidal.instHasMapProdObjFunctorMapBifunctorCurriedTensorSingle₀TensorUnit", "kind": "instance", "module": "Mathlib.CategoryTheory.GradedObject.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.Monoidal.leftUnitor", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.Monoidal.leftUnitor_inv_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.Monoidal.leftUnitor_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Monoidal", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.GradedObject.Monoidal.instHasTensorTensorUnit_1", "kind": "instance", "module": "Mathlib.CategoryTheory.GradedObject.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.Monoidal.instHasMapProdObjFunctorMapBifunctorCurriedTensorSingle₀TensorUnit_1", "kind": "instance", "module": "Mathlib.CategoryTheory.GradedObject.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.Monoidal.rightUnitor", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.Monoidal.rightUnitor_inv_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.Monoidal.rightUnitor_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Monoidal", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.GradedObject.Monoidal.triangle", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Monoidal", "is_tactic_proof": false, "tactics": ["convert", "mapBifunctor_triangle", "all_goals"], "tactic_count": 3}
{"name": "CategoryTheory.GradedObject.monoidalCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.GradedObject.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.instFiniteElemProdNatPreimageHAddFstSndSingletonSet", "kind": "instance", "module": "Mathlib.CategoryTheory.GradedObject.Monoidal", "is_tactic_proof": false, "tactics": ["refine", "rintro", "simpa"], "tactic_count": 3}
{"name": "CategoryTheory.GradedObject.instFiniteElemProdNatSetOfEqHAddFstSnd", "kind": "instance", "module": "Mathlib.CategoryTheory.GradedObject.Monoidal", "is_tactic_proof": false, "tactics": ["refine", "rintro", "simpa"], "tactic_count": 3}
{"name": "CategoryTheory.GradedObject.single", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject.Single", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.single₀", "kind": "abbrev", "module": "Mathlib.CategoryTheory.GradedObject.Single", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.singleObjApplyIsoOfEq", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject.Single", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.singleObjApplyIso", "kind": "abbrev", "module": "Mathlib.CategoryTheory.GradedObject.Single", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.isInitialSingleObjApply", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject.Single", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.GradedObject.singleObjApplyIsoOfEq_inv_single_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Single", "is_tactic_proof": true, "tactics": ["subst", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.GradedObject.single_map_singleObjApplyIsoOfEq_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Single", "is_tactic_proof": true, "tactics": ["subst", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.GradedObject.singleObjApplyIso_inv_single_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Single", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.GradedObject.single_map_singleObjApplyIso_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Single", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.GradedObject.singleCompEval", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject.Single", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.mapTrifunctorObj", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject.Trifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.mapTrifunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject.Trifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.mapTrifunctorMapNatTrans", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject.Trifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.mapTrifunctorMapIso", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject.Trifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.mapTrifunctorMapObj", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject.Trifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.ιMapTrifunctorMapObj", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject.Trifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.mapTrifunctorMapMap", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject.Trifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.ι_mapTrifunctorMapMap", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Trifunctor", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "dsimp", "rw"], "tactic_count": 4}
{"name": "CategoryTheory.GradedObject.mapTrifunctorMapObj_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Trifunctor", "is_tactic_proof": true, "tactics": ["apply", "rintro", "apply"], "tactic_count": 3}
{"name": "CategoryTheory.GradedObject.instHasMapProdObjFunctorMapTrifunctorObjOfMapTrifunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.GradedObject.Trifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.mapTrifunctorMapFunctorObj", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject.Trifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.mapTrifunctorMap", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject.Trifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.HasGoodTrifunctor₁₂Obj", "kind": "abbrev", "module": "Mathlib.CategoryTheory.GradedObject.Trifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.ιMapBifunctor₁₂BifunctorMapObj", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject.Trifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.ιMapBifunctor₁₂BifunctorMapObj_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Trifunctor", "is_tactic_proof": true, "tactics": ["subst", "rfl"], "tactic_count": 2}
{"name": "CategoryTheory.GradedObject.cofan₃MapBifunctor₁₂BifunctorMapObj", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject.Trifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.isColimitCofan₃MapBifunctor₁₂BifunctorMapObj", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject.Trifunctor", "is_tactic_proof": true, "tactics": ["let", "have", "let", "have", "let", "have", "let", "let", "let", "invFun", "left_inv", "obtain", "rfl", "let", "refine", "refine", "obtain", "rfl", "have", "refine", "dsimp", "rw", "rfl"], "tactic_count": 23}
{"name": "CategoryTheory.GradedObject.HasGoodTrifunctor₁₂Obj.hasMap", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Trifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.mapBifunctorComp₁₂MapObjIso", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject.Trifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.ι_mapBifunctorComp₁₂MapObjIso_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Trifunctor", "is_tactic_proof": true, "tactics": ["dsimp", "apply"], "tactic_count": 2}
{"name": "CategoryTheory.GradedObject.ι_mapBifunctorComp₁₂MapObjIso_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Trifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.mapBifunctor₁₂BifunctorMapObj_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Trifunctor", "is_tactic_proof": true, "tactics": ["apply", "rintro", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.GradedObject.mapBifunctor₁₂BifunctorDesc", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject.Trifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.ι_mapBifunctor₁₂BifunctorDesc", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Trifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.HasGoodTrifunctor₂₃Obj", "kind": "abbrev", "module": "Mathlib.CategoryTheory.GradedObject.Trifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.ιMapBifunctorBifunctor₂₃MapObj", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject.Trifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.ιMapBifunctorBifunctor₂₃MapObj_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Trifunctor", "is_tactic_proof": true, "tactics": ["subst", "rfl"], "tactic_count": 2}
{"name": "CategoryTheory.GradedObject.cofan₃MapBifunctorBifunctor₂₃MapObj", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject.Trifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.isColimitCofan₃MapBifunctorBifunctor₂₃MapObj", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject.Trifunctor", "is_tactic_proof": true, "tactics": ["let", "have", "let", "have", "let", "have", "let", "let", "let", "invFun", "left_inv", "obtain", "rfl", "let", "refine", "refine", "obtain", "rfl", "have", "refine", "dsimp", "rw", "rfl"], "tactic_count": 23}
{"name": "CategoryTheory.GradedObject.HasGoodTrifunctor₂₃Obj.hasMap", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Trifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.mapBifunctorComp₂₃MapObjIso", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject.Trifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.ι_mapBifunctorComp₂₃MapObjIso_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Trifunctor", "is_tactic_proof": true, "tactics": ["dsimp", "apply"], "tactic_count": 2}
{"name": "CategoryTheory.GradedObject.ι_mapBifunctorComp₂₃MapObjIso_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Trifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.mapBifunctorBifunctor₂₃MapObj_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Trifunctor", "is_tactic_proof": true, "tactics": ["apply", "rintro", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.GradedObject.mapBifunctorBifunctor₂₃Desc", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject.Trifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.ι_mapBifunctorBifunctor₂₃Desc", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Trifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.mapBifunctorObjSingle₀ObjIso", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject.Unitor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.mapBifunctorObjSingle₀ObjIsInitial", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject.Unitor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.mapBifunctorLeftUnitorCofan", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject.Unitor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.mapBifunctorLeftUnitorCofan_inj", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Unitor", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.GradedObject.mapBifunctorLeftUnitorCofanIsColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject.Unitor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.mapBifunctorLeftUnitor_hasMap", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Unitor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.mapBifunctorLeftUnitor", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject.Unitor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.ι_mapBifunctorLeftUnitor_hom_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Unitor", "is_tactic_proof": true, "tactics": ["dsimp", "erw", "rw"], "tactic_count": 3}
{"name": "CategoryTheory.GradedObject.mapBifunctorLeftUnitor_inv_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Unitor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.mapBifunctorLeftUnitor_inv_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Unitor", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "rw", "dsimp", "rw", "rfl"], "tactic_count": 6}
{"name": "CategoryTheory.GradedObject.mapBifunctorLeftUnitor_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Unitor", "is_tactic_proof": true, "tactics": ["rw", "mapBifunctorLeftUnitor_inv_naturality,"], "tactic_count": 2}
{"name": "CategoryTheory.GradedObject.mapBifunctorObjObjSingle₀Iso", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject.Unitor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.mapBifunctorObjObjSingle₀IsInitial", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject.Unitor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.mapBifunctorRightUnitorCofan", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject.Unitor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.mapBifunctorRightUnitorCofan_inj", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Unitor", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.GradedObject.mapBifunctorRightUnitorCofanIsColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject.Unitor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.mapBifunctorRightUnitor_hasMap", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Unitor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.mapBifunctorRightUnitor", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject.Unitor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.ι_mapBifunctorRightUnitor_hom_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Unitor", "is_tactic_proof": true, "tactics": ["dsimp", "erw", "rw"], "tactic_count": 3}
{"name": "CategoryTheory.GradedObject.mapBifunctorRightUnitor_inv_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Unitor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.mapBifunctorRightUnitor_inv_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Unitor", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "rw", "dsimp", "rw", "erw", "rfl"], "tactic_count": 7}
{"name": "CategoryTheory.GradedObject.mapBifunctorRightUnitor_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Unitor", "is_tactic_proof": true, "tactics": ["rw", "mapBifunctorRightUnitor_inv_naturality,"], "tactic_count": 2}
{"name": "CategoryTheory.GradedObject.TriangleIndexData.r_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Unitor", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.GradedObject.TriangleIndexData.ρ₁₂", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject.Unitor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.TriangleIndexData.ρ₂₃", "kind": "definition", "module": "Mathlib.CategoryTheory.GradedObject.Unitor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GradedObject.mapBifunctor_triangle", "kind": "theorem", "module": "Mathlib.CategoryTheory.GradedObject.Unitor", "is_tactic_proof": true, "tactics": ["rw", "ext", "simp", "congr", "rw", "ι_mapBifunctorAssociator_hom_assoc,", "ιMapBifunctorBifunctor₂₃MapObj_eq_assoc", "ι_mapBifunctorMapMap]", "dsimp", "rw", "ι_mapBifunctorLeftUnitor_hom_apply", "ι_mapBifunctorRightUnitor_hom_apply", "dsimp", "simp", "congr", "symm", "apply"], "tactic_count": 17}
{"name": "CategoryTheory.Grothendieck.ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Grothendieck", "is_tactic_proof": true, "tactics": ["cases", "congr", "dsimp", "cat_disch"], "tactic_count": 4}
{"name": "CategoryTheory.Grothendieck.id", "kind": "definition", "module": "Mathlib.CategoryTheory.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grothendieck.instInhabitedHom", "kind": "instance", "module": "Mathlib.CategoryTheory.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grothendieck.comp", "kind": "definition", "module": "Mathlib.CategoryTheory.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grothendieck.instCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grothendieck.id_base", "kind": "theorem", "module": "Mathlib.CategoryTheory.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grothendieck.id_fiber", "kind": "theorem", "module": "Mathlib.CategoryTheory.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grothendieck.comp_base", "kind": "theorem", "module": "Mathlib.CategoryTheory.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grothendieck.comp_fiber", "kind": "theorem", "module": "Mathlib.CategoryTheory.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grothendieck.congr", "kind": "theorem", "module": "Mathlib.CategoryTheory.Grothendieck", "is_tactic_proof": true, "tactics": ["subst", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Grothendieck.base_eqToHom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Grothendieck", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "CategoryTheory.Grothendieck.fiber_eqToHom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Grothendieck", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "CategoryTheory.Grothendieck.eqToHom_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Grothendieck", "is_tactic_proof": true, "tactics": ["subst", "rfl"], "tactic_count": 2}
{"name": "CategoryTheory.Grothendieck.transport", "kind": "definition", "module": "Mathlib.CategoryTheory.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grothendieck.toTransport", "kind": "definition", "module": "Mathlib.CategoryTheory.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grothendieck.isoMk", "kind": "definition", "module": "Mathlib.CategoryTheory.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grothendieck.transportIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grothendieck.forget", "kind": "definition", "module": "Mathlib.CategoryTheory.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grothendieck.map", "kind": "definition", "module": "Mathlib.CategoryTheory.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grothendieck.map_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grothendieck.map_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Grothendieck", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Grothendieck.functor_comp_forget", "kind": "theorem", "module": "Mathlib.CategoryTheory.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.SmallGroupoid", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Groupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Grpd.free_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.FreeGroupoidOfCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grpd.freeForgetAdjunction", "kind": "definition", "module": "Mathlib.CategoryTheory.Groupoid.FreeGroupoidOfCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grpd.freeForgetAdjunction_homEquiv_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.FreeGroupoidOfCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grpd.freeForgetAdjunction_homEquiv_symm_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.FreeGroupoidOfCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grpd.freeForgetAdjunction_unit_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.FreeGroupoidOfCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grpd.freeForgetAdjunction_counit_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.FreeGroupoidOfCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grpd.instReflectiveCatForgetToCat", "kind": "instance", "module": "Mathlib.CategoryTheory.Groupoid.FreeGroupoidOfCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grpd", "kind": "definition", "module": "Mathlib.CategoryTheory.Groupoid.Grpd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grpd.instInhabited", "kind": "instance", "module": "Mathlib.CategoryTheory.Groupoid.Grpd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grpd.str'", "kind": "instance", "module": "Mathlib.CategoryTheory.Groupoid.Grpd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grpd.instCoeSortType", "kind": "instance", "module": "Mathlib.CategoryTheory.Groupoid.Grpd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grpd.of", "kind": "definition", "module": "Mathlib.CategoryTheory.Groupoid.Grpd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grpd.coe_of", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Grpd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grpd.category", "kind": "instance", "module": "Mathlib.CategoryTheory.Groupoid.Grpd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grpd.objects", "kind": "definition", "module": "Mathlib.CategoryTheory.Groupoid.Grpd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grpd.forgetToCat", "kind": "definition", "module": "Mathlib.CategoryTheory.Groupoid.Grpd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grpd.instGroupoidαCategoryObjCatForgetToCat", "kind": "instance", "module": "Mathlib.CategoryTheory.Groupoid.Grpd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grpd.forgetToCat_full", "kind": "instance", "module": "Mathlib.CategoryTheory.Groupoid.Grpd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grpd.forgetToCat_faithful", "kind": "instance", "module": "Mathlib.CategoryTheory.Groupoid.Grpd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grpd.comp_eq_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Grpd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grpd.id_eq_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Grpd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grpd.id_to_functor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Grpd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grpd.piLimitFan", "kind": "definition", "module": "Mathlib.CategoryTheory.Groupoid.Grpd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grpd.piLimitFanIsLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Groupoid.Grpd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grpd.has_pi", "kind": "instance", "module": "Mathlib.CategoryTheory.Groupoid.Grpd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grpd.piIsoPi", "kind": "definition", "module": "Mathlib.CategoryTheory.Groupoid.Grpd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grpd.piIsoPi_hom_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Grpd.Basic", "is_tactic_proof": true, "tactics": ["simp", "rfl"], "tactic_count": 2}
{"name": "CategoryTheory.Subgroupoid.inv_mem_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": true, "tactics": ["constructor", "intro", "simpa", "apply"], "tactic_count": 4}
{"name": "CategoryTheory.Subgroupoid.mul_mem_cancel_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "suffices", "apply", "apply"], "tactic_count": 5}
{"name": "CategoryTheory.Subgroupoid.mul_mem_cancel_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "suffices", "simpa", "apply", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.Subgroupoid.objs", "kind": "definition", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.mem_objs_of_src", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.mem_objs_of_tgt", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.id_mem_of_nonempty_isotropy", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": true, "tactics": ["rintro", "convert", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.Subgroupoid.id_mem_of_src", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.id_mem_of_tgt", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.asWideQuiver", "kind": "definition", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.coe", "kind": "instance", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.coe_inv_coe'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Subgroupoid.hom", "kind": "definition", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.hom.inj_on_objects", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": true, "tactics": ["rintro", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Subgroupoid.hom.faithful", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "CategoryTheory.Subgroupoid.vertexSubgroup", "kind": "definition", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.toSet", "kind": "definition", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.instSetLikeSigmaHom", "kind": "instance", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.instPartialOrder", "kind": "instance", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.mem_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.le_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Subgroupoid.instTop", "kind": "instance", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.mem_top", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.mem_top_objs", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Subgroupoid.instBot", "kind": "instance", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.instInhabited", "kind": "instance", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.instMin", "kind": "instance", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.instInfSet", "kind": "instance", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.mem_sInf_arrows", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.mem_sInf", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.instCompleteLattice", "kind": "instance", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.le_objs", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.inclusion", "kind": "definition", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.inclusion_inj_on_objects", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.inclusion_faithful", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.inclusion_refl", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.inclusion_trans", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.inclusion_comp_embedding", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.Discrete.Arrows", "kind": "inductive", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.discrete", "kind": "definition", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.mem_discrete_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.isWide_iff_objs_eq_univ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "ext", "apply", "rintro", "refine", "obtain", "exact"], "tactic_count": 8}
{"name": "CategoryTheory.Subgroupoid.IsWide.id_mem", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.IsWide.eqToHom_mem", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "CategoryTheory.Subgroupoid.IsNormal.conj'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.IsNormal.conjugation_bij", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": ["refine", "simpa", "p", "simp"], "tactic_count": 4}
{"name": "CategoryTheory.Subgroupoid.top_isNormal", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.sInf_isNormal", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.discrete_isNormal", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.IsNormal.vertexSubgroup", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.generated", "kind": "definition", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.subset_generated", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": true, "tactics": ["dsimp", "simp", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Subgroupoid.generatedNormal", "kind": "definition", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.generated_le_generatedNormal", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": true, "tactics": ["apply", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Subgroupoid.generatedNormal_isNormal", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.IsNormal.generatedNormal_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "have", "rw", "exact", "rintro", "apply", "exact"], "tactic_count": 8}
{"name": "CategoryTheory.Subgroupoid.comap", "kind": "definition", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.comap_mono", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.isNormal_comap", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.comap_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.ker", "kind": "definition", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.mem_ker_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.ker_isNormal", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.ker_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.Map.Arrows", "kind": "inductive", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.Map.arrows_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "rintro"], "tactic_count": 3}
{"name": "CategoryTheory.Subgroupoid.map", "kind": "definition", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.mem_map_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.galoisConnection_map_comap", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": true, "tactics": ["rintro", "exact", "rintro", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.Subgroupoid.map_mono", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.le_comap_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.map_comap_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.map_le_iff_le_comap", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.mem_map_objs_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": true, "tactics": ["dsimp", "constructor", "rintro", "change", "obtain", "exact", "rintro", "exact"], "tactic_count": 8}
{"name": "CategoryTheory.Subgroupoid.map_objs_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Subgroupoid.im", "kind": "definition", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.mem_im_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "CategoryTheory.Subgroupoid.mem_im_objs_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Subgroupoid.obj_surjective_of_im_eq_top", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": true, "tactics": ["rintro", "rw", "apply"], "tactic_count": 3}
{"name": "CategoryTheory.Subgroupoid.isNormal_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.IsThin", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.isThin_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.IsTotallyDisconnected", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.isTotallyDisconnected_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "exact", "rintro", "simp", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.Subgroupoid.disconnect", "kind": "definition", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.disconnect_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Subgroupoid.disconnect_normal", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.mem_disconnect_objs_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.disconnect_objs", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.disconnect_isTotallyDisconnected", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Subgroupoid.full", "kind": "definition", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.full_objs", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.mem_full_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subgroupoid.mem_full_objs_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Subgroupoid.full_empty", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Subgroupoid.full_univ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Subgroupoid.full_mono", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": true, "tactics": ["rw", "rintro", "simp", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.Subgroupoid.full_arrow_eq_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.Subgroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Groupoid.vertexGroup", "kind": "instance", "module": "Mathlib.CategoryTheory.Groupoid.VertexGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Groupoid.vertexGroup.inv_eq_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Groupoid.VertexGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Groupoid.vertexGroupIsomOfMap", "kind": "definition", "module": "Mathlib.CategoryTheory.Groupoid.VertexGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Groupoid.vertexGroupIsomOfPath", "kind": "definition", "module": "Mathlib.CategoryTheory.Groupoid.VertexGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Groupoid.CategoryTheory.Functor.mapVertexGroup", "kind": "definition", "module": "Mathlib.CategoryTheory.Groupoid.VertexGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.TwoSquare.costructuredArrowRightwards", "kind": "definition", "module": "Mathlib.CategoryTheory.GuitartExact.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.TwoSquare.structuredArrowDownwards", "kind": "definition", "module": "Mathlib.CategoryTheory.GuitartExact.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.TwoSquare.StructuredArrowRightwards", "kind": "abbrev", "module": "Mathlib.CategoryTheory.GuitartExact.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.TwoSquare.CostructuredArrowDownwards", "kind": "abbrev", "module": "Mathlib.CategoryTheory.GuitartExact.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.TwoSquare.StructuredArrowRightwards.mk", "kind": "abbrev", "module": "Mathlib.CategoryTheory.GuitartExact.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.TwoSquare.CostructuredArrowDownwards.mk", "kind": "abbrev", "module": "Mathlib.CategoryTheory.GuitartExact.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.TwoSquare.StructuredArrowRightwards.mk_surjective", "kind": "theorem", "module": "Mathlib.CategoryTheory.GuitartExact.Basic", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "obtain", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.TwoSquare.CostructuredArrowDownwards.mk_surjective", "kind": "theorem", "module": "Mathlib.CategoryTheory.GuitartExact.Basic", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "obtain", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.TwoSquare.EquivalenceJ.functor", "kind": "definition", "module": "Mathlib.CategoryTheory.GuitartExact.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.TwoSquare.EquivalenceJ.inverse", "kind": "definition", "module": "Mathlib.CategoryTheory.GuitartExact.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.TwoSquare.equivalenceJ", "kind": "definition", "module": "Mathlib.CategoryTheory.GuitartExact.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.TwoSquare.isConnected_rightwards_iff_downwards", "kind": "theorem", "module": "Mathlib.CategoryTheory.GuitartExact.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.TwoSquare.costructuredArrowDownwardsPrecomp", "kind": "definition", "module": "Mathlib.CategoryTheory.GuitartExact.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.TwoSquare.guitartExact_iff_isConnected_rightwards", "kind": "theorem", "module": "Mathlib.CategoryTheory.GuitartExact.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.TwoSquare.guitartExact_iff_isConnected_downwards", "kind": "theorem", "module": "Mathlib.CategoryTheory.GuitartExact.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.TwoSquare.instIsConnectedStructuredArrowCostructuredArrowObjCostructuredArrowRightwardsOfGuitartExact", "kind": "instance", "module": "Mathlib.CategoryTheory.GuitartExact.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "CategoryTheory.TwoSquare.instIsConnectedCostructuredArrowStructuredArrowObjStructuredArrowDownwardsOfGuitartExact", "kind": "instance", "module": "Mathlib.CategoryTheory.GuitartExact.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "CategoryTheory.TwoSquare.guitartExact_iff_final", "kind": "theorem", "module": "Mathlib.CategoryTheory.GuitartExact.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.TwoSquare.instFinalCostructuredArrowObjCostructuredArrowRightwardsOfGuitartExact", "kind": "instance", "module": "Mathlib.CategoryTheory.GuitartExact.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "CategoryTheory.TwoSquare.guitartExact_iff_initial", "kind": "theorem", "module": "Mathlib.CategoryTheory.GuitartExact.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.TwoSquare.instInitialStructuredArrowObjStructuredArrowDownwardsOfGuitartExact", "kind": "instance", "module": "Mathlib.CategoryTheory.GuitartExact.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "CategoryTheory.TwoSquare.guitartExact_of_isEquivalence_of_isIso", "kind": "instance", "module": "Mathlib.CategoryTheory.GuitartExact.Basic", "is_tactic_proof": true, "tactics": ["rw", "intro", "have", "have", "have", "dsimp", "infer_instance"], "tactic_count": 7}
{"name": "CategoryTheory.TwoSquare.guitartExact_id", "kind": "instance", "module": "Mathlib.CategoryTheory.GuitartExact.Basic", "is_tactic_proof": true, "tactics": ["rw", "intro", "let", "let", "have", "have", "apply", "intro", "exact"], "tactic_count": 9}
{"name": "CategoryTheory.Functor.LeftExtension.compTwoSquare", "kind": "abbrev", "module": "Mathlib.CategoryTheory.GuitartExact.KanExtension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.LeftExtension.isPointwiseLeftKanExtensionAtCompTwoSquareEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.GuitartExact.KanExtension", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.LeftExtension.nonempty_isPointwiseLeftKanExtensionAt_compTwoSquare_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.GuitartExact.KanExtension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtension.compTwoSquare", "kind": "definition", "module": "Mathlib.CategoryTheory.GuitartExact.KanExtension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.LeftExtension.isPointwiseLeftKanExtensionOfCompTwoSquare", "kind": "definition", "module": "Mathlib.CategoryTheory.GuitartExact.KanExtension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.LeftExtension.isPointwiseLeftKanExtensionEquivOfGuitartExact", "kind": "definition", "module": "Mathlib.CategoryTheory.GuitartExact.KanExtension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.TwoSquare.hasPointwiseLeftKanExtensionAt_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.GuitartExact.KanExtension", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "rfl"], "tactic_count": 3}
{"name": "CategoryTheory.TwoSquare.hasPointwiseLeftKanExtension_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.GuitartExact.KanExtension", "is_tactic_proof": true, "tactics": ["dsimp", "simp", "refine", "rw", "apply"], "tactic_count": 5}
{"name": "CategoryTheory.TwoSquare.hasPointwiseLeftKanExtension", "kind": "theorem", "module": "Mathlib.CategoryTheory.GuitartExact.KanExtension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.TwoSquare.hasLeftKanExtension", "kind": "theorem", "module": "Mathlib.CategoryTheory.GuitartExact.KanExtension", "is_tactic_proof": true, "tactics": ["have", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.TwoSquare.lanBaseChange", "kind": "definition", "module": "Mathlib.CategoryTheory.GuitartExact.KanExtension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.TwoSquare.isIso_lanBaseChange_app_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.GuitartExact.KanExtension", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.TwoSquare.isIso_lanBaseChange_app", "kind": "instance", "module": "Mathlib.CategoryTheory.GuitartExact.KanExtension", "is_tactic_proof": true, "tactics": ["rw", "let", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.TwoSquare.instIsIsoFunctorLanBaseChangeOfGuitartExact", "kind": "instance", "module": "Mathlib.CategoryTheory.GuitartExact.KanExtension", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence.functor", "kind": "definition", "module": "Mathlib.CategoryTheory.GuitartExact.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence.inverse", "kind": "definition", "module": "Mathlib.CategoryTheory.GuitartExact.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.GuitartExact.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.TwoSquare.instGuitartExactOppositeOp", "kind": "instance", "module": "Mathlib.CategoryTheory.GuitartExact.Opposite", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "infer_instance"], "tactic_count": 4}
{"name": "CategoryTheory.TwoSquare.guitartExact_op_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.GuitartExact.Opposite", "is_tactic_proof": true, "tactics": ["constructor", "intro", "let", "let", "have", "rw", "infer_instance", "intro", "infer_instance"], "tactic_count": 9}
{"name": "CategoryTheory.TwoSquare.guitartExact_id'", "kind": "instance", "module": "Mathlib.CategoryTheory.GuitartExact.Opposite", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "CategoryTheory.TwoSquare.overPost", "kind": "abbrev", "module": "Mathlib.CategoryTheory.GuitartExact.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instGuitartExactOverObjOverPostOfHasBinaryProductOfPreservesLimitDiscreteWalkingPairPair", "kind": "instance", "module": "Mathlib.CategoryTheory.GuitartExact.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.TwoSquare.whiskerVertical", "kind": "definition", "module": "Mathlib.CategoryTheory.GuitartExact.VerticalComposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.TwoSquare.GuitartExact.whiskerVertical", "kind": "theorem", "module": "Mathlib.CategoryTheory.GuitartExact.VerticalComposition", "is_tactic_proof": true, "tactics": ["rw", "intro", "let", "structuredArrowDownwards", "w.structuredArrowDownwards", "dsimp", "simp", "rw", "infer_instance"], "tactic_count": 9}
{"name": "CategoryTheory.TwoSquare.GuitartExact.whiskerVertical_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.GuitartExact.VerticalComposition", "is_tactic_proof": true, "tactics": ["constructor", "intro", "have", "ext", "simp", "rw", "exact", "intro", "exact"], "tactic_count": 9}
{"name": "CategoryTheory.TwoSquare.GuitartExact.instWhiskerVerticalOfIsIsoFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.GuitartExact.VerticalComposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.TwoSquare.structuredArrowDownwardsComp", "kind": "definition", "module": "Mathlib.CategoryTheory.GuitartExact.VerticalComposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.TwoSquare.vComp'", "kind": "definition", "module": "Mathlib.CategoryTheory.GuitartExact.VerticalComposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.TwoSquare.GuitartExact.vComp", "kind": "instance", "module": "Mathlib.CategoryTheory.GuitartExact.VerticalComposition", "is_tactic_proof": true, "tactics": ["simp", "intro", "rw", "infer_instance"], "tactic_count": 4}
{"name": "CategoryTheory.TwoSquare.GuitartExact.vComp'", "kind": "instance", "module": "Mathlib.CategoryTheory.GuitartExact.VerticalComposition", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.TwoSquare.GuitartExact.vComp_iff_of_equivalences", "kind": "theorem", "module": "Mathlib.CategoryTheory.GuitartExact.VerticalComposition", "is_tactic_proof": true, "tactics": ["constructor", "intro", "letI", "have", "letI", "let", "let", "let", "have", "ext", "simp", "simp", "simp", "rw", "simp", "rw", "infer_instance", "intro", "exact"], "tactic_count": 19}
{"name": "CategoryTheory.TwoSquare.GuitartExact.vComp'_iff_of_equivalences", "kind": "theorem", "module": "Mathlib.CategoryTheory.GuitartExact.VerticalComposition", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Iso.homCongr", "kind": "definition", "module": "Mathlib.CategoryTheory.HomCongr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.homCongr_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.HomCongr", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Iso.homCongr_refl", "kind": "theorem", "module": "Mathlib.CategoryTheory.HomCongr", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Iso.homCongr_trans", "kind": "theorem", "module": "Mathlib.CategoryTheory.HomCongr", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Iso.homCongr_symm", "kind": "theorem", "module": "Mathlib.CategoryTheory.HomCongr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.isoCongr", "kind": "definition", "module": "Mathlib.CategoryTheory.HomCongr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.isoCongrLeft", "kind": "definition", "module": "Mathlib.CategoryTheory.HomCongr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.isoCongrRight", "kind": "definition", "module": "Mathlib.CategoryTheory.HomCongr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.map_homCongr", "kind": "theorem", "module": "Mathlib.CategoryTheory.HomCongr", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.map_isoCongr", "kind": "theorem", "module": "Mathlib.CategoryTheory.HomCongr", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Idempotents.isIdempotentComplete_iff_hasEqualizer_of_id_and_idempotent", "kind": "theorem", "module": "Mathlib.CategoryTheory.Idempotents.Basic", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rcases", "exact", "isLimit", "apply", "intro", "refine", "constructor", "simp", "intro", "rw", "rw", "simp", "exact", "intro", "refine", "intro", "haveI", "refine", "equalizer.lift_ι", "ext", "simp", "rw"], "tactic_count": 24}
{"name": "CategoryTheory.Idempotents.idem_of_id_sub_idem", "kind": "theorem", "module": "Mathlib.CategoryTheory.Idempotents.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Idempotents.isIdempotentComplete_iff_idempotents_have_kernels", "kind": "theorem", "module": "Mathlib.CategoryTheory.Idempotents.Basic", "is_tactic_proof": true, "tactics": ["rw", "constructor", "intro", "haveI", "convert", "rw", "intro", "haveI", "apply"], "tactic_count": 9}
{"name": "CategoryTheory.Idempotents.isIdempotentComplete_of_abelian", "kind": "instance", "module": "Mathlib.CategoryTheory.Idempotents.Basic", "is_tactic_proof": true, "tactics": ["rw", "intros", "infer_instance"], "tactic_count": 3}
{"name": "CategoryTheory.Idempotents.split_imp_of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Idempotents.Basic", "is_tactic_proof": true, "tactics": ["rcases", "use", "grind"], "tactic_count": 3}
{"name": "CategoryTheory.Idempotents.split_iff_of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Idempotents.Basic", "is_tactic_proof": true, "tactics": ["constructor", "exact", "apply", "rw", "slice_rhs", "simp"], "tactic_count": 6}
{"name": "CategoryTheory.Idempotents.Equivalence.isIdempotentComplete", "kind": "theorem", "module": "Mathlib.CategoryTheory.Idempotents.Basic", "is_tactic_proof": true, "tactics": ["refine", "intro", "let", "erw", "slice_rhs", "rw", "rcases", "use", "constructor", "rw", "simp", "rfl"], "tactic_count": 12}
{"name": "CategoryTheory.Idempotents.isIdempotentComplete_iff_of_equivalence", "kind": "theorem", "module": "Mathlib.CategoryTheory.Idempotents.Basic", "is_tactic_proof": true, "tactics": ["constructor", "exact", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Idempotents.isIdempotentComplete_of_isIdempotentComplete_opposite", "kind": "theorem", "module": "Mathlib.CategoryTheory.Idempotents.Basic", "is_tactic_proof": true, "tactics": ["refine", "intro", "rcases", "use", "constructor", "simp", "rfl", "simp", "rfl"], "tactic_count": 9}
{"name": "CategoryTheory.Idempotents.isIdempotentComplete_iff_opposite", "kind": "theorem", "module": "Mathlib.CategoryTheory.Idempotents.Basic", "is_tactic_proof": true, "tactics": ["constructor", "exact", "intro", "apply", "rw", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.Idempotents.instIsIdempotentCompleteOpposite", "kind": "instance", "module": "Mathlib.CategoryTheory.Idempotents.Basic", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "CategoryTheory.Idempotents.Karoubi.Biproducts.bicone", "kind": "definition", "module": "Mathlib.CategoryTheory.Idempotents.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.Karoubi.karoubi_hasFiniteBiproducts", "kind": "theorem", "module": "Mathlib.CategoryTheory.Idempotents.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.Karoubi.complement", "kind": "definition", "module": "Mathlib.CategoryTheory.Idempotents.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.Karoubi.instHasBinaryBiproductComplement", "kind": "instance", "module": "Mathlib.CategoryTheory.Idempotents.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.Karoubi.decomposition", "kind": "definition", "module": "Mathlib.CategoryTheory.Idempotents.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.app_idem", "kind": "theorem", "module": "Mathlib.CategoryTheory.Idempotents.FunctorCategories", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.app_p_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Idempotents.FunctorCategories", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.app_comp_p", "kind": "theorem", "module": "Mathlib.CategoryTheory.Idempotents.FunctorCategories", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.app_p_comm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Idempotents.FunctorCategories", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.functor_category_isIdempotentComplete", "kind": "instance", "module": "Mathlib.CategoryTheory.Idempotents.FunctorCategories", "is_tactic_proof": true, "tactics": ["refine", "have", "haveI", "hC", "the", "let", "map", "equalizer.lift", "let", "naturality", "let", "naturality", "use", "constructor", "ext", "dsimp", "rw", "ext", "simp"], "tactic_count": 19}
{"name": "CategoryTheory.Idempotents.KaroubiFunctorCategoryEmbedding.obj", "kind": "definition", "module": "Mathlib.CategoryTheory.Idempotents.FunctorCategories", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.KaroubiFunctorCategoryEmbedding.map", "kind": "definition", "module": "Mathlib.CategoryTheory.Idempotents.FunctorCategories", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.karoubiFunctorCategoryEmbedding", "kind": "definition", "module": "Mathlib.CategoryTheory.Idempotents.FunctorCategories", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.instFullKaroubiFunctorKaroubiFunctorCategoryEmbedding", "kind": "instance", "module": "Mathlib.CategoryTheory.Idempotents.FunctorCategories", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.instFaithfulKaroubiFunctorKaroubiFunctorCategoryEmbedding", "kind": "instance", "module": "Mathlib.CategoryTheory.Idempotents.FunctorCategories", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.toKaroubi_comp_karoubiFunctorCategoryEmbedding", "kind": "theorem", "module": "Mathlib.CategoryTheory.Idempotents.FunctorCategories", "is_tactic_proof": true, "tactics": ["apply", "intro", "ext", "simp", "intro", "apply", "intro", "ext", "simp", "intro", "rfl"], "tactic_count": 11}
{"name": "CategoryTheory.Idempotents.natTrans_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Idempotents.FunctorExtension", "is_tactic_proof": true, "tactics": ["rw", "conv_lhs", "congr", "apply"], "tactic_count": 4}
{"name": "CategoryTheory.Idempotents.FunctorExtension₁.obj", "kind": "definition", "module": "Mathlib.CategoryTheory.Idempotents.FunctorExtension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.FunctorExtension₁.map", "kind": "definition", "module": "Mathlib.CategoryTheory.Idempotents.FunctorExtension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.functorExtension₁", "kind": "definition", "module": "Mathlib.CategoryTheory.Idempotents.FunctorExtension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.functorExtension₁CompWhiskeringLeftToKaroubiIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Idempotents.FunctorExtension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.KaroubiUniversal₁.counitIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Idempotents.FunctorExtension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.karoubiUniversal₁", "kind": "definition", "module": "Mathlib.CategoryTheory.Idempotents.FunctorExtension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.functorExtension₁Comp", "kind": "definition", "module": "Mathlib.CategoryTheory.Idempotents.FunctorExtension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.functorExtension₂", "kind": "definition", "module": "Mathlib.CategoryTheory.Idempotents.FunctorExtension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.functorExtension₂CompWhiskeringLeftToKaroubiIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Idempotents.FunctorExtension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.karoubiUniversal₂", "kind": "definition", "module": "Mathlib.CategoryTheory.Idempotents.FunctorExtension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.karoubiUniversal₂_functor_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Idempotents.FunctorExtension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.instIsEquivalenceFunctorKaroubiFunctorExtension₂", "kind": "instance", "module": "Mathlib.CategoryTheory.Idempotents.FunctorExtension", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Idempotents.functorExtension", "kind": "definition", "module": "Mathlib.CategoryTheory.Idempotents.FunctorExtension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.karoubiUniversal", "kind": "definition", "module": "Mathlib.CategoryTheory.Idempotents.FunctorExtension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.karoubiUniversal_functor_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Idempotents.FunctorExtension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.instIsEquivalenceFunctorKaroubiFunctorExtension", "kind": "instance", "module": "Mathlib.CategoryTheory.Idempotents.FunctorExtension", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Idempotents.instIsEquivalenceFunctorKaroubiObjWhiskeringLeftToKaroubi", "kind": "instance", "module": "Mathlib.CategoryTheory.Idempotents.FunctorExtension", "is_tactic_proof": false, "tactics": ["have", "change", "infer_instance", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.Idempotents.whiskeringLeft_obj_preimage_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Idempotents.FunctorExtension", "is_tactic_proof": true, "tactics": ["rw", "congr", "rw", "dsimp", "congr"], "tactic_count": 5}
{"name": "CategoryTheory.Idempotents.whiskeringLeftObjToKaroubiFullyFaithful", "kind": "definition", "module": "Mathlib.CategoryTheory.Idempotents.FunctorExtension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.Karoubi.HomologicalComplex.p_comp_d", "kind": "theorem", "module": "Mathlib.CategoryTheory.Idempotents.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.Karoubi.HomologicalComplex.comp_p_d", "kind": "theorem", "module": "Mathlib.CategoryTheory.Idempotents.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.Karoubi.HomologicalComplex.p_comm_f", "kind": "theorem", "module": "Mathlib.CategoryTheory.Idempotents.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.Karoubi.HomologicalComplex.p_idem", "kind": "theorem", "module": "Mathlib.CategoryTheory.Idempotents.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.KaroubiHomologicalComplexEquivalence.Functor.obj", "kind": "definition", "module": "Mathlib.CategoryTheory.Idempotents.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.KaroubiHomologicalComplexEquivalence.Functor.map", "kind": "definition", "module": "Mathlib.CategoryTheory.Idempotents.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.KaroubiHomologicalComplexEquivalence.functor", "kind": "definition", "module": "Mathlib.CategoryTheory.Idempotents.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.KaroubiHomologicalComplexEquivalence.Inverse.obj", "kind": "definition", "module": "Mathlib.CategoryTheory.Idempotents.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.KaroubiHomologicalComplexEquivalence.Inverse.map", "kind": "definition", "module": "Mathlib.CategoryTheory.Idempotents.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.KaroubiHomologicalComplexEquivalence.inverse", "kind": "definition", "module": "Mathlib.CategoryTheory.Idempotents.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.KaroubiHomologicalComplexEquivalence.counitIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Idempotents.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.KaroubiHomologicalComplexEquivalence.unitIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Idempotents.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.karoubiHomologicalComplexEquivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.Idempotents.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.karoubiChainComplexEquivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.Idempotents.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.karoubiCochainComplexEquivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.Idempotents.HomologicalComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.instIsIdempotentCompleteHomologicalComplex", "kind": "instance", "module": "Mathlib.CategoryTheory.Idempotents.HomologicalComplex", "is_tactic_proof": false, "tactics": ["rw", "isIdempotentComplete_iff_of_equivalence", "infer_instance"], "tactic_count": 3}
{"name": "CategoryTheory.Idempotents.Karoubi.ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Idempotents.Karoubi", "is_tactic_proof": true, "tactics": ["cases", "cases", "dsimp", "subst", "simpa"], "tactic_count": 5}
{"name": "CategoryTheory.Idempotents.Karoubi.instInhabitedHomOfPreadditive", "kind": "instance", "module": "Mathlib.CategoryTheory.Idempotents.Karoubi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.Karoubi.p_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Idempotents.Karoubi", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Idempotents.Karoubi.comp_p", "kind": "theorem", "module": "Mathlib.CategoryTheory.Idempotents.Karoubi", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Idempotents.Karoubi.p_comm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Idempotents.Karoubi", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Idempotents.Karoubi.comp_proof", "kind": "theorem", "module": "Mathlib.CategoryTheory.Idempotents.Karoubi", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Idempotents.Karoubi.instCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Idempotents.Karoubi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.Karoubi.hom_ext_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Idempotents.Karoubi", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "apply"], "tactic_count": 4}
{"name": "CategoryTheory.Idempotents.Karoubi.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Idempotents.Karoubi", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.Idempotents.Karoubi.comp_f", "kind": "theorem", "module": "Mathlib.CategoryTheory.Idempotents.Karoubi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.Karoubi.id_f", "kind": "theorem", "module": "Mathlib.CategoryTheory.Idempotents.Karoubi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.Karoubi.coe", "kind": "instance", "module": "Mathlib.CategoryTheory.Idempotents.Karoubi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.Karoubi.coe_X", "kind": "theorem", "module": "Mathlib.CategoryTheory.Idempotents.Karoubi", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Idempotents.Karoubi.coe_p", "kind": "theorem", "module": "Mathlib.CategoryTheory.Idempotents.Karoubi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.Karoubi.eqToHom_f", "kind": "theorem", "module": "Mathlib.CategoryTheory.Idempotents.Karoubi", "is_tactic_proof": true, "tactics": ["subst", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Idempotents.toKaroubi", "kind": "definition", "module": "Mathlib.CategoryTheory.Idempotents.Karoubi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.instFullKaroubiToKaroubi", "kind": "instance", "module": "Mathlib.CategoryTheory.Idempotents.Karoubi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.instFaithfulKaroubiToKaroubi", "kind": "instance", "module": "Mathlib.CategoryTheory.Idempotents.Karoubi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.instAdd", "kind": "instance", "module": "Mathlib.CategoryTheory.Idempotents.Karoubi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.instNeg", "kind": "instance", "module": "Mathlib.CategoryTheory.Idempotents.Karoubi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.instZero", "kind": "instance", "module": "Mathlib.CategoryTheory.Idempotents.Karoubi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.instAddCommGroupHom", "kind": "instance", "module": "Mathlib.CategoryTheory.Idempotents.Karoubi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.Karoubi.hom_eq_zero_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Idempotents.Karoubi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.Karoubi.inclusionHom", "kind": "definition", "module": "Mathlib.CategoryTheory.Idempotents.Karoubi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.Karoubi.sum_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Idempotents.Karoubi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.instPreadditiveKaroubi", "kind": "instance", "module": "Mathlib.CategoryTheory.Idempotents.Karoubi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.instAdditiveKaroubiToKaroubi", "kind": "instance", "module": "Mathlib.CategoryTheory.Idempotents.Karoubi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.instIsIdempotentCompleteKaroubi", "kind": "instance", "module": "Mathlib.CategoryTheory.Idempotents.Karoubi", "is_tactic_proof": true, "tactics": ["refine", "intro", "simp", "use", "use", "use", "simp"], "tactic_count": 7}
{"name": "CategoryTheory.Idempotents.instEssSurjKaroubiToKaroubiOfIsIdempotentComplete", "kind": "instance", "module": "Mathlib.CategoryTheory.Idempotents.Karoubi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.toKaroubi_isEquivalence", "kind": "instance", "module": "Mathlib.CategoryTheory.Idempotents.Karoubi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.toKaroubiEquivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.Idempotents.Karoubi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.toKaroubiEquivalence_functor_additive", "kind": "instance", "module": "Mathlib.CategoryTheory.Idempotents.Karoubi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.Karoubi.decompId_i", "kind": "definition", "module": "Mathlib.CategoryTheory.Idempotents.Karoubi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.Karoubi.decompId_p", "kind": "definition", "module": "Mathlib.CategoryTheory.Idempotents.Karoubi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.Karoubi.decompId", "kind": "theorem", "module": "Mathlib.CategoryTheory.Idempotents.Karoubi", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Idempotents.Karoubi.decomp_p", "kind": "theorem", "module": "Mathlib.CategoryTheory.Idempotents.Karoubi", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Idempotents.Karoubi.decompId_i_toKaroubi", "kind": "theorem", "module": "Mathlib.CategoryTheory.Idempotents.Karoubi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.Karoubi.decompId_p_toKaroubi", "kind": "theorem", "module": "Mathlib.CategoryTheory.Idempotents.Karoubi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.Karoubi.decompId_i_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Idempotents.Karoubi", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Idempotents.Karoubi.decompId_p_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Idempotents.Karoubi", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Idempotents.Karoubi.zsmul_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Idempotents.Karoubi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.Karoubi.retract", "kind": "definition", "module": "Mathlib.CategoryTheory.Idempotents.Karoubi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.instPreservesEpimorphismsKaroubiToKaroubi", "kind": "instance", "module": "Mathlib.CategoryTheory.Idempotents.Karoubi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.instPreservesMonomorphismsKaroubiToKaroubi", "kind": "instance", "module": "Mathlib.CategoryTheory.Idempotents.Karoubi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.KaroubiKaroubi.idem_f", "kind": "theorem", "module": "Mathlib.CategoryTheory.Idempotents.KaroubiKaroubi", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.Idempotents.KaroubiKaroubi.p_comm_f", "kind": "theorem", "module": "Mathlib.CategoryTheory.Idempotents.KaroubiKaroubi", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.Idempotents.KaroubiKaroubi.inverse", "kind": "definition", "module": "Mathlib.CategoryTheory.Idempotents.KaroubiKaroubi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.KaroubiKaroubi.instAdditiveKaroubiInverse", "kind": "instance", "module": "Mathlib.CategoryTheory.Idempotents.KaroubiKaroubi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.KaroubiKaroubi.unitIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Idempotents.KaroubiKaroubi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.KaroubiKaroubi.counitIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Idempotents.KaroubiKaroubi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.KaroubiKaroubi.equivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.Idempotents.KaroubiKaroubi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.KaroubiKaroubi.equivalence.additive_functor", "kind": "instance", "module": "Mathlib.CategoryTheory.Idempotents.KaroubiKaroubi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.KaroubiKaroubi.equivalence.additive_inverse", "kind": "instance", "module": "Mathlib.CategoryTheory.Idempotents.KaroubiKaroubi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.instIsIdempotentCompleteSimplicialObject", "kind": "instance", "module": "Mathlib.CategoryTheory.Idempotents.SimplicialObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Idempotents.instIsIdempotentCompleteCosimplicialObject", "kind": "instance", "module": "Mathlib.CategoryTheory.Idempotents.SimplicialObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.InducedCategory", "kind": "definition", "module": "Mathlib.CategoryTheory.InducedCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.InducedCategory.hasCoeToSort", "kind": "instance", "module": "Mathlib.CategoryTheory.InducedCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.InducedCategory.instCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.InducedCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.InducedCategory.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.InducedCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.InducedCategory.homMk", "kind": "definition", "module": "Mathlib.CategoryTheory.InducedCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.IsIso.eq_inv_of_hom_inv_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Iso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsIso.id", "kind": "instance", "module": "Mathlib.CategoryTheory.Iso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsIso.inv_isIso", "kind": "instance", "module": "Mathlib.CategoryTheory.Iso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsIso.comp_isIso", "kind": "instance", "module": "Mathlib.CategoryTheory.Iso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsIso.comp_isIso'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Iso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsIso.inv_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Iso", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.IsIso.inv_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Iso", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.IsIso.inv_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Iso", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.IsIso.Iso.inv_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Iso", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.IsIso.inv_comp_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Iso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsIso.eq_inv_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Iso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsIso.of_isIso_comp_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Iso", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.IsIso.of_isIso_fac_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Iso", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.isIso_comp_left_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Iso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.eq_of_inv_eq_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Iso", "is_tactic_proof": true, "tactics": ["apply", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.IsIso.inv_eq_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Iso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.hom_comp_eq_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Iso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.inv_comp_eq_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Iso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isIso_of_hom_comp_eq_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Iso", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Iso.inv_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Iso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.inv_ext'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Iso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.cancel_iso_hom_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Iso", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Iso.cancel_iso_hom_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Iso", "is_tactic_proof": true, "tactics": ["simp", "but"], "tactic_count": 2}
{"name": "CategoryTheory.Iso.cancel_iso_hom_right_assoc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Iso", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Iso.cancel_iso_inv_right_assoc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Iso", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Iso.map_hom_inv_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Iso", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "CategoryTheory.Iso.map_inv_hom_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Iso", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.mapIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Iso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapIso_symm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Iso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapIso_trans", "kind": "theorem", "module": "Mathlib.CategoryTheory.Iso", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.mapIso_refl", "kind": "theorem", "module": "Mathlib.CategoryTheory.Iso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.map_isIso", "kind": "instance", "module": "Mathlib.CategoryTheory.Iso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.map_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Iso", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.map_hom_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Iso", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.IsIsomorphic", "kind": "definition", "module": "Mathlib.CategoryTheory.IsomorphismClasses", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isIsomorphicSetoid", "kind": "definition", "module": "Mathlib.CategoryTheory.IsomorphismClasses", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isomorphismClasses", "kind": "definition", "module": "Mathlib.CategoryTheory.IsomorphismClasses", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Groupoid.isIsomorphic_iff_nonempty_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.IsomorphismClasses", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join", "kind": "inductive", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.term_⋆_", "kind": "definition", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join._aux_Mathlib_CategoryTheory_Join_Basic___macroRules_CategoryTheory_Join_term_⋆__1", "kind": "definition", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join._aux_Mathlib_CategoryTheory_Join_Basic___unexpand_CategoryTheory_Join_1", "kind": "definition", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.Hom", "kind": "definition", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.id", "kind": "definition", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.comp", "kind": "definition", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.instCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.false_of_right_to_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.instUniqueHomLeftRight", "kind": "instance", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.edge", "kind": "definition", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.inclLeft", "kind": "definition", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.inclRight", "kind": "definition", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.homInduction", "kind": "definition", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.homInduction_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.homInduction_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.homInduction_edge", "kind": "theorem", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.inclLeftFullyFaithful", "kind": "definition", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.inclRightFullyFaithful", "kind": "definition", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.inclLeftFull", "kind": "instance", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.inclRightFull", "kind": "instance", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.inclLeftFaithful", "kind": "instance", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.inclRightFaithful", "kind": "instance", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.id_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.id_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.edgeTransform", "kind": "definition", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.mkFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.mkFunctor_obj_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.mkFunctor_obj_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.mkFunctor_map_inclLeft", "kind": "theorem", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.mkFunctorLeft", "kind": "definition", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.mkFunctorRight", "kind": "definition", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.mkFunctor_map_inclRight", "kind": "theorem", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.mkFunctor_edgeTransform", "kind": "theorem", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Join.mkFunctor_map_edge", "kind": "theorem", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.mkNatTrans_app_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.mkNatTrans_app_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.whiskerLeft_inclLeft_mkNatTrans", "kind": "theorem", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.whiskerLeft_inclRight_mkNatTrans", "kind": "theorem", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.natTrans_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": true, "tactics": ["ext", "cases", "left", "right"], "tactic_count": 4}
{"name": "CategoryTheory.Join.eq_mkNatTrans", "kind": "theorem", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Join.mapPair", "kind": "definition", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.mapPair_obj_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.mapPair_obj_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.mapPair_map_inclLeft", "kind": "theorem", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.mapPair_map_inclRight", "kind": "theorem", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.mapPairLeft", "kind": "definition", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.mapPairRight", "kind": "definition", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.isoMkFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.mapPairId", "kind": "definition", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.mapPairComp", "kind": "definition", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.mapPairComp_hom_app_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Join.mapPairComp_hom_app_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Join.mapPairComp_inv_app_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Join.mapPairComp_inv_app_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Join.mapWhiskerRight", "kind": "definition", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.mapWhiskerRight_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Join.mapWhiskerRight_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Join.mapWhiskerLeft", "kind": "definition", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.mapWhiskerLeft_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Join.mapWhiskerLeft_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Join.mapWhisker_exchange", "kind": "theorem", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": true, "tactics": ["ext", "cat_disch"], "tactic_count": 2}
{"name": "CategoryTheory.Join.mapIsoWhiskerLeft", "kind": "definition", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.mapIsoWhiskerRight", "kind": "definition", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.mapIsoWhiskerRight_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.mapIsoWhiskerRight_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": true, "tactics": ["ext", "cases"], "tactic_count": 2}
{"name": "CategoryTheory.Join.mapIsoWhiskerLeft_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.mapIsoWhiskerLeft_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": true, "tactics": ["ext", "cases"], "tactic_count": 2}
{"name": "CategoryTheory.Join.mapPairEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.isEquivalenceMapPair", "kind": "instance", "module": "Mathlib.CategoryTheory.Join.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.costructuredArrowEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Join.Final", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.structuredArrowEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Join.Final", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.instInitialInclLeftOfIsConnected", "kind": "instance", "module": "Mathlib.CategoryTheory.Join.Final", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.instFinalInclRightOfIsConnected", "kind": "instance", "module": "Mathlib.CategoryTheory.Join.Final", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.opEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Join.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.opEquiv_functor_obj_op_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Join.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.opEquiv_functor_obj_op_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Join.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.opEquiv_functor_map_op_inclLeft", "kind": "theorem", "module": "Mathlib.CategoryTheory.Join.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.opEquiv_functor_map_op_inclRight", "kind": "theorem", "module": "Mathlib.CategoryTheory.Join.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.opEquiv_functor_map_op_edge", "kind": "theorem", "module": "Mathlib.CategoryTheory.Join.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.InclLeftCompRightOpOpEquivFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Join.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.InclRightCompRightOpOpEquivFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Join.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.opEquiv_inverse_obj_left_op", "kind": "theorem", "module": "Mathlib.CategoryTheory.Join.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.opEquiv_inverse_obj_right_op", "kind": "theorem", "module": "Mathlib.CategoryTheory.Join.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.opEquiv_inverse_map_inclLeft_op", "kind": "theorem", "module": "Mathlib.CategoryTheory.Join.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.opEquiv_inverse_map_inclRight_op", "kind": "theorem", "module": "Mathlib.CategoryTheory.Join.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.opEquiv_inverse_map_edge_op", "kind": "theorem", "module": "Mathlib.CategoryTheory.Join.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.inclLeftCompOpEquivInverse", "kind": "definition", "module": "Mathlib.CategoryTheory.Join.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.inclRightCompOpEquivInverse", "kind": "definition", "module": "Mathlib.CategoryTheory.Join.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.inclLeftCompOpEquivInverse_hom_app_op", "kind": "theorem", "module": "Mathlib.CategoryTheory.Join.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.inclRightCompOpEquivInverse_hom_app_op", "kind": "theorem", "module": "Mathlib.CategoryTheory.Join.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.inclLeftCompOpEquivInverse_inv_app_op", "kind": "theorem", "module": "Mathlib.CategoryTheory.Join.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.inclRightCompOpEquivInverse_inv_app_op", "kind": "theorem", "module": "Mathlib.CategoryTheory.Join.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.mapCompRight", "kind": "definition", "module": "Mathlib.CategoryTheory.Join.Pseudofunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.mapCompLeft", "kind": "definition", "module": "Mathlib.CategoryTheory.Join.Pseudofunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.mapWhiskerLeft_whiskerLeft", "kind": "theorem", "module": "Mathlib.CategoryTheory.Join.Pseudofunctor", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Join.mapWhiskerRight_whiskerLeft", "kind": "theorem", "module": "Mathlib.CategoryTheory.Join.Pseudofunctor", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Join.mapWhiskerLeft_whiskerRight", "kind": "theorem", "module": "Mathlib.CategoryTheory.Join.Pseudofunctor", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Join.mapWhiskerRight_whiskerRight", "kind": "theorem", "module": "Mathlib.CategoryTheory.Join.Pseudofunctor", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Join.mapWhiskerLeft_associator_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Join.Pseudofunctor", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Join.mapWhiskerRight_associator_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Join.Pseudofunctor", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Join.mapWhiskerLeft_leftUnitor_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Join.Pseudofunctor", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Join.mapWhiskerRight_leftUnitor_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Join.Pseudofunctor", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Join.mapWhiskerLeft_rightUnitor_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Join.Pseudofunctor", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Join.mapWhiskerRight_rightUnitor_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Join.Pseudofunctor", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Join.pseudofunctorRight", "kind": "definition", "module": "Mathlib.CategoryTheory.Join.Pseudofunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.pseudofunctorLeft", "kind": "definition", "module": "Mathlib.CategoryTheory.Join.Pseudofunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.fromSum", "kind": "definition", "module": "Mathlib.CategoryTheory.Join.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.fromSum_map_inl", "kind": "theorem", "module": "Mathlib.CategoryTheory.Join.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.fromSum_map_inr", "kind": "theorem", "module": "Mathlib.CategoryTheory.Join.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.inlCompFromSum", "kind": "definition", "module": "Mathlib.CategoryTheory.Join.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.inrCompFromSum", "kind": "definition", "module": "Mathlib.CategoryTheory.Join.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.instEssSurjSumFromSum", "kind": "instance", "module": "Mathlib.CategoryTheory.Join.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Join.instFaithfulSumFromSum", "kind": "instance", "module": "Mathlib.CategoryTheory.Join.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CommSq.right_adjoint", "kind": "theorem", "module": "Mathlib.CategoryTheory.LiftingProperties.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CommSq.rightAdjointLiftStructEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.LiftingProperties.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CommSq.right_adjoint_hasLift_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.LiftingProperties.Adjunction", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.CommSq.instHasLift", "kind": "instance", "module": "Mathlib.CategoryTheory.LiftingProperties.Adjunction", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.CommSq.left_adjoint", "kind": "theorem", "module": "Mathlib.CategoryTheory.LiftingProperties.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CommSq.leftAdjointLiftStructEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.LiftingProperties.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CommSq.left_adjoint_hasLift_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.LiftingProperties.Adjunction", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.CommSq.instHasLift_1", "kind": "instance", "module": "Mathlib.CategoryTheory.LiftingProperties.Adjunction", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Adjunction.hasLiftingProperty_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.LiftingProperties.Adjunction", "is_tactic_proof": true, "tactics": ["constructor", "rw", "infer_instance", "rw", "infer_instance"], "tactic_count": 5}
{"name": "CategoryTheory.sq_hasLift_of_hasLiftingProperty", "kind": "instance", "module": "Mathlib.CategoryTheory.LiftingProperties.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasLiftingProperty.op", "kind": "theorem", "module": "Mathlib.CategoryTheory.LiftingProperties.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasLiftingProperty.unop", "kind": "theorem", "module": "Mathlib.CategoryTheory.LiftingProperties.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasLiftingProperty.iff_op", "kind": "theorem", "module": "Mathlib.CategoryTheory.LiftingProperties.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasLiftingProperty.iff_unop", "kind": "theorem", "module": "Mathlib.CategoryTheory.LiftingProperties.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasLiftingProperty.of_left_iso", "kind": "instance", "module": "Mathlib.CategoryTheory.LiftingProperties.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasLiftingProperty.of_right_iso", "kind": "instance", "module": "Mathlib.CategoryTheory.LiftingProperties.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasLiftingProperty.of_comp_left", "kind": "instance", "module": "Mathlib.CategoryTheory.LiftingProperties.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasLiftingProperty.of_comp_right", "kind": "instance", "module": "Mathlib.CategoryTheory.LiftingProperties.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasLiftingProperty.of_arrow_iso_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.LiftingProperties.Basic", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.HasLiftingProperty.of_arrow_iso_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.LiftingProperties.Basic", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.HasLiftingProperty.iff_of_arrow_iso_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.LiftingProperties.Basic", "is_tactic_proof": true, "tactics": ["constructor", "exacts"], "tactic_count": 2}
{"name": "CategoryTheory.HasLiftingProperty.iff_of_arrow_iso_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.LiftingProperties.Basic", "is_tactic_proof": true, "tactics": ["constructor", "exacts"], "tactic_count": 2}
{"name": "CategoryTheory.RetractArrow.leftLiftingProperty", "kind": "theorem", "module": "Mathlib.CategoryTheory.LiftingProperties.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.RetractArrow.rightLiftingProperty", "kind": "theorem", "module": "Mathlib.CategoryTheory.LiftingProperties.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Arrow.LiftStruct", "kind": "abbrev", "module": "Mathlib.CategoryTheory.LiftingProperties.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Arrow.hasLiftingProperty_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.LiftingProperties.Basic", "is_tactic_proof": true, "tactics": ["constructor", "intro", "have", "exact", "intro", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.HasLiftingPropertyFixedTop", "kind": "definition", "module": "Mathlib.CategoryTheory.LiftingProperties.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasLiftingPropertyFixedBot", "kind": "definition", "module": "Mathlib.CategoryTheory.LiftingProperties.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPushout.hasLiftingProperty", "kind": "theorem", "module": "Mathlib.CategoryTheory.LiftingProperties.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPullback.hasLiftingProperty", "kind": "theorem", "module": "Mathlib.CategoryTheory.LiftingProperties.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instHasLiftingPropertyInl", "kind": "instance", "module": "Mathlib.CategoryTheory.LiftingProperties.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instHasLiftingPropertyInr", "kind": "instance", "module": "Mathlib.CategoryTheory.LiftingProperties.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instHasLiftingPropertySnd", "kind": "instance", "module": "Mathlib.CategoryTheory.LiftingProperties.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instHasLiftingPropertyFst", "kind": "instance", "module": "Mathlib.CategoryTheory.LiftingProperties.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instHasLiftingPropertyMap", "kind": "instance", "module": "Mathlib.CategoryTheory.LiftingProperties.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instHasLiftingPropertyMap_1", "kind": "instance", "module": "Mathlib.CategoryTheory.LiftingProperties.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CommSq.HasLift.over", "kind": "theorem", "module": "Mathlib.CategoryTheory.LiftingProperties.Over", "is_tactic_proof": true, "tactics": ["let", "dsimp", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.HasLiftingProperty.over", "kind": "theorem", "module": "Mathlib.CategoryTheory.LiftingProperties.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ParametrizedAdjunction.arrowHomEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.LiftingProperties.ParametrizedAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_apply_right_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.LiftingProperties.ParametrizedAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_apply_right_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.LiftingProperties.ParametrizedAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ParametrizedAdjunction.inl_arrowHomEquiv_symm_apply_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.LiftingProperties.ParametrizedAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ParametrizedAdjunction.inr_arrowHomEquiv_symm_apply_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.LiftingProperties.ParametrizedAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ParametrizedAdjunction.liftStructEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.LiftingProperties.ParametrizedAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ParametrizedAdjunction.hasLiftingProperty_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.LiftingProperties.ParametrizedAdjunction", "is_tactic_proof": true, "tactics": ["simp", "constructor", "intro", "obtain", "exact", "intro", "exact"], "tactic_count": 7}
{"name": "CategoryTheory.Bicone", "kind": "inductive", "module": "Mathlib.CategoryTheory.Limits.Bicones", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instDecidableEqBicone", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Bicones", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instInhabitedBicone", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Bicones", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.finBicone", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Bicones", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.BiconeHom", "kind": "inductive", "module": "Mathlib.CategoryTheory.Limits.Bicones", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instInhabitedBiconeHomLeft", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Bicones", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.BiconeHom.decidableEq", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Bicones", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.biconeCategoryStruct", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Bicones", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.biconeCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Bicones", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.biconeMk", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Bicones", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.finBiconeHom", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Bicones", "is_tactic_proof": true, "tactics": ["cases", "exact", "complete", "exact", "complete", "exact", "complete", "exact", "complete", "exact", "complete", "exact", "complete", "exact", "complete", "exact", "complete", "exact", "complete", "rcases", "simp", "use", "simpa"], "tactic_count": 23}
{"name": "CategoryTheory.biconeSmallCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Bicones", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.biconeFinCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Bicones", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.map_id_left_eq_curry_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.ColimitLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.map_id_right_eq_curry_swap_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.ColimitLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.colimitLimitToLimitColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.ColimitLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.ι_colimitLimitToLimitColimit_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.ColimitLimit", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.ι_colimitLimitToLimitColimit_π_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.ColimitLimit", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "dsimp", "rw", "dsimp"], "tactic_count": 5}
{"name": "CategoryTheory.Limits.colimitLimitToLimitColimitCone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.ColimitLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comma.limitAuxiliaryCone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comma.coneOfPreserves", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comma.coneOfPreservesIsLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comma.colimitAuxiliaryCocone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comma.coconeOfPreserves", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comma.coconeOfPreservesIsColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comma.hasLimit", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comma.hasLimitsOfShape", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comma.hasLimitsOfSize", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comma.hasColimit", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comma.hasColimitsOfShape", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comma.hasColimitsOfSize", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comma.preservesColimitsOfShape_fst", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comma.preservesColimitsOfShape_snd", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Arrow.hasLimit", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Comma", "is_tactic_proof": true, "tactics": ["haveI", "haveI", "apply"], "tactic_count": 3}
{"name": "CategoryTheory.Arrow.hasLimitsOfShape", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Arrow.hasLimits", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Arrow.hasColimit", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Comma", "is_tactic_proof": true, "tactics": ["haveI", "haveI", "apply"], "tactic_count": 3}
{"name": "CategoryTheory.Arrow.hasColimitsOfShape", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Arrow.hasColimits", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Arrow.preservesColimitsOfShape_leftFunc", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Comma", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Arrow.preservesColimitsOfShape_rightFunc", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Comma", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.StructuredArrow.hasLimit", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Comma", "is_tactic_proof": true, "tactics": ["haveI", "haveI", "apply"], "tactic_count": 3}
{"name": "CategoryTheory.StructuredArrow.hasLimitsOfShape", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.hasLimitsOfSize", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.createsLimit", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.createsLimitsOfShape", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.createsLimitsOfSize", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.mono_right_of_mono", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.mono_iff_mono_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.hasTerminal", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.hasColimit", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Comma", "is_tactic_proof": true, "tactics": ["haveI", "haveI", "apply"], "tactic_count": 3}
{"name": "CategoryTheory.CostructuredArrow.hasColimitsOfShape", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.hasColimitsOfSize", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.createsColimit", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.createsColimitsOfShape", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.createsColimitsOfSize", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.epi_left_of_epi", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.epi_iff_epi_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.instHasTerminal", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Types.instFullForgetType", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.ConcreteCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Types.instPreservesLimitsOfSizeForgetType", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.ConcreteCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Types.instPreservesColimitsOfSizeForgetType", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.ConcreteCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Types.instReflectsLimitsOfSizeForgetType", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.ConcreteCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Types.instReflectsColimitsOfSizeForgetType", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.ConcreteCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Types.instIsEquivalenceForgetType", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.ConcreteCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Types.instIsCorepresentableForgetType", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.ConcreteCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Concrete.small_sections_of_hasLimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.ConcreteCategory.Basic", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.Concrete.to_product_injective_of_isLimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.ConcreteCategory.Basic", "is_tactic_proof": true, "tactics": ["let", "intro", "apply", "ext", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.Limits.Concrete.isLimit_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.ConcreteCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Concrete.limit_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.ConcreteCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Concrete.surjective_π_app_zero_of_surjective_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.ConcreteCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Concrete.from_union_surjective_of_isColimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.ConcreteCategory.Basic", "is_tactic_proof": true, "tactics": ["intro", "let", "let", "obtain", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.Limits.Concrete.isColimit_exists_rep", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.ConcreteCategory.Basic", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.Concrete.colimit_exists_rep", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.ConcreteCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Concrete.isColimit_rep_eq_of_exists", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.ConcreteCategory.Basic", "is_tactic_proof": true, "tactics": ["let", "obtain", "let", "let", "change", "rw", "exact"], "tactic_count": 7}
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{"name": "CategoryTheory.Limits.Concrete.isColimit_exists_of_rep_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.ConcreteCategory.Basic", "is_tactic_proof": true, "tactics": ["let", "let", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.Concrete.isColimit_rep_eq_iff_exists", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.ConcreteCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Concrete.colimit_exists_of_rep_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.ConcreteCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Concrete.colimit_rep_eq_iff_exists", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.ConcreteCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Concrete.colimit_rep_eq_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.ConcreteCategory.WithAlgebraicStructures", "is_tactic_proof": true, "tactics": ["rw", "obtain", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.Concrete.colimit_no_zero_smul_divisor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.ConcreteCategory.WithAlgebraicStructures", "is_tactic_proof": true, "tactics": ["classical", "obtain", "rw", "obtain", "obtain", "simpa", "congr", "rw"], "tactic_count": 8}
{"name": "CategoryTheory.Limits.Cone.toStructuredArrow", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.ConeCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.limit.toStructuredArrow", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.ConeCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cone.toStructuredArrowIsoToStructuredArrow", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.ConeCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.toStructuredArrowIsoToStructuredArrow", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.ConeCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cone.toStructuredArrowCompProj", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.ConeCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cone.toStructuredArrow_comp_proj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.ConeCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cone.toStructuredArrowCompToUnderCompForget", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.ConeCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cone.toStructuredArrow_comp_toUnder_comp_forget", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.ConeCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cone.toUnder", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.ConeCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.limit.toUnder", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.ConeCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cone.mapConeToUnder", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.ConeCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cone.fromStructuredArrow", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.ConeCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cone.toStructuredArrowCone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.ConeCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cone.toCostructuredArrow", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.ConeCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cone.fromCostructuredArrow", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.ConeCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cone.equivCostructuredArrow", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.ConeCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cone.isLimitEquivIsTerminal", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.ConeCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasLimit_iff_hasTerminal_cone", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.ConeCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasLimitsOfShape_iff_isLeftAdjoint_const", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.ConeCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsLimit.liftConeMorphism_eq_isTerminal_from", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.ConeCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsTerminal.from_eq_liftConeMorphism", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.ConeCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsLimit.ofPreservesConeTerminal", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.ConeCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsLimit.ofReflectsConeTerminal", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.ConeCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cocone.toCostructuredArrow", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.ConeCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.colimit.toCostructuredArrow", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.ConeCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cocone.toCostructuredArrowIsoToCostructuredArrow", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.ConeCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.toCostructuredArrowIsoToCostructuredArrow", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.ConeCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cocone.toCostructuredArrowCompProj", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.ConeCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cocone.toCostructuredArrow_comp_proj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.ConeCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cocone.toCostructuredArrowCompToOverCompForget", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.ConeCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cocone.toCostructuredArrow_comp_toOver_comp_forget", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.ConeCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cocone.toOver", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.ConeCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.colimit.toOver", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.ConeCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cocone.mapCoconeToOver", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.ConeCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cocone.fromCostructuredArrow", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.ConeCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cocone.toCostructuredArrowCocone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.ConeCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cocone.toStructuredArrow", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.ConeCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cocone.fromStructuredArrow", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.ConeCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cocone.equivStructuredArrow", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.ConeCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cocone.isColimitEquivIsInitial", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.ConeCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasColimit_iff_hasInitial_cocone", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.ConeCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasColimitsOfShape_iff_isRightAdjoint_const", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.ConeCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsColimit.descCoconeMorphism_eq_isInitial_to", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.ConeCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsInitial.to_eq_descCoconeMorphism", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.ConeCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsColimit.ofPreservesCoconeInitial", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.ConeCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsColimit.ofReflectsCoconeInitial", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.ConeCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.cones", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Cones", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.cocones", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Cones", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.cones", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Cones", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.cocones", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Cones", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.inhabitedCone", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Cones", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cone.w", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Cones", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.inhabitedCocone", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Cones", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cocone.w", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Cones", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.Cone.equiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Cones", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cone.extensions", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Cones", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cone.extend", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Cones", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cone.whisker", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Cones", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cocone.equiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Cones", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cocone.extensions", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Cones", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cocone.extend", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Cones", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cocone.whisker", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Cones", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.inhabitedConeMorphism", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Cones", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cone.category", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Cones", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.ProdPreservesConnectedLimits.γ₁", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ProdPreservesConnectedLimits.forgetCone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.prod_preservesConnectedLimits", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isBinaryProductOfIsTerminalIsPullback", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isProductOfIsTerminalIsPullback", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.BinaryProducts", "is_tactic_proof": true, "tactics": ["apply", "exact"], "tactic_count": 2}
{"name": "isPullbackOfIsTerminalIsProduct", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.BinaryProducts", "is_tactic_proof": true, "tactics": ["apply", "intro", "use", "use", "use", "intro", "apply", "rintro", "exact", "exact"], "tactic_count": 10}
{"name": "limitConeOfTerminalAndPullbacks", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasBinaryProducts_of_hasTerminal_and_pullbacks", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "preservesBinaryProducts_of_preservesTerminal_and_pullbacks", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "prodIsoPullback", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "prodIsoPullback_hom_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "prodIsoPullback_hom_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "prodIsoPullback_inv_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "prodIsoPullback_inv_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isBinaryCoproductOfIsInitialIsPushout", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCoproductOfIsInitialIsPushout", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.BinaryProducts", "is_tactic_proof": true, "tactics": ["apply", "exact"], "tactic_count": 2}
{"name": "isPushoutOfIsInitialIsCoproduct", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.BinaryProducts", "is_tactic_proof": true, "tactics": ["apply", "intro", "use", "use", "use", "intro", "apply", "rintro", "exact", "exact"], "tactic_count": 10}
{"name": "colimitCoconeOfInitialAndPushouts", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasBinaryCoproducts_of_hasInitial_and_pushouts", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "preservesBinaryCoproducts_of_preservesInitial_and_pushouts", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "coprodIsoPushout", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inl_coprodIsoPushout_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inr_coprodIsoPushout_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inl_coprodIsoPushout_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inr_coprodIsoPushout_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.preserves_mono_of_preservesLimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.EpiMono", "is_tactic_proof": true, "tactics": ["have", "simp_rw", "apply"], "tactic_count": 3}
{"name": "CategoryTheory.preservesMonomorphisms_of_preservesLimitsOfShape", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Constructions.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.reflects_mono_of_reflectsLimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.EpiMono", "is_tactic_proof": true, "tactics": ["have", "simp_rw", "apply"], "tactic_count": 3}
{"name": "CategoryTheory.reflectsMonomorphisms_of_reflectsLimitsOfShape", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Constructions.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.preserves_epi_of_preservesColimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.EpiMono", "is_tactic_proof": true, "tactics": ["have", "simp_rw", "apply"], "tactic_count": 3}
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{"name": "CategoryTheory.reflects_epi_of_reflectsColimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.EpiMono", "is_tactic_proof": true, "tactics": ["have", "simp_rw", "apply"], "tactic_count": 3}
{"name": "CategoryTheory.reflectsEpimorphisms_of_reflectsColimitsOfShape", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Constructions.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.HasEqualizersOfHasPullbacksAndBinaryProducts.constructEqualizer", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Constructions.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.HasEqualizersOfHasPullbacksAndBinaryProducts.pullbackFst", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Constructions.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.HasEqualizersOfHasPullbacksAndBinaryProducts.pullbackFst_eq_pullback_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.Equalizers", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.HasEqualizersOfHasPullbacksAndBinaryProducts.equalizerCone", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Constructions.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.HasEqualizersOfHasPullbacksAndBinaryProducts.equalizerConeIsLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasEqualizers_of_hasPullbacks_and_binary_products", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.preservesEqualizers_of_preservesPullbacks_and_binaryProducts", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.HasCoequalizersOfHasPushoutsAndBinaryCoproducts.constructCoequalizer", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Constructions.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.HasCoequalizersOfHasPushoutsAndBinaryCoproducts.pushoutInl", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Constructions.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.HasCoequalizersOfHasPushoutsAndBinaryCoproducts.pushoutInl_eq_pushout_inr", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.Equalizers", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.HasCoequalizersOfHasPushoutsAndBinaryCoproducts.coequalizerCocone", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Constructions.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.HasCoequalizersOfHasPushoutsAndBinaryCoproducts.coequalizerCoconeIsColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasCoequalizers_of_hasPushouts_and_binary_coproducts", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.preservesCoequalizers_of_preservesPushouts_and_binaryCoproducts", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsEventuallyConstantTo", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.EventuallyConstant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsEventuallyConstantFrom", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.EventuallyConstant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsEventuallyConstantTo.isIso_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.EventuallyConstant", "is_tactic_proof": true, "tactics": ["have", "have", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Functor.IsEventuallyConstantTo.precomp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.EventuallyConstant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsEventuallyConstantTo.isoMap", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.EventuallyConstant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsEventuallyConstantTo.isoMap_hom_inv_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.EventuallyConstant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsEventuallyConstantTo.isoMap_inv_hom_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.EventuallyConstant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsEventuallyConstantTo.coneπApp", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.EventuallyConstant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsEventuallyConstantTo.coneπApp_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.EventuallyConstant", "is_tactic_proof": false, "tactics": ["obtain", "dsimp", "rw", "isoMap_hom,"], "tactic_count": 4}
{"name": "CategoryTheory.Functor.IsEventuallyConstantTo.coneπApp_eq_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.EventuallyConstant", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.IsEventuallyConstantTo.cone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.EventuallyConstant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsEventuallyConstantTo.isLimitCone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.EventuallyConstant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsEventuallyConstantTo.hasLimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.EventuallyConstant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsEventuallyConstantTo.isIso_π_of_isLimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.EventuallyConstant", "is_tactic_proof": false, "tactics": ["simp", "comp_id]", "infer_instance"], "tactic_count": 3}
{"name": "CategoryTheory.Functor.IsEventuallyConstantTo.isIso_π_of_isLimit'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.EventuallyConstant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsEventuallyConstantTo.isLimitOfIsIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.EventuallyConstant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsEventuallyConstantFrom.isIso_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.EventuallyConstant", "is_tactic_proof": true, "tactics": ["have", "have", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Functor.IsEventuallyConstantFrom.postcomp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.EventuallyConstant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsEventuallyConstantFrom.isoMap", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.EventuallyConstant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsEventuallyConstantFrom.isoMap_hom_inv_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.EventuallyConstant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsEventuallyConstantFrom.isoMap_inv_hom_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.EventuallyConstant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsEventuallyConstantFrom.coconeιApp", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.EventuallyConstant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsEventuallyConstantFrom.coconeιApp_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.EventuallyConstant", "is_tactic_proof": true, "tactics": ["obtain", "dsimp", "rw", "cancel_mono", "h₁,"], "tactic_count": 5}
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{"name": "CategoryTheory.Functor.IsEventuallyConstantFrom.cocone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.EventuallyConstant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsEventuallyConstantFrom.isColimitCocone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.EventuallyConstant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsEventuallyConstantFrom.hasColimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.EventuallyConstant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsEventuallyConstantFrom.isIso_ι_of_isColimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.EventuallyConstant", "is_tactic_proof": false, "tactics": ["simp", "id_comp]", "infer_instance"], "tactic_count": 3}
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{"name": "CategoryTheory.Functor.IsEventuallyConstantFrom.isColimitOfIsIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.EventuallyConstant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsCofiltered.instHasLimitOfIsEventuallyConstant", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Constructions.EventuallyConstant", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.IsFiltered.instHasColimitOfIsEventuallyConstant", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Constructions.EventuallyConstant", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.CoproductsFromFiniteFiltered.liftToFinsetObj", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.Filtered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.CoproductsFromFiniteFiltered.liftToFinsetColimitCocone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.Filtered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.CoproductsFromFiniteFiltered.liftToFinset", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.Filtered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.CoproductsFromFiniteFiltered.finiteSubcoproductsCocone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.Filtered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.CoproductsFromFiniteFiltered.isColimitFiniteSubproductsCocone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.Filtered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasCoproducts_of_finite_and_filtered", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.Filtered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.has_colimits_of_finite_and_filtered", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.Filtered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasProducts_of_finite_and_cofiltered", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.Filtered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.has_limits_of_finite_and_cofiltered", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.Filtered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.CoproductsFromFiniteFiltered.liftToFinsetColimIso_aux", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.Filtered", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.CoproductsFromFiniteFiltered.liftToFinsetColimIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.Filtered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.CoproductsFromFiniteFiltered.liftToFinsetEvaluationIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.Filtered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.ProductsFromFiniteCofiltered.liftToFinsetObj", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.Filtered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.ProductsFromFiniteCofiltered.liftToFinsetLimitCone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.Filtered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.ProductsFromFiniteCofiltered.finiteSubproductsCone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.Filtered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.ProductsFromFiniteCofiltered.isLimitFiniteSubproductsCone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.Filtered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.ProductsFromFiniteCofiltered.liftToFinset", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.Filtered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.ProductsFromFiniteCofiltered.liftToFinsetLimIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.Filtered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.ProductsFromFiniteCofiltered.liftToFinsetEvaluationIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.Filtered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.extendFan", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.FiniteProductsOfBinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.extendFanIsLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.FiniteProductsOfBinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.CategoryTheory.Limits.Constructions.FiniteProductsOfBinaryProducts.0.CategoryTheory.hasProduct_fin", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.FiniteProductsOfBinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.hasFiniteProducts_of_has_binary_and_terminal", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.FiniteProductsOfBinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.preservesFinOfPreservesBinaryAndTerminal", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.FiniteProductsOfBinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PreservesFiniteProducts.of_preserves_binary_and_terminal", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.FiniteProductsOfBinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.extendCofan", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.FiniteProductsOfBinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.extendCofanIsColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.FiniteProductsOfBinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.CategoryTheory.Limits.Constructions.FiniteProductsOfBinaryProducts.0.CategoryTheory.hasCoproduct_fin", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.FiniteProductsOfBinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.hasFiniteCoproducts_of_has_binary_and_initial", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.FiniteProductsOfBinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.preserves_fin_of_preserves_binary_and_initial", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.FiniteProductsOfBinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.preservesShape_fin_of_preserves_binary_and_initial", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.FiniteProductsOfBinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.preservesFiniteCoproductsOfPreservesBinaryAndInitial", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.FiniteProductsOfBinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.HasLimitOfHasProductsOfHasEqualizers.buildLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.LimitsOfProductsAndEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.HasLimitOfHasProductsOfHasEqualizers.buildIsLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.LimitsOfProductsAndEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.limitConeOfEqualizerAndProduct", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.LimitsOfProductsAndEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasLimit_of_equalizer_and_product", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.LimitsOfProductsAndEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.limitSubobjectProduct", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.LimitsOfProductsAndEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.limitSubobjectProduct_mono", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Constructions.LimitsOfProductsAndEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.has_limits_of_hasEqualizers_and_products", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.LimitsOfProductsAndEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasFiniteLimits_of_hasEqualizers_and_finite_products", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.LimitsOfProductsAndEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.preservesLimit_of_preservesEqualizers_and_product", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.LimitsOfProductsAndEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.preservesFiniteLimits_of_preservesEqualizers_and_finiteProducts", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.LimitsOfProductsAndEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.preservesLimits_of_preservesEqualizers_and_products", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.LimitsOfProductsAndEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.createsLimitsOfShapeOfCreatesEqualizersAndProducts", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.LimitsOfProductsAndEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.createsFiniteLimitsOfCreatesEqualizersAndFiniteProducts", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.LimitsOfProductsAndEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.createsLimitsOfSizeOfCreatesEqualizersAndProducts", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.LimitsOfProductsAndEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasFiniteLimits_of_hasTerminal_and_pullbacks", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.LimitsOfProductsAndEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.preservesFiniteLimits_of_preservesTerminal_and_pullbacks", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.LimitsOfProductsAndEqualizers", "is_tactic_proof": true, "tactics": ["have", "have", "have", "have", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.Limits.createsFiniteLimitsOfCreatesTerminalAndPullbacks", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.LimitsOfProductsAndEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.HasColimitOfHasCoproductsOfHasCoequalizers.buildColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.LimitsOfProductsAndEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.HasColimitOfHasCoproductsOfHasCoequalizers.buildIsColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.LimitsOfProductsAndEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.colimitCoconeOfCoequalizerAndCoproduct", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.LimitsOfProductsAndEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasColimit_of_coequalizer_and_coproduct", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.LimitsOfProductsAndEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.colimitQuotientCoproduct", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.LimitsOfProductsAndEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.colimitQuotientCoproduct_epi", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Constructions.LimitsOfProductsAndEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.has_colimits_of_hasCoequalizers_and_coproducts", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.LimitsOfProductsAndEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasFiniteColimits_of_hasCoequalizers_and_finite_coproducts", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.LimitsOfProductsAndEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.preservesColimit_of_preservesCoequalizers_and_coproduct", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.LimitsOfProductsAndEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.preservesFiniteColimits_of_preservesCoequalizers_and_finiteCoproducts", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.LimitsOfProductsAndEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.preservesColimits_of_preservesCoequalizers_and_coproducts", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.LimitsOfProductsAndEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.createsColimitsOfShapeOfCreatesCoequalizersAndCoproducts", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.LimitsOfProductsAndEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.createsFiniteColimitsOfCreatesCoequalizersAndFiniteCoproducts", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.LimitsOfProductsAndEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.createsColimitsOfSizeOfCreatesCoequalizersAndCoproducts", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.LimitsOfProductsAndEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasFiniteColimits_of_hasInitial_and_pushouts", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.LimitsOfProductsAndEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.preservesFiniteColimits_of_preservesInitial_and_pushouts", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.LimitsOfProductsAndEqualizers", "is_tactic_proof": true, "tactics": ["haveI", "haveI", "preservesBinaryCoproducts_of_preservesInitial_and_pushouts", "haveI", "refine", "refine", "apply"], "tactic_count": 7}
{"name": "CategoryTheory.Limits.createsFiniteColimitsOfCreatesInitialAndPushouts", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.LimitsOfProductsAndEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.instHasPullbacks", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Constructions.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.instHasEqualizers", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Constructions.Over.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.hasFiniteLimits", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Constructions.Over.Basic", "is_tactic_proof": true, "tactics": ["have", "have", "apply"], "tactic_count": 3}
{"name": "CategoryTheory.Over.hasLimits", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Constructions.Over.Basic", "is_tactic_proof": true, "tactics": ["have", "have", "have", "apply"], "tactic_count": 4}
{"name": "CategoryTheory.CostructuredArrow.CreatesConnected.natTransInCostructuredArrow", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.Over.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.CreatesConnected.raiseCone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.Over.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.CreatesConnected.mapCone_raiseCone", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.Over.Connected", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.CostructuredArrow.CreatesConnected.isLimitRaiseCone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.Over.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.instCreatesLimitsOfShapeProjOfIsConnected", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Constructions.Over.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.instPreservesLimitsOfShapeProjOfIsConnected", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Constructions.Over.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.hasLimitsOfShape_of_isConnected", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Constructions.Over.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.createsLimitsOfShapeForgetOfIsConnected", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Constructions.Over.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.preservesLimitsOfShape_forget_of_isConnected", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Constructions.Over.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.hasLimitsOfShape_of_isConnected", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Constructions.Over.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.conePost", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.Over.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.conePostIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.Over.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.isLimitConePost", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.Over.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullbackConeEquivBinaryFan", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.Over.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsLimit.pullbackConeEquivBinaryFanFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.Over.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsLimit.pullbackConeEquivBinaryFanInverse", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.Over.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pushoutCoconeEquivBinaryCofan", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.Over.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsColimit.pushoutCoconeEquivBinaryCofanFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.Over.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsColimit.pushoutCoconeEquivBinaryCofanInverse", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.Over.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.isPullback_of_binaryFan_isLimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.Over.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.prodLeftIsoPullback", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.Over.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.prodLeftIsoPullback_hom_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.Over.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.prodLeftIsoPullback_hom_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.Over.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.prodLeftIsoPullback_inv_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.Over.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.prodLeftIsoPullback_inv_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.Over.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.ConstructProducts.widePullbackDiagramOfDiagramOver", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Constructions.Over.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.ConstructProducts.conesEquivInverseObj", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.Over.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.ConstructProducts.conesEquivInverse", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.Over.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.ConstructProducts.conesEquivFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.Over.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.ConstructProducts.conesEquivUnitIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.Over.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.ConstructProducts.conesEquivCounitIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.Over.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.ConstructProducts.conesEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.Over.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.ConstructProducts.has_over_limit_discrete_of_widePullback_limit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.Over.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.ConstructProducts.over_product_of_widePullback", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.Over.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.ConstructProducts.over_binaryProduct_of_pullback", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.Over.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.ConstructProducts.over_products_of_widePullbacks", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.Over.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.ConstructProducts.over_finiteProducts_of_finiteWidePullbacks", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.Over.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.over_hasTerminal", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.Over.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasLimit_cospan_of_hasLimit_pair_of_hasLimit_parallelPair", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasPullbacks_of_hasBinaryProducts_of_hasEqualizers", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasColimit_span_of_hasColimit_pair_of_hasColimit_parallelPair", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasPushouts_of_hasBinaryCoproducts_of_hasCoequalizers", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.has_weakly_initial_of_weakly_initial_set_and_hasProducts", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.WeaklyInitial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.hasInitial_of_weakly_initial_and_hasWideEqualizers", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.WeaklyInitial", "is_tactic_proof": true, "tactics": ["let", "let", "haveI", "have", "intro", "refine", "let", "let", "let", "have", "rw", "apply", "rw", "haveI", "rw", "apply", "exact"], "tactic_count": 17}
{"name": "CategoryTheory.Limits.binaryFanZeroLeft", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.ZeroObjects", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.binaryFanZeroLeftIsLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.ZeroObjects", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasBinaryProduct_zero_left", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Constructions.ZeroObjects", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.zeroProdIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.ZeroObjects", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.zeroProdIso_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.ZeroObjects", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.zeroProdIso_inv_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Constructions.ZeroObjects", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.binaryFanZeroRight", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.ZeroObjects", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.binaryFanZeroRightIsLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.ZeroObjects", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits.prodZeroIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Constructions.ZeroObjects", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.ObjectProperty.initial_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Final", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.final_snd", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Final.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.initial_fst", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Final.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits.parallelPair_initial_mk'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Final.ParallelPair", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Functor.sectionsPrecomp", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Final.Type", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.bijective_sectionsPrecomp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Final.Type", "is_tactic_proof": true, "tactics": ["refine", "ext", "let", "have", "have", "have", "dsimp", "rw", "have", "constant_of_preserves_morphisms", "intro", "dsimp", "rw", "dsimp", "rw", "choose", "refine", "let", "simp", "ext", "simpa"], "tactic_count": 21}
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{"name": "CategoryTheory.Functor.colimitTypePrecomp_ιColimitType", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Final.Type", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.FinallySmall.mk'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.FinallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FinalModel", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.FinallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.smallCategoryFinalModel", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.FinallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.fromFinalModel", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.FinallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.final_fromFinalModel", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.FinallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.finallySmall_of_essentiallySmall", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.FinallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.finallySmall_of_final_of_finallySmall", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.FinallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.InitiallySmall.mk'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.FinallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.InitialModel", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.FinallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.smallCategoryInitialModel", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.FinallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.fromInitialModel", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.FinallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.initial_fromInitialModel", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.FinallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.initiallySmall_of_essentiallySmall", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.FinallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.instInitiallySmallOppositeOfFinallySmall", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.FinallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FinallySmall.exists_small_weakly_terminal_set", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.FinallySmall", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact"], "tactic_count": 3}
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{"name": "CategoryTheory.Limits.hasLimitsOfShape_of_initiallySmall", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.FinallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits.FintypeCat.instPreservesFiniteLimitsFintypeCatForget", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.FintypeCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.FintypeCat.productEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.FintypeCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.FintypeCat.productEquiv_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.FintypeCat", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.FintypeCat.productEquiv_symm_comp_π_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.FintypeCat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "CategoryTheory.Limits.FintypeCat.finite_colimitType", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.FintypeCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.FintypeCat.finite_of_isColimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.FintypeCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.FintypeCat.finiteColimitOfFiniteDiagram", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.FintypeCat", "is_tactic_proof": true, "tactics": ["have", "apply"], "tactic_count": 2}
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{"name": "CategoryTheory.Limits.FintypeCat.instCreatesColimitsOfShapeFintypeCatForgetOfFinCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.FintypeCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.FintypeCat.instHasColimitsOfShapeFintypeCatOfFinCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.FintypeCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.FintypeCat.hasFiniteColimits", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.FintypeCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.FintypeCat.inclusion_preservesFiniteColimits", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.FintypeCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.FintypeCat.instPreservesFiniteColimitsFintypeCatForget", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.FintypeCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.FintypeCat.jointly_surjective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.FintypeCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits.FormalCoproduct.hom_ext_iff'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.FormalCoproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.FormalCoproduct.isoOfComponents", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.FormalCoproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits.FormalCoproduct.Hom.asSigma", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.FormalCoproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.FormalCoproduct.Hom.fromIncl_asSigma", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.FormalCoproducts", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.FormalCoproduct.inclHomEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.FormalCoproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.FormalCoproduct.fullyFaithfulIncl", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.FormalCoproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits.FormalCoproduct.instFaithfulIncl", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.FormalCoproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits.FormalCoproduct.cofan", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.FormalCoproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.FormalCoproduct.cofan_inj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.FormalCoproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits.FormalCoproduct.cofanHomEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.FormalCoproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits.FormalCoproduct.coproductIsoCofanPt", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.FormalCoproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.FormalCoproduct.ι_comp_coproductIsoCofanPt", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.FormalCoproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits.FormalCoproduct.cofanPtIsoSelf", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.FormalCoproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits.FormalCoproduct.coproductIsoSelf", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.FormalCoproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits.FormalCoproduct.pullbackCone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.FormalCoproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.FormalCoproduct.pullbackCone_fst_f", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.FormalCoproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.FormalCoproduct.pullbackCone_fst_φ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.FormalCoproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.FormalCoproduct.pullbackCone_snd_f", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.FormalCoproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.FormalCoproduct.pullbackCone_snd_φ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.FormalCoproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.FormalCoproduct.pullbackCone_condition", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.FormalCoproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.FormalCoproduct.homPullbackEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.FormalCoproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.FormalCoproduct.isLimitPullbackCone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.FormalCoproducts", "is_tactic_proof": false, "tactics": ["refine", "convert", "rw", "rfl"], "tactic_count": 4}
{"name": "CategoryTheory.Limits.FormalCoproduct.hasPullback_of_pullbackCone", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.FormalCoproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.FormalCoproduct.isPullback", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.FormalCoproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.FormalCoproduct.instHasPullback", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.FormalCoproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.FormalCoproduct.instHasPullbacks", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.FormalCoproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.FormalCoproduct.eval", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.FormalCoproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.FormalCoproduct.evalCompInclIsoId", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.FormalCoproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.FormalCoproduct.isColimitEvalMapCoconeCofan", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.FormalCoproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.FormalCoproduct.instPreservesColimitDiscreteFunctorObjFunctorEval", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.FormalCoproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.FormalCoproduct.instPreservesColimitsOfShapeDiscreteObjFunctorEval", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.FormalCoproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.FormalCoproduct.evalOp", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.FormalCoproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.FormalCoproduct.evalOpCompInlIsoId", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.FormalCoproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.FormalCoproduct.isLimitEvalMapConeCofanOp", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.FormalCoproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.FormalCoproduct.instPreservesLimitOppositeDiscreteFunctorCompOpObjFunctorEvalOp", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.FormalCoproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.DiagramOfCones.conePoints", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Fubini", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.DiagramOfCocones.coconePoints", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Fubini", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coneOfConeUncurry", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Fubini", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coneOfConeCurry", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Fubini", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coconeOfCoconeUncurry", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Fubini", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coconeOfCoconeCurry", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Fubini", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coneOfConeUncurryIsLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Fubini", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsLimit.ofConeOfConeUncurry", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Fubini", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coconeOfCoconeUncurryIsColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Fubini", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsColimit.ofCoconeUncurry", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Fubini", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.DiagramOfCones.mkOfHasLimits", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Fubini", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.diagramOfConesInhabited", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Fubini", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.DiagramOfCones.mkOfHasLimits_conePoints", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Fubini", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coneOfHasLimitCurryCompLim", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Fubini", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isLimitConeOfHasLimitCurryCompLim", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Fubini", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instHasLimitProd", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Fubini", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.limitUncurryIsoLimitCompLim", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Fubini", "is_tactic_proof": true, "tactics": ["let", "let", "let", "let", "have", "have", "exact"], "tactic_count": 7}
{"name": "CategoryTheory.Limits.limitUncurryIsoLimitCompLim_hom_π_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Fubini", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.limitUncurryIsoLimitCompLim_inv_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Fubini", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.DiagramOfCocones.mkOfHasColimits", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Fubini", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.diagramOfCoconesInhabited", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Fubini", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.DiagramOfCocones.mkOfHasColimits_coconePoints", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Fubini", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coconeOfHasColimitCurryCompColim", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Fubini", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isColimitCoconeOfHasColimitCurryCompColim", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Fubini", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instHasColimitProd", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Fubini", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.colimitUncurryIsoColimitCompColim", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Fubini", "is_tactic_proof": true, "tactics": ["let", "let", "let", "let", "have", "have", "exact"], "tactic_count": 7}
{"name": "CategoryTheory.Limits.colimitUncurryIsoColimitCompColim_ι_ι_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Fubini", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.colimitUncurryIsoColimitCompColim_ι_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Fubini", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.limitFlipCompLimIsoLimitCompLim", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Fubini", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.limitFlipCompLimIsoLimitCompLim_hom_π_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Fubini", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.limitFlipCompLimIsoLimitCompLim_inv_π_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Fubini", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "CategoryTheory.Limits.colimitFlipCompColimIsoColimitCompColim_ι_ι_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Fubini", "is_tactic_proof": true, "tactics": ["dsimp", "slice_lhs", "simp"], "tactic_count": 3}
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{"name": "CategoryTheory.Limits.limitIsoLimitCurryCompLim_inv_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Fubini", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.colimitIsoColimitCurryCompColim", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Fubini", "is_tactic_proof": true, "tactics": ["have", "haveI", "trans", "apply", "exact"], "tactic_count": 5}
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{"name": "CategoryTheory.Limits.limitCurrySwapCompLimIsoLimitCurryCompLim", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Fubini", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.limitCurrySwapCompLimIsoLimitCurryCompLim_hom_π_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Fubini", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "dsimp", "rw", "simp"], "tactic_count": 5}
{"name": "CategoryTheory.Limits.limitCurrySwapCompLimIsoLimitCurryCompLim_inv_π_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Fubini", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.colimitCurrySwapCompColimIsoColimitCurryCompColim", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Fubini", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.colimitCurrySwapCompColimIsoColimitCurryCompColim_ι_ι_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Fubini", "is_tactic_proof": true, "tactics": ["dsimp", "slice_lhs", "simp"], "tactic_count": 3}
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{"name": "CategoryTheory.Limits.createsLimitFullSubcategoryInclusion'", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.FullSubcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits.createsColimitFullSubcategoryInclusion'", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.FullSubcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.createsColimitFullSubcategoryInclusion", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.FullSubcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.createsLimitFullSubcategoryInclusionOfClosed", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.FullSubcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.createsLimitsOfShapeFullSubcategoryInclusion", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.FullSubcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasLimit_of_closedUnderLimits", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.FullSubcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasLimitsOfShape_of_closedUnderLimits", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.FullSubcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.createsColimitFullSubcategoryInclusionOfClosed", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.FullSubcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.createsColimitsOfShapeFullSubcategoryInclusion", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.FullSubcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasColimit_of_closedUnderColimits", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.FullSubcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasColimitsOfShape_of_closedUnderColimits", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.FullSubcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.isClosedUnderColimitsOfShape_of_preservesColimitsOfShape_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.FullSubcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits.instIsClosedUnderLimitsOfShapeEssImageOfHasLimitsOfShapeOfPreservesLimitsOfShapeOfFullOfFaithful", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.FullSubcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instIsClosedUnderColimitsOfShapeEssImageOfHasColimitsOfShapeOfPreservesColimitsOfShapeOfFullOfFaithful", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.FullSubcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.limit.lift_π_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.colimit.ι_desc_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.evaluationJointlyReflectsLimits", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.combineCones", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.evaluateCombinedCones", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.combinedIsLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.evaluationJointlyReflectsColimits", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.combineCocones", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.evaluateCombinedCocones", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.combinedIsColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits.pointwiseIsColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Basic", "is_tactic_proof": true, "tactics": ["apply", "exact"], "tactic_count": 2}
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{"name": "CategoryTheory.Limits.functorCategoryHasLimitsOfShape", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.functorCategoryHasColimit", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.functorCategoryHasColimitsOfShape", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.functorCategoryHasLimitsOfSize", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.functorCategoryHasColimitsOfSize", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasLimitCompEvaluation", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.evaluation_preservesLimit", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.evaluation_preservesLimitsOfShape", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.limitObjIsoLimitCompEvaluation", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.limitObjIsoLimitCompEvaluation_hom_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.limitObjIsoLimitCompEvaluation_inv_π_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.limit_map_limitObjIsoLimitCompEvaluation_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.limitObjIsoLimitCompEvaluation_inv_limit_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.limit_obj_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Basic", "is_tactic_proof": true, "tactics": ["apply", "ext", "simpa"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.limitCompWhiskeringLeftIsoCompLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.limitCompWhiskeringLeftIsoCompLimit_hom_whiskerLeft_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.limitCompWhiskeringLeftIsoCompLimit_inv_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.hasColimitCompEvaluation", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.evaluation_preservesColimit", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.evaluation_preservesColimitsOfShape", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.colimitObjIsoColimitCompEvaluation", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.colimitObjIsoColimitCompEvaluation_ι_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.colimitObjIsoColimitCompEvaluation_ι_app_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.colimitObjIsoColimitCompEvaluation_inv_colimit_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.colimit_map_colimitObjIsoColimitCompEvaluation_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.colimit_obj_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Basic", "is_tactic_proof": true, "tactics": ["apply", "ext", "simpa"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.colimitCompWhiskeringLeftIsoCompColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.ι_colimitCompWhiskeringLeftIsoCompColimit_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.whiskerLeft_ι_colimitCompWhiskeringLeftIsoCompColimit_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.evaluationPreservesLimits", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.preservesLimit_of_evaluation", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.preservesLimitsOfShape_of_evaluation", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.preservesLimits_of_evaluation", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.preservesLimits_const", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.evaluation_preservesColimits", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.preservesColimit_of_evaluation", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.preservesColimitsOfShape_of_evaluation", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.preservesColimits_of_evaluation", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.preservesColimits_const", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.limitIsoFlipCompLim", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.limIsoFlipCompWhiskerLim", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.limitFlipIsoCompLim", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.limCompFlipIsoWhiskerLim", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.limitIsoSwapCompLim", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.colimitIsoFlipCompColim", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.colimIsoFlipCompWhiskerColim", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.colimitFlipIsoCompColim", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.colimCompFlipIsoWhiskerColim", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.colimitIsoSwapCompColim", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instMonoAppOfFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.mono_iff_mono_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instMonoFunctorWhiskerRightOfPreservesMonomorphisms", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.EpiMono", "is_tactic_proof": true, "tactics": ["have", "apply"], "tactic_count": 2}
{"name": "CategoryTheory.instEpiAppOfFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.epi_iff_epi_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instEpiFunctorWhiskerRightOfPreservesEpimorphisms", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.EpiMono", "is_tactic_proof": true, "tactics": ["have", "apply"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.instHasFilteredColimitsOfSizeFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Filtered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instHasCofilteredLimitsOfSizeFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Filtered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instHasFiniteLimitsFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instHasFiniteProductsFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instHasFiniteColimitsFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instHasFiniteCoproductsFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instPreservesFiniteLimitsFunctorObjEvaluationOfHasFiniteLimits", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instPreservesFiniteColimitsFunctorObjEvaluationOfHasFiniteColimits", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FunctorToTypes.monoFactorisation", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FunctorToTypes.monoFactorisationIsImage", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FunctorToTypes.instHasImagesFunctorType", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FunctorToTypes.instHasStrongEpiMonoFactorisationsFunctorType", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.kerIsKernel", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.cokerIsCokernel", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.piObjIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.piObjIso_hom_comp_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Shapes.Products", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.piObjIso_inv_comp_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Shapes.Products", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.sigmaObjIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.ι_comp_sigmaObjIso_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Shapes.Products", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.ι_comp_sigmaObjIso_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Shapes.Products", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.PullbackCone.combine", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Shapes.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PullbackCone.combineIsLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Shapes.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullbackObjIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Shapes.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullbackObjIso_hom_comp_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Shapes.Pullbacks", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.pullbackObjIso_hom_comp_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Shapes.Pullbacks", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.pullbackObjIso_inv_comp_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Shapes.Pullbacks", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.pullbackObjIso_inv_comp_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Shapes.Pullbacks", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.pushoutObjIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Shapes.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.inl_comp_pushoutObjIso_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Shapes.Pullbacks", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.inr_comp_pushoutObjIso_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Shapes.Pullbacks", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.inl_comp_pushoutObjIso_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Shapes.Pullbacks", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.inr_comp_pushoutObjIso_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.FunctorCategory.Shapes.Pullbacks", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.FunctorToTypes.jointly_surjective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.FunctorToTypes", "is_tactic_proof": true, "tactics": ["let", "obtain", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.FunctorToTypes.jointly_surjective'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.FunctorToTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FunctorToTypes.colimit.map_ι_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.FunctorToTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.HasLimit.mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.HasLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.getLimitCone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.HasLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.HasLimits", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.HasLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.HasLimits.has_limits_of_shape", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.HasLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasLimitOfHasLimitsOfShape", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.HasLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasLimitsOfShapeOfHasLimits", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.HasLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.limit.cone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.HasLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.limit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.HasLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.limit.π", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.HasLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.limit.π_comp_eqToHom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.HasLimits", "is_tactic_proof": true, "tactics": ["subst", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.limit.cone_x", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.HasLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.limit.cone_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.HasLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.limit.w", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.HasLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.limit.isLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.HasLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.limit.lift", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.HasLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.limit.isLimit_lift", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.HasLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.limit.lift_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.HasLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.limMap", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.HasLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.limMap_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.HasLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.limit.coneMorphism", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.HasLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.limit.coneMorphism_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.HasLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.limit.coneMorphism_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.HasLimits", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.limit.conePointUniqueUpToIso_hom_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.HasLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.limit.conePointUniqueUpToIso_inv_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.HasLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.limit.existsUnique", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.HasLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.limit.isoLimitCone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.HasLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits.isIndObject_colimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Indization.FilteredColimits", "is_tactic_proof": false, "tactics": ["have", "refine", "have", "choose", "refine", "obtain", "let", "obtain", "refine", "simp", "exact", "refine", "refine", "simp"], "tactic_count": 14}
{"name": "CategoryTheory.Limits.IndObjectPresentation.ofCocone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Indization.IndObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IndObjectPresentation.instSmallCategoryI", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Indization.IndObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IndObjectPresentation.instIsFilteredI", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Indization.IndObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IndObjectPresentation.cocone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Indization.IndObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IndObjectPresentation.coconeIsColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Indization.IndObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IndObjectPresentation.extend", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Indization.IndObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IndObjectPresentation.toCostructuredArrow", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Indization.IndObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IndObjectPresentation.instFinalICostructuredArrowFunctorOppositeTypeYonedaToCostructuredArrow", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Indization.IndObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IndObjectPresentation.yoneda", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Indization.IndObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsIndObject.mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Indization.IndObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isIndObject_yoneda", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Indization.IndObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsIndObject.map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Indization.IndObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsIndObject.iff_of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Indization.IndObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsIndObject.instIsClosedUnderIsomorphismsFunctorOppositeType", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Indization.IndObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsIndObject.presentation", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Indization.IndObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsIndObject.isFiltered", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Indization.IndObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsIndObject.finallySmall", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Indization.IndObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isIndObject_of_isFiltered_of_finallySmall", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Indization.IndObject", "is_tactic_proof": false, "tactics": ["have", "inclusion", "have", "let", "let", "have", "exact"], "tactic_count": 7}
{"name": "CategoryTheory.Limits.isIndObject_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Indization.IndObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isIndObject_limit_comp_yoneda", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Indization.IndObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isIndObject_iff_preservesFiniteLimits", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Indization.IndObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.colimitYonedaHomEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Indization.LocallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.colimitYonedaHomEquiv_π_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Indization.LocallySmall", "is_tactic_proof": false, "tactics": ["simp", "have", "dsimp", "rw", "simp"], "tactic_count": 5}
{"name": "CategoryTheory.instSmallHomFunctorOppositeTypeColimitCompYoneda", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Indization.LocallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instLocallySmallFullSubcategoryFunctorOppositeTypeIsIndObject", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Indization.LocallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instSmallCategoryI", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Indization.ParallelPair", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instIsFilteredI", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Indization.ParallelPair", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NonemptyParallelPairPresentationAux.K", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Indization.ParallelPair", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NonemptyParallelPairPresentationAux.F₁", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Indization.ParallelPair", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NonemptyParallelPairPresentationAux.F₂", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Indization.ParallelPair", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NonemptyParallelPairPresentationAux.ι₁", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Indization.ParallelPair", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NonemptyParallelPairPresentationAux.isColimit₁", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Indization.ParallelPair", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NonemptyParallelPairPresentationAux.ι₂", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Indization.ParallelPair", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NonemptyParallelPairPresentationAux.isColimit₂", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Indization.ParallelPair", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NonemptyParallelPairPresentationAux.ϕ", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Indization.ParallelPair", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NonemptyParallelPairPresentationAux.hf", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Indization.ParallelPair", "is_tactic_proof": true, "tactics": ["refine", "rw", "simpa"], "tactic_count": 3}
{"name": "CategoryTheory.NonemptyParallelPairPresentationAux.ψ", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Indization.ParallelPair", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NonemptyParallelPairPresentationAux.hg", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Indization.ParallelPair", "is_tactic_proof": true, "tactics": ["refine", "rw", "simpa"], "tactic_count": 3}
{"name": "CategoryTheory.NonemptyParallelPairPresentationAux.presentation", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Indization.ParallelPair", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.nonempty_indParallelPairPresentation", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Indization.ParallelPair", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IndParallelPairPresentation.parallelPairIsoParallelPairCompYoneda", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Indization.ParallelPair", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isIndObject_pi", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Indization.Products", "is_tactic_proof": true, "tactics": ["let", "suffices", "refine", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.Limits.isIndObject_limit_of_discrete", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Indization.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isIndObject_limit_of_discrete_of_hasLimitsOfShape", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Indization.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Types.constPUnitFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.IsConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Types.pUnitCocone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.IsConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Types.isColimitPUnitCocone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.IsConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Types.instHasColimitConstPUnitFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.IsConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Types.instSubsingletonColimitPUnit", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.IsConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Types.colimitConstPUnitIsoPUnit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.IsConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Types.zigzag_of_eqvGen_colimitTypeRel", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.IsConnected", "is_tactic_proof": true, "tactics": ["induction", "rel", "refl", "symm", "trans"], "tactic_count": 5}
{"name": "CategoryTheory.Limits.Types.isConnected_iff_colimit_constPUnitFunctor_iso_pUnit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.IsConnected", "is_tactic_proof": true, "tactics": ["refine", "have", "refine", "refine", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.Limits.Types.isConnected_iff_isColimit_pUnitCocone", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.IsConnected", "is_tactic_proof": true, "tactics": ["refine", "let", "have", "simp", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.Functor.isConnected_iff_of_final", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.IsConnected", "is_tactic_proof": false, "tactics": ["rw", "isConnected_iff_colimit_constPUnitFunctor_iso_pUnit.", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Functor.isConnected_iff_of_initial", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.IsConnected", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.isConnected_of_isInitial", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.IsConnected", "is_tactic_proof": true, "tactics": ["letI", "apply", "intro", "use", "simp", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.isConnected_of_isTerminal", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.IsConnected", "is_tactic_proof": true, "tactics": ["letI", "apply", "intro", "use", "simp", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.isConnected_of_hasInitial", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.IsConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isConnected_of_hasTerminal", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.IsConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsLimit.subsingleton", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.IsLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsLimit.map", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.IsLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsLimit.map_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.IsLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsLimit.lift_self", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.IsLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsLimit.liftConeMorphism", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.IsLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsLimit.uniq_cone_morphism", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.IsLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsLimit.existsUnique", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.IsLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsLimit.ofExistsUnique", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.IsLimit", "is_tactic_proof": true, "tactics": ["choose", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.IsLimit.mkConeMorphism", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.IsLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsLimit.uniqueUpToIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.IsLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsLimit.hom_isIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.IsLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.IsLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso_hom_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.IsLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso_inv_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.IsLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsLimit.lift_comp_conePointUniqueUpToIso_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.IsLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsLimit.lift_comp_conePointUniqueUpToIso_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.IsLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsLimit.ofIsoLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.IsLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsLimit.ofIsoLimit_lift", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.IsLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsLimit.equivIsoLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.IsLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsLimit.equivIsoLimit_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.IsLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsLimit.equivIsoLimit_symm_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.IsLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsLimit.ofPointIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.IsLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsLimit.hom_lift", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.IsLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsLimit.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.IsLimit", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.IsLimit.nonempty_isLimit_iff_isIso_lift", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.IsLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsLimit.ofRightAdjoint", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.IsLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsLimit.ofConeEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.IsLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsLimit.ofConeEquiv_apply_desc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.IsLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsLimit.ofConeEquiv_symm_apply_desc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.IsLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsLimit.postcomposeHomEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.IsLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsLimit.postcomposeInvEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.IsLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsLimit.equivOfNatIsoOfIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.IsLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.IsLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_hom_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.IsLimit", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_inv_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.IsLimit", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.IsLimit.lift_comp_conePointsIsoOfNatIso_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.IsLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsLimit.lift_comp_conePointsIsoOfNatIso_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.IsLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsLimit.whiskerEquivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.IsLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsLimit.ofWhiskerEquivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.IsLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsLimit.whiskerEquivalenceEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.IsLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsLimit.extendIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.IsLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsLimit.ofExtendIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.IsLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsLimit.extendIsoEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.IsLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsLimit.conePointsIsoOfEquivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.IsLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits.MonoCoprod.isColimitBinaryCofanSum", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.MonoCoprod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits.MonoCoprod.mono_map'_of_injective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.MonoCoprod", "is_tactic_proof": true, "tactics": ["convert", "apply", "intro", "rw", "simp"], "tactic_count": 5}
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{"name": "CategoryTheory.Limits.MonoCoprod.monoCoprod_of_preservesCoprod_of_reflectsMono", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.MonoCoprod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.MonoCoprod.instOfPreservesColimitsOfShapeDiscreteWalkingPairOfReflectsMonomorphismsForget", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.MonoCoprod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.MorphismProperty.Comma.forgetCreatesLimitOfClosed", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.MorphismProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits.isColimitOfConeOfCoconeRightOp", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits.hasLimit_of_hasColimit_leftOp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits.limitOpIsoOpColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.limitOpIsoOpColimit_inv_comp_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Opposites", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "CategoryTheory.Limits.limitLeftOpIsoUnopColimit_inv_comp_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Opposites", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "CategoryTheory.Limits.limitRightOpIsoOpColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.limitRightOpIsoOpColimit_inv_comp_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Opposites", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "CategoryTheory.Limits.limitUnopIsoUnopColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.limitUnopIsoUnopColimit_inv_comp_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Opposites", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.limitUnopIsoUnopColimit_hom_comp_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Opposites", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "CategoryTheory.Limits.hasLimitsOfShape_of_hasColimitsOfShape_op", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits.hasColimit_of_hasLimit_op", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasColimit_of_hasLimit_rightOp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits.hasColimit_op_of_hasLimit", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasColimit_leftOp_of_hasLimit", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasColimit_rightOp_of_hasLimit", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasColimit_unop_of_hasLimit", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.colimitOpIsoOpLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.ι_comp_colimitOpIsoOpLimit_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Opposites", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.π_comp_colimitOpIsoOpLimit_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Opposites", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.colimitLeftOpIsoUnopLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.ι_comp_colimitLeftOpIsoUnopLimit_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Opposites", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.π_comp_colimitLeftOpIsoUnopLimit_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Opposites", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.colimitRightOpIsoUnopLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.ι_comp_colimitRightOpIsoUnopLimit_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Opposites", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.π_comp_colimitRightOpIsoUnopLimit_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Opposites", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.colimitUnopIsoOpLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.ι_comp_colimitUnopIsoOpLimit_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Opposites", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "CategoryTheory.Limits.hasColimitsOfShape_of_hasLimitsOfShape_op", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasColimits_op_of_hasLimits", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits.hasFiniteColimits_opposite", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Over.instHasColimitsOfShape", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.instHasFiniteColimits", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.instHasColimits", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.instHasFiniteCoproducts", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Over._example", "kind": "example", "module": "Mathlib.CategoryTheory.Limits.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.epi_left_of_epi", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Over.createsColimitsOfSizeMapCompForget", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.preservesColimitsOfSize_map", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.isColimitToOver", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.colimit.isColimitToOver", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.liftCocone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.isColimitLiftCocone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.hasLimit_of_hasLimit_comp_forget", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.instHasLimitsOfShape", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.instHasLimits", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.mono_right_of_mono", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.mono_iff_mono_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.createsLimitsOfSize", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Under._example", "kind": "example", "module": "Mathlib.CategoryTheory.Limits.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.createLimitsOfSizeMapCompForget", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.preservesLimitsOfSize_map", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.isLimitToUnder", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.limit.isLimitToOver", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.liftCone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Under.isLimitLiftCone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.pi.coneCompEval", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.pi.coconeCompEval", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.pi.coneOfConeCompEval", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.pi.coconeOfCoconeCompEval", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.pi.coneOfConeEvalIsLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.pi.coconeOfCoconeEvalIsColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.pi.hasLimit_of_hasLimit_comp_eval", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.pi.hasColimit_of_hasColimit_comp_eval", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Preorder.coneOfLowerBound", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preorder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Preorder.conePt_mem_lowerBounds", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preorder", "is_tactic_proof": true, "tactics": ["intro"], "tactic_count": 1}
{"name": "Preorder.isGLB_of_isLimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preorder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Preorder.isLimitOfIsGLB", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preorder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Preorder.limitConeOfIsGLB", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preorder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Preorder.hasLimit_iff_hasGLB", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preorder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Preorder.coconeOfUpperBound", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preorder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Preorder.coconePt_mem_upperBounds", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preorder", "is_tactic_proof": true, "tactics": ["intro"], "tactic_count": 1}
{"name": "Preorder.isLUB_of_isColimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preorder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Preorder.isColimitOfIsLUB", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preorder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Preorder.colimitCoconeOfIsLUB", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preorder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Preorder.hasColimit_iff_hasLUB", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preorder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsTerminal.orderTop", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preorder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Preorder.orderTopOfHasTerminal", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preorder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Preorder.isTerminalTop", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preorder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Preorder.instHasTerminalOfOrderTop", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Preorder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsInitial.orderBot", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preorder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Preorder.orderBotOfHasInitial", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preorder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Preorder.isInitialBot", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preorder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Preorder.instHasInitialOfOrderBot", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Preorder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Preorder.semilatticeInfOfIsLimitBinaryFan", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preorder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Preorder.semilatticeInfOfHasBinaryProducts", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preorder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Preorder.semilatticeSupOfIsColimitBinaryCofan", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preorder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Preorder.semilatticeSupOfHasBinaryCoproducts", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preorder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Preorder.isLimitBinaryFan", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preorder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Preorder.instHasBinaryProducts", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Preorder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Preorder.instHasBinaryCoproducts", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Preorder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.ColimitPresentation.w", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Presentation", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "CategoryTheory.Limits.ColimitPresentation.hasColimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Presentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits.ColimitPresentation.colimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Presentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.ColimitPresentation.map", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Presentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits.ColimitPresentation.ofIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Presentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits.LimitPresentation.w", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Presentation", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.LimitPresentation.cone", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Presentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.LimitPresentation.hasLimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Presentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.LimitPresentation.self", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Presentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.LimitPresentation.limit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Presentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits.LimitPresentation.ofIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Presentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits.PreservesLimits", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Preserves.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PreservesColimits", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Preserves.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isLimitOfPreserves", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isColimitOfPreserves", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits.id_preservesColimitsOfSize", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Preserves.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instHasLimitCompOfPreservesLimit", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Preserves.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instHasColimitCompOfPreservesColimit", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Preserves.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.comp_preservesLimit", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Preserves.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.comp_preservesLimitsOfShape", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Preserves.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits.comp_preservesColimit", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Preserves.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.comp_preservesColimitsOfShape", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Preserves.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.comp_preservesColimits", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Preserves.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.preservesLimit_of_preserves_limit_cone", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.preservesLimit_of_iso_diagram", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.preservesLimit_of_natIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.preservesLimitsOfShape_of_natIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.preservesLimits_of_natIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.preservesLimitsOfShape_of_equiv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.preservesLimitsOfSize_of_univLE", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.preservesLimitsOfSize_shrink", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.preservesSmallestLimits_of_preservesLimits", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits.preservesSmallestColimits_of_preservesColimits", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits.isLimitOfReflects", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits.HasPullback.of_createsLimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Creates.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits.PreservesFiniteLimitsOfIsFilteredCostructuredArrowYonedaAux.iso_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Presheaf", "is_tactic_proof": true, "tactics": ["dsimp", "simp", "rw", "refine", "simp", "rw", "colimitObjIsoColimitCompEvaluation_ι_inv_assoc", "isoAux_hom_app,", "preservesLimitIso_hom_π_assoc,", "colimit.comp_coconePointUniqueUpToIso_hom]", "have", "dsimp", "rw", "ext", "simp"], "tactic_count": 15}
{"name": "CategoryTheory.Limits.PreservesFiniteLimitsOfIsFilteredCostructuredArrowYonedaAux.isIso_post", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.preservesFiniteLimits_of_isFiltered_costructuredArrow_yoneda", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isFiltered_costructuredArrow_yoneda_iff_nonempty_preservesFiniteLimits", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.PreservesImage.iso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.AbelianImages", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.PreservesImage.iso_hom_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.AbelianImages", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Abelian.PreservesImage.factorThruImage_iso_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.AbelianImages", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Abelian.PreservesImage.iso_inv_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.AbelianImages", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Abelian.PreservesImage.factorThruImage_iso_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.AbelianImages", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Abelian.PreservesCoimage.iso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.AbelianImages", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Abelian.PreservesCoimage.iso_hom_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.AbelianImages", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Abelian.PreservesCoimage.factorThruCoimage_iso_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.AbelianImages", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Abelian.PreservesCoimage.factorThruCoimage_iso_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.AbelianImages", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Abelian.PreservesCoimage.iso_inv_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.AbelianImages", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Abelian.PreservesCoimage.hom_coimageImageComparison", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.AbelianImages", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Abelian.PreservesCoimageImageComparison.iso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.AbelianImages", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isLimitMapConeBinaryFanEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.mapIsLimitOfPreservesOfIsLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isLimitOfReflectsOfMapIsLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isLimitOfHasBinaryProductOfPreservesLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instHasBinaryProductObjOfPreservesLimitDiscreteWalkingPairPair", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PreservesLimitPair.of_iso_prod_comparison", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.BinaryProducts", "is_tactic_proof": true, "tactics": ["apply", "apply", "refine", "apply"], "tactic_count": 4}
{"name": "CategoryTheory.Limits.PreservesLimitPair.iso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PreservesLimitPair.iso_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PreservesLimitPair.iso_inv_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.BinaryProducts", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.PreservesLimitPair.iso_inv_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.BinaryProducts", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.instIsIsoProdComparison", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.BinaryProducts", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.preservesBinaryProducts_of_isIso_prodComparison", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isColimitMapCoconeBinaryCofanEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.mapIsColimitOfPreservesOfIsColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isColimitOfReflectsOfMapIsColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isColimitOfHasBinaryCoproductOfPreservesColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PreservesColimitPair.of_iso_coprod_comparison", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.BinaryProducts", "is_tactic_proof": true, "tactics": ["apply", "apply", "refine", "apply"], "tactic_count": 4}
{"name": "CategoryTheory.Limits.PreservesColimitPair.iso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PreservesColimitPair.iso_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instIsIsoCoprodComparison", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.BinaryProducts", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.preservesBinaryCoproducts_of_isIso_coprodComparison", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapBicone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapBicone_whisker", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapBinaryBicone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isBilimitOfPreserves", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.preservesBiproducts_shrink", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.preservesFiniteBiproductsOfPreservesBiproducts", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isBinaryBilimitOfPreserves", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.preservesBinaryBiproduct_of_preservesBiproduct", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.preservesBinaryBiproducts_of_preservesBiproducts", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.biproductComparison", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.biproductComparison_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.biproductComparison'", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.ι_biproductComparison'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.biproductComparison'_comp_biproductComparison", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Biproducts", "is_tactic_proof": true, "tactics": ["classical", "ext", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.Functor.splitEpiBiproductComparison", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instIsSplitEpiBiproductComparison", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.splitMonoBiproductComparison'", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instIsSplitMonoBiproductComparison'", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.hasBiproduct_of_preserves", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.hasBiproduct_of_preserves'", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapBiproduct", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapBiproduct_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapBiproduct_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.biprodComparison", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.biprodComparison_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.biprodComparison_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.biprodComparison'", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.inl_biprodComparison'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.inr_biprodComparison'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.biprodComparison'_comp_biprodComparison", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Biproducts", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.splitEpiBiprodComparison", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instIsSplitEpiBiprodComparison", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.splitMonoBiprodComparison'", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instIsSplitMonoBiprodComparison'", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.hasBinaryBiproduct_of_preserves", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapBiprod", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapBiprod_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapBiprod_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biproduct.map_lift_mapBiprod", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Biproducts", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.biproduct.mapBiproduct_inv_map_desc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Biproducts", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.biproduct.mapBiproduct_hom_desc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Biproducts", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.biprod.map_lift_mapBiprod", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Biproducts", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.biprod.lift_mapBiprod", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Biproducts", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.biprod.mapBiprod_inv_map_desc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Biproducts", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.biprod.mapBiprod_hom_desc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Biproducts", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.isLimitMapConeForkEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isLimitForkMapOfIsLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isLimitOfIsLimitForkMap", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isLimitOfHasEqualizerOfPreservesLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PreservesEqualizer.of_iso_comparison", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Equalizers", "is_tactic_proof": true, "tactics": ["apply", "apply", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.PreservesEqualizer.iso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PreservesEqualizer.iso_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PreservesEqualizer.iso_inv_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Equalizers", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.instIsIsoEqualizerComparison", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Equalizers", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.isColimitMapCoconeCoforkEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isColimitCoforkMapOfIsColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isColimitOfIsColimitCoforkMap", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isColimitOfHasCoequalizerOfPreservesColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.of_iso_comparison", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Equalizers", "is_tactic_proof": true, "tactics": ["apply", "apply", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.PreservesCoequalizer.iso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PreservesCoequalizer.iso_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instIsIsoCoequalizerComparison", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Equalizers", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.map_π_epi", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.map_π_preserves_coequalizer_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Equalizers", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.map_π_preserves_coequalizer_inv_desc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Equalizers", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.map_π_preserves_coequalizer_inv_colimMap", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Equalizers", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.map_π_preserves_coequalizer_inv_colimMap_desc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Equalizers", "is_tactic_proof": true, "tactics": ["slice_lhs", "slice_lhs"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.preservesSplitCoequalizers", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Equalizers", "is_tactic_proof": true, "tactics": ["apply", "apply"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.preservesSplitEqualizers", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Equalizers", "is_tactic_proof": true, "tactics": ["apply", "apply"], "tactic_count": 2}
{"name": "CategoryTheory.PreservesImage.iso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreservesImage.factorThruImage_comp_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Images", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.PreservesImage.hom_comp_map_image_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Images", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.PreservesImage.inv_comp_image_ι_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Images", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.KernelFork.map_condition", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Kernels", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.KernelFork.map", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.KernelFork.map_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.KernelFork.isLimitMapConeEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Kernels", "is_tactic_proof": true, "tactics": ["refine", "refine", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.KernelFork.mapIsLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isLimitMapConeForkEquiv'", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isLimitForkMapOfIsLimit'", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isLimitOfHasKernelOfPreservesLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instHasKernelMapOfPreservesLimitWalkingParallelPairParallelPairOfNatHom", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PreservesKernel.of_iso_comparison", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Kernels", "is_tactic_proof": true, "tactics": ["apply", "apply", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.PreservesKernel.iso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PreservesKernel.iso_inv_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PreservesKernel.iso_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Kernels", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.instIsIsoKernelComparison", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Kernels", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.kernel_map_comp_preserves_kernel_iso_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Kernels", "is_tactic_proof": true, "tactics": ["rw", "kernelComparison_comp_kernel_map]"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.CokernelCofork.map_condition", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Kernels", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.CokernelCofork.map", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.CokernelCofork.map_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.CokernelCofork.isColimitMapCoconeEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Kernels", "is_tactic_proof": true, "tactics": ["refine", "refine", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.CokernelCofork.mapIsColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isColimitMapCoconeCoforkEquiv'", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isColimitCoforkMapOfIsColimit'", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isColimitOfHasCokernelOfPreservesColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instHasCokernelMapOfPreservesColimitWalkingParallelPairParallelPairOfNatHom", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PreservesCokernel.of_iso_comparison", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Kernels", "is_tactic_proof": true, "tactics": ["apply", "apply", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.PreservesCokernel.iso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PreservesCokernel.π_iso_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PreservesCokernel.iso_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Kernels", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.instIsIsoCokernelComparison", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Kernels", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.preserves_cokernel_iso_comp_cokernel_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Kernels", "is_tactic_proof": true, "tactics": ["rw", "cokernel_map_comp_cokernelComparison,"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.preservesKernel_zero", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.preservesCokernel_zero", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.preservesKernel_zero'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Kernels", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.preservesCokernel_zero'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Kernels", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.MultispanIndex.map", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.MultispanIndex.multispanMapIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Multicofork.map", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Multicofork.isColimitMapEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Multicofork.isColimitMapOfPreserves", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PreservesLimitsOfShape.ofWidePullbacks", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PreservesLimitsOfShape.overPost", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PreservesFiniteLimits.overPost", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PreservesLimitsOfSize.overPost", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PreservesColimitsOfShape.underPost", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PreservesFiniteColimits.underPost", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PreservesColimitsOfSize.underPost", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.preservesColimitsOfShape_of_preservesWellOrderContinuousOfShape", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Preorder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instIsWellOrderContinuousCompOfPreservesWellOrderContinuousOfShape", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Preorder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instPreservesWellOrderContinuousOfShapeComp", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Preorder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instPreservesWellOrderContinuousOfShapeFunctorObjEvaluationOfHasIterationOfShape", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Preorder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instPreservesWellOrderContinuousOfShapeArrowLeftFuncOfHasIterationOfShape", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Preorder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instPreservesWellOrderContinuousOfShapeArrowRightFuncOfHasIterationOfShape", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Preorder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isLimitMapConeFanMkEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Products", "is_tactic_proof": true, "tactics": ["refine", "refine", "refine"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.isLimitFanMkObjOfIsLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isLimitOfIsLimitFanMkObj", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isLimitOfHasProductOfPreservesLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PreservesProduct.of_iso_comparison", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Products", "is_tactic_proof": true, "tactics": ["apply", "apply", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.inv_piComparison_comp_map_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Products", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.PreservesProduct.iso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PreservesProduct.iso_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instIsIsoPiComparison", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Products", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.isColimitMapCoconeCofanMkEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Products", "is_tactic_proof": true, "tactics": ["refine", "refine", "refine"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.isColimitCofanMkObjOfIsColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isColimitOfIsColimitCofanMkObj", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isColimitOfHasCoproductOfPreservesColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PreservesCoproduct.of_iso_comparison", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Products", "is_tactic_proof": true, "tactics": ["apply", "apply", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.map_ι_comp_inv_sigmaComparison", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Products", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.PreservesCoproduct.iso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PreservesCoproduct.inv_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instIsIsoSigmaComparison", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Products", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.preservesLimitsOfShape_of_discrete", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.preservesColimitsOfShape_of_discrete", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PullbackCone.map", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PullbackCone.isLimitMapConeEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isLimitMapConePullbackConeEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isLimitPullbackConeMapOfIsLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isLimitOfIsLimitPullbackConeMap", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isLimitOfHasPullbackOfPreservesLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.preservesPullback_symmetry", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasPullback_of_preservesPullback", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PreservesPullback.iso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PreservesPullback.iso_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PreservesPullback.iso_hom_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Pullbacks", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.PreservesPullback.iso_hom_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Pullbacks", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.PreservesPullback.iso_inv_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Pullbacks", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.PreservesPullback.iso_inv_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Pullbacks", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.PullbackCone.isLimitCoyonedaEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PushoutCocone.map", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PushoutCocone.isColimitMapCoconeEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isColimitMapCoconePushoutCoconeEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isColimitPushoutCoconeMapOfIsColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isColimitOfIsColimitPushoutCoconeMap", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isColimitOfHasPushoutOfPreservesColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.preservesPushout_symmetry", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasPushout_of_preservesPushout", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PreservesPushout.iso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PreservesPushout.iso_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PreservesPushout.inl_iso_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Pullbacks", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.PreservesPushout.inr_iso_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Pullbacks", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.PreservesPushout.inl_iso_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Pullbacks", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.PreservesPushout.inr_iso_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Pullbacks", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.PreservesPullback.of_iso_comparison", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Pullbacks", "is_tactic_proof": true, "tactics": ["apply", "apply", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.instIsIsoPullbackComparison", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Pullbacks", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.PreservesPushout.of_iso_comparison", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Pullbacks", "is_tactic_proof": true, "tactics": ["apply", "apply", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.instIsIsoPushoutComparison", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Pullbacks", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.PushoutCocone.isColimitYonedaEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Square.IsPullback.map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Square.IsPullback.of_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Square.IsPullback.map_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Square.IsPushout.map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Square.IsPushout.of_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Square.IsPushout.map_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Square.isPullback_iff_map_coyoneda_isPullback", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Square.isPushout_iff_op_map_yoneda_isPullback", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Square.IsPullback.iff_of_equiv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square", "is_tactic_proof": true, "tactics": ["rw", "refine", "iff_of_iso", "all_goals", "simpa", "simpa", "simpa", "simpa"], "tactic_count": 8}
{"name": "CategoryTheory.Square.IsPullback.of_equiv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isLimitMapConeEmptyConeEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsTerminal.isTerminalObj", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsTerminal.isTerminalOfObj", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsTerminal.isTerminalIffObj", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.preservesLimitsOfShape_pempty_of_preservesTerminal", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isLimitOfHasTerminalOfPreservesLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasTerminal_of_hasTerminal_of_preservesLimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PreservesTerminal.of_iso_comparison", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Terminal", "is_tactic_proof": true, "tactics": ["apply", "apply", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.preservesTerminal_of_isIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Terminal", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.preservesTerminal_of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PreservesTerminal.iso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PreservesTerminal.iso_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instIsIsoTerminalComparison", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Terminal", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.isColimitMapCoconeEmptyCoconeEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsInitial.isInitialObj", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsInitial.isInitialOfObj", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsInitial.isInitialIffObj", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.preservesColimitsOfShape_pempty_of_preservesInitial", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isColimitOfHasInitialOfPreservesColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasInitial_of_hasInitial_of_preservesColimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PreservesInitial.of_iso_comparison", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Terminal", "is_tactic_proof": true, "tactics": ["apply", "apply", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.preservesInitial_of_isIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Terminal", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.preservesInitial_of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PreservesInitial.iso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PreservesInitial.iso_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instIsIsoInitialComparison", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Terminal", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.map_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.map_isZero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Zero", "is_tactic_proof": true, "tactics": ["simp", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.zero_of_map_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.map_eq_zero_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.preservesZeroMorphisms_of_isLeftAdjoint", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.preservesZeroMorphisms_of_isRightAdjoint", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.preservesZeroMorphisms_of_full", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.preservesZeroMorphisms_comp", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.preservesZeroMorphisms_of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.preservesZeroMorphisms_evaluation_obj", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instPreservesZeroMorphismsFlipOfObj", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instPreservesZeroMorphismsObjFlip", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.whiskerRight_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Zero", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.mapZeroObject", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.preservesZeroMorphisms_of_map_zero_object", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.preservesZeroMorphisms_of_preserves_initial_object", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.preservesZeroMorphisms_of_preserves_terminal_object", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.preservesTerminalObject_of_preservesZeroMorphisms", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.preservesInitialObject_of_preservesZeroMorphisms", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.preservesLimitsOfShape_of_isZero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.preservesColimitsOfShape_of_isZero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.preservesLimitsOfSize_of_isZero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.preservesColimitsOfSize_of_isZero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Types.sectionsEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Ulift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Types.instPreservesLimitsOfSizeUliftFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Preserves.Ulift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Types.instCreatesLimitsOfSizeUliftFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Preserves.Ulift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Types.instPreservesColimitsOfSizeUliftFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Preserves.Ulift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Types.instCreatesColimitsOfSizeUliftFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Preserves.Ulift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.yonedaYonedaColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Preserves.Yoneda", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.yonedaYonedaColimit_app_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Preserves.Yoneda", "is_tactic_proof": true, "tactics": ["dsimp", "simp", "apply", "intro", "rw", "simp", "rw", "simp", "rw", "ext", "simp"], "tactic_count": 11}
{"name": "CategoryTheory.instPreservesColimitFunctorOppositeTypeObjCoyonedaOpYoneda", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Preserves.Yoneda", "is_tactic_proof": true, "tactics": ["suffices", "suffices", "colimit.post", "from", "rw"], "tactic_count": 5}
{"name": "CategoryTheory.Presheaf.restrictedULiftYoneda", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.map_comp_uliftYonedaEquiv_down", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Presheaf", "is_tactic_proof": true, "tactics": ["have", "dsimp", "simp", "simp"], "tactic_count": 4}
{"name": "CategoryTheory.Presheaf.restrictedULiftYonedaHomEquiv'", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.restrictedULiftYonedaHomEquiv'_symm_naturality_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Presheaf", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "CategoryTheory.Presheaf.restrictedULiftYonedaHomEquiv'_symm_app_naturality_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf._example", "kind": "example", "module": "Mathlib.CategoryTheory.Limits.Presheaf", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "CategoryTheory.Presheaf.restrictedULiftYonedaHomEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.uliftYonedaAdjunction", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.uliftYonedaAdjunction_homEquiv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Presheaf", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Presheaf.uliftYonedaAdjunction_unit_app_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Presheaf", "is_tactic_proof": true, "tactics": ["have", "simp", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.Presheaf.preservesColimitsOfSize_of_isLeftKanExtension", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.isIso_of_isLeftKanExtension", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.preservesColimitsOfSize_leftKanExtension", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.instIsIsoFunctorLeftKanExtensionUnitOppositeTypeUliftYoneda", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.isExtensionAlongULiftYoneda", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.functorToRepresentables", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.coconeOfRepresentable", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.coconeOfRepresentable_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Presheaf", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Presheaf.colimitOfRepresentable", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf._example", "kind": "example", "module": "Mathlib.CategoryTheory.Limits.Presheaf", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "CategoryTheory.Presheaf.instIsIsoFunctorOfIsLeftKanExtensionOppositeType", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.isLeftKanExtension_along_uliftYoneda_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Presheaf", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "preservesColimits_of_natIso", "rintro", "apply", "intro", "dsimp", "apply", "let", "functorToRepresentables.", "refine", "exact"], "tactic_count": 13}
{"name": "CategoryTheory.Presheaf.isLeftKanExtension_of_preservesColimits", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Presheaf", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Presheaf.uniqueExtensionAlongULiftYoneda", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.instIsLeftKanExtensionFunctorOppositeTypeIdCompUliftYonedaOfPreservesColimitsOfSizeOfHasPointwiseLeftKanExtension", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.isLeftAdjoint_of_preservesColimits", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.instUniqueHomLeftExtensionOppositeOpObjFunctorTypeYonedaMkYonedaMap", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.instIsLeftKanExtensionOppositeObjFunctorTypeYonedaYonedaMap", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.instUniqueHomLeftExtensionOppositeOpObjFunctorTypeUliftYonedaMkUliftYonedaMap", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.instIsLeftKanExtensionOppositeObjFunctorTypeUliftYonedaUliftYonedaMap", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan_inv_app_app_apply_eq_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.coconeApp", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.coconeApp_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Presheaf", "is_tactic_proof": false, "tactics": ["have", "uliftYonedaEquiv.injective", "have", "congr_fun", "have", "have", "dsimp", "apply", "dsimp", "rw", "simp", "simp"], "tactic_count": 12}
{"name": "CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.presheafHom", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.uliftYonedaEquiv_ι_presheafHom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Presheaf", "is_tactic_proof": true, "tactics": ["obtain", "erw", "dsimp", "apply"], "tactic_count": 4}
{"name": "CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.uliftYonedaEquiv_presheafHom_uliftYoneda_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Presheaf", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.presheafHom_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.natTrans", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.natTrans_app_uliftYoneda_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Presheaf", "is_tactic_proof": true, "tactics": ["dsimp", "apply", "rw", "apply", "rw", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.extensionHom", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Presheaf", "is_tactic_proof": true, "tactics": ["ext", "apply", "apply", "intro", "have", "have", "have", "dsimp", "simp", "congr", "simp", "apply", "dsimp", "rw"], "tactic_count": 14}
{"name": "CategoryTheory.Presheaf.instUniqueHomLeftExtensionFunctorOppositeTypeUliftYonedaCompMkLanOpHomCompULiftYonedaIsoULiftYonedaCompLan", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.instIsLeftKanExtensionFunctorOppositeTypeLanOpHomCompULiftYonedaIsoULiftYonedaCompLan", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.tautologicalCocone'", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.isColimitTautologicalCocone'", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.tautologicalCocone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.isColimitTautologicalCocone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.final_toCostructuredArrow_comp_pre", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Presheaf", "is_tactic_proof": true, "tactics": ["apply", "suffices", "apply", "apply", "refine", "apply", "exact", "apply", "let", "isColimitOfPreserves", "exact"], "tactic_count": 11}
{"name": "Set.instPreservesColimitsOfShapeFunctorToTypesOfIsFilteredOrEmpty", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryBicone.category", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryBiconeMorphism.ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": true, "tactics": ["cases", "cases", "congr"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.BinaryBicones.functoriality", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryBicones.functoriality_full", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryBicones.functoriality_faithful", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryBicone.toCone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryBicone.toCone_pt", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryBicone.toCone_π_app_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryBicone.toCone_π_app_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryBicone.binary_fan_fst_toCone", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryBicone.binary_fan_snd_toCone", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryBicone.toCocone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryBicone.toCocone_pt", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryBicone.toCocone_ι_app_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryBicone.toCocone_ι_app_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryBicone.binary_cofan_inl_toCocone", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryBicone.binary_cofan_inr_toCocone", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryBicone.instIsSplitMonoInl", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryBicone.instIsSplitMonoInr", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryBicone.instIsSplitEpiFst", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryBicone.instIsSplitEpiSnd", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryBicone.toBiconeFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryBicone.toBicone", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryBicone.toBiconeIsLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryBicone.toBiconeIsColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Bicone.toBinaryBiconeFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Bicone.toBinaryBicone", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Bicone.toBinaryBiconeIsLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Bicone.toBinaryBiconeIsColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryBicone.toBiconeIsBilimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Bicone.toBinaryBiconeIsBilimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.HasBinaryBiproduct.mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.getBinaryBiproductData", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryBiproduct.bicone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryBiproduct.isBilimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryBiproduct.isLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryBiproduct.isColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasBinaryBiproducts_of_finite_biproducts", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.HasBinaryBiproduct.hasLimit_pair", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.HasBinaryBiproduct.hasColimit_pair", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasBinaryProducts_of_hasBinaryBiproducts", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasBinaryCoproducts_of_hasBinaryBiproducts", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biprodIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biprod", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.term_⊞_", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits._aux_Mathlib_CategoryTheory_Limits_Shapes_BinaryBiproducts___macroRules_CategoryTheory_Limits_term_⊞__1", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits._aux_Mathlib_CategoryTheory_Limits_Shapes_BinaryBiproducts___unexpand_CategoryTheory_Limits_biprod_1", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biprod.fst", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biprod.snd", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biprod.inl", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biprod.inr", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryBiproduct.bicone_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryBiproduct.bicone_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryBiproduct.bicone_inl", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryBiproduct.bicone_inr", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biprod.inl_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biprod.inl_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biprod.inr_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biprod.inr_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biprod.lift", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biprod.desc", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biprod.lift_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biprod.lift_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biprod.inl_desc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biprod.inr_desc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biprod.mono_lift_of_mono_left", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biprod.mono_lift_of_mono_right", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biprod.epi_desc_of_epi_left", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biprod.epi_desc_of_epi_right", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biprod.map", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biprod.map'", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biprod.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biprod.hom_ext'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biprod.isoProd", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biprod.isoProd_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.biprod.isoProd_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.biprod.isoCoprod", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biprod.isoCoprod_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.biprod_isoCoprod_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.biprod.map_eq_map'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": true, "tactics": ["ext", "simp", "simp", "simp", "simp", "simp", "simp", "simp", "simp"], "tactic_count": 9}
{"name": "CategoryTheory.Limits.biprod.inl_mono", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biprod.inr_mono", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biprod.fst_epi", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biprod.snd_epi", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biprod.map_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biprod.map_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biprod.inl_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.biprod.inr_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.biprod.mapIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biprod.conePointUniqueUpToIso_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biprod.conePointUniqueUpToIso_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": true, "tactics": ["refine", "all_goals", "simp", "rcases", "all_goals"], "tactic_count": 5}
{"name": "CategoryTheory.Limits.biprod.uniqueUpToIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biprod.isIso_inl_iff_id_eq_fst_comp_inl", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": true, "tactics": ["constructor", "intro", "have", "rw", "rw", "intro", "exact"], "tactic_count": 7}
{"name": "CategoryTheory.Limits.biprod.map_epi", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.prod.map_epi", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.biprod.map_mono", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.coprod.map_mono", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.BinaryBicone.fstKernelFork", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryBicone.fstKernelFork_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryBicone.sndKernelFork", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryBicone.sndKernelFork_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryBicone.inlCokernelCofork", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryBicone.inlCokernelCofork_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryBicone.inrCokernelCofork", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryBicone.inrCokernelCofork_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryBicone.isLimitFstKernelFork", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryBicone.isLimitSndKernelFork", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryBicone.isColimitInlCokernelCofork", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryBicone.isColimitInrCokernelCofork", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biprod.fstKernelFork", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biprod.fstKernelFork_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biprod.isKernelFstKernelFork", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biprod.sndKernelFork", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biprod.sndKernelFork_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biprod.isKernelSndKernelFork", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biprod.inlCokernelCofork", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biprod.inlCokernelCofork_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biprod.isCokernelInlCokernelFork", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biprod.inrCokernelCofork", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biprod.inrCokernelCofork_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biprod.isCokernelInrCokernelFork", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instHasKernelFst", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.kernelBiprodFstIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instHasKernelSnd", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.kernelBiprodSndIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instHasCokernelInl", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.cokernelBiprodInlIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instHasCokernelInr", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.cokernelBiprodInrIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isoBiprodZero", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isoZeroBiprod", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biprod_isZero_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": true, "tactics": ["constructor", "intro", "simp", "simp", "show", "rintro", "rw", "apply", "apply", "apply"], "tactic_count": 10}
{"name": "CategoryTheory.Limits.biprod.braiding", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biprod.braiding'", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biprod.braiding'_eq_braiding", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.biprod.braid_natural", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.biprod.braiding_map_braiding", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.biprod.symmetry'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.biprod.symmetry", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.biprod.associator", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biprod.associator_natural", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.biprod.associator_inv_natural", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Indecomposable", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isIso_left_of_isIso_biprod_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isIso_right_of_isIso_biprod_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingPair", "kind": "inductive", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instDecidableEqWalkingPair", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instInhabitedWalkingPair.default", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instInhabitedWalkingPair", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingPair.swap", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingPair.swap_apply_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingPair.swap_apply_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingPair.swap_symm_apply_tt", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingPair.swap_symm_apply_ff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingPair.equivBool", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingPair.equivBool_apply_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingPair.equivBool_apply_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingPair.equivBool_symm_apply_true", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingPair.equivBool_symm_apply_false", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pairFunction", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pairFunction_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pairFunction_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pair", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pair_obj_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pair_obj_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.mapPair", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.mapPair_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.mapPair_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.mapPairIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.diagramIsoPair", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pairComp", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryFan", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryFan.fst", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryFan.snd", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryFan.π_app_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryFan.π_app_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryFan.ext", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryFan.ext_hom_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryFan.IsLimit.mk", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryFan.IsLimit.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryCofan", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryCofan.inl", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryCofan.inr", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryCofan.ext", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryCofan.ext_hom_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryCofan.ι_app_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryCofan.ι_app_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryCofan.IsColimit.mk", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryCofan.IsColimit.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryFan.mk", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryCofan.mk", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryFan.mk_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryFan.mk_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryCofan.mk_inl", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryCofan.mk_inr", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isoBinaryFanMk", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isoBinaryCofanMk", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryFan.isLimitMk", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryCofan.isColimitMk", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryFan.IsLimit.lift'", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryCofan.IsColimit.desc'", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryFan.isLimitFlip", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryFan.isLimit_iff_isIso_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "obtain", "exact", "intro", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.Limits.BinaryFan.isLimit_iff_isIso_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.BinaryFan.isLimitCompLeftIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": true, "tactics": ["fapply", "exact", "simp", "simp", "intro", "apply", "simpa", "simpa"], "tactic_count": 8}
{"name": "CategoryTheory.Limits.BinaryFan.isLimitCompRightIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryCofan.isColimitFlip", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryCofan.isColimit_iff_isIso_inl", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "obtain", "refine", "rw", "have", "rwa", "intro", "exact"], "tactic_count": 9}
{"name": "CategoryTheory.Limits.BinaryCofan.isColimit_iff_isIso_inr", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.BinaryCofan.isColimitCompLeftIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": true, "tactics": ["fapply", "exact", "simp", "simp", "intro", "apply", "rw", "simpa", "simpa"], "tactic_count": 9}
{"name": "CategoryTheory.Limits.BinaryCofan.isColimitCompRightIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.HasBinaryProduct", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.HasBinaryCoproduct", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.prod", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coprod", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.term_⨯_", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits._aux_Mathlib_CategoryTheory_Limits_Shapes_BinaryProducts___macroRules_CategoryTheory_Limits_term_⨯__1", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits._aux_Mathlib_CategoryTheory_Limits_Shapes_BinaryProducts___unexpand_CategoryTheory_Limits_prod_1", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.term_⨿_", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits._aux_Mathlib_CategoryTheory_Limits_Shapes_BinaryProducts___macroRules_CategoryTheory_Limits_term_⨿__1", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits._aux_Mathlib_CategoryTheory_Limits_Shapes_BinaryProducts___unexpand_CategoryTheory_Limits_coprod_1", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.prod.fst", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.prod.snd", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coprod.inl", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coprod.inr", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.prodIsProd", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coprodIsCoprod", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.prod.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coprod.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.prod.lift", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.diag", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coprod.desc", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.codiag", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.prod.lift_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.prod.lift_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coprod.inl_desc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coprod.inr_desc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.prod.mono_lift_of_mono_left", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.prod.mono_lift_of_mono_right", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coprod.epi_desc_of_epi_left", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coprod.epi_desc_of_epi_right", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.prod.lift'", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coprod.desc'", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.prod.map", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coprod.map", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.prod.comp_lift", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.prod.comp_diag", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.prod.map_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.prod.map_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.prod.map_id_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.prod.lift_fst_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.prod.lift_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.prod.lift_fst_comp_snd_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.prod.map_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.prod.map_swap", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.prod.map_comp_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.prod.map_id_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.prod.mapIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isIso_prod", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.prod.map_mono", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.prod.diag_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.prod.diag_map_fst_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.prod.diag_map_fst_snd_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.instIsSplitMonoDiag", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coprod.desc_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.coprod.diag_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.coprod.inl_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coprod.inr_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coprod.map_id_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.coprod.desc_inl_inr", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.coprod.map_desc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.coprod.desc_comp_inl_comp_inr", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.coprod.map_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.coprod.map_swap", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.coprod.map_comp_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.coprod.map_id_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.coprod.mapIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isIso_coprod", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coprod.map_epi", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coprod.map_codiag", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.coprod.map_inl_inr_codiag", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.coprod.map_comp_inl_inr_codiag", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.HasBinaryProducts", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.HasBinaryCoproducts", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasBinaryProducts_of_hasLimit_pair", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasBinaryCoproducts_of_hasColimit_pair", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.prod.braiding", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.braid_natural", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.prod.symmetry'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.prod.symmetry", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.prod.associator", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.prod.pentagon", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.prod.associator_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.prod.leftUnitor", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.prod.rightUnitor", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.prod.leftUnitor_hom_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.prod.leftUnitor_inv_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.prod.rightUnitor_hom_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.prod_rightUnitor_inv_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.prod.triangle", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.coprod.braiding", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coprod.symmetry'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coprod.symmetry", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coprod.associator", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coprod.pentagon", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.coprod.associator_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.coprod.leftUnitor", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coprod.rightUnitor", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coprod.triangle", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.prod.functor", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.prod.functorLeftComp", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coprod.functor", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coprod.functorLeftComp", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.prodComparison", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.prodComparison_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.prodComparison_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.prodComparison_natural", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": true, "tactics": ["rw", "prod.map_fst,"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.prodComparison_natural_of_natTrans", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.prodComparisonNatTrans", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.inv_prodComparison_map_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.inv_prodComparison_map_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.prodComparison_inv_natural", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.prodComparisonNatIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": true, "tactics": ["refine", "apply"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.prodComparison_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": true, "tactics": ["unfold", "ext"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.coprodComparison", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coprodComparison_inl", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coprodComparison_inr", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coprodComparison_natural", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": true, "tactics": ["rw", "coprod.inl_map,"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.coprodComparisonNatTrans", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.map_inl_inv_coprodComparison", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.map_inr_inv_coprodComparison", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.coprodComparison_inv_natural", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.coprodComparisonNatIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.coprodObj", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.coprod", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryFan.op", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryCofan.op", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryFan.unop", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryCofan.unop", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryFan.op_mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryFan.unop_mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryCofan.op_mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryCofan.unop_mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryFan.IsLimit.op", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryCofan.IsColimit.op", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryFan.IsLimit.unop", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryCofan.IsColimit.unop", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryFan.swap", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryFan.swap_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryFan.swap_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsLimit.binaryFanSwap", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.HasBinaryProduct.swap", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryFan.braiding", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryFan.braiding_hom_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryFan.braiding_hom_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryFan.braiding_inv_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryFan.braiding_inv_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryFan.assoc", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryFan.assoc_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryFan.assoc_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryFan.assocInv", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryFan.assocInv_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryFan.assocInv_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsLimit.assoc", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryFan.associator", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryFan.associatorOfLimitCone", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryFan.leftUnitor", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryFan.rightUnitor", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.bicone_ι_π_self", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.bicone_ι_π_ne", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.Bicone.category", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BiconeMorphism.ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": true, "tactics": ["cases", "cases", "congr"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.Bicones.functoriality", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Bicones.functoriality_full", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Bicones.functoriality_faithful", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Bicone.toConeFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Bicone.toCone", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Bicone.toCone_pt", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Bicone.toCone_π_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Bicone.toCone_π_app_mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Bicone.toCone_proj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Bicone.toCoconeFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Bicone.toCocone", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Bicone.toCocone_pt", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Bicone.toCocone_ι_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Bicone.toCocone_inj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Bicone.toCocone_ι_app_mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Bicone.ofLimitCone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Bicone.ι_of_isLimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Bicone.ofColimitCocone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Bicone.π_of_isColimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Bicone.subsingleton_isBilimit", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Bicone.whisker", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Bicone.whiskerToCone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Bicone.whiskerToCocone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Bicone.whiskerIsBilimitIff", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": true, "tactics": ["refine", "let", "let", "exact", "let", "let", "exact", "apply", "apply", "exact", "apply", "apply", "exact"], "tactic_count": 13}
{"name": "CategoryTheory.Limits.HasBiproduct.mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.getBiproductData", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biproduct.bicone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biproduct.isBilimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biproduct.isLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biproduct.isColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasProduct_of_hasBiproduct", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasCoproduct_of_hasBiproduct", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasBiproductsOfShape_of_equiv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasBiproductsOfShape_finite", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": true, "tactics": ["rcases", "haveI", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.hasFiniteProducts_of_hasFiniteBiproducts", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasFiniteCoproducts_of_hasFiniteBiproducts", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasProductsOfShape_of_hasBiproductsOfShape", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasCoproductsOfShape_of_hasBiproductsOfShape", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biproductIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biproduct", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.term⨁_", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits._aux_Mathlib_CategoryTheory_Limits_Shapes_Biproducts___macroRules_CategoryTheory_Limits_term⨁__1", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits._aux_Mathlib_CategoryTheory_Limits_Shapes_Biproducts___unexpand_CategoryTheory_Limits_biproduct_1", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biproduct.π", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biproduct.bicone_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biproduct.ι", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biproduct.bicone_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biproduct.ι_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.biproduct.ι_π_self", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.biproduct.ι_π_ne", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.biproduct.eqToHom_comp_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": true, "tactics": ["cases", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.biproduct.π_comp_eqToHom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.biproduct.lift", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biproduct.desc", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biproduct.lift_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biproduct.ι_desc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biproduct.map", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biproduct.map'", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biproduct.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biproduct.hom_ext'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biproduct.isoProduct", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biproduct.isoProduct_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biproduct.isoProduct_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biproduct.isoCoproduct", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biproduct.isoCoproduct_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biproduct.isoCoproduct_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.HasBiproductsOfShape.colimIsoLim", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biproduct.map_eq_map'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": true, "tactics": ["classical", "ext", "dsimp", "simp", "dsimp", "rw", "split_ifs", "subst", "simp"], "tactic_count": 9}
{"name": "CategoryTheory.Limits.biproduct.map_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biproduct.ι_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.biproduct.map_desc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.biproduct.lift_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.biproduct.mapIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biproduct.map_epi", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": true, "tactics": ["classical", "have", "ext", "simp", "ι_π_assoc]", "split", "all_goals", "rw", "infer_instance"], "tactic_count": 9}
{"name": "CategoryTheory.Limits.Pi.map_epi", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.biproduct.map_mono", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.Sigma.map_mono", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.biproduct.whiskerEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biproduct.whiskerEquiv_hom_eq_lift", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": true, "tactics": ["simp", "ext", "by_cases", "subst", "simp", "simp", "rw", "simp", "rintro", "simp", "exact"], "tactic_count": 11}
{"name": "CategoryTheory.Limits.biproduct.whiskerEquiv_inv_eq_lift", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": true, "tactics": ["simp", "ext", "by_cases", "subst", "simp", "eqToHom_comp_ι,", "simp", "rw", "simp", "exact", "rintro", "simp"], "tactic_count": 12}
{"name": "CategoryTheory.Limits.instHasBiproductSigmaFstSndOfBiproduct", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biproductBiproductIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biproduct.fromSubtype", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biproduct.toSubtype", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biproduct.fromSubtype_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": true, "tactics": ["classical", "ext", "rw", "by_cases", "rw", "split_ifs", "exacts", "rw"], "tactic_count": 8}
{"name": "CategoryTheory.Limits.biproduct.fromSubtype_eq_lift", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biproduct.fromSubtype_π_subtype", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": true, "tactics": ["classical", "ext", "rw", "split_ifs", "exacts"], "tactic_count": 5}
{"name": "CategoryTheory.Limits.biproduct.toSubtype_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biproduct.ι_toSubtype", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": true, "tactics": ["classical", "ext", "rw", "by_cases", "rw", "split_ifs", "exacts", "rw"], "tactic_count": 8}
{"name": "CategoryTheory.Limits.biproduct.toSubtype_eq_desc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biproduct.ι_toSubtype_subtype", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": true, "tactics": ["classical", "ext", "rw", "split_ifs", "exacts"], "tactic_count": 5}
{"name": "CategoryTheory.Limits.biproduct.ι_fromSubtype", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biproduct.fromSubtype_toSubtype", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.biproduct.toSubtype_fromSubtype", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": true, "tactics": ["ext1", "by_cases", "simp", "simp"], "tactic_count": 4}
{"name": "CategoryTheory.Limits.biproduct.isLimitFromSubtype", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instHasKernelπ", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.kernelBiproductπIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biproduct.isColimitToSubtype", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instHasCokernelι", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.cokernelBiproductιIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.kernelForkBiproductToSubtype", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instHasKernelToSubtype", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.kernelBiproductToSubtypeIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.cokernelCoforkBiproductFromSubtype", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instHasCokernelFromSubtype", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.cokernelBiproductFromSubtypeIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biproduct.matrix", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biproduct.matrix_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.biproduct.ι_matrix", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.biproduct.components", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biproduct.matrix_components", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.biproduct.components_matrix", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.biproduct.matrixEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biproduct.ι_mono", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.biproduct.π_epi", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.biproduct.conePointUniqueUpToIso_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biproduct.conePointUniqueUpToIso_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": true, "tactics": ["classical", "refine", "rw", "biproduct.ι_desc,"], "tactic_count": 4}
{"name": "CategoryTheory.Limits.biproduct.uniqueUpToIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasZeroObject_of_hasFiniteBiproducts", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": true, "tactics": ["refine", "intro", "intro"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.limitBiconeOfUnique", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasBiproduct_unique", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biproductUniqueIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Fan.combPairHoms", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.CombinedProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Fan.combPairIsLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.CombinedProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cofan.combPairHoms", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.CombinedProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cofan.combPairIsColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.CombinedProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Concrete.productEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.ConcreteCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Concrete.productEquiv_apply_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ConcreteCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Concrete.productEquiv_symm_apply_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ConcreteCategory", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.Concrete.Pi.map_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ConcreteCategory", "is_tactic_proof": true, "tactics": ["apply", "apply", "intro", "rw", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.Limits.Concrete.uniqueOfTerminalOfPreserves", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.ConcreteCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Concrete.terminalOfUniqueOfReflects", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.ConcreteCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Concrete.terminalIffUnique", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.ConcreteCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Concrete.terminalEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.ConcreteCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Concrete.instUniqueToTypeTerminal", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.ConcreteCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Concrete.empty_of_initial_of_preserves", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ConcreteCategory", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.Concrete.initial_of_empty_of_reflects", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ConcreteCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Concrete.initial_iff_empty_of_preserves_of_reflects", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ConcreteCategory", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.Concrete.prodEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.ConcreteCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Concrete.prodEquiv_apply_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ConcreteCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Concrete.prodEquiv_apply_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ConcreteCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Concrete.prodEquiv_symm_apply_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ConcreteCategory", "is_tactic_proof": true, "tactics": ["obtain", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.Concrete.prodEquiv_symm_apply_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ConcreteCategory", "is_tactic_proof": true, "tactics": ["obtain", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.Concrete.pullbackEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.ConcreteCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Concrete.pullbackMk", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.ConcreteCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Concrete.pullbackMk_surjective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ConcreteCategory", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.Concrete.pullbackMk_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ConcreteCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Concrete.pullbackMk_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ConcreteCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Concrete.widePullback_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ConcreteCategory", "is_tactic_proof": true, "tactics": ["apply", "rintro", "exact", "apply"], "tactic_count": 4}
{"name": "CategoryTheory.Limits.Concrete.widePullback_ext'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ConcreteCategory", "is_tactic_proof": true, "tactics": ["apply", "inhabit", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.Concrete.multiequalizer_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ConcreteCategory", "is_tactic_proof": true, "tactics": ["apply", "rintro", "apply", "rw", "simp"], "tactic_count": 5}
{"name": "CategoryTheory.Limits.Concrete.multiequalizerEquivAux", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.ConcreteCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Concrete.multiequalizerEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.ConcreteCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Concrete.multiequalizerEquiv_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ConcreteCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Concrete.widePushout_exists_rep", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ConcreteCategory", "is_tactic_proof": true, "tactics": ["obtain", "left", "use", "rfl", "right", "use", "rfl"], "tactic_count": 7}
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{"name": "CategoryTheory.Limits.Concrete.cokernel_funext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ConcreteCategory", "is_tactic_proof": true, "tactics": ["ext", "simpa"], "tactic_count": 2}
{"name": "CategoryTheory.instIsConnectedWidePullbackShape", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Connected", "is_tactic_proof": true, "tactics": ["apply", "intro", "suffices", "rintro", "exacts"], "tactic_count": 5}
{"name": "CategoryTheory.instIsConnectedWidePushoutShape", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Connected", "is_tactic_proof": true, "tactics": ["apply", "intro", "suffices", "rintro", "exacts"], "tactic_count": 5}
{"name": "CategoryTheory.Limits.hasFiniteLimits_of_hasCountableLimits", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasCountableLimits_of_hasLimits", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instHasLimitsOfShapeOfHasCountableLimitsOfCountableCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instHasProductsOfShapeOfHasCountableProductsOfCountable", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasCountableProducts_of_hasProducts", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasCountableProducts_of_hasCountableLimits", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasFiniteProducts_of_hasCountableProducts", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasFiniteColimits_of_hasCountableColimits", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasCountableColimits_of_hasColimits", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instHasColimitsOfShapeOfHasCountableColimitsOfCountableCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasCountableCoproducts_of_hasCoproducts", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instHasCoproductsOfShapeOfHasCountableCoproductsOfCountable", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasCountableCoproducts_of_hasCountableColimits", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasFiniteCoproducts_of_hasCountableCoproducts", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsFiltered.sequentialFunctor_obj", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsFiltered.sequentialFunctor_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsFiltered.sequentialFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsFiltered.sequentialFunctor_final_aux", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Countable", "is_tactic_proof": true, "tactics": ["obtain", "refine", "simpa", "leOfHom"], "tactic_count": 4}
{"name": "CategoryTheory.Limits.IsFiltered.sequentialFunctor_final", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsCofiltered.sequentialFunctor_obj", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsCofiltered.sequentialFunctor_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsCofiltered.sequentialFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsCofiltered.sequentialFunctor_initial_aux", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Countable", "is_tactic_proof": true, "tactics": ["obtain", "refine", "simpa", "leOfHom"], "tactic_count": 4}
{"name": "CategoryTheory.Limits.IsCofiltered.sequentialFunctor_initial", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsCofiltered.preorder_of_cofiltered", "kind": "proofWanted", "module": "Mathlib.CategoryTheory.Limits.Shapes.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsCofiltered.preorder_of_cofiltered_countable", "kind": "proofWanted", "module": "Mathlib.CategoryTheory.Limits.Shapes.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsCofiltered.hasCofilteredCountableLimits_of_hasSequentialLimits", "kind": "proofWanted", "module": "Mathlib.CategoryTheory.Limits.Shapes.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsCofiltered.hasCountableLimits_of_hasFiniteLimits_and_hasSequentialLimits", "kind": "proofWanted", "module": "Mathlib.CategoryTheory.Limits.Shapes.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsCofiltered.hasCountableColimits_of_hasFiniteColimits_and_hasSequentialColimits", "kind": "proofWanted", "module": "Mathlib.CategoryTheory.Limits.Shapes.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullback.diagonalObj", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullback.diagonal", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullback.diagonal_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullback.diagonal_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullback.instIsSplitMonoDiagonal", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullback.instIsSplitEpiFst", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullback.instIsSplitEpiSnd", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullback.instIsIsoDiagonalOfMono", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Diagonal", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.pullback.isIso_diagonal_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullback.diagonal_isKernelPair", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullback_diagonal_map_snd_fst_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Diagonal", "is_tactic_proof": true, "tactics": ["conv_rhs", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.pullback_diagonal_map_snd_snd_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Diagonal", "is_tactic_proof": true, "tactics": ["conv_rhs", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.pullbackDiagonalMapIso.hom", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullbackDiagonalMapIso.inv", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullbackDiagonalMapIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullbackDiagonalMapIso.hom_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Diagonal", "is_tactic_proof": true, "tactics": ["delta", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.pullbackDiagonalMapIso.hom_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Diagonal", "is_tactic_proof": true, "tactics": ["delta", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.pullbackDiagonalMapIso.inv_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Diagonal", "is_tactic_proof": true, "tactics": ["delta", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.pullbackDiagonalMapIso.inv_snd_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Diagonal", "is_tactic_proof": true, "tactics": ["delta", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.pullbackDiagonalMapIso.inv_snd_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Diagonal", "is_tactic_proof": true, "tactics": ["delta", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.pullback_fst_map_snd_isPullback", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullbackDiagonalMapIdIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Diagonal", "is_tactic_proof": true, "tactics": ["refine", "refine", "rw", "rw", "rw", "ext", "infer_instance", "refine", "rw", "rw", "infer_instance"], "tactic_count": 11}
{"name": "CategoryTheory.Limits.pullbackDiagonalMapIdIso_hom_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Diagonal", "is_tactic_proof": true, "tactics": ["delta", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.pullbackDiagonalMapIdIso_hom_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Diagonal", "is_tactic_proof": true, "tactics": ["delta", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.pullbackDiagonalMapIdIso_inv_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Diagonal", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.pullbackDiagonalMapIdIso_inv_snd_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Diagonal", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.pullbackDiagonalMapIdIso_inv_snd_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Diagonal", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.pullback.diagonal_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Diagonal", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.pullback.comp_diagonal", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Diagonal", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.pullback_map_diagonal_isPullback", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Diagonal", "is_tactic_proof": true, "tactics": ["apply", "simp", "ext", "constructor", "ext"], "tactic_count": 5}
{"name": "CategoryTheory.Limits.diagonalObjPullbackFstIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.diagonalObjPullbackFstIso_hom_fst_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Diagonal", "is_tactic_proof": true, "tactics": ["delta", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.diagonalObjPullbackFstIso_hom_fst_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Diagonal", "is_tactic_proof": true, "tactics": ["delta", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.diagonalObjPullbackFstIso_hom_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Diagonal", "is_tactic_proof": true, "tactics": ["delta", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.diagonalObjPullbackFstIso_inv_fst_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Diagonal", "is_tactic_proof": true, "tactics": ["delta", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.diagonalObjPullbackFstIso_inv_fst_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Diagonal", "is_tactic_proof": true, "tactics": ["delta", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.diagonalObjPullbackFstIso_inv_snd_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Diagonal", "is_tactic_proof": true, "tactics": ["delta", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.diagonalObjPullbackFstIso_inv_snd_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Diagonal", "is_tactic_proof": true, "tactics": ["delta", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.diagonal_pullback_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Diagonal", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.pullback_lift_diagonal_isPullback", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Diagonal", "is_tactic_proof": true, "tactics": ["let", "let", "pullback", "pullback", "apply", "simp", "ext", "constructor", "ext"], "tactic_count": 9}
{"name": "CategoryTheory.Limits.pullbackFstFstIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullback_map_eq_pullbackFstFstIso_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Diagonal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.pullback_lift_map_isPullback", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isPullback_map_snd_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Diagonal", "is_tactic_proof": true, "tactics": ["refine", "intro", "refine", "simp", "simp", "intro", "apply", "intro", "apply", "intro", "refine", "apply"], "tactic_count": 12}
{"name": "CategoryTheory.Limits.CoproductDisjoint.of_cofan", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.DisjointCoproduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.CoproductDisjoint.of_hasCoproduct", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.DisjointCoproduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Mono.of_coproductDisjoint", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.DisjointCoproduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Mono.ι_of_coproductDisjoint", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.DisjointCoproduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsInitial.ofCoproductDisjointOfIsColimitOfIsLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.DisjointCoproduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsInitial.ofCoproductDisjoint", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.DisjointCoproduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsInitial.ofCoproductDisjointOfIsColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.DisjointCoproduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsInitial.ofCoproductDisjointOfIsLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.DisjointCoproduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsInitial.ofCoproductDisjointOfCommSq", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.DisjointCoproduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryCoproductDisjoint", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.DisjointCoproduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryCoproductDisjoint.of_binaryCofan", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.DisjointCoproduct", "is_tactic_proof": false, "tactics": ["have", "cases", "exact", "exact", "refine", "dsimp", "split", "exact", "exact", "dsimp"], "tactic_count": 10}
{"name": "CategoryTheory.Mono.cofanInl_of_binaryCoproductDisjoint", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.DisjointCoproduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Mono.cofanInr_of_binaryCoproductDisjoint", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.DisjointCoproduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Mono.of_binaryCoproductDisjoint_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.DisjointCoproduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Mono.of_binaryCoproductDisjoint_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.DisjointCoproduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Mono.inl_of_binaryCoproductDisjoint", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.DisjointCoproduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Mono.inr_of_binaryCoproductDisjoint", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.DisjointCoproduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsInitial.ofBinaryCoproductDisjointOfIsColimitOfIsLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.DisjointCoproduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsInitial.ofBinaryCoproductDisjoint", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.DisjointCoproduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsInitial.ofBinaryCoproductDisjointOfIsColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.DisjointCoproduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsInitial.ofBinaryCoproductDisjointOfIsLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.DisjointCoproduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryCoproductsDisjoint", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.DisjointCoproduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.BinaryCoproductsDisjoint.mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.DisjointCoproduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.initialMonoClass_of_coproductsDisjoint", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.DisjointCoproduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.multicospanShapeEnd", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.multispanShapeCoend", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.multicospanIndexEnd", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.multispanIndexCoend", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Wedge", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Wedge.mk", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Wedge.mk_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Wedge.condition", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Wedge.IsLimit.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Wedge.IsLimit.lift", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Wedge.IsLimit.lift_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.End", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.Cowedge", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cowedge.mk", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cowedge.mk_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cowedge.condition", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cowedge.IsColimit.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cowedge.IsColimit.desc", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cowedge.IsColimit.π_desc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.End", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.HasEnd", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.end_", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.end_.π", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.end_.condition", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.End", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.end_.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.end_.lift", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.end_.lift_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.End", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.end_.map", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.end_.map_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.End", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.end_.map_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.End", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.end_.map_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.End", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.endFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.HasCoend", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coend", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coend.ι", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coend.condition", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.End", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.coend.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coend.desc", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coend.ι_desc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.End", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.coend.map", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coend.ι_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.End", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.coend.map_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.End", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.coend.map_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.End", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.coendFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingParallelPair", "kind": "inductive", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instDecidableEqWalkingParallelPair", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instInhabitedWalkingParallelPair.default", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instInhabitedWalkingParallelPair", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingParallelPairHom", "kind": "inductive", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instDecidableEqWalkingParallelPairHom", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instInhabitedWalkingParallelPairHomZeroOne", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingParallelPairHom.comp", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingParallelPairHom.id_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingParallelPairHom.comp_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.WalkingParallelPairHom.assoc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.walkingParallelPairHomCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.walkingParallelPairHom_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.walkingParallelPairOp", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.walkingParallelPairOp_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.walkingParallelPairOp_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.walkingParallelPairOp_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.walkingParallelPairOp_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.walkingParallelPairOpEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.walkingParallelPairOpEquiv_unitIso_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.walkingParallelPairOpEquiv_unitIso_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.walkingParallelPairOpEquiv_counitIso_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.walkingParallelPairOpEquiv_counitIso_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.walkingParallelPairOpEquiv_unitIso_hom_app_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.walkingParallelPairOpEquiv_unitIso_hom_app_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.walkingParallelPairOpEquiv_unitIso_inv_app_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.walkingParallelPairOpEquiv_unitIso_inv_app_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.walkingParallelPairOpEquiv_counitIso_hom_app_op_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.walkingParallelPairOpEquiv_counitIso_hom_app_op_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.walkingParallelPairOpEquiv_counitIso_inv_app_op_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.walkingParallelPairOpEquiv_counitIso_inv_app_op_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.parallelPair", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.parallelPair_obj_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.parallelPair_obj_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.parallelPair_map_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.parallelPair_map_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.parallelPair_functor_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.diagramIsoParallelPair", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.parallelPairHom", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.parallelPairIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.parallelPairHom_app_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.parallelPairHom_app_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.parallelPair.eqOfHomEq", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Fork", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cofork", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Fork.ι", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Fork.app_zero_eq_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cofork.π", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cofork.app_one_eq_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Fork.app_one_eq_ι_comp_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.Fork.app_one_eq_ι_comp_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.Cofork.app_zero_eq_comp_π_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.Cofork.app_zero_eq_comp_π_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.Fork.ofι", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cofork.ofπ", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Fork.ι_ofι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cofork.π_ofπ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Fork.condition", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.Cofork.condition", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.Fork.equalizer_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cofork.coequalizer_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Fork.IsLimit.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cofork.IsColimit.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Fork.IsLimit.lift_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cofork.IsColimit.π_desc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Fork.IsLimit.lift", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Fork.IsLimit.lift_ι'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Fork.IsLimit.lift'", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Fork.IsLimit.mono", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cofork.IsColimit.desc", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cofork.IsColimit.π_desc'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cofork.IsColimit.desc'", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cofork.IsColimit.epi", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Fork.IsLimit.existsUnique", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cofork.IsColimit.existsUnique", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Fork.IsLimit.mk", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Fork.IsLimit.mk'", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cofork.IsColimit.mk", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cofork.IsColimit.mk'", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Fork.IsLimit.ofExistsUnique", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": true, "tactics": ["choose", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.Cofork.IsColimit.ofExistsUnique", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": true, "tactics": ["choose", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.Fork.IsLimit.homIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Fork.IsLimit.homIso_natural", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cofork.IsColimit.homIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cofork.IsColimit.homIso_natural", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cone.ofFork", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cocone.ofCofork", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cone.ofFork_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cocone.ofCofork_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Fork.ofCone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cofork.ofCocone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Fork.ofCone_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cofork.ofCocone_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Fork.ι_postcompose", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cofork.π_precompose", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Fork.mkHom", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.ForkOfι.ext", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Fork.isoForkOfι", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cofork.mkHom", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Fork.hom_comp_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.Fork.π_comp_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.CoforkOfπ.ext", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cofork.isoCoforkOfπ", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.HasEqualizer", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.equalizer", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.equalizer.ι", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.equalizer.fork", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.equalizer.fork_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.equalizer.fork_π_app_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.equalizer.condition", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.equalizerIsEqualizer", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.equalizer.lift", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.equalizer.lift_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.equalizer.lift'", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.equalizer.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.equalizer.existsUnique", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.equalizer.ι_mono", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.mono_of_isLimit_fork", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.idFork", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isLimitIdFork", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isIso_limit_cone_parallelPair_of_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.equalizer.ι_of_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isIso_limit_cone_parallelPair_of_self", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isIso_limit_cone_parallelPair_of_epi", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.eq_of_epi_fork_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.eq_of_epi_equalizer", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasEqualizer_of_self", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.equalizer.ι_of_self", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.equalizer.isoSourceOfSelf", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.equalizer.isoSourceOfSelf_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.equalizer.isoSourceOfSelf_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.precompFork", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.liftPrecomp", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isLimitPrecompFork", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasEqualizer_precomp_of_equalizer", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasEqualizer_precomp_of_hasEqualizer", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.HasCoequalizer", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coequalizer", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coequalizer.π", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coequalizer.cofork", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coequalizer.cofork_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coequalizer.cofork_ι_app_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coequalizer.condition", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coequalizerIsCoequalizer", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coequalizer.desc", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coequalizer.π_desc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coequalizer.π_colimMap_desc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.coequalizer.desc'", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coequalizer.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coequalizer.existsUnique", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coequalizer.π_epi", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.epi_of_isColimit_cofork", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.idCofork", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isColimitIdCofork", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isIso_colimit_cocone_parallelPair_of_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coequalizer.π_of_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isIso_colimit_cocone_parallelPair_of_self", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isIso_limit_cocone_parallelPair_of_epi", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.eq_of_mono_cofork_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.eq_of_mono_coequalizer", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasCoequalizer_of_self", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coequalizer.π_of_self", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coequalizer.isoTargetOfSelf", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coequalizer.isoTargetOfSelf_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.coequalizer.isoTargetOfSelf_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.equalizerComparison", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.equalizerComparison_comp_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.map_lift_equalizerComparison", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.coequalizerComparison", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.ι_comp_coequalizerComparison", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coequalizerComparison_map_desc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.HasEqualizers", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.HasCoequalizers", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasEqualizers_of_hasLimit_parallelPair", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasCoequalizers_of_hasColimit_parallelPair", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coneOfIsSplitMono", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coneOfIsSplitMono_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isSplitMonoEqualizes", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.splitMonoOfEqualizer", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isEqualizerCompMono", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasEqualizer_comp_mono", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.splitMonoOfIdempotentOfIsLimitFork", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.splitMonoOfIdempotentEqualizer", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coconeOfIsSplitEpi", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coconeOfIsSplitEpi_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isSplitEpiCoequalizes", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.splitEpiOfCoequalizer", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isCoequalizerEpiComp", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasCoequalizer_epi_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.splitEpiOfIdempotentOfIsColimitCofork", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.splitEpiOfIdempotentCoequalizer", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.hasInitial_of_equivalence", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.hasInitial_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.hasTerminal_of_equivalence", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.hasTerminal_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasLimitsOfShape_of_hasFiniteLimits", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.FiniteLimits", "is_tactic_proof": true, "tactics": ["apply", "apply"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.hasFiniteLimits_of_hasLimitsOfSize", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.FiniteLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasFiniteLimits_of_hasLimits", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.FiniteLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasFiniteLimits_of_hasLimitsOfSize₀", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.FiniteLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instCategoryULiftHomULiftOfSmallCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.FiniteLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasFiniteLimits_of_hasFiniteLimits_of_size", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.FiniteLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasColimitsOfShape_of_hasFiniteColimits", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.FiniteLimits", "is_tactic_proof": true, "tactics": ["refine", "apply"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.hasFiniteColimits_of_hasColimitsOfSize", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.FiniteLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasFiniteColimits_of_hasColimits", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.FiniteLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasFiniteColimits_of_hasColimitsOfSize₀", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.FiniteLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasFiniteColimits_of_hasFiniteColimits_of_size", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.FiniteLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.fintypeWalkingParallelPair", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.FiniteLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instFintypeWalkingParallelPairHom", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.FiniteLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instFinCategoryWalkingParallelPair", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.FiniteLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits._example", "kind": "example", "module": "Mathlib.CategoryTheory.Limits.Shapes.FiniteLimits", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "CategoryTheory.Limits._example", "kind": "example", "module": "Mathlib.CategoryTheory.Limits.Shapes.FiniteLimits", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.WidePullbackShape.fintypeObj", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.FiniteLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WidePullbackShape.fintypeHom", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.FiniteLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WidePushoutShape.fintypeObj", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.FiniteLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WidePushoutShape.fintypeHom", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.FiniteLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.finCategoryWidePullback", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.FiniteLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.finCategoryWidePushout", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.FiniteLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasLimitsOfShape_widePullbackShape", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.FiniteLimits", "is_tactic_proof": true, "tactics": ["haveI", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.hasColimitsOfShape_widePushoutShape", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.FiniteLimits", "is_tactic_proof": true, "tactics": ["haveI", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.hasFiniteWidePullbacks_of_hasFiniteLimits", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.FiniteLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasFiniteWidePushouts_of_has_finite_limits", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.FiniteLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.fintypeWalkingPair", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.FiniteLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits._example", "kind": "example", "module": "Mathlib.CategoryTheory.Limits.Shapes.FiniteLimits", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "CategoryTheory.Limits._example", "kind": "example", "module": "Mathlib.CategoryTheory.Limits.Shapes.FiniteLimits", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.WalkingMulticospan.instFintype", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.FiniteMultiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingMulticospan.instFinCategoryOfLOfDecidableEqR", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.FiniteMultiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingMultispan.instFintype", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.FiniteMultiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingMultispan.instFinCategoryOfLOfDecidableEqR", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.FiniteMultiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasFiniteProducts_of_hasFiniteLimits", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.FiniteProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasLimitsOfShape_discrete", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.FiniteProducts", "is_tactic_proof": true, "tactics": ["rcases", "haveI", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Limits._example", "kind": "example", "module": "Mathlib.CategoryTheory.Limits.Shapes.FiniteProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasFiniteProducts_of_hasProducts", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.FiniteProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasColimitsOfShape_discrete", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.FiniteProducts", "is_tactic_proof": true, "tactics": ["rcases", "haveI", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.hasFiniteCoproducts_of_hasFiniteColimits", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.FiniteProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasFiniteCoproducts_of_hasCoproducts", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.FiniteProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FunctorToTypes.prod", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.FunctorToTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FunctorToTypes.prod.fst", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.FunctorToTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FunctorToTypes.prod.snd", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.FunctorToTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FunctorToTypes.prod.lift", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.FunctorToTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FunctorToTypes.prod.lift_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.FunctorToTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FunctorToTypes.prod.lift_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.FunctorToTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FunctorToTypes.binaryProductCone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.FunctorToTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FunctorToTypes.binaryProductLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.FunctorToTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FunctorToTypes.binaryProductLimitCone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.FunctorToTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FunctorToTypes.binaryProductIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.FunctorToTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FunctorToTypes.binaryProductIso_hom_comp_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.FunctorToTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FunctorToTypes.binaryProductIso_hom_comp_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.FunctorToTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FunctorToTypes.binaryProductIso_inv_comp_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.FunctorToTypes", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.FunctorToTypes.binaryProductIso_inv_comp_fst_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.FunctorToTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FunctorToTypes.binaryProductIso_inv_comp_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.FunctorToTypes", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.FunctorToTypes.binaryProductIso_inv_comp_snd_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.FunctorToTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FunctorToTypes.prodMk", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.FunctorToTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FunctorToTypes.prodMk_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.FunctorToTypes", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.FunctorToTypes.prodMk_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.FunctorToTypes", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.FunctorToTypes.prod_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.FunctorToTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FunctorToTypes.binaryProductEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.FunctorToTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FunctorToTypes.prod_ext'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.FunctorToTypes", "is_tactic_proof": true, "tactics": ["apply", "aesop"], "tactic_count": 2}
{"name": "CategoryTheory.FunctorToTypes.coprod", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.FunctorToTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FunctorToTypes.coprod.inl", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.FunctorToTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FunctorToTypes.coprod.inr", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.FunctorToTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FunctorToTypes.coprod.desc", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.FunctorToTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FunctorToTypes.coprod.desc_inl", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.FunctorToTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FunctorToTypes.coprod.desc_inr", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.FunctorToTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FunctorToTypes.binaryCoproductCocone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.FunctorToTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FunctorToTypes.binaryCoproductColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.FunctorToTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FunctorToTypes.binaryCoproductColimitCocone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.FunctorToTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FunctorToTypes.binaryCoproductIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.FunctorToTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FunctorToTypes.inl_comp_binaryCoproductIso_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.FunctorToTypes", "is_tactic_proof": true, "tactics": ["simp", "aesop"], "tactic_count": 2}
{"name": "CategoryTheory.FunctorToTypes.inl_comp_binaryCoproductIso_hom_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.FunctorToTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FunctorToTypes.inr_comp_binaryCoproductIso_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.FunctorToTypes", "is_tactic_proof": true, "tactics": ["simp", "aesop"], "tactic_count": 2}
{"name": "CategoryTheory.FunctorToTypes.inr_comp_binaryCoproductIso_hom_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.FunctorToTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FunctorToTypes.inl_comp_binaryCoproductIso_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.FunctorToTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FunctorToTypes.inl_comp_binaryCoproductIso_inv_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.FunctorToTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FunctorToTypes.inr_comp_binaryCoproductIso_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.FunctorToTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FunctorToTypes.inr_comp_binaryCoproductIso_inv_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.FunctorToTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FunctorToTypes.coprodInl", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.FunctorToTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FunctorToTypes.coprodInr", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.FunctorToTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FunctorToTypes.binaryCoproductEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.FunctorToTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasColimit_ι_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.fiberwiseColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.fiberwiseColim", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.natTransIntoForgetCompFiberwiseColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coconeFiberwiseColimitOfCocone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isColimitCoconeFiberwiseColimitOfCocone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasColimit_fiberwiseColimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coconeOfCoconeFiberwiseColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isColimitCoconeOfFiberwiseCocone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasColimit_of_hasColimit_fiberwiseColimit_of_hasColimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.colimitFiberwiseColimitIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.ι_colimitFiberwiseColimitIso_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Grothendieck", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.ι_colimitFiberwiseColimitIso_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Grothendieck", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.hasColimitsOfShape_grothendieck", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.fiberwiseColimCompColimIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.fiberwiseColimCompEvaluationIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.MonoFactorisation.self", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.MonoFactorisation.instInhabitedOfMono", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.MonoFactorisation.ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": true, "tactics": ["obtain", "cases", "replace", "congr", "apply", "rw"], "tactic_count": 6}
{"name": "CategoryTheory.Limits.MonoFactorisation.compMono", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.MonoFactorisation.ofCompIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.MonoFactorisation.isoComp", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.MonoFactorisation.ofIsoComp", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.MonoFactorisation.ofArrowIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.MonoFactorisation.ofIsoI", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.MonoFactorisation.fac_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.IsImage.fac_lift", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsImage.self", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsImage.instInhabitedSelf", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsImage.isoExt", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsImage.isoExt_hom_m", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.IsImage.isoExt_inv_m", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.IsImage.e_isoExt_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.IsImage.e_isoExt_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.IsImage.ofArrowIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsImage.ofIsoI", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.ImageFactorisation.instInhabitedOfMono", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.ImageFactorisation.ofArrowIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.ImageFactorisation.ofIsoI", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.HasImage.mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.HasImage.of_arrow_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.mono_hasImage", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Image.imageFactorisation", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Image.monoFactorisation", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Image.isImage", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.image", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.image.ι", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.image.as_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instMonoι", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.factorThruImage", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.as_factorThruImage", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.image.fac", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.image.lift", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.image.lift_fac", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.image.fac_lift", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.image.isImage_lift", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsImage.lift_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.image.lift_mk_factorThruImage", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.image.lift_mk_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.image.lift_mono", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": true, "tactics": ["refine", "simpa"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.HasImage.uniq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instHasImageCompOfIsIso", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.imageMonoIsoSource", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.imageMonoIsoSource_inv_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.imageMonoIsoSource_hom_self", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": true, "tactics": ["simp", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.image.ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": true, "tactics": ["let", "let", "let", "m", "m_mono", "e", "let", "have", "have", "convert", "rw", "calc", "g"], "tactic_count": 13}
{"name": "CategoryTheory.Limits.instEpiFactorThruImageOfHasLimitWalkingParallelPairParallelPair", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.epi_image_of_epi", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.epi_of_epi_image", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.image.eqToHom", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instIsIsoEqToHom", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.image.eqToIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.image.eq_fac", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": true, "tactics": ["apply", "subst", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.image.preComp", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.image.preComp_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.image.factorThruImage_preComp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.image.preComp_mono", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": true, "tactics": ["refine", "simp", "infer_instance"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.image.preComp_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": true, "tactics": ["apply", "simp", "rw"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.image.preComp_epi_of_epi", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": true, "tactics": ["apply", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.hasImage_iso_comp", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.image.isIso_precomp_iso", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasImage_comp_iso", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.image.compIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.image.compIso_hom_comp_image_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.image.compIso_inv_comp_image_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.instHasImageHomMk", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.inhabitedImageMap", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.ImageMap.factor_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.ImageMap.transport", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.HasImageMap.mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.HasImageMap.transport", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.HasImageMap.imageMap", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasImageMapOfIsIso", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits.ImageMap.map_uniq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.instSubsingletonImageMap", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.image.map", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.image.factor_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.image.map_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.image.map_homMk'_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.imageMapComp", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.image.map_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.imageMapId", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.image.map_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.im", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.strongEpiMonoFactorisationInhabited", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.StrongEpiMonoFactorisation.toMonoIsImage", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.HasStrongEpiMonoFactorisations.mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.strongEpi_of_strongEpiMonoFactorisation", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.strongEpi_factorThruImage_of_strongEpiMonoFactorisation", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasStrongEpiImages_of_hasStrongEpiMonoFactorisations", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasImageMapsOfHasStrongEpiImages", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasStrongEpiImages_of_hasPullbacks_of_hasEqualizers", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.image.isoStrongEpiMono", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits.image.isoStrongEpiMono_inv_comp_mono", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.functorialEpiMonoFactorizationData", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.hasStrongEpiMonoFactorisations_imp_of_isEquivalence", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Images", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.asEmptyCone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.IsTerminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits.IsTerminal", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.IsTerminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits.isTerminalEquivUnique", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.IsTerminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsTerminal.ofUnique", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.IsTerminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsTerminal.ofUniqueHom", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.IsTerminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits.IsTerminal.ofIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.IsTerminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsTerminal.equivOfIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.IsTerminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits.IsInitial.ofUnique", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.IsTerminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsInitial.ofUniqueHom", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.IsTerminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits.IsInitial.ofIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.IsTerminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsInitial.equivOfIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.IsTerminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsTerminal.from", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.IsTerminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsTerminal.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.IsTerminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsTerminal.comp_from", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.IsTerminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsTerminal.from_self", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.IsTerminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsInitial.to", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.IsTerminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsInitial.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.IsTerminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsInitial.to_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.IsTerminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsInitial.to_self", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.IsTerminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsTerminal.isSplitMono_from", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.IsTerminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsInitial.isSplitEpi_to", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.IsTerminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsTerminal.mono_from", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.IsTerminal", "is_tactic_proof": true, "tactics": ["haveI"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.IsInitial.epi_to", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.IsTerminal", "is_tactic_proof": true, "tactics": ["haveI"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.IsTerminal.uniqueUpToIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.IsTerminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsInitial.uniqueUpToIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.IsTerminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isLimitChangeEmptyCone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.IsTerminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isLimitEmptyConeEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.IsTerminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isLimitEquivIsTerminalOfIsEmpty", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.IsTerminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isColimitChangeEmptyCocone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.IsTerminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isColimitEmptyCoconeEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.IsTerminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isColimitEquivIsInitialOfIsEmpty", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.IsTerminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.terminalOpOfInitial", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.IsTerminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.terminalUnopOfInitial", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.IsTerminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.initialOpOfTerminal", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.IsTerminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.initialUnopOfTerminal", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.IsTerminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsInitial.mono_from", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.IsTerminal", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.InitialMonoClass.of_isInitial", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.IsTerminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.InitialMonoClass.of_isTerminal", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.IsTerminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coneOfDiagramInitial", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.IsTerminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.limitOfDiagramInitial", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.IsTerminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coneOfDiagramTerminal", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.IsTerminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.limitOfDiagramTerminal", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.IsTerminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coconeOfDiagramTerminal", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.IsTerminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.colimitOfDiagramTerminal", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.IsTerminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsColimit.isIso_ι_app_of_isTerminal", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.IsTerminal", "is_tactic_proof": true, "tactics": ["change", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.coconeOfDiagramInitial", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.IsTerminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.colimitOfDiagramInitial", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.IsTerminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsLimit.isIso_π_app_of_isInitial", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.IsTerminal", "is_tactic_proof": true, "tactics": ["change", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.isIso_of_isTerminal", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.IsTerminal", "is_tactic_proof": true, "tactics": ["refine", "simp", "apply"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.isIso_of_isInitial", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.IsTerminal", "is_tactic_proof": true, "tactics": ["refine", "simp", "apply"], "tactic_count": 3}
{"name": "CategoryTheory.IsKernelPair", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.KernelPair", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsKernelPair.instSubsingleton", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.KernelPair", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsKernelPair.id_of_mono", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.KernelPair", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsKernelPair.instInhabitedIdOfMono", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.KernelPair", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsKernelPair.lift", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.KernelPair", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsKernelPair.lift_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.KernelPair", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsKernelPair.lift_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.KernelPair", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsKernelPair.lift'", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.KernelPair", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsKernelPair.cancel_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.KernelPair", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsKernelPair.cancel_right_of_mono", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.KernelPair", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsKernelPair.comp_of_mono", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.KernelPair", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsKernelPair.toCoequalizer", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.KernelPair", "is_tactic_proof": true, "tactics": ["let", "have", "have", "refine", "apply", "apply", "exact"], "tactic_count": 7}
{"name": "CategoryTheory.IsKernelPair.toCoequalizer'", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.KernelPair", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsKernelPair.pullback", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.KernelPair", "is_tactic_proof": false, "tactics": ["refine", "pullback.lift", "simp_rw", "simp", "ext", "ext", "simp", "simp", "apply", "simpa", "apply", "simpa", "simpa"], "tactic_count": 13}
{"name": "CategoryTheory.IsKernelPair.mono_of_isIso_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.KernelPair", "is_tactic_proof": true, "tactics": ["obtain", "rw", "rw", "constructor", "intro", "obtain", "rw"], "tactic_count": 7}
{"name": "CategoryTheory.IsKernelPair.mono_of_eq_fst_snd'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.KernelPair", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsKernelPair.mono_of_eq_fst_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.KernelPair", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "CategoryTheory.IsKernelPair.isIso_of_mono", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.KernelPair", "is_tactic_proof": false, "tactics": ["rw", "show", "infer_instance"], "tactic_count": 3}
{"name": "CategoryTheory.IsKernelPair.of_isIso_of_mono", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.KernelPair", "is_tactic_proof": true, "tactics": ["change", "convert", "all_goals"], "tactic_count": 3}
{"name": "CategoryTheory.IsKernelPair.of_hasPullback", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.KernelPair", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.HasKernel", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.HasCokernel", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.KernelFork", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.KernelFork.condition", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.KernelFork.app_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.KernelFork.ofι", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.KernelFork.ι_ofι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isoOfι", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.ofιCongr", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.compNatIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.KernelFork.IsLimit.lift'", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isLimitAux", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.KernelFork.IsLimit.ofι", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.KernelFork.IsLimit.ofι'", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isKernelCompMono", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isKernelCompMono_lift", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isKernelOfComp", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.KernelFork.IsLimit.ofId", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.KernelFork.IsLimit.ofMonoOfIsZero", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.KernelFork.IsLimit.isIso_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.KernelFork.isLimitOfIsLimitOfIff", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.KernelFork.isLimitOfIsLimitOfIff'", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.KernelFork.IsLimit.isZero_of_mono", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": true, "tactics": ["have", "rw", "zero_comp]"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.KernelFork.mapOfIsLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.KernelFork.mapOfIsLimit_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.KernelFork.mapIsoOfIsLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.kernel", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.kernel.ι", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.equalizer_as_kernel", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.kernel.condition", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.kernelIsKernel", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.kernel.lift", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.kernel.lift_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.kernel.lift_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.kernel.lift_mono", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.kernel.lift'", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.kernel.map", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.kernel.map_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.instIsIsoMapOfMono", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.kernel.lift_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.kernel.map_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.kernel.mapIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.kernel.ι_zero_isIso", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.eq_zero_of_epi_kernel", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.kernelZeroIsoSource", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.kernelZeroIsoSource_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.kernelZeroIsoSource_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.kernelIsoOfEq", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.kernelIsoOfEq_refl", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.kernelIsoOfEq_hom_comp_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.kernelIsoOfEq_inv_comp_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.lift_comp_kernelIsoOfEq_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.lift_comp_kernelIsoOfEq_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.kernelIsoOfEq_trans", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.kernel_not_epi_of_nonzero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.kernel_not_iso_of_nonzero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasKernel_comp_mono", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.kernelCompMono", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasKernel_iso_comp", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.kernelIsIsoComp", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.kernel.congr", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isZero_kernel_of_mono", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.kernel.zeroKernelFork", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.kernel.isLimitConeZeroCone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.kernel.ofMono", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.kernel.ι_of_mono", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.zeroKernelOfCancelZero", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsKernel.ofCompIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.kernel.ofCompIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsKernel.isoKernel", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.kernel.isoKernel", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.kernel.ι_of_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.CokernelCofork", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.CokernelCofork.condition", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.CokernelCofork.π_eq_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.CokernelCofork.ofπ", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.CokernelCofork.π_ofπ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isoOfπ", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.ofπCongr", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.CokernelCofork.IsColimit.desc'", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isColimitAux", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.CokernelCofork.IsColimit.ofπ", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.CokernelCofork.IsColimit.ofπ'", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isCokernelEpiComp", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isCokernelEpiComp_desc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isCokernelOfComp", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.CokernelCofork.IsColimit.ofId", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.CokernelCofork.IsColimit.ofEpiOfIsZero", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.CokernelCofork.IsColimit.isIso_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.CokernelCofork.isColimitOfIsColimitOfIff", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.CokernelCofork.isColimitOfIsColimitOfIff'", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.CokernelCofork.IsColimit.isZero_of_epi", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.CokernelCofork.mapOfIsColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.CokernelCofork.π_mapOfIsColimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.CokernelCofork.mapIsoOfIsColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.cokernel", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.cokernel.π", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coequalizer_as_cokernel", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.cokernel.condition", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.cokernelIsCokernel", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.cokernel.desc", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.cokernel.π_desc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.colimit_ι_zero_cokernel_desc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.cokernel.desc_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.cokernel.desc_epi", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.cokernel.desc'", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.cokernel.map", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instIsIsoMapOfEpi", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.cokernel.map_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.cokernel.map_desc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.cokernel.map_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.cokernel.mapIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.cokernel.π_zero_isIso", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.eq_zero_of_mono_cokernel", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.cokernelZeroIsoTarget", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.cokernelZeroIsoTarget_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.cokernelZeroIsoTarget_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.cokernelIsoOfEq", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.cokernelIsoOfEq_refl", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.π_comp_cokernelIsoOfEq_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.π_comp_cokernelIsoOfEq_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.cokernelIsoOfEq_hom_comp_desc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.cokernelIsoOfEq_inv_comp_desc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.cokernelIsoOfEq_trans", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.cokernel_not_mono_of_nonzero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.cokernel_not_iso_of_nonzero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasCokernel_comp_iso", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.cokernelCompIsIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasCokernel_epi_comp", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.cokernelEpiComp", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.cokernel.congr", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isZero_cokernel_of_epi", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.cokernel.zeroCokernelCofork", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.cokernel.isColimitCoconeZeroCocone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.cokernel.ofEpi", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.cokernel.π_of_epi", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.MonoFactorisation.kernel_ι_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.cokernelImageι", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.kernelFactorThruImage", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.kernelFactorThruImage_hom_comp_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.kernelFactorThruImage_inv_comp_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.cokernel.π_of_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.kernel.of_cokernel_of_epi", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.cokernel.of_kernel_of_mono", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.zeroCokernelOfZeroCancel", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsCokernel.ofIsoComp", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.cokernel.ofIsoComp", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsCokernel.cokernelIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.cokernel.cokernelIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.kernelComparison", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.kernelComparison_comp_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.map_lift_kernelComparison", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.kernelComparison_comp_kernel_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.cokernelComparison", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.π_comp_cokernelComparison", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.cokernelComparison_map_desc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.cokernel_map_comp_cokernelComparison", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasKernels_of_hasEqualizers", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasCokernels_of_hasCoequalizers", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.ker", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.ker.ι", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.ker.condition", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.coker", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coker.π", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coker.condition", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Kernels", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.MulticospanShape.prod", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.MultispanShape.prod", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.MultispanShape.ofLinearOrder", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instUniqueLOfLinearOrderBool", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingMulticospan", "kind": "inductive", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingMultispan", "kind": "inductive", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingMulticospan.instInhabitedOfL", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingMulticospan.Hom", "kind": "inductive", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingMulticospan.instInhabitedHom", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingMulticospan.Hom.comp", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingMulticospan.instSmallCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingMulticospan.Hom.id_eq_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingMulticospan.Hom.comp_eq_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingMultispan.instInhabitedOfL", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingMultispan.instSmallOfLOfR", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingMultispan.Hom", "kind": "inductive", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingMultispan.instInhabitedHom", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingMultispan.Hom.comp", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingMultispan.instSmallCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingMultispan.Hom.id_eq_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingMultispan.Hom.comp_eq_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingMultispan.instUniqueHom", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingMultispan.instSubsingletonHomLeft", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": true, "tactics": ["by_cases", "subst", "infer_instance", "have", "infer_instance"], "tactic_count": 5}
{"name": "CategoryTheory.Limits.WalkingMultispan.instSubsingletonHomRight", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": true, "tactics": ["by_cases", "subst", "infer_instance", "have", "infer_instance"], "tactic_count": 5}
{"name": "CategoryTheory.Limits.WalkingMultispan.instIsEmptyHomRightLeft", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingMultispan.instLocallySmall", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingMultispan.equiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingMultispan.arrowEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.MulticospanIndex.multicospan", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.MulticospanIndex.fstPiMapOfIsLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.MulticospanIndex.sndPiMapOfIsLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.MulticospanIndex.fstPiMapOfIsLimit_proj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.MulticospanIndex.sndPiMapOfIsLimit_proj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.MulticospanIndex.parallelPairDiagramOfIsLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.MulticospanIndex.fstPiMap", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.MulticospanIndex.sndPiMap", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.MulticospanIndex.fstPiMap_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.MulticospanIndex.sndPiMap_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.MulticospanIndex.parallelPairDiagram", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.MultispanIndex.multispan", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.MultispanIndex.multispan_obj_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.MultispanIndex.multispan_obj_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.MultispanIndex.multispan_map_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.MultispanIndex.multispan_map_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.MultispanIndex.fstSigmaMapOfIsColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.MultispanIndex.sndSigmaMapOfIsColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.MultispanIndex.inj_fstSigmaMapOfIsColimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.MultispanIndex.inj_sndSigmaMapOfIsColimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.MultispanIndex.parallelPairDiagramOfIsColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.MultispanIndex.fstSigmaMap", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.MultispanIndex.sndSigmaMap", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.MultispanIndex.ι_fstSigmaMap", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.MultispanIndex.ι_sndSigmaMap", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.MultispanIndex.parallelPairDiagram", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Multifork", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Multicofork", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Multifork.ι", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Multifork.app_left_eq_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Multifork.app_right_eq_ι_comp_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.Multifork.app_right_eq_ι_comp_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.Multifork.hom_comp_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Multifork.ofι", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Multifork.ι_ofι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Multifork.condition", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.Multifork.isoOfι", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Multifork.IsLimit.mk", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Multifork.IsLimit.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": true, "tactics": ["apply", "rintro", "apply", "dsimp", "rw"], "tactic_count": 5}
{"name": "CategoryTheory.Limits.Multifork.IsLimit.lift", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Multifork.IsLimit.fac", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Multifork.pi_condition", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.Multifork.toPiFork", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Multifork.toPiFork_π_app_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Multifork.toPiFork_π_app_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Multifork.ofPiFork", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Multifork.ofPiFork_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Multifork.ofPiFork_π_app_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.MulticospanIndex.toPiForkFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.MulticospanIndex.ofPiForkFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiForkOfIsLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.MulticospanIndex.ofParallelHoms", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.MulticospanIndex.multiforkOfParallelHomsEquivFork", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": ["refine", "refine", "rw", "simp", "refine", "rw", "simp"], "tactic_count": 7}
{"name": "CategoryTheory.Limits.MulticospanIndex.multiforkOfParallelHomsEquivFork_functor_obj_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.MulticospanIndex.multiforkOfParallelHomsEquivFork_inverse_obj_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.Multicofork.π", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Multicofork.π_eq_app_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Multicofork.fst_app_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.Multicofork.snd_app_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.Multicofork.π_comp_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Multicofork.ofπ", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Multicofork.condition", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.Multicofork.IsColimit.mk", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Multicofork.IsColimit.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": true, "tactics": ["apply", "rintro"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.Multicofork.IsColimit.desc", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Multicofork.IsColimit.fac", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Multicofork.sigma_condition", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.Multicofork.toSigmaCofork", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Multicofork.toSigmaCofork_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Multicofork.ofSigmaCofork", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Multicofork.ofSigmaCofork_ι_app_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Multicofork.ofSigmaCofork_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Multicofork.isoOfπ", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.MultispanIndex.toSigmaCoforkFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.MultispanIndex.ofSigmaCoforkFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCoforkOfIsColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.HasMultiequalizer", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.multiequalizer", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.HasMulticoequalizer", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.multicoequalizer", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Multiequalizer.ι", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Multiequalizer.multifork", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Multiequalizer.multifork_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Multiequalizer.multifork_π_app_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Multiequalizer.condition", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Multiequalizer.lift", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Multiequalizer.lift_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Multiequalizer.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Multiequalizer.instHasEqualizerFstPiMapSndPiMap", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Multiequalizer.isoEqualizer", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Multiequalizer.ιPi", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Multiequalizer.ιPi_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": true, "tactics": ["rw", "simp", "rfl"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.Multiequalizer.instMonoιPi", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Multicoequalizer.π", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Multicoequalizer.multicofork", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Multicoequalizer.multicofork_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Multicoequalizer.multicofork_ι_app_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Multicoequalizer.multicofork_ι_app_right'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Multicoequalizer.condition", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Multicoequalizer.desc", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Multicoequalizer.π_desc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Multicoequalizer.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Multicoequalizer.instHasCoequalizerFstSigmaMapSndSigmaMap", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Multicoequalizer.isoCoequalizer", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Multicoequalizer.sigmaπ", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Multicoequalizer.ι_sigmaπ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": true, "tactics": ["rw", "simp", "rfl"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.Multicoequalizer.instEpiSigmaπ", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingMultispan.inclusionOfLinearOrder", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.MultispanIndex.toLinearOrder", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.MultispanIndex.toLinearOrderMultispanIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Multicofork.toLinearOrder", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Multicofork.ofLinearOrder", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Multicofork.isColimitToLinearOrder", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Multicofork.IsColimit.isPushout.multicofork", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.MultiequalizerPullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Multicofork.IsColimit.isPushout.multicofork_π_eq_inl", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.MultiequalizerPullback", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.Multicofork.IsColimit.isPushout.multicofork_π_eq_inr", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.MultiequalizerPullback", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.Multicofork.IsColimit.isPushout", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.MultiequalizerPullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.equivalenceReflectsNormalMono", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.NormalMono.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NormalMono.regularMono", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.NormalMono.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instIsRegularMonoOfNormalMono", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.NormalMono.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NormalMono.lift'", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.NormalMono.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.normalOfIsPullbackSndOfNormal", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.NormalMono.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.normalOfIsPullbackFstOfNormal", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.NormalMono.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NormalMono.ofArrowIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.NormalMono.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.normalMonoOfMono", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.NormalMono.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.regularMonoCategoryOfNormalMonoCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.NormalMono.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.equivalenceReflectsNormalEpi", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.NormalMono.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NormalEpi.regularEpi", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.NormalMono.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instIsRegularEpiOfNormalEpi", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.NormalMono.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NormalEpi.desc'", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.NormalMono.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.normalOfIsPushoutSndOfNormal", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.NormalMono.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.normalOfIsPushoutFstOfNormal", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.NormalMono.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NormalEpi.ofArrowIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.NormalMono.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.normalEpiOfNormalMonoUnop", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.NormalMono.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.normalMonoOfNormalEpiUnop", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.NormalMono.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.normalEpiOfEpi", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.NormalMono.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.regularEpiCategoryOfNormalEpiCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.NormalMono.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NormalMonoCategory.pullback_of_mono", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.NormalMono.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.CategoryTheory.Limits.Shapes.NormalMono.Equalizers.0.CategoryTheory.NormalMonoCategory.P", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.NormalMono.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NormalMonoCategory.hasLimit_parallelPair", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.NormalMono.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NormalMonoCategory.hasEqualizers", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.NormalMono.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NormalMonoCategory.epi_of_zero_cokernel", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.NormalMono.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NormalMonoCategory.epi_of_zero_cancel", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.NormalMono.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NormalEpiCategory.pushout_of_epi", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.NormalMono.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.CategoryTheory.Limits.Shapes.NormalMono.Equalizers.0.CategoryTheory.NormalEpiCategory.Q", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.NormalMono.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NormalEpiCategory.hasColimit_parallelPair", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.NormalMono.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NormalEpiCategory.hasCoequalizers", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.NormalMono.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NormalEpiCategory.mono_of_zero_kernel", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.NormalMono.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NormalEpiCategory.mono_of_cancel_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.NormalMono.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasEqualizers_opposite", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasCoequalizers_opposite", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.parallelPairOpIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.parallelPairOpIso_hom_app_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.parallelPairOpIso_hom_app_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.parallelPairOpIso_inv_app_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.parallelPairOpIso_inv_app_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.opParallelPairIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.opParallelPairIso_hom_app_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Equalizers", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.opParallelPairIso_hom_app_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Equalizers", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.opParallelPairIso_inv_app_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Equalizers", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.opParallelPairIso_inv_app_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Equalizers", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.Cofork.unop", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cofork.unop_π_app_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Equalizers", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.Cofork.unop_π_app_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Equalizers", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.Cofork.unop_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Equalizers", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.Cofork.op", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cofork.op_π_app_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Equalizers", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.Cofork.op_π_app_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Equalizers", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.Cofork.op_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Equalizers", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.Fork.unop", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Fork.unop_ι_app_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Equalizers", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.Fork.unop_ι_app_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Equalizers", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.Fork.unop_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Equalizers", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.Fork.op", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Fork.op_ι_app_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Equalizers", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.Fork.op_ι_app_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Equalizers", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.Fork.op_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Equalizers", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.Cofork.op_unop_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Equalizers", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.Cofork.unop_op_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Equalizers", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.Cofork.opUnopIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cofork.unopOpIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Fork.op_unop_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Equalizers", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.Fork.unop_op_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Equalizers", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.Fork.opUnopIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Fork.unopOpIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cofork.isColimitEquivIsLimitOp", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Equalizers", "is_tactic_proof": true, "tactics": ["apply", "intro", "exact", "intro", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.Limits.Cofork.isColimitEquivIsLimitUnop", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Equalizers", "is_tactic_proof": true, "tactics": ["apply", "intro", "exact", "intro", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.Limits.Cofork.ofπOpIsoOfι", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cofork.ofπUnopIsoOfι", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cofork.isColimitOfπEquivIsLimitOp", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cofork.isColimitOfπEquivIsLimitUnop", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Fork.isLimitEquivIsColimitOp", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Fork.isLimitEquivIsColimitUnop", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Fork.ofιOpIsoOfπ", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Fork.ofιUnopIsoOfπ", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Fork.isLimitOfιEquivIsColimitOp", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Fork.isLimitOfιEquivIsColimitUnop", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cofork.isColimitCoforkPushoutEquivIsColimitForkOpPullback", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cofork.isColimitCoforkPushoutEquivIsColimitForkUnopPullback", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Fork.isLimitForkPushoutEquivIsColimitForkOpPullback", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Fork.isLimitForkPushoutEquivIsColimitForkUnopPullback", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.has_cofiltered_limits_op_of_has_filtered_colimits", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Filtered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.has_cofiltered_limits_of_has_filtered_colimits_op", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Filtered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.has_filtered_colimits_op_of_has_cofiltered_limits", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Filtered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.has_filtered_colimits_of_has_cofiltered_limits_op", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Filtered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.CokernelCofork.IsColimit.ofπOp", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.CokernelCofork.IsColimit.ofπUnop", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.KernelFork.IsLimit.ofιOp", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.KernelFork.IsLimit.ofιUnop", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasCoproductsOfShape_opposite", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Products", "is_tactic_proof": true, "tactics": ["haveI", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.hasCoproductsOfShape_of_opposite", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasProductsOfShape_opposite", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasProductsOfShape_of_opposite", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasProducts_opposite", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasProducts_of_opposite", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasCoproducts_opposite", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasCoproducts_of_opposite", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasFiniteCoproducts_opposite", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasFiniteCoproducts_of_opposite", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasFiniteProducts_opposite", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasFiniteProducts_of_opposite", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instHasLimitOppositeDiscreteOpFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instHasLimitDiscreteOppositeCompInverseOppositeOpFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instHasProductOppositeOp", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cofan.op", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cofan.IsColimit.op", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Products", "is_tactic_proof": false, "tactics": ["let", "refine", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.opCoproductIsoProduct'", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.opCoproductIsoProduct", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.opCoproductIsoProduct'_hom_comp_proj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Products", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.opCoproductIsoProduct_hom_comp_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.opCoproductIsoProduct'_inv_comp_inj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.opCoproductIsoProduct'_comp_self", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Products", "is_tactic_proof": true, "tactics": ["apply", "apply", "intro", "change", "simp", "apply", "simp", "rw", "simp", "rfl"], "tactic_count": 10}
{"name": "CategoryTheory.Limits.opCoproductIsoProduct_inv_comp_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.desc_op_comp_opCoproductIsoProduct'_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Products", "is_tactic_proof": true, "tactics": ["refine", "simp", "op_comp,", "erw", "rfl"], "tactic_count": 5}
{"name": "CategoryTheory.Limits.desc_op_comp_opCoproductIsoProduct_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Products", "is_tactic_proof": false, "tactics": ["convert", "simp", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.instHasColimitOppositeDiscreteOpFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instHasColimitDiscreteOppositeCompInverseOppositeOpFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instHasCoproductOppositeOp", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Fan.op", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Fan.IsLimit.op", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Products", "is_tactic_proof": false, "tactics": ["let", "refine", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.opProductIsoCoproduct'", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.opProductIsoCoproduct", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.proj_comp_opProductIsoCoproduct'_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.opProductIsoCoproduct'_comp_self", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Products", "is_tactic_proof": true, "tactics": ["apply", "apply", "intro", "change", "simp", "apply", "simp", "rw", "simp", "rfl"], "tactic_count": 10}
{"name": "CategoryTheory.Limits.π_comp_opProductIsoCoproduct_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.opProductIsoCoproduct'_inv_comp_lift", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Products", "is_tactic_proof": true, "tactics": ["refine", "simp", "op_unop,", "erw", "rfl"], "tactic_count": 5}
{"name": "CategoryTheory.Limits.opProductIsoCoproduct_inv_comp_lift", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Products", "is_tactic_proof": false, "tactics": ["convert", "simp", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.instHasBinaryCoproductOppositeOp", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Products", "is_tactic_proof": true, "tactics": ["have", "change", "convert", "cases"], "tactic_count": 4}
{"name": "CategoryTheory.Limits.opProdIsoCoprod", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.fst_opProdIsoCoprod_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Products", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.snd_opProdIsoCoprod_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Products", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.inl_opProdIsoCoprod_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Products", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.inr_opProdIsoCoprod_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Products", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.opProdIsoCoprod_hom_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Products", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.opProdIsoCoprod_hom_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Products", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.opProdIsoCoprod_inv_inl", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Products", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.opProdIsoCoprod_inv_inr", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Products", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.hasPullbacks_opposite", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Pullbacks", "is_tactic_proof": true, "tactics": ["haveI", "apply"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.hasPushouts_opposite", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Pullbacks", "is_tactic_proof": true, "tactics": ["haveI", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.spanOp", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.opCospan", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.cospanOp", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.opSpan", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PushoutCocone.unop", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PushoutCocone.unop_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Pullbacks", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.PushoutCocone.unop_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Pullbacks", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.PushoutCocone.op", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PushoutCocone.op_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Pullbacks", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.PushoutCocone.op_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Pullbacks", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.PullbackCone.unop", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PullbackCone.unop_inl", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Pullbacks", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.PullbackCone.unop_inr", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Pullbacks", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.PullbackCone.op", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PullbackCone.op_inl", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Pullbacks", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.PullbackCone.op_inr", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Pullbacks", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.PullbackCone.opUnopIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PullbackCone.unopOpIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PushoutCocone.opUnopIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PushoutCocone.unopOpIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PushoutCocone.isColimitEquivIsLimitOp", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Pullbacks", "is_tactic_proof": true, "tactics": ["apply", "intro", "exact", "intro", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.Limits.PushoutCocone.isColimitEquivIsLimitUnop", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Pullbacks", "is_tactic_proof": true, "tactics": ["apply", "intro", "exact", "intro", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.Limits.PullbackCone.isLimitEquivIsColimitOp", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PullbackCone.isLimitEquivIsColimitUnop", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullbackIsoUnopPushout", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullbackIsoUnopPushout_inv_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullbackIsoUnopPushout_inv_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullbackIsoUnopPushout_hom_inl", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullbackIsoUnopPushout_hom_inr", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullbackIsoOpPushout", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullbackIsoOpPushout_inv_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullbackIsoOpPushout_inv_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullbackIsoOpPushout_hom_inl", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullbackIsoOpPushout_hom_inr", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pushoutIsoUnopPullback", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pushoutIsoUnopPullback_inl_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pushoutIsoUnopPullback_inr_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pushoutIsoUnopPullback_inv_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pushoutIsoUnopPullback_inv_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pushoutIsoOpPullback", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pushoutIsoOpPullback_inl_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pushoutIsoOpPullback_inr_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pushoutIsoOpPullback_inv_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pushoutIsoOpPullback_inv_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CommSq.coneOp", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CommSq.coconeOp", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CommSq.coneUnop", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CommSq.coconeUnop", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Opposites.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Pi.binaryFanOfProp", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.PiProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Pi.binaryFanOfPropIsLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.PiProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasBinaryProduct_of_products", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.PiProd", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.Pi.map_eq_prod_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.PiProd", "is_tactic_proof": true, "tactics": ["rw", "dsimp", "cat_disch"], "tactic_count": 3}
{"name": "Preorder.instHasLimitsOfShape", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Preorder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Preorder.instHasColimitsOfShape", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Preorder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.isInitialZero", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Preorder.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.isTerminalLast", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Preorder.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instHasIterationOfShapeOfHasColimitsOfSize", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Preorder.HasIterationOfShape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasColimitsOfShape_of_isSuccLimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Preorder.HasIterationOfShape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasColimitsOfShape_of_isSuccLimit'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Preorder.HasIterationOfShape", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.instHasIterationOfShapeArrow", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Preorder.HasIterationOfShape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instHasIterationOfShapeFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Preorder.HasIterationOfShape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasColimitsOfShape_of_initialSeg", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Preorder.HasIterationOfShape", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "hasColimitsOfShape_of_equivalence", "let", "obtain", "induction", "isMin", "subst", "exact", "succ", "obtain", "have", "le_top", "b", "rw", "exact", "infer_instance", "isSuccLimit", "subst", "exact"], "tactic_count": 20}
{"name": "CategoryTheory.Limits.hasIterationOfShape_of_initialSeg", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Preorder.HasIterationOfShape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instHasIterationOfShapeElemIic", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Preorder.HasIterationOfShape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrincipalSeg.cocone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Preorder.PrincipalSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.TransfiniteCompositionOfShape.ofArrowIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Preorder.TransfiniteCompositionOfShape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.TransfiniteCompositionOfShape.ofComposableArrows", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Preorder.TransfiniteCompositionOfShape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.TransfiniteCompositionOfShape.ofOrderIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Preorder.TransfiniteCompositionOfShape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.TransfiniteCompositionOfShape.map", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Preorder.TransfiniteCompositionOfShape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.TransfiniteCompositionOfShape.iic", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Preorder.TransfiniteCompositionOfShape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.TransfiniteCompositionOfShape.ici", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Preorder.TransfiniteCompositionOfShape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isColimitOfIsWellOrderContinuous", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Preorder.WellOrderContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isColimitOfIsWellOrderContinuous'", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Preorder.WellOrderContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instIsWellOrderContinuousNat", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Preorder.WellOrderContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instIsWellOrderContinuousFin", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Preorder.WellOrderContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isWellOrderContinuous_of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Preorder.WellOrderContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instIsWellOrderContinuousCompFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Preorder.WellOrderContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instIsWellOrderContinuousCompFunctorEquivalence", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Preorder.WellOrderContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsWellOrderContinuous.restriction_setIci", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Preorder.WellOrderContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Fan", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cofan", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Fan.mk", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cofan.mk", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Fan.proj", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cofan.inj", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.fan_mk_proj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.cofan_mk_inj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.HasProduct", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.HasCoproduct", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasCoproduct_of_equiv_of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": false, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.hasProduct_of_equiv_of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": false, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.Fan.IsLimit.lift", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Fan.IsLimit.fac", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Fan.IsLimit.lift_proj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Fan.IsLimit.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cofan.IsColimit.desc", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cofan.IsColimit.fac", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cofan.IsColimit.inj_desc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cofan.IsColimit.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.HasProductsOfShape", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.HasCoproductsOfShape", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.piObj", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.sigmaObj", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.term∏ᶜ_", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits._aux_Mathlib_CategoryTheory_Limits_Shapes_Products___macroRules_CategoryTheory_Limits_term∏ᶜ__1", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits._aux_Mathlib_CategoryTheory_Limits_Shapes_Products___unexpand_CategoryTheory_Limits_piObj_1", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.term∐_", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits._aux_Mathlib_CategoryTheory_Limits_Shapes_Products___macroRules_CategoryTheory_Limits_term∐__1", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits._aux_Mathlib_CategoryTheory_Limits_Shapes_Products___unexpand_CategoryTheory_Limits_sigmaObj_1", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Pi.π", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Sigma.ι", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Pi.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Sigma.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.productIsProduct", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coproductIsCoproduct", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Pi.π_comp_eqToHom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.Sigma.eqToHom_comp_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": true, "tactics": ["cases", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.Pi.lift", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Pi.lift_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.Fan.isLimitOfIsIsoPiLift", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Fan.nonempty_isLimit_iff_isIso_piLift", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Sigma.desc", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Sigma.ι_desc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.instIsIsoDescι", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": true, "tactics": ["convert", "ext", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.Cofan.isColimitOfIsIsoSigmaDesc", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cofan.nonempty_isColimit_iff_isIso_sigmaDesc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cofan.isColimitTrans", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": true, "tactics": ["refine", "exact", "intro", "simp", "erw", "rfl", "intro", "refine", "erw", "simpa"], "tactic_count": 10}
{"name": "CategoryTheory.Limits.Pi.map", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Pi.map_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.Pi.map_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.Pi.map_comp_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.Pi.map_mono", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Pi.map'", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Pi.map'_comp_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Pi.map'_id_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.Pi.map'_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Pi.map'_comp_map'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.Pi.map'_comp_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.Pi.map_comp_map'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.Pi.map'_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.Pi.mapIso", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Pi.map_isIso", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Pi.cone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.productIsProduct'", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Pi.isoLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Pi.isoLimit_inv_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Pi.isoLimit_hom_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Sigma.map", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Sigma.ι_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.Sigma.map_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.Sigma.map_comp_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.Sigma.map_epi", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Sigma.map'", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Sigma.ι_comp_map'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Sigma.map'_id_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.Sigma.map'_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Sigma.map'_comp_map'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.Sigma.map'_comp_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.Sigma.map_comp_map'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.Sigma.map'_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.Sigma.mapIso", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Sigma.map_isIso", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Sigma.cocone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_map_leftUnitor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_map_rightUnitor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjTransformObjSquare", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjTransformObjSquare_iso_hom_naturality₂", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjTransformObjSquare_iso_hom_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjTransformObjSquare_iso_hom_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjPrecomposeObjSquare", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjPrecomposeObjSquare_iso_hom_naturality₂", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjPrecomposeObjSquare_iso_hom_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformPrecomposeObjSquare_iso_hom_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.CatCospanTransform.id", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.CatCospanTransform.comp", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.CatCospanTransform.category", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.CatCospanTransform.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.CatCospanTransformMorphism.left_coherence_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.CatCospanTransformMorphism.right_coherence_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.CatCospanTransformMorphism.whiskerLeft", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.CatCospanTransformMorphism.whiskerRight", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.CatCospanTransform.isIso_left", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.CatCospanTransform.isIso_right", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.CatCospanTransform.isIso_base", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.CatCospanTransform.inv_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform", "is_tactic_proof": true, "tactics": ["symm", "apply", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.CatCospanTransform.inv_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform", "is_tactic_proof": true, "tactics": ["symm", "apply", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.CatCospanTransform.inv_base", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform", "is_tactic_proof": true, "tactics": ["symm", "apply", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.CatCospanTransform.leftIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.CatCospanTransform.rightIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.CatCospanTransform.baseIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.CatCospanTransform.isIso_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.CatCospanTransform.leftUnitor", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.CatCospanTransform.rightUnitor", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.CatCospanTransform.associator", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.CatCospanTransform.term_◁_", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.CatCospanTransform._aux_Mathlib_CategoryTheory_Limits_Shapes_Pullback_Categorical_CatCospanTransform___macroRules_CategoryTheory_Limits_CatCospanTransform_term_◁__1", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.CatCospanTransform._aux_Mathlib_CategoryTheory_Limits_Shapes_Pullback_Categorical_CatCospanTransform___unexpand_CategoryTheory_Limits_CatCospanTransformMorphism_whiskerLeft_1", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.CatCospanTransform.term_▷_", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.CatCospanTransform._aux_Mathlib_CategoryTheory_Limits_Shapes_Pullback_Categorical_CatCospanTransform___macroRules_CategoryTheory_Limits_CatCospanTransform_term_▷__1", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.CatCospanTransform._aux_Mathlib_CategoryTheory_Limits_Shapes_Pullback_Categorical_CatCospanTransform___unexpand_CategoryTheory_Limits_CatCospanTransformMorphism_whiskerRight_1", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.CatCospanTransform.termα_", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.CatCospanTransform._aux_Mathlib_CategoryTheory_Limits_Shapes_Pullback_Categorical_CatCospanTransform___macroRules_CategoryTheory_Limits_CatCospanTransform_termα__1", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.CatCospanTransform._aux_Mathlib_CategoryTheory_Limits_Shapes_Pullback_Categorical_CatCospanTransform___unexpand_CategoryTheory_Limits_CatCospanTransform_associator_1", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.CatCospanTransform.termλ_", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.CatCospanTransform._aux_Mathlib_CategoryTheory_Limits_Shapes_Pullback_Categorical_CatCospanTransform___macroRules_CategoryTheory_Limits_CatCospanTransform_termλ__1", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.CatCospanTransform._aux_Mathlib_CategoryTheory_Limits_Shapes_Pullback_Categorical_CatCospanTransform___unexpand_CategoryTheory_Limits_CatCospanTransform_leftUnitor_1", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.CatCospanTransform.termρ_", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.CatCospanTransform._aux_Mathlib_CategoryTheory_Limits_Shapes_Pullback_Categorical_CatCospanTransform___macroRules_CategoryTheory_Limits_CatCospanTransform_termρ__1", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.CatCospanTransform._aux_Mathlib_CategoryTheory_Limits_Shapes_Pullback_Categorical_CatCospanTransform___unexpand_CategoryTheory_Limits_CatCospanTransform_rightUnitor_1", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.CatCospanTransform.whisker_exchange", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.CatCospanTransform.id_whiskerRight", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.CatCospanTransform.whiskerRight_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.CatCospanTransform.comp_whiskerRight", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.CatCospanTransform.whiskerRight_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.CatCospanTransform.whiskerleft_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.CatCospanTransform.id_whiskerLeft", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.CatCospanTransform.whiskerLeft_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.CatCospanTransform.comp_whiskerLeft", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.CatCospanTransform.pentagon", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.CatCospanTransform.triangle", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.CatCospanTransform.triangle_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.CatCospanTransform.instIsIsoWhiskerLeft", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.CatCospanTransform.inv_whiskerLeft", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.CatCospanTransform.instIsIsoWhiskerRight", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.CatCospanTransform.inv_whiskerRight", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.isLimitOfIsPullbackOfIsConnected", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isColimitOfIsPushoutOfIsConnected", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingCospan", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingCospan.left", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingCospan.right", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingCospan.one", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingSpan", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingSpan.left", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingSpan.right", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingSpan.zero", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingCospan.Hom", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingCospan.Hom.inl", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingCospan.Hom.inr", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingCospan.Hom.id", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingCospan.instSubsingletonHom", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": true, "tactics": ["constructor"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.WalkingSpan.Hom", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingSpan.Hom.fst", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingSpan.Hom.snd", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingSpan.Hom.id", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingSpan.instSubsingletonHom", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": true, "tactics": ["constructor"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.WalkingCospan.ext", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": true, "tactics": ["apply", "rintro", "have", "dsimp", "simp", "have", "dsimp", "simp", "simp_rw", "exact", "exact"], "tactic_count": 11}
{"name": "CategoryTheory.Limits.WalkingSpan.ext", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": true, "tactics": ["apply", "rintro", "have", "dsimp", "simp", "have", "dsimp", "simp", "simp_rw", "exact", "exact"], "tactic_count": 11}
{"name": "CategoryTheory.Limits.cospan", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.span", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.cospan_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.span_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.cospan_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.span_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.cospan_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.span_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.cospan_map_inl", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.span_map_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.cospan_map_inr", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.span_map_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.cospan_map_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.span_map_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.diagramIsoCospan", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.diagramIsoSpan", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.cospanCompIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.cospanCompIso_app_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.cospanCompIso_app_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.cospanCompIso_app_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.cospanCompIso_hom_app_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.cospanCompIso_hom_app_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.cospanCompIso_hom_app_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.cospanCompIso_inv_app_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.cospanCompIso_inv_app_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.cospanCompIso_inv_app_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.spanCompIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.spanCompIso_app_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.spanCompIso_app_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.spanCompIso_app_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.spanCompIso_hom_app_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.spanCompIso_hom_app_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.spanCompIso_hom_app_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.spanCompIso_inv_app_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.spanCompIso_inv_app_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.spanCompIso_inv_app_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.cospanExt", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.cospanExt_app_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.cospanExt_app_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.cospanExt_app_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.cospanExt_hom_app_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.cospanExt_hom_app_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.cospanExt_hom_app_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.cospanExt_inv_app_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.cospanExt_inv_app_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.cospanExt_inv_app_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.spanExt", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.spanExt_app_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.spanExt_app_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.spanExt_app_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.spanExt_hom_app_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.spanExt_hom_app_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.spanExt_hom_app_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.spanExt_inv_app_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.spanExt_inv_app_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.spanExt_inv_app_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isPullback_equalizer_prod", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Equalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isPushout_coequalizer_coprod", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Equalizer", "is_tactic_proof": true, "tactics": ["refine", "refine", "have", "have", "exact", "exact", "exact", "exact"], "tactic_count": 8}
{"name": "CategoryTheory.NatTrans.Equifibered", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Equifibered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.equifibered_of_isIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Equifibered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.Equifibered.comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Equifibered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.Equifibered.whiskerRight", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Equifibered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.Equifibered.whiskerLeft", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Equifibered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.Equifibered.of_discrete", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Equifibered", "is_tactic_proof": true, "tactics": ["rintro", "simp", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.NatTrans.Coequifibered", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Equifibered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.Coequifibered_of_isIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Equifibered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.Coequifibered.comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Equifibered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.Coequifibered.whiskerRight", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Equifibered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.Coequifibered.whiskerLeft", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Equifibered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.Coequifibered.of_discrete", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Equifibered", "is_tactic_proof": true, "tactics": ["rintro", "simp", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.NatTrans.Coequifibered.op", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Equifibered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.Equifibered.op", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Equifibered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.Coequifibered.unop", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Equifibered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.Equifibered.unop", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Equifibered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.HasPullback", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.HasPushout", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullback", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullback.cone", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pushout", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pushout.cocone", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullback.fst", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullback.snd", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pushout.inl", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pushout.inr", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullback.isLimit", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pushout.isColimit", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PullbackCone.fst_limit_cone", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PullbackCone.snd_limit_cone", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PushoutCocone.inl_colimit_cocone", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PushoutCocone.inr_colimit_cocone", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullback.lift_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullback.lift_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pushout.inl_desc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pushout.inr_desc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullback.lift'", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullback.desc'", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullback.condition", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pushout.condition", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullback.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullbackIsPullback", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pushout.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pushoutIsPushout", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullback.lift_fst_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.pushout.desc_inl_inr", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.pullback.map", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullback.mapDesc", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullback.map_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.pullback.map_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.pushout.map", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pushout.mapLift", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pushout.map_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.pushout.map_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.pullback.map_isIso", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": true, "tactics": ["refine", "rw", "rw", "cat_disch", "cat_disch"], "tactic_count": 5}
{"name": "CategoryTheory.Limits.pullback.congrHom", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullback.congrHom_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.pushout.map_isIso", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": true, "tactics": ["refine", "rw", "rw", "cat_disch", "cat_disch"], "tactic_count": 5}
{"name": "CategoryTheory.Limits.pullback.mapDesc_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.pushout.congrHom", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pushout.congrHom_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.pushout.mapLift_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.pullbackComparison", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullbackComparison_comp_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullbackComparison_comp_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.map_lift_pullbackComparison", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.pushoutComparison", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.inl_comp_pushoutComparison", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.inr_comp_pushoutComparison", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pushoutComparison_map_desc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.hasPullback_symmetry", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullbackSymmetry", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullbackSymmetry_hom_comp_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.pullbackSymmetry_hom_comp_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.pullbackSymmetry_inv_comp_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.pullbackSymmetry_inv_comp_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.hasPushout_symmetry", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pushoutSymmetry", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.inl_comp_pushoutSymmetry_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.inr_comp_pushoutSymmetry_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.inl_comp_pushoutSymmetry_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.inr_comp_pushoutSymmetry_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.HasPullbacksAlong", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.HasPushoutsAlong", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.HasPullbacks", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.HasPushouts", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasPullbacks_of_hasLimit_cospan", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasPushouts_of_hasColimit_span", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.walkingSpanOpEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.walkingCospanOpEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasPullbacks_of_hasWidePullbacks", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasPushouts_of_hasWidePushouts", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasPullback_symmetry_of_hasPullbacksAlong", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasPushouts_symmetry_of_hasPushoutsAlong", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullbackProdFstIsoProd", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullbackProdFstIsoProd_hom_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.pullbackProdFstIsoProd_hom_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.pullbackProdFstIsoProd_inv_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.pullbackProdFstIsoProd_inv_snd_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.pullbackProdFstIsoProd_inv_snd_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.pullbackProdSndIsoProd", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullbackProdSndIsoProd_hom_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.pullbackProdSndIsoProd_hom_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.pullbackProdSndIsoProd_inv_fst_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.pullbackProdSndIsoProd_inv_fst_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.pullbackProdSndIsoProd_inv_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.IsPullback.of_is_product", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPullback.of_is_product'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPullback.of_hasBinaryProduct'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPullback.of_iso_pullback", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPullback.of_horiz_isIso_mono", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPullback.of_horiz_isIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPullback.of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPullback.of_iso'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": true, "tactics": ["apply", "simp", "simp", "simp", "simp"], "tactic_count": 5}
{"name": "CategoryTheory.IsPullback.isIso_fst_of_mono", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPullback.isIso_snd_iso_of_mono", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPullback.isIso_fst_of_isIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": true, "tactics": ["have", "rw", "infer_instance"], "tactic_count": 3}
{"name": "CategoryTheory.IsPullback.isIso_snd_of_isIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": true, "tactics": ["have", "rw", "infer_instance"], "tactic_count": 3}
{"name": "CategoryTheory.IsPullback.paste_vert", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPullback.paste_horiz", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPullback.of_bot", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPullback.of_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPullback.paste_vert_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPullback.paste_horiz_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPullback.of_right'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPullback.of_bot'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPullback.instHasPullbackFst", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPullback.of_vert_isIso_mono", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPullback.of_vert_isIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPullback.of_id_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPullback.of_id_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPullback.id_vert", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPullback.id_horiz", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPullback.of_prod_fst_with_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPullback.of_isLimit_binaryFan_of_isTerminal", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPushout.of_is_coproduct", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPushout.of_is_coproduct'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPushout.of_hasBinaryCoproduct'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPushout.of_iso_pushout", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPushout.of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPushout.of_iso'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": true, "tactics": ["apply", "simp", "simp", "simp", "simp"], "tactic_count": 5}
{"name": "CategoryTheory.IsPushout.isIso_inl_iso_of_epi", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPushout.isIso_inr_iso_of_epi", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPushout.isIso_inl_of_isIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": true, "tactics": ["have", "rw", "infer_instance"], "tactic_count": 3}
{"name": "CategoryTheory.IsPushout.isIso_inr_of_isIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": true, "tactics": ["have", "rw", "infer_instance"], "tactic_count": 3}
{"name": "CategoryTheory.IsPushout.paste_vert", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPushout.paste_horiz", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPushout.of_top", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPushout.of_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPushout.paste_vert_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPushout.paste_horiz_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPushout.of_top'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPushout.of_left'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPushout.of_horiz_isIso_epi", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPushout.of_horiz_isIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPushout.of_vert_isIso_epi", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPushout.of_vert_isIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPushout.of_id_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPushout.of_id_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPushout.id_vert", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPushout.id_horiz", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPushout.of_coprod_inl_with_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPushout.of_isColimit_binaryCofan_of_isInitial", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPullback.isLimitFork", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": true, "tactics": ["fapply", "exact", "exact", "intro", "apply"], "tactic_count": 5}
{"name": "CategoryTheory.IsPushout.isLimitFork", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": true, "tactics": ["fapply", "exact", "exact", "intro", "apply"], "tactic_count": 5}
{"name": "CategoryTheory.Functor.map_isPullback", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": false, "tactics": ["refine", "rfl", "simp", "simp"], "tactic_count": 4}
{"name": "CategoryTheory.Functor.map_isPushout", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": false, "tactics": ["refine", "rfl", "simp", "simp"], "tactic_count": 4}
{"name": "CategoryTheory.IsPullback.of_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": true, "tactics": ["refine", "refine", "exacts"], "tactic_count": 3}
{"name": "CategoryTheory.IsPullback.of_map_of_faithful", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPullback.map_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPushout.of_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": true, "tactics": ["refine", "refine", "exacts"], "tactic_count": 3}
{"name": "CategoryTheory.IsPushout.of_map_of_faithful", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPushout.map_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPullback.of_hasBinaryProduct", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.BicartesianSq", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "CategoryTheory.IsPullback.zero_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.BicartesianSq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPullback.zero_top", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.BicartesianSq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPullback.zero_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.BicartesianSq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPullback.zero_bot", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.BicartesianSq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPullback.of_isBilimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.BicartesianSq", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "CategoryTheory.IsPullback.of_has_biproduct", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.BicartesianSq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPullback.inl_snd'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.BicartesianSq", "is_tactic_proof": true, "tactics": ["refine", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.IsPullback.inl_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.BicartesianSq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPullback.inr_fst'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.BicartesianSq", "is_tactic_proof": true, "tactics": ["apply", "refine", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.IsPullback.inr_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.BicartesianSq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPullback.of_is_bilimit'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.BicartesianSq", "is_tactic_proof": true, "tactics": ["refine", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.IsPullback.of_hasBinaryBiproduct", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.BicartesianSq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPullback.hasPullback_biprod_fst_biprod_snd", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.BicartesianSq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPullback.pullbackBiprodInlBiprodInr", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.BicartesianSq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPushout.of_hasBinaryCoproduct", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.BicartesianSq", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "CategoryTheory.IsPushout.zero_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.BicartesianSq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPushout.zero_bot", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.BicartesianSq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPushout.zero_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.BicartesianSq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPushout.zero_top", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.BicartesianSq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPushout.of_isBilimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.BicartesianSq", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "CategoryTheory.IsPushout.of_has_biproduct", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.BicartesianSq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPushout.inl_snd'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.BicartesianSq", "is_tactic_proof": true, "tactics": ["apply", "refine", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.IsPushout.inl_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.BicartesianSq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPushout.inr_fst'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.BicartesianSq", "is_tactic_proof": true, "tactics": ["refine", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.IsPushout.inr_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.BicartesianSq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPushout.of_is_bilimit'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.BicartesianSq", "is_tactic_proof": true, "tactics": ["refine", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.IsPushout.of_hasBinaryBiproduct", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.BicartesianSq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPushout.hasPushout_biprod_fst_biprod_snd", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.BicartesianSq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPushout.pushoutBiprodFstBiprodSnd", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.BicartesianSq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.BicartesianSq.of_isPullback_isPushout", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.BicartesianSq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.BicartesianSq.flip", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.BicartesianSq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.BicartesianSq.of_is_biproduct₁", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.BicartesianSq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.BicartesianSq.of_is_biproduct₂", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.BicartesianSq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.BicartesianSq.of_has_biproduct₁", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.BicartesianSq", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "CategoryTheory.BicartesianSq.of_has_biproduct₂", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.BicartesianSq", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "CategoryTheory.IsPullback.cone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPullback.cone_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPullback.cone_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPullback.isLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPullback.lift", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPullback.lift_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPullback.lift_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPullback.exists_lift", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPullback.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPullback.of_isLimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPullback.of_isLimit'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPullback.of_isLimit_cone", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPullback.hasPullback", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPullback.of_hasPullback", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPullback.isoIsPullback", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPullback.isoIsPullback_hom_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPullback.isoIsPullback_hom_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPullback.isoIsPullback_inv_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.IsPullback.isoIsPullback_inv_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.IsPullback.isoPullback", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPullback.isoPullback_hom_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.IsPullback.isoPullback_hom_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.IsPullback.isoPullback_inv_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.IsPullback.isoPullback_inv_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.IsPushout.cocone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPushout.cocone_inl", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPushout.cocone_inr", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPushout.isColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPushout.desc", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPushout.inl_desc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPushout.inr_desc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPushout.exists_desc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPushout.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPushout.of_isColimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPushout.of_isColimit'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPushout.of_isColimit_cocone", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPushout.hasPushout", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPushout.of_hasPushout", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPushout.isoIsPushout", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPushout.inl_isoIsPushout_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPushout.inr_isoIsPushout_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPushout.inl_isoIsPushout_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.IsPushout.inr_isoIsPushout_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.IsPushout.isoPushout", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPushout.inl_isoPushout_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.IsPushout.inr_isoPushout_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.IsPushout.inl_isoPushout_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.IsPushout.inr_isoPushout_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.IsPullback.flip", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPullback.flip_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPullback.op", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPullback.unop", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPushout.flip", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPushout.flip_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPushout.op", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPushout.unop", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isIso_kernel_map_of_isPullback", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isIso_cokernel_map_of_isPushout", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Kernels", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullbackConeOfLeftIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Iso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullbackConeOfLeftIso_x", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Iso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullbackConeOfLeftIso_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Iso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullbackConeOfLeftIso_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Iso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullbackConeOfLeftIso_π_app_none", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Iso", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.pullbackConeOfLeftIso_π_app_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Iso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullbackConeOfLeftIso_π_app_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Iso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullbackConeOfLeftIsoIsLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Iso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasPullback_of_left_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Iso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullback_snd_iso_of_left_iso", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Iso", "is_tactic_proof": true, "tactics": ["refine", "ext", "simp", "simp"], "tactic_count": 4}
{"name": "CategoryTheory.Limits.pullback_inv_snd_fst_of_left_isIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Iso", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.pullbackConeOfRightIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Iso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullbackConeOfRightIso_x", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Iso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullbackConeOfRightIso_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Iso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullbackConeOfRightIso_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Iso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullbackConeOfRightIso_π_app_none", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Iso", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.pullbackConeOfRightIso_π_app_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Iso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullbackConeOfRightIso_π_app_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Iso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullbackConeOfRightIsoIsLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Iso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasPullback_of_right_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Iso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullback_fst_iso_of_right_iso", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Iso", "is_tactic_proof": true, "tactics": ["refine", "ext", "simp", "simp"], "tactic_count": 4}
{"name": "CategoryTheory.Limits.pullback_inv_fst_snd_of_right_isIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Iso", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.pushoutCoconeOfLeftIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Iso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pushoutCoconeOfLeftIso_x", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Iso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pushoutCoconeOfLeftIso_inl", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Iso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pushoutCoconeOfLeftIso_inr", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Iso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pushoutCoconeOfLeftIso_ι_app_none", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Iso", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.pushoutCoconeOfLeftIso_ι_app_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Iso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pushoutCoconeOfLeftIso_ι_app_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Iso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pushoutCoconeOfLeftIsoIsLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Iso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasPushout_of_left_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Iso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pushout_inr_iso_of_left_iso", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Iso", "is_tactic_proof": true, "tactics": ["refine", "ext", "simp", "simp"], "tactic_count": 4}
{"name": "CategoryTheory.Limits.pushout_inl_inv_inr_of_right_isIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Iso", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.pushoutCoconeOfRightIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Iso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pushoutCoconeOfRightIso_x", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Iso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pushoutCoconeOfRightIso_inl", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Iso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pushoutCoconeOfRightIso_inr", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Iso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pushoutCoconeOfRightIso_ι_app_none", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Iso", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.pushoutCoconeOfRightIso_ι_app_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Iso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pushoutCoconeOfRightIso_ι_app_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Iso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pushoutCoconeOfRightIsoIsLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Iso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasPushout_of_right_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Iso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pushout_inl_iso_of_right_iso", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Iso", "is_tactic_proof": true, "tactics": ["refine", "ext", "simp", "simp"], "tactic_count": 4}
{"name": "CategoryTheory.Limits.pushout_inr_inv_inl_of_right_isIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Iso", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.PullbackCone.mono_snd_of_is_pullback_of_mono", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Mono", "is_tactic_proof": true, "tactics": ["refine", "rw", "apply"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.PullbackCone.mono_fst_of_is_pullback_of_mono", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Mono", "is_tactic_proof": true, "tactics": ["refine", "rw", "apply"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.PullbackCone.isLimitMkIdId", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Mono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PullbackCone.mono_of_isLimitMkIdId", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Mono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PullbackCone.isLimitOfFactors", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Mono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PullbackCone.isLimitOfCompMono", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Mono", "is_tactic_proof": true, "tactics": ["apply", "intro", "rcases", "refine", "intro", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.Limits.pullback.fst_of_mono", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Mono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullback.snd_of_mono", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Mono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.mono_pullback_to_prod", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Mono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullbackIsPullbackOfCompMono", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Mono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasPullback_of_comp_mono", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Mono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasPullback_of_right_factors_mono", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Mono", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.pullback_snd_iso_of_right_factors_mono", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Mono", "is_tactic_proof": true, "tactics": ["have", "convert", "exact", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.Limits.hasPullback_of_left_factors_mono", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Mono", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.pullback_snd_iso_of_left_factors_mono", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Mono", "is_tactic_proof": true, "tactics": ["have", "convert", "exact", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.Limits.has_kernel_pair_of_mono", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Mono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PullbackCone.fst_eq_snd_of_mono_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Mono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.fst_eq_snd_of_mono_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Mono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullbackSymmetry_hom_of_mono_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Mono", "is_tactic_proof": true, "tactics": ["ext", "simp", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.PullbackCone.isIso_fst_of_mono_of_isLimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Mono", "is_tactic_proof": true, "tactics": ["refine", "apply", "simp", "simp"], "tactic_count": 4}
{"name": "CategoryTheory.Limits.PullbackCone.isIso_snd_of_mono_of_isLimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Mono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isIso_fst_of_mono", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Mono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isIso_snd_of_mono", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Mono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PushoutCocone.epi_inr_of_is_pushout_of_epi", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Mono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PushoutCocone.epi_inl_of_is_pushout_of_epi", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Mono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PushoutCocone.isColimitMkIdId", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Mono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PushoutCocone.epi_of_isColimitMkIdId", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Mono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PushoutCocone.isColimitOfFactors", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Mono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PushoutCocone.isColimitOfEpiComp", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Mono", "is_tactic_proof": true, "tactics": ["apply", "intro", "rcases", "refine", "intro", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.Limits.pushout.inl_of_epi", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Mono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pushout.inr_of_epi", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Mono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.epi_coprod_to_pushout", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Mono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pushoutIsPushoutOfEpiComp", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Mono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasPushout_of_epi_comp", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Mono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasPushout_of_right_factors_epi", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Mono", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
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{"name": "CategoryTheory.Limits.pullbackRightPullbackFstIso_inv_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Pasting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullbackRightPullbackFstIso_inv_snd_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Pasting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullbackRightPullbackFstIso_inv_snd_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Pasting", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.hasPullbackVertPaste", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Pasting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullbackLeftPullbackSndIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Pasting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullbackLeftPullbackSndIso_hom_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Pasting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullbackLeftPullbackSndIso_hom_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Pasting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullbackLeftPullbackSndIso_inv_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Pasting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullbackLeftPullbackSndIso_inv_snd_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Pasting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullbackLeftPullbackSndIso_inv_fst_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Pasting", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.instHasPushoutComp", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Pasting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pushoutLeftPushoutInrIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Pasting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.inl_pushoutLeftPushoutInrIso_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Pasting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.inr_pushoutLeftPushoutInrIso_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Pasting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.inr_pushoutLeftPushoutInrIso_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Pasting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.inl_inl_pushoutLeftPushoutInrIso_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Pasting", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.inr_inl_pushoutLeftPushoutInrIso_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Pasting", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.hasPushoutVertPaste", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Pasting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pushoutRightPushoutInlIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Pasting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.inl_pushoutRightPushoutInlIso_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Pasting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.inr_inr_pushoutRightPushoutInlIso_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Pasting", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.inr_pushoutRightPushoutInlIso_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Pasting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.inl_pushoutRightPushoutInlIso_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Pasting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.inr_inl_pushoutRightPushoutInlIso_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Pasting", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.PullbackCone", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PullbackCone.fst", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PullbackCone.snd", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PullbackCone.π_app_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PullbackCone.π_app_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PullbackCone.condition_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": true, "tactics": ["have", "dsimp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.PullbackCone.mk_π_app_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PullbackCone.mk_π_app_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PullbackCone.mk_π_app_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PullbackCone.mk_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PullbackCone.mk_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PullbackCone.condition", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PullbackCone.equalizer_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PullbackCone.eta", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PullbackCone.isLimitAux", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PullbackCone.isLimitAux'", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PullbackCone.IsLimit.mk", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PullbackCone.IsLimit.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PullbackCone.IsLimit.lift", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PullbackCone.IsLimit.lift_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PullbackCone.IsLimit.lift_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PullbackCone.IsLimit.lift'", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PullbackCone.mkSelfIsLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PullbackCone.flip", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PullbackCone.flip_pt", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PullbackCone.flip_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PullbackCone.flip_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PullbackCone.flipFlipIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PullbackCone.flipIsLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PullbackCone.isLimitOfFlip", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cone.ofPullbackCone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PullbackCone.ofCone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PullbackCone.isoMk", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PushoutCocone", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PushoutCocone.inl", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PushoutCocone.inr", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PushoutCocone.ι_app_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PushoutCocone.ι_app_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PushoutCocone.condition_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": true, "tactics": ["have", "dsimp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.PushoutCocone.mk", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PushoutCocone.mk_ι_app_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PushoutCocone.mk_ι_app_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PushoutCocone.mk_ι_app_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PushoutCocone.mk_inl", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PushoutCocone.mk_inr", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PushoutCocone.condition", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PushoutCocone.coequalizer_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PushoutCocone.eta", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PushoutCocone.isColimitAux", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PushoutCocone.isColimitAux'", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PushoutCocone.IsColimit.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PushoutCocone.IsColimit.desc", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PushoutCocone.IsColimit.inl_desc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PushoutCocone.IsColimit.inr_desc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PushoutCocone.IsColimit.desc'", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PushoutCocone.IsColimit.mk", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PushoutCocone.mkSelfIsColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PushoutCocone.flip", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PushoutCocone.flip_pt", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PushoutCocone.flip_inl", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PushoutCocone.flip_inr", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PushoutCocone.flipFlipIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PushoutCocone.flipIsColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PushoutCocone.isColimitOfFlip", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cocone.ofPushoutCocone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PushoutCocone.ofCocone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PushoutCocone.isoMk", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CommSq.cone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CommSq.cocone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CommSq.cone_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CommSq.cone_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CommSq.cocone_inl", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CommSq.cocone_inr", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.PushoutObjObj.ofHasPushout", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackObjObj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.PushoutObjObj.ι", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackObjObj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.PushoutObjObj.inl_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackObjObj", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.PushoutObjObj.inr_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackObjObj", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.PushoutObjObj.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackObjObj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.PushoutObjObj.flip", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackObjObj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.PushoutObjObj.ι_flip", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackObjObj", "is_tactic_proof": true, "tactics": ["apply", "rw", "rw"], "tactic_count": 3}
{"name": "CategoryTheory.Functor.PushoutObjObj.ofHasPushout_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackObjObj", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.PushoutObjObj.mapArrowLeft", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackObjObj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.PushoutObjObj.mapArrowLeft_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackObjObj", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.PushoutObjObj.mapArrowLeft_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackObjObj", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.PushoutObjObj.ι_iso_of_iso_left", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackObjObj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.PushoutObjObj.mapArrowRight", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackObjObj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.PushoutObjObj.mapArrowRight_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackObjObj", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.PushoutObjObj.mapArrowRight_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackObjObj", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.PushoutObjObj.ι_iso_of_iso_right", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackObjObj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.leibnizPushout", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackObjObj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.PullbackObjObj.ofHasPullback", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackObjObj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.PullbackObjObj.π", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackObjObj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.PullbackObjObj.π_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackObjObj", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.PullbackObjObj.π_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackObjObj", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.PullbackObjObj.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackObjObj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.PullbackObjObj.ofHasPullback_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackObjObj", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.PullbackObjObj.mapArrowLeft", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackObjObj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.PullbackObjObj.mapArrowLeft_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackObjObj", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.PullbackObjObj.mapArrowLeft_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackObjObj", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.PullbackObjObj.π_iso_of_iso_left", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackObjObj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.PullbackObjObj.mapArrowRight", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackObjObj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.PullbackObjObj.mapArrowRight_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackObjObj", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.PullbackObjObj.mapArrowRight_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackObjObj", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.PullbackObjObj.π_iso_of_iso_right", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackObjObj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.leibnizPullback", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackObjObj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Square.pullbackCone", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Square", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Square.pushoutCocone", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Square", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Square.IsPullback", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Square", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Square.IsPushout", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Square", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Square.isPullback_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Square", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Square.isPushout_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Square", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Square.IsPullback.mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Square", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Square.IsPushout.mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Square", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Square.IsPullback.isLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Square", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Square.IsPushout.isColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Square", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Square.IsPullback.of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Square", "is_tactic_proof": false, "tactics": ["refine", "all_goals"], "tactic_count": 2}
{"name": "CategoryTheory.Square.IsPullback.iff_of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Square", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Square.IsPushout.of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Square", "is_tactic_proof": false, "tactics": ["refine", "all_goals"], "tactic_count": 2}
{"name": "CategoryTheory.Square.IsPushout.iff_of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Square", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Square.IsPushout.op", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Square", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Square.IsPushout.unop", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Square", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Square.IsPullback.op", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Square", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Square.IsPullback.unop", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Square", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Square.IsPullback.flip", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Square", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Square.IsPullback.mono_f₁₃", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Square", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Square.IsPullback.mono_f₁₂", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Square", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Square.IsPushout.flip", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Square", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Square.IsPushout.epi_f₂₄", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Square", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Square.IsPushout.epi_f₃₄", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Pullback.Square", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.IsReflexivePair.common_section", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsCoreflexivePair.common_retraction", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsReflexivePair.mk'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsCoreflexivePair.mk'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.commonSection", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.section_comp_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.section_comp_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.commonRetraction", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.left_comp_retraction", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.right_comp_retraction", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsKernelPair.isReflexivePair", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsReflexivePair.swap", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsCoreflexivePair.swap", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instIsReflexivePairMapAppCounitObj", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasCoequalizer_of_common_section", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": true, "tactics": ["letI", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.hasEqualizer_of_common_retraction", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": true, "tactics": ["letI", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.hasReflexiveCoequalizers_of_hasCoequalizers", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasCoreflexiveEqualizers_of_hasEqualizers", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingReflexivePair", "kind": "inductive", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instDecidableEqWalkingReflexivePair", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instInhabitedWalkingReflexivePair.default", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instInhabitedWalkingReflexivePair", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingReflexivePair.Hom", "kind": "inductive", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingReflexivePair.instDecidableEqHom", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingReflexivePair.Hom.comp", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingReflexivePair.category", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingReflexivePair.Hom.id_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingReflexivePair.reflexion_comp_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingReflexivePair.reflexion_comp_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingReflexivePair.leftCompReflexion_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingReflexivePair.rightCompReflexion_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingReflexivePair.map_reflexion_comp_map_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.WalkingReflexivePair.map_reflexion_comp_map_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.WalkingParallelPair.inclusionWalkingReflexivePair", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingParallelPair.instNonemptyStructuredArrowWalkingReflexivePairInclusionWalkingReflexivePair", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": true, "tactics": ["cases", "zero", "one"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.WalkingParallelPair.instIsConnectedStructuredArrowWalkingReflexivePairInclusionWalkingReflexivePair", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": true, "tactics": ["cases", "zero", "refine", "rintro", "exact", "exact", "one", "refine", "have", "have", "rintro", "exact", "exact", "all_goals"], "tactic_count": 14}
{"name": "CategoryTheory.Limits.WalkingParallelPair.inclusionWalkingReflexivePair_final", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.reflexivePair_obj_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.reflexivePair_obj_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.reflexivePair_map_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.reflexivePair_map_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.reflexivePair_map_reflexion", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.ofIsReflexivePair", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.ofIsReflexivePair_map_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.ofIsReflexivePair_map_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.inclusionWalkingReflexivePairOfIsReflexivePairIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.reflexivePair.mkNatTrans", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.reflexivePair.mkNatTrans_app_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.reflexivePair.mkNatTrans_app_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.reflexivePair.diagramIsoReflexivePair", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.reflexivePair.compRightIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.reflexivePair.whiskerRightMkNatTrans", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.reflexivePair.to_isReflexivePair", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.ReflexiveCofork", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.ReflexiveCofork.π", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.ReflexiveCofork.mk", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.ReflexiveCofork.mk_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.ReflexiveCofork.condition", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.ReflexiveCofork.app_one_eq_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.ReflexiveCofork.toCofork", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.reflexiveCoforkEquivCofork", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.reflexiveCoforkEquivCofork_functor_obj_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.reflexiveCoforkEquivCofork_inverse_obj_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": false, "tactics": ["dsimp", "rw", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.reflexiveCoforkEquivCoforkObjIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasReflexiveCoequalizer_iff_hasCoequalizer", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.reflexivePair_hasColimit_of_hasCoequalizer", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.ReflexiveCofork.isColimitEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.reflexiveCoequalizerIsoCoequalizer", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.ι_reflexiveCoequalizerIsoCoequalizer_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.π_reflexiveCoequalizerIsoCoequalizer_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": true, "tactics": ["rw", "simp", "colimit.cocone_ι]"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.ofIsReflexivePair_hasColimit_of_hasCoequalizer", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.colimitOfIsReflexivePairIsoCoequalizer", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.ι_colimitOfIsReflexivePairIsoCoequalizer_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.π_colimitOfIsReflexivePairIsoCoequalizer_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasReflexiveCoequalizers_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.RegularMono.mono", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.RegularMono.ofIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.RegularMono.ofArrowIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.regularMono", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.regularMono_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.regularMono.containsIdentities", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.regularMono.respectsIso", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isRegularMono_of_regularMono", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsRegularMono.getStruct", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsRegularMono.Z", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsRegularMono.left", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsRegularMono.right", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsRegularMono.w", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsRegularMono.isLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsRegularMono.lift", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsRegularMono.fac", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsRegularMono.uniq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.RegularMono.equalizer", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instIsRegularMonoι", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.RegularMono.ofIsSplitMono", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instIsRegularMonoOfIsSplitMono", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.RegularMono.lift'", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.regularOfIsPullbackSndOfRegular", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.regularOfIsPullbackFstOfRegular", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.RegularMono.strongMono", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instStrongMonoOfIsRegularMono", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isIso_of_regularMono_of_epi", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.regularMonoOfMono", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.regularMonoCategoryOfSplitMonoCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.strongMonoCategory_of_regularMonoCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.RegularEpi.epi", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.RegularEpi.ofIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.RegularEpi.ofArrowIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.regularEpi", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.regularEpi_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.regularEpi.containsIdentities", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.regularEpi.respectsIso", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isRegularEpi_of_regularEpi", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsRegularEpi.getStruct", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsRegularEpi.W", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsRegularEpi.left", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsRegularEpi.right", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsRegularEpi.w", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsRegularEpi.isColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsRegularEpi.desc", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsRegularEpi.fac", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsRegularEpi.uniq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.coequalizerRegular", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instIsRegularEpiπ", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.regularEpiOfKernelPair", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.effectiveEpiStructOfRegularEpi", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.RegularEpi.effectiveEpi", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instEffectiveEpiOfIsRegularEpi", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.effectiveEpi_of_kernelPair", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isColimitCoforkOfEffectiveEpi", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.regularEpiOfEffectiveEpi", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isRegularEpi_of_EffectiveEpi", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isRegularEpi_iff_effectiveEpi", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.EffectiveEpiStruct.isColimitCoforkOfIsPullback", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.RegularEpi.ofSplitEpi", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instIsRegularEpiOfIsSplitEpi", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.RegularEpi.desc'", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.regularOfIsPushoutSndOfRegular", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.regularOfIsPushoutFstOfRegular", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.strongEpi_of_regularEpi", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isIso_of_regularEpi_of_mono", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.regularEpiOfEpi", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.regularEpiCategoryOfSplitEpiCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.strongEpiCategory_of_regularEpiCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.RegularMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.SequentialProduct.functorObj_eq_pos", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.SequentialProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.SequentialProduct.functorObj_eq_neg", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.SequentialProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.SequentialProduct.functorObj", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.SequentialProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.SequentialProduct.functorObjProj_pos", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.SequentialProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.SequentialProduct.functorObjProj_neg", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.SequentialProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.SequentialProduct.functorMap", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.SequentialProduct", "is_tactic_proof": true, "tactics": ["intro", "refine", "all_goals"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.SequentialProduct.functorMap_commSq_succ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.SequentialProduct", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.SequentialProduct.functorMap_commSq_aux", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.SequentialProduct", "is_tactic_proof": true, "tactics": ["induction", "refl", "specialize", "have", "rw", "slice_lhs", "simp", "dite_eq_ite,", "split_ifs", "simp"], "tactic_count": 10}
{"name": "CategoryTheory.Limits.SequentialProduct.functorMap_commSq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.SequentialProduct", "is_tactic_proof": true, "tactics": ["cases", "zero", "have", "subst", "simp", "succ", "rw", "simp", "have", "simp", "rw", "simp", "congr", "exact"], "tactic_count": 14}
{"name": "CategoryTheory.Limits.SequentialProduct.cone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.SequentialProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.SequentialProduct.cone_π_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.SequentialProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.SequentialProduct.cone_π_app_comp_Pi_π_pos", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.SequentialProduct", "is_tactic_proof": false, "tactics": ["simp", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.SequentialProduct.cone_π_app_comp_Pi_π_neg", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.SequentialProduct", "is_tactic_proof": false, "tactics": ["simp", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.SequentialProduct.isLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.SequentialProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.SequentialProduct.functorMap_epi", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.SequentialProduct", "is_tactic_proof": true, "tactics": ["rw", "apply", "apply", "apply", "apply", "intro", "split", "all_goals", "apply", "apply", "intro", "split", "all_goals"], "tactic_count": 13}
{"name": "CategoryTheory.Limits.SingleObj.instMulActionObjSingleObjStar", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.SingleObj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.SingleObj.Types.sections.equivFixedPoints", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.SingleObj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.SingleObj.Types.limitEquivFixedPoints", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.SingleObj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.SingleObj.colimitTypeRel_iff_orbitRel", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.SingleObj", "is_tactic_proof": true, "tactics": ["conv", "change", "grind"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.SingleObj.colimitTypeRelEquivOrbitRelQuotient", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.SingleObj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.SingleObj.Types.colimitEquivQuotient", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.SingleObj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instInhabitedIsSplitCoequalizerId", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.SplitCoequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsSplitCoequalizer.map", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.SplitCoequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsSplitCoequalizer.asCofork", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.SplitCoequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsSplitCoequalizer.asCofork_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.SplitCoequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsSplitCoequalizer.isCoequalizer", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.SplitCoequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsSplitPair", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.SplitCoequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasSplitCoequalizer.coequalizerOfSplit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.SplitCoequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasSplitCoequalizer.coequalizerπ", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.SplitCoequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasSplitCoequalizer.isSplitCoequalizer", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.SplitCoequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.map_is_split_pair", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.SplitCoequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasCoequalizer_of_hasSplitCoequalizer", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.SplitCoequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instInhabitedIsSplitEqualizerId", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.SplitEqualizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsSplitEqualizer.map", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.SplitEqualizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsSplitEqualizer.asFork", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.SplitEqualizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsSplitEqualizer.asFork_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.SplitEqualizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsSplitEqualizer.isEqualizer", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.SplitEqualizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsCosplitPair", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.SplitEqualizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasSplitEqualizer.equalizerOfSplit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.SplitEqualizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasSplitEqualizer.equalizerι", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.SplitEqualizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasSplitEqualizer.isSplitEqualizer", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.SplitEqualizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.map_is_cosplit_pair", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.SplitEqualizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasEqualizer_of_hasSplitEqualizer", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.SplitEqualizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsInitial.isIso_to", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.StrictInitial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsInitial.strict_hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.StrictInitial", "is_tactic_proof": true, "tactics": ["haveI", "haveI", "exact"], "tactic_count": 3}
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{"name": "CategoryTheory.Limits.IsInitial.ofStrict", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.StrictInitial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.initial_mono_of_strict_initial_objects", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.StrictInitial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.mulIsInitial", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.StrictInitial", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.mulIsInitial_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.StrictInitial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isInitialMul", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.StrictInitial", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.isInitialMul_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.StrictInitial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits.initial.strict_hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.StrictInitial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.initial.subsingleton_to", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.StrictInitial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.mulInitial", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.StrictInitial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.mulInitial_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.StrictInitial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.initialMul", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.StrictInitial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.initialMul_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.StrictInitial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasStrictInitialObjects_of_initial_is_strict", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.StrictInitial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsTerminal.isIso_from", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.StrictInitial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits.IsTerminal.subsingleton_to", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.StrictInitial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits.terminal.strict_hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.StrictInitial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.terminal.subsingleton_to", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.StrictInitial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasStrictTerminalObjects_of_terminal_is_strict", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.StrictInitial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StrongEpi.mk'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.StrongEpi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StrongMono.mk'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.StrongEpi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.epi_of_strongEpi", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.StrongEpi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.strongEpi_of_strongEpi", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.StrongEpi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.strongEpi_of_isIso", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.StrongEpi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.StrongEpi.of_arrow_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.StrongEpi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.StrongEpi.iff_of_arrow_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.StrongEpi", "is_tactic_proof": true, "tactics": ["constructor", "exacts"], "tactic_count": 2}
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{"name": "CategoryTheory.isIso_of_mono_of_strongEpi", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.StrongEpi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.strongEpi_of_epi", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.StrongEpi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.strongMono_of_mono", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.StrongEpi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.balanced_of_strongEpiCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.StrongEpi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.balanced_of_strongMonoCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.StrongEpi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.HasTerminal", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.HasInitial", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasTerminalChangeDiagram", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasTerminalChangeUniverse", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasInitialChangeDiagram", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasInitialChangeUniverse", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.terminal", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.initial", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.term⊤__", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits._aux_Mathlib_CategoryTheory_Limits_Shapes_Terminal___unexpand_CategoryTheory_Limits_terminal_1", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits._aux_Mathlib_CategoryTheory_Limits_Shapes_Terminal___unexpand_CategoryTheory_Limits_initial_1", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasTerminal_of_unique", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsTerminal.hasTerminal", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasInitial_of_unique", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsInitial.hasInitial", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.terminal.from", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits.terminalIsTerminal", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.initialIsInitial", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.uniqueToTerminal", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits.terminal.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Terminal", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
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{"name": "CategoryTheory.Limits.initialIsoIsInitial", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.terminalIsoIsTerminal", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits.initial.isSplitEpi_to", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasInitial_op_of_hasTerminal", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasTerminal_op_of_hasInitial", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasTerminal_of_hasInitial_op", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasInitial_of_hasTerminal_op", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instHasLimitObjFunctorConstTerminal", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.limitConstTerminal", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.limitConstTerminal_inv_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Terminal", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.instHasColimitObjFunctorConstInitial", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.colimitConstInitial", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.ι_colimitConstInitial_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Terminal", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.initial.mono_from", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.InitialMonoClass.of_initial", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.InitialMonoClass.of_terminal", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.terminalComparison", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.initialComparison", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasLimit_of_domain_hasInitial", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.limitOfInitial", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasLimit_of_domain_hasTerminal", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.limitOfTerminal", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasColimit_of_domain_hasTerminal", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.colimitOfTerminal", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasColimit_of_domain_hasInitial", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.colimitOfInitial", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isIso_π_of_isInitial", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isIso_π_initial", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isIso_π_of_isTerminal", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isIso_π_terminal", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isIso_ι_of_isTerminal", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isIso_ι_terminal", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isIso_ι_of_isInitial", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isIso_ι_initial", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.Terminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingParallelFamily", "kind": "inductive", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instInhabitedWalkingParallelFamily.default", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instInhabitedWalkingParallelFamily", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instDecidableEqWalkingParallelFamily", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingParallelFamily.Hom", "kind": "inductive", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingParallelFamily.instDecidableEqHom", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instInhabitedHomZero", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingParallelFamily.Hom.comp", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingParallelFamily.category", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingParallelFamily.hom_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WalkingParallelFamily.arrowEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.parallelFamily", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.parallelFamily_obj_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.parallelFamily_obj_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.parallelFamily_map_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.diagramIsoParallelFamily", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.walkingParallelFamilyEquivWalkingParallelPair", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Trident", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cotrident", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Trident.ι", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cotrident.π", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Trident.ι_eq_app_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cotrident.π_eq_app_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Trident.app_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.Cotrident.app_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.Trident.ofι", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cotrident.ofπ", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Trident.ι_ofι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cotrident.π_ofπ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Trident.condition", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.Cotrident.condition", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.Trident.equalizer_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cotrident.coequalizer_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Trident.IsLimit.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cotrident.IsColimit.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Trident.IsLimit.lift'", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cotrident.IsColimit.desc'", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Trident.IsLimit.mk", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Trident.IsLimit.mk'", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cotrident.IsColimit.mk", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cotrident.IsColimit.mk'", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Trident.IsLimit.homIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Trident.IsLimit.homIso_natural", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cotrident.IsColimit.homIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cotrident.IsColimit.homIso_natural", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cone.ofTrident", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cocone.ofCotrident", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cone.ofTrident_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cocone.ofCotrident_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Trident.ofCone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cotrident.ofCocone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Trident.ofCone_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Cotrident.ofCocone_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.HasWideEqualizer", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.wideEqualizer", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.wideEqualizer.ι", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.wideEqualizer.trident", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.wideEqualizer.trident_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.wideEqualizer.trident_π_app_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.wideEqualizer.condition", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.wideEqualizerIsWideEqualizer", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.wideEqualizer.lift", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.wideEqualizer.lift_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.wideEqualizer.lift'", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.wideEqualizer.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.wideEqualizer.ι_mono", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.mono_of_isLimit_parallelFamily", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.HasWideCoequalizer", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.wideCoequalizer", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.wideCoequalizer.π", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.wideCoequalizer.cotrident", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.wideCoequalizer.cotrident_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.wideCoequalizer.cotrident_ι_app_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.wideCoequalizer.condition", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.wideCoequalizerIsWideCoequalizer", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.wideCoequalizer.desc", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.wideCoequalizer.π_desc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "CategoryTheory.Limits.wideCoequalizer.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.wideCoequalizer.π_epi", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.epi_of_isColimit_parallelFamily", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.HasWideEqualizers", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.HasWideCoequalizers", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasWideEqualizers_of_hasLimit_parallelFamily", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasWideCoequalizers_of_hasColimit_parallelFamily", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasEqualizers_of_hasWideEqualizers", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasCoequalizers_of_hasWideCoequalizers", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WidePullbackShape", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instInhabitedWidePullbackShape", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WidePushoutShape", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instInhabitedWidePushoutShape", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WidePullbackShape.Hom", "kind": "inductive", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WidePullbackShape.instDecidableEqHom", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WidePullbackShape.struct", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WidePullbackShape.Hom.inhabited", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WidePullbackShape.evalCasesBash", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WidePullbackShape.subsingleton_hom", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WidePullbackShape.category", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WidePullbackShape.hom_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WidePullbackShape.wideCospan", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WidePullbackShape.diagramIsoWideCospan", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WidePullbackShape.mkCone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WidePullbackShape.equivalenceOfEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WidePullbackShape.equivalenceOfEquiv_functor_obj_none", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WidePullbackShape.equivalenceOfEquiv_functor_obj_some", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WidePullbackShape.equivalenceOfEquiv_functor_map_term", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WidePullbackShape.uliftEquivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WidePushoutShape.Hom", "kind": "inductive", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WidePushoutShape.instDecidableEqHom", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WidePushoutShape.struct", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits.WidePushoutShape.evalCasesBash'", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WidePushoutShape.subsingleton_hom", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits.WidePushoutShape.hom_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WidePushoutShape.wideSpan", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WidePushoutShape.diagramIsoWideSpan", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WidePushoutShape.mkCocone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WidePushoutShape.equivalenceOfEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WidePushoutShape.uliftEquivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.HasWidePullbacks", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.HasWidePushouts", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.HasWidePullback", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.HasWidePushout", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.widePullback", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.widePushout", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WidePullback.π", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WidePullback.base", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WidePullback.π_arrow", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.WidePullback.lift", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WidePullback.lift_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.WidePullback.lift_base", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.WidePullback.eq_lift_of_comp_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": true, "tactics": ["intro", "apply", "rintro", "apply", "apply"], "tactic_count": 5}
{"name": "CategoryTheory.Limits.WidePullback.hom_eq_lift", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.WidePullback.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": true, "tactics": ["intro", "apply", "rintro", "apply", "apply"], "tactic_count": 5}
{"name": "CategoryTheory.Limits.WidePullbackCone", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WidePullbackCone.π", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WidePullbackCone.base", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WidePullbackCone.condition", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.WidePullbackCone.mk", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WidePullbackCone.mk_base", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WidePullbackCone.mk_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WidePullbackCone.IsLimit.mk", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WidePullbackCone.IsLimit.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": true, "tactics": ["apply", "rintro", "exact", "exact"], "tactic_count": 4}
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{"name": "CategoryTheory.Limits.WidePullbackCone.IsLimit.lift_base", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WidePullbackCone.IsLimit.lift_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WidePullbackCone.reindex", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WidePullbackCone.reindex_base", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WidePullbackCone.reindex_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WidePullbackCone.reindexIsLimitEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WidePushout.ι", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WidePushout.head", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.WidePushout.arrow_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
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{"name": "CategoryTheory.Limits.WidePushout.ι_desc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.WidePushout.head_desc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.WidePushout.eq_desc_of_comp_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": true, "tactics": ["intro", "apply", "rintro", "apply", "apply"], "tactic_count": 5}
{"name": "CategoryTheory.Limits.WidePushout.hom_eq_desc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.WidePushout.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": true, "tactics": ["intro", "apply", "rintro", "apply", "apply"], "tactic_count": 5}
{"name": "CategoryTheory.Limits.widePullbackShapeOpMap", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.widePullbackShapeOp", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.widePushoutShapeOpMap", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.widePushoutShapeOp", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.widePullbackShapeUnop", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.widePushoutShapeUnop", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.widePushoutShapeOpUnop", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.widePushoutShapeUnopOp", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.widePullbackShapeOpUnop", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.widePullbackShapeUnopOp", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.widePushoutShapeOpEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.widePullbackShapeOpEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasWidePushouts_shrink", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasWidePullbacks_shrink", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.comp_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.zero_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasZeroMorphismsPEmpty", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasZeroMorphismsPUnit", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms.0.CategoryTheory.Limits.HasZeroMorphisms.ext_aux", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": false, "tactics": ["have", "funext", "specialize", "apply", "cases", "congr", "apply", "apply"], "tactic_count": 8}
{"name": "CategoryTheory.Limits.HasZeroMorphisms.ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": true, "tactics": ["apply", "intro", "have", "have", "rw"], "tactic_count": 5}
{"name": "CategoryTheory.Limits.HasZeroMorphisms.instSubsingleton", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasZeroMorphismsOpposite", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.op_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.unop_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.zero_of_comp_mono", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.zero_of_epi_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.eq_zero_of_image_eq_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.nonzero_image_of_nonzero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instHasZeroMorphismsFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.zero_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsZero.eq_zero_of_src", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsZero.eq_zero_of_tgt", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsZero.iff_id_eq_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsZero.of_mono_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsZero.of_epi_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsZero.of_mono_eq_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": true, "tactics": ["subst", "apply"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.IsZero.of_epi_eq_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": true, "tactics": ["subst", "apply"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.IsZero.iff_isSplitMono_eq_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": true, "tactics": ["rw", "constructor", "intro", "rw", "intro", "rw", "simp"], "tactic_count": 7}
{"name": "CategoryTheory.Limits.IsZero.iff_isSplitEpi_eq_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": true, "tactics": ["rw", "constructor", "intro", "rw", "intro", "rw", "simp"], "tactic_count": 7}
{"name": "CategoryTheory.Limits.IsZero.of_mono", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": true, "tactics": ["have", "subst", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.IsZero.of_epi", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": true, "tactics": ["have", "subst", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.IsZero.hasZeroMorphisms", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.HasZeroObject.zeroMorphismsOfZeroObject", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.HasZeroObject.zeroIsoIsInitial_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.HasZeroObject.zeroIsoIsInitial_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.HasZeroObject.zeroIsoIsTerminal_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.HasZeroObject.zeroIsoIsTerminal_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.HasZeroObject.zeroIsoInitial_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.HasZeroObject.zeroIsoInitial_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.HasZeroObject.zeroIsoTerminal_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.HasZeroObject.zeroIsoTerminal_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.HasZeroObject.instFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsZero.map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.zero_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.zero_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.id_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.zero_of_to_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.zero_of_target_iso_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.zero_of_from_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.zero_of_source_iso_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.zero_of_source_iso_zero'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.zero_of_target_iso_zero'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.mono_of_source_iso_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.epi_of_target_iso_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.idZeroEquivIsoZero", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.idZeroEquivIsoZero_apply_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.idZeroEquivIsoZero_apply_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isoZeroOfMonoZero", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isoZeroOfEpiZero", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isoZeroOfMonoEqZero", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": true, "tactics": ["subst", "apply"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.isoZeroOfEpiEqZero", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": true, "tactics": ["subst", "apply"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.isoOfIsIsomorphicZero", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isIsoZeroEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isIsoZeroSelfEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.isIsoZeroEquivIsoZero", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": true, "tactics": ["refine", "symm", "fconstructor", "rintro", "fconstructor", "exact", "exact", "rintro", "fconstructor", "exact", "exact", "cat_disch", "cat_disch"], "tactic_count": 13}
{"name": "CategoryTheory.Limits.isIsoZero_iff_source_target_isZero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": true, "tactics": ["constructor", "intro", "let", "exact", "intro", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.Limits.isIso_of_source_target_iso_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.isIsoZeroSelfEquivIsoZero", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasZeroObject_of_hasInitial_object", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": true, "tactics": ["refine", "calc", "f"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.hasZeroObject_of_hasTerminal_object", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": true, "tactics": ["refine", "calc", "f"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.image_ι_comp_eq_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.comp_factorThruImage_eq_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.monoFactorisationZero", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.imageFactorisationZero", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasImage_zero", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.imageZero", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.imageZero'", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.image.ι_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.image.ι_zero'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.isSplitMono_sigma_ι", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.isSplitEpi_pi_π", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.isSplitMono_coprod_inl", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isSplitMono_coprod_inr", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isSplitEpi_prod_fst", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isSplitEpi_prod_snd", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsLimit.ofIsZero", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsColimit.ofIsZero", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsLimit.isZero_pt", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsColimit.isZero_pt", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsTerminal.isZero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.IsInitial.isZero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.Pi.ι", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Pi.ι_π_eq_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.Pi.ι_π_of_ne", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.Pi.ι_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": true, "tactics": ["split_ifs", "subst", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.instMonoι_1", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Sigma.π", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Sigma.ι_π_eq_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.Sigma.ι_π_of_ne", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.Sigma.ι_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": true, "tactics": ["split_ifs", "subst", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.instEpiπ", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.prod.inl", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.prod.inr", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.prod.inl_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.prod.inl_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.prod.inr_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.prod.inr_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.instMonoInl", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instMonoInr", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coprod.fst", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coprod.snd", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.coprod.inl_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.coprod.inr_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.coprod.inl_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.coprod.inr_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.instEpiFst", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instEpiSnd", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsZero.to_", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroObjects", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsZero.eq_to", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroObjects", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsZero.to_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroObjects", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits.IsZero.eq_of_src", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroObjects", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsZero.eq_of_tgt", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroObjects", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits.IsZero.iso", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroObjects", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits.HasZeroObject.zero'", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroObjects", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits.IsZero.hasZeroObject", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroObjects", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits.IsZero.obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Shapes.ZeroObjects", "is_tactic_proof": true, "tactics": ["let", "have", "let", "exact"], "tactic_count": 4}
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{"name": "CategoryTheory.Functor.CoconeTypes.IsColimitCore.fac_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Types.ColimitType", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.CoconeTypes.IsColimitCore.down", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Types.ColimitType", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.CoconeTypes.IsColimitCore.precompose", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Types.ColimitType", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.CoconeTypes.IsColimit.isColimitCore", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Types.ColimitType", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.CoconeTypes.IsColimitCore.isColimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Types.ColimitType", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.CoconeTypes.IsColimit.precompose", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Types.ColimitType", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.CoconeTypes.isColimit_precompose_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Types.ColimitType", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isColimit_coconeTypes", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Types.ColimitType", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.eqvGen_colimitTypeRel_iff_of_isFiltered", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Types.ColimitTypeFiltered", "is_tactic_proof": true, "tactics": ["constructor", "intro", "induction", "rel", "obtain", "exact", "refl", "symm", "obtain", "exact", "trans", "obtain", "obtain", "obtain", "refine", "rw", "rintro", "apply", "exact", "exact"], "tactic_count": 20}
{"name": "CategoryTheory.Functor.ιColimitType_eq_iff_of_isFiltered", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Types.ColimitTypeFiltered", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "CategoryTheory.Functor.CoconeTypes.descColimitType_injective_iff_of_isFiltered", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Types.ColimitTypeFiltered", "is_tactic_proof": true, "tactics": ["constructor", "intro", "have", "rwa", "intro", "obtain", "obtain", "simp", "obtain", "rw"], "tactic_count": 10}
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{"name": "CategoryTheory.Functor.coconeTypesEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Types.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.CoconeTypes.isColimit_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Types.Colimits", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "fac", "uniq", "hm", "hc.funext", "rw", "exact", "rintro", "classical", "refine", "let", "suffices", "have", "ext", "obtain", "exact", "simp", "let", "let", "suffices", "refine", "simpa"], "tactic_count": 24}
{"name": "CategoryTheory.Limits.Types.isColimit_iff_coconeTypesIsColimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Types.Colimits", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.Types.colimitCocone", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Types.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Types.colimitCoconeIsColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Types.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Types.hasColimit_iff_small_colimitType", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Types.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Types.small_colimitType_of_hasColimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Types.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Types.hasColimit", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Types.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Types.hasColimitsOfShape", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Types.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Types.hasColimitsOfSize", "kind": "instance", "module": "Mathlib.CategoryTheory.Limits.Types.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Types._example", "kind": "example", "module": "Mathlib.CategoryTheory.Limits.Types.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Types._example", "kind": "example", "module": "Mathlib.CategoryTheory.Limits.Types.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Types._example", "kind": "example", "module": "Mathlib.CategoryTheory.Limits.Types.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Types._example", "kind": "example", "module": "Mathlib.CategoryTheory.Limits.Types.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Types._example", "kind": "example", "module": "Mathlib.CategoryTheory.Limits.Types.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Types.TypeMax.colimitCocone", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Types.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Types.TypeMax.colimitCoconeIsColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Types.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Types.colimitEquivColimitType", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Types.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Types.colimitEquivColimitType_symm_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Types.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Types.colimitEquivColimitType_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Types.Colimits", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.Types.Colimit.w_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Types.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Types.Colimit.ι_desc_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Types.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Types.Colimit.ι_map_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Types.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Types.colimit_sound", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Types.Colimits", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.Types.colimit_sound'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Types.Colimits", "is_tactic_proof": true, "tactics": ["rw", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.Types.colimit_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Types.Colimits", "is_tactic_proof": true, "tactics": ["apply", "simpa"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.Types.jointly_surjective_of_isColimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Types.Colimits", "is_tactic_proof": true, "tactics": ["by_contra", "simp_rw", "apply", "refine", "ext", "exact", "exact"], "tactic_count": 7}
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{"name": "CategoryTheory.Limits.Types.jointly_surjective'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Types.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Types.nonempty_of_nonempty_colimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Types.Colimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.CofanTypes", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Types.Coproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.CofanTypes.inj", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Limits.Types.Coproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits.CofanTypes.sigma_inj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Types.Coproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.CofanTypes.isColimit_mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Types.Coproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.CofanTypes.isColimit_sigma", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Types.Coproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits.CofanTypes.equivOfIsColimit_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Types.Coproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.CofanTypes.equivOfIsColimit_symm_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Types.Coproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits.CofanTypes.eq_of_inj_apply_eq_of_isColimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Types.Coproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits.Cofan.nonempty_isColimit_iff_bijective_fromSigma", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Types.Coproducts", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "CategoryTheory.Limits.Cofan.eq_of_inj_apply_eq_of_isColimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Types.Coproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Types.initialColimitCocone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Types.Coproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits.Types.initial_iff_empty", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Types.Coproducts", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "intro", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.Limits.Types.binaryCoproductCocone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Types.Coproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Types.binaryCoproductColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Types.Coproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Types.binaryCoproductColimitCocone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Types.Coproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits.Types.binaryCoproductIso_inr_comp_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Types.Coproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits.Types.coproductColimitCocone", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Types.Coproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits.Types.typeEqualizerOfUnique", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Types.Equalizers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits.Types.FilteredColimit.rel_of_colimitTypeRel", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Types.Filtered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Types.FilteredColimit.eqvGen_colimitTypeRel_of_rel", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Types.Filtered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Limits.Types.FilteredColimit.isColimitOf'", "kind": "definition", "module": "Mathlib.CategoryTheory.Limits.Types.Filtered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Types.FilteredColimit.rel_equiv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Types.Filtered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.Types.FilteredColimit.rel_eq_eqvGen_colimitTypeRel", "kind": "theorem", "module": "Mathlib.CategoryTheory.Limits.Types.Filtered", "is_tactic_proof": true, "tactics": ["ext", "constructor", "apply", "rw", "exact"], "tactic_count": 5}
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{"name": "CategoryTheory.Localization.lift₂NatTrans_app_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Bifunctor", "is_tactic_proof": true, "tactics": ["dsimp", "simp", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Localization.natTrans₂_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Bifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.lift₂NatIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.Bifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.isLocal", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.Bousfield", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.isLocal.homEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.Bousfield", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.isoClosure_isLocal", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Bousfield", "is_tactic_proof": true, "tactics": ["ext", "constructor", "intro", "exact", "rintro", "constructor", "intro", "rw", "apply", "simp", "intro", "obtain", "exact"], "tactic_count": 13}
{"name": "CategoryTheory.ObjectProperty.instIsMultiplicativeIsLocal", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.Bousfield", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instHasTwoOutOfThreePropertyIsLocal", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.Bousfield", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.isLocal_of_isIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Bousfield", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.isLocal_iff_isIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Bousfield", "is_tactic_proof": true, "tactics": ["constructor", "intro", "obtain", "exact", "apply"], "tactic_count": 5}
{"name": "CategoryTheory.ObjectProperty.instRespectsIsoIsLocal", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.Bousfield", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.le_isLocal_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Bousfield", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.galoisConnection_isLocal", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Bousfield", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.isColocal", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.Bousfield", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.isColocal.homEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.Bousfield", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.isoClosure_isColocal", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Bousfield", "is_tactic_proof": true, "tactics": ["ext", "constructor", "intro", "exact", "rintro", "constructor", "intro", "rw", "apply", "simp", "intro", "obtain", "exact"], "tactic_count": 13}
{"name": "CategoryTheory.ObjectProperty.instIsMultiplicativeIsColocal", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.Bousfield", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instHasTwoOutOfThreePropertyIsColocal", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.Bousfield", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.isColocal_of_isIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Bousfield", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.isColocal_iff_isIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Bousfield", "is_tactic_proof": true, "tactics": ["constructor", "intro", "obtain", "exact", "apply"], "tactic_count": 5}
{"name": "CategoryTheory.ObjectProperty.instRespectsIsoIsColocal", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.Bousfield", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.le_isColocal_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Bousfield", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.galoisConnection_isColocal", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Bousfield", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.isLocal_adj_unit_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Bousfield", "is_tactic_proof": true, "tactics": ["rintro", "convert", "dsimp", "aesop"], "tactic_count": 4}
{"name": "CategoryTheory.ObjectProperty.isLocal_iff_isIso_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Bousfield", "is_tactic_proof": true, "tactics": ["have", "dsimp", "rw", "isLocal_iff_isIso", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.ObjectProperty.isLocal_eq_inverseImage_isomorphisms", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Bousfield", "is_tactic_proof": true, "tactics": ["ext", "rw", "rfl"], "tactic_count": 3}
{"name": "CategoryTheory.ObjectProperty.isLocalization_isLocal", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Bousfield", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.ObjectProperty.isColocal_adj_counit_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Bousfield", "is_tactic_proof": true, "tactics": ["rintro", "convert", "dsimp", "cat_disch"], "tactic_count": 4}
{"name": "CategoryTheory.ObjectProperty.isColocal_iff_isIso_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Bousfield", "is_tactic_proof": true, "tactics": ["have", "dsimp", "rw", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.ObjectProperty.isColocal_eq_inverseImage_isomorphisms", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Bousfield", "is_tactic_proof": true, "tactics": ["ext", "rw", "rfl"], "tactic_count": 3}
{"name": "CategoryTheory.ObjectProperty.isLocalization_isColocal", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Bousfield", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.ObjectProperty.le_isLocal_isLocal", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Bousfield", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.MorphismProperty.le_isLocal_isLocal", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Bousfield", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.ObjectProperty.le_isColocal_isColocal", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Bousfield", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.MorphismProperty.le_isColocal_isColocal", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Bousfield", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.ObjectProperty.instIsStableUnderTransfiniteCompositionOfShapeIsLocal", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.BousfieldTransfiniteComposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instIsStableUnderTransfiniteCompositionIsLocal", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.BousfieldTransfiniteComposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.LeftFraction.ofHom", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.LeftFraction.ofInv", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.LeftFraction.map", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.LeftFraction.map_comp_map_s", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": true, "tactics": ["letI", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.MorphismProperty.LeftFraction.map_ofHom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MorphismProperty.LeftFraction.map_ofInv_hom_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": true, "tactics": ["letI", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.MorphismProperty.LeftFraction.map_hom_ofInv_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": true, "tactics": ["letI", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.MorphismProperty.LeftFraction.cases", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.RightFraction.ofHom", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.RightFraction.ofInv", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.RightFraction.map", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.RightFraction.map_s_comp_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": true, "tactics": ["letI", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.MorphismProperty.RightFraction.map_ofHom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MorphismProperty.RightFraction.map_ofInv_hom_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": true, "tactics": ["letI", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.MorphismProperty.RightFraction.map_hom_ofInv_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": true, "tactics": ["letI", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.MorphismProperty.RightFraction.cases", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.RightFraction.exists_leftFraction", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.RightFraction.leftFraction", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.RightFraction.leftFraction_fac", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.LeftFraction.exists_rightFraction", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.LeftFraction.rightFraction", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.LeftFraction.rightFraction_fac", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.LeftFractionRel", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.LeftFractionRel.refl", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.LeftFractionRel.symm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.MorphismProperty.LeftFractionRel.trans", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "obtain", "simp", "have", "obtain", "simp", "refine", "rw", "rw", "rw", "exact"], "tactic_count": 12}
{"name": "CategoryTheory.MorphismProperty.equivalenceLeftFractionRel", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.LeftFraction.comp₀", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.LeftFraction.comp₀_rel", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": true, "tactics": ["obtain", "dsimp", "have", "obtain", "simp", "refine", "simp", "simp", "simp", "exact"], "tactic_count": 10}
{"name": "CategoryTheory.MorphismProperty.LeftFraction.Localization.Hom", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.LeftFraction.Localization.Hom.mk", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.LeftFraction.Localization.Hom.mk_surjective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.MorphismProperty.LeftFraction.comp", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.LeftFraction.comp_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.LeftFraction.Localization.Hom.comp", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": true, "tactics": ["refine", "rintro", "obtain", "obtain", "obtain", "obtain", "obtain", "dsimp", "have", "rw", "obtain", "simp", "rw", "apply", "refine", "dsimp", "simp", "dsimp", "simp", "dsimp", "simp", "rw", "exact", "rintro", "obtain", "obtain", "obtain", "obtain", "exists_leftFraction", "let", "let", "dsimp", "simp", "rw", "apply", "refine", "have", "obtain", "simp", "refine", "dsimp", "simp", "dsimp", "simp", "dsimp", "simp", "exact", "obtain", "exists_leftFraction", "dsimp", "simp", "have", "rw", "obtain", "simp", "refine", "simp", "rw", "simp", "exact", "have", "obtain", "simp", "refine", "dsimp", "simp", "dsimp", "simp", "dsimp", "simp", "exact"], "tactic_count": 71}
{"name": "CategoryTheory.MorphismProperty.LeftFraction.Localization.Hom.comp_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.LeftFraction.Localization", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.LeftFraction.Localization.instCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.LeftFraction.Localization.Q", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.LeftFraction.Localization.homMk", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.LeftFraction.Localization.homMk_eq_hom_mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.LeftFraction.Localization.Q_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.LeftFraction.Localization.homMk_comp_homMk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": true, "tactics": ["change", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.MorphismProperty.LeftFraction.Localization.homMk_eq_of_leftFractionRel", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.LeftFraction.Localization.homMk_eq_iff_leftFractionRel", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.LeftFraction.Localization.Qinv", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.LeftFraction.Localization.Q_map_comp_Qinv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.MorphismProperty.LeftFraction.Localization.Qiso", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.LeftFraction.Localization.Qiso_hom_inv_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.LeftFraction.Localization.Qiso_inv_hom_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.LeftFraction.Localization.instIsIsoQinv", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.LeftFraction.Localization.Hom.map", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.LeftFraction.Localization.Hom.map_mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.LeftFraction.Localization.StrictUniversalPropertyFixedTarget.inverts", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.LeftFraction.Localization.StrictUniversalPropertyFixedTarget.lift", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.LeftFraction.Localization.StrictUniversalPropertyFixedTarget.fac", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.LeftFraction.Localization.StrictUniversalPropertyFixedTarget.uniq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.LeftFraction.Localization.strictUniversalPropertyFixedTarget", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.LeftFraction.Localization.instIsLocalizationQ", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.LeftFraction.Localization.homMk_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.MorphismProperty.LeftFraction.Localization.map_eq_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": true, "tactics": ["simp", "constructor", "intro", "rw", "exact", "intro", "congr", "exact"], "tactic_count": 8}
{"name": "CategoryTheory.MorphismProperty.LeftFraction.map_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.LeftFraction.map_compatibility", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": true, "tactics": ["let", "have", "rw", "map_comp_map_s,", "simpa"], "tactic_count": 5}
{"name": "CategoryTheory.MorphismProperty.LeftFraction.map_eq_of_map_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": true, "tactics": ["apply", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.MorphismProperty.LeftFraction.map_comp_map_eq_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": true, "tactics": ["have", "have", "have", "rw", "infer_instance", "dsimp", "rw"], "tactic_count": 7}
{"name": "CategoryTheory.Localization.exists_leftFraction", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": true, "tactics": ["let", "let", "obtain", "obtain", "obtain", "refine", "rw", "g.map_compatibility"], "tactic_count": 8}
{"name": "CategoryTheory.MorphismProperty.LeftFraction.map_eq_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "apply", "intro", "simp", "congr", "exact"], "tactic_count": 8}
{"name": "CategoryTheory.MorphismProperty.map_eq_iff_postcomp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "obtain", "dsimp", "grind", "rintro", "simp"], "tactic_count": 8}
{"name": "CategoryTheory.Localization.essSurj_mapArrow", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.LeftFraction.op", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.RightFraction.op", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.LeftFraction.unop", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.RightFraction.unop", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.RightFraction.op_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.MorphismProperty.LeftFraction.op_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.MorphismProperty.instHasRightCalculusOfFractionsOppositeOpOfHasLeftCalculusOfFractions", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instHasLeftCalculusOfFractionsOppositeOpOfHasRightCalculusOfFractions", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instHasRightCalculusOfFractionsUnopOfHasLeftCalculusOfFractionsOpposite", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instHasLeftCalculusOfFractionsUnopOfHasRightCalculusOfFractionsOpposite", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.RightFractionRel", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.RightFractionRel.op", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.MorphismProperty.RightFractionRel.unop", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.MorphismProperty.LeftFractionRel.op", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.MorphismProperty.LeftFractionRel.unop", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.MorphismProperty.leftFractionRel_op_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.rightFractionRel_op_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.RightFractionRel.refl", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.RightFractionRel.symm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.RightFractionRel.trans", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.equivalenceRightFractionRel", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.exists_rightFraction", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": true, "tactics": ["obtain", "refine", "rw", "rfl"], "tactic_count": 4}
{"name": "CategoryTheory.MorphismProperty.RightFraction.map_eq_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": false, "tactics": ["rw", "constructor", "apply", "apply"], "tactic_count": 4}
{"name": "CategoryTheory.MorphismProperty.map_eq_iff_precomp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "obtain", "dsimp", "grind", "rintro", "simp"], "tactic_count": 8}
{"name": "CategoryTheory.Localization.essSurj_mapArrow_of_hasRightCalculusOfFractions", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.essSurj_mapComposableArrows_of_hasRightCalculusOfFractions", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions.ComposableArrows", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.essSurj_mapComposableArrows", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions.ComposableArrows", "is_tactic_proof": true, "tactics": ["have", "have", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.MorphismProperty.LeftFraction₂Rel", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions.Fractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.LeftFraction₂.fst", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions.Fractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.LeftFraction₂.snd", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions.Fractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.LeftFraction₂.symm", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions.Fractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.LeftFraction₃.fst", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions.Fractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.LeftFraction₃.snd", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions.Fractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.LeftFraction₃.thd", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions.Fractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.LeftFraction₃.forgetFst", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions.Fractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.LeftFraction₃.forgetSnd", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions.Fractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.LeftFraction₃.forgetThd", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions.Fractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.LeftFraction₂Rel.fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions.Fractions", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.MorphismProperty.LeftFraction₂Rel.snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions.Fractions", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.MorphismProperty.LeftFraction₂.map_eq_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions.Fractions", "is_tactic_proof": true, "tactics": ["simp", "constructor", "intro", "obtain", "obtain", "dsimp", "have", "simp", "obtain", "have", "rw", "obtain", "simp", "refine", "rw", "rw", "rw", "rw", "exact", "intro", "exact"], "tactic_count": 21}
{"name": "CategoryTheory.MorphismProperty.RightFraction₂.fst", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions.Fractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.RightFraction₂.snd", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions.Fractions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.RightFraction₂.exists_leftFraction₂", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions.Fractions", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "obtain", "dsimp", "refine", "dsimp", "rw", "rw"], "tactic_count": 8}
{"name": "CategoryTheory.Localization.exists_leftFraction₂", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions.Fractions", "is_tactic_proof": true, "tactics": ["have", "have", "obtain", "let", "f", "f", "s", "hs", "have", "have", "have", "rw", "infer_instance", "refine", "rw", "rw", "nth_rw", "rw"], "tactic_count": 18}
{"name": "CategoryTheory.Localization.exists_leftFraction₃", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions.Fractions", "is_tactic_proof": true, "tactics": ["obtain", "have", "obtain", "dsimp", "let", "f", "f", "f", "s", "hs", "have", "have", "have", "rw", "infer_instance", "refine", "rw", "rw", "rw", "nth_rw", "rw"], "tactic_count": 21}
{"name": "CategoryTheory.Adjunction.hasLeftCalculusOfFractions", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions.OfAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.hasRightCalculusOfFractions", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions.OfAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.isLocalization_leftAdjoint", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions.OfAdjunction", "is_tactic_proof": true, "tactics": ["let", "let", "have", "rw", "intro", "exact", "exact", "e"], "tactic_count": 8}
{"name": "CategoryTheory.Adjunction.isLocalization_rightAdjoint", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions.OfAdjunction", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.Adjunction.functorCategory_inverseImage_isomorphisms_unit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions.OfAdjunction", "is_tactic_proof": true, "tactics": ["intro", "simp", "infer_instance"], "tactic_count": 3}
{"name": "CategoryTheory.Adjunction.functorCategory_inverseImage_isomorphisms_counit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions.OfAdjunction", "is_tactic_proof": true, "tactics": ["intro", "simp", "infer_instance"], "tactic_count": 3}
{"name": "CategoryTheory.Adjunction.isLocalization_leftAdjoint'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions.OfAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.isLocalization_rightAdjoint'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions.OfAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.hasLeftCalculusOfFractions'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions.OfAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.hasRightCalculusOfFractions'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions.OfAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.LeftFraction.neg", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.LeftFraction₂.add", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.LeftFraction₂.symm_add", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions.Preadditive", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "CategoryTheory.MorphismProperty.LeftFraction₂.map_add", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions.Preadditive", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.Localization.Preadditive.neg'", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.Preadditive.neg'_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions.Preadditive", "is_tactic_proof": false, "tactics": ["obtain", "rw", "obtain", "have", "rw", "nth_rw", "rw"], "tactic_count": 7}
{"name": "CategoryTheory.Localization.Preadditive.add'", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.Preadditive.add'_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions.Preadditive", "is_tactic_proof": false, "tactics": ["obtain", "add", "obtain", "have", "rw", "nth_rw", "rw"], "tactic_count": 7}
{"name": "CategoryTheory.Localization.Preadditive.add'_comm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions.Preadditive", "is_tactic_proof": true, "tactics": ["obtain", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.Localization.Preadditive.add'_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions.Preadditive", "is_tactic_proof": true, "tactics": ["obtain", "rw", "have", "rw", "dsimp", "rw"], "tactic_count": 6}
{"name": "CategoryTheory.Localization.Preadditive.zero_add'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions.Preadditive", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Localization.Preadditive.neg'_add'_self", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions.Preadditive", "is_tactic_proof": true, "tactics": ["obtain", "have", "rw", "simp"], "tactic_count": 4}
{"name": "CategoryTheory.Localization.Preadditive.add'_assoc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions.Preadditive", "is_tactic_proof": true, "tactics": ["obtain", "rw", "add'_eq", "add'_eq", "dsimp", "rw"], "tactic_count": 6}
{"name": "CategoryTheory.Localization.Preadditive.add'_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions.Preadditive", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "obtain", "dsimp", "rw", "add'_eq", "rotate_left", "rw", "exact", "rw", "exact", "rw", "dsimp", "rw"], "tactic_count": 14}
{"name": "CategoryTheory.Localization.Preadditive.comp_add'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions.Preadditive", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "obtain", "dsimp", "rw", "add'_eq", "hα,", "dsimp", "rw"], "tactic_count": 9}
{"name": "CategoryTheory.Localization.Preadditive.add'_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.Preadditive.addCommGroup'", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions.Preadditive", "is_tactic_proof": true, "tactics": ["letI", "letI", "letI", "exact", "add_zero", "add_comm", "zero_add", "neg_add_cancel", "nsmul", "zsmul"], "tactic_count": 10}
{"name": "CategoryTheory.Localization.Preadditive.homEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.Preadditive.add", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.Preadditive.add_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions.Preadditive", "is_tactic_proof": true, "tactics": ["obtain", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Localization.Preadditive.comp_add", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions.Preadditive", "is_tactic_proof": true, "tactics": ["obtain", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Localization.Preadditive.add_eq_add", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions.Preadditive", "is_tactic_proof": true, "tactics": ["have", "have", "simp", "simp", "rw"], "tactic_count": 5}
{"name": "CategoryTheory.Localization.Preadditive.addCommGroup", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions.Preadditive", "is_tactic_proof": true, "tactics": ["have", "letI", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Localization.Preadditive.add_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions.Preadditive", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Localization.Preadditive.map_add", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions.Preadditive", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Localization.preadditive", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.functor_additive", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.functor_additive_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions.Preadditive", "is_tactic_proof": true, "tactics": ["constructor", "intro", "infer_instance", "intro", "suffices", "refine", "have", "have", "this", "rw", "add_comp,", "rw", "intro", "obtain", "have", "rw"], "tactic_count": 16}
{"name": "CategoryTheory.Localization.instPreadditiveLocalization", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.instAdditiveLocalizationQ", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.instHasZeroObjectLocalization", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.instPreadditiveLocalization'", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.instAdditiveLocalization'Q'", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.instHasZeroObjectLocalization'", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.CalculusOfFractions.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.StrictUniversalPropertyFixedTarget.comp", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsLocalization.comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Composition", "is_tactic_proof": true, "tactics": ["let", "let", "let", "map", "have", "rw", "rw", "apply", "have", "let", "let", "calc", "isoWhiskerRight", "isoWhiskerLeft", "have", "simpa", "have", "have", "refine", "all_goals", "exact", "exact"], "tactic_count": 22}
{"name": "CategoryTheory.Functor.IsLocalization.of_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Composition", "is_tactic_proof": false, "tactics": ["have", "comp", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Localization.Construction.instQuiverLocQuiver", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.Construction.ιPaths", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.Construction.ψ₁", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.Construction.ψ₂", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.Construction.relations", "kind": "inductive", "module": "Mathlib.CategoryTheory.Localization.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.Localization", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instCategoryLocalization", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.Construction", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.MorphismProperty.Q", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.Construction.wIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.Construction.wInv", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Localization.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.Q_inverts", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.Construction.liftToPathCategory", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.Construction.lift", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.Construction.fac", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.Construction.uniq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Construction", "is_tactic_proof": false, "tactics": ["suffices", "refine", "rintro", "apply", "rintro", "apply", "refine", "ext", "cases", "apply", "rintro", "simpa", "have", "have", "simp", "refine", "all_goals"], "tactic_count": 17}
{"name": "CategoryTheory.Localization.Construction.objEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.Construction.morphismProperty_eq_top", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Construction", "is_tactic_proof": true, "tactics": ["funext", "ext", "constructor", "intro", "apply", "intro", "let", "haveI", "suffices", "rcases", "rcases", "simpa", "intro", "induction", "nil", "let", "rw", "refine", "rcases", "apply", "apply"], "tactic_count": 21}
{"name": "CategoryTheory.Localization.Construction.morphismProperty_eq_top'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.Construction.NatTransExtension.app", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.Construction.NatTransExtension.app_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Construction", "is_tactic_proof": true, "tactics": ["simp", "rfl"], "tactic_count": 2}
{"name": "CategoryTheory.Localization.Construction.natTransExtension", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.Construction.whiskerLeft_natTransExtension", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Construction", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Localization.Construction.natTransExtension_hcomp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Construction", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Localization.Construction.natTrans_hcomp_injective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Construction", "is_tactic_proof": true, "tactics": ["ext", "have", "simp", "rw"], "tactic_count": 4}
{"name": "CategoryTheory.Localization.Construction.WhiskeringLeftEquivalence.functor", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.Construction.WhiskeringLeftEquivalence.inverse", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.Construction.WhiskeringLeftEquivalence.unitIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.Construction.WhiskeringLeftEquivalence.counitIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.Construction.whiskeringLeftEquivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocalizerMorphism.isRightDerivabilityStructure_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.DerivabilityStructure.Basic", "is_tactic_proof": false, "tactics": ["have", "rw", "let", "let", "let", "let", "let", "let", "associator", "let", "have", "ext", "rw", "simp", "dsimp", "rw", "erw", "rfl,", "simp", "rw"], "tactic_count": 20}
{"name": "CategoryTheory.LocalizerMorphism.guitartExact_of_isRightDerivabilityStructure'", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.DerivabilityStructure.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.LocalizerMorphism.guitartExact_of_isRightDerivabilityStructure", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.DerivabilityStructure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocalizerMorphism.instHasRightResolutionsIdOfContainsIdentities", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.DerivabilityStructure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocalizerMorphism.instIsRightDerivabilityStructureIdOfContainsIdentities", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.DerivabilityStructure.Basic", "is_tactic_proof": true, "tactics": ["rw", "dsimp", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.LocalizerMorphism.isLeftDerivabilityStructure_iff_op", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.DerivabilityStructure.Basic", "is_tactic_proof": true, "tactics": ["let", "let", "let", "have", "constructor", "rintro", "rwa", "intro", "have", "rw", "infer_instance", "refine", "rw", "exact"], "tactic_count": 14}
{"name": "CategoryTheory.LocalizerMorphism.isLeftDerivabilityStructure_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.DerivabilityStructure.Basic", "is_tactic_proof": false, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "CategoryTheory.LocalizerMorphism.guitartExact_of_isLeftDerivabilityStructure'", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.DerivabilityStructure.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.LocalizerMorphism.guitartExact_of_isLeftDerivabilityStructure", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.DerivabilityStructure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocalizerMorphism.instHasLeftResolutionsIdOfContainsIdentities", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.DerivabilityStructure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocalizerMorphism.instIsLeftDerivabilityStructureIdOfContainsIdentities", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.DerivabilityStructure.Basic", "is_tactic_proof": true, "tactics": ["rw", "dsimp", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.LocalizerMorphism.IsRightDerivabilityStructure.Constructor.fromRightResolution", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.DerivabilityStructure.Constructor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocalizerMorphism.IsRightDerivabilityStructure.Constructor.isConnected", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.DerivabilityStructure.Constructor", "is_tactic_proof": true, "tactics": ["let", "have", "suffices", "refine", "obtain", "obtain", "exact", "intro", "obtain", "dsimp", "rw", "let", "refine", "have", "zigzag_obj_of_zigzag", "refine", "exact", "apply", "refine", "ext", "dsimp", "rw"], "tactic_count": 22}
{"name": "CategoryTheory.LocalizerMorphism.IsRightDerivabilityStructure.mk'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.DerivabilityStructure.Constructor", "is_tactic_proof": false, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "CategoryTheory.LocalizerMorphism.IsLeftDerivabilityStructure.mk'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.DerivabilityStructure.Constructor", "is_tactic_proof": true, "tactics": ["rw", "have", "let", "exact", "w", "hw", "have", "isConnected_of_equivalent", "exact"], "tactic_count": 9}
{"name": "CategoryTheory.LocalizerMorphism.Derives", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Localization.DerivabilityStructure.Derives", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocalizerMorphism.Derives.hasPointwiseRightDerivedFunctor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.DerivabilityStructure.Derives", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.LocalizerMorphism.Derives.isIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.DerivabilityStructure.Derives", "is_tactic_proof": true, "tactics": ["let", "let", "have", "have", "rw", "infer_instance"], "tactic_count": 6}
{"name": "CategoryTheory.LocalizerMorphism.Derives.isRightDerivedFunctor_of_isIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.DerivabilityStructure.Derives", "is_tactic_proof": true, "tactics": ["have", "have", "have", "let", "have", "have", "rw", "intro", "rw", "dsimp", "simp", "infer_instance", "rw", "infer_instance"], "tactic_count": 14}
{"name": "CategoryTheory.LocalizerMorphism.Derives.isRightDerivedFunctor_iff_isIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.DerivabilityStructure.Derives", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocalizerMorphism.hasRightResolutions_arrow_of_functorial_resolutions", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.DerivabilityStructure.OfFunctorialResolutions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocalizerMorphism.functorialRightResolutions.localizerMorphismInv", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.DerivabilityStructure.OfFunctorialResolutions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocalizerMorphism.functorialRightResolutions.ι", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.DerivabilityStructure.OfFunctorialResolutions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocalizerMorphism.functorialRightResolutions.Φ_functor_map_ι_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.DerivabilityStructure.OfFunctorialResolutions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocalizerMorphism.functorialRightResolutions.W₁_ι_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.DerivabilityStructure.OfFunctorialResolutions", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.LocalizerMorphism.isLocalizedEquivalence_of_functorial_right_resolutions", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.DerivabilityStructure.OfFunctorialResolutions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocalizerMorphism.isConnected_rightResolution_of_functorial_resolutions", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.DerivabilityStructure.OfFunctorialResolutions", "is_tactic_proof": true, "tactics": ["have", "have", "have", "zigzag_isPreconnected", "calc", "comm", "comm", "constructor"], "tactic_count": 8}
{"name": "CategoryTheory.LocalizerMorphism.isRightDerivabilityStructure_of_functorial_resolutions", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.DerivabilityStructure.OfFunctorialResolutions", "is_tactic_proof": true, "tactics": ["have", "have", "have", "have", "apply"], "tactic_count": 5}
{"name": "CategoryTheory.LocalizerMorphism.rightDerivedFunctorComparison", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.DerivabilityStructure.PointwiseRightDerived", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocalizerMorphism.rightDerivedFunctorComparison_fac", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.DerivabilityStructure.PointwiseRightDerived", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.LocalizerMorphism.rightDerivedFunctorComparison_fac_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.DerivabilityStructure.PointwiseRightDerived", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.LocalizerMorphism.hasPointwiseRightDerivedFunctorAt_iff_of_isRightDerivabilityStructure", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.DerivabilityStructure.PointwiseRightDerived", "is_tactic_proof": true, "tactics": ["let", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.LocalizerMorphism.hasPointwiseRightDerivedFunctor_iff_of_isRightDerivabilityStructure", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.DerivabilityStructure.PointwiseRightDerived", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "apply", "intro", "have", "simpa"], "tactic_count": 7}
{"name": "CategoryTheory.LocalizerMorphism.instIsIsoFunctorRightDerivedFunctorComparison", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.DerivabilityStructure.PointwiseRightDerived", "is_tactic_proof": false, "tactics": ["have", "rw", "infer_instance", "dsimp", "rw", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.LocalizerMorphism.isIso_iff_of_isRightDerivabilityStructure", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.DerivabilityStructure.PointwiseRightDerived", "is_tactic_proof": true, "tactics": ["rw", "rightDerivedFunctorComparison_fac_app,"], "tactic_count": 2}
{"name": "CategoryTheory.Localization.equivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.equivalence_counitIso_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Equivalence", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "rw", "dsimp", "rw"], "tactic_count": 5}
{"name": "CategoryTheory.Localization.isEquivalence", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsLocalization.of_equivalence_source", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Equivalence", "is_tactic_proof": false, "tactics": ["have", "obtain", "exact", "exact", "isEquivalence", "calc"], "tactic_count": 6}
{"name": "CategoryTheory.Functor.IsLocalization.of_equivalences", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Equivalence", "is_tactic_proof": true, "tactics": ["haveI", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Localization.HasProductsOfShapeAux.inverts", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.FiniteProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.HasProductsOfShapeAux.limitFunctor", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Localization.FiniteProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.HasProductsOfShapeAux.compLimitFunctorIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.FiniteProducts", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Localization.HasProductsOfShapeAux.instCatCommSqFunctorDiscreteConstObjWhiskeringRight", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.FiniteProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.HasProductsOfShapeAux.instCatCommSqFunctorDiscreteLimObjWhiskeringRightLimitFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.FiniteProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.HasProductsOfShapeAux.adj", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.FiniteProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.HasProductsOfShapeAux.adj_counit_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.FiniteProducts", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Localization.HasProductsOfShapeAux.isLimitMapCone", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.FiniteProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.hasProductsOfShape", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.FiniteProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.preservesProductsOfShape", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.FiniteProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.hasFiniteProducts", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.FiniteProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.preservesFiniteProducts", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.FiniteProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.instHasFiniteProductsLocalization", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.FiniteProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.instPreservesFiniteProductsLocalizationQ", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.FiniteProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.instHasFiniteProductsLocalization'", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.FiniteProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.instPreservesFiniteProductsLocalization'Q'", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.FiniteProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.Localization'", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.HasLocalization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instCategoryLocalization'", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.HasLocalization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.Q'", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.HasLocalization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instIsLocalizationLocalization'Q'", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.HasLocalization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.HasLocalization.standard", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.HasLocalization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocalizerMorphism.homMap", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.HomEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocalizerMorphism.homMap_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.HomEquiv", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.LocalizerMorphism.homMap_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.HomEquiv", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.LocalizerMorphism.homMap_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.HomEquiv", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.LocalizerMorphism.homMap_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.HomEquiv", "is_tactic_proof": true, "tactics": ["let", "let", "change", "letI", "let", "have", "ext", "simp", "simp"], "tactic_count": 9}
{"name": "CategoryTheory.LocalizerMorphism.id_homMap", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.HomEquiv", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.LocalizerMorphism.homMap_homMap", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.HomEquiv", "is_tactic_proof": true, "tactics": ["let", "let", "let", "let", "rw", "dsimp", "simp"], "tactic_count": 7}
{"name": "CategoryTheory.Localization.homEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.HomEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.homEquiv_symm_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.HomEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.homEquiv_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.HomEquiv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Localization.homEquiv_refl", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.HomEquiv", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Localization.homEquiv_trans", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.HomEquiv", "is_tactic_proof": true, "tactics": ["dsimp", "apply"], "tactic_count": 2}
{"name": "CategoryTheory.Localization.homEquiv_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.HomEquiv", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Localization.homEquiv_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.HomEquiv", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Localization.homEquiv_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.HomEquiv", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Localization.homEquiv_isoOfHom_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.HomEquiv", "is_tactic_proof": true, "tactics": ["rw", "isoOfHom_inv_hom_id,"], "tactic_count": 2}
{"name": "CategoryTheory.Localization.linear", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.functor_linear", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Linear", "is_tactic_proof": true, "tactics": ["letI", "constructor", "intro", "change", "simp"], "tactic_count": 5}
{"name": "CategoryTheory.Localization.instLinearLocalization", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.instLinearLocalizationQ", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.instLinearLocalization'", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.instLinearLocalization'Q'", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.functor_linear_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Linear", "is_tactic_proof": true, "tactics": ["constructor", "intro", "have", "have", "rw", "intro", "have", "have", "rw", "dsimp", "rw", "intro", "exact"], "tactic_count": 13}
{"name": "CategoryTheory.LocalizerMorphism.ofEq", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.LocalizerMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocalizerMorphism.id", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.LocalizerMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocalizerMorphism.comp", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.LocalizerMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocalizerMorphism.op", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.LocalizerMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocalizerMorphism.inverts", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.LocalizerMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocalizerMorphism.localizedFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.LocalizerMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocalizerMorphism.liftingLocalizedFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.LocalizerMorphism", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.LocalizerMorphism.catCommSq", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.LocalizerMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocalizerMorphism.isEquivalence_imp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.LocalizerMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocalizerMorphism.isEquivalence_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.LocalizerMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocalizerMorphism.IsLocalizedEquivalence.mk'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.LocalizerMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocalizerMorphism.isEquivalence", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.LocalizerMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocalizerMorphism.instIsLocalizedEquivalenceOppositeOpOp", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.LocalizerMorphism", "is_tactic_proof": true, "tactics": ["let", "letI", "have", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.LocalizerMorphism.localizedFunctor_isEquivalence", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.LocalizerMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocalizerMorphism.IsLocalizedEquivalence.of_isLocalization_of_isLocalization", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.LocalizerMorphism", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.LocalizerMorphism.IsLocalizedEquivalence.of_equivalence", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.LocalizerMorphism", "is_tactic_proof": false, "tactics": ["haveI", "refine", "erw", "rw", "exact", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.LocalizerMorphism.IsLocalizedEquivalence.isLocalization", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.LocalizerMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocalizerMorphism.isLocalizedEquivalence_of_unit_of_unit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.LocalizerMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocalizerMorphism.arrow", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.LocalizerMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.hasLocalizationOfLocallySmall", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.LocallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.definition._@.Mathlib.CategoryTheory.Localization.LocallySmall.822486777._hygCtx._hyg.2", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.LocallySmall", "is_tactic_proof": false, "tactics": ["have", "let", "map", "have", "have", "have", "let", "let", "have", "exact"], "tactic_count": 10}
{"name": "CategoryTheory.MorphismProperty.wrapped._@.Mathlib.CategoryTheory.Localization.LocallySmall.822486777._hygCtx._hyg.2", "kind": "opaque", "module": "Mathlib.CategoryTheory.Localization.LocallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.hasLocalizationOfLocallySmall'", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.LocallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.hasLocalizationOfLocallySmall'_def", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.LocallySmall", "is_tactic_proof": true, "tactics": ["intros", "delta", "rw", "rfl"], "tactic_count": 4}
{"name": "CategoryTheory.MorphismProperty.locallySmall_of_hasLocalization", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.LocallySmall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsMonoidal.mk'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.whiskerLeft_mem", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.whiskerRight_mem", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.tensorHom_mem", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Monoidal.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.MorphismProperty.instIsMonoidalInverseImageOfMonoidalOfRespectsIso", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocalizedMonoidal", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.instCategoryLocalizedMonoidal", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.Monoidal.toMonoidalCategory", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.Monoidal.ε'", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Localization.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.CategoryTheory.Localization.Monoidal.Basic.0.CategoryTheory.Localization.Monoidal.termL'", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.CategoryTheory.Localization.Monoidal.Basic.0.CategoryTheory.Localization.Monoidal._aux_Mathlib_CategoryTheory_Localization_Monoidal_Basic___macroRules__private_Mathlib_CategoryTheory_Localization_Monoidal_Basic_0_CategoryTheory_Localization_Monoidal_termL'_1", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.CategoryTheory.Localization.Monoidal.Basic.0.CategoryTheory.Localization.Monoidal._aux_Mathlib_CategoryTheory_Localization_Monoidal_Basic___unexpand_CategoryTheory_Localization_Monoidal_toMonoidalCategory_1", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.Monoidal.instIsLocalizationLocalizedMonoidalToMonoidalCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.Monoidal.isInvertedBy₂", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Monoidal.Basic", "is_tactic_proof": true, "tactics": ["rintro", "have", "have", "dsimp", "infer_instance"], "tactic_count": 5}
{"name": "CategoryTheory.Localization.Monoidal.tensorBifunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.Monoidal.instLifting₂LocalizedMonoidalToMonoidalCategoryCompFunctorCurriedTensorObjWhiskeringRightTensorBifunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.Monoidal.tensorBifunctorIso", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Localization.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.Monoidal.instLiftingLocalizedMonoidalToMonoidalCategoryCompTensorLeftObjFunctorTensorBifunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.Monoidal.Basic", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Localization.Monoidal.instLiftingLocalizedMonoidalToMonoidalCategoryCompTensorRightObjFunctorFlipTensorBifunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.Monoidal.Basic", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Localization.Monoidal.leftUnitor", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.Monoidal.rightUnitor", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.Monoidal.associator", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.Monoidal.monoidalCategoryStruct", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.Monoidal.μ", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.Monoidal.μ_natural_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.Monoidal.μ_inv_natural_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Monoidal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Localization.Monoidal.μ_natural_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.Monoidal.μ_inv_natural_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Monoidal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Localization.Monoidal.leftUnitor_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Monoidal.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "dsimp", "rw", "change", "simp"], "tactic_count": 6}
{"name": "CategoryTheory.Localization.Monoidal.rightUnitor_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Monoidal.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "dsimp", "rw", "change", "simp"], "tactic_count": 6}
{"name": "CategoryTheory.Localization.Monoidal.associator_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Monoidal.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "simp", "rw", "rfl"], "tactic_count": 4}
{"name": "CategoryTheory.Localization.Monoidal.id_tensorHom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Monoidal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Localization.Monoidal.tensorHom_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Monoidal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Localization.Monoidal.tensor_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Monoidal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Localization.Monoidal.id_tensorHom_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Monoidal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Localization.Monoidal.whiskerLeft_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Monoidal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Localization.Monoidal.whiskerRight_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Monoidal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Localization.Monoidal.whiskerLeft_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Monoidal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Localization.Monoidal.whiskerRight_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Monoidal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Localization.Monoidal.whisker_exchange", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Monoidal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Localization.Monoidal.associator_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Monoidal.Basic", "is_tactic_proof": true, "tactics": ["have", "have", "have", "simp", "dsimp", "rw"], "tactic_count": 6}
{"name": "CategoryTheory.Localization.Monoidal.associator_naturality₁", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Monoidal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Localization.Monoidal.associator_naturality₂", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Monoidal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Localization.Monoidal.associator_naturality₃", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Monoidal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Localization.Monoidal.pentagon_aux₁", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Monoidal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Localization.Monoidal.pentagon_aux₂", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Monoidal.Basic", "is_tactic_proof": true, "tactics": ["simp", "whiskerLeft_id,"], "tactic_count": 2}
{"name": "CategoryTheory.Localization.Monoidal.pentagon_aux₃", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Monoidal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Localization.Monoidal.instEssSurjLocalizedMonoidalToMonoidalCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.Monoidal.pentagon", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Monoidal.Basic", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "obtain", "obtain", "suffices", "dsimp", "refine", "rw", "associator_naturality,", "comp_id", "assoc,", "id_tensorHom_id,", "rw", "e₂.inv_hom_id,", "comp_id]", "dsimp", "have", "pentagon_aux₂", "rw", "whiskerRight_comp,", "reassoc_of%", "pentagon_aux₁", "pentagon_aux₃", "simp", "rw", "simp", "congr", "simp"], "tactic_count": 28}
{"name": "CategoryTheory.Localization.Monoidal.leftUnitor_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Monoidal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Localization.Monoidal.rightUnitor_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.Monoidal.triangle_aux₁", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Monoidal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Localization.Monoidal.triangle_aux₂", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Monoidal.Basic", "is_tactic_proof": true, "tactics": ["simp", "congr", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Localization.Monoidal.triangle_aux₃", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Monoidal.Basic", "is_tactic_proof": true, "tactics": ["simp", "congr", "rw"], "tactic_count": 3}
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{"name": "CategoryTheory.instMonoidalLocalizedMonoidalToMonoidalCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.AreEqualizedByLocalization.map_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Predicate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.AreEqualizedByLocalization.map_eq_of_isInvertedBy", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Predicate", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Localization.StrictUniversalPropertyFixedTarget.prod_uniq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Prod", "is_tactic_proof": true, "tactics": ["apply", "apply", "apply", "apply", "apply", "apply", "simpa"], "tactic_count": 7}
{"name": "CategoryTheory.Localization.StrictUniversalPropertyFixedTarget.prodLift₁", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.StrictUniversalPropertyFixedTarget.prod_fac₁", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.StrictUniversalPropertyFixedTarget.prodLift", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.Prod", "is_tactic_proof": true, "tactics": ["refine", "intro", "haveI", "obtain", "exact", "apply"], "tactic_count": 6}
{"name": "CategoryTheory.Localization.StrictUniversalPropertyFixedTarget.prod_fac₂", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Prod", "is_tactic_proof": true, "tactics": ["simp", "apply"], "tactic_count": 2}
{"name": "CategoryTheory.Localization.StrictUniversalPropertyFixedTarget.prod_fac", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Prod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Localization.StrictUniversalPropertyFixedTarget.prod", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.Construction.prodIsLocalization", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsLocalization.prod", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.Prod", "is_tactic_proof": true, "tactics": ["haveI", "exact", "of_equivalence_target"], "tactic_count": 3}
{"name": "HomRel.FactorsThroughLocalization", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomRel.FactorsThroughLocalization.strictUniversalPropertyFixedTarget", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomRel.FactorsThroughLocalization.strictUniversalPropertyFixedTarget'", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomRel.FactorsThroughLocalization.isLocalizedEquivalence", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocalizerMorphism.RightResolution.mk_surjective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocalizerMorphism.LeftResolution.mk_surjective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocalizerMorphism.HasRightResolutions", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Localization.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocalizerMorphism.HasLeftResolutions", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Localization.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocalizerMorphism.RightResolution.Hom.id", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocalizerMorphism.RightResolution.Hom.comp", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocalizerMorphism.RightResolution.instCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocalizerMorphism.RightResolution.id_f", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocalizerMorphism.RightResolution.comp_f", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocalizerMorphism.RightResolution.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocalizerMorphism.LeftResolution.Hom.id", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocalizerMorphism.LeftResolution.Hom.comp", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocalizerMorphism.LeftResolution.instCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocalizerMorphism.LeftResolution.id_f", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocalizerMorphism.LeftResolution.comp_f", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocalizerMorphism.LeftResolution.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocalizerMorphism.LeftResolution.op", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocalizerMorphism.LeftResolution.unop", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocalizerMorphism.RightResolution.op", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocalizerMorphism.RightResolution.unop", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocalizerMorphism.nonempty_leftResolution_iff_op", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocalizerMorphism.nonempty_rightResolution_iff_op", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocalizerMorphism.hasLeftResolutions_iff_op", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocalizerMorphism.hasRightResolutions_iff_op", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocalizerMorphism.instHasLeftResolutionsOppositeOpOpOfHasRightResolutions", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.Resolution", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "CategoryTheory.LocalizerMorphism.instHasRightResolutionsOppositeOpOpOfHasLeftResolutions", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.Resolution", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "CategoryTheory.LocalizerMorphism.LeftResolution.opFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocalizerMorphism.RightResolution.unopFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocalizerMorphism.LeftResolution.opEquivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocalizerMorphism.essSurj_of_hasRightResolutions", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocalizerMorphism.isIso_iff_of_hasRightResolutions", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Resolution", "is_tactic_proof": true, "tactics": ["constructor", "intros", "infer_instance", "intro", "have", "have", "rw", "apply", "exact"], "tactic_count": 9}
{"name": "CategoryTheory.LocalizerMorphism.essSurj_of_hasLeftResolutions", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocalizerMorphism.isIso_iff_of_hasLeftResolutions", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Resolution", "is_tactic_proof": true, "tactics": ["constructor", "intros", "infer_instance", "intro", "have", "have", "rw", "apply", "exact"], "tactic_count": 9}
{"name": "CategoryTheory.Localization.hasSmallLocalizedHom_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.SmallHom", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "intro", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.Localization.hasSmallLocalizedHom_of_isLocalization", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.SmallHom", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Localization.small_of_hasSmallLocalizedHom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.SmallHom", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "CategoryTheory.Localization.hasSmallLocalizedHom_iff_of_isos", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.SmallHom", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Localization.hasSmallLocalizedHom_of_isos", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.SmallHom", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "CategoryTheory.Localization.hasSmallLocalizedHom_iff_target", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.SmallHom", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Localization.hasSmallLocalizedHom_iff_source", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.SmallHom", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Localization.SmallHom", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.SmallHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.SmallHom.equiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.SmallHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.SmallHom.equiv_equiv_symm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.SmallHom", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "apply"], "tactic_count": 3}
{"name": "CategoryTheory.Localization.SmallHom.mk", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.SmallHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.SmallHom.equiv_mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.SmallHom", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Localization.SmallHom.mkInv", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.SmallHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.SmallHom.equiv_mkInv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.SmallHom", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Localization.SmallHom.comp", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.SmallHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.SmallHom.equiv_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.SmallHom", "is_tactic_proof": true, "tactics": ["letI", "letI", "obtain", "obtain", "dsimp", "rw", "simp"], "tactic_count": 7}
{"name": "CategoryTheory.Localization.SmallHom.mk_comp_mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.SmallHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.SmallHom.comp_mk_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.SmallHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.SmallHom.mk_id_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.SmallHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.SmallHom.comp_assoc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.SmallHom", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Localization.SmallHom.mk_comp_mkInv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.SmallHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.SmallHom.mkInv_comp_mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.SmallHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.SmallHom.chgUniv", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.SmallHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.SmallHom.equiv_chgUniv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.SmallHom", "is_tactic_proof": true, "tactics": ["obtain", "dsimp", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.LocalizerMorphism.smallHomMap", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.SmallHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocalizerMorphism.equiv_smallHomMap", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.SmallHom", "is_tactic_proof": true, "tactics": ["obtain", "simp", "let", "let", "let", "let", "let", "let", "rw", "change", "let", "liftNatIso", "have", "γ.hom.app", "simp", "simp"], "tactic_count": 16}
{"name": "CategoryTheory.LocalizerMorphism.smallHomMap_mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.SmallHom", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.LocalizerMorphism.smallHomMap_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.SmallHom", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.LocalizerMorphism.smallHomMap'", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.SmallHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocalizerMorphism.equiv_smallHomMap'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.SmallHom", "is_tactic_proof": true, "tactics": ["have", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.LocalizerMorphism.smallHomMap'_mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.SmallHom", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.LocalizerMorphism.smallHomMap'_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.SmallHom", "is_tactic_proof": true, "tactics": ["have", "have", "have", "have", "have", "have", "have", "simp", "congr", "rw"], "tactic_count": 10}
{"name": "CategoryTheory.Localization.HasSmallLocalizedShiftedHom", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Localization.SmallShiftedHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.hasSmallLocalizedShiftedHom_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.SmallShiftedHom", "is_tactic_proof": true, "tactics": ["dsimp", "have", "dsimp", "simp"], "tactic_count": 4}
{"name": "CategoryTheory.Localization.hasSmallLocalizedShiftedHom_iff_target", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.SmallShiftedHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.hasSmallLocalizedShiftedHom_iff_source", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.SmallShiftedHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.hasSmallLocalizedHom_of_hasSmallLocalizedShiftedHom₀", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.SmallShiftedHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.instHasSmallLocalizedHomObjShiftFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.SmallShiftedHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.instHasSmallLocalizedHomObjShiftFunctor_1", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.SmallShiftedHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.instHasSmallLocalizedHomObjShiftFunctor_2", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.SmallShiftedHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.instHasSmallLocalizedHomObjShiftFunctor_3", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.SmallShiftedHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.SmallHom.shift", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.SmallShiftedHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.SmallHom.equiv_shift", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.SmallShiftedHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.SmallShiftedHom", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.SmallShiftedHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.SmallShiftedHom.mk", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.SmallShiftedHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.SmallShiftedHom.shift", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.SmallShiftedHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.SmallShiftedHom.comp", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.SmallShiftedHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.SmallShiftedHom.mk₀", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.SmallShiftedHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.SmallShiftedHom.mk₀Inv", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.SmallShiftedHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.SmallShiftedHom.equiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.SmallShiftedHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.SmallShiftedHom.equiv_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.SmallShiftedHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.SmallShiftedHom.equiv_shift'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.SmallShiftedHom", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Localization.SmallShiftedHom.equiv_shift", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.SmallShiftedHom", "is_tactic_proof": true, "tactics": ["dsimp", "erw", "simp", "rfl"], "tactic_count": 4}
{"name": "CategoryTheory.Localization.SmallShiftedHom.equiv_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.SmallShiftedHom", "is_tactic_proof": true, "tactics": ["dsimp", "erw", "simp", "rfl"], "tactic_count": 4}
{"name": "CategoryTheory.Localization.SmallShiftedHom.equiv_mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.SmallShiftedHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.SmallShiftedHom.equiv_mk₀", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.SmallShiftedHom", "is_tactic_proof": true, "tactics": ["subst", "dsimp", "erw", "dsimp", "simp"], "tactic_count": 5}
{"name": "CategoryTheory.Localization.SmallShiftedHom.equiv_mk₀Inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.SmallShiftedHom", "is_tactic_proof": true, "tactics": ["have", "refine", "rw", "simp"], "tactic_count": 4}
{"name": "CategoryTheory.Localization.SmallShiftedHom.comp_assoc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.SmallShiftedHom", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Localization.SmallShiftedHom.mk₀_comp_mk₀Inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.SmallShiftedHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.SmallShiftedHom.mk₀Inv_comp_mk₀", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.SmallShiftedHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.SmallShiftedHom.comp_mk₀_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.SmallShiftedHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.SmallShiftedHom.mk₀_id_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.SmallShiftedHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.SmallShiftedHom.postcompEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.SmallShiftedHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.SmallShiftedHom.precompEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.SmallShiftedHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.SmallShiftedHom.chgUniv", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.SmallShiftedHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.SmallShiftedHom.equiv_chgUniv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.SmallShiftedHom", "is_tactic_proof": true, "tactics": ["dsimp", "congr", "apply"], "tactic_count": 3}
{"name": "CategoryTheory.LocalizerMorphism.smallShiftedHomMap", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.SmallShiftedHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocalizerMorphism.equiv_smallShiftedHomMap", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.SmallShiftedHom", "is_tactic_proof": true, "tactics": ["have", "apply", "simp", "refine", "simp", "assoc,", "nth_rw", "simp"], "tactic_count": 8}
{"name": "CategoryTheory.LocalizerMorphism.smallShiftedHomMap_mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.SmallShiftedHom", "is_tactic_proof": true, "tactics": ["apply", "let", "simp", "nth_rw", "simp"], "tactic_count": 5}
{"name": "CategoryTheory.LocalizerMorphism.smallShiftedHomMap_mk₀", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.SmallShiftedHom", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.LocalizerMorphism.smallShiftedHomMap_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.SmallShiftedHom", "is_tactic_proof": true, "tactics": ["apply", "let", "simp", "rw", "simp"], "tactic_count": 5}
{"name": "CategoryTheory.Localization.structuredArrowEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.StructuredArrow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.CategoryTheory.Localization.StructuredArrow.0.CategoryTheory.Localization.induction_structuredArrow'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.StructuredArrow", "is_tactic_proof": true, "tactics": ["let", "suffices", "obtain", "obtain", "exact", "intro", "induction", "nil", "cons", "obtain", "exact", "simpa"], "tactic_count": 12}
{"name": "CategoryTheory.Localization.induction_structuredArrow", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.StructuredArrow", "is_tactic_proof": true, "tactics": ["let", "rw", "apply", "convert", "simp", "intro", "convert", "simp", "intro", "convert", "simp"], "tactic_count": 11}
{"name": "CategoryTheory.Localization.induction_costructuredArrow", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.StructuredArrow", "is_tactic_proof": true, "tactics": ["let", "change", "induction", "hP₀", "hP₁", "hP₂"], "tactic_count": 6}
{"name": "CategoryTheory.Functor.essImageDistTriang", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.Triangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.essImageDistTriang_mem_of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Triangulated", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.contractible_mem_essImageDistTriang", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Triangulated", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.rotate_essImageDistTriang", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Triangulated", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "exact", "rintro", "exact", "inv_rot_of_distTriang"], "tactic_count": 6}
{"name": "CategoryTheory.Functor.complete_distinguished_essImageDistTriang_morphism", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Triangulated", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "have", "have", "have", "have", "have", "have", "dsimp", "simp", "obtain", "have", "have", "dsimp", "simp", "refine", "rw", "rw", "cancel_mono", "hφ₁,"], "tactic_count": 20}
{"name": "CategoryTheory.Triangulated.Localization.distinguished_cocone_triangle", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Triangulated", "is_tactic_proof": true, "tactics": ["have", "obtain", "obtain", "refine", "refine", "dsimp", "simp"], "tactic_count": 7}
{"name": "CategoryTheory.Triangulated.Localization.complete_distinguished_triangle_morphism", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Triangulated", "is_tactic_proof": true, "tactics": ["refine", "clear", "intro", "obtain", "obtain", "obtain", "have", "have", "dsimp", "obtain", "rw", "rw", "simp", "obtain", "let", "change", "have", "obtain", "let", "have", "refine", "inv", "rw", "dsimp", "rw", "rw", "dsimp", "simp"], "tactic_count": 28}
{"name": "CategoryTheory.Triangulated.Localization.pretriangulated", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.Triangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Triangulated.Localization.isTriangulated_functor", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.Triangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Triangulated.Localization.isTriangulated", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Triangulated", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Triangulated.Localization.instAdditiveLocalizationShiftFunctorInt", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.Triangulated", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Triangulated.Localization.instPretriangulatedLocalization", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.Triangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Triangulated.Localization.instIsTriangulatedLocalization", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.Triangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Triangulated.Localization.instAdditiveLocalization'ShiftFunctorInt", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.Triangulated", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Triangulated.Localization.instPretriangulatedLocalization'", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.Triangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Triangulated.Localization.instIsTriangulatedLocalization'", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.Triangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.distTriang_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Triangulated", "is_tactic_proof": true, "tactics": ["constructor", "intro", "let", "obtain", "exact", "mem⟩", "rintro", "exact"], "tactic_count": 8}
{"name": "CategoryTheory.MorphismProperty.IsInvertedBy₃", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.Trifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.Lifting₃.uncurry", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.Trifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.lift₃", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.Trifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.instLifting₃Lift₃", "kind": "instance", "module": "Mathlib.CategoryTheory.Localization.Trifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.lift₃NatTrans", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.Trifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.lift₃NatTrans_app_app_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Trifunctor", "is_tactic_proof": true, "tactics": ["dsimp", "simp", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Localization.natTrans₃_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Trifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.lift₃NatIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.Trifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.Lifting₃.bifunctorComp₁₂", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.Trifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.Lifting₃.bifunctorComp₂₃", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.Trifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.associator", "kind": "definition", "module": "Mathlib.CategoryTheory.Localization.Trifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Localization.associator_hom_app_app_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Localization.Trifunctor", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "dsimp", "simp"], "tactic_count": 4}
{"name": "CategoryTheory.ChosenPullbacks", "kind": "abbrev", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ChosenPullbacksAlong", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ChosenPullbacksAlong.ofHasPullbacksAlong", "kind": "definition", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ChosenPullbacksAlong", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ChosenPullbacksAlong.id", "kind": "definition", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ChosenPullbacksAlong", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ChosenPullbacksAlong.pullbackId", "kind": "definition", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ChosenPullbacksAlong", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ChosenPullbacksAlong.unit_pullbackId_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ChosenPullbacksAlong", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.ChosenPullbacksAlong.unit_pullbackId_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ChosenPullbacksAlong", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.ChosenPullbacksAlong.pullbackId_hom_counit", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ChosenPullbacksAlong", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.ChosenPullbacksAlong.iso", "kind": "definition", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ChosenPullbacksAlong", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ChosenPullbacksAlong.isoInv", "kind": "definition", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ChosenPullbacksAlong", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ChosenPullbacksAlong.comp", "kind": "definition", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ChosenPullbacksAlong", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ChosenPullbacksAlong.pullbackComp", "kind": "definition", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ChosenPullbacksAlong", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ChosenPullbacksAlong.unit_pullbackComp_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ChosenPullbacksAlong", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.ChosenPullbacksAlong.pullbackComp_hom_counit", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ChosenPullbacksAlong", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategoryToUnit", "kind": "definition", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ChosenPullbacksAlong", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategoryFst", "kind": "definition", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ChosenPullbacksAlong", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategorySnd", "kind": "definition", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ChosenPullbacksAlong", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ChosenPullbacksAlong.pullbackObj", "kind": "abbrev", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ChosenPullbacksAlong", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ChosenPullbacksAlong.fst'", "kind": "abbrev", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ChosenPullbacksAlong", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ChosenPullbacksAlong.fst", "kind": "abbrev", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ChosenPullbacksAlong", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ChosenPullbacksAlong.fst'_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ChosenPullbacksAlong", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ChosenPullbacksAlong.snd", "kind": "abbrev", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ChosenPullbacksAlong", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ChosenPullbacksAlong.snd'", "kind": "abbrev", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ChosenPullbacksAlong", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ChosenPullbacksAlong.snd'_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ChosenPullbacksAlong", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ChosenPullbacksAlong.condition", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ChosenPullbacksAlong", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ChosenPullbacksAlong.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ChosenPullbacksAlong", "is_tactic_proof": true, "tactics": ["let", "let", "let", "let", "have", "apply", "apply", "simpa", "exact"], "tactic_count": 9}
{"name": "CategoryTheory.ChosenPullbacksAlong.lift", "kind": "definition", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ChosenPullbacksAlong", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ChosenPullbacksAlong.lift_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ChosenPullbacksAlong", "is_tactic_proof": true, "tactics": ["let", "let", "have", "simp", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.ChosenPullbacksAlong.lift_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ChosenPullbacksAlong", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.ChosenPullbacksAlong.pullbackMap_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ChosenPullbacksAlong", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.ChosenPullbacksAlong.pullbackCone", "kind": "definition", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ChosenPullbacksAlong", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ChosenPullbacksAlong.pullbackCone_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ChosenPullbacksAlong", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ChosenPullbacksAlong.pullbackCone_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ChosenPullbacksAlong", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ChosenPullbacksAlong.isLimitPullbackCone", "kind": "definition", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ChosenPullbacksAlong", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ChosenPullbacksAlong.isPullback", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ChosenPullbacksAlong", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ChosenPullbacksAlong.chosenPullbacksAlongFst", "kind": "definition", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ChosenPullbacksAlong", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ChosenPullbacksAlong.hasPullbackAlong", "kind": "instance", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ChosenPullbacksAlong", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ChosenPullbacksAlong.hasPullbacks", "kind": "instance", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ChosenPullbacksAlong", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback", "kind": "definition", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ChosenPullbacksAlong", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_hom_app_comp_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ChosenPullbacksAlong", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_hom_app_comp_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ChosenPullbacksAlong", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_inv_app_comp_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ChosenPullbacksAlong", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_inv_app_comp_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ChosenPullbacksAlong", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsExponentiable", "kind": "abbrev", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ExponentiableMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ExponentiableMorphism.isExponentiable", "kind": "instance", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ExponentiableMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ExponentiableMorphism.ev", "kind": "definition", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ExponentiableMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ExponentiableMorphism.coev", "kind": "definition", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ExponentiableMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ExponentiableMorphism.ev_def", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ExponentiableMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ExponentiableMorphism.coev_def", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ExponentiableMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ExponentiableMorphism.ev_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ExponentiableMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ExponentiableMorphism.coev_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ExponentiableMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ExponentiableMorphism.ev_coev", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ExponentiableMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ExponentiableMorphism.coev_ev", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ExponentiableMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ExponentiableMorphism.pushforwardCurry", "kind": "definition", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ExponentiableMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ExponentiableMorphism.pushforwardUncurry", "kind": "definition", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ExponentiableMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ExponentiableMorphism.homEquiv_apply_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ExponentiableMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ExponentiableMorphism.homEquiv_symm_apply_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ExponentiableMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ExponentiableMorphism.pushforward_uncurry_curry", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ExponentiableMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ExponentiableMorphism.pushforward_curry_uncurry", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ExponentiableMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ExponentiableMorphism.instChosenPullbacksAlongHomDiscretePUnitMk", "kind": "instance", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ExponentiableMorphism", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.ExponentiableMorphism.OverMkHom", "kind": "instance", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ExponentiableMorphism", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.ExponentiableMorphism.id", "kind": "definition", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ExponentiableMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ExponentiableMorphism.id_pushforward", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ExponentiableMorphism", "is_tactic_proof": true, "tactics": ["dsimp"], "tactic_count": 1}
{"name": "CategoryTheory.ExponentiableMorphism.pushforwardId", "kind": "definition", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ExponentiableMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ExponentiableMorphism.unit_pushforwardId_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ExponentiableMorphism", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.ExponentiableMorphism.pushforwardId_hom_counit", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ExponentiableMorphism", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.ExponentiableMorphism.comp", "kind": "definition", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ExponentiableMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ExponentiableMorphism.comp_pushforward", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ExponentiableMorphism", "is_tactic_proof": true, "tactics": ["dsimp"], "tactic_count": 1}
{"name": "CategoryTheory.ExponentiableMorphism.pushforwardComp", "kind": "definition", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ExponentiableMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ExponentiableMorphism.unit_pushforwardComp_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ExponentiableMorphism", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.ExponentiableMorphism.pushforwardComp_hom_counit", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.ExponentiableMorphism", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.ChosenPullbacksAlong.binaryFan", "kind": "abbrev", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ChosenPullbacksAlong.binaryFanIsBinaryProduct", "kind": "definition", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategoryOver", "kind": "definition", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ChosenPullbacksAlong.Over.tensorObj_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ChosenPullbacksAlong.Over.tensorObj_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ChosenPullbacksAlong.Over.tensorObj_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ChosenPullbacksAlong.Over.tensorUnit_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ChosenPullbacksAlong.Over.tensorUnit_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ChosenPullbacksAlong.Over.fst_eq_fst'", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ChosenPullbacksAlong.Over.snd_eq_snd'", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ChosenPullbacksAlong.Over.lift_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ChosenPullbacksAlong.Over.toUnit_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ChosenPullbacksAlong.Over.associator_hom_left_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ChosenPullbacksAlong.Over.associator_hom_left_snd_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ChosenPullbacksAlong.Over.associator_hom_left_snd_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ChosenPullbacksAlong.Over.associator_inv_left_fst_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ChosenPullbacksAlong.Over.associator_inv_left_fst_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ChosenPullbacksAlong.Over.associator_inv_left_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ChosenPullbacksAlong.Over.leftUnitor_hom_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ChosenPullbacksAlong.Over.leftUnitor_inv_left_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ChosenPullbacksAlong.Over.leftUnitor_inv_left_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ChosenPullbacksAlong.Over.rightUnitor_hom_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ChosenPullbacksAlong.Over.rightUnitor_inv_left_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ChosenPullbacksAlong.Over.rightUnitor_inv_left_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ChosenPullbacksAlong.Over.whiskerLeft_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ChosenPullbacksAlong.Over.whiskerLeft_left_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ChosenPullbacksAlong.Over.whiskerLeft_left_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ChosenPullbacksAlong.Over.whiskerRight_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ChosenPullbacksAlong.Over.whiskerRight_left_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ChosenPullbacksAlong.Over.whiskerRight_left_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ChosenPullbacksAlong.Over.tensorHom_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ChosenPullbacksAlong.Over.tensorHom_left_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ChosenPullbacksAlong.Over.tensorHom_left_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.toOver", "kind": "definition", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.toOver_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.Over", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.toOverUnit", "kind": "definition", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.equivToOverUnit", "kind": "definition", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.toOverUnitPullback", "kind": "definition", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.forgetAdjToOver", "kind": "definition", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.forgetAdjToOver.homEquiv_symm", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.Over", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.toOverIsoToOverUnit", "kind": "definition", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.toOverPullbackIsoToOver", "kind": "definition", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.toOverIteratedSliceForwardIsoPullback", "kind": "definition", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.curryRightUnitorHom", "kind": "abbrev", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.Sections", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.toUnit_comp_curryRightUnitorHom", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.Sections", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Over.sections", "kind": "definition", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.Sections", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.sectionsCurry", "kind": "definition", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.Sections", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.sectionsUncurry", "kind": "definition", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.Sections", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.sectionsCurry_sectionUncurry", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.Sections", "is_tactic_proof": true, "tactics": ["dsimp", "cat_disch"], "tactic_count": 2}
{"name": "CategoryTheory.Over.sectionsUncurry_sectionsCurry", "kind": "theorem", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.Sections", "is_tactic_proof": true, "tactics": ["dsimp", "ext", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.Over.coreHomEquivToOverSections", "kind": "definition", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.Sections", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.toOverSectionsAdj", "kind": "definition", "module": "Mathlib.CategoryTheory.LocallyCartesianClosed.Sections", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instIsLocallyDirectedDiscrete", "kind": "instance", "module": "Mathlib.CategoryTheory.LocallyDirected", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "simp", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.instIsLocallyDirectedWidePushoutShapeOfMonoObjNoneSomeMapInit", "kind": "instance", "module": "Mathlib.CategoryTheory.LocallyDirected", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "simp", "exact", "simp", "exact", "simp", "exact", "simp", "exact"], "tactic_count": 10}
{"name": "CategoryTheory.MarkovCategory.eq_discard", "kind": "theorem", "module": "Mathlib.CategoryTheory.MarkovCategory.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.MarkovCategory.isTerminalUnit", "kind": "definition", "module": "Mathlib.CategoryTheory.MarkovCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MarkovCategory.instSubsingletonHomTensorUnit", "kind": "instance", "module": "Mathlib.CategoryTheory.MarkovCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.toMonad", "kind": "definition", "module": "Mathlib.CategoryTheory.Monad.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.toComonad", "kind": "definition", "module": "Mathlib.CategoryTheory.Monad.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.adjToMonadIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Monad.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.adjToComonadIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Monad.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.unitAsIsoOfIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Monad.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.isIso_unit_of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monad.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.fullyFaithfulLOfCompIsoId", "kind": "definition", "module": "Mathlib.CategoryTheory.Monad.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.counitAsIsoOfIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Monad.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.isIso_counit_of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monad.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.fullyFaithfulROfCompIsoId", "kind": "definition", "module": "Mathlib.CategoryTheory.Monad.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Monad.comparison", "kind": "definition", "module": "Mathlib.CategoryTheory.Monad.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Monad.comparisonForget", "kind": "definition", "module": "Mathlib.CategoryTheory.Monad.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Monad.left_comparison", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monad.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instFaithfulAlgebraToMonadComparison", "kind": "instance", "module": "Mathlib.CategoryTheory.Monad.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instFullAlgebraToMonadAdjComparison", "kind": "instance", "module": "Mathlib.CategoryTheory.Monad.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instEssSurjAlgebraToMonadAdjComparison", "kind": "instance", "module": "Mathlib.CategoryTheory.Monad.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comonad.comparison", "kind": "definition", "module": "Mathlib.CategoryTheory.Monad.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comonad.comparisonForget", "kind": "definition", "module": "Mathlib.CategoryTheory.Monad.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comonad.left_comparison", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monad.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Comonad.comparison_faithful_of_faithful", "kind": "instance", "module": "Mathlib.CategoryTheory.Monad.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instFullCoalgebraToComonadAdjComparison", "kind": "instance", "module": "Mathlib.CategoryTheory.Monad.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instEssSurjCoalgebraToComonadAdjComparison", "kind": "instance", "module": "Mathlib.CategoryTheory.Monad.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.monadicLeftAdjoint", "kind": "definition", "module": "Mathlib.CategoryTheory.Monad.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.monadicAdjunction", "kind": "definition", "module": "Mathlib.CategoryTheory.Monad.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instIsEquivalenceAlgebraToMonadMonadicAdjunctionComparison", "kind": "instance", "module": "Mathlib.CategoryTheory.Monad.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instIsRightAdjointOfMonadicRightAdjoint", "kind": "instance", "module": "Mathlib.CategoryTheory.Monad.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instMonadicRightAdjointAlgebraForget", "kind": "instance", "module": "Mathlib.CategoryTheory.Monad.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.comonadicRightAdjoint", "kind": "definition", "module": "Mathlib.CategoryTheory.Monad.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.comonadicAdjunction", "kind": "definition", "module": "Mathlib.CategoryTheory.Monad.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instIsEquivalenceCoalgebraToComonadComonadicAdjunctionComparison", "kind": "instance", "module": "Mathlib.CategoryTheory.Monad.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instIsLeftAdjointOfComonadicLeftAdjoint", "kind": "instance", "module": "Mathlib.CategoryTheory.Monad.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instComonadicLeftAdjointCoalgebraForget", "kind": "instance", "module": "Mathlib.CategoryTheory.Monad.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.μ_iso_of_reflective", "kind": "instance", "module": "Mathlib.CategoryTheory.Monad.Adjunction", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.δ_iso_of_coreflective", "kind": "instance", "module": "Mathlib.CategoryTheory.Monad.Adjunction", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Reflective.instIsIsoAppUnitReflectorAdjunctionA", "kind": "instance", "module": "Mathlib.CategoryTheory.Monad.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Reflective.comparison_essSurj", "kind": "instance", "module": "Mathlib.CategoryTheory.Monad.Adjunction", "is_tactic_proof": true, "tactics": ["refine", "symm", "refine", "exact", "dsimp", "rw", "dsimp", "rw", "apply"], "tactic_count": 9}
{"name": "CategoryTheory.Reflective.comparison_full", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monad.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Coreflective.instIsIsoAppCounitCoreflectorAdjunctionA", "kind": "instance", "module": "Mathlib.CategoryTheory.Monad.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Coreflective.comparison_essSurj", "kind": "instance", "module": "Mathlib.CategoryTheory.Monad.Adjunction", "is_tactic_proof": true, "tactics": ["refine", "refine", "exact", "rw", "simp", "simpa"], "tactic_count": 6}
{"name": "CategoryTheory.Coreflective.comparison_full", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monad.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.monadicOfReflective", "kind": "instance", "module": "Mathlib.CategoryTheory.Monad.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.MonoidalCategory.MonoidalRightAction.actionRight", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Monoidal.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.MonoidalCategory.MonoidalRightAction.rightActionOfOppositeRightAction", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Action.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.MonoidalCategory.MonoidalRightAction.oppositeRightAction_actionAssocIso_op", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Action.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.MonoidalRightAction.rightActionOfOppositeRightAction_actionObj_unop", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Action.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.MonoidalRightAction.rightActionOfOppositeRightAction_actionHomLeft_unop", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Action.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.MonoidalRightAction.rightActionOfOppositeRightAction_actionRight_unop", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Action.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.MonoidalRightAction.rightActionOfOppositeRightAction_actionHom_unop", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Action.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.MonoidalRightAction.rightActionOfOppositeRightAction_actionAssocIso_unop", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Action.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "id_tensor_π_preserves_coequalizer_inv_desc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Bimod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "id_tensor_π_preserves_coequalizer_inv_colimMap_desc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Bimod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "π_tensor_id_preserves_coequalizer_inv_desc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Bimod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "π_tensor_id_preserves_coequalizer_inv_colimMap_desc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Bimod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bimod.id'", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Bimod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bimod.homInhabited", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Bimod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bimod.comp", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Bimod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bimod.instCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Bimod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bimod.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Bimod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bimod.id_hom'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Bimod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bimod.comp_hom'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Bimod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bimod.isoOfIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Bimod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bimod.regular", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Bimod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bimod.instInhabited", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Bimod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bimod.forget", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Bimod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bimod.TensorBimod.X", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Bimod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bimod.TensorBimod.actLeft", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Bimod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bimod.TensorBimod.whiskerLeft_π_actLeft", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Bimod", "is_tactic_proof": true, "tactics": ["erw", "simp"], "tactic_count": 2}
{"name": "Bimod.TensorBimod.one_act_left'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Bimod", "is_tactic_proof": true, "tactics": ["refine", "dsimp", "slice_lhs", "slice_lhs", "slice_lhs", "slice_lhs", "slice_rhs", "monoidal"], "tactic_count": 8}
{"name": "Bimod.TensorBimod.left_assoc'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Bimod", "is_tactic_proof": true, "tactics": ["refine", "dsimp", "slice_lhs", "slice_lhs", "slice_lhs", "slice_lhs", "slice_rhs", "slice_rhs", "slice_rhs", "slice_rhs", "monoidal"], "tactic_count": 11}
{"name": "Bimod.TensorBimod.actRight", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Bimod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bimod.TensorBimod.π_tensor_id_actRight", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Bimod", "is_tactic_proof": true, "tactics": ["erw", "simp"], "tactic_count": 2}
{"name": "Bimod.TensorBimod.actRight_one'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Bimod", "is_tactic_proof": true, "tactics": ["refine", "dsimp", "slice_lhs", "slice_lhs", "slice_lhs", "slice_lhs", "simp"], "tactic_count": 7}
{"name": "Bimod.TensorBimod.right_assoc'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Bimod", "is_tactic_proof": true, "tactics": ["refine", "dsimp", "slice_lhs", "slice_lhs", "slice_lhs", "slice_lhs", "slice_rhs", "slice_rhs", "slice_rhs", "simp"], "tactic_count": 10}
{"name": "Bimod.TensorBimod.middle_assoc'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Bimod", "is_tactic_proof": true, "tactics": ["refine", "dsimp", "slice_lhs", "slice_lhs", "slice_lhs", "slice_rhs", "slice_rhs", "slice_rhs", "slice_rhs", "slice_rhs", "simp"], "tactic_count": 11}
{"name": "Bimod.tensorBimod", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Bimod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bimod.whiskerLeft", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Bimod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bimod.whiskerRight", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Bimod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bimod.AssociatorBimod.homAux", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Bimod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bimod.AssociatorBimod.hom", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Bimod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bimod.AssociatorBimod.hom_left_act_hom'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Bimod", "is_tactic_proof": true, "tactics": ["dsimp", "refine", "simp", "slice_lhs", "slice_lhs", "slice_rhs", "refine", "dsimp", "slice_lhs", "slice_lhs", "slice_lhs", "slice_lhs", "slice_rhs", "rw", "whiskerLeft_comp]", "slice_rhs", "slice_rhs", "slice_rhs", "monoidal"], "tactic_count": 19}
{"name": "Bimod.AssociatorBimod.hom_right_act_hom'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Bimod", "is_tactic_proof": true, "tactics": ["dsimp", "refine", "simp", "slice_lhs", "slice_lhs", "slice_rhs", "refine", "dsimp", "slice_lhs", "slice_lhs", "slice_lhs", "slice_lhs", "slice_rhs", "rw", "comp_whiskerRight]", "slice_rhs", "slice_rhs", "dsimp", "slice_rhs", "monoidal"], "tactic_count": 20}
{"name": "Bimod.AssociatorBimod.invAux", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Bimod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bimod.AssociatorBimod.inv", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Bimod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bimod.AssociatorBimod.hom_inv_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Bimod", "is_tactic_proof": true, "tactics": ["dsimp", "apply", "slice_lhs", "refine", "simp", "slice_lhs", "slice_lhs", "slice_lhs", "slice_lhs", "dsimp", "slice_rhs", "rfl"], "tactic_count": 12}
{"name": "Bimod.AssociatorBimod.inv_hom_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Bimod", "is_tactic_proof": true, "tactics": ["dsimp", "apply", "slice_lhs", "refine", "simp", "slice_lhs", "slice_lhs", "slice_lhs", "slice_lhs", "dsimp", "slice_rhs", "rfl"], "tactic_count": 12}
{"name": "Bimod.LeftUnitorBimod.hom", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Bimod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bimod.LeftUnitorBimod.inv", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Bimod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bimod.LeftUnitorBimod.hom_inv_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Bimod", "is_tactic_proof": true, "tactics": ["dsimp", "ext", "slice_lhs", "slice_lhs", "slice_lhs", "slice_lhs", "slice_lhs", "slice_lhs", "slice_lhs", "slice_rhs", "monoidal"], "tactic_count": 11}
{"name": "Bimod.LeftUnitorBimod.inv_hom_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Bimod", "is_tactic_proof": true, "tactics": ["dsimp", "slice_lhs", "rw"], "tactic_count": 3}
{"name": "Bimod.LeftUnitorBimod.hom_left_act_hom'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Bimod", "is_tactic_proof": true, "tactics": ["dsimp", "refine", "dsimp", "slice_lhs", "slice_lhs", "slice_rhs", "rw"], "tactic_count": 7}
{"name": "Bimod.LeftUnitorBimod.hom_right_act_hom'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Bimod", "is_tactic_proof": true, "tactics": ["dsimp", "refine", "dsimp", "slice_lhs", "slice_rhs", "slice_rhs", "simp"], "tactic_count": 7}
{"name": "Bimod.RightUnitorBimod.hom", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Bimod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bimod.RightUnitorBimod.inv", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Bimod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bimod.RightUnitorBimod.hom_inv_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Bimod", "is_tactic_proof": true, "tactics": ["dsimp", "ext", "slice_lhs", "slice_lhs", "slice_lhs", "slice_lhs", "slice_lhs", "slice_lhs", "slice_rhs", "monoidal"], "tactic_count": 10}
{"name": "Bimod.RightUnitorBimod.inv_hom_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Bimod", "is_tactic_proof": true, "tactics": ["dsimp", "slice_lhs", "rw"], "tactic_count": 3}
{"name": "Bimod.RightUnitorBimod.hom_left_act_hom'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Bimod", "is_tactic_proof": true, "tactics": ["dsimp", "refine", "dsimp", "slice_lhs", "slice_lhs", "slice_rhs", "rw"], "tactic_count": 7}
{"name": "Bimod.RightUnitorBimod.hom_right_act_hom'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Bimod", "is_tactic_proof": true, "tactics": ["dsimp", "refine", "dsimp", "slice_lhs", "slice_lhs", "slice_rhs", "rw"], "tactic_count": 7}
{"name": "Bimod.associatorBimod", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Bimod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bimod.leftUnitorBimod", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Bimod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bimod.rightUnitorBimod", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Bimod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bimod.whiskerLeft_id_bimod", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Bimod", "is_tactic_proof": true, "tactics": ["ext", "apply", "simp"], "tactic_count": 3}
{"name": "Bimod.id_whiskerRight_bimod", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Bimod", "is_tactic_proof": true, "tactics": ["ext", "apply", "simp"], "tactic_count": 3}
{"name": "Bimod.whiskerLeft_comp_bimod", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Bimod", "is_tactic_proof": true, "tactics": ["ext", "apply", "simp"], "tactic_count": 3}
{"name": "Bimod.id_whiskerLeft_bimod", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Bimod", "is_tactic_proof": true, "tactics": ["dsimp", "ext", "apply", "dsimp", "slice_lhs", "dsimp", "slice_rhs", "dsimp", "slice_rhs", "slice_rhs", "slice_rhs", "slice_rhs", "slice_rhs", "slice_rhs", "slice_rhs", "have", "grind"], "tactic_count": 17}
{"name": "Bimod.comp_whiskerLeft_bimod", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Bimod", "is_tactic_proof": true, "tactics": ["dsimp", "ext", "apply", "dsimp", "slice_lhs", "dsimp", "slice_rhs", "dsimp", "refine", "simp", "slice_rhs", "slice_rhs", "slice_rhs", "slice_rhs", "dsimp", "slice_rhs", "slice_rhs", "slice_rhs", "slice_rhs", "slice_lhs", "rfl"], "tactic_count": 21}
{"name": "Bimod.comp_whiskerRight_bimod", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Bimod", "is_tactic_proof": true, "tactics": ["ext", "apply", "simp"], "tactic_count": 3}
{"name": "Bimod.whiskerRight_id_bimod", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Bimod", "is_tactic_proof": true, "tactics": ["dsimp", "ext", "apply", "dsimp", "slice_lhs", "dsimp", "slice_rhs", "dsimp", "slice_rhs", "slice_rhs", "slice_rhs", "slice_rhs", "slice_rhs", "slice_rhs", "simp"], "tactic_count": 15}
{"name": "Bimod.whiskerRight_comp_bimod", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Bimod", "is_tactic_proof": true, "tactics": ["dsimp", "ext", "apply", "dsimp", "slice_lhs", "dsimp", "slice_rhs", "dsimp", "refine", "simp", "slice_rhs", "slice_rhs", "slice_rhs", "slice_rhs", "dsimp", "slice_rhs", "slice_rhs", "slice_rhs", "slice_rhs", "slice_lhs", "rfl"], "tactic_count": 21}
{"name": "Bimod.whisker_assoc_bimod", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Bimod", "is_tactic_proof": true, "tactics": ["dsimp", "ext", "apply", "dsimp", "slice_lhs", "dsimp", "slice_rhs", "dsimp", "refine", "simp", "slice_lhs", "slice_rhs", "slice_rhs", "slice_rhs", "dsimp", "slice_rhs", "dsimp", "slice_rhs", "slice_rhs", "simp"], "tactic_count": 20}
{"name": "Bimod.whisker_exchange_bimod", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Bimod", "is_tactic_proof": true, "tactics": ["ext", "apply", "dsimp", "slice_lhs", "slice_lhs", "slice_lhs", "simp"], "tactic_count": 7}
{"name": "Bimod.pentagon_bimod", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Bimod", "is_tactic_proof": true, "tactics": ["dsimp", "ext", "apply", "dsimp", "dsimp", "slice_lhs", "slice_lhs", "slice_rhs", "dsimp", "refine", "dsimp", "slice_lhs", "slice_rhs", "slice_rhs", "refine", "dsimp", "slice_lhs", "rw", "slice_lhs", "dsimp", "slice_lhs", "slice_lhs", "slice_lhs", "slice_lhs", "rw", "slice_rhs", "slice_rhs", "slice_rhs", "slice_rhs", "monoidal"], "tactic_count": 30}
{"name": "Bimod.triangle_bimod", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Bimod", "is_tactic_proof": true, "tactics": ["dsimp", "ext", "apply", "dsimp", "dsimp", "slice_lhs", "dsimp", "slice_rhs", "dsimp", "refine", "dsimp", "slice_lhs", "slice_lhs", "dsimp", "slice_lhs", "slice_rhs", "slice_rhs", "simp"], "tactic_count": 18}
{"name": "Bimod.monBicategory", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Bimod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bimon", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Bimon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bimon.instCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Bimon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bimon.ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Bimon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bimon.id_hom'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Bimon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bimon.comp_hom'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Bimon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bimon.toMon", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Monoidal.Bimon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bimon.forget", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Bimon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bimon.toMon_forget", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Bimon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bimon.toComon", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Bimon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bimon.toComon_forget", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Bimon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bimon.toMonComonObj", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Bimon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bimon.toMonComon", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Bimon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bimon.ofMonComonObjX", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Bimon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bimon.ofMonComonObjX_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Bimon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bimon.ofMonComonObjX_mul", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Bimon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bimon.ofMonComonObj", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Bimon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bimon.ofMonComon", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Bimon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bimon.toMonComon_ofMonComon_obj_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Bimon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bimon.toMonComon_ofMonComon_obj_mul", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Bimon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bimon.equivMonComonUnitIsoAppXAux", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Bimon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bimon.instIsMonHomHomEquivMonComonUnitIsoAppXAux", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Bimon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bimon.equivMonComonUnitIsoAppX", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Bimon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bimon.instIsComonHomMonHomEquivMonComonUnitIsoAppX", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Bimon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bimon.equivMonComonUnitIsoApp", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Bimon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bimon.ofMonComon_toMonComon_obj_counit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Bimon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bimon.ofMonComon_toMonComon_obj_comul", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Bimon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bimon.equivMonComonCounitIsoAppXAux", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Bimon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bimon.instIsComonHomHomEquivMonComonCounitIsoAppXAux", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Bimon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Bimon.instIsMonHomComonHomEquivMonComonCounitIsoAppX", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Bimon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bimon.equivMonComonCounitIsoApp", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Bimon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bimon.equivMonComon", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Bimon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bimon.trivial", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Bimon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bimon.trivialTo", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Bimon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bimon.toTrivial", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Bimon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bimon.BimonObjAux_counit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Bimon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bimon.BimonObjAux_comul", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Bimon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Bimon.one_comul", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Bimon.", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Bimon.mul_counit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Bimon.", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Bimon.compatibility", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Bimon.", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Bimon.mk'X", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Bimon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory._aux_Mathlib_CategoryTheory_Monoidal_Braided_Basic___macroRules_CategoryTheory_termβ__1", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory._aux_Mathlib_CategoryTheory_Monoidal_Braided_Basic___unexpand_CategoryTheory_BraidedCategory_braiding_1", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.BraidedCategory.braiding_tensor_left_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": true, "tactics": ["apply", "apply", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.BraidedCategory.braiding_tensor_right_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": true, "tactics": ["apply", "apply", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.BraidedCategory.braiding_tensor_left_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.BraidedCategory.braiding_tensor_right_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.BraidedCategory.braiding_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp_rw"], "tactic_count": 2}
{"name": "CategoryTheory.BraidedCategory.braiding_inv_naturality_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.BraidedCategory.braiding_inv_naturality_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.BraidedCategory.braiding_inv_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.BraidedCategory.tensorLeftIsoTensorRight", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.BraidedCategory.curriedBraidingNatIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.BraidedCategory.yang_baxter", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": true, "tactics": ["rw", "repeat", "rw"], "tactic_count": 3}
{"name": "CategoryTheory.BraidedCategory.yang_baxter'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": true, "tactics": ["rw", "convert", "all_goals"], "tactic_count": 3}
{"name": "CategoryTheory.BraidedCategory.yang_baxter_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.BraidedCategory.hexagon_forward_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.BraidedCategory.hexagon_reverse_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.BraidedCategory.hexagon_forward_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.BraidedCategory.hexagon_reverse_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.BraidedCategory.ofFullyFaithful", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.braiding_leftUnitor_aux₁", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": true, "tactics": ["monoidal"], "tactic_count": 1}
{"name": "CategoryTheory.braiding_leftUnitor_aux₂", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.braiding_leftUnitor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.braiding_rightUnitor_aux₁", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.braiding_rightUnitor_aux₂", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.braiding_rightUnitor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.braiding_tensorUnit_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.braiding_inv_tensorUnit_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": true, "tactics": ["rw", "rw", "monoidal"], "tactic_count": 3}
{"name": "CategoryTheory.leftUnitor_inv_braiding", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.rightUnitor_inv_braiding", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.braiding_tensorUnit_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.braiding_inv_tensorUnit_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": true, "tactics": ["rw", "rw", "monoidal"], "tactic_count": 3}
{"name": "CategoryTheory.SymmetricCategory.braiding_swap_eq_inv_braiding", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.LaxBraided.id", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.LaxBraided.instComp", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.LaxBraided.ofNatIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LaxBraidedFunctor.of", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LaxBraidedFunctor.toLaxMonoidalFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LaxBraidedFunctor.instCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LaxBraidedFunctor.id_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LaxBraidedFunctor.comp_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LaxBraidedFunctor.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LaxBraidedFunctor.homMk", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LaxBraidedFunctor.isoMk", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LaxBraidedFunctor.forget", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LaxBraidedFunctor.fullyFaithfulForget", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LaxBraidedFunctor.isoOfComponents", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LaxBraidedFunctor.isoOfComponents_hom_hom_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LaxBraidedFunctor.isoOfComponents_inv_hom_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.map_braiding", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.SymmetricCategory.ofFaithful", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SymmetricCategory.ofFullyFaithful", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.Braided.instId", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.Braided.instComp", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.Braided.toMonoidal_injective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "CategoryTheory.instBraidedCategoryDiscrete", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Discrete.monoidalFunctorBraided", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.tensorμ", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.tensorδ", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.tensorμ_tensorδ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": true, "tactics": ["simp", "hom_inv_whiskerRight_assoc,"], "tactic_count": 2}
{"name": "CategoryTheory.MonoidalCategory.tensorδ_tensorμ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": true, "tactics": ["simp", "inv_hom_whiskerRight_assoc,"], "tactic_count": 2}
{"name": "CategoryTheory.MonoidalCategory.tensorμ_natural", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "simp_rw", "slice_lhs", "slice_lhs", "rw", "slice_lhs", "rw", "braiding_naturality,", "slice_lhs", "rw", "slice_lhs", "simp"], "tactic_count": 12}
{"name": "CategoryTheory.MonoidalCategory.tensorμ_natural_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.tensorμ_natural_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.tensor_left_unitality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "have", "slice_rhs", "clear", "slice_rhs", "simp"], "tactic_count": 6}
{"name": "CategoryTheory.MonoidalCategory.tensor_right_unitality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "have", "slice_rhs", "clear", "slice_rhs", "simp"], "tactic_count": 6}
{"name": "CategoryTheory.MonoidalCategory.tensor_associativity", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "simp", "calc"], "tactic_count": 3}
{"name": "CategoryTheory.MonoidalCategory.tensorMonoidal", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.tensor_ε", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.tensor_η", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.tensor_μ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.tensor_δ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.leftUnitor_monoidal", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "have", "rw", "rw", "monoidal"], "tactic_count": 5}
{"name": "CategoryTheory.MonoidalCategory.rightUnitor_monoidal", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "have", "rw", "rw", "monoidal"], "tactic_count": 5}
{"name": "CategoryTheory.MonoidalCategory.associator_monoidal", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "calc"], "tactic_count": 2}
{"name": "CategoryTheory.MonoidalCategory.tensorμ_comp_μ_tensorHom_μ_comp_μ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp", "rw", "comp_whiskerRight_assoc,", "comp_whiskerRight_assoc,", "comp_whiskerRight_assoc,", "comp_whiskerRight_assoc,", "pentagon_inv_assoc,", "associator_inv_naturality_left_assoc,", "simp", "pentagon_inv_hom_hom_hom_inv_assoc]"], "tactic_count": 11}
{"name": "CategoryTheory.instBraidedCategoryOpposite", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.op_braiding", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.unop_braiding", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.op_hom_braiding", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.unop_hom_braiding", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.op_inv_braiding", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.unop_inv_braiding", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalOpposite.instBraiding", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalOpposite.mop_braiding", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalOpposite.unmop_braiding", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalOpposite.mop_hom_braiding", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalOpposite.unmop_hom_braiding", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalOpposite.mop_inv_braiding", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalOpposite.unmop_inv_braiding", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalOpposite.instMonoidalMopFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalOpposite.mopFunctor_ε", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalOpposite.mopFunctor_η", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalOpposite.mopFunctor_μ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalOpposite.mopFunctor_δ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalOpposite.instMonoidalUnmopFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalOpposite.unmopFunctor_ε", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalOpposite.unmopFunctor_η", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalOpposite.unmopFunctor_μ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalOpposite.unmopFunctor_δ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalOpposite.instBraidedMopFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalOpposite.instBraidedUnmopFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.reverseBraiding", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SymmetricCategory.reverseBraiding_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "congr", "funext", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.SymmetricCategory.equivReverseBraiding", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.BraidedCategory.Hexagon.functor₁₂₃", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Multifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.BraidedCategory.Hexagon.functor₁₂₃'", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Multifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.BraidedCategory.Hexagon.functor₂₃₁", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Multifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.BraidedCategory.Hexagon.functor₂₃₁'", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Multifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.BraidedCategory.Hexagon.functor₂₁₃", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Multifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.BraidedCategory.Hexagon.functor₂₁₃'", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Multifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.BraidedCategory.Hexagon.functor₃₁₂'", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Multifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.BraidedCategory.Hexagon.functor₃₁₂", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Multifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.BraidedCategory.Hexagon.functor₁₃₂'", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Multifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.BraidedCategory.Hexagon.functor₁₃₂", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Multifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.BraidedCategory.ofBifunctor._example", "kind": "example", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Multifunctor", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "CategoryTheory.BraidedCategory.ofBifunctor._example", "kind": "example", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Multifunctor", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "CategoryTheory.BraidedCategory.ofBifunctor._example", "kind": "example", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Multifunctor", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "CategoryTheory.BraidedCategory.ofBifunctor.Forward.firstMap₂", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Multifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.BraidedCategory.ofBifunctor.Forward.firstMap₃", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Multifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.BraidedCategory.ofBifunctor.Forward.secondMap₁", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Multifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.BraidedCategory.ofBifunctor.Forward.secondMap₂", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Multifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.BraidedCategory.ofBifunctor.Forward.secondMap₃", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Multifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.BraidedCategory.ofBifunctor.Reverse.firstMap₂", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Multifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.BraidedCategory.ofBifunctor.Reverse.firstMap₃", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Multifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.BraidedCategory.ofBifunctor.Reverse.secondMap₁", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Multifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.BraidedCategory.ofBifunctor.Reverse.secondMap₂", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Multifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.BraidedCategory.ofBifunctor.Reverse.secondMap₃", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Multifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.BraidedCategory.ofBifunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Multifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SymmetricCategory.ofCurried", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Multifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instBraidedCategoryOpposite", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.BraidedCategory.unop_tensorμ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Opposite", "is_tactic_proof": true, "tactics": ["simp", "unop_whiskerRight,"], "tactic_count": 2}
{"name": "CategoryTheory.BraidedCategory.op_tensorμ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Opposite", "is_tactic_proof": true, "tactics": ["simp", "op_hom_braiding,"], "tactic_count": 2}
{"name": "_private.Mathlib.CategoryTheory.Monoidal.Braided.Reflection.0.CategoryTheory.Monoidal.Reflective.adjRetractionAux", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Reflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.CategoryTheory.Monoidal.Braided.Reflection.0.CategoryTheory.Monoidal.Reflective.adjRetraction", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Reflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.CategoryTheory.Monoidal.Braided.Reflection.0.CategoryTheory.Monoidal.Reflective.adjRetraction_is_retraction", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Reflection", "is_tactic_proof": false, "tactics": ["suffices", "simp", "simp", "simp", "slice_lhs", "simp", "slice_lhs", "simp"], "tactic_count": 8}
{"name": "CategoryTheory.Monoidal.Reflective.isIso_tfae", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Reflection", "is_tactic_proof": false, "tactics": ["tfae_have", "h", "have", "intro", "have", "rw", "rw", "simp", "infer_instance", "intro", "have", "simp", "rw", "infer_instance", "tfae_have", "let", "have", "erw", "exact", "tfae_have", "h,", "rw", "intro", "have", "rw", "simp", "have", "rw", "refine", "have", "ext", "simp", "simp", "rw", "simp", "curriedTensor_obj_obj,", "have", "rw", "suffices", "from", "rw", "refine", "constructor", "refine", "ext", "simp", "types_comp_apply,", "have", "rw", "simp", "tfae_have", "conv", "conv", "rw", "rw", "rw", "have", "have", "rw", "ext", "simp", "yoneda_obj_obj,", "rw", "simp", "rw", "simp", "tfae_finish"], "tactic_count": 67}
{"name": "CategoryTheory.Monoidal.Reflective.instIsIsoMapTensorHomAppUnit", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Reflection", "is_tactic_proof": true, "tactics": ["have", "rw", "rw", "infer_instance"], "tactic_count": 4}
{"name": "CategoryTheory.Monoidal.Reflective.instIsIsoAppUnitObjIhom", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Reflection", "is_tactic_proof": true, "tactics": ["revert", "rw", "intro", "infer_instance"], "tactic_count": 4}
{"name": "CategoryTheory.Monoidal.Reflective.closed", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Reflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Monoidal.Reflective.monoidalClosed", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Reflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Monoidal.Transported.instBraidedCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Transport", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.CategoryTheory.Monoidal.Braided.Transport.0.CategoryTheory.Monoidal.termE'_", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Transport", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.CategoryTheory.Monoidal.Braided.Transport.0.CategoryTheory.Monoidal._aux_Mathlib_CategoryTheory_Monoidal_Braided_Transport___macroRules__private_Mathlib_CategoryTheory_Monoidal_Braided_Transport_0_CategoryTheory_Monoidal_termE'__1", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Transport", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.CategoryTheory.Monoidal.Braided.Transport.0.CategoryTheory.Monoidal._aux_Mathlib_CategoryTheory_Monoidal_Braided_Transport___unexpand_CategoryTheory_Monoidal_equivalenceTransported_1", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Transport", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Monoidal.instBraidedTransportedInverseEquivalenceTransported", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Transport", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Monoidal.transportedFunctorCompInverseLaxBraided", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Transport", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Monoidal.transportedFunctorCompInverseBraided", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Transport", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Monoidal.instBraidedTransportedFunctorEquivalenceTransported", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Transport", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Monoidal.Transported.instSymmetricCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Braided.Transport", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SemiCartesianMonoidalCategory.toUnit", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SemiCartesianMonoidalCategory.instUniqueHomTensorUnit", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SemiCartesianMonoidalCategory.default_eq_toUnit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SemiCartesianMonoidalCategory.toUnit_unique", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SemiCartesianMonoidalCategory.toUnit_unit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SemiCartesianMonoidalCategory.comp_toUnit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CartesianMonoidalCategory.ofChosenFiniteProducts.tensorObj", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CartesianMonoidalCategory.ofChosenFiniteProducts.tensorHom", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CartesianMonoidalCategory.ofChosenFiniteProducts.id_tensorHom_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CartesianMonoidalCategory.ofChosenFiniteProducts.tensorHom_comp_tensorHom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CartesianMonoidalCategory.ofChosenFiniteProducts.pentagon", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "apply", "rintro", "simp", "apply", "rintro", "simp", "apply", "rintro"], "tactic_count": 9}
{"name": "CategoryTheory.CartesianMonoidalCategory.ofChosenFiniteProducts.triangle", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CartesianMonoidalCategory.ofChosenFiniteProducts.leftUnitor_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.CartesianMonoidalCategory.ofChosenFiniteProducts.rightUnitor_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.CartesianMonoidalCategory.ofChosenFiniteProducts.associator_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "apply", "rintro", "simp", "apply", "rintro"], "tactic_count": 6}
{"name": "CategoryTheory.CartesianMonoidalCategory.ofChosenFiniteProducts", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CartesianMonoidalCategory.ofHasFiniteProducts", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CartesianMonoidalCategory.lift", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CartesianMonoidalCategory.lift_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CartesianMonoidalCategory.lift_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CartesianMonoidalCategory.mono_lift_of_mono_left", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CartesianMonoidalCategory.mono_lift_of_mono_right", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CartesianMonoidalCategory.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CartesianMonoidalCategory.comp_lift", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.CartesianMonoidalCategory.lift_fst_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.CartesianMonoidalCategory.lift_comp_fst_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.CartesianMonoidalCategory.whiskerLeft_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.CartesianMonoidalCategory.whiskerLeft_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.CartesianMonoidalCategory.whiskerRight_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.CartesianMonoidalCategory.whiskerRight_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.CartesianMonoidalCategory.tensorHom_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.CartesianMonoidalCategory.tensorHom_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.CartesianMonoidalCategory.lift_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.CartesianMonoidalCategory.lift_fst_comp_snd_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.CartesianMonoidalCategory.lift_whiskerRight", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.CartesianMonoidalCategory.lift_whiskerLeft", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.CartesianMonoidalCategory.associator_hom_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.CartesianMonoidalCategory.associator_hom_snd_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.CartesianMonoidalCategory.associator_hom_snd_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.CartesianMonoidalCategory.associator_inv_fst_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.CartesianMonoidalCategory.associator_inv_fst_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.CartesianMonoidalCategory.associator_inv_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.CartesianMonoidalCategory.lift_lift_associator_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.CartesianMonoidalCategory.lift_lift_associator_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.CartesianMonoidalCategory.leftUnitor_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.CartesianMonoidalCategory.rightUnitor_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.CartesianMonoidalCategory.leftUnitor_inv_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CartesianMonoidalCategory.leftUnitor_inv_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.CartesianMonoidalCategory.rightUnitor_inv_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.CartesianMonoidalCategory.rightUnitor_inv_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CartesianMonoidalCategory.whiskerLeft_toUnit_comp_rightUnitor_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.CartesianMonoidalCategory.whiskerRight_toUnit_comp_leftUnitor_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.CartesianMonoidalCategory.lift_leftUnitor_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["rw", "cat_disch"], "tactic_count": 2}
{"name": "CategoryTheory.CartesianMonoidalCategory.lift_rightUnitor_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["rw", "cat_disch"], "tactic_count": 2}
{"name": "CategoryTheory.CartesianMonoidalCategory.homEquivToProd", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CartesianMonoidalCategory.braiding_hom_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.CartesianMonoidalCategory.braiding_hom_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.CartesianMonoidalCategory.braiding_inv_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.CartesianMonoidalCategory.braiding_inv_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.CartesianMonoidalCategory.tensorμ_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.CartesianMonoidalCategory.tensorμ_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.CartesianMonoidalCategory.tensorδ_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.CartesianMonoidalCategory.tensorδ_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.CartesianMonoidalCategory.lift_snd_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.CartesianMonoidalCategory.lift_snd_comp_fst_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.CartesianMonoidalCategory.lift_braiding_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "CategoryTheory.CartesianMonoidalCategory.lift_braiding_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "CategoryTheory.CartesianMonoidalCategory.toSymmetricCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.BraidedCategory.ofCartesianMonoidalCategory", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CartesianMonoidalCategory.instNonemptyBraidedCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CartesianMonoidalCategory.instSubsingletonBraidedCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CartesianMonoidalCategory.instSubsingletonSymmetricCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CartesianMonoidalCategory.instHasFiniteProducts", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CartesianMonoidalCategory.terminalComparison", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CartesianMonoidalCategory.map_toUnit_comp_terminalComparison", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CartesianMonoidalCategory.preservesLimit_empty_of_isIso_terminalComparison", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["apply", "apply", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.CartesianMonoidalCategory.preservesTerminalIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CartesianMonoidalCategory.preservesTerminalIso_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CartesianMonoidalCategory.terminalComparison_isIso_of_preservesLimits", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.CartesianMonoidalCategory.preservesTerminalIso_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.CartesianMonoidalCategory.preservesTerminalIso_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.CartesianMonoidalCategory.prodComparison", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CartesianMonoidalCategory.prodComparison_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CartesianMonoidalCategory.prodComparison_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CartesianMonoidalCategory.inv_prodComparison_map_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.CartesianMonoidalCategory.inv_prodComparison_map_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.CartesianMonoidalCategory.prodComparison_natural", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["apply", "simp", "tensorHom_snd,"], "tactic_count": 3}
{"name": "CategoryTheory.CartesianMonoidalCategory.prodComparison_natural_whiskerLeft", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.CartesianMonoidalCategory.prodComparison_natural_whiskerRight", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.CartesianMonoidalCategory.prodComparison_inv_natural", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.CartesianMonoidalCategory.prodComparison_inv_natural_whiskerLeft", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.CartesianMonoidalCategory.prodComparison_inv_natural_whiskerRight", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.CartesianMonoidalCategory.prodComparison_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["unfold", "ext"], "tactic_count": 2}
{"name": "CategoryTheory.CartesianMonoidalCategory.prodComparison_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CartesianMonoidalCategory.prodComparisonNatTrans", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CartesianMonoidalCategory.prodComparisonNatTrans_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.CartesianMonoidalCategory.prodComparisonNatTrans_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.CartesianMonoidalCategory.prodComparisonBifunctorNatTrans", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CartesianMonoidalCategory.prodComparisonBifunctorNatTrans_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.CartesianMonoidalCategory.instIsIsoFunctorProdComparisonNatTransOfProdComparison", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["letI", "apply"], "tactic_count": 2}
{"name": "CategoryTheory.CartesianMonoidalCategory.instIsIsoFunctorProdComparisonBifunctorNatTransOfProdComparison", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": false, "tactics": ["letI", "apply"], "tactic_count": 2}
{"name": "CategoryTheory.CartesianMonoidalCategory.isLimitCartesianMonoidalCategoryOfPreservesLimits", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CartesianMonoidalCategory.prodComparisonIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CartesianMonoidalCategory.prodComparisonIso_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CartesianMonoidalCategory.isIso_prodComparison_of_preservesLimit_pair", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.CartesianMonoidalCategory.prodComparisonIso_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.CartesianMonoidalCategory.prodComparisonIso_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.CartesianMonoidalCategory.prodComparisonNatIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CartesianMonoidalCategory.prodComparisonBifunctorNatIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CartesianMonoidalCategory.preservesLimit_pair_of_isIso_prodComparison", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["apply", "refine", "dsimp", "simp", "dsimp", "simp"], "tactic_count": 6}
{"name": "CategoryTheory.CartesianMonoidalCategory.preservesLimitsOfShape_discrete_walkingPair_of_isIso_prodComparison", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["constructor", "intro", "refine", "apply"], "tactic_count": 4}
{"name": "CategoryTheory.CartesianMonoidalCategory.tensorLeftIsoProd", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CartesianMonoidalCategory.fullSubcategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.OplaxMonoidal.η_of_cartesianMonoidalCategory", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.OplaxMonoidal.δ_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["trans", "rw", "simp", "simp"], "tactic_count": 4}
{"name": "CategoryTheory.Functor.OplaxMonoidal.δ_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["trans", "rw", "simp", "simp"], "tactic_count": 4}
{"name": "CategoryTheory.Functor.OplaxMonoidal.lift_δ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.OplaxMonoidal.δ_of_cartesianMonoidalCategory", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.OplaxMonoidal.instIsIsoη", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.OplaxMonoidal.instIsIsoδ", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.OplaxMonoidal.ofChosenFiniteProducts", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.OplaxMonoidal.instSubsingleton", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.Monoidal.toUnit_ε", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.Monoidal.lift_μ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.Monoidal.μ_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.Monoidal.μ_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.Monoidal.μ_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.Monoidal.ε_of_cartesianMonoidalCategory", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["change"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.Monoidal.μ_of_cartesianMonoidalCategory", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": true, "tactics": ["change"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.Monoidal.ofChosenFiniteProducts", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.Monoidal.instSubsingleton", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.Monoidal.instPreservesFiniteProducts", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.Monoidal.nonempty_monoidal_iff_preservesFiniteProducts", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.Braided.ofChosenFiniteProducts", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.Braided.instSubsingleton", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.EssImageSubcategory.tensor_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.EssImageSubcategory.lift_def", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.EssImageSubcategory.associator_hom_def", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.EssImageSubcategory.associator_inv_def", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.EssImageSubcategory.toUnit_def", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.IsMonoidal.of_cartesianMonoidalCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.chosenTerminal", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.chosenTerminalIsTerminal", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.fromChosenTerminalEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.prodCone", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.isLimitProdCone", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.instCartesianMonoidalCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat.instBraidedCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Cat._example", "kind": "example", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Cat", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "CategoryTheory.Cat._example", "kind": "example", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Cat", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "CategoryTheory.Monoidal.tensorObj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Monoidal.whiskerLeft", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Monoidal.whiskerLeft_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Monoidal.whiskerLeft_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Monoidal.whiskerRight", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Monoidal.whiskerRight_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Monoidal.whiskerRight_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Monoidal.tensorHom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Monoidal.tensorUnit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Monoidal.associator_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Monoidal.associator_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Monoidal.leftUnitor_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Monoidal.leftUnitor_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Monoidal.rightUnitor_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Monoidal.rightUnitor_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Cat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CommGrpObj.ofRepresentableBy", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.CommGrp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.yonedaCommGrpGrpObj", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.CommGrp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.yonedaCommGrpGrp", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.CommGrp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsCommMonObj.ofRepresentableBy", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.CommMon.", "is_tactic_proof": true, "tactics": ["letI", "have", "constructor", "simp_rw", "op_tensorObj,"], "tactic_count": 5}
{"name": "CategoryTheory.cartesianComon", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Comon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.counit_eq_toUnit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Comon.", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.comul_eq_lift", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Comon.", "is_tactic_proof": true, "tactics": ["ext", "simpa", "simpa"], "tactic_count": 3}
{"name": "CategoryTheory.isoCartesianComon", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Comon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.comonEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Comon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.chosenTerminal", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.FunctorCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.chosenTerminalIsTerminal", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.FunctorCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.chosenProd", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.FunctorCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.chosenProd.fst", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.FunctorCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.chosenProd.snd", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.FunctorCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.chosenProd.isLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.FunctorCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.cartesianMonoidalCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.FunctorCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.Monoidal.tensorObj_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.FunctorCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.Monoidal.tensorObj_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.FunctorCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.Monoidal.fst_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.FunctorCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.Monoidal.snd_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.FunctorCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.Monoidal.leftUnitor_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.FunctorCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.Monoidal.leftUnitor_inv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.FunctorCategory", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.Monoidal.rightUnitor_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.FunctorCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.Monoidal.rightUnitor_inv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.FunctorCategory", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.Monoidal.tensorHom_app_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.FunctorCategory", "is_tactic_proof": true, "tactics": ["change", "rw", "rfl"], "tactic_count": 3}
{"name": "CategoryTheory.Functor.Monoidal.tensorHom_app_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.FunctorCategory", "is_tactic_proof": true, "tactics": ["change", "rw", "rfl"], "tactic_count": 3}
{"name": "CategoryTheory.Functor.Monoidal.whiskerLeft_app_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.FunctorCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.Monoidal.whiskerLeft_app_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.FunctorCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.Monoidal.whiskerRight_app_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.FunctorCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.Monoidal.whiskerRight_app_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.FunctorCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.Monoidal.associator_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.FunctorCategory", "is_tactic_proof": true, "tactics": ["apply", "rw", "simp", "apply", "rw", "simp", "rw", "simp"], "tactic_count": 8}
{"name": "CategoryTheory.Functor.Monoidal.associator_inv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.FunctorCategory", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.Monoidal.instPreservesColimitsOfShapeTensorLeftOfHasColimitsOfShape", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.FunctorCategory", "is_tactic_proof": true, "tactics": ["apply", "intro", "haveI", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.Functor.Monoidal.tensorObjComp", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.FunctorCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.Monoidal.RepresentableBy.tensorObj", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.FunctorCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrpObj.ofRepresentableBy", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Hom.group", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Hom.inv_def", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.yonedaGrpObj", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.yonedaGrpObjRepresentableBy", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrpObj.ofRepresentableBy_yonedaGrpObjRepresentableBy", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Grp.", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.yonedaGrpObjIsoOfRepresentableBy", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.yonedaGrp", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.yonedaGrp_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.yonedaGrpFullyFaithful", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instFullGrpFunctorOppositeGrpCatYonedaGrp", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instFaithfulGrpFunctorOppositeGrpCatYonedaGrp", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.essImage_yonedaGrp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Grp.", "is_tactic_proof": true, "tactics": ["ext", "constructor", "rintro", "exact", "rintro", "letI", "exact"], "tactic_count": 7}
{"name": "CategoryTheory.GrpObj.inv_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Grp.", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.GrpObj.div_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrpObj.zpow_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrpObj.comp_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrpObj.comp_div", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrpObj.comp_zpow", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrpObj.inv_eq_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Grp.", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.GrpObj.one_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Grp.", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.instIsMonHomInvOfIsCommMonObj", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instIsMonHomInvHomOfIsCommMonObj", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grp.instMonObj", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grp.hom_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grp.hom_mul", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grp.Hom.hom_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grp.Hom.hom_mul", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grp.Hom.hom_pow", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Grp.", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "CategoryTheory.Grp.instGrpObj", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grp.Hom.hom_hom_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grp.Hom.hom_hom_div", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grp.Hom.hom_hom_zpow", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Grp.", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "CategoryTheory.Grp.instIsCommMonObj", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grp.instIsMonHom", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Hom.commGroup", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SemilatticeInf.cartesianMonoidalCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.InfSemilattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SemilatticeInf.braidedCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.InfSemilattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SemilatticeInf.tensorObj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.InfSemilattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SemilatticeInf.tensorUnit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.InfSemilattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ModObj.trivialAction", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Mod.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Mod_.trivialAction", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Mod.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonObj.instIsMonHomToUnit", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonObj.instIsMonHomOne", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonObj.lift_lift_assoc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Mon.", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "CategoryTheory.MonObj.lift_comp_one_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Mon.", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "CategoryTheory.MonObj.lift_comp_one_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Mon.", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "CategoryTheory.MonObj.instIsMonHomFst", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonObj.instIsMonHomSnd", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonObj.instIsMonHomLift", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonObj.instIsMonHomMulOfIsCommMonObj", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Mon.instCartesianMonoidalCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Mon.lift_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Mon.fst_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Mon.snd_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Mon.instMonObjOfIsCommMonObjX", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Mon.hom_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Mon.hom_mul", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Mon.instIsCommMonObj", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonObj.ofRepresentableBy", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Hom.monoid", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Hom.one_def", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Hom.mul_def", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.map_mul", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Mon.", "is_tactic_proof": true, "tactics": ["simp", "congr", "rw", "ext"], "tactic_count": 4}
{"name": "CategoryTheory.Functor.map_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Mon.", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.homMonoidHom", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.FullyFaithful.homMulEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Mon.Hom.hom_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Mon.Hom.hom_mul", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Mon.Hom.hom_pow", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Mon.", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "CategoryTheory.yonedaMonObj", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.yonedaMonObjIsoOfRepresentableBy", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.yonedaMon", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.yonedaMon_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.yonedaMonObjRepresentableBy", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonObj.ofRepresentableBy_yonedaMonObjRepresentableBy", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Mon.", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.yonedaMonFullyFaithful", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instFullMonFunctorOppositeMonCatYonedaMon", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instFaithfulMonFunctorOppositeMonCatYonedaMon", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.essImage_yonedaMon", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Mon.", "is_tactic_proof": true, "tactics": ["ext", "constructor", "rintro", "exact", "rintro", "letI", "exact"], "tactic_count": 7}
{"name": "CategoryTheory.MonObj.one_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Mon.", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MonObj.mul_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Mon.", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MonObj.pow_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Mon.", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "CategoryTheory.MonObj.comp_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonObj.comp_mul", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonObj.comp_pow", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Mon.", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "CategoryTheory.MonObj.one_eq_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonObj.mul_eq_mul", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Hom.mulEquivCongrRight", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Over.braidedCategory", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.tensorObj_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.tensorObj_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.tensorObj_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.tensorUnit_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Over.lift_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.toUnit_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.associator_hom_left_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.associator_hom_left_snd_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.associator_hom_left_snd_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.associator_inv_left_fst_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.associator_inv_left_fst_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.associator_inv_left_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.leftUnitor_hom_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.leftUnitor_inv_left_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.leftUnitor_inv_left_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.rightUnitor_hom_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.rightUnitor_inv_left_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.rightUnitor_inv_left_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Over.whiskerLeft_left_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.whiskerLeft_left_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Over.whiskerRight_left_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.whiskerRight_left_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Over.tensorHom_left_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.tensorHom_left_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Over.braiding_inv_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Over.η_pullback_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Over.preservesTerminalIso_pullback", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Over", "is_tactic_proof": true, "tactics": ["ext1"], "tactic_count": 1}
{"name": "CategoryTheory.Over.prodComparisonIso_pullback_inv_left_fst_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Over", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Over.prodComparisonIso_pullback_Spec_inv_left_fst_fst'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.prodComparisonIso_pullback_inv_left_fst_snd'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Over", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Over.prodComparisonIso_pullback_inv_left_snd'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Over", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
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{"name": "CategoryTheory.Over.isCommMonObj_mk_pullbackSnd", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.grpObjMkPullbackSnd", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Over.isMonHom_pullbackFst_id_right", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Cartesian.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.MonoidalCategory.comp_whiskerRight", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.whiskerRight_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.whiskerRight_tensor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["simp", "rw", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.MonoidalCategory.whisker_assoc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["simp", "rw", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.MonoidalCategory.whisker_exchange", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.tensorHom_def'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.whiskerLeft_comp_tensorHom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.whiskerRight_comp_tensorHom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.tensorHom_comp_whiskerLeft", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.tensorHom_comp_whiskerRight", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.leftUnitor_inv_comp_tensorHom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.rightUnitor_inv_comp_tensorHom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.whiskerLeft_hom_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.hom_inv_whiskerRight", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.whiskerLeft_inv_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.inv_hom_whiskerRight", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.whiskerLeft_hom_inv'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.hom_inv_whiskerRight'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.whiskerLeft_inv_hom'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.inv_hom_whiskerRight'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.whiskerLeftIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.whiskerLeft_isIso", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.inv_whiskerLeft", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.whiskerLeftIso_refl", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.whiskerLeftIso_trans", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.whiskerLeftIso_symm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.whiskerRightIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.whiskerRight_isIso", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.inv_whiskerRight", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.whiskerRightIso_refl", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.whiskerRightIso_trans", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.whiskerRightIso_symm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.tensorIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.term_⊗ᵢ_", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory._aux_Mathlib_CategoryTheory_Monoidal_Category___macroRules_CategoryTheory_MonoidalCategory_term_⊗ᵢ__1", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory._aux_Mathlib_CategoryTheory_Monoidal_Category___unexpand_CategoryTheory_MonoidalCategory_tensorIso_1", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.tensorIso_def", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.tensorIso_def'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.tensor_isIso", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.inv_tensor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.whiskerLeft_dite", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["split_ifs"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.dite_whiskerRight", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["split_ifs"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.tensor_dite", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["split_ifs"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.dite_tensor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["split_ifs"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.whiskerLeft_eqToHom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["cases", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.MonoidalCategory.eqToHom_whiskerRight", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["cases", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.MonoidalCategory.associator_naturality_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.associator_inv_naturality_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.whiskerRight_tensor_symm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.associator_naturality_middle", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.associator_inv_naturality_middle", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.whisker_assoc_symm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.associator_naturality_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.associator_inv_naturality_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.tensor_whiskerLeft_symm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.leftUnitor_inv_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.id_whiskerLeft_symm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.rightUnitor_inv_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.whiskerRight_id_symm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.whiskerLeft_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.whiskerRight_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.pentagon_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.pentagon_inv_inv_hom_hom_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.MonoidalCategory.pentagon_inv_hom_hom_hom_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.pentagon_hom_inv_inv_inv_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.pentagon_hom_hom_inv_hom_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.pentagon_hom_inv_inv_inv_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.MonoidalCategory.pentagon_hom_hom_inv_inv_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.pentagon_inv_hom_hom_hom_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.pentagon_inv_inv_hom_inv_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.triangle_assoc_comp_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.triangle_assoc_comp_right_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.triangle_assoc_comp_left_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.leftUnitor_whiskerRight", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["rw", "pentagon_assoc,", "associator_naturality_left]"], "tactic_count": 3}
{"name": "CategoryTheory.MonoidalCategory.leftUnitor_inv_whiskerRight", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.whiskerLeft_rightUnitor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["rw", "pentagon_inv_assoc,", "triangle_assoc_comp_right,"], "tactic_count": 3}
{"name": "CategoryTheory.MonoidalCategory.whiskerLeft_rightUnitor_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.leftUnitor_tensor_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.leftUnitor_tensor_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.rightUnitor_tensor_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.rightUnitor_tensor_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.associator_inv_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.associator_conjugation", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.associator_inv_conjugation", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.id_tensor_associator_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.id_tensor_associator_inv_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.hom_inv_id_tensor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.inv_hom_id_tensor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.tensor_hom_inv_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.tensor_inv_hom_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.hom_inv_id_tensor'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.inv_hom_id_tensor'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.tensor_hom_inv_id'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.tensor_inv_hom_id'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.comp_tensor_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.id_tensor_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.id_tensor_comp_tensor_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.tensor_id_comp_id_tensor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.tensor_left_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.tensor_right_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.tensor", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.leftAssocTensor", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.leftAssocTensor_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.leftAssocTensor_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.rightAssocTensor", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.rightAssocTensor_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.rightAssocTensor_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.curriedTensor", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.tensorLeft", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.tensorRight", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.tensorUnitLeft", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.tensorUnitRight", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.associatorNatIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.leftUnitorNatIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.rightUnitorNatIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.curriedAssociatorNatIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.tensorLeftTensor", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.tensorLeftTensor_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.tensorLeftTensor_inv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "CategoryTheory.MonoidalCategory.instFaithfulFunctorTensoringLeft", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.MonoidalCategory.instFaithfulFunctorTensoringRight", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.tensorRightTensor", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.tensorRightTensor_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Category", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Center.isIso_of_f_isIso", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Center", "is_tactic_proof": true, "tactics": ["change", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Center.tensorObj", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Center.whiskerLeft_comm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Center", "is_tactic_proof": false, "tactics": ["dsimp", "calc", "monoidal"], "tactic_count": 3}
{"name": "CategoryTheory.Center.whiskerLeft", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Center.whiskerRight_comm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Center", "is_tactic_proof": false, "tactics": ["dsimp", "calc", "rw"], "tactic_count": 3}
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{"name": "CategoryTheory.Center.tensorHom", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Center.tensorUnit", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Center.associator", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Center.rightUnitor", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Center.instMonoidalForget", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Center.forget_ε", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Center.forget_μ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Center.instReflectsIsomorphismsForget", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Center.braidedCategoryCenter", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Center.instMonoidalOfBraided", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.unitClosed", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.MonoidalClosed.unitIsoSelf", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.MonoidalClosed.pre_comm_ihom_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "CategoryTheory.MonoidalClosed.internalHomAdjunction₂", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalClosed.ofEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalClosed.ofEquiv_curry_def", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Basic", "is_tactic_proof": true, "tactics": ["change", "dsimp", "rw", "dsimp", "rw", "rfl"], "tactic_count": 6}
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{"name": "CategoryTheory.MonoidalClosed.compTranspose", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalClosed.comp", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalClosed.id_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalClosed.compTranspose_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalClosed.comp_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalClosed.id_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Basic", "is_tactic_proof": true, "tactics": ["apply", "rw", "associator_inv_naturality_middle_assoc,", "triangle_assoc_comp_right_assoc,"], "tactic_count": 4}
{"name": "CategoryTheory.MonoidalClosed.comp_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Basic", "is_tactic_proof": true, "tactics": ["apply", "rw", "associator_inv_naturality_right_assoc,", "rightUnitor_inv_naturality_assoc,", "simp", "rw", "simp"], "tactic_count": 7}
{"name": "CategoryTheory.MonoidalClosed.assoc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Basic", "is_tactic_proof": true, "tactics": ["apply", "simp", "rw", "rw", "rw", "uncurry_curry]", "simp"], "tactic_count": 7}
{"name": "CategoryTheory.MonoidalClosed.curry'", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalClosed.uncurry'", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalClosed.curry'_uncurry'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalClosed.uncurry'_curry'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalClosed.curryHomEquiv'", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalClosed.curry'_injective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalClosed.uncurry'_injective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalClosed.curry'_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "rfl"], "tactic_count": 3}
{"name": "CategoryTheory.MonoidalClosed.whiskerLeft_curry'_ihom_ev_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.MonoidalClosed.curry'_whiskerRight_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply", "rw", "associator_inv_naturality_middle_assoc,", "comp_whiskerRight_assoc,"], "tactic_count": 5}
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{"name": "CategoryTheory.MonoidalClosed.curry'_ihom_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalClosed.curry'_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.CartesianMonoidalCategory.isLeftAdjoint_prod_functor", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Cartesian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CartesianClosed.term_⟹_", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Cartesian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CartesianClosed._aux_Mathlib_CategoryTheory_Monoidal_Closed_Cartesian___macroRules_CategoryTheory_CartesianClosed_term_⟹__1", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Cartesian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CartesianClosed.delabFunctorObjExp", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Cartesian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CartesianClosed.term_^^_", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Cartesian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CartesianClosed._aux_Mathlib_CategoryTheory_Monoidal_Closed_Cartesian___macroRules_CategoryTheory_CartesianClosed_term_^^__1", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Cartesian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.internalizeHom", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Cartesian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.zeroMul", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Cartesian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.mulZero", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Cartesian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.powZero", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Cartesian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.prodCoprodDistrib", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Cartesian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.strict_initial", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Cartesian", "is_tactic_proof": false, "tactics": ["haveI", "rw", "exact", "haveI", "apply"], "tactic_count": 5}
{"name": "CategoryTheory.to_initial_isIso", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Cartesian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.initial_mono", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Cartesian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Initial.mono_to", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Cartesian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.cartesianClosedOfEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Cartesian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalClosed.enrichedCategorySelf", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Enrichment", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalClosed.enrichedCategorySelf_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Enrichment", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalClosed.enrichedCategorySelf_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Enrichment", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalClosed.enrichedCategorySelf_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Enrichment", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalClosed.enrichedOrdinaryCategorySelf", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Enrichment", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalClosed.enrichedOrdinaryCategorySelf_eHomWhiskerLeft", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Enrichment", "is_tactic_proof": true, "tactics": ["change", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.MonoidalClosed.enrichedOrdinaryCategorySelf_eHomWhiskerRight", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Enrichment", "is_tactic_proof": true, "tactics": ["change", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.MonoidalClosed.enrichedOrdinaryCategorySelf_homEquiv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Enrichment", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalClosed.enrichedOrdinaryCategorySelf_homEquiv_symm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Enrichment", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.frobeniusMorphism", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.frobeniusMorphism_iso_of_preserves_binary_products", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.expComparison", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.expComparison_ev", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Functor", "is_tactic_proof": true, "tactics": ["convert", "apply", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.coev_expComparison", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Functor", "is_tactic_proof": true, "tactics": ["convert", "apply", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.uncurry_expComparison", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Functor", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.expComparison_whiskerLeft", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Functor", "is_tactic_proof": true, "tactics": ["unfold", "have", "mateEquiv_conjugateEquiv_vcomp", "have", "conjugateEquiv_mateEquiv_vcomp", "rw", "unfold", "congr", "apply", "ext", "simp", "prodComparisonNatTrans_app]", "rw", "simp"], "tactic_count": 14}
{"name": "CategoryTheory.frobeniusMorphism_mate", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Functor", "is_tactic_proof": true, "tactics": ["unfold", "have", "iterated_mateEquiv_conjugateEquiv", "rw", "congr", "apply", "ext", "unfold", "simp", "prodComparisonNatTrans_app,", "rw", "simp", "apply", "simp", "rw", "slice_lhs", "simp", "unfold", "simp"], "tactic_count": 19}
{"name": "CategoryTheory.frobeniusMorphism_iso_of_expComparison_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Functor", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.expComparison_iso_of_frobeniusMorphism_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Functor", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.cartesianClosedFunctorOfLeftAdjointPreservesBinaryProducts", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalClosed.FunctorCategory.homEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Closed.FunctorCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalClosed.FunctorCategory.homEquiv_naturality_two_symm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Closed.FunctorCategory.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "ext", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.MonoidalClosed.FunctorCategory.homEquiv_naturality_three", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Closed.FunctorCategory.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "ext", "dsimp", "ext", "rw", "whisker_exchange_assoc,", "enrichedOrdinaryCategorySelf_eHomWhiskerLeft]", "dsimp", "rw", "curry_natural_right]", "congr", "symm", "apply"], "tactic_count": 13}
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{"name": "CategoryTheory.MonoidalClosed.FunctorCategory.closed", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Closed.FunctorCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalClosed.FunctorCategory.monoidalClosed", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Closed.FunctorCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.CategoryTheory.Monoidal.Closed.FunctorCategory.Complete.0.CategoryTheory.Functor.incl", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Monoidal.Closed.FunctorCategory.Complete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instReflectsIsomorphismsDiscreteObjWhiskeringLeftIncl", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Closed.FunctorCategory.Complete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instPreservesLimitOfIsCoreflexivePairDiscreteObjWhiskeringLeftIncl", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Closed.FunctorCategory.Complete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instComonadicLeftAdjointDiscreteObjWhiskeringLeftIncl", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Closed.FunctorCategory.Complete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instIsLeftAdjointDiscreteTensorLeftCompIncl", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Closed.FunctorCategory.Complete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.functorCategoryClosed", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Closed.FunctorCategory.Complete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.functorCategoryMonoidalClosed", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Closed.FunctorCategory.Complete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.closedIhom", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Closed.FunctorCategory.Groupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.closedUnit", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Closed.FunctorCategory.Groupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.closedCounit", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Closed.FunctorCategory.Groupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.closed", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Closed.FunctorCategory.Groupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.monoidalClosed", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Closed.FunctorCategory.Groupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.ihom_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Closed.FunctorCategory.Groupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.ihom_ev_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Closed.FunctorCategory.Groupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.ihom_coev_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Closed.FunctorCategory.Groupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FunctorToTypes.functorHomEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Closed.FunctorToTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FunctorToTypes.rightAdj_map", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Closed.FunctorToTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FunctorToTypes.rightAdj", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Closed.FunctorToTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FunctorToTypes.adj", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Closed.FunctorToTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FunctorToTypes.closed", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Closed.FunctorToTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FunctorToTypes.monoidalClosed", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Closed.FunctorToTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ExponentialIdeal.mk'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instExponentialIdealId", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instExponentialIdealSubterminalsSubterminalInclusion", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Ideal", "is_tactic_proof": true, "tactics": ["apply", "intro", "refine", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.exponentialIdealReflective", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Ideal", "is_tactic_proof": true, "tactics": ["symm", "apply", "intro", "haveI", "apply", "simp"], "tactic_count": 6}
{"name": "CategoryTheory.ExponentialIdeal.mk_of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Ideal", "is_tactic_proof": true, "tactics": ["apply", "intro", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.reflective_products", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CartesianMonoidalCategory.ofReflective", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.exponentialIdeal_of_preservesBinaryProducts", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Ideal", "is_tactic_proof": true, "tactics": ["let", "let", "let", "let", "apply", "intro", "let", "apply", "apply", "exact", "have", "dsimp", "rw", "ir.left_triangle_components,", "apply", "haveI", "apply"], "tactic_count": 17}
{"name": "CategoryTheory.cartesianClosedOfReflective'", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.cartesianClosedOfReflective", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.bijection", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.bijection_symm_apply_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Ideal", "is_tactic_proof": false, "tactics": ["simp", "erw", "rw", "prodComparisonIso_hom", "apply", "rw", "apply", "rw", "apply"], "tactic_count": 9}
{"name": "CategoryTheory.bijection_natural", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Ideal", "is_tactic_proof": false, "tactics": ["dsimp", "erw", "homEquiv_symm_apply_eq,", "apply", "rw", "simp", "rw", "uncurry_natural_right,", "uncurry_natural_right,"], "tactic_count": 9}
{"name": "CategoryTheory.prodComparison_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.preservesBinaryProducts_of_exponentialIdeal", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.PreservesFiniteProducts.of_exponentialIdeal", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalClosed.instTransported", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Transport", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Types.tensorProductAdjunction", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Types", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.instMonoidalClosedType", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Types", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instMonoidalClosedFunctorType", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Types", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.cartesianClosedFunctorToTypes", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Types", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instMonoidalClosedFunctorType_1", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Types", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instMonoidalClosedFunctorTypeOfEssentiallySmall", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Types", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.uniqueHomsetOfInitialIsoUnit", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.uniqueHomsetOfZero", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Closed.Zero", "is_tactic_proof": true, "tactics": ["haveI", "apply", "refine"], "tactic_count": 3}
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{"name": "CategoryTheory.MonoidalCategory.leftUnitor_tensor_hom''", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.CoherenceLemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "CategoryTheory.MonoidalCategory.leftUnitor_inv_tensor_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.CoherenceLemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "CategoryTheory.CommComon.instCommComonObjUnit", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.CommComon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.CommComon.forget₂Comon", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.CommComon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.CommGrp.toCommMon", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.CommGrp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.CommGrp.trivial", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.CommGrp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.CommGrp.comp_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.CommGrp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.CommGrp.instFaithfulForget", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.CommGrp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.MonoidalCategory.DayConvolutionUnit.corepresentableByLeft", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.DayConvolutionUnit.corepresentableByRight", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitorCorepresentingIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution", "is_tactic_proof": true, "tactics": ["calc", "coyoneda.obj", "isoWhiskerLeft", "coyoneda.obj", "coyoneda.obj"], "tactic_count": 5}
{"name": "CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitorCorepresentingIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution", "is_tactic_proof": true, "tactics": ["calc", "coyoneda.obj", "isoWhiskerLeft", "coyoneda.obj", "coyoneda.obj"], "tactic_count": 5}
{"name": "CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitor", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitor", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitor_hom_unit_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution", "is_tactic_proof": false, "tactics": ["have", "congrArg", "dsimp", "simp", "simp", "simp"], "tactic_count": 6}
{"name": "CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitor_inv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution", "is_tactic_proof": false, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitor_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution", "is_tactic_proof": true, "tactics": ["apply", "apply", "ext", "simp"], "tactic_count": 4}
{"name": "CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitor_hom_unit_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution", "is_tactic_proof": false, "tactics": ["have", "congrArg", "dsimp", "simp", "simp", "simp"], "tactic_count": 6}
{"name": "CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitor_inv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution", "is_tactic_proof": false, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitor_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution", "is_tactic_proof": true, "tactics": ["apply", "apply", "ext", "simp"], "tactic_count": 4}
{"name": "CategoryTheory.MonoidalCategory.DayConvolution.triangle", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution", "is_tactic_proof": true, "tactics": ["apply", "apply", "have", "extensionUnitLeft", "isPointwiseLeftKanExtensionExtensionUnitLeft", "apply", "extensionUnitLeft", "ext", "dsimp", "simp", "externalProductBifunctor_obj_obj,", "id_tensorHom,", "simp", "simp"], "tactic_count": 14}
{"name": "CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.convolution", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.convolution₂", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.convolution₂'", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.ι_map_tensorHom_hom_eq_tensorHom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution", "is_tactic_proof": true, "tactics": ["apply", "dsimp", "ext", "simp", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.ι_map_associator_hom_eq_associator_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution", "is_tactic_proof": true, "tactics": ["apply", "dsimp", "ext", "simp", "whiskerLeft_id,", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.convolutionUnit", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.ι_map_leftUnitor_hom_eq_leftUnitor_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution", "is_tactic_proof": true, "tactics": ["apply", "dsimp", "ext", "dsimp", "simp", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.ι_map_rightUnitor_hom_eq_rightUnitor_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution", "is_tactic_proof": true, "tactics": ["apply", "dsimp", "ext", "dsimp", "simp", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.MonoidalCategory.monoidalOfLawfulDayConvolutionMonoidalCategoryStruct", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.InducedLawfulDayConvolutionMonoidalCategoryStructCore.convolutions", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.InducedLawfulDayConvolutionMonoidalCategoryStructCore.mkMonoidalCategoryStruct", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.InducedLawfulDayConvolutionMonoidalCategoryStructCore.id_tensorHom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.InducedLawfulDayConvolutionMonoidalCategoryStructCore.tensorHom_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.InducedLawfulDayConvolutionMonoidalCategoryStructCore.ι_map_tensorHom_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "apply", "dsimp", "ext", "dsimp", "simp", "simp"], "tactic_count": 8}
{"name": "CategoryTheory.MonoidalCategory.InducedLawfulDayConvolutionMonoidalCategoryStructCore.mkLawfulDayConvolutionMonoidalCategoryStruct", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.InducedLawfulDayConvolutionMonoidalCategoryStructCore.ofHasDayConvolutions", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.monoidalOfHasDayConvolutions", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.lawfulDayConvolutionMonoidalCategoryStructOfHasDayConvolutions", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.DayConvolution.braidingHomCorepresenting", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution.Braided", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.DayConvolution.braidingInvCorepresenting", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution.Braided", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.DayConvolution.braiding", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution.Braided", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.DayConvolution.unit_app_braiding_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution.Braided", "is_tactic_proof": true, "tactics": ["change", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.MonoidalCategory.DayConvolution.unit_app_braiding_inv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution.Braided", "is_tactic_proof": true, "tactics": ["change", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.MonoidalCategory.DayConvolution.braiding_naturality_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution.Braided", "is_tactic_proof": true, "tactics": ["apply", "ext", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.MonoidalCategory.DayConvolution.braiding_naturality_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution.Braided", "is_tactic_proof": true, "tactics": ["apply", "ext", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.MonoidalCategory.DayConvolution.hexagon_forward", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution.Braided", "is_tactic_proof": true, "tactics": ["apply", "apply", "ext", "dsimp", "simp", "tensor_obj,", "tensorHom_id]", "simp", "simp", "whiskerRight_comp_unit_app_assoc,", "externalProductBifunctor_obj_obj,", "rw", "haveI", "dsimp", "simp", "rw", "simp"], "tactic_count": 17}
{"name": "CategoryTheory.MonoidalCategory.DayConvolution.hexagon_reverse", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution.Braided", "is_tactic_proof": true, "tactics": ["apply", "apply", "ext", "dsimp", "simp", "externalProductBifunctor_obj_obj,", "unit_app_braiding_hom_app_assoc,", "unit_app_map_app_assoc,", "simp", "simp", "whiskerLeft_comp_unit_app_assoc,", "externalProductBifunctor_obj_obj,", "congr", "rw", "haveI", "dsimp", "simp", "rw", "simp"], "tactic_count": 19}
{"name": "CategoryTheory.MonoidalCategory.DayConvolution.symmetry", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution.Braided", "is_tactic_proof": true, "tactics": ["apply", "ext", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.MonoidalCategory.dayConvolutionInternalHomDiagramFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution.Closed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.map", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution.Closed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.map_app_comp_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution.Closed", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.ev_app", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution.Closed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.unit_app_ev_app_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution.Closed", "is_tactic_proof": true, "tactics": ["have", "dsimp", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.ev_naturality_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution.Closed", "is_tactic_proof": true, "tactics": ["apply", "dsimp", "ext", "simp"], "tactic_count": 4}
{"name": "CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.coev_app", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution.Closed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.coev_app_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution.Closed", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.coev_naturality_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution.Closed", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "apply", "intro", "apply", "dsimp", "simp", "simp"], "tactic_count": 8}
{"name": "CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.left_triangle_components", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution.Closed", "is_tactic_proof": true, "tactics": ["apply", "dsimp", "ext", "apply", "simp"], "tactic_count": 5}
{"name": "CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.right_triangle_components", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution.Closed", "is_tactic_proof": true, "tactics": ["ext", "apply", "intro", "apply", "simp"], "tactic_count": 5}
{"name": "CategoryTheory.MonoidalCategory.DayFunctor.term_⊛⥤_", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution.DayFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.DayFunctor._aux_Mathlib_CategoryTheory_Monoidal_DayConvolution_DayFunctor___macroRules_CategoryTheory_MonoidalCategory_DayFunctor_term_⊛⥤__1", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution.DayFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.DayFunctor._aux_Mathlib_CategoryTheory_Monoidal_DayConvolution_DayFunctor___unexpand_CategoryTheory_MonoidalCategory_DayFunctor_1", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution.DayFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.DayFunctor.mk_functor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution.DayFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.DayFunctor.functor_mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution.DayFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.DayFunctor.instCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution.DayFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.DayFunctor.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution.DayFunctor", "is_tactic_proof": true, "tactics": ["cases", "cases", "grind"], "tactic_count": 3}
{"name": "CategoryTheory.MonoidalCategory.DayFunctor.equiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution.DayFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.DayFunctor.inst", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution.DayFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.DayFunctor.instLawfulDayConvolutionMonoidalCategoryStruct", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution.DayFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.DayFunctor.η", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution.DayFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.DayFunctor.instIsLeftKanExtensionProdFunctorTensorObjη", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution.DayFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.DayFunctor.tensor_hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution.DayFunctor", "is_tactic_proof": true, "tactics": ["ext", "apply", "ext", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.MonoidalCategory.DayFunctor.tensorDesc", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution.DayFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.DayFunctor.η_comp_tensorDec", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution.DayFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.DayFunctor.η_comp_tensorDesc_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution.DayFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.DayFunctor.isoPointwiseLeftKanExtension", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution.DayFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.DayFunctor.η_comp_isoPointwiseLeftKanExtension_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution.DayFunctor", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.DayFunctor.ι_comp_isoPointwiseLeftKanExtension_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution.DayFunctor", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalCategory.DayFunctor.ν", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution.DayFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.DayFunctor.νNatTrans", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution.DayFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.DayFunctor.instIsLeftKanExtensionDiscretePUnitFunctorTensorUnitνNatTrans", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution.DayFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.DayFunctor.unit_hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution.DayFunctor", "is_tactic_proof": true, "tactics": ["ext1", "apply", "ext", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.MonoidalCategory.DayFunctor.unitDesc", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution.DayFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.DayFunctor.ν_comp_unitDesc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.DayConvolution.DayFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Discrete.monoidal", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Discrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Discrete.monoidal_tensorUnit_as", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Discrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Discrete.monoidalFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Discrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Discrete.monoidalFunctor_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Discrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Discrete.monoidalFunctorMonoidal", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Discrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Discrete.monoidalFunctor_ε", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Discrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Discrete.monoidalFunctor_η", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Discrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Discrete.monoidalFunctor_μ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Discrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Discrete.monoidalFunctor_δ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Discrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Discrete.monoidalFunctorComp", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Discrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Discrete.monoidalFunctorComp_isMonoidal", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Discrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.endofunctorMonoidalCategory", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.endofunctorMonoidalCategory_tensorUnit_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.endofunctorMonoidalCategory_tensorUnit_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.endofunctorMonoidalCategory_tensorObj_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.endofunctorMonoidalCategory_tensorObj_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.endofunctorMonoidalCategory_tensorMap_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.endofunctorMonoidalCategory_whiskerLeft_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.endofunctorMonoidalCategory_whiskerRight_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.End", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.FreeMonoidalCategory.normalize'", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Free.Coherence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FreeMonoidalCategory.fullNormalize", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Free.Coherence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FreeMonoidalCategory.tensorFunc", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Free.Coherence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FreeMonoidalCategory.tensorFunc_map_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Free.Coherence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FreeMonoidalCategory.tensorFunc_obj_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Free.Coherence", "is_tactic_proof": true, "tactics": ["cases", "cases", "rcases", "dsimp", "subst", "simp"], "tactic_count": 6}
{"name": "CategoryTheory.FreeMonoidalCategory.normalizeIsoApp", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Free.Coherence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FreeMonoidalCategory.normalizeIsoApp'", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Free.Coherence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FreeMonoidalCategory.normalizeIsoApp_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Free.Coherence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FreeMonoidalCategory.normalizeIsoApp_tensor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Free.Coherence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FreeMonoidalCategory.normalizeIsoApp_unitor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Free.Coherence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FreeMonoidalCategory.normalizeIsoAux", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Free.Coherence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FreeMonoidalCategory.normalizeObj_congr", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Free.Coherence", "is_tactic_proof": true, "tactics": ["rcases", "apply", "clear", "induction", "comp", "whiskerLeft", "whiskerRight", "funext", "simp"], "tactic_count": 9}
{"name": "CategoryTheory.FreeMonoidalCategory.normalize_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Free.Coherence", "is_tactic_proof": true, "tactics": ["revert", "induction", "simp", "intro", "dsimp", "whiskerRightIso_hom,", "rw", "simp", "intro", "dsimp", "whiskerRightIso_hom,", "rw", "have", "simp", "all_goals"], "tactic_count": 15}
{"name": "CategoryTheory.FreeMonoidalCategory.normalizeIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Free.Coherence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FreeMonoidalCategory.fullNormalizeIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Free.Coherence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FreeMonoidalCategory.subsingleton_hom", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Free.Coherence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FreeMonoidalCategory.inverseAux", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Free.Coherence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FreeMonoidalCategory.instGroupoid", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Free.Coherence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.LaxMonoidal.μ_natural", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.LaxMonoidal.left_unitality_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.LaxMonoidal.right_unitality_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.LaxMonoidal.associativity_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.LaxMonoidal.ε_tensorHom_comp_μ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.LaxMonoidal.tensorHom_ε_comp_μ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.LaxMonoidal.tensorUnit_whiskerLeft_comp_leftUnitor_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.LaxMonoidal.whiskerRight_tensorUnit_comp_rightUnitor_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.LaxMonoidal.μ_whiskerRight_comp_μ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.LaxMonoidal.whiskerLeft_μ_comp_μ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.LaxMonoidal.ofTensorHom", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.LaxMonoidal.id", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.LaxMonoidal.comp", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.OplaxMonoidal.δ_natural", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.OplaxMonoidal.left_unitality_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": true, "tactics": ["rw", "id_comp]"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.OplaxMonoidal.right_unitality_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": true, "tactics": ["rw", "id_comp]"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.OplaxMonoidal.associativity_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.OplaxMonoidal.δ_comp_η_tensorHom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.OplaxMonoidal.δ_comp_tensorHom_η", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.OplaxMonoidal.δ_comp_δ_whiskerRight", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.OplaxMonoidal.δ_comp_whiskerLeft_δ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.OplaxMonoidal.id", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.OplaxMonoidal.comp", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.Monoidal.εIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.Monoidal.μIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.Monoidal.instIsIsoε", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.Monoidal.instIsIsoη", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.Monoidal.instIsIsoμ", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.Monoidal.instIsIsoδ", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.Monoidal.map_ε_η", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.Monoidal.map_η_ε", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.Monoidal.map_μ_δ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.Monoidal.map_δ_μ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.Monoidal.whiskerRight_ε_η", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.Monoidal.whiskerRight_η_ε", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.Monoidal.whiskerRight_μ_δ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.Monoidal.whiskerRight_δ_μ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.Monoidal.whiskerLeft_ε_η", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.Monoidal.whiskerLeft_η_ε", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.Monoidal.whiskerLeft_μ_δ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.Monoidal.whiskerLeft_δ_μ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.Monoidal.map_tensor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.Monoidal.map_whiskerLeft", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.Monoidal.map_whiskerRight", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.Monoidal.map_associator", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.Monoidal.map_associator_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.Monoidal.map_associator'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.Monoidal.map_associator_inv'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.Monoidal.map_leftUnitor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.Monoidal.map_leftUnitor_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.Monoidal.map_rightUnitor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.Monoidal.map_rightUnitor_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.Monoidal.inv_η", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.Monoidal.inv_ε", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.Monoidal.inv_μ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.Monoidal.inv_δ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.Monoidal.μNatIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.Monoidal.commTensorLeft", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.Monoidal.commTensorRight", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.Monoidal.instId", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.Monoidal.instComp", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.Monoidal.toLaxMonoidal_injective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": true, "tactics": ["intro", "ext1", "exact", "exact", "rw", "rw", "exact", "ext", "rw", "rw", "exact"], "tactic_count": 11}
{"name": "CategoryTheory.Functor.Monoidal.toOplaxMonoidal_injective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": true, "tactics": ["intro", "ext1", "rw", "rw", "exact", "ext", "rw", "rw", "exact", "exact", "exact"], "tactic_count": 11}
{"name": "CategoryTheory.Functor.CoreMonoidal.toLaxMonoidal", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.CoreMonoidal.toOplaxMonoidal", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.CoreMonoidal.toMonoidal", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.CoreMonoidal.ofLaxMonoidal", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.CoreMonoidal.ofOplaxMonoidal", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.Monoidal.ofLaxMonoidal", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.Monoidal.ofOplaxMonoidal", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instLaxMonoidalProdProd", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.prod_ε_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.prod_ε_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.prod_μ_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.prod_μ_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instOplaxMonoidalProdProd", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.prod_η_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.prod_η_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.prod_δ_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.prod_δ_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instMonoidalProdProd", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instMonoidalProdDiag", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.diag_ε", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.diag_η", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.diag_μ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.diag_δ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.LaxMonoidal.prod'", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.prod'_ε_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": true, "tactics": ["change", "rw", "rfl"], "tactic_count": 3}
{"name": "CategoryTheory.Functor.prod'_ε_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": true, "tactics": ["change", "rw", "rfl"], "tactic_count": 3}
{"name": "CategoryTheory.Functor.prod'_μ_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": true, "tactics": ["change", "rw", "rfl"], "tactic_count": 3}
{"name": "CategoryTheory.Functor.prod'_μ_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": true, "tactics": ["change", "rw", "rfl"], "tactic_count": 3}
{"name": "CategoryTheory.Functor.OplaxMonoidal.prod'", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Adjunction.rightAdjointLaxMonoidal", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.instIsMonoidal", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": true, "tactics": ["letI", "constructor", "rfl", "intro", "rfl"], "tactic_count": 5}
{"name": "CategoryTheory.Adjunction.unit_app_unit_comp_map_η", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.unit_app_tensor_comp_map_δ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Adjunction.map_ε_comp_counit_app_unit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Adjunction.map_μ_comp_counit_app_tensor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "CategoryTheory.Adjunction.ε_comp_map_ε", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Adjunction.map_η_comp_η", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "CategoryTheory.Equivalence.unitIso_hom_app_comp_inverse_map_η_functor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Functor.Monoidal.coreMonoidalTransport", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Monoidal.tensorUnit_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.FunctorCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Monoidal.tensorUnit_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.FunctorCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Functor.LaxMonoidal.whiskeringRight", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.FunctorCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.instMonoidalFunctorObjWhiskeringRight", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.FunctorCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.instMonoidalFunctorInverseCongrLeft", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.FunctorCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instIsMonoidalFunctorCongrLeft", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.FunctorCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instLaxMonoidalOfTypeFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Functor.Types", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonObj.termι", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonObj._aux_Mathlib_CategoryTheory_Monoidal_Grp____macroRules_CategoryTheory_MonObj_termι_1", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.GrpObj.instTensorUnit", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grp.toMon", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grp.trivial", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grp.instInhabited", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Grp.id_hom_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.GrpObj.lift_comp_inv_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "CategoryTheory.GrpObj.lift_inv_comp_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
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{"name": "CategoryTheory.GrpObj.eq_lift_inv_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": true, "tactics": ["refine"], "tactic_count": 1}
{"name": "CategoryTheory.GrpObj.lift_inv_right_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "CategoryTheory.GrpObj.inv_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.GrpObj.mul_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": true, "tactics": ["apply", "nth_rw", "rw", "nth_rw", "rw", "comp_toUnit_assoc]"], "tactic_count": 6}
{"name": "CategoryTheory.GrpObj.tensorHom_inv_inv_mul", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.GrpObj.mul_inv_rev", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.GrpObj.mulRight", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrpObj.mulRight_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.GrpObj.isPullback", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrpObj.inv_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": true, "tactics": ["suffices", "apply", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.GrpObj.toMonObj_injective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": true, "tactics": ["intro", "suffices", "apply", "rw", "convert", "exacts"], "tactic_count": 6}
{"name": "CategoryTheory.GrpObj.ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrpObj.tensorObj.instTensorObj", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grp.forget₂Mon", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grp.fullyFaithfulForget₂Mon", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grp.instFullMonForget₂Mon", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grp.instFaithfulMonForget₂Mon", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grp.forget₂Mon_obj_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grp.forget₂Mon_obj_mul", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grp.forget₂Mon_map_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grp.forget", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grp.instFaithfulForget", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grp.forget₂Mon_comp_forget", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grp.instIsIsoHomHomMon", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grp.mkIso'", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grp.uniqueHomFromTrivial", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grp.instHasInitial", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grp.instMonoidalCategoryStruct", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grp.tensorUnit_X", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grp.tensorUnit_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grp.tensorUnit_mul", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grp.tensorObj_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grp.tensorObj_mul", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grp.whiskerLeft_hom_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grp.whiskerRight_hom_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grp.leftUnitor_hom_hom_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grp.leftUnitor_inv_hom_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grp.rightUnitor_hom_hom_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grp.rightUnitor_inv_hom_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grp.associator_hom_hom_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grp.associator_inv_hom_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grp.instMonoidalCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grp.instCartesianMonoidalCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grp.lift_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grp.fst_hom_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grp.snd_hom_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grp.instMonoidalMonForget₂Mon", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grp.instBraidedCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grp.braiding_hom_hom_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Grp.braiding_inv_hom_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.grpObjObj", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.obj.ι_def", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapGrp", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.Faithful.mapGrp", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.FullyFaithful.mapGrp", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.Full.mapGrp", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapGrp_id_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapGrp_id_mul", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.comp_mapGrp_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.comp_mapGrp_mul", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapGrpIdIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapGrpCompIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapGrpNatTrans", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapGrpNatIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapGrpFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.FullyFaithful.grpObj", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.essImage_mapGrp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapGrp.instMonoidal", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapGrp.instBraided", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.mapGrp", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.mapGrp", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Grp.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HopfObj.term𝒮", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Hopf.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HopfObj._aux_Mathlib_CategoryTheory_Monoidal_Hopf____macroRules_CategoryTheory_HopfObj_term𝒮_1", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Hopf.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HopfObj._aux_Mathlib_CategoryTheory_Monoidal_Hopf____unexpand_CategoryTheory_HopfObj_antipode_1", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Hopf.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HopfObj.term𝒮[_]", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Hopf.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HopfObj._aux_Mathlib_CategoryTheory_Monoidal_Hopf____macroRules_CategoryTheory_HopfObj_term𝒮[_]_1", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Hopf.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HopfObj._aux_Mathlib_CategoryTheory_Monoidal_Hopf____unexpand_CategoryTheory_HopfObj_antipode_2", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Hopf.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Hopf.toBimon", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Hopf.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Hopf.instCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Hopf.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HopfObj.hom_antipode", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Hopf.", "is_tactic_proof": true, "tactics": ["apply", "rw", "simp", "slice_lhs", "slice_lhs", "slice_lhs", "slice_lhs", "slice_lhs", "rw", "simp", "slice_lhs", "slice_lhs", "slice_lhs", "slice_lhs", "slice_lhs"], "tactic_count": 15}
{"name": "CategoryTheory.HopfObj.one_antipode", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Hopf.", "is_tactic_proof": true, "tactics": ["have", "conv", "rhs", "rw", "rw", "whisker_exchange_assoc,", "simpa"], "tactic_count": 7}
{"name": "CategoryTheory.HopfObj.antipode_counit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Hopf.", "is_tactic_proof": true, "tactics": ["have", "conv", "rhs", "rw", "rw", "simpa"], "tactic_count": 6}
{"name": "CategoryTheory.HopfObj.antipode_comul₁", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Hopf.", "is_tactic_proof": true, "tactics": ["slice_lhs", "slice_lhs", "slice_lhs", "simp"], "tactic_count": 4}
{"name": "CategoryTheory.HopfObj.antipode_comul₂", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Hopf.", "is_tactic_proof": true, "tactics": ["slice_lhs", "slice_lhs", "slice_lhs", "rw", "whiskerLeft_comp]", "slice_lhs", "slice_lhs", "rw", "whiskerLeft_comp]", "slice_lhs", "slice_lhs", "slice_lhs", "simp", "rw", "simp", "rw", "slice_lhs", "simp", "rw", "simp", "slice_lhs", "simp", "rw", "simp", "rw", "simp", "simp", "slice_lhs", "simp", "rw", "simp", "slice_lhs", "simp", "rw", "simp", "slice_lhs", "simp", "rw", "simp", "slice_lhs", "simp", "whiskerLeft_rightUnitor,", "antipode_right_assoc]", "rw", "monoidal"], "tactic_count": 45}
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{"name": "CategoryTheory.HopfObj.mul_antipode₁", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Hopf.", "is_tactic_proof": true, "tactics": ["slice_lhs", "slice_lhs", "slice_lhs", "slice_lhs", "simp"], "tactic_count": 5}
{"name": "CategoryTheory.HopfObj.mul_antipode₂", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Hopf.", "is_tactic_proof": true, "tactics": ["slice_lhs", "slice_lhs", "slice_lhs", "slice_lhs", "slice_lhs", "slice_lhs", "simp", "rw", "simp", "rw", "rw", "rw", "slice_lhs", "rw", "slice_lhs", "simp", "rw", "simp", "simp", "slice_lhs", "simp", "rw", "simp", "rw", "simp", "slice_lhs", "simp", "rw", "simp", "slice_lhs", "simp", "rw", "simp", "slice_lhs", "simp", "rw", "simp", "rw", "simp", "simp", "slice_lhs", "simp", "rw", "simp", "slice_lhs", "simp", "rw", "simp", "slice_lhs", "simp", "rw", "simp", "rw", "simp", "slice_lhs", "simp", "rw", "simp", "simp", "slice_lhs", "rw", "slice_lhs", "slice_lhs", "simp", "rw", "simp", "slice_lhs", "slice_lhs", "dsimp", "rw", "slice_lhs", "monoidal"], "tactic_count": 72}
{"name": "CategoryTheory.HopfObj.mul_antipode", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Hopf.", "is_tactic_proof": true, "tactics": ["apply", "rw", "simp", "simp", "simp", "exact", "rw", "simp", "simp", "simp", "exact"], "tactic_count": 11}
{"name": "CategoryTheory.HopfObj.antipode_antipode", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Hopf.", "is_tactic_proof": true, "tactics": ["apply", "rw", "simp", "rw", "simp", "rw", "simp"], "tactic_count": 7}
{"name": "CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.functorObjObj", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Internal.FunctorCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.functorObj", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Internal.FunctorCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.functor", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Internal.FunctorCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.inverseObj", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Internal.FunctorCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.inverse", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Internal.FunctorCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.unitIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Internal.FunctorCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.counitIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Internal.FunctorCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Monoidal.monFunctorCategoryEquivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Internal.FunctorCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Monoidal.ComonFunctorCategoryEquivalence.functorObjObj", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Internal.FunctorCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Monoidal.ComonFunctorCategoryEquivalence.functorObj", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Internal.FunctorCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Monoidal.ComonFunctorCategoryEquivalence.functor", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Internal.FunctorCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Monoidal.ComonFunctorCategoryEquivalence.inverseObj", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Internal.FunctorCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.CategoryTheory.Monoidal.Internal.FunctorCategory.0.CategoryTheory.Monoidal.ComonFunctorCategoryEquivalence.inverse", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Internal.FunctorCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.CategoryTheory.Monoidal.Internal.FunctorCategory.0.CategoryTheory.Monoidal.ComonFunctorCategoryEquivalence.unitIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Internal.FunctorCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Monoidal.ComonFunctorCategoryEquivalence.counitIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Internal.FunctorCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.functor", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Internal.FunctorCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Mon.limitCone", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Internal.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Mon.forget_preservesLimitsOfShape", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Internal.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.MonModuleEquivalenceAlgebra.algebraMap", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Internal.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CommMonTypeEquivalenceCommMon.commMonCommMonoid", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Internal.Types.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommMonTypeEquivalenceCommMon.functor", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Internal.Types.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "commMonTypeEquivalenceCommMon", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Internal.Types.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "commMonTypeEquivalenceCommMonForget", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Internal.Types.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.MonoidalLinear.ofFaithful", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.instIsMonHomInvOfHom", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instIsMonHomHomAsIso", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Mon.trivial", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Mon.instInhabited", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonObj.one_mul_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Mon.", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.MonObj.mul_one_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Mon.", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.MonObj.mul_assoc_flip", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Mon.", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MonObj.one_associator", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Mon.", "is_tactic_proof": true, "tactics": ["simp", "slice_lhs", "slice_lhs", "slice_rhs", "slice_lhs", "rw", "slice_lhs", "simp"], "tactic_count": 8}
{"name": "CategoryTheory.MonObj.one_leftUnitor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Mon.", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MonObj.one_rightUnitor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Mon.", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MonObj.Mon_tensor_one_mul", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Mon.", "is_tactic_proof": true, "tactics": ["simp", "slice_lhs", "slice_lhs", "symm", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.MonObj.Mon_tensor_mul_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Mon.", "is_tactic_proof": true, "tactics": ["simp", "slice_lhs", "slice_lhs", "symm", "exact"], "tactic_count": 5}
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{"name": "CategoryTheory.MonObj.mul_rightUnitor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Mon.", "is_tactic_proof": true, "tactics": ["rw", "simp", "slice_lhs", "slice_lhs", "simp"], "tactic_count": 5}
{"name": "CategoryTheory.MonObj.tensorObj.instTensorObj", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonObj.instIsMonHomTensorHom", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonObj.instIsMonHomId", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonObj.instIsMonHomWhiskerLeft", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonObj.instIsMonHomWhiskerRight", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonObj.instIsMonHomHomAssociator", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonObj.instIsMonHomHomLeftUnitor", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonObj.instIsMonHomHomRightUnitor", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonObj.one_braiding", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Mon.", "is_tactic_proof": false, "tactics": ["simp", "monoidal"], "tactic_count": 2}
{"name": "CategoryTheory.Mon.id", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Mon.homInhabited", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Mon.instCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Mon.instIsMonHomHom", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Mon.Hom.ext'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Mon.hom_injective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Mon.id_hom'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Mon.forget_faithful", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Mon.instIsIsoHomOfMapForget", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Mon.instReflectsIsomorphismsForget", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Mon.mkIso'", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Mon.uniqueHomFromTrivial", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Mon.instHasInitial", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Mon.monMonoidalStruct", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Mon.tensorUnit_X", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Mon.tensorUnit_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Mon.tensorUnit_mul", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Mon.tensorObj_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Mon.tensorObj_mul", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Mon.whiskerLeft_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Mon.whiskerRight_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Mon.leftUnitor_hom_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Mon.leftUnitor_inv_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Mon.rightUnitor_hom_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Mon.associator_hom_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Mon.associator_inv_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Mon.tensor_mul", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Mon.instMonoidalForget", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Functor.obj.η_def", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.obj.μ_def", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.monToLaxMonoidalObj", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.instLaxMonoidalDiscretePUnitMonToLaxMonoidalObj", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.monToLaxMonoidalObj_ε", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.unitIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.counitIsoAux", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.monToLaxMonoidal_laxMonoidalToMon_obj_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.NatTrans.IsMonoidal.hcomp", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.NaturalTransformation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.IsMonoidal.whiskerRight", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.NaturalTransformation", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
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{"name": "CategoryTheory.NatTrans.IsMonoidal.instHomFunctorRightUnitor", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.NaturalTransformation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.IsMonoidal.instHomFunctorAssociator", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.NaturalTransformation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.instIsMonoidalProdProd'", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.NaturalTransformation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Adjunction.IsMonoidal.instIsMonoidalUnit", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.NaturalTransformation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.IsMonoidal.instIsMonoidalCounit", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.NaturalTransformation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.Equivalence.instIsMonoidalUnit", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.NaturalTransformation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.Equivalence.instIsMonoidalCounit", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.NaturalTransformation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.LaxMonoidalFunctor.id_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.NaturalTransformation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.MonoidalOpposite.mop_unmop", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalOpposite.unmop_mop", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalOpposite.monoidalOppositeCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.Hom.mop", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.Hom.unmop", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.Hom.mop_inj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.Hom.unmop_inj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.Hom.unmop_mop", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.Hom.mop_unmop", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.mop_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.mop_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.unmop_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.unmop_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.unmop_id_mop", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.mop_id_unmop", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalOpposite.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.mopFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.unmopFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.mop", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.unmop", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsIso.instMonoidalOppositeMop", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsIso.instUnmopOfMonoidalOpposite", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.monoidalCategoryOp", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.op_tensorObj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.unop_tensorObj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.op_tensorUnit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.unop_tensorUnit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.op_tensorHom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.unop_tensorHom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.op_whiskerLeft", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.unop_whiskerLeft", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.op_whiskerRight", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.unop_whiskerRight", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.op_associator", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.unop_associator", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.op_hom_associator", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.unop_hom_associator", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.op_inv_associator", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.unop_inv_associator", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.op_leftUnitor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.unop_leftUnitor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.op_hom_leftUnitor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.unop_hom_leftUnitor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.op_inv_leftUnitor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.unop_inv_leftUnitor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.op_rightUnitor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.unop_rightUnitor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.op_hom_rightUnitor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.unop_hom_rightUnitor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.op_inv_rightUnitor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.unop_inv_rightUnitor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.op_tensor_op", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.unop_tensor_unop", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.monoidalCategoryMop", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.mop_tensorObj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.unmop_tensorObj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.mop_tensorUnit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.unmop_tensorUnit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.mop_tensorHom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.unmop_tensorHom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.mop_whiskerLeft", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.unmop_whiskerLeft", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.mop_whiskerRight", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.unmop_whiskerRight", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.unmop_associator", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.mop_hom_associator", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.unmop_hom_associator", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.mop_inv_associator", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.unmop_inv_associator", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.mop_leftUnitor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.unmop_leftUnitor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.mop_hom_leftUnitor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.unmop_hom_leftUnitor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.unmop_inv_leftUnitor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.unmop_rightUnitor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.mop_hom_rightUnitor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.unmop_hom_rightUnitor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.unmop_inv_rightUnitor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalOpposite.mopEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalOpposite.unmopEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalOpposite.mopMopEquivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalOpposite.mopMopEquivalenceFunctorMonoidal", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalOpposite.mopMopEquivalenceInverseMonoidal", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instIsMonoidalMonoidalOppositeMopMopEquivalence", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.MonoidalOpposite.tensorLeftIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalOpposite.tensorLeftMopIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalOpposite.tensorLeftUnmopIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalOpposite.tensorRightIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalOpposite.tensorRightMopIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalOpposite.tensorRightUnmopIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.monoidalOpOp", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.monoidalUnopUnop", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instMonoidalOppositeFunctorOpOpEquivalence", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instMonoidalOppositeInverseOpOpEquivalence", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instIsMonoidalOppositeOpOpEquivalence", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonObj.mopMonObj", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Opposite.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonObj.mop_isMonHom", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Opposite.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonObj.unmopMonObj", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Opposite.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonObj.unmop_isMonHom", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Opposite.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MonObj.mopEquivCompForgetIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Opposite.Mon.", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalPreadditive.tensor_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Preadditive", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalPreadditive.zero_tensor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Preadditive", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalPreadditive.tensor_add", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Preadditive", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MonoidalPreadditive.add_tensor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Preadditive", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "CategoryTheory.tensorRight_additive", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.monoidalPreadditive_of_faithful", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.whiskerLeft_sum", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.sum_whiskerRight", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.tensor_sum", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Preadditive", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "CategoryTheory.instPreservesFiniteBiproductsTensorLeft", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instPreservesFiniteBiproductsTensorRight", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.BraidedCategory.rigidCategoryOfLeftRigidCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Rigid.Braided", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.leftDualFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Rigid.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.rightDualFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Rigid.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Monoidal.functorHasRightDual", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Rigid.FunctorCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Monoidal.rightRigidFunctorCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Rigid.FunctorCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Monoidal.functorHasLeftDual", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Rigid.FunctorCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Monoidal.leftRigidFunctorCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Rigid.FunctorCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Monoidal.rigidFunctorCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Rigid.FunctorCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ExactPairing.ofFaithful", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Rigid.OfEquivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ExactPairing.ofFullyFaithful", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Rigid.OfEquivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.hasLeftDualOfEquivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Rigid.OfEquivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.hasRightDualOfEquivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Rigid.OfEquivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.leftRigidCategoryOfEquivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Rigid.OfEquivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.rightRigidCategoryOfEquivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Rigid.OfEquivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.rigidCategoryOfEquivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Rigid.OfEquivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.monoidOfSkeletalMonoidal", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Monoidal.Skeleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.commMonoidOfSkeletalBraided", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Monoidal.Skeleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Skeleton.instMonoidalCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Skeleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Skeleton.instMonoid", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Skeleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Skeleton.mul_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Skeleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Skeleton.one_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Skeleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Skeleton.toSkeleton_tensorObj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Skeleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Skeleton.instBraidedCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Skeleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Skeleton.instCommMonoid", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Skeleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instMonoidalSkeletonFunctorSkeletonEquivalence", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Skeleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instMonoidalSkeletonInverseSkeletonEquivalence", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Skeleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instLaxMonoidalSkeletonMapSkeleton", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Skeleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instOplaxMonoidalSkeletonMapSkeleton", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Skeleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instMonoidalSkeletonMapSkeleton", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Skeleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Skeletal.monoidHom", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Skeleton", "is_tactic_proof": true, "tactics": ["intros", "exact", "map_one", "map_mul"], "tactic_count": 4}
{"name": "CategoryTheory.Skeleton.monoidHom", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Skeleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Skeletal.mulEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Skeleton", "is_tactic_proof": true, "tactics": ["intros", "exact", "invFun", "left_inv", "right_inv", "map_mul"], "tactic_count": 6}
{"name": "CategoryTheory.Skeleton.mulEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Skeleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.prop_tensor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Subcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.prop_unit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Subcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.prop_ihom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Subcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instMonoidalCategoryStructFullSubcategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Subcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.fullMonoidalSubcategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Subcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.monoidalι", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Subcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.ι_ε", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Subcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.ι_η", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Subcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.ι_μ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Subcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.ι_δ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Subcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instMonoidalPreadditiveFullSubcategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Subcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instMonoidalLinearFullSubcategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Subcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instMonoidalFullSubcategoryιOfLE", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Subcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.ιOfLE_ε", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Subcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.ιOfLE_η", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Subcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.ιOfLE_μ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Subcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.ιOfLE_δ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Subcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.fullBraidedSubcategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Subcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instBraidedFullSubcategoryι", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Subcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instBraidedFullSubcategoryιOfLE", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Subcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.fullSymmetricSubcategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Subcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.fullMonoidalClosedSubcategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Subcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.ihom_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Subcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.ihom_map_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Subcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Tor", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Tor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Tor'", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Tor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isZero_Tor_succ_of_projective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Tor", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.isZero_Tor'_succ_of_projective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Tor", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Monoidal.induced", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Transport", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Monoidal.fromInducedCoreMonoidal", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Transport", "is_tactic_proof": true, "tactics": ["letI", "exact", "μIso", "μIso_hom_natural_left", "μIso_hom_natural_right", "associativity", "left_unitality", "right_unitality"], "tactic_count": 8}
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{"name": "CategoryTheory.Monoidal.transportStruct", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Transport", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Monoidal.transport", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Transport", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Monoidal.Transported", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Transport", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Monoidal.instCategoryTransported", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Transport", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Monoidal.Transported.instMonoidalCategoryStruct", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Transport", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Monoidal.Transported.instMonoidalCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Transport", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Monoidal.instMonoidalTransportedInverseEquivalenceTransported", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Transport", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Monoidal.instMonoidalTransportedFunctorSymmEquivalenceTransported", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Transport", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Monoidal.instMonoidalTransportedFunctorEquivalenceTransported", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Transport", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Monoidal.instMonoidalTransportedInverseSymmEquivalenceTransported", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Transport", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Monoidal.instIsMonoidalUnitTransportedEquivalenceTransported", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Transport", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Monoidal.instIsMonoidalTransportedCounitEquivalenceTransported", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Transport", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.typesCartesianMonoidalCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Types.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instBraidedCategoryType", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Types.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.types_tensorObj_def", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Types.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.types_tensorUnit_def", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Types.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.tensor_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Types.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.whiskerLeft_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Types.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.whiskerRight_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Types.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.leftUnitor_hom_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Types.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.leftUnitor_inv_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Types.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.rightUnitor_hom_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Types.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.rightUnitor_inv_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Types.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.associator_hom_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Types.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.associator_inv_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Types.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.associator_hom_apply_2_2", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Types.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.associator_inv_apply_1_1", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Types.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.associator_inv_apply_2", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Types.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.braiding_hom_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Types.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.braiding_inv_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Types.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CartesianMonoidalCategory.lift_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Monoidal.Types.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalFunctor.mapPi", "kind": "definition", "module": "Mathlib.CategoryTheory.Monoidal.Types.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instLaxMonoidalObjOppositeFunctorTypeCoyonedaOpTensorUnit", "kind": "instance", "module": "Mathlib.CategoryTheory.Monoidal.Types.Coyoneda", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instCompleteBooleanAlgebra", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.le_def", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instInhabited", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.top_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": true, "tactics": ["funext", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.MorphismProperty.top_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MorphismProperty.of_eq_top", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MorphismProperty.sSup_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "constructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.MorphismProperty.iSup_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": true, "tactics": ["apply", "constructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.MorphismProperty.op", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.unop", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.unop_op", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.op_unop", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.inverseImage", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.inverseImage_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "CategoryTheory.MorphismProperty.op_inverseImage", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.strictMap", "kind": "inductive", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.map_mem_strictMap", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.map", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.map_mem_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.monotone_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": true, "tactics": ["intro", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.MorphismProperty.map_top_eq_top_of_essSurj_of_full", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": true, "tactics": ["rw", "intro", "refine", "exact", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.MorphismProperty.toSet", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.mem_toSet_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.toSet_iSup", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.MorphismProperty.toSet_max", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.homFamily", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.homFamily_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.homFamily_arrow_mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.arrow_mk_mem_toSet_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.of_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": true, "tactics": ["rw", "rwa"], "tactic_count": 2}
{"name": "CategoryTheory.MorphismProperty.ofHoms", "kind": "inductive", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.ofHoms_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "exact", "rintro", "rw", "constructor"], "tactic_count": 6}
{"name": "CategoryTheory.MorphismProperty.ofHoms_homFamily", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": true, "tactics": ["ext", "constructor", "intro", "rw", "obtain", "exact", "intro", "exact"], "tactic_count": 8}
{"name": "CategoryTheory.MorphismProperty.instRespectsOfRespectsLeftOfRespectsRight", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instRespectsRightOppositeOpOfRespectsLeft", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instRespectsLeftOppositeOpOfRespectsRight", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.RespectsLeft.inf", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.RespectsRight.inf", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.isomorphisms", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.monomorphisms", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.epimorphisms", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.op_isomorphisms", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": true, "tactics": ["ext", "apply"], "tactic_count": 2}
{"name": "CategoryTheory.MorphismProperty.RespectsIso", "kind": "abbrev", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.inf", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.RespectsIso.mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.RespectsIso.precomp", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instRespectsIsoTop", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.RespectsIso.postcomp", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.RespectsIso.op", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.RespectsIso.unop", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.isoClosure", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.le_isoClosure", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.isoClosure_respectsIso", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.monotone_isoClosure", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": true, "tactics": ["intro", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.MorphismProperty.cancel_left_of_respectsIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.cancel_right_of_respectsIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.comma_iso_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MorphismProperty.arrow_iso_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.arrow_mk_iso_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.RespectsIso.of_respects_arrow_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.isoClosure_eq_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": true, "tactics": ["refine", "intro", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.MorphismProperty.isoClosure_eq_self", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "CategoryTheory.MorphismProperty.isoClosure_isoClosure", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.isoClosure_le_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": true, "tactics": ["constructor", "exact", "intro", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.MorphismProperty.map_respectsIso", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": true, "tactics": ["apply", "intro", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.MorphismProperty.map_le_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "intro", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.MorphismProperty.map_isoClosure", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": true, "tactics": ["apply", "rw", "intro", "exact", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.MorphismProperty.map_id_eq_isoClosure", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.map_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.MorphismProperty.map_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": true, "tactics": ["apply", "rw", "intro", "exact", "rw", "intro", "exact"], "tactic_count": 7}
{"name": "CategoryTheory.MorphismProperty.RespectsIso.inverseImage", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.map_eq_of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": true, "tactics": ["revert", "suffices", "intro", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.MorphismProperty.map_inverseImage_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.inverseImage_equivalence_inverse_eq_map_functor", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": true, "tactics": ["apply", "intro", "refine", "exact", "rw", "intro", "exact"], "tactic_count": 7}
{"name": "CategoryTheory.MorphismProperty.inverseImage_equivalence_functor_eq_map_inverse", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.map_inverseImage_eq_of_isEquivalence", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": true, "tactics": ["erw"], "tactic_count": 1}
{"name": "CategoryTheory.MorphismProperty.inverseImage_map_eq_of_isEquivalence", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": true, "tactics": ["erw"], "tactic_count": 1}
{"name": "CategoryTheory.MorphismProperty.isomorphisms.iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "CategoryTheory.MorphismProperty.monomorphisms.iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "CategoryTheory.MorphismProperty.epimorphisms.iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "CategoryTheory.MorphismProperty.isomorphisms.infer_property", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.monomorphisms.infer_property", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.epimorphisms.infer_property", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.isomorphisms_op", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.RespectsIso.monomorphisms", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": true, "tactics": ["apply", "intro", "simp", "intro", "apply"], "tactic_count": 5}
{"name": "CategoryTheory.MorphismProperty.RespectsIso.epimorphisms", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": true, "tactics": ["apply", "intro", "simp", "intro", "apply"], "tactic_count": 5}
{"name": "CategoryTheory.MorphismProperty.RespectsIso.isomorphisms", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": true, "tactics": ["apply", "intro", "simp", "intro", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.MorphismProperty.prod", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.pi", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.functorCategory", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.arrow", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.isIso_app_iff_of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.costructuredArrow_iso_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.over_iso_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.commaObj", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.commaObj_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instIsClosedUnderIsomorphismsCommaCommaObjOfRespectsIso", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.costructuredArrowObj", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.costructuredArrowObj_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instIsClosedUnderIsomorphismsCostructuredArrowCostructuredArrowObjOfRespectsIso", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.structuredArrowObj", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.structuredArrowObj_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instIsClosedUnderIsomorphismsStructuredArrowStructuredArrowObjOfRespectsIso", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.over", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.over_eq_inverseImage", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.over_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.under", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.under_eq_inverseImage", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.under_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.overObj", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.overObj_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instIsClosedUnderIsomorphismsOverOverObjOfRespectsIso", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.underObj", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.underObj_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instIsClosedUnderIsomorphismsUnderUnderObjOfRespectsIso", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.Comma.Hom.hom", "kind": "abbrev", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.Comma.Hom.hom_mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.Comma.Hom.hom_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.Comma.Hom.hom_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.Comma.Hom.Simps.hom", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.Comma.id", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.Comma.Hom.comp", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.Comma.instCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.Comma.toCommaMorphism_eq_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.Comma.Hom.ext'", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.Comma.id_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.Comma.comp_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.Comma.comp_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.Comma.comp_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.Comma.homFromCommaOfIsIso", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.Comma.instIsIsoHomFromCommaOfIsIso", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": true, "tactics": ["constructor", "use", "constructor"], "tactic_count": 3}
{"name": "CategoryTheory.MorphismProperty.Comma.isoFromComma", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.Comma.forget", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.Comma.instFaithfulCommaForget", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.Comma.instIsIsoCommaHom", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.Comma.hom_homFromCommaOfIsIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.Comma.inv_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": true, "tactics": ["apply", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.MorphismProperty.Comma.instReflectsIsomorphismsCommaForgetOfRespectsIso", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.Comma.forgetFullyFaithful", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.Comma.instFullTopCommaForget", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.Comma.eqToHom_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": true, "tactics": ["subst", "rfl"], "tactic_count": 2}
{"name": "CategoryTheory.MorphismProperty.Comma.eqToHom_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": true, "tactics": ["subst", "rfl"], "tactic_count": 2}
{"name": "CategoryTheory.MorphismProperty.Comma.changeProp", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.Comma.fullyFaithfulChangeProp", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.Comma.instFaithfulChangeProp", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.Comma.instFullChangeProp", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.Comma.lift", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.Comma.mapLeft", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.Comma.mapRight", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.Over", "kind": "abbrev", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.Over.forget", "kind": "abbrev", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instFaithfulOverTopOverForget", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instFullOverTopOverForget", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.Over.forget_comp_forget_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.Over.Hom.mk", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.Over.mk", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.Over.Hom.ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": true, "tactics": ["ext", "exact", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.MorphismProperty.Over.w", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MorphismProperty.Under", "kind": "abbrev", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.Under.forget", "kind": "abbrev", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instFaithfulUnderTopUnderForget", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instFullUnderTopUnderForget", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.Under.forget_comp_forget_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.Under.Hom.mk", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.Under.mk", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.Under.Hom.ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": true, "tactics": ["ext", "simp", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.MorphismProperty.Under.w", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MorphismProperty.CostructuredArrow", "kind": "abbrev", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.CostructuredArrow.mk", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.CostructuredArrow.Hom.ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.MorphismProperty.CostructuredArrow.forget", "kind": "abbrev", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.CostructuredArrow.toOver", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instFaithfulCostructuredArrowTopOverToOver", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instFullCostructuredArrowTopOverToOver", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": true, "tactics": ["constructor", "intro", "refine", "simpa", "ext"], "tactic_count": 5}
{"name": "CategoryTheory.MorphismProperty.HasFactorization.over", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.id_mem", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.ContainsIdentities.op", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.ContainsIdentities.unop", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.ContainsIdentities.of_op", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.ContainsIdentities.of_unop", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.ContainsIdentities.eqToHom", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": true, "tactics": ["subst", "rw", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.MorphismProperty.ContainsIdentities.inverseImage", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.ContainsIdentities.inf", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.Prod.containsIdentities", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.Pi.containsIdentities", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.of_isIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.isomorphisms_le_of_containsIdentities", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.comp_mem", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instRespectsOfIsStableUnderComposition", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsStableUnderComposition.op", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsStableUnderComposition.unop", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsStableUnderComposition.inf", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.StableUnderInverse", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.StableUnderInverse.op", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.StableUnderInverse.unop", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.respectsIso_of_isStableUnderComposition", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsStableUnderComposition.inverseImage", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.naturalityProperty", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.naturalityProperty.isStableUnderComposition", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.naturalityProperty.stableUnderInverse", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsMultiplicative.op", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsMultiplicative.unop", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsMultiplicative.of_op", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsMultiplicative.of_unop", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsMultiplicative.instTop", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsMultiplicative.instIsomorphisms", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsMultiplicative.instMonomorphisms", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsMultiplicative.instEpimorphisms", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsMultiplicative.instInverseImage", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsMultiplicative.inf", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsMultiplicative.naturalityProperty", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.multiplicativeClosure", "kind": "inductive", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.multiplicativeClosure'", "kind": "inductive", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instIsMultiplicativeMultiplicativeClosure", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instIsMultiplicativeMultiplicativeClosure'", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.le_multiplicativeClosure", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.multiplicativeClosure_eq_self", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": true, "tactics": ["apply", "intro", "induction", "of", "id", "comp_of"], "tactic_count": 6}
{"name": "CategoryTheory.MorphismProperty.multiplicativeClosure_eq_self_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.multiplicativeClosure_le_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.multiplicativeClosure_monotone", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.multiplicativeClosure_eq_multiplicativeClosure'", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.strictMap_multiplicativeClosure_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": true, "tactics": ["intro", "induction", "map", "induction", "of", "id", "comp_of"], "tactic_count": 7}
{"name": "CategoryTheory.MorphismProperty.of_postcomp", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.of_precomp", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.postcomp_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.precomp_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.HasOfPostcompProperty.of_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.HasOfPrecompProperty.of_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instHasOfPrecompPropertyOppositeOpOfHasOfPostcompProperty", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instHasOfPostcompPropertyOppositeOpOfHasOfPrecompProperty", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instHasTwoOutOfThreePropertyOppositeOp", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instHasOfPostcompPropertyTop", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instHasOfPrecompPropertyTop", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instHasTwoOutOfThreePropertyTop", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instHasOfPostcompPropertyMin", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instHasOfPrecompPropertyMin", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instHasTwoOutOfThreePropertyMin", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": true, "tactics": ["have", "have", "have", "have", "constructor"], "tactic_count": 5}
{"name": "CategoryTheory.MorphismProperty.instHasOfPrecompPropertyUnopOfHasOfPostcompPropertyOpposite", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instHasOfPostcompPropertyUnopOfHasOfPrecompPropertyOpposite", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instHasTwoOutOfThreePropertyUnopOfOpposite", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instHasTwoOutOfThreePropertyIsomorphisms", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instHasTwoOutOfThreePropertyInverseImage", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instHasOfPrecompPropertyIsomorphismsOfRespectsIso", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instHasOfPostcompPropertyIsomorphismsOfRespectsIso", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.injective", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Concrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.surjective", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Concrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.bijective", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Concrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.bijective_eq_sup", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Concrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instIsMultiplicativeInjective", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Concrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instIsMultiplicativeSurjective", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Concrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instIsMultiplicativeBijective", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Concrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.injective_respectsIso", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Concrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.surjective_respectsIso", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Concrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.bijective_respectsIso", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Concrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ConcreteCategory.HasSurjectiveInjectiveFactorization", "kind": "abbrev", "module": "Mathlib.CategoryTheory.MorphismProperty.Concrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ConcreteCategory.HasFunctorialSurjectiveInjectiveFactorization", "kind": "abbrev", "module": "Mathlib.CategoryTheory.MorphismProperty.Concrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ConcreteCategory.FunctorialSurjectiveInjectiveFactorizationData", "kind": "abbrev", "module": "Mathlib.CategoryTheory.MorphismProperty.Concrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.functorialSurjectiveInjectiveFactorizationData", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Concrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instHasFunctorialSurjectiveInjectiveFactorizationTypeHomObjForget", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Concrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.of_isPullback_of_descendsAlong", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Descent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.iff_of_isPullback", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Descent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.of_pullback_fst_of_descendsAlong", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Descent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.pullback_fst_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Descent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.of_pullback_snd_of_descendsAlong", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Descent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.pullback_snd_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Descent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.DescendsAlong.top", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Descent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.DescendsAlong.inf", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Descent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.DescendsAlong.of_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Descent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.DescendsAlong.mk'", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Descent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instDescendsAlongOfIsStableUnderBaseChangeOfHasOfPrecompPropertyOfRespectsRight", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Descent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instDescendsAlongDiagonalOfRespectsIsoOfIsStableUnderBaseChange", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Descent", "is_tactic_proof": true, "tactics": ["apply", "introv", "have", "pullback.fst", "apply", "apply", "simp", "rw", "apply", "exact", "rw", "iterate", "rwa"], "tactic_count": 13}
{"name": "CategoryTheory.MorphismProperty.of_isPushout_of_codescendsAlong", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Descent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.iff_of_isPushout", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Descent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.of_pushout_inl_of_codescendsAlong", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Descent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.pushout_inl_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Descent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.of_pushout_inr_of_descendsAlong", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Descent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.pushout_inr_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Descent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.CodescendsAlong.of_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Descent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.CodescendsAlong.top", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Descent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.CodescendsAlong.inf", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Descent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.CodescendsAlong.mk'", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Descent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instCodescendsAlongOfIsStableUnderCobaseChangeOfHasOfPostcompPropertyOfRespectsLeft", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Descent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.MapFactorizationData.op", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Factorization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.FactorizationData", "kind": "abbrev", "module": "Mathlib.CategoryTheory.MorphismProperty.Factorization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.factorizationData", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Factorization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instHasFactorizationOppositeOp", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Factorization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.comp", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Factorization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.comp_eq_top_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Factorization", "is_tactic_proof": true, "tactics": ["constructor", "intro", "refine", "have", "exact", "intro", "ext", "simp", "exact"], "tactic_count": 9}
{"name": "CategoryTheory.MorphismProperty.FunctorialFactorizationData.fac_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Factorization", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.MorphismProperty.FunctorialFactorizationData.ofLE", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Factorization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.FunctorialFactorizationData.factorizationData", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Factorization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.FunctorialFactorizationData.mapZ", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Factorization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.FunctorialFactorizationData.i_mapZ", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Factorization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.FunctorialFactorizationData.mapZ_p", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Factorization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.FunctorialFactorizationData.mapZ_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Factorization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.FunctorialFactorizationData.mapZ_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Factorization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.FunctorialFactorizationData.functorCategory.Z", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Factorization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.FunctorialFactorizationData.functorCategory", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Factorization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.functorialFactorizationData", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Factorization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instHasFactorizationOfHasFunctorialFactorization", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Factorization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instHasFunctorialFactorizationFunctorFunctorCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Factorization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instIsStableUnderRetractsFunctorFunctorCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.FunctorCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsStableUnderLimitsOfShape.functorCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.FunctorCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsStableUnderColimitsOfShape.functorCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.FunctorCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instIsStableUnderBaseChangeFunctorFunctorCategoryOfHasPullbacks", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.FunctorCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instIsStableUnderCobaseChangeFunctorFunctorCategoryOfHasPushouts", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.FunctorCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instIsStableUnderTransfiniteCompositionOfShapeFunctorFunctorCategoryOfHasIterationOfShape", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.FunctorCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.functorCategory_isomorphisms", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.FunctorCategory", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.MorphismProperty.functorCategory_monomorphisms", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.FunctorCategory", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.MorphismProperty.functorCategory_epimorphisms", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.FunctorCategory", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.MorphismProperty.instIsStableUnderTransfiniteCompositionOfShapeFunctorMonomorphismsOfHasPullbacksOfHasIterationOfShape", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.FunctorCategory", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.MorphismProperty.instIsStableUnderCoproductsOfShapeFunctorMonomorphismsOfHasCoproductsOfShapeOfHasPullbacks", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.FunctorCategory", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.MorphismProperty.instIsStableUnderCoproductsFunctorMonomorphismsOfHasCoproductsOfHasPullbacks", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.FunctorCategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.HasCardinalLT", "kind": "abbrev", "module": "Mathlib.CategoryTheory.MorphismProperty.HasCardinalLT", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.hasCardinalLT_ofHoms", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.HasCardinalLT", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.HasCardinalLT.iSup", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.HasCardinalLT", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.MorphismProperty.HasCardinalLT.sup", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.HasCardinalLT", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.MorphismProperty.ind", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Ind", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.exists_hom_of_isFinitelyPresentable", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Ind", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.le_ind", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Ind", "is_tactic_proof": true, "tactics": ["intro", "refine", "exact", "exact", "simpa"], "tactic_count": 5}
{"name": "CategoryTheory.MorphismProperty.ind_iff_ind_underMk", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Ind", "is_tactic_proof": true, "tactics": ["refine", "refine", "exact", "have", "exact", "simp", "refine", "exact", "exact", "exact", "exact", "simp"], "tactic_count": 12}
{"name": "CategoryTheory.MorphismProperty.underObj_ind_eq_ind_underObj", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Ind", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.MorphismProperty.instRespectsLeftInd", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Ind", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instRespectsIsoInd", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Ind", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.ind_underObj_pushout", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Ind", "is_tactic_proof": true, "tactics": ["obtain", "use", "intro", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.MorphismProperty.instIsStableUnderCobaseChangeIndOfHasPushouts", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Ind", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.MorphismProperty.instContainsIdentitiesInd", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Ind", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.ind_ind", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Ind", "is_tactic_proof": true, "tactics": ["refine", "have", "simpa"], "tactic_count": 3}
{"name": "CategoryTheory.MorphismProperty.ind_iff_exists", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Ind", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsStableUnderComposition.ind_of_preIndSpreads", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Ind", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsMultiplicative.ind_of_preIndSpreads", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Ind", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsInvertedBy", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.IsInvertedBy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsInvertedBy.of_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.IsInvertedBy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsInvertedBy.of_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.IsInvertedBy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsInvertedBy.op", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.IsInvertedBy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsInvertedBy.rightOp", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.IsInvertedBy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsInvertedBy.leftOp", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.IsInvertedBy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsInvertedBy.unop", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.IsInvertedBy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsInvertedBy.prod", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.IsInvertedBy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsInvertedBy.pi", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.IsInvertedBy", "is_tactic_proof": true, "tactics": ["intro", "rw", "intro", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.MorphismProperty.FunctorsInverting", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.IsInvertedBy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.FunctorsInverting.ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.IsInvertedBy", "is_tactic_proof": true, "tactics": ["cases", "cases", "subst", "rfl"], "tactic_count": 4}
{"name": "CategoryTheory.MorphismProperty.instCategoryFunctorsInverting", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.IsInvertedBy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.FunctorsInverting.id_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.IsInvertedBy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.FunctorsInverting.comp_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.IsInvertedBy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.FunctorsInverting.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.IsInvertedBy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.FunctorsInverting.mk", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.IsInvertedBy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsInvertedBy.iff_of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.IsInvertedBy", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.MorphismProperty.IsInvertedBy.isoClosure_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.IsInvertedBy", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "intro", "simp", "have", "infer_instance"], "tactic_count": 7}
{"name": "CategoryTheory.MorphismProperty.IsInvertedBy.iff_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.IsInvertedBy", "is_tactic_proof": true, "tactics": ["constructor", "intro", "have", "exact", "intro", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.MorphismProperty.IsInvertedBy.iff_le_inverseImage_isomorphisms", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.IsInvertedBy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsInvertedBy.iff_map_le_isomorphisms", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.IsInvertedBy", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.MorphismProperty.IsInvertedBy.map_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.IsInvertedBy", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MorphismProperty.isSmall_ofHoms", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.IsSmall", "is_tactic_proof": true, "tactics": ["let", "have", "rintro", "exact", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.MorphismProperty.isSmall_iff_eq_ofHoms", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.IsSmall", "is_tactic_proof": true, "tactics": ["constructor", "intro", "refine", "ext", "rw", "constructor", "intro", "exact", "rintro", "simp", "rintro", "infer_instance"], "tactic_count": 12}
{"name": "CategoryTheory.MorphismProperty.llp", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.LiftingProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.rlp", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.LiftingProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.llp_of_isIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.LiftingProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.rlp_of_isIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.LiftingProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.llp_isStableUnderRetracts", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.LiftingProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.rlp_isStableUnderRetracts", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.LiftingProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.llp_isStableUnderCobaseChange", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.LiftingProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.rlp_isStableUnderBaseChange", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.LiftingProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.llp_isMultiplicative", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.LiftingProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.rlp_isMultiplicative", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.LiftingProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.llp_isStableUnderCoproductsOfShape", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.LiftingProperty", "is_tactic_proof": true, "tactics": ["apply", "intro", "have", "infer_instance"], "tactic_count": 4}
{"name": "CategoryTheory.MorphismProperty.rlp_isStableUnderProductsOfShape", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.LiftingProperty", "is_tactic_proof": true, "tactics": ["apply", "intro", "have", "infer_instance"], "tactic_count": 4}
{"name": "CategoryTheory.MorphismProperty.le_llp_iff_le_rlp", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.LiftingProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.gc_llp_rlp", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.LiftingProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.le_llp_rlp", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.LiftingProperty", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.MorphismProperty.rlp_llp_rlp", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.LiftingProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.llp_rlp_llp", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.LiftingProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.antitone_rlp", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.LiftingProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.antitone_llp", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.LiftingProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.pushouts_le_llp_rlp", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.LiftingProperty", "is_tactic_proof": true, "tactics": ["intro", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.MorphismProperty.rlp_pushouts", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.LiftingProperty", "is_tactic_proof": true, "tactics": ["apply", "exact", "rw", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.MorphismProperty.colimitsOfShape_discrete_le_llp_rlp", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.LiftingProperty", "is_tactic_proof": true, "tactics": ["intro", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.MorphismProperty.coproducts_le_llp_rlp", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.LiftingProperty", "is_tactic_proof": true, "tactics": ["intro", "rw", "obtain", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.MorphismProperty.rlp_coproducts", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.LiftingProperty", "is_tactic_proof": true, "tactics": ["apply", "exact", "rw", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.MorphismProperty.retracts_le_llp_rlp", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.LiftingProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.rlp_retracts", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.LiftingProperty", "is_tactic_proof": true, "tactics": ["apply", "exact", "rw", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.MorphismProperty.pullbacks", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.pullbacks_mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.le_pullbacks", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": true, "tactics": ["intro", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.MorphismProperty.pullbacks_monotone", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.MorphismProperty.pushouts", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.pushouts_mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.le_pushouts", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": true, "tactics": ["intro", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.MorphismProperty.pushouts_monotone", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.MorphismProperty.instRespectsIsoPushouts", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instRespectsIsoPullbacks", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.isomorphisms_le_pushouts", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": true, "tactics": ["intro", "obtain", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.MorphismProperty.instIsStableUnderBaseChangePullbacks", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instIsStableUnderCobaseChangePushouts", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instIsStableUnderBaseChangeAlongOfIsStableUnderBaseChange", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.of_isPullback", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.isStableUnderBaseChange_iff_pullbacks_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "intro", "constructor", "intro", "exact"], "tactic_count": 7}
{"name": "CategoryTheory.MorphismProperty.pullbacks_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "CategoryTheory.MorphismProperty.IsStableUnderBaseChange.mk'", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsStableUnderBaseChange.isomorphisms", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsStableUnderBaseChange.monomorphisms", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsStableUnderBaseChange.respectsIso", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": true, "tactics": ["apply", "intro", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.MorphismProperty.pullback_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.pullback_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.baseChange_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.baseChange_map'", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": true, "tactics": ["subst", "refine", "refine", "simpa"], "tactic_count": 4}
{"name": "CategoryTheory.MorphismProperty.baseChange_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": true, "tactics": ["dsimp", "convert"], "tactic_count": 2}
{"name": "CategoryTheory.MorphismProperty.pullback_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": true, "tactics": ["have", "have", "pullback.map", "rw", "apply", "exacts", "baseChange_map"], "tactic_count": 7}
{"name": "CategoryTheory.MorphismProperty.IsStableUnderBaseChange.hasOfPostcompProperty_monomorphisms", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.of_isPushout", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.isStableUnderCobaseChange_iff_pushouts_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "intro", "constructor", "intro", "exact"], "tactic_count": 7}
{"name": "CategoryTheory.MorphismProperty.pushouts_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "CategoryTheory.MorphismProperty.pushouts_le_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": true, "tactics": ["constructor", "exact", "intro", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.MorphismProperty.IsStableUnderCobaseChange.mk'", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsStableUnderCobaseChange.isomorphisms", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsStableUnderCobaseChange.epimorphisms", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsStableUnderCobaseChange.respectsIso", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.pushout_inl", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.pushout_inr", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsStableUnderCobaseChange.hasOfPrecompProperty_epimorphisms", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsStableUnderCobaseChange.op", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsStableUnderCobaseChange.unop", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsStableUnderBaseChange.op", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsStableUnderBaseChange.unop", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsStableUnderBaseChange.inf", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsStableUnderCobaseChange.inf", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instIsStableUnderBaseChangeTop", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instIsStableUnderCobaseChangeTop", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.limitsOfShape", "kind": "inductive", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.limitsOfShape.mk'", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.MorphismProperty.limitsOfShape_monotone", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.MorphismProperty.instRespectsIsoLimitsOfShape", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.limitsOfShape_limMap", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.isStableUnderLimitsOfShape_iff_limitsOfShape_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "exact", "rintro", "constructor", "intro", "exact"], "tactic_count": 7}
{"name": "CategoryTheory.MorphismProperty.limitsOfShape_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "CategoryTheory.MorphismProperty.limMap", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.colimitsOfShape", "kind": "inductive", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.colimitsOfShape.mk'", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.MorphismProperty.colimitsOfShape_monotone", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.MorphismProperty.colimitsOfShape_le_of_final", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": true, "tactics": ["intro", "have", "have", "have", "h₁.desc", "h₁'.hom_ext", "have", "dsimp", "simp", "rw", "exact"], "tactic_count": 11}
{"name": "CategoryTheory.MorphismProperty.colimitsOfShape_eq_of_equivalence", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instRespectsIsoColimitsOfShape", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.colimitsOfShape_colimMap", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.colimitsOfShape.of_isColimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.isStableUnderColimitsOfShape_iff_colimitsOfShape_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "exact", "rintro", "constructor", "intro", "exact"], "tactic_count": 7}
{"name": "CategoryTheory.MorphismProperty.colimitsOfShape_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "CategoryTheory.MorphismProperty.colimMap", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsStableUnderColimitsOfShape.isomorphisms", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instIsStableUnderFilteredColimitsIsomorphisms", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.coproducts", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.colimitsOfShape_le_coproducts", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.coproducts_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MorphismProperty.coproducts_of_small", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": true, "tactics": ["rw", "refine", "rwa"], "tactic_count": 3}
{"name": "CategoryTheory.MorphismProperty.le_colimitsOfShape_punit", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": true, "tactics": ["intro", "have", "let", "let", "have", "have", "have", "hc₁.hom_ext", "obtain", "rw", "simp", "rw", "exact"], "tactic_count": 13}
{"name": "CategoryTheory.MorphismProperty.le_coproducts", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.coproducts_monotone", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": true, "tactics": ["rintro", "rw", "obtain", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.MorphismProperty.IsStableUnderProductsOfShape", "kind": "abbrev", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsStableUnderCoproductsOfShape", "kind": "abbrev", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsStableUnderProductsOfShape.mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsStableUnderCoproductsOfShape.mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.coproducts_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": true, "tactics": ["intro", "rw", "obtain", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.MorphismProperty.coproducts_eq_self", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.coproducts_le_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": true, "tactics": ["constructor", "exact", "intro", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.MorphismProperty.diagonal", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.diagonal_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.RespectsIso.diagonal", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": true, "tactics": ["apply", "introv", "rwa", "introv", "delta", "rwa"], "tactic_count": 6}
{"name": "CategoryTheory.MorphismProperty.diagonal_isStableUnderComposition", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsStableUnderBaseChange.diagonal", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.diagonal_isomorphisms", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.hasOfPostcompProperty_iff_le_diagonal", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": true, "tactics": ["refine", "exact", "set", "have", "rw", "apply", "exact", "exact"], "tactic_count": 8}
{"name": "CategoryTheory.MorphismProperty.universally", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.universally_respectsIso", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": true, "tactics": ["apply", "intro", "have", "exact", "intro", "have", "exact", "hf"], "tactic_count": 8}
{"name": "CategoryTheory.MorphismProperty.universally_isStableUnderBaseChange", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsStableUnderComposition.universally", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.universally_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": true, "tactics": ["intro", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.MorphismProperty.universally_inf", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": true, "tactics": ["ext", "change", "simp_rw", "rfl"], "tactic_count": 4}
{"name": "CategoryTheory.MorphismProperty.universally_eq_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsStableUnderBaseChange.universally_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.universally_mono", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.universally_mk'", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": true, "tactics": ["introv", "have", "rw", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.MorphismProperty.instHasPullbacksOfHasPullbacks", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instHasPullbacksAlongOfHasPullbacks", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instHasPullbacksAlongCompOfIsStableUnderBaseChangeAlong", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instIsStableUnderBaseChangeAlongCompOfHasPullbacksAlong", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsLocalAtTarget.mk_of_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Local", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsLocalAtTarget.mk_of_isStableUnderBaseChange", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Local", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsLocalAtTarget.of_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Local", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsLocalAtTarget.top", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Local", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsLocalAtTarget.of_isPullback", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Local", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.MorphismProperty.IsLocalAtTarget.iff_of_zeroHypercover", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Local", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsLocalAtTarget.inf", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Local", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.of_zeroHypercover_target", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Local", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.MorphismProperty.IsLocalAtSource.mk_of_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Local", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsLocalAtSource.of_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Local", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsLocalAtSource.top", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Local", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsLocalAtSource.iff_of_zeroHypercover", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Local", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsLocalAtSource.inf", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Local", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.of_zeroHypercover_source", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Local", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.MorphismProperty.Over.map", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.OverAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.Over.map_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.OverAdjunction", "is_tactic_proof": true, "tactics": ["fapply", "simp", "intro", "ext", "simp"], "tactic_count": 5}
{"name": "CategoryTheory.MorphismProperty.Over.mapCongr", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.OverAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instHasPullbackHomDiscretePUnitOfHasPullbacksAlong", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.OverAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instHasPullbackSndHomDiscretePUnitOfHasPullbacksAlongOfIsStableUnderBaseChangeAlong", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.OverAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.Over.pullback", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.OverAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.Over.pullbackComp_left_fst_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.OverAdjunction", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MorphismProperty.Over.pullbackCongr", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.OverAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.Over.pullbackCongr_hom_app_left_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.OverAdjunction", "is_tactic_proof": true, "tactics": ["subst", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.MorphismProperty.Over.mapPullbackAdj", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.OverAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instIsLeftAdjointOverTopMapOfHasPullbacksAlongOfIsStableUnderBaseChangeAlong", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.OverAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.HasQuotient.iff_of_eqvGen", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Quotient", "is_tactic_proof": true, "tactics": ["induction", "rel", "refl", "symm", "trans"], "tactic_count": 5}
{"name": "CategoryTheory.MorphismProperty.quotient", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.quotient_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Quotient", "is_tactic_proof": true, "tactics": ["refine", "rw", "rwa"], "tactic_count": 3}
{"name": "CategoryTheory.MorphismProperty.eq_inverseImage_quotientFunctor", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Quotient", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.relativelyRepresentable", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.relativelyRepresentable.pullback", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.relativelyRepresentable.snd", "kind": "abbrev", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.relativelyRepresentable.fst", "kind": "abbrev", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.relativelyRepresentable.fst'", "kind": "abbrev", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.relativelyRepresentable.map_fst'", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.relativelyRepresentable.isPullback", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.relativelyRepresentable.w", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.relativelyRepresentable.isPullback'", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.relativelyRepresentable.w'", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.relativelyRepresentable.isPullback_of_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.relativelyRepresentable.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.relativelyRepresentable.hom_ext'", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.relativelyRepresentable.lift", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.relativelyRepresentable.lift_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.relativelyRepresentable.lift_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.relativelyRepresentable.lift'", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.relativelyRepresentable.lift'_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.relativelyRepresentable.lift'_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.relativelyRepresentable.symmetry", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.relativelyRepresentable.symmetry_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.relativelyRepresentable.symmetry_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.relativelyRepresentable.symmetry_symmetry", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.relativelyRepresentable.symmetryIso", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.relativelyRepresentable.instIsIsoSymmetryOfFaithful", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.relativelyRepresentable.map", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.relativelyRepresentable.of_isIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.relativelyRepresentable.isomorphisms_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.relativelyRepresentable.isMultiplicative", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.relativelyRepresentable.isStableUnderBaseChange", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.relativelyRepresentable.respectsIso", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.relative", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.presheaf", "kind": "abbrev", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.relative.rep", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.relative.property", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.relative.property_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.relative.of_exists", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": true, "tactics": ["refine", "all_goals", "refine", "refine", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.MorphismProperty.relative_of_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.relative_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": true, "tactics": ["apply", "intro", "obtain", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.MorphismProperty.of_relative_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.relative_map_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.relative_monotone", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.relative_isStableUnderBaseChange", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.relative_isStableUnderComposition", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.relative_respectsIso", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.relative_isMultiplicative", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.presheaf_monomorphisms_le_monomorphisms", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.presheaf_mono_of_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.fst'_self_eq_snd", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": true, "tactics": ["have", "apply", "rw"], "tactic_count": 3}
{"name": "CategoryTheory.MorphismProperty.isIso_fst'_self", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.relativelyRepresentable.pullback₃", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.relativelyRepresentable.pullback₃.p₁", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.relativelyRepresentable.pullback₃.p₂", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.relativelyRepresentable.pullback₃.p₃", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.relativelyRepresentable.pullback₃.π", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.relativelyRepresentable.pullback₃.map_p₁_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.relativelyRepresentable.pullback₃.map_p₂_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.relativelyRepresentable.pullback₃.map_p₃_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.relativelyRepresentable.lift₃", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.relativelyRepresentable.lift₃_p₁", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.relativelyRepresentable.lift₃_p₂", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.relativelyRepresentable.lift₃_p₃", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.relativelyRepresentable.pullback₃.fst_fst'_eq_p₁", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.relativelyRepresentable.pullback₃.fst_snd_eq_p₂", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.relativelyRepresentable.pullback₃.snd_snd_eq_p₃", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.relativelyRepresentable.pullback₃.snd_fst'_eq_p₁", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.relativelyRepresentable.pullback₃.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.relativelyRepresentable.of_diag", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": true, "tactics": ["rw", "intro", "obtain", "let", "let", "pasteHorizIsPullback", "pullback.congrHom", "left", "exact"], "tactic_count": 9}
{"name": "CategoryTheory.Functor.relativelyRepresentable.toPullbackTerminal", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": false, "tactics": ["let", "pullback.congrHom", "rw", "apply", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.Functor.relativelyRepresentable.diag_of_map_from_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": true, "tactics": ["rw", "suffices", "intro", "obtain", "obtain", "rfl", "obtain", "pullback.snd", "have", "g", "pullback.lift", "pullback.map", "exact", "hg"], "tactic_count": 14}
{"name": "CategoryTheory.Functor.relativelyRepresentable.diag_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Representable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.of_retract", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Retract", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instIsStableUnderRetractsInverseImage", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Retract", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsStableUnderRetracts.monomorphisms", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Retract", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsStableUnderRetracts.epimorphisms", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Retract", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsStableUnderRetracts.isomorphisms", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Retract", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instIsStableUnderRetractsOppositeOp", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Retract", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instIsStableUnderRetractsUnopOfOpposite", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Retract", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instIsStableUnderRetractsMin", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Retract", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.retracts", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.Retract", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.le_retracts", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Retract", "is_tactic_proof": true, "tactics": ["intro", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.MorphismProperty.retracts_monotone", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Retract", "is_tactic_proof": true, "tactics": ["intro", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.MorphismProperty.isStableUnderRetracts_iff_retracts_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Retract", "is_tactic_proof": true, "tactics": ["rw", "constructor", "intro", "exact", "intro", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.MorphismProperty.retracts_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Retract", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "CategoryTheory.MorphismProperty.retracts_le_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.Retract", "is_tactic_proof": true, "tactics": ["constructor", "exact", "intro", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.MorphismProperty.instRespectsIsoOfIsStableUnderRetracts", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.Retract", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.RetractArrow.ofLeftLiftingProperty", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.RetractArgument", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.RetractArrow.ofRightLiftingProperty", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.RetractArgument", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.llp_eq_of_le_llp_of_hasFactorization_of_isStableUnderRetracts", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.RetractArgument", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.rlp_eq_of_le_rlp_of_hasFactorization_of_isStableUnderRetracts", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.RetractArgument", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.ofArrowIso", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.TransfiniteComposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.ofLE", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.TransfiniteComposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.ofOrderIso", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.TransfiniteComposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.map", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.TransfiniteComposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.iic", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.TransfiniteComposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.ici", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.TransfiniteComposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.ofComposableArrows", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.TransfiniteComposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.id", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.TransfiniteComposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.ofMem", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.TransfiniteComposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.ofComp", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.TransfiniteComposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.transfiniteCompositionsOfShape", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.TransfiniteComposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.transfiniteCompositionsOfShape_monotone", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.TransfiniteComposition", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.MorphismProperty.transfiniteCompositionsOfShape_eq_of_orderIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.TransfiniteComposition", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.MorphismProperty.instRespectsIsoTransfiniteCompositionsOfShape", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.TransfiniteComposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.mem", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.TransfiniteComposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.transfiniteCompositionsOfShape_map_of_preserves", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.TransfiniteComposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.transfiniteCompositionsOfShape_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.TransfiniteComposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.isStableUnderTransfiniteCompositionOfShape_iff_of_orderIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.TransfiniteComposition", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MorphismProperty.IsStableUnderTransfiniteCompositionOfShape.of_isStableUnderColimitsOfShape.mem_map_bot_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.TransfiniteComposition", "is_tactic_proof": true, "tactics": ["obtain", "induction", "isMin", "obtain", "simpa", "succ", "rw", "exact", "isSuccLimit", "hj", "letI", "bot_le", "exact"], "tactic_count": 13}
{"name": "CategoryTheory.MorphismProperty.IsStableUnderTransfiniteCompositionOfShape.of_isStableUnderColimitsOfShape.mem", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.TransfiniteComposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsStableUnderTransfiniteCompositionOfShape.of_isStableUnderColimitsOfShape", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.TransfiniteComposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instIsStableUnderTransfiniteCompositionOfShapeOfIsMultiplicativeOfRespectsIsoOfIsStableUnderFilteredColimits", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.TransfiniteComposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsStableUnderInfiniteComposition", "kind": "abbrev", "module": "Mathlib.CategoryTheory.MorphismProperty.TransfiniteComposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsStableUnderTransfiniteComposition.instOfIsMultiplicativeOfRespectsIsoOfIsStableUnderFilteredColimits", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.TransfiniteComposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsStableUnderTransfiniteComposition._example", "kind": "example", "module": "Mathlib.CategoryTheory.MorphismProperty.TransfiniteComposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsStableUnderTransfiniteComposition.shrink", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.TransfiniteComposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsStableUnderTransfiniteComposition.shrink₀", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.TransfiniteComposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsStableUnderTransfiniteComposition.instIsMultiplicative", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.TransfiniteComposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.transfiniteCompositions", "kind": "definition", "module": "Mathlib.CategoryTheory.MorphismProperty.TransfiniteComposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.transfiniteCompositions_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.TransfiniteComposition", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.MorphismProperty.transfiniteCompositionsOfShape_le_transfiniteCompositions", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.TransfiniteComposition", "is_tactic_proof": true, "tactics": ["intro", "rw", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.MorphismProperty.transfiniteCompositions_monotone", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.TransfiniteComposition", "is_tactic_proof": true, "tactics": ["intro", "rw", "obtain", "exact", "transfiniteCompositionsOfShape_le_transfiniteCompositions"], "tactic_count": 5}
{"name": "CategoryTheory.MorphismProperty.le_transfiniteCompositions", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.TransfiniteComposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.transfiniteCompositions_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.TransfiniteComposition", "is_tactic_proof": true, "tactics": ["intro", "rw", "obtain", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.MorphismProperty.transfiniteCompositions_le_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.TransfiniteComposition", "is_tactic_proof": true, "tactics": ["constructor", "exact", "intro", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.mem_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.TransfiniteComposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.mem_incl_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.TransfiniteComposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape._example", "kind": "example", "module": "Mathlib.CategoryTheory.MorphismProperty.TransfiniteComposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.isIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.TransfiniteComposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.instIsIsoMapF", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.TransfiniteComposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.instIsIsoAppIncl", "kind": "instance", "module": "Mathlib.CategoryTheory.MorphismProperty.TransfiniteComposition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsWeakFactorizationSystem.mk'", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.WeakFactorizationSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.rlp_eq_of_wfs", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.WeakFactorizationSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.llp_eq_of_wfs", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.WeakFactorizationSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.hasLiftingProperty_of_wfs", "kind": "theorem", "module": "Mathlib.CategoryTheory.MorphismProperty.WeakFactorizationSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.app", "kind": "definition", "module": "Mathlib.CategoryTheory.NatIso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.hom_inv_id_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.NatIso", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Iso.inv_hom_id_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.NatIso", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Iso.hom_inv_id_app_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.NatIso", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Iso.inv_hom_id_app_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.NatIso", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Iso.hom_inv_id_app_app_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.NatIso", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Iso.inv_hom_id_app_app_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.NatIso", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.NatIso.trans_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.NatIso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatIso.hom_app_isIso", "kind": "instance", "module": "Mathlib.CategoryTheory.NatIso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatIso.inv_app_isIso", "kind": "instance", "module": "Mathlib.CategoryTheory.NatIso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatIso.cancel_natIso_hom_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.NatIso", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.NatIso.cancel_natIso_inv_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.NatIso", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.NatIso.cancel_natIso_hom_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.NatIso", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.NatIso.cancel_natIso_inv_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.NatIso", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.NatIso.cancel_natIso_hom_right_assoc", "kind": "theorem", "module": "Mathlib.CategoryTheory.NatIso", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.NatIso.cancel_natIso_inv_right_assoc", "kind": "theorem", "module": "Mathlib.CategoryTheory.NatIso", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.NatIso.inv_inv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.NatIso", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.NatIso.naturality_1", "kind": "theorem", "module": "Mathlib.CategoryTheory.NatIso", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.NatIso.naturality_2", "kind": "theorem", "module": "Mathlib.CategoryTheory.NatIso", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.NatIso.naturality_1'", "kind": "theorem", "module": "Mathlib.CategoryTheory.NatIso", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.NatIso.naturality_2'", "kind": "theorem", "module": "Mathlib.CategoryTheory.NatIso", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.NatIso.isIso_app_of_isIso", "kind": "instance", "module": "Mathlib.CategoryTheory.NatIso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatIso.isIso_inv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.NatIso", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.NatIso.inv_map_inv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.NatIso", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.NatIso.ofComponents.app", "kind": "theorem", "module": "Mathlib.CategoryTheory.NatIso", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.NatIso.isIso_of_isIso_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.NatIso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatIso.hcomp", "kind": "definition", "module": "Mathlib.CategoryTheory.NatIso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatIso.isIso_map_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.NatIso", "is_tactic_proof": true, "tactics": ["revert", "suffices", "intro", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.NatTrans.isIso_iff_isIso_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.NatIso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.copyObj", "kind": "definition", "module": "Mathlib.CategoryTheory.NatIso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isoCopyObj", "kind": "definition", "module": "Mathlib.CategoryTheory.NatIso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.naturality_1", "kind": "theorem", "module": "Mathlib.CategoryTheory.NatIso", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.NatTrans.naturality_2", "kind": "theorem", "module": "Mathlib.CategoryTheory.NatIso", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.NatTrans.naturality'", "kind": "theorem", "module": "Mathlib.CategoryTheory.NatTrans", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.congr_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.NatTrans", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.NatTrans.id", "kind": "definition", "module": "Mathlib.CategoryTheory.NatTrans", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.id_app'", "kind": "theorem", "module": "Mathlib.CategoryTheory.NatTrans", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.instInhabited", "kind": "instance", "module": "Mathlib.CategoryTheory.NatTrans", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.vcomp", "kind": "definition", "module": "Mathlib.CategoryTheory.NatTrans", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.vcomp_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.NatTrans", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans._example", "kind": "example", "module": "Mathlib.CategoryTheory.NatTrans", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "CategoryTheory.ObjectProperty", "kind": "abbrev", "module": "Mathlib.CategoryTheory.ObjectProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.le_def", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.prop_of_is", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Basic", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "CategoryTheory.ObjectProperty.is_of_prop", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Basic", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "CategoryTheory.ObjectProperty.ofObj", "kind": "inductive", "module": "Mathlib.CategoryTheory.ObjectProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.ofObj_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.ofObj_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Basic", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.ObjectProperty.ofObj_le_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.ofObj_subtypeVal", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Basic", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.ObjectProperty.singleton", "kind": "abbrev", "module": "Mathlib.CategoryTheory.ObjectProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.singleton_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.ObjectProperty.singleton_le_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.ObjectProperty.pair", "kind": "definition", "module": "Mathlib.CategoryTheory.ObjectProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.pair_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Basic", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "rintro"], "tactic_count": 3}
{"name": "CategoryTheory.ObjectProperty.inverseImage", "kind": "definition", "module": "Mathlib.CategoryTheory.ObjectProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.prop_inverseImage_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.map", "kind": "definition", "module": "Mathlib.CategoryTheory.ObjectProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.prop_map_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.prop_map_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.map_monotone", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Basic", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.ObjectProperty.strictMap", "kind": "inductive", "module": "Mathlib.CategoryTheory.ObjectProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.strictMap_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.strictMap_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.strictMap_monotone", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Basic", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.ObjectProperty.strictMap_le_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Basic", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.ObjectProperty.strictMap_ofObj", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.ObjectProperty.strictMap_singleton", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.ObjectProperty.prop_of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.ClosedUnderIsomorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.prop_iff_of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.ClosedUnderIsomorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.prop_of_isIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.ClosedUnderIsomorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.prop_iff_of_isIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.ClosedUnderIsomorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.isoClosure", "kind": "definition", "module": "Mathlib.CategoryTheory.ObjectProperty.ClosedUnderIsomorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.prop_isoClosure_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.ClosedUnderIsomorphisms", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "CategoryTheory.ObjectProperty.prop_isoClosure", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.ClosedUnderIsomorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.le_isoClosure", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.ClosedUnderIsomorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.monotone_isoClosure", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.ClosedUnderIsomorphisms", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.ObjectProperty.isoClosure_eq_self", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.ClosedUnderIsomorphisms", "is_tactic_proof": true, "tactics": ["apply", "intro", "exact", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.ObjectProperty.isoClosure_le_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.ClosedUnderIsomorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instIsClosedUnderIsomorphismsIsoClosure", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.ClosedUnderIsomorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.isClosedUnderIsomorphisms_iff_isoClosure_eq_self", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.ClosedUnderIsomorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instIsClosedUnderIsomorphismsMap", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.ClosedUnderIsomorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instIsClosedUnderIsomorphismsInverseImage", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.ClosedUnderIsomorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.isoClosure_strictMap", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.ClosedUnderIsomorphisms", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact", "rintro", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.ObjectProperty.map_isoClosure", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.ClosedUnderIsomorphisms", "is_tactic_proof": true, "tactics": ["refine", "rintro", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.ObjectProperty.colimitsCardinalClosure", "kind": "definition", "module": "Mathlib.CategoryTheory.ObjectProperty.ColimitsCardinalClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.le_colimitsCardinalClosure", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.ColimitsCardinalClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instIsClosedUnderIsomorphismsColimitsCardinalClosure", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.ColimitsCardinalClosure", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.ObjectProperty.instEssentiallySmallColimitsCardinalClosureOfLocallySmall", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.ColimitsCardinalClosure", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.ObjectProperty.instIsClosedUnderColimitsOfShapeColimitsCardinalClosureCategoryFamily", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.ColimitsCardinalClosure", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.ObjectProperty.isClosedUnderColimitsOfShape_colimitsCardinalClosure", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.ColimitsCardinalClosure", "is_tactic_proof": true, "tactics": ["obtain", "rw", "infer_instance"], "tactic_count": 3}
{"name": "CategoryTheory.ObjectProperty.colimitsCardinalClosure_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.ColimitsCardinalClosure", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.ObjectProperty.isStableUnderRetracts_colimitsCardinalClosure", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.ColimitsCardinalClosure", "is_tactic_proof": false, "tactics": ["have", "simp", "infer_instance)", "infer_instance"], "tactic_count": 4}
{"name": "CategoryTheory.ObjectProperty.colimitsClosure", "kind": "inductive", "module": "Mathlib.CategoryTheory.ObjectProperty.ColimitsClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.le_colimitsClosure", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.ColimitsClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instIsClosedUnderIsomorphismsColimitsClosure", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.ColimitsClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instIsClosedUnderColimitsOfShapeColimitsClosure", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.ColimitsClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.colimitsClosure_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.ColimitsClosure", "is_tactic_proof": true, "tactics": ["intro", "induction", "of_mem", "of_isoClosure", "of_colimitPresentation"], "tactic_count": 5}
{"name": "CategoryTheory.ObjectProperty.colimitsClosure_monotone", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.ColimitsClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.colimitsClosure_isoClosure", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.ColimitsClosure", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.ObjectProperty.colimitsClosure_eq_unop_limitsClosure", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.ColimitsClosure", "is_tactic_proof": true, "tactics": ["refine", "apply", "rw", "apply", "rw", "apply", "rw", "apply"], "tactic_count": 8}
{"name": "CategoryTheory.ObjectProperty.instEssentiallySmallColimitsClosureOfSmallOfLocallySmall", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.ColimitsClosure", "is_tactic_proof": true, "tactics": ["rw", "have", "infer_instance"], "tactic_count": 3}
{"name": "CategoryTheory.ObjectProperty.strictColimitsOfShape", "kind": "inductive", "module": "Mathlib.CategoryTheory.ObjectProperty.ColimitsOfShape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.strictColimitsOfShape_monotone", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.ColimitsOfShape", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.ObjectProperty.ColimitOfShape.colimit", "kind": "definition", "module": "Mathlib.CategoryTheory.ObjectProperty.ColimitsOfShape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.ColimitOfShape.ofIso", "kind": "definition", "module": "Mathlib.CategoryTheory.ObjectProperty.ColimitsOfShape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.ColimitOfShape.ofLE", "kind": "definition", "module": "Mathlib.CategoryTheory.ObjectProperty.ColimitsOfShape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.ColimitOfShape.reindex", "kind": "definition", "module": "Mathlib.CategoryTheory.ObjectProperty.ColimitsOfShape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.ColimitOfShape.toCostructuredArrow", "kind": "definition", "module": "Mathlib.CategoryTheory.ObjectProperty.ColimitsOfShape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.colimitsOfShape", "kind": "definition", "module": "Mathlib.CategoryTheory.ObjectProperty.ColimitsOfShape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.ColimitOfShape.colimitsOfShape", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.ColimitsOfShape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.strictColimitsOfShape_le_colimitsOfShape", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.ColimitsOfShape", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.ObjectProperty.instIsClosedUnderIsomorphismsColimitsOfShape", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.ColimitsOfShape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.isoClosure_strictColimitsOfShape", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.ColimitsOfShape", "is_tactic_proof": true, "tactics": ["refine", "rw", "apply", "intro", "have", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.ObjectProperty.colimitsOfShape_monotone", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.ColimitsOfShape", "is_tactic_proof": true, "tactics": ["intro", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.ObjectProperty.colimitsOfShape_isoClosure", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.ColimitsOfShape", "is_tactic_proof": true, "tactics": ["refine", "intro", "choose", "exact", "prop_diag_obj"], "tactic_count": 5}
{"name": "CategoryTheory.ObjectProperty.instSmallStrictColimitsOfShapeOfSmallOfLocallySmall", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.ColimitsOfShape", "is_tactic_proof": false, "tactics": ["refine", "small_of_surjective", "letI", "rintro", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.ObjectProperty.IsClosedUnderColimitsOfShape.mk'", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.ColimitsOfShape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.ColimitOfShape.prop", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.ColimitsOfShape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.prop_of_isColimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.ColimitsOfShape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.prop_colimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.ColimitsOfShape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.colimitsOfShape_le_of_final", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.ColimitsOfShape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.colimitsOfShape_congr", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.ColimitsOfShape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.isClosedUnderColimitsOfShape_iff_of_equivalence", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.ColimitsOfShape", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.ObjectProperty.IsClosedUnderColimitsOfShape.of_equivalence", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.ColimitsOfShape", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "CategoryTheory.ObjectProperty.colimitsOfShape_eq_unop_limitsOfShape", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.ColimitsOfShape", "is_tactic_proof": true, "tactics": ["ext", "refine", "exact", "π", "isLimit", "prop_diag_obj", "exact", "ι", "isColimit", "prop_diag_obj"], "tactic_count": 10}
{"name": "CategoryTheory.ObjectProperty.limitsOfShape_eq_unop_colimitsOfShape", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.ColimitsOfShape", "is_tactic_proof": true, "tactics": ["ext", "refine", "exact", "ι", "isColimit", "prop_diag_obj", "exact", "π", "isLimit", "prop_diag_obj"], "tactic_count": 10}
{"name": "CategoryTheory.ObjectProperty.limitsOfShape_op", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.ColimitsOfShape", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.ObjectProperty.colimitsOfShape_op", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.ColimitsOfShape", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.ObjectProperty.isClosedUnderColimitsOfShape_iff_op", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.ColimitsOfShape", "is_tactic_proof": true, "tactics": ["rw", "op_monotone_iff,"], "tactic_count": 2}
{"name": "CategoryTheory.ObjectProperty.isClosedUnderLimitsOfShape_iff_op", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.ColimitsOfShape", "is_tactic_proof": true, "tactics": ["rw", "op_monotone_iff,"], "tactic_count": 2}
{"name": "CategoryTheory.ObjectProperty.isClosedUnderColimitsOfShape_op_iff_op", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.ColimitsOfShape", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.ObjectProperty.isClosedUnderLimitsOfShape_op_iff_op", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.ColimitsOfShape", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.ObjectProperty.instIsClosedUnderLimitsOfShapeOppositeOpOfIsClosedUnderColimitsOfShape", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.ColimitsOfShape", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "CategoryTheory.ObjectProperty.instIsClosedUnderColimitsOfShapeOppositeOpOfIsClosedUnderLimitsOfShape", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.ColimitsOfShape", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "CategoryTheory.ObjectProperty.instIsClosedUnderLimitsOfShapeOppositeOpOfIsClosedUnderColimitsOfShape_1", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.ColimitsOfShape", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "CategoryTheory.ObjectProperty.instIsClosedUnderColimitsOfShapeOppositeOpOfIsClosedUnderLimitsOfShape_1", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.ColimitsOfShape", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "CategoryTheory.ObjectProperty.isClosedUnderColimitsOfShape_iff_unop", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.ColimitsOfShape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.isClosedUnderLimitsOfShape_iff_unop", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.ColimitsOfShape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.isClosedUnderColimitsOfShape_op_iff_unop", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.ColimitsOfShape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.isClosedUnderLimitsOfShape_op_iff_unop", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.ColimitsOfShape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instIsClosedUnderLimitsOfShapeUnopOppositeOfIsClosedUnderColimitsOfShape", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.ColimitsOfShape", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "CategoryTheory.ObjectProperty.instIsClosedUnderColimitsOfShapeUnopOppositeOfIsClosedUnderLimitsOfShape", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.ColimitsOfShape", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "CategoryTheory.ObjectProperty.instIsClosedUnderLimitsOfShapeUnopOfIsClosedUnderColimitsOfShapeOpposite", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.ColimitsOfShape", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "CategoryTheory.ObjectProperty.instIsClosedUnderColimitsOfShapeUnopOfIsClosedUnderLimitsOfShapeOpposite", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.ColimitsOfShape", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "CategoryTheory.ObjectProperty.instIsStableUnderRetractsOfIsClosedUnderColimitsOfShapeWalkingParallelPair", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.ColimitsOfShape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty._example", "kind": "example", "module": "Mathlib.CategoryTheory.ObjectProperty.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.prop_inf_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.prop_sup_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.isoClosure_sup", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.CompleteLattice", "is_tactic_proof": true, "tactics": ["ext", "simp", "constructor", "rintro", "simp", "obtain", "exact", "exact", "rintro", "exact", "exact"], "tactic_count": 11}
{"name": "CategoryTheory.ObjectProperty.instIsClosedUnderIsomorphismsMax", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.CompleteLattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.ObjectProperty.instIsClosedUnderIsomorphismsMin", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instIsClosedUnderIsomorphismsTop", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.prop_iSup_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.CompleteLattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.ObjectProperty.isoClosure_iSup", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.CompleteLattice", "is_tactic_proof": true, "tactics": ["refine", "rintro", "simp", "obtain", "exact", "simp", "intro", "rw", "exact"], "tactic_count": 9}
{"name": "CategoryTheory.ObjectProperty.instIsClosedUnderIsomorphismsISup", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.CompleteLattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.ObjectProperty.ι_map_top", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.CompleteLattice", "is_tactic_proof": true, "tactics": ["ext", "constructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.ObjectProperty.exists_prop_of_containsZero", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.ContainsZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.prop_of_isZero", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.ContainsZero", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.ObjectProperty.prop_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.ContainsZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instContainsZeroTopOfHasZeroObject", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.ContainsZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instContainsZeroIsZeroOfHasZeroObject", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.ContainsZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instContainsZeroMapOfPreservesZeroMorphisms", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.ContainsZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instContainsZeroInverseImageOfIsClosedUnderIsomorphismsOfPreservesZeroMorphismsOfHasZeroObject", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.ContainsZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instContainsZeroIsoClosure", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.ContainsZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instContainsZeroMinOfIsClosedUnderIsomorphisms", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.ContainsZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instContainsZeroOppositeOp", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.ContainsZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instContainsZeroUnopOfOpposite", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.ContainsZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instHasZeroObjectFullSubcategoryOfContainsZero", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.ContainsZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.kernel", "kind": "abbrev", "module": "Mathlib.CategoryTheory.ObjectProperty.ContainsZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.prop_of_mono", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instIsClosedUnderIsomorphisms", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.prop_X₁_of_shortExact", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.EpiMono", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.ObjectProperty.instIsClosedUnderSubobjectsInverseImageOfPreservesMonomorphisms", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.prop_of_epi", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instIsClosedUnderIsomorphisms_1", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.prop_X₃_of_shortExact", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.EpiMono", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.ObjectProperty.instIsClosedUnderQuotientsInverseImageOfPreservesEpimorphisms", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instIsClosedUnderSubobjectsTop", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instIsClosedUnderQuotientsTop", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instIsClosedUnderSubobjectsIsZeroOfHasZeroMorphisms", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instIsClosedUnderQuotientsIsZeroOfHasZeroMorphisms", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.essSurj_ιOfLE_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Equivalence", "is_tactic_proof": true, "tactics": ["refine", "exact", "obtain", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.ObjectProperty.isEquivalence_ιOfLE_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Equivalence", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.ObjectProperty.instIsEquivalenceFullSubcategoryIsoClosureιOfLE", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.Equivalence", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.ObjectProperty.topEquivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.ObjectProperty.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.congrFullSubcategory", "kind": "definition", "module": "Mathlib.CategoryTheory.ObjectProperty.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.prop_X₂_of_shortExact", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Extensions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instIsClosedUnderExtensionsTop", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.Extensions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instIsClosedUnderExtensionsIsZero", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.Extensions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instIsClosedUnderExtensionsInverseImageOfPreservesZeroMorphismsOfPreservesFiniteLimitsOfPreservesFiniteColimits", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.Extensions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.prop_biprod", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Extensions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.IsClosedUnderBinaryProducts", "kind": "abbrev", "module": "Mathlib.CategoryTheory.ObjectProperty.FiniteProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.prop_prod", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.FiniteProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.prop_of_isTerminal", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.FiniteProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.IsClosedUnderBinaryProducts.closedUnderIsomorphisms", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.FiniteProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instIsClosedUnderLimitsOfShapeDiscreteOfIsClosedUnderFiniteProductsOfFinite", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.FiniteProducts", "is_tactic_proof": true, "tactics": ["obtain", "have", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.ObjectProperty.instIsClosedUnderLimitsOfShapeDiscretePEmptyOfContainsZeroOfIsClosedUnderIsomorphisms", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.FiniteProducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.IsClosedUnderFiniteProducts.mk'", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.FiniteProducts", "is_tactic_proof": true, "tactics": ["have", "have", "have", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.ObjectProperty.FullSubcategory.category", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.FullSubcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.FullSubcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.ι", "kind": "definition", "module": "Mathlib.CategoryTheory.ObjectProperty.FullSubcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.ι_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.FullSubcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.ι_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.FullSubcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.prop_ι_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.FullSubcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.FullSubcategory.id_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.FullSubcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.FullSubcategory.comp_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.FullSubcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.homMk", "kind": "definition", "module": "Mathlib.CategoryTheory.ObjectProperty.FullSubcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.homMk_surjective", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.FullSubcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.fullyFaithfulι", "kind": "abbrev", "module": "Mathlib.CategoryTheory.ObjectProperty.FullSubcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.full_ι", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.FullSubcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.faithful_ι", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.FullSubcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.isoMk", "kind": "definition", "module": "Mathlib.CategoryTheory.ObjectProperty.FullSubcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.isoHom_inv_id_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.FullSubcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.isoInv_hom_id_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.FullSubcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.ιOfLE", "kind": "definition", "module": "Mathlib.CategoryTheory.ObjectProperty.FullSubcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.fullyFaithfulιOfLE", "kind": "definition", "module": "Mathlib.CategoryTheory.ObjectProperty.FullSubcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.full_ιOfLE", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.FullSubcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.faithful_ιOfLE", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.FullSubcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.ιOfLECompιIso", "kind": "definition", "module": "Mathlib.CategoryTheory.ObjectProperty.FullSubcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.lift", "kind": "definition", "module": "Mathlib.CategoryTheory.ObjectProperty.FullSubcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.liftCompιIso", "kind": "definition", "module": "Mathlib.CategoryTheory.ObjectProperty.FullSubcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.ι_obj_lift_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.FullSubcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.ι_obj_lift_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.FullSubcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instFaithfulFullSubcategoryLift", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.FullSubcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instFullFullSubcategoryLift", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.FullSubcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.liftCompιOfLEIso", "kind": "definition", "module": "Mathlib.CategoryTheory.ObjectProperty.FullSubcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.preservesLimit", "kind": "abbrev", "module": "Mathlib.CategoryTheory.ObjectProperty.FunctorCategory.PreservesLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.preservesLimit_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.FunctorCategory.PreservesLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.congr_preservesLimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.FunctorCategory.PreservesLimits", "is_tactic_proof": true, "tactics": ["ext", "simp_rw", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.ObjectProperty.preservesColimit", "kind": "abbrev", "module": "Mathlib.CategoryTheory.ObjectProperty.FunctorCategory.PreservesLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.preservesColimit_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.FunctorCategory.PreservesLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.congr_preservesColimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.FunctorCategory.PreservesLimits", "is_tactic_proof": true, "tactics": ["ext", "simp_rw", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.ObjectProperty.preservesLimitsOfShape", "kind": "abbrev", "module": "Mathlib.CategoryTheory.ObjectProperty.FunctorCategory.PreservesLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.preservesLimitsOfShape_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.FunctorCategory.PreservesLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.preservesLimitsOfShape_eq_iSup", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.FunctorCategory.PreservesLimits", "is_tactic_proof": true, "tactics": ["ext", "simp", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.ObjectProperty.congr_preservesLimitsOfShape", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.FunctorCategory.PreservesLimits", "is_tactic_proof": true, "tactics": ["ext", "simp", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.ObjectProperty.preservesColimitsOfShape", "kind": "abbrev", "module": "Mathlib.CategoryTheory.ObjectProperty.FunctorCategory.PreservesLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.preservesColimitsOfShape_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.FunctorCategory.PreservesLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.preservesColimitsOfShape_eq_iSup", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.FunctorCategory.PreservesLimits", "is_tactic_proof": true, "tactics": ["ext", "simp", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.ObjectProperty.congr_preservesColimitsOfShape", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.FunctorCategory.PreservesLimits", "is_tactic_proof": true, "tactics": ["ext", "simp", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.ObjectProperty.preservesFiniteLimits", "kind": "abbrev", "module": "Mathlib.CategoryTheory.ObjectProperty.FunctorCategory.PreservesLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.preservesFiniteLimits_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.FunctorCategory.PreservesLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.preservesFiniteColimits", "kind": "abbrev", "module": "Mathlib.CategoryTheory.ObjectProperty.FunctorCategory.PreservesLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.preservesFiniteColimits_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.FunctorCategory.PreservesLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instIsClosedUnderColimitsOfShapeFunctorPreservesLimitsOfShapeOfPreservesLimitsOfShapeColim", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.FunctorCategory.PreservesLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instIsClosedUnderColimitsOfShapeFunctorPreservesFiniteLimitsOfHasExactColimitsOfShape", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.FunctorCategory.PreservesLimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.HasCardinalLT", "kind": "abbrev", "module": "Mathlib.CategoryTheory.ObjectProperty.HasCardinalLT", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.hasCardinalLT_subtype_ofObj", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.HasCardinalLT", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.HasCardinalLT.iSup", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.HasCardinalLT", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.HasCardinalLT.sup", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.HasCardinalLT", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.ind", "kind": "definition", "module": "Mathlib.CategoryTheory.ObjectProperty.Ind", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.le_ind", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Ind", "is_tactic_proof": true, "tactics": ["intro", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.ObjectProperty.instIsClosedUnderIsomorphismsInd", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.Ind", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.ind_ind", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Ind", "is_tactic_proof": true, "tactics": ["refine", "choose", "have", "have", "exact", "simp"], "tactic_count": 6}
{"name": "CategoryTheory.ObjectProperty.of_essentiallySmall_index", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Ind", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.ind_iff_exists", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Ind", "is_tactic_proof": true, "tactics": ["refine", "have", "obtain", "exact", "let", "have", "obtain", "exact", "have", "have", "obtain", "have", "essentiallySmall_of_fully_faithful", "exact"], "tactic_count": 14}
{"name": "CategoryTheory.ObjectProperty.InheritedFromSource.instIsomorphismsOfIsClosedUnderIsomorphisms", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.InheritedFromHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.InheritedFromSource.op", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.InheritedFromHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.InheritedFromSource.instMin", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.InheritedFromHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.InheritedFromSource.of_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.InheritedFromHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.InheritedFromTarget.instIsomorphismsOfIsClosedUnderIsomorphisms", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.InheritedFromHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.InheritedFromTarget.op", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.InheritedFromHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.InheritedFromTarget.instMin", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.InheritedFromHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.InheritedFromTarget.of_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.InheritedFromHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.IsClosedUnderIsomorphisms.of_inheritedFromSource", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.InheritedFromHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.IsClosedUnderIsomorphisms.of_inheritedFromTarget", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.InheritedFromHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.limitsClosure", "kind": "inductive", "module": "Mathlib.CategoryTheory.ObjectProperty.LimitsClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.le_limitsClosure", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.LimitsClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instIsClosedUnderIsomorphismsLimitsClosure", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.LimitsClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instIsClosedUnderLimitsOfShapeLimitsClosure", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.LimitsClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.limitsClosure_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.LimitsClosure", "is_tactic_proof": true, "tactics": ["intro", "induction", "of_mem", "of_isoClosure", "of_limitPresentation"], "tactic_count": 5}
{"name": "CategoryTheory.ObjectProperty.limitsClosure_monotone", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.LimitsClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.limitsClosure_isoClosure", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.LimitsClosure", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.ObjectProperty.strictLimitsClosureStep", "kind": "definition", "module": "Mathlib.CategoryTheory.ObjectProperty.LimitsClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.le_strictLimitsClosureStep", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.LimitsClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.strictLimitsClosureStep_monotone", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.LimitsClosure", "is_tactic_proof": true, "tactics": ["dsimp", "simp", "exact", "le_iSup"], "tactic_count": 4}
{"name": "CategoryTheory.ObjectProperty.strictLimitsClosureIter", "kind": "abbrev", "module": "Mathlib.CategoryTheory.ObjectProperty.LimitsClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.le_strictLimitsClosureIter", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.LimitsClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.strictLimitsClosureIter_le_limitsClosure", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.LimitsClosure", "is_tactic_proof": true, "tactics": ["induction", "isMin", "obtain", "simp", "succ", "hb", "rw", "exact", "isSuccLimit", "hb", "simp", "intro", "exact"], "tactic_count": 13}
{"name": "CategoryTheory.ObjectProperty.instSmallStrictLimitsClosureIterOfLocallySmallOfSmallElemIio", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.LimitsClosure", "is_tactic_proof": false, "tactics": ["have", "small_of_injective", "induction", "isMin", "obtain", "simp", "infer_instance", "succ", "have", "rw", "infer_instance", "isSuccLimit", "simp", "have", "have", "exact", "infer_instance"], "tactic_count": 17}
{"name": "CategoryTheory.ObjectProperty.strictLimitsClosureStep_strictLimitsClosureIter_eq_self", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.LimitsClosure", "is_tactic_proof": true, "tactics": ["have", "have", "refine", "simp", "obtain", "exact", "simp", "prop_iSup_iff,", "choose", "obtain", "refine", "rw", "exact", "obtain", "exact", "refine", "monotone_transfiniteIterate", "dsimp", "rw", "simp", "exact", "monotone_transfiniteIterate"], "tactic_count": 22}
{"name": "CategoryTheory.ObjectProperty.isoClosure_strictLimitsClosureIter_eq_limitsClosure", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.LimitsClosure", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact", "have", "conv_rhs", "rw", "exact", "refine"], "tactic_count": 8}
{"name": "CategoryTheory.ObjectProperty.isEssentiallySmall_limitsClosure", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.LimitsClosure", "is_tactic_proof": true, "tactics": ["obtain", "have", "rw", "infer_instance", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.ObjectProperty.instEssentiallySmallLimitsClosureOfSmallOfLocallySmall", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.LimitsClosure", "is_tactic_proof": true, "tactics": ["obtain", "have", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.ObjectProperty.strictLimitsOfShape", "kind": "inductive", "module": "Mathlib.CategoryTheory.ObjectProperty.LimitsOfShape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.strictLimitsOfShape_monotone", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.LimitsOfShape", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.ObjectProperty.LimitOfShape.limit", "kind": "definition", "module": "Mathlib.CategoryTheory.ObjectProperty.LimitsOfShape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.LimitOfShape.ofIso", "kind": "definition", "module": "Mathlib.CategoryTheory.ObjectProperty.LimitsOfShape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.LimitOfShape.ofLE", "kind": "definition", "module": "Mathlib.CategoryTheory.ObjectProperty.LimitsOfShape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.LimitOfShape.reindex", "kind": "definition", "module": "Mathlib.CategoryTheory.ObjectProperty.LimitsOfShape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.LimitOfShape.toStructuredArrow", "kind": "definition", "module": "Mathlib.CategoryTheory.ObjectProperty.LimitsOfShape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.limitsOfShape", "kind": "definition", "module": "Mathlib.CategoryTheory.ObjectProperty.LimitsOfShape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.LimitOfShape.limitsOfShape", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.LimitsOfShape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.strictLimitsOfShape_le_limitsOfShape", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.LimitsOfShape", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.ObjectProperty.instIsClosedUnderIsomorphismsLimitsOfShape", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.LimitsOfShape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.isoClosure_strictLimitsOfShape", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.LimitsOfShape", "is_tactic_proof": true, "tactics": ["refine", "rw", "apply", "intro", "have", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.ObjectProperty.limitsOfShape_monotone", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.LimitsOfShape", "is_tactic_proof": true, "tactics": ["intro", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.ObjectProperty.limitsOfShape_isoClosure", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.LimitsOfShape", "is_tactic_proof": true, "tactics": ["refine", "intro", "choose", "exact", "prop_diag_obj"], "tactic_count": 5}
{"name": "CategoryTheory.ObjectProperty.instSmallStrictLimitsOfShapeOfSmallOfLocallySmall", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.LimitsOfShape", "is_tactic_proof": false, "tactics": ["refine", "small_of_surjective", "letI", "rintro", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.ObjectProperty.instEssentiallySmallLimitsOfShapeOfSmallOfSmallOfLocallySmall", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.LimitsOfShape", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.ObjectProperty.IsClosedUnderLimitsOfShape.mk'", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.LimitsOfShape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.LimitOfShape.prop", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.LimitsOfShape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.prop_of_isLimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.LimitsOfShape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.prop_limit", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.LimitsOfShape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.limitsOfShape_le_of_initial", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.LimitsOfShape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.limitsOfShape_congr", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.LimitsOfShape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.isClosedUnderLimitsOfShape_iff_of_equivalence", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.LimitsOfShape", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.ObjectProperty.IsClosedUnderLimitsOfShape.of_equivalence", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.LimitsOfShape", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "CategoryTheory.MorphismProperty.isLocal", "kind": "definition", "module": "Mathlib.CategoryTheory.ObjectProperty.Local", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.isLocal_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Local", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.isColocal", "kind": "definition", "module": "Mathlib.CategoryTheory.ObjectProperty.Local", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.isColocal_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Local", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instIsClosedUnderIsomorphismsIsLocal", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.Local", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instIsClosedUnderIsomorphismsIsColocal", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.Local", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instIsClosedUnderLimitsOfShapeIsLocal", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.Local", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instIsClosedUnderColimitsOfShapeIsColocal", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.Local", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.op", "kind": "definition", "module": "Mathlib.CategoryTheory.ObjectProperty.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.unop", "kind": "definition", "module": "Mathlib.CategoryTheory.ObjectProperty.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.op_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.unop_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.op_unop", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.unop_op", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.op_injective", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Opposite", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.ObjectProperty.unop_injective", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Opposite", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.ObjectProperty.op_injective_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.unop_injective_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.op_monotone", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.unop_monotone", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.op_monotone_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.unop_monotone_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.subtypeOpEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.ObjectProperty.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.op_ofObj", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Opposite", "is_tactic_proof": true, "tactics": ["ext", "simp", "constructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 7}
{"name": "CategoryTheory.ObjectProperty.unop_ofObj", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.op_singleton", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Opposite", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.ObjectProperty.unop_singleton", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Opposite", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.ObjectProperty.instIsClosedUnderIsomorphismsOppositeOp", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instIsClosedUnderIsomorphismsUnopOfOpposite", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.op_isoClosure", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Opposite", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.ObjectProperty.unop_isoClosure", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Opposite", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.ObjectProperty.rightOrthogonal", "kind": "definition", "module": "Mathlib.CategoryTheory.ObjectProperty.Orthogonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.rightOrthogonal_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Orthogonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.leftOrthogonal", "kind": "definition", "module": "Mathlib.CategoryTheory.ObjectProperty.Orthogonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.leftOrthogonal_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Orthogonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instIsClosedUnderIsomorphismsRightOrthogonal", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.Orthogonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instIsClosedUnderIsomorphismsLeftOrthogonal", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.Orthogonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instContainsZeroRightOrthogonalOfHasZeroObject", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.Orthogonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instContainsZeroLeftOrthogonalOfHasZeroObject", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.Orthogonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.prop_of_retract", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Retract", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.retractClosure", "kind": "definition", "module": "Mathlib.CategoryTheory.ObjectProperty.Retract", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.prop_retractClosure_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Retract", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "CategoryTheory.ObjectProperty.prop_retractClosure", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Retract", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.le_retractClosure", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Retract", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.monotone_retractClosure", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Retract", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.ObjectProperty.retractClosure_eq_self", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Retract", "is_tactic_proof": true, "tactics": ["apply", "intro", "exact", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.ObjectProperty.retractClosure_le_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Retract", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.retractClosure_isoClosure", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Retract", "is_tactic_proof": true, "tactics": ["refine", "rintro", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.ObjectProperty.instIsStableUnderRetractsRetractClosure", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.Retract", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instEssentiallySmallRetractClosureOfLocallySmall", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.Retract", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.shift", "kind": "definition", "module": "Mathlib.CategoryTheory.ObjectProperty.Shift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.prop_shift_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Shift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instIsClosedUnderIsomorphismsShift", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.Shift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.shift_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Shift", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.ObjectProperty.shift_shift", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Shift", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.ObjectProperty.le_shift", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Shift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instIsStableUnderShiftByIsoClosure", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.Shift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instIsStableUnderShiftByMin", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.Shift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instIsStableUnderShiftIsoClosure", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.Shift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instIsStableUnderShiftMin", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.Shift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.prop_shift_iff_of_isStableUnderShift", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Shift", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.ObjectProperty.hasShift", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.Shift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.commShiftι", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.Shift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instCommShiftFullSubcategoryLift", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.Shift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instCommShiftHomFunctorLiftCompιIso", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.Shift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instIsStableUnderShiftInverseImageOfIsClosedUnderIsomorphismsOfCommShift", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.Shift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instAdditiveFullSubcategoryShiftFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.ShiftAdditive", "is_tactic_proof": true, "tactics": ["have", "apply"], "tactic_count": 2}
{"name": "CategoryTheory.ObjectProperty.iff_of_presieve", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.SiteLocal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.IsLocal.mk_of_zeroHypercover", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.SiteLocal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.IsLocal.of_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.SiteLocal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.IsLocal.top", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.SiteLocal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.IsLocal.inf", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.SiteLocal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.of_zeroHypercover", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.SiteLocal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.iff_of_zeroHypercover", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.SiteLocal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.Small", "kind": "abbrev", "module": "Mathlib.CategoryTheory.ObjectProperty.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instSmallFullSubcategoryOfSmall", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.Small.of_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instSmallOppositeOp", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instSmallUnopOfOpposite", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.Small", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.ObjectProperty.instSmallOfObjOfSmall", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instSmallPair", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.Small", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.ObjectProperty.instSmallMin", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instSmallMin_1", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instSmallMax", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instSmallISupOfSmall", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.small_op_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.small_unop_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Small", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.ObjectProperty.instSmallOppositeOp_1", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.Small", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.ObjectProperty.instSmallUnopOfOpposite_1", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.Small", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.ObjectProperty.EssentiallySmall.exists_small_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Small", "is_tactic_proof": true, "tactics": ["obtain", "let", "have", "choose", "refine", "exact", "intro", "simp", "obtain", "exact", "intro", "obtain", "let", "exact"], "tactic_count": 14}
{"name": "CategoryTheory.ObjectProperty.instEssentiallySmallOfSmall", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instEssentiallySmallIsoClosure", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.EssentiallySmall.exists_small", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Small", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.ObjectProperty.EssentiallySmall.of_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instEssentiallySmallMax", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.Small", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "refine", "simp", "constructor", "exact", "exact"], "tactic_count": 7}
{"name": "CategoryTheory.ObjectProperty.instEssentiallySmallISupOfSmall", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.essentiallySmall_op_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Small", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact", "obtain", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.ObjectProperty.essentiallySmall_unop_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Small", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.ObjectProperty.instEssentiallySmallOppositeOp", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.Small", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.ObjectProperty.instEssentiallySmallUnopOfOpposite", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.Small", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.ObjectProperty.instEssentiallySmallFullSubcategoryOfLocallySmallOfEssentiallySmall", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.Small", "is_tactic_proof": true, "tactics": ["obtain", "have", "rw", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.ObjectProperty.instEssentiallySmallTopOfEssentiallySmall", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instSmallStrictMap", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instEssentiallySmallMap", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.Small", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.ObjectProperty.instEssentiallySmallFullSubcategoryOfLocallySmallOfEssentiallySmall_1", "kind": "instance", "module": "Mathlib.CategoryTheory.ObjectProperty.Small", "is_tactic_proof": true, "tactics": ["obtain", "have", "rw", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.ObjectProperty.exists_equivalence_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Small", "is_tactic_proof": true, "tactics": ["refine", "exact", "obtain", "rw", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.exists_equivalence_iff_of_locallySmall", "kind": "theorem", "module": "Mathlib.CategoryTheory.ObjectProperty.Small", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Quiver.Hom.op_inj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.Hom.unop_inj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.Hom.unop_op", "kind": "theorem", "module": "Mathlib.CategoryTheory.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.Hom.unop_op'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.Hom.op_unop", "kind": "theorem", "module": "Mathlib.CategoryTheory.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.Hom.unop_mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CategoryStruct.opposite", "kind": "instance", "module": "Mathlib.CategoryTheory.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.unop_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.op_id_unop", "kind": "theorem", "module": "Mathlib.CategoryTheory.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.op_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.op_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.unop_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.unop_id_op", "kind": "theorem", "module": "Mathlib.CategoryTheory.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.op_comp_unop", "kind": "theorem", "module": "Mathlib.CategoryTheory.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Category.opposite", "kind": "instance", "module": "Mathlib.CategoryTheory.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.op_comp_assoc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Opposites", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.unop_comp_assoc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Opposites", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.unopUnop", "kind": "definition", "module": "Mathlib.CategoryTheory.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.opOp", "kind": "definition", "module": "Mathlib.CategoryTheory.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.opOpEquivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instIsEquivalenceOppositeOpOp", "kind": "instance", "module": "Mathlib.CategoryTheory.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instIsEquivalenceOppositeUnopUnop", "kind": "instance", "module": "Mathlib.CategoryTheory.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isIso_op", "kind": "instance", "module": "Mathlib.CategoryTheory.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isIso_of_op", "kind": "theorem", "module": "Mathlib.CategoryTheory.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isIso_op_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isIso_unop_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Opposites", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.isIso_unop", "kind": "instance", "module": "Mathlib.CategoryTheory.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.op_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Opposites", "is_tactic_proof": true, "tactics": ["apply", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.unop_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Opposites", "is_tactic_proof": true, "tactics": ["apply", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.op", "kind": "definition", "module": "Mathlib.CategoryTheory.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.unop", "kind": "definition", "module": "Mathlib.CategoryTheory.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.opUnopIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.unopOpIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.opHom", "kind": "definition", "module": "Mathlib.CategoryTheory.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.opInv", "kind": "definition", "module": "Mathlib.CategoryTheory.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.opComp", "kind": "definition", "module": "Mathlib.CategoryTheory.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.unopComp", "kind": "definition", "module": "Mathlib.CategoryTheory.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.opId", "kind": "definition", "module": "Mathlib.CategoryTheory.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.unopId", "kind": "definition", "module": "Mathlib.CategoryTheory.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.leftOp", "kind": "definition", "module": "Mathlib.CategoryTheory.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.rightOp", "kind": "definition", "module": "Mathlib.CategoryTheory.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.rightOp_map_unop", "kind": "theorem", "module": "Mathlib.CategoryTheory.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instFullOppositeOp", "kind": "instance", "module": "Mathlib.CategoryTheory.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Functor.rightOp_faithful", "kind": "instance", "module": "Mathlib.CategoryTheory.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Functor.rightOp_full", "kind": "instance", "module": "Mathlib.CategoryTheory.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Functor.rightOpComp", "kind": "definition", "module": "Mathlib.CategoryTheory.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Functor.rightOpId", "kind": "definition", "module": "Mathlib.CategoryTheory.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.leftOpId", "kind": "definition", "module": "Mathlib.CategoryTheory.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.leftOpRightOpIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Functor.rightOp_leftOp_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Opposites", "is_tactic_proof": true, "tactics": ["cases", "rfl"], "tactic_count": 2}
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{"name": "CategoryTheory.NatTrans.unop_whiskerRight", "kind": "theorem", "module": "Mathlib.CategoryTheory.Opposites", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
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{"name": "CategoryTheory.NatTrans.removeOp", "kind": "definition", "module": "Mathlib.CategoryTheory.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.removeOp_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.NatTrans.removeUnop_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.leftOp", "kind": "definition", "module": "Mathlib.CategoryTheory.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.leftOp_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.NatTrans.leftOpWhiskerRight", "kind": "theorem", "module": "Mathlib.CategoryTheory.Opposites", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
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{"name": "CategoryTheory.NatTrans.removeLeftOp_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.NatTrans.rightOp_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.NatTrans.rightOpWhiskerRight", "kind": "theorem", "module": "Mathlib.CategoryTheory.Opposites", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
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{"name": "CategoryTheory.NatTrans.removeRightOp_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.NatIso.unop", "kind": "definition", "module": "Mathlib.CategoryTheory.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.decidableEqOfUnop", "kind": "instance", "module": "Mathlib.CategoryTheory.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isoOpEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.opUnopEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.leftOpRightOpEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.instIsEmptyDiscrete", "kind": "instance", "module": "Mathlib.CategoryTheory.PEmpty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.functorOfIsEmpty", "kind": "definition", "module": "Mathlib.CategoryTheory.PEmpty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isEmptyExt", "kind": "definition", "module": "Mathlib.CategoryTheory.PEmpty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.pathsHomRel", "kind": "definition", "module": "Mathlib.CategoryTheory.PathCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.toQuotientPaths", "kind": "definition", "module": "Mathlib.CategoryTheory.PathCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.quotientPathsTo", "kind": "definition", "module": "Mathlib.CategoryTheory.PathCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.quotientPathsEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.PathCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Paths.morphismProperty_eq_top", "kind": "theorem", "module": "Mathlib.CategoryTheory.PathCategory.MorphismProperty", "is_tactic_proof": true, "tactics": ["ext", "simp", "exact"], "tactic_count": 3}
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{"name": "CategoryTheory.Paths.liftNatIso", "kind": "definition", "module": "Mathlib.CategoryTheory.PathCategory.MorphismProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Pi.sumElimCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Pi.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Pi.isoMk", "kind": "definition", "module": "Mathlib.CategoryTheory.Pi.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pi.isoApp", "kind": "definition", "module": "Mathlib.CategoryTheory.Pi.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Functor.pi", "kind": "definition", "module": "Mathlib.CategoryTheory.Pi.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Functor.eqToHom_proj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Pi.Basic", "is_tactic_proof": true, "tactics": ["subst", "rfl"], "tactic_count": 2}
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{"name": "CategoryTheory.Functor.preservesFiniteCoproductsOfAdditive", "kind": "instance", "module": "Mathlib.CategoryTheory.Preadditive.AdditiveFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.AdditiveFunctor.of", "kind": "definition", "module": "Mathlib.CategoryTheory.Preadditive.AdditiveFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.AdditiveFunctor.of_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.AdditiveFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.AdditiveFunctor.forget_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.AdditiveFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.AdditiveFunctor.forget_obj_of", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.AdditiveFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.AdditiveFunctor.forget_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.AdditiveFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instAdditiveAdditiveFunctorFunctorForget", "kind": "instance", "module": "Mathlib.CategoryTheory.Preadditive.AdditiveFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instAdditiveObjFunctorAdditiveFunctor_1", "kind": "instance", "module": "Mathlib.CategoryTheory.Preadditive.AdditiveFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.leftExactFunctor_le_additiveFunctor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.AdditiveFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.rightExactFunctor_le_additiveFunctor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.AdditiveFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.exactFunctor_le_additiveFunctor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.AdditiveFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.AdditiveFunctor.ofLeftExact", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Preadditive.AdditiveFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.AdditiveFunctor.ofRightExact", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Preadditive.AdditiveFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.AdditiveFunctor.ofExact", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Preadditive.AdditiveFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.AdditiveFunctor.ofLeftExact_obj_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.AdditiveFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.AdditiveFunctor.ofRightExact_obj_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.AdditiveFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.AdditiveFunctor.ofExact_obj_fst", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.AdditiveFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.AdditiveFunctor.ofLeftExact_map_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.AdditiveFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.AdditiveFunctor.ofRightExact_map_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.AdditiveFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.AdditiveFunctor.ofExact_map_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.AdditiveFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.inducedCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.InducedCategory.homAddEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.fullSubcategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.instAddCommGroupEnd", "kind": "instance", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Preadditive.leftComp", "kind": "definition", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.rightComp", "kind": "definition", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.compHom", "kind": "definition", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.sub_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.comp_sub", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.neg_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.comp_neg", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.neg_comp_neg", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Preadditive.nsmul_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.comp_nsmul", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.zsmul_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.comp_zsmul", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.comp_sum", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.sum_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.sum_comp'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": true, "tactics": ["simp", "apply"], "tactic_count": 2}
{"name": "CategoryTheory.Preadditive.instEpiNegHom", "kind": "instance", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.instMonoNegHom", "kind": "instance", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.preadditiveHasZeroMorphisms", "kind": "instance", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.instSemiringEnd", "kind": "instance", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.instRingEnd", "kind": "instance", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.moduleEndRight", "kind": "instance", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.mono_of_cancel_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.mono_iff_cancel_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.mono_of_kernel_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.mono_of_isZero_kernel'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.mono_iff_isZero_kernel'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.mono_of_isZero_kernel", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.mono_iff_isZero_kernel", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.epi_of_cancel_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.epi_iff_cancel_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.epi_of_cokernel_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.epi_of_isZero_cokernel'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.epi_iff_isZero_cokernel'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.epi_of_isZero_cokernel", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.epi_iff_isZero_cokernel", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.IsIso.comp_left_eq_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Preadditive.IsIso.comp_right_eq_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Preadditive.mono_of_kernel_iso_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.epi_of_cokernel_iso_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.forkOfKernelFork", "kind": "definition", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.forkOfKernelFork_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.kernelForkOfFork", "kind": "definition", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.kernelForkOfFork_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.kernelForkOfFork_ofι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.isLimitForkOfKernelFork", "kind": "definition", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.isLimitForkOfKernelFork_lift", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.isLimitKernelForkOfFork", "kind": "definition", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.hasEqualizer_of_hasKernel", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.hasKernel_of_hasEqualizer", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.coforkOfCokernelCofork", "kind": "definition", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.coforkOfCokernelCofork_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.cokernelCoforkOfCofork", "kind": "definition", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.cokernelCoforkOfCofork_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.cokernelCoforkOfCofork_ofπ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.isColimitCoforkOfCokernelCofork", "kind": "definition", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.isColimitCoforkOfCokernelCofork_desc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.isColimitCokernelCoforkOfCofork", "kind": "definition", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.hasCoequalizer_of_hasCokernel", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.hasCokernel_of_hasCoequalizer", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.hasEqualizers_of_hasKernels", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.hasCoequalizers_of_hasCokernels", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.instSMulUnitsIntIso", "kind": "instance", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.smul_iso_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.smul_iso_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.instNegIso", "kind": "instance", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.neg_iso_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.neg_iso_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isBilimitOfTotal", "kind": "definition", "module": "Mathlib.CategoryTheory.Preadditive.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsBilimit.total", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.hasBiproduct_of_total", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isBilimitOfIsLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Preadditive.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biconeIsBilimitOfLimitConeOfIsLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Preadditive.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isBilimitOfIsColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Preadditive.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biconeIsBilimitOfColimitCoconeOfIsColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Preadditive.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.HasBiproduct.of_hasProduct", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Biproducts", "is_tactic_proof": true, "tactics": ["cases", "exact", "isBilimit"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.HasBiproduct.of_hasCoproduct", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Biproducts", "is_tactic_proof": true, "tactics": ["cases", "exact", "isBilimit"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.HasFiniteBiproducts.of_hasFiniteProducts", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.HasFiniteBiproducts.of_hasFiniteCoproducts", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biproduct.total", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.biproduct.lift_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Biproducts", "is_tactic_proof": true, "tactics": ["classical", "ext", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.biproduct.desc_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Biproducts", "is_tactic_proof": true, "tactics": ["classical", "ext", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.biproduct.lift_desc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Biproducts", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.biproduct.map_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Biproducts", "is_tactic_proof": true, "tactics": ["classical", "ext", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.biproduct.lift_matrix", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Biproducts", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.biproduct.matrix_desc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Biproducts", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.biproduct.matrix_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Biproducts", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
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{"name": "CategoryTheory.Limits.biproduct.reindex", "kind": "definition", "module": "Mathlib.CategoryTheory.Preadditive.Biproducts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.HomOrthogonal.matrixDecompositionAddEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Preadditive.HomOrthogonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HomOrthogonal.matrixDecomposition_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.HomOrthogonal", "is_tactic_proof": true, "tactics": ["ext", "simp", "simp", "split_ifs", "cases", "simp", "simp", "convert", "simpa"], "tactic_count": 9}
{"name": "CategoryTheory.HomOrthogonal.matrixDecomposition_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.HomOrthogonal", "is_tactic_proof": true, "tactics": ["ext", "simp", "simp", "conv_lhs", "simp", "apply", "simp", "intro", "simp", "simp", "convert", "convert", "convert", "convert", "simp"], "tactic_count": 15}
{"name": "CategoryTheory.HomOrthogonal.matrixDecompositionLinearEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Preadditive.HomOrthogonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HomOrthogonal.equiv_of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.HomOrthogonal", "is_tactic_proof": true, "tactics": ["classical", "refine", "intro", "apply", "apply", "cases", "simp", "exact", "rw", "simp)", "rw", "simp)"], "tactic_count": 12}
{"name": "CategoryTheory.instPreadditiveInd", "kind": "instance", "module": "Mathlib.CategoryTheory.Preadditive.Indization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instHasFiniteBiproductsInd", "kind": "instance", "module": "Mathlib.CategoryTheory.Preadditive.Indization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isInjective", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Preadditive.Injective.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.IsZero.injective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Injective.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Injective.factorThru", "kind": "definition", "module": "Mathlib.CategoryTheory.Preadditive.Injective.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Injective.comp_factorThru", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Injective.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Injective.zero_injective", "kind": "instance", "module": "Mathlib.CategoryTheory.Preadditive.Injective.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Injective.of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Injective.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Injective.iso_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Injective.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Injective.instOfNonempty", "kind": "instance", "module": "Mathlib.CategoryTheory.Preadditive.Injective.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Injective.Type.enoughInjectives", "kind": "instance", "module": "Mathlib.CategoryTheory.Preadditive.Injective.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Injective.instProd", "kind": "instance", "module": "Mathlib.CategoryTheory.Preadditive.Injective.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Injective.instPiObj", "kind": "instance", "module": "Mathlib.CategoryTheory.Preadditive.Injective.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Injective.instBiprod", "kind": "instance", "module": "Mathlib.CategoryTheory.Preadditive.Injective.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Injective.instBiproduct", "kind": "instance", "module": "Mathlib.CategoryTheory.Preadditive.Injective.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Injective.instUnopOfProjectiveOpposite", "kind": "instance", "module": "Mathlib.CategoryTheory.Preadditive.Injective.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Injective.instProjectiveUnopOfOpposite", "kind": "instance", "module": "Mathlib.CategoryTheory.Preadditive.Injective.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Injective.instProjectiveOppositeOp", "kind": "instance", "module": "Mathlib.CategoryTheory.Preadditive.Injective.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Injective.instOppositeOpOfProjective", "kind": "instance", "module": "Mathlib.CategoryTheory.Preadditive.Injective.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Injective.injective_iff_projective_op", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Injective.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Injective.projective_iff_injective_op", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Injective.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Injective.injective_iff_preservesEpimorphisms_yoneda_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Injective.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Injective.injective_of_adjoint", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Injective.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Injective.exists_presentation", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Injective.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "have", "exact", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.Injective.under", "kind": "definition", "module": "Mathlib.CategoryTheory.Preadditive.Injective.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Injective.injective_under", "kind": "instance", "module": "Mathlib.CategoryTheory.Preadditive.Injective.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Injective.ι", "kind": "definition", "module": "Mathlib.CategoryTheory.Preadditive.Injective.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Injective.ι_mono", "kind": "instance", "module": "Mathlib.CategoryTheory.Preadditive.Injective.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Injective.isZero_under", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Injective.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Injective.syzygies", "kind": "definition", "module": "Mathlib.CategoryTheory.Preadditive.Injective.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Injective.d", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Preadditive.Injective.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Injective.instEnoughProjectivesOppositeOfEnoughInjectives", "kind": "instance", "module": "Mathlib.CategoryTheory.Preadditive.Injective.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Injective.instEnoughInjectivesOppositeOfEnoughProjectives", "kind": "instance", "module": "Mathlib.CategoryTheory.Preadditive.Injective.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Injective.enoughProjectives_of_enoughInjectives_op", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Injective.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Injective.enoughInjectives_of_enoughProjectives_op", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Injective.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.map_injective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Injective.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.injective_of_map_injective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Injective.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Adjunction.injectivePresentationOfMap", "kind": "definition", "module": "Mathlib.CategoryTheory.Preadditive.Injective.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.injective_of_map_injective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Injective.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.EnoughInjectives.of_adjunction", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Injective.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.EnoughInjectives.of_equivalence", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Injective.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.map_injective_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Injective.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.injectivePresentationOfMapInjectivePresentation", "kind": "definition", "module": "Mathlib.CategoryTheory.Preadditive.Injective.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.enoughInjectives_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Injective.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Injective.hasLiftingProperty_of_isZero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Injective.LiftingProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.injective_iff_rlp_monomorphisms_of_isZero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Injective.LiftingProperties", "is_tactic_proof": true, "tactics": ["obtain", "constructor", "intro", "exact", "intro", "constructor", "intro", "have", "have", "exact"], "tactic_count": 10}
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{"name": "CategoryTheory.Functor.preservesInjectiveObjects_of_adjunction_of_preservesMonomorphisms", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Injective.Preserves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.preservesInjectiveObjects_of_isEquivalence", "kind": "instance", "module": "Mathlib.CategoryTheory.Preadditive.Injective.Preserves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.preservesMonomorphisms_of_adjunction_of_preservesInjectiveObjects", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Injective.Preserves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.InjectiveResolution.cocomplex_exactAt_succ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Injective.Resolution", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.InjectiveResolution.exact_succ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Injective.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.InjectiveResolution.ι_f_succ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Injective.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.InjectiveResolution.ι_f_zero_comp_complex_d", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Injective.Resolution", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.InjectiveResolution.complex_d_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Injective.Resolution", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.InjectiveResolution.kernelFork", "kind": "definition", "module": "Mathlib.CategoryTheory.Preadditive.Injective.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.InjectiveResolution.isLimitKernelFork", "kind": "definition", "module": "Mathlib.CategoryTheory.Preadditive.Injective.Resolution", "is_tactic_proof": true, "tactics": ["refine", "refine", "rw", "cancel_epi", "simp"], "tactic_count": 5}
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{"name": "CategoryTheory.InjectiveResolution.Hom.ι_comp_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Injective.Resolution", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.isLimitMapConeBinaryFanOfPreservesKernels", "kind": "definition", "module": "Mathlib.CategoryTheory.Preadditive.LeftExact", "is_tactic_proof": true, "tactics": ["let", "let", "let", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.Functor.preservesBinaryProduct_of_preservesKernels", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.LeftExact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.preservesBinaryProducts_of_preservesKernels", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.LeftExact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.preservesEqualizer_of_preservesKernels", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.LeftExact", "is_tactic_proof": true, "tactics": ["letI", "haveI", "constructor", "let", "dsimp", "let", "constructor", "apply", "apply", "let", "exact"], "tactic_count": 11}
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{"name": "CategoryTheory.Functor.isColimitMapCoconeBinaryCofanOfPreservesCokernels", "kind": "definition", "module": "Mathlib.CategoryTheory.Preadditive.LeftExact", "is_tactic_proof": true, "tactics": ["let", "let", "let", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.Functor.preservesCoproduct_of_preservesCokernels", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.LeftExact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.preservesBinaryCoproducts_of_preservesCokernels", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.LeftExact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.preservesCoequalizer_of_preservesCokernels", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.LeftExact", "is_tactic_proof": true, "tactics": ["letI", "haveI", "constructor", "intro", "let", "dsimp", "let", "constructor", "apply", "apply", "let", "parallelPair.ext", "exact"], "tactic_count": 13}
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{"name": "CategoryTheory.Functor.projective_obj_of_projective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Projective.Preserves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.preservesProjectiveObjects_comp", "kind": "instance", "module": "Mathlib.CategoryTheory.Preadditive.Projective.Preserves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.preservesProjectiveObjects_of_adjunction_of_preservesEpimorphisms", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Projective.Preserves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.preservesProjectiveObjects_of_isEquivalence", "kind": "instance", "module": "Mathlib.CategoryTheory.Preadditive.Projective.Preserves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.preservesEpimorphisms_of_adjunction_of_preservesProjectiveObjects", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Projective.Preserves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ProjectiveResolution.complex_exactAt_succ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Projective.Resolution", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.ProjectiveResolution.exact_succ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Projective.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ProjectiveResolution.π_f_succ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Projective.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ProjectiveResolution.complex_d_comp_π_f_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Projective.Resolution", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.ProjectiveResolution.complex_d_succ_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Projective.Resolution", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.ProjectiveResolution.cokernelCofork", "kind": "definition", "module": "Mathlib.CategoryTheory.Preadditive.Projective.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ProjectiveResolution.isColimitCokernelCofork", "kind": "definition", "module": "Mathlib.CategoryTheory.Preadditive.Projective.Resolution", "is_tactic_proof": true, "tactics": ["refine", "refine", "rw", "dsimp", "simp", "isoHomologyι_inv_hom_id,"], "tactic_count": 6}
{"name": "CategoryTheory.ProjectiveResolution.instEpiFNatπ", "kind": "instance", "module": "Mathlib.CategoryTheory.Preadditive.Projective.Resolution", "is_tactic_proof": true, "tactics": ["cases", "exact", "rw"], "tactic_count": 3}
{"name": "CategoryTheory.ProjectiveResolution.self", "kind": "definition", "module": "Mathlib.CategoryTheory.Preadditive.Projective.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ProjectiveResolution.Hom.hom_comp_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Projective.Resolution", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.mapProjectiveResolution", "kind": "definition", "module": "Mathlib.CategoryTheory.Preadditive.Projective.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.mono_of_nonzero_from_simple", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Schur", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isIso_of_hom_simple", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Schur", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isIso_iff_nonzero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Schur", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instDivisionRingEndOfHasKernelsOfSimple", "kind": "instance", "module": "Mathlib.CategoryTheory.Preadditive.Schur", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.finrank_hom_simple_simple_eq_zero_of_not_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Schur", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.finrank_endomorphism_eq_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Schur", "is_tactic_proof": true, "tactics": ["have", "refine", "intro", "have", "have", "obtain", "use", "rw", "exact"], "tactic_count": 9}
{"name": "CategoryTheory.finrank_endomorphism_simple_eq_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Schur", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.endomorphism_simple_eq_smul_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Schur", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.fieldEndOfFiniteDimensional", "kind": "definition", "module": "Mathlib.CategoryTheory.Preadditive.Schur", "is_tactic_proof": true, "tactics": ["classical", "exact", "mul_comm", "obtain", "obtain", "simp"], "tactic_count": 6}
{"name": "CategoryTheory.finrank_hom_simple_simple_le_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Schur", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact", "obtain", "haveI", "refine", "intro", "obtain", "exact"], "tactic_count": 9}
{"name": "CategoryTheory.finrank_hom_simple_simple_eq_one_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Schur", "is_tactic_proof": true, "tactics": ["fconstructor", "intro", "rw", "obtain", "rw", "exact", "rintro", "have", "have", "finrank_pos_iff_exists_ne_zero.mpr", "lia"], "tactic_count": 11}
{"name": "CategoryTheory.finrank_hom_simple_simple_eq_zero_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Schur", "is_tactic_proof": true, "tactics": ["rw", "have", "lia"], "tactic_count": 3}
{"name": "CategoryTheory.finrank_hom_simple_simple", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Schur", "is_tactic_proof": true, "tactics": ["split_ifs", "exact", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.instPreadditiveSingleObj", "kind": "instance", "module": "Mathlib.CategoryTheory.Preadditive.SingleObj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Preadditive.ofFullyFaithful", "kind": "definition", "module": "Mathlib.CategoryTheory.Preadditive.Transfer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.FullyFaithful.additive_ofFullyFaithful", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Transfer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.additive_inverse_of_FullyFaithful", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Transfer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.preadditiveYonedaObj", "kind": "definition", "module": "Mathlib.CategoryTheory.Preadditive.Yoneda.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.preadditiveYoneda", "kind": "definition", "module": "Mathlib.CategoryTheory.Preadditive.Yoneda.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.preadditiveCoyonedaObj", "kind": "definition", "module": "Mathlib.CategoryTheory.Preadditive.Yoneda.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.preadditiveCoyoneda", "kind": "definition", "module": "Mathlib.CategoryTheory.Preadditive.Yoneda.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.additive_yonedaObj", "kind": "instance", "module": "Mathlib.CategoryTheory.Preadditive.Yoneda.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.additive_yonedaObj'", "kind": "instance", "module": "Mathlib.CategoryTheory.Preadditive.Yoneda.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.additive_coyonedaObj", "kind": "instance", "module": "Mathlib.CategoryTheory.Preadditive.Yoneda.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.additive_coyonedaObj'", "kind": "instance", "module": "Mathlib.CategoryTheory.Preadditive.Yoneda.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.whiskering_preadditiveYoneda", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Yoneda.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.whiskering_preadditiveCoyoneda", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Yoneda.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.full_preadditiveYoneda", "kind": "instance", "module": "Mathlib.CategoryTheory.Preadditive.Yoneda.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.full_preadditiveCoyoneda", "kind": "instance", "module": "Mathlib.CategoryTheory.Preadditive.Yoneda.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.faithful_preadditiveYoneda", "kind": "instance", "module": "Mathlib.CategoryTheory.Preadditive.Yoneda.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.faithful_preadditiveCoyoneda", "kind": "instance", "module": "Mathlib.CategoryTheory.Preadditive.Yoneda.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.preadditiveYonedaMap", "kind": "definition", "module": "Mathlib.CategoryTheory.Preadditive.Yoneda.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGrpCat.preadditiveCoyonedaIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Preadditive.Yoneda.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Injective.injective_iff_preservesEpimorphisms_preadditiveYoneda_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Yoneda.Injective", "is_tactic_proof": true, "tactics": ["rw", "refine", "exact", "intro", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.Injective.injective_iff_preservesEpimorphisms_preadditive_yoneda_obj'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Yoneda.Injective", "is_tactic_proof": true, "tactics": ["rw", "refine", "exact", "intro", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.preservesLimits_preadditiveYonedaObj", "kind": "instance", "module": "Mathlib.CategoryTheory.Preadditive.Yoneda.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.preservesLimits_preadditiveCoyonedaObj", "kind": "instance", "module": "Mathlib.CategoryTheory.Preadditive.Yoneda.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.preservesLimits_preadditiveYoneda_obj", "kind": "instance", "module": "Mathlib.CategoryTheory.Preadditive.Yoneda.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.preservesLimits_preadditiveCoyoneda_obj", "kind": "instance", "module": "Mathlib.CategoryTheory.Preadditive.Yoneda.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Projective.projective_iff_preservesEpimorphisms_preadditiveCoyoneda_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Yoneda.Projective", "is_tactic_proof": true, "tactics": ["rw", "refine", "exact", "intro", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.Projective.projective_iff_preservesEpimorphisms_preadditiveCoyonedaObj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Preadditive.Yoneda.Projective", "is_tactic_proof": true, "tactics": ["rw", "refine", "exact", "intro", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.Adjunction.isCardinalPresentable_leftAdjoint_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.Adjunction", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Adjunction.isCardinalFilteredGenerator", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.hasCardinalFilteredGenerator", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.isCardinalLocallyPresentable", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.isCardinalAccessibleCategory", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.hasCardinalFilteredGenerator", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.isCardinalLocallyPresentable", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.isCardinalAccessibleCategory", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.isLocallyPresentable", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.Adjunction", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Equivalence.isAccessibleCategory", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.Adjunction", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.preservesColimitsOfShape_of_isCardinalAccessible", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.preservesColimitsOfShape_of_isCardinalAccessible_of_essentiallySmall", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.Basic", "is_tactic_proof": true, "tactics": ["have", "have", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Functor.isCardinalAccessible_of_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isCardinalAccessible_of_natIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instIsCardinalAccessibleId", "kind": "instance", "module": "Mathlib.CategoryTheory.Presentable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instIsCardinalAccessibleComp", "kind": "instance", "module": "Mathlib.CategoryTheory.Presentable.Basic", "is_tactic_proof": true, "tactics": ["have", "have", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Functor.instIsCardinalAccessibleOfPreservesColimitsOfSize", "kind": "instance", "module": "Mathlib.CategoryTheory.Presentable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instIsCardinalAccessibleObjConst", "kind": "instance", "module": "Mathlib.CategoryTheory.Presentable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isAccessible_of_isCardinalAccessible", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instIsAccessibleComp", "kind": "instance", "module": "Mathlib.CategoryTheory.Presentable.Basic", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "have", "have", "have", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.Functor.instIsAccessibleObjConst", "kind": "instance", "module": "Mathlib.CategoryTheory.Presentable.Basic", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.IsCardinalPresentable", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Presentable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isCardinalPresentable", "kind": "definition", "module": "Mathlib.CategoryTheory.Presentable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instIsCardinalPresentableObjIsCardinalPresentable", "kind": "instance", "module": "Mathlib.CategoryTheory.Presentable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instIsCardinalPresentableObjFullSubcategoryIsCardinalPresentableι", "kind": "instance", "module": "Mathlib.CategoryTheory.Presentable.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.isCardinalPresentable_iff_isCardinalAccessible_coyoneda_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isCardinalPresentable_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.preservesColimitsOfShape_of_isCardinalPresentable", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.preservesColimitsOfShape_of_isCardinalPresentable_of_essentiallySmall", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isCardinalPresentable_of_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isCardinalPresentable_monotone", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.Basic", "is_tactic_proof": true, "tactics": ["intro", "rw", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.isCardinalPresentable_of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instIsClosedUnderIsomorphismsIsCardinalPresentable", "kind": "instance", "module": "Mathlib.CategoryTheory.Presentable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isCardinalPresentable_of_equivalence", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.Basic", "is_tactic_proof": true, "tactics": ["refine", "have", "suffices", "have", "coyoneda.obj", "intro", "ext", "simp", "exact"], "tactic_count": 9}
{"name": "CategoryTheory.isCardinalPresentable_of_isEquivalence", "kind": "instance", "module": "Mathlib.CategoryTheory.Presentable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isCardinalPresentable_iff_of_isEquivalence", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.Basic", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "intro", "infer_instance"], "tactic_count": 5}
{"name": "CategoryTheory.IsCardinalPresentable.exists_hom_of_isColimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.Basic", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.IsCardinalPresentable.exists_eq_of_isColimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.Basic", "is_tactic_proof": true, "tactics": ["have", "have", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.IsCardinalPresentable.exists_eq_of_isColimit'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.Basic", "is_tactic_proof": true, "tactics": ["have", "have", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.isCardinalPresentable_iff_isCardinalAccessible_uliftCoyoneda_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.Basic", "is_tactic_proof": true, "tactics": ["change", "refine", "have", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.instIsCardinalAccessibleObjOppositeFunctorTypeUliftCoyonedaOpOfIsCardinalPresentable", "kind": "instance", "module": "Mathlib.CategoryTheory.Presentable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsPresentable", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Presentable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isPresentable_of_isCardinalPresentable", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instHasCardinalFilteredColimitsOfHasColimitsOfSize", "kind": "instance", "module": "Mathlib.CategoryTheory.Presentable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.ColimitPresentation.isCardinalPresentable", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.CardinalFilteredPresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.ColimitOfShape.isCardinalPresentable", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.CardinalFilteredPresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.IsCardinalFilteredGenerator.of_le_isoClosure", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.CardinalFilteredPresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.IsCardinalFilteredGenerator.isoClosure", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.CardinalFilteredPresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.IsCardinalFilteredGenerator.isoClosure_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.CardinalFilteredPresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.IsCardinalFilteredGenerator.presentable", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.CardinalFilteredPresentation", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "obtain", "exact", "have", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.ObjectProperty.IsCardinalFilteredGenerator.isStrongGenerator", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.CardinalFilteredPresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.IsCardinalFilteredGenerator.isPresentable_eq_retractClosure", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.CardinalFilteredPresentation", "is_tactic_proof": true, "tactics": ["refine", "rw", "obtain", "have", "obtain", "exact", "simpa"], "tactic_count": 7}
{"name": "CategoryTheory.ObjectProperty.IsCardinalFilteredGenerator.essentiallySmall_isPresentable", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.CardinalFilteredPresentation", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.ObjectProperty.IsCardinalFilteredGenerator.hasCardinalFilteredGenerator", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.CardinalFilteredPresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasCardinalFilteredGenerator.exists_small_generator", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.CardinalFilteredPresentation", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.instEssentiallySmallIsCardinalPresentableOfHasCardinalFilteredGenerator", "kind": "instance", "module": "Mathlib.CategoryTheory.Presentable.CardinalFilteredPresentation", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.ColimitPresentation.Total", "kind": "definition", "module": "Mathlib.CategoryTheory.Presentable.ColimitPresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.ColimitPresentation.Total.mk", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Presentable.ColimitPresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.ColimitPresentation.Total.Hom.comp", "kind": "definition", "module": "Mathlib.CategoryTheory.Presentable.ColimitPresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.ColimitPresentation.instCategoryTotal", "kind": "instance", "module": "Mathlib.CategoryTheory.Presentable.ColimitPresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.ColimitPresentation.instLocallySmallTotal", "kind": "instance", "module": "Mathlib.CategoryTheory.Presentable.ColimitPresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.ColimitPresentation.Total.exists_hom_of_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.ColimitPresentation", "is_tactic_proof": true, "tactics": ["obtain", "use"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.ColimitPresentation.instNonemptyTotalOfIsFiltered", "kind": "instance", "module": "Mathlib.CategoryTheory.Presentable.ColimitPresentation", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.ColimitPresentation.instIsFilteredTotalOfIsFinitelyPresentableObjDiag", "kind": "instance", "module": "Mathlib.CategoryTheory.Presentable.ColimitPresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.ColimitPresentation.bind", "kind": "definition", "module": "Mathlib.CategoryTheory.Presentable.ColimitPresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isCardinalFilteredGenerator_isCardinalPresentable", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.Dense", "is_tactic_proof": true, "tactics": ["obtain", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.IsCardinalAccessibleCategory.final_toCostructuredArrow", "kind": "instance", "module": "Mathlib.CategoryTheory.Presentable.Dense", "is_tactic_proof": true, "tactics": ["have", "rw", "refine", "obtain", "exact", "obtain", "exact"], "tactic_count": 7}
{"name": "CategoryTheory.IsCardinalAccessibleCategory.instIsDenseFullSubcategoryIsCardinalPresentableι", "kind": "instance", "module": "Mathlib.CategoryTheory.Presentable.Dense", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsCardinalAccessibleCategory.instIsCardinalFilteredCostructuredArrowFullSubcategoryIsCardinalPresentableι", "kind": "instance", "module": "Mathlib.CategoryTheory.Presentable.Dense", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.IsFinitelyAccessibleCategory.instIsFilteredCostructuredArrowFullSubcategoryIsFinitelyPresentableι", "kind": "instance", "module": "Mathlib.CategoryTheory.Presentable.Dense", "is_tactic_proof": false, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.IsFinitelyAccessibleCategory.instIsDenseFullSubcategoryIsFinitelyPresentableι", "kind": "instance", "module": "Mathlib.CategoryTheory.Presentable.Dense", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.IsFinitelyAccessibleCategory.instEssentiallySmallIsFinitelyPresentable", "kind": "instance", "module": "Mathlib.CategoryTheory.Presentable.Dense", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.Diagram.IsTerminal.prop", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.Directed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.Diagram.IsTerminal.lift_self", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.Directed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.Diagram.IsTerminal.instSubsingleton", "kind": "instance", "module": "Mathlib.CategoryTheory.Presentable.Directed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.Diagram.IsTerminal.ofExistsUnique", "kind": "definition", "module": "Mathlib.CategoryTheory.Presentable.Directed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.DiagramWithUniqueTerminal.ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.Directed", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "obtain", "obtain", "obtain", "rfl"], "tactic_count": 6}
{"name": "CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.instPartialOrderDiagramWithUniqueTerminal", "kind": "instance", "module": "Mathlib.CategoryTheory.Presentable.Directed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.functorMap", "kind": "definition", "module": "Mathlib.CategoryTheory.Presentable.Directed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.functorMap_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.Directed", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.functorMap_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.Directed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.functor", "kind": "definition", "module": "Mathlib.CategoryTheory.Presentable.Directed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.Diagram.single", "kind": "definition", "module": "Mathlib.CategoryTheory.Presentable.Directed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.instFiniteSubtypePSingle", "kind": "instance", "module": "Mathlib.CategoryTheory.Presentable.Directed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.DiagramWithUniqueTerminal.single", "kind": "definition", "module": "Mathlib.CategoryTheory.Presentable.Directed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.Diagram.iSup", "kind": "definition", "module": "Mathlib.CategoryTheory.Presentable.Directed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.Diagram.sup", "kind": "definition", "module": "Mathlib.CategoryTheory.Presentable.Directed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.isCardinalFiltered_aux", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.Directed", "is_tactic_proof": true, "tactics": ["choose", "let", "let", "let", "let", "let", "fst", "snd", "let", "right", "fst", "snd", "have", "have", "have", "hasCardinalLT_prod", "refine", "rintro", "rw", "dsimp", "obtain", "obtain", "obtain", "rfl", "have", "have", "rw", "hasCardinalLT_sum_iff", "hasCardinalLT_sum_iff", "refine", "let", "exact", "simpa"], "tactic_count": 33}
{"name": "CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.D₁", "kind": "definition", "module": "Mathlib.CategoryTheory.Presentable.Directed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.D₂", "kind": "definition", "module": "Mathlib.CategoryTheory.Presentable.Directed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.eq_id_of_D₂_W", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.Directed", "is_tactic_proof": true, "tactics": ["simp", "obtain", "simp", "obtain", "exact", "rfl", "rw", "obtain", "obtain", "exact"], "tactic_count": 10}
{"name": "CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.isCardinalFiltered", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.Directed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.D₃", "kind": "definition", "module": "Mathlib.CategoryTheory.Presentable.Directed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.D₄", "kind": "definition", "module": "Mathlib.CategoryTheory.Presentable.Directed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.final_functor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.Directed", "is_tactic_proof": true, "tactics": ["have", "have", "have", "rw", "refine", "obtain", "obtain", "have", "let", "have", "obtain", "exact", "exact", "rfl", "have", "obtain", "exact", "rfl", "rw", "obtain", "obtain", "exact", "let", "rintro", "exact", "exact", "rintro", "obtain", "obtain", "rfl", "rw", "rintro", "exact", "exact", "exact", "have", "let", "top", "isTerminal", "uniq_terminal", "hj", "obtain", "exact", "rfl", "exact", "simpa"], "tactic_count": 46}
{"name": "CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.aux", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.Directed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsCardinalFiltered.exists_cardinal_directed", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.Directed", "is_tactic_proof": true, "tactics": ["have", "obtain", "exists_cardinal_directed.aux", "have", "exact", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.IsFiltered.exists_directed", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.Directed", "is_tactic_proof": true, "tactics": ["have", "obtain", "have", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.ObjectProperty.IsCardinalFilteredGenerator.essentiallyLarge_top", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.EssentiallyLarge", "is_tactic_proof": true, "tactics": ["let", "let", "let", "refine", "obtain", "let", "let", "have", "have", "let", "exact"], "tactic_count": 11}
{"name": "CategoryTheory.HasCardinalFilteredGenerator.exists_equivalence", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.EssentiallyLarge", "is_tactic_proof": true, "tactics": ["rw", "obtain", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Functor.IsFinitelyAccessible", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Presentable.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsFinitelyAccessible_iff_preservesFilteredColimitsOfSize", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.Finite", "is_tactic_proof": true, "tactics": ["refine"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.isFinitelyAccessible_iff_preservesFilteredColimits", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsFinitelyPresentable", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Presentable.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.isFinitelyPresentable", "kind": "definition", "module": "Mathlib.CategoryTheory.Presentable.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.isFinitelyPresentable_eq_isCardinalPresentable", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.isFinitelyPresentable", "kind": "definition", "module": "Mathlib.CategoryTheory.Presentable.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isFinitelyPresentable_iff_preservesFilteredColimitsOfSize", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isFinitelyPresentable_iff_preservesFilteredColimits", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instPreservesFilteredColimitsOfSizeObjOppositeFunctorTypeCoyonedaOpOfIsFinitelyPresentable", "kind": "instance", "module": "Mathlib.CategoryTheory.Presentable.Finite", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.instIsFinitelyPresentableObjFullSubcategoryIsFinitelyPresentableι", "kind": "instance", "module": "Mathlib.CategoryTheory.Presentable.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsFinitelyPresentable.exists_hom_of_isColimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsFinitelyPresentable.exists_eq_of_isColimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsFinitelyPresentable.exists_hom_of_isColimit_under", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasCardinalFilteredColimits_iff_hasFilteredColimitsOfSize", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.Finite", "is_tactic_proof": true, "tactics": ["refine"], "tactic_count": 1}
{"name": "CategoryTheory.HasCardinalFilteredColimits_iff_hasFilteredColimits", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.hasCardinalLT_arrow_walkingParallelFamily", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.IsCardinalFiltered", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.IsCardinalFiltered.cocone", "kind": "definition", "module": "Mathlib.CategoryTheory.Presentable.IsCardinalFiltered", "is_tactic_proof": true, "tactics": ["have", "have", "have", "let", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.IsCardinalFiltered.of_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.IsCardinalFiltered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsCardinalFiltered.of_equivalence", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.IsCardinalFiltered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsCardinalFiltered.max", "kind": "definition", "module": "Mathlib.CategoryTheory.Presentable.IsCardinalFiltered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsCardinalFiltered.toMax", "kind": "definition", "module": "Mathlib.CategoryTheory.Presentable.IsCardinalFiltered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsCardinalFiltered.coeq", "kind": "definition", "module": "Mathlib.CategoryTheory.Presentable.IsCardinalFiltered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsCardinalFiltered.coeqHom", "kind": "definition", "module": "Mathlib.CategoryTheory.Presentable.IsCardinalFiltered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsCardinalFiltered.toCoeq", "kind": "definition", "module": "Mathlib.CategoryTheory.Presentable.IsCardinalFiltered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsCardinalFiltered.coeq_condition", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.IsCardinalFiltered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsCardinalFiltered.wideSpan", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.IsCardinalFiltered", "is_tactic_proof": true, "tactics": ["let", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.isFiltered_of_isCardinalFiltered", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.IsCardinalFiltered", "is_tactic_proof": true, "tactics": ["rw", "intro", "have", "refine", "simp", "infer_instance", "exact"], "tactic_count": 7}
{"name": "CategoryTheory.IsCardinalFiltered.nonempty", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.IsCardinalFiltered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isCardinalFiltered_aleph0_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.IsCardinalFiltered", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "intro", "constructor", "intro", "rw", "have", "exact"], "tactic_count": 9}
{"name": "CategoryTheory.isCardinalFiltered_preorder", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.IsCardinalFiltered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instIsCardinalFilteredToTypeOrd", "kind": "instance", "module": "Mathlib.CategoryTheory.Presentable.IsCardinalFiltered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isCardinalFiltered_under", "kind": "instance", "module": "Mathlib.CategoryTheory.Presentable.IsCardinalFiltered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isCardinalFiltered_prod", "kind": "instance", "module": "Mathlib.CategoryTheory.Presentable.IsCardinalFiltered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isCardinalFiltered_pi", "kind": "instance", "module": "Mathlib.CategoryTheory.Presentable.IsCardinalFiltered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isCardinalFiltered_iff_aux₁", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.IsCardinalFiltered", "is_tactic_proof": true, "tactics": ["obtain", "let", "obtain", "exact"], "tactic_count": 4}
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{"name": "CategoryTheory.IsCardinalFiltered.multicoequalizer", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.IsCardinalFiltered", "is_tactic_proof": true, "tactics": ["have", "obtain", "exact"], "tactic_count": 3}
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{"name": "CategoryTheory.Limits.IsTerminal.isCardinalFiltered", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.IsCardinalFiltered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isCardinalFiltered_of_hasTerminal", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.IsCardinalFiltered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.Accessible.Limits.isColimitMapCocone.surjective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.Limits", "is_tactic_proof": true, "tactics": ["have", "obtain", "obtain", "have", "let", "let", "have", "exact", "rw", "obtain", "have", "dsimp", "simpa", "let", "let", "have", "obtain", "let", "let", "refine", "simpa", "exact", "let", "property", "φ", "dsimp", "rw", "refine", "apply", "rw", "ext", "have", "have", "dsimp", "rw"], "tactic_count": 35}
{"name": "CategoryTheory.Functor.Accessible.Limits.isColimitMapCocone.injective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.Limits", "is_tactic_proof": true, "tactics": ["have", "let", "let", "have", "have", "have", "simp", "dsimp", "simp", "let", "let", "have", "have", "let", "refine", "apply", "ext", "simp", "have", "have", "dsimp", "simp"], "tactic_count": 22}
{"name": "CategoryTheory.Functor.Accessible.Limits.isColimitMapCocone", "kind": "definition", "module": "Mathlib.CategoryTheory.Presentable.Limits", "is_tactic_proof": true, "tactics": ["have", "apply", "exact", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.Functor.isCardinalAccessible_of_isLimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isCardinalPresentable_of_isColimit'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.Limits", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.isCardinalPresentable_of_isColimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.Limits", "is_tactic_proof": true, "tactics": ["let", "have", "rw", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.isClosedUnderColimitsOfShape_isCardinalPresentable", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory._example", "kind": "example", "module": "Mathlib.CategoryTheory.Presentable.LocallyPresentable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instIsCardinalAccessibleCategoryOfIsCardinalLocallyPresentable", "kind": "instance", "module": "Mathlib.CategoryTheory.Presentable.LocallyPresentable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory._example", "kind": "example", "module": "Mathlib.CategoryTheory.Presentable.LocallyPresentable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsLocallyFinitelyPresentable", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Presentable.LocallyPresentable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsFinitelyAccessibleCategory", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Presentable.LocallyPresentable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instIsAccessibleCategoryOfIsLocallyPresentable", "kind": "instance", "module": "Mathlib.CategoryTheory.Presentable.LocallyPresentable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instIsPresentableOfIsAccessibleCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Presentable.LocallyPresentable", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "apply"], "tactic_count": 3}
{"name": "CategoryTheory._example", "kind": "example", "module": "Mathlib.CategoryTheory.Presentable.LocallyPresentable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.isClosedUnderColimitsOfShape_isLocal", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.OrthogonalReflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.isCardinalAccessible_ι_isLocal", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.OrthogonalReflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OrthogonalReflection.D₁", "kind": "definition", "module": "Mathlib.CategoryTheory.Presentable.OrthogonalReflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OrthogonalReflection.instSmallD₁OfIsSmallOfLocallySmall", "kind": "instance", "module": "Mathlib.CategoryTheory.Presentable.OrthogonalReflection", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.OrthogonalReflection.D₁.hasCoproductsOfShape", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.OrthogonalReflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OrthogonalReflection.D₁.obj₁", "kind": "definition", "module": "Mathlib.CategoryTheory.Presentable.OrthogonalReflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OrthogonalReflection.D₁.obj₂", "kind": "definition", "module": "Mathlib.CategoryTheory.Presentable.OrthogonalReflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OrthogonalReflection.D₁.l", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Presentable.OrthogonalReflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OrthogonalReflection.D₁.ιLeft", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Presentable.OrthogonalReflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OrthogonalReflection.D₁.ιLeft_comp_l", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.OrthogonalReflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OrthogonalReflection.D₁.t", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Presentable.OrthogonalReflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OrthogonalReflection.D₁.ιRight", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Presentable.OrthogonalReflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OrthogonalReflection.D₁.ι_comp_t", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.OrthogonalReflection", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.OrthogonalReflection.D₁.ιLeft_comp_t", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.OrthogonalReflection", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.OrthogonalReflection.step", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Presentable.OrthogonalReflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OrthogonalReflection.toStep", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Presentable.OrthogonalReflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OrthogonalReflection.D₂", "kind": "definition", "module": "Mathlib.CategoryTheory.Presentable.OrthogonalReflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OrthogonalReflection.D₂.multispanShape", "kind": "definition", "module": "Mathlib.CategoryTheory.Presentable.OrthogonalReflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OrthogonalReflection.instSmallD₂", "kind": "instance", "module": "Mathlib.CategoryTheory.Presentable.OrthogonalReflection", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.OrthogonalReflection.instSmallLMultispanShape", "kind": "instance", "module": "Mathlib.CategoryTheory.Presentable.OrthogonalReflection", "is_tactic_proof": true, "tactics": ["dsimp"], "tactic_count": 1}
{"name": "CategoryTheory.OrthogonalReflection.D₂.hasColimitsOfShape", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.OrthogonalReflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OrthogonalReflection.D₂.multispanIndex", "kind": "definition", "module": "Mathlib.CategoryTheory.Presentable.OrthogonalReflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OrthogonalReflection.succ", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Presentable.OrthogonalReflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OrthogonalReflection.fromStep", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Presentable.OrthogonalReflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OrthogonalReflection.D₂.condition", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.OrthogonalReflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OrthogonalReflection.toSucc", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Presentable.OrthogonalReflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OrthogonalReflection.toSucc_injectivity", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.OrthogonalReflection", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.OrthogonalReflection.toSucc_surjectivity", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.OrthogonalReflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OrthogonalReflection.isLocal_isLocal_toSucc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.OrthogonalReflection", "is_tactic_proof": true, "tactics": ["refine", "ext", "simp", "dsimp", "ext", "apply", "simp", "exact", "choose", "exact"], "tactic_count": 10}
{"name": "CategoryTheory.OrthogonalReflection.isIso_toSucc_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.OrthogonalReflection", "is_tactic_proof": true, "tactics": ["refine", "refine", "simpa", "have", "simp", "exact", "simp", "obtain", "dsimp", "refine", "ext", "dsimp", "ext", "simp", "simp", "refine", "rw", "simp"], "tactic_count": 18}
{"name": "CategoryTheory.OrthogonalReflection.succStruct", "kind": "definition", "module": "Mathlib.CategoryTheory.Presentable.OrthogonalReflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OrthogonalReflection.reflectionObj", "kind": "definition", "module": "Mathlib.CategoryTheory.Presentable.OrthogonalReflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OrthogonalReflection.reflection", "kind": "definition", "module": "Mathlib.CategoryTheory.Presentable.OrthogonalReflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OrthogonalReflection.transfiniteCompositionOfShapeReflection", "kind": "definition", "module": "Mathlib.CategoryTheory.Presentable.OrthogonalReflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OrthogonalReflection.iteration", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Presentable.OrthogonalReflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OrthogonalReflection.iterationObjSuccIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Presentable.OrthogonalReflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OrthogonalReflection.iteration_map_succ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.OrthogonalReflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OrthogonalReflection.iteration_map_succ_injectivity", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.OrthogonalReflection", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.OrthogonalReflection.iteration_map_succ_surjectivity", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.OrthogonalReflection", "is_tactic_proof": true, "tactics": ["simp", "obtain", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.OrthogonalReflection.isLocal_isLocal_reflection", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.OrthogonalReflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OrthogonalReflection.isLocal_reflectionObj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.OrthogonalReflection", "is_tactic_proof": true, "tactics": ["let", "intro", "obtain", "refine", "obtain", "obtain", "obtain", "exact", "dsimp", "obtain", "have", "simp", "have", "simp", "simp", "rw", "obtain", "obtain", "exact"], "tactic_count": 19}
{"name": "CategoryTheory.OrthogonalReflection.corepresentableBy", "kind": "definition", "module": "Mathlib.CategoryTheory.Presentable.OrthogonalReflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OrthogonalReflection.isRightAdjoint_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.OrthogonalReflection", "is_tactic_proof": true, "tactics": ["rw", "ext", "simpa"], "tactic_count": 3}
{"name": "CategoryTheory.MorphismProperty.isRightAdjoint_ι_isLocal", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.OrthogonalReflection", "is_tactic_proof": true, "tactics": ["let", "have", "have", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.MorphismProperty.isLocallyPresentable_isLocal", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.OrthogonalReflection", "is_tactic_proof": true, "tactics": ["have", "have", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Presheaf.instIsCardinalPresentableFunctorOppositeFreeYonedaOfHasColimitsOfSize", "kind": "instance", "module": "Mathlib.CategoryTheory.Presentable.Presheaf", "is_tactic_proof": false, "tactics": ["let", "constructor", "intro", "have", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.Presheaf.instIsCardinalPresentableFunctorOppositeTypeObjUliftYonedaOfHasColimitsOfSize", "kind": "instance", "module": "Mathlib.CategoryTheory.Presentable.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.isStrongGenerator", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.Presheaf", "is_tactic_proof": true, "tactics": ["rw", "obtain", "refine", "rw", "rintro", "refine", "obtain", "obtain", "hi", "exact"], "tactic_count": 10}
{"name": "CategoryTheory.Presheaf.instIsCardinalLocallyPresentableFunctorOppositeOfHasPullbacks", "kind": "instance", "module": "Mathlib.CategoryTheory.Presentable.Presheaf", "is_tactic_proof": true, "tactics": ["have", "obtain", "rw", "refine", "rintro", "have", "rw", "infer_instance"], "tactic_count": 8}
{"name": "CategoryTheory.Presheaf.instIsLocallyPresentableFunctorOppositeOfHasPullbacks", "kind": "instance", "module": "Mathlib.CategoryTheory.Presentable.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Retract.isCardinalPresentable", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.Retracts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instIsStableUnderRetractsIsCardinalPresentable", "kind": "instance", "module": "Mathlib.CategoryTheory.Presentable.Retracts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsCardinalFilteredGenerator.of_isDense", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.StrongGenerator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsCardinalFilteredGenerator.of_isDense_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.StrongGenerator", "is_tactic_proof": true, "tactics": ["rw", "have", "simpa"], "tactic_count": 3}
{"name": "CategoryTheory.ObjectProperty.isCardinalFiltered_costructuredArrow_colimitsCardinalClosure_ι", "kind": "instance", "module": "Mathlib.CategoryTheory.Presentable.StrongGenerator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.isFiltered_costructuredArrow_colimitsCardinalClosure_ι", "kind": "instance", "module": "Mathlib.CategoryTheory.Presentable.StrongGenerator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.IsStrongGenerator.isDense_colimitsCardinalClosure_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.StrongGenerator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.colimitsCardinalClosure_le_isCardinalPresentable", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.StrongGenerator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsStrongGenerator.colimitsCardinalClosure_eq_isCardinalPresentable", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.StrongGenerator", "is_tactic_proof": true, "tactics": ["refine", "have", "intro", "rw", "rw", "obtain", "exact"], "tactic_count": 7}
{"name": "CategoryTheory.IsCardinalLocallyPresentable.iff_exists_isStrongGenerator", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.StrongGenerator", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact", "have", "have", "exists_generator", "constructor"], "tactic_count": 7}
{"name": "CategoryTheory.IsCardinalLocallyPresentable.of_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.StrongGenerator", "is_tactic_proof": true, "tactics": ["rw", "obtain", "exact"], "tactic_count": 3}
{"name": "HasCardinalLT.isCardinalPresentable", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.Type", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasCardinalLT.Set", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Presentable.Type", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasCardinalLT.Set.instIsCardinalFiltered", "kind": "instance", "module": "Mathlib.CategoryTheory.Presentable.Type", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasCardinalLT.Set.instIsFilteredOfFactIsRegular", "kind": "instance", "module": "Mathlib.CategoryTheory.Presentable.Type", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasCardinalLT.Set.isFiltered_of_aleph0_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.Type", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasCardinalLT.Set.functor", "kind": "definition", "module": "Mathlib.CategoryTheory.Presentable.Type", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasCardinalLT.Set.cocone", "kind": "definition", "module": "Mathlib.CategoryTheory.Presentable.Type", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasCardinalLT.Set.isColimitCocone", "kind": "definition", "module": "Mathlib.CategoryTheory.Presentable.Type", "is_tactic_proof": true, "tactics": ["have", "refine", "exact", "rintro", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.Types.isCardinalPresentable_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Presentable.Type", "is_tactic_proof": true, "tactics": ["refine", "have", "obtain", "obtain", "ext", "have", "dsimp", "rw", "simp", "exact"], "tactic_count": 10}
{"name": "CategoryTheory.Types.instIsPresentable", "kind": "instance", "module": "Mathlib.CategoryTheory.Presentable.Type", "is_tactic_proof": true, "tactics": ["obtain", "have", "have", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.prod.associator", "kind": "definition", "module": "Mathlib.CategoryTheory.Products.Associator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.prod.inverseAssociator", "kind": "definition", "module": "Mathlib.CategoryTheory.Products.Associator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.prod.associativity", "kind": "definition", "module": "Mathlib.CategoryTheory.Products.Associator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.prod.associatorIsEquivalence", "kind": "instance", "module": "Mathlib.CategoryTheory.Products.Associator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.prod.inverseAssociatorIsEquivalence", "kind": "instance", "module": "Mathlib.CategoryTheory.Products.Associator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.prod.prodFunctorToFunctorProdAssociator", "kind": "definition", "module": "Mathlib.CategoryTheory.Products.Associator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.prod.functorProdToProdFunctorAssociator", "kind": "definition", "module": "Mathlib.CategoryTheory.Products.Associator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.prod", "kind": "instance", "module": "Mathlib.CategoryTheory.Products.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Prod.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Products.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Prod.mkHom", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Products.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Prod.term_×ₘ_", "kind": "definition", "module": "Mathlib.CategoryTheory.Products.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Prod._aux_Mathlib_CategoryTheory_Products_Basic___macroRules_CategoryTheory_Prod_term_×ₘ__1", "kind": "definition", "module": "Mathlib.CategoryTheory.Products.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Prod._aux_Mathlib_CategoryTheory_Products_Basic___unexpand_CategoryTheory_Prod_mkHom_1", "kind": "definition", "module": "Mathlib.CategoryTheory.Products.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Prod.mkHom_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Products.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.prod_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Products.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.prod_id'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Products.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.prod_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Products.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.prod'", "kind": "instance", "module": "Mathlib.CategoryTheory.Products.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isIso_prod_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Products.Basic", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "rcases", "rcases", "exact", "rintro", "dsimp", "refine"], "tactic_count": 8}
{"name": "CategoryTheory.prod.etaIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Products.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.prod", "kind": "definition", "module": "Mathlib.CategoryTheory.Products.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.uniformProd", "kind": "instance", "module": "Mathlib.CategoryTheory.Products.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Prod.sectL", "kind": "definition", "module": "Mathlib.CategoryTheory.Products.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Prod.sectR", "kind": "definition", "module": "Mathlib.CategoryTheory.Products.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Prod.fst", "kind": "definition", "module": "Mathlib.CategoryTheory.Products.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Prod.snd", "kind": "definition", "module": "Mathlib.CategoryTheory.Products.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Prod.swap", "kind": "definition", "module": "Mathlib.CategoryTheory.Products.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Prod.symmetry", "kind": "definition", "module": "Mathlib.CategoryTheory.Products.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Prod.braiding", "kind": "definition", "module": "Mathlib.CategoryTheory.Products.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Prod.swapIsEquivalence", "kind": "instance", "module": "Mathlib.CategoryTheory.Products.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Prod.fac", "kind": "theorem", "module": "Mathlib.CategoryTheory.Products.Basic", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
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{"name": "CategoryTheory.evaluation", "kind": "definition", "module": "Mathlib.CategoryTheory.Products.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.evaluationUncurried", "kind": "definition", "module": "Mathlib.CategoryTheory.Products.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.constCompEvaluationObj", "kind": "definition", "module": "Mathlib.CategoryTheory.Products.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.prod", "kind": "definition", "module": "Mathlib.CategoryTheory.Products.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.prod'", "kind": "definition", "module": "Mathlib.CategoryTheory.Products.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.prod'CompFst", "kind": "definition", "module": "Mathlib.CategoryTheory.Products.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.prod'CompSnd", "kind": "definition", "module": "Mathlib.CategoryTheory.Products.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.diag", "kind": "definition", "module": "Mathlib.CategoryTheory.Products.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.prod", "kind": "definition", "module": "Mathlib.CategoryTheory.Products.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.prod'", "kind": "definition", "module": "Mathlib.CategoryTheory.Products.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.prodFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Products.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatIso.prod", "kind": "definition", "module": "Mathlib.CategoryTheory.Products.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.prod", "kind": "definition", "module": "Mathlib.CategoryTheory.Products.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.flipCompEvaluation", "kind": "definition", "module": "Mathlib.CategoryTheory.Products.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.flip_comp_evaluation", "kind": "theorem", "module": "Mathlib.CategoryTheory.Products.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.compEvaluation", "kind": "definition", "module": "Mathlib.CategoryTheory.Products.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.comp_evaluation", "kind": "theorem", "module": "Mathlib.CategoryTheory.Products.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.whiskeringLeftCompEvaluation", "kind": "definition", "module": "Mathlib.CategoryTheory.Products.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.whiskeringLeft_comp_evaluation", "kind": "theorem", "module": "Mathlib.CategoryTheory.Products.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.whiskeringRightCompEvaluation", "kind": "definition", "module": "Mathlib.CategoryTheory.Products.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.whiskeringRight_comp_evaluation", "kind": "theorem", "module": "Mathlib.CategoryTheory.Products.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.prodFunctorToFunctorProd", "kind": "definition", "module": "Mathlib.CategoryTheory.Products.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.functorProdToProdFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Products.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.functorProdFunctorEquivUnitIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Products.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.functorProdFunctorEquivCounitIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Products.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.functorProdFunctorEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Products.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.prodOpEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Products.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bifunctor.map_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Products.Bifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Bifunctor.map_id_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Products.Bifunctor", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Bifunctor.map_comp_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Products.Bifunctor", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Bifunctor.diagonal", "kind": "theorem", "module": "Mathlib.CategoryTheory.Products.Bifunctor", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Bifunctor.diagonal'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Products.Bifunctor", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.prod.leftUnitor", "kind": "definition", "module": "Mathlib.CategoryTheory.Products.Unitor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.prod.rightUnitor", "kind": "definition", "module": "Mathlib.CategoryTheory.Products.Unitor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.prod.leftInverseUnitor", "kind": "definition", "module": "Mathlib.CategoryTheory.Products.Unitor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.prod.rightInverseUnitor", "kind": "definition", "module": "Mathlib.CategoryTheory.Products.Unitor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.prod.leftUnitorEquivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.Products.Unitor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.prod.rightUnitorEquivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.Products.Unitor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.prod.leftUnitor_isEquivalence", "kind": "instance", "module": "Mathlib.CategoryTheory.Products.Unitor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.prod.rightUnitor_isEquivalence", "kind": "instance", "module": "Mathlib.CategoryTheory.Products.Unitor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomRel", "kind": "definition", "module": "Mathlib.CategoryTheory.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.homRel", "kind": "definition", "module": "Mathlib.CategoryTheory.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.homRel_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HomRel.CompClosure", "kind": "inductive", "module": "Mathlib.CategoryTheory.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HomRel.CompClosure.of", "kind": "theorem", "module": "Mathlib.CategoryTheory.Quotient", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.HomRel.instIsStableUnderPrecompCompClosure", "kind": "instance", "module": "Mathlib.CategoryTheory.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HomRel.instIsStableUnderPostcompCompClosure", "kind": "instance", "module": "Mathlib.CategoryTheory.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HomRel.compClosure_iff_self", "kind": "theorem", "module": "Mathlib.CategoryTheory.Quotient", "is_tactic_proof": true, "tactics": ["refine", "rintro", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.HomRel.compClosure_eq_self", "kind": "theorem", "module": "Mathlib.CategoryTheory.Quotient", "is_tactic_proof": true, "tactics": ["dsimp", "ext", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.Functor.congruence_homRel", "kind": "instance", "module": "Mathlib.CategoryTheory.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instInhabitedQuotient", "kind": "instance", "module": "Mathlib.CategoryTheory.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Quotient.Hom", "kind": "definition", "module": "Mathlib.CategoryTheory.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Quotient.instInhabitedHom", "kind": "instance", "module": "Mathlib.CategoryTheory.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Quotient.comp", "kind": "definition", "module": "Mathlib.CategoryTheory.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Quotient.comp_mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Quotient.category", "kind": "instance", "module": "Mathlib.CategoryTheory.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Quotient.equiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Quotient.inv", "kind": "definition", "module": "Mathlib.CategoryTheory.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Quotient.inv_mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Quotient.groupoid", "kind": "instance", "module": "Mathlib.CategoryTheory.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Quotient.functor", "kind": "definition", "module": "Mathlib.CategoryTheory.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Quotient.full_functor", "kind": "instance", "module": "Mathlib.CategoryTheory.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Quotient.essSurj_functor", "kind": "instance", "module": "Mathlib.CategoryTheory.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Quotient.instUnique", "kind": "instance", "module": "Mathlib.CategoryTheory.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Quotient.instSubsingletonHom", "kind": "instance", "module": "Mathlib.CategoryTheory.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Quotient.induction", "kind": "theorem", "module": "Mathlib.CategoryTheory.Quotient", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
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{"name": "CategoryTheory.Quotient.functor_homRel_eq_compClosure_eqvGen", "kind": "theorem", "module": "Mathlib.CategoryTheory.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Quotient.compClosure.congruence", "kind": "theorem", "module": "Mathlib.CategoryTheory.Quotient", "is_tactic_proof": true, "tactics": ["convert", "ext", "rw"], "tactic_count": 3}
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{"name": "CategoryTheory.Quotient.lift_spec", "kind": "theorem", "module": "Mathlib.CategoryTheory.Quotient", "is_tactic_proof": true, "tactics": ["tauto"], "tactic_count": 1}
{"name": "CategoryTheory.Quotient.lift_unique", "kind": "theorem", "module": "Mathlib.CategoryTheory.Quotient", "is_tactic_proof": true, "tactics": ["subst_vars", "fapply", "rintro", "dsimp", "congr", "rintro", "dsimp", "refine", "simp", "congr"], "tactic_count": 10}
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{"name": "CategoryTheory.Quotient.lift.isLift_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Quotient.lift.isLift_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Quotient.lift_obj_functor_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Quotient.natTrans_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Quotient.natTransLift", "kind": "definition", "module": "Mathlib.CategoryTheory.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Quotient.natTransLift_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Quotient.comp_natTransLift", "kind": "theorem", "module": "Mathlib.CategoryTheory.Quotient", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Quotient.natTransLift_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Quotient", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Quotient.natIsoLift", "kind": "definition", "module": "Mathlib.CategoryTheory.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Quotient.full_whiskeringLeft_functor", "kind": "instance", "module": "Mathlib.CategoryTheory.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Quotient.faithful_whiskeringLeft_functor", "kind": "instance", "module": "Mathlib.CategoryTheory.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Quotient.Linear.smul", "kind": "definition", "module": "Mathlib.CategoryTheory.Quotient.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Quotient.Linear.smul_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Quotient.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Quotient.Preadditive.add", "kind": "definition", "module": "Mathlib.CategoryTheory.Quotient.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Quotient.Preadditive.neg", "kind": "definition", "module": "Mathlib.CategoryTheory.Quotient.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Quotient.functor_additive", "kind": "theorem", "module": "Mathlib.CategoryTheory.Quotient.Preadditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.instIsRegularEpiFst", "kind": "instance", "module": "Mathlib.CategoryTheory.RegularCategory.Basic", "is_tactic_proof": true, "tactics": ["apply", "dsimp", "infer_instance"], "tactic_count": 3}
{"name": "CategoryTheory.instPreregular", "kind": "instance", "module": "Mathlib.CategoryTheory.RegularCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Regular.instHasCoequalizerFstSnd", "kind": "instance", "module": "Mathlib.CategoryTheory.RegularCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Regular.strongEpiMonoFactorisation", "kind": "definition", "module": "Mathlib.CategoryTheory.RegularCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Regular.instIsRegularEpiEStrongEpiMonoFactorisation", "kind": "instance", "module": "Mathlib.CategoryTheory.RegularCategory.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
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{"name": "CategoryTheory.Regular.regularEpiOfExtremalEpi", "kind": "definition", "module": "Mathlib.CategoryTheory.RegularCategory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Functor.IsRepresentedBy.iff_isIso_uliftYonedaEquiv", "kind": "theorem", "module": "Mathlib.CategoryTheory.RepresentedBy", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "rfl"], "tactic_count": 4}
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{"name": "CategoryTheory.Functor.IsRepresentedBy.representableBy_homEquiv_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.RepresentedBy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Functor.IsRepresentedBy.iff_exists_representableBy", "kind": "theorem", "module": "Mathlib.CategoryTheory.RepresentedBy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsRepresentedBy.of_natIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.RepresentedBy", "is_tactic_proof": true, "tactics": ["rw", "use", "simp"], "tactic_count": 3}
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{"name": "CategoryTheory.Functor.IsRepresentedBy.of_isoObj", "kind": "theorem", "module": "Mathlib.CategoryTheory.RepresentedBy", "is_tactic_proof": true, "tactics": ["rw", "use", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.Functor.IsRepresentedBy.iff_of_isoObj", "kind": "theorem", "module": "Mathlib.CategoryTheory.RepresentedBy", "is_tactic_proof": true, "tactics": ["refine", "have", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Functor.IsRepresentedBy.of_isRepresentable", "kind": "theorem", "module": "Mathlib.CategoryTheory.RepresentedBy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsRepresentable.iff_exists_isRepresentedBy", "kind": "theorem", "module": "Mathlib.CategoryTheory.RepresentedBy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Retract.splitEpi", "kind": "definition", "module": "Mathlib.CategoryTheory.Retract", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Retract.splitMono", "kind": "definition", "module": "Mathlib.CategoryTheory.Retract", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Retract.instIsSplitEpiR", "kind": "instance", "module": "Mathlib.CategoryTheory.Retract", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Retract.instIsSplitMonoI", "kind": "instance", "module": "Mathlib.CategoryTheory.Retract", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Retract.refl", "kind": "definition", "module": "Mathlib.CategoryTheory.Retract", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Retract.trans", "kind": "definition", "module": "Mathlib.CategoryTheory.Retract", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Retract.ofIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Retract", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.RetractArrow", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Retract", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.RetractArrow.i_w", "kind": "theorem", "module": "Mathlib.CategoryTheory.Retract", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.RetractArrow.r_w", "kind": "theorem", "module": "Mathlib.CategoryTheory.Retract", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.RetractArrow.right", "kind": "definition", "module": "Mathlib.CategoryTheory.Retract", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.RetractArrow.retract_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Retract", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.RetractArrow.retract_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Retract", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.RetractArrow.instIsSplitEpiLeftRArrow", "kind": "instance", "module": "Mathlib.CategoryTheory.Retract", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.RetractArrow.instIsSplitEpiRightRArrow", "kind": "instance", "module": "Mathlib.CategoryTheory.Retract", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.RetractArrow.instIsSplitMonoLeftIArrow", "kind": "instance", "module": "Mathlib.CategoryTheory.Retract", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.RetractArrow.instIsSplitMonoRightIArrow", "kind": "instance", "module": "Mathlib.CategoryTheory.Retract", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.RetractArrow.map", "kind": "definition", "module": "Mathlib.CategoryTheory.Retract", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.RetractArrow.op", "kind": "definition", "module": "Mathlib.CategoryTheory.Retract", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.RetractArrow.unop", "kind": "definition", "module": "Mathlib.CategoryTheory.Retract", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.retract", "kind": "definition", "module": "Mathlib.CategoryTheory.Retract", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.retractArrowApp", "kind": "definition", "module": "Mathlib.CategoryTheory.Retract", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.CommShift.CompatibilityUnit", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Shift.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.CommShift.CompatibilityCounit", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Shift.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.CommShift.compatibilityCounit_of_compatibilityUnit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Adjunction", "is_tactic_proof": true, "tactics": ["intro", "have", "simp", "apply", "dsimp", "rw", "simp", "erw", "dsimp", "simp"], "tactic_count": 10}
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{"name": "CategoryTheory.Adjunction.CommShift.compatibilityUnit_unique_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Adjunction", "is_tactic_proof": true, "tactics": ["rw", "ext", "rw"], "tactic_count": 3}
{"name": "CategoryTheory.Adjunction.CommShift.compatibilityUnit_unique_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Adjunction", "is_tactic_proof": true, "tactics": ["ext", "rw", "compatibilityCounit_left"], "tactic_count": 3}
{"name": "CategoryTheory.Adjunction.CommShift.compatibilityUnit_isoZero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Adjunction", "is_tactic_proof": true, "tactics": ["intro", "simp", "unit_naturality_assoc,"], "tactic_count": 3}
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{"name": "CategoryTheory.Adjunction.unit_app_shift_commShiftIso_inv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Adjunction", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "CategoryTheory.Adjunction.CommShift.instId", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.CommShift.instComp", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.shift_unit_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Adjunction", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
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{"name": "CategoryTheory.Adjunction.RightAdjointCommShift.iso'", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.RightAdjointCommShift.iso", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.RightAdjointCommShift.iso_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Adjunction", "is_tactic_proof": true, "tactics": ["obtain", "simp"], "tactic_count": 2}
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{"name": "CategoryTheory.Adjunction.rightAdjointCommShift", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.commShift_of_leftAdjoint", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Adjunction", "is_tactic_proof": true, "tactics": ["letI", "refine", "ext", "dsimp", "simpa"], "tactic_count": 5}
{"name": "CategoryTheory.Adjunction.LeftAdjointCommShift.iso'", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.LeftAdjointCommShift.iso", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.LeftAdjointCommShift.iso_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Adjunction", "is_tactic_proof": true, "tactics": ["obtain", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Adjunction.LeftAdjointCommShift.iso_inv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Adjunction", "is_tactic_proof": true, "tactics": ["obtain", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Adjunction.LeftAdjointCommShift.compatibilityUnit_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Adjunction", "is_tactic_proof": true, "tactics": ["intro", "rw", "simp", "unit_naturality_assoc,", "slice_rhs", "simp", "rw", "simp"], "tactic_count": 8}
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{"name": "CategoryTheory.Adjunction.commShift_of_rightAdjoint", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Adjunction", "is_tactic_proof": true, "tactics": ["letI", "refine", "ext", "dsimp", "simpa"], "tactic_count": 5}
{"name": "CategoryTheory.Equivalence.CommShift", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Shift.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.CommShift.instCommShiftHomFunctorUnitIso", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.CommShift.instCommShiftHomFunctorCounitIso", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.CommShift.instCommShiftInverseSymmOfFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.CommShift.instCommShiftFunctorSymmOfInverse", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.CommShift.mk'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.CommShift.instCommShiftFunctorRefl", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.Adjunction", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Equivalence.CommShift.instCommShiftInverseRefl", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.Adjunction", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Equivalence.CommShift.instRefl", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.Adjunction", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
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{"name": "CategoryTheory.Equivalence.CommShift.mk''", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.CommShift.instCommShiftFunctorTrans", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.Adjunction", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Equivalence.CommShift.instCommShiftInverseTrans", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.Adjunction", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Equivalence.CommShift.instTrans", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.commShiftInverse", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.commShift_of_functor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Adjunction", "is_tactic_proof": true, "tactics": ["letI", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Equivalence.commShiftFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.commShift_of_inverse", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Adjunction", "is_tactic_proof": true, "tactics": ["letI", "have", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.ShiftMkCore.assoc_inv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": false, "tactics": ["rw", "h.assoc_hom_app,", "rfl"], "tactic_count": 3}
{"name": "CategoryTheory.ShiftMkCore.zero_add_inv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.ShiftMkCore.add_zero_inv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.instMonoidalDiscreteFunctorFunctorF", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.hasShiftMk", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.shiftMonoidalFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instMonoidalDiscreteFunctorShiftMonoidalFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.shiftFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.shiftFunctorAdd", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.shiftFunctorAdd'", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.shiftFunctorAdd'_eq_shiftFunctorAdd", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": true, "tactics": ["ext1", "apply"], "tactic_count": 2}
{"name": "CategoryTheory.shiftFunctorZero", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.shiftFunctorZero'", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShiftMkCore.shiftFunctor_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShiftMkCore.shiftFunctorZero_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShiftMkCore.shiftFunctorAdd_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.term_⟦_⟧", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory._aux_Mathlib_CategoryTheory_Shift_Basic___macroRules_CategoryTheory_term_⟦_⟧'_1", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.shiftFunctorAdd'_zero_add", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "simp", "rfl"], "tactic_count": 4}
{"name": "CategoryTheory.shiftFunctorAdd'_add_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "simp", "rfl"], "tactic_count": 4}
{"name": "CategoryTheory.shiftFunctorAdd'_assoc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": true, "tactics": ["subst", "ext", "dsimp", "simp", "dsimp", "simp", "dsimp", "simp", "erw", "rfl"], "tactic_count": 10}
{"name": "CategoryTheory.shiftFunctorAdd_assoc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": true, "tactics": ["ext", "simpa"], "tactic_count": 2}
{"name": "CategoryTheory.shiftFunctorAdd'_zero_add_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.shiftFunctorAdd_zero_add_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.shiftFunctorAdd'_zero_add_inv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.shiftFunctorAdd_zero_add_inv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.shiftFunctorAdd'_add_zero_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.shiftFunctorAdd_add_zero_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.shiftFunctorAdd'_add_zero_inv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.shiftFunctorAdd_add_zero_inv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.shiftFunctorAdd'_assoc_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.shiftFunctorAdd'_assoc_inv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.shiftFunctorAdd_assoc_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.shiftFunctorAdd_assoc_inv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.shiftAdd", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.shift_shift'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.shiftZero", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.shiftZero'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": true, "tactics": ["symm", "rw", "apply"], "tactic_count": 3}
{"name": "CategoryTheory.shiftFunctorCompIsoId", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.shiftEquiv'", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.shiftEquiv", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instIsEquivalenceShiftFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": true, "tactics": ["change", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.shiftShiftNeg", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.shiftNegShift", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.shift_shift_neg'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.shift_neg_shift'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.shift_equiv_triangle", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.shift_shiftFunctorCompIsoId_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "simpa", "shiftFunctorAdd'_assoc_inv_app"], "tactic_count": 3}
{"name": "CategoryTheory.shift_shiftFunctorCompIsoId_inv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": false, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "CategoryTheory.shift_shiftFunctorCompIsoId_add_neg_cancel_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.shift_shiftFunctorCompIsoId_add_neg_cancel_inv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.shift_shiftFunctorCompIsoId_neg_add_cancel_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.shift_shiftFunctorCompIsoId_neg_add_cancel_inv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.shiftFunctorCompIsoId_zero_zero_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.shiftFunctorCompIsoId_zero_zero_inv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.shiftFunctorCompIsoId_add'_inv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "simp", "congr", "rw", "dsimp", "rw", "shiftFunctorAdd'_assoc_inv_app", "shiftFunctorAdd'_assoc_inv_app", "shiftFunctorAdd'_add_zero_hom_app,"], "tactic_count": 9}
{"name": "CategoryTheory.shiftFunctorCompIsoId_add'_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": false, "tactics": ["rw", "shiftFunctorCompIsoId_add'_inv_app", "dsimp", "rw"], "tactic_count": 4}
{"name": "CategoryTheory.shift_zero_eq_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.shiftFunctorComm", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.shiftFunctorComm_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": true, "tactics": ["subst", "rw", "rfl"], "tactic_count": 3}
{"name": "CategoryTheory.shiftFunctorComm_eq_refl", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.shiftFunctorComm_symm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": true, "tactics": ["ext1", "dsimp", "rw", "rfl"], "tactic_count": 4}
{"name": "CategoryTheory.shiftComm", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.shiftComm_symm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.shiftComm'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": true, "tactics": ["erw", "dsimp", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.shiftComm_hom_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.shiftFunctorZero_hom_app_shift", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": true, "tactics": ["rw", "dsimp", "rw"], "tactic_count": 3}
{"name": "CategoryTheory.shiftFunctorZero_inv_app_shift", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": false, "tactics": ["rw", "shiftFunctorZero_hom_app_shift,", "dsimp", "rw"], "tactic_count": 4}
{"name": "CategoryTheory.shiftFunctorComm_zero_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.shiftFunctorComm_hom_app_comp_shift_shiftFunctorAdd_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": false, "tactics": ["rw", "cancel_mono", "simp", "dsimp", "simp", "dsimp", "simp", "dsimp", "simp", "shiftFunctorAdd'_assoc_hom_app_assoc", "shiftFunctorAdd'_assoc_hom_app_assoc", "shiftFunctorAdd'_assoc_hom_app"], "tactic_count": 12}
{"name": "CategoryTheory.shiftFunctorComm_hom_app_of_add_eq_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.shiftFunctorComm_inv_app_of_add_eq_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.FullyFaithful.hasShift.zero", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.FullyFaithful.hasShift.map_zero_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.FullyFaithful.hasShift.map_zero_inv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.FullyFaithful.hasShift.add", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.FullyFaithful.hasShift.map_add_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.FullyFaithful.hasShift.map_add_inv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.FullyFaithful.hasShift", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.CommShift.isoZero", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.CommShift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.CommShift.isoZero'", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.CommShift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.CommShift.isoZero'_eq_isoZero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.CommShift", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.CommShift.isoAdd'", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.CommShift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.CommShift.isoAdd", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.CommShift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.CommShift.isoAdd_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.CommShift", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.CommShift.isoAdd_inv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.CommShift", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.CommShift.isoAdd'_isoZero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.CommShift", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.CommShift.isoZero_isoAdd'_", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.CommShift", "is_tactic_proof": true, "tactics": ["ext", "have", "dsimp", "simp"], "tactic_count": 4}
{"name": "CategoryTheory.Functor.CommShift.isoAdd'_assoc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.CommShift", "is_tactic_proof": true, "tactics": ["ext", "have", "dsimp", "simp", "rw", "shiftFunctorAdd'_assoc_hom_app", "simp_rw", "simp"], "tactic_count": 8}
{"name": "CategoryTheory.Functor.commShiftIso_hom_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.CommShift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.commShiftIso_inv_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.CommShift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.commShiftIso_zero'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.CommShift", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.commShiftIso_add'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.CommShift", "is_tactic_proof": true, "tactics": ["subst", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.CommShift.id", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.CommShift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.CommShift.comp", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.CommShift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.map_shiftFunctorComm_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.CommShift", "is_tactic_proof": true, "tactics": ["have", "simp", "simp", "dsimp", "simp", "dsimp", "rw", "simp"], "tactic_count": 8}
{"name": "CategoryTheory.Functor.map_shiftFunctorCompIsoId_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.CommShift", "is_tactic_proof": true, "tactics": ["dsimp", "have", "simp", "rw", "simp"], "tactic_count": 5}
{"name": "CategoryTheory.Functor.map_shiftFunctorCompIsoId_inv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.CommShift", "is_tactic_proof": false, "tactics": ["rw", "map_shiftFunctorCompIsoId_hom_app]", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.NatTrans.CommShiftCore.shift_app_comm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.CommShift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.CommShiftCore.shift_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.CommShift", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.NatTrans.CommShiftCore.app_shift", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.CommShift", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.NatTrans.CommShiftCore.zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.CommShift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.CommShiftCore.add", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.CommShift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.CommShift.of_core", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.CommShift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.shift_comm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.CommShift", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.NatTrans.shift_app_comm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.CommShift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.shift_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.CommShift", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.NatTrans.app_shift", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.CommShift", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.NatTrans.CommShift.of_iso_inv", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.CommShift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.CommShift.of_iso_symm", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.CommShift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.CommShift.of_isIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.CommShift", "is_tactic_proof": true, "tactics": ["haveI", "change", "infer_instance"], "tactic_count": 3}
{"name": "CategoryTheory.NatTrans.CommShift.id", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.CommShift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.CommShift.comp", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.CommShift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.CommShift.whiskerRight", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.CommShift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.CommShift.whiskerLeft", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.CommShift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.CommShift.associator", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.CommShift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.CommShift.leftUnitor", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.CommShift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.CommShift.rightUnitor", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.CommShift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.CommShift.ofIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.CommShift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.CommShift.ofIso_compatibility", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.CommShift", "is_tactic_proof": true, "tactics": ["letI", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.CommShift.ofHasShiftOfFullyFaithful", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.CommShift", "is_tactic_proof": true, "tactics": ["letI", "exact", "commShiftIso_zero", "ext", "simp", "commShiftIso_add", "ext", "simp"], "tactic_count": 8}
{"name": "CategoryTheory.Functor.shiftFunctorIso_ofHasShiftOfFullyFaithful", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.CommShift", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.map_shiftFunctorComm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.CommShift", "is_tactic_proof": true, "tactics": ["have", "simp", "simp", "dsimp", "simp", "simp"], "tactic_count": 6}
{"name": "CategoryTheory.Functor.CommShift.OfComp.iso", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.CommShift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.CommShift.OfComp.map_iso_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.CommShift", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.CommShift.OfComp.map_iso_inv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.CommShift", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.CommShift.ofComp", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.CommShift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.CommShift.ofComp_compatibility", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.CommShift", "is_tactic_proof": true, "tactics": ["letI", "refine", "ext", "simp"], "tactic_count": 4}
{"name": "CategoryTheory.NatTrans.CommShift.verticalComposition", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.CommShift", "is_tactic_proof": true, "tactics": ["subst", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.CommShift₂Setup.int", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.CommShiftTwo", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.CommShift₂Int", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Shift.CommShiftTwo", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.CommShift₂.precomp₁", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.CommShiftTwo", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.CommShift₂.precomp₂", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.CommShiftTwo", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.CommShift₂.instIdFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.CommShiftTwo", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.CommShift₂.instCompFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.CommShiftTwo", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.CommShift₂Int", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Shift.CommShiftTwo", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasShift.Induced.zero", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.Induced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasShift.Induced.add", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.Induced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasShift.Induced.zero_hom_app_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Induced", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.HasShift.Induced.zero_inv_app_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Induced", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.HasShift.Induced.add_hom_app_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Induced", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.HasShift.Induced.add_inv_app_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Induced", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.HasShift.induced", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.Induced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.shiftFunctor_of_induced", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Induced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.shiftFunctorZero_hom_app_obj_of_induced", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Induced", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.shiftFunctorZero_inv_app_obj_of_induced", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Induced", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.shiftFunctorAdd_hom_app_obj_of_induced", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Induced", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.shiftFunctorAdd_inv_app_obj_of_induced", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Induced", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.CommShift.ofInduced", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.Induced", "is_tactic_proof": true, "tactics": ["letI", "exact", "commShiftIso_zero", "ext", "dsimp", "simp", "commShiftIso_add", "ext", "dsimp", "simp", "rw", "dsimp", "rw"], "tactic_count": 13}
{"name": "CategoryTheory.Functor.commShiftIso_eq_ofInduced", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Induced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.ShiftSequence.induced.isoZero", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.InducedShiftSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.ShiftSequence.induced.isoZero_hom_app_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.InducedShiftSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.ShiftSequence.induced.shiftIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.InducedShiftSequence", "is_tactic_proof": true, "tactics": ["exact", "isoWhiskerRight"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.ShiftSequence.induced.shiftIso_hom_app_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.InducedShiftSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.ShiftSequence.induced", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.InducedShiftSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.ShiftSequence.induced_isoShiftZero_hom_app_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.InducedShiftSequence", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.ShiftSequence.induced_shiftIso_hom_app_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.InducedShiftSequence", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.ShiftSequence.induced_shiftMap", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.InducedShiftSequence", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "nth_rw", "simp", "rw", "rfl"], "tactic_count": 6}
{"name": "CategoryTheory.Shift.linear_of_localization", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Linear", "is_tactic_proof": true, "tactics": ["have", "rw", "infer_instance"], "tactic_count": 3}
{"name": "CategoryTheory.Shift.instLinearLocalizationShiftFunctorOfCommShiftOfQ", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Shift.instLinearLocalization'ShiftFunctorOfCommShiftOfQ'", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.IsCompatibleWithShift.iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Localization", "is_tactic_proof": true, "tactics": ["conv_rhs", "rfl"], "tactic_count": 2}
{"name": "CategoryTheory.MorphismProperty.IsCompatibleWithShift.shiftFunctor_comp_inverts", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.shift", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Localization", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.MorphismProperty.shiftLocalizerMorphism", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Shift.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasShift.localized", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.CommShift.localized", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasShift.localization", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.commShift_Q", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasShift.localization'", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.commShift_Q'", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.commShiftOfLocalization.iso", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.commShiftOfLocalization.iso_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Localization", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.commShiftOfLocalization.iso_inv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Localization", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.commShiftOfLocalization", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.commShiftOfLocalization_iso_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Localization", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.commShiftOfLocalization_iso_inv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Localization", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.NatTrans.commShift_iso_hom_of_localization", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.Localization", "is_tactic_proof": true, "tactics": ["letI", "constructor", "intro", "ext", "simp"], "tactic_count": 5}
{"name": "CategoryTheory.LocalizerMorphism.commShift", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.Localization", "is_tactic_proof": true, "tactics": ["letI", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.LocalizerMorphism.commShift_iso_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Localization", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.LocalizerMorphism.commShift_iso_inv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Localization", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.LocalizerMorphism.natTransCommShift_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Localization", "is_tactic_proof": true, "tactics": ["letI", "refine", "ext", "simp"], "tactic_count": 4}
{"name": "CategoryTheory.LocalizerMorphism.instCommShiftLocalizedFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.LocalizerMorphism.instCommShiftLocalizationHomFunctorIsoFunctorQLocalizedFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasShift.mkShiftCoreOp", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OppositeShift", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instCategoryOppositeShift", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instHasShiftOppositeShift", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instHasZeroObjectOppositeShift", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.Opposite", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.instPreadditiveOppositeShift", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instAdditiveOppositeShiftShiftFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.Opposite", "is_tactic_proof": true, "tactics": ["change", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.oppositeShiftFunctorZero_inv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.oppositeShiftFunctorZero_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Opposite", "is_tactic_proof": false, "tactics": ["rw", "oppositeShiftFunctorZero_inv_app,", "rfl"], "tactic_count": 3}
{"name": "CategoryTheory.oppositeShiftFunctorAdd_inv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.oppositeShiftFunctorAdd_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Opposite", "is_tactic_proof": false, "tactics": ["rw", "oppositeShiftFunctorAdd_inv_app,", "rfl"], "tactic_count": 3}
{"name": "CategoryTheory.oppositeShiftFunctorAdd'_inv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Opposite", "is_tactic_proof": true, "tactics": ["subst", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.oppositeShiftFunctorAdd'_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Opposite", "is_tactic_proof": true, "tactics": ["subst", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.OppositeShift.functor", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OppositeShift.natTrans", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.commShiftOp", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.commShiftOp_iso_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.commShiftUnop", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.commShift_op", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.OppositeShift.natIsoId", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.instCommShiftOppositeShiftHomFunctorNatIsoId", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.OppositeShift.natIsoComp", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.instCommShiftOppositeShiftHomFunctorNatIsoComp", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.OppositeShift.adjunction", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.commShift_op", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PullbackShift", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.Pullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instCategoryPullbackShift", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.Pullback", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.instHasShiftPullbackShift", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.Pullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instHasZeroObjectPullbackShift", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.Pullback", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.instPreadditivePullbackShift", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.Pullback", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.instAdditivePullbackShiftShiftFunctorOfCoeAddMonoidHom", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.Pullback", "is_tactic_proof": true, "tactics": ["change", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.pullbackShiftIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.Pullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.pullbackShiftFunctorZero_inv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Pullback", "is_tactic_proof": true, "tactics": ["change", "dsimp", "congr", "apply"], "tactic_count": 4}
{"name": "CategoryTheory.pullbackShiftFunctorZero_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Pullback", "is_tactic_proof": false, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "CategoryTheory.pullbackShiftFunctorZero'_inv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Pullback", "is_tactic_proof": true, "tactics": ["rw", "simp", "erw"], "tactic_count": 3}
{"name": "CategoryTheory.pullbackShiftFunctorZero'_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Pullback", "is_tactic_proof": false, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "CategoryTheory.pullbackShiftFunctorAdd'_inv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Pullback", "is_tactic_proof": true, "tactics": ["subst", "obtain", "simp", "erw", "change", "congr", "rw", "dsimp", "congr", "apply"], "tactic_count": 10}
{"name": "CategoryTheory.pullbackShiftFunctorAdd'_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Pullback", "is_tactic_proof": false, "tactics": ["rw", "pullbackShiftFunctorAdd'_inv_app", "rfl"], "tactic_count": 3}
{"name": "CategoryTheory.PullbackShift.functor", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.Pullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PullbackShift.natTrans", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.Pullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.commShiftPullback", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.Pullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.commShiftPullback_iso_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Pullback", "is_tactic_proof": true, "tactics": ["obtain", "rfl"], "tactic_count": 2}
{"name": "CategoryTheory.NatTrans.commShiftPullback", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.Pullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.PullbackShift.natIsoId", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.Pullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.instCommShiftPullbackShiftHomFunctorNatIsoId", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.Pullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.PullbackShift.natIsoComp", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.Pullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.instCommShiftPullbackShiftHomFunctorNatIsoComp", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.Pullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PullbackShift.adjunction", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.Pullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.commShiftPullback", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.Pullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasShift.quotient", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Quotient.functor_commShift", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Quotient.LiftCommShift.iso", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Quotient.LiftCommShift.iso_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Quotient", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "dsimp", "erw"], "tactic_count": 4}
{"name": "CategoryTheory.Quotient.LiftCommShift.iso_inv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Quotient", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "dsimp", "erw"], "tactic_count": 4}
{"name": "CategoryTheory.Quotient.liftCommShift", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Quotient.liftCommShift_compatibility", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.ShiftSequence.tautological", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.ShiftSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.shift", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.ShiftSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.shiftIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.ShiftSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.shiftIso_hom_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.ShiftSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.shiftIso_inv_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.ShiftSequence", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.isoShiftZero", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.ShiftSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isoShift", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.ShiftSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isoShift_hom_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.ShiftSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isoShift_inv_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.ShiftSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.shiftIso_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.ShiftSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.shiftIso_zero_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.ShiftSequence", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.shiftIso_zero_inv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.ShiftSequence", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.shiftIso_add", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.ShiftSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.shiftIso_add_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.ShiftSequence", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.shiftIso_add_inv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.ShiftSequence", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.shiftIso_add'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.ShiftSequence", "is_tactic_proof": true, "tactics": ["subst", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.shiftIso_add'_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.ShiftSequence", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.shiftIso_add'_inv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.ShiftSequence", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.shiftIso_hom_app_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.ShiftSequence", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.shiftMap", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.ShiftSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.shiftMap_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.ShiftSequence", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.shiftMap_comp'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.ShiftSequence", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.shiftIso_hom_app_comp_shiftMap", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.ShiftSequence", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.shiftIso_hom_app_comp_shiftMap_of_add_eq_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.ShiftSequence", "is_tactic_proof": true, "tactics": ["have", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.instPreservesZeroMorphismsShift", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.ShiftSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.shiftMap_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.ShiftSequence", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.instAdditiveShift", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.ShiftSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShiftedHom", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Shift.ShiftedHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShiftedHom.comp", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.ShiftedHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShiftedHom.comp_assoc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.ShiftedHom", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.ShiftedHom.mk₀", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.ShiftedHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShiftedHom.homEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.ShiftedHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShiftedHom.mk₀_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.ShiftedHom", "is_tactic_proof": true, "tactics": ["subst", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.ShiftedHom.mk₀_id_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.ShiftedHom", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.ShiftedHom.comp_mk₀", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.ShiftedHom", "is_tactic_proof": true, "tactics": ["subst", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.ShiftedHom.comp_mk₀_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.ShiftedHom", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.ShiftedHom.mk₀_comp_mk₀", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.ShiftedHom", "is_tactic_proof": true, "tactics": ["subst", "obtain", "rw"], "tactic_count": 3}
{"name": "CategoryTheory.ShiftedHom.mk₀_comp_mk₀_assoc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.ShiftedHom", "is_tactic_proof": true, "tactics": ["subst", "rw", "all_goals"], "tactic_count": 3}
{"name": "CategoryTheory.ShiftedHom.mk₀_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.ShiftedHom", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.ShiftedHom.comp_add", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.ShiftedHom", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.ShiftedHom.add_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.ShiftedHom", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.ShiftedHom.comp_neg", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.ShiftedHom", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.ShiftedHom.neg_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.ShiftedHom", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.ShiftedHom.comp_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.ShiftedHom", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.ShiftedHom.zero_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.ShiftedHom", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.ShiftedHom.map", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.ShiftedHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShiftedHom.map_mk₀", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.ShiftedHom", "is_tactic_proof": true, "tactics": ["subst", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.ShiftedHom.id_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.ShiftedHom", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.ShiftedHom.comp_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.ShiftedHom", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.ShiftedHom.map_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.ShiftedHom", "is_tactic_proof": true, "tactics": ["dsimp", "simp", "erw", "simp"], "tactic_count": 4}
{"name": "CategoryTheory.ShiftedHom.map_add", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.ShiftedHom", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.ShiftedHom.map_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.ShiftedHom", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.ShiftedHom.comp_smul", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.ShiftedHom", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.ShiftedHom.smul_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.ShiftedHom", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.ShiftedHom.mk₀_smul", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.ShiftedHom", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.ShiftedHom.map_smul", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.ShiftedHom", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.ShiftedHom.opEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.ShiftedHomOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShiftedHom.opEquiv_symm_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.ShiftedHomOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShiftedHom.opEquiv_symm_apply_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.ShiftedHomOpposite", "is_tactic_proof": true, "tactics": ["rw", "dsimp", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.ShiftedHom.opEquiv_symm_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.ShiftedHomOpposite", "is_tactic_proof": false, "tactics": ["rw", "opShiftFunctorEquivalence_add_unitIso_inv_app_eq", "dsimp", "rw", "dsimp", "rw", "dsimp", "rw", "rw", "erw", "rfl"], "tactic_count": 11}
{"name": "CategoryTheory.ShiftedHom.opEquiv'", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.ShiftedHomOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShiftedHom.opEquiv'_symm_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.ShiftedHomOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShiftedHom.opEquiv'_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.ShiftedHomOpposite", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "CategoryTheory.ShiftedHom.opEquiv'_symm_op_opShiftFunctorEquivalence_counitIso_inv_app_op_shift", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.ShiftedHomOpposite", "is_tactic_proof": true, "tactics": ["rw", "dsimp", "apply", "simp", "erw"], "tactic_count": 5}
{"name": "CategoryTheory.ShiftedHom.opEquiv'_symm_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.ShiftedHomOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ShiftedHom.opEquiv'_zero_add_symm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.ShiftedHomOpposite", "is_tactic_proof": true, "tactics": ["simp", "opShiftFunctorEquivalence_zero_unitIso_inv_app]"], "tactic_count": 2}
{"name": "CategoryTheory.ShiftedHom.opEquiv'_add_symm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.ShiftedHomOpposite", "is_tactic_proof": false, "tactics": ["simp", "opShiftFunctorEquivalence_add_unitIso_inv_app_eq", "dsimp", "simp", "shiftFunctorAdd'_assoc_inv_app", "rfl"], "tactic_count": 6}
{"name": "CategoryTheory.ShiftedHom.opEquiv_symm_add", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.ShiftedHomOpposite", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.ShiftedHom.opEquiv'_symm_add", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.ShiftedHomOpposite", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.SingleFunctors.shiftIso_add_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.SingleFunctors", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.SingleFunctors.shiftIso_add_inv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.SingleFunctors", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.SingleFunctors.shiftIso_add'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.SingleFunctors", "is_tactic_proof": true, "tactics": ["subst", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.SingleFunctors.shiftIso_add'_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.SingleFunctors", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.SingleFunctors.shiftIso_add'_inv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.SingleFunctors", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.SingleFunctors.shiftIso_zero_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.SingleFunctors", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "CategoryTheory.SingleFunctors.shiftIso_zero_inv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.SingleFunctors", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "CategoryTheory.SingleFunctors.Hom.id", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.SingleFunctors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SingleFunctors.Hom.comp", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.SingleFunctors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SingleFunctors.instCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.SingleFunctors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SingleFunctors.id_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.SingleFunctors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SingleFunctors.comp_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.SingleFunctors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SingleFunctors.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.SingleFunctors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SingleFunctors.isoMk", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.SingleFunctors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SingleFunctors.evaluation", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.SingleFunctors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SingleFunctors.hom_inv_id_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.SingleFunctors", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.SingleFunctors.inv_hom_id_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.SingleFunctors", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.SingleFunctors.hom_inv_id_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.SingleFunctors", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.SingleFunctors.inv_hom_id_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.SingleFunctors", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.SingleFunctors.instIsIsoFunctorHom", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.SingleFunctors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SingleFunctors.postcomp", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.SingleFunctors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SingleFunctors.postcompFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.SingleFunctors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SingleFunctors.postcompPostcompIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.SingleFunctors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SingleFunctors.postcompIsoOfIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.SingleFunctors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.TwistShiftData.z_zero_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Twist", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.TwistShiftData.z_zero_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Twist", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.TwistShiftData.shift_z_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Twist", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.TwistShiftData.Category", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.Twist", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.TwistShiftData.instCategoryCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.Twist", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.TwistShiftData.shiftMkCore", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.Twist", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.TwistShiftData.hasShift", "kind": "instance", "module": "Mathlib.CategoryTheory.Shift.Twist", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.TwistShiftData.shiftIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Shift.Twist", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.TwistShiftData.shiftFunctor_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Twist", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.TwistShiftData.shiftFunctorZero_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Twist", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.TwistShiftData.shiftFunctorZero_inv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Twist", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.TwistShiftData.shiftFunctorAdd'_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Twist", "is_tactic_proof": false, "tactics": ["have", "dsimp", "cat_disch", "rw", "congr", "change", "simp"], "tactic_count": 7}
{"name": "CategoryTheory.TwistShiftData.shiftFunctorAdd'_inv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Shift.Twist", "is_tactic_proof": false, "tactics": ["have", "dsimp", "cat_disch", "rw", "congr", "change", "simp"], "tactic_count": 7}
{"name": "CategoryTheory.FunctorToTypes.Small", "kind": "abbrev", "module": "Mathlib.CategoryTheory.ShrinkYoneda", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FunctorToTypes.shrink", "kind": "definition", "module": "Mathlib.CategoryTheory.ShrinkYoneda", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FunctorToTypes.shrinkMap", "kind": "definition", "module": "Mathlib.CategoryTheory.ShrinkYoneda", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instSmallOppositeObjFunctorTypeYoneda", "kind": "instance", "module": "Mathlib.CategoryTheory.ShrinkYoneda", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.shrinkYoneda", "kind": "definition", "module": "Mathlib.CategoryTheory.ShrinkYoneda", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.shrinkYonedaObjObjEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.ShrinkYoneda", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.shrinkYonedaEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.ShrinkYoneda", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.map_shrinkYonedaEquiv", "kind": "theorem", "module": "Mathlib.CategoryTheory.ShrinkYoneda", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.shrinkYonedaEquiv_shrinkYoneda_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.ShrinkYoneda", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.shrinkYonedaEquiv_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.ShrinkYoneda", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.shrinkYonedaEquiv_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.ShrinkYoneda", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.shrinkYonedaEquiv_symm_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.ShrinkYoneda", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.fullyFaithfulShrinkYoneda", "kind": "definition", "module": "Mathlib.CategoryTheory.ShrinkYoneda", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instFaithfulFunctorOppositeTypeShrinkYoneda", "kind": "instance", "module": "Mathlib.CategoryTheory.ShrinkYoneda", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instFullFunctorOppositeTypeShrinkYoneda", "kind": "instance", "module": "Mathlib.CategoryTheory.ShrinkYoneda", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sigma.SigmaHom", "kind": "inductive", "module": "Mathlib.CategoryTheory.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sigma.SigmaHom.id", "kind": "definition", "module": "Mathlib.CategoryTheory.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sigma.SigmaHom.instInhabited", "kind": "instance", "module": "Mathlib.CategoryTheory.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sigma.SigmaHom.comp", "kind": "definition", "module": "Mathlib.CategoryTheory.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sigma.SigmaHom.instCategoryStructSigma", "kind": "instance", "module": "Mathlib.CategoryTheory.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sigma.SigmaHom.comp_def", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sigma.SigmaHom.assoc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sigma.SigmaHom.id_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sigma.SigmaHom.comp_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sigma.sigma", "kind": "instance", "module": "Mathlib.CategoryTheory.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sigma.incl", "kind": "definition", "module": "Mathlib.CategoryTheory.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sigma.incl_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sigma.instFullSigmaIncl", "kind": "instance", "module": "Mathlib.CategoryTheory.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sigma.instFaithfulSigmaIncl", "kind": "instance", "module": "Mathlib.CategoryTheory.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sigma.natTrans", "kind": "definition", "module": "Mathlib.CategoryTheory.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sigma.natTrans_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sigma.descMap", "kind": "definition", "module": "Mathlib.CategoryTheory.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sigma.desc", "kind": "definition", "module": "Mathlib.CategoryTheory.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sigma.desc_map_mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sigma.inclDesc", "kind": "definition", "module": "Mathlib.CategoryTheory.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sigma.inclDesc_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sigma.inclDesc_inv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sigma.descUniq", "kind": "definition", "module": "Mathlib.CategoryTheory.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sigma.descUniq_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sigma.descUniq_inv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sigma.natIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sigma.map", "kind": "definition", "module": "Mathlib.CategoryTheory.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sigma.map_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sigma.map_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sigma.inclCompMap", "kind": "definition", "module": "Mathlib.CategoryTheory.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sigma.mapId", "kind": "definition", "module": "Mathlib.CategoryTheory.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sigma.mapComp", "kind": "definition", "module": "Mathlib.CategoryTheory.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sigma.Functor.sigma", "kind": "definition", "module": "Mathlib.CategoryTheory.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sigma.natTrans.sigma", "kind": "definition", "module": "Mathlib.CategoryTheory.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isIso_of_mono_of_nonzero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Simple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Simple.of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Simple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Simple.iff_of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Simple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.kernel_zero_of_nonzero_from_simple", "kind": "theorem", "module": "Mathlib.CategoryTheory.Simple", "is_tactic_proof": true, "tactics": ["classical", "by_contra", "haveI", "exact", "w"], "tactic_count": 5}
{"name": "CategoryTheory.epi_of_nonzero_to_simple", "kind": "theorem", "module": "Mathlib.CategoryTheory.Simple", "is_tactic_proof": true, "tactics": ["rw", "haveI", "apply"], "tactic_count": 3}
{"name": "CategoryTheory.mono_to_simple_zero_of_not_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Simple", "is_tactic_proof": true, "tactics": ["classical", "by_contra", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.id_nonzero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Simple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instNontrivialEndOfSimple", "kind": "instance", "module": "Mathlib.CategoryTheory.Simple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Simple.not_isZero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Simple", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.zero_not_simple", "kind": "theorem", "module": "Mathlib.CategoryTheory.Simple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.simple_of_cosimple", "kind": "theorem", "module": "Mathlib.CategoryTheory.Simple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isIso_of_epi_of_nonzero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Simple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.cokernel_zero_of_nonzero_to_simple", "kind": "theorem", "module": "Mathlib.CategoryTheory.Simple", "is_tactic_proof": true, "tactics": ["classical", "by_contra", "haveI", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.epi_from_simple_zero_of_not_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Simple", "is_tactic_proof": true, "tactics": ["classical", "by_contra", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Biprod.isIso_inl_iff_isZero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Simple", "is_tactic_proof": true, "tactics": ["rw", "constructor", "intro", "replace", "simpa", "intro", "rw", "rw"], "tactic_count": 8}
{"name": "CategoryTheory.indecomposable_of_simple", "kind": "theorem", "module": "Mathlib.CategoryTheory.Simple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instNontrivialSubobjectOfSimple", "kind": "instance", "module": "Mathlib.CategoryTheory.Simple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instIsSimpleOrderSubobjectOfSimple", "kind": "instance", "module": "Mathlib.CategoryTheory.Simple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.simple_of_isSimpleOrder_subobject", "kind": "theorem", "module": "Mathlib.CategoryTheory.Simple", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "intro", "rw", "exact", "intro", "rcases", "rw", "exact", "exact"], "tactic_count": 11}
{"name": "CategoryTheory.simple_iff_subobject_isSimpleOrder", "kind": "theorem", "module": "Mathlib.CategoryTheory.Simple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.subobject_simple_iff_isAtom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Simple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SingleObj", "kind": "abbrev", "module": "Mathlib.CategoryTheory.SingleObj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SingleObj.categoryStruct", "kind": "instance", "module": "Mathlib.CategoryTheory.SingleObj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SingleObj.category", "kind": "instance", "module": "Mathlib.CategoryTheory.SingleObj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SingleObj.id_as_one", "kind": "theorem", "module": "Mathlib.CategoryTheory.SingleObj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SingleObj.comp_as_mul", "kind": "theorem", "module": "Mathlib.CategoryTheory.SingleObj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SingleObj.finCategoryOfFintype", "kind": "instance", "module": "Mathlib.CategoryTheory.SingleObj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SingleObj.groupoid", "kind": "instance", "module": "Mathlib.CategoryTheory.SingleObj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SingleObj.inv_as_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.SingleObj", "is_tactic_proof": true, "tactics": ["apply", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.SingleObj.star", "kind": "abbrev", "module": "Mathlib.CategoryTheory.SingleObj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SingleObj.toEnd", "kind": "definition", "module": "Mathlib.CategoryTheory.SingleObj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SingleObj.toEnd_def", "kind": "theorem", "module": "Mathlib.CategoryTheory.SingleObj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SingleObj.mapHom", "kind": "definition", "module": "Mathlib.CategoryTheory.SingleObj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SingleObj.mapHom_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.SingleObj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SingleObj.mapHom_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.SingleObj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SingleObj.differenceFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.SingleObj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SingleObj.functor", "kind": "definition", "module": "Mathlib.CategoryTheory.SingleObj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SingleObj.natTrans", "kind": "definition", "module": "Mathlib.CategoryTheory.SingleObj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.toFunctor", "kind": "abbrev", "module": "Mathlib.CategoryTheory.SingleObj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.comp_toFunctor", "kind": "theorem", "module": "Mathlib.CategoryTheory.SingleObj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.id_toFunctor", "kind": "theorem", "module": "Mathlib.CategoryTheory.SingleObj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.toSingleObjEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.SingleObj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.toAut", "kind": "definition", "module": "Mathlib.CategoryTheory.SingleObj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.toAut_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.SingleObj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.toAut_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.SingleObj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonCat.toCat", "kind": "definition", "module": "Mathlib.CategoryTheory.SingleObj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonCat.toCat_full", "kind": "instance", "module": "Mathlib.CategoryTheory.SingleObj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonCat.toCat_faithful", "kind": "instance", "module": "Mathlib.CategoryTheory.SingleObj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.sheafIsAbelian", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.presheafToSheaf_additive", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.sheafForget", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Sites.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.adjunction", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.adjunction_unit_app_val", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Adjunction", "is_tactic_proof": true, "tactics": ["change", "simp", "whiskeringRight_obj_map,", "rfl"], "tactic_count": 4}
{"name": "CategoryTheory.Sheaf.adjunction_counit_app_val", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Adjunction", "is_tactic_proof": true, "tactics": ["change", "simp", "whiskeringRight_obj_map,", "sheafifyMap_sheafifyLift,"], "tactic_count": 4}
{"name": "CategoryTheory.Sheaf.instIsRightAdjointSheafComposeOfHasWeakSheafify", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.instIsLeftAdjointComposeAndSheafify", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.preservesSheafification_of_adjunction", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.instPreservesSheafificationOfIsLeftAdjoint", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf._example", "kind": "example", "module": "Mathlib.CategoryTheory.Sites.Adjunction", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "CategoryTheory.Sheaf.isSheafFor_bind", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Canonical", "is_tactic_proof": true, "tactics": ["intro", "let", "s", "have", "intro", "apply", "apply", "let", "have", "have", "rw", "intro", "apply", "intro", "apply", "intro", "have", "trans", "have", "rw", "grind", "have", "conv_lhs", "rw", "simp", "refine", "rintro", "rw", "apply", "intro", "apply", "intro", "apply", "intro", "rw"], "tactic_count": 35}
{"name": "CategoryTheory.Sheaf.isSheafFor_trans", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Canonical", "is_tactic_proof": false, "tactics": ["have", "rintro", "apply", "apply", "apply", "intro", "rw", "apply", "intro", "have", "ext", "constructor", "rintro", "rw", "simp", "intro", "refine", "simp", "rw", "apply"], "tactic_count": 20}
{"name": "CategoryTheory.Sheaf.finestTopologySingle", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.finestTopology", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.sheaf_for_finestTopology", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.le_finestTopology", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Canonical", "is_tactic_proof": true, "tactics": ["rintro", "intro", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Sheaf.canonicalTopology", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.isSheaf_yoneda_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.isSheaf_of_isRepresentable", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Canonical", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "refine", "rw", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.GrothendieckTopology.le_canonical", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.instSubcanonicalCanonicalTopology", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Subcanonical.of_isSheaf_yoneda_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Subcanonical.isSheaf_of_isRepresentable", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.yoneda", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.uliftYoneda", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.uliftYonedaIsoYoneda", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.yonedaCompSheafToPresheaf", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.uliftYonedaCompSheafToPresheaf", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.yonedaFullyFaithful", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.instFullSheafTypeYoneda", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.instFaithfulSheafTypeYoneda", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.fullyFaithfulUliftYoneda", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.instFullSheafTypeUliftYoneda", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.instFaithfulSheafTypeUliftYoneda", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Canonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instMonoidalClosedSheafOfHasSheafifyOfFunctorOpposite", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.CartesianClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.tensorProd_isSheaf", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.CartesianMonoidal", "is_tactic_proof": false, "tactics": ["apply", "isSheaf_of_isLimit", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Sheaf.tensorUnit_isSheaf", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.CartesianMonoidal", "is_tactic_proof": true, "tactics": ["apply", "exact", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Sheaf.cartesianMonoidalCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.CartesianMonoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.cartesianMonoidalCategoryFst_val", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.CartesianMonoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.cartesianMonoidalCategorySnd_val", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.CartesianMonoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.cartesianMonoidalCategoryLift_val", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.CartesianMonoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.cartesianMonoidalCategoryWhiskerLeft_val", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.CartesianMonoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.cartesianMonoidalCategoryWhiskerRight_val", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.CartesianMonoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.sheafToPresheafMonoidal", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.CartesianMonoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.sheafToPresheaf_ε", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.CartesianMonoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.sheafToPresheaf_η", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.CartesianMonoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.sheafToPresheaf_μ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.CartesianMonoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.sheafToPresheaf_δ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.CartesianMonoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.close", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Closed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.le_close", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Closed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.IsClosed", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Closed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.covers_iff_mem_of_isClosed", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Closed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.isClosed_pullback", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Closed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.le_close_of_isClosed", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Closed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.close_isClosed", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Closed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.closureOperator", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Closed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.isClosed_iff_close_eq_self", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Closed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.close_eq_self_of_isClosed", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Closed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.pullback_close", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Closed", "is_tactic_proof": true, "tactics": ["apply", "refine", "apply", "intro", "change", "rw", "apply"], "tactic_count": 7}
{"name": "CategoryTheory.GrothendieckTopology.monotone_close", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Closed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.close_close", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Closed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.close_eq_top_iff_mem", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Closed", "is_tactic_proof": true, "tactics": ["constructor", "intro", "apply", "intro", "change", "rwa", "intro", "rw", "intro", "apply"], "tactic_count": 10}
{"name": "CategoryTheory.Functor.closedSieves", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Closed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.classifier_isSheaf", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Closed", "is_tactic_proof": true, "tactics": ["intro", "rw", "refine", "rintro", "simp", "ext", "dsimp", "rw", "have", "congr_arg", "have", "ext", "rw", "simp", "apply", "intro", "rw", "constructor", "intro", "rw", "apply", "rw", "apply", "intro", "rw", "apply", "rw", "apply", "intro", "rw", "let", "have", "intro", "apply", "rintro", "rw", "show", "conv_lhs", "rw", "rw", "apply", "apply", "refine", "intro", "simp", "ext1", "dsimp", "rw", "apply"], "tactic_count": 49}
{"name": "CategoryTheory.le_topology_of_closedSieves_isSheaf", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Closed", "is_tactic_proof": true, "tactics": ["intro", "rw", "have", "intro", "trivial", "suffices", "rw", "exact", "apply", "intro", "simp", "ext1", "dsimp", "rw", "apply"], "tactic_count": 15}
{"name": "CategoryTheory.topology_eq_iff_same_sheaves", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Closed", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "intro", "rfl", "intro", "apply", "apply", "rw", "apply", "apply", "rw", "apply"], "tactic_count": 12}
{"name": "CategoryTheory.topologyOfClosureOperator", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Closed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.topologyOfClosureOperator_self", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Closed", "is_tactic_proof": true, "tactics": ["ext", "apply"], "tactic_count": 2}
{"name": "CategoryTheory.topologyOfClosureOperator_close", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Closed", "is_tactic_proof": true, "tactics": ["ext", "change", "rw"], "tactic_count": 3}
{"name": "CategoryTheory.coherentCoverage", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Coherent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.coherentTopology", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Coherent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.regularCoverage", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Coherent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.regularTopology", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Coherent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.extensiveCoverage", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Coherent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.extensiveTopology", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Coherent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isSheaf_coherent", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coherent.CoherentSheaves", "is_tactic_proof": true, "tactics": ["constructor", "intro", "simp", "apply", "exact", "intro", "simp", "rintro", "exact"], "tactic_count": 9}
{"name": "CategoryTheory.coherentTopology.isSheaf_yoneda_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coherent.CoherentSheaves", "is_tactic_proof": true, "tactics": ["rw", "intro", "have", "rw", "intro", "let", "have", "let", "obtain", "refine", "convert", "exact", "exact"], "tactic_count": 13}
{"name": "CategoryTheory.coherentTopology.subcanonical", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Coherent.CoherentSheaves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.coherentTopology.mem_sieves_of_hasEffectiveEpiFamily", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coherent.CoherentTopology", "is_tactic_proof": true, "tactics": ["intro", "apply", "exact", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.EffectiveEpiFamily.transitive_of_finite", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coherent.CoherentTopology", "is_tactic_proof": true, "tactics": ["rw", "suffices", "change", "rw", "exact", "apply", "apply", "use", "intro", "rw", "apply", "apply", "obtain", "exact"], "tactic_count": 14}
{"name": "CategoryTheory.precoherentEffectiveEpiFamilyCompEffectiveEpis", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Coherent.CoherentTopology", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.coherentTopology.mem_sieves_iff_hasEffectiveEpiFamily", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coherent.CoherentTopology", "is_tactic_proof": true, "tactics": ["constructor", "intro", "induction", "of", "obtain", "refine", "obtain", "exact", "top", "transitive", "obtain", "choose", "exact", "exact"], "tactic_count": 14}
{"name": "CategoryTheory.instPreregularOfPrecoherentOfHasFiniteCoproducts", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Coherent.Comparison", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instPrecoherentOfFinitaryPreExtensiveOfPreregular", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Coherent.Comparison", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.extensive_regular_generate_coherent", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coherent.Comparison", "is_tactic_proof": true, "tactics": ["ext", "refine", "induction", "of", "apply", "simp", "exact", "top", "transitive", "induction", "of", "obtain", "apply", "apply", "simp", "exact", "rintro", "change", "rw", "apply", "have", "generate", "rintro", "exact", "apply", "apply", "refine", "convert", "aesop", "top", "transitive"], "tactic_count": 31}
{"name": "CategoryTheory.Equivalence.precoherent", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coherent.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.instPrecoherentSmallModel", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Coherent.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.instIsDenseSubsiteCoherentTopologyInverse", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Coherent.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.sheafCongrPrecoherent", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Coherent.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.precoherent_isSheaf_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coherent.Equivalence", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.Equivalence.precoherent_isSheaf_iff_of_essentiallySmall", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coherent.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.preregular", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coherent.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.instPreregularSmallModel", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Coherent.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.instIsDenseSubsiteRegularTopologyInverse", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Coherent.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.sheafCongrPreregular", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Coherent.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.preregular_isSheaf_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coherent.Equivalence", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.Equivalence.preregular_isSheaf_iff_of_essentiallySmall", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coherent.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isSheaf_pointwiseColimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coherent.ExtensiveColimits", "is_tactic_proof": true, "tactics": ["rw", "dsimp", "apply", "have", "rw", "exact", "exact", "preservesLimitsOfShape_of_evaluation", "inferInstanceAs"], "tactic_count": 9}
{"name": "CategoryTheory.instPreservesFiniteProductsFunctorColimOfPreadditive", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Coherent.ExtensiveColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instPreservesColimitsOfShapeSheafExtensiveTopologyFunctorOppositeSheafToPresheafOfPreservesFiniteProductsColim", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Coherent.ExtensiveColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instPreservesFiniteColimitsSheafExtensiveTopologyFunctorOppositeSheafToPresheafOfPreadditiveOfHasFiniteColimits", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Coherent.ExtensiveColimits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instHasPairwisePullbacksOfExtensive", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Coherent.ExtensiveSheaves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isSheafFor_extensive_of_preservesFiniteProducts", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coherent.ExtensiveSheaves", "is_tactic_proof": true, "tactics": ["obtain", "have", "cases", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.instExtensiveOfArrowsι", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Coherent.ExtensiveSheaves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.extensiveTopology.isSheaf_yoneda_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coherent.ExtensiveSheaves", "is_tactic_proof": true, "tactics": ["rw", "intro", "have", "have", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.extensiveTopology.subcanonical", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Coherent.ExtensiveSheaves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.isSheaf_iff_preservesFiniteProducts", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coherent.ExtensiveSheaves", "is_tactic_proof": true, "tactics": ["refine", "rw", "let", "have", "inferInstanceAs", "have", "inferInstanceAs", "let", "let", "exact", "apply", "refine", "ext", "cases", "simp", "refine", "suffices", "ext", "simp", "rw", "intro", "have", "have", "exact"], "tactic_count": 24}
{"name": "CategoryTheory.Presheaf.isSheaf_iff_preservesFiniteProducts", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coherent.ExtensiveSheaves", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "refine", "constructor", "apply", "intro", "specialize", "rw", "exact", "intro", "rw", "exact"], "tactic_count": 13}
{"name": "CategoryTheory.instPreservesFiniteProductsOppositeVal", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Coherent.ExtensiveSheaves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.extensiveTopology.mem_sieves_iff_contains_colimit_cofan", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coherent.ExtensiveTopology", "is_tactic_proof": true, "tactics": ["constructor", "intro", "induction", "of", "obtain", "refine", "have", "exact", "obtain", "exact", "top", "refine", "have", "have", "exact", "exact", "transitive", "obtain", "choose", "exact", "intro", "apply", "exact", "refine", "rw", "exact"], "tactic_count": 26}
{"name": "CategoryTheory.regularTopology.isLocallySurjective_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coherent.LocallySurjective", "is_tactic_proof": true, "tactics": ["constructor", "intro", "specialize", "rw", "obtain", "exact", "intro", "refine", "obtain", "rw", "exact"], "tactic_count": 11}
{"name": "CategoryTheory.extensiveTopology.surjective_of_isLocallySurjective_sheaf_of_types", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coherent.LocallySurjective", "is_tactic_proof": true, "tactics": ["intro", "replace", "rw", "obtain", "let", "let", "let", "let", "let", "ht.conePointsIsoOfNatIso", "refine", "apply", "intro", "simp", "rw", "erw", "change", "erw", "rfl"], "tactic_count": 19}
{"name": "CategoryTheory.extensiveTopology.presheafIsLocallySurjective_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coherent.LocallySurjective", "is_tactic_proof": true, "tactics": ["constructor", "rw", "exact", "intro", "refine", "obtain", "convert", "rw", "simpa"], "tactic_count": 9}
{"name": "CategoryTheory.extensiveTopology.isLocallySurjective_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coherent.LocallySurjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.regularTopology.isLocallySurjective_sheaf_of_types", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coherent.LocallySurjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.coherentTopology.presheafIsLocallySurjective_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coherent.LocallySurjective", "is_tactic_proof": true, "tactics": ["constructor", "rw", "exact", "refine", "rw", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.coherentTopology.isLocallySurjective_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coherent.LocallySurjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.reflects_precoherent", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coherent.ReflectsPrecoherent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.reflects_preregular", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coherent.ReflectsPreregular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.regularTopology.equalizerCondition_w", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coherent.RegularSheaves", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.regularTopology.SingleEqualizerCondition", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Coherent.RegularSheaves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.regularTopology.EqualizerCondition", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Coherent.RegularSheaves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.regularTopology.equalizerCondition_of_natIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coherent.RegularSheaves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.regularTopology.equalizerCondition_precomp_of_preservesPullback", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coherent.RegularSheaves", "is_tactic_proof": true, "tactics": ["intro", "have", "refine", "simp", "refine", "simp", "exact"], "tactic_count": 7}
{"name": "CategoryTheory.regularTopology.mapToEqualizer", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Coherent.RegularSheaves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.regularTopology.EqualizerCondition.bijective_mapToEqualizer_pullback'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coherent.RegularSheaves", "is_tactic_proof": true, "tactics": ["specialize", "rw", "rw", "intro", "obtain", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.regularTopology.EqualizerCondition.bijective_mapToEqualizer_pullback", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coherent.RegularSheaves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.regularTopology.EqualizerCondition.mk'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coherent.RegularSheaves", "is_tactic_proof": true, "tactics": ["intro", "specialize", "rw", "rw", "intro", "obtain", "exact"], "tactic_count": 7}
{"name": "CategoryTheory.regularTopology.EqualizerCondition.mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coherent.RegularSheaves", "is_tactic_proof": true, "tactics": ["intro", "have", "specialize", "rw", "rw", "intro", "have", "have", "rw", "simp", "obtain", "refine", "simpa", "simpa"], "tactic_count": 14}
{"name": "CategoryTheory.regularTopology.equalizerCondition_w'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coherent.RegularSheaves", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.regularTopology.mapToEqualizer_eq_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coherent.RegularSheaves", "is_tactic_proof": true, "tactics": ["rw", "apply", "aesop"], "tactic_count": 3}
{"name": "CategoryTheory.regularTopology.equalizerCondition_iff_isIso_lift", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coherent.RegularSheaves", "is_tactic_proof": true, "tactics": ["constructor", "intro", "have", "rw", "exact", "intro", "apply", "intro", "rw", "infer_instance"], "tactic_count": 10}
{"name": "CategoryTheory.regularTopology.equalizerCondition_iff_of_equivalence", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coherent.RegularSheaves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.regularTopology.parallelPair_pullback_initial", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coherent.RegularSheaves", "is_tactic_proof": true, "tactics": ["apply", "intro", "obtain", "let", "let", "exact", "intro", "have", "have", "dsimp", "let", "refine", "all_goals"], "tactic_count": 13}
{"name": "CategoryTheory.regularTopology.isLimit_forkOfι_equiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Coherent.RegularSheaves", "is_tactic_proof": true, "tactics": ["let", "let", "let", "let", "let", "let", "let", "let", "have", "let", "refine", "refine", "rintro", "all_goals"], "tactic_count": 14}
{"name": "CategoryTheory.regularTopology.equalizerConditionMap_iff_nonempty_isLimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coherent.RegularSheaves", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "intro", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.regularTopology.equalizerCondition_iff_isSheaf", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coherent.RegularSheaves", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "constructor", "rintro", "exact", "intro", "exact"], "tactic_count": 7}
{"name": "CategoryTheory.regularTopology.isSheafFor_regular_of_projective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coherent.RegularSheaves", "is_tactic_proof": true, "tactics": ["obtain", "rw", "refine", "simpa", "simp"], "tactic_count": 5}
{"name": "CategoryTheory.regularTopology.isSheaf_of_projective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coherent.RegularSheaves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.regularTopology.isSheaf_yoneda_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coherent.RegularSheaves", "is_tactic_proof": true, "tactics": ["rw", "intro", "have", "obtain", "have", "rw", "intro", "let", "have", "let", "obtain", "refine", "convert", "exact", "exact"], "tactic_count": 15}
{"name": "CategoryTheory.regularTopology.subcanonical", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Coherent.RegularSheaves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.regularTopology.mem_sieves_of_hasEffectiveEpi", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coherent.RegularTopology", "is_tactic_proof": true, "tactics": ["rintro", "have", "rw", "apply", "intro", "refine", "cases", "exact", "apply", "exact"], "tactic_count": 10}
{"name": "CategoryTheory.regularTopology.instEffectiveEpiComp", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Coherent.RegularTopology", "is_tactic_proof": true, "tactics": ["rw", "suffices", "change", "rw", "exact", "apply", "apply", "use", "intro", "rw", "apply", "apply", "cases", "exact"], "tactic_count": 14}
{"name": "CategoryTheory.regularTopology.mem_sieves_iff_hasEffectiveEpi", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coherent.RegularTopology", "is_tactic_proof": true, "tactics": ["constructor", "intro", "induction", "of", "rcases", "refine", "rcases", "exact", "top", "transitive", "rcases", "choose", "exact", "exact"], "tactic_count": 14}
{"name": "_private.Mathlib.CategoryTheory.Sites.Coherent.SequentialLimit.0.CategoryTheory.coherentTopology.exists_effectiveEpi", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coherent.SequentialLimit", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "_private.Mathlib.CategoryTheory.Sites.Coherent.SequentialLimit.0.CategoryTheory.coherentTopology.preimage", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Coherent.SequentialLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.CategoryTheory.Sites.Coherent.SequentialLimit.0.CategoryTheory.coherentTopology.preimageStruct", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Coherent.SequentialLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.CategoryTheory.Sites.Coherent.SequentialLimit.0.CategoryTheory.coherentTopology.preimageDiagram", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Coherent.SequentialLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.CategoryTheory.Sites.Coherent.SequentialLimit.0.CategoryTheory.coherentTopology.cone", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Coherent.SequentialLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.coherentTopology.isLocallySurjective_π_app_zero_of_isLocallySurjective_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coherent.SequentialLimit", "is_tactic_proof": true, "tactics": ["rw", "intro", "have", "h", "refine", "simp", "rfl"], "tactic_count": 7}
{"name": "CategoryTheory.coherentTopology.epi_π_app_zero_of_epi", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coherent.SequentialLimit", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.coherentTopology.instIsCoverDense", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Coherent.SheafComparison", "is_tactic_proof": true, "tactics": ["refine", "apply", "refine", "funext", "ext", "refine", "rintro", "simp", "rw", "infer_instance"], "tactic_count": 10}
{"name": "CategoryTheory.coherentTopology.exists_effectiveEpiFamily_iff_mem_induced", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coherent.SheafComparison", "is_tactic_proof": true, "tactics": ["refine", "apply", "refine", "exact", "obtain", "refine", "let", "let", "have", "refine", "refine", "simpa", "obtain", "rw", "convert", "exact"], "tactic_count": 16}
{"name": "CategoryTheory.coherentTopology.eq_induced", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coherent.SheafComparison", "is_tactic_proof": true, "tactics": ["ext", "have", "rw", "rw"], "tactic_count": 4}
{"name": "CategoryTheory.coherentTopology.instIsDenseSubsite", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Coherent.SheafComparison", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.coherentTopology.coverPreserving", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coherent.SheafComparison", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.coherentTopology.equivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Coherent.SheafComparison", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.coherentTopology.equivalence'", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Coherent.SheafComparison", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.regularTopology.instIsCoverDense", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Coherent.SheafComparison", "is_tactic_proof": true, "tactics": ["refine", "apply", "refine", "funext", "ext", "refine", "rintro", "simp"], "tactic_count": 8}
{"name": "CategoryTheory.regularTopology.exists_effectiveEpi_iff_mem_induced", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coherent.SheafComparison", "is_tactic_proof": true, "tactics": ["refine", "apply", "refine", "exact", "obtain", "let", "refine", "refine", "simp", "infer_instance", "obtain", "rw", "convert", "exact"], "tactic_count": 14}
{"name": "CategoryTheory.regularTopology.eq_induced", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coherent.SheafComparison", "is_tactic_proof": true, "tactics": ["ext", "have", "rw", "rw"], "tactic_count": 4}
{"name": "CategoryTheory.regularTopology.instIsDenseSubsite", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Coherent.SheafComparison", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.regularTopology.coverPreserving", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coherent.SheafComparison", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.regularTopology.equivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Coherent.SheafComparison", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.isSheaf_coherent_iff_regular_and_extensive", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coherent.SheafComparison", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Presheaf.isSheaf_iff_preservesFiniteProducts_and_equalizerCondition", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coherent.SheafComparison", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Presheaf.instPreservesFiniteProductsOppositeVal", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Coherent.SheafComparison", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.isSheaf_iff_preservesFiniteProducts_of_projective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coherent.SheafComparison", "is_tactic_proof": true, "tactics": ["rw", "isSheaf_iff_preservesFiniteProducts]"], "tactic_count": 2}
{"name": "CategoryTheory.Presheaf.isSheaf_iff_extensiveSheaf_of_projective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coherent.SheafComparison", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Presheaf.coherentExtensiveEquivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Coherent.SheafComparison", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.isSheaf_coherent_of_hasPullbacks_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coherent.SheafComparison", "is_tactic_proof": true, "tactics": ["rw", "have", "refine", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.Presheaf.isSheaf_coherent_of_hasPullbacks_of_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coherent.SheafComparison", "is_tactic_proof": true, "tactics": ["rw", "obtain", "refine", "exact", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.Presheaf.isSheaf_coherent_of_projective_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coherent.SheafComparison", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Presheaf.isSheaf_coherent_of_projective_of_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coherent.SheafComparison", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Presheaf.instHasSheafComposeCoherentTopologyOfForallEffectiveEpiHasPullbackOfPreservesFiniteLimits", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Coherent.SheafComparison", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.instHasSheafComposeCoherentTopologyOfProjectiveOfPreservesFiniteProducts", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Coherent.SheafComparison", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.diagramCompIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.CompatiblePlus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.diagramCompIso_hom_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.CompatiblePlus", "is_tactic_proof": true, "tactics": ["delta", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.GrothendieckTopology.plusCompIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.CompatiblePlus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.ι_plusCompIso_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.CompatiblePlus", "is_tactic_proof": true, "tactics": ["delta", "simp", "erw", "simp"], "tactic_count": 4}
{"name": "CategoryTheory.GrothendieckTopology.plusCompIso_whiskerLeft", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.CompatiblePlus", "is_tactic_proof": true, "tactics": ["ext", "apply", "intro", "dsimp", "simp", "simp", "congr", "cat_disch"], "tactic_count": 8}
{"name": "CategoryTheory.GrothendieckTopology.plusFunctorWhiskerLeftIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.CompatiblePlus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.plusCompIso_whiskerRight", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.CompatiblePlus", "is_tactic_proof": true, "tactics": ["ext", "apply", "intro", "dsimp", "simp", "simp", "dsimp", "simp", "dsimp", "simp", "simp", "congr", "dsimp", "ext", "dsimp", "simp", "simp"], "tactic_count": 17}
{"name": "CategoryTheory.GrothendieckTopology.plusFunctorWhiskerRightIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.CompatiblePlus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.whiskerRight_toPlus_comp_plusCompIso_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.CompatiblePlus", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "simp", "simp", "congr", "dsimp", "ext", "rw", "simp"], "tactic_count": 9}
{"name": "CategoryTheory.GrothendieckTopology.toPlus_comp_plusCompIso_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.CompatiblePlus", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.GrothendieckTopology.plusCompIso_inv_eq_plusLift", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.CompatiblePlus", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.GrothendieckTopology.sheafifyCompIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.CompatibleSheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.sheafificationWhiskerLeftIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.CompatibleSheafification", "is_tactic_proof": true, "tactics": ["refine", "refine", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.GrothendieckTopology.sheafificationWhiskerLeftIso_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.CompatibleSheafification", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.GrothendieckTopology.sheafificationWhiskerLeftIso_inv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.CompatibleSheafification", "is_tactic_proof": true, "tactics": ["dsimp", "erw"], "tactic_count": 2}
{"name": "CategoryTheory.GrothendieckTopology.sheafificationWhiskerRightIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.CompatibleSheafification", "is_tactic_proof": true, "tactics": ["refine", "refine", "refine", "refine", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.GrothendieckTopology.sheafificationWhiskerRightIso_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.CompatibleSheafification", "is_tactic_proof": true, "tactics": ["dsimp", "simp", "erw"], "tactic_count": 3}
{"name": "CategoryTheory.GrothendieckTopology.sheafificationWhiskerRightIso_inv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.CompatibleSheafification", "is_tactic_proof": true, "tactics": ["dsimp", "simp", "erw"], "tactic_count": 3}
{"name": "CategoryTheory.GrothendieckTopology.whiskerRight_toSheafify_sheafifyCompIso_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.CompatibleSheafification", "is_tactic_proof": true, "tactics": ["dsimp", "erw", "slice_lhs", "rw", "whiskerRight_toPlus_comp_plusCompIso_hom]", "rfl"], "tactic_count": 6}
{"name": "CategoryTheory.GrothendieckTopology.toSheafify_comp_sheafifyCompIso_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.CompatibleSheafification", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.GrothendieckTopology.sheafifyCompIso_inv_eq_sheafifyLift", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.CompatibleSheafification", "is_tactic_proof": true, "tactics": ["apply", "rw", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.Meq", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.ConcreteSheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Meq.instCoeFunForallToTypeObjOppositeOpY", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.ConcreteSheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Meq.congr_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.ConcreteSheafification", "is_tactic_proof": true, "tactics": ["subst", "rfl"], "tactic_count": 2}
{"name": "CategoryTheory.Meq.ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.ConcreteSheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Meq.condition", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.ConcreteSheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Meq.refine", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.ConcreteSheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Meq.refine_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.ConcreteSheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Meq.pullback", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.ConcreteSheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Meq.pullback_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.ConcreteSheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Meq.pullback_refine", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.ConcreteSheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Meq.mk", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.ConcreteSheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Meq.mk_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.ConcreteSheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Meq.equiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.ConcreteSheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Meq.equiv_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.ConcreteSheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Meq.equiv_symm_eq_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.ConcreteSheafification", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.GrothendieckTopology.Plus.mk", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.ConcreteSheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Plus.res_mk_eq_mk_pullback", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.ConcreteSheafification", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "comp_apply", "apply", "apply", "dsimp", "rw", "ext", "simp", "rw", "erw", "cases"], "tactic_count": 12}
{"name": "CategoryTheory.GrothendieckTopology.Plus.toPlus_mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.ConcreteSheafification", "is_tactic_proof": true, "tactics": ["dsimp", "let", "rw", "delta", "rw", "apply", "dsimp", "apply", "intro", "simp", "rfl"], "tactic_count": 11}
{"name": "CategoryTheory.GrothendieckTopology.Plus.toPlus_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.ConcreteSheafification", "is_tactic_proof": true, "tactics": ["dsimp", "delta", "dsimp", "rw", "dsimp", "let", "rw", "apply", "apply", "intro", "dsimp", "rw", "erw", "simpa"], "tactic_count": 14}
{"name": "CategoryTheory.GrothendieckTopology.Plus.toPlus_eq_mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.ConcreteSheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Plus.exists_rep", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.ConcreteSheafification", "is_tactic_proof": true, "tactics": ["obtain", "use", "rw", "dsimp", "simp"], "tactic_count": 5}
{"name": "CategoryTheory.GrothendieckTopology.Plus.eq_mk_iff_exists", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.ConcreteSheafification", "is_tactic_proof": true, "tactics": ["constructor", "intro", "obtain", "use", "ext", "apply_fun", "convert", "all_goals", "dsimp", "rw", "erw", "cases", "rintro", "apply", "use", "apply", "intro", "apply_fun", "convert", "all_goals", "dsimp", "rw", "erw", "cases"], "tactic_count": 24}
{"name": "CategoryTheory.GrothendieckTopology.Plus.sep", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.ConcreteSheafification", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "simp", "choose", "rw", "let", "use", "let", "homOfLE", "rintro", "rw", "apply", "exact", "let", "homOfLE", "rintro", "rw", "apply", "exact", "use", "ext1", "let", "specialize", "let", "apply_fun", "convert", "exact", "exact"], "tactic_count": 28}
{"name": "CategoryTheory.GrothendieckTopology.Plus.inj_of_sep", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.ConcreteSheafification", "is_tactic_proof": true, "tactics": ["intro", "simp", "rw", "obtain", "apply", "intro", "apply_fun", "exact"], "tactic_count": 8}
{"name": "CategoryTheory.GrothendieckTopology.Plus.meqOfSep", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.ConcreteSheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Plus.exists_of_sep", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.ConcreteSheafification", "is_tactic_proof": true, "tactics": ["have", "choose", "exists_rep", "let", "choose", "let", "use", "ext", "dsimp", "rw", "apply", "intro", "simp", "use", "let", "homOfLE", "intro", "apply", "cases", "exact", "use", "ext", "let", "let", "let", "let", "change", "apply", "rw", "erw", "rw", "let", "exact"], "tactic_count": 33}
{"name": "CategoryTheory.GrothendieckTopology.Plus.isSheaf_of_sep", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.ConcreteSheafification", "is_tactic_proof": true, "tactics": ["rw", "intro", "apply", "rw", "constructor", "intro", "apply", "intro", "apply_fun", "apply_fun", "dsimp", "convert", "rintro", "obtain", "use", "apply", "rw", "ext", "dsimp", "rw", "rfl"], "tactic_count": 21}
{"name": "CategoryTheory.GrothendieckTopology.Plus.isSheaf_plus_plus", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.ConcreteSheafification", "is_tactic_proof": true, "tactics": ["apply", "intro", "apply"], "tactic_count": 3}
{"name": "CategoryTheory.GrothendieckTopology.sheafify", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.ConcreteSheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.toSheafify", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.ConcreteSheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.sheafifyMap", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.ConcreteSheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.sheafifyMap_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.ConcreteSheafification", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.GrothendieckTopology.sheafifyMap_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.ConcreteSheafification", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.GrothendieckTopology.toSheafify_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.ConcreteSheafification", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.GrothendieckTopology.sheafification", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.ConcreteSheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.sheafification_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.ConcreteSheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.sheafification_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.ConcreteSheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.toSheafification", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.ConcreteSheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.toSheafification_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.ConcreteSheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.isIso_toSheafify", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.ConcreteSheafification", "is_tactic_proof": true, "tactics": ["dsimp", "haveI", "change", "infer_instance"], "tactic_count": 4}
{"name": "CategoryTheory.GrothendieckTopology.isoSheafify", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.ConcreteSheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.isoSheafify_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.ConcreteSheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.sheafifyLift", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.ConcreteSheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.toSheafify_sheafifyLift", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.ConcreteSheafification", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.GrothendieckTopology.sheafifyLift_unique", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.ConcreteSheafification", "is_tactic_proof": true, "tactics": ["intro", "apply", "apply", "rw", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.GrothendieckTopology.isoSheafify_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.ConcreteSheafification", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.GrothendieckTopology.sheafify_hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.ConcreteSheafification", "is_tactic_proof": true, "tactics": ["apply", "apply", "rw", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.GrothendieckTopology.sheafifyMap_sheafifyLift", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.ConcreteSheafification", "is_tactic_proof": true, "tactics": ["apply", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.GrothendieckTopology.sheafify_isSheaf", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.ConcreteSheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.plusPlusSheaf", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.ConcreteSheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.plusPlusSheaf_preservesZeroMorphisms", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.ConcreteSheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.plusPlusAdjunction", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.ConcreteSheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.sheafToPresheaf_isRightAdjoint", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.ConcreteSheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.presheaf_mono_of_mono", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.ConcreteSheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.Hom.mono_iff_presheaf_mono", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.ConcreteSheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.constantPresheafAdj", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.ConstantSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.constantSheaf", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.ConstantSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.constantSheafAdj", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.ConstantSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.mem_essImage_of_isConstant", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.ConstantSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.isConstant_congr", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.ConstantSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.isConstant_of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.ConstantSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.isConstant_iff_mem_essImage", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.ConstantSheaf", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Sheaf.isConstant_of_isIso_counit_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.ConstantSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.instIsIsoAppCounitConstantSheafAdjOfFaithfulOfFullConstantSheafOfIsConstant", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.ConstantSheaf", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Sheaf.isConstant_iff_isIso_counit_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.ConstantSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.isConstant_iff_isIso_counit_app'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.ConstantSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.equivCommuteConstant", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.ConstantSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.equivCommuteConstant'", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.ConstantSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.isConstant_iff_of_equivalence", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.ConstantSheaf", "is_tactic_proof": true, "tactics": ["constructor", "exact", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.constantCommuteCompose", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.ConstantSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.constantCommuteCompose_hom_app_val", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.ConstantSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.constantSheafAdj_counit_w", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.ConstantSheaf", "is_tactic_proof": true, "tactics": ["apply", "rw", "apply", "ext", "simp", "simp"], "tactic_count": 6}
{"name": "CategoryTheory.Sheaf.isConstant_of_forget", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.ConstantSheaf", "is_tactic_proof": false, "tactics": ["have", "rw", "infer_instance", "rw", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.instIsConstantObjSheafSheafCompose", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.ConstantSheaf", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Sheaf.isConstant_iff_forget", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.ConstantSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreOneHypercover.map", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreOneHypercover.isLimitMapMultiforkEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Continuous", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "CategoryTheory.GrothendieckTopology.OneHypercover.map", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.OneHypercover.instIsPreservedById", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.PreservesOneHypercovers", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Sites.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.op_comp_isSheaf_of_types", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.op_comp_isSheaf", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isContinuous_of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isContinuous_id", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isContinuous_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isContinuous_comp'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Continuous", "is_tactic_proof": true, "tactics": ["have", "apply"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.instIsContinuousCompId", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Continuous", "is_tactic_proof": true, "tactics": ["assumption"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.instIsContinuousCompId_1", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Continuous", "is_tactic_proof": true, "tactics": ["assumption"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.op_comp_isSheaf_of_preservesOneHypercovers", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Continuous", "is_tactic_proof": true, "tactics": ["rw", "intro", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Functor.isContinuous_of_preservesOneHypercovers", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instIsContinuousOfPreservesOneHypercovers", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.sheafPushforwardContinuous", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.sheafPushforwardContinuousCompSheafToPresheafIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.sheafPushforwardContinuousId", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.sheafPushforwardContinuousComp", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.sheafPushforwardContinuousNatTrans", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.sheafPushforwardContinuousIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.sheafPushforwardContinuousId'", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.sheafPushforwardContinuousComp'", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.cover_lift", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.CoverLifting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isCocontinuous_id", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.CoverLifting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isCocontinuous_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.CoverLifting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.RanIsSheafOfIsCocontinuous.liftAux", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.CoverLifting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.RanIsSheafOfIsCocontinuous.liftAux_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.CoverLifting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.RanIsSheafOfIsCocontinuous.liftAux_map'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.CoverLifting", "is_tactic_proof": true, "tactics": ["apply", "rintro", "dsimp", "have", "have", "dsimp", "simp", "simp"], "tactic_count": 8}
{"name": "CategoryTheory.RanIsSheafOfIsCocontinuous.lift", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.CoverLifting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.RanIsSheafOfIsCocontinuous.fac'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.CoverLifting", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.RanIsSheafOfIsCocontinuous.fac", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.CoverLifting", "is_tactic_proof": true, "tactics": ["apply", "intro", "have", "dsimp", "simp", "rw", "simpa"], "tactic_count": 7}
{"name": "CategoryTheory.RanIsSheafOfIsCocontinuous.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.CoverLifting", "is_tactic_proof": true, "tactics": ["apply", "intro", "apply", "intro", "have", "dsimp", "simp", "rw"], "tactic_count": 8}
{"name": "CategoryTheory.RanIsSheafOfIsCocontinuous.isLimitMultifork", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.CoverLifting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ran_isSheaf_of_isCocontinuous", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.CoverLifting", "is_tactic_proof": true, "tactics": ["rw", "intro", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Functor.sheafPushforwardCocontinuous", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.CoverLifting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.sheafPushforwardCocontinuousCompSheafToPresheafIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.CoverLifting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.sheafAdjunctionCocontinuous", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.CoverLifting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.sheafAdjunctionCocontinuous_unit_app_val", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.CoverLifting", "is_tactic_proof": false, "tactics": ["apply", "dsimp", "erw", "change", "simp"], "tactic_count": 5}
{"name": "CategoryTheory.Functor.sheafAdjunctionCocontinuous_counit_app_val", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.CoverLifting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.sheafAdjunctionCocontinuous_homEquiv_apply_val", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.CoverLifting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.pushforwardContinuousSheafificationCompatibility", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.CoverLifting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.toSheafify_pullbackSheafificationCompatibility", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.CoverLifting", "is_tactic_proof": true, "tactics": ["let", "let", "let", "let", "change", "adj₂.unit.app", "apply", "have", "rw", "rw", "apply", "simp", "congr", "exact"], "tactic_count": 14}
{"name": "CategoryTheory.Functor.pushforwardContinuousSheafificationCompatibility_hom_app_val", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.CoverLifting", "is_tactic_proof": true, "tactics": ["apply", "apply"], "tactic_count": 2}
{"name": "CategoryTheory.idCoverPreserving", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.CoverPreserving", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CoverPreserving.comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.CoverPreserving", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.FamilyOfElements.Compatible.functorPushforward", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.CoverPreserving", "is_tactic_proof": true, "tactics": ["rintro", "unfold", "rcases", "rcases", "suffices", "apply", "simpa"], "tactic_count": 7}
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{"name": "CategoryTheory.compatiblePreservingOfDownwardsClosed", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.CoverPreserving", "is_tactic_proof": true, "tactics": ["constructor", "introv", "obtain", "apply", "simp", "simpa"], "tactic_count": 6}
{"name": "CategoryTheory.Functor.isContinuous_of_coverPreserving", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.CoverPreserving", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.FactorsThruAlong", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Coverage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.FactorsThruAlong.pullbackArrows", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coverage", "is_tactic_proof": true, "tactics": ["intro", "have", "refine"], "tactic_count": 3}
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{"name": "CategoryTheory.Presieve.factorsThruAlong_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coverage", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Presieve.factorsThru_of_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coverage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.le_of_factorsThru_sieve", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coverage", "is_tactic_proof": true, "tactics": ["rintro", "obtain", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Presieve.factorsThru_top", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coverage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.GrothendieckTopology.toCoverage", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Coverage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.mem_toCoverage_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coverage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Coverage.Saturate", "kind": "inductive", "module": "Mathlib.CategoryTheory.Sites.Coverage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Coverage.eq_top_pullback", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coverage", "is_tactic_proof": true, "tactics": ["ext", "simp", "apply", "apply", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.Coverage.saturate_of_superset", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coverage", "is_tactic_proof": true, "tactics": ["apply", "intro", "rw", "apply", "assumption"], "tactic_count": 5}
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{"name": "CategoryTheory.Coverage.saturate_iff_saturate_toPrecoverage", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coverage", "is_tactic_proof": true, "tactics": ["constructor", "induction", "induction"], "tactic_count": 3}
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{"name": "CategoryTheory.Coverage.mem_toGrothendieck", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coverage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Coverage.instPartialOrder", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Coverage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Coverage.gi", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Coverage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Coverage.toGrothendieck_eq_sInf", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coverage", "is_tactic_proof": true, "tactics": ["apply", "apply", "intro", "induction", "of", "top", "transitive", "apply", "intro", "apply"], "tactic_count": 10}
{"name": "CategoryTheory.Coverage.instSemilatticeSup", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Coverage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Coverage.sup_covering", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coverage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Coverage.mem_toGrothendieck_sieves_of_superset", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coverage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretopology.toCoverage", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Coverage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretopology.mem_toCoverage", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coverage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.GrothendieckTopology.mem_toPrecoverage_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coverage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.instHasIsosToPrecoverage", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Coverage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.instIsStableUnderCompositionToPrecoverage", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Coverage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.instIsStableUnderBaseChangeToPrecoverage", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Coverage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Precoverage.toGrothendieck_le_iff_le_toPrecoverage", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coverage", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Coverage.toGrothendieck_toPrecoverage", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coverage", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Presieve.isSheaf_coverage", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coverage", "is_tactic_proof": true, "tactics": ["rw", "constructor", "intro", "simpa", "intro", "obtain", "apply", "intro", "obtain", "exact", "apply", "intro", "obtain", "exact"], "tactic_count": 14}
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{"name": "CategoryTheory.Presheaf.isSheaf_iff_isLimit_coverage", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Coverage", "is_tactic_proof": false, "tactics": ["simp", "aesop"], "tactic_count": 2}
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{"name": "CategoryTheory.GrothendieckTopology.CoversTop", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.CoversTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.coversTop_iff_of_isTerminal", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.CoversTop", "is_tactic_proof": true, "tactics": ["constructor", "tauto", "intro", "apply", "rintro", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.GrothendieckTopology.CoversTop.cover", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Sites.CoversTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.CoversTop.ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.CoversTop", "is_tactic_proof": true, "tactics": ["refine", "rintro", "simpa"], "tactic_count": 3}
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{"name": "CategoryTheory.Presheaf.FamilyOfElementsOnObjects", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.CoversTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.FamilyOfElementsOnObjects.IsCompatible", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.CoversTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.FamilyOfElementsOnObjects.familyOfElements", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.CoversTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.FamilyOfElementsOnObjects.IsCompatible.familyOfElements_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.CoversTop", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Presheaf.FamilyOfElementsOnObjects.IsCompatible.familyOfElements_isCompatible", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.CoversTop", "is_tactic_proof": true, "tactics": ["intro", "simpa"], "tactic_count": 2}
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{"name": "CategoryTheory.Presieve.coverByImage", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.DenseSubsite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.coverByImage", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.DenseSubsite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.in_coverByImage", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.DenseSubsite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.is_cover_of_isCoverDense", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.DenseSubsite.Basic", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.isCoverDense_of_generate_singleton_functor_π_mem", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.DenseSubsite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsCoverDense.ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.DenseSubsite.Basic", "is_tactic_proof": false, "tactics": ["apply", "rintro", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.Functor.IsCoverDense.functorPullback_pushforward_covering", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.DenseSubsite.Basic", "is_tactic_proof": true, "tactics": ["refine", "apply", "rintro", "rw", "apply", "rintro", "exact"], "tactic_count": 7}
{"name": "CategoryTheory.Functor.IsCoverDense.homOver", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.DenseSubsite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsCoverDense.isoOver", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.DenseSubsite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsCoverDense.sheaf_eq_amalgamation", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.DenseSubsite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsCoverDense.Types.naturality_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.DenseSubsite.Basic", "is_tactic_proof": false, "tactics": ["have", "exact", "refine", "simp"], "tactic_count": 4}
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{"name": "CategoryTheory.Functor.IsCoverDense.Types.pushforwardFamily", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.DenseSubsite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsCoverDense.Types.pushforwardFamily_def", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.DenseSubsite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsCoverDense.Types.pushforwardFamily_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.DenseSubsite.Basic", "is_tactic_proof": true, "tactics": ["simp", "generalize", "obtain", "simp"], "tactic_count": 4}
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{"name": "CategoryTheory.Functor.IsCoverDense.Types.appHom", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.DenseSubsite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsCoverDense.Types.appHom_restrict", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.DenseSubsite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsCoverDense.Types.appHom_valid_glue", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.DenseSubsite.Basic", "is_tactic_proof": true, "tactics": ["ext", "apply"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.IsCoverDense.Types.appIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.DenseSubsite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsCoverDense.Types.presheafHom", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.DenseSubsite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsCoverDense.Types.presheafIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.DenseSubsite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsCoverDense.Types.sheafIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.DenseSubsite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsCoverDense.sheafCoyonedaHom", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.DenseSubsite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsCoverDense.sheafYonedaHom", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.DenseSubsite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsCoverDense.sheafHom", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.DenseSubsite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Functor.IsCoverDense.iso_of_restrict_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.DenseSubsite.Basic", "is_tactic_proof": true, "tactics": ["convert", "ext1", "apply"], "tactic_count": 3}
{"name": "CategoryTheory.Functor.IsCoverDense.compatiblePreserving", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.DenseSubsite.Basic", "is_tactic_proof": true, "tactics": ["constructor", "intro", "apply", "intro", "refine", "refine", "refine", "intro", "simp", "apply", "simpa"], "tactic_count": 11}
{"name": "CategoryTheory.Functor.IsCoverDense.isContinuous", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.DenseSubsite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsCoverDense.full_sheafPushforwardContinuous", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.DenseSubsite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsCoverDense.faithful_sheafPushforwardContinuous", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.DenseSubsite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.whiskerLeft_obj_map_bijective_of_isCoverDense", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.DenseSubsite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Functor.IsDenseSubsite.isCoverDense", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.DenseSubsite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsDenseSubsite.isLocallyFull", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.DenseSubsite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsDenseSubsite.isLocallyFaithful", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.DenseSubsite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsDenseSubsite.coverPreserving", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.DenseSubsite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsDenseSubsite.instIsContinuous", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.DenseSubsite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsDenseSubsite.instIsCocontinuous", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.DenseSubsite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsDenseSubsite.full_sheafPushforwardContinuous", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.DenseSubsite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsDenseSubsite.faithful_sheafPushforwardContinuous", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.DenseSubsite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsDenseSubsite.imageSieve_mem", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.DenseSubsite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsDenseSubsite.equalizer_mem", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.DenseSubsite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.pushforward_cover_iff_cover_pullback", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.DenseSubsite.InducedTopology", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "rintro", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.Functor.inducedTopology", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.DenseSubsite.InducedTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mem_inducedTopology_sieves_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.DenseSubsite.InducedTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.inducedTopology_isCocontinuous", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.DenseSubsite.InducedTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.inducedTopology_coverPreserving", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.DenseSubsite.InducedTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.locallyCoverDense_of_isCoverDense", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.DenseSubsite.InducedTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instIsDenseSubsiteInducedTopologyOfIsCoverDense", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.DenseSubsite.InducedTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.over_forget_locallyCoverDense", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.DenseSubsite.InducedTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.sheafInducedTopologyEquivOfIsCoverDense", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.DenseSubsite.InducedTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsDenseSubsite.isIso_ranCounit_app_of_isDenseSubsite", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.DenseSubsite.SheafEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsDenseSubsite.instIsIsoSheafAppCounitSheafAdjunctionCocontinuous", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.DenseSubsite.SheafEquiv", "is_tactic_proof": true, "tactics": ["apply", "rw", "intro", "apply", "rw", "intro", "simp", "sheafToPresheaf_map,", "exact"], "tactic_count": 9}
{"name": "CategoryTheory.Functor.IsDenseSubsite.sheafEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.DenseSubsite.SheafEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsDenseSubsite.instIsEquivalenceSheafSheafPushforwardContinuous", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.DenseSubsite.SheafEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsDenseSubsite.sheafEquivSheafificationCompatibility", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Sites.DenseSubsite.SheafEquiv", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Pseudofunctor.DescentData.instIsIsoαCategoryObjLocallyDiscreteOppositeCatMkOpHom", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Descent.DescentData", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pseudofunctor.DescentData.instCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Descent.DescentData", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pseudofunctor.DescentData.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Descent.DescentData", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pseudofunctor.DescentData.id_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Descent.DescentData", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pseudofunctor.DescentData.comp_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Descent.DescentData", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pseudofunctor.DescentData.ofObj", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Descent.DescentData", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pseudofunctor.toDescentData", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Descent.DescentData", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pseudofunctor.DescentData.pullFunctorObj", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Descent.DescentData", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pseudofunctor.DescentData.pullFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Descent.DescentData", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pseudofunctor.DescentData.toDescentDataCompPullFunctorIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Descent.DescentData", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pseudofunctor.DescentData.pullFunctorIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Descent.DescentData", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pseudofunctor.DescentData.pullFunctorIdIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Descent.DescentData", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pseudofunctor.DescentData.pullFunctorEquivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Descent.DescentData", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pseudofunctor.DescentData.exists_equivalence_of_sieve_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Descent.DescentData", "is_tactic_proof": false, "tactics": ["have", "obtain", "exact", "have", "obtain", "exact", "choose", "choose", "exact"], "tactic_count": 9}
{"name": "CategoryTheory.Pseudofunctor.DescentData.nonempty_fullyFaithful_toDescentData_iff_of_sieve_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Descent.DescentData", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Pseudofunctor.DescentData.isEquivalence_toDescentData_iff_of_sieve_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Descent.DescentData", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Pseudofunctor.DescentData.subtypeCompatibleHomEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Descent.DescentData", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pseudofunctor.DescentData.subtypeCompatibleHomEquiv_toCompatible_presheafHomObjHomEquiv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Descent.DescentData", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Pseudofunctor.IsPrestackFor.fullyFaithful", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Descent.DescentData", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pseudofunctor.isPrestackFor_iff_of_sieve_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Descent.DescentData", "is_tactic_proof": true, "tactics": ["simp", "obtain", "obtain", "apply", "simpa"], "tactic_count": 5}
{"name": "CategoryTheory.Pseudofunctor.IsPrestackFor_generate_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Descent.DescentData", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pseudofunctor.isPrestackFor_ofArrows_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Descent.DescentData", "is_tactic_proof": true, "tactics": ["simp", "apply", "rw"], "tactic_count": 3}
{"name": "CategoryTheory.Pseudofunctor.IsStackFor.isPrestackFor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Descent.DescentData", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pseudofunctor.isStackFor_iff_of_sieve_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Descent.DescentData", "is_tactic_proof": true, "tactics": ["simp", "obtain", "obtain", "apply", "simpa"], "tactic_count": 5}
{"name": "CategoryTheory.Pseudofunctor.IsStackFor_generate_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Descent.DescentData", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pseudofunctor.isStackFor_ofArrows_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Descent.DescentData", "is_tactic_proof": true, "tactics": ["simp", "apply", "rw"], "tactic_count": 3}
{"name": "CategoryTheory.Pseudofunctor.bijective_toDescentData_map_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Descent.DescentData", "is_tactic_proof": false, "tactics": ["rw", "convert", "ext", "apply"], "tactic_count": 4}
{"name": "CategoryTheory.Pseudofunctor.isPrestackFor_iff_isSheafFor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Descent.DescentData", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "convert", "refine", "rintro", "obtain", "obtain", "exact", "rintro", "exact"], "tactic_count": 11}
{"name": "CategoryTheory.Pseudofunctor.isPrestackFor_iff_isSheafFor'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Descent.DescentData", "is_tactic_proof": true, "tactics": ["rw", "refine", "replace", "rw", "convert", "refine", "intro", "exact", "rintro", "replace", "dsimp", "rw", "change", "simpa"], "tactic_count": 14}
{"name": "CategoryTheory.Pseudofunctor.IsPrestackFor.isSheafFor'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Descent.DescentData", "is_tactic_proof": true, "tactics": ["rw", "obtain", "simpa"], "tactic_count": 3}
{"name": "CategoryTheory.Pseudofunctor.fullyFaithfulToDescentData", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Descent.DescentData", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pseudofunctor.isPrestackFor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Descent.DescentData", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Pseudofunctor.isPrestackFor'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Descent.DescentData", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pseudofunctor.IsPrestack.of_isPrestackFor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Descent.DescentData", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pseudofunctor.LocallyDiscreteOpToCat.map_eq_pullHom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Descent.IsPrestack", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Pseudofunctor.LocallyDiscreteOpToCat.pullHom_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Descent.IsPrestack", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Pseudofunctor.presheafHom", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Descent.IsPrestack", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pseudofunctor.presheafHomObjHomEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Descent.IsPrestack", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pseudofunctor.overMapCompPresheafHomIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Descent.IsPrestack", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pseudofunctor.sheafHom", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Descent.IsPrestack", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pseudofunctor.isStackFor'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Descent.IsStack", "is_tactic_proof": true, "tactics": ["rw", "have", "have", "have", "have", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.Pseudofunctor.isStackFor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Descent.IsStack", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.Pseudofunctor.isEquivalence_toDescentData", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Descent.IsStack", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Pseudofunctor.IsStack.of_isStackFor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Descent.IsStack", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pseudofunctor.DescentData.full_pullFunctor.sieve", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Sites.Descent.Precoverage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pseudofunctor.DescentData.full_pullFunctor.sieve_mem", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Descent.Precoverage", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.Pseudofunctor.DescentData.full_pullFunctor.sieve.exists_fac", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Descent.Precoverage", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Pseudofunctor.DescentData.full_pullFunctor.sieve.idx", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Descent.Precoverage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pseudofunctor.DescentData.full_pullFunctor.sieve.hom", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Descent.Precoverage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pseudofunctor.DescentData.full_pullFunctor.sieve.fac", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Descent.Precoverage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pseudofunctor.DescentData.full_pullFunctor.familyOfElements", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Descent.Precoverage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pseudofunctor.DescentData.full_pullFunctor.compatible_familyOfElements", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Descent.Precoverage", "is_tactic_proof": true, "tactics": ["intro", "obtain", "obtain", "obtain", "obtain", "obtain", "obtain", "dsimp", "rw", "mor_precomp", "apply"], "tactic_count": 11}
{"name": "CategoryTheory.Pseudofunctor.DescentData.full_pullFunctor.hom", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Descent.Precoverage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pseudofunctor.DescentData.full_pullFunctor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Descent.Precoverage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.EffectiveEpimorphic", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.EffectiveEpimorphic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.EffectiveEpimorphic", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Sites.EffectiveEpimorphic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.generateSingleton", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.EffectiveEpimorphic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.generateSingleton_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.EffectiveEpimorphic", "is_tactic_proof": true, "tactics": ["ext", "constructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.isColimitOfEffectiveEpiStruct", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.EffectiveEpimorphic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.effectiveEpiStructOfIsColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.EffectiveEpimorphic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.effectiveEpimorphic_singleton", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.EffectiveEpimorphic", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "constructor", "apply", "rintro", "change", "rw", "apply"], "tactic_count": 9}
{"name": "CategoryTheory.Sieve.generateFamily", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.EffectiveEpimorphic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.generateFamily_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.EffectiveEpimorphic", "is_tactic_proof": true, "tactics": ["ext", "constructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.isColimitOfEffectiveEpiFamilyStruct", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.EffectiveEpimorphic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.effectiveEpiFamilyStructOfIsColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.EffectiveEpimorphic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.effectiveEpimorphic_family", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.EffectiveEpimorphic", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "constructor", "apply", "rintro", "change", "rw", "apply"], "tactic_count": 9}
{"name": "CategoryTheory.Sheaf.locallyInjective", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.locallySurjective", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.functorialLocallySurjectiveInjectiveFactorization", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.instIsLocallySurjectiveAppArrowILocallySurjectiveLocallyInjectiveFunctorialLocallySurjectiveInjectiveFactorization", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.EpiMono", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Sheaf.instIsLocallyInjectiveAppArrowPLocallySurjectiveLocallyInjectiveFunctorialLocallySurjectiveInjectiveFactorization", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.EpiMono", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Sheaf.instEpiAppArrowILocallySurjectiveLocallyInjectiveFunctorialLocallySurjectiveInjectiveFactorization", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.EpiMono", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Sheaf.instMonoAppArrowPLocallySurjectiveLocallyInjectiveFunctorialLocallySurjectiveInjectiveFactorization", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.EpiMono", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Sheaf.instHasFunctorialFactorizationLocallySurjectiveLocallyInjective", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.EpiMono", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.isLocallySurjective_iff_epi'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.EpiMono", "is_tactic_proof": true, "tactics": ["constructor", "intro", "infer_instance", "intro", "let", "have", "have", "have", "have", "have", "rw", "infer_instance"], "tactic_count": 12}
{"name": "CategoryTheory.Equalizer.FirstObj", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.EqualizerSheafCondition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equalizer.FirstObj.ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.EqualizerSheafCondition", "is_tactic_proof": true, "tactics": ["apply", "rintro", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Equalizer.firstObjEqFamily", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.EqualizerSheafCondition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equalizer.instInhabitedFirstObjBotPresieve", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.EqualizerSheafCondition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equalizer.instInhabitedFirstObjArrowsBotSieve", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.EqualizerSheafCondition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equalizer.forkMap", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.EqualizerSheafCondition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equalizer.Sieve.SecondObj", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.EqualizerSheafCondition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equalizer.Sieve.SecondObj.ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.EqualizerSheafCondition", "is_tactic_proof": true, "tactics": ["apply", "rintro", "apply"], "tactic_count": 3}
{"name": "CategoryTheory.Equalizer.Sieve.firstMap", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.EqualizerSheafCondition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equalizer.Sieve.instInhabitedSecondObjBotSieve", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.EqualizerSheafCondition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equalizer.Sieve.secondMap", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.EqualizerSheafCondition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equalizer.Sieve.w", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.EqualizerSheafCondition", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Equalizer.Sieve.compatible_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.EqualizerSheafCondition", "is_tactic_proof": true, "tactics": ["rw", "constructor", "intro", "apply", "intro", "simpa", "intro", "rw", "simpa"], "tactic_count": 9}
{"name": "CategoryTheory.Equalizer.Sieve.equalizer_sheaf_condition", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.EqualizerSheafCondition", "is_tactic_proof": false, "tactics": ["rw", "simp_rw", "simp", "apply", "intro", "apply", "intro", "rw", "rw", "constructor", "intro", "funext", "simpa", "intro", "rw", "simp"], "tactic_count": 16}
{"name": "CategoryTheory.Equalizer.Presieve.SecondObj", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.EqualizerSheafCondition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equalizer.Presieve.firstMap", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.EqualizerSheafCondition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equalizer.Presieve.instInhabitedSecondObjBotPresieve", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.EqualizerSheafCondition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equalizer.Presieve.secondMap", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.EqualizerSheafCondition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equalizer.Presieve.w", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.EqualizerSheafCondition", "is_tactic_proof": true, "tactics": ["dsimp", "ext", "simp", "simp", "haveI", "rw", "simp"], "tactic_count": 7}
{"name": "CategoryTheory.Equalizer.Presieve.compatible_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.EqualizerSheafCondition", "is_tactic_proof": true, "tactics": ["rw", "constructor", "intro", "apply", "rintro", "simpa", "intro", "rw", "simpa"], "tactic_count": 9}
{"name": "CategoryTheory.Equalizer.Presieve.sheaf_condition", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.EqualizerSheafCondition", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "apply", "intro", "apply", "intro", "rw", "constructor", "intro", "funext", "simpa", "intro", "rw", "simp"], "tactic_count": 14}
{"name": "CategoryTheory.Equalizer.Presieve.Arrows.FirstObj", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.EqualizerSheafCondition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equalizer.Presieve.Arrows.FirstObj.ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.EqualizerSheafCondition", "is_tactic_proof": true, "tactics": ["apply", "rintro", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Equalizer.Presieve.Arrows.SecondObj", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.EqualizerSheafCondition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equalizer.Presieve.Arrows.SecondObj.ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.EqualizerSheafCondition", "is_tactic_proof": true, "tactics": ["apply", "rintro", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Equalizer.Presieve.Arrows.forkMap", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.EqualizerSheafCondition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equalizer.Presieve.Arrows.firstMap", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.EqualizerSheafCondition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equalizer.Presieve.Arrows.secondMap", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.EqualizerSheafCondition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equalizer.Presieve.Arrows.w", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.EqualizerSheafCondition", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Equalizer.Presieve.Arrows.compatible_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.EqualizerSheafCondition", "is_tactic_proof": true, "tactics": ["rw", "constructor", "intro", "ext", "simpa", "intro", "apply_fun", "simpa"], "tactic_count": 8}
{"name": "CategoryTheory.Equalizer.Presieve.Arrows.compatible_iff_of_small", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.EqualizerSheafCondition", "is_tactic_proof": true, "tactics": ["rw", "refine", "ext", "simpa", "apply_fun", "simpa"], "tactic_count": 6}
{"name": "CategoryTheory.Equalizer.Presieve.Arrows.sheaf_condition", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.EqualizerSheafCondition", "is_tactic_proof": true, "tactics": ["rw", "simp", "rw", "simp_rw", "apply", "intro", "apply", "intro", "rw", "constructor", "intro", "funext", "simpa", "intro", "rw", "simp"], "tactic_count": 16}
{"name": "CategoryTheory.Equalizer.Presieve.isSheafFor_singleton_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.EqualizerSheafCondition", "is_tactic_proof": false, "tactics": ["have", "refine", "rw", "simp", "rw", "simp_rw"], "tactic_count": 6}
{"name": "CategoryTheory.Equalizer.Presieve.isSheafFor_singleton_iff_of_hasPullback", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.EqualizerSheafCondition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.instIsCoverDenseOfIsEquivalence", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.instIsDenseSubsiteInducedTopologyInverseFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Equivalence", "is_tactic_proof": false, "tactics": ["have", "ext", "rw", "congr", "nth_rw", "infer_instance"], "tactic_count": 6}
{"name": "CategoryTheory.Equivalence.eq_inducedTopology_of_isDenseSubsite", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Equivalence", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Equivalence.isDenseSubsite_functor_of_isCocontinuous", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.isDenseSubsite_inverse_of_isCocontinuous", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.instIsDenseSubsiteFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Equivalence", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Equivalence.sheafCongr.functor", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.sheafCongr.inverse", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.sheafCongr.unitIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.sheafCongr.counitIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.sheafCongr", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.transportAndSheafify", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.transportIsoSheafToPresheaf", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.transportSheafificationAdjunction", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.instPreservesFiniteLimitsFunctorOppositeSheafTransportAndSheafify", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.hasSheafify", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.hasSheafCompose", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.smallSheafify", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.smallSheafificationAdjunction", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.hasSheafifyEssentiallySmallSite", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.hasSheafComposeEssentiallySmallSite", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.hasLimitsEssentiallySmallSite", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.hasColimitsEssentiallySmallSite", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.W_inverseImage_whiskeringLeft", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Equivalence", "is_tactic_proof": true, "tactics": ["ext", "have", "rw", "conv_rhs", "apply", "ext", "constructor", "rintro", "exact", "rintro", "exact", "have", "rw", "exact", "rw", "constructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 20}
{"name": "CategoryTheory.GrothendieckTopology.W_whiskerLeft_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Equivalence", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "CategoryTheory.GrothendieckTopology.PreservesSheafification.transport", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.WEqualsLocallyBijective.transport", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.WEqualsLocallyBijective.ofEssentiallySmall", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.instPreservesSheafification_1", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Precoverage.finite", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Precoverage.mem_finite_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Precoverage.ofArrows_mem_finite", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Finite", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.Precoverage.instHasIsosFinite", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretopology.finite", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretopology.ofArrows_mem_finite", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasGlobalSectionsFunctor", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Sites.GlobalSections", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.Γ", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.GlobalSections", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.constantSheafΓAdj", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.GlobalSections", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instIsRightAdjointSheafΓ", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.GlobalSections", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "CategoryTheory.hasGlobalSectionsFunctor_of_hasTerminal", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.GlobalSections", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.ΓNatIsoSheafSections", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.GlobalSections", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.hasGlobalSectionsFunctor_of_hasLimitsOfShape", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.GlobalSections", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.ΓNatIsoLim", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.GlobalSections", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.ΓHomEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.GlobalSections", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.ΓHomEquiv_naturality_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.GlobalSections", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.ΓHomEquiv_naturality_left_symm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.GlobalSections", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.ΓHomEquiv_naturality_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.GlobalSections", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.ΓHomEquiv_naturality_right_symm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.GlobalSections", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.coneΓ", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.GlobalSections", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.isLimitConeΓ", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.GlobalSections", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.ΓRes", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.GlobalSections", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.ΓRes_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.GlobalSections", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.coneΓ_π_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.GlobalSections", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.ΓRes_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.GlobalSections", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Sheaf.natTransΓRes", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.GlobalSections", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.ΓObjEquivSections", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.GlobalSections", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.ΓObjEquivSections_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.GlobalSections", "is_tactic_proof": true, "tactics": ["dsimp", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Sheaf.ΓObjEquivSections_naturality_symm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.GlobalSections", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.ΓNatIsoSectionsFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.GlobalSections", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.ΓObjEquivHom", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.GlobalSections", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.ΓObjEquivHom_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.GlobalSections", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.ΓObjEquivHom_naturality_symm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.GlobalSections", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.ΓNatIsoCoyoneda", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.GlobalSections", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.instDFunLikeSetSieve", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.mem_sieves_iff_coe", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.top_mem", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.pullback_stable", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.pullback_mem_iff_of_isIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": true, "tactics": ["refine", "convert", "rw"], "tactic_count": 3}
{"name": "CategoryTheory.GrothendieckTopology.transitive", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.covering_of_eq_top", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.copy", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.sieves_copy", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.coe_copy", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.copy_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.superset_covering", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": true, "tactics": ["apply", "intro", "apply", "rw", "apply"], "tactic_count": 5}
{"name": "CategoryTheory.GrothendieckTopology.intersection_covering", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": true, "tactics": ["apply", "intro", "rw", "simp"], "tactic_count": 4}
{"name": "CategoryTheory.GrothendieckTopology.intersection_covering_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.bind_covering", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.bindOfArrows", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.GrothendieckTopology.Covers", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.covers_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.covering_iff_covers_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.GrothendieckTopology.arrow_max", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "CategoryTheory.GrothendieckTopology.arrow_stable", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.GrothendieckTopology.arrow_trans", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": true, "tactics": ["intro", "apply", "intro", "rw", "apply"], "tactic_count": 5}
{"name": "CategoryTheory.GrothendieckTopology.arrow_intersect", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.GrothendieckTopology.trivial", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.discrete", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.trivial_covering", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.instLEGrothendieckTopology", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.le_def", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.instPartialOrder", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.instInfSet", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.mem_sInf", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": true, "tactics": ["change", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.GrothendieckTopology.isGLB_sInf", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": true, "tactics": ["refine", "rfl", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.GrothendieckTopology.instCompleteLattice", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.instInhabited", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.trivial_eq_bot", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.discrete_eq_top", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.bot_covering", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.top_covering", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.bot_covers", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.GrothendieckTopology.top_covers", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.GrothendieckTopology.dense", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.dense_covering", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.RightOreCondition", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.right_ore_of_pullbacks", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.atomic", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Cover", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Cover.instCoeOutSieve", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Cover.instCoeFunForallForallHomProp", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Cover.condition", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Cover.ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Cover.instOrderTop", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Cover.instSemilatticeInf", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Cover.instInhabited", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Cover.Arrow.precomp", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Cover.Arrow.precompRelation", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Cover.Arrow.map", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Cover.Arrow.Relation.map", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Cover.pullback", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Cover.Arrow.base", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Cover.Arrow.Relation.base", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Cover.coe_pullback", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Cover.pullbackId", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Cover.pullbackComp", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Cover.bind", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Cover.bindToBase", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Cover.Arrow.middle", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Cover.Arrow.toMiddleHom", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Cover.Arrow.fromMiddleHom", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Cover.Arrow.from_middle_condition", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Cover.Arrow.fromMiddle", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Cover.Arrow.to_middle_condition", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Cover.Arrow.toMiddle", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Cover.Arrow.middle_spec", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Cover.Relation.mk'", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Cover.shape", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Cover.index", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Cover.multifork", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Cover.toMultiequalizer", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.pullback", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.pullbackId", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.pullbackComp", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Grothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreOneHypercover.Homotopy.mapMultiforkOfIsLimit_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Homotopy", "is_tactic_proof": true, "tactics": ["refine", "have", "simp", "multicospanShape_snd,", "simp"], "tactic_count": 5}
{"name": "CategoryTheory.PreOneHypercover.cylinderX", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Homotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreOneHypercover.cylinderf", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Homotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreOneHypercover.cylinder", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Homotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreOneHypercover.toPullback_cylinder", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Homotopy", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.PreOneHypercover.sieve₀_cylinder", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Homotopy", "is_tactic_proof": true, "tactics": ["refine", "rw", "rintro", "refine", "simp", "exact", "rw", "rintro", "exact"], "tactic_count": 9}
{"name": "CategoryTheory.PreOneHypercover.sieve₁'_cylinder", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Homotopy", "is_tactic_proof": true, "tactics": ["refine", "rw", "rintro", "refine", "simp", "rw", "rintro", "simp_rw", "apply", "rw", "convert", "simp"], "tactic_count": 12}
{"name": "CategoryTheory.PreOneHypercover.cylinderHom", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Homotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreOneHypercover.cylinderHomotopy", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Homotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreOneHypercover.exists_nonempty_homotopy", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Homotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.OneHypercover.cylinder", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Homotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.OneHypercover.exists_nonempty_homotopy", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Homotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.OneHypercover.homotopicRel", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Homotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.HOneHypercover", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Homotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.OneHypercover.toHOneHypercover", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Homotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreOneHypercover.Homotopy.map_eq_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Homotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.HOneHypercover.instNonempty", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Homotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.HOneHypercover.isCofiltered_of_hasPullbacks", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Homotopy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.OneHypercoverFamily", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Sites.Hypercover.IsSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.OneHypercoverFamily.exists_oneHypercover", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.IsSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.OneHypercoverFamily.IsSheafIff.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.IsSheaf", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.GrothendieckTopology.OneHypercoverFamily.IsSheafIff.lift", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.IsSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.OneHypercoverFamily.IsSheafIff.fac'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.IsSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.OneHypercoverFamily.IsSheafIff.fac", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.IsSheaf", "is_tactic_proof": true, "tactics": ["apply", "intro", "rintro", "rw", "exact", "snd", "r"], "tactic_count": 7}
{"name": "CategoryTheory.GrothendieckTopology.OneHypercoverFamily.IsSheafIff.isLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.IsSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.OneHypercoverFamily.isSheaf_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.IsSheaf", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "intro", "rw", "rintro", "obtain", "exact"], "tactic_count": 8}
{"name": "CategoryTheory.GrothendieckTopology.IsGeneratedByOneHypercovers", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Sites.Hypercover.IsSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.instIsGeneratedByOneHypercovers", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Hypercover.IsSheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.isSheaf_iff_of_isGeneratedByOneHypercovers", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.IsSheaf", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.PreOneHypercover.sieve₁", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.One", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreOneHypercover.toPullback", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Sites.Hypercover.One", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreOneHypercover.sieve₁'", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.One", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreOneHypercover.sieve₁_eq_pullback_sieve₁'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.One", "is_tactic_proof": true, "tactics": ["ext", "constructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.PreOneHypercover.sieve₁'_eq_sieve₁", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.One", "is_tactic_proof": true, "tactics": ["rw", "congr", "cat_disch"], "tactic_count": 3}
{"name": "CategoryTheory.PreOneHypercover.I₁'", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Sites.Hypercover.One", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreOneHypercover.Y'", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.One", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreOneHypercover.Y'_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.One", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreOneHypercover.multicospanShape", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.One", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreOneHypercover.multicospanIndex", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.One", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreOneHypercover.multifork", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.One", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreOneHypercover.multifork_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.One", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreOneHypercover.forkOfIsColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.One", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreOneHypercover.forkOfIsColimit_ι_map_inj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.One", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.PreOneHypercover.isLimitMultiforkEquivIsLimitFork", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.One", "is_tactic_proof": true, "tactics": ["letI", "letI", "letI", "letI", "refine", "refine", "refine", "simp", "rw", "simp", "refine", "simp", "rw", "simp", "refine", "simp", "simp"], "tactic_count": 17}
{"name": "CategoryTheory.PreOneHypercover.sigmaOfIsColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.One", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreOneHypercover.p₁_sigmaOfIsColimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.One", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.PreOneHypercover.p₂_sigmaOfIsColimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.One", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.PreOneHypercover.instUniqueLMulticospanShapeSigmaOfIsColimit", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Hypercover.One", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreOneHypercover.instUniqueRMulticospanShapeSigmaOfIsColimit", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Hypercover.One", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreOneHypercover.isLimitSigmaOfIsColimitEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.One", "is_tactic_proof": false, "tactics": ["refine", "exact", "exact", "exact", "all_goals"], "tactic_count": 5}
{"name": "CategoryTheory.PreOneHypercover.trivial", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.One", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreOneHypercover.sieve₀_trivial", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.One", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.PreOneHypercover.sieve₁_trivial", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.One", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.PreOneHypercover.instNonempty", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Hypercover.One", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreOneHypercover.inter", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.One", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreOneHypercover.sieve₁_inter", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.One", "is_tactic_proof": true, "tactics": ["ext", "let", "refine", "refine", "apply", "apply", "apply", "refine", "have", "simp", "have", "simp", "exact", "simp", "subst", "refine", "simp", "simp", "apply", "simp", "simpa", "apply", "simp", "simpa"], "tactic_count": 24}
{"name": "CategoryTheory.PreOneHypercover.Hom.id", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.One", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreOneHypercover.Hom.comp", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.One", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreOneHypercover.Hom.s₁'", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.One", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreOneHypercover.instCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Hypercover.One", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreOneHypercover.oneToZero", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.One", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreOneHypercover.Hom.mapMultiforkOfIsLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.One", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreOneHypercover.Hom.mapMultiforkOfIsLimit_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.One", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.PreOneHypercover.interFst", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.One", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreOneHypercover.interSnd", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.One", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreOneHypercover.interLift", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.One", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.OneHypercover.mem_sieve₁'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.One", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.GrothendieckTopology.OneHypercover.mk'", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.One", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.OneHypercover.multiforkLift", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.One", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.OneHypercover.multiforkLift_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.One", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.GrothendieckTopology.OneHypercover.isLimitMultifork", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.One", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.OneHypercover.toZeroHypercover", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.One", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.OneHypercover.trivial", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.One", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.OneHypercover.instNonempty", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Hypercover.One", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.OneHypercover.inter", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.One", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.OneHypercover.Hom", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Sites.Hypercover.One", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.OneHypercover.instCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Hypercover.One", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.OneHypercover.isoMk", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.One", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.OneHypercover.isSheafFor_presieve₀", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.One", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.GrothendieckTopology.OneHypercover.arrowsCompatible", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.One", "is_tactic_proof": true, "tactics": ["rintro", "refine", "rw", "conv_rhs", "simp"], "tactic_count": 5}
{"name": "CategoryTheory.GrothendieckTopology.OneHypercover.amalgamate", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.One", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.OneHypercover.map_amalgamate", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.One", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.GrothendieckTopology.Cover.preOneHypercover", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.One", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Cover.preOneHypercover_sieve₀", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.One", "is_tactic_proof": true, "tactics": ["ext", "constructor", "rintro", "exact", "intro", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.GrothendieckTopology.Cover.preOneHypercover_sieve₁", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.One", "is_tactic_proof": true, "tactics": ["ext", "simp", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.GrothendieckTopology.Cover.oneHypercover", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.One", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreZeroHypercover.ext_of_isSeparatedFor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.One", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreZeroHypercover.toPreOneHypercover", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.One", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instHasPullbacksToPreOneHypercover", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Hypercover.One", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.sieve₁'_toPreOneHypercover_eq_top", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.One", "is_tactic_proof": true, "tactics": ["rw", "intro", "refine", "refine", "apply"], "tactic_count": 5}
{"name": "CategoryTheory.Precoverage.ZeroHypercover.toOneHypercover", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.One", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.OneHypercover.glueMorphisms", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Subcanonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.OneHypercover.f_glueMorphisms", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Subcanonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Precoverage.ZeroHypercover.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Subcanonical", "is_tactic_proof": false, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Precoverage.ZeroHypercover.glueMorphisms", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Subcanonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Precoverage.ZeroHypercover.f_glueMorphisms", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Subcanonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Precoverage.ZeroHypercover.instIsLocalAtTargetIsomorphisms", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Subcanonical", "is_tactic_proof": true, "tactics": ["refine", "refine", "let", "pullback.map", "rw", "simp", "exact", "exact"], "tactic_count": 8}
{"name": "CategoryTheory.Precoverage.ZeroHypercover.isPullback_of_forall_isPullback", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Subcanonical", "is_tactic_proof": false, "tactics": ["have", "suffices", "simp_rw", "isomorphisms.iff]", "intro", "let", "have", "simpa", "have", "rw", "simpa", "have", "pullback.snd", "rw", "cat_disch", "rw", "infer_instance"], "tactic_count": 17}
{"name": "CategoryTheory.PreZeroHypercover.HasPullbacks", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreZeroHypercover.presieve₀", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreZeroHypercover.presieve₀_f", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreZeroHypercover.sieve₀", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreZeroHypercover.sieve₀_f", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreZeroHypercover.singleton", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreZeroHypercover.presieve₀_singleton", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.PreZeroHypercover.instUniqueI₀Singleton", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreZeroHypercover.pullback₁", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreZeroHypercover.pullback₂", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreZeroHypercover.presieve₀_pullback₁", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": true, "tactics": ["refine", "rintro", "use", "rintro", "use"], "tactic_count": 5}
{"name": "CategoryTheory.PreZeroHypercover.pullbackCoverOfLeft", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreZeroHypercover.pullbackCoverOfRight", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreZeroHypercover.bind", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreZeroHypercover.restrictIndex", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreZeroHypercover.presieve₀_restrictIndex_equiv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.PreZeroHypercover.reindex", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreZeroHypercover.presieve₀_reindex", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.PreZeroHypercover.inter", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreZeroHypercover.inter_def", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreZeroHypercover.sum", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreZeroHypercover.sum_X_inl", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreZeroHypercover.sum_X_inr", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreZeroHypercover.sum_f_inl", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreZeroHypercover.sum_f_inr", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreZeroHypercover.presieve₀_sum", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": true, "tactics": ["rw", "apply", "intro", "cases", "exact", "exact", "rintro", "exact", "exact"], "tactic_count": 9}
{"name": "CategoryTheory.PreZeroHypercover.add", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreZeroHypercover.add_X_some", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreZeroHypercover.add_X_none", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreZeroHypercover.add_f_some", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreZeroHypercover.add_f_nome", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreZeroHypercover.presieve₀_add", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.PreZeroHypercover.sigmaOfIsColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreZeroHypercover.inj_sigmaOfIsColimit_f", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.PreZeroHypercover.Hom.id", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreZeroHypercover.Hom.comp", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreZeroHypercover.instCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreZeroHypercover.Hom.ext'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": true, "tactics": ["cases", "cases", "simp", "cat_disch"], "tactic_count": 4}
{"name": "CategoryTheory.PreZeroHypercover.Hom.ext'_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreZeroHypercover.hom_inv_s₀_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreZeroHypercover.inv_hom_s₀_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreZeroHypercover.hom_inv_h₀", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": true, "tactics": ["obtain", "simpa"], "tactic_count": 2}
{"name": "CategoryTheory.PreZeroHypercover.inv_hom_h₀", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": true, "tactics": ["obtain", "simpa"], "tactic_count": 2}
{"name": "CategoryTheory.PreZeroHypercover.instIsIsoH₀Hom", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": true, "tactics": ["use", "rw", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.PreZeroHypercover.instIsIsoH₀Inv", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreZeroHypercover.inv_hom_h₀_comp_f", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.PreZeroHypercover.inv_inv_h₀_comp_f", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.PreZeroHypercover.map", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreZeroHypercover.presieve₀_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreZeroHypercover.pullbackIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreZeroHypercover.sumInl", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreZeroHypercover.sumInr", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreZeroHypercover.sumLift", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreZeroHypercover.interFst", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreZeroHypercover.interSnd", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreZeroHypercover.interLift", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreZeroHypercover.pullbackCoverOfLeftIsoPullback₁", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreZeroHypercover.pullbackCoverOfRightIsoPullback₂", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.preZeroHypercover", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.presieve₀_preZeroHypercover", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": true, "tactics": ["refine", "rintro", "exact", "intro", "let", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.Presieve.exists_eq_preZeroHypercover", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreZeroHypercover.shrink", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreZeroHypercover.presieve₀_shrink", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreZeroHypercover.shrink_eq_shrink_of_presieve₀_eq_presieve₀", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.PreZeroHypercover.presieve₀_eq_presieve₀_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.PreZeroHypercover.toShrink", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreZeroHypercover.fromShrink", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Precoverage.RespectsIso.of_forall_exists_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": true, "tactics": ["choose", "choose", "let", "f", "i", "let", "f", "i", "let", "refine", "cases", "have", "refine", "rintro", "have", "refine", "rintro", "rw", "apply", "rwa"], "tactic_count": 20}
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{"name": "CategoryTheory.Precoverage.ZeroHypercover.singleton", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Precoverage.ZeroHypercover.pullback₁", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Precoverage.ZeroHypercover.pullback₂", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Precoverage.ZeroHypercover.bind", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Precoverage.ZeroHypercover.inter", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Precoverage.ZeroHypercover.reindex", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Precoverage.ZeroHypercover.sum", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Precoverage.ZeroHypercover.add", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Precoverage.ZeroHypercover.weaken", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Precoverage.ZeroHypercover.instHasPullbacksPresieve₀OfHasPullbacks", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Precoverage.ZeroHypercover.instHasPullbackFOfHasPullbacksPresieve₀", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Precoverage.ZeroHypercover.instHasPullbackFOfHasPullbacksPresieve₀_1", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Precoverage.ZeroHypercover.Hom", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Precoverage.ZeroHypercover.instCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Precoverage.ZeroHypercover.isoMk", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Precoverage.ZeroHypercover.map", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Precoverage.ZeroHypercover.presieve₀_mem_of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Precoverage.ZeroHypercover.instSmallOfSmallI₀", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Precoverage.ZeroHypercover.Small.Index", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Precoverage.ZeroHypercover.Small.restrictFun", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Precoverage.ZeroHypercover.Small.mem₀", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Precoverage.ZeroHypercover.instSmall", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Precoverage.ZeroHypercover.restrictIndexOfSmall", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Precoverage.ZeroHypercover.instSmallPullback₁", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": true, "tactics": ["use", "have", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Precoverage.mem_iff_exists_zeroHypercover", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": true, "tactics": ["refine", "obtain", "use"], "tactic_count": 3}
{"name": "CategoryTheory.Precoverage.le_of_zeroHypercover", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": true, "tactics": ["intro", "obtain", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Precoverage.instSmallOfSmall", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": ["have", "let", "use", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.Precoverage.instRespectsIsoOfIsStableUnderBaseChange", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Precoverage.ZeroHypercover.pullbackCoverOfLeft", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Precoverage.ZeroHypercover.pullbackCoverOfRight", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instCoeFunPreZeroHypercoverFamilyForallForallPreZeroHypercoverProp", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Hypercover.ZeroFamily", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreZeroHypercoverFamily.presieve", "kind": "inductive", "module": "Mathlib.CategoryTheory.Sites.Hypercover.ZeroFamily", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreZeroHypercoverFamily.precoverage", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.ZeroFamily", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreZeroHypercoverFamily.mem_precoverage_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.ZeroFamily", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PreZeroHypercover.presieve₀_mem_precoverage_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.ZeroFamily", "is_tactic_proof": true, "tactics": ["refine", "rw", "obtain", "rw", "rwa"], "tactic_count": 5}
{"name": "CategoryTheory.Precoverage.preZeroHypercoverFamily", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.ZeroFamily", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Precoverage.equivPreZeroHypercoverFamily", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Hypercover.ZeroFamily", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Precoverage.HasIsos.of_preZeroHypercoverFamily", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.ZeroFamily", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Precoverage.IsStableUnderBaseChange.of_preZeroHypercoverFamily_of_isClosedUnderIsomorphisms", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.ZeroFamily", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Precoverage.IsStableUnderComposition.of_preZeroHypercoverFamily", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.ZeroFamily", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Precoverage.IsStableUnderSup.of_preZeroHypercoverFamily", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Hypercover.ZeroFamily", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.FamilyOfElements", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.instInhabitedFamilyOfElementsBot", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.FamilyOfElements.ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": true, "tactics": ["funext", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Presieve.FamilyOfElements.restrict", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.FamilyOfElements.map", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.FamilyOfElements.map_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.FamilyOfElements.restrict_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.FamilyOfElements.singletonEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.FamilyOfElements.singletonEquiv_symm_apply_self", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Presieve.FamilyOfElements.Compatible", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.FamilyOfElements.PullbackCompatible", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.pullbackCompatible_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": true, "tactics": ["constructor", "intro", "apply", "haveI", "apply", "intro", "haveI", "rw"], "tactic_count": 8}
{"name": "CategoryTheory.Presieve.FamilyOfElements.Compatible.restrict", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.FamilyOfElements.sieveExtend", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.FamilyOfElements.Compatible.sieveExtend", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": true, "tactics": ["intro", "iterate", "apply", "simp"], "tactic_count": 4}
{"name": "CategoryTheory.Presieve.extend_agrees", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": true, "tactics": ["have", "unfold", "rw", "simp", "rw", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.Presieve.restrict_extend", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": true, "tactics": ["funext", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Presieve.FamilyOfElements.SieveCompatible", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.compatible_iff_sieveCompatible", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": true, "tactics": ["constructor", "intro", "simpa", "intro", "simp_rw", "congr"], "tactic_count": 6}
{"name": "CategoryTheory.Presieve.FamilyOfElements.Compatible.to_sieveCompatible", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.extend_restrict", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": true, "tactics": ["rw", "funext", "apply", "congr", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.Presieve.restrict_inj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.compatibleEquivGenerateSieveCompatible", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.FamilyOfElements.comp_of_compatible", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.Presieve.FamilyOfElements.compatible_singleton_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": true, "tactics": ["refine", "rintro", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Presieve.FamilyOfElements.functorPullback", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.FamilyOfElements.Compatible.functorPullback", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": true, "tactics": ["intro", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Presieve.FamilyOfElements.functorPushforward", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.FamilyOfElements.pullback", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.FamilyOfElements.Compatible.pullback", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": true, "tactics": ["simp", "intro", "unfold", "rw", "congr", "simp"], "tactic_count": 6}
{"name": "CategoryTheory.Presieve.FamilyOfElements.compPresheafMap", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.FamilyOfElements.map_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.FamilyOfElements.map_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "CategoryTheory.Presieve.FamilyOfElements.Compatible.map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": true, "tactics": ["intro", "unfold", "rwa"], "tactic_count": 3}
{"name": "CategoryTheory.Presieve.FamilyOfElements.IsAmalgamation", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.FamilyOfElements.IsAmalgamation.map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": true, "tactics": ["intro", "dsimp", "change", "rw"], "tactic_count": 4}
{"name": "CategoryTheory.Presieve.is_compatible_of_exists_amalgamation", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": true, "tactics": ["obtain", "intro", "rw", "simp"], "tactic_count": 4}
{"name": "CategoryTheory.Presieve.isAmalgamation_restrict", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.isAmalgamation_sieveExtend", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": true, "tactics": ["intro", "dsimp", "rw"], "tactic_count": 3}
{"name": "CategoryTheory.Presieve.FamilyOfElements.isAmalgamation_singleton_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": true, "tactics": ["refine", "rintro", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Presieve.IsSeparatedFor", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.IsSeparatedFor.ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.isSeparatedFor_iff_generate", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": true, "tactics": ["constructor", "intro", "apply", "exact", "exact", "intro", "apply", "exact", "exact"], "tactic_count": 9}
{"name": "CategoryTheory.Presieve.isSeparatedFor_top", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.IsSheafFor", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.YonedaSheafCondition", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.natTransEquivCompatibleFamily", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.extension_iff_amalgamation", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": true, "tactics": ["change", "constructor", "rintro", "rw", "simp", "intro", "ext", "convert", "rw", "simp"], "tactic_count": 10}
{"name": "CategoryTheory.Presieve.isSheafFor_iff_yonedaSheafCondition", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "rw", "rw", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.Presieve.IsSheafFor.extend", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.IsSheafFor.functorInclusion_comp_extend", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.IsSheafFor.unique_extend", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.IsSheafFor.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.isSeparatedFor_and_exists_isAmalgamation_iff_isSheafFor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": true, "tactics": ["rw", "apply", "intro", "constructor", "intro", "exact", "intro", "refine", "intro", "apply", "exact"], "tactic_count": 11}
{"name": "CategoryTheory.Presieve.IsSeparatedFor.isSheafFor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Presieve.IsSheafFor.isSeparatedFor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.IsSheafFor.amalgamate", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.IsSheafFor.isAmalgamation", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.IsSheafFor.valid_glue", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.isSheafFor_iff_generate", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": true, "tactics": ["rw", "rw", "rw", "apply", "constructor", "intro", "apply", "intro", "simpa", "intro", "apply", "intro", "simpa"], "tactic_count": 13}
{"name": "CategoryTheory.Presieve.isSheafFor_singleton_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": true, "tactics": ["intro", "refine", "rintro", "simp", "intro", "simpa"], "tactic_count": 6}
{"name": "CategoryTheory.Presieve.isSheafFor_top", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": true, "tactics": ["rw", "rw", "apply"], "tactic_count": 3}
{"name": "CategoryTheory.Presieve.isSheafFor_of_nat_equiv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.isSheafFor_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.isSheafFor_iff_of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.isSeparatedFor_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": true, "tactics": ["intro", "simpa"], "tactic_count": 2}
{"name": "CategoryTheory.Presieve.isSheafFor_subsieve_aux", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": true, "tactics": ["rw", "constructor", "intro", "exact", "intro", "use", "intro", "apply", "intro", "rw", "hx", "simp"], "tactic_count": 12}
{"name": "CategoryTheory.Presieve.isSheafFor_subsieve", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.Arrows.Compatible", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.FamilyOfElements.isAmalgamation_iff_ofArrows", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.Arrows.Compatible.exists_familyOfElements", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": true, "tactics": ["choose", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Presieve.Arrows.Compatible.familyOfElements", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.Arrows.Compatible.familyOfElements_ofArrows_mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.Arrows.Compatible.familyOfElements_compatible", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": true, "tactics": ["rintro", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Presieve.isSheafFor_arrows_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": true, "tactics": ["refine", "obtain", "refine", "rw", "rw", "obtain", "h", "exact"], "tactic_count": 8}
{"name": "CategoryTheory.Presieve.Arrows.toCompatible", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.isSheafFor_ofArrows_iff_bijective_toCompabible", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": true, "tactics": ["rw", "refine", "obtain", "exact", "obtain", "rw", "dsimp", "subst", "exact"], "tactic_count": 9}
{"name": "CategoryTheory.Presieve.isSheafFor_pullback_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": true, "tactics": ["obtain", "have", "dsimp", "let", "s", "simp", "exact", "invFun", "s", "replace", "simp", "exact", "simp", "convert", "ext", "simp"], "tactic_count": 16}
{"name": "CategoryTheory.Presieve.isSheafFor_over_map_op_comp_ofArrows_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": false, "tactics": ["let", "s", "replace", "dsimp", "have", "s.property", "have", "dsimp", "rw", "let", "replace", "dsimp", "simp", "convert", "invFun", "s", "s.property", "simp", "rfl"], "tactic_count": 19}
{"name": "CategoryTheory.Presieve.isSheafFor_over_map_op_comp_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": true, "tactics": ["obtain", "rw", "isSheafFor_iff_generate]", "convert", "refine", "rintro", "refine", "simpa", "cat_disch", "rintro", "exact"], "tactic_count": 11}
{"name": "CategoryTheory.Presieve.Arrows.PullbackCompatible", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.Arrows.pullbackCompatible_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": true, "tactics": ["refine", "apply", "exact", "rw", "op_comp,"], "tactic_count": 5}
{"name": "CategoryTheory.Presieve.isSheafFor_arrows_iff_pullbacks", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "CategoryTheory.Presieve.isSeparatedFor_singleton", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "aesop"], "tactic_count": 3}
{"name": "CategoryTheory.Presieve.isSheafFor_singleton", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.IsSheafFor", "is_tactic_proof": true, "tactics": ["rw", "simp_rw"], "tactic_count": 2}
{"name": "CategoryTheory.Types.jointlySurjectivePrecoverage", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.JointlySurjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Types.mem_jointlySurjectivePrecoverage_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.JointlySurjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Types.singleton_mem_jointlySurjectivePrecoverage_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.JointlySurjective", "is_tactic_proof": true, "tactics": ["rw", "refine", "obtain", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.Types.ofArrows_mem_jointlySurjectivePrecoverage_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.JointlySurjective", "is_tactic_proof": true, "tactics": ["refine", "obtain", "use", "obtain", "use"], "tactic_count": 5}
{"name": "CategoryTheory.Types.instHasIsosJointlySurjectivePrecoverage", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.JointlySurjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Types.instIsStableUnderCompositionJointlySurjectivePrecoverage", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.JointlySurjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Types.instIsStableUnderSupJointlySurjectivePrecoverage", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.JointlySurjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.mem_comap_jointlySurjectivePrecoverage_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.JointlySurjective", "is_tactic_proof": true, "tactics": ["rw", "refine", "obtain", "exact", "obtain", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.Presieve.ofArrows_mem_comap_jointlySurjectivePrecoverage_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.JointlySurjective", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.isStableUnderBaseChange_comap_jointlySurjectivePrecoverage", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.JointlySurjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instIsStableUnderBaseChangeJointlySurjectivePrecoverage", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.JointlySurjective", "is_tactic_proof": true, "tactics": ["rw", "apply", "intro", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.GrothendieckTopology.coneCompEvaluationOfConeCompDiagramFunctorCompEvaluation", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.LeftExact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.liftToDiagramLimitObjAux", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.LeftExact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.liftToDiagramLimitObjAux_fac", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.LeftExact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.liftToDiagramLimitObj", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Sites.LeftExact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.preservesLimit_diagramFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.LeftExact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.preservesLimitsOfShape_diagramFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.LeftExact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.preservesLimits_diagramFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.LeftExact", "is_tactic_proof": true, "tactics": ["constructor", "intro", "apply"], "tactic_count": 3}
{"name": "CategoryTheory.GrothendieckTopology.liftToPlusObjLimitObj", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.LeftExact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.liftToPlusObjLimitObj_fac", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.LeftExact", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "congr", "dsimp", "rw", "refine", "dsimp", "simp", "dsimp", "rw", "dsimp", "rw", "simp_rw", "rw", "congr", "rw", "erw", "rfl"], "tactic_count": 18}
{"name": "CategoryTheory.GrothendieckTopology.preservesLimitsOfShape_plusFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.LeftExact", "is_tactic_proof": true, "tactics": ["constructor", "apply", "refine", "intro", "apply", "intro", "dsimp", "simp_rw", "refine", "simp", "congr", "refine", "dsimp", "erw", "conv_lhs", "simp", "rw", "simp", "conv_lhs", "rw", "rfl"], "tactic_count": 21}
{"name": "CategoryTheory.GrothendieckTopology.preserveFiniteLimits_plusFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.LeftExact", "is_tactic_proof": true, "tactics": ["apply", "intro", "have", "apply"], "tactic_count": 4}
{"name": "CategoryTheory.GrothendieckTopology.preservesLimitsOfShape_sheafification", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.LeftExact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.preservesFiniteLimits_sheafification", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.LeftExact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.preservesLimitsOfShape_presheafToSheaf", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.LeftExact", "is_tactic_proof": true, "tactics": ["let", "haveI", "haveI", "constructor", "change", "infer_instance", "intro", "change", "infer_instance", "refine", "constructor", "apply", "have", "reflectsLimitsOfShape_of_reflectsIsomorphisms", "apply"], "tactic_count": 15}
{"name": "CategoryTheory.preservesFiniteLimits_presheafToSheaf", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.LeftExact", "is_tactic_proof": true, "tactics": ["apply", "intros", "infer_instance"], "tactic_count": 3}
{"name": "CategoryTheory.plusPlusSheafIsoPresheafToSheaf", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.LeftExact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.plusPlusFunctorIsoSheafification", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.LeftExact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.plusPlusIsoSheafify", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.LeftExact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.toSheafify_plusPlusIsoSheafify_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.LeftExact", "is_tactic_proof": true, "tactics": ["convert", "ext1", "dsimp", "rw"], "tactic_count": 4}
{"name": "CategoryTheory.instHasSheafifyOfPreservesLimitsForgetOfHasFiniteLimitsOfSmallOppositeCover", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.LeftExact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instHasSheafifyType", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.LeftExact", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "CategoryTheory.instFinitaryExtensiveSheafOfHasPullbacksOfHasSheafify", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.LeftExact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instAdhesiveSheafOfHasPullbacksOfHasPushoutsOfHasSheafify", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.LeftExact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SheafOfTypes.finitary_extensive", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.LeftExact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SheafOfTypes.adhesive", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.LeftExact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SheafOfTypes.balanced", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.LeftExact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.multiforkEvaluationCone", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.isLimitMultiforkOfIsLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.isSheaf_of_isLimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Limits", "is_tactic_proof": true, "tactics": ["rw", "intro", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Sheaf.instCreatesLimitFunctorOppositeSheafToPresheaf", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.createsLimitsOfShape", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.instHasLimitsOfShape", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.instHasFiniteProducts", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.instHasFiniteLimits", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.createsLimits", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.hasLimitsOfSize", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.instPreservesFiniteLimitsFunctorOppositeSheafToPresheafOfHasFiniteLimits", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf._example", "kind": "example", "module": "Mathlib.CategoryTheory.Sites.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.sheafifyCocone", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.sheafifyCocone_ι_app_val", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Limits", "is_tactic_proof": true, "tactics": ["rw", "dsimp", "rw", "dsimp", "rw", "sheafifyLift_id_toSheafify_assoc]"], "tactic_count": 6}
{"name": "CategoryTheory.Sheaf.isColimitSheafifyCocone", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.instHasColimitsOfShape", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.instHasFiniteCoproducts", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.instHasFiniteColimits", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.instHasColimitsOfSize", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.createsColimitOfIsSheaf", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf._example", "kind": "example", "module": "Mathlib.CategoryTheory.Sites.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.W", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Sites.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.W_eq_isLocal_range_sheafToPresheaf_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Localization", "is_tactic_proof": true, "tactics": ["apply", "ext", "constructor", "intro", "exact", "rintro", "exact"], "tactic_count": 7}
{"name": "CategoryTheory.GrothendieckTopology.W_sheafToPresheaf_map_iff_isIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Localization", "is_tactic_proof": true, "tactics": ["rw", "isIso_iff_of_reflects_iso]"], "tactic_count": 2}
{"name": "CategoryTheory.GrothendieckTopology.W_adj_unit_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Localization", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.GrothendieckTopology.W_iff_isIso_map_of_adjunction", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Localization", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.GrothendieckTopology.W_eq_inverseImage_isomorphisms_of_adjunction", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Localization", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.GrothendieckTopology.W_toSheafify", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.W_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.W_eq_inverseImage_isomorphisms", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.instIsLocalizationFunctorOppositeSheafPresheafToSheafW", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Localization", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "_private.Mathlib.CategoryTheory.Sites.LocallyBijective.0.CategoryTheory.Sheaf.isLocallyBijective_iff_isIso'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.LocallyBijective", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "rw", "suffices", "rw", "intro", "rw", "exact", "intro", "have", "let", "have", "intro", "apply", "have", "have", "have", "have", "refine", "erw", "simp", "refine", "apply", "intro", "rw", "exact", "intro", "constructor"], "tactic_count": 28}
{"name": "CategoryTheory.Sheaf.isLocallyBijective_iff_isIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.LocallyBijective", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "rw", "constructor", "intro", "constructor"], "tactic_count": 6}
{"name": "CategoryTheory.GrothendieckTopology.W_iff_isLocallyBijective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.LocallyBijective", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.GrothendieckTopology.W_of_isLocallyBijective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.LocallyBijective", "is_tactic_proof": true, "tactics": ["rw", "constructor"], "tactic_count": 2}
{"name": "CategoryTheory.GrothendieckTopology.W.isLocallyInjective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.LocallyBijective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.W.isLocallySurjective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.LocallyBijective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.instIsLocallyInjectiveToSheafify", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.LocallyBijective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.instIsLocallySurjectiveToSheafify", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.LocallyBijective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.WEqualsLocallyBijective.mk'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.LocallyBijective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.instWEqualsLocallyBijectiveOfHasWeakSheafifyOfHasSheafComposeOfPreservesSheafificationOfReflectsIsomorphismsForget", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.LocallyBijective", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.GrothendieckTopology.instWEqualsLocallyBijectiveTypeHomObjForget", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.LocallyBijective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.isLocallyInjective_presheafToSheaf_map_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.LocallyBijective", "is_tactic_proof": true, "tactics": ["rw", "comp_isLocallyInjective_iff"], "tactic_count": 2}
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{"name": "CategoryTheory.Functor.imageSieve", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.LocallyFullyFaithful", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.imageSieve_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.LocallyFullyFaithful", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Sieve.equalizer", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.LocallyFullyFaithful", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.equalizer_self", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.LocallyFullyFaithful", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Sieve.equalizer_eq_equalizerSieve", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.LocallyFullyFaithful", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.imageSieve_eq_imageSieve", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.LocallyFullyFaithful", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.functorPushforward_imageSieve_mem", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.LocallyFullyFaithful", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Functor.IsLocallyFull.ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.LocallyFullyFaithful", "is_tactic_proof": false, "tactics": ["apply", "rintro", "simp"], "tactic_count": 3}
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{"name": "CategoryTheory.Presheaf.equalizerSieve", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.LocallyInjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.equalizerSieve_self_eq_top", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.LocallyInjective", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "CategoryTheory.Presheaf.equalizerSieve_eq_top_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.LocallyInjective", "is_tactic_proof": true, "tactics": ["constructor", "intro", "simpa", "rintro", "apply"], "tactic_count": 5}
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{"name": "CategoryTheory.Presheaf.isLocallyInjective_of_injective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.LocallyInjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.instIsLocallyInjectiveOfIsIsoFunctorOpposite", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.LocallyInjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.isLocallyInjective_forget", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.LocallyInjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Presheaf.isLocallyInjective_iff_equalizerSieve_mem_imp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.LocallyInjective", "is_tactic_proof": true, "tactics": ["constructor", "intro", "let", "let", "equalizerSieve", "refine", "rintro", "simpa", "intro", "refine", "rw", "exact", "intro", "exact"], "tactic_count": 14}
{"name": "CategoryTheory.Presheaf.equalizerSieve_mem_of_equalizerSieve_app_mem", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.LocallyInjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.isLocallyInjective_comp", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.LocallyInjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.isLocallyInjective_of_isLocallyInjective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.LocallyInjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.isLocallyInjective_of_isLocallyInjective_fac", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.LocallyInjective", "is_tactic_proof": true, "tactics": ["subst", "exact"], "tactic_count": 2}
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{"name": "CategoryTheory.Presheaf.isLocallyInjective_iff_injective_of_separated", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.LocallyInjective", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "apply"], "tactic_count": 4}
{"name": "CategoryTheory.Presheaf.instIsLocallyInjectiveHomObjForgetTypeιOpposite", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.LocallyInjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.isLocallyInjective_toPlus", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.LocallyInjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.isLocallyInjective_toSheafify", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.LocallyInjective", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "infer_instance"], "tactic_count": 3}
{"name": "CategoryTheory.Presheaf.isLocallyInjective_toSheafify'", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.LocallyInjective", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Sheaf.IsLocallyInjective", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Sites.LocallyInjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.isLocallyInjective_sheafToPresheaf_map_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.LocallyInjective", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "CategoryTheory.Sheaf.isLocallyInjective_of_iso", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.LocallyInjective", "is_tactic_proof": true, "tactics": ["change", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Sheaf.mono_of_injective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.LocallyInjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.isLocallyInjective_forget", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.LocallyInjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.isLocallyInjective_iff_injective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.LocallyInjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.mono_of_isLocallyInjective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.LocallyInjective", "is_tactic_proof": true, "tactics": ["apply", "rw", "infer_instance"], "tactic_count": 3}
{"name": "CategoryTheory.Sheaf.instIsLocallyInjectiveHomObjForgetTypeImageι", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.LocallyInjective", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Presheaf.imageSieve", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.LocallySurjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.imageSieve_eq_sieveOfSection", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.LocallySurjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.imageSieve_whisker_forget", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.LocallySurjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.imageSieve_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.LocallySurjective", "is_tactic_proof": true, "tactics": ["ext", "simp", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Presheaf.localPreimage", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.LocallySurjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.app_localPreimage", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.LocallySurjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.imageSieve_mem", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.LocallySurjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.instIsLocallySurjectiveHomObjForgetTypeWhiskerRightOpposite", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.LocallySurjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.isLocallySurjective_iff_range_sheafify_eq_top", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.LocallySurjective", "is_tactic_proof": false, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Presheaf.isLocallySurjective_iff_range_sheafify_eq_top'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.LocallySurjective", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Presheaf.isLocallySurjective_iff_whisker_forget", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.LocallySurjective", "is_tactic_proof": true, "tactics": ["simp", "rfl"], "tactic_count": 2}
{"name": "CategoryTheory.Presheaf.isLocallySurjective_of_surjective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.LocallySurjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.isLocallySurjective_of_iso", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.LocallySurjective", "is_tactic_proof": true, "tactics": ["apply", "intro", "apply", "rw", "infer_instance"], "tactic_count": 5}
{"name": "CategoryTheory.Presheaf.isLocallySurjective_comp", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.LocallySurjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.isLocallySurjective_of_isLocallySurjective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.LocallySurjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.isLocallySurjective_of_isLocallySurjective_fac", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.LocallySurjective", "is_tactic_proof": true, "tactics": ["subst", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Presheaf.isLocallySurjective_iff_of_fac", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.LocallySurjective", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "intro", "rw", "infer_instance"], "tactic_count": 6}
{"name": "CategoryTheory.Presheaf.comp_isLocallySurjective_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.LocallySurjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.isLocallySurjective_of_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.LocallySurjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.isLocallyInjective_of_isLocallyInjective_of_isLocallySurjective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.LocallySurjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.isLocallyInjective_of_isLocallyInjective_of_isLocallySurjective_fac", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.LocallySurjective", "is_tactic_proof": true, "tactics": ["subst", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Presheaf.isLocallySurjective_of_isLocallySurjective_of_isLocallyInjective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.LocallySurjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Presheaf.comp_isLocallyInjective_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.LocallySurjective", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "intro", "infer_instance"], "tactic_count": 5}
{"name": "CategoryTheory.Presheaf.isLocallySurjective_comp_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.LocallySurjective", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "intro", "infer_instance"], "tactic_count": 5}
{"name": "CategoryTheory.Presheaf.instIsLocallySurjectiveHomObjForgetTypeToRangeSheafify", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.LocallySurjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.sheafificationIsoImagePresheaf", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.LocallySurjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.isLocallySurjective_toPlus", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.LocallySurjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.isLocallySurjective_toSheafify", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.LocallySurjective", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "infer_instance"], "tactic_count": 3}
{"name": "CategoryTheory.Presheaf.isLocallySurjective_toSheafify'", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.LocallySurjective", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Sheaf.IsLocallySurjective", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Sites.LocallySurjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.isLocallySurjective_sheafToPresheaf_map_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.LocallySurjective", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "CategoryTheory.Sheaf.isLocallySurjective_comp", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.LocallySurjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.isLocallySurjective_of_iso", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.LocallySurjective", "is_tactic_proof": true, "tactics": ["have", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Sheaf.instIsLocallySurjectiveHomObjForgetTypeToImage", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.LocallySurjective", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Sheaf.instIsLocallySurjectiveHomObjForgetTypeMapSheafCompose", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.LocallySurjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.isLocallySurjective_iff_isIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.LocallySurjective", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Sheaf.epi_of_isLocallySurjective'", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.LocallySurjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.epi_of_isLocallySurjective", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.LocallySurjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.isLocallySurjective_iff_epi", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.LocallySurjective", "is_tactic_proof": true, "tactics": ["constructor", "intro", "infer_instance", "intro", "have", "rw", "apply"], "tactic_count": 7}
{"name": "CategoryTheory.Presieve.FamilyOfElements.localPreimage", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.LocallySurjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.FamilyOfElements.isAmalgamation_map_localPreimage", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.LocallySurjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.isPullback_square_op_map_yoneda_presheafToSheaf_yoneda_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.MayerVietorisSquare", "is_tactic_proof": false, "tactics": ["refine", "all_goals", "ext", "dsimp", "rw", "erw", "rfl"], "tactic_count": 7}
{"name": "CategoryTheory.GrothendieckTopology.MayerVietorisSquare.mk'", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.MayerVietorisSquare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.MayerVietorisSquare.mk_of_isPullback", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.MayerVietorisSquare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.MayerVietorisSquare.isPushoutAddCommGrpFreeSheaf", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.MayerVietorisSquare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.MayerVietorisSquare.SheafCondition", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.MayerVietorisSquare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.MayerVietorisSquare.sheafCondition_iff_comp_coyoneda", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.MayerVietorisSquare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.MayerVietorisSquare.toPullbackObj", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Sites.MayerVietorisSquare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.MayerVietorisSquare.sheafCondition_iff_bijective_toPullbackObj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.MayerVietorisSquare", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.GrothendieckTopology.MayerVietorisSquare.SheafCondition.bijective_toPullbackObj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.MayerVietorisSquare", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "CategoryTheory.GrothendieckTopology.MayerVietorisSquare.SheafCondition.ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.MayerVietorisSquare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.MayerVietorisSquare.SheafCondition.glue", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.MayerVietorisSquare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.MayerVietorisSquare.SheafCondition.map_f₂₄_op_glue", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.MayerVietorisSquare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.MayerVietorisSquare.SheafCondition.map_f₃₄_op_glue", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.MayerVietorisSquare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.MayerVietorisSquare.sheafCondition_of_sheaf", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.MayerVietorisSquare", "is_tactic_proof": true, "tactics": ["rw", "intro", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.GrothendieckTopology.MayerVietorisSquare.shortComplex", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.MayerVietorisSquare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.MayerVietorisSquare.instMonoSheafAddCommGrpCatFShortComplex", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.MayerVietorisSquare", "is_tactic_proof": false, "tactics": ["have", "dsimp", "simp", "infer_instance", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.GrothendieckTopology.MayerVietorisSquare.instEpiSheafAddCommGrpCatGShortComplex", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.MayerVietorisSquare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.MayerVietorisSquare.shortComplex_exact", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.MayerVietorisSquare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.MayerVietorisSquare.shortComplex_shortExact", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.MayerVietorisSquare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.functorEnrichedHomCoyonedaObjEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.functorEnrichedHomCoyonedaObjEquiv_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Monoidal", "is_tactic_proof": true, "tactics": ["dsimp", "ext", "simp", "rfl"], "tactic_count": 4}
{"name": "CategoryTheory.Presheaf.isSheaf_functorEnrichedHom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.W.transport_isMonoidal", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Monoidal", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.GrothendieckTopology.W.whiskerLeft", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.W.whiskerRight", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.W.monoidal", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.monoidalCategory", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.braidedCategory", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.symmetricCategory", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.instMonoidalFunctorOppositePresheafToSheaf", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.instBraidedFunctorOppositePresheafToSheaf", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf._example", "kind": "example", "module": "Mathlib.CategoryTheory.Sites.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf._example", "kind": "example", "module": "Mathlib.CategoryTheory.Sites.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf._example", "kind": "example", "module": "Mathlib.CategoryTheory.Sites.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.precoverage", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.MorphismProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.ofArrows_mem_precoverage", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.MorphismProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instHasIsosPrecoverageOfContainsIdentitiesOfRespectsIso", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.MorphismProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instIsStableUnderBaseChangePrecoverageOfIsStableUnderBaseChange", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.MorphismProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instIsStableUnderCompositionPrecoverageOfIsStableUnderComposition", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.MorphismProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instSmallPrecoverage", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.MorphismProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.precoverage_monotone", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.MorphismProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.precoverage_inf", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.MorphismProperty", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.MorphismProperty.comap_precoverage", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.MorphismProperty", "is_tactic_proof": true, "tactics": ["ext", "obtain", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.MorphismProperty.coverage", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.MorphismProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.grothendieckTopology", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Sites.MorphismProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.pretopology", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.MorphismProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.coverage_eq_toCoverage_pretopology", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.MorphismProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.grothendieckTopology_eq_toGrothendieck_pretopology", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.MorphismProperty", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.MorphismProperty.pretopology_monotone", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.MorphismProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.pretopology_inf", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.MorphismProperty", "is_tactic_proof": true, "tactics": ["ext", "simp", "rfl"], "tactic_count": 3}
{"name": "CategoryTheory.PresheafOfGroups.ZeroCochain", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.NonabelianCohomology.H1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PresheafOfGroups.instGroupZeroCochain", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.NonabelianCohomology.H1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PresheafOfGroups.Cochain₀.one_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.NonabelianCohomology.H1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PresheafOfGroups.Cochain₀.inv_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.NonabelianCohomology.H1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PresheafOfGroups.Cochain₀.mul_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.NonabelianCohomology.H1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PresheafOfGroups.OneCochain.instOne", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.NonabelianCohomology.H1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PresheafOfGroups.OneCochain.one_ev", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.NonabelianCohomology.H1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PresheafOfGroups.OneCochain.instMul", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.NonabelianCohomology.H1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PresheafOfGroups.OneCochain.mul_ev", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.NonabelianCohomology.H1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PresheafOfGroups.OneCochain.instInv", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.NonabelianCohomology.H1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PresheafOfGroups.OneCochain.inv_ev", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.NonabelianCohomology.H1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PresheafOfGroups.OneCochain.instGroup", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.NonabelianCohomology.H1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PresheafOfGroups.OneCocycle.instOne", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.NonabelianCohomology.H1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PresheafOfGroups.OneCocycle.one_toOneCochain", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.NonabelianCohomology.H1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PresheafOfGroups.OneCocycle.ev_refl", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.NonabelianCohomology.H1", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.PresheafOfGroups.OneCocycle.ev_symm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.NonabelianCohomology.H1", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.PresheafOfGroups.OneCohomologyRelation", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.NonabelianCohomology.H1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PresheafOfGroups.OneCohomologyRelation.refl", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.NonabelianCohomology.H1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PresheafOfGroups.OneCohomologyRelation.symm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.NonabelianCohomology.H1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PresheafOfGroups.OneCohomologyRelation.trans", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.NonabelianCohomology.H1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PresheafOfGroups.OneCocycle.IsCohomologous", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.NonabelianCohomology.H1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PresheafOfGroups.OneCocycle.equivalence_isCohomologous", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.NonabelianCohomology.H1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PresheafOfGroups.H1", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.NonabelianCohomology.H1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PresheafOfGroups.OneCocycle.class", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.NonabelianCohomology.H1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PresheafOfGroups.instOneH1", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.NonabelianCohomology.H1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PresheafOfGroups.OneCocycle.class_eq_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.NonabelianCohomology.H1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PresheafOfGroups.OneCocycle.IsCohomologous.class_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.NonabelianCohomology.H1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.map_functorPullback_overForget", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Over", "is_tactic_proof": true, "tactics": ["refine", "let", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Sieve.overEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.overEquiv_top", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Over", "is_tactic_proof": true, "tactics": ["ext", "simp", "dsimp", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.Sieve.overEquiv_symm_top", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.overEquiv_le_overEquiv_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Over", "is_tactic_proof": true, "tactics": ["refine", "replace", "simpa"], "tactic_count": 3}
{"name": "CategoryTheory.Sieve.overEquiv_pullback", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Over", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "constructor", "rintro", "exact", "rintro", "let", "let", "let", "refine", "rw", "exact"], "tactic_count": 12}
{"name": "CategoryTheory.Sieve.overEquiv_symm_pullback", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.overEquiv_symm_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Over", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "CategoryTheory.Sieve.overEquiv_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Over", "is_tactic_proof": true, "tactics": ["obtain", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Sieve.overEquiv_generate", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.overEquiv_symm_generate", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Over", "is_tactic_proof": true, "tactics": ["refine", "rw", "obtain", "refine", "ext", "exact", "rw", "exact"], "tactic_count": 8}
{"name": "CategoryTheory.Sieve.functorPushforward_over_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Over", "is_tactic_proof": true, "tactics": ["ext", "constructor", "rintro", "exact", "intro", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.GrothendieckTopology.over", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.mem_over_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Over", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "CategoryTheory.GrothendieckTopology.overEquiv_symm_mem_over", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Over", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.GrothendieckTopology.over_forget_coverPreserving", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.over_forget_compatiblePreserving", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.instIsCocontinuousOverForgetOver", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.instIsContinuousOverForgetOver", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.overPullback", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Sites.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.over_map_coverPreserving", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.over_map_compatiblePreserving", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.instIsContinuousOverMapOver", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.overMapPullback", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Sites.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.overMapPullbackCongr", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.overMapPullbackCongr_eq_eqToIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Over", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "CategoryTheory.GrothendieckTopology.overMapPullbackId", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.overMapPullbackComp", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.overMapPullback_comp_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Over", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "simp", "congr", "cat_disch"], "tactic_count": 5}
{"name": "CategoryTheory.GrothendieckTopology.overMapPullback_id_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Over", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "simp", "congr", "cat_disch"], "tactic_count": 5}
{"name": "CategoryTheory.GrothendieckTopology.overMapPullback_assoc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Over", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "simp", "congr", "cat_disch"], "tactic_count": 5}
{"name": "CategoryTheory.Sheaf.over", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Sites.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.over_toGrothendieck_eq_toGrothendieck_comap_forget", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Over", "is_tactic_proof": true, "tactics": ["refine", "intro", "obtain", "simp", "induction", "of", "rw", "exact", "top", "rw", "simp", "transitive", "ih", "refine", "obtain", "rw", "exact", "rw", "intro", "rw", "rw", "exact"], "tactic_count": 22}
{"name": "CategoryTheory.instIsDenseSubsiteOverLeftDiscretePUnitOverInverseIteratedSliceEquiv", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instIsContinuousOverLeftDiscretePUnitIteratedSliceForwardOver", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instIsCocontinuousOverLeftDiscretePUnitIteratedSliceForwardOver", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instIsContinuousOverLeftDiscretePUnitIteratedSliceBackwardOver", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instIsCocontinuousOverLeftDiscretePUnitIteratedSliceBackwardOver", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.diagram", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Plus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.diagramPullback", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Plus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.diagramNatTrans", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Plus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.diagramNatTrans_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Plus", "is_tactic_proof": true, "tactics": ["ext", "refine", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.GrothendieckTopology.diagramNatTrans_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Plus", "is_tactic_proof": true, "tactics": ["ext", "refine", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.GrothendieckTopology.diagramNatTrans_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Plus", "is_tactic_proof": true, "tactics": ["ext", "refine", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.GrothendieckTopology.diagramFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Plus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.plusObj", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Plus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.plusMap", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Plus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.plusMap_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Plus", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "rw", "ext", "simp"], "tactic_count": 5}
{"name": "CategoryTheory.GrothendieckTopology.plusMap_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Plus", "is_tactic_proof": true, "tactics": ["ext", "refine", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.GrothendieckTopology.plusMap_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Plus", "is_tactic_proof": true, "tactics": ["ext", "refine", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.GrothendieckTopology.plusFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Plus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.toPlus", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Plus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.toPlus_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Plus", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "delta", "simp", "simp_rw", "congr", "exact"], "tactic_count": 7}
{"name": "CategoryTheory.GrothendieckTopology.toPlusNatTrans", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Plus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.plusMap_toPlus", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Plus", "is_tactic_proof": true, "tactics": ["ext", "refine", "dsimp", "let", "rw", "congr", "refine", "erw", "simp", "let", "erw", "congr", "refine", "convert", "all_goals"], "tactic_count": 15}
{"name": "CategoryTheory.GrothendieckTopology.isIso_toPlus_of_isSheaf", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Plus", "is_tactic_proof": true, "tactics": ["rw", "suffices", "intro", "refine", "suffices", "isIso_ι_of_isInitial", "intro", "have", "have", "rw", "infer_instance"], "tactic_count": 11}
{"name": "CategoryTheory.GrothendieckTopology.isoToPlus", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Plus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.isoToPlus_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Plus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.plusLift", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Plus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.toPlus_plusLift", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Plus", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "rw", "dsimp", "rw"], "tactic_count": 5}
{"name": "CategoryTheory.GrothendieckTopology.plusLift_unique", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Plus", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.GrothendieckTopology.plus_hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Plus", "is_tactic_proof": false, "tactics": ["have", "apply", "rfl", "rw", "apply", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.GrothendieckTopology.isoToPlus_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Plus", "is_tactic_proof": true, "tactics": ["apply", "rw", "rfl"], "tactic_count": 3}
{"name": "CategoryTheory.GrothendieckTopology.plusMap_plusLift", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Plus", "is_tactic_proof": true, "tactics": ["apply", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.GrothendieckTopology.plusFunctor_preservesZeroMorphisms", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Plus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Point.instHasColimitsOfShapeOppositeElementsFiber", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Point.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Point.instHasExactColimitsOfShapeOppositeElementsFiberOfLocallySmallOfAB5OfSizeOfHasFiniteLimits", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Point.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Point.presheafFiber", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Point.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Point.toPresheafFiber", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Point.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Point.presheafFiber_hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Point.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Point.toPresheafFiberNatTrans", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Point.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_w", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Point.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Point.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Point.presheafFiberDesc", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Point.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_presheafFiberDesc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Point.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Point.instPreservesColimitsOfShapeOppositeElementsFiberForget", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Point.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_jointly_surjective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Point.Basic", "is_tactic_proof": false, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_jointly_surjective₂", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Point.Basic", "is_tactic_proof": false, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_eq_iff'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Point.Basic", "is_tactic_proof": false, "tactics": ["refine", "isColimitOfPreserves", "constructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 7}
{"name": "CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_map_surjective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Point.Basic", "is_tactic_proof": true, "tactics": ["intro", "obtain", "obtain", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_map_injective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Point.Basic", "is_tactic_proof": false, "tactics": ["suffices", "rintro", "obtain", "simp", "obtain", "simp", "simpa", "intro", "obtain", "simp_all"], "tactic_count": 10}
{"name": "CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_map_bijective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Point.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Point.W_isInvertedBy_presheafFiber", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Point.Basic", "is_tactic_proof": true, "tactics": ["intro", "obtain", "rw", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.GrothendieckTopology.Point.sheafFiber", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Sites.Point.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Point.instIsIsoMapFunctorOppositePresheafFiberToSheafify", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Point.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Point.presheafToSheafCompSheafFiber", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Point.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Point.instPreservesFiniteLimitsFunctorOppositePresheafFiberOfLocallySmallOfHasFiniteLimitsOfAB5OfSize", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Point.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Point.instPreservesFiniteLimitsSheafSheafFiberOfLocallySmallOfHasFiniteLimitsOfAB5OfSize", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Point.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Point.instPreservesColimitsOfSizeFunctorOppositePresheafFiber", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Point.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Point.instPreservesColimitsOfSizeSheafSheafFiberOfHasSheafifyOfWEqualsLocallyBijectiveOfReflectsIsomorphismsOfPreservesFilteredColimitsOfSizeForgetOfLocallySmall", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Point.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Point.instCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Point.Category", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Point.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Point.Category", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Point.id_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Point.Category", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Point.comp_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Point.Category", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Point.Hom.presheafFiber", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Point.Category", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Point.Hom.presheafFiber_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Point.Category", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.GrothendieckTopology.Point.Hom.presheafFiber_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Point.Category", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.GrothendieckTopology.Point.Hom.sheafFiber", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Sites.Point.Category", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Point.Hom.sheafFiber_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Point.Category", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.GrothendieckTopology.Point.Hom.sheafFiber_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Point.Category", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Precoverage.instCoeFunForallSetPresieve", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Precoverage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Precoverage.instPartialOrder", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Precoverage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Precoverage.instMin", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Precoverage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Precoverage.instMax", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Precoverage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Precoverage.instSupSet", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Precoverage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Precoverage.instInfSet", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Precoverage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Precoverage.instTop", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Precoverage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Precoverage.instBot", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Precoverage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Precoverage.instCompleteLattice", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Precoverage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Precoverage.mem_coverings_of_isPullback", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Precoverage", "is_tactic_proof": true, "tactics": ["let", "i.elim", "convert_to", "refine", "exact", "refine", "convert", "refine", "exact"], "tactic_count": 9}
{"name": "CategoryTheory.Precoverage.comp_mem_coverings", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Precoverage", "is_tactic_proof": true, "tactics": ["let", "let", "let", "let", "let", "let", "let", "convert_to", "refine", "exact", "refine", "convert", "refine", "exact", "convert", "refine"], "tactic_count": 16}
{"name": "CategoryTheory.Precoverage.instHasPullbacksOfHasPullbacks", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Precoverage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Precoverage.pullbackArrows_mem", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Precoverage", "is_tactic_proof": true, "tactics": ["obtain", "have", "rw", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.Precoverage.instHasIsosMin", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Precoverage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Precoverage.instIsStableUnderBaseChangeMin", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Precoverage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Precoverage.instIsStableUnderCompositionMin", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Precoverage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Precoverage.instIsStableUnderSupMin", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Precoverage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Precoverage.comap", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Precoverage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Precoverage.mem_comap_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Precoverage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Precoverage.comap_inf", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Precoverage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Precoverage.comap_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Precoverage", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Precoverage.comap_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Precoverage", "is_tactic_proof": true, "tactics": ["ext", "obtain", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.Precoverage.instHasIsosComap", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Precoverage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Precoverage.instIsStableUnderCompositionComap", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Precoverage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Precoverage.instIsStableUnderBaseChangeComapOfPreservesLimitsOfShapeWalkingCospan", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Precoverage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Precoverage.instHasPullbacksComapOfCreatesLimitsOfShapeWalkingCospan", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Precoverage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Precoverage.Saturate", "kind": "inductive", "module": "Mathlib.CategoryTheory.Sites.PrecoverageToGrothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Precoverage.toGrothendieck", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.PrecoverageToGrothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Precoverage.mem_toGrothendieck_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.PrecoverageToGrothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Precoverage.generate_mem_toGrothendieck", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.PrecoverageToGrothendieck", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Precoverage.toGrothendieck_eq_sInf", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.PrecoverageToGrothendieck", "is_tactic_proof": true, "tactics": ["refine", "rw", "intro", "induction", "of", "top", "pullback", "transitive", "exact"], "tactic_count": 9}
{"name": "CategoryTheory.Precoverage.isSheaf_toGrothendieck_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.PrecoverageToGrothendieck", "is_tactic_proof": true, "tactics": ["constructor", "refine", "rw", "exact", "intro", "suffices", "induction", "of", "top", "pullback", "intro", "rw", "exact", "transitive", "intro", "simp", "choose", "choose", "refine", "intro", "refine", "refine", "simp", "simp", "rw", "simpa", "let", "have", "intro", "rw", "rw", "choose", "let", "have", "intro", "apply", "intro", "simp", "rw", "dsimp", "simpa", "simpa", "obtain", "refine", "refine", "rw", "on_goal", "refine", "rw", "on_goal", "refine", "rw", "apply", "simp"], "tactic_count": 54}
{"name": "CategoryTheory.Precoverage.mem_toGrothendieck_iff_of_isStableUnderComposition", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.PrecoverageToGrothendieck", "is_tactic_proof": true, "tactics": ["refine", "induction", "of", "use", "exact", "top", "pullback", "obtain", "have", "refine", "rw", "apply", "rwa", "transitive", "obtain", "rw", "obtain", "replace", "obtain", "rw", "obtain", "use", "choose", "refine", "rw", "intro", "exact", "rw", "apply", "exact"], "tactic_count": 30}
{"name": "CategoryTheory.Precoverage.toGrothendieck_toPretopology_eq_toGrothendieck", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.PrecoverageToGrothendieck", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Presieve.IsSheaf.isSheafFor_of_mem_precoverage", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.PrecoverageToGrothendieck", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "CategoryTheory.Presieve.isTerminal_of_isSheafFor_empty_presieve", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Preserves", "is_tactic_proof": true, "tactics": ["refine", "choose", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Presieve.preservesTerminal_of_isSheaf_for_empty", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Preserves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.piComparison_fac", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Preserves", "is_tactic_proof": true, "tactics": ["have", "dsimp", "have", "rw", "have", "simp", "rw", "simp"], "tactic_count": 8}
{"name": "CategoryTheory.Presieve.isSheafFor_of_preservesProduct", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Preserves", "is_tactic_proof": true, "tactics": ["rw", "have", "have", "rw", "intro", "obtain", "refine", "apply_fun", "simp", "ht₂"], "tactic_count": 10}
{"name": "CategoryTheory.Presieve.firstMap_eq_secondMap", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Preserves", "is_tactic_proof": true, "tactics": ["ext", "simp", "by_cases", "rw", "have", "apply_fun", "injective_of_mono", "ext", "exact"], "tactic_count": 9}
{"name": "CategoryTheory.Presieve.preservesProduct_of_isSheafFor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Preserves", "is_tactic_proof": true, "tactics": ["have", "refine", "rw", "refine", "rw", "rw", "exact"], "tactic_count": 7}
{"name": "CategoryTheory.Presieve.isSheafFor_iff_preservesProduct", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Preserves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.isLocallyInjective_whisker", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.PreservesLocallyBijective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.isLocallyInjective_of_whisker", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.PreservesLocallyBijective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.isLocallyInjective_whisker_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.PreservesLocallyBijective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.isLocallySurjective_whisker", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.PreservesLocallyBijective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.isLocallySurjective_of_whisker", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.PreservesLocallyBijective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.isLocallySurjective_whisker_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.PreservesLocallyBijective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.W_of_preservesSheafification", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.PreservesSheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.W_isInvertedBy_whiskeringRight_presheafToSheaf", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.PreservesSheafification", "is_tactic_proof": true, "tactics": ["intro", "dsimp", "rw", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.Sheaf.composeAndSheafify", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Sites.PreservesSheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.toPresheafToSheafCompComposeAndSheafify", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.PreservesSheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instIsIsoFunctorOppositeSheafToPresheafToSheafCompComposeAndSheafify", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.PreservesSheafification", "is_tactic_proof": true, "tactics": ["rw", "intro", "dsimp", "simpa"], "tactic_count": 4}
{"name": "CategoryTheory.presheafToSheafCompComposeAndSheafifyIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.PreservesSheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instLiftingFunctorOppositeSheafPresheafToSheafWCompObjWhiskeringRightComposeAndSheafify", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.PreservesSheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.preservesSheafification_iff_of_adjunctions", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.PreservesSheafification", "is_tactic_proof": true, "tactics": ["simp", "constructor", "intro", "apply", "rw", "infer_instance", "intro", "constructor", "intro", "rw", "dsimp", "rw", "erw", "dsimp", "rw", "apply"], "tactic_count": 16}
{"name": "CategoryTheory.sheafComposeNatTrans", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.PreservesSheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.sheafComposeNatTrans_fac", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.PreservesSheafification", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.sheafComposeNatTrans_app_uniq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.PreservesSheafification", "is_tactic_proof": true, "tactics": ["apply", "dsimp", "erw", "rw", "apply"], "tactic_count": 5}
{"name": "CategoryTheory.GrothendieckTopology.preservesSheafification_iff_of_adjunctions_of_hasSheafCompose", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.PreservesSheafification", "is_tactic_proof": true, "tactics": ["rw", "apply", "intro", "rw", "sheafComposeNatTrans_fac"], "tactic_count": 5}
{"name": "CategoryTheory.instIsIsoFunctorOppositeSheafSheafComposeNatTrans", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.PreservesSheafification", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.sheafComposeNatIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.PreservesSheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.sheafifyComposeIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.PreservesSheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.sheafComposeIso_hom_fac", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.PreservesSheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.sheafComposeIso_inv_fac", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.PreservesSheafification", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.GrothendieckTopology.sheafToPresheaf_map_sheafComposeNatTrans_eq_sheafifyCompIso_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.PreservesSheafification", "is_tactic_proof": false, "tactics": ["suffices", "rw", "rfl", "apply", "convert", "dsimp", "simp"], "tactic_count": 7}
{"name": "CategoryTheory.GrothendieckTopology.instIsIsoSheafAppFunctorOppositeSheafComposeNatTransPlusPlusAdjunction", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.PreservesSheafification", "is_tactic_proof": false, "tactics": ["rw", "sheafToPresheaf_map_sheafComposeNatTrans_eq_sheafifyCompIso_inv]", "infer_instance"], "tactic_count": 3}
{"name": "CategoryTheory.GrothendieckTopology.instIsIsoFunctorOppositeSheafSheafComposeNatTransPlusPlusAdjunction", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.PreservesSheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.instPreservesSheafification", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.PreservesSheafification", "is_tactic_proof": false, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.GrothendieckTopology.instPreservesSheafificationForgetOfPreservesLimitsOfHasColimitsOfShapeOfPreservesColimitsOfShapeOppositeCoverOfHasLimitsOfShapeWalkingMulticospanOfReflectsIsomorphisms", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.PreservesSheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretopology.instCoeFunForallSetPresieve", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Pretopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretopology.LE", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Pretopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretopology.le_def", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Pretopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretopology.instPartialOrder", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Pretopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretopology.orderTop", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Pretopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretopology.instInhabited", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Pretopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretopology.toGrothendieck", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Pretopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretopology.mem_toGrothendieck", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Pretopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.toPretopology", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Pretopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretopology.gi", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Pretopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.mem_toPretopology", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Pretopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretopology.trivial", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Pretopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretopology.orderBot", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Pretopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretopology.toGrothendieck_bot", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Pretopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretopology.instInfSet", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Pretopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretopology.mem_sInf", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Pretopology", "is_tactic_proof": true, "tactics": ["change", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Pretopology.sInf_ofGrothendieck", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Pretopology", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Pretopology.isGLB_sInf", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Pretopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretopology.instCompleteLattice", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Pretopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretopology.mem_inf", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Pretopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Precoverage.toPretopology", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Pretopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.pseudofunctorOver", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.PseudofunctorSheafOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.sheafPullback", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Pullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.sheafAdjunctionContinuous", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Pullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.sheafPullbackConstruction.sheafPullback", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Pullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.sheafPullbackConstruction.sheafAdjunctionContinuous", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Pullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.sheafPullbackConstruction.instIsRightAdjointSheafSheafPushforwardContinuousOfHasWeakSheafify", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Pullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.sheafPullbackConstruction.sheafPullbackIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Pullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.sheafPullbackConstruction.instPreservesFiniteLimitsSheafSheafPullback", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Pullback", "is_tactic_proof": true, "tactics": ["have", "apply"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.sheafPullbackConstruction.preservesFiniteLimits", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Pullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.SmallCategories._example", "kind": "example", "module": "Mathlib.CategoryTheory.Sites.Pullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.SmallCategories.instPreservesFiniteLimitsSheafSheafPullbackOfRepresentablyFlat", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Pullback", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.isRegularEpiCategory_sheaf", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.RegularEpi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instIsRegularEpiCategorySheafTypeOfHasSheafify", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.RegularEpi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory._example", "kind": "example", "module": "Mathlib.CategoryTheory.Sites.RegularEpi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.IsSheaf", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.IsSeparated", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.conesEquivSieveCompatibleFamily", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.FamilyOfElements.SieveCompatible.cone", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.homEquivAmalgamation", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.isLimit_iff_isSheafFor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "rw", "intro", "specialize", "rw", "exact", "rintro", "let", "rw", "erw", "rw", "exact"], "tactic_count": 13}
{"name": "CategoryTheory.Presheaf.subsingleton_iff_isSeparatedFor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": true, "tactics": ["constructor", "intro", "have", "rw", "specialize", "rcases", "simpa", "rintro", "let", "constructor", "rw", "intro", "let", "apply", "ext", "apply"], "tactic_count": 16}
{"name": "CategoryTheory.Presheaf.isSheaf_iff_isLimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.isSeparated_iff_subsingleton", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.isLimit_iff_isSheafFor_presieve", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.isSheaf_iff_isLimit_pretopology", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": true, "tactics": ["dsimp", "simp_rw", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Presheaf.IsSheaf.amalgamate", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.IsSheaf.amalgamate_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Presheaf.IsSheaf.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.IsSheaf.hom_ext_ofArrows", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": true, "tactics": ["apply", "rintro", "dsimp", "rw"], "tactic_count": 4}
{"name": "CategoryTheory.Presheaf.IsSheaf.existsUnique_amalgamation_ofArrows", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.IsSheaf.amalgamateOfArrows", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.IsSheaf.amalgamateOfArrows_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.isSheaf_of_iso_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.isSheaf_of_isTerminal", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.instCategorySheaf", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.instInhabitedHom", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.sheafToPresheaf", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.sheafSections", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.sheafSectionsNatIsoEvaluation", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.fullyFaithfulSheafToPresheaf", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.homEquiv", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.sheafToPresheafCompYonedaCompWhiskeringLeftSheafToPresheaf", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.sheafToPresheafCompYonedaCompWhiskeringLeftSheafToPresheaf_app_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.sheafToPresheafCompCoyonedaCompWhiskeringLeftSheafToPresheaf", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.sheafToPresheafCompCoyonedaCompWhiskeringLeftSheafToPresheaf_app_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instFullSheafFunctorOppositeSheafToPresheaf", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instFaithfulSheafFunctorOppositeSheafToPresheaf", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instReflectsIsomorphismsSheafFunctorOppositeSheafToPresheaf", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.Hom.mono_of_presheaf_mono", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.Hom.epi_of_presheaf_epi", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isSheaf_iff_isSheaf_of_type", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": true, "tactics": ["constructor", "intro", "refine", "exact", "intro", "refine", "intro", "exact", "intro", "funext", "apply", "intro", "funext", "apply", "intro", "rw", "rfl"], "tactic_count": 17}
{"name": "CategoryTheory.sheafOver", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.IsSheaf.isSheafFor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Presheaf.isSheaf_bot", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.sheafBotEquivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instInhabitedSheafBotGrothendieckTopologyType", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.isTerminalOfBotCover", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": true, "tactics": ["refine", "intro", "choose", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.sheafHomHasZSMul", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instSubHomSheaf", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instNegHomSheaf", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.sheafHomHasNSMul", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instZeroHomSheaf", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instAddHomSheaf", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.Hom.add_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.Hom.addCommGroup", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instPreadditiveSheaf", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.isLimitOfIsSheaf", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.isSheaf_iff_multifork", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": true, "tactics": ["refine", "intro", "let", "obtain", "let", "use", "dsimp", "intro", "apply", "intro", "apply", "rintro", "apply", "rw", "congr", "apply"], "tactic_count": 16}
{"name": "CategoryTheory.Presheaf.IsSheaf.isLimitMultifork", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Presheaf.isSheaf_iff_multiequalizer", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": true, "tactics": ["rw", "refine", "rintro", "let", "exact", "intro", "refine", "apply", "intro", "symm", "simp"], "tactic_count": 11}
{"name": "CategoryTheory.Presheaf.firstObj", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.forkMap", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.secondObj", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.firstMap", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.secondMap", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.w", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": true, "tactics": ["apply", "rintro", "simp", "rw", "simp"], "tactic_count": 5}
{"name": "CategoryTheory.Presheaf.IsSheaf'", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.isSheafForIsSheafFor'", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": false, "tactics": ["let", "parallelPair", "parallelPair", "refine", "parallelPair.ext", "dsimp", "simp", "piComparison_comp_π_assoc]", "dsimp", "simp", "piComparison_comp_π_assoc]", "refine", "refine", "dsimp", "simp"], "tactic_count": 15}
{"name": "CategoryTheory.Presheaf.isSheaf_iff_isSheaf'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": true, "tactics": ["constructor", "intro", "refine", "apply", "intro", "have", "rw", "rw", "replace", "apply", "intro", "rw", "refine", "refine", "letI", "apply", "apply", "simpa"], "tactic_count": 18}
{"name": "CategoryTheory.Presheaf.isSheaf_of_isSheaf_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Presheaf.isSheaf_comp_of_isSheaf", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "CategoryTheory.Presheaf.isSheaf_iff_isSheaf_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": true, "tactics": ["letI", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Presheaf.isSheaf_iff_isSheaf_forget", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sheaf", "is_tactic_proof": true, "tactics": ["have", "have", "apply"], "tactic_count": 3}
{"name": "CategoryTheory.Sheaf.H", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.SheafCohomology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.instAddCommGroupH", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.SheafCohomology.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Sheaf.cohomologyPresheafFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.SheafCohomology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.cohomologyPresheaf", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Sites.SheafCohomology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.presheafHom", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.SheafHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.presheafHom_map_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.SheafHom", "is_tactic_proof": true, "tactics": ["subst", "rfl"], "tactic_count": 2}
{"name": "CategoryTheory.presheafHom_map_app_op_mk_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.SheafHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.presheafHomSectionsEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.SheafHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PresheafHom.isAmalgamation_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.SheafHom", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "intro", "dsimp", "ext", "refine", "have", "dsimp", "simp", "rw", "rfl"], "tactic_count": 12}
{"name": "CategoryTheory.PresheafHom.IsSheafFor.exists_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.SheafHom", "is_tactic_proof": false, "tactics": ["let", "π", "naturality", "rintro", "dsimp", "rw", "have", "simp", "let", "have", "dsimp", "erw", "use", "intro", "exact"], "tactic_count": 15}
{"name": "CategoryTheory.PresheafHom.IsSheafFor.app", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.SheafHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PresheafHom.IsSheafFor.app_cond", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.SheafHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.presheafHom_isSheafFor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.SheafHom", "is_tactic_proof": true, "tactics": ["intro", "apply", "refine", "naturality", "rintro", "apply", "rintro", "dsimp", "rw", "rw", "congr", "simp", "rw", "intro", "dsimp", "have", "rw", "exact", "intro", "rw", "apply", "ext", "apply", "rintro", "dsimp", "let", "refine", "rw"], "tactic_count": 28}
{"name": "CategoryTheory.Presheaf.IsSheaf.hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.SheafHom", "is_tactic_proof": true, "tactics": ["rw", "intro", "exact", "presheafHom_isSheafFor"], "tactic_count": 4}
{"name": "CategoryTheory.sheafHom'", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.SheafHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.sheafHom'Iso", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.SheafHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.sheafHom", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.SheafHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.sheafHomSectionsEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.SheafHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.sheafHomSectionsEquiv_symm_apply_coe_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.SheafHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.IsSeparated", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.SheafOfTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.IsSheaf", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.SheafOfTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.IsSheaf.isSheafFor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.SheafOfTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.isSheaf_of_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.SheafOfTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.isSeparated_of_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.SheafOfTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.IsSheaf.isSeparated", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.SheafOfTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.IsSeparated.isSheaf", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.SheafOfTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.isSheaf_of_nat_equiv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.SheafOfTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.isSheaf_iff_of_nat_equiv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.SheafOfTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.isSheaf_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.SheafOfTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.isSeparated_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.SheafOfTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.isSheaf_of_yoneda", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.SheafOfTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.isSheaf_pretopology", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.SheafOfTypes", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "apply", "rintro", "have", "apply", "rwa", "apply", "intro", "rw", "exact"], "tactic_count": 12}
{"name": "CategoryTheory.Presieve.isSheaf_bot", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.SheafOfTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.isSheaf_comp_uliftFunctor_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.SheafOfTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.isSheaf_comp_uliftFunctor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.SheafOfTypes", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "CategoryTheory.Presieve.compatibleYonedaFamily_toCocone", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.SheafOfTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.yonedaFamilyOfElements_fromCocone", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.SheafOfTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.yonedaFamily_fromCocone_compatible", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.SheafOfTypes", "is_tactic_proof": true, "tactics": ["intro", "have", "simp", "dsimp", "have", "have", "let", "let", "let", "have", "have", "have", "cat_disch"], "tactic_count": 13}
{"name": "CategoryTheory.Sieve.forallYonedaIsSheaf_iff_colimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.SheafOfTypes", "is_tactic_proof": true, "tactics": ["constructor", "intro", "refine", "exact", "fac", "intro", "replace", "have", "cat_disch", "uniq", "intro", "replace", "apply", "exact", "intro", "replace", "let", "use", "constructor", "exact", "exact"], "tactic_count": 21}
{"name": "CategoryTheory.HasWeakSheafify", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Sites.Sheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instHasWeakSheafifyOfHasSheafify", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Sheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instPreservesFiniteLimitsFunctorOppositeSheafLeftAdjointSheafToPresheaf", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Sheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasSheafify.mk'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.presheafToSheaf", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Sheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instPreservesFiniteLimitsFunctorOppositeSheafPresheafToSheaf", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Sheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.sheafificationAdjunction", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Sheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instIsLeftAdjointFunctorOppositeSheafPresheafToSheaf", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Sheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instReflectiveFunctorOppositeSheafSheafToPresheafOfHasWeakSheafify", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Sheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instPreservesFiniteLimitsFunctorOppositeSheafReflectorSheafToPresheaf", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Sheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.sheafify", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Sites.Sheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.toSheafify", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Sites.Sheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.sheafificationAdjunction_unit_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.sheafifyMap", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Sites.Sheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.sheafifyMap_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sheafification", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.sheafifyMap_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sheafification", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.toSheafify_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.sheafification", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Sites.Sheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.sheafification_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.sheafification_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.toSheafification", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Sites.Sheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.toSheafification_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isIso_toSheafify", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sheafification", "is_tactic_proof": true, "tactics": ["refine", "change", "rw", "rfl", "change", "change", "rw", "simp"], "tactic_count": 8}
{"name": "CategoryTheory.isoSheafify", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Sheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isoSheafify_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.sheafifyLift", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Sheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.sheafificationAdjunction_counit_app_val", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sheafification", "is_tactic_proof": true, "tactics": ["unfold", "rw", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.toSheafify_sheafifyLift", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sheafification", "is_tactic_proof": true, "tactics": ["rw", "change", "simp", "change", "change", "rw", "simp"], "tactic_count": 7}
{"name": "CategoryTheory.sheafifyLift_unique", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sheafification", "is_tactic_proof": true, "tactics": ["intro", "rw", "rw", "let", "change", "rw", "exact"], "tactic_count": 7}
{"name": "CategoryTheory.isoSheafify_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sheafification", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.sheafify_hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sheafification", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.sheafifyMap_sheafifyLift", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sheafification", "is_tactic_proof": true, "tactics": ["apply", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.sheafificationIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Sheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isIso_sheafificationAdjunction_counit", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Sheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instIsIsoFunctorOppositeValAppSheafCounitSheafificationAdjunction", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Sheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.sheafification_reflective", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Sheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.sheafifyLift_id_toSheafify", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sheafification", "is_tactic_proof": true, "tactics": ["rw", "cat_disch"], "tactic_count": 2}
{"name": "CategoryTheory.sheafificationNatIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Sheafification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instCompleteLatticePresieve", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.top_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.instInhabited", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.category", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.categoryMk", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.diagram", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.cocone", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.bind", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.bind.bindStruct", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.BindStruct.bind", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.bind_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.singleton", "kind": "inductive", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.singleton_eq_iff_domain", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "rfl", "rintro", "apply"], "tactic_count": 5}
{"name": "CategoryTheory.Presieve.singleton_self", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.instHasPullbacksOfHasPullbacks", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.instHasPullbacksSingletonOfHasPullback", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.pullbackArrows", "kind": "inductive", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.pullback_singleton", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["funext", "ext", "constructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 7}
{"name": "CategoryTheory.Presieve.ofArrows", "kind": "inductive", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.ofArrows.mk'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["subst", "simp", "subst", "constructor"], "tactic_count": 4}
{"name": "CategoryTheory.Presieve.ofArrows_pUnit", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["funext", "ext", "constructor", "rintro", "apply", "rintro", "exact"], "tactic_count": 7}
{"name": "CategoryTheory.Presieve.instHasPullbacksOfArrowsOfHasPullback", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.ofArrows_pullback", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["funext", "ext", "constructor", "rintro", "exact", "rintro", "apply"], "tactic_count": 7}
{"name": "CategoryTheory.Presieve.ofArrows_bind", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["funext", "ext", "constructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 7}
{"name": "CategoryTheory.Presieve.ofArrows_surj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Presieve.exists_eq_ofArrows", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["let", "use", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Presieve.ofArrows_category", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["refine", "rintro", "exact", "rintro", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.Presieve.ofArrows.idx", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.ofArrows.obj_idx", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.ofArrows.eq_eqToHom_comp_hom_idx", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.ofArrows.hom_idx", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Presieve.ofArrows_comp_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["rintro", "use"], "tactic_count": 2}
{"name": "CategoryTheory.Presieve.ofArrows_comp_eq_of_surjective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["refine", "rintro", "obtain", "use"], "tactic_count": 4}
{"name": "CategoryTheory.Presieve.ofArrows_le_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.bindOfArrows", "kind": "inductive", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.bindOfArrows_ofArrows", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["refine", "rintro", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Presieve.functorPullback", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.functorPullback_mem", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.functorPullback_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.instHasPairwisePullbacksOfHasPullbacks", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.instHasPullbackOfHasPairwisePullbacksOfArrows", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.functorPushforward", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.getFunctorPushforwardStructure", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["choose", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Presieve.functorPushforward_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["funext", "ext", "constructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 7}
{"name": "CategoryTheory.Presieve.image_mem_functorPushforward", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.map", "kind": "inductive", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.map_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.map_ofArrows", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["refine", "obtain", "obtain", "simpa"], "tactic_count": 4}
{"name": "CategoryTheory.Presieve.map_singleton", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Presieve.map_functorPullback", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.map_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.map_monotone", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.uncurry", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.uncurry_singleton", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["ext", "rintro", "intro", "rw", "obtain"], "tactic_count": 5}
{"name": "CategoryTheory.Presieve.uncurry_pullbackArrows", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["ext", "rintro", "rintro", "rw", "obtain", "rw", "exact"], "tactic_count": 7}
{"name": "CategoryTheory.Presieve.uncurry_bind", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["ext", "rintro", "exact", "rintro", "rw", "obtain", "rw", "exact"], "tactic_count": 8}
{"name": "CategoryTheory.Presieve.uncurry_ofArrows", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["ext", "rintro", "rintro"], "tactic_count": 3}
{"name": "CategoryTheory.Presieve.ofArrows_eq_ofArrows_uncurry", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Sieve.instCoeFunPresieve", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.arrows_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["rintro", "rfl"], "tactic_count": 2}
{"name": "CategoryTheory.Sieve.ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.sup", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.inf", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.union", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.inter", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.instCompleteLattice", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.sieveInhabited", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.sInf_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.sSup_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Sieve.inter_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.union_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.top_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.arrows_top", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.arrows_eq_top_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.generate", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.arrows_generate_map_eq_functorPushforward", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["refine", "rintro", "rintro"], "tactic_count": 3}
{"name": "CategoryTheory.Sieve.bind", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.BindStruct", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.generate_le_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.giGenerate", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.le_generate", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.generate_sieve", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.id_mem_iff_eq_top", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.generate_of_contains_isSplitEpi", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Sieve.generate_of_singleton_isSplitEpi", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.generate_top", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.comp_mem_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["refine", "convert", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.Sieve.ofArrows", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.ofArrows_mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.mem_ofArrows_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "exact", "rintro", "apply"], "tactic_count": 5}
{"name": "CategoryTheory.Sieve.ofArrows.exists", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Sieve.ofArrows.i", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.ofArrows.h", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.ofArrows.fac", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.ofArrows_category'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["refine", "rw", "rintro", "exact", "rintro", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.Sieve.ofArrows_category", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Sieve.exists_eq_ofArrows", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.ofTwoArrows", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.ofObjects", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.mem_ofObjects_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "CategoryTheory.Sieve.ofArrows_le_ofObjects", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["intro", "rw", "obtain", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.Sieve.ofArrows_eq_ofObjects", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["refine", "rw", "rintro", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.Sieve.pullback", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.pullback_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Sieve.pullback_top", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.pullback_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Sieve.pullback_inter", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Sieve.pullback_ofArrows_of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["rw", "intro", "constructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 7}
{"name": "CategoryTheory.Sieve.mem_iff_pullback_eq_top", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Sieve.pullback_eq_top_of_mem", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.pullback_ofObjects_eq_top", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["ext", "simp", "rw", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.Sieve.pushforward", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.pushforward_apply_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.pushforward_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.galoisConnection", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.pullback_monotone", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.pushforward_monotone", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.le_pushforward_pullback", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.pullback_pushforward_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.pushforward_union", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.pushforward_le_bind_of_mem", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Sieve.le_pullback_bind", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "CategoryTheory.Sieve.galoisCoinsertionOfMono", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["apply", "rintro", "rw", "rwa"], "tactic_count": 4}
{"name": "CategoryTheory.Sieve.galoisInsertionOfIsSplitEpi", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["apply", "intro", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Sieve.pullbackArrows_comm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["ext", "constructor", "rintro", "have", "rw", "exact", "rintro", "have", "exact"], "tactic_count": 9}
{"name": "CategoryTheory.Sieve.functorPullback", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.functorPullback_arrows", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.functorPullback_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "CategoryTheory.Sieve.functorPullback_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "CategoryTheory.Sieve.generate_functorPullback_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["rw", "intro", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Sieve.functorPullback_pullback", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Sieve.functorPushforward_extend_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["funext", "ext", "constructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 7}
{"name": "CategoryTheory.Sieve.functorPushforward", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.generate_map_eq_functorPushforward", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["ext", "rw", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.Sieve.functorPushforward_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["ext", "constructor", "intro", "obtain", "exact", "intro", "exact"], "tactic_count": 7}
{"name": "CategoryTheory.Sieve.functorPushforward_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Sieve.functor_galoisConnection", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["intro", "constructor", "intro", "apply", "refine", "rw", "rintro", "apply", "exact"], "tactic_count": 9}
{"name": "CategoryTheory.Sieve.functorPushforward_le_iff_le_functorPullback", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.functorPullback_monotone", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.functorPushforward_monotone", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.le_functorPushforward_pullback", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.functorPullback_pushforward_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.functorPushforward_union", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.functorPullback_union", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.functorPullback_inter", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.functorPushforward_bot", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.functorPushforward_top", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["refine", "apply", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Sieve.functorPullback_bot", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.functorPullback_top", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.image_mem_functorPushforward", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.functorPushforward_pullback_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["rw", "apply", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Sieve.essSurjFullFunctorGaloisInsertion", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["apply", "intro", "refine", "simpa"], "tactic_count": 4}
{"name": "CategoryTheory.Sieve.fullyFaithfulFunctorGaloisCoinsertion", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["apply", "rintro", "rw", "rw", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.Sieve.functorPushforward_functor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["ext", "constructor", "rintro", "simpa", "intro", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.Sieve.mem_functorPushforward_functor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.functorPushforward_inverse", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.mem_functorPushforward_inverse", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.functorPushforward_equivalence_eq_pullback", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Sieve.pullback_functorPushforward_equivalence_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Sieve.mem_functorPushforward_iff_of_full", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["refine", "obtain", "use", "simp", "apply", "use", "simp"], "tactic_count": 7}
{"name": "CategoryTheory.Sieve.mem_functorPushforward_iff_of_full_of_faithful", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["rw", "refine", "rwa"], "tactic_count": 3}
{"name": "CategoryTheory.Sieve.functor", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.natTransOfLe", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.functorInclusion", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.toFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.natTransOfLe_comm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.functorInclusion_is_mono", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.sieveOfSubfunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.sieveOfSubfunctor_functorInclusion", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["ext", "simp", "constructor", "rintro", "exact", "intro", "exact"], "tactic_count": 7}
{"name": "CategoryTheory.Sieve.functorInclusion_top_isIso", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sieve.ofArrows_eq_pullback_of_isPullback", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["refine", "rw", "rintro", "use", "exact", "rintro", "use", "simp"], "tactic_count": 8}
{"name": "CategoryTheory.Presieve.bind_ofArrows_le_bindOfArrows", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Sieves", "is_tactic_proof": true, "tactics": ["rintro", "rw", "exact"], "tactic_count": 3}
{"name": "Opens.grothendieckTopology", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Spaces", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Opens.pretopology", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Spaces", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Opens.toPretopology_grothendieckTopology", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Spaces", "is_tactic_proof": true, "tactics": ["apply", "intro", "rcases", "exact", "intro", "rcases", "exact"], "tactic_count": 7}
{"name": "Opens.pretopology_toGrothendieck", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Spaces", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "CategoryTheory.GrothendieckTopology.yonedaEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Subcanonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.yonedaEquiv_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Subcanonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.yonedaEquiv_symm_app_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Subcanonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.yonedaEquiv_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Subcanonical", "is_tactic_proof": true, "tactics": ["simp", "rfl"], "tactic_count": 2}
{"name": "CategoryTheory.GrothendieckTopology.yonedaEquiv_naturality'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Subcanonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.yonedaEquiv_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Subcanonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.yonedaEquiv_yoneda_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Subcanonical", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.GrothendieckTopology.yonedaEquiv_symm_naturality_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Subcanonical", "is_tactic_proof": true, "tactics": ["apply", "simp", "rw"], "tactic_count": 3}
{"name": "CategoryTheory.GrothendieckTopology.yonedaEquiv_symm_naturality_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Subcanonical", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.GrothendieckTopology.map_yonedaEquiv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Subcanonical", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.GrothendieckTopology.map_yonedaEquiv'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Subcanonical", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.GrothendieckTopology.yonedaEquiv_symm_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Subcanonical", "is_tactic_proof": true, "tactics": ["obtain", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.GrothendieckTopology.hom_ext_yoneda", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Subcanonical", "is_tactic_proof": true, "tactics": ["ext", "simpa"], "tactic_count": 2}
{"name": "CategoryTheory.GrothendieckTopology.yonedaOpCompCoyoneda", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Subcanonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.uliftYonedaEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Subcanonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Subcanonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_symm_app_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Subcanonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Subcanonical", "is_tactic_proof": true, "tactics": ["change", "rw", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_naturality'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Subcanonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Subcanonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_uliftYoneda_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Subcanonical", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_symm_naturality_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Subcanonical", "is_tactic_proof": true, "tactics": ["apply", "simp", "rw", "rfl"], "tactic_count": 4}
{"name": "CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_symm_naturality_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Subcanonical", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.GrothendieckTopology.map_uliftYonedaEquiv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Subcanonical", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.GrothendieckTopology.map_uliftYonedaEquiv'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Subcanonical", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_symm_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Subcanonical", "is_tactic_proof": true, "tactics": ["obtain", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.GrothendieckTopology.hom_ext_uliftYoneda", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Subcanonical", "is_tactic_proof": true, "tactics": ["ext", "simpa", "congr_arg"], "tactic_count": 3}
{"name": "CategoryTheory.GrothendieckTopology.uliftYonedaOpCompCoyoneda", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Subcanonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.uliftYonedaOpCompCoyoneda_inv_app_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Subcanonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.uliftYonedaOpCompCoyoneda_app_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Subcanonical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.preservesLimitsOfSize_yoneda", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Subcanonical", "is_tactic_proof": true, "tactics": ["refine", "have", "inferInstanceAs", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.GrothendieckTopology.isColimitCofanMkYoneda", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Subcanonical", "is_tactic_proof": false, "tactics": ["have", "by_cases", "subst", "rw", "obtain", "have", "exact", "refine", "refine", "refine", "intro", "ext", "dsimp", "rw", "exact", "ext", "let", "have", "dsimp", "simp", "ext", "have", "exact", "ext", "dsimp", "apply", "ext", "simp"], "tactic_count": 28}
{"name": "CategoryTheory.GrothendieckTopology.preservesColimitsOfShape_yoneda_of_ofArrows_inj_mem", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Subcanonical", "is_tactic_proof": true, "tactics": ["apply", "refine", "have", "refine", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.Subfunctor.isSeparated", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Subsheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subfunctor.sheafify", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Subsheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subfunctor.le_sheafify", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Subsheaf", "is_tactic_proof": true, "tactics": ["intro", "change", "convert", "rw", "rintro", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.Subfunctor.eq_sheafify", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Subsheaf", "is_tactic_proof": true, "tactics": ["apply", "intro", "suffices", "rw", "exact", "apply", "intro", "exact"], "tactic_count": 8}
{"name": "CategoryTheory.Subfunctor.sheafify_isSheaf", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Subsheaf", "is_tactic_proof": true, "tactics": ["refine", "let", "have", "choose", "dsimp", "let", "have", "intro", "refine", "apply", "intro", "have", "have", "rw", "exact", "have", "intro", "rw", "exact", "congr_arg", "obtain", "refine", "refine", "intro", "dsimp", "rw", "exact"], "tactic_count": 27}
{"name": "CategoryTheory.Subfunctor.eq_sheafify_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Subsheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subfunctor.isSheaf_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Subsheaf", "is_tactic_proof": true, "tactics": ["rw", "change", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Subfunctor.sheafify_sheafify", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Subsheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subfunctor.sheafifyLift", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Subsheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subfunctor.to_sheafifyLift", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Subsheaf", "is_tactic_proof": true, "tactics": ["ext", "apply", "intro", "have", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.Subfunctor.to_sheafify_lift_unique", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Subsheaf", "is_tactic_proof": true, "tactics": ["ext", "apply", "rintro", "dsimp", "rw", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.Subfunctor.sheafify_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Subsheaf", "is_tactic_proof": true, "tactics": ["intro", "convert", "apply", "intro", "have", "congr_arg", "convert", "rw", "rfl"], "tactic_count": 9}
{"name": "CategoryTheory.Subfunctor.toRangeSheafify", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Subsheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.image", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Subsheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.toImage", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Subsheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.imageι", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Subsheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.toImage_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Subsheaf", "is_tactic_proof": true, "tactics": ["ext1", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.instMonoSheafTypeImageι", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Subsheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instEpiSheafTypeToImage", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Subsheaf", "is_tactic_proof": true, "tactics": ["refine", "ext", "apply", "rintro", "change", "rw", "have", "have", "dsimp", "convert"], "tactic_count": 10}
{"name": "CategoryTheory.imageMonoFactorization", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Subsheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.imageFactorization", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Subsheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instHasImagesSheafType", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Subsheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.typesGrothendieckTopology", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Types", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.discreteSieve", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Types", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.discreteSieve_mem", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Types", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.discretePresieve", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Types", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.generate_discretePresieve_mem", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Types", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presieve.isSheaf_yoneda'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Types", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Presheaf.isSheaf_yoneda'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Types", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.yoneda'", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Types", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.yoneda'_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Types", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.eval", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Types", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.typesGlue", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Types", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.eval_typesGlue", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Types", "is_tactic_proof": true, "tactics": ["funext", "apply", "convert"], "tactic_count": 3}
{"name": "CategoryTheory.typesGlue_eval", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Types", "is_tactic_proof": true, "tactics": ["apply", "intro", "apply", "apply", "rw", "suffices", "funext", "exact"], "tactic_count": 8}
{"name": "CategoryTheory.evalEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Types", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.eval_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Types", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "CategoryTheory.equivYoneda", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Types", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.equivYoneda'", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Types", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.eval_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Types", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.typeEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Types", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.subcanonical_typesGrothendieckTopology", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Types", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.typesGrothendieckTopology_eq_canonical", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Types", "is_tactic_proof": true, "tactics": ["refine", "refine", "funext", "ext", "refine", "by_contra", "have", "simp"], "tactic_count": 8}
{"name": "CategoryTheory.sheafCompose", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Whiskering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instFaithfulSheafFunctorOppositeCompSheafComposeSheafToPresheaf", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Whiskering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instFullSheafFunctorOppositeCompSheafComposeSheafToPresheafOfFaithful", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Whiskering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.fullyFaithfulSheafComposeCompSheafToPresheaf", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Whiskering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instFaithfulSheafSheafCompose", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Whiskering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instFullSheafSheafComposeOfFaithful", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Whiskering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.fullyFaithfulSheafCompose", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Whiskering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instReflectsIsomorphismsSheafSheafCompose", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Whiskering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.sheafCompose_map", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Whiskering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.sheafCompose_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Whiskering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.sheafCompose_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Whiskering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Cover.multicospanComp", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Whiskering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.GrothendieckTopology.Cover.mapMultifork", "kind": "definition", "module": "Mathlib.CategoryTheory.Sites.Whiskering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.hasSheafCompose_of_preservesMulticospan", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Whiskering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.hasSheafCompose_of_preservesLimitsOfSize", "kind": "instance", "module": "Mathlib.CategoryTheory.Sites.Whiskering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sheaf.isSeparated", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Whiskering", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Presheaf.IsSheaf.isSeparated", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sites.Whiskering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Skeletal", "kind": "definition", "module": "Mathlib.CategoryTheory.Skeletal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.eq_of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Skeletal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.functor_skeletal", "kind": "theorem", "module": "Mathlib.CategoryTheory.Skeletal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Skeleton", "kind": "definition", "module": "Mathlib.CategoryTheory.Skeletal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.fromSkeleton", "kind": "definition", "module": "Mathlib.CategoryTheory.Skeletal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instFullSkeletonFromSkeleton", "kind": "instance", "module": "Mathlib.CategoryTheory.Skeletal", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.instFaithfulSkeletonFromSkeleton", "kind": "instance", "module": "Mathlib.CategoryTheory.Skeletal", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.instEssSurjSkeletonFromSkeleton", "kind": "instance", "module": "Mathlib.CategoryTheory.Skeletal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.fromSkeleton.isEquivalence", "kind": "instance", "module": "Mathlib.CategoryTheory.Skeletal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.toSkeleton", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Skeletal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.fromSkeletonToSkeletonIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Skeletal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Skeleton.comp_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Skeletal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.toSkeletonFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Skeletal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.skeletonEquivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.Skeletal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.skeleton_skeletal", "kind": "theorem", "module": "Mathlib.CategoryTheory.Skeletal", "is_tactic_proof": true, "tactics": ["rintro", "have", "simpa"], "tactic_count": 3}
{"name": "CategoryTheory.skeleton_isSkeleton", "kind": "theorem", "module": "Mathlib.CategoryTheory.Skeletal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.toSkeleton_fromSkeleton_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Skeletal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.toSkeleton_eq_toSkeleton_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Skeletal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.congr_toSkeleton_of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Skeletal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Skeleton.isoOfEq", "kind": "definition", "module": "Mathlib.CategoryTheory.Skeletal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.toSkeleton_eq_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Skeletal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapSkeleton", "kind": "definition", "module": "Mathlib.CategoryTheory.Skeletal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapSkeleton_obj_toSkeleton", "kind": "theorem", "module": "Mathlib.CategoryTheory.Skeletal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instFullSkeletonMapSkeleton", "kind": "instance", "module": "Mathlib.CategoryTheory.Skeletal", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.instFaithfulSkeletonMapSkeleton", "kind": "instance", "module": "Mathlib.CategoryTheory.Skeletal", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.instEssSurjSkeletonMapSkeleton", "kind": "instance", "module": "Mathlib.CategoryTheory.Skeletal", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.toSkeletonFunctorCompMapSkeletonIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Skeletal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapSkeleton_injective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Skeletal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapSkeleton_surjective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Skeletal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.skeletonEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Skeletal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ThinSkeleton", "kind": "definition", "module": "Mathlib.CategoryTheory.Skeletal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ThinSkeleton.mk", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Skeletal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.inhabitedThinSkeleton", "kind": "instance", "module": "Mathlib.CategoryTheory.Skeletal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ThinSkeleton.preorder", "kind": "instance", "module": "Mathlib.CategoryTheory.Skeletal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.toThinSkeleton", "kind": "definition", "module": "Mathlib.CategoryTheory.Skeletal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ThinSkeleton.thin", "kind": "instance", "module": "Mathlib.CategoryTheory.Skeletal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ThinSkeleton.map", "kind": "definition", "module": "Mathlib.CategoryTheory.Skeletal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ThinSkeleton.comp_toThinSkeleton", "kind": "theorem", "module": "Mathlib.CategoryTheory.Skeletal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ThinSkeleton.mapNatTrans", "kind": "definition", "module": "Mathlib.CategoryTheory.Skeletal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ThinSkeleton.map₂ObjMap", "kind": "definition", "module": "Mathlib.CategoryTheory.Skeletal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ThinSkeleton.map₂Functor", "kind": "definition", "module": "Mathlib.CategoryTheory.Skeletal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ThinSkeleton.map₂NatTrans", "kind": "definition", "module": "Mathlib.CategoryTheory.Skeletal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ThinSkeleton.map₂", "kind": "definition", "module": "Mathlib.CategoryTheory.Skeletal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ThinSkeleton.toThinSkeleton_faithful", "kind": "instance", "module": "Mathlib.CategoryTheory.Skeletal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ThinSkeleton.fromThinSkeleton", "kind": "definition", "module": "Mathlib.CategoryTheory.Skeletal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ThinSkeleton.equivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.Skeletal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ThinSkeleton.fromThinSkeleton_isEquivalence", "kind": "instance", "module": "Mathlib.CategoryTheory.Skeletal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ThinSkeleton.equiv_of_both_ways", "kind": "theorem", "module": "Mathlib.CategoryTheory.Skeletal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ThinSkeleton.thinSkeletonPartialOrder", "kind": "instance", "module": "Mathlib.CategoryTheory.Skeletal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ThinSkeleton.skeletal", "kind": "theorem", "module": "Mathlib.CategoryTheory.Skeletal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ThinSkeleton.map_comp_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Skeletal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ThinSkeleton.map_id_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Skeletal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ThinSkeleton.map_iso_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Skeletal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ThinSkeleton.fromThinSkeletonCompToThinSkeletonIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Skeletal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ThinSkeleton.mapCompFromThinSkeletonIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Skeletal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ThinSkeleton.thinSkeleton_isSkeleton", "kind": "theorem", "module": "Mathlib.CategoryTheory.Skeletal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ThinSkeleton.isSkeletonOfInhabited", "kind": "instance", "module": "Mathlib.CategoryTheory.Skeletal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ThinSkeleton.lowerAdjunction", "kind": "definition", "module": "Mathlib.CategoryTheory.Skeletal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.thinSkeletonOrderIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Skeletal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.smallObjectκ", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.smallObjectκ_isRegular", "kind": "instance", "module": "Mathlib.CategoryTheory.SmallObject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instOrderBotToTypeOrdSmallObjectκ", "kind": "instance", "module": "Mathlib.CategoryTheory.SmallObject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.isCardinalForSmallObjectArgument_smallObjectκ", "kind": "instance", "module": "Mathlib.CategoryTheory.SmallObject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.instHasFunctorialFactorizationLlpRlp", "kind": "instance", "module": "Mathlib.CategoryTheory.SmallObject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.llp_rlp_of_hasSmallObjectArgument'", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.llp_rlp_of_hasSmallObjectArgument", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.functorObjSrcFamily", "kind": "abbrev", "module": "Mathlib.CategoryTheory.SmallObject.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.functorObjTgtFamily", "kind": "abbrev", "module": "Mathlib.CategoryTheory.SmallObject.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.functorObjLeftFamily", "kind": "abbrev", "module": "Mathlib.CategoryTheory.SmallObject.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.functorObjTop", "kind": "abbrev", "module": "Mathlib.CategoryTheory.SmallObject.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.functorObjLeft", "kind": "abbrev", "module": "Mathlib.CategoryTheory.SmallObject.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.functorObj", "kind": "abbrev", "module": "Mathlib.CategoryTheory.SmallObject.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.ιFunctorObj", "kind": "abbrev", "module": "Mathlib.CategoryTheory.SmallObject.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.ρFunctorObj", "kind": "abbrev", "module": "Mathlib.CategoryTheory.SmallObject.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.functorObj_comm", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.functorObj_isPushout", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.FunctorObjIndex.comm", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Construction", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.SmallObject.π'FunctorObj", "kind": "abbrev", "module": "Mathlib.CategoryTheory.SmallObject.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.πFunctorObj", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.ρFunctorObj_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Construction", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.SmallObject.ιFunctorObj_πFunctorObj", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Construction", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.SmallObject.attachCellsιFunctorObj", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.instSmallFunctorObjIndex", "kind": "instance", "module": "Mathlib.CategoryTheory.SmallObject.Construction", "is_tactic_proof": false, "tactics": ["let", "have", "rintro", "obtain", "simpa", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.SmallObject.instSmallιAttachCellsιFunctorObj", "kind": "instance", "module": "Mathlib.CategoryTheory.SmallObject.Construction", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.SmallObject.attachCellsιFunctorObjOfSmall", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.functorMapSrc", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.ι_functorMapSrc", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Construction", "is_tactic_proof": true, "tactics": ["subst", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.SmallObject.functorMapSrc_functorObjTop", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Construction", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.SmallObject.functorMapTgt", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.ι_functorMapTgt", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Construction", "is_tactic_proof": true, "tactics": ["subst", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.SmallObject.functorMap_comm", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Construction", "is_tactic_proof": true, "tactics": ["ext", "simp", "ι_functorMapSrc_assoc"], "tactic_count": 3}
{"name": "CategoryTheory.SmallObject.functorMap", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.functorMap_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Construction", "is_tactic_proof": true, "tactics": ["ext", "simp", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.SmallObject.functorMap_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Construction", "is_tactic_proof": true, "tactics": ["ext", "simp", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.SmallObject.ιFunctorObj_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Construction", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.SmallObject.ιFunctorObj_extension", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.ιFunctorObj_extension'", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Construction", "is_tactic_proof": false, "tactics": ["obtain", "ιFunctorObj_extension", "refine", "rw", "rw"], "tactic_count": 5}
{"name": "CategoryTheory.SmallObject.functor", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.ε", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.isSmall", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.IsCardinalForSmallObjectArgument", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.locallySmall", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.IsCardinalForSmallObjectArgument", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.hasIterationOfShape", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.IsCardinalForSmallObjectArgument", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.hasPushouts", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.IsCardinalForSmallObjectArgument", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.hasCoproducts", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.IsCardinalForSmallObjectArgument", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.preservesColimit", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.IsCardinalForSmallObjectArgument", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.hasColimitsOfShape_discrete", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.IsCardinalForSmallObjectArgument", "is_tactic_proof": true, "tactics": ["haveI", "haveI", "haveI", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.SmallObject.succStruct", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.IsCardinalForSmallObjectArgument", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.attachCellsOfSuccStructProp", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.IsCardinalForSmallObjectArgument", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.propArrow", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.IsCardinalForSmallObjectArgument", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.succStruct_prop_le_propArrow", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.IsCardinalForSmallObjectArgument", "is_tactic_proof": true, "tactics": ["haveI", "haveI", "haveI", "haveI", "intro", "constructor", "nth_rw", "apply", "exact", "rw", "dsimp", "infer_instance"], "tactic_count": 12}
{"name": "CategoryTheory.SmallObject.iterationFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.IsCardinalForSmallObjectArgument", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.iteration", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.IsCardinalForSmallObjectArgument", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.ιIteration", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.IsCardinalForSmallObjectArgument", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.transfiniteCompositionOfShapeSuccStructPropιIteration", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.IsCardinalForSmallObjectArgument", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.transfiniteCompositionOfShapeSuccStructPropιIteration_F", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.IsCardinalForSmallObjectArgument", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.transfiniteCompositionOfShapeιIterationAppRight", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.IsCardinalForSmallObjectArgument", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.instIsIsoRightAppArrowιIteration", "kind": "instance", "module": "Mathlib.CategoryTheory.SmallObject.IsCardinalForSmallObjectArgument", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.instIsIsoRightAppArrowMapToTypeOrdFunctorIterationFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.SmallObject.IsCardinalForSmallObjectArgument", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.iterationObjRightIso", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.IsCardinalForSmallObjectArgument", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.iterationFunctorObjObjRightIso", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.IsCardinalForSmallObjectArgument", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.iterationFunctorObjObjRightIso_ιIteration_app_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.IsCardinalForSmallObjectArgument", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.SmallObject.prop_iterationFunctor_map_succ", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.IsCardinalForSmallObjectArgument", "is_tactic_proof": true, "tactics": ["have", "have", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.SmallObject.iterationFunctorMapSuccAppArrowIso", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.IsCardinalForSmallObjectArgument", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.iterationFunctorMapSuccAppArrowIso_hom_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.IsCardinalForSmallObjectArgument", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.iterationFunctorMapSuccAppArrowIso_hom_right_right_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.IsCardinalForSmallObjectArgument", "is_tactic_proof": true, "tactics": ["have", "dsimp", "rw"], "tactic_count": 3}
{"name": "CategoryTheory.SmallObject.obj", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.IsCardinalForSmallObjectArgument", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.ιObj", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.IsCardinalForSmallObjectArgument", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.πObj", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.IsCardinalForSmallObjectArgument", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.πObj_ιIteration_app_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.IsCardinalForSmallObjectArgument", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.SmallObject.ιObj_πObj", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.IsCardinalForSmallObjectArgument", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.SmallObject.relativeCellComplexιObj", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.IsCardinalForSmallObjectArgument", "is_tactic_proof": true, "tactics": ["have", "let", "exact", "attachCells"], "tactic_count": 4}
{"name": "CategoryTheory.SmallObject.transfiniteCompositionsOfShape_ιObj", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.IsCardinalForSmallObjectArgument", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.llp_rlp_ιObj", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.IsCardinalForSmallObjectArgument", "is_tactic_proof": true, "tactics": ["apply", "apply"], "tactic_count": 2}
{"name": "CategoryTheory.SmallObject.relativeCellComplexιObjFObjSuccIso", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.IsCardinalForSmallObjectArgument", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.ιFunctorObj_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.IsCardinalForSmallObjectArgument", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.SmallObject.πFunctorObj_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.IsCardinalForSmallObjectArgument", "is_tactic_proof": true, "tactics": ["have", "have", "dsimp", "rw", "rw", "cancel_mono", "πObj_ιIteration_app_right,", "cancel_epi", "dsimp", "simp", "iterationFunctorMapSuccAppArrowIso_hom_right_right_comp_assoc]"], "tactic_count": 11}
{"name": "CategoryTheory.SmallObject.hasRightLiftingProperty_πObj", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.IsCardinalForSmallObjectArgument", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.rlp_πObj", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.IsCardinalForSmallObjectArgument", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.objMap", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.IsCardinalForSmallObjectArgument", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.objMap_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.IsCardinalForSmallObjectArgument", "is_tactic_proof": true, "tactics": ["simp", "rfl"], "tactic_count": 2}
{"name": "CategoryTheory.SmallObject.objMap_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.IsCardinalForSmallObjectArgument", "is_tactic_proof": true, "tactics": ["simp", "rfl"], "tactic_count": 2}
{"name": "CategoryTheory.SmallObject.ιObj_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.IsCardinalForSmallObjectArgument", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.πObj_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.IsCardinalForSmallObjectArgument", "is_tactic_proof": true, "tactics": ["let", "let", "change", "have", "have", "dsimp", "rw", "apply", "simp", "rw", "apply"], "tactic_count": 11}
{"name": "CategoryTheory.SmallObject.functorialFactorizationData", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.IsCardinalForSmallObjectArgument", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.hasFunctorialFactorization", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.IsCardinalForSmallObjectArgument", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.llp_rlp_of_isCardinalForSmallObjectArgument'", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.IsCardinalForSmallObjectArgument", "is_tactic_proof": true, "tactics": ["refine", "intro", "have", "have", "refine", "exact", "r"], "tactic_count": 7}
{"name": "CategoryTheory.SmallObject.llp_rlp_of_isCardinalForSmallObjectArgument", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.IsCardinalForSmallObjectArgument", "is_tactic_proof": true, "tactics": ["refine", "rw", "apply", "apply"], "tactic_count": 4}
{"name": "CategoryTheory.SmallObject.restrictionLT", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.restrictionLT_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.restrictionLT_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.coconeOfLE", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.restrictionLE", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.restrictionLE_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.restrictionLE_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.ofNatTrans", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.prop", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.prop_toSucc", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.toSuccArrow", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.prop_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.Basic", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "rfl", "intro", "rw", "apply"], "tactic_count": 6}
{"name": "CategoryTheory.SmallObject.SuccStruct.prop.succ_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.Basic", "is_tactic_proof": true, "tactics": ["cases", "rfl"], "tactic_count": 2}
{"name": "CategoryTheory.SmallObject.SuccStruct.prop.fac", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.Basic", "is_tactic_proof": true, "tactics": ["cases", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.SmallObject.SuccStruct.prop.arrowIso", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.arrowMap", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.arrowMap_refl", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.SmallObject.SuccStruct.arrowMap_restrictionLE", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.arrowSucc", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.arrowSucc_def", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.arrowι", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.arrowι_def", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.Iteration.obj_succ", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.Iteration.prop_map_succ", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.SmallObject.SuccStruct.Iteration.obj_limit", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.Iteration.isColimit", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.Basic", "is_tactic_proof": true, "tactics": ["letI", "refine", "rintro", "apply", "dsimp", "rw", "simp"], "tactic_count": 7}
{"name": "CategoryTheory.SmallObject.SuccStruct.Iteration.trunc", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.Iteration.subsingleton.MapEq", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.Iteration.subsingleton.MapEq.src", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.Iteration.subsingleton.MapEq.tgt", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.Iteration.subsingleton.MapEq.w", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.Basic", "is_tactic_proof": true, "tactics": ["have", "tauto"], "tactic_count": 2}
{"name": "CategoryTheory.SmallObject.SuccStruct.Iteration.subsingleton.mapEq_refl", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.SmallObject.SuccStruct.Iteration.subsingleton.mapEq_trans", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.Basic", "is_tactic_proof": true, "tactics": ["simp", "refine", "rw", "simp"], "tactic_count": 4}
{"name": "CategoryTheory.SmallObject.SuccStruct.Iteration.subsingleton.ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.Basic", "is_tactic_proof": true, "tactics": ["apply", "rintro", "apply"], "tactic_count": 3}
{"name": "CategoryTheory.SmallObject.SuccStruct.Iteration.subsingleton", "kind": "instance", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.Iteration.congr_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.Basic", "is_tactic_proof": true, "tactics": ["wlog", "exact", "rw", "dsimp"], "tactic_count": 4}
{"name": "CategoryTheory.SmallObject.SuccStruct.Iteration.congr_arrowMap", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.Basic", "is_tactic_proof": true, "tactics": ["wlog", "simp", "rw", "rfl"], "tactic_count": 4}
{"name": "CategoryTheory.SmallObject.SuccStruct.Iteration.congr_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.Basic", "is_tactic_proof": true, "tactics": ["have", "tauto"], "tactic_count": 2}
{"name": "CategoryTheory.SmallObject.SuccStruct.Iteration.mapObj", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.Iteration.arrow_mk_mapObj", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.SmallObject.SuccStruct.Iteration.mapObj_refl", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.SmallObject.SuccStruct.Iteration.mapObj_trans", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.SmallObject.SuccStruct.extendToSucc.obj", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.ExtendToSucc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.extendToSucc.obj_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.ExtendToSucc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.extendToSucc.objIso", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.ExtendToSucc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.extendToSucc.obj_succ_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.ExtendToSucc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.extendToSucc.objSuccIso", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.ExtendToSucc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.extendToSucc.map", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.ExtendToSucc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.extendToSucc.map_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.ExtendToSucc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.extendToSucc.map_self_succ", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.ExtendToSucc", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.SmallObject.SuccStruct.extendToSucc.map_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.ExtendToSucc", "is_tactic_proof": true, "tactics": ["dsimp", "by_cases", "rw", "obtain", "rw"], "tactic_count": 5}
{"name": "CategoryTheory.SmallObject.SuccStruct.extendToSucc.map_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.ExtendToSucc", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "obtain", "obtain", "rw", "rw", "dsimp", "rw", "rw"], "tactic_count": 9}
{"name": "CategoryTheory.SmallObject.SuccStruct.extendToSucc", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.ExtendToSucc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.extendToSucc_obj_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.ExtendToSucc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.extendToSuccObjIso", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.ExtendToSucc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.extendToSucc_obj_succ_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.ExtendToSucc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.extendToSuccObjSuccIso", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.ExtendToSucc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.extendToSuccObjIso_hom_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.ExtendToSucc", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.SmallObject.SuccStruct.extendToSuccRestrictionLEIso", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.ExtendToSucc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.extendToSucc_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.ExtendToSucc", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.SmallObject.SuccStruct.extendToSucc_map_le_succ", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.ExtendToSucc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.arrowMap_extendToSucc", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.ExtendToSucc", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.SmallObject.SuccStruct.arrowSucc_extendToSucc", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.ExtendToSucc", "is_tactic_proof": true, "tactics": ["simp", "extendToSucc.objSuccIso]"], "tactic_count": 2}
{"name": "CategoryTheory.SmallObject.SuccStruct.ofCocone.obj", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.FunctorOfCocone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.ofCocone.objIso", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.FunctorOfCocone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.ofCocone.objIsoPt", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.FunctorOfCocone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.ofCocone.map", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.FunctorOfCocone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.ofCocone.map_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.FunctorOfCocone", "is_tactic_proof": true, "tactics": ["dsimp", "grind"], "tactic_count": 2}
{"name": "CategoryTheory.SmallObject.SuccStruct.ofCocone.map_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.FunctorOfCocone", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "dsimp", "obtain", "rw", "rw", "comp_id,", "rw", "rw"], "tactic_count": 9}
{"name": "CategoryTheory.SmallObject.SuccStruct.ofCocone", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.FunctorOfCocone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.ofCocone_obj_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.FunctorOfCocone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.ofCoconeObjIso", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.FunctorOfCocone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.ofCocone_obj_eq_pt", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.FunctorOfCocone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.ofCoconeObjIsoPt", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.FunctorOfCocone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.ofCocone_map_to_top", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.FunctorOfCocone", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.SmallObject.SuccStruct.ofCocone_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.FunctorOfCocone", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.SmallObject.SuccStruct.ofCoconeObjIso_hom_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.FunctorOfCocone", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.SmallObject.SuccStruct.restrictionLTOfCoconeIso", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.FunctorOfCocone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.isColimitCoconeOfLEOfCocone", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.FunctorOfCocone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.arrowMap_ofCocone", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.FunctorOfCocone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.arrowMap_ofCocone_to_top", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.FunctorOfCocone", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.SmallObject.SuccStruct.Iteration.mkOfBot", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.Nonempty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.Iteration.mkOfSucc", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.Nonempty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.Iteration.mkOfLimit.inductiveSystem", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.Nonempty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.Iteration.mkOfLimit.functor", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.Nonempty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.Iteration.mkOfLimit.functor_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.Nonempty", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "apply"], "tactic_count": 3}
{"name": "CategoryTheory.SmallObject.SuccStruct.Iteration.mkOfLimit.arrowMap_functor", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.Nonempty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.Iteration.mkOfLimit.arrowMap_functor_to_top", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.Nonempty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.Iteration.mkOfLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.Nonempty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.Iteration.nonempty", "kind": "instance", "module": "Mathlib.CategoryTheory.SmallObject.Iteration.Nonempty", "is_tactic_proof": true, "tactics": ["induction", "isMin", "obtain", "exact", "succ", "isSuccLimit"], "tactic_count": 6}
{"name": "CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.TransfiniteCompositionLifting", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.sq", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.TransfiniteCompositionLifting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.map", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.TransfiniteCompositionLifting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasLiftingProperty.transfiniteComposition.sqFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.TransfiniteCompositionLifting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasLiftingProperty.transfiniteComposition.wellOrderInductionData.liftHom", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.TransfiniteCompositionLifting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasLiftingProperty.transfiniteComposition.wellOrderInductionData.liftHom_fac", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.TransfiniteCompositionLifting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasLiftingProperty.transfiniteComposition.wellOrderInductionData.lift", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.TransfiniteCompositionLifting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasLiftingProperty.transfiniteComposition.wellOrderInductionData.map_lift", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.TransfiniteCompositionLifting", "is_tactic_proof": true, "tactics": ["ext", "apply"], "tactic_count": 2}
{"name": "CategoryTheory.HasLiftingProperty.transfiniteComposition.wellOrderInductionData", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.TransfiniteCompositionLifting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasLiftingProperty.transfiniteComposition.hasLift", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.TransfiniteCompositionLifting", "is_tactic_proof": true, "tactics": ["obtain", "replace", "dsimp", "let", "naturality", "let", "have", "exact", "l", "fac_left", "fac_right"], "tactic_count": 11}
{"name": "CategoryTheory.HasLiftingProperty.transfiniteComposition.hasLiftingPropertyFixedBot_ι_app_bot", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.TransfiniteCompositionLifting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasLiftingProperty.transfiniteComposition.hasLiftingProperty_ι_app_bot", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.TransfiniteCompositionLifting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MorphismProperty.isStableUnderTransfiniteCompositionOfShape_llp", "kind": "instance", "module": "Mathlib.CategoryTheory.SmallObject.TransfiniteCompositionLifting", "is_tactic_proof": true, "tactics": ["rw", "rintro", "have", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.MorphismProperty.transfiniteCompositionsOfShape_le_llp_rlp", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.TransfiniteCompositionLifting", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.MorphismProperty.transfiniteCompositionsOfShape_pushouts_coproducts_le_llp_rlp", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.TransfiniteCompositionLifting", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.MorphismProperty.retracts_transfiniteCompositionsOfShape_pushouts_coproducts_le_llp_rlp", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.TransfiniteCompositionLifting", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "CategoryTheory.MorphismProperty.transfiniteCompositions_le_llp_rlp", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.TransfiniteCompositionLifting", "is_tactic_proof": true, "tactics": ["intro", "rw", "obtain", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.MorphismProperty.transfiniteCompositions_pushouts_coproducts_le_llp_rlp", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.TransfiniteCompositionLifting", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.MorphismProperty.retracts_transfiniteComposition_pushouts_coproducts_le_llp_rlp", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.TransfiniteCompositionLifting", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "CategoryTheory.SmallObject.SuccStruct.iter", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.TransfiniteIteration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.iterationFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.TransfiniteIteration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.iteration", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.TransfiniteIteration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.iterationCocone", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.TransfiniteIteration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.iterationCocone_pt", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.TransfiniteIteration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.isColimitIterationCocone", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.TransfiniteIteration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.iterationFunctor_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.TransfiniteIteration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.arrowMk_iterationFunctor_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.TransfiniteIteration", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.SmallObject.SuccStruct.instIsWellOrderContinuousIterationFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.SmallObject.TransfiniteIteration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.iterationFunctorObjBotIso", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.TransfiniteIteration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.ιIterationFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.TransfiniteIteration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.ιIteration", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.TransfiniteIteration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.transfiniteCompositionOfShapeιIteration", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.TransfiniteIteration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.prop_iterationFunctor_map_succ", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.TransfiniteIteration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.iterationFunctorObjSuccIso", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.TransfiniteIteration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallObject.SuccStruct.iterationFunctor_map_succ", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.TransfiniteIteration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.WellOrderInductionData.ofExists", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.WellOrderInductionData", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.WellOrderInductionData.Extension.ofLE", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.WellOrderInductionData", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.WellOrderInductionData.Extension.val_injective", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.WellOrderInductionData", "is_tactic_proof": true, "tactics": ["cases", "cases", "subst", "rfl"], "tactic_count": 4}
{"name": "CategoryTheory.Functor.WellOrderInductionData.Extension.instSubsingletonOfWellFoundedLT", "kind": "instance", "module": "Mathlib.CategoryTheory.SmallObject.WellOrderInductionData", "is_tactic_proof": true, "tactics": ["induction", "isMin", "obtain", "refine", "have", "have", "simp", "rw", "succ", "refine", "have", "have", "simp", "rw", "congr", "exact", "isSuccLimit", "refine", "have", "have", "simp", "rw", "congr", "ext", "have", "exact"], "tactic_count": 26}
{"name": "CategoryTheory.Functor.WellOrderInductionData.Extension.compatibility", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.WellOrderInductionData", "is_tactic_proof": true, "tactics": ["obtain", "rfl"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.WellOrderInductionData.Extension.zero", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.WellOrderInductionData", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.WellOrderInductionData.Extension.succ", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.WellOrderInductionData", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.WellOrderInductionData.Extension.limit", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.WellOrderInductionData", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.WellOrderInductionData.Extension.instNonempty", "kind": "instance", "module": "Mathlib.CategoryTheory.SmallObject.WellOrderInductionData", "is_tactic_proof": true, "tactics": ["induction", "isMin", "obtain", "exact", "succ", "isSuccLimit"], "tactic_count": 6}
{"name": "CategoryTheory.Functor.WellOrderInductionData.Extension.instUnique", "kind": "instance", "module": "Mathlib.CategoryTheory.SmallObject.WellOrderInductionData", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.WellOrderInductionData.sectionsMk", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallObject.WellOrderInductionData", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.WellOrderInductionData.sectionsMk_val_op_bot", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.WellOrderInductionData", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.WellOrderInductionData.surjective", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallObject.WellOrderInductionData", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallCategoryOfSet.instSmallCategoryElemObj", "kind": "instance", "module": "Mathlib.CategoryTheory.SmallRepresentatives", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallCategoryOfSet.categoryFamily", "kind": "abbrev", "module": "Mathlib.CategoryTheory.SmallRepresentatives", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CoreSmallCategoryOfSet.smallCategoryOfSet", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallRepresentatives", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CoreSmallCategoryOfSet.functor", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallRepresentatives", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CoreSmallCategoryOfSet.fullyFaithfulFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallRepresentatives", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CoreSmallCategoryOfSet.instIsEquivalenceElemObjSmallCategoryOfSetFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.SmallRepresentatives", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CoreSmallCategoryOfSet.equivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallRepresentatives", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CoreSmallCategoryOfSet.arrowEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallRepresentatives", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallCategoryOfSet.exists_equivalence", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallRepresentatives", "is_tactic_proof": true, "tactics": ["let", "let", "let", "let", "hom", "objEquiv", "homEquiv", "exact"], "tactic_count": 8}
{"name": "CategoryTheory.SmallCategoryCardinalLT", "kind": "definition", "module": "Mathlib.CategoryTheory.SmallRepresentatives", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallCategoryCardinalLT.categoryFamily", "kind": "abbrev", "module": "Mathlib.CategoryTheory.SmallRepresentatives", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallCategoryCardinalLT.hasCardinalLT", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallRepresentatives", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.SmallCategoryCardinalLT.exists_equivalence", "kind": "theorem", "module": "Mathlib.CategoryTheory.SmallRepresentatives", "is_tactic_proof": true, "tactics": ["let", "have", "rw", "simpa", "have", "rw", "refine", "intro", "exact", "have", "rw", "refine", "intro", "simpa", "let", "let", "let", "let", "hom", "objEquiv", "homEquiv", "refine", "rwa"], "tactic_count": 23}
{"name": "CategoryTheory.Square.commSq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Square", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Square.Hom.id", "kind": "definition", "module": "Mathlib.CategoryTheory.Square", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Square.Hom.comp", "kind": "definition", "module": "Mathlib.CategoryTheory.Square", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Square.category", "kind": "instance", "module": "Mathlib.CategoryTheory.Square", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Square.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Square", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Square.isoMk", "kind": "definition", "module": "Mathlib.CategoryTheory.Square", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Square.flip", "kind": "definition", "module": "Mathlib.CategoryTheory.Square", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Square.flipFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Square", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Square.flipEquivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.Square", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Square.toArrowArrowFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Square", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Square.fromArrowArrowFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Square", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Square.arrowArrowEquivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.Square", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Square.toArrowArrowFunctor'", "kind": "definition", "module": "Mathlib.CategoryTheory.Square", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Square.fromArrowArrowFunctor'", "kind": "definition", "module": "Mathlib.CategoryTheory.Square", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Square.arrowArrowEquivalence'", "kind": "definition", "module": "Mathlib.CategoryTheory.Square", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Square.evaluation₁", "kind": "definition", "module": "Mathlib.CategoryTheory.Square", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Square.evaluation₂", "kind": "definition", "module": "Mathlib.CategoryTheory.Square", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Square.evaluation₃", "kind": "definition", "module": "Mathlib.CategoryTheory.Square", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Square.evaluation₄", "kind": "definition", "module": "Mathlib.CategoryTheory.Square", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Square.op", "kind": "definition", "module": "Mathlib.CategoryTheory.Square", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Square.unop", "kind": "definition", "module": "Mathlib.CategoryTheory.Square", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Square.opFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Square", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Square.unopFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Square", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Square.opEquivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.Square", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Square.map", "kind": "definition", "module": "Mathlib.CategoryTheory.Square", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapSquare", "kind": "definition", "module": "Mathlib.CategoryTheory.Square", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.mapSquare", "kind": "definition", "module": "Mathlib.CategoryTheory.Square", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Square.mapFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Square", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instPartialOrderSubfunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.Subfunctor.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instCompleteLatticeSubfunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.Subfunctor.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subfunctor.le_def", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subfunctor.top_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subfunctor.bot_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subfunctor.sSup_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subfunctor.sInf_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subfunctor.iSup_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Subfunctor.iInf_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Subfunctor.max_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subfunctor.min_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subfunctor.max_min", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.Basic", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "CategoryTheory.Subfunctor.iSup_min", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.Basic", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "CategoryTheory.Subfunctor.instNonempty", "kind": "instance", "module": "Mathlib.CategoryTheory.Subfunctor.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subfunctor.toFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Subfunctor.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subfunctor.instCoeHeadObjToFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.Subfunctor.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subfunctor.ι", "kind": "definition", "module": "Mathlib.CategoryTheory.Subfunctor.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subfunctor.instMonoFunctorTypeι", "kind": "instance", "module": "Mathlib.CategoryTheory.Subfunctor.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subfunctor.homOfLe", "kind": "definition", "module": "Mathlib.CategoryTheory.Subfunctor.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subfunctor.instMonoFunctorTypeHomOfLe", "kind": "instance", "module": "Mathlib.CategoryTheory.Subfunctor.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subfunctor.homOfLe_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.Basic", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "CategoryTheory.Subfunctor.instIsIsoFunctorTypeιTop", "kind": "instance", "module": "Mathlib.CategoryTheory.Subfunctor.Basic", "is_tactic_proof": true, "tactics": ["refine", "intro", "rw", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.Subfunctor.eq_top_iff_isIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.Basic", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "infer_instance", "intro", "ext", "apply", "rw", "exact"], "tactic_count": 8}
{"name": "CategoryTheory.Subfunctor.nat_trans_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subfunctor.equalizer", "kind": "definition", "module": "Mathlib.CategoryTheory.Subfunctor.Equalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subfunctor.equalizer_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.Equalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subfunctor.equalizer_self", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.Equalizer", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "CategoryTheory.Subfunctor.mem_equalizer_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.Equalizer", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Subfunctor.range_le_equalizer_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.Equalizer", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Subfunctor.equalizer_eq_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.Equalizer", "is_tactic_proof": true, "tactics": ["have", "simp", "rw", "constructor", "intro", "rw", "intro", "exact"], "tactic_count": 8}
{"name": "CategoryTheory.Subfunctor.equalizer.ι", "kind": "definition", "module": "Mathlib.CategoryTheory.Subfunctor.Equalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subfunctor.instMonoFunctorTypeι_1", "kind": "instance", "module": "Mathlib.CategoryTheory.Subfunctor.Equalizer", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Subfunctor.equalizer.ι_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.Equalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subfunctor.equalizer.condition", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.Equalizer", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Subfunctor.equalizer.lift", "kind": "definition", "module": "Mathlib.CategoryTheory.Subfunctor.Equalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subfunctor.equalizer.lift_ι'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.Equalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subfunctor.equalizer.lift_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.Equalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subfunctor.equalizer.fork", "kind": "definition", "module": "Mathlib.CategoryTheory.Subfunctor.Equalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subfunctor.equalizer.fork_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.Equalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subfunctor.equalizer.forkIsLimit", "kind": "definition", "module": "Mathlib.CategoryTheory.Subfunctor.Equalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subfunctor.IsGeneratedBy", "kind": "definition", "module": "Mathlib.CategoryTheory.Subfunctor.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subfunctor.isGeneratedBy_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subfunctor.IsGeneratedBy.iSup_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subfunctor.IsGeneratedBy.ofSection_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.Finite", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Subfunctor.IsGeneratedBy.mem", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.Finite", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Subfunctor.IsGeneratedBy.of_equiv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.Finite", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Subfunctor.IsGeneratedBy.image", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.Finite", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Subfunctor.IsFinite.Index", "kind": "definition", "module": "Mathlib.CategoryTheory.Subfunctor.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subfunctor.IsFinite.instFiniteIndex", "kind": "instance", "module": "Mathlib.CategoryTheory.Subfunctor.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subfunctor.IsFinite.X", "kind": "definition", "module": "Mathlib.CategoryTheory.Subfunctor.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subfunctor.IsFinite.x", "kind": "definition", "module": "Mathlib.CategoryTheory.Subfunctor.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subfunctor.isGeneratedBy_of_isFinite", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subfunctor.IsGeneratedBy.isFinite", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.Finite", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Subfunctor.image_isFinite", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PresheafIsGeneratedBy", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Subfunctor.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.PresheafIsGeneratedBy.range", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.Finite", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.PresheafIsGeneratedBy.of_epi", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.Finite", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.PresheafIsFinite", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Subfunctor.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.presheafIsGeneratedBy_of_isFinite", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subfunctor.range_isFinite", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.presheafIsFinite_of_epi", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.yoneda_obj_isGeneratedBy", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.Finite", "is_tactic_proof": true, "tactics": ["simp", "ext", "simp", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.instPresheafIsFiniteObjFunctorOppositeTypeYoneda", "kind": "instance", "module": "Mathlib.CategoryTheory.Subfunctor.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subfunctor.range", "kind": "definition", "module": "Mathlib.CategoryTheory.Subfunctor.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subfunctor.range_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.Image", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "CategoryTheory.Subfunctor.range_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.Image", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "CategoryTheory.Subfunctor.lift", "kind": "definition", "module": "Mathlib.CategoryTheory.Subfunctor.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subfunctor.lift_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subfunctor.toRange", "kind": "definition", "module": "Mathlib.CategoryTheory.Subfunctor.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subfunctor.toRange_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subfunctor.toRange_app_val", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.Image", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Subfunctor.range_toRange", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.Image", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "simp", "simp", "obtain", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.Subfunctor.epi_iff_range_eq_top", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.Image", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Subfunctor.range_eq_top", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.Image", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "CategoryTheory.Subfunctor.instEpiFunctorTypeToRange", "kind": "instance", "module": "Mathlib.CategoryTheory.Subfunctor.Image", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Subfunctor.instIsIsoFunctorTypeToRangeOfMono", "kind": "instance", "module": "Mathlib.CategoryTheory.Subfunctor.Image", "is_tactic_proof": true, "tactics": ["have", "rw", "intro", "rw", "constructor", "rw", "infer_instance", "rw", "infer_instance"], "tactic_count": 9}
{"name": "CategoryTheory.Subfunctor.range_comp_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subfunctor.image", "kind": "definition", "module": "Mathlib.CategoryTheory.Subfunctor.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subfunctor.image_top", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.Image", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "CategoryTheory.Subfunctor.image_iSup", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.Image", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "CategoryTheory.Subfunctor.image_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.Image", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "CategoryTheory.Subfunctor.range_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.Image", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "CategoryTheory.Subfunctor.preimage", "kind": "definition", "module": "Mathlib.CategoryTheory.Subfunctor.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subfunctor.preimage_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.Image", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "CategoryTheory.Subfunctor.preimage_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.Image", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "CategoryTheory.Subfunctor.image_le_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.Image", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Subfunctor.fromPreimage", "kind": "definition", "module": "Mathlib.CategoryTheory.Subfunctor.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subfunctor.fromPreimage_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subfunctor.preimage_eq_top_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.Image", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Subfunctor.preimage_image_of_epi", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.Image", "is_tactic_proof": true, "tactics": ["apply", "rw", "intro", "simp", "obtain", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.Subfunctor.ofSection", "kind": "definition", "module": "Mathlib.CategoryTheory.Subfunctor.OfSection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subfunctor.mem_ofSection_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.OfSection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subfunctor.ofSection_le_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.OfSection", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "rintro", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.Subfunctor.ofSection_image", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.OfSection", "is_tactic_proof": true, "tactics": ["apply", "rw", "exact", "simp", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.Subfunctor.ofSection_eq_range", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.OfSection", "is_tactic_proof": true, "tactics": ["ext", "simp", "constructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 7}
{"name": "CategoryTheory.Subfunctor.range_eq_ofSection", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.OfSection", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Subfunctor.ofSection_eq_range'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.OfSection", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "simp", "constructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 8}
{"name": "CategoryTheory.Subfunctor.range_eq_ofSection'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.OfSection", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Subfunctor.sieveOfSection", "kind": "definition", "module": "Mathlib.CategoryTheory.Subfunctor.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subfunctor.familyOfElementsOfSection", "kind": "definition", "module": "Mathlib.CategoryTheory.Subfunctor.Sieves", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subfunctor.family_of_elements_compatible", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.Sieves", "is_tactic_proof": true, "tactics": ["intro", "refine", "change", "rw"], "tactic_count": 4}
{"name": "CategoryTheory.Subfunctor.equivalenceMonoOver", "kind": "definition", "module": "Mathlib.CategoryTheory.Subfunctor.Subobject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subfunctor.range_subobjectMk_ι", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.Subobject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subfunctor.subobjectMk_range_arrow", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subfunctor.Subobject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subfunctor.orderIsoSubobject", "kind": "definition", "module": "Mathlib.CategoryTheory.Subfunctor.Subobject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isArtinianObject", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.ArtinianObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsArtinianObject", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Subobject.ArtinianObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instWellFoundedLTSubobjectOfIsArtinianObject", "kind": "instance", "module": "Mathlib.CategoryTheory.Subobject.ArtinianObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isArtinianObject_iff_antitone_chain_condition", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.ArtinianObject", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.antitone_chain_condition_of_isArtinianObject", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.ArtinianObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isArtinianObject_iff_not_strictAnti", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.ArtinianObject", "is_tactic_proof": true, "tactics": ["refine", "dsimp", "rw", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.not_strictAnti_of_isArtinianObject", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.ArtinianObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isArtinianObject_iff_isEventuallyConstant", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.ArtinianObject", "is_tactic_proof": true, "tactics": ["rw", "refine", "obtain", "refine", "rw", "exact", "obtain", "refine", "simpa"], "tactic_count": 9}
{"name": "CategoryTheory.isEventuallyConstant_of_isArtinianObject", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.ArtinianObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isArtinianObject_of_isZero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.ArtinianObject", "is_tactic_proof": true, "tactics": ["rw", "have", "intro", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.instContainsZeroIsArtinianObjectOfHasZeroObject", "kind": "instance", "module": "Mathlib.CategoryTheory.Subobject.ArtinianObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isArtinianObject_of_mono", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.ArtinianObject", "is_tactic_proof": true, "tactics": ["rw", "intro", "obtain", "antitone_chain_condition_of_isArtinianObject", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.instIsClosedUnderSubobjectsIsArtinianObject", "kind": "instance", "module": "Mathlib.CategoryTheory.Subobject.ArtinianObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.exists_simple_subobject", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.ArtinianObject", "is_tactic_proof": true, "tactics": ["have", "obtain", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.simpleSubobject", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.ArtinianObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.simpleSubobjectArrow", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.ArtinianObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.mono_simpleSubobjectArrow", "kind": "instance", "module": "Mathlib.CategoryTheory.Subobject.ArtinianObject", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.instSimpleSimpleSubobject", "kind": "instance", "module": "Mathlib.CategoryTheory.Subobject.ArtinianObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instPartialOrderSubobject", "kind": "instance", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.skeletal", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.mk", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.ind", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": true, "tactics": ["apply", "intro", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Subobject.ind₂", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": true, "tactics": ["apply", "intro", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Subobject.lift", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.lift_mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.equivMonoOver", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.representative", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.instIsEquivalenceMonoOverRepresentative", "kind": "instance", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.representativeIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.underlying", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.instCoeOut", "kind": "instance", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.underlyingIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.arrow", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.arrow_mono", "kind": "instance", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.arrow_congr", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": true, "tactics": ["induction", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Subobject.representative_coe", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.representative_arrow", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.underlying_arrow", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.underlyingIso_arrow", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.underlyingIso_hom_comp_eq_mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.eq_of_comp_arrow_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.mk_le_mk_of_comm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.mk_arrow", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.le_of_comm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "CategoryTheory.Subobject.le_mk_of_comm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.mk_le_of_comm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.eq_of_comm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.eq_mk_of_comm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.mk_eq_of_comm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.mk_eq_mk_of_comm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.mk_surjective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.ofLE", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.ofLE_arrow", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.instMonoOfLE", "kind": "instance", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": true, "tactics": ["fconstructor", "intro", "replace", "ext", "simpa"], "tactic_count": 5}
{"name": "CategoryTheory.Subobject.ofLE_mk_le_mk_of_comm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Subobject.ofLEMk", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.instMonoOfLEMk", "kind": "instance", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Subobject.ofLEMk_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Subobject.ofMkLE", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.instMonoOfMkLE", "kind": "instance", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Subobject.ofMkLE_arrow", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Subobject.ofMkLEMk", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.instMonoOfMkLEMk", "kind": "instance", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Subobject.ofMkLEMk_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Subobject.ofLE_comp_ofLE", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": true, "tactics": ["simp", "congr"], "tactic_count": 2}
{"name": "CategoryTheory.Subobject.ofLE_comp_ofLEMk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": true, "tactics": ["simp", "congr"], "tactic_count": 2}
{"name": "CategoryTheory.Subobject.ofLEMk_comp_ofMkLE", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": true, "tactics": ["simp", "congr"], "tactic_count": 2}
{"name": "CategoryTheory.Subobject.ofLEMk_comp_ofMkLEMk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": true, "tactics": ["simp", "congr"], "tactic_count": 2}
{"name": "CategoryTheory.Subobject.ofMkLE_comp_ofLE", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": true, "tactics": ["simp", "congr"], "tactic_count": 2}
{"name": "CategoryTheory.Subobject.ofMkLE_comp_ofLEMk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": true, "tactics": ["simp", "congr"], "tactic_count": 2}
{"name": "CategoryTheory.Subobject.ofMkLEMk_comp_ofMkLE", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": true, "tactics": ["simp", "congr"], "tactic_count": 2}
{"name": "CategoryTheory.Subobject.ofMkLEMk_comp_ofMkLEMk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": true, "tactics": ["simp", "congr"], "tactic_count": 2}
{"name": "CategoryTheory.Subobject.ofLE_refl", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Subobject.ofMkLEMk_refl", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Subobject.isoOfEq", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.isoOfEqMk", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.isoOfMkEq", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.isoOfMkEqMk", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.mk_lt_mk_of_comm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": true, "tactics": ["obtain", "assumption", "exfalso", "apply", "convert", "rw"], "tactic_count": 6}
{"name": "CategoryTheory.Subobject.mk_lt_mk_iff_of_comm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.subobjectMk_le_mk_of_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.isIso_hom_left_iff_subobjectMk_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.isIso_iff_subobjectMk_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Subobject.lower", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.lower_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.lower₂", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.lower_comm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.lowerCompRepresentativeIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.lowerAdjunction", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.lowerEquivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.hasLimitsOfShape", "kind": "instance", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Subobject.hasFiniteLimits", "kind": "instance", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.hasLimitsOfSize", "kind": "instance", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.hasColimitsOfSize", "kind": "instance", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Subobject.pullback", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.pullback_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": ["induction", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Subobject.pullback_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": ["induction", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Subobject.pullback_obj_mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.pullback_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact", "mk_eq_mk_of_comm"], "tactic_count": 4}
{"name": "CategoryTheory.Subobject.instFaithfulPullback", "kind": "instance", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.isPullback_aux", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exists", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.Subobject.pullbackπ", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.isPullback", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.map", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.map_mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.map_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": ["induction", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Subobject.map_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": ["induction", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Subobject.map_obj_injective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.mapIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.mapIsoToOrderIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.mapPullbackAdj", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.pullback_map_self", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": true, "tactics": ["revert", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Subobject.map_pullback", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": true, "tactics": ["revert", "apply", "intro", "apply", "apply", "refine", "simp", "refine", "rw", "rfl", "dsimp", "rw", "apply"], "tactic_count": 13}
{"name": "CategoryTheory.Subobject.exists", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.exists_iso_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.existsPullbackAdj", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.existsCompRepresentativeIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.existsIsoImage", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.imageFactorisation", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.projectSubobject", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Comma", "is_tactic_proof": true, "tactics": ["refine", "intro", "refine", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.StructuredArrow.projectSubobject_mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.projectSubobject_factors", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.liftSubobject", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.lift_projectSubobject", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.subobjectEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.StructuredArrow.wellPowered_structuredArrow", "kind": "instance", "module": "Mathlib.CategoryTheory.Subobject.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.projectQuotient", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Comma", "is_tactic_proof": true, "tactics": ["refine", "intro", "refine", "have", "simpa"], "tactic_count": 5}
{"name": "CategoryTheory.CostructuredArrow.projectQuotient_mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.projectQuotient_factors", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.liftQuotient", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.unop_left_comp_underlyingIso_hom_unop", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Comma", "is_tactic_proof": false, "tactics": ["conv_lhs", "congr", "rw", "rw"], "tactic_count": 4}
{"name": "CategoryTheory.CostructuredArrow.lift_projectQuotient", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.unop_left_comp_ofMkLEMk_unop", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Comma", "is_tactic_proof": false, "tactics": ["conv_lhs", "congr", "rw", "rw", "simp"], "tactic_count": 5}
{"name": "CategoryTheory.CostructuredArrow.quotientEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.CostructuredArrow.well_copowered_costructuredArrow", "kind": "instance", "module": "Mathlib.CategoryTheory.Subobject.Comma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.Factors", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.FactorThru", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.factors_congr", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.FactorThru", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.factorThru", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.FactorThru", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.Factors", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.FactorThru", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.mk_factors_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.FactorThru", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.mk_factors_self", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.FactorThru", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.factors_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.FactorThru", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.factors_self", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.FactorThru", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.factors_comp_arrow", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.FactorThru", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.factors_of_factors_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.FactorThru", "is_tactic_proof": true, "tactics": ["induction", "obtain", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Subobject.factors_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.FactorThru", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.factors_of_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.FactorThru", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Subobject.factorThru", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.FactorThru", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.factorThru_arrow", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.FactorThru", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.factorThru_self", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.FactorThru", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Subobject.factorThru_mk_self", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.FactorThru", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Subobject.factorThru_comp_arrow", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.FactorThru", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Subobject.factorThru_eq_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.FactorThru", "is_tactic_proof": true, "tactics": ["fconstructor", "intro", "replace", "simpa", "rintro", "ext", "simp"], "tactic_count": 7}
{"name": "CategoryTheory.Subobject.factorThru_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.FactorThru", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Subobject.factorThru_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.FactorThru", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Subobject.factorThru_ofLE", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.FactorThru", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Subobject.le_of_factors", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.FactorThru", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.homOfFactors", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.FactorThru", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.factors_add", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.FactorThru", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.factorThru_add", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.FactorThru", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Subobject.factors_left_of_factors_add", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.FactorThru", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.factorThru_add_sub_factorThru_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.FactorThru", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Subobject.factors_right_of_factors_add", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.FactorThru", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.factorThru_add_sub_factorThru_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.FactorThru", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Subobject.hasCardinalLT_of_mono", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.HasCardinalLT", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.instTop", "kind": "instance", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.instInhabited", "kind": "instance", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.leTop", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.top_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.top_arrow", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.mapTop", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.pullbackTop", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.topLEPullbackSelf", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.pullbackSelf", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.instBot", "kind": "instance", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.bot_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.bot_arrow", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.botLE", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.mapBot", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.botCoeIsoZero", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.bot_arrow_eq_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.initialTo_b_eq_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.MonoOver.inf", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.infLELeft", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.infLERight", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.leInf", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.sup", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.leSupLeft", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": true, "tactics": ["refine", "erw", "rfl"], "tactic_count": 3}
{"name": "CategoryTheory.MonoOver.leSupRight", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": true, "tactics": ["refine", "erw", "rfl"], "tactic_count": 3}
{"name": "CategoryTheory.MonoOver.supLe", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": true, "tactics": ["intro", "refine", "apply", "ext", "simp", "simp", "apply"], "tactic_count": 7}
{"name": "CategoryTheory.Subobject.orderTop", "kind": "instance", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.instInhabited", "kind": "instance", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.top_eq_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.underlyingIso_top_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Subobject.top_arrow_isIso", "kind": "instance", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Subobject.underlyingIso_inv_top_arrow", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.map_top", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.top_factors", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.isIso_iff_mk_eq_top", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.isIso_arrow_iff_eq_top", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Subobject.isIso_top_arrow", "kind": "instance", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Subobject.mk_eq_top_of_isIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.eq_top_of_isIso_arrow", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.epi_iff_mk_eq_top", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Subobject.pullback_top", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.pullback_self", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.orderBot", "kind": "instance", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.bot_eq_initial_to", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.botCoeIsoInitial", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.map_bot", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.botCoeIsoZero", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.bot_eq_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.bot_arrow", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.bot_factors_iff_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.mk_eq_bot_iff_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.functor", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.inf", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.inf_le_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.inf_le_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.le_inf", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.semilatticeInf", "kind": "instance", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.factors_left_of_inf_factors", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.factors_right_of_inf_factors", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.inf_factors", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.inf_isPullback", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": ["refine", "simpa", "cat_disch", "ext", "simp", "ext", "simp"], "tactic_count": 7}
{"name": "CategoryTheory.Subobject.inf_arrow_factors_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.inf_arrow_factors_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.finset_inf_factors", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "insert", "simp"], "tactic_count": 5}
{"name": "CategoryTheory.Subobject.finset_inf_arrow_factors", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": true, "tactics": ["classical", "revert", "induction", "empty", "insert", "intro", "rw", "simp", "rcases", "rw", "exact", "rw", "apply", "exact"], "tactic_count": 14}
{"name": "CategoryTheory.Subobject.inf_eq_map_pullback'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": true, "tactics": ["induction", "rfl"], "tactic_count": 2}
{"name": "CategoryTheory.Subobject.inf_eq_map_pullback", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.prod_eq_inf", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": true, "tactics": ["apply", "refine", "apply", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.Subobject.inf_def", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.inf_pullback", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": true, "tactics": ["revert", "apply", "intro", "erw", "map_pullback", "rfl"], "tactic_count": 6}
{"name": "CategoryTheory.Subobject.inf_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": true, "tactics": ["revert", "apply", "intro", "erw", "dsimp", "rw"], "tactic_count": 6}
{"name": "CategoryTheory.Subobject.sup", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.semilatticeSup", "kind": "instance", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.sup_factors_of_factors_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.sup_factors_of_factors_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.finset_sup_factors", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": true, "tactics": ["classical", "revert", "induction", "empty", "insert", "rintro", "simp", "simp", "rcases", "exact", "exact"], "tactic_count": 11}
{"name": "CategoryTheory.Subobject.boundedOrder", "kind": "instance", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.instLattice", "kind": "instance", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.wideCospan", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.wideCospan_map_term", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.leInfCone", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.leInfCone_π_app_none", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.widePullback", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.widePullbackι", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.widePullbackι_mono", "kind": "instance", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.sInf", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.sInf_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": true, "tactics": ["fapply", "exact", "eqToHom", "dsimp", "simp", "convert", "simp"], "tactic_count": 7}
{"name": "CategoryTheory.Subobject.le_sInf", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": true, "tactics": ["fapply", "exact", "dsimp", "rw"], "tactic_count": 4}
{"name": "CategoryTheory.Subobject.completeSemilatticeInf", "kind": "instance", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.smallCoproductDesc", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.sSup", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.le_sSup", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": true, "tactics": ["fapply", "refine", "eqToHom", "factorThruImage", "exact", "simp"], "tactic_count": 6}
{"name": "CategoryTheory.Subobject.symm_apply_mem_iff_mem_image", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.sSup_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": true, "tactics": ["fapply", "refine", "refine", "rintro", "refine", "simpa", "ext", "dsimp", "simp", "dsimp", "rw"], "tactic_count": 11}
{"name": "CategoryTheory.Subobject.completeSemilatticeSup", "kind": "instance", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.instCompleteLattice", "kind": "instance", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.subsingleton_of_isInitial", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": true, "tactics": ["suffices", "intro", "obtain", "have", "let", "inv", "hom_inv_id", "inv_hom_id", "exact"], "tactic_count": 9}
{"name": "CategoryTheory.Subobject.subsingleton_of_isZero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.nontrivial_of_not_isZero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Subobject.subobjectOrderIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullback_factors", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullback_factors_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Limits", "is_tactic_proof": true, "tactics": ["refine", "rw", "use", "simp"], "tactic_count": 4}
{"name": "CategoryTheory.Limits.equalizerSubobject", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Subobject.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.equalizerSubobjectIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.equalizerSubobject_arrow", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Limits", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.equalizerSubobject_arrow'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Limits", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.equalizerSubobject_arrow_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Limits", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.equalizerSubobject_factors", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.equalizerSubobject_factors_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.pullback_equalizer", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Limits", "is_tactic_proof": true, "tactics": ["refine", "apply", "have", "rw", "reassoc_of%", "apply", "apply", "rw"], "tactic_count": 8}
{"name": "CategoryTheory.Limits.kernelSubobject", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Subobject.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.kernelSubobjectIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.kernelSubobject_arrow", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Limits", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.kernelSubobject_arrow'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Limits", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.kernelSubobject_arrow_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Limits", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.kernelSubobject_factors", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.kernelSubobject_factors_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.factorThruKernelSubobject", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.factorThruKernelSubobject_comp_arrow", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Limits", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.factorThruKernelSubobject_comp_kernelSubobjectIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.kernelSubobjectMap", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.kernelSubobjectMap_arrow", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Limits", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.kernelSubobjectMap_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Limits", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.kernelSubobjectMap_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Limits", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.kernel_map_comp_kernelSubobjectIso_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Limits", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.kernelSubobjectIso_comp_kernel_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Limits", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.kernelSubobject_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.isIso_kernelSubobject_zero_arrow", "kind": "instance", "module": "Mathlib.CategoryTheory.Subobject.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.le_kernelSubobject", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.kernelSubobjectIsoComp", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.kernelSubobjectIsoComp_hom_arrow", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Limits", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.kernelSubobjectIsoComp_inv_arrow", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Limits", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.kernelSubobject_comp_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.kernelSubobject_comp_mono", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.kernelSubobject_comp_mono_isIso", "kind": "instance", "module": "Mathlib.CategoryTheory.Subobject.Limits", "is_tactic_proof": true, "tactics": ["rw", "infer_instance", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.cokernelOrderHom", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.kernelOrderHom", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.imageSubobject", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Subobject.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.imageSubobjectIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.imageSubobject_arrow", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Limits", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.imageSubobject_arrow'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Limits", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.factorThruImageSubobject", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.instEpiFactorThruImageSubobjectOfHasEqualizers", "kind": "instance", "module": "Mathlib.CategoryTheory.Subobject.Limits", "is_tactic_proof": true, "tactics": ["dsimp", "apply"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.imageSubobject_arrow_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Limits", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.imageSubobject_arrow_comp_eq_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.imageSubobject_factors_comp_self", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.factorThruImageSubobject_comp_self", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Limits", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.factorThruImageSubobject_comp_self_assoc", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Limits", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.imageSubobject_comp_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.imageSubobject_zero_arrow", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Limits", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.imageSubobject_zero", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.imageSubobject_comp_le_epi_of_epi", "kind": "instance", "module": "Mathlib.CategoryTheory.Subobject.Limits", "is_tactic_proof": true, "tactics": ["rw", "infer_instance", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.Limits.imageSubobjectCompIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.imageSubobjectCompIso_hom_arrow", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Limits", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.imageSubobjectCompIso_inv_arrow", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Limits", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Limits.imageSubobject_mono", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.imageSubobject_iso_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.imageSubobject_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.imageSubobject_le_mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.imageSubobjectMap", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Limits.imageSubobjectMap_arrow", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Limits", "is_tactic_proof": true, "tactics": ["simp", "erw"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.image_map_comp_imageSubobjectIso_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Limits", "is_tactic_proof": true, "tactics": ["ext", "simpa"], "tactic_count": 2}
{"name": "CategoryTheory.Limits.imageSubobjectIso_comp_image_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.Limits", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Over.isMono", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Subobject.MonoOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Subobject.MonoOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.mono_obj_hom", "kind": "instance", "module": "Mathlib.CategoryTheory.Subobject.MonoOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.mk", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.MonoOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.forget", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Subobject.MonoOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.instCoeOut", "kind": "instance", "module": "Mathlib.CategoryTheory.Subobject.MonoOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.forget_obj_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.MonoOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.mk_coe", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.MonoOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.arrow", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Subobject.MonoOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.mk_arrow", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.MonoOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.forget_obj_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.MonoOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.fullyFaithfulForget", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.MonoOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.mono", "kind": "instance", "module": "Mathlib.CategoryTheory.Subobject.MonoOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.instMonoHomDiscretePUnitObjOverForget", "kind": "instance", "module": "Mathlib.CategoryTheory.Subobject.MonoOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.isThin", "kind": "instance", "module": "Mathlib.CategoryTheory.Subobject.MonoOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.w", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.MonoOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.mkArrowIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.MonoOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.instIsIsoLeftDiscretePUnitHomFullSubcategoryOverIsMono", "kind": "instance", "module": "Mathlib.CategoryTheory.Subobject.MonoOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.isIso_iff_isIso_hom_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.MonoOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.lift", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.MonoOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.liftIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.MonoOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.liftComp", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.MonoOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.liftId", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.MonoOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.lift_comm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.MonoOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.lift_obj_arrow", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.MonoOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.slice", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.MonoOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.instIsClosedUnderLimitsOfShapeOverIsMono", "kind": "instance", "module": "Mathlib.CategoryTheory.Subobject.MonoOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.hasLimit", "kind": "instance", "module": "Mathlib.CategoryTheory.Subobject.MonoOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.hasLimitsOfShape", "kind": "instance", "module": "Mathlib.CategoryTheory.Subobject.MonoOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.hasFiniteLimits", "kind": "instance", "module": "Mathlib.CategoryTheory.Subobject.MonoOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.hasLimitsOfSize", "kind": "instance", "module": "Mathlib.CategoryTheory.Subobject.MonoOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.strongEpiMonoFactorisationSigmaDesc", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.MonoOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.coconeOfHasStrongEpiMonoFactorisation", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.MonoOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.commSqOfHasStrongEpiMonoFactorisation", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.MonoOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.liftStructOfHasStrongEpiMonoFactorisation", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.MonoOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.isColimitCoconeOfHasStrongEpiMonoFactorisation", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.MonoOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.hasColimitsOfSize_of_hasStrongEpiMonoFactorisations", "kind": "instance", "module": "Mathlib.CategoryTheory.Subobject.MonoOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.pullback", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.MonoOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.pullbackComp", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.MonoOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.pullbackId", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.MonoOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.pullback_obj_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.MonoOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.pullback_obj_arrow", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.MonoOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.pullbackObjIsoOfIsPullback", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.MonoOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.map", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.MonoOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.mapComp", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.MonoOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.mapId", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.MonoOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.map_obj_left", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.MonoOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.map_obj_arrow", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.MonoOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.MonoOver.faithful_map", "kind": "instance", "module": "Mathlib.CategoryTheory.Subobject.MonoOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.mapIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.MonoOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.congr", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.MonoOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.mapPullbackAdj", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.MonoOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.pullbackMapSelf", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.MonoOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.imageMonoOver", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.MonoOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.imageMonoOver_arrow", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.MonoOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.image", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.MonoOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.imageForgetAdj", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.MonoOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.instIsRightAdjointOverForget", "kind": "instance", "module": "Mathlib.CategoryTheory.Subobject.MonoOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.MonoOver.forgetImage", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.MonoOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.exists", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.MonoOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.faithful_exists", "kind": "instance", "module": "Mathlib.CategoryTheory.Subobject.MonoOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.existsIsoMap", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.MonoOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoOver.existsPullbackAdj", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.MonoOver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isNoetherianObject", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.NoetherianObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsNoetherianObject", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Subobject.NoetherianObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instWellFoundedGTSubobjectOfIsNoetherianObject", "kind": "instance", "module": "Mathlib.CategoryTheory.Subobject.NoetherianObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isNoetherianObject_iff_monotone_chain_condition", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subobject.NoetherianObject", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
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{"name": "Subobject.presheaf", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Types.monoOverEquivalenceSet", "kind": "definition", "module": "Mathlib.CategoryTheory.Subobject.Types", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instWellPoweredType", "kind": "instance", "module": "Mathlib.CategoryTheory.Subobject.Types", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.subterminalInclusion", "kind": "definition", "module": "Mathlib.CategoryTheory.Subterminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.instFullSubterminalsSubterminalInclusion", "kind": "instance", "module": "Mathlib.CategoryTheory.Subterminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.subterminalsEquivMonoOverTerminal", "kind": "definition", "module": "Mathlib.CategoryTheory.Subterminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.subterminals_to_monoOver_terminal_comp_forget", "kind": "theorem", "module": "Mathlib.CategoryTheory.Subterminal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.sum.inverseAssociator", "kind": "definition", "module": "Mathlib.CategoryTheory.Sums.Associator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.sum.inverseAssociator_obj_inl", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sums.Associator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.sum.inverseAssociator_obj_inr_inr", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sums.Associator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.sum.inverseAssociator_map_inl", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sums.Associator", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.sum.inverseAssociator_map_inr_inl", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sums.Associator", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.sum.inverseAssociator_map_inr_inr", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sums.Associator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.sum.inlCompInrCompInverseAssociator", "kind": "definition", "module": "Mathlib.CategoryTheory.Sums.Associator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Sum.inr_", "kind": "definition", "module": "Mathlib.CategoryTheory.Sums.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sum.homInduction", "kind": "definition", "module": "Mathlib.CategoryTheory.Sums.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Functor.sum'", "kind": "definition", "module": "Mathlib.CategoryTheory.Sums.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Functor.sumIsoExt_hom_app_inl", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sums.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.sumIsoExt_hom_app_inr", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sums.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.sumIsoExt_inv_app_inl", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sums.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.sumIsoExt_inv_app_inr", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sums.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isoSum", "kind": "definition", "module": "Mathlib.CategoryTheory.Sums.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isoSum_hom_app_inl", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sums.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isoSum_hom_app_inr", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sums.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isoSum_inv_app_inl", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sums.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isoSum_inv_app_inr", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sums.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.sum'", "kind": "definition", "module": "Mathlib.CategoryTheory.Sums.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.sum'_app_inl", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sums.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.sum'_app_inr", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sums.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.sum", "kind": "definition", "module": "Mathlib.CategoryTheory.Sums.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.sum_app_inl", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sums.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.NatTrans.sum_app_inr", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sums.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sum.swap", "kind": "definition", "module": "Mathlib.CategoryTheory.Sums.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sum.swap_obj_inl", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sums.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sum.swap_obj_inr", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sums.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sum.swap_map_inl", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sums.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sum.swap_map_inr", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sums.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sum.swapCompInl", "kind": "definition", "module": "Mathlib.CategoryTheory.Sums.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sum.swapCompInr", "kind": "definition", "module": "Mathlib.CategoryTheory.Sums.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sum.Swap.equivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.Sums.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sum.Swap.isEquivalence", "kind": "instance", "module": "Mathlib.CategoryTheory.Sums.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sum.Swap.symmetry", "kind": "definition", "module": "Mathlib.CategoryTheory.Sums.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sum.functorEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Sums.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sum.functorEquiv_unit_app_app_inl", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sums.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sum.functorEquiv_unit_app_app_inr", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sums.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sum.functorEquiv_unitIso_inv_app_app_inl", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sums.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sum.functorEquiv_unitIso_inv_app_app_inr", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sums.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sum.functorEquivFunctorCompFstIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Sums.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sum.functorEquivFunctorCompSndIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Sums.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sum.functorEquivInverseCompWhiskeringLeftInlIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Sums.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Sum.natTransOfWhiskerLeftInlInr", "kind": "definition", "module": "Mathlib.CategoryTheory.Sums.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sum.natTransOfWhiskerLeftInlInr_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sums.Products", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
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{"name": "CategoryTheory.Sum.natIsoOfWhiskerLeftInlInr", "kind": "definition", "module": "Mathlib.CategoryTheory.Sums.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sum.natIsoOfWhiskerLeftInlInr_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Sums.Products", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
{"name": "CategoryTheory.Sum.Swap.equivalenceFunctorEquivFunctorIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Sums.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Sum.associativityFunctorEquivNaturalityFunctorIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Sums.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.thin_category", "kind": "definition", "module": "Mathlib.CategoryTheory.Thin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.subsingleton_iso", "kind": "instance", "module": "Mathlib.CategoryTheory.Thin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Classifier.mkOfTerminalΩ₀", "kind": "definition", "module": "Mathlib.CategoryTheory.Topos.Classifier", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Classifier.instUniqueHomΩ₀", "kind": "instance", "module": "Mathlib.CategoryTheory.Topos.Classifier", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Classifier.isTerminalΩ₀", "kind": "definition", "module": "Mathlib.CategoryTheory.Topos.Classifier", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Classifier.isTerminalFrom_eq_χ₀", "kind": "theorem", "module": "Mathlib.CategoryTheory.Topos.Classifier", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasClassifier.Ω₀", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Topos.Classifier", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasClassifier.Ω", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Topos.Classifier", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasClassifier.truth", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Topos.Classifier", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasClassifier.χ", "kind": "definition", "module": "Mathlib.CategoryTheory.Topos.Classifier", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasClassifier.isPullback_χ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Topos.Classifier", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasClassifier.comm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Topos.Classifier", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasClassifier.unique", "kind": "theorem", "module": "Mathlib.CategoryTheory.Topos.Classifier", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasClassifier.truthIsSplitMono", "kind": "instance", "module": "Mathlib.CategoryTheory.Topos.Classifier", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasClassifier.truthIsRegularMono", "kind": "definition", "module": "Mathlib.CategoryTheory.Topos.Classifier", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasClassifier.instIsRegularMonoTruth", "kind": "instance", "module": "Mathlib.CategoryTheory.Topos.Classifier", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasClassifier.isRegularMonoCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Topos.Classifier", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasClassifier.reflectsIsomorphisms", "kind": "instance", "module": "Mathlib.CategoryTheory.Topos.Classifier", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.HasClassifier.reflectsIsomorphismsOp", "kind": "instance", "module": "Mathlib.CategoryTheory.Topos.Classifier", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Classifier.truth_as_subobject", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Topos.Classifier", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Classifier.surjective_χ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Topos.Classifier", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Classifier.pullback_χ_obj_mk_truth", "kind": "theorem", "module": "Mathlib.CategoryTheory.Topos.Classifier", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Classifier.χ_pullback_obj_mk_truth_arrow", "kind": "theorem", "module": "Mathlib.CategoryTheory.Topos.Classifier", "is_tactic_proof": true, "tactics": ["obtain", "refine", "refine", "dsimp", "rw", "rfl"], "tactic_count": 6}
{"name": "CategoryTheory.Classifier.representableBy", "kind": "definition", "module": "Mathlib.CategoryTheory.Topos.Classifier", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Classifier.SubobjectRepresentableBy", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Topos.Classifier", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Classifier.SubobjectRepresentableBy.Ω₀", "kind": "definition", "module": "Mathlib.CategoryTheory.Topos.Classifier", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Classifier.SubobjectRepresentableBy.homEquiv_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Topos.Classifier", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.Classifier.SubobjectRepresentableBy.pullback_homEquiv_symm_obj_Ω₀", "kind": "theorem", "module": "Mathlib.CategoryTheory.Topos.Classifier", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "CategoryTheory.Classifier.SubobjectRepresentableBy.iso", "kind": "definition", "module": "Mathlib.CategoryTheory.Topos.Classifier", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Classifier.SubobjectRepresentableBy.π", "kind": "definition", "module": "Mathlib.CategoryTheory.Topos.Classifier", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Classifier.SubobjectRepresentableBy.iso_inv_left_π", "kind": "theorem", "module": "Mathlib.CategoryTheory.Topos.Classifier", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "convert", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.Classifier.SubobjectRepresentableBy.iso_inv_hom_left_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Topos.Classifier", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Classifier.SubobjectRepresentableBy.isPullback", "kind": "theorem", "module": "Mathlib.CategoryTheory.Topos.Classifier", "is_tactic_proof": false, "tactics": ["fapply", "all_goals"], "tactic_count": 2}
{"name": "CategoryTheory.Classifier.SubobjectRepresentableBy.uniq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Topos.Classifier", "is_tactic_proof": true, "tactics": ["apply", "simp", "simpa"], "tactic_count": 3}
{"name": "CategoryTheory.Classifier.SubobjectRepresentableBy.isTerminalΩ₀", "kind": "definition", "module": "Mathlib.CategoryTheory.Topos.Classifier", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Classifier.SubobjectRepresentableBy.hasTerminal", "kind": "theorem", "module": "Mathlib.CategoryTheory.Topos.Classifier", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Classifier.SubobjectRepresentableBy.isoΩ₀", "kind": "definition", "module": "Mathlib.CategoryTheory.Topos.Classifier", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Classifier.SubobjectRepresentableBy.classifier", "kind": "definition", "module": "Mathlib.CategoryTheory.Topos.Classifier", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isRepresentable_hasClassifier_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Topos.Classifier", "is_tactic_proof": true, "tactics": ["constructor", "obtain", "apply", "exact", "obtain", "constructor", "exact"], "tactic_count": 7}
{"name": "CategoryTheory.Adjunction.isTriangulated_rightAdjoint", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Adjunction.isTriangulated_leftAdjoint", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Adjunction", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
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{"name": "CategoryTheory.Equivalence.IsTriangulated", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Triangulated.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.IsTriangulated.instIsTriangulatedFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.IsTriangulated.instIsTriangulatedInverse", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.IsTriangulated.instIsTriangulatedInverseSymmOfFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.IsTriangulated.instIsTriangulatedFunctorSymmOfInverse", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.IsTriangulated.mk'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.IsTriangulated.mk''", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.IsTriangulated.refl", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Adjunction", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "infer_instance"], "tactic_count": 3}
{"name": "CategoryTheory.Equivalence.IsTriangulated.symm", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Adjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Equivalence.IsTriangulated.trans", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Adjunction", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "infer_instance"], "tactic_count": 3}
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{"name": "CategoryTheory.Pretriangulated.instInhabitedTriangle", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.contractibleTriangle", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.triangleMorphismId", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.instInhabitedTriangleMorphism", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.TriangleMorphism.comp", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.triangleCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Triangle.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Pretriangulated.id_hom₂", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Pretriangulated.comp_hom₁", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.comp_hom₂", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.comp_hom₃", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Triangle.isIso_of_isIsos", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Basic", "is_tactic_proof": true, "tactics": ["let", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Iso.hom_inv_id_triangle_hom₁", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Iso.hom_inv_id_triangle_hom₂", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Iso.hom_inv_id_triangle_hom₃", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Iso.inv_hom_id_triangle_hom₁", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Iso.inv_hom_id_triangle_hom₂", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Iso.inv_hom_id_triangle_hom₃", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Pretriangulated.Triangle.eqToHom_hom₁", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Basic", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "CategoryTheory.Pretriangulated.Triangle.eqToHom_hom₂", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Basic", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "CategoryTheory.Pretriangulated.Triangle.eqToHom_hom₃", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Basic", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "CategoryTheory.Pretriangulated.Triangle.instZeroHom", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Triangle.instAddHom", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Triangle.instNegHom", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Triangle.instSubHom", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Triangle.instSMulHom", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Triangle.instAddCommGroupHom", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Triangle.instPreadditive", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Triangle.instModuleHom", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Triangle.instLinear", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.binaryBiproductTriangle", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.binaryProductTriangle", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.binaryProductTriangleIsoBinaryBiproductTriangle", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.productTriangle", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.productTriangle.π", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.productTriangle.fan", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.productTriangle.lift", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.productTriangle.isLimitFan", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.productTriangle.zero₃₁", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Basic", "is_tactic_proof": false, "tactics": ["have", "dsimp", "change", "rw", "ext", "simp"], "tactic_count": 6}
{"name": "CategoryTheory.Pretriangulated.contractibleTriangleFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Triangle.π₁", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Triangle.π₂", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Triangle.π₃", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Triangle.π₁Toπ₂", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Triangle.π₂Toπ₃", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Triangle.π₃Toπ₁", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Triangle.instIsIsoHom₁", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Triangle.instIsIsoHom₂", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Triangle.instIsIsoHom₃", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Triangle.functorMk", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Triangle.functorHomMk'", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Triangle.functorIsoMk", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Triangle.functorIsoMk'", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapTriangle", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instFaithfulTriangleMapTriangle", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instFullTriangleMapTriangleOfFaithful", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapTriangleCommShiftIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.CategoryTheory.Triangulated.Functor.0.CategoryTheory.Functor.mapTriangleCommShiftIso_add", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Functor", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.instCommShiftTriangleMapTriangleInt", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapTriangleRotateIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapTriangleInvRotateIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapTriangleIdIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapTriangleCompIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapTriangleIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.map_distinguished", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsTriangulated.instPreservesZeroMorphisms", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsTriangulated.instPreservesLimitsOfShapeDiscreteWalkingPair", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Functor", "is_tactic_proof": false, "tactics": ["suffices", "have", "exact", "intro", "let", "hom₂", "hom₃", "comm₁", "dsimp", "ext", "simp", "simp", "comm₂", "comm₃", "exact", "isIso₂_of_isIso₁₃"], "tactic_count": 16}
{"name": "CategoryTheory.Functor.IsTriangulated.instAdditive", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsTriangulated.instId", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsTriangulated.instComp", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.map_distinguished_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Functor", "is_tactic_proof": true, "tactics": ["refine", "obtain", "refine", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.Functor.isTriangulated_of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isTriangulated_iff_of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Functor", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "intro", "have", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.Functor.isTriangulated_iff_comp_right", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Functor", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.Functor.mem_mapTriangle_essImage_of_distinguished", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Functor", "is_tactic_proof": false, "tactics": ["obtain", "let", "exact", "obtain", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.Functor.isTriangulated_of_precomp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isTriangulated_of_precomp_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Functor", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Triangulated.Octahedron.map", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isTriangulated_of_essSurj_mapComposableArrows_two", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Functor", "is_tactic_proof": true, "tactics": ["apply", "intro", "obtain", "obtain", "obtain", "obtain", "obtain", "exact"], "tactic_count": 8}
{"name": "CategoryTheory.IsTriangulated.of_fully_faithful_triangulated_functor", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.homologicalKernel", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.HomologicalFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mem_homologicalKernel_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.HomologicalFunctor", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.map_distinguished_exact", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.HomologicalFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instIsHomologicalCompOfIsTriangulated", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.HomologicalFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsHomological.mk'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.HomologicalFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.IsHomological.of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.HomologicalFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instIsClosedUnderIsomorphismsHomologicalKernel", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.HomologicalFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instIsTriangulatedHomologicalKernel", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.HomologicalFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instPreservesLimitsOfShapeDiscreteWalkingPairOfIsHomological", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.HomologicalFunctor", "is_tactic_proof": false, "tactics": ["suffices", "intro", "have", "have", "rw", "intro", "let", "have", "have", "obtain", "dsimp", "replace", "simp", "rw", "have", "apply"], "tactic_count": 16}
{"name": "CategoryTheory.Functor.instAdditiveOfIsHomological", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.HomologicalFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isHomological_of_localization", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.HomologicalFunctor", "is_tactic_proof": false, "tactics": ["have", "preservesZeroMorphisms_of_map_zero_object", "have", "refine", "rw", "obtain", "exact"], "tactic_count": 7}
{"name": "CategoryTheory.Functor.homologySequenceδ", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.HomologicalFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.homologySequenceδ_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.HomologicalFunctor", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.comp_homologySequenceδ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.HomologicalFunctor", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.homologySequenceδ_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.HomologicalFunctor", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.homologySequence_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.HomologicalFunctor", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.homologySequence_exact₂", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.HomologicalFunctor", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.homologySequence_exact₃", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.HomologicalFunctor", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.homologySequence_exact₁", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.HomologicalFunctor", "is_tactic_proof": true, "tactics": ["refine", "refine", "dsimp", "simp"], "tactic_count": 4}
{"name": "CategoryTheory.Functor.homologySequence_epi_shift_map_mor₁_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.HomologicalFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.homologySequence_mono_shift_map_mor₁_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.HomologicalFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.homologySequence_epi_shift_map_mor₂_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.HomologicalFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.homologySequence_mono_shift_map_mor₂_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.HomologicalFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mem_homologicalKernel_trW_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.HomologicalFunctor", "is_tactic_proof": true, "tactics": ["obtain", "apply", "have", "have", "have", "dsimp", "simp", "constructor", "intro", "obtain", "have", "have", "apply", "intros", "constructor"], "tactic_count": 15}
{"name": "CategoryTheory.Functor.homologySequenceComposableArrows₅", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.HomologicalFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.homologySequenceComposableArrows₅_exact", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.HomologicalFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.CategoryTheory.Triangulated.Opposite.Basic.0.CategoryTheory.Pretriangulated.Opposite.OppositeShiftAux", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Opposite.instHasShiftOppositeInt", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Opposite.instAdditiveOppositeShiftFunctorInt", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.shiftFunctorOpIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.shiftFunctorZero_op_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.shiftFunctorZero_op_inv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.Basic", "is_tactic_proof": true, "tactics": ["rw", "op_comp_assoc,"], "tactic_count": 2}
{"name": "CategoryTheory.Pretriangulated.shiftFunctorAdd'_op_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.Basic", "is_tactic_proof": false, "tactics": ["erw", "rw", "rfl"], "tactic_count": 3}
{"name": "CategoryTheory.Pretriangulated.shiftFunctorAdd'_op_inv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.Basic", "is_tactic_proof": false, "tactics": ["rw", "shiftFunctorAdd'_op_hom_app", "erw", "rw"], "tactic_count": 4}
{"name": "CategoryTheory.Pretriangulated.opShiftFunctorEquivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_hom_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_inv_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_zero_unitIso_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.Basic", "is_tactic_proof": true, "tactics": ["apply", "dsimp", "rw", "shiftFunctorCompIsoId_zero_zero_hom_app,"], "tactic_count": 4}
{"name": "CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_zero_unitIso_inv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.Basic", "is_tactic_proof": true, "tactics": ["apply", "dsimp", "rw", "shiftFunctorCompIsoId_zero_zero_inv_app,"], "tactic_count": 4}
{"name": "CategoryTheory.Pretriangulated.shift_unop_opShiftFunctorEquivalence_counitIso_inv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.shift_unop_opShiftFunctorEquivalence_counitIso_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_inv_app_shift", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_hom_app_shift", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.opShiftFunctorEquivalenceSymmHomEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.opShiftFunctorEquivalenceSymmHomEquiv_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.opShiftFunctorEquivalenceSymmHomEquiv_left_inv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.shift_opShiftFunctorEquivalenceSymmHomEquiv_unop", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Pretriangulated.Opposite.commShiftFunctorOpInt", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Opposite.commShift_natTrans_op_int", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Opposite.commShift_adjunction_op_int", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.Functor", "is_tactic_proof": false, "tactics": ["have", "adj.op", "ext", "dsimp", "simp", "rw", "exact", "inferInstanceAs"], "tactic_count": 8}
{"name": "CategoryTheory.Functor.op_commShiftIso_hom_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.Functor", "is_tactic_proof": true, "tactics": ["obtain", "rfl"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.op_commShiftIso_inv_app", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.Functor", "is_tactic_proof": false, "tactics": ["rw", "assoc]", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.Functor.shift_map_op", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.map_shift_unop", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.Functor", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.map_opShiftFunctorEquivalence_unitIso_hom_app_unop", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.Functor", "is_tactic_proof": true, "tactics": ["dsimp", "simp", "commShiftIso_hom_naturality_assoc,", "congr", "rw", "dsimp", "rw"], "tactic_count": 7}
{"name": "CategoryTheory.Functor.map_opShiftFunctorEquivalence_unitIso_inv_app_unop", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.Functor", "is_tactic_proof": false, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Functor.map_opShiftFunctorEquivalence_counitIso_hom_app_unop", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.Functor", "is_tactic_proof": true, "tactics": ["apply", "dsimp", "rw", "map_shiftFunctorCompIsoId_inv_app_assoc,"], "tactic_count": 4}
{"name": "CategoryTheory.Functor.map_opShiftFunctorEquivalence_counitIso_inv_app_unop", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.Functor", "is_tactic_proof": false, "tactics": ["rw", "dsimp", "simp", "simp"], "tactic_count": 4}
{"name": "CategoryTheory.Functor.mapTriangleOpCompTriangleOpEquivalenceFunctorApp", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapTriangleOpCompTriangleOpEquivalenceFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instCatCommSqOppositeTriangleOpMapTriangleFunctorTriangleOpEquivalence", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.instCatCommSqTriangleOppositeMapTriangleOpInverseTriangleOpEquivalence", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.opMapTriangleCompTriangleOpEquivalenceInverse", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Opposite.functor_isTriangulated_op", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isTriangulated_of_op", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.op_isTriangulated_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Opposite.OpOpCommShift.iso", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.OpOp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Opposite.UnopUnopCommShift.iso", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.OpOp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Opposite.instCommShiftOppositeOpOpInt", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.OpOp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Opposite.instCommShiftOppositeUnopUnopInt", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.OpOp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.instCommShiftOppositeFunctorOpOpEquivalenceInt", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.OpOp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.instCommShiftOppositeInverseOpOpEquivalenceInt", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.OpOp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.instCommShiftOppositeOpOpEquivalenceInt", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.OpOp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.instIsTriangulatedOppositeOpOp", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.OpOp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.instIsTriangulatedOppositeOpOpEquivalence", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.OpOp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.instIsTriangulatedOppositeUnopUnop", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.OpOp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Opposite.distinguishedTriangles", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.Pretriangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Opposite.mem_distinguishedTriangles_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.Pretriangulated", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "CategoryTheory.Pretriangulated.Opposite.mem_distinguishedTriangles_iff'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.Pretriangulated", "is_tactic_proof": true, "tactics": ["rw", "constructor", "intro", "exact", "rintro", "refine", "exact"], "tactic_count": 7}
{"name": "CategoryTheory.Pretriangulated.Opposite.isomorphic_distinguished", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.Pretriangulated", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Pretriangulated.Opposite.contractibleTriangleIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.Pretriangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Opposite.contractible_distinguished", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.Pretriangulated", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Pretriangulated.Opposite.rotateTriangleOpEquivalenceInverseObjRotateUnopIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.Pretriangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Opposite.rotate_distinguished_triangle", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.Pretriangulated", "is_tactic_proof": false, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Pretriangulated.Opposite.distinguished_cocone_triangle", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.Pretriangulated", "is_tactic_proof": true, "tactics": ["obtain", "refine", "simp", "refine", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.Pretriangulated.Opposite.complete_distinguished_triangle_morphism", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.Pretriangulated", "is_tactic_proof": true, "tactics": ["rw", "obtain", "dsimp", "replace", "dsimp", "simp", "refine", "apply", "rw", "unop_comp_assoc,", "simp"], "tactic_count": 11}
{"name": "CategoryTheory.Pretriangulated.Opposite.instOpposite", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.Pretriangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.mem_distTriang_op_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.Pretriangulated", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "CategoryTheory.Pretriangulated.mem_distTriang_op_iff'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.Pretriangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.op_distinguished", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.Pretriangulated", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Pretriangulated.unop_distinguished", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.Pretriangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.map_distinguished_op_exact", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.Pretriangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.TriangleOpEquivalence.functor", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.Triangle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.TriangleOpEquivalence.inverse", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.Triangle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.TriangleOpEquivalence.unitIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.Triangle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.TriangleOpEquivalence.counitIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.Triangle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.triangleOpEquivalence", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.Triangle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Opposite.instIsTriangulatedOpposite", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Opposite.Triangulated", "is_tactic_proof": false, "tactics": ["have", "intro", "obtain", "obtain", "obtain", "exact", "refine", "obtain", "refine", "opShiftFunctorEquivalenceSymmHomEquiv", "v₁₃.op,", "rw", "refine", "refine", "simpa", "rw", "refine", "refine", "simpa", "rw", "refine", "refine", "simpa", "obtain", "obtain", "exact", "m₃", "comm₁", "comm₂", "have", "dsimp", "rw", "rw", "shift_opShiftFunctorEquivalenceSymmHomEquiv_unop,", "comm₃", "comm₄", "have", "rw", "dsimp", "rw", "shift_opShiftFunctorEquivalenceSymmHomEquiv_unop,", "unop_comp_assoc,", "mem", "rw", "refine", "have", "have", "dsimp", "simp", "neg_comp,", "rw", "reassoc_of%", "simp"], "tactic_count": 53}
{"name": "CategoryTheory.ObjectProperty.instIsStableUnderShiftRightOrthogonal", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Orthogonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instIsStableUnderShiftLeftOrthogonal", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Orthogonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instIsTriangulatedClosed₂RightOrthogonal", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Orthogonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instIsTriangulatedClosed₂LeftOrthogonal", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Orthogonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instIsTriangulatedRightOrthogonalOfIsStableUnderShiftInt", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Orthogonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instIsTriangulatedLeftOrthogonalOfIsStableUnderShiftInt", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Orthogonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty._example", "kind": "example", "module": "Mathlib.CategoryTheory.Triangulated.Orthogonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty._example", "kind": "example", "module": "Mathlib.CategoryTheory.Triangulated.Orthogonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.isLocal_trW", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Orthogonal", "is_tactic_proof": true, "tactics": ["ext", "refine", "exact", "suffices", "simpa", "intro", "obtain", "simp", "obtain", "exact"], "tactic_count": 10}
{"name": "CategoryTheory.ObjectProperty.isColocal_trW", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Orthogonal", "is_tactic_proof": true, "tactics": ["ext", "refine", "exact", "rw", "obtain", "refine", "suffices", "simpa", "intro", "obtain", "simp", "obtain", "exact"], "tactic_count": 13}
{"name": "CategoryTheory.ObjectProperty.rightOrthogonal.map_bijective_of_isTriangulated", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Orthogonal", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "obtain", "exact", "obtain", "have", "obtain", "refine", "rw"], "tactic_count": 10}
{"name": "CategoryTheory.ObjectProperty.leftOrthogonal.map_bijective_of_isTriangulated", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Orthogonal", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "obtain", "exact", "obtain", "have", "obtain", "refine", "rw"], "tactic_count": 10}
{"name": "CategoryTheory.Pretriangulated.termDistTriang_", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated._aux_Mathlib_CategoryTheory_Triangulated_Pretriangulated___macroRules_CategoryTheory_Pretriangulated_termDistTriang__1", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.distinguished_iff_of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.rot_of_distTriang", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.inv_rot_of_distTriang", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.comp_distTriang_mor_zero₁₂", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": false, "tactics": ["obtain", "complete_distinguished_triangle_morphism", "simpa"], "tactic_count": 3}
{"name": "CategoryTheory.Pretriangulated.comp_distTriang_mor_zero₂₃", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.comp_distTriang_mor_zero₃₁", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "CategoryTheory.Pretriangulated.shortComplexOfDistTriangle", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.shortComplexOfDistTriangleIsoOfIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.distinguished_cocone_triangle₁", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Pretriangulated.distinguished_cocone_triangle₂", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": true, "tactics": ["obtain", "let", "refine", "isomorphic_distinguished", "exact"], "tactic_count": 5}
{"name": "CategoryTheory.Pretriangulated.complete_distinguished_triangle_morphism₁", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": false, "tactics": ["obtain", "complete_distinguished_triangle_morphism", "refine", "apply", "dsimp", "rw", "simpa", "simpa"], "tactic_count": 8}
{"name": "CategoryTheory.Pretriangulated.complete_distinguished_triangle_morphism₂", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": false, "tactics": ["obtain", "complete_distinguished_triangle_morphism", "dsimp", "simp", "refine", "dsimp", "rw", "simp"], "tactic_count": 8}
{"name": "CategoryTheory.Pretriangulated.contractible_distinguished₁", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Pretriangulated.contractible_distinguished₂", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Pretriangulated.Triangle.yoneda_exact₂", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": false, "tactics": ["obtain", "complete_distinguished_triangle_morphism", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Pretriangulated.Triangle.yoneda_exact₃", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Triangle.coyoneda_exact₂", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": false, "tactics": ["obtain", "complete_distinguished_triangle_morphism₁", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.Pretriangulated.Triangle.coyoneda_exact₁", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Triangle.coyoneda_exact₃", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Triangle.mor₃_eq_zero_iff_epi₂", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "intro", "obtain", "rw", "intro", "rw"], "tactic_count": 8}
{"name": "CategoryTheory.Pretriangulated.Triangle.mor₂_eq_zero_iff_epi₁", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": true, "tactics": ["have", "dsimp", "rw"], "tactic_count": 3}
{"name": "CategoryTheory.Pretriangulated.Triangle.mor₁_eq_zero_iff_epi₃", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": true, "tactics": ["have", "dsimp", "rw", "constructor", "intro", "simp", "intro", "rw"], "tactic_count": 8}
{"name": "CategoryTheory.Pretriangulated.Triangle.mor₃_eq_zero_of_epi₂", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Triangle.mor₂_eq_zero_of_epi₁", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Triangle.mor₁_eq_zero_of_epi₃", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Triangle.epi₂", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Triangle.epi₁", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Triangle.epi₃", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Triangle.mor₁_eq_zero_iff_mono₂", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "intro", "obtain", "rw", "intro", "rw"], "tactic_count": 8}
{"name": "CategoryTheory.Pretriangulated.Triangle.mor₂_eq_zero_iff_mono₃", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Triangle.mor₃_eq_zero_iff_mono₁", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": true, "tactics": ["have", "dsimp", "rw", "constructor", "intro", "simp", "intro", "rw"], "tactic_count": 8}
{"name": "CategoryTheory.Pretriangulated.Triangle.mor₁_eq_zero_of_mono₂", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Triangle.mor₂_eq_zero_of_mono₃", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Triangle.mor₃_eq_zero_of_mono₁", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Triangle.mono₂", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Triangle.mono₃", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Triangle.mono₁", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Triangle.isZero₂_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "intro", "obtain", "rw"], "tactic_count": 6}
{"name": "CategoryTheory.Pretriangulated.Triangle.isZero₁_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": true, "tactics": ["refine", "dsimp", "simp", "tauto"], "tactic_count": 4}
{"name": "CategoryTheory.Pretriangulated.Triangle.isZero₃_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": true, "tactics": ["refine", "dsimp", "tauto"], "tactic_count": 3}
{"name": "CategoryTheory.Pretriangulated.Triangle.isZero₁_of_isZero₂₃", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Pretriangulated.Triangle.isZero₂_of_isZero₁₃", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.Pretriangulated.Triangle.isZero₃_of_isZero₁₂", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Triangle.isZero₁_iff_isIso₂", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": true, "tactics": ["rw", "constructor", "intro", "have", "obtain", "exact", "intro", "rw", "constructor"], "tactic_count": 9}
{"name": "CategoryTheory.Pretriangulated.Triangle.isZero₂_iff_isIso₃", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Triangle.isZero₃_iff_isIso₁", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": true, "tactics": ["refine", "dsimp", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.Pretriangulated.Triangle.isZero₁_of_isIso₂", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Triangle.isZero₂_of_isIso₃", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Triangle.isZero₃_of_isIso₁", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Triangle.shift_distinguished", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": true, "tactics": ["revert", "let", "change", "have", "have", "isomorphic_distinguished", "have", "isomorphic_distinguished", "have", "isomorphic_distinguished", "obtain", "induction", "zero", "succ", "induction", "zero", "succ"], "tactic_count": 17}
{"name": "CategoryTheory.Pretriangulated.Triangle.shift_distinguished_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Triangle.distinguished_iff_of_isZero₃", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Triangle.distinguished_iff_of_isZero₁", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": false, "tactics": ["rw", "distinguished_iff_of_isZero₃", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.Pretriangulated.Triangle.distinguished_iff_of_isZero₂", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.Pretriangulated.instSplitEpiCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.instSplitMonoCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.isIso₂_of_isIso₁₃", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": false, "tactics": ["have", "rw", "intro", "obtain", "rw", "obtain", "obtain", "refine", "have", "dsimp", "rw", "erw", "refine", "intro", "simpa", "intro", "obtain", "obtain", "rw", "comp_distTriang_mor_zero₂₃", "obtain", "obtain", "refine", "dsimp", "rw"], "tactic_count": 25}
{"name": "CategoryTheory.Pretriangulated.isIso₃_of_isIso₁₂", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.isIso₁_of_isIso₂₃", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.binaryBiproductData", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": true, "tactics": ["have", "have", "exact", "fst", "snd", "inl", "inr", "inl_fst", "simp", "comp_distTriang_mor_zero₁₂_assoc", "inl_snd", "inr_fst", "simp", "inr_snd", "isBilimit"], "tactic_count": 15}
{"name": "CategoryTheory.Pretriangulated.instHasBinaryBiproducts", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.instHasFiniteProducts", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.instHasFiniteCoproducts", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.instHasFiniteBiproducts", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.exists_iso_binaryBiproduct_of_distTriang", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": true, "tactics": ["have", "have", "obtain", "let", "refine", "ext", "simpa", "simpa"], "tactic_count": 8}
{"name": "CategoryTheory.Pretriangulated.binaryBiproductTriangle_distinguished", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "dsimp", "refine", "refine"], "tactic_count": 5}
{"name": "CategoryTheory.Pretriangulated.binaryProductTriangle_distinguished", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.completeDistinguishedTriangleMorphism", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.productTriangle_distinguished", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": true, "tactics": ["and", "let", "obtain", "let", "change", "let", "completeDistinguishedTriangleMorphism", "let", "have", "have", "have", "have", "suffices", "have", "apply", "all_goals", "exact", "refine", "isIso_of_yoneda_map_bijective", "suffices", "intro", "simpa", "rw", "intro", "have", "rw", "obtain", "have", "have", "rw", "simpa", "have", "let", "have", "have", "rw", "intro", "obtain", "have", "rw", "productTriangle.zero₃₁]", "intro", "exact", "have", "exact", "have", "simp", "erw", "rw", "rw", "let", "have", "have", "have", "rw", "exact"], "tactic_count": 56}
{"name": "CategoryTheory.Pretriangulated.exists_iso_of_arrow_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": true, "tactics": ["let", "have", "have", "have", "have", "apply", "all_goals", "exact"], "tactic_count": 8}
{"name": "CategoryTheory.Pretriangulated.isoTriangleOfIso₁₂", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": true, "tactics": ["have", "exact", "have", "dsimp", "conv_rhs", "have", "dsimp", "conv_lhs"], "tactic_count": 8}
{"name": "CategoryTheory.Pretriangulated.isoTriangleOfIso₁₃", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Pretriangulated", "is_tactic_proof": false, "tactics": ["have", "exists_iso_of_arrow_iso", "have", "dsimp", "simp", "simp", "let", "have", "have", "have", "have", "dsimp", "refine", "convert", "simp"], "tactic_count": 15}
{"name": "CategoryTheory.Pretriangulated.Triangle.rotate", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Rotate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Triangle.invRotate", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Rotate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.rotate", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Rotate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.invRotate", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Rotate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.rotCompInvRot", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Rotate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.invRotCompRot", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Rotate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.triangleRotation", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Rotate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.instIsEquivalenceTriangleRotate", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Rotate", "is_tactic_proof": true, "tactics": ["change", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Pretriangulated.instIsEquivalenceTriangleInvRotate", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Rotate", "is_tactic_proof": true, "tactics": ["change", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Triangulated.SpectralObject.ω₂", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.SpectralObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Triangulated.SpectralObject.ω₂_obj_distinguished", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.SpectralObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Triangulated.SpectralObject.δ", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.SpectralObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Triangulated.SpectralObject.triangle", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.SpectralObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Triangulated.SpectralObject.triangle_distinguished", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.SpectralObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Triangulated.SpectralObject.precomp", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.SpectralObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Triangulated.SpectralObject.mapTriangulatedFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.SpectralObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Triangulated.SpectralObject.mapTriangulatedFunctor_δ", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.SpectralObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Triangulated.SpectralObject.instCategory", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.SpectralObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Triangulated.SpectralObject.hom_ext", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.SpectralObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Triangulated.SpectralObject.id_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.SpectralObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Triangulated.SpectralObject.comp_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.SpectralObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.mapTriangulatedSpectralObject", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.SpectralObject", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.ext_of_isTriangulatedClosed₁'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Subcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.ext_of_isTriangulatedClosed₂'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Subcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.ext_of_isTriangulatedClosed₃'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Subcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.ext_of_isTriangulatedClosed₁", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Subcategory", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.ObjectProperty.ext_of_isTriangulatedClosed₂", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Subcategory", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.ObjectProperty.ext_of_isTriangulatedClosed₃", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Subcategory", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CategoryTheory.ObjectProperty.IsTriangulatedClosed₁.mk'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Subcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.IsTriangulatedClosed₂.mk'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Subcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.IsTriangulatedClosed₃.mk'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Subcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.ObjectProperty.instIsTriangulatedClosed₁OfIsTriangulated", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Subcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instIsTriangulatedClosed₃OfIsTriangulated", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Subcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instIsTriangulatedIsoClosure", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Subcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.trW", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Subcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.trW_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Subcategory", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "CategoryTheory.ObjectProperty.trW_iff'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Subcategory", "is_tactic_proof": true, "tactics": ["rw", "constructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.ObjectProperty.trW.mk", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Subcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.trW.mk'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Subcategory", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.ObjectProperty.trW_isoClosure", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Subcategory", "is_tactic_proof": true, "tactics": ["ext", "constructor", "rintro", "refine", "exact", "rintro", "exact"], "tactic_count": 7}
{"name": "CategoryTheory.ObjectProperty.instRespectsIsoTrW", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Subcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instContainsIdentitiesTrWOfContainsZero", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Subcategory", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.ObjectProperty.trW_of_isIso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Subcategory", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.ObjectProperty.smul_mem_trW_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Subcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.trW.shift", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Subcategory", "is_tactic_proof": true, "tactics": ["rw", "obtain", "exact"], "tactic_count": 3}
{"name": "CategoryTheory.ObjectProperty.trW.unshift", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Subcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instIsCompatibleWithShiftTrWIntOfIsStableUnderShift", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Subcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instIsMultiplicativeTrWOfIsTriangulatedOfIsTriangulated", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Subcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.trW_iff_of_distinguished", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Subcategory", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "obtain", "exact", "intro", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.ObjectProperty.instHasLeftCalculusOfFractionsTrWOfIsTriangulatedOfIsTriangulated", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Subcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instHasRightCalculusOfFractionsTrWOfIsTriangulatedOfIsTriangulated", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Subcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ObjectProperty.instIsCompatibleWithTriangulationTrWOfIsTriangulatedOfIsTriangulated", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Subcategory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Triangulated.TStructure.exists_triangle", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.TStructure.Basic", "is_tactic_proof": true, "tactics": ["obtain", "let", "let", "have", "refine", "refine", "all_goals", "exact"], "tactic_count": 8}
{"name": "CategoryTheory.Triangulated.TStructure.shift_le", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.TStructure.Basic", "is_tactic_proof": true, "tactics": ["ext", "constructor", "intro", "exact", "intro", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.Triangulated.TStructure.shift_ge", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.TStructure.Basic", "is_tactic_proof": true, "tactics": ["ext", "constructor", "intro", "exact", "intro", "exact"], "tactic_count": 6}
{"name": "CategoryTheory.Triangulated.TStructure.le_monotone", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.TStructure.Basic", "is_tactic_proof": true, "tactics": ["let", "suffices", "intro", "obtain", "obtain", "apply", "have", "simp", "rfl", "have", "rw", "rw", "exact", "have", "intro", "rw", "exact", "intro", "induction", "zero", "succ"], "tactic_count": 21}
{"name": "CategoryTheory.Triangulated.TStructure.ge_antitone", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.TStructure.Basic", "is_tactic_proof": true, "tactics": ["let", "suffices", "intro", "obtain", "obtain", "apply", "have", "simp", "rfl", "have", "rw", "rw", "exact", "have", "intro", "rw", "exact", "intro", "induction", "zero", "succ"], "tactic_count": 21}
{"name": "CategoryTheory.Triangulated.TStructure.le_of_isLE", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.TStructure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Triangulated.TStructure.ge_of_isGE", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.TStructure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Triangulated.TStructure.isLE_of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.TStructure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Triangulated.TStructure.isGE_of_iso", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.TStructure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Triangulated.TStructure.zero_of_isLE_of_isGE", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.TStructure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Triangulated.TStructure.minus", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.TStructure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Triangulated.TStructure.plus", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.TStructure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Triangulated.TStructure.bounded", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.TStructure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Triangulated.TStructure.instIsClosedUnderIsomorphismsMinus", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.TStructure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Triangulated.TStructure.instIsStableUnderShiftMinusInt", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.TStructure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Triangulated.TStructure.instIsClosedUnderIsomorphismsPlus", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.TStructure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Triangulated.TStructure.instIsStableUnderShiftPlusInt", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.TStructure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Triangulated.TStructure.instIsClosedUnderIsomorphismsBounded", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.TStructure.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Triangulated.TStructure.instIsStableUnderShiftBoundedInt", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.TStructure.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Triangulated.TStructure.TruncAux.triangle", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.TStructure.TruncLTGE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Triangulated.TStructure.TruncAux.triangle_distinguished", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.TStructure.TruncLTGE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Triangulated.TStructure.TruncAux.triangle_obj₁_isLE", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.TStructure.TruncLTGE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Triangulated.TStructure.TruncAux.triangle_obj₃_isGE", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.TStructure.TruncLTGE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Triangulated.TStructure.TruncAux.triangleMap", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.TStructure.TruncLTGE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Triangulated.TStructure.TruncAux.triangleFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.TStructure.TruncLTGE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Triangulated.TStructure.TruncAux.triangleFunctor_obj_distinguished", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.TStructure.TruncLTGE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Triangulated.TStructure.TruncAux.isLE_triangleFunctor_obj_obj₁", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.TStructure.TruncLTGE", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Triangulated.TStructure.TruncAux.isGE_triangleFunctor_obj_obj₃", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.TStructure.TruncLTGE", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Triangulated.TStructure.TruncAux.instAdditiveTriangleTriangleFunctor", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.TStructure.TruncLTGE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Triangulated.TStructure.truncLT", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.TStructure.TruncLTGE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Triangulated.TStructure.truncLTι", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.TStructure.TruncLTGE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Triangulated.TStructure.truncGE", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.TStructure.TruncLTGE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Triangulated.TStructure.instAdditiveTruncGE", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.TStructure.TruncLTGE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Triangulated.TStructure.truncGEπ", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.TStructure.TruncLTGE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Triangulated.TStructure.instIsLEObjTruncLTHSubIntOfNat", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.TStructure.TruncLTGE", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Triangulated.TStructure.instIsGEObjTruncGE", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.TStructure.TruncLTGE", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Triangulated.TStructure.truncGEδLT", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.TStructure.TruncLTGE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Triangulated.TStructure.triangleLTGE", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.TStructure.TruncLTGE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Triangulated.TStructure.triangleLTGE_distinguished", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.TStructure.TruncLTGE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Triangulated.TStructure.instIsLEObj₁ObjTriangleTriangleLTGEHSubIntOfNat", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.TStructure.TruncLTGE", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Triangulated.TStructure.instIsGEObj₃ObjTriangleTriangleLTGE", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.TStructure.TruncLTGE", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "CategoryTheory.Pretriangulated.Triangle.shiftFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.TriangleShift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Triangle.shiftFunctorZero", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.TriangleShift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Triangle.shiftFunctorAdd'", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.TriangleShift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.rotateRotateRotateIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.TriangleShift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.invRotateInvRotateInvRotateIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.TriangleShift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.invRotateIsoRotateRotateShiftFunctorNegOne", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.TriangleShift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Triangle.instHasShiftInt", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.TriangleShift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Triangle.shiftFunctor_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.TriangleShift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Triangle.shiftFunctorZero_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.TriangleShift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Triangle.shiftFunctorAdd_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.TriangleShift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.Triangle.shiftFunctorAdd'_eq", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.TriangleShift", "is_tactic_proof": true, "tactics": ["subst", "rw", "apply"], "tactic_count": 3}
{"name": "CategoryTheory.Triangulated.instNonemptyOctahedron", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Triangulated", "is_tactic_proof": false, "tactics": ["refine", "isomorphic_distinguished", "all_goals"], "tactic_count": 3}
{"name": "CategoryTheory.Triangulated.Octahedron.triangle", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Triangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Triangulated.Octahedron.triangleMorphism₁", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Triangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Triangulated.Octahedron.triangleMorphism₂", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Triangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Triangulated.Octahedron.ofIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Triangulated", "is_tactic_proof": true, "tactics": ["let", "let", "let", "isoTriangleOfIso₁₂", "have", "have", "have", "have", "have", "have", "have", "have", "have", "have", "dsimp", "rw", "rw", "refine", "rw", "eq₁₃,", "dsimp", "rw", "rw", "rel₁₃]", "rw", "eq₂₃]", "dsimp", "rw", "rw", "rel₂₃,", "refine", "refine", "dsimp", "rw"], "tactic_count": 34}
{"name": "CategoryTheory.Triangulated.someOctahedron'", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Triangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Triangulated.someOctahedron", "kind": "definition", "module": "Mathlib.CategoryTheory.Triangulated.Triangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.IsTriangulated.mk'", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Triangulated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.instIsHomologicalAddCommGrpCatObjOppositeFunctorPreadditiveCoyoneda", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Yoneda", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.instIsHomologicalOppositeAddCommGrpCatObjFunctorPreadditiveYoneda", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Yoneda", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.preadditiveYoneda_map_distinguished", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Yoneda", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.instShiftSequenceAddCommGrpCatObjOppositeFunctorPreadditiveCoyonedaInt", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Yoneda", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.preadditiveCoyoneda_homologySequenceδ_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Yoneda", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CategoryTheory.Pretriangulated.instShiftSequenceOppositeAddCommGrpCatObjFunctorPreadditiveYonedaInt", "kind": "instance", "module": "Mathlib.CategoryTheory.Triangulated.Yoneda", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Pretriangulated.preadditiveYoneda_shiftMap_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Yoneda", "is_tactic_proof": true, "tactics": ["symm", "apply"], "tactic_count": 2}
{"name": "CategoryTheory.Pretriangulated.preadditiveYoneda_homologySequenceδ_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Triangulated.Yoneda", "is_tactic_proof": true, "tactics": ["simp", "congr", "apply", "rw", "rfl"], "tactic_count": 5}
{"name": "CategoryTheory.types", "kind": "instance", "module": "Mathlib.CategoryTheory.Types.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.types_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Types.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.types_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Types.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.types_id_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Types.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.types_comp_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Types.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.hom_inv_id_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Types.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.inv_hom_id_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Types.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.asHom", "kind": "abbrev", "module": "Mathlib.CategoryTheory.Types.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.term↾_", "kind": "definition", "module": "Mathlib.CategoryTheory.Types.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory._aux_Mathlib_CategoryTheory_Types_Basic___macroRules_CategoryTheory_term↾__1", "kind": "definition", "module": "Mathlib.CategoryTheory.Types.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory._aux_Mathlib_CategoryTheory_Types_Basic___unexpand_CategoryTheory_asHom_1", "kind": "definition", "module": "Mathlib.CategoryTheory.Types.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory._example", "kind": "example", "module": "Mathlib.CategoryTheory.Types.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory._example", "kind": "example", "module": "Mathlib.CategoryTheory.Types.Basic", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "CategoryTheory._example", "kind": "example", "module": "Mathlib.CategoryTheory.Types.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.sections", "kind": "definition", "module": "Mathlib.CategoryTheory.Types.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.sections_property", "kind": "theorem", "module": "Mathlib.CategoryTheory.Types.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.sections_ext_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Types.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.sectionsFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Types.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.FunctorToTypes.map_comp_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Types.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "CategoryTheory.FunctorToTypes.eqToHom_map_comp_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Types.Basic", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
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{"name": "CategoryTheory.uliftTrivial", "kind": "definition", "module": "Mathlib.CategoryTheory.Types.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.uliftFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Types.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.uliftFunctor_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Types.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.uliftFunctor_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Types.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.fullyFaithfulULiftFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Types.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.uliftFunctor_full", "kind": "instance", "module": "Mathlib.CategoryTheory.Types.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.uliftFunctor_faithful", "kind": "instance", "module": "Mathlib.CategoryTheory.Types.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.uliftFunctorTrivial", "kind": "definition", "module": "Mathlib.CategoryTheory.Types.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.homOfElement", "kind": "definition", "module": "Mathlib.CategoryTheory.Types.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.homOfElement_eq_iff", "kind": "theorem", "module": "Mathlib.CategoryTheory.Types.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.epi_iff_surjective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Types.Basic", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "refine", "rw", "apply", "change", "rw", "exact"], "tactic_count": 8}
{"name": "CategoryTheory.surjective_of_epi", "kind": "theorem", "module": "Mathlib.CategoryTheory.Types.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ofTypeFunctor", "kind": "definition", "module": "Mathlib.CategoryTheory.Types.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ofTypeFunctor_obj", "kind": "theorem", "module": "Mathlib.CategoryTheory.Types.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.ofTypeFunctor_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Types.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.toIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Types.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.toIso_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Types.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Iso.toEquiv_fun", "kind": "theorem", "module": "Mathlib.CategoryTheory.Types.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.toEquiv_symm_fun", "kind": "theorem", "module": "Mathlib.CategoryTheory.Types.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.instSplitEpiCategoryType", "kind": "instance", "module": "Mathlib.CategoryTheory.Types.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isSplitEpi_iff_surjective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Types.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "equivIsoIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Types.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "equivEquivIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Types.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Types.instIsStableUnderCobaseChangeMonomorphismsType", "kind": "instance", "module": "Mathlib.CategoryTheory.Types.Monomorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Types.instIsStableUnderFilteredColimitsMonomorphismsType", "kind": "instance", "module": "Mathlib.CategoryTheory.Types.Monomorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Types.instIsStableUnderCoproductsOfShapeMonomorphismsType", "kind": "instance", "module": "Mathlib.CategoryTheory.Types.Monomorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Types.instIsStableUnderCoproductsMonomorphismsType", "kind": "instance", "module": "Mathlib.CategoryTheory.Types.Monomorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.functorToTypes", "kind": "definition", "module": "Mathlib.CategoryTheory.Types.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UnivLE.ofEssSurj", "kind": "theorem", "module": "Mathlib.CategoryTheory.UnivLE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EssSurj.ofUnivLE", "kind": "instance", "module": "Mathlib.CategoryTheory.UnivLE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UnivLE_iff_essSurj", "kind": "theorem", "module": "Mathlib.CategoryTheory.UnivLE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsEquivalenceUliftFunctorOfUnivLE", "kind": "instance", "module": "Mathlib.CategoryTheory.UnivLE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UnivLE.witness", "kind": "definition", "module": "Mathlib.CategoryTheory.UnivLE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFaithfulWitness", "kind": "instance", "module": "Mathlib.CategoryTheory.UnivLE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Functor.id_hcomp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Whiskering", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
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{"name": "CategoryTheory.Functor.hcomp_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Whiskering", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
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{"name": "CategoryTheory.Functor.faithful_whiskeringRight_obj", "kind": "instance", "module": "Mathlib.CategoryTheory.Whiskering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Functor.whiskeringLeftObjCompIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Whiskering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.whiskeringRight_obj_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Whiskering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.whiskeringRightObjIdIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Whiskering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Functor.whiskeringRightObjCompIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Whiskering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.full_whiskeringRight_obj", "kind": "instance", "module": "Mathlib.CategoryTheory.Whiskering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.whiskerLeft_id", "kind": "theorem", "module": "Mathlib.CategoryTheory.Whiskering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Functor.whiskerLeft_comp_whiskerRight", "kind": "theorem", "module": "Mathlib.CategoryTheory.Whiskering", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
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{"name": "CategoryTheory.Functor.isoWhiskerLeft_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Whiskering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Functor.isoWhiskerRight", "kind": "definition", "module": "Mathlib.CategoryTheory.Whiskering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.isoWhiskerRight_hom", "kind": "theorem", "module": "Mathlib.CategoryTheory.Whiskering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CategoryTheory.Functor.isoWhiskerRight_refl", "kind": "theorem", "module": "Mathlib.CategoryTheory.Whiskering", "is_tactic_proof": true, "tactics": ["cat_disch"], "tactic_count": 1}
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{"name": "CategoryTheory.isIso_of_yoneda_map_bijective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Yoneda", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.isIso_iff_yoneda_map_bijective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Yoneda", "is_tactic_proof": true, "tactics": ["refine", "intro", "rw", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.isIso_iff_isIso_yoneda_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Yoneda", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.uliftYonedaEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Yoneda", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.uliftYonedaEquiv_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Yoneda", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.uliftYonedaEquiv_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Yoneda", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.uliftYonedaEquiv_symm_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Yoneda", "is_tactic_proof": true, "tactics": ["obtain", "rw", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.uliftYonedaEquiv_uliftYoneda_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Yoneda", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.hom_ext_uliftYoneda", "kind": "theorem", "module": "Mathlib.CategoryTheory.Yoneda", "is_tactic_proof": true, "tactics": ["ext", "simpa"], "tactic_count": 2}
{"name": "CategoryTheory.uliftYonedaOpCompCoyoneda", "kind": "definition", "module": "Mathlib.CategoryTheory.Yoneda", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.coyonedaEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Yoneda", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.coyonedaEquiv_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Yoneda", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.coyonedaEquiv_symm_app_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Yoneda", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.coyonedaEquiv_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Yoneda", "is_tactic_proof": true, "tactics": ["change", "rw", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.coyonedaEquiv_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Yoneda", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "CategoryTheory.coyonedaEquiv_coyoneda_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Yoneda", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.map_coyonedaEquiv", "kind": "theorem", "module": "Mathlib.CategoryTheory.Yoneda", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CategoryTheory.coyonedaEquiv_symm_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Yoneda", "is_tactic_proof": true, "tactics": ["obtain", "simp"], "tactic_count": 2}
{"name": "CategoryTheory.coyonedaEvaluation", "kind": "definition", "module": "Mathlib.CategoryTheory.Yoneda", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.coyonedaEvaluation_map_down", "kind": "theorem", "module": "Mathlib.CategoryTheory.Yoneda", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.coyonedaPairing", "kind": "definition", "module": "Mathlib.CategoryTheory.Yoneda", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.coyonedaPairingExt", "kind": "theorem", "module": "Mathlib.CategoryTheory.Yoneda", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.coyonedaPairing_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Yoneda", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.coyonedaLemma", "kind": "definition", "module": "Mathlib.CategoryTheory.Yoneda", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.curriedCoyonedaLemma", "kind": "definition", "module": "Mathlib.CategoryTheory.Yoneda", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.largeCurriedCoyonedaLemma", "kind": "definition", "module": "Mathlib.CategoryTheory.Yoneda", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.coyonedaCompYonedaObj", "kind": "definition", "module": "Mathlib.CategoryTheory.Yoneda", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.curriedCoyonedaLemma'", "kind": "definition", "module": "Mathlib.CategoryTheory.Yoneda", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.isIso_of_coyoneda_map_bijective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Yoneda", "is_tactic_proof": true, "tactics": ["obtain", "refine", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.isIso_iff_coyoneda_map_bijective", "kind": "theorem", "module": "Mathlib.CategoryTheory.Yoneda", "is_tactic_proof": true, "tactics": ["refine", "intro", "rw", "exact"], "tactic_count": 4}
{"name": "CategoryTheory.isIso_iff_isIso_coyoneda_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Yoneda", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CategoryTheory.uliftCoyonedaEquiv", "kind": "definition", "module": "Mathlib.CategoryTheory.Yoneda", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.uliftCoyonedaEquiv_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Yoneda", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.uliftCoyonedaEquiv_comp", "kind": "theorem", "module": "Mathlib.CategoryTheory.Yoneda", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.uliftCoyonedaEquiv_symm_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Yoneda", "is_tactic_proof": true, "tactics": ["obtain", "rw", "simp"], "tactic_count": 3}
{"name": "CategoryTheory.uliftCoyonedaEquiv_uliftCoyoneda_map", "kind": "theorem", "module": "Mathlib.CategoryTheory.Yoneda", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CategoryTheory.hom_ext_uliftCoyoneda", "kind": "theorem", "module": "Mathlib.CategoryTheory.Yoneda", "is_tactic_proof": true, "tactics": ["ext", "simpa"], "tactic_count": 2}
{"name": "CategoryTheory.uliftCoyonedaRightOpCompCoyoneda", "kind": "definition", "module": "Mathlib.CategoryTheory.Yoneda", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.yonedaMap", "kind": "definition", "module": "Mathlib.CategoryTheory.Yoneda", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.yonedaMap_app_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Yoneda", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.uliftYonedaMap", "kind": "definition", "module": "Mathlib.CategoryTheory.Yoneda", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.uliftYonedaMap_app_apply", "kind": "theorem", "module": "Mathlib.CategoryTheory.Yoneda", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.sectionsEquivHom", "kind": "definition", "module": "Mathlib.CategoryTheory.Yoneda", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.sectionsEquivHom_naturality", "kind": "theorem", "module": "Mathlib.CategoryTheory.Yoneda", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "CategoryTheory.Functor.sectionsEquivHom_naturality_symm", "kind": "theorem", "module": "Mathlib.CategoryTheory.Yoneda", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "CategoryTheory.sectionsFunctorNatIsoCoyoneda", "kind": "definition", "module": "Mathlib.CategoryTheory.Yoneda", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.FullyFaithful.homNatIso", "kind": "definition", "module": "Mathlib.CategoryTheory.Yoneda", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.FullyFaithful.homNatIsoMaxRight", "kind": "definition", "module": "Mathlib.CategoryTheory.Yoneda", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.FullyFaithful.compUliftYonedaCompWhiskeringLeft", "kind": "definition", "module": "Mathlib.CategoryTheory.Yoneda", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.FullyFaithful.compYonedaCompWhiskeringLeftMaxRight", "kind": "definition", "module": "Mathlib.CategoryTheory.Yoneda", "is_tactic_proof": true, "tactics": ["refine", "isoWhiskerLeft", "hF.compUliftYonedaCompWhiskeringLeft"], "tactic_count": 3}
{"name": "CategoryTheory.Functor.FullyFaithful.homNatIso'", "kind": "definition", "module": "Mathlib.CategoryTheory.Yoneda", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Functor.FullyFaithful.compUliftCoyonedaCompWhiskeringLeft", "kind": "definition", "module": "Mathlib.CategoryTheory.Yoneda", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "threeAPFree_frontier", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Behrend", "is_tactic_proof": true, "tactics": ["intro", "obtain", "rwa", "have", "simp", "ring_nf", "simp"], "tactic_count": 7}
{"name": "threeAPFree_sphere", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Behrend", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact", "convert", "exact"], "tactic_count": 5}
{"name": "Behrend.box", "kind": "definition", "module": "Mathlib.Combinatorics.Additive.AP.Three.Behrend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Behrend.mem_box", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Behrend", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Behrend.card_box", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Behrend", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Behrend.box_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Behrend", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Behrend.sphere", "kind": "definition", "module": "Mathlib.Combinatorics.Additive.AP.Three.Behrend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Behrend.sphere_zero_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Behrend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Behrend.sphere_zero_right", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Behrend", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Behrend.sphere_subset_box", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Behrend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Behrend.norm_of_mem_sphere", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Behrend", "is_tactic_proof": true, "tactics": ["rw", "dsimp", "simp_rw"], "tactic_count": 3}
{"name": "Behrend.sphere_subset_preimage_metric_sphere", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Behrend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Behrend.map", "kind": "definition", "module": "Mathlib.Combinatorics.Additive.AP.Three.Behrend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Behrend.map_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Behrend", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Behrend.map_succ", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Behrend", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Behrend.map_succ'", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Behrend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Behrend.map_monotone", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Behrend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Behrend.map_mod", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Behrend", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Behrend.map_eq_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Behrend", "is_tactic_proof": true, "tactics": ["refine", "have", "rw", "exact"], "tactic_count": 4}
{"name": "Behrend.map_injOn", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Behrend", "is_tactic_proof": true, "tactics": ["intro", "induction", "zero", "succ", "ext", "have", "exact"], "tactic_count": 7}
{"name": "Behrend.map_le_of_mem_box", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Behrend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Behrend.threeAPFree_sphere", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Behrend", "is_tactic_proof": false, "tactics": ["set", "map_zero", "map_add", "refine", "refine", "rw", "exact"], "tactic_count": 7}
{"name": "Behrend.threeAPFree_image_sphere", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Behrend", "is_tactic_proof": true, "tactics": ["rw", "apply", "threeAPFree_sphere", "rw", "rintro", "have", "have", "rw", "exact"], "tactic_count": 9}
{"name": "Behrend.sum_sq_le_of_mem_box", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Behrend", "is_tactic_proof": true, "tactics": ["rw", "have", "exact"], "tactic_count": 3}
{"name": "Behrend.sum_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Behrend", "is_tactic_proof": true, "tactics": ["refine", "rw", "add_tsub_cancel_right,"], "tactic_count": 3}
{"name": "Behrend.sum_lt", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Behrend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Behrend.card_sphere_le_rothNumberNat", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Behrend", "is_tactic_proof": true, "tactics": ["cases", "dsimp", "cases", "simp", "apply", "simp", "rintro", "exact", "apply", "simp", "exact"], "tactic_count": 11}
{"name": "Behrend.exists_large_sphere_aux", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Behrend", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact", "rw", "exact"], "tactic_count": 5}
{"name": "Behrend.exists_large_sphere", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Behrend", "is_tactic_proof": true, "tactics": ["obtain", "refine", "obtain", "simp", "obtain", "simp", "refine", "exact", "exact", "simp", "sub_add,", "apply", "rwa", "rw", "norm_num", "exact"], "tactic_count": 16}
{"name": "Behrend.bound_aux'", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Behrend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Behrend.bound_aux", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Behrend", "is_tactic_proof": true, "tactics": ["convert", "rw", "rwa"], "tactic_count": 3}
{"name": "Behrend.log_two_mul_two_le_sqrt_log_eight", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Behrend", "is_tactic_proof": true, "tactics": ["rw", "apply", "rw", "gcongr", "linarith"], "tactic_count": 5}
{"name": "Behrend.two_div_one_sub_two_div_e_le_eight", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Behrend", "is_tactic_proof": true, "tactics": ["rw", "linarith", "rw"], "tactic_count": 3}
{"name": "Behrend.le_sqrt_log", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Behrend", "is_tactic_proof": true, "tactics": ["calc", "gcongr", "field_simp", "simp", "norm_num1", "exact", "simp", "apply", "nlinarith", "gcongr", "exact"], "tactic_count": 11}
{"name": "Behrend.exp_neg_two_mul_le", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Behrend", "is_tactic_proof": true, "tactics": ["have", "have", "calc", "rw", "sub_add_add_cancel,", "exact"], "tactic_count": 6}
{"name": "Behrend.div_lt_floor", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Behrend", "is_tactic_proof": true, "tactics": ["apply", "have", "rw", "exact", "rwa", "mul_div_assoc',", "exact", "exact"], "tactic_count": 8}
{"name": "Behrend.ceil_lt_mul", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Behrend", "is_tactic_proof": true, "tactics": ["refine", "rw", "have", "rwa", "norm_num1"], "tactic_count": 5}
{"name": "Behrend.nValue", "kind": "definition", "module": "Mathlib.Combinatorics.Additive.AP.Three.Behrend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Behrend.dValue", "kind": "definition", "module": "Mathlib.Combinatorics.Additive.AP.Three.Behrend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Behrend.nValue_pos", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Behrend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Behrend.three_le_nValue", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Behrend", "is_tactic_proof": true, "tactics": ["rw", "apply", "have", "rw", "exact", "apply", "rw", "exact", "norm_num1"], "tactic_count": 9}
{"name": "Behrend.dValue_pos", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Behrend", "is_tactic_proof": true, "tactics": ["have", "rw", "sub_nonneg,", "have", "apply", "rw", "apply", "rw", "exact", "apply", "rw", "apply", "apply", "exact", "exact", "exact", "exact", "exact"], "tactic_count": 18}
{"name": "Behrend.le_N", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Behrend", "is_tactic_proof": true, "tactics": ["have", "apply", "suffices", "suffices", "rw", "apply", "rw", "rw", "apply", "rw", "exact", "apply"], "tactic_count": 12}
{"name": "Behrend.bound", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Behrend", "is_tactic_proof": true, "tactics": ["apply", "rw", "grw", "rw", "norm_num", "norm_num1", "rw", "refine", "rw", "exact", "apply", "have", "rw", "exact", "refine", "rw", "exact", "norm_num1", "rw", "exact", "refine", "rw", "exact", "positivity"], "tactic_count": 24}
{"name": "Behrend.roth_lower_bound_explicit", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Behrend", "is_tactic_proof": true, "tactics": ["let", "have", "have", "have", "have", "have", "calc", "rw", "cast_sub", "div_eq_mul_inv]", "gcongr", "rw", "have", "rw", "norm_num", "rw", "gcongr", "rw", "neg_le_neg_iff,", "gcongr", "apply", "refine", "rw", "exact", "refine", "rw", "exact"], "tactic_count": 27}
{"name": "Behrend.exp_four_lt", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Behrend", "is_tactic_proof": false, "tactics": ["rw", "lt_log_iff_exp_lt", "exact", "simp"], "tactic_count": 4}
{"name": "Behrend.four_zero_nine_six_lt_exp_sixteen", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Behrend", "is_tactic_proof": false, "tactics": ["rw", "log_rpow", "linarith"], "tactic_count": 3}
{"name": "Behrend.lower_bound_le_one'", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Behrend", "is_tactic_proof": false, "tactics": ["rw", "log_mul", "sqrt_le_left", "norm_num1", "apply", "exact"], "tactic_count": 6}
{"name": "Behrend.lower_bound_le_one", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Behrend", "is_tactic_proof": true, "tactics": ["obtain", "simp", "exact"], "tactic_count": 3}
{"name": "Behrend.roth_lower_bound", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Behrend", "is_tactic_proof": true, "tactics": ["obtain", "simp", "obtain", "exact", "apply", "simpa"], "tactic_count": 6}
{"name": "ThreeGPFree", "kind": "definition", "module": "Mathlib.Combinatorics.Additive.AP.Three.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ThreeGPFree.instDecidable", "kind": "instance", "module": "Mathlib.Combinatorics.Additive.AP.Three.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ThreeGPFree.mono", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "threeGPFree_empty", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Subsingleton.threeGPFree", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "threeGPFree_singleton", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ThreeGPFree.prod", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "threeGPFree_pi", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ThreeGPFree.of_image", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "threeGPFree_image", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Defs", "is_tactic_proof": true, "tactics": ["rw", "have", "simp", "hf.mul_eq_mul"], "tactic_count": 4}
{"name": "IsMulFreimanHom.threeGPFree", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMulFreimanIso.threeGPFree_congr", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ThreeGPFree.image'", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Defs", "is_tactic_proof": true, "tactics": ["rintro", "rw"], "tactic_count": 2}
{"name": "ThreeGPFree.eq_right", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Defs", "is_tactic_proof": true, "tactics": ["rintro", "obtain", "simpa"], "tactic_count": 3}
{"name": "threeGPFree_insert", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Defs", "is_tactic_proof": false, "tactics": ["refine", "hs", "rintro", "rw", "obtain", "rfl", "all_goals", "exact", "exact", "exact", "exact", "obtain", "exact", "exact"], "tactic_count": 14}
{"name": "ThreeGPFree.smul_set", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Defs", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "threeGPFree_smul_set", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "threeGPFree_insert_of_lt", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Defs", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "ThreeGPFree.smul_set₀", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Defs", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "threeGPFree_smul_set₀", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "threeAPFree_iff_eq_right", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Defs", "is_tactic_proof": true, "tactics": ["refine", "rintro", "exact", "rintro", "simp_rw", "exact"], "tactic_count": 6}
{"name": "mulRothNumber", "kind": "definition", "module": "Mathlib.Combinatorics.Additive.AP.Three.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mulRothNumber_le", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mulRothNumber_spec", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ThreeGPFree.le_mulRothNumber", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ThreeGPFree.mulRothNumber_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mulRothNumber_empty", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mulRothNumber_singleton", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Defs", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "mulRothNumber_union_le", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_mulRothNumber_product", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Defs", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "rw", "refine", "rw", "exact"], "tactic_count": 6}
{"name": "mulRothNumber_lt_of_forall_not_threeGPFree", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Defs", "is_tactic_proof": true, "tactics": ["obtain", "rw", "intro", "obtain", "exact"], "tactic_count": 5}
{"name": "IsMulFreimanHom.mulRothNumber_mono", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Defs", "is_tactic_proof": true, "tactics": ["obtain", "have", "have", "rw", "refine", "rw", "simpa"], "tactic_count": 7}
{"name": "IsMulFreimanIso.mulRothNumber_congr", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Defs", "is_tactic_proof": true, "tactics": ["refine", "obtain", "rw", "have", "have", "rw", "rw", "refine", "rw", "exact"], "tactic_count": 10}
{"name": "mulRothNumber_map_mul_left", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Defs", "is_tactic_proof": true, "tactics": ["refine", "obtain", "rw", "obtain", "rw", "rw", "exact", "obtain", "have", "convert", "rw"], "tactic_count": 11}
{"name": "mulRothNumber_map_mul_right", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "rothNumberNat", "kind": "definition", "module": "Mathlib.Combinatorics.Additive.AP.Three.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "rothNumberNat_def", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "rothNumberNat_le", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "rothNumberNat_spec", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ThreeAPFree.le_rothNumberNat", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "rothNumberNat_add_le", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Defs", "is_tactic_proof": true, "tactics": ["simp_rw", "rw", "exact"], "tactic_count": 3}
{"name": "rothNumberNat_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "addRothNumber_Ico", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Defs", "is_tactic_proof": true, "tactics": ["obtain", "rw", "convert", "rw", "convert", "exact"], "tactic_count": 6}
{"name": "Fin.addRothNumber_eq_rothNumberNat", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.addRothNumber_le_rothNumberNat", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.AP.Three.Defs", "is_tactic_proof": false, "tactics": ["suffices", "exact", "refine", "simpa", "simp", "exact"], "tactic_count": 6}
{"name": "IsApproximateSubgroup.nonempty", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.ApproximateSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsApproximateSubgroup.one_le", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.ApproximateSubgroup", "is_tactic_proof": true, "tactics": ["obtain", "grw", "have", "simpa"], "tactic_count": 4}
{"name": "IsApproximateSubgroup.mono", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.ApproximateSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsApproximateSubgroup.card_pow_le", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.ApproximateSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsApproximateSubgroup.card_mul_self_le", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.ApproximateSubgroup", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsApproximateSubgroup.image", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.ApproximateSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsApproximateSubgroup.subgroup", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.ApproximateSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsApproximateSubgroup.of_small_tripling", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.ApproximateSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsApproximateSubgroup.pow_inter_pow_covBySMul_sq_inter_sq", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.ApproximateSubgroup", "is_tactic_proof": true, "tactics": ["classical", "obtain", "obtain", "have", "choose", "refine", "calc", "calc", "gcongr", "simp_rw", "simp_rw", "rw", "simp_rw"], "tactic_count": 13}
{"name": "IsApproximateSubgroup.pow_inter_pow", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.ApproximateSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isApproximateSubgroup_one", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.ApproximateSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.Additive.CauchyDavenport.0.DevosMulRel", "kind": "definition", "module": "Mathlib.Combinatorics.Additive.CauchyDavenport", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.Additive.CauchyDavenport.0.devosMulRel_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.CauchyDavenport", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "_private.Mathlib.Combinatorics.Additive.CauchyDavenport.0.devosMulRel_of_le", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.CauchyDavenport", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.Additive.CauchyDavenport.0.devosMulRel_of_le_of_le", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.CauchyDavenport", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.Additive.CauchyDavenport.0.wellFoundedOn_devosMulRel", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.CauchyDavenport", "is_tactic_proof": false, "tactics": ["refine", "wellFounded_lt.onFun.wellFoundedOn.prod_lex_of_wellFoundedOn_fiber", "exact", "wellFounded_lt.onFun.wellFoundedOn.mono", "tsub_lt_tsub_left_of_le", "add_le_add"], "tactic_count": 6}
{"name": "cauchy_davenport_minOrder_mul", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.CauchyDavenport", "is_tactic_proof": true, "tactics": ["set", "clear_value", "simp", "obtain", "refine", "wellFoundedOn_devosMulRel.induction", "min", "clear", "rintro", "simp", "obtain", "simpa", "ih", "obtain", "simp", "obtain", "obtain", "have", "refine", "forall_mem_zpowers.2", "rw", "exact", "simp", "rwa", "refine", "rw", "simp", "replace", "card_lt_card", "hsg", "replace", "replace", "card_mono", "mulETransformRight.fst_mul_snd_subset", "obtain", "rw", "right", "grw", "exact", "obtain", "exact", "exact"], "tactic_count": 42}
{"name": "cauchy_davenport_of_isMulTorsionFree", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.CauchyDavenport", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ZMod.cauchy_davenport", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.CauchyDavenport", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "cauchy_davenport_mul_of_linearOrder_isCancelMul", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.CauchyDavenport", "is_tactic_proof": false, "tactics": ["suffices", "rw", "card_singleton", "exact", "card_mono", "mul_subset_mul_right", "refine", "eq_singleton_iff_unique_mem.2", "simp", "forall_apply_eq_imp_iff₂,", "exact"], "tactic_count": 11}
{"name": "Finset.convolution", "kind": "definition", "module": "Mathlib.Combinatorics.Additive.Convolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_smul_inter_smul", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.Convolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_inter_smul", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.Convolution", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.card_smul_inter", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.Convolution", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.card_mul_inv_eq_convolution_inv", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.Convolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.convolution_pos", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.Convolution", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Finset.convolution_ne_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.Convolution", "is_tactic_proof": true, "tactics": ["suffices", "lia"], "tactic_count": 2}
{"name": "Finset.convolution_eq_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.Convolution", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.convolution_le_card_left", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.Convolution", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finset.convolution_le_card_right", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.Convolution", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finset.convolution_inv", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.Convolution", "is_tactic_proof": true, "tactics": ["nth_rw", "rw"], "tactic_count": 2}
{"name": "Finset.op_smul_convolution_eq_convolution_smul", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.Convolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.smul_convolution_eq_convolution_inv_mul", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.Convolution", "is_tactic_proof": true, "tactics": ["nth_rw", "rw"], "tactic_count": 2}
{"name": "Finset.convolution_op_smul_eq_convolution_mul_inv", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.Convolution", "is_tactic_proof": true, "tactics": ["nth_rw", "rw"], "tactic_count": 2}
{"name": "IsCornerFree", "kind": "definition", "module": "Mathlib.Combinatorics.Additive.Corner.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCornerFree_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.Corner.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCorner.mono", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.Corner.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCornerFree.mono", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.Corner.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_isCorner_empty", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.Corner.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.Subsingleton.isCornerFree", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.Corner.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCornerFree_empty", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.Corner.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCornerFree_singleton", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.Corner.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCorner.image", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.Corner.Defs", "is_tactic_proof": true, "tactics": ["obtain", "exact", "hf.add_eq_add"], "tactic_count": 3}
{"name": "IsCornerFree.of_image", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.Corner.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCorner_image", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.Corner.Defs", "is_tactic_proof": true, "tactics": ["have", "rw", "congr", "exact", "exact", "exact", "exact"], "tactic_count": 7}
{"name": "isCornerFree_image", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.Corner.Defs", "is_tactic_proof": false, "tactics": ["have", "rw", "simp"], "tactic_count": 3}
{"name": "_private.Mathlib.Combinatorics.Additive.Corner.Roth.0.Corners.triangleIndices", "kind": "definition", "module": "Mathlib.Combinatorics.Additive.Corner.Roth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.Additive.Corner.Roth.0.Corners.mk_mem_triangleIndices", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.Corner.Roth", "is_tactic_proof": true, "tactics": ["simp", "refine", "rintro", "exact"], "tactic_count": 4}
{"name": "_private.Mathlib.Combinatorics.Additive.Corner.Roth.0.Corners.card_triangleIndices", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.Corner.Roth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.Additive.Corner.Roth.0.Corners.triangleIndices.instExplicitDisjoint", "kind": "instance", "module": "Mathlib.Combinatorics.Additive.Corner.Roth", "is_tactic_proof": true, "tactics": ["constructor", "all_goals", "simp", "rintro", "simp"], "tactic_count": 5}
{"name": "_private.Mathlib.Combinatorics.Additive.Corner.Roth.0.Corners.noAccidental", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.Corner.Roth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.Additive.Corner.Roth.0.Corners.farFromTriangleFree_graph", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.Corner.Roth", "is_tactic_proof": true, "tactics": ["refine", "simp_rw", "ring_nf", "simpa"], "tactic_count": 4}
{"name": "cornersTheoremBound", "kind": "definition", "module": "Mathlib.Combinatorics.Additive.Corner.Roth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "corners_theorem", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.Corner.Roth", "is_tactic_proof": true, "tactics": ["rintro", "rw", "have", "have", "simp", "rwa", "positivity", "have", "rw", "refine", "classical", "have", "rw", "convert"], "tactic_count": 14}
{"name": "corners_theorem_nat", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.Corner.Roth", "is_tactic_proof": true, "tactics": ["rintro", "rw", "have", "rw", "simp", "rintro", "have", "simp", "lia", "rw", "have", "have", "hA.of_image", "refine", "simp", "exact", "rw", "refine", "calc", "rw", "have", "exact"], "tactic_count": 22}
{"name": "roth_3ap_theorem", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.Corner.Roth", "is_tactic_proof": true, "tactics": ["rintro", "classical", "let", "have", "calc", "norm_cast", "rw", "exact", "obtain", "simpa", "have", "hA", "rw", "add_comm]", "exact"], "tactic_count": 15}
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{"name": "rothNumberNat_isLittleO_id", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.Corner.Roth", "is_tactic_proof": true, "tactics": ["simp", "refine", "obtain", "rw", "exact"], "tactic_count": 5}
{"name": "CovBySMul", "kind": "definition", "module": "Mathlib.Combinatorics.Additive.CovBySMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CovBySMul.rfl", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.CovBySMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CovBySMul.of_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.CovBySMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CovBySMul.nonneg", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.CovBySMul", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "covBySMul_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.CovBySMul", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CovBySMul.mono", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.CovBySMul", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "CovBySMul.trans", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.CovBySMul", "is_tactic_proof": true, "tactics": ["classical", "have", "obtain", "obtain", "refine", "calc", "calc"], "tactic_count": 7}
{"name": "CovBySMul.subset_left", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.CovBySMul", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CovBySMul.subset_right", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.CovBySMul", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CovBySMul.subset", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.CovBySMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulDissociated", "kind": "definition", "module": "Mathlib.Combinatorics.Additive.Dissociation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mulDissociated_iff_sum_eq_subsingleton", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.Dissociation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulDissociated.subset", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.Dissociation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mulDissociated_empty", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.Dissociation", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "mulDissociated_singleton", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.Dissociation", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "not_mulDissociated", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.Dissociation", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "not_mulDissociated_iff_exists_disjoint", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.Dissociation", "is_tactic_proof": true, "tactics": ["classical", "refine", "rintro", "refine", "push_cast", "exact"], "tactic_count": 6}
{"name": "MulEquiv.mulDissociated_preimage", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.Dissociation", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "mulDissociated_inv", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.Dissociation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mulSpan", "kind": "definition", "module": "Mathlib.Combinatorics.Additive.Dissociation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_mulSpan", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.Dissociation", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.subset_mulSpan", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.Dissociation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_div_prod_mem_mulSpan", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.Dissociation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.exists_subset_mulSpan_card_le_of_forall_mulDissociated", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.Dissociation", "is_tactic_proof": true, "tactics": ["classical", "obtain", "simp", "refine", "by_cases", "exact", "obtain", "not_mulDissociated_iff_exists_disjoint.1", "hs'.not_gt", "by_cases", "have", "rw", "exact", "prod_div_prod_mem_mulSpan", "rw", "by_cases", "have", "rw", "exact", "rw", "cases"], "tactic_count": 21}
{"name": "Finset.mulConst", "kind": "definition", "module": "Mathlib.Combinatorics.Additive.DoublingConst", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.divConst", "kind": "definition", "module": "Mathlib.Combinatorics.Additive.DoublingConst", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Combinatorics.Additive.termσₘ[_,_]", "kind": "definition", "module": "Mathlib.Combinatorics.Additive.DoublingConst", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Combinatorics.Additive._aux_Mathlib_Combinatorics_Additive_DoublingConst___macroRules_Combinatorics_Additive_termσₘ[_,_]_1", "kind": "definition", "module": "Mathlib.Combinatorics.Additive.DoublingConst", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Combinatorics.Additive._aux_Mathlib_Combinatorics_Additive_DoublingConst___delab_app_Combinatorics_Additive_termσₘ[_,_]_1", "kind": "definition", "module": "Mathlib.Combinatorics.Additive.DoublingConst", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Combinatorics.Additive.termσₘ[_]", "kind": "definition", "module": "Mathlib.Combinatorics.Additive.DoublingConst", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Combinatorics.Additive._aux_Mathlib_Combinatorics_Additive_DoublingConst___macroRules_Combinatorics_Additive_termσₘ[_]_1", "kind": "definition", "module": "Mathlib.Combinatorics.Additive.DoublingConst", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Combinatorics.Additive._aux_Mathlib_Combinatorics_Additive_DoublingConst___delab_app_Combinatorics_Additive_termσₘ[_]_1", "kind": "definition", "module": "Mathlib.Combinatorics.Additive.DoublingConst", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Combinatorics.Additive.termσ[_,_]", "kind": "definition", "module": "Mathlib.Combinatorics.Additive.DoublingConst", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Combinatorics.Additive._aux_Mathlib_Combinatorics_Additive_DoublingConst___macroRules_Combinatorics_Additive_termσ[_,_]_1", "kind": "definition", "module": "Mathlib.Combinatorics.Additive.DoublingConst", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Combinatorics.Additive._aux_Mathlib_Combinatorics_Additive_DoublingConst___delab_app_Combinatorics_Additive_termσ[_,_]_1", "kind": "definition", "module": "Mathlib.Combinatorics.Additive.DoublingConst", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Combinatorics.Additive.termσ[_]", "kind": "definition", "module": "Mathlib.Combinatorics.Additive.DoublingConst", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Combinatorics.Additive._aux_Mathlib_Combinatorics_Additive_DoublingConst___macroRules_Combinatorics_Additive_termσ[_]_1", "kind": "definition", "module": "Mathlib.Combinatorics.Additive.DoublingConst", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Combinatorics.Additive._aux_Mathlib_Combinatorics_Additive_DoublingConst___delab_app_Combinatorics_Additive_termσ[_]_1", "kind": "definition", "module": "Mathlib.Combinatorics.Additive.DoublingConst", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Combinatorics.Additive.termδₘ[_,_]", "kind": "definition", "module": "Mathlib.Combinatorics.Additive.DoublingConst", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Combinatorics.Additive._aux_Mathlib_Combinatorics_Additive_DoublingConst___macroRules_Combinatorics_Additive_termδₘ[_,_]_1", "kind": "definition", "module": "Mathlib.Combinatorics.Additive.DoublingConst", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Combinatorics.Additive._aux_Mathlib_Combinatorics_Additive_DoublingConst___delab_app_Combinatorics_Additive_termδₘ[_,_]_1", "kind": "definition", "module": "Mathlib.Combinatorics.Additive.DoublingConst", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Combinatorics.Additive.termδₘ[_]", "kind": "definition", "module": "Mathlib.Combinatorics.Additive.DoublingConst", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Combinatorics.Additive._aux_Mathlib_Combinatorics_Additive_DoublingConst___macroRules_Combinatorics_Additive_termδₘ[_]_1", "kind": "definition", "module": "Mathlib.Combinatorics.Additive.DoublingConst", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Combinatorics.Additive._aux_Mathlib_Combinatorics_Additive_DoublingConst___delab_app_Combinatorics_Additive_termδₘ[_]_1", "kind": "definition", "module": "Mathlib.Combinatorics.Additive.DoublingConst", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Combinatorics.Additive.termδ[_,_]", "kind": "definition", "module": "Mathlib.Combinatorics.Additive.DoublingConst", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Combinatorics.Additive._aux_Mathlib_Combinatorics_Additive_DoublingConst___macroRules_Combinatorics_Additive_termδ[_,_]_1", "kind": "definition", "module": "Mathlib.Combinatorics.Additive.DoublingConst", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Combinatorics.Additive._aux_Mathlib_Combinatorics_Additive_DoublingConst___delab_app_Combinatorics_Additive_termδ[_,_]_1", "kind": "definition", "module": "Mathlib.Combinatorics.Additive.DoublingConst", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Combinatorics.Additive.termδ[_]", "kind": "definition", "module": "Mathlib.Combinatorics.Additive.DoublingConst", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Combinatorics.Additive._aux_Mathlib_Combinatorics_Additive_DoublingConst___macroRules_Combinatorics_Additive_termδ[_]_1", "kind": "definition", "module": "Mathlib.Combinatorics.Additive.DoublingConst", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Combinatorics.Additive._aux_Mathlib_Combinatorics_Additive_DoublingConst___delab_app_Combinatorics_Additive_termδ[_]_1", "kind": "definition", "module": "Mathlib.Combinatorics.Additive.DoublingConst", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mulConst_mul_card", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.DoublingConst", "is_tactic_proof": true, "tactics": ["obtain", "simp", "exact"], "tactic_count": 3}
{"name": "Finset.divConst_mul_card", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.DoublingConst", "is_tactic_proof": true, "tactics": ["obtain", "simp", "exact"], "tactic_count": 3}
{"name": "Finset.card_mul_mulConst", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.DoublingConst", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.card_mul_divConst", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.DoublingConst", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.mulConst_empty_left", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.DoublingConst", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.divConst_empty_left", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.DoublingConst", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.mulConst_empty_right", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.DoublingConst", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.divConst_empty_right", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.DoublingConst", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.mulConst_inv_right", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.DoublingConst", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.divConst_inv_right", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.DoublingConst", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.one_le_mulConst", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.DoublingConst", "is_tactic_proof": true, "tactics": ["rw", "exact", "simpa"], "tactic_count": 3}
{"name": "Finset.one_le_mulConst_self", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.DoublingConst", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.one_le_divConst", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.DoublingConst", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "Finset.one_le_divConst_self", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.DoublingConst", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mulConst_le_card", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.DoublingConst", "is_tactic_proof": true, "tactics": ["obtain", "simp", "rw", "exact"], "tactic_count": 4}
{"name": "Finset.divConst_le_card", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.DoublingConst", "is_tactic_proof": true, "tactics": ["obtain", "simp", "rw", "exact"], "tactic_count": 4}
{"name": "Finset.mulConst_le_inv_dens", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.DoublingConst", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.divConst_le_inv_dens", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.DoublingConst", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.cast_addConst", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.DoublingConst", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.cast_subConst", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.DoublingConst", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.cast_mulConst", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.DoublingConst", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.cast_divConst", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.DoublingConst", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.cast_addConst_mul_card", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.DoublingConst", "is_tactic_proof": true, "tactics": ["norm_cast"], "tactic_count": 1}
{"name": "Finset.cast_subConst_mul_card", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.DoublingConst", "is_tactic_proof": true, "tactics": ["norm_cast"], "tactic_count": 1}
{"name": "Finset.card_mul_cast_addConst", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.DoublingConst", "is_tactic_proof": true, "tactics": ["norm_cast"], "tactic_count": 1}
{"name": "Finset.card_mul_cast_subConst", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.DoublingConst", "is_tactic_proof": true, "tactics": ["norm_cast"], "tactic_count": 1}
{"name": "Finset.cast_mulConst_mul_card", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.DoublingConst", "is_tactic_proof": true, "tactics": ["norm_cast"], "tactic_count": 1}
{"name": "Finset.cast_divConst_mul_card", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.DoublingConst", "is_tactic_proof": true, "tactics": ["norm_cast"], "tactic_count": 1}
{"name": "Finset.card_mul_cast_mulConst", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.DoublingConst", "is_tactic_proof": true, "tactics": ["norm_cast"], "tactic_count": 1}
{"name": "Finset.card_mul_cast_divConst", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.DoublingConst", "is_tactic_proof": true, "tactics": ["norm_cast"], "tactic_count": 1}
{"name": "Finset.divConst_le_mulConst_sq", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.DoublingConst", "is_tactic_proof": true, "tactics": ["obtain", "simp", "refine", "calc"], "tactic_count": 4}
{"name": "Finset.mulConst_inv_left", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.DoublingConst", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.divConst_inv_left", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.DoublingConst", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.mulConst_le_divConst_sq", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.DoublingConst", "is_tactic_proof": true, "tactics": ["obtain", "simp", "refine", "calc"], "tactic_count": 4}
{"name": "Finset.mulDysonETransform", "kind": "definition", "module": "Mathlib.Combinatorics.Additive.ETransform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mulDysonETransform.subset", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.ETransform", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "Finset.mulDysonETransform.card", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.ETransform", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "card_smul_finset]"], "tactic_count": 3}
{"name": "Finset.mulDysonETransform_idem", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.ETransform", "is_tactic_proof": true, "tactics": ["ext", "rw", "exact", "rw", "exact"], "tactic_count": 5}
{"name": "Finset.mulDysonETransform.smul_finset_snd_subset_fst", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.ETransform", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "exact"], "tactic_count": 3}
{"name": "Finset.mulETransformLeft", "kind": "definition", "module": "Mathlib.Combinatorics.Additive.ETransform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mulETransformRight", "kind": "definition", "module": "Mathlib.Combinatorics.Additive.ETransform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mulETransformLeft_one", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.ETransform", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.mulETransformRight_one", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.ETransform", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.mulETransformLeft.fst_mul_snd_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.ETransform", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "Finset.mulETransformRight.fst_mul_snd_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.ETransform", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "Finset.mulETransformLeft.card", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.ETransform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mulETransformRight.card", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.ETransform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.MulETransform.card", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.ETransform", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.mulETransformLeft_inv", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.ETransform", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.mulETransformRight_inv", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.ETransform", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.mulEnergy", "kind": "definition", "module": "Mathlib.Combinatorics.Additive.Energy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Combinatorics.Additive.termEₘ[_,_]", "kind": "definition", "module": "Mathlib.Combinatorics.Additive.Energy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Combinatorics.Additive._aux_Mathlib_Combinatorics_Additive_Energy___macroRules_Combinatorics_Additive_termEₘ[_,_]_1", "kind": "definition", "module": "Mathlib.Combinatorics.Additive.Energy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Combinatorics.Additive._aux_Mathlib_Combinatorics_Additive_Energy___delab_app_Combinatorics_Additive_termEₘ[_,_]_1", "kind": "definition", "module": "Mathlib.Combinatorics.Additive.Energy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Combinatorics.Additive.termE[_,_]", "kind": "definition", "module": "Mathlib.Combinatorics.Additive.Energy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Combinatorics.Additive._aux_Mathlib_Combinatorics_Additive_Energy___macroRules_Combinatorics_Additive_termE[_,_]_1", "kind": "definition", "module": "Mathlib.Combinatorics.Additive.Energy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Combinatorics.Additive._aux_Mathlib_Combinatorics_Additive_Energy___delab_app_Combinatorics_Additive_termE[_,_]_1", "kind": "definition", "module": "Mathlib.Combinatorics.Additive.Energy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Combinatorics.Additive.termEₘ[_]", "kind": "definition", "module": "Mathlib.Combinatorics.Additive.Energy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Combinatorics.Additive._aux_Mathlib_Combinatorics_Additive_Energy___macroRules_Combinatorics_Additive_termEₘ[_]_1", "kind": "definition", "module": "Mathlib.Combinatorics.Additive.Energy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Combinatorics.Additive._aux_Mathlib_Combinatorics_Additive_Energy___delab_app_Combinatorics_Additive_termEₘ[_]_1", "kind": "definition", "module": "Mathlib.Combinatorics.Additive.Energy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Combinatorics.Additive.termE[_]", "kind": "definition", "module": "Mathlib.Combinatorics.Additive.Energy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Combinatorics.Additive._aux_Mathlib_Combinatorics_Additive_Energy___macroRules_Combinatorics_Additive_termE[_]_1", "kind": "definition", "module": "Mathlib.Combinatorics.Additive.Energy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Combinatorics.Additive._aux_Mathlib_Combinatorics_Additive_Energy___delab_app_Combinatorics_Additive_termE[_]_1", "kind": "definition", "module": "Mathlib.Combinatorics.Additive.Energy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mulEnergy_mono", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.Energy", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "Finset.mulEnergy_mono_left", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.Energy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mulEnergy_mono_right", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.Energy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.le_mulEnergy", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.Energy", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finset.le_mulEnergy_self", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.Energy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mulEnergy_pos", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.Energy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mulEnergy_self_pos", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.Energy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mulEnergy_empty_left", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.Energy", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.mulEnergy_empty_right", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.Energy", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.mulEnergy_pos_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.Energy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mulEnergy_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.Energy", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.mulEnergy_self_pos_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.Energy", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.mulEnergy_self_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.Energy", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.mulEnergy_eq_card_filter", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.Energy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mulEnergy_eq_sum_sq'", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.Energy", "is_tactic_proof": true, "tactics": ["simp_rw", "rw", "swap", "aesop", "congr", "aesop"], "tactic_count": 6}
{"name": "Finset.mulEnergy_eq_sum_sq", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.Energy", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finset.card_sq_le_card_mul_mulEnergy", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.Energy", "is_tactic_proof": true, "tactics": ["calc", "refine", "aesop"], "tactic_count": 3}
{"name": "Finset.le_card_mul_mul_mulEnergy", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.Energy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mulEnergy_comm", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.Energy", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Finset.mulEnergy_univ_left", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.Energy", "is_tactic_proof": true, "tactics": ["simp", "let", "have", "rintro", "simp_rw", "obtain", "rw", "rw", "congr", "simp", "refine", "rintro", "simpa"], "tactic_count": 13}
{"name": "Finset.mulEnergy_univ_right", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.Energy", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "_private.Mathlib.Combinatorics.Additive.ErdosGinzburgZiv.0.f₁", "kind": "definition", "module": "Mathlib.Combinatorics.Additive.ErdosGinzburgZiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.Additive.ErdosGinzburgZiv.0.f₂", "kind": "definition", "module": "Mathlib.Combinatorics.Additive.ErdosGinzburgZiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.Additive.ErdosGinzburgZiv.0.totalDegree_f₁_add_totalDegree_f₂", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.ErdosGinzburgZiv", "is_tactic_proof": true, "tactics": ["calc", "gcongr", "exact", "exact"], "tactic_count": 4}
{"name": "_private.Mathlib.Combinatorics.Additive.ErdosGinzburgZiv.0.ZMod.erdos_ginzburg_ziv_prime", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.ErdosGinzburgZiv", "is_tactic_proof": true, "tactics": ["haveI", "classical", "set", "let", "have", "have", "simp", "have", "char_dvd_card_solutions_of_add_lt", "obtain", "refine", "simp", "rw", "refine", "rw", "exact", "rw", "simpa", "x.2.1", "rw", "exact", "simpa"], "tactic_count": 22}
{"name": "_private.Mathlib.Combinatorics.Additive.ErdosGinzburgZiv.0.Int.erdos_ginzburg_ziv_prime", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.ErdosGinzburgZiv", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Int.erdos_ginzburg_ziv", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.ErdosGinzburgZiv", "is_tactic_proof": true, "tactics": ["classical", "induction", "zero", "exact", "one", "prime", "haveI", "obtain", "obtain", "exact", "composite", "suffices", "obtain", "obtain", "refine", "rw", "rwa", "exact", "exact", "exact", "rintro", "induction", "zero", "succ", "obtain", "ih", "have", "calc", "rw", "le_card_sdiff", "obtain", "have", "rintro", "obtain", "simpa", "lia", "refine", "simp", "exact", "simp", "exact"], "tactic_count": 41}
{"name": "ZMod.erdos_ginzburg_ziv", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.ErdosGinzburgZiv", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Int.erdos_ginzburg_ziv_multiset", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.ErdosGinzburgZiv", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "ZMod.erdos_ginzburg_ziv_multiset", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.ErdosGinzburgZiv", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "IsMulFreimanIso.isMulFreimanHom", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.FreimanHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMulFreimanHom.congr", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.FreimanHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMulFreimanIso.congr", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.FreimanHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMulFreimanHom.mul_eq_mul", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.FreimanHom", "is_tactic_proof": true, "tactics": ["simp_rw", "refine"], "tactic_count": 2}
{"name": "IsMulFreimanIso.mul_eq_mul", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.FreimanHom", "is_tactic_proof": true, "tactics": ["simp_rw", "refine"], "tactic_count": 2}
{"name": "isMulFreimanHom_two", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.FreimanHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isMulFreimanIso_two", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.FreimanHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isMulFreimanHom_id", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.FreimanHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isMulFreimanIso_id", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.FreimanHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMulFreimanHom.comp", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.FreimanHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMulFreimanIso.comp", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.FreimanHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMulFreimanHom.subset", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.FreimanHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMulFreimanHom.superset", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.FreimanHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMulFreimanIso.subset", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.FreimanHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isMulFreimanHom_const", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.FreimanHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isMulFreimanHom_zero_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.FreimanHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isMulFreimanIso_zero_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.FreimanHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isMulFreimanHom_one_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.FreimanHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isMulFreimanIso_one_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.FreimanHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isMulFreimanHom_empty", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.FreimanHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isMulFreimanIso_empty", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.FreimanHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMulFreimanHom.mul", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.FreimanHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHomClass.isMulFreimanHom", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.FreimanHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquivClass.isMulFreimanIso", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.FreimanHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMulFreimanHom.subtypeVal", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.FreimanHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMulFreimanHom.mono", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.FreimanHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMulFreimanIso.mono", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.FreimanHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMulFreimanHom.inv", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.FreimanHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMulFreimanHom.div", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.FreimanHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMulFreimanHom.prodMap", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.FreimanHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMulFreimanIso.prodMap", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.FreimanHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.Additive.FreimanHom.0.Fin.aux", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.FreimanHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.isAddFreimanIso_Iic", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.FreimanHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.isAddFreimanIso_Iio", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.FreimanHom", "is_tactic_proof": true, "tactics": ["obtain", "simp", "have", "convert", "simp", "simp_rw", "rw", "simp"], "tactic_count": 8}
{"name": "Finset.ruzsa_triangle_inequality_div_div_div", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.PluenneckeRuzsa", "is_tactic_proof": true, "tactics": ["rw", "refine", "card_mul_le_card_mul", "card_le_one_iff.2", "obtain", "refine", "rw", "exact", "exact", "exact"], "tactic_count": 10}
{"name": "Finset.ruzsa_triangle_inequality_mulInv_mulInv_mulInv", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.PluenneckeRuzsa", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.ruzsa_triangle_inequality_invMul_invMul_invMul", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.PluenneckeRuzsa", "is_tactic_proof": true, "tactics": ["simpa", "ruzsa_triangle_inequality_div_div_div"], "tactic_count": 2}
{"name": "Finset.ruzsa_triangle_inequality_div_mul_mul", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.PluenneckeRuzsa", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.ruzsa_triangle_inequality_mulInv_mul_mul", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.PluenneckeRuzsa", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.ruzsa_triangle_inequality_invMul_mul_mul", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.PluenneckeRuzsa", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.ruzsa_triangle_inequality_mul_div_mul", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.PluenneckeRuzsa", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.ruzsa_triangle_inequality_mul_mulInv_mul", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.PluenneckeRuzsa", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.ruzsa_triangle_inequality_mul_mul_invMul", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.PluenneckeRuzsa", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.pluennecke_petridis_inequality_mul", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.PluenneckeRuzsa", "is_tactic_proof": true, "tactics": ["induction", "empty", "insert", "set", "set", "have", "rw", "have", "rw", "refine", "rw", "gcongr", "exact", "have", "calc", "gcongr", "rw", "refine", "rw", "card_singleton_mul,", "exact", "rw", "card_singleton_mul"], "tactic_count": 23}
{"name": "_private.Mathlib.Combinatorics.Additive.PluenneckeRuzsa.0.Finset.mul_aux", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.PluenneckeRuzsa", "is_tactic_proof": true, "tactics": ["rintro", "obtain", "simp", "have", "have", "exact", "mod_cast"], "tactic_count": 7}
{"name": "Finset.ruzsa_triangle_inequality_mul_mul_mul", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.PluenneckeRuzsa", "is_tactic_proof": true, "tactics": ["obtain", "simp", "have", "obtain", "rw", "refine", "push_cast", "rw", "refine", "refine", "le_trans", "rw", "mul_comm", "exact"], "tactic_count": 14}
{"name": "Finset.ruzsa_triangle_inequality_mul_div_div", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.PluenneckeRuzsa", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finset.ruzsa_triangle_inequality_div_mul_div", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.PluenneckeRuzsa", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finset.card_div_mul_le_card_div_mul_card_mul", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.PluenneckeRuzsa", "is_tactic_proof": true, "tactics": ["rw", "exact", "ruzsa_triangle_inequality_mul_div_div"], "tactic_count": 3}
{"name": "_private.Mathlib.Combinatorics.Additive.PluenneckeRuzsa.0.Finset.card_mul_pow_le", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.PluenneckeRuzsa", "is_tactic_proof": true, "tactics": ["obtain", "simp", "induction", "zero", "succ", "refine", "calc"], "tactic_count": 7}
{"name": "Finset.pluennecke_ruzsa_inequality_pow_div_pow_mul", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.PluenneckeRuzsa", "is_tactic_proof": true, "tactics": ["have", "obtain", "rw", "obtain", "refine", "calc", "gcongr"], "tactic_count": 7}
{"name": "Finset.pluennecke_ruzsa_inequality_pow_div_pow_div", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.PluenneckeRuzsa", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finset.pluennecke_ruzsa_inequality_pow_mul", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.PluenneckeRuzsa", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.pluennecke_ruzsa_inequality_pow_div", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.PluenneckeRuzsa", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "AddDissociated.randomisation", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.Randomisation", "is_tactic_proof": true, "tactics": ["refine", "push_cast", "calc", "simp_rw", "simp", "pow_eq_zero_iff',", "refine", "calc", "simp_rw", "rw", "prod_ne_zero_iff,", "exact"], "tactic_count": 12}
{"name": "Finset.ruzsa_covering_mul", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.RuzsaCovering", "is_tactic_proof": true, "tactics": ["haveI", "set", "obtain", "simp", "obtain", "refine", "calc", "by_cases", "exact", "by_cases", "refine", "rw", "exact", "simp_rw", "obtain", "exact"], "tactic_count": 16}
{"name": "Set.ruzsa_covering_mul", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.RuzsaCovering", "is_tactic_proof": true, "tactics": ["lift", "lift", "classical", "obtain", "exact"], "tactic_count": 5}
{"name": "_private.Mathlib.Combinatorics.Additive.SmallTripling.0.Finset.inductive_claim_mul", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.SmallTripling", "is_tactic_proof": true, "tactics": ["induction", "base", "succ", "obtain", "simp", "have", "have", "obtain", "simp", "have", "let", "let", "let", "refine", "calc", "simp", "simp", "gcongr", "exact", "exact"], "tactic_count": 20}
{"name": "_private.Mathlib.Combinatorics.Additive.SmallTripling.0.Finset.small_neg_pos_pos_mul", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.SmallTripling", "is_tactic_proof": true, "tactics": ["obtain", "simp", "have", "refine", "calc", "gcongr", "calc"], "tactic_count": 7}
{"name": "_private.Mathlib.Combinatorics.Additive.SmallTripling.0.Finset.small_neg_neg_pos_mul", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.SmallTripling", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "_private.Mathlib.Combinatorics.Additive.SmallTripling.0.Finset.small_pos_neg_neg_mul", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.SmallTripling", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "_private.Mathlib.Combinatorics.Additive.SmallTripling.0.Finset.small_pos_pos_neg_mul", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.SmallTripling", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "_private.Mathlib.Combinatorics.Additive.SmallTripling.0.Finset.small_pos_neg_pos_mul", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.SmallTripling", "is_tactic_proof": true, "tactics": ["obtain", "simp", "refine", "calc", "simpa", "gcongr", "exact", "calc"], "tactic_count": 8}
{"name": "_private.Mathlib.Combinatorics.Additive.SmallTripling.0.Finset.small_neg_pos_neg_mul", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.SmallTripling", "is_tactic_proof": true, "tactics": ["rw", "simpa", "small_pos_neg_pos_mul"], "tactic_count": 3}
{"name": "Finset.small_alternating_pow_of_small_tripling", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.SmallTripling", "is_tactic_proof": true, "tactics": ["have", "have", "obtain", "simp", "have", "one_le_of_le_mul_right₀", "rw", "refine", "simp", "succ_one_eq_two,", "simp", "have", "have", "gcongr", "exact", "simp", "obtain", "simp", "nlinarith", "nlinarith", "nlinarith", "nlinarith", "nlinarith", "nlinarith", "nlinarith", "simp", "nlinarith"], "tactic_count": 27}
{"name": "Finset.small_pow_of_small_tripling", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.SmallTripling", "is_tactic_proof": true, "tactics": ["have", "calc"], "tactic_count": 2}
{"name": "Finset.subsetSum", "kind": "definition", "module": "Mathlib.Combinatorics.Additive.SubsetSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_subsetSum_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.SubsetSum", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.zero_mem_subsetSum", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.SubsetSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.subsetSum_nonempty", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.SubsetSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.subset_subsetSum", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.SubsetSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.subsetSum_mono", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.SubsetSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.subsetSum_erase_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.SubsetSum", "is_tactic_proof": true, "tactics": ["refine", "obtain", "refine", "exact"], "tactic_count": 4}
{"name": "Finset.vadd_finset_subsetSum_subset_subsetSum_insert", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.SubsetSum", "is_tactic_proof": true, "tactics": ["simp_rw", "rintro", "exact"], "tactic_count": 3}
{"name": "Finset.nonneg_of_mem_subsetSum", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.SubsetSum", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.card_add_card_subsetSum_lt_card_subsetSum_insert_max", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.SubsetSum", "is_tactic_proof": true, "tactics": ["have", "have", "simpa", "have", "exact", "have", "vadd_finset_subsetSum_subset_subsetSum_insert", "calc", "grw"], "tactic_count": 9}
{"name": "Finset.card_succ_choose_two_lt_card_subsetSum_of_pos", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.SubsetSum", "is_tactic_proof": true, "tactics": ["induction", "h0", "step", "have", "grw", "add_right_comm,", "exact"], "tactic_count": 7}
{"name": "Finset.card_choose_two_lt_card_subsetSum_of_nonneg", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.SubsetSum", "is_tactic_proof": true, "tactics": ["calc"], "tactic_count": 1}
{"name": "_private.Mathlib.Combinatorics.Additive.VerySmallDoubling.0.Finset.smul_stabilizer_of_no_doubling_aux", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.VerySmallDoubling", "is_tactic_proof": true, "tactics": ["have", "have", "have", "have", "rw", "smul_eq_mul]", "let", "have", "ext", "rw", "refine", "simpa", "norm_cast", "rwa", "refine", "rw", "rw", "norm_cast", "rw"], "tactic_count": 19}
{"name": "Finset.smul_stabilizer_of_no_doubling", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.VerySmallDoubling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.op_smul_stabilizer_of_no_doubling", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.VerySmallDoubling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.Additive.VerySmallDoubling.0.Finset.big_intersection", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.VerySmallDoubling", "is_tactic_proof": false, "tactics": ["have", "gcongr", "rw", "exact", "grw", "simp"], "tactic_count": 6}
{"name": "_private.Mathlib.Combinatorics.Additive.VerySmallDoubling.0.Finset.le_card_smul_inter_smul", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.VerySmallDoubling", "is_tactic_proof": true, "tactics": ["have"], "tactic_count": 1}
{"name": "_private.Mathlib.Combinatorics.Additive.VerySmallDoubling.0.Finset.lt_card_smul_inter_smul", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.VerySmallDoubling", "is_tactic_proof": true, "tactics": ["have"], "tactic_count": 1}
{"name": "_private.Mathlib.Combinatorics.Additive.VerySmallDoubling.0.Finset.le_card_mul_inv_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.VerySmallDoubling", "is_tactic_proof": true, "tactics": ["simp", "obtain", "rw", "simpa"], "tactic_count": 4}
{"name": "_private.Mathlib.Combinatorics.Additive.VerySmallDoubling.0.Finset.lt_card_mul_inv_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.VerySmallDoubling", "is_tactic_proof": true, "tactics": ["simp", "obtain", "rw", "simpa"], "tactic_count": 4}
{"name": "_private.Mathlib.Combinatorics.Additive.VerySmallDoubling.0.Finset.mul_inv_eq_inv_mul_of_doubling_lt_two_aux", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.VerySmallDoubling", "is_tactic_proof": true, "tactics": ["intro", "simp", "rintro", "have", "simp", "obtain", "refine", "rw"], "tactic_count": 8}
{"name": "Finset.mul_inv_eq_inv_mul_of_doubling_lt_two", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.VerySmallDoubling", "is_tactic_proof": true, "tactics": ["refine", "simpa"], "tactic_count": 2}
{"name": "_private.Mathlib.Combinatorics.Additive.VerySmallDoubling.0.Finset.weaken_doubling", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.VerySmallDoubling", "is_tactic_proof": true, "tactics": ["rw", "linarith"], "tactic_count": 2}
{"name": "_private.Mathlib.Combinatorics.Additive.VerySmallDoubling.0.Finset.nonempty_of_doubling", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.VerySmallDoubling", "is_tactic_proof": true, "tactics": ["by_contra", "simp"], "tactic_count": 2}
{"name": "Finset.invMulSubgroup", "kind": "definition", "module": "Mathlib.Combinatorics.Additive.VerySmallDoubling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.invMulSubgroup_eq_inv_mul", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.VerySmallDoubling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.invMulSubgroup_eq_mul_inv", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.VerySmallDoubling", "is_tactic_proof": true, "tactics": ["rw", "norm_cast", "exact"], "tactic_count": 3}
{"name": "Finset.instFintypeSubtypeMemSubgroupInvMulSubgroup", "kind": "instance", "module": "Mathlib.Combinatorics.Additive.VerySmallDoubling", "is_tactic_proof": true, "tactics": ["simp", "infer_instance"], "tactic_count": 2}
{"name": "_private.Mathlib.Combinatorics.Additive.VerySmallDoubling.0.Finset.weak_invMulSubgroup_bound", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.VerySmallDoubling", "is_tactic_proof": true, "tactics": ["have", "have", "convert", "norm_num", "simp", "have", "rw", "simp", "intro", "exact", "have", "rw", "refine", "simp", "rw", "nlinarith"], "tactic_count": 16}
{"name": "_private.Mathlib.Combinatorics.Additive.VerySmallDoubling.0.Finset.A_subset_aH", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.VerySmallDoubling", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "_private.Mathlib.Combinatorics.Additive.VerySmallDoubling.0.Finset.subgroup_strong_bound_left", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.VerySmallDoubling", "is_tactic_proof": false, "tactics": ["have", "rw", "have", "rw", "rw", "refine", "rw", "exact"], "tactic_count": 8}
{"name": "_private.Mathlib.Combinatorics.Additive.VerySmallDoubling.0.Finset.subgroup_strong_bound_right", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.VerySmallDoubling", "is_tactic_proof": true, "tactics": ["intro", "simp", "obtain", "let", "let", "have", "rw", "have", "rw", "simp", "refine", "simp", "have", "rw", "subset_smul_finset_iff]", "simp", "refine", "simp", "have", "rw", "exact", "have", "have", "have", "refine", "rw", "exact", "have", "rw", "linarith", "simp", "rw", "exact"], "tactic_count": 33}
{"name": "Finset.smul_inv_mul_opSMul_eq_mul_of_doubling_lt_three_halves", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.VerySmallDoubling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_inv_mul_of_doubling_lt_three_halves", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.VerySmallDoubling", "is_tactic_proof": true, "tactics": ["obtain", "simp_rw"], "tactic_count": 2}
{"name": "Finset.smul_inv_mul_eq_inv_mul_opSMul", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.VerySmallDoubling", "is_tactic_proof": true, "tactics": ["refine", "rw", "calc", "a", "simp_rw", "rw", "invMulSubgroup_eq_inv_mul]", "rw", "calc", "a⁻¹", "rw", "simp_rw", "rw", "invMulSubgroup_eq_mul_inv"], "tactic_count": 14}
{"name": "Finset.doubling_lt_three_halves", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.VerySmallDoubling", "is_tactic_proof": true, "tactics": ["let", "refine", "simp", "rwa", "rw", "exact_mod_cast", "simpa", "smul_inv_mul_eq_inv_mul_opSMul"], "tactic_count": 8}
{"name": "_private.Mathlib.Combinatorics.Additive.VerySmallDoubling.0.Finset.op_smul_eq_iff_mem", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.VerySmallDoubling", "is_tactic_proof": false, "tactics": ["refine", "obtain", "change", "rw", "rwa"], "tactic_count": 5}
{"name": "_private.Mathlib.Combinatorics.Additive.VerySmallDoubling.0.Finset.op_smul_eq_op_smul_iff_mem", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.VerySmallDoubling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.Additive.VerySmallDoubling.0.Finset.exists_subset_mul_eq_mul_injOn", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.VerySmallDoubling", "is_tactic_proof": true, "tactics": ["obtain", "lift", "refine", "simpa"], "tactic_count": 4}
{"name": "_private.Mathlib.Combinatorics.Additive.VerySmallDoubling.0.Finset.card_mul_eq_mul_card_of_injOn_opSMul", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.VerySmallDoubling", "is_tactic_proof": true, "tactics": ["rw", "simp", "rintro", "simp", "obtain", "hZ", "simp_all"], "tactic_count": 7}
{"name": "Finset.doubling_lt_golden_ratio", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.VerySmallDoubling", "is_tactic_proof": true, "tactics": ["classical", "have", "have", "have", "have", "have", "have", "positivity", "obtain", "exact", "let", "let", "have", "have", "cases", "have", "simp", "obtain", "have", "have", "have", "simpa", "refine", "suffices", "calc", "have", "simp", "let", "have", "simp", "calc", "simp", "set", "have", "calc", "norm_cast", "exact", "simp_rw", "gcongr", "exact", "simp_all", "simp", "ring", "have", "replace", "calc", "ring", "calc", "have", "have", "rw", "gcongr", "linarith", "field", "gcongr", "simp", "rintro", "rw", "rintro", "have", "simpa", "le_card_mul_inv_eq", "rw", "simp", "have", "have", "have", "exact", "have", "mod_cast", "linarith", "simpa"], "tactic_count": 72}
{"name": "_private.Mathlib.Combinatorics.Additive.VerySmallDoubling.0.Finset.expansion", "kind": "definition", "module": "Mathlib.Combinatorics.Additive.VerySmallDoubling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.Additive.VerySmallDoubling.0.Finset.expansion_empty", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.VerySmallDoubling", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "_private.Mathlib.Combinatorics.Additive.VerySmallDoubling.0.Finset.mul_card_le_expansion", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.VerySmallDoubling", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "_private.Mathlib.Combinatorics.Additive.VerySmallDoubling.0.Finset.expansion_nonneg", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.VerySmallDoubling", "is_tactic_proof": true, "tactics": ["nlinarith"], "tactic_count": 1}
{"name": "_private.Mathlib.Combinatorics.Additive.VerySmallDoubling.0.Finset.expansion_pos", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.VerySmallDoubling", "is_tactic_proof": true, "tactics": ["have", "nlinarith"], "tactic_count": 2}
{"name": "_private.Mathlib.Combinatorics.Additive.VerySmallDoubling.0.Finset.expansion_pos_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.VerySmallDoubling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.Additive.VerySmallDoubling.0.Finset.expansion_smul_finset", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.VerySmallDoubling", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "_private.Mathlib.Combinatorics.Additive.VerySmallDoubling.0.Finset.expansion_submodularity", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.VerySmallDoubling", "is_tactic_proof": true, "tactics": ["have", "have", "have", "mod_cast", "have", "simp_rw", "nlinarith"], "tactic_count": 7}
{"name": "_private.Mathlib.Combinatorics.Additive.VerySmallDoubling.0.Finset.bddBelow_expansion", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.VerySmallDoubling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.Additive.VerySmallDoubling.0.Finset.connectivity", "kind": "definition", "module": "Mathlib.Combinatorics.Additive.VerySmallDoubling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.Additive.VerySmallDoubling.0.Finset.le_connectivity_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.VerySmallDoubling", "is_tactic_proof": true, "tactics": ["have", "simp"], "tactic_count": 2}
{"name": "_private.Mathlib.Combinatorics.Additive.VerySmallDoubling.0.Finset.connectivity_lt_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.VerySmallDoubling", "is_tactic_proof": true, "tactics": ["have", "simp"], "tactic_count": 2}
{"name": "_private.Mathlib.Combinatorics.Additive.VerySmallDoubling.0.Finset.connectivity_le_expansion", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.VerySmallDoubling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.Additive.VerySmallDoubling.0.Finset.connectivity_nonneg", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.VerySmallDoubling", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "_private.Mathlib.Combinatorics.Additive.VerySmallDoubling.0.Finset.IsFragment", "kind": "definition", "module": "Mathlib.Combinatorics.Additive.VerySmallDoubling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.Additive.VerySmallDoubling.0.Finset.IsAtom", "kind": "definition", "module": "Mathlib.Combinatorics.Additive.VerySmallDoubling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.Additive.VerySmallDoubling.0.Finset.IsAtom.isFragment", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.VerySmallDoubling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.Additive.VerySmallDoubling.0.Finset.isFragment_smul_finset", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.VerySmallDoubling", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "_private.Mathlib.Combinatorics.Additive.VerySmallDoubling.0.Finset.isAtom_smul_finset", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.VerySmallDoubling", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "_private.Mathlib.Combinatorics.Additive.VerySmallDoubling.0.Finset.IsFragment.smul_finset", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.VerySmallDoubling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.Additive.VerySmallDoubling.0.Finset.IsAtom.smul_finset", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.VerySmallDoubling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.Additive.VerySmallDoubling.0.Finset.IsFragment.inter", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.VerySmallDoubling", "is_tactic_proof": true, "tactics": ["unfold", "have", "have", "have", "linarith"], "tactic_count": 5}
{"name": "_private.Mathlib.Combinatorics.Additive.VerySmallDoubling.0.Finset.IsAtom.eq_of_inter_nonempty", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.VerySmallDoubling", "is_tactic_proof": true, "tactics": ["replace", "replace", "replace", "replace", "replace", "exact"], "tactic_count": 6}
{"name": "_private.Mathlib.Combinatorics.Additive.VerySmallDoubling.0.Finset.exists_nonempty_isFragment", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.VerySmallDoubling", "is_tactic_proof": true, "tactics": ["by_contra", "let", "let", "have", "have", "linarith", "let", "have", "rw", "calc", "κ", "let", "have", "rw", "refine", "apply", "exact", "apply", "apply", "exact", "mem_Icc.2", "have", "let", "have", "simp", "obtain", "have", "have", "exact"], "tactic_count": 29}
{"name": "_private.Mathlib.Combinatorics.Additive.VerySmallDoubling.0.Finset.exists_isFragment", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.VerySmallDoubling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.Additive.VerySmallDoubling.0.Finset.exists_isAtom", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.VerySmallDoubling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.Additive.VerySmallDoubling.0.Finset.connectivity_pos", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.VerySmallDoubling", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "_private.Mathlib.Combinatorics.Additive.VerySmallDoubling.0.Finset.not_isFragment_empty", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.VerySmallDoubling", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "_private.Mathlib.Combinatorics.Additive.VerySmallDoubling.0.Finset.IsFragment.nonempty", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.VerySmallDoubling", "is_tactic_proof": true, "tactics": ["by_contra", "simp"], "tactic_count": 2}
{"name": "_private.Mathlib.Combinatorics.Additive.VerySmallDoubling.0.Finset.IsAtom.nonempty", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.VerySmallDoubling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.Additive.VerySmallDoubling.0.Finset.exists_subgroup_isAtom", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.VerySmallDoubling", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "have", "have", "apply", "simpa", "let", "one_mem", "mul_mem", "hb", "rw", "apply", "rw", "have", "simpa", "hb", "inv_mem", "ha", "rw", "apply", "rw", "have", "simpa", "self_mem_smul_carrier", "refine", "simpa", "simpa"], "tactic_count": 27}
{"name": "Finset.card_mul_finset_lt_two", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.VerySmallDoubling", "is_tactic_proof": true, "tactics": ["let", "have", "let", "let", "obtain", "obtain", "obtain", "have", "calc", "ex", "refine", "rw", "calc", "ε", "field", "cardZ", "calc", "simp", "gcongr", "rw", "suffices", "simp", "rw", "calc", "grw", "gcongr", "linarith", "simp"], "tactic_count": 28}
{"name": "Finset.doubling_lt_two", "kind": "theorem", "module": "Mathlib.Combinatorics.Additive.VerySmallDoubling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.instInhabitedColex", "kind": "instance", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.toColex_ofColex", "kind": "theorem", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.ofColex_toColex", "kind": "theorem", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.toColex_inj", "kind": "theorem", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.ofColex_inj", "kind": "theorem", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Finset.toColex_ne_toColex", "kind": "theorem", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.ofColex_ne_ofColex", "kind": "theorem", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.toColex_injective", "kind": "theorem", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.ofColex_injective", "kind": "theorem", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Colex.instLE", "kind": "instance", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.Colex.0.Finset.Colex.trans_aux", "kind": "theorem", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": true, "tactics": ["classical", "let", "have", "simp", "have", "by_cases", "exact", "have", "have", "refine", "exact"], "tactic_count": 11}
{"name": "_private.Mathlib.Combinatorics.Colex.0.Finset.Colex.antisymm_aux", "kind": "theorem", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": true, "tactics": ["intro", "by_contra", "have", "exact"], "tactic_count": 4}
{"name": "Finset.Colex.instPartialOrder", "kind": "instance", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Colex.le_def", "kind": "theorem", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Colex.toColex_le_toColex", "kind": "theorem", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Colex.toColex_lt_toColex", "kind": "theorem", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.Colex.toColex_mono", "kind": "theorem", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Colex.toColex_strictMono", "kind": "theorem", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Colex.toColex_le_toColex_of_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Colex.toColex_lt_toColex_of_ssubset", "kind": "theorem", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Colex.instOrderBot", "kind": "instance", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Colex.toColex_empty", "kind": "theorem", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Colex.ofColex_bot", "kind": "theorem", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Colex.forall_le_mono", "kind": "theorem", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": true, "tactics": ["rintro", "by_cases", "exact", "obtain", "exact"], "tactic_count": 5}
{"name": "Finset.Colex.forall_lt_mono", "kind": "theorem", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": true, "tactics": ["rintro", "by_cases", "exact", "obtain", "exact"], "tactic_count": 5}
{"name": "Finset.Colex.toColex_le_singleton", "kind": "theorem", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": true, "tactics": ["simp", "refine"], "tactic_count": 2}
{"name": "Finset.Colex.toColex_lt_singleton", "kind": "theorem", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": true, "tactics": ["rw", "refine", "rintro", "refine", "simp"], "tactic_count": 5}
{"name": "Finset.Colex.singleton_le_toColex", "kind": "theorem", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.Colex.singleton_le_singleton", "kind": "theorem", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.Colex.singleton_lt_singleton", "kind": "theorem", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.Colex.le_iff_sdiff_subset_lowerClosure", "kind": "theorem", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.Colex.instDecidableLE", "kind": "instance", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Colex.instDecidableLT", "kind": "instance", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Colex.toColex_sdiff_le_toColex_sdiff", "kind": "theorem", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": true, "tactics": ["simp_rw", "sdiff_sdiff_sdiff_cancel_right"], "tactic_count": 2}
{"name": "Finset.Colex.toColex_sdiff_lt_toColex_sdiff", "kind": "theorem", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Colex.toColex_sdiff_le_toColex_sdiff'", "kind": "theorem", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.Colex.toColex_sdiff_lt_toColex_sdiff'", "kind": "theorem", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.Colex.cons_le_cons", "kind": "theorem", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": true, "tactics": ["obtain", "simp", "classical", "rw"], "tactic_count": 4}
{"name": "Finset.Colex.cons_lt_cons", "kind": "theorem", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Colex.insert_le_insert", "kind": "theorem", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.Colex.insert_lt_insert", "kind": "theorem", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.Colex.erase_le_erase", "kind": "theorem", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": true, "tactics": ["obtain", "simp", "classical", "rw", "singleton_le_singleton]"], "tactic_count": 5}
{"name": "Finset.Colex.erase_lt_erase", "kind": "theorem", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Colex.instLinearOrder", "kind": "instance", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.Colex.0.Finset.Colex.max_mem_aux", "kind": "theorem", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.Colex.toColex_lt_toColex_iff_exists_forall_lt", "kind": "theorem", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Finset.Colex.lt_iff_exists_forall_lt", "kind": "theorem", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Colex.toColex_le_toColex_iff_max'_mem", "kind": "theorem", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": true, "tactics": ["refine", "set", "by_contra", "have", "have", "exact", "lt_irrefl", "have", "refine", "simpa"], "tactic_count": 10}
{"name": "Finset.Colex.le_iff_max'_mem", "kind": "theorem", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Colex.toColex_lt_toColex_iff_max'_mem", "kind": "theorem", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.Colex.lt_iff_max'_mem", "kind": "theorem", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.Colex.lt_iff_exists_filter_lt", "kind": "theorem", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": true, "tactics": ["simp", "refine", "let", "have", "have", "let", "have", "refine", "by_contra", "have", "exact", "rintro", "refine", "by_contra", "exact"], "tactic_count": 15}
{"name": "Finset.Colex.erase_le_erase_min'", "kind": "theorem", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": true, "tactics": ["generalize_proofs", "set", "obtain", "exact", "replace", "simp", "obtain", "obtain", "have", "refine", "change", "rw", "obtain", "assumption", "by_contra", "exact", "obtain", "have", "rintro", "rw", "exact", "rw", "rw", "exact", "tsub_le_tsub_right", "refine", "change", "rw", "obtain", "assumption", "by_contra", "exact"], "tactic_count": 32}
{"name": "Finset.Colex.toColex_image_le_toColex_image", "kind": "theorem", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.Colex.toColex_image_lt_toColex_image", "kind": "theorem", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Colex.toColex_image_ofColex_strictMono", "kind": "theorem", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Colex.instBoundedOrder", "kind": "instance", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Colex.toColex_univ", "kind": "theorem", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Colex.ofColex_top", "kind": "theorem", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Colex.IsInitSeg", "kind": "definition", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Colex.isInitSeg_empty", "kind": "theorem", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.Colex.IsInitSeg.total", "kind": "theorem", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": true, "tactics": ["classical", "simp_rw", "by_contra", "have", "rw", "obtain", "exact", "simp", "exact", "exact"], "tactic_count": 10}
{"name": "Finset.Colex.initSeg", "kind": "definition", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Colex.mem_initSeg", "kind": "theorem", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.Colex.mem_initSeg_self", "kind": "theorem", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.Colex.initSeg_nonempty", "kind": "theorem", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Colex.isInitSeg_initSeg", "kind": "theorem", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "Finset.Colex.IsInitSeg.exists_initSeg", "kind": "theorem", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": true, "tactics": ["have", "refine", "ext", "rw", "refine", "rw", "exact", "rintro", "obtain", "rwa", "exact"], "tactic_count": 11}
{"name": "Finset.Colex.isInitSeg_iff_exists_initSeg", "kind": "theorem", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": true, "tactics": ["refine", "rintro", "exact"], "tactic_count": 3}
{"name": "Finset.geomSum_ofColex_strictMono", "kind": "theorem", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": true, "tactics": ["intro", "rw", "obtain", "rw", "exact"], "tactic_count": 5}
{"name": "Finset.geomSum_le_geomSum_iff_toColex_le_toColex", "kind": "theorem", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.geomSum_lt_geomSum_iff_toColex_lt_toColex", "kind": "theorem", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.geomSum_injective", "kind": "theorem", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": true, "tactics": ["intro", "rwa", "le_antisymm_iff]"], "tactic_count": 3}
{"name": "Finset.lt_geomSum_of_mem", "kind": "theorem", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.toFinset_bitIndices_twoPowSum", "kind": "theorem", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.twoPowSum_toFinset_bitIndices", "kind": "theorem", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.equivBitIndices", "kind": "definition", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.orderIsoColex", "kind": "definition", "module": "Mathlib.Combinatorics.Colex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Configuration.Dual", "kind": "definition", "module": "Mathlib.Combinatorics.Configuration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Configuration.instInhabitedDual", "kind": "instance", "module": "Mathlib.Combinatorics.Configuration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Configuration.instFiniteDual", "kind": "instance", "module": "Mathlib.Combinatorics.Configuration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Configuration.instFintypeDual", "kind": "instance", "module": "Mathlib.Combinatorics.Configuration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Configuration.instMembershipDual", "kind": "instance", "module": "Mathlib.Combinatorics.Configuration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Configuration.Dual.Nondegenerate", "kind": "instance", "module": "Mathlib.Combinatorics.Configuration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Configuration.Dual.hasLines", "kind": "instance", "module": "Mathlib.Combinatorics.Configuration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Configuration.Dual.hasPoints", "kind": "instance", "module": "Mathlib.Combinatorics.Configuration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Configuration.HasPoints.existsUnique_point", "kind": "theorem", "module": "Mathlib.Combinatorics.Configuration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Configuration.HasLines.existsUnique_line", "kind": "theorem", "module": "Mathlib.Combinatorics.Configuration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Configuration.Nondegenerate.exists_injective_of_card_le", "kind": "theorem", "module": "Mathlib.Combinatorics.Configuration", "is_tactic_proof": true, "tactics": ["classical", "let", "suffices", "obtain", "exact", "intro", "by_cases", "simp_rw", "by_cases", "obtain", "obtain", "rw", "exact", "suffices", "rw", "replace", "rwa", "add_le_add_iff_right]", "have", "refine", "simp_rw", "obtain", "exact", "by_cases", "rw", "rw", "rw", "rw", "exact", "exact", "hs₂.trans"], "tactic_count": 31}
{"name": "Configuration.lineCount", "kind": "definition", "module": "Mathlib.Combinatorics.Configuration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Configuration.pointCount", "kind": "definition", "module": "Mathlib.Combinatorics.Configuration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Configuration.sum_lineCount_eq_sum_pointCount", "kind": "theorem", "module": "Mathlib.Combinatorics.Configuration", "is_tactic_proof": true, "tactics": ["classical", "simp", "apply", "calc"], "tactic_count": 4}
{"name": "Configuration.HasLines.pointCount_le_lineCount", "kind": "theorem", "module": "Mathlib.Combinatorics.Configuration", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "haveI", "cases", "rw", "have", "exact"], "tactic_count": 7}
{"name": "Configuration.HasPoints.lineCount_le_pointCount", "kind": "theorem", "module": "Mathlib.Combinatorics.Configuration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Configuration.HasLines.card_le", "kind": "theorem", "module": "Mathlib.Combinatorics.Configuration", "is_tactic_proof": true, "tactics": ["classical", "by_contra", "obtain", "have", "calc", "obtain", "refine", "simpa", "rw", "obtain", "exact", "let", "exact"], "tactic_count": 13}
{"name": "Configuration.HasPoints.card_le", "kind": "theorem", "module": "Mathlib.Combinatorics.Configuration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Configuration.HasLines.exists_bijective_of_card_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Configuration", "is_tactic_proof": true, "tactics": ["classical", "obtain", "have", "exact", "mem_univ"], "tactic_count": 5}
{"name": "Configuration.HasLines.lineCount_eq_pointCount", "kind": "theorem", "module": "Mathlib.Combinatorics.Configuration", "is_tactic_proof": true, "tactics": ["classical", "obtain", "let", "have", "rw", "simp_rw", "have", "rw", "on_goal", "rw", "refine", "simp_rw", "change", "rw", "all_goals", "have", "rwa", "rw", "exact", "step3.symm"], "tactic_count": 20}
{"name": "Configuration.HasPoints.lineCount_eq_pointCount", "kind": "theorem", "module": "Mathlib.Combinatorics.Configuration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Configuration.HasLines.hasPoints", "kind": "definition", "module": "Mathlib.Combinatorics.Configuration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Configuration.HasPoints.hasLines", "kind": "definition", "module": "Mathlib.Combinatorics.Configuration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Configuration.ProjectivePlane.instDual", "kind": "instance", "module": "Mathlib.Combinatorics.Configuration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Configuration.ProjectivePlane.order", "kind": "definition", "module": "Mathlib.Combinatorics.Configuration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Configuration.ProjectivePlane.card_points_eq_card_lines", "kind": "theorem", "module": "Mathlib.Combinatorics.Configuration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Configuration.ProjectivePlane.lineCount_eq_lineCount", "kind": "theorem", "module": "Mathlib.Combinatorics.Configuration", "is_tactic_proof": true, "tactics": ["cases", "cases", "obtain", "have", "let", "have", "have", "have", "have", "have", "have", "suffices", "refine", "refine", "rw"], "tactic_count": 15}
{"name": "Configuration.ProjectivePlane.pointCount_eq_pointCount", "kind": "theorem", "module": "Mathlib.Combinatorics.Configuration", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "Configuration.ProjectivePlane.lineCount_eq_pointCount", "kind": "theorem", "module": "Mathlib.Combinatorics.Configuration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Configuration.ProjectivePlane.Dual.order", "kind": "theorem", "module": "Mathlib.Combinatorics.Configuration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Configuration.ProjectivePlane.lineCount_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Configuration", "is_tactic_proof": true, "tactics": ["classical", "obtain", "cases", "rw", "exact"], "tactic_count": 5}
{"name": "Configuration.ProjectivePlane.pointCount_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Configuration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Configuration.ProjectivePlane.one_lt_order", "kind": "theorem", "module": "Mathlib.Combinatorics.Configuration", "is_tactic_proof": true, "tactics": ["obtain", "cases", "rw", "simp_rw", "have", "exact", "ne_of_mem_of_not_mem"], "tactic_count": 7}
{"name": "Configuration.ProjectivePlane.two_lt_lineCount", "kind": "theorem", "module": "Mathlib.Combinatorics.Configuration", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Configuration.ProjectivePlane.two_lt_pointCount", "kind": "theorem", "module": "Mathlib.Combinatorics.Configuration", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Configuration.ProjectivePlane.card_points", "kind": "theorem", "module": "Mathlib.Combinatorics.Configuration", "is_tactic_proof": true, "tactics": ["cases", "obtain", "let", "invFun", "right_inv", "rfl", "classical", "have", "apply", "convert", "have", "intro", "rw", "refine", "rw", "simp_rw", "simp_rw", "rw"], "tactic_count": 18}
{"name": "Configuration.ProjectivePlane.card_lines", "kind": "theorem", "module": "Mathlib.Combinatorics.Configuration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Configuration.ofField.instMembershipProjectivizationForallFinOfNatNat", "kind": "instance", "module": "Mathlib.Combinatorics.Configuration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Configuration.ofField.mem_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Configuration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Configuration.ofField.crossProduct_eq_zero_of_dotProduct_eq_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.Configuration", "is_tactic_proof": true, "tactics": ["by_contra", "simp_rw", "rw", "let", "let", "have", "ext", "fin_cases", "replace", "rw", "contradiction"], "tactic_count": 11}
{"name": "Configuration.ofField.eq_or_eq_of_orthogonal", "kind": "theorem", "module": "Mathlib.Combinatorics.Configuration", "is_tactic_proof": true, "tactics": ["induction", "h", "induction", "h", "induction", "h", "induction", "h", "rw", "exact"], "tactic_count": 10}
{"name": "Configuration.ofField.instNondegenerateProjectivizationForallFinOfNatNat", "kind": "instance", "module": "Mathlib.Combinatorics.Configuration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Configuration.ofField.instProjectivePlaneProjectivizationForallFinOfNatNatOfDecidableEq", "kind": "instance", "module": "Mathlib.Combinatorics.Configuration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "derangements", "kind": "definition", "module": "Mathlib.Combinatorics.Derangements.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_derangements_iff_fixedPoints_eq_empty", "kind": "theorem", "module": "Mathlib.Combinatorics.Derangements.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.derangementsCongr", "kind": "definition", "module": "Mathlib.Combinatorics.Derangements.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "derangements.subtypeEquiv", "kind": "definition", "module": "Mathlib.Combinatorics.Derangements.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "derangements.atMostOneFixedPointEquivSum_derangements", "kind": "definition", "module": "Mathlib.Combinatorics.Derangements.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "derangements.Equiv.RemoveNone.fiber", "kind": "definition", "module": "Mathlib.Combinatorics.Derangements.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "derangements.Equiv.RemoveNone.mem_fiber", "kind": "theorem", "module": "Mathlib.Combinatorics.Derangements.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "derangements.Equiv.RemoveNone.fiber_none", "kind": "theorem", "module": "Mathlib.Combinatorics.Derangements.Basic", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "rcases", "exact"], "tactic_count": 5}
{"name": "derangements.Equiv.RemoveNone.fiber_some", "kind": "theorem", "module": "Mathlib.Combinatorics.Derangements.Basic", "is_tactic_proof": true, "tactics": ["ext", "constructor", "rw", "rintro", "rw", "apply_fun", "rcases", "rwa", "exfalso", "rw", "exact", "intro", "use", "constructor", "intro", "apply_fun", "simp", "rcases", "simp", "simp", "by_cases", "rw", "apply", "have", "have", "rw", "intro", "exact", "rw"], "tactic_count": 29}
{"name": "derangements.derangementsOptionEquivSigmaAtMostOneFixedPoint", "kind": "definition", "module": "Mathlib.Combinatorics.Derangements.Basic", "is_tactic_proof": false, "tactics": ["have", "rw", "exact", "calc", "derangements", "simp_rw", "rfl"], "tactic_count": 7}
{"name": "derangements.derangementsRecursionEquiv", "kind": "definition", "module": "Mathlib.Combinatorics.Derangements.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "numDerangements_tendsto_inv_e", "kind": "theorem", "module": "Mathlib.Combinatorics.Derangements.Exponential", "is_tactic_proof": true, "tactics": ["let", "suffices", "simp_rw", "rw", "apply", "rw", "exact", "intro", "rw", "push_cast", "rw", "refine", "intro", "have", "rw", "push_cast", "field"], "tactic_count": 17}
{"name": "instDecidablePredPermDerangements", "kind": "instance", "module": "Mathlib.Combinatorics.Derangements.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFintypeElemPermDerangements", "kind": "instance", "module": "Mathlib.Combinatorics.Derangements.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "card_derangements_invariant", "kind": "theorem", "module": "Mathlib.Combinatorics.Derangements.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "card_derangements_fin_add_two", "kind": "theorem", "module": "Mathlib.Combinatorics.Derangements.Finite", "is_tactic_proof": true, "tactics": ["have", "intro", "simp", "add_tsub_cancel_right,", "have", "simp", "simp", "card_sigma,"], "tactic_count": 8}
{"name": "numDerangements", "kind": "definition", "module": "Mathlib.Combinatorics.Derangements.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "numDerangements_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.Derangements.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "numDerangements_one", "kind": "theorem", "module": "Mathlib.Combinatorics.Derangements.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "numDerangements_add_two", "kind": "theorem", "module": "Mathlib.Combinatorics.Derangements.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "numDerangements_succ", "kind": "theorem", "module": "Mathlib.Combinatorics.Derangements.Finite", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "simp", "ring"], "tactic_count": 5}
{"name": "card_derangements_fin_eq_numDerangements", "kind": "theorem", "module": "Mathlib.Combinatorics.Derangements.Finite", "is_tactic_proof": false, "tactics": ["induction", "ind", "rcases", "rfl", "rfl", "rw"], "tactic_count": 6}
{"name": "card_derangements_eq_numDerangements", "kind": "theorem", "module": "Mathlib.Combinatorics.Derangements.Finite", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "numDerangements_sum", "kind": "theorem", "module": "Mathlib.Combinatorics.Derangements.Finite", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "hn", "rw", "intro", "have", "rw"], "tactic_count": 8}
{"name": "Digraph.mk'", "kind": "definition", "module": "Mathlib.Combinatorics.Digraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDecidableRelAdjCoeEmbeddingForallForallBoolDigraphMk'", "kind": "instance", "module": "Mathlib.Combinatorics.Digraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFintypeDigraphOfDecidableEq", "kind": "instance", "module": "Mathlib.Combinatorics.Digraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Digraph.completeDigraph", "kind": "definition", "module": "Mathlib.Combinatorics.Digraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Digraph.emptyDigraph", "kind": "definition", "module": "Mathlib.Combinatorics.Digraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Digraph.completeBipartiteGraph", "kind": "definition", "module": "Mathlib.Combinatorics.Digraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Digraph.adj_injective", "kind": "theorem", "module": "Mathlib.Combinatorics.Digraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Digraph.adj_inj", "kind": "theorem", "module": "Mathlib.Combinatorics.Digraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Digraph.IsSubgraph", "kind": "definition", "module": "Mathlib.Combinatorics.Digraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Digraph.instLE", "kind": "instance", "module": "Mathlib.Combinatorics.Digraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Digraph.isSubgraph_eq_le", "kind": "theorem", "module": "Mathlib.Combinatorics.Digraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Digraph.instMax", "kind": "instance", "module": "Mathlib.Combinatorics.Digraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Digraph.sup_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.Digraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Digraph.instMin", "kind": "instance", "module": "Mathlib.Combinatorics.Digraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Digraph.inf_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.Digraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Digraph.instCompl", "kind": "instance", "module": "Mathlib.Combinatorics.Digraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Digraph.compl_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.Digraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Digraph.sdiff", "kind": "instance", "module": "Mathlib.Combinatorics.Digraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Digraph.sdiff_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.Digraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Digraph.supSet", "kind": "instance", "module": "Mathlib.Combinatorics.Digraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Digraph.infSet", "kind": "instance", "module": "Mathlib.Combinatorics.Digraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Digraph.sSup_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.Digraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Digraph.sInf_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.Digraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Digraph.iSup_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.Digraph.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Digraph.iInf_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.Digraph.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Digraph.distribLattice", "kind": "instance", "module": "Mathlib.Combinatorics.Digraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Digraph.completeAtomicBooleanAlgebra", "kind": "instance", "module": "Mathlib.Combinatorics.Digraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Digraph.top_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.Digraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Digraph.bot_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.Digraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Digraph.completeDigraph_eq_top", "kind": "theorem", "module": "Mathlib.Combinatorics.Digraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Digraph.emptyDigraph_eq_bot", "kind": "theorem", "module": "Mathlib.Combinatorics.Digraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Digraph.instInhabited", "kind": "instance", "module": "Mathlib.Combinatorics.Digraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Digraph.instUniqueOfIsEmpty", "kind": "instance", "module": "Mathlib.Combinatorics.Digraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Digraph.instNontrivialOfNonempty", "kind": "instance", "module": "Mathlib.Combinatorics.Digraph.Basic", "is_tactic_proof": true, "tactics": ["use", "have", "exact"], "tactic_count": 3}
{"name": "Digraph.Bot.adjDecidable", "kind": "instance", "module": "Mathlib.Combinatorics.Digraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Digraph.Sup.adjDecidable", "kind": "instance", "module": "Mathlib.Combinatorics.Digraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Digraph.Inf.adjDecidable", "kind": "instance", "module": "Mathlib.Combinatorics.Digraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Digraph.SDiff.adjDecidable", "kind": "instance", "module": "Mathlib.Combinatorics.Digraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Digraph.Top.adjDecidable", "kind": "instance", "module": "Mathlib.Combinatorics.Digraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Digraph.Compl.adjDecidable", "kind": "instance", "module": "Mathlib.Combinatorics.Digraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Digraph.toSimpleGraphInclusive", "kind": "definition", "module": "Mathlib.Combinatorics.Digraph.Orientation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Digraph.toSimpleGraphStrict", "kind": "definition", "module": "Mathlib.Combinatorics.Digraph.Orientation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Digraph.toSimpleGraphStrict_subgraph_toSimpleGraphInclusive", "kind": "theorem", "module": "Mathlib.Combinatorics.Digraph.Orientation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Digraph.toSimpleGraphInclusive_mono", "kind": "theorem", "module": "Mathlib.Combinatorics.Digraph.Orientation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Digraph.toSimpleGraphStrict_mono", "kind": "theorem", "module": "Mathlib.Combinatorics.Digraph.Orientation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Digraph.toSimpleGraphInclusive_top", "kind": "theorem", "module": "Mathlib.Combinatorics.Digraph.Orientation", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Digraph.toSimpleGraphStrict_top", "kind": "theorem", "module": "Mathlib.Combinatorics.Digraph.Orientation", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Digraph.toSimpleGraphInclusive_bot", "kind": "theorem", "module": "Mathlib.Combinatorics.Digraph.Orientation", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Digraph.toSimpleGraphStrict_bot", "kind": "theorem", "module": "Mathlib.Combinatorics.Digraph.Orientation", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Multiset.bell", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.Bell", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.bell_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Bell", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.Enumerative.Bell.0.Multiset.bell_mul_eq_lemma", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Bell", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.bell_mul_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Bell", "is_tactic_proof": true, "tactics": ["unfold", "rw", "simp", "rw", "simp", "rw", "apply", "rw", "suffices", "by_cases", "rw", "rw", "simp", "exact", "nth_rewrite", "nth_rewrite", "exact", "rw", "apply", "intro", "rw", "simp", "simp", "apply", "rw", "simp"], "tactic_count": 26}
{"name": "Multiset.bell_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Bell", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact", "rw", "apply", "rw", "apply", "simp", "forall_apply_eq_imp_iff₂]", "exact", "apply", "exact"], "tactic_count": 12}
{"name": "Nat.uniformBell", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.Bell", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.uniformBell_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Bell", "is_tactic_proof": true, "tactics": ["unfold", "rw", "split_ifs", "simp", "by_cases", "simp", "rw", "simp"], "tactic_count": 8}
{"name": "Nat.uniformBell_zero_left", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Bell", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.uniformBell_zero_right", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Bell", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.uniformBell_succ_left", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Bell", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.uniformBell_one_left", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Bell", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.uniformBell_one_right", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Bell", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.uniformBell_mul_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Bell", "is_tactic_proof": true, "tactics": ["convert", "simp", "simp", "split_ifs", "rw", "rw", "rw", "simp", "simp"], "tactic_count": 9}
{"name": "Nat.uniformBell_eq_div", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Bell", "is_tactic_proof": true, "tactics": ["rw", "apply", "exact", "rw"], "tactic_count": 4}
{"name": "Nat.bell", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.Bell", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.bell_succ", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Bell", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.bell_succ'", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Bell", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.bell_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Bell", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.bell_one", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Bell", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.bell_two", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Bell", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "catalan", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.Catalan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "catalan_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Catalan", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "catalan_succ", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Catalan", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "catalan_succ'", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Catalan", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "catalan_one", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Catalan", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "_private.Mathlib.Combinatorics.Enumerative.Catalan.0.gosperCatalan", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.Catalan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.Enumerative.Catalan.0.gosper_trick", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Catalan", "is_tactic_proof": true, "tactics": ["have", "have", "have", "have", "have", "mod_cast", "have", "mod_cast", "simp", "push_cast", "rw", "rw", "field"], "tactic_count": 13}
{"name": "_private.Mathlib.Combinatorics.Enumerative.Catalan.0.gosper_catalan_sub_eq_central_binom_div", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Catalan", "is_tactic_proof": false, "tactics": ["simp", "field"], "tactic_count": 2}
{"name": "catalan_eq_centralBinom_div", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Catalan", "is_tactic_proof": false, "tactics": ["suffices", "have", "exact", "induction", "zero", "ind", "simp_rw", "trans", "congr", "ext1", "have", "have", "rw", "norm_cast", "trans", "refine", "rw", "rw", "rw", "norm_cast"], "tactic_count": 20}
{"name": "succ_mul_catalan_eq_centralBinom", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Catalan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "catalan_two", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Catalan", "is_tactic_proof": true, "tactics": ["norm_num"], "tactic_count": 1}
{"name": "catalan_three", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Catalan", "is_tactic_proof": true, "tactics": ["norm_num"], "tactic_count": 1}
{"name": "Tree.pairwiseNode", "kind": "abbrev", "module": "Mathlib.Combinatorics.Enumerative.Catalan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tree.treesOfNumNodesEq", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.Catalan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tree.treesOfNumNodesEq_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Catalan", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Tree.treesOfNumNodesEq_succ", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Catalan", "is_tactic_proof": true, "tactics": ["rw", "ext", "simp"], "tactic_count": 3}
{"name": "Tree.mem_treesOfNumNodesEq", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Catalan", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "Tree.mem_treesOfNumNodesEq_numNodes", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Catalan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tree.coe_treesOfNumNodesEq", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Catalan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tree.treesOfNumNodesEq_card_eq_catalan", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Catalan", "is_tactic_proof": true, "tactics": ["induction", "hz", "hi", "rw", "apply", "rintro", "rw", "simp_rw", "aesop"], "tactic_count": 9}
{"name": "instDecidableEqComposition", "kind": "instance", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDecidableEqCompositionAsSet", "kind": "instance", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInhabitedCompositionAsSet", "kind": "instance", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Composition.instToString", "kind": "instance", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Composition.length", "kind": "abbrev", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Composition.blocks_length", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Composition.blocksFun", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Composition.ofFn_blocksFun", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Composition.sum_blocksFun", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": true, "tactics": ["conv_rhs"], "tactic_count": 1}
{"name": "Composition.blocksFun_mem_blocks", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Composition.one_le_blocks", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Composition.blocks_le", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Composition.one_le_blocks'", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Composition.blocks_pos'", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Composition.one_le_blocksFun", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Composition.blocksFun_le", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Composition.length_le", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": true, "tactics": ["conv_rhs", "exact"], "tactic_count": 2}
{"name": "Composition.blocks_eq_nil", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": true, "tactics": ["constructor", "intro", "simpa", "rintro", "rw", "exact"], "tactic_count": 6}
{"name": "Composition.length_eq_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Composition.length_pos_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Composition.sizeUpTo", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Composition.sizeUpTo_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Composition.sizeUpTo_ofLength_le", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": true, "tactics": ["dsimp", "convert", "exact"], "tactic_count": 3}
{"name": "Composition.sizeUpTo_length", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Composition.sizeUpTo_le", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": true, "tactics": ["conv_rhs", "exact"], "tactic_count": 2}
{"name": "Composition.sizeUpTo_succ", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": true, "tactics": ["simp", "rw"], "tactic_count": 2}
{"name": "Composition.sizeUpTo_succ'", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Composition.sizeUpTo_strict_mono", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Composition.monotone_sizeUpTo", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Composition.boundary", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Composition.boundary_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Composition.boundary_last", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Composition.boundaries", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Composition.card_boundaries_eq_succ_length", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Composition.toCompositionAsSet", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Composition.orderEmbOfFin_boundaries", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "Composition.embedding", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Composition.coe_embedding", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Composition.index_exists", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": true, "tactics": ["have", "have", "have", "refine", "have", "simp"], "tactic_count": 6}
{"name": "Composition.index", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Composition.lt_sizeUpTo_index_succ", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Composition.sizeUpTo_index_le", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": true, "tactics": ["by_contra", "set", "have", "by_contra", "revert", "simp", "let", "have", "have", "have", "simp_all"], "tactic_count": 11}
{"name": "Composition.invEmbedding", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Composition.coe_invEmbedding", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Composition.embedding_comp_inv", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "Composition.mem_range_embedding_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rcases", "rw", "dsimp", "rw", "simp", "intro", "apply", "refine", "rw", "exact", "exact", "rw", "exact"], "tactic_count": 15}
{"name": "Composition.disjoint_range", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": true, "tactics": ["classical", "wlog", "exact", "by_contra", "obtain", "have", "apply", "calc"], "tactic_count": 8}
{"name": "Composition.mem_range_embedding", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "Composition.mem_range_embedding_iff'", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": true, "tactics": ["constructor", "rw", "intro", "exact", "intro", "rw", "exact"], "tactic_count": 7}
{"name": "Composition.index_embedding", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": true, "tactics": ["symm", "rw", "apply"], "tactic_count": 3}
{"name": "Composition.invEmbedding_comp", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Composition.blocksFinEquiv", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Composition.blocksFun_congr", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": true, "tactics": ["cases", "rw", "cases", "congr", "rwa"], "tactic_count": 5}
{"name": "Composition.sigma_eq_iff_blocks_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": true, "tactics": ["refine", "rcases", "rcases", "have", "induction", "congr", "ext1", "exact"], "tactic_count": 8}
{"name": "Composition.ones", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Composition.instInhabited", "kind": "instance", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Composition.ones_length", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Composition.ones_blocks", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Composition.ones_blocksFun", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Composition.ones_sizeUpTo", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Composition.ones_embedding", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": true, "tactics": ["ext", "simpa"], "tactic_count": 2}
{"name": "Composition.eq_ones_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "exact", "intro", "ext1", "have", "have", "conv_rhs", "simp", "rw"], "tactic_count": 10}
{"name": "Composition.ne_ones_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": true, "tactics": ["refine", "have", "simp"], "tactic_count": 3}
{"name": "Composition.eq_ones_iff_length", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "exact", "contrapose", "intro", "apply", "calc", "n", "obtain", "rw", "obtain", "rw", "exact"], "tactic_count": 13}
{"name": "Composition.eq_ones_iff_le_length", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Composition.single", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Composition.single_length", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Composition.single_blocks", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Composition.single_blocksFun", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Composition.single_embedding", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Composition.eq_single_iff_length", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "exact", "intro", "ext1", "have", "have", "rw", "simpa"], "tactic_count": 10}
{"name": "Composition.ne_single_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": true, "tactics": ["contrapose", "constructor", "rintro", "exact", "rintro", "rw", "have", "intro", "by_contra", "apply", "calc", "simpa"], "tactic_count": 12}
{"name": "Composition.cast", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Composition.cast_rfl", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Composition.cast_heq", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "Composition.cast_eq_cast", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": true, "tactics": ["subst", "rfl"], "tactic_count": 2}
{"name": "Composition.append", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Composition.reverse", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Composition.reverse_reverse", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Composition.reverse_involutive", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Composition.reverse_bijective", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Composition.reverse_injective", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Composition.reverse_surjective", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Composition.reverse_inj", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Composition.reverse_ones", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": true, "tactics": ["ext1"], "tactic_count": 1}
{"name": "Composition.reverse_single", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": true, "tactics": ["ext1"], "tactic_count": 1}
{"name": "Composition.reverse_eq_ones", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Composition.reverse_eq_single", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Composition.reverse_append", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Composition.recOnSingleAppend", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Composition.recOnAppendSingle", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.splitWrtCompositionAux", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.splitWrtComposition", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.splitWrtCompositionAux_cons", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.length_splitWrtCompositionAux", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": true, "tactics": ["induction", "simp", "simp"], "tactic_count": 3}
{"name": "List.length_splitWrtComposition", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.map_length_splitWrtCompositionAux", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "List.map_length_splitWrtComposition", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.length_pos_of_mem_splitWrtComposition", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "List.sum_take_map_length_splitWrtComposition", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": true, "tactics": ["congr", "exact"], "tactic_count": 2}
{"name": "List.getElem_splitWrtCompositionAux", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "rcases", "simp", "simp", "rw"], "tactic_count": 7}
{"name": "List.getElem_splitWrtComposition'", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.getElem_splitWrtComposition", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.flatten_splitWrtCompositionAux", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "intro", "simp", "rw", "simp", "rw"], "tactic_count": 8}
{"name": "List.flatten_splitWrtComposition", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.splitWrtComposition_flatten", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "compositionAsSetEquiv", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "compositionAsSetFintype", "kind": "instance", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "compositionAsSet_card", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "CompositionAsSet.boundaries_nonempty", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompositionAsSet.card_boundaries_pos", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompositionAsSet.length", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompositionAsSet.card_boundaries_eq_succ_length", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompositionAsSet.length_lt_card_boundaries", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CompositionAsSet.lt_length", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompositionAsSet.lt_length'", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompositionAsSet.boundary", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompositionAsSet.boundary_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CompositionAsSet.boundary_length", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": true, "tactics": ["convert", "exact"], "tactic_count": 2}
{"name": "CompositionAsSet.blocksFun", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompositionAsSet.blocksFun_pos", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompositionAsSet.blocks", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompositionAsSet.blocks_length", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompositionAsSet.blocks_partial_sum", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "have", "rw", "simp", "have", "rw", "simp"], "tactic_count": 9}
{"name": "CompositionAsSet.mem_boundaries_iff_exists_blocks_sum_take_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rcases", "rw", "refine", "dsimp", "rw", "rfl", "rintro", "convert", "have", "exact"], "tactic_count": 12}
{"name": "CompositionAsSet.blocks_sum", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": true, "tactics": ["have", "rw", "rfl"], "tactic_count": 3}
{"name": "CompositionAsSet.toComposition", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Composition.toCompositionAsSet_length", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CompositionAsSet.toComposition_length", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Composition.toCompositionAsSet_blocks", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": true, "tactics": ["let", "change", "have", "suffices", "intro", "have", "simpa", "have", "have", "have", "d.boundaries.orderEmbOfFin", "c.boundaries.orderEmbOfFin", "rfl", "have", "rw"], "tactic_count": 15}
{"name": "CompositionAsSet.toComposition_blocks", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompositionAsSet.toComposition_boundaries", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Composition.toCompositionAsSet_boundaries", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "compositionEquiv", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "compositionFintype", "kind": "instance", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "composition_card", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Composition", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finset.bipartiteBelow", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.DoubleCounting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.bipartiteAbove", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.DoubleCounting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.bipartiteBelow_swap", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.DoubleCounting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.bipartiteAbove_swap", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.DoubleCounting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.coe_bipartiteBelow", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.DoubleCounting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.coe_bipartiteAbove", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.DoubleCounting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_bipartiteBelow", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.DoubleCounting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_bipartiteAbove", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.DoubleCounting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_prod_bipartiteAbove_eq_prod_prod_bipartiteBelow", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.DoubleCounting", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Finset.sum_card_bipartiteAbove_eq_sum_card_bipartiteBelow", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.DoubleCounting", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Finset.card_nsmul_le_card_nsmul", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.DoubleCounting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_nsmul_le_card_nsmul'", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.DoubleCounting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_nsmul_lt_card_nsmul_of_lt_of_le", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.DoubleCounting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_nsmul_lt_card_nsmul_of_le_of_lt", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.DoubleCounting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_nsmul_lt_card_nsmul_of_lt_of_le'", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.DoubleCounting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_nsmul_lt_card_nsmul_of_le_of_lt'", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.DoubleCounting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_mul_le_card_mul", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.DoubleCounting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_mul_le_card_mul'", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.DoubleCounting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_mul_eq_card_mul", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.DoubleCounting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_le_card_of_forall_subsingleton", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.DoubleCounting", "is_tactic_proof": true, "tactics": ["classical", "rw", "exact", "card_mul_le_card_mul", "card_pos.2", "rw", "exact", "card_le_one.2", "simp_rw", "exact"], "tactic_count": 10}
{"name": "Finset.card_le_card_of_forall_subsingleton'", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.DoubleCounting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_le_card_of_leftTotal_unique", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.DoubleCounting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_le_card_of_rightTotal_unique", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.DoubleCounting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DyckStep", "kind": "inductive", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInhabitedDyckStep.default", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInhabitedDyckStep", "kind": "instance", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDecidableEqDyckStep", "kind": "instance", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DyckStep.dichotomy", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "instDecidableEqDyckWord", "kind": "instance", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCoeDyckWordListDyckStep", "kind": "instance", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instAddDyckWord", "kind": "instance", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instZeroDyckWord", "kind": "instance", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instAddCancelMonoidDyckWord", "kind": "instance", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DyckWord.toList_eq_nil", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "DyckWord.toList_ne_nil", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DyckWord.instUniqueAddUnits", "kind": "instance", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DyckWord.head_eq_U", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": true, "tactics": ["rcases", "rw", "by_contra", "rename_i", "simpa"], "tactic_count": 5}
{"name": "DyckWord.getLast_eq_D", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": true, "tactics": ["by_contra", "rw", "simp_rw", "have"], "tactic_count": 4}
{"name": "DyckWord.cons_tail_dropLast_concat", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": true, "tactics": ["have", "have", "rcases", "tauto", "rename_i", "cases", "tauto", "nth_rw", "rw", "rfl"], "tactic_count": 10}
{"name": "DyckWord.take", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DyckWord.drop", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DyckWord.nest", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DyckWord.nest_ne_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DyckWord.IsNested", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DyckWord.IsNested.nest", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DyckWord.denest", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DyckWord.nest_denest", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "DyckWord.denest_nest", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "DyckWord.semilength", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DyckWord.semilength_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DyckWord.semilength_add", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DyckWord.semilength_nest", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DyckWord.semilength_eq_count_D", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "DyckWord.two_mul_semilength_eq_length", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": true, "tactics": ["nth_rw", "convert", "rw"], "tactic_count": 3}
{"name": "DyckWord.firstReturn", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DyckWord.firstReturn_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DyckWord.firstReturn_pos", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": true, "tactics": ["rw", "simp", "rw", "simp", "rw", "exact"], "tactic_count": 6}
{"name": "DyckWord.firstReturn_lt_length", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": true, "tactics": ["have", "rw", "apply", "simp", "use", "exact"], "tactic_count": 6}
{"name": "DyckWord.count_take_firstReturn_add_one", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "DyckWord.count_D_lt_count_U_of_lt_firstReturn", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "DyckWord.firstReturn_add", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": true, "tactics": ["split_ifs", "have", "rw", "simp_rw", "have", "constructor", "rw", "count_take_firstReturn_add_one", "intro", "rw", "simpa", "rw", "exact"], "tactic_count": 13}
{"name": "DyckWord.firstReturn_nest", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": true, "tactics": ["have", "rw", "simp_rw", "constructor", "rw", "intro", "simp_rw", "take_append,", "have", "simp", "lia", "simp_rw", "exact"], "tactic_count": 13}
{"name": "DyckWord.insidePart", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DyckWord.outsidePart", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DyckWord.insidePart_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DyckWord.outsidePart_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DyckWord.insidePart_add", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": false, "tactics": ["simp_rw", "congr", "exact"], "tactic_count": 3}
{"name": "DyckWord.outsidePart_add", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": false, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "DyckWord.insidePart_nest", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": true, "tactics": ["simp_rw", "convert", "simp_rw"], "tactic_count": 3}
{"name": "DyckWord.outsidePart_nest", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": true, "tactics": ["simp_rw", "rw", "simp_rw"], "tactic_count": 3}
{"name": "DyckWord.nest_insidePart_add_outsidePart", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": true, "tactics": ["simp_rw", "apply"], "tactic_count": 2}
{"name": "DyckWord.semilength_insidePart_add_semilength_outsidePart_add_one", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "DyckWord.semilength_insidePart_lt", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": true, "tactics": ["have", "lia"], "tactic_count": 2}
{"name": "DyckWord.semilength_outsidePart_lt", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": true, "tactics": ["have", "lia"], "tactic_count": 2}
{"name": "DyckWord.instPreorder", "kind": "instance", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DyckWord.le_add_self", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "have", "exact", "termination_by"], "tactic_count": 5}
{"name": "DyckWord.zero_le", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DyckWord.infix_of_le", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": true, "tactics": ["induction", "refl", "tail", "rename_i", "rcases", "rw", "rwa", "have", "grind"], "tactic_count": 9}
{"name": "DyckWord.le_of_suffix", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": true, "tactics": ["obtain", "have", "have", "rw", "rw", "simp", "let", "have", "rw"], "tactic_count": 9}
{"name": "DyckWord.instPartialOrder", "kind": "instance", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DyckWord.pos_iff_ne_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "DyckWord.monotone_semilength", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DyckWord.strictMono_semilength", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.Enumerative.DyckWord.0.DyckWord.equivTreeToFun", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.Enumerative.DyckWord.0.DyckWord.equivTreeInvFun", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.Enumerative.DyckWord.0.DyckWord.equivTree_left_inv", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "rw", "simp_rw", "have", "have", "rw", "exact", "termination_by"], "tactic_count": 9}
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{"name": "DyckWord.equivTree", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DyckWord.semilength_eq_numNodes_equivTree", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "rw", "simp_rw", "have", "have", "rw", "semilength_eq_numNodes_equivTree", "rfl", "termination_by"], "tactic_count": 10}
{"name": "DyckWord.equivTreesOfNumNodesEq", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DyckWord.instFintypeSubtypeEqNatSemilength", "kind": "instance", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DyckWord.card_dyckWord_semilength_eq_catalan", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": true, "tactics": ["rw", "convert"], "tactic_count": 2}
{"name": "Mathlib.Meta.Positivity.evalDyckWordFirstReturn", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.DyckWord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IncidenceAlgebra.instFunLike", "kind": "instance", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IncidenceAlgebra.apply_eq_zero_of_not_le", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IncidenceAlgebra.le_of_ne_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IncidenceAlgebra.toFun_eq_coe", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IncidenceAlgebra.coe_mk", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "IncidenceAlgebra.instZero", "kind": "instance", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IncidenceAlgebra.instInhabited", "kind": "instance", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IncidenceAlgebra.coe_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IncidenceAlgebra.zero_apply", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IncidenceAlgebra.instAdd", "kind": "instance", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "IncidenceAlgebra.add_apply", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IncidenceAlgebra.instSmulZeroClassRight", "kind": "instance", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IncidenceAlgebra.coe_constSMul", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IncidenceAlgebra.constSMul_apply", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IncidenceAlgebra.instAddMonoid", "kind": "instance", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IncidenceAlgebra.instAddCommMonoid", "kind": "instance", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IncidenceAlgebra.instNeg", "kind": "instance", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IncidenceAlgebra.instSub", "kind": "instance", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "IncidenceAlgebra.neg_apply", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IncidenceAlgebra.sub_apply", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IncidenceAlgebra.instAddGroup", "kind": "instance", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IncidenceAlgebra.instAddCommGroup", "kind": "instance", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IncidenceAlgebra.instOne", "kind": "instance", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IncidenceAlgebra.one_apply", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IncidenceAlgebra.instMul", "kind": "instance", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IncidenceAlgebra.mul_apply", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IncidenceAlgebra.instNonUnitalNonAssocSemiring", "kind": "instance", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IncidenceAlgebra.instNonAssocSemiring", "kind": "instance", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IncidenceAlgebra.instSemiring", "kind": "instance", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IncidenceAlgebra.instRing", "kind": "instance", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IncidenceAlgebra.instSMul", "kind": "instance", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IncidenceAlgebra.smul_apply", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IncidenceAlgebra.instIsScalarTower", "kind": "instance", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IncidenceAlgebra.instModule", "kind": "instance", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IncidenceAlgebra.smulWithZeroRight", "kind": "instance", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IncidenceAlgebra.moduleRight", "kind": "instance", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IncidenceAlgebra.algebraRight", "kind": "instance", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IncidenceAlgebra.lambda", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IncidenceAlgebra.zeta", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IncidenceAlgebra.zeta_apply", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IncidenceAlgebra.zeta_of_le", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IncidenceAlgebra.zeta_mul_zeta", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "rw"], "tactic_count": 4}
{"name": "_private.Mathlib.Combinatorics.Enumerative.IncidenceAlgebra.0.IncidenceAlgebra.muFun", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.Enumerative.IncidenceAlgebra.0.IncidenceAlgebra.muFun_apply", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IncidenceAlgebra.mu", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IncidenceAlgebra.mu_apply", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IncidenceAlgebra.mu_self", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IncidenceAlgebra.mu_eq_neg_sum_Ico_of_ne", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IncidenceAlgebra.eulerChar", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IncidenceAlgebra.sum_Icc_mu_right", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": true, "tactics": ["split_ifs", "simp", "by_cases", "simp", "exact"], "tactic_count": 5}
{"name": "_private.Mathlib.Combinatorics.Enumerative.IncidenceAlgebra.0.IncidenceAlgebra.muFun'", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.Enumerative.IncidenceAlgebra.0.IncidenceAlgebra.muFun'_apply", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "_private.Mathlib.Combinatorics.Enumerative.IncidenceAlgebra.0.IncidenceAlgebra.mu'", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.Enumerative.IncidenceAlgebra.0.IncidenceAlgebra.mu'_apply", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "_private.Mathlib.Combinatorics.Enumerative.IncidenceAlgebra.0.IncidenceAlgebra.mu'_apply_self", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "_private.Mathlib.Combinatorics.Enumerative.IncidenceAlgebra.0.IncidenceAlgebra.mu'_eq_sum_Ioc_of_ne", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "_private.Mathlib.Combinatorics.Enumerative.IncidenceAlgebra.0.IncidenceAlgebra.sum_Icc_mu'_left", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": true, "tactics": ["split_ifs", "simp", "by_cases", "simp", "exact"], "tactic_count": 5}
{"name": "IncidenceAlgebra.mu_mul_zeta", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": true, "tactics": ["ext", "calc"], "tactic_count": 2}
{"name": "_private.Mathlib.Combinatorics.Enumerative.IncidenceAlgebra.0.IncidenceAlgebra.zeta_mul_mu'", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": true, "tactics": ["ext", "calc"], "tactic_count": 2}
{"name": "_private.Mathlib.Combinatorics.Enumerative.IncidenceAlgebra.0.IncidenceAlgebra.mu_eq_mu'", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "IncidenceAlgebra.mu_eq_neg_sum_Ioc_of_ne", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IncidenceAlgebra.zeta_mul_mu", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IncidenceAlgebra.sum_Icc_mu_left", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IncidenceAlgebra.mu_toDual", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": true, "tactics": ["letI", "let", "eq_zero_of_not_le", "suffices", "suffices", "rw", "apply_fun", "symm", "simpa", "clear", "ext", "simp", "calc", "exact"], "tactic_count": 14}
{"name": "IncidenceAlgebra.mu_ofDual", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IncidenceAlgebra.eulerChar_orderDual", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IncidenceAlgebra.moebius_inversion_top", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": true, "tactics": ["letI", "symm", "calc", "congr", "rw", "rw", "rw", "rw", "simp", "apply", "simp", "exact", "simp", "exact"], "tactic_count": 14}
{"name": "IncidenceAlgebra.moebius_inversion_bot", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "IncidenceAlgebra.zeta_prod_apply", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IncidenceAlgebra.zeta_prod_mk", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IncidenceAlgebra.prod", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IncidenceAlgebra.prod_mk", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IncidenceAlgebra.prod_apply", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IncidenceAlgebra.prod_mul_prod'", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "IncidenceAlgebra.one_prod_one", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "IncidenceAlgebra.zeta_prod_zeta", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "IncidenceAlgebra.prod_mul_prod", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IncidenceAlgebra.mu_prod_mu", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "IncidenceAlgebra.eulerChar_prod", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.IncidenceAlgebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.prod_indicator_biUnion_sub_indicator", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.InclusionExclusion", "is_tactic_proof": true, "tactics": ["by_cases", "have", "simp", "obtain", "apply", "obtain", "have", "exact"], "tactic_count": 8}
{"name": "Finset.indicator_biUnion_eq_sum_powerset", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.InclusionExclusion", "is_tactic_proof": true, "tactics": ["classical", "by_cases", "simp", "symm", "apply", "simp", "intro", "rw", "simp", "contrapose", "simp", "rcases", "simp", "exact", "rw", "calc", "simp", "congr", "simp", "simp", "have", "rw", "simp", "rcases", "exact"], "tactic_count": 25}
{"name": "Finset.prod_indicator_biUnion_finset_sub_indicator", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.InclusionExclusion", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "Finset.inclusion_exclusion_sum_biUnion", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.InclusionExclusion", "is_tactic_proof": true, "tactics": ["classical", "rw", "calc", "rw", "simp", "congr", "split_ifs", "obtain", "simp", "simp", "zero_smul,", "congr", "aesop", "obtain", "simp", "congr", "obtain"], "tactic_count": 17}
{"name": "Finset.inclusion_exclusion_card_biUnion", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.InclusionExclusion", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.inclusion_exclusion_sum_inf_compl", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.InclusionExclusion", "is_tactic_proof": true, "tactics": ["classical", "calc", "rw", "simp", "pow_succ]"], "tactic_count": 5}
{"name": "Finset.inclusion_exclusion_card_inf_compl", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.InclusionExclusion", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Nat.instDecidableEqPartition", "kind": "instance", "module": "Mathlib.Combinatorics.Enumerative.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Partition.le_of_mem_parts", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Partition.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Nat.Partition.ofComposition", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Partition.ofComposition_surj", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Partition.Basic", "is_tactic_proof": true, "tactics": ["rintro", "induction", "exact"], "tactic_count": 3}
{"name": "Nat.Partition.ofSums", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Partition.ofMultiset", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Partition.ofSym", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Partition.ofSym_map", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Partition.Basic", "is_tactic_proof": true, "tactics": ["simp", "rw", "simp", "congr", "rw"], "tactic_count": 5}
{"name": "Nat.Partition.ofSymShapeEquiv", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Partition.toFinsuppAntidiag", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Partition.toFinsuppAntidiag_injective", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Partition.Basic", "is_tactic_proof": true, "tactics": ["unfold", "intro", "rw", "obtain", "rw", "intro", "obtain", "grind", "exact"], "tactic_count": 9}
{"name": "Nat.Partition.toFinsuppAntidiag_mem_finsuppAntidiag", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Partition.Basic", "is_tactic_proof": true, "tactics": ["have", "suffices", "convert", "rw", "apply", "suffices", "grind"], "tactic_count": 7}
{"name": "Nat.Partition.indiscrete", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Partition.instInhabited", "kind": "instance", "module": "Mathlib.Combinatorics.Enumerative.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Partition.indiscrete_parts", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Partition.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.Partition.partition_zero_parts", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Partition.UniquePartitionZero", "kind": "instance", "module": "Mathlib.Combinatorics.Enumerative.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Partition.partition_one_parts", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Partition.Basic", "is_tactic_proof": false, "tactics": ["have", "eq_replicate_card.2", "have", "rw"], "tactic_count": 4}
{"name": "Nat.Partition.UniquePartitionOne", "kind": "instance", "module": "Mathlib.Combinatorics.Enumerative.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Partition.ofSym_one", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Partition.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Nat.Partition.count_ofSums_of_ne_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Partition.count_ofSums_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Partition.instFintype", "kind": "instance", "module": "Mathlib.Combinatorics.Enumerative.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Partition.restricted", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Partition.countRestricted", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Partition.odds", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Partition.distincts", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Partition.countRestricted_two", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Partition.Basic", "is_tactic_proof": true, "tactics": ["congrm", "rw", "grind"], "tactic_count": 3}
{"name": "Nat.Partition.oddDistincts", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Partition.genFun", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.Partition.GenFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Partition.coeff_genFun", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Partition.GenFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Partition.tendsto_order_genFun_term_atTop_nhds_top", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Partition.GenFun", "is_tactic_proof": true, "tactics": ["refine", "intro", "grw", "refine", "nontriviality", "rw", "norm_cast", "grind"], "tactic_count": 8}
{"name": "Nat.Partition.summable_genFun_term", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Partition.GenFun", "is_tactic_proof": true, "tactics": ["apply", "apply"], "tactic_count": 2}
{"name": "Nat.Partition.summable_genFun_term'", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Partition.GenFun", "is_tactic_proof": true, "tactics": ["obtain", "apply"], "tactic_count": 2}
{"name": "_private.Mathlib.Combinatorics.Enumerative.Partition.GenFun.0.Nat.Partition.aux_dvd_of_coeff_ne_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Partition.GenFun", "is_tactic_proof": true, "tactics": ["by_cases", "specialize", "contrapose", "have", "rw", "rw", "congrm", "suffices", "contrapose", "simp", "rw", "apply", "suffices", "contrapose", "simp", "suffices", "contrapose", "exact"], "tactic_count": 18}
{"name": "_private.Mathlib.Combinatorics.Enumerative.Partition.GenFun.0.Nat.Partition.aux_prod_coeff_eq_zero_of_notMem_range", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Partition.GenFun", "is_tactic_proof": false, "tactics": ["suffices", "obtain", "apply", "contrapose", "rw", "have", "refine", "contrapose", "exact", "exact", "refine", "simpa", "suffices", "exact", "obtain", "refine", "suffices", "apply", "exact", "ext", "simpa"], "tactic_count": 21}
{"name": "_private.Mathlib.Combinatorics.Enumerative.Partition.GenFun.0.Nat.Partition.aux_prod_f_eq_prod_coeff", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Partition.GenFun", "is_tactic_proof": true, "tactics": ["simp_rw", "apply", "grind", "intro", "rw", "have", "have", "simp", "intro", "rw", "have", "rw", "suffices", "f", "simpa", "rw", "rw", "simp", "intro", "suffices", "rw", "grind"], "tactic_count": 22}
{"name": "Nat.Partition.hasProd_genFun", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Partition.GenFun", "is_tactic_proof": true, "tactics": ["rw", "refine", "have", "rw", "have", "intro", "suffices", "intro", "refine", "rw", "refine", "intro", "exact", "exact", "exact"], "tactic_count": 15}
{"name": "Nat.Partition.multipliable_genFun", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Partition.GenFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Partition.genFun_eq_tprod", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Partition.GenFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Partition.hasProd_powerSeriesMk_card_restricted", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Partition.Glaisher", "is_tactic_proof": true, "tactics": ["convert", "ext1", "split_ifs", "rw", "simp", "simp_rw", "apply", "exact", "simp", "simp_rw", "simp"], "tactic_count": 11}
{"name": "Nat.Partition.multipliable_powerSeriesMk_card_restricted", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Partition.Glaisher", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Partition.powerSeriesMk_card_restricted_eq_tprod", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Partition.Glaisher", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Partition.hasProd_powerSeriesMk_card_countRestricted", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Partition.Glaisher", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Partition.multipliable_powerSeriesMk_card_countRestricted", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Partition.Glaisher", "is_tactic_proof": true, "tactics": ["rcases", "simpa", "exact"], "tactic_count": 3}
{"name": "Nat.Partition.powerSeriesMk_card_countRestricted_eq_tprod", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Partition.Glaisher", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.Enumerative.Partition.Glaisher.0.Nat.Partition.aux_mul_one_sub_X_pow", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Partition.Glaisher", "is_tactic_proof": true, "tactics": ["nontriviality", "rw", "simp_rw", "conv", "ext", "rw", "refine", "intro", "rw", "exact", "suffices", "intro", "obtain", "refine", "rw", "intro", "have", "simp"], "tactic_count": 18}
{"name": "Nat.Partition.powerSeriesMk_card_restricted_eq_powerSeriesMk_card_countRestricted", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Partition.Glaisher", "is_tactic_proof": true, "tactics": ["nontriviality", "let", "have", "rw", "rw", "apply", "rw", "rw", "exact"], "tactic_count": 9}
{"name": "Nat.Partition.card_restricted_eq_card_countRestricted", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Partition.Glaisher", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Nat.Partition.card_odds_eq_card_distincts", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Partition.Glaisher", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Nat.largeSchroder", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.Schroder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.largeSchroder_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Schroder", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.largeSchroder_one", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Schroder", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.largeSchroder_two", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Schroder", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.largeSchroder_succ", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Schroder", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.even_largeSchroder", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Schroder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.smallSchroder", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.Schroder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.smallSchroder_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Schroder", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.smallSchroder_one", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Schroder", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.smallSchroder_succ_eq_largeSchroder_div_two", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Schroder", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.two_mul_smallSchroder_succ", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Schroder", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.smallSchroder_succ", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Schroder", "is_tactic_proof": true, "tactics": ["obtain", "simp", "simp", "refine", "calc", "rw", "sum_Ioo_add_eq_sum_Ioc]", "simp", "lia", "congr", "simp", "rw", "rw", "simp", "lia"], "tactic_count": 15}
{"name": "Nat.stirlingFirst", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.Stirling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.stirlingFirst_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Stirling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.stirlingFirst_zero_succ", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Stirling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.stirlingFirst_succ_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Stirling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.stirlingFirst_succ_left", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Stirling", "is_tactic_proof": true, "tactics": ["obtain", "rfl"], "tactic_count": 2}
{"name": "Nat.stirlingFirst_succ_right", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Stirling", "is_tactic_proof": true, "tactics": ["obtain", "rfl"], "tactic_count": 2}
{"name": "Nat.stirlingFirst_succ_succ", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Stirling", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "Nat.stirlingFirst_eq_zero_of_lt", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Stirling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.stirlingFirst_self", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Stirling", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "Nat.stirlingFirst_succ_self_left", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Stirling", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw"], "tactic_count": 4}
{"name": "Nat.stirlingFirst_one_right", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Stirling", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "simp"], "tactic_count": 5}
{"name": "Nat.stirlingSecond", "kind": "definition", "module": "Mathlib.Combinatorics.Enumerative.Stirling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.stirlingSecond_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Stirling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.stirlingSecond_zero_succ", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Stirling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.stirlingSecond_succ_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Stirling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.stirlingSecond_succ_left", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Stirling", "is_tactic_proof": true, "tactics": ["obtain", "rfl"], "tactic_count": 2}
{"name": "Nat.stirlingSecond_succ_right", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Stirling", "is_tactic_proof": true, "tactics": ["obtain", "rfl"], "tactic_count": 2}
{"name": "Nat.stirlingSecond_succ_succ", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Stirling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.stirlingSecond_eq_zero_of_lt", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Stirling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.stirlingSecond_self", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Stirling", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "Nat.stirlingSecond_one_right", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Stirling", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Nat.stirlingSecond_succ_self_left", "kind": "theorem", "module": "Mathlib.Combinatorics.Enumerative.Stirling", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw"], "tactic_count": 4}
{"name": "ruzsaSzemerediNumber", "kind": "definition", "module": "Mathlib.Combinatorics.Extremal.RuzsaSzemeredi", "is_tactic_proof": true, "tactics": ["classical", "exact"], "tactic_count": 2}
{"name": "ruzsaSzemerediNumber_le", "kind": "theorem", "module": "Mathlib.Combinatorics.Extremal.RuzsaSzemeredi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ruzsaSzemerediNumber_spec", "kind": "theorem", "module": "Mathlib.Combinatorics.Extremal.RuzsaSzemeredi", "is_tactic_proof": true, "tactics": ["classical", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.LocallyLinear.le_ruzsaSzemerediNumber", "kind": "theorem", "module": "Mathlib.Combinatorics.Extremal.RuzsaSzemeredi", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "ruzsaSzemerediNumber_mono", "kind": "theorem", "module": "Mathlib.Combinatorics.Extremal.RuzsaSzemeredi", "is_tactic_proof": true, "tactics": ["classical", "refine", "rintro", "refine", "rw", "decide"], "tactic_count": 6}
{"name": "ruzsaSzemerediNumber_congr", "kind": "theorem", "module": "Mathlib.Combinatorics.Extremal.RuzsaSzemeredi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ruzsaSzemerediNumberNat", "kind": "definition", "module": "Mathlib.Combinatorics.Extremal.RuzsaSzemeredi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ruzsaSzemerediNumberNat_card", "kind": "theorem", "module": "Mathlib.Combinatorics.Extremal.RuzsaSzemeredi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ruzsaSzemerediNumberNat_mono", "kind": "theorem", "module": "Mathlib.Combinatorics.Extremal.RuzsaSzemeredi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ruzsaSzemerediNumberNat_le", "kind": "theorem", "module": "Mathlib.Combinatorics.Extremal.RuzsaSzemeredi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ruzsaSzemerediNumberNat_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.Extremal.RuzsaSzemeredi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ruzsaSzemerediNumberNat_one", "kind": "theorem", "module": "Mathlib.Combinatorics.Extremal.RuzsaSzemeredi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ruzsaSzemerediNumberNat_two", "kind": "theorem", "module": "Mathlib.Combinatorics.Extremal.RuzsaSzemeredi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.Extremal.RuzsaSzemeredi.0.triangleIndices", "kind": "definition", "module": "Mathlib.Combinatorics.Extremal.RuzsaSzemeredi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.Extremal.RuzsaSzemeredi.0.mem_triangleIndices", "kind": "theorem", "module": "Mathlib.Combinatorics.Extremal.RuzsaSzemeredi", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "_private.Mathlib.Combinatorics.Extremal.RuzsaSzemeredi.0.card_triangleIndices", "kind": "theorem", "module": "Mathlib.Combinatorics.Extremal.RuzsaSzemeredi", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "_private.Mathlib.Combinatorics.Extremal.RuzsaSzemeredi.0.noAccidental", "kind": "theorem", "module": "Mathlib.Combinatorics.Extremal.RuzsaSzemeredi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.Extremal.RuzsaSzemeredi.0.instExplicitDisjointTriangleIndices", "kind": "instance", "module": "Mathlib.Combinatorics.Extremal.RuzsaSzemeredi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.Extremal.RuzsaSzemeredi.0.locallyLinear", "kind": "theorem", "module": "Mathlib.Combinatorics.Extremal.RuzsaSzemeredi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.Extremal.RuzsaSzemeredi.0.card_edgeFinset", "kind": "theorem", "module": "Mathlib.Combinatorics.Extremal.RuzsaSzemeredi", "is_tactic_proof": true, "tactics": ["haveI", "rw"], "tactic_count": 2}
{"name": "addRothNumber_le_ruzsaSzemerediNumber", "kind": "theorem", "module": "Mathlib.Combinatorics.Extremal.RuzsaSzemeredi", "is_tactic_proof": true, "tactics": ["obtain", "haveI", "rw", "exact"], "tactic_count": 4}
{"name": "rothNumberNat_le_ruzsaSzemerediNumberNat", "kind": "theorem", "module": "Mathlib.Combinatorics.Extremal.RuzsaSzemeredi", "is_tactic_proof": true, "tactics": ["let", "have", "haveI", "open", "calc", "rw", "simp_rw", "ring_nf"], "tactic_count": 8}
{"name": "rothNumberNat_le_ruzsaSzemerediNumberNat'", "kind": "theorem", "module": "Mathlib.Combinatorics.Extremal.RuzsaSzemeredi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ruzsaSzemerediNumberNat_lower_bound", "kind": "theorem", "module": "Mathlib.Combinatorics.Extremal.RuzsaSzemeredi", "is_tactic_proof": true, "tactics": ["rw", "obtain", "exact", "exact"], "tactic_count": 4}
{"name": "ruzsaSzemerediNumberNat_asymptotic_lower_bound", "kind": "theorem", "module": "Mathlib.Combinatorics.Extremal.RuzsaSzemeredi", "is_tactic_proof": true, "tactics": ["trans", "simp_rw", "refine", "trans", "simp_rw", "exact", "refine", "simpa", "rw", "refine", "simp", "exact", "rw", "refine", "simp", "mul_le_mul_iff_right₀,", "refine", "gcongr", "simp", "lia", "lia", "refine", "filter_upwards", "have", "simpa"], "tactic_count": 25}
{"name": "Graph.termV(_)", "kind": "definition", "module": "Mathlib.Combinatorics.Graph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Graph._aux_Mathlib_Combinatorics_Graph_Basic___macroRules_Graph_termV(_)_1", "kind": "definition", "module": "Mathlib.Combinatorics.Graph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Graph._aux_Mathlib_Combinatorics_Graph_Basic___unexpand_Graph_vertexSet_1", "kind": "definition", "module": "Mathlib.Combinatorics.Graph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Graph.termE(_)", "kind": "definition", "module": "Mathlib.Combinatorics.Graph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Graph._aux_Mathlib_Combinatorics_Graph_Basic___macroRules_Graph_termE(_)_1", "kind": "definition", "module": "Mathlib.Combinatorics.Graph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Graph._aux_Mathlib_Combinatorics_Graph_Basic___unexpand_Graph_edgeSet_1", "kind": "definition", "module": "Mathlib.Combinatorics.Graph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Graph.IsLink.edge_mem", "kind": "theorem", "module": "Mathlib.Combinatorics.Graph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Graph.IsLink.symm", "kind": "theorem", "module": "Mathlib.Combinatorics.Graph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Graph.IsLink.left_mem", "kind": "theorem", "module": "Mathlib.Combinatorics.Graph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Graph.IsLink.right_mem", "kind": "theorem", "module": "Mathlib.Combinatorics.Graph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Graph.isLink_comm", "kind": "theorem", "module": "Mathlib.Combinatorics.Graph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Graph.exists_isLink_of_mem_edgeSet", "kind": "theorem", "module": "Mathlib.Combinatorics.Graph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Graph.edgeSet_eq_setOf_exists_isLink", "kind": "theorem", "module": "Mathlib.Combinatorics.Graph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Graph.IsLink.left_eq_or_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Graph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Graph.IsLink.right_eq_or_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Graph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Graph.IsLink.left_eq_of_right_ne", "kind": "theorem", "module": "Mathlib.Combinatorics.Graph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Graph.IsLink.right_unique", "kind": "theorem", "module": "Mathlib.Combinatorics.Graph.Basic", "is_tactic_proof": true, "tactics": ["obtain", "rfl", "obtain"], "tactic_count": 3}
{"name": "Graph.IsLink.left_unique", "kind": "theorem", "module": "Mathlib.Combinatorics.Graph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Graph.IsLink.eq_and_eq_or_eq_and_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Graph.Basic", "is_tactic_proof": true, "tactics": ["obtain", "simp", "simp"], "tactic_count": 3}
{"name": "Graph.IsLink.isLink_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Graph.Basic", "is_tactic_proof": true, "tactics": ["refine", "rintro", "assumption", "exact"], "tactic_count": 4}
{"name": "Graph.IsLink.isLink_iff_sym2_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Graph.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Graph.Inc", "kind": "definition", "module": "Mathlib.Combinatorics.Graph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Graph.Inc.edge_mem", "kind": "theorem", "module": "Mathlib.Combinatorics.Graph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Graph.Inc.vertex_mem", "kind": "theorem", "module": "Mathlib.Combinatorics.Graph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Graph.IsLink.inc_left", "kind": "theorem", "module": "Mathlib.Combinatorics.Graph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Graph.IsLink.inc_right", "kind": "theorem", "module": "Mathlib.Combinatorics.Graph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Graph.Inc.eq_or_eq_of_isLink", "kind": "theorem", "module": "Mathlib.Combinatorics.Graph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Graph.Inc.eq_of_isLink_of_ne_left", "kind": "theorem", "module": "Mathlib.Combinatorics.Graph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Graph.IsLink.isLink_iff_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Graph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Graph.isLink_iff_inc", "kind": "theorem", "module": "Mathlib.Combinatorics.Graph.Basic", "is_tactic_proof": true, "tactics": ["refine", "rintro", "obtain", "obtain", "assumption", "exact", "assumption"], "tactic_count": 7}
{"name": "Graph.Inc.other", "kind": "definition", "module": "Mathlib.Combinatorics.Graph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Graph.Inc.isLink_other", "kind": "theorem", "module": "Mathlib.Combinatorics.Graph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Graph.Inc.inc_other", "kind": "theorem", "module": "Mathlib.Combinatorics.Graph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Graph.Inc.eq_or_eq_or_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Graph.Basic", "is_tactic_proof": true, "tactics": ["by_contra", "obtain", "obtain", "obtain", "exact"], "tactic_count": 5}
{"name": "Graph.IsLoopAt", "kind": "definition", "module": "Mathlib.Combinatorics.Graph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Graph.isLink_self_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Graph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Graph.IsLoopAt.inc", "kind": "theorem", "module": "Mathlib.Combinatorics.Graph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Graph.IsLoopAt.eq_of_inc", "kind": "theorem", "module": "Mathlib.Combinatorics.Graph.Basic", "is_tactic_proof": true, "tactics": ["obtain", "rfl"], "tactic_count": 2}
{"name": "Graph.IsLoopAt.edge_mem", "kind": "theorem", "module": "Mathlib.Combinatorics.Graph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Graph.IsLoopAt.vertex_mem", "kind": "theorem", "module": "Mathlib.Combinatorics.Graph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Graph.IsNonloopAt", "kind": "definition", "module": "Mathlib.Combinatorics.Graph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Graph.IsNonloopAt.inc", "kind": "theorem", "module": "Mathlib.Combinatorics.Graph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Graph.IsNonloopAt.edge_mem", "kind": "theorem", "module": "Mathlib.Combinatorics.Graph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Graph.IsNonloopAt.vertex_mem", "kind": "theorem", "module": "Mathlib.Combinatorics.Graph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Graph.IsLoopAt.not_isNonloopAt", "kind": "theorem", "module": "Mathlib.Combinatorics.Graph.Basic", "is_tactic_proof": true, "tactics": ["rintro", "rw", "exact"], "tactic_count": 3}
{"name": "Graph.IsNonloopAt.not_isLoopAt", "kind": "theorem", "module": "Mathlib.Combinatorics.Graph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Graph.isNonloopAt_iff_inc_not_isLoopAt", "kind": "theorem", "module": "Mathlib.Combinatorics.Graph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Graph.isLoopAt_iff_inc_not_isNonloopAt", "kind": "theorem", "module": "Mathlib.Combinatorics.Graph.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Graph.Inc.isLoopAt_or_isNonloopAt", "kind": "theorem", "module": "Mathlib.Combinatorics.Graph.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Graph.Adj", "kind": "definition", "module": "Mathlib.Combinatorics.Graph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Graph.Adj.symm", "kind": "theorem", "module": "Mathlib.Combinatorics.Graph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Graph.adj_comm", "kind": "theorem", "module": "Mathlib.Combinatorics.Graph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Graph.Adj.left_mem", "kind": "theorem", "module": "Mathlib.Combinatorics.Graph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Graph.Adj.right_mem", "kind": "theorem", "module": "Mathlib.Combinatorics.Graph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Graph.IsLink.adj", "kind": "theorem", "module": "Mathlib.Combinatorics.Graph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Graph.mk_eq_self", "kind": "theorem", "module": "Mathlib.Combinatorics.Graph.Basic", "is_tactic_proof": true, "tactics": ["obtain", "cases"], "tactic_count": 2}
{"name": "Graph.ext", "kind": "theorem", "module": "Mathlib.Combinatorics.Graph.Basic", "is_tactic_proof": true, "tactics": ["rw", "convert", "exact", "simp", "simp"], "tactic_count": 5}
{"name": "Graph.ext_inc", "kind": "theorem", "module": "Mathlib.Combinatorics.Graph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Graph.incidenceSet", "kind": "definition", "module": "Mathlib.Combinatorics.Graph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Graph.mem_incidenceSet", "kind": "theorem", "module": "Mathlib.Combinatorics.Graph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Graph.incidenceSet_subset_edgeSet", "kind": "theorem", "module": "Mathlib.Combinatorics.Graph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Graph.loopSet", "kind": "definition", "module": "Mathlib.Combinatorics.Graph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Graph.mem_loopSet", "kind": "theorem", "module": "Mathlib.Combinatorics.Graph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Graph.loopSet_subset_incidenceSet", "kind": "theorem", "module": "Mathlib.Combinatorics.Graph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Combinatorics.Subspace.instInhabited", "kind": "instance", "module": "Mathlib.Combinatorics.HalesJewett", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Combinatorics.Subspace.toFun", "kind": "definition", "module": "Mathlib.Combinatorics.HalesJewett", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Combinatorics.Subspace.instCoeFun", "kind": "instance", "module": "Mathlib.Combinatorics.HalesJewett", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Combinatorics.Subspace.coe_apply", "kind": "theorem", "module": "Mathlib.Combinatorics.HalesJewett", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Combinatorics.Subspace.coe_injective", "kind": "theorem", "module": "Mathlib.Combinatorics.HalesJewett", "is_tactic_proof": true, "tactics": ["classical", "rintro", "ext", "simp", "cases", "inl", "obtain", "cases", "inr", "cases", "inl", "obtain", "simpa", "inr", "obtain", "simp", "by_contra", "simpa"], "tactic_count": 18}
{"name": "Combinatorics.Subspace.apply_def", "kind": "theorem", "module": "Mathlib.Combinatorics.HalesJewett", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Combinatorics.Subspace.apply_inl", "kind": "theorem", "module": "Mathlib.Combinatorics.HalesJewett", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Combinatorics.Subspace.apply_inr", "kind": "theorem", "module": "Mathlib.Combinatorics.HalesJewett", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Combinatorics.Subspace.IsMono", "kind": "definition", "module": "Mathlib.Combinatorics.HalesJewett", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Combinatorics.Subspace.reindex", "kind": "definition", "module": "Mathlib.Combinatorics.HalesJewett", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Combinatorics.Subspace.reindex_apply", "kind": "theorem", "module": "Mathlib.Combinatorics.HalesJewett", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Combinatorics.Subspace.reindex_isMono", "kind": "theorem", "module": "Mathlib.Combinatorics.HalesJewett", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Combinatorics.Subspace.IsMono.reindex", "kind": "theorem", "module": "Mathlib.Combinatorics.HalesJewett", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Combinatorics.Line.toFun", "kind": "definition", "module": "Mathlib.Combinatorics.HalesJewett", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Combinatorics.Line.instCoeFun", "kind": "instance", "module": "Mathlib.Combinatorics.HalesJewett", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Combinatorics.Line.coe_apply", "kind": "theorem", "module": "Mathlib.Combinatorics.HalesJewett", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Combinatorics.Line.coe_injective", "kind": "theorem", "module": "Mathlib.Combinatorics.HalesJewett", "is_tactic_proof": true, "tactics": ["rintro", "ext", "obtain", "simp", "refine", "cases", "cases"], "tactic_count": 7}
{"name": "Combinatorics.Line.IsMono", "kind": "definition", "module": "Mathlib.Combinatorics.HalesJewett", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Combinatorics.Line.toSubspaceUnit", "kind": "definition", "module": "Mathlib.Combinatorics.HalesJewett", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Combinatorics.Line.toSubspaceUnit_apply", "kind": "theorem", "module": "Mathlib.Combinatorics.HalesJewett", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Combinatorics.Line.toSubspaceUnit_isMono", "kind": "theorem", "module": "Mathlib.Combinatorics.HalesJewett", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Combinatorics.Line.toSubspace", "kind": "definition", "module": "Mathlib.Combinatorics.HalesJewett", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Combinatorics.Line.toSubspace_apply", "kind": "theorem", "module": "Mathlib.Combinatorics.HalesJewett", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Combinatorics.Line.toSubspace_isMono", "kind": "theorem", "module": "Mathlib.Combinatorics.HalesJewett", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Combinatorics.Line.diagonal", "kind": "definition", "module": "Mathlib.Combinatorics.HalesJewett", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Combinatorics.Line.instInhabitedOfNonempty", "kind": "instance", "module": "Mathlib.Combinatorics.HalesJewett", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Combinatorics.Line.instInhabitedAlmostMonoDefaultOfNonempty", "kind": "instance", "module": "Mathlib.Combinatorics.HalesJewett", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Combinatorics.Line.instInhabitedColorFocused", "kind": "instance", "module": "Mathlib.Combinatorics.HalesJewett", "is_tactic_proof": true, "tactics": ["refine", "simp"], "tactic_count": 2}
{"name": "Combinatorics.Line.map", "kind": "definition", "module": "Mathlib.Combinatorics.HalesJewett", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "hallMatchingsOn", "kind": "definition", "module": "Mathlib.Combinatorics.Hall.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Hindman.FS", "kind": "inductive", "module": "Mathlib.Combinatorics.Hindman", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Matroid.IsBase.exchange", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Matroid.IsBase.eq_of_subset_isBase", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Matroid.IsBase.insert_not_isBase", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsBase.encard_diff_comm", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsBase.ncard_diff_comm", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "Matroid.IsBase.finite_of_finite", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsBase.infinite_of_infinite", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": true, "tactics": ["contrapose"], "tactic_count": 1}
{"name": "Matroid.IsBase.finite", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Matroid.IsBase.rankPos_of_nonempty", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": true, "tactics": ["rw", "intro", "obtain", "simp"], "tactic_count": 4}
{"name": "Matroid.IsBase.rankFinite_of_finite", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsBase.rankInfinite_of_infinite", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.not_rankFinite", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": true, "tactics": ["intro"], "tactic_count": 1}
{"name": "Matroid.not_rankInfinite", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": true, "tactics": ["intro"], "tactic_count": 1}
{"name": "Matroid.rankFinite_or_rankInfinite", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.not_rankFinite_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.not_rankInfinite_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.IsBase.diff_finite_comm", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsBase.diff_infinite_comm", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.ext_isBase", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": ["have", "ext"], "tactic_count": 2}
{"name": "Matroid.ext_iff_isBase", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.Dep", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.indep_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.setOf_indep_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Matroid.Indep.exists_isBase_superset", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.dep_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.setOf_dep_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.Indep.subset_ground", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Matroid.Dep.subset_ground", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.Indep.not_dep", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.Dep.not_indep", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.indep_iff_not_dep", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Matroid.Indep.subset", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Matroid.IsBase.indep", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.empty_indep", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.Dep.nonempty", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.Indep.finite", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.Indep.rankPos_of_nonempty", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Matroid.Indep.inter_right", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.Indep.inter_left", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.Indep.diff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsBase.eq_of_subset_indep", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.isBase_iff_maximal_indep", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "obtain", "rwa"], "tactic_count": 4}
{"name": "Matroid.Indep.isBase_of_maximal", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Matroid.IsBase.mem_of_insert_indep", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsBase.eq_exchange_of_diff_eq_singleton", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": true, "tactics": ["obtain", "have", "rw", "refine", "rw", "exact"], "tactic_count": 6}
{"name": "Matroid.IsBase.exchange_isBase_of_indep", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": true, "tactics": ["obtain", "have", "rw", "obtain", "rw", "exact", "rw", "obtain", "obtain", "simp_rw", "exact"], "tactic_count": 11}
{"name": "Matroid.IsBase.exchange_isBase_of_indep'", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "Matroid.insert_isBase_of_insert_indep", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": true, "tactics": ["obtain", "assumption", "simpa"], "tactic_count": 3}
{"name": "Matroid.IsBase.insert_dep", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Matroid.Indep.exists_insert_of_not_isBase", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "by_cases", "exact", "obtain", "exact"], "tactic_count": 6}
{"name": "Matroid.Indep.exists_insert_of_not_maximal", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": true, "tactics": ["simp", "refine", "obtain", "exact", "exact"], "tactic_count": 5}
{"name": "Matroid.Indep.isBase_of_forall_insert", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": true, "tactics": ["by_contra", "obtain", "obtain", "exact"], "tactic_count": 4}
{"name": "Matroid.ground_indep_iff_isBase", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsBase.exists_insert_of_ssubset", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.ext_indep", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.ext_iff_indep", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.ext_isBase_indep", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact", "obtain", "exact"], "tactic_count": 5}
{"name": "Matroid.indep_of_forall_finite_subset_indep", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.indep_iff_forall_finite_subset_indep", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.finitary_of_rankFinite", "kind": "instance", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.existsMaximalSubsetProperty_indep", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.copy", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.copyIndep", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.copyBase", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsBasis", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsBasis'", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsBasis'.indep", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsBasis.indep", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsBasis.subset", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsBasis.isBasis'", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsBasis'.subset", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsBasis.subset_ground", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsBasis.isBasis_inter_ground", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "Matroid.IsBasis.left_subset_ground", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsBasis.eq_of_subset_indep", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsBasis.Finite", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.isBasis_iff'", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": true, "tactics": ["rw", "tauto"], "tactic_count": 2}
{"name": "Matroid.isBasis'_iff_isBasis_inter_ground", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact", "exact"], "tactic_count": 3}
{"name": "Matroid.isBasis_iff_isBasis'_subset_ground", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsBasis'.isBasis_inter_ground", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsBasis'.eq_of_subset_indep", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsBasis'.insert_not_indep", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsBasis.isBasis_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Matroid.isBasis_self_iff_indep", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Matroid.Indep.isBasis_self", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.isBasis_empty_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsBasis.dep_of_ssubset", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "Matroid.IsBasis.insert_dep", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsBasis.mem_of_insert_indep", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsBasis'.mem_of_insert_indep", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsBasis.not_isBasis_of_ssubset", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.Indep.subset_isBasis'_of_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Matroid.exists_isBasis'", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.Indep.eq_of_isBasis", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsBasis.exists_isBase", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.isBasis_ground_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": true, "tactics": ["rw", "maximal_and_iff_right_of_imp"], "tactic_count": 2}
{"name": "Matroid.IsBase.isBasis_ground", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.Indep.isBasis_iff_forall_insert_dep", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp", "hI.subset_ground]", "exact"], "tactic_count": 4}
{"name": "Matroid.Indep.isBasis_of_forall_insert", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.Indep.isBasis_insert_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": ["simp_rw", "and_iff_left", "tauto"], "tactic_count": 3}
{"name": "Matroid.IsBasis.iUnion_isBasis_iUnion", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": true, "tactics": ["refine", "rintro", "rw", "refine", "rw", "exact"], "tactic_count": 6}
{"name": "Matroid.IsBasis.isBasis_iUnion", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": true, "tactics": ["convert", "exact"], "tactic_count": 2}
{"name": "Matroid.IsBasis.isBasis_sUnion", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": true, "tactics": ["rw", "have", "exact"], "tactic_count": 3}
{"name": "Matroid.Indep.isBasis_setOf_insert_isBasis", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": ["refine", "hI.isBasis_of_forall_insert", "rw", "simpa"], "tactic_count": 4}
{"name": "Matroid.IsBasis.union_isBasis_union", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp", "rwa"], "tactic_count": 4}
{"name": "Matroid.IsBasis.isBasis_union", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "Matroid.IsBasis.isBasis_union_of_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": true, "tactics": ["convert", "assumption"], "tactic_count": 2}
{"name": "Matroid.IsBasis.insert_isBasis_insert", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Matroid.IsBase.isBase_of_isBasis_superset", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": true, "tactics": ["by_contra", "obtain", "exact"], "tactic_count": 3}
{"name": "Matroid.Indep.exists_isBase_subset_union_isBase", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Matroid.IsBasis.inter_eq_of_subset_indep", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsBasis'.inter_eq_of_subset_indep", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": true, "tactics": ["rw", "inter_eq_self_of_subset_left"], "tactic_count": 2}
{"name": "Matroid.finite_setOf_matroid", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": true, "tactics": ["set", "have", "refine", "rw", "exact", "rw", "refine", "rintro", "simp", "exact"], "tactic_count": 10}
{"name": "Matroid.finite_setOf_matroid'", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsCircuit", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.isCircuit_def", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsCircuit.dep", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsCircuit.not_indep", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsCircuit.minimal", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsCircuit.subset_ground", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsCircuit.nonempty", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.empty_not_isCircuit", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.isCircuit_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Matroid.IsCircuit.ssubset_indep", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Matroid.IsCircuit.minimal_not_indep", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Matroid.isCircuit_iff_minimal_not_indep", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsCircuit.diff_singleton_indep", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.isCircuit_iff_forall_ssubset", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Matroid.isCircuit_antichain", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsCircuit.eq_of_not_indep_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsCircuit.eq_of_dep_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsCircuit.not_ssubset", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsCircuit.eq_of_subset_isCircuit", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsCircuit.eq_of_superset_isCircuit", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.isCircuit_iff_dep_forall_diff_singleton_indep", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": true, "tactics": ["wlog", "exact", "simp", "minimal_iff_forall_diff_singleton"], "tactic_count": 4}
{"name": "Matroid.Indep.insert_isCircuit_of_forall", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": true, "tactics": ["rw", "rintro", "simpa", "rw", "exact"], "tactic_count": 5}
{"name": "Matroid.Indep.insert_isCircuit_of_forall_of_nontrivial", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact"], "tactic_count": 3}
{"name": "Matroid.IsCircuit.diff_singleton_isBasis", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": true, "tactics": ["nth_rw", "rw", "insert_eq_of_mem", "exact"], "tactic_count": 4}
{"name": "Matroid.IsCircuit.isBasis_iff_eq_diff_singleton", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact", "rintro", "exact"], "tactic_count": 5}
{"name": "Matroid.IsCircuit.isBasis_iff_insert_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "rw"], "tactic_count": 4}
{"name": "Matroid.IsCircuit.isCircuit_restrict_of_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Matroid.fundCircuit", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.fundCircuit_eq_sInter", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "singleton_subset_iff]", "rw"], "tactic_count": 4}
{"name": "Matroid.fundCircuit_subset_insert", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.mem_fundCircuit", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.fundCircuit_diff_eq_inter", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.fundCircuit_eq_of_mem", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": false, "tactics": ["suffices", "simpa", "exact"], "tactic_count": 3}
{"name": "Matroid.fundCircuit_eq_of_notMem_ground", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": false, "tactics": ["suffices", "simpa", "simp_rw", "exact"], "tactic_count": 4}
{"name": "Matroid.Indep.fundCircuit_isCircuit", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": true, "tactics": ["have", "rw", "refine", "simp", "rw", "simp", "simp", "exact"], "tactic_count": 8}
{"name": "Matroid.Indep.mem_fundCircuit_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": true, "tactics": ["obtain", "simp", "suffices", "simpa", "mem_ground_of_mem_closure", "refine", "exact"], "tactic_count": 7}
{"name": "Matroid.IsBase.fundCircuit_isCircuit", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsCircuit.eq_fundCircuit_of_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": true, "tactics": ["obtain", "exact", "suffices", "refine", "rw", "exact", "exact", "have", "have", "rw", "refine", "exact"], "tactic_count": 12}
{"name": "Matroid.fundCircuit_restrict", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": true, "tactics": ["simp_rw", "apply", "gcongr", "simp", "refine", "rwa", "gcongr", "refine", "rw", "simp", "exact"], "tactic_count": 11}
{"name": "Matroid.fundCircuit_restrict_univ", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": false, "tactics": ["have", "refine", "refine", "simp", "simp"], "tactic_count": 5}
{"name": "Matroid.Dep.exists_isCircuit_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "exact", "hI.indep.fundCircuit_isCircuit"], "tactic_count": 4}
{"name": "Matroid.dep_iff_superset_isCircuit'", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.indep_iff_forall_subset_not_isCircuit'", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": true, "tactics": ["simp_rw", "aesop"], "tactic_count": 2}
{"name": "Matroid.IsCircuit.closure_diff_singleton_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsCircuit.subset_closure_diff_singleton", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Matroid.IsCircuit.mem_closure_diff_singleton_of_mem", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.exists_isCircuit_of_mem_closure", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.mem_closure_iff_exists_isCircuit", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.ext_isCircuit", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": false, "tactics": ["have", "iff_of_false", "refine", "simp_rw"], "tactic_count": 4}
{"name": "Matroid.ext_isCircuit_not_indep", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": true, "tactics": ["refine", "obtain", "rwa", "obtain", "rwa"], "tactic_count": 5}
{"name": "Matroid.ext_iff_isCircuit", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsCircuit.strong_multi_elimination_insert", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": true, "tactics": ["obtain", "exact", "suffices", "rw", "obtain", "refine", "rwa", "have", "simpa", "rw", "refine", "mem_of_mem_of_subset", "rw", "exact"], "tactic_count": 14}
{"name": "Matroid.IsCircuit.strong_multi_elimination", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": false, "tactics": ["have", "obtain", "refine", "refine", "union_subset", "subset_diff.2", "rw", "rintro", "obtain", "simp", "simpa", "rwa", "rintro", "exact", "rintro", "exact", "simp", "exact"], "tactic_count": 18}
{"name": "Matroid.IsCircuit.strong_multi_elimination_set", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": true, "tactics": ["choose", "simp", "have", "obtain", "refine", "simpa", "simpa", "simpa", "simp", "exact", "simp", "refine", "simpa", "simpa"], "tactic_count": 14}
{"name": "Matroid.IsCircuit.strong_elimination", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": false, "tactics": ["obtain", "hC₁.strong_multi_elimination", "exact"], "tactic_count": 3}
{"name": "Matroid.IsCircuit.elimination", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": true, "tactics": ["have", "obtain", "by_cases", "by_cases", "obtain", "exact", "exact", "exact"], "tactic_count": 8}
{"name": "Matroid.IsCircuit.finite", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": true, "tactics": ["have", "rw", "obtain", "rwa"], "tactic_count": 4}
{"name": "Matroid.finitary_iff_forall_isCircuit_finite", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact", "simpa"], "tactic_count": 4}
{"name": "Matroid.exists_mem_finite_closure_of_mem_closure", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": true, "tactics": ["by_cases", "obtain", "exact", "obtain", "exact"], "tactic_count": 5}
{"name": "Matroid.exists_subset_finite_closure_of_subset_closure", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": false, "tactics": ["suffices", "obtain", "obtain", "exact", "refine", "obtain", "exact", "insert_subset"], "tactic_count": 8}
{"name": "Matroid.IsCocircuit", "kind": "abbrev", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.isCocircuit_def", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsCocircuit.isCircuit", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsCircuit.isCocircuit", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Matroid.IsCocircuit.nonempty", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsCocircuit.subset_ground", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.dual_isCocircuit_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.coindep_iff_forall_subset_not_isCocircuit", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.isCocircuit_iff_minimal", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": true, "tactics": ["have", "rw", "refine", "minimal_iff_minimal_of_imp_of_forall", "rw", "exact"], "tactic_count": 6}
{"name": "Matroid.isCocircuit_iff_minimal_compl_nonspanning", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": true, "tactics": ["convert", "simp_rw", "not_disjoint_iff_nonempty_inter,"], "tactic_count": 3}
{"name": "Matroid.IsBase.compl_closure_diff_singleton_isCocircuit", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": false, "tactics": ["rw", "closure_spanning_iff", "have", "refine", "rw", "refine", "rw", "suffices", "refine", "hsp.spanning.superset", "rw", "apply", "exact"], "tactic_count": 13}
{"name": "Matroid.isCocircuit_iff_minimal_compl_nonspanning'", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": true, "tactics": ["rw", "exact", "minimal_iff_minimal_of_imp_of_forall"], "tactic_count": 3}
{"name": "Matroid.IsCircuit.inter_isCocircuit_ne_singleton", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": true, "tactics": ["intro", "have", "simp_rw", "have", "apply", "rw", "nth_rw", "refine", "rw", "closure_union_congr_right", "rw", "exact", "rw", "exact"], "tactic_count": 14}
{"name": "Matroid.IsCircuit.isCocircuit_inter_nontrivial", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact"], "tactic_count": 3}
{"name": "Matroid.IsCircuit.isCocircuit_disjoint_or_nontrivial_inter", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Matroid.dual_rankPos_iff_exists_isCircuit", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": false, "tactics": ["rw", "indep_iff_forall_subset_not_isCircuit]", "exact"], "tactic_count": 3}
{"name": "Matroid.IsCircuit.dual_rankPos", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.exists_isCircuit", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.rankPos_iff_exists_isCocircuit", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.fundCocircuit", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.fundCocircuit_isCocircuit", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": true, "tactics": ["apply", "rw", "exact"], "tactic_count": 3}
{"name": "Matroid.mem_fundCocircuit", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.fundCocircuit_subset_insert_compl", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.fundCocircuit_inter_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": true, "tactics": ["refine", "refine", "simp"], "tactic_count": 3}
{"name": "Matroid.fundCocircuit_eq_of_notMem_ground", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Matroid.fundCocircuit_eq_of_notMem", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "exact", "rw"], "tactic_count": 4}
{"name": "Matroid.Indep.exists_isCocircuit_inter_eq_mem", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": true, "tactics": ["obtain", "refine", "rw", "singleton_subset_iff,", "exact"], "tactic_count": 5}
{"name": "Matroid.IsBase.mem_fundCocircuit_iff_mem_fundCircuit", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Circuit", "is_tactic_proof": true, "tactics": ["suffices", "aux", "clear", "intro", "obtain", "simp", "have", "obtain", "rw", "contradiction", "obtain", "rw", "contradiction", "obtain", "rw", "rw", "have", "refine", "simp", "rw", "union_singleton", "simp"], "tactic_count": 22}
{"name": "Matroid.ground_isFlat", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsFlat.iInter", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": false, "tactics": ["refine", "obtain", "refine", "convert", "rw"], "tactic_count": 5}
{"name": "Matroid.subtypeClosure", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.isFlat_iff_isClosed", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Matroid.isClosed_iff_isFlat", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matroid.closure", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.closure_def", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.instNonemptyElemSetSetOfAndIsFlatSubsetInterE", "kind": "instance", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.closure_eq_subtypeClosure", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": false, "tactics": ["suffices", "exact", "h"], "tactic_count": 3}
{"name": "Matroid.closure_subset_ground", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.ground_subset_closure_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matroid.closure_inter_ground", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Matroid.inter_ground_subset_closure", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Matroid.IsFlat.closure", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.isFlat_closure", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.isFlat_iff_closure_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.closure_ground", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.closure_univ", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.closure_subset_closure", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.closure_mono", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.closure_closure", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.closure_subset_closure_of_subset_closure", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.exists_of_closure_ssubset", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["by_contra", "exact"], "tactic_count": 2}
{"name": "Matroid.notMem_of_mem_diff_closure", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.mem_ground_of_mem_closure", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.closure_iUnion_closure_eq_closure_iUnion", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["simp_rw", "convert", "simp"], "tactic_count": 3}
{"name": "Matroid.closure_iUnion_congr", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matroid.closure_biUnion_closure_eq_closure_sUnion", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.closure_biUnion_closure_eq_closure_biUnion", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.closure_biUnion_congr", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.closure_closure_union_closure_eq_closure_union", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["rw", "simp_rw"], "tactic_count": 2}
{"name": "Matroid.closure_union_closure_right_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.closure_union_closure_left_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.closure_insert_closure_eq_closure_insert", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Matroid.closure_union_congr_left", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.closure_union_congr_right", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.closure_insert_congr_right", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matroid.closure_union_closure_empty_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.closure_empty_union_closure_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.closure_insert_eq_of_mem_closure", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.Indep.closure_eq_setOf_isBasis_insert", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["set", "have", "have", "refine", "exact", "rw", "rintro", "rw", "obtain", "exact", "exact"], "tactic_count": 11}
{"name": "Matroid.Indep.insert_isBasis_iff_mem_closure", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.Indep.isBasis_closure", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.IsBasis.closure_eq_closure", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "Matroid.IsBasis.closure_eq_right", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsBasis'.closure_eq_closure", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.IsBasis.subset_closure", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.IsBasis'.isBasis_closure_right", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.IsBasis.isBasis_closure_right", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.Indep.mem_closure_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Matroid.Indep.mem_closure_iff'", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["rw", "have", "aesop"], "tactic_count": 3}
{"name": "Matroid.Indep.insert_dep_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["rw", "intro"], "tactic_count": 2}
{"name": "Matroid.Indep.mem_closure_iff_of_notMem", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.Indep.insert_indep_iff_of_notMem", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": false, "tactics": ["rw", "and_iff_left", "exact"], "tactic_count": 3}
{"name": "Matroid.Indep.insert_indep_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["obtain", "simp_rw", "rw"], "tactic_count": 3}
{"name": "Matroid.insert_indep_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "simp"], "tactic_count": 3}
{"name": "Matroid.Indep.insert_diff_indep_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["obtain", "simp", "rw"], "tactic_count": 3}
{"name": "Matroid.Indep.isBasis_of_subset_of_subset_closure", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.isBasis_iff_indep_subset_closure", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.Indep.isBase_of_ground_subset_closure", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.IsBase.closure_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.IsBase.closure_of_superset", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.isBase_iff_indep_closure_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Matroid.Indep.isBase_iff_ground_subset_closure", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.Indep.closure_inter_eq_self_of_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["have", "rw", "rintro", "exact"], "tactic_count": 4}
{"name": "Matroid.Indep.closure_sInter_eq_biInter_closure_of_forall_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["rw", "have", "have", "refine", "rw", "have", "refine", "refine", "rw", "exact", "rw", "obtain", "he'.subset_isBasis_of_subset", "have", "rw", "exact", "obtain", "obtain", "hI.eq_of_isBasis", "refine", "obtain", "refine", "specialize", "rw", "exact", "exact"], "tactic_count": 26}
{"name": "Matroid.closure_iInter_eq_iInter_closure_of_iUnion_indep", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "Matroid.closure_sInter_eq_biInter_closure_of_sUnion_indep", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.closure_biInter_eq_biInter_closure_of_biUnion_indep", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["have", "convert"], "tactic_count": 2}
{"name": "Matroid.Indep.closure_iInter_eq_biInter_closure_of_forall_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.Indep.closure_inter_eq_inter_closure", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["rw", "exact", "rwa"], "tactic_count": 3}
{"name": "Matroid.Indep.inter_isBasis_biInter", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["refine", "simp_rw", "closure_biInter_eq_biInter_closure_of_biUnion_indep", "subset_iInter_iff]", "exact"], "tactic_count": 5}
{"name": "Matroid.Indep.inter_isBasis_iInter", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["convert", "hI.inter_isBasis_biInter", "simp", "exact"], "tactic_count": 4}
{"name": "Matroid.Indep.inter_isBasis_sInter", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Matroid.isBasis_iff_isBasis_closure_of_subset'", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.isBasis'_iff_isBasis_closure", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["rw", "exact", "h.1.isBasis_subset"], "tactic_count": 3}
{"name": "Matroid.exists_isBasis_inter_ground_isBasis_closure", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["obtain", "have", "exact"], "tactic_count": 3}
{"name": "Matroid.isBasis_union_iff_indep_closure", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.isBasis_iff_indep_closure", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.Indep.inter_isBasis_closure_iff_subset_closure_inter", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsBasis.closure_inter_isBasis_closure", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Matroid.IsBasis.eq_of_closure_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Matroid.empty_isBasis_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.indep_iff_forall_notMem_closure_diff'", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.Indep.notMem_closure_diff_of_mem", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.Indep.closure_insert_diff_eq_of_mem_closure", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["apply", "simp", "rintro", "exacts", "intro", "obtain", "exacts"], "tactic_count": 7}
{"name": "Matroid.Indep.indep_insert_diff_of_mem_closure", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["simp", "obtain", "exact", "rw", "refine", "exact"], "tactic_count": 6}
{"name": "Matroid.IsBasis.isBasis_insert_diff_of_mem_closure", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["rw", "exact", "hB.2.1.trans_eq", "diff_subset.trans"], "tactic_count": 4}
{"name": "Matroid.IsBase.isBase_insert_diff_of_mem_closure", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["rw", "by_cases", "exact", "obtain", "simpa", "rw", "cases"], "tactic_count": 7}
{"name": "Matroid.indep_iff_forall_closure_diff_ne", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "inter_comm,", "nth_rw", "rw"], "tactic_count": 6}
{"name": "Matroid.Indep.union_indep_iff_forall_notMem_closure_right", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["refine", "rwa", "obtain", "obtain", "exact", "exfalso", "obtain", "have", "rw", "exact", "refine", "rw", "exact"], "tactic_count": 13}
{"name": "Matroid.Indep.union_indep_iff_forall_notMem_closure_left", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Matroid.Indep.closure_ssubset_closure", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["obtain", "exact", "heJ"], "tactic_count": 3}
{"name": "Matroid.Indep.closure_diff_ssubset", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["refine", "rw", "simp"], "tactic_count": 3}
{"name": "Matroid.Indep.closure_diff_singleton_ssubset", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.mem_closure_insert", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["rw", "have", "have", "rw", "obtain", "rw", "rw", "he.1.mem_closure_iff]", "rw", "and_iff_left", "intro", "rw", "subst"], "tactic_count": 13}
{"name": "Matroid.closure_exchange", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.closure_exchange_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.closure_insert_congr", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["have", "rw", "closure_closure,", "closure_closure]"], "tactic_count": 4}
{"name": "Matroid.closure_diff_eq_self", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["rw", "union_eq_self_of_subset_right"], "tactic_count": 2}
{"name": "Matroid.closure_diff_singleton_eq_closure", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.ext_closure", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.Spanning.closure_eq_of_superset", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Matroid.IsBase.spanning", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.ground_spanning", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.spanning_iff_exists_isBase_subset'", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["refine", "obtain", "have", "rw", "exact"], "tactic_count": 5}
{"name": "Matroid.Spanning.exists_isBase_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Matroid.Coindep.compl_spanning", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.Coindep.closure_compl", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.Indep.isBase_of_spanning", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "Matroid.Spanning.isBase_of_indep", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.Indep.eq_of_spanning_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsBasis.spanning_iff_spanning", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.Spanning.isBase_restrict_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["rw", "refine", "exact", "rw", "exact"], "tactic_count": 5}
{"name": "Matroid.Spanning.compl_coindep", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Matroid.IsBasis.isBase_of_spanning", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.Indep.exists_isBase_subset_spanning", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Matroid.Restriction.isBase_iff_of_spanning", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["obtain", "rw"], "tactic_count": 2}
{"name": "Matroid.ext_spanning", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": false, "tactics": ["have", "ext", "refine", "rw", "intro", "rw"], "tactic_count": 6}
{"name": "Matroid.IsBase.eq_of_superset_spanning", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.isBase_iff_minimal_spanning", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["rw", "refine", "obtain", "rwa"], "tactic_count": 4}
{"name": "Matroid.Spanning.isBase_of_minimal", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Matroid.restrict_closure_eq'", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "ext", "rw", "hI'.indep.mem_closure_iff',", "by_cases", "simp", "tauto"], "tactic_count": 8}
{"name": "Matroid.emptyOn_closure_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.loopyOn_closure_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matroid.loopyOn_spanning_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.freeOn_closure_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matroid.uniqueBaseOn_closure_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["rw", "inter_right_comm,"], "tactic_count": 2}
{"name": "Matroid.closure_empty_eq_ground_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["refine", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "Matroid.comap_closure_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "simp_rw", "mem_preimage,", "image_insert_eq]", "intro", "by_cases", "simp", "simp"], "tactic_count": 9}
{"name": "Matroid.map_closure_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": true, "tactics": ["suffices", "obtain", "rw", "image_preimage_inter,", "refine", "simp", "hI.mem_closure_iff']", "constructor", "rintro", "refine", "obtain", "rw", "rwa", "rintro", "refine", "replace", "have", "rwa"], "tactic_count": 18}
{"name": "Matroid.restrict_spanning_iff'", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Closure", "is_tactic_proof": false, "tactics": ["rw", "union_inter_distrib_right,", "intro", "rw"], "tactic_count": 4}
{"name": "Matroid.emptyOn", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.emptyOn_ground", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.emptyOn_isBase_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.emptyOn_indep_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.ground_eq_empty_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Constructions", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Matroid.emptyOn_dual_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Constructions", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.restrict_empty", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Constructions", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matroid.eq_emptyOn_or_nonempty", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Constructions", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Matroid.eq_emptyOn", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Constructions", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Matroid.finite_emptyOn", "kind": "instance", "module": "Mathlib.Combinatorics.Matroid.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.loopyOn", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.loopyOn_ground", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.loopyOn_empty", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Constructions", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.loopyOn_indep_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Constructions", "is_tactic_proof": true, "tactics": ["simp", "rintro"], "tactic_count": 2}
{"name": "Matroid.eq_loopyOn_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Constructions", "is_tactic_proof": true, "tactics": ["simp", "rintro", "refine"], "tactic_count": 3}
{"name": "Matroid.loopyOn_isBase_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Constructions", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matroid.loopyOn_isBasis_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.loopyOn_rankFinite", "kind": "instance", "module": "Mathlib.Combinatorics.Matroid.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.Finite.loopyOn_finite", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.loopyOn_restrict", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Constructions", "is_tactic_proof": true, "tactics": ["refine", "simp", "exact"], "tactic_count": 3}
{"name": "Matroid.empty_isBase_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Constructions", "is_tactic_proof": false, "tactics": ["simp", "true_and,", "exact"], "tactic_count": 3}
{"name": "Matroid.eq_loopyOn_or_rankPos", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Constructions", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.not_rankPos_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Constructions", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.freeOn", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.freeOn_ground", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.freeOn_dual_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Constructions", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.loopyOn_dual_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.freeOn_empty", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Constructions", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matroid.freeOn_isBase_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Constructions", "is_tactic_proof": true, "tactics": ["simp", "eq_comm"], "tactic_count": 2}
{"name": "Matroid.freeOn_indep_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Constructions", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matroid.freeOn_indep", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.freeOn_isBasis_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Constructions", "is_tactic_proof": true, "tactics": ["use", "rintro", "exact"], "tactic_count": 3}
{"name": "Matroid.freeOn_isBasis'_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Constructions", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.eq_freeOn_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Constructions", "is_tactic_proof": true, "tactics": ["refine", "rintro", "simp", "exact"], "tactic_count": 4}
{"name": "Matroid.ground_indep_iff_eq_freeOn", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Constructions", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matroid.freeOn_restrict", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Constructions", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matroid.restrict_eq_freeOn_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Constructions", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.Indep.restrict_eq_freeOn", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Constructions", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Matroid.freeOn_finitary", "kind": "instance", "module": "Mathlib.Combinatorics.Matroid.Constructions", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Matroid.freeOn_rankPos", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Constructions", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matroid.uniqueBaseOn", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.uniqueBaseOn_ground", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.uniqueBaseOn_isBase_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Constructions", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.uniqueBaseOn_inter_ground_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Constructions", "is_tactic_proof": true, "tactics": ["simp", "tauto"], "tactic_count": 2}
{"name": "Matroid.uniqueBaseOn_indep_iff'", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Constructions", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.uniqueBaseOn_indep_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Constructions", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Matroid.uniqueBaseOn_isBasis_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Constructions", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Matroid.uniqueBaseOn_inter_isBasis", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Constructions", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.uniqueBaseOn_dual_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Constructions", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "uniqueBaseOn_ground]", "exact"], "tactic_count": 5}
{"name": "Matroid.uniqueBaseOn_self", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Constructions", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.uniqueBaseOn_empty", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Constructions", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.uniqueBaseOn_restrict'", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Constructions", "is_tactic_proof": false, "tactics": ["simp_rw", "uniqueBaseOn_indep_iff',", "tauto"], "tactic_count": 3}
{"name": "Matroid.uniqueBaseOn_restrict", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Constructions", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.uniqueBaseOn_rankFinite", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Constructions", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "Matroid.uniqueBaseOn_finitary", "kind": "instance", "module": "Mathlib.Combinatorics.Matroid.Constructions", "is_tactic_proof": true, "tactics": ["refine", "simp", "exact"], "tactic_count": 3}
{"name": "Matroid.uniqueBaseOn_rankPos", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.dualIndepMatroid", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Dual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.dual", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Dual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.term_✶", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Dual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid._aux_Mathlib_Combinatorics_Matroid_Dual___macroRules_Matroid_term_✶_1", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Dual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid._aux_Mathlib_Combinatorics_Matroid_Dual___unexpand_Matroid_dual_1", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Dual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.dual_indep_iff_exists'", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Dual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.dual_ground", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Dual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.dual_dep_iff_forall", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Dual", "is_tactic_proof": true, "tactics": ["simp_rw", "not_disjoint_iff_nonempty_inter,"], "tactic_count": 2}
{"name": "Matroid.dual_finite", "kind": "instance", "module": "Mathlib.Combinatorics.Matroid.Dual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.dual_nonempty", "kind": "instance", "module": "Mathlib.Combinatorics.Matroid.Dual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.dual_isBase_iff'", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Dual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.setOf_dual_isBase_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Dual", "is_tactic_proof": true, "tactics": ["ext", "simp", "refine", "rwa"], "tactic_count": 4}
{"name": "Matroid.dual_dual", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Dual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.dual_involutive", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Dual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.dual_injective", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Dual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.dual_inj", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Dual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.eq_dual_comm", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Dual", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.eq_dual_iff_dual_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Dual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsBase.compl_isBase_of_dual", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Dual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsBase.compl_isBase_dual", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Dual", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Matroid.IsBase.compl_inter_isBasis_of_inter_isBasis", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Dual", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact", "simp", "simp_rw", "and_iff_left", "refine", "rw", "singleton_inter_eq_empty,", "diff_eq_empty]", "obtain", "have", "refine", "simp_rw", "iff_false_intro", "exact"], "tactic_count": 16}
{"name": "Matroid.ground_not_isBase", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Dual", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Matroid.IsBase.ssubset_ground", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Dual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.Indep.ssubset_ground", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Dual", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "Matroid.Coindep", "kind": "abbrev", "module": "Mathlib.Combinatorics.Matroid.Dual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.coindep_def", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Dual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.Coindep.indep", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Dual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.dual_coindep_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Dual", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.Indep.coindep", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Dual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.coindep_iff_exists'", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Dual", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Matroid.coindep_iff_subset_compl_isBase", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Dual", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Matroid.Coindep.subset_ground", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Dual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.Coindep.exists_isBase_subset_compl", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Dual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.Coindep.exists_subset_compl_isBase", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Dual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IndepMatroid.matroid", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.IndepAxioms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IndepMatroid.matroid_indep_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.IndepAxioms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IndepMatroid.ofFinitary", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.IndepAxioms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IndepMatroid.ofFinitary_indep", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.IndepAxioms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IndepMatroid.ofFinitary_finitary", "kind": "instance", "module": "Mathlib.Combinatorics.Matroid.IndepAxioms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IndepMatroid.ofFinitaryCardAugment", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.IndepAxioms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IndepMatroid.ofFinitaryCardAugment_indep", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.IndepAxioms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IndepMatroid.ofFinitaryCardAugment_finitary", "kind": "instance", "module": "Mathlib.Combinatorics.Matroid.IndepAxioms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.existsMaximalSubsetProperty_of_bdd", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.IndepAxioms", "is_tactic_proof": true, "tactics": ["obtain", "rintro", "have", "rw", "simp_rw", "use", "rintro", "obtain", "rwa", "obtain", "refine", "have", "refine", "exact"], "tactic_count": 14}
{"name": "IndepMatroid.ofBdd", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.IndepAxioms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IndepMatroid.ofBdd_indep", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.IndepAxioms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IndepMatroid.instRankFiniteMatroidOfBdd", "kind": "instance", "module": "Mathlib.Combinatorics.Matroid.IndepAxioms", "is_tactic_proof": true, "tactics": ["obtain", "refine", "obtain", "exact"], "tactic_count": 4}
{"name": "IndepMatroid.ofBddAugment", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.IndepAxioms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IndepMatroid.ofBddAugment_E", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.IndepAxioms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IndepMatroid.ofBddAugment_indep", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.IndepAxioms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IndepMatroid.ofBddAugment_rankFinite", "kind": "instance", "module": "Mathlib.Combinatorics.Matroid.IndepAxioms", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "IndepMatroid.ofFinite", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.IndepAxioms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IndepMatroid.ofFinite_E", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.IndepAxioms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IndepMatroid.ofFinite_indep", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.IndepAxioms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IndepMatroid.ofFinite_finite", "kind": "instance", "module": "Mathlib.Combinatorics.Matroid.IndepAxioms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IndepMatroid.ofFinset", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.IndepAxioms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IndepMatroid.ofFinset_E", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.IndepAxioms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IndepMatroid.ofFinset_indep", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.IndepAxioms", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "IndepMatroid.ofFinset_indep'", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.IndepAxioms", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matroid.ofExistsMatroid", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.IndepAxioms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.ofBase", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.IndepAxioms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.ofExistsFiniteIsBase", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.IndepAxioms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.ofExistsFiniteIsBase_isBase", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.IndepAxioms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.ofExistsFiniteIsBase_rankFinite", "kind": "instance", "module": "Mathlib.Combinatorics.Matroid.IndepAxioms", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Matroid.ofIsBaseOfFinite", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.IndepAxioms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.ofIsBaseOfFinite_E", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.IndepAxioms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.ofIsBaseOfFinite_isBase", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.IndepAxioms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.ofBaseOfFinite_finite", "kind": "instance", "module": "Mathlib.Combinatorics.Matroid.IndepAxioms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "initFn._@.Mathlib.Combinatorics.Matroid.Init.3819442404._hygCtx._hyg.3", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.loops", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.loops_subset_ground", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsLoop", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.isLoop_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.closure_empty", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsLoop.mem_ground", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.isLoop_tfae", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["tfae_have", "tfae_have", "simp", "ssubset_singleton_iff]", "tfae_have", "tfae_have", "simp", "refine", "obtain", "exact", "tfae_finish"], "tactic_count": 11}
{"name": "Matroid.singleton_dep", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.singleton_isCircuit", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.isLoop_iff_forall_mem_compl_isBase", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsLoop.mem_closure", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsLoop.mem_of_isFlat", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsFlat.loops_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsLoop.not_indep_of_mem", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsLoop.notMem_of_indep", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsLoop.eq_of_isCircuit_mem", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.Indep.disjoint_loops", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": ["let"], "tactic_count": 1}
{"name": "Matroid.Indep.eq_empty_of_subset_loops", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.isBasis_loops_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.closure_eq_loops_of_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.isBasis_iff_empty_of_subset_loops", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["refine", "have", "simpa"], "tactic_count": 3}
{"name": "Matroid.IsLoop.closure", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.isLoop_iff_closure_eq_loops_and_mem_ground", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.closure_loops", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.closure_union_loops_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.closure_loops_union_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matroid.closure_diff_loops_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["rw", "union_empty]"], "tactic_count": 2}
{"name": "Matroid.restrict_loops_eq'", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.restrict_loops_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.restrict_isLoop_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["simp", "tauto"], "tactic_count": 2}
{"name": "Matroid.IsRestriction.isLoop_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["obtain", "simp", "exact"], "tactic_count": 3}
{"name": "Matroid.IsLoop.of_isRestriction", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsLoop.isLoop_isRestriction", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.map_loops", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matroid.mapEmbedding_isLoop_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matroid.comap_loops", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.comap_isLoop_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matroid.loopyOn_isLoop_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matroid.eq_loopyOn_iff_loops", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.restrict_subset_loops_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["rw", "union_eq_self_of_subset_right"], "tactic_count": 2}
{"name": "Matroid.freeOn_not_isLoop", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matroid.uniqueBaseOn_isLoop_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matroid.eq_loopyOn_iff_loops_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsLoop.not_isNonloop", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.compl_loops_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matroid.isNonloop_iff_mem_compl_loops", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.setOf_isNonloop_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.not_isNonloop_iff_closure", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "simp"], "tactic_count": 3}
{"name": "Matroid.indep_singleton", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Matroid.Indep.isNonloop_of_mem", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.IsNonloop.exists_mem_isBase", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Matroid.IsCocircuit.isNonloop_of_mem", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["rw", "intro", "obtain", "exact"], "tactic_count": 4}
{"name": "Matroid.IsCircuit.isNonloop_of_mem", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsCircuit.isNonloop_of_mem_of_one_lt_card", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "Matroid.IsNonloop.mem_closure_singleton", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Matroid.IsNonloop.mem_closure_comm", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsNonloop.isNonloop_of_mem_closure", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["rw", "by_contra", "rw", "obtain", "rw", "rw"], "tactic_count": 6}
{"name": "Matroid.IsNonloop.closure_eq_of_mem_closure", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["rw", "closure_closure", "closure_insert_closure_eq_closure_insert,"], "tactic_count": 3}
{"name": "Matroid.IsNonloop.closure_eq_closure_iff_isCircuit_of_ne", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["refine", "have", "rw", "singleton_subset_iff,", "suffices", "rw", "simp", "have", "rwa"], "tactic_count": 9}
{"name": "Matroid.IsNonloop.closure_eq_closure_iff_eq_or_dep", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["obtain", "exact", "simp_rw", "isCircuit_iff_dep_forall_diff_singleton_indep,", "and_iff_left", "rintro", "rwa", "rwa"], "tactic_count": 8}
{"name": "Matroid.exists_isNonloop", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsNonloop.rankPos", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.restrict_isNonloop_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.IsNonloop.of_restrict", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsNonloop.of_isRestriction", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "Matroid.isNonloop_iff_restrict_of_mem", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.comap_isNonloop_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.freeOn_isNonloop_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.uniqueBaseOn_isNonloop_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.IsNonloop.exists_mem_isCocircuit", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Matroid.closure_inter_setOf_isNonloop_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.IsColoop", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.coloops", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsColoop.mem_ground", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.coloops_subset_ground", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.isColoop_iff_mem_coloops", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.dual_loops", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.dual_coloops", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.IsColoop.dual_isLoop", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsColoop.isCocircuit", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsLoop.dual_isColoop", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Matroid.dual_isColoop_iff_isLoop", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.dual_isLoop_iff_isColoop", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.singleton_isCocircuit", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matroid.isColoop_tfae", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["tfae_have", "tfae_have", "tfae_have", "simp_rw", "refine", "obtain", "assumption", "tfae_have", "tfae_have", "refine", "rw", "obtain", "exact", "tfae_have", "refine", "obtain", "exact", "simpa", "tfae_have", "wlog", "exact", "rw", "diff_diff_cancel_left", "tfae_finish"], "tactic_count": 24}
{"name": "Matroid.isColoop_iff_forall_mem_isBase", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsBase.mem_of_isColoop", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsColoop.mem_of_isBase", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsBase.coloops_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsColoop.isNonloop", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsLoop.not_isColoop", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Matroid.IsColoop.notMem_isCircuit", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsCircuit.disjoint_coloops", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.isColoop_iff_forall_mem_compl_isCircuit", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "obtain", "exact"], "tactic_count": 4}
{"name": "Matroid.IsCircuit.not_isColoop_of_mem", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.isColoop_iff_forall_mem_closure_iff_mem", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.isColoop_iff_forall_mem_closure_iff_mem'", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": ["refine", "isColoop_iff_forall_mem_closure_iff_mem.2", "rw"], "tactic_count": 3}
{"name": "Matroid.IsColoop.mem_closure_iff_mem", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsColoop.mem_of_mem_closure", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.isColoop_iff_diff_not_spanning", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.isColoop_iff_diff_closure", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.IsBase.isColoop_iff_forall_notMem_fundCircuit", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["refine", "have", "rintro", "obtain", "exact", "have", "refine", "simpa", "simp", "rw", "exact"], "tactic_count": 11}
{"name": "Matroid.IsBasis'.inter_coloops_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["intro", "rwa"], "tactic_count": 2}
{"name": "Matroid.IsBasis.inter_coloops_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.exists_mem_isCircuit_of_not_isColoop", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["simp", "obtain", "exact"], "tactic_count": 3}
{"name": "Matroid.closure_inter_coloops_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["simp_rw", "intro", "rw"], "tactic_count": 3}
{"name": "Matroid.closure_inter_eq_of_subset_coloops", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["nth_rw", "rw"], "tactic_count": 2}
{"name": "Matroid.closure_union_eq_of_subset_coloops", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": ["rw", "eq_empty_iff_forall_notMem]", "refine", "obtain", "rw", "exact"], "tactic_count": 6}
{"name": "Matroid.closure_insert_isColoop_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.closure_eq_of_subset_coloops", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.closure_diff_eq_of_subset_coloops", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["nth_rw", "rw", "diff_eq_empty.mpr", "rintro", "rw", "exact"], "tactic_count": 6}
{"name": "Matroid.closure_disjoint_of_disjoint_of_subset_coloops", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Matroid.closure_disjoint_coloops_of_disjoint_coloops", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.closure_union_coloops_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsColoop.notMem_closure_of_notMem", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsColoop.insert_indep_of_indep", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "Matroid.union_indep_iff_indep_of_subset_coloops", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact"], "tactic_count": 3}
{"name": "Matroid.diff_indep_iff_indep_of_subset_coloops", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.union_coloops_indep_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.diff_coloops_indep_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.coloops_indep", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Matroid.restrict_isColoop_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["wlog", "exact", "rw", "simp", "aesop"], "tactic_count": 5}
{"name": "Matroid.ext_indep_disjoint_loops_coloops", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["refine", "rw", "obtain", "rw", "rw", "exact", "obtain", "refine", "rw", "rw", "exact"], "tactic_count": 11}
{"name": "Matroid.loops_eq_empty", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.not_isLoop", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.loopless_iff_forall_isNonloop", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.loopless_iff_forall_not_isLoop", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.loopless_iff_forall_isCircuit", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": ["suffices", "rw", "contrapose", "exact", "refine", "obtain", "simpa", "exact"], "tactic_count": 8}
{"name": "Matroid.Loopless.ground_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsRestriction.loopless", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["obtain", "rw"], "tactic_count": 2}
{"name": "Matroid.instRankPosOfNonemptyOfLoopless", "kind": "instance", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.loopyOn_isLoopless_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matroid.removeLoops", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.removeLoops_eq_restrict", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.removeLoops_ground_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.removeLoops_loopless", "kind": "instance", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matroid.removeLoops_eq_self", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.removeLoops_eq_self_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["refine", "rw", "infer_instance"], "tactic_count": 3}
{"name": "Matroid.removeLoops_isRestriction", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.eq_restrict_removeLoops", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["rw", "simp", "exact"], "tactic_count": 3}
{"name": "Matroid.removeLoops_indep_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["ext", "rw", "exact"], "tactic_count": 3}
{"name": "Matroid.removeLoops_isBasis'_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Matroid.removeLoops_isBase_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "Matroid.removeLoops_isNonloop_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "Matroid.IsNonloop.removeLoops_isNonloop", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Matroid.removeLoops_idem", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matroid.removeLoops_restrict_eq_restrict", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Matroid.restrict_univ_removeLoops_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Matroid.IsRestriction.isRestriction_removeLoops", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Matroid.removeLoops_mono_isRestriction", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Loop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.comap", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.comap_indep_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.comap_ground_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.comap_dep_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": true, "tactics": ["rw", "refine", "rintro", "exact", "rw", "simpa"], "tactic_count": 6}
{"name": "Matroid.comap_id", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.comap_indep_iff_of_injOn", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": true, "tactics": ["rw", "refine", "apply"], "tactic_count": 3}
{"name": "Matroid.comap_emptyOn", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matroid.comap_loopyOn", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.comap_isBasis_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": true, "tactics": ["refine", "obtain", "refine", "simp", "obtain", "have", "replace", "simp", "not_and,", "exact", "refine", "simp", "have", "simp_rw", "exact", "suffices", "simpa", "exact"], "tactic_count": 18}
{"name": "Matroid.comap_isBase_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.comap_isBasis'_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": false, "tactics": ["simp", "subset_inter_iff,", "exact"], "tactic_count": 3}
{"name": "Matroid.comap_finitary", "kind": "instance", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": true, "tactics": ["refine", "rw", "simp", "refine", "obtain", "rw", "exact"], "tactic_count": 7}
{"name": "Matroid.comap_rankFinite", "kind": "instance", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": true, "tactics": ["obtain", "refine", "simp", "exact"], "tactic_count": 4}
{"name": "Matroid.comapOn", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.comapOn_preimage_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.comapOn_indep_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matroid.comapOn_ground_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.comapOn_isBase_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.comapOn_isBase_iff_of_surjOn", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": true, "tactics": ["simp_rw", "inter_eq_self_of_subset_right"], "tactic_count": 2}
{"name": "Matroid.comapOn_isBase_iff_of_bijOn", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": false, "tactics": ["rw", "suffices", "exact"], "tactic_count": 3}
{"name": "Matroid.comapOn_dual_eq_of_bijOn", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": true, "tactics": ["refine", "rw", "comapOn_ground_eq,", "h.image_eq]", "exact"], "tactic_count": 5}
{"name": "Matroid.comapOn_finitary", "kind": "instance", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.comapOn_rankFinite", "kind": "instance", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.mapSetEmbedding", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.mapSetEmbedding_ground", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.mapSetEmbedding_indep_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.Indep.exists_eq_image_of_mapSetEmbedding", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.mapSetEmbedding_indep_iff'", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": true, "tactics": ["simp", "constructor", "rintro", "exact", "rintro", "rw", "exact"], "tactic_count": 7}
{"name": "Matroid.map", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.map_ground", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.map_indep_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.Indep.map", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.Indep.exists_bijOn_of_map", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Matroid.map_image_indep_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw"], "tactic_count": 3}
{"name": "Matroid.map_isBase_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": true, "tactics": ["rw", "refine", "obtain", "refine", "rw", "exact", "rintro", "rw", "refine", "obtain", "rw", "rw"], "tactic_count": 12}
{"name": "Matroid.IsBase.map", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.map_dep_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": true, "tactics": ["simp", "constructor", "rintro", "exact", "rintro", "refine", "rw", "subst"], "tactic_count": 8}
{"name": "Matroid.map_image_isBase_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw"], "tactic_count": 3}
{"name": "Matroid.IsBasis.map", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": true, "tactics": ["refine", "rintro", "have", "rw", "simp", "intro", "rw", "obtain", "exact"], "tactic_count": 9}
{"name": "Matroid.map_isBasis_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": true, "tactics": ["refine", "obtain", "rw", "obtain", "have", "refine", "have", "rw", "exact"], "tactic_count": 9}
{"name": "Matroid.map_isBasis_iff'", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": true, "tactics": ["refine", "obtain", "obtain", "rw", "exact", "rintro", "exact"], "tactic_count": 7}
{"name": "Matroid.map_dual", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": true, "tactics": ["apply", "simp", "dual_isBase_iff']", "intro", "simp_rw", "dual_isBase_iff", "exact"], "tactic_count": 7}
{"name": "Matroid.map_emptyOn", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matroid.map_loopyOn", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matroid.map_freeOn", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.map_id", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matroid.map_comap", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": true, "tactics": ["refine", "simp", "exact"], "tactic_count": 3}
{"name": "Matroid.comap_map", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matroid.instNonemptyMap", "kind": "instance", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.instFiniteMap", "kind": "instance", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.instFinitaryMap", "kind": "instance", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": true, "tactics": ["refine", "simp", "have", "intro", "obtain", "exact", "obtain", "refine", "specialize", "rwa"], "tactic_count": 10}
{"name": "Matroid.instRankFiniteMap", "kind": "instance", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.instRankPosMap", "kind": "instance", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.mapSetEquiv", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.mapSetEquiv_indep_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.mapSetEquiv.ground", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.mapEmbedding", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.mapEmbedding_ground_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.mapEmbedding_indep_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": true, "tactics": ["rw", "refine", "rintro", "rw", "exact"], "tactic_count": 5}
{"name": "Matroid.Indep.mapEmbedding", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Matroid.IsBase.mapEmbedding", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Matroid.IsBasis.mapEmbedding", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "Matroid.mapEmbedding_isBase_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": true, "tactics": ["rw", "refine", "rintro", "rw", "exact"], "tactic_count": 5}
{"name": "Matroid.mapEmbedding_isBasis_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": true, "tactics": ["rw", "refine", "rintro", "simp", "obtain", "obtain", "exact"], "tactic_count": 7}
{"name": "Matroid.instNonemptyMapEmbedding", "kind": "instance", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.instFiniteMapEmbedding", "kind": "instance", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.instFinitaryMapEmbedding", "kind": "instance", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.instRankFiniteMapEmbedding", "kind": "instance", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.instRankPosMapEmbedding", "kind": "instance", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.mapEquiv", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.mapEquiv_ground_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.mapEquiv_eq_map", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.mapEquiv_indep_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Matroid.mapEquiv_dep_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Matroid.mapEquiv_isBase_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Matroid.mapEquiv_isBasis_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": true, "tactics": ["rw", "refine", "obtain", "simpa"], "tactic_count": 4}
{"name": "Matroid.instNonemptyMapEquiv", "kind": "instance", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.instFiniteMapEquiv", "kind": "instance", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.instFinitaryMapEquiv", "kind": "instance", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.instRankFiniteMapEquiv", "kind": "instance", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.instRankPosMapEquiv", "kind": "instance", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.restrictSubtype", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.restrictSubtype_ground", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matroid.restrictSubtype_indep_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matroid.restrictSubtype_indep_iff_of_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.restrictSubtype_inter_indep_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matroid.restrictSubtype_isBasis_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": false, "tactics": ["rw", "isBasis_restrict_iff',", "simp", "exact"], "tactic_count": 4}
{"name": "Matroid.restrictSubtype_isBase_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Matroid.restrictSubtype_ground_isBase_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.restrictSubtype_ground_isBasis_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.eq_of_restrictSubtype_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": true, "tactics": ["subst", "refine", "rwa"], "tactic_count": 3}
{"name": "Matroid.restrictSubtype_dual", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": false, "tactics": ["rw", "comapOn_preimage_eq,", "exact"], "tactic_count": 3}
{"name": "Matroid.restrictSubtype_dual'", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.map_val_restrictSubtype_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matroid.map_val_restrictSubtype_ground_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matroid.instFinitaryElemRestrictSubtype", "kind": "instance", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.instRankFiniteElemRestrictSubtype", "kind": "instance", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.instFiniteElemERestrictSubtype", "kind": "instance", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.instNonemptyElemERestrictSubtype", "kind": "instance", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.instRankPosElemERestrictSubtype", "kind": "instance", "module": "Mathlib.Combinatorics.Matroid.Map", "is_tactic_proof": true, "tactics": ["obtain", "have", "exact"], "tactic_count": 3}
{"name": "Matroid.contract", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.term_／_", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid._aux_Mathlib_Combinatorics_Matroid_Minor_Contract___macroRules_Matroid_term_／__1", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid._aux_Mathlib_Combinatorics_Matroid_Minor_Contract___unexpand_Matroid_contract_1", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.contract_ground", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.dual_delete_dual", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.dual_delete", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.dual_contract", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.dual_contract_dual", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matroid.contract_contract", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matroid.contract_comm", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matroid.dual_contract_delete", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matroid.dual_delete_contract", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matroid.contract_eq_self_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.contractElem_eq_self", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.contract_empty", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.contract_contract_eq_contract_diff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matroid.contract_eq_contract_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.contract_inter_ground_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.contract_ground_subset_ground", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.coindep_contract_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.Coindep.coindep_contract_of_disjoint", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.contract_isCocircuit_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.Indep.contract_isBase_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": false, "tactics": ["rw", "and_congr_left_iff,", "union_subset_iff,", "simp", "rwa"], "tactic_count": 5}
{"name": "Matroid.Indep.contract_indep_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Matroid.IsNonloop.contractElem_indep_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matroid.Indep.union_indep_iff_contract_indep", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.Indep.diff_indep_contract_of_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Matroid.Indep.contract_dep_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": false, "tactics": ["rw", "and_iff_left", "tauto"], "tactic_count": 3}
{"name": "Matroid.IsBasis.contract_eq_contract_delete", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": false, "tactics": ["nth_rw", "delete_delete,", "refine", "have", "rw", "and_iff_right", "exact", "rw", "and_comm]"], "tactic_count": 9}
{"name": "Matroid.Indep.union_isBasis_union_of_contract_isBasis", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "rw", "rw", "diff_union_of_subset"], "tactic_count": 5}
{"name": "Matroid.IsBasis'.contract_isBasis'_diff_diff_of_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": false, "tactics": ["suffices", "simpa", "disjoint_sdiff_left,", "subset_antisymm_iff,", "exact"], "tactic_count": 5}
{"name": "Matroid.IsBasis'.contract_isBasis'_diff_of_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Matroid.IsBasis.contract_isBasis_diff_diff_of_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "Matroid.IsBasis.contract_diff_isBasis_diff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["refine", "rw", "hIX.eq_of_subset_indep", "diff_self_inter]", "exact", "refine"], "tactic_count": 6}
{"name": "Matroid.IsBasis'.contract_isBasis_union_union", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Matroid.IsBasis.contract_isBasis_union_union", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "Matroid.IsBasis'.contract_eq_contract_delete", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["rw", "delete_inter_ground_eq,"], "tactic_count": 2}
{"name": "Matroid.IsBasis'.contract_indep_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["rw", "disjoint_union_right,"], "tactic_count": 2}
{"name": "Matroid.IsBasis.contract_indep_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsBasis'.contract_dep_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["rw", "disjoint_union_right,"], "tactic_count": 2}
{"name": "Matroid.IsBasis.contract_dep_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsBasis.contract_indep_iff_of_disjoint", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.IsBasis.contract_indep_diff_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.IsBasis'.contract_indep_diff_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.IsBasis.contract_isBasis_of_isBasis'", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "refine", "rotate_left", "rw", "closure_union_congr_left", "exact", "subset_closure_of_subset", "all_goals"], "tactic_count": 10}
{"name": "Matroid.IsBasis'.contract_isBasis'", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Matroid.IsBasis.contract_isBasis", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsBasis.contract_isBasis_of_disjoint", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "Matroid.IsBasis'.contract_isBasis_of_indep", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsBasis.contract_isBasis_of_indep", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsBasis.contract_isBasis_of_disjoint_indep", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Matroid.Indep.of_contract", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.contract_finite", "kind": "instance", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "Matroid.contract_rankFinite", "kind": "instance", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.contract_finitary", "kind": "instance", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["obtain", "suffices", "rw", "infer_instance", "exact", "hJ.indep.contract_indep_iff.2", "indep_of_forall_finite_subset_indep"], "tactic_count": 7}
{"name": "Matroid.contract_eq_delete_of_subset_loops", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matroid.contract_eq_delete_of_subset_coloops", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.contract_isLoop_iff_mem_closure", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["obtain", "rw", "hI.indep.insert_dep_iff,", "by_cases", "simp", "simp"], "tactic_count": 6}
{"name": "Matroid.contract_loops_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matroid.contract_coloops_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.contract_isColoop_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matroid.IsNonloop.of_contract", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Matroid.contract_isNonloop_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "Matroid.IsBasis.diff_subset_loops_contract", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Matroid.contract_closure_eq_contract_delete", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["wlog", "rw", "diff_eq_empty.2", "obtain", "rw", "diff_union_diff_cancel"], "tactic_count": 6}
{"name": "Matroid.contract_closure_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": false, "tactics": ["rw", "contract_contract,", "diff_subset_iff]", "simp", "refine"], "tactic_count": 5}
{"name": "Matroid.contract_spanning_iff'", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "Matroid.Spanning.contract", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "Matroid.Spanning.contract_eq_loopyOn", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Matroid.IsCircuit.contract_isCircuit", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": false, "tactics": ["suffices", "simpa", "diff_union_of_subset", "exact"], "tactic_count": 4}
{"name": "Matroid.IsCircuit.contractElem_isCircuit", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsCircuit.contract_dep", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["obtain", "rw", "contract_ground,", "exact"], "tactic_count": 4}
{"name": "Matroid.IsCircuit.contract_dep_of_not_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["have", "simp", "have", "rwa"], "tactic_count": 4}
{"name": "Matroid.IsCircuit.contract_diff_isCircuit", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["simpa", "hC.contract_isCircuit"], "tactic_count": 2}
{"name": "Matroid.IsCircuit.exists_subset_isCircuit_of_contract", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["wlog", "obtain", "rw", "obtain", "exact", "obtain", "obtain", "refine", "have", "rw", "refine", "rw", "exact"], "tactic_count": 13}
{"name": "Matroid.IsCocircuit.of_contract", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Matroid.IsCocircuit.delete_isCocircuit", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Matroid.IsCocircuit.delete_diff_isCocircuit", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Matroid.contract_delete_diff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.contract_restrict_eq_restrict_contract", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["refine", "obtain", "have", "simpa", "rw", "have", "tauto_set"], "tactic_count": 7}
{"name": "Matroid.restrict_contract_eq_contract_restrict", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Matroid.contract_delete_comm", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["wlog", "rw", "inter_assoc,", "rw", "restrict_contract_eq_contract_restrict"], "tactic_count": 5}
{"name": "Matroid.contract_delete_comm'", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.delete_contract_eq_diff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.delete_contract_comm'", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.contract_delete_contract'", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.contract_delete_contract", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.contract_delete_contract_delete'", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.contract_delete_contract_delete", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.delete_contract_delete'", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.delete_contract_delete", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Contract", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.delete", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Minor.Delete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.term_＼_", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Minor.Delete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid._aux_Mathlib_Combinatorics_Matroid_Minor_Delete___macroRules_Matroid_term_＼__1", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Minor.Delete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid._aux_Mathlib_Combinatorics_Matroid_Minor_Delete___unexpand_Matroid_delete_1", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Minor.Delete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.delete_eq_restrict", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Delete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.restrict_compl", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Delete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.delete_isRestriction", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Delete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsRestriction.exists_eq_delete", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Delete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.isRestriction_iff_exists_eq_delete", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Delete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.delete_ground", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Delete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.delete_subset_ground", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Delete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.delete_eq_self_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Delete", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.deleteElem_eq_self", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Delete", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Matroid.delete_delete", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Delete", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Matroid.delete_comm", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Delete", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.delete_inter_ground_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Delete", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.delete_eq_delete_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Delete", "is_tactic_proof": true, "tactics": ["rw", "refine", "apply_fun", "simp_rw", "assumption"], "tactic_count": 5}
{"name": "Matroid.delete_empty", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Delete", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Matroid.delete_delete_eq_delete_diff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Delete", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matroid.IsRestriction.restrict_delete_of_disjoint", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Delete", "is_tactic_proof": true, "tactics": ["obtain", "refine", "rwa"], "tactic_count": 3}
{"name": "Matroid.IsRestriction.isRestriction_deleteElem", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Delete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.delete_indep_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Delete", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.deleteElem_indep_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Delete", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matroid.Indep.of_delete", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Delete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.Indep.indep_delete_of_disjoint", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Delete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.indep_iff_delete_of_disjoint", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Delete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.delete_dep_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Delete", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.delete_isBase_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Delete", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.delete_isBasis_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Delete", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.delete_isBasis'_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Delete", "is_tactic_proof": false, "tactics": ["rw", "diff_eq,", "exact"], "tactic_count": 3}
{"name": "Matroid.IsBasis.of_delete", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Delete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsBasis.delete", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Delete", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.Coindep.delete_isBase_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Delete", "is_tactic_proof": true, "tactics": ["rw", "refine", "have", "rw", "have", "rw", "exact", "exact"], "tactic_count": 8}
{"name": "Matroid.Coindep.delete_rankPos", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Delete", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Matroid.Coindep.delete_spanning_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Delete", "is_tactic_proof": false, "tactics": ["simp", "and_congr_left_iff,", "refine", "exact"], "tactic_count": 4}
{"name": "Matroid.delete_isLoop_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Delete", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.delete_isNonloop_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Delete", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.IsNonloop.of_delete", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Delete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.isNonloop_iff_delete_of_notMem", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Delete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.delete_loops_eq_removeLoops", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Delete", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.delete_isCircuit_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Delete", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Matroid.IsCircuit.of_delete", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Delete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.circuit_iff_delete_of_disjoint", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Delete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.delete_closure_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Delete", "is_tactic_proof": false, "tactics": ["rw", "inter_assoc", "exact"], "tactic_count": 3}
{"name": "Matroid.delete_closure_eq_of_disjoint", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Delete", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.delete_loops_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Delete", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matroid.delete_isColoop_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Delete", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Matroid.delete_finitary", "kind": "instance", "module": "Mathlib.Combinatorics.Matroid.Minor.Delete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.delete_finite", "kind": "instance", "module": "Mathlib.Combinatorics.Matroid.Minor.Delete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.delete_rankFinite", "kind": "instance", "module": "Mathlib.Combinatorics.Matroid.Minor.Delete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsMinor", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Minor.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.term_≤m_", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Minor.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid._aux_Mathlib_Combinatorics_Matroid_Minor_Order___macroRules_Matroid_term_≤m__1", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Minor.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid._aux_Mathlib_Combinatorics_Matroid_Minor_Order___unexpand_Matroid_IsMinor_1", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Minor.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.contract_delete_isMinor", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsMinor.exists_eq_contract_delete_disjoint", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Order", "is_tactic_proof": true, "tactics": ["obtain", "exact", "disjoint_sdiff_right.mono_left"], "tactic_count": 3}
{"name": "Matroid.IsStrictMinor", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Minor.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.term_<m_", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Minor.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid._aux_Mathlib_Combinatorics_Matroid_Minor_Order___macroRules_Matroid_term_<m__1", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Minor.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid._aux_Mathlib_Combinatorics_Matroid_Minor_Order___unexpand_Matroid_IsStrictMinor_1", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Minor.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsMinor.subset", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Order", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Matroid.IsMinor.refl", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsMinor.trans", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Order", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "exact"], "tactic_count": 3}
{"name": "Matroid.IsMinor.eq_of_ground_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Order", "is_tactic_proof": true, "tactics": ["obtain", "rw", "rw", "delete_empty]"], "tactic_count": 4}
{"name": "Matroid.IsMinor.antisymm", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.instPartialOrder", "kind": "instance", "module": "Mathlib.Combinatorics.Matroid.Minor.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsMinor.le", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsStrictMinor.lt", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.le_eq_isMinor", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.lt_eq_isStrictMinor", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.isStrictMinor_iff_isMinor_ne", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsStrictMinor.ne", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.isStrictMinor_irrefl", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsStrictMinor.isMinor", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsStrictMinor.not_isMinor", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsStrictMinor.ssubset", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.isStrictMinor_iff_isMinor_ssubset", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsStrictMinor.trans_isMinor", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsMinor.trans_isStrictMinor", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsStrictMinor.trans", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.Indep.of_isMinor", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Order", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Matroid.IsNonloop.of_isMinor", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Order", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Matroid.Dep.of_isMinor", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsLoop.of_isMinor", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Order", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Matroid.restrictIndepMatroid", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.restrict", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.term_↾_", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid._aux_Mathlib_Combinatorics_Matroid_Minor_Restrict___macroRules_Matroid_term_↾__1", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid._aux_Mathlib_Combinatorics_Matroid_Minor_Restrict___unexpand_Matroid_restrict_1", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.restrict_indep_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.Indep.indep_restrict_of_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.Indep.of_restrict", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.restrict_ground_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.restrict_finite", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.restrict_dep_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.restrict_ground_eq_self", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": true, "tactics": ["refine"], "tactic_count": 1}
{"name": "Matroid.restrict_restrict_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": true, "tactics": ["refine", "simp", "exact"], "tactic_count": 3}
{"name": "Matroid.restrict_idem", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.isBase_restrict_iff'", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Matroid.IsBasis'.isBase_restrict", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsBasis.restrict_isBase", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.restrict_rankFinite", "kind": "instance", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.restrict_finitary", "kind": "instance", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": true, "tactics": ["refine", "simp", "rw", "exact"], "tactic_count": 4}
{"name": "Matroid.IsBasis.isBase_restrict", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsBasis.isBasis_restrict_of_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Matroid.isBasis'_restrict_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": true, "tactics": ["simp_rw", "tauto"], "tactic_count": 2}
{"name": "Matroid.isBasis_restrict_iff'", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": false, "tactics": ["rw", "isBasis'_iff_isBasis_inter_ground]", "intro", "rw", "exact"], "tactic_count": 5}
{"name": "Matroid.isBasis'_iff_isBasis_restrict_univ", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.restrict_eq_restrict_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": true, "tactics": ["refine", "rw", "restrict_indep_iff]", "rw"], "tactic_count": 4}
{"name": "Matroid.restrict_eq_self_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsRestriction", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsStrictRestriction", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.term_≤r_", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid._aux_Mathlib_Combinatorics_Matroid_Minor_Restrict___macroRules_Matroid_term_≤r__1", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid._aux_Mathlib_Combinatorics_Matroid_Minor_Restrict___unexpand_Matroid_IsRestriction_1", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.term_<r_", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid._aux_Mathlib_Combinatorics_Matroid_Minor_Restrict___macroRules_Matroid_term_<r__1", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid._aux_Mathlib_Combinatorics_Matroid_Minor_Restrict___unexpand_Matroid_IsStrictRestriction_1", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.instCoeOutMatroidᵣ", "kind": "instance", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.Matroidᵣ.coe_inj", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.instPartialOrderMatroidᵣ", "kind": "instance", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.Matroidᵣ.le_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.Matroidᵣ.lt_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.ofMatroid_le_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matroid.ofMatroid_lt_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matroid.IsRestriction.refl", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsRestriction.antisymm", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Matroid.IsRestriction.trans", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsRestriction.eq_restrict", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "Matroid.IsRestriction.subset", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "Matroid.IsRestriction.exists_eq_restrict", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsRestriction.of_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.isRestriction_iff_exists", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": true, "tactics": ["use"], "tactic_count": 1}
{"name": "Matroid.IsStrictRestriction.isRestriction", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsStrictRestriction.ne", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "Matroid.IsStrictRestriction.irrefl", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsStrictRestriction.ssubset", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": true, "tactics": ["obtain", "refine", "rw"], "tactic_count": 3}
{"name": "Matroid.IsStrictRestriction.eq_restrict", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsStrictRestriction.exists_eq_restrict", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsRestriction.isStrictRestriction_of_ne", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsRestriction.eq_or_isStrictRestriction", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Matroid.restrict_isStrictRestriction", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "Matroid.IsRestriction.isStrictRestriction_of_ground_ne", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Matroid.IsStrictRestriction.of_ssubset", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsRestriction.finite", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Matroid.IsRestriction.rankFinite", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": true, "tactics": ["obtain", "infer_instance"], "tactic_count": 2}
{"name": "Matroid.IsRestriction.finitary", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": true, "tactics": ["obtain", "infer_instance"], "tactic_count": 2}
{"name": "Matroid.finite_setOf_isRestriction", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.Indep.of_isRestriction", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "Matroid.Indep.indep_isRestriction", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "Matroid.IsRestriction.indep_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsBasis.isBasis_isRestriction", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "Matroid.IsBasis.of_isRestriction", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "Matroid.IsBase.isBasis_of_isRestriction", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "Matroid.IsRestriction.base_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsRestriction.isBasis_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.Dep.of_isRestriction", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact"], "tactic_count": 3}
{"name": "Matroid.IsRestriction.dep_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsBasis.transfer", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Matroid.IsBasis.isBasis_of_isBasis_of_subset_of_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": true, "tactics": ["have", "have", "exact"], "tactic_count": 3}
{"name": "Matroid.Indep.exists_isBasis_subset_union_isBasis", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": false, "tactics": ["obtain", "rw", "exact"], "tactic_count": 3}
{"name": "Matroid.Indep.exists_insert_of_not_isBasis", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": true, "tactics": ["rw", "obtain", "exact"], "tactic_count": 3}
{"name": "Matroid.IsBasis.isBase_of_isBase_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsBasis.exchange", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Matroid.IsBasis.eq_exchange_of_diff_eq_singleton", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.IsBasis'.encard_eq_encard", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.IsBasis.encard_eq_encard", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.Indep.augment", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": true, "tactics": ["by_contra", "have", "simp_rw", "insert_subset_iff,", "exact", "obtain", "rw", "exact"], "tactic_count": 8}
{"name": "Matroid.Indep.augment_finset", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Minor.Restrict", "is_tactic_proof": true, "tactics": ["obtain", "simp", "exact"], "tactic_count": 3}
{"name": "Matroid.cRank", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Rank.Cardinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.cRk", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Rank.Cardinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsBase.cardinalMk_le_cRank", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Cardinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.Indep.cardinalMk_le_cRank", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Cardinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.cRank_eq_iSup_cardinalMk_indep", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Cardinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsBasis'.cardinalMk_le_cRk", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Cardinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsBasis.cardinalMk_le_cRk", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Cardinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.cRank_le_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Cardinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.cRk_le_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Cardinal", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Matroid.Indep.cardinalMk_le_cRk_of_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Cardinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.cRk_le_cardinalMk", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Cardinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.cRk_ground", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Cardinal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.cRank_restrict", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Cardinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.cRk_mono", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Cardinal", "is_tactic_proof": true, "tactics": ["simp", "intro", "obtain", "exact"], "tactic_count": 4}
{"name": "Matroid.cRk_le_of_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Cardinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.cRk_inter_ground", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Cardinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.cRk_restrict_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Cardinal", "is_tactic_proof": false, "tactics": ["have", "simp_rw", "exact", "simp_rw", "exact"], "tactic_count": 5}
{"name": "Matroid.cRk_restrict", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Cardinal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.Indep.cRk_eq_cardinalMk", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Cardinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.cRk_map_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Cardinal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.cRk_comap_lift", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Cardinal", "is_tactic_proof": true, "tactics": ["nth_rw", "nth_rw", "simp", "refine", "rw", "exact", "obtain", "show", "obtain", "refine", "rw", "rw", "exact"], "tactic_count": 13}
{"name": "Matroid.cRk_comap", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Cardinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsBasis.cardinalMk_diff_comm", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Cardinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsBasis'.cardinalMk_diff_comm", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Cardinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsBase.cardinalMk_diff_comm", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Cardinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsBasis.cardinalMk_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Cardinal", "is_tactic_proof": true, "tactics": ["rw", "hIX.cardinalMk_diff_comm", "diff_union_inter]"], "tactic_count": 3}
{"name": "Matroid.IsBasis'.cardinalMk_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Cardinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsBase.cardinalMk_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Cardinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.Indep.cardinalMk_le_isBase", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Cardinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.Indep.cardinalMk_le_isBasis'", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Cardinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.Indep.cardinalMk_le_isBasis", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Cardinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsBase.cardinalMk_eq_cRank", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Cardinal", "is_tactic_proof": true, "tactics": ["have", "simp"], "tactic_count": 2}
{"name": "Matroid.invariantCardinalRank_restrict", "kind": "instance", "module": "Mathlib.Combinatorics.Matroid.Rank.Cardinal", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "Matroid.IsBasis'.cardinalMk_eq_cRk", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Cardinal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.IsBasis.cardinalMk_eq_cRk", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Cardinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.cRk_closure", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Cardinal", "is_tactic_proof": true, "tactics": ["obtain", "rw"], "tactic_count": 2}
{"name": "Matroid.cRk_closure_congr", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Cardinal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.Spanning.cRank_le_cardinalMk", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Cardinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.cRk_union_closure_right_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Cardinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.cRk_union_closure_left_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Cardinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.cRk_insert_closure_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Cardinal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.cRk_union_closure_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Cardinal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matroid.cRk_inter_add_cRk_union_le", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Cardinal", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "obtain", "rw", "hIi.cardinalMk_eq_cRk,", "exact"], "tactic_count": 6}
{"name": "Matroid.invariantCardinalRank_of_finitary", "kind": "instance", "module": "Mathlib.Combinatorics.Matroid.Rank.Cardinal", "is_tactic_proof": false, "tactics": ["suffices", "from", "intro", "by_cases", "rw", "exact", "rw", "have", "have", "contrapose", "exact", "choose", "let", "suffices", "refine", "simp", "exact", "rw", "have", "by_contra", "have", "have", "refine", "exact"], "tactic_count": 24}
{"name": "Matroid.invariantCardinalRank_map", "kind": "instance", "module": "Mathlib.Combinatorics.Matroid.Rank.Cardinal", "is_tactic_proof": true, "tactics": ["refine", "obtain", "obtain", "obtain", "have", "rwa", "mk_image_eq_of_injOn_lift", "hf.image_inter"], "tactic_count": 8}
{"name": "Matroid.invariantCardinalRank_comap", "kind": "instance", "module": "Mathlib.Combinatorics.Matroid.Rank.Cardinal", "is_tactic_proof": true, "tactics": ["refine", "obtain", "obtain", "rw", "mk_image_eq_of_injOn_lift", "diff_union_diff_cancel", "mk_union_of_disjoint,", "diff_union_diff_cancel", "mk_union_of_disjoint,", "exact"], "tactic_count": 10}
{"name": "Matroid.rankFinite_iff_cRank_lt_aleph0", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Cardinal", "is_tactic_proof": true, "tactics": ["refine", "have", "exact", "have", "simp_rw", "exact"], "tactic_count": 6}
{"name": "Matroid.rankInfinite_iff_aleph0_le_cRank", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Cardinal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.isRkFinite_iff_cRk_lt_aleph0", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Cardinal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.Indep.isBase_of_cRank_le", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Cardinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.Spanning.isBase_of_le_cRank", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Cardinal", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "Matroid.Indep.isBase_of_cRank_le_of_finite", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Cardinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.Spanning.isBase_of_le_cRank_of_finite", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Cardinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.toENat_cRank_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Cardinal", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "rw", "simp"], "tactic_count": 4}
{"name": "Matroid.toENat_cRk_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Cardinal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.eRank", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.eRk", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.eRank_def", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.eRk_ground", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.eRank_restrict", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsBase.encard_eq_eRank", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matroid.IsBasis'.encard_eq_eRk", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsBasis.encard_eq_eRk", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.Indep.eRk_eq_encard", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsBasis'.eRk_eq_eRk", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.IsBasis.eRk_eq_eRk", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.IsBasis'.eRk_eq_encard", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.IsBasis.eRk_eq_encard", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.IsBase.eRk_eq_eRank", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.eRk_inter_ground", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["obtain", "rw"], "tactic_count": 2}
{"name": "Matroid.eRk_ground_inter", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.eRk_union_ground", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.eRk_ground_union", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.eRk_insert_of_notMem_ground", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.eRk_eq_eRank", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.eRk_compl_union_of_disjoint", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["rw", "union_eq_self_of_subset_right"], "tactic_count": 2}
{"name": "Matroid.one_le_eRank", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact"], "tactic_count": 3}
{"name": "Matroid.eRk_univ_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.eRk_empty", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.eRk_closure_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["obtain", "rw"], "tactic_count": 2}
{"name": "Matroid.eRk_union_closure_right_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.eRk_union_closure_left_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.eRk_insert_closure_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.restrict_eRk_eq'", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["obtain", "rw", "rw", "rw"], "tactic_count": 4}
{"name": "Matroid.restrict_eRk_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.IsBasis'.eRk_eq_eRk_union", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.IsBasis'.eRk_eq_eRk_insert", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.IsBasis.eRk_eq_eRk_union", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsBasis.eRk_eq_eRk_insert", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.eRk_le_encard", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact"], "tactic_count": 3}
{"name": "Matroid.eRank_le_encard_ground", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.eRk_mono", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["rintro", "obtain", "obtain", "rw", "exact"], "tactic_count": 5}
{"name": "Matroid.eRk_le_eRank", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.eRk_eq_eRk_of_subset_of_le", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.le_eRk_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["refine", "obtain", "rw", "obtain", "exact", "rw", "exact"], "tactic_count": 7}
{"name": "Matroid.eRk_le_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["refine", "obtain", "rw", "exact"], "tactic_count": 4}
{"name": "Matroid.Indep.encard_le_eRk_of_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.Indep.encard_le_eRank", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Matroid.eRk_eq_zero_iff'", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["obtain", "rw", "refine", "exact"], "tactic_count": 4}
{"name": "Matroid.eRk_loops", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matroid.eRk_inter_add_eRk_union_le", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "obtain", "rw", "hIY.encard_eq_eRk,", "exact"], "tactic_count": 6}
{"name": "Matroid.eRk_insert_inter_add_eRk_insert_union_le", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "Matroid.eRk_compl_union_add_eRk_compl_inter_le", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "Matroid.eRk_compl_insert_union_add_eRk_compl_insert_inter_le", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Matroid.eRk_union_le_eRk_add_eRk", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.eRk_eq_eRk_union_eRk_le_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.eRk_eq_eRk_diff_eRk_le_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.eRk_le_eRk_inter_add_eRk_diff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["nth_rw"], "tactic_count": 1}
{"name": "Matroid.eRk_le_eRk_add_eRk_diff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["nth_rw"], "tactic_count": 1}
{"name": "Matroid.eRk_union_le_encard_add_eRk", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.eRk_union_le_eRk_add_encard", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.eRank_le_encard_add_eRk_compl", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.eRank_ne_top_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact"], "tactic_count": 3}
{"name": "Matroid.eRank_eq_top_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.eRank_lt_top_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matroid.eRank_eq_top", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.eRk_eq_top_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["obtain", "rw"], "tactic_count": 2}
{"name": "Matroid.eRk_ne_top_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matroid.eRk_lt_top_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.IsRkFinite.eRk_lt_top", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsRkFinite.isBasis_of_subset_closure_of_subset_of_encard_le", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["obtain", "have", "rw", "replace", "have", "rw", "rwa"], "tactic_count": 7}
{"name": "Matroid.IsRkFinite.closure_eq_closure_of_subset_of_eRk_ge_eRk", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "rw", "rw", "hJ.isBasis_inter_ground.closure_eq_closure,"], "tactic_count": 5}
{"name": "Matroid.eRk_insert_le_add_one", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.eRk_insert_eq_add_one", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["obtain", "rw", "rw"], "tactic_count": 3}
{"name": "Matroid.exists_eRk_insert_eq_add_one_of_lt", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": false, "tactics": ["have", "contrapose", "simpa", "obtain", "refine"], "tactic_count": 5}
{"name": "Matroid.IsRkFinite.closure_eq_closure_of_subset_of_forall_insert", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["refine", "obtain", "simpa"], "tactic_count": 3}
{"name": "Matroid.eRk_eq_of_eRk_insert_le_forall", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "rw"], "tactic_count": 3}
{"name": "Matroid.indep_iff_eRk_eq_encard_of_finite", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["refine", "obtain", "rw", "exact", "rw"], "tactic_count": 5}
{"name": "Matroid.indep_iff_eRk_eq_encard", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["refine", "obtain", "rwa", "rw", "exact"], "tactic_count": 5}
{"name": "Matroid.IsRkFinite.indep_of_encard_le_eRk", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["rw", "exact", "simpa"], "tactic_count": 3}
{"name": "Matroid.eRk_lt_encard_of_dep_of_finite", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.Dep.eRk_lt_encard", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "Matroid.Indep.exists_insert_of_encard_lt", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.isBasis'_iff_indep_encard_eq_of_finite", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["refine", "obtain", "rwa"], "tactic_count": 3}
{"name": "Matroid.Indep.isBasis'_of_eRk_ge", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.Indep.isBase_of_eRk_ge", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Matroid.IsCircuit.eRk_add_one_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "rw"], "tactic_count": 3}
{"name": "Matroid.IsLoop.eRk_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.IsNonloop.eRk_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.eRk_singleton_le", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.eRk_singleton_eq_one_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["refine", "rwa"], "tactic_count": 2}
{"name": "Matroid.Spanning.eRk_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Matroid.spanning_iff_eRk_le'", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact"], "tactic_count": 3}
{"name": "Matroid.Spanning.eRank_restrict", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.eRank_map", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["obtain", "rw"], "tactic_count": 2}
{"name": "Matroid.eRk_comap", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "rw"], "tactic_count": 3}
{"name": "Matroid.eRk_loopyOn", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["obtain", "rw"], "tactic_count": 2}
{"name": "Matroid.eRank_loopyOn", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.eRank_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["refine", "obtain", "rw", "rw"], "tactic_count": 4}
{"name": "Matroid.exists_of_eRank_eq_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.eRank_emptyOn", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.eq_loopyOn_iff_eRank", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.eRank_freeOn", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.eRk_freeOn", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["obtain", "rw"], "tactic_count": 2}
{"name": "Matroid.IsBase.encard_compl_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.eRk_dual_add_eRank'", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.eRank_add_eRank_dual", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.ENat", "is_tactic_proof": true, "tactics": ["obtain", "rw", "union_diff_cancel"], "tactic_count": 3}
{"name": "Matroid.IsRkFinite", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Rank.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsRkFinite.rankFinite", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.RankFinite.isRkFinite", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsBasis'.finite_iff_isRkFinite", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsBasis.finite_iff_isRkFinite", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsBasis'.isRkFinite_of_finite", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsBasis.isRkFinite_of_finite", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsRkFinite.finite_of_isBasis'", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsRkFinite.finite_of_isBasis", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsRkFinite.exists_finite_isBasis'", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsRkFinite.exists_finset_isBasis'", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.isRkFinite_iff_exists_isBasis'", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsRkFinite.subset", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Finite", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "exact"], "tactic_count": 3}
{"name": "Matroid.isRkFinite_inter_ground_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsRkFinite.inter_ground", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.Indep.isRkFinite_iff_finite", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.isRkFinite_of_finite", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.Indep.subset_finite_isBasis'_of_subset_of_isRkFinite", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.isRkFinite_singleton", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Finite", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matroid.IsRkFinite.empty", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsRkFinite.finite_of_indep_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.isRkFinite_ground_iff_rankFinite", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Finite", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.isRkFinite_ground", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Finite", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Matroid.Indep.finite_of_subset_isRkFinite", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsRkFinite.closure", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.isRkFinite_closure_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Finite", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Matroid.IsRkFinite.union", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Finite", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "rw", "refine", "rw", "exact"], "tactic_count": 6}
{"name": "Matroid.IsRkFinite.isRkFinite_union_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsRkFinite.isRkFinite_diff_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Finite", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.IsRkFinite.inter_right", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsRkFinite.inter_left", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsRkFinite.diff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsRkFinite.insert", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Finite", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Matroid.isRkFinite_insert_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Finite", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.IsRkFinite.diff_singleton_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Finite", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matroid.isRkFinite_set", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.IsRkFinite.iUnion", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Rank.Finite", "is_tactic_proof": true, "tactics": ["choose", "have", "refine", "rw", "exact"], "tactic_count": 5}
{"name": "Matroid.sigma", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.sigma_indep_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.sigma_isBase_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.sigma_ground_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.sigma_isBasis_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Sum", "is_tactic_proof": false, "tactics": ["simp", "and_congr_right_iff]", "refine", "refine", "specialize", "simp", "true_implies]", "rw", "exact", "intro", "obtain", "rwa", "rw", "apply", "exact", "exact", "refine", "simpa", "exact"], "tactic_count": 19}
{"name": "Matroid.Finitary.sigma", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Sum", "is_tactic_proof": true, "tactics": ["refine", "simp", "intro", "apply", "intro", "convert", "rw"], "tactic_count": 7}
{"name": "Matroid.sum'", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.sum'_indep_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Sum", "is_tactic_proof": true, "tactics": ["simp", "convert", "ext", "simp"], "tactic_count": 4}
{"name": "Matroid.sum'_ground_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Sum", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Matroid.sum'_isBase_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Sum", "is_tactic_proof": true, "tactics": ["simp", "convert", "ext", "simp"], "tactic_count": 4}
{"name": "Matroid.sum'_isBasis_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Sum", "is_tactic_proof": true, "tactics": ["simp", "convert"], "tactic_count": 2}
{"name": "Matroid.Finitary.sum'", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Sum", "is_tactic_proof": true, "tactics": ["have", "rw", "infer_instance"], "tactic_count": 3}
{"name": "Matroid.disjointSigma", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.disjointSigma_ground_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Sum", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Matroid.disjointSigma_indep_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Sum", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matroid.disjointSigma_isBase_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Sum", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matroid.disjointSigma_isBasis_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Sum", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matroid.sum", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.sum_ground", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Sum", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matroid.sum_indep_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Sum", "is_tactic_proof": false, "tactics": ["simp", "sigma_indep_iff,", "convert"], "tactic_count": 3}
{"name": "Matroid.sum_isBase_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Sum", "is_tactic_proof": false, "tactics": ["simp", "sigma_isBase_iff,", "convert"], "tactic_count": 3}
{"name": "Matroid.sum_isBasis_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Sum", "is_tactic_proof": false, "tactics": ["simp", "sigma_isBasis_iff,", "convert"], "tactic_count": 3}
{"name": "Matroid.disjointSum", "kind": "definition", "module": "Mathlib.Combinatorics.Matroid.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matroid.disjointSum_ground_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Sum", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matroid.disjointSum_indep_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Sum", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matroid.disjointSum_isBase_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Sum", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matroid.disjointSum_isBasis_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Sum", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matroid.disjointSum_comm", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Sum", "is_tactic_proof": true, "tactics": ["ext", "simp", "repeat", "simpa"], "tactic_count": 4}
{"name": "Matroid.Indep.eq_union_image_of_disjointSum", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Sum", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw"], "tactic_count": 3}
{"name": "Matroid.IsBase.eq_union_image_of_disjointSum", "kind": "theorem", "module": "Mathlib.Combinatorics.Matroid.Sum", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw"], "tactic_count": 3}
{"name": "MvPolynomial.eq_zero_of_eval_zero_at_prod_finset", "kind": "theorem", "module": "Mathlib.Combinatorics.Nullstellensatz", "is_tactic_proof": true, "tactics": ["induction", "h", "suffices", "have", "rw", "rwa", "apply", "intro", "classical", "convert", "conv_lhs", "intro", "simp", "apply", "intro", "simp", "convert", "simp", "h_empty", "suffices", "specialize", "rw", "rw", "ext", "suffices", "ext", "set", "suffices", "have", "apply", "intro", "rw", "apply", "simp", "apply", "rw", "intro", "simp", "rw", "convert", "ext", "simp", "set", "rw", "rw", "by_contra", "apply", "rw", "rw", "convert", "exact", "ext", "simp", "suffices", "apply", "intro", "apply", "simp", "intro", "set", "rw", "rw", "convert", "rw", "intro", "specialize", "rw", "simpa"], "tactic_count": 68}
{"name": "_private.Mathlib.Combinatorics.Nullstellensatz.0.MvPolynomial.Alon.P", "kind": "definition", "module": "Mathlib.Combinatorics.Nullstellensatz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.Nullstellensatz.0.MvPolynomial.Alon.degree_P", "kind": "theorem", "module": "Mathlib.Combinatorics.Nullstellensatz", "is_tactic_proof": true, "tactics": ["simp", "rw", "simp", "intro", "rw", "exact"], "tactic_count": 6}
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{"name": "Quiver.IsSStronglyConnected.exists_pos_path", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.ConnectedComponent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.IsSStronglyConnected.exists_pos_cycle", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.ConnectedComponent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.IsSStronglyConnected.isStronglyConnected", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.ConnectedComponent", "is_tactic_proof": true, "tactics": ["intro"], "tactic_count": 1}
{"name": "Quiver.stronglyConnectedSetoid", "kind": "definition", "module": "Mathlib.Combinatorics.Quiver.ConnectedComponent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.StronglyConnectedComponent", "kind": "definition", "module": "Mathlib.Combinatorics.Quiver.ConnectedComponent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.StronglyConnectedComponent.mk", "kind": "definition", "module": "Mathlib.Combinatorics.Quiver.ConnectedComponent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.StronglyConnectedComponent.instCoe", "kind": "instance", "module": "Mathlib.Combinatorics.Quiver.ConnectedComponent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.StronglyConnectedComponent.instInhabited", "kind": "instance", "module": "Mathlib.Combinatorics.Quiver.ConnectedComponent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.StronglyConnectedComponent.eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.ConnectedComponent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.StronglyConnectedComponent.mk_eq_mk", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.ConnectedComponent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.StronglyConnectedComponent.IsSStronglyConnected.pos_cycle", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.ConnectedComponent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.stronglyConnectedComponent_eq_of_path", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.ConnectedComponent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.exists_path_of_stronglyConnectedComponent_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.ConnectedComponent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.stronglyConnectedComponent_singleton_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.ConnectedComponent", "is_tactic_proof": true, "tactics": ["constructor", "intro", "obtain", "have", "stronglyConnectedComponent_eq_of_path", "obtain", "contradiction", "intro", "by_contra", "obtain", "exact"], "tactic_count": 11}
{"name": "Quiver.IsStronglyConnected.isStronglyConnected_symmetrify", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.ConnectedComponent", "is_tactic_proof": true, "tactics": ["intro", "obtain", "induction", "nil", "cons"], "tactic_count": 5}
{"name": "Quiver.IsStronglyConnected.isSStronglyConnected_of_hom", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.ConnectedComponent", "is_tactic_proof": true, "tactics": ["intro", "obtain", "obtain", "let", "have", "simpa", "exact"], "tactic_count": 7}
{"name": "Quiver.Star", "kind": "abbrev", "module": "Mathlib.Combinatorics.Quiver.Covering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.Star.mk", "kind": "abbrev", "module": "Mathlib.Combinatorics.Quiver.Covering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.Costar", "kind": "abbrev", "module": "Mathlib.Combinatorics.Quiver.Covering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.Costar.mk", "kind": "abbrev", "module": "Mathlib.Combinatorics.Quiver.Covering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prefunctor.star", "kind": "definition", "module": "Mathlib.Combinatorics.Quiver.Covering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prefunctor.costar", "kind": "definition", "module": "Mathlib.Combinatorics.Quiver.Covering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prefunctor.star_apply", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Covering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prefunctor.costar_apply", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Covering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prefunctor.star_comp", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Covering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prefunctor.costar_comp", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Covering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prefunctor.IsCovering.map_injective", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Covering", "is_tactic_proof": true, "tactics": ["rintro", "have", "simpa"], "tactic_count": 3}
{"name": "Prefunctor.IsCovering.comp", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Covering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prefunctor.IsCovering.of_comp_right", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Covering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prefunctor.IsCovering.of_comp_left", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Covering", "is_tactic_proof": true, "tactics": ["refine", "exacts"], "tactic_count": 2}
{"name": "Quiver.symmetrifyStar", "kind": "definition", "module": "Mathlib.Combinatorics.Quiver.Covering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.symmetrifyCostar", "kind": "definition", "module": "Mathlib.Combinatorics.Quiver.Covering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prefunctor.symmetrifyStar", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Covering", "is_tactic_proof": true, "tactics": ["rw", "ext", "simp", "erw", "simp"], "tactic_count": 5}
{"name": "Prefunctor.symmetrifyCostar", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Covering", "is_tactic_proof": true, "tactics": ["rw", "ext", "simp", "erw", "simp"], "tactic_count": 5}
{"name": "Prefunctor.IsCovering.symmetrify", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Covering", "is_tactic_proof": true, "tactics": ["refine", "simp"], "tactic_count": 2}
{"name": "Quiver.PathStar", "kind": "abbrev", "module": "Mathlib.Combinatorics.Quiver.Covering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.PathStar.mk", "kind": "abbrev", "module": "Mathlib.Combinatorics.Quiver.Covering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prefunctor.pathStar", "kind": "definition", "module": "Mathlib.Combinatorics.Quiver.Covering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prefunctor.pathStar_apply", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Covering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prefunctor.pathStar_injective", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Covering", "is_tactic_proof": true, "tactics": ["dsimp", "rintro", "induction", "nil", "rintro", "rcases", "intro", "rfl", "intro", "simp", "exfalso", "obtain", "rw", "exact", "cons", "rename_i", "rintro", "rcases", "intro", "simp", "exfalso", "obtain", "rw", "exact", "rename_i", "intro", "simp", "obtain", "rw", "have", "have", "have", "have", "simp", "cases", "have", "exact", "cases", "rfl"], "tactic_count": 39}
{"name": "Prefunctor.pathStar_surjective", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Covering", "is_tactic_proof": true, "tactics": ["dsimp", "rintro", "induction", "nil", "use", "simp", "cons", "obtain", "simp", "obtain", "obtain", "simp", "obtain", "simp", "subst", "use", "simp"], "tactic_count": 17}
{"name": "Prefunctor.pathStar_bijective", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Covering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prefunctor.IsCovering.pathStar_bijective", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Covering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.starEquivCostar", "kind": "definition", "module": "Mathlib.Combinatorics.Quiver.Covering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.starEquivCostar_apply", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Covering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.starEquivCostar_symm_apply", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Covering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prefunctor.costar_conj_star", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Covering", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Prefunctor.bijective_costar_iff_bijective_star", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Covering", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Prefunctor.isCovering_of_bijective_star", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Covering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prefunctor.isCovering_of_bijective_costar", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Covering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.Path", "kind": "inductive", "module": "Mathlib.Combinatorics.Quiver.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.Hom.toPath", "kind": "definition", "module": "Mathlib.Combinatorics.Quiver.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.Path.nil_ne_cons", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.Path.cons_ne_nil", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.Path.obj_eq_of_cons_eq_cons", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Path", "is_tactic_proof": true, "tactics": ["injection"], "tactic_count": 1}
{"name": "Quiver.Path.heq_of_cons_eq_cons", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Path", "is_tactic_proof": true, "tactics": ["injection"], "tactic_count": 1}
{"name": "Quiver.Path.hom_heq_of_cons_eq_cons", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Path", "is_tactic_proof": true, "tactics": ["injection"], "tactic_count": 1}
{"name": "Quiver.Path.length", "kind": "definition", "module": "Mathlib.Combinatorics.Quiver.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.Path.instInhabited", "kind": "instance", "module": "Mathlib.Combinatorics.Quiver.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.Path.length_nil", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.Path.length_cons", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.Path.eq_of_length_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Path", "is_tactic_proof": true, "tactics": ["cases", "rfl", "cases"], "tactic_count": 3}
{"name": "Quiver.Path.eq_nil_of_length_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Path", "is_tactic_proof": true, "tactics": ["cases", "rfl", "simp"], "tactic_count": 3}
{"name": "Quiver.Path.length_toPath", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.Path.comp", "kind": "definition", "module": "Mathlib.Combinatorics.Quiver.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.Path.comp_cons", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.Path.comp_nil", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.Path.nil_comp", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.Path.comp_assoc", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.Path.length_comp", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.Path.comp_inj", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Path", "is_tactic_proof": true, "tactics": ["refine", "induction", "nil", "rcases", "exact", "cases", "cons", "rcases", "cases", "simp", "obtain", "obtain", "rw", "exact"], "tactic_count": 14}
{"name": "Quiver.Path.comp_inj'", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.Path.comp_injective_left", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.Path.comp_injective_right", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.Path.comp_inj_left", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.Path.comp_inj_right", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.Path.eq_toPath_comp_of_length_eq_succ", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Path", "is_tactic_proof": true, "tactics": ["induction", "nil", "cases", "rw", "obtain", "obtain", "exact", "rw", "obtain", "exact"], "tactic_count": 10}
{"name": "Quiver.Path.length_ne_zero_iff_eq_comp", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Path", "is_tactic_proof": true, "tactics": ["refine", "have", "obtain", "exact", "rintro", "simp"], "tactic_count": 6}
{"name": "Quiver.Path.length_ne_zero_iff_eq_cons", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Path", "is_tactic_proof": true, "tactics": ["refine", "cases", "nil", "cons", "rintro", "simp"], "tactic_count": 6}
{"name": "Quiver.Path.comp_toPath_eq_cons", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.Path.toList", "kind": "definition", "module": "Mathlib.Combinatorics.Quiver.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.Path.toList_comp", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.Path.isChain_toList_nonempty", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.Path.isChain_cons_toList_nonempty", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.Path.toList_injective", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.Path.toList_inj", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.Path.BoundedPaths", "kind": "definition", "module": "Mathlib.Combinatorics.Quiver.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.Path.instSubsingletonBddPaths", "kind": "instance", "module": "Mathlib.Combinatorics.Quiver.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.Path.decidableEqBddPathsZero", "kind": "definition", "module": "Mathlib.Combinatorics.Quiver.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.Path.decidableEqBddPathsOfDecidableEq", "kind": "definition", "module": "Mathlib.Combinatorics.Quiver.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.Path.decidableEqBoundedPaths", "kind": "instance", "module": "Mathlib.Combinatorics.Quiver.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.Path.instDecidableEq", "kind": "instance", "module": "Mathlib.Combinatorics.Quiver.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prefunctor.mapPath", "kind": "definition", "module": "Mathlib.Combinatorics.Quiver.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prefunctor.mapPath_nil", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prefunctor.mapPath_cons", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prefunctor.mapPath_comp", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prefunctor.mapPath_toPath", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prefunctor.mapPath_id", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prefunctor.mapPath_comp_apply", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Path", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "Quiver.Path.exists_notMem_mem_hom_path_path_of_notMem_mem", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Path.Decomposition", "is_tactic_proof": true, "tactics": ["induction", "zero", "obtain", "exact", "succ", "have", "obtain", "by_cases", "have", "obtain", "refine", "simp", "refine", "simp"], "tactic_count": 14}
{"name": "Quiver.Path.exists_mem_notMem_hom_path_path_of_notMem_mem", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Path.Decomposition", "is_tactic_proof": true, "tactics": ["classical", "have", "have", "obtain", "exists_notMem_mem_hom_path_path_of_notMem_mem", "simp", "refine"], "tactic_count": 7}
{"name": "Quiver.Path.end", "kind": "definition", "module": "Mathlib.Combinatorics.Quiver.Path.Vertices", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.Path.end_cons", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Path.Vertices", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.Path.vertices", "kind": "definition", "module": "Mathlib.Combinatorics.Quiver.Path.Vertices", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.Path.vertices_nil", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Path.Vertices", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.Path.vertices_cons", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Path.Vertices", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.Path.mem_vertices_cons", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Path.Vertices", "is_tactic_proof": true, "tactics": ["simp", "simp_all"], "tactic_count": 2}
{"name": "Quiver.Path.verticesSet_nil", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Path.Vertices", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Quiver.Path.vertices_length", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Path.Vertices", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "Quiver.Path.length_vertices_pos", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Path.Vertices", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Quiver.Path.vertices_ne_nil", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Path.Vertices", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Quiver.Path.start_mem_vertices", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Path.Vertices", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "Quiver.Path.vertices_head?", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Path.Vertices", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "Quiver.Path.getElem_vertices_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Path.Vertices", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "Quiver.Path.dropLast_append_end_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Path.Vertices", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Quiver.Path.vertices_comp", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Path.Vertices", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "Quiver.Path.length_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Path.Vertices", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Quiver.Path.vertices_toPath", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Path.Vertices", "is_tactic_proof": true, "tactics": ["change", "simp"], "tactic_count": 2}
{"name": "Quiver.Path.vertices_toPath_tail", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Path.Vertices", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Quiver.Path.nil_of_comp_eq_nil_left", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Path.Vertices", "is_tactic_proof": true, "tactics": ["have", "have", "exact"], "tactic_count": 3}
{"name": "Quiver.Path.nil_of_comp_eq_nil_right", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Path.Vertices", "is_tactic_proof": true, "tactics": ["have", "have", "exact"], "tactic_count": 3}
{"name": "Quiver.Path.comp_eq_nil_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Path.Vertices", "is_tactic_proof": true, "tactics": ["refine", "induction", "nil", "cons"], "tactic_count": 4}
{"name": "Quiver.Path.end_mem_vertices", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Path.Vertices", "is_tactic_proof": true, "tactics": ["have", "have", "simpa"], "tactic_count": 3}
{"name": "Quiver.Path.exists_eq_comp_of_le_length", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Path.Vertices", "is_tactic_proof": true, "tactics": ["induction", "nil", "obtain", "exact", "rw", "rcases", "obtain", "exact", "exact"], "tactic_count": 9}
{"name": "Quiver.Path.exists_eq_comp_and_length_eq_of_lt_length", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Path.Vertices", "is_tactic_proof": false, "tactics": ["have", "rw", "exact", "obtain", "exact"], "tactic_count": 5}
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{"name": "Quiver.Path.exists_eq_comp_and_notMem_tail_of_mem_vertices", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Path.Vertices", "is_tactic_proof": true, "tactics": ["induction", "nil", "have", "subst", "exact", "simp", "cons", "ih", "have", "have", "v", "rintro", "exact", "have", "v", "v", "intro", "obtain", "let", "have", "exact", "cases", "inl", "by_cases", "exact", "exact", "inr"], "tactic_count": 27}
{"name": "Quiver.Path.weight", "kind": "definition", "module": "Mathlib.Combinatorics.Quiver.Path.Weight", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.Path.addWeight", "kind": "definition", "module": "Mathlib.Combinatorics.Quiver.Path.Weight", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.Path.weightOfEPs", "kind": "definition", "module": "Mathlib.Combinatorics.Quiver.Path.Weight", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.Path.weight_nil", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Path.Weight", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Quiver.Path.weight_cons", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Path.Weight", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "Quiver.Path.weightOfEPs_cons", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Path.Weight", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
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{"name": "Quiver.Path.weight_pos", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Path.Weight", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "have", "simpa"], "tactic_count": 5}
{"name": "Quiver.Path.weight_nonneg", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Path.Weight", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "have", "simpa"], "tactic_count": 5}
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{"name": "Prefunctor.mk_map", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Prefunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Prefunctor.instInhabited", "kind": "instance", "module": "Mathlib.Combinatorics.Quiver.Prefunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prefunctor.comp", "kind": "definition", "module": "Mathlib.Combinatorics.Quiver.Prefunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Quiver.Push.of", "kind": "definition", "module": "Mathlib.Combinatorics.Quiver.Push", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.Push.of_obj", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Push", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.Push.lift", "kind": "definition", "module": "Mathlib.Combinatorics.Quiver.Push", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "WideSubquiver.toType", "kind": "definition", "module": "Mathlib.Combinatorics.Quiver.Subquiver", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Prefunctor.mapReverseId", "kind": "instance", "module": "Mathlib.Combinatorics.Quiver.Symmetric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Quiver.Hom.toNeg", "kind": "abbrev", "module": "Mathlib.Combinatorics.Quiver.Symmetric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.Path.reverse", "kind": "definition", "module": "Mathlib.Combinatorics.Quiver.Symmetric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quiver.Path.reverse_toPath", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Symmetric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Prefunctor.symmetrify_mapReverse", "kind": "instance", "module": "Mathlib.Combinatorics.Quiver.Symmetric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Quiver.Push.of_reverse", "kind": "theorem", "module": "Mathlib.Combinatorics.Quiver.Symmetric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "schnirelmannDensity", "kind": "definition", "module": "Mathlib.Combinatorics.Schnirelmann", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "schnirelmannDensity_nonneg", "kind": "theorem", "module": "Mathlib.Combinatorics.Schnirelmann", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "schnirelmannDensity_le_div", "kind": "theorem", "module": "Mathlib.Combinatorics.Schnirelmann", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "schnirelmannDensity_mul_le_card_filter", "kind": "theorem", "module": "Mathlib.Combinatorics.Schnirelmann", "is_tactic_proof": true, "tactics": ["rcases", "simp", "exact"], "tactic_count": 3}
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{"name": "schnirelmannDensity_le_one", "kind": "theorem", "module": "Mathlib.Combinatorics.Schnirelmann", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "schnirelmannDensity_le_iff_forall", "kind": "theorem", "module": "Mathlib.Combinatorics.Schnirelmann", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "schnirelmannDensity_congr'", "kind": "theorem", "module": "Mathlib.Combinatorics.Schnirelmann", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "schnirelmannDensity_insert_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.Schnirelmann", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "schnirelmannDensity_diff_singleton_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.Schnirelmann", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "schnirelmannDensity_congr", "kind": "theorem", "module": "Mathlib.Combinatorics.Schnirelmann", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_of_schnirelmannDensity_eq_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.Schnirelmann", "is_tactic_proof": true, "tactics": ["by_contra", "rw", "linarith"], "tactic_count": 3}
{"name": "schnirelmannDensity_empty", "kind": "theorem", "module": "Mathlib.Combinatorics.Schnirelmann", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "schnirelmannDensity_finset", "kind": "theorem", "module": "Mathlib.Combinatorics.Schnirelmann", "is_tactic_proof": true, "tactics": ["refine", "simp", "intro", "wlog", "obtain", "exact", "let", "have", "use", "rw", "exact"], "tactic_count": 11}
{"name": "schnirelmannDensity_finite", "kind": "theorem", "module": "Mathlib.Combinatorics.Schnirelmann", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "schnirelmannDensity_univ", "kind": "theorem", "module": "Mathlib.Combinatorics.Schnirelmann", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "schnirelmannDensity_setOf_even", "kind": "theorem", "module": "Mathlib.Combinatorics.Schnirelmann", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "schnirelmannDensity_setOf_prime", "kind": "theorem", "module": "Mathlib.Combinatorics.Schnirelmann", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "schnirelmannDensity_setOf_mod_eq_one", "kind": "theorem", "module": "Mathlib.Combinatorics.Schnirelmann", "is_tactic_proof": true, "tactics": ["rcases", "simp", "refine", "simp", "apply", "rw", "gcongr", "simp", "and_imp]", "use", "intro", "rcases", "simp", "rwa", "rw", "intro", "simp", "have", "simp", "rintro", "have", "simp", "exact", "rw", "apply", "rw", "have", "rwa", "intro", "simp"], "tactic_count": 30}
{"name": "schnirelmannDensity_setOf_modeq_one", "kind": "theorem", "module": "Mathlib.Combinatorics.Schnirelmann", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rw", "simp"], "tactic_count": 4}
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{"name": "_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.binomial_sum_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.AhlswedeZhang", "is_tactic_proof": true, "tactics": ["set", "suffices", "rw", "simp", "intro", "rw", "have", "have", "have", "have", "have", "push_cast", "dsimp", "rw", "have", "push_cast", "rw", "have", "have", "simp"], "tactic_count": 20}
{"name": "_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Fintype.sum_div_mul_card_choose_card", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.AhlswedeZhang", "is_tactic_proof": true, "tactics": ["rw", "have", "intro", "rw", "simp_rw", "rw", "add_comm", "have", "rw", "exact", "simp", "convert", "rw"], "tactic_count": 13}
{"name": "_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Finset.sup_aux", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.AhlswedeZhang", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Finset.lower_aux", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.AhlswedeZhang", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.truncatedSup", "kind": "definition", "module": "Mathlib.Combinatorics.SetFamily.AhlswedeZhang", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.truncatedSup_of_mem", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.AhlswedeZhang", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.truncatedSup_of_notMem", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.AhlswedeZhang", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.truncatedSup_empty", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.AhlswedeZhang", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.truncatedSup_singleton", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.AhlswedeZhang", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.le_truncatedSup", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.AhlswedeZhang", "is_tactic_proof": true, "tactics": ["rw", "split_ifs", "obtain", "exact", "exact"], "tactic_count": 5}
{"name": "Finset.map_truncatedSup", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.AhlswedeZhang", "is_tactic_proof": true, "tactics": ["have", "simp_rw", "congr", "simp", "sup'_map]"], "tactic_count": 5}
{"name": "Finset.truncatedSup_of_isAntichain", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.AhlswedeZhang", "is_tactic_proof": true, "tactics": ["refine", "simp_rw", "rintro", "exact"], "tactic_count": 4}
{"name": "Finset.truncatedSup_union", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.AhlswedeZhang", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.truncatedSup_union_left", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.AhlswedeZhang", "is_tactic_proof": true, "tactics": ["simp", "simp"], "tactic_count": 2}
{"name": "Finset.truncatedSup_union_right", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.AhlswedeZhang", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.truncatedSup_union_of_notMem", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.AhlswedeZhang", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Finset.inf_aux", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.AhlswedeZhang", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Finset.upper_aux", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.AhlswedeZhang", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.truncatedInf", "kind": "definition", "module": "Mathlib.Combinatorics.SetFamily.AhlswedeZhang", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.truncatedInf_of_mem", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.AhlswedeZhang", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.truncatedInf_of_notMem", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.AhlswedeZhang", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.truncatedInf_le", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.AhlswedeZhang", "is_tactic_proof": true, "tactics": ["unfold", "split_ifs", "obtain", "exact", "exact"], "tactic_count": 5}
{"name": "Finset.truncatedInf_empty", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.AhlswedeZhang", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.truncatedInf_singleton", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.AhlswedeZhang", "is_tactic_proof": true, "tactics": ["simp", "split_ifs"], "tactic_count": 2}
{"name": "Finset.map_truncatedInf", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.AhlswedeZhang", "is_tactic_proof": true, "tactics": ["have", "simp_rw", "congr", "simp", "inf'_map]"], "tactic_count": 5}
{"name": "Finset.truncatedInf_of_isAntichain", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.AhlswedeZhang", "is_tactic_proof": true, "tactics": ["refine", "simp_rw", "rintro", "exact"], "tactic_count": 4}
{"name": "Finset.truncatedInf_union", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.AhlswedeZhang", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.truncatedInf_union_left", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.AhlswedeZhang", "is_tactic_proof": true, "tactics": ["simp", "simp"], "tactic_count": 2}
{"name": "Finset.truncatedInf_union_right", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.AhlswedeZhang", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.truncatedInf_union_of_notMem", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.AhlswedeZhang", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Finset.infs_aux", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.AhlswedeZhang", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Finset.sups_aux", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.AhlswedeZhang", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.truncatedSup_infs", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.AhlswedeZhang", "is_tactic_proof": true, "tactics": ["simp", "simp_rw", "rw", "simp"], "tactic_count": 4}
{"name": "Finset.truncatedInf_sups", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.AhlswedeZhang", "is_tactic_proof": true, "tactics": ["simp", "simp_rw", "rw", "simp"], "tactic_count": 4}
{"name": "Finset.truncatedSup_infs_of_notMem", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.AhlswedeZhang", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.truncatedInf_sups_of_notMem", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.AhlswedeZhang", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.compl_truncatedSup", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.AhlswedeZhang", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.compl_truncatedInf", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.AhlswedeZhang", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_truncatedSup_union_add_card_truncatedSup_infs", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.AhlswedeZhang", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "exact", "rw", "rw", "rw", "truncatedSup_infs_of_notMem"], "tactic_count": 7}
{"name": "Finset.card_truncatedInf_union_add_card_truncatedInf_sups", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.AhlswedeZhang", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "exact", "rw", "rw", "rw", "truncatedInf_sups_of_notMem"], "tactic_count": 7}
{"name": "AhlswedeZhang.infSum", "kind": "definition", "module": "Mathlib.Combinatorics.SetFamily.AhlswedeZhang", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AhlswedeZhang.supSum", "kind": "definition", "module": "Mathlib.Combinatorics.SetFamily.AhlswedeZhang", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AhlswedeZhang.supSum_union_add_supSum_infs", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.AhlswedeZhang", "is_tactic_proof": true, "tactics": ["unfold", "rw", "simp_rw", "simp"], "tactic_count": 4}
{"name": "AhlswedeZhang.infSum_union_add_infSum_sups", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.AhlswedeZhang", "is_tactic_proof": true, "tactics": ["unfold", "rw", "simp_rw", "simp"], "tactic_count": 4}
{"name": "AhlswedeZhang.IsAntichain.le_infSum", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.AhlswedeZhang", "is_tactic_proof": false, "tactics": ["calc", "refine", "rw", "have", "positivity"], "tactic_count": 5}
{"name": "AhlswedeZhang.supSum_singleton", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.AhlswedeZhang", "is_tactic_proof": false, "tactics": ["have", "rintro", "simp_rw", "split_ifs", "simp_rw", "rw", "binomial_sum_eq", "refine", "rw", "exact"], "tactic_count": 10}
{"name": "AhlswedeZhang.infSum_compls_add_supSum", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.AhlswedeZhang", "is_tactic_proof": true, "tactics": ["unfold", "rw", "simp", "cast_sub"], "tactic_count": 4}
{"name": "AhlswedeZhang.supSum_of_univ_notMem", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.AhlswedeZhang", "is_tactic_proof": true, "tactics": ["set", "clear_value", "induction", "ind", "replace", "obtain", "refine", "simpa", "cases", "cases", "obtain", "have", "rw", "supSum_singleton", "exact", "exact", "simpa", "exact", "exact", "exact"], "tactic_count": 20}
{"name": "AhlswedeZhang.infSum_eq_one", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.AhlswedeZhang", "is_tactic_proof": false, "tactics": ["rw", "add_sub_cancel_left]", "simpa"], "tactic_count": 3}
{"name": "Finset.nonMemberSubfamily", "kind": "definition", "module": "Mathlib.Combinatorics.SetFamily.Compression.Down", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.memberSubfamily", "kind": "definition", "module": "Mathlib.Combinatorics.SetFamily.Compression.Down", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_nonMemberSubfamily", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Compression.Down", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.mem_memberSubfamily", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Compression.Down", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "rintro", "rw", "exact"], "tactic_count": 5}
{"name": "Finset.nonMemberSubfamily_inter", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Compression.Down", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.memberSubfamily_inter", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Compression.Down", "is_tactic_proof": true, "tactics": ["unfold", "rw", "simp"], "tactic_count": 3}
{"name": "Finset.nonMemberSubfamily_union", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Compression.Down", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.memberSubfamily_union", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Compression.Down", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Finset.card_memberSubfamily_add_card_nonMemberSubfamily", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Compression.Down", "is_tactic_proof": true, "tactics": ["rw", "conv_rhs", "apply", "simp"], "tactic_count": 4}
{"name": "Finset.memberSubfamily_union_nonMemberSubfamily", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Compression.Down", "is_tactic_proof": true, "tactics": ["ext", "simp", "constructor", "rintro", "exact", "exact", "rintro", "by_cases", "exact", "exact"], "tactic_count": 10}
{"name": "Finset.memberSubfamily_memberSubfamily", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Compression.Down", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Finset.memberSubfamily_nonMemberSubfamily", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Compression.Down", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Finset.nonMemberSubfamily_memberSubfamily", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Compression.Down", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Finset.nonMemberSubfamily_nonMemberSubfamily", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Compression.Down", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Finset.memberSubfamily_image_insert", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Compression.Down", "is_tactic_proof": true, "tactics": ["ext", "simp", "refine", "rintro", "rwa"], "tactic_count": 5}
{"name": "Finset.nonMemberSubfamily_image_insert", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Compression.Down", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.memberSubfamily_image_erase", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Compression.Down", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.image_insert_memberSubfamily", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Compression.Down", "is_tactic_proof": true, "tactics": ["ext", "simp", "refine", "rintro", "exact", "rwa"], "tactic_count": 6}
{"name": "Finset.memberFamily_induction_on", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Compression.Down", "is_tactic_proof": true, "tactics": ["set", "have", "clear_value", "induction", "empty", "simp_rw", "rw", "obtain", "insert", "refine", "simp", "exact", "simp", "exact"], "tactic_count": 14}
{"name": "Finset.family_induction_on", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Compression.Down", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "Down.compression", "kind": "definition", "module": "Mathlib.Combinatorics.SetFamily.Compression.Down", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinsetFamily.term𝓓", "kind": "definition", "module": "Mathlib.Combinatorics.SetFamily.Compression.Down", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinsetFamily._aux_Mathlib_Combinatorics_SetFamily_Compression_Down___macroRules_FinsetFamily_term𝓓_1", "kind": "definition", "module": "Mathlib.Combinatorics.SetFamily.Compression.Down", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinsetFamily._aux_Mathlib_Combinatorics_SetFamily_Compression_Down___unexpand_Down_compression_1", "kind": "definition", "module": "Mathlib.Combinatorics.SetFamily.Compression.Down", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Down.mem_compression", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Compression.Down", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "or_congr_right", "rintro", "rwa"], "tactic_count": 5}
{"name": "Down.erase_mem_compression", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Compression.Down", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "rwa"], "tactic_count": 3}
{"name": "Down.erase_mem_compression_of_mem_compression", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Compression.Down", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "rwa"], "tactic_count": 3}
{"name": "Down.mem_compression_of_insert_mem_compression", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Compression.Down", "is_tactic_proof": true, "tactics": ["by_cases", "rwa", "rw", "exact"], "tactic_count": 4}
{"name": "Down.compression_idem", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Compression.Down", "is_tactic_proof": true, "tactics": ["ext", "refine", "rintro", "exact", "cases"], "tactic_count": 5}
{"name": "Down.card_compression", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Compression.Down", "is_tactic_proof": false, "tactics": ["rw", "card_union_of_disjoint]", "conv_rhs", "exact", "intro", "rw", "exact"], "tactic_count": 7}
{"name": "sup_sdiff_injOn", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Compression.UV", "is_tactic_proof": true, "tactics": ["rintro", "have", "dsimp", "rw", "rwa", "sdiff_sup_cancel"], "tactic_count": 6}
{"name": "UV.compress", "kind": "definition", "module": "Mathlib.Combinatorics.SetFamily.Compression.UV", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UV.compress_of_disjoint_of_le", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Compression.UV", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UV.compress_of_disjoint_of_le'", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Compression.UV", "is_tactic_proof": true, "tactics": ["rw", "sdiff_sup_cancel"], "tactic_count": 2}
{"name": "UV.compress_self", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Compression.UV", "is_tactic_proof": true, "tactics": ["unfold", "split_ifs", "exact", "rfl"], "tactic_count": 4}
{"name": "UV.compress_sdiff_sdiff", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Compression.UV", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "UV.compress_idem", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Compression.UV", "is_tactic_proof": true, "tactics": ["unfold", "split_ifs", "rw", "rfl", "rfl"], "tactic_count": 5}
{"name": "UV.compression", "kind": "definition", "module": "Mathlib.Combinatorics.SetFamily.Compression.UV", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinsetFamily.term𝓒", "kind": "definition", "module": "Mathlib.Combinatorics.SetFamily.Compression.UV", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinsetFamily._aux_Mathlib_Combinatorics_SetFamily_Compression_UV___macroRules_FinsetFamily_term𝓒_1", "kind": "definition", "module": "Mathlib.Combinatorics.SetFamily.Compression.UV", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinsetFamily._aux_Mathlib_Combinatorics_SetFamily_Compression_UV___unexpand_UV_compression_1", "kind": "definition", "module": "Mathlib.Combinatorics.SetFamily.Compression.UV", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UV.IsCompressed", "kind": "definition", "module": "Mathlib.Combinatorics.SetFamily.Compression.UV", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UV.compress_injOn", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Compression.UV", "is_tactic_proof": true, "tactics": ["intro", "rw", "rw", "split_ifs", "rw", "split_ifs", "exact", "exact", "exact"], "tactic_count": 9}
{"name": "UV.mem_compression", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Compression.UV", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "UV.IsCompressed.eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Compression.UV", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UV.compression_self", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Compression.UV", "is_tactic_proof": true, "tactics": ["unfold", "convert", "ext", "rw", "refine", "simp_rw", "obtain", "exact"], "tactic_count": 8}
{"name": "UV.isCompressed_self", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Compression.UV", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UV.compress_disjoint", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Compression.UV", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UV.compress_mem_compression", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Compression.UV", "is_tactic_proof": true, "tactics": ["rw", "by_cases", "rw", "exact", "exact"], "tactic_count": 5}
{"name": "UV.compress_mem_compression_of_mem_compression", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Compression.UV", "is_tactic_proof": true, "tactics": ["rw", "simp", "obtain", "exact", "exact"], "tactic_count": 5}
{"name": "UV.compression_idem", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Compression.UV", "is_tactic_proof": false, "tactics": ["have", "filter_false_of_mem", "rw", "exact"], "tactic_count": 4}
{"name": "UV.card_compression", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Compression.UV", "is_tactic_proof": true, "tactics": ["rw", "card_union_of_disjoint"], "tactic_count": 2}
{"name": "UV.le_of_mem_compression_of_notMem", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Compression.UV", "is_tactic_proof": true, "tactics": ["rw", "obtain", "cases", "unfold", "split_ifs", "rw", "exact", "cases"], "tactic_count": 8}
{"name": "UV.disjoint_of_mem_compression_of_notMem", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Compression.UV", "is_tactic_proof": true, "tactics": ["rw", "obtain", "cases", "unfold", "split_ifs", "rw", "exact", "cases"], "tactic_count": 8}
{"name": "UV.sup_sdiff_mem_of_mem_compression_of_notMem", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Compression.UV", "is_tactic_proof": true, "tactics": ["rw", "obtain", "cases", "unfold", "split_ifs", "rwa", "cases"], "tactic_count": 7}
{"name": "UV.sup_sdiff_mem_of_mem_compression", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Compression.UV", "is_tactic_proof": true, "tactics": ["rw", "obtain", "exact", "have", "suffices", "refine", "rw", "exact", "have", "rw", "apply", "rw", "exact", "rwa"], "tactic_count": 14}
{"name": "UV.mem_of_mem_compression", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Compression.UV", "is_tactic_proof": true, "tactics": ["rw", "obtain", "exact", "unfold", "split_ifs", "rw", "rwa", "rwa"], "tactic_count": 8}
{"name": "UV.card_compress", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Compression.UV", "is_tactic_proof": true, "tactics": ["unfold", "split_ifs", "rw", "add_tsub_cancel_right]", "rfl"], "tactic_count": 5}
{"name": "Set.Sized.uvCompression", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Compression.UV", "is_tactic_proof": true, "tactics": ["simp_rw", "rintro", "exact", "rw"], "tactic_count": 4}
{"name": "_private.Mathlib.Combinatorics.SetFamily.Compression.UV.0.UV.aux", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Compression.UV", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "UV.shadow_compression_subset_compression_shadow", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Compression.UV", "is_tactic_proof": true, "tactics": ["set", "suffices", "rintro", "rw", "by_cases", "swap", "obtain", "exact", "refine", "rw", "split_ifs", "swap", "exact", "rw", "obtain", "have", "have", "have", "by_cases", "obtain", "refine", "rw", "have", "rwa", "erase_union_of_mem", "refine", "mem_shadow_iff.2", "rw", "exact", "simp", "intro", "have", "obtain", "have", "have", "have", "have", "have", "have", "have", "have", "intro", "obtain", "apply", "m", "have", "refine", "sup_sdiff_mem_of_mem_compression", "rw", "exact", "convert", "rw", "erase_eq_of_notMem", "have", "rwa", "simp_rw", "refine", "exact", "rwa", "rintro", "have", "by_cases", "obtain", "apply", "have", "have", "refine", "rw", "exact", "convert", "rw", "sdiff_erase", "rw", "apply", "have", "sup_sdiff_mem_of_mem_compression", "convert", "rw", "insert_sdiff_of_notMem"], "tactic_count": 79}
{"name": "UV.card_shadow_compression_le", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Compression.UV", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.SetFamily.FourFunctions.0.ineq", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.FourFunctions", "is_tactic_proof": false, "tactics": ["calc", "obtain", "rw", "rw", "refine", "calc"], "tactic_count": 6}
{"name": "_private.Mathlib.Combinatorics.SetFamily.FourFunctions.0.collapse", "kind": "definition", "module": "Mathlib.Combinatorics.SetFamily.FourFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.SetFamily.FourFunctions.0.erase_eq_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.FourFunctions", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "_private.Mathlib.Combinatorics.SetFamily.FourFunctions.0.filter_collapse_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.FourFunctions", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "collapse_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.FourFunctions", "is_tactic_proof": true, "tactics": ["rw", "split_ifs"], "tactic_count": 2}
{"name": "collapse_of_mem", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.FourFunctions", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "le_collapse_of_mem", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.FourFunctions", "is_tactic_proof": true, "tactics": ["subst", "rw", "split_ifs", "exact", "rw"], "tactic_count": 5}
{"name": "le_collapse_of_insert_mem", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.FourFunctions", "is_tactic_proof": true, "tactics": ["rw", "split_ifs", "exact", "rw"], "tactic_count": 4}
{"name": "collapse_nonneg", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.FourFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "collapse_modular", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.FourFunctions", "is_tactic_proof": true, "tactics": ["rintro", "have", "have", "have", "have", "have", "have", "have", "have", "rw", "split_ifs", "rw", "split_ifs", "rw", "collapse_of_mem", "refine", "simpa", "simpa", "simpa", "rw", "refine", "rw", "insert_inter_of_notMem", "gcongr", "exacts", "rw", "refine", "rw", "union_insert,", "gcongr", "exacts", "le_collapse_of_insert_mem", "rw", "exact", "rw", "split_ifs", "refine", "rw", "inter_insert_of_notMem", "exact", "mul_le_mul_of_nonneg_right", "add_nonneg", "rw", "exact", "mul_le_mul", "collapse_nonneg", "rw", "refine", "mul_le_mul", "collapse_nonneg", "exact", "le_collapse_of_mem", "simp_rw", "exact", "rw", "split_ifs", "refine", "rw", "insert_inter_of_notMem", "exact", "mul_le_mul_of_nonneg_left", "add_nonneg", "rw", "refine", "mul_le_mul", "collapse_nonneg", "rw", "exact", "mul_le_mul", "collapse_nonneg", "simp_rw", "exact", "simp_rw", "exact"], "tactic_count": 74}
{"name": "sum_collapse", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.FourFunctions", "is_tactic_proof": false, "tactics": ["calc", "rw", "exact", "exact", "congr", "simp", "refine", "rintro", "exact", "rw", "rw", "exact", "rw", "union_sdiff_of_subset"], "tactic_count": 14}
{"name": "Finset.four_functions_theorem", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.FourFunctions", "is_tactic_proof": true, "tactics": ["induction", "empty", "simp", "obtain", "insert", "ih", "specialize", "ih", "have", "have", "simpa"], "tactic_count": 11}
{"name": "_private.Mathlib.Combinatorics.SetFamily.FourFunctions.0.four_functions_theorem_aux", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.FourFunctions", "is_tactic_proof": true, "tactics": ["have", "refine"], "tactic_count": 2}
{"name": "four_functions_theorem", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.FourFunctions", "is_tactic_proof": true, "tactics": ["classical", "set", "have", "set", "set", "have", "simpa", "subset_latticeClosure", "have", "simpa", "subset_latticeClosure", "clear_value", "obtain", "have", "four_functions_theorem_aux", "simpa", "rintro", "classical", "obtain", "obtain", "simp_rw", "exact", "simpa", "mul_nonneg", "simpa", "mul_nonneg"], "tactic_count": 26}
{"name": "Finset.le_card_infs_mul_card_sups", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.FourFunctions", "is_tactic_proof": true, "tactics": ["simpa", "four_functions_theorem"], "tactic_count": 2}
{"name": "four_functions_theorem_univ", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.FourFunctions", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "holley", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.FourFunctions", "is_tactic_proof": true, "tactics": ["classical", "obtain", "simp", "simp", "obtain", "simp", "simp", "have", "four_functions_theorem", "univ", "simpa", "simp_rw", "rw", "exact"], "tactic_count": 14}
{"name": "fkg", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.FourFunctions", "is_tactic_proof": false, "tactics": ["refine", "four_functions_theorem_univ", "dsimp", "rw", "exact", "mul_le_mul", "mul_nonneg"], "tactic_count": 7}
{"name": "Finset.le_card_diffs_mul_card_diffs", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.FourFunctions", "is_tactic_proof": false, "tactics": ["have", "s.map", "rintro", "simp_rw", "exact", "simpa"], "tactic_count": 6}
{"name": "Finset.card_le_card_diffs", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.FourFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLowerSet.nonMemberSubfamily", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.HarrisKleitman", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLowerSet.memberSubfamily", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.HarrisKleitman", "is_tactic_proof": true, "tactics": ["rintro", "simp_rw", "exact"], "tactic_count": 3}
{"name": "IsLowerSet.memberSubfamily_subset_nonMemberSubfamily", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.HarrisKleitman", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLowerSet.le_card_inter_finset'", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.HarrisKleitman", "is_tactic_proof": true, "tactics": ["induction", "empty", "simp_rw", "obtain", "simp", "obtain", "simp", "simp", "insert", "ih", "rw", "card_memberSubfamily_add_card_nonMemberSubfamily", "add_add_add_comm]", "grw", "card_le_card", "have", "rintro", "rw", "exact", "have", "rintro", "rw", "exact", "gcongr", "refine", "ih", "rw", "card_memberSubfamily_add_card_nonMemberSubfamily]"], "tactic_count": 28}
{"name": "IsLowerSet.le_card_inter_finset", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.HarrisKleitman", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUpperSet.card_inter_le_finset", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.HarrisKleitman", "is_tactic_proof": true, "tactics": ["rw", "have", "rwa", "card_sdiff_of_subset"], "tactic_count": 4}
{"name": "IsLowerSet.card_inter_le_finset", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.HarrisKleitman", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsUpperSet.le_card_inter_finset", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.HarrisKleitman", "is_tactic_proof": true, "tactics": ["rw", "have", "rwa", "card_sdiff_of_subset", "grw", "grw"], "tactic_count": 6}
{"name": "Set.Intersecting", "kind": "definition", "module": "Mathlib.Combinatorics.SetFamily.Intersecting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Intersecting.mono", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Intersecting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Intersecting.bot_notMem", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Intersecting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Intersecting.ne_bot", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Intersecting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.intersecting_empty", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Intersecting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.intersecting_singleton", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Intersecting", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.Intersecting.insert", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Intersecting", "is_tactic_proof": true, "tactics": ["rintro", "rwa", "exact", "exact", "exact"], "tactic_count": 5}
{"name": "Set.intersecting_insert", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Intersecting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.intersecting_iff_pairwise_not_disjoint", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Intersecting", "is_tactic_proof": true, "tactics": ["refine", "rintro", "exact", "have", "rw", "rw", "exact"], "tactic_count": 7}
{"name": "Set.Subsingleton.intersecting", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Intersecting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.intersecting_iff_eq_empty_of_subsingleton", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Intersecting", "is_tactic_proof": false, "tactics": ["refine", "subsingleton_of_subsingleton.intersecting.trans", "obtain", "rwa", "rintro", "exact"], "tactic_count": 6}
{"name": "Set.Intersecting.isUpperSet", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Intersecting", "is_tactic_proof": true, "tactics": ["classical", "rintro", "rw", "exact", "exact"], "tactic_count": 5}
{"name": "Set.Intersecting.isUpperSet'", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Intersecting", "is_tactic_proof": true, "tactics": ["classical", "rintro", "rw", "exact", "rw", "exact"], "tactic_count": 6}
{"name": "Set.Intersecting.exists_mem_set", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Intersecting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Intersecting.exists_mem_finset", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Intersecting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Intersecting.compl_notMem", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Intersecting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Intersecting.notMem", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Intersecting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Intersecting.disjoint_map_compl", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Intersecting", "is_tactic_proof": true, "tactics": ["rw", "rintro", "obtain", "exact"], "tactic_count": 4}
{"name": "Set.Intersecting.card_le", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Intersecting", "is_tactic_proof": true, "tactics": ["classical", "refine", "rw"], "tactic_count": 3}
{"name": "Set.Intersecting.is_max_iff_card_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Intersecting", "is_tactic_proof": true, "tactics": ["classical", "refine", "suffices", "rw", "rw", "image_eq_preimage_of_inverse", "refine", "simp_rw", "by_contra", "refine", "rw", "refine", "rintro", "have", "rw", "rw", "exact"], "tactic_count": 17}
{"name": "Set.Intersecting.exists_card_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Intersecting", "is_tactic_proof": true, "tactics": ["have", "rw", "revert", "refine", "rintro", "by_cases", "exact", "obtain", "refine", "rw", "exact"], "tactic_count": 11}
{"name": "Finset.card_biUnion_le_of_intersecting", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Kleitman", "is_tactic_proof": true, "tactics": ["have", "obtain", "rw", "refine", "biUnion_subset.2", "rw", "induction", "empty", "cons", "ih", "set", "have", "rintro", "simp_rw", "exact", "have", "refine", "rw", "exact", "refine", "nth_rw", "rw", "refine", "rw", "refine", "rw", "refine", "rw", "exact", "rw", "exact", "rw", "add_tsub_cancel_left,", "gcongr", "refine", "rw", "add_tsub_assoc_of_le", "card_cons,"], "tactic_count": 38}
{"name": "Finset.Colex.shadow_initSeg", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.KruskalKatona", "is_tactic_proof": true, "tactics": ["ext", "simp", "constructor", "rintro", "constructor", "rw", "simpa", "erase_le_erase_min", "simp_rw", "simp", "rintro", "refine", "rw", "exact", "set", "min", "have", "have", "have", "rw", "refine", "obtain", "refine", "simpa", "refine", "rcases", "apply", "rw", "refine", "apply", "rw", "apply", "rw", "by_contra", "apply", "rwa"], "tactic_count": 36}
{"name": "Finset.Colex.IsInitSeg.shadow", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.KruskalKatona", "is_tactic_proof": true, "tactics": ["cases", "obtain", "have", "have", "simp", "simp", "obtain", "simp", "obtain", "rw", "exact"], "tactic_count": 11}
{"name": "Finset.UV.toColex_compress_lt_toColex", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.KruskalKatona", "is_tactic_proof": true, "tactics": ["rw", "rw", "simp_rw", "refine", "have", "have", "simp"], "tactic_count": 7}
{"name": "_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.UV.UsefulCompression", "kind": "definition", "module": "Mathlib.Combinatorics.SetFamily.KruskalKatona", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.UV.UsefulCompression.instDecidableRel", "kind": "instance", "module": "Mathlib.Combinatorics.SetFamily.KruskalKatona", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.UV.compression_improved", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.KruskalKatona", "is_tactic_proof": true, "tactics": ["obtain", "refine", "obtain", "rw", "have", "have", "rw", "exact", "refine", "rw", "rwa", "rwa", "exact", "le_max"], "tactic_count": 14}
{"name": "Finset.UV.isInitSeg_of_compressed", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.KruskalKatona", "is_tactic_proof": true, "tactics": ["refine", "rintro", "by_contra", "have", "have", "have", "have", "have", "have", "obtain", "rw", "cases", "exact", "assumption", "refine", "rw", "exact"], "tactic_count": 17}
{"name": "_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.UV.familyMeasure", "kind": "definition", "module": "Mathlib.Combinatorics.SetFamily.KruskalKatona", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.UV.familyMeasure_compression_lt_familyMeasure", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.KruskalKatona", "is_tactic_proof": true, "tactics": ["rw", "have", "have", "have", "contrapose", "rw", "rwa", "rw", "conv_rhs", "rw", "refine", "simp_rw", "rw", "exact"], "tactic_count": 14}
{"name": "_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.UV.kruskal_katona_helper", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.KruskalKatona", "is_tactic_proof": true, "tactics": ["classical", "set", "obtain", "refine", "rw", "by_contra", "exact", "husable", "mem_filter.2", "obtain", "rw", "have", "rintro", "by_contra", "exact", "have", "obtain", "have", "obtain", "exact", "termination_by"], "tactic_count": 21}
{"name": "Finset.kruskal_katona", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.KruskalKatona", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "suffices", "have", "obtain", "exact", "exact"], "tactic_count": 7}
{"name": "Finset.iterated_kk", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.KruskalKatona", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "refine", "convert"], "tactic_count": 5}
{"name": "Finset.kruskal_katona_lovasz_form", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.KruskalKatona", "is_tactic_proof": true, "tactics": ["set", "set", "have", "calc", "k.choose", "congr", "ext", "rw", "constructor", "rintro", "have", "exists_subsuperset_card_eq", "rwa", "obtain", "rw", "refine", "rw", "rintro", "rw", "refine", "rw", "refine", "rwa", "simp_rw", "rintro", "refine", "rw", "have", "rwa", "apply", "simp_rw", "rintro", "simpa"], "tactic_count": 33}
{"name": "Finset.erdos_ko_rado", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.KruskalKatona", "is_tactic_proof": true, "tactics": ["rcases", "convert", "rw", "refine", "rw", "exact", "refine", "le_of_not_gt", "have", "disjoint_right.2", "simp", "obtain", "exact", "have", "have", "have", "rwa", "have", "have", "kruskal_katona_lovasz_form", "have", "rw", "have", "calc", "n.choose", "convert", "apply", "convert", "rw", "rw", "refine", "convert", "lia"], "tactic_count": 33}
{"name": "Finset.local_lubell_yamamoto_meshalkin_inequality_mul", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.LYM", "is_tactic_proof": true, "tactics": ["let", "refine", "rw", "refine", "simp_rw", "exact", "refine", "rw", "refine", "rw", "have", "rw", "rintro", "rw", "exact", "have", "exists_eq_insert_iff.2", "rcases", "exact"], "tactic_count": 19}
{"name": "Finset.local_lubell_yamamoto_meshalkin_inequality_div", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.LYM", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact", "replace", "rw", "rcases", "exact", "rw", "apply", "convert", "simpa", "simp", "exact", "exact", "exact"], "tactic_count": 15}
{"name": "Finset.falling", "kind": "definition", "module": "Mathlib.Combinatorics.SetFamily.LYM", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_falling", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.LYM", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.sized_falling", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.LYM", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.slice_subset_falling", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.LYM", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.falling_zero_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.LYM", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.slice_union_shadow_falling_succ", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.LYM", "is_tactic_proof": true, "tactics": ["ext", "simp_rw", "constructor", "rintro", "exact", "refine", "rw", "rfl", "rintro", "by_cases", "exact", "obtain", "refine", "rw"], "tactic_count": 14}
{"name": "Finset.IsAntichain.disjoint_slice_shadow_falling", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.LYM", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.le_card_falling_div_choose", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.LYM", "is_tactic_proof": true, "tactics": ["induction", "zero", "simp", "sum_singleton,", "exact", "succ", "ih", "rw", "card_union_of_disjoint", "rw", "grw", "local_lubell_yamamoto_meshalkin_inequality_div", "sized_falling"], "tactic_count": 13}
{"name": "Finset.lubell_yamamoto_meshalkin_inequality_sum_card_div_choose", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.LYM", "is_tactic_proof": true, "tactics": ["classical", "rw", "refine", "rw", "simpa", "rw", "exact"], "tactic_count": 7}
{"name": "Finset.lubell_yamamoto_meshalkin_inequality_sum_inv_choose", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.LYM", "is_tactic_proof": true, "tactics": ["calc", "rw"], "tactic_count": 2}
{"name": "IsAntichain.sperner", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.LYM", "is_tactic_proof": false, "tactics": ["have", "have", "calc", "gcongr", "exact", "exact", "simpa"], "tactic_count": 7}
{"name": "Finset.shadow", "kind": "definition", "module": "Mathlib.Combinatorics.SetFamily.Shadow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinsetFamily.term∂", "kind": "definition", "module": "Mathlib.Combinatorics.SetFamily.Shadow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinsetFamily._aux_Mathlib_Combinatorics_SetFamily_Shadow___macroRules_FinsetFamily_term∂_1", "kind": "definition", "module": "Mathlib.Combinatorics.SetFamily.Shadow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinsetFamily._aux_Mathlib_Combinatorics_SetFamily_Shadow___unexpand_Finset_shadow_1", "kind": "definition", "module": "Mathlib.Combinatorics.SetFamily.Shadow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.shadow_empty", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Shadow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.shadow_iterate_empty", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Shadow", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "Finset.shadow_singleton_empty", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Shadow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.shadow_singleton", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Shadow", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.shadow_monotone", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Shadow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.shadow_mono", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Shadow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_shadow_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Shadow", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.erase_mem_shadow", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Shadow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_shadow_iff_exists_sdiff", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Shadow", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Finset.mem_shadow_iff_insert_mem", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Shadow", "is_tactic_proof": true, "tactics": ["simp_rw", "aesop"], "tactic_count": 2}
{"name": "Finset.mem_shadow_iff_exists_mem_card_add_one", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Shadow", "is_tactic_proof": false, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "Finset.mem_shadow_iterate_iff_exists_card", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Shadow", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "simp", "aesop"], "tactic_count": 5}
{"name": "Finset.mem_shadow_iterate_iff_exists_sdiff", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Shadow", "is_tactic_proof": true, "tactics": ["rw", "constructor", "rintro", "exact", "rintro", "refine", "rwa"], "tactic_count": 7}
{"name": "Finset.mem_shadow_iterate_iff_exists_mem_card_add", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Shadow", "is_tactic_proof": false, "tactics": ["refine", "mem_shadow_iterate_iff_exists_sdiff.trans", "exists_congr", "rw", "exact"], "tactic_count": 5}
{"name": "Set.Sized.shadow", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Shadow", "is_tactic_proof": true, "tactics": ["intro", "obtain", "rw"], "tactic_count": 3}
{"name": "Set.Sized.shadow_iterate", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Shadow", "is_tactic_proof": true, "tactics": ["simp_rw", "rintro", "rw"], "tactic_count": 3}
{"name": "Finset.sized_shadow_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Shadow", "is_tactic_proof": true, "tactics": ["refine", "obtain", "rw"], "tactic_count": 3}
{"name": "Finset.exists_subset_of_mem_shadow", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Shadow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.upShadow", "kind": "definition", "module": "Mathlib.Combinatorics.SetFamily.Shadow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinsetFamily.term∂⁺", "kind": "definition", "module": "Mathlib.Combinatorics.SetFamily.Shadow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinsetFamily._aux_Mathlib_Combinatorics_SetFamily_Shadow___macroRules_FinsetFamily_term∂⁺_1", "kind": "definition", "module": "Mathlib.Combinatorics.SetFamily.Shadow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinsetFamily._aux_Mathlib_Combinatorics_SetFamily_Shadow___unexpand_Finset_upShadow_1", "kind": "definition", "module": "Mathlib.Combinatorics.SetFamily.Shadow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.upShadow_empty", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Shadow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.upShadow_monotone", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Shadow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_upShadow_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Shadow", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Finset.insert_mem_upShadow", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Shadow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_upShadow_iff_exists_sdiff", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Shadow", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Finset.mem_upShadow_iff_erase_mem", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Shadow", "is_tactic_proof": true, "tactics": ["simp_rw", "aesop"], "tactic_count": 2}
{"name": "Finset.mem_upShadow_iff_exists_mem_card_add_one", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Shadow", "is_tactic_proof": false, "tactics": ["refine", "mem_upShadow_iff_exists_sdiff.trans", "rw", "exact"], "tactic_count": 4}
{"name": "Finset.mem_upShadow_iterate_iff_exists_card", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Shadow", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "ih", "simp", "erase_sdiff_comm,", "constructor", "rintro", "exact", "rintro", "rw", "exact"], "tactic_count": 12}
{"name": "Finset.mem_upShadow_iterate_iff_exists_sdiff", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Shadow", "is_tactic_proof": true, "tactics": ["rw", "constructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 6}
{"name": "Finset.mem_upShadow_iterate_iff_exists_mem_card_add", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Shadow", "is_tactic_proof": false, "tactics": ["refine", "mem_upShadow_iterate_iff_exists_sdiff.trans", "exists_congr", "rw", "exact"], "tactic_count": 5}
{"name": "Set.Sized.upShadow", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Shadow", "is_tactic_proof": true, "tactics": ["intro", "obtain", "rw"], "tactic_count": 3}
{"name": "Finset.exists_subset_of_mem_upShadow", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Shadow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_upShadow_iff_exists_mem_card_add", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Shadow", "is_tactic_proof": true, "tactics": ["induction", "zero", "refine", "rintro", "rwa", "succ", "simp", "refine", "clear", "constructor", "rintro", "obtain", "refine", "rw", "rfl", "rintro", "obtain", "refine", "rw", "rfl"], "tactic_count": 20}
{"name": "Finset.shadow_compls", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Shadow", "is_tactic_proof": true, "tactics": ["ext", "simp", "refine", "simp"], "tactic_count": 4}
{"name": "Finset.upShadow_compls", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Shadow", "is_tactic_proof": true, "tactics": ["ext", "simp", "refine", "simp"], "tactic_count": 4}
{"name": "Finset.Shatters", "kind": "definition", "module": "Mathlib.Combinatorics.SetFamily.Shatter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.instDecidablePredShatters", "kind": "instance", "module": "Mathlib.Combinatorics.SetFamily.Shatter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Shatters.exists_inter_eq_singleton", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Shatter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Shatters.mono_left", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Shatter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Shatters.mono_right", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Shatter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Shatters.exists_superset", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Shatter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.shatters_of_forall_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Shatter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Shatters.nonempty", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Shatter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.shatters_empty", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Shatter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Shatters.subset_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Shatter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.shatters_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Shatter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.univ_shatters", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Shatter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.shatters_univ", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Shatter", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.shatterer", "kind": "definition", "module": "Mathlib.Combinatorics.SetFamily.Shatter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_shatterer", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Shatter", "is_tactic_proof": true, "tactics": ["refine", "simp_rw", "exact"], "tactic_count": 3}
{"name": "Finset.shatterer_mono", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Shatter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.subset_shatterer", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Shatter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.isLowerSet_shatterer", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Shatter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.shatterer_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Shatter", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact", "obtain", "exact"], "tactic_count": 5}
{"name": "Finset.shatterer_idem", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Shatter", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.shatters_shatterer", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Shatter", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "_private.Mathlib.Combinatorics.SetFamily.Shatter.0.Finset.aux", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Shatter", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "Finset.card_le_card_shatterer", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Shatter", "is_tactic_proof": true, "tactics": ["refine", "simp", "rfl", "intro", "set", "have", "refine", "simp", "exact", "rw", "refine", "rw", "swap", "simp", "rintro", "exact", "exact", "refine", "simp", "rintro", "obtain", "rw", "refine", "obtain", "rw", "rw", "exact", "refine", "simp", "rw", "by_cases", "obtain", "rw", "refine", "rw", "obtain", "rw", "refine", "rwa"], "tactic_count": 39}
{"name": "Finset.Shatters.of_compression", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Shatter", "is_tactic_proof": true, "tactics": ["intro", "obtain", "rw", "obtain", "exact", "by_cases", "obtain", "rw", "obtain", "refine", "rw", "rintro", "rw", "exact", "rw", "cases", "rw", "exact", "refine", "rw"], "tactic_count": 20}
{"name": "Finset.shatterer_compress_subset_shatterer", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Shatter", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.vcDim", "kind": "definition", "module": "Mathlib.Combinatorics.SetFamily.Shatter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.vcDim_mono", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Shatter", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "Finset.Shatters.card_le_vcDim", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Shatter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.vcDim_compress_le", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Shatter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_shatterer_le_sum_vcDim", "kind": "theorem", "module": "Mathlib.Combinatorics.SetFamily.Shatter", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.IsAcyclic", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Acyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.isAcyclic_bot", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Acyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsAcyclic.comap", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Acyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsAcyclic.embedding", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Acyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Iso.isAcyclic_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Acyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Iso.isTree_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Acyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsAcyclic.of_map", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Acyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsAcyclic.of_comap", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Acyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsAcyclic.induce", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Acyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsAcyclic.subgraph", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Acyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsAcyclic.anti", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Acyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.Walk.exists_mem_contains_edges_of_directed", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Acyclic", "is_tactic_proof": true, "tactics": ["induction", "nil", "obtain", "obtain", "obtain", "simpa"], "tactic_count": 6}
{"name": "SimpleGraph.isAcyclic_sSup_of_isAcyclic_directedOn", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Acyclic", "is_tactic_proof": true, "tactics": ["rcases", "simp", "intro", "obtain", "exact"], "tactic_count": 5}
{"name": "SimpleGraph.exists_maximal_isAcyclic_of_le_isAcyclic", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Acyclic", "is_tactic_proof": true, "tactics": ["refine", "refine", "grind", "exact"], "tactic_count": 4}
{"name": "SimpleGraph.IsAcyclic.isTree_connectedComponent", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Acyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsAcyclic.of_subsingleton", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Acyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.isAcyclic_coe_bot", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Acyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsTree.of_subsingleton", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Acyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsTree.coe_singletonSubgraph", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Acyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsTree.coe_subgraphOfAdj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Acyclic", "is_tactic_proof": true, "tactics": ["refine", "have", "have", "grind"], "tactic_count": 4}
{"name": "SimpleGraph.isAcyclic_iff_forall_adj_isBridge", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Acyclic", "is_tactic_proof": true, "tactics": ["simp_rw", "constructor", "intro", "apply", "intro", "cases", "rintro", "exact", "apply", "rw", "apply"], "tactic_count": 11}
{"name": "SimpleGraph.isAcyclic_iff_forall_edge_isBridge", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Acyclic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.IsAcyclic.path_unique", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Acyclic", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "rw", "induction", "nil", "cases", "rfl", "cons", "rw", "specialize", "rw", "replace", "simp", "rcases", "cases", "nil", "cons", "rw", "simp", "rcases", "cases", "rfl", "simp", "exact", "rw", "exact"], "tactic_count": 26}
{"name": "SimpleGraph.isAcyclic_of_path_unique", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Acyclic", "is_tactic_proof": true, "tactics": ["intro", "simp", "cases", "nil", "cons", "simp", "specialize", "rw", "simp"], "tactic_count": 9}
{"name": "SimpleGraph.isAcyclic_iff_path_unique", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Acyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsAcyclic.mem_support_of_ne_mem_support_of_adj_of_isPath", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Acyclic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.IsAcyclic.ne_mem_support_of_support_of_adj_of_isPath", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Acyclic", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.IsAcyclic.path_concat", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Acyclic", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.isTree_iff_existsUnique_path", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Acyclic", "is_tactic_proof": true, "tactics": ["classical", "rw", "constructor", "rintro", "refine", "intro", "let", "use", "simp", "intro", "specialize", "exact", "rintro", "refine", "intro", "obtain", "exact", "rintro", "simp"], "tactic_count": 19}
{"name": "SimpleGraph.IsTree.existsUnique_path", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Acyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsAcyclic.isPath_iff_isChain", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Acyclic", "is_tactic_proof": true, "tactics": ["classical", "refine", "induction", "nil", "have", "refine", "rcases", "simp", "by_contra", "apply", "simp", "support_cons,", "have", "tail.isPath_def.mp", "refine", "by_contra", "refine", "rw", "have", "simp"], "tactic_count": 20}
{"name": "SimpleGraph.IsAcyclic.isPath_iff_isTrail", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Acyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsTree.card_edgeFinset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Acyclic", "is_tactic_proof": true, "tactics": ["have", "inhabit", "classical", "have", "rw", "rw", "choose", "refine", "exact", "simp", "intro", "wlog", "exact", "rw", "obtain", "exact", "have", "have", "rw", "lia", "simp", "exact", "simp", "intro", "wlog", "rw", "exact", "refine", "rintro", "rw", "length_cons,", "simp", "rw", "simp", "contra", "suffices", "rw", "simp", "refine", "simp"], "tactic_count": 40}
{"name": "SimpleGraph.isTree_of_minimal_connected", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Acyclic", "is_tactic_proof": true, "tactics": ["rw", "exact", "by_contra", "h.not_prop_of_lt", "h.prop.connected_delete_edge_of_not_isBridge"], "tactic_count": 5}
{"name": "SimpleGraph.isTree_iff_minimal_connected", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Acyclic", "is_tactic_proof": true, "tactics": ["refine", "have", "have", "congrArg", "congrArg", "simp", "simp"], "tactic_count": 7}
{"name": "SimpleGraph.Connected.exists_isTree_le", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Acyclic", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.isAcyclic_add_edge_iff_of_not_reachable", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Acyclic", "is_tactic_proof": true, "tactics": ["refine", "have", "have", "have", "rw", "intro", "let", "have", "simpa", "exact"], "tactic_count": 10}
{"name": "SimpleGraph.reachable_eq_of_maximal_isAcyclic", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Acyclic", "is_tactic_proof": true, "tactics": ["obtain", "replace", "ext", "refine", "contrapose", "obtain", "let", "have", "have", "obtain", "suffices", "refine", "have", "simp", "grind", "rw", "push_neg", "refine", "simpa", "have", "grind", "suffices", "suffices", "rw", "exact", "simp_rw", "grind"], "tactic_count": 27}
{"name": "SimpleGraph.maximal_isAcyclic_iff_reachable_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Acyclic", "is_tactic_proof": true, "tactics": ["refine", "by_contra", "obtain", "obtain", "have", "apply", "refine", "rw", "grind", "have", "have", "apply", "simp", "simp", "cases", "simp", "suffices", "apply", "apply", "simpa"], "tactic_count": 20}
{"name": "SimpleGraph.Connected.maximal_le_isAcyclic_iff_isTree", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Acyclic", "is_tactic_proof": true, "tactics": ["have", "refine", "rw", "exact", "rw", "replace", "rw", "exact", "replace", "rw", "exact", "rw"], "tactic_count": 12}
{"name": "SimpleGraph.maximal_isAcyclic_iff_isTree", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Acyclic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Connected.card_vert_le_card_edgeSet_add_one", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Acyclic", "is_tactic_proof": true, "tactics": ["obtain", "simp", "have", "obtain", "rw", "exact"], "tactic_count": 6}
{"name": "SimpleGraph.isTree_iff_connected_and_card", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Acyclic", "is_tactic_proof": true, "tactics": ["have", "classical", "refine", "simp_rw", "refine", "by_contra", "rw", "add_lt_add_iff_right]", "exact"], "tactic_count": 9}
{"name": "SimpleGraph.IsTree.minDegree_eq_one_of_nontrivial", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Acyclic", "is_tactic_proof": true, "tactics": ["by_cases", "have", "have", "have", "gcongr", "exact", "rw", "lia", "have", "lia"], "tactic_count": 10}
{"name": "SimpleGraph.IsTree.exists_vert_degree_one_of_nontrivial", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Acyclic", "is_tactic_proof": true, "tactics": ["obtain", "use", "rw", "exact"], "tactic_count": 4}
{"name": "SimpleGraph.Connected.induce_compl_singleton_of_degree_eq_one", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Acyclic", "is_tactic_proof": true, "tactics": ["obtain", "refine", "via", "intro", "obtain", "obtain", "rw", "classical", "use", "is", "intro", "rw", "obtain", "by_contra", "subst_vars", "refine", "rw", "have", "simp", "have", "rw", "lia"], "tactic_count": 22}
{"name": "SimpleGraph.Connected.exists_connected_induce_compl_singleton_of_finite_nontrivial", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Acyclic", "is_tactic_proof": true, "tactics": ["obtain", "have", "have", "classical", "obtain", "exact"], "tactic_count": 6}
{"name": "SimpleGraph.Connected.exists_preconnected_induce_compl_singleton_of_finite", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Acyclic", "is_tactic_proof": true, "tactics": ["nontriviality", "obtain", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.IsAcyclic.dist_ne_of_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Acyclic", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "rw", "by_cases", "rw", "exact", "have", "rw", "exact"], "tactic_count": 9}
{"name": "SimpleGraph.IsTree.dist_ne_of_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Acyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsAcyclic.dist_eq_dist_add_one_of_adj_of_reachable", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Acyclic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "SimpleGraph.IsTree.dist_eq_dist_add_one_of_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Acyclic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "SimpleGraph.IsTree.coloringTwoOfVert", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Acyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsTree.coloringTwo", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Acyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsTree.isBipartite", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Acyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsAcyclic.coloringTwoOfVerts", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Acyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsAcyclic.coloringTwo", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Acyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsAcyclic.isBipartite", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Acyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.IsAdjMatrix.apply_diag_ne", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.AdjMatrix", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.IsAdjMatrix.apply_ne_one_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.AdjMatrix", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "Matrix.IsAdjMatrix.apply_ne_zero_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.AdjMatrix", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matrix.IsAdjMatrix.toGraph", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.AdjMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.IsAdjMatrix.instDecidableRelAdjToGraphOfDecidableEq", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.AdjMatrix", "is_tactic_proof": true, "tactics": ["simp", "infer_instance"], "tactic_count": 2}
{"name": "Matrix.isAdjMatrix_iff_hadamard", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.AdjMatrix", "is_tactic_proof": false, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Matrix.compl", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.AdjMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.compl_apply_diag", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.AdjMatrix", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.compl_apply", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.AdjMatrix", "is_tactic_proof": true, "tactics": ["unfold", "split_ifs"], "tactic_count": 2}
{"name": "Matrix.isSymm_compl", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.AdjMatrix", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Matrix.isAdjMatrix_compl", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.AdjMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.IsAdjMatrix.compl", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.AdjMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.IsAdjMatrix.toGraph_compl_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.AdjMatrix", "is_tactic_proof": true, "tactics": ["ext", "rcases"], "tactic_count": 2}
{"name": "SimpleGraph.adjMatrix", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.AdjMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.adjMatrix_apply", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.AdjMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.transpose_adjMatrix", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.AdjMatrix", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "SimpleGraph.isSymm_adjMatrix", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.AdjMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.isAdjMatrix_adjMatrix", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.AdjMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.toGraph_adjMatrix_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.AdjMatrix", "is_tactic_proof": true, "tactics": ["ext", "simp", "apply"], "tactic_count": 3}
{"name": "SimpleGraph.one_add_adjMatrix_add_compl_adjMatrix_eq_allOnes", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.AdjMatrix", "is_tactic_proof": true, "tactics": ["ext", "unfold", "rw", "by_cases", "aesop", "split_ifs"], "tactic_count": 6}
{"name": "SimpleGraph.adjMatrix_dotProduct", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.AdjMatrix", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.dotProduct_adjMatrix", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.AdjMatrix", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.adjMatrix_mulVec_apply", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.AdjMatrix", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.adjMatrix_vecMul_apply", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.AdjMatrix", "is_tactic_proof": true, "tactics": ["simp", "refine", "rw"], "tactic_count": 3}
{"name": "SimpleGraph.adjMatrix_mul_apply", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.AdjMatrix", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.mul_adjMatrix_apply", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.AdjMatrix", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.trace_adjMatrix", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.AdjMatrix", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.adjMatrix_mul_self_apply_self", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.AdjMatrix", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.adjMatrix_mulVec_const_apply", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.AdjMatrix", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.adjMatrix_mulVec_const_apply_of_regular", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.AdjMatrix", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.adjMatrix_pow_apply_eq_card_walk", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.AdjMatrix", "is_tactic_proof": true, "tactics": ["rw", "induction", "zero", "succ", "simp", "rw", "norm_cast", "simp", "apply", "rintro", "rw", "intro", "simp", "obtain", "cases", "simp"], "tactic_count": 16}
{"name": "SimpleGraph.dotProduct_mulVec_adjMatrix", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.AdjMatrix", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.IsAdjMatrix.adjMatrix_toGraph_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.AdjMatrix", "is_tactic_proof": true, "tactics": ["ext", "obtain"], "tactic_count": 2}
{"name": "aesop_graph", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Combinatorics_SimpleGraph_Basic___macroRules_aesop_graph_1", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "aesop_graph?", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Combinatorics_SimpleGraph_Basic___macroRules_aesop_graph?_1", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "aesop_graph_nonterminal", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Combinatorics_SimpleGraph_Basic___macroRules_aesop_graph_nonterminal_1", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.mk'", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFintypeSimpleGraphOfDecidableEq", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.instFinite", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.fromRel", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.fromRel_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDecidableRelAdjFromRelOfDecidableEq", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "completeBipartiteGraph", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.irrefl", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.adj_comm", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.adj_symm", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Adj.symm", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ne_of_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.Adj.ne", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Adj.ne'", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ne_of_adj_of_not_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.adj_injective", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.adj_inj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.adj_congr_of_sym2", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": true, "tactics": ["simp", "rcases", "rw", "rw"], "tactic_count": 4}
{"name": "SimpleGraph.symm_adj", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsSubgraph", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.instLE", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.le_iff_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.isSubgraph_eq_le", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.instMax", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.sup_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.instMin", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.inf_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.instCompl", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.compl_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.sdiff", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.sdiff_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.supSet", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.infSet", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.sSup_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.sInf_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.iSup_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.iInf_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.sInf_adj_of_nonempty", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.iInf_adj_of_nonempty", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.distribLattice", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.completeAtomicBooleanAlgebra", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.completeGraph", "kind": "abbrev", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.emptyGraph", "kind": "abbrev", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.top_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.bot_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.completeGraph_eq_top", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.emptyGraph_eq_bot", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.eq_bot_iff_forall_not_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.ne_bot_iff_exists_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.eq_top_iff_forall_ne_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.ne_top_iff_exists_not_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.instInhabited", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.uniqueOfSubsingleton", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.instNontrivial", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Bot.adjDecidable", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Sup.adjDecidable", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Inf.adjDecidable", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Sdiff.adjDecidable", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Top.adjDecidable", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Compl.adjDecidable", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.support", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.mem_support", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.support_mono", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.support_top_of_nontrivial", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.support_bot", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.support_eq_bot_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.support_of_subsingleton", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.neighborSet", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.neighborSet.memDecidable", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.neighborSet_subset_support", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.edgeSetEmbedding", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.edgeSet", "kind": "abbrev", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.mem_edgeSet", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.not_isDiag_of_mem_edgeSet", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.not_mem_edgeSet_of_isDiag", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.edgeSet_inj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.edgeSet_subset_edgeSet", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.edgeSet_ssubset_edgeSet", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.edgeSet_injective", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.edgeSet_bot", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.edgeSet_top", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.edgeSet_subset_compl_diagSet", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "SimpleGraph.edgeSet_sup", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "SimpleGraph.edgeSet_inf", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "SimpleGraph.edgeSet_sdiff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "SimpleGraph.disjoint_edgeSet", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.edgeSet_eq_empty", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.edgeSet_nonempty", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.edgeSet_sdiff_sdiff_isDiag", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "SimpleGraph.adj_iff_exists_edge", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": true, "tactics": ["refine", "rintro", "rw", "subst", "rwa"], "tactic_count": 5}
{"name": "SimpleGraph.adj_iff_exists_edge_coe", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.edge_other_ne", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.decidableMemEdgeSet", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.fintypeEdgeSet", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.fintypeEdgeSetBot", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "SimpleGraph.fintypeEdgeSetSup", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "SimpleGraph.fintypeEdgeSetInf", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.fintypeEdgeSetSdiff", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.fromEdgeSet", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.instDecidableRelAdjFromEdgeSetOfDecidablePredSym2MemSetOfDecidableEq", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.fromEdgeSet_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.edgeSet_fromEdgeSet", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.fromEdgeSet_edgeSet", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.fromEdgeSet_le", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.edgeSet_eq_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.fromEdgeSet_empty", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "SimpleGraph.fromEdgeSet_not_isDiag", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "SimpleGraph.fromEdgeSet_univ", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "SimpleGraph.fromEdgeSet_inter", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp", "tauto"], "tactic_count": 3}
{"name": "SimpleGraph.fromEdgeSet_union", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "SimpleGraph.fromEdgeSet_sdiff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": true, "tactics": ["ext", "constructor"], "tactic_count": 2}
{"name": "SimpleGraph.fromEdgeSet_mono", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "SimpleGraph.disjoint_fromEdgeSet", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": true, "tactics": ["conv_rhs", "rw", "grind"], "tactic_count": 3}
{"name": "SimpleGraph.fromEdgeSet_disjoint", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.instFintypeElemSym2EdgeSetFromEdgeSetOfDecidableEq", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "SimpleGraph.disjoint_left", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.incidenceSet", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.incidenceSet_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.mk'_mem_incidenceSet_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.mk'_mem_incidenceSet_left_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.mk'_mem_incidenceSet_right_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.edge_mem_incidenceSet_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.incidenceSet_inter_incidenceSet_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.incidenceSet_inter_incidenceSet_of_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": true, "tactics": ["refine", "rintro", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.adj_of_mem_incidenceSet", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "SimpleGraph.incidenceSet_inter_incidenceSet_of_not_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "intro", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.decidableMemIncidenceSet", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.mem_neighborSet", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.notMem_neighborSet_self", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.mem_incidenceSet", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.mem_incidence_iff_neighbor", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.adj_incidenceSet_inter", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp", "refine", "rw", "exact", "rintro", "exact"], "tactic_count": 7}
{"name": "SimpleGraph.compl_neighborSet_disjoint", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": true, "tactics": ["rw", "rintro", "rw", "exact"], "tactic_count": 4}
{"name": "SimpleGraph.neighborSet_union_compl_neighborSet_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": true, "tactics": ["ext", "have", "simp_rw", "tauto"], "tactic_count": 4}
{"name": "SimpleGraph.card_neighborSet_union_compl_neighborSet", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": true, "tactics": ["classical", "simp_rw"], "tactic_count": 2}
{"name": "SimpleGraph.neighborSet_compl", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "SimpleGraph.commonNeighbors", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.commonNeighbors_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.mem_commonNeighbors", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.commonNeighbors_symm", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.notMem_commonNeighbors_left", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.notMem_commonNeighbors_right", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.commonNeighbors_subset_neighborSet_left", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.commonNeighbors_subset_neighborSet_right", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.decidableMemCommonNeighbors", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.commonNeighbors_top_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "SimpleGraph.otherVertexOfIncident", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.edge_other_incident_set", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": true, "tactics": ["use", "simp"], "tactic_count": 2}
{"name": "SimpleGraph.incidence_other_prop", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": true, "tactics": ["obtain", "rwa"], "tactic_count": 2}
{"name": "SimpleGraph.incidence_other_neighbor_edge", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.incidenceSetEquivNeighborSet", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsCompleteBetween", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsCompleteBetween.disjoint", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.isCompleteBetween_comm", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.subsingleton_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": true, "tactics": ["refine", "contrapose", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.nontrivial_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Basic", "is_tactic_proof": true, "tactics": ["refine", "contrapose", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.IsBipartiteWith.symm", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Bipartite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.isBipartiteWith_comm", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Bipartite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsBipartiteWith.mem_of_mem_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Bipartite", "is_tactic_proof": true, "tactics": ["apply", "have", "simpa"], "tactic_count": 3}
{"name": "SimpleGraph.isBipartiteWith_neighborSet", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Bipartite", "is_tactic_proof": true, "tactics": ["ext", "rw", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.isBipartiteWith_neighborSet_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Bipartite", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.isBipartiteWith_neighborSet_disjoint", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Bipartite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsBipartiteWith.mem_of_mem_adj'", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Bipartite", "is_tactic_proof": true, "tactics": ["apply", "have", "simpa"], "tactic_count": 3}
{"name": "SimpleGraph.isBipartiteWith_neighborSet'", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Bipartite", "is_tactic_proof": true, "tactics": ["ext", "rw", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.isBipartiteWith_neighborSet_subset'", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Bipartite", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.isBipartiteWith_support_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Bipartite", "is_tactic_proof": true, "tactics": ["intro", "apply", "tauto"], "tactic_count": 3}
{"name": "SimpleGraph.isBipartiteWith_neighborSet_disjoint'", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Bipartite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.isBipartiteWith_neighborFinset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Bipartite", "is_tactic_proof": true, "tactics": ["ext", "rw", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.isBipartiteWith_neighborFinset'", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Bipartite", "is_tactic_proof": true, "tactics": ["ext", "rw", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.isBipartiteWith_bipartiteAbove", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Bipartite", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.isBipartiteWith_bipartiteBelow", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Bipartite", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.isBipartiteWith_neighborFinset_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Bipartite", "is_tactic_proof": true, "tactics": ["classical", "rw", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.isBipartiteWith_neighborFinset_disjoint", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Bipartite", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.isBipartiteWith_degree_le", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Bipartite", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.isBipartiteWith_neighborFinset_subset'", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Bipartite", "is_tactic_proof": true, "tactics": ["classical", "rw", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.isBipartiteWith_neighborFinset_disjoint'", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Bipartite", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.isBipartiteWith_degree_le'", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Bipartite", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.isBipartiteWith_sum_degrees_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Bipartite", "is_tactic_proof": true, "tactics": ["classical", "simp_rw", "conv_lhs", "rhs", "rw", "conv_rhs", "rhs", "rw", "simp_rw", "exact"], "tactic_count": 10}
{"name": "SimpleGraph.isBipartiteWith_sum_degrees_eq_twice_card_edges", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Bipartite", "is_tactic_proof": true, "tactics": ["have", "rw", "rw", "intro", "rwa"], "tactic_count": 5}
{"name": "SimpleGraph.isBipartiteWith_sum_degrees_eq_card_edges", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Bipartite", "is_tactic_proof": true, "tactics": ["classical", "rw", "sum_union", "exact"], "tactic_count": 4}
{"name": "SimpleGraph.isBipartiteWith_sum_degrees_eq_card_edges'", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Bipartite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsBipartite", "kind": "abbrev", "module": "Mathlib.Combinatorics.SimpleGraph.Bipartite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsBipartite.exists_isBipartiteWith", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Bipartite", "is_tactic_proof": true, "tactics": ["obtain", "refine", "rintro", "apply", "simp", "lia"], "tactic_count": 6}
{"name": "SimpleGraph.IsBipartiteWith.isBipartite", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Bipartite", "is_tactic_proof": true, "tactics": ["refine", "obtain"], "tactic_count": 2}
{"name": "SimpleGraph.isBipartite_iff_exists_isBipartiteWith", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Bipartite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Copy.completeBipartiteGraph", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Bipartite", "is_tactic_proof": false, "tactics": ["have", "rw", "exact", "let", "have", "rw", "exact", "let", "let", "refine", "refine", "rcases", "all_goals", "rw", "exact", "rw", "exact"], "tactic_count": 17}
{"name": "SimpleGraph.completeBipartiteGraph_isContained_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Bipartite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.between", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Bipartite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.between_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Bipartite", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "SimpleGraph.between_le", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Bipartite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.between_comm", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Bipartite", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.instDecidableRelAdjBetweenOfDecidablePredMemSet", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Bipartite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.between_isBipartiteWith", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Bipartite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.between_isBipartite", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Bipartite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.neighborSet_subset_between_union", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Bipartite", "is_tactic_proof": true, "tactics": ["intro", "rw", "by_cases", "exact", "exact"], "tactic_count": 5}
{"name": "SimpleGraph.neighborSet_subset_between_union_compl", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Bipartite", "is_tactic_proof": true, "tactics": ["intro", "rw", "by_cases", "exact", "exact"], "tactic_count": 5}
{"name": "SimpleGraph.neighborFinset_subset_between_union", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Bipartite", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "SimpleGraph.degree_le_between_add", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Bipartite", "is_tactic_proof": false, "tactics": ["have", "simpa", "simp_rw", "card_union_of_disjoint", "exact"], "tactic_count": 5}
{"name": "SimpleGraph.neighborFinset_subset_between_union_compl", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Bipartite", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "SimpleGraph.degree_le_between_add_compl", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Bipartite", "is_tactic_proof": false, "tactics": ["have", "simpa", "simp_rw", "card_union_of_disjoint", "exact"], "tactic_count": 5}
{"name": "SimpleGraph.circulantGraph", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Circulant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.circulantGraph_eq_erase_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Circulant", "is_tactic_proof": true, "tactics": ["ext", "simp", "intro", "apply", "intro", "cases", "inl", "inr", "intro", "cases", "inl", "inr"], "tactic_count": 12}
{"name": "SimpleGraph.circulantGraph_eq_symm", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Circulant", "is_tactic_proof": true, "tactics": ["ext", "simp", "grind"], "tactic_count": 3}
{"name": "SimpleGraph.instDecidableRelAdjCirculantGraphOfDecidableEqOfDecidablePredMemSet", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Circulant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.circulantGraph_adj_translate", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Circulant", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.cycleGraph", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Circulant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.instDecidableRelFinAdjCycleGraph", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Circulant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.cycleGraph_zero_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Circulant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.cycleGraph_zero_eq_bot", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Circulant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.cycleGraph_one_eq_bot", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Circulant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.cycleGraph_zero_eq_top", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Circulant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.cycleGraph_one_eq_top", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Circulant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.cycleGraph_two_eq_top", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Circulant", "is_tactic_proof": true, "tactics": ["simp", "decide"], "tactic_count": 2}
{"name": "SimpleGraph.cycleGraph_three_eq_top", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Circulant", "is_tactic_proof": true, "tactics": ["simp", "decide"], "tactic_count": 2}
{"name": "SimpleGraph.cycleGraph_one_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Circulant", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.cycleGraph_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Circulant", "is_tactic_proof": true, "tactics": ["simp", "intro", "simp_all"], "tactic_count": 3}
{"name": "SimpleGraph.cycleGraph_adj'", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Circulant", "is_tactic_proof": true, "tactics": ["n"], "tactic_count": 1}
{"name": "SimpleGraph.cycleGraph_neighborSet", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Circulant", "is_tactic_proof": true, "tactics": ["ext", "simp", "rw"], "tactic_count": 3}
{"name": "SimpleGraph.cycleGraph_neighborFinset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Circulant", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.cycleGraph_degree_two_le", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Circulant", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.cycleGraph_degree_three_le", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Circulant", "is_tactic_proof": true, "tactics": ["rw", "simp", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.pathGraph_le_cycleGraph", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Circulant", "is_tactic_proof": true, "tactics": ["n", "intro", "rw", "rw", "cases", "inl", "inr"], "tactic_count": 7}
{"name": "SimpleGraph.cycleGraph_preconnected", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Circulant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.cycleGraph_connected", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Circulant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.SimpleGraph.Circulant.0.SimpleGraph.cycleGraph_EulerianCircuit_cons", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Circulant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.cycleGraph_EulerianCircuit", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Circulant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.SimpleGraph.Circulant.0.SimpleGraph.cycleGraph_EulerianCircuit_cons_length", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Circulant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.cycleGraph_EulerianCircuit_length", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Circulant", "is_tactic_proof": true, "tactics": ["unfold", "simp"], "tactic_count": 2}
{"name": "SimpleGraph.IsClique", "kind": "abbrev", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.isClique_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.not_isClique_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SimpleGraph.isClique_iff_induce_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["rw", "constructor", "intro", "ext", "simp", "exact", "intro", "have", "conv_lhs", "simp", "exact"], "tactic_count": 11}
{"name": "SimpleGraph.isClique_iff_isChain_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.instDecidableIsCliqueCoeFinsetOfDecidableEqOfDecidableRelAdj", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.isClique_empty", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.isClique_singleton", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.IsClique.of_subsingleton", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.isClique_pair", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.isClique_insert", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.isClique_insert_of_notMem", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsClique.insert", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsClique.mono", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsClique.subset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.isClique_bot_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsClique.map", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.isClique_map_iff_of_nontrivial", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["refine", "rintro", "obtain", "rw", "rwa", "rw", "intro", "obtain", "obtain", "exact"], "tactic_count": 10}
{"name": "SimpleGraph.isClique_map_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["obtain", "simp", "simp"], "tactic_count": 3}
{"name": "SimpleGraph.isClique_map_image_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["rw", "obtain", "simp", "simp"], "tactic_count": 4}
{"name": "SimpleGraph.isClique_map_finset_iff_of_nontrivial", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["constructor", "rw", "rintro", "obtain", "exact", "rintro", "simpa"], "tactic_count": 7}
{"name": "SimpleGraph.isClique_map_finset_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["obtain", "simp", "exact", "rw", "simp", "exact"], "tactic_count": 6}
{"name": "SimpleGraph.IsClique.finsetMap", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "SimpleGraph.IsClique.of_induce", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["simp", "intro", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.IsClique.sdiff_of_sup_edge", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["intro", "have", "simp_all"], "tactic_count": 3}
{"name": "SimpleGraph.isClique_sup_edge_of_ne_sdiff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["intro", "by_cases", "obtain", "exact", "exact", "exact"], "tactic_count": 6}
{"name": "SimpleGraph.isClique_sup_edge_of_ne_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.isClique_range_copy_top", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["intro", "rw", "rwa", "f.topEmbedding.map_adj_iff]"], "tactic_count": 4}
{"name": "SimpleGraph.isNClique_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.instDecidableIsNCliqueOfDecidableEqOfDecidableRelAdj", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.isNClique_empty", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.isNClique_singleton", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.IsNClique.mono", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.IsNClique.map", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.isNClique_map_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": false, "tactics": ["rw", "constructor", "rintro", "simp", "rintro", "simp"], "tactic_count": 6}
{"name": "SimpleGraph.isNClique_bot_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["rw", "refine", "rintro", "exact"], "tactic_count": 4}
{"name": "SimpleGraph.isNClique_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.isNClique_one", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.IsNClique.insert", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["constructor", "push_cast", "exact", "rw"], "tactic_count": 4}
{"name": "SimpleGraph.IsNClique.erase_of_mem", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsNClique.insert_erase", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["cases", "zero", "succ"], "tactic_count": 3}
{"name": "SimpleGraph.is3Clique_triple_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["simp", "by_cases"], "tactic_count": 2}
{"name": "SimpleGraph.is3Clique_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["refine", "obtain", "refine", "rwa", "rintro", "exact"], "tactic_count": 6}
{"name": "SimpleGraph.is3Clique_iff_exists_cycle_length_three", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["classical", "simp_rw", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.IsNClique.of_induce", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["rw", "simp", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.IsNClique.erase_of_sup_edge_of_mem", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.isNClique_map_copy_top", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.CliqueFree", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsNClique.not_cliqueFree", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.not_cliqueFree_of_top_embedding", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["simp", "use", "simp", "ext", "simp", "obtain", "obtain", "simp_rw"], "tactic_count": 8}
{"name": "SimpleGraph.topEmbeddingOfNotCliqueFree", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["simp", "obtain", "have", "apply", "simpa", "rw", "convert", "exact"], "tactic_count": 8}
{"name": "SimpleGraph.not_cliqueFree_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.cliqueFree_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["contrapose"], "tactic_count": 1}
{"name": "SimpleGraph.cliqueFree_iff_top_free", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.not_cliqueFree_card_of_top_embedding", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.not_cliqueFree_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.cliqueFree_bot", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["intro", "have", "contradiction"], "tactic_count": 3}
{"name": "SimpleGraph.CliqueFree.mono", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["intro", "obtain", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.CliqueFree.anti", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.CliqueFree.comap", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["intro", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.cliqueFree_map_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "simp", "simp", "simp"], "tactic_count": 5}
{"name": "SimpleGraph.cliqueFree_of_card_lt", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["rw", "contrapose", "simpa"], "tactic_count": 3}
{"name": "SimpleGraph.cliqueFree_completeMultipartiteGraph", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["rw", "intro", "obtain", "rw", "exact"], "tactic_count": 5}
{"name": "SimpleGraph.completeMultipartiteGraph.topEmbedding", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.completeMultipartiteGraph.not_cliqueFree_of_le_card", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.completeMultipartiteGraph.not_cliqueFree_of_infinite", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.completeMultipartiteGraph.not_cliqueFree_of_le_enatCard", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "have", "rw", "exact"], "tactic_count": 5}
{"name": "SimpleGraph.CliqueFree.replaceVertex", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["contrapose", "obtain", "rw", "by_cases", "obtain", "by_cases", "obtain", "have", "simp_rw", "rwa", "unfold", "use", "intro", "simp", "rw", "convert", "use", "simp_rw", "conv", "exact"], "tactic_count": 20}
{"name": "SimpleGraph.cliqueFree_one", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.cliqueFree_two", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["classical", "constructor", "simp_rw", "exact", "rintro", "exact"], "tactic_count": 6}
{"name": "SimpleGraph.CliqueFree.mem_of_sup_edge_isNClique", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["by_contra", "have", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.CliqueFree.sup_edge", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsNClique.exists_not_adj_of_cliqueFree_succ", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["classical", "by_contra", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.exists_of_maximal_cliqueFree_not_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["obtain", "use", "have", "have", "rw", "insert_erase", "exact"], "tactic_count": 7}
{"name": "SimpleGraph.CliqueFreeOn", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.CliqueFreeOn.subset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.CliqueFreeOn.mono", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["rintro", "obtain", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.CliqueFreeOn.anti", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.cliqueFreeOn_empty", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.cliqueFreeOn_singleton", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "SimpleGraph.cliqueFreeOn_univ", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.CliqueFree.cliqueFreeOn", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.cliqueFreeOn_of_card_lt", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.cliqueFreeOn_two", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["classical", "refine", "push_cast", "exact", "simp", "rintro", "simp", "refine"], "tactic_count": 8}
{"name": "SimpleGraph.CliqueFreeOn.of_succ", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["classical", "refine", "push_cast", "exact"], "tactic_count": 4}
{"name": "SimpleGraph.cliqueSet", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.mem_cliqueSet_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.cliqueSet_eq_empty_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "SimpleGraph.cliqueSet_mono", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.cliqueSet_mono'", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.cliqueSet_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.cliqueSet_one", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.cliqueSet_bot", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.cliqueSet_map", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["ext", "constructor", "rintro", "have", "classical", "rw", "rintro", "obtain", "obtain", "exact", "refine", "rw", "exact", "rintro", "exact"], "tactic_count": 15}
{"name": "SimpleGraph.cliqueSet_map_of_equiv", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["obtain", "ext", "simp", "exact"], "tactic_count": 4}
{"name": "SimpleGraph.cliqueNum", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.finite_cliqueNum_bddAbove", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["have", "use", "rintro", "rw", "rw", "exact"], "tactic_count": 6}
{"name": "SimpleGraph.IsClique.card_le_cliqueNum", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "SimpleGraph.exists_isNClique_cliqueNum", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "simp"], "tactic_count": 3}
{"name": "SimpleGraph.isMaximumClique_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.isMaximalClique_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsMaximumClique.isMaximalClique", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.maximumClique_card_eq_cliqueNum", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.maximumClique_exists", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.cliqueFinset", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.mem_cliqueFinset_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.coe_cliqueFinset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.cliqueFinset_eq_empty_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "SimpleGraph.card_cliqueFinset_le", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["rw", "refine", "simpa"], "tactic_count": 3}
{"name": "SimpleGraph.cliqueFinset_mono", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.cliqueFinset_map", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.cliqueFinset_map_of_equiv", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsIndepSet", "kind": "abbrev", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.isIndepSet_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.isIndepSet_iff_isAntichain_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.isClique_compl", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["rw", "simp_all"], "tactic_count": 2}
{"name": "SimpleGraph.isIndepSet_compl", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["rw", "simp_all"], "tactic_count": 2}
{"name": "SimpleGraph.instDecidableIsIndepSetCoeFinsetOfDecidableEqOfDecidableRelAdj", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsIndepSet.nonempty_mem_compl_mem_edge", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["obtain", "by_contra", "refine", "exact", "exact"], "tactic_count": 5}
{"name": "SimpleGraph.isIndepSet_neighborSet_of_triangleFree", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["classical", "by_contra", "rw", "push_neg", "simp_rw", "obtain", "exact"], "tactic_count": 7}
{"name": "SimpleGraph.isIndepSet_induce", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.isNClique_compl", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "SimpleGraph.isNIndepSet_compl", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "SimpleGraph.instDecidableIsNIndepSetOfDecidableEqOfDecidableRelAdj", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.isNIndepSet_induce", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.IndepSetFree", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.cliqueFree_compl", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.indepSetFree_compl", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.IndepSetFreeOn", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.indepSetSet", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.mem_indepSetSet_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.indepNum", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.cliqueNum_compl", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.indepNum_compl", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.IsIndepSet.card_le_indepNum", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.exists_isNIndepSet_indepNum", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.isMaximumClique_compl", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.isMaximumIndepSet_compl", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.isMaximalIndepSet_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.isMaximalClique_compl", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.isMaximalIndepSet_compl", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.IsMaximumIndepSet.isMaximalIndepSet", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.maximumIndepSet_card_eq_indepNum", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.maximumIndepSet_exists", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.indepSetFinset", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.mem_indepSetFinset_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Clique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Coloring", "kind": "abbrev", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Coloring.valid", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Coloring.injective_comp_of_pairwise_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Coloring.mk", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Coloring.colorClass", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Coloring.colorClasses", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Coloring.mem_colorClass", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Coloring.colorClasses_isPartition", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Coloring.mem_colorClasses", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Coloring.colorClasses_finite", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Coloring.card_colorClasses_le", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": true, "tactics": ["simp", "convert"], "tactic_count": 2}
{"name": "SimpleGraph.Coloring.not_adj_of_mem_colorClass", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Coloring.color_classes_independent", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.instFintypeColoring", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": true, "tactics": ["classical", "change", "apply"], "tactic_count": 3}
{"name": "SimpleGraph.instDecidablePredMemSetColorClassOfDecidableEq", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Colorable", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Coloring.ofIsEmpty", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Colorable.of_isEmpty", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.isEmpty_of_colorable_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": true, "tactics": ["constructor", "intro", "obtain", "exact"], "tactic_count": 4}
{"name": "SimpleGraph.colorable_zero_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Colorable.map", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": true, "tactics": ["obtain", "use", "intro", "rw", "exact"], "tactic_count": 5}
{"name": "SimpleGraph.Colorable.card_le_of_pairwise_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": true, "tactics": ["obtain", "simpa"], "tactic_count": 2}
{"name": "SimpleGraph.selfColoring", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.chromaticNumber", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.le_chromaticNumber_iff_colorable", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.le_chromaticNumber_iff_coloring", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.le_chromaticNumber_of_pairwise_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.chromaticNumber_eq_biInf", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.chromaticNumber_eq_iInf", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.Colorable.chromaticNumber_eq_sInf", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.recolorOfEmbedding", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.coe_recolorOfEmbedding", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.recolorOfEquiv", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.coe_recolorOfEquiv", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.recolorOfCardLE", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.coe_recolorOfCardLE", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Colorable.mono", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Coloring.colorable", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.colorable_of_fintype", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Colorable.toColoring", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.Colorable.of_hom", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Colorable.of_embedding", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.colorable_iff_exists_bdd_nat_coloring", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "have", "let", "use", "intro", "exact", "rintro", "refine", "exact", "rintro", "simp", "exact"], "tactic_count": 13}
{"name": "SimpleGraph.colorable_iff_forall_connectedComponents", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.colorable_set_nonempty_of_colorable", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.chromaticNumber_bddBelow", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Colorable.chromaticNumber_le", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": true, "tactics": ["rw", "norm_cast", "apply", "exact"], "tactic_count": 4}
{"name": "SimpleGraph.chromaticNumber_ne_top_iff_exists", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": true, "tactics": ["rw", "convert_to", "rw", "rw", "simp"], "tactic_count": 5}
{"name": "SimpleGraph.chromaticNumber_le_iff_colorable", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": true, "tactics": ["refine", "have", "rw", "obtain", "rw", "have", "rw", "exact"], "tactic_count": 8}
{"name": "SimpleGraph.chromaticNumber_eq_iff_colorable_not_colorable", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.colorable_chromaticNumber", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": true, "tactics": ["classical", "rw", "apply", "exact"], "tactic_count": 4}
{"name": "SimpleGraph.colorable_chromaticNumber_of_fintype", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": true, "tactics": ["cases", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.chromaticNumber_le_one_of_subsingleton", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": true, "tactics": ["rw", "refine", "intro", "cases", "simp"], "tactic_count": 5}
{"name": "SimpleGraph.chromaticNumber_pos", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": true, "tactics": ["rw", "apply", "intro", "by_contra", "simp", "obtain", "have", "exact"], "tactic_count": 8}
{"name": "SimpleGraph.colorable_of_chromaticNumber_ne_top", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": true, "tactics": ["rw", "obtain", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.chromaticNumber_eq_zero_of_isEmpty", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.isEmpty_of_chromaticNumber_eq_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.Colorable.mono_left", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.chromaticNumber_le_of_forall_imp", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": true, "tactics": ["rw", "simp", "intro", "have", "rw", "exact"], "tactic_count": 6}
{"name": "SimpleGraph.chromaticNumber_mono", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.chromaticNumber_mono_of_hom", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.chromaticNumber_mono_of_embedding", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.card_le_chromaticNumber_iff_forall_surjective", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": true, "tactics": ["refine", "rw", "intro", "by_contra", "let", "classical", "exact", "simp", "rintro", "contrapose", "refine", "dsimp", "simpa"], "tactic_count": 13}
{"name": "SimpleGraph.le_chromaticNumber_iff_forall_surjective", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.chromaticNumber_eq_card_iff_forall_surjective", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.chromaticNumber_eq_iff_forall_surjective", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.chromaticNumber_bot", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.chromaticNumber_top", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "intro", "contrapose", "intro", "exact"], "tactic_count": 7}
{"name": "SimpleGraph.chromaticNumber_top_eq_top_of_infinite", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": true, "tactics": ["by_contra", "rw", "obtain", "exact"], "tactic_count": 4}
{"name": "SimpleGraph.eq_top_of_chromaticNumber_eq_card", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": true, "tactics": ["classical", "by_contra", "have", "obtain", "apply", "suffices", "apply", "grind", "rw", "have", "grind"], "tactic_count": 11}
{"name": "SimpleGraph.chromaticNumber_eq_card_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.chromaticNumber_le_card", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.two_le_chromaticNumber_of_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.chromaticNumber_eq_one_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": true, "tactics": ["refine", "contrapose", "obtain", "have", "contrapose", "simp", "refine", "contrapose", "have", "simp_all"], "tactic_count": 10}
{"name": "SimpleGraph.two_le_chromaticNumber_iff_ne_bot", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": true, "tactics": ["refine", "contrapose", "by_cases", "simp", "simp", "obtain", "exact"], "tactic_count": 7}
{"name": "SimpleGraph.CompleteBipartiteGraph.bicoloring", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.CompleteBipartiteGraph.chromaticNumber", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": false, "tactics": ["rw", "chromaticNumber_eq_iff_forall_surjective", "intro", "have", "have", "have", "by_cases", "exact", "by_cases", "exact", "simpa"], "tactic_count": 11}
{"name": "SimpleGraph.IsClique.card_le_of_colorable", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "SimpleGraph.IsClique.card_le_of_coloring", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsClique.card_le_chromaticNumber", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.cliqueNum_le_chromaticNumber", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.Colorable.cliqueFree", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": true, "tactics": ["by_contra", "simp", "obtain", "exact"], "tactic_count": 4}
{"name": "SimpleGraph.cliqueFree_of_chromaticNumber_lt", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": true, "tactics": ["have", "obtain", "have", "refine", "rw", "rw", "simpa"], "tactic_count": 7}
{"name": "SimpleGraph.Coloring.surjOn_of_card_le_isClique", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": true, "tactics": ["intro", "obtain", "card_le_chromaticNumber_iff_forall_surjective.mp", "exact"], "tactic_count": 4}
{"name": "SimpleGraph.completeMultipartiteGraph.coloring", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.completeMultipartiteGraph.colorable", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.completeMultipartiteGraph.chromaticNumber", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": true, "tactics": ["apply", "by_contra", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.completeMultipartiteGraph.colorable_of_cliqueFree", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": true, "tactics": ["cases", "zero", "succ", "have", "apply", "have", "contrapose", "exact"], "tactic_count": 8}
{"name": "SimpleGraph.free_of_colorable", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Coloring", "is_tactic_proof": true, "tactics": ["contrapose", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.IsCompleteMultipartite", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.bot_isCompleteMultipartite", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.IsCompleteMultipartite.setoid", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.completeMultipartiteGraph.isCompleteMultipartite", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite", "is_tactic_proof": true, "tactics": ["intro", "simp_all"], "tactic_count": 2}
{"name": "SimpleGraph.IsCompleteMultipartite.iso", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.isCompleteMultipartite_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite", "is_tactic_proof": true, "tactics": ["constructor", "exact", "obtain", "intro", "rw", "exact"], "tactic_count": 6}
{"name": "SimpleGraph.IsCompleteMultipartite.colorable_of_cliqueFree", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsPathGraph3Compl.ne_fst", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsPathGraph3Compl.ne_snd", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsPathGraph3Compl.fst_ne_snd", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsPathGraph3Compl.symm", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.exists_isPathGraph3Compl_of_not_isCompleteMultipartite", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite", "is_tactic_proof": true, "tactics": ["rw", "push_neg", "obtain", "rw", "exact"], "tactic_count": 5}
{"name": "SimpleGraph.not_isCompleteMultipartite_iff_exists_isPathGraph3Compl", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsPathGraph3Compl.pathGraph3ComplEmbedding", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.pathGraph3ComplEmbeddingOf", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.not_isCompleteMultipartite_of_pathGraph3ComplEmbedding", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite", "is_tactic_proof": true, "tactics": ["intro", "have", "have", "have", "exact"], "tactic_count": 5}
{"name": "SimpleGraph.IsCompleteMultipartite.comap", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite", "is_tactic_proof": true, "tactics": ["intro", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.completeEquipartiteGraph", "kind": "abbrev", "module": "Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.completeEquipartiteGraph_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "SimpleGraph.completeEquipartiteGraph.completeMultipartiteGraph", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.completeEquipartiteGraph.turanGraph", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.completeEquipartiteGraph_eq_bot_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite", "is_tactic_proof": true, "tactics": ["contrapose", "rw", "refine", "induction", "rw", "exact", "use", "rw", "exact"], "tactic_count": 9}
{"name": "SimpleGraph.completeEquipartiteGraph.isCompleteMultipartite", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite", "is_tactic_proof": true, "tactics": ["rcases", "rw", "exact", "rw", "use", "simp_rw", "exact"], "tactic_count": 7}
{"name": "SimpleGraph.neighborSet_completeEquipartiteGraph", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "SimpleGraph.neighborFinset_completeEquipartiteGraph", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "SimpleGraph.degree_completeEquipartiteGraph", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite", "is_tactic_proof": true, "tactics": ["rw", "card_singleton,"], "tactic_count": 2}
{"name": "SimpleGraph.card_edgeFinset_completeEquipartiteGraph", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite", "is_tactic_proof": true, "tactics": ["rw", "conv_lhs", "rhs", "rw", "rw", "conv_rhs", "rw"], "tactic_count": 7}
{"name": "SimpleGraph.isContained_completeEquipartiteGraph_of_colorable", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite", "is_tactic_proof": false, "tactics": ["have", "rw", "exact", "have", "have", "let", "have", "apply", "rw", "rw", "simp", "rw", "simpa", "use", "intro", "rw", "exact"], "tactic_count": 17}
{"name": "SimpleGraph.chromaticNumber_le_two_iff_isBipartite", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.ConcreteColorings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.chromaticNumber_eq_two_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.ConcreteColorings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.pathGraph.bicoloring", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.ConcreteColorings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.pathGraph_two_embedding", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.ConcreteColorings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.chromaticNumber_pathGraph", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.ConcreteColorings", "is_tactic_proof": true, "tactics": ["have", "apply", "exact", "have", "exact"], "tactic_count": 5}
{"name": "SimpleGraph.Coloring.even_length_iff_congr", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.ConcreteColorings", "is_tactic_proof": true, "tactics": ["induction", "nil", "simp", "have", "rw", "exact", "tauto"], "tactic_count": 7}
{"name": "SimpleGraph.Coloring.odd_length_iff_not_congr", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.ConcreteColorings", "is_tactic_proof": true, "tactics": ["rw", "tauto"], "tactic_count": 2}
{"name": "SimpleGraph.Walk.three_le_chromaticNumber_of_odd_loop", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.ConcreteColorings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.cycleGraph.bicoloring_of_even", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.ConcreteColorings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.chromaticNumber_cycleGraph_of_even", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.ConcreteColorings", "is_tactic_proof": true, "tactics": ["have", "apply", "apply", "have", "exact"], "tactic_count": 5}
{"name": "SimpleGraph.cycleGraph.tricoloring", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.ConcreteColorings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.chromaticNumber_cycleGraph_of_odd", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.ConcreteColorings", "is_tactic_proof": true, "tactics": ["have", "apply", "apply", "have", "refine", "intro", "rw", "exact", "let", "have", "rw", "exact", "rw", "exact"], "tactic_count": 14}
{"name": "SimpleGraph.Coloring.completeEquipartiteGraph", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.ConcreteColorings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.completeEquipartiteGraph_colorable", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.ConcreteColorings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.two_colorable_iff_forall_loop_even", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.ConcreteColorings", "is_tactic_proof": true, "tactics": ["simp_rw", "constructor", "intro", "have", "norm_cast", "apply", "intro", "obtain", "use", "intro", "apply", "h", "c.toSimpleGraph_hom", "rw", "have", "exact"], "tactic_count": 16}
{"name": "SimpleGraph.Reachable", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.reachable_iff_nonempty_univ", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.not_reachable_iff_isEmpty_walk", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Reachable.elim", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Reachable.elim_path", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.reachable", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Adj.reachable", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.adj_le_reachable", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Reachable.refl", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Reachable.rfl", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Reachable.symm", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.reachable_comm", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Reachable.trans", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.reachable_iff_reflTransGen", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "induction", "nil", "cons", "intro", "induction", "refl", "tail"], "tactic_count": 9}
{"name": "SimpleGraph.reachable_eq_reflTransGen", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.reachable_fromEdgeSet_eq_reflTransGen_toRel", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": true, "tactics": ["rw", "congr", "ext", "simpa"], "tactic_count": 4}
{"name": "SimpleGraph.reachable_fromEdgeSet_fromRel_eq_reflTransGen", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Reachable.map", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Reachable.mono", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Reachable.mono'", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Reachable.exists_isPath", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": true, "tactics": ["classical", "obtain", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.Iso.reachable_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Iso.symm_apply_reachable", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.Reachable.mem_subgraphVerts", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": ["let", "by_cases", "exact", "exact", "termination_by", "decreasing_by", "rw", "lia", "exact"], "tactic_count": 9}
{"name": "SimpleGraph.reachable_is_equivalence", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.reachable_bot", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.reachable_top", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": true, "tactics": ["obtain", "simp", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.Reachable.of_subsingleton", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.not_reachable_of_left_degree_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": true, "tactics": ["rintro", "contradiction", "have", "rw", "contradiction"], "tactic_count": 5}
{"name": "SimpleGraph.not_reachable_of_right_degree_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.reachableSetoid", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Preconnected", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Preconnected.map", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Preconnected.mono", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.preconnected_iff_reachable_eq_top", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SimpleGraph.preconnected_bot_iff_subsingleton", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": true, "tactics": ["refine", "contrapose", "simp"], "tactic_count": 3}
{"name": "SimpleGraph.preconnected_bot", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.not_preconnected_bot", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.preconnected_top", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Preconnected.of_subsingleton", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Iso.preconnected_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Preconnected.support_eq_univ", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": true, "tactics": ["simp", "intro", "obtain", "obtain", "cases", "nil"], "tactic_count": 6}
{"name": "SimpleGraph.Preconnected.degree_pos_of_nontrivial", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Preconnected.minDegree_pos_of_nontrivial", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.adj_of_mem_walk_support", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "SimpleGraph.mem_support_of_mem_walk_support", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.mem_support_of_reachable", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": true, "tactics": ["let", "have", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.Preconnected.exists_isPath", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.connected_iff_exists_forall_reachable", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": true, "tactics": ["rw", "constructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 6}
{"name": "SimpleGraph.instCoeFunConnectedForallForallReachable", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Connected.map", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Connected.mono", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Connected.exists_isPath", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.connected_bot_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.not_connected_bot", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.connected_top_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.connected_top", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "SimpleGraph.Connected.of_subsingleton", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Iso.connected_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.reachable_or_compl_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.reachable_or_reachable_compl", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": true, "tactics": ["refine", "by_cases", "have", "have", "exact", "exact"], "tactic_count": 6}
{"name": "SimpleGraph.connected_or_preconnected_compl", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": true, "tactics": ["rw", "intro", "push_neg", "have", "exact"], "tactic_count": 5}
{"name": "SimpleGraph.connected_or_connected_compl", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ConnectedComponent", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.connectedComponentMk", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ConnectedComponent.inhabited", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ConnectedComponent.isEmpty", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ConnectedComponent.instSubsingleton", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ConnectedComponent.instUnique", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ConnectedComponent.instNonempty", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ConnectedComponent.instFinite", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ConnectedComponent.ind", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ConnectedComponent.ind₂", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ConnectedComponent.sound", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ConnectedComponent.exact", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ConnectedComponent.eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ConnectedComponent.connectedComponentMk_eq_of_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ConnectedComponent.lift", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ConnectedComponent.lift_mk", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ConnectedComponent.exists", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ConnectedComponent.forall", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Preconnected.subsingleton_connectedComponent", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ConnectedComponent.recOn", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ConnectedComponent.map", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ConnectedComponent.map_mk", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ConnectedComponent.map_id", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ConnectedComponent.map_comp", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ConnectedComponent.surjective_map_ofLE", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ConnectedComponent.iso_image_comp_eq_map_iff_eq_comp", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": true, "tactics": ["refine", "simp"], "tactic_count": 2}
{"name": "SimpleGraph.ConnectedComponent.iso_inv_image_comp_eq_iff_eq_map", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": true, "tactics": ["refine", "simp"], "tactic_count": 2}
{"name": "SimpleGraph.Iso.connectedComponentEquiv", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Iso.connectedComponentEquiv_refl", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "SimpleGraph.Iso.connectedComponentEquiv_symm", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "SimpleGraph.Iso.connectedComponentEquiv_trans", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "SimpleGraph.ConnectedComponent.supp", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ConnectedComponent.supp_injective", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": true, "tactics": ["refine", "simp", "intro", "rw"], "tactic_count": 4}
{"name": "SimpleGraph.ConnectedComponent.supp_inj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ConnectedComponent.instSetLike", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ConnectedComponent.mem_supp_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ConnectedComponent.mem_supp_congr_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": true, "tactics": ["simp", "constructor", "exact", "exact"], "tactic_count": 4}
{"name": "SimpleGraph.ConnectedComponent.connectedComponentMk_mem", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ConnectedComponent.nonempty_supp", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ConnectedComponent.isoEquivSupp", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ConnectedComponent.mem_coe_supp_of_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": true, "tactics": ["obtain", "use", "rw", "exact"], "tactic_count": 4}
{"name": "SimpleGraph.ConnectedComponent.eq_of_common_vertex", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": true, "tactics": ["simp", "rw"], "tactic_count": 2}
{"name": "SimpleGraph.ConnectedComponent.connectedComponentMk_supp_subset_supp", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": true, "tactics": ["intro", "simp", "rw", "exact"], "tactic_count": 4}
{"name": "SimpleGraph.ConnectedComponent.biUnion_supp_eq_supp", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": true, "tactics": ["ext", "simp_rw", "refine", "intro", "use", "use", "simp"], "tactic_count": 7}
{"name": "SimpleGraph.ConnectedComponent.top_supp_eq_univ", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": true, "tactics": ["obtain", "ext", "simpa"], "tactic_count": 3}
{"name": "SimpleGraph.ConnectedComponent.reachable_of_mem_supp", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.ConnectedComponent.mem_supp_of_adj_mem_supp", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ConnectedComponent.toSimpleGraph", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ConnectedComponent.toSimpleGraph_hom", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ConnectedComponent.toSimpleGraph_hom_apply", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ConnectedComponent.toSimpleGraph_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.ConnectedComponent.adj_spanningCoe_toSimpleGraph", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": true, "tactics": ["apply", "intro", "simp_all", "obtain", "subst", "exact", "simp", "intro", "exact"], "tactic_count": 9}
{"name": "_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": true, "tactics": ["cases", "nil", "have", "have", "exact"], "tactic_count": 5}
{"name": "SimpleGraph.ConnectedComponent.reachable_toSimpleGraph", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ConnectedComponent.connected_toSimpleGraph", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ConnectedComponent.maximal_connected_induce_supp", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": true, "tactics": ["refine", "refine", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.ConnectedComponent.maximal_connected_induce_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": true, "tactics": ["refine", "have", "suffices", "exact", "exact"], "tactic_count": 5}
{"name": "SimpleGraph.homOfConnectedComponents", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.pairwise_disjoint_supp_connectedComponent", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": true, "tactics": ["simp_rw", "intro", "rw", "rw", "exact"], "tactic_count": 5}
{"name": "SimpleGraph.iUnion_connectedComponentSupp", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": true, "tactics": ["refine", "simp", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.Preconnected.set_univ_walk_nonempty", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.Connected.set_univ_walk_nonempty", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Preconnected.exists_adj_of_nontrivial", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": true, "tactics": ["have", "have", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.IsBridge", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.isBridge_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.reachable_delete_edges_iff_exists_walk", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "use", "simp_rw", "rintro", "simpa", "rintro", "refine", "simp", "exact"], "tactic_count": 10}
{"name": "SimpleGraph.isBridge_iff_adj_and_forall_walk_mem_edges", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": true, "tactics": ["rw", "rw"], "tactic_count": 2}
{"name": "SimpleGraph.reachable_deleteEdges_iff_exists_cycle.aux", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": true, "tactics": ["have", "let", "let", "let", "have", "simp", "have", "have", "rw", "rw", "exact"], "tactic_count": 11}
{"name": "SimpleGraph.adj_and_reachable_delete_edges_iff_exists_cycle", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": true, "tactics": ["classical", "rw", "constructor", "rintro", "refine", "apply", "rw", "intro", "cases", "simp", "rintro", "refine", "by_contra", "have", "intro", "simpa", "have", "refine", "reachable_deleteEdges_iff_exists_cycle.aux", "rwa"], "tactic_count": 20}
{"name": "SimpleGraph.isBridge_iff_adj_and_forall_cycle_notMem", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": true, "tactics": ["rw", "intro", "contrapose", "rw", "simp"], "tactic_count": 5}
{"name": "SimpleGraph.isBridge_iff_mem_and_forall_cycle_notMem", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Connected.connected_delete_edge_of_not_isBridge", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": true, "tactics": ["classical", "simp", "obtain", "rwa", "refine", "obtain", "obtain", "exact", "have", "let", "have", "have", "exact"], "tactic_count": 13}
{"name": "SimpleGraph.IsBridge.anti_of_mem_edgeSet", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.exists_mem_edges_of_not_reachable_deleteEdges", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": true, "tactics": ["contrapose"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.mem_edges_of_not_reachable_deleteEdges", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.IsTrail.not_mem_edges_of_not_reachable", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": true, "tactics": ["classical", "exact", "hw.disjoint_edges_takeUntil_dropUntil"], "tactic_count": 3}
{"name": "SimpleGraph.Walk.IsTrail.not_mem_support_of_not_reachable", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": true, "tactics": ["classical", "exact", "hw.not_mem_edges_of_not_reachable", "w.edges_takeUntil_subset"], "tactic_count": 4}
{"name": "SimpleGraph.Walk.IsTrail.not_mem_support_of_subsingleton_neighborSet", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": true, "tactics": ["rintro", "obtain", "refine", "rintro", "obtain", "simpa", "exact"], "tactic_count": 7}
{"name": "SimpleGraph.Preconnected.induce_of_degree_eq_one", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected", "is_tactic_proof": true, "tactics": ["rintro", "obtain", "constructor", "convert", "rintro", "by_contra", "exact"], "tactic_count": 7}
{"name": "SimpleGraph.IsEdgeReachable", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.EdgeConnectivity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsEdgeConnected", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.EdgeConnectivity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsEdgeReachable.refl", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.EdgeConnectivity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsEdgeReachable.symm", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.EdgeConnectivity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.isEdgeReachable_comm", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.EdgeConnectivity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsEdgeReachable.trans", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.EdgeConnectivity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsEdgeReachable.mono", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.EdgeConnectivity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsEdgeReachable.anti", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.EdgeConnectivity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsEdgeReachable.zero", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.EdgeConnectivity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.IsEdgeConnected.zero", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.EdgeConnectivity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.isEdgeReachable_one", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.EdgeConnectivity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.isEdgeConnected_one", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.EdgeConnectivity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.IsEdgeReachable.reachable", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.EdgeConnectivity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsEdgeConnected.preconnected", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.EdgeConnectivity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsEdgeConnected.connected", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.EdgeConnectivity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.isEdgeReachable_add_one", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.EdgeConnectivity", "is_tactic_proof": true, "tactics": ["refine", "rw", "apply", "grw", "exact", "obtain", "simpa", "rw", "refine", "rwa"], "tactic_count": 10}
{"name": "SimpleGraph.isEdgeConnected_add_one", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.EdgeConnectivity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.isBridge_iff_adj_and_not_isEdgeConnected_two", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.EdgeConnectivity", "is_tactic_proof": true, "tactics": ["refine", "exact", "refine", "by_cases", "apply", "exact", "obtain", "by_cases", "exact", "exact"], "tactic_count": 10}
{"name": "SimpleGraph.isEdgeReachable_two", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.EdgeConnectivity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.isEdgeConnected_two", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.EdgeConnectivity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.IsTrail.not_mem_edges_of_not_isEdgeReachable_two", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.EdgeConnectivity", "is_tactic_proof": true, "tactics": ["classical", "obtain", "have", "exact", "hw.disjoint_edges_takeUntil_dropUntil"], "tactic_count": 5}
{"name": "SimpleGraph.ConnectedComponent.Represents", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Represents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ConnectedComponent.Represents.image_out", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Represents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ConnectedComponent.Represents.existsUnique_rep", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Represents", "is_tactic_proof": true, "tactics": ["obtain", "use", "simp", "exact"], "tactic_count": 4}
{"name": "SimpleGraph.ConnectedComponent.Represents.exists_inter_eq_singleton", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Represents", "is_tactic_proof": true, "tactics": ["obtain", "aesop"], "tactic_count": 2}
{"name": "SimpleGraph.ConnectedComponent.Represents.disjoint_supp_of_notMem", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Represents", "is_tactic_proof": true, "tactics": ["rw", "intro", "simp", "subst", "exact"], "tactic_count": 5}
{"name": "SimpleGraph.ConnectedComponent.Represents.ncard_inter", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Represents", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.ConnectedComponent.Represents.ncard_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Represents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ConnectedComponent.Represents.ncard_sdiff_of_mem", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Represents", "is_tactic_proof": true, "tactics": ["obtain", "rw", "simp"], "tactic_count": 3}
{"name": "SimpleGraph.ConnectedComponent.Represents.ncard_sdiff_of_notMem", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Represents", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.ConnectedComponent.even_ncard_supp_sdiff_rep", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Represents", "is_tactic_proof": true, "tactics": ["by_cases", "simpa", "have", "rw", "simpa"], "tactic_count": 5}
{"name": "SimpleGraph.Subgraph.instCoePreconnectedPreconnectedElemVertsCoe", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.instCoeFunPreconnectedForallForallReachableElemVertsCoe", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.preconnected_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.instCoeConnectedConnectedElemVertsCoe", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.instCoeFunConnectedForallForallReachableElemVertsCoe", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.connected_iff'", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.connected_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.Subgraph.Connected.preconnected", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.Subgraph.Connected.nonempty", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.Subgraph.singletonSubgraph_connected", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": true, "tactics": ["refine", "rintro", "simp", "subst_vars", "rfl"], "tactic_count": 5}
{"name": "SimpleGraph.Subgraph.subgraphOfAdj_connected", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": true, "tactics": ["refine", "rintro", "simp", "obtain", "first", "rfl"], "tactic_count": 6}
{"name": "SimpleGraph.Subgraph.top_induce_pair_connected_of_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.Subgraph.Connected.mono", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": true, "tactics": ["rw", "refine", "rintro", "exact"], "tactic_count": 4}
{"name": "SimpleGraph.Subgraph.Connected.mono'", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "SimpleGraph.Subgraph.connected_sup", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": true, "tactics": ["rw", "obtain", "exists", "rintro", "exact", "exact"], "tactic_count": 6}
{"name": "SimpleGraph.Subgraph.Connected.sup", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.Preconnected.degree_zero_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": true, "tactics": ["refine", "have", "simpa"], "tactic_count": 3}
{"name": "SimpleGraph.Subgraph.Preconnected.exists_adj_of_nontrivial", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": true, "tactics": ["have", "tauto"], "tactic_count": 2}
{"name": "SimpleGraph.Subgraph.Connected.exists_verts_eq_connectedComponentSupp", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": true, "tactics": ["rw", "obtain", "use", "ext", "simp", "exact"], "tactic_count": 6}
{"name": "SimpleGraph.ConnectedComponent.toSubgraph", "kind": "abbrev", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ConnectedComponent.coe_toSubgraph", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ConnectedComponent.spanningCoe_toSubgraph", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ConnectedComponent.connected_toSubgraph", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ConnectedComponent.maximal_connected_toSubgraph", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": true, "tactics": ["refine", "refine", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.ConnectedComponent.maximal_subgraph_connected_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": true, "tactics": ["refine", "have", "suffices", "exact", "le_trans", "exact"], "tactic_count": 6}
{"name": "SimpleGraph.Walk.toSubgraph", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.toSubgraph_cons_nil_eq_subgraphOfAdj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.mem_verts_toSubgraph", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "rename_i", "have", "simp"], "tactic_count": 6}
{"name": "SimpleGraph.Walk.not_nil_of_adj_toSubgraph", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.start_mem_verts_toSubgraph", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.end_mem_verts_toSubgraph", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.verts_toSubgraph", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.mem_edges_toSubgraph", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.edgeSet_toSubgraph", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.toSubgraph_append", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.toSubgraph_reverse", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "simp", "rw", "congr", "ext"], "tactic_count": 7}
{"name": "SimpleGraph.Walk.toSubgraph_rotate", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.toSubgraph_map", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.adj_toSubgraph_mapLe", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.finite_neighborSet_toSubgraph", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": true, "tactics": ["induction", "nil", "rw", "apply", "cons", "rw", "refine", "refine", "apply"], "tactic_count": 9}
{"name": "SimpleGraph.Walk.toSubgraph_le_induce_support", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": true, "tactics": ["convert", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.Walk.toSubgraph_adj_getVert", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "cases", "simp", "true_or]", "simp", "right", "exact"], "tactic_count": 9}
{"name": "SimpleGraph.Walk.toSubgraph_adj_snd", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.toSubgraph_adj_penultimate", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "SimpleGraph.Walk.toSubgraph_adj_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": true, "tactics": ["constructor", "intro", "unfold", "p", "simp", "cases", "inl", "use", "simp", "refine", "exact", "inr", "obtain", "use", "simp", "constructor", "exact", "simp", "rintro", "rw", "exact"], "tactic_count": 21}
{"name": "SimpleGraph.Walk.mem_support_of_adj_toSubgraph", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.adj_toSubgraph_iff_mem_edges", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.toSubgraph_bypass_le_toSubgraph", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": true, "tactics": ["constructor", "simpa", "simpa"], "tactic_count": 3}
{"name": "SimpleGraph.Walk.mapToSubgraph", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.map_mapToSubgraph_hom", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.map_mapToSubgraph_eq_induce", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.map_mapToSubgraph_eq_induce_id", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.IsPath.neighborSet_toSubgraph_startpoint", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": true, "tactics": ["have", "ext", "simp_all", "grind"], "tactic_count": 4}
{"name": "SimpleGraph.Walk.IsPath.neighborSet_toSubgraph_endpoint", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.IsPath.neighborSet_toSubgraph_internal", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": true, "tactics": ["have", "ext", "simp_all", "refine", "rintro", "apply", "aesop"], "tactic_count": 7}
{"name": "SimpleGraph.Walk.IsPath.ncard_neighborSet_toSubgraph_internal_eq_two", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": true, "tactics": ["rw", "have", "intro", "have", "lia", "simp_all"], "tactic_count": 6}
{"name": "SimpleGraph.Walk.IsPath.snd_of_toSubgraph_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": true, "tactics": ["have", "simp", "rcases", "have", "apply", "rw", "simp", "have", "apply", "rw", "contradiction"], "tactic_count": 11}
{"name": "SimpleGraph.Walk.IsCycle.neighborSet_toSubgraph_endpoint", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": true, "tactics": ["have", "ext", "simp_all", "grind"], "tactic_count": 4}
{"name": "SimpleGraph.Walk.IsCycle.neighborSet_toSubgraph_internal", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": true, "tactics": ["have", "ext", "simp_all", "refine", "rintro", "apply", "simp_all", "apply", "aesop"], "tactic_count": 9}
{"name": "SimpleGraph.Walk.IsCycle.ncard_neighborSet_toSubgraph_eq_two", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": true, "tactics": ["simp", "obtain", "by_cases", "have", "rw", "exact", "rw", "exact"], "tactic_count": 8}
{"name": "SimpleGraph.Walk.IsCycle.exists_isCycle_snd_verts_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": true, "tactics": ["have", "rw", "push", "obtain", "exact", "use", "rw", "exact"], "tactic_count": 8}
{"name": "SimpleGraph.Walk.exists_mem_support_mem_erase_mem_support_takeUntil_eq_empty", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": true, "tactics": ["simp", "induction", "simp", "obtain", "obtain", "use", "have", "rw", "have", "lia", "obtain", "use", "rwa", "simp", "rintro", "exact"], "tactic_count": 16}
{"name": "SimpleGraph.Walk.exists_mem_support_forall_mem_support_imp_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": true, "tactics": ["obtain", "use", "suffices", "rwa"], "tactic_count": 4}
{"name": "SimpleGraph.Walk.toSubgraph_connected", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": true, "tactics": ["induction", "nil", "ih", "apply", "exists", "simp"], "tactic_count": 6}
{"name": "SimpleGraph.Subgraph.induce_union_connected", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.connected_induce_top_sup", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": true, "tactics": ["refine", "exact", "exact", "exact"], "tactic_count": 4}
{"name": "SimpleGraph.Subgraph.Connected.adj_union", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.preconnected_iff_forall_exists_walk_subgraph", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": true, "tactics": ["constructor", "intro", "refine", "exists", "simp", "intro", "rw", "rintro", "obtain", "exact"], "tactic_count": 10}
{"name": "SimpleGraph.Subgraph.connected_iff_forall_exists_walk_subgraph", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.preconnected_induce_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.connected_induce_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.induce_union_connected", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.induce_pair_connected_of_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.Subgraph.Connected.induce_verts", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.Walk.connected_induce_support", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.connected_induce_union", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": true, "tactics": ["rw", "rw", "apply", "simp", "apply", "simp", "simp", "rw", "simp"], "tactic_count": 9}
{"name": "SimpleGraph.induce_connected_adj_union", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.induce_connected_of_patches", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": true, "tactics": ["rw", "refine", "rintro", "obtain", "exact"], "tactic_count": 5}
{"name": "SimpleGraph.induce_sUnion_connected_of_pairwise_not_disjoint", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "apply", "rintro", "simp", "obtain", "refine", "induce_union_connected"], "tactic_count": 8}
{"name": "SimpleGraph.extend_finset_to_connected", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": true, "tactics": ["classical", "obtain", "refine", "simp", "exact", "apply", "simp", "exact", "intro", "simp", "obtain", "refine", "simp", "exact", "simp", "refine"], "tactic_count": 16}
{"name": "SimpleGraph.Reachable.coe_toSubgraph", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Preconnected.toSubgraph", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Connected.toSubgraph", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Reachable.coe_subgraphMap", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Reachable.coe_coeSubgraph", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.Preconnected.map", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": true, "tactics": ["rw", "intro", "simp_rw", "exact"], "tactic_count": 4}
{"name": "SimpleGraph.Subgraph.Connected.map", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.Preconnected.coeSubgraph", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.Connected.coeSubgraph", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.set_walk_self_length_zero_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkCounting", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.set_walk_length_zero_eq_of_ne", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkCounting", "is_tactic_proof": true, "tactics": ["ext", "simp", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.set_walk_length_succ_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkCounting", "is_tactic_proof": true, "tactics": ["ext", "cases", "nil", "cons", "pwv", "simp", "grind"], "tactic_count": 7}
{"name": "SimpleGraph.walkLengthTwoEquivCommonNeighbors", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkCounting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.finsetWalkLength", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkCounting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.coe_finsetWalkLength_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkCounting", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "ih", "simp", "ext", "simp", "congr", "rename_i", "have", "simp", "rw"], "tactic_count": 12}
{"name": "SimpleGraph.mem_finsetWalkLength_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkCounting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.finsetWalkLengthLT", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkCounting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.coe_finsetWalkLengthLT_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkCounting", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "SimpleGraph.mem_finsetWalkLengthLT_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkCounting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.fintypeSetWalkLength", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkCounting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.fintypeSubtypeWalkLength", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkCounting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.set_walk_length_toFinset_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkCounting", "is_tactic_proof": true, "tactics": ["simp", "power"], "tactic_count": 2}
{"name": "SimpleGraph.card_set_walk_length_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkCounting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.fintypeSetWalkLengthLT", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkCounting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.fintypeSubtypeWalkLengthLT", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkCounting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.fintypeSetPathLength", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkCounting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.fintypeSubtypePathLength", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkCounting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.fintypeSetPathLengthLT", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkCounting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.fintypeSubtypePathLengthLT", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkCounting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ConnectedComponent.card_le_card_of_le", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkCounting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.reachable_iff_exists_finsetWalkLength_nonempty", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkCounting", "is_tactic_proof": true, "tactics": ["constructor", "intro", "refine", "refine", "simp", "rintro", "exact"], "tactic_count": 7}
{"name": "SimpleGraph.instDecidableRelReachable", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkCounting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.instFintypeConnectedComponent", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkCounting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.instDecidablePreconnected", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkCounting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.instDecidableConnected", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkCounting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Path.instFintype", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkCounting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.instDecidableMemSupp", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkCounting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.disjiUnion_supp_toFinset_eq_supp_toFinset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkCounting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.oddComponents", "kind": "abbrev", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkCounting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ConnectedComponent.odd_oddComponents_ncard_subset_supp", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkCounting", "is_tactic_proof": true, "tactics": ["simp_rw", "classical", "cases", "rw", "simp", "rw", "congr", "ext", "simp_rw", "and_comm]"], "tactic_count": 10}
{"name": "SimpleGraph.odd_ncard_oddComponents", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkCounting", "is_tactic_proof": true, "tactics": ["classical", "cases", "rw", "simp", "rw", "simp_rw", "exact"], "tactic_count": 7}
{"name": "SimpleGraph.ncard_oddComponents_mono", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkCounting", "is_tactic_proof": false, "tactics": ["have", "refine", "simpa", "let", "refine", "simp", "exact"], "tactic_count": 7}
{"name": "SimpleGraph.Walk.takeUntil", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkDecomp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.takeUntil_nil", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkDecomp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.takeUntil_cons", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkDecomp", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.takeUntil_first", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkDecomp", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.nil_takeUntil", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkDecomp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.dropUntil", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkDecomp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.take_spec", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkDecomp", "is_tactic_proof": true, "tactics": ["induction", "rw", "subst", "rfl", "cases", "simp", "simp", "split_ifs"], "tactic_count": 8}
{"name": "SimpleGraph.Walk.isSubwalk_takeUntil", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkDecomp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.isSubwalk_dropUntil", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkDecomp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.mem_support_iff_exists_append", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkDecomp", "is_tactic_proof": true, "tactics": ["classical", "constructor", "exact", "rintro", "simp"], "tactic_count": 5}
{"name": "SimpleGraph.Walk.count_support_takeUntil_eq_one", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkDecomp", "is_tactic_proof": true, "tactics": ["induction", "rw", "subst", "simp", "cases", "simp", "simp", "split_ifs"], "tactic_count": 8}
{"name": "SimpleGraph.Walk.count_edges_takeUntil_le_one", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkDecomp", "is_tactic_proof": true, "tactics": ["induction", "nil", "rw", "subst", "simp", "cons", "cases", "simp", "simp", "split_ifs", "subst", "simp", "rw", "split_ifs", "simp", "obtain", "exact", "cases", "apply"], "tactic_count": 19}
{"name": "SimpleGraph.Walk.takeUntil_copy", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkDecomp", "is_tactic_proof": true, "tactics": ["subst_vars", "rfl"], "tactic_count": 2}
{"name": "SimpleGraph.Walk.dropUntil_copy", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkDecomp", "is_tactic_proof": true, "tactics": ["subst_vars", "rfl"], "tactic_count": 2}
{"name": "SimpleGraph.Walk.support_takeUntil_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkDecomp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.support_dropUntil_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkDecomp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.darts_takeUntil_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkDecomp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.darts_dropUntil_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkDecomp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.edges_takeUntil_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkDecomp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.edges_dropUntil_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkDecomp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.length_takeUntil_le", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkDecomp", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.Walk.length_dropUntil_le", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkDecomp", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.Walk.takeUntil_append_of_mem_left", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkDecomp", "is_tactic_proof": true, "tactics": ["induction", "nil", "rw", "by_cases", "subst_vars", "have", "simp_rw", "simpa"], "tactic_count": 8}
{"name": "SimpleGraph.Walk.getVert_takeUntil", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkDecomp", "is_tactic_proof": true, "tactics": ["conv_rhs", "cases"], "tactic_count": 2}
{"name": "SimpleGraph.Walk.snd_takeUntil", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkDecomp", "is_tactic_proof": true, "tactics": ["apply", "by_contra", "simp", "exact"], "tactic_count": 4}
{"name": "SimpleGraph.Walk.getVert_length_takeUntil", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkDecomp", "is_tactic_proof": true, "tactics": ["have", "grind"], "tactic_count": 2}
{"name": "SimpleGraph.Walk.getVert_lt_length_takeUntil_ne", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkDecomp", "is_tactic_proof": true, "tactics": ["rintro", "have", "have", "simp_rw", "have", "grind"], "tactic_count": 6}
{"name": "SimpleGraph.Walk.getVert_le_length_takeUntil_eq_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkDecomp", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.length_takeUntil_lt", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkDecomp", "is_tactic_proof": true, "tactics": ["rw", "exact", "huw", "simpa"], "tactic_count": 4}
{"name": "SimpleGraph.Walk.takeUntil_takeUntil", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkDecomp", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.notMem_support_takeUntil_support_takeUntil_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkDecomp", "is_tactic_proof": true, "tactics": ["rw", "intro", "have", "have", "simp", "lia"], "tactic_count": 6}
{"name": "SimpleGraph.Walk.rotate", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkDecomp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.support_rotate", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkDecomp", "is_tactic_proof": true, "tactics": ["simp", "apply", "rw"], "tactic_count": 3}
{"name": "SimpleGraph.Walk.mem_support_rotate_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkDecomp", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.rotate_darts", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkDecomp", "is_tactic_proof": true, "tactics": ["simp", "apply", "rw"], "tactic_count": 3}
{"name": "SimpleGraph.Walk.rotate_edges", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkDecomp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.mem_support_iff_exists_getVert", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkDecomp", "is_tactic_proof": true, "tactics": ["classical", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.Hom.toCopy", "kind": "abbrev", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Embedding.toCopy", "kind": "abbrev", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Iso.toCopy", "kind": "abbrev", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Copy.instFunLike", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Copy.injective", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Copy.ext", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Copy.coe_toHom", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Copy.toHom_apply", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Copy.coe_mk", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Copy.mapEdgeSet", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Copy.mapNeighborSet", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Copy.toEmbedding", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Copy.id", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Copy.coe_id", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Copy.comp", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": true, "tactics": ["use", "rw", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.Copy.comp_apply", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Copy.ofLE", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Copy.coe_comp", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "SimpleGraph.Copy.coe_ofLE", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Copy.ofLE_refl", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "SimpleGraph.Copy.ofLE_comp", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "SimpleGraph.Copy.induce", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Copy.bot", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Copy.isoSubgraphMap", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": true, "tactics": ["use", "simp_rw", "f.injective.eq_iff,"], "tactic_count": 3}
{"name": "SimpleGraph.Copy.toSubgraph", "kind": "abbrev", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Copy.isoToSubgraph", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Copy.range_toSubgraph", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": true, "tactics": ["ext", "constructor", "rintro", "simpa", "rintro", "refine", "simp"], "tactic_count": 7}
{"name": "SimpleGraph.Copy.toSubgraph_surjOn", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Copy.instSubsingletonOfForall", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Copy.instFintypeOfSubtypeHomInjectiveCoe", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Copy.topEmbedding", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.coeCopy", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsContained", "kind": "abbrev", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.term_⊑_", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph._aux_Mathlib_Combinatorics_SimpleGraph_Copy___macroRules_SimpleGraph_term_⊑__1", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph._aux_Mathlib_Combinatorics_SimpleGraph_Copy___unexpand_SimpleGraph_IsContained_1", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsContained.refl", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsContained.rfl", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsContained.of_le", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsContained.trans", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsContained.trans'", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsContained.mono_right", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsContained.mono_left", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.isContained_congr", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.isContained_congr_left", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.isContained_congr_right", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsContained.of_isEmpty", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.bot_isContained_iff_card_le", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.coe_isContained", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.isContained_iff_exists_iso_subgraph", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Free", "kind": "abbrev", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.not_free", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.free_congr", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.free_congr_left", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.free_congr_right", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.free_bot", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": true, "tactics": ["rw", "intro", "absurd", "rw", "exact"], "tactic_count": 5}
{"name": "SimpleGraph.IsIndContained", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.term_⊴_", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph._aux_Mathlib_Combinatorics_SimpleGraph_Copy___macroRules_SimpleGraph_term_⊴__1", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph._aux_Mathlib_Combinatorics_SimpleGraph_Copy___unexpand_SimpleGraph_IsIndContained_1", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsIndContained.isContained", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Iso.isIndContained", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Iso.isIndContained'", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Iso.isContained", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.IsInduced.isIndContained", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsIndContained.refl", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsIndContained.rfl", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsIndContained.trans", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsIndContained.of_isEmpty", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.isIndContained_iff_exists_iso_subgraph", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "refine", "simp", "rintro", "exact"], "tactic_count": 6}
{"name": "SimpleGraph.top_isIndContained_iff_top_isContained", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.compl_isIndContained_compl", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.labelledCopyCount", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "SimpleGraph.labelledCopyCount_of_isEmpty", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": true, "tactics": ["convert", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.labelledCopyCount_eq_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.labelledCopyCount_pos", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.copyCount", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "SimpleGraph.copyCount_eq_card_image_copyToSubgraph", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": true, "tactics": ["rw", "congr", "refine", "simpa"], "tactic_count": 4}
{"name": "SimpleGraph.copyCount_eq_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.copyCount_pos", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.copyCount_le_labelledCopyCount", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "SimpleGraph.copyCount_bot", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": true, "tactics": ["classical", "rw", "convert", "card_singleton", "adj_sub", "edge_vert", "simp", "refine", "ext", "simp", "exact"], "tactic_count": 11}
{"name": "SimpleGraph.copyCount_of_isEmpty", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": true, "tactics": ["cases", "exact", "copyCount_pos.2"], "tactic_count": 3}
{"name": "_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.aux", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.definition._@.Mathlib.Combinatorics.SimpleGraph.Copy.3082331781._hygCtx._hyg.14", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": true, "tactics": ["classical", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.killCopies_le_left", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.killCopies_bot", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.killCopies_of_ne_bot", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.killCopies_eq_left", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": ["simp", "deleteEdges_eq_self,", "exact", "forall_congr"], "tactic_count": 4}
{"name": "SimpleGraph.Free.killCopies_eq_left", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": true, "tactics": ["obtain", "exact", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.free_killCopies", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": true, "tactics": ["rw", "rintro", "have", "rw", "exact", "set", "have", "clear_value", "rw", "subst", "obtain", "let", "have", "rw", "have", "simp", "not_exists]", "refine", "rw", "congr", "exact"], "tactic_count": 21}
{"name": "SimpleGraph.killCopies.edgeSet.instFintype", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.le_card_edgeFinset_killCopies", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": true, "tactics": ["classical", "obtain", "simp", "let", "calc", "simp", "rw", "simp", "simp"], "tactic_count": 9}
{"name": "SimpleGraph.le_card_edgeFinset_killCopies_add_copyCount", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.instDecidableEqDart", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Dart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Dart.ext_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Dart", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "SimpleGraph.Dart.ext", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Dart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Dart.fst_ne_snd", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Dart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Dart.snd_ne_fst", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Dart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Dart.toProd_injective", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Dart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Dart.fintype", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Dart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Dart.edge", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Dart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Dart.edge_mk", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Dart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Dart.edge_mem", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Dart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Dart.symm", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Dart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Dart.symm_mk", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Dart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Dart.edge_symm", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Dart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Dart.edge_comp_symm", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Dart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Dart.symm_symm", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Dart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Dart.symm_involutive", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Dart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Dart.symm_ne", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Dart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.dart_edge_eq_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Dart", "is_tactic_proof": true, "tactics": ["rintro", "simp"], "tactic_count": 2}
{"name": "SimpleGraph.dart_edge_eq_mk'_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Dart", "is_tactic_proof": true, "tactics": ["rintro", "apply"], "tactic_count": 2}
{"name": "SimpleGraph.dart_edge_eq_mk'_iff'", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Dart", "is_tactic_proof": true, "tactics": ["rintro", "rw", "simp"], "tactic_count": 3}
{"name": "SimpleGraph.DartAdj", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Dart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.dartOfNeighborSet", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Dart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.dartOfNeighborSet_injective", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Dart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.nonempty_dart_top", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Dart", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.dart_fst_fiber", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.DegreeSum", "is_tactic_proof": true, "tactics": ["ext", "simp", "constructor", "rintro", "exact", "rintro", "rfl"], "tactic_count": 7}
{"name": "SimpleGraph.dart_fst_fiber_card_eq_degree", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.DegreeSum", "is_tactic_proof": true, "tactics": ["simpa", "card_image_of_injective"], "tactic_count": 2}
{"name": "SimpleGraph.dart_card_eq_sum_degrees", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.DegreeSum", "is_tactic_proof": true, "tactics": ["haveI", "simp", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.Dart.edge_fiber", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.DegreeSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.dart_edge_fiber_card", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.DegreeSum", "is_tactic_proof": true, "tactics": ["obtain", "let", "convert", "rw", "rw", "exact"], "tactic_count": 6}
{"name": "SimpleGraph.dart_card_eq_twice_card_edges", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.DegreeSum", "is_tactic_proof": true, "tactics": ["classical", "rw", "rw", "apply", "rw", "intro", "apply", "rwa"], "tactic_count": 8}
{"name": "SimpleGraph.sum_degrees_eq_twice_card_edges", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.DegreeSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.two_mul_card_edgeFinset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.DegreeSum", "is_tactic_proof": true, "tactics": ["rw", "refine"], "tactic_count": 2}
{"name": "SimpleGraph.sum_degrees_support_eq_twice_card_edges", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.DegreeSum", "is_tactic_proof": true, "tactics": ["classical", "simp_rw", "apply", "intro", "rw", "rwa"], "tactic_count": 6}
{"name": "SimpleGraph.even_card_odd_degree_vertices", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.DegreeSum", "is_tactic_proof": true, "tactics": ["classical", "have", "simp", "rw", "rw", "simp", "rw", "convert", "exact", "intro", "rw", "tauto"], "tactic_count": 12}
{"name": "SimpleGraph.odd_card_odd_degree_vertices_ne", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.DegreeSum", "is_tactic_proof": true, "tactics": ["rcases", "have", "have", "use", "rw", "exact", "rwa", "exact", "have", "ext", "rw", "simp", "rw", "refine", "lia", "rwa"], "tactic_count": 16}
{"name": "SimpleGraph.exists_ne_odd_degree_of_exists_odd_degree", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.DegreeSum", "is_tactic_proof": true, "tactics": ["haveI", "rcases", "have", "rw", "apply", "rcases", "rw", "exact"], "tactic_count": 8}
{"name": "SimpleGraph.deleteEdges", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.DeleteEdges", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.instDecidableRelAdjDeleteEdgesOfDecidablePredSym2MemSetOfDecidableEq", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.DeleteEdges", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.deleteEdges_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.DeleteEdges", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.deleteEdges_edgeSet", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.DeleteEdges", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "SimpleGraph.deleteEdges_deleteEdges", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.DeleteEdges", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.deleteEdges_empty", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.DeleteEdges", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.deleteEdges_univ", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.DeleteEdges", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.deleteEdges_le", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.DeleteEdges", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.deleteEdges_anti", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.DeleteEdges", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.deleteEdges_mono", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.DeleteEdges", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.deleteEdges_eq_self", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.DeleteEdges", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.deleteEdges_eq_inter_edgeSet", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.DeleteEdges", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "SimpleGraph.deleteEdges_of_subset_diagSet", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.DeleteEdges", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "SimpleGraph.deleteEdges_sdiff_eq_of_le", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.DeleteEdges", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.edgeSet_deleteEdges", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.DeleteEdges", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.edgeFinset_deleteEdges", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.DeleteEdges", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "SimpleGraph.deleteEdges_sup", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.DeleteEdges", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.deleteEdges_fromEdgeSet", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.DeleteEdges", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "SimpleGraph.deleteIncidenceSet", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.DeleteEdges", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.deleteIncidenceSet_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.DeleteEdges", "is_tactic_proof": true, "tactics": ["rw", "tauto"], "tactic_count": 2}
{"name": "SimpleGraph.deleteIncidenceSet_le", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.DeleteEdges", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.edgeSet_fromEdgeSet_incidenceSet", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.DeleteEdges", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.edgeSet_deleteIncidenceSet", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.DeleteEdges", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "SimpleGraph.support_deleteIncidenceSet_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.DeleteEdges", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.induce_deleteIncidenceSet_of_notMem", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.DeleteEdges", "is_tactic_proof": true, "tactics": ["ext", "simp_rw", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.instDecidableRelAdjDeleteIncidenceSet", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.DeleteEdges", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.card_edgeFinset_induce_compl_singleton", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.DeleteEdges", "is_tactic_proof": true, "tactics": ["have", "simp_rw", "apply", "trans", "exact", "rw", "exact"], "tactic_count": 7}
{"name": "SimpleGraph.edgeFinset_deleteIncidenceSet_eq_sdiff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.DeleteEdges", "is_tactic_proof": true, "tactics": ["apply", "push_cast", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.card_edgeFinset_deleteIncidenceSet", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.DeleteEdges", "is_tactic_proof": true, "tactics": ["simp_rw", "edgeFinset_deleteIncidenceSet_eq_sdiff]"], "tactic_count": 2}
{"name": "SimpleGraph.edgeFinset_deleteIncidenceSet_eq_filter", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.DeleteEdges", "is_tactic_proof": true, "tactics": ["rw", "apply", "intro", "rw", "left", "rwa"], "tactic_count": 6}
{"name": "SimpleGraph.card_support_deleteIncidenceSet", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.DeleteEdges", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "apply", "rw", "exact"], "tactic_count": 5}
{"name": "SimpleGraph.DeleteFar", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.DeleteEdges", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.deleteFar_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.DeleteEdges", "is_tactic_proof": true, "tactics": ["classical", "refine", "have", "simp", "coe_edgeFinset,", "exact", "classical", "simpa", "h"], "tactic_count": 9}
{"name": "SimpleGraph.DeleteFar.mono", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.DeleteEdges", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.DeleteFar.le_card_edgeFinset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.DeleteEdges", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rel.interedges", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Density", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rel.edgeDensity", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Density", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rel.mem_interedges_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Density", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Rel.mk_mem_interedges_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Density", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rel.interedges_empty_left", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Density", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Rel.interedges_mono", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Density", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rel.card_interedges_add_card_interedges_compl", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Density", "is_tactic_proof": true, "tactics": ["classical", "rw", "exact"], "tactic_count": 3}
{"name": "Rel.interedges_disjoint_left", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Density", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "exact"], "tactic_count": 4}
{"name": "Rel.interedges_disjoint_right", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Density", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "exact"], "tactic_count": 4}
{"name": "Rel.interedges_eq_biUnion", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Density", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Rel.interedges_biUnion_left", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Density", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Rel.interedges_biUnion_right", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Density", "is_tactic_proof": true, "tactics": ["ext", "simp", "exact"], "tactic_count": 3}
{"name": "Rel.interedges_biUnion", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Density", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Rel.card_interedges_le_mul", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Density", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rel.edgeDensity_nonneg", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Density", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "Rel.edgeDensity_le_one", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Density", "is_tactic_proof": true, "tactics": ["apply", "exact", "exact"], "tactic_count": 3}
{"name": "Rel.edgeDensity_add_edgeDensity_compl", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Density", "is_tactic_proof": true, "tactics": ["rw", "exact", "exact"], "tactic_count": 3}
{"name": "Rel.edgeDensity_empty_left", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Density", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Rel.edgeDensity_empty_right", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Density", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Rel.card_interedges_finpartition_left", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Density", "is_tactic_proof": true, "tactics": ["classical", "simp_rw", "rw", "exact"], "tactic_count": 4}
{"name": "Rel.card_interedges_finpartition_right", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Density", "is_tactic_proof": true, "tactics": ["classical", "simp_rw", "rw", "exact"], "tactic_count": 4}
{"name": "Rel.card_interedges_finpartition", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Density", "is_tactic_proof": true, "tactics": ["rw", "congr", "rw"], "tactic_count": 3}
{"name": "Rel.mul_edgeDensity_le_edgeDensity", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Density", "is_tactic_proof": true, "tactics": ["have", "rw", "gcongr", "exact"], "tactic_count": 4}
{"name": "Rel.edgeDensity_sub_edgeDensity_le_one_sub_mul", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Density", "is_tactic_proof": true, "tactics": ["refine", "refine", "rw", "refine", "exact", "apply", "exact"], "tactic_count": 7}
{"name": "Rel.abs_edgeDensity_sub_edgeDensity_le_one_sub_mul", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Density", "is_tactic_proof": true, "tactics": ["refine", "rw", "add_sub_cancel_right", "edgeDensity_add_edgeDensity_compl", "sub_sub_sub_cancel_left]", "exact"], "tactic_count": 6}
{"name": "Rel.abs_edgeDensity_sub_edgeDensity_le_two_mul_sub_sq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Density", "is_tactic_proof": false, "tactics": ["have", "rw", "gcongr", "exact", "rw", "obtain", "rw", "simpa", "obtain", "rw", "simpa", "have", "rw", "norm_cast", "refine", "push_cast", "have", "have", "gcongr", "refine", "exact", "refine", "exact"], "tactic_count": 23}
{"name": "Rel.abs_edgeDensity_sub_edgeDensity_le_two_mul", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Density", "is_tactic_proof": true, "tactics": ["rcases", "exact", "rw", "refine", "rw", "exact", "exact"], "tactic_count": 7}
{"name": "Rel.swap_mem_interedges_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Density", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Rel.mk_mem_interedges_comm", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Density", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rel.card_interedges_comm", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Density", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rel.edgeDensity_comm", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Density", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.interedges", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Density", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.edgeDensity", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Density", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.interedges_def", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Density", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.edgeDensity_def", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Density", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.card_interedges_div_card", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Density", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.mem_interedges_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Density", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.mk_mem_interedges_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Density", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.interedges_empty_left", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Density", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.interedges_mono", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Density", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.interedges_disjoint_left", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Density", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.interedges_disjoint_right", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Density", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.interedges_biUnion_left", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Density", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.interedges_biUnion_right", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Density", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.interedges_biUnion", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Density", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.card_interedges_add_card_interedges_compl", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Density", "is_tactic_proof": true, "tactics": ["rw", "have", "refine", "rw", "rw", "rw", "exact"], "tactic_count": 7}
{"name": "SimpleGraph.edgeDensity_add_edgeDensity_compl", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Density", "is_tactic_proof": true, "tactics": ["rw", "exact", "positivity"], "tactic_count": 3}
{"name": "SimpleGraph.card_interedges_le_mul", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Density", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.edgeDensity_nonneg", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Density", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.edgeDensity_le_one", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Density", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.edgeDensity_empty_left", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Density", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.edgeDensity_empty_right", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Density", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.swap_mem_interedges_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Density", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.mk_mem_interedges_comm", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Density", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.edgeDensity_comm", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Density", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.eccent", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.eccent_def", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.edist_le_eccent", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.exists_edist_eq_eccent_of_finite", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.eccent_eq_top_of_not_connected", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": true, "tactics": ["rw", "push_neg", "obtain", "rw", "exact"], "tactic_count": 5}
{"name": "SimpleGraph.eccent_eq_zero_of_subsingleton", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "SimpleGraph.eccent_ne_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": true, "tactics": ["obtain", "contrapose", "simp", "exact"], "tactic_count": 4}
{"name": "SimpleGraph.eccent_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": true, "tactics": ["refine", "contrapose", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.eccent_pos_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.eccent_bot", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.eccent_top", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": true, "tactics": ["apply", "rw", "intro", "cases"], "tactic_count": 4}
{"name": "SimpleGraph.eq_top_iff_forall_eccent_eq_one", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": true, "tactics": ["refine", "ext", "refine", "rw", "apply", "rw", "exact"], "tactic_count": 7}
{"name": "SimpleGraph.eccent_le_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.eccent_le_one_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": true, "tactics": ["constructor", "intro", "have", "have", "exact", "intro", "rw", "intro", "rw", "exact"], "tactic_count": 10}
{"name": "SimpleGraph.eccent_eq_one_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.ediam", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ediam_eq_iSup_iSup_edist", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ediam_def", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.eccent_le_ediam", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.edist_le_ediam", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ediam_le_of_edist_le", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ediam_le_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ediam_eq_top", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.ediam_eq_zero_of_subsingleton", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "SimpleGraph.nontrivial_of_ediam_ne_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": true, "tactics": ["contrapose", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.ediam_ne_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": true, "tactics": ["obtain", "contrapose", "simp", "exact"], "tactic_count": 4}
{"name": "SimpleGraph.subsingleton_of_ediam_eq_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": true, "tactics": ["contrapose", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.ediam_ne_zero_iff_nontrivial", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ediam_eq_zero_iff_subsingleton", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ediam_eq_top_of_not_connected", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": true, "tactics": ["rw", "push_neg", "obtain", "rw", "exact"], "tactic_count": 5}
{"name": "SimpleGraph.ediam_eq_top_of_not_preconnected", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": true, "tactics": ["cases", "exfalso", "exact", "apply", "rw", "tauto"], "tactic_count": 6}
{"name": "SimpleGraph.preconnected_of_ediam_ne_top", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.connected_of_ediam_ne_top", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.exists_eccent_eq_ediam_of_ne_top", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.exists_eccent_eq_ediam_of_finite", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.exists_edist_eq_ediam_of_ne_top", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.exists_edist_eq_ediam_of_finite", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.connected_iff_ediam_ne_top", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ediam_anti", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ediam_bot", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ediam_top", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.ediam_eq_one", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": true, "tactics": ["refine", "rw", "intro", "apply", "rw", "exact"], "tactic_count": 6}
{"name": "SimpleGraph.diam", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.diam_def", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.dist_le_diam", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.nontrivial_of_diam_ne_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": true, "tactics": ["contrapose", "simp"], "tactic_count": 2}
{"name": "SimpleGraph.diam_eq_zero_of_not_connected", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": true, "tactics": ["cases", "rw", "rw"], "tactic_count": 3}
{"name": "SimpleGraph.diam_eq_zero_of_ediam_eq_top", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.ediam_ne_top_of_diam_ne_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.exists_dist_eq_diam", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "obtain", "use", "rw"], "tactic_count": 5}
{"name": "SimpleGraph.diam_ne_zero_of_ediam_ne_top", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.diam_anti_of_ediam_ne_top", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.diam_bot", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": true, "tactics": ["rw", "cases", "exact", "exact"], "tactic_count": 4}
{"name": "SimpleGraph.diam_top", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.diam_eq_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.diam_eq_one", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.diam_eq_zero_iff_ediam_eq_top", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.connected_iff_diam_ne_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.radius", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.radius_eq_iInf_iSup_edist", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.radius_le_eccent", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.exists_eccent_eq_radius", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.exists_edist_eq_radius_of_finite", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "use", "rw"], "tactic_count": 4}
{"name": "SimpleGraph.radius_eq_top_of_not_connected", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.radius_eq_top_of_isEmpty", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.radius_ne_top_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": true, "tactics": ["refine", "obtain", "rw", "exact"], "tactic_count": 4}
{"name": "SimpleGraph.radius_ne_zero_of_nontrivial", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": true, "tactics": ["rw", "apply", "simp"], "tactic_count": 3}
{"name": "SimpleGraph.radius_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": true, "tactics": ["refine", "contrapose", "simp", "contrapose", "simp", "rw", "use", "simpa"], "tactic_count": 8}
{"name": "SimpleGraph.radius_le_ediam", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ediam_le_two_mul_radius", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": true, "tactics": ["cases", "rw", "exact", "by_cases", "obtain", "obtain", "apply", "rw", "exact", "rw", "exact"], "tactic_count": 11}
{"name": "SimpleGraph.radius_eq_ediam_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": true, "tactics": ["refine", "use", "intro", "exact", "obtain", "have", "rw", "exact"], "tactic_count": 8}
{"name": "SimpleGraph.radius_bot", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.radius_top", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.center", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.center_nonempty", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.mem_center_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.center_eq_univ_iff_radius_eq_ediam", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": true, "tactics": ["rw", "refine", "use", "exact", "obtain", "intro", "rw", "exact"], "tactic_count": 8}
{"name": "SimpleGraph.center_eq_univ_of_subsingleton", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "tauto"], "tactic_count": 4}
{"name": "SimpleGraph.center_bot", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": true, "tactics": ["cases", "exact", "rw", "intro", "rw"], "tactic_count": 5}
{"name": "SimpleGraph.center_top", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Diam", "is_tactic_proof": true, "tactics": ["cases", "exact", "rw", "intro", "rw"], "tactic_count": 5}
{"name": "SimpleGraph.EdgeLabeling", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.EdgeLabeling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.instFintypeEdgeLabelingOfDecidableEqOfElemSym2EdgeSet", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.EdgeLabeling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.instFiniteEdgeLabelingOfElemSym2EdgeSet", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.EdgeLabeling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.instNonemptyEdgeLabeling", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.EdgeLabeling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.instInhabitedEdgeLabeling", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.EdgeLabeling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.instSubsingletonEdgeLabeling", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.EdgeLabeling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.instNontrivialEdgeLabelingOfNonemptyElemSym2EdgeSet", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.EdgeLabeling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.instUniqueEdgeLabeling", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.EdgeLabeling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.TopEdgeLabeling", "kind": "abbrev", "module": "Mathlib.Combinatorics.SimpleGraph.EdgeLabeling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.card_topEdgeLabeling", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.EdgeLabeling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.EdgeLabeling.get", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.EdgeLabeling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.EdgeLabeling.get_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.EdgeLabeling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.EdgeLabeling.get_comm", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.EdgeLabeling", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.EdgeLabeling.ext_get", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.EdgeLabeling", "is_tactic_proof": true, "tactics": ["funext", "induction", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.EdgeLabeling.compRight", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.EdgeLabeling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.EdgeLabeling.pullback", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.EdgeLabeling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.EdgeLabeling.pullback_apply", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.EdgeLabeling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.EdgeLabeling.get_pullback", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.EdgeLabeling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.EdgeLabeling.compRight_apply", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.EdgeLabeling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.EdgeLabeling.compRight_get", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.EdgeLabeling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.EdgeLabeling.mk", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.EdgeLabeling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.EdgeLabeling.get_mk", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.EdgeLabeling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.EdgeLabeling.labelGraph", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.EdgeLabeling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.EdgeLabeling.labelGraph_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.EdgeLabeling", "is_tactic_proof": true, "tactics": ["rw", "simp", "grind"], "tactic_count": 3}
{"name": "SimpleGraph.EdgeLabeling.instDecidableRelAdjLabelGraphOfDecidableEq", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.EdgeLabeling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.EdgeLabeling.labelGraph_le", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.EdgeLabeling", "is_tactic_proof": true, "tactics": ["intro", "grind"], "tactic_count": 2}
{"name": "SimpleGraph.EdgeLabeling.pairwise_disjoint_labelGraph", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.EdgeLabeling", "is_tactic_proof": true, "tactics": ["intro", "rw", "grind"], "tactic_count": 3}
{"name": "SimpleGraph.EdgeLabeling.pairwiseDisjoint_univ_labelGraph", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.EdgeLabeling", "is_tactic_proof": true, "tactics": ["intro", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.EdgeLabeling.iSup_labelGraph", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.EdgeLabeling", "is_tactic_proof": true, "tactics": ["ext", "simp", "grind"], "tactic_count": 3}
{"name": "SimpleGraph.TopEdgeLabeling.pullback", "kind": "abbrev", "module": "Mathlib.Combinatorics.SimpleGraph.EdgeLabeling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.TopEdgeLabeling.labelGraph_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.EdgeLabeling", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.toTopEdgeLabeling", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.EdgeLabeling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.toTopEdgeLabeling_get", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.EdgeLabeling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.toTopEdgeLabeling_labelGraph", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.EdgeLabeling", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "SimpleGraph.toTopEdgeLabeling_labelGraph_compl", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.EdgeLabeling", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "SimpleGraph.TopEdgeLabeling.labelGraph_toTopEdgeLabeling", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.EdgeLabeling", "is_tactic_proof": true, "tactics": ["refine", "grind"], "tactic_count": 2}
{"name": "SimpleGraph.ComponentCompl", "kind": "abbrev", "module": "Mathlib.Combinatorics.SimpleGraph.Ends.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.componentComplMk", "kind": "abbrev", "module": "Mathlib.Combinatorics.SimpleGraph.Ends.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ComponentCompl.supp", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Ends.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ComponentCompl.supp_injective", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Ends.Defs", "is_tactic_proof": true, "tactics": ["refine", "rintro", "simp", "exact"], "tactic_count": 4}
{"name": "SimpleGraph.ComponentCompl.supp_inj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Ends.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ComponentCompl.setLike", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Ends.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.instPartialOrderComponentCompl", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Ends.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ComponentCompl.mem_supp_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Ends.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.componentComplMk_mem", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Ends.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.componentComplMk_eq_of_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Ends.Defs", "is_tactic_proof": true, "tactics": ["rw", "apply", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.componentCompl_nonempty_of_infinite", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Ends.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ComponentCompl.lift", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Ends.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ComponentCompl.ind", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Ends.Defs", "is_tactic_proof": true, "tactics": ["apply", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.ComponentCompl.coeGraph", "kind": "abbrev", "module": "Mathlib.Combinatorics.SimpleGraph.Ends.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ComponentCompl.coe_inj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Ends.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ComponentCompl.nonempty", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Ends.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ComponentCompl.exists_eq_mk", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Ends.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ComponentCompl.disjoint_right", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Ends.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.ComponentCompl.notMem_of_mem", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Ends.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ComponentCompl.pairwise_disjoint", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Ends.Defs", "is_tactic_proof": true, "tactics": ["rintro", "rw", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.ComponentCompl.mem_of_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Ends.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ComponentCompl.exists_adj_boundary_pair", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Ends.Defs", "is_tactic_proof": true, "tactics": ["refine", "let", "let", "by_contra", "suffices", "symm", "rw", "rintro", "by_contra", "obtain", "obtain", "exact"], "tactic_count": 12}
{"name": "SimpleGraph.ComponentCompl.hom", "kind": "abbrev", "module": "Mathlib.Combinatorics.SimpleGraph.Ends.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ComponentCompl.subset_hom", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Ends.Defs", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.componentComplMk_mem_hom", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Ends.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ComponentCompl.hom_eq_iff_le", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Ends.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ComponentCompl.hom_eq_iff_not_disjoint", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Ends.Defs", "is_tactic_proof": true, "tactics": ["rw", "constructor", "rintro", "refine", "exact", "refine", "rintro", "rw", "rfl"], "tactic_count": 9}
{"name": "SimpleGraph.ComponentCompl.hom_refl", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Ends.Defs", "is_tactic_proof": true, "tactics": ["change", "rw"], "tactic_count": 2}
{"name": "SimpleGraph.ComponentCompl.hom_trans", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Ends.Defs", "is_tactic_proof": true, "tactics": ["change", "rw", "rfl"], "tactic_count": 3}
{"name": "SimpleGraph.ComponentCompl.hom_mk", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Ends.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ComponentCompl.hom_infinite", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Ends.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.ComponentCompl.infinite_iff_in_all_ranges", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Ends.Defs", "is_tactic_proof": true, "tactics": ["classical", "constructor", "rintro", "obtain", "exact", "rintro", "obtain", "obtain", "let", "simp_rw", "exact"], "tactic_count": 11}
{"name": "SimpleGraph.componentCompl_finite", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Ends.Defs", "is_tactic_proof": true, "tactics": ["classical", "rcases", "dsimp", "rw", "have", "exact", "let", "let", "have", "h'.symm", "have", "refine", "apply", "simp", "apply"], "tactic_count": 15}
{"name": "SimpleGraph.componentComplFunctor", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Ends.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.end", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Ends.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.end_hom_mk_of_mk", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Ends.Defs", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "SimpleGraph.infinite_iff_in_eventualRange", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Ends.Defs", "is_tactic_proof": false, "tactics": ["simp", "componentComplFunctor_map]", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.instIsEmptyElemForallObjOppositeFinsetComponentComplFunctorEndOfFinite", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Ends.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.end_componentCompl_infinite", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Ends.Properties", "is_tactic_proof": true, "tactics": ["refine", "change", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.componentComplFunctor_nonempty_of_infinite", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Ends.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.componentComplFunctor_finite", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Ends.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.nonempty_ends_of_infinite", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Ends.Properties", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "SimpleGraph.IsExtremal", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Extremal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsExtremal.prop", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Extremal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.exists_isExtremal_iff_exists", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Extremal.Basic", "is_tactic_proof": true, "tactics": ["refine", "obtain", "apply", "use", "use", "exact"], "tactic_count": 6}
{"name": "SimpleGraph.exists_isExtremal_free", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Extremal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsExtremal.le_iff_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Extremal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.extremalNumber", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Extremal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.extremalNumber_of_fintypeCard_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Extremal.Basic", "is_tactic_proof": true, "tactics": ["let", "rw", "and_intros", "on_goal", "all_goals", "rw", "intro", "let", "replace", "rw", "simpa", "rw", "convert"], "tactic_count": 13}
{"name": "SimpleGraph.card_edgeFinset_le_extremalNumber", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Extremal.Basic", "is_tactic_proof": true, "tactics": ["rw", "convert"], "tactic_count": 2}
{"name": "SimpleGraph.IsContained.of_extremalNumber_lt_card_edgeFinset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Extremal.Basic", "is_tactic_proof": true, "tactics": ["contrapose", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.extremalNumber_le_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Extremal.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.lt_extremalNumber_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Extremal.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.extremalNumber_le_iff_of_nonneg", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Extremal.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.lt_extremalNumber_iff_of_nonneg", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Extremal.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.IsContained.extremalNumber_le", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Extremal.Basic", "is_tactic_proof": true, "tactics": ["rw", "intro", "contrapose", "exact"], "tactic_count": 4}
{"name": "SimpleGraph.extremalNumber_congr", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Extremal.Basic", "is_tactic_proof": true, "tactics": ["rw", "and_intros", "on_goal", "all_goals", "rw", "intro", "apply", "contrapose", "exact"], "tactic_count": 9}
{"name": "SimpleGraph.extremalNumber_congr_right", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Extremal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.isExtremal_free_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Extremal.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.card_edgeFinset_of_isExtremal_free", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Extremal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.card_edgeFinset_deleteIncidenceSet_le_extremalNumber", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Extremal.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply", "contrapose", "exact"], "tactic_count": 4}
{"name": "SimpleGraph.IsTuranMaximal", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Extremal.Turan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.turanGraph", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Extremal.Turan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.turanGraph_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Extremal.Turan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.instDecidableRelFinAdjTuranGraph", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Extremal.Turan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.turanGraph_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Extremal.Turan", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.turanGraph_eq_top", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Extremal.Turan", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "contrapose", "use", "simp", "rintro", "simp", "rw"], "tactic_count": 8}
{"name": "SimpleGraph.turanGraph_cliqueFree", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Extremal.Turan", "is_tactic_proof": true, "tactics": ["rw", "by_contra", "simp_rw", "obtain", "rw", "exact"], "tactic_count": 6}
{"name": "SimpleGraph.not_cliqueFree_of_isTuranMaximal", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Extremal.Turan", "is_tactic_proof": true, "tactics": ["rintro", "obtain", "obtain", "simpa", "exists_and_right]", "exact", "hGab", "le_sup_right.trans_eq"], "tactic_count": 8}
{"name": "SimpleGraph.exists_isTuranMaximal", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Extremal.Turan", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "SimpleGraph.IsTuranMaximal.degree_eq_of_not_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Extremal.Turan", "is_tactic_proof": true, "tactics": ["rw", "wlog", "replace", "exact", "classical", "use", "have", "lia"], "tactic_count": 8}
{"name": "SimpleGraph.IsTuranMaximal.not_adj_trans", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Extremal.Turan", "is_tactic_proof": true, "tactics": ["have", "have", "have", "rw", "classical", "use", "have", "have", "have", "rw", "have", "unfold", "simp_rw", "by_cases", "simpa", "rw", "have", "rw", "congr", "simp_rw", "split_ifs", "have", "lia"], "tactic_count": 23}
{"name": "SimpleGraph.IsTuranMaximal.equivalence_not_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Extremal.Turan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsTuranMaximal.setoid", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Extremal.Turan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsTuranMaximal.instDecidableRelR", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Extremal.Turan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsTuranMaximal.finpartition", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Extremal.Turan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsTuranMaximal.not_adj_iff_part_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Extremal.Turan", "is_tactic_proof": true, "tactics": ["change", "rw", "let", "change", "rw"], "tactic_count": 5}
{"name": "SimpleGraph.IsTuranMaximal.degree_eq_card_sub_part_card", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Extremal.Turan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsTuranMaximal.isEquipartition", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Extremal.Turan", "is_tactic_proof": true, "tactics": ["set", "by_contra", "rw", "obtain", "obtain", "obtain", "apply", "rw", "use", "have", "have", "have", "by_contra", "rw", "rw", "degree_eq_card_sub_part_card", "have", "lia"], "tactic_count": 18}
{"name": "SimpleGraph.IsTuranMaximal.card_parts_le", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Extremal.Turan", "is_tactic_proof": true, "tactics": ["by_contra", "obtain", "have", "refine", "contrapose", "exact", "rw", "exact"], "tactic_count": 8}
{"name": "SimpleGraph.IsTuranMaximal.card_parts", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Extremal.Turan", "is_tactic_proof": true, "tactics": ["set", "apply", "by_contra", "rw", "obtain", "apply", "rw", "have", "simp_rw", "and_comm,", "intro", "exact", "use", "convert", "convert", "rwa"], "tactic_count": 16}
{"name": "SimpleGraph.IsTuranMaximal.nonempty_iso_turanGraph", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Extremal.Turan", "is_tactic_proof": true, "tactics": ["classical", "obtain", "use", "intro", "simp_rw", "have", "rw", "rw", "rcases", "rw", "have", "rw", "rfl"], "tactic_count": 13}
{"name": "SimpleGraph.isTuranMaximal_of_iso", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Extremal.Turan", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "rw", "use"], "tactic_count": 4}
{"name": "SimpleGraph.IsTuranMaximal.iso", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Extremal.Turan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.isTuranMaximal_turanGraph", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Extremal.Turan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.isTuranMaximal_iff_nonempty_iso_turanGraph", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Extremal.Turan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.isExtremal_top_free_iff_isTuranMaximal", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Extremal.Turan", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "SimpleGraph.isExtremal_top_free_turanGraph", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Extremal.Turan", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.extremalNumber_top", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Extremal.Turan", "is_tactic_proof": false, "tactics": ["conv", "enter", "rw", "exact"], "tactic_count": 4}
{"name": "SimpleGraph.card_edgeFinset_eq_extremalNumber_top_iff_nonempty_iso_turanGraph", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Extremal.Turan", "is_tactic_proof": true, "tactics": ["rw", "isExtremal_top_free_iff_isTuranMaximal,"], "tactic_count": 2}
{"name": "_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.sum_ne_add_mod_eq_sub_one", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Extremal.Turan", "is_tactic_proof": true, "tactics": ["rcases", "suffices", "rw", "rw", "apply", "change", "rw", "simp", "have", "rw", "change", "rwa", "rw", "simp", "rw"], "tactic_count": 15}
{"name": "SimpleGraph.card_edgeFinset_turanGraph_add", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Extremal.Turan", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "conv_lhs", "enter", "rw", "rw", "add_assoc,", "congr", "rw", "conv_rhs", "congr", "rw", "conv_rhs", "rw", "congr"], "tactic_count": 15}
{"name": "SimpleGraph.card_edgeFinset_turanGraph", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Extremal.Turan", "is_tactic_proof": true, "tactics": ["rcases", "rw", "have", "rw", "have", "nth_rw", "show", "rw", "rcases", "rw", "have", "rw", "rw", "let", "have", "rw", "congr", "have", "rw", "have", "n", "n", "rw", "rw", "rw", "add_comm", "congr", "rw"], "tactic_count": 28}
{"name": "SimpleGraph.mul_card_edgeFinset_turanGraph_le", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Extremal.Turan", "is_tactic_proof": true, "tactics": ["grw", "rw", "grw", "exact", "rw", "gcongr", "rcases", "rw", "exact"], "tactic_count": 9}
{"name": "SimpleGraph.CliqueFree.card_edgeFinset_le", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Extremal.Turan", "is_tactic_proof": true, "tactics": ["rcases", "rw", "simp_rw", "exact", "obtain", "convert", "rw"], "tactic_count": 7}
{"name": "SimpleGraph.antitoneOn_extremalNumber_div_choose_two", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Extremal.TuranDensity", "is_tactic_proof": true, "tactics": ["apply", "intro", "conv_lhs", "enter", "rw", "rw", "intro", "rw", "mul_comm", "mul_le_mul_iff_right₀", "conv_rhs", "rw", "apply", "card_nsmul_le_card_nsmul", "intro", "simp_rw", "card_compl,", "intro", "simpa"], "tactic_count": 19}
{"name": "SimpleGraph.turanDensity", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Extremal.TuranDensity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.tendsto_turanDensity", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Extremal.TuranDensity", "is_tactic_proof": true, "tactics": ["let", "suffices", "obtain", "simpa", "use", "apply", "rw", "exact", "use", "intro", "rw", "positivity"], "tactic_count": 12}
{"name": "SimpleGraph.isEquivalent_extremalNumber", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Extremal.TuranDensity", "is_tactic_proof": true, "tactics": ["have", "apply", "simp_rw", "have", "rw", "use", "intro", "simp", "simpa"], "tactic_count": 9}
{"name": "SimpleGraph.edgeFinset", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.coe_edgeFinset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.mem_edgeFinset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.not_isDiag_of_mem_edgeFinset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.card_toFinset_mem_edgeFinset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.edgeFinset_inj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.edgeFinset_subset_edgeFinset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.edgeFinset_ssubset_edgeFinset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.edgeFinset_bot", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.edgeFinset_sup", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.edgeFinset_inf", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.edgeFinset_sdiff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.disjoint_edgeFinset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "SimpleGraph.edgeFinset_eq_empty", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.edgeFinset_nonempty", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.edgeFinset_card", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.card_edgeSet", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.edgeSet_univ_card", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.edgeFinset_top", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.card_edgeFinset_top_eq_card_choose_two", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "SimpleGraph.card_edgeFinset_le_card_choose_two", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": true, "tactics": ["classical", "rw", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.neighborFinset", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.neighborFinset_def", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.coe_neighborFinset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.mem_neighborFinset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.notMem_neighborFinset_self", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.neighborFinset_disjoint_singleton", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.singleton_disjoint_neighborFinset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.degree", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.card_neighborFinset_eq_degree", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.card_neighborSet_eq_degree", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.degree_pos_iff_exists_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.degree_pos_iff_nonempty", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Adj.degree_pos_left", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Adj.degree_pos_right", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.degree_pos_iff_mem_support", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.degree_eq_zero_iff_notMem_support", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.degree_eq_zero_of_subsingleton", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": true, "tactics": ["have", "simp_all"], "tactic_count": 2}
{"name": "SimpleGraph.degree_eq_one_iff_existsUnique_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "SimpleGraph.nontrivial_of_degree_ne_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": true, "tactics": ["by_contra", "simp_all"], "tactic_count": 2}
{"name": "SimpleGraph.degree_compl", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": true, "tactics": ["classical", "rw", "simp"], "tactic_count": 3}
{"name": "SimpleGraph.incidenceSetFintype", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.incidenceFinset", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.card_incidenceSet_eq_degree", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "SimpleGraph.coe_incidenceFinset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.card_incidenceFinset_eq_degree", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "SimpleGraph.mem_incidenceFinset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.incidenceFinset_eq_filter", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": true, "tactics": ["ext", "induction", "simp"], "tactic_count": 3}
{"name": "SimpleGraph.incidenceFinset_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.degree_le_card_edgeFinset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": true, "tactics": ["classical", "rw", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.degree_le_of_le", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.LocallyFinite", "kind": "abbrev", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsRegularOfDegree", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsRegularOfDegree.degree_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsRegularOfDegree.compl", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": true, "tactics": ["intro", "rw"], "tactic_count": 2}
{"name": "SimpleGraph.neighborSetFintype", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.neighborFinset_eq_filter", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "SimpleGraph.neighborFinset_compl", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.complete_graph_degree", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": true, "tactics": ["simp_rw", "rw"], "tactic_count": 2}
{"name": "SimpleGraph.bot_degree", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.IsRegularOfDegree.top", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": true, "tactics": ["intro", "simp"], "tactic_count": 2}
{"name": "SimpleGraph.minDegree", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.exists_minimal_degree_vertex", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.minDegree_le_degree", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": true, "tactics": ["obtain", "have", "rwa"], "tactic_count": 3}
{"name": "SimpleGraph.le_minDegree_of_forall_le_degree", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": true, "tactics": ["rcases", "rw", "apply"], "tactic_count": 3}
{"name": "SimpleGraph.minDegree_of_isEmpty", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "SimpleGraph.minDegree_le_minDegree", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": true, "tactics": ["by_cases", "apply", "exact", "simp"], "tactic_count": 4}
{"name": "SimpleGraph.minDegree_lt_card", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": true, "tactics": ["obtain", "rw", "have", "contrapose", "rw", "exact"], "tactic_count": 6}
{"name": "SimpleGraph.maxDegree", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.exists_maximal_degree_vertex", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": true, "tactics": ["obtain", "have", "simp", "rcases", "refine", "rw"], "tactic_count": 6}
{"name": "SimpleGraph.degree_le_maxDegree", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": true, "tactics": ["obtain", "have", "rwa"], "tactic_count": 3}
{"name": "SimpleGraph.maxDegree_of_isEmpty", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.maxDegree_le_of_forall_degree_le", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "obtain", "exact"], "tactic_count": 4}
{"name": "SimpleGraph.maxDegree_bot_eq_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.minDegree_le_maxDegree", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.minDegree_bot_eq_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.degree_lt_card_verts", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": true, "tactics": ["classical", "apply", "rw", "exact"], "tactic_count": 4}
{"name": "SimpleGraph.maxDegree_lt_card_verts", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": true, "tactics": ["obtain", "rw", "apply"], "tactic_count": 3}
{"name": "SimpleGraph.card_commonNeighbors_le_degree_left", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.card_commonNeighbors_le_degree_right", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "SimpleGraph.card_commonNeighbors_lt_card_verts", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Adj.card_commonNeighbors_lt_degree", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": true, "tactics": ["classical", "rw", "apply", "rw", "use", "constructor", "rw", "apply", "rw", "constructor", "simpa", "rw", "exact"], "tactic_count": 13}
{"name": "SimpleGraph.card_commonNeighbors_top", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": true, "tactics": ["simp", "simp"], "tactic_count": 2}
{"name": "SimpleGraph.Iso.card_edgeFinset_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": true, "tactics": ["apply", "simp", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.Iso.degree_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.Iso.minDegree_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": true, "tactics": ["rcases", "simp", "have", "apply", "obtain", "simpa", "obtain", "simpa"], "tactic_count": 8}
{"name": "SimpleGraph.Iso.maxDegree_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": true, "tactics": ["rcases", "simp", "have", "apply", "obtain", "simpa", "obtain", "simpa"], "tactic_count": 8}
{"name": "SimpleGraph.edgeFinset_subset_sym2_of_support_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": true, "tactics": ["simp_rw", "intro", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.instDecidablePredMemSetSupport", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.map_edgeFinset_induce", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SimpleGraph.map_edgeFinset_induce_of_support_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "SimpleGraph.card_edgeFinset_induce_of_support_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.card_edgeFinset_induce_support", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.map_neighborFinset_induce", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "SimpleGraph.map_neighborFinset_induce_of_neighborSet_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": true, "tactics": ["classical", "rwa"], "tactic_count": 2}
{"name": "SimpleGraph.degree_induce_of_neighborSet_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "SimpleGraph.degree_induce_of_support_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.degree_induce_support", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.edgeFinset_map", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": true, "tactics": ["rw", "push_cast", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.card_edgeFinset_map", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finite", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.Finsubgraph", "kind": "abbrev", "module": "Mathlib.Combinatorics.SimpleGraph.Finsubgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.FinsubgraphHom", "kind": "abbrev", "module": "Mathlib.Combinatorics.SimpleGraph.Finsubgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.SimpleGraph.Finsubgraph.0.SimpleGraph.term_→fg_", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Finsubgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.SimpleGraph.Finsubgraph.0.SimpleGraph._aux_Mathlib_Combinatorics_SimpleGraph_Finsubgraph___macroRules__private_Mathlib_Combinatorics_SimpleGraph_Finsubgraph_0_SimpleGraph_term_→fg__1", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Finsubgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.SimpleGraph.Finsubgraph.0.SimpleGraph._aux_Mathlib_Combinatorics_SimpleGraph_Finsubgraph___unexpand_SimpleGraph_FinsubgraphHom_1", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Finsubgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Finsubgraph.instOrderBot", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Finsubgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Finsubgraph.instMax", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Finsubgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Finsubgraph.instMin", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Finsubgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Finsubgraph.instSDiff", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Finsubgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Finsubgraph.coe_bot", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finsubgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Finsubgraph.coe_sup", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finsubgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Finsubgraph.coe_inf", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finsubgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Finsubgraph.coe_sdiff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finsubgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Finsubgraph.instGeneralizedCoheytingAlgebra", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Finsubgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Finsubgraph.instTop", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Finsubgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Finsubgraph.instCompl", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Finsubgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Finsubgraph.instHNot", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Finsubgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Finsubgraph.instHImp", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Finsubgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Finsubgraph.instSupSet", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Finsubgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Finsubgraph.instInfSet", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Finsubgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Finsubgraph.coe_top", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finsubgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Finsubgraph.coe_compl", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finsubgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Finsubgraph.coe_hnot", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finsubgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Finsubgraph.coe_himp", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finsubgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Finsubgraph.coe_sSup", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finsubgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Finsubgraph.coe_sInf", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finsubgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Finsubgraph.coe_iSup", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finsubgraph", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.Finsubgraph.coe_iInf", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finsubgraph", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.Finsubgraph.instCompletelyDistribLattice", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Finsubgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.singletonFinsubgraph", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Finsubgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.finsubgraphOfAdj", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Finsubgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.singletonFinsubgraph_le_adj_left", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finsubgraph", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.singletonFinsubgraph_le_adj_right", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finsubgraph", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.FinsubgraphHom.restrict", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Finsubgraph", "is_tactic_proof": true, "tactics": ["refine", "rintro", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.finsubgraphHomFunctor", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Finsubgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.nonempty_hom_of_forall_finite_subgraph_hom", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Finsubgraph", "is_tactic_proof": true, "tactics": ["cases", "haveI", "haveI", "intro", "haveI", "haveI", "exact", "obtain", "refine", "exact", "unfold", "simp⟩", "intro", "simp", "target", "have", "have", "rw", "apply", "simp"], "tactic_count": 20}
{"name": "_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.term‖_‖", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.FiveWheelLike", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0._aux_Mathlib_Combinatorics_SimpleGraph_FiveWheelLike___macroRules__private_Mathlib_Combinatorics_SimpleGraph_FiveWheelLike_0_term‖_‖_1", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.FiveWheelLike", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0._aux_Mathlib_Combinatorics_SimpleGraph_FiveWheelLike___unexpand_Fintype_card_1", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.FiveWheelLike", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsNClique.insert_insert", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.FiveWheelLike", "is_tactic_proof": true, "tactics": ["apply", "obtain", "exact", "exact"], "tactic_count": 4}
{"name": "_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsNClique.insert_insert_erase", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.FiveWheelLike", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.exists_isFiveWheelLike_of_maximal_cliqueFree_not_isCompleteMultipartite", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.FiveWheelLike", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "obtain", "exact"], "tactic_count": 4}
{"name": "SimpleGraph.FiveWheelLikeFree", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.FiveWheelLike", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsFiveWheelLike.symm", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.FiveWheelLike", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsFiveWheelLike.fst_notMem_right", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.FiveWheelLike", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsFiveWheelLike.snd_notMem_left", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.FiveWheelLike", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsFiveWheelLike.not_colorable_succ", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.FiveWheelLike", "is_tactic_proof": true, "tactics": ["intro", "have", "have", "obtain", "obtain", "rw", "cases", "inl", "cases", "inl", "subst_vars", "inr", "apply", "exact", "inr", "apply", "exact"], "tactic_count": 17}
{"name": "SimpleGraph.IsFiveWheelLike.card_left", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.FiveWheelLike", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.IsFiveWheelLike.card_right", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.FiveWheelLike", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsFiveWheelLike.card_inter_lt_of_cliqueFree", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.FiveWheelLike", "is_tactic_proof": true, "tactics": ["contrapose", "have", "have", "exact", "hw.isPathGraph3Compl.adj).not_cliqueFree"], "tactic_count": 5}
{"name": "SimpleGraph.exists_max_isFiveWheelLike_of_maximal_cliqueFree_not_isCompleteMultipartite", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.FiveWheelLike", "is_tactic_proof": true, "tactics": ["obtain", "let", "have", "classical", "obtain", "exact", "hj.not_ge"], "tactic_count": 7}
{"name": "SimpleGraph.CliqueFree.fiveWheelLikeFree_of_le", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.FiveWheelLike", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.colorable_iff_isCompleteMultipartite_of_maximal_cliqueFree", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.FiveWheelLike", "is_tactic_proof": true, "tactics": ["classical", "r", "refine", "contrapose", "obtain", "exact"], "tactic_count": 6}
{"name": "_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.sum_degree_le_of_le_not_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.FiveWheelLike", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsFiveWheelLike.exist_not_adj_of_adj_inter", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.FiveWheelLike", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "obtain", "obtain", "exact"], "tactic_count": 5}
{"name": "SimpleGraph.IsFiveWheelLike.exists_isFiveWheelLike_succ_of_not_adj_le_two", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.FiveWheelLike", "is_tactic_proof": false, "tactics": ["obtain", "hw.exist_not_adj_of_adj_inter", "let", "have", "by_contra", "apply", "by_cases", "exact", "exact", "simp_rw", "have", "have", "refine", "by_cases", "grind", "exact", "by_cases", "grind", "exact", "by_cases", "grind", "exact", "have", "intro", "by_contra", "apply", "exact", "two_lt_card.2", "hbz.symm⟩", "have", "grind", "refine", "exact", "hw.isNClique_left.insert_insert_erase", "wa", "hbv", "exact", "hw.isNClique_fst_left.insert_insert_erase", "wa", "exact", "hw.isNClique_right.insert_insert_erase", "wa", "exact", "hw.isNClique_snd_right.insert_insert_erase", "wa", "rw", "erase_eq_of_notMem", "hw.card_inter]"], "tactic_count": 48}
{"name": "SimpleGraph.IsFiveWheelLike.minDegree_le_of_cliqueFree_fiveWheelLikeFree_succ", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.FiveWheelLike", "is_tactic_proof": true, "tactics": ["let", "let", "have", "intro", "by_contra", "obtain", "hw.exists_isFiveWheelLike_succ_of_not_adj_le_two", "exact", "have", "let", "card_pos.2", "have", "sum_degree_le_of_le_not_adj", "have", "intro", "apply", "obtain", "contrapose", "simpa", "exact", "have", "rw", "rw", "have", "grind", "calc", "simp_rw", "card_eq_sum_ones,", "gcongr", "by_cases", "k", "have", "rw", "exact", "subst", "rw", "simp", "have", "two_lt_card.2", "hw.isPathGraph3Compl.ne_snd,", "have", "rw", "gcongr", "lia"], "tactic_count": 44}
{"name": "SimpleGraph.colorable_of_cliqueFree_lt_minDegree", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.FiveWheelLike", "is_tactic_proof": true, "tactics": ["r", "classical", "obtain", "apply", "by_contra", "have", "hnotcol", "hc.colorable_of_cliqueFree", "hmcf.1", "obtain", "exists_max_isFiveWheelLike_of_maximal_cliqueFree_not_isCompleteMultipartite", "have", "have", "apply", "rw", "apply", "nlinarith", "exact"], "tactic_count": 18}
{"name": "SimpleGraph.egirth", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Girth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.le_egirth", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Girth", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.egirth_le_length", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Girth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.egirth_eq_top", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Girth", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.egirth_anti", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Girth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.exists_egirth_eq_length", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Girth", "is_tactic_proof": true, "tactics": ["refine", "rintro", "exact", "simp_rw", "exact"], "tactic_count": 5}
{"name": "SimpleGraph.three_le_egirth", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Girth", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "SimpleGraph.egirth_bot", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Girth", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.girth", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Girth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.girth_le_length", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Girth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.three_le_girth", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Girth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.girth_eq_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Girth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.girth_anti", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Girth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.exists_girth_eq_length", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Girth", "is_tactic_proof": true, "tactics": ["refine", "obtain", "simp_all", "tauto"], "tactic_count": 4}
{"name": "SimpleGraph.girth_bot", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Girth", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "_private.Mathlib.Combinatorics.SimpleGraph.Hall.0.SimpleGraph.hall_subgraph", "kind": "abbrev", "module": "Mathlib.Combinatorics.SimpleGraph.Hall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.exists_isMatching_of_forall_ncard_le", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Hall", "is_tactic_proof": true, "tactics": ["classical", "obtain", "have", "rw", "simpa", "have", "h₁.disjoint", "use", "refine", "simp", "rcases", "exact", "use", "have", "simp", "exact"], "tactic_count": 16}
{"name": "SimpleGraph.union_eq_univ_of_forall_ncard_le", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Hall", "is_tactic_proof": true, "tactics": ["classical", "obtain", "have", "simpa", "refine", "have", "grind"], "tactic_count": 7}
{"name": "SimpleGraph.exists_bijective_of_forall_ncard_le", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Hall", "is_tactic_proof": true, "tactics": ["classical", "obtain", "have", "simpa", "have", "h₁.disjoint", "have", "h₁.disjoint", "have", "let", "let", "refine", "exact", "exact", "exact", "exact"], "tactic_count": 16}
{"name": "SimpleGraph.exists_isPerfectMatching_of_forall_ncard_le", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Hall", "is_tactic_proof": true, "tactics": ["classical", "obtain", "use", "have", "rw", "exact", "refine", "simp", "split", "exact", "obtain", "exact"], "tactic_count": 12}
{"name": "SimpleGraph.Walk.IsHamiltonian", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Hamiltonian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.IsHamiltonian.map", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Hamiltonian", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.IsHamiltonian.mem_support", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Hamiltonian", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.IsHamiltonian.isPath", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Hamiltonian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.IsPath.isHamiltonian_of_mem", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Hamiltonian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.IsPath.isHamiltonian_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Hamiltonian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.IsHamiltonian.of_subsingleton", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Hamiltonian", "is_tactic_proof": true, "tactics": ["intro", "rw"], "tactic_count": 2}
{"name": "SimpleGraph.Walk.IsHamiltonian.fintype", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Hamiltonian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.IsHamiltonian.support_toFinset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Hamiltonian", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.IsHamiltonian.length_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Hamiltonian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.IsHamiltonian.length_support", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Hamiltonian", "is_tactic_proof": true, "tactics": ["have", "grind"], "tactic_count": 2}
{"name": "SimpleGraph.Walk.IsHamiltonian.supportGetEquiv", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Hamiltonian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.IsHamiltonian.getVertEquiv", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Hamiltonian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.isHamiltonian_iff_support_get_bijective", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Hamiltonian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.IsHamiltonian.getVert_surjective", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Hamiltonian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.IsHamiltonianCycle.isCycle", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Hamiltonian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.IsHamiltonianCycle.map", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Hamiltonian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.isHamiltonianCycle_isCycle_and_isHamiltonian_tail", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Hamiltonian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.isHamiltonianCycle_iff_isCycle_and_support_count_tail_eq_one", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Hamiltonian", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.IsHamiltonianCycle.mem_support", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Hamiltonian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.IsHamiltonianCycle.length_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Hamiltonian", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.Walk.IsHamiltonianCycle.count_support_self", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Hamiltonian", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.IsHamiltonianCycle.support_count_of_ne", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Hamiltonian", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.IsHamiltonian", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Hamiltonian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsHamiltonian.mono", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Hamiltonian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsHamiltonian.connected", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Hamiltonian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsHamiltonian.of_card_eq_one", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Hamiltonian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsHamiltonian.of_unique", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Hamiltonian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.not_isHamiltonian_of_isBridge", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Hamiltonian", "is_tactic_proof": true, "tactics": ["classical", "refine", "intro", "have", "haveI", "have", "have", "exact", "obtain", "have", "have", "let", "have", "have", "he_not_in_cycle", "have", "by_cases", "subst", "exact", "have", "have", "have", "rw", "have", "have", "exact", "let", "have", "exact"], "tactic_count": 29}
{"name": "SimpleGraph.hasse", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Hasse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.hasse_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Hasse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.hasseDualIso", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Hasse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.hasseDualIso_apply", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Hasse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.hasseDualIso_symm_apply", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Hasse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.hasse_prod", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Hasse", "is_tactic_proof": true, "tactics": ["ext", "simp_rw"], "tactic_count": 2}
{"name": "SimpleGraph.hasse_preconnected_of_succ", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Hasse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.hasse_preconnected_of_pred", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Hasse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.pathGraph", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Hasse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.pathGraph_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Hasse", "is_tactic_proof": true, "tactics": ["simp", "simp_rw"], "tactic_count": 2}
{"name": "SimpleGraph.pathGraph_preconnected", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Hasse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.pathGraph_connected", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Hasse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.pathGraph_two_eq_top", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Hasse", "is_tactic_proof": true, "tactics": ["ext", "fin_cases"], "tactic_count": 2}
{"name": "SimpleGraph.incMatrix", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.IncMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.incMatrix_apply", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.IncMatrix", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.incMatrix_apply'", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.IncMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.incMatrix_apply_mul_incMatrix_apply", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.IncMatrix", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.incMatrix_apply_mul_incMatrix_apply_of_not_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.IncMatrix", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.incMatrix_of_notMem_incidenceSet", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.IncMatrix", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.incMatrix_of_mem_incidenceSet", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.IncMatrix", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.incMatrix_apply_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.IncMatrix", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.incMatrix_apply_eq_one_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.IncMatrix", "is_tactic_proof": true, "tactics": ["convert", "infer_instance"], "tactic_count": 2}
{"name": "SimpleGraph.sum_incMatrix_apply", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.IncMatrix", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.incMatrix_mul_transpose_diag", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.IncMatrix", "is_tactic_proof": true, "tactics": ["rw", "simp", "simp_all"], "tactic_count": 3}
{"name": "SimpleGraph.sum_incMatrix_apply_of_mem_edgeSet", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.IncMatrix", "is_tactic_proof": true, "tactics": ["refine", "intro", "rw", "rw", "simp", "congr", "ext", "simp"], "tactic_count": 8}
{"name": "SimpleGraph.sum_incMatrix_apply_of_notMem_edgeSet", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.IncMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.incMatrix_transpose_mul_diag", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.IncMatrix", "is_tactic_proof": false, "tactics": ["simp", "and_self_iff]", "split_ifs", "revert", "refine", "intro", "rw", "simp", "congr", "ext", "simp", "revert", "refine", "intro", "simp"], "tactic_count": 15}
{"name": "SimpleGraph.incMatrix_mul_transpose_apply_of_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.IncMatrix", "is_tactic_proof": false, "tactics": ["simp_rw", "convert", "convert", "rw", "exact"], "tactic_count": 5}
{"name": "SimpleGraph.incMatrix_mul_transpose", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.IncMatrix", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "split_ifs", "subst", "exact", "exact", "simp", "sum_const_zero]"], "tactic_count": 8}
{"name": "initFn._@.Mathlib.Combinatorics.SimpleGraph.Init.3578731502._hygCtx._hyg.3", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.degree_eq_sum_if_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.LapMatrix", "is_tactic_proof": true, "tactics": ["unfold", "rw"], "tactic_count": 2}
{"name": "SimpleGraph.degMatrix", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.LapMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.lapMatrix", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.LapMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.isSymm_degMatrix", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.LapMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.isSymm_lapMatrix", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.LapMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.degMatrix_mulVec_apply", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.LapMatrix", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.lapMatrix_mulVec_apply", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.LapMatrix", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "SimpleGraph.lapMatrix_mulVec_const_eq_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.LapMatrix", "is_tactic_proof": true, "tactics": ["ext1", "rw", "simp"], "tactic_count": 3}
{"name": "SimpleGraph.dotProduct_mulVec_degMatrix", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.LapMatrix", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.lapMatrix_toLinearMap₂'", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.LapMatrix", "is_tactic_proof": false, "tactics": ["simp_rw", "dotProduct_mulVec_adjMatrix,", "sum_sub_distrib,", "rw", "conv_lhs", "conv_lhs", "simp_rw", "congr", "congr", "ring_nf"], "tactic_count": 10}
{"name": "SimpleGraph.posSemidef_lapMatrix", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.LapMatrix", "is_tactic_proof": true, "tactics": ["refine", "rw", "rw", "positivity"], "tactic_count": 4}
{"name": "SimpleGraph.lapMatrix_toLinearMap₂'_apply'_eq_zero_iff_forall_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.LapMatrix", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.lapMatrix_mulVec_eq_zero_iff_forall_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.LapMatrix", "is_tactic_proof": true, "tactics": ["rw", "lapMatrix_toLinearMap₂'_apply'_eq_zero_iff_forall_adj]"], "tactic_count": 2}
{"name": "SimpleGraph.lapMatrix_toLinearMap₂'_apply'_eq_zero_iff_forall_reachable", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.LapMatrix", "is_tactic_proof": true, "tactics": ["rw", "refine", "intro", "induction", "nil", "cons"], "tactic_count": 6}
{"name": "SimpleGraph.lapMatrix_mulVec_eq_zero_iff_forall_reachable", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.LapMatrix", "is_tactic_proof": true, "tactics": ["rw", "lapMatrix_toLinearMap₂'_apply'_eq_zero_iff_forall_reachable]"], "tactic_count": 2}
{"name": "SimpleGraph.det_lapMatrix_eq_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.LapMatrix", "is_tactic_proof": true, "tactics": ["rw", "use", "refine", "rw", "use", "simp"], "tactic_count": 6}
{"name": "SimpleGraph.mem_ker_toLin'_lapMatrix_of_connectedComponent", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.LapMatrix", "is_tactic_proof": true, "tactics": ["rw", "intro", "split_ifs", "rfl", "rw", "exact", "rw", "exact", "rfl"], "tactic_count": 9}
{"name": "SimpleGraph.lapMatrix_ker_basis_aux", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.LapMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.linearIndependent_lapMatrix_ker_basis_aux", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.LapMatrix", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "have", "simp", "repeat", "ext", "simp", "rw", "intro", "obtain", "exact"], "tactic_count": 12}
{"name": "SimpleGraph.top_le_span_range_lapMatrix_ker_basis_aux", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.LapMatrix", "is_tactic_proof": true, "tactics": ["intro", "rw", "use", "ext", "simp", "rw", "simp", "mem_univ,", "rfl"], "tactic_count": 9}
{"name": "SimpleGraph.lapMatrix_ker_basis", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.LapMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.card_connectedComponent_eq_finrank_ker_toLin'_lapMatrix", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.LapMatrix", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "SimpleGraph.lineGraph", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.LineGraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.lineGraph_adj_iff_exists", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.LineGraph", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.lineGraph_bot", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.LineGraph", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SimpleGraph.map", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.instDecidableMapAdj", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.map_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.edgeSet_map", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": true, "tactics": ["ext", "induction", "rw", "constructor", "intro", "use", "rw", "intro", "induction", "rw", "exact"], "tactic_count": 11}
{"name": "SimpleGraph.map_adj_apply", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.map_monotone", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.map_id", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.map_map", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.support_map", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "SimpleGraph.comap", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.comap_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.comap_id", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.comap_comap", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.instDecidableComapAdj", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.comap_symm", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": true, "tactics": ["ext", "simp", "exists_eq_right]"], "tactic_count": 3}
{"name": "SimpleGraph.map_symm", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.comap_monotone", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.comap_bot", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.comap_top", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "SimpleGraph.comap_map_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "SimpleGraph.leftInverse_comap_map", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.map_injective", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.comap_surjective", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.map_le_iff_le_comap", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.map_comap_le", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.le_comap_of_subsingleton", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": true, "tactics": ["intro"], "tactic_count": 1}
{"name": "SimpleGraph.map_le_of_subsingleton", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.completeMultipartiteGraph", "kind": "abbrev", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.simpleGraph", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.simpleGraph_refl", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Equiv.simpleGraph_trans", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.symm_simpleGraph", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.induce", "kind": "abbrev", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.induce_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.induce_top", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.induce_singleton_eq_top", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.spanningCoe", "kind": "abbrev", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.induce_spanningCoe", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.spanningCoe_induce_le", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsCompleteBetween.induce", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": true, "tactics": ["intro", "rw", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.Hom", "kind": "abbrev", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Embedding", "kind": "abbrev", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Iso", "kind": "abbrev", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.term_→g_", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph._aux_Mathlib_Combinatorics_SimpleGraph_Maps___macroRules_SimpleGraph_term_→g__1", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph._aux_Mathlib_Combinatorics_SimpleGraph_Maps___unexpand_SimpleGraph_Hom_1", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.term_↪g_", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph._aux_Mathlib_Combinatorics_SimpleGraph_Maps___macroRules_SimpleGraph_term_↪g__1", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph._aux_Mathlib_Combinatorics_SimpleGraph_Maps___unexpand_SimpleGraph_Embedding_1", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.term_≃g_", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph._aux_Mathlib_Combinatorics_SimpleGraph_Maps___macroRules_SimpleGraph_term_≃g__1", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph._aux_Mathlib_Combinatorics_SimpleGraph_Maps___unexpand_SimpleGraph_Iso_1", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.HomClass", "kind": "abbrev", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Hom.id", "kind": "abbrev", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Hom.coe_id", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Hom.instSubsingletonOfForall", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Hom.instUniqueOfIsEmpty", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Hom.instFinite", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Hom.map_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Hom.map_mem_edgeSet", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Hom.apply_mem_neighborSet", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Hom.mapEdgeSet", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Hom.mapNeighborSet", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Hom.mapDart", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Hom.mapDart_apply", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Hom.ofLE", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Hom.coe_ofLE", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Hom.ofLE_apply", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Hom.mapEdgeSet.injective", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": true, "tactics": ["rintro", "dsimp", "repeat", "apply"], "tactic_count": 4}
{"name": "SimpleGraph.Hom.injective_of_top_hom", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": true, "tactics": ["intro", "contrapose", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.Hom.comap", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Hom.comp", "kind": "abbrev", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Hom.coe_comp", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Embedding.refl", "kind": "abbrev", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Embedding.toHom", "kind": "abbrev", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Embedding.coe_toHom", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Embedding.map_adj_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Embedding.map_mem_edgeSet_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Embedding.apply_mem_neighborSet_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Embedding.mapEdgeSet", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Embedding.mapNeighborSet", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Embedding.comap", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Embedding.comap_apply", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Embedding.map", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Embedding.map_apply", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Embedding.induce", "kind": "abbrev", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Embedding.spanningCoe", "kind": "abbrev", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Embedding.completeGraph", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Embedding.coe_completeGraph", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Embedding.comp", "kind": "abbrev", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Embedding.coe_comp", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Embedding.complEquiv", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.induceHom", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.coe_induceHom", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.induceHom_id", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "SimpleGraph.induceHom_comp", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "SimpleGraph.induceHom_injective", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "SimpleGraph.induceHomOfLE", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.induceHomOfLE_apply", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.induceHomOfLE_toHom", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "SimpleGraph.Iso.refl", "kind": "abbrev", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Iso.toEmbedding", "kind": "abbrev", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Iso.toHom", "kind": "abbrev", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Iso.symm", "kind": "abbrev", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Iso.map_adj_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Iso.map_mem_edgeSet_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Iso.apply_mem_neighborSet_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Iso.symm_toHom_comp_toHom", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "SimpleGraph.Iso.toHom_comp_symm_toHom", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "SimpleGraph.Iso.mapEdgeSet", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Iso.mapNeighborSet", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Iso.card_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": true, "tactics": ["rw", "convert"], "tactic_count": 2}
{"name": "SimpleGraph.Iso.comap", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Iso.comap_apply", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Iso.comap_symm_apply", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Iso.map", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Iso.map_apply", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Iso.map_symm_apply", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Iso.completeGraph", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Iso.toEmbedding_completeGraph", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Iso.comp", "kind": "abbrev", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Iso.coe_comp", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.induceUnivIso", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.overFin", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.overFinIso", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Maps", "is_tactic_proof": true, "tactics": ["use"], "tactic_count": 1}
{"name": "SimpleGraph.Subgraph.IsMatching", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Matching", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.IsMatching.toEdge", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Matching", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.IsMatching.toEdge_eq_of_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Matching", "is_tactic_proof": true, "tactics": ["simp", "congr", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.Subgraph.IsMatching.toEdge.surjective", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Matching", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.Subgraph.IsMatching.toEdge_eq_toEdge_of_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Matching", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.Subgraph.IsMatching.map_ofLE", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Matching", "is_tactic_proof": true, "tactics": ["intro", "obtain", "obtain", "use", "simpa"], "tactic_count": 5}
{"name": "SimpleGraph.Subgraph.IsMatching.eq_of_adj_left", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Matching", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.IsMatching.eq_of_adj_right", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Matching", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.IsMatching.not_adj_left_of_ne", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Matching", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.IsMatching.not_adj_right_of_ne", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Matching", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.IsMatching.sup", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Matching", "is_tactic_proof": true, "tactics": ["intro", "have", "obtain", "use", "refine", "intro", "cases", "inl", "inr", "rw", "simpa", "cases", "inl", "inr", "rw", "exact"], "tactic_count": 16}
{"name": "SimpleGraph.Subgraph.IsMatching.iSup", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Matching", "is_tactic_proof": true, "tactics": ["intro", "obtain", "obtain", "use", "refine", "intro", "obtain", "by_cases", "exact", "have", "simp", "simpa"], "tactic_count": 12}
{"name": "SimpleGraph.Subgraph.IsMatching.subgraphOfAdj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Matching", "is_tactic_proof": true, "tactics": ["intro", "rw", "cases", "inl", "inr"], "tactic_count": 5}
{"name": "SimpleGraph.Subgraph.IsMatching.coeSubgraph", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Matching", "is_tactic_proof": true, "tactics": ["intro", "obtain", "use", "refine", "obtain", "simp", "exact", "obtain", "rw"], "tactic_count": 9}
{"name": "SimpleGraph.Subgraph.IsMatching.exists_of_disjoint_sets_of_equiv", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Matching", "is_tactic_proof": false, "tactics": ["use", "verts", "adj_sub", "intro", "obtain", "exact", "exact", "edge_vert", "simp", "intro", "rcases", "use", "simp", "rintro", "rfl", "exact", "use", "simp", "rintro", "exact", "simp"], "tactic_count": 21}
{"name": "SimpleGraph.Subgraph.IsMatching.map", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Matching", "is_tactic_proof": true, "tactics": ["rintro", "obtain", "use", "refine", "rintro", "cases", "rw"], "tactic_count": 7}
{"name": "SimpleGraph.Subgraph.Iso.isMatching_map", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Matching", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.IsPerfectMatching", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Matching", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.IsMatching.support_eq_verts", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Matching", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.Subgraph.isMatching_iff_forall_degree", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Matching", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Subgraph.IsMatching.even_card", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Matching", "is_tactic_proof": true, "tactics": ["classical", "rw", "use", "rw", "simp"], "tactic_count": 5}
{"name": "SimpleGraph.Subgraph.isPerfectMatching_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Matching", "is_tactic_proof": true, "tactics": ["refine", "rintro", "exact", "obtain", "exact"], "tactic_count": 5}
{"name": "SimpleGraph.Subgraph.isPerfectMatching_iff_forall_degree", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Matching", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Subgraph.IsPerfectMatching.even_card", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Matching", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "SimpleGraph.Subgraph.IsMatching.induce_connectedComponent", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Matching", "is_tactic_proof": true, "tactics": ["intro", "obtain", "obtain", "use", "simpa"], "tactic_count": 5}
{"name": "SimpleGraph.Subgraph.IsPerfectMatching.induce_connectedComponent_isMatching", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Matching", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "SimpleGraph.Subgraph.IsPerfectMatching.toSubgraph_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Matching", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.IsClique.even_iff_exists_isMatching", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Matching", "is_tactic_proof": false, "tactics": ["refine", "rintro", "simpa", "obtain", "obtain", "rw", "exact", "exact", "hc"], "tactic_count": 9}
{"name": "SimpleGraph.ConnectedComponent.even_card_of_isPerfectMatching", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Matching", "is_tactic_proof": false, "tactics": ["some", "blocked", "using", "letI", "simpa"], "tactic_count": 5}
{"name": "SimpleGraph.ConnectedComponent.odd_matches_node_outside", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Matching", "is_tactic_proof": true, "tactics": ["by_contra", "have", "intro", "obtain", "obtain", "use", "have", "refine", "apply", "simp", "hwnu,", "trivial", "apply", "haveI", "classical", "haveI", "simpa"], "tactic_count": 17}
{"name": "SimpleGraph.IsMatchingFree", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Matching", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsMatchingFree.mono", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Matching", "is_tactic_proof": true, "tactics": ["intro", "by_contra", "apply", "refine", "intro", "simp", "exact"], "tactic_count": 7}
{"name": "SimpleGraph.exists_maximal_isMatchingFree", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Matching", "is_tactic_proof": true, "tactics": ["simp_rw", "obtain", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.IsCycles", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Matching", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsCycles.other_adj_of_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Matching", "is_tactic_proof": true, "tactics": ["simp_rw", "have", "obtain", "exact"], "tactic_count": 4}
{"name": "SimpleGraph.IsCycles.existsUnique_ne_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Matching", "is_tactic_proof": true, "tactics": ["obtain", "use", "refine", "intro", "obtain", "simp_rw", "aesop"], "tactic_count": 7}
{"name": "SimpleGraph.IsCycles.toSimpleGraph", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Matching", "is_tactic_proof": true, "tactics": ["intro", "rw", "rw", "congr", "ext", "simp"], "tactic_count": 6}
{"name": "SimpleGraph.Walk.IsCycle.isCycles_spanningCoe_toSubgraph", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Matching", "is_tactic_proof": true, "tactics": ["intro", "apply", "obtain", "exact"], "tactic_count": 4}
{"name": "SimpleGraph.Walk.IsPath.isCycles_spanningCoe_toSubgraph_sup_edge", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Matching", "is_tactic_proof": true, "tactics": ["let", "have", "ext", "simp", "subgraphOfAdj_adj,", "aesop", "exact"], "tactic_count": 7}
{"name": "SimpleGraph.Walk.IsCycle.adj_toSubgraph_iff_of_isCycles", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Matching", "is_tactic_proof": true, "tactics": ["refine", "have", "rw", "hcyc", "this]"], "tactic_count": 5}
{"name": "SimpleGraph.Subgraph.IsPerfectMatching.symmDiff_isCycles", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Matching", "is_tactic_proof": true, "tactics": ["intro", "obtain", "obtain", "simp", "not_or,", "by_cases", "simp_all", "right", "use", "aesop"], "tactic_count": 10}
{"name": "SimpleGraph.IsCycles.snd_of_mem_support_of_isPath_of_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Matching", "is_tactic_proof": true, "tactics": ["classical", "apply", "rw", "obtain", "by_cases", "aesop", "have", "refine", "rw", "hp.ncard_neighborSet_toSubgraph_internal_eq_two", "rw", "exact"], "tactic_count": 12}
{"name": "_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.IsCycles.reachable_sdiff_toSubgraph_spanningCoe_aux", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Matching", "is_tactic_proof": true, "tactics": ["classical", "by_cases", "subst", "use", "have", "obtain", "have", "intro", "exact", "hw'1", "by_cases", "subst", "have", "simp", "exact", "exact", "have", "apply", "simp", "have", "rw", "refine", "exact", "have", "simp", "refine", "exact", "use", "termination_by", "decreasing_by", "have", "simp_wf", "have", "lia"], "tactic_count": 34}
{"name": "SimpleGraph.IsCycles.reachable_sdiff_toSubgraph_spanningCoe", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Matching", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.IsCycles.reachable_deleteEdges", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Matching", "is_tactic_proof": false, "tactics": ["have", "simp", "exact", "rw", "exact"], "tactic_count": 5}
{"name": "SimpleGraph.IsCycles.exists_cycle_toSubgraph_verts_eq_connectedComponentSupp", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Matching", "is_tactic_proof": true, "tactics": ["classical", "obtain", "obtain", "have", "have", "obtain", "p.toSubgraph_connected.exists_verts_eq_connectedComponentSupp", "intro", "refine", "have", "rw", "refine", "rw", "lia", "refine", "rw", "hp.1.ncard_neighborSet_toSubgraph_eq_two", "rw", "have", "rw", "exact", "simp_all", "use", "rw", "exact"], "tactic_count": 25}
{"name": "SimpleGraph.IsAlternating", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Matching", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsAlternating.mono", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Matching", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsAlternating.spanningCoe", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Matching", "is_tactic_proof": true, "tactics": ["intro", "simp", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.IsAlternating.sup_edge", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Matching", "is_tactic_proof": true, "tactics": ["by_cases", "rwa", "intro", "simp", "obtain", "exact", "rw", "simp", "rcases", "subst", "exact", "simp_all", "rw", "simp", "rcases", "subst", "exact", "aesop", "aesop"], "tactic_count": 19}
{"name": "SimpleGraph.Subgraph.IsPerfectMatching.symmDiff_of_isAlternating", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Matching", "is_tactic_proof": true, "tactics": ["rw", "intro", "simp", "obtain", "by_cases", "obtain", "have", "use", "simp", "not_true_eq_false,", "rintro", "aesop", "obtain", "by_contra", "simp_all", "use", "simp", "and_self,", "rintro", "exact", "have", "simp_all"], "tactic_count": 22}
{"name": "SimpleGraph.Subgraph.IsPerfectMatching.isAlternating_symmDiff_left", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Matching", "is_tactic_proof": true, "tactics": ["intro", "obtain", "obtain", "simp", "aesop"], "tactic_count": 5}
{"name": "SimpleGraph.Subgraph.IsPerfectMatching.isAlternating_symmDiff_right", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Matching", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "SimpleGraph.edist", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.edist_eq_sInf", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Reachable.exists_walk_length_eq_edist", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Connected.exists_walk_length_eq_edist", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.edist_le", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.edist_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Metric", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "SimpleGraph.edist_self", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.edist_pos_of_ne", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.edist_eq_top_of_not_reachable", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Metric", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.reachable_of_edist_ne_top", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.exists_walk_of_edist_ne_top", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.edist_triangle", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Metric", "is_tactic_proof": true, "tactics": ["cases", "inl", "inr", "cases", "inl", "inr", "obtain", "obtain", "rw", "exact"], "tactic_count": 10}
{"name": "SimpleGraph.edist_comm", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Metric", "is_tactic_proof": false, "tactics": ["rw", "simp_rw"], "tactic_count": 2}
{"name": "SimpleGraph.exists_walk_of_edist_eq_coe", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.edist_ne_top_iff_reachable", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Metric", "is_tactic_proof": true, "tactics": ["refine", "by_contra", "simp", "exact"], "tactic_count": 4}
{"name": "SimpleGraph.edist_eq_one_iff_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Metric", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact", "exact"], "tactic_count": 4}
{"name": "SimpleGraph.edist_le_one_iff_adj_or_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Metric", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "simp", "have", "rw", "exact"], "tactic_count": 6}
{"name": "SimpleGraph.edist_bot_of_ne", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Metric", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "SimpleGraph.edist_bot", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Metric", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "SimpleGraph.edist_top_of_ne", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Metric", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.edist_top", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Metric", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "SimpleGraph.edist_anti", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Metric", "is_tactic_proof": true, "tactics": ["by_cases", "obtain", "rw", "apply", "exact"], "tactic_count": 5}
{"name": "SimpleGraph.dist", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.dist_eq_sInf", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Reachable.coe_dist_eq_edist", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Reachable.exists_walk_length_eq_dist", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Connected.exists_walk_length_eq_dist", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.dist_le", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.dist_eq_zero_iff_eq_or_not_reachable", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Metric", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.dist_self", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Metric", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Reachable.dist_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Metric", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Reachable.pos_dist_of_ne", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Reachable.one_lt_dist_of_ne_of_not_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Connected.dist_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Metric", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Connected.pos_dist_of_ne", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Connected.one_lt_dist_of_ne_of_not_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.dist_eq_zero_of_not_reachable", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Metric", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.nonempty_of_pos_dist", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Metric", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "SimpleGraph.Connected.dist_triangle", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Metric", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "rw", "apply"], "tactic_count": 4}
{"name": "SimpleGraph.Reachable.dist_triangle_left", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Metric", "is_tactic_proof": true, "tactics": ["by_cases", "grind", "rw", "grind"], "tactic_count": 4}
{"name": "SimpleGraph.Reachable.dist_triangle_right", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Metric", "is_tactic_proof": true, "tactics": ["by_cases", "grind", "rw", "grind"], "tactic_count": 4}
{"name": "SimpleGraph.dist_comm", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Metric", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.dist_ne_zero_iff_ne_and_reachable", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Metric", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Reachable.of_dist_ne_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.exists_walk_of_dist_ne_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.dist_eq_one_iff_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Metric", "is_tactic_proof": true, "tactics": ["rw", "decide"], "tactic_count": 2}
{"name": "SimpleGraph.Adj.diff_dist_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Metric", "is_tactic_proof": true, "tactics": ["by_cases", "grind", "have", "have", "have", "have", "lia"], "tactic_count": 7}
{"name": "SimpleGraph.Connected.diff_dist_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Metric", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.isPath_of_length_eq_dist", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Metric", "is_tactic_proof": true, "tactics": ["classical", "have", "apply", "calc", "p.length", "rw", "apply"], "tactic_count": 7}
{"name": "SimpleGraph.Reachable.exists_path_of_dist", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Metric", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.Connected.exists_path_of_dist", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Metric", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.dist_bot", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Metric", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "SimpleGraph.dist_top_of_ne", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Metric", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.dist_top", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Metric", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "SimpleGraph.length_eq_dist_of_subwalk", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Metric", "is_tactic_proof": true, "tactics": ["refine", "obtain", "obtain", "let", "have", "have", "have", "lia"], "tactic_count": 8}
{"name": "SimpleGraph.Reachable.dist_anti", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Metric", "is_tactic_proof": true, "tactics": ["obtain", "rw", "apply"], "tactic_count": 3}
{"name": "SimpleGraph.Walk.exists_adj_adj_not_adj_ne", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Metric", "is_tactic_proof": true, "tactics": ["use", "have", "have", "rw", "p.tail.length_tail_add_one", "simp", "lia)]", "lia", "have", "by_cases", "have", "lia", "by_cases", "have", "lia", "exact"], "tactic_count": 16}
{"name": "SimpleGraph.replaceVertex", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.not_adj_replaceVertex_same", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.replaceVertex_self", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Operations", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "SimpleGraph.adj_replaceVertex_iff_of_ne_left", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.adj_replaceVertex_iff_of_ne_right", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.adj_replaceVertex_iff_of_ne", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.edgeSet_replaceVertex_of_not_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Operations", "is_tactic_proof": true, "tactics": ["ext", "simp", "intros"], "tactic_count": 3}
{"name": "SimpleGraph.edgeSet_replaceVertex_of_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Operations", "is_tactic_proof": true, "tactics": ["ext", "simp", "intros"], "tactic_count": 3}
{"name": "SimpleGraph.instDecidableRelAdjReplaceVertex", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Operations", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "SimpleGraph.edgeFinset_replaceVertex_of_not_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Operations", "is_tactic_proof": true, "tactics": ["apply", "push_cast", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.edgeFinset_replaceVertex_of_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Operations", "is_tactic_proof": true, "tactics": ["apply", "push_cast", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.disjoint_sdiff_neighborFinset_image", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Operations", "is_tactic_proof": true, "tactics": ["rw", "intro", "have", "rw", "obtain", "contrapose", "simp_all", "aesop"], "tactic_count": 8}
{"name": "SimpleGraph.card_edgeFinset_replaceVertex_of_not_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Operations", "is_tactic_proof": true, "tactics": ["have", "rw", "card_sdiff_of_subset", "congr", "rw", "unfold", "aesop"], "tactic_count": 7}
{"name": "SimpleGraph.card_edgeFinset_replaceVertex_of_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Operations", "is_tactic_proof": true, "tactics": ["have", "rw", "card_union_of_disjoint", "congr", "rw", "unfold", "aesop"], "tactic_count": 7}
{"name": "SimpleGraph.edge", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.edge_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.adj_edge", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Operations", "is_tactic_proof": true, "tactics": ["simp", "tauto"], "tactic_count": 2}
{"name": "SimpleGraph.edge_comm", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.instDecidableRelAdjEdge", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.edge_self_eq_bot", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Operations", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "SimpleGraph.sup_edge_self", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.lt_sup_edge", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.edge_le_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Operations", "is_tactic_proof": true, "tactics": ["obtain", "simp", "refine", "aesop"], "tactic_count": 4}
{"name": "SimpleGraph.edge_edgeSet_of_ne", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Operations", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "SimpleGraph.sup_edge_of_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Operations", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "SimpleGraph.disjoint_edge", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Operations", "is_tactic_proof": true, "tactics": ["by_cases", "subst", "simp", "simp"], "tactic_count": 4}
{"name": "SimpleGraph.sdiff_edge", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Subgraph.spanningCoe_sup_edge_le", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Operations", "is_tactic_proof": true, "tactics": ["intro", "have", "simp", "by_cases", "exact", "aesop"], "tactic_count": 6}
{"name": "SimpleGraph.instFintypeElemSym2EdgeSetEdge", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.edgeFinset_sup_edge", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Operations", "is_tactic_proof": true, "tactics": ["letI", "rw", "simp_rw"], "tactic_count": 3}
{"name": "SimpleGraph.card_edgeFinset_sup_edge", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.Partition.PartsCardLe", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Partition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Partitionable", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Partition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Partition.partOfVertex", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Partition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Partition.partOfVertex_mem", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Partition", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.Partition.mem_partOfVertex", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Partition", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.Partition.partOfVertex_ne_of_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Partition", "is_tactic_proof": true, "tactics": ["intro", "have", "rw", "exact"], "tactic_count": 4}
{"name": "SimpleGraph.Partition.toColoring", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Partition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Partition.toColoring'", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Partition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Partition.colorable", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Partition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Coloring.toPartition", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Partition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Partition.instInhabited", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Partition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.partitionable_iff_colorable", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Partition", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "have", "rw", "apply", "rintro", "refine", "generalize_proofs", "change", "have", "rw", "exact"], "tactic_count": 12}
{"name": "SimpleGraph.Walk.isTrail_copy", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["subst_vars", "rfl"], "tactic_count": 2}
{"name": "SimpleGraph.Walk.IsPath.mk'", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.isPath_def", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.isPath_iff_injective_get_support", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.isPath_copy", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["subst_vars", "rfl"], "tactic_count": 2}
{"name": "SimpleGraph.Walk.isCircuit_copy", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["subst_vars", "rfl"], "tactic_count": 2}
{"name": "SimpleGraph.Walk.IsCircuit.not_nil", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.isCycle_def", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.isCycle_copy", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["subst_vars", "rfl"], "tactic_count": 2}
{"name": "SimpleGraph.Walk.IsCycle.not_nil", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.IsTrail.nil", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.IsTrail.of_cons", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.isTrail_cons", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.IsTrail.cons", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.IsTrail.reverse", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.reverse_isTrail_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["constructor", "intro", "convert", "try"], "tactic_count": 4}
{"name": "SimpleGraph.Walk.IsTrail.of_append_left", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.Walk.IsTrail.of_append_right", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.Walk.IsTrail.count_edges_le_one", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.IsTrail.count_edges_eq_one", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.IsTrail.length_le_card_edgeFinset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["classical", "let", "have", "rw", "have", "intro", "refine", "apply", "simpa", "exact"], "tactic_count": 10}
{"name": "SimpleGraph.Walk.IsPath.nil", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["constructor"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.IsPath.of_cons", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.cons_isPath_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["constructor"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.IsPath.cons", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.isPath_iff_eq_nil", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.IsPath.reverse", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.isPath_reverse_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["constructor"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.IsPath.of_append_left", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.Walk.IsPath.of_append_right", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["rw", "rw", "apply"], "tactic_count": 3}
{"name": "SimpleGraph.Walk.isTrail_of_isSubwalk", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.Walk.isPath_of_isSubwalk", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.Walk.IsPath.of_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.concat_isPath_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": false, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.Walk.IsPath.concat", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.IsPath.mem_support_iff_exists_append", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["refine", "obtain", "have", "exact"], "tactic_count": 4}
{"name": "SimpleGraph.Walk.IsPath.disjoint_support_of_append", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["have", "rw", "rw", "exact"], "tactic_count": 4}
{"name": "SimpleGraph.Walk.IsPath.ne_of_mem_support_of_append", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["rintro", "have", "intro", "simp", "have", "rw", "rw", "exact", "exact"], "tactic_count": 9}
{"name": "SimpleGraph.Walk.IsCycle.not_of_nil", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.IsCycle.ne_bot", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.IsCycle.three_le_length", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["have"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.not_nil_of_isCycle_cons", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["have", "rw", "lia"], "tactic_count": 3}
{"name": "SimpleGraph.Walk.cons_isCycle_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": false, "tactics": ["simp", "have", "tauto"], "tactic_count": 3}
{"name": "SimpleGraph.Walk.IsCycle.reverse", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.Walk.isCycle_reverse", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.IsCycle.isPath_of_append_right", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["have", "rw", "rw", "exact"], "tactic_count": 4}
{"name": "SimpleGraph.Walk.IsCycle.isPath_of_append_left", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.IsPath.tail", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["cases", "nil", "cons"], "tactic_count": 3}
{"name": "SimpleGraph.Walk.exists_isTrail_forall_isTrail_length_le_length", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["have", "let", "have", "obtain", "obtain", "refine", "have", "lia"], "tactic_count": 8}
{"name": "SimpleGraph.Walk.exists_isPath_forall_isPath_length_le_length", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["have", "let", "have", "hn", "obtain", "obtain", "refine", "have", "lia"], "tactic_count": 9}
{"name": "SimpleGraph.Walk.instDecidableIsPathOfDecidableEq", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "SimpleGraph.Walk.IsPath.length_lt", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.Walk.IsPath.getVert_injOn", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["intro", "induction", "nil", "simp", "by_cases", "lia", "simp", "have", "exact", "simp", "have", "exact", "simp", "have", "lia"], "tactic_count": 15}
{"name": "SimpleGraph.Walk.IsPath.getVert_eq_start_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["refine", "intro", "by_cases", "exact", "apply", "simp"], "tactic_count": 6}
{"name": "SimpleGraph.Walk.IsPath.getVert_eq_end_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["have", "simp", "rw", "lia"], "tactic_count": 4}
{"name": "SimpleGraph.Walk.IsPath.getVert_injOn_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["refine", "induction", "nil", "cons", "intro", "rw", "refine", "intro", "simp", "have", "hinj", "lia),", "obtain", "have", "hinj", "lia"], "tactic_count": 16}
{"name": "SimpleGraph.Walk.IsPath.eq_snd_of_mem_edges", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["have", "rw", "have", "grind"], "tactic_count": 4}
{"name": "SimpleGraph.Walk.IsPath.eq_penultimate_of_mem_edges", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.IsCycle.getVert_injOn", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "have", "lia"], "tactic_count": 5}
{"name": "SimpleGraph.Walk.IsCycle.getVert_injOn'", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["intro", "simp", "have", "have", "hpc.reverse.getVert_injOn", "simp", "show", "lia"], "tactic_count": 8}
{"name": "SimpleGraph.Walk.IsCycle.snd_ne_penultimate", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["intro", "have", "apply", "lia"], "tactic_count": 4}
{"name": "SimpleGraph.Walk.IsCycle.getVert_endpoint_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["refine", "rw", "intro", "exact", "hpc.getVert_injOn"], "tactic_count": 5}
{"name": "SimpleGraph.Walk.IsCycle.getVert_sub_one_ne_getVert_add_one", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["intro", "have", "by_cases", "rw", "lia", "have", "hpc.getVert_injOn", "lia"], "tactic_count": 8}
{"name": "SimpleGraph.Walk.IsTrail.takeUntil", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.IsTrail.dropUntil", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.IsPath.takeUntil", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.IsPath.dropUntil", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.IsTrail.disjoint_edges_takeUntil_dropUntil", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.IsTrail.rotate", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.Walk.IsCircuit.rotate", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["refine", "cases", "exact", "intro", "have", "rw", "simp"], "tactic_count": 7}
{"name": "SimpleGraph.Walk.IsCycle.rotate", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.Walk.IsCycle.isPath_takeUntil", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["by_cases", "subst", "simp", "rw", "exact"], "tactic_count": 5}
{"name": "SimpleGraph.Walk.IsCycle.count_support", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["have", "have", "grind"], "tactic_count": 3}
{"name": "SimpleGraph.Walk.IsCycle.count_support_of_mem", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["have", "have", "have", "grind"], "tactic_count": 4}
{"name": "SimpleGraph.Walk.endpoint_notMem_support_takeUntil", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["intro", "rw", "obtain", "rw", "have", "have", "lia"], "tactic_count": 7}
{"name": "SimpleGraph.Path", "kind": "abbrev", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Path.isPath", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Path.isTrail", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Path.nil", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Path.singleton", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Path.mk'_mem_edges_singleton", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Path.reverse", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Path.count_support_eq_one", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Path.count_edges_eq_one", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Path.nodup_support", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Path.loop_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["obtain", "rfl", "simp"], "tactic_count": 3}
{"name": "SimpleGraph.Path.notMem_edges_of_loop", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Path.cons_isCycle", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.bypass", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.bypass_copy", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["subst_vars", "rfl"], "tactic_count": 2}
{"name": "SimpleGraph.Walk.bypass_isPath", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "simp", "split_ifs", "exact", "simp"], "tactic_count": 7}
{"name": "SimpleGraph.Walk.length_bypass_le", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "simp", "split_ifs", "trans", "apply", "rw", "lia", "rw", "exact"], "tactic_count": 11}
{"name": "SimpleGraph.Walk.bypass_eq_self_of_length_le", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "simp", "split_ifs", "exfalso", "simp", "apply", "calc", "p.length", "simp", "rw"], "tactic_count": 12}
{"name": "SimpleGraph.Walk.toPath", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.support_bypass_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "simp", "split_ifs", "apply", "apply", "assumption", "rw", "apply", "assumption"], "tactic_count": 11}
{"name": "SimpleGraph.Walk.support_toPath_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.darts_bypass_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "simp", "split_ifs", "apply", "apply", "rw", "exact"], "tactic_count": 9}
{"name": "SimpleGraph.Walk.edges_bypass_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.darts_toPath_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.edges_toPath_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.cycleBypass", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.cycleBypass_nil", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.edges_cycleBypass_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.IsTrail.isCycle_cycleBypass", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.map_isPath_of_injective", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "rw", "simp", "intro", "cases", "exact"], "tactic_count": 8}
{"name": "SimpleGraph.Walk.IsPath.of_map", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "SimpleGraph.Walk.map_isPath_iff_of_injective", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.map_isTrail_iff_of_injective", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "rw", "apply", "rw"], "tactic_count": 6}
{"name": "SimpleGraph.Walk.map_isCycle_iff_of_injective", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.mapLe_isTrail", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.mapLe_isPath", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.mapLe_isCycle", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Path.map", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Path.map_injective", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["rintro", "simp", "simp"], "tactic_count": 3}
{"name": "SimpleGraph.Path.mapEmbedding", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Path.mapEmbedding_injective", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.IsPath.transfer", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "simp", "exact"], "tactic_count": 5}
{"name": "SimpleGraph.Walk.IsCycle.transfer", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["cases", "nil", "cons", "simp", "simp", "exact"], "tactic_count": 6}
{"name": "SimpleGraph.Walk.IsPath.toDeleteEdges", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.IsCycle.toDeleteEdges", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.toDeleteEdges_copy", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Paths", "is_tactic_proof": true, "tactics": ["subst_vars", "rfl"], "tactic_count": 2}
{"name": "SimpleGraph.boxProd", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.term_□_", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph._aux_Mathlib_Combinatorics_SimpleGraph_Prod___macroRules_SimpleGraph_term_□__1", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph._aux_Mathlib_Combinatorics_SimpleGraph_Prod___unexpand_SimpleGraph_boxProd_1", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.boxProd_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.boxProd_adj_left", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.boxProd_adj_right", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.neighborSet_boxProd", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Prod", "is_tactic_proof": true, "tactics": ["ext", "simp", "simp"], "tactic_count": 3}
{"name": "SimpleGraph.boxProdComm", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.boxProdAssoc", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.boxProdLeft", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.boxProdRight", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Iso.boxProdSumDistrib", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Iso.sumBoxProdDistrib", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.boxProdLeft", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.boxProdRight", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.ofBoxProdLeft", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.ofBoxProdRight", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.ofBoxProdLeft_boxProdLeft", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.ofBoxProdRight_boxProdRight", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.length_boxProd", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Prod", "is_tactic_proof": true, "tactics": ["unfold", "rw", "have", "rcases", "simp", "rw", "congr", "simp", "congr"], "tactic_count": 9}
{"name": "SimpleGraph.Preconnected.boxProd", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Prod", "is_tactic_proof": true, "tactics": ["rintro", "obtain", "obtain", "exact"], "tactic_count": 4}
{"name": "SimpleGraph.Preconnected.ofBoxProdLeft", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Prod", "is_tactic_proof": true, "tactics": ["classical", "rintro", "obtain", "exact"], "tactic_count": 4}
{"name": "SimpleGraph.Preconnected.ofBoxProdRight", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Prod", "is_tactic_proof": true, "tactics": ["classical", "rintro", "obtain", "exact"], "tactic_count": 4}
{"name": "SimpleGraph.Connected.boxProd", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Prod", "is_tactic_proof": true, "tactics": ["haveI", "haveI", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.Connected.ofBoxProdLeft", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Prod", "is_tactic_proof": true, "tactics": ["haveI", "haveI", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.Connected.ofBoxProdRight", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Prod", "is_tactic_proof": true, "tactics": ["haveI", "haveI", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.connected_boxProd", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.boxProdFintypeNeighborSet", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.neighborFinset_boxProd", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Prod", "is_tactic_proof": true, "tactics": ["letI", "convert_to", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.degree_boxProd", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Prod", "is_tactic_proof": true, "tactics": ["rw", "simp_rw"], "tactic_count": 2}
{"name": "SimpleGraph.reachable_boxProd", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Prod", "is_tactic_proof": true, "tactics": ["classical", "constructor", "intro", "exact", "intro", "exact"], "tactic_count": 6}
{"name": "SimpleGraph.edist_boxProd", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Prod", "is_tactic_proof": true, "tactics": ["classical", "have", "simp_rw", "by_cases", "rw", "aesop", "have", "have", "have", "let", "have", "refine", "calc", "have", "rw", "exact"], "tactic_count": 16}
{"name": "SzemerediRegularity.stepBound", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Bound", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SzemerediRegularity.le_stepBound", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Bound", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SzemerediRegularity.stepBound_mono", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Bound", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SzemerediRegularity.stepBound_pos_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Bound", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SzemerediRegularity.coe_stepBound", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Bound", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Bound.0.termM", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Bound", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Bound.0._aux_Mathlib_Combinatorics_SimpleGraph_Regularity_Bound___macroRules__private_Mathlib_Combinatorics_SimpleGraph_Regularity_Bound_0_termM_1", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Bound", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Bound.0._aux_Mathlib_Combinatorics_SimpleGraph_Regularity_Bound___delab_app__private_Mathlib_Combinatorics_SimpleGraph_Regularity_Bound_0_termM_1", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Bound", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Bound.0.termA", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Bound", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Bound.0._aux_Mathlib_Combinatorics_SimpleGraph_Regularity_Bound___macroRules__private_Mathlib_Combinatorics_SimpleGraph_Regularity_Bound_0_termA_1", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Bound", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Bound.0._aux_Mathlib_Combinatorics_SimpleGraph_Regularity_Bound___delab_app__private_Mathlib_Combinatorics_SimpleGraph_Regularity_Bound_0_termA_1", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Bound", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Bound.0.SzemerediRegularity.Positivity.eps_pos", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Bound", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Bound.0.SzemerediRegularity.Positivity.m_pos", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Bound", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SzemerediRegularity.Positivity.tacticSz_positivity", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Bound", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SzemerediRegularity.Positivity._aux_Mathlib_Combinatorics_SimpleGraph_Regularity_Bound___macroRules_SzemerediRegularity_Positivity_tacticSz_positivity_1", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Bound", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SzemerediRegularity.m_pos", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Bound", "is_tactic_proof": true, "tactics": ["sz_positivity"], "tactic_count": 1}
{"name": "SzemerediRegularity.coe_m_add_one_pos", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Bound", "is_tactic_proof": true, "tactics": ["positivity"], "tactic_count": 1}
{"name": "SzemerediRegularity.one_le_m_coe", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Bound", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SzemerediRegularity.eps_pow_five_pos", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Bound", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SzemerediRegularity.eps_pos", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Bound", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SzemerediRegularity.hundred_div_ε_pow_five_le_m", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Bound", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SzemerediRegularity.hundred_le_m", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Bound", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SzemerediRegularity.a_add_one_le_four_pow_parts_card", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Bound", "is_tactic_proof": true, "tactics": ["have", "rw", "conv_rhs", "rw", "exact"], "tactic_count": 5}
{"name": "SzemerediRegularity.card_aux₁", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Bound", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SzemerediRegularity.card_aux₂", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Bound", "is_tactic_proof": false, "tactics": ["have", "rw", "exact", "rw", "rw"], "tactic_count": 5}
{"name": "SzemerediRegularity.pow_mul_m_le_card_part", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Bound", "is_tactic_proof": true, "tactics": ["norm_cast", "rw", "exact"], "tactic_count": 3}
{"name": "SzemerediRegularity.initialBound", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Bound", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SzemerediRegularity.le_initialBound", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Bound", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SzemerediRegularity.seven_le_initialBound", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Bound", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SzemerediRegularity.initialBound_pos", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Bound", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SzemerediRegularity.hundred_lt_pow_initialBound_mul", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Bound", "is_tactic_proof": false, "tactics": ["rw", "push_cast", "exact", "exact", "exact"], "tactic_count": 5}
{"name": "SzemerediRegularity.bound", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Bound", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SzemerediRegularity.initialBound_le_bound", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Bound", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SzemerediRegularity.le_bound", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Bound", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SzemerediRegularity.bound_pos", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Bound", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SzemerediRegularity.mul_sq_le_sum_sq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Bound", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SzemerediRegularity.add_div_le_sum_sq_div_card", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Bound", "is_tactic_proof": true, "tactics": ["obtain", "simpa", "have", "have", "have", "apply", "rw", "grw", "rw", "have", "grw", "simp", "div_le_iff₀", "nsmul_eq_mul,", "ring_nf", "rfl"], "tactic_count": 16}
{"name": "Mathlib.Meta.Positivity.evalInitialBound", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Bound", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity._example", "kind": "example", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Bound", "is_tactic_proof": true, "tactics": ["positivity"], "tactic_count": 1}
{"name": "Mathlib.Meta.Positivity.evalBound", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Bound", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity._example", "kind": "example", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Bound", "is_tactic_proof": true, "tactics": ["positivity"], "tactic_count": 1}
{"name": "_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.termM", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SzemerediRegularity.chunk", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SzemerediRegularity.star", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SzemerediRegularity.biUnion_star_subset_nonuniformWitness", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SzemerediRegularity.star_subset_chunk", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.card_nonuniformWitness_sdiff_biUnion_star", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk", "is_tactic_proof": false, "tactics": ["have", "nonuniformWitness_mem_nonuniformWitnesses", "have", "intro", "rw", "simp", "obtain", "exact", "apply", "trans", "suffices", "intro", "unfold", "split_ifs", "convert", "convert", "grw", "filter_subset]", "simp"], "tactic_count": 19}
{"name": "_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.one_sub_eps_mul_card_nonuniformWitness_le_card_star", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "swap", "sz_positivity", "refine", "calc", "rw", "refine", "rw", "calc", "gcongr", "exact", "calc", "rw", "refine", "have", "rw", "rw", "gcongr", "exact", "have", "sz_positivity", "rw", "card_sdiff_of_subset", "exact"], "tactic_count": 26}
{"name": "SzemerediRegularity.card_chunk", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk", "is_tactic_proof": true, "tactics": ["unfold", "split_ifs", "rw", "exact", "rw"], "tactic_count": 5}
{"name": "SzemerediRegularity.card_eq_of_mem_parts_chunk", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk", "is_tactic_proof": true, "tactics": ["unfold", "split_ifs"], "tactic_count": 2}
{"name": "SzemerediRegularity.m_le_card_of_mem_chunk_parts", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SzemerediRegularity.card_le_m_add_one_of_mem_chunk_parts", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SzemerediRegularity.card_biUnion_star_le_m_add_one_card_star_mul", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.le_sum_card_subset_chunk_parts", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk", "is_tactic_proof": true, "tactics": ["rw", "gcongr", "rw", "exact", "exact"], "tactic_count": 5}
{"name": "_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.sum_card_subset_chunk_parts_le", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk", "is_tactic_proof": true, "tactics": ["rw", "gcongr", "norm_cast", "refine", "apply", "exact"], "tactic_count": 6}
{"name": "_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.one_sub_le_m_div_m_add_one_sq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk", "is_tactic_proof": true, "tactics": ["have", "rw", "refine", "rw", "one_div_div]", "refine", "norm_num", "apply", "sz_positivity"], "tactic_count": 9}
{"name": "_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.m_add_one_div_m_le_one_add", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk", "is_tactic_proof": true, "tactics": ["have", "rw", "calc", "gcongr", "rw", "exact"], "tactic_count": 6}
{"name": "_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.density_sub_eps_le_sum_density_div_card", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk", "is_tactic_proof": false, "tactics": ["have", "rw", "refine", "exact", "refine", "conv_rhs", "simp", "conv_lhs", "rw", "simp", "push_cast", "apply", "simp", "rintro", "rw", "refine", "rw", "refine", "refine", "exact", "rw", "gcongr", "apply", "apply", "refine", "exacts"], "tactic_count": 26}
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{"name": "_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.average_density_near_total_density", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk", "is_tactic_proof": true, "tactics": ["rw", "constructor", "rw", "exact", "suffices", "ε", "apply", "gcongr", "rw", "apply"], "tactic_count": 10}
{"name": "_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.edgeDensity_chunk_aux", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk", "is_tactic_proof": true, "tactics": ["obtain", "refine", "exact", "exact", "exact", "rw", "have", "calc", "exact", "gcongr", "have", "have", "refine", "rw", "rw", "norm_cast"], "tactic_count": 16}
{"name": "_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.abs_density_star_sub_density_le_eps", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk", "is_tactic_proof": false, "tactics": ["convert", "abs_edgeDensity_sub_edgeDensity_le_two_mul", "linarith"], "tactic_count": 3}
{"name": "_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.eps_le_card_star_div", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk", "is_tactic_proof": true, "tactics": ["have", "have", "have", "calc", "gcongr", "exacts", "rw", "gcongr", "exact", "gcongr", "exact", "gcongr", "sz_positivity", "exact", "rw", "refine", "have", "rw", "linarith"], "tactic_count": 19}
{"name": "_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.edgeDensity_star_not_uniform", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk", "is_tactic_proof": true, "tactics": ["rw", "set", "set", "set", "set", "set", "have", "have", "unfold", "exact", "have", "have", "have", "average_density_near_total_density", "simp_rw", "norm_num", "exact", "have", "rw", "rw", "cases", "left", "right"], "tactic_count": 23}
{"name": "SzemerediRegularity.edgeDensity_chunk_not_uniform", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SzemerediRegularity.edgeDensity_chunk_uniform", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk", "is_tactic_proof": true, "tactics": ["apply", "have", "rw", "norm_cast", "simp_rw", "convert"], "tactic_count": 6}
{"name": "Finpartition.energy", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Energy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.energy_nonneg", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Energy", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "Finpartition.energy_le_one", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Energy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.coe_energy", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Energy", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finpartition.equitabilise_aux", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Equitabilise", "is_tactic_proof": true, "tactics": ["obtain", "refine", "simp", "exact", "induction", "by_cases", "simp", "subst", "exact", "simp_rw", "set", "obtain", "n", "rw", "split_ifs", "refine", "rw", "refine", "rw", "which", "least", "of", "induction", "by_cases", "obtain", "have", "have", "rw", "obtain", "hcard", "refine", "simp", "exact", "exact", "simp_rw", "split_ifs", "rw", "rw", "exact", "intro", "obtain", "obtain", "have", "have", "rw", "obtain", "refine", "simp", "exact", "conv", "simp", "refine", "simp", "obtain", "rw", "exact", "refine", "simpa", "apply", "exact", "simp", "exact", "simp", "split_ifs", "rw", "rw", "intro"], "tactic_count": 67}
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{"name": "Finpartition.card_eq_of_mem_parts_equitabilise", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Equitabilise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.equitabilise_isEquipartition", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Equitabilise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.card_filter_equitabilise_big", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Equitabilise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.card_filter_equitabilise_small", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Equitabilise", "is_tactic_proof": true, "tactics": ["refine", "rw", "have", "rw", "exact", "nth_rw", "rw", "refine", "intro", "apply", "exact"], "tactic_count": 11}
{"name": "Finpartition.card_parts_equitabilise", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Equitabilise", "is_tactic_proof": false, "tactics": ["rw", "aesop"], "tactic_count": 2}
{"name": "Finpartition.card_parts_equitabilise_subset_le", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Equitabilise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.exists_equipartition_card_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Equitabilise", "is_tactic_proof": true, "tactics": ["rw", "have", "rw", "add_comm,", "refine", "rw"], "tactic_count": 6}
{"name": "_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.termM", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Increment", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0._aux_Mathlib_Combinatorics_SimpleGraph_Regularity_Increment___macroRules__private_Mathlib_Combinatorics_SimpleGraph_Regularity_Increment_0_termM_1", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Increment", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0._aux_Mathlib_Combinatorics_SimpleGraph_Regularity_Increment___delab_app__private_Mathlib_Combinatorics_SimpleGraph_Regularity_Increment_0_termM_1", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Increment", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SzemerediRegularity.increment", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Increment", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SzemerediRegularity.card_increment", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Increment", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "simp_rw", "rw", "any_goals", "rw", "congr", "rw"], "tactic_count": 9}
{"name": "SzemerediRegularity.increment_isEquipartition", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Increment", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "rw", "obtain", "exact"], "tactic_count": 5}
{"name": "_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.SzemerediRegularity.distinctPairs", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Increment", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.SzemerediRegularity.distinctPairs_increment", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Increment", "is_tactic_proof": true, "tactics": ["rintro", "simp", "true_and,", "refine", "rintro", "obtain", "exact"], "tactic_count": 7}
{"name": "_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.SzemerediRegularity.pairwiseDisjoint_distinctPairs", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Increment", "is_tactic_proof": false, "tactics": ["simp", "rintro", "rw", "obtain", "obtain", "exact", "hst"], "tactic_count": 7}
{"name": "SzemerediRegularity.le_sum_distinctPairs_edgeDensity_sq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Increment", "is_tactic_proof": true, "tactics": ["rw", "split_ifs", "rw", "exact", "exact"], "tactic_count": 5}
{"name": "SzemerediRegularity.energy_increment", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Increment", "is_tactic_proof": false, "tactics": ["calc", "rw", "norm_num", "rw", "gcongr", "rw", "exact", "gcongr", "rw", "calc", "rw", "nsmul_eq_mul,", "gcongr", "calc", "gcongr", "rw", "norm_cast", "rw", "refine", "nlinarith", "norm_num"], "tactic_count": 21}
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{"name": "SimpleGraph.IsUniform", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsUniform.instDecidableRel", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "SimpleGraph.IsUniform.mono", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SimpleGraph.isUniform_one", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform", "is_tactic_proof": true, "tactics": ["intro", "rw", "rw", "abs_zero]", "exact"], "tactic_count": 5}
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{"name": "SimpleGraph.isUniform_singleton", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform", "is_tactic_proof": true, "tactics": ["refine", "rw", "obtain", "replace", "exact", "obtain", "replace", "exact", "rwa"], "tactic_count": 9}
{"name": "SimpleGraph.not_isUniform_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.not_isUniform_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform", "is_tactic_proof": true, "tactics": ["unfold", "simp"], "tactic_count": 2}
{"name": "SimpleGraph.nonuniformWitnesses", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.left_nonuniformWitnesses_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.left_nonuniformWitnesses_card", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.right_nonuniformWitnesses_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.right_nonuniformWitnesses_card", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.nonuniformWitnesses_spec", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.nonuniformWitness", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.nonuniformWitness_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform", "is_tactic_proof": true, "tactics": ["unfold", "split_ifs", "exact", "exact"], "tactic_count": 4}
{"name": "SimpleGraph.le_card_nonuniformWitness", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform", "is_tactic_proof": true, "tactics": ["unfold", "split_ifs", "exact", "exact"], "tactic_count": 4}
{"name": "SimpleGraph.nonuniformWitness_spec", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform", "is_tactic_proof": true, "tactics": ["unfold", "rcases", "rw", "exact", "cases", "rw", "apply"], "tactic_count": 7}
{"name": "Finpartition.sparsePairs", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.mk_mem_sparsePairs", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finpartition.sparsePairs_mono", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.nonUniforms", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.mk_mem_nonUniforms", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finpartition.nonUniforms_mono", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.nonUniforms_bot", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform", "is_tactic_proof": true, "tactics": ["rw", "rintro", "simp", "rintro", "rwa"], "tactic_count": 5}
{"name": "Finpartition.IsUniform", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.bot_isUniform", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finpartition.isUniform_one", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw"], "tactic_count": 3}
{"name": "Finpartition.IsUniform.mono", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.isUniformOfEmpty", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finpartition.nonempty_of_not_uniform", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.nonuniformWitnesses", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.card_nonuniformWitnesses_le", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.nonuniformWitness_mem_nonuniformWitnesses", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.IsEquipartition.card_interedges_sparsePairs_le'", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform", "is_tactic_proof": false, "tactics": ["calc", "gcongr", "obtain", "simp", "refine", "exact", "mul_pos", "norm_cast", "gcongr", "calc", "simp", "rintro", "exact_mod_cast", "rw", "exact"], "tactic_count": 15}
{"name": "Finpartition.IsEquipartition.card_interedges_sparsePairs_le", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform", "is_tactic_proof": true, "tactics": ["calc"], "tactic_count": 1}
{"name": "_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform.0.Finpartition.aux", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform", "is_tactic_proof": true, "tactics": ["have", "apply", "rw", "gcongr", "apply"], "tactic_count": 5}
{"name": "Finpartition.IsEquipartition.card_biUnion_offDiag_le'", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform", "is_tactic_proof": true, "tactics": ["obtain", "simp", "calc", "mod_cast", "simpa", "suffices", "rwa", "have", "refine", "simp"], "tactic_count": 10}
{"name": "Finpartition.IsEquipartition.card_biUnion_offDiag_le", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform", "is_tactic_proof": true, "tactics": ["obtain", "simp", "apply", "rw", "have", "refine", "suffices", "rw", "convert", "rwa", "positivity"], "tactic_count": 11}
{"name": "Finpartition.IsEquipartition.sum_nonUniforms_lt'", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform", "is_tactic_proof": false, "tactics": ["calc", "simp", "rintro", "rw", "exact", "rw", "apply", "norm_cast", "exact"], "tactic_count": 9}
{"name": "Finpartition.IsEquipartition.sum_nonUniforms_lt", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform", "is_tactic_proof": true, "tactics": ["calc"], "tactic_count": 1}
{"name": "SimpleGraph.regularityReduced", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.regularityReduced.instDecidableRel_adj", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "SimpleGraph.regularityReduced_le", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.regularityReduced_mono", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.regularityReduced_anti", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.unreduced_edges_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform", "is_tactic_proof": true, "tactics": ["rintro", "simp", "mem_interedges_iff]", "intro", "replace", "obtain", "obtain", "obtain", "exact", "by_cases", "exact", "exact"], "tactic_count": 12}
{"name": "SimpleGraph.bot_strongly_regular", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.StronglyRegular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.conway_99", "kind": "proofWanted", "module": "Mathlib.Combinatorics.SimpleGraph.StronglyRegular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsSRGWith.top", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.StronglyRegular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsSRGWith.card_neighborFinset_union_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.StronglyRegular", "is_tactic_proof": true, "tactics": ["apply", "rw", "simp", "apply", "simp"], "tactic_count": 5}
{"name": "SimpleGraph.IsSRGWith.card_neighborFinset_union_of_not_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.StronglyRegular", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.IsSRGWith.card_neighborFinset_union_of_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.StronglyRegular", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.compl_neighborFinset_sdiff_inter_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.StronglyRegular", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "SimpleGraph.sdiff_compl_neighborFinset_inter_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.StronglyRegular", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "SimpleGraph.IsSRGWith.compl_is_regular", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.StronglyRegular", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.IsSRGWith.card_commonNeighbors_eq_of_adj_compl", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.StronglyRegular", "is_tactic_proof": false, "tactics": ["simp", "simp_rw", "have", "rw", "rw", "rw", "simp", "intro", "simp", "rintro"], "tactic_count": 10}
{"name": "SimpleGraph.IsSRGWith.card_commonNeighbors_eq_of_not_adj_compl", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.StronglyRegular", "is_tactic_proof": false, "tactics": ["simp", "simp", "have", "simp_rw", "rwa"], "tactic_count": 5}
{"name": "SimpleGraph.IsSRGWith.compl", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.StronglyRegular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.IsSRGWith.param_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.StronglyRegular", "is_tactic_proof": true, "tactics": ["letI", "rw", "obtain", "convert", "simp", "simp", "intro", "rw", "simp_rw", "have", "rw", "exact", "rw", "card_singleton,", "congr", "simp", "simp_rw", "congr", "intro", "simp_rw", "simp_rw", "congr"], "tactic_count": 22}
{"name": "SimpleGraph.IsSRGWith.matrix_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.StronglyRegular", "is_tactic_proof": true, "tactics": ["ext", "simp", "compl_adj]", "rw", "obtain", "rw", "simp", "simp", "by_cases", "simp", "not_false_eq_true,", "rw", "rw"], "tactic_count": 13}
{"name": "SimpleGraph.singletonSubgraph", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.subgraphOfAdj", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.loopless", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.adj_comm", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.adj_symm", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.Adj.symm", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.Adj.adj_sub", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.Adj.fst_mem", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.Adj.snd_mem", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.Adj.ne", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.adj_congr_of_sym2", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["simp", "rcases", "rw", "rw"], "tactic_count": 4}
{"name": "SimpleGraph.Subgraph.coe", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.Adj.adj_sub'", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.coe_adj_sub", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.Adj.coe", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.instDecidableRelElemVertsAdjCoeOfAdj", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.IsSpanning", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.isSpanning_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.spanningCoe", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.spanningCoe_coe", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["ext", "simp", "grind"], "tactic_count": 3}
{"name": "SimpleGraph.Subgraph.Adj.of_spanningCoe", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.spanningCoe_le", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.spanningCoe_inj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Subgraph.mem_of_adj_spanningCoe", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SimpleGraph.Subgraph.spanningCoe_subgraphOfAdj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["ext", "aesop"], "tactic_count": 2}
{"name": "SimpleGraph.Subgraph.spanningCoeEquivCoeOfSpanning", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.IsInduced", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.IsInduced.adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.support", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.mem_support", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.support_subset_verts", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.neighborSet", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.neighborSet_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.neighborSet_subset_verts", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.mem_neighborSet", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.coeNeighborSetEquiv", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.edgeSet", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.edgeSet_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.mem_edgeSet", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.edgeSet_coe", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "SimpleGraph.Subgraph.image_coe_edgeSet_coe", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["rw", "rintro", "induction", "h", "rw", "exact"], "tactic_count": 6}
{"name": "SimpleGraph.Subgraph.mem_verts_of_mem_edge", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["induction", "rcases", "exact", "exact"], "tactic_count": 4}
{"name": "SimpleGraph.Subgraph.incidenceSet", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.incidenceSet_subset_incidenceSet", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.incidenceSet_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.vert", "kind": "abbrev", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.copy", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.copy_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.instMax", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.instMin", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.instTop", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.instBot", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.instSupSet", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.instInfSet", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.sup_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.inf_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.top_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.not_bot_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.verts_sup", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.verts_inf", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.verts_top", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.verts_bot", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.eq_bot_iff_verts_eq_empty", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.ne_bot_iff_nonempty_verts", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.sSup_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.sInf_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.iSup_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Subgraph.iInf_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Subgraph.sInf_adj_of_nonempty", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.iInf_adj_of_nonempty", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "SimpleGraph.Subgraph.verts_sSup", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.verts_sInf", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.verts_iSup", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Subgraph.verts_iInf", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Subgraph.coe_bot", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.IsInduced.top", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.topIso", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.verts_spanningCoe_injective", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["intro", "rw", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.Subgraph.distribLattice", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.instBoundedOrder", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.completelyDistribLatticeMinimalAxioms", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.instCompletelyDistribLattice", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.verts_mono", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.verts_monotone", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.subgraphInhabited", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.neighborSet_sup", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.neighborSet_inf", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.neighborSet_top", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.neighborSet_bot", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.neighborSet_sSup", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "SimpleGraph.Subgraph.neighborSet_sInf", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "SimpleGraph.Subgraph.neighborSet_iSup", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Subgraph.neighborSet_iInf", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Subgraph.edgeSet_top", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.edgeSet_bot", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.edgeSet_inf", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.edgeSet_sup", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.edgeSet_sSup", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["ext", "induction", "simp"], "tactic_count": 3}
{"name": "SimpleGraph.Subgraph.edgeSet_sInf", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["ext", "induction", "simp"], "tactic_count": 3}
{"name": "SimpleGraph.Subgraph.edgeSet_iSup", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Subgraph.edgeSet_iInf", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Subgraph.spanningCoe_top", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.spanningCoe_bot", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.toSubgraph", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.support_mono", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.toSubgraph.isSpanning", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.spanningCoe_le_of_le", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.sup_spanningCoe", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.botIso", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.edgeSet_mono", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Disjoint.edgeSet", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.map", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.map_id", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "SimpleGraph.Subgraph.map_comp", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "SimpleGraph.Subgraph.map_mono", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["constructor", "intro", "simp", "rintro", "exact", "rintro", "exact"], "tactic_count": 7}
{"name": "SimpleGraph.Subgraph.map_monotone", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.map_sup", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "SimpleGraph.Subgraph.map_iso_top", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "SimpleGraph.Subgraph.edgeSet_map", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.comap", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.comap_monotone", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["intro", "constructor", "intro", "simp", "apply", "intro", "simp", "intro", "apply"], "tactic_count": 9}
{"name": "SimpleGraph.Subgraph.comap_equiv_top", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "SimpleGraph.Subgraph.map_le_iff_le_comap", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["refine", "simp", "exact", "simp", "exact", "simp", "rintro", "exact", "simp", "rintro", "exact"], "tactic_count": 11}
{"name": "SimpleGraph.Subgraph.instFintypeOfDecidableEqOfDecidableRelAdj", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": ["refine", "rintro", "simp", "classical", "exact", "simpa"], "tactic_count": 6}
{"name": "SimpleGraph.Subgraph.instFinite", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "SimpleGraph.Subgraph.inclusion", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.inclusion.injective", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["intro", "rw", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.Subgraph.hom", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.coe_hom", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.hom_injective", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.map_hom_top", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SimpleGraph.Subgraph.spanningHom", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.spanningHom_injective", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.neighborSet_subset_of_subgraph", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.neighborSet.decidablePred", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.finiteAt", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.finiteAtOfSubgraph", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.instFintypeElemNeighborSetOfVertsOfDecidablePredMemSet", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.coeFiniteAt", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.IsSpanning.card_verts", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["simp", "congr"], "tactic_count": 2}
{"name": "SimpleGraph.Subgraph.degree", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.finset_card_neighborSet_eq_degree", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.Subgraph.degree_of_notMem_verts", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["rw", "intro", "by_contra", "exact"], "tactic_count": 4}
{"name": "SimpleGraph.Subgraph.degree_le", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.Subgraph.degree_le'", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.coe_degree", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.Subgraph.degree_spanningCoe", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["rw", "congr"], "tactic_count": 2}
{"name": "SimpleGraph.Subgraph.degree_pos_iff_exists_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Subgraph.degree_eq_zero_of_subsingleton", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "have", "exact", "exact"], "tactic_count": 5}
{"name": "SimpleGraph.Subgraph.degree_eq_one_iff_existsUnique_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "SimpleGraph.Subgraph.nontrivial_verts_of_degree_ne_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["by_contra", "simp_all"], "tactic_count": 2}
{"name": "SimpleGraph.Subgraph.neighborSet_eq_of_equiv", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["lift", "lift", "refine", "rw", "exact"], "tactic_count": 5}
{"name": "SimpleGraph.Subgraph.adj_iff_of_neighborSet_equiv", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.card_neighborSet_toSubgraph", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["refine", "simp", "rfl"], "tactic_count": 3}
{"name": "SimpleGraph.degree_toSubgraph", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.nonempty_singletonSubgraph_verts", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.instUniqueElemVertsSingletonSubgraph", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.singletonSubgraph_le_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["refine", "intro", "constructor", "rwa", "exact"], "tactic_count": 5}
{"name": "SimpleGraph.map_singletonSubgraph", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": ["ext", "simp", "and_iff_left_iff_imp,", "exact"], "tactic_count": 4}
{"name": "SimpleGraph.neighborSet_singletonSubgraph", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.edgeSet_singletonSubgraph", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.eq_singletonSubgraph_iff_verts_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["refine", "ext", "rw", "simp", "intro", "have", "have", "rw", "subst_vars", "exact"], "tactic_count": 10}
{"name": "SimpleGraph.nonempty_subgraphOfAdj_verts", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.edgeSet_subgraphOfAdj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["ext", "refine", "simp"], "tactic_count": 3}
{"name": "SimpleGraph.subgraphOfAdj_le_of_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rintro", "simp", "rintro"], "tactic_count": 5}
{"name": "SimpleGraph.subgraphOfAdj_symm", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "SimpleGraph.map_subgraphOfAdj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "SimpleGraph.neighborSet_subgraphOfAdj_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.neighborSet_fst_subgraphOfAdj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["ext", "suffices", "rw"], "tactic_count": 3}
{"name": "SimpleGraph.neighborSet_snd_subgraphOfAdj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.neighborSet_subgraphOfAdj_of_ne_of_ne", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "SimpleGraph.neighborSet_subgraphOfAdj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["split_ifs"], "tactic_count": 1}
{"name": "SimpleGraph.singletonSubgraph_fst_le_subgraphOfAdj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.singletonSubgraph_snd_le_subgraphOfAdj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.support_subgraphOfAdj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["ext", "rw", "simp", "refine", "rintro", "exact"], "tactic_count": 6}
{"name": "SimpleGraph.Subgraph.coeSubgraph", "kind": "abbrev", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.restrict", "kind": "abbrev", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.verts_coeSubgraph", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.coeSubgraph_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Subgraph.restrict_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.restrict_coeSubgraph", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["ext", "simp", "rw", "simpa"], "tactic_count": 4}
{"name": "SimpleGraph.Subgraph.coeSubgraph_injective", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.coeSubgraph_le", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["constructor", "simp", "rintro", "exact"], "tactic_count": 4}
{"name": "SimpleGraph.Subgraph.coeSubgraph_restrict_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["ext", "simp", "simp_rw", "simp", "intro", "simp"], "tactic_count": 6}
{"name": "SimpleGraph.Subgraph.deleteEdges", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.deleteEdges_verts", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.deleteEdges_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.deleteEdges_deleteEdges", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "SimpleGraph.Subgraph.deleteEdges_empty_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "SimpleGraph.Subgraph.deleteEdges_spanningCoe_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "SimpleGraph.Subgraph.deleteEdges_coe_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["ext", "simp", "and_congr_right_iff]", "intro", "constructor", "intro", "refine", "rintro", "simp", "contrapose", "rintro", "intro", "exact"], "tactic_count": 13}
{"name": "SimpleGraph.Subgraph.coe_deleteEdges_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "SimpleGraph.Subgraph.deleteEdges_le", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["constructor"], "tactic_count": 1}
{"name": "SimpleGraph.Subgraph.deleteEdges_le_of_le", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["constructor", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.Subgraph.deleteEdges_inter_edgeSet_left_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "SimpleGraph.Subgraph.deleteEdges_inter_edgeSet_right_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "SimpleGraph.Subgraph.coe_deleteEdges_le", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["intro", "simp"], "tactic_count": 2}
{"name": "SimpleGraph.Subgraph.spanningCoe_deleteEdges_le", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.induce", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.induce_eq_coe_induce_top", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "SimpleGraph.spanningCoe_induce_top", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "SimpleGraph.Subgraph.IsInduced.induce_top_verts", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.isInduced_iff_exists_eq_induce_top", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.Subgraph.induce_mono", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["constructor", "simp", "simp", "intro", "exact"], "tactic_count": 5}
{"name": "SimpleGraph.Subgraph.induce_mono_left", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.induce_mono_right", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.induce_empty", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "SimpleGraph.Subgraph.induce_self_verts", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["ext", "simp", "constructor", "exact"], "tactic_count": 4}
{"name": "SimpleGraph.Subgraph.le_induce_top_verts", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.le_induce_union", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["constructor", "simp", "simp", "rintro"], "tactic_count": 4}
{"name": "SimpleGraph.Subgraph.le_induce_union_left", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "SimpleGraph.Subgraph.le_induce_union_right", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "SimpleGraph.Subgraph.singletonSubgraph_eq_induce", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "SimpleGraph.Subgraph.subgraphOfAdj_eq_induce", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["ext", "simp", "constructor", "intro", "simp", "obtain", "intro", "simp", "obtain", "first", "exact", "simp"], "tactic_count": 12}
{"name": "SimpleGraph.Subgraph.instDecidableRel_induce_adj", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.coeInduceIso", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.deleteVerts", "kind": "abbrev", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.deleteVerts_verts", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.deleteVerts_adj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Subgraph.deleteVerts_deleteVerts", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "SimpleGraph.Subgraph.deleteVerts_empty", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Subgraph.deleteVerts_le", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["constructor"], "tactic_count": 1}
{"name": "SimpleGraph.Subgraph.deleteVerts_mono", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.deleteVerts_mono'", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["intro", "aesop"], "tactic_count": 2}
{"name": "SimpleGraph.Subgraph.deleteVerts_anti", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.deleteVerts_inter_verts_left_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "SimpleGraph.Subgraph.deleteVerts_inter_verts_set_right_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "SimpleGraph.Subgraph.instDecidableRel_deleteVerts_adj", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.coeDeleteVertsIso", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Subgraph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.sum", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.term_⊕g_", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph._aux_Mathlib_Combinatorics_SimpleGraph_Sum___macroRules_SimpleGraph_term_⊕g__1", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph._aux_Mathlib_Combinatorics_SimpleGraph_Sum___unexpand_SimpleGraph_sum_1", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Iso.sumComm", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Iso.sumAssoc", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Embedding.sumInl", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Embedding.sumInr", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Coloring.sum", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Coloring.sumLeft", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Coloring.sumRight", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Coloring.sumLeft_sum", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Coloring.sumRight_sum", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Coloring.sum_sumLeft_sumRight", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Sum", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "SimpleGraph.Coloring.sumEquiv", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Coloring.sumFin", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Colorable.sum_max", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Colorable.of_sum_left", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Colorable.of_sum_right", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.colorable_sum", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.chromaticNumber_le_sum_left", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.chromaticNumber_le_sum_right", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.chromaticNumber_sum", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Sum", "is_tactic_proof": true, "tactics": ["refine", "cases", "top", "coe", "let", "let", "exact"], "tactic_count": 7}
{"name": "SimpleGraph.Walk.IsTrail.edgesFinset", "kind": "abbrev", "module": "Mathlib.Combinatorics.SimpleGraph.Trails", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.IsTrail.even_countP_edges_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Trails", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "rw", "specialize", "simp", "split_ifs", "rw", "obtain", "rw", "simp", "false_and,", "rintro", "exact", "have", "grind"], "tactic_count": 16}
{"name": "SimpleGraph.Walk.IsEulerian", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Trails", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.IsEulerian.isTrail", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Trails", "is_tactic_proof": true, "tactics": ["rw", "intro", "by_cases", "exact", "simp"], "tactic_count": 5}
{"name": "SimpleGraph.Walk.IsEulerian.mem_edges_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Trails", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.IsEulerian.fintypeEdgeSet", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Trails", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.IsTrail.isEulerian_of_forall_mem", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Trails", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.isEulerian_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Trails", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "rintro", "exact"], "tactic_count": 5}
{"name": "SimpleGraph.Walk.IsTrail.isEulerian_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Trails", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.IsEulerian.edgeSet_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Trails", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.IsEulerian.edgesFinset_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Trails", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "SimpleGraph.Walk.IsEulerian.even_degree_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Trails", "is_tactic_proof": true, "tactics": ["convert", "rw", "change", "congr", "convert_to", "rw"], "tactic_count": 6}
{"name": "SimpleGraph.Walk.IsEulerian.card_filter_odd_degree", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Trails", "is_tactic_proof": true, "tactics": ["subst", "simp", "simp", "obtain", "simp", "right", "convert_to", "simp", "congr", "ext", "simp"], "tactic_count": 11}
{"name": "SimpleGraph.Walk.IsEulerian.card_odd_degree", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Trails", "is_tactic_proof": true, "tactics": ["rw", "apply", "simp"], "tactic_count": 3}
{"name": "SimpleGraph.EdgeDisjointTriangles", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.LocallyLinear", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.LocallyLinear.edgeDisjointTriangles", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.EdgeDisjointTriangles.mono", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.edgeDisjointTriangles_bot", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.locallyLinear_bot", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.EdgeDisjointTriangles.map", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Basic", "is_tactic_proof": true, "tactics": ["rw", "classical", "rintro", "dsimp", "rw", "exact"], "tactic_count": 6}
{"name": "SimpleGraph.LocallyLinear.map", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Basic", "is_tactic_proof": true, "tactics": ["refine", "rintro", "obtain", "exact"], "tactic_count": 4}
{"name": "SimpleGraph.locallyLinear_comap", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact", "rw", "exact"], "tactic_count": 5}
{"name": "SimpleGraph.edgeDisjointTriangles_iff_mem_sym2_subsingleton", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Basic", "is_tactic_proof": true, "tactics": ["classical", "have", "ext", "simp", "is3Clique_iff]", "constructor", "rintro", "simp", "obtain", "any_goals", "any_goals", "first", "exact", "exact", "exact", "simp", "exact", "simp", "exact", "simp", "exact", "rintro", "refine", "constructor", "rw", "rintro", "simp", "rw", "rintro", "refine", "simp", "rintro", "refine", "hG", "simp"], "tactic_count": 35}
{"name": "SimpleGraph.EdgeDisjointTriangles.instDecidable", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.LocallyLinear.instDecidable", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.EdgeDisjointTriangles.card_edgeFinset_le", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp", "rintro", "have", "refine", "rw", "refine", "simp", "simpa", "mem_cliqueSet_iff]"], "tactic_count": 11}
{"name": "SimpleGraph.LocallyLinear.card_edgeFinset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "refine", "simpa", "simp", "rintro", "calc", "simp", "and_imp,", "rintro"], "tactic_count": 10}
{"name": "SimpleGraph.FarFromTriangleFree", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.farFromTriangleFree_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.FarFromTriangleFree.mono", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.FarFromTriangleFree.cliqueFinset_nonempty'", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.farFromTriangleFree_of_disjoint_triangles_aux", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Basic", "is_tactic_proof": true, "tactics": ["rw", "by_contra", "have", "by_contra", "refine", "simp", "obtain", "rw", "refine", "choose", "let", "have", "obtain", "dsimp", "have", "rw", "obtain", "exact", "exact"], "tactic_count": 19}
{"name": "SimpleGraph.farFromTriangleFree_of_disjoint_triangles", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Basic", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "exact"], "tactic_count": 4}
{"name": "SimpleGraph.EdgeDisjointTriangles.farFromTriangleFree", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.FarFromTriangleFree.lt_half", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Basic", "is_tactic_proof": true, "tactics": ["refine", "calc", "ε"], "tactic_count": 3}
{"name": "SimpleGraph.FarFromTriangleFree.lt_one", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.FarFromTriangleFree.nonpos", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Basic", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.CliqueFree.not_farFromTriangleFree", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.FarFromTriangleFree.not_cliqueFree", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.FarFromTriangleFree.cliqueFinset_nonempty", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.badVertices", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Counting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.card_interedges_badVertices_le", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Counting", "is_tactic_proof": true, "tactics": ["classical", "refine", "simp_rw", "exact"], "tactic_count": 4}
{"name": "_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.edgeDensity_badVertices_le", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Counting", "is_tactic_proof": true, "tactics": ["rw", "push_cast", "refine", "rw", "exact"], "tactic_count": 5}
{"name": "_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.card_badVertices_le", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Counting", "is_tactic_proof": false, "tactics": ["have", "by_contra", "have", "hst", "rw", "linarith"], "tactic_count": 6}
{"name": "_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triangle_split_helper", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Counting", "is_tactic_proof": true, "tactics": ["rintro", "simp", "and_imp,", "rintro", "exact"], "tactic_count": 5}
{"name": "_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.good_vertices_triangle_card", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Counting", "is_tactic_proof": true, "tactics": ["simp", "rw", "simp", "obtain", "have", "have", "rw", "have", "have", "rw", "push_cast", "have", "refine", "refine", "ring"], "tactic_count": 15}
{"name": "SimpleGraph.triangle_counting'", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Counting", "is_tactic_proof": true, "tactics": ["classical", "have", "have", "let", "have", "triangle_split_helper", "refine", "rw", "apply", "rw", "have", "suffices", "exact", "have", "rw", "mul_comm", "refine", "rw", "gcongr", "rintro", "rw", "simp", "aesop"], "tactic_count": 23}
{"name": "_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triple_eq_triple_of_mem", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Counting", "is_tactic_proof": true, "tactics": ["simp", "grind"], "tactic_count": 2}
{"name": "SimpleGraph.triangle_counting", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Counting", "is_tactic_proof": true, "tactics": ["apply", "rw", "refine", "rintro", "simp", "rintro", "simp", "apply"], "tactic_count": 8}
{"name": "SimpleGraph.triangleRemovalBound", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Removal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.triangleRemovalBound_pos", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Removal", "is_tactic_proof": true, "tactics": ["have", "unfold", "positivity"], "tactic_count": 3}
{"name": "SimpleGraph.triangleRemovalBound_nonpos", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Removal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.triangleRemovalBound_mul_cube_lt", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Removal", "is_tactic_proof": true, "tactics": ["calc"], "tactic_count": 1}
{"name": "SimpleGraph.triangleRemovalBound_le", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Removal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Removal.0.SimpleGraph.aux", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Removal", "is_tactic_proof": false, "tactics": ["rw", "add_lt_add_iff_right]", "apply", "simpa"], "tactic_count": 4}
{"name": "_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Removal.0.SimpleGraph.card_bound", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Removal", "is_tactic_proof": true, "tactics": ["cases", "simp", "have", "calc"], "tactic_count": 4}
{"name": "_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Removal.0.SimpleGraph.triangle_removal_aux", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Removal", "is_tactic_proof": true, "tactics": ["rw", "obtain", "ht", "cases", "cases", "cases", "have", "have", "have", "have", "have", "linarith", "calc", "exact"], "tactic_count": 14}
{"name": "SimpleGraph.regularityReduced_edges_card_aux", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Removal", "is_tactic_proof": true, "tactics": ["let", "let", "let", "calc", "rw", "norm_cast", "rw", "gcongr", "exact", "gcongr", "exact", "exact"], "tactic_count": 12}
{"name": "SimpleGraph.FarFromTriangleFree.le_card_cliqueFinset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Removal", "is_tactic_proof": true, "tactics": ["cases", "simp", "obtain", "apply", "let", "have", "rcases", "calc", "obtain", "have", "have", "rw", "replace", "obtain", "exact"], "tactic_count": 15}
{"name": "SimpleGraph.triangle_removal", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Removal", "is_tactic_proof": true, "tactics": ["by_contra", "refine", "intro", "exact"], "tactic_count": 4}
{"name": "Mathlib.Meta.Positivity.evalTriangleRemovalBound", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Removal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity._example", "kind": "example", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Removal", "is_tactic_proof": true, "tactics": ["positivity"], "tactic_count": 1}
{"name": "SimpleGraph.TripartiteFromTriangles.Rel", "kind": "inductive", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.TripartiteFromTriangles.rel_irrefl", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.TripartiteFromTriangles.rel_symm", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.TripartiteFromTriangles.graph", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.TripartiteFromTriangles.Graph.not_in₀₀", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.TripartiteFromTriangles.Graph.not_in₁₁", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.TripartiteFromTriangles.Graph.not_in₂₂", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.TripartiteFromTriangles.Graph.in₀₁_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.TripartiteFromTriangles.Graph.in₁₀_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.TripartiteFromTriangles.Graph.in₀₂_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.TripartiteFromTriangles.Graph.in₂₀_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.TripartiteFromTriangles.Graph.in₁₂_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.TripartiteFromTriangles.Graph.in₂₁_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.TripartiteFromTriangles.Graph.in₀₁_iff'", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.TripartiteFromTriangles.Graph.in₁₀_iff'", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.TripartiteFromTriangles.Graph.in₀₂_iff'", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.TripartiteFromTriangles.Graph.in₂₀_iff'", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.TripartiteFromTriangles.Graph.in₁₂_iff'", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.TripartiteFromTriangles.Graph.in₂₁_iff'", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.TripartiteFromTriangles.graph.instDecidableRelAdj", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.TripartiteFromTriangles.graph_triple", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite", "is_tactic_proof": true, "tactics": ["rintro", "refine", "constructor", "assumption"], "tactic_count": 4}
{"name": "SimpleGraph.TripartiteFromTriangles.toTriangle", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.TripartiteFromTriangles.toTriangle_is3Clique", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.TripartiteFromTriangles.exists_mem_toTriangle", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "SimpleGraph.TripartiteFromTriangles.is3Clique_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite", "is_tactic_proof": true, "tactics": ["refine", "rw", "obtain", "obtain", "refine", "obtain", "obtain", "obtain", "obtain", "rintro", "exact"], "tactic_count": 11}
{"name": "SimpleGraph.TripartiteFromTriangles.toTriangle_surjOn", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.TripartiteFromTriangles.map_toTriangle_disjoint", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite", "is_tactic_proof": true, "tactics": ["intro", "simp", "rintro", "have", "simp", "simp", "suffices", "refine", "rintro", "exact", "rintro", "exact", "rintro", "exact"], "tactic_count": 14}
{"name": "SimpleGraph.TripartiteFromTriangles.cliqueSet_eq_image", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "SimpleGraph.TripartiteFromTriangles.cliqueFinset_eq_image", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.TripartiteFromTriangles.cliqueFinset_eq_map", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.TripartiteFromTriangles.card_triangles", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.TripartiteFromTriangles.farFromTriangleFree", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.TripartiteFromTriangles.locallyLinear", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite", "is_tactic_proof": true, "tactics": ["classical", "refine", "unfold", "convert", "rw", "obtain", "exact"], "tactic_count": 7}
{"name": "SimpleGraph.IsTutteViolator", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Tutte", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Combinatorics.SimpleGraph.Tutte.0.SimpleGraph.tutte_exists_isAlternating_isCycles", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Tutte", "is_tactic_proof": false, "tactics": ["refine", "sup_le_iff.mpr", "simpa", "refine", "rw", "simp", "simp", "simpa"], "tactic_count": 8}
{"name": "SimpleGraph.IsTutteViolator.mono", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Tutte", "is_tactic_proof": true, "tactics": ["simp", "have", "simp", "lia"], "tactic_count": 4}
{"name": "_private.Mathlib.Combinatorics.SimpleGraph.Tutte.0.SimpleGraph.Subgraph.IsMatching.exists_verts_compl_subset_universalVerts", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Tutte", "is_tactic_proof": true, "tactics": ["classical", "have", "obtain", "simp", "rwa", "have", "have", "rw", "exact", "choose", "let", "have", "refine", "rw", "hcomplMatch_compl", "exact", "have", "rw", "exact", "have", "rw", "intro", "by_cases", "exact", "right", "simp", "use", "aesop", "exact"], "tactic_count": 29}
{"name": "SimpleGraph.Subgraph.IsPerfectMatching.exists_of_isClique_supp", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Tutte", "is_tactic_proof": true, "tactics": ["classical", "cases", "obtain", "obtain", "refine", "simp", "rw", "exact"], "tactic_count": 8}
{"name": "SimpleGraph.IsTutteViolator.empty", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Tutte", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.not_isTutteViolator_of_isPerfectMatching", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Tutte", "is_tactic_proof": true, "tactics": ["choose", "have", "replace", "exact", "simpa"], "tactic_count": 5}
{"name": "_private.Mathlib.Combinatorics.SimpleGraph.Tutte.0.SimpleGraph.tutte_exists_isPerfectMatching_of_near_matchings", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Tutte", "is_tactic_proof": true, "tactics": ["classical", "by_cases", "use", "exact", "by_cases", "use", "exact", "simp", "have", "have", "aesop", "suffices", "obtain", "have", "apply", "simp", "use", "apply", "let", "have", "have", "have", "have", "have", "have", "refine", "simp", "exact", "le_trans", "by_cases", "use", "refine", "simp", "refine", "rw", "rw", "simp_all", "have", "have", "have", "rw", "exact", "obtain", "obtain", "obtain", "hp.1.exists_isCycle_snd_verts_eq", "obtain", "use", "simp", "rwa", "refine", "simp", "htw", "have", "apply", "rw", "aesop", "rwa", "simp", "obtain", "exacts", "have", "rw", "intro", "apply", "have", "simp", "aesop", "have", "refine", "obtain", "obtain", "rw", "exact", "rw", "exact", "simp", "obtain", "exact", "tutte_exists_isAlternating_isCycles", "conv", "enter", "rw", "rw", "exact", "tutte_exists_isAlternating_isCycles"], "tactic_count": 86}
{"name": "SimpleGraph.exists_isTutteViolator", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Tutte", "is_tactic_proof": true, "tactics": ["classical", "cases", "obtain", "refine", "by_contra", "simp", "by_cases", "rw", "simp_rw", "push_neg", "obtain", "exact", "obtain", "obtain", "obtain", "obtain", "simp", "obtain", "have", "obtain", "hMaximal", "left_lt_sup.mpr", "rw", "simp", "obtain", "have", "obtain", "tutte_exists_isPerfectMatching_of_near_matchings", "hc.1", "exact"], "tactic_count": 30}
{"name": "SimpleGraph.tutte", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Tutte", "is_tactic_proof": true, "tactics": ["classical", "refine", "contrapose", "intro", "by_cases", "exact", "exact"], "tactic_count": 7}
{"name": "SimpleGraph.UnitDistEmbedding.bot", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.UnitDistance.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.UnitDistEmbedding.subsingleton", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.UnitDistance.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.UnitDistEmbedding.copy", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.UnitDistance.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.UnitDistEmbedding.embed", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.UnitDistance.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.UnitDistEmbedding.iso", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.UnitDistance.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.universalVerts", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.UniversalVerts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.isClique_universalVerts", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.UniversalVerts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.deleteUniversalVerts", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.UniversalVerts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Subgraph.IsMatching.exists_of_universalVerts", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.UniversalVerts", "is_tactic_proof": true, "tactics": ["obtain", "refine", "obtain", "letI", "have", "exact"], "tactic_count": 6}
{"name": "SimpleGraph.disjoint_image_val_universalVerts", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.UniversalVerts", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "SimpleGraph.even_ncard_image_val_supp_sdiff_image_val_rep_union", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.UniversalVerts", "is_tactic_proof": true, "tactics": ["simp", "sdiff_eq_left.mpr"], "tactic_count": 2}
{"name": "SimpleGraph.IsVertexCover", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.VertexCover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.isVertexCover_empty", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.VertexCover", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.isVertexCover_univ", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.VertexCover", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.isVertexCover_bot", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.VertexCover", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.IsVertexCover.subset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.VertexCover", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "SimpleGraph.IsVertexCover.mono", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.VertexCover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.isIndepSet_compl_iff_isVertexCover", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.VertexCover", "is_tactic_proof": true, "tactics": ["refine", "by_contra", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.isVertexCover_compl", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.VertexCover", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.IsVertexCover.preimage", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.VertexCover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.isVertexCover_preimage_iso", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.VertexCover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.isVertexCover_image_iso", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.VertexCover", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.vertexCoverNum", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.VertexCover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.vertexCoverNum_le_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.VertexCover", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.IsVertexCover.vertexCoverNum_le", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.VertexCover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.vertexCoverNum_exists", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.VertexCover", "is_tactic_proof": true, "tactics": ["have", "obtain", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.exists_of_le_vertexCoverNum", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.VertexCover", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "exact"], "tactic_count": 3}
{"name": "SimpleGraph.vertexCoverNum_bot", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.VertexCover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.vertexCoverNum_of_subsingleton", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.VertexCover", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.vertexCoverNum_eq_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.VertexCover", "is_tactic_proof": true, "tactics": ["refine", "simpa"], "tactic_count": 2}
{"name": "SimpleGraph.vertexCoverNum_le_card_sub_one", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.VertexCover", "is_tactic_proof": true, "tactics": ["nontriviality", "obtain", "refine", "simp", "have", "simpa"], "tactic_count": 6}
{"name": "SimpleGraph.vertexCoverNum_ne_top_of_finite", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.VertexCover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.vertexCoverNum_lt_card", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.VertexCover", "is_tactic_proof": true, "tactics": ["refine", "grw", "enat_to_nat", "exact"], "tactic_count": 4}
{"name": "SimpleGraph.vertexCoverNum_le_encard_edgeSet", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.VertexCover", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "refine", "simp", "have", "grind"], "tactic_count": 6}
{"name": "SimpleGraph.vertexCoverNum_ne_top_of_finite_edgeSet", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.VertexCover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.vertexCoverNum_top", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.VertexCover", "is_tactic_proof": true, "tactics": ["nontriviality", "refine", "grw", "by_contra", "have", "grw", "simp", "obtain", "have", "refine", "rw", "refine", "refine", "grw", "simp", "obtain", "have", "grind"], "tactic_count": 18}
{"name": "SimpleGraph.IsContained.vertexCoverNum_le_vertexCoverNum", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.VertexCover", "is_tactic_proof": true, "tactics": ["have", "obtain", "have", "have", "have", "grw", "exact"], "tactic_count": 7}
{"name": "SimpleGraph.vertexCoverNum_le_vertexCoverNum_of_injective", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.VertexCover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.vertexCoverNum_mono", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.VertexCover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.vertexCoverNum_congr", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.VertexCover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk", "kind": "inductive", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.instDecidableEqWalk", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.instInhabited", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Adj.toWalk", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.nil'", "kind": "abbrev", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.cons'", "kind": "abbrev", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.exists_eq_cons_of_ne", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.length", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.length_nil", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.length_cons", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.eq_of_length_eq_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.adj_of_length_eq_one", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.exists_length_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.exists_length_eq_one_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": true, "tactics": ["refine", "induction", "nil", "cons", "simp", "exact"], "tactic_count": 6}
{"name": "SimpleGraph.Walk.length_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.support", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.darts", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.edges", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.support_nil", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.support_cons", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.support_ne_nil", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.head_support", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.getLast_support", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.support_eq_cons", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.start_mem_support", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.end_mem_support", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.support_nonempty", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.mem_support_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.mem_support_nil_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.end_mem_tail_support_of_ne", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": true, "tactics": ["obtain", "simp"], "tactic_count": 2}
{"name": "SimpleGraph.Walk.support_subset_support_cons", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.coe_support", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.isChain_adj_cons_support", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.isChain_adj_support", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.isChain_dartAdj_cons_darts", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "SimpleGraph.Walk.isChain_dartAdj_darts", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.edges_subset_edgeSet", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.adj_of_mem_edges", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.darts_nil", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.darts_cons", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.cons_map_snd_darts", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.map_snd_darts", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.map_fst_darts_append", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.map_fst_darts", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.edges_nil", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.edges_cons", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.length_support", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.length_darts", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.length_edges", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.fst_darts_getElem", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.snd_darts_getElem", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.mem_darts_iff_infix_support", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": true, "tactics": ["refine", "have", "exact", "have", "have", "convert"], "tactic_count": 6}
{"name": "SimpleGraph.Walk.mem_darts_iff_fst_snd_infix_support", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.dart_fst_mem_support_of_mem_darts", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.mem_support_iff_exists_mem_edges", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.darts_nodup_of_support_nodup", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "simp", "exact"], "tactic_count": 5}
{"name": "SimpleGraph.Walk.edges_eq_zipWith_support", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "SimpleGraph.Walk.edges_injective", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.darts_injective", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.edgeSet", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.mem_edgeSet", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.edgeSet_nil", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.edgeSet_cons", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.coe_edges_toFinset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.Nil", "kind": "inductive", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.nil_nil", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.not_nil_cons", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.instDecidableNil", "kind": "instance", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.Nil.eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.not_nil_of_ne", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.nil_iff_support_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.darts_eq_nil", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.edges_eq_nil", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.nil_iff_length_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.not_nil_iff_lt_length", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.not_nil_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.nil_iff_eq_nil", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.nil_of_subsingleton", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.notNilRec", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.notNilRec_cons", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.end_mem_tail_support", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.mem_support_iff_exists_mem_edges_of_not_nil", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "SimpleGraph.Walk.exists_boundary_dart", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Basic", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "rename_i", "by_cases", "obtain", "exact", "exact"], "tactic_count": 8}
{"name": "SimpleGraph.Walk.map", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.map_nil", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.map_cons", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.map_copy", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Maps", "is_tactic_proof": true, "tactics": ["subst_vars", "rfl"], "tactic_count": 2}
{"name": "SimpleGraph.Walk.map_id", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Maps", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.map_map", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Maps", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.map_eq_of_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Maps", "is_tactic_proof": true, "tactics": ["subst_vars", "rfl"], "tactic_count": 2}
{"name": "SimpleGraph.Walk.map_eq_nil_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Maps", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.length_map", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Maps", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.map_append", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Maps", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.reverse_map", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Maps", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.support_map", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Maps", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.darts_map", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Maps", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.edges_map", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Maps", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.edgeSet_map", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Maps", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.getVert_map", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Maps", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.map_injective_of_injective", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Maps", "is_tactic_proof": true, "tactics": ["intro", "induction", "nil", "cons", "cases", "nil", "cons", "simp", "grind"], "tactic_count": 9}
{"name": "SimpleGraph.Walk.mapLe", "kind": "abbrev", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.support_mapLe_eq_support", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Maps", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.edges_mapLe_eq_edges", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Maps", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.edgeSet_mapLe_eq_edgeSet", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Maps", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.transfer", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.transfer_self", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Maps", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.transfer_eq_map_ofLE", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Maps", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.edges_transfer", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Maps", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.edgeSet_transfer", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Maps", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.support_transfer", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Maps", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.length_transfer", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Maps", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.transfer_transfer", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Maps", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.transfer_append", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Maps", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.reverse_transfer", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Maps", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.induce", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.induce_nil", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.induce_cons", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.support_induce", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.map_induce", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.map_induce_induceHomOfLE", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.toDeleteEdges", "kind": "abbrev", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.toDeleteEdges_nil", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.toDeleteEdges_cons", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.toDeleteEdge", "kind": "abbrev", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.map_toDeleteEdges_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Maps", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "SimpleGraph.Walk.copy", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.copy_rfl_rfl", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.copy_copy", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["subst_vars", "rfl"], "tactic_count": 2}
{"name": "SimpleGraph.Walk.copy_nil", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["subst_vars", "rfl"], "tactic_count": 2}
{"name": "SimpleGraph.Walk.copy_cons", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["subst_vars", "rfl"], "tactic_count": 2}
{"name": "SimpleGraph.Walk.cons_copy", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["subst_vars", "rfl"], "tactic_count": 2}
{"name": "SimpleGraph.Walk.append", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.concat", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.concat_eq_append", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.reverseAux", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.reverse", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.cons_append", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.cons_nil_append", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.nil_append", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.append_nil", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.append_assoc", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.append_copy_copy", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["subst_vars", "rfl"], "tactic_count": 2}
{"name": "SimpleGraph.Walk.concat_nil", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.concat_cons", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.append_concat", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.concat_append", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.exists_cons_eq_concat", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "obtain", "exact"], "tactic_count": 5}
{"name": "SimpleGraph.Walk.exists_concat_eq_cons", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.reverse_nil", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.reverse_singleton", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.reverse_toWalk", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.cons_reverseAux", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.append_reverseAux", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "SimpleGraph.Walk.reverseAux_append", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "SimpleGraph.Walk.reverseAux_eq_reverse_append", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.reverse_cons", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.reverse_copy", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["subst_vars", "rfl"], "tactic_count": 2}
{"name": "SimpleGraph.Walk.reverse_append", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.reverse_concat", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.reverse_reverse", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "SimpleGraph.Walk.reverse_surjective", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.reverse_injective", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.reverse_bijective", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.length_copy", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["subst_vars", "rfl"], "tactic_count": 2}
{"name": "SimpleGraph.Walk.length_append", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.length_concat", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.length_reverseAux", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "SimpleGraph.Walk.length_reverse", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.getVert_append", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.getVert_reverse", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "simp", "split_ifs", "simp", "obtain", "simp", "rw", "simp"], "tactic_count": 10}
{"name": "SimpleGraph.Walk.concatRecAux", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.concatRec", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.concatRec_nil", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.concatRec_concat", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["simp", "apply", "trans", "congr", "simp", "rw", "congr"], "tactic_count": 7}
{"name": "SimpleGraph.Walk.concat_ne_nil", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.concat_inj", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["induction", "nil", "cases", "exact", "simp", "obtain", "exact", "cons", "rw", "cases", "simp", "obtain", "exact", "rw", "obtain", "obtain", "exact"], "tactic_count": 17}
{"name": "SimpleGraph.Walk.support_concat", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.support_copy", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["subst_vars", "rfl"], "tactic_count": 2}
{"name": "SimpleGraph.Walk.support_append", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.support_reverse", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.support_append_eq_support_dropLast_append", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.tail_support_append", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.support_eq_concat", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["cases", "nil", "cons", "obtain", "simp"], "tactic_count": 5}
{"name": "SimpleGraph.Walk.ext_support", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["refine", "have", "have", "grind"], "tactic_count": 4}
{"name": "SimpleGraph.Walk.mem_tail_support_append_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.mem_support_append_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["simp", "obtain", "simp"], "tactic_count": 3}
{"name": "SimpleGraph.Walk.support_subset_support_concat", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.subset_support_append_left", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.subset_support_append_right", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["intro", "simp"], "tactic_count": 2}
{"name": "SimpleGraph.Walk.coe_support_append", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.coe_support_append'", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["simp_rw", "add_tsub_cancel_right]"], "tactic_count": 2}
{"name": "SimpleGraph.Walk.darts_concat", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.darts_copy", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["subst_vars", "rfl"], "tactic_count": 2}
{"name": "SimpleGraph.Walk.darts_append", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.darts_reverse", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.mem_darts_reverse", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.edges_concat", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.edges_copy", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["subst_vars", "rfl"], "tactic_count": 2}
{"name": "SimpleGraph.Walk.edges_append", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.edges_reverse", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.dart_snd_mem_support_of_mem_darts", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.fst_mem_support_of_mem_edges", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["obtain", "rw", "rcases", "exact", "exact"], "tactic_count": 5}
{"name": "SimpleGraph.Walk.snd_mem_support_of_mem_edges", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.mem_support_of_mem_edges", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.edges_nodup_of_support_nodup", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "simp", "exact"], "tactic_count": 5}
{"name": "SimpleGraph.Walk.nodup_tail_support_reverse", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["refine", "rw", "getVert_eq_support_getElem", "simp"], "tactic_count": 4}
{"name": "SimpleGraph.Walk.edgeSet_reverse", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.edgeSet_concat", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.edgeSet_append", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.edgeSet_copy", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.nil_append_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.Nil.append", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.nil_reverse", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.drop", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.drop_length", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.drop_getVert", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.drop_add_heq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["rw", "induction"], "tactic_count": 2}
{"name": "SimpleGraph.Walk.drop_add_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.nil_drop_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.darts_drop", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.edges_drop", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.take", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.take_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.take_length", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.take_getVert", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.take_add_heq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["rw", "induction", "grind"], "tactic_count": 3}
{"name": "SimpleGraph.Walk.take_add_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.nil_take_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.take_support_eq_support_take_succ", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.darts_take", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.edges_take", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.penultimate_concat", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.snd_reverse", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.penultimate_reverse", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.tail", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.drop_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.drop_support_eq_support_drop_min", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.append_take_drop_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["apply", "rw", "by_cases", "simp", "rw", "simp"], "tactic_count": 6}
{"name": "SimpleGraph.Walk.dropLast", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.tail_nil", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.tail_cons_nil", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.tail_cons", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.dropLast_nil", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.dropLast_cons_nil", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.dropLast_cons_cons", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.dropLast_cons_of_not_nil", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.dropLast_concat", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["induction", "rfl", "simp_rw", "rw"], "tactic_count": 4}
{"name": "SimpleGraph.Walk.cons_tail_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.concat_dropLast", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "cases", "nil"], "tactic_count": 5}
{"name": "SimpleGraph.Walk.cons_support_tail", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.length_tail_add_one", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.Nil.tail", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.not_nil_of_tail_not_nil", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.nil_copy", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["subst_vars", "rfl"], "tactic_count": 2}
{"name": "SimpleGraph.Walk.support_tail_of_not_nil", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.getVert_copy", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["subst_vars", "rfl"], "tactic_count": 2}
{"name": "SimpleGraph.Walk.getVert_tail", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.getVert_mem_tail_support", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.support_injective", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.ext_getVert_le_length", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["suffices", "intro", "cases", "inl", "rw", "exact", "inr", "replace", "have", "rw", "rw"], "tactic_count": 11}
{"name": "SimpleGraph.Walk.ext_getVert", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Operations", "is_tactic_proof": true, "tactics": ["wlog", "exact", "refine", "by_contra", "exact"], "tactic_count": 5}
{"name": "SimpleGraph.Walk.IsSubwalk", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Subwalks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.isSubwalk_rfl", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Subwalks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.nil_isSubwalk", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Subwalks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.IsSubwalk.cons", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Subwalks", "is_tactic_proof": true, "tactics": ["obtain", "use", "simp"], "tactic_count": 3}
{"name": "SimpleGraph.Walk.isSubwalk_cons", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Subwalks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.IsSubwalk.concat", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Subwalks", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.Walk.isSubwalk_concat", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Subwalks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.IsSubwalk.trans", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Subwalks", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "use", "simp"], "tactic_count": 4}
{"name": "SimpleGraph.Walk.isSubwalk_nil_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Subwalks", "is_tactic_proof": true, "tactics": ["cases", "nil", "constructor", "rintro", "simp", "rintro", "simp", "cons", "constructor", "rintro", "rintro"], "tactic_count": 11}
{"name": "SimpleGraph.Walk.nil_isSubwalk_iff_exists", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Subwalks", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.length_le_of_isSubwalk", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Subwalks", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.isSubwalk_of_append_left", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Subwalks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.isSubwalk_of_append_right", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Subwalks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.isSubwalk_take", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Subwalks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.isSubwalk_drop", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Subwalks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.isSubwalk_iff_support_isInfix", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Subwalks", "is_tactic_proof": true, "tactics": ["refine", "grind", "have", "refine", "simp", "simp", "apply", "simp", "drop_support_eq_support_drop_min,", "rw", "simp"], "tactic_count": 11}
{"name": "SimpleGraph.Walk.isSubwalk_antisymm", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Subwalks", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SimpleGraph.Walk.IsSubwalk.support_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Subwalks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.IsSubwalk.edges_isInfix", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Subwalks", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.IsSubwalk.edges_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Subwalks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.IsSubwalk.darts_isInfix", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Subwalks", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.IsSubwalk.darts_subset", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Subwalks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.IsSubwalk.map", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Subwalks", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.IsSubwalk.dropLast", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Subwalks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.IsSubwalk.tail", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Subwalks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.getVert", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Traversal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.getVert_zero", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Traversal", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.getVert_nil", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Traversal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.getVert_of_length_le", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Traversal", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "cases", "cases", "exact"], "tactic_count": 6}
{"name": "SimpleGraph.Walk.getVert_length", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Traversal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.adj_getVert_succ", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Traversal", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "cases", "simp", "exact"], "tactic_count": 6}
{"name": "SimpleGraph.Walk.getVert_cons_succ", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Traversal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.getVert_cons", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Traversal", "is_tactic_proof": true, "tactics": ["obtain", "rw"], "tactic_count": 2}
{"name": "SimpleGraph.Walk.getVert_mem_support", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Traversal", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.getVert_eq_support_getElem", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Traversal", "is_tactic_proof": true, "tactics": ["cases", "nil", "cons", "cases", "zero", "succ", "simp_rw", "exact"], "tactic_count": 8}
{"name": "SimpleGraph.Walk.support_getElem_eq_getVert", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Traversal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.getVert_eq_support_getElem?", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Traversal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.getVert_eq_getD_support", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Traversal", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "grind"], "tactic_count": 3}
{"name": "SimpleGraph.Walk.getVert_comp_val_eq_get_support", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Traversal", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.range_getVert_eq_range_support_getElem", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Traversal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.darts_getElem_eq_getVert", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Traversal", "is_tactic_proof": true, "tactics": ["rw", "ext", "simp", "by_cases", "cases", "contradiction", "simp", "have", "grind", "simp"], "tactic_count": 10}
{"name": "SimpleGraph.Walk.adj_of_infix_support", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Traversal", "is_tactic_proof": true, "tactics": ["have", "have", "have", "rw", "exact"], "tactic_count": 5}
{"name": "SimpleGraph.Walk.snd", "kind": "abbrev", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Traversal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.adj_snd", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Traversal", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.snd_cons", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Traversal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.snd_mem_tail_support", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Traversal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.support_getElem_one", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Traversal", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.snd_eq_support_getElem_one", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Traversal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.penultimate", "kind": "abbrev", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Traversal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.penultimate_nil", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Traversal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.penultimate_cons_nil", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Traversal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.penultimate_cons_cons", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Traversal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.penultimate_cons_of_not_nil", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Traversal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.adj_penultimate", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Traversal", "is_tactic_proof": true, "tactics": ["conv", "rw", "convert"], "tactic_count": 3}
{"name": "SimpleGraph.Walk.penultimate_mem_dropLast_support", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Traversal", "is_tactic_proof": true, "tactics": ["have", "grind"], "tactic_count": 2}
{"name": "SimpleGraph.Walk.support_getElem_length_sub_one_eq_penultimate", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Traversal", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.firstDart", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Traversal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.lastDart", "kind": "definition", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Traversal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.edge_firstDart", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Traversal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.edge_lastDart", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Traversal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.firstDart_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Traversal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.lastDart_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Traversal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.head_darts_eq_firstDart", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Traversal", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.firstDart_eq_head_darts", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Traversal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.head_darts_fst", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Traversal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.firstDart_mem_darts", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Traversal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.getLast_darts_eq_lastDart", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Traversal", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.lastDart_eq_getLast_darts", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Traversal", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.getLast_darts_snd", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Traversal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.lastDart_mem_darts", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Traversal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.head_edges_eq_mk_start_snd", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Traversal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.mk_start_snd_eq_head_edges", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Traversal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.mk_start_snd_mem_edges", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Traversal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.getLast_edges_eq_mk_penultimate_end", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Traversal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SimpleGraph.Walk.mk_penultimate_end_eq_getLast_edges", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Traversal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SimpleGraph.Walk.mk_penultimate_end_mem_edges", "kind": "theorem", "module": "Mathlib.Combinatorics.SimpleGraph.Walks.Traversal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteTiling.Prototile.instInhabited", "kind": "instance", "module": "Mathlib.Combinatorics.Tiling.Tile", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteTiling.Prototile.instCoeOutSet", "kind": "instance", "module": "Mathlib.Combinatorics.Tiling.Tile", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteTiling.Prototile.instMembership", "kind": "instance", "module": "Mathlib.Combinatorics.Tiling.Tile", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteTiling.Prototile.coe_mk", "kind": "theorem", "module": "Mathlib.Combinatorics.Tiling.Tile", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteTiling.Prototile.mem_coe", "kind": "theorem", "module": "Mathlib.Combinatorics.Tiling.Tile", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteTiling.Protoset.instInhabited", "kind": "instance", "module": "Mathlib.Combinatorics.Tiling.Tile", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteTiling.Protoset.instCoeFunForallPrototile", "kind": "instance", "module": "Mathlib.Combinatorics.Tiling.Tile", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteTiling.Protoset.coe_mk", "kind": "theorem", "module": "Mathlib.Combinatorics.Tiling.Tile", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteTiling.Protoset.coe_inj", "kind": "theorem", "module": "Mathlib.Combinatorics.Tiling.Tile", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteTiling.Protoset.coe_injective", "kind": "theorem", "module": "Mathlib.Combinatorics.Tiling.Tile", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteTiling.PlacedTile.instNonempty", "kind": "instance", "module": "Mathlib.Combinatorics.Tiling.Tile", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteTiling.PlacedTile.induction_on", "kind": "theorem", "module": "Mathlib.Combinatorics.Tiling.Tile", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "DiscreteTiling.PlacedTile.ext_iff_of_exists", "kind": "theorem", "module": "Mathlib.Combinatorics.Tiling.Tile", "is_tactic_proof": true, "tactics": ["refine", "subst", "simp", "refine", "rw", "rcases", "rcases", "dsimp", "subst", "ext", "rfl", "exact"], "tactic_count": 12}
{"name": "DiscreteTiling.PlacedTile.ext_iff_of_preimage", "kind": "theorem", "module": "Mathlib.Combinatorics.Tiling.Tile", "is_tactic_proof": true, "tactics": ["refine", "subst", "simp", "rcases", "rcases", "dsimp", "subst", "ext", "rfl", "exact"], "tactic_count": 10}
{"name": "DiscreteTiling.PlacedTile.coeSet", "kind": "definition", "module": "Mathlib.Combinatorics.Tiling.Tile", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteTiling.PlacedTile.instCoeOutSet", "kind": "instance", "module": "Mathlib.Combinatorics.Tiling.Tile", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteTiling.PlacedTile.instMembership", "kind": "instance", "module": "Mathlib.Combinatorics.Tiling.Tile", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteTiling.PlacedTile.mem_coe", "kind": "theorem", "module": "Mathlib.Combinatorics.Tiling.Tile", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteTiling.PlacedTile.coe_mk_mk", "kind": "theorem", "module": "Mathlib.Combinatorics.Tiling.Tile", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteTiling.PlacedTile.coe_mk_coe", "kind": "theorem", "module": "Mathlib.Combinatorics.Tiling.Tile", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteTiling.PlacedTile.coe_nonempty_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Tiling.Tile", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rw", "simp"], "tactic_count": 4}
{"name": "DiscreteTiling.PlacedTile.coe_mk_nonempty_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Tiling.Tile", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteTiling.PlacedTile.coe_finite_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Tiling.Tile", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rw", "simp"], "tactic_count": 4}
{"name": "DiscreteTiling.PlacedTile.coe_mk_finite_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Tiling.Tile", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteTiling.PlacedTile.instSMul", "kind": "instance", "module": "Mathlib.Combinatorics.Tiling.Tile", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteTiling.PlacedTile.smul_mk_mk", "kind": "theorem", "module": "Mathlib.Combinatorics.Tiling.Tile", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteTiling.PlacedTile.smul_mk_coe", "kind": "theorem", "module": "Mathlib.Combinatorics.Tiling.Tile", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteTiling.PlacedTile.smul_index", "kind": "theorem", "module": "Mathlib.Combinatorics.Tiling.Tile", "is_tactic_proof": true, "tactics": ["induction", "rfl"], "tactic_count": 2}
{"name": "DiscreteTiling.PlacedTile.coe_smul", "kind": "theorem", "module": "Mathlib.Combinatorics.Tiling.Tile", "is_tactic_proof": true, "tactics": ["induction", "simp"], "tactic_count": 2}
{"name": "DiscreteTiling.PlacedTile.instMulAction", "kind": "instance", "module": "Mathlib.Combinatorics.Tiling.Tile", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteTiling.PlacedTile.smul_mem_smul_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Tiling.Tile", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "DiscreteTiling.PlacedTile.mem_smul_iff_smul_inv_mem", "kind": "theorem", "module": "Mathlib.Combinatorics.Tiling.Tile", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "DiscreteTiling.PlacedTile.mem_inv_smul_iff_smul_mem", "kind": "theorem", "module": "Mathlib.Combinatorics.Tiling.Tile", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "SemistandardYoungTableau.instFunLike", "kind": "instance", "module": "Mathlib.Combinatorics.Young.SemistandardTableau", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemistandardYoungTableau.to_fun_eq_coe", "kind": "theorem", "module": "Mathlib.Combinatorics.Young.SemistandardTableau", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemistandardYoungTableau.ext", "kind": "theorem", "module": "Mathlib.Combinatorics.Young.SemistandardTableau", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemistandardYoungTableau.copy", "kind": "definition", "module": "Mathlib.Combinatorics.Young.SemistandardTableau", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemistandardYoungTableau.coe_copy", "kind": "theorem", "module": "Mathlib.Combinatorics.Young.SemistandardTableau", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemistandardYoungTableau.copy_eq", "kind": "theorem", "module": "Mathlib.Combinatorics.Young.SemistandardTableau", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemistandardYoungTableau.row_weak", "kind": "theorem", "module": "Mathlib.Combinatorics.Young.SemistandardTableau", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemistandardYoungTableau.col_strict", "kind": "theorem", "module": "Mathlib.Combinatorics.Young.SemistandardTableau", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemistandardYoungTableau.zeros", "kind": "theorem", "module": "Mathlib.Combinatorics.Young.SemistandardTableau", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemistandardYoungTableau.row_weak_of_le", "kind": "theorem", "module": "Mathlib.Combinatorics.Young.SemistandardTableau", "is_tactic_proof": true, "tactics": ["rcases", "rw", "exact"], "tactic_count": 3}
{"name": "SemistandardYoungTableau.col_weak", "kind": "theorem", "module": "Mathlib.Combinatorics.Young.SemistandardTableau", "is_tactic_proof": true, "tactics": ["rcases", "rw", "exact"], "tactic_count": 3}
{"name": "SemistandardYoungTableau.highestWeight", "kind": "definition", "module": "Mathlib.Combinatorics.Young.SemistandardTableau", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemistandardYoungTableau.highestWeight_apply", "kind": "theorem", "module": "Mathlib.Combinatorics.Young.SemistandardTableau", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemistandardYoungTableau.instInhabited", "kind": "instance", "module": "Mathlib.Combinatorics.Young.SemistandardTableau", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "YoungDiagram.instSetLikeProdNat", "kind": "instance", "module": "Mathlib.Combinatorics.Young.YoungDiagram", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "YoungDiagram.instPartialOrder", "kind": "instance", "module": "Mathlib.Combinatorics.Young.YoungDiagram", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "YoungDiagram.mem_cells", "kind": "theorem", "module": "Mathlib.Combinatorics.Young.YoungDiagram", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "YoungDiagram.mem_mk", "kind": "theorem", "module": "Mathlib.Combinatorics.Young.YoungDiagram", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "YoungDiagram.decidableMem", "kind": "instance", "module": "Mathlib.Combinatorics.Young.YoungDiagram", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "YoungDiagram.up_left_mem", "kind": "theorem", "module": "Mathlib.Combinatorics.Young.YoungDiagram", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "YoungDiagram.cells_subset_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Young.YoungDiagram", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "YoungDiagram.cells_ssubset_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Young.YoungDiagram", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "YoungDiagram.instMax", "kind": "instance", "module": "Mathlib.Combinatorics.Young.YoungDiagram", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "YoungDiagram.cells_sup", "kind": "theorem", "module": "Mathlib.Combinatorics.Young.YoungDiagram", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "YoungDiagram.coe_sup", "kind": "theorem", "module": "Mathlib.Combinatorics.Young.YoungDiagram", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "YoungDiagram.mem_sup", "kind": "theorem", "module": "Mathlib.Combinatorics.Young.YoungDiagram", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "YoungDiagram.instMin", "kind": "instance", "module": "Mathlib.Combinatorics.Young.YoungDiagram", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "YoungDiagram.cells_inf", "kind": "theorem", "module": "Mathlib.Combinatorics.Young.YoungDiagram", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "YoungDiagram.coe_inf", "kind": "theorem", "module": "Mathlib.Combinatorics.Young.YoungDiagram", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "YoungDiagram.mem_inf", "kind": "theorem", "module": "Mathlib.Combinatorics.Young.YoungDiagram", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "YoungDiagram.instOrderBot", "kind": "instance", "module": "Mathlib.Combinatorics.Young.YoungDiagram", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "YoungDiagram.cells_bot", "kind": "theorem", "module": "Mathlib.Combinatorics.Young.YoungDiagram", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "YoungDiagram.notMem_bot", "kind": "theorem", "module": "Mathlib.Combinatorics.Young.YoungDiagram", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "YoungDiagram.coe_bot", "kind": "theorem", "module": "Mathlib.Combinatorics.Young.YoungDiagram", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "YoungDiagram.instInhabited", "kind": "instance", "module": "Mathlib.Combinatorics.Young.YoungDiagram", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "YoungDiagram.instDistribLattice", "kind": "instance", "module": "Mathlib.Combinatorics.Young.YoungDiagram", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "YoungDiagram.card", "kind": "abbrev", "module": "Mathlib.Combinatorics.Young.YoungDiagram", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "YoungDiagram.transpose", "kind": "definition", "module": "Mathlib.Combinatorics.Young.YoungDiagram", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "YoungDiagram.mem_transpose", "kind": "theorem", "module": "Mathlib.Combinatorics.Young.YoungDiagram", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "YoungDiagram.transpose_transpose", "kind": "theorem", "module": "Mathlib.Combinatorics.Young.YoungDiagram", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "YoungDiagram.transpose_eq_iff_eq_transpose", "kind": "theorem", "module": "Mathlib.Combinatorics.Young.YoungDiagram", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "simp"], "tactic_count": 3}
{"name": "YoungDiagram.transpose_eq_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Young.YoungDiagram", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "YoungDiagram.le_of_transpose_le", "kind": "theorem", "module": "Mathlib.Combinatorics.Young.YoungDiagram", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "YoungDiagram.transpose_le_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Young.YoungDiagram", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "YoungDiagram.transpose_mono", "kind": "theorem", "module": "Mathlib.Combinatorics.Young.YoungDiagram", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "YoungDiagram.transposeOrderIso", "kind": "definition", "module": "Mathlib.Combinatorics.Young.YoungDiagram", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "YoungDiagram.row", "kind": "definition", "module": "Mathlib.Combinatorics.Young.YoungDiagram", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "YoungDiagram.mem_row_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Young.YoungDiagram", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "YoungDiagram.mk_mem_row_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Young.YoungDiagram", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "YoungDiagram.exists_notMem_row", "kind": "theorem", "module": "Mathlib.Combinatorics.Young.YoungDiagram", "is_tactic_proof": false, "tactics": ["obtain", "cases", "rfl)", "rw", "exact"], "tactic_count": 5}
{"name": "YoungDiagram.rowLen", "kind": "definition", "module": "Mathlib.Combinatorics.Young.YoungDiagram", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "YoungDiagram.mem_iff_lt_rowLen", "kind": "theorem", "module": "Mathlib.Combinatorics.Young.YoungDiagram", "is_tactic_proof": true, "tactics": ["rw", "push_neg", "exact"], "tactic_count": 3}
{"name": "YoungDiagram.row_eq_prod", "kind": "theorem", "module": "Mathlib.Combinatorics.Young.YoungDiagram", "is_tactic_proof": true, "tactics": ["ext", "simp", "and_congr_right_iff]", "rintro", "rfl"], "tactic_count": 5}
{"name": "YoungDiagram.rowLen_eq_card", "kind": "theorem", "module": "Mathlib.Combinatorics.Young.YoungDiagram", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "YoungDiagram.rowLen_anti", "kind": "theorem", "module": "Mathlib.Combinatorics.Young.YoungDiagram", "is_tactic_proof": true, "tactics": ["by_contra", "rw", "rw", "exact"], "tactic_count": 4}
{"name": "YoungDiagram.col", "kind": "definition", "module": "Mathlib.Combinatorics.Young.YoungDiagram", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "YoungDiagram.mem_col_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Young.YoungDiagram", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "YoungDiagram.mk_mem_col_iff", "kind": "theorem", "module": "Mathlib.Combinatorics.Young.YoungDiagram", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "YoungDiagram.exists_notMem_col", "kind": "theorem", "module": "Mathlib.Combinatorics.Young.YoungDiagram", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "YoungDiagram.colLen", "kind": "definition", "module": "Mathlib.Combinatorics.Young.YoungDiagram", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "YoungDiagram.colLen_transpose", "kind": "theorem", "module": "Mathlib.Combinatorics.Young.YoungDiagram", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "YoungDiagram.rowLen_transpose", "kind": "theorem", "module": "Mathlib.Combinatorics.Young.YoungDiagram", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "YoungDiagram.mem_iff_lt_colLen", "kind": "theorem", "module": "Mathlib.Combinatorics.Young.YoungDiagram", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "YoungDiagram.col_eq_prod", "kind": "theorem", "module": "Mathlib.Combinatorics.Young.YoungDiagram", "is_tactic_proof": true, "tactics": ["ext", "simp", "and_congr_right_iff]", "rintro", "rfl"], "tactic_count": 5}
{"name": "YoungDiagram.colLen_eq_card", "kind": "theorem", "module": "Mathlib.Combinatorics.Young.YoungDiagram", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "YoungDiagram.colLen_anti", "kind": "theorem", "module": "Mathlib.Combinatorics.Young.YoungDiagram", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "YoungDiagram.rowLens", "kind": "definition", "module": "Mathlib.Combinatorics.Young.YoungDiagram", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "YoungDiagram.get_rowLens", "kind": "theorem", "module": "Mathlib.Combinatorics.Young.YoungDiagram", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "YoungDiagram.length_rowLens", "kind": "theorem", "module": "Mathlib.Combinatorics.Young.YoungDiagram", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "YoungDiagram.rowLens_sorted", "kind": "theorem", "module": "Mathlib.Combinatorics.Young.YoungDiagram", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "YoungDiagram.pos_of_mem_rowLens", "kind": "theorem", "module": "Mathlib.Combinatorics.Young.YoungDiagram", "is_tactic_proof": true, "tactics": ["rw", "obtain", "rwa"], "tactic_count": 3}
{"name": "YoungDiagram.cellsOfRowLens", "kind": "definition", "module": "Mathlib.Combinatorics.Young.YoungDiagram", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "YoungDiagram.mem_cellsOfRowLens", "kind": "theorem", "module": "Mathlib.Combinatorics.Young.YoungDiagram", "is_tactic_proof": true, "tactics": ["induction", "simp", "rcases"], "tactic_count": 3}
{"name": "YoungDiagram.ofRowLens", "kind": "definition", "module": "Mathlib.Combinatorics.Young.YoungDiagram", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "YoungDiagram.mem_ofRowLens", "kind": "theorem", "module": "Mathlib.Combinatorics.Young.YoungDiagram", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "YoungDiagram.rowLens_length_ofRowLens", "kind": "theorem", "module": "Mathlib.Combinatorics.Young.YoungDiagram", "is_tactic_proof": false, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "YoungDiagram.rowLen_ofRowLens", "kind": "theorem", "module": "Mathlib.Combinatorics.Young.YoungDiagram", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "YoungDiagram.ofRowLens_to_rowLens_eq_self", "kind": "theorem", "module": "Mathlib.Combinatorics.Young.YoungDiagram", "is_tactic_proof": true, "tactics": ["ext", "simp", "simpa"], "tactic_count": 3}
{"name": "YoungDiagram.rowLens_ofRowLens_eq_self", "kind": "theorem", "module": "Mathlib.Combinatorics.Young.YoungDiagram", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "YoungDiagram.equivListRowLens", "kind": "definition", "module": "Mathlib.Combinatorics.Young.YoungDiagram", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ack", "kind": "definition", "module": "Mathlib.Computability.Ackermann", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ack_zero", "kind": "theorem", "module": "Mathlib.Computability.Ackermann", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ack_succ_zero", "kind": "theorem", "module": "Mathlib.Computability.Ackermann", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ack_succ_succ", "kind": "theorem", "module": "Mathlib.Computability.Ackermann", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ack_one", "kind": "theorem", "module": "Mathlib.Computability.Ackermann", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "ack_two", "kind": "theorem", "module": "Mathlib.Computability.Ackermann", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "ack_three", "kind": "theorem", "module": "Mathlib.Computability.Ackermann", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "calc"], "tactic_count": 5}
{"name": "ack_pos", "kind": "theorem", "module": "Mathlib.Computability.Ackermann", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_lt_ack_succ_left", "kind": "theorem", "module": "Mathlib.Computability.Ackermann", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_lt_ack_succ_right", "kind": "theorem", "module": "Mathlib.Computability.Ackermann", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ack_strictMono_right", "kind": "theorem", "module": "Mathlib.Computability.Ackermann", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ack_mono_right", "kind": "theorem", "module": "Mathlib.Computability.Ackermann", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ack_injective_right", "kind": "theorem", "module": "Mathlib.Computability.Ackermann", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ack_lt_iff_right", "kind": "theorem", "module": "Mathlib.Computability.Ackermann", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ack_le_iff_right", "kind": "theorem", "module": "Mathlib.Computability.Ackermann", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ack_inj_right", "kind": "theorem", "module": "Mathlib.Computability.Ackermann", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "max_ack_right", "kind": "theorem", "module": "Mathlib.Computability.Ackermann", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "add_lt_ack", "kind": "theorem", "module": "Mathlib.Computability.Ackermann", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "add_add_one_le_ack", "kind": "theorem", "module": "Mathlib.Computability.Ackermann", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lt_ack_left", "kind": "theorem", "module": "Mathlib.Computability.Ackermann", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lt_ack_right", "kind": "theorem", "module": "Mathlib.Computability.Ackermann", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Computability.Ackermann.0.ack_strict_mono_left'", "kind": "theorem", "module": "Mathlib.Computability.Ackermann", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ack_strictMono_left", "kind": "theorem", "module": "Mathlib.Computability.Ackermann", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ack_mono_left", "kind": "theorem", "module": "Mathlib.Computability.Ackermann", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ack_injective_left", "kind": "theorem", "module": "Mathlib.Computability.Ackermann", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ack_lt_iff_left", "kind": "theorem", "module": "Mathlib.Computability.Ackermann", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ack_le_iff_left", "kind": "theorem", "module": "Mathlib.Computability.Ackermann", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ack_inj_left", "kind": "theorem", "module": "Mathlib.Computability.Ackermann", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "max_ack_left", "kind": "theorem", "module": "Mathlib.Computability.Ackermann", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ack_le_ack", "kind": "theorem", "module": "Mathlib.Computability.Ackermann", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ack_succ_right_le_ack_succ_left", "kind": "theorem", "module": "Mathlib.Computability.Ackermann", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rw", "apply", "lia"], "tactic_count": 5}
{"name": "_private.Mathlib.Computability.Ackermann.0.sq_le_two_pow_add_one_minus_three", "kind": "theorem", "module": "Mathlib.Computability.Ackermann", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "ack_add_one_sq_lt_ack_add_three", "kind": "theorem", "module": "Mathlib.Computability.Ackermann", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ack_ack_lt_ack_max_add_two", "kind": "theorem", "module": "Mathlib.Computability.Ackermann", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ack_add_one_sq_lt_ack_add_four", "kind": "theorem", "module": "Mathlib.Computability.Ackermann", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ack_pair_lt", "kind": "theorem", "module": "Mathlib.Computability.Ackermann", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_lt_ack_of_nat_primrec", "kind": "theorem", "module": "Mathlib.Computability.Ackermann", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "refine", "rw", "apply", "left", "refine", "rw", "exact", "right", "refine", "rw", "exact", "obtain", "refine", "calc", "pair", "comp", "obtain", "exact", "obtain", "have", "intro", "induction", "zero", "apply", "lia", "succ", "simp", "apply", "rcases", "rw", "gcongr", "rw", "apply", "rcases", "rw", "exact", "rw", "apply", "rw", "exact", "ack_mono_left", "exact"], "tactic_count": 45}
{"name": "not_nat_primrec_ack_self", "kind": "theorem", "module": "Mathlib.Computability.Ackermann", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_primrec_ack_self", "kind": "theorem", "module": "Mathlib.Computability.Ackermann", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "not_primrec₂_ack", "kind": "theorem", "module": "Mathlib.Computability.Ackermann", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Partrec.Code.pappAck", "kind": "definition", "module": "Mathlib.Computability.Ackermann", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Partrec.Code.primrec_pappAck_step", "kind": "theorem", "module": "Mathlib.Computability.Ackermann", "is_tactic_proof": true, "tactics": ["apply_rules"], "tactic_count": 1}
{"name": "Nat.Partrec.Code.eval_pappAck_step_zero", "kind": "theorem", "module": "Mathlib.Computability.Ackermann", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.Partrec.Code.eval_pappAck_step_succ", "kind": "theorem", "module": "Mathlib.Computability.Ackermann", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.Partrec.Code.primrec_pappAck", "kind": "theorem", "module": "Mathlib.Computability.Ackermann", "is_tactic_proof": false, "tactics": ["suffices", "induction", "apply_rules"], "tactic_count": 3}
{"name": "Nat.Partrec.Code.eval_pappAck", "kind": "theorem", "module": "Mathlib.Computability.Ackermann", "is_tactic_proof": true, "tactics": ["induction", "case1", "case2", "case3"], "tactic_count": 4}
{"name": "computable₂_ack", "kind": "theorem", "module": "Mathlib.Computability.Ackermann", "is_tactic_proof": false, "tactics": ["apply", "change", "apply_rules", "simp"], "tactic_count": 4}
{"name": "_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.termε", "kind": "definition", "module": "Mathlib.Computability.AkraBazzi.AkraBazzi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence._aux_Mathlib_Computability_AkraBazzi_AkraBazzi___macroRules__private_Mathlib_Computability_AkraBazzi_AkraBazzi_0_AkraBazziRecurrence_termε_1", "kind": "definition", "module": "Mathlib.Computability.AkraBazzi.AkraBazzi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence._aux_Mathlib_Computability_AkraBazzi_AkraBazzi___unexpand_AkraBazziRecurrence_smoothingFn_1", "kind": "definition", "module": "Mathlib.Computability.AkraBazzi.AkraBazzi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AkraBazziRecurrence.eventually_deriv_rpow_p_mul_one_sub_smoothingFn", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.AkraBazzi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AkraBazziRecurrence.eventually_deriv_rpow_p_mul_one_add_smoothingFn", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.AkraBazzi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AkraBazziRecurrence.isEquivalent_deriv_rpow_p_mul_one_sub_smoothingFn", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.AkraBazzi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AkraBazziRecurrence.isEquivalent_deriv_rpow_p_mul_one_add_smoothingFn", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.AkraBazzi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AkraBazziRecurrence.isTheta_deriv_rpow_p_mul_one_sub_smoothingFn", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.AkraBazzi", "is_tactic_proof": true, "tactics": ["refine", "calc"], "tactic_count": 2}
{"name": "AkraBazziRecurrence.isTheta_deriv_rpow_p_mul_one_add_smoothingFn", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.AkraBazzi", "is_tactic_proof": true, "tactics": ["refine", "calc"], "tactic_count": 2}
{"name": "AkraBazziRecurrence.growsPolynomially_deriv_rpow_p_mul_one_sub_smoothingFn", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.AkraBazzi", "is_tactic_proof": true, "tactics": ["cases", "inl", "have", "filter_upwards", "have", "simp", "refine", "refine", "filter_upwards", "inr", "refine", "filter_upwards", "positivity"], "tactic_count": 13}
{"name": "AkraBazziRecurrence.growsPolynomially_deriv_rpow_p_mul_one_add_smoothingFn", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.AkraBazzi", "is_tactic_proof": true, "tactics": ["cases", "inl", "have", "filter_upwards", "have", "simp", "refine", "refine", "filter_upwards", "inr", "refine", "filter_upwards", "positivity"], "tactic_count": 13}
{"name": "AkraBazziRecurrence.isBigO_apply_r_sub_b", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.AkraBazzi", "is_tactic_proof": true, "tactics": ["let", "have", "have", "calc", "b", "have", "have", "calc", "b", "obtain", "rw", "refine", "have", "filter_upwards", "rw", "refine", "refine", "calc", "refine", "calc", "b"], "tactic_count": 21}
{"name": "AkraBazziRecurrence.rpow_p_mul_one_sub_smoothingFn_le", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.AkraBazzi", "is_tactic_proof": true, "tactics": ["rw", "intro", "let", "have", "refine", "differentiableOn_one_sub_smoothingFn", "rw", "rw", "exact", "have", "calc", "deriv", "filter_upwards", "rw", "refine", "calc", "calc", "filter_upwards", "rw", "have", "refine", "calc", "filter_upwards", "have", "simp", "refine", "simp_rw", "refine", "have", "have", "calc", "filter_upwards", "refine", "have", "have", "refine", "rwa", "calc", "calc", "b", "positivity", "filter_upwards", "have", "q", "have", "simp", "ring", "change", "rw", "exact"], "tactic_count": 50}
{"name": "AkraBazziRecurrence.rpow_p_mul_one_add_smoothingFn_ge", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.AkraBazzi", "is_tactic_proof": true, "tactics": ["rw", "intro", "let", "have", "refine", "differentiableOn_one_add_smoothingFn", "rw", "rw", "exact", "have", "calc", "deriv", "filter_upwards", "rw", "refine", "calc", "calc", "filter_upwards", "rw", "have", "refine", "calc", "exact", "filter_upwards", "have", "simp", "refine", "simp_rw", "refine", "have", "have", "calc", "exact", "filter_upwards", "refine", "have", "have", "refine", "change", "rw", "exact", "calc", "calc", "b", "positivity", "filter_upwards", "have", "q", "have", "simp", "ring", "change", "rw", "exact"], "tactic_count": 54}
{"name": "AkraBazziRecurrence.base_nonempty", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.AkraBazzi", "is_tactic_proof": true, "tactics": ["let", "have", "simp_rw", "have", "calc", "exact_mod_cast"], "tactic_count": 6}
{"name": "AkraBazziRecurrence.T_isBigO_smoothingFn_mul_asympBound", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.AkraBazzi", "is_tactic_proof": true, "tactics": ["let", "have", "rw", "obtain", "filter_upwards", "eventually_ge_atTop", "eventually_forall_ge_atTop.mpr", "eventually_forall_ge_atTop.mpr", "eventually_forall_ge_atTop.mpr", "eventually_forall_ge_atTop.mpr", "eventually_gt_atTop", "eventually_forall_ge_atTop.mpr", "eventually_forall_ge_atTop.mpr", "eventually_forall_ge_atTop.mpr", "eventually_forall_ge_atTop.mpr", "h_asympBound_pos", "h_sumTransform", "have", "let", "set", "refine", "have", "intro", "rw", "have", "have", "rw", "rw", "calc", "have", "have", "rw", "induction", "ind", "h_ind", "have", "exact_mod_cast", "calc", "have", "calc", "gcongr", "exact", "by_cases", "exact", "h_base", "simp_all", "mem_Ico,", "exact", "h_ind", "a", "g", "g", "g", "gcongr", "positivity", "refine", "rw", "exact", "exact", "g", "congr", "refine", "rw", "exact", "n", "g", "g", "gcongr", "positivity", "positivity", "exact", "ring", "rw", "gcongr", "refine", "rw", "calc", "gcongr", "rw", "exact"], "tactic_count": 80}
{"name": "AkraBazziRecurrence.smoothingFn_mul_asympBound_isBigO_T", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.AkraBazzi", "is_tactic_proof": true, "tactics": ["let", "have", "rw", "obtain", "filter_upwards", "eventually_ge_atTop", "eventually_forall_ge_atTop.mpr", "eventually_forall_ge_atTop.mpr", "eventually_forall_ge_atTop.mpr", "eventually_gt_atTop", "eventually_forall_ge_atTop.mpr", "eventually_forall_ge_atTop.mpr", "eventually_forall_ge_atTop.mpr", "eventually_forall_ge_atTop.mpr", "eventually_forall_ge_atTop.mpr", "h_smoothing_pos", "h_smoothingFn_floor", "have", "set", "base_min_def", "let", "have", "refine", "obtain", "calc", "have", "have", "rw", "exact", "have", "refine", "calc", "positivity", "refine", "have", "intro", "rw", "have", "have", "rw", "rw", "calc", "have", "have", "rw", "induction", "ind", "h_ind", "have", "exact_mod_cast", "calc", "have", "calc", "gcongr", "exact", "cases", "inl", "inr", "exact", "h_ind", "a", "g", "g", "g", "gcongr", "positivity", "refine", "rw", "exact", "exact", "g", "congr", "refine", "rw", "exact", "n", "g", "g", "gcongr", "positivity", "positivity", "exact", "ring", "rw", "gcongr", "refine", "rw", "calc", "gcongr", "refine", "calc", "exp"], "tactic_count": 92}
{"name": "AkraBazziRecurrence.isBigO_asympBound", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.AkraBazzi", "is_tactic_proof": true, "tactics": ["calc", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "AkraBazziRecurrence.isBigO_symm_asympBound", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.AkraBazzi", "is_tactic_proof": true, "tactics": ["calc", "asympBound", "refine", "rw", "exact"], "tactic_count": 5}
{"name": "AkraBazziRecurrence.isTheta_asympBound", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.AkraBazzi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AkraBazziRecurrence.GrowsPolynomially", "kind": "definition", "module": "Mathlib.Computability.AkraBazzi.GrowsPolynomially", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AkraBazziRecurrence.GrowsPolynomially.congr_of_eventuallyEq", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.GrowsPolynomially", "is_tactic_proof": true, "tactics": ["intro", "have", "obtain", "refine", "filter_upwards", "intro", "rw", "exact"], "tactic_count": 8}
{"name": "AkraBazziRecurrence.GrowsPolynomially.iff_eventuallyEq", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.GrowsPolynomially", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_le", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.GrowsPolynomially", "is_tactic_proof": true, "tactics": ["obtain", "refine", "filter_upwards", "exact"], "tactic_count": 4}
{"name": "AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_le_nat", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.GrowsPolynomially", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_ge", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.GrowsPolynomially", "is_tactic_proof": true, "tactics": ["obtain", "refine", "filter_upwards", "exact"], "tactic_count": 4}
{"name": "AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_ge_nat", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.GrowsPolynomially", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "AkraBazziRecurrence.GrowsPolynomially.eventually_zero_of_frequently_zero", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.GrowsPolynomially", "is_tactic_proof": true, "tactics": ["obtain", "rw", "filter_upwards", "obtain", "have", "calc", "have", "intro", "induction", "zero", "simp", "specialize", "simp", "refine", "simp", "simp", "succ", "intro", "simp", "have", "calc", "x", "specialize", "specialize", "rw", "gcongr", "norm_num", "lia", "simp", "refine", "rw", "have", "have", "rw", "rw", "exact", "have", "simp", "exact", "refine", "rw", "refine", "rw", "simp", "calc", "rw", "refine", "rw", "simp", "have", "rw", "refine", "rw", "exact", "exact_mod_cast"], "tactic_count": 55}
{"name": "AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.GrowsPolynomially", "is_tactic_proof": true, "tactics": ["obtain", "left", "filter_upwards", "have", "rw", "exact", "have", "have", "rw", "have", "exact", "right", "filter_upwards", "have", "rw", "exact", "have", "have", "rw", "have", "exact", "have", "simp", "rw", "obtain", "refine", "rw", "refine", "refine", "grind", "intro", "have", "have", "grind", "obtain", "cases", "inl", "inr", "right", "filter_upwards", "exact"], "tactic_count": 41}
{"name": "AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_zero_or_pos_or_neg", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.GrowsPolynomially", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "cases", "inl", "refine", "simp", "rw", "exact", "inr", "refine", "simp", "rw", "exact"], "tactic_count": 13}
{"name": "AkraBazziRecurrence.GrowsPolynomially.neg", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.GrowsPolynomially", "is_tactic_proof": true, "tactics": ["intro", "obtain", "refine", "filter_upwards", "intro", "simp", "exact"], "tactic_count": 7}
{"name": "AkraBazziRecurrence.GrowsPolynomially.neg_iff", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.GrowsPolynomially", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AkraBazziRecurrence.GrowsPolynomially.abs", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.GrowsPolynomially", "is_tactic_proof": true, "tactics": ["cases", "inl", "hf", "have", "filter_upwards", "rw", "rw", "exact", "inr", "hf", "have", "filter_upwards", "simp", "rw", "exact"], "tactic_count": 15}
{"name": "AkraBazziRecurrence.GrowsPolynomially.norm", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.GrowsPolynomially", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "AkraBazziRecurrence.growsPolynomially_const", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.GrowsPolynomially", "is_tactic_proof": true, "tactics": ["refine", "filter_upwards", "simp"], "tactic_count": 3}
{"name": "AkraBazziRecurrence.growsPolynomially_id", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.GrowsPolynomially", "is_tactic_proof": true, "tactics": ["intro", "refine", "refine", "filter_upwards", "simp", "exact"], "tactic_count": 6}
{"name": "AkraBazziRecurrence.GrowsPolynomially.mul", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.GrowsPolynomially", "is_tactic_proof": false, "tactics": ["suffices", "cases", "inl", "cases", "inl", "hg", "have", "filter_upwards", "rw", "rwa", "inr", "hg", "have", "filter_upwards", "simp", "simp", "exact", "inr", "cases", "inl", "hg", "have", "filter_upwards", "rw", "simp", "exact", "inr", "hg", "have", "filter_upwards", "simp", "simp", "exact", "intro", "have", "have", "obtain", "obtain", "refine", "refine", "filter_upwards", "intro", "refine", "calc", "c₁", "gcongr", "exact", "exact", "calc", "f", "gcongr", "exact", "exact"], "tactic_count": 53}
{"name": "AkraBazziRecurrence.GrowsPolynomially.const_mul", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.GrowsPolynomially", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AkraBazziRecurrence.GrowsPolynomially.add", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.GrowsPolynomially", "is_tactic_proof": true, "tactics": ["intro", "have", "have", "obtain", "obtain", "refine", "refine", "filter_upwards", "intro", "have", "calc", "b", "have", "have", "refine", "calc", "min", "gcongr", "exact", "exact", "gcongr", "exact", "exact", "calc", "max", "gcongr", "exact", "exact", "gcongr", "exact", "exact"], "tactic_count": 31}
{"name": "AkraBazziRecurrence.GrowsPolynomially.add_isLittleO", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.GrowsPolynomially", "is_tactic_proof": true, "tactics": ["intro", "have", "rw", "cases", "inl", "have", "obtain", "specialize", "refine", "filter_upwards", "hx_nonneg", "have", "have", "calc", "have", "calc", "have", "calc", "f", "intro", "have", "have", "calc", "refine", "calc", "f", "calc", "inr", "have", "obtain", "specialize", "refine", "filter_upwards", "hx_nonneg", "have", "have", "calc", "have", "calc", "have", "calc", "f", "rw", "gcongr", "refine", "rwa", "intro", "have", "have", "calc", "refine", "calc", "f", "rw", "gcongr", "refine", "rwa", "calc", "rw", "gcongr", "rwa"], "tactic_count": 61}
{"name": "AkraBazziRecurrence.GrowsPolynomially.inv", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.GrowsPolynomially", "is_tactic_proof": true, "tactics": ["cases", "inl", "refine", "have", "filter_upwards", "intro", "simp", "inr", "hf_pos_or_neg", "suffices", "cases", "inl", "hf", "have", "filter_upwards", "rw", "rwa", "inr", "hf", "have", "filter_upwards", "simp", "rw", "exact", "have", "cases", "inl", "inr", "simp", "have", "intro", "have", "obtain", "refine", "refine", "filter_upwards", "intro", "have", "refine", "rw", "gcongr", "exact", "rw", "gcongr", "exact"], "tactic_count": 45}
{"name": "AkraBazziRecurrence.GrowsPolynomially.div", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.GrowsPolynomially", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "AkraBazziRecurrence.GrowsPolynomially.rpow", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.GrowsPolynomially", "is_tactic_proof": true, "tactics": ["intro", "obtain", "have", "have", "cases", "inl", "refine", "refine", "filter_upwards", "intro", "have", "refine", "calc", "c₁", "calc", "inr", "refine", "filter_upwards", "intro", "simp", "simp", "rw", "refine", "refine", "filter_upwards", "intro", "refine", "calc", "c₂", "calc", "have", "rw", "exact"], "tactic_count": 33}
{"name": "AkraBazziRecurrence.GrowsPolynomially.pow", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.GrowsPolynomially", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "AkraBazziRecurrence.GrowsPolynomially.zpow", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.GrowsPolynomially", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "AkraBazziRecurrence.growsPolynomially_rpow", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.GrowsPolynomially", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AkraBazziRecurrence.growsPolynomially_pow", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.GrowsPolynomially", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AkraBazziRecurrence.growsPolynomially_zpow", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.GrowsPolynomially", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AkraBazziRecurrence.growsPolynomially_log", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.GrowsPolynomially", "is_tactic_proof": true, "tactics": ["intro", "have", "refine", "refine", "have", "filter_upwards", "h_tendsto.eventually", "x", "intro", "refine", "calc", "rw", "gcongr", "calc", "exact"], "tactic_count": 15}
{"name": "AkraBazziRecurrence.GrowsPolynomially.of_isTheta", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.GrowsPolynomially", "is_tactic_proof": true, "tactics": ["intro", "have", "have", "have", "obtain", "obtain", "have", "obtain", "obtain", "have", "have", "refine", "refine", "have", "have", "filter_upwards", "hg_bound", "intro", "have", "calc", "b", "have", "refine", "calc", "c₁", "exact", "rw", "exact", "calc", "f", "gcongr", "rw", "exact"], "tactic_count": 33}
{"name": "AkraBazziRecurrence.GrowsPolynomially.of_isEquivalent", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.GrowsPolynomially", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "AkraBazziRecurrence.GrowsPolynomially.of_isEquivalent_const", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.GrowsPolynomially", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AkraBazziRecurrence.min_bi", "kind": "definition", "module": "Mathlib.Computability.AkraBazzi.SumTransform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AkraBazziRecurrence.max_bi", "kind": "definition", "module": "Mathlib.Computability.AkraBazzi.SumTransform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AkraBazziRecurrence.min_bi_le", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.SumTransform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AkraBazziRecurrence.max_bi_le", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.SumTransform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AkraBazziRecurrence.isLittleO_self_div_log_id", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.SumTransform", "is_tactic_proof": true, "tactics": ["calc", "refine", "refine", "calc"], "tactic_count": 4}
{"name": "AkraBazziRecurrence.dist_r_b'", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.SumTransform", "is_tactic_proof": true, "tactics": ["rw", "intro", "simpa"], "tactic_count": 3}
{"name": "AkraBazziRecurrence.eventually_b_le_r", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.SumTransform", "is_tactic_proof": true, "tactics": ["filter_upwards", "have", "rw", "calc"], "tactic_count": 4}
{"name": "AkraBazziRecurrence.eventually_r_le_b", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.SumTransform", "is_tactic_proof": true, "tactics": ["filter_upwards", "calc", "r"], "tactic_count": 3}
{"name": "AkraBazziRecurrence.eventually_r_lt_n", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.SumTransform", "is_tactic_proof": true, "tactics": ["filter_upwards"], "tactic_count": 1}
{"name": "AkraBazziRecurrence.eventually_bi_mul_le_r", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.SumTransform", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "have", "filter_upwards", "simp", "calc", "b", "congr", "exact"], "tactic_count": 10}
{"name": "AkraBazziRecurrence.bi_min_div_two_lt_one", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.SumTransform", "is_tactic_proof": true, "tactics": ["have", "calc", "b"], "tactic_count": 3}
{"name": "AkraBazziRecurrence.bi_min_div_two_pos", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.SumTransform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AkraBazziRecurrence.exists_eventually_const_mul_le_r", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.SumTransform", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "AkraBazziRecurrence.eventually_r_ge", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.SumTransform", "is_tactic_proof": true, "tactics": ["obtain", "filter_upwards", "have", "calc", "rw", "exact"], "tactic_count": 6}
{"name": "AkraBazziRecurrence.tendsto_atTop_r", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.SumTransform", "is_tactic_proof": true, "tactics": ["rw", "intro", "have", "rw", "exact_mod_cast"], "tactic_count": 5}
{"name": "AkraBazziRecurrence.tendsto_atTop_r_real", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.SumTransform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AkraBazziRecurrence.exists_eventually_r_le_const_mul", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.SumTransform", "is_tactic_proof": true, "tactics": ["let", "have", "have", "have", "linarith", "have", "have", "have", "calc", "b", "refine", "have", "rw", "have", "filter_upwards", "intro", "rw", "simp", "calc", "r"], "tactic_count": 20}
{"name": "AkraBazziRecurrence.eventually_r_pos", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.SumTransform", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "AkraBazziRecurrence.eventually_log_b_mul_pos", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.SumTransform", "is_tactic_proof": true, "tactics": ["rw", "intro", "have", "exact"], "tactic_count": 4}
{"name": "AkraBazziRecurrence.T_pos", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.SumTransform", "is_tactic_proof": true, "tactics": ["induction", "ind", "cases", "inl", "inr", "rw", "have", "refine", "exact"], "tactic_count": 9}
{"name": "AkraBazziRecurrence.T_nonneg", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.SumTransform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AkraBazziRecurrence.smoothingFn", "kind": "definition", "module": "Mathlib.Computability.AkraBazzi.SumTransform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Computability.AkraBazzi.SumTransform.0.AkraBazziRecurrence.termε", "kind": "definition", "module": "Mathlib.Computability.AkraBazzi.SumTransform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Computability.AkraBazzi.SumTransform.0.AkraBazziRecurrence._aux_Mathlib_Computability_AkraBazzi_SumTransform___macroRules__private_Mathlib_Computability_AkraBazzi_SumTransform_0_AkraBazziRecurrence_termε_1", "kind": "definition", "module": "Mathlib.Computability.AkraBazzi.SumTransform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Computability.AkraBazzi.SumTransform.0.AkraBazziRecurrence._aux_Mathlib_Computability_AkraBazzi_SumTransform___unexpand_AkraBazziRecurrence_smoothingFn_1", "kind": "definition", "module": "Mathlib.Computability.AkraBazzi.SumTransform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AkraBazziRecurrence.one_add_smoothingFn_le_two", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.SumTransform", "is_tactic_proof": true, "tactics": ["simp", "gcongr", "have", "calc", "rw", "calc"], "tactic_count": 6}
{"name": "AkraBazziRecurrence.isLittleO_smoothingFn_one", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.SumTransform", "is_tactic_proof": true, "tactics": ["unfold", "refine", "simp", "exact"], "tactic_count": 4}
{"name": "AkraBazziRecurrence.isEquivalent_one_add_smoothingFn_one", "kind": "theorem", "module": "Mathlib.Computability.AkraBazzi.SumTransform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ContextFreeGrammar.generates_reverse_comm", "kind": "theorem", "module": "Mathlib.Computability.ContextFreeGrammar", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContextFreeGrammar.language_reverse", "kind": "theorem", "module": "Mathlib.Computability.ContextFreeGrammar", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Language.IsContextFree.reverse", "kind": "theorem", "module": "Mathlib.Computability.ContextFreeGrammar", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "DFA.instInhabited", "kind": "instance", "module": "Mathlib.Computability.DFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFA.evalFrom", "kind": "definition", "module": "Mathlib.Computability.DFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFA.evalFrom_nil", "kind": "theorem", "module": "Mathlib.Computability.DFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFA.evalFrom_cons", "kind": "theorem", "module": "Mathlib.Computability.DFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFA.evalFrom_singleton", "kind": "theorem", "module": "Mathlib.Computability.DFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFA.evalFrom_append_singleton", "kind": "theorem", "module": "Mathlib.Computability.DFA", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DFA.eval", "kind": "definition", "module": "Mathlib.Computability.DFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFA.eval_nil", "kind": "theorem", "module": "Mathlib.Computability.DFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFA.eval_singleton", "kind": "theorem", "module": "Mathlib.Computability.DFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFA.eval_append_singleton", "kind": "theorem", "module": "Mathlib.Computability.DFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFA.evalFrom_of_append", "kind": "theorem", "module": "Mathlib.Computability.DFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFA.acceptsFrom", "kind": "definition", "module": "Mathlib.Computability.DFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFA.mem_acceptsFrom", "kind": "theorem", "module": "Mathlib.Computability.DFA", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "DFA.accepts", "kind": "definition", "module": "Mathlib.Computability.DFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFA.mem_accepts", "kind": "theorem", "module": "Mathlib.Computability.DFA", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "DFA.evalFrom_split", "kind": "theorem", "module": "Mathlib.Computability.DFA", "is_tactic_proof": false, "tactics": ["obtain", "wlog", "exact", "refine", "rw", "simp", "omega", "intro", "have", "simp", "omega", "have", "rw", "min_eq_left", "use", "rwa"], "tactic_count": 16}
{"name": "DFA.evalFrom_of_pow", "kind": "theorem", "module": "Mathlib.Computability.DFA", "is_tactic_proof": true, "tactics": ["rw", "rcases", "induction", "nil", "cons", "have", "rw", "rw", "apply", "intro", "exact"], "tactic_count": 11}
{"name": "DFA.pumping_lemma", "kind": "theorem", "module": "Mathlib.Computability.DFA", "is_tactic_proof": true, "tactics": ["obtain", "use", "intro", "rw", "rcases", "rw", "rcases", "rw", "substs", "have", "rwa"], "tactic_count": 11}
{"name": "DFA.comap", "kind": "definition", "module": "Mathlib.Computability.DFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFA.comap_id", "kind": "theorem", "module": "Mathlib.Computability.DFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFA.evalFrom_comap", "kind": "theorem", "module": "Mathlib.Computability.DFA", "is_tactic_proof": true, "tactics": ["induction", "nil", "append_singleton"], "tactic_count": 3}
{"name": "DFA.eval_comap", "kind": "theorem", "module": "Mathlib.Computability.DFA", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DFA.accepts_comap", "kind": "theorem", "module": "Mathlib.Computability.DFA", "is_tactic_proof": true, "tactics": ["ext", "conv", "rhs", "rw", "simp"], "tactic_count": 5}
{"name": "DFA.reindex", "kind": "definition", "module": "Mathlib.Computability.DFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFA.reindex_refl", "kind": "theorem", "module": "Mathlib.Computability.DFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFA.symm_reindex", "kind": "theorem", "module": "Mathlib.Computability.DFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFA.evalFrom_reindex", "kind": "theorem", "module": "Mathlib.Computability.DFA", "is_tactic_proof": true, "tactics": ["induction", "nil", "append_singleton"], "tactic_count": 3}
{"name": "DFA.eval_reindex", "kind": "theorem", "module": "Mathlib.Computability.DFA", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DFA.accepts_reindex", "kind": "theorem", "module": "Mathlib.Computability.DFA", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "DFA.comap_reindex", "kind": "theorem", "module": "Mathlib.Computability.DFA", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DFA.instCompl", "kind": "instance", "module": "Mathlib.Computability.DFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFA.compl_def", "kind": "theorem", "module": "Mathlib.Computability.DFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFA.acceptsFrom_compl", "kind": "theorem", "module": "Mathlib.Computability.DFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFA.accepts_compl", "kind": "theorem", "module": "Mathlib.Computability.DFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFA.union", "kind": "definition", "module": "Mathlib.Computability.DFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFA.acceptsFrom_union", "kind": "theorem", "module": "Mathlib.Computability.DFA", "is_tactic_proof": true, "tactics": ["ext", "simp", "rw", "simp_rw", "induction", "nil", "cons"], "tactic_count": 7}
{"name": "DFA.accepts_union", "kind": "theorem", "module": "Mathlib.Computability.DFA", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DFA.inter", "kind": "definition", "module": "Mathlib.Computability.DFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFA.acceptsFrom_inter", "kind": "theorem", "module": "Mathlib.Computability.DFA", "is_tactic_proof": true, "tactics": ["ext", "simp", "simp_rw", "induction", "nil", "cons"], "tactic_count": 6}
{"name": "DFA.accepts_inter", "kind": "theorem", "module": "Mathlib.Computability.DFA", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Language.IsRegular", "kind": "definition", "module": "Mathlib.Computability.DFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Computability.DFA.0.Language.isRegular_iff.helper", "kind": "theorem", "module": "Mathlib.Computability.DFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.isRegular_iff", "kind": "theorem", "module": "Mathlib.Computability.DFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.IsRegular.compl", "kind": "theorem", "module": "Mathlib.Computability.DFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.IsRegular.of_compl", "kind": "theorem", "module": "Mathlib.Computability.DFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.IsRegular_compl", "kind": "theorem", "module": "Mathlib.Computability.DFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.IsRegular.add", "kind": "theorem", "module": "Mathlib.Computability.DFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.IsRegular.inf", "kind": "theorem", "module": "Mathlib.Computability.DFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computability.Encoding.encode_injective", "kind": "theorem", "module": "Mathlib.Computability.Encoding", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "Computability.Γ.fintype", "kind": "instance", "module": "Mathlib.Computability.Encoding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computability.Γ'", "kind": "inductive", "module": "Mathlib.Computability.Encoding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computability.instDecidableEqΓ'", "kind": "instance", "module": "Mathlib.Computability.Encoding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computability.instFintypeΓ'", "kind": "instance", "module": "Mathlib.Computability.Encoding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computability.inhabitedΓ'", "kind": "instance", "module": "Mathlib.Computability.Encoding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computability.inclusionBoolΓ'", "kind": "definition", "module": "Mathlib.Computability.Encoding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computability.sectionΓ'Bool", "kind": "definition", "module": "Mathlib.Computability.Encoding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computability.sectionΓ'Bool_inclusionBoolΓ'", "kind": "theorem", "module": "Mathlib.Computability.Encoding", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Computability.inclusionBoolΓ'_injective", "kind": "theorem", "module": "Mathlib.Computability.Encoding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computability.encodePosNum", "kind": "definition", "module": "Mathlib.Computability.Encoding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computability.encodeNum", "kind": "definition", "module": "Mathlib.Computability.Encoding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computability.encodeNat", "kind": "definition", "module": "Mathlib.Computability.Encoding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computability.decodePosNum", "kind": "definition", "module": "Mathlib.Computability.Encoding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computability.decodeNum", "kind": "definition", "module": "Mathlib.Computability.Encoding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computability.decodeNat", "kind": "definition", "module": "Mathlib.Computability.Encoding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computability.encodePosNum_nonempty", "kind": "theorem", "module": "Mathlib.Computability.Encoding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computability.decode_encodePosNum", "kind": "theorem", "module": "Mathlib.Computability.Encoding", "is_tactic_proof": true, "tactics": ["induction", "one", "bit1", "rw", "exact", "bit0"], "tactic_count": 6}
{"name": "Computability.decode_encodeNum", "kind": "theorem", "module": "Mathlib.Computability.Encoding", "is_tactic_proof": true, "tactics": ["obtain", "rfl", "rw", "rw", "exact"], "tactic_count": 5}
{"name": "Computability.decode_encodeNat", "kind": "theorem", "module": "Mathlib.Computability.Encoding", "is_tactic_proof": true, "tactics": ["conv_rhs", "exact"], "tactic_count": 2}
{"name": "Computability.encodingNatBool", "kind": "definition", "module": "Mathlib.Computability.Encoding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computability.finEncodingNatBool", "kind": "definition", "module": "Mathlib.Computability.Encoding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computability.encodingNatΓ'", "kind": "definition", "module": "Mathlib.Computability.Encoding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computability.finEncodingNatΓ'", "kind": "definition", "module": "Mathlib.Computability.Encoding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computability.unaryEncodeNat", "kind": "definition", "module": "Mathlib.Computability.Encoding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computability.unaryDecodeNat", "kind": "definition", "module": "Mathlib.Computability.Encoding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computability.unary_decode_encode_nat", "kind": "theorem", "module": "Mathlib.Computability.Encoding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computability.unaryFinEncodingNat", "kind": "definition", "module": "Mathlib.Computability.Encoding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computability.encodeBool", "kind": "definition", "module": "Mathlib.Computability.Encoding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computability.decodeBool", "kind": "definition", "module": "Mathlib.Computability.Encoding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computability.decode_encodeBool", "kind": "theorem", "module": "Mathlib.Computability.Encoding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computability.finEncodingBoolBool", "kind": "definition", "module": "Mathlib.Computability.Encoding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computability.inhabitedFinEncoding", "kind": "instance", "module": "Mathlib.Computability.Encoding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computability.inhabitedEncoding", "kind": "instance", "module": "Mathlib.Computability.Encoding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computability.Encoding.card_le_card_list", "kind": "theorem", "module": "Mathlib.Computability.Encoding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computability.Encoding.card_le_aleph0", "kind": "theorem", "module": "Mathlib.Computability.Encoding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computability.FinEncoding.card_le_aleph0", "kind": "theorem", "module": "Mathlib.Computability.Encoding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "εNFA.εClosure", "kind": "inductive", "module": "Mathlib.Computability.EpsilonNFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "εNFA.subset_εClosure", "kind": "theorem", "module": "Mathlib.Computability.EpsilonNFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "εNFA.εClosure_empty", "kind": "theorem", "module": "Mathlib.Computability.EpsilonNFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "εNFA.εClosure_univ", "kind": "theorem", "module": "Mathlib.Computability.EpsilonNFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "εNFA.mem_εClosure_iff_exists", "kind": "theorem", "module": "Mathlib.Computability.EpsilonNFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "εNFA.stepSet", "kind": "definition", "module": "Mathlib.Computability.EpsilonNFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "εNFA.mem_stepSet_iff", "kind": "theorem", "module": "Mathlib.Computability.EpsilonNFA", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "εNFA.stepSet_empty", "kind": "theorem", "module": "Mathlib.Computability.EpsilonNFA", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "εNFA.evalFrom", "kind": "definition", "module": "Mathlib.Computability.EpsilonNFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "εNFA.evalFrom_nil", "kind": "theorem", "module": "Mathlib.Computability.EpsilonNFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "εNFA.evalFrom_singleton", "kind": "theorem", "module": "Mathlib.Computability.EpsilonNFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "εNFA.evalFrom_append_singleton", "kind": "theorem", "module": "Mathlib.Computability.EpsilonNFA", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "εNFA.evalFrom_empty", "kind": "theorem", "module": "Mathlib.Computability.EpsilonNFA", "is_tactic_proof": true, "tactics": ["induction", "nil", "append_singleton"], "tactic_count": 3}
{"name": "εNFA.mem_evalFrom_iff_exists", "kind": "theorem", "module": "Mathlib.Computability.EpsilonNFA", "is_tactic_proof": true, "tactics": ["induction", "nil", "append_singleton", "simp_rw", "tauto"], "tactic_count": 5}
{"name": "εNFA.eval", "kind": "definition", "module": "Mathlib.Computability.EpsilonNFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "εNFA.eval_nil", "kind": "theorem", "module": "Mathlib.Computability.EpsilonNFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "εNFA.eval_singleton", "kind": "theorem", "module": "Mathlib.Computability.EpsilonNFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "εNFA.eval_append_singleton", "kind": "theorem", "module": "Mathlib.Computability.EpsilonNFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "εNFA.accepts", "kind": "definition", "module": "Mathlib.Computability.EpsilonNFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "εNFA.IsPath", "kind": "inductive", "module": "Mathlib.Computability.EpsilonNFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "εNFA.isPath_nil", "kind": "theorem", "module": "Mathlib.Computability.EpsilonNFA", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "εNFA.isPath_singleton", "kind": "theorem", "module": "Mathlib.Computability.EpsilonNFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "εNFA.isPath_append", "kind": "theorem", "module": "Mathlib.Computability.EpsilonNFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "εNFA.mem_εClosure_iff_exists_path", "kind": "theorem", "module": "Mathlib.Computability.EpsilonNFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "εNFA.mem_evalFrom_iff_exists_path", "kind": "theorem", "module": "Mathlib.Computability.EpsilonNFA", "is_tactic_proof": true, "tactics": ["induction", "nil", "rw", "constructor", "intro", "use", "rw", "trivial", "simp_rw", "intro", "exact", "append_singleton", "rw", "constructor", "intro", "obtain", "rw", "simp_rw", "obtain", "use", "rw", "tauto", "simp_rw", "intro", "rw", "obtain", "use", "rw", "simp_rw", "tauto"], "tactic_count": 30}
{"name": "εNFA.mem_accepts_iff_exists_path", "kind": "theorem", "module": "Mathlib.Computability.EpsilonNFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "εNFA.toNFA", "kind": "definition", "module": "Mathlib.Computability.EpsilonNFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "εNFA.toNFA_evalFrom_match", "kind": "theorem", "module": "Mathlib.Computability.EpsilonNFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "εNFA.toNFA_correct", "kind": "theorem", "module": "Mathlib.Computability.EpsilonNFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "εNFA.pumping_lemma", "kind": "theorem", "module": "Mathlib.Computability.EpsilonNFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NFA.toεNFA", "kind": "definition", "module": "Mathlib.Computability.EpsilonNFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NFA.toεNFA_εClosure", "kind": "theorem", "module": "Mathlib.Computability.EpsilonNFA", "is_tactic_proof": true, "tactics": ["ext", "refine", "rintro", "exact", "cases"], "tactic_count": 5}
{"name": "NFA.toεNFA_evalFrom_match", "kind": "theorem", "module": "Mathlib.Computability.EpsilonNFA", "is_tactic_proof": true, "tactics": ["rw", "suffices", "ext", "simp", "apply", "simp", "intro", "rw", "rfl"], "tactic_count": 9}
{"name": "NFA.toεNFA_correct", "kind": "theorem", "module": "Mathlib.Computability.EpsilonNFA", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "εNFA.instZero", "kind": "instance", "module": "Mathlib.Computability.EpsilonNFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "εNFA.instOne", "kind": "instance", "module": "Mathlib.Computability.EpsilonNFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "εNFA.instInhabited", "kind": "instance", "module": "Mathlib.Computability.EpsilonNFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "εNFA.step_zero", "kind": "theorem", "module": "Mathlib.Computability.EpsilonNFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "εNFA.step_one", "kind": "theorem", "module": "Mathlib.Computability.EpsilonNFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "εNFA.start_zero", "kind": "theorem", "module": "Mathlib.Computability.EpsilonNFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "εNFA.start_one", "kind": "theorem", "module": "Mathlib.Computability.EpsilonNFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "εNFA.accept_zero", "kind": "theorem", "module": "Mathlib.Computability.EpsilonNFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "εNFA.accept_one", "kind": "theorem", "module": "Mathlib.Computability.EpsilonNFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Partrec.merge'", "kind": "theorem", "module": "Mathlib.Computability.Halting", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "have", "refine", "have", "x", "intro", "obtain", "revert", "simp", "rcases", "exact", "subst", "exact", "refine", "intro", "rw", "simp", "obtain", "refine", "simp", "refine", "rcases", "exact", "exact"], "tactic_count": 25}
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{"name": "Partrec.cond", "kind": "theorem", "module": "Mathlib.Computability.Halting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Partrec.sumCasesOn", "kind": "theorem", "module": "Mathlib.Computability.Halting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComputablePred", "kind": "definition", "module": "Mathlib.Computability.Halting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComputablePred.decide", "kind": "theorem", "module": "Mathlib.Computability.Halting", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "Computable.computablePred", "kind": "theorem", "module": "Mathlib.Computability.Halting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "computablePred_iff_computable_decide", "kind": "theorem", "module": "Mathlib.Computability.Halting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimrecPred.computablePred", "kind": "theorem", "module": "Mathlib.Computability.Halting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "REPred", "kind": "definition", "module": "Mathlib.Computability.Halting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "REPred.of_eq", "kind": "theorem", "module": "Mathlib.Computability.Halting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Partrec.dom_re", "kind": "theorem", "module": "Mathlib.Computability.Halting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComputablePred.of_eq", "kind": "theorem", "module": "Mathlib.Computability.Halting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComputablePred.computable_iff", "kind": "theorem", "module": "Mathlib.Computability.Halting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComputablePred.not", "kind": "theorem", "module": "Mathlib.Computability.Halting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComputablePred.ite", "kind": "theorem", "module": "Mathlib.Computability.Halting", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ComputablePred.to_re", "kind": "theorem", "module": "Mathlib.Computability.Halting", "is_tactic_proof": true, "tactics": ["obtain", "unfold", "dsimp", "refine", "cases"], "tactic_count": 5}
{"name": "ComputablePred.rice", "kind": "theorem", "module": "Mathlib.Computability.Halting", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "fixed_point₂", "simp", "by_cases", "simp", "change", "rwa", "simp", "rw", "contradiction"], "tactic_count": 11}
{"name": "ComputablePred.rice₂", "kind": "theorem", "module": "Mathlib.Computability.Halting", "is_tactic_proof": true, "tactics": ["classical", "exact", "have", "or_iff_not_imp_left.2", "let", "rice"], "tactic_count": 6}
{"name": "ComputablePred.halting_problem_re", "kind": "theorem", "module": "Mathlib.Computability.Halting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComputablePred.halting_problem", "kind": "theorem", "module": "Mathlib.Computability.Halting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComputablePred.computable_iff_re_compl_re", "kind": "theorem", "module": "Mathlib.Computability.Halting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComputablePred.computable_iff_re_compl_re'", "kind": "theorem", "module": "Mathlib.Computability.Halting", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "ComputablePred.halting_problem_not_re", "kind": "theorem", "module": "Mathlib.Computability.Halting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Partrec'", "kind": "inductive", "module": "Mathlib.Computability.Halting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Partrec'.to_part", "kind": "theorem", "module": "Mathlib.Computability.Halting", "is_tactic_proof": true, "tactics": ["induction", "prim", "comp", "rfind", "have", "have", "exact"], "tactic_count": 7}
{"name": "Nat.Partrec'.of_eq", "kind": "theorem", "module": "Mathlib.Computability.Halting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Partrec'.of_prim", "kind": "theorem", "module": "Mathlib.Computability.Halting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Partrec'.head", "kind": "theorem", "module": "Mathlib.Computability.Halting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Partrec'.tail", "kind": "theorem", "module": "Mathlib.Computability.Halting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Partrec'.bind", "kind": "theorem", "module": "Mathlib.Computability.Halting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Partrec'.map", "kind": "theorem", "module": "Mathlib.Computability.Halting", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Nat.Partrec'.Vec", "kind": "definition", "module": "Mathlib.Computability.Halting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Partrec'.Vec.prim", "kind": "theorem", "module": "Mathlib.Computability.Halting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Partrec'.nil", "kind": "theorem", "module": "Mathlib.Computability.Halting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Partrec'.cons", "kind": "theorem", "module": "Mathlib.Computability.Halting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Partrec'.idv", "kind": "theorem", "module": "Mathlib.Computability.Halting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Partrec'.comp'", "kind": "theorem", "module": "Mathlib.Computability.Halting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Partrec'.comp₁", "kind": "theorem", "module": "Mathlib.Computability.Halting", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Nat.Partrec'.rfindOpt", "kind": "theorem", "module": "Mathlib.Computability.Halting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Partrec'.of_part", "kind": "theorem", "module": "Mathlib.Computability.Halting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Partrec'.part_iff", "kind": "theorem", "module": "Mathlib.Computability.Halting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Partrec'.part_iff₁", "kind": "theorem", "module": "Mathlib.Computability.Halting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Partrec'.part_iff₂", "kind": "theorem", "module": "Mathlib.Computability.Halting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Partrec'.vec_iff", "kind": "theorem", "module": "Mathlib.Computability.Halting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language", "kind": "definition", "module": "Mathlib.Computability.Language", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.instMembershipList", "kind": "instance", "module": "Mathlib.Computability.Language", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.instSingletonList", "kind": "instance", "module": "Mathlib.Computability.Language", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.instInsertList", "kind": "instance", "module": "Mathlib.Computability.Language", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.instCompleteAtomicBooleanAlgebra", "kind": "instance", "module": "Mathlib.Computability.Language", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.instZero", "kind": "instance", "module": "Mathlib.Computability.Language", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.instOne", "kind": "instance", "module": "Mathlib.Computability.Language", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.instInhabited", "kind": "instance", "module": "Mathlib.Computability.Language", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.instAdd", "kind": "instance", "module": "Mathlib.Computability.Language", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.instSub", "kind": "instance", "module": "Mathlib.Computability.Language", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.instMul", "kind": "instance", "module": "Mathlib.Computability.Language", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.zero_def", "kind": "theorem", "module": "Mathlib.Computability.Language", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.one_def", "kind": "theorem", "module": "Mathlib.Computability.Language", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.add_def", "kind": "theorem", "module": "Mathlib.Computability.Language", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.sub_def", "kind": "theorem", "module": "Mathlib.Computability.Language", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.mul_def", "kind": "theorem", "module": "Mathlib.Computability.Language", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.instKStar", "kind": "instance", "module": "Mathlib.Computability.Language", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.kstar_def", "kind": "theorem", "module": "Mathlib.Computability.Language", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.ext", "kind": "theorem", "module": "Mathlib.Computability.Language", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.notMem_zero", "kind": "theorem", "module": "Mathlib.Computability.Language", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.mem_one", "kind": "theorem", "module": "Mathlib.Computability.Language", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "Language.nil_mem_one", "kind": "theorem", "module": "Mathlib.Computability.Language", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.mem_add", "kind": "theorem", "module": "Mathlib.Computability.Language", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.mem_sub", "kind": "theorem", "module": "Mathlib.Computability.Language", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.mem_mul", "kind": "theorem", "module": "Mathlib.Computability.Language", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.append_mem_mul", "kind": "theorem", "module": "Mathlib.Computability.Language", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.mem_kstar", "kind": "theorem", "module": "Mathlib.Computability.Language", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.join_mem_kstar", "kind": "theorem", "module": "Mathlib.Computability.Language", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.nil_mem_kstar", "kind": "theorem", "module": "Mathlib.Computability.Language", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.instOrderedSub", "kind": "instance", "module": "Mathlib.Computability.Language", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.instSemiring", "kind": "instance", "module": "Mathlib.Computability.Language", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.add_self", "kind": "theorem", "module": "Mathlib.Computability.Language", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.map", "kind": "definition", "module": "Mathlib.Computability.Language", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.map_id", "kind": "theorem", "module": "Mathlib.Computability.Language", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Language.map_map", "kind": "theorem", "module": "Mathlib.Computability.Language", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Language.mem_kstar_iff_exists_nonempty", "kind": "theorem", "module": "Mathlib.Computability.Language", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "refine", "simp", "exact", "rintro", "exact"], "tactic_count": 7}
{"name": "Language.kstar_def_nonempty", "kind": "theorem", "module": "Mathlib.Computability.Language", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Language.le_iff", "kind": "theorem", "module": "Mathlib.Computability.Language", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.instMulLeftMono", "kind": "instance", "module": "Mathlib.Computability.Language", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.instMulRightMono", "kind": "instance", "module": "Mathlib.Computability.Language", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.le_mul_congr", "kind": "theorem", "module": "Mathlib.Computability.Language", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.mem_iSup", "kind": "theorem", "module": "Mathlib.Computability.Language", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.iSup_mul", "kind": "theorem", "module": "Mathlib.Computability.Language", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.mul_iSup", "kind": "theorem", "module": "Mathlib.Computability.Language", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.iSup_add", "kind": "theorem", "module": "Mathlib.Computability.Language", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.add_iSup", "kind": "theorem", "module": "Mathlib.Computability.Language", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.iSup_sub", "kind": "theorem", "module": "Mathlib.Computability.Language", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.sub_iSup", "kind": "theorem", "module": "Mathlib.Computability.Language", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.mem_pow", "kind": "theorem", "module": "Mathlib.Computability.Language", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "simp", "constructor", "rintro", "exact", "rintro", "rw", "exact"], "tactic_count": 10}
{"name": "Language.kstar_eq_iSup_pow", "kind": "theorem", "module": "Mathlib.Computability.Language", "is_tactic_proof": true, "tactics": ["ext", "simp", "grind"], "tactic_count": 3}
{"name": "Language.map_kstar", "kind": "theorem", "module": "Mathlib.Computability.Language", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "exact"], "tactic_count": 3}
{"name": "Language.mul_self_kstar_comm", "kind": "theorem", "module": "Mathlib.Computability.Language", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Language.one_add_self_mul_kstar_eq_kstar", "kind": "theorem", "module": "Mathlib.Computability.Language", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Language.one_add_kstar_mul_self_eq_kstar", "kind": "theorem", "module": "Mathlib.Computability.Language", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Language.instKleeneAlgebra", "kind": "instance", "module": "Mathlib.Computability.Language", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.le_add_congr", "kind": "theorem", "module": "Mathlib.Computability.Language", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.self_eq_mul_add_iff", "kind": "theorem", "module": "Mathlib.Computability.Language", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.reverse", "kind": "definition", "module": "Mathlib.Computability.Language", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.mem_reverse", "kind": "theorem", "module": "Mathlib.Computability.Language", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.reverse_mem_reverse", "kind": "theorem", "module": "Mathlib.Computability.Language", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Language.reverse_eq_image", "kind": "theorem", "module": "Mathlib.Computability.Language", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.reverse_zero", "kind": "theorem", "module": "Mathlib.Computability.Language", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.reverse_one", "kind": "theorem", "module": "Mathlib.Computability.Language", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Language.reverse_involutive", "kind": "theorem", "module": "Mathlib.Computability.Language", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.reverse_bijective", "kind": "theorem", "module": "Mathlib.Computability.Language", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.reverse_injective", "kind": "theorem", "module": "Mathlib.Computability.Language", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.reverse_surjective", "kind": "theorem", "module": "Mathlib.Computability.Language", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.reverse_reverse", "kind": "theorem", "module": "Mathlib.Computability.Language", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.reverse_add", "kind": "theorem", "module": "Mathlib.Computability.Language", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.reverse_mul", "kind": "theorem", "module": "Mathlib.Computability.Language", "is_tactic_proof": true, "tactics": ["simp", "apply"], "tactic_count": 2}
{"name": "Language.reverse_iSup", "kind": "theorem", "module": "Mathlib.Computability.Language", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.reverse_iInf", "kind": "theorem", "module": "Mathlib.Computability.Language", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.reverseIso", "kind": "definition", "module": "Mathlib.Computability.Language", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.reverse_pow", "kind": "theorem", "module": "Mathlib.Computability.Language", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.reverse_kstar", "kind": "theorem", "module": "Mathlib.Computability.Language", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Language.mem_inf", "kind": "theorem", "module": "Mathlib.Computability.Language", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "Language.compl_compl", "kind": "theorem", "module": "Mathlib.Computability.Language", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Symbol", "kind": "inductive", "module": "Mathlib.Computability.Language", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDecidableEqSymbol", "kind": "instance", "module": "Mathlib.Computability.Language", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instReprSymbol", "kind": "instance", "module": "Mathlib.Computability.Language", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFintypeSymbol", "kind": "instance", "module": "Mathlib.Computability.Language", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.leftQuotient", "kind": "definition", "module": "Mathlib.Computability.MyhillNerode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.leftQuotient_nil", "kind": "theorem", "module": "Mathlib.Computability.MyhillNerode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.leftQuotient_append", "kind": "theorem", "module": "Mathlib.Computability.MyhillNerode", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Language.mem_leftQuotient", "kind": "theorem", "module": "Mathlib.Computability.MyhillNerode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.leftQuotient_accepts_apply", "kind": "theorem", "module": "Mathlib.Computability.MyhillNerode", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Language.leftQuotient_accepts", "kind": "theorem", "module": "Mathlib.Computability.MyhillNerode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.IsRegular.finite_range_leftQuotient", "kind": "theorem", "module": "Mathlib.Computability.MyhillNerode", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "Language.toDFA", "kind": "definition", "module": "Mathlib.Computability.MyhillNerode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.mem_accept_toDFA", "kind": "theorem", "module": "Mathlib.Computability.MyhillNerode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.step_toDFA", "kind": "theorem", "module": "Mathlib.Computability.MyhillNerode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.start_toDFA", "kind": "theorem", "module": "Mathlib.Computability.MyhillNerode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.accepts_toDFA", "kind": "theorem", "module": "Mathlib.Computability.MyhillNerode", "is_tactic_proof": true, "tactics": ["ext", "rw", "suffices", "induction", "nil", "append_singleton"], "tactic_count": 6}
{"name": "Language.IsRegular.of_finite_range_leftQuotient", "kind": "theorem", "module": "Mathlib.Computability.MyhillNerode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.isRegular_iff_finite_range_leftQuotient", "kind": "theorem", "module": "Mathlib.Computability.MyhillNerode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NFA.instInhabited", "kind": "instance", "module": "Mathlib.Computability.NFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NFA.stepSet", "kind": "definition", "module": "Mathlib.Computability.NFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NFA.mem_stepSet", "kind": "theorem", "module": "Mathlib.Computability.NFA", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NFA.stepSet_empty", "kind": "theorem", "module": "Mathlib.Computability.NFA", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NFA.stepSet_singleton", "kind": "theorem", "module": "Mathlib.Computability.NFA", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NFA.stepSet_union", "kind": "theorem", "module": "Mathlib.Computability.NFA", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "NFA.evalFrom", "kind": "definition", "module": "Mathlib.Computability.NFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NFA.evalFrom_nil", "kind": "theorem", "module": "Mathlib.Computability.NFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NFA.evalFrom_singleton", "kind": "theorem", "module": "Mathlib.Computability.NFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NFA.evalFrom_cons", "kind": "theorem", "module": "Mathlib.Computability.NFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NFA.evalFrom_append", "kind": "theorem", "module": "Mathlib.Computability.NFA", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NFA.evalFrom_append_singleton", "kind": "theorem", "module": "Mathlib.Computability.NFA", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NFA.evalFrom_union", "kind": "theorem", "module": "Mathlib.Computability.NFA", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "NFA.evalFrom_iUnion", "kind": "theorem", "module": "Mathlib.Computability.NFA", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "NFA.evalFrom_iUnion₂", "kind": "theorem", "module": "Mathlib.Computability.NFA", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NFA.evalFrom_biUnion", "kind": "theorem", "module": "Mathlib.Computability.NFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NFA.evalFrom_eq_biUnion_singleton", "kind": "theorem", "module": "Mathlib.Computability.NFA", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NFA.mem_evalFrom_iff_exists", "kind": "theorem", "module": "Mathlib.Computability.NFA", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "NFA.acceptsFrom", "kind": "definition", "module": "Mathlib.Computability.NFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NFA.mem_acceptsFrom", "kind": "theorem", "module": "Mathlib.Computability.NFA", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "NFA.nil_mem_acceptsFrom", "kind": "theorem", "module": "Mathlib.Computability.NFA", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NFA.cons_mem_acceptsFrom", "kind": "theorem", "module": "Mathlib.Computability.NFA", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NFA.cons_preimage_acceptsFrom", "kind": "theorem", "module": "Mathlib.Computability.NFA", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "NFA.append_mem_acceptsFrom", "kind": "theorem", "module": "Mathlib.Computability.NFA", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NFA.append_preimage_acceptsFrom", "kind": "theorem", "module": "Mathlib.Computability.NFA", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "NFA.acceptsFrom_union", "kind": "theorem", "module": "Mathlib.Computability.NFA", "is_tactic_proof": true, "tactics": ["rw", "simp", "constructor", "rintro", "left", "right", "rintro"], "tactic_count": 7}
{"name": "NFA.acceptsFrom_iUnion", "kind": "theorem", "module": "Mathlib.Computability.NFA", "is_tactic_proof": true, "tactics": ["ext", "simp", "simp_rw"], "tactic_count": 3}
{"name": "NFA.acceptsFrom_iUnion₂", "kind": "theorem", "module": "Mathlib.Computability.NFA", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "_private.Mathlib.Computability.NFA.0.NFA.mem_acceptsFrom_sep_fact", "kind": "theorem", "module": "Mathlib.Computability.NFA", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "ih", "have", "simp", "simp"], "tactic_count": 7}
{"name": "NFA.eval", "kind": "definition", "module": "Mathlib.Computability.NFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NFA.eval_nil", "kind": "theorem", "module": "Mathlib.Computability.NFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NFA.eval_singleton", "kind": "theorem", "module": "Mathlib.Computability.NFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NFA.eval_append_singleton", "kind": "theorem", "module": "Mathlib.Computability.NFA", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NFA.accepts", "kind": "definition", "module": "Mathlib.Computability.NFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NFA.mem_accepts", "kind": "theorem", "module": "Mathlib.Computability.NFA", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "NFA.accepts_eq_acceptsFrom_start", "kind": "theorem", "module": "Mathlib.Computability.NFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NFA.Path", "kind": "inductive", "module": "Mathlib.Computability.NFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NFA.Path.supp", "kind": "definition", "module": "Mathlib.Computability.NFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NFA.mem_evalFrom_iff_nonempty_path", "kind": "theorem", "module": "Mathlib.Computability.NFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NFA.accepts_iff_exists_path", "kind": "theorem", "module": "Mathlib.Computability.NFA", "is_tactic_proof": true, "tactics": ["simp", "tauto"], "tactic_count": 2}
{"name": "NFA.toDFA", "kind": "definition", "module": "Mathlib.Computability.NFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NFA.toDFA_correct", "kind": "theorem", "module": "Mathlib.Computability.NFA", "is_tactic_proof": true, "tactics": ["ext", "rw", "constructor"], "tactic_count": 3}
{"name": "NFA.pumping_lemma", "kind": "theorem", "module": "Mathlib.Computability.NFA", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "DFA.toNFA", "kind": "definition", "module": "Mathlib.Computability.NFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFA.toNFA_evalFrom_match", "kind": "theorem", "module": "Mathlib.Computability.NFA", "is_tactic_proof": true, "tactics": ["change", "induction", "nil", "cons", "ih", "rw", "tauto"], "tactic_count": 7}
{"name": "DFA.toNFA_correct", "kind": "theorem", "module": "Mathlib.Computability.NFA", "is_tactic_proof": true, "tactics": ["ext", "rw", "constructor", "rintro", "rwa", "exact"], "tactic_count": 6}
{"name": "NFA.reverse", "kind": "definition", "module": "Mathlib.Computability.NFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NFA.reverse_reverse", "kind": "theorem", "module": "Mathlib.Computability.NFA", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NFA.disjoint_stepSet_reverse", "kind": "theorem", "module": "Mathlib.Computability.NFA", "is_tactic_proof": true, "tactics": ["rw", "simp", "tauto"], "tactic_count": 3}
{"name": "NFA.disjoint_evalFrom_reverse", "kind": "theorem", "module": "Mathlib.Computability.NFA", "is_tactic_proof": true, "tactics": ["simp", "induction", "nil", "rw", "exact", "cons", "rw", "rw", "exact"], "tactic_count": 9}
{"name": "NFA.disjoint_evalFrom_reverse_iff", "kind": "theorem", "module": "Mathlib.Computability.NFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NFA.mem_accepts_reverse", "kind": "theorem", "module": "Mathlib.Computability.NFA", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Language.IsRegular.reverse", "kind": "theorem", "module": "Mathlib.Computability.NFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.IsRegular.of_reverse", "kind": "theorem", "module": "Mathlib.Computability.NFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Language.isRegular_reverse_iff", "kind": "theorem", "module": "Mathlib.Computability.NFA", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Computability.Partrec.0.Nat.lbp", "kind": "definition", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Computability.Partrec.0.Nat.wf_lbp", "kind": "definition", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.rfindX", "kind": "definition", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.rfind", "kind": "definition", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.rfind_spec", "kind": "theorem", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.rfind_min", "kind": "theorem", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.rfind_dom", "kind": "theorem", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.rfind_dom'", "kind": "theorem", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.mem_rfind", "kind": "theorem", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.rfind_min'", "kind": "theorem", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.rfind_zero_none", "kind": "theorem", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.rfindOpt", "kind": "definition", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.rfindOpt_spec", "kind": "theorem", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.rfindOpt_dom", "kind": "theorem", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.rfindOpt_mono", "kind": "theorem", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Partrec", "kind": "inductive", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Partrec.of_eq", "kind": "theorem", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Partrec.of_eq_tot", "kind": "theorem", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Partrec.of_primrec", "kind": "theorem", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "left", "right", "pair", "refine", "simp", "comp", "prec", "refine", "simp", "induction", "zero", "succ", "simp", "exact"], "tactic_count": 17}
{"name": "Nat.Partrec.some", "kind": "theorem", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Partrec.none", "kind": "theorem", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Partrec.prec'", "kind": "theorem", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Partrec.ppred", "kind": "theorem", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Partrec", "kind": "definition", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Partrec₂", "kind": "definition", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computable", "kind": "definition", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computable₂", "kind": "definition", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.to_comp", "kind": "theorem", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec₂.to_comp", "kind": "theorem", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computable.partrec", "kind": "theorem", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computable₂.partrec₂", "kind": "theorem", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computable.of_eq", "kind": "theorem", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computable.const", "kind": "theorem", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computable.ofOption", "kind": "theorem", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computable.to₂", "kind": "theorem", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computable.id", "kind": "theorem", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computable.fst", "kind": "theorem", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computable.snd", "kind": "theorem", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computable.pair", "kind": "theorem", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computable.unpair", "kind": "theorem", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computable.succ", "kind": "theorem", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computable.pred", "kind": "theorem", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computable.nat_bodd", "kind": "theorem", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computable.nat_div2", "kind": "theorem", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computable.sumInl", "kind": "theorem", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computable.sumInr", "kind": "theorem", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computable.list_cons", "kind": "theorem", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computable.list_reverse", "kind": "theorem", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computable.list_getElem?", "kind": "theorem", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computable.list_append", "kind": "theorem", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computable.list_concat", "kind": "theorem", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computable.list_length", "kind": "theorem", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computable.vector_cons", "kind": "theorem", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computable.vector_toList", "kind": "theorem", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computable.vector_length", "kind": "theorem", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computable.vector_head", "kind": "theorem", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computable.vector_tail", "kind": "theorem", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computable.vector_get", "kind": "theorem", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computable.vector_ofFn'", "kind": "theorem", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computable.fin_app", "kind": "theorem", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computable.encode", "kind": "theorem", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computable.decode", "kind": "theorem", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computable.ofNat", "kind": "theorem", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computable.encode_iff", "kind": "theorem", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computable.option_some", "kind": "theorem", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Partrec.of_eq", "kind": "theorem", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Partrec.of_eq_tot", "kind": "theorem", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Partrec.none", "kind": "theorem", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Partrec.some", "kind": "theorem", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Decidable.Partrec.const'", "kind": "theorem", "module": "Mathlib.Computability.Partrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Turing.FRespects", "kind": "definition", "module": "Mathlib.Computability.PostTuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.frespects_eq", "kind": "theorem", "module": "Mathlib.Computability.PostTuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.fun_respects", "kind": "theorem", "module": "Mathlib.Computability.PostTuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.tr_eval'", "kind": "theorem", "module": "Mathlib.Computability.PostTuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM0.Stmt", "kind": "inductive", "module": "Mathlib.Computability.PostTuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Turing.TM0.Machine", "kind": "definition", "module": "Mathlib.Computability.PostTuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Turing.TM0.step", "kind": "definition", "module": "Mathlib.Computability.PostTuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM0.Reaches", "kind": "definition", "module": "Mathlib.Computability.PostTuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM0.init", "kind": "definition", "module": "Mathlib.Computability.PostTuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM0.eval", "kind": "definition", "module": "Mathlib.Computability.PostTuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM0.Supports", "kind": "definition", "module": "Mathlib.Computability.PostTuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM0.step_supports", "kind": "theorem", "module": "Mathlib.Computability.PostTuringMachine", "is_tactic_proof": true, "tactics": ["intro", "rcases", "exact"], "tactic_count": 3}
{"name": "Turing.TM0.univ_supports", "kind": "theorem", "module": "Mathlib.Computability.PostTuringMachine", "is_tactic_proof": true, "tactics": ["constructor"], "tactic_count": 1}
{"name": "Turing.TM0.Stmt.map", "kind": "definition", "module": "Mathlib.Computability.PostTuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM0.Cfg.map", "kind": "definition", "module": "Mathlib.Computability.PostTuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM0.Machine.map", "kind": "definition", "module": "Mathlib.Computability.PostTuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM0.Machine.map_step", "kind": "theorem", "module": "Mathlib.Computability.PostTuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Turing.TM1.Stmt", "kind": "inductive", "module": "Mathlib.Computability.PostTuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Turing.TM1.stepAux", "kind": "definition", "module": "Mathlib.Computability.PostTuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM1.step", "kind": "definition", "module": "Mathlib.Computability.PostTuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM1.SupportsStmt", "kind": "definition", "module": "Mathlib.Computability.PostTuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM1.stmts₁", "kind": "definition", "module": "Mathlib.Computability.PostTuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM1.stmts₁_self", "kind": "theorem", "module": "Mathlib.Computability.PostTuringMachine", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
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{"name": "Turing.TM1.stmts", "kind": "definition", "module": "Mathlib.Computability.PostTuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM1.stmts_trans", "kind": "theorem", "module": "Mathlib.Computability.PostTuringMachine", "is_tactic_proof": false, "tactics": ["simp", "exists_imp,", "exact"], "tactic_count": 3}
{"name": "Turing.TM1.Supports", "kind": "definition", "module": "Mathlib.Computability.PostTuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM1.stmts_supportsStmt", "kind": "theorem", "module": "Mathlib.Computability.PostTuringMachine", "is_tactic_proof": false, "tactics": ["simp", "exists_imp,", "exact"], "tactic_count": 3}
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{"name": "Turing.TM1.init", "kind": "definition", "module": "Mathlib.Computability.PostTuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM1.eval", "kind": "definition", "module": "Mathlib.Computability.PostTuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM1to0.Λ'", "kind": "definition", "module": "Mathlib.Computability.PostTuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM1to0.instInhabitedΛ'", "kind": "instance", "module": "Mathlib.Computability.PostTuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM1to0.trAux", "kind": "definition", "module": "Mathlib.Computability.PostTuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM1to0.tr", "kind": "definition", "module": "Mathlib.Computability.PostTuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM1to0.trCfg", "kind": "definition", "module": "Mathlib.Computability.PostTuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM1to0.tr_respects", "kind": "theorem", "module": "Mathlib.Computability.PostTuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM1to0.tr_eval", "kind": "theorem", "module": "Mathlib.Computability.PostTuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM1to0.trStmts", "kind": "definition", "module": "Mathlib.Computability.PostTuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Turing.TM1to1.exists_enc_dec", "kind": "theorem", "module": "Mathlib.Computability.PostTuringMachine", "is_tactic_proof": true, "tactics": ["rcases", "letI", "let", "let", "let", "exact"], "tactic_count": 6}
{"name": "Turing.TM1to1.Λ'", "kind": "inductive", "module": "Mathlib.Computability.PostTuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Turing.TM1to1.readAux", "kind": "definition", "module": "Mathlib.Computability.PostTuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM1to1.move", "kind": "definition", "module": "Mathlib.Computability.PostTuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM1to1.read", "kind": "definition", "module": "Mathlib.Computability.PostTuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM1to1.write", "kind": "definition", "module": "Mathlib.Computability.PostTuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM1to1.trNormal", "kind": "definition", "module": "Mathlib.Computability.PostTuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM1to1.stepAux_move", "kind": "theorem", "module": "Mathlib.Computability.PostTuringMachine", "is_tactic_proof": true, "tactics": ["suffices", "intro", "induction", "zero", "succ", "rw", "simp", "rw"], "tactic_count": 8}
{"name": "Turing.TM1to1.supportsStmt_move", "kind": "theorem", "module": "Mathlib.Computability.PostTuringMachine", "is_tactic_proof": true, "tactics": ["suffices", "intro"], "tactic_count": 2}
{"name": "Turing.TM1to1.supportsStmt_write", "kind": "theorem", "module": "Mathlib.Computability.PostTuringMachine", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "Turing.TM1to1.supportsStmt_read", "kind": "theorem", "module": "Mathlib.Computability.PostTuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM1to1.trTape'", "kind": "definition", "module": "Mathlib.Computability.PostTuringMachine", "is_tactic_proof": true, "tactics": ["refine", "simp"], "tactic_count": 2}
{"name": "Turing.TM1to1.trTape", "kind": "definition", "module": "Mathlib.Computability.PostTuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM1to1.trTape_mk'", "kind": "theorem", "module": "Mathlib.Computability.PostTuringMachine", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Turing.TM1to1.tr", "kind": "definition", "module": "Mathlib.Computability.PostTuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Turing.TM1to1.trTape'_move_left", "kind": "theorem", "module": "Mathlib.Computability.PostTuringMachine", "is_tactic_proof": true, "tactics": ["obtain", "simp", "suffices", "intro", "induction", "nil", "cons", "simp", "convert", "simp"], "tactic_count": 10}
{"name": "Turing.TM1to1.trTape'_move_right", "kind": "theorem", "module": "Mathlib.Computability.PostTuringMachine", "is_tactic_proof": false, "tactics": ["suffices", "refine", "simp", "intro", "induction", "zero", "succ"], "tactic_count": 7}
{"name": "Turing.TM1to1.stepAux_write", "kind": "theorem", "module": "Mathlib.Computability.PostTuringMachine", "is_tactic_proof": true, "tactics": ["simp", "suffices", "stepAux", "stepAux", "clear", "intro", "induction", "nil", "cons", "rcases", "rw", "simp"], "tactic_count": 12}
{"name": "Turing.TM1to1.stepAux_read", "kind": "theorem", "module": "Mathlib.Computability.PostTuringMachine", "is_tactic_proof": false, "tactics": ["suffices", "rw", "simp", "obtain", "simp", "suffices", "stepAux", "stepAux", "intro", "exact", "clear", "intro", "subst", "induction", "nil", "cons", "trans", "dsimp", "simp", "cases", "rw", "rfl"], "tactic_count": 22}
{"name": "Turing.TM1to1.tr_respects", "kind": "theorem", "module": "Mathlib.Computability.PostTuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM1to1.writes", "kind": "definition", "module": "Mathlib.Computability.PostTuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM1to1.trSupp", "kind": "definition", "module": "Mathlib.Computability.PostTuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM1to1.tr_supports", "kind": "theorem", "module": "Mathlib.Computability.PostTuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM0to1.Λ'", "kind": "inductive", "module": "Mathlib.Computability.PostTuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM0to1.instInhabitedΛ'", "kind": "instance", "module": "Mathlib.Computability.PostTuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM0to1.tr", "kind": "definition", "module": "Mathlib.Computability.PostTuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM0to1.trCfg", "kind": "definition", "module": "Mathlib.Computability.PostTuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM0to1.tr_respects", "kind": "theorem", "module": "Mathlib.Computability.PostTuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.unpaired", "kind": "definition", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Primrec", "kind": "inductive", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Primrec.of_eq", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Primrec.const", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Primrec.id", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Primrec.prec1", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Primrec.casesOn1", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Primrec.casesOn'", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Primrec.swap", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Primrec.swap'", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Primrec.pred", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Primrec.add", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Primrec.sub", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Primrec.mul", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Primrec.pow", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primcodable.ofDenumerable", "kind": "instance", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primcodable.ofEquiv", "kind": "definition", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primcodable.empty", "kind": "instance", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primcodable.unit", "kind": "instance", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primcodable.option", "kind": "instance", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primcodable.bool", "kind": "instance", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec", "kind": "definition", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.encode", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.decode", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.dom_denumerable", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.nat_iff", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.encdec", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.option_some", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.of_eq", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.const", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.id", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.comp", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.succ", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.pred", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.encode_iff", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.ofNat_iff", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.ofNat", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.option_some_iff", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.of_equiv", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.of_equiv_symm", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.of_equiv_iff", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.of_equiv_symm_iff", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primcodable.prod", "kind": "instance", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.fst", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.snd", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.pair", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.unpair", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.list_getElem?₁", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec₂", "kind": "definition", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimrecPred", "kind": "definition", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimrecRel", "kind": "definition", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec₂.mk", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec₂.of_eq", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec₂.const", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec₂.pair", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec₂.left", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec₂.right", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec₂.natPair", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Primrec₂.unpaired", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec₂.unpaired'", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec₂.encode_iff", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec₂.option_some_iff", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec₂.ofNat_iff", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec₂.uncurry", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Primrec₂.curry", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Primrec.comp₂", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec₂.comp", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec₂.comp₂", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimrecPred.decide", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "Primrec.primrecPred", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "primrecPred_iff_primrec_decide", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimrecPred.comp", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimrecRel.decide", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec₂.primrecRel", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "primrecRel_iff_primrec_decide", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimrecRel.comp", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimrecRel.comp₂", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimrecPred.of_eq", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimrecRel.of_eq", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec₂.swap", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimrecRel.swap", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec₂.nat_iff", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": ["have", "simp"], "tactic_count": 2}
{"name": "Primrec₂.nat_iff'", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.to₂", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimrecPred.primrecRel", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.nat_rec", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.nat_rec'", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.nat_rec₁", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.nat_casesOn'", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.nat_casesOn", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.nat_casesOn₁", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.nat_iterate", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.option_casesOn", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.option_bind", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.option_bind₁", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.option_map", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.option_map₁", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.option_getD", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.option_getD_default", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.option_iget", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.option_isSome", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.bind_decode_iff", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.map_decode_iff", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Primrec.nat_add", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.nat_sub", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.nat_mul", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.cond", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.ite", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Primrec.nat_le", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.nat_min", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.nat_max", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.dom_bool", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.dom_bool₂", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.not", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.and", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.or", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimrecPred.not", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimrecPred.and", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimrecPred.or", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.eq", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.beq", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.nat_lt", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.option_guard", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.option_orElse", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.decode₂", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.list_findIdx₁", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.list_idxOf₁", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.dom_finite", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.PrimrecBounded", "kind": "definition", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.nat_findGreatest", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.of_graph", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": true, "tactics": ["rcases", "refine", "exact"], "tactic_count": 3}
{"name": "Primrec.nat_div", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": true, "tactics": ["refine", "have", "refine", "rintro", "have", "rw", "simpa"], "tactic_count": 7}
{"name": "Primrec.nat_mod", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.nat_bodd", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.nat_div2", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.nat_double", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.nat_double_succ", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primcodable.sum", "kind": "instance", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.sumInl", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.sumInr", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.sumCasesOn", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimrecRel.not", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primcodable.subtype", "kind": "definition", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primcodable.fin", "kind": "instance", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primcodable.mem_range_encode", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primcodable.ulower", "kind": "instance", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.subtype_val", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": true, "tactics": ["letI", "refine", "rcases"], "tactic_count": 3}
{"name": "Primrec.subtype_val_iff", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": true, "tactics": ["letI", "refine", "refine", "rcases", "simp"], "tactic_count": 5}
{"name": "Primrec.subtype_mk", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.option_get", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": true, "tactics": ["intro", "refine", "generalize", "cases"], "tactic_count": 4}
{"name": "Primrec.ulower_down", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.ulower_up", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.fin_val_iff", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": true, "tactics": ["letI", "exact"], "tactic_count": 2}
{"name": "Primrec.fin_val", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.fin_succ", "kind": "theorem", "module": "Mathlib.Computability.Primrec.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Computability.Primrec.List.0.prim", "kind": "definition", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Computability.Primrec.List.0.list_casesOn'", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Computability.Primrec.List.0.list_foldl'", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": true, "tactics": ["letI", "let", "have", "list_casesOn", "to₂", "let", "have", "suffices", "refine", "rw", "introv", "dsimp", "generalize", "generalize", "induction", "zero", "succ", "simp", "rcases"], "tactic_count": 19}
{"name": "_private.Mathlib.Computability.Primrec.List.0.list_cons'", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Computability.Primrec.List.0.list_reverse'", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primcodable.list", "kind": "instance", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.list_cons", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.list_casesOn", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.list_foldl", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.list_reverse", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.list_foldr", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.list_head?", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.list_headI", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.list_tail", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.list_rec", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.list_getElem?", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.list_getD", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Primrec.list_getI", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.list_append", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.list_concat", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.list_map", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.list_range", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.list_flatten", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.list_flatMap", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.optionToList", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.listFilterMap", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.list_length", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.listFilter", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": true, "tactics": ["rw", "apply", "simp", "exact"], "tactic_count": 4}
{"name": "Primrec.list_findIdx", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.list_idxOf", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.nat_strong_rec", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.listLookup", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.nat_omega_rec'", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": true, "tactics": ["haveI", "let", "let", "let", "i.rec", "have", "to₂", "have", "nat_rec", "have", "to₂", "nat_rec", "to₂", "listFilterMap", "to₂", "option_map", "have", "option_map", "exact", "option_some_iff.mp", "this.of_eq", "have", "graph", "have", "have", "induction", "succ", "have", "mapGraph", "induction", "cons", "have", "rcases", "simpa", "have", "graph", "have", "induction", "zero", "succ", "ih", "simp", "bindList_succ,", "apply", "intro", "exact", "exact", "simp"], "tactic_count": 48}
{"name": "Primrec.nat_omega_rec", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimrecPred.exists_mem_list", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimrecPred.forall_mem_list", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimrecPred.exists_lt", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimrecPred.forall_lt", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimrecPred.listFilter_listRange", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": true, "tactics": ["simp", "refine", "refine", "exact"], "tactic_count": 4}
{"name": "PrimrecRel.listFilter", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": true, "tactics": ["simp", "refine", "exact", "exact"], "tactic_count": 4}
{"name": "PrimrecRel.exists_mem_list", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": true, "tactics": ["classical", "have", "refine", "exact"], "tactic_count": 4}
{"name": "PrimrecRel.forall_mem_list", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": true, "tactics": ["classical", "have", "apply", "exact"], "tactic_count": 4}
{"name": "PrimrecRel.exists_lt", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimrecRel.forall_lt", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primcodable.vector", "kind": "instance", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primcodable.finArrow", "kind": "instance", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.vector_toList", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.vector_toList_iff", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.vector_cons", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.vector_length", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.vector_head", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.vector_tail", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.vector_get", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.list_ofFn", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.vector_ofFn", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.vector_get'", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.vector_ofFn'", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.fin_app", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.fin_curry₁", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.fin_curry", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Primrec'", "kind": "inductive", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Primrec'.to_prim", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "get", "comp", "exact"], "tactic_count": 6}
{"name": "Nat.Primrec'.of_eq", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Primrec'.const", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Primrec'.head", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Primrec'.tail", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Primrec'.Vec", "kind": "definition", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Primrec'.nil", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Primrec'.cons", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Primrec'.idv", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Primrec'.comp'", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Primrec'.comp₁", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Primrec'.comp₂", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Nat.Primrec'.prec'", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Nat.Primrec'.pred", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Primrec'.add", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Primrec'.sub", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": ["have", "refine", "simp", "simpa"], "tactic_count": 4}
{"name": "Nat.Primrec'.mul", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Primrec'.if_lt", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Primrec'.natPair", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Primrec'.encode", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Primrec'.sqrt", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": ["suffices", "simp", "have", "have", "exact", "head", "exact", "have", "have", "exact", "introv", "induction", "zero", "succ", "dsimp", "exact", "exact"], "tactic_count": 17}
{"name": "Nat.Primrec'.unpair₁", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": true, "tactics": ["have", "have", "refine", "simp"], "tactic_count": 4}
{"name": "Nat.Primrec'.unpair₂", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": true, "tactics": ["have", "have", "refine", "simp"], "tactic_count": 4}
{"name": "Nat.Primrec'.of_prim", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Primrec'.prim_iff", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Primrec'.prim_iff₁", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Primrec'.prim_iff₂", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Primrec'.vec_iff", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Primrec.nat_sqrt", "kind": "theorem", "module": "Mathlib.Computability.Primrec.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ManyOneReducible", "kind": "definition", "module": "Mathlib.Computability.Reduce", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "term_≤₀_", "kind": "definition", "module": "Mathlib.Computability.Reduce", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Computability_Reduce___macroRules_term_≤₀__1", "kind": "definition", "module": "Mathlib.Computability.Reduce", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Computability_Reduce___unexpand_ManyOneReducible_1", "kind": "definition", "module": "Mathlib.Computability.Reduce", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ManyOneReducible.mk", "kind": "theorem", "module": "Mathlib.Computability.Reduce", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "manyOneReducible_refl", "kind": "theorem", "module": "Mathlib.Computability.Reduce", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ManyOneReducible.trans", "kind": "theorem", "module": "Mathlib.Computability.Reduce", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "reflexive_manyOneReducible", "kind": "theorem", "module": "Mathlib.Computability.Reduce", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "transitive_manyOneReducible", "kind": "theorem", "module": "Mathlib.Computability.Reduce", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OneOneReducible", "kind": "definition", "module": "Mathlib.Computability.Reduce", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "term_≤₁_", "kind": "definition", "module": "Mathlib.Computability.Reduce", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Computability_Reduce___macroRules_term_≤₁__1", "kind": "definition", "module": "Mathlib.Computability.Reduce", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Computability_Reduce___unexpand_OneOneReducible_1", "kind": "definition", "module": "Mathlib.Computability.Reduce", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OneOneReducible.mk", "kind": "theorem", "module": "Mathlib.Computability.Reduce", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "oneOneReducible_refl", "kind": "theorem", "module": "Mathlib.Computability.Reduce", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OneOneReducible.trans", "kind": "theorem", "module": "Mathlib.Computability.Reduce", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OneOneReducible.to_many_one", "kind": "theorem", "module": "Mathlib.Computability.Reduce", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OneOneReducible.of_equiv", "kind": "theorem", "module": "Mathlib.Computability.Reduce", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OneOneReducible.of_equiv_symm", "kind": "theorem", "module": "Mathlib.Computability.Reduce", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "reflexive_oneOneReducible", "kind": "theorem", "module": "Mathlib.Computability.Reduce", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "transitive_oneOneReducible", "kind": "theorem", "module": "Mathlib.Computability.Reduce", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComputablePred.computable_of_manyOneReducible", "kind": "theorem", "module": "Mathlib.Computability.Reduce", "is_tactic_proof": true, "tactics": ["rcases", "rw", "rcases", "exact"], "tactic_count": 4}
{"name": "ComputablePred.computable_of_oneOneReducible", "kind": "theorem", "module": "Mathlib.Computability.Reduce", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ManyOneEquiv", "kind": "definition", "module": "Mathlib.Computability.Reduce", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OneOneEquiv", "kind": "definition", "module": "Mathlib.Computability.Reduce", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "manyOneEquiv_refl", "kind": "theorem", "module": "Mathlib.Computability.Reduce", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ManyOneEquiv.symm", "kind": "theorem", "module": "Mathlib.Computability.Reduce", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ManyOneEquiv.trans", "kind": "theorem", "module": "Mathlib.Computability.Reduce", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "equivalence_of_manyOneEquiv", "kind": "theorem", "module": "Mathlib.Computability.Reduce", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "oneOneEquiv_refl", "kind": "theorem", "module": "Mathlib.Computability.Reduce", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OneOneEquiv.symm", "kind": "theorem", "module": "Mathlib.Computability.Reduce", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OneOneEquiv.trans", "kind": "theorem", "module": "Mathlib.Computability.Reduce", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "equivalence_of_oneOneEquiv", "kind": "theorem", "module": "Mathlib.Computability.Reduce", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OneOneEquiv.to_many_one", "kind": "theorem", "module": "Mathlib.Computability.Reduce", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Computable", "kind": "definition", "module": "Mathlib.Computability.Reduce", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Computable.symm", "kind": "theorem", "module": "Mathlib.Computability.Reduce", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Computable.trans", "kind": "theorem", "module": "Mathlib.Computability.Reduce", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computable.eqv", "kind": "theorem", "module": "Mathlib.Computability.Reduce", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computable.equiv₂", "kind": "theorem", "module": "Mathlib.Computability.Reduce", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OneOneEquiv.of_equiv", "kind": "theorem", "module": "Mathlib.Computability.Reduce", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ManyOneEquiv.of_equiv", "kind": "theorem", "module": "Mathlib.Computability.Reduce", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ManyOneEquiv.le_congr_left", "kind": "theorem", "module": "Mathlib.Computability.Reduce", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ManyOneEquiv.le_congr_right", "kind": "theorem", "module": "Mathlib.Computability.Reduce", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OneOneEquiv.le_congr_left", "kind": "theorem", "module": "Mathlib.Computability.Reduce", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OneOneEquiv.le_congr_right", "kind": "theorem", "module": "Mathlib.Computability.Reduce", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ManyOneEquiv.congr_left", "kind": "theorem", "module": "Mathlib.Computability.Reduce", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ManyOneEquiv.congr_right", "kind": "theorem", "module": "Mathlib.Computability.Reduce", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OneOneEquiv.congr_left", "kind": "theorem", "module": "Mathlib.Computability.Reduce", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ULower.down_computable", "kind": "theorem", "module": "Mathlib.Computability.Reduce", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Turing.ToPartrec.Code.pred", "kind": "definition", "module": "Mathlib.Computability.TMConfig", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.ToPartrec.Code.pred_eval", "kind": "theorem", "module": "Mathlib.Computability.TMConfig", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Turing.ToPartrec.Code.rfind", "kind": "definition", "module": "Mathlib.Computability.TMConfig", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.ToPartrec.Code.prec", "kind": "definition", "module": "Mathlib.Computability.TMConfig", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.ToPartrec.Code.exists_code.comp", "kind": "theorem", "module": "Mathlib.Computability.TMConfig", "is_tactic_proof": false, "tactics": ["rsuffices", "obtain", "exact", "simp", "rfl⟩", "clear", "induction", "zero", "succ", "obtain", "obtain", "exact", "simp", "rfl⟩"], "tactic_count": 14}
{"name": "Turing.ToPartrec.Code.exists_code", "kind": "theorem", "module": "Mathlib.Computability.TMConfig", "is_tactic_proof": true, "tactics": ["induction", "prim", "induction", "zero", "succ", "get", "refine", "exact", "obtain", "exact", "comp", "obtain", "obtain", "simp", "refine", "rw", "specialize", "replace", "simp", "simp", "simp", "induction", "succ", "suffices", "a", "have", "simp_all", "intro", "induction", "zero", "refine", "simp", "rfl", "succ", "refine", "simp", "exact", "comp", "obtain", "replace", "simp", "show", "refine", "simp", "succ_eval,", "constructor", "rintro", "suffices", "v", "v₁", "clear", "intro", "refine", "clear", "rintro", "have", "simp", "split_ifs", "simp", "reduceCtorEq]", "subst", "exact", "refine", "obtain", "exacts", "rintro", "refine", "have", "generalize", "clear", "induction", "zero", "succ", "refine", "simp"], "tactic_count": 75}
{"name": "Turing.ToPartrec.Cont", "kind": "inductive", "module": "Mathlib.Computability.TMConfig", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.ToPartrec.instInhabitedCont.default", "kind": "definition", "module": "Mathlib.Computability.TMConfig", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.ToPartrec.instInhabitedCont", "kind": "instance", "module": "Mathlib.Computability.TMConfig", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.ToPartrec.Cont.eval", "kind": "definition", "module": "Mathlib.Computability.TMConfig", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.ToPartrec.Cfg", "kind": "inductive", "module": "Mathlib.Computability.TMConfig", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.ToPartrec.instInhabitedCfg.default", "kind": "definition", "module": "Mathlib.Computability.TMConfig", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.ToPartrec.instInhabitedCfg", "kind": "instance", "module": "Mathlib.Computability.TMConfig", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.ToPartrec.stepNormal", "kind": "definition", "module": "Mathlib.Computability.TMConfig", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.ToPartrec.stepRet", "kind": "definition", "module": "Mathlib.Computability.TMConfig", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.ToPartrec.step", "kind": "definition", "module": "Mathlib.Computability.TMConfig", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.ToPartrec.Cont.then", "kind": "definition", "module": "Mathlib.Computability.TMConfig", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.ToPartrec.Cont.then_eval", "kind": "theorem", "module": "Mathlib.Computability.TMConfig", "is_tactic_proof": true, "tactics": ["induction", "halt", "cons₁", "cons₂", "comp", "fix", "simp", "split_ifs"], "tactic_count": 8}
{"name": "Turing.ToPartrec.Cfg.then", "kind": "definition", "module": "Mathlib.Computability.TMConfig", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.ToPartrec.stepNormal_then", "kind": "theorem", "module": "Mathlib.Computability.TMConfig", "is_tactic_proof": true, "tactics": ["induction", "cons", "comp", "cases", "fix"], "tactic_count": 5}
{"name": "Turing.ToPartrec.stepRet_then", "kind": "theorem", "module": "Mathlib.Computability.TMConfig", "is_tactic_proof": true, "tactics": ["induction", "cons₁", "rw", "rfl", "comp", "fix", "split_ifs", "rw", "rw", "rfl"], "tactic_count": 10}
{"name": "Turing.ToPartrec.Code.Ok", "kind": "definition", "module": "Mathlib.Computability.TMConfig", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.ToPartrec.Code.Ok.zero", "kind": "theorem", "module": "Mathlib.Computability.TMConfig", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Turing.ToPartrec.stepNormal.is_ret", "kind": "theorem", "module": "Mathlib.Computability.TMConfig", "is_tactic_proof": true, "tactics": ["induction", "cons", "comp", "rw", "simp", "cases", "fix"], "tactic_count": 7}
{"name": "Turing.ToPartrec.cont_eval_fix", "kind": "theorem", "module": "Mathlib.Computability.TMConfig", "is_tactic_proof": true, "tactics": ["refine", "simp", "constructor", "suffices", "x", "c", "intro", "obtain", "refine", "simp", "split_ifs", "rw", "exact", "exact", "refine", "rintro", "have", "rw", "obtain", "rw", "swap", "exact", "cases", "refine", "rw", "revert", "by_cases", "refine", "rw", "exact", "exact", "obtain", "have", "rw", "simp", "obtain", "refine", "simp", "split_ifs", "exact", "rintro", "rw", "swap", "exact", "refine", "rw", "obtain", "obtain", "split_ifs", "refine", "rw", "swap", "exact", "rwa", "obtain", "split_ifs", "clear", "refine", "rw", "swap", "exact", "rw", "exact"], "tactic_count": 63}
{"name": "Turing.ToPartrec.code_is_ok", "kind": "theorem", "module": "Mathlib.Computability.TMConfig", "is_tactic_proof": true, "tactics": ["induction", "cons", "rw", "simp", "rw", "exact", "rw", "refine", "exact", "comp", "rw", "simp", "rw", "exact", "rw", "simp", "cases", "fix"], "tactic_count": 18}
{"name": "Turing.ToPartrec.stepNormal_eval", "kind": "theorem", "module": "Mathlib.Computability.TMConfig", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.ToPartrec.stepRet_eval", "kind": "theorem", "module": "Mathlib.Computability.TMConfig", "is_tactic_proof": true, "tactics": ["induction", "halt", "simp", "exact", "cons₁", "rw", "simp", "rw", "exact", "rw", "cons₂", "comp", "rw", "simp", "rw", "exact", "rw", "fix", "rw", "split_ifs", "simp", "congr", "exact"], "tactic_count": 23}
{"name": "Turing.PartrecToTM2.Γ'", "kind": "inductive", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.instDecidableEqΓ'", "kind": "instance", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.instInhabitedΓ'.default", "kind": "definition", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.instInhabitedΓ'", "kind": "instance", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.instFintypeΓ'", "kind": "instance", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.default_Γ'", "kind": "theorem", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.K'", "kind": "inductive", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.instDecidableEqK'", "kind": "instance", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.instInhabitedK'.default", "kind": "definition", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.instInhabitedK'", "kind": "instance", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.Cont'", "kind": "inductive", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.instDecidableEqCont'", "kind": "instance", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.instInhabitedCont'.default", "kind": "definition", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.instInhabitedCont'", "kind": "instance", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.Λ'", "kind": "inductive", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.Λ'.instInhabited", "kind": "instance", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.Λ'.instDecidableEq", "kind": "instance", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.Stmt'", "kind": "definition", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.Cfg'", "kind": "definition", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.natEnd", "kind": "definition", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.pop'", "kind": "definition", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.peek'", "kind": "definition", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.push'", "kind": "definition", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.unrev", "kind": "definition", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.moveExcl", "kind": "definition", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.move₂", "kind": "definition", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.head", "kind": "definition", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.trNormal", "kind": "definition", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.tr", "kind": "definition", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.tr_move", "kind": "theorem", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.tr_push", "kind": "theorem", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.tr_read", "kind": "theorem", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.tr_clear", "kind": "theorem", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.tr_copy", "kind": "theorem", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.tr_succ", "kind": "theorem", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.tr_pred", "kind": "theorem", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.tr_ret_cons₁", "kind": "theorem", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.tr_ret_cons₂", "kind": "theorem", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.tr_ret_comp", "kind": "theorem", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.tr_ret_fix", "kind": "theorem", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.tr_ret_halt", "kind": "theorem", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.trCont", "kind": "definition", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.trPosNum", "kind": "definition", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.trNum", "kind": "definition", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.trNat", "kind": "definition", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.trNat_zero", "kind": "theorem", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Turing.PartrecToTM2.trNat_default", "kind": "theorem", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.trList", "kind": "definition", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.trLList", "kind": "definition", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.contStack", "kind": "definition", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.trContStack", "kind": "definition", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.K'.elim", "kind": "definition", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.K'.elim_main", "kind": "theorem", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.K'.elim_rev", "kind": "theorem", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.K'.elim_aux", "kind": "theorem", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.K'.elim_stack", "kind": "theorem", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.K'.elim_update_main", "kind": "theorem", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": true, "tactics": ["funext"], "tactic_count": 1}
{"name": "Turing.PartrecToTM2.K'.elim_update_rev", "kind": "theorem", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": true, "tactics": ["funext"], "tactic_count": 1}
{"name": "Turing.PartrecToTM2.K'.elim_update_aux", "kind": "theorem", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": true, "tactics": ["funext"], "tactic_count": 1}
{"name": "Turing.PartrecToTM2.K'.elim_update_stack", "kind": "theorem", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": true, "tactics": ["funext"], "tactic_count": 1}
{"name": "Turing.PartrecToTM2.halt", "kind": "definition", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.TrCfg", "kind": "definition", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.splitAtPred", "kind": "definition", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.splitAtPred_eq", "kind": "theorem", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.splitAtPred_false", "kind": "theorem", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.move_ok", "kind": "theorem", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": true, "tactics": ["induction", "nil", "rw", "swap", "rw", "refine", "simp", "grind", "cons", "refine", "rw", "rcases", "cases", "cases", "swap", "cases", "rcases", "rw", "cases", "simp", "convert", "simp", "simp"], "tactic_count": 23}
{"name": "Turing.PartrecToTM2.unrev_ok", "kind": "theorem", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.move₂_ok", "kind": "theorem", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": true, "tactics": ["refine", "simp", "cases", "convert", "simp", "rw", "simp", "simp", "convert", "simp", "rw", "simp"], "tactic_count": 12}
{"name": "Turing.PartrecToTM2.clear_ok", "kind": "theorem", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": true, "tactics": ["induction", "nil", "refine", "rw", "revert", "cases", "rfl", "simp", "revert", "cases", "rcases", "rw", "cons", "refine", "rw", "rcases", "cases", "cases", "swap", "cases", "rcases", "rw", "cases", "simp", "convert"], "tactic_count": 25}
{"name": "Turing.PartrecToTM2.copy_ok", "kind": "theorem", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": true, "tactics": ["induction", "nil", "refine", "simp", "cons", "refine", "rw", "simp", "elim_update_rev,", "pop',", "exact"], "tactic_count": 11}
{"name": "Turing.PartrecToTM2.trPosNum_natEnd", "kind": "theorem", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.trNum_natEnd", "kind": "theorem", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.trNat_natEnd", "kind": "theorem", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.trList_ne_consₗ", "kind": "theorem", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.head_main_ok", "kind": "theorem", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": true, "tactics": ["let", "refine", "cases", "rw", "simp", "trList]", "rw", "refine", "exact", "convert"], "tactic_count": 10}
{"name": "Turing.PartrecToTM2.head_stack_ok", "kind": "theorem", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": true, "tactics": ["rcases", "refine", "rw", "simp", "elim_rev,", "convert", "simp", "refine", "simp", "elim_update_rev,", "refine", "convert", "simp"], "tactic_count": 13}
{"name": "Turing.PartrecToTM2.succ_ok", "kind": "theorem", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": true, "tactics": ["simp", "rcases", "refine", "simp", "convert", "simp", "rfl", "simp", "suffices", "obtain", "simp", "refine", "convert", "simp", "induction", "one", "refine", "simp", "bit1", "obtain", "refine", "simp", "rfl", "bit0", "refine", "simp", "simp", "rfl"], "tactic_count": 28}
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{"name": "Turing.PartrecToTM2.codeSupp'", "kind": "definition", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.codeSupp'_self", "kind": "theorem", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": true, "tactics": ["cases", "first", "rfl", "exact"], "tactic_count": 4}
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{"name": "Turing.PartrecToTM2.codeSupp", "kind": "definition", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.codeSupp_self", "kind": "theorem", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.codeSupp_zero", "kind": "theorem", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Turing.PartrecToTM2.codeSupp_cons", "kind": "theorem", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Turing.PartrecToTM2.codeSupp_comp", "kind": "theorem", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": true, "tactics": ["simp", "rw"], "tactic_count": 2}
{"name": "Turing.PartrecToTM2.codeSupp_case", "kind": "theorem", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Turing.PartrecToTM2.codeSupp_fix", "kind": "theorem", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Turing.PartrecToTM2.contSupp_cons₁", "kind": "theorem", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Turing.PartrecToTM2.contSupp_cons₂", "kind": "theorem", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.contSupp_comp", "kind": "theorem", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.contSupp_fix", "kind": "theorem", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Turing.PartrecToTM2.contSupp_halt", "kind": "theorem", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.Λ'.Supports", "kind": "definition", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.Supports", "kind": "definition", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.PartrecToTM2.supports_insert", "kind": "theorem", "module": "Mathlib.Computability.TMToPartrec", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "Turing.BlankRel.equivalence", "kind": "theorem", "module": "Mathlib.Computability.Tape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.BlankRel.setoid", "kind": "definition", "module": "Mathlib.Computability.Tape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Turing.Tape.move", "kind": "definition", "module": "Mathlib.Computability.Tape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.Tape.move_left_right", "kind": "theorem", "module": "Mathlib.Computability.Tape", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Turing.Tape.move_right_left", "kind": "theorem", "module": "Mathlib.Computability.Tape", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Turing.Tape.mk'", "kind": "definition", "module": "Mathlib.Computability.Tape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.Tape.mk'_left", "kind": "theorem", "module": "Mathlib.Computability.Tape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.Tape.mk'_head", "kind": "theorem", "module": "Mathlib.Computability.Tape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.Tape.mk'_right", "kind": "theorem", "module": "Mathlib.Computability.Tape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.Tape.mk'_right₀", "kind": "theorem", "module": "Mathlib.Computability.Tape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.Tape.mk'_left_right₀", "kind": "theorem", "module": "Mathlib.Computability.Tape", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Turing.Tape.exists_mk'", "kind": "theorem", "module": "Mathlib.Computability.Tape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.Tape.move_left_mk'", "kind": "theorem", "module": "Mathlib.Computability.Tape", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Turing.Tape.move_right_mk'", "kind": "theorem", "module": "Mathlib.Computability.Tape", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Turing.Tape.mk₂", "kind": "definition", "module": "Mathlib.Computability.Tape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.Tape.mk₁", "kind": "definition", "module": "Mathlib.Computability.Tape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.Tape.nth", "kind": "definition", "module": "Mathlib.Computability.Tape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.Tape.nth_zero", "kind": "theorem", "module": "Mathlib.Computability.Tape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.Tape.right₀_nth", "kind": "theorem", "module": "Mathlib.Computability.Tape", "is_tactic_proof": true, "tactics": ["cases", "simp"], "tactic_count": 2}
{"name": "Turing.Tape.mk'_nth_nat", "kind": "theorem", "module": "Mathlib.Computability.Tape", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Turing.Tape.move_left_nth", "kind": "theorem", "module": "Mathlib.Computability.Tape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.Tape.move_right_nth", "kind": "theorem", "module": "Mathlib.Computability.Tape", "is_tactic_proof": true, "tactics": ["conv", "rw"], "tactic_count": 2}
{"name": "Turing.Tape.move_right_n_head", "kind": "theorem", "module": "Mathlib.Computability.Tape", "is_tactic_proof": true, "tactics": ["induction", "rfl", "simp"], "tactic_count": 3}
{"name": "Turing.Tape.write", "kind": "definition", "module": "Mathlib.Computability.Tape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.Tape.write_self", "kind": "theorem", "module": "Mathlib.Computability.Tape", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "Turing.Tape.write_nth", "kind": "theorem", "module": "Mathlib.Computability.Tape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.Tape.write_mk", "kind": "theorem", "module": "Mathlib.Computability.Tape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.Tape.write_mk'", "kind": "theorem", "module": "Mathlib.Computability.Tape", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Turing.Tape.map", "kind": "definition", "module": "Mathlib.Computability.Tape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.Tape.map_fst", "kind": "theorem", "module": "Mathlib.Computability.Tape", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "Turing.Tape.map_write", "kind": "theorem", "module": "Mathlib.Computability.Tape", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "Turing.Tape.write_move_right_n", "kind": "theorem", "module": "Mathlib.Computability.Tape", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "Turing.Tape.map_move", "kind": "theorem", "module": "Mathlib.Computability.Tape", "is_tactic_proof": true, "tactics": ["cases", "cases"], "tactic_count": 2}
{"name": "Turing.Tape.map_mk'", "kind": "theorem", "module": "Mathlib.Computability.Tape", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Turing.Tape.map_mk₂", "kind": "theorem", "module": "Mathlib.Computability.Tape", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Turing.Tape.map_mk₁", "kind": "theorem", "module": "Mathlib.Computability.Tape", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RecursiveIn", "kind": "inductive", "module": "Mathlib.Computability.TuringDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TuringReducible", "kind": "abbrev", "module": "Mathlib.Computability.TuringDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TuringEquivalent", "kind": "abbrev", "module": "Mathlib.Computability.TuringDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computability.term_≤ᵀ_", "kind": "definition", "module": "Mathlib.Computability.TuringDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computability._aux_Mathlib_Computability_TuringDegree___macroRules_Computability_term_≤ᵀ__1", "kind": "definition", "module": "Mathlib.Computability.TuringDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computability._aux_Mathlib_Computability_TuringDegree___unexpand_TuringReducible_1", "kind": "definition", "module": "Mathlib.Computability.TuringDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computability.term_≡ᵀ_", "kind": "definition", "module": "Mathlib.Computability.TuringDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computability._aux_Mathlib_Computability_TuringDegree___macroRules_Computability_term_≡ᵀ__1", "kind": "definition", "module": "Mathlib.Computability.TuringDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computability._aux_Mathlib_Computability_TuringDegree___unexpand_TuringEquivalent_1", "kind": "definition", "module": "Mathlib.Computability.TuringDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Partrec.turingReducible", "kind": "theorem", "module": "Mathlib.Computability.TuringDegree", "is_tactic_proof": true, "tactics": ["induction", "repeat", "pair", "comp", "prec", "rfind"], "tactic_count": 6}
{"name": "TuringReducible.partrec_of_zero", "kind": "theorem", "module": "Mathlib.Computability.TuringDegree", "is_tactic_proof": true, "tactics": ["induction", "repeat", "oracle", "pair", "comp", "prec", "rfind", "repeat"], "tactic_count": 8}
{"name": "partrec_iff_forall_turingReducible", "kind": "theorem", "module": "Mathlib.Computability.TuringDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TuringReducible.refl", "kind": "theorem", "module": "Mathlib.Computability.TuringDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TuringReducible.rfl", "kind": "theorem", "module": "Mathlib.Computability.TuringDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TuringReducible.trans", "kind": "theorem", "module": "Mathlib.Computability.TuringDegree", "is_tactic_proof": true, "tactics": ["induction", "repeat", "oracle", "pair", "comp", "prec", "rfind"], "tactic_count": 7}
{"name": "instIsPreorderPFunNatTuringReducible", "kind": "instance", "module": "Mathlib.Computability.TuringDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TuringEquivalent.equivalence", "kind": "theorem", "module": "Mathlib.Computability.TuringDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TuringEquivalent.refl", "kind": "theorem", "module": "Mathlib.Computability.TuringDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TuringEquivalent.symm", "kind": "theorem", "module": "Mathlib.Computability.TuringDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TuringEquivalent.trans", "kind": "theorem", "module": "Mathlib.Computability.TuringDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TuringDegree", "kind": "abbrev", "module": "Mathlib.Computability.TuringDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Computability.TuringDegree.0.instPreorderPFunNat", "kind": "instance", "module": "Mathlib.Computability.TuringDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TuringDegree.instPartialOrder", "kind": "instance", "module": "Mathlib.Computability.TuringDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "recursiveIn_empty_iff_partrec", "kind": "theorem", "module": "Mathlib.Computability.TuringDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM2.Stmt", "kind": "inductive", "module": "Mathlib.Computability.TuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM2.Stmt.inhabited", "kind": "instance", "module": "Mathlib.Computability.TuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM2.Cfg.inhabited", "kind": "instance", "module": "Mathlib.Computability.TuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM2.stepAux", "kind": "definition", "module": "Mathlib.Computability.TuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM2.step", "kind": "definition", "module": "Mathlib.Computability.TuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM2.Reaches", "kind": "definition", "module": "Mathlib.Computability.TuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM2.SupportsStmt", "kind": "definition", "module": "Mathlib.Computability.TuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM2.stmts₁", "kind": "definition", "module": "Mathlib.Computability.TuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM2.stmts₁_self", "kind": "theorem", "module": "Mathlib.Computability.TuringMachine", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
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{"name": "Turing.TM2.stmts₁_supportsStmt_mono", "kind": "theorem", "module": "Mathlib.Computability.TuringMachine", "is_tactic_proof": true, "tactics": ["induction", "branch", "goto", "halt", "load"], "tactic_count": 5}
{"name": "Turing.TM2.stmts", "kind": "definition", "module": "Mathlib.Computability.TuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM2.stmts_trans", "kind": "theorem", "module": "Mathlib.Computability.TuringMachine", "is_tactic_proof": false, "tactics": ["simp", "exists_imp,", "exact"], "tactic_count": 3}
{"name": "Turing.TM2.Supports", "kind": "definition", "module": "Mathlib.Computability.TuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM2.stmts_supportsStmt", "kind": "theorem", "module": "Mathlib.Computability.TuringMachine", "is_tactic_proof": false, "tactics": ["simp", "exists_imp,", "exact"], "tactic_count": 3}
{"name": "Turing.TM2.step_supports", "kind": "theorem", "module": "Mathlib.Computability.TuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM2.init", "kind": "definition", "module": "Mathlib.Computability.TuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM2.eval", "kind": "definition", "module": "Mathlib.Computability.TuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM2to1.stk_nth_val", "kind": "theorem", "module": "Mathlib.Computability.TuringMachine", "is_tactic_proof": true, "tactics": ["rw", "cases"], "tactic_count": 2}
{"name": "Turing.TM2to1.Γ'", "kind": "definition", "module": "Mathlib.Computability.TuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM2to1.Γ'.inhabited", "kind": "instance", "module": "Mathlib.Computability.TuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM2to1.Γ'.fintype", "kind": "instance", "module": "Mathlib.Computability.TuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM2to1.addBottom", "kind": "definition", "module": "Mathlib.Computability.TuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM2to1.addBottom_map", "kind": "theorem", "module": "Mathlib.Computability.TuringMachine", "is_tactic_proof": true, "tactics": ["simp", "convert", "generalize", "refine"], "tactic_count": 4}
{"name": "Turing.TM2to1.addBottom_modifyNth", "kind": "theorem", "module": "Mathlib.Computability.TuringMachine", "is_tactic_proof": true, "tactics": ["cases", "congr"], "tactic_count": 2}
{"name": "Turing.TM2to1.addBottom_nth_snd", "kind": "theorem", "module": "Mathlib.Computability.TuringMachine", "is_tactic_proof": true, "tactics": ["conv"], "tactic_count": 1}
{"name": "Turing.TM2to1.addBottom_nth_succ_fst", "kind": "theorem", "module": "Mathlib.Computability.TuringMachine", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Turing.TM2to1.addBottom_head_fst", "kind": "theorem", "module": "Mathlib.Computability.TuringMachine", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Turing.TM2to1.StAct", "kind": "inductive", "module": "Mathlib.Computability.TuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM2to1.StAct.inhabited", "kind": "instance", "module": "Mathlib.Computability.TuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM2to1.stRun", "kind": "definition", "module": "Mathlib.Computability.TuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM2to1.stVar", "kind": "definition", "module": "Mathlib.Computability.TuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM2to1.stWrite", "kind": "definition", "module": "Mathlib.Computability.TuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM2to1.stmtStRec", "kind": "definition", "module": "Mathlib.Computability.TuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM2to1.supports_run", "kind": "theorem", "module": "Mathlib.Computability.TuringMachine", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Turing.TM2to1.Λ'", "kind": "inductive", "module": "Mathlib.Computability.TuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM2to1.Λ'.inhabited", "kind": "instance", "module": "Mathlib.Computability.TuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM2to1.trStAct", "kind": "definition", "module": "Mathlib.Computability.TuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM2to1.trInit", "kind": "definition", "module": "Mathlib.Computability.TuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM2to1.step_run", "kind": "theorem", "module": "Mathlib.Computability.TuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM2to1.trNormal", "kind": "definition", "module": "Mathlib.Computability.TuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM2to1.trNormal_run", "kind": "theorem", "module": "Mathlib.Computability.TuringMachine", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Turing.TM2to1.trStmts₁", "kind": "definition", "module": "Mathlib.Computability.TuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM2to1.trStmts₁_run", "kind": "theorem", "module": "Mathlib.Computability.TuringMachine", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Turing.TM2to1.tr_respects_aux₂", "kind": "theorem", "module": "Mathlib.Computability.TuringMachine", "is_tactic_proof": true, "tactics": ["simp", "cases", "push", "have", "refine", "rw", "erw", "rw", "rfl⟩", "refine", "rw", "by_cases", "subst", "split_ifs", "rw", "simp", "rw", "rcases", "rw", "simpa", "rw", "simp", "split_ifs", "rw", "peek", "rw", "use", "cases", "rw", "addBottom_nth_snd,", "rfl", "pop", "rcases", "simp", "iterate_zero_apply,", "rw", "exact", "refine", "erw", "iterate_succ',", "addBottom_modifyNth", "show", "rw", "refine", "rw", "by_cases", "subst", "split_ifs", "rw", "rfl", "rw", "rw", "rcases", "rw", "simpa", "rw", "simp", "split_ifs", "rw"], "tactic_count": 59}
{"name": "Turing.TM2to1.tr", "kind": "definition", "module": "Mathlib.Computability.TuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM2to1.TrCfg", "kind": "inductive", "module": "Mathlib.Computability.TuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM2to1.tr_respects_aux₁", "kind": "theorem", "module": "Mathlib.Computability.TuringMachine", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "apply", "rw", "simp", "rw", "rfl", "rwa"], "tactic_count": 9}
{"name": "Turing.TM2to1.tr_respects_aux₃", "kind": "theorem", "module": "Mathlib.Computability.TuringMachine", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "refine", "simp", "rw", "iterate_succ',", "rfl"], "tactic_count": 8}
{"name": "Turing.TM2to1.tr_respects_aux", "kind": "theorem", "module": "Mathlib.Computability.TuringMachine", "is_tactic_proof": true, "tactics": ["simp", "have", "obtain", "have", "rw", "obtain", "refine", "rw", "exact"], "tactic_count": 9}
{"name": "Turing.TM2to1.tr_respects", "kind": "theorem", "module": "Mathlib.Computability.TuringMachine", "is_tactic_proof": true, "tactics": ["intro", "obtain", "rsuffices", "exact", "simp", "generalize", "induction", "run", "load", "branch", "unfold", "beta_reduce", "cases", "goto", "halt"], "tactic_count": 15}
{"name": "Turing.TM2to1.trCfg_init", "kind": "theorem", "module": "Mathlib.Computability.TuringMachine", "is_tactic_proof": true, "tactics": ["rw", "refine", "refine", "rw", "have", "rfl", "rw", "simp", "by_cases", "subst", "simp", "rw", "simp", "rw", "cases", "rw", "congr", "simp", "rfl"], "tactic_count": 19}
{"name": "Turing.TM2to1.tr_eval_dom", "kind": "theorem", "module": "Mathlib.Computability.TuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM2to1.tr_eval", "kind": "theorem", "module": "Mathlib.Computability.TuringMachine", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "obtain", "cases", "exact"], "tactic_count": 5}
{"name": "Turing.TM2to1.trSupp", "kind": "definition", "module": "Mathlib.Computability.TuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Turing.TM2to1.tr_supports", "kind": "theorem", "module": "Mathlib.Computability.TuringMachine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Condensed.hasExactColimitsOfShape", "kind": "theorem", "module": "Mathlib.Condensed.AB", "is_tactic_proof": false, "tactics": ["let", "exact"], "tactic_count": 2}
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{"name": "CompHausLike.LocallyConstant.instIsIsoFunctorTypeUnitSheafCoherentTopologyAdjunction", "kind": "instance", "module": "Mathlib.Condensed.Discrete.LocallyConstant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CondensedSet.LocallyConstant.functorFullyFaithful", "kind": "definition", "module": "Mathlib.Condensed.Discrete.LocallyConstant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CondensedSet.LocallyConstant.instFaithfulFunctor", "kind": "instance", "module": "Mathlib.Condensed.Discrete.LocallyConstant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CondensedSet.LocallyConstant.instFullFunctor", "kind": "instance", "module": "Mathlib.Condensed.Discrete.LocallyConstant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CondensedSet.LocallyConstant.instFaithfulCondensedTypeDiscrete", "kind": "instance", "module": "Mathlib.Condensed.Discrete.LocallyConstant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CondensedSet.LocallyConstant.instFullCondensedTypeDiscrete", "kind": "instance", "module": "Mathlib.Condensed.Discrete.LocallyConstant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondSet.LocallyConstant.functor", "kind": "abbrev", "module": "Mathlib.Condensed.Discrete.LocallyConstant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondSet.LocallyConstant.instHasPropAndTotallyDisconnectedSpaceCarrierSecondCountableTopologySubtypeToTop", "kind": "instance", "module": "Mathlib.Condensed.Discrete.LocallyConstant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondSet.LocallyConstant.iso", "kind": "definition", "module": "Mathlib.Condensed.Discrete.LocallyConstant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondSet.LocallyConstant.functorFullyFaithful", "kind": "definition", "module": "Mathlib.Condensed.Discrete.LocallyConstant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondSet.LocallyConstant.instFaithfulFunctor", "kind": "instance", "module": "Mathlib.Condensed.Discrete.LocallyConstant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondSet.LocallyConstant.instFullFunctor", "kind": "instance", "module": "Mathlib.Condensed.Discrete.LocallyConstant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondSet.LocallyConstant.instFaithfulLightCondensedTypeDiscrete", "kind": "instance", "module": "Mathlib.Condensed.Discrete.LocallyConstant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondSet.LocallyConstant.instFullLightCondensedTypeDiscrete", "kind": "instance", "module": "Mathlib.Condensed.Discrete.LocallyConstant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.LocallyConstantModule.functorToPresheaves", "kind": "definition", "module": "Mathlib.Condensed.Discrete.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.LocallyConstantModule.functor", "kind": "definition", "module": "Mathlib.Condensed.Discrete.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CondensedMod.LocallyConstant.functorToPresheaves", "kind": "abbrev", "module": "Mathlib.Condensed.Discrete.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CondensedMod.LocallyConstant.functor", "kind": "abbrev", "module": "Mathlib.Condensed.Discrete.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CondensedMod.LocallyConstant.functorIsoDiscreteAux₁", "kind": "definition", "module": "Mathlib.Condensed.Discrete.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CondensedMod.LocallyConstant.functorIsoDiscreteAux₂", "kind": "definition", "module": "Mathlib.Condensed.Discrete.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CondensedMod.LocallyConstant.instIsIsoCondensedSetMapForgetAppCondensedModuleCatCounitDiscreteUnderlyingAdjObjFunctor", "kind": "instance", "module": "Mathlib.Condensed.Discrete.Module", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "refine", "have", "have", "rw", "constructor", "change", "rw", "exact"], "tactic_count": 10}
{"name": "CondensedMod.LocallyConstant.functorIsoDiscreteComponents", "kind": "definition", "module": "Mathlib.Condensed.Discrete.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CondensedMod.LocallyConstant.functorIsoDiscrete", "kind": "definition", "module": "Mathlib.Condensed.Discrete.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CondensedMod.LocallyConstant.adjunction", "kind": "definition", "module": "Mathlib.Condensed.Discrete.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CondensedMod.LocallyConstant.fullyFaithfulFunctor", "kind": "definition", "module": "Mathlib.Condensed.Discrete.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CondensedMod.LocallyConstant.instFaithfulModuleCatFunctor", "kind": "instance", "module": "Mathlib.Condensed.Discrete.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CondensedMod.LocallyConstant.instFullModuleCatFunctor", "kind": "instance", "module": "Mathlib.Condensed.Discrete.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CondensedMod.LocallyConstant.instFaithfulModuleCatCondensedDiscrete", "kind": "instance", "module": "Mathlib.Condensed.Discrete.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CondensedMod.LocallyConstant.instFaithfulModuleCatSheafCompHausCoherentTopologyConstantSheaf", "kind": "instance", "module": "Mathlib.Condensed.Discrete.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CondensedMod.LocallyConstant.instFullModuleCatCondensedDiscrete", "kind": "instance", "module": "Mathlib.Condensed.Discrete.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CondensedMod.LocallyConstant.instFullModuleCatSheafCompHausCoherentTopologyConstantSheaf", "kind": "instance", "module": "Mathlib.Condensed.Discrete.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CondensedMod.LocallyConstant.instFaithfulSheafCompHausCoherentTopologyTypeConstantSheaf", "kind": "instance", "module": "Mathlib.Condensed.Discrete.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CondensedMod.LocallyConstant.instFullSheafCompHausCoherentTopologyTypeConstantSheaf", "kind": "instance", "module": "Mathlib.Condensed.Discrete.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondMod.LocallyConstant.functorToPresheaves", "kind": "abbrev", "module": "Mathlib.Condensed.Discrete.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LightCondMod.LocallyConstant.functorIsoDiscreteAux₁", "kind": "definition", "module": "Mathlib.Condensed.Discrete.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LightCondMod.LocallyConstant.instIsIsoLightCondSetMapForgetAppLightCondensedModuleCatCounitDiscreteUnderlyingAdjObjFunctor", "kind": "instance", "module": "Mathlib.Condensed.Discrete.Module", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "refine", "have", "inferInstanceAs", "have", "rw", "constructor", "change", "rw", "exact"], "tactic_count": 11}
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{"name": "LightCondMod.LocallyConstant.fullyFaithfulFunctor", "kind": "definition", "module": "Mathlib.Condensed.Discrete.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondMod.LocallyConstant.instFaithfulModuleCatFunctor", "kind": "instance", "module": "Mathlib.Condensed.Discrete.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondMod.LocallyConstant.instFullModuleCatFunctor", "kind": "instance", "module": "Mathlib.Condensed.Discrete.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondMod.LocallyConstant.instFaithfulModuleCatLightCondensedDiscrete", "kind": "instance", "module": "Mathlib.Condensed.Discrete.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondMod.LocallyConstant.instFaithfulModuleCatSheafLightProfiniteCoherentTopologyConstantSheaf", "kind": "instance", "module": "Mathlib.Condensed.Discrete.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondMod.LocallyConstant.instFullModuleCatLightCondensedDiscrete", "kind": "instance", "module": "Mathlib.Condensed.Discrete.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondMod.LocallyConstant.instFullModuleCatSheafLightProfiniteCoherentTopologyConstantSheaf", "kind": "instance", "module": "Mathlib.Condensed.Discrete.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondMod.LocallyConstant.instFaithfulSheafLightProfiniteCoherentTopologyTypeConstantSheaf", "kind": "instance", "module": "Mathlib.Condensed.Discrete.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondMod.LocallyConstant.instFullSheafLightProfiniteCoherentTopologyTypeConstantSheaf", "kind": "instance", "module": "Mathlib.Condensed.Discrete.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instPreservesEpimorphismsCompHausCondensedSetCompHausToCondensed", "kind": "instance", "module": "Mathlib.Condensed.EffectiveEpi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsRegularEpiCategoryCondensedSet", "kind": "instance", "module": "Mathlib.Condensed.EffectiveEpi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_example", "kind": "example", "module": "Mathlib.Condensed.EffectiveEpi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Condensed.epi_iff_locallySurjective_on_compHaus", "kind": "theorem", "module": "Mathlib.Condensed.Epi", "is_tactic_proof": false, "tactics": ["rw", "simp_rw"], "tactic_count": 2}
{"name": "Condensed.epi_iff_surjective_on_stonean", "kind": "theorem", "module": "Mathlib.Condensed.Epi", "is_tactic_proof": false, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CondensedSet.epi_iff_locallySurjective_on_compHaus", "kind": "theorem", "module": "Mathlib.Condensed.Epi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CondensedSet.epi_iff_surjective_on_stonean", "kind": "theorem", "module": "Mathlib.Condensed.Epi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CondensedMod.epi_iff_locallySurjective_on_compHaus", "kind": "theorem", "module": "Mathlib.Condensed.Epi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Condensed.StoneanCompHaus.equivalence", "kind": "definition", "module": "Mathlib.Condensed.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Condensed.StoneanProfinite.instPreservesEffectiveEpisStoneanProfiniteToProfinite", "kind": "instance", "module": "Mathlib.Condensed.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Condensed.StoneanProfinite.instReflectsEffectiveEpisStoneanProfiniteToProfinite", "kind": "instance", "module": "Mathlib.Condensed.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Condensed.StoneanProfinite.stoneanToProfiniteEffectivePresentation", "kind": "definition", "module": "Mathlib.Condensed.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Condensed.StoneanProfinite.instEffectivelyEnoughStoneanProfiniteToProfinite", "kind": "instance", "module": "Mathlib.Condensed.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Condensed.StoneanProfinite.equivalence", "kind": "definition", "module": "Mathlib.Condensed.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Condensed.ProfiniteCompHaus.equivalence", "kind": "definition", "module": "Mathlib.Condensed.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Condensed.isSheafProfinite", "kind": "theorem", "module": "Mathlib.Condensed.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Condensed.isSheafStonean", "kind": "theorem", "module": "Mathlib.Condensed.Equivalence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Condensed.ofSheafStonean", "kind": "definition", "module": "Mathlib.Condensed.Explicit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Condensed.ofSheafForgetStonean", "kind": "definition", "module": "Mathlib.Condensed.Explicit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Condensed.ofSheafProfinite", "kind": "definition", "module": "Mathlib.Condensed.Explicit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Condensed.ofSheafForgetProfinite", "kind": "definition", "module": "Mathlib.Condensed.Explicit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Condensed.ofSheafCompHaus", "kind": "definition", "module": "Mathlib.Condensed.Explicit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Condensed.ofSheafForgetCompHaus", "kind": "definition", "module": "Mathlib.Condensed.Explicit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Condensed.equalizerCondition", "kind": "theorem", "module": "Mathlib.Condensed.Explicit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Condensed.instPreservesFiniteProductsOppositeCompHausVal", "kind": "instance", "module": "Mathlib.Condensed.Explicit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Condensed.instPreservesFiniteProductsOppositeProfiniteVal", "kind": "instance", "module": "Mathlib.Condensed.Explicit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Condensed.equalizerCondition_profinite", "kind": "theorem", "module": "Mathlib.Condensed.Explicit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Condensed.instPreservesFiniteProductsOppositeStoneanVal", "kind": "instance", "module": "Mathlib.Condensed.Explicit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CondensedSet.ofSheafStonean", "kind": "abbrev", "module": "Mathlib.Condensed.Explicit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CondensedSet.ofSheafProfinite", "kind": "abbrev", "module": "Mathlib.Condensed.Explicit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CondensedSet.ofSheafCompHaus", "kind": "abbrev", "module": "Mathlib.Condensed.Explicit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CondensedMod.ofSheafStonean", "kind": "abbrev", "module": "Mathlib.Condensed.Explicit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CondensedMod.ofSheafProfinite", "kind": "abbrev", "module": "Mathlib.Condensed.Explicit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CondensedMod.ofSheafCompHaus", "kind": "abbrev", "module": "Mathlib.Condensed.Explicit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Condensed.ulift", "kind": "definition", "module": "Mathlib.Condensed.Functors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFullCondensedTypeCondensedSetUlift", "kind": "instance", "module": "Mathlib.Condensed.Functors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFaithfulCondensedTypeCondensedSetUlift", "kind": "instance", "module": "Mathlib.Condensed.Functors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "compHausToCondensed'", "kind": "definition", "module": "Mathlib.Condensed.Functors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "compHausToCondensed", "kind": "definition", "module": "Mathlib.Condensed.Functors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHaus.toCondensed", "kind": "abbrev", "module": "Mathlib.Condensed.Functors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "profiniteToCondensed", "kind": "definition", "module": "Mathlib.Condensed.Functors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.toCondensed", "kind": "abbrev", "module": "Mathlib.Condensed.Functors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "stoneanToCondensed", "kind": "definition", "module": "Mathlib.Condensed.Functors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stonean.toCondensed", "kind": "abbrev", "module": "Mathlib.Condensed.Functors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFullCompHausCondensedTypeCompHausToCondensed'", "kind": "instance", "module": "Mathlib.Condensed.Functors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFaithfulCompHausCondensedTypeCompHausToCondensed'", "kind": "instance", "module": "Mathlib.Condensed.Functors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFullCompHausCondensedSetCompHausToCondensed", "kind": "instance", "module": "Mathlib.Condensed.Functors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFaithfulCompHausCondensedSetCompHausToCondensed", "kind": "instance", "module": "Mathlib.Condensed.Functors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondensed.instCountableAB4StarLightCondMod", "kind": "instance", "module": "Mathlib.Condensed.Light.AB", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondensed.instIsGrothendieckAbelianLightCondMod", "kind": "instance", "module": "Mathlib.Condensed.Light.AB", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondensed", "kind": "definition", "module": "Mathlib.Condensed.Light.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCategoryLightCondensed", "kind": "instance", "module": "Mathlib.Condensed.Light.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondSet", "kind": "abbrev", "module": "Mathlib.Condensed.Light.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondensed.id_val", "kind": "theorem", "module": "Mathlib.Condensed.Light.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondensed.comp_val", "kind": "theorem", "module": "Mathlib.Condensed.Light.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondensed.hom_ext", "kind": "theorem", "module": "Mathlib.Condensed.Light.Basic", "is_tactic_proof": true, "tactics": ["apply", "ext", "exact"], "tactic_count": 3}
{"name": "LightCondSet.hom_naturality_apply", "kind": "theorem", "module": "Mathlib.Condensed.Light.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCartesianMonoidalCategoryLightCondSet", "kind": "instance", "module": "Mathlib.Condensed.Light.CartesianClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instMonoidalClosedLightCondSet", "kind": "instance", "module": "Mathlib.Condensed.Light.CartesianClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instPreservesEpimorphismsLightProfiniteLightCondSetLightProfiniteToLightCondSet", "kind": "instance", "module": "Mathlib.Condensed.Light.EffectiveEpi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsRegularEpiCategoryLightCondSet", "kind": "instance", "module": "Mathlib.Condensed.Light.EffectiveEpi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_example", "kind": "example", "module": "Mathlib.Condensed.Light.EffectiveEpi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondensed.isLocallySurjective_iff_locallySurjective_on_lightProfinite", "kind": "theorem", "module": "Mathlib.Condensed.Light.Epi", "is_tactic_proof": true, "tactics": ["rw", "simp_rw"], "tactic_count": 2}
{"name": "LightCondSet.epi_iff_locallySurjective_on_lightProfinite", "kind": "theorem", "module": "Mathlib.Condensed.Light.Epi", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "LightCondMod.epi_iff_locallySurjective_on_lightProfinite", "kind": "theorem", "module": "Mathlib.Condensed.Light.Epi", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "LightCondMod.instReflectsEpimorphismsLightCondSetForget", "kind": "instance", "module": "Mathlib.Condensed.Light.Epi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondMod.instPreservesEpimorphismsLightCondSetForget", "kind": "instance", "module": "Mathlib.Condensed.Light.Epi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondensed.epi_π_app_zero_of_epi", "kind": "theorem", "module": "Mathlib.Condensed.Light.Epi", "is_tactic_proof": true, "tactics": ["apply", "change", "apply", "simp", "exact", "have", "exact", "exact"], "tactic_count": 8}
{"name": "LightCondensed.instEpiLightCondModMapNat", "kind": "instance", "module": "Mathlib.Condensed.Light.Epi", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "LightCondensed.instPreservesEpimorphismsFunctorDiscreteNatLightCondModLim", "kind": "instance", "module": "Mathlib.Condensed.Light.Epi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondensed.ofSheafLightProfinite", "kind": "definition", "module": "Mathlib.Condensed.Light.Explicit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondensed.ofSheafForgetLightProfinite", "kind": "definition", "module": "Mathlib.Condensed.Light.Explicit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondensed.equalizerCondition", "kind": "theorem", "module": "Mathlib.Condensed.Light.Explicit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondensed.instPreservesFiniteProductsOppositeLightProfiniteVal", "kind": "instance", "module": "Mathlib.Condensed.Light.Explicit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondSet.ofSheafLightProfinite", "kind": "abbrev", "module": "Mathlib.Condensed.Light.Explicit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondMod.ofSheafLightProfinite", "kind": "abbrev", "module": "Mathlib.Condensed.Light.Explicit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondAb.ofSheafLightProfinite", "kind": "abbrev", "module": "Mathlib.Condensed.Light.Explicit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lightProfiniteToLightCondSet", "kind": "definition", "module": "Mathlib.Condensed.Light.Functors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightProfinite.toCondensed", "kind": "abbrev", "module": "Mathlib.Condensed.Light.Functors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lightProfiniteToLightCondSetFullyFaithful", "kind": "abbrev", "module": "Mathlib.Condensed.Light.Functors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFullLightProfiniteLightCondSetLightProfiniteToLightCondSet", "kind": "instance", "module": "Mathlib.Condensed.Light.Functors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFaithfulLightProfiniteLightCondSetLightProfiniteToLightCondSet", "kind": "instance", "module": "Mathlib.Condensed.Light.Functors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lightProfiniteToLightCondSetIsoTopCatToLightCondSet", "kind": "definition", "module": "Mathlib.Condensed.Light.Functors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instPreservesLimitsOfShapeLightProfiniteLightCondSetLightProfiniteToLightCondSetOfCountableCategory", "kind": "instance", "module": "Mathlib.Condensed.Light.Functors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instPreservesFiniteLimitsLightProfiniteLightCondSetLightProfiniteToLightCondSet", "kind": "instance", "module": "Mathlib.Condensed.Light.Functors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instMonoidalLightProfiniteLightCondSetLightProfiniteToLightCondSet", "kind": "instance", "module": "Mathlib.Condensed.Light.Functors", "is_tactic_proof": false, "tactics": ["have", "rw", "infer_instance", "exact"], "tactic_count": 4}
{"name": "LightProfinite.hasSheafify", "kind": "instance", "module": "Mathlib.Condensed.Light.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightProfinite.hasSheafify_type", "kind": "instance", "module": "Mathlib.Condensed.Light.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightProfinite.instWEqualsLocallyBijectiveCoherentTopology", "kind": "instance", "module": "Mathlib.Condensed.Light.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondensed.ihomPoints", "kind": "definition", "module": "Mathlib.Condensed.Light.InternallyProjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondensed.ihomPoints_apply", "kind": "theorem", "module": "Mathlib.Condensed.Light.InternallyProjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondensed.ihomPoints_symm_apply", "kind": "theorem", "module": "Mathlib.Condensed.Light.InternallyProjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondensed.ihom_map_val_app", "kind": "theorem", "module": "Mathlib.Condensed.Light.InternallyProjective", "is_tactic_proof": true, "tactics": ["apply", "simp", "congr", "cat_disch"], "tactic_count": 4}
{"name": "LightCondensed.ihomPoints_symm_comp", "kind": "theorem", "module": "Mathlib.Condensed.Light.InternallyProjective", "is_tactic_proof": false, "tactics": ["have", "simp", "rfl"], "tactic_count": 3}
{"name": "LightCondensed.internallyProjective_iff_tensor_condition", "kind": "theorem", "module": "Mathlib.Condensed.Light.InternallyProjective", "is_tactic_proof": true, "tactics": ["refine", "have", "rw", "specialize", "obtain", "refine", "rw", "apply", "rw", "exact", "rw", "intro", "specialize", "obtain", "refine", "rw", "have", "dsimp", "rw", "simp"], "tactic_count": 20}
{"name": "LightCondensed.internallyProjective_iff_tensor_condition'", "kind": "theorem", "module": "Mathlib.Condensed.Light.InternallyProjective", "is_tactic_proof": true, "tactics": ["rw", "refine", "specialize", "obtain", "refine", "simp", "specialize", "obtain", "refine", "simp"], "tactic_count": 10}
{"name": "LightCondensed.free_internallyProjective_iff_tensor_condition", "kind": "theorem", "module": "Mathlib.Condensed.Light.InternallyProjective", "is_tactic_proof": true, "tactics": ["rw", "refine", "specialize", "obtain", "refine", "rw", "simp", "simp", "specialize", "obtain", "refine", "rw", "simp"], "tactic_count": 13}
{"name": "LightCondensed.free_internallyProjective_iff_tensor_condition'", "kind": "theorem", "module": "Mathlib.Condensed.Light.InternallyProjective", "is_tactic_proof": true, "tactics": ["rw", "refine", "specialize", "obtain", "refine", "rw", "simp", "specialize", "obtain", "refine", "rw", "simp"], "tactic_count": 12}
{"name": "LightCondensed.free_lightProfinite_internallyProjective_iff_tensor_condition", "kind": "theorem", "module": "Mathlib.Condensed.Light.InternallyProjective", "is_tactic_proof": true, "tactics": ["rw", "refine", "specialize", "obtain", "refine", "rw", "simp", "specialize", "obtain", "refine", "rw", "simp"], "tactic_count": 12}
{"name": "LightCondensed.free_lightProfinite_internallyProjective_iff_tensor_condition'", "kind": "theorem", "module": "Mathlib.Condensed.Light.InternallyProjective", "is_tactic_proof": true, "tactics": ["rw", "refine", "specialize", "obtain", "refine", "rw", "simp", "specialize", "obtain", "refine", "rw", "simp"], "tactic_count": 12}
{"name": "instHasLimitsOfSizeLightCondSet", "kind": "instance", "module": "Mathlib.Condensed.Light.Limits", "is_tactic_proof": true, "tactics": ["change", "infer_instance"], "tactic_count": 2}
{"name": "instHasFiniteLimitsLightCondSet", "kind": "instance", "module": "Mathlib.Condensed.Light.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instHasLimitsOfSizeLightCondMod", "kind": "instance", "module": "Mathlib.Condensed.Light.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instHasLimitsOfSizeLightCondMod_1", "kind": "instance", "module": "Mathlib.Condensed.Light.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instHasFiniteLimitsLightCondMod", "kind": "instance", "module": "Mathlib.Condensed.Light.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondMod", "kind": "abbrev", "module": "Mathlib.Condensed.Light.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instAbelianLightCondMod", "kind": "instance", "module": "Mathlib.Condensed.Light.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondensed.forget", "kind": "definition", "module": "Mathlib.Condensed.Light.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondensed.free", "kind": "definition", "module": "Mathlib.Condensed.Light.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondensed.freeForgetAdjunction", "kind": "definition", "module": "Mathlib.Condensed.Light.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondAb", "kind": "abbrev", "module": "Mathlib.Condensed.Light.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_example", "kind": "example", "module": "Mathlib.Condensed.Light.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondMod.hom_naturality_apply", "kind": "theorem", "module": "Mathlib.Condensed.Light.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondensed.instIsMonoidalFunctorOppositeLightProfiniteModuleCatWCoherentTopology", "kind": "instance", "module": "Mathlib.Condensed.Light.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondensed.instMonoidalCategoryLightCondMod", "kind": "instance", "module": "Mathlib.Condensed.Light.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondensed.instMonoidalCategorySheafLightProfiniteCoherentTopologyModuleCat", "kind": "instance", "module": "Mathlib.Condensed.Light.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondensed.instSymmetricCategoryLightCondMod", "kind": "instance", "module": "Mathlib.Condensed.Light.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondensed.instMonoidalClosedFunctorOppositeLightProfiniteModuleCat", "kind": "instance", "module": "Mathlib.Condensed.Light.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondensed.instMonoidalClosedSheafLightProfiniteCoherentTopologyModuleCat", "kind": "instance", "module": "Mathlib.Condensed.Light.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondensed.instMonoidalClosedLightCondMod", "kind": "instance", "module": "Mathlib.Condensed.Light.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondensed.instMonoidalFunctorOppositeLightProfiniteModuleCatSheafCoherentTopologyPresheafToSheaf", "kind": "instance", "module": "Mathlib.Condensed.Light.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondensed.instMonoidalLightCondSetLightCondModFree", "kind": "instance", "module": "Mathlib.Condensed.Light.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondensed.equivSmall", "kind": "abbrev", "module": "Mathlib.Condensed.Light.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondensed.instSmallHom", "kind": "instance", "module": "Mathlib.Condensed.Light.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondensed.equivSmallSheafificationIso", "kind": "definition", "module": "Mathlib.Condensed.Light.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondensed.equivSmallFreeIso", "kind": "definition", "module": "Mathlib.Condensed.Light.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Condensed.Light.TopCatAdjunction.0.LightCondSet.coinducingCoprod", "kind": "definition", "module": "Mathlib.Condensed.Light.TopCatAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondSet.underlyingTopologicalSpace", "kind": "instance", "module": "Mathlib.Condensed.Light.TopCatAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondSet.toTopCat", "kind": "abbrev", "module": "Mathlib.Condensed.Light.TopCatAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondSet.continuous_coinducingCoprod", "kind": "theorem", "module": "Mathlib.Condensed.Light.TopCatAdjunction", "is_tactic_proof": false, "tactics": ["suffices", "from", "rw", "apply"], "tactic_count": 4}
{"name": "LightCondSet.toTopCatMap", "kind": "definition", "module": "Mathlib.Condensed.Light.TopCatAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lightCondSetToTopCat", "kind": "definition", "module": "Mathlib.Condensed.Light.TopCatAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondSet.topCatAdjunctionCounit", "kind": "definition", "module": "Mathlib.Condensed.Light.TopCatAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondSet.topCatAdjunctionCounitEquiv", "kind": "definition", "module": "Mathlib.Condensed.Light.TopCatAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondSet.topCatAdjunctionCounit_bijective", "kind": "theorem", "module": "Mathlib.Condensed.Light.TopCatAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondSet.topCatAdjunctionUnit", "kind": "definition", "module": "Mathlib.Condensed.Light.TopCatAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondSet.topCatAdjunction", "kind": "definition", "module": "Mathlib.Condensed.Light.TopCatAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondSet.instEpiTopCatAppCounitTopCatAdjunction", "kind": "instance", "module": "Mathlib.Condensed.Light.TopCatAdjunction", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "LightCondSet.instFaithfulTopCatTopCatToLightCondSet", "kind": "instance", "module": "Mathlib.Condensed.Light.TopCatAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondSet.instSequentialSpaceCarrierToTopCat", "kind": "instance", "module": "Mathlib.Condensed.Light.TopCatAdjunction", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "LightCondSet.instSequentialSpaceCarrierObjTopCatLightCondSetToTopCat", "kind": "instance", "module": "Mathlib.Condensed.Light.TopCatAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondSet.lightCondSetToSequential", "kind": "definition", "module": "Mathlib.Condensed.Light.TopCatAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondSet.sequentialToLightCondSet", "kind": "definition", "module": "Mathlib.Condensed.Light.TopCatAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondSet.sequentialAdjunction", "kind": "definition", "module": "Mathlib.Condensed.Light.TopCatAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondSet.sequentialAdjunctionHomeo", "kind": "definition", "module": "Mathlib.Condensed.Light.TopCatAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondSet.sequentialAdjunctionCounitIso", "kind": "definition", "module": "Mathlib.Condensed.Light.TopCatAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightCondSet.instIsIsoFunctorSequentialCounitSequentialAdjunction", "kind": "instance", "module": "Mathlib.Condensed.Light.TopCatAdjunction", "is_tactic_proof": true, "tactics": ["rw", "intro", "exact"], "tactic_count": 3}
{"name": "LightCondSet.fullyFaithfulSequentialToLightCondSet", "kind": "definition", "module": "Mathlib.Condensed.Light.TopCatAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.toLightCondSet", "kind": "abbrev", "module": "Mathlib.Condensed.Light.TopComparison", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "topCatToLightCondSet", "kind": "abbrev", "module": "Mathlib.Condensed.Light.TopComparison", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instHasLimitsCondensedSet", "kind": "instance", "module": "Mathlib.Condensed.Limits", "is_tactic_proof": true, "tactics": ["change", "infer_instance"], "tactic_count": 2}
{"name": "instHasLimitsOfSizeCondensedSet", "kind": "instance", "module": "Mathlib.Condensed.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instHasLimitsCondensedMod", "kind": "instance", "module": "Mathlib.Condensed.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instHasColimitsCondensedMod", "kind": "instance", "module": "Mathlib.Condensed.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instHasLimitsOfSizeCondensedMod", "kind": "instance", "module": "Mathlib.Condensed.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instHasColimitsOfShapeCondensedOfHasWeakSheafifyCompHausCoherentTopology", "kind": "instance", "module": "Mathlib.Condensed.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instHasLimitsOfShapeCondensed", "kind": "instance", "module": "Mathlib.Condensed.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instHasFiniteLimitsCondensed", "kind": "instance", "module": "Mathlib.Condensed.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instHasFiniteColimitsCondensedOfHasWeakSheafifyCompHausCoherentTopology", "kind": "instance", "module": "Mathlib.Condensed.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CondensedMod", "kind": "abbrev", "module": "Mathlib.Condensed.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instAbelianCondensedMod", "kind": "instance", "module": "Mathlib.Condensed.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Condensed.forget", "kind": "definition", "module": "Mathlib.Condensed.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Condensed.free", "kind": "definition", "module": "Mathlib.Condensed.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Condensed.freeForgetAdjunction", "kind": "definition", "module": "Mathlib.Condensed.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CondensedAb", "kind": "abbrev", "module": "Mathlib.Condensed.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_example", "kind": "example", "module": "Mathlib.Condensed.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Condensed.abForget", "kind": "abbrev", "module": "Mathlib.Condensed.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Condensed.freeAb", "kind": "abbrev", "module": "Mathlib.Condensed.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Condensed.setAbAdjunction", "kind": "abbrev", "module": "Mathlib.Condensed.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CondensedMod.hom_naturality_apply", "kind": "theorem", "module": "Mathlib.Condensed.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Condensed.finFree", "kind": "abbrev", "module": "Mathlib.Condensed.Solid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Condensed.profiniteFree", "kind": "abbrev", "module": "Mathlib.Condensed.Solid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Condensed.profiniteSolid", "kind": "definition", "module": "Mathlib.Condensed.Solid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Condensed.profiniteSolidCounit", "kind": "definition", "module": "Mathlib.Condensed.Solid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Condensed.instIsRightKanExtensionFintypeCatCondensedModProfiniteProfiniteSolidProfiniteSolidCounit", "kind": "instance", "module": "Mathlib.Condensed.Solid", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "Condensed.profiniteSolidIsPointwiseRightKanExtension", "kind": "definition", "module": "Mathlib.Condensed.Solid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Condensed.profiniteSolidification", "kind": "definition", "module": "Mathlib.Condensed.Solid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Condensed.TopCatAdjunction.0.CondensedSet.coinducingCoprod", "kind": "definition", "module": "Mathlib.Condensed.TopCatAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instTopologicalSpaceObjOppositeCompHausValOpOfPUnit", "kind": "instance", "module": "Mathlib.Condensed.TopCatAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CondensedSet.toTopCat", "kind": "abbrev", "module": "Mathlib.Condensed.TopCatAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CondensedSet.continuous_coinducingCoprod", "kind": "theorem", "module": "Mathlib.Condensed.TopCatAdjunction", "is_tactic_proof": false, "tactics": ["suffices", "this", "rw", "apply"], "tactic_count": 4}
{"name": "CondensedSet.toTopCatMap", "kind": "definition", "module": "Mathlib.Condensed.TopCatAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "condensedSetToTopCat", "kind": "definition", "module": "Mathlib.Condensed.TopCatAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CondensedSet.topCatAdjunctionCounit", "kind": "definition", "module": "Mathlib.Condensed.TopCatAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CondensedSet.topCatAdjunctionCounit_hom_apply", "kind": "theorem", "module": "Mathlib.Condensed.TopCatAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CondensedSet.topCatAdjunctionCounitEquiv", "kind": "definition", "module": "Mathlib.Condensed.TopCatAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CondensedSet.topCatAdjunctionCounit_bijective", "kind": "theorem", "module": "Mathlib.Condensed.TopCatAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CondensedSet.topCatAdjunctionUnit", "kind": "definition", "module": "Mathlib.Condensed.TopCatAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CondensedSet.topCatAdjunction", "kind": "definition", "module": "Mathlib.Condensed.TopCatAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CondensedSet.instEpiTopCatAppCounitTopCatAdjunction", "kind": "instance", "module": "Mathlib.Condensed.TopCatAdjunction", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CondensedSet.instFaithfulTopCatTopCatToCondensedSet", "kind": "instance", "module": "Mathlib.Condensed.TopCatAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CondensedSet.instUCompactlyGeneratedSpaceCarrierToTopCat", "kind": "instance", "module": "Mathlib.Condensed.TopCatAdjunction", "is_tactic_proof": true, "tactics": ["apply", "intro", "rw", "exact"], "tactic_count": 4}
{"name": "CondensedSet.instUCompactlyGeneratedSpaceCarrierObjTopCatCondensedSetToTopCat", "kind": "instance", "module": "Mathlib.Condensed.TopCatAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CondensedSet.condensedSetToCompactlyGenerated", "kind": "definition", "module": "Mathlib.Condensed.TopCatAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CondensedSet.compactlyGeneratedToCondensedSet", "kind": "definition", "module": "Mathlib.Condensed.TopCatAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CondensedSet.compactlyGeneratedAdjunction", "kind": "definition", "module": "Mathlib.Condensed.TopCatAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CondensedSet.compactlyGeneratedAdjunctionCounitHomeo", "kind": "definition", "module": "Mathlib.Condensed.TopCatAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CondensedSet.compactlyGeneratedAdjunctionCounitIso", "kind": "definition", "module": "Mathlib.Condensed.TopCatAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CondensedSet.instIsIsoFunctorCompactlyGeneratedCounitCompactlyGeneratedAdjunction", "kind": "instance", "module": "Mathlib.Condensed.TopCatAdjunction", "is_tactic_proof": true, "tactics": ["rw", "intro", "exact"], "tactic_count": 3}
{"name": "CondensedSet.fullyFaithfulCompactlyGeneratedToCondensedSet", "kind": "definition", "module": "Mathlib.Condensed.TopCatAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "factorsThrough_of_pullbackCondition", "kind": "theorem", "module": "Mathlib.Condensed.TopComparison", "is_tactic_proof": true, "tactics": ["intro", "let", "have", "dsimp", "have", "have", "rw", "simpa"], "tactic_count": 8}
{"name": "equalizerCondition_yonedaPresheaf", "kind": "theorem", "module": "Mathlib.Condensed.TopComparison", "is_tactic_proof": true, "tactics": ["apply", "intro", "refine", "simp", "simp", "ext", "obtain", "rw", "exact", "simp", "simp", "simp", "refine", "congr", "exact"], "tactic_count": 15}
{"name": "instPreservesFiniteProductsOppositeYonedaPresheafOfPreservesFiniteCoproductsTopCat", "kind": "instance", "module": "Mathlib.Condensed.TopComparison", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.toSheafCompHausLike", "kind": "definition", "module": "Mathlib.Condensed.TopComparison", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "topCatToSheafCompHausLike", "kind": "definition", "module": "Mathlib.Condensed.TopComparison", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.toCondensedSet", "kind": "abbrev", "module": "Mathlib.Condensed.TopComparison", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "topCatToCondensedSet", "kind": "abbrev", "module": "Mathlib.Condensed.TopComparison", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Applicative.map_seq_map", "kind": "theorem", "module": "Mathlib.Control.Applicative", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Applicative.pure_seq_eq_map'", "kind": "theorem", "module": "Mathlib.Control.Applicative", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Applicative.ext", "kind": "theorem", "module": "Mathlib.Control.Applicative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCommApplicativeId", "kind": "instance", "module": "Mathlib.Control.Applicative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Functor.Comp.map_pure", "kind": "theorem", "module": "Mathlib.Control.Applicative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Functor.Comp.seq_pure", "kind": "theorem", "module": "Mathlib.Control.Applicative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Functor.Comp.seq_assoc", "kind": "theorem", "module": "Mathlib.Control.Applicative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Functor.Comp.pure_seq_eq_map", "kind": "theorem", "module": "Mathlib.Control.Applicative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Functor.Comp.instLawfulApplicativeComp", "kind": "instance", "module": "Mathlib.Control.Applicative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Functor.Comp.applicative_id_comp", "kind": "theorem", "module": "Mathlib.Control.Applicative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Functor.Comp.applicative_comp_id", "kind": "theorem", "module": "Mathlib.Control.Applicative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Functor.Comp.instCommApplicative", "kind": "instance", "module": "Mathlib.Control.Applicative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Comp.seq_mk", "kind": "theorem", "module": "Mathlib.Control.Applicative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instApplicativeConstOfOneOfMul", "kind": "instance", "module": "Mathlib.Control.Applicative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instLawfulApplicativeConst", "kind": "instance", "module": "Mathlib.Control.Applicative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instApplicativeAddConstOfZeroOfAdd", "kind": "instance", "module": "Mathlib.Control.Applicative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instLawfulApplicativeAddConst", "kind": "instance", "module": "Mathlib.Control.Applicative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zipWithM", "kind": "definition", "module": "Mathlib.Control.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zipWithM'", "kind": "definition", "module": "Mathlib.Control.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pure_id'_seq", "kind": "theorem", "module": "Mathlib.Control.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "seq_map_assoc", "kind": "theorem", "module": "Mathlib.Control.Basic", "is_tactic_proof": true, "tactics": ["simp", "simp", "simp", "rfl"], "tactic_count": 4}
{"name": "map_seq", "kind": "theorem", "module": "Mathlib.Control.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "seq_bind_eq", "kind": "theorem", "module": "Mathlib.Control.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fish_pure", "kind": "theorem", "module": "Mathlib.Control.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "List.mapAccumRM", "kind": "definition", "module": "Mathlib.Control.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.mapAccumLM", "kind": "definition", "module": "Mathlib.Control.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "joinM_map_map", "kind": "theorem", "module": "Mathlib.Control.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "joinM_map_joinM", "kind": "theorem", "module": "Mathlib.Control.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "succeeds", "kind": "definition", "module": "Mathlib.Control.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tryM", "kind": "definition", "module": "Mathlib.Control.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "try?", "kind": "definition", "module": "Mathlib.Control.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "guard_true", "kind": "theorem", "module": "Mathlib.Control.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "Sum.bind", "kind": "definition", "module": "Mathlib.Control.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.instMonad_mathlib", "kind": "instance", "module": "Mathlib.Control.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.instLawfulFunctor_mathlib", "kind": "instance", "module": "Mathlib.Control.Basic", "is_tactic_proof": true, "tactics": ["constructor"], "tactic_count": 1}
{"name": "Sum.instLawfulMonad_mathlib", "kind": "instance", "module": "Mathlib.Control.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommApplicative.commutative_map", "kind": "theorem", "module": "Mathlib.Control.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bifunctor.fst", "kind": "abbrev", "module": "Mathlib.Control.Bifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bifunctor.snd", "kind": "abbrev", "module": "Mathlib.Control.Bifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bifunctor.id_fst", "kind": "theorem", "module": "Mathlib.Control.Bifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Bifunctor.snd_fst", "kind": "theorem", "module": "Mathlib.Control.Bifunctor", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Bifunctor.comp_snd", "kind": "theorem", "module": "Mathlib.Control.Bifunctor", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Prod.bifunctor", "kind": "instance", "module": "Mathlib.Control.Bifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Bifunctor.const", "kind": "instance", "module": "Mathlib.Control.Bifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LawfulBifunctor.const", "kind": "instance", "module": "Mathlib.Control.Bifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bifunctor.flip", "kind": "instance", "module": "Mathlib.Control.Bifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Bifunctor.functor", "kind": "instance", "module": "Mathlib.Control.Bifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bifunctor.lawfulFunctor", "kind": "instance", "module": "Mathlib.Control.Bifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.bicompl.bifunctor", "kind": "instance", "module": "Mathlib.Control.Bifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.bicompl.lawfulBifunctor", "kind": "instance", "module": "Mathlib.Control.Bifunctor", "is_tactic_proof": true, "tactics": ["constructor"], "tactic_count": 1}
{"name": "Function.bicompr.bifunctor", "kind": "instance", "module": "Mathlib.Control.Bifunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.bicompr.lawfulBifunctor", "kind": "instance", "module": "Mathlib.Control.Bifunctor", "is_tactic_proof": true, "tactics": ["constructor"], "tactic_count": 1}
{"name": "bisequence", "kind": "definition", "module": "Mathlib.Control.Bitraversable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.bitraverse", "kind": "definition", "module": "Mathlib.Control.Bitraversable.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instBitraversableProd", "kind": "instance", "module": "Mathlib.Control.Bitraversable.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instLawfulBitraversableProd", "kind": "instance", "module": "Mathlib.Control.Bitraversable.Instances", "is_tactic_proof": true, "tactics": ["constructor"], "tactic_count": 1}
{"name": "Sum.bitraverse", "kind": "definition", "module": "Mathlib.Control.Bitraversable.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instBitraversableSum", "kind": "instance", "module": "Mathlib.Control.Bitraversable.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instLawfulBitraversableSum", "kind": "instance", "module": "Mathlib.Control.Bitraversable.Instances", "is_tactic_proof": true, "tactics": ["constructor"], "tactic_count": 1}
{"name": "Const.bitraverse", "kind": "definition", "module": "Mathlib.Control.Bitraversable.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bitraversable.const", "kind": "instance", "module": "Mathlib.Control.Bitraversable.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LawfulBitraversable.const", "kind": "instance", "module": "Mathlib.Control.Bitraversable.Instances", "is_tactic_proof": true, "tactics": ["constructor"], "tactic_count": 1}
{"name": "flip.bitraverse", "kind": "definition", "module": "Mathlib.Control.Bitraversable.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bitraversable.flip", "kind": "instance", "module": "Mathlib.Control.Bitraversable.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LawfulBitraversable.flip", "kind": "instance", "module": "Mathlib.Control.Bitraversable.Instances", "is_tactic_proof": true, "tactics": ["constructor"], "tactic_count": 1}
{"name": "Bitraversable.traversable", "kind": "instance", "module": "Mathlib.Control.Bitraversable.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bitraversable.isLawfulTraversable", "kind": "instance", "module": "Mathlib.Control.Bitraversable.Instances", "is_tactic_proof": true, "tactics": ["constructor", "simp", "simp"], "tactic_count": 3}
{"name": "Bicompl.bitraverse", "kind": "definition", "module": "Mathlib.Control.Bitraversable.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instBitraversableBicompl", "kind": "instance", "module": "Mathlib.Control.Bitraversable.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instLawfulBitraversableBicomplOfLawfulTraversable", "kind": "instance", "module": "Mathlib.Control.Bitraversable.Instances", "is_tactic_proof": false, "tactics": ["constructor", "simp", "simp", "dsimp", "simp"], "tactic_count": 5}
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{"name": "instBitraversableBicompr", "kind": "instance", "module": "Mathlib.Control.Bitraversable.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instLawfulBitraversableBicomprOfLawfulTraversable", "kind": "instance", "module": "Mathlib.Control.Bitraversable.Instances", "is_tactic_proof": true, "tactics": ["constructor", "simp", "dsimp", "simp"], "tactic_count": 4}
{"name": "Bitraversable.tfst", "kind": "abbrev", "module": "Mathlib.Control.Bitraversable.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bitraversable.tsnd", "kind": "abbrev", "module": "Mathlib.Control.Bitraversable.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bitraversable.id_tfst", "kind": "theorem", "module": "Mathlib.Control.Bitraversable.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bitraversable.id_tsnd", "kind": "theorem", "module": "Mathlib.Control.Bitraversable.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bitraversable.comp_tfst", "kind": "theorem", "module": "Mathlib.Control.Bitraversable.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Bitraversable.tfst_tsnd", "kind": "theorem", "module": "Mathlib.Control.Bitraversable.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Bitraversable.tsnd_tfst", "kind": "theorem", "module": "Mathlib.Control.Bitraversable.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Bitraversable.comp_tsnd", "kind": "theorem", "module": "Mathlib.Control.Bitraversable.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "simp", "rfl"], "tactic_count": 3}
{"name": "Bitraversable.tfst_eq_fst_id", "kind": "theorem", "module": "Mathlib.Control.Bitraversable.Lemmas", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "Bitraversable.tsnd_eq_snd_id", "kind": "theorem", "module": "Mathlib.Control.Bitraversable.Lemmas", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "joinM", "kind": "definition", "module": "Mathlib.Control.Combinators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "condM", "kind": "definition", "module": "Mathlib.Control.Combinators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EquivFunctor.mapEquiv", "kind": "definition", "module": "Mathlib.Control.EquivFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EquivFunctor.mapEquiv_apply", "kind": "theorem", "module": "Mathlib.Control.EquivFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EquivFunctor.mapEquiv_symm_apply", "kind": "theorem", "module": "Mathlib.Control.EquivFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EquivFunctor.mapEquiv_refl", "kind": "theorem", "module": "Mathlib.Control.EquivFunctor", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "EquivFunctor.mapEquiv_symm", "kind": "theorem", "module": "Mathlib.Control.EquivFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EquivFunctor.mapEquiv_trans", "kind": "theorem", "module": "Mathlib.Control.EquivFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EquivFunctor.ofLawfulFunctor", "kind": "instance", "module": "Mathlib.Control.EquivFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EquivFunctor.mapEquiv.injective", "kind": "theorem", "module": "Mathlib.Control.EquivFunctor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EquivFunctorUnique", "kind": "instance", "module": "Mathlib.Control.EquivFunctor.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EquivFunctorPerm", "kind": "instance", "module": "Mathlib.Control.EquivFunctor.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EquivFunctorFinset", "kind": "instance", "module": "Mathlib.Control.EquivFunctor.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ContT.run_withContT", "kind": "theorem", "module": "Mathlib.Control.Monad.Cont", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ContT.instLawfulMonad", "kind": "instance", "module": "Mathlib.Control.Monad.Cont", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ContT.instLawfulMonadCont", "kind": "instance", "module": "Mathlib.Control.Monad.Cont", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "instLawfulMonadContExceptT", "kind": "instance", "module": "Mathlib.Control.Monad.Cont", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "instLawfulMonadContOptionT", "kind": "instance", "module": "Mathlib.Control.Monad.Cont", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "instMonadContWriterTOfMonadOfMonoid", "kind": "instance", "module": "Mathlib.Control.Monad.Cont", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "instMonadWriterAdapterWriterTOfMonad", "kind": "instance", "module": "Mathlib.Control.Monad.Writer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "instMonadLiftTRandGTOfMonadLift", "kind": "instance", "module": "Mathlib.Control.Random", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Filter.Realizer.prod", "kind": "definition", "module": "Mathlib.Data.Analysis.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Realizer.le_iff", "kind": "theorem", "module": "Mathlib.Data.Analysis.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Realizer.tendsto_iff", "kind": "theorem", "module": "Mathlib.Data.Analysis.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Realizer.ne_bot_iff", "kind": "theorem", "module": "Mathlib.Data.Analysis.Filter", "is_tactic_proof": true, "tactics": ["rw", "simp", "exact", "let"], "tactic_count": 4}
{"name": "instInhabitedCtopSet", "kind": "instance", "module": "Mathlib.Data.Analysis.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ctop.instCoeFunForallSet", "kind": "instance", "module": "Mathlib.Data.Analysis.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ctop.coe_mk", "kind": "theorem", "module": "Mathlib.Data.Analysis.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ctop.ofEquiv", "kind": "definition", "module": "Mathlib.Data.Analysis.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ctop.ofEquiv_val", "kind": "theorem", "module": "Mathlib.Data.Analysis.Topology", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Ctop.toTopsp", "kind": "definition", "module": "Mathlib.Data.Analysis.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ctop.toTopsp_isTopologicalBasis", "kind": "theorem", "module": "Mathlib.Data.Analysis.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ctop.mem_nhds_toTopsp", "kind": "theorem", "module": "Mathlib.Data.Analysis.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ctop.toRealizer", "kind": "definition", "module": "Mathlib.Data.Analysis.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInhabitedRealizer", "kind": "instance", "module": "Mathlib.Data.Analysis.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ctop.Realizer.is_basis", "kind": "theorem", "module": "Mathlib.Data.Analysis.Topology", "is_tactic_proof": true, "tactics": ["have"], "tactic_count": 1}
{"name": "Ctop.Realizer.mem_nhds", "kind": "theorem", "module": "Mathlib.Data.Analysis.Topology", "is_tactic_proof": true, "tactics": ["have"], "tactic_count": 1}
{"name": "Ctop.Realizer.isOpen_iff", "kind": "theorem", "module": "Mathlib.Data.Analysis.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ctop.Realizer.isClosed_iff", "kind": "theorem", "module": "Mathlib.Data.Analysis.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ctop.Realizer.mem_interior_iff", "kind": "theorem", "module": "Mathlib.Data.Analysis.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ctop.Realizer.isOpen", "kind": "theorem", "module": "Mathlib.Data.Analysis.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ctop.Realizer.ext'", "kind": "theorem", "module": "Mathlib.Data.Analysis.Topology", "is_tactic_proof": true, "tactics": ["refine", "ext", "rw"], "tactic_count": 3}
{"name": "Ctop.Realizer.ext", "kind": "theorem", "module": "Mathlib.Data.Analysis.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ctop.Realizer.id", "kind": "definition", "module": "Mathlib.Data.Analysis.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ctop.Realizer.ofEquiv", "kind": "definition", "module": "Mathlib.Data.Analysis.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ctop.Realizer.ofEquiv_σ", "kind": "theorem", "module": "Mathlib.Data.Analysis.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ctop.Realizer.ofEquiv_F", "kind": "theorem", "module": "Mathlib.Data.Analysis.Topology", "is_tactic_proof": true, "tactics": ["delta"], "tactic_count": 1}
{"name": "Ctop.Realizer.nhds", "kind": "definition", "module": "Mathlib.Data.Analysis.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ctop.Realizer.nhds_σ", "kind": "theorem", "module": "Mathlib.Data.Analysis.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ctop.Realizer.nhds_F", "kind": "theorem", "module": "Mathlib.Data.Analysis.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ctop.Realizer.tendsto_nhds_iff", "kind": "theorem", "module": "Mathlib.Data.Analysis.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyFinite.Realizer.to_locallyFinite", "kind": "theorem", "module": "Mathlib.Data.Analysis.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "locallyFinite_iff_exists_realizer", "kind": "theorem", "module": "Mathlib.Data.Analysis.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instNonemptyRealizerOfFinite", "kind": "instance", "module": "Mathlib.Data.Analysis.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Compact.Realizer", "kind": "definition", "module": "Mathlib.Data.Analysis.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInhabitedRealizerEmptyCollectionSet", "kind": "instance", "module": "Mathlib.Data.Analysis.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Array.cyclicPermute!", "kind": "definition", "module": "Mathlib.Data.Array.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Array.permute!", "kind": "definition", "module": "Mathlib.Data.Array.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BitVec.ofFin_intCast", "kind": "theorem", "module": "Mathlib.Data.BitVec", "is_tactic_proof": true, "tactics": ["cases", "simp", "apply", "rw", "rw", "have", "rw", "omega"], "tactic_count": 8}
{"name": "BitVec.toFin_intCast", "kind": "theorem", "module": "Mathlib.Data.BitVec", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "BitVec.toNat_injective", "kind": "theorem", "module": "Mathlib.Data.BitVec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BitVec.toFin_injective", "kind": "theorem", "module": "Mathlib.Data.BitVec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BitVec.toFin_nsmul", "kind": "theorem", "module": "Mathlib.Data.BitVec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BitVec.toFin_zsmul", "kind": "theorem", "module": "Mathlib.Data.BitVec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BitVec.toFin_pow", "kind": "theorem", "module": "Mathlib.Data.BitVec", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "BitVec._example", "kind": "example", "module": "Mathlib.Data.BitVec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BitVec.instCommSemiring", "kind": "instance", "module": "Mathlib.Data.BitVec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BitVec.instCommRing", "kind": "instance", "module": "Mathlib.Data.BitVec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BitVec.equivFin", "kind": "definition", "module": "Mathlib.Data.BitVec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.all_iff_forall_prop", "kind": "theorem", "module": "Mathlib.Data.Bool.AllAny", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.any_iff_exists_prop", "kind": "theorem", "module": "Mathlib.Data.Bool.AllAny", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.any_of_mem", "kind": "theorem", "module": "Mathlib.Data.Bool.AllAny", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bool.true_eq_false_eq_False", "kind": "theorem", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "Bool.false_eq_true_eq_False", "kind": "theorem", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "Bool.eq_false_eq_not_eq_true", "kind": "theorem", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Bool.eq_true_eq_not_eq_false", "kind": "theorem", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Bool.eq_false_of_not_eq_true", "kind": "theorem", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bool.eq_true_of_not_eq_false", "kind": "theorem", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bool.and_eq_true_eq_eq_true_and_eq_true", "kind": "theorem", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Bool.or_eq_true_eq_eq_true_or_eq_true", "kind": "theorem", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Bool.not_eq_true_eq_eq_false", "kind": "theorem", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Bool.and_eq_false_eq_eq_false_or_eq_false", "kind": "theorem", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Bool.or_eq_false_eq_eq_false_and_eq_false", "kind": "theorem", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Bool.not_eq_false_eq_eq_true", "kind": "theorem", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Bool.coe_false", "kind": "theorem", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Bool.coe_true", "kind": "theorem", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Bool.coe_sort_false", "kind": "theorem", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Bool.coe_sort_true", "kind": "theorem", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Bool.decide_iff", "kind": "theorem", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Bool.decide_true", "kind": "theorem", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bool.of_decide_true", "kind": "theorem", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bool.bool_iff_false", "kind": "theorem", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Bool.bool_eq_false", "kind": "theorem", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bool.decide_false_iff", "kind": "theorem", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bool.decide_false", "kind": "theorem", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bool.of_decide_false", "kind": "theorem", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bool.decide_congr", "kind": "theorem", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bool.coe_xor_iff", "kind": "theorem", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Bool.dichotomy", "kind": "theorem", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Bool.not_ne_id", "kind": "theorem", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bool.or_inl", "kind": "theorem", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Bool.or_inr", "kind": "theorem", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Bool.and_elim_left", "kind": "theorem", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "Bool.and_intro", "kind": "theorem", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "Bool.and_elim_right", "kind": "theorem", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "Bool.eq_not_iff", "kind": "theorem", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "Bool.not_eq_iff", "kind": "theorem", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "Bool.ne_not", "kind": "theorem", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bool.not_ne_self", "kind": "theorem", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "Bool.self_ne_not", "kind": "theorem", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "Bool.eq_or_eq_not", "kind": "theorem", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "Bool.not_iff_not", "kind": "theorem", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Bool.eq_true_of_not_eq_false'", "kind": "theorem", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Bool.eq_false_of_not_eq_true'", "kind": "theorem", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Bool.bne_eq_xor", "kind": "theorem", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": true, "tactics": ["constructor"], "tactic_count": 1}
{"name": "Bool.xor_iff_ne", "kind": "theorem", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "Bool.linearOrder", "kind": "instance", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bool.lt_iff", "kind": "theorem", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "Bool.false_lt_true", "kind": "theorem", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bool.le_iff_imp", "kind": "theorem", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "Bool.and_le_left", "kind": "theorem", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "Bool.and_le_right", "kind": "theorem", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "Bool.le_and", "kind": "theorem", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "Bool.left_le_or", "kind": "theorem", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "Bool.right_le_or", "kind": "theorem", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "Bool.or_le", "kind": "theorem", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "Bool.ofNat", "kind": "definition", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bool.ofNat_zero", "kind": "theorem", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bool.ofNat_add_one", "kind": "theorem", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bool.toNat_beq_zero", "kind": "theorem", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Bool.toNat_bne_zero", "kind": "theorem", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Bool.toNat_beq_one", "kind": "theorem", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Bool.toNat_bne_one", "kind": "theorem", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Bool.ofNat_le_ofNat", "kind": "theorem", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": true, "tactics": ["simp", "cases", "isTrue", "isFalse"], "tactic_count": 4}
{"name": "Bool.toNat_le_toNat", "kind": "theorem", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Bool.ofNat_toNat", "kind": "theorem", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Bool.injective_iff", "kind": "theorem", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bool.apply_apply_apply", "kind": "theorem", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Bool.xor3", "kind": "definition", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bool.carry", "kind": "definition", "module": "Mathlib.Data.Bool.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.count_not_add_count", "kind": "theorem", "module": "Mathlib.Data.Bool.Count", "is_tactic_proof": true, "tactics": ["have", "aesop"], "tactic_count": 2}
{"name": "List.count_add_count_not", "kind": "theorem", "module": "Mathlib.Data.Bool.Count", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "List.count_false_add_count_true", "kind": "theorem", "module": "Mathlib.Data.Bool.Count", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.count_true_add_count_false", "kind": "theorem", "module": "Mathlib.Data.Bool.Count", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.IsChain.count_not_cons", "kind": "theorem", "module": "Mathlib.Data.Bool.Count", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.IsChain.count_not_eq_count", "kind": "theorem", "module": "Mathlib.Data.Bool.Count", "is_tactic_proof": true, "tactics": ["rcases", "rfl", "rw", "suffices", "rw"], "tactic_count": 5}
{"name": "List.IsChain.count_false_eq_count_true", "kind": "theorem", "module": "Mathlib.Data.Bool.Count", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.IsChain.count_not_le_count_add_one", "kind": "theorem", "module": "Mathlib.Data.Bool.Count", "is_tactic_proof": true, "tactics": ["rcases", "exact", "obtain", "rw", "lia", "rw", "lia"], "tactic_count": 7}
{"name": "List.IsChain.count_false_le_count_true_add_one", "kind": "theorem", "module": "Mathlib.Data.Bool.Count", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.IsChain.count_true_le_count_false_add_one", "kind": "theorem", "module": "Mathlib.Data.Bool.Count", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.IsChain.two_mul_count_bool_of_even", "kind": "theorem", "module": "Mathlib.Data.Bool.Count", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.IsChain.two_mul_count_bool_eq_ite", "kind": "theorem", "module": "Mathlib.Data.Bool.Count", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "rcases", "exact", "simp", "rw", "replace", "rw", "cases"], "tactic_count": 9}
{"name": "List.IsChain.length_sub_one_le_two_mul_count_bool", "kind": "theorem", "module": "Mathlib.Data.Bool.Count", "is_tactic_proof": true, "tactics": ["rw", "split_ifs"], "tactic_count": 2}
{"name": "List.IsChain.length_div_two_le_count_bool", "kind": "theorem", "module": "Mathlib.Data.Bool.Count", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
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{"name": "Bool.range_eq", "kind": "theorem", "module": "Mathlib.Data.Bool.Set", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Bool.compl_singleton", "kind": "theorem", "module": "Mathlib.Data.Bool.Set", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "term⁅_,_⁆", "kind": "definition", "module": "Mathlib.Data.Bracket", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Data_Bracket___macroRules_term⁅_,_⁆_1", "kind": "definition", "module": "Mathlib.Data.Bracket", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Data_Bracket___unexpand_Bracket_bracket_1", "kind": "definition", "module": "Mathlib.Data.Bracket", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bundle.instInhabitedTotalSpaceOfDefault", "kind": "instance", "module": "Mathlib.Data.Bundle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bundle.termπ__", "kind": "definition", "module": "Mathlib.Data.Bundle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bundle._aux_Mathlib_Data_Bundle___macroRules_Bundle_termπ___1", "kind": "definition", "module": "Mathlib.Data.Bundle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bundle._aux_Mathlib_Data_Bundle___unexpand_Bundle_TotalSpace_proj_1", "kind": "definition", "module": "Mathlib.Data.Bundle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bundle.TotalSpace.mk'", "kind": "abbrev", "module": "Mathlib.Data.Bundle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bundle.TotalSpace.mk_cast", "kind": "theorem", "module": "Mathlib.Data.Bundle", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "Bundle.TotalSpace.mk_inj", "kind": "theorem", "module": "Mathlib.Data.Bundle", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Bundle.TotalSpace.mk_injective", "kind": "theorem", "module": "Mathlib.Data.Bundle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bundle.instCoeTCTotalSpace", "kind": "instance", "module": "Mathlib.Data.Bundle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bundle.TotalSpace.eta", "kind": "theorem", "module": "Mathlib.Data.Bundle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bundle.TotalSpace.exists", "kind": "theorem", "module": "Mathlib.Data.Bundle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bundle.TotalSpace.range_mk", "kind": "theorem", "module": "Mathlib.Data.Bundle", "is_tactic_proof": true, "tactics": ["apply", "rintro", "rfl", "rintro", "exact"], "tactic_count": 5}
{"name": "Bundle.term_×ᵇ_", "kind": "definition", "module": "Mathlib.Data.Bundle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bundle._aux_Mathlib_Data_Bundle___macroRules_Bundle_term_×ᵇ__1", "kind": "definition", "module": "Mathlib.Data.Bundle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bundle.Trivial", "kind": "definition", "module": "Mathlib.Data.Bundle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bundle.TotalSpace.trivialSnd", "kind": "definition", "module": "Mathlib.Data.Bundle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bundle.TotalSpace.toProd", "kind": "definition", "module": "Mathlib.Data.Bundle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bundle.Pullback", "kind": "definition", "module": "Mathlib.Data.Bundle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bundle.term_*ᵖ_", "kind": "definition", "module": "Mathlib.Data.Bundle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bundle._aux_Mathlib_Data_Bundle___macroRules_Bundle_term_*ᵖ__1", "kind": "definition", "module": "Mathlib.Data.Bundle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bundle._aux_Mathlib_Data_Bundle___unexpand_Bundle_Pullback_1", "kind": "definition", "module": "Mathlib.Data.Bundle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bundle.instNonemptyPullback", "kind": "instance", "module": "Mathlib.Data.Bundle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bundle.pullbackTotalSpaceEmbedding", "kind": "definition", "module": "Mathlib.Data.Bundle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bundle.Pullback.lift", "kind": "definition", "module": "Mathlib.Data.Bundle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bundle.Pullback.lift_mk", "kind": "theorem", "module": "Mathlib.Data.Bundle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instLinearOrderChar", "kind": "instance", "module": "Mathlib.Data.Char", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "termℂ", "kind": "definition", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Data_Complex_Basic___macroRules_termℂ_1", "kind": "definition", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Data_Complex_Basic___unexpand_Complex_1", "kind": "definition", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.instDecidableEq", "kind": "instance", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.equivRealProd", "kind": "definition", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.eta", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.ext", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.forall", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Complex.exists", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Complex.re_surjective", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.im_surjective", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.range_re", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.range_im", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.ofReal", "kind": "definition", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.instCoeReal", "kind": "instance", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.ofReal_re", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.ofReal_im", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.ofReal_def", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.ofReal_inj", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.ofReal_injective", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.canLift", "kind": "instance", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.reProdIm", "kind": "definition", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.term_×ℂ_", "kind": "definition", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex._aux_Mathlib_Data_Complex_Basic___macroRules_Complex_term_×ℂ__1", "kind": "definition", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex._aux_Mathlib_Data_Complex_Basic___unexpand_Complex_reProdIm_1", "kind": "definition", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.mem_reProdIm", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.instZero", "kind": "instance", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.instInhabited", "kind": "instance", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.zero_re", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.zero_im", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.ofReal_zero", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.ofReal_eq_zero", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.ofReal_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.instOne", "kind": "instance", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.one_re", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.one_im", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.ofReal_one", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.ofReal_eq_one", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.ofReal_ne_one", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.instAdd", "kind": "instance", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.add_re", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.add_im", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.ofReal_add", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.instNeg", "kind": "instance", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.neg_re", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.neg_im", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.ofReal_neg", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.instSub", "kind": "instance", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.instMul", "kind": "instance", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.mul_re", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.mul_im", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.ofReal_mul", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.re_ofReal_mul", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.im_ofReal_mul", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.re_mul_ofReal", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.im_mul_ofReal", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.ofReal_mul'", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.I", "kind": "definition", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.I_re", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.I_im", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.I_mul_I", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.I_mul", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.I_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.mk_eq_add_mul_I", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.re_add_im", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.mul_I_re", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.mul_I_im", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.I_mul_re", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.I_mul_im", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.equivRealProd_symm_apply", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Complex.equivRealProdAddHom", "kind": "definition", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.equivRealProdAddHom_symm_apply", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.instNontrivial", "kind": "instance", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.SMul.instSMulRealComplex", "kind": "instance", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.smul_re", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.smul_im", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.real_smul", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.addCommGroup", "kind": "instance", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.instNatCast", "kind": "instance", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.instIntCast", "kind": "instance", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.instNNRatCast", "kind": "instance", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.instRatCast", "kind": "instance", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.ofReal_ofNat", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.ofReal_natCast", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.ofReal_intCast", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.ofReal_nnratCast", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.ofReal_ratCast", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.re_ofNat", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.im_ofNat", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.natCast_re", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.natCast_im", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.intCast_re", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.intCast_im", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.re_nnratCast", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.im_nnratCast", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.ratCast_re", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.ratCast_im", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.addGroupWithOne", "kind": "instance", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.commRing", "kind": "instance", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.instRing", "kind": "instance", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Complex.instCommSemiring", "kind": "instance", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.instSemiring", "kind": "instance", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.reAddGroupHom", "kind": "definition", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.coe_reAddGroupHom", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.imAddGroupHom", "kind": "definition", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.coe_imAddGroupHom", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.re_nsmul", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.im_nsmul", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.re_zsmul", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.im_zsmul", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.re_nnqsmul", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.im_nnqsmul", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.re_qsmul", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.im_qsmul", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.ofReal_nsmul", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.ofReal_zsmul", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.instStarRing", "kind": "instance", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.conj_re", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.conj_im", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.conj_ofReal", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.conj_I", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.conj_natCast", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.conj_ofNat", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.conj_neg_I", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.conj_eq_iff_real", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.conj_eq_iff_re", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.conj_eq_iff_im", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.star_def", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.normSq", "kind": "definition", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.normSq_apply", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.normSq_ofReal", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.normSq_natCast", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.normSq_intCast", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.normSq_ratCast", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.normSq_ofNat", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.normSq_mk", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.normSq_add_mul_I", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.normSq_eq_conj_mul_self", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Complex.normSq_zero", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.normSq_one", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.normSq_I", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.normSq_nonneg", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.normSq_eq_zero", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.normSq_pos", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.normSq_neg", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.normSq_conj", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.normSq_mul", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.normSq_add", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": true, "tactics": ["dsimp"], "tactic_count": 1}
{"name": "Complex.re_sq_le_normSq", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.im_sq_le_normSq", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.mul_conj", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.add_conj", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.ofRealHom", "kind": "definition", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.ofRealHom_eq_coe", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.ofReal_comp_add", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.ofReal_comp_sub", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.ofReal_comp_neg", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.ofReal_comp_nsmul", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.ofReal_comp_zsmul", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.ofReal_comp_mul", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.ofReal_comp_pow", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.I_sq", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.I_pow_three", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.I_pow_four", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.I_pow_eq_pow_mod", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": true, "tactics": ["conv_lhs", "simp"], "tactic_count": 2}
{"name": "Complex.sub_re", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.sub_im", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.ofReal_sub", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.ofReal_pow", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "Complex.sub_conj", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.normSq_sub", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp", "ring"], "tactic_count": 3}
{"name": "Complex.instInv", "kind": "instance", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.inv_def", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.inv_re", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.inv_im", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.ofReal_inv", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.inv_zero", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.mul_inv_cancel", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.instDivInvMonoid", "kind": "instance", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.div_re", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.div_im", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.instField", "kind": "instance", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.ofReal_nnqsmul", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.ofReal_qsmul", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.conj_inv", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.ofReal_div", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.ofReal_zpow", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.div_I", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.inv_I", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.normSq_inv", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.normSq_div", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.div_ofReal", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Complex.div_natCast", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.div_intCast", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.div_ratCast", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.div_ofNat", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.div_ofReal_re", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.div_ofReal_im", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.div_natCast_re", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.div_natCast_im", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.div_intCast_re", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.div_intCast_im", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.div_ratCast_re", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.div_ratCast_im", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complex.div_ofNat_re", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.div_ofNat_im", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.instCharZero", "kind": "instance", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.instIsAddTorsionFree", "kind": "instance", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.re_eq_add_conj", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.im_eq_sub_conj", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": true, "tactics": ["simp", "mul_div_cancel_left₀"], "tactic_count": 2}
{"name": "Complex.instRepr", "kind": "instance", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.preimage_equivRealProd_prod", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.reProdIm_subset_iff", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Complex.reProdIm_subset_iff'", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": true, "tactics": ["convert", "exact"], "tactic_count": 2}
{"name": "Complex.reProdIm_nonempty", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.reProdIm_eq_empty", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.Rectangle", "kind": "definition", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.horizontalSegment_eq", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": true, "tactics": ["rw", "ext", "constructor", "intro", "obtain", "simp", "intro", "obtain", "refine"], "tactic_count": 9}
{"name": "Complex.verticalSegment_eq", "kind": "theorem", "module": "Mathlib.Data.Complex.Basic", "is_tactic_proof": true, "tactics": ["rw", "ext", "constructor", "intro", "obtain", "simp", "intro", "simp", "obtain", "refine"], "tactic_count": 10}
{"name": "Complex.ofReal_prod", "kind": "theorem", "module": "Mathlib.Data.Complex.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.ofReal_sum", "kind": "theorem", "module": "Mathlib.Data.Complex.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.ofReal_expect", "kind": "theorem", "module": "Mathlib.Data.Complex.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.ofReal_balance", "kind": "theorem", "module": "Mathlib.Data.Complex.BigOperators", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.ofReal_comp_balance", "kind": "theorem", "module": "Mathlib.Data.Complex.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.re_sum", "kind": "theorem", "module": "Mathlib.Data.Complex.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.re_expect", "kind": "theorem", "module": "Mathlib.Data.Complex.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.re_balance", "kind": "theorem", "module": "Mathlib.Data.Complex.BigOperators", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.re_comp_balance", "kind": "theorem", "module": "Mathlib.Data.Complex.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.im_sum", "kind": "theorem", "module": "Mathlib.Data.Complex.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.im_expect", "kind": "theorem", "module": "Mathlib.Data.Complex.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.im_balance", "kind": "theorem", "module": "Mathlib.Data.Complex.BigOperators", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.im_comp_balance", "kind": "theorem", "module": "Mathlib.Data.Complex.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCountableInt", "kind": "instance", "module": "Mathlib.Data.Countable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "countable_iff_nonempty_embedding", "kind": "theorem", "module": "Mathlib.Data.Countable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uncountable_iff_isEmpty_embedding", "kind": "theorem", "module": "Mathlib.Data.Countable.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "nonempty_embedding_nat", "kind": "theorem", "module": "Mathlib.Data.Countable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.countable", "kind": "theorem", "module": "Mathlib.Data.Countable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.uncountable", "kind": "theorem", "module": "Mathlib.Data.Countable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCountableSum", "kind": "instance", "module": "Mathlib.Data.Countable.Basic", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "exact"], "tactic_count": 3}
{"name": "Sum.uncountable_inl", "kind": "instance", "module": "Mathlib.Data.Countable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.uncountable_inr", "kind": "instance", "module": "Mathlib.Data.Countable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Option.instCountable", "kind": "instance", "module": "Mathlib.Data.Countable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "instUncountableProdOfNonempty_1", "kind": "instance", "module": "Mathlib.Data.Countable.Basic", "is_tactic_proof": true, "tactics": ["inhabit", "exact"], "tactic_count": 2}
{"name": "countable_left_of_prod_of_nonempty", "kind": "theorem", "module": "Mathlib.Data.Countable.Basic", "is_tactic_proof": true, "tactics": ["contrapose", "infer_instance"], "tactic_count": 2}
{"name": "countable_right_of_prod_of_nonempty", "kind": "theorem", "module": "Mathlib.Data.Countable.Basic", "is_tactic_proof": true, "tactics": ["contrapose", "infer_instance"], "tactic_count": 2}
{"name": "countable_prod_swap", "kind": "theorem", "module": "Mathlib.Data.Countable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCountableSigma", "kind": "instance", "module": "Mathlib.Data.Countable.Basic", "is_tactic_proof": true, "tactics": ["rcases", "choose", "exact"], "tactic_count": 3}
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{"name": "instUncountableSigmaOfNonempty", "kind": "instance", "module": "Mathlib.Data.Countable.Basic", "is_tactic_proof": true, "tactics": ["inhabit"], "tactic_count": 1}
{"name": "SetCoe.countable", "kind": "instance", "module": "Mathlib.Data.Countable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCountablePSum", "kind": "instance", "module": "Mathlib.Data.Countable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCountablePProd", "kind": "instance", "module": "Mathlib.Data.Countable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCountablePSigma", "kind": "instance", "module": "Mathlib.Data.Countable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCountableForallOfFinite", "kind": "instance", "module": "Mathlib.Data.Countable.Basic", "is_tactic_proof": false, "tactics": ["have", "induction", "zero", "succ", "rcases", "have", "exact"], "tactic_count": 7}
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{"name": "instCountablePUnit", "kind": "instance", "module": "Mathlib.Data.Countable.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "DFinsupp.liftAddHom_singleAddHom", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.liftAddHom_apply_single", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.BigOperators", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "DFinsupp.subtypeDomain_finsupp_sum", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MonoidHom.dfinsuppProd_apply", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.map_dfinsuppSumAddHom", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.dfinsuppSumAddHom_apply", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.coe_dfinsuppSumAddHom", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.map_dfinsuppSumAddHom", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddEquiv.map_dfinsuppSumAddHom", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "_aux_Mathlib_Data_DFinsupp_Defs___macroRules_termΠ₀_,__1", "kind": "definition", "module": "Mathlib.Data.DFinsupp.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "DFinsupp.instInhabited", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.coe_mk'", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "DFinsupp.zero_apply", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.mapRange", "kind": "definition", "module": "Mathlib.Data.DFinsupp.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.mapRange_apply", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "DFinsupp.support_single_subset", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.mapRange_def", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Defs", "is_tactic_proof": true, "tactics": ["ext", "simp_all"], "tactic_count": 2}
{"name": "DFinsupp.mapRange_single", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.mapRange_injective", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.mapRange_surjective", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.support_mapRange", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DFinsupp.zipWith_def", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Defs", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "DFinsupp.support_zipWith", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Defs", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "DFinsupp.erase_def", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Defs", "is_tactic_proof": true, "tactics": ["ext", "grind"], "tactic_count": 2}
{"name": "DFinsupp.support_erase", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Defs", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "DFinsupp.support_update_ne_zero", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Defs", "is_tactic_proof": true, "tactics": ["ext", "rcases", "simp", "simp"], "tactic_count": 4}
{"name": "DFinsupp.support_update", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Defs", "is_tactic_proof": true, "tactics": ["ext", "split_ifs", "subst", "simp", "rw"], "tactic_count": 5}
{"name": "DFinsupp.filter_def", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Defs", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "DFinsupp.support_filter", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Defs", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "DFinsupp.subtypeDomain_def", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Defs", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "DFinsupp.support_subtypeDomain", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Defs", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "DFinsupp.support_add", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.support_neg", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Defs", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "DFinsupp.instDecidableEq", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.comapDomain", "kind": "definition", "module": "Mathlib.Data.DFinsupp.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.comapDomain_apply", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.comapDomain_zero", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Defs", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "DFinsupp.comapDomain_add", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Defs", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "DFinsupp.comapDomain_single", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Defs", "is_tactic_proof": true, "tactics": ["ext", "rw", "obtain", "rw", "rw"], "tactic_count": 5}
{"name": "DFinsupp.comapDomain'", "kind": "definition", "module": "Mathlib.Data.DFinsupp.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.comapDomain'_apply", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.comapDomain'_zero", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Defs", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "DFinsupp.comapDomain'_add", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Defs", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "DFinsupp.comapDomain'_single", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Defs", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "DFinsupp.equivCongrLeft", "kind": "definition", "module": "Mathlib.Data.DFinsupp.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.hasAdd₂", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.addZeroClass₂", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.addMonoid₂", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.extendWith", "kind": "definition", "module": "Mathlib.Data.DFinsupp.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.extendWith_none", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.extendWith_some", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.extendWith_single_zero", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Defs", "is_tactic_proof": true, "tactics": ["ext", "rw", "rw", "obtain", "rw", "rw"], "tactic_count": 6}
{"name": "DFinsupp.extendWith_zero", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Defs", "is_tactic_proof": true, "tactics": ["ext", "rw", "rw"], "tactic_count": 3}
{"name": "DFinsupp.equivProdDFinsupp", "kind": "definition", "module": "Mathlib.Data.DFinsupp.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.equivProdDFinsupp_add", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.mapRange_add", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Defs", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "DFinsupp.mapRange.addMonoidHom", "kind": "definition", "module": "Mathlib.Data.DFinsupp.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.mapRange.addMonoidHom_id", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.mapRange.addMonoidHom_comp", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Defs", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "DFinsupp.mapRange.addEquiv", "kind": "definition", "module": "Mathlib.Data.DFinsupp.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.mapRange.addEquiv_refl", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.mapRange.addEquiv_trans", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Defs", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "DFinsupp.mapRange.addEquiv_symm", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instEncodableDFinsuppOfDecidableNeOfNat", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Encodable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCountableDFinsupp", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Encodable", "is_tactic_proof": true, "tactics": ["classical", "let", "let", "infer_instance"], "tactic_count": 4}
{"name": "DFinsupp.add_closure_iUnion_range_single", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Ext", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.addHom_ext", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Ext", "is_tactic_proof": true, "tactics": ["refine", "simp", "rcases", "apply"], "tactic_count": 4}
{"name": "DFinsupp.addHom_ext'", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Ext", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.fintype", "kind": "instance", "module": "Mathlib.Data.DFinsupp.FiniteInfinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.infinite_of_left", "kind": "instance", "module": "Mathlib.Data.DFinsupp.FiniteInfinite", "is_tactic_proof": true, "tactics": ["letI", "exact"], "tactic_count": 2}
{"name": "DFinsupp.infinite_of_exists_right", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.FiniteInfinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.infinite_of_right", "kind": "instance", "module": "Mathlib.Data.DFinsupp.FiniteInfinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.dfinsupp", "kind": "definition", "module": "Mathlib.Data.DFinsupp.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_dfinsupp", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_dfinsupp_iff", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Interval", "is_tactic_proof": true, "tactics": ["refine", "rintro", "rw", "refine", "convert", "exact", "refine", "ext", "dsimp", "exact"], "tactic_count": 10}
{"name": "Finset.mem_dfinsupp_iff_of_support_subset", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Interval", "is_tactic_proof": false, "tactics": ["refine", "mem_dfinsupp_iff.trans", "forall_congr", "by_cases", "exact", "rw", "exact", "rwa"], "tactic_count": 8}
{"name": "DFinsupp.singleton", "kind": "definition", "module": "Mathlib.Data.DFinsupp.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.mem_singleton_apply_iff", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.rangeIcc", "kind": "definition", "module": "Mathlib.Data.DFinsupp.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.rangeIcc_apply", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.mem_rangeIcc_apply_iff", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.support_rangeIcc_subset", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Interval", "is_tactic_proof": true, "tactics": ["refine", "by_contra", "refine", "rw", "notMem_support_iff.1", "exact"], "tactic_count": 6}
{"name": "DFinsupp.pi", "kind": "definition", "module": "Mathlib.Data.DFinsupp.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.mem_pi", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.card_pi", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Interval", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "DFinsupp.instLocallyFiniteOrder", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.Icc_eq", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.card_Icc", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.card_Ico", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Interval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "DFinsupp.card_Ioc", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Interval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "DFinsupp.card_Ioo", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Interval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "DFinsupp.card_uIcc", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Interval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "DFinsupp.card_Iic", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Interval", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "DFinsupp.card_Iio", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Interval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "DFinsupp.Lex", "kind": "definition", "module": "Mathlib.Data.DFinsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.lex_eq_dfinsupp_lex", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.lex_def", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.instLTLex", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.instLTColex", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.Lex.lt_iff", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.Colex.lt_iff", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.lex_lt_of_lt_of_preorder", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Lex", "is_tactic_proof": true, "tactics": ["obtain", "classical", "have", "obtain", "refine", "exact"], "tactic_count": 6}
{"name": "DFinsupp.lex_lt_of_lt", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Lex", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "DFinsupp.lex_iff_of_unique", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.Lex.lt_iff_of_unique", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.colex_lt_iff_of_unique", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.Lex.isStrictOrder", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.Colex.isStrictOrder", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.Lex.partialOrder", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.Colex.partialOrder", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.Lex.le_iff_of_unique", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.Colex.le_iff_of_unique", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.DFinsupp.Lex.0.DFinsupp.lt_trichotomy_rec", "kind": "definition", "module": "Mathlib.Data.DFinsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.Lex.total_le", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.Colex.total_le", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.Lex.decidableLE", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.Colex.decidableLE", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.Lex.decidableLT", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.Colex.decidableLT", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.Lex.linearOrder", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.Colex.linearOrder", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.toLex_monotone", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Lex", "is_tactic_proof": true, "tactics": ["intro", "refine", "classical", "exact"], "tactic_count": 4}
{"name": "DFinsupp.toColex_monotone", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.lt_of_forall_lt_of_lt", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.Lex.addLeftStrictMono", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.Colex.addLeftStrictMono", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.Lex.addLeftMono", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.Colex.addLeftMono", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.Lex.addRightStrictMono", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.Colex.addRightStrictMono", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.Lex.addRightMono", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.Colex.addRightMono", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.Lex.orderBot", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.Colex.orderBot", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.Lex.isOrderedCancelAddMonoid", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.Colex.isOrderedCancelAddMonoid", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.Lex.isOrderedAddMonoid", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.Colex.isOrderedAddMonoid", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.instSMulZeroClass", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.smul_apply", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.coe_smul", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.smulCommClass", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.isScalarTower", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.isCentralScalar", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.distribMulAction", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.module", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.coeFnLinearMap", "kind": "definition", "module": "Mathlib.Data.DFinsupp.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.coeFnLinearMap_apply", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.filter_smul", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Module", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "DFinsupp.filterLinearMap", "kind": "definition", "module": "Mathlib.Data.DFinsupp.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.subtypeDomain_smul", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.subtypeDomainLinearMap", "kind": "definition", "module": "Mathlib.Data.DFinsupp.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.mk_smul", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.single_smul", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.support_smul", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.comapDomain_smul", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Module", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "DFinsupp.comapDomain'_smul", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Module", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "DFinsupp.distribMulAction₂", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.equivProdDFinsupp_smul", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.addZeroClass'", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.toMultiset", "kind": "definition", "module": "Mathlib.Data.DFinsupp.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.toMultiset_single", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.toDFinsupp", "kind": "definition", "module": "Mathlib.Data.DFinsupp.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.toDFinsupp_apply", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.toDFinsupp_support", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.toDFinsupp_replicate", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Multiset", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "simp"], "tactic_count": 3}
{"name": "Multiset.toDFinsupp_singleton", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Multiset", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.equivDFinsupp", "kind": "definition", "module": "Mathlib.Data.DFinsupp.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.toDFinsupp_toMultiset", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.toDFinsupp_injective", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.toDFinsupp_inj", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.toDFinsupp_le_toDFinsupp", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Multiset", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.toDFinsupp_lt_toDFinsupp", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.toDFinsupp_inter", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Multiset", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Multiset.toDFinsupp_union", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Multiset", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "DFinsupp.toMultiset_toDFinsupp", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.toMultiset_injective", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.toMultiset_inj", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.toMultiset_le_toMultiset", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Multiset", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "DFinsupp.toMultiset_lt_toMultiset", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Multiset", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "DFinsupp.toMultiset_inf", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.toMultiset_sup", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.neLocus", "kind": "definition", "module": "Mathlib.Data.DFinsupp.NeLocus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.mem_neLocus", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.NeLocus", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "DFinsupp.notMem_neLocus", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.NeLocus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.coe_neLocus", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.NeLocus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.neLocus_eq_empty", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.NeLocus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.nonempty_neLocus_iff", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.NeLocus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.neLocus_comm", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.NeLocus", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "DFinsupp.neLocus_zero_right", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.NeLocus", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "DFinsupp.neLocus_zero_left", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.NeLocus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.subset_mapRange_neLocus", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.NeLocus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.zipWith_neLocus_eq_left", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.NeLocus", "is_tactic_proof": true, "tactics": ["ext", "simpa"], "tactic_count": 2}
{"name": "DFinsupp.zipWith_neLocus_eq_right", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.NeLocus", "is_tactic_proof": true, "tactics": ["ext", "simpa"], "tactic_count": 2}
{"name": "DFinsupp.mapRange_neLocus_eq", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.NeLocus", "is_tactic_proof": true, "tactics": ["ext", "simpa"], "tactic_count": 2}
{"name": "DFinsupp.neLocus_add_left", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.NeLocus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.neLocus_add_right", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.NeLocus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.neLocus_neg_neg", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.NeLocus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.neLocus_neg", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.NeLocus", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "DFinsupp.neLocus_eq_support_sub", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.NeLocus", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "DFinsupp.neLocus_sub_left", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.NeLocus", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DFinsupp.neLocus_sub_right", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.NeLocus", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "DFinsupp.neLocus_self_add_right", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.NeLocus", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "DFinsupp.neLocus_self_add_left", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.NeLocus", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "DFinsupp.neLocus_self_sub_right", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.NeLocus", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "DFinsupp.neLocus_self_sub_left", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.NeLocus", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "DFinsupp.Internal.elabSingle₀", "kind": "definition", "module": "Mathlib.Data.DFinsupp.Notation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.Internal.elabUpdate₀", "kind": "definition", "module": "Mathlib.Data.DFinsupp.Notation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.singleUnexpander", "kind": "definition", "module": "Mathlib.Data.DFinsupp.Notation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.updateUnexpander", "kind": "definition", "module": "Mathlib.Data.DFinsupp.Notation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.instRepr", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Notation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.instLE", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.le_def", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.coe_le_coe", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.orderEmbeddingToFun", "kind": "definition", "module": "Mathlib.Data.DFinsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.coe_orderEmbeddingToFun", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.orderEmbeddingToFun_apply", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.instPreorder", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.lt_def", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.coe_lt_coe", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.coe_mono", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.coe_strictMono", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.instPartialOrder", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.instSemilatticeInf", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.coe_inf", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.inf_apply", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.instSemilatticeSup", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.coe_sup", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.sup_apply", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.lattice", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.support_inf_union_support_sup", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.support_sup_union_support_inf", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.instIsOrderedAddMonoid", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.instIsOrderedCancelAddMonoid", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.instAddLeftReflectLE", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.instPosSMulMono", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.instSMulPosMono", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.instPosSMulReflectLE", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.instSMulPosReflectLE", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.instPosSMulStrictMono", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.instSMulPosStrictMono", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.instSMulPosReflectLT", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.instOrderBot", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.bot_eq_zero", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.add_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Order", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DFinsupp.le_iff'", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.le_iff", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.support_monotone", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.support_mono", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.decidableLE", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.single_le_iff", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Order", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "DFinsupp.tsub", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.tsub_apply", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.coe_tsub", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Order", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "DFinsupp.instOrderedSub", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.instCanonicallyOrderedAddOfAddLeftMono", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.single_tsub", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Order", "is_tactic_proof": true, "tactics": ["ext", "obtain", "rw", "rw"], "tactic_count": 4}
{"name": "DFinsupp.support_tsub", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Order", "is_tactic_proof": true, "tactics": ["simp", "zero_le,"], "tactic_count": 2}
{"name": "DFinsupp.subset_support_tsub", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Order", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DFinsupp.support_inf", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Order", "is_tactic_proof": true, "tactics": ["ext", "simp", "simp"], "tactic_count": 3}
{"name": "DFinsupp.support_sup", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Order", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "DFinsupp.disjoint_iff", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Order", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "DFinsupp.sigmaCurry", "kind": "definition", "module": "Mathlib.Data.DFinsupp.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.sigmaCurry_apply", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.sigmaCurry_zero", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.sigmaCurry_add", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Sigma", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "DFinsupp.sigmaCurry_smul", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Sigma", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "DFinsupp.sigmaCurry_single", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Sigma", "is_tactic_proof": true, "tactics": ["obtain", "ext", "dsimp", "rw", "obtain", "rw", "obtain", "rw", "rw", "simpa", "simp"], "tactic_count": 11}
{"name": "DFinsupp.sigmaUncurry", "kind": "definition", "module": "Mathlib.Data.DFinsupp.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.sigmaUncurry_apply", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.sigmaUncurry_zero", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.sigmaUncurry_add", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.sigmaUncurry_smul", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.sigmaUncurry_single", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Sigma", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "rw", "obtain", "rw", "obtain", "rw", "rw", "simpa", "simp"], "tactic_count": 10}
{"name": "DFinsupp.sigmaCurryEquiv", "kind": "definition", "module": "Mathlib.Data.DFinsupp.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.small", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.small", "kind": "instance", "module": "Mathlib.Data.DFinsupp.Small", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "dfinsuppProd_mem", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Submonoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dfinsuppSumAddHom_mem", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Submonoid", "is_tactic_proof": true, "tactics": ["classical", "rw", "exact"], "tactic_count": 3}
{"name": "AddSubmonoid.iSup_eq_mrange_dfinsuppSumAddHom", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Submonoid", "is_tactic_proof": true, "tactics": ["apply", "apply", "intro", "exact", "rintro", "exact"], "tactic_count": 6}
{"name": "AddSubmonoid.bsupr_eq_mrange_dfinsuppSumAddHom", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Submonoid", "is_tactic_proof": true, "tactics": ["apply", "refine", "rw", "exact", "rintro", "refine", "refine", "by_cases", "simp", "simp"], "tactic_count": 10}
{"name": "AddSubmonoid.mem_iSup_iff_exists_dfinsupp", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Submonoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.mem_iSup_iff_exists_dfinsupp'", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Submonoid", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "rfl"], "tactic_count": 3}
{"name": "AddSubmonoid.mem_bsupr_iff_exists_dfinsupp", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.Submonoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.lex_fibration", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.WellFounded", "is_tactic_proof": true, "tactics": ["rintro", "simp_rw", "split_ifs", "refine", "simp", "simp", "split_ifs", "rwa", "assumption", "ext1", "simp", "split_ifs", "rw", "rw", "rw", "refine", "simp", "exact", "split_ifs", "rwa", "assumption", "ext1", "simp", "split_ifs", "rw", "rw", "simpa"], "tactic_count": 27}
{"name": "DFinsupp.Lex.acc_of_single_erase", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.WellFounded", "is_tactic_proof": true, "tactics": ["classical", "convert", "convert"], "tactic_count": 3}
{"name": "DFinsupp.Lex.acc_zero", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.WellFounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.Lex.acc_of_single", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.WellFounded", "is_tactic_proof": true, "tactics": ["generalize", "classical", "induction", "empty", "intro", "rw", "exact", "insert", "refine", "refine", "rw", "exact"], "tactic_count": 12}
{"name": "DFinsupp.Lex.acc_single", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.WellFounded", "is_tactic_proof": false, "tactics": ["induction", "refine", "refine", "rintro", "rw", "split_ifs", "swap", "exact", "subst", "classical", "refine", "obtain", "exact", "by_cases", "rw", "exact", "exact"], "tactic_count": 17}
{"name": "DFinsupp.Lex.acc", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.WellFounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.Lex.wellFounded", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.WellFounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.Lex.wellFounded'", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.WellFounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.Lex.wellFoundedLT", "kind": "instance", "module": "Mathlib.Data.DFinsupp.WellFounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.Lex.wellFounded", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.WellFounded", "is_tactic_proof": true, "tactics": ["obtain", "convert", "letI", "haveI", "refine", "exacts"], "tactic_count": 6}
{"name": "Pi.Lex.wellFoundedLT", "kind": "instance", "module": "Mathlib.Data.DFinsupp.WellFounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Lex.wellFoundedLT", "kind": "instance", "module": "Mathlib.Data.DFinsupp.WellFounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.Lex.wellFounded_of_finite", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.WellFounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.Lex.wellFoundedLT_of_finite", "kind": "instance", "module": "Mathlib.Data.DFinsupp.WellFounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.wellFoundedLT", "kind": "theorem", "module": "Mathlib.Data.DFinsupp.WellFounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.wellFoundedLT'", "kind": "instance", "module": "Mathlib.Data.DFinsupp.WellFounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.wellFoundedLT", "kind": "instance", "module": "Mathlib.Data.DFinsupp.WellFounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.wellFoundedLT", "kind": "instance", "module": "Mathlib.Data.DFinsupp.WellFounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.wellFoundedLT_of_finite", "kind": "instance", "module": "Mathlib.Data.DFinsupp.WellFounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Batteries.DList.listEquivDList", "kind": "definition", "module": "Mathlib.Data.DList.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Batteries.instTraversableDList", "kind": "instance", "module": "Mathlib.Data.DList.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Batteries.instLawfulTraversableDList", "kind": "instance", "module": "Mathlib.Data.DList.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.instMulActionNNReal", "kind": "instance", "module": "Mathlib.Data.ENNReal.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.smul_def", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.instIsScalarTowerNNReal", "kind": "instance", "module": "Mathlib.Data.ENNReal.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.smulCommClass_left", "kind": "instance", "module": "Mathlib.Data.ENNReal.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.smulCommClass_right", "kind": "instance", "module": "Mathlib.Data.ENNReal.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.instDistribMulActionNNReal", "kind": "instance", "module": "Mathlib.Data.ENNReal.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.instModuleNNReal", "kind": "instance", "module": "Mathlib.Data.ENNReal.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.instAlgebraNNReal", "kind": "instance", "module": "Mathlib.Data.ENNReal.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal._example", "kind": "example", "module": "Mathlib.Data.ENNReal.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal._example", "kind": "example", "module": "Mathlib.Data.ENNReal.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.coe_smul", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Action", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.smul_top", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Action", "is_tactic_proof": true, "tactics": ["rw", "simp_rw"], "tactic_count": 2}
{"name": "ENNReal.nnreal_smul_lt_top", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.nnreal_smul_ne_top", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.nnreal_smul_ne_top_iff", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.nnreal_smul_lt_top_iff", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Action", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.smul_toNNReal", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Action", "is_tactic_proof": true, "tactics": ["change", "simp"], "tactic_count": 2}
{"name": "ENNReal.toReal_smul", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Action", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "ENNReal.instPosSMulStrictMonoNNReal", "kind": "instance", "module": "Mathlib.Data.ENNReal.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.instSMulPosMonoNNReal", "kind": "instance", "module": "Mathlib.Data.ENNReal.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal", "kind": "definition", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.termℝ≥0∞", "kind": "definition", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal._aux_Mathlib_Data_ENNReal_Basic___macroRules_ENNReal_termℝ≥0∞_1", "kind": "definition", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal._aux_Mathlib_Data_ENNReal_Basic___unexpand_ENNReal_1", "kind": "definition", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.term∞", "kind": "definition", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal._aux_Mathlib_Data_ENNReal_Basic___macroRules_ENNReal_term∞_1", "kind": "definition", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.instOrderBot", "kind": "instance", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.instOrderTop", "kind": "instance", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.instBoundedOrder", "kind": "instance", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.instCharZero", "kind": "instance", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.instMin", "kind": "instance", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.instMax", "kind": "instance", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.instCommSemiring", "kind": "instance", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.instPartialOrder", "kind": "instance", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.instIsOrderedRing", "kind": "instance", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.instCanonicallyOrderedAdd", "kind": "instance", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.instNoZeroDivisors", "kind": "instance", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.instCompleteLinearOrder", "kind": "instance", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.instDenselyOrdered", "kind": "instance", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.instAddCommMonoid", "kind": "instance", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.instLinearOrder", "kind": "instance", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.instIsOrderedAddMonoid", "kind": "instance", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.instSub", "kind": "instance", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.instOrderedSub", "kind": "instance", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.instLinearOrderedAddCommMonoidWithTop", "kind": "instance", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.instInv", "kind": "instance", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.instDivInvMonoid", "kind": "instance", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.instIsOrderedMonoid", "kind": "instance", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.instUniqueAddUnits", "kind": "instance", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.instInhabited", "kind": "instance", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.ofNNReal", "kind": "definition", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.instCoeNNReal", "kind": "instance", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.recTopCoe", "kind": "definition", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.canLift", "kind": "instance", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.none_eq_top", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.some_eq_coe", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.some_eq_coe'", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.coe_injective", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.coe_inj", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.coe_ne_coe", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.range_coe'", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.range_coe", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.instNNRatCast", "kind": "instance", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.coe_nnratCast", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.toNNReal", "kind": "definition", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.toReal", "kind": "definition", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.ofReal", "kind": "definition", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.toNNReal_coe", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.coe_toNNReal", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.coe_comp_toNNReal_comp", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "ENNReal.ofReal_toReal", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.toReal_ofReal", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.toReal_ofReal'", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.coe_toNNReal_le_self", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.coe_nnreal_eq", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.ofReal_eq_coe_nnreal", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.ofNNReal_toNNReal", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.ofReal_coe_nnreal", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.coe_zero", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.coe_one", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.toReal_nonneg", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.coe_toNNReal_eq_toReal", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.toNNReal_toReal_eq", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "ENNReal.toNNReal_top", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.toReal_top", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.toReal_one", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.toNNReal_one", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.coe_toReal", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.toNNReal_zero", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.toReal_zero", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.ofReal_zero", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.ofReal_one", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.ofReal_toReal_le", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.forall_ennreal", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.forall_ne_top", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.exists_ne_top", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.toNNReal_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.toReal_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.toNNReal_ne_zero", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.toReal_ne_zero", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.toNNReal_eq_one_iff", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.toReal_eq_one_iff", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.toNNReal_ne_one", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.toReal_ne_one", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.coe_ne_top", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.top_ne_coe", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.coe_lt_top", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.ofReal_ne_top", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.ofReal_lt_top", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.top_ne_ofReal", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.ofReal_toReal_eq_iff", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.toReal_ofReal_eq_iff", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.zero_ne_top", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.top_ne_zero", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.one_ne_top", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.top_ne_one", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.zero_lt_top", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.coe_le_coe", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.coe_lt_coe", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.coe_mono", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.coe_strictMono", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.coe_eq_zero", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.zero_eq_coe", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.coe_eq_one", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.one_eq_coe", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.coe_pos", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.coe_ne_zero", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.coe_ne_one", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.coe_add", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.coe_mul", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.coe_nsmul", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.coe_pow", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.coe_ofNat", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.coe_two", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.toNNReal_eq_toNNReal_iff", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.toReal_eq_toReal_iff", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.toNNReal_eq_toNNReal_iff'", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.toReal_eq_toReal_iff'", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.one_lt_two", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fact_one_le_one_ennreal", "kind": "instance", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fact_one_le_two_ennreal", "kind": "instance", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fact_one_le_top_ennreal", "kind": "instance", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.neTopEquivNNReal", "kind": "definition", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.cinfi_ne_top", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.iInf_ne_top", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.csupr_ne_top", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.iSup_ne_top", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.iInf_ennreal", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.iSup_ennreal", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.ofNNRealHom", "kind": "definition", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.coe_ofNNRealHom", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.bot_eq_zero", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.not_top_le_coe", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.one_le_coe_iff", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.coe_le_one_iff", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.coe_lt_one_iff", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.one_lt_coe_iff", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.coe_natCast", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.ofReal_natCast", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.ofReal_ofNat", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.natCast_ne_top", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.natCast_lt_top", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.ofNat_ne_top", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.ofNat_lt_top", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.top_ne_natCast", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.top_ne_ofNat", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.natCast_le_ofNNReal", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.ofNNReal_le_natCast", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.ofNNReal_add_natCast", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.ofNNReal_natCast_add", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.ofNNReal_sub_natCast", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.ofNNReal_natCast_sub", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.one_lt_top", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.toNNReal_natCast", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.toNNReal_ofNat", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.toReal_natCast", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.toReal_ofNat", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.toNNReal_natCast_eq_toNNReal", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.le_coe_iff", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.coe_le_iff", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.lt_iff_exists_coe", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.toReal_le_coe_of_le_coe", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": true, "tactics": ["lift", "simpa"], "tactic_count": 2}
{"name": "ENNReal.max_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.min_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.max_zero_left", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.max_zero_right", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.lt_iff_exists_rat_btwn", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.lt_iff_exists_real_btwn", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.lt_iff_exists_nnreal_btwn", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.lt_iff_exists_add_pos_lt", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": true, "tactics": ["refine", "rcases", "lift", "rw", "refine", "rwa"], "tactic_count": 6}
{"name": "ENNReal.le_of_forall_pos_le_add", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": true, "tactics": ["contrapose", "rcases", "exact"], "tactic_count": 3}
{"name": "ENNReal.natCast_lt_coe", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.coe_lt_natCast", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.exists_nat_gt", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": true, "tactics": ["lift", "rcases", "exact"], "tactic_count": 3}
{"name": "ENNReal.iUnion_Iio_coe_nat", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": true, "tactics": ["ext", "rw", "exact"], "tactic_count": 3}
{"name": "ENNReal.iUnion_Iic_coe_nat", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.iUnion_Ioc_coe_nat", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.iUnion_Ioo_coe_nat", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.iUnion_Icc_coe_nat", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.iUnion_Ico_coe_nat", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.iInter_Ici_coe_nat", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.iInter_Ioi_coe_nat", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.coe_min", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.coe_max", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.le_of_top_imp_top_of_toNNReal_le", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": true, "tactics": ["by_contra", "lift", "lift", "refine", "simpa"], "tactic_count": 5}
{"name": "ENNReal.abs_toReal", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "ENNReal.coe_sSup", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.coe_sInf", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.coe_iSup", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.coe_iInf", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.coe_mem_upperBounds", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.iSup_coe_eq_top", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.iSup_coe_lt_top", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.iInf_coe_eq_top", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.iInf_coe_lt_top", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.OrdConnected.preimage_coe_nnreal_ennreal", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.OrdConnected.image_coe_nnreal_ennreal", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": true, "tactics": ["refine", "rcases", "exact"], "tactic_count": 3}
{"name": "Set.OrdConnected.preimage_ennreal_ofReal", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.OrdConnected.image_ennreal_ofReal", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "instReprENNReal", "kind": "instance", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalENNRealtoReal", "kind": "definition", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalENNRealOfNNReal", "kind": "definition", "module": "Mathlib.Data.ENNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.coe_finset_sum", "kind": "theorem", "module": "Mathlib.Data.ENNReal.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.coe_finset_prod", "kind": "theorem", "module": "Mathlib.Data.ENNReal.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.toNNReal_prod", "kind": "theorem", "module": "Mathlib.Data.ENNReal.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.toReal_prod", "kind": "theorem", "module": "Mathlib.Data.ENNReal.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.ofReal_prod_of_nonneg", "kind": "theorem", "module": "Mathlib.Data.ENNReal.BigOperators", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "ENNReal.iInf_sum", "kind": "theorem", "module": "Mathlib.Data.ENNReal.BigOperators", "is_tactic_proof": true, "tactics": ["induction", "empty", "cons", "simp", "refine", "refine", "rw", "exact"], "tactic_count": 8}
{"name": "ENNReal.prod_ne_top", "kind": "theorem", "module": "Mathlib.Data.ENNReal.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.prod_lt_top", "kind": "theorem", "module": "Mathlib.Data.ENNReal.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.sum_eq_top", "kind": "theorem", "module": "Mathlib.Data.ENNReal.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.sum_ne_top", "kind": "theorem", "module": "Mathlib.Data.ENNReal.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.sum_lt_top", "kind": "theorem", "module": "Mathlib.Data.ENNReal.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.lt_top_of_sum_ne_top", "kind": "theorem", "module": "Mathlib.Data.ENNReal.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.toNNReal_sum", "kind": "theorem", "module": "Mathlib.Data.ENNReal.BigOperators", "is_tactic_proof": true, "tactics": ["rw", "intro", "exact", "exact"], "tactic_count": 4}
{"name": "ENNReal.toReal_sum", "kind": "theorem", "module": "Mathlib.Data.ENNReal.BigOperators", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "ENNReal.ofReal_sum_of_nonneg", "kind": "theorem", "module": "Mathlib.Data.ENNReal.BigOperators", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "ENNReal.sum_lt_sum_of_nonempty", "kind": "theorem", "module": "Mathlib.Data.ENNReal.BigOperators", "is_tactic_proof": true, "tactics": ["induction", "singleton", "cons", "simp", "exact"], "tactic_count": 5}
{"name": "ENNReal.exists_le_of_sum_le", "kind": "theorem", "module": "Mathlib.Data.ENNReal.BigOperators", "is_tactic_proof": true, "tactics": ["contrapose", "apply"], "tactic_count": 2}
{"name": "ENNReal.prod_inv_distrib", "kind": "theorem", "module": "Mathlib.Data.ENNReal.BigOperators", "is_tactic_proof": false, "tactics": ["induction", "empty", "cons", "simp", "refine", "exact", "exact"], "tactic_count": 7}
{"name": "ENNReal.prod_div_distrib", "kind": "theorem", "module": "Mathlib.Data.ENNReal.BigOperators", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.prod_div_distrib_of_ne_top", "kind": "theorem", "module": "Mathlib.Data.ENNReal.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.prod_div_distrib_of_ne_zero", "kind": "theorem", "module": "Mathlib.Data.ENNReal.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.finsetSum_iSup", "kind": "theorem", "module": "Mathlib.Data.ENNReal.BigOperators", "is_tactic_proof": true, "tactics": ["induction", "empty", "cons", "simp_rw", "refine", "gcongr", "exacts"], "tactic_count": 7}
{"name": "ENNReal.finsetSum_iSup_of_monotone", "kind": "theorem", "module": "Mathlib.Data.ENNReal.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.HolderConjugate", "kind": "abbrev", "module": "Mathlib.Data.ENNReal.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.holderConjugate_iff", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Holder", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.HolderTriple.of", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.HolderTriple.symm", "kind": "instance", "module": "Mathlib.Data.ENNReal.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.HolderTriple.instInfty", "kind": "instance", "module": "Mathlib.Data.ENNReal.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.HolderTriple.instZero", "kind": "instance", "module": "Mathlib.Data.ENNReal.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.HolderTriple.inv_eq", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.HolderTriple.unique", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Holder", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.HolderTriple.one_div_add_one_div", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Holder", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ENNReal.HolderTriple.one_div_eq", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.HolderTriple.inv_inv_add_inv", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Holder", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.HolderTriple.le", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Holder", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.HolderTriple.inv_le_inv", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Holder", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.HolderTriple.inv_sub_inv_eq_inv", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Holder", "is_tactic_proof": true, "tactics": ["apply", "calc", "q⁻¹"], "tactic_count": 3}
{"name": "ENNReal.HolderTriple.inv_sub_inv_eq_inv'", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Holder", "is_tactic_proof": true, "tactics": ["obtain", "suffices", "by_contra", "have", "calc", "simp_all", "exact"], "tactic_count": 7}
{"name": "ENNReal.HolderTriple.unique_of_ne_zero", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Holder", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.HolderTriple.holderConjugate_div_div", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.HolderConjugate.symm", "kind": "instance", "module": "Mathlib.Data.ENNReal.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.HolderConjugate.instTwoTwo", "kind": "instance", "module": "Mathlib.Data.ENNReal.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.HolderConjugate.instOneInfty", "kind": "instance", "module": "Mathlib.Data.ENNReal.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.HolderConjugate.one_le", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.HolderConjugate.pos", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.HolderConjugate.ne_zero", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.HolderConjugate.inv_add_inv_eq_one", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.HolderConjugate.one_sub_inv", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.HolderConjugate.unique", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.HolderConjugate.eq_top_iff_eq_one", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Holder", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "rw", "simp", "rintro", "rw", "simp"], "tactic_count": 7}
{"name": "ENNReal.HolderConjugate.ne_top_iff_ne_one", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Holder", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.HolderConjugate.lt_top_iff_one_lt", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Holder", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "ENNReal.HolderConjugate.sub_one_mul_inv", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Holder", "is_tactic_proof": true, "tactics": ["have", "rw", "simp"], "tactic_count": 3}
{"name": "ENNReal.div_eq_inv_mul", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.div_right_comm", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.inv_zero", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.inv_top", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.coe_inv_le", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.coe_inv", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.coe_inv_two", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.coe_div", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.coe_div_le", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ENNReal.div_zero", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.instDivInvOneMonoid", "kind": "instance", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.inv_pow", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.mul_inv_cancel", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["lift", "norm_cast", "exact"], "tactic_count": 3}
{"name": "ENNReal.inv_mul_cancel", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.inv_mul_cancel_left'", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["obtain", "simp_all", "obtain", "simp_all", "simp"], "tactic_count": 5}
{"name": "ENNReal.inv_mul_cancel_left", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.mul_inv_cancel_left'", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["obtain", "simp_all", "obtain", "simp_all", "simp"], "tactic_count": 5}
{"name": "ENNReal.mul_inv_cancel_left", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.mul_inv_cancel_right'", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["obtain", "simp_all", "obtain", "simp_all", "simp"], "tactic_count": 5}
{"name": "ENNReal.mul_inv_cancel_right", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.inv_mul_cancel_right'", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["obtain", "simp_all", "obtain", "simp_all", "simp"], "tactic_count": 5}
{"name": "ENNReal.inv_mul_cancel_right", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.mul_div_cancel_right'", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.mul_div_cancel_right", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.div_mul_cancel'", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.div_mul_cancel", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.mul_div_cancel'", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.mul_div_cancel", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.mul_comm_div", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.mul_div_right_comm", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.instInvolutiveInv", "kind": "instance", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.inv_eq_one", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.inv_eq_top", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.inv_ne_top", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.inv_lt_top", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.div_lt_top", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.div_ne_top", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.inv_eq_zero", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.inv_ne_zero", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.div_pos", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.inv_mul_le_iff", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.mul_inv_le_iff", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.div_le_iff", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.div_le_iff'", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.mul_inv", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["cases", "simp_all", "cases", "simp_all", "top_mul,", "grind"], "tactic_count": 6}
{"name": "ENNReal.inv_div", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["rw", "rw", "rw"], "tactic_count": 3}
{"name": "ENNReal.mul_div_mul_left", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.mul_div_mul_right", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.sub_div", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "ENNReal.inv_pos", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.inv_strictAnti", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["intro", "lift", "cases", "rw", "rcases", "rw", "exact"], "tactic_count": 7}
{"name": "ENNReal.inv_lt_inv", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.inv_lt_iff_inv_lt", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ENNReal.lt_inv_iff_lt_inv", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ENNReal.inv_le_inv", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.inv_le_iff_inv_le", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ENNReal.le_inv_iff_le_inv", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ENNReal.inv_le_inv'", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.inv_lt_inv'", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.inv_le_one", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.one_le_inv", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.inv_lt_one", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.one_lt_inv", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "OrderIso.invENNReal", "kind": "definition", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.invENNReal_symm_apply", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.div_top", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.top_div", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.top_div_of_ne_top", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.top_div_coe", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.top_div_of_lt_top", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.zero_div", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.div_eq_top", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.div_div_cancel'", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["obtain", "simp", "obtain", "simp", "rw"], "tactic_count": 5}
{"name": "ENNReal.div_div_cancel", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.le_div_iff_mul_le", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": ["cases", "top", "lift", "rw", "rcases", "coe", "rcases", "have", "simp", "rw", "rw"], "tactic_count": 11}
{"name": "ENNReal.div_le_iff_le_mul", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["suffices", "refine"], "tactic_count": 2}
{"name": "ENNReal.lt_div_iff_mul_lt", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.div_le_of_le_mul", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["by_cases", "have", "simp", "by_cases", "exact"], "tactic_count": 5}
{"name": "ENNReal.div_le_of_le_mul'", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.div_self_le_one", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.mul_inv_le_one", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.inv_mul_le_one", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.mul_inv_ne_top", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.inv_mul_ne_top", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.mul_le_of_le_div", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ENNReal.mul_le_of_le_div'", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.div_lt_iff", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.mul_lt_of_lt_div", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["contrapose", "exact"], "tactic_count": 2}
{"name": "ENNReal.mul_lt_of_lt_div'", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.div_lt_of_lt_mul", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.div_lt_of_lt_mul'", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.div_lt_div_iff_left", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.div_lt_div_iff_right", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.div_lt_div_right", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.div_lt_div_left", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.exists_pos_mul_lt", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["obtain", "exact", "refine", "gcongr", "exacts"], "tactic_count": 5}
{"name": "ENNReal.inv_le_iff_le_mul", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["rw", "exacts"], "tactic_count": 2}
{"name": "ENNReal.le_inv_iff_mul_le", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["rw", "right", "simp"], "tactic_count": 3}
{"name": "ENNReal.div_le_div", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.div_le_div_left", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.div_le_div_right", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.eq_inv_of_mul_eq_one_left", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["rw", "rintro", "simp"], "tactic_count": 3}
{"name": "ENNReal.mul_le_iff_le_inv", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.le_of_forall_nnreal_lt", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["refine", "lift", "exact"], "tactic_count": 3}
{"name": "ENNReal.eq_of_forall_nnreal_le_iff", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.eq_of_forall_le_nnreal_iff", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.le_of_forall_pos_nnreal_lt", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.eq_top_of_forall_nnreal_le", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.add_div", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.div_add_div_same", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.div_self", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.mul_div_le", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.eq_div_iff", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.div_eq_div_iff", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["rw", "conv_rhs", "rw"], "tactic_count": 3}
{"name": "ENNReal.div_eq_one_iff", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.inv_two_add_inv_two", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.inv_three_add_inv_three", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["rw", "ring"], "tactic_count": 2}
{"name": "ENNReal.add_halves", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.add_thirds", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.div_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.div_pos_iff", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.div_ne_zero", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.div_mul", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["simp", "rw", "ring", "simpa", "simpa"], "tactic_count": 5}
{"name": "ENNReal.mul_div_mul_comm", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["simp", "ring"], "tactic_count": 2}
{"name": "ENNReal.half_pos", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.one_half_lt_one", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.half_lt_self", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["lift", "rw", "rw", "exacts"], "tactic_count": 4}
{"name": "ENNReal.half_le_self", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.sub_half", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.one_sub_inv_two", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.exists_lt_mul_left", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.exists_lt_mul_right", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "ENNReal.mul_le_of_forall_lt", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["refine", "obtain", "obtain", "exact"], "tactic_count": 4}
{"name": "ENNReal.le_mul_of_forall_lt", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["rw", "exact", "mul_le_of_forall_lt"], "tactic_count": 3}
{"name": "ENNReal.orderIsoIicOneBirational", "kind": "definition", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": ["refine", "simpa", "have", "simp"], "tactic_count": 4}
{"name": "ENNReal.orderIsoIicOneBirational_symm_apply", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.orderIsoIicCoe", "kind": "definition", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.orderIsoIicCoe_symm_apply_coe", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.orderIsoUnitIntervalBirational", "kind": "definition", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.orderIsoUnitIntervalBirational_apply_coe", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.exists_inv_nat_lt", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.exists_nat_pos_mul_gt", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.exists_nat_mul_gt", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.exists_nat_pos_inv_mul_lt", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["rcases", "use", "rw", "exact"], "tactic_count": 4}
{"name": "ENNReal.exists_nnreal_pos_mul_lt", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["rcases", "use", "simp"], "tactic_count": 3}
{"name": "ENNReal.exists_inv_two_pow_lt", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["rcases", "refine", "rw", "norm_cast", "exact"], "tactic_count": 5}
{"name": "ENNReal.coe_zpow", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["rcases", "simp", "have", "simp"], "tactic_count": 4}
{"name": "ENNReal.zero_zpow_def", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "ENNReal.top_zpow_def", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "ENNReal.zpow_pos", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["cases", "simpa", "simp"], "tactic_count": 3}
{"name": "ENNReal.zpow_lt_top", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["cases", "simpa", "simp"], "tactic_count": 3}
{"name": "ENNReal.zpow_ne_top", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.exists_mem_Ico_zpow", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["lift", "lift", "have", "obtain", "refine", "simpa", "refine", "rwa", "rwa"], "tactic_count": 9}
{"name": "ENNReal.exists_mem_Ioc_zpow", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["lift", "lift", "have", "obtain", "refine", "simpa", "refine", "rwa", "rwa"], "tactic_count": 9}
{"name": "ENNReal.Ioo_zero_top_eq_iUnion_Ico_zpow", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["ext", "simp", "constructor", "rintro", "exact", "rintro", "constructor", "apply", "exact", "apply", "exact"], "tactic_count": 11}
{"name": "ENNReal.zpow_le_of_le", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["obtain", "simp", "exact", "apply", "exact", "simp", "refine", "simp", "apply", "simpa"], "tactic_count": 10}
{"name": "ENNReal.monotone_zpow", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.zpow_add", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["lift", "replace", "simp"], "tactic_count": 3}
{"name": "ENNReal.zpow_neg", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "obtain", "obtain", "exact"], "tactic_count": 5}
{"name": "ENNReal.zpow_sub", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.inv_zpow", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "ENNReal.inv_zpow'", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.zpow_le_one_of_nonpos", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["obtain", "lift", "rw", "exact"], "tactic_count": 4}
{"name": "ENNReal.isUnit_iff", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.mulLeftOrderIso", "kind": "definition", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.mulRightOrderIso", "kind": "definition", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.mul_iSup", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "obtain", "simp", "obtain", "obtain", "simpa", "exact"], "tactic_count": 8}
{"name": "ENNReal.iSup_mul", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.mul_sSup", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.sSup_mul", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.iSup_div", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.sSup_div", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.mul_iInf'", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["obtain", "simp", "obtain", "obtain", "rw", "rw", "exact", "exact"], "tactic_count": 8}
{"name": "ENNReal.iInf_mul'", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ENNReal.mul_iInf_of_ne", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.iInf_mul_of_ne", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.mul_iInf", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.iInf_mul", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.iInf_div'", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.iInf_div_of_ne", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.iInf_div", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.inv_iInf", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.inv_iSup", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.inv_sInf", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.inv_sSup", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.le_iInf_mul", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.iSup_mul_le", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.le_iInf_mul_iInf", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["rw", "have", "have", "replace", "rw", "rintro", "simpa"], "tactic_count": 7}
{"name": "ENNReal.iInf_mul_iInf", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": false, "tactics": ["refine", "obtain", "exact"], "tactic_count": 3}
{"name": "ENNReal.smul_iSup", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.smul_sSup", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "ENNReal.ofReal_inv_of_pos", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.ofReal_div_of_pos", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.toNNReal_inv", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["cases", "top", "coe", "rcases", "rw"], "tactic_count": 5}
{"name": "ENNReal.toNNReal_div", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.toReal_inv", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.toReal_div", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Inv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.coe_indicator", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.coe_finset_sup", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.mul_lt_mul", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.pow_right_strictMono", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.pow_le_pow_left_iff", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.pow_lt_pow_left_iff", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.pow_le_pow_left", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.mul_left_strictMono", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.mul_right_strictMono", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.mul_lt_mul_right", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.mul_lt_mul_left", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.mul_right_inj", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.mul_left_inj", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.mul_le_mul_iff_right", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.mul_le_mul_iff_left", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.mul_lt_mul_iff_right", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.mul_lt_mul_iff_left", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.mul_eq_left", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ENNReal.mul_eq_right", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ENNReal.pow_pos", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.pow_ne_zero", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ENNReal.not_lt_zero", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.le_of_add_le_add_left", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.le_of_add_le_add_right", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.add_lt_add_left", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.add_lt_add_right", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.add_le_add_iff_left", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.add_le_add_iff_right", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.add_lt_add_iff_left", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.add_lt_add_iff_right", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.add_lt_add_of_le_of_lt", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.add_lt_add_of_lt_of_le", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.addLeftReflectLT", "kind": "instance", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.lt_add_right", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "ENNReal.add_eq_top", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.add_lt_top", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.toNNReal_add", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": true, "tactics": ["lift", "lift", "rfl"], "tactic_count": 3}
{"name": "ENNReal.toReal_le_add'", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": true, "tactics": ["refine", "simpa"], "tactic_count": 2}
{"name": "ENNReal.toReal_le_add", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.not_lt_top", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.add_ne_top", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ENNReal.Finiteness.add_ne_top", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.mul_top'", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "ENNReal.mul_top", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.top_mul'", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "ENNReal.top_mul", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.top_mul_top", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.mul_eq_top", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.mul_lt_top", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.mul_ne_top", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.lt_top_of_mul_ne_top_left", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.lt_top_of_mul_ne_top_right", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.mul_lt_top_iff", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "intro", "exact", "rintro"], "tactic_count": 6}
{"name": "ENNReal.mul_self_lt_top_iff", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": true, "tactics": ["rw", "rintro", "exact"], "tactic_count": 3}
{"name": "ENNReal.mul_pos_iff", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.mul_pos", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.top_pow", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.pow_eq_top_iff", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.pow_ne_top_iff", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.pow_lt_top_iff", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.eq_top_of_pow", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.pow_ne_top", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.pow_lt_top", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.add_lt_add", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.addLECancellable_iff_ne", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.cancel_of_ne", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.cancel_of_lt", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.cancel_of_lt'", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.cancel_coe", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.add_right_inj", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.add_left_inj", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.sub_eq_sInf", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.coe_sub", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.top_sub_coe", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.top_sub", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": true, "tactics": ["lift"], "tactic_count": 1}
{"name": "ENNReal.sub_top", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.sub_eq_top_iff", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.sub_ne_top_iff", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.sub_ne_top", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.natCast_sub", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.sub_eq_of_eq_add", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.sub_eq_of_eq_add'", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.eq_sub_of_add_eq", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.eq_sub_of_add_eq'", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.sub_eq_of_eq_add_rev", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.sub_eq_of_eq_add_rev'", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.add_sub_cancel_left", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.add_sub_cancel_right", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.sub_add_eq_add_sub", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": true, "tactics": ["by_cases", "simpa", "refine", "simp", "simpa"], "tactic_count": 5}
{"name": "ENNReal.lt_add_of_sub_lt_left", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact", "exact"], "tactic_count": 4}
{"name": "ENNReal.lt_add_of_sub_lt_right", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.le_sub_of_add_le_left", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.le_sub_of_add_le_right", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.sub_lt_of_lt_add", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.sub_lt_iff_lt_right", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.sub_lt_iff_lt_left", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.le_sub_iff_add_le_left", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.le_sub_iff_add_le_right", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.sub_lt_self", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.sub_lt_self_iff", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.sub_lt_of_sub_lt", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.sub_sub_cancel", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.sub_right_inj", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.sub_mul", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "exact"], "tactic_count": 3}
{"name": "ENNReal.mul_sub", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "ENNReal.sub_le_sub_iff_left", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.le_toReal_sub", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": true, "tactics": ["lift", "induction", "simp", "simp", "exact"], "tactic_count": 5}
{"name": "ENNReal.toNNReal_sub", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": true, "tactics": ["lift"], "tactic_count": 1}
{"name": "ENNReal.toReal_sub_of_le", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.ofReal_sub", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": true, "tactics": ["obtain", "rw", "refine", "rw"], "tactic_count": 4}
{"name": "ENNReal.sub_sub_sub_cancel_left", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": true, "tactics": ["have", "lift", "lift", "cases", "simp", "norm_cast", "rw", "exact"], "tactic_count": 8}
{"name": "ENNReal.Ico_eq_Iio", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.mem_Iio_self_add", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.mem_Ioo_self_sub_add", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.image_coe_Iic", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.image_coe_Ici", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.image_coe_Iio", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.image_coe_Ioi", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.image_coe_Icc", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.image_coe_Ico", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.image_coe_Ioc", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.image_coe_Ioo", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.image_coe_uIcc", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.image_coe_uIoc", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.image_coe_uIoo", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.toNNReal_iInf", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": true, "tactics": ["cases", "rw", "lift", "simp_rw"], "tactic_count": 4}
{"name": "ENNReal.toNNReal_sInf", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "ENNReal.toReal_iInf", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.toReal_sInf", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.ofReal_iInf", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": true, "tactics": ["obtain", "rw", "simp", "replace", "refine", "obtain", "simp", "rw", "exact", "exact"], "tactic_count": 10}
{"name": "ENNReal.iInf_add", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.sub_iInf", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": true, "tactics": ["refine", "rw", "simp"], "tactic_count": 3}
{"name": "ENNReal.sInf_add", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.add_iInf", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.iInf_add_iInf", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.iInf_add_iInf_of_monotone", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.add_iInf₂", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.iInf₂_add", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.add_sInf", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.le_iInf_add_iInf", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "ENNReal.le_iInf₂_add_iInf₂", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "ENNReal.iInf_gt_eq_self", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": true, "tactics": ["refine", "refine", "obtain", "exact"], "tactic_count": 4}
{"name": "ENNReal.exists_add_lt_of_add_lt", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": true, "tactics": ["contrapose", "simpa"], "tactic_count": 2}
{"name": "ENNReal.toNNReal_iSup", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": true, "tactics": ["lift", "simp_rw", "by_cases", "rw", "rw"], "tactic_count": 5}
{"name": "ENNReal.toNNReal_sSup", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "ENNReal.toReal_iSup", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.toReal_sSup", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.iSup_sub", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.iSup_eq_zero", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.iSup_zero", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.iSup_natCast", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.add_iSup", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": true, "tactics": ["obtain", "simp", "refine", "refine", "exact"], "tactic_count": 5}
{"name": "ENNReal.iSup_add", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.add_biSup'", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": true, "tactics": ["haveI", "simp"], "tactic_count": 2}
{"name": "ENNReal.biSup_add'", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.add_biSup", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.biSup_add", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.add_sSup", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.sSup_add", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.iSup_add_iSup_le", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "ENNReal.biSup_add_biSup_le'", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "ENNReal.biSup_add_biSup_le", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.iSup_add_iSup", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": true, "tactics": ["cases", "simp", "refine", "refine", "rcases", "exact"], "tactic_count": 6}
{"name": "ENNReal.iSup_add_iSup_of_monotone", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.sub_iSup", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact", "simp_rw", "refine", "le_antisymm", "add_le_of_le_tsub_right_of_le", "rw", "exact"], "tactic_count": 9}
{"name": "ENNReal.iSup_lt_eq_self", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": true, "tactics": ["refine", "refine", "obtain", "exact"], "tactic_count": 4}
{"name": "ENNReal.exists_lt_add_of_lt_add", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Operations", "is_tactic_proof": true, "tactics": ["contrapose", "simpa"], "tactic_count": 2}
{"name": "ENNReal.toReal_add", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": true, "tactics": ["lift", "lift", "rfl"], "tactic_count": 3}
{"name": "ENNReal.toReal_add_le", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.ofReal_add", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.ofReal_add_le", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.toReal_le_toReal", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": true, "tactics": ["lift", "lift", "norm_cast"], "tactic_count": 3}
{"name": "ENNReal.toReal_mono", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.toReal_mono'", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": true, "tactics": ["rcases", "exact", "exact"], "tactic_count": 3}
{"name": "ENNReal.toReal_lt_toReal", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": true, "tactics": ["lift", "lift", "norm_cast"], "tactic_count": 3}
{"name": "ENNReal.toReal_strict_mono", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.toNNReal_mono", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.le_toNNReal_of_coe_le", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.toNNReal_le_toNNReal", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.toNNReal_strict_mono", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ENNReal.toNNReal_lt_toNNReal", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.toNNReal_lt_of_lt_coe", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.toReal_max", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.toReal_min", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.toReal_sup", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.toReal_inf", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.toNNReal_pos_iff", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "ENNReal.toNNReal_pos", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.toReal_pos_iff", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.toReal_pos", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.ofReal_le_ofReal", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.ofReal_mono", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.ofReal_le_of_le_toReal", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.ofReal_le_ofReal_iff", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.ofReal_le_ofReal_iff'", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.ofReal_le_coe", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.ofReal_lt_ofReal_iff'", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.ofReal_eq_ofReal_iff", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.ofReal_lt_ofReal_iff", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.ofReal_lt_ofReal_iff_of_nonneg", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.ofReal_pos", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.ofReal_eq_zero", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.ofReal_min", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.ofReal_max", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.ofReal_ne_zero_iff", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.zero_eq_ofReal", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.ofReal_lt_natCast", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "ENNReal.ofReal_lt_one", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "ENNReal.ofReal_lt_ofNat", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.natCast_le_ofReal", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.one_le_ofReal", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "ENNReal.ofNat_le_ofReal", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.ofReal_le_natCast", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.ofReal_le_one", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.ofReal_le_ofNat", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.natCast_lt_ofReal", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.one_lt_ofReal", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.ofNat_lt_ofReal", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.ofReal_eq_natCast", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.ofReal_eq_one", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.ofReal_eq_ofNat", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.ofReal_le_iff_le_toReal", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": true, "tactics": ["lift", "simpa"], "tactic_count": 2}
{"name": "ENNReal.ofReal_lt_iff_lt_toReal", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": true, "tactics": ["lift", "simpa"], "tactic_count": 2}
{"name": "ENNReal.ofReal_lt_coe_iff", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.le_ofReal_iff_toReal_le", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": true, "tactics": ["lift", "simpa"], "tactic_count": 2}
{"name": "ENNReal.toReal_le_of_le_ofReal", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.lt_ofReal_iff_toReal_lt", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": true, "tactics": ["lift", "simpa"], "tactic_count": 2}
{"name": "ENNReal.toReal_lt_of_lt_ofReal", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.ofReal_mul", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.ofReal_mul'", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.ofReal_pow", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.ofReal_nsmul", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.toNNReal_mul", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.toNNReal_mul_top", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.toNNReal_top_mul", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.toNNRealHom", "kind": "definition", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.toNNReal_pow", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.toRealHom", "kind": "definition", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.toReal_mul", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.toReal_nsmul", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.toReal_pow", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.toReal_ofReal_mul", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.toReal_mul_top", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.toReal_top_mul", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ENNReal.trichotomy", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ENNReal.trichotomy₂", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": true, "tactics": ["rcases", "simpa", "rcases", "simpa", "have", "have", "simp"], "tactic_count": 7}
{"name": "ENNReal.dichotomy", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.toReal_pos_iff_ne_top", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.sup_eq_zero", "kind": "theorem", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalENNRealOfReal", "kind": "definition", "module": "Mathlib.Data.ENNReal.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.some_eq_coe", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.coe_inj", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.instSuccAddOrder", "kind": "instance", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.coe_zero", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.coe_one", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.coe_add", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.coe_sub", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.coe_mul", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.mul_top", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.top_mul", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.mul_top'", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.top_mul'", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.top_pow", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.pow_eq_top_iff", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.pow_ne_top_iff", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.pow_lt_top_iff", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.eq_top_of_pow", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.lift", "kind": "definition", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.coe_lift", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.lift_coe", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.lift_lt_iff", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.lift_le_iff", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.lt_lift_iff", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.le_lift_iff", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.lift_zero", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.lift_one", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.lift_ofNat", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.add_lt_top", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.lift_add", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "ENat.canLift", "kind": "instance", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.instWellFoundedRelation", "kind": "instance", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.toNat", "kind": "definition", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.toNatHom", "kind": "definition", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.coe_toNatHom", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.toNatHom_apply", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.toNat_coe", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.toNat_zero", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.toNat_one", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.toNat_ofNat", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.toNat_top", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.toNat_eq_zero", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.lift_eq_toNat_of_lt_top", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": true, "tactics": ["rcases", "contradiction", "rfl"], "tactic_count": 3}
{"name": "ENat.recTopCoe_zero", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.recTopCoe_one", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.recTopCoe_ofNat", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.top_ne_coe", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.top_ne_ofNat", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.top_ne_zero", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.top_ne_one", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.coe_ne_top", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.ofNat_ne_top", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.zero_ne_top", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.one_ne_top", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.top_sub_coe", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.top_sub_one", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.top_sub_ofNat", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.top_pos", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.one_lt_top", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.sub_top", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.coe_toNat_eq_self", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.toNat_eq_iff_eq_coe", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": true, "tactics": ["cases", "simpa", "simp"], "tactic_count": 3}
{"name": "ENat.coe_toNat_le_self", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.toNat_add", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": true, "tactics": ["lift", "lift", "rfl"], "tactic_count": 3}
{"name": "ENat.toNat_sub", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": true, "tactics": ["lift", "induction", "rw", "rw"], "tactic_count": 4}
{"name": "ENat.toNat_mul", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": true, "tactics": ["cases", "simp", "rename_i", "rename_i", "simp"], "tactic_count": 5}
{"name": "ENat.toNat_eq_iff", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "ENat.toNat_le_of_le_coe", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": true, "tactics": ["lift", "simpa"], "tactic_count": 2}
{"name": "ENat.toNat_le_toNat", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.succ_def", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.add_one_le_iff", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.one_le_iff_ne_zero", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.lt_one_iff_eq_zero", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.lt_add_one_iff", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.add_le_add_iff_left", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.add_le_add_iff_right", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.lt_add_one_iff'", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENat.lt_coe_add_one_iff", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.le_coe_iff", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.not_lt_zero", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.coe_lt_top", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.coe_lt_coe", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENat.coe_le_coe", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENat.nat_induction", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": true, "tactics": ["have", "cases", "exact", "exact"], "tactic_count": 4}
{"name": "ENat.add_one_pos", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.natCast_lt_succ", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ENat.add_lt_add_iff_right", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.add_lt_add_iff_left", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.ne_top_iff_exists", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.eq_top_iff_forall_ne", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.forall_ne_top", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.exists_ne_top", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.eq_top_iff_forall_gt", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.eq_top_iff_forall_ge", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.forall_natCast_le_iff_le", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.eq_of_forall_natCast_le_iff", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.exists_nat_gt", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "ENat.sub_eq_top_iff", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.sub_ne_top_iff", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.addLECancellable_of_ne_top", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.addLECancellable_of_lt_top", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.addLECancellable_coe", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.le_sub_of_add_le_left", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.le_sub_of_add_le_right", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.le_sub_one_of_lt", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": true, "tactics": ["cases", "simp", "exact"], "tactic_count": 3}
{"name": "ENat.sub_sub_cancel", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.add_left_injective_of_ne_top", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": true, "tactics": ["intro", "exact"], "tactic_count": 2}
{"name": "ENat.add_right_injective_of_ne_top", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "ENat.mul_right_strictMono", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.mul_left_strictMono", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.mul_le_mul_left_iff", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.mul_le_mul_right_iff", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.mul_le_mul_of_le_right", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ENat.self_le_mul_right", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": true, "tactics": ["obtain", "simp", "obtain", "simp", "nth_rewrite", "assumption"], "tactic_count": 6}
{"name": "ENat.self_le_mul_left", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ENat.instUniqueUnits", "kind": "instance", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.add_one_natCast_le_withTop_of_lt", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": true, "tactics": [], "tactic_count": 0}
{"name": "ENat.coe_top_add_one", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.add_one_eq_coe_top_iff", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": true, "tactics": ["norm_cast", "simp"], "tactic_count": 2}
{"name": "ENat.natCast_ne_coe_top", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.one_le_iff_ne_zero_withTop", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.natCast_le_of_coe_top_le_withTop", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.natCast_lt_of_coe_top_le_withTop", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.map", "kind": "definition", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.map_top", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.map_coe", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.map_zero", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.map_one", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.map_ofNat", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.map_eq_top_iff", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.strictMono_map_iff", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.monotone_map_iff", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.map_natCast_nonneg", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "ENat.map_natCast_strictMono", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.map_natCast_injective", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.map_natCast_inj", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.map_natCast_eq_zero", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENat.map_add", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OneHom.ENatMap", "kind": "definition", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroHom.ENatMap", "kind": "definition", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddHom.ENatMap", "kind": "definition", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.ENatMap", "kind": "definition", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.ENatMap", "kind": "definition", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.ENatMap", "kind": "definition", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.map_natCast_mul", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.lt_add_one_iff", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": true, "tactics": ["rw", "cases", "simp", "rw"], "tactic_count": 4}
{"name": "WithBot.add_one_le_iff", "kind": "theorem", "module": "Mathlib.Data.ENat.Basic", "is_tactic_proof": true, "tactics": ["rw", "cases", "simp", "rw"], "tactic_count": 4}
{"name": "ENat.sum_iSup", "kind": "theorem", "module": "Mathlib.Data.ENat.BigOperators", "is_tactic_proof": true, "tactics": ["induction", "empty", "cons", "simp_rw", "refine", "gcongr", "exacts"], "tactic_count": 7}
{"name": "ENat.sum_iSup_of_monotone", "kind": "theorem", "module": "Mathlib.Data.ENat.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat", "kind": "definition", "module": "Mathlib.Data.ENat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "termℕ∞", "kind": "definition", "module": "Mathlib.Data.ENat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Data_ENat_Defs___macroRules_termℕ∞_1", "kind": "definition", "module": "Mathlib.Data.ENat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Data_ENat_Defs___unexpand_ENat_1", "kind": "definition", "module": "Mathlib.Data.ENat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.instNatCast", "kind": "instance", "module": "Mathlib.Data.ENat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.recTopCoe", "kind": "definition", "module": "Mathlib.Data.ENat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.recTopCoe_top", "kind": "theorem", "module": "Mathlib.Data.ENat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.recTopCoe_coe", "kind": "theorem", "module": "Mathlib.Data.ENat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCompleteLinearOrderWithBotENat", "kind": "instance", "module": "Mathlib.Data.ENat.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.iSup_coe_eq_top", "kind": "theorem", "module": "Mathlib.Data.ENat.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.iSup_coe_ne_top", "kind": "theorem", "module": "Mathlib.Data.ENat.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.iSup_coe_lt_top", "kind": "theorem", "module": "Mathlib.Data.ENat.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.iInf_coe_eq_top", "kind": "theorem", "module": "Mathlib.Data.ENat.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.iInf_coe_ne_top", "kind": "theorem", "module": "Mathlib.Data.ENat.Lattice", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENat.iInf_coe_lt_top", "kind": "theorem", "module": "Mathlib.Data.ENat.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.coe_sSup", "kind": "theorem", "module": "Mathlib.Data.ENat.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.coe_sInf", "kind": "theorem", "module": "Mathlib.Data.ENat.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.coe_iSup", "kind": "theorem", "module": "Mathlib.Data.ENat.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.coe_iInf", "kind": "theorem", "module": "Mathlib.Data.ENat.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.iInf_eq_top_of_isEmpty", "kind": "theorem", "module": "Mathlib.Data.ENat.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.iInf_toNat", "kind": "theorem", "module": "Mathlib.Data.ENat.Lattice", "is_tactic_proof": true, "tactics": ["cases", "simp", "norm_cast"], "tactic_count": 3}
{"name": "ENat.iInf_eq_zero", "kind": "theorem", "module": "Mathlib.Data.ENat.Lattice", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ENat.sSup_eq_zero", "kind": "theorem", "module": "Mathlib.Data.ENat.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.sInf_eq_zero", "kind": "theorem", "module": "Mathlib.Data.ENat.Lattice", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "ENat.sSup_eq_zero'", "kind": "theorem", "module": "Mathlib.Data.ENat.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.iSup_eq_zero", "kind": "theorem", "module": "Mathlib.Data.ENat.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.iSup_zero", "kind": "theorem", "module": "Mathlib.Data.ENat.Lattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENat.sSup_eq_top_of_infinite", "kind": "theorem", "module": "Mathlib.Data.ENat.Lattice", "is_tactic_proof": true, "tactics": ["apply", "intro", "cases", "top", "coe", "contrapose", "apply", "intro", "specialize", "have", "use", "simp"], "tactic_count": 12}
{"name": "ENat.finite_of_sSup_lt_top", "kind": "theorem", "module": "Mathlib.Data.ENat.Lattice", "is_tactic_proof": true, "tactics": ["contrapose", "simp", "exact"], "tactic_count": 3}
{"name": "ENat.sSup_mem_of_nonempty_of_lt_top", "kind": "theorem", "module": "Mathlib.Data.ENat.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.exists_eq_iSup_of_lt_top", "kind": "theorem", "module": "Mathlib.Data.ENat.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.exists_eq_iInf", "kind": "theorem", "module": "Mathlib.Data.ENat.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.exists_eq_iSup₂_of_lt_top", "kind": "theorem", "module": "Mathlib.Data.ENat.Lattice", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ENat.iSup_natCast", "kind": "theorem", "module": "Mathlib.Data.ENat.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.mul_iSup", "kind": "theorem", "module": "Mathlib.Data.ENat.Lattice", "is_tactic_proof": false, "tactics": ["refine", "obtain", "simp", "obtain", "simp", "cases", "top", "coe", "d", "have", "rw", "intro", "obtain", "exact", "obtain", "rw", "apply"], "tactic_count": 17}
{"name": "ENat.iSup_mul", "kind": "theorem", "module": "Mathlib.Data.ENat.Lattice", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "ENat.mul_sSup", "kind": "theorem", "module": "Mathlib.Data.ENat.Lattice", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "ENat.sSup_mul", "kind": "theorem", "module": "Mathlib.Data.ENat.Lattice", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "ENat.mul_iInf", "kind": "theorem", "module": "Mathlib.Data.ENat.Lattice", "is_tactic_proof": true, "tactics": ["refine", "obtain", "rw", "exact"], "tactic_count": 4}
{"name": "ENat.iInf_mul", "kind": "theorem", "module": "Mathlib.Data.ENat.Lattice", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "ENat.mul_iInf'", "kind": "theorem", "module": "Mathlib.Data.ENat.Lattice", "is_tactic_proof": true, "tactics": ["obtain", "suffices", "aesop", "rw"], "tactic_count": 4}
{"name": "ENat.iInf_mul'", "kind": "theorem", "module": "Mathlib.Data.ENat.Lattice", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "ENat.mul_iInf_of_ne", "kind": "theorem", "module": "Mathlib.Data.ENat.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.iInf_mul_of_ne", "kind": "theorem", "module": "Mathlib.Data.ENat.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.add_iSup", "kind": "theorem", "module": "Mathlib.Data.ENat.Lattice", "is_tactic_proof": true, "tactics": ["obtain", "simp", "refine", "refine", "exact"], "tactic_count": 5}
{"name": "ENat.iSup_add", "kind": "theorem", "module": "Mathlib.Data.ENat.Lattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENat.add_biSup'", "kind": "theorem", "module": "Mathlib.Data.ENat.Lattice", "is_tactic_proof": true, "tactics": ["haveI", "simp"], "tactic_count": 2}
{"name": "ENat.biSup_add'", "kind": "theorem", "module": "Mathlib.Data.ENat.Lattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENat.add_biSup", "kind": "theorem", "module": "Mathlib.Data.ENat.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.biSup_add", "kind": "theorem", "module": "Mathlib.Data.ENat.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.add_sSup", "kind": "theorem", "module": "Mathlib.Data.ENat.Lattice", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENat.sSup_add", "kind": "theorem", "module": "Mathlib.Data.ENat.Lattice", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENat.iSup_add_iSup_le", "kind": "theorem", "module": "Mathlib.Data.ENat.Lattice", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "ENat.biSup_add_biSup_le'", "kind": "theorem", "module": "Mathlib.Data.ENat.Lattice", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "ENat.biSup_add_biSup_le", "kind": "theorem", "module": "Mathlib.Data.ENat.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.iSup_add_iSup", "kind": "theorem", "module": "Mathlib.Data.ENat.Lattice", "is_tactic_proof": true, "tactics": ["cases", "simp", "refine", "refine", "rcases", "exact"], "tactic_count": 6}
{"name": "ENat.iSup_add_iSup_of_monotone", "kind": "theorem", "module": "Mathlib.Data.ENat.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.smul_iSup", "kind": "theorem", "module": "Mathlib.Data.ENat.Lattice", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ENat.smul_sSup", "kind": "theorem", "module": "Mathlib.Data.ENat.Lattice", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "ENat.sub_iSup", "kind": "theorem", "module": "Mathlib.Data.ENat.Lattice", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact", "simp_rw", "refine", "le_antisymm", "add_le_of_le_tsub_right_of_le", "rw", "exact"], "tactic_count": 9}
{"name": "ENat.instPow", "kind": "instance", "module": "Mathlib.Data.ENat.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.epow_natCast", "kind": "theorem", "module": "Mathlib.Data.ENat.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.zero_epow_top", "kind": "theorem", "module": "Mathlib.Data.ENat.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.zero_epow", "kind": "theorem", "module": "Mathlib.Data.ENat.Pow", "is_tactic_proof": true, "tactics": ["induction", "top", "coe"], "tactic_count": 3}
{"name": "ENat.one_epow", "kind": "theorem", "module": "Mathlib.Data.ENat.Pow", "is_tactic_proof": true, "tactics": ["induction", "top", "coe"], "tactic_count": 3}
{"name": "ENat.top_epow_top", "kind": "theorem", "module": "Mathlib.Data.ENat.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.top_epow", "kind": "theorem", "module": "Mathlib.Data.ENat.Pow", "is_tactic_proof": true, "tactics": ["induction", "top", "coe"], "tactic_count": 3}
{"name": "ENat.epow_zero", "kind": "theorem", "module": "Mathlib.Data.ENat.Pow", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENat.epow_one", "kind": "theorem", "module": "Mathlib.Data.ENat.Pow", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENat.epow_top", "kind": "theorem", "module": "Mathlib.Data.ENat.Pow", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENat.epow_right_mono", "kind": "theorem", "module": "Mathlib.Data.ENat.Pow", "is_tactic_proof": true, "tactics": ["intro", "induction", "rw", "induction", "rcases", "exact", "simp", "simp", "exact"], "tactic_count": 9}
{"name": "ENat.one_le_epow", "kind": "theorem", "module": "Mathlib.Data.ENat.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.epow_left_mono", "kind": "theorem", "module": "Mathlib.Data.ENat.Pow", "is_tactic_proof": true, "tactics": ["intro", "simp", "induction", "rcases", "rw", "rw", "rw", "simp"], "tactic_count": 8}
{"name": "ENat.epow_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Data.ENat.Pow", "is_tactic_proof": true, "tactics": ["refine", "by_contra", "exact", "rw"], "tactic_count": 4}
{"name": "ENat.epow_eq_one_iff", "kind": "theorem", "module": "Mathlib.Data.ENat.Pow", "is_tactic_proof": true, "tactics": ["refine", "rcases", "rw", "rfl", "have", "simp", "exact"], "tactic_count": 7}
{"name": "ENat.epow_add", "kind": "theorem", "module": "Mathlib.Data.ENat.Pow", "is_tactic_proof": true, "tactics": ["rcases", "rw", "rcases", "simp", "rw", "exact", "simp", "induction", "rw", "exact", "induction", "rw", "exact", "simp"], "tactic_count": 14}
{"name": "ENat.mul_epow", "kind": "theorem", "module": "Mathlib.Data.ENat.Pow", "is_tactic_proof": true, "tactics": ["induction", "rcases", "simp", "simp", "rcases", "simp", "simp", "rw", "exact", "simp"], "tactic_count": 10}
{"name": "ENat.epow_mul", "kind": "theorem", "module": "Mathlib.Data.ENat.Pow", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rcases", "simp", "rcases", "rw", "simp", "induction", "rw", "induction", "rw", "apply", "apply", "simp", "simp"], "tactic_count": 15}
{"name": "EReal", "kind": "definition", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instZeroLEOneClassEReal", "kind": "instance", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instSupSetEReal", "kind": "instance", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInfSetEReal", "kind": "instance", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCompleteLinearOrderEReal", "kind": "instance", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instLinearOrderEReal", "kind": "instance", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsOrderedAddMonoidEReal", "kind": "instance", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instAddCommMonoidWithOneEReal", "kind": "instance", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDenselyOrderedEReal", "kind": "instance", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCharZeroEReal", "kind": "instance", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.toEReal", "kind": "definition", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.decidableLT", "kind": "instance", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.instTop", "kind": "instance", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.instCoeReal", "kind": "instance", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.coe_strictMono", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.coe_injective", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.coe_le_coe_iff", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.coe_lt_coe_iff", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.coe_eq_coe_iff", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.coe_ne_coe_iff", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.coe_natCast", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.toEReal", "kind": "definition", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.hasCoeENNReal", "kind": "instance", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.instInhabited", "kind": "instance", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.coe_zero", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.coe_one", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.rec", "kind": "definition", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.forall", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.exists", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.mul", "kind": "definition", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.instMul", "kind": "instance", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.coe_mul", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.induction₂", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.induction₂_symm", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.mul_comm", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": ["induction", "try", "rw"], "tactic_count": 3}
{"name": "EReal.one_mul", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.zero_mul", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.instMulZeroOneClass", "kind": "instance", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.canLift", "kind": "instance", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.toReal", "kind": "definition", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.toReal_top", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.toReal_bot", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.toReal_zero", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.toReal_one", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.toReal_coe", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.bot_lt_coe", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.coe_ne_bot", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.bot_ne_coe", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.coe_lt_top", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.coe_ne_top", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.top_ne_coe", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.bot_lt_zero", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.bot_ne_zero", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.zero_ne_bot", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.zero_lt_top", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.zero_ne_top", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.top_ne_zero", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.range_coe", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": true, "tactics": ["ext", "induction"], "tactic_count": 2}
{"name": "EReal.range_coe_eq_Ioo", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": true, "tactics": ["ext", "induction"], "tactic_count": 2}
{"name": "EReal.coe_add", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.coe_nsmul", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.coe_eq_zero", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.coe_eq_one", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.coe_ne_zero", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.coe_ne_one", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.coe_nonneg", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.coe_nonpos", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.coe_pos", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.coe_neg'", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.toReal_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "EReal.toReal_ne_zero_iff", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "EReal.toReal_eq_toReal", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": true, "tactics": ["lift", "lift", "simp"], "tactic_count": 3}
{"name": "EReal.toReal_nonneg", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": true, "tactics": ["cases", "simp", "exact", "simp"], "tactic_count": 4}
{"name": "EReal.toReal_nonpos", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": true, "tactics": ["cases", "simp", "exact", "simp"], "tactic_count": 4}
{"name": "EReal.toReal_pos", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": true, "tactics": ["lift", "simpa"], "tactic_count": 2}
{"name": "EReal.toReal_neg", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": true, "tactics": ["lift", "simpa"], "tactic_count": 2}
{"name": "EReal.toReal_image_Ioo_zero_top", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": true, "tactics": ["ext", "constructor", "rintro", "lift", "simpa", "intro", "use", "simpa"], "tactic_count": 8}
{"name": "EReal.toReal_image_Ioo_bot_zero", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": true, "tactics": ["ext", "constructor", "rintro", "lift", "simpa", "intro", "use", "simpa"], "tactic_count": 8}
{"name": "EReal.toReal_le_toReal", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": true, "tactics": ["lift", "lift", "simpa"], "tactic_count": 3}
{"name": "EReal.coe_toReal", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": true, "tactics": ["lift", "rfl"], "tactic_count": 2}
{"name": "EReal.le_coe_toReal", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "simp"], "tactic_count": 3}
{"name": "EReal.coe_toReal_le", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "simp"], "tactic_count": 3}
{"name": "EReal.eq_top_iff_forall_lt", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "exact", "contrapose", "intro", "exact"], "tactic_count": 6}
{"name": "EReal.eq_bot_iff_forall_lt", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "exact", "contrapose", "intro", "exact"], "tactic_count": 6}
{"name": "EReal.exists_between_coe_real", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": true, "tactics": ["obtain", "induction", "bot", "coe", "top"], "tactic_count": 5}
{"name": "EReal.image_coe_Icc", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "rfl"], "tactic_count": 3}
{"name": "EReal.image_coe_Ico", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "rfl"], "tactic_count": 3}
{"name": "EReal.image_coe_Ici", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "rfl"], "tactic_count": 3}
{"name": "EReal.image_coe_Ioc", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "rfl"], "tactic_count": 3}
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{"name": "EReal.image_coe_Ioi", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "rfl"], "tactic_count": 3}
{"name": "EReal.image_coe_Iic", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "rfl"], "tactic_count": 3}
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{"name": "EReal.preimage_coe_Ici", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": true, "tactics": ["change", "refine", "simp"], "tactic_count": 3}
{"name": "EReal.preimage_coe_Ioi", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": true, "tactics": ["change", "refine", "simp"], "tactic_count": 3}
{"name": "EReal.preimage_coe_Ioi_bot", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": true, "tactics": ["change", "refine", "simp"], "tactic_count": 3}
{"name": "EReal.preimage_coe_Iic", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": true, "tactics": ["change", "refine", "simp"], "tactic_count": 3}
{"name": "EReal.preimage_coe_Iio", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": true, "tactics": ["change", "refine", "simp"], "tactic_count": 3}
{"name": "EReal.preimage_coe_Iio_top", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": true, "tactics": ["change", "refine", "simp"], "tactic_count": 3}
{"name": "EReal.preimage_coe_Icc", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "simp"], "tactic_count": 2}
{"name": "EReal.preimage_coe_Ico", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "simp"], "tactic_count": 2}
{"name": "EReal.preimage_coe_Ioc", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "simp"], "tactic_count": 2}
{"name": "EReal.preimage_coe_Ioo", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "simp"], "tactic_count": 2}
{"name": "EReal.preimage_coe_Ico_top", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "EReal.preimage_coe_Ioo_top", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "EReal.preimage_coe_Ioc_bot", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "EReal.preimage_coe_Ioo_bot", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "EReal.preimage_coe_Ioo_bot_top", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "EReal.toReal_coe_ennreal", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.coe_ennreal_ofReal", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.coe_ennreal_toReal", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": true, "tactics": ["lift", "rfl"], "tactic_count": 2}
{"name": "EReal.coe_nnreal_eq_coe_real", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.coe_ennreal_zero", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.coe_ennreal_one", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.coe_ennreal_top", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.coe_ennreal_strictMono", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.coe_ennreal_injective", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.coe_ennreal_eq_top_iff", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.coe_nnreal_ne_top", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.coe_nnreal_lt_top", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.coe_ennreal_le_coe_ennreal_iff", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.coe_ennreal_lt_coe_ennreal_iff", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.coe_ennreal_eq_coe_ennreal_iff", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.coe_ennreal_ne_coe_ennreal_iff", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.coe_ennreal_eq_zero", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EReal.coe_ennreal_eq_one", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EReal.coe_ennreal_ne_zero", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.coe_ennreal_ne_one", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.coe_ennreal_nonneg", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.range_coe_ennreal", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.instCanLiftENNRealToERealLeOfNat", "kind": "instance", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.coe_ennreal_pos", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EReal.coe_ennreal_pos_iff_ne_zero", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EReal.bot_lt_coe_ennreal", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.coe_ennreal_ne_bot", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.coe_ennreal_add", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "_private.Mathlib.Data.EReal.Basic.0.EReal.coe_ennreal_top_mul", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rw", "exact"], "tactic_count": 4}
{"name": "EReal.coe_ennreal_mul", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.coe_ennreal_nsmul", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.toENNReal", "kind": "definition", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.toENNReal_top", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.toENNReal_of_ne_top", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.toENNReal_eq_top_iff", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "simp"], "tactic_count": 3}
{"name": "EReal.toENNReal_ne_top_iff", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.toENNReal_of_nonpos", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact", "exact"], "tactic_count": 3}
{"name": "EReal.toENNReal_bot", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.toENNReal_zero", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.toENNReal_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "EReal.toENNReal_ne_zero_iff", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "EReal.toENNReal_pos_iff", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EReal.coe_toENNReal", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": true, "tactics": ["rw", "by_cases", "rw", "rfl", "rw", "simp", "exact"], "tactic_count": 7}
{"name": "EReal.coe_toENNReal_eq_max", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": true, "tactics": ["rcases", "rw", "rw"], "tactic_count": 3}
{"name": "EReal.toENNReal_coe", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "rwa", "simp"], "tactic_count": 4}
{"name": "EReal.real_coe_toENNReal", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.toReal_toENNReal", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "simp"], "tactic_count": 3}
{"name": "EReal.toENNReal_eq_toENNReal", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "EReal.toENNReal_le_toENNReal", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": true, "tactics": ["induction", "simp", "by_cases", "simp", "simp", "exact", "simp_all"], "tactic_count": 7}
{"name": "EReal.toENNReal_lt_toENNReal", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.coe_coe_eq_natCast", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.natCast_ne_bot", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.natCast_ne_top", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.natCast_eq_iff", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EReal.natCast_ne_iff", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.natCast_le_iff", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EReal.natCast_lt_iff", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EReal.natCast_mul", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EReal.exists_rat_btwn_of_lt", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.lt_iff_exists_rat_btwn", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.lt_iff_exists_real_btwn", "kind": "theorem", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.neTopBotEquivReal", "kind": "definition", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalRealToEReal", "kind": "definition", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalENNRealToEReal", "kind": "definition", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalERealToReal", "kind": "definition", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalERealToENNReal", "kind": "definition", "module": "Mathlib.Data.EReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.abs", "kind": "definition", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.abs_top", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.abs_bot", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.abs_def", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.abs_coe_lt_top", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.abs_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": true, "tactics": ["induction", "simp", "simp", "simp"], "tactic_count": 4}
{"name": "EReal.abs_zero", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EReal.coe_abs", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EReal.abs_neg", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.abs_mul", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": true, "tactics": ["induction", "top_zero", "top_top", "symm", "coe_coe", "top_pos", "rw", "rw", "exact", "neg_left"], "tactic_count": 10}
{"name": "EReal.sign_top", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.sign_bot", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.sign_coe", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "EReal.coe_coe_sign", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "EReal.sign_neg", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.sign_mul", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": true, "tactics": ["induction", "top_zero", "top_top", "symm", "coe_coe", "top_pos", "neg_left"], "tactic_count": 7}
{"name": "EReal.sign_mul_abs", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.abs_mul_sign", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EReal.sign_eq_and_abs_eq_iff_eq", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "rw", "rintro", "exact"], "tactic_count": 5}
{"name": "EReal.le_iff_sign", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": true, "tactics": ["constructor", "intro", "refine", "rw", "cases", "simp", "left", "right", "rintro", "exact", "all_goals"], "tactic_count": 11}
{"name": "EReal.instCommMonoidWithZero", "kind": "instance", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.instPosMulMono", "kind": "instance", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.instMulPosMono", "kind": "instance", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.instPosMulReflectLT", "kind": "instance", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.instMulPosReflectLT", "kind": "instance", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.mul_le_mul_of_nonpos_right", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": true, "tactics": ["rw", "rw", "gcongr"], "tactic_count": 3}
{"name": "EReal.coe_pow", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.coe_ennreal_pow", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.exists_nat_ge_mul", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.min_neg_neg", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "EReal.max_neg_neg", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "EReal.inv", "kind": "definition", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.instInv", "kind": "instance", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.instDivInvMonoid", "kind": "instance", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.inv_bot", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.inv_top", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.coe_inv", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.inv_zero", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": true, "tactics": ["change", "rw"], "tactic_count": 2}
{"name": "EReal.instDivInvOneMonoid", "kind": "instance", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.inv_neg", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": true, "tactics": ["induction", "rw", "rw", "exact", "rw"], "tactic_count": 5}
{"name": "EReal.inv_inv", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EReal.mul_inv", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": true, "tactics": ["induction", "top_top", "top_zero", "top_bot", "zero_bot", "bot_bot", "top_pos", "top_neg", "pos_bot", "coe_coe", "neg_bot"], "tactic_count": 11}
{"name": "EReal.sign_mul_inv_abs", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": true, "tactics": ["induction", "bot", "top", "coe", "rcases", "rw", "max_eq_left", "rw", "rw", "simp", "congr", "exact"], "tactic_count": 12}
{"name": "EReal.sign_mul_inv_abs'", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": true, "tactics": ["induction", "bot", "top", "coe", "rcases", "rw", "ofReal_inv_of_pos", "coe_neg", "simp", "rw", "ofReal_inv_of_pos", "coe_inv", "congr", "exact"], "tactic_count": 14}
{"name": "EReal.bot_lt_inv", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": true, "tactics": ["cases", "bot", "top", "coe"], "tactic_count": 4}
{"name": "EReal.inv_lt_top", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": true, "tactics": ["cases", "bot", "top", "coe"], "tactic_count": 4}
{"name": "EReal.inv_nonneg_of_nonneg", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": true, "tactics": ["cases", "bot", "top", "coe"], "tactic_count": 4}
{"name": "EReal.inv_nonpos_of_nonpos", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": true, "tactics": ["cases", "bot", "top", "coe"], "tactic_count": 4}
{"name": "EReal.inv_pos_of_pos_ne_top", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": true, "tactics": ["lift", "rw"], "tactic_count": 2}
{"name": "EReal.inv_neg_of_neg_ne_bot", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": true, "tactics": ["lift", "rw"], "tactic_count": 2}
{"name": "EReal.inv_strictAntiOn", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": true, "tactics": ["intro", "push", "lift", "rw", "exact"], "tactic_count": 5}
{"name": "EReal.div_eq_inv_mul", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.coe_div", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.natCast_div_le", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "EReal.div_bot", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.div_top", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.div_zero", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": true, "tactics": ["change", "rw"], "tactic_count": 2}
{"name": "EReal.zero_div", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.top_div_of_pos_ne_top", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.top_div_of_neg_ne_bot", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.bot_div_of_pos_ne_top", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.bot_div_of_neg_ne_bot", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.div_self", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": true, "tactics": ["rw", "rw"], "tactic_count": 2}
{"name": "EReal.mul_div", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": true, "tactics": ["change", "rw"], "tactic_count": 2}
{"name": "EReal.mul_div_right", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EReal.mul_div_left_comm", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EReal.div_div", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": true, "tactics": ["change", "rw"], "tactic_count": 2}
{"name": "EReal.div_mul_div_comm", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EReal.div_mul_cancel", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EReal.mul_div_cancel", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EReal.mul_div_mul_cancel", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EReal.div_eq_iff", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": true, "tactics": ["refine", "rw", "rw"], "tactic_count": 3}
{"name": "EReal.monotone_div_right_of_nonneg", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.div_le_div_right_of_nonneg", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.strictMono_div_right_of_pos", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": true, "tactics": ["intro", "apply", "intro", "apply", "rw"], "tactic_count": 5}
{"name": "EReal.div_lt_div_right_of_pos", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.antitone_div_right_of_nonpos", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": true, "tactics": ["intro", "change", "rw", "neg_mul", "have", "exact"], "tactic_count": 6}
{"name": "EReal.div_le_div_right_of_nonpos", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.strictAnti_div_right_of_neg", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": true, "tactics": ["intro", "simp", "apply", "intro", "apply", "rw"], "tactic_count": 6}
{"name": "EReal.div_lt_div_right_of_neg", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.le_div_iff_mul_le", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": true, "tactics": ["nth_rw", "rw", "exact"], "tactic_count": 3}
{"name": "EReal.div_le_iff_le_mul", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": true, "tactics": ["nth_rw", "rw", "exact"], "tactic_count": 3}
{"name": "EReal.lt_div_iff", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": true, "tactics": ["nth_rw", "rw", "exact"], "tactic_count": 3}
{"name": "EReal.div_lt_iff", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": true, "tactics": ["nth_rw", "rw", "exact"], "tactic_count": 3}
{"name": "EReal.div_nonneg", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.div_pos", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.div_nonpos_of_nonpos_of_nonneg", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.div_nonpos_of_nonneg_of_nonpos", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.div_nonneg_of_nonpos_of_nonpos", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.EReal.Inv.0.EReal.exists_lt_mul_left_of_nonneg", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "rw", "exact", "obtain", "use", "rw", "rwa", "have", "obtain", "exact"], "tactic_count": 11}
{"name": "_private.Mathlib.Data.EReal.Inv.0.EReal.exists_lt_mul_right_of_nonneg", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": true, "tactics": ["have", "simp_rw", "exact"], "tactic_count": 3}
{"name": "_private.Mathlib.Data.EReal.Inv.0.EReal.exists_mul_left_lt", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": true, "tactics": ["rcases", "rw", "rcases", "obtain", "exact", "rcases", "rcases", "obtain", "rw", "refine", "rw", "rw", "obtain", "exact"], "tactic_count": 14}
{"name": "_private.Mathlib.Data.EReal.Inv.0.EReal.exists_mul_right_lt", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "EReal.le_mul_of_forall_lt", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": true, "tactics": ["refine", "obtain", "replace", "replace", "obtain", "exact"], "tactic_count": 6}
{"name": "EReal.mul_le_of_forall_lt_of_nonneg", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": true, "tactics": ["refine", "rcases", "exact", "obtain", "obtain", "exact"], "tactic_count": 6}
{"name": "EReal.div_right_distrib_of_nonneg", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.add_div_of_nonneg_right", "kind": "theorem", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "Mathlib.Meta.Positivity.evalERealInv", "kind": "definition", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalERealDiv", "kind": "definition", "module": "Mathlib.Data.EReal.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.add_bot", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.bot_add", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.add_eq_bot_iff", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.add_ne_bot_iff", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.bot_lt_add_iff", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "EReal.top_add_top", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.top_add_coe", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.top_add_of_ne_bot", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": true, "tactics": ["induction", "exfalso", "exact", "exact"], "tactic_count": 4}
{"name": "EReal.top_add_iff_ne_bot", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "rw", "exact", "cases", "bot", "top", "coe"], "tactic_count": 8}
{"name": "EReal.add_top_of_ne_bot", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EReal.add_top_iff_ne_bot", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EReal.add_pos_of_pos_of_nonneg", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.add_pos", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.coe_add_top", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.toReal_add", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": true, "tactics": ["lift", "lift", "rfl"], "tactic_count": 3}
{"name": "EReal.toENNReal_add", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": ["induction", "try", "norm_cast", "simp_rw", "simp_all"], "tactic_count": 5}
{"name": "EReal.toENNReal_add_le", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": ["induction", "try", "exact"], "tactic_count": 3}
{"name": "EReal.addLECancellable_coe", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.add_lt_add_right_coe", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.add_lt_add_left_coe", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "EReal.add_lt_add", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": true, "tactics": ["rcases", "simp", "lift", "calc"], "tactic_count": 4}
{"name": "EReal.add_lt_add_of_lt_of_le'", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "obtain", "simpa", "lift", "exact", "exact"], "tactic_count": 7}
{"name": "EReal.add_lt_add_of_lt_of_le", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.add_lt_top", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.add_ne_top", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.add_ne_top_iff_ne_top₂", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": true, "tactics": ["refine", "cases", "cases", "simp_all"], "tactic_count": 4}
{"name": "EReal.add_ne_top_iff_ne_top_left", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "EReal.add_ne_top_iff_ne_top_right", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.add_ne_top_iff_of_ne_bot_of_ne_top", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "EReal.neg", "kind": "definition", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.instNeg", "kind": "instance", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.instSubNegZeroMonoid", "kind": "instance", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.neg_top", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.neg_bot", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.coe_neg", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.coe_sub", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.coe_zsmul", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.instInvolutiveNeg", "kind": "instance", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.toReal_neg_eq", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.neg_eq_top_iff", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.neg_eq_bot_iff", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.neg_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.neg_strictAnti", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.neg_le_neg_iff", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.neg_lt_neg_iff", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.neg_le", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EReal.neg_le_of_neg_le", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.le_neg", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EReal.le_neg_of_le_neg", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.neg_lt_comm", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EReal.neg_lt_of_neg_lt", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.lt_neg_comm", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EReal.neg_lt_zero", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EReal.neg_le_zero", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EReal.neg_pos", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EReal.neg_nonneg", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EReal.lt_neg_of_lt_neg", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.negOrderIso", "kind": "definition", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.neg_add", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": true, "tactics": ["induction", "rw"], "tactic_count": 2}
{"name": "EReal.neg_sub", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EReal.recENNReal", "kind": "definition", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.recENNReal_coe_ennreal", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": true, "tactics": ["suffices", "intro", "have", "obtain", "simp"], "tactic_count": 5}
{"name": "EReal.recENNReal_neg_coe_ennreal", "kind": "proofWanted", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.bot_sub", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.sub_top", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.top_sub_bot", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.top_sub_coe", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.coe_sub_bot", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.sub_bot", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "EReal.top_sub", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "EReal.sub_self", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "EReal.sub_self_le_zero", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "EReal.sub_nonneg", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "EReal.sub_nonpos", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "EReal.sub_pos", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "EReal.sub_neg", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "EReal.sub_le_sub", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.sub_lt_sub_of_lt_of_le", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.coe_real_ereal_eq_coe_toNNReal_sub_coe_toNNReal", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": true, "tactics": ["rcases", "lift", "rw", "sub_zero]", "rfl", "rw", "zero_sub,", "exact"], "tactic_count": 8}
{"name": "EReal.toReal_sub", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": true, "tactics": ["lift", "lift", "rfl"], "tactic_count": 3}
{"name": "EReal.toENNReal_sub", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": ["induction", "try", "rename_i", "by_cases", "rw", "exact", "rw", "simp"], "tactic_count": 8}
{"name": "EReal.add_sub_cancel_right", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": true, "tactics": ["cases", "exact"], "tactic_count": 2}
{"name": "EReal.add_sub_cancel_left", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EReal.sub_add_cancel", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EReal.sub_add_cancel_right", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": true, "tactics": ["cases", "exact"], "tactic_count": 2}
{"name": "EReal.sub_add_cancel_left", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EReal.le_sub_iff_add_le", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": true, "tactics": ["induction", "bot", "simp", "simp", "coe", "top", "simp", "refine", "by_contra", "exact"], "tactic_count": 10}
{"name": "EReal.sub_le_iff_le_add", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": true, "tactics": ["suffices", "refine"], "tactic_count": 2}
{"name": "EReal.lt_sub_iff_add_lt", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.sub_le_of_le_add", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": true, "tactics": ["induction", "bot", "coe", "top"], "tactic_count": 4}
{"name": "EReal.sub_le_of_le_add'", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.add_le_of_le_sub", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "EReal.sub_lt_iff", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.add_lt_of_lt_sub", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": true, "tactics": ["contrapose", "exact"], "tactic_count": 2}
{"name": "EReal.sub_lt_of_lt_add", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.sub_lt_of_lt_add'", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.le_of_forall_lt_iff_le", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": true, "tactics": ["refine", "rw", "aesop"], "tactic_count": 3}
{"name": "EReal.ge_of_forall_gt_iff_ge", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": true, "tactics": ["refine", "rw", "aesop"], "tactic_count": 3}
{"name": "_private.Mathlib.Data.EReal.Operations.0.EReal.exists_lt_add_left", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": true, "tactics": ["obtain", "refine", "contrapose", "exact"], "tactic_count": 4}
{"name": "_private.Mathlib.Data.EReal.Operations.0.EReal.exists_lt_add_right", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "EReal.add_le_of_forall_lt", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": true, "tactics": ["refine", "obtain", "obtain", "exact"], "tactic_count": 4}
{"name": "EReal.le_add_of_forall_gt", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "ENNReal.toEReal_sub", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": true, "tactics": ["lift", "cases", "top", "coe"], "tactic_count": 4}
{"name": "EReal.top_mul_top", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.top_mul_bot", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.bot_mul_top", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.bot_mul_bot", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.coe_mul_top_of_pos", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.coe_mul_top_of_neg", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.top_mul_coe_of_pos", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.top_mul_coe_of_neg", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.mul_top_of_pos", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.mul_top_of_neg", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.top_mul_of_pos", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "EReal.top_mul_of_neg", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "EReal.top_mul_coe_ennreal", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.coe_ennreal_mul_top", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EReal.coe_mul_bot_of_pos", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.coe_mul_bot_of_neg", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.bot_mul_coe_of_pos", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.bot_mul_coe_of_neg", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.mul_bot_of_pos", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.mul_bot_of_neg", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.bot_mul_of_pos", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "EReal.bot_mul_of_neg", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "EReal.toReal_mul", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": true, "tactics": ["induction", "top_zero", "zero_bot", "top_top", "top_bot", "bot_bot", "symm", "coe_coe", "top_pos", "top_neg", "pos_bot", "neg_bot"], "tactic_count": 12}
{"name": "EReal.instNoZeroDivisors", "kind": "instance", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.mul_pos_iff", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": true, "tactics": ["induction", "symm", "top_top", "top_pos", "top_zero", "top_neg", "top_bot", "pos_bot", "coe_coe", "zero_bot", "neg_bot", "bot_bot"], "tactic_count": 12}
{"name": "EReal.mul_nonneg_iff", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": true, "tactics": ["simp_rw", "rcases", "simp", "tauto"], "tactic_count": 4}
{"name": "EReal.mul_nonneg", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.mul_pos", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.induction₂_neg_left", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.induction₂_symm_neg", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.neg_mul", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": true, "tactics": ["induction", "top_zero", "zero_top", "zero_bot", "top_top", "top_bot", "neg_left", "coe_coe", "top_pos", "pos_top", "top_neg", "pos_bot"], "tactic_count": 12}
{"name": "EReal.instHasDistribNeg", "kind": "instance", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.mul_neg_iff", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": true, "tactics": ["nth_rw", "rw"], "tactic_count": 2}
{"name": "EReal.mul_nonpos_iff", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": true, "tactics": ["nth_rw", "rw"], "tactic_count": 2}
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{"name": "EReal.mul_eq_bot", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": ["rw", "tauto"], "tactic_count": 2}
{"name": "EReal.mul_ne_bot", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": true, "tactics": ["rw", "push_neg", "rfl"], "tactic_count": 3}
{"name": "EReal.toENNReal_mul", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": false, "tactics": ["induction", "try", "rcases", "simp", "simp_all", "rename_i", "rcases", "simp_all", "simp", "simp_all"], "tactic_count": 10}
{"name": "EReal.toENNReal_mul'", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EReal.right_distrib_of_nonneg", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": true, "tactics": ["lift", "lift", "cases", "coe", "neg_coe", "simp", "rw"], "tactic_count": 7}
{"name": "EReal.left_distrib_of_nonneg", "kind": "theorem", "module": "Mathlib.Data.EReal.Operations", "is_tactic_proof": true, "tactics": ["nth_rewrite", "exact"], "tactic_count": 2}
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{"name": "FinEnum.equiv_down", "kind": "theorem", "module": "Mathlib.Data.FinEnum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinEnum.up_equiv_symm", "kind": "theorem", "module": "Mathlib.Data.FinEnum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinEnum.down_equiv_symm", "kind": "theorem", "module": "Mathlib.Data.FinEnum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinEnum.pempty", "kind": "instance", "module": "Mathlib.Data.FinEnum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinEnum.empty", "kind": "instance", "module": "Mathlib.Data.FinEnum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinEnum.punit", "kind": "instance", "module": "Mathlib.Data.FinEnum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinEnum.prod", "kind": "instance", "module": "Mathlib.Data.FinEnum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinEnum.sum", "kind": "instance", "module": "Mathlib.Data.FinEnum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinEnum.fin", "kind": "instance", "module": "Mathlib.Data.FinEnum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinEnum.card_fin", "kind": "theorem", "module": "Mathlib.Data.FinEnum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinEnum.Quotient.enum", "kind": "instance", "module": "Mathlib.Data.FinEnum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinEnum.Finset.enum", "kind": "definition", "module": "Mathlib.Data.FinEnum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinEnum.Finset.mem_enum", "kind": "theorem", "module": "Mathlib.Data.FinEnum", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "ih", "simp", "refine", "simp", "simp"], "tactic_count": 8}
{"name": "FinEnum.Finset.finEnum", "kind": "instance", "module": "Mathlib.Data.FinEnum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinEnum.Subtype.finEnum", "kind": "instance", "module": "Mathlib.Data.FinEnum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinEnum.instSigma", "kind": "instance", "module": "Mathlib.Data.FinEnum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinEnum.PSigma.finEnum", "kind": "instance", "module": "Mathlib.Data.FinEnum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinEnum.PSigma.finEnumPropLeft", "kind": "instance", "module": "Mathlib.Data.FinEnum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinEnum.PSigma.finEnumPropRight", "kind": "instance", "module": "Mathlib.Data.FinEnum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinEnum.PSigma.finEnumPropProp", "kind": "instance", "module": "Mathlib.Data.FinEnum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinEnum.instSubtypeMemListOfDecidableEq", "kind": "instance", "module": "Mathlib.Data.FinEnum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinEnum.instFintype", "kind": "instance", "module": "Mathlib.Data.FinEnum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinEnum.card_eq_fintypeCard", "kind": "theorem", "module": "Mathlib.Data.FinEnum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinEnum.card_unique", "kind": "theorem", "module": "Mathlib.Data.FinEnum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinEnum.card_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Data.FinEnum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinEnum.card_eq_zero", "kind": "theorem", "module": "Mathlib.Data.FinEnum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinEnum.card_pos_iff", "kind": "theorem", "module": "Mathlib.Data.FinEnum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinEnum.card_pos", "kind": "theorem", "module": "Mathlib.Data.FinEnum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinEnum.card_ne_zero", "kind": "theorem", "module": "Mathlib.Data.FinEnum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinEnum.card_eq_one", "kind": "theorem", "module": "Mathlib.Data.FinEnum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinEnum.instUniqueOfIsEmpty", "kind": "instance", "module": "Mathlib.Data.FinEnum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinEnum.ofIsEmpty", "kind": "definition", "module": "Mathlib.Data.FinEnum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinEnum.instUnique", "kind": "instance", "module": "Mathlib.Data.FinEnum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinEnum.ofUnique", "kind": "definition", "module": "Mathlib.Data.FinEnum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.mem_pi_toList", "kind": "theorem", "module": "Mathlib.Data.FinEnum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Pi.enum", "kind": "definition", "module": "Mathlib.Data.FinEnum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Pi.mem_enum", "kind": "theorem", "module": "Mathlib.Data.FinEnum", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "List.Pi.finEnum", "kind": "instance", "module": "Mathlib.Data.FinEnum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.pfunFinEnum", "kind": "instance", "module": "Mathlib.Data.FinEnum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinEnum.insertNone", "kind": "definition", "module": "Mathlib.Data.FinEnum.Option", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinEnum.instFinEnumOptionLast", "kind": "instance", "module": "Mathlib.Data.FinEnum.Option", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinEnum.recEmptyOption", "kind": "definition", "module": "Mathlib.Data.FinEnum.Option", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinEnum.recEmptyOption_of_card_eq_zero", "kind": "theorem", "module": "Mathlib.Data.FinEnum.Option", "is_tactic_proof": true, "tactics": ["unfold", "split", "congr", "exact"], "tactic_count": 4}
{"name": "FinEnum.recEmptyOption_of_card_pos", "kind": "theorem", "module": "Mathlib.Data.FinEnum.Option", "is_tactic_proof": true, "tactics": ["conv", "split", "exact", "rcases"], "tactic_count": 4}
{"name": "FinEnum.recOnEmptyOption", "kind": "abbrev", "module": "Mathlib.Data.FinEnum.Option", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.forall_lt_iff_fin", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.exists_lt_iff_fin", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finZeroElim", "kind": "definition", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.mk_eq_one", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.one_eq_mk", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.instCanLiftNatValLt", "kind": "instance", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.rec0", "kind": "definition", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.val_injective", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.size_positive", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.size_positive'", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.prop", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.lt_last_iff_ne_last", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.ne_zero_of_lt", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.ne_last_of_lt", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.equivSubtype", "kind": "definition", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.neZero", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.val_eq_val", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.ne_iff_vne", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.mk_eq_mk", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.heq_fun_iff", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": true, "tactics": ["subst", "simp"], "tactic_count": 2}
{"name": "Fin.heq_fun₂_iff", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": true, "tactics": ["subst", "subst", "simp"], "tactic_count": 3}
{"name": "Fin.heq_ext_iff", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": true, "tactics": ["subst", "simp"], "tactic_count": 2}
{"name": "Fin.le_iff_val_le_val", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.val_fin_lt", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.val_fin_le", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.min_val", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.max_val", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.instWellFoundedRelation_mathlib", "kind": "instance", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.mk_zero'", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.val_pos_iff", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.pos_iff_ne_zero'", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.cast_eq_self", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.cast_eq_zero", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.cast_injective", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.last_pos'", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.one_lt_last", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Fin.coe_int_sub_eq_ite", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": true, "tactics": ["rw", "split", "rw", "rw"], "tactic_count": 4}
{"name": "Fin.coe_int_sub_eq_mod", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": true, "tactics": ["rw", "split", "rw", "rw"], "tactic_count": 4}
{"name": "Fin.coe_int_add_eq_ite", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": true, "tactics": ["rw", "split", "rw", "rw"], "tactic_count": 4}
{"name": "Fin.coe_int_add_eq_mod", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": true, "tactics": ["omega"], "tactic_count": 1}
{"name": "Fin.tacticFin_omega", "kind": "definition", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin._aux_Mathlib_Data_Fin_Basic___macroRules_Fin_tacticFin_omega_1", "kind": "definition", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.val_one'", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.nontrivial_iff_two_le", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.instNontrivial", "kind": "instance", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.exists_ne_and_ne_of_two_lt", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": true, "tactics": ["have", "rcases", "rcases", "simp_rw", "by_cases", "exact", "by_cases", "exact", "refine", "dsimp", "lia"], "tactic_count": 11}
{"name": "Fin.inhabitedFinOneAdd", "kind": "instance", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.default_eq_zero", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.val_add_eq_ite", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.val_add_eq_of_add_lt", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Fin.intCast_val_sub_eq_sub_add_ite", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": true, "tactics": ["split"], "tactic_count": 1}
{"name": "Fin.sub_val_lt_sub", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.castLT_sub_nezero", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": true, "tactics": ["refine", "simpa"], "tactic_count": 2}
{"name": "Fin.one_le_of_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": true, "tactics": ["have", "intro", "obtain", "cases", "zero", "succ"], "tactic_count": 6}
{"name": "Fin.val_sub_one_of_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": true, "tactics": ["have", "intro", "obtain", "rw"], "tactic_count": 4}
{"name": "Fin.ofNat_eq_cast", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.val_natCast", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.val_cast_of_lt", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.cast_val_eq_self", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.natCast_self", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Fin.natCast_eq_zero", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.natCast_zero", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.natCast_eq_last", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Fin.natCast_eq_mk", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.one_eq_mk_of_lt", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.le_val_last", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Fin.natCast_le_natCast", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Fin.natCast_lt_natCast", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.natCast_mono", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.natCast_strictMono", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.castLE_natCast", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp", "rw"], "tactic_count": 3}
{"name": "Fin.modNat_rev", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": true, "tactics": ["ext", "have", "have", "simp", "calc", "rw", "exact"], "tactic_count": 7}
{"name": "Fin.liftFun_iff_succ", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "refine", "simp", "intro", "rw", "obtain", "obtain", "exact", "exact"], "tactic_count": 11}
{"name": "Fin.eq_zero", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.eq_one_of_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": true, "tactics": ["lia"], "tactic_count": 1}
{"name": "Fin.coe_neg_one", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": true, "tactics": ["cases", "simp", "rw", "constructor"], "tactic_count": 4}
{"name": "Fin.last_sub", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.add_one_le_of_lt", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Fin.exists_eq_add_of_le", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": true, "tactics": ["obtain", "have", "refine", "simp"], "tactic_count": 4}
{"name": "Fin.exists_eq_add_of_lt", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": true, "tactics": ["cases", "lia", "obtain", "have", "refine", "simp"], "tactic_count": 6}
{"name": "Fin.pos_of_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.sub_succ_le_sub_of_le", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": true, "tactics": ["fin_omega"], "tactic_count": 1}
{"name": "Fin.coe_natCast_eq_mod", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.coe_ofNat_eq_mod", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.val_add_one_of_lt'", "kind": "theorem", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Fin.instNeZeroHAddNatOfNat_mathlib", "kind": "instance", "module": "Mathlib.Data.Fin.Basic", "is_tactic_proof": true, "tactics": ["suffices", "apply", "simpa"], "tactic_count": 3}
{"name": "Fin.valEmbedding", "kind": "definition", "module": "Mathlib.Data.Fin.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.equivSubtype_symm_trans_valEmbedding", "kind": "theorem", "module": "Mathlib.Data.Fin.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.succEmb", "kind": "definition", "module": "Mathlib.Data.Fin.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.coe_succEmb", "kind": "theorem", "module": "Mathlib.Data.Fin.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.castLEEmb", "kind": "definition", "module": "Mathlib.Data.Fin.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.coe_castLEEmb", "kind": "theorem", "module": "Mathlib.Data.Fin.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.nonempty_embedding_iff", "kind": "theorem", "module": "Mathlib.Data.Fin.Embedding", "is_tactic_proof": true, "tactics": ["refine", "induction", "zero", "succ", "obtain", "rcases", "refine", "refine", "simpa"], "tactic_count": 9}
{"name": "Fin.equiv_iff_eq", "kind": "theorem", "module": "Mathlib.Data.Fin.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.castAddEmb", "kind": "definition", "module": "Mathlib.Data.Fin.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.coe_castAddEmb", "kind": "theorem", "module": "Mathlib.Data.Fin.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.castAddEmb_apply", "kind": "theorem", "module": "Mathlib.Data.Fin.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.castSuccEmb", "kind": "definition", "module": "Mathlib.Data.Fin.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.coe_castSuccEmb", "kind": "theorem", "module": "Mathlib.Data.Fin.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.castSuccEmb_apply", "kind": "theorem", "module": "Mathlib.Data.Fin.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.addNatEmb", "kind": "definition", "module": "Mathlib.Data.Fin.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.natAddEmb", "kind": "definition", "module": "Mathlib.Data.Fin.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.succAboveEmb", "kind": "definition", "module": "Mathlib.Data.Fin.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.coe_succAboveEmb", "kind": "theorem", "module": "Mathlib.Data.Fin.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.natAdd_castLEEmb", "kind": "definition", "module": "Mathlib.Data.Fin.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.range_natAdd_castLEEmb", "kind": "theorem", "module": "Mathlib.Data.Fin.Embedding", "is_tactic_proof": true, "tactics": ["simp", "ext", "exact"], "tactic_count": 3}
{"name": "Fin2", "kind": "inductive", "module": "Mathlib.Data.Fin.Fin2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin2.cases'", "kind": "definition", "module": "Mathlib.Data.Fin.Fin2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin2.elim0", "kind": "definition", "module": "Mathlib.Data.Fin.Fin2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin2.toNat", "kind": "definition", "module": "Mathlib.Data.Fin.Fin2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin2.optOfNat", "kind": "definition", "module": "Mathlib.Data.Fin.Fin2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin2.add", "kind": "definition", "module": "Mathlib.Data.Fin.Fin2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin2.left", "kind": "definition", "module": "Mathlib.Data.Fin.Fin2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin2.insertPerm", "kind": "definition", "module": "Mathlib.Data.Fin.Fin2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin2.remapLeft", "kind": "definition", "module": "Mathlib.Data.Fin.Fin2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin2.IsLT.zero", "kind": "instance", "module": "Mathlib.Data.Fin.Fin2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin2.IsLT.succ", "kind": "instance", "module": "Mathlib.Data.Fin.Fin2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin2.ofNat'", "kind": "definition", "module": "Mathlib.Data.Fin.Fin2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin2.castSucc", "kind": "definition", "module": "Mathlib.Data.Fin.Fin2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin2.last", "kind": "definition", "module": "Mathlib.Data.Fin.Fin2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin2.rev", "kind": "definition", "module": "Mathlib.Data.Fin.Fin2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin2.rev_last", "kind": "theorem", "module": "Mathlib.Data.Fin.Fin2", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "Fin2.rev_castSucc", "kind": "theorem", "module": "Mathlib.Data.Fin.Fin2", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "Fin2.rev_rev", "kind": "theorem", "module": "Mathlib.Data.Fin.Fin2", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "Fin2.rev_involutive", "kind": "theorem", "module": "Mathlib.Data.Fin.Fin2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.Fin.Fin2.0.Fin2.term&_", "kind": "definition", "module": "Mathlib.Data.Fin.Fin2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.Fin.Fin2.0.Fin2._aux_Mathlib_Data_Fin_Fin2___macroRules__private_Mathlib_Data_Fin_Fin2_0_Fin2_term&__1", "kind": "definition", "module": "Mathlib.Data.Fin.Fin2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.Fin.Fin2.0.Fin2._aux_Mathlib_Data_Fin_Fin2___unexpand_Fin2_ofNat'_1", "kind": "definition", "module": "Mathlib.Data.Fin.Fin2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin2.instInhabitedOfNatNat", "kind": "instance", "module": "Mathlib.Data.Fin.Fin2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin2.instFintype", "kind": "instance", "module": "Mathlib.Data.Fin.Fin2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin2.toFin", "kind": "definition", "module": "Mathlib.Data.Fin.Fin2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin2.toFin_fz", "kind": "theorem", "module": "Mathlib.Data.Fin.Fin2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin2.toFin_fs", "kind": "theorem", "module": "Mathlib.Data.Fin.Fin2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin2.ofFin", "kind": "definition", "module": "Mathlib.Data.Fin.Fin2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin2.ofFin_zero", "kind": "theorem", "module": "Mathlib.Data.Fin.Fin2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin2.ofFin_succ", "kind": "theorem", "module": "Mathlib.Data.Fin.Fin2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin2.toFin_ofFin", "kind": "theorem", "module": "Mathlib.Data.Fin.Fin2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin2.ofFin_toFin", "kind": "theorem", "module": "Mathlib.Data.Fin.Fin2", "is_tactic_proof": true, "tactics": ["induction", "fz", "fs"], "tactic_count": 3}
{"name": "Fin2.equivFin", "kind": "definition", "module": "Mathlib.Data.Fin.Fin2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMaxChain.range_fin_of_covBy", "kind": "theorem", "module": "Mathlib.Data.Fin.FlagRange", "is_tactic_proof": true, "tactics": ["have", "refine", "rw", "suffices", "intro", "induction", "zero", "succ", "rw", "exact"], "tactic_count": 10}
{"name": "Flag.rangeFin", "kind": "definition", "module": "Mathlib.Data.Fin.FlagRange", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Flag.mem_rangeFin", "kind": "theorem", "module": "Mathlib.Data.Fin.FlagRange", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.even_succAbove_add_predAbove", "kind": "theorem", "module": "Mathlib.Data.Fin.Parity", "is_tactic_proof": true, "tactics": ["rcases", "have", "simp", "simp", "not_iff_comm,"], "tactic_count": 5}
{"name": "Fin.neg_one_pow_succAbove_add_predAbove", "kind": "theorem", "module": "Mathlib.Data.Fin.Parity", "is_tactic_proof": true, "tactics": ["rw", "rw"], "tactic_count": 2}
{"name": "Fin.even_of_val", "kind": "theorem", "module": "Mathlib.Data.Fin.Parity", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "Fin.odd_of_val", "kind": "theorem", "module": "Mathlib.Data.Fin.Parity", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Fin.even_of_odd", "kind": "theorem", "module": "Mathlib.Data.Fin.Parity", "is_tactic_proof": true, "tactics": ["have", "rcases", "exact", "simpa"], "tactic_count": 4}
{"name": "Fin.odd_of_odd", "kind": "theorem", "module": "Mathlib.Data.Fin.Parity", "is_tactic_proof": true, "tactics": ["rcases", "simpa", "exact"], "tactic_count": 3}
{"name": "Fin.even_iff_of_even", "kind": "theorem", "module": "Mathlib.Data.Fin.Parity", "is_tactic_proof": true, "tactics": ["rcases", "refine", "rintro", "rw", "split_ifs"], "tactic_count": 5}
{"name": "Fin.odd_iff_of_even", "kind": "theorem", "module": "Mathlib.Data.Fin.Parity", "is_tactic_proof": true, "tactics": ["rcases", "refine", "rintro", "rw", "simp", "rw", "simp"], "tactic_count": 7}
{"name": "Fin.even_iff", "kind": "theorem", "module": "Mathlib.Data.Fin.Parity", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "Fin.even_iff_imp", "kind": "theorem", "module": "Mathlib.Data.Fin.Parity", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Fin.odd_iff", "kind": "theorem", "module": "Mathlib.Data.Fin.Parity", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "Fin.odd_iff_imp", "kind": "theorem", "module": "Mathlib.Data.Fin.Parity", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Fin.even_iff_mod_of_even", "kind": "theorem", "module": "Mathlib.Data.Fin.Parity", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Fin.odd_iff_mod_of_even", "kind": "theorem", "module": "Mathlib.Data.Fin.Parity", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Fin.not_odd_iff_even_of_even", "kind": "theorem", "module": "Mathlib.Data.Fin.Parity", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Fin.not_even_iff_odd_of_even", "kind": "theorem", "module": "Mathlib.Data.Fin.Parity", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Fin.odd_add_one_iff_even", "kind": "theorem", "module": "Mathlib.Data.Fin.Parity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.even_add_one_iff_odd", "kind": "theorem", "module": "Mathlib.Data.Fin.Parity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.le_of_injective", "kind": "theorem", "module": "Mathlib.Data.Fin.Pigeonhole", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Fin.le_of_embedding", "kind": "theorem", "module": "Mathlib.Data.Fin.Pigeonhole", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Fin.lt_of_injective_of_notMem", "kind": "theorem", "module": "Mathlib.Data.Fin.Pigeonhole", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Fin.le_of_surjective", "kind": "theorem", "module": "Mathlib.Data.Fin.Pigeonhole", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Fin.card_range_le", "kind": "theorem", "module": "Mathlib.Data.Fin.Pigeonhole", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Fin.rev_involutive", "kind": "theorem", "module": "Mathlib.Data.Fin.Rev", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.revPerm", "kind": "definition", "module": "Mathlib.Data.Fin.Rev", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.rev_injective", "kind": "theorem", "module": "Mathlib.Data.Fin.Rev", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.rev_surjective", "kind": "theorem", "module": "Mathlib.Data.Fin.Rev", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.rev_bijective", "kind": "theorem", "module": "Mathlib.Data.Fin.Rev", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.revPerm_symm", "kind": "theorem", "module": "Mathlib.Data.Fin.Rev", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.cast_rev", "kind": "theorem", "module": "Mathlib.Data.Fin.Rev", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "Fin.rev_eq_iff", "kind": "theorem", "module": "Mathlib.Data.Fin.Rev", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.rev_ne_iff", "kind": "theorem", "module": "Mathlib.Data.Fin.Rev", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.rev_lt_iff", "kind": "theorem", "module": "Mathlib.Data.Fin.Rev", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.rev_le_iff", "kind": "theorem", "module": "Mathlib.Data.Fin.Rev", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.lt_rev_iff", "kind": "theorem", "module": "Mathlib.Data.Fin.Rev", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.le_rev_iff", "kind": "theorem", "module": "Mathlib.Data.Fin.Rev", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.val_rev_zero", "kind": "theorem", "module": "Mathlib.Data.Fin.Rev", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.succAbove_rev_left", "kind": "theorem", "module": "Mathlib.Data.Fin.Rev", "is_tactic_proof": true, "tactics": ["obtain", "rw", "rw", "rev_rev]"], "tactic_count": 4}
{"name": "Fin.succAbove_rev_right", "kind": "theorem", "module": "Mathlib.Data.Fin.Rev", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.rev_succAbove", "kind": "theorem", "module": "Mathlib.Data.Fin.Rev", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.predAbove_rev_left", "kind": "theorem", "module": "Mathlib.Data.Fin.Rev", "is_tactic_proof": true, "tactics": ["obtain", "rw", "castPred_inj,", "rw", "pred_inj,"], "tactic_count": 5}
{"name": "Fin.predAbove_rev_right", "kind": "theorem", "module": "Mathlib.Data.Fin.Rev", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.rev_predAbove", "kind": "theorem", "module": "Mathlib.Data.Fin.Rev", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.add_rev_cast", "kind": "theorem", "module": "Mathlib.Data.Fin.Rev", "is_tactic_proof": true, "tactics": ["obtain", "simp"], "tactic_count": 2}
{"name": "Fin.rev_add_cast", "kind": "theorem", "module": "Mathlib.Data.Fin.Rev", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.succ_injective", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.exists_succ_eq", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.exists_succ_eq_of_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.succ_zero_eq_one'", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["cases", "exact", "rfl"], "tactic_count": 3}
{"name": "Fin.one_pos'", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.zero_ne_one'", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.succ_one_eq_two'", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["cases", "exact", "rfl"], "tactic_count": 3}
{"name": "Fin.le_zero_iff'", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.castLE_inj", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.castAdd_inj", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.castLE_injective", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.castAdd_injective", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.castSucc_injective", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.castLE_castSucc", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.castLE_comp_castSucc", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.castLE_rfl", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.range_castLE", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.coe_of_injective_castLE_symm", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Fin.leftInverse_cast", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.rightInverse_cast", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.cast_inj", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.cast_lt_cast", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.cast_le_cast", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finCongr", "kind": "definition", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finCongr_apply_mk", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finCongr_symm", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finCongr_apply_coe", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finCongr_symm_apply_coe", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finCongr_eq_equivCast", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "Fin.cast_eq_cast", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Fin.castSucc_le_succ", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.castSucc_le_castSucc_iff", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.succ_le_castSucc_iff", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.castSucc_lt_succ_iff", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.le_of_castSucc_lt_of_succ_lt", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.castSucc_lt_or_lt_succ", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Fin.succ_le_or_le_castSucc", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Fin.eq_castSucc_of_ne_last", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.forall_fin_succ'", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.eq_castSucc_or_eq_last", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.castSucc_ne_last", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.exists_fin_succ'", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.castSucc_zero'", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.castSucc_pos_iff", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.castSucc_ne_zero_of_lt", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["cases", "exact", "grind"], "tactic_count": 3}
{"name": "Fin.succ_ne_last_iff", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.succ_ne_last_of_lt", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Fin.coe_eq_castSucc", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "Fin.coe_succ_lt_iff_lt", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.range_castSucc", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.coe_of_injective_castSucc_symm", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Fin.castSucc_castAdd", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.succ_castAdd", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["split_ifs", "exacts"], "tactic_count": 2}
{"name": "Fin.succ_natAdd", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.pred_lt_iff", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.lt_pred_iff", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.pred_le_iff", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.le_pred_iff", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.castSucc_pred_eq_pred_castSucc", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.castSucc_pred_add_one_eq", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.le_pred_castSucc_iff", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.pred_castSucc_lt_iff", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.pred_castSucc_lt", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.le_castSucc_pred_iff", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.castSucc_pred_lt_iff", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.castSucc_pred_lt", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.castPred", "kind": "definition", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.coe_castPred", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.castSucc_castPred", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["rcases", "rw"], "tactic_count": 2}
{"name": "Fin.castPred_eq_iff_eq_castSucc", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.castPred_le_castPred_iff", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.castPred_le_castPred", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.castPred_lt_castPred_iff", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.castPred_lt_castPred", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.castPred_lt_iff", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.lt_castPred_iff", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.castPred_le_iff", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.le_castPred_iff", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.castPred_inj", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Fin.castPred_zero", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.castPred_eq_zero", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.castPred_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.castPred_one", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["cases", "exact", "rfl"], "tactic_count": 3}
{"name": "Fin.succ_castPred_eq_add_one", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["cases", "exact", "rw"], "tactic_count": 3}
{"name": "Fin.castpred_succ_le_iff", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.lt_castPred_succ_iff", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.lt_castPred_succ", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.succ_castPred_le_iff", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.lt_succ_castPred_iff", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.lt_succ_castPred", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.castPred_le_pred_iff", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.pred_lt_castPred_iff", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.pred_lt_castPred", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.succAbove", "kind": "definition", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.succAbove_of_castSucc_lt", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.succAbove_of_succ_le", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.succAbove_of_le_castSucc", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.succAbove_of_lt_succ", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.succAbove_succ_of_lt", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.succAbove_succ_of_le", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.succAbove_succ_self", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.succAbove_castSucc_of_lt", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.succAbove_castSucc_of_le", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.succAbove_castSucc_self", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.succAbove_pred_of_lt", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.succAbove_pred_of_le", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.succAbove_pred_self", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.succAbove_castPred_of_lt", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.succAbove_castPred_of_le", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.succAbove_castPred_self", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.succAbove_ne", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["rcases", "rw", "exact", "rw", "exact"], "tactic_count": 5}
{"name": "Fin.ne_succAbove", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.succAbove_right_injective", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["rintro", "unfold", "split_ifs", "exact", "rw", "cases", "rw", "cases", "exact"], "tactic_count": 9}
{"name": "Fin.succAbove_right_inj", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.succAbove_ne_zero_zero", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["rw", "exact", "exact"], "tactic_count": 3}
{"name": "Fin.succAbove_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.succAbove_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.succAbove_zero", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.succAbove_zero_apply", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.succAbove_ne_last_last", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.succAbove_eq_last_iff", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.succAbove_ne_last", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.succAbove_last", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Fin.succAbove_last_apply", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.succAbove_lt_iff_castSucc_lt", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["rcases", "rwa", "rw", "exact"], "tactic_count": 4}
{"name": "Fin.succAbove_lt_iff_succ_le", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.lt_succAbove_iff_le_castSucc", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["rcases", "rw", "exact", "rwa"], "tactic_count": 4}
{"name": "Fin.lt_succAbove_iff_lt_castSucc", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.succAbove_pos", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["by_cases", "simpa", "simp"], "tactic_count": 3}
{"name": "Fin.exists_succAbove_eq", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["obtain", "exacts"], "tactic_count": 2}
{"name": "Fin.exists_succAbove_eq_iff", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.range_succAbove", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.range_succ", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.succAbove_left_injective", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.succAbove_left_inj", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.zero_succAbove", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.succ_succAbove_zero", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.succ_succAbove_succ", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["obtain", "rw", "rwa"], "tactic_count": 3}
{"name": "Fin.castSucc_succAbove_castSucc", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["rcases", "rw", "rw"], "tactic_count": 3}
{"name": "Fin.one_succAbove_zero", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.succ_succAbove_one", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Fin.one_succAbove_succ", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["have"], "tactic_count": 1}
{"name": "Fin.one_succAbove_one", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["simpa", "succ_succAbove_succ"], "tactic_count": 2}
{"name": "Fin.predAbove", "kind": "definition", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.predAbove_of_le_castSucc", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.predAbove_of_lt_succ", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.predAbove_of_castSucc_lt", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.predAbove_of_succ_le", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.predAbove_succ_of_lt", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.predAbove_succ_of_le", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.predAbove_succ_self", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.predAbove_castSucc_of_lt", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.predAbove_castSucc_of_le", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.predAbove_castSucc_self", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.predAbove_pred_of_lt", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.predAbove_pred_of_le", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.predAbove_pred_self", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.predAbove_castPred_of_lt", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.predAbove_castPred_of_le", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.predAbove_castPred_self", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.predAbove_right_zero", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["cases", "exact", "rw"], "tactic_count": 3}
{"name": "Fin.predAbove_zero_succ", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.predAbove_zero_of_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Fin.succ_predAbove_zero", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.predAbove_zero", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["split_ifs", "rw", "rw"], "tactic_count": 3}
{"name": "Fin.predAbove_right_last", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.predAbove_last_castSucc", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.predAbove_last_of_ne_last", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["rw", "rcases", "exact"], "tactic_count": 3}
{"name": "Fin.predAbove_last_apply", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["split_ifs", "rw", "rw"], "tactic_count": 3}
{"name": "Fin.predAbove_surjective", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["intro", "by_cases", "exact", "rw", "exact"], "tactic_count": 5}
{"name": "Fin.succAbove_predAbove", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["obtain", "rw", "rw"], "tactic_count": 3}
{"name": "Fin.succ_succAbove_predAbove", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["obtain", "rw", "rw"], "tactic_count": 3}
{"name": "Fin.predAbove_succAbove", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["obtain", "rw", "rw"], "tactic_count": 3}
{"name": "Fin.succ_predAbove_succ", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["obtain", "rw", "rw"], "tactic_count": 3}
{"name": "Fin.castSucc_predAbove_castSucc", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["obtain", "rw", "rw"], "tactic_count": 3}
{"name": "Fin.predAbove_predAbove_succAbove", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["cases", "inl", "h", "rw", "rwa", "inr", "h", "rw", "rwa"], "tactic_count": 9}
{"name": "Fin.succAbove_succAbove_predAbove", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["cases", "inl", "inr"], "tactic_count": 3}
{"name": "Fin.succAbove_succAbove_succAbove_predAbove", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPred", "is_tactic_proof": true, "tactics": ["we", "ext", "simp", "apply_ite", "split_ifs"], "tactic_count": 5}
{"name": "Fin.instSuccOrder", "kind": "instance", "module": "Mathlib.Data.Fin.SuccPredOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.orderSucc_eq", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPredOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.orderSucc_apply", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPredOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.orderSucc_last", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPredOrder", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.orderSucc_castSucc", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPredOrder", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.instPredOrder", "kind": "instance", "module": "Mathlib.Data.Fin.SuccPredOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.orderPred_eq", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPredOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.orderPred_apply", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPredOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.orderPred_zero", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPredOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.orderPred_succ", "kind": "theorem", "module": "Mathlib.Data.Fin.SuccPredOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin._example", "kind": "example", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Fin.tuple0_le", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.tail", "kind": "definition", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.tail_def", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.cons", "kind": "definition", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.tail_cons", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.cons_succ", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.cons_zero", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.cons_one", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.cons_last", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.cons_update", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["ext", "cases"], "tactic_count": 2}
{"name": "Fin.cons_injective2", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.cons_inj", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.cons_left_injective", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.cons_right_injective", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.update_cons_zero", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["ext", "cases"], "tactic_count": 2}
{"name": "Fin.cons_self_tail", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["ext", "cases"], "tactic_count": 2}
{"name": "Fin.consEquiv", "kind": "definition", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.consCases", "kind": "definition", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.consCases_cons", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["rw", "congr"], "tactic_count": 2}
{"name": "Fin.consInduction", "kind": "definition", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.cons_injective_of_injective", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["intro", "cases"], "tactic_count": 2}
{"name": "Fin.cons_injective_iff", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["refine", "rintro", "replace", "simp", "simpa"], "tactic_count": 5}
{"name": "Fin.exists_cons", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.forall_fin_zero_pi", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.exists_fin_zero_pi", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.forall_fin_succ_pi", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.exists_fin_succ_pi", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.tail_update_zero", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Fin.tail_update_succ", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "rw", "simp", "simp"], "tactic_count": 5}
{"name": "Fin.comp_cons", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "rw", "rfl", "let", "have", "rw"], "tactic_count": 7}
{"name": "Fin.comp_tail", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Fin.le_cons", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.cons_le", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.cons_le_cons", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.range_fin_succ", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.range_cons", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.append", "kind": "definition", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.append_left", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.append_left'", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.append_right", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.append_right_nil", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "refine", "simp", "exact"], "tactic_count": 5}
{"name": "Fin.append_elim0", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.append_left_nil", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["refine", "exact", "rw", "refine", "simp"], "tactic_count": 5}
{"name": "Fin.elim0_append", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.append_assoc", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["ext", "rw", "refine", "rw", "refine", "rw", "simp", "rw", "simp", "rw", "simp"], "tactic_count": 11}
{"name": "Fin.append_left_eq_cons", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["ext", "refine", "intro", "rw", "exact", "intro", "rw", "exact"], "tactic_count": 8}
{"name": "Fin.cons_eq_append", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["funext"], "tactic_count": 1}
{"name": "Fin.append_cast_left", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "Fin.append_cast_right", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "Fin.append_rev", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["rcases", "rw", "induction", "simp", "simp"], "tactic_count": 5}
{"name": "Fin.append_comp_rev", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.append_castAdd_natAdd", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["unfold", "simp"], "tactic_count": 2}
{"name": "Fin.addCases_castAdd_natAdd", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["ext", "cases"], "tactic_count": 2}
{"name": "Fin.append_comp_sumElim", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Fin.append_injective_iff", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["let", "invFun", "left_inv", "right_inv", "rw"], "tactic_count": 5}
{"name": "Fin.repeat", "kind": "definition", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.repeat_apply", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.repeat_zero", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.repeat_one", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["generalize_proofs", "apply", "rw", "intro", "simp"], "tactic_count": 5}
{"name": "Fin.repeat_succ", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["generalize_proofs", "apply", "rw", "refine", "simp", "simp"], "tactic_count": 6}
{"name": "Fin.repeat_add", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["generalize_proofs", "apply", "rw", "refine", "simp", "simp"], "tactic_count": 6}
{"name": "Fin.repeat_rev", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.repeat_comp_rev", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.init", "kind": "definition", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.init_def", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.snoc", "kind": "definition", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.init_snoc", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp", "convert"], "tactic_count": 3}
{"name": "Fin.snoc_castSucc", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["simp", "convert"], "tactic_count": 2}
{"name": "Fin.snoc_apply_zero", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.snoc_comp_castSucc", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.snoc_last", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.snoc_zero", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.snoc_comp_natAdd", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["ext", "refine", "simp", "rw", "simp", "rw"], "tactic_count": 6}
{"name": "Fin.snoc_castAdd", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.snoc_comp_castAdd", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.snoc_update", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["ext", "cases", "cast", "last"], "tactic_count": 4}
{"name": "Fin.update_snoc_last", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["ext", "cases"], "tactic_count": 2}
{"name": "Fin.range_snoc", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Fin.snoc_injective2", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.snoc_inj", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.snoc_right_injective", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.snoc_left_injective", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.snoc_init_self", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["ext", "cases"], "tactic_count": 2}
{"name": "Fin.init_update_last", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Fin.init_update_castSucc", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "rw", "simp", "simp"], "tactic_count": 5}
{"name": "Fin.tail_init_eq_init_tail", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Fin.cons_snoc_eq_snoc_cons", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["ext", "cases", "zero", "succ", "cases", "last", "cast", "rw", "simp"], "tactic_count": 9}
{"name": "Fin.comp_snoc", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "simp", "rw", "simp"], "tactic_count": 5}
{"name": "Fin.append_right_eq_snoc", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["ext", "refine", "intro", "rw", "exact", "intro", "rw", "exact"], "tactic_count": 8}
{"name": "Fin.snoc_eq_append", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.append_left_snoc", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.append_right_cons", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.append_cons", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["funext", "rcases", "simp", "rcases", "simp", "split_ifs", "have", "simp", "have", "simp"], "tactic_count": 10}
{"name": "Fin.append_snoc", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["funext", "rcases", "simp", "castLT_mk]", "split_ifs", "have", "contradiction", "obtain", "simp", "have", "contradiction"], "tactic_count": 11}
{"name": "Fin.comp_init", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Fin.snocEquiv", "kind": "definition", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.snocCases", "kind": "definition", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.snocCases_snoc", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.snocInduction", "kind": "definition", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.snoc_injective_of_injective", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.snoc_injective_iff", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["refine", "simpa", "rintro", "rw", "exact"], "tactic_count": 5}
{"name": "Fin.succAboveCases", "kind": "definition", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.forall_iff_castSucc", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.forall_fin_add", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.forall_fin_add_pi", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.exists_iff_castSucc", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.forall_iff_succAbove", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.exists_iff_succAbove", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.eq_self_or_eq_succAbove", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.removeNth", "kind": "definition", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.insertNth", "kind": "definition", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.insertNth_apply_same", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.insertNth_apply_succAbove", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["simp", "split_ifs", "generalize_proofs", "generalize", "rw", "intro", "generalize_proofs", "generalize", "rw", "intro"], "tactic_count": 10}
{"name": "Fin.succAbove_cases_eq_insertNth", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.removeNth_apply", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.removeNth_fun_const", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.removeNth_insertNth", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Fin.removeNth_zero", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Fin.removeNth_last", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Fin.insertNth_comp_succAbove", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.insertNth_eq_iff", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.eq_insertNth_iff", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Fin.insertNth_injective2", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.insertNth_inj", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.insertNth_left_injective", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.insertNth_right_injective", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.insertNth_apply_below", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.insertNth_apply_above", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.insertNth_zero", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["refine", "ext", "convert"], "tactic_count": 3}
{"name": "Fin.insertNth_zero'", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.insertNth_last", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["refine", "ext", "apply", "trans", "rw", "exact", "apply", "rw"], "tactic_count": 8}
{"name": "Fin.insertNth_last'", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.insertNth_rev", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["induction", "exact", "simp", "simp"], "tactic_count": 4}
{"name": "Fin.insertNth_comp_rev", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["funext", "apply"], "tactic_count": 2}
{"name": "Fin.insertNth_succ_cons", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["ext", "cases", "x", "p", "simp", "cases"], "tactic_count": 6}
{"name": "Fin.cons_rev", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Fin.cons_comp_rev", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["funext"], "tactic_count": 1}
{"name": "Fin.snoc_rev", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Fin.snoc_comp_rev", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.insertNth_binop", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.insertNth_le_iff", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.le_insertNth_iff", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.removeNth_update", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Fin.removeNth_update_succAbove", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["ext", "rcases"], "tactic_count": 2}
{"name": "Fin.insertNth_removeNth", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.insertNth_self_removeNth", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.update_insertNth", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.insertNth_update", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.insertNthEquiv", "kind": "definition", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.insertNthEquiv_zero", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.insertNthEquiv_last", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Fin.removeNth_removeNth_heq_swap", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["apply", "simp", "rintro", "unfold", "apply", "rw"], "tactic_count": 6}
{"name": "Fin.removeNth_removeNth_eq_swap", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX", "kind": "definition", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.find", "kind": "definition", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.find_spec", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.find_min", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.find_le_of_pos", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.find_eq_iff", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["refine", "have", "grind"], "tactic_count": 3}
{"name": "Fin.val_find", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.find_nat_lt", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["rw", "have"], "tactic_count": 2}
{"name": "Fin.find_lt_iff", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.find_le_iff", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.lt_find_iff", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Fin.le_find_iff", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Fin.find_eq_zero", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.find_of_not_zero", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Fin.find_eq_dite", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["split_ifs", "grind", "grind"], "tactic_count": 3}
{"name": "Fin.find_mono_of_le", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.find_mono", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.find_congr", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.find_congr'", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.find_le", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.find_pos", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.find_of_find_le", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": ["have", "refine", "cases", "left", "right", "exact", "rw", "exact"], "tactic_count": 8}
{"name": "Fin.find?_eq_dite", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["split_ifs"], "tactic_count": 1}
{"name": "Fin.find?_decide_eq_dite", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Fin.get_find?_eq_find_of_eq_true", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Fin.find?_decide_get_eq_find", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Fin.find_mem_find?_decide", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Fin.mem_find?_iff", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.find?_eq_some_find_of_exists", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Fin.find?_eq_some_find_of_isSome", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Fin.contractNth", "kind": "definition", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.contractNth_apply_of_lt", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.contractNth_apply_of_eq", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "Fin.contractNth_apply_of_gt", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.contractNth_apply_of_ne", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["rcases", "rwa", "rwa", "exact", "rwa", "exact"], "tactic_count": 6}
{"name": "Fin.comp_contractNth", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": true, "tactics": ["ext", "rcases", "simp", "simp", "simp"], "tactic_count": 5}
{"name": "Fin.sigma_eq_of_eq_comp_cast", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.sigma_eq_iff_eq_comp_cast", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "piFinTwoEquiv", "kind": "definition", "module": "Mathlib.Data.Fin.Tuple.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tuple.bubble_sort_induction'", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.BubbleSortInduction", "is_tactic_proof": true, "tactics": ["letI", "refine", "obtain", "exact"], "tactic_count": 4}
{"name": "Tuple.bubble_sort_induction", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.BubbleSortInduction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.FromTypes.uncurry", "kind": "definition", "module": "Mathlib.Data.Fin.Tuple.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.FromTypes.curry", "kind": "definition", "module": "Mathlib.Data.Fin.Tuple.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.FromTypes.uncurry_apply_cons", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.FromTypes.uncurry_apply_succ", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.FromTypes.curry_apply_cons", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.FromTypes.curry_apply_succ", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.FromTypes.curry_uncurry", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Curry", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Function.FromTypes.uncurry_curry", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Curry", "is_tactic_proof": true, "tactics": ["ext", "induction", "zero", "succ"], "tactic_count": 4}
{"name": "Function.FromTypes.curryEquiv", "kind": "definition", "module": "Mathlib.Data.Fin.Tuple.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.FromTypes.curry_two_eq_curry", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.FromTypes.uncurry_two_eq_uncurry", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.OfArity.uncurry", "kind": "definition", "module": "Mathlib.Data.Fin.Tuple.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.OfArity.curry", "kind": "definition", "module": "Mathlib.Data.Fin.Tuple.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.OfArity.curry_uncurry", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.OfArity.uncurry_curry", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.OfArity.curryEquiv", "kind": "definition", "module": "Mathlib.Data.Fin.Tuple.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.OfArity.curry_two_eq_curry", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.OfArity.uncurry_two_eq_uncurry", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.Embedding.tail", "kind": "definition", "module": "Mathlib.Data.Fin.Tuple.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.Embedding.coe_tail", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.Embedding.cons", "kind": "definition", "module": "Mathlib.Data.Fin.Tuple.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.Embedding.coe_cons", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.Embedding.tail_cons", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.Embedding.init", "kind": "definition", "module": "Mathlib.Data.Fin.Tuple.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.Embedding.snoc", "kind": "definition", "module": "Mathlib.Data.Fin.Tuple.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.Embedding.coe_snoc", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.Embedding.init_snoc", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Embedding", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.Embedding.snoc_castSucc", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Embedding", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.Embedding.snoc_last", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Embedding", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.Embedding.append", "kind": "definition", "module": "Mathlib.Data.Fin.Tuple.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.Embedding.coe_append", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.twoEmbeddingEquiv", "kind": "definition", "module": "Mathlib.Data.Fin.Tuple.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.embFinTwo", "kind": "definition", "module": "Mathlib.Data.Fin.Tuple.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.embFinTwo_apply_zero", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.embFinTwo_apply_one", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.mem_piFinset_iff_zero_tail", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Finset", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.mem_piFinset_iff_last_init", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Finset", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.mem_piFinset_iff_pivot_removeNth", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Finset", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.cons_mem_piFinset_cons", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Finset", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Fin.snoc_mem_piFinset_snoc", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Finset", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Fin.insertNth_mem_piFinset_insertNth", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Finset", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.map_consEquiv_filter_piFinset", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Finset", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "Finset.map_snocEquiv_filter_piFinset", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Finset", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "Finset.map_insertNthEquiv_filter_piFinset", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Finset", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "Finset.filter_piFinset_eq_map_consEquiv", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Finset", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.filter_piFinset_eq_map_snocEquiv", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Finset", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.filter_piFinset_eq_map_insertNthEquiv", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Finset", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.card_consEquiv_filter_piFinset", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Finset", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.card_snocEquiv_filter_piFinset", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Finset", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.card_insertNthEquiv_filter_piFinset", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Finset", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.Nat.antidiagonalTuple", "kind": "definition", "module": "Mathlib.Data.Fin.Tuple.NatAntidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Nat.antidiagonalTuple_zero_zero", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.NatAntidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Nat.antidiagonalTuple_zero_succ", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.NatAntidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Nat.mem_antidiagonalTuple", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.NatAntidiagonal", "is_tactic_proof": true, "tactics": ["induction", "elim0", "cases", "decide", "simp", "cons", "simp_rw", "exists_eq_right_right,"], "tactic_count": 8}
{"name": "List.Nat.nodup_antidiagonalTuple", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.NatAntidiagonal", "is_tactic_proof": false, "tactics": ["induction", "zero", "succ", "simp_rw", "constructor", "intro", "exact", "induction", "zero", "succ", "rw", "refine", "rw", "obtain", "rw", "injection", "rw", "obtain", "dsimp", "rw", "obtain", "rw", "exact"], "tactic_count": 23}
{"name": "List.Nat.antidiagonalTuple_zero_right", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.NatAntidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Nat.antidiagonalTuple_one", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.NatAntidiagonal", "is_tactic_proof": false, "tactics": ["simp_rw", "conv_rhs", "congr", "simp_rw", "intro", "obtain", "rw"], "tactic_count": 7}
{"name": "List.Nat.antidiagonalTuple_two", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.NatAntidiagonal", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "rw", "rfl"], "tactic_count": 4}
{"name": "List.Nat.antidiagonalTuple_pairwise_pi_lex", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.NatAntidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Nat.antidiagonalTuple", "kind": "definition", "module": "Mathlib.Data.Fin.Tuple.NatAntidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Nat.antidiagonalTuple_zero_zero", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.NatAntidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Nat.antidiagonalTuple_zero_succ", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.NatAntidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Nat.mem_antidiagonalTuple", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.NatAntidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Nat.nodup_antidiagonalTuple", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.NatAntidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Nat.antidiagonalTuple_zero_right", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.NatAntidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Nat.antidiagonalTuple_one", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.NatAntidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Nat.antidiagonalTuple_two", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.NatAntidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Nat.antidiagonalTuple", "kind": "definition", "module": "Mathlib.Data.Fin.Tuple.NatAntidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Nat.antidiagonalTuple_zero_zero", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.NatAntidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Nat.antidiagonalTuple_zero_succ", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.NatAntidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Nat.mem_antidiagonalTuple", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.NatAntidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Nat.antidiagonalTuple_zero_right", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.NatAntidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Nat.antidiagonalTuple_one", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.NatAntidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Nat.antidiagonalTuple_two", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.NatAntidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Nat.sigmaAntidiagonalTupleEquivTuple", "kind": "definition", "module": "Mathlib.Data.Fin.Tuple.NatAntidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinVec.seq", "kind": "definition", "module": "Mathlib.Data.Fin.Tuple.Reflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinVec.seq_eq", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Reflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinVec._example", "kind": "example", "module": "Mathlib.Data.Fin.Tuple.Reflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinVec.map", "kind": "definition", "module": "Mathlib.Data.Fin.Tuple.Reflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinVec.map_eq", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Reflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinVec._example", "kind": "example", "module": "Mathlib.Data.Fin.Tuple.Reflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinVec.etaExpand", "kind": "definition", "module": "Mathlib.Data.Fin.Tuple.Reflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinVec.etaExpand_eq", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Reflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinVec._example", "kind": "example", "module": "Mathlib.Data.Fin.Tuple.Reflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinVec.Forall", "kind": "definition", "module": "Mathlib.Data.Fin.Tuple.Reflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinVec.forall_iff", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Reflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinVec._example", "kind": "example", "module": "Mathlib.Data.Fin.Tuple.Reflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinVec.Exists", "kind": "definition", "module": "Mathlib.Data.Fin.Tuple.Reflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinVec.exists_iff", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Reflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinVec._example", "kind": "example", "module": "Mathlib.Data.Fin.Tuple.Reflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinVec.sum", "kind": "definition", "module": "Mathlib.Data.Fin.Tuple.Reflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinVec.prod", "kind": "definition", "module": "Mathlib.Data.Fin.Tuple.Reflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinVec.prod_eq", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Reflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinVec._example", "kind": "example", "module": "Mathlib.Data.Fin.Tuple.Reflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinVec._example", "kind": "example", "module": "Mathlib.Data.Fin.Tuple.Reflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinVec.mkProdEqQ", "kind": "definition", "module": "Mathlib.Data.Fin.Tuple.Reflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinVec.mkSumEqQ", "kind": "definition", "module": "Mathlib.Data.Fin.Tuple.Reflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.prod_univ_ofNat", "kind": "definition", "module": "Mathlib.Data.Fin.Tuple.Reflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.sum_univ_ofNat", "kind": "definition", "module": "Mathlib.Data.Fin.Tuple.Reflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tuple.graph", "kind": "definition", "module": "Mathlib.Data.Fin.Tuple.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tuple.graph.proj", "kind": "definition", "module": "Mathlib.Data.Fin.Tuple.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tuple.graph.card", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Sort", "is_tactic_proof": true, "tactics": ["rw", "exact", "intro", "rw", "simp"], "tactic_count": 5}
{"name": "Tuple.graphEquiv₁", "kind": "definition", "module": "Mathlib.Data.Fin.Tuple.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tuple.proj_equiv₁'", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tuple.graphEquiv₂", "kind": "definition", "module": "Mathlib.Data.Fin.Tuple.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tuple.sort", "kind": "definition", "module": "Mathlib.Data.Fin.Tuple.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tuple.graphEquiv₂_apply", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tuple.self_comp_sort", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tuple.monotone_proj", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Sort", "is_tactic_proof": true, "tactics": ["rintro", "exact", "simp"], "tactic_count": 3}
{"name": "Tuple.monotone_sort", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Sort", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Tuple.lt_card_le_iff_apply_le_of_monotone", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tuple.lt_card_ge_iff_apply_ge_of_antitone", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tuple.lt_card_lt_iff_apply_lt_of_monotone", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tuple.lt_card_gt_iff_apply_gt_of_antitone", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tuple.unique_monotone", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tuple.unique_antitone", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tuple.eq_sort_iff'", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Sort", "is_tactic_proof": true, "tactics": ["constructor", "rw", "exact", "have", "ext1", "exact"], "tactic_count": 6}
{"name": "Tuple.eq_sort_iff", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Sort", "is_tactic_proof": true, "tactics": ["rw", "refine", "exact", "obtain", "exacts"], "tactic_count": 5}
{"name": "Tuple.sort_eq_refl_iff_monotone", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Sort", "is_tactic_proof": true, "tactics": ["rw", "simp", "exact"], "tactic_count": 3}
{"name": "Tuple.comp_sort_eq_comp_iff_monotone", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tuple.comp_perm_comp_sort_eq_comp_sort", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Sort", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Tuple.antitone_pair_of_not_sorted'", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Sort", "is_tactic_proof": true, "tactics": ["contrapose", "exact"], "tactic_count": 2}
{"name": "Tuple.antitone_pair_of_not_sorted", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tuple.sort_perm", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Sort", "is_tactic_proof": true, "tactics": ["apply", "simpa", "intro", "exact"], "tactic_count": 4}
{"name": "Equiv.Perm.monotone_iff", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Sort", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.take", "kind": "definition", "module": "Mathlib.Data.Fin.Tuple.Take", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.take_apply", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Take", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.take_zero", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Take", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Fin.take_one", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Take", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Fin.take_eq_init", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Take", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.take_eq_self", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Take", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Fin.take_take", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Take", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.take_init", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Take", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.take_repeat", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Take", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Fin.take_succ_eq_snoc", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Take", "is_tactic_proof": true, "tactics": ["ext", "induction", "zero", "have", "subst", "simp", "succ", "induction", "last", "cast"], "tactic_count": 10}
{"name": "Fin.take_update_of_lt", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Take", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "rw", "simp", "have", "simp"], "tactic_count": 6}
{"name": "Fin.take_update_of_ge", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Take", "is_tactic_proof": true, "tactics": ["ext", "have", "refine", "simp", "exact", "simp"], "tactic_count": 6}
{"name": "Fin.take_addCases_left", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Take", "is_tactic_proof": true, "tactics": ["ext", "have", "simp", "congr"], "tactic_count": 4}
{"name": "Fin.take_append_left", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Take", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.take_addCases_right", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Take", "is_tactic_proof": true, "tactics": ["ext", "simp", "by_cases", "simp", "congr", "simp"], "tactic_count": 6}
{"name": "Fin.take_append_right", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Take", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.ofFn_take_eq_take_ofFn", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Take", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.ofFn_take_get", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Take", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.get_take_eq_take_get_comp_cast", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Take", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Fin.get_take_ofFn_eq_take_comp_cast", "kind": "theorem", "module": "Mathlib.Data.Fin.Tuple.Take", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
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{"name": "Matrix.vecNotation", "kind": "definition", "module": "Mathlib.Data.Fin.VecNotation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix._aux_Mathlib_Data_Fin_VecNotation___macroRules_Matrix_vecNotation_1", "kind": "definition", "module": "Mathlib.Data.Fin.VecNotation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.vecConsUnexpander", "kind": "definition", "module": "Mathlib.Data.Fin.VecNotation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.vecEmptyUnexpander", "kind": "definition", "module": "Mathlib.Data.Fin.VecNotation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.vecHead", "kind": "definition", "module": "Mathlib.Data.Fin.VecNotation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.vecTail", "kind": "definition", "module": "Mathlib.Data.Fin.VecNotation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiFin.hasRepr", "kind": "instance", "module": "Mathlib.Data.Fin.VecNotation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.empty_eq", "kind": "theorem", "module": "Mathlib.Data.Fin.VecNotation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.head_fin_const", "kind": "theorem", "module": "Mathlib.Data.Fin.VecNotation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.cons_val_zero", "kind": "theorem", "module": "Mathlib.Data.Fin.VecNotation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.cons_val_zero'", "kind": "theorem", "module": "Mathlib.Data.Fin.VecNotation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.cons_val_succ", "kind": "theorem", "module": "Mathlib.Data.Fin.VecNotation", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.cons_val_succ'", "kind": "theorem", "module": "Mathlib.Data.Fin.VecNotation", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.matchVecConsPrefix", "kind": "definition", "module": "Mathlib.Data.Fin.VecNotation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.cons_val", "kind": "definition", "module": "Mathlib.Data.Fin.VecNotation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.head_cons", "kind": "theorem", "module": "Mathlib.Data.Fin.VecNotation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.tail_cons", "kind": "theorem", "module": "Mathlib.Data.Fin.VecNotation", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Matrix.empty_val'", "kind": "theorem", "module": "Mathlib.Data.Fin.VecNotation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.cons_head_tail", "kind": "theorem", "module": "Mathlib.Data.Fin.VecNotation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.range_cons", "kind": "theorem", "module": "Mathlib.Data.Fin.VecNotation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.range_empty", "kind": "theorem", "module": "Mathlib.Data.Fin.VecNotation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.range_cons_empty", "kind": "theorem", "module": "Mathlib.Data.Fin.VecNotation", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matrix.range_cons_cons_empty", "kind": "theorem", "module": "Mathlib.Data.Fin.VecNotation", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matrix.vecCons_const", "kind": "theorem", "module": "Mathlib.Data.Fin.VecNotation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.vec_single_eq_const", "kind": "theorem", "module": "Mathlib.Data.Fin.VecNotation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.cons_val_one", "kind": "theorem", "module": "Mathlib.Data.Fin.VecNotation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.cons_val_two", "kind": "theorem", "module": "Mathlib.Data.Fin.VecNotation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.cons_val_three", "kind": "theorem", "module": "Mathlib.Data.Fin.VecNotation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.cons_val_four", "kind": "theorem", "module": "Mathlib.Data.Fin.VecNotation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.cons_val_fin_one", "kind": "theorem", "module": "Mathlib.Data.Fin.VecNotation", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Matrix.cons_fin_one", "kind": "theorem", "module": "Mathlib.Data.Fin.VecNotation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.vecCons_inj", "kind": "theorem", "module": "Mathlib.Data.Fin.VecNotation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiFin.mkLiteralQ", "kind": "definition", "module": "Mathlib.Data.Fin.VecNotation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiFin.toExpr", "kind": "instance", "module": "Mathlib.Data.Fin.VecNotation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.vecAppend", "kind": "definition", "module": "Mathlib.Data.Fin.VecNotation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.vecAppend_eq_ite", "kind": "theorem", "module": "Mathlib.Data.Fin.VecNotation", "is_tactic_proof": true, "tactics": ["ext", "rw", "congr", "simp", "rfl"], "tactic_count": 5}
{"name": "Matrix.vecAppend_apply_zero", "kind": "theorem", "module": "Mathlib.Data.Fin.VecNotation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.empty_vecAppend", "kind": "theorem", "module": "Mathlib.Data.Fin.VecNotation", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Matrix.vecAppend_empty", "kind": "theorem", "module": "Mathlib.Data.Fin.VecNotation", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Matrix.cons_vecAppend", "kind": "theorem", "module": "Mathlib.Data.Fin.VecNotation", "is_tactic_proof": true, "tactics": ["ext", "simp_rw", "split_ifs", "rcases", "simp", "simp", "simp", "rcases", "simp", "rw", "simp"], "tactic_count": 11}
{"name": "Matrix.vecAlt0", "kind": "definition", "module": "Mathlib.Data.Fin.VecNotation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.vecAlt1", "kind": "definition", "module": "Mathlib.Data.Fin.VecNotation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.vecAlt0_vecAppend", "kind": "theorem", "module": "Mathlib.Data.Fin.VecNotation", "is_tactic_proof": true, "tactics": ["ext", "simp_rw", "split_ifs", "rw", "exact", "rw", "simp", "refine", "lia"], "tactic_count": 9}
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{"name": "Matrix.vecHead_vecAlt0", "kind": "theorem", "module": "Mathlib.Data.Fin.VecNotation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.vecHead_vecAlt1", "kind": "theorem", "module": "Mathlib.Data.Fin.VecNotation", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.cons_vec_bit0_eq_alt0", "kind": "theorem", "module": "Mathlib.Data.Fin.VecNotation", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matrix.cons_vec_bit1_eq_alt1", "kind": "theorem", "module": "Mathlib.Data.Fin.VecNotation", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "Matrix.cons_vecAlt1", "kind": "theorem", "module": "Mathlib.Data.Fin.VecNotation", "is_tactic_proof": true, "tactics": ["ext", "simp_rw", "rcases", "rfl", "simp"], "tactic_count": 5}
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{"name": "Matrix.const_fin1_eq", "kind": "theorem", "module": "Mathlib.Data.Fin.VecNotation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finite.equivFin", "kind": "definition", "module": "Mathlib.Data.Finite.Card", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "Finite.equivFinOfCardEq", "kind": "definition", "module": "Mathlib.Data.Finite.Card", "is_tactic_proof": true, "tactics": ["subst", "apply"], "tactic_count": 2}
{"name": "Nat.card_eq", "kind": "theorem", "module": "Mathlib.Data.Finite.Card", "is_tactic_proof": true, "tactics": ["cases", "letI", "simp", "simp"], "tactic_count": 4}
{"name": "Finite.card_pos_iff", "kind": "theorem", "module": "Mathlib.Data.Finite.Card", "is_tactic_proof": true, "tactics": ["haveI", "rw"], "tactic_count": 2}
{"name": "Finite.card_pos", "kind": "theorem", "module": "Mathlib.Data.Finite.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finite.card_eq", "kind": "theorem", "module": "Mathlib.Data.Finite.Card", "is_tactic_proof": true, "tactics": ["haveI", "haveI", "simp"], "tactic_count": 3}
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{"name": "Finite.one_lt_card_iff_nontrivial", "kind": "theorem", "module": "Mathlib.Data.Finite.Card", "is_tactic_proof": true, "tactics": ["haveI", "simp"], "tactic_count": 2}
{"name": "Finite.one_lt_card", "kind": "theorem", "module": "Mathlib.Data.Finite.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finite.card_option", "kind": "theorem", "module": "Mathlib.Data.Finite.Card", "is_tactic_proof": true, "tactics": ["haveI", "simp"], "tactic_count": 2}
{"name": "Finite.card_le_of_embedding", "kind": "theorem", "module": "Mathlib.Data.Finite.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finite.card_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Data.Finite.Card", "is_tactic_proof": true, "tactics": ["haveI", "simp"], "tactic_count": 2}
{"name": "Finite.card_le_of_injective'", "kind": "theorem", "module": "Mathlib.Data.Finite.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finite.card_le_of_embedding'", "kind": "theorem", "module": "Mathlib.Data.Finite.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finite.card_le_of_surjective'", "kind": "theorem", "module": "Mathlib.Data.Finite.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finite.card_eq_zero_of_surjective", "kind": "theorem", "module": "Mathlib.Data.Finite.Card", "is_tactic_proof": true, "tactics": ["cases", "haveI", "haveI", "exact", "haveI", "exact"], "tactic_count": 6}
{"name": "Finite.card_eq_zero_of_injective", "kind": "theorem", "module": "Mathlib.Data.Finite.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finite.card_eq_zero_of_embedding", "kind": "theorem", "module": "Mathlib.Data.Finite.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finite.card_image_le", "kind": "theorem", "module": "Mathlib.Data.Finite.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finite.card_range_le", "kind": "theorem", "module": "Mathlib.Data.Finite.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finite.card_subtype_le", "kind": "theorem", "module": "Mathlib.Data.Finite.Card", "is_tactic_proof": true, "tactics": ["classical", "haveI", "simpa"], "tactic_count": 3}
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{"name": "ENat.card_eq_coe_natCard", "kind": "theorem", "module": "Mathlib.Data.Finite.Card", "is_tactic_proof": true, "tactics": ["unfold", "apply", "rw", "exact"], "tactic_count": 4}
{"name": "Set.card_union_le", "kind": "theorem", "module": "Mathlib.Data.Finite.Card", "is_tactic_proof": true, "tactics": ["rcases", "rw", "cases", "rw", "exact", "exact"], "tactic_count": 6}
{"name": "Set.Finite.card_lt_card", "kind": "theorem", "module": "Mathlib.Data.Finite.Card", "is_tactic_proof": true, "tactics": ["have", "have", "simp", "exact"], "tactic_count": 4}
{"name": "Set.Finite.eq_of_subset_of_card_le", "kind": "theorem", "module": "Mathlib.Data.Finite.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.equiv_image_eq_iff_subset", "kind": "theorem", "module": "Mathlib.Data.Finite.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.eq_top_of_card_le_of_finite", "kind": "theorem", "module": "Mathlib.Data.Finite.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finite", "kind": "classInductive", "module": "Mathlib.Data.Finite.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finite_iff_exists_equiv_fin", "kind": "theorem", "module": "Mathlib.Data.Finite.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finite.exists_equiv_fin", "kind": "theorem", "module": "Mathlib.Data.Finite.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finite.of_equiv", "kind": "theorem", "module": "Mathlib.Data.Finite.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.finite_iff", "kind": "theorem", "module": "Mathlib.Data.Finite.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Bijective.finite_iff", "kind": "theorem", "module": "Mathlib.Data.Finite.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finite.ofBijective", "kind": "theorem", "module": "Mathlib.Data.Finite.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finite.nonempty_decidableEq", "kind": "theorem", "module": "Mathlib.Data.Finite.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFinitePLift", "kind": "instance", "module": "Mathlib.Data.Finite.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFiniteULift", "kind": "instance", "module": "Mathlib.Data.Finite.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_finite_iff_infinite", "kind": "theorem", "module": "Mathlib.Data.Finite.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_infinite_iff_finite", "kind": "theorem", "module": "Mathlib.Data.Finite.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.infinite_iff", "kind": "theorem", "module": "Mathlib.Data.Finite.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInfinitePLift", "kind": "instance", "module": "Mathlib.Data.Finite.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInfiniteULift", "kind": "instance", "module": "Mathlib.Data.Finite.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finite_or_infinite", "kind": "theorem", "module": "Mathlib.Data.Finite.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_finite", "kind": "theorem", "module": "Mathlib.Data.Finite.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finite.false", "kind": "theorem", "module": "Mathlib.Data.Finite.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Infinite.false", "kind": "theorem", "module": "Mathlib.Data.Finite.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bool.instFinite", "kind": "instance", "module": "Mathlib.Data.Finite.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prop.instFinite", "kind": "instance", "module": "Mathlib.Data.Finite.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite", "kind": "definition", "module": "Mathlib.Data.Finite.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.finite_coe_iff", "kind": "theorem", "module": "Mathlib.Data.Finite.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.toFinite", "kind": "theorem", "module": "Mathlib.Data.Finite.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.to_subtype", "kind": "theorem", "module": "Mathlib.Data.Finite.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Infinite", "kind": "definition", "module": "Mathlib.Data.Finite.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.not_finite", "kind": "theorem", "module": "Mathlib.Data.Finite.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.not_infinite", "kind": "theorem", "module": "Mathlib.Data.Finite.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Infinite.not_finite", "kind": "theorem", "module": "Mathlib.Data.Finite.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.finite_or_infinite", "kind": "theorem", "module": "Mathlib.Data.Finite.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.infinite_or_finite", "kind": "theorem", "module": "Mathlib.Data.Finite.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.set_finite_iff", "kind": "theorem", "module": "Mathlib.Data.Finite.Defs", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.infinite_coe_iff", "kind": "theorem", "module": "Mathlib.Data.Finite.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.card_perm", "kind": "theorem", "module": "Mathlib.Data.Finite.Perm", "is_tactic_proof": true, "tactics": ["classical", "have", "rw"], "tactic_count": 3}
{"name": "Finite.instProd", "kind": "instance", "module": "Mathlib.Data.Finite.Prod", "is_tactic_proof": true, "tactics": ["haveI", "haveI", "infer_instance"], "tactic_count": 3}
{"name": "Finite.instPProd", "kind": "instance", "module": "Mathlib.Data.Finite.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finite.prod_left", "kind": "theorem", "module": "Mathlib.Data.Finite.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finite.prod_right", "kind": "theorem", "module": "Mathlib.Data.Finite.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.finite_iff", "kind": "theorem", "module": "Mathlib.Data.Finite.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.finite", "kind": "instance", "module": "Mathlib.Data.Finite.Prod", "is_tactic_proof": true, "tactics": ["classical", "haveI", "haveI", "exact"], "tactic_count": 4}
{"name": "Function.Embedding.finite", "kind": "instance", "module": "Mathlib.Data.Finite.Prod", "is_tactic_proof": true, "tactics": ["rcases", "infer_instance", "refine", "haveI", "exact"], "tactic_count": 5}
{"name": "Equiv.finite_right", "kind": "instance", "module": "Mathlib.Data.Finite.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.finite_left", "kind": "instance", "module": "Mathlib.Data.Finite.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.finite_left", "kind": "instance", "module": "Mathlib.Data.Finite.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.finite_right", "kind": "instance", "module": "Mathlib.Data.Finite.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.fintypeProd", "kind": "instance", "module": "Mathlib.Data.Finite.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.fintypeOffDiag", "kind": "instance", "module": "Mathlib.Data.Finite.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.fintypeImage2", "kind": "instance", "module": "Mathlib.Data.Finite.Prod", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "Finite.Set.finite_prod", "kind": "instance", "module": "Mathlib.Data.Finite.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finite.Set.finite_image2", "kind": "instance", "module": "Mathlib.Data.Finite.Prod", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "Set.Finite.prod", "kind": "theorem", "module": "Mathlib.Data.Finite.Prod", "is_tactic_proof": true, "tactics": ["have", "have", "apply"], "tactic_count": 3}
{"name": "Set.Finite.of_prod_left", "kind": "theorem", "module": "Mathlib.Data.Finite.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.of_prod_right", "kind": "theorem", "module": "Mathlib.Data.Finite.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Infinite.prod_left", "kind": "theorem", "module": "Mathlib.Data.Finite.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Infinite.prod_right", "kind": "theorem", "module": "Mathlib.Data.Finite.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.infinite_prod", "kind": "theorem", "module": "Mathlib.Data.Finite.Prod", "is_tactic_proof": true, "tactics": ["refine", "simp_rw", "by_contra", "exact", "rintro", "exact", "exact"], "tactic_count": 7}
{"name": "Set.finite_prod", "kind": "theorem", "module": "Mathlib.Data.Finite.Prod", "is_tactic_proof": true, "tactics": ["contrapose"], "tactic_count": 1}
{"name": "Set.Finite.offDiag", "kind": "theorem", "module": "Mathlib.Data.Finite.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.image2", "kind": "theorem", "module": "Mathlib.Data.Finite.Prod", "is_tactic_proof": true, "tactics": ["have", "have", "apply"], "tactic_count": 3}
{"name": "Set.Finite.toFinset_prod", "kind": "theorem", "module": "Mathlib.Data.Finite.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.toFinset_offDiag", "kind": "theorem", "module": "Mathlib.Data.Finite.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.finite_image_fst_and_snd_iff", "kind": "theorem", "module": "Mathlib.Data.Finite.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Infinite.image2_left", "kind": "theorem", "module": "Mathlib.Data.Finite.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Infinite.image2_right", "kind": "theorem", "module": "Mathlib.Data.Finite.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.infinite_image2", "kind": "theorem", "module": "Mathlib.Data.Finite.Prod", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact", "rintro", "exact", "exact"], "tactic_count": 6}
{"name": "Set.finite_image2", "kind": "theorem", "module": "Mathlib.Data.Finite.Prod", "is_tactic_proof": true, "tactics": ["contrapose", "rw", "grind"], "tactic_count": 3}
{"name": "Finite.Set.finite_of_finite_image", "kind": "theorem", "module": "Mathlib.Data.Finite.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finite.of_injective_finite_range", "kind": "theorem", "module": "Mathlib.Data.Finite.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finite.instSigma", "kind": "instance", "module": "Mathlib.Data.Finite.Sigma", "is_tactic_proof": true, "tactics": ["letI", "letI", "infer_instance"], "tactic_count": 3}
{"name": "Finite.instPSigma", "kind": "instance", "module": "Mathlib.Data.Finite.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finite.instSum", "kind": "instance", "module": "Mathlib.Data.Finite.Sum", "is_tactic_proof": true, "tactics": ["haveI", "haveI", "infer_instance"], "tactic_count": 3}
{"name": "Finite.sum_left", "kind": "theorem", "module": "Mathlib.Data.Finite.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finite.sum_right", "kind": "theorem", "module": "Mathlib.Data.Finite.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finite.instPSum", "kind": "instance", "module": "Mathlib.Data.Finite.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finite.psum_left", "kind": "theorem", "module": "Mathlib.Data.Finite.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finite.psum_right", "kind": "theorem", "module": "Mathlib.Data.Finite.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.finite", "kind": "instance", "module": "Mathlib.Data.Finite.Vector", "is_tactic_proof": true, "tactics": ["haveI", "infer_instance"], "tactic_count": 2}
{"name": "instFiniteSym", "kind": "instance", "module": "Mathlib.Data.Finite.Vector", "is_tactic_proof": true, "tactics": ["classical", "haveI", "infer_instance"], "tactic_count": 3}
{"name": "Multiset.keys", "kind": "definition", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.coe_keys", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.keys_zero", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.keys_cons", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.keys_singleton", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.NodupKeys", "kind": "definition", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.coe_nodupKeys", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.nodup_keys", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "Multiset.NodupKeys.nodup", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AList.toFinmap", "kind": "definition", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.Finmap.0.term⟦_⟧", "kind": "definition", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.Finmap.0._aux_Mathlib_Data_Finmap___macroRules__private_Mathlib_Data_Finmap_0_term⟦_⟧_1", "kind": "definition", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.Finmap.0._aux_Mathlib_Data_Finmap___unexpand_AList_toFinmap_1", "kind": "definition", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AList.toFinmap_eq", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": true, "tactics": ["cases", "cases", "simp"], "tactic_count": 3}
{"name": "AList.toFinmap_entries", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.toFinmap", "kind": "definition", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.nodup_entries", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.liftOn", "kind": "definition", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": ["refine", "exact", "have", "revert", "rcases", "exact"], "tactic_count": 6}
{"name": "Finmap.liftOn_toFinmap", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": true, "tactics": ["cases", "rfl"], "tactic_count": 2}
{"name": "Finmap.liftOn₂", "kind": "definition", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.liftOn₂_toFinmap", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.induction_on", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "Finmap.induction_on₂", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.induction_on₃", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.ext", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.ext_iff'", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.instMembership", "kind": "instance", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.mem_def", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.mem_toFinmap", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.keys", "kind": "definition", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.keys_val", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.keys_ext", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finmap.mem_keys", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.instEmptyCollection", "kind": "instance", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.instInhabited", "kind": "instance", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.empty_toFinmap", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.toFinmap_nil", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.notMem_empty", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.keys_empty", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.singleton", "kind": "definition", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.keys_singleton", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.mem_singleton", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finmap.decidableEq", "kind": "instance", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.lookup", "kind": "definition", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.lookup_toFinmap", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.dlookup_list_toFinmap", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finmap.lookup_empty", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.lookup_isSome", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.lookup_eq_none", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.mem_lookup_iff", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "Finmap.lookup_eq_some_iff", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.sigma_keys_lookup", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": true, "tactics": ["ext", "have", "simpa"], "tactic_count": 3}
{"name": "Finmap.lookup_singleton_eq", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finmap.instDecidableMem", "kind": "instance", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.mem_iff", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.mem_of_lookup_eq_some", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.ext_lookup", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.keysLookupEquiv", "kind": "definition", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.keysLookupEquiv_symm_apply_keys", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.keysLookupEquiv_symm_apply_lookup", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.replace", "kind": "definition", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.replace_toFinmap", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finmap.keys_replace", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.mem_replace", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.foldl", "kind": "definition", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.any", "kind": "definition", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.all", "kind": "definition", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.erase", "kind": "definition", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.erase_toFinmap", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finmap.keys_erase_toFinset", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finmap.keys_erase", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.mem_erase", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.notMem_erase_self", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": true, "tactics": ["rw", "left", "rfl"], "tactic_count": 3}
{"name": "Finmap.lookup_erase", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.lookup_erase_ne", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.erase_erase", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.sdiff", "kind": "definition", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.instSDiff", "kind": "instance", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.insert", "kind": "definition", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.insert_toFinmap", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finmap.entries_insert_of_notMem", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.mem_insert", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.lookup_insert", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.lookup_insert_of_ne", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.insert_insert", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.insert_insert_of_ne", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.toFinmap_cons", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.mem_list_toFinmap", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "obtain", "simp", "refine", "rintro", "simp"], "tactic_count": 8}
{"name": "Finmap.insert_singleton_eq", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finmap.extract", "kind": "definition", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.extract_eq_lookup_erase", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.union", "kind": "definition", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.instUnion", "kind": "instance", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.mem_union", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.union_toFinmap", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finmap.keys_union", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.lookup_union_left", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.lookup_union_right", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.lookup_union_left_of_not_in", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "rw"], "tactic_count": 3}
{"name": "Finmap.mem_lookup_union'", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.mem_lookup_union", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.mem_lookup_union_middle", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.insert_union", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.union_assoc", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.empty_union", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.union_empty", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.erase_union_singleton", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.Disjoint", "kind": "definition", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.disjoint_empty", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.Disjoint.symm", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.Disjoint.symm_iff", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.instDecidableRelDisjoint", "kind": "instance", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.disjoint_union_left", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finmap.disjoint_union_right", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finmap.union_comm_of_disjoint", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finmap.union_cancel", "kind": "theorem", "module": "Mathlib.Data.Finmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.attach", "kind": "definition", "module": "Mathlib.Data.Finset.Attach", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.attach_val", "kind": "theorem", "module": "Mathlib.Data.Finset.Attach", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_attach", "kind": "theorem", "module": "Mathlib.Data.Finset.Attach", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.coe_attach", "kind": "theorem", "module": "Mathlib.Data.Finset.Attach", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "initFn._@.Mathlib.Data.Finset.Attr.3237354494._hygCtx._hyg.3", "kind": "definition", "module": "Mathlib.Data.Finset.Attr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.disjUnion_eq_union", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.disjoint_union_left", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.disjoint_union_right", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.not_disjoint_iff_nonempty_inter", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.disjoint_or_nonempty_inter", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finset.disjoint_of_subset_iff_left_eq_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.pairwiseDisjoint_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.isDirected_le", "kind": "instance", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finset.isDirected_subset", "kind": "instance", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.erase_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Nontrivial.erase_nonempty", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.erase_nonempty", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["simp", "refine", "rintro", "exact"], "tactic_count": 4}
{"name": "Finset.erase_singleton", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.erase_insert_eq_erase", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.erase_insert", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.erase_insert_of_ne", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.erase_cons_of_ne", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.insert_erase", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.erase_eq_iff_eq_insert", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Finset.insert_erase_invOn", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.erase_ssubset", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.ssubset_iff_exists_subset_erase", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.erase_ssubset_insert", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.erase_cons", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.subset_insert_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.erase_insert_subset", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.insert_erase_subset", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.subset_insert_iff_of_notMem", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.erase_subset_iff_of_mem", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.erase_injOn'", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Nontrivial.exists_cons_eq", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["classical", "obtain", "have", "refine"], "tactic_count": 4}
{"name": "Finset.erase_sdiff_erase", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["ext", "aesop"], "tactic_count": 2}
{"name": "Finset.sdiff_singleton_eq_erase", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.erase_eq", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.disjoint_erase_comm", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Finset.disjoint_insert_erase", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.disjoint_erase_insert", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.disjoint_of_erase_left", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finset.disjoint_of_erase_right", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finset.inter_erase", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.erase_inter", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.erase_sdiff_comm", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.erase_inter_comm", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.erase_union_distrib", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.insert_inter_distrib", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.erase_sdiff_distrib", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.erase_union_of_mem", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.union_erase_of_mem", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.sdiff_union_erase_cancel", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.sdiff_insert", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.sdiff_insert_insert_of_mem_of_notMem", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.sdiff_erase", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.sdiff_erase_self", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.erase_eq_empty_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.sdiff_disjoint", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.disjoint_sdiff", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.disjoint_sdiff_inter", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.attach_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.attach_nonempty_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.attach_eq_empty_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.filter_singleton", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.filter_cons_of_pos", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.filter_cons_of_neg", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.disjoint_filter", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["constructor"], "tactic_count": 1}
{"name": "Finset.disjoint_filter_filter'", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "rintro", "rw", "simpa"], "tactic_count": 4}
{"name": "Finset.disjoint_filter_filter_not", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.filter_disjUnion", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.filter_cons", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.disjoint_disjUnion_left", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.disjoint_disjUnion_right", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.filter_union", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.filter_union_right", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.filter_mem_eq_inter", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.filter_notMem_eq_sdiff", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.filter_inter_distrib", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.filter_inter", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.inter_filter", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.filter_insert", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.filter_erase", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.filter_or", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.filter_and", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.filter_not", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.filter_and_not", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.sdiff_eq_filter", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.subset_union_elim", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["classical", "refine", "grind", "grind", "intro", "simp", "intro", "exact"], "tactic_count": 8}
{"name": "Finset.filter_eq", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.filter_eq'", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.filter_ne", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.filter_ne'", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.filter_union_filter_of_codisjoint", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.filter_union_filter_not_eq", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.range_filter_eq", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.range_inter_range", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finset.range_union_range", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Multiset.toFinset_add", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.toFinset_inter", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.toFinset_union", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Multiset.toFinset_eq_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.toFinset_nonempty", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.toFinset_filter", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "List.toFinset_union", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "List.toFinset_inter", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "List.toFinset_filter", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finset.toList_eq_nil", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.empty_toList", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.toList_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Nonempty.toList_ne_nil", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Nonempty.not_empty_toList", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.chooseX", "kind": "definition", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.choose", "kind": "definition", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.choose_spec", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.choose_mem", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.choose_property", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Finset.union", "kind": "definition", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Finset.union_symm_inl", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Finset.union_symm_inr", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.piFinsetUnion", "kind": "definition", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.equivToSet", "kind": "definition", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.toFinset_replicate", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp", "split_ifs"], "tactic_count": 3}
{"name": "Finset.mem_union_of_disjoint", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw", "have", "tauto"], "tactic_count": 3}
{"name": "Finset.univ_finset_of_isEmpty", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.isEmpty_of_forall_eq_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.univ_finset_eq_singleton_empty_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Nonempty.eq_univ", "kind": "theorem", "module": "Mathlib.Data.Finset.BooleanAlgebra", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "Finset.univ_nonempty_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.BooleanAlgebra", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.univ_nonempty", "kind": "theorem", "module": "Mathlib.Data.Finset.BooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.univ_eq_empty_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.BooleanAlgebra", "is_tactic_proof": true, "tactics": ["contrapose"], "tactic_count": 1}
{"name": "Finset.univ_nontrivial_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.BooleanAlgebra", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.univ_nontrivial", "kind": "theorem", "module": "Mathlib.Data.Finset.BooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.singleton_ne_univ", "kind": "theorem", "module": "Mathlib.Data.Finset.BooleanAlgebra", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "Finset.univ_eq_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.BooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.univ_unique", "kind": "theorem", "module": "Mathlib.Data.Finset.BooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.boundedOrder", "kind": "instance", "module": "Mathlib.Data.Finset.BooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.top_eq_univ", "kind": "theorem", "module": "Mathlib.Data.Finset.BooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.ssubset_univ_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.BooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.univ_subset_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.BooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.codisjoint_left", "kind": "theorem", "module": "Mathlib.Data.Finset.BooleanAlgebra", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finset.codisjoint_right", "kind": "theorem", "module": "Mathlib.Data.Finset.BooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.booleanAlgebra", "kind": "instance", "module": "Mathlib.Data.Finset.BooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sdiff_eq_inter_compl", "kind": "theorem", "module": "Mathlib.Data.Finset.BooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.compl_eq_univ_sdiff", "kind": "theorem", "module": "Mathlib.Data.Finset.BooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_compl", "kind": "theorem", "module": "Mathlib.Data.Finset.BooleanAlgebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.notMem_compl", "kind": "theorem", "module": "Mathlib.Data.Finset.BooleanAlgebra", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.coe_compl", "kind": "theorem", "module": "Mathlib.Data.Finset.BooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.compl_subset_compl", "kind": "theorem", "module": "Mathlib.Data.Finset.BooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.compl_ssubset_compl", "kind": "theorem", "module": "Mathlib.Data.Finset.BooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.subset_compl_comm", "kind": "theorem", "module": "Mathlib.Data.Finset.BooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.subset_compl_iff_disjoint_right", "kind": "theorem", "module": "Mathlib.Data.Finset.BooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.subset_compl_iff_disjoint_left", "kind": "theorem", "module": "Mathlib.Data.Finset.BooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.subset_compl_singleton", "kind": "theorem", "module": "Mathlib.Data.Finset.BooleanAlgebra", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.compl_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.BooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.compl_univ", "kind": "theorem", "module": "Mathlib.Data.Finset.BooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.compl_eq_empty_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.BooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.compl_eq_univ_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.BooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.union_compl", "kind": "theorem", "module": "Mathlib.Data.Finset.BooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inter_compl", "kind": "theorem", "module": "Mathlib.Data.Finset.BooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.compl_union", "kind": "theorem", "module": "Mathlib.Data.Finset.BooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.compl_inter", "kind": "theorem", "module": "Mathlib.Data.Finset.BooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.compl_erase", "kind": "theorem", "module": "Mathlib.Data.Finset.BooleanAlgebra", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Finset.compl_insert", "kind": "theorem", "module": "Mathlib.Data.Finset.BooleanAlgebra", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Finset.insert_compl_insert", "kind": "theorem", "module": "Mathlib.Data.Finset.BooleanAlgebra", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Finset.insert_compl_self", "kind": "theorem", "module": "Mathlib.Data.Finset.BooleanAlgebra", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.compl_filter", "kind": "theorem", "module": "Mathlib.Data.Finset.BooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.compl_ne_univ_iff_nonempty", "kind": "theorem", "module": "Mathlib.Data.Finset.BooleanAlgebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.compl_singleton", "kind": "theorem", "module": "Mathlib.Data.Finset.BooleanAlgebra", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.insert_inj_on'", "kind": "theorem", "module": "Mathlib.Data.Finset.BooleanAlgebra", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finset.image_univ_of_surjective", "kind": "theorem", "module": "Mathlib.Data.Finset.BooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image_univ_equiv", "kind": "theorem", "module": "Mathlib.Data.Finset.BooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.univ_inter", "kind": "theorem", "module": "Mathlib.Data.Finset.BooleanAlgebra", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finset.inter_univ", "kind": "theorem", "module": "Mathlib.Data.Finset.BooleanAlgebra", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.inter_eq_univ", "kind": "theorem", "module": "Mathlib.Data.Finset.BooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.singleton_eq_univ", "kind": "theorem", "module": "Mathlib.Data.Finset.BooleanAlgebra", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finset.map_univ_of_surjective", "kind": "theorem", "module": "Mathlib.Data.Finset.BooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.map_univ_equiv", "kind": "theorem", "module": "Mathlib.Data.Finset.BooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.univ_map_equiv_to_embedding", "kind": "theorem", "module": "Mathlib.Data.Finset.BooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.univ_filter_exists", "kind": "theorem", "module": "Mathlib.Data.Finset.BooleanAlgebra", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Finset.univ_filter_mem_range", "kind": "theorem", "module": "Mathlib.Data.Finset.BooleanAlgebra", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.coe_filter_univ", "kind": "theorem", "module": "Mathlib.Data.Finset.BooleanAlgebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.subtype_eq_univ", "kind": "theorem", "module": "Mathlib.Data.Finset.BooleanAlgebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.subtype_univ", "kind": "theorem", "module": "Mathlib.Data.Finset.BooleanAlgebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.univ_map_subtype", "kind": "theorem", "module": "Mathlib.Data.Finset.BooleanAlgebra", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.univ_val_map_subtype_val", "kind": "theorem", "module": "Mathlib.Data.Finset.BooleanAlgebra", "is_tactic_proof": true, "tactics": ["apply", "apply", "apply"], "tactic_count": 3}
{"name": "Finset.univ_val_map_subtype_restrict", "kind": "theorem", "module": "Mathlib.Data.Finset.BooleanAlgebra", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.filter_univ_mem", "kind": "theorem", "module": "Mathlib.Data.Finset.BooleanAlgebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.decidableCodisjoint", "kind": "instance", "module": "Mathlib.Data.Finset.BooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.decidableIsCompl", "kind": "instance", "module": "Mathlib.Data.Finset.BooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card", "kind": "definition", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.term#_", "kind": "definition", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset._aux_Mathlib_Data_Finset_Card___macroRules_Finset_term#__1", "kind": "definition", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset._aux_Mathlib_Data_Finset_Card___unexpand_Finset_card_1", "kind": "definition", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_def", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_val", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_mk", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_le_card", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_mono", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "Finset.card_eq_zero", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_pos", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.one_le_card", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_ne_zero_of_mem", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_singleton", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_singleton_inter", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.card_cons", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_insert_of_notMem", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.card_insert_of_mem", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.card_insert_le", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.card_le_two", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_le_three", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_le_four", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_le_five", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_le_six", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_insert_eq_ite", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.card_pair_eq_one_or_two", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.card_pair", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.card_erase_of_mem", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_erase_add_one", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_erase_lt_of_mem", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_erase_le", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.pred_card_le_card_erase", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.card_erase_eq_ite", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_range", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_attach", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.card_toFinset", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.toFinset_card_le", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.toFinset_card_of_nodup", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.dedup_card_eq_card_iff_nodup", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.toFinset_card_eq_card_iff_nodup", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.card_toFinset", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.toFinset_card_le", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.toFinset_card_of_nodup", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.length_toList", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.card_image_le", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.card_image_of_injOn", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.injOn_of_card_image_eq", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["rw", "dsimp", "have", "refine", "simp", "rw", "exact"], "tactic_count": 7}
{"name": "Finset.card_image_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_image_of_injective", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.fiber_card_ne_zero_iff_mem_image", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.card_filter_le_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_map", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_subtype", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.card_filter_le", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.eq_of_subset_of_card_le", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.eq_iff_card_le_of_subset", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.eq_of_superset_of_card_ge", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.eq_iff_card_ge_of_superset", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.subset_iff_eq_of_card_le", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.map_eq_of_subset", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_filter_eq_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.card_filter_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.card_lt_card", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_strictMono", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_eq_of_bijective", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["classical", "have", "ext", "suffices", "simpa", "constructor", "intro", "rintro", "calc", "apply", "intro", "exact"], "tactic_count": 12}
{"name": "Finset.card_bij", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["classical", "calc", "apply", "intro", "simpa", "congr", "ext", "constructor", "obtain", "obtain"], "tactic_count": 10}
{"name": "Finset.card_bij'", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["refine", "rw", "simp"], "tactic_count": 3}
{"name": "Finset.card_nbij", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_nbij'", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_equiv", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["refine"], "tactic_count": 1}
{"name": "Finset.card_bijective", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.BijOn.finsetCard_eq", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_le_card_of_injOn", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["classical", "calc"], "tactic_count": 2}
{"name": "Finset.card_le_card_of_injective", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["rcases", "simp", "classical", "let", "apply", "aesop", "intro", "rw", "simp", "exact"], "tactic_count": 10}
{"name": "Finset.card_le_card_of_surjOn", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finset.exists_ne_map_eq_of_card_lt_of_maps_to", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["classical", "by_contra", "refine", "intro", "contrapose", "exact"], "tactic_count": 6}
{"name": "Finset.exists_ne_map_eq_of_card_image_lt", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.not_injOn_of_card_image_lt", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.le_card_of_inj_on_range", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.surjOn_of_injOn_of_card_le", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["classical", "suffices", "have", "exact"], "tactic_count": 4}
{"name": "Finset.surj_on_of_inj_on_of_card_le", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["let", "have", "have", "intro", "obtain", "exact"], "tactic_count": 6}
{"name": "Finset.injOn_of_surjOn_of_card_le", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["classical", "have", "have", "have", "rw", "lia"], "tactic_count": 6}
{"name": "Finset.inj_on_of_surj_on_of_card_le", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["let", "have", "have", "exact"], "tactic_count": 4}
{"name": "Finset.card_disjUnion", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_union_add_card_inter", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_inter_add_card_union", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.card_union", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.card_inter", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.card_union_le", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.card_union_eq_card_add_card", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.card_sdiff_of_subset", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["suffices", "rw"], "tactic_count": 2}
{"name": "Finset.card_sdiff", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.card_sdiff_add_card_eq_card", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.card_sub_card_eq", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.le_card_sdiff", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.card_le_card_sdiff_add_card", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.card_sdiff_add_card", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.sdiff_nonempty_of_card_lt_card", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.exists_mem_notMem_of_card_lt_card", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finset.card_sdiff_add_card_inter", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.card_inter_add_card_sdiff", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.card_sdiff_le_card_sdiff_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.card_sdiff_lt_card_sdiff_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.card_sdiff_eq_card_sdiff_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.inter_nonempty_of_card_lt_card_add_card", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["contrapose", "calc"], "tactic_count": 2}
{"name": "Finset.card_filter_add_card_filter_not", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finset.exists_subsuperset_card_eq", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["classical", "refine", "intro", "obtain", "exact"], "tactic_count": 5}
{"name": "Finset.exists_subset_card_eq", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.le_card_iff_exists_subset_card", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "Finset.exists_subset_or_subset_of_two_mul_lt_card", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["have", "have", "obtain", "exact", "exact"], "tactic_count": 5}
{"name": "Finset.card_eq_one", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["cases", "simp"], "tactic_count": 2}
{"name": "Finset.exists_eq_insert_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["constructor", "grind", "rintro", "obtain", "exact"], "tactic_count": 5}
{"name": "Finset.card_le_one", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["obtain", "simp", "refine", "grind", "exact"], "tactic_count": 5}
{"name": "Finset.card_le_one_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.card_le_one_iff_subsingleton_coe", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_le_one_iff_subset_singleton", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact", "exact", "rintro", "rw", "exact"], "tactic_count": 7}
{"name": "Finset.exists_mem_ne", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["have", "by_contra", "exact"], "tactic_count": 3}
{"name": "Finset.card_le_one_of_subsingleton", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.one_lt_card", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["contrapose"], "tactic_count": 1}
{"name": "Finset.one_lt_card_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Finset.one_lt_card_iff_nontrivial", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["rw", "card_le_one_iff_subsingleton_coe,"], "tactic_count": 2}
{"name": "Finset.exists_of_one_lt_card_pi", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["simp_rw", "obtain", "refine", "rw", "obtain", "exacts"], "tactic_count": 6}
{"name": "Finset.card_eq_succ_iff_cons", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_eq_succ", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_eq_two", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["constructor", "rw", "grind", "grind"], "tactic_count": 4}
{"name": "Finset.card_eq_three", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["constructor", "rw", "grind", "grind"], "tactic_count": 4}
{"name": "Finset.card_eq_four", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["constructor", "rw", "grind", "grind"], "tactic_count": 4}
{"name": "Finset.two_lt_card_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["classical", "simp_rw", "exists_comm", "constructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 8}
{"name": "Finset.two_lt_card", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Finset.three_lt_card_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["classical", "simp_rw", "exists_comm", "constructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 8}
{"name": "Finset.three_lt_card", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Finset.strongInduction", "kind": "definition", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.strongInduction_eq", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.strongInductionOn", "kind": "definition", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.strongInductionOn_eq", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "Finset.case_strong_induction_on", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Nonempty.strong_induction", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.strongDownwardInduction", "kind": "definition", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.strongDownwardInduction_eq", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.strongDownwardInductionOn", "kind": "definition", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.strongDownwardInductionOn_eq", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "Finset.lt_wf", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.eraseInduction", "kind": "theorem", "module": "Mathlib.Data.Finset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.cast_card_erase_of_mem", "kind": "theorem", "module": "Mathlib.Data.Finset.CastCard", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.cast_card_inter", "kind": "theorem", "module": "Mathlib.Data.Finset.CastCard", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.cast_card_union", "kind": "theorem", "module": "Mathlib.Data.Finset.CastCard", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.cast_card_sdiff", "kind": "theorem", "module": "Mathlib.Data.Finset.CastCard", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.dedup_eq_self", "kind": "theorem", "module": "Mathlib.Data.Finset.Dedup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.toFinset", "kind": "definition", "module": "Mathlib.Data.Finset.Dedup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.toFinset_val", "kind": "theorem", "module": "Mathlib.Data.Finset.Dedup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.toFinset_eq", "kind": "theorem", "module": "Mathlib.Data.Finset.Dedup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Nodup.toFinset_inj", "kind": "theorem", "module": "Mathlib.Data.Finset.Dedup", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Multiset.mem_toFinset", "kind": "theorem", "module": "Mathlib.Data.Finset.Dedup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.toFinset_subset", "kind": "theorem", "module": "Mathlib.Data.Finset.Dedup", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.toFinset_ssubset", "kind": "theorem", "module": "Mathlib.Data.Finset.Dedup", "is_tactic_proof": true, "tactics": ["simp_rw", "rfl"], "tactic_count": 2}
{"name": "Multiset.toFinset_dedup", "kind": "theorem", "module": "Mathlib.Data.Finset.Dedup", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Multiset.isWellFounded_ssubset", "kind": "instance", "module": "Mathlib.Data.Finset.Dedup", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finset.val_toFinset", "kind": "theorem", "module": "Mathlib.Data.Finset.Dedup", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "Finset.val_le_iff_val_subset", "kind": "theorem", "module": "Mathlib.Data.Finset.Dedup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.toFinset", "kind": "definition", "module": "Mathlib.Data.Finset.Dedup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.toFinset_val", "kind": "theorem", "module": "Mathlib.Data.Finset.Dedup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.toFinset_coe", "kind": "theorem", "module": "Mathlib.Data.Finset.Dedup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.toFinset_eq", "kind": "theorem", "module": "Mathlib.Data.Finset.Dedup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.mem_toFinset", "kind": "theorem", "module": "Mathlib.Data.Finset.Dedup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.coe_toFinset", "kind": "theorem", "module": "Mathlib.Data.Finset.Dedup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.toFinset_surj_on", "kind": "theorem", "module": "Mathlib.Data.Finset.Dedup", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "List.toFinset_surjective", "kind": "theorem", "module": "Mathlib.Data.Finset.Dedup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.toFinset_eq_iff_perm_dedup", "kind": "theorem", "module": "Mathlib.Data.Finset.Dedup", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.toFinset.ext_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Dedup", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "List.toFinset_eq_of_perm", "kind": "theorem", "module": "Mathlib.Data.Finset.Dedup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.perm_of_nodup_nodup_toFinset_eq", "kind": "theorem", "module": "Mathlib.Data.Finset.Dedup", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "List.toFinset_reverse", "kind": "theorem", "module": "Mathlib.Data.Finset.Dedup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.toList", "kind": "definition", "module": "Mathlib.Data.Finset.Dedup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.nodup_toList", "kind": "theorem", "module": "Mathlib.Data.Finset.Dedup", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finset.mem_toList", "kind": "theorem", "module": "Mathlib.Data.Finset.Dedup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.coe_toList", "kind": "theorem", "module": "Mathlib.Data.Finset.Dedup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.toList_toFinset", "kind": "theorem", "module": "Mathlib.Data.Finset.Dedup", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
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{"name": "Finset.exists_list_nodup_eq", "kind": "theorem", "module": "Mathlib.Data.Finset.Dedup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.perm_toList", "kind": "theorem", "module": "Mathlib.Data.Finset.Dedup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.canLiftFinset", "kind": "instance", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.eq_of_veq", "kind": "theorem", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.val_injective", "kind": "theorem", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.val_inj", "kind": "theorem", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.decidableEq", "kind": "instance", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.instMembership", "kind": "instance", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_def", "kind": "theorem", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_val", "kind": "theorem", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_mk", "kind": "theorem", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.decidableMem", "kind": "instance", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.forall_mem_not_eq", "kind": "theorem", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.forall_mem_not_eq'", "kind": "theorem", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.instSetLike", "kind": "instance", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.instPartialOrder", "kind": "instance", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.toSet", "kind": "abbrev", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_coe", "kind": "theorem", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.setOf_mem", "kind": "theorem", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.coe_mem", "kind": "theorem", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mk_coe", "kind": "theorem", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Finset.ext", "kind": "theorem", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.coe_inj", "kind": "theorem", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Finset.forall_coe", "kind": "theorem", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.exists_coe", "kind": "theorem", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.PiFinsetCoe.canLift", "kind": "instance", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.PiFinsetCoe.canLift'", "kind": "instance", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Finset.coe_sort_coe", "kind": "theorem", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.instHasSubset", "kind": "instance", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.instHasSSubset", "kind": "instance", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.partialOrder", "kind": "instance", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.subset_of_le", "kind": "theorem", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.instReflSubset", "kind": "instance", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.instIsTransSubset", "kind": "instance", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.instAntisymmSubset", "kind": "instance", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.instIrreflSSubset", "kind": "instance", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.instIsTransSSubset", "kind": "instance", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.instAsymmSSubset", "kind": "instance", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.instIsNonstrictStrictOrderSubsetSSubset", "kind": "instance", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.subset_def", "kind": "theorem", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.ssubset_def", "kind": "theorem", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Subset.refl", "kind": "theorem", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Subset.rfl", "kind": "theorem", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.subset_of_eq", "kind": "theorem", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Subset.trans", "kind": "theorem", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Superset.trans", "kind": "theorem", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_of_subset", "kind": "theorem", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.notMem_mono", "kind": "theorem", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Subset.antisymm", "kind": "theorem", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.subset_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Finset.val_le_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Subset.antisymm_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.not_subset", "kind": "theorem", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.le_eq_subset", "kind": "theorem", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Finset.le_iff_subset", "kind": "theorem", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.lt_iff_ssubset", "kind": "theorem", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.coe_ssubset", "kind": "theorem", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "Finset.val_strictMono", "kind": "theorem", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.ssubset_iff_subset_ne", "kind": "theorem", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.ssubset_iff_of_subset", "kind": "theorem", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.ssubset_of_ssubset_of_subset", "kind": "theorem", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.ssubset_of_subset_of_ssubset", "kind": "theorem", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.exists_of_ssubset", "kind": "theorem", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.isWellFounded_ssubset", "kind": "instance", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.wellFoundedLT", "kind": "instance", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.coeEmb", "kind": "definition", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.coe_coeEmb", "kind": "theorem", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.decidableDforallFinset", "kind": "instance", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.instDecidableRelSubset", "kind": "instance", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.instDecidableRelSSubset", "kind": "instance", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.instDecidableLE", "kind": "instance", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.instDecidableLT", "kind": "instance", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.decidableDExistsFinset", "kind": "instance", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.decidableExistsAndFinset", "kind": "instance", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.decidableExistsAndFinsetCoe", "kind": "instance", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.decidableEqPiFinset", "kind": "instance", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.instDecidableMapsToCoeFinsetOfDecidablePredMemSet", "kind": "instance", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.instDecidableSurjOnCoeFinsetOfDecidableEq", "kind": "instance", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.pairwise_subtype_iff_pairwise_finset'", "kind": "theorem", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.pairwise_subtype_iff_pairwise_finset", "kind": "theorem", "module": "Mathlib.Data.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.exists_between", "kind": "theorem", "module": "Mathlib.Data.Finset.DenselyOrdered", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
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{"name": "Finset.dens", "kind": "definition", "module": "Mathlib.Data.Finset.Density", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.dens_eq_card_div_card", "kind": "theorem", "module": "Mathlib.Data.Finset.Density", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.dens_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.Density", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.dens_singleton", "kind": "theorem", "module": "Mathlib.Data.Finset.Density", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.dens_cons", "kind": "theorem", "module": "Mathlib.Data.Finset.Density", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.dens_disjUnion", "kind": "theorem", "module": "Mathlib.Data.Finset.Density", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Finset.dens_eq_zero", "kind": "theorem", "module": "Mathlib.Data.Finset.Density", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.dens_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Finset.Density", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.dens_pos", "kind": "theorem", "module": "Mathlib.Data.Finset.Density", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.dens_le_dens", "kind": "theorem", "module": "Mathlib.Data.Finset.Density", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Finset.dens_mono", "kind": "theorem", "module": "Mathlib.Data.Finset.Density", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.dens_strictMono", "kind": "theorem", "module": "Mathlib.Data.Finset.Density", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.dens_map_le", "kind": "theorem", "module": "Mathlib.Data.Finset.Density", "is_tactic_proof": true, "tactics": ["cases", "simp", "simp_rw", "gcongr", "exact", "exact"], "tactic_count": 6}
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{"name": "Finset.dens_image", "kind": "theorem", "module": "Mathlib.Data.Finset.Density", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.card_mul_dens", "kind": "theorem", "module": "Mathlib.Data.Finset.Density", "is_tactic_proof": true, "tactics": ["cases", "simp", "rw", "exact"], "tactic_count": 4}
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{"name": "Finset.natCast_card_mul_nnratCast_dens", "kind": "theorem", "module": "Mathlib.Data.Finset.Density", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Finset.dens_eq_one", "kind": "theorem", "module": "Mathlib.Data.Finset.Density", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "Finset.dens_union_add_dens_inter", "kind": "theorem", "module": "Mathlib.Data.Finset.Density", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
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{"name": "Finset.dens_union_of_disjoint", "kind": "theorem", "module": "Mathlib.Data.Finset.Density", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.dens_sdiff_add_dens_eq_dens", "kind": "theorem", "module": "Mathlib.Data.Finset.Density", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.dens_sdiff_add_dens", "kind": "theorem", "module": "Mathlib.Data.Finset.Density", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.dens_sdiff_comm", "kind": "theorem", "module": "Mathlib.Data.Finset.Density", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.dens_sdiff_add_dens_inter", "kind": "theorem", "module": "Mathlib.Data.Finset.Density", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.dens_inter_add_dens_sdiff", "kind": "theorem", "module": "Mathlib.Data.Finset.Density", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.dens_filter_add_dens_filter_not_eq_dens", "kind": "theorem", "module": "Mathlib.Data.Finset.Density", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finset.dens_union_le", "kind": "theorem", "module": "Mathlib.Data.Finset.Density", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.dens_le_dens_sdiff_add_dens", "kind": "theorem", "module": "Mathlib.Data.Finset.Density", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.dens_sdiff", "kind": "theorem", "module": "Mathlib.Data.Finset.Density", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.le_dens_sdiff", "kind": "theorem", "module": "Mathlib.Data.Finset.Density", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.disjoint_left", "kind": "theorem", "module": "Mathlib.Data.Finset.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.disjoint_right", "kind": "theorem", "module": "Mathlib.Data.Finset.Disjoint", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.disjoint_iff_ne", "kind": "theorem", "module": "Mathlib.Data.Finset.Disjoint", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.disjoint_val", "kind": "theorem", "module": "Mathlib.Data.Finset.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Disjoint.forall_ne_finset", "kind": "theorem", "module": "Mathlib.Data.Finset.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.not_disjoint_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.disjoint_of_subset_left", "kind": "theorem", "module": "Mathlib.Data.Finset.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.disjoint_of_subset_right", "kind": "theorem", "module": "Mathlib.Data.Finset.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.disjoint_empty_left", "kind": "theorem", "module": "Mathlib.Data.Finset.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.disjoint_empty_right", "kind": "theorem", "module": "Mathlib.Data.Finset.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.disjoint_singleton_left", "kind": "theorem", "module": "Mathlib.Data.Finset.Disjoint", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.disjoint_singleton_right", "kind": "theorem", "module": "Mathlib.Data.Finset.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.disjoint_singleton", "kind": "theorem", "module": "Mathlib.Data.Finset.Disjoint", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.disjoint_self_iff_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.disjoint_coe", "kind": "theorem", "module": "Mathlib.Data.Finset.Disjoint", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.pairwiseDisjoint_coe", "kind": "theorem", "module": "Mathlib.Data.Finset.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.pairwiseDisjoint_singleton_iff_injOn", "kind": "theorem", "module": "Mathlib.Data.Finset.Disjoint", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.decidableDisjoint", "kind": "instance", "module": "Mathlib.Data.Finset.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.disjUnion", "kind": "definition", "module": "Mathlib.Data.Finset.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_disjUnion", "kind": "theorem", "module": "Mathlib.Data.Finset.Disjoint", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "Finset.coe_disjUnion", "kind": "theorem", "module": "Mathlib.Data.Finset.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.disjUnion_comm", "kind": "theorem", "module": "Mathlib.Data.Finset.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.disjUnion_inj_left", "kind": "theorem", "module": "Mathlib.Data.Finset.Disjoint", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.disjUnion_inj_right", "kind": "theorem", "module": "Mathlib.Data.Finset.Disjoint", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.singleton_disjUnion", "kind": "theorem", "module": "Mathlib.Data.Finset.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.disjUnion_singleton", "kind": "theorem", "module": "Mathlib.Data.Finset.Disjoint", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.disjoint_insert_left", "kind": "theorem", "module": "Mathlib.Data.Finset.Disjoint", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.disjoint_insert_right", "kind": "theorem", "module": "Mathlib.Data.Finset.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.disjoint_toFinset", "kind": "theorem", "module": "Mathlib.Data.Finset.Disjoint", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.disjoint_toFinset_iff_disjoint", "kind": "theorem", "module": "Mathlib.Data.Finset.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Nonempty", "kind": "definition", "module": "Mathlib.Data.Finset.Empty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.nonempty_def", "kind": "theorem", "module": "Mathlib.Data.Finset.Empty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.decidableNonempty", "kind": "instance", "module": "Mathlib.Data.Finset.Empty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.coe_nonempty", "kind": "theorem", "module": "Mathlib.Data.Finset.Empty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.nonempty_coe_sort", "kind": "theorem", "module": "Mathlib.Data.Finset.Empty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Nonempty.exists_mem", "kind": "theorem", "module": "Mathlib.Data.Finset.Empty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Nonempty.mono", "kind": "theorem", "module": "Mathlib.Data.Finset.Empty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Nonempty.forall_const", "kind": "theorem", "module": "Mathlib.Data.Finset.Empty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Nonempty.to_subtype", "kind": "theorem", "module": "Mathlib.Data.Finset.Empty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Nonempty.to_type", "kind": "theorem", "module": "Mathlib.Data.Finset.Empty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.empty", "kind": "definition", "module": "Mathlib.Data.Finset.Empty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.instEmptyCollection", "kind": "instance", "module": "Mathlib.Data.Finset.Empty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inhabitedFinset", "kind": "instance", "module": "Mathlib.Data.Finset.Empty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.empty_val", "kind": "theorem", "module": "Mathlib.Data.Finset.Empty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.notMem_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.Empty", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.not_nonempty_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.Empty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mk_zero", "kind": "theorem", "module": "Mathlib.Data.Finset.Empty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.ne_empty_of_mem", "kind": "theorem", "module": "Mathlib.Data.Finset.Empty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Nonempty.ne_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.Empty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.empty_subset", "kind": "theorem", "module": "Mathlib.Data.Finset.Empty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.eq_empty_of_forall_notMem", "kind": "theorem", "module": "Mathlib.Data.Finset.Empty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.eq_empty_iff_forall_notMem", "kind": "theorem", "module": "Mathlib.Data.Finset.Empty", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.val_eq_zero", "kind": "theorem", "module": "Mathlib.Data.Finset.Empty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.subset_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.Empty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.not_ssubset_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.Empty", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.nonempty_of_ne_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.Empty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.nonempty_iff_ne_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.Empty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.not_nonempty_iff_eq_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.Empty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.eq_empty_or_nonempty", "kind": "theorem", "module": "Mathlib.Data.Finset.Empty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.coe_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.Empty", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.coe_eq_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.Empty", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.isEmpty_coe_sort", "kind": "theorem", "module": "Mathlib.Data.Finset.Empty", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.instIsEmpty", "kind": "instance", "module": "Mathlib.Data.Finset.Empty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.eq_empty_of_isEmpty", "kind": "theorem", "module": "Mathlib.Data.Finset.Empty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.instOrderBot", "kind": "instance", "module": "Mathlib.Data.Finset.Empty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.bot_eq_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.Empty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.empty_ssubset", "kind": "theorem", "module": "Mathlib.Data.Finset.Empty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.exists_mem_empty_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Empty", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.forall_mem_empty_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Empty", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Mathlib.Meta.proveFinsetNonempty", "kind": "definition", "module": "Mathlib.Data.Finset.Empty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.erase", "kind": "definition", "module": "Mathlib.Data.Finset.Erase", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.erase_val", "kind": "theorem", "module": "Mathlib.Data.Finset.Erase", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_erase", "kind": "theorem", "module": "Mathlib.Data.Finset.Erase", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.notMem_erase", "kind": "theorem", "module": "Mathlib.Data.Finset.Erase", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.ne_of_mem_erase", "kind": "theorem", "module": "Mathlib.Data.Finset.Erase", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_of_mem_erase", "kind": "theorem", "module": "Mathlib.Data.Finset.Erase", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_erase_of_ne_of_mem", "kind": "theorem", "module": "Mathlib.Data.Finset.Erase", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.eq_of_mem_of_notMem_erase", "kind": "theorem", "module": "Mathlib.Data.Finset.Erase", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.erase_eq_of_notMem", "kind": "theorem", "module": "Mathlib.Data.Finset.Erase", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.erase_eq_self", "kind": "theorem", "module": "Mathlib.Data.Finset.Erase", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.erase_ne_self", "kind": "theorem", "module": "Mathlib.Data.Finset.Erase", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.erase_subset_erase", "kind": "theorem", "module": "Mathlib.Data.Finset.Erase", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.erase_subset", "kind": "theorem", "module": "Mathlib.Data.Finset.Erase", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.subset_erase", "kind": "theorem", "module": "Mathlib.Data.Finset.Erase", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.coe_erase", "kind": "theorem", "module": "Mathlib.Data.Finset.Erase", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.erase_idem", "kind": "theorem", "module": "Mathlib.Data.Finset.Erase", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.erase_right_comm", "kind": "theorem", "module": "Mathlib.Data.Finset.Erase", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.erase_inj", "kind": "theorem", "module": "Mathlib.Data.Finset.Erase", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.erase_injOn", "kind": "theorem", "module": "Mathlib.Data.Finset.Erase", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.filter", "kind": "definition", "module": "Mathlib.Data.Finset.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.knownToBeFinsetNotSet", "kind": "definition", "module": "Mathlib.Data.Finset.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.elabFinsetBuilderSep", "kind": "definition", "module": "Mathlib.Data.Finset.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.filter_val", "kind": "theorem", "module": "Mathlib.Data.Finset.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.filter_subset", "kind": "theorem", "module": "Mathlib.Data.Finset.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_filter", "kind": "theorem", "module": "Mathlib.Data.Finset.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_of_mem_filter", "kind": "theorem", "module": "Mathlib.Data.Finset.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.filter_ssubset", "kind": "theorem", "module": "Mathlib.Data.Finset.Filter", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.filter_filter", "kind": "theorem", "module": "Mathlib.Data.Finset.Filter", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.filter_comm", "kind": "theorem", "module": "Mathlib.Data.Finset.Filter", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.filter_congr_decidable", "kind": "theorem", "module": "Mathlib.Data.Finset.Filter", "is_tactic_proof": true, "tactics": ["congr"], "tactic_count": 1}
{"name": "Finset.filter_true", "kind": "theorem", "module": "Mathlib.Data.Finset.Filter", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finset.filter_false", "kind": "theorem", "module": "Mathlib.Data.Finset.Filter", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finset.filter_eq_self", "kind": "theorem", "module": "Mathlib.Data.Finset.Filter", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.filter_eq_empty_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Filter", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.filter_nonempty_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Filter", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.filter_true_of_mem", "kind": "theorem", "module": "Mathlib.Data.Finset.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.filter_false_of_mem", "kind": "theorem", "module": "Mathlib.Data.Finset.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.filter_const", "kind": "theorem", "module": "Mathlib.Data.Finset.Filter", "is_tactic_proof": true, "tactics": ["split_ifs"], "tactic_count": 1}
{"name": "Finset.filter_congr", "kind": "theorem", "module": "Mathlib.Data.Finset.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.filter_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.filter_subset_filter", "kind": "theorem", "module": "Mathlib.Data.Finset.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.monotone_filter_left", "kind": "theorem", "module": "Mathlib.Data.Finset.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.monotone_filter_right", "kind": "theorem", "module": "Mathlib.Data.Finset.Filter", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.coe_filter", "kind": "theorem", "module": "Mathlib.Data.Finset.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.subset_coe_filter_of_subset_forall", "kind": "theorem", "module": "Mathlib.Data.Finset.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.disjoint_filter_filter", "kind": "theorem", "module": "Mathlib.Data.Finset.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.pairwiseDisjoint_filter", "kind": "theorem", "module": "Mathlib.Data.Finset.Filter", "is_tactic_proof": true, "tactics": ["rintro", "obtain", "obtain", "contradiction"], "tactic_count": 4}
{"name": "Finset.disjoint_filter_and_not_filter", "kind": "theorem", "module": "Mathlib.Data.Finset.Filter", "is_tactic_proof": true, "tactics": ["intro", "simp", "by_contra", "exact"], "tactic_count": 4}
{"name": "Finset.filter_inj", "kind": "theorem", "module": "Mathlib.Data.Finset.Filter", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.filter_inj'", "kind": "theorem", "module": "Mathlib.Data.Finset.Filter", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.attachFin", "kind": "definition", "module": "Mathlib.Data.Finset.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_attachFin", "kind": "theorem", "module": "Mathlib.Data.Finset.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.coe_attachFin", "kind": "theorem", "module": "Mathlib.Data.Finset.Fin", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finset.card_attachFin", "kind": "theorem", "module": "Mathlib.Data.Finset.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image_val_attachFin", "kind": "theorem", "module": "Mathlib.Data.Finset.Fin", "is_tactic_proof": true, "tactics": ["apply", "rw", "exact"], "tactic_count": 3}
{"name": "Finset.map_valEmbedding_attachFin", "kind": "theorem", "module": "Mathlib.Data.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.attachFin_subset_attachFin_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.attachFin_subset_attachFin", "kind": "theorem", "module": "Mathlib.Data.Finset.Fin", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.attachFin_ssubset_attachFin_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.attachFin_ssubset_attachFin", "kind": "theorem", "module": "Mathlib.Data.Finset.Fin", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.finsupp", "kind": "definition", "module": "Mathlib.Data.Finset.Finsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_finsupp_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Finsupp", "is_tactic_proof": true, "tactics": ["classical", "refine", "rintro", "refine", "convert", "exact", "refine", "ext", "exact"], "tactic_count": 9}
{"name": "Finset.mem_finsupp_iff_of_support_subset", "kind": "theorem", "module": "Mathlib.Data.Finset.Finsupp", "is_tactic_proof": false, "tactics": ["refine", "mem_finsupp_iff.trans", "forall_congr", "by_cases", "exact", "rw", "exact", "rwa"], "tactic_count": 8}
{"name": "Finset.card_finsupp", "kind": "theorem", "module": "Mathlib.Data.Finset.Finsupp", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finsupp.pi", "kind": "definition", "module": "Mathlib.Data.Finset.Finsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.mem_pi", "kind": "theorem", "module": "Mathlib.Data.Finset.Finsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.card_pi", "kind": "theorem", "module": "Mathlib.Data.Finset.Finsupp", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "_private.Mathlib.Data.Finset.Fold.0.Finset.term_*_", "kind": "definition", "module": "Mathlib.Data.Finset.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.Finset.Fold.0.Finset._aux_Mathlib_Data_Finset_Fold___macroRules__private_Mathlib_Data_Finset_Fold_0_Finset_term_*__1", "kind": "definition", "module": "Mathlib.Data.Finset.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.fold", "kind": "definition", "module": "Mathlib.Data.Finset.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.fold_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.fold_cons", "kind": "theorem", "module": "Mathlib.Data.Finset.Fold", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "Finset.fold_insert", "kind": "theorem", "module": "Mathlib.Data.Finset.Fold", "is_tactic_proof": true, "tactics": ["unfold", "rw"], "tactic_count": 2}
{"name": "Finset.fold_singleton", "kind": "theorem", "module": "Mathlib.Data.Finset.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.fold_map", "kind": "theorem", "module": "Mathlib.Data.Finset.Fold", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.fold_image", "kind": "theorem", "module": "Mathlib.Data.Finset.Fold", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.fold_congr", "kind": "theorem", "module": "Mathlib.Data.Finset.Fold", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.fold_op_distrib", "kind": "theorem", "module": "Mathlib.Data.Finset.Fold", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.fold_const", "kind": "theorem", "module": "Mathlib.Data.Finset.Fold", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "insert", "simp", "split_ifs", "rw", "exact"], "tactic_count": 8}
{"name": "Finset.fold_hom", "kind": "theorem", "module": "Mathlib.Data.Finset.Fold", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Finset.fold_disjUnion", "kind": "theorem", "module": "Mathlib.Data.Finset.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.fold_union_inter", "kind": "theorem", "module": "Mathlib.Data.Finset.Fold", "is_tactic_proof": true, "tactics": ["unfold", "rw"], "tactic_count": 2}
{"name": "Finset.fold_insert_idem", "kind": "theorem", "module": "Mathlib.Data.Finset.Fold", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "simp", "apply"], "tactic_count": 4}
{"name": "Finset.fold_image_idem", "kind": "theorem", "module": "Mathlib.Data.Finset.Fold", "is_tactic_proof": true, "tactics": ["induction", "empty", "cons", "haveI", "rw", "simp"], "tactic_count": 6}
{"name": "Finset.fold_ite'", "kind": "theorem", "module": "Mathlib.Data.Finset.Fold", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "insert", "simp", "split_ifs", "have", "simp", "have", "simp"], "tactic_count": 10}
{"name": "Finset.fold_ite", "kind": "theorem", "module": "Mathlib.Data.Finset.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.fold_op_rel_iff_and", "kind": "theorem", "module": "Mathlib.Data.Finset.Fold", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "insert", "rw", "simp"], "tactic_count": 6}
{"name": "Finset.fold_op_rel_iff_or", "kind": "theorem", "module": "Mathlib.Data.Finset.Fold", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "insert", "rw", "simp"], "tactic_count": 6}
{"name": "Finset.fold_union_empty_singleton", "kind": "theorem", "module": "Mathlib.Data.Finset.Fold", "is_tactic_proof": true, "tactics": ["induction", "empty", "insert"], "tactic_count": 3}
{"name": "Finset.fold_sup_bot_singleton", "kind": "theorem", "module": "Mathlib.Data.Finset.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.le_fold_min", "kind": "theorem", "module": "Mathlib.Data.Finset.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.fold_min_le", "kind": "theorem", "module": "Mathlib.Data.Finset.Fold", "is_tactic_proof": true, "tactics": ["change", "apply", "intro", "change", "exact"], "tactic_count": 5}
{"name": "Finset.lt_fold_min", "kind": "theorem", "module": "Mathlib.Data.Finset.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.fold_min_lt", "kind": "theorem", "module": "Mathlib.Data.Finset.Fold", "is_tactic_proof": true, "tactics": ["change", "apply", "intro", "change", "exact"], "tactic_count": 5}
{"name": "Finset.fold_max_le", "kind": "theorem", "module": "Mathlib.Data.Finset.Fold", "is_tactic_proof": true, "tactics": ["change", "apply", "intro", "change", "exact"], "tactic_count": 5}
{"name": "Finset.le_fold_max", "kind": "theorem", "module": "Mathlib.Data.Finset.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.fold_max_lt", "kind": "theorem", "module": "Mathlib.Data.Finset.Fold", "is_tactic_proof": true, "tactics": ["change", "apply", "intro", "change", "exact"], "tactic_count": 5}
{"name": "Finset.lt_fold_max", "kind": "theorem", "module": "Mathlib.Data.Finset.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.functor", "kind": "instance", "module": "Mathlib.Data.Finset.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.lawfulFunctor", "kind": "instance", "module": "Mathlib.Data.Finset.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.fmap_def", "kind": "theorem", "module": "Mathlib.Data.Finset.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.pure", "kind": "instance", "module": "Mathlib.Data.Finset.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.pure_def", "kind": "theorem", "module": "Mathlib.Data.Finset.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.applicative", "kind": "instance", "module": "Mathlib.Data.Finset.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.seq_def", "kind": "theorem", "module": "Mathlib.Data.Finset.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.seqLeft_def", "kind": "theorem", "module": "Mathlib.Data.Finset.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.seqRight_def", "kind": "theorem", "module": "Mathlib.Data.Finset.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image₂_def", "kind": "theorem", "module": "Mathlib.Data.Finset.Functor", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Finset.lawfulApplicative", "kind": "instance", "module": "Mathlib.Data.Finset.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.commApplicative", "kind": "instance", "module": "Mathlib.Data.Finset.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.instMonad", "kind": "instance", "module": "Mathlib.Data.Finset.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.bind_def", "kind": "theorem", "module": "Mathlib.Data.Finset.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.instLawfulMonad", "kind": "instance", "module": "Mathlib.Data.Finset.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.instAlternativeMonad", "kind": "instance", "module": "Mathlib.Data.Finset.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.instLawfulAlternative", "kind": "instance", "module": "Mathlib.Data.Finset.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.traverse", "kind": "definition", "module": "Mathlib.Data.Finset.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.id_traverse", "kind": "theorem", "module": "Mathlib.Data.Finset.Functor", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finset.map_comp_coe", "kind": "theorem", "module": "Mathlib.Data.Finset.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.map_comp_coe_apply", "kind": "theorem", "module": "Mathlib.Data.Finset.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.map_traverse", "kind": "theorem", "module": "Mathlib.Data.Finset.Functor", "is_tactic_proof": true, "tactics": ["unfold", "simp"], "tactic_count": 2}
{"name": "Multiset.covBy_cons", "kind": "theorem", "module": "Mathlib.Data.Finset.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CovBy.exists_multiset_cons", "kind": "theorem", "module": "Mathlib.Data.Finset.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.covBy_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CovBy.card_multiset", "kind": "theorem", "module": "Mathlib.Data.Finset.Grade", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "Multiset.isAtom_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Grade", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.isAtom_singleton", "kind": "theorem", "module": "Mathlib.Data.Finset.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.instGradeMinOrder", "kind": "instance", "module": "Mathlib.Data.Finset.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.grade_eq", "kind": "theorem", "module": "Mathlib.Data.Finset.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.ordConnected_range_val", "kind": "theorem", "module": "Mathlib.Data.Finset.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.ordConnected_range_coe", "kind": "theorem", "module": "Mathlib.Data.Finset.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.val_wcovBy_val", "kind": "theorem", "module": "Mathlib.Data.Finset.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.val_covBy_val", "kind": "theorem", "module": "Mathlib.Data.Finset.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.coe_wcovBy_coe", "kind": "theorem", "module": "Mathlib.Data.Finset.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.coe_covBy_coe", "kind": "theorem", "module": "Mathlib.Data.Finset.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.covBy_cons", "kind": "theorem", "module": "Mathlib.Data.Finset.Grade", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CovBy.exists_finset_cons", "kind": "theorem", "module": "Mathlib.Data.Finset.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.covBy_iff_exists_cons", "kind": "theorem", "module": "Mathlib.Data.Finset.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CovBy.card_finset", "kind": "theorem", "module": "Mathlib.Data.Finset.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.wcovBy_insert", "kind": "theorem", "module": "Mathlib.Data.Finset.Grade", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.erase_wcovBy", "kind": "theorem", "module": "Mathlib.Data.Finset.Grade", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.covBy_insert", "kind": "theorem", "module": "Mathlib.Data.Finset.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.empty_covBy_singleton", "kind": "theorem", "module": "Mathlib.Data.Finset.Grade", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finset.erase_covBy", "kind": "theorem", "module": "Mathlib.Data.Finset.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CovBy.exists_finset_insert", "kind": "theorem", "module": "Mathlib.Data.Finset.Grade", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CovBy.exists_finset_erase", "kind": "theorem", "module": "Mathlib.Data.Finset.Grade", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.covBy_iff_exists_insert", "kind": "theorem", "module": "Mathlib.Data.Finset.Grade", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.covBy_iff_card_sdiff_eq_one", "kind": "theorem", "module": "Mathlib.Data.Finset.Grade", "is_tactic_proof": true, "tactics": ["rw", "constructor", "rintro", "simp", "simp_rw", "rintro", "refine", "rw"], "tactic_count": 8}
{"name": "Finset.covBy_iff_exists_erase", "kind": "theorem", "module": "Mathlib.Data.Finset.Grade", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.isAtom_singleton", "kind": "theorem", "module": "Mathlib.Data.Finset.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.isAtom_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Grade", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.isCoatom_compl_singleton", "kind": "theorem", "module": "Mathlib.Data.Finset.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.isCoatom_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Grade", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Finset.instGradeMinOrder_multiset", "kind": "instance", "module": "Mathlib.Data.Finset.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.grade_multiset_eq", "kind": "theorem", "module": "Mathlib.Data.Finset.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.instGradeMinOrder_nat", "kind": "instance", "module": "Mathlib.Data.Finset.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.grade_eq", "kind": "theorem", "module": "Mathlib.Data.Finset.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.map", "kind": "definition", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.map_val", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.map_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_map", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_map_equiv", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": true, "tactics": ["simp", "grind"], "tactic_count": 2}
{"name": "Finset.mem_map'", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_map_mk", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_map_of_mem", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.forall_mem_map", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.apply_coe_mem_map", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.coe_map", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.coe_map_subset_range", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.map_perm", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.map_toFinset", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.map_refl", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.map_cast_heq", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": true, "tactics": ["subst", "simp"], "tactic_count": 2}
{"name": "Finset.map_map", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.map_comm", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Function.Semiconj.finset_map", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Commute.finset_map", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.map_subset_map", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.subset_map_symm", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": true, "tactics": ["constructor", "simp", "simpa", "simp", "exact"], "tactic_count": 5}
{"name": "Finset.map_symm_subset", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.mapEmbedding", "kind": "definition", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.map_inj", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.map_injective", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.map_ssubset_map", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mapEmbedding_apply", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.filter_map", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.map_filter'", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.filter_attach'", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.filter_attach", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.map_filter", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.disjoint_map", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.map_union", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.map_inter", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.map_sdiff", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.map_singleton", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.map_insert", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.map_cons", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.map_eq_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.map_nonempty", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.map_nontrivial", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.attach_map_val", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.range_add_one'", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finset.image", "kind": "definition", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image_val", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_image", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.mem_image_of_mem", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.forall_mem_image", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.exists_mem_image", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.map_eq_image", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_image_const", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.mem_image_const_self", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.canLift", "kind": "instance", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image_congr", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": true, "tactics": ["ext", "simp_rw", "exact"], "tactic_count": 3}
{"name": "Function.Injective.mem_finset_image", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.coe_image", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image_nonempty", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Nonempty.image", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image_toFinset", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image_val_of_injOn", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image_id", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image_id'", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image_image", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image_comm", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Function.Semiconj.finset_image", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Commute.finset_image", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image_subset_image", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.image_subset_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image_mono", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image_injective", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.image_inj", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image_subset_image_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image_ssubset_image", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Finset.coe_image_subset_range", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.filter_image", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.fiber_nonempty_iff_mem_image", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.image_union", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image_inter_subset", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image_inter_of_injOn", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image_inter", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image_singleton", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.image_insert", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.erase_image_subset_image_erase", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.image_erase", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.image_eq_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image_sdiff", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image_sdiff_of_injOn", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Disjoint.of_image_finset", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_range_iff_mem_finset_range_of_mod_eq'", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "simp", "exact", "rintro", "simp", "rcases", "exact"], "tactic_count": 8}
{"name": "Finset.mem_range_iff_mem_finset_range_of_mod_eq", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.attach_image_val", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.attach_cons", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finset.attach_insert", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finset.disjoint_image", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image_const", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.map_erase", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Finset.filterMap", "kind": "definition", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.filterMap_val", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.filterMap_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_filterMap", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.coe_filterMap", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.filterMap_some", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.filterMap_mono", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "List.toFinset_filterMap", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.subtype", "kind": "definition", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_subtype", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.subtype_eq_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.subtype_mono", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.subtype_map", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Finset.subtype_map_of_mem", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.property_of_mem_map_subtype", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "Finset.notMem_map_subtype_of_not_property", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.map_subtype_subset", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": true, "tactics": ["intro", "rw", "convert"], "tactic_count": 3}
{"name": "Finset.subset_set_image_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": true, "tactics": ["constructor", "intro", "letI", "lift", "refine", "ext", "grind"], "tactic_count": 7}
{"name": "Finset.subset_image_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.subset_univ_image_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.range_sdiff_zero", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "conv_rhs", "rw", "simp"], "tactic_count": 6}
{"name": "Multiset.toFinset_map", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.finsetCongr", "kind": "definition", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.finsetCongr_apply", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.finsetCongr_refl", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Equiv.finsetCongr_symm", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.finsetCongr_trans", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Equiv.finsetCongr_toEmbedding", "kind": "theorem", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.finsetSubtypeComm", "kind": "definition", "module": "Mathlib.Data.Finset.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.instSingleton", "kind": "instance", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.singleton_val", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_singleton", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.eq_of_mem_singleton", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.notMem_singleton", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_singleton_self", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.val_eq_singleton_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Finset.singleton_injective", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.singleton_inj", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.singleton_nonempty", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.singleton_ne_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.empty_ne_singleton", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.empty_ssubset_singleton", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.coe_singleton", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.coe_eq_singleton", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.coe_subset_singleton", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.singleton_subset_coe", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.eq_singleton_iff_unique_mem", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.eq_singleton_iff_nonempty_unique_mem", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.nonempty_iff_eq_singleton_default", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.singleton_iff_unique_mem", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.singleton_subset_set_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.singleton_subset_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.subset_singleton_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.singleton_subset_singleton", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.Nonempty.subset_singleton_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.subset_singleton_iff'", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.ssubset_singleton_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.eq_empty_of_ssubset_singleton", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Nontrivial", "kind": "abbrev", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.nontrivial_def", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Nontrivial.nonempty", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.not_nontrivial_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.not_nontrivial_singleton", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.Nontrivial.ne_singleton", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "Finset.Nontrivial.exists_ne", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.eq_singleton_or_nontrivial", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.nontrivial_iff_ne_singleton", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Nonempty.exists_eq_singleton_or_nontrivial", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.nontrivial_coe", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Nontrivial.not_subset_singleton", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.instNontrivial", "kind": "instance", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.instUniqueOfIsEmpty", "kind": "instance", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.instUniqueSubtypeMemSingleton", "kind": "instance", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.default_singleton", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Nontrivial.instDecidablePred", "kind": "instance", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.cons", "kind": "definition", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_cons", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_cons_of_mem", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_cons_self", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.cons_val", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.eq_of_mem_cons_of_notMem", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_of_mem_cons_of_ne", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.forall_mem_cons", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.forall_of_forall_cons", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mk_cons", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.cons_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.cons_nonempty", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.cons_ne_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.nonempty_mk", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "Finset.coe_cons", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Finset.subset_cons", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.ssubset_cons", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.cons_subset", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.cons_subset_cons", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Finset.ssubset_iff_exists_cons_subset", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.cons_swap", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.consPiProd", "kind": "definition", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prodPiCons", "kind": "definition", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.consPiProdEquiv", "kind": "definition", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.instInsert", "kind": "instance", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.insert_def", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.insert_val", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.insert_val'", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.insert_val_of_notMem", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.mem_insert", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_insert_self", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_insert_of_mem", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_of_mem_insert_of_ne", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.eq_of_mem_insert_of_notMem", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.insert_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.cons_eq_insert", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.coe_insert", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.mem_insert_coe", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.instLawfulSingleton", "kind": "instance", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.insert_eq_of_mem", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.insert_eq_self", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.insert_ne_self", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.pair_eq_singleton", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.insert_comm", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.coe_pair", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.coe_eq_pair", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.pair_comm", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.insert_idem", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.insert_nonempty", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.insert_ne_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.instNonemptyElemCoeInsert", "kind": "instance", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.ne_insert_of_notMem", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": true, "tactics": ["contrapose", "simp"], "tactic_count": 2}
{"name": "Finset.insert_subset_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.insert_subset", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.subset_insert", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.insert_subset_insert", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.insert_subset_insert_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Finset.insert_inj", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.insert_inj_on", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.ssubset_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.ssubset_insert", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.cons_induction", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.cons_induction_on", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.induction", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.induction_on", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.induction_on'", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Nonempty.cons_induction", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": true, "tactics": ["induction", "empty", "cons", "obtain", "exact", "exact", "cons"], "tactic_count": 7}
{"name": "Finset.Nonempty.exists_cons_eq", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.subtypeInsertEquivOption", "kind": "definition", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.insertPiProd", "kind": "definition", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prodPiInsert", "kind": "definition", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.insertPiProdEquiv", "kind": "definition", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.exists_mem_insert", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.forall_mem_insert", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.forall_of_forall_insert", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.toFinset_zero", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.toFinset_cons", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.toFinset_singleton", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.toFinset_nil", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.toFinset_cons", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.toFinset_replicate_of_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "List.toFinset_eq_empty_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "List.toFinset_nonempty_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.toList_eq_singleton_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.toList_singleton", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.toList_cons", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.toList_insert", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.pairwise_cons'", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": true, "tactics": ["simp", "grind"], "tactic_count": 2}
{"name": "Finset.pairwise_cons", "kind": "theorem", "module": "Mathlib.Data.Finset.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.instLocallyFiniteOrder", "kind": "instance", "module": "Mathlib.Data.Finset.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Icc_eq_filter_powerset", "kind": "theorem", "module": "Mathlib.Data.Finset.Interval", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finset.Ico_eq_filter_ssubsets", "kind": "theorem", "module": "Mathlib.Data.Finset.Interval", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finset.Ioc_eq_filter_powerset", "kind": "theorem", "module": "Mathlib.Data.Finset.Interval", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finset.Ioo_eq_filter_ssubsets", "kind": "theorem", "module": "Mathlib.Data.Finset.Interval", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finset.Iic_eq_powerset", "kind": "theorem", "module": "Mathlib.Data.Finset.Interval", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finset.Iio_eq_ssubsets", "kind": "theorem", "module": "Mathlib.Data.Finset.Interval", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finset.Icc_eq_image_powerset", "kind": "theorem", "module": "Mathlib.Data.Finset.Interval", "is_tactic_proof": true, "tactics": ["unfold", "ext", "simp"], "tactic_count": 3}
{"name": "Finset.Ico_eq_image_ssubsets", "kind": "theorem", "module": "Mathlib.Data.Finset.Interval", "is_tactic_proof": true, "tactics": ["ext", "simp_rw", "constructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 7}
{"name": "Finset.card_Icc_finset", "kind": "theorem", "module": "Mathlib.Data.Finset.Interval", "is_tactic_proof": true, "tactics": ["unfold", "simp"], "tactic_count": 2}
{"name": "Finset.card_Ico_finset", "kind": "theorem", "module": "Mathlib.Data.Finset.Interval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.card_Ioc_finset", "kind": "theorem", "module": "Mathlib.Data.Finset.Interval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.card_Ioo_finset", "kind": "theorem", "module": "Mathlib.Data.Finset.Interval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.card_Iic_finset", "kind": "theorem", "module": "Mathlib.Data.Finset.Interval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.card_Iio_finset", "kind": "theorem", "module": "Mathlib.Data.Finset.Interval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.monotone_iff_forall_le_cons", "kind": "theorem", "module": "Mathlib.Data.Finset.Interval", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finset.antitone_iff_forall_cons_le", "kind": "theorem", "module": "Mathlib.Data.Finset.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.strictMono_iff_forall_lt_cons", "kind": "theorem", "module": "Mathlib.Data.Finset.Interval", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finset.strictAnti_iff_forall_cons_lt", "kind": "theorem", "module": "Mathlib.Data.Finset.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.monotone_iff_forall_le_insert", "kind": "theorem", "module": "Mathlib.Data.Finset.Interval", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.antitone_iff_forall_insert_le", "kind": "theorem", "module": "Mathlib.Data.Finset.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.strictMono_iff_forall_lt_insert", "kind": "theorem", "module": "Mathlib.Data.Finset.Interval", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.strictAnti_iff_forall_lt_insert", "kind": "theorem", "module": "Mathlib.Data.Finset.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.instUnion", "kind": "instance", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.instInter", "kind": "instance", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.instLattice", "kind": "instance", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sup_eq_union'", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sup_eq_union", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inf_eq_inter'", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inf_eq_inter", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.union_val_nd", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.union_val", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_union", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_union_left", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_union_right", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.forall_mem_union", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.notMem_union", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.coe_union", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.union_subset", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.subset_union_left", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.subset_union_right", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.union_subset_union", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.union_subset_union_left", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.union_subset_union_right", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.union_comm", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.instCommutativeUnion", "kind": "instance", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.union_assoc", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.instAssociativeUnion", "kind": "instance", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.union_idempotent", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.instIdempotentOpUnion", "kind": "instance", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.union_subset_left", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.union_subset_right", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.union_left_comm", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.union_right_comm", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.union_self", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.union_eq_left", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.left_eq_union", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.union_eq_right", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.right_eq_union", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.union_congr_left", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.union_congr_right", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.union_eq_union_iff_left", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.union_eq_union_iff_right", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inter_val_nd", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inter_val", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_inter", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_of_mem_inter_left", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_of_mem_inter_right", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_inter_of_mem", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inter_subset_left", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inter_subset_right", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.subset_inter", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.coe_inter", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.union_inter_cancel_left", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.union_inter_cancel_right", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.inter_comm", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.inter_assoc", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.inter_left_comm", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.inter_right_comm", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.inter_self", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inter_union_self", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.inter_subset_inter", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.inter_subset_inter_left", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inter_subset_inter_right", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inter_subset_union", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.instDistribLattice", "kind": "instance", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.union_left_idem", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.union_right_idem", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inter_left_idem", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inter_right_idem", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inter_union_distrib_left", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.union_inter_distrib_right", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.union_inter_distrib_left", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inter_union_distrib_right", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.union_union_distrib_left", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.union_union_distrib_right", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inter_inter_distrib_left", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inter_inter_distrib_right", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.union_union_union_comm", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inter_inter_inter_comm", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.union_subset_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.subset_inter_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inter_eq_left", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inter_eq_right", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inter_congr_left", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inter_congr_right", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inter_eq_inter_iff_left", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inter_eq_inter_iff_right", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.ite_subset_union", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inter_subset_ite", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sup", "kind": "definition", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sup_def", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sup_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sup_cons", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sup_insert", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sup_image", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sup_map", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sup_singleton", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sup_sup", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": true, "tactics": ["induction", "empty", "cons", "rw", "exact"], "tactic_count": 5}
{"name": "Finset.sup_congr", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": true, "tactics": ["subst", "exact"], "tactic_count": 2}
{"name": "map_finset_sup", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sup_le_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": true, "tactics": ["apply", "simp", "exact"], "tactic_count": 3}
{"name": "Finset.sup_const_le", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.le_sup", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.isLUB_sup", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.isLUB_sup_id", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.le_sup_of_le", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sup_union", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sup_const", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sup_bot", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": true, "tactics": ["obtain", "exact", "exact"], "tactic_count": 3}
{"name": "Finset.sup_ite", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sup_mono_fun", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sup_mono", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sup_comm", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sup_attach", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sup_erase_bot", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact", "exact"], "tactic_count": 4}
{"name": "Finset.sup_sdiff_right", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": true, "tactics": ["induction", "empty", "cons"], "tactic_count": 3}
{"name": "Finset.comp_sup_eq_sup_comp", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sup_coe", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": true, "tactics": ["letI", "letI", "apply"], "tactic_count": 3}
{"name": "Finset.sup_toFinset", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.foldr_sup_eq_sup_toFinset", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Finset.subset_range_sup_succ", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sup_induction", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": true, "tactics": ["induction", "empty", "cons", "simp", "exact"], "tactic_count": 5}
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{"name": "Finset.sup_mem", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sup_eq_bot_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finset.sup_disjSum", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sup_eq_bot_of_isEmpty", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finset.le_sup_dite_pos", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.le_sup_dite_neg", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.sup_eq_iSup", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sup_id_eq_sSup", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.sup_id_set_eq_sUnion", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sup_set_eq_biUnion", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sup_eq_sSup_image", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finset.exists_sup_ge", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": true, "tactics": ["cases", "exact", "obtain", "refine", "classical", "have", "rwa"], "tactic_count": 7}
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{"name": "Finset.inf", "kind": "definition", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inf_def", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inf_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inf_cons", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inf_insert", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Finset.inf_inf", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "map_finset_inf", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.le_inf_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.le_inf_const_le", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inf_le", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.isGLB_inf", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.isGLB_inf_id", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.inf_le_of_le", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Finset.inf_top", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Finset.inf_mono_fun", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Finset.inf_attach", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inf_erase_top", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.comp_inf_eq_inf_comp", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inf_coe", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.foldr_inf_eq_inf_toFinset", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Finset.inf_induction", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Finset.inf_eq_top_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Finset.inf_dite_pos_le", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": true, "tactics": ["have", "rw", "apply"], "tactic_count": 3}
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{"name": "Finset.toDual_sup", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.toDual_inf", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.ofDual_sup", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.ofDual_inf", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sup_inf_distrib_left", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": true, "tactics": ["induction", "empty", "cons"], "tactic_count": 3}
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{"name": "Finset.codisjoint_inf_right", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Finset.comp_sup_eq_sup_comp_of_is_total", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Finset.Nonempty.sup_eq_top_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": true, "tactics": ["cases", "simpa", "exact"], "tactic_count": 3}
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{"name": "Finset.sup_mem_of_nonempty", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "insert", "rw", "cases", "inl", "inr", "simp", "rcases", "rw", "exact", "rw", "apply"], "tactic_count": 14}
{"name": "Finset.comp_inf_eq_inf_comp_of_is_total", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Finset.inf_eq_bot_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Nonempty.inf_eq_bot_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inf_lt_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Finset.inf_eq_iInf", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inf_id_eq_sInf", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inf_id_set_eq_sInter", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inf_set_eq_iInter", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inf_eq_sInf_image", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.exists_inf_le", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.exists_inf_eq_iInf", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sup_of_mem", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Finset.coe_sup'", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.sup'_cons", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Finset.sup'_insert", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Finset.sup'_singleton", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Finset.isLUB_sup'", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.le_sup'_of_le", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sup'_eq_of_forall", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sup'_const", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Finset.comp_sup'_eq_sup'_comp", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": true, "tactics": ["refine"], "tactic_count": 1}
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{"name": "Finset.sup'_comp_eq_image", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Finset.inf_of_mem", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Finset.isGLB_inf'", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Finset.inf'_congr", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Finset.inf'_comp_eq_image", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Finset.coe_sup_of_nonempty", "kind": "theorem", "module": "Mathlib.Data.Finset.Lattice.Fold", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "Finset.coe_image₂", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Finset.image₂_empty_right", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image₂_eq_empty_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": true, "tactics": ["contrapose"], "tactic_count": 1}
{"name": "Finset.image₂_singleton_left", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image₂_singleton_right", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image₂_singleton_left'", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image₂_singleton", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.image₂_union_left", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image₂_union_right", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image₂_insert_left", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image₂_insert_right", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image₂_inter_left", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image₂_inter_right", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image₂_inter_subset_left", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image₂_inter_subset_right", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image₂_congr", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image₂_congr'", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_image₂_singleton_left", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.card_image₂_singleton_right", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.image₂_singleton_inter", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Finset.image₂_inter_singleton", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Finset.card_le_card_image₂_left", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_le_card_image₂_right", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.biUnion_image_left", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.biUnion_image_right", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image_image₂", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image₂_image_left", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image₂_image_right", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image₂_mk_eq_product", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finset.image₂_curry", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image_uncurry_product", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image₂_swap", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image₂_left", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image₂_right", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image₂_assoc", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image₂_comm", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image₂_left_comm", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image₂_right_comm", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image₂_image₂_image₂_comm", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image_image₂_distrib", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image_image₂_distrib_left", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image_image₂_distrib_right", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image₂_image_left_comm", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image_image₂_right_comm", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image₂_distrib_subset_left", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image₂_distrib_subset_right", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image_image₂_antidistrib", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finset.image_image₂_antidistrib_left", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image_image₂_antidistrib_right", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image₂_image_left_anticomm", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image_image₂_right_anticomm", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image₂_left_identity", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image₂_right_identity", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.card_dvd_card_image₂_right", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "insert", "specialize", "rw", "by_cases", "rw", "exact", "simp_rw", "obtain", "rwa", "exact", "h).trans_subset"], "tactic_count": 14}
{"name": "Finset.card_dvd_card_image₂_left", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.subset_set_image₂", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": true, "tactics": ["rw", "rcases", "classical", "use", "simp", "exact"], "tactic_count": 6}
{"name": "Finset.image₂_inter_union_subset_union", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image₂_union_inter_subset_union", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image₂_inter_union_subset", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image₂_union_inter_subset", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sup'_image₂_le", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.sup'_image₂_left", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.sup'_image₂_right", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.sup_image₂_le", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.sup_image₂_left", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.sup_image₂_right", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.le_inf'_image₂", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.inf'_image₂_left", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inf'_image₂_right", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.le_inf_image₂", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inf_image₂_left", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inf_image₂_right", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.piFinset_image₂", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Set.toFinset_image2", "kind": "theorem", "module": "Mathlib.Data.Finset.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Nat.instHasAntidiagonal", "kind": "instance", "module": "Mathlib.Data.Finset.NatAntidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Nat.antidiagonal_eq_map", "kind": "theorem", "module": "Mathlib.Data.Finset.NatAntidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Nat.antidiagonal_eq_map'", "kind": "theorem", "module": "Mathlib.Data.Finset.NatAntidiagonal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.Nat.antidiagonal_eq_image", "kind": "theorem", "module": "Mathlib.Data.Finset.NatAntidiagonal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.Nat.antidiagonal_eq_image'", "kind": "theorem", "module": "Mathlib.Data.Finset.NatAntidiagonal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.Nat.card_antidiagonal", "kind": "theorem", "module": "Mathlib.Data.Finset.NatAntidiagonal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.Nat.antidiagonal_zero", "kind": "theorem", "module": "Mathlib.Data.Finset.NatAntidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Nat.antidiagonal_succ", "kind": "theorem", "module": "Mathlib.Data.Finset.NatAntidiagonal", "is_tactic_proof": true, "tactics": ["apply", "rw", "apply"], "tactic_count": 3}
{"name": "Finset.Nat.antidiagonal_succ'", "kind": "theorem", "module": "Mathlib.Data.Finset.NatAntidiagonal", "is_tactic_proof": true, "tactics": ["apply", "rw", "exact"], "tactic_count": 3}
{"name": "Finset.Nat.antidiagonal_succ_succ'", "kind": "theorem", "module": "Mathlib.Data.Finset.NatAntidiagonal", "is_tactic_proof": true, "tactics": ["simp_rw", "rfl"], "tactic_count": 2}
{"name": "Finset.Nat.antidiagonal.fst_lt", "kind": "theorem", "module": "Mathlib.Data.Finset.NatAntidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Nat.antidiagonal.snd_lt", "kind": "theorem", "module": "Mathlib.Data.Finset.NatAntidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Nat.antidiagonal_filter_snd_le_of_le", "kind": "theorem", "module": "Mathlib.Data.Finset.NatAntidiagonal", "is_tactic_proof": true, "tactics": ["ext", "suffices", "refine", "rw", "rintro", "refine", "rw", "exact"], "tactic_count": 8}
{"name": "Finset.Nat.antidiagonal_filter_fst_le_of_le", "kind": "theorem", "module": "Mathlib.Data.Finset.NatAntidiagonal", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "simp_rw", "ext", "simpa"], "tactic_count": 6}
{"name": "Finset.Nat.antidiagonal_filter_le_fst_of_le", "kind": "theorem", "module": "Mathlib.Data.Finset.NatAntidiagonal", "is_tactic_proof": true, "tactics": ["ext", "suffices", "refine", "rw", "rintro", "refine", "rw", "exact"], "tactic_count": 8}
{"name": "Finset.Nat.antidiagonal_filter_le_snd_of_le", "kind": "theorem", "module": "Mathlib.Data.Finset.NatAntidiagonal", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "simp_rw", "ext", "simpa"], "tactic_count": 6}
{"name": "Finset.Nat.antidiagonalEquivFin", "kind": "definition", "module": "Mathlib.Data.Finset.NatAntidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.divisors_mul", "kind": "theorem", "module": "Mathlib.Data.Finset.NatDivisors", "is_tactic_proof": true, "tactics": ["ext", "simp_rw", "simp"], "tactic_count": 3}
{"name": "Nat.divisorsHom", "kind": "definition", "module": "Mathlib.Data.Finset.NatDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Prime.divisors_sq", "kind": "theorem", "module": "Mathlib.Data.Finset.NatDivisors", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.nat_divisors_prod", "kind": "theorem", "module": "Mathlib.Data.Finset.NatDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.nat_divisors_prod", "kind": "theorem", "module": "Mathlib.Data.Finset.NatDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.nat_divisors_prod", "kind": "theorem", "module": "Mathlib.Data.Finset.NatDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.noncommFoldr", "kind": "definition", "module": "Mathlib.Data.Finset.NoncommProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.noncommFoldr_coe", "kind": "theorem", "module": "Mathlib.Data.Finset.NoncommProd", "is_tactic_proof": true, "tactics": ["simp", "rw", "simp"], "tactic_count": 3}
{"name": "Multiset.noncommFoldr_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.NoncommProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.noncommFoldr_cons", "kind": "theorem", "module": "Mathlib.Data.Finset.NoncommProd", "is_tactic_proof": true, "tactics": ["induction", "simp"], "tactic_count": 2}
{"name": "Multiset.noncommFoldr_eq_foldr", "kind": "theorem", "module": "Mathlib.Data.Finset.NoncommProd", "is_tactic_proof": true, "tactics": ["induction", "simp"], "tactic_count": 2}
{"name": "Multiset.noncommFold", "kind": "definition", "module": "Mathlib.Data.Finset.NoncommProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.noncommFold_coe", "kind": "theorem", "module": "Mathlib.Data.Finset.NoncommProd", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.noncommFold_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.NoncommProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.noncommFold_cons", "kind": "theorem", "module": "Mathlib.Data.Finset.NoncommProd", "is_tactic_proof": true, "tactics": ["induction", "simp"], "tactic_count": 2}
{"name": "Multiset.noncommFold_eq_fold", "kind": "theorem", "module": "Mathlib.Data.Finset.NoncommProd", "is_tactic_proof": true, "tactics": ["induction", "simp"], "tactic_count": 2}
{"name": "Multiset.noncommProd", "kind": "definition", "module": "Mathlib.Data.Finset.NoncommProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.noncommProd_coe", "kind": "theorem", "module": "Mathlib.Data.Finset.NoncommProd", "is_tactic_proof": true, "tactics": ["rw", "simp", "induction", "nil", "cons", "rw", "intro", "exact"], "tactic_count": 8}
{"name": "Multiset.noncommProd_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.NoncommProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.noncommProd_cons", "kind": "theorem", "module": "Mathlib.Data.Finset.NoncommProd", "is_tactic_proof": true, "tactics": ["induction", "simp"], "tactic_count": 2}
{"name": "Multiset.noncommProd_cons'", "kind": "theorem", "module": "Mathlib.Data.Finset.NoncommProd", "is_tactic_proof": false, "tactics": ["induction", "simp", "induction", "nil", "cons", "rw", "congr", "apply", "intro", "simp", "apply", "cases", "cases"], "tactic_count": 13}
{"name": "Multiset.noncommProd_add", "kind": "theorem", "module": "Mathlib.Data.Finset.NoncommProd", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "simp"], "tactic_count": 3}
{"name": "Multiset.noncommProd_induction", "kind": "theorem", "module": "Mathlib.Data.Finset.NoncommProd", "is_tactic_proof": false, "tactics": ["induction", "simp", "exact"], "tactic_count": 3}
{"name": "Multiset.map_noncommProd_aux", "kind": "theorem", "module": "Mathlib.Data.Finset.NoncommProd", "is_tactic_proof": true, "tactics": ["simp", "rintro", "exact"], "tactic_count": 3}
{"name": "Multiset.map_noncommProd", "kind": "theorem", "module": "Mathlib.Data.Finset.NoncommProd", "is_tactic_proof": true, "tactics": ["induction", "simpa"], "tactic_count": 2}
{"name": "Multiset.noncommProd_eq_pow_card", "kind": "theorem", "module": "Mathlib.Data.Finset.NoncommProd", "is_tactic_proof": true, "tactics": ["induction", "simp", "exact"], "tactic_count": 3}
{"name": "Multiset.noncommProd_eq_prod", "kind": "theorem", "module": "Mathlib.Data.Finset.NoncommProd", "is_tactic_proof": true, "tactics": ["induction", "simp"], "tactic_count": 2}
{"name": "Multiset.noncommProd_commute", "kind": "theorem", "module": "Mathlib.Data.Finset.NoncommProd", "is_tactic_proof": true, "tactics": ["induction", "simp", "exact"], "tactic_count": 3}
{"name": "Finset.noncommProd_lemma", "kind": "theorem", "module": "Mathlib.Data.Finset.NoncommProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.noncommProd", "kind": "definition", "module": "Mathlib.Data.Finset.NoncommProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.noncommProd_induction", "kind": "theorem", "module": "Mathlib.Data.Finset.NoncommProd", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact"], "tactic_count": 3}
{"name": "Finset.noncommProd_congr", "kind": "theorem", "module": "Mathlib.Data.Finset.NoncommProd", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Finset.noncommProd_toFinset", "kind": "theorem", "module": "Mathlib.Data.Finset.NoncommProd", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Finset.noncommProd_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.NoncommProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.noncommProd_cons", "kind": "theorem", "module": "Mathlib.Data.Finset.NoncommProd", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Finset.noncommProd_cons'", "kind": "theorem", "module": "Mathlib.Data.Finset.NoncommProd", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Finset.noncommProd_insert_of_notMem", "kind": "theorem", "module": "Mathlib.Data.Finset.NoncommProd", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.noncommProd_insert_of_notMem'", "kind": "theorem", "module": "Mathlib.Data.Finset.NoncommProd", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.noncommProd_singleton", "kind": "theorem", "module": "Mathlib.Data.Finset.NoncommProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.map_noncommProd", "kind": "theorem", "module": "Mathlib.Data.Finset.NoncommProd", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.noncommProd_eq_pow_card", "kind": "theorem", "module": "Mathlib.Data.Finset.NoncommProd", "is_tactic_proof": true, "tactics": ["rw", "simp", "simpa"], "tactic_count": 3}
{"name": "Finset.noncommProd_commute", "kind": "theorem", "module": "Mathlib.Data.Finset.NoncommProd", "is_tactic_proof": true, "tactics": ["apply", "intro", "rw", "rintro", "exact"], "tactic_count": 5}
{"name": "Finset.noncommProd_eq_prod", "kind": "theorem", "module": "Mathlib.Data.Finset.NoncommProd", "is_tactic_proof": true, "tactics": ["induction", "empty", "cons"], "tactic_count": 3}
{"name": "Finset.noncommProd_union_of_disjoint", "kind": "theorem", "module": "Mathlib.Data.Finset.NoncommProd", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "rw", "calc", "noncommProd", "noncommProd", "noncommProd"], "tactic_count": 7}
{"name": "Finset.noncommProd_mul_distrib_aux", "kind": "theorem", "module": "Mathlib.Data.Finset.NoncommProd", "is_tactic_proof": true, "tactics": ["intro", "apply", "exact", "exact", "exact", "exact"], "tactic_count": 6}
{"name": "Finset.noncommProd_mul_distrib", "kind": "theorem", "module": "Mathlib.Data.Finset.NoncommProd", "is_tactic_proof": true, "tactics": ["induction", "empty", "cons", "ih", "rw", "ih", "exact"], "tactic_count": 7}
{"name": "Finset.noncommProd_mulSingle", "kind": "theorem", "module": "Mathlib.Data.Finset.NoncommProd", "is_tactic_proof": true, "tactics": ["ext", "apply", "intro", "exact", "convert", "intro", "exact", "intro", "rw", "mul_one]", "simp", "intro", "simp", "simp", "intro", "simp"], "tactic_count": 16}
{"name": "MonoidHom.pi_ext", "kind": "theorem", "module": "Mathlib.Data.Finset.NoncommProd", "is_tactic_proof": true, "tactics": ["cases", "ext", "rw", "congr"], "tactic_count": 4}
{"name": "Option.toFinset", "kind": "definition", "module": "Mathlib.Data.Finset.Option", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Option.toFinset_none", "kind": "theorem", "module": "Mathlib.Data.Finset.Option", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Option.toFinset_some", "kind": "theorem", "module": "Mathlib.Data.Finset.Option", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Option.mem_toFinset", "kind": "theorem", "module": "Mathlib.Data.Finset.Option", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Option.card_toFinset", "kind": "theorem", "module": "Mathlib.Data.Finset.Option", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Finset.insertNone", "kind": "definition", "module": "Mathlib.Data.Finset.Option", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_insertNone", "kind": "theorem", "module": "Mathlib.Data.Finset.Option", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.forall_mem_insertNone", "kind": "theorem", "module": "Mathlib.Data.Finset.Option", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.some_mem_insertNone", "kind": "theorem", "module": "Mathlib.Data.Finset.Option", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.none_mem_insertNone", "kind": "theorem", "module": "Mathlib.Data.Finset.Option", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.insertNone_nonempty", "kind": "theorem", "module": "Mathlib.Data.Finset.Option", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_insertNone", "kind": "theorem", "module": "Mathlib.Data.Finset.Option", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.eraseNone", "kind": "definition", "module": "Mathlib.Data.Finset.Option", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_eraseNone", "kind": "theorem", "module": "Mathlib.Data.Finset.Option", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.forall_mem_eraseNone", "kind": "theorem", "module": "Mathlib.Data.Finset.Option", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.eraseNone_eq_biUnion", "kind": "theorem", "module": "Mathlib.Data.Finset.Option", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Finset.eraseNone_map_some", "kind": "theorem", "module": "Mathlib.Data.Finset.Option", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Finset.eraseNone_image_some", "kind": "theorem", "module": "Mathlib.Data.Finset.Option", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.coe_eraseNone", "kind": "theorem", "module": "Mathlib.Data.Finset.Option", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.eraseNone_union", "kind": "theorem", "module": "Mathlib.Data.Finset.Option", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Finset.eraseNone_inter", "kind": "theorem", "module": "Mathlib.Data.Finset.Option", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Finset.eraseNone_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.Option", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Finset.eraseNone_none", "kind": "theorem", "module": "Mathlib.Data.Finset.Option", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Finset.image_some_eraseNone", "kind": "theorem", "module": "Mathlib.Data.Finset.Option", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finset.map_some_eraseNone", "kind": "theorem", "module": "Mathlib.Data.Finset.Option", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.insertNone_eraseNone", "kind": "theorem", "module": "Mathlib.Data.Finset.Option", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finset.eraseNone_insertNone", "kind": "theorem", "module": "Mathlib.Data.Finset.Option", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Finset.card_eraseNone_eq_card_erase", "kind": "theorem", "module": "Mathlib.Data.Finset.Option", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.card_eraseNone_le", "kind": "theorem", "module": "Mathlib.Data.Finset.Option", "is_tactic_proof": true, "tactics": ["classical", "rw", "apply"], "tactic_count": 3}
{"name": "Finset.card_eraseNone_of_mem", "kind": "theorem", "module": "Mathlib.Data.Finset.Option", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finset.card_eraseNone_of_not_mem", "kind": "theorem", "module": "Mathlib.Data.Finset.Option", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Directed.finset_le", "kind": "theorem", "module": "Mathlib.Data.Finset.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.exists_le", "kind": "theorem", "module": "Mathlib.Data.Finset.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.toFinset", "kind": "definition", "module": "Mathlib.Data.Finset.PImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.mem_toFinset", "kind": "theorem", "module": "Mathlib.Data.Finset.PImage", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Part.toFinset_none", "kind": "theorem", "module": "Mathlib.Data.Finset.PImage", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Part.toFinset_some", "kind": "theorem", "module": "Mathlib.Data.Finset.PImage", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Part.coe_toFinset", "kind": "theorem", "module": "Mathlib.Data.Finset.PImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.pimage", "kind": "definition", "module": "Mathlib.Data.Finset.PImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_pimage", "kind": "theorem", "module": "Mathlib.Data.Finset.PImage", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.coe_pimage", "kind": "theorem", "module": "Mathlib.Data.Finset.PImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.pimage_some", "kind": "theorem", "module": "Mathlib.Data.Finset.PImage", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Finset.pimage_congr", "kind": "theorem", "module": "Mathlib.Data.Finset.PImage", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Finset.pimage_eq_image_filter", "kind": "theorem", "module": "Mathlib.Data.Finset.PImage", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Finset.pimage_union", "kind": "theorem", "module": "Mathlib.Data.Finset.PImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.pimage_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.PImage", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Finset.pimage_subset", "kind": "theorem", "module": "Mathlib.Data.Finset.PImage", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.pimage_mono", "kind": "theorem", "module": "Mathlib.Data.Finset.PImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.pimage_inter", "kind": "theorem", "module": "Mathlib.Data.Finset.PImage", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "instDecidablePairwiseCoeFinsetOfDecidableEqOfDecidableRel", "kind": "instance", "module": "Mathlib.Data.Finset.Pairwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.pairwiseDisjoint_range_singleton", "kind": "theorem", "module": "Mathlib.Data.Finset.Pairwise", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "Set.PairwiseDisjoint.elim_finset", "kind": "theorem", "module": "Mathlib.Data.Finset.Pairwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.PairwiseDisjoint.image_finset_of_le", "kind": "theorem", "module": "Mathlib.Data.Finset.Pairwise", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.PairwiseDisjoint.attach", "kind": "theorem", "module": "Mathlib.Data.Finset.Pairwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.PairwiseDisjoint.biUnion_finset", "kind": "theorem", "module": "Mathlib.Data.Finset.Pairwise", "is_tactic_proof": true, "tactics": ["rintro", "simp_rw", "obtain", "obtain", "obtain", "exact", "exact"], "tactic_count": 7}
{"name": "List.pairwise_of_coe_toFinset_pairwise", "kind": "theorem", "module": "Mathlib.Data.Finset.Pairwise", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "List.pairwise_iff_coe_toFinset_pairwise", "kind": "theorem", "module": "Mathlib.Data.Finset.Pairwise", "is_tactic_proof": true, "tactics": ["letI", "rw"], "tactic_count": 2}
{"name": "List.pairwise_disjoint_of_coe_toFinset_pairwiseDisjoint", "kind": "theorem", "module": "Mathlib.Data.Finset.Pairwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.pairwiseDisjoint_iff_coe_toFinset_pairwise_disjoint", "kind": "theorem", "module": "Mathlib.Data.Finset.Pairwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Pi.empty", "kind": "definition", "module": "Mathlib.Data.Finset.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.pi", "kind": "definition", "module": "Mathlib.Data.Finset.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.pi_val", "kind": "theorem", "module": "Mathlib.Data.Finset.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_pi", "kind": "theorem", "module": "Mathlib.Data.Finset.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Pi.cons", "kind": "definition", "module": "Mathlib.Data.Finset.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Pi.cons_same", "kind": "theorem", "module": "Mathlib.Data.Finset.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Pi.cons_ne", "kind": "theorem", "module": "Mathlib.Data.Finset.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Pi.cons_injective", "kind": "theorem", "module": "Mathlib.Data.Finset.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.pi_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.pi_nonempty", "kind": "theorem", "module": "Mathlib.Data.Finset.Pi", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.pi_eq_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.Pi", "is_tactic_proof": true, "tactics": ["contrapose"], "tactic_count": 1}
{"name": "Finset.pi_insert", "kind": "theorem", "module": "Mathlib.Data.Finset.Pi", "is_tactic_proof": true, "tactics": ["apply", "rw", "refine", "dedup", "dedup", "dedup", "subst", "congr", "exact"], "tactic_count": 9}
{"name": "Finset.pi_singletons", "kind": "theorem", "module": "Mathlib.Data.Finset.Pi", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.pi_const_singleton", "kind": "theorem", "module": "Mathlib.Data.Finset.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.pi_subset", "kind": "theorem", "module": "Mathlib.Data.Finset.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.pi_disjoint_of_disjoint", "kind": "theorem", "module": "Mathlib.Data.Finset.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.piDiag", "kind": "definition", "module": "Mathlib.Data.Finset.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_piDiag", "kind": "theorem", "module": "Mathlib.Data.Finset.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_piDiag", "kind": "theorem", "module": "Mathlib.Data.Finset.Pi", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.restrict", "kind": "definition", "module": "Mathlib.Data.Finset.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.restrict_def", "kind": "theorem", "module": "Mathlib.Data.Finset.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.piCongrLeft_comp_restrict", "kind": "theorem", "module": "Mathlib.Data.Finset.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.piCongrLeft_comp_restrict", "kind": "theorem", "module": "Mathlib.Data.Finset.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.restrict₂", "kind": "definition", "module": "Mathlib.Data.Finset.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.restrict₂_def", "kind": "theorem", "module": "Mathlib.Data.Finset.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.restrict₂_comp_restrict", "kind": "theorem", "module": "Mathlib.Data.Finset.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.restrict₂_comp_restrict₂", "kind": "theorem", "module": "Mathlib.Data.Finset.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.dependsOn_restrict", "kind": "theorem", "module": "Mathlib.Data.Finset.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.restrict_preimage_univ", "kind": "theorem", "module": "Mathlib.Data.Finset.Pi", "is_tactic_proof": true, "tactics": ["ext", "simp_all"], "tactic_count": 2}
{"name": "Finset.restrict_preimage", "kind": "theorem", "module": "Mathlib.Data.Finset.Pi", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.restrict₂_preimage", "kind": "theorem", "module": "Mathlib.Data.Finset.Pi", "is_tactic_proof": true, "tactics": ["ext", "simp", "refine", "split_ifs", "exact", "exact"], "tactic_count": 6}
{"name": "Finset.induction_on_pi_of_choice", "kind": "theorem", "module": "Mathlib.Data.Finset.PiInduction", "is_tactic_proof": true, "tactics": ["cases", "induction", "subst", "rcases", "convert", "simpa", "rcases", "rcases", "set", "clear_value", "have", "rw", "apply", "rw", "rw", "clear", "rw", "refine", "rw", "exacts"], "tactic_count": 20}
{"name": "Finset.induction_on_pi", "kind": "theorem", "module": "Mathlib.Data.Finset.PiInduction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.induction_on_pi_max", "kind": "theorem", "module": "Mathlib.Data.Finset.PiInduction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.induction_on_pi_min", "kind": "theorem", "module": "Mathlib.Data.Finset.PiInduction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.piecewise", "kind": "definition", "module": "Mathlib.Data.Finset.Piecewise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.piecewise_insert_self", "kind": "theorem", "module": "Mathlib.Data.Finset.Piecewise", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.piecewise_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.Piecewise", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Finset.piecewise_coe", "kind": "theorem", "module": "Mathlib.Data.Finset.Piecewise", "is_tactic_proof": true, "tactics": ["ext", "congr"], "tactic_count": 2}
{"name": "Finset.piecewise_eq_of_mem", "kind": "theorem", "module": "Mathlib.Data.Finset.Piecewise", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.piecewise_eq_of_notMem", "kind": "theorem", "module": "Mathlib.Data.Finset.Piecewise", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.piecewise_congr", "kind": "theorem", "module": "Mathlib.Data.Finset.Piecewise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.piecewise_insert_of_ne", "kind": "theorem", "module": "Mathlib.Data.Finset.Piecewise", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.piecewise_insert", "kind": "theorem", "module": "Mathlib.Data.Finset.Piecewise", "is_tactic_proof": true, "tactics": ["classical", "ext", "congr", "simp"], "tactic_count": 4}
{"name": "Finset.piecewise_cases", "kind": "theorem", "module": "Mathlib.Data.Finset.Piecewise", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "Finset.piecewise_singleton", "kind": "theorem", "module": "Mathlib.Data.Finset.Piecewise", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.piecewise_piecewise_of_subset_left", "kind": "theorem", "module": "Mathlib.Data.Finset.Piecewise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.piecewise_idem_left", "kind": "theorem", "module": "Mathlib.Data.Finset.Piecewise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.piecewise_piecewise_of_subset_right", "kind": "theorem", "module": "Mathlib.Data.Finset.Piecewise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.piecewise_idem_right", "kind": "theorem", "module": "Mathlib.Data.Finset.Piecewise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.update_eq_piecewise", "kind": "theorem", "module": "Mathlib.Data.Finset.Piecewise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.update_piecewise", "kind": "theorem", "module": "Mathlib.Data.Finset.Piecewise", "is_tactic_proof": true, "tactics": ["ext", "rcases"], "tactic_count": 2}
{"name": "Finset.update_piecewise_of_mem", "kind": "theorem", "module": "Mathlib.Data.Finset.Piecewise", "is_tactic_proof": true, "tactics": ["rw", "refine", "exact"], "tactic_count": 3}
{"name": "Finset.update_piecewise_of_notMem", "kind": "theorem", "module": "Mathlib.Data.Finset.Piecewise", "is_tactic_proof": true, "tactics": ["rw", "refine", "exact"], "tactic_count": 3}
{"name": "Finset.piecewise_same", "kind": "theorem", "module": "Mathlib.Data.Finset.Piecewise", "is_tactic_proof": true, "tactics": ["ext", "by_cases"], "tactic_count": 2}
{"name": "Finset.piecewise_univ", "kind": "theorem", "module": "Mathlib.Data.Finset.Piecewise", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Finset.piecewise_compl", "kind": "theorem", "module": "Mathlib.Data.Finset.Piecewise", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Finset.piecewise_erase_univ", "kind": "theorem", "module": "Mathlib.Data.Finset.Piecewise", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.piecewise_mem_set_pi", "kind": "theorem", "module": "Mathlib.Data.Finset.Piecewise", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finset.piecewise_le_of_le_of_le", "kind": "theorem", "module": "Mathlib.Data.Finset.Piecewise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.le_piecewise_of_le_of_le", "kind": "theorem", "module": "Mathlib.Data.Finset.Piecewise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.piecewise_le_piecewise'", "kind": "theorem", "module": "Mathlib.Data.Finset.Piecewise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.piecewise_le_piecewise", "kind": "theorem", "module": "Mathlib.Data.Finset.Piecewise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.piecewise_mem_Icc_of_mem_of_mem", "kind": "theorem", "module": "Mathlib.Data.Finset.Piecewise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.piecewise_mem_Icc", "kind": "theorem", "module": "Mathlib.Data.Finset.Piecewise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.piecewise_mem_Icc'", "kind": "theorem", "module": "Mathlib.Data.Finset.Piecewise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.powerset", "kind": "definition", "module": "Mathlib.Data.Finset.Powerset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_powerset", "kind": "theorem", "module": "Mathlib.Data.Finset.Powerset", "is_tactic_proof": true, "tactics": ["cases", "simp"], "tactic_count": 2}
{"name": "Finset.coe_powerset", "kind": "theorem", "module": "Mathlib.Data.Finset.Powerset", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Finset.empty_mem_powerset", "kind": "theorem", "module": "Mathlib.Data.Finset.Powerset", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.mem_powerset_self", "kind": "theorem", "module": "Mathlib.Data.Finset.Powerset", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.powerset_nonempty", "kind": "theorem", "module": "Mathlib.Data.Finset.Powerset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.powerset_mono", "kind": "theorem", "module": "Mathlib.Data.Finset.Powerset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.powerset_injective", "kind": "theorem", "module": "Mathlib.Data.Finset.Powerset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.powerset_inj", "kind": "theorem", "module": "Mathlib.Data.Finset.Powerset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.powerset_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.Powerset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.powerset_eq_singleton_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.Powerset", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.image_injOn_powerset_of_injOn", "kind": "theorem", "module": "Mathlib.Data.Finset.Powerset", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "Finset.image_surjOn_powerset", "kind": "theorem", "module": "Mathlib.Data.Finset.Powerset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.powerset_image", "kind": "theorem", "module": "Mathlib.Data.Finset.Powerset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_powerset", "kind": "theorem", "module": "Mathlib.Data.Finset.Powerset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.notMem_of_mem_powerset_of_notMem", "kind": "theorem", "module": "Mathlib.Data.Finset.Powerset", "is_tactic_proof": true, "tactics": ["apply", "apply"], "tactic_count": 2}
{"name": "Finset.powerset_insert", "kind": "theorem", "module": "Mathlib.Data.Finset.Powerset", "is_tactic_proof": true, "tactics": ["ext", "simp", "grind"], "tactic_count": 3}
{"name": "Finset.pairwiseDisjoint_pair_insert", "kind": "theorem", "module": "Mathlib.Data.Finset.Powerset", "is_tactic_proof": true, "tactics": ["simp_rw", "rintro", "simp", "exists_eq_left,", "refine", "cases"], "tactic_count": 6}
{"name": "Finset.decidableExistsOfDecidableSubsets", "kind": "instance", "module": "Mathlib.Data.Finset.Powerset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.decidableForallOfDecidableSubsets", "kind": "instance", "module": "Mathlib.Data.Finset.Powerset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.decidableExistsOfDecidableSubsets'", "kind": "instance", "module": "Mathlib.Data.Finset.Powerset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.decidableForallOfDecidableSubsets'", "kind": "instance", "module": "Mathlib.Data.Finset.Powerset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.ssubsets", "kind": "definition", "module": "Mathlib.Data.Finset.Powerset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_ssubsets", "kind": "theorem", "module": "Mathlib.Data.Finset.Powerset", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.empty_mem_ssubsets", "kind": "theorem", "module": "Mathlib.Data.Finset.Powerset", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finset.decidableExistsOfDecidableSSubsets", "kind": "definition", "module": "Mathlib.Data.Finset.Powerset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.decidableForallOfDecidableSSubsets", "kind": "definition", "module": "Mathlib.Data.Finset.Powerset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.decidableExistsOfDecidableSSubsets'", "kind": "definition", "module": "Mathlib.Data.Finset.Powerset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.decidableForallOfDecidableSSubsets'", "kind": "definition", "module": "Mathlib.Data.Finset.Powerset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.powersetCard", "kind": "definition", "module": "Mathlib.Data.Finset.Powerset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_powersetCard", "kind": "theorem", "module": "Mathlib.Data.Finset.Powerset", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Finset.powersetCard_mono", "kind": "theorem", "module": "Mathlib.Data.Finset.Powerset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_powersetCard", "kind": "theorem", "module": "Mathlib.Data.Finset.Powerset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.powersetCard_zero", "kind": "theorem", "module": "Mathlib.Data.Finset.Powerset", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.powersetCard_empty_subsingleton", "kind": "theorem", "module": "Mathlib.Data.Finset.Powerset", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.map_val_val_powersetCard", "kind": "theorem", "module": "Mathlib.Data.Finset.Powerset", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.powersetCard_one", "kind": "theorem", "module": "Mathlib.Data.Finset.Powerset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.powersetCard_eq_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.Powerset", "is_tactic_proof": true, "tactics": ["refine", "contrapose", "exact"], "tactic_count": 3}
{"name": "Finset.powersetCard_card_add", "kind": "theorem", "module": "Mathlib.Data.Finset.Powerset", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.powersetCard_eq_filter", "kind": "theorem", "module": "Mathlib.Data.Finset.Powerset", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Finset.powersetCard_succ_insert", "kind": "theorem", "module": "Mathlib.Data.Finset.Powerset", "is_tactic_proof": true, "tactics": ["rw", "grind"], "tactic_count": 2}
{"name": "Finset.powersetCard_nonempty", "kind": "theorem", "module": "Mathlib.Data.Finset.Powerset", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Finset.powersetCard_self", "kind": "theorem", "module": "Mathlib.Data.Finset.Powerset", "is_tactic_proof": true, "tactics": ["ext", "rw", "constructor", "exact", "rintro", "simp"], "tactic_count": 6}
{"name": "Finset.pairwise_disjoint_powersetCard", "kind": "theorem", "module": "Mathlib.Data.Finset.Powerset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.powerset_card_disjiUnion", "kind": "theorem", "module": "Mathlib.Data.Finset.Powerset", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact", "mem_powersetCard.mpr", "rcases", "exact"], "tactic_count": 6}
{"name": "Finset.powerset_card_biUnion", "kind": "theorem", "module": "Mathlib.Data.Finset.Powerset", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.powersetCard_sup", "kind": "theorem", "module": "Mathlib.Data.Finset.Powerset", "is_tactic_proof": true, "tactics": ["apply", "simp_rw", "rintro", "exact", "rw", "intro", "simp", "obtain", "powersetCard_nonempty.2", "refine", "rw", "exact"], "tactic_count": 12}
{"name": "Finset.powersetCard_map", "kind": "theorem", "module": "Mathlib.Data.Finset.Powerset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.preimage", "kind": "definition", "module": "Mathlib.Data.Finset.Preimage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_preimage", "kind": "theorem", "module": "Mathlib.Data.Finset.Preimage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.coe_preimage", "kind": "theorem", "module": "Mathlib.Data.Finset.Preimage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.preimage_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.Preimage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.preimage_univ", "kind": "theorem", "module": "Mathlib.Data.Finset.Preimage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.preimage_inter", "kind": "theorem", "module": "Mathlib.Data.Finset.Preimage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.preimage_union", "kind": "theorem", "module": "Mathlib.Data.Finset.Preimage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.preimage_compl'", "kind": "theorem", "module": "Mathlib.Data.Finset.Preimage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.preimage_compl", "kind": "theorem", "module": "Mathlib.Data.Finset.Preimage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.preimage_map", "kind": "theorem", "module": "Mathlib.Data.Finset.Preimage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.monotone_preimage", "kind": "theorem", "module": "Mathlib.Data.Finset.Preimage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image_subset_iff_subset_preimage", "kind": "theorem", "module": "Mathlib.Data.Finset.Preimage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.map_subset_iff_subset_preimage", "kind": "theorem", "module": "Mathlib.Data.Finset.Preimage", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finset.card_preimage", "kind": "theorem", "module": "Mathlib.Data.Finset.Preimage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image_preimage", "kind": "theorem", "module": "Mathlib.Data.Finset.Preimage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image_preimage_of_bij", "kind": "theorem", "module": "Mathlib.Data.Finset.Preimage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.preimage_subset_of_subset_image", "kind": "theorem", "module": "Mathlib.Data.Finset.Preimage", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.preimage_subset", "kind": "theorem", "module": "Mathlib.Data.Finset.Preimage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.subset_map_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Preimage", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finset.sigma_preimage_mk", "kind": "theorem", "module": "Mathlib.Data.Finset.Preimage", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Finset.sigma_preimage_mk_of_subset", "kind": "theorem", "module": "Mathlib.Data.Finset.Preimage", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.sigma_image_fst_preimage_mk", "kind": "theorem", "module": "Mathlib.Data.Finset.Preimage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.preimage_inl", "kind": "theorem", "module": "Mathlib.Data.Finset.Preimage", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finset.preimage_inr", "kind": "theorem", "module": "Mathlib.Data.Finset.Preimage", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Equiv.restrictPreimageFinset", "kind": "definition", "module": "Mathlib.Data.Finset.Preimage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.restrict_comp_piCongrLeft", "kind": "theorem", "module": "Mathlib.Data.Finset.Preimage", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Finset.product", "kind": "definition", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.instSProd", "kind": "instance", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.product_eq_sprod", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.product_val", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_product", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mk_mem_product", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.coe_product", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.subset_product_image_fst", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.subset_product_image_snd", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.product_image_fst", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Finset.product_image_snd", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Finset.subset_product", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.product_subset_product", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.product_subset_product_left", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.product_subset_product_right", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prodMap_image_product", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prodMap_map_product", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.map_swap_product", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image_swap_product", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.product_eq_biUnion", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.product_eq_biUnion_right", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.product_biUnion", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.card_product", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.nontrivial_prod_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Finset.filter_product", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.filter_product_left", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.filter_product_right", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.filter_product_card", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": true, "tactics": ["classical", "rw", "apply", "grind", "apply", "exact"], "tactic_count": 6}
{"name": "Finset.empty_product", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.product_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Nonempty.product", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Nonempty.fst", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Nonempty.snd", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.nonempty_product", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.product_eq_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": true, "tactics": ["contrapose"], "tactic_count": 1}
{"name": "Finset.singleton_product", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Finset.product_singleton", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Finset.singleton_product_singleton", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.union_product", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.product_union", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.inter_product", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.product_inter", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.product_inter_product", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.disjoint_product", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Finset.disjUnion_product", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.product_disjUnion", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.diag", "kind": "definition", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.offDiag", "kind": "definition", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_diag", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Finset.mem_offDiag", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "Finset.diag_nonempty", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.diag_eq_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.diag_eq_filter", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finset.image_diag", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.coe_offDiag", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.diag_card", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.offDiag_card", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": true, "tactics": ["rw", "rcases", "apply"], "tactic_count": 3}
{"name": "Finset.diag_mono", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.offDiag_mono", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.diag_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.offDiag_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.diag_union_offDiag", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.disjoint_diag_offDiag", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.product_sdiff_diag", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.product_sdiff_offDiag", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.diag_inter", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.offDiag_inter", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.diag_union", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.offDiag_union", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.offDiag_singleton", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.diag_singleton", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.diag_insert", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.offDiag_insert", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.offDiag_filter_lt_eq_filter_le", "kind": "theorem", "module": "Mathlib.Data.Finset.Prod", "is_tactic_proof": true, "tactics": ["ext", "simpa"], "tactic_count": 2}
{"name": "Finset.range", "kind": "definition", "module": "Mathlib.Data.Finset.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.range_val", "kind": "theorem", "module": "Mathlib.Data.Finset.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_range", "kind": "theorem", "module": "Mathlib.Data.Finset.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.coe_range", "kind": "theorem", "module": "Mathlib.Data.Finset.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.range_zero", "kind": "theorem", "module": "Mathlib.Data.Finset.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.range_one", "kind": "theorem", "module": "Mathlib.Data.Finset.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.range_add_one", "kind": "theorem", "module": "Mathlib.Data.Finset.Range", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.range_succ", "kind": "theorem", "module": "Mathlib.Data.Finset.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.notMem_range_self", "kind": "theorem", "module": "Mathlib.Data.Finset.Range", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.self_mem_range_succ", "kind": "theorem", "module": "Mathlib.Data.Finset.Range", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.range_subset", "kind": "theorem", "module": "Mathlib.Data.Finset.Range", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.subset_range", "kind": "theorem", "module": "Mathlib.Data.Finset.Range", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.range_subset_range", "kind": "theorem", "module": "Mathlib.Data.Finset.Range", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.range_mono", "kind": "theorem", "module": "Mathlib.Data.Finset.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_range_succ_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Range", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.mem_range_le", "kind": "theorem", "module": "Mathlib.Data.Finset.Range", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.mem_range_sub_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Finset.Range", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.nonempty_range_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.range_eq_empty_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Range", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.nonempty_range_add_one", "kind": "theorem", "module": "Mathlib.Data.Finset.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.range_nontrivial", "kind": "theorem", "module": "Mathlib.Data.Finset.Range", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finset.exists_nat_subset_range", "kind": "theorem", "module": "Mathlib.Data.Finset.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "notMemRangeEquiv", "kind": "definition", "module": "Mathlib.Data.Finset.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "coe_notMemRangeEquiv", "kind": "theorem", "module": "Mathlib.Data.Finset.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "coe_notMemRangeEquiv_symm", "kind": "theorem", "module": "Mathlib.Data.Finset.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.instSDiff", "kind": "instance", "module": "Mathlib.Data.Finset.SDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sdiff_val", "kind": "theorem", "module": "Mathlib.Data.Finset.SDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_sdiff", "kind": "theorem", "module": "Mathlib.Data.Finset.SDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inter_sdiff_self", "kind": "theorem", "module": "Mathlib.Data.Finset.SDiff", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.instGeneralizedBooleanAlgebra", "kind": "instance", "module": "Mathlib.Data.Finset.SDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.notMem_sdiff_of_mem_right", "kind": "theorem", "module": "Mathlib.Data.Finset.SDiff", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.notMem_sdiff_of_notMem_left", "kind": "theorem", "module": "Mathlib.Data.Finset.SDiff", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.union_sdiff_of_subset", "kind": "theorem", "module": "Mathlib.Data.Finset.SDiff", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.sdiff_union_of_subset", "kind": "theorem", "module": "Mathlib.Data.Finset.SDiff", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.inter_sdiff_assoc", "kind": "theorem", "module": "Mathlib.Data.Finset.SDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sdiff_inter_right_comm", "kind": "theorem", "module": "Mathlib.Data.Finset.SDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inter_sdiff_left_comm", "kind": "theorem", "module": "Mathlib.Data.Finset.SDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sdiff_inter_self", "kind": "theorem", "module": "Mathlib.Data.Finset.SDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sdiff_self", "kind": "theorem", "module": "Mathlib.Data.Finset.SDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sdiff_inter_distrib_right", "kind": "theorem", "module": "Mathlib.Data.Finset.SDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sdiff_inter_self_left", "kind": "theorem", "module": "Mathlib.Data.Finset.SDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sdiff_inter_self_right", "kind": "theorem", "module": "Mathlib.Data.Finset.SDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sdiff_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.SDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sdiff_subset_sdiff", "kind": "theorem", "module": "Mathlib.Data.Finset.SDiff", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.sdiff_subset_sdiff_iff_subset", "kind": "theorem", "module": "Mathlib.Data.Finset.SDiff", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.coe_sdiff", "kind": "theorem", "module": "Mathlib.Data.Finset.SDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.union_sdiff_self_eq_union", "kind": "theorem", "module": "Mathlib.Data.Finset.SDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sdiff_union_self_eq_union", "kind": "theorem", "module": "Mathlib.Data.Finset.SDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.union_sdiff_left", "kind": "theorem", "module": "Mathlib.Data.Finset.SDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.union_sdiff_right", "kind": "theorem", "module": "Mathlib.Data.Finset.SDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.union_sdiff_cancel_left", "kind": "theorem", "module": "Mathlib.Data.Finset.SDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.union_sdiff_cancel_right", "kind": "theorem", "module": "Mathlib.Data.Finset.SDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.union_sdiff_symm", "kind": "theorem", "module": "Mathlib.Data.Finset.SDiff", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.sdiff_union_inter", "kind": "theorem", "module": "Mathlib.Data.Finset.SDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sdiff_idem", "kind": "theorem", "module": "Mathlib.Data.Finset.SDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.subset_sdiff", "kind": "theorem", "module": "Mathlib.Data.Finset.SDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sdiff_eq_empty_iff_subset", "kind": "theorem", "module": "Mathlib.Data.Finset.SDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sdiff_nonempty", "kind": "theorem", "module": "Mathlib.Data.Finset.SDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.empty_sdiff", "kind": "theorem", "module": "Mathlib.Data.Finset.SDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.insert_sdiff_of_notMem", "kind": "theorem", "module": "Mathlib.Data.Finset.SDiff", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.insert_sdiff_of_mem", "kind": "theorem", "module": "Mathlib.Data.Finset.SDiff", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.insert_sdiff_self_of_mem", "kind": "theorem", "module": "Mathlib.Data.Finset.SDiff", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.insert_sdiff_cancel", "kind": "theorem", "module": "Mathlib.Data.Finset.SDiff", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.insert_sdiff_insert", "kind": "theorem", "module": "Mathlib.Data.Finset.SDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.insert_sdiff_insert'", "kind": "theorem", "module": "Mathlib.Data.Finset.SDiff", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finset.cons_sdiff_cons", "kind": "theorem", "module": "Mathlib.Data.Finset.SDiff", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.sdiff_insert_of_notMem", "kind": "theorem", "module": "Mathlib.Data.Finset.SDiff", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.sdiff_subset", "kind": "theorem", "module": "Mathlib.Data.Finset.SDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sdiff_ssubset", "kind": "theorem", "module": "Mathlib.Data.Finset.SDiff", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.union_sdiff_distrib", "kind": "theorem", "module": "Mathlib.Data.Finset.SDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sdiff_union_distrib", "kind": "theorem", "module": "Mathlib.Data.Finset.SDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.union_sdiff_self", "kind": "theorem", "module": "Mathlib.Data.Finset.SDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Nontrivial.sdiff_singleton_nonempty", "kind": "theorem", "module": "Mathlib.Data.Finset.SDiff", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.sdiff_sdiff_left'", "kind": "theorem", "module": "Mathlib.Data.Finset.SDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sdiff_union_sdiff_cancel", "kind": "theorem", "module": "Mathlib.Data.Finset.SDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sdiff_sdiff_eq_sdiff_union", "kind": "theorem", "module": "Mathlib.Data.Finset.SDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sdiff_sdiff_self_left", "kind": "theorem", "module": "Mathlib.Data.Finset.SDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sdiff_sdiff_eq_self", "kind": "theorem", "module": "Mathlib.Data.Finset.SDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sdiff_eq_sdiff_iff_inter_eq_inter", "kind": "theorem", "module": "Mathlib.Data.Finset.SDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.union_eq_sdiff_union_sdiff_union_inter", "kind": "theorem", "module": "Mathlib.Data.Finset.SDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sdiff_eq_self_iff_disjoint", "kind": "theorem", "module": "Mathlib.Data.Finset.SDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sdiff_eq_self_of_disjoint", "kind": "theorem", "module": "Mathlib.Data.Finset.SDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.IsPWO.smul", "kind": "theorem", "module": "Mathlib.Data.Finset.SMulAntidiagonal", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.IsWF.smul", "kind": "theorem", "module": "Mathlib.Data.Finset.SMulAntidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.IsWF.min_smul", "kind": "theorem", "module": "Mathlib.Data.Finset.SMulAntidiagonal", "is_tactic_proof": true, "tactics": ["refine", "rw", "rintro", "exact"], "tactic_count": 4}
{"name": "Finset.SMulAntidiagonal", "kind": "definition", "module": "Mathlib.Data.Finset.SMulAntidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_smulAntidiagonal", "kind": "theorem", "module": "Mathlib.Data.Finset.SMulAntidiagonal", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Finset.smulAntidiagonal_mono_left", "kind": "theorem", "module": "Mathlib.Data.Finset.SMulAntidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.smulAntidiagonal_mono_right", "kind": "theorem", "module": "Mathlib.Data.Finset.SMulAntidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.support_smulAntidiagonal_subset_smul", "kind": "theorem", "module": "Mathlib.Data.Finset.SMulAntidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.isPWO_support_smulAntidiagonal", "kind": "theorem", "module": "Mathlib.Data.Finset.SMulAntidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.smulAntidiagonal_min_smul_min", "kind": "theorem", "module": "Mathlib.Data.Finset.SMulAntidiagonal", "is_tactic_proof": true, "tactics": ["ext", "simp", "constructor", "rintro", "obtain", "exact", "rintro", "exact"], "tactic_count": 8}
{"name": "Finset.sigma", "kind": "definition", "module": "Mathlib.Data.Finset.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_sigma", "kind": "theorem", "module": "Mathlib.Data.Finset.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.coe_sigma", "kind": "theorem", "module": "Mathlib.Data.Finset.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sigma_nonempty", "kind": "theorem", "module": "Mathlib.Data.Finset.Sigma", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.sigma_eq_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.Sigma", "is_tactic_proof": true, "tactics": ["contrapose"], "tactic_count": 1}
{"name": "Finset.sigma_mono", "kind": "theorem", "module": "Mathlib.Data.Finset.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.pairwiseDisjoint_map_sigmaMk", "kind": "theorem", "module": "Mathlib.Data.Finset.Sigma", "is_tactic_proof": true, "tactics": ["intro", "rw", "simp_rw", "rintro", "exact"], "tactic_count": 5}
{"name": "Finset.disjiUnion_map_sigma_mk", "kind": "theorem", "module": "Mathlib.Data.Finset.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sigma_eq_biUnion", "kind": "theorem", "module": "Mathlib.Data.Finset.Sigma", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Finset.sup_sigma", "kind": "theorem", "module": "Mathlib.Data.Finset.Sigma", "is_tactic_proof": true, "tactics": ["simp", "exact", "le_sup"], "tactic_count": 3}
{"name": "Finset.inf_sigma", "kind": "theorem", "module": "Mathlib.Data.Finset.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "biSup_finsetSigma", "kind": "theorem", "module": "Mathlib.Data.Finset.Sigma", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "biSup_finsetSigma'", "kind": "theorem", "module": "Mathlib.Data.Finset.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "biInf_finsetSigma", "kind": "theorem", "module": "Mathlib.Data.Finset.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "biInf_finsetSigma'", "kind": "theorem", "module": "Mathlib.Data.Finset.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.biUnion_finsetSigma", "kind": "theorem", "module": "Mathlib.Data.Finset.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.biUnion_finsetSigma'", "kind": "theorem", "module": "Mathlib.Data.Finset.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.biInter_finsetSigma", "kind": "theorem", "module": "Mathlib.Data.Finset.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.biInter_finsetSigma'", "kind": "theorem", "module": "Mathlib.Data.Finset.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sigmaLift", "kind": "definition", "module": "Mathlib.Data.Finset.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_sigmaLift", "kind": "theorem", "module": "Mathlib.Data.Finset.Sigma", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "constructor", "simp_rw", "simp", "rintro", "exact", "rintro", "rw", "exact", "rw", "refine", "rintro", "exact"], "tactic_count": 14}
{"name": "Finset.mk_mem_sigmaLift", "kind": "theorem", "module": "Mathlib.Data.Finset.Sigma", "is_tactic_proof": true, "tactics": ["rw", "refine", "rintro", "exact"], "tactic_count": 4}
{"name": "Finset.notMem_sigmaLift_of_ne_left", "kind": "theorem", "module": "Mathlib.Data.Finset.Sigma", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finset.notMem_sigmaLift_of_ne_right", "kind": "theorem", "module": "Mathlib.Data.Finset.Sigma", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finset.sigmaLift_nonempty", "kind": "theorem", "module": "Mathlib.Data.Finset.Sigma", "is_tactic_proof": true, "tactics": ["simp_rw", "split_ifs"], "tactic_count": 2}
{"name": "Finset.sigmaLift_eq_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.Sigma", "is_tactic_proof": true, "tactics": ["simp_rw", "split_ifs", "simp", "simp"], "tactic_count": 4}
{"name": "Finset.sigmaLift_mono", "kind": "theorem", "module": "Mathlib.Data.Finset.Sigma", "is_tactic_proof": true, "tactics": ["rintro", "rw", "obtain", "exact"], "tactic_count": 4}
{"name": "Finset.card_sigmaLift", "kind": "theorem", "module": "Mathlib.Data.Finset.Sigma", "is_tactic_proof": true, "tactics": ["simp_rw", "split_ifs"], "tactic_count": 2}
{"name": "Set.Sized", "kind": "definition", "module": "Mathlib.Data.Finset.Slice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Sized.mono", "kind": "theorem", "module": "Mathlib.Data.Finset.Slice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sized_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.Slice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.sized_singleton", "kind": "theorem", "module": "Mathlib.Data.Finset.Slice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.sized_union", "kind": "theorem", "module": "Mathlib.Data.Finset.Slice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sized_iUnion", "kind": "theorem", "module": "Mathlib.Data.Finset.Slice", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Set.sized_iUnion₂", "kind": "theorem", "module": "Mathlib.Data.Finset.Slice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.Sized.isAntichain", "kind": "theorem", "module": "Mathlib.Data.Finset.Slice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Sized.subsingleton", "kind": "theorem", "module": "Mathlib.Data.Finset.Slice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Sized.subsingleton'", "kind": "theorem", "module": "Mathlib.Data.Finset.Slice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Sized.empty_mem_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Slice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Sized.univ_mem_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Slice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sized_powersetCard", "kind": "theorem", "module": "Mathlib.Data.Finset.Slice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.subset_powersetCard_univ_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Slice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Sized.card_le", "kind": "theorem", "module": "Mathlib.Data.Finset.Slice", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finset.slice", "kind": "definition", "module": "Mathlib.Data.Finset.Slice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.term_#_", "kind": "definition", "module": "Mathlib.Data.Finset.Slice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset._aux_Mathlib_Data_Finset_Slice___macroRules_Finset_term_#__1", "kind": "definition", "module": "Mathlib.Data.Finset.Slice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset._aux_Mathlib_Data_Finset_Slice___unexpand_Finset_slice_1", "kind": "definition", "module": "Mathlib.Data.Finset.Slice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_slice", "kind": "theorem", "module": "Mathlib.Data.Finset.Slice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.slice_subset", "kind": "theorem", "module": "Mathlib.Data.Finset.Slice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sized_slice", "kind": "theorem", "module": "Mathlib.Data.Finset.Slice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.eq_of_mem_slice", "kind": "theorem", "module": "Mathlib.Data.Finset.Slice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.ne_of_mem_slice", "kind": "theorem", "module": "Mathlib.Data.Finset.Slice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.pairwiseDisjoint_slice", "kind": "theorem", "module": "Mathlib.Data.Finset.Slice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.biUnion_slice", "kind": "theorem", "module": "Mathlib.Data.Finset.Slice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sum_card_slice", "kind": "theorem", "module": "Mathlib.Data.Finset.Slice", "is_tactic_proof": true, "tactics": ["letI", "rw", "exact"], "tactic_count": 3}
{"name": "Finset.sort_val", "kind": "theorem", "module": "Mathlib.Data.Finset.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.pairwise_sort", "kind": "theorem", "module": "Mathlib.Data.Finset.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sort_eq", "kind": "theorem", "module": "Mathlib.Data.Finset.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sort_nodup", "kind": "theorem", "module": "Mathlib.Data.Finset.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sort_toFinset", "kind": "theorem", "module": "Mathlib.Data.Finset.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sort_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sort_singleton", "kind": "theorem", "module": "Mathlib.Data.Finset.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.map_sort", "kind": "theorem", "module": "Mathlib.Data.Finset.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMonoOn.map_finsetSort", "kind": "theorem", "module": "Mathlib.Data.Finset.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sort_range", "kind": "theorem", "module": "Mathlib.Data.Finset.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sort_perm_toList", "kind": "theorem", "module": "Mathlib.Data.Finset.Sort", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "List.toFinset_sort", "kind": "theorem", "module": "Mathlib.Data.Finset.Sort", "is_tactic_proof": true, "tactics": ["refine", "intro", "rw", "exact"], "tactic_count": 4}
{"name": "Finset.sort_mk", "kind": "theorem", "module": "Mathlib.Data.Finset.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_sort", "kind": "theorem", "module": "Mathlib.Data.Finset.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.length_sort", "kind": "theorem", "module": "Mathlib.Data.Finset.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sort_cons", "kind": "theorem", "module": "Mathlib.Data.Finset.Sort", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.sort_insert", "kind": "theorem", "module": "Mathlib.Data.Finset.Sort", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.sortedLT_sort", "kind": "theorem", "module": "Mathlib.Data.Finset.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sortedGT_sort", "kind": "theorem", "module": "Mathlib.Data.Finset.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sorted_zero_eq_min'_aux", "kind": "theorem", "module": "Mathlib.Data.Finset.Sort", "is_tactic_proof": true, "tactics": ["let", "apply", "have", "obtain", "rw", "exact", "have", "exact"], "tactic_count": 8}
{"name": "Finset.sorted_zero_eq_min'", "kind": "theorem", "module": "Mathlib.Data.Finset.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.min'_eq_sorted_zero", "kind": "theorem", "module": "Mathlib.Data.Finset.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sorted_last_eq_max'_aux", "kind": "theorem", "module": "Mathlib.Data.Finset.Sort", "is_tactic_proof": true, "tactics": ["let", "apply", "have", "exact", "have", "obtain", "rw", "exact"], "tactic_count": 8}
{"name": "Finset.sorted_last_eq_max'", "kind": "theorem", "module": "Mathlib.Data.Finset.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.max'_eq_sorted_last", "kind": "theorem", "module": "Mathlib.Data.Finset.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.orderIsoOfFin", "kind": "definition", "module": "Mathlib.Data.Finset.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.orderEmbOfFin", "kind": "definition", "module": "Mathlib.Data.Finset.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.coe_orderIsoOfFin_apply", "kind": "theorem", "module": "Mathlib.Data.Finset.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.orderIsoOfFin_symm_apply", "kind": "theorem", "module": "Mathlib.Data.Finset.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.orderEmbOfFin_apply", "kind": "theorem", "module": "Mathlib.Data.Finset.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.orderEmbOfFin_mem", "kind": "theorem", "module": "Mathlib.Data.Finset.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.range_orderEmbOfFin", "kind": "theorem", "module": "Mathlib.Data.Finset.Sort", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.image_orderEmbOfFin_univ", "kind": "theorem", "module": "Mathlib.Data.Finset.Sort", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "Finset.map_orderEmbOfFin_univ", "kind": "theorem", "module": "Mathlib.Data.Finset.Sort", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.listMap_orderEmbOfFin_finRange", "kind": "theorem", "module": "Mathlib.Data.Finset.Sort", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Finset.orderEmbOfFin_zero", "kind": "theorem", "module": "Mathlib.Data.Finset.Sort", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.orderEmbOfFin_last", "kind": "theorem", "module": "Mathlib.Data.Finset.Sort", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.orderEmbOfFin_singleton", "kind": "theorem", "module": "Mathlib.Data.Finset.Sort", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.orderEmbOfFin_unique", "kind": "theorem", "module": "Mathlib.Data.Finset.Sort", "is_tactic_proof": false, "tactics": ["rw", "coe_inj]", "refine", "rcases", "exact", "rw"], "tactic_count": 6}
{"name": "Finset.orderEmbOfFin_unique'", "kind": "theorem", "module": "Mathlib.Data.Finset.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.orderEmbOfFin_eq_orderEmbOfFin_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Sort", "is_tactic_proof": true, "tactics": ["substs", "exact"], "tactic_count": 2}
{"name": "Finset.orderEmbOfCardLe", "kind": "definition", "module": "Mathlib.Data.Finset.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.orderEmbOfCardLe_mem", "kind": "theorem", "module": "Mathlib.Data.Finset.Sort", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.orderEmbOfFin_compl_singleton", "kind": "theorem", "module": "Mathlib.Data.Finset.Sort", "is_tactic_proof": true, "tactics": ["apply", "rw", "convert", "simp", "simp"], "tactic_count": 5}
{"name": "Finset.orderEmbOfFin_compl_singleton_eq_succAboveOrderEmb", "kind": "theorem", "module": "Mathlib.Data.Finset.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.orderEmbOfFin_compl_singleton_apply", "kind": "theorem", "module": "Mathlib.Data.Finset.Sort", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Finset.instRepr", "kind": "instance", "module": "Mathlib.Data.Finset.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.sort_univ", "kind": "theorem", "module": "Mathlib.Data.Finset.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.orderIsoFinOfCardEq", "kind": "definition", "module": "Mathlib.Data.Finset.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nonempty_orderEmbedding_of_finite_infinite", "kind": "theorem", "module": "Mathlib.Data.Finset.Sort", "is_tactic_proof": true, "tactics": ["haveI", "obtain", "exact"], "tactic_count": 3}
{"name": "Finset.disjSum", "kind": "definition", "module": "Mathlib.Data.Finset.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.val_disjSum", "kind": "theorem", "module": "Mathlib.Data.Finset.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.empty_disjSum", "kind": "theorem", "module": "Mathlib.Data.Finset.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.disjSum_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_disjSum", "kind": "theorem", "module": "Mathlib.Data.Finset.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.disjoint_map_inl_map_inr", "kind": "theorem", "module": "Mathlib.Data.Finset.Sum", "is_tactic_proof": true, "tactics": ["simp_rw", "rintro"], "tactic_count": 2}
{"name": "Finset.map_inl_disjUnion_map_inr", "kind": "theorem", "module": "Mathlib.Data.Finset.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_disjSum", "kind": "theorem", "module": "Mathlib.Data.Finset.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inl_mem_disjSum", "kind": "theorem", "module": "Mathlib.Data.Finset.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inr_mem_disjSum", "kind": "theorem", "module": "Mathlib.Data.Finset.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.disjSum_eq_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.Sum", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.disjSum_mono", "kind": "theorem", "module": "Mathlib.Data.Finset.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.disjSum_mono_left", "kind": "theorem", "module": "Mathlib.Data.Finset.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.disjSum_mono_right", "kind": "theorem", "module": "Mathlib.Data.Finset.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.disjSum_ssubset_disjSum_of_ssubset_of_subset", "kind": "theorem", "module": "Mathlib.Data.Finset.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.disjSum_ssubset_disjSum_of_subset_of_ssubset", "kind": "theorem", "module": "Mathlib.Data.Finset.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.disjSum_strictMono_left", "kind": "theorem", "module": "Mathlib.Data.Finset.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.disjSum_strictMono_right", "kind": "theorem", "module": "Mathlib.Data.Finset.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.disjSum_inj", "kind": "theorem", "module": "Mathlib.Data.Finset.Sum", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.Injective2_disjSum", "kind": "theorem", "module": "Mathlib.Data.Finset.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.toLeft", "kind": "definition", "module": "Mathlib.Data.Finset.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Finset.mem_toRight", "kind": "theorem", "module": "Mathlib.Data.Finset.Sum", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.toLeft_subset_toLeft", "kind": "theorem", "module": "Mathlib.Data.Finset.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.toRight_subset_toRight", "kind": "theorem", "module": "Mathlib.Data.Finset.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.toLeft_monotone", "kind": "theorem", "module": "Mathlib.Data.Finset.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.toRight_monotone", "kind": "theorem", "module": "Mathlib.Data.Finset.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.toLeft_disjSum_toRight", "kind": "theorem", "module": "Mathlib.Data.Finset.Sum", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finset.card_toLeft_add_card_toRight", "kind": "theorem", "module": "Mathlib.Data.Finset.Sum", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.card_toLeft_le", "kind": "theorem", "module": "Mathlib.Data.Finset.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_toRight_le", "kind": "theorem", "module": "Mathlib.Data.Finset.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.toLeft_disjSum", "kind": "theorem", "module": "Mathlib.Data.Finset.Sum", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finset.toRight_disjSum", "kind": "theorem", "module": "Mathlib.Data.Finset.Sum", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finset.disjSum_eq_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.eq_disjSum_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.disjSum_subset", "kind": "theorem", "module": "Mathlib.Data.Finset.Sum", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.subset_disjSum", "kind": "theorem", "module": "Mathlib.Data.Finset.Sum", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.subset_map_inl", "kind": "theorem", "module": "Mathlib.Data.Finset.Sum", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.subset_map_inr", "kind": "theorem", "module": "Mathlib.Data.Finset.Sum", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.map_inl_subset_iff_subset_toLeft", "kind": "theorem", "module": "Mathlib.Data.Finset.Sum", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.map_inr_subset_iff_subset_toRight", "kind": "theorem", "module": "Mathlib.Data.Finset.Sum", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.gc_map_inl_toLeft", "kind": "theorem", "module": "Mathlib.Data.Finset.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.gc_map_inr_toRight", "kind": "theorem", "module": "Mathlib.Data.Finset.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.toLeft_map_sumComm", "kind": "theorem", "module": "Mathlib.Data.Finset.Sum", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finset.toRight_map_sumComm", "kind": "theorem", "module": "Mathlib.Data.Finset.Sum", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finset.toLeft_cons_inl", "kind": "theorem", "module": "Mathlib.Data.Finset.Sum", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finset.toLeft_cons_inr", "kind": "theorem", "module": "Mathlib.Data.Finset.Sum", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finset.toRight_cons_inl", "kind": "theorem", "module": "Mathlib.Data.Finset.Sum", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finset.toRight_cons_inr", "kind": "theorem", "module": "Mathlib.Data.Finset.Sum", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finset.toLeft_image_swap", "kind": "theorem", "module": "Mathlib.Data.Finset.Sum", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finset.toRight_image_swap", "kind": "theorem", "module": "Mathlib.Data.Finset.Sum", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finset.toLeft_insert_inl", "kind": "theorem", "module": "Mathlib.Data.Finset.Sum", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finset.toLeft_insert_inr", "kind": "theorem", "module": "Mathlib.Data.Finset.Sum", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finset.toRight_insert_inl", "kind": "theorem", "module": "Mathlib.Data.Finset.Sum", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finset.toRight_insert_inr", "kind": "theorem", "module": "Mathlib.Data.Finset.Sum", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finset.toLeft_inter", "kind": "theorem", "module": "Mathlib.Data.Finset.Sum", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finset.toRight_inter", "kind": "theorem", "module": "Mathlib.Data.Finset.Sum", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finset.toLeft_union", "kind": "theorem", "module": "Mathlib.Data.Finset.Sum", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finset.toRight_union", "kind": "theorem", "module": "Mathlib.Data.Finset.Sum", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finset.toLeft_sdiff", "kind": "theorem", "module": "Mathlib.Data.Finset.Sum", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
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{"name": "Finset.sumEquiv", "kind": "definition", "module": "Mathlib.Data.Finset.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sumEquiv_symm_apply", "kind": "theorem", "module": "Mathlib.Data.Finset.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.map_disjSum", "kind": "theorem", "module": "Mathlib.Data.Finset.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.fold_disjSum", "kind": "theorem", "module": "Mathlib.Data.Finset.Sum", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
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{"name": "Finset.sym2_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.Sym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sym2_eq_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.Sym", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.sym2_nonempty", "kind": "theorem", "module": "Mathlib.Data.Finset.Sym", "is_tactic_proof": true, "tactics": ["contrapose"], "tactic_count": 1}
{"name": "Finset.sym2_singleton", "kind": "theorem", "module": "Mathlib.Data.Finset.Sym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_sym2", "kind": "theorem", "module": "Mathlib.Data.Finset.Sym", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.sym2_eq_image", "kind": "theorem", "module": "Mathlib.Data.Finset.Sym", "is_tactic_proof": true, "tactics": ["ext", "refine", "grind"], "tactic_count": 3}
{"name": "Finset.isDiag_mk_of_mem_diag", "kind": "theorem", "module": "Mathlib.Data.Finset.Sym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.not_isDiag_mk_of_mem_offDiag", "kind": "theorem", "module": "Mathlib.Data.Finset.Sym", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finset.diag_mem_sym2_mem_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Sym", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finset.diag_mem_sym2_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Sym", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.image_diag_union_image_offDiag", "kind": "theorem", "module": "Mathlib.Data.Finset.Sym", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.sym", "kind": "definition", "module": "Mathlib.Data.Finset.Sym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sym_zero", "kind": "theorem", "module": "Mathlib.Data.Finset.Sym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sym_succ", "kind": "theorem", "module": "Mathlib.Data.Finset.Sym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_sym_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.Sym", "is_tactic_proof": false, "tactics": ["induction", "zero", "refine", "rintro", "exact", "succ", "refine", "rintro", "rw", "obtain", "rw", "obtain", "exact", "exact", "obtain", "exact"], "tactic_count": 16}
{"name": "Finset.sym_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.Sym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.replicate_mem_sym", "kind": "theorem", "module": "Mathlib.Data.Finset.Sym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Nonempty.sym", "kind": "theorem", "module": "Mathlib.Data.Finset.Sym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sym_singleton", "kind": "theorem", "module": "Mathlib.Data.Finset.Sym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.eq_empty_of_sym_eq_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.Sym", "is_tactic_proof": true, "tactics": ["contrapose"], "tactic_count": 1}
{"name": "Finset.sym_eq_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.Sym", "is_tactic_proof": true, "tactics": ["cases", "exact", "refine", "rintro", "exact"], "tactic_count": 5}
{"name": "Finset.sym_nonempty", "kind": "theorem", "module": "Mathlib.Data.Finset.Sym", "is_tactic_proof": true, "tactics": ["contrapose"], "tactic_count": 1}
{"name": "Finset.sym_univ", "kind": "theorem", "module": "Mathlib.Data.Finset.Sym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sym_mono", "kind": "theorem", "module": "Mathlib.Data.Finset.Sym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sym_inter", "kind": "theorem", "module": "Mathlib.Data.Finset.Sym", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Finset.sym_union", "kind": "theorem", "module": "Mathlib.Data.Finset.Sym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sym_fill_mem", "kind": "theorem", "module": "Mathlib.Data.Finset.Sym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sym_filterNe_mem", "kind": "theorem", "module": "Mathlib.Data.Finset.Sym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.symInsertEquiv", "kind": "definition", "module": "Mathlib.Data.Finset.Sym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_symmDiff", "kind": "theorem", "module": "Mathlib.Data.Finset.SymmDiff", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Finset.coe_symmDiff", "kind": "theorem", "module": "Mathlib.Data.Finset.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.symmDiff_eq_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.symmDiff_nonempty", "kind": "theorem", "module": "Mathlib.Data.Finset.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image_symmDiff", "kind": "theorem", "module": "Mathlib.Data.Finset.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.symmDiff_subset_sdiff", "kind": "theorem", "module": "Mathlib.Data.Finset.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.symmDiff_subset_sdiff'", "kind": "theorem", "module": "Mathlib.Data.Finset.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.symmDiff_subset_union", "kind": "theorem", "module": "Mathlib.Data.Finset.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.symmDiff_eq_union_iff", "kind": "theorem", "module": "Mathlib.Data.Finset.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.symmDiff_eq_union", "kind": "theorem", "module": "Mathlib.Data.Finset.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.disjiUnion", "kind": "definition", "module": "Mathlib.Data.Finset.Union", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.disjiUnion_val", "kind": "theorem", "module": "Mathlib.Data.Finset.Union", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.disjiUnion_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.Union", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_disjiUnion", "kind": "theorem", "module": "Mathlib.Data.Finset.Union", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.coe_disjiUnion", "kind": "theorem", "module": "Mathlib.Data.Finset.Union", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.disjiUnion_cons", "kind": "theorem", "module": "Mathlib.Data.Finset.Union", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.singleton_disjiUnion", "kind": "theorem", "module": "Mathlib.Data.Finset.Union", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.disjiUnion_disjiUnion", "kind": "theorem", "module": "Mathlib.Data.Finset.Union", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sUnion_disjiUnion", "kind": "theorem", "module": "Mathlib.Data.Finset.Union", "is_tactic_proof": true, "tactics": ["ext", "simp", "tauto"], "tactic_count": 3}
{"name": "_private.Mathlib.Data.Finset.Union.0.Finset.pairwiseDisjoint_fibers", "kind": "theorem", "module": "Mathlib.Data.Finset.Union", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.disjiUnion_filter_eq", "kind": "theorem", "module": "Mathlib.Data.Finset.Union", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.disjiUnion_filter_eq_of_maps_to", "kind": "theorem", "module": "Mathlib.Data.Finset.Union", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.map_disjiUnion", "kind": "theorem", "module": "Mathlib.Data.Finset.Union", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.disjiUnion_map", "kind": "theorem", "module": "Mathlib.Data.Finset.Union", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.disjiUnion_singleton_eq_self", "kind": "theorem", "module": "Mathlib.Data.Finset.Union", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.fold_disjiUnion", "kind": "theorem", "module": "Mathlib.Data.Finset.Union", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.pairwiseDisjoint_filter", "kind": "theorem", "module": "Mathlib.Data.Finset.Union", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.filter_disjiUnion", "kind": "theorem", "module": "Mathlib.Data.Finset.Union", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.disjiUnion_singleton", "kind": "theorem", "module": "Mathlib.Data.Finset.Union", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finset.disjoint_disjiUnion_left", "kind": "theorem", "module": "Mathlib.Data.Finset.Union", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "Finset.disjoint_disjiUnion_right", "kind": "theorem", "module": "Mathlib.Data.Finset.Union", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.pairwiseDisjoint_disjUnion", "kind": "theorem", "module": "Mathlib.Data.Finset.Union", "is_tactic_proof": true, "tactics": ["intros", "simp"], "tactic_count": 2}
{"name": "Finset.disjiUnion_disjUnion", "kind": "theorem", "module": "Mathlib.Data.Finset.Union", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.biUnion", "kind": "definition", "module": "Mathlib.Data.Finset.Union", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.biUnion_val", "kind": "theorem", "module": "Mathlib.Data.Finset.Union", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.biUnion_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.Union", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_biUnion", "kind": "theorem", "module": "Mathlib.Data.Finset.Union", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.coe_biUnion", "kind": "theorem", "module": "Mathlib.Data.Finset.Union", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.biUnion_insert", "kind": "theorem", "module": "Mathlib.Data.Finset.Union", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Finset.biUnion_congr", "kind": "theorem", "module": "Mathlib.Data.Finset.Union", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.disjiUnion_eq_biUnion", "kind": "theorem", "module": "Mathlib.Data.Finset.Union", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.biUnion_subset", "kind": "theorem", "module": "Mathlib.Data.Finset.Union", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.singleton_biUnion", "kind": "theorem", "module": "Mathlib.Data.Finset.Union", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.biUnion_inter", "kind": "theorem", "module": "Mathlib.Data.Finset.Union", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.inter_biUnion", "kind": "theorem", "module": "Mathlib.Data.Finset.Union", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.biUnion_biUnion", "kind": "theorem", "module": "Mathlib.Data.Finset.Union", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.bind_toFinset", "kind": "theorem", "module": "Mathlib.Data.Finset.Union", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.biUnion_mono", "kind": "theorem", "module": "Mathlib.Data.Finset.Union", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.biUnion_subset_biUnion_of_subset_left", "kind": "theorem", "module": "Mathlib.Data.Finset.Union", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.subset_biUnion_of_mem", "kind": "theorem", "module": "Mathlib.Data.Finset.Union", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.biUnion_subset_iff_forall_subset", "kind": "theorem", "module": "Mathlib.Data.Finset.Union", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.biUnion_singleton_eq_self", "kind": "theorem", "module": "Mathlib.Data.Finset.Union", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.filter_biUnion", "kind": "theorem", "module": "Mathlib.Data.Finset.Union", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.biUnion_filter_eq_of_maps_to", "kind": "theorem", "module": "Mathlib.Data.Finset.Union", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.erase_biUnion", "kind": "theorem", "module": "Mathlib.Data.Finset.Union", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.biUnion_nonempty", "kind": "theorem", "module": "Mathlib.Data.Finset.Union", "is_tactic_proof": true, "tactics": ["simp", "rw", "simp"], "tactic_count": 3}
{"name": "Finset.Nonempty.biUnion", "kind": "theorem", "module": "Mathlib.Data.Finset.Union", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.disjoint_biUnion_left", "kind": "theorem", "module": "Mathlib.Data.Finset.Union", "is_tactic_proof": true, "tactics": ["classical", "refine", "simp", "intro", "simp"], "tactic_count": 5}
{"name": "Finset.disjoint_biUnion_right", "kind": "theorem", "module": "Mathlib.Data.Finset.Union", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.image_biUnion", "kind": "theorem", "module": "Mathlib.Data.Finset.Union", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.biUnion_image", "kind": "theorem", "module": "Mathlib.Data.Finset.Union", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image_biUnion_filter_eq", "kind": "theorem", "module": "Mathlib.Data.Finset.Union", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.union_biUnion", "kind": "theorem", "module": "Mathlib.Data.Finset.Union", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.biUnion_union", "kind": "theorem", "module": "Mathlib.Data.Finset.Union", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.biUnion_singleton", "kind": "theorem", "module": "Mathlib.Data.Finset.Union", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Function.updateFinset", "kind": "definition", "module": "Mathlib.Data.Finset.Update", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.updateFinset_def", "kind": "theorem", "module": "Mathlib.Data.Finset.Update", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.updateFinset_empty", "kind": "theorem", "module": "Mathlib.Data.Finset.Update", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.updateFinset_singleton", "kind": "theorem", "module": "Mathlib.Data.Finset.Update", "is_tactic_proof": true, "tactics": ["congr", "by_cases", "cases", "simp", "simp"], "tactic_count": 5}
{"name": "Function.update_eq_updateFinset", "kind": "theorem", "module": "Mathlib.Data.Finset.Update", "is_tactic_proof": true, "tactics": ["congr", "by_cases", "cases", "simp", "exact", "simp"], "tactic_count": 6}
{"name": "DependsOn.updateFinset", "kind": "theorem", "module": "Mathlib.Data.Finset.Update", "is_tactic_proof": true, "tactics": ["refine", "simp", "split_ifs", "simp_all"], "tactic_count": 4}
{"name": "DependsOn.update", "kind": "theorem", "module": "Mathlib.Data.Finset.Update", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Function.updateFinset_updateFinset", "kind": "theorem", "module": "Mathlib.Data.Finset.Update", "is_tactic_proof": true, "tactics": ["set", "ext", "by_cases", "simp", "exfalso", "exact", "exact"], "tactic_count": 7}
{"name": "Function.updateFinset_updateFinset_of_subset", "kind": "theorem", "module": "Mathlib.Data.Finset.Update", "is_tactic_proof": true, "tactics": ["ext", "simp", "split_ifs", "exact"], "tactic_count": 4}
{"name": "Function.restrict_updateFinset_of_subset", "kind": "theorem", "module": "Mathlib.Data.Finset.Update", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Function.restrict_updateFinset", "kind": "theorem", "module": "Mathlib.Data.Finset.Update", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Function.updateFinset_restrict", "kind": "theorem", "module": "Mathlib.Data.Finset.Update", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Finsupp.toAList", "kind": "definition", "module": "Mathlib.Data.Finsupp.AList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.toAList_keys_toFinset", "kind": "theorem", "module": "Mathlib.Data.Finsupp.AList", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Finsupp.mem_toAlist", "kind": "theorem", "module": "Mathlib.Data.Finsupp.AList", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "AList.lookupFinsupp", "kind": "definition", "module": "Mathlib.Data.Finsupp.AList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AList.lookupFinsupp_apply", "kind": "theorem", "module": "Mathlib.Data.Finsupp.AList", "is_tactic_proof": true, "tactics": ["simp", "congr"], "tactic_count": 2}
{"name": "AList.lookupFinsupp_support", "kind": "theorem", "module": "Mathlib.Data.Finsupp.AList", "is_tactic_proof": true, "tactics": ["dsimp", "congr"], "tactic_count": 2}
{"name": "AList.lookupFinsupp_eq_iff_of_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Finsupp.AList", "is_tactic_proof": true, "tactics": ["rw", "rcases"], "tactic_count": 2}
{"name": "AList.lookupFinsupp_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Data.Finsupp.AList", "is_tactic_proof": true, "tactics": ["rw", "rcases"], "tactic_count": 2}
{"name": "AList.empty_lookupFinsupp", "kind": "theorem", "module": "Mathlib.Data.Finsupp.AList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AList.insert_lookupFinsupp", "kind": "theorem", "module": "Mathlib.Data.Finsupp.AList", "is_tactic_proof": true, "tactics": ["ext", "by_cases"], "tactic_count": 2}
{"name": "AList.singleton_lookupFinsupp", "kind": "theorem", "module": "Mathlib.Data.Finsupp.AList", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finsupp.toAList_lookupFinsupp", "kind": "theorem", "module": "Mathlib.Data.Finsupp.AList", "is_tactic_proof": true, "tactics": ["ext", "classical", "by_cases", "suffices", "simp", "suffices", "apply", "simpa"], "tactic_count": 8}
{"name": "AList.lookupFinsupp_surjective", "kind": "theorem", "module": "Mathlib.Data.Finsupp.AList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.antidiagonal'", "kind": "definition", "module": "Mathlib.Data.Finsupp.Antidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.instHasAntidiagonal", "kind": "instance", "module": "Mathlib.Data.Finsupp.Antidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.antidiagonal_zero", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Antidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.prod_antidiagonal_swap", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Antidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.antidiagonal_single", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Antidiagonal", "is_tactic_proof": true, "tactics": ["ext", "simp", "constructor", "intro", "refine", "simp_rw", "intro", "replace", "simp_rw", "obtain", "exact", "simp_rw", "exact", "rintro", "exact"], "tactic_count": 15}
{"name": "Finsupp.graph", "kind": "definition", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.mk_mem_graph_iff", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "constructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 6}
{"name": "Finsupp.mem_graph_iff", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": true, "tactics": ["cases", "exact"], "tactic_count": 2}
{"name": "Finsupp.mk_mem_graph", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.apply_eq_of_mem_graph", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.notMem_graph_snd_zero", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.image_fst_graph", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finsupp.graph_injective", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": true, "tactics": ["intro", "classical", "have", "refine", "exact"], "tactic_count": 5}
{"name": "Finsupp.graph_inj", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.graph_zero", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finsupp.graph_eq_empty", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.mapRange_multiset_sum", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.mapRange_finset_sum", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.equivMapDomain", "kind": "definition", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.equivMapDomain_apply", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.equivMapDomain_symm_apply", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.equivMapDomain_refl", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finsupp.equivMapDomain_refl'", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finsupp.equivMapDomain_trans", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finsupp.equivMapDomain_trans'", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finsupp.equivMapDomain_single", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": true, "tactics": ["classical", "ext", "simp"], "tactic_count": 3}
{"name": "Finsupp.equivMapDomain_zero", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finsupp.prod_equivMapDomain", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finsupp.equivCongrLeft", "kind": "definition", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": true, "tactics": ["refine", "simp"], "tactic_count": 2}
{"name": "Finsupp.equivCongrLeft_apply", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.equivCongrLeft_symm", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.cast_finsuppProd", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.cast_finsupp_sum", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.cast_finsuppProd", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.cast_finsupp_sum", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.cast_finsupp_sum", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.cast_finsuppProd", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.mapDomain", "kind": "definition", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.mapDomain_apply", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": true, "tactics": ["rw", "intro", "exact", "intro", "rw"], "tactic_count": 5}
{"name": "Finsupp.mapDomain_notin_range", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finsupp.mapDomain_id", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.mapDomain_comp", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": true, "tactics": ["refine", "intro", "exact", "intro", "exact", "refine", "exact"], "tactic_count": 7}
{"name": "Finsupp.mapDomain_single", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.mapDomain_zero", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.mapDomain_congr", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.mapDomain_add", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.mapDomain_equiv_apply", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": true, "tactics": ["conv_lhs", "exact"], "tactic_count": 2}
{"name": "Finsupp.mapDomain.addMonoidHom", "kind": "definition", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.mapDomain.addMonoidHom_id", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.mapDomain.addMonoidHom_comp", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.mapDomain_finset_sum", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.mapDomain_sum", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.mapDomain_support", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.mapDomain_apply'", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": true, "tactics": ["classical", "rw", "simp_rw", "by_cases", "rw", "convert", "refine", "exact", "rw", "refine", "exact"], "tactic_count": 11}
{"name": "Finsupp.mapDomain_support_of_injOn", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.mapDomain_support_of_injective", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.prod_mapDomain_index", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.sum_mapDomain_index_addMonoidHom", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.embDomain_eq_mapDomain", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "rcases", "rw", "rw"], "tactic_count": 5}
{"name": "Finsupp.prod_mapDomain_index_inj", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finsupp.mapDomain_injective", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": true, "tactics": ["intro", "ext", "have", "rwa"], "tactic_count": 4}
{"name": "Finsupp.mapDomain_surjective", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": true, "tactics": ["intro", "use", "rw"], "tactic_count": 3}
{"name": "Finsupp.mapDomainEmbedding", "kind": "definition", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.mapDomain.addMonoidHom_comp_mapRange", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Finsupp.mapDomain_mapRange", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.sum_update_add", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": true, "tactics": ["rw", "conv_rhs", "rw", "congr", "rw"], "tactic_count": 5}
{"name": "Finsupp.mapDomain_injOn", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": true, "tactics": ["intro", "ext", "classical", "by_cases", "rw", "apply", "exact", "simp_all"], "tactic_count": 8}
{"name": "Finsupp.equivMapDomain_eq_mapDomain", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finsupp.comapDomain", "kind": "definition", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.comapDomain_apply", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.sum_comapDomain", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.eq_zero_of_comapDomain_eq_zero", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "intro", "obtain", "exact"], "tactic_count": 5}
{"name": "Finsupp.embDomain_comapDomain", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "obtain", "rw", "replace", "rw"], "tactic_count": 6}
{"name": "Finsupp.comapDomain_single", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simp_rw", "rw", "support_single_ne_zero", "rw", "exact"], "tactic_count": 6}
{"name": "Finsupp.comapDomain_surjective", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": true, "tactics": ["classical", "intro", "cases", "exact", "obtain", "exact"], "tactic_count": 6}
{"name": "Finsupp.comapDomain_add", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Finsupp.comapDomain_add_of_injective", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.comapDomain.addMonoidHom", "kind": "definition", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.mapDomain_comapDomain", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": true, "tactics": ["conv_rhs", "rfl"], "tactic_count": 2}
{"name": "Finsupp.mapDomain_comapDomain_nat_add_one", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": true, "tactics": ["refine", "congr", "simp_all"], "tactic_count": 3}
{"name": "Finsupp.comapDomain_mapDomain", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finsupp.mem_range_mapDomain_iff", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": true, "tactics": ["refine", "refine", "by_contra", "simp", "exact"], "tactic_count": 5}
{"name": "Finsupp.filter", "kind": "definition", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.filter_apply", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.filter_eq_indicator", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Finsupp.filter_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finsupp.filter_eq_self_iff", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finsupp.filter_apply_pos", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.filter_apply_neg", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.support_filter", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.filter_zero", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finsupp.filter_single_of_pos", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.filter_single_of_neg", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.prod_filter_index", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "rw"], "tactic_count": 3}
{"name": "Finsupp.prod_filter_mul_prod_filter_not", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Finsupp.prod_div_prod_filter", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.filter_pos_add_filter_neg", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.frange", "kind": "definition", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.mem_frange", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finsupp.zero_notMem_frange", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.frange_single", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finsupp.mem_frange_of_mem", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": true, "tactics": ["simp_all"], "tactic_count": 1}
{"name": "Finsupp.range_subset_insert_frange", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finsupp.finite_range", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.subtypeDomain", "kind": "definition", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.support_subtypeDomain", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finsupp.subtypeDomain_apply", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.subtypeDomain_zero", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.subtypeDomain_eq_iff_forall", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Finsupp.subtypeDomain_eq_iff", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.subtypeDomain_eq_zero_iff'", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.subtypeDomain_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.prod_subtypeDomain_index", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": true, "tactics": ["refine"], "tactic_count": 1}
{"name": "Finsupp.subtypeDomain_add", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.subtypeDomainAddMonoidHom", "kind": "definition", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.filterAddHom", "kind": "definition", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.filter_add", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.subtypeDomain_sum", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.subtypeDomain_finsupp_sum", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.filter_sum", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.filter_eq_sum", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.subtypeDomain_neg", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.subtypeDomain_sub", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.filter_neg", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.filter_sub", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.mem_support_multiset_sum", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Finsupp.uncurry", "kind": "definition", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Finsupp.sumFinsuppEquivProdFinsupp", "kind": "definition", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.fst_sumFinsuppEquivProdFinsupp", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Finsupp.extendDomain_eq_embDomain_subtype", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "refine", "simp", "simp"], "tactic_count": 5}
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{"name": "Finsupp.restrictSupportEquiv_symm_apply_coe", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "Finsupp.mem_splitSupport_iff_nonzero", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Basic", "is_tactic_proof": false, "tactics": ["classical", "rw", "simp"], "tactic_count": 3}
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{"name": "Finsupp.mapRange_injective", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Defs", "is_tactic_proof": true, "tactics": ["intro", "rw", "simpa"], "tactic_count": 3}
{"name": "Finsupp.mapRange_surjective", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Defs", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Finsupp.mapRange.equiv", "kind": "definition", "module": "Mathlib.Data.Finsupp.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.mapRange.equiv_refl", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Defs", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finsupp.mapRange.equiv_trans", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Defs", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finsupp.mapRange.equiv_symm", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.embDomain", "kind": "definition", "module": "Mathlib.Data.Finsupp.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.support_embDomain", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.embDomain_zero", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.embDomain_apply", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Defs", "is_tactic_proof": false, "tactics": ["simp", "split_ifs"], "tactic_count": 2}
{"name": "Finsupp.embDomain_apply_self", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Defs", "is_tactic_proof": true, "tactics": ["classical", "simp_rw", "split_ifs", "refine", "exact", "exact"], "tactic_count": 6}
{"name": "Finsupp.embDomain_notin_range", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Defs", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finsupp.embDomain_injective", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.embDomain_inj", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.embDomain_eq_zero", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.embDomain_mapRange", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Defs", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finsupp.zipWith", "kind": "definition", "module": "Mathlib.Data.Finsupp.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.zipWith_apply", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.support_zipWith", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Defs", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "instEncodableFinsuppOfDecidableNeOfNat", "kind": "instance", "module": "Mathlib.Data.Finsupp.Encodable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCountableFinsupp", "kind": "instance", "module": "Mathlib.Data.Finsupp.Encodable", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finsupp.add_closure_setOf_eq_single", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Ext", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.addHom_ext", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Ext", "is_tactic_proof": true, "tactics": ["refine", "rintro", "apply"], "tactic_count": 3}
{"name": "Finsupp.addHom_ext'", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Ext", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.mulHom_ext", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Ext", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.mulHom_ext'", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Ext", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.tail", "kind": "definition", "module": "Mathlib.Data.Finsupp.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.cons", "kind": "definition", "module": "Mathlib.Data.Finsupp.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.tail_apply", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.cons_zero", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.cons_succ", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.tail_cons", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.tail_update_zero", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finsupp.tail_update_succ", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Fin", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finsupp.cons_tail", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Fin", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "rw", "rw"], "tactic_count": 4}
{"name": "Finsupp.cons_zero_zero", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Fin", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "simp", "rw", "simp"], "tactic_count": 5}
{"name": "Finsupp.cons_ne_zero_of_left", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Fin", "is_tactic_proof": true, "tactics": ["contrapose", "rw"], "tactic_count": 2}
{"name": "Finsupp.cons_ne_zero_of_right", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Fin", "is_tactic_proof": true, "tactics": ["contrapose", "ext", "simp"], "tactic_count": 3}
{"name": "Finsupp.cons_ne_zero_iff", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Fin", "is_tactic_proof": true, "tactics": ["refine", "refine", "rw"], "tactic_count": 3}
{"name": "Finsupp.cons_support", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Fin", "is_tactic_proof": true, "tactics": ["intro", "suffices", "apply", "rintro", "simpa"], "tactic_count": 5}
{"name": "Finsupp.cons_right_injective", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.fintype", "kind": "instance", "module": "Mathlib.Data.Finsupp.Fintype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.infinite_of_left", "kind": "instance", "module": "Mathlib.Data.Finsupp.Fintype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.infinite_of_right", "kind": "instance", "module": "Mathlib.Data.Finsupp.Fintype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_finsupp", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Fintype", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finsupp.indicator", "kind": "definition", "module": "Mathlib.Data.Finsupp.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.indicator_of_mem", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.indicator_of_notMem", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.indicator_apply", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Indicator", "is_tactic_proof": true, "tactics": ["simp", "congr"], "tactic_count": 2}
{"name": "Finsupp.indicator_injective", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Indicator", "is_tactic_proof": true, "tactics": ["intro", "ext", "rw", "exact"], "tactic_count": 4}
{"name": "Finsupp.support_indicator_subset", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Indicator", "is_tactic_proof": true, "tactics": ["intro", "rw", "by_contra", "exact"], "tactic_count": 4}
{"name": "Finsupp.single_eq_indicator", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Indicator", "is_tactic_proof": true, "tactics": ["classical", "ext", "simp"], "tactic_count": 3}
{"name": "Finsupp.rangeSingleton", "kind": "definition", "module": "Mathlib.Data.Finsupp.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.mem_rangeSingleton_apply_iff", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.rangeIcc", "kind": "definition", "module": "Mathlib.Data.Finsupp.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.coe_rangeIcc", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.rangeIcc_support", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.mem_rangeIcc_apply_iff", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.instLocallyFiniteOrder", "kind": "instance", "module": "Mathlib.Data.Finsupp.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.Icc_eq", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.card_Icc", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Interval", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Finsupp.card_Ico", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Interval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finsupp.card_Ioc", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Interval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finsupp.card_Ioo", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Interval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finsupp.card_uIcc", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Interval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finsupp.card_Iic", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Interval", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finsupp.card_Iio", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Interval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finsupp.Lex", "kind": "definition", "module": "Mathlib.Data.Finsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.lex_eq_finsupp_lex", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.lex_def", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.lex_eq_invImage_dfinsupp_lex", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.instLTLex", "kind": "instance", "module": "Mathlib.Data.Finsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.instLTColex", "kind": "instance", "module": "Mathlib.Data.Finsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.Lex.lt_iff", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.Colex.lt_iff", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.lex_lt_of_lt_of_preorder", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.lex_lt_of_lt", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.lex_iff_of_unique", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.Lex.lt_iff_of_unique", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.Colex.lt_iff_of_unique", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.Lex.isStrictOrder", "kind": "instance", "module": "Mathlib.Data.Finsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.Colex.isStrictOrder", "kind": "instance", "module": "Mathlib.Data.Finsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.Lex.partialOrder", "kind": "instance", "module": "Mathlib.Data.Finsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.Colex.partialOrder", "kind": "instance", "module": "Mathlib.Data.Finsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.Lex.linearOrder", "kind": "instance", "module": "Mathlib.Data.Finsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.Colex.linearOrder", "kind": "instance", "module": "Mathlib.Data.Finsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.Lex.le_iff_of_unique", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.Colex.le_iff_of_unique", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.Lex.single_strictAnti", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Lex", "is_tactic_proof": true, "tactics": ["intro", "simp", "simp", "use", "constructor", "intro", "simp", "simp"], "tactic_count": 8}
{"name": "Finsupp.Colex.single_strictMono", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.Lex.single_lt_iff", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.Colex.single_lt_iff", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.Lex.single_le_iff", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.Colex.single_le_iff", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.Lex.single_antitone", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.toLex_monotone", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.toColex_monotone", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.lt_of_forall_lt_of_lt", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.Lex.addLeftStrictMono", "kind": "instance", "module": "Mathlib.Data.Finsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.Colex.addLeftStrictMono", "kind": "instance", "module": "Mathlib.Data.Finsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.Lex.addLeftMono", "kind": "instance", "module": "Mathlib.Data.Finsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.Colex.addLeftMono", "kind": "instance", "module": "Mathlib.Data.Finsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.Lex.addRightStrictMono", "kind": "instance", "module": "Mathlib.Data.Finsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.Colex.addRightStrictMono", "kind": "instance", "module": "Mathlib.Data.Finsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.Lex.addRightMono", "kind": "instance", "module": "Mathlib.Data.Finsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.Colex.addRightMono", "kind": "instance", "module": "Mathlib.Data.Finsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.Lex.orderBot", "kind": "instance", "module": "Mathlib.Data.Finsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.Colex.orderBot", "kind": "instance", "module": "Mathlib.Data.Finsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.Lex.isOrderedCancelAddMonoid", "kind": "instance", "module": "Mathlib.Data.Finsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.Colex.isOrderedCancelAddMonoid", "kind": "instance", "module": "Mathlib.Data.Finsupp.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonomialOrder.le_add_right", "kind": "theorem", "module": "Mathlib.Data.Finsupp.MonomialOrder", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MonomialOrder.orderBot", "kind": "instance", "module": "Mathlib.Data.Finsupp.MonomialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonomialOrder.bot_eq_zero", "kind": "theorem", "module": "Mathlib.Data.Finsupp.MonomialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonomialOrder.zero_le", "kind": "theorem", "module": "Mathlib.Data.Finsupp.MonomialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonomialOrder.eq_zero_iff", "kind": "theorem", "module": "Mathlib.Data.Finsupp.MonomialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonomialOrder.toSyn_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Data.Finsupp.MonomialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonomialOrder.toSyn_lt_iff_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Finsupp.MonomialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonomialOrder.toSyn_strictMono", "kind": "theorem", "module": "Mathlib.Data.Finsupp.MonomialOrder", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "MonomialOrder.term_≺[_]_", "kind": "definition", "module": "Mathlib.Data.Finsupp.MonomialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonomialOrder._aux_Mathlib_Data_Finsupp_MonomialOrder___macroRules_MonomialOrder_term_≺[_]__1", "kind": "definition", "module": "Mathlib.Data.Finsupp.MonomialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonomialOrder.term_≼[_]_", "kind": "definition", "module": "Mathlib.Data.Finsupp.MonomialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonomialOrder._aux_Mathlib_Data_Finsupp_MonomialOrder___macroRules_MonomialOrder_term_≼[_]__1", "kind": "definition", "module": "Mathlib.Data.Finsupp.MonomialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsOrderedCancelAddMonoidLexFinsupp", "kind": "instance", "module": "Mathlib.Data.Finsupp.MonomialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_example", "kind": "example", "module": "Mathlib.Data.Finsupp.MonomialOrder", "is_tactic_proof": true, "tactics": ["use"], "tactic_count": 1}
{"name": "_example", "kind": "example", "module": "Mathlib.Data.Finsupp.MonomialOrder", "is_tactic_proof": true, "tactics": ["use"], "tactic_count": 1}
{"name": "_example", "kind": "example", "module": "Mathlib.Data.Finsupp.MonomialOrder", "is_tactic_proof": true, "tactics": ["use"], "tactic_count": 1}
{"name": "MonomialOrder.lex", "kind": "definition", "module": "Mathlib.Data.Finsupp.MonomialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonomialOrder.lex_le_iff", "kind": "theorem", "module": "Mathlib.Data.Finsupp.MonomialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonomialOrder.lex_lt_iff", "kind": "theorem", "module": "Mathlib.Data.Finsupp.MonomialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonomialOrder.lex_lt_iff_of_unique", "kind": "theorem", "module": "Mathlib.Data.Finsupp.MonomialOrder", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MonomialOrder.lex_le_iff_of_unique", "kind": "theorem", "module": "Mathlib.Data.Finsupp.MonomialOrder", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DegLex", "kind": "definition", "module": "Mathlib.Data.Finsupp.MonomialOrder.DegLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toDegLex", "kind": "definition", "module": "Mathlib.Data.Finsupp.MonomialOrder.DegLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toDegLex_injective", "kind": "theorem", "module": "Mathlib.Data.Finsupp.MonomialOrder.DegLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toDegLex_inj", "kind": "theorem", "module": "Mathlib.Data.Finsupp.MonomialOrder.DegLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofDegLex", "kind": "definition", "module": "Mathlib.Data.Finsupp.MonomialOrder.DegLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofDegLex_injective", "kind": "theorem", "module": "Mathlib.Data.Finsupp.MonomialOrder.DegLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofDegLex_inj", "kind": "theorem", "module": "Mathlib.Data.Finsupp.MonomialOrder.DegLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofDegLex_symm_eq", "kind": "theorem", "module": "Mathlib.Data.Finsupp.MonomialOrder.DegLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toDegLex_symm_eq", "kind": "theorem", "module": "Mathlib.Data.Finsupp.MonomialOrder.DegLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofDegLex_toDegLex", "kind": "theorem", "module": "Mathlib.Data.Finsupp.MonomialOrder.DegLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toDegLex_ofDegLex", "kind": "theorem", "module": "Mathlib.Data.Finsupp.MonomialOrder.DegLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DegLex.rec", "kind": "definition", "module": "Mathlib.Data.Finsupp.MonomialOrder.DegLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DegLex.forall_iff", "kind": "theorem", "module": "Mathlib.Data.Finsupp.MonomialOrder.DegLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DegLex.exists_iff", "kind": "theorem", "module": "Mathlib.Data.Finsupp.MonomialOrder.DegLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instAddCommMonoidDegLex", "kind": "instance", "module": "Mathlib.Data.Finsupp.MonomialOrder.DegLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toDegLex_add", "kind": "theorem", "module": "Mathlib.Data.Finsupp.MonomialOrder.DegLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofDegLex_add", "kind": "theorem", "module": "Mathlib.Data.Finsupp.MonomialOrder.DegLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.DegLex", "kind": "definition", "module": "Mathlib.Data.Finsupp.MonomialOrder.DegLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.degLex_def", "kind": "theorem", "module": "Mathlib.Data.Finsupp.MonomialOrder.DegLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.DegLex.wellFounded", "kind": "theorem", "module": "Mathlib.Data.Finsupp.MonomialOrder.DegLex", "is_tactic_proof": true, "tactics": ["have", "rw", "unfold", "rw", "exact"], "tactic_count": 5}
{"name": "Finsupp.DegLex.instLTDegLexNat", "kind": "instance", "module": "Mathlib.Data.Finsupp.MonomialOrder.DegLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.DegLex.lt_def", "kind": "theorem", "module": "Mathlib.Data.Finsupp.MonomialOrder.DegLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.DegLex.lt_iff", "kind": "theorem", "module": "Mathlib.Data.Finsupp.MonomialOrder.DegLex", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finsupp.DegLex.isStrictOrder", "kind": "instance", "module": "Mathlib.Data.Finsupp.MonomialOrder.DegLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.DegLex.instLinearOrderDegLexNat", "kind": "instance", "module": "Mathlib.Data.Finsupp.MonomialOrder.DegLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.DegLex.le_iff", "kind": "theorem", "module": "Mathlib.Data.Finsupp.MonomialOrder.DegLex", "is_tactic_proof": true, "tactics": ["simp", "by_cases", "simp", "by_cases", "simp", "simp"], "tactic_count": 6}
{"name": "Finsupp.DegLex.instIsOrderedCancelAddMonoidDegLexNat", "kind": "instance", "module": "Mathlib.Data.Finsupp.MonomialOrder.DegLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.DegLex.single_strictAnti", "kind": "theorem", "module": "Mathlib.Data.Finsupp.MonomialOrder.DegLex", "is_tactic_proof": true, "tactics": ["intro", "simp"], "tactic_count": 2}
{"name": "Finsupp.DegLex.single_antitone", "kind": "theorem", "module": "Mathlib.Data.Finsupp.MonomialOrder.DegLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.DegLex.single_lt_iff", "kind": "theorem", "module": "Mathlib.Data.Finsupp.MonomialOrder.DegLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.DegLex.single_le_iff", "kind": "theorem", "module": "Mathlib.Data.Finsupp.MonomialOrder.DegLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.DegLex.monotone_degree", "kind": "theorem", "module": "Mathlib.Data.Finsupp.MonomialOrder.DegLex", "is_tactic_proof": true, "tactics": ["intro", "rw", "rintro", "apply", "apply"], "tactic_count": 5}
{"name": "Finsupp.DegLex.orderBot", "kind": "instance", "module": "Mathlib.Data.Finsupp.MonomialOrder.DegLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.DegLex.wellFoundedLT", "kind": "instance", "module": "Mathlib.Data.Finsupp.MonomialOrder.DegLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonomialOrder.degLex", "kind": "definition", "module": "Mathlib.Data.Finsupp.MonomialOrder.DegLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonomialOrder.degLex_le_iff", "kind": "theorem", "module": "Mathlib.Data.Finsupp.MonomialOrder.DegLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonomialOrder.degLex_lt_iff", "kind": "theorem", "module": "Mathlib.Data.Finsupp.MonomialOrder.DegLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonomialOrder.degLex_single_le_iff", "kind": "theorem", "module": "Mathlib.Data.Finsupp.MonomialOrder.DegLex", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MonomialOrder.degLex_single_lt_iff", "kind": "theorem", "module": "Mathlib.Data.Finsupp.MonomialOrder.DegLex", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "_example", "kind": "example", "module": "Mathlib.Data.Finsupp.MonomialOrder.DegLex", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "_example", "kind": "example", "module": "Mathlib.Data.Finsupp.MonomialOrder.DegLex", "is_tactic_proof": true, "tactics": ["rw", "simp", "true_and,", "use", "simp"], "tactic_count": 5}
{"name": "_example", "kind": "example", "module": "Mathlib.Data.Finsupp.MonomialOrder.DegLex", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finsupp.toMultiset", "kind": "definition", "module": "Mathlib.Data.Finsupp.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.toMultiset_zero", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.toMultiset_add", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.toMultiset_apply", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.toMultiset_single", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Multiset", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finsupp.toMultiset_sum", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.toMultiset_sum_single", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Multiset", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Finsupp.card_toMultiset", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Multiset", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finsupp.toMultiset_map", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Multiset", "is_tactic_proof": true, "tactics": ["refine", "rw", "intro", "rw", "toMultiset_single,", "rfl"], "tactic_count": 6}
{"name": "Finsupp.prod_toMultiset", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Multiset", "is_tactic_proof": true, "tactics": ["refine", "rw", "intro", "rw", "exact"], "tactic_count": 5}
{"name": "Finsupp.toFinset_toMultiset", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Multiset", "is_tactic_proof": true, "tactics": ["refine", "rw", "intro", "rw", "refine", "rwa"], "tactic_count": 6}
{"name": "Finsupp.count_toMultiset", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.toMultiset_sup", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Multiset", "is_tactic_proof": true, "tactics": ["ext", "simp_rw"], "tactic_count": 2}
{"name": "Finsupp.toMultiset_inf", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Multiset", "is_tactic_proof": true, "tactics": ["ext", "simp_rw"], "tactic_count": 2}
{"name": "Finsupp.mem_toMultiset", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Multiset", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Multiset.toFinsupp", "kind": "definition", "module": "Mathlib.Data.Finsupp.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.toFinsupp_support", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.toFinsupp_apply", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.toFinsupp_zero", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.toFinsupp_add", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.toFinsupp_singleton", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Multiset", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Multiset.toFinsupp_toMultiset", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.toFinsupp_eq_iff", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.toFinsupp_union", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Multiset", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Multiset.toFinsupp_inter", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Multiset", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Multiset.toFinsupp_sum_eq", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Multiset", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finsupp.toMultiset_toFinsupp", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.toMultiset_eq_iff", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.orderIsoMultiset", "kind": "definition", "module": "Mathlib.Data.Finsupp.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.coe_orderIsoMultiset", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.coe_orderIsoMultiset_symm", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.toMultiset_strictMono", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Multiset", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finsupp.sum_id_lt_of_lt", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Multiset", "is_tactic_proof": true, "tactics": ["rw", "apply", "exact"], "tactic_count": 3}
{"name": "Finsupp.lt_wf", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.instWellFoundedRelationNat", "kind": "instance", "module": "Mathlib.Data.Finsupp.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.toFinsupp_strictMono", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym.equivNatSum", "kind": "definition", "module": "Mathlib.Data.Finsupp.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym.coe_equivNatSum_apply_apply", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym.coe_equivNatSum_symm_apply", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym.equivNatSumOfFintype", "kind": "definition", "module": "Mathlib.Data.Finsupp.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym.coe_equivNatSumOfFintype_apply_apply", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym.coe_equivNatSumOfFintype_symm_apply", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Multiset", "is_tactic_proof": true, "tactics": ["obtain", "change", "ext", "rw", "simp"], "tactic_count": 5}
{"name": "Finsupp.neLocus", "kind": "definition", "module": "Mathlib.Data.Finsupp.NeLocus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.mem_neLocus", "kind": "theorem", "module": "Mathlib.Data.Finsupp.NeLocus", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finsupp.notMem_neLocus", "kind": "theorem", "module": "Mathlib.Data.Finsupp.NeLocus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.coe_neLocus", "kind": "theorem", "module": "Mathlib.Data.Finsupp.NeLocus", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "Finsupp.neLocus_eq_empty", "kind": "theorem", "module": "Mathlib.Data.Finsupp.NeLocus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.nonempty_neLocus_iff", "kind": "theorem", "module": "Mathlib.Data.Finsupp.NeLocus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.neLocus_comm", "kind": "theorem", "module": "Mathlib.Data.Finsupp.NeLocus", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Finsupp.neLocus_zero_right", "kind": "theorem", "module": "Mathlib.Data.Finsupp.NeLocus", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "Finsupp.neLocus_zero_left", "kind": "theorem", "module": "Mathlib.Data.Finsupp.NeLocus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.subset_mapRange_neLocus", "kind": "theorem", "module": "Mathlib.Data.Finsupp.NeLocus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.zipWith_neLocus_eq_left", "kind": "theorem", "module": "Mathlib.Data.Finsupp.NeLocus", "is_tactic_proof": true, "tactics": ["ext", "simpa"], "tactic_count": 2}
{"name": "Finsupp.zipWith_neLocus_eq_right", "kind": "theorem", "module": "Mathlib.Data.Finsupp.NeLocus", "is_tactic_proof": true, "tactics": ["ext", "simpa"], "tactic_count": 2}
{"name": "Finsupp.mapRange_neLocus_eq", "kind": "theorem", "module": "Mathlib.Data.Finsupp.NeLocus", "is_tactic_proof": true, "tactics": ["ext", "simpa"], "tactic_count": 2}
{"name": "Finsupp.neLocus_add_left", "kind": "theorem", "module": "Mathlib.Data.Finsupp.NeLocus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.neLocus_add_right", "kind": "theorem", "module": "Mathlib.Data.Finsupp.NeLocus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.neLocus_neg_neg", "kind": "theorem", "module": "Mathlib.Data.Finsupp.NeLocus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.neLocus_neg", "kind": "theorem", "module": "Mathlib.Data.Finsupp.NeLocus", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finsupp.neLocus_eq_support_sub", "kind": "theorem", "module": "Mathlib.Data.Finsupp.NeLocus", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finsupp.neLocus_sub_left", "kind": "theorem", "module": "Mathlib.Data.Finsupp.NeLocus", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finsupp.neLocus_sub_right", "kind": "theorem", "module": "Mathlib.Data.Finsupp.NeLocus", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finsupp.neLocus_self_add_right", "kind": "theorem", "module": "Mathlib.Data.Finsupp.NeLocus", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finsupp.neLocus_self_add_left", "kind": "theorem", "module": "Mathlib.Data.Finsupp.NeLocus", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finsupp.neLocus_self_sub_right", "kind": "theorem", "module": "Mathlib.Data.Finsupp.NeLocus", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finsupp.neLocus_self_sub_left", "kind": "theorem", "module": "Mathlib.Data.Finsupp.NeLocus", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finsupp.fun₀.matchAlts", "kind": "definition", "module": "Mathlib.Data.Finsupp.Notation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.fun₀", "kind": "definition", "module": "Mathlib.Data.Finsupp.Notation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.Internal.stxSingle₀", "kind": "definition", "module": "Mathlib.Data.Finsupp.Notation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.Internal.stxUpdate₀", "kind": "definition", "module": "Mathlib.Data.Finsupp.Notation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.Internal.elabSingle₀", "kind": "definition", "module": "Mathlib.Data.Finsupp.Notation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.Internal.elabUpdate₀", "kind": "definition", "module": "Mathlib.Data.Finsupp.Notation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.Internal._aux_Mathlib_Data_Finsupp_Notation___macroRules_Finsupp_fun₀_1", "kind": "definition", "module": "Mathlib.Data.Finsupp.Notation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.singleUnexpander", "kind": "definition", "module": "Mathlib.Data.Finsupp.Notation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.updateUnexpander", "kind": "definition", "module": "Mathlib.Data.Finsupp.Notation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.instRepr", "kind": "instance", "module": "Mathlib.Data.Finsupp.Notation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.some", "kind": "definition", "module": "Mathlib.Data.Finsupp.Option", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.some_apply", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Option", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.some_zero", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Option", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Finsupp.some_add", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Option", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Finsupp.some_single_none", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Option", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Finsupp.some_single_some", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Option", "is_tactic_proof": true, "tactics": ["classical", "ext", "simp"], "tactic_count": 3}
{"name": "Finsupp.some_embDomain_some", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Option", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finsupp.embDomain_some_none", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Option", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.embDomain_some_some", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Option", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finsupp.some_update_none", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Option", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Finsupp.optionEquiv", "kind": "definition", "module": "Mathlib.Data.Finsupp.Option", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.optionElim", "kind": "definition", "module": "Mathlib.Data.Finsupp.Option", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.optionElim_apply_none", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Option", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finsupp.optionElim_apply_some", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Option", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finsupp.optionElim_apply_eq_elim", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Option", "is_tactic_proof": true, "tactics": ["cases", "none", "some"], "tactic_count": 3}
{"name": "Finsupp.optionElim_eq_elim'", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Option", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finsupp.some_optionElim", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Option", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Finsupp.optionElim_some", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Option", "is_tactic_proof": true, "tactics": ["ext", "cases", "rw", "simp"], "tactic_count": 4}
{"name": "Finsupp.optionElim_zero", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Option", "is_tactic_proof": true, "tactics": ["ext", "cases", "simp", "simp"], "tactic_count": 4}
{"name": "Finsupp.optionElim_ne_zero_of_left", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Option", "is_tactic_proof": true, "tactics": ["contrapose", "have", "simp", "exact"], "tactic_count": 4}
{"name": "Finsupp.optionElim_ne_zero_of_right", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Option", "is_tactic_proof": true, "tactics": ["contrapose", "ext", "have", "simp", "exact"], "tactic_count": 5}
{"name": "Finsupp.optionElim_ne_zero_iff", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Option", "is_tactic_proof": true, "tactics": ["constructor", "intro", "contrapose", "rcases", "rw", "intro", "cases", "inl", "inr"], "tactic_count": 9}
{"name": "Finsupp.eq_option_embedding_update_none_iff", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Option", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.prod_option_index", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Option", "is_tactic_proof": true, "tactics": ["classical", "induction", "zero", "add", "rw", "simp", "rw", "all_goals", "single"], "tactic_count": 9}
{"name": "Finsupp.sum_option_index_smul", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Option", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.sum_le_sum", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.sum_nonneg", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.sum_nonneg'", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.sum_nonpos", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.sum_pos", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.sum_pos'", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.single_le_single", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Order", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finsupp.single_mono", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.single_nonneg", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Order", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finsupp.single_nonpos", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Order", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finsupp.sum_le_sum_index", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Order", "is_tactic_proof": true, "tactics": ["classical", "rw", "exact"], "tactic_count": 3}
{"name": "Finsupp.isOrderedAddMonoid", "kind": "instance", "module": "Mathlib.Data.Finsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.mapDomain_mono", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Order", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finsupp.mapDomain_nonneg", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Order", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finsupp.mapDomain_nonpos", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Order", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finsupp.isOrderedCancelAddMonoid", "kind": "instance", "module": "Mathlib.Data.Finsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.addLeftReflectLE", "kind": "instance", "module": "Mathlib.Data.Finsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.instPosSMulMono", "kind": "instance", "module": "Mathlib.Data.Finsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.instSMulPosMono", "kind": "instance", "module": "Mathlib.Data.Finsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.instPosSMulReflectLE", "kind": "instance", "module": "Mathlib.Data.Finsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.instSMulPosReflectLE", "kind": "instance", "module": "Mathlib.Data.Finsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.instPosSMulStrictMono", "kind": "instance", "module": "Mathlib.Data.Finsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.instSMulPosStrictMono", "kind": "instance", "module": "Mathlib.Data.Finsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.instSMulPosReflectLT", "kind": "instance", "module": "Mathlib.Data.Finsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.orderBot", "kind": "instance", "module": "Mathlib.Data.Finsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.bot_eq_zero", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.add_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Order", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finsupp.le_iff'", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.le_iff", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.support_monotone", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.support_mono", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.decidableLE", "kind": "instance", "module": "Mathlib.Data.Finsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.decidableLT", "kind": "instance", "module": "Mathlib.Data.Finsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.single_le_iff", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.tsub", "kind": "instance", "module": "Mathlib.Data.Finsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.orderedSub", "kind": "instance", "module": "Mathlib.Data.Finsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.instCanonicallyOrderedAddOfAddLeftMono", "kind": "instance", "module": "Mathlib.Data.Finsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.coe_tsub", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.tsub_apply", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.single_tsub", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Order", "is_tactic_proof": true, "tactics": ["ext", "obtain", "rw", "rw"], "tactic_count": 4}
{"name": "Finsupp.support_tsub", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Order", "is_tactic_proof": true, "tactics": ["simp", "zero_le,"], "tactic_count": 2}
{"name": "Finsupp.subset_support_tsub", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Order", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finsupp.support_inf", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Order", "is_tactic_proof": true, "tactics": ["ext", "simp", "simp"], "tactic_count": 3}
{"name": "Finsupp.support_sup", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Order", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Finsupp.disjoint_iff", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Order", "is_tactic_proof": true, "tactics": ["classical", "rw", "rfl"], "tactic_count": 3}
{"name": "Finsupp.sub_single_one_add", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.add_sub_single_one", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.sub_add_single_one_cancel", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Order", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finsupp.wellQuasiOrderedLE", "kind": "instance", "module": "Mathlib.Data.Finsupp.PWO", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.isPWO", "kind": "theorem", "module": "Mathlib.Data.Finsupp.PWO", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.instMul", "kind": "instance", "module": "Mathlib.Data.Finsupp.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.coe_mul", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.mul_apply", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.single_mul", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.support_mul_subset_left", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.support_mul_subset_right", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.support_mul", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.instMulZeroClass", "kind": "instance", "module": "Mathlib.Data.Finsupp.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.instSemigroupWithZero", "kind": "instance", "module": "Mathlib.Data.Finsupp.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.instNonUnitalNonAssocSemiring", "kind": "instance", "module": "Mathlib.Data.Finsupp.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.instNonUnitalSemiring", "kind": "instance", "module": "Mathlib.Data.Finsupp.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.instNonUnitalCommSemiring", "kind": "instance", "module": "Mathlib.Data.Finsupp.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.instNonUnitalNonAssocRing", "kind": "instance", "module": "Mathlib.Data.Finsupp.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.instNonUnitalRing", "kind": "instance", "module": "Mathlib.Data.Finsupp.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.instNonUnitalCommRing", "kind": "instance", "module": "Mathlib.Data.Finsupp.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.pointwiseScalar", "kind": "instance", "module": "Mathlib.Data.Finsupp.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.coe_pointwise_smul", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.pointwiseModule", "kind": "instance", "module": "Mathlib.Data.Finsupp.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.finite_vaddAntidiagonal", "kind": "theorem", "module": "Mathlib.Data.Finsupp.PointwiseSMul", "is_tactic_proof": true, "tactics": ["refine", "intro", "exact", "intro", "rw", "exact"], "tactic_count": 6}
{"name": "Finsupp.vaddAntidiagonal", "kind": "definition", "module": "Mathlib.Data.Finsupp.PointwiseSMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.mem_vaddAntidiagonal_iff", "kind": "theorem", "module": "Mathlib.Data.Finsupp.PointwiseSMul", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finsupp.mem_vaddAntidiagonal_of_addGroup", "kind": "theorem", "module": "Mathlib.Data.Finsupp.PointwiseSMul", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finsupp.instSMulForallOfIsLeftCancelVAddOfSMulWithZero", "kind": "instance", "module": "Mathlib.Data.Finsupp.PointwiseSMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.smul_eq", "kind": "theorem", "module": "Mathlib.Data.Finsupp.PointwiseSMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.smul_apply_addAction", "kind": "theorem", "module": "Mathlib.Data.Finsupp.PointwiseSMul", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "simp", "intro", "rw", "exact", "intro", "have", "rcases", "intro", "rw", "rw"], "tactic_count": 13}
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{"name": "Finsupp.comapSMul_def", "kind": "theorem", "module": "Mathlib.Data.Finsupp.SMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.comapSMul_single", "kind": "theorem", "module": "Mathlib.Data.Finsupp.SMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.comapMulAction", "kind": "definition", "module": "Mathlib.Data.Finsupp.SMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Finsupp.comapSMul_apply", "kind": "theorem", "module": "Mathlib.Data.Finsupp.SMul", "is_tactic_proof": true, "tactics": ["conv_lhs", "exact"], "tactic_count": 2}
{"name": "IsSMulRegular.finsupp", "kind": "theorem", "module": "Mathlib.Data.Finsupp.SMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.faithfulSMul", "kind": "instance", "module": "Mathlib.Data.Finsupp.SMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.distribMulAction", "kind": "instance", "module": "Mathlib.Data.Finsupp.SMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.module", "kind": "instance", "module": "Mathlib.Data.Finsupp.SMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.support_smul_eq", "kind": "theorem", "module": "Mathlib.Data.Finsupp.SMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.filter_smul", "kind": "theorem", "module": "Mathlib.Data.Finsupp.SMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.mapDomain_smul", "kind": "theorem", "module": "Mathlib.Data.Finsupp.SMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.smul_single'", "kind": "theorem", "module": "Mathlib.Data.Finsupp.SMul", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finsupp.smul_single_one", "kind": "theorem", "module": "Mathlib.Data.Finsupp.SMul", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finsupp.comapDomain_smul_of_injective", "kind": "theorem", "module": "Mathlib.Data.Finsupp.SMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.sum_smul_index", "kind": "theorem", "module": "Mathlib.Data.Finsupp.SMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.sum_smul_index'", "kind": "theorem", "module": "Mathlib.Data.Finsupp.SMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.sum_smul_index_addMonoidHom", "kind": "theorem", "module": "Mathlib.Data.Finsupp.SMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.moduleIsTorsionFree", "kind": "instance", "module": "Mathlib.Data.Finsupp.SMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.DistribMulActionHom.single", "kind": "definition", "module": "Mathlib.Data.Finsupp.SMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.distribMulActionHom_ext", "kind": "theorem", "module": "Mathlib.Data.Finsupp.SMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.distribMulActionHom_ext'", "kind": "theorem", "module": "Mathlib.Data.Finsupp.SMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.smulZeroClass", "kind": "instance", "module": "Mathlib.Data.Finsupp.SMulWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.coe_smul", "kind": "theorem", "module": "Mathlib.Data.Finsupp.SMulWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.smul_apply", "kind": "theorem", "module": "Mathlib.Data.Finsupp.SMulWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.instSMulWithZero", "kind": "instance", "module": "Mathlib.Data.Finsupp.SMulWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.distribSMul", "kind": "instance", "module": "Mathlib.Data.Finsupp.SMulWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.isScalarTower", "kind": "instance", "module": "Mathlib.Data.Finsupp.SMulWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.smulCommClass", "kind": "instance", "module": "Mathlib.Data.Finsupp.SMulWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.isCentralScalar", "kind": "instance", "module": "Mathlib.Data.Finsupp.SMulWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.support_smul", "kind": "theorem", "module": "Mathlib.Data.Finsupp.SMulWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.smul_single", "kind": "theorem", "module": "Mathlib.Data.Finsupp.SMulWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.mapRange_smul'", "kind": "theorem", "module": "Mathlib.Data.Finsupp.SMulWithZero", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Finsupp.mapRange_smul", "kind": "theorem", "module": "Mathlib.Data.Finsupp.SMulWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.embSigma", "kind": "definition", "module": "Mathlib.Data.Finsupp.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.embSigma_apply", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Sigma", "is_tactic_proof": true, "tactics": ["rcases", "split_ifs", "subst", "simp", "apply", "simp", "rw", "simp_all"], "tactic_count": 8}
{"name": "Finsupp.embSigma_apply_self", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Sigma", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finsupp.embSigma_apply_of_ne", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Sigma", "is_tactic_proof": true, "tactics": ["apply", "grind"], "tactic_count": 2}
{"name": "Finsupp.support_embSigma", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Sigma", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finsupp.embSigma_zero", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Sigma", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finsupp.embSigma_eq_zero", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Sigma", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finsupp.embSigma_injective", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Sigma", "is_tactic_proof": true, "tactics": ["intro", "ext", "have", "simpa"], "tactic_count": 4}
{"name": "Finsupp.embSigma_inj", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.embSigma_add", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Sigma", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "subst", "simp", "simp"], "tactic_count": 5}
{"name": "Finsupp.embSigma_single", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Sigma", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finsupp.split_embSigma_self", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Sigma", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Finsupp.split_embSigma_of_ne", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Sigma", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Finsupp.single", "kind": "definition", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.single_apply", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finsupp.single_apply_left", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finsupp.single_eq_set_indicator", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": true, "tactics": ["classical", "ext", "simp"], "tactic_count": 3}
{"name": "Finsupp.Set.indicator_singleton_eq", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": true, "tactics": ["classical", "ext", "simp", "split_ifs"], "tactic_count": 4}
{"name": "Finsupp.single_eq_same", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finsupp.single_eq_of_ne", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finsupp.single_eq_of_ne'", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finsupp.single_eq_update", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finsupp.single_eq_pi_single", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.single_zero", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.single_of_single_apply", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finsupp.support_single_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.support_single_subset", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finsupp.single_apply_mem", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finsupp.range_single_subset", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.single_injective", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.single_apply_eq_zero", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finsupp.single_apply_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finsupp.mem_support_single", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finsupp.eq_single_iff", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": true, "tactics": ["refine", "rintro", "ext", "by_cases", "exact"], "tactic_count": 5}
{"name": "Finsupp.single_eq_single_iff", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": true, "tactics": ["classical", "constructor", "intro", "by_cases", "refine", "rwa", "rw", "have", "have", "grind", "grind"], "tactic_count": 11}
{"name": "Finsupp.single_left_injective", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.single_left_inj", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.apply_surjective", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.support_single_ne_bot", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finsupp.support_single_disjoint", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finsupp.single_eq_zero", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finsupp.single_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.single_swap", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finsupp.instNontrivial", "kind": "instance", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": true, "tactics": ["inhabit", "rcases", "exact"], "tactic_count": 3}
{"name": "Finsupp.unique_single", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.unique_single_eq_iff", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finsupp.apply_single'", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finsupp.support_eq_singleton", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.support_eq_singleton'", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.card_support_eq_one", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finsupp.card_support_eq_one'", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finsupp.support_subset_singleton", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.support_subset_singleton'", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.card_support_le_one", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finsupp.card_support_le_one'", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finsupp.equivFunOnFinite_single", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finsupp.equivFunOnFinite_symm_single", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finsupp.update", "kind": "definition", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.update_apply", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": true, "tactics": ["delta", "grind"], "tactic_count": 2}
{"name": "Finsupp.coe_update", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finsupp.update_self", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finsupp.zero_update", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.support_update", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finsupp.support_update_zero", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finsupp.support_update_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finsupp.support_update_subset", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finsupp.update_comm", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finsupp.update_idem", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finsupp.erase", "kind": "definition", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.erase_apply", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Finsupp.support_erase", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finsupp.erase_same", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finsupp.erase_ne", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finsupp.erase_single", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finsupp.erase_single_ne", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finsupp.erase_of_notMem_support", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finsupp.erase_zero", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finsupp.erase_eq_update_zero", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": true, "tactics": ["classical", "grind"], "tactic_count": 2}
{"name": "Finsupp.erase_update_of_ne", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": true, "tactics": ["classical", "grind"], "tactic_count": 2}
{"name": "Finsupp.erase_idem", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finsupp.update_erase_eq_update", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finsupp.erase_update_eq_erase", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finsupp.mapRange_single", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finsupp.single_of_embDomain_single", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": true, "tactics": ["classical", "have", "have", "rcases", "use", "constructor", "ext", "rw", "grind", "exact"], "tactic_count": 10}
{"name": "Finsupp.embDomain_single", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": true, "tactics": ["classical", "ext", "by_cases"], "tactic_count": 3}
{"name": "Finsupp.zipWith_single_single", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Single", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finsupp.toDFinsupp", "kind": "definition", "module": "Mathlib.Data.Finsupp.ToDFinsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.toDFinsupp_coe", "kind": "theorem", "module": "Mathlib.Data.Finsupp.ToDFinsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.toDFinsupp_single", "kind": "theorem", "module": "Mathlib.Data.Finsupp.ToDFinsupp", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "toDFinsupp_support", "kind": "theorem", "module": "Mathlib.Data.Finsupp.ToDFinsupp", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "DFinsupp.toFinsupp", "kind": "definition", "module": "Mathlib.Data.Finsupp.ToDFinsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.toFinsupp_coe", "kind": "theorem", "module": "Mathlib.Data.Finsupp.ToDFinsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.toFinsupp_support", "kind": "theorem", "module": "Mathlib.Data.Finsupp.ToDFinsupp", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "DFinsupp.toFinsupp_single", "kind": "theorem", "module": "Mathlib.Data.Finsupp.ToDFinsupp", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Finsupp.toDFinsupp_toFinsupp", "kind": "theorem", "module": "Mathlib.Data.Finsupp.ToDFinsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.toFinsupp_toDFinsupp", "kind": "theorem", "module": "Mathlib.Data.Finsupp.ToDFinsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.toDFinsupp_zero", "kind": "theorem", "module": "Mathlib.Data.Finsupp.ToDFinsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.toDFinsupp_add", "kind": "theorem", "module": "Mathlib.Data.Finsupp.ToDFinsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.toDFinsupp_neg", "kind": "theorem", "module": "Mathlib.Data.Finsupp.ToDFinsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.toDFinsupp_sub", "kind": "theorem", "module": "Mathlib.Data.Finsupp.ToDFinsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.toDFinsupp_smul", "kind": "theorem", "module": "Mathlib.Data.Finsupp.ToDFinsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.toFinsupp_zero", "kind": "theorem", "module": "Mathlib.Data.Finsupp.ToDFinsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.toFinsupp_add", "kind": "theorem", "module": "Mathlib.Data.Finsupp.ToDFinsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.toFinsupp_neg", "kind": "theorem", "module": "Mathlib.Data.Finsupp.ToDFinsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.toFinsupp_sub", "kind": "theorem", "module": "Mathlib.Data.Finsupp.ToDFinsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.toFinsupp_smul", "kind": "theorem", "module": "Mathlib.Data.Finsupp.ToDFinsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finsuppEquivDFinsupp", "kind": "definition", "module": "Mathlib.Data.Finsupp.ToDFinsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finsuppAddEquivDFinsupp", "kind": "definition", "module": "Mathlib.Data.Finsupp.ToDFinsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finsuppLequivDFinsupp", "kind": "definition", "module": "Mathlib.Data.Finsupp.ToDFinsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finsuppLequivDFinsupp_apply_apply", "kind": "theorem", "module": "Mathlib.Data.Finsupp.ToDFinsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finsuppLequivDFinsupp_symm_apply", "kind": "theorem", "module": "Mathlib.Data.Finsupp.ToDFinsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sigmaFinsuppEquivDFinsupp", "kind": "definition", "module": "Mathlib.Data.Finsupp.ToDFinsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sigmaFinsuppEquivDFinsupp_apply", "kind": "theorem", "module": "Mathlib.Data.Finsupp.ToDFinsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sigmaFinsuppEquivDFinsupp_symm_apply", "kind": "theorem", "module": "Mathlib.Data.Finsupp.ToDFinsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sigmaFinsuppEquivDFinsupp_support", "kind": "theorem", "module": "Mathlib.Data.Finsupp.ToDFinsupp", "is_tactic_proof": true, "tactics": ["ext", "rw", "exact"], "tactic_count": 3}
{"name": "sigmaFinsuppEquivDFinsupp_single", "kind": "theorem", "module": "Mathlib.Data.Finsupp.ToDFinsupp", "is_tactic_proof": true, "tactics": ["obtain", "ext", "by_cases", "subst", "classical", "suffices", "have", "classical", "rw"], "tactic_count": 9}
{"name": "sigmaFinsuppEquivDFinsupp_add", "kind": "theorem", "module": "Mathlib.Data.Finsupp.ToDFinsupp", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "sigmaFinsuppAddEquivDFinsupp", "kind": "definition", "module": "Mathlib.Data.Finsupp.ToDFinsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sigmaFinsuppEquivDFinsupp_smul", "kind": "theorem", "module": "Mathlib.Data.Finsupp.ToDFinsupp", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "sigmaFinsuppLequivDFinsupp", "kind": "definition", "module": "Mathlib.Data.Finsupp.ToDFinsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.weight", "kind": "definition", "module": "Mathlib.Data.Finsupp.Weight", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.weight_apply", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Weight", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.weight_single_index", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Weight", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.weight_single_one_apply", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Weight", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finsupp.weight_single", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Weight", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.nonTorsionWeight_of", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Weight", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.NonTorsionWeight.ne_zero", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Weight", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.weight_sub_single_add", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Weight", "is_tactic_proof": true, "tactics": ["conv_rhs", "rw", "exacts"], "tactic_count": 3}
{"name": "Finsupp.le_weight", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Weight", "is_tactic_proof": true, "tactics": ["classical", "simp", "by_cases", "rw", "refine", "apply", "exact", "simp", "rw", "apply"], "tactic_count": 10}
{"name": "Finsupp.le_weight_of_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Weight", "is_tactic_proof": true, "tactics": ["classical", "simp", "trans", "apply", "exact", "rw", "rw", "exact"], "tactic_count": 8}
{"name": "Finsupp.le_weight_of_ne_zero'", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Weight", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.weight_eq_zero_iff_eq_zero", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Weight", "is_tactic_proof": true, "tactics": ["classical", "constructor", "intro", "ext", "simp", "by_contra", "apply", "rw", "exact", "intro", "rw"], "tactic_count": 11}
{"name": "Finsupp.finite_of_nat_weight_le", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Weight", "is_tactic_proof": true, "tactics": ["classical", "set", "suffices", "exact", "intro", "rw", "simp", "exists_eq_right]", "use", "ext", "dsimp", "grw", "simp"], "tactic_count": 13}
{"name": "Finsupp.degree", "kind": "definition", "module": "Mathlib.Data.Finsupp.Weight", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.degree_apply", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Weight", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.degree_eq_sum", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Weight", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finsupp.degree_single", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Weight", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.degree_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Weight", "is_tactic_proof": true, "tactics": ["simp", "coe_zero,"], "tactic_count": 2}
{"name": "Finsupp.le_degree", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Weight", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "simp", "simp"], "tactic_count": 4}
{"name": "Finsupp.degree_eq_weight_one", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Weight", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Finsupp.finite_of_degree_le", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Weight", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "intro", "simp"], "tactic_count": 4}
{"name": "Finsupp.range_single_one", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Weight", "is_tactic_proof": true, "tactics": ["refine", "simp", "intro", "obtain", "use"], "tactic_count": 5}
{"name": "Finsupp.degree_mono", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Weight", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.exists_le_degree_eq", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Weight", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "obtain", "obtain", "obtain", "exact"], "tactic_count": 7}
{"name": "Finsupp.degree_preimage_add", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Weight", "is_tactic_proof": true, "tactics": ["refine", "rintro", "obtain", "obtain", "exact"], "tactic_count": 5}
{"name": "Finsupp.degree_preimage_nsmul", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Weight", "is_tactic_proof": true, "tactics": ["obtain", "induction"], "tactic_count": 2}
{"name": "Finsupp.nsmul_single_one_image", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Weight", "is_tactic_proof": true, "tactics": ["classical", "induction", "zero", "succ", "rw", "refine", "simp", "obtain", "obtain", "exact"], "tactic_count": 10}
{"name": "Finsupp.image_pow_eq_finsuppProd_image", "kind": "theorem", "module": "Mathlib.Data.Finsupp.Weight", "is_tactic_proof": true, "tactics": ["classical", "suffices", "simp", "intro", "refine", "simp"], "tactic_count": 6}
{"name": "Finsupp.Lex.acc", "kind": "theorem", "module": "Mathlib.Data.Finsupp.WellFounded", "is_tactic_proof": true, "tactics": ["rw", "classical", "refine", "simpa"], "tactic_count": 4}
{"name": "Finsupp.Lex.wellFounded", "kind": "theorem", "module": "Mathlib.Data.Finsupp.WellFounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.Lex.wellFounded'", "kind": "theorem", "module": "Mathlib.Data.Finsupp.WellFounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.Lex.wellFoundedLT", "kind": "instance", "module": "Mathlib.Data.Finsupp.WellFounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.Lex.wellFounded_of_finite", "kind": "theorem", "module": "Mathlib.Data.Finsupp.WellFounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.Lex.wellFoundedLT_of_finite", "kind": "theorem", "module": "Mathlib.Data.Finsupp.WellFounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.wellFoundedLT", "kind": "theorem", "module": "Mathlib.Data.Finsupp.WellFounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.wellFoundedLT'", "kind": "instance", "module": "Mathlib.Data.Finsupp.WellFounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.wellFoundedLT_of_finite", "kind": "instance", "module": "Mathlib.Data.Finsupp.WellFounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.fintype", "kind": "instance", "module": "Mathlib.Data.Fintype.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.univ_def", "kind": "theorem", "module": "Mathlib.Data.Fintype.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.val_univ_fin", "kind": "theorem", "module": "Mathlib.Data.Fintype.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nonempty_fintype", "kind": "theorem", "module": "Mathlib.Data.Fintype.Basic", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "List.toFinset_finRange", "kind": "theorem", "module": "Mathlib.Data.Fintype.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Fin.univ_val_map", "kind": "theorem", "module": "Mathlib.Data.Fintype.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.univ_image_def", "kind": "theorem", "module": "Mathlib.Data.Fintype.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.univ_map_def", "kind": "theorem", "module": "Mathlib.Data.Fintype.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.image_succAbove_univ", "kind": "theorem", "module": "Mathlib.Data.Fintype.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Fin.image_succ_univ", "kind": "theorem", "module": "Mathlib.Data.Fintype.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.image_castSucc", "kind": "theorem", "module": "Mathlib.Data.Fintype.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.univ_succ", "kind": "theorem", "module": "Mathlib.Data.Fintype.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.univ_castSuccEmb", "kind": "theorem", "module": "Mathlib.Data.Fintype.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.univ_succAbove", "kind": "theorem", "module": "Mathlib.Data.Fintype.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.univ_image_get", "kind": "theorem", "module": "Mathlib.Data.Fintype.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.univ_image_getElem'", "kind": "theorem", "module": "Mathlib.Data.Fintype.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.univ_image_get'", "kind": "theorem", "module": "Mathlib.Data.Fintype.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Unique.fintype", "kind": "definition", "module": "Mathlib.Data.Fintype.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.subtypeEq", "kind": "instance", "module": "Mathlib.Data.Fintype.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.subtypeEq'", "kind": "instance", "module": "Mathlib.Data.Fintype.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.univ_empty", "kind": "theorem", "module": "Mathlib.Data.Fintype.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.univ_pempty", "kind": "theorem", "module": "Mathlib.Data.Fintype.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unit.fintype", "kind": "instance", "module": "Mathlib.Data.Fintype.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.univ_unit", "kind": "theorem", "module": "Mathlib.Data.Fintype.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PUnit.fintype", "kind": "instance", "module": "Mathlib.Data.Fintype.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.univ_punit", "kind": "theorem", "module": "Mathlib.Data.Fintype.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.univ_bool", "kind": "theorem", "module": "Mathlib.Data.Fintype.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.prodLeft", "kind": "definition", "module": "Mathlib.Data.Fintype.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.prodRight", "kind": "definition", "module": "Mathlib.Data.Fintype.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.fintype", "kind": "instance", "module": "Mathlib.Data.Fintype.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PLift.fintype", "kind": "instance", "module": "Mathlib.Data.Fintype.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PLift.fintypeProp", "kind": "instance", "module": "Mathlib.Data.Fintype.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quotient.fintype", "kind": "instance", "module": "Mathlib.Data.Fintype.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSigma.fintypePropLeft", "kind": "instance", "module": "Mathlib.Data.Fintype.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSigma.fintypePropRight", "kind": "instance", "module": "Mathlib.Data.Fintype.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSigma.fintypePropProp", "kind": "instance", "module": "Mathlib.Data.Fintype.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pfunFintype", "kind": "instance", "module": "Mathlib.Data.Fintype.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "truncOfMultisetExistsMem", "kind": "definition", "module": "Mathlib.Data.Fintype.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "truncOfNonemptyFintype", "kind": "definition", "module": "Mathlib.Data.Fintype.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "truncSigmaOfExists", "kind": "definition", "module": "Mathlib.Data.Fintype.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.count_univ", "kind": "theorem", "module": "Mathlib.Data.Fintype.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.map_univ_val_equiv", "kind": "theorem", "module": "Mathlib.Data.Fintype.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.bijective_iff_map_univ_eq_univ", "kind": "theorem", "module": "Mathlib.Data.Fintype.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "seqOfForallFinsetExistsAux", "kind": "definition", "module": "Mathlib.Data.Fintype.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_seq_of_forall_finset_exists", "kind": "theorem", "module": "Mathlib.Data.Fintype.Basic", "is_tactic_proof": true, "tactics": ["classical", "have", "rcases", "exact", "choose", "have", "set", "have", "intro", "induction", "have", "rw", "exact", "refine", "conv_rhs", "rw", "apply", "exact"], "tactic_count": 18}
{"name": "exists_seq_of_forall_finset_exists'", "kind": "theorem", "module": "Mathlib.Data.Fintype.Basic", "is_tactic_proof": true, "tactics": ["rcases", "refine", "rcases", "exact", "exact", "unfold", "apply", "exact"], "tactic_count": 8}
{"name": "Fintype.prod_bool", "kind": "theorem", "module": "Mathlib.Data.Fintype.BigOperators", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fintype.card_eq_sum_ones", "kind": "theorem", "module": "Mathlib.Data.Fintype.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.prod_extend_by_one", "kind": "theorem", "module": "Mathlib.Data.Fintype.BigOperators", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fintype.prod_eq_one", "kind": "theorem", "module": "Mathlib.Data.Fintype.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.prod_congr", "kind": "theorem", "module": "Mathlib.Data.Fintype.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.prod_eq_single", "kind": "theorem", "module": "Mathlib.Data.Fintype.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.prod_eq_mul", "kind": "theorem", "module": "Mathlib.Data.Fintype.BigOperators", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "Fintype.eq_of_subsingleton_of_prod_eq", "kind": "theorem", "module": "Mathlib.Data.Fintype.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.prod_option", "kind": "theorem", "module": "Mathlib.Data.Fintype.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.prod_eq_mul_prod_subtype_ne", "kind": "theorem", "module": "Mathlib.Data.Fintype.BigOperators", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Finset.card_pi", "kind": "theorem", "module": "Mathlib.Data.Fintype.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_piFinset", "kind": "theorem", "module": "Mathlib.Data.Fintype.BigOperators", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fintype.card_piFinset_const", "kind": "theorem", "module": "Mathlib.Data.Fintype.BigOperators", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fintype.card_pi", "kind": "theorem", "module": "Mathlib.Data.Fintype.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_pi_const", "kind": "theorem", "module": "Mathlib.Data.Fintype.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.prod_sigma", "kind": "theorem", "module": "Mathlib.Data.Fintype.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.prod_sigma'", "kind": "theorem", "module": "Mathlib.Data.Fintype.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_sigma", "kind": "theorem", "module": "Mathlib.Data.Fintype.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_filter_piFinset_eq_of_mem", "kind": "theorem", "module": "Mathlib.Data.Fintype.BigOperators", "is_tactic_proof": true, "tactics": ["calc", "rw"], "tactic_count": 2}
{"name": "Fintype.card_filter_piFinset_const_eq_of_mem", "kind": "theorem", "module": "Mathlib.Data.Fintype.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_filter_piFinset_eq", "kind": "theorem", "module": "Mathlib.Data.Fintype.BigOperators", "is_tactic_proof": true, "tactics": ["split_ifs", "rw", "rw"], "tactic_count": 3}
{"name": "Fintype.card_filter_piFinset_const", "kind": "theorem", "module": "Mathlib.Data.Fintype.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_fun", "kind": "theorem", "module": "Mathlib.Data.Fintype.BigOperators", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "card_vector", "kind": "theorem", "module": "Mathlib.Data.Fintype.BigOperators", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.prod_univ_eq_prod_range", "kind": "theorem", "module": "Mathlib.Data.Fintype.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_fin_eq_prod_range", "kind": "theorem", "module": "Mathlib.Data.Fintype.BigOperators", "is_tactic_proof": true, "tactics": ["rw", "rintro", "simp"], "tactic_count": 3}
{"name": "Finset.prod_toFinset_eq_subtype", "kind": "theorem", "module": "Mathlib.Data.Fintype.BigOperators", "is_tactic_proof": true, "tactics": ["rw", "simp_rw"], "tactic_count": 2}
{"name": "Fintype.prod_dite", "kind": "theorem", "module": "Mathlib.Data.Fintype.BigOperators", "is_tactic_proof": true, "tactics": ["simp", "congr", "exact", "exact"], "tactic_count": 4}
{"name": "Fintype.prod_sumElim", "kind": "theorem", "module": "Mathlib.Data.Fintype.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.prod_sum_type", "kind": "theorem", "module": "Mathlib.Data.Fintype.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.prod_prod_type", "kind": "theorem", "module": "Mathlib.Data.Fintype.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.prod_prod_type'", "kind": "theorem", "module": "Mathlib.Data.Fintype.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.prod_prod_type_right", "kind": "theorem", "module": "Mathlib.Data.Fintype.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.prod_prod_type_right'", "kind": "theorem", "module": "Mathlib.Data.Fintype.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card", "kind": "definition", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.subtype_card", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_of_subtype", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": true, "tactics": ["rw", "congr"], "tactic_count": 2}
{"name": "Fintype.card_ofFinset", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_of_finset'", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fintype.ofEquiv_card", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_congr", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fintype.card_congr'", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_ofSubsingleton", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_unique", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_ofIsEmpty", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.toFinset_card", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_univ", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.eq_univ_of_card", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_eq_iff_eq_univ", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_le_univ", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_lt_univ_of_notMem", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_lt_iff_ne_univ", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_compl_lt_iff_nonempty", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_univ_diff", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.card_compl", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_add_card_compl", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.card_compl_add_card", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fintype.card_compl_set", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Fintype.card_subtype_eq", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_subtype_eq'", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_empty", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_pempty", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_unit", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_punit", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_bool", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_ulift", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_plift", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_orderDual", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_lex", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_setUniv", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "Fintype.card_subtype_true", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "Fintype.sumLeft", "kind": "definition", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.sumRight", "kind": "definition", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finite.exists_univ_list", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": true, "tactics": ["cases", "obtain", "have", "exact"], "tactic_count": 4}
{"name": "List.Nodup.length_le_card", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Fintype.card_le_of_injective", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.not_injective_of_card_lt", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_le_of_embedding", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_lt_of_injective_of_notMem", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_lt_of_injective_not_surjective", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_le_of_surjective", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_range_le", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_range", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fintype.card_eq_zero", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.cardEqZeroEquivEquivEmpty", "kind": "definition", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_pos_iff", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_pos", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.instNeZeroNatCardOfNonempty", "kind": "instance", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.existsUnique_iff_card_one", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp"], "tactic_count": 3}
{"name": "Fintype.two_lt_card_iff", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Fintype.card_of_bijective", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finite.surjective_of_injective", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": true, "tactics": ["intro", "have", "cases", "have", "eq_of_subset_of_card_le", "have", "obtain", "exact"], "tactic_count": 8}
{"name": "Finite.injective_iff_surjective", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finite.injective_iff_bijective", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finite.surjective_iff_bijective", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finite.injective_iff_surjective_of_equiv", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_coe", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.exists_superset_card_eq", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Fintype.card_prop", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "set_fintype_card_le_univ", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "set_fintype_card_eq_univ_iff", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fintype.card_subtype_le", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_subtype_lt", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_subtype", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": true, "tactics": ["refine", "simp"], "tactic_count": 2}
{"name": "Fintype.card_subtype_compl", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": true, "tactics": ["classical", "rw", "intro", "simp"], "tactic_count": 4}
{"name": "Fintype.card_subtype_mono", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_compl_eq_card_compl", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": true, "tactics": ["cases", "simp"], "tactic_count": 2}
{"name": "Fintype.card_quotient_le", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "univ_eq_singleton_of_card_one", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": true, "tactics": ["symm", "apply", "simp"], "tactic_count": 3}
{"name": "Finite.wellFounded_of_trans_of_irrefl", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": true, "tactics": ["classical", "cases", "have", "simp_rw", "exact", "exact"], "tactic_count": 6}
{"name": "Finite.to_wellFoundedLT", "kind": "instance", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finite.to_wellFoundedGT", "kind": "instance", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bool.instWellFoundedLT", "kind": "instance", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bool.instWellFoundedGT", "kind": "instance", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prop.instWellFoundedLT", "kind": "instance", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prop.instWellFoundedGT", "kind": "instance", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "truncOfCardPos", "kind": "definition", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.induction_subsingleton_or_nontrivial", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": true, "tactics": ["obtain", "induction", "rcases", "apply", "apply", "intro", "rw", "exact"], "tactic_count": 8}
{"name": "Fintype.card_fin", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_fin_lt_of_le", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": true, "tactics": ["conv_rhs", "apply", "exact", "invFun"], "tactic_count": 4}
{"name": "Finset.card_fin", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "fin_injective", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.val_eq_val_of_heq", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.cast_eq_cast'", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": true, "tactics": ["cases", "rfl"], "tactic_count": 2}
{"name": "card_finset_fin_le", "kind": "theorem", "module": "Mathlib.Data.Fintype.Card", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "_private.Mathlib.Data.Fintype.CardEmbedding.0.term|_|", "kind": "definition", "module": "Mathlib.Data.Fintype.CardEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.Fintype.CardEmbedding.0._aux_Mathlib_Data_Fintype_CardEmbedding___macroRules__private_Mathlib_Data_Fintype_CardEmbedding_0_term|_|_1", "kind": "definition", "module": "Mathlib.Data.Fintype.CardEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.Fintype.CardEmbedding.0._aux_Mathlib_Data_Fintype_CardEmbedding___unexpand_Finset_card_1", "kind": "definition", "module": "Mathlib.Data.Fintype.CardEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.Fintype.CardEmbedding.0.term‖_‖", "kind": "definition", "module": "Mathlib.Data.Fintype.CardEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.Fintype.CardEmbedding.0._aux_Mathlib_Data_Fintype_CardEmbedding___macroRules__private_Mathlib_Data_Fintype_CardEmbedding_0_term‖_‖_1", "kind": "definition", "module": "Mathlib.Data.Fintype.CardEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.Fintype.CardEmbedding.0._aux_Mathlib_Data_Fintype_CardEmbedding___unexpand_Fintype_card_1", "kind": "definition", "module": "Mathlib.Data.Fintype.CardEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_embedding_eq_of_unique", "kind": "theorem", "module": "Mathlib.Data.Fintype.CardEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_embedding_eq", "kind": "theorem", "module": "Mathlib.Data.Fintype.CardEmbedding", "is_tactic_proof": true, "tactics": ["rw", "refine", "dsimp", "clear", "letI", "rw", "rw", "exact", "classical", "rw", "simp", "mul_comm]"], "tactic_count": 12}
{"name": "Fintype.card_embedding_eq_of_infinite", "kind": "theorem", "module": "Mathlib.Data.Fintype.CardEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.nodup_map_iff_injOn", "kind": "theorem", "module": "Mathlib.Data.Fintype.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.instDecidableInjOnCoeFinsetOfDecidableEq", "kind": "instance", "module": "Mathlib.Data.Fintype.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.instDecidableBijOnCoeFinsetOfDecidableEq", "kind": "instance", "module": "Mathlib.Data.Fintype.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.univ", "kind": "definition", "module": "Mathlib.Data.Fintype.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_univ", "kind": "theorem", "module": "Mathlib.Data.Fintype.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_univ_val", "kind": "theorem", "module": "Mathlib.Data.Fintype.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.eq_univ_iff_forall", "kind": "theorem", "module": "Mathlib.Data.Fintype.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.eq_univ_of_forall", "kind": "theorem", "module": "Mathlib.Data.Fintype.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.coe_univ", "kind": "theorem", "module": "Mathlib.Data.Fintype.Defs", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finset.coe_eq_univ", "kind": "theorem", "module": "Mathlib.Data.Fintype.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.subset_univ", "kind": "theorem", "module": "Mathlib.Data.Fintype.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_filter_univ", "kind": "theorem", "module": "Mathlib.Data.Fintype.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Meta.elabFinsetBuilderSetOf", "kind": "definition", "module": "Mathlib.Data.Fintype.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.delabFinsetFilter", "kind": "definition", "module": "Mathlib.Data.Fintype.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.decidablePiFintype", "kind": "instance", "module": "Mathlib.Data.Fintype.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.decidableForallFintype", "kind": "instance", "module": "Mathlib.Data.Fintype.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.decidableExistsFintype", "kind": "instance", "module": "Mathlib.Data.Fintype.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.decidableMemRangeFintype", "kind": "instance", "module": "Mathlib.Data.Fintype.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.decidableSubsingleton", "kind": "instance", "module": "Mathlib.Data.Fintype.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.decidableEqEquivFintype", "kind": "instance", "module": "Mathlib.Data.Fintype.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.decidableEqEmbeddingFintype", "kind": "instance", "module": "Mathlib.Data.Fintype.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.nodup_map_univ_iff_injective", "kind": "theorem", "module": "Mathlib.Data.Fintype.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fintype.decidableInjectiveFintype", "kind": "instance", "module": "Mathlib.Data.Fintype.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.decidableSurjectiveFintype", "kind": "instance", "module": "Mathlib.Data.Fintype.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.decidableBijectiveFintype", "kind": "instance", "module": "Mathlib.Data.Fintype.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.decidableRightInverseFintype", "kind": "instance", "module": "Mathlib.Data.Fintype.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.decidableLeftInverseFintype", "kind": "instance", "module": "Mathlib.Data.Fintype.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.subsingleton", "kind": "instance", "module": "Mathlib.Data.Fintype.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.instFastSubsingleton", "kind": "instance", "module": "Mathlib.Data.Fintype.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.subtype", "kind": "definition", "module": "Mathlib.Data.Fintype.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.ofFinset", "kind": "definition", "module": "Mathlib.Data.Fintype.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bool.fintype", "kind": "instance", "module": "Mathlib.Data.Fintype.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordering.fintype", "kind": "instance", "module": "Mathlib.Data.Fintype.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.fintype", "kind": "instance", "module": "Mathlib.Data.Fintype.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.finite", "kind": "instance", "module": "Mathlib.Data.Fintype.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lex.fintype", "kind": "instance", "module": "Mathlib.Data.Fintype.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.truncEquivFin", "kind": "definition", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": true, "tactics": ["unfold", "exact"], "tactic_count": 2}
{"name": "Fintype.equivFin", "kind": "definition", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.truncFinBijection", "kind": "definition", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": true, "tactics": ["unfold", "refine"], "tactic_count": 2}
{"name": "Fintype.truncEquivFinOfCardEq", "kind": "definition", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.equivFinOfCardEq", "kind": "definition", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.truncEquivOfCardEq", "kind": "definition", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.equivOfCardEq", "kind": "definition", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": true, "tactics": ["letI", "letI", "exact"], "tactic_count": 3}
{"name": "Fintype.card_eq", "kind": "theorem", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.finite", "kind": "theorem", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finite.of_fintype", "kind": "instance", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finite_iff_nonempty_fintype", "kind": "theorem", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.ofFinite", "kind": "definition", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finite.of_injective", "kind": "theorem", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": true, "tactics": ["rcases", "classical"], "tactic_count": 2}
{"name": "Finite.of_subsingleton", "kind": "instance", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFiniteProp", "kind": "instance", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.finite", "kind": "instance", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finite.of_surjective", "kind": "theorem", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quot.finite", "kind": "instance", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quotient.finite", "kind": "instance", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_eq_one_iff", "kind": "theorem", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Fintype.card_eq_one_iff_nonempty_unique", "kind": "theorem", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_le_one_iff", "kind": "theorem", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_le_one_iff_subsingleton", "kind": "theorem", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.one_lt_card_iff_nontrivial", "kind": "theorem", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": true, "tactics": ["contrapose"], "tactic_count": 1}
{"name": "Fintype.exists_ne_of_one_lt_card", "kind": "theorem", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.exists_pair_of_one_lt_card", "kind": "theorem", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_eq_one_of_forall_eq", "kind": "theorem", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.one_lt_card", "kind": "theorem", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.one_lt_card_iff", "kind": "theorem", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.bijective_iff_injective_and_card", "kind": "theorem", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.bijective_iff_surjective_and_card", "kind": "theorem", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.LeftInverse.rightInverse_of_card_le", "kind": "theorem", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.RightInverse.leftInverse_of_card_le", "kind": "theorem", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.ofLeftInverseOfCardLE", "kind": "definition", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.ofRightInverseOfCardLE", "kind": "definition", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.equivFin", "kind": "definition", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.equivFinOfCardEq", "kind": "definition", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_eq_of_equiv_fin", "kind": "theorem", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_eq_of_equiv_fintype", "kind": "theorem", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.equivOfCardEq", "kind": "definition", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_eq_of_equiv", "kind": "theorem", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.equivOfFiniteSelfEmbedding", "kind": "definition", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.toEmbedding_equivOfFiniteSelfEmbedding", "kind": "theorem", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "Equiv.embeddingEquivOfFinite", "kind": "definition", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.truncOfCardLE", "kind": "definition", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.nonempty_of_card_le", "kind": "theorem", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Function.Embedding.nonempty_iff_card_le", "kind": "theorem", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.exists_of_card_le_finset", "kind": "theorem", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": true, "tactics": ["rw", "rcases", "exact"], "tactic_count": 3}
{"name": "Function.Embedding.exists_of_card_eq_finset", "kind": "theorem", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": true, "tactics": ["obtain", "use", "apply", "simp", "simp"], "tactic_count": 5}
{"name": "Finset.univ_map_embedding", "kind": "theorem", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fintype.card_lt_of_surjective_not_injective", "kind": "theorem", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.false", "kind": "theorem", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isEmpty_fintype", "kind": "theorem", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fintypeOfNotInfinite", "kind": "definition", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fintypeOrInfinite", "kind": "definition", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Infinite.of_not_fintype", "kind": "theorem", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Infinite.of_injective_to_set", "kind": "theorem", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Infinite.of_surjective_from_set", "kind": "theorem", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Infinite.exists_notMem_finset", "kind": "theorem", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Infinite.instNontrivial", "kind": "instance", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Infinite.nonempty", "kind": "theorem", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Infinite.of_injective", "kind": "theorem", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Infinite.of_surjective", "kind": "theorem", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Infinite.instSigmaOfNonempty", "kind": "instance", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Infinite.sigma_of_right", "kind": "theorem", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Infinite.instSigmaOfNonempty_1", "kind": "instance", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInfiniteNat", "kind": "instance", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.infinite", "kind": "instance", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInfiniteMultisetOfNonempty", "kind": "instance", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInfiniteListOfNonempty", "kind": "instance", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "String.infinite", "kind": "instance", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Infinite.set", "kind": "instance", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInfiniteFinset", "kind": "instance", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInfiniteOption", "kind": "instance", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.infinite_of_left", "kind": "instance", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.infinite_of_right", "kind": "instance", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.infinite_of_right", "kind": "instance", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.infinite_of_left", "kind": "instance", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInfinitePerm", "kind": "instance", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": true, "tactics": ["classical", "obtain", "exact"], "tactic_count": 3}
{"name": "_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.natEmbeddingAux", "kind": "definition", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.natEmbeddingAux_injective", "kind": "theorem", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": true, "tactics": ["rintro", "letI", "wlog", "exact", "by_contra", "have", "refine", "refine", "rw"], "tactic_count": 9}
{"name": "Infinite.natEmbedding", "kind": "definition", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Infinite.exists_subset_card_eq", "kind": "theorem", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Infinite.exists_superset_card_eq", "kind": "theorem", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rcases", "exact", "obtain", "obtain", "refine", "simp"], "tactic_count": 9}
{"name": "fintypeOfFinsetCardLe", "kind": "definition", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": true, "tactics": ["apply", "intro", "obtain", "specialize", "rw", "exact"], "tactic_count": 6}
{"name": "not_injective_infinite_finite", "kind": "theorem", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.is_empty", "kind": "instance", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_surjective_finite_infinite", "kind": "theorem", "module": "Mathlib.Data.Fintype.EquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.map_valEmbedding_univ", "kind": "theorem", "module": "Mathlib.Data.Fintype.Fin", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Fin.Ioi_zero_eq_map", "kind": "theorem", "module": "Mathlib.Data.Fintype.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.Iio_last_eq_map", "kind": "theorem", "module": "Mathlib.Data.Fintype.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.Ioi_succ", "kind": "theorem", "module": "Mathlib.Data.Fintype.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.Iio_castSucc", "kind": "theorem", "module": "Mathlib.Data.Fintype.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.card_filter_val_lt", "kind": "theorem", "module": "Mathlib.Data.Fintype.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.card_filter_univ_succ", "kind": "theorem", "module": "Mathlib.Data.Fintype.Fin", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.card_filter_univ_succ'", "kind": "theorem", "module": "Mathlib.Data.Fintype.Fin", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.card_filter_univ_eq_vector_get_eq_count", "kind": "theorem", "module": "Mathlib.Data.Fintype.Fin", "is_tactic_proof": true, "tactics": ["induction", "nil", "simp_rw"], "tactic_count": 3}
{"name": "Fin.lt_card_filter_univ_iff_apply_of_imp", "kind": "theorem", "module": "Mathlib.Data.Fintype.Fin", "is_tactic_proof": false, "tactics": ["have", "rw", "exact", "refine", "by_contra", "let", "have", "have", "grind"], "tactic_count": 9}
{"name": "Function.Injective.invOfMemRange", "kind": "definition", "module": "Mathlib.Data.Fintype.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.left_inv_of_invOfMemRange", "kind": "theorem", "module": "Mathlib.Data.Fintype.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.right_inv_of_invOfMemRange", "kind": "theorem", "module": "Mathlib.Data.Fintype.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.invFun_restrict", "kind": "theorem", "module": "Mathlib.Data.Fintype.Inv", "is_tactic_proof": true, "tactics": ["ext", "apply", "simp"], "tactic_count": 3}
{"name": "Function.Injective.invOfMemRange_surjective", "kind": "theorem", "module": "Mathlib.Data.Fintype.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.invOfMemRange", "kind": "definition", "module": "Mathlib.Data.Fintype.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.left_inv_of_invOfMemRange", "kind": "theorem", "module": "Mathlib.Data.Fintype.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.right_inv_of_invOfMemRange", "kind": "theorem", "module": "Mathlib.Data.Fintype.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.invFun_restrict", "kind": "theorem", "module": "Mathlib.Data.Fintype.Inv", "is_tactic_proof": true, "tactics": ["ext", "apply", "simp"], "tactic_count": 3}
{"name": "Function.Embedding.invOfMemRange_surjective", "kind": "theorem", "module": "Mathlib.Data.Fintype.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.chooseX", "kind": "definition", "module": "Mathlib.Data.Fintype.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.choose", "kind": "definition", "module": "Mathlib.Data.Fintype.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.choose_spec", "kind": "theorem", "module": "Mathlib.Data.Fintype.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.bijInv", "kind": "definition", "module": "Mathlib.Data.Fintype.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.leftInverse_bijInv", "kind": "theorem", "module": "Mathlib.Data.Fintype.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.rightInverse_bijInv", "kind": "theorem", "module": "Mathlib.Data.Fintype.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.bijective_bijInv", "kind": "theorem", "module": "Mathlib.Data.Fintype.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sup_univ_eq_iSup", "kind": "theorem", "module": "Mathlib.Data.Fintype.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inf_univ_eq_iInf", "kind": "theorem", "module": "Mathlib.Data.Fintype.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.fold_inf_univ", "kind": "theorem", "module": "Mathlib.Data.Fintype.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.fold_sup_univ", "kind": "theorem", "module": "Mathlib.Data.Fintype.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_inf", "kind": "theorem", "module": "Mathlib.Data.Fintype.Lattice", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "Finite.exists_max", "kind": "theorem", "module": "Mathlib.Data.Fintype.Lattice", "is_tactic_proof": true, "tactics": ["cases", "simpa"], "tactic_count": 2}
{"name": "Finite.exists_min", "kind": "theorem", "module": "Mathlib.Data.Fintype.Lattice", "is_tactic_proof": true, "tactics": ["cases", "simpa"], "tactic_count": 2}
{"name": "Multiset.lists", "kind": "definition", "module": "Mathlib.Data.Fintype.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.lists_coe", "kind": "theorem", "module": "Mathlib.Data.Fintype.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.lists_nodup_finset", "kind": "theorem", "module": "Mathlib.Data.Fintype.List", "is_tactic_proof": true, "tactics": ["have", "rw", "rw", "exact"], "tactic_count": 4}
{"name": "Multiset.mem_lists_iff", "kind": "theorem", "module": "Mathlib.Data.Fintype.List", "is_tactic_proof": true, "tactics": ["induction", "simpa"], "tactic_count": 2}
{"name": "fintypeNodupList", "kind": "instance", "module": "Mathlib.Data.Fintype.List", "is_tactic_proof": true, "tactics": ["refine", "let", "let", "refine", "simp", "unfold", "use", "constructor", "simp", "rfl", "convert", "ext", "unfold", "refine", "intro", "simp", "rw", "have", "rw", "rw", "simp", "rw", "constructor", "intro", "by_contra", "rw", "contrapose", "use", "simp", "intro", "simp", "intro", "by_contra", "absurd", "rw", "exact", "intro", "simp", "constructor", "intro", "rcases", "convert", "rw", "rfl", "intro", "exact"], "tactic_count": 46}
{"name": "Fintype.ofMultiset", "kind": "definition", "module": "Mathlib.Data.Fintype.OfMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.ofList", "kind": "definition", "module": "Mathlib.Data.Fintype.OfMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.ofBijective", "kind": "definition", "module": "Mathlib.Data.Fintype.OfMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.ofSurjective", "kind": "definition", "module": "Mathlib.Data.Fintype.OfMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.ofInjective", "kind": "definition", "module": "Mathlib.Data.Fintype.OfMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.ofEquiv", "kind": "definition", "module": "Mathlib.Data.Fintype.OfMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.ofSubsingleton", "kind": "definition", "module": "Mathlib.Data.Fintype.OfMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.univ_ofSubsingleton", "kind": "theorem", "module": "Mathlib.Data.Fintype.OfMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.ofIsEmpty", "kind": "definition", "module": "Mathlib.Data.Fintype.OfMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.univ_ofIsEmpty", "kind": "theorem", "module": "Mathlib.Data.Fintype.OfMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.instEmpty", "kind": "instance", "module": "Mathlib.Data.Fintype.OfMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.instPEmpty", "kind": "instance", "module": "Mathlib.Data.Fintype.OfMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFintypeOption", "kind": "instance", "module": "Mathlib.Data.Fintype.Option", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFiniteOption", "kind": "instance", "module": "Mathlib.Data.Fintype.Option", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "univ_option", "kind": "theorem", "module": "Mathlib.Data.Fintype.Option", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_option", "kind": "theorem", "module": "Mathlib.Data.Fintype.Option", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fintypeOfOption", "kind": "definition", "module": "Mathlib.Data.Fintype.Option", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fintypeOfOptionEquiv", "kind": "definition", "module": "Mathlib.Data.Fintype.Option", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.truncRecEmptyOption", "kind": "definition", "module": "Mathlib.Data.Fintype.Option", "is_tactic_proof": false, "tactics": ["suffices", "apply", "intro", "apply", "intro", "exact", "intro", "induction", "zero", "have", "apply", "intro", "apply", "exact", "succ", "ih", "have", "apply", "intro", "apply", "intro", "exact"], "tactic_count": 22}
{"name": "Fintype.induction_empty_option", "kind": "theorem", "module": "Mathlib.Data.Fintype.Option", "is_tactic_proof": false, "tactics": ["obtain", "let", "let", "rintro", "convert", "exact", "p"], "tactic_count": 7}
{"name": "Finite.induction_empty_option", "kind": "theorem", "module": "Mathlib.Data.Fintype.Option", "is_tactic_proof": true, "tactics": ["cases", "refine", "exacts"], "tactic_count": 3}
{"name": "Fintype.toOrderBot", "kind": "abbrev", "module": "Mathlib.Data.Fintype.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.toOrderTop", "kind": "abbrev", "module": "Mathlib.Data.Fintype.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.toBoundedOrder", "kind": "abbrev", "module": "Mathlib.Data.Fintype.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.toCompleteLattice", "kind": "abbrev", "module": "Mathlib.Data.Fintype.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.toCompleteDistribLatticeMinimalAxioms", "kind": "abbrev", "module": "Mathlib.Data.Fintype.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.toCompleteDistribLattice", "kind": "abbrev", "module": "Mathlib.Data.Fintype.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.toCompleteLinearOrder", "kind": "abbrev", "module": "Mathlib.Data.Fintype.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.toCompleteBooleanAlgebra", "kind": "abbrev", "module": "Mathlib.Data.Fintype.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.toCompleteAtomicBooleanAlgebra", "kind": "abbrev", "module": "Mathlib.Data.Fintype.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.toCompleteLatticeOfNonempty", "kind": "abbrev", "module": "Mathlib.Data.Fintype.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.toCompleteLinearOrderOfNonempty", "kind": "abbrev", "module": "Mathlib.Data.Fintype.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.completeLinearOrder", "kind": "instance", "module": "Mathlib.Data.Fintype.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bool.completeBooleanAlgebra", "kind": "instance", "module": "Mathlib.Data.Fintype.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bool.completeLinearOrder", "kind": "instance", "module": "Mathlib.Data.Fintype.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bool.completeAtomicBooleanAlgebra", "kind": "instance", "module": "Mathlib.Data.Fintype.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Directed.finite_set_le", "kind": "theorem", "module": "Mathlib.Data.Fintype.Order", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "Directed.finite_le", "kind": "theorem", "module": "Mathlib.Data.Fintype.Order", "is_tactic_proof": true, "tactics": ["classical", "obtain", "exact"], "tactic_count": 3}
{"name": "Finite.exists_le", "kind": "theorem", "module": "Mathlib.Data.Fintype.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finite.exists_ge", "kind": "theorem", "module": "Mathlib.Data.Fintype.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.exists_le", "kind": "theorem", "module": "Mathlib.Data.Fintype.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.exists_ge", "kind": "theorem", "module": "Mathlib.Data.Fintype.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finite.bddAbove_range", "kind": "theorem", "module": "Mathlib.Data.Fintype.Order", "is_tactic_proof": true, "tactics": ["obtain", "refine", "obtain", "exact"], "tactic_count": 4}
{"name": "Finite.bddBelow_range", "kind": "theorem", "module": "Mathlib.Data.Fintype.Order", "is_tactic_proof": true, "tactics": ["obtain", "refine", "obtain", "exact"], "tactic_count": 4}
{"name": "Fintype.IsSquare.decidablePred", "kind": "instance", "module": "Mathlib.Data.Fintype.Parity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_fin_two", "kind": "instance", "module": "Mathlib.Data.Fintype.Parity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "permsOfList", "kind": "definition", "module": "Mathlib.Data.Fintype.Perm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "length_permsOfList", "kind": "theorem", "module": "Mathlib.Data.Fintype.Perm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_permsOfList_of_mem", "kind": "theorem", "module": "Mathlib.Data.Fintype.Perm", "is_tactic_proof": true, "tactics": ["induction", "nil", "simp", "exact", "cons", "by_cases", "refine", "rintro", "exact", "have", "have", "intro", "have", "rintro", "apply", "simp", "refine", "simp", "split_ifs", "exacts", "suffices", "simpa", "refine", "exact", "rw"], "tactic_count": 25}
{"name": "mem_of_mem_permsOfList", "kind": "theorem", "module": "Mathlib.Data.Fintype.Perm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_permsOfList_iff", "kind": "theorem", "module": "Mathlib.Data.Fintype.Perm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nodup_permsOfList", "kind": "theorem", "module": "Mathlib.Data.Fintype.Perm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "permsOfFinset", "kind": "definition", "module": "Mathlib.Data.Fintype.Perm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_perms_of_finset_iff", "kind": "theorem", "module": "Mathlib.Data.Fintype.Perm", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "card_perms_of_finset", "kind": "theorem", "module": "Mathlib.Data.Fintype.Perm", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "fintypePerm", "kind": "definition", "module": "Mathlib.Data.Fintype.Perm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.instFintype", "kind": "instance", "module": "Mathlib.Data.Fintype.Perm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.instFintype", "kind": "instance", "module": "Mathlib.Data.Fintype.Perm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_perm", "kind": "theorem", "module": "Mathlib.Data.Fintype.Perm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_equiv", "kind": "theorem", "module": "Mathlib.Data.Fintype.Perm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.piFinset", "kind": "definition", "module": "Mathlib.Data.Fintype.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.mem_piFinset", "kind": "theorem", "module": "Mathlib.Data.Fintype.Pi", "is_tactic_proof": true, "tactics": ["constructor", "simp", "rintro", "rw", "exact", "simp", "exact"], "tactic_count": 7}
{"name": "Fintype.coe_piFinset", "kind": "theorem", "module": "Mathlib.Data.Fintype.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.piFinset_subset", "kind": "theorem", "module": "Mathlib.Data.Fintype.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.piFinset_eq_empty", "kind": "theorem", "module": "Mathlib.Data.Fintype.Pi", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fintype.piFinset_empty", "kind": "theorem", "module": "Mathlib.Data.Fintype.Pi", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fintype.piFinset_nonempty", "kind": "theorem", "module": "Mathlib.Data.Fintype.Pi", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.Nonempty.piFinset_const", "kind": "theorem", "module": "Mathlib.Data.Fintype.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.piFinset_of_isEmpty", "kind": "theorem", "module": "Mathlib.Data.Fintype.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.piFinset_singleton", "kind": "theorem", "module": "Mathlib.Data.Fintype.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.piFinset_subsingleton", "kind": "theorem", "module": "Mathlib.Data.Fintype.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.piFinset_disjoint_of_disjoint", "kind": "theorem", "module": "Mathlib.Data.Fintype.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.piFinset_image", "kind": "theorem", "module": "Mathlib.Data.Fintype.Pi", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Fintype.eval_image_piFinset_subset", "kind": "theorem", "module": "Mathlib.Data.Fintype.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.eval_image_piFinset", "kind": "theorem", "module": "Mathlib.Data.Fintype.Pi", "is_tactic_proof": true, "tactics": ["refine", "choose", "exact"], "tactic_count": 3}
{"name": "Fintype.eval_image_piFinset_const", "kind": "theorem", "module": "Mathlib.Data.Fintype.Pi", "is_tactic_proof": true, "tactics": ["obtain", "haveI", "simp", "exact"], "tactic_count": 4}
{"name": "Fintype.filter_piFinset_of_notMem", "kind": "theorem", "module": "Mathlib.Data.Fintype.Pi", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Fintype.piFinset_update_eq_filter_piFinset_mem", "kind": "theorem", "module": "Mathlib.Data.Fintype.Pi", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Fintype.piFinset_update_singleton_eq_filter_piFinset_eq", "kind": "theorem", "module": "Mathlib.Data.Fintype.Pi", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Pi.instFintype", "kind": "instance", "module": "Mathlib.Data.Fintype.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.piFinset_univ", "kind": "theorem", "module": "Mathlib.Data.Fintype.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.fintype", "kind": "instance", "module": "Mathlib.Data.Fintype.Pi", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "RelHom.instFintype", "kind": "instance", "module": "Mathlib.Data.Fintype.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelEmbedding.instFintype", "kind": "instance", "module": "Mathlib.Data.Fintype.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.univ_pi_univ", "kind": "theorem", "module": "Mathlib.Data.Fintype.Pi", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finset.piFinset_filter_const", "kind": "theorem", "module": "Mathlib.Data.Fintype.Pi", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Finset.piDiag_subset_piFinset", "kind": "theorem", "module": "Mathlib.Data.Fintype.Pi", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.Finite.pi", "kind": "theorem", "module": "Mathlib.Data.Fintype.Pi", "is_tactic_proof": true, "tactics": ["cases", "lift", "classical", "rw", "apply"], "tactic_count": 5}
{"name": "Set.Finite.pi'", "kind": "theorem", "module": "Mathlib.Data.Fintype.Pi", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.forall_finite_image_eval_iff", "kind": "theorem", "module": "Mathlib.Data.Fintype.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.exists_ne_map_eq_of_card_lt", "kind": "theorem", "module": "Mathlib.Data.Fintype.Pigeonhole", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.isEmpty_of_card_lt", "kind": "theorem", "module": "Mathlib.Data.Fintype.Pigeonhole", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finite.exists_ne_map_eq_of_infinite", "kind": "theorem", "module": "Mathlib.Data.Fintype.Pigeonhole", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finite.exists_infinite_fiber", "kind": "theorem", "module": "Mathlib.Data.Fintype.Pigeonhole", "is_tactic_proof": true, "tactics": ["classical", "by_contra", "cases", "let", "complete", "exact"], "tactic_count": 6}
{"name": "Finset.fintype", "kind": "instance", "module": "Mathlib.Data.Fintype.Powerset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_finset", "kind": "theorem", "module": "Mathlib.Data.Fintype.Powerset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.powerset_univ", "kind": "theorem", "module": "Mathlib.Data.Fintype.Powerset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.filter_subset_univ", "kind": "theorem", "module": "Mathlib.Data.Fintype.Powerset", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finset.powerset_eq_univ", "kind": "theorem", "module": "Mathlib.Data.Fintype.Powerset", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.mem_powersetCard_univ", "kind": "theorem", "module": "Mathlib.Data.Fintype.Powerset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.univ_filter_card_eq", "kind": "theorem", "module": "Mathlib.Data.Fintype.Powerset", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Fintype.card_finset_len", "kind": "theorem", "module": "Mathlib.Data.Fintype.Powerset", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.fintype", "kind": "instance", "module": "Mathlib.Data.Fintype.Powerset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instFinite", "kind": "instance", "module": "Mathlib.Data.Fintype.Powerset", "is_tactic_proof": true, "tactics": ["cases", "infer_instance"], "tactic_count": 2}
{"name": "Fintype.card_set", "kind": "theorem", "module": "Mathlib.Data.Fintype.Powerset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.toFinset_prod", "kind": "theorem", "module": "Mathlib.Data.Fintype.Prod", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Set.toFinset_offDiag", "kind": "theorem", "module": "Mathlib.Data.Fintype.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFintypeProd", "kind": "instance", "module": "Mathlib.Data.Fintype.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.univ_product_univ", "kind": "theorem", "module": "Mathlib.Data.Fintype.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.product_eq_univ", "kind": "theorem", "module": "Mathlib.Data.Fintype.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fintype.card_prod", "kind": "theorem", "module": "Mathlib.Data.Fintype.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "infinite_prod", "kind": "theorem", "module": "Mathlib.Data.Fintype.Prod", "is_tactic_proof": false, "tactics": ["refine", "rw", "rcases", "contrapose", "infer_instance"], "tactic_count": 5}
{"name": "Pi.infinite_of_left", "kind": "instance", "module": "Mathlib.Data.Fintype.Prod", "is_tactic_proof": true, "tactics": ["classical", "choose", "refine", "simp_rw", "exact"], "tactic_count": 5}
{"name": "Pi.infinite_of_exists_right", "kind": "theorem", "module": "Mathlib.Data.Fintype.Prod", "is_tactic_proof": true, "tactics": ["classical", "let", "exact"], "tactic_count": 3}
{"name": "Pi.infinite_of_right", "kind": "instance", "module": "Mathlib.Data.Fintype.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.infinite_of_left", "kind": "instance", "module": "Mathlib.Data.Fintype.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.infinite_of_right", "kind": "instance", "module": "Mathlib.Data.Fintype.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quotient.listChoice", "kind": "definition", "module": "Mathlib.Data.Fintype.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quotient.listChoice_mk", "kind": "theorem", "module": "Mathlib.Data.Fintype.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quotient.list_ind", "kind": "theorem", "module": "Mathlib.Data.Fintype.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quotient.ind_fintype_pi", "kind": "theorem", "module": "Mathlib.Data.Fintype.Quotient", "is_tactic_proof": false, "tactics": ["have", "induction", "exact", "exact"], "tactic_count": 4}
{"name": "Quotient.induction_on_fintype_pi", "kind": "theorem", "module": "Mathlib.Data.Fintype.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quotient.finChoice", "kind": "definition", "module": "Mathlib.Data.Fintype.Quotient", "is_tactic_proof": false, "tactics": ["let", "refine", "exact", "intro", "refine", "simp_rw"], "tactic_count": 6}
{"name": "Quotient.finChoice_eq", "kind": "theorem", "module": "Mathlib.Data.Fintype.Quotient", "is_tactic_proof": true, "tactics": ["dsimp", "obtain", "simp_rw", "rfl"], "tactic_count": 4}
{"name": "Quotient.eval_finChoice", "kind": "theorem", "module": "Mathlib.Data.Fintype.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quotient.finLiftOn", "kind": "definition", "module": "Mathlib.Data.Fintype.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quotient.finLiftOn_empty", "kind": "theorem", "module": "Mathlib.Data.Fintype.Quotient", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "induction", "exact"], "tactic_count": 4}
{"name": "Quotient.finLiftOn_mk", "kind": "theorem", "module": "Mathlib.Data.Fintype.Quotient", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "rw", "rfl"], "tactic_count": 4}
{"name": "Quotient.finChoiceEquiv", "kind": "definition", "module": "Mathlib.Data.Fintype.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quotient.finHRecOn", "kind": "definition", "module": "Mathlib.Data.Fintype.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quotient.finRecOn", "kind": "definition", "module": "Mathlib.Data.Fintype.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quotient.finHRecOn_mk", "kind": "theorem", "module": "Mathlib.Data.Fintype.Quotient", "is_tactic_proof": true, "tactics": ["ext", "refine", "rw", "rfl"], "tactic_count": 4}
{"name": "Quotient.finRecOn_mk", "kind": "theorem", "module": "Mathlib.Data.Fintype.Quotient", "is_tactic_proof": true, "tactics": ["unfold", "simp"], "tactic_count": 2}
{"name": "Trunc.finChoice", "kind": "definition", "module": "Mathlib.Data.Fintype.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trunc.finChoice_eq", "kind": "theorem", "module": "Mathlib.Data.Fintype.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trunc.finLiftOn", "kind": "definition", "module": "Mathlib.Data.Fintype.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trunc.finLiftOn_empty", "kind": "theorem", "module": "Mathlib.Data.Fintype.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trunc.finLiftOn_mk", "kind": "theorem", "module": "Mathlib.Data.Fintype.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trunc.finChoiceEquiv", "kind": "definition", "module": "Mathlib.Data.Fintype.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trunc.finRecOn", "kind": "definition", "module": "Mathlib.Data.Fintype.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trunc.finRecOn_mk", "kind": "theorem", "module": "Mathlib.Data.Fintype.Quotient", "is_tactic_proof": true, "tactics": ["unfold", "simp"], "tactic_count": 2}
{"name": "Set.toFinset", "kind": "definition", "module": "Mathlib.Data.Fintype.Sets", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.toFinset_congr", "kind": "theorem", "module": "Mathlib.Data.Fintype.Sets", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "Set.mem_toFinset", "kind": "theorem", "module": "Mathlib.Data.Fintype.Sets", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.toFinset_ofFinset", "kind": "theorem", "module": "Mathlib.Data.Fintype.Sets", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.decidableMemOfFintype", "kind": "definition", "module": "Mathlib.Data.Fintype.Sets", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.coe_toFinset", "kind": "theorem", "module": "Mathlib.Data.Fintype.Sets", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.toFinset_nonempty", "kind": "theorem", "module": "Mathlib.Data.Fintype.Sets", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.toFinset_inj", "kind": "theorem", "module": "Mathlib.Data.Fintype.Sets", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.toFinset_subset_toFinset", "kind": "theorem", "module": "Mathlib.Data.Fintype.Sets", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.toFinset_ssubset", "kind": "theorem", "module": "Mathlib.Data.Fintype.Sets", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.subset_toFinset", "kind": "theorem", "module": "Mathlib.Data.Fintype.Sets", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.ssubset_toFinset", "kind": "theorem", "module": "Mathlib.Data.Fintype.Sets", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.toFinset_ssubset_toFinset", "kind": "theorem", "module": "Mathlib.Data.Fintype.Sets", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.toFinset_subset", "kind": "theorem", "module": "Mathlib.Data.Fintype.Sets", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.disjoint_toFinset", "kind": "theorem", "module": "Mathlib.Data.Fintype.Sets", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.toFinset_nontrivial", "kind": "theorem", "module": "Mathlib.Data.Fintype.Sets", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.subsingleton_toFinset_iff", "kind": "theorem", "module": "Mathlib.Data.Fintype.Sets", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.toFinset_inter", "kind": "theorem", "module": "Mathlib.Data.Fintype.Sets", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Set.toFinset_union", "kind": "theorem", "module": "Mathlib.Data.Fintype.Sets", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Set.toFinset_diff", "kind": "theorem", "module": "Mathlib.Data.Fintype.Sets", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Set.toFinset_symmDiff", "kind": "theorem", "module": "Mathlib.Data.Fintype.Sets", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Set.toFinset_compl", "kind": "theorem", "module": "Mathlib.Data.Fintype.Sets", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Set.toFinset_empty", "kind": "theorem", "module": "Mathlib.Data.Fintype.Sets", "is_tactic_proof": true, "tactics": ["ext", "simp", "it"], "tactic_count": 3}
{"name": "Set.toFinset_univ", "kind": "theorem", "module": "Mathlib.Data.Fintype.Sets", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Set.toFinset_eq_empty", "kind": "theorem", "module": "Mathlib.Data.Fintype.Sets", "is_tactic_proof": true, "tactics": ["let", "rw"], "tactic_count": 2}
{"name": "Set.toFinset_eq_univ", "kind": "theorem", "module": "Mathlib.Data.Fintype.Sets", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.toFinset_setOf", "kind": "theorem", "module": "Mathlib.Data.Fintype.Sets", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Set.toFinset_ssubset_univ", "kind": "theorem", "module": "Mathlib.Data.Fintype.Sets", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.toFinset_image", "kind": "theorem", "module": "Mathlib.Data.Fintype.Sets", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.toFinset_range", "kind": "theorem", "module": "Mathlib.Data.Fintype.Sets", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Set.toFinset_singleton", "kind": "theorem", "module": "Mathlib.Data.Fintype.Sets", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Set.toFinset_insert", "kind": "theorem", "module": "Mathlib.Data.Fintype.Sets", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Set.filter_mem_univ_eq_toFinset", "kind": "theorem", "module": "Mathlib.Data.Fintype.Sets", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "Finset.toFinset_coe", "kind": "theorem", "module": "Mathlib.Data.Fintype.Sets", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.fintypeCoeSort", "kind": "instance", "module": "Mathlib.Data.Fintype.Sets", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.univ_eq_attach", "kind": "theorem", "module": "Mathlib.Data.Fintype.Sets", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.coe_image_univ", "kind": "theorem", "module": "Mathlib.Data.Fintype.Sets", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.Subtype.fintype", "kind": "instance", "module": "Mathlib.Data.Fintype.Sets", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Subtype.fintype", "kind": "instance", "module": "Mathlib.Data.Fintype.Sets", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Subtype.fintype", "kind": "instance", "module": "Mathlib.Data.Fintype.Sets", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinsetCoe.fintype", "kind": "instance", "module": "Mathlib.Data.Fintype.Sets", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.attach_eq_univ", "kind": "theorem", "module": "Mathlib.Data.Fintype.Sets", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prop.fintype", "kind": "instance", "module": "Mathlib.Data.Fintype.Sets", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.univ_Prop", "kind": "theorem", "module": "Mathlib.Data.Fintype.Sets", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.fintype", "kind": "instance", "module": "Mathlib.Data.Fintype.Sets", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "setFintype", "kind": "definition", "module": "Mathlib.Data.Fintype.Sets", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.finsetEquivSet", "kind": "definition", "module": "Mathlib.Data.Fintype.Sets", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.coe_finsetEquivSet", "kind": "theorem", "module": "Mathlib.Data.Fintype.Sets", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.finsetEquivSet_apply", "kind": "theorem", "module": "Mathlib.Data.Fintype.Sets", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.finsetEquivSet_symm_apply", "kind": "theorem", "module": "Mathlib.Data.Fintype.Sets", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fintype.finsetOrderIsoSet", "kind": "definition", "module": "Mathlib.Data.Fintype.Sets", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.coe_finsetOrderIsoSet", "kind": "theorem", "module": "Mathlib.Data.Fintype.Sets", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.coe_finsetOrderIsoSet_symm", "kind": "theorem", "module": "Mathlib.Data.Fintype.Sets", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_image_univ_iff_mem_range", "kind": "theorem", "module": "Mathlib.Data.Fintype.Sets", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "finsetStx", "kind": "definition", "module": "Mathlib.Data.Fintype.Sets", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Data_Fintype_Sets___elabRules_finsetStx_1", "kind": "definition", "module": "Mathlib.Data.Fintype.Sets", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "precheckFinsetStx", "kind": "definition", "module": "Mathlib.Data.Fintype.Sets", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Shrink.instFintype", "kind": "instance", "module": "Mathlib.Data.Fintype.Shrink", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Shrink.instFinite", "kind": "instance", "module": "Mathlib.Data.Fintype.Shrink", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_shrink", "kind": "theorem", "module": "Mathlib.Data.Fintype.Shrink", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.biUnion_finsetSigma_univ", "kind": "theorem", "module": "Mathlib.Data.Fintype.Sigma", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Set.biUnion_finsetSigma_univ'", "kind": "theorem", "module": "Mathlib.Data.Fintype.Sigma", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Set.biInter_finsetSigma_univ", "kind": "theorem", "module": "Mathlib.Data.Fintype.Sigma", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Set.biInter_finsetSigma_univ'", "kind": "theorem", "module": "Mathlib.Data.Fintype.Sigma", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Sigma.instFintype", "kind": "instance", "module": "Mathlib.Data.Fintype.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSigma.instFintype", "kind": "instance", "module": "Mathlib.Data.Fintype.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.univ_sigma_univ", "kind": "theorem", "module": "Mathlib.Data.Fintype.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monoEquivOfFin", "kind": "definition", "module": "Mathlib.Data.Fintype.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finSumEquivOfFinset", "kind": "definition", "module": "Mathlib.Data.Fintype.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finSumEquivOfFinset_inl", "kind": "theorem", "module": "Mathlib.Data.Fintype.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finSumEquivOfFinset_inr", "kind": "theorem", "module": "Mathlib.Data.Fintype.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFintypeSum", "kind": "instance", "module": "Mathlib.Data.Fintype.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.toLeft_eq_univ", "kind": "theorem", "module": "Mathlib.Data.Fintype.Sum", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.toRight_eq_empty", "kind": "theorem", "module": "Mathlib.Data.Fintype.Sum", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.toRight_eq_univ", "kind": "theorem", "module": "Mathlib.Data.Fintype.Sum", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.toLeft_eq_empty", "kind": "theorem", "module": "Mathlib.Data.Fintype.Sum", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.univ_disjSum_univ", "kind": "theorem", "module": "Mathlib.Data.Fintype.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.toLeft_univ", "kind": "theorem", "module": "Mathlib.Data.Fintype.Sum", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finset.toRight_univ", "kind": "theorem", "module": "Mathlib.Data.Fintype.Sum", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Fintype.card_sum", "kind": "theorem", "module": "Mathlib.Data.Fintype.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fintypeOfFintypeNe", "kind": "definition", "module": "Mathlib.Data.Fintype.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "image_subtype_ne_univ_eq_image_erase", "kind": "theorem", "module": "Mathlib.Data.Fintype.Sum", "is_tactic_proof": true, "tactics": ["apply", "rw", "intro", "apply", "intro", "rw", "rcases", "subst", "exact"], "tactic_count": 9}
{"name": "image_subtype_univ_ssubset_image_univ", "kind": "theorem", "module": "Mathlib.Data.Fintype.Sum", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.exists_equiv_extend_of_card_eq", "kind": "theorem", "module": "Mathlib.Data.Fintype.Sum", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "obtain", "use", "simp", "insert", "have", "have", "obtain", "have", "use", "simp_rw", "rintro", "simp", "rw", "exact", "ne_of_apply_ne", "hfs.ne", "exact"], "tactic_count": 20}
{"name": "Set.MapsTo.exists_equiv_extend_of_card_eq", "kind": "theorem", "module": "Mathlib.Data.Fintype.Sum", "is_tactic_proof": true, "tactics": ["classical", "let", "have", "have", "obtain", "refine", "apply", "simpa"], "tactic_count": 8}
{"name": "Fintype.card_subtype_or", "kind": "theorem", "module": "Mathlib.Data.Fintype.Sum", "is_tactic_proof": true, "tactics": ["classical", "convert", "rw"], "tactic_count": 3}
{"name": "Fintype.card_subtype_or_disjoint", "kind": "theorem", "module": "Mathlib.Data.Fintype.Sum", "is_tactic_proof": true, "tactics": ["classical", "convert", "simp"], "tactic_count": 3}
{"name": "Fintype.card_subtype_eq_or_eq_of_ne", "kind": "theorem", "module": "Mathlib.Data.Fintype.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "infinite_sum", "kind": "theorem", "module": "Mathlib.Data.Fintype.Sum", "is_tactic_proof": true, "tactics": ["refine", "contrapose", "infer_instance"], "tactic_count": 3}
{"name": "UnitsInt.fintype", "kind": "instance", "module": "Mathlib.Data.Fintype.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UnitsInt.univ", "kind": "theorem", "module": "Mathlib.Data.Fintype.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_units_int", "kind": "theorem", "module": "Mathlib.Data.Fintype.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFintypeUnitsOfDecidableEq", "kind": "instance", "module": "Mathlib.Data.Fintype.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFiniteUnits", "kind": "instance", "module": "Mathlib.Data.Fintype.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.card_units", "kind": "theorem", "module": "Mathlib.Data.Fintype.Units", "is_tactic_proof": true, "tactics": ["classical", "rw", "rcases", "rw", "rw"], "tactic_count": 5}
{"name": "Nat.card_eq_card_units_add_one", "kind": "theorem", "module": "Mathlib.Data.Fintype.Units", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fintype.card_units", "kind": "theorem", "module": "Mathlib.Data.Fintype.Units", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fintype.card_eq_card_units_add_one", "kind": "theorem", "module": "Mathlib.Data.Fintype.Units", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Vector.fintype", "kind": "instance", "module": "Mathlib.Data.Fintype.Vector", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFintypeSym'OfDecidableEq", "kind": "instance", "module": "Mathlib.Data.Fintype.Vector", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFintypeSymOfDecidableEq", "kind": "instance", "module": "Mathlib.Data.Fintype.Vector", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFintypeWithTop", "kind": "instance", "module": "Mathlib.Data.Fintype.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFiniteWithTop", "kind": "instance", "module": "Mathlib.Data.Fintype.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFintypeWithBot", "kind": "instance", "module": "Mathlib.Data.Fintype.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFiniteWithBot", "kind": "instance", "module": "Mathlib.Data.Fintype.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FunLike", "kind": "abbrev", "module": "Mathlib.Data.FunLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFunLike.hasCoeToFun", "kind": "instance", "module": "Mathlib.Data.FunLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFunLike.coe_eq_coe_fn", "kind": "theorem", "module": "Mathlib.Data.FunLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFunLike.coe_injective", "kind": "theorem", "module": "Mathlib.Data.FunLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFunLike.coe_fn_eq", "kind": "theorem", "module": "Mathlib.Data.FunLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFunLike.ext'", "kind": "theorem", "module": "Mathlib.Data.FunLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFunLike.ext'_iff", "kind": "theorem", "module": "Mathlib.Data.FunLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "DFunLike.ext_iff", "kind": "theorem", "module": "Mathlib.Data.FunLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "DFunLike.ne_iff", "kind": "theorem", "module": "Mathlib.Data.FunLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFunLike.exists_ne", "kind": "theorem", "module": "Mathlib.Data.FunLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFunLike.subsingleton_cod", "kind": "theorem", "module": "Mathlib.Data.FunLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFunLike.subsingleton_dom", "kind": "theorem", "module": "Mathlib.Data.FunLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFunLike.congr", "kind": "theorem", "module": "Mathlib.Data.FunLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFunLike.congr_arg", "kind": "theorem", "module": "Mathlib.Data.FunLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFunLike.dite_apply", "kind": "theorem", "module": "Mathlib.Data.FunLike.Basic", "is_tactic_proof": true, "tactics": ["split_ifs"], "tactic_count": 1}
{"name": "DFunLike.ite_apply", "kind": "theorem", "module": "Mathlib.Data.FunLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EmbeddingLike.injective", "kind": "theorem", "module": "Mathlib.Data.FunLike.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EmbeddingLike.apply_eq_iff_eq", "kind": "theorem", "module": "Mathlib.Data.FunLike.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EmbeddingLike.comp_injective", "kind": "theorem", "module": "Mathlib.Data.FunLike.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EquivLike.inv_injective", "kind": "theorem", "module": "Mathlib.Data.FunLike.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EquivLike.toFunLike", "kind": "instance", "module": "Mathlib.Data.FunLike.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EquivLike.coe_apply", "kind": "theorem", "module": "Mathlib.Data.FunLike.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EquivLike.inv_apply_eq", "kind": "theorem", "module": "Mathlib.Data.FunLike.Equiv", "is_tactic_proof": true, "tactics": ["constructor", "exacts"], "tactic_count": 2}
{"name": "EquivLike.toEmbeddingLike", "kind": "instance", "module": "Mathlib.Data.FunLike.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EquivLike.injective", "kind": "theorem", "module": "Mathlib.Data.FunLike.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EquivLike.surjective", "kind": "theorem", "module": "Mathlib.Data.FunLike.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EquivLike.bijective", "kind": "theorem", "module": "Mathlib.Data.FunLike.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EquivLike.apply_eq_iff_eq", "kind": "theorem", "module": "Mathlib.Data.FunLike.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EquivLike.injective_comp", "kind": "theorem", "module": "Mathlib.Data.FunLike.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EquivLike.surjective_comp", "kind": "theorem", "module": "Mathlib.Data.FunLike.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EquivLike.bijective_comp", "kind": "theorem", "module": "Mathlib.Data.FunLike.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EquivLike.inv_apply_apply", "kind": "theorem", "module": "Mathlib.Data.FunLike.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EquivLike.apply_inv_apply", "kind": "theorem", "module": "Mathlib.Data.FunLike.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EquivLike.comp_injective", "kind": "theorem", "module": "Mathlib.Data.FunLike.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EquivLike.comp_surjective", "kind": "theorem", "module": "Mathlib.Data.FunLike.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EquivLike.comp_bijective", "kind": "theorem", "module": "Mathlib.Data.FunLike.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EquivLike.subsingleton_dom", "kind": "theorem", "module": "Mathlib.Data.FunLike.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFunLike.fintype", "kind": "definition", "module": "Mathlib.Data.FunLike.Fintype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "FunLike.finite", "kind": "theorem", "module": "Mathlib.Data.FunLike.Fintype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FunLike.toDecidableEq", "kind": "instance", "module": "Mathlib.Data.FunLike.Fintype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HolorIndex", "kind": "definition", "module": "Mathlib.Data.Holor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "HolorIndex.drop", "kind": "definition", "module": "Mathlib.Data.Holor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "HolorIndex.drop_take", "kind": "theorem", "module": "Mathlib.Data.Holor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HolorIndex.drop_drop", "kind": "theorem", "module": "Mathlib.Data.Holor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Holor", "kind": "definition", "module": "Mathlib.Data.Holor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Holor.instAdd", "kind": "instance", "module": "Mathlib.Data.Holor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Holor.instNeg", "kind": "instance", "module": "Mathlib.Data.Holor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Holor.instAddSemigroup", "kind": "instance", "module": "Mathlib.Data.Holor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Holor.instAddCommSemigroup", "kind": "instance", "module": "Mathlib.Data.Holor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Holor.instAddMonoid", "kind": "instance", "module": "Mathlib.Data.Holor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Holor.instAddCommMonoid", "kind": "instance", "module": "Mathlib.Data.Holor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Holor.instAddGroup", "kind": "instance", "module": "Mathlib.Data.Holor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Holor.instAddCommGroup", "kind": "instance", "module": "Mathlib.Data.Holor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Holor.instSMulOfMul", "kind": "instance", "module": "Mathlib.Data.Holor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Holor.instModule", "kind": "instance", "module": "Mathlib.Data.Holor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Holor.mul", "kind": "definition", "module": "Mathlib.Data.Holor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.Holor.0.Holor.term_⊗_", "kind": "definition", "module": "Mathlib.Data.Holor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.Holor.0.Holor._aux_Mathlib_Data_Holor___macroRules__private_Mathlib_Data_Holor_0_Holor_term_⊗__1", "kind": "definition", "module": "Mathlib.Data.Holor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.Holor.0.Holor._aux_Mathlib_Data_Holor___unexpand_Holor_mul_1", "kind": "definition", "module": "Mathlib.Data.Holor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Holor.assocRight", "kind": "definition", "module": "Mathlib.Data.Holor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Holor.assocLeft", "kind": "definition", "module": "Mathlib.Data.Holor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Holor.mul_assoc0", "kind": "theorem", "module": "Mathlib.Data.Holor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Holor.mul_assoc", "kind": "theorem", "module": "Mathlib.Data.Holor", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Holor.mul_left_distrib", "kind": "theorem", "module": "Mathlib.Data.Holor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Holor.mul_right_distrib", "kind": "theorem", "module": "Mathlib.Data.Holor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Holor.zero_mul", "kind": "theorem", "module": "Mathlib.Data.Holor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Holor.mul_zero", "kind": "theorem", "module": "Mathlib.Data.Holor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Holor.mul_scalar_mul", "kind": "theorem", "module": "Mathlib.Data.Holor", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Holor.slice", "kind": "definition", "module": "Mathlib.Data.Holor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Holor.holor_index_cons_decomp", "kind": "theorem", "module": "Mathlib.Data.Holor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Holor.slice_eq", "kind": "theorem", "module": "Mathlib.Data.Holor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Holor.slice_unitVec_mul", "kind": "theorem", "module": "Mathlib.Data.Holor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Holor.slice_add", "kind": "theorem", "module": "Mathlib.Data.Holor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Holor.slice_zero", "kind": "theorem", "module": "Mathlib.Data.Holor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Holor.slice_sum", "kind": "theorem", "module": "Mathlib.Data.Holor", "is_tactic_proof": true, "tactics": ["letI", "refine", "simp", "intro", "rw"], "tactic_count": 5}
{"name": "Holor.sum_unitVec_mul_slice", "kind": "theorem", "module": "Mathlib.Data.Holor", "is_tactic_proof": true, "tactics": ["apply", "ext", "rw", "simp", "rw", "simp", "intro", "have", "simp", "intro", "exfalso", "exact"], "tactic_count": 12}
{"name": "Holor.CPRankMax1", "kind": "inductive", "module": "Mathlib.Data.Holor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Holor.CPRankMax", "kind": "inductive", "module": "Mathlib.Data.Holor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Holor.cprankMax_nil", "kind": "theorem", "module": "Mathlib.Data.Holor", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "Holor.cprankMax_1", "kind": "theorem", "module": "Mathlib.Data.Holor", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "Holor.cprankMax_add", "kind": "theorem", "module": "Mathlib.Data.Holor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Holor.cprankMax_mul", "kind": "theorem", "module": "Mathlib.Data.Holor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Holor.cprankMax_sum", "kind": "theorem", "module": "Mathlib.Data.Holor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Holor.cprankMax_upper_bound", "kind": "theorem", "module": "Mathlib.Data.Holor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Holor.cprank", "kind": "definition", "module": "Mathlib.Data.Holor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Holor.cprank_upper_bound", "kind": "theorem", "module": "Mathlib.Data.Holor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Ineq", "kind": "inductive", "module": "Mathlib.Data.Ineq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.instDecidableEqIneq", "kind": "instance", "module": "Mathlib.Data.Ineq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.instInhabitedIneq.default", "kind": "definition", "module": "Mathlib.Data.Ineq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.instInhabitedIneq", "kind": "instance", "module": "Mathlib.Data.Ineq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.instReprIneq", "kind": "instance", "module": "Mathlib.Data.Ineq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Ineq.max", "kind": "definition", "module": "Mathlib.Data.Ineq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Ineq.cmp", "kind": "definition", "module": "Mathlib.Data.Ineq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Ineq.toString", "kind": "definition", "module": "Mathlib.Data.Ineq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Ineq.instToString", "kind": "instance", "module": "Mathlib.Data.Ineq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Ineq.instToFormat", "kind": "instance", "module": "Mathlib.Data.Ineq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lean.Expr.ineq?", "kind": "definition", "module": "Mathlib.Data.Ineq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lean.Expr.ineqOrNotIneq?", "kind": "definition", "module": "Mathlib.Data.Ineq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AbsoluteValue.map_units_int", "kind": "theorem", "module": "Mathlib.Data.Int.AbsoluteValue", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "AbsoluteValue.map_units_intCast", "kind": "theorem", "module": "Mathlib.Data.Int.AbsoluteValue", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "AbsoluteValue.map_units_int_smul", "kind": "theorem", "module": "Mathlib.Data.Int.AbsoluteValue", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "Int.natAbs_eq_iff_associated", "kind": "theorem", "module": "Mathlib.Data.Int.Associated", "is_tactic_proof": true, "tactics": ["refine", "constructor", "rintro", "rfl", "exact", "rintro", "obtain", "exact", "exact"], "tactic_count": 9}
{"name": "Int.instNontrivial", "kind": "instance", "module": "Mathlib.Data.Int.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.ofNat_injective", "kind": "theorem", "module": "Mathlib.Data.Int.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.inductionOn'_add_one", "kind": "theorem", "module": "Mathlib.Data.Int.Basic", "is_tactic_proof": true, "tactics": ["apply", "lift", "rw", "have", "subst", "convert", "rw"], "tactic_count": 7}
{"name": "Int.strongRec_of_ge", "kind": "theorem", "module": "Mathlib.Data.Int.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "congr", "refine", "rw", "rw", "rw", "rw", "rw", "exact"], "tactic_count": 10}
{"name": "Int.natAbs_surjective", "kind": "theorem", "module": "Mathlib.Data.Int.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.pow_right_injective", "kind": "theorem", "module": "Mathlib.Data.Int.Basic", "is_tactic_proof": true, "tactics": ["refine", "convert", "rw"], "tactic_count": 3}
{"name": "Int.ofNat_dvd_natCast", "kind": "theorem", "module": "Mathlib.Data.Int.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.natCast_dvd_ofNat", "kind": "theorem", "module": "Mathlib.Data.Int.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.natCast_dvd", "kind": "theorem", "module": "Mathlib.Data.Int.Basic", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "Int.dvd_natCast", "kind": "theorem", "module": "Mathlib.Data.Int.Basic", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "Int.eq_zero_of_dvd_of_nonneg_of_lt", "kind": "theorem", "module": "Mathlib.Data.Int.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.eq_of_mod_eq_of_natAbs_sub_lt_natAbs", "kind": "theorem", "module": "Mathlib.Data.Int.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.natAbs_le_of_dvd_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Int.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.gcd_emod", "kind": "theorem", "module": "Mathlib.Data.Int.Basic", "is_tactic_proof": true, "tactics": ["conv_rhs"], "tactic_count": 1}
{"name": "Int.div2", "kind": "definition", "module": "Mathlib.Data.Int.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.bodd", "kind": "definition", "module": "Mathlib.Data.Int.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.bit", "kind": "definition", "module": "Mathlib.Data.Int.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.natBitwise", "kind": "definition", "module": "Mathlib.Data.Int.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.bitwise", "kind": "definition", "module": "Mathlib.Data.Int.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.lnot", "kind": "definition", "module": "Mathlib.Data.Int.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.lor", "kind": "definition", "module": "Mathlib.Data.Int.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.land", "kind": "definition", "module": "Mathlib.Data.Int.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.ldiff", "kind": "definition", "module": "Mathlib.Data.Int.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.xor", "kind": "definition", "module": "Mathlib.Data.Int.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.instShiftLeft_mathlib", "kind": "instance", "module": "Mathlib.Data.Int.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.instShiftRight_mathlib", "kind": "instance", "module": "Mathlib.Data.Int.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.bodd_zero", "kind": "theorem", "module": "Mathlib.Data.Int.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.bodd_one", "kind": "theorem", "module": "Mathlib.Data.Int.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.bodd_two", "kind": "theorem", "module": "Mathlib.Data.Int.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.bodd_coe", "kind": "theorem", "module": "Mathlib.Data.Int.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.bodd_subNatNat", "kind": "theorem", "module": "Mathlib.Data.Int.Bitwise", "is_tactic_proof": true, "tactics": ["apply", "simp", "cases", "simp"], "tactic_count": 4}
{"name": "Int.bodd_negOfNat", "kind": "theorem", "module": "Mathlib.Data.Int.Bitwise", "is_tactic_proof": true, "tactics": ["cases", "rfl"], "tactic_count": 2}
{"name": "Int.bodd_neg", "kind": "theorem", "module": "Mathlib.Data.Int.Bitwise", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Int.bodd_add", "kind": "theorem", "module": "Mathlib.Data.Int.Bitwise", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simp"], "tactic_count": 3}
{"name": "Int.bodd_mul", "kind": "theorem", "module": "Mathlib.Data.Int.Bitwise", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simp"], "tactic_count": 3}
{"name": "Int.bodd_add_div2", "kind": "theorem", "module": "Mathlib.Data.Int.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.div2_val", "kind": "theorem", "module": "Mathlib.Data.Int.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.bit_val", "kind": "theorem", "module": "Mathlib.Data.Int.Bitwise", "is_tactic_proof": true, "tactics": ["cases", "apply", "rfl"], "tactic_count": 3}
{"name": "Int.bit_decomp", "kind": "theorem", "module": "Mathlib.Data.Int.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.bitCasesOn", "kind": "definition", "module": "Mathlib.Data.Int.Bitwise", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "Int.bit_zero", "kind": "theorem", "module": "Mathlib.Data.Int.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.bit_coe_nat", "kind": "theorem", "module": "Mathlib.Data.Int.Bitwise", "is_tactic_proof": true, "tactics": ["rw", "cases"], "tactic_count": 2}
{"name": "Int.bit_negSucc", "kind": "theorem", "module": "Mathlib.Data.Int.Bitwise", "is_tactic_proof": true, "tactics": ["rw", "cases"], "tactic_count": 2}
{"name": "Int.bodd_bit", "kind": "theorem", "module": "Mathlib.Data.Int.Bitwise", "is_tactic_proof": true, "tactics": ["rw", "cases"], "tactic_count": 2}
{"name": "Int.testBit_bit_zero", "kind": "theorem", "module": "Mathlib.Data.Int.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.testBit_bit_succ", "kind": "theorem", "module": "Mathlib.Data.Int.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.bitwise_or", "kind": "theorem", "module": "Mathlib.Data.Int.Bitwise", "is_tactic_proof": true, "tactics": ["funext", "rcases", "try", "simp", "rw", "congr", "funext", "cases", "simp", "congr", "simp"], "tactic_count": 11}
{"name": "Int.bitwise_and", "kind": "theorem", "module": "Mathlib.Data.Int.Bitwise", "is_tactic_proof": true, "tactics": ["funext", "rcases", "try", "simp", "rw", "congr", "funext", "cases", "congr", "simp"], "tactic_count": 10}
{"name": "Int.bitwise_diff", "kind": "theorem", "module": "Mathlib.Data.Int.Bitwise", "is_tactic_proof": true, "tactics": ["funext", "rcases", "try", "simp", "congr", "simp", "congr", "simp", "rw", "congr", "funext", "cases", "rfl"], "tactic_count": 13}
{"name": "Int.bitwise_xor", "kind": "theorem", "module": "Mathlib.Data.Int.Bitwise", "is_tactic_proof": true, "tactics": ["funext", "rcases", "try", "simp", "simp"], "tactic_count": 5}
{"name": "Int.bitwise_bit", "kind": "theorem", "module": "Mathlib.Data.Int.Bitwise", "is_tactic_proof": false, "tactics": ["rcases", "simp", "by_cases", "by_cases", "by_cases", "by_cases"], "tactic_count": 6}
{"name": "Int.lor_bit", "kind": "theorem", "module": "Mathlib.Data.Int.Bitwise", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.land_bit", "kind": "theorem", "module": "Mathlib.Data.Int.Bitwise", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.ldiff_bit", "kind": "theorem", "module": "Mathlib.Data.Int.Bitwise", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.lxor_bit", "kind": "theorem", "module": "Mathlib.Data.Int.Bitwise", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.lnot_bit", "kind": "theorem", "module": "Mathlib.Data.Int.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.testBit_bitwise", "kind": "theorem", "module": "Mathlib.Data.Int.Bitwise", "is_tactic_proof": true, "tactics": ["cases", "by_cases", "by_cases", "by_cases", "by_cases"], "tactic_count": 5}
{"name": "Int.testBit_lor", "kind": "theorem", "module": "Mathlib.Data.Int.Bitwise", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.testBit_land", "kind": "theorem", "module": "Mathlib.Data.Int.Bitwise", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.testBit_ldiff", "kind": "theorem", "module": "Mathlib.Data.Int.Bitwise", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.testBit_lxor", "kind": "theorem", "module": "Mathlib.Data.Int.Bitwise", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.testBit_lnot", "kind": "theorem", "module": "Mathlib.Data.Int.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.shiftLeft_neg", "kind": "theorem", "module": "Mathlib.Data.Int.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.shiftRight_neg", "kind": "theorem", "module": "Mathlib.Data.Int.Bitwise", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.shiftLeft_natCast", "kind": "theorem", "module": "Mathlib.Data.Int.Bitwise", "is_tactic_proof": true, "tactics": ["unfold_projs"], "tactic_count": 1}
{"name": "Int.shiftRight_natCast", "kind": "theorem", "module": "Mathlib.Data.Int.Bitwise", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Int.shiftLeft_negSucc", "kind": "theorem", "module": "Mathlib.Data.Int.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.shiftRight_negSucc", "kind": "theorem", "module": "Mathlib.Data.Int.Bitwise", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Int.shiftRight_add'", "kind": "theorem", "module": "Mathlib.Data.Int.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.shiftLeft_natCast_right", "kind": "theorem", "module": "Mathlib.Data.Int.Bitwise", "is_tactic_proof": true, "tactics": ["rw", "unfold_projs", "cases", "simp", "mul_def]", "grind", "simp", "grind"], "tactic_count": 8}
{"name": "Int.shiftRight_natCast_right", "kind": "theorem", "module": "Mathlib.Data.Int.Bitwise", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Int.shiftLeft_add'", "kind": "theorem", "module": "Mathlib.Data.Int.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.shiftLeft_sub", "kind": "theorem", "module": "Mathlib.Data.Int.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.shiftLeft_eq_mul_pow", "kind": "theorem", "module": "Mathlib.Data.Int.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.one_shiftLeft", "kind": "theorem", "module": "Mathlib.Data.Int.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.zero_shiftLeft'", "kind": "theorem", "module": "Mathlib.Data.Int.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.zero_shiftRight'", "kind": "theorem", "module": "Mathlib.Data.Int.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.Ico_filter_modEq_eq", "kind": "theorem", "module": "Mathlib.Data.Int.CardIntervalMod", "is_tactic_proof": true, "tactics": ["ext", "simp_rw", "modEq_iff_dvd,"], "tactic_count": 3}
{"name": "Int.Ioc_filter_modEq_eq", "kind": "theorem", "module": "Mathlib.Data.Int.CardIntervalMod", "is_tactic_proof": true, "tactics": ["ext", "simp_rw", "modEq_iff_dvd,"], "tactic_count": 3}
{"name": "Int.Ico_filter_dvd_eq", "kind": "theorem", "module": "Mathlib.Data.Int.CardIntervalMod", "is_tactic_proof": true, "tactics": ["ext", "simp", "cast_pos.2", "aesop"], "tactic_count": 4}
{"name": "Int.Ioc_filter_dvd_eq", "kind": "theorem", "module": "Mathlib.Data.Int.CardIntervalMod", "is_tactic_proof": true, "tactics": ["ext", "simp", "cast_pos.2", "aesop"], "tactic_count": 4}
{"name": "Int.Ico_filter_dvd_card", "kind": "theorem", "module": "Mathlib.Data.Int.CardIntervalMod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.Ioc_filter_dvd_card", "kind": "theorem", "module": "Mathlib.Data.Int.CardIntervalMod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.Ico_filter_modEq_card", "kind": "theorem", "module": "Mathlib.Data.Int.CardIntervalMod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Int.Ioc_filter_modEq_card", "kind": "theorem", "module": "Mathlib.Data.Int.CardIntervalMod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.Ico_filter_modEq_cast", "kind": "theorem", "module": "Mathlib.Data.Int.CardIntervalMod", "is_tactic_proof": true, "tactics": ["ext", "simp", "constructor", "simp_rw", "intro"], "tactic_count": 5}
{"name": "Nat.Ioc_filter_modEq_cast", "kind": "theorem", "module": "Mathlib.Data.Int.CardIntervalMod", "is_tactic_proof": true, "tactics": ["ext", "simp", "constructor", "simp_rw", "intro"], "tactic_count": 5}
{"name": "Nat.Ico_filter_modEq_card", "kind": "theorem", "module": "Mathlib.Data.Int.CardIntervalMod", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Nat.Ioc_filter_modEq_card", "kind": "theorem", "module": "Mathlib.Data.Int.CardIntervalMod", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Nat.count_modEq_card_eq_ceil", "kind": "theorem", "module": "Mathlib.Data.Int.CardIntervalMod", "is_tactic_proof": true, "tactics": ["have", "rw", "max_eq_left", "conv_lhs", "rw", "tactic", "rw", "rw", "neg_lt_neg_iff,", "exact"], "tactic_count": 10}
{"name": "Nat.count_modEq_card", "kind": "theorem", "module": "Mathlib.Data.Int.CardIntervalMod", "is_tactic_proof": true, "tactics": ["have", "rw", "conv_lhs", "rw", "rw", "split_ifs", "rw", "cast_pos,", "exact", "rw", "neg_eq_neg_one_mul,", "exact"], "tactic_count": 12}
{"name": "Nat.cast_sub", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.cast_pred", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.cast_ite", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.cast_negSucc", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.cast_zero", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.cast_natCast", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.cast_ofNat", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Int.cast_one", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.cast_neg", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.cast_subNatNat", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Basic", "is_tactic_proof": true, "tactics": ["unfold", "cases", "simp", "rw"], "tactic_count": 4}
{"name": "Int.cast_negOfNat", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Int.cast_add", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.cast_sub", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Int.cast_two", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.cast_three", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.cast_four", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zsmul_one", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Int.castDef", "kind": "definition", "module": "Mathlib.Data.Int.Cast.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.cast_neg_natCast", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Field", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Int.cast_div", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Field", "is_tactic_proof": true, "tactics": ["rcases", "have", "rw"], "tactic_count": 3}
{"name": "Int.ofNatHom", "kind": "definition", "module": "Mathlib.Data.Int.Cast.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.castAddHom", "kind": "definition", "module": "Mathlib.Data.Int.Cast.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.coe_castAddHom", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Even.intCast", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.cast_eq_zero", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.cast_inj", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.cast_injective", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.cast_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.cast_eq_one", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.cast_ne_one", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.castRingHom", "kind": "definition", "module": "Mathlib.Data.Int.Cast.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.coe_castRingHom", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.cast_commute", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.cast_comm", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.commute_cast", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zsmul_eq_mul", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zsmul_eq_mul'", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Odd.intCast", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.cast_dvd_cast", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiconjBy.intCast_mul_right", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiconjBy.intCast_mul_left", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiconjBy.intCast_mul_intCast_mul", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Commute.intCast_left", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.intCast_right", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.intCast_mul_right", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Commute.intCast_mul_left", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Commute.intCast_mul_intCast_mul", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.self_intCast_mul", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.intCast_mul_self", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.self_intCast_mul_intCast_mul", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.ext_int", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.eq_intCastAddHom", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddEquiv.ext_int", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_intCast'", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "map_intCast'", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.castAddHom_int", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.ext_mint", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.ext_int", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Lemmas", "is_tactic_proof": true, "tactics": ["ext", "exact", "rw", "congr", "exact"], "tactic_count": 5}
{"name": "MonoidWithZeroHom.ext_int", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ext_int'", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zmultiplesHom", "kind": "definition", "module": "Mathlib.Data.Int.Cast.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zpowersHom", "kind": "definition", "module": "Mathlib.Data.Int.Cast.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zmultiplesHom_apply", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zmultiplesHom_symm_apply", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zpowersHom_apply", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zpowersHom_symm_apply", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.apply_mint", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AddMonoidHom.apply_int", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "zmultiplesAddHom", "kind": "definition", "module": "Mathlib.Data.Int.Cast.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zpowersMulHom", "kind": "definition", "module": "Mathlib.Data.Int.Cast.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zpowersMulHom_apply", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zpowersMulHom_symm_apply", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zmultiplesAddHom_apply", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zmultiplesAddHom_symm_apply", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_intCast", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "map_intCast", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.eq_intCast'", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.ext_int", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.Int.subsingleton_ringHom", "kind": "instance", "module": "Mathlib.Data.Int.Cast.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.castRingHom_int", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instIntCast", "kind": "instance", "module": "Mathlib.Data.Int.Cast.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.intCast_apply", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.intCast_def", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.elim_intCast_intCast", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instAddGroupWithOne", "kind": "instance", "module": "Mathlib.Data.Int.Cast.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.fst_intCast", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.snd_intCast", "kind": "theorem", "module": "Mathlib.Data.Int.Cast.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.cast_div_charZero", "kind": "theorem", "module": "Mathlib.Data.Int.CharZero", "is_tactic_proof": true, "tactics": ["rcases", "simp", "exact", "cast_div"], "tactic_count": 4}
{"name": "Int.cast_div_ofNat_charZero", "kind": "theorem", "module": "Mathlib.Data.Int.CharZero", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RingHom.injective_int", "kind": "theorem", "module": "Mathlib.Data.Int.CharZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.support_intCast", "kind": "theorem", "module": "Mathlib.Data.Int.CharZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.mulSupport_intCast", "kind": "theorem", "module": "Mathlib.Data.Int.CharZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instConditionallyCompleteLinearOrder", "kind": "instance", "module": "Mathlib.Data.Int.ConditionallyCompleteOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.csSup_eq_greatestOfBdd", "kind": "theorem", "module": "Mathlib.Data.Int.ConditionallyCompleteOrder", "is_tactic_proof": true, "tactics": ["have", "simp", "convert"], "tactic_count": 3}
{"name": "Int.csSup_empty", "kind": "theorem", "module": "Mathlib.Data.Int.ConditionallyCompleteOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.csSup_of_not_bddAbove", "kind": "theorem", "module": "Mathlib.Data.Int.ConditionallyCompleteOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.csInf_eq_leastOfBdd", "kind": "theorem", "module": "Mathlib.Data.Int.ConditionallyCompleteOrder", "is_tactic_proof": true, "tactics": ["have", "simp", "convert"], "tactic_count": 3}
{"name": "Int.csInf_empty", "kind": "theorem", "module": "Mathlib.Data.Int.ConditionallyCompleteOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.csInf_of_not_bddBelow", "kind": "theorem", "module": "Mathlib.Data.Int.ConditionallyCompleteOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.csSup_mem", "kind": "theorem", "module": "Mathlib.Data.Int.ConditionallyCompleteOrder", "is_tactic_proof": true, "tactics": ["convert", "exact"], "tactic_count": 2}
{"name": "Int.csInf_mem", "kind": "theorem", "module": "Mathlib.Data.Int.ConditionallyCompleteOrder", "is_tactic_proof": true, "tactics": ["convert", "exact"], "tactic_count": 2}
{"name": "_example", "kind": "example", "module": "Mathlib.Data.Int.ConditionallyCompleteOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.mul_ediv_le_mul_ediv_assoc", "kind": "theorem", "module": "Mathlib.Data.Int.DivMod", "is_tactic_proof": true, "tactics": ["obtain", "simp", "rw", "exact"], "tactic_count": 4}
{"name": "Int.fdiv_fdiv_eq_fdiv_mul", "kind": "theorem", "module": "Mathlib.Data.Int.DivMod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.emod_eq_sub_self_emod", "kind": "theorem", "module": "Mathlib.Data.Int.DivMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.fib", "kind": "definition", "module": "Mathlib.Data.Int.Fib.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.fib_natCast", "kind": "theorem", "module": "Mathlib.Data.Int.Fib.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.fib_zero", "kind": "theorem", "module": "Mathlib.Data.Int.Fib.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.fib_one", "kind": "theorem", "module": "Mathlib.Data.Int.Fib.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.fib_two", "kind": "theorem", "module": "Mathlib.Data.Int.Fib.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.fib_neg_one", "kind": "theorem", "module": "Mathlib.Data.Int.Fib.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.fib_neg_two", "kind": "theorem", "module": "Mathlib.Data.Int.Fib.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.fib_of_nonneg", "kind": "theorem", "module": "Mathlib.Data.Int.Fib.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Int.fib_of_odd", "kind": "theorem", "module": "Mathlib.Data.Int.Fib.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Int.fib_two_mul_add_one_eq_natFib_natAbs", "kind": "theorem", "module": "Mathlib.Data.Int.Fib.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.fib_two_mul_add_one_pos", "kind": "theorem", "module": "Mathlib.Data.Int.Fib.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Int.fib_neg_natCast", "kind": "theorem", "module": "Mathlib.Data.Int.Fib.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simp"], "tactic_count": 3}
{"name": "Int.fib_neg", "kind": "theorem", "module": "Mathlib.Data.Int.Fib.Basic", "is_tactic_proof": true, "tactics": ["obtain", "aesop"], "tactic_count": 2}
{"name": "Int.coe_fib_neg", "kind": "theorem", "module": "Mathlib.Data.Int.Fib.Basic", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Int.fib_add_two", "kind": "theorem", "module": "Mathlib.Data.Int.Fib.Basic", "is_tactic_proof": true, "tactics": ["rcases", "dsimp", "rw", "rw", "simp", "add_neg_cancel_comm_assoc,", "symm", "calc", "have", "obtain", "rw", "simp", "rw", "simp"], "tactic_count": 14}
{"name": "Int.fib_eq_fib_add_two_sub_fib_add_one", "kind": "theorem", "module": "Mathlib.Data.Int.Fib.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Int.fib_add_one", "kind": "theorem", "module": "Mathlib.Data.Int.Fib.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Int.fib_eq_zero", "kind": "theorem", "module": "Mathlib.Data.Int.Fib.Basic", "is_tactic_proof": true, "tactics": ["obtain", "simp"], "tactic_count": 2}
{"name": "_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_natCast_add", "kind": "theorem", "module": "Mathlib.Data.Int.Fib.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_add_natCast", "kind": "theorem", "module": "Mathlib.Data.Int.Fib.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_neg_natCast_add_neg_natCast", "kind": "theorem", "module": "Mathlib.Data.Int.Fib.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.fib_add", "kind": "theorem", "module": "Mathlib.Data.Int.Fib.Basic", "is_tactic_proof": true, "tactics": ["obtain", "exact", "obtain", "exact", "exact"], "tactic_count": 5}
{"name": "Int.fib_two_mul", "kind": "theorem", "module": "Mathlib.Data.Int.Fib.Basic", "is_tactic_proof": true, "tactics": ["rw", "grind"], "tactic_count": 2}
{"name": "Int.fib_two_mul_add_one", "kind": "theorem", "module": "Mathlib.Data.Int.Fib.Basic", "is_tactic_proof": true, "tactics": ["have", "grind"], "tactic_count": 2}
{"name": "Int.fib_two_mul_add_two", "kind": "theorem", "module": "Mathlib.Data.Int.Fib.Basic", "is_tactic_proof": true, "tactics": ["rw", "grind"], "tactic_count": 2}
{"name": "Int.gcd_fib", "kind": "theorem", "module": "Mathlib.Data.Int.Fib.Basic", "is_tactic_proof": true, "tactics": ["obtain", "simp"], "tactic_count": 2}
{"name": "Int.fib_gcd", "kind": "theorem", "module": "Mathlib.Data.Int.Fib.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_natCast_dvd", "kind": "theorem", "module": "Mathlib.Data.Int.Fib.Basic", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Int.fib_dvd", "kind": "theorem", "module": "Mathlib.Data.Int.Fib.Basic", "is_tactic_proof": true, "tactics": ["obtain", "exact", "simp"], "tactic_count": 3}
{"name": "Int.fib_natCast_succ_mul_fib_natCast_pred_sub_fib_natCast_sq", "kind": "theorem", "module": "Mathlib.Data.Int.Fib.Lemmas", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Int.fib_succ_mul_fib_pred_sub_fib_sq", "kind": "theorem", "module": "Mathlib.Data.Int.Fib.Lemmas", "is_tactic_proof": true, "tactics": ["obtain", "exact", "obtain", "simp_rw", "grind"], "tactic_count": 5}
{"name": "Int.fib_add_sq_sub_fib_mul_fib_add_two_mul", "kind": "theorem", "module": "Mathlib.Data.Int.Fib.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.xgcdAux", "kind": "definition", "module": "Mathlib.Data.Int.GCD", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.xgcd_zero_left", "kind": "theorem", "module": "Mathlib.Data.Int.GCD", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.xgcdAux_rec", "kind": "theorem", "module": "Mathlib.Data.Int.GCD", "is_tactic_proof": true, "tactics": ["obtain", "rw", "rfl"], "tactic_count": 3}
{"name": "Nat.xgcd", "kind": "definition", "module": "Mathlib.Data.Int.GCD", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.gcdA", "kind": "definition", "module": "Mathlib.Data.Int.GCD", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.gcdB", "kind": "definition", "module": "Mathlib.Data.Int.GCD", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.gcdA_zero_left", "kind": "theorem", "module": "Mathlib.Data.Int.GCD", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.gcdB_zero_left", "kind": "theorem", "module": "Mathlib.Data.Int.GCD", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.gcdA_zero_right", "kind": "theorem", "module": "Mathlib.Data.Int.GCD", "is_tactic_proof": true, "tactics": ["obtain", "rfl"], "tactic_count": 2}
{"name": "Nat.gcdB_zero_right", "kind": "theorem", "module": "Mathlib.Data.Int.GCD", "is_tactic_proof": true, "tactics": ["obtain", "rfl"], "tactic_count": 2}
{"name": "Nat.xgcdAux_fst", "kind": "theorem", "module": "Mathlib.Data.Int.GCD", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.xgcdAux_val", "kind": "theorem", "module": "Mathlib.Data.Int.GCD", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.xgcd_val", "kind": "theorem", "module": "Mathlib.Data.Int.GCD", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "_private.Mathlib.Data.Int.GCD.0.Nat.P", "kind": "definition", "module": "Mathlib.Data.Int.GCD", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.Int.GCD.0.Nat.xgcdAux_P", "kind": "theorem", "module": "Mathlib.Data.Int.GCD", "is_tactic_proof": true, "tactics": ["induction", "intro", "rw", "rw", "rw", "mul_assoc,"], "tactic_count": 6}
{"name": "Nat.gcd_eq_gcd_ab", "kind": "theorem", "module": "Mathlib.Data.Int.GCD", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "Nat.exists_mul_mod_eq_gcd", "kind": "theorem", "module": "Mathlib.Data.Int.GCD", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.exists_mul_mod_eq_one_of_coprime", "kind": "theorem", "module": "Mathlib.Data.Int.GCD", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Nat.exists_mul_mod_eq_of_coprime", "kind": "theorem", "module": "Mathlib.Data.Int.GCD", "is_tactic_proof": true, "tactics": ["obtain", "simp", "obtain", "use", "rw"], "tactic_count": 5}
{"name": "Int.gcd_def", "kind": "theorem", "module": "Mathlib.Data.Int.GCD", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.gcdA", "kind": "definition", "module": "Mathlib.Data.Int.GCD", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.gcdB", "kind": "definition", "module": "Mathlib.Data.Int.GCD", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.gcd_eq_gcd_ab", "kind": "theorem", "module": "Mathlib.Data.Int.GCD", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.lcm_def", "kind": "theorem", "module": "Mathlib.Data.Int.GCD", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.gcd_eq_one_of_gcd_mul_right_eq_one_left", "kind": "theorem", "module": "Mathlib.Data.Int.GCD", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.gcd_eq_one_of_gcd_mul_right_eq_one_right", "kind": "theorem", "module": "Mathlib.Data.Int.GCD", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.ne_zero_of_gcd", "kind": "theorem", "module": "Mathlib.Data.Int.GCD", "is_tactic_proof": true, "tactics": ["contrapose", "rw"], "tactic_count": 2}
{"name": "Int.exists_gcd_one", "kind": "theorem", "module": "Mathlib.Data.Int.GCD", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.exists_gcd_one'", "kind": "theorem", "module": "Mathlib.Data.Int.GCD", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.gcd_dvd_iff", "kind": "theorem", "module": "Mathlib.Data.Int.GCD", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "exact", "rintro", "rw", "exact"], "tactic_count": 7}
{"name": "Int.gcd_greatest", "kind": "theorem", "module": "Mathlib.Data.Int.GCD", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.dvd_of_dvd_mul_left_of_gcd_one", "kind": "theorem", "module": "Mathlib.Data.Int.GCD", "is_tactic_proof": true, "tactics": ["have", "simp", "have", "rw", "exact"], "tactic_count": 5}
{"name": "Int.dvd_of_dvd_mul_right_of_gcd_one", "kind": "theorem", "module": "Mathlib.Data.Int.GCD", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Int.gcd_least_linear", "kind": "theorem", "module": "Mathlib.Data.Int.GCD", "is_tactic_proof": true, "tactics": ["simp_rw", "constructor", "simpa", "simp", "exact"], "tactic_count": 5}
{"name": "pow_gcd_eq_one", "kind": "theorem", "module": "Mathlib.Data.Int.GCD", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pow_eq_one_iff_of_coprime", "kind": "theorem", "module": "Mathlib.Data.Int.GCD", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "pow_intGCD_eq_one", "kind": "theorem", "module": "Mathlib.Data.Int.GCD", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "Commute.pow_eq_pow_iff_of_coprime", "kind": "theorem", "module": "Mathlib.Data.Int.GCD", "is_tactic_proof": true, "tactics": ["refine", "by_cases", "by_cases", "by_cases", "by_cases", "refine", "refine", "conv_lhs", "simp", "mul_comm", "simp", "exact"], "tactic_count": 12}
{"name": "pow_eq_pow_iff_of_coprime", "kind": "theorem", "module": "Mathlib.Data.Int.GCD", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pow_mem_range_pow_of_coprime", "kind": "theorem", "module": "Mathlib.Data.Int.GCD", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Int.neg_eq_neg", "kind": "theorem", "module": "Mathlib.Data.Int.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.succ", "kind": "definition", "module": "Mathlib.Data.Int.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.pred", "kind": "definition", "module": "Mathlib.Data.Int.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.pred_succ", "kind": "theorem", "module": "Mathlib.Data.Int.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.succ_pred", "kind": "theorem", "module": "Mathlib.Data.Int.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.neg_succ", "kind": "theorem", "module": "Mathlib.Data.Int.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.succ_neg_succ", "kind": "theorem", "module": "Mathlib.Data.Int.Init", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.neg_pred", "kind": "theorem", "module": "Mathlib.Data.Int.Init", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.pred_neg_pred", "kind": "theorem", "module": "Mathlib.Data.Int.Init", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.pred_nat_succ", "kind": "theorem", "module": "Mathlib.Data.Int.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.neg_nat_succ", "kind": "theorem", "module": "Mathlib.Data.Int.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.succ_neg_natCast_succ", "kind": "theorem", "module": "Mathlib.Data.Int.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.natCast_pred_of_pos", "kind": "theorem", "module": "Mathlib.Data.Int.Init", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Int.lt_succ_self", "kind": "theorem", "module": "Mathlib.Data.Int.Init", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "Int.pred_self_lt", "kind": "theorem", "module": "Mathlib.Data.Int.Init", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "Int.induction_on", "kind": "theorem", "module": "Mathlib.Data.Int.Init", "is_tactic_proof": true, "tactics": ["cases", "ofNat", "induction", "zero", "succ", "negSucc", "suffices", "intro", "induction", "zero", "succ"], "tactic_count": 11}
{"name": "Int.inductionOn'", "kind": "definition", "module": "Mathlib.Data.Int.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.inductionOn'_self", "kind": "theorem", "module": "Mathlib.Data.Int.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.inductionOn'_sub_one", "kind": "theorem", "module": "Mathlib.Data.Int.Init", "is_tactic_proof": true, "tactics": ["apply", "obtain", "rw", "obtain", "change", "have", "subst", "have", "subst", "refine", "congr", "symm", "rw"], "tactic_count": 13}
{"name": "Int.negInduction", "kind": "definition", "module": "Mathlib.Data.Int.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.le_induction", "kind": "theorem", "module": "Mathlib.Data.Int.Init", "is_tactic_proof": true, "tactics": ["refine"], "tactic_count": 1}
{"name": "Int.le_induction_down", "kind": "theorem", "module": "Mathlib.Data.Int.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.strongRec", "kind": "definition", "module": "Mathlib.Data.Int.Init", "is_tactic_proof": true, "tactics": ["refine", "intro", "exact", "exact"], "tactic_count": 4}
{"name": "Int.strongRec_of_lt", "kind": "theorem", "module": "Mathlib.Data.Int.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.sign_mul_self_eq_natAbs", "kind": "theorem", "module": "Mathlib.Data.Int.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.natCast_div", "kind": "theorem", "module": "Mathlib.Data.Int.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.ediv_of_neg_of_pos", "kind": "theorem", "module": "Mathlib.Data.Int.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.natCast_mod", "kind": "theorem", "module": "Mathlib.Data.Int.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.div_le_iff_of_dvd_of_pos", "kind": "theorem", "module": "Mathlib.Data.Int.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.div_le_iff_of_dvd_of_neg", "kind": "theorem", "module": "Mathlib.Data.Int.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.div_lt_iff_of_dvd_of_pos", "kind": "theorem", "module": "Mathlib.Data.Int.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.div_lt_iff_of_dvd_of_neg", "kind": "theorem", "module": "Mathlib.Data.Int.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.le_div_iff_of_dvd_of_pos", "kind": "theorem", "module": "Mathlib.Data.Int.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.le_div_iff_of_dvd_of_neg", "kind": "theorem", "module": "Mathlib.Data.Int.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.lt_div_iff_of_dvd_of_pos", "kind": "theorem", "module": "Mathlib.Data.Int.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.lt_div_iff_of_dvd_of_neg", "kind": "theorem", "module": "Mathlib.Data.Int.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.div_le_div_iff_of_dvd_of_pos_of_pos", "kind": "theorem", "module": "Mathlib.Data.Int.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.div_le_div_iff_of_dvd_of_pos_of_neg", "kind": "theorem", "module": "Mathlib.Data.Int.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.div_le_div_iff_of_dvd_of_neg_of_pos", "kind": "theorem", "module": "Mathlib.Data.Int.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.div_le_div_iff_of_dvd_of_neg_of_neg", "kind": "theorem", "module": "Mathlib.Data.Int.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.div_lt_div_iff_of_dvd_of_pos", "kind": "theorem", "module": "Mathlib.Data.Int.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.div_lt_div_iff_of_dvd_of_pos_of_neg", "kind": "theorem", "module": "Mathlib.Data.Int.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.div_lt_div_iff_of_dvd_of_neg_of_pos", "kind": "theorem", "module": "Mathlib.Data.Int.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.div_lt_div_iff_of_dvd_of_neg_of_neg", "kind": "theorem", "module": "Mathlib.Data.Int.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.emod_two_eq_zero_or_one", "kind": "theorem", "module": "Mathlib.Data.Int.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.ext_ediv_emod", "kind": "theorem", "module": "Mathlib.Data.Int.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.ext_ediv_emod_iff", "kind": "theorem", "module": "Mathlib.Data.Int.Init", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Int.dvd_mul_of_div_dvd", "kind": "theorem", "module": "Mathlib.Data.Int.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.div_dvd_iff_dvd_mul", "kind": "theorem", "module": "Mathlib.Data.Int.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.mul_dvd_of_dvd_div", "kind": "theorem", "module": "Mathlib.Data.Int.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.dvd_div_of_mul_dvd", "kind": "theorem", "module": "Mathlib.Data.Int.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.dvd_div_iff_mul_dvd", "kind": "theorem", "module": "Mathlib.Data.Int.Init", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Int.exists_lt_and_lt_iff_not_dvd", "kind": "theorem", "module": "Mathlib.Data.Int.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.eq_mul_div_of_mul_eq_mul_of_dvd_left", "kind": "theorem", "module": "Mathlib.Data.Int.Init", "is_tactic_proof": true, "tactics": ["obtain", "rw", "rwa"], "tactic_count": 3}
{"name": "Int.ofNat_add_negSucc_of_ge", "kind": "theorem", "module": "Mathlib.Data.Int.Init", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.le_iff_pos_of_dvd", "kind": "theorem", "module": "Mathlib.Data.Int.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.le_add_iff_lt_of_dvd_sub", "kind": "theorem", "module": "Mathlib.Data.Int.Init", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.sign_add_eq_of_sign_eq", "kind": "theorem", "module": "Mathlib.Data.Int.Init", "is_tactic_proof": true, "tactics": ["lia"], "tactic_count": 1}
{"name": "Int.toNat_pred_coe_of_pos", "kind": "theorem", "module": "Mathlib.Data.Int.Init", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Int.toNat_lt_of_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Int.Init", "is_tactic_proof": true, "tactics": ["lia"], "tactic_count": 1}
{"name": "Int.natMod", "kind": "definition", "module": "Mathlib.Data.Int.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.natMod_lt", "kind": "theorem", "module": "Mathlib.Data.Int.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.pow_eq", "kind": "theorem", "module": "Mathlib.Data.Int.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.gcd_ofNat_negSucc", "kind": "theorem", "module": "Mathlib.Data.Int.Init", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Int.gcd_negSucc_ofNat", "kind": "theorem", "module": "Mathlib.Data.Int.Init", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Int.gcd_negSucc_negSucc", "kind": "theorem", "module": "Mathlib.Data.Int.Init", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Int.instLocallyFiniteOrder", "kind": "instance", "module": "Mathlib.Data.Int.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.Icc_eq_finset_map", "kind": "theorem", "module": "Mathlib.Data.Int.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.Ico_eq_finset_map", "kind": "theorem", "module": "Mathlib.Data.Int.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.Ioc_eq_finset_map", "kind": "theorem", "module": "Mathlib.Data.Int.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.Ioo_eq_finset_map", "kind": "theorem", "module": "Mathlib.Data.Int.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.uIcc_eq_finset_map", "kind": "theorem", "module": "Mathlib.Data.Int.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.card_Icc", "kind": "theorem", "module": "Mathlib.Data.Int.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.card_Ico", "kind": "theorem", "module": "Mathlib.Data.Int.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.card_Ioc", "kind": "theorem", "module": "Mathlib.Data.Int.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.card_Ioo", "kind": "theorem", "module": "Mathlib.Data.Int.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.card_uIcc", "kind": "theorem", "module": "Mathlib.Data.Int.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.card_Icc_of_le", "kind": "theorem", "module": "Mathlib.Data.Int.Interval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.card_Ico_of_le", "kind": "theorem", "module": "Mathlib.Data.Int.Interval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.card_Ioc_of_le", "kind": "theorem", "module": "Mathlib.Data.Int.Interval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.card_Ioo_of_lt", "kind": "theorem", "module": "Mathlib.Data.Int.Interval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.Icc_eq_pair", "kind": "theorem", "module": "Mathlib.Data.Int.Interval", "is_tactic_proof": true, "tactics": ["ext", "simp", "omega"], "tactic_count": 3}
{"name": "Int.card_fintype_Icc_of_le", "kind": "theorem", "module": "Mathlib.Data.Int.Interval", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Int.card_fintype_Ico_of_le", "kind": "theorem", "module": "Mathlib.Data.Int.Interval", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Int.card_fintype_Ioc_of_le", "kind": "theorem", "module": "Mathlib.Data.Int.Interval", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Int.card_fintype_Ioo_of_lt", "kind": "theorem", "module": "Mathlib.Data.Int.Interval", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Int.image_Ico_emod", "kind": "theorem", "module": "Mathlib.Data.Int.Interval", "is_tactic_proof": true, "tactics": ["obtain", "simp", "ext", "simp", "constructor", "rintro", "exact", "rintro", "have", "obtain", "refine", "calc", "n", "calc", "i", "rw", "refine", "exact", "rw", "refine", "simp", "exact", "rw"], "tactic_count": 23}
{"name": "Finset.Icc_succ_succ", "kind": "theorem", "module": "Mathlib.Data.Int.Interval", "is_tactic_proof": true, "tactics": ["ext", "simp", "omega"], "tactic_count": 3}
{"name": "Finset.Ico_succ_succ", "kind": "theorem", "module": "Mathlib.Data.Int.Interval", "is_tactic_proof": true, "tactics": ["ext", "simp", "omega"], "tactic_count": 3}
{"name": "Finset.Ioc_succ_succ", "kind": "theorem", "module": "Mathlib.Data.Int.Interval", "is_tactic_proof": true, "tactics": ["ext", "simp", "lia"], "tactic_count": 3}
{"name": "Finset.Ioo_succ_succ", "kind": "theorem", "module": "Mathlib.Data.Int.Interval", "is_tactic_proof": true, "tactics": ["ext", "simp", "lia"], "tactic_count": 3}
{"name": "Int.leastOfBdd", "kind": "definition", "module": "Mathlib.Data.Int.LeastGreatest", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.isLeast_coe_leastOfBdd", "kind": "theorem", "module": "Mathlib.Data.Int.LeastGreatest", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.exists_least_of_bdd", "kind": "theorem", "module": "Mathlib.Data.Int.LeastGreatest", "is_tactic_proof": true, "tactics": ["classical", "let", "let", "exact"], "tactic_count": 4}
{"name": "Int.coe_leastOfBdd_eq", "kind": "theorem", "module": "Mathlib.Data.Int.LeastGreatest", "is_tactic_proof": false, "tactics": ["rcases", "rcases", "exact"], "tactic_count": 3}
{"name": "Int.greatestOfBdd", "kind": "definition", "module": "Mathlib.Data.Int.LeastGreatest", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.isGreatest_coe_greatestOfBdd", "kind": "theorem", "module": "Mathlib.Data.Int.LeastGreatest", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.exists_greatest_of_bdd", "kind": "theorem", "module": "Mathlib.Data.Int.LeastGreatest", "is_tactic_proof": true, "tactics": ["classical", "let", "let", "exact"], "tactic_count": 4}
{"name": "Int.coe_greatestOfBdd_eq", "kind": "theorem", "module": "Mathlib.Data.Int.LeastGreatest", "is_tactic_proof": false, "tactics": ["rcases", "rcases", "exact"], "tactic_count": 3}
{"name": "Int.le_natCast_sub", "kind": "theorem", "module": "Mathlib.Data.Int.Lemmas", "is_tactic_proof": true, "tactics": ["lia"], "tactic_count": 1}
{"name": "Int.succ_natCast_pos", "kind": "theorem", "module": "Mathlib.Data.Int.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.natAbs_eq_iff_sq_eq", "kind": "theorem", "module": "Mathlib.Data.Int.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Int.natAbs_lt_iff_sq_lt", "kind": "theorem", "module": "Mathlib.Data.Int.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Int.natAbs_le_iff_sq_le", "kind": "theorem", "module": "Mathlib.Data.Int.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Int.natAbs_inj_of_nonneg_of_nonneg", "kind": "theorem", "module": "Mathlib.Data.Int.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.natAbs_inj_of_nonpos_of_nonpos", "kind": "theorem", "module": "Mathlib.Data.Int.Lemmas", "is_tactic_proof": true, "tactics": ["simpa", "natAbs_inj_of_nonneg_of_nonneg"], "tactic_count": 2}
{"name": "Int.natAbs_inj_of_nonneg_of_nonpos", "kind": "theorem", "module": "Mathlib.Data.Int.Lemmas", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Int.natAbs_inj_of_nonpos_of_nonneg", "kind": "theorem", "module": "Mathlib.Data.Int.Lemmas", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Int.natAbs_coe_sub_coe_le_of_le", "kind": "theorem", "module": "Mathlib.Data.Int.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Int.natAbs_coe_sub_coe_lt_of_lt", "kind": "theorem", "module": "Mathlib.Data.Int.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Int.strictMonoOn_natAbs", "kind": "theorem", "module": "Mathlib.Data.Int.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.strictAntiOn_natAbs", "kind": "theorem", "module": "Mathlib.Data.Int.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.injOn_natAbs_Ici", "kind": "theorem", "module": "Mathlib.Data.Int.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.injOn_natAbs_Iic", "kind": "theorem", "module": "Mathlib.Data.Int.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.div2_bit", "kind": "theorem", "module": "Mathlib.Data.Int.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "cases", "decide", "change", "rw", "decide"], "tactic_count": 6}
{"name": "Int.ediv_emod_unique''", "kind": "theorem", "module": "Mathlib.Data.Int.Lemmas", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "intro", "constructor", "rw", "simp", "rw"], "tactic_count": 8}
{"name": "Int.log", "kind": "definition", "module": "Mathlib.Data.Int.Log", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.log_of_one_le_right", "kind": "theorem", "module": "Mathlib.Data.Int.Log", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.log_of_right_le_one", "kind": "theorem", "module": "Mathlib.Data.Int.Log", "is_tactic_proof": true, "tactics": ["obtain", "rw", "neg_zero]", "exact"], "tactic_count": 4}
{"name": "Int.log_natCast", "kind": "theorem", "module": "Mathlib.Data.Int.Log", "is_tactic_proof": true, "tactics": ["cases", "simp", "rw", "simp"], "tactic_count": 4}
{"name": "Int.log_ofNat", "kind": "theorem", "module": "Mathlib.Data.Int.Log", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.log_of_left_le_one", "kind": "theorem", "module": "Mathlib.Data.Int.Log", "is_tactic_proof": true, "tactics": ["rcases", "rw", "rw"], "tactic_count": 3}
{"name": "Int.log_of_right_le_zero", "kind": "theorem", "module": "Mathlib.Data.Int.Log", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.zpow_log_le_self", "kind": "theorem", "module": "Mathlib.Data.Int.Log", "is_tactic_proof": true, "tactics": ["rcases", "rw", "rw", "exact", "rw", "exact"], "tactic_count": 6}
{"name": "Int.lt_zpow_succ_log_self", "kind": "theorem", "module": "Mathlib.Data.Int.Log", "is_tactic_proof": true, "tactics": ["rcases", "rw", "exact", "rcases", "rw", "rw", "apply", "exact", "rw", "have", "have", "rw", "lt_inv_comm₀", "refine", "exact"], "tactic_count": 15}
{"name": "Int.log_zero_right", "kind": "theorem", "module": "Mathlib.Data.Int.Log", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.log_one_right", "kind": "theorem", "module": "Mathlib.Data.Int.Log", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.log_zero_left", "kind": "theorem", "module": "Mathlib.Data.Int.Log", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Int.log_one_left", "kind": "theorem", "module": "Mathlib.Data.Int.Log", "is_tactic_proof": true, "tactics": ["by_cases", "simp_all", "simp"], "tactic_count": 3}
{"name": "Int.log_zpow", "kind": "theorem", "module": "Mathlib.Data.Int.Log", "is_tactic_proof": true, "tactics": ["obtain", "rw", "rw", "zpow_neg,"], "tactic_count": 4}
{"name": "Int.log_mono_right", "kind": "theorem", "module": "Mathlib.Data.Int.Log", "is_tactic_proof": true, "tactics": ["rcases", "have", "rw", "exact", "rw", "exact", "obtain", "rfl", "rw", "exact"], "tactic_count": 10}
{"name": "Int.zpowLogGi", "kind": "definition", "module": "Mathlib.Data.Int.Log", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.lt_zpow_iff_log_lt", "kind": "theorem", "module": "Mathlib.Data.Int.Log", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.zpow_le_iff_le_log", "kind": "theorem", "module": "Mathlib.Data.Int.Log", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.clog", "kind": "definition", "module": "Mathlib.Data.Int.Log", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.clog_of_one_le_right", "kind": "theorem", "module": "Mathlib.Data.Int.Log", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.clog_of_right_le_one", "kind": "theorem", "module": "Mathlib.Data.Int.Log", "is_tactic_proof": true, "tactics": ["obtain", "rw", "neg_zero]", "exact"], "tactic_count": 4}
{"name": "Int.clog_of_right_le_zero", "kind": "theorem", "module": "Mathlib.Data.Int.Log", "is_tactic_proof": true, "tactics": ["rw", "rcases", "exact", "refine", "exact"], "tactic_count": 5}
{"name": "Int.clog_inv", "kind": "theorem", "module": "Mathlib.Data.Int.Log", "is_tactic_proof": true, "tactics": ["rcases", "obtain", "rw", "rw", "rw"], "tactic_count": 5}
{"name": "Int.log_inv", "kind": "theorem", "module": "Mathlib.Data.Int.Log", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.neg_log_inv_eq_clog", "kind": "theorem", "module": "Mathlib.Data.Int.Log", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.neg_clog_inv_eq_log", "kind": "theorem", "module": "Mathlib.Data.Int.Log", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.clog_natCast", "kind": "theorem", "module": "Mathlib.Data.Int.Log", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rw"], "tactic_count": 3}
{"name": "Int.clog_ofNat", "kind": "theorem", "module": "Mathlib.Data.Int.Log", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.clog_of_left_le_one", "kind": "theorem", "module": "Mathlib.Data.Int.Log", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.self_le_zpow_clog", "kind": "theorem", "module": "Mathlib.Data.Int.Log", "is_tactic_proof": true, "tactics": ["rcases", "rw", "exact", "rw", "exact", "exact"], "tactic_count": 6}
{"name": "Int.zpow_pred_clog_lt_self", "kind": "theorem", "module": "Mathlib.Data.Int.Log", "is_tactic_proof": true, "tactics": ["rw", "exact", "exact"], "tactic_count": 3}
{"name": "Int.clog_zero_right", "kind": "theorem", "module": "Mathlib.Data.Int.Log", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.clog_one_right", "kind": "theorem", "module": "Mathlib.Data.Int.Log", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.clog_zero_left", "kind": "theorem", "module": "Mathlib.Data.Int.Log", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "simp"], "tactic_count": 3}
{"name": "Int.clog_one_left", "kind": "theorem", "module": "Mathlib.Data.Int.Log", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Int.clog_zpow", "kind": "theorem", "module": "Mathlib.Data.Int.Log", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.clog_mono_right", "kind": "theorem", "module": "Mathlib.Data.Int.Log", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "Int.clogZPowGi", "kind": "definition", "module": "Mathlib.Data.Int.Log", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.zpow_lt_iff_lt_clog", "kind": "theorem", "module": "Mathlib.Data.Int.Log", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.le_zpow_iff_clog_le", "kind": "theorem", "module": "Mathlib.Data.Int.Log", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.ModEq", "kind": "definition", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "term_≡_[ZMOD_]", "kind": "definition", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Data_Int_ModEq___macroRules_term_≡_[ZMOD_]_1", "kind": "definition", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Data_Int_ModEq___unexpand_Int_ModEq_1", "kind": "definition", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGroup.modEq_iff_intModEq", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "AddCommGroup.intCast_modEq_intCast", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGroup.intCast_modEq_intCast'", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Int.instDecidableModEq", "kind": "instance", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.ModEq.refl", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.ModEq.rfl", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.ModEq.instRefl", "kind": "instance", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.ModEq.symm", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.ModEq.trans", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.ModEq.instIsTrans", "kind": "instance", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.ModEq.eq", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.modEq_comm", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.natCast_modEq_iff", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "Int.modEq_zero_iff_dvd", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Dvd.dvd.modEq_zero_int", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dvd.dvd.zero_modEq_int", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.modEq_iff_dvd", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Int.modEq_iff_add_fac", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Int.mod_modEq", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.neg_modEq_neg", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Int.modEq_neg", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Int.ModEq.of_dvd", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.ModEq.mul_left'", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": true, "tactics": ["obtain", "rw", "simp", "simp", "simp"], "tactic_count": 5}
{"name": "Int.ModEq.mul_right'", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.ModEq.add", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.ModEq.add_left", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.ModEq.add_right", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.ModEq.add_left_cancel", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.ModEq.add_left_cancel'", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.ModEq.add_right_cancel", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Int.ModEq.add_right_cancel'", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.ModEq.neg", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.ModEq.sub", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Int.ModEq.sub_left", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.ModEq.sub_right", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.ModEq.mul_left", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.ModEq.mul_right", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.ModEq.mul", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.ModEq.pow", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Int.ModEq.of_mul_left", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.ModEq.of_mul_right", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.ModEq.cancel_right_div_gcd", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": true, "tactics": ["letI", "rw", "refine", "rw", "exact", "rw"], "tactic_count": 6}
{"name": "Int.ModEq.cancel_left_div_gcd", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.ModEq.of_div", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "Int.ModEq.mul_left_cancel'", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Int.ModEq.mul_left_cancel_iff'", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.ModEq.mul_right_cancel'", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Int.ModEq.mul_right_cancel_iff'", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.ModEq.dvd_iff", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Int.modulus_modEq_zero", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Int.modEq_abs", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Int.modEq_natAbs", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Int.add_modEq_left_iff", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Int.add_modEq_right_iff", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.left_modEq_add_iff", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.right_modEq_add_iff", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.add_modulus_modEq_iff", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Int.modulus_add_modEq_iff", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.modEq_add_modulus_iff", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Int.modEq_modulus_add_iff", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Int.add_mul_modulus_modEq_iff", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Int.mul_modulus_add_modEq_iff", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.modEq_add_mul_modulus_iff", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Int.modEq_mul_modulus_add_iff", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.add_modulus_mul_modEq_iff", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Int.modulus_mul_add_modEq_iff", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.modEq_add_modulus_mul_iff", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Int.modEq_modulus_mul_add_iff", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.sub_modulus_modEq_iff", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.sub_modulus_mul_modEq_iff", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.modEq_sub_modulus_iff", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.modEq_sub_modulus_mul_iff", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.modEq_one", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.modEq_sub", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.modEq_zero_iff", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.add_modEq_left", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Int.add_modEq_right", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Int.modEq_and_modEq_iff_modEq_lcm", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Int.modEq_and_modEq_iff_modEq_mul", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "Int.gcd_a_modEq", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Int.modEq_add_fac", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Int.modEq_sub_fac", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Int.modEq_add_fac_self", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Int.mod_coprime", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.existsUnique_equiv", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.existsUnique_equiv_nat", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.mod_mul_right_mod", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.mod_mul_left_mod", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.ext_ediv_modEq", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.ext_ediv_modEq_iff", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.modEq_iff_eq_of_div_eq", "kind": "theorem", "module": "Mathlib.Data.Int.ModEq", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Int.natAbsHom", "kind": "definition", "module": "Mathlib.Data.Int.NatAbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.natAbs_natCast_sub_natCast_of_ge", "kind": "theorem", "module": "Mathlib.Data.Int.NatAbs", "is_tactic_proof": true, "tactics": ["lia"], "tactic_count": 1}
{"name": "Int.natAbs_natCast_sub_natCast_of_le", "kind": "theorem", "module": "Mathlib.Data.Int.NatAbs", "is_tactic_proof": true, "tactics": ["lia"], "tactic_count": 1}
{"name": "Int.not_prime_of_int_mul", "kind": "theorem", "module": "Mathlib.Data.Int.NatPrime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.succ_dvd_or_succ_dvd_of_succ_sum_dvd_mul", "kind": "theorem", "module": "Mathlib.Data.Int.NatPrime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.Prime.dvd_natAbs_of_coe_dvd_sq", "kind": "theorem", "module": "Mathlib.Data.Int.NatPrime", "is_tactic_proof": true, "tactics": ["apply", "rwa"], "tactic_count": 2}
{"name": "termℤ", "kind": "definition", "module": "Mathlib.Data.Int.Notation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Data_Int_Notation___macroRules_termℤ_1", "kind": "definition", "module": "Mathlib.Data.Int.Notation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Data_Int_Notation___unexpand_Int_1", "kind": "definition", "module": "Mathlib.Data.Int.Notation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.le.elim", "kind": "theorem", "module": "Mathlib.Data.Int.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.lt.elim", "kind": "theorem", "module": "Mathlib.Data.Int.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.instLinearOrder", "kind": "instance", "module": "Mathlib.Data.Int.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.eq_zero_or_eq_zero_of_mul_eq_zero", "kind": "theorem", "module": "Mathlib.Data.Int.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.nonneg_or_nonpos_of_mul_nonneg", "kind": "theorem", "module": "Mathlib.Data.Int.Order.Basic", "is_tactic_proof": true, "tactics": ["intro", "by_cases", "exact", "refine", "obtain", "all_goals", "refine", "obtain", "all_goals", "exact"], "tactic_count": 10}
{"name": "Int.mul_nonneg_of_nonneg_or_nonpos", "kind": "theorem", "module": "Mathlib.Data.Int.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.mul_nonneg_iff", "kind": "theorem", "module": "Mathlib.Data.Int.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.natAbs_eq_iff_mul_self_eq", "kind": "theorem", "module": "Mathlib.Data.Int.Order.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Int.natAbs_lt_iff_mul_self_lt", "kind": "theorem", "module": "Mathlib.Data.Int.Order.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Int.natAbs_le_iff_mul_self_le", "kind": "theorem", "module": "Mathlib.Data.Int.Order.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Int.abs_le_sqrt", "kind": "theorem", "module": "Mathlib.Data.Int.Order.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.abs_le_sqrt_iff_sq_le", "kind": "theorem", "module": "Mathlib.Data.Int.Order.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.isUnit_iff_abs_eq", "kind": "theorem", "module": "Mathlib.Data.Int.Order.Units", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.isUnit_sq", "kind": "theorem", "module": "Mathlib.Data.Int.Order.Units", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.units_sq", "kind": "theorem", "module": "Mathlib.Data.Int.Order.Units", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.units_mul_self", "kind": "theorem", "module": "Mathlib.Data.Int.Order.Units", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.units_inv_eq_self", "kind": "theorem", "module": "Mathlib.Data.Int.Order.Units", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.units_div_eq_mul", "kind": "theorem", "module": "Mathlib.Data.Int.Order.Units", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.units_coe_mul_self", "kind": "theorem", "module": "Mathlib.Data.Int.Order.Units", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.neg_one_pow_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Int.Order.Units", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Int.sq_eq_one_of_sq_lt_four", "kind": "theorem", "module": "Mathlib.Data.Int.Order.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.sq_eq_one_of_sq_le_three", "kind": "theorem", "module": "Mathlib.Data.Int.Order.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.units_pow_eq_pow_mod_two", "kind": "theorem", "module": "Mathlib.Data.Int.Order.Units", "is_tactic_proof": true, "tactics": ["conv", "lhs", "rw", "rw"], "tactic_count": 4}
{"name": "Int.range", "kind": "definition", "module": "Mathlib.Data.Int.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.mem_range_iff", "kind": "theorem", "module": "Mathlib.Data.Int.Range", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Int.decidableLELT", "kind": "instance", "module": "Mathlib.Data.Int.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.decidableLELE", "kind": "instance", "module": "Mathlib.Data.Int.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.decidableLTLT", "kind": "instance", "module": "Mathlib.Data.Int.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.decidableLTLE", "kind": "instance", "module": "Mathlib.Data.Int.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.sqrt", "kind": "definition", "module": "Mathlib.Data.Int.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.sqrt_eq", "kind": "theorem", "module": "Mathlib.Data.Int.Sqrt", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.exists_mul_self", "kind": "theorem", "module": "Mathlib.Data.Int.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.sqrt_nonneg", "kind": "theorem", "module": "Mathlib.Data.Int.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.sqrt_natCast", "kind": "theorem", "module": "Mathlib.Data.Int.Sqrt", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.sqrt_ofNat", "kind": "theorem", "module": "Mathlib.Data.Int.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.addSubmonoid_closure_range_pow", "kind": "theorem", "module": "Mathlib.Data.Int.Star", "is_tactic_proof": true, "tactics": ["refine", "have", "rw", "exact"], "tactic_count": 4}
{"name": "Int.addSubmonoid_closure_range_mul_self", "kind": "theorem", "module": "Mathlib.Data.Int.Star", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Int.instStarOrderedRing", "kind": "instance", "module": "Mathlib.Data.Int.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.instSuccOrder", "kind": "abbrev", "module": "Mathlib.Data.Int.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.instSuccAddOrder", "kind": "instance", "module": "Mathlib.Data.Int.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.instPredOrder", "kind": "abbrev", "module": "Mathlib.Data.Int.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.instPredSubOrder", "kind": "instance", "module": "Mathlib.Data.Int.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.succ_eq_succ", "kind": "theorem", "module": "Mathlib.Data.Int.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.pred_eq_pred", "kind": "theorem", "module": "Mathlib.Data.Int.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.instIsSuccArchimedean", "kind": "instance", "module": "Mathlib.Data.Int.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.instIsPredArchimedean", "kind": "instance", "module": "Mathlib.Data.Int.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.natCast_covBy", "kind": "theorem", "module": "Mathlib.Data.Int.SuccPred", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "WithZeroMulInt.toNNReal", "kind": "definition", "module": "Mathlib.Data.Int.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZeroMulInt.toNNReal_pos_apply", "kind": "theorem", "module": "Mathlib.Data.Int.WithZero", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WithZeroMulInt.toNNReal_neg_apply", "kind": "theorem", "module": "Mathlib.Data.Int.WithZero", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WithZeroMulInt.toNNReal_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Int.WithZero", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WithZeroMulInt.toNNReal_pos", "kind": "theorem", "module": "Mathlib.Data.Int.WithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZeroMulInt.toNNReal_strictMono", "kind": "theorem", "module": "Mathlib.Data.Int.WithZero", "is_tactic_proof": true, "tactics": ["intro", "simp", "split_ifs", "simp", "exact", "simp", "rw", "exact"], "tactic_count": 8}
{"name": "WithZeroMulInt.toNNReal_eq_one_iff", "kind": "theorem", "module": "Mathlib.Data.Int.WithZero", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "refine", "rw", "rw"], "tactic_count": 5}
{"name": "WithZeroMulInt.toNNReal_lt_one_iff", "kind": "theorem", "module": "Mathlib.Data.Int.WithZero", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "WithZeroMulInt.toNNReal_le_one_iff", "kind": "theorem", "module": "Mathlib.Data.Int.WithZero", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.toAList", "kind": "definition", "module": "Mathlib.Data.List.AList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AList.ext", "kind": "theorem", "module": "Mathlib.Data.List.AList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AList.instDecidableEq", "kind": "instance", "module": "Mathlib.Data.List.AList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AList.keys", "kind": "definition", "module": "Mathlib.Data.List.AList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AList.keys_nodup", "kind": "theorem", "module": "Mathlib.Data.List.AList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AList.keys_mk", "kind": "theorem", "module": "Mathlib.Data.List.AList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AList.instMembership", "kind": "instance", "module": "Mathlib.Data.List.AList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AList.mem_keys", "kind": "theorem", "module": "Mathlib.Data.List.AList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AList.mem_of_perm", "kind": "theorem", "module": "Mathlib.Data.List.AList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AList.mem_mk", "kind": "theorem", "module": "Mathlib.Data.List.AList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AList.instEmptyCollection", "kind": "instance", "module": "Mathlib.Data.List.AList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AList.instInhabited", "kind": "instance", "module": "Mathlib.Data.List.AList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AList.notMem_empty", "kind": "theorem", "module": "Mathlib.Data.List.AList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AList.empty_entries", "kind": "theorem", "module": "Mathlib.Data.List.AList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AList.keys_empty", "kind": "theorem", "module": "Mathlib.Data.List.AList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AList.singleton", "kind": "definition", "module": "Mathlib.Data.List.AList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AList.singleton_entries", "kind": "theorem", "module": "Mathlib.Data.List.AList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AList.keys_singleton", "kind": "theorem", "module": "Mathlib.Data.List.AList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AList.lookup", "kind": "definition", "module": "Mathlib.Data.List.AList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AList.lookup_empty", "kind": "theorem", "module": "Mathlib.Data.List.AList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AList.lookup_isSome", "kind": "theorem", "module": "Mathlib.Data.List.AList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AList.lookup_eq_none", "kind": "theorem", "module": "Mathlib.Data.List.AList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AList.mem_lookup_iff", "kind": "theorem", "module": "Mathlib.Data.List.AList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AList.perm_lookup", "kind": "theorem", "module": "Mathlib.Data.List.AList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AList.instDecidableMem", "kind": "instance", "module": "Mathlib.Data.List.AList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AList.keys_subset_keys_of_entries_subset_entries", "kind": "theorem", "module": "Mathlib.Data.List.AList", "is_tactic_proof": true, "tactics": ["intro", "letI", "have", "rw", "rw", "exact"], "tactic_count": 6}
{"name": "AList.replace", "kind": "definition", "module": "Mathlib.Data.List.AList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AList.keys_replace", "kind": "theorem", "module": "Mathlib.Data.List.AList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AList.mem_replace", "kind": "theorem", "module": "Mathlib.Data.List.AList", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AList.perm_replace", "kind": "theorem", "module": "Mathlib.Data.List.AList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AList.foldl", "kind": "definition", "module": "Mathlib.Data.List.AList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AList.erase", "kind": "definition", "module": "Mathlib.Data.List.AList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AList.keys_erase", "kind": "theorem", "module": "Mathlib.Data.List.AList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AList.mem_erase", "kind": "theorem", "module": "Mathlib.Data.List.AList", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AList.perm_erase", "kind": "theorem", "module": "Mathlib.Data.List.AList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AList.lookup_erase", "kind": "theorem", "module": "Mathlib.Data.List.AList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AList.lookup_erase_ne", "kind": "theorem", "module": "Mathlib.Data.List.AList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AList.erase_erase", "kind": "theorem", "module": "Mathlib.Data.List.AList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AList.insert", "kind": "definition", "module": "Mathlib.Data.List.AList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AList.entries_insert", "kind": "theorem", "module": "Mathlib.Data.List.AList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AList.entries_insert_of_notMem", "kind": "theorem", "module": "Mathlib.Data.List.AList", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AList.insert_of_notMem", "kind": "theorem", "module": "Mathlib.Data.List.AList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AList.insert_empty", "kind": "theorem", "module": "Mathlib.Data.List.AList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AList.mem_insert", "kind": "theorem", "module": "Mathlib.Data.List.AList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AList.keys_insert", "kind": "theorem", "module": "Mathlib.Data.List.AList", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AList.perm_insert", "kind": "theorem", "module": "Mathlib.Data.List.AList", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AList.lookup_insert", "kind": "theorem", "module": "Mathlib.Data.List.AList", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AList.lookup_insert_ne", "kind": "theorem", "module": "Mathlib.Data.List.AList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AList.lookup_insert_eq_none", "kind": "theorem", "module": "Mathlib.Data.List.AList", "is_tactic_proof": true, "tactics": ["by_cases", "subst", "simp_all"], "tactic_count": 3}
{"name": "AList.lookup_to_alist", "kind": "theorem", "module": "Mathlib.Data.List.AList", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AList.insert_insert", "kind": "theorem", "module": "Mathlib.Data.List.AList", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "AList.insert_insert_of_ne", "kind": "theorem", "module": "Mathlib.Data.List.AList", "is_tactic_proof": true, "tactics": ["simp", "rw"], "tactic_count": 2}
{"name": "AList.insert_singleton_eq", "kind": "theorem", "module": "Mathlib.Data.List.AList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AList.entries_toAList", "kind": "theorem", "module": "Mathlib.Data.List.AList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AList.toAList_cons", "kind": "theorem", "module": "Mathlib.Data.List.AList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AList.mk_cons_eq_insert", "kind": "theorem", "module": "Mathlib.Data.List.AList", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "AList.insertRec", "kind": "definition", "module": "Mathlib.Data.List.AList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AList._example", "kind": "example", "module": "Mathlib.Data.List.AList", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "AList.insertRec_empty", "kind": "theorem", "module": "Mathlib.Data.List.AList", "is_tactic_proof": true, "tactics": ["change", "rw"], "tactic_count": 2}
{"name": "AList.insertRec_insert", "kind": "theorem", "module": "Mathlib.Data.List.AList", "is_tactic_proof": true, "tactics": ["obtain", "suffices", "cases", "apply", "convert", "rw", "apply"], "tactic_count": 7}
{"name": "AList.insertRec_insert_mk", "kind": "theorem", "module": "Mathlib.Data.List.AList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AList.extract", "kind": "definition", "module": "Mathlib.Data.List.AList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AList.extract_eq_lookup_erase", "kind": "theorem", "module": "Mathlib.Data.List.AList", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AList.union", "kind": "definition", "module": "Mathlib.Data.List.AList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AList.instUnion", "kind": "instance", "module": "Mathlib.Data.List.AList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AList.union_entries", "kind": "theorem", "module": "Mathlib.Data.List.AList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AList.empty_union", "kind": "theorem", "module": "Mathlib.Data.List.AList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AList.union_empty", "kind": "theorem", "module": "Mathlib.Data.List.AList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AList.mem_union", "kind": "theorem", "module": "Mathlib.Data.List.AList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AList.perm_union", "kind": "theorem", "module": "Mathlib.Data.List.AList", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AList.union_erase", "kind": "theorem", "module": "Mathlib.Data.List.AList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AList.lookup_union_left", "kind": "theorem", "module": "Mathlib.Data.List.AList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AList.lookup_union_right", "kind": "theorem", "module": "Mathlib.Data.List.AList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AList.mem_lookup_union", "kind": "theorem", "module": "Mathlib.Data.List.AList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AList.lookup_union_eq_some", "kind": "theorem", "module": "Mathlib.Data.List.AList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AList.mem_lookup_union_middle", "kind": "theorem", "module": "Mathlib.Data.List.AList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AList.insert_union", "kind": "theorem", "module": "Mathlib.Data.List.AList", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "AList.union_assoc", "kind": "theorem", "module": "Mathlib.Data.List.AList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AList.Disjoint", "kind": "definition", "module": "Mathlib.Data.List.AList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AList.union_comm_of_disjoint", "kind": "theorem", "module": "Mathlib.Data.List.AList", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.uniqueOfIsEmpty", "kind": "instance", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.instLawfulIdentityAppendNil_mathlib", "kind": "instance", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.instAssociativeAppend_mathlib", "kind": "instance", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.cons_injective", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.singleton_injective", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.set_of_mem_cons", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Decidable.List.eq_or_ne_mem_of_mem", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "exact"], "tactic_count": 3}
{"name": "List.mem_pair", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.mem_map_of_injective", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Involutive.exists_mem_and_apply_eq_iff", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.mem_map_of_involutive", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.length_pos_iff_ne_nil", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.exists_of_length_succ", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.length_injective_iff", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["constructor", "intro", "intro", "induction", "rfl", "cases", "cases", "congr", "subsingleton", "apply"], "tactic_count": 10}
{"name": "List.length_injective", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.length_eq_two", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.length_eq_three", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.length_eq_four", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.instSingletonList", "kind": "instance", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.instInsertOfDecidableEq_mathlib", "kind": "instance", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.instLawfulSingleton_mathlib", "kind": "instance", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.singleton_eq", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.insert_neg", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.insert_pos", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.doubleton_eq", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["rw", "rwa"], "tactic_count": 2}
{"name": "List.forall_mem_of_forall_mem_cons", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.exists_mem_cons_of", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.exists_mem_cons_of_exists", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.or_exists_of_exists_mem_cons", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "List.exists_mem_cons_iff", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "List.cons_subset_of_subset_of_mem", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.append_subset_of_subset_of_subset", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.map_subset_iff", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["refine", "rcases", "cases"], "tactic_count": 3}
{"name": "List.append_eq_has_append", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.append_right_injective", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.append_left_injective", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.eq_replicate_length", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.replicate_add", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.replicate_subset_singleton", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.subset_singleton_iff", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.replicate_right_injective", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.replicate_right_inj", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.replicate_right_inj'", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.replicate_left_injective", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.replicate_left_inj", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.head?_flatten_replicate", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["obtain", "induction"], "tactic_count": 2}
{"name": "List.getLast?_flatten_replicate", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["rw", "head?_flatten_replicate"], "tactic_count": 2}
{"name": "List.mem_pure", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.bind_eq_flatMap", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.reverse_cons'", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.reverse_concat'", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.reverse_singleton", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.reverse_involutive", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.reverse_injective", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.reverse_surjective", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.reverse_bijective", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.concat_eq_reverse_cons", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "List.map_reverseAux", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.reverse_perm'", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.perm_reverse", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.getLast_append_singleton", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.getLast_append_of_right_ne_nil", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.getLast_concat'", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.getLast_singleton'", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.dropLast_append_getLast", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.getLast_congr", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "List.getLast_replicate_succ", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "List.mem_getLast?_eq_getLast", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.getLast?_eq_getLast_of_ne_nil", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.mem_getLast?_cons", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.dropLast_append_getLast?", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.getLastI_eq_getLast?_getD", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.getLastI_eq_getLast?", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.getLast?_append_cons", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.getLast?_append_of_ne_nil", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.mem_getLast?_append_of_mem_getLast?", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "List.mem_dropLast_of_mem_of_ne_getLast", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "List.mem_dropLast_of_mem_of_ne_getLastD", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.mem_dropLast_of_mem_of_ne_getLast?", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.head!_nil", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.head_cons_tail", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.head_eq_getElem_zero", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.head!_eq_head?_getD", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "List.head!_eq_head?", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.surjective_head!", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.surjective_head?", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.surjective_tail", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.eq_cons_of_mem_head?", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.head!_cons", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.head!_append", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["induction", "contradiction", "rfl"], "tactic_count": 3}
{"name": "List.mem_head?_append_of_mem_head?", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "List.head?_append_of_ne_nil", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.tail_append_singleton_of_ne_nil", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "List.cons_head?_tail", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.head!_mem_head?", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.cons_head!_tail", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.head!_mem_self", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "List.get_eq_getElem?", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.exists_mem_iff_getElem", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "List.exists_mem_iff_get", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.forall_mem_iff_getElem", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.forall_mem_iff_get", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.get_surjective_iff", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.getElem_fin_surjective_iff", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.getElem?_surjective_iff", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["refine", "cases", "none", "some"], "tactic_count": 4}
{"name": "List.Sublist.cons_cons", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.cons_sublist_cons'", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "List.sublist_cons_of_sublist", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sublist_singleton", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["constructor"], "tactic_count": 1}
{"name": "List.Sublist.antisymm", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Sublist.of_cons_of_ne", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.idxOf_cons_eq", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.idxOf_cons_ne", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.idxOf_eq_length_iff", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "List.idxOf_of_notMem", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.idxOf_eq_zero_iff_eq_nil_or_head_eq", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["cases", "simp", "grind"], "tactic_count": 3}
{"name": "List.idxOf_eq_zero_iff_head_eq", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.idxOf_append_of_mem", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "List.idxOf_append_of_notMem", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "List.IsPrefix.idxOf_le", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["obtain", "grind"], "tactic_count": 2}
{"name": "List.IsPrefix.idxOf_eq_of_mem", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "List.IsPrefix.mem_iff_idxOf_lt_length", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["refine", "exact", "have", "grind"], "tactic_count": 4}
{"name": "List.IsSuffix.idxOf_le", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["obtain", "grind"], "tactic_count": 2}
{"name": "List.IsSuffix.idxOf_add_length_le", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["obtain", "grind"], "tactic_count": 2}
{"name": "List.mem_take_iff_idxOf_lt", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["rw", "grind"], "tactic_count": 2}
{"name": "List.mem_dropLast_iff_idxOf_lt", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.succ_idxOf_lt_length_of_mem_dropLast", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["have", "grind"], "tactic_count": 2}
{"name": "List.idxOf_getLast", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.getElem?_length", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.getElem_map_rev", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.get_length_sub_one", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.take_one_drop_eq_of_lt_length", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "List.ext_getElem?'", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["apply", "grind"], "tactic_count": 2}
{"name": "List.ext_get_iff", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "exact", "intro", "exact"], "tactic_count": 5}
{"name": "List.ext_getElem?_iff'", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.ext_getElem!", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.idxOf_get", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.getElem?_idxOf", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.idxOf_inj", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "simp"], "tactic_count": 3}
{"name": "List.get_reverse'", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.eq_cons_of_length_one", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["refine"], "tactic_count": 1}
{"name": "List.getElem_set_of_ne", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.flatMap_pure_eq_map", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.flatMap_congr", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.infix_flatMap_of_mem", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.map_eq_map", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.comp_map", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.map_comp_map", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Function.LeftInverse.list_map", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.RightInverse.list_map", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Involutive.list_map", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.map_leftInverse_iff", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.map_rightInverse_iff", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.map_involutive_iff", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.list_map", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.map_injective_iff", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["refine", "suffices", "apply", "simp"], "tactic_count": 4}
{"name": "Function.Surjective.list_map", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.map_surjective_iff", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["refine", "let", "exact"], "tactic_count": 3}
{"name": "Function.Bijective.list_map", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.map_bijective_iff", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "List.eq_of_mem_map_const", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.eq_nil_or_concat'", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "List.foldl_ext", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "unfold", "rw"], "tactic_count": 5}
{"name": "List.foldr_ext", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": ["induction", "nil", "cons", "simp", "simp"], "tactic_count": 5}
{"name": "List.foldl_concat", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.foldr_concat", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.foldl_fixed'", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.foldr_fixed'", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.foldl_fixed", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.foldr_fixed", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.reverse_foldl", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.foldl_hom₂", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.foldr_hom₂", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["revert", "induction"], "tactic_count": 2}
{"name": "List.injective_foldl_comp", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "apply", "apply", "apply"], "tactic_count": 6}
{"name": "List.append_cons_inj_of_notMem", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["constructor", "simp", "rintro", "rintro", "rfl"], "tactic_count": 5}
{"name": "List.foldl1_eq_foldr1", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.foldl_eq_of_comm_of_assoc", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.foldl_eq_foldr", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.foldl_eq_of_comm'", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.foldl_eq_foldr'", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.foldr_eq_of_comm'", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.List.Basic.0.List.term_⋆_", "kind": "definition", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.List.Basic.0.List._aux_Mathlib_Data_List_Basic___macroRules__private_Mathlib_Data_List_Basic_0_List_term_⋆__1", "kind": "definition", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.List.Basic.0.List.term_<*>_", "kind": "definition", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.List.Basic.0.List._aux_Mathlib_Data_List_Basic___macroRules__private_Mathlib_Data_List_Basic_0_List_term_<*>__1", "kind": "definition", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.List.Basic.0.List._aux_Mathlib_Data_List_Basic___unexpand_List_foldl_1", "kind": "definition", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.foldl_op_eq_op_foldr_assoc", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.foldl_assoc_comm_cons", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.foldrM_eq_foldr", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.foldlM_eq_foldl", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": ["suffices", "simp", "induction", "nil", "cons"], "tactic_count": 5}
{"name": "List.length_eq_length_filter_add", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "List.filterMap_eq_flatMap_toList", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": ["induction", "nil", "cons", "simp", "rcases"], "tactic_count": 5}
{"name": "List.filterMap_congr", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.filterMap_eq_map_iff_forall_eq_some", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.filter_singleton", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.filter_eq_foldr", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.filter_subset'", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.of_mem_filter", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.mem_of_mem_filter", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.mem_filter_of_mem", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.monotone_filter_right", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.map_filter", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.filter_attach'", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["classical", "refine", "simp"], "tactic_count": 3}
{"name": "List.filter_attach", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.filter_comm", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.filter_true", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.filter_false", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.length_eraseP_add_one", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "List.length_erase_add_one", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.map_erase", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "List.map_foldl_erase", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.erase_getElem", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "List.length_eraseIdx_add_one", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "List.map_diff", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.choose_spec", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.choose_mem", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.choose_property", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.forall_cons", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.forall_append", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.forall_iff_forall_mem", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Forall.imp", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.forall_map_iff", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.instDecidablePredForall", "kind": "instance", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.get_attach", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.disjoint_pmap", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["simp", "rintro", "apply", "rwa"], "tactic_count": 4}
{"name": "List.disjoint_map", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "List.Disjoint.of_map", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Disjoint.map_iff", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Perm.disjoint_left", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "List.Perm.disjoint_right", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "List.disjoint_reverse_left", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.disjoint_reverse_right", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.lookup_graph", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.range'_0", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "List.left_le_of_mem_range'", "kind": "theorem", "module": "Mathlib.Data.List.Basic", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "List.isChain_nil", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.isChain_singleton", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.isChain_cons_iff", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.IsChain.imp_of_mem_tail_imp", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.IsChain.imp_of_mem_imp", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.IsChain.iff", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.IsChain.iff_of_mem_imp", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.IsChain.iff_of_mem_tail_imp", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.IsChain.iff_mem", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.IsChain.iff_mem_mem_tail", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.isChain_pair", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.isChain_isInfix", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.isChain_split", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.isChain_cons_split", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "List.isChain_append_cons_cons", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.isChain_cons_append_cons_cons", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.isChain_iff_forall_rel_of_append_cons_cons", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": true, "tactics": ["refine", "induction", "nil", "singleton", "cons_cons", "ih", "refine", "apply", "rw"], "tactic_count": 9}
{"name": "List.isChain_iff_forall₂", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.isChain_cons_iff_forall₂", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "List.isChain_cons_append_singleton_iff_forall₂", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "List.isChain_map", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.isChain_of_isChain_map", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.isChain_map_of_isChain", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.isChain_cons_map", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.isChain_cons_of_isChain_cons_map", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.isChain_cons_map_of_isChain_cons", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.isChain_pmap", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.isChain_pmap_of_isChain", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.isChain_of_isChain_pmap", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.isChain_cons_pmap", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.isChain_cons_pmap_of_isChain_cons", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.isChain_cons_of_isChain_cons_pmap", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.IsChain.sublist", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "List.IsChain.rel_cons", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "List.IsChain.of_cons", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.IsChain.tail", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "List.IsChain.rel_head", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.IsChain.rel_head?", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "List.IsChain.cons", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.IsChain.cons_of_ne_nil", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "List.isChain_cons", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.isChain_append", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.IsChain.append", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.IsChain.left_of_append", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.IsChain.right_of_append", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.IsChain.infix", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "List.IsChain.suffix", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.IsChain.prefix", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.IsChain.drop", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.IsChain.dropLast", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.IsChain.take", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.IsChain.imp_head", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.isChain_iff_get", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.isChain_cons_iff_get", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.exists_not_getElem_of_not_isChain", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": true, "tactics": ["simp_all"], "tactic_count": 1}
{"name": "List.isChain_reverse", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": true, "tactics": ["induction", "nil", "singleton", "cons_cons", "rw", "reverse_cons,"], "tactic_count": 6}
{"name": "List.IsChain.append_overlap", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.isChain_flatten", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.isChain_attachWith", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.isChain_attach", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.exists_isChain_cons_of_relationReflTransGen", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": true, "tactics": ["refine", "exact", "intro", "obtain", "refine", "rwa"], "tactic_count": 6}
{"name": "List.exists_isChain_ne_nil_of_relationReflTransGen", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "List.IsChain.induction", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.IsChain.cons_induction", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.IsChain.concat_induction", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.IsChain.concat_induction_head", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.IsChain.backwards_induction", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": true, "tactics": ["have", "replace", "grind"], "tactic_count": 3}
{"name": "List.IsChain.backwards_concat_induction", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.IsChain.backwards_cons_induction", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.IsChain.backwards_cons_induction_head", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.relationReflTransGen_of_exists_isChain", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.relationReflTransGen_of_exists_isChain_cons", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.IsChain.cons_of_le", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": true, "tactics": ["cases", "nil", "cons", "apply", "cases", "nil", "simp", "exact", "cons", "rw", "refine", "rw", "rcases", "by_contra", "rw", "apply", "apply", "exact", "simp_all"], "tactic_count": 19}
{"name": "List.IsChain.isChain_cons", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "List.IsChain.iterate_eq_of_apply_eq", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "rw", "apply"], "tactic_count": 6}
{"name": "List.isChain_replicate_of_rel", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.isChain_eq_iff_eq_replicate", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": true, "tactics": ["induction", "nil", "singleton", "cons_cons"], "tactic_count": 4}
{"name": "List.isChain_cons_eq_iff_eq_replicate", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.chains", "kind": "abbrev", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.lex_chains", "kind": "abbrev", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Acc.list_chain'", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": true, "tactics": ["obtain", "apply", "specialize", "rw", "induction", "intro", "have", "let", "have", "rcases", "apply", "rintro", "apply", "ih", "revert", "rw", "clear_value", "induction", "intro", "intro", "apply", "rintro", "apply", "apply", "apply"], "tactic_count": 25}
{"name": "WellFounded.list_chain'", "kind": "theorem", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsWellFoundedChainsLex_chains", "kind": "instance", "module": "Mathlib.Data.List.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.isChain_ofFn", "kind": "theorem", "module": "Mathlib.Data.List.ChainOfFn", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "List.countP_lt_length_iff", "kind": "theorem", "module": "Mathlib.Data.List.Count", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.count_lt_length_iff", "kind": "theorem", "module": "Mathlib.Data.List.Count", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.countP_erase", "kind": "theorem", "module": "Mathlib.Data.List.Count", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "List.count_diff", "kind": "theorem", "module": "Mathlib.Data.List.Count", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.countP_diff", "kind": "theorem", "module": "Mathlib.Data.List.Count", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "List.count_map_of_injective", "kind": "theorem", "module": "Mathlib.Data.List.Count", "is_tactic_proof": true, "tactics": ["simp", "unfold", "simp"], "tactic_count": 3}
{"name": "List.nextOr", "kind": "definition", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.nextOr_nil", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.nextOr_singleton", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.nextOr_self_cons_cons", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.nextOr_cons_of_ne", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": true, "tactics": ["rcases", "rfl", "exact"], "tactic_count": 3}
{"name": "List.nextOr_eq_nextOr_of_mem_dropLast", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": ["induction", "nil", "cons", "rcases", "simp", "by_cases", "rw", "rw", "simpa"], "tactic_count": 9}
{"name": "List.mem_of_nextOr_ne", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": ["induction", "nil", "cons", "rcases", "simp", "by_cases", "simp", "rw", "simpa"], "tactic_count": 9}
{"name": "List.nextOr_concat", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "obtain", "rw"], "tactic_count": 5}
{"name": "List.nextOr_mem", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": true, "tactics": ["revert", "suffices", "intro", "induction", "nil", "cons", "rcases", "exact", "rw", "split_ifs", "exact", "exact"], "tactic_count": 12}
{"name": "List.next", "kind": "definition", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.prev", "kind": "definition", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.next_singleton", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.prev_singleton", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.next_cons_cons_eq'", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.next_cons_cons_eq", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.next_cons_eq_next_of_mem_dropLast", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "List.next_getLast_cons", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": true, "tactics": ["rw", "subst", "intro", "obtain", "grind", "suffices", "rcases", "simp", "rw", "rw", "refine", "rw", "rw", "rw", "simp", "getElem_cons_succ]", "simp", "lia", "simpa"], "tactic_count": 19}
{"name": "List.prev_getLast_cons'", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "List.prev_getLast_cons", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.prev_head_eq_getLast", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": true, "tactics": ["cases", "nil", "cons"], "tactic_count": 3}
{"name": "List.prev_cons_cons_eq'", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.prev_cons_cons_eq", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.prev_cons_cons_of_ne'", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": true, "tactics": ["cases", "simp", "rw"], "tactic_count": 3}
{"name": "List.prev_cons_cons_of_ne", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.prev_ne_cons_cons", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": true, "tactics": ["cases", "simp", "rw"], "tactic_count": 3}
{"name": "List.next_mem", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.prev_mem", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": true, "tactics": ["rcases", "simp", "induction", "nil", "cons", "by_cases", "simp", "exact", "rw", "split_ifs", "exact", "exact"], "tactic_count": 12}
{"name": "List.nextOr_eq_getElem?_idxOf_succ_of_mem_dropLast", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": true, "tactics": ["nil", "x", "rw", "split_ifs", "grind", "rw", "grind"], "tactic_count": 7}
{"name": "List.nextOr_eq_getElem_idxOf_succ_of_mem_dropLast", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.nextOr_infix_of_mem_dropLast", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": true, "tactics": ["refine", "have", "grind", "by_cases", "grind", "grind"], "tactic_count": 6}
{"name": "List.nextOr_getLast_of_notMem_dropLast", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": true, "tactics": ["nil", "x", "unfold", "split_ifs", "grind", "apply", "grind"], "tactic_count": 7}
{"name": "List.next_getLast_eq_head_of_notMem_dropLast", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.next_eq_getElem", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": true, "tactics": ["have", "by_cases", "simp", "grind"], "tactic_count": 4}
{"name": "List.next_getElem", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "List.prev_eq_getElem?_idxOf_pred_of_ne_head", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": true, "tactics": ["nil", "x", "have", "grind"], "tactic_count": 4}
{"name": "List.prev_eq_getElem_idxOf_pred_of_ne_head", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.prev_infix_of_mem_tail", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": true, "tactics": ["have", "refine", "by_cases", "subst", "grind", "grind"], "tactic_count": 6}
{"name": "List.prev_eq_getElem", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": true, "tactics": ["cases", "nil", "cons", "by_cases", "subst", "simp", "grind", "rw", "congr", "rw", "all_goals"], "tactic_count": 11}
{"name": "List.prev_getElem", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "List.next_getLast_eq_head", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": true, "tactics": ["have", "simp"], "tactic_count": 2}
{"name": "List.pmap_next_eq_rotate_one", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": true, "tactics": ["apply", "simp", "intros", "rw"], "tactic_count": 4}
{"name": "List.pmap_prev_eq_rotate_length_sub_one", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": true, "tactics": ["apply", "simp", "intro", "rw"], "tactic_count": 4}
{"name": "List.prev_next", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": true, "tactics": ["obtain", "simp", "rcases", "simp", "have", "rw", "rw", "simp"], "tactic_count": 8}
{"name": "List.next_prev", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": true, "tactics": ["obtain", "simp", "rcases", "simp", "have", "rw", "rw", "simp"], "tactic_count": 8}
{"name": "List.prev_reverse_eq_next", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": true, "tactics": ["obtain", "have", "have", "rw", "simp_rw", "rw", "simp_rw", "rw", "simp", "simpa"], "tactic_count": 10}
{"name": "List.next_reverse_eq_prev", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": true, "tactics": ["convert", "exact"], "tactic_count": 2}
{"name": "List.isRotated_next_eq", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "rw", "simp_rw", "rw", "simp"], "tactic_count": 6}
{"name": "List.isRotated_prev_eq", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Cycle", "kind": "definition", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.ofList", "kind": "definition", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.instCoeList", "kind": "instance", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.coe_eq_coe", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.mk_eq_coe", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.mk''_eq_coe", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.coe_cons_eq_coe_append", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.nil", "kind": "definition", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.coe_nil", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.coe_eq_nil", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.instEmptyCollection", "kind": "instance", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.empty_eq", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.instInhabited", "kind": "instance", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.induction_on", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.Mem", "kind": "definition", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.instMembership", "kind": "instance", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.mem_coe_iff", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.notMem_nil", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.instDecidableEq", "kind": "instance", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.instDecidableMemOfDecidableEq", "kind": "instance", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.reverse", "kind": "definition", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.reverse_coe", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.mem_reverse_iff", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.reverse_reverse", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.reverse_nil", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.length", "kind": "definition", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.length_coe", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.length_nil", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.length_reverse", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.Subsingleton", "kind": "definition", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.subsingleton_nil", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.length_subsingleton_iff", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.subsingleton_reverse_iff", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Cycle.Subsingleton.congr", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": ["induction", "simp", "length_eq_one_iff,", "rcases"], "tactic_count": 4}
{"name": "Cycle.Nontrivial", "kind": "definition", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.nontrivial_coe_nodup_iff", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": true, "tactics": ["rw", "rcases", "simp", "simp", "simp", "refine", "simp", "exact"], "tactic_count": 8}
{"name": "Cycle.nontrivial_reverse_iff", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Cycle.length_nontrivial", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": true, "tactics": ["obtain", "induction", "rcases", "simp", "simp", "simp", "simp"], "tactic_count": 7}
{"name": "Cycle.Nodup", "kind": "definition", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.nodup_nil", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.nodup_coe_iff", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.nodup_reverse_iff", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.Subsingleton.nodup", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": ["induction", "obtain", "simp", "have", "simp"], "tactic_count": 5}
{"name": "Cycle.Nodup.nontrivial_iff", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": true, "tactics": ["rw", "induction", "simp", "simp"], "tactic_count": 4}
{"name": "Cycle.toMultiset", "kind": "definition", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.coe_toMultiset", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.nil_toMultiset", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.card_toMultiset", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.toMultiset_eq_nil", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.map", "kind": "definition", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.map_nil", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.map_coe", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.map_eq_nil", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.mem_map", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.lists", "kind": "definition", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.lists_coe", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.mem_lists_iff_coe_eq", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.lists_nil", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cycle.decidableNontrivialCoe", "kind": "definition", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.instDecidableNontrivial", "kind": "instance", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.instDecidableNodup", "kind": "instance", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.fintypeNodupCycle", "kind": "instance", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.fintypeNodupNontrivialCycle", "kind": "instance", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.toFinset", "kind": "definition", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.toFinset_toMultiset", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.coe_toFinset", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.nil_toFinset", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.toFinset_eq_nil", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.next", "kind": "definition", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.prev", "kind": "definition", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.prev_reverse_eq_next", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.prev_reverse_eq_next'", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.next_reverse_eq_prev", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Cycle.next_reverse_eq_prev'", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Cycle.next_mem", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": true, "tactics": ["induction", "apply"], "tactic_count": 2}
{"name": "Cycle.prev_mem", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "Cycle.prev_next", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.next_prev", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.instRepr", "kind": "instance", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.Chain", "kind": "definition", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.Chain.nil", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": true, "tactics": ["trivial"], "tactic_count": 1}
{"name": "Cycle.chain_coe_cons", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.chain_singleton", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cycle.chain_ne_nil", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.chain_map", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.chain_range_succ", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cycle.Chain.imp", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": true, "tactics": ["induction", "trivial", "rw", "exact"], "tactic_count": 4}
{"name": "Cycle.chain_mono", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.chain_of_pairwise", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": ["induction", "nil", "cons", "intro", "have", "have", "rw", "apply", "rw", "refine", "pairwise_append.2", "rw", "rcases", "exact", "rw", "rw", "exact", "rw", "rw", "exact"], "tactic_count": 20}
{"name": "Cycle.chain_iff_pairwise", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.Chain.eq_nil_of_irrefl", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "have", "exact"], "tactic_count": 5}
{"name": "Cycle.Chain.eq_nil_of_well_founded", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.forall_eq_of_chain", "kind": "theorem", "module": "Mathlib.Data.List.Cycle", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "List.dedup_nil", "kind": "theorem", "module": "Mathlib.Data.List.Dedup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.dedup_cons_of_mem'", "kind": "theorem", "module": "Mathlib.Data.List.Dedup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.dedup_cons_of_notMem'", "kind": "theorem", "module": "Mathlib.Data.List.Dedup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.dedup_cons'", "kind": "theorem", "module": "Mathlib.Data.List.Dedup", "is_tactic_proof": true, "tactics": ["split"], "tactic_count": 1}
{"name": "List.mem_dedup", "kind": "theorem", "module": "Mathlib.Data.List.Dedup", "is_tactic_proof": true, "tactics": ["have", "simpa", "intro", "exact"], "tactic_count": 4}
{"name": "List.dedup_cons_of_mem", "kind": "theorem", "module": "Mathlib.Data.List.Dedup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.dedup_cons_of_notMem", "kind": "theorem", "module": "Mathlib.Data.List.Dedup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.dedup_cons", "kind": "theorem", "module": "Mathlib.Data.List.Dedup", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "List.dedup_sublist", "kind": "theorem", "module": "Mathlib.Data.List.Dedup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.dedup_subset", "kind": "theorem", "module": "Mathlib.Data.List.Dedup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.subset_dedup", "kind": "theorem", "module": "Mathlib.Data.List.Dedup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.nodup_dedup", "kind": "theorem", "module": "Mathlib.Data.List.Dedup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.headI_dedup", "kind": "theorem", "module": "Mathlib.Data.List.Dedup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.tail_dedup", "kind": "theorem", "module": "Mathlib.Data.List.Dedup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.dedup_eq_self", "kind": "theorem", "module": "Mathlib.Data.List.Dedup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.dedup_eq_cons", "kind": "theorem", "module": "Mathlib.Data.List.Dedup", "is_tactic_proof": true, "tactics": ["refine", "refine", "have", "have", "rw", "lia", "have", "have", "rw", "exact"], "tactic_count": 10}
{"name": "List.dedup_eq_nil", "kind": "theorem", "module": "Mathlib.Data.List.Dedup", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "by_cases", "simp", "simp"], "tactic_count": 6}
{"name": "List.Nodup.dedup", "kind": "theorem", "module": "Mathlib.Data.List.Dedup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.dedup_idem", "kind": "theorem", "module": "Mathlib.Data.List.Dedup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.dedup_append", "kind": "theorem", "module": "Mathlib.Data.List.Dedup", "is_tactic_proof": false, "tactics": ["induction", "nil", "cons", "simp", "rw", "by_cases", "rw", "rw"], "tactic_count": 8}
{"name": "List.dedup_map_of_injective", "kind": "theorem", "module": "Mathlib.Data.List.Dedup", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "rw", "by_cases", "rw", "rw"], "tactic_count": 7}
{"name": "List.Subset.dedup_append_right", "kind": "theorem", "module": "Mathlib.Data.List.Dedup", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.Disjoint.union_eq", "kind": "theorem", "module": "Mathlib.Data.List.Dedup", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "rw", "rw", "by_cases", "rw", "rw", "rw", "exact"], "tactic_count": 10}
{"name": "List.Disjoint.dedup_append", "kind": "theorem", "module": "Mathlib.Data.List.Dedup", "is_tactic_proof": true, "tactics": ["rw", "intro", "exact"], "tactic_count": 3}
{"name": "List.replicate_dedup", "kind": "theorem", "module": "Mathlib.Data.List.Dedup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.count_dedup", "kind": "theorem", "module": "Mathlib.Data.List.Dedup", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "List.Perm.dedup", "kind": "theorem", "module": "Mathlib.Data.List.Dedup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.instSDiffOfDecidableEq_mathlib", "kind": "instance", "module": "Mathlib.Data.List.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.getI", "kind": "definition", "module": "Mathlib.Data.List.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.headI", "kind": "definition", "module": "Mathlib.Data.List.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.headI_nil", "kind": "theorem", "module": "Mathlib.Data.List.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.headI_cons", "kind": "theorem", "module": "Mathlib.Data.List.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.getLastI", "kind": "definition", "module": "Mathlib.Data.List.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.takeI", "kind": "definition", "module": "Mathlib.Data.List.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.findM", "kind": "definition", "module": "Mathlib.Data.List.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.findM?'", "kind": "definition", "module": "Mathlib.Data.List.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.orM", "kind": "definition", "module": "Mathlib.Data.List.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.andM", "kind": "definition", "module": "Mathlib.Data.List.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.foldlIdxM", "kind": "definition", "module": "Mathlib.Data.List.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.foldrIdxM", "kind": "definition", "module": "Mathlib.Data.List.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.mapIdxMAux'", "kind": "definition", "module": "Mathlib.Data.List.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.mapIdxM'", "kind": "definition", "module": "Mathlib.Data.List.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Forall", "kind": "definition", "module": "Mathlib.Data.List.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.permutationsAux2", "kind": "definition", "module": "Mathlib.Data.List.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.permutationsAux.rec", "kind": "definition", "module": "Mathlib.Data.List.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.permutationsAux", "kind": "definition", "module": "Mathlib.Data.List.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.permutations", "kind": "definition", "module": "Mathlib.Data.List.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.permutations'Aux", "kind": "definition", "module": "Mathlib.Data.List.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.permutations'", "kind": "definition", "module": "Mathlib.Data.List.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.extractp", "kind": "definition", "module": "Mathlib.Data.List.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.instSProd", "kind": "instance", "module": "Mathlib.Data.List.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.dedup", "kind": "definition", "module": "Mathlib.Data.List.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.destutter'", "kind": "definition", "module": "Mathlib.Data.List.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.destutter", "kind": "definition", "module": "Mathlib.Data.List.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.chooseX", "kind": "definition", "module": "Mathlib.Data.List.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.choose", "kind": "definition", "module": "Mathlib.Data.List.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.mapDiagM'", "kind": "definition", "module": "Mathlib.Data.List.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.map₂Left'", "kind": "definition", "module": "Mathlib.Data.List.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.map₂Right'", "kind": "definition", "module": "Mathlib.Data.List.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.map₂Left", "kind": "definition", "module": "Mathlib.Data.List.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.map₂Right", "kind": "definition", "module": "Mathlib.Data.List.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.zipWith3", "kind": "definition", "module": "Mathlib.Data.List.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.zipWith4", "kind": "definition", "module": "Mathlib.Data.List.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.zipWith5", "kind": "definition", "module": "Mathlib.Data.List.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.replaceIf", "kind": "definition", "module": "Mathlib.Data.List.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.iterate", "kind": "definition", "module": "Mathlib.Data.List.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.iterateTR", "kind": "definition", "module": "Mathlib.Data.List.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.iterateTR_loop_eq", "kind": "theorem", "module": "Mathlib.Data.List.Defs", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.iterate_eq_iterateTR", "kind": "theorem", "module": "Mathlib.Data.List.Defs", "is_tactic_proof": true, "tactics": ["funext", "exact"], "tactic_count": 2}
{"name": "List.mapAccumr", "kind": "definition", "module": "Mathlib.Data.List.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.length_mapAccumr", "kind": "theorem", "module": "Mathlib.Data.List.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.mapAccumr₂", "kind": "definition", "module": "Mathlib.Data.List.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.length_mapAccumr₂", "kind": "theorem", "module": "Mathlib.Data.List.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.destutter'_nil", "kind": "theorem", "module": "Mathlib.Data.List.Destutter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.destutter'_cons", "kind": "theorem", "module": "Mathlib.Data.List.Destutter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.destutter'_cons_pos", "kind": "theorem", "module": "Mathlib.Data.List.Destutter", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.destutter'_cons_neg", "kind": "theorem", "module": "Mathlib.Data.List.Destutter", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.destutter'_singleton", "kind": "theorem", "module": "Mathlib.Data.List.Destutter", "is_tactic_proof": true, "tactics": ["split_ifs"], "tactic_count": 1}
{"name": "List.destutter'_sublist", "kind": "theorem", "module": "Mathlib.Data.List.Destutter", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "rw", "split_ifs", "exact", "exact"], "tactic_count": 7}
{"name": "List.mem_destutter'", "kind": "theorem", "module": "Mathlib.Data.List.Destutter", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "rw", "split_ifs", "simp", "assumption"], "tactic_count": 7}
{"name": "List.isChain_destutter'", "kind": "theorem", "module": "Mathlib.Data.List.Destutter", "is_tactic_proof": true, "tactics": ["induction", "nil", "singleton", "cons_cons", "simp_rw", "simp_rw", "if_true_right,", "exact"], "tactic_count": 8}
{"name": "List.isChain_cons_destutter'_of_rel", "kind": "theorem", "module": "Mathlib.Data.List.Destutter", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "List.destutter'_of_isChain_cons", "kind": "theorem", "module": "Mathlib.Data.List.Destutter", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "obtain", "rw"], "tactic_count": 5}
{"name": "List.destutter'_eq_self_iff", "kind": "theorem", "module": "Mathlib.Data.List.Destutter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.destutter'_ne_nil", "kind": "theorem", "module": "Mathlib.Data.List.Destutter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.destutter_nil", "kind": "theorem", "module": "Mathlib.Data.List.Destutter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.destutter_cons'", "kind": "theorem", "module": "Mathlib.Data.List.Destutter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.destutter_cons_cons", "kind": "theorem", "module": "Mathlib.Data.List.Destutter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.destutter_singleton", "kind": "theorem", "module": "Mathlib.Data.List.Destutter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.destutter_pair", "kind": "theorem", "module": "Mathlib.Data.List.Destutter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.destutter_sublist", "kind": "theorem", "module": "Mathlib.Data.List.Destutter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.isChain_destutter", "kind": "theorem", "module": "Mathlib.Data.List.Destutter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.destutter_of_isChain", "kind": "theorem", "module": "Mathlib.Data.List.Destutter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.destutter_eq_self_iff", "kind": "theorem", "module": "Mathlib.Data.List.Destutter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.destutter_idem", "kind": "theorem", "module": "Mathlib.Data.List.Destutter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.destutter_eq_nil", "kind": "theorem", "module": "Mathlib.Data.List.Destutter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.map_destutter", "kind": "theorem", "module": "Mathlib.Data.List.Destutter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.map_destutter_ne", "kind": "theorem", "module": "Mathlib.Data.List.Destutter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.length_destutter'_cotrans_ge", "kind": "theorem", "module": "Mathlib.Data.List.Destutter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.length_destutter'_congr", "kind": "theorem", "module": "Mathlib.Data.List.Destutter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.le_length_destutter'_cons", "kind": "theorem", "module": "Mathlib.Data.List.Destutter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.length_destutter_le_length_destutter_cons", "kind": "theorem", "module": "Mathlib.Data.List.Destutter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.length_destutter_ne_le_length_destutter_cons", "kind": "theorem", "module": "Mathlib.Data.List.Destutter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.IsChain.length_le_length_destutter", "kind": "theorem", "module": "Mathlib.Data.List.Destutter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.IsChain.length_le_length_destutter_ne", "kind": "theorem", "module": "Mathlib.Data.List.Destutter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Pairwise.destutter_eq_dedup", "kind": "theorem", "module": "Mathlib.Data.List.Destutter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.rdrop", "kind": "definition", "module": "Mathlib.Data.List.DropRight", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.rdrop_nil", "kind": "theorem", "module": "Mathlib.Data.List.DropRight", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.rdrop_zero", "kind": "theorem", "module": "Mathlib.Data.List.DropRight", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.rdrop_eq_reverse_drop_reverse", "kind": "theorem", "module": "Mathlib.Data.List.DropRight", "is_tactic_proof": true, "tactics": ["rw", "induction", "nil", "append_singleton", "cases", "simp", "simp"], "tactic_count": 7}
{"name": "List.rdrop_concat_succ", "kind": "theorem", "module": "Mathlib.Data.List.DropRight", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.rtake", "kind": "definition", "module": "Mathlib.Data.List.DropRight", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.rtake_nil", "kind": "theorem", "module": "Mathlib.Data.List.DropRight", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.rtake_zero", "kind": "theorem", "module": "Mathlib.Data.List.DropRight", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.rtake_eq_reverse_take_reverse", "kind": "theorem", "module": "Mathlib.Data.List.DropRight", "is_tactic_proof": true, "tactics": ["rw", "induction", "nil", "append_singleton", "cases", "exact", "simp"], "tactic_count": 7}
{"name": "List.rtake_concat_succ", "kind": "theorem", "module": "Mathlib.Data.List.DropRight", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.rdropWhile", "kind": "definition", "module": "Mathlib.Data.List.DropRight", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.rdropWhile_nil", "kind": "theorem", "module": "Mathlib.Data.List.DropRight", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.rdropWhile_concat", "kind": "theorem", "module": "Mathlib.Data.List.DropRight", "is_tactic_proof": true, "tactics": ["simp", "split_ifs"], "tactic_count": 2}
{"name": "List.rdropWhile_concat_pos", "kind": "theorem", "module": "Mathlib.Data.List.DropRight", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.rdropWhile_concat_neg", "kind": "theorem", "module": "Mathlib.Data.List.DropRight", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.rdropWhile_singleton", "kind": "theorem", "module": "Mathlib.Data.List.DropRight", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.rdropWhile_last_not", "kind": "theorem", "module": "Mathlib.Data.List.DropRight", "is_tactic_proof": true, "tactics": ["simp_rw", "rw", "simp"], "tactic_count": 3}
{"name": "List.rdropWhile_prefix", "kind": "theorem", "module": "Mathlib.Data.List.DropRight", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "List.rdropWhile_eq_nil_iff", "kind": "theorem", "module": "Mathlib.Data.List.DropRight", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.rdropWhile_eq_self_iff", "kind": "theorem", "module": "Mathlib.Data.List.DropRight", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.dropWhile_idempotent", "kind": "theorem", "module": "Mathlib.Data.List.DropRight", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "List.rdropWhile_idempotent", "kind": "theorem", "module": "Mathlib.Data.List.DropRight", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.rdropWhile_reverse", "kind": "theorem", "module": "Mathlib.Data.List.DropRight", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "List.rtakeWhile", "kind": "definition", "module": "Mathlib.Data.List.DropRight", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.rtakeWhile_nil", "kind": "theorem", "module": "Mathlib.Data.List.DropRight", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.rtakeWhile_concat", "kind": "theorem", "module": "Mathlib.Data.List.DropRight", "is_tactic_proof": true, "tactics": ["simp", "split_ifs"], "tactic_count": 2}
{"name": "List.rtakeWhile_concat_pos", "kind": "theorem", "module": "Mathlib.Data.List.DropRight", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.rtakeWhile_concat_neg", "kind": "theorem", "module": "Mathlib.Data.List.DropRight", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.rtakeWhile_suffix", "kind": "theorem", "module": "Mathlib.Data.List.DropRight", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "List.rtakeWhile_eq_self_iff", "kind": "theorem", "module": "Mathlib.Data.List.DropRight", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.rtakeWhile_eq_nil_iff", "kind": "theorem", "module": "Mathlib.Data.List.DropRight", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.mem_rtakeWhile_imp", "kind": "theorem", "module": "Mathlib.Data.List.DropRight", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "List.rtakeWhile_idempotent", "kind": "theorem", "module": "Mathlib.Data.List.DropRight", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.rtakeWhile_reverse", "kind": "theorem", "module": "Mathlib.Data.List.DropRight", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "List.rdropWhile_append_rtakeWhile", "kind": "theorem", "module": "Mathlib.Data.List.DropRight", "is_tactic_proof": true, "tactics": ["simp", "rw"], "tactic_count": 2}
{"name": "List.rdrop_add", "kind": "theorem", "module": "Mathlib.Data.List.DropRight", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "List.rdrop_append_length", "kind": "theorem", "module": "Mathlib.Data.List.DropRight", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.rdrop_append_of_le_length", "kind": "theorem", "module": "Mathlib.Data.List.DropRight", "is_tactic_proof": true, "tactics": ["intro", "rw", "rw", "rdrop_eq_reverse_drop_reverse]"], "tactic_count": 4}
{"name": "List.rdrop_append_length_add", "kind": "theorem", "module": "Mathlib.Data.List.DropRight", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.Duplicate", "kind": "inductive", "module": "Mathlib.Data.List.Duplicate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.List.Duplicate.0.List.term_∈+_", "kind": "definition", "module": "Mathlib.Data.List.Duplicate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.List.Duplicate.0.List._aux_Mathlib_Data_List_Duplicate___macroRules__private_Mathlib_Data_List_Duplicate_0_List_term_∈+__1", "kind": "definition", "module": "Mathlib.Data.List.Duplicate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.List.Duplicate.0.List._aux_Mathlib_Data_List_Duplicate___unexpand_List_Duplicate_1", "kind": "definition", "module": "Mathlib.Data.List.Duplicate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Mem.duplicate_cons_self", "kind": "theorem", "module": "Mathlib.Data.List.Duplicate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Duplicate.duplicate_cons", "kind": "theorem", "module": "Mathlib.Data.List.Duplicate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Duplicate.mem", "kind": "theorem", "module": "Mathlib.Data.List.Duplicate", "is_tactic_proof": true, "tactics": ["induction", "cons_mem", "cons_duplicate"], "tactic_count": 3}
{"name": "List.Duplicate.mem_cons_self", "kind": "theorem", "module": "Mathlib.Data.List.Duplicate", "is_tactic_proof": true, "tactics": ["obtain", "exact", "exact"], "tactic_count": 3}
{"name": "List.duplicate_cons_self_iff", "kind": "theorem", "module": "Mathlib.Data.List.Duplicate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Duplicate.ne_nil", "kind": "theorem", "module": "Mathlib.Data.List.Duplicate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.not_duplicate_nil", "kind": "theorem", "module": "Mathlib.Data.List.Duplicate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Duplicate.ne_singleton", "kind": "theorem", "module": "Mathlib.Data.List.Duplicate", "is_tactic_proof": true, "tactics": ["induction", "cons_mem", "cons_duplicate"], "tactic_count": 3}
{"name": "List.not_duplicate_singleton", "kind": "theorem", "module": "Mathlib.Data.List.Duplicate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Duplicate.elim_nil", "kind": "theorem", "module": "Mathlib.Data.List.Duplicate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Duplicate.elim_singleton", "kind": "theorem", "module": "Mathlib.Data.List.Duplicate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.duplicate_cons_iff", "kind": "theorem", "module": "Mathlib.Data.List.Duplicate", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact", "exact", "rcases", "simpa", "exact"], "tactic_count": 7}
{"name": "List.Duplicate.of_duplicate_cons", "kind": "theorem", "module": "Mathlib.Data.List.Duplicate", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "List.duplicate_cons_iff_of_ne", "kind": "theorem", "module": "Mathlib.Data.List.Duplicate", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.Duplicate.mono_sublist", "kind": "theorem", "module": "Mathlib.Data.List.Duplicate", "is_tactic_proof": true, "tactics": ["induction", "slnil", "cons", "cons₂", "rw", "rcases", "simp", "simp"], "tactic_count": 8}
{"name": "List.duplicate_iff_sublist", "kind": "theorem", "module": "Mathlib.Data.List.Duplicate", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "by_cases", "simp", "rw", "refine", "cases", "assumption", "contradiction"], "tactic_count": 10}
{"name": "List.nodup_iff_forall_not_duplicate", "kind": "theorem", "module": "Mathlib.Data.List.Duplicate", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "List.exists_duplicate_iff_not_nodup", "kind": "theorem", "module": "Mathlib.Data.List.Duplicate", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.Duplicate.not_nodup", "kind": "theorem", "module": "Mathlib.Data.List.Duplicate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.duplicate_iff_two_le_count", "kind": "theorem", "module": "Mathlib.Data.List.Duplicate", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.decidableDuplicate", "kind": "instance", "module": "Mathlib.Data.List.Duplicate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.forall_mem_zipIdx", "kind": "theorem", "module": "Mathlib.Data.List.Enum", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.forall_mem_zipIdx'", "kind": "theorem", "module": "Mathlib.Data.List.Enum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.exists_mem_zipIdx", "kind": "theorem", "module": "Mathlib.Data.List.Enum", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.exists_mem_zipIdx'", "kind": "theorem", "module": "Mathlib.Data.List.Enum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.count_finRange", "kind": "theorem", "module": "Mathlib.Data.List.FinRange", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.idxOf_finRange", "kind": "theorem", "module": "Mathlib.Data.List.FinRange", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "List.finRange_succ_eq_map", "kind": "theorem", "module": "Mathlib.Data.List.FinRange", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.ofFn_eq_pmap", "kind": "theorem", "module": "Mathlib.Data.List.FinRange", "is_tactic_proof": true, "tactics": ["ext", "grind"], "tactic_count": 2}
{"name": "List.ofFn_id", "kind": "theorem", "module": "Mathlib.Data.List.FinRange", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.ofFn_eq_map", "kind": "theorem", "module": "Mathlib.Data.List.FinRange", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.nodup_ofFn_ofInjective", "kind": "theorem", "module": "Mathlib.Data.List.FinRange", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "List.nodup_ofFn", "kind": "theorem", "module": "Mathlib.Data.List.FinRange", "is_tactic_proof": true, "tactics": ["refine", "refine", "intro", "exact", "intro", "rw", "simp_rw", "exact"], "tactic_count": 8}
{"name": "Equiv.Perm.map_finRange_perm", "kind": "theorem", "module": "Mathlib.Data.List.FinRange", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "Equiv.Perm.ofFn_comp_perm", "kind": "theorem", "module": "Mathlib.Data.List.FinRange", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "List.Sublist.flatten", "kind": "theorem", "module": "Mathlib.Data.List.Flatten", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.Sublist.flatMap", "kind": "theorem", "module": "Mathlib.Data.List.Flatten", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Sublist.flatMap_right", "kind": "theorem", "module": "Mathlib.Data.List.Flatten", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.drop_take_succ_eq_cons_getElem", "kind": "theorem", "module": "Mathlib.Data.List.Flatten", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.append_flatten_map_append", "kind": "theorem", "module": "Mathlib.Data.List.Flatten", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.head_head_eq_head_flatten", "kind": "theorem", "module": "Mathlib.Data.List.Flatten", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "List.head_flatten_eq_head_head", "kind": "theorem", "module": "Mathlib.Data.List.Flatten", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.getLast_flatten_of_getLast_ne_nil", "kind": "theorem", "module": "Mathlib.Data.List.Flatten", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "List.getLast_flatten_of_flatten_ne_nil", "kind": "theorem", "module": "Mathlib.Data.List.Flatten", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Forall₂.imp", "kind": "theorem", "module": "Mathlib.Data.List.Forall2", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.Forall₂.mp", "kind": "theorem", "module": "Mathlib.Data.List.Forall2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Forall₂.flip", "kind": "theorem", "module": "Mathlib.Data.List.Forall2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.forall₂_same", "kind": "theorem", "module": "Mathlib.Data.List.Forall2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.forall₂_refl", "kind": "theorem", "module": "Mathlib.Data.List.Forall2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.forall₂_eq_eq_eq", "kind": "theorem", "module": "Mathlib.Data.List.Forall2", "is_tactic_proof": true, "tactics": ["funext", "constructor", "intro", "induction", "rfl", "simp", "rintro", "exact"], "tactic_count": 8}
{"name": "List.forall₂_nil_left_iff", "kind": "theorem", "module": "Mathlib.Data.List.Forall2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.forall₂_nil_right_iff", "kind": "theorem", "module": "Mathlib.Data.List.Forall2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.forall₂_cons_left_iff", "kind": "theorem", "module": "Mathlib.Data.List.Forall2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.forall₂_cons_right_iff", "kind": "theorem", "module": "Mathlib.Data.List.Forall2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.forall₂_and_left", "kind": "theorem", "module": "Mathlib.Data.List.Forall2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.forall₂_map_left_iff", "kind": "theorem", "module": "Mathlib.Data.List.Forall2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.forall₂_map_right_iff", "kind": "theorem", "module": "Mathlib.Data.List.Forall2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.left_unique_forall₂'", "kind": "theorem", "module": "Mathlib.Data.List.Forall2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Relator.LeftUnique.forall₂", "kind": "theorem", "module": "Mathlib.Data.List.Forall2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.right_unique_forall₂'", "kind": "theorem", "module": "Mathlib.Data.List.Forall2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Relator.RightUnique.forall₂", "kind": "theorem", "module": "Mathlib.Data.List.Forall2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Relator.BiUnique.forall₂", "kind": "theorem", "module": "Mathlib.Data.List.Forall2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Forall₂.length_eq", "kind": "theorem", "module": "Mathlib.Data.List.Forall2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Forall₂.get", "kind": "theorem", "module": "Mathlib.Data.List.Forall2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.forall₂_of_length_eq_of_get", "kind": "theorem", "module": "Mathlib.Data.List.Forall2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.forall₂_iff_get", "kind": "theorem", "module": "Mathlib.Data.List.Forall2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.forall₂_zip", "kind": "theorem", "module": "Mathlib.Data.List.Forall2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.forall₂_iff_zip", "kind": "theorem", "module": "Mathlib.Data.List.Forall2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.forall₂_take", "kind": "theorem", "module": "Mathlib.Data.List.Forall2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.forall₂_drop", "kind": "theorem", "module": "Mathlib.Data.List.Forall2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.forall₂_take_append", "kind": "theorem", "module": "Mathlib.Data.List.Forall2", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "List.forall₂_drop_append", "kind": "theorem", "module": "Mathlib.Data.List.Forall2", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "List.rel_mem", "kind": "theorem", "module": "Mathlib.Data.List.Forall2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.rel_map", "kind": "theorem", "module": "Mathlib.Data.List.Forall2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.rel_append", "kind": "theorem", "module": "Mathlib.Data.List.Forall2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.rel_reverse", "kind": "theorem", "module": "Mathlib.Data.List.Forall2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.forall₂_reverse_iff", "kind": "theorem", "module": "Mathlib.Data.List.Forall2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.rel_flatten", "kind": "theorem", "module": "Mathlib.Data.List.Forall2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.rel_flatMap", "kind": "theorem", "module": "Mathlib.Data.List.Forall2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.rel_foldl", "kind": "theorem", "module": "Mathlib.Data.List.Forall2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.rel_foldr", "kind": "theorem", "module": "Mathlib.Data.List.Forall2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.rel_filter", "kind": "theorem", "module": "Mathlib.Data.List.Forall2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.rel_filterMap", "kind": "theorem", "module": "Mathlib.Data.List.Forall2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.SublistForall₂", "kind": "inductive", "module": "Mathlib.Data.List.Forall2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sublistForall₂_iff", "kind": "theorem", "module": "Mathlib.Data.List.Forall2", "is_tactic_proof": true, "tactics": ["constructor", "induction", "nil", "obtain", "exact", "cons_right", "obtain", "exact", "obtain", "revert", "induction", "slnil", "intro", "rw", "exact", "cons", "cons₂", "intro", "obtain", "exact"], "tactic_count": 20}
{"name": "List.SublistForall₂.is_refl", "kind": "instance", "module": "Mathlib.Data.List.Forall2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.SublistForall₂.is_trans", "kind": "instance", "module": "Mathlib.Data.List.Forall2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Sublist.sublistForall₂", "kind": "theorem", "module": "Mathlib.Data.List.Forall2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.tail_sublistForall₂_self", "kind": "theorem", "module": "Mathlib.Data.List.Forall2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sublistForall₂_map_left_iff", "kind": "theorem", "module": "Mathlib.Data.List.Forall2", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.sublistForall₂_map_right_iff", "kind": "theorem", "module": "Mathlib.Data.List.Forall2", "is_tactic_proof": true, "tactics": ["simp", "constructor", "rintro", "obtain", "use", "simpa", "rintro", "use", "simp"], "tactic_count": 9}
{"name": "List.getD_eq_getElem", "kind": "theorem", "module": "Mathlib.Data.List.GetD", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "List.getD_eq_getElem?", "kind": "theorem", "module": "Mathlib.Data.List.GetD", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.getD_eq_get", "kind": "theorem", "module": "Mathlib.Data.List.GetD", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.getD_map", "kind": "theorem", "module": "Mathlib.Data.List.GetD", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.getD_eq_default", "kind": "theorem", "module": "Mathlib.Data.List.GetD", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "List.getD_reverse", "kind": "theorem", "module": "Mathlib.Data.List.GetD", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "List.decidableGetDNilNe", "kind": "definition", "module": "Mathlib.Data.List.GetD", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.getElem?_getD_singleton_default_eq", "kind": "theorem", "module": "Mathlib.Data.List.GetD", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "List.getElem?_getD_replicate_default_eq", "kind": "theorem", "module": "Mathlib.Data.List.GetD", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "List.getD_replicate", "kind": "theorem", "module": "Mathlib.Data.List.GetD", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "List.getD_append", "kind": "theorem", "module": "Mathlib.Data.List.GetD", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "List.getD_append_right", "kind": "theorem", "module": "Mathlib.Data.List.GetD", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "List.getD_surjective_iff", "kind": "theorem", "module": "Mathlib.Data.List.GetD", "is_tactic_proof": true, "tactics": ["apply", "have", "simp", "this,", "grind"], "tactic_count": 5}
{"name": "List.getD_surjective", "kind": "theorem", "module": "Mathlib.Data.List.GetD", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.getI_nil", "kind": "theorem", "module": "Mathlib.Data.List.GetD", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.getI_cons_zero", "kind": "theorem", "module": "Mathlib.Data.List.GetD", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.getI_cons_succ", "kind": "theorem", "module": "Mathlib.Data.List.GetD", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.getI_eq_getElem", "kind": "theorem", "module": "Mathlib.Data.List.GetD", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.getI_eq_default", "kind": "theorem", "module": "Mathlib.Data.List.GetD", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.getD_default_eq_getI", "kind": "theorem", "module": "Mathlib.Data.List.GetD", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.getI_append", "kind": "theorem", "module": "Mathlib.Data.List.GetD", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.getI_append_right", "kind": "theorem", "module": "Mathlib.Data.List.GetD", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.getI_eq_getElem?_getD", "kind": "theorem", "module": "Mathlib.Data.List.GetD", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.getI_eq_iget_getElem?", "kind": "theorem", "module": "Mathlib.Data.List.GetD", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.getI_zero_eq_headI", "kind": "theorem", "module": "Mathlib.Data.List.GetD", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "List.mapIdx_append_one", "kind": "theorem", "module": "Mathlib.Data.List.Indexes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.mapIdx_eq_ofFn", "kind": "theorem", "module": "Mathlib.Data.List.Indexes", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "List.mapIdxMAux'_eq_mapIdxMGo", "kind": "theorem", "module": "Mathlib.Data.List.Indexes", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "ih", "simp", "pure_bind,", "generalize", "have", "rw", "simp"], "tactic_count": 10}
{"name": "List.mapIdxM'_eq_mapIdxM", "kind": "theorem", "module": "Mathlib.Data.List.Indexes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.reverseRecOn", "kind": "definition", "module": "Mathlib.Data.List.Induction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.reverseRecOn_nil", "kind": "theorem", "module": "Mathlib.Data.List.Induction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.reverseRecOn_concat", "kind": "theorem", "module": "Mathlib.Data.List.Induction", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "List.bidirectionalRec", "kind": "definition", "module": "Mathlib.Data.List.Induction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.bidirectionalRec_nil", "kind": "theorem", "module": "Mathlib.Data.List.Induction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.bidirectionalRec_singleton", "kind": "theorem", "module": "Mathlib.Data.List.Induction", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.bidirectionalRec_cons_append", "kind": "theorem", "module": "Mathlib.Data.List.Induction", "is_tactic_proof": true, "tactics": ["conv_lhs", "cases"], "tactic_count": 2}
{"name": "List.bidirectionalRecOn", "kind": "abbrev", "module": "Mathlib.Data.List.Induction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.recNeNil", "kind": "definition", "module": "Mathlib.Data.List.Induction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.recNeNil_singleton", "kind": "theorem", "module": "Mathlib.Data.List.Induction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.recNeNil_cons", "kind": "theorem", "module": "Mathlib.Data.List.Induction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.recOnNeNil", "kind": "abbrev", "module": "Mathlib.Data.List.Induction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.twoStepInduction", "kind": "definition", "module": "Mathlib.Data.List.Induction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.twoStepInduction_nil", "kind": "theorem", "module": "Mathlib.Data.List.Induction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.twoStepInduction_singleton", "kind": "theorem", "module": "Mathlib.Data.List.Induction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.twoStepInduction_cons_cons", "kind": "theorem", "module": "Mathlib.Data.List.Induction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.IsPrefix.take", "kind": "theorem", "module": "Mathlib.Data.List.Infix", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "List.IsPrefix.drop", "kind": "theorem", "module": "Mathlib.Data.List.Infix", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.isPrefix_append_of_length", "kind": "theorem", "module": "Mathlib.Data.List.Infix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.take_isPrefix_take", "kind": "theorem", "module": "Mathlib.Data.List.Infix", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.IsPrefix.flatten", "kind": "theorem", "module": "Mathlib.Data.List.Infix", "is_tactic_proof": true, "tactics": ["rcases", "simp"], "tactic_count": 2}
{"name": "List.IsPrefix.flatMap", "kind": "theorem", "module": "Mathlib.Data.List.Infix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.IsSuffix.flatten", "kind": "theorem", "module": "Mathlib.Data.List.Infix", "is_tactic_proof": true, "tactics": ["rcases", "simp"], "tactic_count": 2}
{"name": "List.IsSuffix.flatMap", "kind": "theorem", "module": "Mathlib.Data.List.Infix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.IsInfix.flatten", "kind": "theorem", "module": "Mathlib.Data.List.Infix", "is_tactic_proof": true, "tactics": ["rcases", "simp"], "tactic_count": 2}
{"name": "List.IsInfix.flatMap", "kind": "theorem", "module": "Mathlib.Data.List.Infix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.dropSlice_sublist", "kind": "theorem", "module": "Mathlib.Data.List.Infix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.dropSlice_subset", "kind": "theorem", "module": "Mathlib.Data.List.Infix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.mem_of_mem_dropSlice", "kind": "theorem", "module": "Mathlib.Data.List.Infix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.tail_subset", "kind": "theorem", "module": "Mathlib.Data.List.Infix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.mem_of_mem_dropLast", "kind": "theorem", "module": "Mathlib.Data.List.Infix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.concat_get_prefix", "kind": "theorem", "module": "Mathlib.Data.List.Infix", "is_tactic_proof": true, "tactics": ["use", "nth_rw", "convert", "rw"], "tactic_count": 4}
{"name": "List.prefix_append_drop", "kind": "theorem", "module": "Mathlib.Data.List.Infix", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "cases", "nil", "cons", "obtain", "simpa"], "tactic_count": 8}
{"name": "List.decidableInfix", "kind": "instance", "module": "Mathlib.Data.List.Infix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.IsPrefix.reduceOption", "kind": "theorem", "module": "Mathlib.Data.List.Infix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.singleton_infix_iff", "kind": "theorem", "module": "Mathlib.Data.List.Infix", "is_tactic_proof": true, "tactics": ["rw", "congr", "simp"], "tactic_count": 3}
{"name": "List.singleton_infix_singleton_iff", "kind": "theorem", "module": "Mathlib.Data.List.Infix", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "rintro"], "tactic_count": 3}
{"name": "List.infix_singleton_iff", "kind": "theorem", "module": "Mathlib.Data.List.Infix", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "simp"], "tactic_count": 3}
{"name": "List.infix_antisymm", "kind": "theorem", "module": "Mathlib.Data.List.Infix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.instIsPartialOrderIsPrefix", "kind": "instance", "module": "Mathlib.Data.List.Infix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.instIsPartialOrderIsSuffix", "kind": "instance", "module": "Mathlib.Data.List.Infix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.instIsPartialOrderIsInfix", "kind": "instance", "module": "Mathlib.Data.List.Infix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.mem_inits", "kind": "theorem", "module": "Mathlib.Data.List.Infix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.mem_tails", "kind": "theorem", "module": "Mathlib.Data.List.Infix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.inits_cons", "kind": "theorem", "module": "Mathlib.Data.List.Infix", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.tails_cons", "kind": "theorem", "module": "Mathlib.Data.List.Infix", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.inits_append", "kind": "theorem", "module": "Mathlib.Data.List.Infix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.tails_append", "kind": "theorem", "module": "Mathlib.Data.List.Infix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.inits_eq_tails", "kind": "theorem", "module": "Mathlib.Data.List.Infix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.tails_eq_inits", "kind": "theorem", "module": "Mathlib.Data.List.Infix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.inits_reverse", "kind": "theorem", "module": "Mathlib.Data.List.Infix", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "List.tails_reverse", "kind": "theorem", "module": "Mathlib.Data.List.Infix", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "List.map_reverse_inits", "kind": "theorem", "module": "Mathlib.Data.List.Infix", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "List.map_reverse_tails", "kind": "theorem", "module": "Mathlib.Data.List.Infix", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "List.length_tails", "kind": "theorem", "module": "Mathlib.Data.List.Infix", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "List.length_inits", "kind": "theorem", "module": "Mathlib.Data.List.Infix", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.getElem_tails", "kind": "theorem", "module": "Mathlib.Data.List.Infix", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "cases", "zero", "succ"], "tactic_count": 6}
{"name": "List.get_tails", "kind": "theorem", "module": "Mathlib.Data.List.Infix", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.getElem_inits", "kind": "theorem", "module": "Mathlib.Data.List.Infix", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "cases", "zero", "succ"], "tactic_count": 6}
{"name": "List.get_inits", "kind": "theorem", "module": "Mathlib.Data.List.Infix", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.map_inits", "kind": "theorem", "module": "Mathlib.Data.List.Infix", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.map_tails", "kind": "theorem", "module": "Mathlib.Data.List.Infix", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.take_inits", "kind": "theorem", "module": "Mathlib.Data.List.Infix", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "List.insert_eq_ite", "kind": "theorem", "module": "Mathlib.Data.List.Infix", "is_tactic_proof": true, "tactics": ["simp", "rfl"], "tactic_count": 2}
{"name": "List.suffix_insert", "kind": "theorem", "module": "Mathlib.Data.List.Infix", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "simp"], "tactic_count": 3}
{"name": "List.infix_insert", "kind": "theorem", "module": "Mathlib.Data.List.Infix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sublist_insert", "kind": "theorem", "module": "Mathlib.Data.List.Infix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.subset_insert", "kind": "theorem", "module": "Mathlib.Data.List.Infix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sublist_insertIdx", "kind": "theorem", "module": "Mathlib.Data.List.InsertIdx", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "List.subset_insertIdx", "kind": "theorem", "module": "Mathlib.Data.List.InsertIdx", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.insertIdx_eraseIdx_self", "kind": "theorem", "module": "Mathlib.Data.List.InsertIdx", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.insertIdx_eraseIdx_getElem", "kind": "theorem", "module": "Mathlib.Data.List.InsertIdx", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.eq_or_mem_of_mem_insertIdx", "kind": "theorem", "module": "Mathlib.Data.List.InsertIdx", "is_tactic_proof": true, "tactics": ["cases", "inl", "rw", "exact", "inr"], "tactic_count": 5}
{"name": "List.insertIdx_subset_cons", "kind": "theorem", "module": "Mathlib.Data.List.InsertIdx", "is_tactic_proof": true, "tactics": ["intro", "simpa"], "tactic_count": 2}
{"name": "List.insertIdx_pmap", "kind": "theorem", "module": "Mathlib.Data.List.InsertIdx", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "List.map_insertIdx", "kind": "theorem", "module": "Mathlib.Data.List.InsertIdx", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "List.eraseIdx_pmap", "kind": "theorem", "module": "Mathlib.Data.List.InsertIdx", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.eraseIdx_map", "kind": "theorem", "module": "Mathlib.Data.List.InsertIdx", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "List.insertIdx_injective", "kind": "theorem", "module": "Mathlib.Data.List.InsertIdx", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.take_insertIdx_eq_take_of_le", "kind": "theorem", "module": "Mathlib.Data.List.InsertIdx", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.take_eraseIdx_eq_take_of_le", "kind": "theorem", "module": "Mathlib.Data.List.InsertIdx", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Ico", "kind": "definition", "module": "Mathlib.Data.List.Intervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Ico.zero_bot", "kind": "theorem", "module": "Mathlib.Data.List.Intervals", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.Ico.length", "kind": "theorem", "module": "Mathlib.Data.List.Intervals", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "List.Ico.pairwise_lt", "kind": "theorem", "module": "Mathlib.Data.List.Intervals", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "List.Ico.nodup", "kind": "theorem", "module": "Mathlib.Data.List.Intervals", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "List.Ico.mem", "kind": "theorem", "module": "Mathlib.Data.List.Intervals", "is_tactic_proof": true, "tactics": ["suffices", "lia"], "tactic_count": 2}
{"name": "List.Ico.eq_nil_of_le", "kind": "theorem", "module": "Mathlib.Data.List.Intervals", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.Ico.map_add", "kind": "theorem", "module": "Mathlib.Data.List.Intervals", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.Ico.map_sub", "kind": "theorem", "module": "Mathlib.Data.List.Intervals", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.Ico.self_empty", "kind": "theorem", "module": "Mathlib.Data.List.Intervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Ico.eq_empty_iff", "kind": "theorem", "module": "Mathlib.Data.List.Intervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Ico.append_consecutive", "kind": "theorem", "module": "Mathlib.Data.List.Intervals", "is_tactic_proof": true, "tactics": ["dsimp", "convert", "rw", "lia"], "tactic_count": 4}
{"name": "List.Ico.inter_consecutive", "kind": "theorem", "module": "Mathlib.Data.List.Intervals", "is_tactic_proof": true, "tactics": ["apply", "intro", "simp", "intro", "exfalso", "exact"], "tactic_count": 6}
{"name": "List.Ico.bagInter_consecutive", "kind": "theorem", "module": "Mathlib.Data.List.Intervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Ico.succ_singleton", "kind": "theorem", "module": "Mathlib.Data.List.Intervals", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "List.Ico.succ_top", "kind": "theorem", "module": "Mathlib.Data.List.Intervals", "is_tactic_proof": true, "tactics": ["rwa", "exact"], "tactic_count": 2}
{"name": "List.Ico.eq_cons", "kind": "theorem", "module": "Mathlib.Data.List.Intervals", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "List.Ico.pred_singleton", "kind": "theorem", "module": "Mathlib.Data.List.Intervals", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.Ico.isChain_succ", "kind": "theorem", "module": "Mathlib.Data.List.Intervals", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "unfold", "exact", "rw", "exact"], "tactic_count": 6}
{"name": "List.Ico.notMem_top", "kind": "theorem", "module": "Mathlib.Data.List.Intervals", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.Ico.filter_lt_of_top_le", "kind": "theorem", "module": "Mathlib.Data.List.Intervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Ico.filter_lt_of_le_bot", "kind": "theorem", "module": "Mathlib.Data.List.Intervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Ico.filter_lt_of_ge", "kind": "theorem", "module": "Mathlib.Data.List.Intervals", "is_tactic_proof": true, "tactics": ["rcases", "rw", "append_nil]", "rw"], "tactic_count": 4}
{"name": "List.Ico.filter_lt", "kind": "theorem", "module": "Mathlib.Data.List.Intervals", "is_tactic_proof": true, "tactics": ["rcases", "rw", "rw"], "tactic_count": 3}
{"name": "List.Ico.filter_le_of_le_bot", "kind": "theorem", "module": "Mathlib.Data.List.Intervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Ico.filter_le_of_top_le", "kind": "theorem", "module": "Mathlib.Data.List.Intervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Ico.filter_le_of_le", "kind": "theorem", "module": "Mathlib.Data.List.Intervals", "is_tactic_proof": true, "tactics": ["rcases", "rw", "nil_append]", "rw"], "tactic_count": 4}
{"name": "List.Ico.filter_le", "kind": "theorem", "module": "Mathlib.Data.List.Intervals", "is_tactic_proof": true, "tactics": ["rcases", "rw", "rw"], "tactic_count": 3}
{"name": "List.Ico.filter_lt_of_succ_bot", "kind": "theorem", "module": "Mathlib.Data.List.Intervals", "is_tactic_proof": true, "tactics": ["have", "simp"], "tactic_count": 2}
{"name": "List.Ico.filter_le_of_bot", "kind": "theorem", "module": "Mathlib.Data.List.Intervals", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "List.Ico.trichotomy", "kind": "theorem", "module": "Mathlib.Data.List.Intervals", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "List.length_iterate", "kind": "theorem", "module": "Mathlib.Data.List.Iterate", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.iterate_eq_nil", "kind": "theorem", "module": "Mathlib.Data.List.Iterate", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.getElem?_iterate", "kind": "theorem", "module": "Mathlib.Data.List.Iterate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.getElem_iterate", "kind": "theorem", "module": "Mathlib.Data.List.Iterate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.mem_iterate", "kind": "theorem", "module": "Mathlib.Data.List.Iterate", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.range_map_iterate", "kind": "theorem", "module": "Mathlib.Data.List.Iterate", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "List.iterate_add", "kind": "theorem", "module": "Mathlib.Data.List.Iterate", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "List.take_iterate", "kind": "theorem", "module": "Mathlib.Data.List.Iterate", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.Disjoint.symm", "kind": "theorem", "module": "Mathlib.Data.List.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.mem_union_left", "kind": "theorem", "module": "Mathlib.Data.List.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.mem_union_right", "kind": "theorem", "module": "Mathlib.Data.List.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sublist_suffix_of_union", "kind": "theorem", "module": "Mathlib.Data.List.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.suffix_union_right", "kind": "theorem", "module": "Mathlib.Data.List.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.union_sublist_append", "kind": "theorem", "module": "Mathlib.Data.List.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.forall_mem_union", "kind": "theorem", "module": "Mathlib.Data.List.Lattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.forall_mem_of_forall_mem_union_left", "kind": "theorem", "module": "Mathlib.Data.List.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.forall_mem_of_forall_mem_union_right", "kind": "theorem", "module": "Mathlib.Data.List.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Subset.union_eq_right", "kind": "theorem", "module": "Mathlib.Data.List.Lattice", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "rw"], "tactic_count": 4}
{"name": "List.inter_nil", "kind": "theorem", "module": "Mathlib.Data.List.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.inter_cons_of_mem", "kind": "theorem", "module": "Mathlib.Data.List.Lattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.inter_cons_of_notMem", "kind": "theorem", "module": "Mathlib.Data.List.Lattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.inter_cons", "kind": "theorem", "module": "Mathlib.Data.List.Lattice", "is_tactic_proof": true, "tactics": ["split_ifs"], "tactic_count": 1}
{"name": "List.inter_nil'", "kind": "theorem", "module": "Mathlib.Data.List.Lattice", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.mem_of_mem_inter_left", "kind": "theorem", "module": "Mathlib.Data.List.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.mem_of_mem_inter_right", "kind": "theorem", "module": "Mathlib.Data.List.Lattice", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "List.mem_inter_of_mem_of_mem", "kind": "theorem", "module": "Mathlib.Data.List.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.inter_subset_left", "kind": "theorem", "module": "Mathlib.Data.List.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.inter_subset_right", "kind": "theorem", "module": "Mathlib.Data.List.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.subset_inter", "kind": "theorem", "module": "Mathlib.Data.List.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.inter_eq_nil_iff_disjoint", "kind": "theorem", "module": "Mathlib.Data.List.Lattice", "is_tactic_proof": true, "tactics": ["simp", "rfl"], "tactic_count": 2}
{"name": "List.forall_mem_inter_of_forall_left", "kind": "theorem", "module": "Mathlib.Data.List.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.forall_mem_inter_of_forall_right", "kind": "theorem", "module": "Mathlib.Data.List.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.inter_reverse", "kind": "theorem", "module": "Mathlib.Data.List.Lattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.Subset.inter_eq_left", "kind": "theorem", "module": "Mathlib.Data.List.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.nil_bagInter", "kind": "theorem", "module": "Mathlib.Data.List.Lattice", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "List.bagInter_nil", "kind": "theorem", "module": "Mathlib.Data.List.Lattice", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "List.cons_bagInter_of_pos", "kind": "theorem", "module": "Mathlib.Data.List.Lattice", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "List.cons_bagInter_of_neg", "kind": "theorem", "module": "Mathlib.Data.List.Lattice", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "List.cons_bagInteger", "kind": "theorem", "module": "Mathlib.Data.List.Lattice", "is_tactic_proof": true, "tactics": ["split_ifs"], "tactic_count": 1}
{"name": "List.mem_bagInter", "kind": "theorem", "module": "Mathlib.Data.List.Lattice", "is_tactic_proof": true, "tactics": ["fun_induction"], "tactic_count": 1}
{"name": "List.count_bagInter", "kind": "theorem", "module": "Mathlib.Data.List.Lattice", "is_tactic_proof": true, "tactics": ["fun_induction"], "tactic_count": 1}
{"name": "List.bagInter_sublist_left", "kind": "theorem", "module": "Mathlib.Data.List.Lattice", "is_tactic_proof": true, "tactics": ["fun_induction"], "tactic_count": 1}
{"name": "List.bagInter_nil_iff_inter_nil", "kind": "theorem", "module": "Mathlib.Data.List.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.setOf_mem_eq_empty_iff", "kind": "theorem", "module": "Mathlib.Data.List.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.injOn_insertIdx_index_of_notMem", "kind": "theorem", "module": "Mathlib.Data.List.Lemmas", "is_tactic_proof": true, "tactics": ["intro", "induction", "nil", "cons", "simp", "simp", "cases", "rfl", "simp", "simp", "simp", "rw", "refine", "simpa", "simpa"], "tactic_count": 15}
{"name": "List.foldr_range_subset_of_range_subset", "kind": "theorem", "module": "Mathlib.Data.List.Lemmas", "is_tactic_proof": true, "tactics": ["rintro", "induction", "nil", "cons", "obtain", "obtain", "rw", "exact"], "tactic_count": 8}
{"name": "List.foldl_range_subset_of_range_subset", "kind": "theorem", "module": "Mathlib.Data.List.Lemmas", "is_tactic_proof": false, "tactics": ["change", "simp_rw", "exact"], "tactic_count": 3}
{"name": "List.foldr_range_eq_of_range_eq", "kind": "theorem", "module": "Mathlib.Data.List.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.foldl_range_eq_of_range_eq", "kind": "theorem", "module": "Mathlib.Data.List.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.mapAccumr_eq_foldr", "kind": "theorem", "module": "Mathlib.Data.List.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.mapAccumr₂_eq_foldr", "kind": "theorem", "module": "Mathlib.Data.List.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.lex_cons_iff", "kind": "theorem", "module": "Mathlib.Data.List.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.lex_nil_or_eq_nil", "kind": "theorem", "module": "Mathlib.Data.List.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.lex_singleton_iff", "kind": "theorem", "module": "Mathlib.Data.List.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Lex.isOrderConnected", "kind": "instance", "module": "Mathlib.Data.List.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Lex.isTrichotomous", "kind": "instance", "module": "Mathlib.Data.List.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Lex.asymm", "kind": "instance", "module": "Mathlib.Data.List.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Lex.decidableRel", "kind": "instance", "module": "Mathlib.Data.List.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Lex.append_right", "kind": "theorem", "module": "Mathlib.Data.List.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Lex.append_left", "kind": "theorem", "module": "Mathlib.Data.List.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Lex.imp", "kind": "theorem", "module": "Mathlib.Data.List.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Lex.to_ne", "kind": "theorem", "module": "Mathlib.Data.List.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Decidable.List.Lex.ne_iff", "kind": "theorem", "module": "Mathlib.Data.List.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Lex.ne_iff", "kind": "theorem", "module": "Mathlib.Data.List.Lex", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "List.instLinearOrder", "kind": "instance", "module": "Mathlib.Data.List.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.LE'", "kind": "instance", "module": "Mathlib.Data.List.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.lt_iff_lex_lt", "kind": "theorem", "module": "Mathlib.Data.List.Lex", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.head_le_of_lt", "kind": "theorem", "module": "Mathlib.Data.List.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.head!_le_of_lt", "kind": "theorem", "module": "Mathlib.Data.List.Lex", "is_tactic_proof": true, "tactics": ["replace", "by_cases", "simp", "rw", "exact"], "tactic_count": 5}
{"name": "List.cons_le_cons", "kind": "theorem", "module": "Mathlib.Data.List.Lex", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "_private.Mathlib.Data.List.Lookmap.0.List.lookmap.go_append", "kind": "theorem", "module": "Mathlib.Data.List.Lookmap", "is_tactic_proof": true, "tactics": ["cases", "nil", "cons", "rw", "cases", "none", "simp", "rfl", "some"], "tactic_count": 9}
{"name": "List.lookmap_nil", "kind": "theorem", "module": "Mathlib.Data.List.Lookmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.lookmap_cons_none", "kind": "theorem", "module": "Mathlib.Data.List.Lookmap", "is_tactic_proof": true, "tactics": ["simp", "rw"], "tactic_count": 2}
{"name": "List.lookmap_cons_some", "kind": "theorem", "module": "Mathlib.Data.List.Lookmap", "is_tactic_proof": true, "tactics": ["simp", "rw"], "tactic_count": 2}
{"name": "List.lookmap_cons", "kind": "theorem", "module": "Mathlib.Data.List.Lookmap", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "List.lookmap_some", "kind": "theorem", "module": "Mathlib.Data.List.Lookmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.lookmap_none", "kind": "theorem", "module": "Mathlib.Data.List.Lookmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.lookmap_congr", "kind": "theorem", "module": "Mathlib.Data.List.Lookmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.lookmap_of_forall_not", "kind": "theorem", "module": "Mathlib.Data.List.Lookmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.lookmap_map_eq", "kind": "theorem", "module": "Mathlib.Data.List.Lookmap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.lookmap_id'", "kind": "theorem", "module": "Mathlib.Data.List.Lookmap", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.length_lookmap", "kind": "theorem", "module": "Mathlib.Data.List.Lookmap", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.perm_lookmap", "kind": "theorem", "module": "Mathlib.Data.List.Lookmap", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "cases", "simpa", "simp", "swap", "rcases", "simpa", "simpa", "simpa", "rcases", "exact", "trans", "refine", "grind"], "tactic_count": 16}
{"name": "List.map₂Left'_nil_right", "kind": "theorem", "module": "Mathlib.Data.List.Map2", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "List.map₂Right'_nil_left", "kind": "theorem", "module": "Mathlib.Data.List.Map2", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "List.map₂Right'_nil_right", "kind": "theorem", "module": "Mathlib.Data.List.Map2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.map₂Right'_nil_cons", "kind": "theorem", "module": "Mathlib.Data.List.Map2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.map₂Right'_cons_cons", "kind": "theorem", "module": "Mathlib.Data.List.Map2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.nil_zipWith", "kind": "theorem", "module": "Mathlib.Data.List.Map2", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "List.zipWith_nil", "kind": "theorem", "module": "Mathlib.Data.List.Map2", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "List.zipWith_flip", "kind": "theorem", "module": "Mathlib.Data.List.Map2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.zipLeft'_nil_right", "kind": "theorem", "module": "Mathlib.Data.List.Map2", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "List.zipLeft'_nil_left", "kind": "theorem", "module": "Mathlib.Data.List.Map2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.zipLeft'_cons_nil", "kind": "theorem", "module": "Mathlib.Data.List.Map2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.zipLeft'_cons_cons", "kind": "theorem", "module": "Mathlib.Data.List.Map2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.zipRight'_nil_left", "kind": "theorem", "module": "Mathlib.Data.List.Map2", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "List.zipRight'_nil_right", "kind": "theorem", "module": "Mathlib.Data.List.Map2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.zipRight'_nil_cons", "kind": "theorem", "module": "Mathlib.Data.List.Map2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.zipRight'_cons_cons", "kind": "theorem", "module": "Mathlib.Data.List.Map2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.map₂Left_nil_right", "kind": "theorem", "module": "Mathlib.Data.List.Map2", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "List.map₂Left_eq_map₂Left'", "kind": "theorem", "module": "Mathlib.Data.List.Map2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.map₂Left_eq_zipWith", "kind": "theorem", "module": "Mathlib.Data.List.Map2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.map₂Right_nil_left", "kind": "theorem", "module": "Mathlib.Data.List.Map2", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "List.map₂Right_nil_right", "kind": "theorem", "module": "Mathlib.Data.List.Map2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.map₂Right_nil_cons", "kind": "theorem", "module": "Mathlib.Data.List.Map2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.map₂Right_cons_cons", "kind": "theorem", "module": "Mathlib.Data.List.Map2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.map₂Right_eq_map₂Right'", "kind": "theorem", "module": "Mathlib.Data.List.Map2", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.map₂Right_eq_zipWith", "kind": "theorem", "module": "Mathlib.Data.List.Map2", "is_tactic_proof": true, "tactics": ["have", "simp"], "tactic_count": 2}
{"name": "List.zipLeft_nil_right", "kind": "theorem", "module": "Mathlib.Data.List.Map2", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "List.zipLeft_nil_left", "kind": "theorem", "module": "Mathlib.Data.List.Map2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.zipLeft_cons_nil", "kind": "theorem", "module": "Mathlib.Data.List.Map2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.zipLeft_cons_cons", "kind": "theorem", "module": "Mathlib.Data.List.Map2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.zipLeft_eq_zipLeft'", "kind": "theorem", "module": "Mathlib.Data.List.Map2", "is_tactic_proof": true, "tactics": ["rw", "cases", "nil", "cons", "cases", "nil", "cons", "rw", "exact"], "tactic_count": 9}
{"name": "List.zipRight_nil_left", "kind": "theorem", "module": "Mathlib.Data.List.Map2", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "List.zipRight_nil_right", "kind": "theorem", "module": "Mathlib.Data.List.Map2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.zipRight_nil_cons", "kind": "theorem", "module": "Mathlib.Data.List.Map2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.zipRight_cons_cons", "kind": "theorem", "module": "Mathlib.Data.List.Map2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.zipRight_eq_zipRight'", "kind": "theorem", "module": "Mathlib.Data.List.Map2", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.argAux", "kind": "definition", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.foldl_argAux_eq_none", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.List.MinMax.0.List.foldl_argAux_mem", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.argAux_self", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.not_of_mem_foldl_argAux", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": ["induction", "nil", "append_singleton", "intro", "rw", "rcases", "rw", "rw", "simp_all", "rw", "dsimp", "split_ifs", "exact", "simp_all", "exact", "simp_all"], "tactic_count": 16}
{"name": "List.argmax", "kind": "definition", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.argmin", "kind": "definition", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.argmax_nil", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.argmin_nil", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.argmax_singleton", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.argmin_singleton", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.not_lt_of_mem_argmax", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.not_lt_of_mem_argmin", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.argmax_concat", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.argmin_concat", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.argmax_mem", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.argmin_mem", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.argmax_eq_none", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.argmin_eq_none", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.le_of_mem_argmax", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.le_of_mem_argmin", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.argmax_cons", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.argmin_cons", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.index_of_argmax", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.index_of_argmin", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.mem_argmax_iff", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.argmax_eq_some_iff", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.mem_argmin_iff", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.argmin_eq_some_iff", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.maximum", "kind": "definition", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.minimum", "kind": "definition", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.maximum_nil", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.minimum_nil", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.maximum_singleton", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.minimum_singleton", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.maximum_mem", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.minimum_mem", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.maximum_eq_bot", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.minimum_eq_top", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.not_maximum_lt_of_mem", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.not_lt_minimum_of_mem", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.not_maximum_lt_of_mem'", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "List.not_lt_minimum_of_mem'", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "List.maximum_concat", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": true, "tactics": ["simp", "cases", "exact", "simp"], "tactic_count": 4}
{"name": "List.le_maximum_of_mem", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.minimum_le_of_mem", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.le_maximum_of_mem'", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.minimum_le_of_mem'", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.minimum_concat", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.maximum_cons", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.minimum_cons", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.maximum_append", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "List.minimum_append", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.maximum_le_of_forall_le", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "simp", "exact"], "tactic_count": 5}
{"name": "List.le_minimum_of_forall_le", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "simp", "exact"], "tactic_count": 5}
{"name": "List.maximum_mono", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.minimum_anti", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.maximum_eq_coe_iff", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": true, "tactics": ["rw", "simp", "intro", "rw"], "tactic_count": 4}
{"name": "List.minimum_eq_coe_iff", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.coe_le_maximum_iff", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.minimum_le_coe_iff", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.maximum_ne_bot_of_ne_nil", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.minimum_ne_top_of_ne_nil", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.maximum_ne_bot_of_length_pos", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.minimum_ne_top_of_length_pos", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.maximum_of_length_pos", "kind": "definition", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.minimum_of_length_pos", "kind": "definition", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.coe_maximum_of_length_pos", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.coe_minimum_of_length_pos", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.le_maximum_of_length_pos_iff", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.minimum_of_length_pos_le_iff", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.maximum_of_length_pos_mem", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "List.minimum_of_length_pos_mem", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.le_maximum_of_length_pos_of_mem", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "List.minimum_of_length_pos_le_of_mem", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.getD_max?_eq_unbotD_maximum", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": true, "tactics": ["cases", "bot", "coe", "rw", "simp", "cases", "none", "some", "have", "rw", "rw", "exact", "all_goals"], "tactic_count": 13}
{"name": "List.getD_min?_eq_untopD_minimum", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.foldr_max_of_ne_nil", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "rw", "by_cases", "simp", "simp"], "tactic_count": 7}
{"name": "List.max_le_of_forall_le", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "List.le_max_of_le", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "obtain", "simp", "exact", "exact"], "tactic_count": 7}
{"name": "List.foldr_min_of_ne_nil", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.le_min_of_forall_le", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.min_le_of_le", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.le_max_of_le'", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "simp", "obtain", "exact", "exact"], "tactic_count": 7}
{"name": "List.min_le_of_le'", "kind": "theorem", "module": "Mathlib.Data.List.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.List.ModifyLast.0.List.modifyLast.go_concat", "kind": "theorem", "module": "Mathlib.Data.List.ModifyLast", "is_tactic_proof": true, "tactics": ["cases", "nil", "cons", "simp", "rw", "exact", "rw", "simp"], "tactic_count": 8}
{"name": "List.modifyLast_concat", "kind": "theorem", "module": "Mathlib.Data.List.ModifyLast", "is_tactic_proof": true, "tactics": ["cases", "nil", "cons", "simp", "rw", "exact", "rw", "nil_append,", "exact"], "tactic_count": 9}
{"name": "List.modifyLast_append_of_right_ne_nil", "kind": "theorem", "module": "Mathlib.Data.List.ModifyLast", "is_tactic_proof": true, "tactics": ["cases", "nil", "cons", "cases", "nil", "cons", "tl", "rw", "modifyLast_append_of_right_ne_nil", "modifyLast_append_of_right_ne_nil", "all_goals"], "tactic_count": 11}
{"name": "List.instMonad", "kind": "instance", "module": "Mathlib.Data.List.Monad", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.pure_def", "kind": "theorem", "module": "Mathlib.Data.List.Monad", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.instLawfulMonad", "kind": "instance", "module": "Mathlib.Data.List.Monad", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.instAlternativeMonad_mathlib", "kind": "instance", "module": "Mathlib.Data.List.Monad", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.instLawfulAlternative_mathlib", "kind": "instance", "module": "Mathlib.Data.List.Monad", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Nat.antidiagonal", "kind": "definition", "module": "Mathlib.Data.List.NatAntidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Nat.mem_antidiagonal", "kind": "theorem", "module": "Mathlib.Data.List.NatAntidiagonal", "is_tactic_proof": true, "tactics": ["rcases", "simp", "grind"], "tactic_count": 3}
{"name": "List.Nat.length_antidiagonal", "kind": "theorem", "module": "Mathlib.Data.List.NatAntidiagonal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.Nat.antidiagonal_zero", "kind": "theorem", "module": "Mathlib.Data.List.NatAntidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Nat.nodup_antidiagonal", "kind": "theorem", "module": "Mathlib.Data.List.NatAntidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Nat.antidiagonal_succ", "kind": "theorem", "module": "Mathlib.Data.List.NatAntidiagonal", "is_tactic_proof": false, "tactics": ["simp", "apply", "ext"], "tactic_count": 3}
{"name": "List.Nat.antidiagonal_succ'", "kind": "theorem", "module": "Mathlib.Data.List.NatAntidiagonal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.Nat.antidiagonal_succ_succ'", "kind": "theorem", "module": "Mathlib.Data.List.NatAntidiagonal", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "List.Nat.map_swap_antidiagonal", "kind": "theorem", "module": "Mathlib.Data.List.NatAntidiagonal", "is_tactic_proof": true, "tactics": ["rw", "apply", "simp"], "tactic_count": 3}
{"name": "List.Pairwise.nodup", "kind": "theorem", "module": "Mathlib.Data.List.Nodup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.rel_nodup", "kind": "theorem", "module": "Mathlib.Data.List.Nodup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Nodup.cons", "kind": "theorem", "module": "Mathlib.Data.List.Nodup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.nodup_singleton", "kind": "theorem", "module": "Mathlib.Data.List.Nodup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Nodup.of_cons", "kind": "theorem", "module": "Mathlib.Data.List.Nodup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Nodup.notMem", "kind": "theorem", "module": "Mathlib.Data.List.Nodup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.not_nodup_cons_of_mem", "kind": "theorem", "module": "Mathlib.Data.List.Nodup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.not_nodup_pair", "kind": "theorem", "module": "Mathlib.Data.List.Nodup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.nodup_iff_sublist", "kind": "theorem", "module": "Mathlib.Data.List.Nodup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.nodup_mergeSort", "kind": "theorem", "module": "Mathlib.Data.List.Nodup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.nodup_iff_injective_getElem", "kind": "theorem", "module": "Mathlib.Data.List.Nodup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.nodup_iff_injective_get", "kind": "theorem", "module": "Mathlib.Data.List.Nodup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Nodup.injective_get", "kind": "theorem", "module": "Mathlib.Data.List.Nodup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.nodup", "kind": "theorem", "module": "Mathlib.Data.List.Nodup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Nodup.get_inj_iff", "kind": "theorem", "module": "Mathlib.Data.List.Nodup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Nodup.getElem_inj_iff", "kind": "theorem", "module": "Mathlib.Data.List.Nodup", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "List.nodup_iff_getElem?_ne_getElem?", "kind": "theorem", "module": "Mathlib.Data.List.Nodup", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "List.Nodup.ne_singleton_iff", "kind": "theorem", "module": "Mathlib.Data.List.Nodup", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "specialize", "by_cases", "simpa", "rw", "rcases", "simp", "suffices", "exact"], "tactic_count": 11}
{"name": "List.not_nodup_of_get_eq_of_ne", "kind": "theorem", "module": "Mathlib.Data.List.Nodup", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "List.idxOf_getElem", "kind": "theorem", "module": "Mathlib.Data.List.Nodup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.get_idxOf", "kind": "theorem", "module": "Mathlib.Data.List.Nodup", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.nodup_iff_count_le_one", "kind": "theorem", "module": "Mathlib.Data.List.Nodup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.nodup_iff_count_eq_one", "kind": "theorem", "module": "Mathlib.Data.List.Nodup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.get_bijective_iff", "kind": "theorem", "module": "Mathlib.Data.List.Nodup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.getElem_bijective_iff", "kind": "theorem", "module": "Mathlib.Data.List.Nodup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.count_eq_one_of_mem", "kind": "theorem", "module": "Mathlib.Data.List.Nodup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Nodup.of_append_left", "kind": "theorem", "module": "Mathlib.Data.List.Nodup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Nodup.of_append_right", "kind": "theorem", "module": "Mathlib.Data.List.Nodup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.nodup_append'", "kind": "theorem", "module": "Mathlib.Data.List.Nodup", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.disjoint_of_nodup_append", "kind": "theorem", "module": "Mathlib.Data.List.Nodup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Nodup.append", "kind": "theorem", "module": "Mathlib.Data.List.Nodup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.nodup_append_comm", "kind": "theorem", "module": "Mathlib.Data.List.Nodup", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.nodup_middle", "kind": "theorem", "module": "Mathlib.Data.List.Nodup", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.Nodup.of_map", "kind": "theorem", "module": "Mathlib.Data.List.Nodup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Nodup.map_on", "kind": "theorem", "module": "Mathlib.Data.List.Nodup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.inj_on_of_nodup_map", "kind": "theorem", "module": "Mathlib.Data.List.Nodup", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "simp", "simp", "rintro", "rfl", "apply", "apply", "apply"], "tactic_count": 10}
{"name": "List.nodup_map_iff_inj_on", "kind": "theorem", "module": "Mathlib.Data.List.Nodup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Nodup.map", "kind": "theorem", "module": "Mathlib.Data.List.Nodup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.nodup_map_iff", "kind": "theorem", "module": "Mathlib.Data.List.Nodup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.nodup_attach", "kind": "theorem", "module": "Mathlib.Data.List.Nodup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Nodup.pmap", "kind": "theorem", "module": "Mathlib.Data.List.Nodup", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "List.Nodup.filter", "kind": "theorem", "module": "Mathlib.Data.List.Nodup", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "List.nodup_reverse", "kind": "theorem", "module": "Mathlib.Data.List.Nodup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.nodup_concat", "kind": "theorem", "module": "Mathlib.Data.List.Nodup", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "List.nodup_tail_reverse", "kind": "theorem", "module": "Mathlib.Data.List.Nodup", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "by_cases", "simp_all", "simp_all", "simp", "rw", "simp"], "tactic_count": 9}
{"name": "List.Nodup.erase_getElem", "kind": "theorem", "module": "Mathlib.Data.List.Nodup", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "cases", "zero", "succ"], "tactic_count": 6}
{"name": "List.Nodup.erase_get", "kind": "theorem", "module": "Mathlib.Data.List.Nodup", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.Nodup.diff", "kind": "theorem", "module": "Mathlib.Data.List.Nodup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.nodup_flatten", "kind": "theorem", "module": "Mathlib.Data.List.Nodup", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.nodup_flatMap", "kind": "theorem", "module": "Mathlib.Data.List.Nodup", "is_tactic_proof": true, "tactics": ["simp", "rw", "forall_swap.trans"], "tactic_count": 3}
{"name": "List.Nodup.product", "kind": "theorem", "module": "Mathlib.Data.List.Nodup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Nodup.sigma", "kind": "theorem", "module": "Mathlib.Data.List.Nodup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Nodup.filterMap", "kind": "theorem", "module": "Mathlib.Data.List.Nodup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Nodup.concat", "kind": "theorem", "module": "Mathlib.Data.List.Nodup", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.Nodup.insert", "kind": "theorem", "module": "Mathlib.Data.List.Nodup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Nodup.union", "kind": "theorem", "module": "Mathlib.Data.List.Nodup", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "List.Nodup.inter", "kind": "theorem", "module": "Mathlib.Data.List.Nodup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Nodup.diff_eq_filter", "kind": "theorem", "module": "Mathlib.Data.List.Nodup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Nodup.mem_diff_iff", "kind": "theorem", "module": "Mathlib.Data.List.Nodup", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.Nodup.set", "kind": "theorem", "module": "Mathlib.Data.List.Nodup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Nodup.map_update", "kind": "theorem", "module": "Mathlib.Data.List.Nodup", "is_tactic_proof": false, "tactics": ["induction", "nil", "cons", "rw", "simp", "by_cases", "subst", "simp", "simp"], "tactic_count": 9}
{"name": "List.Nodup.pairwise_of_forall_ne", "kind": "theorem", "module": "Mathlib.Data.List.Nodup", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "List.Nodup.take_eq_filter_mem", "kind": "theorem", "module": "Mathlib.Data.List.Nodup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Option.toList_nodup", "kind": "theorem", "module": "Mathlib.Data.List.Nodup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Nodup.getBijectionOfForallMemList", "kind": "definition", "module": "Mathlib.Data.List.NodupEquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Nodup.getEquiv", "kind": "definition", "module": "Mathlib.Data.List.NodupEquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Nodup.getEquivOfForallMemList", "kind": "definition", "module": "Mathlib.Data.List.NodupEquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.getEquivOfForallCountEqOne", "kind": "definition", "module": "Mathlib.Data.List.NodupEquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.SortedLT.getIso", "kind": "definition", "module": "Mathlib.Data.List.NodupEquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.SortedLT.coe_getIso_apply", "kind": "theorem", "module": "Mathlib.Data.List.NodupEquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.SortedLT.coe_getIso_symm_apply", "kind": "theorem", "module": "Mathlib.Data.List.NodupEquivFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sublist_of_orderEmbedding_getElem?_eq", "kind": "theorem", "module": "Mathlib.Data.List.NodupEquivFin", "is_tactic_proof": false, "tactics": ["induction", "nil", "cons", "have", "rw", "obtain", "let", "dsimp", "rw", "rw", "exact", "have", "intro", "rw", "simp", "rw", "exact", "rw", "apply", "rw", "exact"], "tactic_count": 21}
{"name": "List.sublist_iff_exists_orderEmbedding_getElem?_eq", "kind": "theorem", "module": "Mathlib.Data.List.NodupEquivFin", "is_tactic_proof": true, "tactics": ["constructor", "intro", "induction", "slnil", "cons", "obtain", "refine", "simpa", "cons₂", "obtain", "refine", "rintro", "rintro", "simp", "simpa", "rintro", "exact"], "tactic_count": 17}
{"name": "List.sublist_iff_exists_fin_orderEmbedding_get_eq", "kind": "theorem", "module": "Mathlib.Data.List.NodupEquivFin", "is_tactic_proof": true, "tactics": ["rw", "constructor", "rintro", "have", "intro", "specialize", "rw", "obtain", "exact", "refine", "simp", "intro", "apply", "simpa", "rintro", "refine", "intro", "dsimp", "split_ifs", "rwa", "lia", "exact", "simpa", "grind"], "tactic_count": 24}
{"name": "List.duplicate_iff_exists_distinct_get", "kind": "theorem", "module": "Mathlib.Data.List.NodupEquivFin", "is_tactic_proof": true, "tactics": ["classical", "rw", "constructor", "rintro", "refine", "rw", "rintro", "refine", "rintro", "simp", "simp", "simp", "simp", "simp", "rintro", "simpa", "simpa"], "tactic_count": 17}
{"name": "List.get_ofFn", "kind": "theorem", "module": "Mathlib.Data.List.OfFn", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.map_ofFn", "kind": "theorem", "module": "Mathlib.Data.List.OfFn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.ofFn_comp'", "kind": "theorem", "module": "Mathlib.Data.List.OfFn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.ofFn_congr", "kind": "theorem", "module": "Mathlib.Data.List.OfFn", "is_tactic_proof": true, "tactics": ["subst", "simp_rw"], "tactic_count": 2}
{"name": "List.ofFn_succ'", "kind": "theorem", "module": "Mathlib.Data.List.OfFn", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "simp"], "tactic_count": 5}
{"name": "List.ofFn_fin_append", "kind": "theorem", "module": "Mathlib.Data.List.OfFn", "is_tactic_proof": true, "tactics": ["simp_rw", "simp"], "tactic_count": 2}
{"name": "List.ofFn_mul", "kind": "theorem", "module": "Mathlib.Data.List.OfFn", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "simp_rw", "simp", "rfl"], "tactic_count": 6}
{"name": "List.ofFn_mul'", "kind": "theorem", "module": "Mathlib.Data.List.OfFn", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "List.ofFn_get", "kind": "theorem", "module": "Mathlib.Data.List.OfFn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.ofFn_getElem", "kind": "theorem", "module": "Mathlib.Data.List.OfFn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.ofFn_getElem_eq_map", "kind": "theorem", "module": "Mathlib.Data.List.OfFn", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.mem_ofFn'", "kind": "theorem", "module": "Mathlib.Data.List.OfFn", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "List.forall_mem_ofFn_iff", "kind": "theorem", "module": "Mathlib.Data.List.OfFn", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.ofFn_const", "kind": "theorem", "module": "Mathlib.Data.List.OfFn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.ofFn_fin_repeat", "kind": "theorem", "module": "Mathlib.Data.List.OfFn", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "List.pairwise_ofFn", "kind": "theorem", "module": "Mathlib.Data.List.OfFn", "is_tactic_proof": true, "tactics": ["simp", "forall_comm"], "tactic_count": 2}
{"name": "List.getLast_ofFn_succ", "kind": "theorem", "module": "Mathlib.Data.List.OfFn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.ofFn_cons", "kind": "theorem", "module": "Mathlib.Data.List.OfFn", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "List.find?_ofFn_eq_some", "kind": "theorem", "module": "Mathlib.Data.List.OfFn", "is_tactic_proof": true, "tactics": ["rw", "exact", "simpa"], "tactic_count": 3}
{"name": "List.find?_ofFn_eq_some_of_injective", "kind": "theorem", "module": "Mathlib.Data.List.OfFn", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.equivSigmaTuple", "kind": "definition", "module": "Mathlib.Data.List.OfFn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.ofFnRec", "kind": "definition", "module": "Mathlib.Data.List.OfFn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.ofFnRec_ofFn", "kind": "theorem", "module": "Mathlib.Data.List.OfFn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.exists_iff_exists_tuple", "kind": "theorem", "module": "Mathlib.Data.List.OfFn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.forall_iff_forall_tuple", "kind": "theorem", "module": "Mathlib.Data.List.OfFn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.ofFn_inj'", "kind": "theorem", "module": "Mathlib.Data.List.OfFn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.ofFn_injective", "kind": "theorem", "module": "Mathlib.Data.List.OfFn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.ofFn_inj", "kind": "theorem", "module": "Mathlib.Data.List.OfFn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.offDiag", "kind": "definition", "module": "Mathlib.Data.List.OffDiag", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.offDiag_nil", "kind": "theorem", "module": "Mathlib.Data.List.OffDiag", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.offDiag_cons_perm", "kind": "theorem", "module": "Mathlib.Data.List.OffDiag", "is_tactic_proof": true, "tactics": ["simp", "have", "conv_rhs", "simp"], "tactic_count": 4}
{"name": "List.offDiag_singleton", "kind": "theorem", "module": "Mathlib.Data.List.OffDiag", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.length_offDiag'", "kind": "theorem", "module": "Mathlib.Data.List.OffDiag", "is_tactic_proof": false, "tactics": ["have", "length_eraseIdx_of_lt", "simp"], "tactic_count": 3}
{"name": "List.length_offDiag", "kind": "theorem", "module": "Mathlib.Data.List.OffDiag", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.mem_offDiag_iff_getElem", "kind": "theorem", "module": "Mathlib.Data.List.OffDiag", "is_tactic_proof": true, "tactics": ["rcases", "simp"], "tactic_count": 2}
{"name": "List.count_offDiag_eq_mul_sub_ite", "kind": "theorem", "module": "Mathlib.Data.List.OffDiag", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "ihl", "have", "split_ifs", "rw", "simp", "have", "split_ifs", "rw", "simp", "simp", "have", "split_ifs"], "tactic_count": 15}
{"name": "List.Perm.offDiag", "kind": "theorem", "module": "Mathlib.Data.List.OffDiag", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "List.Nodup.offDiag", "kind": "theorem", "module": "Mathlib.Data.List.OffDiag", "is_tactic_proof": true, "tactics": ["letI", "rw", "rintro", "rw", "grind"], "tactic_count": 5}
{"name": "List.Nodup.of_offDiag", "kind": "theorem", "module": "Mathlib.Data.List.OffDiag", "is_tactic_proof": true, "tactics": ["letI", "simp", "intro", "specialize", "contrapose", "rw", "suffices", "calc", "rw", "exact"], "tactic_count": 10}
{"name": "List.nodup_offDiag", "kind": "theorem", "module": "Mathlib.Data.List.OffDiag", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Nodup.mem_offDiag", "kind": "theorem", "module": "Mathlib.Data.List.OffDiag", "is_tactic_proof": true, "tactics": ["rcases", "simp_rw", "constructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 7}
{"name": "List.map_prodMap_offDiag", "kind": "theorem", "module": "Mathlib.Data.List.OffDiag", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.Pairwise.forall_of_forall", "kind": "theorem", "module": "Mathlib.Data.List.Pairwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Pairwise.forall", "kind": "theorem", "module": "Mathlib.Data.List.Pairwise", "is_tactic_proof": true, "tactics": ["apply", "exact", "exact", "exact"], "tactic_count": 4}
{"name": "List.Pairwise.set_pairwise", "kind": "theorem", "module": "Mathlib.Data.List.Pairwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.pairwise_of_reflexive_of_forall_ne", "kind": "theorem", "module": "Mathlib.Data.List.Pairwise", "is_tactic_proof": true, "tactics": ["rw", "intro", "apply", "exact"], "tactic_count": 4}
{"name": "List.Pairwise.rel_head_tail", "kind": "theorem", "module": "Mathlib.Data.List.Pairwise", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "List.Pairwise.rel_head_of_rel_head_head", "kind": "theorem", "module": "Mathlib.Data.List.Pairwise", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "List.Pairwise.rel_head", "kind": "theorem", "module": "Mathlib.Data.List.Pairwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Pairwise.rel_dropLast_getLast", "kind": "theorem", "module": "Mathlib.Data.List.Pairwise", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "List.Pairwise.rel_getLast_of_rel_getLast_getLast", "kind": "theorem", "module": "Mathlib.Data.List.Pairwise", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "List.Pairwise.rel_getLast", "kind": "theorem", "module": "Mathlib.Data.List.Pairwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Pairwise.head!_le", "kind": "theorem", "module": "Mathlib.Data.List.Pairwise", "is_tactic_proof": true, "tactics": ["cases", "contradiction", "cases", "head", "tail"], "tactic_count": 5}
{"name": "List.pairwise_replicate_of_refl", "kind": "theorem", "module": "Mathlib.Data.List.Pairwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.pairwise_cons_cons_iff_of_trans", "kind": "theorem", "module": "Mathlib.Data.List.Pairwise", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "List.Pairwise.cons_cons_of_trans", "kind": "theorem", "module": "Mathlib.Data.List.Pairwise", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "List.Pairwise.rel_get_of_lt", "kind": "theorem", "module": "Mathlib.Data.List.Pairwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Pairwise.rel_get_of_le", "kind": "theorem", "module": "Mathlib.Data.List.Pairwise", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "List.Pairwise.decide", "kind": "theorem", "module": "Mathlib.Data.List.Pairwise", "is_tactic_proof": true, "tactics": ["refine"], "tactic_count": 1}
{"name": "List.Palindrome", "kind": "inductive", "module": "Mathlib.Data.List.Palindrome", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Palindrome.reverse_eq", "kind": "theorem", "module": "Mathlib.Data.List.Palindrome", "is_tactic_proof": true, "tactics": ["induction", "simpa"], "tactic_count": 2}
{"name": "List.Palindrome.of_reverse_eq", "kind": "theorem", "module": "Mathlib.Data.List.Palindrome", "is_tactic_proof": true, "tactics": ["refine", "intro", "rw", "rw", "have", "exact"], "tactic_count": 6}
{"name": "List.Palindrome.iff_reverse_eq", "kind": "theorem", "module": "Mathlib.Data.List.Palindrome", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Palindrome.append_reverse", "kind": "theorem", "module": "Mathlib.Data.List.Palindrome", "is_tactic_proof": true, "tactics": ["apply", "rw"], "tactic_count": 2}
{"name": "List.Palindrome.map", "kind": "theorem", "module": "Mathlib.Data.List.Palindrome", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Palindrome.instDecidableOfDecidableEq", "kind": "instance", "module": "Mathlib.Data.List.Palindrome", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.HasPeriod", "kind": "definition", "module": "Mathlib.Data.List.PeriodicityLemma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.hasPeriod_iff_getElem?", "kind": "theorem", "module": "Mathlib.Data.List.PeriodicityLemma", "is_tactic_proof": true, "tactics": ["constructor", "rw", "intro", "have", "have", "have", "have", "simp_all", "intro", "rw", "have", "simp", "intro", "have", "simp_all", "rw", "simp_all"], "tactic_count": 17}
{"name": "List.hasPeriod_zero", "kind": "theorem", "module": "Mathlib.Data.List.PeriodicityLemma", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.hasPeriod_of_length_le", "kind": "theorem", "module": "Mathlib.Data.List.PeriodicityLemma", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.hasPeriod_empty", "kind": "theorem", "module": "Mathlib.Data.List.PeriodicityLemma", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.HasPeriod.getElem?_mod", "kind": "theorem", "module": "Mathlib.Data.List.PeriodicityLemma", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "cases", "inl", "have", "rw", "inr", "have", "have", "rw", "have", "have", "simp", "have", "aesop"], "tactic_count": 15}
{"name": "List.hasPeriod_iff_forall_getElem?_mod", "kind": "theorem", "module": "Mathlib.Data.List.PeriodicityLemma", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "intro", "rw", "intro", "rw"], "tactic_count": 7}
{"name": "List.HasPeriod.factor", "kind": "theorem", "module": "Mathlib.Data.List.PeriodicityLemma", "is_tactic_proof": true, "tactics": ["suffices", "intro", "have", "rw", "all_goals", "have", "have", "rw", "rw", "exact", "lia", "lia", "have", "simp_all", "rw", "exact"], "tactic_count": 16}
{"name": "List.HasPeriod.infix", "kind": "theorem", "module": "Mathlib.Data.List.PeriodicityLemma", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "List.HasPeriod.drop_prefix", "kind": "theorem", "module": "Mathlib.Data.List.PeriodicityLemma", "is_tactic_proof": true, "tactics": ["rw", "simp_all"], "tactic_count": 2}
{"name": "List.HasPeriod.take_append", "kind": "theorem", "module": "Mathlib.Data.List.PeriodicityLemma", "is_tactic_proof": true, "tactics": ["rcases", "simp_all", "rcases", "simp_all", "rw", "have", "suffices", "intro", "have", "intro", "by_cases", "calc", "have", "have", "have", "calc", "calc", "have", "rw"], "tactic_count": 19}
{"name": "List.HasPeriod.drop_of_hasPeriod_add", "kind": "theorem", "module": "Mathlib.Data.List.PeriodicityLemma", "is_tactic_proof": true, "tactics": ["rw", "simp", "intro", "calc", "w"], "tactic_count": 5}
{"name": "List.HasPeriod.gcd", "kind": "theorem", "module": "Mathlib.Data.List.PeriodicityLemma", "is_tactic_proof": true, "tactics": ["rcases", "simp_all", "rcases", "simp_all", "cases", "lt", "have", "exact", "eq", "gt", "have", "have", "have", "exact", "have", "have", "exact", "have", "apply", "all_goals", "have", "have", "rw", "have", "lia", "have", "let", "convert_to", "rw", "exact", "have", "convert_to", "rw", "exact", "termination_by", "decreasing_by"], "tactic_count": 36}
{"name": "List.perm_rfl", "kind": "theorem", "module": "Mathlib.Data.List.Perm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.instSymmPerm_mathlib", "kind": "instance", "module": "Mathlib.Data.List.Perm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Perm.subset_congr_left", "kind": "theorem", "module": "Mathlib.Data.List.Perm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Perm.subset_congr_right", "kind": "theorem", "module": "Mathlib.Data.List.Perm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.set_perm_cons_eraseIdx", "kind": "theorem", "module": "Mathlib.Data.List.Perm.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply", "rw", "exact"], "tactic_count": 4}
{"name": "List.getElem_cons_eraseIdx_perm", "kind": "theorem", "module": "Mathlib.Data.List.Perm.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "List.perm_insertIdx_iff_of_le", "kind": "theorem", "module": "Mathlib.Data.List.Perm.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.perm_insertIdx_iff", "kind": "theorem", "module": "Mathlib.Data.List.Perm.Basic", "is_tactic_proof": true, "tactics": ["wlog", "rw", "cases", "inl", "rw", "cases", "inl", "inr", "apply", "intro", "rw", "grind", "grind", "inr"], "tactic_count": 14}
{"name": "List.Perm.insertIdx", "kind": "theorem", "module": "Mathlib.Data.List.Perm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.perm_eraseIdx_of_getElem?_eq", "kind": "theorem", "module": "Mathlib.Data.List.Perm.Basic", "is_tactic_proof": true, "tactics": ["cases", "inl", "rw", "cases", "intro", "rw", "rel_congr_right", "inr", "rw", "rw"], "tactic_count": 10}
{"name": "_private.Mathlib.Data.List.Perm.Basic.0.List.term_∘r_", "kind": "definition", "module": "Mathlib.Data.List.Perm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.List.Perm.Basic.0.List._aux_Mathlib_Data_List_Perm_Basic___macroRules__private_Mathlib_Data_List_Perm_Basic_0_List_term_∘r__1", "kind": "definition", "module": "Mathlib.Data.List.Perm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.List.Perm.Basic.0.List._aux_Mathlib_Data_List_Perm_Basic___unexpand_Relation_Comp_1", "kind": "definition", "module": "Mathlib.Data.List.Perm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.perm_comp_perm", "kind": "theorem", "module": "Mathlib.Data.List.Perm.Basic", "is_tactic_proof": true, "tactics": ["funext", "constructor", "exact", "exact"], "tactic_count": 4}
{"name": "List.perm_comp_forall₂", "kind": "theorem", "module": "Mathlib.Data.List.Perm.Basic", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "obtain", "rcases", "exact", "swap", "obtain", "obtain", "exact", "trans", "rcases", "rcases", "exact"], "tactic_count": 14}
{"name": "List.forall₂_comp_perm_eq_perm_comp_forall₂", "kind": "theorem", "module": "Mathlib.Data.List.Perm.Basic", "is_tactic_proof": true, "tactics": ["funext", "constructor", "intro", "rcases", "have", "rcases", "exact", "exact"], "tactic_count": 8}
{"name": "List.eq_map_comp_perm", "kind": "theorem", "module": "Mathlib.Data.List.Perm.Basic", "is_tactic_proof": true, "tactics": ["conv_rhs", "simp"], "tactic_count": 2}
{"name": "List.rel_perm_imp", "kind": "theorem", "module": "Mathlib.Data.List.Perm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.rel_perm", "kind": "theorem", "module": "Mathlib.Data.List.Perm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.count_eq_count_filter_add", "kind": "theorem", "module": "Mathlib.Data.List.Perm.Basic", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "List.Perm.foldl_eq", "kind": "theorem", "module": "Mathlib.Data.List.Perm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Perm.foldr_eq", "kind": "theorem", "module": "Mathlib.Data.List.Perm.Basic", "is_tactic_proof": true, "tactics": ["intro", "induction", "nil", "cons", "swap", "trans"], "tactic_count": 6}
{"name": "_private.Mathlib.Data.List.Perm.Basic.0.List.term_*_", "kind": "definition", "module": "Mathlib.Data.List.Perm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.List.Perm.Basic.0.List._aux_Mathlib_Data_List_Perm_Basic___macroRules__private_Mathlib_Data_List_Perm_Basic_0_List_term_*__1", "kind": "definition", "module": "Mathlib.Data.List.Perm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.List.Perm.Basic.0.List.term_<*>_", "kind": "definition", "module": "Mathlib.Data.List.Perm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.List.Perm.Basic.0.List._aux_Mathlib_Data_List_Perm_Basic___macroRules__private_Mathlib_Data_List_Perm_Basic_0_List_term_<*>__1", "kind": "definition", "module": "Mathlib.Data.List.Perm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.List.Perm.Basic.0.List._aux_Mathlib_Data_List_Perm_Basic___unexpand_List_foldl_1", "kind": "definition", "module": "Mathlib.Data.List.Perm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Perm.foldl_op_eq", "kind": "theorem", "module": "Mathlib.Data.List.Perm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Perm.foldr_op_eq", "kind": "theorem", "module": "Mathlib.Data.List.Perm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.perm_option_toList", "kind": "theorem", "module": "Mathlib.Data.List.Perm.Basic", "is_tactic_proof": true, "tactics": ["refine", "rcases", "cases", "cases", "exact"], "tactic_count": 5}
{"name": "List.perm_replicate_append_replicate", "kind": "theorem", "module": "Mathlib.Data.List.Perm.Basic", "is_tactic_proof": true, "tactics": ["rw", "suffices", "simp", "trans", "simp", "exact"], "tactic_count": 6}
{"name": "List.map_perm_map_iff", "kind": "theorem", "module": "Mathlib.Data.List.Perm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Perm.flatMap_left", "kind": "theorem", "module": "Mathlib.Data.List.Perm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Perm.flatMap", "kind": "theorem", "module": "Mathlib.Data.List.Perm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.flatMap_append_perm", "kind": "theorem", "module": "Mathlib.Data.List.Perm.Basic", "is_tactic_proof": false, "tactics": ["induction", "nil", "cons", "simp", "refine", "rw", "exact"], "tactic_count": 7}
{"name": "List.map_append_flatMap_perm", "kind": "theorem", "module": "Mathlib.Data.List.Perm.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "List.Perm.product_right", "kind": "theorem", "module": "Mathlib.Data.List.Perm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Perm.product_left", "kind": "theorem", "module": "Mathlib.Data.List.Perm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Perm.product", "kind": "theorem", "module": "Mathlib.Data.List.Perm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Perm.bagInter_right", "kind": "theorem", "module": "Mathlib.Data.List.Perm.Lattice", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.Perm.bagInter_left", "kind": "theorem", "module": "Mathlib.Data.List.Perm.Lattice", "is_tactic_proof": false, "tactics": ["induction", "nil", "cons", "by_cases", "simp", "simp"], "tactic_count": 6}
{"name": "List.Perm.bagInter", "kind": "theorem", "module": "Mathlib.Data.List.Perm.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Perm.inter_append", "kind": "theorem", "module": "Mathlib.Data.List.Perm.Lattice", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "by_cases", "have", "simp", "by_cases", "simp", "refine", "change", "rw", "solve_by_elim", "simp"], "tactic_count": 13}
{"name": "List.Perm.take_inter", "kind": "theorem", "module": "Mathlib.Data.List.Perm.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Perm.drop_inter", "kind": "theorem", "module": "Mathlib.Data.List.Perm.Lattice", "is_tactic_proof": true, "tactics": ["by_cases", "let", "have", "have", "rw", "apply", "rw", "apply", "apply", "grind"], "tactic_count": 10}
{"name": "List.Perm.dropSlice_inter", "kind": "theorem", "module": "Mathlib.Data.List.Perm.Lattice", "is_tactic_proof": true, "tactics": ["simp", "have", "have", "apply", "exact", "exact"], "tactic_count": 6}
{"name": "List.subperm_iff_count", "kind": "theorem", "module": "Mathlib.Data.List.Perm.Subperm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.subperm_iff", "kind": "theorem", "module": "Mathlib.Data.List.Perm.Subperm", "is_tactic_proof": true, "tactics": ["refine", "rintro", "obtain", "exact"], "tactic_count": 4}
{"name": "List.subperm_singleton_iff", "kind": "theorem", "module": "Mathlib.Data.List.Perm.Subperm", "is_tactic_proof": true, "tactics": ["constructor", "rw", "rintro", "rwa", "rintro", "exacts"], "tactic_count": 6}
{"name": "List.subperm_cons_self", "kind": "theorem", "module": "Mathlib.Data.List.Perm.Subperm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Nodup.subperm", "kind": "theorem", "module": "Mathlib.Data.List.Perm.Subperm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.permutationsAux2_fst", "kind": "theorem", "module": "Mathlib.Data.List.Permutation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.permutationsAux2_snd_nil", "kind": "theorem", "module": "Mathlib.Data.List.Permutation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.permutationsAux2_snd_cons", "kind": "theorem", "module": "Mathlib.Data.List.Permutation", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.permutationsAux2_append", "kind": "theorem", "module": "Mathlib.Data.List.Permutation", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.permutationsAux2_comp_append", "kind": "theorem", "module": "Mathlib.Data.List.Permutation", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "List.map_permutationsAux2'", "kind": "theorem", "module": "Mathlib.Data.List.Permutation", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "simp", "rw", "refine", "simp", "intro"], "tactic_count": 8}
{"name": "List.map_permutationsAux2", "kind": "theorem", "module": "Mathlib.Data.List.Permutation", "is_tactic_proof": true, "tactics": ["rw", "rfl", "simp"], "tactic_count": 3}
{"name": "List.permutationsAux2_snd_eq", "kind": "theorem", "module": "Mathlib.Data.List.Permutation", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.map_map_permutationsAux2", "kind": "theorem", "module": "Mathlib.Data.List.Permutation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.map_map_permutations'Aux", "kind": "theorem", "module": "Mathlib.Data.List.Permutation", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "List.permutations'Aux_eq_permutationsAux2", "kind": "theorem", "module": "Mathlib.Data.List.Permutation", "is_tactic_proof": false, "tactics": ["induction", "nil", "cons", "simp", "simp", "simp"], "tactic_count": 6}
{"name": "List.mem_permutationsAux2", "kind": "theorem", "module": "Mathlib.Data.List.Permutation", "is_tactic_proof": false, "tactics": ["induction", "nil", "cons", "rw", "constructor", "rintro", "exact", "exact", "rintro", "simp", "simp", "rcases", "exact"], "tactic_count": 13}
{"name": "List.mem_permutationsAux2'", "kind": "theorem", "module": "Mathlib.Data.List.Permutation", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.length_permutationsAux2", "kind": "theorem", "module": "Mathlib.Data.List.Permutation", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.foldr_permutationsAux2", "kind": "theorem", "module": "Mathlib.Data.List.Permutation", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "List.mem_foldr_permutationsAux2", "kind": "theorem", "module": "Mathlib.Data.List.Permutation", "is_tactic_proof": false, "tactics": ["have", "rw", "simp"], "tactic_count": 3}
{"name": "List.length_foldr_permutationsAux2", "kind": "theorem", "module": "Mathlib.Data.List.Permutation", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.length_foldr_permutationsAux2'", "kind": "theorem", "module": "Mathlib.Data.List.Permutation", "is_tactic_proof": true, "tactics": ["rw", "induction", "nil", "cons", "ih", "have", "have", "simp"], "tactic_count": 8}
{"name": "List.permutationsAux_nil", "kind": "theorem", "module": "Mathlib.Data.List.Permutation", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.permutationsAux_cons", "kind": "theorem", "module": "Mathlib.Data.List.Permutation", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.permutations_nil", "kind": "theorem", "module": "Mathlib.Data.List.Permutation", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.map_permutationsAux", "kind": "theorem", "module": "Mathlib.Data.List.Permutation", "is_tactic_proof": true, "tactics": ["refine", "introv", "simp", "append_assoc,"], "tactic_count": 4}
{"name": "List.map_permutations", "kind": "theorem", "module": "Mathlib.Data.List.Permutation", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.map_permutations'", "kind": "theorem", "module": "Mathlib.Data.List.Permutation", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "List.permutationsAux_append", "kind": "theorem", "module": "Mathlib.Data.List.Permutation", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "ih", "simp", "append_assoc]", "congr", "funext", "rw", "simp", "simp"], "tactic_count": 11}
{"name": "List.permutations_append", "kind": "theorem", "module": "Mathlib.Data.List.Permutation", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.perm_of_mem_permutationsAux", "kind": "theorem", "module": "Mathlib.Data.List.Permutation", "is_tactic_proof": true, "tactics": ["show", "refine", "introv", "rw", "rcases", "exact", "have", "simp", "rcases", "simp", "exact", "exact"], "tactic_count": 12}
{"name": "List.perm_of_mem_permutations", "kind": "theorem", "module": "Mathlib.Data.List.Permutation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.length_permutationsAux", "kind": "theorem", "module": "Mathlib.Data.List.Permutation", "is_tactic_proof": true, "tactics": ["refine", "intro", "have", "simp", "rw", "permutations,"], "tactic_count": 6}
{"name": "List.length_permutations", "kind": "theorem", "module": "Mathlib.Data.List.Permutation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.mem_permutations_of_perm_lemma", "kind": "theorem", "module": "Mathlib.Data.List.Permutation", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "List.mem_permutationsAux_of_perm", "kind": "theorem", "module": "Mathlib.Data.List.Permutation", "is_tactic_proof": false, "tactics": ["show", "refine", "intro", "rw", "rcases", "clear", "subst", "rcases", "subst", "have", "rcases", "exact", "exact", "exact"], "tactic_count": 14}
{"name": "List.mem_permutations", "kind": "theorem", "module": "Mathlib.Data.List.Permutation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.perm_permutations'Aux_comm", "kind": "theorem", "module": "Mathlib.Data.List.Permutation", "is_tactic_proof": false, "tactics": ["induction", "nil", "cons", "simp", "apply", "have", "map", "map", "intro", "simp", "change", "refine", "rw", "exact", "refine", "rw", "exact"], "tactic_count": 17}
{"name": "List.Perm.permutations'", "kind": "theorem", "module": "Mathlib.Data.List.Permutation", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "swap", "dsimp", "rw", "apply", "intro", "apply", "trans"], "tactic_count": 10}
{"name": "List.permutations_perm_permutations'", "kind": "theorem", "module": "Mathlib.Data.List.Permutation", "is_tactic_proof": true, "tactics": ["obtain", "induction", "zero", "succ", "refine", "rw", "have", "simp", "refine", "rw", "refine", "refine", "congr", "funext", "rw"], "tactic_count": 15}
{"name": "List.mem_permutations'", "kind": "theorem", "module": "Mathlib.Data.List.Permutation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Perm.permutations", "kind": "theorem", "module": "Mathlib.Data.List.Permutation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.perm_permutations_iff", "kind": "theorem", "module": "Mathlib.Data.List.Permutation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.perm_permutations'_iff", "kind": "theorem", "module": "Mathlib.Data.List.Permutation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.getElem_permutations'Aux", "kind": "theorem", "module": "Mathlib.Data.List.Permutation", "is_tactic_proof": true, "tactics": ["induction", "nil", "simp", "simp", "cons", "cases", "simp", "simpa"], "tactic_count": 8}
{"name": "List.get_permutations'Aux", "kind": "theorem", "module": "Mathlib.Data.List.Permutation", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "_private.Mathlib.Data.List.Permutation.0.List.DecEq_eq", "kind": "theorem", "module": "Mathlib.Data.List.Permutation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.count_permutations'Aux_self", "kind": "theorem", "module": "Mathlib.Data.List.Permutation", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "rw", "by_cases", "subst", "simpa", "rw", "simp", "count_eq_zero_of_not_mem,"], "tactic_count": 10}
{"name": "List.length_permutations'Aux", "kind": "theorem", "module": "Mathlib.Data.List.Permutation", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "List.injective_permutations'Aux", "kind": "theorem", "module": "Mathlib.Data.List.Permutation", "is_tactic_proof": true, "tactics": ["intro", "apply", "dsimp", "have", "rw", "simp"], "tactic_count": 6}
{"name": "List.nodup_permutations'Aux_of_notMem", "kind": "theorem", "module": "Mathlib.Data.List.Permutation", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "simp", "simp", "refine", "rw", "exact", "simp"], "tactic_count": 9}
{"name": "List.nodup_permutations'Aux_iff", "kind": "theorem", "module": "Mathlib.Data.List.Permutation", "is_tactic_proof": true, "tactics": ["refine", "obtain", "rw", "apply", "have", "have", "rw", "rw", "have", "rw", "exact"], "tactic_count": 11}
{"name": "List.nodup_permutations", "kind": "theorem", "module": "Mathlib.Data.List.Permutation", "is_tactic_proof": true, "tactics": ["rw", "induction", "nil", "rw", "rw", "constructor", "intro", "rw", "rw", "exact", "refine", "rw", "rintro", "obtain", "obtain", "rw", "have", "simp", "rw", "have", "simp", "have", "simp", "rcases", "suffices", "rw", "exact", "simp", "rw", "exact", "suffices", "rw", "exact"], "tactic_count": 33}
{"name": "List.permutations_take_two", "kind": "theorem", "module": "Mathlib.Data.List.Permutation", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.nodup_permutations_iff", "kind": "theorem", "module": "Mathlib.Data.List.Permutation", "is_tactic_proof": true, "tactics": ["refine", "contrapose", "rw", "intro", "rw", "obtain", "rw", "use", "rw", "exact", "take_sublist"], "tactic_count": 11}
{"name": "List.Pi.nil", "kind": "definition", "module": "Mathlib.Data.List.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Pi.head", "kind": "definition", "module": "Mathlib.Data.List.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Pi.tail", "kind": "definition", "module": "Mathlib.Data.List.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Pi.cons", "kind": "definition", "module": "Mathlib.Data.List.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Pi.cons_def", "kind": "theorem", "module": "Mathlib.Data.List.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Pi.cons_coe", "kind": "theorem", "module": "Mathlib.Data.List.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Pi.cons_eta", "kind": "theorem", "module": "Mathlib.Data.List.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Pi.cons_map", "kind": "theorem", "module": "Mathlib.Data.List.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Pi.forall_rel_cons_ext", "kind": "theorem", "module": "Mathlib.Data.List.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.pi", "kind": "definition", "module": "Mathlib.Data.List.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.pi_nil", "kind": "theorem", "module": "Mathlib.Data.List.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.pi_cons", "kind": "theorem", "module": "Mathlib.Data.List.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.pi_coe", "kind": "theorem", "module": "Mathlib.Data.List.Pi", "is_tactic_proof": true, "tactics": ["induction", "nil", "simp", "ext", "simp", "cons"], "tactic_count": 6}
{"name": "List.mem_pi", "kind": "theorem", "module": "Mathlib.Data.List.Pi", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Prime.dvd_prod_iff", "kind": "theorem", "module": "Mathlib.Data.List.Prime", "is_tactic_proof": true, "tactics": ["constructor", "intro", "induction", "nil", "rw", "exact", "cons", "rw", "rcases", "exact", "obtain", "exact", "exact"], "tactic_count": 13}
{"name": "Prime.not_dvd_prod", "kind": "theorem", "module": "Mathlib.Data.List.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_list_primes_of_dvd_prod", "kind": "theorem", "module": "Mathlib.Data.List.Prime", "is_tactic_proof": true, "tactics": ["obtain", "rwa"], "tactic_count": 2}
{"name": "perm_of_prod_eq_prod", "kind": "theorem", "module": "Mathlib.Data.List.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.nil_product", "kind": "theorem", "module": "Mathlib.Data.List.ProdSigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.product_cons", "kind": "theorem", "module": "Mathlib.Data.List.ProdSigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.product_nil", "kind": "theorem", "module": "Mathlib.Data.List.ProdSigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.mem_product", "kind": "theorem", "module": "Mathlib.Data.List.ProdSigma", "is_tactic_proof": true, "tactics": ["simp_all"], "tactic_count": 1}
{"name": "List.length_product", "kind": "theorem", "module": "Mathlib.Data.List.ProdSigma", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "simp"], "tactic_count": 4}
{"name": "List.nil_sigma", "kind": "theorem", "module": "Mathlib.Data.List.ProdSigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sigma_cons", "kind": "theorem", "module": "Mathlib.Data.List.ProdSigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sigma_nil", "kind": "theorem", "module": "Mathlib.Data.List.ProdSigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.mem_sigma", "kind": "theorem", "module": "Mathlib.Data.List.ProdSigma", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.mem_map_swap", "kind": "theorem", "module": "Mathlib.Data.List.ProdSigma", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.getElem_range'_1", "kind": "theorem", "module": "Mathlib.Data.List.Range", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.isChain_range", "kind": "theorem", "module": "Mathlib.Data.List.Range", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "simp", "cases", "zero", "succ", "n", "simp", "isChain_append_cons_cons,", "rw"], "tactic_count": 11}
{"name": "List.isChain_range_succ", "kind": "theorem", "module": "Mathlib.Data.List.Range", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.isChain_cons_range_succ", "kind": "theorem", "module": "Mathlib.Data.List.Range", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "List.ranges", "kind": "definition", "module": "Mathlib.Data.List.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.ranges_disjoint", "kind": "theorem", "module": "Mathlib.Data.List.Range", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "simp", "constructor", "intro", "obtain", "intro", "rw", "rw", "lia", "rw", "apply", "intro", "apply", "exact"], "tactic_count": 16}
{"name": "List.ranges_length", "kind": "theorem", "module": "Mathlib.Data.List.Range", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "simp", "conv_rhs", "apply", "intro", "simp"], "tactic_count": 8}
{"name": "List.reduceOption_cons_of_some", "kind": "theorem", "module": "Mathlib.Data.List.ReduceOption", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.reduceOption_cons_of_none", "kind": "theorem", "module": "Mathlib.Data.List.ReduceOption", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.reduceOption_nil", "kind": "theorem", "module": "Mathlib.Data.List.ReduceOption", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.reduceOption_map", "kind": "theorem", "module": "Mathlib.Data.List.ReduceOption", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "List.reduceOption_append", "kind": "theorem", "module": "Mathlib.Data.List.ReduceOption", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.reduceOption_replicate_none", "kind": "theorem", "module": "Mathlib.Data.List.ReduceOption", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "List.reduceOption_eq_nil_iff", "kind": "theorem", "module": "Mathlib.Data.List.ReduceOption", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "constructor", "intro", "exact", "grind"], "tactic_count": 6}
{"name": "List.reduceOption_eq_singleton_iff", "kind": "theorem", "module": "Mathlib.Data.List.ReduceOption", "is_tactic_proof": true, "tactics": ["dsimp", "constructor", "intro", "rw", "obtain", "rw", "apply", "apply", "rw", "use", "intro", "simp"], "tactic_count": 12}
{"name": "List.reduceOption_eq_append_iff", "kind": "theorem", "module": "Mathlib.Data.List.ReduceOption", "is_tactic_proof": true, "tactics": ["dsimp", "exact"], "tactic_count": 2}
{"name": "List.reduceOption_eq_concat_iff", "kind": "theorem", "module": "Mathlib.Data.List.ReduceOption", "is_tactic_proof": true, "tactics": ["rw", "constructor", "intro", "rw", "obtain", "rw", "obtain", "use", "simp_rw", "intro", "rw"], "tactic_count": 11}
{"name": "List.reduceOption_length_eq", "kind": "theorem", "module": "Mathlib.Data.List.ReduceOption", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "List.length_eq_reduceOption_length_add_filter_none", "kind": "theorem", "module": "Mathlib.Data.List.ReduceOption", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "List.reduceOption_length_le", "kind": "theorem", "module": "Mathlib.Data.List.ReduceOption", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "List.reduceOption_length_eq_iff", "kind": "theorem", "module": "Mathlib.Data.List.ReduceOption", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.reduceOption_length_lt_iff", "kind": "theorem", "module": "Mathlib.Data.List.ReduceOption", "is_tactic_proof": true, "tactics": ["rw", "induction", "simp", "grind"], "tactic_count": 4}
{"name": "List.reduceOption_singleton", "kind": "theorem", "module": "Mathlib.Data.List.ReduceOption", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "List.reduceOption_concat", "kind": "theorem", "module": "Mathlib.Data.List.ReduceOption", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "simp", "cases"], "tactic_count": 5}
{"name": "List.reduceOption_concat_of_some", "kind": "theorem", "module": "Mathlib.Data.List.ReduceOption", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.reduceOption_mem_iff", "kind": "theorem", "module": "Mathlib.Data.List.ReduceOption", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.reduceOption_getElem?_iff", "kind": "theorem", "module": "Mathlib.Data.List.ReduceOption", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.rotate_mod", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.rotate_nil", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.rotate_zero", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.rotate'_nil", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.rotate'_zero", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "List.rotate'_cons_succ", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.length_rotate'", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.rotate'_eq_drop_append_take", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.rotate'_rotate'", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.rotate'_length", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.rotate'_length_mul", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.rotate'_mod", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.rotate_eq_rotate'", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.rotate_cons_succ", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.mem_rotate", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.length_rotate", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.rotate_replicate", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.rotate_eq_drop_append_take", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.rotate_eq_drop_append_take_mod", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rw"], "tactic_count": 3}
{"name": "List.rotate_append_length_eq", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": true, "tactics": ["rw", "induction", "simp", "simp_all"], "tactic_count": 4}
{"name": "List.rotate_rotate", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.rotate_length", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.rotate_length_mul", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.rotate_perm", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": true, "tactics": ["rw", "induction", "zero", "succ", "rcases", "simp", "rw", "exact"], "tactic_count": 8}
{"name": "List.nodup_rotate", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.rotate_eq_nil_iff", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rcases", "simp", "simp"], "tactic_count": 6}
{"name": "List.nil_eq_rotate_iff", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.rotate_singleton", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.zipWith_rotate_distrib", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": false, "tactics": ["rw", "rw"], "tactic_count": 2}
{"name": "List.zipWith_rotate_one", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.getElem?_rotate", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": true, "tactics": ["rw", "rcases", "rw", "rw", "rw", "have", "rw", "congr", "rw", "have", "have", "rw", "exact", "conv_rhs", "lia", "rwa"], "tactic_count": 16}
{"name": "List.getElem_rotate", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "List.get_rotate", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.head?_rotate", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.get_rotate_one", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.getElem_eq_getElem_rotate", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp", "rw", "exacts"], "tactic_count": 5}
{"name": "List.get_eq_get_rotate", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "List.rotate_eq_self_iff_eq_replicate", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.rotate_one_eq_self_iff_eq_replicate", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.rotate_injective", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": true, "tactics": ["rintro", "have", "rw", "obtain", "rw"], "tactic_count": 5}
{"name": "List.rotate_eq_rotate", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.rotate_eq_iff", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": true, "tactics": ["rw", "rcases", "rw", "rcases", "simp", "rw", "exact"], "tactic_count": 7}
{"name": "List.rotate_eq_singleton_iff", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.singleton_eq_rotate_iff", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.reverse_rotate", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": true, "tactics": ["rw", "induction", "zero", "succ", "rcases", "simp", "rw", "simp"], "tactic_count": 8}
{"name": "List.rotate_reverse", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "rw", "let", "rcases", "simp_all", "rcases", "simp", "rw", "exact", "exact"], "tactic_count": 11}
{"name": "List.map_rotate", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rcases", "simp", "simp"], "tactic_count": 6}
{"name": "List.Nodup.rotate_congr", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "List.Nodup.rotate_congr_iff", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simp", "refine", "rw"], "tactic_count": 5}
{"name": "List.Nodup.rotate_eq_self_iff", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.IsRotated", "kind": "definition", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.term_~r_", "kind": "definition", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List._aux_Mathlib_Data_List_Rotate___macroRules_List_term_~r__1", "kind": "definition", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List._aux_Mathlib_Data_List_Rotate___unexpand_List_IsRotated_1", "kind": "definition", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.IsRotated.refl", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.IsRotated.symm", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": true, "tactics": ["obtain", "rcases", "exists", "use", "rw", "exact"], "tactic_count": 6}
{"name": "List.isRotated_comm", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.IsRotated.forall", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.IsRotated.trans", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.IsRotated.eqv", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.IsRotated.setoid", "kind": "definition", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.IsRotated.perm", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.IsRotated.nodup_iff", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.IsRotated.mem_iff", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.isRotated_nil_iff", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.isRotated_nil_iff'", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.isRotated_singleton_iff", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.isRotated_singleton_iff'", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.isRotated_concat", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.isRotated_append", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.IsRotated.reverse", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "List.isRotated_reverse_comm_iff", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": true, "tactics": ["constructor", "intro", "simpa"], "tactic_count": 3}
{"name": "List.isRotated_reverse_iff", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.isRotated_iff_mod", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": true, "tactics": ["refine", "obtain", "rcases", "simp", "refine", "refine", "simp"], "tactic_count": 7}
{"name": "List.isRotated_iff_mem_map_range", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "List.IsRotated.map", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": true, "tactics": ["obtain", "rw", "use"], "tactic_count": 3}
{"name": "List.IsRotated.cons_append_singleton", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "List.IsRotated.cons_getLast_dropLast", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": true, "tactics": ["induction", "nil", "append_singleton", "simp", "apply", "apply"], "tactic_count": 6}
{"name": "List.IsRotated.dropLast_tail", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.cyclicPermutations", "kind": "definition", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.cyclicPermutations_nil", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.cyclicPermutations_cons", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.cyclicPermutations_of_ne_nil", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "List.length_cyclicPermutations_cons", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.length_cyclicPermutations_of_ne_nil", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.cyclicPermutations_ne_nil", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.getElem_cyclicPermutations", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": true, "tactics": ["cases", "nil", "cons", "l", "simp", "rw"], "tactic_count": 6}
{"name": "List.get_cyclicPermutations", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.head_cyclicPermutations", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "List.head?_cyclicPermutations", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.cyclicPermutations_injective", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.cyclicPermutations_inj", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.length_mem_cyclicPermutations", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": true, "tactics": ["obtain", "simp"], "tactic_count": 2}
{"name": "List.mem_cyclicPermutations_self", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "List.cyclicPermutations_rotate", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": false, "tactics": ["have", "cases", "simp", "rw", "refine", "rw", "cases"], "tactic_count": 7}
{"name": "List.mem_cyclicPermutations_iff", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": true, "tactics": ["constructor", "simp_rw", "rintro", "exact", "rintro", "rw", "apply"], "tactic_count": 7}
{"name": "List.cyclicPermutations_eq_nil_iff", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.cyclicPermutations_eq_singleton_iff", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Nodup.cyclicPermutations", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rw", "rintro", "simp", "simpa"], "tactic_count": 6}
{"name": "List.IsRotated.cyclicPermutations", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "List.isRotated_cyclicPermutations_iff", "kind": "theorem", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.isRotatedDecidable", "kind": "instance", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.instDecidableR_mathlib", "kind": "instance", "module": "Mathlib.Data.List.Rotate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.mem_sections", "kind": "theorem", "module": "Mathlib.Data.List.Sections", "is_tactic_proof": true, "tactics": ["refine", "induction", "cases", "exact", "simp", "rcases", "simp", "induction", "nil", "simp", "exact"], "tactic_count": 11}
{"name": "List.mem_sections_length", "kind": "theorem", "module": "Mathlib.Data.List.Sections", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.rel_sections", "kind": "theorem", "module": "Mathlib.Data.List.Sections", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Shortlex", "kind": "definition", "module": "Mathlib.Data.List.Shortlex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Shortlex.of_length_lt", "kind": "theorem", "module": "Mathlib.Data.List.Shortlex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Shortlex.of_lex", "kind": "theorem", "module": "Mathlib.Data.List.Shortlex", "is_tactic_proof": true, "tactics": ["apply", "right", "exact"], "tactic_count": 3}
{"name": "List.shortlex_def", "kind": "theorem", "module": "Mathlib.Data.List.Shortlex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.shortlex_iff_lex", "kind": "theorem", "module": "Mathlib.Data.List.Shortlex", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.shortlex_cons_iff", "kind": "theorem", "module": "Mathlib.Data.List.Shortlex", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.not_shortlex_nil_right", "kind": "theorem", "module": "Mathlib.Data.List.Shortlex", "is_tactic_proof": true, "tactics": ["rw", "rintro", "simp", "exact"], "tactic_count": 4}
{"name": "List.shortlex_nil_or_eq_nil", "kind": "theorem", "module": "Mathlib.Data.List.Shortlex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.shortlex_singleton_iff", "kind": "theorem", "module": "Mathlib.Data.List.Shortlex", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.Shortlex.isTrichotomous", "kind": "instance", "module": "Mathlib.Data.List.Shortlex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Shortlex.asymm", "kind": "instance", "module": "Mathlib.Data.List.Shortlex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Shortlex.append_right", "kind": "theorem", "module": "Mathlib.Data.List.Shortlex", "is_tactic_proof": true, "tactics": ["rcases", "apply", "rw", "lia", "cases", "nil", "rw", "exact", "cons", "apply", "rw", "lia"], "tactic_count": 12}
{"name": "List.Shortlex.append_left", "kind": "theorem", "module": "Mathlib.Data.List.Shortlex", "is_tactic_proof": true, "tactics": ["rcases", "apply", "rw", "lia", "cases", "nil", "rw", "exact", "cons", "apply", "simp", "exact", "exact"], "tactic_count": 13}
{"name": "_private.Mathlib.Data.List.Shortlex.0.Acc.shortlex", "kind": "theorem", "module": "Mathlib.Data.List.Shortlex", "is_tactic_proof": true, "tactics": ["induction", "intro", "induction", "intro", "refine", "rcases", "exact", "cases", "nil", "simp", "refine", "apply", "rw", "exact", "simp", "refine", "apply", "rw", "exact"], "tactic_count": 19}
{"name": "List.Shortlex.wf", "kind": "theorem", "module": "Mathlib.Data.List.Shortlex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.keys", "kind": "definition", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.keys_nil", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.keys_cons", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.keys_append", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.mem_keys_of_mem", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.exists_of_mem_keys", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": true, "tactics": ["have", "grind"], "tactic_count": 2}
{"name": "List.mem_keys", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.notMem_keys", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "List.ne_key", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "List.NodupKeys", "kind": "definition", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.nodupKeys_iff_pairwise", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.NodupKeys.pairwise_ne", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.nodupKeys_nil", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.nodupKeys_cons", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.nodupKeys_middle", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": true, "tactics": ["simp_all"], "tactic_count": 1}
{"name": "List.notMem_keys_of_nodupKeys_cons", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "List.nodupKeys_of_nodupKeys_cons", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.NodupKeys.eq_of_fst_eq", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.NodupKeys.eq_of_mk_mem", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "List.nodupKeys_singleton", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.NodupKeys.sublist", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.NodupKeys.nodup", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.perm_nodupKeys", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.nodupKeys_flatten", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp"], "tactic_count": 3}
{"name": "List.nodup_zipIdx_map_snd", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.mem_ext", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "List.dlookup", "kind": "definition", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.dlookup_nil", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.dlookup_cons_eq", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.dlookup_cons_ne", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.dlookup_isSome", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "List.dlookup_eq_none", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.of_mem_dlookup", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "List.mem_dlookup", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": true, "tactics": ["obtain", "cases", "exact"], "tactic_count": 3}
{"name": "List.map_dlookup_eq_find", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "List.mem_dlookup_iff", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.perm_dlookup", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": true, "tactics": ["have", "ext"], "tactic_count": 2}
{"name": "List.lookup_ext", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "List.dlookup_map", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "have", "by_cases"], "tactic_count": 5}
{"name": "List.dlookup_map₁", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": true, "tactics": ["have", "grind"], "tactic_count": 2}
{"name": "List.dlookup_map₂", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.NodupKeys.map₁", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": true, "tactics": ["classical", "induction", "nil", "cons", "have", "grind"], "tactic_count": 6}
{"name": "List.map₂_keys", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.NodupKeys.map₂", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": true, "tactics": ["simp_all"], "tactic_count": 1}
{"name": "List.dlookup_append", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "List.sublist_dlookup", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "List.lookupAll", "kind": "definition", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.lookupAll_nil", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.lookupAll_cons_eq", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.lookupAll_cons_ne", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.lookupAll_eq_nil", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.head?_lookupAll", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.mem_lookupAll", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.lookupAll_sublist", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.lookupAll_length_le_one", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": true, "tactics": ["have", "rw", "rwa"], "tactic_count": 3}
{"name": "List.lookupAll_eq_dlookup", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": true, "tactics": ["rw", "have", "rcases", "exact"], "tactic_count": 4}
{"name": "List.lookupAll_nodup", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": true, "tactics": [], "tactic_count": 0}
{"name": "List.perm_lookupAll", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": true, "tactics": ["have", "simp"], "tactic_count": 2}
{"name": "List.kreplace", "kind": "definition", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.kreplace_of_forall_not", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.kreplace_self", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": true, "tactics": ["refine", "rintro", "dsimp", "split_ifs", "subst", "simp", "simp_all", "simp_all", "rfl", "simp"], "tactic_count": 10}
{"name": "List.keys_kreplace", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.kreplace_nodupKeys", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.Perm.kreplace", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.kerase", "kind": "definition", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.kerase_nil", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.kerase_cons_eq", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.kerase_cons_ne", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.kerase_of_notMem_keys", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "List.kerase_sublist", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.kerase_keys_subset", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.mem_keys_of_mem_keys_kerase", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.exists_of_kerase", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "by_cases", "subst", "exact", "simp", "rcases", "exact", "rcases", "exact"], "tactic_count": 11}
{"name": "List.mem_keys_kerase_of_ne", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.keys_kerase", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": true, "tactics": ["rw", "congr"], "tactic_count": 2}
{"name": "List.kerase_kerase", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": true, "tactics": ["by_cases", "subst", "induction", "nil", "cons", "by_cases", "subst", "simp", "by_cases", "subst", "simp", "simp"], "tactic_count": 12}
{"name": "List.NodupKeys.kerase", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Perm.kerase", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": true, "tactics": ["apply", "apply", "intros"], "tactic_count": 3}
{"name": "List.notMem_keys_kerase", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "simp", "by_cases", "subst", "simp", "simp"], "tactic_count": 8}
{"name": "List.dlookup_kerase", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.dlookup_kerase_ne", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "obtain", "by_cases", "substs", "cases", "subst", "simp", "subst", "simp", "simp"], "tactic_count": 12}
{"name": "List.kerase_append_left", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.kerase_append_right", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.kerase_comm", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sizeOf_kerase", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": true, "tactics": ["simp", "induction", "nil", "cons"], "tactic_count": 4}
{"name": "List.kinsert", "kind": "definition", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.kinsert_def", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.mem_keys_kinsert", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "List.kinsert_nodupKeys", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Perm.kinsert", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.dlookup_kinsert", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.dlookup_kinsert_ne", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.kextract", "kind": "definition", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.kextract_eq_dlookup_kerase", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.dedupKeys", "kind": "definition", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.dedupKeys_cons", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.nodupKeys_dedupKeys", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": true, "tactics": ["dsimp", "generalize", "have", "rw", "apply", "clear", "induction", "nil", "cons", "cases", "simp", "constructor", "simp", "apply", "exact"], "tactic_count": 15}
{"name": "List.dlookup_dedupKeys", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "obtain", "by_cases", "subst", "rw", "rw", "exact"], "tactic_count": 9}
{"name": "List.sizeOf_dedupKeys", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": true, "tactics": ["simp", "induction", "nil", "cons", "simp", "trans", "apply", "assumption"], "tactic_count": 8}
{"name": "List.kunion", "kind": "definition", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.nil_kunion", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.kunion_nil", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.kunion_cons", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.mem_keys_kunion", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "List.kunion_kerase", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.NodupKeys.kunion", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "simp", "simp"], "tactic_count": 5}
{"name": "List.Perm.kunion_right", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "swap", "trans"], "tactic_count": 5}
{"name": "List.Perm.kunion_left", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Perm.kunion", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.dlookup_kunion_left", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "simp", "rcases", "simp", "rw", "by_cases", "subst", "simp", "simp"], "tactic_count": 11}
{"name": "List.dlookup_kunion_right", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "List.mem_dlookup_kunion", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "obtain", "by_cases", "subst", "simp", "simp"], "tactic_count": 8}
{"name": "List.dlookup_kunion_eq_some", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.mem_dlookup_kunion_middle", "kind": "theorem", "module": "Mathlib.Data.List.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.List.Sort.0.List.term_≼_", "kind": "definition", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.List.Sort.0.List._aux_Mathlib_Data_List_Sort___macroRules__private_Mathlib_Data_List_Sort_0_List_term_≼__1", "kind": "definition", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.List.Sort.0.List.term_≼__1", "kind": "definition", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.List.Sort.0.List._aux_Mathlib_Data_List_Sort___macroRules__private_Mathlib_Data_List_Sort_0_List_term_≼__1_1", "kind": "definition", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.orderedInsert", "kind": "definition", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.orderedInsert_nil", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.orderedInsert_cons", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.orderedInsert_cons_of_le", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.orderedInsert_of_not_le", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.insertionSort", "kind": "definition", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.insertionSort_nil", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.insertionSort_cons", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List._example", "kind": "example", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.orderedInsert_length", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.orderedInsert_eq_take_drop", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.insertionSort_cons_eq_take_drop", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.mem_orderedInsert", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.map_orderedInsert", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.perm_orderedInsert", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.orderedInsert_count", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "List.perm_insertionSort", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.mem_insertionSort", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.length_insertionSort", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.insertionSort_cons_of_forall_rel", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": true, "tactics": ["rw", "cases", "nil", "cons", "rw", "apply", "rw", "exact"], "tactic_count": 8}
{"name": "List.map_insertionSort", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "simp_rw", "simp_rw", "rw", "simpa", "simpa"], "tactic_count": 8}
{"name": "List.Pairwise.insertionSort_eq", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.erase_orderedInsert", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.erase_orderedInsert_of_notMem", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.orderedInsert_erase", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.sublist_orderedInsert", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.cons_sublist_orderedInsert", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.Sublist.orderedInsert_sublist", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": true, "tactics": ["cases", "nil", "cons", "cases", "nil", "cons", "unfold", "cases", "exact", "have", "simp", "exact", "have", "exact", "have", "rw", "exact", "simp_all", "exact"], "tactic_count": 19}
{"name": "List.Pairwise.orderedInsert", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.pairwise_insertionSort", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sublist_insertionSort", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "cases", "cons", "cons₂", "obtain", "exact"], "tactic_count": 8}
{"name": "List.pair_sublist_insertionSort", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sublist_insertionSort'", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": true, "tactics": ["classical", "obtain", "induction", "nil", "cons", "cases", "cons", "cons₂", "specialize", "have", "have", "exact"], "tactic_count": 12}
{"name": "List.pair_sublist_insertionSort'", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List._example", "kind": "example", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.Perm.eq_of_pairwise'", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sublist_of_subperm_of_pairwise", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": true, "tactics": ["let", "exact"], "tactic_count": 2}
{"name": "List.Subset.antisymm_of_pairwise", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Pairwise.eq_of_mem_iff", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Pairwise.merge", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": true, "tactics": ["simpa", "pairwise_merge"], "tactic_count": 2}
{"name": "List.pairwise_mergeSort'", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "List.mergeSort_eq_self", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.mergeSort_eq_insertionSort", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.SortedLE", "kind": "definition", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.SortedGE", "kind": "definition", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.SortedLT", "kind": "definition", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.SortedGT", "kind": "definition", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sortedLE_iff_monotone_get", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sortedGE_iff_antitone_get", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sortedLT_iff_strictMono_get", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sortedGT_iff_strictAnti_get", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sortedLE_iff_pairwise", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": true, "tactics": ["simp", "grind"], "tactic_count": 2}
{"name": "List.sortedGE_iff_pairwise", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": true, "tactics": ["simp", "grind"], "tactic_count": 2}
{"name": "List.sortedLT_iff_pairwise", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": true, "tactics": ["simp", "grind"], "tactic_count": 2}
{"name": "List.sortedGT_iff_pairwise", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": true, "tactics": ["simp", "grind"], "tactic_count": 2}
{"name": "List.sortedLE_iff_isChain", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sortedGE_iff_isChain", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sortedLT_iff_isChain", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sortedGT_iff_isChain", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.decidableSortedLE", "kind": "instance", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.decidableSortedGE", "kind": "instance", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.decidableSortedLT", "kind": "instance", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.decidableSortedGT", "kind": "instance", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sortedLE_iff_getElem_le_getElem_of_le", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sortedGE_iff_getElem_ge_getElem_of_le", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sortedLT_iff_getElem_lt_getElem_of_lt", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sortedGT_iff_getElem_gt_getElem_of_lt", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.SortedLT.sortedLE", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.SortedGT.sortedGE", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.SortedLT.nodup", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.SortedGT.nodup", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sortedLE_replicate", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sortedLT_finRange", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sortedLT_range", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sorted_le_range", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sortedLT_range'", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sorted_le_range'", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sortedLE_range'", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sortedLE_ofFn_iff", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.sortedGE_ofFn_iff", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.sortedLT_ofFn_iff", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.sortedGT_ofFn_iff", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.sortedLE_reverse", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "List.sortedGE_reverse", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "List.sortedLT_reverse", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "List.sortedGT_reverse", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "List.sortedLE_map_ofDual", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "List.sortedGE_map_ofDual", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "List.sortedLT_map_ofDual", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "List.sortedGT_map_ofDual", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "List.sortedLE_map_toDual", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "List.sortedGE_map_toDual", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "List.sortedLT_map_toDual", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "List.sortedGT_map_toDual", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "List.SortedLE.sortedLT_of_nodup", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.SortedGE.sortedGT_of_nodup", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sortedLT_iff_nodup_and_sortedLE", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sortedGT_iff_nodup_and_sortedGE", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Perm.eq_of_sortedLE", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Perm.eq_of_sortedGE", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Subset.antisymm_of_sortedLT", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Subset.antisymm_of_sortedGT", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.SortedLT.eq_of_mem_iff", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.SortedGT.eq_of_mem_iff", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Perm.eq_reverse_of_sortedLE_of_sortedGE", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.SortedLT.eq_reverse_of_mem_iff_of_sortedGT", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.SortedGT.eq_reverse_of_mem_iff_of_sortedLT", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sublist_of_subperm_of_sortedLE", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sublist_of_subperm_of_sortedGE", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sortedLE_mergeSort", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sortedGE_mergeSort", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sortedLE_insertionSort", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sortedGE_insertionSort", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.SortedLT.getElem_le_getElem_iff", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.SortedGT.getElem_le_getElem_iff", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.SortedLT.getElem_lt_getElem_iff", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.SortedGT.getElem_lt_getElem_iff", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelEmbedding.pairwise_listMap", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RelEmbedding.pairwise_swap_listMap", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RelIso.pairwise_listMap", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelIso.pairwise_swap_listMap", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderEmbedding.sortedLE_listMap", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "OrderEmbedding.sortedLT_listMap", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "OrderEmbedding.sortedGE_listMap", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "OrderEmbedding.sortedGT_listMap", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "OrderIso.sortedLT_listMap", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.sortedGT_listMap", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.sortedLE_listMap", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.sortedGE_listMap", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.sortedLT_listMap", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.sortedGT_listMap", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictAnti.sortedLE_listMap", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": true, "tactics": ["have", "grind"], "tactic_count": 2}
{"name": "StrictAnti.sortedGE_listMap", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": true, "tactics": ["have", "grind"], "tactic_count": 2}
{"name": "StrictAnti.sortedLT_listMap", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": true, "tactics": ["have", "grind"], "tactic_count": 2}
{"name": "StrictAnti.sortedGT_listMap", "kind": "theorem", "module": "Mathlib.Data.List.Sort", "is_tactic_proof": true, "tactics": ["have", "grind"], "tactic_count": 2}
{"name": "List.splitBy_nil", "kind": "theorem", "module": "Mathlib.Data.List.SplitBy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.List.SplitBy.0.List.splitByLoop_eq_append", "kind": "theorem", "module": "Mathlib.Data.List.SplitBy", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "simp_rw", "split", "conv_rhs", "simp"], "tactic_count": 7}
{"name": "_private.Mathlib.Data.List.SplitBy.0.List.flatten_splitByLoop", "kind": "theorem", "module": "Mathlib.Data.List.SplitBy", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "rw", "split"], "tactic_count": 5}
{"name": "List.flatten_splitBy", "kind": "theorem", "module": "Mathlib.Data.List.SplitBy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.List.SplitBy.0.List.nil_notMem_splitByLoop", "kind": "theorem", "module": "Mathlib.Data.List.SplitBy", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "rw", "split", "exact", "rw", "simpa"], "tactic_count": 8}
{"name": "List.nil_notMem_splitBy", "kind": "theorem", "module": "Mathlib.Data.List.SplitBy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.ne_nil_of_mem_splitBy", "kind": "theorem", "module": "Mathlib.Data.List.SplitBy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.List.SplitBy.0.List.isChain_of_mem_splitByLoop", "kind": "theorem", "module": "Mathlib.Data.List.SplitBy", "is_tactic_proof": true, "tactics": ["induction", "nil", "rw", "obtain", "cases", "apply", "rw", "exact", "cons", "simp", "split", "apply", "grind", "rw", "obtain", "apply", "rw", "exact", "grind"], "tactic_count": 19}
{"name": "List.isChain_of_mem_splitBy", "kind": "theorem", "module": "Mathlib.Data.List.SplitBy", "is_tactic_proof": true, "tactics": ["a"], "tactic_count": 1}
{"name": "_private.Mathlib.Data.List.SplitBy.0.List.isChain_getLast_head_splitByLoop", "kind": "theorem", "module": "Mathlib.Data.List.SplitBy", "is_tactic_proof": true, "tactics": ["induction", "nil", "rw", "apply", "simpa", "cons", "rw", "split", "apply", "intro", "obtain", "refine", "rwa", "apply", "simpa", "rw", "apply", "simpa"], "tactic_count": 18}
{"name": "List.isChain_getLast_head_splitBy", "kind": "theorem", "module": "Mathlib.Data.List.SplitBy", "is_tactic_proof": true, "tactics": ["cases", "nil", "cons", "apply", "rintro"], "tactic_count": 5}
{"name": "List.splitLengths", "kind": "definition", "module": "Mathlib.Data.List.SplitLengths", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.length_splitLengths", "kind": "theorem", "module": "Mathlib.Data.List.SplitLengths", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.splitLengths_nil", "kind": "theorem", "module": "Mathlib.Data.List.SplitLengths", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.splitLengths_cons", "kind": "theorem", "module": "Mathlib.Data.List.SplitLengths", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.take_splitLength", "kind": "theorem", "module": "Mathlib.Data.List.SplitLengths", "is_tactic_proof": true, "tactics": ["induction", "simp", "cases", "simp", "simp"], "tactic_count": 5}
{"name": "List.length_splitLengths_getElem_le", "kind": "theorem", "module": "Mathlib.Data.List.SplitLengths", "is_tactic_proof": true, "tactics": ["induction", "simp", "simp", "cases", "simp", "simp"], "tactic_count": 6}
{"name": "List.flatten_splitLengths", "kind": "theorem", "module": "Mathlib.Data.List.SplitLengths", "is_tactic_proof": true, "tactics": ["induction", "simp_all", "simp", "rw", "simpa"], "tactic_count": 5}
{"name": "List.map_splitLengths_length", "kind": "theorem", "module": "Mathlib.Data.List.SplitLengths", "is_tactic_proof": true, "tactics": ["induction", "simp", "simp", "simp", "rw", "simp", "simp"], "tactic_count": 7}
{"name": "List.length_splitLengths_getElem_eq", "kind": "theorem", "module": "Mathlib.Data.List.SplitLengths", "is_tactic_proof": true, "tactics": ["rw", "simp", "conv_rhs", "rw", "simp", "rw"], "tactic_count": 6}
{"name": "List.splitLengths_length_getElem", "kind": "theorem", "module": "Mathlib.Data.List.SplitLengths", "is_tactic_proof": true, "tactics": ["have", "rw", "simp", "simpa"], "tactic_count": 4}
{"name": "List.length_mem_splitLengths", "kind": "theorem", "module": "Mathlib.Data.List.SplitLengths", "is_tactic_proof": true, "tactics": ["rw", "intro", "have", "have", "lia"], "tactic_count": 5}
{"name": "List.splitOn_nil", "kind": "theorem", "module": "Mathlib.Data.List.SplitOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.splitOnP_nil", "kind": "theorem", "module": "Mathlib.Data.List.SplitOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.splitOnP.go_ne_nil", "kind": "theorem", "module": "Mathlib.Data.List.SplitOn", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.splitOnP.go_acc", "kind": "theorem", "module": "Mathlib.Data.List.SplitOn", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "simp", "simp", "rw", "congr"], "tactic_count": 7}
{"name": "List.splitOnP_ne_nil", "kind": "theorem", "module": "Mathlib.Data.List.SplitOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.splitOnP_cons", "kind": "theorem", "module": "Mathlib.Data.List.SplitOn", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.splitOnP_spec", "kind": "theorem", "module": "Mathlib.Data.List.SplitOn", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "rw", "by_cases", "rw", "exact", "rw", "flatten_zipWith", "exact", "flatten", "a", "cases", "nil", "cons", "cases", "nil", "cons"], "tactic_count": 18}
{"name": "List.splitOnP_eq_single", "kind": "theorem", "module": "Mathlib.Data.List.SplitOn", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "simp", "ih"], "tactic_count": 5}
{"name": "List.splitOnP_append_cons", "kind": "theorem", "module": "Mathlib.Data.List.SplitOn", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "obtain", "by_cases"], "tactic_count": 5}
{"name": "List.splitOnP_first", "kind": "theorem", "module": "Mathlib.Data.List.SplitOn", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.intercalate_splitOn", "kind": "theorem", "module": "Mathlib.Data.List.SplitOn", "is_tactic_proof": true, "tactics": ["simp", "induction", "nil", "cons", "rcases", "rw", "rw", "split_ifs", "rw", "subst", "simp", "cases"], "tactic_count": 12}
{"name": "List.splitOn_intercalate", "kind": "theorem", "module": "Mathlib.Data.List.SplitOn", "is_tactic_proof": true, "tactics": ["simp", "induction", "nil", "cons", "cases", "suffices", "exact", "simp", "specialize", "grind", "grind", "simp", "have", "rw"], "tactic_count": 14}
{"name": "List.sublists'_nil", "kind": "theorem", "module": "Mathlib.Data.List.Sublists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sublists'_singleton", "kind": "theorem", "module": "Mathlib.Data.List.Sublists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sublists'Aux", "kind": "definition", "module": "Mathlib.Data.List.Sublists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sublists'Aux_eq_array_foldl", "kind": "theorem", "module": "Mathlib.Data.List.Sublists", "is_tactic_proof": true, "tactics": ["intro", "rw", "have", "r₂.toArray)", "simpa"], "tactic_count": 5}
{"name": "List.sublists'_eq_sublists'Aux", "kind": "theorem", "module": "Mathlib.Data.List.Sublists", "is_tactic_proof": true, "tactics": ["simp", "rw", "intros"], "tactic_count": 3}
{"name": "List.sublists'Aux_eq_map", "kind": "theorem", "module": "Mathlib.Data.List.Sublists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sublists'_cons", "kind": "theorem", "module": "Mathlib.Data.List.Sublists", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.mem_sublists'", "kind": "theorem", "module": "Mathlib.Data.List.Sublists", "is_tactic_proof": false, "tactics": ["induction", "nil", "simp", "exact", "cons", "simp", "constructor", "rcases", "exact", "exact", "obtain", "exact", "exact"], "tactic_count": 13}
{"name": "List.length_sublists'", "kind": "theorem", "module": "Mathlib.Data.List.Sublists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sublists_nil", "kind": "theorem", "module": "Mathlib.Data.List.Sublists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sublists_singleton", "kind": "theorem", "module": "Mathlib.Data.List.Sublists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sublistsAux", "kind": "definition", "module": "Mathlib.Data.List.Sublists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sublistsAux_eq_array_foldl", "kind": "theorem", "module": "Mathlib.Data.List.Sublists", "is_tactic_proof": true, "tactics": ["funext", "simp", "have", "foldl_hom", "simpa"], "tactic_count": 5}
{"name": "List.sublistsAux_eq_flatMap", "kind": "theorem", "module": "Mathlib.Data.List.Sublists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sublists_append", "kind": "theorem", "module": "Mathlib.Data.List.Sublists", "is_tactic_proof": true, "tactics": ["simp", "induction", "nil", "cons", "rw", "simp"], "tactic_count": 6}
{"name": "List.sublists_cons", "kind": "theorem", "module": "Mathlib.Data.List.Sublists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sublists_concat", "kind": "theorem", "module": "Mathlib.Data.List.Sublists", "is_tactic_proof": true, "tactics": ["rw", "map_id"], "tactic_count": 2}
{"name": "List.sublists_reverse", "kind": "theorem", "module": "Mathlib.Data.List.Sublists", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "simp", "map_map,"], "tactic_count": 5}
{"name": "List.sublists_eq_sublists'", "kind": "theorem", "module": "Mathlib.Data.List.Sublists", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.sublists'_reverse", "kind": "theorem", "module": "Mathlib.Data.List.Sublists", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.sublists'_eq_sublists", "kind": "theorem", "module": "Mathlib.Data.List.Sublists", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.mem_sublists", "kind": "theorem", "module": "Mathlib.Data.List.Sublists", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.length_sublists", "kind": "theorem", "module": "Mathlib.Data.List.Sublists", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.map_pure_sublist_sublists", "kind": "theorem", "module": "Mathlib.Data.List.Sublists", "is_tactic_proof": true, "tactics": ["induction", "simp", "exact", "singleton_sublist.2"], "tactic_count": 4}
{"name": "List.sublistsLenAux", "kind": "definition", "module": "Mathlib.Data.List.Sublists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sublistsLen", "kind": "definition", "module": "Mathlib.Data.List.Sublists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sublistsLenAux_append", "kind": "theorem", "module": "Mathlib.Data.List.Sublists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sublistsLenAux_eq", "kind": "theorem", "module": "Mathlib.Data.List.Sublists", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.sublistsLenAux_zero", "kind": "theorem", "module": "Mathlib.Data.List.Sublists", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "List.sublistsLen_zero", "kind": "theorem", "module": "Mathlib.Data.List.Sublists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sublistsLen_succ_nil", "kind": "theorem", "module": "Mathlib.Data.List.Sublists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sublistsLen_succ_cons", "kind": "theorem", "module": "Mathlib.Data.List.Sublists", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.sublistsLen_one", "kind": "theorem", "module": "Mathlib.Data.List.Sublists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.length_sublistsLen", "kind": "theorem", "module": "Mathlib.Data.List.Sublists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sublistsLen_sublist_sublists'", "kind": "theorem", "module": "Mathlib.Data.List.Sublists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sublistsLen_sublist_of_sublist", "kind": "theorem", "module": "Mathlib.Data.List.Sublists", "is_tactic_proof": false, "tactics": ["induction", "zero", "succ", "induction", "slnil", "cons", "refine", "rw", "apply", "cons₂"], "tactic_count": 10}
{"name": "List.length_of_sublistsLen", "kind": "theorem", "module": "Mathlib.Data.List.Sublists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.mem_sublistsLen_self", "kind": "theorem", "module": "Mathlib.Data.List.Sublists", "is_tactic_proof": true, "tactics": ["induction", "slnil", "rcases", "simp", "rw", "exact", "cons₂", "rw", "exact"], "tactic_count": 9}
{"name": "List.mem_sublistsLen", "kind": "theorem", "module": "Mathlib.Data.List.Sublists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sublistsLen_of_length_lt", "kind": "theorem", "module": "Mathlib.Data.List.Sublists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sublistsLen_length", "kind": "theorem", "module": "Mathlib.Data.List.Sublists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Pairwise.sublists'", "kind": "theorem", "module": "Mathlib.Data.List.Sublists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.pairwise_sublists", "kind": "theorem", "module": "Mathlib.Data.List.Sublists", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "List.nodup_sublists", "kind": "theorem", "module": "Mathlib.Data.List.Sublists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.nodup_sublists'", "kind": "theorem", "module": "Mathlib.Data.List.Sublists", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.nodup_sublistsLen", "kind": "theorem", "module": "Mathlib.Data.List.Sublists", "is_tactic_proof": false, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "List.sublists_map", "kind": "theorem", "module": "Mathlib.Data.List.Sublists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sublists'_map", "kind": "theorem", "module": "Mathlib.Data.List.Sublists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sublists_perm_sublists'", "kind": "theorem", "module": "Mathlib.Data.List.Sublists", "is_tactic_proof": true, "tactics": ["rw", "apply", "apply", "simp", "exact", "exact"], "tactic_count": 6}
{"name": "List.sublists_cons_perm_append", "kind": "theorem", "module": "Mathlib.Data.List.Sublists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.revzip_sublists", "kind": "theorem", "module": "Mathlib.Data.List.Sublists", "is_tactic_proof": true, "tactics": ["rw", "induction", "nil", "have", "simp", "append_singleton", "ih", "rw", "simp", "rcases", "rw", "exact", "rw", "apply", "rw", "exact"], "tactic_count": 16}
{"name": "List.revzip_sublists'", "kind": "theorem", "module": "Mathlib.Data.List.Sublists", "is_tactic_proof": true, "tactics": ["rw", "induction", "nil", "simp_all", "cons", "rw", "simp]", "rcases", "exact", "exact"], "tactic_count": 10}
{"name": "List.range_bind_sublistsLen_perm", "kind": "theorem", "module": "Mathlib.Data.List.Sublists", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "l_ih", "simp_rw", "refine", "simp_rw", "rw", "refine", "rw", "range_succ_eq_map]", "exact"], "tactic_count": 12}
{"name": "List.sym2", "kind": "definition", "module": "Mathlib.Data.List.Sym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sym2_map", "kind": "theorem", "module": "Mathlib.Data.List.Sym", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "List.mem_sym2_cons_iff", "kind": "theorem", "module": "Mathlib.Data.List.Sym", "is_tactic_proof": true, "tactics": ["simp", "simp"], "tactic_count": 2}
{"name": "List.sym2_eq_nil_iff", "kind": "theorem", "module": "Mathlib.Data.List.Sym", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "List.left_mem_of_mk_mem_sym2", "kind": "theorem", "module": "Mathlib.Data.List.Sym", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "rw", "rw", "obtain", "rw", "exact", "rw", "obtain", "exact"], "tactic_count": 11}
{"name": "List.right_mem_of_mk_mem_sym2", "kind": "theorem", "module": "Mathlib.Data.List.Sym", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "List.mk_mem_sym2", "kind": "theorem", "module": "Mathlib.Data.List.Sym", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "rw", "grind"], "tactic_count": 5}
{"name": "List.mk_mem_sym2_iff", "kind": "theorem", "module": "Mathlib.Data.List.Sym", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "rintro", "exact"], "tactic_count": 5}
{"name": "List.mem_sym2_iff", "kind": "theorem", "module": "Mathlib.Data.List.Sym", "is_tactic_proof": true, "tactics": ["refine", "simp"], "tactic_count": 2}
{"name": "List.setOf_mem_sym2", "kind": "theorem", "module": "Mathlib.Data.List.Sym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Nodup.sym2", "kind": "theorem", "module": "Mathlib.Data.List.Sym", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "rw", "specialize", "rw", "refine", "intro", "simp", "obtain", "intro", "simp", "intro", "simp", "rintro"], "tactic_count": 15}
{"name": "List.map_mk_sublist_sym2", "kind": "theorem", "module": "Mathlib.Data.List.Sym", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "simp", "cases", "head", "tail", "refine", "rw", "refine", "rw", "exact"], "tactic_count": 12}
{"name": "List.map_mk_disjoint_sym2", "kind": "theorem", "module": "Mathlib.Data.List.Sym", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "simp", "rw", "refine", "refine", "simp", "simp_rw", "intro", "simp_rw", "rintro", "exact", "exact", "simp", "simp", "intro", "rw", "obtain", "obtain", "simp", "obtain", "exact", "exact"], "tactic_count": 24}
{"name": "List.dedup_sym2", "kind": "theorem", "module": "Mathlib.Data.List.Sym", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "simp", "obtain", "rw", "refine", "rw", "exact", "rw", "exact", "exact", "simp"], "tactic_count": 13}
{"name": "List.Perm.sym2", "kind": "theorem", "module": "Mathlib.Data.List.Sym", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "simp", "exact", "swap", "simp", "conv", "rw", "refine", "simp", "simp", "trans"], "tactic_count": 13}
{"name": "List.Sublist.sym2", "kind": "theorem", "module": "Mathlib.Data.List.Sym", "is_tactic_proof": true, "tactics": ["induction", "slnil", "cons", "simp", "exact", "cons₂", "simp", "exact"], "tactic_count": 8}
{"name": "List.Subperm.sym2", "kind": "theorem", "module": "Mathlib.Data.List.Sym", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "List.length_sym2", "kind": "theorem", "module": "Mathlib.Data.List.Sym", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "rw"], "tactic_count": 4}
{"name": "List.sym", "kind": "definition", "module": "Mathlib.Data.List.Sym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sym_one_eq", "kind": "theorem", "module": "Mathlib.Data.List.Sym", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "List.sym2_eq_sym_two", "kind": "theorem", "module": "Mathlib.Data.List.Sym", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "rw", "rfl"], "tactic_count": 5}
{"name": "List.sym_map", "kind": "theorem", "module": "Mathlib.Data.List.Sym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Sublist.sym", "kind": "theorem", "module": "Mathlib.Data.List.Sym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.sym_sublist_sym_cons", "kind": "theorem", "module": "Mathlib.Data.List.Sym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.mem_of_mem_of_mem_sym", "kind": "theorem", "module": "Mathlib.Data.List.Sym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.first_mem_of_cons_mem_sym", "kind": "theorem", "module": "Mathlib.Data.List.Sym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Nodup.sym", "kind": "theorem", "module": "Mathlib.Data.List.Sym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.length_sym", "kind": "theorem", "module": "Mathlib.Data.List.Sym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.TFAE", "kind": "definition", "module": "Mathlib.Data.List.TFAE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.tfae_nil", "kind": "theorem", "module": "Mathlib.Data.List.TFAE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.tfae_singleton", "kind": "theorem", "module": "Mathlib.Data.List.TFAE", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.tfae_cons_of_mem", "kind": "theorem", "module": "Mathlib.Data.List.TFAE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.tfae_cons_cons", "kind": "theorem", "module": "Mathlib.Data.List.TFAE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.tfae_cons_self", "kind": "theorem", "module": "Mathlib.Data.List.TFAE", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.tfae_of_forall", "kind": "theorem", "module": "Mathlib.Data.List.TFAE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.tfae_of_cycle", "kind": "theorem", "module": "Mathlib.Data.List.TFAE", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "simp", "rcases", "have", "exact"], "tactic_count": 7}
{"name": "List.forall_tfae", "kind": "theorem", "module": "Mathlib.Data.List.TFAE", "is_tactic_proof": true, "tactics": ["simp", "intro", "exact"], "tactic_count": 3}
{"name": "List.exists_tfae", "kind": "theorem", "module": "Mathlib.Data.List.TFAE", "is_tactic_proof": true, "tactics": ["simp", "intro", "exact"], "tactic_count": 3}
{"name": "List.tfae_not_iff", "kind": "theorem", "module": "Mathlib.Data.List.TFAE", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "List.take_one_drop_eq_of_lt_length", "kind": "theorem", "module": "Mathlib.Data.List.TakeDrop", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "List.take_eq_self_iff", "kind": "theorem", "module": "Mathlib.Data.List.TakeDrop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.take_self_eq_iff", "kind": "theorem", "module": "Mathlib.Data.List.TakeDrop", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.take_eq_left_iff", "kind": "theorem", "module": "Mathlib.Data.List.TakeDrop", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.left_eq_take_iff", "kind": "theorem", "module": "Mathlib.Data.List.TakeDrop", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.drop_take_append_drop", "kind": "theorem", "module": "Mathlib.Data.List.TakeDrop", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.drop_take_append_drop'", "kind": "theorem", "module": "Mathlib.Data.List.TakeDrop", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.take_concat_get'", "kind": "theorem", "module": "Mathlib.Data.List.TakeDrop", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.cons_getElem_drop_succ", "kind": "theorem", "module": "Mathlib.Data.List.TakeDrop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.cons_get_drop_succ", "kind": "theorem", "module": "Mathlib.Data.List.TakeDrop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.drop_length_sub_one", "kind": "theorem", "module": "Mathlib.Data.List.TakeDrop", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "by_cases", "simp_all", "rw", "simp"], "tactic_count": 7}
{"name": "List.takeI_length", "kind": "theorem", "module": "Mathlib.Data.List.TakeDrop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.takeI_nil", "kind": "theorem", "module": "Mathlib.Data.List.TakeDrop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.takeI_eq_take", "kind": "theorem", "module": "Mathlib.Data.List.TakeDrop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.takeI_left", "kind": "theorem", "module": "Mathlib.Data.List.TakeDrop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.takeI_left'", "kind": "theorem", "module": "Mathlib.Data.List.TakeDrop", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.takeD_length", "kind": "theorem", "module": "Mathlib.Data.List.TakeDrop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.takeD_eq_take", "kind": "theorem", "module": "Mathlib.Data.List.TakeDrop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.takeD_left", "kind": "theorem", "module": "Mathlib.Data.List.TakeDrop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.takeD_left'", "kind": "theorem", "module": "Mathlib.Data.List.TakeDrop", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "_private.Mathlib.Data.List.TakeDrop.0.List.span.loop_eq_take_drop", "kind": "theorem", "module": "Mathlib.Data.List.TakeDrop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.span_eq_takeWhile_dropWhile", "kind": "theorem", "module": "Mathlib.Data.List.TakeDrop", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "List.dropSlice_eq", "kind": "theorem", "module": "Mathlib.Data.List.TakeDrop", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.length_dropSlice", "kind": "theorem", "module": "Mathlib.Data.List.TakeDrop", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.length_dropSlice_lt", "kind": "theorem", "module": "Mathlib.Data.List.TakeDrop", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "List.dropWhile_get_zero_not", "kind": "theorem", "module": "Mathlib.Data.List.TakeWhile", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "simp", "by_cases", "simp_all", "apply", "simp_all", "simp"], "tactic_count": 9}
{"name": "List.length_dropWhile_le", "kind": "theorem", "module": "Mathlib.Data.List.TakeWhile", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "simp", "split", "lia", "simp"], "tactic_count": 7}
{"name": "List.dropWhile_eq_nil_iff", "kind": "theorem", "module": "Mathlib.Data.List.TakeWhile", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "List.dropWhile_eq_self_iff", "kind": "theorem", "module": "Mathlib.Data.List.TakeWhile", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rw", "by_cases", "simp", "intro", "replace", "have", "simp", "lia", "simp"], "tactic_count": 11}
{"name": "List.takeWhile_eq_self_iff", "kind": "theorem", "module": "Mathlib.Data.List.TakeWhile", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "List.takeWhile_eq_nil_iff", "kind": "theorem", "module": "Mathlib.Data.List.TakeWhile", "is_tactic_proof": true, "tactics": ["induction", "nil", "simp", "intro", "simp", "cons"], "tactic_count": 6}
{"name": "List.mem_takeWhile_imp", "kind": "theorem", "module": "Mathlib.Data.List.TakeWhile", "is_tactic_proof": true, "tactics": ["induction", "cons", "cases", "simp", "rw", "rcases", "exact", "exact"], "tactic_count": 8}
{"name": "List.takeWhile_takeWhile", "kind": "theorem", "module": "Mathlib.Data.List.TakeWhile", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "List.takeWhile_idem", "kind": "theorem", "module": "Mathlib.Data.List.TakeWhile", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "List.find?_eq_head?_dropWhile_not", "kind": "theorem", "module": "Mathlib.Data.List.TakeWhile", "is_tactic_proof": true, "tactics": ["induction", "simp", "set", "rcases", "have", "rw", "exact", "simpa", "rw", "simp", "simpa"], "tactic_count": 11}
{"name": "List.find?_not_eq_head?_dropWhile", "kind": "theorem", "module": "Mathlib.Data.List.TakeWhile", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "List.find?_eq_head_dropWhile_not", "kind": "theorem", "module": "Mathlib.Data.List.TakeWhile", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.find?_not_eq_head_dropWhile", "kind": "theorem", "module": "Mathlib.Data.List.TakeWhile", "is_tactic_proof": true, "tactics": ["convert", "simp", "simpa"], "tactic_count": 3}
{"name": "List.toFinsupp", "kind": "definition", "module": "Mathlib.Data.List.ToFinsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.coe_toFinsupp", "kind": "theorem", "module": "Mathlib.Data.List.ToFinsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.toFinsupp_apply", "kind": "theorem", "module": "Mathlib.Data.List.ToFinsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.toFinsupp_support", "kind": "theorem", "module": "Mathlib.Data.List.ToFinsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.toFinsupp_apply_lt", "kind": "theorem", "module": "Mathlib.Data.List.ToFinsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.toFinsupp_apply_fin", "kind": "theorem", "module": "Mathlib.Data.List.ToFinsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.toFinsupp_apply_le", "kind": "theorem", "module": "Mathlib.Data.List.ToFinsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.toFinsupp_nil", "kind": "theorem", "module": "Mathlib.Data.List.ToFinsupp", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "List.toFinsupp_singleton", "kind": "theorem", "module": "Mathlib.Data.List.ToFinsupp", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "List.toFinsupp_append", "kind": "theorem", "module": "Mathlib.Data.List.ToFinsupp", "is_tactic_proof": true, "tactics": ["ext", "simp", "cases", "inl", "rw", "rintro", "lia", "inr", "rcases", "rw", "exact"], "tactic_count": 11}
{"name": "List.toFinsupp_cons_eq_single_add_embDomain", "kind": "theorem", "module": "Mathlib.Data.List.ToFinsupp", "is_tactic_proof": true, "tactics": ["classical", "convert", "exact", "ext", "exact"], "tactic_count": 5}
{"name": "List.toFinsupp_concat_eq_toFinsupp_add_single", "kind": "theorem", "module": "Mathlib.Data.List.ToFinsupp", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "List.toFinsupp_eq_sum_mapIdx_single", "kind": "theorem", "module": "Mathlib.Data.List.ToFinsupp", "is_tactic_proof": true, "tactics": ["revert", "induction", "nil", "append_singleton"], "tactic_count": 4}
{"name": "List.Triplewise", "kind": "inductive", "module": "Mathlib.Data.List.Triplewise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.triplewise_cons", "kind": "theorem", "module": "Mathlib.Data.List.Triplewise", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "List.triplewise_singleton", "kind": "theorem", "module": "Mathlib.Data.List.Triplewise", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.triplewise_pair", "kind": "theorem", "module": "Mathlib.Data.List.Triplewise", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.triplewise_triple", "kind": "theorem", "module": "Mathlib.Data.List.Triplewise", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.Triplewise.imp", "kind": "theorem", "module": "Mathlib.Data.List.Triplewise", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "List.triplewise_map", "kind": "theorem", "module": "Mathlib.Data.List.Triplewise", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "List.Triplewise.of_map", "kind": "theorem", "module": "Mathlib.Data.List.Triplewise", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "List.Triplewise.map", "kind": "theorem", "module": "Mathlib.Data.List.Triplewise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.triplewise_iff_getElem", "kind": "theorem", "module": "Mathlib.Data.List.Triplewise", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "simp", "refine", "grind", "simpa", "simpa"], "tactic_count": 8}
{"name": "List.triplewise_append", "kind": "theorem", "module": "Mathlib.Data.List.Triplewise", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.triplewise_reverse", "kind": "theorem", "module": "Mathlib.Data.List.Triplewise", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "List.rightInverse_unzip_zip", "kind": "theorem", "module": "Mathlib.Data.List.Zip", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "List.zip_swap", "kind": "theorem", "module": "Mathlib.Data.List.Zip", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.forall_zipWith", "kind": "theorem", "module": "Mathlib.Data.List.Zip", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.unzip_swap", "kind": "theorem", "module": "Mathlib.Data.List.Zip", "is_tactic_proof": true, "tactics": ["simp", "rfl"], "tactic_count": 2}
{"name": "List.zipWith_congr", "kind": "theorem", "module": "Mathlib.Data.List.Zip", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "List.zipWith_zipWith_left", "kind": "theorem", "module": "Mathlib.Data.List.Zip", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.zipWith_zipWith_right", "kind": "theorem", "module": "Mathlib.Data.List.Zip", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.zipWith3_same_left", "kind": "theorem", "module": "Mathlib.Data.List.Zip", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.zipWith3_same_mid", "kind": "theorem", "module": "Mathlib.Data.List.Zip", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.zipWith3_same_right", "kind": "theorem", "module": "Mathlib.Data.List.Zip", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.instIsSymmOpZipWith", "kind": "instance", "module": "Mathlib.Data.List.Zip", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.length_revzip", "kind": "theorem", "module": "Mathlib.Data.List.Zip", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.unzip_revzip", "kind": "theorem", "module": "Mathlib.Data.List.Zip", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.revzip_map_fst", "kind": "theorem", "module": "Mathlib.Data.List.Zip", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.revzip_map_snd", "kind": "theorem", "module": "Mathlib.Data.List.Zip", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.reverse_revzip", "kind": "theorem", "module": "Mathlib.Data.List.Zip", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "List.revzip_swap", "kind": "theorem", "module": "Mathlib.Data.List.Zip", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.mem_zip_inits_tails", "kind": "theorem", "module": "Mathlib.Data.List.Zip", "is_tactic_proof": true, "tactics": ["induction", "simp", "constructor", "rintro", "simp", "simp", "rcases", "simp", "intro", "right", "use", "simp_all"], "tactic_count": 12}
{"name": "Matrix.instModuleForall", "kind": "instance", "module": "Mathlib.Data.Matrix.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.smul_eq_mulVec", "kind": "theorem", "module": "Mathlib.Data.Matrix.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.instSMulCommClassForall", "kind": "instance", "module": "Mathlib.Data.Matrix.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.instSMulCommClassForall_1", "kind": "instance", "module": "Mathlib.Data.Matrix.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.instIsScalarTowerForall", "kind": "instance", "module": "Mathlib.Data.Matrix.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.instModuleMulOppositeForall", "kind": "instance", "module": "Mathlib.Data.Matrix.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.op_smul_eq_vecMul", "kind": "theorem", "module": "Mathlib.Data.Matrix.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.instSMulCommClassMulOppositeForallOfIsScalarTower", "kind": "instance", "module": "Mathlib.Data.Matrix.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.instSMulCommClassMulOppositeForallOfIsScalarTower_1", "kind": "instance", "module": "Mathlib.Data.Matrix.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.instIsScalarTowerMulOppositeForallOfSMulCommClass", "kind": "instance", "module": "Mathlib.Data.Matrix.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.decidableEq", "kind": "instance", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.instFintypeOfDecidableEq", "kind": "instance", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.instFinite", "kind": "instance", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.instIsStablyFiniteRingOfFinite", "kind": "instance", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.ofLinearEquiv", "kind": "definition", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.coe_ofLinearEquiv", "kind": "theorem", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.coe_ofLinearEquiv_symm", "kind": "theorem", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.sum_apply", "kind": "theorem", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.diagonalAddMonoidHom", "kind": "definition", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.diagonalLinearMap", "kind": "definition", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.zero_le_one_elem", "kind": "theorem", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "subst", "simp", "simp"], "tactic_count": 4}
{"name": "Matrix.zero_le_one_row", "kind": "theorem", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.diagAddMonoidHom", "kind": "definition", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.diagLinearMap", "kind": "definition", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.diag_list_sum", "kind": "theorem", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.diag_multiset_sum", "kind": "theorem", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.diag_sum", "kind": "theorem", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.diagonalRingHom", "kind": "definition", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.diagonal_pow", "kind": "theorem", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.scalar", "kind": "definition", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.scalar_apply", "kind": "theorem", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.scalar_inj", "kind": "theorem", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.scalar_comm_iff", "kind": "theorem", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Matrix.scalar_commute_iff", "kind": "theorem", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Matrix.scalar_commute", "kind": "theorem", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.instAlgebra", "kind": "instance", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.algebraMap_matrix_apply", "kind": "theorem", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.algebraMap_eq_diagonal", "kind": "theorem", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.algebraMap_eq_diagonalRingHom", "kind": "theorem", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.map_algebraMap", "kind": "theorem", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Matrix.diagonalAlgHom", "kind": "definition", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.scalarAlgHom", "kind": "definition", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.scalarAlgHom_apply", "kind": "theorem", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.entryAddHom", "kind": "definition", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.entryAddHom_eq_comp", "kind": "theorem", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.entryAddMonoidHom", "kind": "definition", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.entryAddMonoidHom_eq_comp", "kind": "theorem", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "Matrix.evalAddMonoidHom_comp_diagAddMonoidHom", "kind": "theorem", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.entryAddMonoidHom_toAddHom", "kind": "theorem", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.entryLinearMap", "kind": "definition", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.entryLinearMap_eq_comp", "kind": "theorem", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "Matrix.proj_comp_diagLinearMap", "kind": "theorem", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.entryLinearMap_toAddMonoidHom", "kind": "theorem", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.entryLinearMap_toAddHom", "kind": "theorem", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.mapMatrix", "kind": "definition", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.mapMatrix_refl", "kind": "theorem", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.mapMatrix_symm", "kind": "theorem", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.mapMatrix_trans", "kind": "theorem", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.mapMatrix", "kind": "definition", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.mapMatrix_id", "kind": "theorem", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.mapMatrix_comp", "kind": "theorem", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.entryAddMonoidHom_comp_mapMatrix", "kind": "theorem", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.mapMatrix_zero", "kind": "theorem", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.mapMatrix_add", "kind": "theorem", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.mapMatrix_sub", "kind": "theorem", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.mapMatrix_neg", "kind": "theorem", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.mapMatrix_smul", "kind": "theorem", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddEquiv.mapMatrix", "kind": "definition", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddEquiv.mapMatrix_refl", "kind": "theorem", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddEquiv.mapMatrix_symm", "kind": "theorem", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddEquiv.mapMatrix_trans", "kind": "theorem", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddEquiv.entryAddHom_comp_mapMatrix", "kind": "theorem", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.mapMatrix", "kind": "definition", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.mapMatrix_id", "kind": "theorem", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.mapMatrix_comp", "kind": "theorem", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.entryLinearMap_comp_mapMatrix", "kind": "theorem", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.mapMatrix_zero", "kind": "theorem", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.mapMatrix_add", "kind": "theorem", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.mapMatrix_smul", "kind": "theorem", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.mapMatrixLinear", "kind": "definition", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.mapMatrix_sub", "kind": "theorem", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.mapMatrix_neg", "kind": "theorem", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.mapMatrix", "kind": "definition", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.mapMatrix_refl", "kind": "theorem", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.mapMatrix_symm", "kind": "theorem", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.mapMatrix_trans", "kind": "theorem", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.mapMatrix_toLinearMap", "kind": "theorem", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "LinearEquiv.entryLinearMap_comp_mapMatrix", "kind": "theorem", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RingHom.mapMatrix", "kind": "definition", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.mapMatrix_id", "kind": "theorem", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.mapMatrix_comp", "kind": "theorem", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.map_pow", "kind": "theorem", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.mapMatrix", "kind": "definition", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.mapMatrix_refl", "kind": "theorem", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.mapMatrix_symm", "kind": "theorem", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.mapMatrix_trans", "kind": "theorem", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.mopMatrix", "kind": "definition", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsStablyFiniteRingMulOpposite", "kind": "instance", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.isStablyFiniteRing_iff", "kind": "theorem", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.mapMatrix", "kind": "definition", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.mapMatrix_id", "kind": "theorem", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.mapMatrix_comp", "kind": "theorem", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.mapMatrix", "kind": "definition", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.mapMatrix_refl", "kind": "theorem", "module": "Mathlib.Data.Matrix.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Matrix.fromBlocks_conjTranspose", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.fromBlocks_submatrix_sum_swap_left", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": true, "tactics": ["ext", "cases"], "tactic_count": 2}
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{"name": "Matrix.fromBlocks_zero", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": true, "tactics": ["ext", "rcases"], "tactic_count": 2}
{"name": "Matrix.fromBlocks_add", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Matrix.fromBlocks_multiply", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": true, "tactics": ["ext", "rcases", "simp"], "tactic_count": 3}
{"name": "Matrix.fromBlocks_diagonal_pow", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Matrix.fromBlocks_mulVec", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": true, "tactics": ["ext", "cases"], "tactic_count": 2}
{"name": "Matrix.vecMul_fromBlocks", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": true, "tactics": ["ext", "cases"], "tactic_count": 2}
{"name": "Matrix.toBlock_diagonal_self", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "simp", "simp"], "tactic_count": 4}
{"name": "Matrix.toBlock_diagonal_disjoint", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": true, "tactics": ["ext", "have", "simp"], "tactic_count": 3}
{"name": "Matrix.fromBlocks_diagonal", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": true, "tactics": ["ext", "rcases"], "tactic_count": 2}
{"name": "Matrix.toBlocks₁₁_diagonal", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": true, "tactics": ["unfold", "funext", "simp"], "tactic_count": 3}
{"name": "Matrix.toBlocks₂₂_diagonal", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": true, "tactics": ["unfold", "funext", "simp"], "tactic_count": 3}
{"name": "Matrix.toBlocks₁₂_diagonal", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.toBlocks₂₁_diagonal", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.fromBlocks_one", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": true, "tactics": ["ext", "rcases"], "tactic_count": 2}
{"name": "Matrix.toBlock_one_self", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.toBlock_one_disjoint", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.blockDiagonal", "kind": "definition", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.blockDiagonal_apply'", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.blockDiagonal_apply", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.blockDiagonal_apply_eq", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.blockDiagonal_apply_ne", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.blockDiagonal_map", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": true, "tactics": ["ext", "simp", "rw"], "tactic_count": 3}
{"name": "Matrix.blockDiagonal_transpose", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": true, "tactics": ["ext", "simp", "split_ifs", "rw", "rfl"], "tactic_count": 5}
{"name": "Matrix.blockDiagonal_conjTranspose", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": true, "tactics": ["simp", "rw"], "tactic_count": 2}
{"name": "Matrix.blockDiagonal_zero", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Matrix.blockDiagonal_diagonal", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": true, "tactics": ["ext", "simp", "congr", "rw"], "tactic_count": 4}
{"name": "Matrix.blockDiagonal_one", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.blockDiagonal_add", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": true, "tactics": ["ext", "simp", "split_ifs"], "tactic_count": 3}
{"name": "Matrix.blockDiagonalAddMonoidHom", "kind": "definition", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.blockDiagonal_neg", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.blockDiagonal_sub", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.blockDiagonal_mul", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": true, "tactics": ["ext", "simp", "split_ifs"], "tactic_count": 3}
{"name": "Matrix.blockDiagonalRingHom", "kind": "definition", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.blockDiagonal_pow", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.blockDiagonal_smul", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": true, "tactics": ["ext", "simp", "split_ifs"], "tactic_count": 3}
{"name": "Matrix.blockDiag", "kind": "definition", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.blockDiag_apply", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.blockDiag_map", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.blockDiag_transpose", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.blockDiag_conjTranspose", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.blockDiag_zero", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.blockDiag_diagonal", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.blockDiag_blockDiagonal", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.blockDiagonal_injective", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.blockDiagonal_inj", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.blockDiag_one", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.blockDiag_add", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.blockDiagAddMonoidHom", "kind": "definition", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.blockDiag_neg", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.blockDiag_sub", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.blockDiag_smul", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.blockDiagonal'", "kind": "definition", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.blockDiagonal'_apply'", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.blockDiagonal'_eq_blockDiagonal", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.blockDiagonal'_submatrix_eq_blockDiagonal", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.blockDiagonal'_apply", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.blockDiagonal'_apply_eq", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.blockDiagonal'_apply_ne", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.blockDiagonal'_map", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": true, "tactics": ["ext", "simp", "rw"], "tactic_count": 3}
{"name": "Matrix.blockDiagonal'_transpose", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": true, "tactics": ["ext", "simp", "split_ifs"], "tactic_count": 3}
{"name": "Matrix.blockDiagonal'_conjTranspose", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Matrix.blockDiagonal'_zero", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Matrix.blockDiagonal'_diagonal", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": true, "tactics": ["ext", "simp", "obtain", "simp", "simp"], "tactic_count": 5}
{"name": "Matrix.blockDiagonal'_one", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.blockDiagonal'_add", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": true, "tactics": ["ext", "simp", "split_ifs"], "tactic_count": 3}
{"name": "Matrix.blockDiagonal'AddMonoidHom", "kind": "definition", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.blockDiagonal'_neg", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.blockDiagonal'_sub", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.blockDiagonal'_mul", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": true, "tactics": ["ext", "simp", "rw", "simp", "split_ifs", "intro", "exact"], "tactic_count": 7}
{"name": "Matrix.blockDiagonal'RingHom", "kind": "definition", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.blockDiagonal'_pow", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.blockDiagonal'_smul", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": true, "tactics": ["ext", "simp", "split_ifs"], "tactic_count": 3}
{"name": "Matrix.blockDiag'", "kind": "definition", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.blockDiag'_apply", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.blockDiag'_map", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.blockDiag'_transpose", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.blockDiag'_conjTranspose", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.blockDiag'_zero", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.blockDiag'_diagonal", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.blockDiag'_blockDiagonal'", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.blockDiagonal'_injective", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.blockDiagonal'_inj", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.blockDiag'_one", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.blockDiag'_add", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.blockDiag'AddMonoidHom", "kind": "definition", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.blockDiag'_neg", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.blockDiag'_sub", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.blockDiag'_smul", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.toBlock_mul_eq_mul", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": true, "tactics": ["ext", "simp", "rw", "simp"], "tactic_count": 4}
{"name": "Matrix.toBlock_mul_eq_add", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": true, "tactics": ["classical", "ext", "simp", "exact"], "tactic_count": 4}
{"name": "Matrix.map_toSquareBlock", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.comp_toSquareBlock", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.comp_diagonal", "kind": "theorem", "module": "Mathlib.Data.Matrix.Block", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CartanMatrix.E₆", "kind": "definition", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CartanMatrix.E₇", "kind": "definition", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CartanMatrix.E₈", "kind": "definition", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CartanMatrix.F₄", "kind": "definition", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CartanMatrix.G₂", "kind": "definition", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CartanMatrix.A", "kind": "definition", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CartanMatrix.B", "kind": "definition", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CartanMatrix.C", "kind": "definition", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CartanMatrix.D", "kind": "definition", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CartanMatrix.A_diag", "kind": "theorem", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CartanMatrix.B_diag", "kind": "theorem", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CartanMatrix.C_diag", "kind": "theorem", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CartanMatrix.D_diag", "kind": "theorem", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CartanMatrix.A_apply_le_zero_of_ne", "kind": "theorem", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CartanMatrix.B_off_diag_nonpos", "kind": "theorem", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CartanMatrix.C_off_diag_nonpos", "kind": "theorem", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CartanMatrix.D_off_diag_nonpos", "kind": "theorem", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CartanMatrix.A_transpose", "kind": "theorem", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CartanMatrix.A_isSymm", "kind": "theorem", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CartanMatrix.B_transpose", "kind": "theorem", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CartanMatrix.C_transpose", "kind": "theorem", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CartanMatrix.D_transpose", "kind": "theorem", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CartanMatrix.D_isSymm", "kind": "theorem", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CartanMatrix.A_one", "kind": "theorem", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "CartanMatrix.A_two", "kind": "theorem", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "CartanMatrix.A_three", "kind": "theorem", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "CartanMatrix.B_one", "kind": "theorem", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "CartanMatrix.C_one", "kind": "theorem", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "CartanMatrix.D_one", "kind": "theorem", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "CartanMatrix.D_two", "kind": "theorem", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "CartanMatrix.B_two", "kind": "theorem", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "CartanMatrix.C_two", "kind": "theorem", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "CartanMatrix.D_three", "kind": "theorem", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "CartanMatrix.D_three'", "kind": "theorem", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "CartanMatrix.D_four", "kind": "theorem", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "CartanMatrix.E₆_diag", "kind": "theorem", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": true, "tactics": ["fin_cases"], "tactic_count": 1}
{"name": "CartanMatrix.E₇_diag", "kind": "theorem", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": true, "tactics": ["fin_cases"], "tactic_count": 1}
{"name": "CartanMatrix.E₈_diag", "kind": "theorem", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": true, "tactics": ["fin_cases"], "tactic_count": 1}
{"name": "CartanMatrix.F₄_diag", "kind": "theorem", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": true, "tactics": ["fin_cases"], "tactic_count": 1}
{"name": "CartanMatrix.G₂_diag", "kind": "theorem", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": true, "tactics": ["fin_cases"], "tactic_count": 1}
{"name": "CartanMatrix.E₆_off_diag_nonpos", "kind": "theorem", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": true, "tactics": ["fin_cases"], "tactic_count": 1}
{"name": "CartanMatrix.E₇_off_diag_nonpos", "kind": "theorem", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": true, "tactics": ["fin_cases"], "tactic_count": 1}
{"name": "CartanMatrix.E₈_off_diag_nonpos", "kind": "theorem", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": true, "tactics": ["fin_cases"], "tactic_count": 1}
{"name": "CartanMatrix.F₄_off_diag_nonpos", "kind": "theorem", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": true, "tactics": ["fin_cases"], "tactic_count": 1}
{"name": "CartanMatrix.G₂_off_diag_nonpos", "kind": "theorem", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": true, "tactics": ["fin_cases"], "tactic_count": 1}
{"name": "CartanMatrix.E₆_transpose", "kind": "theorem", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "CartanMatrix.E₇_transpose", "kind": "theorem", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "CartanMatrix.E₈_transpose", "kind": "theorem", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "CartanMatrix.E₆_isSymm", "kind": "theorem", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CartanMatrix.E₇_isSymm", "kind": "theorem", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CartanMatrix.E₈_isSymm", "kind": "theorem", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CartanMatrix.G₂_det", "kind": "theorem", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "CartanMatrix.F₄_det", "kind": "theorem", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "CartanMatrix.E₆_det", "kind": "proofWanted", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CartanMatrix.E₇_det", "kind": "proofWanted", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CartanMatrix.E₈_det", "kind": "proofWanted", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.IsSimplyLaced", "kind": "definition", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CartanMatrix.instDecidablePredMatrixIntIsSimplyLacedOfFintypeOfDecidableEq", "kind": "instance", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.isSimplyLaced_iff_of_linearOrder", "kind": "theorem", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "intro", "obtain", "simpa", "exact"], "tactic_count": 7}
{"name": "Matrix.isSimplyLaced_transpose", "kind": "theorem", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": true, "tactics": ["rw", "aesop"], "tactic_count": 2}
{"name": "CartanMatrix.isSimplyLaced_A", "kind": "theorem", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": true, "tactics": ["intro", "simp", "grind"], "tactic_count": 3}
{"name": "CartanMatrix.isSimplyLaced_D", "kind": "theorem", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": true, "tactics": ["intro", "simp", "grind"], "tactic_count": 3}
{"name": "CartanMatrix.isSimplyLaced_E₆", "kind": "theorem", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CartanMatrix.isSimplyLaced_E₇", "kind": "theorem", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CartanMatrix.isSimplyLaced_E₈", "kind": "theorem", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CartanMatrix.not_isSimplyLaced_F₄", "kind": "theorem", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "CartanMatrix.not_isSimplyLaced_G₂", "kind": "theorem", "module": "Mathlib.Data.Matrix.Cartan", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "Matrix.fromRows", "kind": "definition", "module": "Mathlib.Data.Matrix.ColumnRowPartitioned", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.fromCols", "kind": "definition", "module": "Mathlib.Data.Matrix.ColumnRowPartitioned", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.toCols₁", "kind": "definition", "module": "Mathlib.Data.Matrix.ColumnRowPartitioned", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.toCols₂", "kind": "definition", "module": "Mathlib.Data.Matrix.ColumnRowPartitioned", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.toRows₁", "kind": "definition", "module": "Mathlib.Data.Matrix.ColumnRowPartitioned", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.toRows₂", "kind": "definition", "module": "Mathlib.Data.Matrix.ColumnRowPartitioned", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.fromRows_apply_inl", "kind": "theorem", "module": "Mathlib.Data.Matrix.ColumnRowPartitioned", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.fromRows_apply_inr", "kind": "theorem", "module": "Mathlib.Data.Matrix.ColumnRowPartitioned", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.fromCols_apply_inl", "kind": "theorem", "module": "Mathlib.Data.Matrix.ColumnRowPartitioned", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.fromCols_apply_inr", "kind": "theorem", "module": "Mathlib.Data.Matrix.ColumnRowPartitioned", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.toRows₁_apply", "kind": "theorem", "module": "Mathlib.Data.Matrix.ColumnRowPartitioned", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.toRows₂_apply", "kind": "theorem", "module": "Mathlib.Data.Matrix.ColumnRowPartitioned", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.toRows₁_fromRows", "kind": "theorem", "module": "Mathlib.Data.Matrix.ColumnRowPartitioned", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.toRows₂_fromRows", "kind": "theorem", "module": "Mathlib.Data.Matrix.ColumnRowPartitioned", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.toCols₁_apply", "kind": "theorem", "module": "Mathlib.Data.Matrix.ColumnRowPartitioned", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.toCols₂_apply", "kind": "theorem", "module": "Mathlib.Data.Matrix.ColumnRowPartitioned", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.toCols₁_fromCols", "kind": "theorem", "module": "Mathlib.Data.Matrix.ColumnRowPartitioned", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.toCols₂_fromCols", "kind": "theorem", "module": "Mathlib.Data.Matrix.ColumnRowPartitioned", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.fromCols_toCols", "kind": "theorem", "module": "Mathlib.Data.Matrix.ColumnRowPartitioned", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Matrix.fromRows_toRows", "kind": "theorem", "module": "Mathlib.Data.Matrix.ColumnRowPartitioned", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Matrix.fromRows_inj", "kind": "theorem", "module": "Mathlib.Data.Matrix.ColumnRowPartitioned", "is_tactic_proof": true, "tactics": ["intro", "simp"], "tactic_count": 2}
{"name": "Matrix.fromCols_inj", "kind": "theorem", "module": "Mathlib.Data.Matrix.ColumnRowPartitioned", "is_tactic_proof": true, "tactics": ["intro", "simp", "simp_all"], "tactic_count": 3}
{"name": "Matrix.fromCols_ext_iff", "kind": "theorem", "module": "Mathlib.Data.Matrix.ColumnRowPartitioned", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.fromRows_ext_iff", "kind": "theorem", "module": "Mathlib.Data.Matrix.ColumnRowPartitioned", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.transpose_fromCols", "kind": "theorem", "module": "Mathlib.Data.Matrix.ColumnRowPartitioned", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Matrix.transpose_fromRows", "kind": "theorem", "module": "Mathlib.Data.Matrix.ColumnRowPartitioned", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Matrix.fromRows_map", "kind": "theorem", "module": "Mathlib.Data.Matrix.ColumnRowPartitioned", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Matrix.fromCols_map", "kind": "theorem", "module": "Mathlib.Data.Matrix.ColumnRowPartitioned", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Matrix.fromRows_neg", "kind": "theorem", "module": "Mathlib.Data.Matrix.ColumnRowPartitioned", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Matrix.fromCols_neg", "kind": "theorem", "module": "Mathlib.Data.Matrix.ColumnRowPartitioned", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Matrix.fromCols_fromRows_eq_fromBlocks", "kind": "theorem", "module": "Mathlib.Data.Matrix.ColumnRowPartitioned", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Matrix.fromRows_fromCols_eq_fromBlocks", "kind": "theorem", "module": "Mathlib.Data.Matrix.ColumnRowPartitioned", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Matrix.fromRows_mulVec", "kind": "theorem", "module": "Mathlib.Data.Matrix.ColumnRowPartitioned", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Matrix.vecMul_fromCols", "kind": "theorem", "module": "Mathlib.Data.Matrix.ColumnRowPartitioned", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Matrix.sumElim_vecMul_fromRows", "kind": "theorem", "module": "Mathlib.Data.Matrix.ColumnRowPartitioned", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Matrix.vecMul_fromRows", "kind": "theorem", "module": "Mathlib.Data.Matrix.ColumnRowPartitioned", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.fromCols_mulVec_sumElim", "kind": "theorem", "module": "Mathlib.Data.Matrix.ColumnRowPartitioned", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Matrix.fromCols_mulVec", "kind": "theorem", "module": "Mathlib.Data.Matrix.ColumnRowPartitioned", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.fromRows_mul", "kind": "theorem", "module": "Mathlib.Data.Matrix.ColumnRowPartitioned", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Matrix.mul_fromCols", "kind": "theorem", "module": "Mathlib.Data.Matrix.ColumnRowPartitioned", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Matrix.fromRows_zero", "kind": "theorem", "module": "Mathlib.Data.Matrix.ColumnRowPartitioned", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Matrix.fromCols_zero", "kind": "theorem", "module": "Mathlib.Data.Matrix.ColumnRowPartitioned", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Matrix.fromRows_mul_fromCols", "kind": "theorem", "module": "Mathlib.Data.Matrix.ColumnRowPartitioned", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Matrix.fromCols_mul_fromRows", "kind": "theorem", "module": "Mathlib.Data.Matrix.ColumnRowPartitioned", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Matrix.fromCols_mul_fromBlocks", "kind": "theorem", "module": "Mathlib.Data.Matrix.ColumnRowPartitioned", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Matrix.fromBlocks_mul_fromRows", "kind": "theorem", "module": "Mathlib.Data.Matrix.ColumnRowPartitioned", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Matrix.fromCols_mul_fromRows_eq_one_comm", "kind": "theorem", "module": "Mathlib.Data.Matrix.ColumnRowPartitioned", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.equiv_compl_fromCols_mul_fromRows_eq_one_comm", "kind": "theorem", "module": "Mathlib.Data.Matrix.ColumnRowPartitioned", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.conjTranspose_fromCols_eq_fromRows_conjTranspose", "kind": "theorem", "module": "Mathlib.Data.Matrix.ColumnRowPartitioned", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Matrix.conjTranspose_fromRows_eq_fromCols_conjTranspose", "kind": "theorem", "module": "Mathlib.Data.Matrix.ColumnRowPartitioned", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Matrix.comp", "kind": "definition", "module": "Mathlib.Data.Matrix.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.comp_one", "kind": "theorem", "module": "Mathlib.Data.Matrix.Composition", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Matrix.comp_map_map", "kind": "theorem", "module": "Mathlib.Data.Matrix.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.comp_single_single", "kind": "theorem", "module": "Mathlib.Data.Matrix.Composition", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "obtain", "rw", "obtain", "rw", "rw", "obtain", "rw", "obtain", "rw", "rw"], "tactic_count": 12}
{"name": "Matrix.comp_symm_single", "kind": "theorem", "module": "Mathlib.Data.Matrix.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.comp_diagonal_diagonal", "kind": "theorem", "module": "Mathlib.Data.Matrix.Composition", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "obtain", "rw", "rw", "obtain", "rw", "rw"], "tactic_count": 8}
{"name": "Matrix.comp_symm_diagonal", "kind": "theorem", "module": "Mathlib.Data.Matrix.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.comp_transpose", "kind": "theorem", "module": "Mathlib.Data.Matrix.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.comp_map_transpose", "kind": "theorem", "module": "Mathlib.Data.Matrix.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.comp_symm_transpose", "kind": "theorem", "module": "Mathlib.Data.Matrix.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.compAddEquiv", "kind": "definition", "module": "Mathlib.Data.Matrix.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.compAddEquiv_apply", "kind": "theorem", "module": "Mathlib.Data.Matrix.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.compAddEquiv_symm_apply", "kind": "theorem", "module": "Mathlib.Data.Matrix.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.compRingEquiv", "kind": "definition", "module": "Mathlib.Data.Matrix.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.compRingEquiv_apply", "kind": "theorem", "module": "Mathlib.Data.Matrix.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.compRingEquiv_symm_apply", "kind": "theorem", "module": "Mathlib.Data.Matrix.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.instIsStablyFiniteRing", "kind": "instance", "module": "Mathlib.Data.Matrix.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.compLinearEquiv", "kind": "definition", "module": "Mathlib.Data.Matrix.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.compAlgEquiv", "kind": "definition", "module": "Mathlib.Data.Matrix.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.compAlgEquiv_apply", "kind": "theorem", "module": "Mathlib.Data.Matrix.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.compAlgEquiv_symm_apply", "kind": "theorem", "module": "Mathlib.Data.Matrix.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.isUnit_comp_iff", "kind": "theorem", "module": "Mathlib.Data.Matrix.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.isUnit_comp_symm_iff", "kind": "theorem", "module": "Mathlib.Data.Matrix.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DMatrix", "kind": "definition", "module": "Mathlib.Data.Matrix.DMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DMatrix.ext_iff", "kind": "theorem", "module": "Mathlib.Data.Matrix.DMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DMatrix.ext", "kind": "theorem", "module": "Mathlib.Data.Matrix.DMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DMatrix.map", "kind": "definition", "module": "Mathlib.Data.Matrix.DMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DMatrix.map_apply", "kind": "theorem", "module": "Mathlib.Data.Matrix.DMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DMatrix.map_map", "kind": "theorem", "module": "Mathlib.Data.Matrix.DMatrix", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "DMatrix.transpose", "kind": "definition", "module": "Mathlib.Data.Matrix.DMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DMatrix.term_ᵀ", "kind": "definition", "module": "Mathlib.Data.Matrix.DMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DMatrix._aux_Mathlib_Data_Matrix_DMatrix___macroRules_DMatrix_term_ᵀ_1", "kind": "definition", "module": "Mathlib.Data.Matrix.DMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DMatrix._aux_Mathlib_Data_Matrix_DMatrix___unexpand_DMatrix_transpose_1", "kind": "definition", "module": "Mathlib.Data.Matrix.DMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DMatrix.col", "kind": "definition", "module": "Mathlib.Data.Matrix.DMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DMatrix.row", "kind": "definition", "module": "Mathlib.Data.Matrix.DMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DMatrix.instInhabited", "kind": "instance", "module": "Mathlib.Data.Matrix.DMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DMatrix.instAdd", "kind": "instance", "module": "Mathlib.Data.Matrix.DMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DMatrix.instAddSemigroup", "kind": "instance", "module": "Mathlib.Data.Matrix.DMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DMatrix.instAddCommSemigroup", "kind": "instance", "module": "Mathlib.Data.Matrix.DMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DMatrix.instZero", "kind": "instance", "module": "Mathlib.Data.Matrix.DMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DMatrix.instAddMonoid", "kind": "instance", "module": "Mathlib.Data.Matrix.DMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DMatrix.instAddCommMonoid", "kind": "instance", "module": "Mathlib.Data.Matrix.DMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DMatrix.instNeg", "kind": "instance", "module": "Mathlib.Data.Matrix.DMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DMatrix.instSub", "kind": "instance", "module": "Mathlib.Data.Matrix.DMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DMatrix.instAddGroup", "kind": "instance", "module": "Mathlib.Data.Matrix.DMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DMatrix.instAddCommGroup", "kind": "instance", "module": "Mathlib.Data.Matrix.DMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DMatrix.instUnique", "kind": "instance", "module": "Mathlib.Data.Matrix.DMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DMatrix.instSubsingleton", "kind": "instance", "module": "Mathlib.Data.Matrix.DMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DMatrix.zero_apply", "kind": "theorem", "module": "Mathlib.Data.Matrix.DMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DMatrix.neg_apply", "kind": "theorem", "module": "Mathlib.Data.Matrix.DMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DMatrix.add_apply", "kind": "theorem", "module": "Mathlib.Data.Matrix.DMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DMatrix.sub_apply", "kind": "theorem", "module": "Mathlib.Data.Matrix.DMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DMatrix.map_zero", "kind": "theorem", "module": "Mathlib.Data.Matrix.DMatrix", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "DMatrix.map_add", "kind": "theorem", "module": "Mathlib.Data.Matrix.DMatrix", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "DMatrix.map_sub", "kind": "theorem", "module": "Mathlib.Data.Matrix.DMatrix", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "DMatrix.subsingleton_of_empty_left", "kind": "instance", "module": "Mathlib.Data.Matrix.DMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DMatrix.subsingleton_of_empty_right", "kind": "instance", "module": "Mathlib.Data.Matrix.DMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.mapDMatrix", "kind": "definition", "module": "Mathlib.Data.Matrix.DMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.mapDMatrix_apply", "kind": "theorem", "module": "Mathlib.Data.Matrix.DMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.diagonal", "kind": "definition", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.diagonal_apply", "kind": "theorem", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.diagonal_apply_eq", "kind": "theorem", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.diagonal_apply_ne", "kind": "theorem", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.diagonal_apply_ne'", "kind": "theorem", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.diagonal_eq_diagonal_iff", "kind": "theorem", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.diagonal_injective", "kind": "theorem", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.diagonal_zero", "kind": "theorem", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Matrix.diagonal_zero'", "kind": "theorem", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.diagonal_transpose", "kind": "theorem", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "simp", "simp"], "tactic_count": 4}
{"name": "Matrix.diagonal_add", "kind": "theorem", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": true, "tactics": ["ext", "by_cases"], "tactic_count": 2}
{"name": "Matrix.diagonal_smul", "kind": "theorem", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": true, "tactics": ["ext", "by_cases"], "tactic_count": 2}
{"name": "Matrix.diagonal_neg", "kind": "theorem", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": true, "tactics": ["ext", "by_cases"], "tactic_count": 2}
{"name": "Matrix.diagonal_sub", "kind": "theorem", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": true, "tactics": ["ext", "by_cases"], "tactic_count": 2}
{"name": "Matrix.diagonal_mem_matrix_iff", "kind": "theorem", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": true, "tactics": ["simp", "conv_lhs", "simp"], "tactic_count": 3}
{"name": "Matrix.instNatCastOfZero", "kind": "instance", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.diagonal_natCast", "kind": "theorem", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.diagonal_natCast'", "kind": "theorem", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.diagonal_ofNat", "kind": "theorem", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.diagonal_ofNat'", "kind": "theorem", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.instIntCastOfZero", "kind": "instance", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.diagonal_intCast", "kind": "theorem", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.diagonal_intCast'", "kind": "theorem", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.diagonal_map", "kind": "theorem", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": true, "tactics": ["ext", "simp", "split_ifs"], "tactic_count": 3}
{"name": "Matrix.map_natCast", "kind": "theorem", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.map_ofNat", "kind": "theorem", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.natCast_apply", "kind": "theorem", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matrix.ofNat_apply", "kind": "theorem", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.map_intCast", "kind": "theorem", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.intCast_apply", "kind": "theorem", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matrix.diagonal_unique", "kind": "theorem", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "Matrix.col_diagonal", "kind": "theorem", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Matrix.row_diagonal", "kind": "theorem", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Matrix.one", "kind": "instance", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.diagonal_one", "kind": "theorem", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.diagonal_one'", "kind": "theorem", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.one_apply", "kind": "theorem", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.one_apply_eq", "kind": "theorem", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.one_apply_ne", "kind": "theorem", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.one_apply_ne'", "kind": "theorem", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.map_one", "kind": "theorem", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": true, "tactics": ["ext", "simp", "split_ifs"], "tactic_count": 3}
{"name": "Matrix.one_eq_pi_single", "kind": "theorem", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.instAddMonoidWithOne", "kind": "instance", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.instAddGroupWithOne", "kind": "instance", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.instAddCommMonoidWithOne", "kind": "instance", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.instAddCommGroupWithOne", "kind": "instance", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.diag", "kind": "definition", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.diag_apply", "kind": "theorem", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.diag_diagonal", "kind": "theorem", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.diag_transpose", "kind": "theorem", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.diag_zero", "kind": "theorem", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.diag_add", "kind": "theorem", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.diag_sub", "kind": "theorem", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.diag_neg", "kind": "theorem", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.diag_smul", "kind": "theorem", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.diag_one", "kind": "theorem", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.diag_map", "kind": "theorem", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.transpose_eq_diagonal", "kind": "theorem", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.transpose_one", "kind": "theorem", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.transpose_eq_one", "kind": "theorem", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.transpose_natCast", "kind": "theorem", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.transpose_eq_natCast", "kind": "theorem", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.transpose_ofNat", "kind": "theorem", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.transpose_eq_ofNat", "kind": "theorem", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.transpose_intCast", "kind": "theorem", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.transpose_eq_intCast", "kind": "theorem", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.submatrix_diagonal", "kind": "theorem", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.submatrix_one", "kind": "theorem", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.diag_submatrix", "kind": "theorem", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.submatrix_diagonal_embedding", "kind": "theorem", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.submatrix_diagonal_equiv", "kind": "theorem", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.submatrix_one_embedding", "kind": "theorem", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.submatrix_one_equiv", "kind": "theorem", "module": "Mathlib.Data.Matrix.Diagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.dualNumberEquiv", "kind": "definition", "module": "Mathlib.Data.Matrix.DualNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.invOf_mul_cancel_left", "kind": "theorem", "module": "Mathlib.Data.Matrix.Invertible", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matrix.mul_invOf_cancel_left", "kind": "theorem", "module": "Mathlib.Data.Matrix.Invertible", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matrix.invOf_mul_cancel_right", "kind": "theorem", "module": "Mathlib.Data.Matrix.Invertible", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matrix.mul_invOf_cancel_right", "kind": "theorem", "module": "Mathlib.Data.Matrix.Invertible", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matrix.invOf_mul_eq_iff_eq_mul_left", "kind": "theorem", "module": "Mathlib.Data.Matrix.Invertible", "is_tactic_proof": true, "tactics": ["refine", "rw", "rw"], "tactic_count": 3}
{"name": "Matrix.mul_left_eq_iff_eq_invOf_mul", "kind": "theorem", "module": "Mathlib.Data.Matrix.Invertible", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matrix.mul_invOf_eq_iff_eq_mul_right", "kind": "theorem", "module": "Mathlib.Data.Matrix.Invertible", "is_tactic_proof": true, "tactics": ["refine", "rw", "rw"], "tactic_count": 3}
{"name": "Matrix.mul_right_eq_iff_eq_mul_invOf", "kind": "theorem", "module": "Mathlib.Data.Matrix.Invertible", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matrix.invertibleConjTranspose", "kind": "instance", "module": "Mathlib.Data.Matrix.Invertible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.conjTranspose_invOf", "kind": "theorem", "module": "Mathlib.Data.Matrix.Invertible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.invertibleOfInvertibleConjTranspose", "kind": "definition", "module": "Mathlib.Data.Matrix.Invertible", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "Matrix.isUnit_conjTranspose", "kind": "theorem", "module": "Mathlib.Data.Matrix.Invertible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.invertibleTranspose", "kind": "instance", "module": "Mathlib.Data.Matrix.Invertible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.transpose_invOf", "kind": "theorem", "module": "Mathlib.Data.Matrix.Invertible", "is_tactic_proof": true, "tactics": ["letI", "convert"], "tactic_count": 2}
{"name": "Matrix.invertibleOfInvertibleTranspose", "kind": "definition", "module": "Mathlib.Data.Matrix.Invertible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.transposeInvertibleEquivInvertible", "kind": "definition", "module": "Mathlib.Data.Matrix.Invertible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.isUnit_transpose", "kind": "theorem", "module": "Mathlib.Data.Matrix.Invertible", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.add_mul_mul_invOf_mul_eq_one", "kind": "theorem", "module": "Mathlib.Data.Matrix.Invertible", "is_tactic_proof": true, "tactics": ["calc", "rw", "abel", "rw", "congr", "simp", "rw", "abel"], "tactic_count": 8}
{"name": "Matrix.add_mul_mul_invOf_mul_eq_one'", "kind": "theorem", "module": "Mathlib.Data.Matrix.Invertible", "is_tactic_proof": true, "tactics": ["calc", "rw", "abel", "rw", "simp_rw", "simp", "rw", "abel"], "tactic_count": 8}
{"name": "Matrix.invertibleAddMulMul", "kind": "definition", "module": "Mathlib.Data.Matrix.Invertible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.invOf_add_mul_mul", "kind": "theorem", "module": "Mathlib.Data.Matrix.Invertible", "is_tactic_proof": true, "tactics": ["letI", "convert"], "tactic_count": 2}
{"name": "Matrix.add_mul_mul_mul_invOf_eq_one", "kind": "theorem", "module": "Mathlib.Data.Matrix.Invertible", "is_tactic_proof": true, "tactics": ["simp", "rw", "simp", "simp", "congr", "rw", "simp"], "tactic_count": 7}
{"name": "Matrix.add_mul_mul_mul_invOf_eq_one'", "kind": "theorem", "module": "Mathlib.Data.Matrix.Invertible", "is_tactic_proof": true, "tactics": ["simp", "rw", "simp", "congr", "rw", "rw", "simp", "simp"], "tactic_count": 8}
{"name": "Matrix.invertibleAddMulMul'", "kind": "definition", "module": "Mathlib.Data.Matrix.Invertible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.invOf_add_mul_mul'", "kind": "theorem", "module": "Mathlib.Data.Matrix.Invertible", "is_tactic_proof": true, "tactics": ["letI", "convert"], "tactic_count": 2}
{"name": "dotProduct", "kind": "definition", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "term_⬝ᵥ_", "kind": "definition", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Data_Matrix_Mul___macroRules_term_⬝ᵥ__1", "kind": "definition", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Data_Matrix_Mul___unexpand_dotProduct_1", "kind": "definition", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dotProduct_assoc", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "dotProduct_comm", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "dotProduct_pUnit", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "dotProduct_one", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "one_dotProduct", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "dotProduct_zero", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "dotProduct_zero'", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zero_dotProduct", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "zero_dotProduct'", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "add_dotProduct", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "dotProduct_add", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "sumElim_dotProduct_sumElim", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "comp_equiv_symm_dotProduct", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dotProduct_comp_equiv_symm", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "comp_equiv_dotProduct_comp_equiv", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "dotProduct_sum", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["simp", "rw"], "tactic_count": 2}
{"name": "sum_dotProduct", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["simp", "rw"], "tactic_count": 2}
{"name": "diagonal_dotProduct", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["have", "convert"], "tactic_count": 2}
{"name": "dotProduct_diagonal", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["have", "convert"], "tactic_count": 2}
{"name": "dotProduct_diagonal'", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["have", "convert"], "tactic_count": 2}
{"name": "single_dotProduct", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["have", "convert"], "tactic_count": 2}
{"name": "dotProduct_single", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["have", "convert"], "tactic_count": 2}
{"name": "one_dotProduct_one", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "dotProduct_single_one", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "single_one_dotProduct", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "neg_dotProduct", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "dotProduct_neg", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "neg_dotProduct_neg", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "sub_dotProduct", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "dotProduct_sub", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "smul_dotProduct", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "dotProduct_smul", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "exists_ne_zero_dotProduct_eq_zero", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["obtain", "classical", "use", "split_ifs", "simp", "simp", "refine", "simp"], "tactic_count": 8}
{"name": "not_injective_dotProduct_left", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["intro", "obtain", "simpa"], "tactic_count": 3}
{"name": "not_injective_dotProduct_right", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["intro", "obtain", "simpa"], "tactic_count": 3}
{"name": "Matrix.instHMulOfFintypeOfMulOfAddCommMonoid", "kind": "instance", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.mul_apply", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.instMulOfFintypeOfAddCommMonoid", "kind": "instance", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.instMulOneOfFintypeOfDecidableEqOfAddCommMonoid", "kind": "instance", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.mul_apply'", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.two_mul_expl", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["refine", "rw", "simp"], "tactic_count": 3}
{"name": "Matrix.smul_mul", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["ext", "apply"], "tactic_count": 2}
{"name": "Matrix.mul_smul", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["ext", "apply"], "tactic_count": 2}
{"name": "Matrix.mul_zero", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["ext", "apply"], "tactic_count": 2}
{"name": "Matrix.zero_mul", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["ext", "apply"], "tactic_count": 2}
{"name": "Matrix.mul_add", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["ext", "apply"], "tactic_count": 2}
{"name": "Matrix.add_mul", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["ext", "apply"], "tactic_count": 2}
{"name": "Matrix.nonUnitalNonAssocSemiring", "kind": "instance", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.diagonal_mul", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.mul_diagonal", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "Matrix.diagonal_mul_diagonal", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["ext", "by_cases"], "tactic_count": 2}
{"name": "Matrix.diagonal_mul_diagonal'", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.commute_diagonal", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Matrix.smul_eq_diagonal_mul", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Matrix.op_smul_eq_mul_diagonal", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Matrix.addMonoidHomMulLeft", "kind": "definition", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.addMonoidHomMulRight", "kind": "definition", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.sum_mul", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.mul_sum", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.Semiring.isScalarTower", "kind": "instance", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.Semiring.smulCommClass", "kind": "instance", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.map_mul", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Matrix.one_mul", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "Matrix.mul_one", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "Matrix.nonAssocSemiring", "kind": "instance", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.smul_one_eq_diagonal", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Matrix.op_smul_one_eq_diagonal", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Matrix.mul_assoc", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["ext", "apply"], "tactic_count": 2}
{"name": "Matrix.nonUnitalSemiring", "kind": "instance", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.semiring", "kind": "instance", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.neg_mul", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["ext", "apply"], "tactic_count": 2}
{"name": "Matrix.mul_neg", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["ext", "apply"], "tactic_count": 2}
{"name": "Matrix.sub_mul", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matrix.mul_sub", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matrix.nonUnitalNonAssocRing", "kind": "instance", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.instNonUnitalRing", "kind": "instance", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.instNonAssocRing", "kind": "instance", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.instRing", "kind": "instance", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.mul_mul_left", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.pow_apply_nonneg", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "intro", "exact"], "tactic_count": 5}
{"name": "Matrix.smul_eq_mul_diagonal", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Matrix.mul_mul_right", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsDedekindFiniteMonoidOfIsStablyFiniteRing", "kind": "instance", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsStablyFiniteRing.of_injective", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.isStablyFiniteRing_iff", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsStablyFiniteRingSubtypeMem", "kind": "instance", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.vecMulVec", "kind": "definition", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.vecMulVec_apply", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.row_vecMulVec", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.col_vecMulVec", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.zero_vecMulVec", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.vecMulVec_zero", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.vecMulVec_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.vecMulVec_eq_zero", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["simp", "forall_or_right]"], "tactic_count": 2}
{"name": "Matrix.add_vecMulVec", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.vecMulVec_add", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.neg_vecMulVec", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.vecMulVec_neg", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.smul_vecMulVec", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.vecMulVec_smul", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.vecMulVec_smul'", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.transpose_vecMulVec", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.diag_vecMulVec", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.mulVec", "kind": "definition", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.term_*ᵥ_", "kind": "definition", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix._aux_Mathlib_Data_Matrix_Mul___macroRules_Matrix_term_*ᵥ__1", "kind": "definition", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix._aux_Mathlib_Data_Matrix_Mul___unexpand_Matrix_mulVec_1", "kind": "definition", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.vecMul", "kind": "definition", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.term_ᵥ*_", "kind": "definition", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix._aux_Mathlib_Data_Matrix_Mul___macroRules_Matrix_term_ᵥ*__1", "kind": "definition", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix._aux_Mathlib_Data_Matrix_Mul___unexpand_Matrix_vecMul_1", "kind": "definition", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.mulVec.addMonoidHomLeft", "kind": "definition", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.mul_apply_eq_vecMul", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.vecMul_eq_sum", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.mulVec_eq_sum", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.mulVec_diagonal", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.vecMul_diagonal", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.dotProduct_mulVec", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Matrix.mulVec_zero", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Matrix.zero_vecMul", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Matrix.zero_mulVec", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Matrix.vecMul_zero", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Matrix.mulVec_add", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["ext", "apply"], "tactic_count": 2}
{"name": "Matrix.add_mulVec", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["ext", "apply"], "tactic_count": 2}
{"name": "Matrix.vecMul_add", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["ext", "apply"], "tactic_count": 2}
{"name": "Matrix.add_vecMul", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["ext", "apply"], "tactic_count": 2}
{"name": "Matrix.mulVec_smul", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "Matrix.smul_mulVec", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "Matrix.smul_vecMul", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "Matrix.vecMul_smul", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "Matrix.mulVec_single", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.single_vecMul", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.mulVec_single_one", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Matrix.single_one_vecMul", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Matrix.diagonal_mulVec_single", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["ext", "rw", "exact"], "tactic_count": 3}
{"name": "Matrix.single_vecMul_diagonal", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["ext", "rw", "exact"], "tactic_count": 3}
{"name": "Matrix.vecMul_vecMul", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["ext", "apply"], "tactic_count": 2}
{"name": "Matrix.mulVec_mulVec", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["ext", "symm", "apply"], "tactic_count": 3}
{"name": "Matrix.mul_mul_apply", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Matrix.vecMul_vecMulVec", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Matrix.vecMulVec_mulVec", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Matrix.mul_vecMulVec", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["ext", "simp_rw"], "tactic_count": 2}
{"name": "Matrix.vecMulVec_mul", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["ext", "simp_rw"], "tactic_count": 2}
{"name": "Matrix.vecMulVec_mul_vecMulVec", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matrix.mul_right_injective_iff_mulVec_injective", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["refine", "inhabit", "suffices", "exact"], "tactic_count": 4}
{"name": "Matrix.mul_left_injective_iff_vecMul_injective", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["refine", "inhabit", "suffices", "exact"], "tactic_count": 4}
{"name": "Matrix.isLeftRegular_iff_mulVec_injective", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["cases", "simp", "exact"], "tactic_count": 3}
{"name": "Matrix.isRightRegular_iff_vecMul_injective", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["cases", "simp", "exact"], "tactic_count": 3}
{"name": "Matrix.mulVec_one", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Matrix.one_vecMul", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Matrix.ext_of_mulVec_single", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["ext", "simp_rw", "exact"], "tactic_count": 3}
{"name": "Matrix.ext_of_single_vecMul", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["ext", "simp_rw", "exact"], "tactic_count": 3}
{"name": "Matrix.mulVec_injective", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["intro", "ext", "classical"], "tactic_count": 3}
{"name": "Matrix.ext_iff_mulVec", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.vecMul_injective", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["intro", "ext", "classical"], "tactic_count": 3}
{"name": "Matrix.ext_iff_vecMul", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.one_mulVec", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "Matrix.vecMul_one", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "Matrix.diagonal_const_mulVec", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Matrix.vecMul_diagonal_const", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Matrix.natCast_mulVec", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.vecMul_natCast", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.ofNat_mulVec", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.vecMul_ofNat", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.neg_vecMul", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["ext", "apply"], "tactic_count": 2}
{"name": "Matrix.vecMul_neg", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["ext", "apply"], "tactic_count": 2}
{"name": "Matrix.neg_vecMul_neg", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matrix.neg_mulVec", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["ext", "apply"], "tactic_count": 2}
{"name": "Matrix.mulVec_neg", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["ext", "apply"], "tactic_count": 2}
{"name": "Matrix.neg_mulVec_neg", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matrix.mulVec_sub", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["ext", "apply"], "tactic_count": 2}
{"name": "Matrix.sub_mulVec", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.vecMul_sub", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.sub_vecMul", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["ext", "apply"], "tactic_count": 2}
{"name": "Matrix.sub_vecMulVec", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.vecMulVec_sub", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.mulVec_transpose", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["ext", "apply"], "tactic_count": 2}
{"name": "Matrix.vecMul_transpose", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["ext", "apply"], "tactic_count": 2}
{"name": "Matrix.mulVec_vecMul", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matrix.vecMul_mulVec", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matrix.mulVec_injective_of_isUnit", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.vecMul_injective_of_isUnit", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.pow_row_eq_zero_of_le", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["replace", "rw", "rw"], "tactic_count": 3}
{"name": "Matrix.pow_col_eq_zero_of_le", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["replace", "rw", "rw"], "tactic_count": 3}
{"name": "Matrix.mulVec_smul_assoc", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.intCast_mulVec", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.vecMul_intCast", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.transpose_mul", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["ext", "apply"], "tactic_count": 2}
{"name": "Matrix.submatrix_mul", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.submatrix_mul_equiv", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.submatrix_mulVec_equiv", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.submatrix_id_mul_left", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Matrix.submatrix_id_mul_right", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Matrix.submatrix_vecMul_equiv", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.mul_submatrix_one", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["cases", "let", "have", "simp", "rw", "simp"], "tactic_count": 6}
{"name": "Matrix.one_submatrix_mul", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["cases", "let", "have", "simp", "rw", "simp"], "tactic_count": 6}
{"name": "Matrix.submatrix_mul_transpose_submatrix", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matrix.instIsDedekindFiniteMonoidOfIsStablyFiniteRing", "kind": "instance", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.mul_eq_one_comm_of_equiv", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.mul_eq_one_comm_of_card_eq", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.map_matrix_mul", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RingHom.map_dotProduct", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RingHom.map_vecMul", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RingHom.map_mulVec", "kind": "theorem", "module": "Mathlib.Data.Matrix.Mul", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PEquiv.toMatrix", "kind": "definition", "module": "Mathlib.Data.Matrix.PEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PEquiv.toMatrix_apply", "kind": "theorem", "module": "Mathlib.Data.Matrix.PEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PEquiv.toMatrix_mul_apply", "kind": "theorem", "module": "Mathlib.Data.Matrix.PEquiv", "is_tactic_proof": true, "tactics": ["dsimp", "rcases", "simp", "rw"], "tactic_count": 4}
{"name": "PEquiv.mul_toMatrix_apply", "kind": "theorem", "module": "Mathlib.Data.Matrix.PEquiv", "is_tactic_proof": true, "tactics": ["dsimp", "rcases", "simp", "rw", "simp", "rintro", "simp", "simp"], "tactic_count": 8}
{"name": "PEquiv.toMatrix_symm", "kind": "theorem", "module": "Mathlib.Data.Matrix.PEquiv", "is_tactic_proof": true, "tactics": ["ext", "simp", "congr"], "tactic_count": 3}
{"name": "PEquiv.toMatrix_refl", "kind": "theorem", "module": "Mathlib.Data.Matrix.PEquiv", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "PEquiv.toMatrix_toPEquiv_apply", "kind": "theorem", "module": "Mathlib.Data.Matrix.PEquiv", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "PEquiv.transpose_toMatrix_toPEquiv_apply", "kind": "theorem", "module": "Mathlib.Data.Matrix.PEquiv", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "PEquiv.toMatrix_toPEquiv_mul", "kind": "theorem", "module": "Mathlib.Data.Matrix.PEquiv", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "PEquiv.mul_toMatrix_toPEquiv", "kind": "theorem", "module": "Mathlib.Data.Matrix.PEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PEquiv.toMatrix_toPEquiv_mulVec", "kind": "theorem", "module": "Mathlib.Data.Matrix.PEquiv", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "PEquiv.vecMul_toMatrix_toPEquiv", "kind": "theorem", "module": "Mathlib.Data.Matrix.PEquiv", "is_tactic_proof": true, "tactics": ["classical", "ext", "simp"], "tactic_count": 3}
{"name": "PEquiv.toMatrix_trans", "kind": "theorem", "module": "Mathlib.Data.Matrix.PEquiv", "is_tactic_proof": true, "tactics": ["ext", "rw", "dsimp", "cases"], "tactic_count": 4}
{"name": "PEquiv.toMatrix_bot", "kind": "theorem", "module": "Mathlib.Data.Matrix.PEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PEquiv.toMatrix_injective", "kind": "theorem", "module": "Mathlib.Data.Matrix.PEquiv", "is_tactic_proof": true, "tactics": ["intro", "refine", "simp", "intro", "use", "rcases", "rcases", "rw", "use", "simp", "use", "simp"], "tactic_count": 12}
{"name": "PEquiv.toMatrix_swap", "kind": "theorem", "module": "Mathlib.Data.Matrix.PEquiv", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "split_ifs"], "tactic_count": 3}
{"name": "PEquiv.single_mul_single", "kind": "theorem", "module": "Mathlib.Data.Matrix.PEquiv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PEquiv.single_mul_single_of_ne", "kind": "theorem", "module": "Mathlib.Data.Matrix.PEquiv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PEquiv.single_mul_single_right", "kind": "theorem", "module": "Mathlib.Data.Matrix.PEquiv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PEquiv.toMatrix_toPEquiv_eq", "kind": "theorem", "module": "Mathlib.Data.Matrix.PEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PEquiv.map_toMatrix", "kind": "theorem", "module": "Mathlib.Data.Matrix.PEquiv", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Matrix.Forall", "kind": "definition", "module": "Mathlib.Data.Matrix.Reflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.forall_iff", "kind": "theorem", "module": "Mathlib.Data.Matrix.Reflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix._example", "kind": "example", "module": "Mathlib.Data.Matrix.Reflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.Exists", "kind": "definition", "module": "Mathlib.Data.Matrix.Reflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.exists_iff", "kind": "theorem", "module": "Mathlib.Data.Matrix.Reflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix._example", "kind": "example", "module": "Mathlib.Data.Matrix.Reflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.transposeᵣ", "kind": "definition", "module": "Mathlib.Data.Matrix.Reflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.transposeᵣ_eq", "kind": "theorem", "module": "Mathlib.Data.Matrix.Reflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix._example", "kind": "example", "module": "Mathlib.Data.Matrix.Reflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.dotProductᵣ", "kind": "definition", "module": "Mathlib.Data.Matrix.Reflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.dotProductᵣ_eq", "kind": "theorem", "module": "Mathlib.Data.Matrix.Reflection", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Matrix._example", "kind": "example", "module": "Mathlib.Data.Matrix.Reflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.mulᵣ", "kind": "definition", "module": "Mathlib.Data.Matrix.Reflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.mulᵣ_eq", "kind": "theorem", "module": "Mathlib.Data.Matrix.Reflection", "is_tactic_proof": true, "tactics": ["simp", "rfl"], "tactic_count": 2}
{"name": "Matrix._example", "kind": "example", "module": "Mathlib.Data.Matrix.Reflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.mulVecᵣ", "kind": "definition", "module": "Mathlib.Data.Matrix.Reflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.mulVecᵣ_eq", "kind": "theorem", "module": "Mathlib.Data.Matrix.Reflection", "is_tactic_proof": true, "tactics": ["simp", "rfl"], "tactic_count": 2}
{"name": "Matrix._example", "kind": "example", "module": "Mathlib.Data.Matrix.Reflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.vecMulᵣ", "kind": "definition", "module": "Mathlib.Data.Matrix.Reflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.vecMulᵣ_eq", "kind": "theorem", "module": "Mathlib.Data.Matrix.Reflection", "is_tactic_proof": true, "tactics": ["simp", "rfl"], "tactic_count": 2}
{"name": "Matrix._example", "kind": "example", "module": "Mathlib.Data.Matrix.Reflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.etaExpand", "kind": "definition", "module": "Mathlib.Data.Matrix.Reflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.etaExpand_eq", "kind": "theorem", "module": "Mathlib.Data.Matrix.Reflection", "is_tactic_proof": true, "tactics": ["simp_rw", "grind"], "tactic_count": 2}
{"name": "Matrix._example", "kind": "example", "module": "Mathlib.Data.Matrix.Reflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.add", "kind": "definition", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.instAdd", "kind": "instance", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.coe_add", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.singleton_add", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.add_le_add_iff_left", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.add_le_add_iff_right", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.add_comm", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.add_assoc", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.zero_add", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.add_zero", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.le_add_right", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Multiset.le_add_left", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Multiset.subset_add_left", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.subset_add_right", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.le_iff_exists_add", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.cons_add", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.add_cons", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.mem_add", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.countP_add", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.count_add", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.add_left_inj", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Multiset.add_right_inj", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Multiset.card_add", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.erase", "kind": "definition", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.coe_erase", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.erase_zero", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.erase_cons_head", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.erase_cons_tail", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.erase_singleton", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.erase_of_notMem", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.cons_erase", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.erase_cons_tail_of_mem", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": true, "tactics": ["rcases", "simp", "exact"], "tactic_count": 3}
{"name": "Multiset.le_cons_erase", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.add_singleton_eq_iff", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": true, "tactics": ["rw", "constructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 6}
{"name": "Multiset.erase_add_left_pos", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.erase_add_right_pos", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.erase_add_right_neg", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.erase_add_left_neg", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.erase_le", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.erase_lt", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.erase_subset", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.mem_erase_of_ne", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.mem_of_mem_erase", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.erase_comm", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.instRightCommutativeErase", "kind": "instance", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.erase_le_erase", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.erase_le_iff_le_cons", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.card_erase_of_mem", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.card_erase_add_one", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.card_erase_lt_of_mem", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.card_erase_le", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.card_erase_eq_ite", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": true, "tactics": ["by_cases", "rwa", "rwa"], "tactic_count": 3}
{"name": "Multiset.count_erase_self", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.count_erase_of_ne", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.sub", "kind": "definition", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.instSub", "kind": "instance", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.coe_sub", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.sub_zero", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.sub_cons", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.zero_sub", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.countP_sub", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.count_sub", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.sub_le_iff_le_add", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": true, "tactics": ["induction", "empty", "cons"], "tactic_count": 3}
{"name": "Multiset.sub_le_iff_le_add'", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.sub_le_self", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Multiset.add_sub_assoc", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Multiset.add_sub_cancel", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Multiset.sub_add_cancel", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Multiset.sub_add_eq_sub_sub", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Multiset.le_sub_add", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.le_add_sub", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.sub_le_sub_right", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.add_sub_cancel_right", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Multiset.eq_sub_of_add_eq", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.cons_sub_of_le", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.card_sub", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.sub_singleton", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": true, "tactics": ["ext", "simp", "split"], "tactic_count": 3}
{"name": "Multiset.mem_sub", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.Rel.add", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": true, "tactics": ["induction", "zero", "cons"], "tactic_count": 3}
{"name": "Multiset.rel_add_left", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.rel_add_right", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.nodup_singleton", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.not_nodup_pair", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Nodup.erase", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.mem_sub_of_nodup", "kind": "theorem", "module": "Mathlib.Data.Multiset.AddSub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.antidiagonal", "kind": "definition", "module": "Mathlib.Data.Multiset.Antidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.antidiagonal_coe", "kind": "theorem", "module": "Mathlib.Data.Multiset.Antidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.antidiagonal_coe'", "kind": "theorem", "module": "Mathlib.Data.Multiset.Antidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.mem_antidiagonal", "kind": "theorem", "module": "Mathlib.Data.Multiset.Antidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.antidiagonal_map_fst", "kind": "theorem", "module": "Mathlib.Data.Multiset.Antidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.antidiagonal_map_snd", "kind": "theorem", "module": "Mathlib.Data.Multiset.Antidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.antidiagonal_zero", "kind": "theorem", "module": "Mathlib.Data.Multiset.Antidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.antidiagonal_cons", "kind": "theorem", "module": "Mathlib.Data.Multiset.Antidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.antidiagonal_eq_map_powerset", "kind": "theorem", "module": "Mathlib.Data.Multiset.Antidiagonal", "is_tactic_proof": true, "tactics": ["induction", "empty", "cons", "hs", "simp_rw", "erase_cons_head]", "rw", "congr", "refine", "rw"], "tactic_count": 10}
{"name": "Multiset.card_antidiagonal", "kind": "theorem", "module": "Mathlib.Data.Multiset.Antidiagonal", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "Multiset.toList", "kind": "definition", "module": "Mathlib.Data.Multiset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.coe_toList", "kind": "theorem", "module": "Mathlib.Data.Multiset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.toList_eq_nil", "kind": "theorem", "module": "Mathlib.Data.Multiset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.empty_toList", "kind": "theorem", "module": "Mathlib.Data.Multiset.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.toList_zero", "kind": "theorem", "module": "Mathlib.Data.Multiset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.mem_toList", "kind": "theorem", "module": "Mathlib.Data.Multiset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.toList_eq_singleton_iff", "kind": "theorem", "module": "Mathlib.Data.Multiset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.toList_singleton", "kind": "theorem", "module": "Mathlib.Data.Multiset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.length_toList", "kind": "theorem", "module": "Mathlib.Data.Multiset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.strongInductionOn", "kind": "definition", "module": "Mathlib.Data.Multiset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.strongInductionOn_eq", "kind": "theorem", "module": "Mathlib.Data.Multiset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.case_strongInductionOn", "kind": "theorem", "module": "Mathlib.Data.Multiset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.strongDownwardInduction", "kind": "definition", "module": "Mathlib.Data.Multiset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.strongDownwardInduction_eq", "kind": "theorem", "module": "Mathlib.Data.Multiset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.strongDownwardInductionOn", "kind": "definition", "module": "Mathlib.Data.Multiset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.strongDownwardInductionOn_eq", "kind": "theorem", "module": "Mathlib.Data.Multiset.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "Multiset.chooseX", "kind": "definition", "module": "Mathlib.Data.Multiset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.choose", "kind": "definition", "module": "Mathlib.Data.Multiset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.choose_spec", "kind": "theorem", "module": "Mathlib.Data.Multiset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.choose_mem", "kind": "theorem", "module": "Mathlib.Data.Multiset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.choose_property", "kind": "theorem", "module": "Mathlib.Data.Multiset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.subsingletonEquiv", "kind": "definition", "module": "Mathlib.Data.Multiset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.coe_subsingletonEquiv", "kind": "theorem", "module": "Mathlib.Data.Multiset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.join", "kind": "definition", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.coe_join", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.join_zero", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.join_cons", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.join_add", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.singleton_join", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.mem_join", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.card_join", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.map_join", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": true, "tactics": ["induction", "empty", "cons"], "tactic_count": 3}
{"name": "Multiset.prod_join", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": true, "tactics": ["induction", "empty", "cons"], "tactic_count": 3}
{"name": "Multiset.rel_join", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": true, "tactics": ["induction", "zero", "cons"], "tactic_count": 3}
{"name": "Multiset.filter_join", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": true, "tactics": ["induction", "empty", "cons"], "tactic_count": 3}
{"name": "Multiset.filterMap_join", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": true, "tactics": ["induction", "empty", "cons"], "tactic_count": 3}
{"name": "Multiset.bind", "kind": "definition", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.coe_bind", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Multiset.zero_bind", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.cons_bind", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.singleton_bind", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.add_bind", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.bind_zero", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.bind_add", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.bind_cons", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.bind_singleton", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.mem_bind", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.card_bind", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.bind_congr", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.bind_hcongr", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": true, "tactics": ["subst", "simp", "simp"], "tactic_count": 3}
{"name": "Multiset.map_bind", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.bind_map", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.bind_assoc", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.bind_bind", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.bind_map_comm", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.filter_eq_bind", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": true, "tactics": ["induction", "empty", "cons"], "tactic_count": 3}
{"name": "Multiset.bind_filter", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": true, "tactics": ["simp", "apply", "split_ifs"], "tactic_count": 3}
{"name": "Multiset.filter_bind", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.filterMap_eq_bind", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": true, "tactics": ["induction", "empty", "cons"], "tactic_count": 3}
{"name": "Multiset.bind_filterMap", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": true, "tactics": ["simp", "apply", "cases", "none", "some"], "tactic_count": 5}
{"name": "Multiset.filterMap_bind", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.prod_bind", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.rel_bind", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": true, "tactics": ["apply", "rw", "exact"], "tactic_count": 3}
{"name": "Multiset.count_sum", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.count_bind", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.le_bind", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": true, "tactics": ["classical", "refine", "obtain", "rw", "exact"], "tactic_count": 5}
{"name": "Multiset.attach_bind_coe", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.nodup_bind", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": true, "tactics": ["have", "choose", "have", "have", "exact", "unfold", "simp"], "tactic_count": 7}
{"name": "Multiset.dedup_bind_dedup", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": true, "tactics": ["ext", "simp_rw", "congr", "simp"], "tactic_count": 4}
{"name": "Multiset.fold_bind", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": true, "tactics": ["induction", "empty", "cons"], "tactic_count": 3}
{"name": "Multiset.product", "kind": "definition", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.instSProd", "kind": "instance", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.coe_product", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "simp"], "tactic_count": 3}
{"name": "Multiset.zero_product", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.cons_product", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.product_zero", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.product_cons", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.product_singleton", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.add_product", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.product_add", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.card_product", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.mem_product", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Nodup.product", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.map_swap_product", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "Multiset.prod_map_product_eq_prod_prod", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "Multiset.sigma", "kind": "definition", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.coe_sigma", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Multiset.zero_sigma", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.cons_sigma", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.sigma_singleton", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.add_sigma", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.sigma_add", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.card_sigma", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.mem_sigma", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Nodup.sigma", "kind": "theorem", "module": "Mathlib.Data.Multiset.Bind", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.countP", "kind": "definition", "module": "Mathlib.Data.Multiset.Count", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.coe_countP", "kind": "theorem", "module": "Mathlib.Data.Multiset.Count", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.countP_zero", "kind": "theorem", "module": "Mathlib.Data.Multiset.Count", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.countP_cons_of_pos", "kind": "theorem", "module": "Mathlib.Data.Multiset.Count", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.countP_cons_of_neg", "kind": "theorem", "module": "Mathlib.Data.Multiset.Count", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.countP_cons", "kind": "theorem", "module": "Mathlib.Data.Multiset.Count", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.countP_le_card", "kind": "theorem", "module": "Mathlib.Data.Multiset.Count", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.card_eq_countP_add_countP", "kind": "theorem", "module": "Mathlib.Data.Multiset.Count", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.countP_le_of_le", "kind": "theorem", "module": "Mathlib.Data.Multiset.Count", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.countP_True", "kind": "theorem", "module": "Mathlib.Data.Multiset.Count", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.countP_False", "kind": "theorem", "module": "Mathlib.Data.Multiset.Count", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.countP_attach", "kind": "theorem", "module": "Mathlib.Data.Multiset.Count", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.countP_pos", "kind": "theorem", "module": "Mathlib.Data.Multiset.Count", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.countP_eq_zero", "kind": "theorem", "module": "Mathlib.Data.Multiset.Count", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.countP_eq_card", "kind": "theorem", "module": "Mathlib.Data.Multiset.Count", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.countP_pos_of_mem", "kind": "theorem", "module": "Mathlib.Data.Multiset.Count", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.countP_congr", "kind": "theorem", "module": "Mathlib.Data.Multiset.Count", "is_tactic_proof": true, "tactics": ["revert", "exact", "simp", "apply", "simpa"], "tactic_count": 5}
{"name": "Multiset.count", "kind": "definition", "module": "Mathlib.Data.Multiset.Count", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.coe_count", "kind": "theorem", "module": "Mathlib.Data.Multiset.Count", "is_tactic_proof": true, "tactics": ["simp_rw", "rfl"], "tactic_count": 2}
{"name": "Multiset.count_zero", "kind": "theorem", "module": "Mathlib.Data.Multiset.Count", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.count_cons_self", "kind": "theorem", "module": "Mathlib.Data.Multiset.Count", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.count_cons_of_ne", "kind": "theorem", "module": "Mathlib.Data.Multiset.Count", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.count_le_card", "kind": "theorem", "module": "Mathlib.Data.Multiset.Count", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.count_le_of_le", "kind": "theorem", "module": "Mathlib.Data.Multiset.Count", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.count_le_count_cons", "kind": "theorem", "module": "Mathlib.Data.Multiset.Count", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.count_cons", "kind": "theorem", "module": "Mathlib.Data.Multiset.Count", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.count_singleton_self", "kind": "theorem", "module": "Mathlib.Data.Multiset.Count", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.count_singleton", "kind": "theorem", "module": "Mathlib.Data.Multiset.Count", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.count_attach", "kind": "theorem", "module": "Mathlib.Data.Multiset.Count", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.count_pos", "kind": "theorem", "module": "Mathlib.Data.Multiset.Count", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.one_le_count_iff_mem", "kind": "theorem", "module": "Mathlib.Data.Multiset.Count", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.count_eq_zero_of_notMem", "kind": "theorem", "module": "Mathlib.Data.Multiset.Count", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.count_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Multiset.Count", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.count_eq_zero", "kind": "theorem", "module": "Mathlib.Data.Multiset.Count", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.count_eq_card", "kind": "theorem", "module": "Mathlib.Data.Multiset.Count", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.ext", "kind": "theorem", "module": "Mathlib.Data.Multiset.Count", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.ext'", "kind": "theorem", "module": "Mathlib.Data.Multiset.Count", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.count_injective", "kind": "theorem", "module": "Mathlib.Data.Multiset.Count", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.le_iff_count", "kind": "theorem", "module": "Mathlib.Data.Multiset.Count", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Rel.countP_eq", "kind": "theorem", "module": "Mathlib.Data.Multiset.Count", "is_tactic_proof": true, "tactics": ["induction", "empty", "cons", "obtain", "rw", "simp", "exact"], "tactic_count": 7}
{"name": "Multiset.nodup_iff_count_le_one", "kind": "theorem", "module": "Mathlib.Data.Multiset.Count", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.nodup_iff_count_eq_one", "kind": "theorem", "module": "Mathlib.Data.Multiset.Count", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.count_eq_one_of_mem", "kind": "theorem", "module": "Mathlib.Data.Multiset.Count", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.count_eq_of_nodup", "kind": "theorem", "module": "Mathlib.Data.Multiset.Count", "is_tactic_proof": true, "tactics": ["split_ifs", "exact", "exact"], "tactic_count": 3}
{"name": "Multiset.dedup", "kind": "definition", "module": "Mathlib.Data.Multiset.Dedup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.coe_dedup", "kind": "theorem", "module": "Mathlib.Data.Multiset.Dedup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.dedup_zero", "kind": "theorem", "module": "Mathlib.Data.Multiset.Dedup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.mem_dedup", "kind": "theorem", "module": "Mathlib.Data.Multiset.Dedup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.dedup_cons_of_mem", "kind": "theorem", "module": "Mathlib.Data.Multiset.Dedup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.dedup_cons_of_notMem", "kind": "theorem", "module": "Mathlib.Data.Multiset.Dedup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.dedup_le", "kind": "theorem", "module": "Mathlib.Data.Multiset.Dedup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.dedup_subset", "kind": "theorem", "module": "Mathlib.Data.Multiset.Dedup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.subset_dedup", "kind": "theorem", "module": "Mathlib.Data.Multiset.Dedup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.dedup_subset'", "kind": "theorem", "module": "Mathlib.Data.Multiset.Dedup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.subset_dedup'", "kind": "theorem", "module": "Mathlib.Data.Multiset.Dedup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.nodup_dedup", "kind": "theorem", "module": "Mathlib.Data.Multiset.Dedup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.dedup_eq_self", "kind": "theorem", "module": "Mathlib.Data.Multiset.Dedup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.count_dedup", "kind": "theorem", "module": "Mathlib.Data.Multiset.Dedup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.dedup_idem", "kind": "theorem", "module": "Mathlib.Data.Multiset.Dedup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.dedup_eq_zero", "kind": "theorem", "module": "Mathlib.Data.Multiset.Dedup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.dedup_singleton", "kind": "theorem", "module": "Mathlib.Data.Multiset.Dedup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.le_dedup", "kind": "theorem", "module": "Mathlib.Data.Multiset.Dedup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.le_dedup_self", "kind": "theorem", "module": "Mathlib.Data.Multiset.Dedup", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.dedup_ext", "kind": "theorem", "module": "Mathlib.Data.Multiset.Dedup", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.dedup_map_of_injective", "kind": "theorem", "module": "Mathlib.Data.Multiset.Dedup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.dedup_map_dedup_eq", "kind": "theorem", "module": "Mathlib.Data.Multiset.Dedup", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.Nodup.le_dedup_iff_le", "kind": "theorem", "module": "Mathlib.Data.Multiset.Dedup", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.Subset.dedup_add_right", "kind": "theorem", "module": "Mathlib.Data.Multiset.Dedup", "is_tactic_proof": true, "tactics": ["induction", "exact"], "tactic_count": 2}
{"name": "Multiset.Subset.dedup_add_left", "kind": "theorem", "module": "Mathlib.Data.Multiset.Dedup", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.Disjoint.dedup_add", "kind": "theorem", "module": "Mathlib.Data.Multiset.Dedup", "is_tactic_proof": true, "tactics": ["induction", "exact"], "tactic_count": 2}
{"name": "List.Subset.dedup_append_left", "kind": "theorem", "module": "Mathlib.Data.Multiset.Dedup", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset", "kind": "definition", "module": "Mathlib.Data.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.ofList", "kind": "definition", "module": "Mathlib.Data.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.instCoeList", "kind": "instance", "module": "Mathlib.Data.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.quot_mk_to_coe", "kind": "theorem", "module": "Mathlib.Data.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.quot_mk_to_coe'", "kind": "theorem", "module": "Mathlib.Data.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.quot_mk_to_coe''", "kind": "theorem", "module": "Mathlib.Data.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.lift_coe", "kind": "theorem", "module": "Mathlib.Data.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.coe_eq_coe", "kind": "theorem", "module": "Mathlib.Data.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.instDecidableEquivListOfDecidableEq", "kind": "instance", "module": "Mathlib.Data.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.instDecidableRListOfDecidableEq", "kind": "instance", "module": "Mathlib.Data.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.decidableEq", "kind": "instance", "module": "Mathlib.Data.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Mem", "kind": "definition", "module": "Mathlib.Data.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.instMembership", "kind": "instance", "module": "Mathlib.Data.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.mem_coe", "kind": "theorem", "module": "Mathlib.Data.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.decidableMem", "kind": "instance", "module": "Mathlib.Data.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Subset", "kind": "definition", "module": "Mathlib.Data.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.instHasSubset", "kind": "instance", "module": "Mathlib.Data.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.instHasSSubset", "kind": "instance", "module": "Mathlib.Data.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.instIsNonstrictStrictOrder", "kind": "instance", "module": "Mathlib.Data.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.coe_subset", "kind": "theorem", "module": "Mathlib.Data.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Subset.refl", "kind": "theorem", "module": "Mathlib.Data.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Subset.trans", "kind": "theorem", "module": "Mathlib.Data.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.subset_iff", "kind": "theorem", "module": "Mathlib.Data.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.mem_of_subset", "kind": "theorem", "module": "Mathlib.Data.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Le", "kind": "definition", "module": "Mathlib.Data.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.instPartialOrder", "kind": "instance", "module": "Mathlib.Data.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.decidableLE", "kind": "instance", "module": "Mathlib.Data.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.subset_of_le", "kind": "theorem", "module": "Mathlib.Data.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.mem_of_le", "kind": "theorem", "module": "Mathlib.Data.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.notMem_mono", "kind": "theorem", "module": "Mathlib.Data.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.coe_le", "kind": "theorem", "module": "Mathlib.Data.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.leInductionOn", "kind": "theorem", "module": "Mathlib.Data.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.card", "kind": "definition", "module": "Mathlib.Data.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.coe_card", "kind": "theorem", "module": "Mathlib.Data.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.card_le_card", "kind": "theorem", "module": "Mathlib.Data.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.eq_of_le_of_card_le", "kind": "theorem", "module": "Mathlib.Data.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.card_lt_card", "kind": "theorem", "module": "Mathlib.Data.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.card_mono", "kind": "theorem", "module": "Mathlib.Data.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.card_strictMono", "kind": "theorem", "module": "Mathlib.Data.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.instWellFoundedLT", "kind": "instance", "module": "Mathlib.Data.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.coe_reverse", "kind": "theorem", "module": "Mathlib.Data.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.pmap", "kind": "definition", "module": "Mathlib.Data.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.coe_pmap", "kind": "theorem", "module": "Mathlib.Data.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.pmap_congr", "kind": "theorem", "module": "Mathlib.Data.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.mem_pmap", "kind": "theorem", "module": "Mathlib.Data.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.card_pmap", "kind": "theorem", "module": "Mathlib.Data.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.attach", "kind": "definition", "module": "Mathlib.Data.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.coe_attach", "kind": "theorem", "module": "Mathlib.Data.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.mem_attach", "kind": "theorem", "module": "Mathlib.Data.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.card_attach", "kind": "theorem", "module": "Mathlib.Data.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.decidableForallMultiset", "kind": "definition", "module": "Mathlib.Data.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.decidableDforallMultiset", "kind": "instance", "module": "Mathlib.Data.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.decidableEqPiMultiset", "kind": "instance", "module": "Mathlib.Data.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.decidableExistsMultiset", "kind": "definition", "module": "Mathlib.Data.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.decidableDexistsMultiset", "kind": "instance", "module": "Mathlib.Data.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Pairwise", "kind": "definition", "module": "Mathlib.Data.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.pairwise_coe_iff", "kind": "theorem", "module": "Mathlib.Data.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.pairwise_coe_iff_pairwise", "kind": "theorem", "module": "Mathlib.Data.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Nodup", "kind": "definition", "module": "Mathlib.Data.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.coe_nodup", "kind": "theorem", "module": "Mathlib.Data.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Nodup.ext", "kind": "theorem", "module": "Mathlib.Data.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.le_iff_subset", "kind": "theorem", "module": "Mathlib.Data.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.nodup_of_le", "kind": "theorem", "module": "Mathlib.Data.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.nodupDecidable", "kind": "instance", "module": "Mathlib.Data.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.sizeOf", "kind": "definition", "module": "Mathlib.Data.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.instSizeOf", "kind": "instance", "module": "Mathlib.Data.Multiset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.IsDershowitzMannaLT", "kind": "definition", "module": "Mathlib.Data.Multiset.DershowitzManna", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.IsDershowitzMannaLT.trans", "kind": "theorem", "module": "Mathlib.Data.Multiset.DershowitzManna", "is_tactic_proof": true, "tactics": ["classical", "rintro", "rw", "refine", "simpa", "rwa", "rw", "rwa", "simp", "refine", "obtain", "by_cases", "obtain", "exact", "exact", "obtain", "exact"], "tactic_count": 17}
{"name": "_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset.OneStep", "kind": "definition", "module": "Mathlib.Data.Multiset.DershowitzManna", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset.isDershowitzMannaLT_of_oneStep", "kind": "theorem", "module": "Mathlib.Data.Multiset.DershowitzManna", "is_tactic_proof": true, "tactics": ["rintro", "use", "simpa"], "tactic_count": 3}
{"name": "_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset.isDershowitzMannaLT_singleton_insert", "kind": "theorem", "module": "Mathlib.Data.Multiset.DershowitzManna", "is_tactic_proof": true, "tactics": ["classical", "obtain", "obtain", "refine", "simpa", "refine", "rw", "rw", "have", "simpa", "rw", "have", "simpa"], "tactic_count": 13}
{"name": "_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset.acc_oneStep_cons_of_acc_lt", "kind": "theorem", "module": "Mathlib.Data.Multiset.DershowitzManna", "is_tactic_proof": false, "tactics": ["induction", "rintro", "induction", "refine", "obtain", "exact", "clear", "induction", "empty", "simp", "obtain", "exact"], "tactic_count": 12}
{"name": "_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset.acc_oneStep_of_acc_lt", "kind": "theorem", "module": "Mathlib.Data.Multiset.DershowitzManna", "is_tactic_proof": true, "tactics": ["induction", "empty", "constructor", "simp", "cons", "exact"], "tactic_count": 6}
{"name": "_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset.isDershowitzMannaLT_singleton_wf", "kind": "theorem", "module": "Mathlib.Data.Multiset.DershowitzManna", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset.transGen_oneStep_of_isDershowitzMannaLT", "kind": "theorem", "module": "Mathlib.Data.Multiset.DershowitzManna", "is_tactic_proof": true, "tactics": ["classical", "rintro", "induction", "empty", "cons", "obtain", "exact", "let", "refine", "rw", "simp", "simpa"], "tactic_count": 12}
{"name": "_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset.isDershowitzMannaLT_of_transGen_oneStep", "kind": "theorem", "module": "Mathlib.Data.Multiset.DershowitzManna", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset.transGen_oneStep_eq_isDershowitzMannaLT", "kind": "theorem", "module": "Mathlib.Data.Multiset.DershowitzManna", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "Multiset.wellFounded_isDershowitzMannaLT", "kind": "theorem", "module": "Mathlib.Data.Multiset.DershowitzManna", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Multiset.instWellFoundedIsDershowitzMannaLT", "kind": "instance", "module": "Mathlib.Data.Multiset.DershowitzManna", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.filter", "kind": "definition", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.filter_coe", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.filter_zero", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.filter_congr", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.filter_add", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.filter_le", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.filter_subset", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.filter_le_filter", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.monotone_filter_left", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.monotone_filter_right", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.filter_cons_of_pos", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.filter_cons_of_neg", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.mem_filter", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.of_mem_filter", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.mem_of_mem_filter", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.mem_filter_of_mem", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.filter_eq_self", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.filter_eq_nil", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.filter_true", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.filter_false", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.le_filter", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.filter_cons", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": true, "tactics": ["split_ifs", "rw", "rw"], "tactic_count": 3}
{"name": "Multiset.filter_singleton", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.filter_filter", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.filter_comm", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.filter_add_filter", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.filter_add_not", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": true, "tactics": ["rw", "simp", "simp", "simp"], "tactic_count": 4}
{"name": "Multiset.filter_map", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.map_filter'", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.card_filter_le_iff", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": true, "tactics": ["fconstructor", "intro", "by_contra", "have", "exact", "contrapose", "exact"], "tactic_count": 7}
{"name": "Multiset.filterMap", "kind": "definition", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.filterMap_coe", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.filterMap_zero", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.filterMap_cons_none", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.filterMap_cons_some", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.filterMap_cons", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": true, "tactics": ["cases", "none", "some"], "tactic_count": 3}
{"name": "Multiset.filterMap_add", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.filterMap_eq_map", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.filterMap_eq_filter", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.filterMap_filterMap", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.map_filterMap", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.filterMap_map", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.filter_filterMap", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.filterMap_filter", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.filterMap_some", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.mem_filterMap", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.map_filterMap_of_inv", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.filterMap_le_filterMap", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.map_filter_eq_filterMap", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": true, "tactics": ["induction", "empty", "cons", "simp", "split_ifs"], "tactic_count": 5}
{"name": "Multiset.countP_eq_card_filter", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.countP_filter", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.countP_eq_countP_filter_add", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.countP_map", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": true, "tactics": ["refine", "rw", "rw"], "tactic_count": 3}
{"name": "Multiset.filter_attach", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.count_filter_of_pos", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.count_filter_of_neg", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.count_filter", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": true, "tactics": ["split_ifs", "exact", "exact"], "tactic_count": 3}
{"name": "Multiset.count_map", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.count_map_eq_count", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": false, "tactics": ["suffices", "rw", "exact", "rw", "simp", "simp"], "tactic_count": 6}
{"name": "Multiset.count_map_eq_count'", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "rw", "rintro", "rw", "contradiction"], "tactic_count": 6}
{"name": "Multiset.filter_eq'", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.filter_eq", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Multiset.filter_sub", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": true, "tactics": ["revert", "rw", "by_cases", "rw", "congr", "by_cases", "rw", "rw", "rw", "by_cases", "rw", "rw"], "tactic_count": 12}
{"name": "Multiset.sub_filter_eq_filter_not", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Multiset.map_le_map_iff", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": true, "tactics": ["classical", "refine", "simpa"], "tactic_count": 3}
{"name": "Multiset.mapEmbedding", "kind": "definition", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.count_eq_card_filter_eq", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.map_count_True_eq_filter_card", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.filter_attach'", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": true, "tactics": ["classical", "refine", "rw", "simp"], "tactic_count": 4}
{"name": "Multiset.Nodup.filter", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Nodup.erase_eq_filter", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Nodup.filterMap", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Nodup.mem_erase_iff", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.Nodup.notMem_erase", "kind": "theorem", "module": "Mathlib.Data.Multiset.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.ndinsert", "kind": "definition", "module": "Mathlib.Data.Multiset.FinsetOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.coe_ndinsert", "kind": "theorem", "module": "Mathlib.Data.Multiset.FinsetOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.ndinsert_zero", "kind": "theorem", "module": "Mathlib.Data.Multiset.FinsetOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.ndinsert_of_mem", "kind": "theorem", "module": "Mathlib.Data.Multiset.FinsetOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.ndinsert_of_notMem", "kind": "theorem", "module": "Mathlib.Data.Multiset.FinsetOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.mem_ndinsert", "kind": "theorem", "module": "Mathlib.Data.Multiset.FinsetOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.le_ndinsert_self", "kind": "theorem", "module": "Mathlib.Data.Multiset.FinsetOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.mem_ndinsert_self", "kind": "theorem", "module": "Mathlib.Data.Multiset.FinsetOps", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.mem_ndinsert_of_mem", "kind": "theorem", "module": "Mathlib.Data.Multiset.FinsetOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.length_ndinsert_of_mem", "kind": "theorem", "module": "Mathlib.Data.Multiset.FinsetOps", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.length_ndinsert_of_notMem", "kind": "theorem", "module": "Mathlib.Data.Multiset.FinsetOps", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.dedup_cons", "kind": "theorem", "module": "Mathlib.Data.Multiset.FinsetOps", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "Multiset.Nodup.ndinsert", "kind": "theorem", "module": "Mathlib.Data.Multiset.FinsetOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.ndinsert_le", "kind": "theorem", "module": "Mathlib.Data.Multiset.FinsetOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.attach_ndinsert", "kind": "theorem", "module": "Mathlib.Data.Multiset.FinsetOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.disjoint_ndinsert_left", "kind": "theorem", "module": "Mathlib.Data.Multiset.FinsetOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.disjoint_ndinsert_right", "kind": "theorem", "module": "Mathlib.Data.Multiset.FinsetOps", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.ndunion", "kind": "definition", "module": "Mathlib.Data.Multiset.FinsetOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.coe_ndunion", "kind": "theorem", "module": "Mathlib.Data.Multiset.FinsetOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.zero_ndunion", "kind": "theorem", "module": "Mathlib.Data.Multiset.FinsetOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.cons_ndunion", "kind": "theorem", "module": "Mathlib.Data.Multiset.FinsetOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.mem_ndunion", "kind": "theorem", "module": "Mathlib.Data.Multiset.FinsetOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.le_ndunion_right", "kind": "theorem", "module": "Mathlib.Data.Multiset.FinsetOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.subset_ndunion_right", "kind": "theorem", "module": "Mathlib.Data.Multiset.FinsetOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.ndunion_le_add", "kind": "theorem", "module": "Mathlib.Data.Multiset.FinsetOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.ndunion_le", "kind": "theorem", "module": "Mathlib.Data.Multiset.FinsetOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.subset_ndunion_left", "kind": "theorem", "module": "Mathlib.Data.Multiset.FinsetOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.le_ndunion_left", "kind": "theorem", "module": "Mathlib.Data.Multiset.FinsetOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.ndunion_le_union", "kind": "theorem", "module": "Mathlib.Data.Multiset.FinsetOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Nodup.ndunion", "kind": "theorem", "module": "Mathlib.Data.Multiset.FinsetOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.ndunion_eq_union", "kind": "theorem", "module": "Mathlib.Data.Multiset.FinsetOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.dedup_add", "kind": "theorem", "module": "Mathlib.Data.Multiset.FinsetOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Disjoint.ndunion_eq", "kind": "theorem", "module": "Mathlib.Data.Multiset.FinsetOps", "is_tactic_proof": true, "tactics": ["induction", "exact"], "tactic_count": 2}
{"name": "Multiset.Subset.ndunion_eq_right", "kind": "theorem", "module": "Mathlib.Data.Multiset.FinsetOps", "is_tactic_proof": true, "tactics": ["induction", "exact"], "tactic_count": 2}
{"name": "Multiset.ndinter", "kind": "definition", "module": "Mathlib.Data.Multiset.FinsetOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.coe_ndinter", "kind": "theorem", "module": "Mathlib.Data.Multiset.FinsetOps", "is_tactic_proof": true, "tactics": ["simp", "apply"], "tactic_count": 2}
{"name": "Multiset.zero_ndinter", "kind": "theorem", "module": "Mathlib.Data.Multiset.FinsetOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.cons_ndinter_of_mem", "kind": "theorem", "module": "Mathlib.Data.Multiset.FinsetOps", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.ndinter_cons_of_notMem", "kind": "theorem", "module": "Mathlib.Data.Multiset.FinsetOps", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.mem_ndinter", "kind": "theorem", "module": "Mathlib.Data.Multiset.FinsetOps", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.Nodup.ndinter", "kind": "theorem", "module": "Mathlib.Data.Multiset.FinsetOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.le_ndinter", "kind": "theorem", "module": "Mathlib.Data.Multiset.FinsetOps", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.ndinter_le_left", "kind": "theorem", "module": "Mathlib.Data.Multiset.FinsetOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.ndinter_subset_left", "kind": "theorem", "module": "Mathlib.Data.Multiset.FinsetOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.ndinter_subset_right", "kind": "theorem", "module": "Mathlib.Data.Multiset.FinsetOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.ndinter_le_right", "kind": "theorem", "module": "Mathlib.Data.Multiset.FinsetOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.inter_le_ndinter", "kind": "theorem", "module": "Mathlib.Data.Multiset.FinsetOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.ndinter_eq_inter", "kind": "theorem", "module": "Mathlib.Data.Multiset.FinsetOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Nodup.inter", "kind": "theorem", "module": "Mathlib.Data.Multiset.FinsetOps", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Multiset.ndinter_eq_zero_iff_disjoint", "kind": "theorem", "module": "Mathlib.Data.Multiset.FinsetOps", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.Subset.ndinter_eq_left", "kind": "theorem", "module": "Mathlib.Data.Multiset.FinsetOps", "is_tactic_proof": true, "tactics": ["induction", "rw"], "tactic_count": 2}
{"name": "Multiset.ToType", "kind": "definition", "module": "Mathlib.Data.Multiset.Fintype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.instCoeSortType", "kind": "instance", "module": "Mathlib.Data.Multiset.Fintype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset._example", "kind": "example", "module": "Mathlib.Data.Multiset.Fintype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.mkToType", "kind": "definition", "module": "Mathlib.Data.Multiset.Fintype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.instCoeSortMultisetType.instCoeOutToType", "kind": "instance", "module": "Mathlib.Data.Multiset.Fintype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.coe_mk", "kind": "theorem", "module": "Mathlib.Data.Multiset.Fintype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.coe_mem", "kind": "theorem", "module": "Mathlib.Data.Multiset.Fintype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.forall_coe", "kind": "theorem", "module": "Mathlib.Data.Multiset.Fintype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.exists_coe", "kind": "theorem", "module": "Mathlib.Data.Multiset.Fintype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.instFintypeElemProdNatSetOfLtSndCountFst", "kind": "instance", "module": "Mathlib.Data.Multiset.Fintype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.toEnumFinset", "kind": "definition", "module": "Mathlib.Data.Multiset.Fintype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.mem_toEnumFinset", "kind": "theorem", "module": "Mathlib.Data.Multiset.Fintype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.mem_of_mem_toEnumFinset", "kind": "theorem", "module": "Mathlib.Data.Multiset.Fintype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.toEnumFinset_filter_eq", "kind": "theorem", "module": "Mathlib.Data.Multiset.Fintype", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Multiset.map_toEnumFinset_fst", "kind": "theorem", "module": "Mathlib.Data.Multiset.Fintype", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Multiset.image_toEnumFinset_fst", "kind": "theorem", "module": "Mathlib.Data.Multiset.Fintype", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.map_fst_le_of_subset_toEnumFinset", "kind": "theorem", "module": "Mathlib.Data.Multiset.Fintype", "is_tactic_proof": true, "tactics": ["simp_rw", "rintro", "obtain", "rw", "exact", "obtain", "by_contra", "replace", "simpa", "h", "have", "simpa", "lia", "exact"], "tactic_count": 14}
{"name": "Multiset.toEnumFinset_mono", "kind": "theorem", "module": "Mathlib.Data.Multiset.Fintype", "is_tactic_proof": true, "tactics": ["intro", "simp", "exact"], "tactic_count": 3}
{"name": "Multiset.toEnumFinset_subset_iff", "kind": "theorem", "module": "Mathlib.Data.Multiset.Fintype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.coeEmbedding", "kind": "definition", "module": "Mathlib.Data.Multiset.Fintype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.coeEquiv", "kind": "definition", "module": "Mathlib.Data.Multiset.Fintype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.toEmbedding_coeEquiv_trans", "kind": "theorem", "module": "Mathlib.Data.Multiset.Fintype", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Multiset.fintypeCoe", "kind": "instance", "module": "Mathlib.Data.Multiset.Fintype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.map_univ_coeEmbedding", "kind": "theorem", "module": "Mathlib.Data.Multiset.Fintype", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Multiset.map_univ_coe", "kind": "theorem", "module": "Mathlib.Data.Multiset.Fintype", "is_tactic_proof": true, "tactics": ["have", "rw", "simpa"], "tactic_count": 3}
{"name": "Multiset.map_univ_comp_coe", "kind": "theorem", "module": "Mathlib.Data.Multiset.Fintype", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.map_univ", "kind": "theorem", "module": "Mathlib.Data.Multiset.Fintype", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Multiset.card_toEnumFinset", "kind": "theorem", "module": "Mathlib.Data.Multiset.Fintype", "is_tactic_proof": true, "tactics": ["rw", "congr", "exact"], "tactic_count": 3}
{"name": "Multiset.card_coe", "kind": "theorem", "module": "Mathlib.Data.Multiset.Fintype", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Multiset.prod_eq_prod_coe", "kind": "theorem", "module": "Mathlib.Data.Multiset.Fintype", "is_tactic_proof": true, "tactics": ["congr", "simp"], "tactic_count": 2}
{"name": "Multiset.prod_eq_prod_toEnumFinset", "kind": "theorem", "module": "Mathlib.Data.Multiset.Fintype", "is_tactic_proof": true, "tactics": ["congr", "simp"], "tactic_count": 2}
{"name": "Multiset.prod_toEnumFinset", "kind": "theorem", "module": "Mathlib.Data.Multiset.Fintype", "is_tactic_proof": true, "tactics": ["rw", "rw", "intro", "rfl"], "tactic_count": 4}
{"name": "Multiset.cast", "kind": "definition", "module": "Mathlib.Data.Multiset.Fintype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.instIsEmptyToTypeOfNat", "kind": "instance", "module": "Mathlib.Data.Multiset.Fintype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.instIsEmptyToTypeEmptyCollection", "kind": "instance", "module": "Mathlib.Data.Multiset.Fintype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.consEquiv", "kind": "definition", "module": "Mathlib.Data.Multiset.Fintype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.consEquiv_symm_none", "kind": "theorem", "module": "Mathlib.Data.Multiset.Fintype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.consEquiv_symm_some", "kind": "theorem", "module": "Mathlib.Data.Multiset.Fintype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.coe_consEquiv_of_ne", "kind": "theorem", "module": "Mathlib.Data.Multiset.Fintype", "is_tactic_proof": true, "tactics": ["simp", "rfl"], "tactic_count": 2}
{"name": "Multiset.coe_consEquiv_of_eq_of_eq", "kind": "theorem", "module": "Mathlib.Data.Multiset.Fintype", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.coe_consEquiv_of_eq_of_lt", "kind": "theorem", "module": "Mathlib.Data.Multiset.Fintype", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.mapEquiv_aux", "kind": "definition", "module": "Mathlib.Data.Multiset.Fintype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.mapEquiv", "kind": "definition", "module": "Mathlib.Data.Multiset.Fintype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.mapEquiv_apply", "kind": "theorem", "module": "Mathlib.Data.Multiset.Fintype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.Multiset.Fold.0.Multiset.term_*_", "kind": "definition", "module": "Mathlib.Data.Multiset.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.Multiset.Fold.0.Multiset._aux_Mathlib_Data_Multiset_Fold___macroRules__private_Mathlib_Data_Multiset_Fold_0_Multiset_term_*__1", "kind": "definition", "module": "Mathlib.Data.Multiset.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.fold", "kind": "definition", "module": "Mathlib.Data.Multiset.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.fold_eq_foldr", "kind": "theorem", "module": "Mathlib.Data.Multiset.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.coe_fold_r", "kind": "theorem", "module": "Mathlib.Data.Multiset.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.coe_fold_l", "kind": "theorem", "module": "Mathlib.Data.Multiset.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.fold_eq_foldl", "kind": "theorem", "module": "Mathlib.Data.Multiset.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.fold_zero", "kind": "theorem", "module": "Mathlib.Data.Multiset.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.fold_cons_left", "kind": "theorem", "module": "Mathlib.Data.Multiset.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.fold_cons_right", "kind": "theorem", "module": "Mathlib.Data.Multiset.Fold", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.fold_cons'_right", "kind": "theorem", "module": "Mathlib.Data.Multiset.Fold", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.fold_cons'_left", "kind": "theorem", "module": "Mathlib.Data.Multiset.Fold", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.fold_add", "kind": "theorem", "module": "Mathlib.Data.Multiset.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.fold_singleton", "kind": "theorem", "module": "Mathlib.Data.Multiset.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.fold_distrib", "kind": "theorem", "module": "Mathlib.Data.Multiset.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.fold_hom", "kind": "theorem", "module": "Mathlib.Data.Multiset.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.fold_union_inter", "kind": "theorem", "module": "Mathlib.Data.Multiset.Fold", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.fold_dedup_idem", "kind": "theorem", "module": "Mathlib.Data.Multiset.Fold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.functor", "kind": "instance", "module": "Mathlib.Data.Multiset.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.fmap_def", "kind": "theorem", "module": "Mathlib.Data.Multiset.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.instLawfulFunctor", "kind": "instance", "module": "Mathlib.Data.Multiset.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.traverse", "kind": "definition", "module": "Mathlib.Data.Multiset.Functor", "is_tactic_proof": true, "tactics": ["refine", "introv", "induction", "nil", "h", "have", "simpa", "swap", "l", "have", "rw", "congr", "funext", "simpa", "simp", "trans"], "tactic_count": 16}
{"name": "Multiset.instMonad", "kind": "instance", "module": "Mathlib.Data.Multiset.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.pure_def", "kind": "theorem", "module": "Mathlib.Data.Multiset.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.bind_def", "kind": "theorem", "module": "Mathlib.Data.Multiset.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.instLawfulMonad", "kind": "instance", "module": "Mathlib.Data.Multiset.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.map_comp_coe", "kind": "theorem", "module": "Mathlib.Data.Multiset.Functor", "is_tactic_proof": true, "tactics": ["funext"], "tactic_count": 1}
{"name": "Multiset.id_traverse", "kind": "theorem", "module": "Mathlib.Data.Multiset.Functor", "is_tactic_proof": true, "tactics": ["refine", "intro", "simp"], "tactic_count": 3}
{"name": "Multiset.comp_traverse", "kind": "theorem", "module": "Mathlib.Data.Multiset.Functor", "is_tactic_proof": true, "tactics": ["refine", "intro", "simp"], "tactic_count": 3}
{"name": "Multiset.map_traverse", "kind": "theorem", "module": "Mathlib.Data.Multiset.Functor", "is_tactic_proof": true, "tactics": ["refine", "intro", "simp", "rw", "simp"], "tactic_count": 5}
{"name": "Multiset.traverse_map", "kind": "theorem", "module": "Mathlib.Data.Multiset.Functor", "is_tactic_proof": true, "tactics": ["refine", "intro", "simp", "rw"], "tactic_count": 4}
{"name": "Multiset.naturality", "kind": "theorem", "module": "Mathlib.Data.Multiset.Functor", "is_tactic_proof": true, "tactics": ["refine", "intro", "simp"], "tactic_count": 3}
{"name": "Multiset.instLocallyFiniteOrder", "kind": "instance", "module": "Mathlib.Data.Multiset.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Icc_eq", "kind": "theorem", "module": "Mathlib.Data.Multiset.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.uIcc_eq", "kind": "theorem", "module": "Mathlib.Data.Multiset.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.card_Icc", "kind": "theorem", "module": "Mathlib.Data.Multiset.Interval", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Multiset.card_Ico", "kind": "theorem", "module": "Mathlib.Data.Multiset.Interval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.card_Ioc", "kind": "theorem", "module": "Mathlib.Data.Multiset.Interval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.card_Ioo", "kind": "theorem", "module": "Mathlib.Data.Multiset.Interval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.card_uIcc", "kind": "theorem", "module": "Mathlib.Data.Multiset.Interval", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Multiset.card_Iic", "kind": "theorem", "module": "Mathlib.Data.Multiset.Interval", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Multiset.sup", "kind": "definition", "module": "Mathlib.Data.Multiset.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.sup_coe", "kind": "theorem", "module": "Mathlib.Data.Multiset.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.sup_zero", "kind": "theorem", "module": "Mathlib.Data.Multiset.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.sup_cons", "kind": "theorem", "module": "Mathlib.Data.Multiset.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.sup_singleton", "kind": "theorem", "module": "Mathlib.Data.Multiset.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.sup_add", "kind": "theorem", "module": "Mathlib.Data.Multiset.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.sup_le", "kind": "theorem", "module": "Mathlib.Data.Multiset.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.le_sup", "kind": "theorem", "module": "Mathlib.Data.Multiset.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.sup_mono", "kind": "theorem", "module": "Mathlib.Data.Multiset.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.sup_dedup", "kind": "theorem", "module": "Mathlib.Data.Multiset.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.sup_ndunion", "kind": "theorem", "module": "Mathlib.Data.Multiset.Lattice", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.sup_union", "kind": "theorem", "module": "Mathlib.Data.Multiset.Lattice", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.sup_ndinsert", "kind": "theorem", "module": "Mathlib.Data.Multiset.Lattice", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.nodup_sup_iff", "kind": "theorem", "module": "Mathlib.Data.Multiset.Lattice", "is_tactic_proof": true, "tactics": ["induction", "empty", "cons"], "tactic_count": 3}
{"name": "Multiset.inf", "kind": "definition", "module": "Mathlib.Data.Multiset.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.inf_coe", "kind": "theorem", "module": "Mathlib.Data.Multiset.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.inf_zero", "kind": "theorem", "module": "Mathlib.Data.Multiset.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.inf_cons", "kind": "theorem", "module": "Mathlib.Data.Multiset.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.inf_singleton", "kind": "theorem", "module": "Mathlib.Data.Multiset.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.inf_add", "kind": "theorem", "module": "Mathlib.Data.Multiset.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.le_inf", "kind": "theorem", "module": "Mathlib.Data.Multiset.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.inf_le", "kind": "theorem", "module": "Mathlib.Data.Multiset.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.inf_mono", "kind": "theorem", "module": "Mathlib.Data.Multiset.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.inf_dedup", "kind": "theorem", "module": "Mathlib.Data.Multiset.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.inf_ndunion", "kind": "theorem", "module": "Mathlib.Data.Multiset.Lattice", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.inf_union", "kind": "theorem", "module": "Mathlib.Data.Multiset.Lattice", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.inf_ndinsert", "kind": "theorem", "module": "Mathlib.Data.Multiset.Lattice", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.map", "kind": "definition", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.map_congr", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": true, "tactics": ["rintro", "induction", "exact"], "tactic_count": 3}
{"name": "Multiset.map_hcongr", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": true, "tactics": ["subst", "simp"], "tactic_count": 2}
{"name": "Multiset.forall_mem_map_iff", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.map_coe", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.map_zero", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.map_cons", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.map_comp_cons", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Multiset.map_singleton", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.map_replicate", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.map_add", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.canLift", "kind": "instance", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.mem_map", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.card_map", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.map_eq_zero", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.mem_map_of_mem", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.map_eq_singleton", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": true, "tactics": ["constructor", "intro", "obtain", "refine", "rw", "rintro", "simp"], "tactic_count": 7}
{"name": "Multiset.map_eq_cons", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "rw", "intro", "have", "rw", "exact", "obtain", "obtain", "rw", "refine", "rw"], "tactic_count": 12}
{"name": "Multiset.mem_map_of_injective", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.map_map", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.map_id", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.map_id'", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.map_const", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.map_const'", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.eq_of_mem_map_const", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.map_le_map", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.map_lt_map", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "Multiset.map_mono", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.map_strictMono", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.map_subset_map", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.map_erase", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": false, "tactics": ["induction", "empty", "cons", "by_cases", "cases", "simp", "rw"], "tactic_count": 7}
{"name": "Multiset.map_erase_of_mem", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": false, "tactics": ["induction", "empty", "cons", "rcases", "simp", "replace", "rw"], "tactic_count": 7}
{"name": "Multiset.map_surjective_of_surjective", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": true, "tactics": ["intro", "induction", "empty", "cons", "obtain", "obtain", "exact"], "tactic_count": 7}
{"name": "Multiset.foldl", "kind": "definition", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.foldl_zero", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.foldl_cons", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.foldl_add", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.foldr", "kind": "definition", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.foldr_zero", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.foldr_cons", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.foldr_singleton", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.foldr_add", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.coe_foldr", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.coe_foldl", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.coe_foldr_swap", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.foldr_swap", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.foldl_swap", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.foldr_induction'", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": true, "tactics": ["induction", "empty", "cons", "simp", "exact"], "tactic_count": 5}
{"name": "Multiset.foldr_induction", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.foldl_induction'", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Multiset.foldl_induction", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.pmap_eq_map", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.map_pmap", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.pmap_eq_map_attach", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.attach_map_val'", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.attach_map_val", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.attach_cons", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.erase_attach_map_val", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.erase_attach_map", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": true, "tactics": ["simp", "rw"], "tactic_count": 2}
{"name": "Multiset.sub_eq_fold_erase", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.rel_map_left", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.rel_map_right", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.rel_map", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.map_eq_map", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Multiset.map_injective", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.map_mk_eq_map_mk_of_rel", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.exists_multiset_eq_map_quot_mk", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.induction_on_multiset_quot", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Nodup.of_map", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Nodup.map_on", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Nodup.map", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.nodup_map_iff_of_inj_on", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.nodup_map_iff_of_injective", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.inj_on_of_nodup_map", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.nodup_map_iff_inj_on", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Nodup.pmap", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.nodup_attach", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.map_eq_map_of_bij_of_nodup", "kind": "theorem", "module": "Mathlib.Data.Multiset.MapFold", "is_tactic_proof": false, "tactics": ["have", "rw", "aesop", "exact", "calc", "s.map"], "tactic_count": 6}
{"name": "Multiset.Nat.antidiagonal", "kind": "definition", "module": "Mathlib.Data.Multiset.NatAntidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Nat.mem_antidiagonal", "kind": "theorem", "module": "Mathlib.Data.Multiset.NatAntidiagonal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.Nat.card_antidiagonal", "kind": "theorem", "module": "Mathlib.Data.Multiset.NatAntidiagonal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.Nat.antidiagonal_zero", "kind": "theorem", "module": "Mathlib.Data.Multiset.NatAntidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Nat.nodup_antidiagonal", "kind": "theorem", "module": "Mathlib.Data.Multiset.NatAntidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Nat.antidiagonal_succ", "kind": "theorem", "module": "Mathlib.Data.Multiset.NatAntidiagonal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.Nat.antidiagonal_succ'", "kind": "theorem", "module": "Mathlib.Data.Multiset.NatAntidiagonal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.Nat.antidiagonal_succ_succ'", "kind": "theorem", "module": "Mathlib.Data.Multiset.NatAntidiagonal", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Multiset.Nat.map_swap_antidiagonal", "kind": "theorem", "module": "Mathlib.Data.Multiset.NatAntidiagonal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.instIsOrderedCancelAddMonoid", "kind": "instance", "module": "Mathlib.Data.Multiset.OrderedMonoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.instCanonicallyOrderedAdd", "kind": "instance", "module": "Mathlib.Data.Multiset.OrderedMonoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Pairwise.forall", "kind": "theorem", "module": "Mathlib.Data.Multiset.Pairwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Pi.empty", "kind": "definition", "module": "Mathlib.Data.Multiset.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Pi.cons", "kind": "definition", "module": "Mathlib.Data.Multiset.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Pi.cons_same", "kind": "theorem", "module": "Mathlib.Data.Multiset.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Pi.cons_ne", "kind": "theorem", "module": "Mathlib.Data.Multiset.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Pi.cons_swap", "kind": "theorem", "module": "Mathlib.Data.Multiset.Pi", "is_tactic_proof": true, "tactics": ["apply", "simp", "rintro", "refine", "rcases", "on_goal", "all_goals"], "tactic_count": 7}
{"name": "Multiset.Pi.cons_eta", "kind": "theorem", "module": "Mathlib.Data.Multiset.Pi", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "subst", "rw", "rw"], "tactic_count": 5}
{"name": "Multiset.Pi.cons_map", "kind": "theorem", "module": "Mathlib.Data.Multiset.Pi", "is_tactic_proof": true, "tactics": ["ext", "refine", "ext", "rfl"], "tactic_count": 4}
{"name": "Multiset.Pi.forall_rel_cons_ext", "kind": "theorem", "module": "Mathlib.Data.Multiset.Pi", "is_tactic_proof": true, "tactics": ["intro", "dsimp", "split_ifs", "cases", "exact", "exact"], "tactic_count": 6}
{"name": "Multiset.Pi.cons_injective", "kind": "theorem", "module": "Mathlib.Data.Multiset.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.pi", "kind": "definition", "module": "Mathlib.Data.Multiset.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.pi_zero", "kind": "theorem", "module": "Mathlib.Data.Multiset.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.pi_cons", "kind": "theorem", "module": "Mathlib.Data.Multiset.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.card_pi", "kind": "theorem", "module": "Mathlib.Data.Multiset.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Nodup.pi", "kind": "theorem", "module": "Mathlib.Data.Multiset.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.mem_pi", "kind": "theorem", "module": "Mathlib.Data.Multiset.Pi", "is_tactic_proof": false, "tactics": ["induction", "empty", "have", "simp", "intro", "cons", "simp_rw", "constructor", "rintro", "by_cases", "subst", "rwa", "rw", "apply", "intro", "refine", "rw"], "tactic_count": 17}
{"name": "Multiset.powersetAux", "kind": "definition", "module": "Mathlib.Data.Multiset.Powerset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.powersetAux_eq_map_coe", "kind": "theorem", "module": "Mathlib.Data.Multiset.Powerset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.mem_powersetAux", "kind": "theorem", "module": "Mathlib.Data.Multiset.Powerset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.powersetAux'", "kind": "definition", "module": "Mathlib.Data.Multiset.Powerset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.powersetAux_perm_powersetAux'", "kind": "theorem", "module": "Mathlib.Data.Multiset.Powerset", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.powersetAux'_nil", "kind": "theorem", "module": "Mathlib.Data.Multiset.Powerset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.powersetAux'_cons", "kind": "theorem", "module": "Mathlib.Data.Multiset.Powerset", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.powerset_aux'_perm", "kind": "theorem", "module": "Mathlib.Data.Multiset.Powerset", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "simp", "exact", "swap", "simp", "apply", "rw", "exact", "trans"], "tactic_count": 11}
{"name": "Multiset.powersetAux_perm", "kind": "theorem", "module": "Mathlib.Data.Multiset.Powerset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.powerset", "kind": "definition", "module": "Mathlib.Data.Multiset.Powerset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.powerset_coe", "kind": "theorem", "module": "Mathlib.Data.Multiset.Powerset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.powerset_coe'", "kind": "theorem", "module": "Mathlib.Data.Multiset.Powerset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.powerset_zero", "kind": "theorem", "module": "Mathlib.Data.Multiset.Powerset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.powerset_cons", "kind": "theorem", "module": "Mathlib.Data.Multiset.Powerset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.mem_powerset", "kind": "theorem", "module": "Mathlib.Data.Multiset.Powerset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.map_single_le_powerset", "kind": "theorem", "module": "Mathlib.Data.Multiset.Powerset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.card_powerset", "kind": "theorem", "module": "Mathlib.Data.Multiset.Powerset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.revzip_powersetAux", "kind": "theorem", "module": "Mathlib.Data.Multiset.Powerset", "is_tactic_proof": true, "tactics": ["rw", "simp", "rcases", "exact"], "tactic_count": 4}
{"name": "Multiset.revzip_powersetAux'", "kind": "theorem", "module": "Mathlib.Data.Multiset.Powerset", "is_tactic_proof": true, "tactics": ["rw", "simp", "rcases", "exact"], "tactic_count": 4}
{"name": "Multiset.revzip_powersetAux_lemma", "kind": "theorem", "module": "Mathlib.Data.Multiset.Powerset", "is_tactic_proof": false, "tactics": ["have", "rw", "rintro", "dsimp", "rw", "rw", "simpa"], "tactic_count": 7}
{"name": "Multiset.revzip_powersetAux_perm_aux'", "kind": "theorem", "module": "Mathlib.Data.Multiset.Powerset", "is_tactic_proof": true, "tactics": ["haveI", "rw", "exact"], "tactic_count": 3}
{"name": "Multiset.revzip_powersetAux_perm", "kind": "theorem", "module": "Mathlib.Data.Multiset.Powerset", "is_tactic_proof": true, "tactics": ["haveI", "simp", "exact"], "tactic_count": 3}
{"name": "Multiset.powersetCardAux", "kind": "definition", "module": "Mathlib.Data.Multiset.Powerset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.powersetCardAux_eq_map_coe", "kind": "theorem", "module": "Mathlib.Data.Multiset.Powerset", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.mem_powersetCardAux", "kind": "theorem", "module": "Mathlib.Data.Multiset.Powerset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.powersetCardAux_zero", "kind": "theorem", "module": "Mathlib.Data.Multiset.Powerset", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.powersetCardAux_nil", "kind": "theorem", "module": "Mathlib.Data.Multiset.Powerset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.powersetCardAux_cons", "kind": "theorem", "module": "Mathlib.Data.Multiset.Powerset", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.powersetCardAux_perm", "kind": "theorem", "module": "Mathlib.Data.Multiset.Powerset", "is_tactic_proof": false, "tactics": ["induction", "zero", "succ", "induction", "nil", "cons", "simp", "exact", "swap", "simp", "apply", "cases", "simp", "simp", "rw", "exact", "trans"], "tactic_count": 17}
{"name": "Multiset.powersetCard", "kind": "definition", "module": "Mathlib.Data.Multiset.Powerset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.powersetCard_coe'", "kind": "theorem", "module": "Mathlib.Data.Multiset.Powerset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.powersetCard_coe", "kind": "theorem", "module": "Mathlib.Data.Multiset.Powerset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.powersetCard_zero_left", "kind": "theorem", "module": "Mathlib.Data.Multiset.Powerset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.powersetCard_zero_right", "kind": "theorem", "module": "Mathlib.Data.Multiset.Powerset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.powersetCard_cons", "kind": "theorem", "module": "Mathlib.Data.Multiset.Powerset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.powersetCard_one", "kind": "theorem", "module": "Mathlib.Data.Multiset.Powerset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.mem_powersetCard", "kind": "theorem", "module": "Mathlib.Data.Multiset.Powerset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.card_powersetCard", "kind": "theorem", "module": "Mathlib.Data.Multiset.Powerset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.powersetCard_le_powerset", "kind": "theorem", "module": "Mathlib.Data.Multiset.Powerset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.powersetCard_mono", "kind": "theorem", "module": "Mathlib.Data.Multiset.Powerset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.powersetCard_eq_empty", "kind": "theorem", "module": "Mathlib.Data.Multiset.Powerset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.powersetCard_card_add", "kind": "theorem", "module": "Mathlib.Data.Multiset.Powerset", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.powersetCard_map", "kind": "theorem", "module": "Mathlib.Data.Multiset.Powerset", "is_tactic_proof": true, "tactics": ["induction", "empty", "cons"], "tactic_count": 3}
{"name": "Multiset.pairwise_disjoint_powersetCard", "kind": "theorem", "module": "Mathlib.Data.Multiset.Powerset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.bind_powerset_len", "kind": "theorem", "module": "Mathlib.Data.Multiset.Powerset", "is_tactic_proof": true, "tactics": ["induction", "simp_rw", "exact"], "tactic_count": 3}
{"name": "Multiset.nodup_powerset", "kind": "theorem", "module": "Mathlib.Data.Multiset.Powerset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Nodup.powersetCard", "kind": "theorem", "module": "Mathlib.Data.Multiset.Powerset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.range", "kind": "definition", "module": "Mathlib.Data.Multiset.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.coe_range", "kind": "theorem", "module": "Mathlib.Data.Multiset.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.range_zero", "kind": "theorem", "module": "Mathlib.Data.Multiset.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.range_succ", "kind": "theorem", "module": "Mathlib.Data.Multiset.Range", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.card_range", "kind": "theorem", "module": "Mathlib.Data.Multiset.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.range_subset", "kind": "theorem", "module": "Mathlib.Data.Multiset.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.mem_range", "kind": "theorem", "module": "Mathlib.Data.Multiset.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.notMem_range_self", "kind": "theorem", "module": "Mathlib.Data.Multiset.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.self_mem_range_succ", "kind": "theorem", "module": "Mathlib.Data.Multiset.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.range_add", "kind": "theorem", "module": "Mathlib.Data.Multiset.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.range_disjoint_map_add", "kind": "theorem", "module": "Mathlib.Data.Multiset.Range", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "obtain", "exact"], "tactic_count": 5}
{"name": "Multiset.range_add_eq_union", "kind": "theorem", "module": "Mathlib.Data.Multiset.Range", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "Multiset.nodup_range", "kind": "theorem", "module": "Mathlib.Data.Multiset.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.range_le", "kind": "theorem", "module": "Mathlib.Data.Multiset.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.replicate", "kind": "definition", "module": "Mathlib.Data.Multiset.Replicate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.coe_replicate", "kind": "theorem", "module": "Mathlib.Data.Multiset.Replicate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.replicate_zero", "kind": "theorem", "module": "Mathlib.Data.Multiset.Replicate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.replicate_succ", "kind": "theorem", "module": "Mathlib.Data.Multiset.Replicate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.replicate_add", "kind": "theorem", "module": "Mathlib.Data.Multiset.Replicate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.replicate_one", "kind": "theorem", "module": "Mathlib.Data.Multiset.Replicate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.card_replicate", "kind": "theorem", "module": "Mathlib.Data.Multiset.Replicate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.mem_replicate", "kind": "theorem", "module": "Mathlib.Data.Multiset.Replicate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.eq_of_mem_replicate", "kind": "theorem", "module": "Mathlib.Data.Multiset.Replicate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.eq_replicate_card", "kind": "theorem", "module": "Mathlib.Data.Multiset.Replicate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.eq_replicate", "kind": "theorem", "module": "Mathlib.Data.Multiset.Replicate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.replicate_right_injective", "kind": "theorem", "module": "Mathlib.Data.Multiset.Replicate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.replicate_right_inj", "kind": "theorem", "module": "Mathlib.Data.Multiset.Replicate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.replicate_left_injective", "kind": "theorem", "module": "Mathlib.Data.Multiset.Replicate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.replicate_subset_singleton", "kind": "theorem", "module": "Mathlib.Data.Multiset.Replicate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.replicate_le_coe", "kind": "theorem", "module": "Mathlib.Data.Multiset.Replicate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.replicate_le_replicate", "kind": "theorem", "module": "Mathlib.Data.Multiset.Replicate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.replicate_mono", "kind": "theorem", "module": "Mathlib.Data.Multiset.Replicate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.le_replicate_iff", "kind": "theorem", "module": "Mathlib.Data.Multiset.Replicate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.lt_replicate_succ", "kind": "theorem", "module": "Mathlib.Data.Multiset.Replicate", "is_tactic_proof": true, "tactics": ["rw", "constructor", "rintro", "have", "rwa", "intro", "rw", "exact"], "tactic_count": 8}
{"name": "Multiset.count_replicate_self", "kind": "theorem", "module": "Mathlib.Data.Multiset.Replicate", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "Multiset.count_replicate", "kind": "theorem", "module": "Mathlib.Data.Multiset.Replicate", "is_tactic_proof": true, "tactics": ["convert", "rw", "simp"], "tactic_count": 3}
{"name": "Multiset.le_count_iff_replicate_le", "kind": "theorem", "module": "Mathlib.Data.Multiset.Replicate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.rel_replicate_left", "kind": "theorem", "module": "Mathlib.Data.Multiset.Replicate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.rel_replicate_right", "kind": "theorem", "module": "Mathlib.Data.Multiset.Replicate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.nodup_iff_le", "kind": "theorem", "module": "Mathlib.Data.Multiset.Replicate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.nodup_iff_ne_cons_cons", "kind": "theorem", "module": "Mathlib.Data.Multiset.Replicate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.nodup_iff_pairwise", "kind": "theorem", "module": "Mathlib.Data.Multiset.Replicate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Nodup.pairwise", "kind": "theorem", "module": "Mathlib.Data.Multiset.Replicate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Sections", "kind": "definition", "module": "Mathlib.Data.Multiset.Sections", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.sections_zero", "kind": "theorem", "module": "Mathlib.Data.Multiset.Sections", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.sections_cons", "kind": "theorem", "module": "Mathlib.Data.Multiset.Sections", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.coe_sections", "kind": "theorem", "module": "Mathlib.Data.Multiset.Sections", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.sections_add", "kind": "theorem", "module": "Mathlib.Data.Multiset.Sections", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.mem_sections", "kind": "theorem", "module": "Mathlib.Data.Multiset.Sections", "is_tactic_proof": true, "tactics": ["induction", "empty", "cons"], "tactic_count": 3}
{"name": "Multiset.card_sections", "kind": "theorem", "module": "Mathlib.Data.Multiset.Sections", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.coe_sort", "kind": "theorem", "module": "Mathlib.Data.Multiset.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.pairwise_sort", "kind": "theorem", "module": "Mathlib.Data.Multiset.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.sort_eq", "kind": "theorem", "module": "Mathlib.Data.Multiset.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.sort_zero", "kind": "theorem", "module": "Mathlib.Data.Multiset.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.sort_singleton", "kind": "theorem", "module": "Mathlib.Data.Multiset.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.map_sort", "kind": "theorem", "module": "Mathlib.Data.Multiset.Sort", "is_tactic_proof": true, "tactics": ["revert", "exact"], "tactic_count": 2}
{"name": "Multiset.sort_cons", "kind": "theorem", "module": "Mathlib.Data.Multiset.Sort", "is_tactic_proof": true, "tactics": ["refine", "simpa"], "tactic_count": 2}
{"name": "Multiset.sort_range", "kind": "theorem", "module": "Mathlib.Data.Multiset.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.mem_sort", "kind": "theorem", "module": "Mathlib.Data.Multiset.Sort", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.length_sort", "kind": "theorem", "module": "Mathlib.Data.Multiset.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.instToExprOfToLevel", "kind": "instance", "module": "Mathlib.Data.Multiset.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.instRepr", "kind": "instance", "module": "Mathlib.Data.Multiset.Sort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.disjSum", "kind": "definition", "module": "Mathlib.Data.Multiset.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.zero_disjSum", "kind": "theorem", "module": "Mathlib.Data.Multiset.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.disjSum_zero", "kind": "theorem", "module": "Mathlib.Data.Multiset.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.card_disjSum", "kind": "theorem", "module": "Mathlib.Data.Multiset.Sum", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.mem_disjSum", "kind": "theorem", "module": "Mathlib.Data.Multiset.Sum", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Multiset.inl_mem_disjSum", "kind": "theorem", "module": "Mathlib.Data.Multiset.Sum", "is_tactic_proof": true, "tactics": ["rw", "simp", "rintro", "exact"], "tactic_count": 4}
{"name": "Multiset.inr_mem_disjSum", "kind": "theorem", "module": "Mathlib.Data.Multiset.Sum", "is_tactic_proof": true, "tactics": ["rw", "simp", "rintro", "exact"], "tactic_count": 4}
{"name": "Multiset.disjSum_mono", "kind": "theorem", "module": "Mathlib.Data.Multiset.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.disjSum_mono_left", "kind": "theorem", "module": "Mathlib.Data.Multiset.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.disjSum_mono_right", "kind": "theorem", "module": "Mathlib.Data.Multiset.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.disjSum_lt_disjSum_of_lt_of_le", "kind": "theorem", "module": "Mathlib.Data.Multiset.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.disjSum_lt_disjSum_of_le_of_lt", "kind": "theorem", "module": "Mathlib.Data.Multiset.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.disjSum_strictMono_left", "kind": "theorem", "module": "Mathlib.Data.Multiset.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.disjSum_strictMono_right", "kind": "theorem", "module": "Mathlib.Data.Multiset.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Nodup.disjSum", "kind": "theorem", "module": "Mathlib.Data.Multiset.Sum", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "Multiset.map_disjSum", "kind": "theorem", "module": "Mathlib.Data.Multiset.Sum", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Multiset.sym2", "kind": "definition", "module": "Mathlib.Data.Multiset.Sym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.sym2_coe", "kind": "theorem", "module": "Mathlib.Data.Multiset.Sym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.sym2_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Data.Multiset.Sym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.sym2_zero", "kind": "theorem", "module": "Mathlib.Data.Multiset.Sym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.sym2_cons", "kind": "theorem", "module": "Mathlib.Data.Multiset.Sym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.sym2_map", "kind": "theorem", "module": "Mathlib.Data.Multiset.Sym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.mk_mem_sym2_iff", "kind": "theorem", "module": "Mathlib.Data.Multiset.Sym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.mem_sym2_iff", "kind": "theorem", "module": "Mathlib.Data.Multiset.Sym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.setOf_mem_sym2", "kind": "theorem", "module": "Mathlib.Data.Multiset.Sym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Nodup.sym2", "kind": "theorem", "module": "Mathlib.Data.Multiset.Sym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.sym2_mono", "kind": "theorem", "module": "Mathlib.Data.Multiset.Sym", "is_tactic_proof": true, "tactics": ["refine", "suffices", "simpa"], "tactic_count": 3}
{"name": "Multiset.monotone_sym2", "kind": "theorem", "module": "Mathlib.Data.Multiset.Sym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.card_sym2", "kind": "theorem", "module": "Mathlib.Data.Multiset.Sym", "is_tactic_proof": true, "tactics": ["refine", "simp"], "tactic_count": 2}
{"name": "Multiset.dedup_sym2", "kind": "theorem", "module": "Mathlib.Data.Multiset.Sym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.union", "kind": "definition", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.instUnion", "kind": "instance", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.union_def", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.le_union_left", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.le_union_right", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.eq_union_left", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.union_le_union_right", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.union_le", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.mem_union", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.map_union", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.zero_union", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.union_zero", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.count_union", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.filter_union", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.inter", "kind": "definition", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.instInter", "kind": "instance", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.inter_zero", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.zero_inter", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.cons_inter_of_pos", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.cons_inter_of_neg", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.inter_le_left", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.inter_le_right", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": true, "tactics": ["induction", "empty", "cons", "by_cases", "simpa", "simp"], "tactic_count": 6}
{"name": "Multiset.le_inter", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": true, "tactics": ["revert", "simpa", "by_cases", "rw", "exact", "rw", "exact"], "tactic_count": 7}
{"name": "Multiset.mem_inter", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.instLattice", "kind": "instance", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.sup_eq_union", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.inf_eq_inter", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.le_inter_iff", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.union_le_iff", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.union_comm", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.inter_comm", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.eq_union_right", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.union_le_union_left", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.union_le_add", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.union_add_distrib", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": true, "tactics": ["simpa", "show"], "tactic_count": 2}
{"name": "Multiset.add_union_distrib", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.cons_union_distrib", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Multiset.inter_add_distrib", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": true, "tactics": ["by_contra", "obtain", "lt_iff_cons_le.1", "h.lt_of_le", "rw", "exact", "le_inter"], "tactic_count": 7}
{"name": "Multiset.add_inter_distrib", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.cons_inter_distrib", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.union_add_inter", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": true, "tactics": ["apply", "rw", "refine", "rw", "exact", "rw", "refine", "rw", "exact"], "tactic_count": 9}
{"name": "Multiset.sub_add_inter", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": true, "tactics": ["rw", "revert", "by_cases", "rw", "rw"], "tactic_count": 5}
{"name": "Multiset.sub_inter", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.count_inter", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": true, "tactics": ["apply", "rw"], "tactic_count": 2}
{"name": "Multiset.coe_inter", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Multiset.instDistribLattice", "kind": "instance", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.filter_inter", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.replicate_inter", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": true, "tactics": ["ext", "rw", "by_cases", "simp", "simp"], "tactic_count": 5}
{"name": "Multiset.inter_replicate", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.inter_add_sub_of_add_eq_add", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": true, "tactics": ["ext", "rw", "have", "rw", "simp_all", "omega"], "tactic_count": 6}
{"name": "Multiset.disjoint_left", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": true, "tactics": ["refine", "simpa", "rw", "exact"], "tactic_count": 4}
{"name": "Multiset.coe_disjoint", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.disjoint_right", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.disjoint_iff_ne", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.disjoint_of_subset_left", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.disjoint_of_subset_right", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.zero_disjoint", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.singleton_disjoint", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.disjoint_singleton", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.disjoint_add_left", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.disjoint_add_right", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.disjoint_cons_left", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.disjoint_cons_right", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.inter_eq_zero_iff_disjoint", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.disjoint_union_left", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.disjoint_union_right", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.add_eq_union_iff_disjoint", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Multiset.add_eq_union_left_of_le", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "exact", "rintro", "exact", "rintro", "exact"], "tactic_count": 8}
{"name": "Multiset.add_eq_union_right_of_le", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Multiset.disjoint_map_map", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.map_set_pairwise", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.nodup_add", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.disjoint_of_nodup_add", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Nodup.add_iff", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.Nodup.inter_left", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Nodup.inter_right", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.nodup_union", "kind": "theorem", "module": "Mathlib.Data.Multiset.UnionInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.zero", "kind": "definition", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.instZero", "kind": "instance", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.instEmptyCollection", "kind": "instance", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.inhabitedMultiset", "kind": "instance", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.instUniqueOfIsEmpty", "kind": "instance", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.coe_nil", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.empty_eq_zero", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.coe_eq_zero", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.coe_eq_zero_iff_isEmpty", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.cons", "kind": "definition", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.term_::ₘ_", "kind": "definition", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset._aux_Mathlib_Data_Multiset_ZeroCons___macroRules_Multiset_term_::ₘ__1", "kind": "definition", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset._aux_Mathlib_Data_Multiset_ZeroCons___unexpand_Multiset_cons_1", "kind": "definition", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.instInsert", "kind": "instance", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.insert_eq_cons", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.cons_coe", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.cons_inj_left", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.cons_inj_right", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "Multiset.induction", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": true, "tactics": ["rintro", "induction", "nil", "cons"], "tactic_count": 4}
{"name": "Multiset.induction_on", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.cons_swap", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.rec", "kind": "definition", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.recOn", "kind": "definition", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.recOn_0", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.recOn_cons", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.mem_cons", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.mem_cons_of_mem", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.mem_cons_self", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.forall_mem_cons", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.exists_cons_of_mem", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.notMem_zero", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.eq_zero_of_forall_notMem", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.eq_zero_iff_forall_notMem", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.exists_mem_of_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.empty_or_exists_mem", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.zero_ne_cons", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.cons_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.cons_eq_cons", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": true, "tactics": ["haveI", "constructor", "intro", "by_cases", "subst", "simp_all", "have", "have", "rcases", "simp", "have", "have", "simpa", "intro", "rcases", "simp", "simp"], "tactic_count": 17}
{"name": "Multiset.instSingleton", "kind": "instance", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.instLawfulSingleton", "kind": "instance", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.cons_zero", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.coe_singleton", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.mem_singleton", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.mem_singleton_self", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Multiset.singleton_inj", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Multiset.coe_eq_singleton", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.singleton_eq_cons_iff", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Multiset.pair_comm", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.zero_subset", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.subset_cons", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.ssubset_cons", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.cons_subset", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.cons_subset_cons", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.eq_zero_of_subset_zero", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.subset_zero", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.zero_ssubset", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.singleton_subset", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.induction_on'", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.zero_le", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.instOrderBot", "kind": "instance", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.bot_eq_zero", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.le_zero", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.lt_cons_self", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.le_cons_self", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.cons_le_cons_iff", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.cons_le_cons", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.cons_lt_cons_iff", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.cons_lt_cons", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.le_cons_of_notMem", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": true, "tactics": ["refine", "suffices", "introv", "revert", "refine", "introv", "rcases", "exact"], "tactic_count": 8}
{"name": "Multiset.cons_le_of_notMem", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": true, "tactics": ["apply", "rintro", "exact"], "tactic_count": 3}
{"name": "Multiset.singleton_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.zero_ne_singleton", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.singleton_le", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.le_singleton", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.lt_singleton", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": true, "tactics": ["simp", "rintro", "exact"], "tactic_count": 3}
{"name": "Multiset.ssubset_singleton_iff", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": true, "tactics": ["refine", "obtain", "rwa", "rintro", "simp"], "tactic_count": 5}
{"name": "Multiset.card_zero", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.card_cons", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.card_singleton", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.card_pair", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.card_eq_one", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.lt_iff_cons_le", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.card_eq_zero", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.card_pos", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.card_pos_iff_exists_mem", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.card_eq_two", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.card_eq_three", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.card_eq_four", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.pmap_zero", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.pmap_cons", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.attach_zero", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Rel", "kind": "inductive", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.Multiset.ZeroCons.0.Multiset.rel_flip_aux", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.rel_flip", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.rel_refl_of_refl_on", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": true, "tactics": ["refine", "intros", "apply", "intro", "exact"], "tactic_count": 5}
{"name": "Multiset.rel_eq_refl", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.rel_eq", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": true, "tactics": ["constructor", "intro", "induction", "intro", "subst", "exact"], "tactic_count": 6}
{"name": "Multiset.Rel.mono", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": true, "tactics": ["induction", "zero", "ih", "apply", "exact"], "tactic_count": 5}
{"name": "Multiset.rel_flip_eq", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.rel_zero_left", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.rel_zero_right", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.rel_cons_left", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": true, "tactics": ["constructor", "generalize", "intro", "induction", "zero", "ih", "rcases", "subst", "subst", "exact", "rcases", "exact", "exact"], "tactic_count": 13}
{"name": "Multiset.rel_cons_right", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw"], "tactic_count": 3}
{"name": "Multiset.card_eq_card_of_rel", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "Multiset.exists_mem_of_rel_of_mem", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": true, "tactics": ["induction", "zero", "intro", "rcases", "exact", "rcases", "exact"], "tactic_count": 7}
{"name": "Multiset.rel_of_forall", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": true, "tactics": ["revert", "refine", "intro", "rw", "intro", "rw", "obtain", "obtain", "refine", "exact", "simpa"], "tactic_count": 11}
{"name": "Multiset.Rel.trans", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": true, "tactics": ["induction", "empty", "cons", "obtain", "obtain", "exact"], "tactic_count": 6}
{"name": "Multiset.pairwise_zero", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.nodup_zero", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.nodup_cons", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Nodup.cons", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Nodup.of_cons", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Nodup.notMem", "kind": "theorem", "module": "Mathlib.Data.Multiset.ZeroCons", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.cast_listSum", "kind": "theorem", "module": "Mathlib.Data.NNRat.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.cast_listProd", "kind": "theorem", "module": "Mathlib.Data.NNRat.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.cast_multisetSum", "kind": "theorem", "module": "Mathlib.Data.NNRat.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.cast_sum", "kind": "theorem", "module": "Mathlib.Data.NNRat.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.cast_multisetProd", "kind": "theorem", "module": "Mathlib.Data.NNRat.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.cast_prod", "kind": "theorem", "module": "Mathlib.Data.NNRat.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.toNNRat_sum_of_nonneg", "kind": "theorem", "module": "Mathlib.Data.NNRat.BigOperators", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "NNRat.toNNRat_prod_of_nonneg", "kind": "theorem", "module": "Mathlib.Data.NNRat.BigOperators", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "LibraryNote.specialised_high_priority_simp_lemma", "kind": "definition", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.instPosMulMono", "kind": "instance", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.instNontrivial", "kind": "instance", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.instOrderBot", "kind": "instance", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.val_eq_cast", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.instCharZero", "kind": "instance", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.canLift", "kind": "instance", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.ext", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.coe_injective", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.coe_inj", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.ne_iff", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.coe_mk", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.forall", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.exists", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.toNNRat", "kind": "definition", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.coe_toNNRat", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.le_coe_toNNRat", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.coe_nonneg", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.coe_zero", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.num_zero", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.den_zero", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.coe_one", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.num_one", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.den_one", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.coe_add", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.coe_mul", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.coe_pow", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.num_pow", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NNRat.den_pow", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.coe_sub", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.coe_eq_zero", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": true, "tactics": ["norm_cast"], "tactic_count": 1}
{"name": "NNRat.coe_ne_zero", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.mk_zero", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.coe_le_coe", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.coe_lt_coe", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.coe_pos", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.coe_mono", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.toNNRat_mono", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.toNNRat_coe", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.toNNRat_coe_nat", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.gi", "kind": "definition", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.coeHom", "kind": "definition", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.coe_natCast", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.mk_natCast", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.coe_coeHom", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.nsmul_coe", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.bddAbove_coe", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.bddBelow_coe", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.coe_max", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.coe_min", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.sub_def", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.abs_coe", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.nonpos_iff_eq_zero", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.toNNRat_zero", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.toNNRat_one", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.toNNRat_pos", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Rat.toNNRat_eq_zero", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Rat.toNNRat_le_toNNRat_iff", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Rat.toNNRat_lt_toNNRat_iff'", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Rat.toNNRat_lt_toNNRat_iff", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.toNNRat_lt_toNNRat_iff_of_nonneg", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.toNNRat_add", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.toNNRat_add_le", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.toNNRat_le_iff_le_coe", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.le_toNNRat_iff_coe_le", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Rat.le_toNNRat_iff_coe_le'", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.toNNRat_lt_iff_lt_coe", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Rat.lt_toNNRat_iff_coe_lt", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.toNNRat_mul", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": true, "tactics": ["rcases", "ext", "have", "rw"], "tactic_count": 4}
{"name": "Rat.nnabs", "kind": "definition", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.coe_nnabs", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.num_coe", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NNRat.natAbs_num_coe", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.den_coe", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.num_ne_zero", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NNRat.num_pos", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "NNRat.den_pos", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.den_ne_zero", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.coprime_num_den", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "NNRat.num_natCast", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.den_natCast", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.num_ofNat", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.den_ofNat", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.ext_num_den", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": true, "tactics": ["refine", "simpa"], "tactic_count": 2}
{"name": "NNRat.ext_num_den_iff", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.divNat", "kind": "definition", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.coe_divNat", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.mk_divInt", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.divNat_inj", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NNRat.divNat_zero", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NNRat.num_divNat_den", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.natCast_eq_divNat", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.divNat_mul_divNat", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "NNRat.divNat_mul_left", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "NNRat.divNat_mul_right", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "NNRat.mul_den_eq_num", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": true, "tactics": ["ext", "push_cast", "rw", "exact"], "tactic_count": 4}
{"name": "NNRat.den_mul_eq_num", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NNRat.numDenCasesOn", "kind": "definition", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NNRat.add_def", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "NNRat.mul_def", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "NNRat.lt_def", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NNRat.le_def", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Qify.nnratCast_eq", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Qify.nnratCast_le", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Qify.nnratCast_lt", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Qify.nnratCast_ne", "kind": "theorem", "module": "Mathlib.Data.NNRat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.instFloorSemiring", "kind": "instance", "module": "Mathlib.Data.NNRat.Floor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.floor_coe", "kind": "theorem", "module": "Mathlib.Data.NNRat.Floor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.ceil_coe", "kind": "theorem", "module": "Mathlib.Data.NNRat.Floor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.coe_floor", "kind": "theorem", "module": "Mathlib.Data.NNRat.Floor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.coe_ceil", "kind": "theorem", "module": "Mathlib.Data.NNRat.Floor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.floor_def", "kind": "theorem", "module": "Mathlib.Data.NNRat.Floor", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NNRat.floor_cast", "kind": "theorem", "module": "Mathlib.Data.NNRat.Floor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.ceil_cast", "kind": "theorem", "module": "Mathlib.Data.NNRat.Floor", "is_tactic_proof": true, "tactics": ["obtain", "simp", "refine"], "tactic_count": 3}
{"name": "NNRat.intFloor_cast", "kind": "theorem", "module": "Mathlib.Data.NNRat.Floor", "is_tactic_proof": true, "tactics": ["rw", "norm_cast", "norm_cast", "rw"], "tactic_count": 4}
{"name": "NNRat.intCeil_cast", "kind": "theorem", "module": "Mathlib.Data.NNRat.Floor", "is_tactic_proof": true, "tactics": ["rw", "constructor", "have", "rw", "refine", "norm_cast", "rw", "exact"], "tactic_count": 8}
{"name": "NNRat.floor_natCast_div_natCast", "kind": "theorem", "module": "Mathlib.Data.NNRat.Floor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.IsNat.natCeil", "kind": "theorem", "module": "Mathlib.Data.NNRat.Floor", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "Mathlib.Meta.NormNum.IsInt.natCeil", "kind": "theorem", "module": "Mathlib.Data.NNRat.Floor", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "Mathlib.Meta.NormNum.IsNNRat.natCeil", "kind": "theorem", "module": "Mathlib.Data.NNRat.Floor", "is_tactic_proof": true, "tactics": ["constructor", "rw", "simp"], "tactic_count": 3}
{"name": "Mathlib.Meta.NormNum.IsRat.natCeil", "kind": "theorem", "module": "Mathlib.Data.NNRat.Floor", "is_tactic_proof": true, "tactics": ["constructor", "simp"], "tactic_count": 2}
{"name": "Mathlib.Meta.NormNum.evalNatCeil", "kind": "definition", "module": "Mathlib.Data.NNRat.Floor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.coe_indicator", "kind": "theorem", "module": "Mathlib.Data.NNRat.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.toNNRat_inv", "kind": "theorem", "module": "Mathlib.Data.NNRat.Lemmas", "is_tactic_proof": true, "tactics": ["obtain", "rw", "nth_rw", "rw"], "tactic_count": 4}
{"name": "Rat.toNNRat_div", "kind": "theorem", "module": "Mathlib.Data.NNRat.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Rat.toNNRat_div'", "kind": "theorem", "module": "Mathlib.Data.NNRat.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NNRat.rec", "kind": "definition", "module": "Mathlib.Data.NNRat.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NNRat.mul_num", "kind": "theorem", "module": "Mathlib.Data.NNRat.Lemmas", "is_tactic_proof": true, "tactics": ["zify", "convert"], "tactic_count": 2}
{"name": "NNRat.mul_den", "kind": "theorem", "module": "Mathlib.Data.NNRat.Lemmas", "is_tactic_proof": true, "tactics": ["convert", "norm_cast"], "tactic_count": 2}
{"name": "NNRat.den_mul_den_eq_den_mul_gcd", "kind": "theorem", "module": "Mathlib.Data.NNRat.Lemmas", "is_tactic_proof": true, "tactics": ["convert", "norm_cast"], "tactic_count": 2}
{"name": "NNRat.num_mul_num_eq_num_mul_gcd", "kind": "theorem", "module": "Mathlib.Data.NNRat.Lemmas", "is_tactic_proof": true, "tactics": ["zify", "convert"], "tactic_count": 2}
{"name": "instIsStrictOrderedRingNNRat", "kind": "instance", "module": "Mathlib.Data.NNRat.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.instOrderedSub", "kind": "instance", "module": "Mathlib.Data.NNRat.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.instCanonicallyOrderedAdd", "kind": "instance", "module": "Mathlib.Data.NNRat.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.instFloorSemiring", "kind": "instance", "module": "Mathlib.Data.NNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.coe_mulIndicator", "kind": "theorem", "module": "Mathlib.Data.NNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.coe_indicator", "kind": "theorem", "module": "Mathlib.Data.NNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.coe_mulSingle", "kind": "theorem", "module": "Mathlib.Data.NNReal.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "NNReal.coe_single", "kind": "theorem", "module": "Mathlib.Data.NNReal.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "NNReal.coe_list_sum", "kind": "theorem", "module": "Mathlib.Data.NNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.coe_list_prod", "kind": "theorem", "module": "Mathlib.Data.NNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.coe_multiset_sum", "kind": "theorem", "module": "Mathlib.Data.NNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.coe_multiset_prod", "kind": "theorem", "module": "Mathlib.Data.NNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.coe_sum", "kind": "theorem", "module": "Mathlib.Data.NNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.coe_expect", "kind": "theorem", "module": "Mathlib.Data.NNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.toNNReal_sum_of_nonneg", "kind": "theorem", "module": "Mathlib.Data.NNReal.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "NNReal.coe_prod", "kind": "theorem", "module": "Mathlib.Data.NNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.toNNReal_prod_of_nonneg", "kind": "theorem", "module": "Mathlib.Data.NNReal.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "NNReal.le_iInf_add_iInf", "kind": "theorem", "module": "Mathlib.Data.NNReal.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "NNReal.mul_finset_sup", "kind": "theorem", "module": "Mathlib.Data.NNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.finset_sup_mul", "kind": "theorem", "module": "Mathlib.Data.NNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.finset_sup_div", "kind": "theorem", "module": "Mathlib.Data.NNReal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NNReal.bddAbove_natCast_image_iff", "kind": "theorem", "module": "Mathlib.Data.NNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.bddAbove_range_natCast_iff", "kind": "theorem", "module": "Mathlib.Data.NNReal.Basic", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "NNReal.sub_div", "kind": "theorem", "module": "Mathlib.Data.NNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.iInf_mul", "kind": "theorem", "module": "Mathlib.Data.NNReal.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "NNReal.mul_iInf", "kind": "theorem", "module": "Mathlib.Data.NNReal.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "NNReal.mul_iSup", "kind": "theorem", "module": "Mathlib.Data.NNReal.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "NNReal.iSup_mul", "kind": "theorem", "module": "Mathlib.Data.NNReal.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp_rw"], "tactic_count": 2}
{"name": "NNReal.iSup_div", "kind": "theorem", "module": "Mathlib.Data.NNReal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NNReal.mul_iSup_le", "kind": "theorem", "module": "Mathlib.Data.NNReal.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "NNReal.iSup_mul_le", "kind": "theorem", "module": "Mathlib.Data.NNReal.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "NNReal.iSup_mul_iSup_le", "kind": "theorem", "module": "Mathlib.Data.NNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.le_mul_iInf", "kind": "theorem", "module": "Mathlib.Data.NNReal.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "NNReal.le_iInf_mul", "kind": "theorem", "module": "Mathlib.Data.NNReal.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "NNReal.le_iInf_mul_iInf", "kind": "theorem", "module": "Mathlib.Data.NNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.natCast_iSup", "kind": "theorem", "module": "Mathlib.Data.NNReal.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "apply", "simp", "simp"], "tactic_count": 4}
{"name": "NNReal.natCast_iInf", "kind": "theorem", "module": "Mathlib.Data.NNReal.Basic", "is_tactic_proof": true, "tactics": ["obtain", "simp", "apply", "simp"], "tactic_count": 4}
{"name": "NNReal.range_coe", "kind": "theorem", "module": "Mathlib.Data.NNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.image_coe_Ici", "kind": "theorem", "module": "Mathlib.Data.NNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.image_coe_Iic", "kind": "theorem", "module": "Mathlib.Data.NNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.image_coe_Ioi", "kind": "theorem", "module": "Mathlib.Data.NNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.image_coe_Iio", "kind": "theorem", "module": "Mathlib.Data.NNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.image_coe_Icc", "kind": "theorem", "module": "Mathlib.Data.NNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.image_coe_Ioc", "kind": "theorem", "module": "Mathlib.Data.NNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.image_coe_Ico", "kind": "theorem", "module": "Mathlib.Data.NNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.image_coe_Ioo", "kind": "theorem", "module": "Mathlib.Data.NNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.image_coe_uIcc", "kind": "theorem", "module": "Mathlib.Data.NNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.image_coe_uIoc", "kind": "theorem", "module": "Mathlib.Data.NNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.image_coe_uIoo", "kind": "theorem", "module": "Mathlib.Data.NNReal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal", "kind": "definition", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.termℝ≥0", "kind": "definition", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal._aux_Mathlib_Data_NNReal_Defs___macroRules_NNReal_termℝ≥0_1", "kind": "definition", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal._aux_Mathlib_Data_NNReal_Defs___unexpand_NNReal_1", "kind": "definition", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.toReal", "kind": "definition", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.instCoeReal", "kind": "instance", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.instCanonicallyOrderedAdd", "kind": "instance", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.instNoZeroDivisors", "kind": "instance", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.instDenselyOrdered", "kind": "instance", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.instOrderBot", "kind": "instance", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.instArchimedean", "kind": "instance", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.instMulArchimedean", "kind": "instance", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.instMin", "kind": "instance", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.instMax", "kind": "instance", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.instSub", "kind": "instance", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.instOrderedSub", "kind": "instance", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.instNNRatCast", "kind": "instance", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.instLinearOrder", "kind": "instance", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.instInv", "kind": "instance", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.instDiv", "kind": "instance", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.instSMulNNRat", "kind": "instance", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.zpow", "kind": "instance", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.instSemifield", "kind": "instance", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.instIsOrderedRing", "kind": "instance", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.instIsStrictOrderedRing", "kind": "instance", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.instLinearOrderedCommGroupWithZero", "kind": "instance", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal._example", "kind": "example", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["with_reducible_and_instances"], "tactic_count": 1}
{"name": "NNReal.val_eq_coe", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.canLift", "kind": "instance", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.eq", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.ne_iff", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.forall", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.exists", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.toNNReal", "kind": "definition", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.coe_toNNReal", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.toNNReal_of_nonneg", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Real.le_coe_toNNReal", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.coe_nonneg", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.coe_mk", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal._example", "kind": "example", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "NNReal._example", "kind": "example", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "NNReal._example", "kind": "example", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "NNReal._example", "kind": "example", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "NNReal._example", "kind": "example", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "NNReal._example", "kind": "example", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "NNReal._example", "kind": "example", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "NNReal._example", "kind": "example", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "NNReal._example", "kind": "example", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "NNReal._example", "kind": "example", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "NNReal._example", "kind": "example", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "NNReal.coe_injective", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.coe_inj", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.coe_zero", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.coe_one", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.mk_zero", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.mk_one", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.coe_add", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.coe_mul", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.coe_inv", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.coe_div", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.coe_two", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.coe_sub", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.coe_eq_zero", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NNReal.coe_eq_one", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NNReal.coe_ne_zero", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.coe_ne_one", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal._example", "kind": "example", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "NNReal.toRealHom", "kind": "definition", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.coe_toRealHom", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.instMulActionOfReal", "kind": "instance", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.smul_def", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.instIsScalarTowerOfReal", "kind": "instance", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.smulCommClass_left", "kind": "instance", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.smulCommClass_right", "kind": "instance", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.instDistribMulActionOfReal", "kind": "instance", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.instModuleOfReal", "kind": "instance", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.instAlgebraOfReal", "kind": "instance", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal._example", "kind": "example", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "NNReal._example", "kind": "example", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "NNReal._example", "kind": "example", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "NNReal._example", "kind": "example", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "NNReal._example", "kind": "example", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "NNReal.coe_pow", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.coe_zpow", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.coe_nsmul", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.coe_nnqsmul", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.coe_natCast", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.coe_ofNat", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.coe_ofScientific", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.algebraMap_eq_coe", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal._example", "kind": "example", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "NNReal.coe_le_coe", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.coe_lt_coe", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.coe_pos", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.one_le_coe", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NNReal.one_lt_coe", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NNReal.coe_le_one", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NNReal.coe_lt_one", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NNReal.coe_mono", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.toNNReal_monotone", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.toNNReal_mono", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.toNNReal_coe", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.mk_natCast", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.toNNReal_coe_nat", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.toNNReal_ofNat", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.gi", "kind": "definition", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal._example", "kind": "example", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "NNReal._example", "kind": "example", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "NNReal._example", "kind": "example", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "NNReal._example", "kind": "example", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "NNReal._example", "kind": "example", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "NNReal._example", "kind": "example", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "NNReal._example", "kind": "example", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "NNReal._example", "kind": "example", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "NNReal._example", "kind": "example", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "NNReal._example", "kind": "example", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal._example", "kind": "example", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "NNReal._example", "kind": "example", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "NNReal._example", "kind": "example", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "NNReal.instPosSMulStrictMono", "kind": "instance", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.instSMulPosStrictMono", "kind": "instance", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.orderIsoIccZeroCoe", "kind": "definition", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.orderIsoIccZeroCoe_apply_coe_coe", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.orderIsoIccZeroCoe_symm_apply_coe", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.coe_image", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.bddAbove_coe", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.bddBelow_coe", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.instConditionallyCompleteLinearOrderBot", "kind": "instance", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.coe_sSup", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["rcases", "simp", "by_cases", "have", "apply", "rintro", "exact", "exact", "simp", "apply", "contrapose", "exact"], "tactic_count": 12}
{"name": "NNReal.coe_iSup", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NNReal.coe_sInf", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["rcases", "simp", "exact", "have", "apply", "rintro", "exact", "exact"], "tactic_count": 8}
{"name": "NNReal.sInf_empty", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NNReal.coe_iInf", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "NNReal.addLeftMono", "kind": "instance", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.addLeftReflectLT", "kind": "instance", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.mulLeftMono", "kind": "instance", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.lt_iff_exists_rat_btwn", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.bot_eq_zero", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.mul_sup", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.sup_mul", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.coe_max", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.coe_min", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.zero_le_coe", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.instIsStrictOrderedModule", "kind": "instance", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.coe_toNNReal'", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.toNNReal_zero", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.toNNReal_one", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.toNNReal_pos", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.toNNReal_eq_zero", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.toNNReal_of_nonpos", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.toNNReal_eq_iff_eq_coe", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.toNNReal_eq_one", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.toNNReal_eq_natCast", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.toNNReal_eq_ofNat", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.toNNReal_le_toNNReal_iff", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.toNNReal_le_one", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.one_lt_toNNReal", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.toNNReal_le_natCast", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.natCast_lt_toNNReal", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.toNNReal_le_ofNat", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.ofNat_lt_toNNReal", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.toNNReal_eq_toNNReal_iff", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.toNNReal_lt_toNNReal_iff'", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.toNNReal_lt_toNNReal_iff", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.lt_of_toNNReal_lt", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.toNNReal_lt_toNNReal_iff_of_nonneg", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.toNNReal_le_toNNReal_iff'", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Real.toNNReal_le_toNNReal_iff_of_pos", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.one_le_toNNReal", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.toNNReal_lt_one", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.natCastle_toNNReal'", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.toNNReal_lt_natCast'", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.natCast_le_toNNReal", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.toNNReal_lt_natCast", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.toNNReal_lt_ofNat", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.ofNat_le_toNNReal", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.toNNReal_add", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.toNNReal_add_toNNReal", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.toNNReal_le_toNNReal", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.toNNReal_add_le", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.toNNReal_le_iff_le_coe", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.le_toNNReal_iff_coe_le", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.le_toNNReal_iff_coe_le'", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.toNNReal_lt_iff_lt_coe", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.lt_toNNReal_iff_coe_lt", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.toNNReal_pow", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.toNNReal_zpow", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.toNNReal_mul", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.mul_eq_mul_left", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NNReal.pow_antitone_exp", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.exists_pow_lt_of_lt_one", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "NNReal.exists_mem_Ico_zpow", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.exists_mem_Ioc_zpow", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.sub_def", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.coe_sub_def", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal._example", "kind": "example", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "NNReal.inv_le", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NNReal.inv_le_of_le_mul", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "NNReal.le_inv_iff_mul_le", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NNReal.lt_inv_iff_mul_lt", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NNReal.div_le_of_le_mul", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.div_le_of_le_mul'", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.mul_lt_of_lt_div", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.le_of_forall_lt_one_mul_le", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.half_le_self", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.half_lt_self", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.div_lt_one_of_lt", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Real.toNNReal_inv", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["rcases", "nth_rw", "rw", "rw"], "tactic_count": 4}
{"name": "Real.toNNReal_div", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.toNNReal_div'", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NNReal.inv_lt_one_iff", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NNReal.inv_lt_inv", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.exists_nat_pos_inv_lt", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.abs_eq", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.le_toNNReal_of_coe_le", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.sSup_of_not_bddAbove", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "NNReal.iSup_of_not_bddAbove", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.iSup_empty", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.iInf_empty", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NNReal.iSup_eq_zero", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["cases", "simp", "simp"], "tactic_count": 3}
{"name": "NNReal.iInf_const_zero", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.OrdConnected.preimage_coe_nnreal_real", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.OrdConnected.image_coe_nnreal_real", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.OrdConnected.image_real_toNNReal", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["refine", "rcases", "rw", "exact", "lift", "rw", "exact"], "tactic_count": 7}
{"name": "Set.OrdConnected.preimage_real_toNNReal", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.nnabs", "kind": "definition", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.coe_nnabs", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.nnabs_of_nonneg", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "Real.nnabs_coe", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.coe_toNNReal_le", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.toNNReal_abs", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cast_natAbs_eq_nnabs_cast", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "Real.nnabs_pos", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.nnreal_dichotomy", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["obtain", "all_goals", "rw", "lift", "aesop"], "tactic_count": 5}
{"name": "Real.nnreal_trichotomy", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["obtain", "rw", "aesop"], "tactic_count": 3}
{"name": "Real.nnreal_induction_on", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["obtain", "all_goals"], "tactic_count": 2}
{"name": "Real.nnreal_induction_on'", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["obtain", "all_goals"], "tactic_count": 2}
{"name": "NNReal.exists_lt_of_strictMono", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["obtain", "set", "have", "rw", "split_ifs", "rw", "have", "have", "rw", "exact", "obtain", "use", "rwa"], "tactic_count": 13}
{"name": "Real.exists_lt_of_strictMono", "kind": "theorem", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": true, "tactics": ["set", "have", "exact"], "tactic_count": 3}
{"name": "instReprNNReal", "kind": "instance", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalNNRealtoReal", "kind": "definition", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalRealToNNReal", "kind": "definition", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalRealNNAbs", "kind": "definition", "module": "Mathlib.Data.NNReal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instStarRingNNReal", "kind": "instance", "module": "Mathlib.Data.NNReal.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instTrivialStarNNReal", "kind": "instance", "module": "Mathlib.Data.NNReal.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instStarModuleNNRealReal", "kind": "instance", "module": "Mathlib.Data.NNReal.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instStarModuleNNRealOfReal", "kind": "instance", "module": "Mathlib.Data.NNReal.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.instLinearOrder", "kind": "instance", "module": "Mathlib.Data.Nat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.instPreorder", "kind": "instance", "module": "Mathlib.Data.Nat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.instPartialOrder", "kind": "instance", "module": "Mathlib.Data.Nat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.instNontrivial", "kind": "instance", "module": "Mathlib.Data.Nat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.succ_injective", "kind": "theorem", "module": "Mathlib.Data.Nat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.div_right_comm", "kind": "theorem", "module": "Mathlib.Data.Nat.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.pow_left_injective", "kind": "theorem", "module": "Mathlib.Data.Nat.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.pow_right_injective", "kind": "theorem", "module": "Mathlib.Data.Nat.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.pow_sub_one", "kind": "theorem", "module": "Mathlib.Data.Nat.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.leRecOn_injective", "kind": "theorem", "module": "Mathlib.Data.Nat.Basic", "is_tactic_proof": true, "tactics": ["induction", "refl", "intro", "rwa", "step", "intro", "rw", "exact"], "tactic_count": 8}
{"name": "Nat.leRecOn_surjective", "kind": "theorem", "module": "Mathlib.Data.Nat.Basic", "is_tactic_proof": true, "tactics": ["induction", "refl", "intro", "refine", "rw", "step", "intro", "obtain", "obtain", "refine", "rw"], "tactic_count": 11}
{"name": "Nat.set_induction_bounded", "kind": "theorem", "module": "Mathlib.Data.Nat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.set_induction", "kind": "theorem", "module": "Mathlib.Data.Nat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.dvd_left_injective", "kind": "theorem", "module": "Mathlib.Data.Nat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.dvd_sub_self_left", "kind": "theorem", "module": "Mathlib.Data.Nat.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rcases", "simp", "simp", "refine"], "tactic_count": 6}
{"name": "Nat.dvd_sub_self_right", "kind": "theorem", "module": "Mathlib.Data.Nat.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simp"], "tactic_count": 3}
{"name": "Nat.bit", "kind": "definition", "module": "Mathlib.Data.Nat.BinaryRec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.shiftRight_one", "kind": "theorem", "module": "Mathlib.Data.Nat.BinaryRec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.bit_decide_mod_two_eq_one_shiftRight_one", "kind": "theorem", "module": "Mathlib.Data.Nat.BinaryRec", "is_tactic_proof": true, "tactics": ["simp", "cases"], "tactic_count": 2}
{"name": "Nat.bit_testBit_zero_shiftRight_one", "kind": "theorem", "module": "Mathlib.Data.Nat.BinaryRec", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.bit_false", "kind": "theorem", "module": "Mathlib.Data.Nat.BinaryRec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.bit_true", "kind": "theorem", "module": "Mathlib.Data.Nat.BinaryRec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.bit_false_apply", "kind": "theorem", "module": "Mathlib.Data.Nat.BinaryRec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.bit_true_apply", "kind": "theorem", "module": "Mathlib.Data.Nat.BinaryRec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.bit_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Data.Nat.BinaryRec", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Nat.bit_ne_zero_iff", "kind": "theorem", "module": "Mathlib.Data.Nat.BinaryRec", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.bitCasesOn", "kind": "definition", "module": "Mathlib.Data.Nat.BinaryRec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.bit_lt_two_pow_succ_iff", "kind": "theorem", "module": "Mathlib.Data.Nat.BinaryRec", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Nat.log2_eq_succ_log2_shiftRight", "kind": "theorem", "module": "Mathlib.Data.Nat.BinaryRec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.binaryRec", "kind": "definition", "module": "Mathlib.Data.Nat.BinaryRec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.binaryRec'", "kind": "definition", "module": "Mathlib.Data.Nat.BinaryRec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.binaryRecFromOne", "kind": "definition", "module": "Mathlib.Data.Nat.BinaryRec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.bit_val", "kind": "theorem", "module": "Mathlib.Data.Nat.BinaryRec", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Nat.bit_div_two", "kind": "theorem", "module": "Mathlib.Data.Nat.BinaryRec", "is_tactic_proof": true, "tactics": ["rw", "cases", "decide"], "tactic_count": 3}
{"name": "Nat.bit_mod_two", "kind": "theorem", "module": "Mathlib.Data.Nat.BinaryRec", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Nat.bit_shiftRight_one", "kind": "theorem", "module": "Mathlib.Data.Nat.BinaryRec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.testBit_bit_zero", "kind": "theorem", "module": "Mathlib.Data.Nat.BinaryRec", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.bitCasesOn_bit", "kind": "theorem", "module": "Mathlib.Data.Nat.BinaryRec", "is_tactic_proof": true, "tactics": ["change", "generalize", "rw", "intros"], "tactic_count": 4}
{"name": "Nat.binaryRec_zero", "kind": "theorem", "module": "Mathlib.Data.Nat.BinaryRec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.binaryRec_one", "kind": "theorem", "module": "Mathlib.Data.Nat.BinaryRec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.binaryRec_eq", "kind": "theorem", "module": "Mathlib.Data.Nat.BinaryRec", "is_tactic_proof": true, "tactics": ["by_cases", "obtain", "simp", "unfold", "exact", "rw", "change", "generalize", "rw", "intros"], "tactic_count": 10}
{"name": "Nat.binaryRec'_zero", "kind": "theorem", "module": "Mathlib.Data.Nat.BinaryRec", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.binaryRec'_one", "kind": "theorem", "module": "Mathlib.Data.Nat.BinaryRec", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.binaryRec'_eq", "kind": "theorem", "module": "Mathlib.Data.Nat.BinaryRec", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.binaryRecFromOne_zero", "kind": "theorem", "module": "Mathlib.Data.Nat.BinaryRec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.binaryRecFromOne_one", "kind": "theorem", "module": "Mathlib.Data.Nat.BinaryRec", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.binaryRecFromOne_eq", "kind": "theorem", "module": "Mathlib.Data.Nat.BinaryRec", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.bitIndices", "kind": "definition", "module": "Mathlib.Data.Nat.BitIndices", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.bitIndices_zero", "kind": "theorem", "module": "Mathlib.Data.Nat.BitIndices", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.bitIndices_one", "kind": "theorem", "module": "Mathlib.Data.Nat.BitIndices", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.bitIndices_bit_true", "kind": "theorem", "module": "Mathlib.Data.Nat.BitIndices", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.bitIndices_bit_false", "kind": "theorem", "module": "Mathlib.Data.Nat.BitIndices", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.bitIndices_two_mul_add_one", "kind": "theorem", "module": "Mathlib.Data.Nat.BitIndices", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.bitIndices_two_mul", "kind": "theorem", "module": "Mathlib.Data.Nat.BitIndices", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.bitIndices_sorted", "kind": "theorem", "module": "Mathlib.Data.Nat.BitIndices", "is_tactic_proof": true, "tactics": ["induction", "zero", "bit", "hs", "suffices", "cases", "exact"], "tactic_count": 7}
{"name": "Nat.bitIndices_nodup", "kind": "theorem", "module": "Mathlib.Data.Nat.BitIndices", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.bitIndices_two_pow_mul", "kind": "theorem", "module": "Mathlib.Data.Nat.BitIndices", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "ih", "rw", "simp"], "tactic_count": 6}
{"name": "Nat.bitIndices_two_pow", "kind": "theorem", "module": "Mathlib.Data.Nat.BitIndices", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.twoPowSum_bitIndices", "kind": "theorem", "module": "Mathlib.Data.Nat.BitIndices", "is_tactic_proof": true, "tactics": ["induction", "zero", "bit", "hs", "have", "cases", "simpa", "simp"], "tactic_count": 8}
{"name": "Nat.bitIndices_twoPowsum", "kind": "theorem", "module": "Mathlib.Data.Nat.BitIndices", "is_tactic_proof": true, "tactics": ["cases", "nil", "cons", "obtain", "simp_rw", "have", "refine", "rwa", "simp", "exact", "have", "simp", "simp", "obtain", "have", "simp", "simp", "nth_rw", "rw", "simp", "termination_by"], "tactic_count": 21}
{"name": "Nat.two_pow_le_of_mem_bitIndices", "kind": "theorem", "module": "Mathlib.Data.Nat.BitIndices", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Nat.notMem_bitIndices_self", "kind": "theorem", "module": "Mathlib.Data.Nat.BitIndices", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.Nat.Bits.0.termBxor", "kind": "definition", "module": "Mathlib.Data.Nat.Bits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.Nat.Bits.0._aux_Mathlib_Data_Nat_Bits___macroRules__private_Mathlib_Data_Nat_Bits_0_termBxor_1", "kind": "definition", "module": "Mathlib.Data.Nat.Bits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.Nat.Bits.0._aux_Mathlib_Data_Nat_Bits___unexpand_Bool_xor_1", "kind": "definition", "module": "Mathlib.Data.Nat.Bits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.boddDiv2", "kind": "definition", "module": "Mathlib.Data.Nat.Bits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.div2", "kind": "definition", "module": "Mathlib.Data.Nat.Bits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.bodd", "kind": "definition", "module": "Mathlib.Data.Nat.Bits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.bodd_zero", "kind": "theorem", "module": "Mathlib.Data.Nat.Bits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.bodd_one", "kind": "theorem", "module": "Mathlib.Data.Nat.Bits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.bodd_two", "kind": "theorem", "module": "Mathlib.Data.Nat.Bits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.bodd_succ", "kind": "theorem", "module": "Mathlib.Data.Nat.Bits", "is_tactic_proof": true, "tactics": ["simp", "let", "cases"], "tactic_count": 3}
{"name": "Nat.bodd_add", "kind": "theorem", "module": "Mathlib.Data.Nat.Bits", "is_tactic_proof": true, "tactics": ["induction", "simp", "simp"], "tactic_count": 3}
{"name": "Nat.bodd_mul", "kind": "theorem", "module": "Mathlib.Data.Nat.Bits", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "simp", "cases"], "tactic_count": 5}
{"name": "Nat.mod_two_of_bodd", "kind": "theorem", "module": "Mathlib.Data.Nat.Bits", "is_tactic_proof": true, "tactics": ["have", "rw", "rcases"], "tactic_count": 3}
{"name": "Nat.div2_zero", "kind": "theorem", "module": "Mathlib.Data.Nat.Bits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.div2_one", "kind": "theorem", "module": "Mathlib.Data.Nat.Bits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.div2_two", "kind": "theorem", "module": "Mathlib.Data.Nat.Bits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.div2_succ", "kind": "theorem", "module": "Mathlib.Data.Nat.Bits", "is_tactic_proof": true, "tactics": ["simp", "rcases"], "tactic_count": 2}
{"name": "Nat.bodd_add_div2", "kind": "theorem", "module": "Mathlib.Data.Nat.Bits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.div2_val", "kind": "theorem", "module": "Mathlib.Data.Nat.Bits", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "Nat.bit_bodd_div2", "kind": "theorem", "module": "Mathlib.Data.Nat.Bits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.bit_false_zero", "kind": "theorem", "module": "Mathlib.Data.Nat.Bits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.shiftLeft'", "kind": "definition", "module": "Mathlib.Data.Nat.Bits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.shiftLeft'_false", "kind": "theorem", "module": "Mathlib.Data.Nat.Bits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.shiftLeft_eq'", "kind": "theorem", "module": "Mathlib.Data.Nat.Bits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.shiftRight_eq", "kind": "theorem", "module": "Mathlib.Data.Nat.Bits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.binaryRec_decreasing", "kind": "theorem", "module": "Mathlib.Data.Nat.Bits", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Nat.size", "kind": "definition", "module": "Mathlib.Data.Nat.Bits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.bits", "kind": "definition", "module": "Mathlib.Data.Nat.Bits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.ldiff", "kind": "definition", "module": "Mathlib.Data.Nat.Bits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.bodd_bit", "kind": "theorem", "module": "Mathlib.Data.Nat.Bits", "is_tactic_proof": true, "tactics": ["rw", "simp", "cases"], "tactic_count": 3}
{"name": "Nat.div2_bit", "kind": "theorem", "module": "Mathlib.Data.Nat.Bits", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.shiftLeft'_add", "kind": "theorem", "module": "Mathlib.Data.Nat.Bits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.shiftLeft'_sub", "kind": "theorem", "module": "Mathlib.Data.Nat.Bits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.shiftLeft_sub", "kind": "theorem", "module": "Mathlib.Data.Nat.Bits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.bodd_eq_one_and_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Nat.Bits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.testBit_bit_succ", "kind": "theorem", "module": "Mathlib.Data.Nat.Bits", "is_tactic_proof": false, "tactics": ["have", "simp", "simp", "rw", "simp", "exact"], "tactic_count": 6}
{"name": "Nat.boddDiv2_eq", "kind": "theorem", "module": "Mathlib.Data.Nat.Bits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.div2_bit0", "kind": "theorem", "module": "Mathlib.Data.Nat.Bits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.div2_bit1", "kind": "theorem", "module": "Mathlib.Data.Nat.Bits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.bit_add", "kind": "theorem", "module": "Mathlib.Data.Nat.Bits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.bit_add'", "kind": "theorem", "module": "Mathlib.Data.Nat.Bits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.bit_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Nat.Bits", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Nat.bitCasesOn_bit0", "kind": "theorem", "module": "Mathlib.Data.Nat.Bits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.bitCasesOn_bit1", "kind": "theorem", "module": "Mathlib.Data.Nat.Bits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.bit_cases_on_injective", "kind": "theorem", "module": "Mathlib.Data.Nat.Bits", "is_tactic_proof": true, "tactics": ["intro", "ext", "simpa"], "tactic_count": 3}
{"name": "Nat.bit_cases_on_inj", "kind": "theorem", "module": "Mathlib.Data.Nat.Bits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.bit_le", "kind": "theorem", "module": "Mathlib.Data.Nat.Bits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.bit_lt_bit", "kind": "theorem", "module": "Mathlib.Data.Nat.Bits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.zero_bits", "kind": "theorem", "module": "Mathlib.Data.Nat.Bits", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.bits_append_bit", "kind": "theorem", "module": "Mathlib.Data.Nat.Bits", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "Nat.bit0_bits", "kind": "theorem", "module": "Mathlib.Data.Nat.Bits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.bit1_bits", "kind": "theorem", "module": "Mathlib.Data.Nat.Bits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.one_bits", "kind": "theorem", "module": "Mathlib.Data.Nat.Bits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.bodd_eq_bits_head", "kind": "theorem", "module": "Mathlib.Data.Nat.Bits", "is_tactic_proof": true, "tactics": ["induction", "zero", "bit"], "tactic_count": 3}
{"name": "Nat.div2_bits_eq_tail", "kind": "theorem", "module": "Mathlib.Data.Nat.Bits", "is_tactic_proof": true, "tactics": ["induction", "zero", "bit"], "tactic_count": 3}
{"name": "Nat.bitwise_zero_left", "kind": "theorem", "module": "Mathlib.Data.Nat.Bitwise", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.bitwise_zero_right", "kind": "theorem", "module": "Mathlib.Data.Nat.Bitwise", "is_tactic_proof": true, "tactics": ["unfold", "simp", "rintro", "split_ifs"], "tactic_count": 4}
{"name": "Nat.bitwise_zero", "kind": "theorem", "module": "Mathlib.Data.Nat.Bitwise", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.bitwise_of_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Nat.Bitwise", "is_tactic_proof": true, "tactics": ["conv_lhs", "have", "simp"], "tactic_count": 3}
{"name": "Nat.binaryRec_of_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Nat.Bitwise", "is_tactic_proof": true, "tactics": ["cases", "bit", "rw", "generalize_proofs", "rw", "simp"], "tactic_count": 6}
{"name": "Nat.bit_mod_two_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Data.Nat.Bitwise", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.bit_mod_two_eq_one_iff", "kind": "theorem", "module": "Mathlib.Data.Nat.Bitwise", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.lor_bit", "kind": "theorem", "module": "Mathlib.Data.Nat.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.land_bit", "kind": "theorem", "module": "Mathlib.Data.Nat.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.ldiff_bit", "kind": "theorem", "module": "Mathlib.Data.Nat.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.xor_bit", "kind": "theorem", "module": "Mathlib.Data.Nat.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.testBit_lor", "kind": "theorem", "module": "Mathlib.Data.Nat.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.testBit_land", "kind": "theorem", "module": "Mathlib.Data.Nat.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.testBit_ldiff", "kind": "theorem", "module": "Mathlib.Data.Nat.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.bitwise_bit'", "kind": "theorem", "module": "Mathlib.Data.Nat.Bitwise", "is_tactic_proof": true, "tactics": ["conv_lhs", "rw", "simp", "conv_rhs"], "tactic_count": 4}
{"name": "Nat.bitwise_eq_binaryRec", "kind": "theorem", "module": "Mathlib.Data.Nat.Bitwise", "is_tactic_proof": true, "tactics": ["funext", "induction", "zero", "bit", "rw", "simp_rw", "induction", "zero", "bit", "rw", "simp_rw", "eq_rec_constant,"], "tactic_count": 12}
{"name": "Nat.zero_of_testBit_eq_false", "kind": "theorem", "module": "Mathlib.Data.Nat.Bitwise", "is_tactic_proof": false, "tactics": ["induction", "zero", "bit", "have", "rw"], "tactic_count": 5}
{"name": "Nat.testBit_eq_false_of_lt", "kind": "theorem", "module": "Mathlib.Data.Nat.Bitwise", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.testBit_eq_inth", "kind": "theorem", "module": "Mathlib.Data.Nat.Bitwise", "is_tactic_proof": true, "tactics": ["induction", "zero", "simp", "cases", "succ", "conv_lhs", "rw", "cases"], "tactic_count": 8}
{"name": "Nat.exists_most_significant_bit", "kind": "theorem", "module": "Mathlib.Data.Nat.Bitwise", "is_tactic_proof": false, "tactics": ["induction", "zero", "bit", "by_cases", "subst", "rw", "revert", "cases", "refine", "obtain", "rw", "obtain", "refine", "obtain", "exact"], "tactic_count": 15}
{"name": "Nat.lt_of_testBit", "kind": "theorem", "module": "Mathlib.Data.Nat.Bitwise", "is_tactic_proof": true, "tactics": ["induction", "zero", "rw", "rintro", "simp", "bit", "induction", "zero", "bit", "by_cases", "subst", "simp", "have", "eq_of_testBit_eq", "rw", "exact", "obtain", "simp", "have", "exact"], "tactic_count": 20}
{"name": "Nat.bitwise_swap", "kind": "theorem", "module": "Mathlib.Data.Nat.Bitwise", "is_tactic_proof": true, "tactics": ["funext", "simp", "induction", "ind", "rcases", "specialize", "simp"], "tactic_count": 7}
{"name": "Nat.bitwise_comm", "kind": "theorem", "module": "Mathlib.Data.Nat.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.lor_comm", "kind": "theorem", "module": "Mathlib.Data.Nat.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.land_comm", "kind": "theorem", "module": "Mathlib.Data.Nat.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.and_two_pow", "kind": "theorem", "module": "Mathlib.Data.Nat.Bitwise", "is_tactic_proof": true, "tactics": ["refine", "obtain", "simp", "simp", "simp", "simp"], "tactic_count": 6}
{"name": "Nat.two_pow_and", "kind": "theorem", "module": "Mathlib.Data.Nat.Bitwise", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.tacticBitwise_assoc_tac", "kind": "definition", "module": "Mathlib.Data.Nat.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat._aux_Mathlib_Data_Nat_Bitwise___macroRules_Nat_tacticBitwise_assoc_tac_1", "kind": "definition", "module": "Mathlib.Data.Nat.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.land_assoc", "kind": "theorem", "module": "Mathlib.Data.Nat.Bitwise", "is_tactic_proof": true, "tactics": ["bitwise_assoc_tac"], "tactic_count": 1}
{"name": "Nat.lor_assoc", "kind": "theorem", "module": "Mathlib.Data.Nat.Bitwise", "is_tactic_proof": true, "tactics": ["bitwise_assoc_tac"], "tactic_count": 1}
{"name": "Nat.xor_cancel_right", "kind": "theorem", "module": "Mathlib.Data.Nat.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.xor_cancel_left", "kind": "theorem", "module": "Mathlib.Data.Nat.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.xor_eq_zero", "kind": "theorem", "module": "Mathlib.Data.Nat.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.xor_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Nat.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.xor_trichotomy", "kind": "theorem", "module": "Mathlib.Data.Nat.Bitwise", "is_tactic_proof": true, "tactics": ["set", "have", "have", "have", "rw", "obtain", "have", "contrapose", "simp_rw", "rw", "rfl", "obtain", "on_goal", "on_goal", "on_goal", "all_goals", "refine", "rw", "rfl", "simp"], "tactic_count": 20}
{"name": "Nat.lt_xor_cases", "kind": "theorem", "module": "Mathlib.Data.Nat.Bitwise", "is_tactic_proof": true, "tactics": ["obtain", "exacts"], "tactic_count": 2}
{"name": "Nat.xor_mod_two_eq", "kind": "theorem", "module": "Mathlib.Data.Nat.Bitwise", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "lia", "simp", "simp", "lia"], "tactic_count": 6}
{"name": "Nat.even_xor", "kind": "theorem", "module": "Mathlib.Data.Nat.Bitwise", "is_tactic_proof": true, "tactics": ["simp", "lia"], "tactic_count": 2}
{"name": "Nat.xor_one_of_even", "kind": "theorem", "module": "Mathlib.Data.Nat.Bitwise", "is_tactic_proof": true, "tactics": ["cases", "zero", "succ"], "tactic_count": 3}
{"name": "Nat.xor_one_of_odd", "kind": "theorem", "module": "Mathlib.Data.Nat.Bitwise", "is_tactic_proof": true, "tactics": ["cases", "zero", "succ", "simp", "grind"], "tactic_count": 5}
{"name": "Nat.xor_range", "kind": "theorem", "module": "Mathlib.Data.Nat.Bitwise", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "nth_rw", "rw", "rw", "rw", "rfl", "rw", "refine", "rw", "rfl"], "tactic_count": 12}
{"name": "Nat.shiftLeft_lt", "kind": "theorem", "module": "Mathlib.Data.Nat.Bitwise", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.append_lt", "kind": "theorem", "module": "Mathlib.Data.Nat.Bitwise", "is_tactic_proof": true, "tactics": ["apply", "rw", "apply"], "tactic_count": 3}
{"name": "Nat.castAddMonoidHom", "kind": "definition", "module": "Mathlib.Data.Nat.Cast.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.coe_castAddMonoidHom", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Even.natCast", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.cast_mul", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Basic", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "Nat.castRingHom", "kind": "definition", "module": "Mathlib.Data.Nat.Cast.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.coe_castRingHom", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nsmul_eq_mul'", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Nat.ofNat_nsmul_eq_mul", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.cast_pow", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.cast_dvd_cast", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_natCast'", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "map_natCast'", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "map_ofNat'", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ext_nat''", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Basic", "is_tactic_proof": true, "tactics": ["apply", "rintro", "simp", "exact"], "tactic_count": 4}
{"name": "MonoidWithZeroHom.ext_nat", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_natCast", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "map_natCast", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "map_ofNat", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ext_nat", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NeZero.nat_of_neZero", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.eq_natCast'", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.cast_id", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.castRingHom_nat", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.uniqueRingHom", "kind": "instance", "module": "Mathlib.Data.Nat.Cast.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instNatCast", "kind": "instance", "module": "Mathlib.Data.Nat.Cast.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.natCast_apply", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.natCast_def", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instOfNat", "kind": "instance", "module": "Mathlib.Data.Nat.Cast.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.ofNat_apply", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.ofNat_def", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.elim_natCast_natCast", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.cast_commute", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Commute", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Commute.ofNat_left", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Commute", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.cast_comm", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Commute", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.commute_cast", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Commute", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.ofNat_right", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Commute", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiconjBy.natCast_mul_right", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Commute", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiconjBy.natCast_mul_left", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Commute", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiconjBy.natCast_mul_natCast_mul", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Commute", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Commute.natCast_mul_right", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Commute", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.natCast_mul_left", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Commute", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.natCast_mul_natCast_mul", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Commute", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Commute.self_natCast_mul", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Commute", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.natCast_mul_self", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Commute", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.self_natCast_mul_natCast_mul", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Commute", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.unaryCast", "kind": "definition", "module": "Mathlib.Data.Nat.Cast.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instOfNatAtLeastTwo", "kind": "instance", "module": "Mathlib.Data.Nat.Cast.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LibraryNote.no_index_around_OfNat.ofNat", "kind": "definition", "module": "Mathlib.Data.Nat.Cast.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.cast_ofNat", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.cast_zero", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.cast_succ", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.cast_add_one", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.cast_ite", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Defs", "is_tactic_proof": true, "tactics": ["split_ifs"], "tactic_count": 1}
{"name": "Nat.cast_one", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.cast_add", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Defs", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Nat.binCast", "kind": "definition", "module": "Mathlib.Data.Nat.Cast.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.binCast_eq", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Defs", "is_tactic_proof": false, "tactics": ["induction", "ind", "cases", "zero", "succ", "rw", "by_cases", "conv", "rw", "rw", "conv", "rw", "have", "rw", "simp"], "tactic_count": 15}
{"name": "Nat.cast_two", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.cast_three", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.cast_four", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidWithOne.unary", "kind": "abbrev", "module": "Mathlib.Data.Nat.Cast.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidWithOne.binary", "kind": "abbrev", "module": "Mathlib.Data.Nat.Cast.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_add_one_eq_two", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Defs", "is_tactic_proof": true, "tactics": ["rw", "apply", "decide"], "tactic_count": 3}
{"name": "two_add_one_eq_three", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Defs", "is_tactic_proof": true, "tactics": ["rw", "apply", "decide"], "tactic_count": 3}
{"name": "three_add_one_eq_four", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Defs", "is_tactic_proof": false, "tactics": ["rw", "apply", "decide"], "tactic_count": 3}
{"name": "two_add_two_eq_four", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "nsmul_one", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.cast_div", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Field", "is_tactic_proof": true, "tactics": ["obtain", "have", "rw"], "tactic_count": 3}
{"name": "Nat.cast_div_charZero", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Field", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "Nat.cast_div_div_div_cancel_right", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Field", "is_tactic_proof": true, "tactics": ["rcases", "replace", "rw"], "tactic_count": 3}
{"name": "NeZero.one_le", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.NeZero", "is_tactic_proof": true, "tactics": ["have"], "tactic_count": 1}
{"name": "NeZero.natCast_ne", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.NeZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NeZero.of_neZero_natCast", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.NeZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NeZero.pos_of_neZero_natCast", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.NeZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.mono_cast", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.cast_nonneg'", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.ofNat_nonneg'", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.cast_add_one_pos", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Order.Basic", "is_tactic_proof": true, "tactics": ["apply", "convert"], "tactic_count": 2}
{"name": "Nat.cast_pos'", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Order.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Nat.strictMono_cast", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.castOrderEmbedding", "kind": "definition", "module": "Mathlib.Data.Nat.Cast.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.cast_le", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.cast_lt", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.one_lt_cast", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Order.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.one_le_cast", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Order.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.one_le_cast_iff_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.cast_lt_one", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Order.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.cast_le_one", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Order.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.cast_nonpos", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Order.Basic", "is_tactic_proof": true, "tactics": ["norm_cast"], "tactic_count": 1}
{"name": "Nat.ofNat_le_cast", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.ofNat_lt_cast", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.cast_le_ofNat", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.cast_lt_ofNat", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.one_lt_ofNat", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.one_le_ofNat", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.not_ofNat_le_one", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.not_ofNat_lt_one", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.ofNat_le", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.ofNat_lt", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instNontrivialOfCharZero", "kind": "instance", "module": "Mathlib.Data.Nat.Cast.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NeZero.nat_of_injective", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.cast_inv_le_one", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Order.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.cast_div_le", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Order.Field", "is_tactic_proof": true, "tactics": ["cases", "rw", "rw", "exact", "exact"], "tactic_count": 5}
{"name": "Nat.inv_pos_of_nat", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Order.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.one_div_pos_of_nat", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Order.Field", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Nat.one_div_le_one_div", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Order.Field", "is_tactic_proof": true, "tactics": ["refine", "exact", "simpa"], "tactic_count": 3}
{"name": "Nat.one_div_lt_one_div", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Order.Field", "is_tactic_proof": true, "tactics": ["refine", "exact", "simpa"], "tactic_count": 3}
{"name": "Nat.one_div_cast_pos", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Order.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.one_div_cast_nonneg", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Order.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.one_div_cast_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Order.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.one_sub_one_div_cast_nonneg", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Order.Field", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Nat.one_sub_one_div_cast_le_one", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Order.Field", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Nat.cast_nonneg", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Order.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.ofNat_nonneg", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Order.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.cast_min", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Order.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.cast_max", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Order.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.cast_pos", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Order.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.ofNat_pos'", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Order.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.ofNat_pos", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Order.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.cast_tsub", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Order.Ring", "is_tactic_proof": true, "tactics": ["rcases", "rw", "exact", "rcases", "rw"], "tactic_count": 5}
{"name": "Nat.abs_cast", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Order.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.abs_ofNat", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Order.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.neg_cast_eq_cast", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Order.Ring", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.cast_eq_neg_cast", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Order.Ring", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.mul_le_pow", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Order.Ring", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "rcases", "simp", "simp", "rw", "rcases", "simp", "refine", "rw", "refine", "exact"], "tactic_count": 14}
{"name": "Nat.two_mul_sq_add_one_le_two_pow_two_mul", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Order.Ring", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "hk", "grw", "gcongr", "rw", "exact"], "tactic_count": 8}
{"name": "Prod.instAddMonoidWithOne", "kind": "instance", "module": "Mathlib.Data.Nat.Cast.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.fst_natCast", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Prod", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "Prod.fst_ofNat", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.snd_natCast", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Prod", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "Prod.snd_ofNat", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.range_cast_int", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.SetInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.image_cast_int_Icc", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.SetInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.image_cast_int_Ico", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.SetInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.image_cast_int_Ioc", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.SetInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.image_cast_int_Ioo", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.SetInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.image_cast_int_Iic", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.SetInterval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.image_cast_int_Iio", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.SetInterval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.image_cast_int_Ici", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.SetInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.image_cast_int_Ioi", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.SetInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instNatCastOrderDual", "kind": "instance", "module": "Mathlib.Data.Nat.Cast.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instAddMonoidWithOneOrderDual", "kind": "instance", "module": "Mathlib.Data.Nat.Cast.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instAddCommMonoidWithOneOrderDual", "kind": "instance", "module": "Mathlib.Data.Nat.Cast.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toDual_natCast", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toDual_ofNat", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofDual_natCast", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofDual_ofNat", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instNatCastLex", "kind": "instance", "module": "Mathlib.Data.Nat.Cast.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instAddMonoidWithOneLex", "kind": "instance", "module": "Mathlib.Data.Nat.Cast.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instAddCommMonoidWithOneLex", "kind": "instance", "module": "Mathlib.Data.Nat.Cast.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toLex_natCast", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toLex_ofNat", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofLex_natCast", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofLex_ofNat", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instWellFoundedRelationWithTopNat", "kind": "instance", "module": "Mathlib.Data.Nat.Cast.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.cast_withTop", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.cast_withBot", "kind": "theorem", "module": "Mathlib.Data.Nat.Cast.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.modEq_list_prod_iff", "kind": "theorem", "module": "Mathlib.Data.Nat.ChineseRemainder", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "have", "simp", "constructor", "rintro", "cases", "intro"], "tactic_count": 9}
{"name": "Nat.modEq_list_map_prod_iff", "kind": "theorem", "module": "Mathlib.Data.Nat.ChineseRemainder", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "ih", "have", "simp", "intro", "exact", "simp"], "tactic_count": 9}
{"name": "Nat.chineseRemainderOfList", "kind": "definition", "module": "Mathlib.Data.Nat.ChineseRemainder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.chineseRemainderOfList_nil", "kind": "theorem", "module": "Mathlib.Data.Nat.ChineseRemainder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.chineseRemainderOfList_lt_prod", "kind": "theorem", "module": "Mathlib.Data.Nat.ChineseRemainder", "is_tactic_proof": true, "tactics": ["cases", "nil", "cons", "simp", "have", "simp", "intro", "exact", "refine", "simp", "intro", "exact"], "tactic_count": 12}
{"name": "Nat.chineseRemainderOfList_modEq_unique", "kind": "theorem", "module": "Mathlib.Data.Nat.ChineseRemainder", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "simp", "have", "simp", "intro", "exact", "exact", "chineseRemainder_modEq_unique"], "tactic_count": 10}
{"name": "Nat.chineseRemainderOfList_perm", "kind": "theorem", "module": "Mathlib.Data.Nat.ChineseRemainder", "is_tactic_proof": true, "tactics": ["let", "have", "exact", "rw", "exact"], "tactic_count": 5}
{"name": "Nat.chineseRemainderOfMultiset", "kind": "definition", "module": "Mathlib.Data.Nat.ChineseRemainder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.chineseRemainderOfMultiset_lt_prod", "kind": "theorem", "module": "Mathlib.Data.Nat.ChineseRemainder", "is_tactic_proof": false, "tactics": ["induction", "unfold", "simpa"], "tactic_count": 3}
{"name": "Nat.chineseRemainderOfFinset", "kind": "definition", "module": "Mathlib.Data.Nat.ChineseRemainder", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Nat.chineseRemainderOfFinset_lt_prod", "kind": "theorem", "module": "Mathlib.Data.Nat.ChineseRemainder", "is_tactic_proof": true, "tactics": ["simpa", "chineseRemainderOfMultiset_lt_prod"], "tactic_count": 2}
{"name": "Nat.choose", "kind": "definition", "module": "Mathlib.Data.Nat.Choose.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.choose_zero_right", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Nat.choose_zero_succ", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.choose_succ_succ", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.choose_succ_succ'", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.choose_succ_left", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Basic", "is_tactic_proof": true, "tactics": ["obtain", "rfl"], "tactic_count": 2}
{"name": "Nat.choose_succ_right", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Basic", "is_tactic_proof": true, "tactics": ["obtain", "rfl"], "tactic_count": 2}
{"name": "Nat.choose_eq_choose_pred_add", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Basic", "is_tactic_proof": true, "tactics": ["obtain", "rw"], "tactic_count": 2}
{"name": "Nat.choose_eq_zero_of_lt", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.choose_self", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Basic", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "Nat.choose_succ_self", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.choose_one_right", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Basic", "is_tactic_proof": true, "tactics": ["induction", "simp"], "tactic_count": 2}
{"name": "Nat.triangle_succ", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Basic", "is_tactic_proof": true, "tactics": ["rw", "cases"], "tactic_count": 2}
{"name": "Nat.choose_two_right", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "simp"], "tactic_count": 5}
{"name": "Nat.choose_pos", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.choose_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.choose_ne_zero_iff", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.choose_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.add_one_mul_choose_eq", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.succ_mul_choose_eq", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.choose_mul_factorial_mul_factorial", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.choose_mul", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Basic", "is_tactic_proof": true, "tactics": ["obtain", "grind", "have", "apply", "calc", "grind"], "tactic_count": 6}
{"name": "Nat.choose_eq_factorial_div_factorial", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Nat.add_choose", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.add_choose_mul_factorial_mul_factorial", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.factorial_mul_factorial_dvd_factorial", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.factorial_mul_factorial_dvd_factorial_add", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Basic", "is_tactic_proof": true, "tactics": ["suffices", "exact"], "tactic_count": 2}
{"name": "Nat.choose_symm", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.choose_symm_of_eq_add", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Basic", "is_tactic_proof": true, "tactics": ["suffices", "exact"], "tactic_count": 2}
{"name": "Nat.choose_symm_add", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Nat.cast_choose", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Cast", "is_tactic_proof": true, "tactics": ["have", "rw", "rw_mod_cast"], "tactic_count": 3}
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{"name": "Nat.cast_choose_two", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Cast", "is_tactic_proof": true, "tactics": ["rw", "eq_div_iff_mul_eq"], "tactic_count": 2}
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{"name": "Nat.centralBinom_eq_two_mul_choose", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Central", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Nat.centralBinom_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Central", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.centralBinom_zero", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Central", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.choose_le_centralBinom", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Central", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.two_le_centralBinom", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Central", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.succ_mul_centralBinom_succ", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Central", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.four_pow_lt_mul_centralBinom", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Central", "is_tactic_proof": false, "tactics": ["induction", "rcases", "clear", "norm_num", "obtain", "calc"], "tactic_count": 6}
{"name": "Nat.four_pow_le_two_mul_self_mul_centralBinom", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Central", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.two_dvd_centralBinom_succ", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Central", "is_tactic_proof": true, "tactics": ["use", "rw"], "tactic_count": 2}
{"name": "Nat.two_dvd_centralBinom_of_one_le", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Central", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
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{"name": "Nat.Prime.dvd_choose_add", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Dvd", "is_tactic_proof": true, "tactics": ["have", "rw", "hp.dvd_factorial]", "exact"], "tactic_count": 4}
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{"name": "Nat.Prime.dvd_choose_self", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Dvd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Prime.coprime_choose_of_lt", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Dvd", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Nat.factorization_factorial", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Factorization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Nat.factorization_le_factorization_choose_add", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Factorization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Nat.factorization_choose_le_log", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Factorization", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "have", "have", "refine", "simp", "rw", "exact"], "tactic_count": 8}
{"name": "Nat.pow_factorization_choose_le", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Factorization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.factorization_choose_le_one", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Factorization", "is_tactic_proof": true, "tactics": ["apply", "rcases", "exact"], "tactic_count": 3}
{"name": "Nat.factorization_choose_of_lt_three_mul", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Factorization", "is_tactic_proof": true, "tactics": ["rcases", "exact", "rcases", "simp", "simp", "and_imp]", "intro", "rcases", "rw", "exact", "lt_of_le_of_lt", "replace", "have", "calc", "n", "rwa"], "tactic_count": 16}
{"name": "Nat.factorization_centralBinom_of_two_mul_self_lt_three_mul", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Factorization", "is_tactic_proof": true, "tactics": ["refine", "lia", "rw"], "tactic_count": 3}
{"name": "Nat.factorization_factorial_eq_zero_of_lt", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Factorization", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "hn"], "tactic_count": 5}
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{"name": "Nat.factorization_centralBinom_eq_zero_of_two_mul_lt", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Factorization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Nat.prod_pow_factorization_choose", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Factorization", "is_tactic_proof": true, "tactics": ["conv_rhs", "rw", "apply", "intro", "rw", "contrapose", "rw", "intro", "simp"], "tactic_count": 9}
{"name": "Nat.prod_pow_factorization_centralBinom", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Factorization", "is_tactic_proof": true, "tactics": ["apply", "lia"], "tactic_count": 2}
{"name": "Choose.choose_modEq_choose_mod_mul_choose_div", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Lucas", "is_tactic_proof": false, "tactics": ["have", "simpa", "simp", "simp", "conv_lhs", "enter", "rw", "have", "intro", "rw", "constructor", "simp", "have", "rw", "exact", "rw", "simp", "rw", "split_ifs", "simp", "rw", "cases"], "tactic_count": 22}
{"name": "Choose.choose_modEq_choose_mod_mul_choose_div_nat", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Lucas", "is_tactic_proof": true, "tactics": ["rw", "exact_mod_cast"], "tactic_count": 2}
{"name": "Choose.choose_modEq_choose_mul_prod_range_choose", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Lucas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Choose.choose_modEq_prod_range_choose", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Lucas", "is_tactic_proof": true, "tactics": ["apply", "simp_rw"], "tactic_count": 2}
{"name": "Choose.choose_modEq_prod_range_choose_nat", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Lucas", "is_tactic_proof": true, "tactics": ["rw", "exact_mod_cast"], "tactic_count": 2}
{"name": "Nat.multinomial", "kind": "definition", "module": "Mathlib.Data.Nat.Choose.Multinomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.multinomial_pos", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Multinomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.multinomial_spec", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Multinomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.multinomial_empty", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Multinomial", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.multinomial_cons", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Multinomial", "is_tactic_proof": false, "tactics": ["rw", "mul_assoc,", "positivity"], "tactic_count": 3}
{"name": "Nat.multinomial_insert", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Multinomial", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.multinomial_singleton", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Multinomial", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.multinomial_insert_one", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Multinomial", "is_tactic_proof": true, "tactics": ["simp", "rw", "simp", "rw"], "tactic_count": 4}
{"name": "Nat.multinomial_congr", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Multinomial", "is_tactic_proof": true, "tactics": ["simp", "rw", "exact"], "tactic_count": 3}
{"name": "Nat.binomial_eq", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Multinomial", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.binomial_eq_choose", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Multinomial", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.binomial_spec", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Multinomial", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Nat.binomial_one", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Multinomial", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.binomial_succ_succ", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Multinomial", "is_tactic_proof": true, "tactics": ["simp", "rw", "rw", "ring"], "tactic_count": 4}
{"name": "Nat.succ_mul_binomial", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Multinomial", "is_tactic_proof": false, "tactics": ["rw", "rw"], "tactic_count": 2}
{"name": "Nat.multinomial_univ_two", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Multinomial", "is_tactic_proof": true, "tactics": ["rw", "dsimp"], "tactic_count": 2}
{"name": "Nat.multinomial_univ_three", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Multinomial", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Finsupp.multinomial", "kind": "definition", "module": "Mathlib.Data.Nat.Choose.Multinomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.multinomial_eq", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Multinomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.multinomial_eq_of_support_subset", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Multinomial", "is_tactic_proof": true, "tactics": ["simp", "congr", "simp", "rw", "grind"], "tactic_count": 5}
{"name": "Finsupp.multinomial_update", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Multinomial", "is_tactic_proof": true, "tactics": ["simp", "classical", "by_cases", "rw", "support_update_zero]", "congr", "exact", "rw", "rw"], "tactic_count": 9}
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{"name": "Multiset.multinomial_filter_ne", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Multinomial", "is_tactic_proof": true, "tactics": ["dsimp", "convert", "rw", "ext1", "rw", "split_ifs", "rw", "rw"], "tactic_count": 8}
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{"name": "Finset.sum_pow_eq_sum_piAntidiag_of_commute", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Multinomial", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "cons", "rw", "simp", "sum_add_distrib,", "suffices", "p", "s.noncommProd", "n.choose", "rw", "simp", "rw", "hc", "simp", "refine", "rw", "refine", "rw", "rw", "congr", "rw", "rw", "intro", "rw", "exact", "refine", "rw", "exact"], "tactic_count": 30}
{"name": "Finset.sum_pow_of_commute", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Multinomial", "is_tactic_proof": false, "tactics": ["induction", "empty", "rw", "rintro", "rw", "swap", "exact", "convert", "convert", "simp", "rw", "haveI", "apply", "insert", "intro", "rw", "exact", "simp_rw", "refine", "rw", "conv", "simp_rw", "rw", "rw", "congr"], "tactic_count": 25}
{"name": "Finset.sum_pow_eq_sum_piAntidiag", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Multinomial", "is_tactic_proof": true, "tactics": ["simp_rw", "rw"], "tactic_count": 2}
{"name": "Finset.sum_pow", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Multinomial", "is_tactic_proof": true, "tactics": ["conv_rhs", "convert", "rw"], "tactic_count": 3}
{"name": "Nat.multinomial_two_mul_le_mul_multinomial", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Multinomial", "is_tactic_proof": true, "tactics": ["rw", "refine", "calc", "rw", "gcongr", "rw", "exact"], "tactic_count": 7}
{"name": "Sym.multinomial_coe_fill_of_notMem", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Multinomial", "is_tactic_proof": true, "tactics": ["rw", "rw", "refine", "rw", "refine", "rw", "rw", "rw", "rw", "exact", "exact"], "tactic_count": 11}
{"name": "Commute.add_pow", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Sum", "is_tactic_proof": true, "tactics": ["let", "change", "have", "simp", "have", "have", "intro", "have", "dsimp", "rw", "congr", "rw", "rw", "by_cases", "rw", "rw", "rw", "induction", "zero", "rw", "dsimp", "rw", "succ", "ih", "rw", "add_mul,", "congr", "rw"], "tactic_count": 28}
{"name": "Commute.add_pow'", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Sum", "is_tactic_proof": true, "tactics": ["simp_rw", "h.add_pow]"], "tactic_count": 2}
{"name": "add_pow", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sub_pow", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Sum", "is_tactic_proof": true, "tactics": ["rw", "congr", "have", "rw", "simp", "rw", "ring"], "tactic_count": 7}
{"name": "Nat.sum_range_choose", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Sum", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "Nat.sum_range_choose_halfway", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.choose_middle_le_pow", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Sum", "is_tactic_proof": false, "tactics": ["have", "single_le_sum", "simpa"], "tactic_count": 3}
{"name": "Nat.four_pow_le_two_mul_add_one_mul_central_binom", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Sum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.sum_Icc_choose", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Sum", "is_tactic_proof": true, "tactics": ["rcases", "rw", "induction", "base", "succ", "rw"], "tactic_count": 6}
{"name": "Nat.sum_range_add_choose", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Sum", "is_tactic_proof": true, "tactics": ["rw", "convert", "rw"], "tactic_count": 3}
{"name": "Nat.sum_range_mul_choose", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Sum", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "apply", "calc", "congr", "rw", "rw", "congr", "rw"], "tactic_count": 9}
{"name": "Nat.sum_range_multichoose", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Sum", "is_tactic_proof": true, "tactics": ["cases", "zero", "succ"], "tactic_count": 3}
{"name": "Int.alternating_sum_range_choose_eq_choose", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Sum", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "grind"], "tactic_count": 5}
{"name": "Int.alternating_sum_range_choose", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Sum", "is_tactic_proof": true, "tactics": ["cases", "zero", "succ"], "tactic_count": 3}
{"name": "Int.alternating_sum_range_choose_of_ne", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Sum", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.sum_powerset_apply_card", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Sum", "is_tactic_proof": true, "tactics": ["trans", "refine", "intro", "rw", "rw", "exact", "refine", "rw", "refine", "rw"], "tactic_count": 10}
{"name": "Finset.sum_powerset_neg_one_pow_card", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Sum", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Finset.sum_powerset_neg_one_pow_card_of_nonempty", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Sum", "is_tactic_proof": true, "tactics": ["classical", "rw", "exact"], "tactic_count": 3}
{"name": "Finset.prod_pow_choose_succ", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Sum", "is_tactic_proof": false, "tactics": ["have", "rw", "simpa"], "tactic_count": 3}
{"name": "Finset.prod_antidiagonal_pow_choose_succ", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Sum", "is_tactic_proof": true, "tactics": ["simp", "have", "congr", "refine", "rw", "refine", "rw"], "tactic_count": 7}
{"name": "Finset.sum_choose_succ_mul", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Sum", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.sum_antidiagonal_choose_succ_mul", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Sum", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.sum_antidiagonal_choose_add", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Sum", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Nat.add_choose_eq", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Vandermonde", "is_tactic_proof": true, "tactics": ["calc", "rw", "simp"], "tactic_count": 3}
{"name": "Nat.sum_range_choose_sq", "kind": "theorem", "module": "Mathlib.Data.Nat.Choose.Vandermonde", "is_tactic_proof": true, "tactics": ["rw", "congr", "rw"], "tactic_count": 3}
{"name": "Nat.count", "kind": "definition", "module": "Mathlib.Data.Nat.Count", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.count_zero", "kind": "theorem", "module": "Mathlib.Data.Nat.Count", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.CountSet.fintype", "kind": "definition", "module": "Mathlib.Data.Nat.Count", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.count_eq_card_filter_range", "kind": "theorem", "module": "Mathlib.Data.Nat.Count", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Nat.count_eq_card_fintype", "kind": "theorem", "module": "Mathlib.Data.Nat.Count", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Nat.count_le", "kind": "theorem", "module": "Mathlib.Data.Nat.Count", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Nat.count_succ", "kind": "theorem", "module": "Mathlib.Data.Nat.Count", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Nat.count_monotone", "kind": "theorem", "module": "Mathlib.Data.Nat.Count", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.count_add", "kind": "theorem", "module": "Mathlib.Data.Nat.Count", "is_tactic_proof": false, "tactics": ["have", "grind", "simp_rw", "addLeftEmbedding,"], "tactic_count": 4}
{"name": "Nat.count_add'", "kind": "theorem", "module": "Mathlib.Data.Nat.Count", "is_tactic_proof": true, "tactics": ["rw", "simp_rw"], "tactic_count": 2}
{"name": "Nat.count_one", "kind": "theorem", "module": "Mathlib.Data.Nat.Count", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.count_succ'", "kind": "theorem", "module": "Mathlib.Data.Nat.Count", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.count_lt_count_succ_iff", "kind": "theorem", "module": "Mathlib.Data.Nat.Count", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Nat.count_succ_eq_succ_count_iff", "kind": "theorem", "module": "Mathlib.Data.Nat.Count", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Nat.count_succ_eq_count_iff", "kind": "theorem", "module": "Mathlib.Data.Nat.Count", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Nat.lt_of_count_lt_count", "kind": "theorem", "module": "Mathlib.Data.Nat.Count", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.count_strict_mono", "kind": "theorem", "module": "Mathlib.Data.Nat.Count", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.count_injective", "kind": "theorem", "module": "Mathlib.Data.Nat.Count", "is_tactic_proof": true, "tactics": ["by_contra", "wlog", "exact", "simpa"], "tactic_count": 4}
{"name": "Nat.count_le_card", "kind": "theorem", "module": "Mathlib.Data.Nat.Count", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Nat.count_lt_card", "kind": "theorem", "module": "Mathlib.Data.Nat.Count", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.count_iff_forall", "kind": "theorem", "module": "Mathlib.Data.Nat.Count", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Nat.count_true", "kind": "theorem", "module": "Mathlib.Data.Nat.Count", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.count_iff_forall_not", "kind": "theorem", "module": "Mathlib.Data.Nat.Count", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.count_ne_iff_exists", "kind": "theorem", "module": "Mathlib.Data.Nat.Count", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.count_false", "kind": "theorem", "module": "Mathlib.Data.Nat.Count", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.exists_of_count_lt_count", "kind": "theorem", "module": "Mathlib.Data.Nat.Count", "is_tactic_proof": true, "tactics": ["obtain", "rw", "obtain", "simp_rw", "exact"], "tactic_count": 5}
{"name": "Nat.count_mono_left", "kind": "theorem", "module": "Mathlib.Data.Nat.Count", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.digitsAux0", "kind": "definition", "module": "Mathlib.Data.Nat.Digits.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.digitsAux1", "kind": "definition", "module": "Mathlib.Data.Nat.Digits.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.digitsAux", "kind": "definition", "module": "Mathlib.Data.Nat.Digits.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.digitsAux_zero", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.digitsAux_def", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Defs", "is_tactic_proof": true, "tactics": ["cases", "cases", "rw"], "tactic_count": 3}
{"name": "Nat.digits", "kind": "definition", "module": "Mathlib.Data.Nat.Digits.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.digits_zero", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Defs", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "Nat.digits_zero_zero", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.digits_zero_succ", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.digits_zero_succ'", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.digits_one", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.digits_one_succ", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.digits_add_two_add_one", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.digits_of_two_le_of_pos", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.digits_def'", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.digits_of_lt", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Defs", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "rw"], "tactic_count": 3}
{"name": "Nat.digits_add", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Defs", "is_tactic_proof": true, "tactics": ["rcases", "cases", "simp", "dsimp", "rw", "congr", "simp", "simp", "apply"], "tactic_count": 9}
{"name": "Nat.ofDigits", "kind": "definition", "module": "Mathlib.Data.Nat.Digits.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.ofDigits_eq_foldr", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Defs", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "Nat.ofDigits_nil", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.ofDigits_singleton", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.ofDigits_one_cons", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.ofDigits_cons", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.ofDigits_append", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Defs", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "rw", "ring"], "tactic_count": 5}
{"name": "Nat.ofDigits_append_zero", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.ofDigits_replicate_zero", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Defs", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Nat.ofDigits_append_replicate_zero", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Defs", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Nat.ofDigits_reverse_cons", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Defs", "is_tactic_proof": true, "tactics": ["simp", "rw", "simp"], "tactic_count": 3}
{"name": "Nat.ofDigits_reverse_zero_cons", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.coe_ofDigits", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Defs", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "Nat.digits_zero_of_eq_zero", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.digits_ofDigits", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Defs", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "dsimp", "replace", "rw", "rw", "intro", "apply", "exact", "intro", "rw", "convert", "exact", "by_cases", "rcases", "left", "simpa", "right", "contrapose", "refine", "rw", "exact"], "tactic_count": 23}
{"name": "Nat.ofDigits_digits", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Defs", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "rfl", "simp", "rcases", "induction", "zero", "succ", "rw", "simp", "induction", "ind", "cases", "rw", "rfl", "simp", "dsimp", "rw", "rw"], "tactic_count": 19}
{"name": "Nat.ofDigits_one", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Defs", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "Nat.digits_eq_nil_iff_eq_zero", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Defs", "is_tactic_proof": true, "tactics": ["constructor", "intro", "have", "convert", "rw", "rintro", "simp"], "tactic_count": 7}
{"name": "Nat.digits_ne_nil_iff_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.digits_eq_cons_digits_div", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.digits_getLast", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Defs", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "simp", "rw"], "tactic_count": 4}
{"name": "Nat.digits.injective", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.digits_inj_iff", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.mul_ofDigits", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Defs", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "rw", "ring"], "tactic_count": 5}
{"name": "Nat.ofDigits_inj_of_len_eq", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Defs", "is_tactic_proof": false, "tactics": ["induction", "nil", "simp", "exact", "cons", "obtain", "simp", "simp", "have", "have", "simpa", "simp", "have", "rw"], "tactic_count": 14}
{"name": "Nat.ofDigits_add_ofDigits_eq_ofDigits_zipWith_of_length_eq", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Defs", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "induction", "nil", "cons", "ih₂", "simp_all", "rw", "ac_rfl"], "tactic_count": 10}
{"name": "Nat.digits_lt_base'", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Defs", "is_tactic_proof": false, "tactics": ["induction", "ind", "intro", "rcases", "rw", "cases", "rw", "cases", "exact", "apply", "apply", "assumption"], "tactic_count": 12}
{"name": "Nat.digits_lt_base", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Defs", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "Nat.ofDigits_lt_base_pow_length'", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Defs", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "rw", "have", "mul_le_mul", "suffices", "exact"], "tactic_count": 8}
{"name": "Nat.ofDigits_lt_base_pow_length", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Defs", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "Nat.lt_base_pow_length_digits'", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Defs", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "Nat.lt_base_pow_length_digits", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Defs", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "Nat.digits_base_mul", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Defs", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Nat.digits_base_pow_mul", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Defs", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw"], "tactic_count": 4}
{"name": "Nat.ofDigits_digits_append_digits", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.ofDigits_monotone", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Defs", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "simp", "exact"], "tactic_count": 5}
{"name": "Nat.sum_le_ofDigits", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.digit_sum_le", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Defs", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "induction", "zero", "succ", "nth_rw", "rw", "exact"], "tactic_count": 9}
{"name": "Nat.ofDigits_div_eq_ofDigits_tail", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Defs", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "refine", "rw"], "tactic_count": 5}
{"name": "Nat.ofDigits_div_pow_eq_ofDigits_drop", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Defs", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "ofDigits_div_eq_ofDigits_tail"], "tactic_count": 5}
{"name": "Nat.self_div_pow_eq_ofDigits_drop", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Defs", "is_tactic_proof": true, "tactics": ["convert", "exact"], "tactic_count": 2}
{"name": "Nat.ofDigits_mod_pow_eq_ofDigits_take", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Defs", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "cases", "nil", "cons", "tl", "rw", "add_mod,", "mul_mod_mul_left,", "apply", "apply", "exact", "rw", "exact"], "tactic_count": 15}
{"name": "Nat.self_mod_pow_eq_ofDigits_take", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Defs", "is_tactic_proof": true, "tactics": ["convert", "exact"], "tactic_count": 2}
{"name": "Nat.toDigitsCore_lens_eq_aux", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Defs", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "simp", "specialize", "simp", "exact"], "tactic_count": 7}
{"name": "Nat.toDigitsCore_lens_eq", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Defs", "is_tactic_proof": true, "tactics": ["induction", "succ"], "tactic_count": 2}
{"name": "Nat.nat_repr_len_aux", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Defs", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Nat.toDigitsCore_length", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Defs", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "simp", "cases", "zero", "succ", "cases", "zero", "rw", "simp", "succ", "specialize", "split_ifs", "simp", "simp"], "tactic_count": 16}
{"name": "Nat.toDigits_length", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.repr_length", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Nat.modEq_three_digits_sum", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Div", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.modEq_nine_digits_sum", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Div", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.modEq_eleven_digits_sum", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Div", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "Nat.dvd_iff_dvd_digits_sum", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Div", "is_tactic_proof": true, "tactics": ["rw", "conv_lhs", "rw"], "tactic_count": 3}
{"name": "Nat.three_dvd_iff", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Div", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.nine_dvd_iff", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Div", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.dvd_iff_dvd_ofDigits", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Div", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Nat.eleven_dvd_iff", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Div", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "Nat.eleven_dvd_of_palindrome", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Div", "is_tactic_proof": true, "tactics": ["let", "replace", "refine", "have", "rw", "exact"], "tactic_count": 6}
{"name": "Nat.ofDigits_eq_sum_mapIdx_aux", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Lemmas", "is_tactic_proof": false, "tactics": ["suffices", "l.zipWith", "l.zipWith", "congr"], "tactic_count": 4}
{"name": "Nat.ofDigits_eq_sum_mapIdx", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Lemmas", "is_tactic_proof": false, "tactics": ["rw", "induction", "nil", "cons"], "tactic_count": 4}
{"name": "Nat.digits_len", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Lemmas", "is_tactic_proof": false, "tactics": ["induction", "rw", "by_cases", "simp", "aesop", "have", "rw", "refine", "contrapose", "exact"], "tactic_count": 10}
{"name": "Nat.digits_length_le_iff", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Lemmas", "is_tactic_proof": true, "tactics": ["by_cases", "have", "simpa", "rw", "exact"], "tactic_count": 5}
{"name": "Nat.lt_digits_length_iff", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Lemmas", "is_tactic_proof": true, "tactics": ["contrapose", "exact"], "tactic_count": 2}
{"name": "Nat.getLast_digit_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Lemmas", "is_tactic_proof": true, "tactics": ["rcases", "cases", "cases", "simp", "cases", "cases", "simp", "exact", "revert", "induction", "ind", "intro", "by_cases", "simpa", "rw", "refine", "rw", "exact"], "tactic_count": 18}
{"name": "Nat.digits_append_digits", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Lemmas", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rw", "refine", "rcases", "by_cases", "simp", "exact", "exact"], "tactic_count": 9}
{"name": "Nat.digits_append_zeroes_append_digits", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "simp", "ring"], "tactic_count": 3}
{"name": "Nat.digits_len_le_digits_len_succ", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Lemmas", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rcases", "interval_cases", "simpa"], "tactic_count": 5}
{"name": "Nat.le_digits_len_le", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.pow_length_le_mul_ofDigits", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "simp", "ofDigits_singleton,", "apply", "refine", "have", "convert", "rw"], "tactic_count": 8}
{"name": "Nat.base_pow_length_digits_le'", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Lemmas", "is_tactic_proof": true, "tactics": ["have", "convert", "rw"], "tactic_count": 3}
{"name": "Nat.base_pow_length_digits_le", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Lemmas", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "Nat.sub_one_mul_sum_div_pow_eq_sub_sum_digits", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Lemmas", "is_tactic_proof": true, "tactics": ["obtain", "induction", "nil", "cons", "ih", "simp", "digits_ofDigits", "simp", "rw", "simp", "obtain", "simp", "have", "have", "have", "simp", "have", "rw", "have", "rw", "sum_Ico_consecutive", "mul_add,", "nth_rw", "rw", "simp", "simp", "cases", "rfl", "simp"], "tactic_count": 29}
{"name": "Nat.sub_one_mul_sum_log_div_pow_eq_sub_sum_digits", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Lemmas", "is_tactic_proof": true, "tactics": ["obtain", "rcases", "simp", "convert", "sub_one_mul_sum_div_pow_eq_sub_sum_digits", "refine", "all_goals", "simp", "simp", "cases", "all_goals"], "tactic_count": 11}
{"name": "Nat.digits_two_eq_bits", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Lemmas", "is_tactic_proof": true, "tactics": ["induction", "zero", "one", "bit", "rw", "cases", "rw", "simpa", "simpa", "simpa"], "tactic_count": 10}
{"name": "Nat.dvd_ofDigits_sub_ofDigits", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Lemmas", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "simp", "exact"], "tactic_count": 5}
{"name": "Nat.ofDigits_modEq'", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Lemmas", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "dsimp", "dsimp", "conv_lhs", "conv_rhs"], "tactic_count": 7}
{"name": "Nat.ofDigits_modEq", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.ofDigits_mod", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.ofDigits_mod_eq_head!", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Lemmas", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "Nat.head!_digits", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Lemmas", "is_tactic_proof": true, "tactics": ["by_cases", "rcases", "simp", "nth_rw", "rw", "exact", "rcases"], "tactic_count": 7}
{"name": "Nat.ofDigits_zmodeq'", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Lemmas", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "dsimp", "dsimp", "conv_lhs", "conv_rhs"], "tactic_count": 7}
{"name": "Nat.ofDigits_zmodeq", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.ofDigits_zmod", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.modEq_digits_sum", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "conv", "congr", "skip", "rw", "convert", "exact"], "tactic_count": 7}
{"name": "Nat.zmodeq_ofDigits_digits", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Lemmas", "is_tactic_proof": false, "tactics": ["conv", "congr", "skip", "rw", "rw", "apply"], "tactic_count": 6}
{"name": "Nat.ofDigits_neg_one", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.getD_digits", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Lemmas", "is_tactic_proof": true, "tactics": ["obtain", "clear", "rw", "induction", "zero", "ind", "rcases", "rw", "simp", "simp"], "tactic_count": 10}
{"name": "Nat.digitsAppend", "kind": "definition", "module": "Mathlib.Data.Nat.Digits.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.length_digitsAppend", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "rwa"], "tactic_count": 2}
{"name": "Nat.lt_of_mem_digitsAppend", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "obtain", "exact", "linarith"], "tactic_count": 4}
{"name": "Nat.mapsTo_ofDigits", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.mapsTo_digitsAppend", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.injOn_ofDigits", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.setInvOn_digitsAppend_ofDigits", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Lemmas", "is_tactic_proof": true, "tactics": ["refine", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "Nat.bijOn_ofDigits", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.bijOn_digitsAppend", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.sum_digits_ofDigits_eq_sum", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Lemmas", "is_tactic_proof": true, "tactics": ["nth_rewrite", "rw"], "tactic_count": 2}
{"name": "List.fixedLengthDigits", "kind": "definition", "module": "Mathlib.Data.Nat.Digits.Lemmas", "is_tactic_proof": false, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "List.mem_fixedLengthDigits_iff", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.bijOn_ofDigits'", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "convert", "ext"], "tactic_count": 3}
{"name": "Nat.bijOn_digitsAppend'", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "convert", "ext"], "tactic_count": 3}
{"name": "List.fixedLengthDigits_zero", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Lemmas", "is_tactic_proof": true, "tactics": ["ext", "simpa"], "tactic_count": 2}
{"name": "List.fixedLengthDigits_one", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Lemmas", "is_tactic_proof": true, "tactics": ["ext", "rw", "grind"], "tactic_count": 3}
{"name": "List.card_fixedLengthDigits", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.consFixedLengthDigits", "kind": "definition", "module": "Mathlib.Data.Nat.Digits.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.ne_empty_of_mem_consFixedLengthDigits", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Lemmas", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "List.consFixedLengthDigits_head", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Lemmas", "is_tactic_proof": true, "tactics": ["obtain", "rw"], "tactic_count": 2}
{"name": "List.cons_mem_fixedLengthDigits_succ", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Lemmas", "is_tactic_proof": true, "tactics": ["refine", "simpa", "intro", "obtain", "exact", "exact"], "tactic_count": 6}
{"name": "List.pairwiseDisjoint_consFixedLengthDigits", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Lemmas", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "List.fixedLengthDigits_succ_eq_disjiUnion", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Lemmas", "is_tactic_proof": true, "tactics": ["ext", "simp_rw", "refine", "have", "have", "have", "refine", "refine", "rw", "exact", "rintro", "exact"], "tactic_count": 12}
{"name": "List.sum_fixedLengthDigits_sum", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Lemmas", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "by_cases", "simp", "rw", "simp", "sum_cons]", "rw", "simp_rw", "rw", "ring"], "tactic_count": 12}
{"name": "Nat.sum_sum_digits_eq", "kind": "theorem", "module": "Mathlib.Data.Nat.Digits.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw"], "tactic_count": 3}
{"name": "Nat.dist", "kind": "definition", "module": "Mathlib.Data.Nat.Dist", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.dist_comm", "kind": "theorem", "module": "Mathlib.Data.Nat.Dist", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.dist_self", "kind": "theorem", "module": "Mathlib.Data.Nat.Dist", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.eq_of_dist_eq_zero", "kind": "theorem", "module": "Mathlib.Data.Nat.Dist", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "Nat.dist_eq_zero", "kind": "theorem", "module": "Mathlib.Data.Nat.Dist", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "Nat.dist_eq_sub_of_le", "kind": "theorem", "module": "Mathlib.Data.Nat.Dist", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "Nat.dist_eq_sub_of_le_right", "kind": "theorem", "module": "Mathlib.Data.Nat.Dist", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "Nat.dist_tri_left", "kind": "theorem", "module": "Mathlib.Data.Nat.Dist", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "Nat.dist_tri_right", "kind": "theorem", "module": "Mathlib.Data.Nat.Dist", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "Nat.dist_tri_left'", "kind": "theorem", "module": "Mathlib.Data.Nat.Dist", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "Nat.dist_tri_right'", "kind": "theorem", "module": "Mathlib.Data.Nat.Dist", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "Nat.dist_zero_right", "kind": "theorem", "module": "Mathlib.Data.Nat.Dist", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "Nat.dist_zero_left", "kind": "theorem", "module": "Mathlib.Data.Nat.Dist", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "Nat.dist_add_add_right", "kind": "theorem", "module": "Mathlib.Data.Nat.Dist", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "Nat.dist_add_add_left", "kind": "theorem", "module": "Mathlib.Data.Nat.Dist", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "Nat.dist_eq_intro", "kind": "theorem", "module": "Mathlib.Data.Nat.Dist", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "Nat.dist.triangle_inequality", "kind": "theorem", "module": "Mathlib.Data.Nat.Dist", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "Nat.dist_mul_right", "kind": "theorem", "module": "Mathlib.Data.Nat.Dist", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.dist_mul_left", "kind": "theorem", "module": "Mathlib.Data.Nat.Dist", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.dist_eq_max_sub_min", "kind": "theorem", "module": "Mathlib.Data.Nat.Dist", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Nat.dist_succ_succ", "kind": "theorem", "module": "Mathlib.Data.Nat.Dist", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "Nat.dist_pos_of_ne", "kind": "theorem", "module": "Mathlib.Data.Nat.Dist", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "Nat.evenOddRec", "kind": "definition", "module": "Mathlib.Data.Nat.EvenOddRec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.evenOddRec_zero", "kind": "theorem", "module": "Mathlib.Data.Nat.EvenOddRec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.evenOddRec_even", "kind": "theorem", "module": "Mathlib.Data.Nat.EvenOddRec", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
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{"name": "Nat.prod_factorization_eq_prod_primeFactors", "kind": "theorem", "module": "Mathlib.Data.Nat.Factorization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Nat.ordProj_of_not_prime", "kind": "theorem", "module": "Mathlib.Data.Nat.Factorization.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "Nat.Prime.pow_dvd_iff_dvd_ordProj", "kind": "theorem", "module": "Mathlib.Data.Nat.Factorization.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.Prime.dvd_iff_one_le_factorization", "kind": "theorem", "module": "Mathlib.Data.Nat.Factorization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.exists_factorization_lt_of_lt", "kind": "theorem", "module": "Mathlib.Data.Nat.Factorization.Basic", "is_tactic_proof": true, "tactics": ["have", "contrapose", "rw", "exact"], "tactic_count": 4}
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{"name": "Nat.dvd_iff_div_factorization_eq_tsub", "kind": "theorem", "module": "Mathlib.Data.Nat.Factorization.Basic", "is_tactic_proof": true, "tactics": ["refine", "rcases", "have", "intro", "rw", "by_contra", "obtain", "rwa"], "tactic_count": 8}
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{"name": "Nat.setOf_pow_dvd_eq_Icc_factorization", "kind": "theorem", "module": "Mathlib.Data.Nat.Factorization.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
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{"name": "Nat.Prime.factorization_pos_of_dvd", "kind": "theorem", "module": "Mathlib.Data.Nat.Factorization.Defs", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
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{"name": "Nat.factorizationLCMRight_zero_right", "kind": "theorem", "module": "Mathlib.Data.Nat.Factorization.LCM", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "Nat.factorizationLCMLeft_dvd_left", "kind": "theorem", "module": "Mathlib.Data.Nat.Factorization.LCM", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rcases", "simp", "nth_rewrite", "rw", "apply", "rw", "apply", "intro", "rw", "intros"], "tactic_count": 12}
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{"name": "IsPrimePow.minFac_pow_factorization_eq", "kind": "theorem", "module": "Mathlib.Data.Nat.Factorization.PrimePow", "is_tactic_proof": true, "tactics": ["obtain", "rw", "rw"], "tactic_count": 3}
{"name": "isPrimePow_of_minFac_pow_factorization_eq", "kind": "theorem", "module": "Mathlib.Data.Nat.Factorization.PrimePow", "is_tactic_proof": true, "tactics": ["rcases", "simp_all", "refine", "simp"], "tactic_count": 4}
{"name": "isPrimePow_iff_minFac_pow_factorization_eq", "kind": "theorem", "module": "Mathlib.Data.Nat.Factorization.PrimePow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "isPrimePow_iff_card_primeFactors_eq_one", "kind": "theorem", "module": "Mathlib.Data.Nat.Factorization.PrimePow", "is_tactic_proof": true, "tactics": ["simp_rw", "pos_iff_ne_zero]"], "tactic_count": 2}
{"name": "Nat.not_isPrimePow_iff_nontrivial_of_two_le", "kind": "theorem", "module": "Mathlib.Data.Nat.Factorization.PrimePow", "is_tactic_proof": true, "tactics": ["rw", "grind"], "tactic_count": 2}
{"name": "IsPrimePow.exists_ordCompl_eq_one", "kind": "theorem", "module": "Mathlib.Data.Nat.Factorization.PrimePow", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "rcases", "refine", "simp", "refine", "refine", "rw", "simp"], "tactic_count": 9}
{"name": "exists_ordCompl_eq_one_iff_isPrimePow", "kind": "theorem", "module": "Mathlib.Data.Nat.Factorization.PrimePow", "is_tactic_proof": true, "tactics": ["refine", "rcases", "rw", "rw", "refine", "contrapose", "simp"], "tactic_count": 7}
{"name": "isPrimePow_iff_unique_prime_dvd", "kind": "theorem", "module": "Mathlib.Data.Nat.Factorization.PrimePow", "is_tactic_proof": true, "tactics": ["rw", "constructor", "rintro", "refine", "rintro", "exact", "rintro", "rcases", "cases", "refine", "simp", "apply", "apply", "rw", "intro", "rw", "cases", "simp"], "tactic_count": 18}
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{"name": "Nat.Coprime.isPrimePow_dvd_mul", "kind": "theorem", "module": "Mathlib.Data.Nat.Factorization.PrimePow", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rcases", "simp", "refine", "i.trans", "obtain", "simp", "hp.pow_dvd_iff_le_factorization", "have", "rw", "intro", "simpa", "rcases"], "tactic_count": 14}
{"name": "Nat.mul_divisors_filter_prime_pow", "kind": "theorem", "module": "Mathlib.Data.Nat.Factorization.PrimePow", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simp", "rcases", "simp", "simp", "ext", "simp", "not_false_iff,", "apply"], "tactic_count": 10}
{"name": "IsPrimePow.factorization_minFac_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Nat.Factorization.PrimePow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Primes.prodNatEquiv", "kind": "definition", "module": "Mathlib.Data.Nat.Factorization.PrimePow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Primes.prodNatEquiv_apply", "kind": "theorem", "module": "Mathlib.Data.Nat.Factorization.PrimePow", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "Nat.Primes.coe_prodNatEquiv_apply", "kind": "theorem", "module": "Mathlib.Data.Nat.Factorization.PrimePow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Primes.prodNatEquiv_symm_apply", "kind": "theorem", "module": "Mathlib.Data.Nat.Factorization.PrimePow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.exponent_eq_exponent_mul_factorization_of_prime_pow_eq_base_pow", "kind": "theorem", "module": "Mathlib.Data.Nat.Factorization.PrimePow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.exponent_dvd_of_prime_pow_eq_pow", "kind": "theorem", "module": "Mathlib.Data.Nat.Factorization.PrimePow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.exists_base_eq_prime_pow_of_prime_pow_eq_base_pow", "kind": "theorem", "module": "Mathlib.Data.Nat.Factorization.PrimePow", "is_tactic_proof": true, "tactics": ["rcases", "rw", "use", "exact"], "tactic_count": 4}
{"name": "Nat.floorRoot", "kind": "definition", "module": "Mathlib.Data.Nat.Factorization.Root", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.floorRoot_def", "kind": "theorem", "module": "Mathlib.Data.Nat.Factorization.Root", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "Nat.floorRoot_zero_left", "kind": "theorem", "module": "Mathlib.Data.Nat.Factorization.Root", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.floorRoot_zero_right", "kind": "theorem", "module": "Mathlib.Data.Nat.Factorization.Root", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.floorRoot_one_left", "kind": "theorem", "module": "Mathlib.Data.Nat.Factorization.Root", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.floorRoot_one_right", "kind": "theorem", "module": "Mathlib.Data.Nat.Factorization.Root", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.floorRoot_pow_self", "kind": "theorem", "module": "Mathlib.Data.Nat.Factorization.Root", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.floorRoot_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Nat.Factorization.Root", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.floorRoot_eq_zero", "kind": "theorem", "module": "Mathlib.Data.Nat.Factorization.Root", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.factorization_floorRoot", "kind": "theorem", "module": "Mathlib.Data.Nat.Factorization.Root", "is_tactic_proof": true, "tactics": ["rw", "split_ifs", "obtain", "refine", "have", "exact"], "tactic_count": 6}
{"name": "Nat.pow_dvd_iff_dvd_floorRoot", "kind": "theorem", "module": "Mathlib.Data.Nat.Factorization.Root", "is_tactic_proof": true, "tactics": ["obtain", "simp", "obtain", "simp", "obtain", "simp", "rw", "factorization_pow,"], "tactic_count": 8}
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{"name": "Nat.ceilRoot", "kind": "definition", "module": "Mathlib.Data.Nat.Factorization.Root", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Nat.ceilRoot_zero_left", "kind": "theorem", "module": "Mathlib.Data.Nat.Factorization.Root", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.ceilRoot_zero_right", "kind": "theorem", "module": "Mathlib.Data.Nat.Factorization.Root", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.ceilRoot_one_left", "kind": "theorem", "module": "Mathlib.Data.Nat.Factorization.Root", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.ceilRoot_one_right", "kind": "theorem", "module": "Mathlib.Data.Nat.Factorization.Root", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.ceilRoot_pow_self", "kind": "theorem", "module": "Mathlib.Data.Nat.Factorization.Root", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.ceilRoot_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Nat.Factorization.Root", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.ceilRoot_eq_zero", "kind": "theorem", "module": "Mathlib.Data.Nat.Factorization.Root", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.factorization_ceilRoot", "kind": "theorem", "module": "Mathlib.Data.Nat.Factorization.Root", "is_tactic_proof": true, "tactics": ["rw", "split_ifs", "obtain", "refine", "have", "exact"], "tactic_count": 6}
{"name": "Nat.dvd_pow_iff_ceilRoot_dvd", "kind": "theorem", "module": "Mathlib.Data.Nat.Factorization.Root", "is_tactic_proof": true, "tactics": ["obtain", "aesop", "obtain", "simp", "rw", "factorization_pow,"], "tactic_count": 6}
{"name": "Nat.dvd_ceilRoot_pow", "kind": "theorem", "module": "Mathlib.Data.Nat.Factorization.Root", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.primeFactorsList", "kind": "definition", "module": "Mathlib.Data.Nat.Factors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.primeFactorsList_zero", "kind": "theorem", "module": "Mathlib.Data.Nat.Factors", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.primeFactorsList_one", "kind": "theorem", "module": "Mathlib.Data.Nat.Factors", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.primeFactorsList_two", "kind": "theorem", "module": "Mathlib.Data.Nat.Factors", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.prime_of_mem_primeFactorsList", "kind": "theorem", "module": "Mathlib.Data.Nat.Factors", "is_tactic_proof": true, "tactics": ["k", "intro", "let", "have", "have", "exact"], "tactic_count": 6}
{"name": "Nat.pos_of_mem_primeFactorsList", "kind": "theorem", "module": "Mathlib.Data.Nat.Factors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.prod_primeFactorsList", "kind": "theorem", "module": "Mathlib.Data.Nat.Factors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.primeFactorsList_prime", "kind": "theorem", "module": "Mathlib.Data.Nat.Factors", "is_tactic_proof": true, "tactics": ["have", "rw", "simp", "have", "simp"], "tactic_count": 5}
{"name": "Nat.isChain_cons_primeFactorsList", "kind": "theorem", "module": "Mathlib.Data.Nat.Factors", "is_tactic_proof": true, "tactics": ["k", "intro", "let", "have", "rw", "refine", "exact"], "tactic_count": 7}
{"name": "Nat.isChain_two_cons_primeFactorsList", "kind": "theorem", "module": "Mathlib.Data.Nat.Factors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.isChain_primeFactorsList", "kind": "theorem", "module": "Mathlib.Data.Nat.Factors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.primeFactorsList_sorted", "kind": "theorem", "module": "Mathlib.Data.Nat.Factors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.primeFactorsList_add_two", "kind": "theorem", "module": "Mathlib.Data.Nat.Factors", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.primeFactorsList_eq_nil", "kind": "theorem", "module": "Mathlib.Data.Nat.Factors", "is_tactic_proof": true, "tactics": ["constructor", "rcases", "exact", "exact", "rw", "injection", "rcases", "exact", "exact"], "tactic_count": 9}
{"name": "Nat.primeFactorsList_ne_nil", "kind": "theorem", "module": "Mathlib.Data.Nat.Factors", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.eq_of_perm_primeFactorsList", "kind": "theorem", "module": "Mathlib.Data.Nat.Factors", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Nat.mem_primeFactorsList_iff_dvd", "kind": "theorem", "module": "Mathlib.Data.Nat.Factors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.dvd_of_mem_primeFactorsList", "kind": "theorem", "module": "Mathlib.Data.Nat.Factors", "is_tactic_proof": true, "tactics": ["rcases", "exact", "rwa"], "tactic_count": 3}
{"name": "Nat.mem_primeFactorsList", "kind": "theorem", "module": "Mathlib.Data.Nat.Factors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.mem_primeFactorsList'", "kind": "theorem", "module": "Mathlib.Data.Nat.Factors", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Nat.le_of_mem_primeFactorsList", "kind": "theorem", "module": "Mathlib.Data.Nat.Factors", "is_tactic_proof": true, "tactics": ["rcases", "rw", "cases", "exact"], "tactic_count": 4}
{"name": "Nat.primeFactorsList_unique", "kind": "theorem", "module": "Mathlib.Data.Nat.Factors", "is_tactic_proof": true, "tactics": ["refine", "rw", "refine", "rintro", "rw", "exact", "simp_rw", "exact", "simp_rw", "exact"], "tactic_count": 10}
{"name": "Nat.Prime.primeFactorsList_pow", "kind": "theorem", "module": "Mathlib.Data.Nat.Factors", "is_tactic_proof": true, "tactics": ["symm", "rw", "apply", "intro", "rwa"], "tactic_count": 5}
{"name": "Nat.eq_prime_pow_of_unique_prime_dvd", "kind": "theorem", "module": "Mathlib.Data.Nat.Factors", "is_tactic_proof": true, "tactics": ["set", "rw", "eq_replicate_of_mem"], "tactic_count": 3}
{"name": "Nat.perm_primeFactorsList_mul", "kind": "theorem", "module": "Mathlib.Data.Nat.Factors", "is_tactic_proof": true, "tactics": ["refine", "rw", "intro", "rw", "rcases"], "tactic_count": 5}
{"name": "Nat.perm_primeFactorsList_mul_of_coprime", "kind": "theorem", "module": "Mathlib.Data.Nat.Factors", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rcases", "simp", "exact"], "tactic_count": 5}
{"name": "Nat.primeFactorsList_sublist_right", "kind": "theorem", "module": "Mathlib.Data.Nat.Factors", "is_tactic_proof": true, "tactics": ["rcases", "simp", "apply", "simp", "exact"], "tactic_count": 5}
{"name": "Nat.primeFactorsList_sublist_of_dvd", "kind": "theorem", "module": "Mathlib.Data.Nat.Factors", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Nat.primeFactorsList_subset_right", "kind": "theorem", "module": "Mathlib.Data.Nat.Factors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.primeFactorsList_subset_of_dvd", "kind": "theorem", "module": "Mathlib.Data.Nat.Factors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.dvd_of_primeFactorsList_subperm", "kind": "theorem", "module": "Mathlib.Data.Nat.Factors", "is_tactic_proof": true, "tactics": ["rcases", "exact", "rcases", "exact", "exact", "use", "nth_rw", "rw"], "tactic_count": 8}
{"name": "Nat.replicate_subperm_primeFactorsList_iff", "kind": "theorem", "module": "Mathlib.Data.Nat.Factors", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "constructor", "rw", "rintro", "rw", "exact", "rintro", "rw", "rw", "primeFactorsList_prime", "exact"], "tactic_count": 13}
{"name": "Nat.mem_primeFactorsList_mul", "kind": "theorem", "module": "Mathlib.Data.Nat.Factors", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "Nat.coprime_primeFactorsList_disjoint", "kind": "theorem", "module": "Mathlib.Data.Nat.Factors", "is_tactic_proof": true, "tactics": ["intro", "apply", "rw", "exact"], "tactic_count": 4}
{"name": "Nat.mem_primeFactorsList_mul_of_coprime", "kind": "theorem", "module": "Mathlib.Data.Nat.Factors", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rcases", "simp", "rw"], "tactic_count": 5}
{"name": "Nat.mem_primeFactorsList_mul_left", "kind": "theorem", "module": "Mathlib.Data.Nat.Factors", "is_tactic_proof": true, "tactics": ["rcases", "simp", "apply"], "tactic_count": 3}
{"name": "Nat.mem_primeFactorsList_mul_right", "kind": "theorem", "module": "Mathlib.Data.Nat.Factors", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Nat.eq_two_pow_or_exists_odd_prime_and_dvd", "kind": "theorem", "module": "Mathlib.Data.Nat.Factors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.four_dvd_or_exists_odd_prime_and_dvd_of_two_lt", "kind": "theorem", "module": "Mathlib.Data.Nat.Factors", "is_tactic_proof": true, "tactics": ["obtain", "contradiction", "contradiction", "simp", "exact"], "tactic_count": 5}
{"name": "Nat.fib", "kind": "definition", "module": "Mathlib.Data.Nat.Fib.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.fib_zero", "kind": "theorem", "module": "Mathlib.Data.Nat.Fib.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.fib_one", "kind": "theorem", "module": "Mathlib.Data.Nat.Fib.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.fib_two", "kind": "theorem", "module": "Mathlib.Data.Nat.Fib.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.fib_add_two", "kind": "theorem", "module": "Mathlib.Data.Nat.Fib.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.fib_add_one", "kind": "theorem", "module": "Mathlib.Data.Nat.Fib.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.fib_le_fib_succ", "kind": "theorem", "module": "Mathlib.Data.Nat.Fib.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Nat.fib_mono", "kind": "theorem", "module": "Mathlib.Data.Nat.Fib.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.fib_eq_zero", "kind": "theorem", "module": "Mathlib.Data.Nat.Fib.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.fib_pos", "kind": "theorem", "module": "Mathlib.Data.Nat.Fib.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.fib_add_two_sub_fib_add_one", "kind": "theorem", "module": "Mathlib.Data.Nat.Fib.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.fib_lt_fib_succ", "kind": "theorem", "module": "Mathlib.Data.Nat.Fib.Basic", "is_tactic_proof": true, "tactics": ["rcases", "rw", "exact"], "tactic_count": 3}
{"name": "Nat.fib_add_two_strictMono", "kind": "theorem", "module": "Mathlib.Data.Nat.Fib.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "Nat.fib_strictMonoOn", "kind": "theorem", "module": "Mathlib.Data.Nat.Fib.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.fib_lt_fib", "kind": "theorem", "module": "Mathlib.Data.Nat.Fib.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.le_fib_self", "kind": "theorem", "module": "Mathlib.Data.Nat.Fib.Basic", "is_tactic_proof": true, "tactics": ["induction", "refl", "rfl", "rw", "calc", "n"], "tactic_count": 6}
{"name": "Nat.le_fib_add_one", "kind": "theorem", "module": "Mathlib.Data.Nat.Fib.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.fib_coprime_fib_succ", "kind": "theorem", "module": "Mathlib.Data.Nat.Fib.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Nat.fib_add", "kind": "theorem", "module": "Mathlib.Data.Nat.Fib.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "specialize", "rw", "simp", "ring"], "tactic_count": 7}
{"name": "Nat.fib_two_mul", "kind": "theorem", "module": "Mathlib.Data.Nat.Fib.Basic", "is_tactic_proof": true, "tactics": ["cases", "simp", "rw", "simp", "ring"], "tactic_count": 5}
{"name": "Nat.fib_two_mul_add_one", "kind": "theorem", "module": "Mathlib.Data.Nat.Fib.Basic", "is_tactic_proof": true, "tactics": ["rw", "ring"], "tactic_count": 2}
{"name": "Nat.fib_two_mul_add_two", "kind": "theorem", "module": "Mathlib.Data.Nat.Fib.Basic", "is_tactic_proof": true, "tactics": ["rw", "have", "zify", "ring"], "tactic_count": 4}
{"name": "Nat.fastFibAux", "kind": "definition", "module": "Mathlib.Data.Nat.Fib.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.fastFib", "kind": "definition", "module": "Mathlib.Data.Nat.Fib.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.fast_fib_aux_bit_ff", "kind": "theorem", "module": "Mathlib.Data.Nat.Fib.Basic", "is_tactic_proof": true, "tactics": ["rw", "rfl", "simp"], "tactic_count": 3}
{"name": "Nat.fast_fib_aux_bit_tt", "kind": "theorem", "module": "Mathlib.Data.Nat.Fib.Basic", "is_tactic_proof": true, "tactics": ["rw", "rfl", "simp"], "tactic_count": 3}
{"name": "Nat.fast_fib_aux_eq", "kind": "theorem", "module": "Mathlib.Data.Nat.Fib.Basic", "is_tactic_proof": true, "tactics": ["refine", "simp", "rintro", "simp", "simp"], "tactic_count": 5}
{"name": "Nat.fast_fib_eq", "kind": "theorem", "module": "Mathlib.Data.Nat.Fib.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.gcd_fib_add_self", "kind": "theorem", "module": "Mathlib.Data.Nat.Fib.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simp", "replace", "calc", "gcd", "rw", "ring_nf"], "tactic_count": 7}
{"name": "Nat.gcd_fib_add_mul_self", "kind": "theorem", "module": "Mathlib.Data.Nat.Fib.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.fib_gcd", "kind": "theorem", "module": "Mathlib.Data.Nat.Fib.Basic", "is_tactic_proof": true, "tactics": ["induction", "rw", "conv_rhs", "rwa"], "tactic_count": 4}
{"name": "Nat.fib_dvd", "kind": "theorem", "module": "Mathlib.Data.Nat.Fib.Basic", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Nat.fib_succ_eq_sum_choose", "kind": "theorem", "module": "Mathlib.Data.Nat.Fib.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.fib_succ_eq_succ_sum", "kind": "theorem", "module": "Mathlib.Data.Nat.Fib.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "calc", "fib"], "tactic_count": 5}
{"name": "instIsTransNatLeHAddOfNat", "kind": "instance", "module": "Mathlib.Data.Nat.Fib.Zeckendorf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.IsZeckendorfRep", "kind": "definition", "module": "Mathlib.Data.Nat.Fib.Zeckendorf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.IsZeckendorfRep_nil", "kind": "theorem", "module": "Mathlib.Data.Nat.Fib.Zeckendorf", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.IsZeckendorfRep.sum_fib_lt", "kind": "theorem", "module": "Mathlib.Data.Nat.Fib.Zeckendorf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.greatestFib", "kind": "definition", "module": "Mathlib.Data.Nat.Fib.Zeckendorf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.fib_greatestFib_le", "kind": "theorem", "module": "Mathlib.Data.Nat.Fib.Zeckendorf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.greatestFib_mono", "kind": "theorem", "module": "Mathlib.Data.Nat.Fib.Zeckendorf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.le_greatestFib", "kind": "theorem", "module": "Mathlib.Data.Nat.Fib.Zeckendorf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.greatestFib_lt", "kind": "theorem", "module": "Mathlib.Data.Nat.Fib.Zeckendorf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.lt_fib_greatestFib_add_one", "kind": "theorem", "module": "Mathlib.Data.Nat.Fib.Zeckendorf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.greatestFib_fib", "kind": "theorem", "module": "Mathlib.Data.Nat.Fib.Zeckendorf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.greatestFib_eq_zero", "kind": "theorem", "module": "Mathlib.Data.Nat.Fib.Zeckendorf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.greatestFib_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Nat.Fib.Zeckendorf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.greatestFib_pos", "kind": "theorem", "module": "Mathlib.Data.Nat.Fib.Zeckendorf", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.greatestFib_sub_fib_greatestFib_le_greatestFib", "kind": "theorem", "module": "Mathlib.Data.Nat.Fib.Zeckendorf", "is_tactic_proof": false, "tactics": ["rw", "exact", "simpa", "simpa"], "tactic_count": 4}
{"name": "_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.Nat.zeckendorf_aux", "kind": "theorem", "module": "Mathlib.Data.Nat.Fib.Zeckendorf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.zeckendorf", "kind": "definition", "module": "Mathlib.Data.Nat.Fib.Zeckendorf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.zeckendorf_zero", "kind": "theorem", "module": "Mathlib.Data.Nat.Fib.Zeckendorf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.zeckendorf_succ", "kind": "theorem", "module": "Mathlib.Data.Nat.Fib.Zeckendorf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.zeckendorf_of_pos", "kind": "theorem", "module": "Mathlib.Data.Nat.Fib.Zeckendorf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.isZeckendorfRep_zeckendorf", "kind": "theorem", "module": "Mathlib.Data.Nat.Fib.Zeckendorf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.zeckendorf_sum_fib", "kind": "theorem", "module": "Mathlib.Data.Nat.Fib.Zeckendorf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.sum_zeckendorf_fib", "kind": "theorem", "module": "Mathlib.Data.Nat.Fib.Zeckendorf", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "Nat.zeckendorfEquiv", "kind": "definition", "module": "Mathlib.Data.Nat.Fib.Zeckendorf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.Nat.Find.0.Nat.lbp", "kind": "definition", "module": "Mathlib.Data.Nat.Find", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.Nat.Find.0.Nat.wf_lbp", "kind": "definition", "module": "Mathlib.Data.Nat.Find", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.findX", "kind": "definition", "module": "Mathlib.Data.Nat.Find", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.find", "kind": "definition", "module": "Mathlib.Data.Nat.Find", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.find_spec", "kind": "theorem", "module": "Mathlib.Data.Nat.Find", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.find_min", "kind": "theorem", "module": "Mathlib.Data.Nat.Find", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.find_min'", "kind": "theorem", "module": "Mathlib.Data.Nat.Find", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.find_eq_iff", "kind": "theorem", "module": "Mathlib.Data.Nat.Find", "is_tactic_proof": true, "tactics": ["constructor", "grind", "rintro", "have", "grind"], "tactic_count": 5}
{"name": "Nat.find_lt_iff", "kind": "theorem", "module": "Mathlib.Data.Nat.Find", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.find_le_iff", "kind": "theorem", "module": "Mathlib.Data.Nat.Find", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.le_find_iff", "kind": "theorem", "module": "Mathlib.Data.Nat.Find", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.lt_find_iff", "kind": "theorem", "module": "Mathlib.Data.Nat.Find", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.find_eq_zero", "kind": "theorem", "module": "Mathlib.Data.Nat.Find", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.find_mono_of_le", "kind": "theorem", "module": "Mathlib.Data.Nat.Find", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.find_mono", "kind": "theorem", "module": "Mathlib.Data.Nat.Find", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.find_congr", "kind": "theorem", "module": "Mathlib.Data.Nat.Find", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.find_congr'", "kind": "theorem", "module": "Mathlib.Data.Nat.Find", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.find_le", "kind": "theorem", "module": "Mathlib.Data.Nat.Find", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.find_comp_succ", "kind": "theorem", "module": "Mathlib.Data.Nat.Find", "is_tactic_proof": true, "tactics": ["refine", "cases", "exacts"], "tactic_count": 3}
{"name": "Nat.find_pos", "kind": "theorem", "module": "Mathlib.Data.Nat.Find", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.find_add", "kind": "theorem", "module": "Mathlib.Data.Nat.Find", "is_tactic_proof": true, "tactics": ["refine", "have", "refine", "rwa", "rw", "refine", "rw", "exact"], "tactic_count": 8}
{"name": "Nat.findGreatest", "kind": "definition", "module": "Mathlib.Data.Nat.Find", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.findGreatest_zero", "kind": "theorem", "module": "Mathlib.Data.Nat.Find", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.findGreatest_succ", "kind": "theorem", "module": "Mathlib.Data.Nat.Find", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.findGreatest_eq", "kind": "theorem", "module": "Mathlib.Data.Nat.Find", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.findGreatest_of_not", "kind": "theorem", "module": "Mathlib.Data.Nat.Find", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.findGreatest_eq_iff", "kind": "theorem", "module": "Mathlib.Data.Nat.Find", "is_tactic_proof": true, "tactics": ["induction", "zero", "rw", "simp", "rintro", "exact", "succ", "by_cases", "rw", "constructor", "rintro", "exact", "rintro", "rcases", "exacts", "rw", "grind"], "tactic_count": 17}
{"name": "Nat.findGreatest_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Data.Nat.Find", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.findGreatest_pos", "kind": "theorem", "module": "Mathlib.Data.Nat.Find", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.findGreatest_spec", "kind": "theorem", "module": "Mathlib.Data.Nat.Find", "is_tactic_proof": true, "tactics": ["by_cases", "cases", "rwa", "exact", "exact"], "tactic_count": 5}
{"name": "Nat.findGreatest_le", "kind": "theorem", "module": "Mathlib.Data.Nat.Find", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.le_findGreatest", "kind": "theorem", "module": "Mathlib.Data.Nat.Find", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.findGreatest_mono_right", "kind": "theorem", "module": "Mathlib.Data.Nat.Find", "is_tactic_proof": true, "tactics": ["induction", "refl", "step", "rw", "split_ifs", "exact", "exact"], "tactic_count": 7}
{"name": "Nat.findGreatest_mono_left", "kind": "theorem", "module": "Mathlib.Data.Nat.Find", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "by_cases", "rw", "rw", "exact"], "tactic_count": 7}
{"name": "Nat.findGreatest_mono", "kind": "theorem", "module": "Mathlib.Data.Nat.Find", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.findGreatest_is_greatest", "kind": "theorem", "module": "Mathlib.Data.Nat.Find", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.findGreatest_of_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Nat.Find", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.gcd_greatest", "kind": "theorem", "module": "Mathlib.Data.Nat.GCD.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.pow_sub_one_mod_pow_sub_one", "kind": "theorem", "module": "Mathlib.Data.Nat.GCD.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rcases", "simp", "rcases", "simp", "rcases", "rw", "rwa", "suffices", "rw", "mod_mod,", "rw"], "tactic_count": 13}
{"name": "Nat.pow_sub_one_gcd_pow_sub_one", "kind": "theorem", "module": "Mathlib.Data.Nat.GCD.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simp", "replace", "rw"], "tactic_count": 4}
{"name": "Nat.dvd_lcm_of_dvd_left", "kind": "theorem", "module": "Mathlib.Data.Nat.GCD.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.dvd_of_lcm_right_dvd", "kind": "theorem", "module": "Mathlib.Data.Nat.GCD.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.dvd_lcm_of_dvd_right", "kind": "theorem", "module": "Mathlib.Data.Nat.GCD.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.dvd_of_lcm_left_dvd", "kind": "theorem", "module": "Mathlib.Data.Nat.GCD.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Coprime.lcm_eq_mul", "kind": "theorem", "module": "Mathlib.Data.Nat.GCD.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.Coprime.symmetric", "kind": "theorem", "module": "Mathlib.Data.Nat.GCD.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Coprime.dvd_mul_right", "kind": "theorem", "module": "Mathlib.Data.Nat.GCD.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Coprime.dvd_mul_left", "kind": "theorem", "module": "Mathlib.Data.Nat.GCD.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.coprime_add_self_right", "kind": "theorem", "module": "Mathlib.Data.Nat.GCD.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.coprime_self_add_right", "kind": "theorem", "module": "Mathlib.Data.Nat.GCD.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.coprime_add_self_left", "kind": "theorem", "module": "Mathlib.Data.Nat.GCD.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.coprime_self_add_left", "kind": "theorem", "module": "Mathlib.Data.Nat.GCD.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.coprime_add_mul_right_right", "kind": "theorem", "module": "Mathlib.Data.Nat.GCD.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.coprime_add_mul_left_right", "kind": "theorem", "module": "Mathlib.Data.Nat.GCD.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.coprime_mul_right_add_right", "kind": "theorem", "module": "Mathlib.Data.Nat.GCD.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.coprime_mul_left_add_right", "kind": "theorem", "module": "Mathlib.Data.Nat.GCD.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.coprime_add_mul_right_left", "kind": "theorem", "module": "Mathlib.Data.Nat.GCD.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.coprime_add_mul_left_left", "kind": "theorem", "module": "Mathlib.Data.Nat.GCD.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.coprime_mul_right_add_left", "kind": "theorem", "module": "Mathlib.Data.Nat.GCD.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.coprime_mul_left_add_left", "kind": "theorem", "module": "Mathlib.Data.Nat.GCD.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "Nat.add_coprime_iff_right", "kind": "theorem", "module": "Mathlib.Data.Nat.GCD.Basic", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
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{"name": "hyperoperation", "kind": "definition", "module": "Mathlib.Data.Nat.Hyperoperation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "hyperoperation_two_two_eq_four", "kind": "theorem", "module": "Mathlib.Data.Nat.Hyperoperation", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
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{"name": "Nat.two_le_iff", "kind": "theorem", "module": "Mathlib.Data.Nat.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Nat.ModEq.add_left_cancel", "kind": "theorem", "module": "Mathlib.Data.Nat.ModEq", "is_tactic_proof": true, "tactics": ["simp", "rw", "convert", "rw"], "tactic_count": 4}
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{"name": "Nat.ModEq.sub_right", "kind": "theorem", "module": "Mathlib.Data.Nat.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Nat.ModEq.mul_left_cancel_iff'", "kind": "theorem", "module": "Mathlib.Data.Nat.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.ModEq.mul_right_cancel'", "kind": "theorem", "module": "Mathlib.Data.Nat.ModEq", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Nat.ModEq.mul_right_cancel_iff'", "kind": "theorem", "module": "Mathlib.Data.Nat.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.ModEq.of_mul_left", "kind": "theorem", "module": "Mathlib.Data.Nat.ModEq", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Nat.ModEq.of_mul_right", "kind": "theorem", "module": "Mathlib.Data.Nat.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Nat.modulus_modEq_zero", "kind": "theorem", "module": "Mathlib.Data.Nat.ModEq", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.add_modEq_left_iff", "kind": "theorem", "module": "Mathlib.Data.Nat.ModEq", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "Nat.right_modEq_add_iff", "kind": "theorem", "module": "Mathlib.Data.Nat.ModEq", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.add_modulus_modEq_iff", "kind": "theorem", "module": "Mathlib.Data.Nat.ModEq", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.modulus_add_modEq_iff", "kind": "theorem", "module": "Mathlib.Data.Nat.ModEq", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.modEq_add_modulus_iff", "kind": "theorem", "module": "Mathlib.Data.Nat.ModEq", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "Nat.mul_modulus_add_modEq_iff", "kind": "theorem", "module": "Mathlib.Data.Nat.ModEq", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "Nat.sub_modulus_modEq_iff", "kind": "theorem", "module": "Mathlib.Data.Nat.ModEq", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "Nat.modEq_zero_iff", "kind": "theorem", "module": "Mathlib.Data.Nat.ModEq", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "Nat.modEq_iff_exists_eq_add", "kind": "theorem", "module": "Mathlib.Data.Nat.ModEq", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Nat.ModEq.le_of_lt_add", "kind": "theorem", "module": "Mathlib.Data.Nat.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Nat.chineseRemainder'", "kind": "definition", "module": "Mathlib.Data.Nat.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.chineseRemainder", "kind": "definition", "module": "Mathlib.Data.Nat.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.chineseRemainder'_lt_lcm", "kind": "theorem", "module": "Mathlib.Data.Nat.ModEq", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "have", "exact"], "tactic_count": 4}
{"name": "Nat.chineseRemainder_lt_mul", "kind": "theorem", "module": "Mathlib.Data.Nat.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.mod_lcm", "kind": "theorem", "module": "Mathlib.Data.Nat.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.chineseRemainder_modEq_unique", "kind": "theorem", "module": "Mathlib.Data.Nat.ModEq", "is_tactic_proof": true, "tactics": ["simpa", "mod_lcm"], "tactic_count": 2}
{"name": "Nat.modEq_and_modEq_iff_modEq_mul", "kind": "theorem", "module": "Mathlib.Data.Nat.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.coprime_of_mul_modEq_one", "kind": "theorem", "module": "Mathlib.Data.Nat.ModEq", "is_tactic_proof": true, "tactics": ["obtain", "rw", "calc"], "tactic_count": 3}
{"name": "Nat.add_mod_add_ite", "kind": "theorem", "module": "Mathlib.Data.Nat.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.add_mod_of_add_mod_lt", "kind": "theorem", "module": "Mathlib.Data.Nat.ModEq", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.add_mod_add_of_le_add_mod", "kind": "theorem", "module": "Mathlib.Data.Nat.ModEq", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.add_div_eq_of_add_mod_lt", "kind": "theorem", "module": "Mathlib.Data.Nat.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.add_div_of_dvd_right", "kind": "theorem", "module": "Mathlib.Data.Nat.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.add_div_of_dvd_left", "kind": "theorem", "module": "Mathlib.Data.Nat.ModEq", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Nat.add_div_eq_of_le_mod_add_mod", "kind": "theorem", "module": "Mathlib.Data.Nat.ModEq", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.add_div_le_add_div", "kind": "theorem", "module": "Mathlib.Data.Nat.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Nat.odd_mul_odd", "kind": "theorem", "module": "Mathlib.Data.Nat.ModEq", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Nat.odd_mul_odd_div_two", "kind": "theorem", "module": "Mathlib.Data.Nat.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.odd_of_mod_four_eq_one", "kind": "theorem", "module": "Mathlib.Data.Nat.ModEq", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Nat.odd_of_mod_four_eq_three", "kind": "theorem", "module": "Mathlib.Data.Nat.ModEq", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Nat.odd_mod_four_iff", "kind": "theorem", "module": "Mathlib.Data.Nat.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.mod_eq_of_modEq", "kind": "theorem", "module": "Mathlib.Data.Nat.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.ext_div_modEq", "kind": "theorem", "module": "Mathlib.Data.Nat.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.ext_div_modEq_iff", "kind": "theorem", "module": "Mathlib.Data.Nat.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.modEq_iff_eq_of_div_eq", "kind": "theorem", "module": "Mathlib.Data.Nat.ModEq", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Nat.emultiplicity_eq_card_pow_dvd", "kind": "theorem", "module": "Mathlib.Data.Nat.Multiplicity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Nat.Prime.emultiplicity_mul", "kind": "theorem", "module": "Mathlib.Data.Nat.Multiplicity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Prime.emultiplicity_pow", "kind": "theorem", "module": "Mathlib.Data.Nat.Multiplicity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Prime.emultiplicity_self", "kind": "theorem", "module": "Mathlib.Data.Nat.Multiplicity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Prime.emultiplicity_pow_self", "kind": "theorem", "module": "Mathlib.Data.Nat.Multiplicity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Prime.emultiplicity_factorial", "kind": "theorem", "module": "Mathlib.Data.Nat.Multiplicity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Prime.sub_one_mul_multiplicity_factorial", "kind": "theorem", "module": "Mathlib.Data.Nat.Multiplicity", "is_tactic_proof": true, "tactics": ["simp", "emultiplicity_factorial"], "tactic_count": 2}
{"name": "Nat.Prime.emultiplicity_factorial_mul_succ", "kind": "theorem", "module": "Mathlib.Data.Nat.Multiplicity", "is_tactic_proof": true, "tactics": ["have", "have", "have", "have", "have", "have", "rw", "exact", "revert", "have", "intro", "rw", "rw", "exact", "simp_rw", "intro", "rw", "sum_const_zero,"], "tactic_count": 18}
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{"name": "Nat.Prime.multiplicity_factorial_pow", "kind": "theorem", "module": "Mathlib.Data.Nat.Multiplicity", "is_tactic_proof": false, "tactics": ["rw", "induction", "zero", "succ"], "tactic_count": 4}
{"name": "Nat.Prime.pow_dvd_factorial_iff", "kind": "theorem", "module": "Mathlib.Data.Nat.Multiplicity", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.Prime.emultiplicity_factorial_le_div_pred", "kind": "theorem", "module": "Mathlib.Data.Nat.Multiplicity", "is_tactic_proof": true, "tactics": ["rw", "apply", "exact"], "tactic_count": 3}
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{"name": "Nat.Prime.emultiplicity_choose", "kind": "theorem", "module": "Mathlib.Data.Nat.Multiplicity", "is_tactic_proof": true, "tactics": ["have", "convert", "rw", "exact"], "tactic_count": 4}
{"name": "Nat.Prime.emultiplicity_le_emultiplicity_choose_add", "kind": "theorem", "module": "Mathlib.Data.Nat.Multiplicity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Prime.emultiplicity_choose_prime_pow_add_emultiplicity", "kind": "theorem", "module": "Mathlib.Data.Nat.Multiplicity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Prime.emultiplicity_choose_prime_pow", "kind": "theorem", "module": "Mathlib.Data.Nat.Multiplicity", "is_tactic_proof": true, "tactics": ["push_cast", "rw", "norm_cast", "rw"], "tactic_count": 4}
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{"name": "Nat.pair_lt_pair_left", "kind": "theorem", "module": "Mathlib.Data.Nat.Pairing", "is_tactic_proof": true, "tactics": ["by_cases", "by_cases", "simp", "simp", "apply", "exact", "exact", "simp", "simp", "apply", "exact", "apply"], "tactic_count": 12}
{"name": "Nat.pair_lt_pair_right", "kind": "theorem", "module": "Mathlib.Data.Nat.Pairing", "is_tactic_proof": true, "tactics": ["by_cases", "simpa", "simp", "by_cases", "simp", "rw", "rwa", "exact"], "tactic_count": 8}
{"name": "Nat.pair_lt_max_add_one_sq", "kind": "theorem", "module": "Mathlib.Data.Nat.Pairing", "is_tactic_proof": true, "tactics": ["simp", "split_ifs"], "tactic_count": 2}
{"name": "Nat.max_sq_add_min_le_pair", "kind": "theorem", "module": "Mathlib.Data.Nat.Pairing", "is_tactic_proof": true, "tactics": ["rw", "rcases", "rw", "rw", "exact"], "tactic_count": 5}
{"name": "Nat.add_le_pair", "kind": "theorem", "module": "Mathlib.Data.Nat.Pairing", "is_tactic_proof": true, "tactics": ["simp", "split_ifs", "have", "lia", "exact"], "tactic_count": 5}
{"name": "Nat.unpair_add_le", "kind": "theorem", "module": "Mathlib.Data.Nat.Pairing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_unpair", "kind": "theorem", "module": "Mathlib.Data.Nat.Pairing", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "iInf_unpair", "kind": "theorem", "module": "Mathlib.Data.Nat.Pairing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_unpair_prod", "kind": "theorem", "module": "Mathlib.Data.Nat.Pairing", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.iUnion_unpair", "kind": "theorem", "module": "Mathlib.Data.Nat.Pairing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iInter_unpair", "kind": "theorem", "module": "Mathlib.Data.Nat.Pairing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat", "kind": "definition", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.some", "kind": "definition", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.instZero", "kind": "instance", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.instInhabited", "kind": "instance", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.instOne", "kind": "instance", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.instAdd", "kind": "instance", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.instDecidableDomNatSome", "kind": "instance", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.dom_some", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.addCommMonoid", "kind": "instance", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.instAddCommMonoidWithOne", "kind": "instance", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.some_eq_natCast", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.instCharZero", "kind": "instance", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.natCast_inj", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.dom_natCast", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.dom_ofNat", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.dom_zero", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.dom_one", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.instCanLiftNatCastDom", "kind": "instance", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.instLE", "kind": "instance", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.instTop", "kind": "instance", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.instBot", "kind": "instance", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.instMax", "kind": "instance", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.le_def", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.casesOn'", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.casesOn", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "PartENat.top_add", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.add_top", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PartENat.natCast_get", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "PartENat.get_natCast'", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PartENat.get_natCast", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.coe_add_get", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "PartENat.get_add", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.get_zero", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.get_one", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.get_ofNat'", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.get_eq_iff_eq_some", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.get_eq_iff_eq_coe", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "PartENat.dom_of_le_of_dom", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.dom_of_le_some", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.dom_of_le_natCast", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "PartENat.decidableLe", "kind": "instance", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.partialOrder", "kind": "instance", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.lt_def", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": true, "tactics": ["rw", "constructor", "rintro", "by_cases", "use", "intro", "specialize", "specialize", "rw", "lia", "specialize", "rw", "obtain", "exact", "rintro", "exact"], "tactic_count": 16}
{"name": "PartENat.isOrderedAddMonoid", "kind": "instance", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.semilatticeSup", "kind": "instance", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.orderBot", "kind": "instance", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.orderTop", "kind": "instance", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.instZeroLEOneClass", "kind": "instance", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.coe_le_coe", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.coe_lt_coe", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.get_le_get", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": true, "tactics": ["conv", "lhs", "rw"], "tactic_count": 3}
{"name": "PartENat.le_coe_iff", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": true, "tactics": ["change", "simp"], "tactic_count": 2}
{"name": "PartENat.lt_coe_iff", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PartENat.coe_le_iff", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": true, "tactics": ["rw", "simp", "rfl"], "tactic_count": 3}
{"name": "PartENat.coe_lt_iff", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": true, "tactics": ["rw", "simp", "rfl"], "tactic_count": 3}
{"name": "PartENat.eq_zero_iff", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.ne_zero_iff", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.dom_of_lt", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.top_eq_none", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.natCast_lt_top", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.zero_lt_top", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.one_lt_top", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.ofNat_lt_top", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.natCast_ne_top", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.zero_ne_top", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.one_ne_top", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.ofNat_ne_top", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.not_isMax_natCast", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.ne_top_iff", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "PartENat.ne_top_iff_dom", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "PartENat.not_dom_iff_eq_top", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.ne_top_of_lt", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.eq_top_iff_forall_lt", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "exact", "contrapose", "rw", "rintro", "exact"], "tactic_count": 7}
{"name": "PartENat.eq_top_iff_forall_le", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.pos_iff_one_le", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.isTotal", "kind": "instance", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.linearOrder", "kind": "instance", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.boundedOrder", "kind": "instance", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.lattice", "kind": "instance", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.instCanonicallyOrderedAdd", "kind": "instance", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.eq_natCast_sub_of_add_eq_natCast", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": true, "tactics": ["lift", "lift", "rw", "rw"], "tactic_count": 4}
{"name": "PartENat.add_lt_add_right", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "induction", "rw", "exact_mod_cast", "intro", "norm_cast", "exact"], "tactic_count": 8}
{"name": "PartENat.add_lt_add_iff_right", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.add_lt_add_iff_left", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PartENat.lt_add_iff_pos_right", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": true, "tactics": ["conv_rhs", "rw"], "tactic_count": 2}
{"name": "PartENat.lt_add_one", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": true, "tactics": ["rw", "norm_cast"], "tactic_count": 2}
{"name": "PartENat.le_of_lt_add_one", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": true, "tactics": ["induction", "apply", "intro", "rcases", "exact_mod_cast"], "tactic_count": 5}
{"name": "PartENat.add_one_le_of_lt", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": true, "tactics": ["induction", "apply", "intro", "rcases", "exact_mod_cast"], "tactic_count": 5}
{"name": "PartENat.add_one_le_iff_lt", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": true, "tactics": ["refine", "rcases", "induction", "apply", "intro", "exact_mod_cast"], "tactic_count": 6}
{"name": "PartENat.coe_succ_le_iff", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PartENat.lt_add_one_iff_lt", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": true, "tactics": ["refine", "rcases", "induction", "rw", "apply", "intro", "exact_mod_cast"], "tactic_count": 7}
{"name": "PartENat.lt_coe_succ_iff_le", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PartENat.add_eq_top_iff", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": true, "tactics": ["refine", "simp"], "tactic_count": 2}
{"name": "PartENat.add_right_cancel_iff", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": true, "tactics": ["rcases", "refine", "simp", "simp"], "tactic_count": 4}
{"name": "PartENat.add_left_cancel_iff", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PartENat.toWithTop", "kind": "definition", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.toWithTop_top", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.toWithTop_top'", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "PartENat.toWithTop_zero", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.toWithTop_zero'", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "PartENat.toWithTop_one", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.toWithTop_one'", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "PartENat.toWithTop_some", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.toWithTop_natCast", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": true, "tactics": ["simp", "congr"], "tactic_count": 2}
{"name": "PartENat.toWithTop_natCast'", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PartENat.toWithTop_ofNat", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.toWithTop_le", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": true, "tactics": ["induction", "simp", "induction", "simp", "simp"], "tactic_count": 5}
{"name": "PartENat.toWithTop_lt", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.ofENat", "kind": "definition", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.instCoeENat", "kind": "instance", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat._example", "kind": "example", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.ofENat_top", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.ofENat_coe", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.ofENat_zero", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.ofENat_one", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.ofENat_ofNat", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.toWithTop_ofENat", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": true, "tactics": ["cases", "top", "coe"], "tactic_count": 3}
{"name": "PartENat.ofENat_toWithTop", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "PartENat.ofENat_le", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "PartENat.ofENat_lt", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "PartENat.toWithTop_add", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": true, "tactics": ["refine"], "tactic_count": 1}
{"name": "PartENat.withTopEquiv", "kind": "definition", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.withTopEquiv_top", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PartENat.withTopEquiv_natCast", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PartENat.withTopEquiv_zero", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PartENat.withTopEquiv_one", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PartENat.withTopEquiv_ofNat", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PartENat.withTopEquiv_le", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PartENat.withTopEquiv_lt", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PartENat.withTopEquiv_symm_top", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PartENat.withTopEquiv_symm_coe", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PartENat.withTopEquiv_symm_zero", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PartENat.withTopEquiv_symm_one", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PartENat.withTopEquiv_symm_ofNat", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PartENat.withTopEquiv_symm_le", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PartENat.withTopEquiv_symm_lt", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PartENat.withTopOrderIso", "kind": "definition", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.withTopAddEquiv", "kind": "definition", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.lt_wf", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": true, "tactics": ["classical", "change", "simp_rw", "exact"], "tactic_count": 4}
{"name": "PartENat.instWellFoundedLT", "kind": "instance", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.wellFoundedRelation", "kind": "instance", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.find", "kind": "definition", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.find_get", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.find_dom", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.lt_find", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "have", "revert", "contrapose", "exact"], "tactic_count": 7}
{"name": "PartENat.lt_find_iff", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": true, "tactics": ["refine", "intro", "by_cases", "apply", "rw", "specialize", "exact", "exact"], "tactic_count": 8}
{"name": "PartENat.find_le", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "PartENat.find_eq_top_iff", "kind": "theorem", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.instLinearOrderedAddCommMonoidWithTop", "kind": "instance", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartENat.instCompleteLinearOrder", "kind": "instance", "module": "Mathlib.Data.Nat.PartENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.periodic_gcd", "kind": "theorem", "module": "Mathlib.Data.Nat.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.periodic_coprime", "kind": "theorem", "module": "Mathlib.Data.Nat.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.periodic_mod", "kind": "theorem", "module": "Mathlib.Data.Nat.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Periodic.map_mod_nat", "kind": "theorem", "module": "Mathlib.Data.Nat.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.filter_multiset_Ico_card_eq_of_periodic", "kind": "theorem", "module": "Mathlib.Data.Nat.Periodic", "is_tactic_proof": false, "tactics": ["rw", "map_count_True_eq_filter_card,", "congr", "exact"], "tactic_count": 4}
{"name": "Nat.filter_Ico_card_eq_of_periodic", "kind": "theorem", "module": "Mathlib.Data.Nat.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.infinite_setOf_prime", "kind": "theorem", "module": "Mathlib.Data.Nat.PrimeFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Primes.infinite", "kind": "instance", "module": "Mathlib.Data.Nat.PrimeFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Primes.countable", "kind": "instance", "module": "Mathlib.Data.Nat.PrimeFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.primeFactors", "kind": "definition", "module": "Mathlib.Data.Nat.PrimeFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.toFinset_factors", "kind": "theorem", "module": "Mathlib.Data.Nat.PrimeFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.mem_primeFactors", "kind": "theorem", "module": "Mathlib.Data.Nat.PrimeFin", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Nat.mem_primeFactors_of_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Nat.PrimeFin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.Prime.mem_primeFactors", "kind": "theorem", "module": "Mathlib.Data.Nat.PrimeFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Prime.mem_primeFactors'", "kind": "theorem", "module": "Mathlib.Data.Nat.PrimeFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Prime.mem_primeFactors_self", "kind": "theorem", "module": "Mathlib.Data.Nat.PrimeFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.primeFactors_mono", "kind": "theorem", "module": "Mathlib.Data.Nat.PrimeFin", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Nat.mem_primeFactors_iff_mem_primeFactorsList", "kind": "theorem", "module": "Mathlib.Data.Nat.PrimeFin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.prime_of_mem_primeFactors", "kind": "theorem", "module": "Mathlib.Data.Nat.PrimeFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.dvd_of_mem_primeFactors", "kind": "theorem", "module": "Mathlib.Data.Nat.PrimeFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.pos_of_mem_primeFactors", "kind": "theorem", "module": "Mathlib.Data.Nat.PrimeFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.le_of_mem_primeFactors", "kind": "theorem", "module": "Mathlib.Data.Nat.PrimeFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.primeFactors_zero", "kind": "theorem", "module": "Mathlib.Data.Nat.PrimeFin", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Nat.primeFactors_one", "kind": "theorem", "module": "Mathlib.Data.Nat.PrimeFin", "is_tactic_proof": true, "tactics": ["ext", "simpa"], "tactic_count": 2}
{"name": "Nat.primeFactors_eq_empty", "kind": "theorem", "module": "Mathlib.Data.Nat.PrimeFin", "is_tactic_proof": true, "tactics": ["constructor", "contrapose", "rintro", "obtain", "exact", "rintro"], "tactic_count": 6}
{"name": "Nat.nonempty_primeFactors", "kind": "theorem", "module": "Mathlib.Data.Nat.PrimeFin", "is_tactic_proof": true, "tactics": ["contrapose", "rw"], "tactic_count": 2}
{"name": "Nat.Prime.primeFactors", "kind": "theorem", "module": "Mathlib.Data.Nat.PrimeFin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.primeFactors_mul", "kind": "theorem", "module": "Mathlib.Data.Nat.PrimeFin", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Nat.Coprime.primeFactors_mul", "kind": "theorem", "module": "Mathlib.Data.Nat.PrimeFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.primeFactors_gcd", "kind": "theorem", "module": "Mathlib.Data.Nat.PrimeFin", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Nat.disjoint_primeFactors", "kind": "theorem", "module": "Mathlib.Data.Nat.PrimeFin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.Coprime.disjoint_primeFactors", "kind": "theorem", "module": "Mathlib.Data.Nat.PrimeFin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.primeFactors_pow_succ", "kind": "theorem", "module": "Mathlib.Data.Nat.PrimeFin", "is_tactic_proof": true, "tactics": ["rcases", "simp", "induction", "zero", "succ"], "tactic_count": 5}
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{"name": "Nat.primeFactors_prime_pow", "kind": "theorem", "module": "Mathlib.Data.Nat.PrimeFin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.prime_mul_iff", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.not_prime_mul", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.not_prime_of_mul_eq", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Prime.dvd_iff_eq", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Basic", "is_tactic_proof": true, "tactics": ["refine", "rintro", "rcases", "exact", "exact"], "tactic_count": 5}
{"name": "Nat.Prime.eq_two_or_odd", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Prime.eq_two_or_odd'", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Prime.five_le_of_ne_two_of_ne_three", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Basic", "is_tactic_proof": true, "tactics": ["by_contra", "revert", "decide"], "tactic_count": 3}
{"name": "Nat.Prime.pred_pos", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.succ_pred_prime", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.exists_dvd_of_not_prime", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.exists_dvd_of_not_prime2", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.not_prime_of_dvd_of_ne", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.not_prime_of_dvd_of_lt", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.not_prime_iff_exists_dvd_ne", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.not_prime_iff_exists_dvd_lt", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.not_prime_iff_exists_mul_eq", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.dvd_of_forall_prime_mul_dvd", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Basic", "is_tactic_proof": true, "tactics": ["obtain", "apply", "obtain", "exact"], "tactic_count": 4}
{"name": "Nat.Prime.even_iff", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.Prime.odd_of_ne_two", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Prime.even_sub_one", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Prime.mod_two_eq_one_iff_ne_two", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "simp"], "tactic_count": 3}
{"name": "Nat.coprime_of_dvd'", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Prime.dvd_iff_not_coprime", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Prime.not_coprime_iff_dvd", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Basic", "is_tactic_proof": true, "tactics": ["apply", "intro", "exact", "intro", "obtain", "apply"], "tactic_count": 6}
{"name": "Nat.coprime_of_lt_minFac", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Basic", "is_tactic_proof": true, "tactics": ["rw", "push_neg", "exact"], "tactic_count": 3}
{"name": "Nat.gcd_eq_one_of_lt_minFac", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Prime.not_dvd_mul", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.coprime_two_left", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.coprime_two_right", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Prime.dvd_of_dvd_pow", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Prime.not_prime_pow'", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Prime.not_prime_pow", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Prime.eq_one_of_pow", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Prime.pow_eq_iff", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "rw"], "tactic_count": 3}
{"name": "Nat.Prime.mul_eq_prime_sq_iff", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Basic", "is_tactic_proof": true, "tactics": ["refine", "have", "simp", "suffices", "obtain", "apply", "assumption", "rintro", "have", "obtain", "subst", "rw", "subst", "simp", "subst", "exact", "refine", "subst", "subst", "rw", "exact"], "tactic_count": 21}
{"name": "Nat.Prime.coprime_pow_of_not_dvd", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.coprime_primes", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.coprime_pow_primes", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.coprime_or_dvd_of_prime", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.coprime_of_lt_prime", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.eq_or_coprime_of_le_prime", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.prime_eq_prime_of_dvd_pow", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.dvd_prime_pow", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Nat.Prime.dvd_mul_of_dvd_ne", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.eq_prime_pow_of_dvd_least_prime_pow", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Basic", "is_tactic_proof": true, "tactics": ["obtain", "congr", "exact"], "tactic_count": 3}
{"name": "Nat.ne_one_iff_exists_prime_dvd", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.eq_one_iff_not_exists_prime_dvd", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Nat.succ_dvd_or_succ_dvd_of_succ_sum_dvd_mul", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Basic", "is_tactic_proof": false, "tactics": ["have", "let", "rwa", "have", "have", "have", "have", "suffices", "exact", "hpd5.elim"], "tactic_count": 10}
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{"name": "Nat.not_prime_one", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Nat.Prime.one_le", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Nat.Prime.ne_one", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Prime.eq_one_or_self_of_dvd", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Defs", "is_tactic_proof": true, "tactics": ["obtain", "have", "rw", "apply", "rintro", "rw"], "tactic_count": 6}
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{"name": "Nat.prime_def_le_sqrt", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.prime_iff_not_exists_mul_eq", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Defs", "is_tactic_proof": true, "tactics": ["push_neg", "simp_rw", "refine", "simp_rw", "refine", "have", "exact"], "tactic_count": 7}
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{"name": "Nat.decidablePrime", "kind": "instance", "module": "Mathlib.Data.Nat.Prime.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.prime_two", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Defs", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
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{"name": "Nat.dvd_prime", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.dvd_prime_two_le", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.prime_dvd_prime_iff_eq", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Prime.not_dvd_one", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.minFac_lemma", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.minFacAux", "kind": "definition", "module": "Mathlib.Data.Nat.Prime.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Nat.minFac_zero", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Nat.minFac_two", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.minFac_eq", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Nat.minFacAux_has_prop", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Nat.minFac_prime", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Nat.le_minFac'", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.prime_def_minFac", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Prime.minFac_eq", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.decidablePrime'", "kind": "definition", "module": "Mathlib.Data.Nat.Prime.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.decidablePrime_csimp", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Defs", "is_tactic_proof": true, "tactics": ["subsingleton"], "tactic_count": 1}
{"name": "Nat.not_prime_iff_minFac_lt", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.minFac_le_div", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.minFac_sq_le_self", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Nat.exists_prime_and_dvd", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.coprime_of_dvd", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Defs", "is_tactic_proof": true, "tactics": ["rw", "by_contra", "obtain", "apply", "exact", "exact"], "tactic_count": 6}
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{"name": "Nat.irreducible_iff_prime", "kind": "theorem", "module": "Mathlib.Data.Nat.Prime.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Nat.Primes.coeNat", "kind": "instance", "module": "Mathlib.Data.Nat.Prime.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Nat.monoid.primePow", "kind": "instance", "module": "Mathlib.Data.Nat.Prime.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Nat.zero_union_range_succ", "kind": "theorem", "module": "Mathlib.Data.Nat.Set", "is_tactic_proof": true, "tactics": ["ext", "cases"], "tactic_count": 2}
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{"name": "Nat.shiftLeft_eq_mul_pow", "kind": "theorem", "module": "Mathlib.Data.Nat.Size", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Nat.prime_iff_card_units", "kind": "theorem", "module": "Mathlib.Data.Nat.Totient", "is_tactic_proof": true, "tactics": ["rcases", "subst", "simp", "suffices", "simp", "rw"], "tactic_count": 6}
{"name": "Nat.totient_two", "kind": "theorem", "module": "Mathlib.Data.Nat.Totient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.odd_totient_iff", "kind": "theorem", "module": "Mathlib.Data.Nat.Totient", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "Nat.totient_eq_one_iff", "kind": "theorem", "module": "Mathlib.Data.Nat.Totient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.dvd_two_of_totient_le_one", "kind": "theorem", "module": "Mathlib.Data.Nat.Totient", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "Nat.odd_totient_iff_eq_one", "kind": "theorem", "module": "Mathlib.Data.Nat.Totient", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.totient_coprime_totient_iff", "kind": "theorem", "module": "Mathlib.Data.Nat.Totient", "is_tactic_proof": true, "tactics": ["constructor", "rw", "simp_rw", "exact", "simp_rw", "rintro", "exacts"], "tactic_count": 7}
{"name": "Nat.totient_eq_prod_factorization", "kind": "theorem", "module": "Mathlib.Data.Nat.Totient", "is_tactic_proof": true, "tactics": ["rw", "apply", "intro", "have", "rw"], "tactic_count": 5}
{"name": "Nat.totient_mul_prod_primeFactors", "kind": "theorem", "module": "Mathlib.Data.Nat.Totient", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "nth_rw", "simp", "refine", "rw", "rw"], "tactic_count": 7}
{"name": "Nat.totient_eq_div_primeFactors_mul", "kind": "theorem", "module": "Mathlib.Data.Nat.Totient", "is_tactic_proof": false, "tactics": ["rw", "mul_comm]", "exact"], "tactic_count": 3}
{"name": "Nat.totient_eq_mul_prod_factors", "kind": "theorem", "module": "Mathlib.Data.Nat.Totient", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "have", "have", "rw", "exact", "simp", "mul_comm_div,", "refine", "have", "have", "rw"], "tactic_count": 12}
{"name": "Nat.totient_gcd_mul_totient_mul", "kind": "theorem", "module": "Mathlib.Data.Nat.Totient", "is_tactic_proof": false, "tactics": ["have", "intro", "calc", "a1", "congr", "exact", "simp", "rw", "rotate_left", "repeat", "simp", "rw", "exact"], "tactic_count": 13}
{"name": "Nat.totient_super_multiplicative", "kind": "theorem", "module": "Mathlib.Data.Nat.Totient", "is_tactic_proof": true, "tactics": ["let", "rcases", "simp", "have", "apply", "grw"], "tactic_count": 6}
{"name": "Nat.totient_dvd_of_dvd", "kind": "theorem", "module": "Mathlib.Data.Nat.Totient", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rcases", "simp", "have", "rw", "refine", "exact"], "tactic_count": 8}
{"name": "Nat.totient_mul_of_prime_of_dvd", "kind": "theorem", "module": "Mathlib.Data.Nat.Totient", "is_tactic_proof": true, "tactics": ["have", "rw", "simpa"], "tactic_count": 3}
{"name": "Nat.totient_mul_of_prime_of_not_dvd", "kind": "theorem", "module": "Mathlib.Data.Nat.Totient", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "Nat.totient_two_mul_of_even", "kind": "theorem", "module": "Mathlib.Data.Nat.Totient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.totient_two_mul_of_odd", "kind": "theorem", "module": "Mathlib.Data.Nat.Totient", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.eq_or_eq_of_totient_eq_totient", "kind": "theorem", "module": "Mathlib.Data.Nat.Totient", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "simp", "by_cases", "rw", "exact", "obtain", "suffices", "rw", "obtain", "simp", "simp", "refine", "rintro", "suffices", "rw", "exact", "rw", "refine", "rw", "exact", "exact", "exact"], "tactic_count": 23}
{"name": "Even.eq_of_totient_eq_totient", "kind": "theorem", "module": "Mathlib.Data.Nat.Totient", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "rw", "refine", "rw", "mul_eq_right", "lia"], "tactic_count": 7}
{"name": "Nat.prime_pow_pow_totient_ediv_prod", "kind": "theorem", "module": "Mathlib.Data.Nat.Totient", "is_tactic_proof": false, "tactics": ["have", "rw", "refine", "exact", "simp_rw", "rw", "simp_rw", "ring_nf"], "tactic_count": 8}
{"name": "Nat.prod_primeFactors_pow_totient_ediv_dvd", "kind": "theorem", "module": "Mathlib.Data.Nat.Totient", "is_tactic_proof": true, "tactics": ["have", "rw", "refine", "exact"], "tactic_count": 4}
{"name": "Mathlib.Meta.Positivity.evalNatTotient", "kind": "definition", "module": "Mathlib.Data.Nat.Totient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Upto", "kind": "abbrev", "module": "Mathlib.Data.Nat.Upto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Upto.GT", "kind": "definition", "module": "Mathlib.Data.Nat.Upto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Upto.instLT", "kind": "instance", "module": "Mathlib.Data.Nat.Upto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Upto.wf", "kind": "theorem", "module": "Mathlib.Data.Nat.Upto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Upto.zero", "kind": "definition", "module": "Mathlib.Data.Nat.Upto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Upto.succ", "kind": "definition", "module": "Mathlib.Data.Nat.Upto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.WithBot.instWellFoundedRelationWithBot", "kind": "instance", "module": "Mathlib.Data.Nat.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.WithBot.add_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Data.Nat.WithBot", "is_tactic_proof": true, "tactics": ["cases", "simp", "cases", "simp", "simp"], "tactic_count": 5}
{"name": "Nat.WithBot.add_eq_one_iff", "kind": "theorem", "module": "Mathlib.Data.Nat.WithBot", "is_tactic_proof": true, "tactics": ["cases", "simp", "cases", "simp", "simp"], "tactic_count": 5}
{"name": "Nat.WithBot.add_eq_two_iff", "kind": "theorem", "module": "Mathlib.Data.Nat.WithBot", "is_tactic_proof": true, "tactics": ["cases", "simp", "cases", "simp", "simp"], "tactic_count": 5}
{"name": "Nat.WithBot.add_eq_three_iff", "kind": "theorem", "module": "Mathlib.Data.Nat.WithBot", "is_tactic_proof": true, "tactics": ["cases", "simp", "cases", "simp", "simp"], "tactic_count": 5}
{"name": "Nat.WithBot.coe_nonneg", "kind": "theorem", "module": "Mathlib.Data.Nat.WithBot", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Nat.WithBot.lt_zero_iff", "kind": "theorem", "module": "Mathlib.Data.Nat.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.WithBot.one_le_iff_zero_lt", "kind": "theorem", "module": "Mathlib.Data.Nat.WithBot", "is_tactic_proof": true, "tactics": ["refine", "cases", "exact", "rwa"], "tactic_count": 4}
{"name": "Nat.WithBot.lt_one_iff_le_zero", "kind": "theorem", "module": "Mathlib.Data.Nat.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.WithBot.add_one_le_of_lt", "kind": "theorem", "module": "Mathlib.Data.Nat.WithBot", "is_tactic_proof": true, "tactics": ["cases", "simp", "cases", "exact", "rwa"], "tactic_count": 5}
{"name": "PosNum", "kind": "inductive", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDecidableEqPosNum", "kind": "instance", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instOnePosNum", "kind": "instance", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInhabitedPosNum", "kind": "instance", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num", "kind": "inductive", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDecidableEqNum", "kind": "instance", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instZeroNum", "kind": "instance", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instOneNum", "kind": "instance", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInhabitedNum", "kind": "instance", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZNum", "kind": "inductive", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDecidableEqZNum", "kind": "instance", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instZeroZNum", "kind": "instance", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instOneZNum", "kind": "instance", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInhabitedZNum", "kind": "instance", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.bit", "kind": "definition", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.succ", "kind": "definition", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.isOne", "kind": "definition", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.add", "kind": "definition", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.instAdd", "kind": "instance", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.pred'", "kind": "definition", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.pred", "kind": "definition", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.size", "kind": "definition", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.natSize", "kind": "definition", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.mul", "kind": "definition", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.instMul", "kind": "instance", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.ofNatSucc", "kind": "definition", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.ofNat", "kind": "definition", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.instOfNatHAddNatOfNat", "kind": "instance", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.cmp", "kind": "definition", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.instLT", "kind": "instance", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.instLE", "kind": "instance", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.decidableLT", "kind": "instance", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.decidableLE", "kind": "instance", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "castPosNum", "kind": "definition", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "castNum", "kind": "definition", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "posNumCoe", "kind": "instance", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "numNatCoe", "kind": "instance", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instReprPosNum", "kind": "instance", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instReprNum", "kind": "instance", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.succ'", "kind": "definition", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.succ", "kind": "definition", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.add", "kind": "definition", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.instAdd", "kind": "instance", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.bit0", "kind": "definition", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.bit1", "kind": "definition", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.bit", "kind": "definition", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.size", "kind": "definition", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.natSize", "kind": "definition", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.mul", "kind": "definition", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.instMul", "kind": "instance", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.cmp", "kind": "definition", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.instLT", "kind": "instance", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.instLE", "kind": "instance", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.decidableLT", "kind": "instance", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.decidableLE", "kind": "instance", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.toZNum", "kind": "definition", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.toZNumNeg", "kind": "definition", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.ofNat'", "kind": "definition", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZNum.zNeg", "kind": "definition", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZNum.instNeg", "kind": "instance", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZNum.abs", "kind": "definition", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZNum.succ", "kind": "definition", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZNum.pred", "kind": "definition", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZNum.bit0", "kind": "definition", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZNum.bit1", "kind": "definition", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZNum.bitm1", "kind": "definition", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZNum.ofInt'", "kind": "definition", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.sub'", "kind": "definition", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.ofZNum'", "kind": "definition", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.ofZNum", "kind": "definition", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.sub", "kind": "definition", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.instSub", "kind": "instance", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.ppred", "kind": "definition", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Num.div2", "kind": "definition", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.ofZNum'", "kind": "definition", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Num.psub", "kind": "definition", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ZNum.add", "kind": "definition", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ZNum.mul", "kind": "definition", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ZNum.cmp", "kind": "definition", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "PosNum.divModAux", "kind": "definition", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.divMod", "kind": "definition", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.div'", "kind": "definition", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.mod'", "kind": "definition", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.Num.Basic.0.PosNum.sqrtAux1", "kind": "definition", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.Num.Basic.0.PosNum.sqrtAux", "kind": "definition", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.div", "kind": "definition", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.mod", "kind": "definition", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.instDiv", "kind": "instance", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.instMod", "kind": "instance", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.gcdAux", "kind": "definition", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.gcd", "kind": "definition", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZNum.div", "kind": "definition", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZNum.mod", "kind": "definition", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZNum.instDiv", "kind": "instance", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZNum.instMod", "kind": "instance", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZNum.gcd", "kind": "definition", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "castZNum", "kind": "definition", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "znumCoe", "kind": "instance", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instReprZNum", "kind": "instance", "module": "Mathlib.Data.Num.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.lor", "kind": "definition", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.instOrOp", "kind": "instance", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.lor_eq_or", "kind": "theorem", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.land", "kind": "definition", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.instHAndNum", "kind": "instance", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.land_eq_and", "kind": "theorem", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.ldiff", "kind": "definition", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.lxor", "kind": "definition", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.instHXorNum", "kind": "instance", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.lxor_eq_xor", "kind": "theorem", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.testBit", "kind": "definition", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.oneBits", "kind": "definition", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.shiftl", "kind": "definition", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.instHShiftLeftNat", "kind": "instance", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.shiftl_eq_shiftLeft", "kind": "theorem", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.shiftl_succ_eq_bit0_shiftl", "kind": "theorem", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.shiftr", "kind": "definition", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.instHShiftRightNatNum", "kind": "instance", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.shiftr_eq_shiftRight", "kind": "theorem", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.lor", "kind": "definition", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.instOrOp", "kind": "instance", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.lor_eq_or", "kind": "theorem", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.land", "kind": "definition", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.instAndOp", "kind": "instance", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.land_eq_and", "kind": "theorem", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.ldiff", "kind": "definition", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.lxor", "kind": "definition", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.instXorOp", "kind": "instance", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.lxor_eq_xor", "kind": "theorem", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.shiftl", "kind": "definition", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.instHShiftLeftNat", "kind": "instance", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.shiftl_eq_shiftLeft", "kind": "theorem", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.shiftr", "kind": "definition", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.instHShiftRightNat", "kind": "instance", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.shiftr_eq_shiftRight", "kind": "theorem", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.testBit", "kind": "definition", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.oneBits", "kind": "definition", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NzsNum", "kind": "inductive", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDecidableEqNzsNum", "kind": "instance", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SNum", "kind": "inductive", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDecidableEqSNum", "kind": "instance", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCoeNzsNumSNum", "kind": "instance", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instZeroSNum", "kind": "instance", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instOneNzsNum", "kind": "instance", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instOneSNum", "kind": "instance", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInhabitedNzsNum", "kind": "instance", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInhabitedSNum", "kind": "instance", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NzsNum.term_::_", "kind": "definition", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NzsNum._aux_Mathlib_Data_Num_Bitwise___macroRules_NzsNum_term_::__1", "kind": "definition", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NzsNum._aux_Mathlib_Data_Num_Bitwise___unexpand_NzsNum_bit_1", "kind": "definition", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NzsNum.sign", "kind": "definition", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NzsNum.not", "kind": "definition", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NzsNum.term~_", "kind": "definition", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NzsNum._aux_Mathlib_Data_Num_Bitwise___macroRules_NzsNum_term~__1", "kind": "definition", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NzsNum._aux_Mathlib_Data_Num_Bitwise___unexpand_NzsNum_not_1", "kind": "definition", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NzsNum.bit0", "kind": "definition", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NzsNum.bit1", "kind": "definition", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NzsNum.head", "kind": "definition", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NzsNum.tail", "kind": "definition", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SNum.sign", "kind": "definition", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SNum.not", "kind": "definition", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SNum.term~_", "kind": "definition", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SNum._aux_Mathlib_Data_Num_Bitwise___macroRules_SNum_term~__1", "kind": "definition", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SNum._aux_Mathlib_Data_Num_Bitwise___unexpand_SNum_not_1", "kind": "definition", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SNum.bit", "kind": "definition", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SNum.term_::_", "kind": "definition", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SNum._aux_Mathlib_Data_Num_Bitwise___macroRules_SNum_term_::__1", "kind": "definition", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SNum._aux_Mathlib_Data_Num_Bitwise___unexpand_SNum_bit_1", "kind": "definition", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SNum.bit0", "kind": "definition", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SNum.bit1", "kind": "definition", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SNum.bit_zero", "kind": "theorem", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "SNum.bit_one", "kind": "theorem", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "NzsNum.drec'", "kind": "definition", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SNum.head", "kind": "definition", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SNum.tail", "kind": "definition", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SNum.drec'", "kind": "definition", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SNum.rec'", "kind": "definition", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SNum.testBit", "kind": "definition", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SNum.succ", "kind": "definition", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SNum.pred", "kind": "definition", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SNum.neg", "kind": "definition", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SNum.instNeg", "kind": "instance", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SNum.czAdd", "kind": "definition", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SNum.bits", "kind": "definition", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SNum.cAdd", "kind": "definition", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SNum.add", "kind": "definition", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SNum.instAdd", "kind": "instance", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SNum.sub", "kind": "definition", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SNum.instSub", "kind": "instance", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SNum.mul", "kind": "definition", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SNum.instMul", "kind": "instance", "module": "Mathlib.Data.Num.Bitwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.cast_one", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.cast_one'", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.cast_bit0", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.cast_bit1", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.cast_to_nat", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.to_nat_to_int", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.cast_to_int", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PosNum.succ_to_nat", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.one_add", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "PosNum.add_one", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "PosNum.add_to_nat", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.add_succ", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.bit0_of_bit0", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.bit1_of_bit1", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.mul_to_nat", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.to_nat_pos", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.cmp_to_nat_lemma", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.cmp_swap", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": true, "tactics": ["induction", "one", "bit1", "bit0", "intro", "obtain", "unfold", "try", "rw", "cases", "rfl"], "tactic_count": 11}
{"name": "PosNum.cmp_to_nat", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.lt_to_nat", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.le_to_nat", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Num.add_zero", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Num.zero_add", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Num.add_one", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.add_succ", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.bit0_of_bit0", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.bit1_of_bit1", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.ofNat'_zero", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Num.ofNat'_bit", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.ofNat'_one", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Num.bit1_succ", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.ofNat'_succ", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.add_ofNat'", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": true, "tactics": ["induction", "simp", "simp"], "tactic_count": 3}
{"name": "Num.cast_zero", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.cast_zero'", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.cast_one", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.cast_pos", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.succ'_to_nat", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.succ_to_nat", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.cast_to_nat", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.add_to_nat", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.mul_to_nat", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.cmp_to_nat", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.lt_to_nat", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.le_to_nat", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PosNum.of_to_nat'", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.of_to_nat'", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.toNat_injective", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.to_nat_inj", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.transfer_rw", "kind": "definition", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num._aux_Mathlib_Data_Num_Lemmas___macroRules_Num_transfer_rw_1", "kind": "definition", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.transfer", "kind": "definition", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num._aux_Mathlib_Data_Num_Lemmas___macroRules_Num_transfer_1", "kind": "definition", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.addMonoid", "kind": "instance", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.addMonoidWithOne", "kind": "instance", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.commSemiring", "kind": "instance", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.partialOrder", "kind": "instance", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.isOrderedCancelAddMonoid", "kind": "instance", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.linearOrder", "kind": "instance", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.isStrictOrderedRing", "kind": "instance", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.add_of_nat", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.to_nat_to_int", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.cast_to_int", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Num.to_of_nat", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.of_natCast", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Num.of_nat_inj", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.of_to_nat", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.dvd_to_nat", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.of_to_nat", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.to_nat_inj", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.pred'_to_nat", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.pred'_succ'", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.succ'_pred'", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.dvd", "kind": "instance", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.dvd_to_nat", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.size_to_nat", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.size_eq_natSize", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.natSize_to_nat", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PosNum.natSize_pos", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "PosNum.transfer_rw", "kind": "definition", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum._aux_Mathlib_Data_Num_Lemmas___macroRules_PosNum_transfer_rw_1", "kind": "definition", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.transfer", "kind": "definition", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum._aux_Mathlib_Data_Num_Lemmas___macroRules_PosNum_transfer_1", "kind": "definition", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.addCommSemigroup", "kind": "instance", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.commMonoid", "kind": "instance", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.distrib", "kind": "instance", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.linearOrder", "kind": "instance", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.cast_to_num", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PosNum.bit_to_nat", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "PosNum.cast_add", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PosNum.cast_succ", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PosNum.cast_inj", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PosNum.one_le_cast", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PosNum.cast_pos", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.cast_mul", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PosNum.cmp_eq", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": true, "tactics": ["have", "revert", "cases", "try", "simp"], "tactic_count": 5}
{"name": "PosNum.cast_lt", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PosNum.cast_le", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Num.bit_to_nat", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Num.cast_succ'", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Num.cast_succ", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.cast_add", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Num.cast_bit0", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Num.cast_bit1", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Num.cast_mul", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.size_to_nat", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.size_eq_natSize", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.natSize_to_nat", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Num.ofNat'_eq", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.zneg_toZNum", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Num.zneg_toZNumNeg", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Num.toZNum_inj", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.cast_toZNum", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.cast_toZNumNeg", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.add_toZNum", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "PosNum.pred_to_nat", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": true, "tactics": ["unfold", "cases", "have", "rw", "exact", "rw", "rfl"], "tactic_count": 7}
{"name": "PosNum.sub'_one", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "PosNum.one_sub'", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "PosNum.lt_iff_cmp", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.le_iff_cmp", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.pred_to_nat", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.ppred_to_nat", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.cmp_swap", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": true, "tactics": ["cases", "try", "apply"], "tactic_count": 3}
{"name": "Num.cmp_eq", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": true, "tactics": ["have", "revert", "cases", "try", "simp"], "tactic_count": 5}
{"name": "Num.cast_lt", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Num.cast_le", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Num.cast_inj", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Num.lt_iff_cmp", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.le_iff_cmp", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.castNum_eq_bitwise", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": true, "tactics": ["intro", "obtain", "rw", "rw", "cases", "rw", "cases", "rw", "have", "have", "induction", "one", "bit1", "bit0", "obtain", "any_goals", "simp", "show", "all_goals", "repeat", "rw", "any_goals", "any_goals", "any_goals", "all_goals", "rw", "rw"], "tactic_count": 27}
{"name": "Num.castNum_or", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": true, "tactics": ["apply", "intros", "rfl"], "tactic_count": 3}
{"name": "Num.castNum_and", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "Num.castNum_ldiff", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "Num.castNum_xor", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "Num.castNum_shiftLeft", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": true, "tactics": ["cases", "symm", "apply", "simp", "induction", "zero", "succ", "simp"], "tactic_count": 8}
{"name": "Num.castNum_shiftRight", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": true, "tactics": ["obtain", "symm", "apply", "induction", "zero", "succ", "have", "obtain", "rw", "symm", "apply", "simp", "trans", "apply", "change", "rw", "apply", "simp", "trans", "apply", "change", "rw", "apply", "simp"], "tactic_count": 24}
{"name": "Num.castNum_testBit", "kind": "theorem", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": true, "tactics": ["cases", "zero", "pos", "rw", "induction", "rfl", "rw", "rw", "simp", "rw", "rw"], "tactic_count": 11}
{"name": "Int.ofSnum", "kind": "definition", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.snumCoe", "kind": "instance", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SNum.lt", "kind": "instance", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SNum.le", "kind": "instance", "module": "Mathlib.Data.Num.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.minFacAux", "kind": "definition", "module": "Mathlib.Data.Num.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.minFacAux_to_nat", "kind": "theorem", "module": "Mathlib.Data.Num.Prime", "is_tactic_proof": true, "tactics": ["induction", "rw", "simp", "simp_rw", "simp", "split_ifs", "rw", "simp"], "tactic_count": 8}
{"name": "PosNum.minFac", "kind": "definition", "module": "Mathlib.Data.Num.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.minFac_to_nat", "kind": "theorem", "module": "Mathlib.Data.Num.Prime", "is_tactic_proof": true, "tactics": ["obtain", "simp", "rw", "swap", "simp", "rw", "rfl", "simp", "rw", "calc", "rw", "rfl", "simp"], "tactic_count": 13}
{"name": "PosNum.Prime", "kind": "definition", "module": "Mathlib.Data.Num.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.decidablePrime", "kind": "instance", "module": "Mathlib.Data.Num.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.minFac", "kind": "definition", "module": "Mathlib.Data.Num.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.minFac_to_nat", "kind": "theorem", "module": "Mathlib.Data.Num.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.Prime", "kind": "definition", "module": "Mathlib.Data.Num.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.decidablePrime", "kind": "instance", "module": "Mathlib.Data.Num.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZNum.cast_zero", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZNum.cast_zero'", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZNum.cast_one", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZNum.cast_pos", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZNum.cast_neg", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZNum.cast_zneg", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZNum.neg_zero", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZNum.zneg_pos", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZNum.zneg_neg", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZNum.zneg_zneg", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "ZNum.zneg_bit1", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "ZNum.zneg_bitm1", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "ZNum.zneg_succ", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": true, "tactics": ["cases", "try", "rw"], "tactic_count": 3}
{"name": "ZNum.zneg_pred", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ZNum.abs_to_nat", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZNum.abs_toZNum", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZNum.cast_to_int", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZNum.bit0_of_bit0", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZNum.bit1_of_bit1", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZNum.cast_bit0", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZNum.cast_bit1", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZNum.cast_bitm1", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": ["conv", "lhs", "rw", "rw", "have", "simpa"], "tactic_count": 6}
{"name": "ZNum.add_zero", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "ZNum.zero_add", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "ZNum.add_one", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.cast_to_znum", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.cast_sub'", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.to_nat_eq_succ_pred", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PosNum.to_int_eq_succ_pred", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Num.cast_sub'", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.toZNum_succ", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.toZNumNeg_succ", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.pred_succ", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.succ_ofInt'", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.ofInt'_toZNum", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.mem_ofZNum'", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.ofZNum'_toNat", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.ofZNum_toNat", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.cast_ofZNum", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Num.sub_to_nat", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZNum.cast_add", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZNum.cast_succ", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ZNum.mul_to_int", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZNum.cast_mul", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ZNum.ofInt'_neg", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZNum.of_to_int'", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZNum.to_int_inj", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZNum.cmp_to_int", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZNum.lt_to_int", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZNum.le_to_int", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ZNum.cast_lt", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ZNum.cast_le", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ZNum.cast_inj", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ZNum.transfer_rw", "kind": "definition", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZNum._aux_Mathlib_Data_Num_ZNum___macroRules_ZNum_transfer_rw_1", "kind": "definition", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZNum.transfer", "kind": "definition", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZNum._aux_Mathlib_Data_Num_ZNum___macroRules_ZNum_transfer_1", "kind": "definition", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZNum.linearOrder", "kind": "instance", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZNum.addMonoid", "kind": "instance", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZNum.addCommGroup", "kind": "instance", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZNum.addMonoidWithOne", "kind": "instance", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.Num.ZNum.0.ZNum.mul_comm", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": true, "tactics": ["transfer"], "tactic_count": 1}
{"name": "ZNum.commRing", "kind": "instance", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZNum.nontrivial", "kind": "instance", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZNum.zeroLEOneClass", "kind": "instance", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZNum.isOrderedAddMonoid", "kind": "instance", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZNum.isStrictOrderedRing", "kind": "instance", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZNum.cast_sub", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ZNum.neg_of_int", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZNum.ofInt'_eq", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZNum.of_nat_toZNum", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZNum.of_to_int", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ZNum.to_of_int", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZNum.of_nat_toZNumNeg", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ZNum.of_intCast", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ZNum.of_natCast", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ZNum.dvd_to_int", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.divMod_to_nat_aux", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": true, "tactics": ["unfold", "have", "intro", "apply", "rw", "simp", "rcases", "rw", "refine", "obtain", "rw", "cases", "have", "simp", "constructor", "rwa", "rwa"], "tactic_count": 17}
{"name": "PosNum.divMod_to_nat", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": true, "tactics": ["rw", "induction", "one", "bit1", "unfold", "revert", "simp", "apply", "rw", "lia", "bit0", "unfold", "revert", "simp", "apply", "simp", "rw", "simpa"], "tactic_count": 18}
{"name": "PosNum.div'_to_nat", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.mod'_to_nat", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.div_zero", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.div_to_nat", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.mod_zero", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.mod_to_nat", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.gcd_to_nat_aux", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Num.gcd_to_nat", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": ["have", "intros", "simp", "rw", "exact", "intros", "unfold", "split_ifs", "exact", "rw", "exact"], "tactic_count": 11}
{"name": "Num.dvd_iff_mod_eq_zero", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Num.decidableDvd", "kind": "instance", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PosNum.decidableDvd", "kind": "instance", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZNum.div_zero", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZNum.div_to_int", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZNum.mod_to_int", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZNum.gcd_to_nat", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZNum.dvd_iff_mod_eq_zero", "kind": "theorem", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ZNum.decidableDvd", "kind": "instance", "module": "Mathlib.Data.Num.ZNum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Opposite.unexpander_op", "kind": "definition", "module": "Mathlib.Data.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "term_ᵒᵖ", "kind": "definition", "module": "Mathlib.Data.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Data_Opposite___macroRules_term_ᵒᵖ_1", "kind": "definition", "module": "Mathlib.Data.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Data_Opposite___unexpand_Opposite_1", "kind": "definition", "module": "Mathlib.Data.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Opposite.op_injective", "kind": "theorem", "module": "Mathlib.Data.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Opposite.unop_injective", "kind": "theorem", "module": "Mathlib.Data.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Opposite.op_unop", "kind": "theorem", "module": "Mathlib.Data.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Opposite.unop_op", "kind": "theorem", "module": "Mathlib.Data.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Opposite.op_inj_iff", "kind": "theorem", "module": "Mathlib.Data.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Opposite.unop_inj_iff", "kind": "theorem", "module": "Mathlib.Data.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Opposite.equivToOpposite", "kind": "definition", "module": "Mathlib.Data.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Opposite.op_surjective", "kind": "theorem", "module": "Mathlib.Data.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Opposite.unop_surjective", "kind": "theorem", "module": "Mathlib.Data.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Opposite.equivToOpposite_coe", "kind": "theorem", "module": "Mathlib.Data.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Opposite.equivToOpposite_symm_coe", "kind": "theorem", "module": "Mathlib.Data.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Opposite.op_eq_iff_eq_unop", "kind": "theorem", "module": "Mathlib.Data.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Opposite.unop_eq_iff_eq_op", "kind": "theorem", "module": "Mathlib.Data.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Opposite.instInhabited", "kind": "instance", "module": "Mathlib.Data.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Opposite.instNonempty", "kind": "instance", "module": "Mathlib.Data.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Opposite.instSubsingleton", "kind": "instance", "module": "Mathlib.Data.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Opposite.small", "kind": "instance", "module": "Mathlib.Data.Opposite", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Option.coe_def", "kind": "theorem", "module": "Mathlib.Data.Option.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Option.mem_map", "kind": "theorem", "module": "Mathlib.Data.Option.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Option.mem_map_of_injective", "kind": "theorem", "module": "Mathlib.Data.Option.Basic", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Option.forall_mem_map", "kind": "theorem", "module": "Mathlib.Data.Option.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Option.exists_mem_map", "kind": "theorem", "module": "Mathlib.Data.Option.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Option.coe_get", "kind": "theorem", "module": "Mathlib.Data.Option.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Option.eq_of_mem_of_mem", "kind": "theorem", "module": "Mathlib.Data.Option.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Option.Mem.leftUnique", "kind": "theorem", "module": "Mathlib.Data.Option.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Option.some_injective", "kind": "theorem", "module": "Mathlib.Data.Option.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Option.map_comp_some", "kind": "theorem", "module": "Mathlib.Data.Option.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Option.bind_congr'", "kind": "theorem", "module": "Mathlib.Data.Option.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Option.joinM_eq_join", "kind": "theorem", "module": "Mathlib.Data.Option.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Option.bind_eq_bind'", "kind": "theorem", "module": "Mathlib.Data.Option.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Option.map_coe", "kind": "theorem", "module": "Mathlib.Data.Option.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Option.map_coe'", "kind": "theorem", "module": "Mathlib.Data.Option.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Option.map_injective'", "kind": "theorem", "module": "Mathlib.Data.Option.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Option.map_inj", "kind": "theorem", "module": "Mathlib.Data.Option.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Option.map_eq_id", "kind": "theorem", "module": "Mathlib.Data.Option.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Option.map_comm", "kind": "theorem", "module": "Mathlib.Data.Option.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Option.mem_pmem", "kind": "theorem", "module": "Mathlib.Data.Option.Basic", "is_tactic_proof": true, "tactics": ["rw", "subst", "rfl"], "tactic_count": 3}
{"name": "Option.pmap_bind", "kind": "theorem", "module": "Mathlib.Data.Option.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Option.bind_pmap", "kind": "theorem", "module": "Mathlib.Data.Option.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Option.pbind_eq_none", "kind": "theorem", "module": "Mathlib.Data.Option.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Option.join_pmap_eq_pmap_join", "kind": "theorem", "module": "Mathlib.Data.Option.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Option.pmap_bind_id_eq_pmap_join", "kind": "theorem", "module": "Mathlib.Data.Option.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Option.seq_some", "kind": "theorem", "module": "Mathlib.Data.Option.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Option.iget_mem", "kind": "theorem", "module": "Mathlib.Data.Option.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Option.iget_of_mem", "kind": "theorem", "module": "Mathlib.Data.Option.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Option.getD_default_eq_iget", "kind": "theorem", "module": "Mathlib.Data.Option.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Option.failure_eq_none", "kind": "theorem", "module": "Mathlib.Data.Option.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Option.guard_eq_some'", "kind": "theorem", "module": "Mathlib.Data.Option.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Option.casesOn'", "kind": "definition", "module": "Mathlib.Data.Option.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Option.casesOn'_none", "kind": "theorem", "module": "Mathlib.Data.Option.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Option.casesOn'_some", "kind": "theorem", "module": "Mathlib.Data.Option.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Option.casesOn'_coe", "kind": "theorem", "module": "Mathlib.Data.Option.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Option.casesOn'_none_coe", "kind": "theorem", "module": "Mathlib.Data.Option.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Option.casesOn'_eq_elim", "kind": "theorem", "module": "Mathlib.Data.Option.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Option.orElse_eq_some", "kind": "theorem", "module": "Mathlib.Data.Option.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Option.orElse_eq_none", "kind": "theorem", "module": "Mathlib.Data.Option.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Option.choice_eq_none", "kind": "theorem", "module": "Mathlib.Data.Option.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Option.elim_none_some", "kind": "theorem", "module": "Mathlib.Data.Option.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Option.elim_comp", "kind": "theorem", "module": "Mathlib.Data.Option.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Option.elim_comp₂", "kind": "theorem", "module": "Mathlib.Data.Option.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Option.elim_apply", "kind": "theorem", "module": "Mathlib.Data.Option.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Option.elim'_update", "kind": "theorem", "module": "Mathlib.Data.Option.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Option.getD_comp_some", "kind": "theorem", "module": "Mathlib.Data.Option.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Option.traverse", "kind": "definition", "module": "Mathlib.Data.Option.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Option.elim'", "kind": "definition", "module": "Mathlib.Data.Option.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Option.elim'_none", "kind": "theorem", "module": "Mathlib.Data.Option.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Option.elim'_some", "kind": "theorem", "module": "Mathlib.Data.Option.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Option.elim'_none_some", "kind": "theorem", "module": "Mathlib.Data.Option.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Option.elim'_eq_elim", "kind": "theorem", "module": "Mathlib.Data.Option.Defs", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Option.iget", "kind": "abbrev", "module": "Mathlib.Data.Option.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Option.iget_some", "kind": "theorem", "module": "Mathlib.Data.Option.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Option.map₂", "kind": "definition", "module": "Mathlib.Data.Option.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Option.map₂_def", "kind": "theorem", "module": "Mathlib.Data.Option.NAry", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Option.map₂_some_some", "kind": "theorem", "module": "Mathlib.Data.Option.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Option.map₂_coe_coe", "kind": "theorem", "module": "Mathlib.Data.Option.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Option.map₂_none_left", "kind": "theorem", "module": "Mathlib.Data.Option.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Option.map₂_none_right", "kind": "theorem", "module": "Mathlib.Data.Option.NAry", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Option.map₂_coe_left", "kind": "theorem", "module": "Mathlib.Data.Option.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Option.map₂_coe_right", "kind": "theorem", "module": "Mathlib.Data.Option.NAry", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Option.mem_map₂_iff", "kind": "theorem", "module": "Mathlib.Data.Option.NAry", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Option.map₂_eq_some_iff", "kind": "theorem", "module": "Mathlib.Data.Option.NAry", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Option.map₂_eq_none_iff", "kind": "theorem", "module": "Mathlib.Data.Option.NAry", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Option.map₂_swap", "kind": "theorem", "module": "Mathlib.Data.Option.NAry", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Option.map_map₂", "kind": "theorem", "module": "Mathlib.Data.Option.NAry", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Option.map₂_map_left", "kind": "theorem", "module": "Mathlib.Data.Option.NAry", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Option.map₂_map_right", "kind": "theorem", "module": "Mathlib.Data.Option.NAry", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Option.map₂_curry", "kind": "theorem", "module": "Mathlib.Data.Option.NAry", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Option.map_uncurry", "kind": "theorem", "module": "Mathlib.Data.Option.NAry", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Option.map₂_assoc", "kind": "theorem", "module": "Mathlib.Data.Option.NAry", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Option.map₂_comm", "kind": "theorem", "module": "Mathlib.Data.Option.NAry", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Option.map₂_left_comm", "kind": "theorem", "module": "Mathlib.Data.Option.NAry", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Option.map₂_right_comm", "kind": "theorem", "module": "Mathlib.Data.Option.NAry", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Option.map_map₂_distrib", "kind": "theorem", "module": "Mathlib.Data.Option.NAry", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Option.map_map₂_distrib_left", "kind": "theorem", "module": "Mathlib.Data.Option.NAry", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Option.map_map₂_distrib_right", "kind": "theorem", "module": "Mathlib.Data.Option.NAry", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Option.map₂_map_left_comm", "kind": "theorem", "module": "Mathlib.Data.Option.NAry", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Option.map_map₂_right_comm", "kind": "theorem", "module": "Mathlib.Data.Option.NAry", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Option.map_map₂_antidistrib", "kind": "theorem", "module": "Mathlib.Data.Option.NAry", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Option.map_map₂_antidistrib_left", "kind": "theorem", "module": "Mathlib.Data.Option.NAry", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Option.map_map₂_antidistrib_right", "kind": "theorem", "module": "Mathlib.Data.Option.NAry", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Option.map₂_map_left_anticomm", "kind": "theorem", "module": "Mathlib.Data.Option.NAry", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Option.map_map₂_right_anticomm", "kind": "theorem", "module": "Mathlib.Data.Option.NAry", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Option.map₂_left_identity", "kind": "theorem", "module": "Mathlib.Data.Option.NAry", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Option.map₂_right_identity", "kind": "theorem", "module": "Mathlib.Data.Option.NAry", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Ordering.Compares", "kind": "definition", "module": "Mathlib.Data.Ordering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordering.compares_lt", "kind": "theorem", "module": "Mathlib.Data.Ordering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordering.compares_eq", "kind": "theorem", "module": "Mathlib.Data.Ordering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordering.compares_gt", "kind": "theorem", "module": "Mathlib.Data.Ordering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordering.dthen", "kind": "definition", "module": "Mathlib.Data.Ordering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cmpUsing", "kind": "definition", "module": "Mathlib.Data.Ordering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cmp", "kind": "definition", "module": "Mathlib.Data.Ordering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordering.ite_eq_lt_distrib", "kind": "theorem", "module": "Mathlib.Data.Ordering.Lemmas", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "Ordering.ite_eq_eq_distrib", "kind": "theorem", "module": "Mathlib.Data.Ordering.Lemmas", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "Ordering.ite_eq_gt_distrib", "kind": "theorem", "module": "Mathlib.Data.Ordering.Lemmas", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "Ordering.dthen_eq_then", "kind": "theorem", "module": "Mathlib.Data.Ordering.Lemmas", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "cmpUsing_eq_lt", "kind": "theorem", "module": "Mathlib.Data.Ordering.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "cmpUsing_eq_gt", "kind": "theorem", "module": "Mathlib.Data.Ordering.Lemmas", "is_tactic_proof": false, "tactics": ["simp", "reduceCtorEq]", "exact"], "tactic_count": 3}
{"name": "cmpUsing_eq_eq", "kind": "theorem", "module": "Mathlib.Data.Ordering.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Ordnode.not_le_delta", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.delta_lt_false", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.realSize", "kind": "definition", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.Sized", "kind": "definition", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.Sized.node'", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.Sized.eq_node'", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordnode.Sized.size_eq", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.Sized.induction", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": true, "tactics": ["induction", "nil", "node", "rw", "exact"], "tactic_count": 5}
{"name": "Ordnode.size_eq_realSize", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.Sized.size_eq_zero", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Ordnode.Sized.pos", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordnode.dual_dual", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.size_dual", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Ordnode.BalancedSz", "kind": "definition", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.BalancedSz.dec", "kind": "instance", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.Balanced", "kind": "definition", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.Balanced.dec", "kind": "instance", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.BalancedSz.symm", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.balancedSz_zero", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Ordnode.balancedSz_up", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": true, "tactics": ["refine", "refine", "cases", "inl", "cases", "cases", "exact", "inr"], "tactic_count": 8}
{"name": "Ordnode.balancedSz_down", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.Balanced.dual", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.node3L", "kind": "definition", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.node3R", "kind": "definition", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.node4L", "kind": "definition", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.node4R", "kind": "definition", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.rotateL", "kind": "definition", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.rotateL_node", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.rotateL_nil", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.rotateR", "kind": "definition", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.rotateR_node", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.rotateR_nil", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.balanceL'", "kind": "definition", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.balanceR'", "kind": "definition", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.balance'", "kind": "definition", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.dual_node'", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Ordnode.dual_node3L", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Ordnode.dual_node3R", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Ordnode.dual_node4L", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Ordnode.dual_node4R", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Ordnode.dual_rotateL", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Ordnode.dual_rotateR", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordnode.dual_balance'", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": true, "tactics": ["simp", "cases"], "tactic_count": 2}
{"name": "Ordnode.dual_balanceL", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": true, "tactics": ["unfold", "obtain", "obtain", "obtain", "try", "split_ifs", "obtain", "dsimp", "split_ifs", "obtain", "dsimp", "split_ifs"], "tactic_count": 12}
{"name": "Ordnode.dual_balanceR", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordnode.Sized.node3L", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.Sized.node3R", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.Sized.node4L", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Ordnode.node3L_size", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": true, "tactics": ["dsimp"], "tactic_count": 1}
{"name": "Ordnode.node3R_size", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": true, "tactics": ["dsimp"], "tactic_count": 1}
{"name": "Ordnode.node4L_size", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": true, "tactics": ["cases", "simp", "abel", "simp"], "tactic_count": 4}
{"name": "Ordnode.Sized.dual", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.Sized.dual_iff", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.Sized.rotateL", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": true, "tactics": ["cases", "rw", "exact", "exact"], "tactic_count": 4}
{"name": "Ordnode.Sized.rotateR", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.Sized.rotateL_size", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": true, "tactics": ["cases", "simp", "split_ifs"], "tactic_count": 3}
{"name": "Ordnode.Sized.rotateR_size", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordnode.Sized.balance'", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": true, "tactics": ["unfold", "exact", "exact", "exact", "exact"], "tactic_count": 5}
{"name": "Ordnode.size_balance'", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": true, "tactics": ["unfold", "rfl", "exact", "exact", "rfl"], "tactic_count": 5}
{"name": "Ordnode.All.imp", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.Any.imp", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.all_singleton", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.any_singleton", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.all_dual", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.all_iff_forall", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.any_iff_exists", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.emem_iff_all", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.all_node'", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.all_node3L", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Ordnode.all_node3R", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.all_node4L", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Ordnode.all_node4R", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Ordnode.all_rotateL", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Ordnode.all_rotateR", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordnode.all_balance'", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordnode.foldr_cons_eq_toList", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.toList_nil", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.toList_node", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordnode.emem_iff_mem_toList", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "Ordnode.length_toList'", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.length_toList", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordnode.equiv_iff", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.pos_size_of_mem", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Ordnode.findMin'_dual", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.findMax'_dual", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordnode.findMin_dual", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.findMax_dual", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordnode.dual_eraseMin", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.dual_eraseMax", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordnode.splitMin_eq", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.splitMax_eq", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.findMin'_all", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.findMax'_all", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.merge_nil_left", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Ordnode.merge_nil_right", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.merge_node", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.dual_insert", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.balance_eq_balance'", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "rfl", "rw", "obtain", "rfl", "have", "have", "rwa", "cases", "cases", "obtain", "rw", "all_goals", "have", "have", "rwa", "cases", "cases", "obtain", "rw", "all_goals", "symm", "dsimp", "simp", "simp", "exact", "obtain", "rw", "obtain", "rfl", "have", "have", "rwa", "cases", "cases", "obtain", "rw", "all_goals", "have", "have", "rwa", "cases", "cases", "obtain", "rw", "all_goals", "symm", "dsimp", "simp", "simp", "exact", "simp", "symm", "split_ifs", "have", "have", "rwa", "obtain", "rw", "exact", "obtain", "exact", "dsimp", "simp", "simp", "have", "have", "rwa", "obtain", "rw", "exact", "obtain", "exact", "dsimp", "simp", "simp", "simp", "exact"], "tactic_count": 79}
{"name": "Ordnode.balanceL_eq_balance", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": true, "tactics": ["obtain", "rfl", "obtain", "have", "have", "rwa", "cases", "cases", "rw", "replace", "simp"], "tactic_count": 11}
{"name": "Ordnode.Raised", "kind": "definition", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.raised_iff", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "exact", "exact", "rintro", "rcases", "exact", "exact"], "tactic_count": 8}
{"name": "Ordnode.Raised.dist_le", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "Ordnode.Raised.dist_le'", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordnode.Raised.add_left", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": true, "tactics": ["rcases", "exact", "exact"], "tactic_count": 3}
{"name": "Ordnode.Raised.add_right", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordnode.Raised.right", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": true, "tactics": ["rw", "rcases", "exact", "exact"], "tactic_count": 4}
{"name": "Ordnode.balanceL_eq_balance'", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": true, "tactics": ["rw", "intro", "rcases", "exact", "exact", "intro", "rcases", "exact", "exact", "cases", "exact"], "tactic_count": 11}
{"name": "Ordnode.balance_sz_dual", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Ordnode.size_balanceL", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordnode.all_balanceL", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordnode.balanceR_eq_balance'", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": true, "tactics": ["rw", "balanceL_eq_balance"], "tactic_count": 2}
{"name": "Ordnode.size_balanceR", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordnode.all_balanceR", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordnode.Bounded", "kind": "definition", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.Bounded.dual", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.Bounded.dual_iff", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.Bounded.weak_left", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.Bounded.weak_right", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.Bounded.weak", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.Bounded.mono_left", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.Bounded.mono_right", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.Bounded.to_lt", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.Bounded.to_nil", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.Bounded.trans_left", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.Bounded.trans_right", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.Bounded.mem_lt", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.Bounded.mem_gt", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.Bounded.of_lt", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.Bounded.of_gt", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.Bounded.to_sep", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Invariants", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "Ordnode", "kind": "inductive", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.instEmptyCollection", "kind": "instance", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.instInhabited", "kind": "instance", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.delta", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.ratio", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.singleton", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.Ordmap.Ordnode.0.Ordnode.termι_", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.Ordmap.Ordnode.0.Ordnode._aux_Mathlib_Data_Ordmap_Ordnode___macroRules__private_Mathlib_Data_Ordmap_Ordnode_0_Ordnode_termι__1", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.Ordmap.Ordnode.0.Ordnode._aux_Mathlib_Data_Ordmap_Ordnode___unexpand_Ordnode_singleton_1", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.instSingleton", "kind": "instance", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.size", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.size_nil", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.size_node", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.empty", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.dual", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.node'", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.repr", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.instRepr", "kind": "instance", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.balanceL", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "exact", "rcases", "rcases", "exact", "exact", "rcases", "exact", "exact", "rcases", "exact", "refine", "rcases", "exact", "rcases", "exact", "exact"], "tactic_count": 18}
{"name": "Ordnode.balanceR", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "exact", "rcases", "rcases", "exact", "exact", "rcases", "exact", "exact", "rcases", "exact", "refine", "rcases", "exact", "rcases", "exact", "exact"], "tactic_count": 18}
{"name": "Ordnode.balance", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "exact", "rcases", "cases", "exact", "exact", "rcases", "exact", "exact", "rcases", "rcases", "rcases", "exact", "exact", "rcases", "exact", "exact", "refine", "rcases", "exact", "rcases", "exact", "exact", "rcases", "exact", "rcases", "exact", "exact"], "tactic_count": 29}
{"name": "Ordnode.All", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.All.decidable", "kind": "instance", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.Any", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.Any.decidable", "kind": "instance", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.Emem", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.Emem.decidable", "kind": "instance", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": true, "tactics": ["dsimp"], "tactic_count": 1}
{"name": "Ordnode.Amem", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.Amem.decidable", "kind": "instance", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": true, "tactics": ["dsimp"], "tactic_count": 1}
{"name": "Ordnode.findMin'", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.findMin", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.findMax'", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.findMax", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.eraseMin", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.eraseMax", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.splitMin'", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.splitMin", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.splitMax'", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.splitMax", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.glue", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.merge", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.insertMax", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.insertMin", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.link", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.filter", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.partition", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.map", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.fold", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.foldl", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.foldr", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.toList", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.toRevList", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.instToString", "kind": "instance", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.instToFormat", "kind": "instance", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.Equiv", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.instDecidableRelEquivOfDecidableEq", "kind": "instance", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.powerset", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.prod", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.copair", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.pmap", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.attach'", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.nth", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.removeNth", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.takeAux", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.take", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.dropAux", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.drop", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.splitAtAux", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.splitAt", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.takeWhile", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.dropWhile", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.span", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.ofAscListAux₁", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.ofAscListAux₂", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.ofAscList", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.mem", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.find", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.instMembership", "kind": "instance", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.mem.decidable", "kind": "instance", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.insertWith", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.adjustWith", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.updateWith", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.alter", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.insert", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.instInsert", "kind": "instance", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.insert'", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.split", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.split3", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.erase", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.findLtAux", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.findLt", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.findGtAux", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.findGt", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.findLeAux", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.findLe", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.findGeAux", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.findGe", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.findIndexAux", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.findIndex", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.isSubsetAux", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.isSubset", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.disjoint", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.union", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.diff", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.inter", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.ofList", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.ofList'", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.image", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordnode", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.Valid", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.Valid'.mono_left", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.Valid'.mono_right", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.Valid'.trans_left", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.Valid'.trans_right", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.Valid'.of_lt", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.Valid'.of_gt", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.Valid'.valid", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.valid'_nil", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.valid_nil", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.Valid'.node", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.Valid'.dual", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.Valid'.dual_iff", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.Valid.dual", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.Valid.dual_iff", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.Valid'.left", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.Valid'.right", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.Valid.left", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.Valid.right", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.Valid.size_eq", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.Valid'.node'", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.valid'_singleton", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.valid_singleton", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.Valid'.node3L", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.Valid'.node3R", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.Valid'.node4L_lemma₁", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": true, "tactics": ["lia"], "tactic_count": 1}
{"name": "Ordnode.Valid'.node4L_lemma₂", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": true, "tactics": ["lia"], "tactic_count": 1}
{"name": "Ordnode.Valid'.node4L_lemma₃", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": true, "tactics": ["lia"], "tactic_count": 1}
{"name": "Ordnode.Valid'.node4L_lemma₄", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": true, "tactics": ["lia"], "tactic_count": 1}
{"name": "Ordnode.Valid'.node4L_lemma₅", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": true, "tactics": ["lia"], "tactic_count": 1}
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{"name": "Ordnode.Valid'.rotateL_lemma₁", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": true, "tactics": ["lia"], "tactic_count": 1}
{"name": "Ordnode.Valid'.rotateL_lemma₂", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": true, "tactics": ["lia"], "tactic_count": 1}
{"name": "Ordnode.Valid'.rotateL_lemma₃", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": true, "tactics": ["lia"], "tactic_count": 1}
{"name": "Ordnode.Valid'.rotateL_lemma₄", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": true, "tactics": ["lia"], "tactic_count": 1}
{"name": "Ordnode.Valid'.rotateL", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": true, "tactics": ["obtain", "rw", "rw", "replace", "have", "have", "have", "have", "absurd", "rw", "have", "suffices", "exact", "rcases", "rw", "have", "rcases", "rw", "rw", "decide", "have", "rw", "rw", "decide", "replace", "rcases", "refine", "exact", "exact", "exact", "exact", "rcases", "rw", "replace", "rw", "rw", "cases", "refine", "rcases", "replace", "rcases", "have", "rw", "exact", "exact", "exact"], "tactic_count": 46}
{"name": "Ordnode.Valid'.rotateR", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": true, "tactics": ["refine", "rw", "refine", "rwa", "rwa", "rwa"], "tactic_count": 6}
{"name": "Ordnode.Valid'.balance'_aux", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": true, "tactics": ["rw", "exact", "exact", "exact", "exact"], "tactic_count": 5}
{"name": "Ordnode.Valid'.balance'_lemma", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": true, "tactics": ["suffices", "rcases", "exact", "exact", "exact", "rw", "exact"], "tactic_count": 7}
{"name": "Ordnode.Valid'.balance'", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.Valid'.balance", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordnode.Valid'.balanceL_aux", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": true, "tactics": ["rw", "refine", "rcases", "rw", "rcases", "rw", "replace"], "tactic_count": 7}
{"name": "Ordnode.Valid'.balanceL", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": true, "tactics": ["rw", "refine", "rcases", "exact", "exact"], "tactic_count": 5}
{"name": "Ordnode.Valid'.balanceR_aux", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": true, "tactics": ["rw", "have", "rw", "exact"], "tactic_count": 4}
{"name": "Ordnode.Valid'.balanceR", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordnode.Valid'.eraseMax_aux", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": true, "tactics": ["have", "induction", "nil", "node", "have", "rcases", "refine", "rw", "rw"], "tactic_count": 9}
{"name": "Ordnode.Valid'.eraseMin_aux", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "Ordnode.eraseMin.valid", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.eraseMax.valid", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordnode.Valid'.glue_aux", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "dsimp", "rw", "obtain", "suffices", "refine", "refine", "exact", "exact", "rw", "refine", "rwa", "rw", "obtain", "suffices", "refine", "refine", "exact", "exact", "rw", "refine", "rwa"], "tactic_count": 23}
{"name": "Ordnode.Valid'.glue", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.Valid'.merge_lemma", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": true, "tactics": ["lia"], "tactic_count": 1}
{"name": "Ordnode.Valid'.merge_aux₁", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": true, "tactics": ["rw", "rw", "rcases", "suffices", "suffices", "refine", "rw", "rw", "size_balance", "abel", "rw", "intro"], "tactic_count": 12}
{"name": "Ordnode.Valid'.merge_aux", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": false, "tactics": ["induction", "nil", "node", "induction", "nil", "node", "rw", "obtain", "exact", "obtain", "have", "rw", "exact", "refine"], "tactic_count": 14}
{"name": "Ordnode.Valid.merge", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.insertWith.valid_aux", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.insertWith.valid", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.insert_eq_insertWith", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.insert.valid", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordnode.insert'_eq_insertWith", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.insert'.valid", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "Ordnode.map.valid", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.Valid'.erase_aux", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": true, "tactics": ["induction", "nil", "node", "simp", "have", "have", "clear", "obtain", "obtain", "cases", "suffices", "constructor", "exact", "rw", "repeat", "exact", "left", "have", "obtain", "constructor", "exact", "right", "suffices", "constructor", "exact", "rw", "apply", "apply", "exact", "right"], "tactic_count": 30}
{"name": "Ordnode.erase.valid", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordnode.size_erase_of_mem", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": true, "tactics": ["induction", "nil", "node", "have", "have", "clear", "dsimp", "unfold", "revert", "have", "clear", "have", "obtain", "rw", "rw", "have", "revert", "cases", "simp", "rw", "have", "clear", "have", "obtain", "rw", "rw", "have", "revert", "cases", "simp"], "tactic_count": 30}
{"name": "Ordset", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordset.nil", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordset.size", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordset.singleton", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordset.instEmptyCollection", "kind": "instance", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordset.instInhabited", "kind": "instance", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordset.instSingleton", "kind": "instance", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordset.Empty", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordset.empty_iff", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordset.Empty.instDecidablePred", "kind": "instance", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordset.insert", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordset.instInsert", "kind": "instance", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordset.insert'", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordset.mem", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordset.find", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordset.instMembership", "kind": "instance", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordset.mem.decidable", "kind": "instance", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordset.pos_size_of_mem", "kind": "theorem", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": true, "tactics": ["simp", "apply"], "tactic_count": 2}
{"name": "Ordset.erase", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordset.map", "kind": "definition", "module": "Mathlib.Data.Ordmap.Ordset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "term_≃._", "kind": "definition", "module": "Mathlib.Data.PEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Data_PEquiv___macroRules_term_≃.__1", "kind": "definition", "module": "Mathlib.Data.PEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Data_PEquiv___unexpand_PEquiv_1", "kind": "definition", "module": "Mathlib.Data.PEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PEquiv.instFunLikeOption", "kind": "instance", "module": "Mathlib.Data.PEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PEquiv.coe_mk", "kind": "theorem", "module": "Mathlib.Data.PEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PEquiv.coe_mk_apply", "kind": "theorem", "module": "Mathlib.Data.PEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PEquiv.ext", "kind": "theorem", "module": "Mathlib.Data.PEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PEquiv.refl", "kind": "definition", "module": "Mathlib.Data.PEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PEquiv.symm", "kind": "definition", "module": "Mathlib.Data.PEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PEquiv.mem_iff_mem", "kind": "theorem", "module": "Mathlib.Data.PEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PEquiv.eq_some_iff", "kind": "theorem", "module": "Mathlib.Data.PEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PEquiv.trans", "kind": "definition", "module": "Mathlib.Data.PEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PEquiv.refl_apply", "kind": "theorem", "module": "Mathlib.Data.PEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PEquiv.symm_refl", "kind": "theorem", "module": "Mathlib.Data.PEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PEquiv.symm_symm", "kind": "theorem", "module": "Mathlib.Data.PEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PEquiv.symm_bijective", "kind": "theorem", "module": "Mathlib.Data.PEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PEquiv.symm_injective", "kind": "theorem", "module": "Mathlib.Data.PEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PEquiv.trans_assoc", "kind": "theorem", "module": "Mathlib.Data.PEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PEquiv.mem_trans", "kind": "theorem", "module": "Mathlib.Data.PEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PEquiv.trans_eq_some", "kind": "theorem", "module": "Mathlib.Data.PEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PEquiv.trans_eq_none", "kind": "theorem", "module": "Mathlib.Data.PEquiv", "is_tactic_proof": true, "tactics": ["simp", "push_neg", "exact"], "tactic_count": 3}
{"name": "PEquiv.refl_trans", "kind": "theorem", "module": "Mathlib.Data.PEquiv", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "PEquiv.trans_refl", "kind": "theorem", "module": "Mathlib.Data.PEquiv", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "PEquiv.inj", "kind": "theorem", "module": "Mathlib.Data.PEquiv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PEquiv.injective_of_forall_ne_isSome", "kind": "theorem", "module": "Mathlib.Data.PEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PEquiv.injective_of_forall_isSome", "kind": "theorem", "module": "Mathlib.Data.PEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PEquiv.ofSet", "kind": "definition", "module": "Mathlib.Data.PEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PEquiv.mem_ofSet_self_iff", "kind": "theorem", "module": "Mathlib.Data.PEquiv", "is_tactic_proof": true, "tactics": ["dsimp"], "tactic_count": 1}
{"name": "PEquiv.mem_ofSet_iff", "kind": "theorem", "module": "Mathlib.Data.PEquiv", "is_tactic_proof": true, "tactics": ["dsimp", "grind"], "tactic_count": 2}
{"name": "PEquiv.ofSet_eq_some_iff", "kind": "theorem", "module": "Mathlib.Data.PEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PEquiv.ofSet_eq_some_self_iff", "kind": "theorem", "module": "Mathlib.Data.PEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PEquiv.ofSet_symm", "kind": "theorem", "module": "Mathlib.Data.PEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PEquiv.ofSet_univ", "kind": "theorem", "module": "Mathlib.Data.PEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PEquiv.ofSet_eq_refl", "kind": "theorem", "module": "Mathlib.Data.PEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PEquiv.symm_trans_rev", "kind": "theorem", "module": "Mathlib.Data.PEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PEquiv.self_trans_symm", "kind": "theorem", "module": "Mathlib.Data.PEquiv", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "simp", "constructor", "rintro", "exact", "simp"], "tactic_count": 7}
{"name": "PEquiv.symm_trans_self", "kind": "theorem", "module": "Mathlib.Data.PEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PEquiv.trans_symm_eq_iff_forall_isSome", "kind": "theorem", "module": "Mathlib.Data.PEquiv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PEquiv.instBotPEquiv", "kind": "instance", "module": "Mathlib.Data.PEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PEquiv.instInhabited", "kind": "instance", "module": "Mathlib.Data.PEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PEquiv.bot_apply", "kind": "theorem", "module": "Mathlib.Data.PEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PEquiv.symm_bot", "kind": "theorem", "module": "Mathlib.Data.PEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PEquiv.trans_bot", "kind": "theorem", "module": "Mathlib.Data.PEquiv", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "PEquiv.bot_trans", "kind": "theorem", "module": "Mathlib.Data.PEquiv", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "PEquiv.isSome_symm_get", "kind": "theorem", "module": "Mathlib.Data.PEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PEquiv.single", "kind": "definition", "module": "Mathlib.Data.PEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PEquiv.mem_single", "kind": "theorem", "module": "Mathlib.Data.PEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PEquiv.mem_single_iff", "kind": "theorem", "module": "Mathlib.Data.PEquiv", "is_tactic_proof": true, "tactics": ["dsimp"], "tactic_count": 1}
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{"name": "PEquiv.single_apply", "kind": "theorem", "module": "Mathlib.Data.PEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PEquiv.single_apply_of_ne", "kind": "theorem", "module": "Mathlib.Data.PEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PEquiv.single_trans_of_mem", "kind": "theorem", "module": "Mathlib.Data.PEquiv", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "split_ifs"], "tactic_count": 3}
{"name": "PEquiv.trans_single_of_mem", "kind": "theorem", "module": "Mathlib.Data.PEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PEquiv.single_trans_single", "kind": "theorem", "module": "Mathlib.Data.PEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PEquiv.single_subsingleton_eq_refl", "kind": "theorem", "module": "Mathlib.Data.PEquiv", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "rw"], "tactic_count": 3}
{"name": "PEquiv.trans_single_of_eq_none", "kind": "theorem", "module": "Mathlib.Data.PEquiv", "is_tactic_proof": true, "tactics": ["ext", "simp", "dsimp", "simp", "intros", "split_ifs"], "tactic_count": 6}
{"name": "PEquiv.single_trans_of_eq_none", "kind": "theorem", "module": "Mathlib.Data.PEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PEquiv.single_trans_single_of_ne", "kind": "theorem", "module": "Mathlib.Data.PEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PEquiv.instPartialOrderPEquiv", "kind": "instance", "module": "Mathlib.Data.PEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PEquiv.le_def", "kind": "theorem", "module": "Mathlib.Data.PEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PEquiv.instOrderBot", "kind": "instance", "module": "Mathlib.Data.PEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PEquiv.instSemilatticeInfOfDecidableEq", "kind": "instance", "module": "Mathlib.Data.PEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.toPEquiv", "kind": "definition", "module": "Mathlib.Data.PEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.toPEquiv_refl", "kind": "theorem", "module": "Mathlib.Data.PEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.toPEquiv_trans", "kind": "theorem", "module": "Mathlib.Data.PEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.toPEquiv_symm", "kind": "theorem", "module": "Mathlib.Data.PEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.toPEquiv_apply", "kind": "theorem", "module": "Mathlib.Data.PEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PFun", "kind": "definition", "module": "Mathlib.Data.PFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "term_→._", "kind": "definition", "module": "Mathlib.Data.PFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Data_PFun___macroRules_term_→.__1", "kind": "definition", "module": "Mathlib.Data.PFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Data_PFun___unexpand_PFun_1", "kind": "definition", "module": "Mathlib.Data.PFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PFun.inhabited", "kind": "instance", "module": "Mathlib.Data.PFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PFun.Dom", "kind": "definition", "module": "Mathlib.Data.PFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PFun.mem_dom", "kind": "theorem", "module": "Mathlib.Data.PFun", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PFun.dom_mk", "kind": "theorem", "module": "Mathlib.Data.PFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PFun.dom_eq", "kind": "theorem", "module": "Mathlib.Data.PFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PFun.fn", "kind": "definition", "module": "Mathlib.Data.PFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PFun.fn_apply", "kind": "theorem", "module": "Mathlib.Data.PFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PFun.evalOpt", "kind": "definition", "module": "Mathlib.Data.PFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "PFun.ext", "kind": "theorem", "module": "Mathlib.Data.PFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PFun.asSubtype", "kind": "definition", "module": "Mathlib.Data.PFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PFun.equivSubtype", "kind": "definition", "module": "Mathlib.Data.PFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PFun.asSubtype_eq_of_mem", "kind": "theorem", "module": "Mathlib.Data.PFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PFun.lift", "kind": "definition", "module": "Mathlib.Data.PFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PFun.coe", "kind": "instance", "module": "Mathlib.Data.PFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "PFun.graph", "kind": "definition", "module": "Mathlib.Data.PFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "PFun.mem_restrict", "kind": "theorem", "module": "Mathlib.Data.PFun", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PFun.res", "kind": "definition", "module": "Mathlib.Data.PFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PFun.mem_res", "kind": "theorem", "module": "Mathlib.Data.PFun", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "PFun.dom_iff_graph", "kind": "theorem", "module": "Mathlib.Data.PFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "PFun.pure", "kind": "definition", "module": "Mathlib.Data.PFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "PFun.bind_apply", "kind": "theorem", "module": "Mathlib.Data.PFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PFun.map", "kind": "definition", "module": "Mathlib.Data.PFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PFun.monad", "kind": "instance", "module": "Mathlib.Data.PFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PFun.lawfulMonad", "kind": "instance", "module": "Mathlib.Data.PFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "PFun.preimage_asSubtype", "kind": "theorem", "module": "Mathlib.Data.PFun", "is_tactic_proof": true, "tactics": ["ext", "simp", "show", "exact", "have"], "tactic_count": 5}
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{"name": "MvPFunctor.wPathDestLeft", "kind": "definition", "module": "Mathlib.Data.PFunctor.Multivariate.W", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPFunctor.wPathDestRight", "kind": "definition", "module": "Mathlib.Data.PFunctor.Multivariate.W", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPFunctor.wPathDestLeft_wPathCasesOn", "kind": "theorem", "module": "Mathlib.Data.PFunctor.Multivariate.W", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPFunctor.wPathDestRight_wPathCasesOn", "kind": "theorem", "module": "Mathlib.Data.PFunctor.Multivariate.W", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPFunctor.wPathCasesOn_eta", "kind": "theorem", "module": "Mathlib.Data.PFunctor.Multivariate.W", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "MvPFunctor.comp_wPathCasesOn", "kind": "theorem", "module": "Mathlib.Data.PFunctor.Multivariate.W", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "MvPFunctor.wp", "kind": "definition", "module": "Mathlib.Data.PFunctor.Multivariate.W", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPFunctor.W", "kind": "definition", "module": "Mathlib.Data.PFunctor.Multivariate.W", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MvPFunctor.wpRec", "kind": "definition", "module": "Mathlib.Data.PFunctor.Multivariate.W", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPFunctor.wpRec_eq", "kind": "theorem", "module": "Mathlib.Data.PFunctor.Multivariate.W", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPFunctor.wp_ind", "kind": "theorem", "module": "Mathlib.Data.PFunctor.Multivariate.W", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPFunctor.wMk", "kind": "definition", "module": "Mathlib.Data.PFunctor.Multivariate.W", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPFunctor.wRec", "kind": "definition", "module": "Mathlib.Data.PFunctor.Multivariate.W", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPFunctor.wRec_eq", "kind": "theorem", "module": "Mathlib.Data.PFunctor.Multivariate.W", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MvPFunctor.wMap", "kind": "definition", "module": "Mathlib.Data.PFunctor.Multivariate.W", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPFunctor.wMk_eq", "kind": "theorem", "module": "Mathlib.Data.PFunctor.Multivariate.W", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MvPFunctor.objAppend1", "kind": "abbrev", "module": "Mathlib.Data.PFunctor.Multivariate.W", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPFunctor.map_objAppend1", "kind": "theorem", "module": "Mathlib.Data.PFunctor.Multivariate.W", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MvPFunctor.wMk'", "kind": "definition", "module": "Mathlib.Data.PFunctor.Multivariate.W", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPFunctor.wDest'", "kind": "definition", "module": "Mathlib.Data.PFunctor.Multivariate.W", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPFunctor.wDest'_wMk", "kind": "theorem", "module": "Mathlib.Data.PFunctor.Multivariate.W", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MvPFunctor.wDest'_wMk'", "kind": "theorem", "module": "Mathlib.Data.PFunctor.Multivariate.W", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
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{"name": "PFunctor.Obj", "kind": "definition", "module": "Mathlib.Data.PFunctor.Univariate.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PFunctor.instCoeFunForallType", "kind": "instance", "module": "Mathlib.Data.PFunctor.Univariate.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "PFunctor.instFunctorObj", "kind": "instance", "module": "Mathlib.Data.PFunctor.Univariate.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "PFunctor.instLawfulFunctorObj", "kind": "instance", "module": "Mathlib.Data.PFunctor.Univariate.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PFunctor.W", "kind": "definition", "module": "Mathlib.Data.PFunctor.Univariate.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PFunctor.W.head", "kind": "definition", "module": "Mathlib.Data.PFunctor.Univariate.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PFunctor.W.children", "kind": "definition", "module": "Mathlib.Data.PFunctor.Univariate.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "PFunctor.fst_map", "kind": "theorem", "module": "Mathlib.Data.PFunctor.Univariate.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
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{"name": "PFunctor.liftp_iff", "kind": "theorem", "module": "Mathlib.Data.PFunctor.Univariate.Basic", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "rcases", "refine", "rw", "congr", "rintro", "use", "rw"], "tactic_count": 9}
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{"name": "PFunctor.Approx.AllAgree", "kind": "definition", "module": "Mathlib.Data.PFunctor.Univariate.M", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PFunctor.Approx.agree_trivial", "kind": "theorem", "module": "Mathlib.Data.PFunctor.Univariate.M", "is_tactic_proof": true, "tactics": ["constructor"], "tactic_count": 1}
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{"name": "PFunctor.Approx.truncate", "kind": "definition", "module": "Mathlib.Data.PFunctor.Univariate.M", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "PFunctor.Approx.Path", "kind": "definition", "module": "Mathlib.Data.PFunctor.Univariate.M", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "PFunctor.M", "kind": "definition", "module": "Mathlib.Data.PFunctor.Univariate.M", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "PFunctor.M.cases", "kind": "definition", "module": "Mathlib.Data.PFunctor.Univariate.M", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "PFunctor.M.agree'_refl", "kind": "theorem", "module": "Mathlib.Data.PFunctor.Univariate.M", "is_tactic_proof": false, "tactics": ["induction", "zero", "succ", "induction", "constructor", "try", "intro"], "tactic_count": 7}
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{"name": "PFunctor.M.iselect_nil", "kind": "theorem", "module": "Mathlib.Data.PFunctor.Univariate.M", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "PFunctor.M.dest_corec", "kind": "theorem", "module": "Mathlib.Data.PFunctor.Univariate.M", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "PNat.instCommMonoid", "kind": "instance", "module": "Mathlib.Data.PNat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.instIsOrderedCancelMonoid", "kind": "instance", "module": "Mathlib.Data.PNat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.instCancelCommMonoid", "kind": "instance", "module": "Mathlib.Data.PNat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.instWellFoundedLT", "kind": "instance", "module": "Mathlib.Data.PNat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.one_add_natPred", "kind": "theorem", "module": "Mathlib.Data.PNat.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PNat.natPred_add_one", "kind": "theorem", "module": "Mathlib.Data.PNat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.natPred_strictMono", "kind": "theorem", "module": "Mathlib.Data.PNat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.natPred_monotone", "kind": "theorem", "module": "Mathlib.Data.PNat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.natPred_injective", "kind": "theorem", "module": "Mathlib.Data.PNat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.natPred_lt_natPred", "kind": "theorem", "module": "Mathlib.Data.PNat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.natPred_le_natPred", "kind": "theorem", "module": "Mathlib.Data.PNat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.natPred_inj", "kind": "theorem", "module": "Mathlib.Data.PNat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.val_ofNat", "kind": "theorem", "module": "Mathlib.Data.PNat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.mk_ofNat", "kind": "theorem", "module": "Mathlib.Data.PNat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.succPNat_strictMono", "kind": "theorem", "module": "Mathlib.Data.PNat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.succPNat_mono", "kind": "theorem", "module": "Mathlib.Data.PNat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.succPNat_lt_succPNat", "kind": "theorem", "module": "Mathlib.Data.PNat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.succPNat_le_succPNat", "kind": "theorem", "module": "Mathlib.Data.PNat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "PNat.coe_inj", "kind": "theorem", "module": "Mathlib.Data.PNat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.add_coe", "kind": "theorem", "module": "Mathlib.Data.PNat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.coeAddHom", "kind": "definition", "module": "Mathlib.Data.PNat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.addLeftMono", "kind": "instance", "module": "Mathlib.Data.PNat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.addLeftStrictMono", "kind": "instance", "module": "Mathlib.Data.PNat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.addLeftReflectLE", "kind": "instance", "module": "Mathlib.Data.PNat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.addLeftReflectLT", "kind": "instance", "module": "Mathlib.Data.PNat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.pnatIsoNat", "kind": "definition", "module": "Mathlib.Data.PNat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.pnatIsoNat_symm_apply", "kind": "theorem", "module": "Mathlib.Data.PNat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.lt_add_one_iff", "kind": "theorem", "module": "Mathlib.Data.PNat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "PNat.instOrderBot", "kind": "instance", "module": "Mathlib.Data.PNat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "PNat.coeMonoidHom", "kind": "definition", "module": "Mathlib.Data.PNat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "PNat.lt_add_left", "kind": "theorem", "module": "Mathlib.Data.PNat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.lt_add_right", "kind": "theorem", "module": "Mathlib.Data.PNat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.pow_coe", "kind": "theorem", "module": "Mathlib.Data.PNat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "PNat.instSub", "kind": "instance", "module": "Mathlib.Data.PNat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "PNat.add_sub", "kind": "theorem", "module": "Mathlib.Data.PNat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "PNat.modDivAux_spec", "kind": "theorem", "module": "Mathlib.Data.PNat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.mod_add_div", "kind": "theorem", "module": "Mathlib.Data.PNat.Basic", "is_tactic_proof": true, "tactics": ["let", "have", "rintro", "rw", "exact", "have", "exact"], "tactic_count": 7}
{"name": "PNat.div_add_mod", "kind": "theorem", "module": "Mathlib.Data.PNat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "PNat.dvd_antisymm", "kind": "theorem", "module": "Mathlib.Data.PNat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "instOnePNat", "kind": "instance", "module": "Mathlib.Data.PNat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instOfNatPNatOfNeZeroNat", "kind": "instance", "module": "Mathlib.Data.PNat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "PNat.natPred_eq_pred", "kind": "theorem", "module": "Mathlib.Data.PNat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.succPNat", "kind": "definition", "module": "Mathlib.Data.PNat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Nat.toPNat'_zero", "kind": "theorem", "module": "Mathlib.Data.PNat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "PNat.ne_zero", "kind": "theorem", "module": "Mathlib.Data.PNat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "PNat.toPNat'_coe", "kind": "theorem", "module": "Mathlib.Data.PNat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.coe_toPNat'", "kind": "theorem", "module": "Mathlib.Data.PNat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.one_le", "kind": "theorem", "module": "Mathlib.Data.PNat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.not_lt_one", "kind": "theorem", "module": "Mathlib.Data.PNat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.instInhabited", "kind": "instance", "module": "Mathlib.Data.PNat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.mk_one", "kind": "theorem", "module": "Mathlib.Data.PNat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.one_coe", "kind": "theorem", "module": "Mathlib.Data.PNat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.coe_eq_one_iff", "kind": "theorem", "module": "Mathlib.Data.PNat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.instWellFoundedRelation", "kind": "instance", "module": "Mathlib.Data.PNat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.strongInductionOn", "kind": "definition", "module": "Mathlib.Data.PNat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.modDivAux", "kind": "definition", "module": "Mathlib.Data.PNat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.modDiv", "kind": "definition", "module": "Mathlib.Data.PNat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.mod", "kind": "definition", "module": "Mathlib.Data.PNat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.div", "kind": "definition", "module": "Mathlib.Data.PNat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.mod_coe", "kind": "theorem", "module": "Mathlib.Data.PNat.Defs", "is_tactic_proof": true, "tactics": ["dsimp", "cases", "zero", "rw", "rfl", "succ", "rw", "rfl"], "tactic_count": 8}
{"name": "PNat.div_coe", "kind": "theorem", "module": "Mathlib.Data.PNat.Defs", "is_tactic_proof": true, "tactics": ["dsimp", "cases", "zero", "rw", "rfl", "succ", "rw", "rfl"], "tactic_count": 8}
{"name": "PNat.divExact", "kind": "definition", "module": "Mathlib.Data.PNat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.canLiftPNat", "kind": "instance", "module": "Mathlib.Data.PNat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.canLiftPNat", "kind": "instance", "module": "Mathlib.Data.PNat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.pnatEquivNat", "kind": "definition", "module": "Mathlib.Data.PNat.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeMultiset", "kind": "definition", "module": "Mathlib.Data.PNat.Factors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeMultiset.instRepr", "kind": "instance", "module": "Mathlib.Data.PNat.Factors", "is_tactic_proof": true, "tactics": ["delta"], "tactic_count": 1}
{"name": "PrimeMultiset.ofPrime", "kind": "definition", "module": "Mathlib.Data.PNat.Factors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeMultiset.card_ofPrime", "kind": "theorem", "module": "Mathlib.Data.PNat.Factors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeMultiset.toNatMultiset", "kind": "definition", "module": "Mathlib.Data.PNat.Factors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeMultiset.coeNat", "kind": "instance", "module": "Mathlib.Data.PNat.Factors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeMultiset.coeNatMonoidHom", "kind": "definition", "module": "Mathlib.Data.PNat.Factors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeMultiset.coe_coeNatMonoidHom", "kind": "theorem", "module": "Mathlib.Data.PNat.Factors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeMultiset.coeNat_injective", "kind": "theorem", "module": "Mathlib.Data.PNat.Factors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeMultiset.coeNat_ofPrime", "kind": "theorem", "module": "Mathlib.Data.PNat.Factors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeMultiset.coeNat_prime", "kind": "theorem", "module": "Mathlib.Data.PNat.Factors", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "PrimeMultiset.toPNatMultiset", "kind": "definition", "module": "Mathlib.Data.PNat.Factors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeMultiset.coePNat", "kind": "instance", "module": "Mathlib.Data.PNat.Factors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeMultiset.coePNatMonoidHom", "kind": "definition", "module": "Mathlib.Data.PNat.Factors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeMultiset.coe_coePNatMonoidHom", "kind": "theorem", "module": "Mathlib.Data.PNat.Factors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeMultiset.coePNat_injective", "kind": "theorem", "module": "Mathlib.Data.PNat.Factors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeMultiset.coePNat_ofPrime", "kind": "theorem", "module": "Mathlib.Data.PNat.Factors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeMultiset.coePNat_prime", "kind": "theorem", "module": "Mathlib.Data.PNat.Factors", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "PrimeMultiset.coeMultisetPNatNat", "kind": "instance", "module": "Mathlib.Data.PNat.Factors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeMultiset.coePNat_nat", "kind": "theorem", "module": "Mathlib.Data.PNat.Factors", "is_tactic_proof": true, "tactics": ["change", "rw", "rfl"], "tactic_count": 3}
{"name": "PrimeMultiset.prod", "kind": "definition", "module": "Mathlib.Data.PNat.Factors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeMultiset.coe_prod", "kind": "theorem", "module": "Mathlib.Data.PNat.Factors", "is_tactic_proof": false, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "PrimeMultiset.prod_ofPrime", "kind": "theorem", "module": "Mathlib.Data.PNat.Factors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeMultiset.ofNatMultiset", "kind": "definition", "module": "Mathlib.Data.PNat.Factors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeMultiset.mem_ofNatMultiset", "kind": "theorem", "module": "Mathlib.Data.PNat.Factors", "is_tactic_proof": false, "tactics": ["simp", "simp"], "tactic_count": 2}
{"name": "PrimeMultiset.to_ofNatMultiset", "kind": "theorem", "module": "Mathlib.Data.PNat.Factors", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "PrimeMultiset.prod_ofNatMultiset", "kind": "theorem", "module": "Mathlib.Data.PNat.Factors", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PrimeMultiset.ofPNatMultiset", "kind": "definition", "module": "Mathlib.Data.PNat.Factors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeMultiset.to_ofPNatMultiset", "kind": "theorem", "module": "Mathlib.Data.PNat.Factors", "is_tactic_proof": true, "tactics": ["dsimp", "have", "funext", "apply", "rfl", "rw"], "tactic_count": 6}
{"name": "PrimeMultiset.prod_ofPNatMultiset", "kind": "theorem", "module": "Mathlib.Data.PNat.Factors", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "PrimeMultiset.ofNatList", "kind": "definition", "module": "Mathlib.Data.PNat.Factors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeMultiset.mem_ofNatList", "kind": "theorem", "module": "Mathlib.Data.PNat.Factors", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PrimeMultiset.prod_ofNatList", "kind": "theorem", "module": "Mathlib.Data.PNat.Factors", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "PrimeMultiset.ofPNatList", "kind": "definition", "module": "Mathlib.Data.PNat.Factors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeMultiset.toPNatMultiset_ofPNatList", "kind": "theorem", "module": "Mathlib.Data.PNat.Factors", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PrimeMultiset.prod_ofPNatList", "kind": "theorem", "module": "Mathlib.Data.PNat.Factors", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "PrimeMultiset.prod_zero", "kind": "theorem", "module": "Mathlib.Data.PNat.Factors", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "PrimeMultiset.prod_add", "kind": "theorem", "module": "Mathlib.Data.PNat.Factors", "is_tactic_proof": true, "tactics": ["change", "rw", "exact"], "tactic_count": 3}
{"name": "PrimeMultiset.prod_smul", "kind": "theorem", "module": "Mathlib.Data.PNat.Factors", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "PNat.factorMultiset", "kind": "definition", "module": "Mathlib.Data.PNat.Factors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.prod_factorMultiset", "kind": "theorem", "module": "Mathlib.Data.PNat.Factors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.coeNat_factorMultiset", "kind": "theorem", "module": "Mathlib.Data.PNat.Factors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.mem_factorMultiset", "kind": "theorem", "module": "Mathlib.Data.PNat.Factors", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PrimeMultiset.factorMultiset_prod", "kind": "theorem", "module": "Mathlib.Data.PNat.Factors", "is_tactic_proof": true, "tactics": ["apply", "rw", "rcases", "dsimp", "let", "have", "simp", "obtain", "exact", "exact"], "tactic_count": 10}
{"name": "PNat.factorMultisetEquiv", "kind": "definition", "module": "Mathlib.Data.PNat.Factors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.factorMultiset_one", "kind": "theorem", "module": "Mathlib.Data.PNat.Factors", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PNat.factorMultiset_mul", "kind": "theorem", "module": "Mathlib.Data.PNat.Factors", "is_tactic_proof": true, "tactics": ["let", "let", "have", "have", "rw", "repeat"], "tactic_count": 6}
{"name": "PNat.factorMultiset_pow", "kind": "theorem", "module": "Mathlib.Data.PNat.Factors", "is_tactic_proof": true, "tactics": ["let", "have", "rw", "repeat"], "tactic_count": 4}
{"name": "PNat.factorMultiset_ofPrime", "kind": "theorem", "module": "Mathlib.Data.PNat.Factors", "is_tactic_proof": true, "tactics": ["apply", "change", "rw"], "tactic_count": 3}
{"name": "PNat.factorMultiset_le_iff", "kind": "theorem", "module": "Mathlib.Data.PNat.Factors", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "apply", "rw", "intro", "rw", "exact"], "tactic_count": 8}
{"name": "PNat.factorMultiset_le_iff'", "kind": "theorem", "module": "Mathlib.Data.PNat.Factors", "is_tactic_proof": true, "tactics": ["let", "rw", "exact"], "tactic_count": 3}
{"name": "PrimeMultiset.prod_dvd_iff", "kind": "theorem", "module": "Mathlib.Data.PNat.Factors", "is_tactic_proof": true, "tactics": ["let", "rw", "exact"], "tactic_count": 3}
{"name": "PrimeMultiset.prod_dvd_iff'", "kind": "theorem", "module": "Mathlib.Data.PNat.Factors", "is_tactic_proof": true, "tactics": ["let", "rw", "exact"], "tactic_count": 3}
{"name": "PNat.factorMultiset_gcd", "kind": "theorem", "module": "Mathlib.Data.PNat.Factors", "is_tactic_proof": true, "tactics": ["apply", "apply", "exact", "exact", "rw", "apply", "exact", "exact"], "tactic_count": 8}
{"name": "PNat.factorMultiset_lcm", "kind": "theorem", "module": "Mathlib.Data.PNat.Factors", "is_tactic_proof": true, "tactics": ["apply", "rw", "apply", "exact", "exact", "apply", "exact", "exact"], "tactic_count": 8}
{"name": "PNat.count_factorMultiset", "kind": "theorem", "module": "Mathlib.Data.PNat.Factors", "is_tactic_proof": true, "tactics": ["rw", "congr", "apply", "constructor", "rw", "intro", "rw", "exact"], "tactic_count": 8}
{"name": "PrimeMultiset.prod_inf", "kind": "theorem", "module": "Mathlib.Data.PNat.Factors", "is_tactic_proof": true, "tactics": ["let", "let", "change", "have", "have", "rw"], "tactic_count": 6}
{"name": "PrimeMultiset.prod_sup", "kind": "theorem", "module": "Mathlib.Data.PNat.Factors", "is_tactic_proof": true, "tactics": ["let", "let", "change", "have", "have", "rw"], "tactic_count": 6}
{"name": "PNat.decidablePredExistsNat", "kind": "instance", "module": "Mathlib.Data.PNat.Find", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.findX", "kind": "definition", "module": "Mathlib.Data.PNat.Find", "is_tactic_proof": true, "tactics": ["have", "have", "refine", "obtain", "rw", "exact", "obtain", "simpa", "exact"], "tactic_count": 9}
{"name": "PNat.find", "kind": "definition", "module": "Mathlib.Data.PNat.Find", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.find_spec", "kind": "theorem", "module": "Mathlib.Data.PNat.Find", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.find_min", "kind": "theorem", "module": "Mathlib.Data.PNat.Find", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.find_min'", "kind": "theorem", "module": "Mathlib.Data.PNat.Find", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.find_eq_iff", "kind": "theorem", "module": "Mathlib.Data.PNat.Find", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 5}
{"name": "PNat.find_lt_iff", "kind": "theorem", "module": "Mathlib.Data.PNat.Find", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.find_le_iff", "kind": "theorem", "module": "Mathlib.Data.PNat.Find", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PNat.le_find_iff", "kind": "theorem", "module": "Mathlib.Data.PNat.Find", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PNat.lt_find_iff", "kind": "theorem", "module": "Mathlib.Data.PNat.Find", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PNat.find_eq_one", "kind": "theorem", "module": "Mathlib.Data.PNat.Find", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PNat.one_le_find", "kind": "theorem", "module": "Mathlib.Data.PNat.Find", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PNat.find_mono", "kind": "theorem", "module": "Mathlib.Data.PNat.Find", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.find_le", "kind": "theorem", "module": "Mathlib.Data.PNat.Find", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.find_comp_succ", "kind": "theorem", "module": "Mathlib.Data.PNat.Find", "is_tactic_proof": true, "tactics": ["refine", "induction", "one", "succ", "intro", "simp", "exact"], "tactic_count": 7}
{"name": "PNat.instLocallyFiniteOrder", "kind": "instance", "module": "Mathlib.Data.PNat.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.Icc_eq_finset_subtype", "kind": "theorem", "module": "Mathlib.Data.PNat.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.Ico_eq_finset_subtype", "kind": "theorem", "module": "Mathlib.Data.PNat.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.Ioc_eq_finset_subtype", "kind": "theorem", "module": "Mathlib.Data.PNat.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.Ioo_eq_finset_subtype", "kind": "theorem", "module": "Mathlib.Data.PNat.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.uIcc_eq_finset_subtype", "kind": "theorem", "module": "Mathlib.Data.PNat.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.map_subtype_embedding_Icc", "kind": "theorem", "module": "Mathlib.Data.PNat.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.map_subtype_embedding_Ico", "kind": "theorem", "module": "Mathlib.Data.PNat.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.map_subtype_embedding_Ioc", "kind": "theorem", "module": "Mathlib.Data.PNat.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.map_subtype_embedding_Ioo", "kind": "theorem", "module": "Mathlib.Data.PNat.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.map_subtype_embedding_uIcc", "kind": "theorem", "module": "Mathlib.Data.PNat.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.card_Icc", "kind": "theorem", "module": "Mathlib.Data.PNat.Interval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PNat.card_Ico", "kind": "theorem", "module": "Mathlib.Data.PNat.Interval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PNat.card_Ioc", "kind": "theorem", "module": "Mathlib.Data.PNat.Interval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PNat.card_Ioo", "kind": "theorem", "module": "Mathlib.Data.PNat.Interval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PNat.card_uIcc", "kind": "theorem", "module": "Mathlib.Data.PNat.Interval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PNat.card_fintype_Icc", "kind": "theorem", "module": "Mathlib.Data.PNat.Interval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PNat.card_fintype_Ico", "kind": "theorem", "module": "Mathlib.Data.PNat.Interval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PNat.card_fintype_Ioc", "kind": "theorem", "module": "Mathlib.Data.PNat.Interval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PNat.card_fintype_Ioo", "kind": "theorem", "module": "Mathlib.Data.PNat.Interval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PNat.card_fintype_uIcc", "kind": "theorem", "module": "Mathlib.Data.PNat.Interval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PNat", "kind": "definition", "module": "Mathlib.Data.PNat.Notation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "termℕ+", "kind": "definition", "module": "Mathlib.Data.PNat.Notation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Data_PNat_Notation___macroRules_termℕ+_1", "kind": "definition", "module": "Mathlib.Data.PNat.Notation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Data_PNat_Notation___unexpand_PNat_1", "kind": "definition", "module": "Mathlib.Data.PNat.Notation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.val", "kind": "definition", "module": "Mathlib.Data.PNat.Notation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "coePNatNat", "kind": "instance", "module": "Mathlib.Data.PNat.Notation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instReprPNat", "kind": "instance", "module": "Mathlib.Data.PNat.Notation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.instSuccOrder", "kind": "instance", "module": "Mathlib.Data.PNat.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.instSuccAddOrder", "kind": "instance", "module": "Mathlib.Data.PNat.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.instNoMaxOrder", "kind": "instance", "module": "Mathlib.Data.PNat.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.succ_eq_add_one", "kind": "theorem", "module": "Mathlib.Data.PNat.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Primes.toPNat", "kind": "definition", "module": "Mathlib.Data.PNat.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Primes.coePNat", "kind": "instance", "module": "Mathlib.Data.PNat.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Primes.coe_pnat_nat", "kind": "theorem", "module": "Mathlib.Data.PNat.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Primes.coe_pnat_injective", "kind": "theorem", "module": "Mathlib.Data.PNat.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Primes.coe_pnat_inj", "kind": "theorem", "module": "Mathlib.Data.PNat.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.gcd", "kind": "definition", "module": "Mathlib.Data.PNat.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.lcm", "kind": "definition", "module": "Mathlib.Data.PNat.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.gcd_coe", "kind": "theorem", "module": "Mathlib.Data.PNat.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.lcm_coe", "kind": "theorem", "module": "Mathlib.Data.PNat.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.gcd_dvd_left", "kind": "theorem", "module": "Mathlib.Data.PNat.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.gcd_dvd_right", "kind": "theorem", "module": "Mathlib.Data.PNat.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.dvd_gcd", "kind": "theorem", "module": "Mathlib.Data.PNat.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.dvd_lcm_left", "kind": "theorem", "module": "Mathlib.Data.PNat.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.dvd_lcm_right", "kind": "theorem", "module": "Mathlib.Data.PNat.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.lcm_dvd", "kind": "theorem", "module": "Mathlib.Data.PNat.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.gcd_mul_lcm", "kind": "theorem", "module": "Mathlib.Data.PNat.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.eq_one_of_lt_two", "kind": "theorem", "module": "Mathlib.Data.PNat.Prime", "is_tactic_proof": true, "tactics": ["intro", "apply", "exact"], "tactic_count": 3}
{"name": "PNat.Prime", "kind": "definition", "module": "Mathlib.Data.PNat.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.Prime.one_lt", "kind": "theorem", "module": "Mathlib.Data.PNat.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.prime_two", "kind": "theorem", "module": "Mathlib.Data.PNat.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.instFactPrimeValOfPrime", "kind": "instance", "module": "Mathlib.Data.PNat.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.fact_prime_two", "kind": "instance", "module": "Mathlib.Data.PNat.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.prime_three", "kind": "theorem", "module": "Mathlib.Data.PNat.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.fact_prime_three", "kind": "instance", "module": "Mathlib.Data.PNat.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.prime_five", "kind": "theorem", "module": "Mathlib.Data.PNat.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.fact_prime_five", "kind": "instance", "module": "Mathlib.Data.PNat.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.dvd_prime", "kind": "theorem", "module": "Mathlib.Data.PNat.Prime", "is_tactic_proof": true, "tactics": ["rw", "rw", "simp"], "tactic_count": 3}
{"name": "PNat.Prime.ne_one", "kind": "theorem", "module": "Mathlib.Data.PNat.Prime", "is_tactic_proof": true, "tactics": ["intro", "apply", "rw", "apply"], "tactic_count": 4}
{"name": "PNat.not_prime_one", "kind": "theorem", "module": "Mathlib.Data.PNat.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.Prime.not_dvd_one", "kind": "theorem", "module": "Mathlib.Data.PNat.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.exists_prime_and_dvd", "kind": "theorem", "module": "Mathlib.Data.PNat.Prime", "is_tactic_proof": true, "tactics": ["obtain", "exists"], "tactic_count": 2}
{"name": "PNat.Coprime", "kind": "definition", "module": "Mathlib.Data.PNat.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.coprime_coe", "kind": "theorem", "module": "Mathlib.Data.PNat.Prime", "is_tactic_proof": true, "tactics": ["unfold", "rw", "simp"], "tactic_count": 3}
{"name": "PNat.Coprime.mul", "kind": "theorem", "module": "Mathlib.Data.PNat.Prime", "is_tactic_proof": true, "tactics": ["repeat", "rw", "apply"], "tactic_count": 3}
{"name": "PNat.Coprime.mul_right", "kind": "theorem", "module": "Mathlib.Data.PNat.Prime", "is_tactic_proof": true, "tactics": ["repeat", "rw", "apply"], "tactic_count": 3}
{"name": "PNat.gcd_comm", "kind": "theorem", "module": "Mathlib.Data.PNat.Prime", "is_tactic_proof": true, "tactics": ["apply", "simp", "apply"], "tactic_count": 3}
{"name": "PNat.gcd_eq_left_iff_dvd", "kind": "theorem", "module": "Mathlib.Data.PNat.Prime", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "PNat.gcd_eq_right_iff_dvd", "kind": "theorem", "module": "Mathlib.Data.PNat.Prime", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "PNat.Coprime.gcd_mul_left_cancel", "kind": "theorem", "module": "Mathlib.Data.PNat.Prime", "is_tactic_proof": true, "tactics": ["intro", "apply"], "tactic_count": 2}
{"name": "PNat.Coprime.gcd_mul_right_cancel", "kind": "theorem", "module": "Mathlib.Data.PNat.Prime", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PNat.Coprime.gcd_mul_left_cancel_right", "kind": "theorem", "module": "Mathlib.Data.PNat.Prime", "is_tactic_proof": true, "tactics": ["intro", "apply"], "tactic_count": 2}
{"name": "PNat.Coprime.gcd_mul_right_cancel_right", "kind": "theorem", "module": "Mathlib.Data.PNat.Prime", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "PNat.one_gcd", "kind": "theorem", "module": "Mathlib.Data.PNat.Prime", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "PNat.gcd_one", "kind": "theorem", "module": "Mathlib.Data.PNat.Prime", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "PNat.Coprime.symm", "kind": "theorem", "module": "Mathlib.Data.PNat.Prime", "is_tactic_proof": true, "tactics": ["unfold", "rw", "simp"], "tactic_count": 3}
{"name": "PNat.one_coprime", "kind": "theorem", "module": "Mathlib.Data.PNat.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.coprime_one", "kind": "theorem", "module": "Mathlib.Data.PNat.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.Coprime.coprime_dvd_left", "kind": "theorem", "module": "Mathlib.Data.PNat.Prime", "is_tactic_proof": true, "tactics": ["rw", "repeat", "apply"], "tactic_count": 3}
{"name": "PNat.Coprime.factor_eq_gcd_left", "kind": "theorem", "module": "Mathlib.Data.PNat.Prime", "is_tactic_proof": true, "tactics": ["rw", "conv_lhs", "rw", "apply", "apply"], "tactic_count": 5}
{"name": "PNat.Coprime.factor_eq_gcd_right", "kind": "theorem", "module": "Mathlib.Data.PNat.Prime", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PNat.Coprime.factor_eq_gcd_left_right", "kind": "theorem", "module": "Mathlib.Data.PNat.Prime", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PNat.Coprime.factor_eq_gcd_right_right", "kind": "theorem", "module": "Mathlib.Data.PNat.Prime", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "PNat.Coprime.gcd_mul", "kind": "theorem", "module": "Mathlib.Data.PNat.Prime", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "PNat.Coprime.pow", "kind": "theorem", "module": "Mathlib.Data.PNat.Prime", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PNat.instInhabitedXgcdType.default", "kind": "definition", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.instInhabitedXgcdType", "kind": "instance", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.XgcdType.instSizeOf", "kind": "instance", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.XgcdType.instRepr", "kind": "instance", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.XgcdType.mk'", "kind": "definition", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.XgcdType.w", "kind": "definition", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.XgcdType.z", "kind": "definition", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.XgcdType.a", "kind": "definition", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.XgcdType.b", "kind": "definition", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.XgcdType.r", "kind": "definition", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.XgcdType.q", "kind": "definition", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.XgcdType.qp", "kind": "definition", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.XgcdType.vp", "kind": "definition", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.XgcdType.v", "kind": "definition", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.XgcdType.succ₂", "kind": "definition", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.XgcdType.v_eq_succ_vp", "kind": "theorem", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "PNat.XgcdType.IsSpecial", "kind": "definition", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.XgcdType.IsSpecial'", "kind": "definition", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.XgcdType.isSpecial_iff", "kind": "theorem", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": true, "tactics": ["dsimp", "let", "constructor", "simp", "simp_all", "simp", "rw"], "tactic_count": 7}
{"name": "PNat.XgcdType.IsReduced", "kind": "definition", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.XgcdType.IsReduced'", "kind": "definition", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.XgcdType.isReduced_iff", "kind": "theorem", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.XgcdType.flip", "kind": "definition", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.XgcdType.flip_w", "kind": "theorem", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.XgcdType.flip_x", "kind": "theorem", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.XgcdType.flip_y", "kind": "theorem", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.XgcdType.flip_z", "kind": "theorem", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.XgcdType.flip_a", "kind": "theorem", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.XgcdType.flip_b", "kind": "theorem", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.XgcdType.flip_isReduced", "kind": "theorem", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": true, "tactics": ["dsimp", "constructor"], "tactic_count": 2}
{"name": "PNat.XgcdType.flip_isSpecial", "kind": "theorem", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "PNat.XgcdType.flip_v", "kind": "theorem", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": true, "tactics": ["dsimp", "ext", "simp", "ring", "simp", "ring"], "tactic_count": 6}
{"name": "PNat.XgcdType.rq_eq", "kind": "theorem", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.XgcdType.qp_eq", "kind": "theorem", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": true, "tactics": ["by_cases", "let", "rw", "cases", "exact"], "tactic_count": 5}
{"name": "PNat.XgcdType.start", "kind": "definition", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.XgcdType.start_isSpecial", "kind": "theorem", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": true, "tactics": ["dsimp"], "tactic_count": 1}
{"name": "PNat.XgcdType.start_v", "kind": "theorem", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": true, "tactics": ["dsimp", "have", "have", "lia"], "tactic_count": 4}
{"name": "PNat.XgcdType.finish", "kind": "definition", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.XgcdType.finish_isReduced", "kind": "theorem", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": true, "tactics": ["dsimp", "rfl"], "tactic_count": 2}
{"name": "PNat.XgcdType.finish_isSpecial", "kind": "theorem", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "ring"], "tactic_count": 3}
{"name": "PNat.XgcdType.finish_v", "kind": "theorem", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": true, "tactics": ["let", "rw", "ext", "change", "have", "rw", "ring", "change", "rw", "ring"], "tactic_count": 10}
{"name": "PNat.XgcdType.step", "kind": "definition", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.XgcdType.step_wf", "kind": "theorem", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": true, "tactics": ["change", "have", "have", "rw", "exact"], "tactic_count": 5}
{"name": "PNat.XgcdType.step_isSpecial", "kind": "theorem", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "ring"], "tactic_count": 3}
{"name": "PNat.XgcdType.step_v", "kind": "theorem", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": true, "tactics": ["let", "let", "ext", "change", "rw", "ring", "change", "rw", "ring"], "tactic_count": 9}
{"name": "PNat.XgcdType.reduce", "kind": "definition", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.XgcdType.reduce_a", "kind": "theorem", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "PNat.XgcdType.reduce_b", "kind": "theorem", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "PNat.XgcdType.reduce_isReduced", "kind": "theorem", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.XgcdType.reduce_isReduced'", "kind": "theorem", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.XgcdType.reduce_isSpecial", "kind": "theorem", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.XgcdType.reduce_isSpecial'", "kind": "theorem", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.XgcdType.reduce_v", "kind": "theorem", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.xgcd", "kind": "definition", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.gcdD", "kind": "definition", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.gcdW", "kind": "definition", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.gcdX", "kind": "definition", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.gcdY", "kind": "definition", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.gcdZ", "kind": "definition", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.gcdA'", "kind": "definition", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.gcdB'", "kind": "definition", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.gcdA'_coe", "kind": "theorem", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "PNat.gcdB'_coe", "kind": "theorem", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "PNat.gcd_props", "kind": "theorem", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": true, "tactics": ["intro", "let", "let", "have", "have", "have", "have", "constructor", "exact", "have", "let", "rw", "have", "have", "constructor", "exact", "constructor", "exact", "have", "rw", "ring", "have", "rw", "ring", "constructor", "apply", "rw", "constructor", "apply", "rw", "grind"], "tactic_count": 31}
{"name": "PNat.gcd_eq", "kind": "theorem", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": true, "tactics": ["rcases", "apply", "apply", "exact", "exact", "have", "have", "rw", "rw", "exact"], "tactic_count": 10}
{"name": "PNat.gcd_det_eq", "kind": "theorem", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.gcd_a_eq", "kind": "theorem", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.gcd_b_eq", "kind": "theorem", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.gcd_rel_left'", "kind": "theorem", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.gcd_rel_right'", "kind": "theorem", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.gcd_rel_left", "kind": "theorem", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.gcd_rel_right", "kind": "theorem", "module": "Mathlib.Data.PNat.Xgcd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSigma.termΣₗ'_,_", "kind": "definition", "module": "Mathlib.Data.PSigma.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSigma._aux_Mathlib_Data_PSigma_Order___macroRules_PSigma_termΣₗ'_,__1", "kind": "definition", "module": "Mathlib.Data.PSigma.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSigma._aux_Mathlib_Data_PSigma_Order___delab_app_PSigma_termΣₗ'_,__1", "kind": "definition", "module": "Mathlib.Data.PSigma.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSigma.Lex.le", "kind": "instance", "module": "Mathlib.Data.PSigma.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSigma.Lex.lt", "kind": "instance", "module": "Mathlib.Data.PSigma.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSigma.Lex.preorder", "kind": "instance", "module": "Mathlib.Data.PSigma.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSigma.Lex.partialOrder", "kind": "instance", "module": "Mathlib.Data.PSigma.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSigma.Lex.linearOrder", "kind": "instance", "module": "Mathlib.Data.PSigma.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSigma.Lex.orderBot", "kind": "instance", "module": "Mathlib.Data.PSigma.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSigma.Lex.orderTop", "kind": "instance", "module": "Mathlib.Data.PSigma.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSigma.Lex.boundedOrder", "kind": "instance", "module": "Mathlib.Data.PSigma.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSigma.Lex.denselyOrdered", "kind": "instance", "module": "Mathlib.Data.PSigma.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSigma.Lex.denselyOrdered_of_noMaxOrder", "kind": "instance", "module": "Mathlib.Data.PSigma.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSigma.Lex.denselyOrdered_of_noMinOrder", "kind": "instance", "module": "Mathlib.Data.PSigma.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSigma.Lex.noMaxOrder_of_nonempty", "kind": "instance", "module": "Mathlib.Data.PSigma.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSigma.Lex.noMinOrder_of_nonempty", "kind": "instance", "module": "Mathlib.Data.PSigma.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSigma.Lex.noMaxOrder", "kind": "instance", "module": "Mathlib.Data.PSigma.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSigma.Lex.noMinOrder", "kind": "instance", "module": "Mathlib.Data.PSigma.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.toOption", "kind": "definition", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.toOption_isSome", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "Part.toOption_eq_none", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "Part.ext'", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.eta", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.Mem", "kind": "definition", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.instMembership", "kind": "instance", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.mem_eq", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.dom_iff_mem", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.get_mem", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.mem_mk_iff", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.ext", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.none", "kind": "definition", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.instInhabited", "kind": "instance", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.notMem_none", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.some", "kind": "definition", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.some_dom", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.mem_unique", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.mem_right_unique", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.Mem.left_unique", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.Mem.right_unique", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.get_eq_of_mem", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.subsingleton", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.get_some", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.mem_some", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.mem_some_iff", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.eq_some_iff", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.eq_none_iff", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.eq_none_iff'", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.not_none_dom", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.some_ne_none", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": true, "tactics": ["intro", "exact"], "tactic_count": 2}
{"name": "Part.none_ne_some", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.ne_none_iff", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": true, "tactics": ["constructor", "rw", "exact", "rintro", "apply"], "tactic_count": 5}
{"name": "Part.eq_none_or_eq_some", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.some_injective", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.some_inj", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.some_get", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.get_eq_iff_eq_some", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.get_eq_get_of_eq", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": true, "tactics": ["congr"], "tactic_count": 1}
{"name": "Part.get_eq_iff_mem", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.eq_get_iff_mem", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.eq_of_get_eq_get", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.eq_iff_of_dom", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.eq_of_mem", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "Part.none_toOption", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.some_toOption", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.noneDecidable", "kind": "instance", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.someDecidable", "kind": "instance", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.getOrElse", "kind": "definition", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.getOrElse_of_dom", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.getOrElse_of_not_dom", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.getOrElse_none", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.getOrElse_some", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.mem_toOption", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": true, "tactics": ["unfold", "by_cases", "simpa", "simp", "exact"], "tactic_count": 5}
{"name": "Part.toOption_eq_some_iff", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Part.Dom.toOption", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.toOption_eq_none_iff", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.elim_toOption", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": true, "tactics": ["split_ifs", "rw", "rfl", "rw", "rfl"], "tactic_count": 5}
{"name": "Part.ofOption", "kind": "definition", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.mem_ofOption", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.ofOption_dom", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.ofOption_eq_get", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.instCoeOption", "kind": "instance", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.mem_coe", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.coe_none", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.coe_some", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.induction_on", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.ofOptionDecidable", "kind": "instance", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.to_ofOption", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Part.of_toOption", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.equivOption", "kind": "definition", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.instPartialOrder", "kind": "instance", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.instOrderBot", "kind": "instance", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.le_total_of_le_of_le", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": true, "tactics": ["rcases", "rw", "left", "apply", "right", "rw", "have", "have", "exact"], "tactic_count": 9}
{"name": "Part.assert", "kind": "definition", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.bind", "kind": "definition", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.map", "kind": "definition", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.mem_map", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.mem_map_iff", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.map_none", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.map_some", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.mem_assert", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.mem_assert_iff", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.assert_pos", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": true, "tactics": ["ext", "simp_all"], "tactic_count": 2}
{"name": "Part.assert_neg", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": true, "tactics": ["ext", "simp_all"], "tactic_count": 2}
{"name": "Part.mem_bind", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.mem_bind_iff", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.Dom.bind", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": true, "tactics": ["ext", "simp", "refine", "rintro", "rwa"], "tactic_count": 5}
{"name": "Part.Dom.of_bind", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.bind_none", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.bind_some", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.bind_of_mem", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Part.bind_some_eq_map", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.bind_toOption", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": true, "tactics": ["by_cases", "simp_rw", "rfl", "rw", "exact"], "tactic_count": 5}
{"name": "Part.bind_assoc", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.bind_map", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Part.map_bind", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Part.map_map", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Part.instMonad", "kind": "instance", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.instLawfulMonad", "kind": "instance", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.map_id'", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Part.bind_some_right", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Part.pure_eq_some", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.ret_eq_some", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.map_eq_map", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.bind_eq_bind", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.bind_le", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": true, "tactics": ["constructor", "intro", "have", "simp", "apply", "intro", "simp", "rcases", "apply"], "tactic_count": 9}
{"name": "Part.restrict", "kind": "definition", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.mem_restrict", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": true, "tactics": ["dsimp", "rintro", "exact", "rintro"], "tactic_count": 4}
{"name": "Part.unwrap", "kind": "definition", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.assert_defined", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.bind_defined", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.bind_dom", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.instOne", "kind": "instance", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.instMul", "kind": "instance", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.instInv", "kind": "instance", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.instDiv", "kind": "instance", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.instMod", "kind": "instance", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.instAppend", "kind": "instance", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.instInter", "kind": "instance", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.instUnion", "kind": "instance", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.instSDiff", "kind": "instance", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.mul_def", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.one_def", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.inv_def", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.div_def", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.mod_def", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.append_def", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.inter_def", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.union_def", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.sdiff_def", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.one_mem_one", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.mul_mem_mul", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.left_dom_of_mul_dom", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.right_dom_of_mul_dom", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.mul_get_eq", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.some_mul_some", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Part.inv_mem_inv", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Part.inv_some", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.div_mem_div", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Part.left_dom_of_div_dom", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.right_dom_of_div_dom", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.div_get_eq", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Part.some_div_some", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Part.mod_mem_mod", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Part.left_dom_of_mod_dom", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.right_dom_of_mod_dom", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.mod_get_eq", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Part.some_mod_some", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Part.append_mem_append", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Part.left_dom_of_append_dom", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.right_dom_of_append_dom", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.append_get_eq", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Part.some_append_some", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Part.inter_mem_inter", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Part.left_dom_of_inter_dom", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.right_dom_of_inter_dom", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.inter_get_eq", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Part.some_inter_some", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Part.union_mem_union", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Part.left_dom_of_union_dom", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.right_dom_of_union_dom", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.union_get_eq", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Part.some_union_some", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Part.sdiff_mem_sdiff", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Part.left_dom_of_sdiff_dom", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.right_dom_of_sdiff_dom", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Part.sdiff_get_eq", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Part.some_sdiff_some", "kind": "theorem", "module": "Mathlib.Data.Part", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Pi.instLocallyFiniteOrder", "kind": "instance", "module": "Mathlib.Data.Pi.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.Icc_eq", "kind": "theorem", "module": "Mathlib.Data.Pi.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.card_Icc", "kind": "theorem", "module": "Mathlib.Data.Pi.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.card_Ico", "kind": "theorem", "module": "Mathlib.Data.Pi.Interval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Pi.card_Ioc", "kind": "theorem", "module": "Mathlib.Data.Pi.Interval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Pi.card_Ioo", "kind": "theorem", "module": "Mathlib.Data.Pi.Interval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Pi.instLocallyFiniteOrderBot", "kind": "instance", "module": "Mathlib.Data.Pi.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.card_Iic", "kind": "theorem", "module": "Mathlib.Data.Pi.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.card_Iio", "kind": "theorem", "module": "Mathlib.Data.Pi.Interval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Pi.instLocallyFiniteOrderTop", "kind": "instance", "module": "Mathlib.Data.Pi.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.card_Ici", "kind": "theorem", "module": "Mathlib.Data.Pi.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.card_Ioi", "kind": "theorem", "module": "Mathlib.Data.Pi.Interval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Pi.uIcc_eq", "kind": "theorem", "module": "Mathlib.Data.Pi.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.card_uIcc", "kind": "theorem", "module": "Mathlib.Data.Pi.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.swap_eq_iff_eq_swap", "kind": "theorem", "module": "Mathlib.Data.Prod.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Prod.mk.injArrow", "kind": "definition", "module": "Mathlib.Data.Prod.Basic", "is_tactic_proof": true, "tactics": ["intros", "cases", "exact"], "tactic_count": 3}
{"name": "Prod.mk.eta", "kind": "theorem", "module": "Mathlib.Data.Prod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.forall'", "kind": "theorem", "module": "Mathlib.Data.Prod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.exists'", "kind": "theorem", "module": "Mathlib.Data.Prod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.snd_comp_mk", "kind": "theorem", "module": "Mathlib.Data.Prod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.fst_comp_mk", "kind": "theorem", "module": "Mathlib.Data.Prod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.map_apply'", "kind": "theorem", "module": "Mathlib.Data.Prod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.map_fst'", "kind": "theorem", "module": "Mathlib.Data.Prod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.map_snd'", "kind": "theorem", "module": "Mathlib.Data.Prod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.mk_inj", "kind": "theorem", "module": "Mathlib.Data.Prod.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Prod.mk_right_injective", "kind": "theorem", "module": "Mathlib.Data.Prod.Basic", "is_tactic_proof": true, "tactics": ["intro", "simpa"], "tactic_count": 2}
{"name": "Prod.mk_left_injective", "kind": "theorem", "module": "Mathlib.Data.Prod.Basic", "is_tactic_proof": true, "tactics": ["intro", "simpa"], "tactic_count": 2}
{"name": "Prod.mk_right_inj", "kind": "theorem", "module": "Mathlib.Data.Prod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.mk_left_inj", "kind": "theorem", "module": "Mathlib.Data.Prod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.map_def", "kind": "theorem", "module": "Mathlib.Data.Prod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.id_prod", "kind": "theorem", "module": "Mathlib.Data.Prod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.map_iterate", "kind": "theorem", "module": "Mathlib.Data.Prod.Basic", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "Prod.fst_surjective", "kind": "theorem", "module": "Mathlib.Data.Prod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.snd_surjective", "kind": "theorem", "module": "Mathlib.Data.Prod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.fst_injective", "kind": "theorem", "module": "Mathlib.Data.Prod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.snd_injective", "kind": "theorem", "module": "Mathlib.Data.Prod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.swap_leftInverse", "kind": "theorem", "module": "Mathlib.Data.Prod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.swap_rightInverse", "kind": "theorem", "module": "Mathlib.Data.Prod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.swap_injective", "kind": "theorem", "module": "Mathlib.Data.Prod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.swap_surjective", "kind": "theorem", "module": "Mathlib.Data.Prod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.swap_bijective", "kind": "theorem", "module": "Mathlib.Data.Prod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Semiconj.swap_map", "kind": "theorem", "module": "Mathlib.Data.Prod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.eq_iff_fst_eq_snd_eq", "kind": "theorem", "module": "Mathlib.Data.Prod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.fst_eq_iff", "kind": "theorem", "module": "Mathlib.Data.Prod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.snd_eq_iff", "kind": "theorem", "module": "Mathlib.Data.Prod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.lex_iff", "kind": "theorem", "module": "Mathlib.Data.Prod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.Lex.decidable", "kind": "instance", "module": "Mathlib.Data.Prod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.Lex.refl_left", "kind": "theorem", "module": "Mathlib.Data.Prod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instReflLex_mathlib", "kind": "instance", "module": "Mathlib.Data.Prod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.Lex.refl_right", "kind": "theorem", "module": "Mathlib.Data.Prod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instReflLex_mathlib_1", "kind": "instance", "module": "Mathlib.Data.Prod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instIrreflLex_mathlib", "kind": "instance", "module": "Mathlib.Data.Prod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.Lex.trans", "kind": "theorem", "module": "Mathlib.Data.Prod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instIsTransLex", "kind": "instance", "module": "Mathlib.Data.Prod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instAntisymmLexOfIsStrictOrder", "kind": "instance", "module": "Mathlib.Data.Prod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.total_left", "kind": "instance", "module": "Mathlib.Data.Prod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.total_right", "kind": "instance", "module": "Mathlib.Data.Prod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.IsTrichotomous", "kind": "instance", "module": "Mathlib.Data.Prod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instAsymmLex_mathlib", "kind": "instance", "module": "Mathlib.Data.Prod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.prodMap", "kind": "theorem", "module": "Mathlib.Data.Prod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.prodMap", "kind": "theorem", "module": "Mathlib.Data.Prod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Bijective.prodMap", "kind": "theorem", "module": "Mathlib.Data.Prod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.LeftInverse.prodMap", "kind": "theorem", "module": "Mathlib.Data.Prod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.RightInverse.prodMap", "kind": "theorem", "module": "Mathlib.Data.Prod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Involutive.prodMap", "kind": "theorem", "module": "Mathlib.Data.Prod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.map_injective", "kind": "theorem", "module": "Mathlib.Data.Prod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.map_surjective", "kind": "theorem", "module": "Mathlib.Data.Prod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.map_bijective", "kind": "theorem", "module": "Mathlib.Data.Prod.Basic", "is_tactic_proof": true, "tactics": ["haveI", "haveI", "exact"], "tactic_count": 3}
{"name": "Prod.map_leftInverse", "kind": "theorem", "module": "Mathlib.Data.Prod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.map_rightInverse", "kind": "theorem", "module": "Mathlib.Data.Prod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.map_involutive", "kind": "theorem", "module": "Mathlib.Data.Prod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.PrettyPrinting.initFn._@.Mathlib.Data.Prod.Basic.1114368346._hygCtx._hyg.4", "kind": "definition", "module": "Mathlib.Data.Prod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.PrettyPrinting.pp.numericProj.prod", "kind": "opaque", "module": "Mathlib.Data.Prod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.PrettyPrinting.getPPNumericProjProd", "kind": "definition", "module": "Mathlib.Data.Prod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.PrettyPrinting.delabProdFst", "kind": "definition", "module": "Mathlib.Data.Prod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.PrettyPrinting.delabProdSnd", "kind": "definition", "module": "Mathlib.Data.Prod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.Lex.term_×ₗ_", "kind": "definition", "module": "Mathlib.Data.Prod.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.Lex._aux_Mathlib_Data_Prod_Lex___macroRules_Prod_Lex_term_×ₗ__1", "kind": "definition", "module": "Mathlib.Data.Prod.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.Lex._aux_Mathlib_Data_Prod_Lex___unexpand_Lex_1", "kind": "definition", "module": "Mathlib.Data.Prod.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.Lex.instLE", "kind": "instance", "module": "Mathlib.Data.Prod.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.Lex.instLT", "kind": "instance", "module": "Mathlib.Data.Prod.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.Lex.toLex_le_toLex", "kind": "theorem", "module": "Mathlib.Data.Prod.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.Lex.toLex_lt_toLex", "kind": "theorem", "module": "Mathlib.Data.Prod.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.Lex.le_iff", "kind": "theorem", "module": "Mathlib.Data.Prod.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.Lex.lt_iff", "kind": "theorem", "module": "Mathlib.Data.Prod.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.Lex.instWellFoundedLTLex", "kind": "instance", "module": "Mathlib.Data.Prod.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.Lex.instWellFoundedRelationLexOfWellFoundedLT", "kind": "instance", "module": "Mathlib.Data.Prod.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "WCovBy.fst_ofLex", "kind": "theorem", "module": "Mathlib.Data.Prod.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.Lex.toLex_covBy_toLex_iff", "kind": "theorem", "module": "Mathlib.Data.Prod.Lex", "is_tactic_proof": false, "tactics": ["simp", "isMin_iff_forall_not_lt]", "grind"], "tactic_count": 3}
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{"name": "Prod.Lex.toLex_strictMono", "kind": "theorem", "module": "Mathlib.Data.Prod.Lex", "is_tactic_proof": true, "tactics": ["rintro", "obtain", "exact", "exact"], "tactic_count": 4}
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{"name": "Prod.Lex.instOrdLexProd", "kind": "instance", "module": "Mathlib.Data.Prod.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.Lex.compare_def", "kind": "theorem", "module": "Mathlib.Data.Prod.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lexOrd_eq", "kind": "theorem", "module": "Mathlib.Data.Prod.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Prod.Lex.instTransOrdLex", "kind": "instance", "module": "Mathlib.Data.Prod.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.Lex.instLinearOrder", "kind": "instance", "module": "Mathlib.Data.Prod.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.Lex.orderBot", "kind": "instance", "module": "Mathlib.Data.Prod.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.Lex.orderTop", "kind": "instance", "module": "Mathlib.Data.Prod.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.Lex.boundedOrder", "kind": "instance", "module": "Mathlib.Data.Prod.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.Lex.instDenselyOrderedLex", "kind": "instance", "module": "Mathlib.Data.Prod.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.Lex.noMaxOrder_of_left", "kind": "instance", "module": "Mathlib.Data.Prod.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.Lex.noMinOrder_of_left", "kind": "instance", "module": "Mathlib.Data.Prod.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.Lex.noMaxOrder_of_right", "kind": "instance", "module": "Mathlib.Data.Prod.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "PProd.mk.injArrow", "kind": "definition", "module": "Mathlib.Data.Prod.PProd", "is_tactic_proof": true, "tactics": ["intros", "cases", "exact"], "tactic_count": 3}
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{"name": "List.TProd.piEquivTProd", "kind": "definition", "module": "Mathlib.Data.Prod.TProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MvQPF.Cofix.mvfunctor", "kind": "instance", "module": "Mathlib.Data.QPF.Multivariate.Constructions.Cofix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "QPF.mem_supp", "kind": "theorem", "module": "Mathlib.Data.QPF.Univariate.Basic", "is_tactic_proof": true, "tactics": ["rw", "intro", "have", "rw", "exact", "exact", "intro", "rintro", "rcases", "rw"], "tactic_count": 10}
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{"name": "QPF.LiftpPreservation", "kind": "definition", "module": "Mathlib.Data.QPF.Univariate.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "QPF.supp_eq_of_isUniform", "kind": "theorem", "module": "Mathlib.Data.QPF.Univariate.Basic", "is_tactic_proof": true, "tactics": ["ext", "intro", "apply", "intro", "rw"], "tactic_count": 5}
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{"name": "Quotient.surjective_liftOn'", "kind": "theorem", "module": "Mathlib.Data.Quot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quotient.liftOn₂'", "kind": "definition", "module": "Mathlib.Data.Quot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quotient.liftOn₂'_mk''", "kind": "theorem", "module": "Mathlib.Data.Quot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quotient.ind'", "kind": "theorem", "module": "Mathlib.Data.Quot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quotient.ind₂'", "kind": "theorem", "module": "Mathlib.Data.Quot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quotient.inductionOn'", "kind": "theorem", "module": "Mathlib.Data.Quot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quotient.inductionOn₂'", "kind": "theorem", "module": "Mathlib.Data.Quot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quotient.inductionOn₃'", "kind": "theorem", "module": "Mathlib.Data.Quot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quotient.recOnSubsingleton'", "kind": "definition", "module": "Mathlib.Data.Quot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quotient.recOnSubsingleton₂'", "kind": "definition", "module": "Mathlib.Data.Quot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quotient.hrecOn'", "kind": "definition", "module": "Mathlib.Data.Quot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quotient.hrecOn'_mk''", "kind": "theorem", "module": "Mathlib.Data.Quot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quotient.hrecOn₂'", "kind": "definition", "module": "Mathlib.Data.Quot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quotient.hrecOn₂'_mk''", "kind": "theorem", "module": "Mathlib.Data.Quot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quotient.map'", "kind": "definition", "module": "Mathlib.Data.Quot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quotient.map'_mk''", "kind": "theorem", "module": "Mathlib.Data.Quot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quotient.map₂'", "kind": "definition", "module": "Mathlib.Data.Quot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quotient.map₂'_mk''", "kind": "theorem", "module": "Mathlib.Data.Quot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quotient.exact'", "kind": "theorem", "module": "Mathlib.Data.Quot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quotient.sound'", "kind": "theorem", "module": "Mathlib.Data.Quot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quotient.eq'", "kind": "theorem", "module": "Mathlib.Data.Quot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quotient.eq''", "kind": "theorem", "module": "Mathlib.Data.Quot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quotient.out_eq'", "kind": "theorem", "module": "Mathlib.Data.Quot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quotient.mk_out'", "kind": "theorem", "module": "Mathlib.Data.Quot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quotient.mk''_eq_mk", "kind": "theorem", "module": "Mathlib.Data.Quot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quotient.liftOn'_mk", "kind": "theorem", "module": "Mathlib.Data.Quot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quotient.liftOn₂'_mk", "kind": "theorem", "module": "Mathlib.Data.Quot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quotient.map'_mk", "kind": "theorem", "module": "Mathlib.Data.Quot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quotient.instDecidableLiftOn'OfDecidablePred", "kind": "instance", "module": "Mathlib.Data.Quot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quotient.instDecidableLiftOn₂'OfDecidablePred", "kind": "instance", "module": "Mathlib.Data.Quot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equivalence.quot_mk_eq_iff", "kind": "theorem", "module": "Mathlib.Data.Quot", "is_tactic_proof": true, "tactics": ["constructor", "rw", "intro", "induction", "rel", "refl", "symm", "trans", "exact"], "tactic_count": 9}
{"name": "Rat.cast_list_sum", "kind": "theorem", "module": "Mathlib.Data.Rat.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.cast_multiset_sum", "kind": "theorem", "module": "Mathlib.Data.Rat.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.cast_sum", "kind": "theorem", "module": "Mathlib.Data.Rat.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.cast_list_prod", "kind": "theorem", "module": "Mathlib.Data.Rat.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.cast_multiset_prod", "kind": "theorem", "module": "Mathlib.Data.Rat.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.cast_prod", "kind": "theorem", "module": "Mathlib.Data.Rat.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mkRat", "kind": "theorem", "module": "Mathlib.Data.Rat.Cardinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.cast_injective", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.CharZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.cast_inj", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.CharZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.cast_eq_zero", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.CharZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.cast_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.CharZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.cast_add", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.CharZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.cast_sub", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.CharZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.cast_mul", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.CharZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.castHom", "kind": "definition", "module": "Mathlib.Data.Rat.Cast.CharZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.coe_castHom", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.CharZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.cast_inv", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.CharZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.cast_div", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.CharZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.cast_zpow", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.CharZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.cast_divInt", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.CharZero", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NNRat.cast_injective", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.CharZero", "is_tactic_proof": true, "tactics": ["rintro", "rw", "on_goal", "norm_cast", "any_goals", "any_goals", "exact"], "tactic_count": 7}
{"name": "NNRat.cast_inj", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.CharZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.cast_eq_zero", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.CharZero", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NNRat.cast_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.CharZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.cast_add", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.CharZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.cast_mul", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.CharZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.castHom", "kind": "definition", "module": "Mathlib.Data.Rat.Cast.CharZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.coe_castHom", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.CharZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.cast_inv", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.CharZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.cast_div", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.CharZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.cast_zpow", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.CharZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.cast_divNat", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.CharZero", "is_tactic_proof": true, "tactics": ["rw", "congr", "ext", "apply"], "tactic_count": 4}
{"name": "NNRat.cast_natCast", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NNRat.cast_ofNat", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.cast_zero", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.cast_one", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.cast_commute", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "NNRat.commute_cast", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.cast_comm", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.cast_divNat_of_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Defs", "is_tactic_proof": true, "tactics": ["rcases", "rw", "lift", "have", "refine", "have", "obtain", "simp", "have", "simp_rw", "rw", "dsimp", "rw", "norm_cast", "rw", "exact"], "tactic_count": 16}
{"name": "NNRat.cast_add_of_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Defs", "is_tactic_proof": false, "tactics": ["rw", "push_cast", "rfl", "push_cast", "exact"], "tactic_count": 5}
{"name": "NNRat.cast_mul_of_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Defs", "is_tactic_proof": false, "tactics": ["rw", "push_cast", "rfl", "push_cast", "exact"], "tactic_count": 5}
{"name": "NNRat.cast_inv_of_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NNRat.cast_div_of_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Defs", "is_tactic_proof": false, "tactics": ["rw", "push_cast", "rfl", "push_cast", "exact"], "tactic_count": 5}
{"name": "Rat.cast_intCast", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.cast_natCast", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Rat.cast_ofNat", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Rat.cast_zero", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.cast_one", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.cast_commute", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Rat.cast_comm", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.commute_cast", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.cast_divInt_of_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Defs", "is_tactic_proof": false, "tactics": ["have", "refine", "simp", "rcases", "have", "intro", "have", "rcases", "have", "rw", "contradiction", "rw", "have", "rw", "rw", "mul_assoc,"], "tactic_count": 16}
{"name": "Rat.cast_mkRat_of_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Rat.cast_add_of_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Defs", "is_tactic_proof": false, "tactics": ["rw", "push_cast", "rfl", "push_cast", "exact"], "tactic_count": 5}
{"name": "Rat.cast_neg", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Rat.cast_sub_of_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Rat.cast_mul_of_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Defs", "is_tactic_proof": false, "tactics": ["rw", "push_cast", "rfl", "push_cast", "exact"], "tactic_count": 5}
{"name": "Rat.cast_inv_of_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Rat.cast_div_of_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Defs", "is_tactic_proof": false, "tactics": ["rw", "push_cast", "rfl", "push_cast", "exact"], "tactic_count": 5}
{"name": "map_nnratCast", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Defs", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "eq_nnratCast", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "map_ratCast", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "eq_ratCast", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MonoidWithZeroHomClass.ext_nnrat'", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHomClass.ext_nnrat", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHomClass.ext_nnrat_on_pnat", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHomClass.ext_rat'", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHomClass.ext_rat", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHomClass.ext_rat_on_pnat", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.ext_rat", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.subsingleton_ringHom", "kind": "instance", "module": "Mathlib.Data.Rat.Cast.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.subsingleton_ringHom", "kind": "instance", "module": "Mathlib.Data.Rat.Cast.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.cast_pow", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Rat.cast_inv_nat", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Lemmas", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rw"], "tactic_count": 3}
{"name": "Rat.cast_inv_int", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Lemmas", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simp"], "tactic_count": 3}
{"name": "Rat.cast_nnratCast", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "have", "on_goal", "simpa", "simp", "rw"], "tactic_count": 6}
{"name": "Rat.cast_ofScientific", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NNRat.cast_pow", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NNRat.cast_zpow_of_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Lemmas", "is_tactic_proof": true, "tactics": ["obtain", "simp", "simp_rw", "congr", "rw"], "tactic_count": 5}
{"name": "NNRat.cast_mk", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Lemmas", "is_tactic_proof": true, "tactics": ["simp", "rw"], "tactic_count": 2}
{"name": "NNRat.Nonneg.coe_ofScientific", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instLawfulOfScientificOfCharZero", "kind": "instance", "module": "Mathlib.Data.Rat.Cast.OfScientific", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.castHom_rat", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.cast_pos_of_pos", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Rat.cast_strictMono", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.cast_mono", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.castOrderEmbedding", "kind": "definition", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.cast_le", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.cast_lt", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.cast_nonneg", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": true, "tactics": ["norm_cast"], "tactic_count": 1}
{"name": "Rat.cast_nonpos", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": true, "tactics": ["norm_cast"], "tactic_count": 1}
{"name": "Rat.cast_pos", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": true, "tactics": ["norm_cast"], "tactic_count": 1}
{"name": "Rat.cast_lt_zero", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": true, "tactics": ["norm_cast"], "tactic_count": 1}
{"name": "Rat.cast_le_natCast", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Rat.natCast_le_cast", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Rat.cast_le_intCast", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Rat.intCast_le_cast", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Rat.cast_lt_natCast", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Rat.natCast_lt_cast", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Rat.cast_lt_intCast", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Rat.intCast_lt_cast", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Rat.cast_min", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.cast_max", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.cast_abs", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Rat.preimage_cast_Icc", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.preimage_cast_Ico", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.preimage_cast_Ioc", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.preimage_cast_Ioo", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.preimage_cast_Ici", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.preimage_cast_Iic", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.preimage_cast_Ioi", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.preimage_cast_Iio", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.preimage_cast_uIcc", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.preimage_cast_uIoc", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.cast_strictMono", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.cast_mono", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.castOrderEmbedding", "kind": "definition", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.cast_le", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.cast_lt", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.cast_nonpos", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": true, "tactics": ["norm_cast"], "tactic_count": 1}
{"name": "NNRat.cast_pos", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": true, "tactics": ["norm_cast"], "tactic_count": 1}
{"name": "NNRat.cast_lt_zero", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": true, "tactics": ["norm_cast"], "tactic_count": 1}
{"name": "NNRat.not_cast_lt_zero", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.cast_le_one", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": true, "tactics": ["norm_cast"], "tactic_count": 1}
{"name": "NNRat.one_le_cast", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": true, "tactics": ["norm_cast"], "tactic_count": 1}
{"name": "NNRat.cast_lt_one", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": true, "tactics": ["norm_cast"], "tactic_count": 1}
{"name": "NNRat.one_lt_cast", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": true, "tactics": ["norm_cast"], "tactic_count": 1}
{"name": "NNRat.cast_le_ofNat", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NNRat.ofNat_le_cast", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NNRat.cast_lt_ofNat", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NNRat.ofNat_lt_cast", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NNRat.cast_le_natCast", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NNRat.natCast_le_cast", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NNRat.cast_lt_natCast", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NNRat.natCast_lt_cast", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NNRat.cast_min", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.cast_max", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.preimage_cast_Icc", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.preimage_cast_Ico", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.preimage_cast_Ioc", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.preimage_cast_Ioo", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.preimage_cast_Ici", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.preimage_cast_Iic", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.preimage_cast_Ioi", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.preimage_cast_Iio", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.preimage_cast_uIcc", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.preimage_cast_uIoc", "kind": "theorem", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalRatCast", "kind": "definition", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalNNRatCast", "kind": "definition", "module": "Mathlib.Data.Rat.Cast.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.pos", "kind": "theorem", "module": "Mathlib.Data.Rat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.mk'_num_den", "kind": "theorem", "module": "Mathlib.Data.Rat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.ofInt_eq_cast", "kind": "theorem", "module": "Mathlib.Data.Rat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.intCast_injective", "kind": "theorem", "module": "Mathlib.Data.Rat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.natCast_injective", "kind": "theorem", "module": "Mathlib.Data.Rat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.intCast_eq_one_iff", "kind": "theorem", "module": "Mathlib.Data.Rat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.natCast_eq_one_iff", "kind": "theorem", "module": "Mathlib.Data.Rat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.mkRat_eq_divInt", "kind": "theorem", "module": "Mathlib.Data.Rat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.mk'_zero", "kind": "theorem", "module": "Mathlib.Data.Rat.Defs", "is_tactic_proof": true, "tactics": ["congr"], "tactic_count": 1}
{"name": "Rat.num_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Rat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.den_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Rat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.divInt_eq_zero", "kind": "theorem", "module": "Mathlib.Data.Rat.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Rat.divInt_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Rat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.intCast_eq_divInt", "kind": "theorem", "module": "Mathlib.Data.Rat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.lift_binop_eq", "kind": "theorem", "module": "Mathlib.Data.Rat.Defs", "is_tactic_proof": true, "tactics": ["generalize", "generalize", "rw", "have", "have", "exact"], "tactic_count": 6}
{"name": "Rat.neg_def", "kind": "theorem", "module": "Mathlib.Data.Rat.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Rat.divInt_neg", "kind": "theorem", "module": "Mathlib.Data.Rat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.mk'_mul_mk'", "kind": "theorem", "module": "Mathlib.Data.Rat.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Rat.mul_eq_mkRat", "kind": "theorem", "module": "Mathlib.Data.Rat.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Rat.pow_eq_mkRat", "kind": "theorem", "module": "Mathlib.Data.Rat.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Rat.pow_eq_divInt", "kind": "theorem", "module": "Mathlib.Data.Rat.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Rat.mk'_pow", "kind": "theorem", "module": "Mathlib.Data.Rat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.inv_mkRat", "kind": "theorem", "module": "Mathlib.Data.Rat.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Rat.divInt_div_divInt", "kind": "theorem", "module": "Mathlib.Data.Rat.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Rat.div_def'", "kind": "theorem", "module": "Mathlib.Data.Rat.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Rat.divInt_one", "kind": "theorem", "module": "Mathlib.Data.Rat.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Rat.divInt_one_one", "kind": "theorem", "module": "Mathlib.Data.Rat.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Rat.zero_ne_one", "kind": "theorem", "module": "Mathlib.Data.Rat.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Rat.nontrivial", "kind": "instance", "module": "Mathlib.Data.Rat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.addCommGroup", "kind": "instance", "module": "Mathlib.Data.Rat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.addGroup", "kind": "instance", "module": "Mathlib.Data.Rat.Defs", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Rat.addCommMonoid", "kind": "instance", "module": "Mathlib.Data.Rat.Defs", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Rat.addMonoid", "kind": "instance", "module": "Mathlib.Data.Rat.Defs", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Rat.addLeftCancelSemigroup", "kind": "instance", "module": "Mathlib.Data.Rat.Defs", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Rat.addRightCancelSemigroup", "kind": "instance", "module": "Mathlib.Data.Rat.Defs", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Rat.addCommSemigroup", "kind": "instance", "module": "Mathlib.Data.Rat.Defs", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Rat.addSemigroup", "kind": "instance", "module": "Mathlib.Data.Rat.Defs", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Rat.commMonoid", "kind": "instance", "module": "Mathlib.Data.Rat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.monoid", "kind": "instance", "module": "Mathlib.Data.Rat.Defs", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Rat.commSemigroup", "kind": "instance", "module": "Mathlib.Data.Rat.Defs", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Rat.semigroup", "kind": "instance", "module": "Mathlib.Data.Rat.Defs", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Rat.eq_iff_mul_eq_mul", "kind": "theorem", "module": "Mathlib.Data.Rat.Defs", "is_tactic_proof": false, "tactics": ["conv", "lhs", "rw", "apply", "rw", "apply"], "tactic_count": 6}
{"name": "Rat.den_neg_eq_den", "kind": "theorem", "module": "Mathlib.Data.Rat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.num_neg_eq_neg_num", "kind": "theorem", "module": "Mathlib.Data.Rat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.num_zero", "kind": "theorem", "module": "Mathlib.Data.Rat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.den_zero", "kind": "theorem", "module": "Mathlib.Data.Rat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.zero_of_num_zero", "kind": "theorem", "module": "Mathlib.Data.Rat.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Rat.zero_iff_num_zero", "kind": "theorem", "module": "Mathlib.Data.Rat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.num_one", "kind": "theorem", "module": "Mathlib.Data.Rat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.den_one", "kind": "theorem", "module": "Mathlib.Data.Rat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.mk_num_ne_zero_of_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Rat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.mk_denom_ne_zero_of_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Rat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.divInt_ne_zero_of_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Rat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.add_divInt", "kind": "theorem", "module": "Mathlib.Data.Rat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.intCast_div_eq_divInt", "kind": "theorem", "module": "Mathlib.Data.Rat.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Rat.natCast_div_eq_divInt", "kind": "theorem", "module": "Mathlib.Data.Rat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.divInt_mul_divInt_cancel", "kind": "theorem", "module": "Mathlib.Data.Rat.Defs", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "simp", "rw"], "tactic_count": 4}
{"name": "Rat.coe_int_num_of_den_eq_one", "kind": "theorem", "module": "Mathlib.Data.Rat.Defs", "is_tactic_proof": true, "tactics": ["conv_rhs", "rw", "rfl"], "tactic_count": 3}
{"name": "Rat.eq_num_of_isInt", "kind": "theorem", "module": "Mathlib.Data.Rat.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Rat.den_eq_one_iff", "kind": "theorem", "module": "Mathlib.Data.Rat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.canLift", "kind": "instance", "module": "Mathlib.Data.Rat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.coe_int_inj", "kind": "theorem", "module": "Mathlib.Data.Rat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.divCasesOn", "kind": "definition", "module": "Mathlib.Data.Rat.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.instDenumerable", "kind": "instance", "module": "Mathlib.Data.Rat.Denumerable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.instEncodable", "kind": "instance", "module": "Mathlib.Data.Rat.Encodable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.le_floor", "kind": "theorem", "module": "Mathlib.Data.Rat.Floor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.instFloorRing", "kind": "instance", "module": "Mathlib.Data.Rat.Floor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.floor_def'", "kind": "theorem", "module": "Mathlib.Data.Rat.Floor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.ceil_def'", "kind": "theorem", "module": "Mathlib.Data.Rat.Floor", "is_tactic_proof": true, "tactics": ["change", "rw"], "tactic_count": 2}
{"name": "Rat.floor_intCast_div_natCast", "kind": "theorem", "module": "Mathlib.Data.Rat.Floor", "is_tactic_proof": true, "tactics": ["rw", "obtain", "simp", "set", "obtain", "rw", "exact", "rw", "refine", "rwa"], "tactic_count": 10}
{"name": "Rat.ceil_intCast_div_natCast", "kind": "theorem", "module": "Mathlib.Data.Rat.Floor", "is_tactic_proof": true, "tactics": ["conv_lhs", "rw"], "tactic_count": 2}
{"name": "Rat.floor_natCast_div_natCast", "kind": "theorem", "module": "Mathlib.Data.Rat.Floor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.ceil_natCast_div_natCast", "kind": "theorem", "module": "Mathlib.Data.Rat.Floor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.natFloor_natCast_div_natCast", "kind": "theorem", "module": "Mathlib.Data.Rat.Floor", "is_tactic_proof": true, "tactics": ["rw", "push_cast", "exact"], "tactic_count": 3}
{"name": "Rat.floor_cast", "kind": "theorem", "module": "Mathlib.Data.Rat.Floor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.ceil_cast", "kind": "theorem", "module": "Mathlib.Data.Rat.Floor", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Rat.round_cast", "kind": "theorem", "module": "Mathlib.Data.Rat.Floor", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "Rat.cast_fract", "kind": "theorem", "module": "Mathlib.Data.Rat.Floor", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Rat.den_intFract", "kind": "theorem", "module": "Mathlib.Data.Rat.Floor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.isNat_intFloor", "kind": "theorem", "module": "Mathlib.Data.Rat.Floor", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "Rat.isInt_intFloor", "kind": "theorem", "module": "Mathlib.Data.Rat.Floor", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "Rat.isNat_intFloor_ofIsNNRat", "kind": "theorem", "module": "Mathlib.Data.Rat.Floor", "is_tactic_proof": true, "tactics": ["rintro", "constructor", "simp", "rw", "cast_natCast]"], "tactic_count": 5}
{"name": "Rat.isInt_intFloor_ofIsRat_neg", "kind": "theorem", "module": "Mathlib.Data.Rat.Floor", "is_tactic_proof": true, "tactics": ["rintro", "constructor", "simp", "rw", "rw", "natCast_toNat_eq_self.mpr", "ceil_intCast_div_natCast", "floor_intCast_div_natCast"], "tactic_count": 8}
{"name": "Rat.evalIntFloor", "kind": "definition", "module": "Mathlib.Data.Rat.Floor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.isNat_intCeil", "kind": "theorem", "module": "Mathlib.Data.Rat.Floor", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "Rat.isInt_intCeil", "kind": "theorem", "module": "Mathlib.Data.Rat.Floor", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "Rat.isNat_intCeil_ofIsNNRat", "kind": "theorem", "module": "Mathlib.Data.Rat.Floor", "is_tactic_proof": true, "tactics": ["rintro", "constructor", "simp", "rw"], "tactic_count": 4}
{"name": "Rat.isInt_intCeil_ofIsRat_neg", "kind": "theorem", "module": "Mathlib.Data.Rat.Floor", "is_tactic_proof": true, "tactics": ["rintro", "constructor", "simp", "rw", "floor_natCast_div_natCast", "ceil_intCast_div_natCast"], "tactic_count": 6}
{"name": "Rat.evalIntCeil", "kind": "definition", "module": "Mathlib.Data.Rat.Floor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.isNat_intFract_of_isNat", "kind": "theorem", "module": "Mathlib.Data.Rat.Floor", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "Rat.isNat_intFract_of_isInt", "kind": "theorem", "module": "Mathlib.Data.Rat.Floor", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "Rat.isNNRat_intFract_of_isNNRat", "kind": "theorem", "module": "Mathlib.Data.Rat.Floor", "is_tactic_proof": true, "tactics": ["rintro", "refine", "simp"], "tactic_count": 3}
{"name": "Rat.isRat_intFract_of_isRat_negOfNat", "kind": "theorem", "module": "Mathlib.Data.Rat.Floor", "is_tactic_proof": true, "tactics": ["rintro", "refine", "simp"], "tactic_count": 3}
{"name": "Rat.evalIntFract", "kind": "definition", "module": "Mathlib.Data.Rat.Floor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.isNat_round", "kind": "theorem", "module": "Mathlib.Data.Rat.Floor", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "Rat.isInt_round", "kind": "theorem", "module": "Mathlib.Data.Rat.Floor", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "Rat.IsRat.isInt_round", "kind": "theorem", "module": "Mathlib.Data.Rat.Floor", "is_tactic_proof": true, "tactics": ["rintro", "subst", "constructor", "rw", "norm_cast"], "tactic_count": 5}
{"name": "_private.Mathlib.Data.Rat.Floor.0.Rat.instFloorRing_1", "kind": "instance", "module": "Mathlib.Data.Rat.Floor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.evalRound", "kind": "definition", "module": "Mathlib.Data.Rat.Floor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.mod_nat_eq_sub_mul_floor_rat_div", "kind": "theorem", "module": "Mathlib.Data.Rat.Floor", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.coprime_sub_mul_floor_rat_div_of_coprime", "kind": "theorem", "module": "Mathlib.Data.Rat.Floor", "is_tactic_proof": true, "tactics": ["have", "rw", "have", "rwa"], "tactic_count": 4}
{"name": "Rat.num_lt_succ_floor_mul_den", "kind": "theorem", "module": "Mathlib.Data.Rat.Floor", "is_tactic_proof": true, "tactics": ["suffices", "suffices", "have", "rwa", "suffices", "have", "calc", "rwa", "suffices", "rw", "simpa", "have", "have", "have", "rwa", "exact"], "tactic_count": 16}
{"name": "Rat.fract_inv_num_lt_num_of_pos", "kind": "theorem", "module": "Mathlib.Data.Rat.Floor", "is_tactic_proof": true, "tactics": ["have", "have", "set", "have", "suffices", "suffices", "simp", "field_simp", "simp", "suffices", "have", "suffices", "mod_cast", "have", "simpa", "rwa", "have", "have", "have", "rwa", "have", "have", "have", "rw", "rw", "constructor", "exact", "suffices", "rw", "exact", "rwa"], "tactic_count": 31}
{"name": "termℚ", "kind": "definition", "module": "Mathlib.Data.Rat.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Data_Rat_Init___macroRules_termℚ_1", "kind": "definition", "module": "Mathlib.Data.Rat.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Data_Rat_Init___unexpand_Rat_1", "kind": "definition", "module": "Mathlib.Data.Rat.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat", "kind": "definition", "module": "Mathlib.Data.Rat.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "termℚ≥0", "kind": "definition", "module": "Mathlib.Data.Rat.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Data_Rat_Init___macroRules_termℚ≥0_1", "kind": "definition", "module": "Mathlib.Data.Rat.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Data_Rat_Init___unexpand_NNRat_1", "kind": "definition", "module": "Mathlib.Data.Rat.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.instNNRatCast", "kind": "instance", "module": "Mathlib.Data.Rat.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.cast", "kind": "definition", "module": "Mathlib.Data.Rat.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRatCast.toCoeTail", "kind": "instance", "module": "Mathlib.Data.Rat.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRatCast.toCoeHTCT", "kind": "instance", "module": "Mathlib.Data.Rat.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.instNNRatCast", "kind": "instance", "module": "Mathlib.Data.Rat.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.num", "kind": "definition", "module": "Mathlib.Data.Rat.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.den", "kind": "definition", "module": "Mathlib.Data.Rat.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.num_mk", "kind": "theorem", "module": "Mathlib.Data.Rat.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.den_mk", "kind": "theorem", "module": "Mathlib.Data.Rat.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.cast_id", "kind": "theorem", "module": "Mathlib.Data.Rat.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.cast_eq_id", "kind": "theorem", "module": "Mathlib.Data.Rat.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.cast_id", "kind": "theorem", "module": "Mathlib.Data.Rat.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.cast_eq_id", "kind": "theorem", "module": "Mathlib.Data.Rat.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.num_dvd", "kind": "theorem", "module": "Mathlib.Data.Rat.Lemmas", "is_tactic_proof": true, "tactics": ["rcases", "rw", "refine", "have", "simp"], "tactic_count": 5}
{"name": "Rat.den_dvd", "kind": "theorem", "module": "Mathlib.Data.Rat.Lemmas", "is_tactic_proof": true, "tactics": ["by_cases", "rcases", "rw", "refine", "rw"], "tactic_count": 5}
{"name": "Rat.num_den_mk", "kind": "theorem", "module": "Mathlib.Data.Rat.Lemmas", "is_tactic_proof": true, "tactics": ["obtain", "simp", "have", "refine", "exact", "rwa", "have", "rw", "exact", "refine", "rw", "refine", "rw", "exact"], "tactic_count": 14}
{"name": "Rat.num_mk", "kind": "theorem", "module": "Mathlib.Data.Rat.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.den_mk", "kind": "theorem", "module": "Mathlib.Data.Rat.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.add_den_dvd_lcm", "kind": "theorem", "module": "Mathlib.Data.Rat.Lemmas", "is_tactic_proof": false, "tactics": ["rw", "refine", "rw", "apply", "exact"], "tactic_count": 5}
{"name": "Rat.sub_den_dvd_lcm", "kind": "theorem", "module": "Mathlib.Data.Rat.Lemmas", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Rat.add_den_dvd", "kind": "theorem", "module": "Mathlib.Data.Rat.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.sub_den_dvd", "kind": "theorem", "module": "Mathlib.Data.Rat.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.mul_den_dvd", "kind": "theorem", "module": "Mathlib.Data.Rat.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "apply", "apply"], "tactic_count": 3}
{"name": "Rat.mul_num", "kind": "theorem", "module": "Mathlib.Data.Rat.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Rat.mul_den", "kind": "theorem", "module": "Mathlib.Data.Rat.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Rat.add_intCast_den", "kind": "theorem", "module": "Mathlib.Data.Rat.Lemmas", "is_tactic_proof": true, "tactics": ["apply", "simpa", "simpa"], "tactic_count": 3}
{"name": "Rat.intCast_add_den", "kind": "theorem", "module": "Mathlib.Data.Rat.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Rat.sub_intCast_den", "kind": "theorem", "module": "Mathlib.Data.Rat.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Rat.intCast_sub_den", "kind": "theorem", "module": "Mathlib.Data.Rat.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Rat.add_natCast_den", "kind": "theorem", "module": "Mathlib.Data.Rat.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.natCast_add_den", "kind": "theorem", "module": "Mathlib.Data.Rat.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.sub_natCast_den", "kind": "theorem", "module": "Mathlib.Data.Rat.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.natCast_sub_den", "kind": "theorem", "module": "Mathlib.Data.Rat.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.add_ofNat_den", "kind": "theorem", "module": "Mathlib.Data.Rat.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.ofNat_add_den", "kind": "theorem", "module": "Mathlib.Data.Rat.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.sub_ofNat_den", "kind": "theorem", "module": "Mathlib.Data.Rat.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.ofNat_sub_den", "kind": "theorem", "module": "Mathlib.Data.Rat.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.den_mul_den_eq_den_mul_gcd", "kind": "theorem", "module": "Mathlib.Data.Rat.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Rat.num_mul_num_eq_num_mul_gcd", "kind": "theorem", "module": "Mathlib.Data.Rat.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "Rat.mul_self_num", "kind": "theorem", "module": "Mathlib.Data.Rat.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Rat.mul_self_den", "kind": "theorem", "module": "Mathlib.Data.Rat.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Rat.add_num_den", "kind": "theorem", "module": "Mathlib.Data.Rat.Lemmas", "is_tactic_proof": true, "tactics": ["have", "have", "conv_lhs", "rw"], "tactic_count": 4}
{"name": "Rat.isSquare_iff", "kind": "theorem", "module": "Mathlib.Data.Rat.Lemmas", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "rw", "simp", "rintro", "refine", "rw"], "tactic_count": 7}
{"name": "Rat.isSquare_natCast_iff", "kind": "theorem", "module": "Mathlib.Data.Rat.Lemmas", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Rat.isSquare_intCast_iff", "kind": "theorem", "module": "Mathlib.Data.Rat.Lemmas", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Rat.isSquare_ofNat_iff", "kind": "theorem", "module": "Mathlib.Data.Rat.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.mkRat_add_mkRat_of_den", "kind": "theorem", "module": "Mathlib.Data.Rat.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Rat.exists_eq_mul_div_num_and_eq_mul_div_den", "kind": "theorem", "module": "Mathlib.Data.Rat.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.mul_num_den'", "kind": "theorem", "module": "Mathlib.Data.Rat.Lemmas", "is_tactic_proof": true, "tactics": ["let", "have", "obtain", "rw", "nth_rw", "rw", "intro", "have", "rw", "rw"], "tactic_count": 10}
{"name": "Rat.add_num_den'", "kind": "theorem", "module": "Mathlib.Data.Rat.Lemmas", "is_tactic_proof": true, "tactics": ["let", "have", "obtain", "rw", "nth_rw", "repeat", "apply", "rw", "intro", "have", "rw", "rw", "rw", "apply", "rw"], "tactic_count": 15}
{"name": "Rat.substr_num_den'", "kind": "theorem", "module": "Mathlib.Data.Rat.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Rat.inv_neg", "kind": "theorem", "module": "Mathlib.Data.Rat.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Rat.num_div_eq_of_coprime", "kind": "theorem", "module": "Mathlib.Data.Rat.Lemmas", "is_tactic_proof": true, "tactics": ["lift", "simp", "rw"], "tactic_count": 3}
{"name": "Rat.den_div_eq_of_coprime", "kind": "theorem", "module": "Mathlib.Data.Rat.Lemmas", "is_tactic_proof": true, "tactics": ["lift", "simp", "rw"], "tactic_count": 3}
{"name": "Rat.div_int_inj", "kind": "theorem", "module": "Mathlib.Data.Rat.Lemmas", "is_tactic_proof": true, "tactics": ["apply", "rw", "rw"], "tactic_count": 3}
{"name": "Rat.intCast_div_self", "kind": "theorem", "module": "Mathlib.Data.Rat.Lemmas", "is_tactic_proof": true, "tactics": ["by_cases", "subst", "simp", "have", "simp"], "tactic_count": 5}
{"name": "Rat.natCast_div_self", "kind": "theorem", "module": "Mathlib.Data.Rat.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.intCast_div", "kind": "theorem", "module": "Mathlib.Data.Rat.Lemmas", "is_tactic_proof": true, "tactics": ["rcases", "rw"], "tactic_count": 2}
{"name": "Rat.natCast_div", "kind": "theorem", "module": "Mathlib.Data.Rat.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.den_div_intCast_eq_one_iff", "kind": "theorem", "module": "Mathlib.Data.Rat.Lemmas", "is_tactic_proof": true, "tactics": ["replace", "constructor", "rw", "exact", "exact"], "tactic_count": 5}
{"name": "Rat.den_div_natCast_eq_one_iff", "kind": "theorem", "module": "Mathlib.Data.Rat.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.inv_intCast_num_of_pos", "kind": "theorem", "module": "Mathlib.Data.Rat.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Rat.inv_natCast_num_of_pos", "kind": "theorem", "module": "Mathlib.Data.Rat.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.inv_intCast_den_of_pos", "kind": "theorem", "module": "Mathlib.Data.Rat.Lemmas", "is_tactic_proof": true, "tactics": ["simp", "grind"], "tactic_count": 2}
{"name": "Rat.inv_natCast_den_of_pos", "kind": "theorem", "module": "Mathlib.Data.Rat.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "rwa"], "tactic_count": 2}
{"name": "Rat.inv_intCast_num", "kind": "theorem", "module": "Mathlib.Data.Rat.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Rat.inv_natCast_num", "kind": "theorem", "module": "Mathlib.Data.Rat.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Rat.inv_ofNat_num", "kind": "theorem", "module": "Mathlib.Data.Rat.Lemmas", "is_tactic_proof": true, "tactics": ["have", "simp", "change", "lia"], "tactic_count": 4}
{"name": "Rat.inv_intCast_den", "kind": "theorem", "module": "Mathlib.Data.Rat.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Rat.inv_natCast_den", "kind": "theorem", "module": "Mathlib.Data.Rat.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Rat.inv_ofNat_den", "kind": "theorem", "module": "Mathlib.Data.Rat.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Rat.den_inv_of_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Rat.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Rat.forall", "kind": "theorem", "module": "Mathlib.Data.Rat.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.exists", "kind": "theorem", "module": "Mathlib.Data.Rat.Lemmas", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Rat.pnatDen", "kind": "definition", "module": "Mathlib.Data.Rat.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.coe_pnatDen", "kind": "theorem", "module": "Mathlib.Data.Rat.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.pnatDen_eq_iff_den_eq", "kind": "theorem", "module": "Mathlib.Data.Rat.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.pnatDen_one", "kind": "theorem", "module": "Mathlib.Data.Rat.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.pnatDen_zero", "kind": "theorem", "module": "Mathlib.Data.Rat.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.ratSqrt", "kind": "definition", "module": "Mathlib.Data.Rat.NatSqrt.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.ratSqrt_nonneg", "kind": "theorem", "module": "Mathlib.Data.Rat.NatSqrt.Defs", "is_tactic_proof": true, "tactics": ["unfold", "positivity"], "tactic_count": 2}
{"name": "Nat.ratSqrt_sq_le", "kind": "theorem", "module": "Mathlib.Data.Rat.NatSqrt.Defs", "is_tactic_proof": true, "tactics": ["unfold", "rw", "norm_cast", "exact"], "tactic_count": 4}
{"name": "Nat.lt_ratSqrt_add_inv_prec_sq", "kind": "theorem", "module": "Mathlib.Data.Rat.NatSqrt.Defs", "is_tactic_proof": true, "tactics": ["unfold", "rw", "rw", "rw", "norm_cast", "exact", "all_goals"], "tactic_count": 7}
{"name": "Nat.ratSqrt_le_realSqrt", "kind": "theorem", "module": "Mathlib.Data.Rat.NatSqrt.Real", "is_tactic_proof": true, "tactics": ["have", "have", "have", "rwa", "simpa"], "tactic_count": 5}
{"name": "Nat.realSqrt_lt_ratSqrt_add_inv_prec", "kind": "theorem", "module": "Mathlib.Data.Rat.NatSqrt.Real", "is_tactic_proof": true, "tactics": ["have", "have", "have", "rw", "push_cast", "exact", "push_cast", "exact"], "tactic_count": 8}
{"name": "Nat.realSqrt_mem_Ico", "kind": "theorem", "module": "Mathlib.Data.Rat.NatSqrt.Real", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Nat.ratSqrt_mem_Ioc", "kind": "theorem", "module": "Mathlib.Data.Rat.NatSqrt.Real", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Rat.sqrt", "kind": "definition", "module": "Mathlib.Data.Rat.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.sqrt_eq", "kind": "theorem", "module": "Mathlib.Data.Rat.Sqrt", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Rat.exists_mul_self", "kind": "theorem", "module": "Mathlib.Data.Rat.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.sqrt_nonneg", "kind": "theorem", "module": "Mathlib.Data.Rat.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.instDecidablePredIsSquare", "kind": "instance", "module": "Mathlib.Data.Rat.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.sqrt_intCast", "kind": "theorem", "module": "Mathlib.Data.Rat.Sqrt", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Rat.sqrt_natCast", "kind": "theorem", "module": "Mathlib.Data.Rat.Sqrt", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Rat.sqrt_ofNat", "kind": "theorem", "module": "Mathlib.Data.Rat.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.addSubmonoid_closure_range_pow", "kind": "theorem", "module": "Mathlib.Data.Rat.Star", "is_tactic_proof": true, "tactics": ["refine", "suffices", "rw", "exact", "rw", "push_cast", "rw", "num_div_den]", "all_goals"], "tactic_count": 9}
{"name": "NNRat.addSubmonoid_closure_range_mul_self", "kind": "theorem", "module": "Mathlib.Data.Rat.Star", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "NNRat.instStarOrderedRing", "kind": "instance", "module": "Mathlib.Data.Rat.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.addSubmonoid_closure_range_pow", "kind": "theorem", "module": "Mathlib.Data.Rat.Star", "is_tactic_proof": true, "tactics": ["convert", "have", "simp", "ext", "simp"], "tactic_count": 5}
{"name": "Rat.addSubmonoid_closure_range_mul_self", "kind": "theorem", "module": "Mathlib.Data.Rat.Star", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Rat.instStarOrderedRing", "kind": "instance", "module": "Mathlib.Data.Rat.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.instArchimedean", "kind": "instance", "module": "Mathlib.Data.Real.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.instFloorRing", "kind": "instance", "module": "Mathlib.Data.Real.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.isCauSeq_iff_lift", "kind": "theorem", "module": "Mathlib.Data.Real.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.of_near", "kind": "theorem", "module": "Mathlib.Data.Real.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.exists_floor", "kind": "theorem", "module": "Mathlib.Data.Real.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.exists_isLUB", "kind": "theorem", "module": "Mathlib.Data.Real.Archimedean", "is_tactic_proof": true, "tactics": ["rcases", "have", "obtain", "refine", "rcases", "refine", "push_cast", "exact", "choose", "have", "let", "have", "intro", "have", "simp", "rwa", "exact", "have", "intro", "suffices", "refine", "rw", "exact", "intro", "replace", "replace", "have", "have", "rcases", "refine", "simpa", "let", "refine", "refine", "obtain", "refine", "replace", "replace", "have", "refine", "rwa", "exact", "mk_le_of_forall_le", "let", "le_trans"], "tactic_count": 45}
{"name": "Real.exists_isGLB", "kind": "theorem", "module": "Mathlib.Data.Real.Archimedean", "is_tactic_proof": true, "tactics": ["have", "have", "use", "rw", "exact"], "tactic_count": 5}
{"name": "Real.instSupSet", "kind": "instance", "module": "Mathlib.Data.Real.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sSup_def", "kind": "theorem", "module": "Mathlib.Data.Real.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.isLUB_sSup", "kind": "theorem", "module": "Mathlib.Data.Real.Archimedean", "is_tactic_proof": true, "tactics": ["simp", "apply"], "tactic_count": 2}
{"name": "Real.instInfSet", "kind": "instance", "module": "Mathlib.Data.Real.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sInf_def", "kind": "theorem", "module": "Mathlib.Data.Real.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.isGLB_sInf", "kind": "theorem", "module": "Mathlib.Data.Real.Archimedean", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Real.instConditionallyCompleteLinearOrder", "kind": "instance", "module": "Mathlib.Data.Real.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.lt_sInf_add_pos", "kind": "theorem", "module": "Mathlib.Data.Real.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.add_neg_lt_sSup", "kind": "theorem", "module": "Mathlib.Data.Real.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sInf_le_iff", "kind": "theorem", "module": "Mathlib.Data.Real.Archimedean", "is_tactic_proof": true, "tactics": ["rw", "constructor", "exact", "rcases", "exact"], "tactic_count": 5}
{"name": "Real.le_sSup_iff", "kind": "theorem", "module": "Mathlib.Data.Real.Archimedean", "is_tactic_proof": true, "tactics": ["rw", "refine", "exact", "rcases", "exact"], "tactic_count": 5}
{"name": "Real.sSup_empty", "kind": "theorem", "module": "Mathlib.Data.Real.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sInf_univ", "kind": "theorem", "module": "Mathlib.Data.Real.Archimedean", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.iSup_of_isEmpty", "kind": "theorem", "module": "Mathlib.Data.Real.Archimedean", "is_tactic_proof": true, "tactics": ["dsimp", "convert", "rw", "infer_instance"], "tactic_count": 4}
{"name": "Real.iSup_const_zero", "kind": "theorem", "module": "Mathlib.Data.Real.Archimedean", "is_tactic_proof": true, "tactics": ["cases", "exact", "exact"], "tactic_count": 3}
{"name": "Real.sSup_of_not_bddAbove", "kind": "theorem", "module": "Mathlib.Data.Real.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.iSup_of_not_bddAbove", "kind": "theorem", "module": "Mathlib.Data.Real.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sSup_univ", "kind": "theorem", "module": "Mathlib.Data.Real.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sInf_empty", "kind": "theorem", "module": "Mathlib.Data.Real.Archimedean", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.iInf_of_isEmpty", "kind": "theorem", "module": "Mathlib.Data.Real.Archimedean", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.iInf_const_zero", "kind": "theorem", "module": "Mathlib.Data.Real.Archimedean", "is_tactic_proof": true, "tactics": ["cases", "exact", "exact"], "tactic_count": 3}
{"name": "Real.sInf_of_not_bddBelow", "kind": "theorem", "module": "Mathlib.Data.Real.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.iInf_of_not_bddBelow", "kind": "theorem", "module": "Mathlib.Data.Real.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sSup_neg", "kind": "theorem", "module": "Mathlib.Data.Real.Archimedean", "is_tactic_proof": true, "tactics": ["obtain", "by_cases", "rw", "rw", "neg_zero]"], "tactic_count": 5}
{"name": "Real.sInf_neg", "kind": "theorem", "module": "Mathlib.Data.Real.Archimedean", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.sSup_le", "kind": "theorem", "module": "Mathlib.Data.Real.Archimedean", "is_tactic_proof": true, "tactics": ["obtain", "exacts"], "tactic_count": 2}
{"name": "Real.iSup_le", "kind": "theorem", "module": "Mathlib.Data.Real.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.le_sInf", "kind": "theorem", "module": "Mathlib.Data.Real.Archimedean", "is_tactic_proof": true, "tactics": ["obtain", "exacts"], "tactic_count": 2}
{"name": "Real.le_iInf", "kind": "theorem", "module": "Mathlib.Data.Real.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sSup_nonpos", "kind": "theorem", "module": "Mathlib.Data.Real.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.iSup_nonpos", "kind": "theorem", "module": "Mathlib.Data.Real.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sInf_nonneg", "kind": "theorem", "module": "Mathlib.Data.Real.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.iInf_nonneg", "kind": "theorem", "module": "Mathlib.Data.Real.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sSup_nonneg'", "kind": "theorem", "module": "Mathlib.Data.Real.Archimedean", "is_tactic_proof": true, "tactics": ["classical", "obtain", "exact"], "tactic_count": 3}
{"name": "Real.iSup_nonneg'", "kind": "theorem", "module": "Mathlib.Data.Real.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sInf_nonpos'", "kind": "theorem", "module": "Mathlib.Data.Real.Archimedean", "is_tactic_proof": true, "tactics": ["classical", "obtain", "exact"], "tactic_count": 3}
{"name": "Real.iInf_nonpos'", "kind": "theorem", "module": "Mathlib.Data.Real.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sSup_nonneg", "kind": "theorem", "module": "Mathlib.Data.Real.Archimedean", "is_tactic_proof": true, "tactics": ["obtain", "exact", "exact"], "tactic_count": 3}
{"name": "Real.iSup_nonneg", "kind": "theorem", "module": "Mathlib.Data.Real.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sInf_nonpos", "kind": "theorem", "module": "Mathlib.Data.Real.Archimedean", "is_tactic_proof": true, "tactics": ["obtain", "exact", "exact"], "tactic_count": 3}
{"name": "Real.iInf_nonpos", "kind": "theorem", "module": "Mathlib.Data.Real.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sInf_le_sSup", "kind": "theorem", "module": "Mathlib.Data.Real.Archimedean", "is_tactic_proof": true, "tactics": ["rcases", "rw", "exact"], "tactic_count": 3}
{"name": "Real.cauSeq_converges", "kind": "theorem", "module": "Mathlib.Data.Real.Archimedean", "is_tactic_proof": true, "tactics": ["let", "have", "have", "have", "refine", "rcases", "refine", "refine", "rw", "exact", "rcases", "refine", "refine", "rw", "exact"], "tactic_count": 15}
{"name": "Real.instIsCompleteAbs", "kind": "instance", "module": "Mathlib.Data.Real.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.iInf_Ioi_eq_iInf_rat_gt", "kind": "theorem", "module": "Mathlib.Data.Real.Archimedean", "is_tactic_proof": true, "tactics": ["refine", "have", "obtain", "exact", "refine", "obtain", "refine", "exact_mod_cast", "refine", "have", "rw", "obtain", "refine", "refine", "rintro", "suffices", "exact", "exact", "refine", "norm_cast"], "tactic_count": 20}
{"name": "Real.not_bddAbove_coe", "kind": "theorem", "module": "Mathlib.Data.Real.Archimedean", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "ext", "simpa"], "tactic_count": 4}
{"name": "Real.not_bddBelow_coe", "kind": "theorem", "module": "Mathlib.Data.Real.Archimedean", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "ext", "simpa"], "tactic_count": 4}
{"name": "Real.iUnion_Iic_rat", "kind": "theorem", "module": "Mathlib.Data.Real.Archimedean", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "Real.iInter_Iic_rat", "kind": "theorem", "module": "Mathlib.Data.Real.Archimedean", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "Real.exists_natCast_add_one_lt_pow_of_one_lt", "kind": "theorem", "module": "Mathlib.Data.Real.Archimedean", "is_tactic_proof": false, "tactics": ["obtain", "contrapose", "refine", "intro", "refine", "rw", "norm_cast", "rw", "rw", "norm_cast", "lia", "use", "calc"], "tactic_count": 13}
{"name": "Real.exists_nat_pos_inv_lt", "kind": "theorem", "module": "Mathlib.Data.Real.Archimedean", "is_tactic_proof": true, "tactics": ["refine", "have", "refine", "rwa"], "tactic_count": 4}
{"name": "termℝ", "kind": "definition", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Data_Real_Basic___macroRules_termℝ_1", "kind": "definition", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Data_Real_Basic___unexpand_Real_1", "kind": "definition", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauSeq.Completion.ofRat_rat", "kind": "theorem", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.ext_cauchy_iff", "kind": "theorem", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.ext_cauchy", "kind": "theorem", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.equivCauchy", "kind": "definition", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.definition._@.Mathlib.Data.Real.Basic.1850581184._hygCtx._hyg.8", "kind": "definition", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.wrapped._@.Mathlib.Data.Real.Basic.1850581184._hygCtx._hyg.8", "kind": "opaque", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.Real.Basic.0.Real.zero", "kind": "definition", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.Real.Basic.0.Real.zero_def", "kind": "theorem", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": true, "tactics": ["intros", "delta", "rw", "rfl"], "tactic_count": 4}
{"name": "Real.definition._@.Mathlib.Data.Real.Basic.1279875089._hygCtx._hyg.8", "kind": "definition", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.wrapped._@.Mathlib.Data.Real.Basic.1279875089._hygCtx._hyg.8", "kind": "opaque", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.Real.Basic.0.Real.one", "kind": "definition", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.Real.Basic.0.Real.one_def", "kind": "theorem", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": true, "tactics": ["intros", "delta", "rw", "rfl"], "tactic_count": 4}
{"name": "Real.definition._@.Mathlib.Data.Real.Basic.1138242547._hygCtx._hyg.8", "kind": "definition", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.wrapped._@.Mathlib.Data.Real.Basic.1138242547._hygCtx._hyg.8", "kind": "opaque", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.Real.Basic.0.Real.add", "kind": "definition", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.Real.Basic.0.Real.add_def", "kind": "theorem", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": true, "tactics": ["intros", "delta", "rw", "rfl"], "tactic_count": 4}
{"name": "Real.definition._@.Mathlib.Data.Real.Basic.2451848184._hygCtx._hyg.8", "kind": "definition", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.wrapped._@.Mathlib.Data.Real.Basic.2451848184._hygCtx._hyg.8", "kind": "opaque", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.Real.Basic.0.Real.neg", "kind": "definition", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.Real.Basic.0.Real.neg_def", "kind": "theorem", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": true, "tactics": ["intros", "delta", "rw", "rfl"], "tactic_count": 4}
{"name": "Real.definition._@.Mathlib.Data.Real.Basic.4214226450._hygCtx._hyg.8", "kind": "definition", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.wrapped._@.Mathlib.Data.Real.Basic.4214226450._hygCtx._hyg.8", "kind": "opaque", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.Real.Basic.0.Real.mul", "kind": "definition", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.Real.Basic.0.Real.mul_def", "kind": "theorem", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": true, "tactics": ["intros", "delta", "rw", "rfl"], "tactic_count": 4}
{"name": "Real.definition._@.Mathlib.Data.Real.Basic.4277896327._hygCtx._hyg.8", "kind": "definition", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.wrapped._@.Mathlib.Data.Real.Basic.4277896327._hygCtx._hyg.8", "kind": "opaque", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.Real.Basic.0.Real.inv'", "kind": "definition", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.Real.Basic.0.Real.inv'_def", "kind": "theorem", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": true, "tactics": ["intros", "delta", "rw", "rfl"], "tactic_count": 4}
{"name": "Real.instZero", "kind": "instance", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.instOne", "kind": "instance", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.instAdd", "kind": "instance", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.instNeg", "kind": "instance", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.instMul", "kind": "instance", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.instSub", "kind": "instance", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.instInv", "kind": "instance", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.ofCauchy_zero", "kind": "theorem", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.ofCauchy_one", "kind": "theorem", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.ofCauchy_add", "kind": "theorem", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.ofCauchy_neg", "kind": "theorem", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.ofCauchy_sub", "kind": "theorem", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Real.ofCauchy_mul", "kind": "theorem", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.ofCauchy_inv", "kind": "theorem", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cauchy_zero", "kind": "theorem", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cauchy_one", "kind": "theorem", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cauchy_add", "kind": "theorem", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cauchy_neg", "kind": "theorem", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cauchy_mul", "kind": "theorem", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cauchy_sub", "kind": "theorem", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cauchy_inv", "kind": "theorem", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.instNatCast", "kind": "instance", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.instIntCast", "kind": "instance", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.instNNRatCast", "kind": "instance", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.instRatCast", "kind": "instance", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.ofCauchy_natCast", "kind": "theorem", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.ofCauchy_intCast", "kind": "theorem", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.ofCauchy_nnratCast", "kind": "theorem", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.ofCauchy_ratCast", "kind": "theorem", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cauchy_natCast", "kind": "theorem", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cauchy_intCast", "kind": "theorem", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cauchy_nnratCast", "kind": "theorem", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cauchy_ratCast", "kind": "theorem", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.commRing", "kind": "instance", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.ringEquivCauchy", "kind": "definition", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.instRing", "kind": "instance", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Real.instCommSemiring", "kind": "instance", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Real.semiring", "kind": "instance", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Real.instCommMonoidWithZero", "kind": "instance", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Real.instMonoidWithZero", "kind": "instance", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Real.instAddCommGroup", "kind": "instance", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Real.instAddGroup", "kind": "instance", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Real.instAddCommMonoid", "kind": "instance", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Real.instAddMonoid", "kind": "instance", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Real.instAddLeftCancelSemigroup", "kind": "instance", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Real.instAddRightCancelSemigroup", "kind": "instance", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Real.instAddCommSemigroup", "kind": "instance", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Real.instAddSemigroup", "kind": "instance", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Real.instCommMonoid", "kind": "instance", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Real.instMonoid", "kind": "instance", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Real.instCommSemigroup", "kind": "instance", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Real.instSemigroup", "kind": "instance", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Real.instInhabited", "kind": "instance", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.mk", "kind": "definition", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.mk_eq", "kind": "theorem", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.definition._@.Mathlib.Data.Real.Basic.1175651576._hygCtx._hyg.8", "kind": "definition", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.wrapped._@.Mathlib.Data.Real.Basic.1175651576._hygCtx._hyg.8", "kind": "opaque", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.Real.Basic.0.Real.lt", "kind": "definition", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.Real.Basic.0.Real.lt_def", "kind": "theorem", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": true, "tactics": ["intros", "delta", "rw", "rfl"], "tactic_count": 4}
{"name": "Real.instLT", "kind": "instance", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.lt_cauchy", "kind": "theorem", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.mk_lt", "kind": "theorem", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.mk_zero", "kind": "theorem", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.mk_one", "kind": "theorem", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.mk_add", "kind": "theorem", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.mk_mul", "kind": "theorem", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.mk_neg", "kind": "theorem", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.mk_pos", "kind": "theorem", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Real.mk_const", "kind": "theorem", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.definition._@.Mathlib.Data.Real.Basic.702802587._hygCtx._hyg.8", "kind": "definition", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.wrapped._@.Mathlib.Data.Real.Basic.702802587._hygCtx._hyg.8", "kind": "opaque", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.Real.Basic.0.Real.le", "kind": "definition", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.Real.Basic.0.Real.le_def", "kind": "theorem", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": true, "tactics": ["intros", "delta", "rw", "rfl"], "tactic_count": 4}
{"name": "Real.instLE", "kind": "instance", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.Real.Basic.0.Real.le_def'", "kind": "theorem", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.mk_le", "kind": "theorem", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.ind_mk", "kind": "theorem", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": true, "tactics": ["obtain", "induction", "exact"], "tactic_count": 3}
{"name": "Real.partialOrder", "kind": "instance", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.instPreorder", "kind": "instance", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Real.ratCast_lt", "kind": "theorem", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Real.zero_lt_one", "kind": "theorem", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "Real.instNontrivial", "kind": "instance", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.instZeroLEOneClass", "kind": "instance", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.instIsOrderedAddMonoid", "kind": "instance", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.instIsStrictOrderedRing", "kind": "instance", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.instIsOrderedRing", "kind": "instance", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.instIsOrderedCancelAddMonoid", "kind": "instance", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.definition._@.Mathlib.Data.Real.Basic.3793047190._hygCtx._hyg.8", "kind": "definition", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.wrapped._@.Mathlib.Data.Real.Basic.3793047190._hygCtx._hyg.8", "kind": "opaque", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.Real.Basic.0.Real.sup", "kind": "definition", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.Real.Basic.0.Real.sup_def", "kind": "theorem", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": true, "tactics": ["intros", "delta", "rw", "rfl"], "tactic_count": 4}
{"name": "Real.instMax", "kind": "instance", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.ofCauchy_sup", "kind": "theorem", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.mk_sup", "kind": "theorem", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.definition._@.Mathlib.Data.Real.Basic.1934218611._hygCtx._hyg.8", "kind": "definition", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.wrapped._@.Mathlib.Data.Real.Basic.1934218611._hygCtx._hyg.8", "kind": "opaque", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.Real.Basic.0.Real.inf", "kind": "definition", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.Real.Basic.0.Real.inf_def", "kind": "theorem", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": true, "tactics": ["intros", "delta", "rw", "rfl"], "tactic_count": 4}
{"name": "Real.instMin", "kind": "instance", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.ofCauchy_inf", "kind": "theorem", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.mk_inf", "kind": "theorem", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.instDistribLattice", "kind": "instance", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.lattice", "kind": "instance", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.instSemilatticeInf", "kind": "instance", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.instSemilatticeSup", "kind": "instance", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.leTotal_R", "kind": "instance", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.linearOrder", "kind": "instance", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.instIsDomain", "kind": "instance", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.instDivInvMonoid", "kind": "instance", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.ofCauchy_div", "kind": "theorem", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Real.instField", "kind": "instance", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.instDivisionRing", "kind": "instance", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Real.decidableLT", "kind": "instance", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Real.decidableLE", "kind": "instance", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Real.decidableEq", "kind": "instance", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Real.instRepr", "kind": "instance", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.le_mk_of_forall_le", "kind": "theorem", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": true, "tactics": ["intro", "induction", "apply", "rw", "rintro", "obtain", "apply", "rw", "refine", "have", "rwa"], "tactic_count": 11}
{"name": "Real.mk_le_of_forall_le", "kind": "theorem", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact"], "tactic_count": 3}
{"name": "Real.mk_near_of_forall_near", "kind": "theorem", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.mul_add_one_le_add_one_pow", "kind": "theorem", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simp", "clear", "induction", "zero", "succ", "calc", "a", "gcongr", "norm_num", "exact"], "tactic_count": 11}
{"name": "IsPowMul", "kind": "definition", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPowMul.map_one_le_one", "kind": "theorem", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": true, "tactics": ["have", "rcases", "exact"], "tactic_count": 3}
{"name": "RingHom.IsBoundedWrt", "kind": "definition", "module": "Mathlib.Data.Real.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instConditionallyCompleteLinearOrderedFieldReal", "kind": "instance", "module": "Mathlib.Data.Real.CompleteField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.RingHom.unique", "kind": "instance", "module": "Mathlib.Data.Real.CompleteField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.ringHom_apply", "kind": "theorem", "module": "Mathlib.Data.Real.CompleteField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.HolderConjugate", "kind": "abbrev", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.conjExponent", "kind": "definition", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.HolderTriple.of_pos", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.HolderTriple.symm", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.HolderTriple.pos", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.HolderTriple.nonneg", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.HolderTriple.ne_zero", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.HolderTriple.inv_pos", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.HolderTriple.inv_nonneg", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.HolderTriple.inv_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.HolderTriple.one_div_pos", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.HolderTriple.one_div_nonneg", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.HolderTriple.one_div_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.HolderTriple.pos'", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.HolderTriple.nonneg'", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.HolderTriple.ne_zero'", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.HolderTriple.inv_pos'", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.HolderTriple.inv_nonneg'", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.HolderTriple.inv_ne_zero'", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.HolderTriple.one_div_pos'", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.HolderTriple.one_div_nonneg'", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.HolderTriple.one_div_ne_zero'", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.HolderTriple.inv_eq", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.HolderTriple.one_div_add_one_div", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.HolderTriple.one_div_eq", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.HolderTriple.inv_inv_add_inv", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.HolderTriple.inv_lt_inv", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.HolderTriple.lt", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.HolderTriple.inv_sub_inv_eq_inv", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.HolderTriple.holderConjugate_div_div", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.HolderConjugate.two_two", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.HolderConjugate.symm", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.HolderConjugate.inv_add_inv_eq_one", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.HolderConjugate.sub_one_pos", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.HolderConjugate.sub_one_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.HolderConjugate.conjugate_eq", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.HolderConjugate.conjExponent_eq", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.HolderConjugate.one_sub_inv", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.HolderConjugate.inv_sub_one", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.HolderConjugate.sub_one_mul_conj", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.HolderConjugate.mul_eq_add", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.HolderConjugate.div_conj_eq_sub_one", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": true, "tactics": ["field_simp", "linear_combination"], "tactic_count": 2}
{"name": "Real.HolderConjugate.inv_add_inv_ennreal", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.holderConjugate_iff", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": true, "tactics": ["refine", "rintro", "have", "refine", "rw", "exact"], "tactic_count": 6}
{"name": "Real.HolderConjugate.inv_inv", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.HolderConjugate.inv_one_sub_inv", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.HolderConjugate.one_sub_inv_inv", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.holderConjugate_comm", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.holderConjugate_iff_eq_conjExponent", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.HolderConjugate.conjExponent", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.holderConjugate_one_div", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "NNReal.HolderConjugate", "kind": "abbrev", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.conjExponent", "kind": "definition", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.holderTriple_coe_iff", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": true, "tactics": ["rw_mod_cast"], "tactic_count": 1}
{"name": "NNReal.holderConjugate_coe_iff", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.HolderTriple.of_pos", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.HolderTriple.symm", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.HolderTriple.pos", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.HolderTriple.nonneg", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.HolderTriple.ne_zero", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.HolderTriple.inv_pos", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.HolderTriple.inv_nonneg", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.HolderTriple.inv_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.HolderTriple.one_div_pos", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.HolderTriple.one_div_nonneg", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.HolderTriple.one_div_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.HolderTriple.pos'", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.HolderTriple.nonneg'", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.HolderTriple.ne_zero'", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.HolderTriple.inv_pos'", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.HolderTriple.inv_nonneg'", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.HolderTriple.inv_ne_zero'", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.HolderTriple.one_div_pos'", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.HolderTriple.one_div_nonneg'", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.HolderTriple.one_div_ne_zero'", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.HolderTriple.inv_eq", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.HolderTriple.one_div_add_one_div", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": true, "tactics": ["exact_mod_cast"], "tactic_count": 1}
{"name": "NNReal.HolderTriple.one_div_eq", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.HolderTriple.inv_inv_add_inv", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": true, "tactics": ["exact_mod_cast"], "tactic_count": 1}
{"name": "NNReal.HolderTriple.inv_lt_inv", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.HolderTriple.lt", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.HolderTriple.inv_sub_inv_eq_inv", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": true, "tactics": ["have", "exact_mod_cast"], "tactic_count": 2}
{"name": "NNReal.HolderTriple.holderConjugate_div_div", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.HolderConjugate.two_two", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.HolderConjugate.symm", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.HolderConjugate.inv_add_inv_eq_one", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.HolderConjugate.sub_one_pos", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.HolderConjugate.sub_one_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.HolderConjugate.conjugate_eq", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": true, "tactics": ["have", "exact_mod_cast"], "tactic_count": 2}
{"name": "NNReal.HolderConjugate.conjExponent_eq", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.HolderConjugate.one_sub_inv", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.HolderConjugate.sub_one_mul_conj", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.HolderConjugate.mul_eq_add", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "NNReal.HolderConjugate.div_conj_eq_sub_one", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": true, "tactics": ["field_simp", "linear_combination"], "tactic_count": 2}
{"name": "NNReal.HolderConjugate.inv_add_inv_ennreal", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": true, "tactics": ["norm_cast"], "tactic_count": 1}
{"name": "NNReal.holderConjugate_iff", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": true, "tactics": ["rw", "exact_mod_cast"], "tactic_count": 2}
{"name": "NNReal.HolderConjugate.inv_inv", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.HolderConjugate.inv_one_sub_inv", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.HolderConjugate.one_sub_inv_inv", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.holderConjugate_comm", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.holderConjugate_iff_eq_conjExponent", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": ["rw", "exact_mod_cast"], "tactic_count": 2}
{"name": "NNReal.HolderConjugate.conjExponent", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.holderConjugate_one_div", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.HolderTriple.toNNReal", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.HolderConjugate.toNNReal", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ENNReal.conjExponent", "kind": "definition", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.coe_conjExponent", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": true, "tactics": ["rw", "norm_cast", "rw", "norm_cast", "field_simp", "rw"], "tactic_count": 6}
{"name": "ENNReal.holderTriple_coe_iff", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": true, "tactics": ["refine", "rw", "obtain", "constructor", "all_goals", "rintro", "apply", "exact_mod_cast", "exact", "rw", "have", "have", "exact_mod_cast"], "tactic_count": 13}
{"name": "ENNReal.holderConjugate_coe_iff", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.HolderTriple.ennrealOfReal", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": true, "tactics": ["simpa", "congr"], "tactic_count": 2}
{"name": "Real.HolderConjugate.ennrealOfReal", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ENNReal.HolderTriple.of_toReal", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": true, "tactics": ["have", "have", "have", "rw", "simpa"], "tactic_count": 5}
{"name": "ENNReal.HolderTriple.toReal_iff", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": true, "tactics": ["refine", "rw", "simpa"], "tactic_count": 3}
{"name": "ENNReal.HolderTriple.toReal", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.HolderTriple.of_toNNReal", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.HolderTriple.toNNReal_iff", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": true, "tactics": ["simp_rw", "apply", "all_goals"], "tactic_count": 3}
{"name": "ENNReal.HolderTriple.toNNReal", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.HolderConjugate.of_toReal", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ENNReal.HolderConjugate.toReal_iff", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": true, "tactics": ["refine", "have", "rw", "refine", "contrapose", "exact", "simpa"], "tactic_count": 7}
{"name": "ENNReal.HolderConjugate.toReal", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.HolderConjugate.of_toNNReal", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.HolderConjugate.toNNReal_iff", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": true, "tactics": ["simp_rw", "apply", "all_goals"], "tactic_count": 3}
{"name": "ENNReal.HolderConjugate.toNNReal", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.HolderConjugate.conjExponent", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": true, "tactics": ["have", "rw", "refine", "rw", "obtain", "simp", "obtain", "simp", "calc", "rw", "rw", "simp"], "tactic_count": 12}
{"name": "ENNReal.HolderConjugate.instConjExponentOfFactLeOfNat", "kind": "instance", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.HolderConjugate.conjExponent_eq", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.HolderConjugate.conj_eq", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.HolderConjugate.mul_eq_add", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": true, "tactics": ["obtain", "simp", "obtain", "simp", "simpa"], "tactic_count": 5}
{"name": "ENNReal.HolderConjugate.div_conj_eq_sub_one", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "simp", "refine", "rw"], "tactic_count": 5}
{"name": "ENNReal.HolderConjugate.inv_inv", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.HolderConjugate.inv_one_sub_inv", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.HolderConjugate.inv_one_sub_inv'", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ENNReal.HolderConjugate.one_sub_inv_inv", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.HolderConjugate.top_one", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.HolderConjugate.one_top", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.isConjExponent_comm", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.isConjExponent_iff_eq_conjExponent", "kind": "theorem", "module": "Mathlib.Data.Real.ConjExponents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.toENNReal", "kind": "definition", "module": "Mathlib.Data.Real.ENatENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.hasCoeENNReal", "kind": "instance", "module": "Mathlib.Data.Real.ENatENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.map_coe_nnreal", "kind": "theorem", "module": "Mathlib.Data.Real.ENatENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.toENNRealOrderEmbedding", "kind": "definition", "module": "Mathlib.Data.Real.ENatENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.toENNRealRingHom", "kind": "definition", "module": "Mathlib.Data.Real.ENatENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.toENNReal_top", "kind": "theorem", "module": "Mathlib.Data.Real.ENatENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.toENNReal_coe", "kind": "theorem", "module": "Mathlib.Data.Real.ENatENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.toENNReal_ofNat", "kind": "theorem", "module": "Mathlib.Data.Real.ENatENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.toENNReal_inj", "kind": "theorem", "module": "Mathlib.Data.Real.ENatENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.toENNReal_eq_top", "kind": "theorem", "module": "Mathlib.Data.Real.ENatENNReal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENat.toENNReal_ne_top", "kind": "theorem", "module": "Mathlib.Data.Real.ENatENNReal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENat.toENNReal_le", "kind": "theorem", "module": "Mathlib.Data.Real.ENatENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.toENNReal_lt", "kind": "theorem", "module": "Mathlib.Data.Real.ENatENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.toENNReal_lt_top", "kind": "theorem", "module": "Mathlib.Data.Real.ENatENNReal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENat.toENNReal_mono", "kind": "theorem", "module": "Mathlib.Data.Real.ENatENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.toENNReal_strictMono", "kind": "theorem", "module": "Mathlib.Data.Real.ENatENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.toENNReal_zero", "kind": "theorem", "module": "Mathlib.Data.Real.ENatENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.toENNReal_add", "kind": "theorem", "module": "Mathlib.Data.Real.ENatENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.toENNReal_one", "kind": "theorem", "module": "Mathlib.Data.Real.ENatENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.toENNReal_mul", "kind": "theorem", "module": "Mathlib.Data.Real.ENatENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.toENNReal_pow", "kind": "theorem", "module": "Mathlib.Data.Real.ENatENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.toENNReal_min", "kind": "theorem", "module": "Mathlib.Data.Real.ENatENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.toENNReal_max", "kind": "theorem", "module": "Mathlib.Data.Real.ENatENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.toENNReal_sub", "kind": "theorem", "module": "Mathlib.Data.Real.ENatENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_smul_one_lt_iff", "kind": "theorem", "module": "Mathlib.Data.Real.Embedding", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "num_smul_one_lt_den_smul_add", "kind": "theorem", "module": "Mathlib.Data.Real.Embedding", "is_tactic_proof": false, "tactics": ["have", "simpa", "suffices", "refine", "rwa", "rw", "rw", "rw", "exact"], "tactic_count": 9}
{"name": "num_le_nat_mul_den", "kind": "theorem", "module": "Mathlib.Data.Real.Embedding", "is_tactic_proof": true, "tactics": ["refine", "rw", "simpa"], "tactic_count": 3}
{"name": "Archimedean.ratLt", "kind": "abbrev", "module": "Mathlib.Data.Real.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Archimedean.mkRat_mem_ratLt", "kind": "theorem", "module": "Mathlib.Data.Real.Embedding", "is_tactic_proof": true, "tactics": ["rw", "obtain", "conv", "conv", "exact"], "tactic_count": 5}
{"name": "Archimedean.ratLt'", "kind": "abbrev", "module": "Mathlib.Data.Real.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Archimedean.embedRealFun", "kind": "abbrev", "module": "Mathlib.Data.Real.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Archimedean.ratLt_bddAbove", "kind": "theorem", "module": "Mathlib.Data.Real.Embedding", "is_tactic_proof": true, "tactics": ["obtain", "use", "rw", "intro", "rw", "suffices", "intro", "exact"], "tactic_count": 8}
{"name": "Archimedean.ratLt_nonempty", "kind": "theorem", "module": "Mathlib.Data.Real.Embedding", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "use", "suffices", "exact", "exact", "obtain", "use", "simpa"], "tactic_count": 9}
{"name": "Archimedean.ratLt_add", "kind": "theorem", "module": "Mathlib.Data.Real.Embedding", "is_tactic_proof": true, "tactics": ["ext", "rw", "constructor", "such", "and", "intro", "rw", "obtain", "have", "contrapose", "simp", "have", "obtain", "refine", "rw", "simpa", "have", "rw", "rw", "convert", "abel", "have", "lt_of_lt_of_le", "rw", "exact", "rw", "rw", "intro", "rw", "rw", "exact"], "tactic_count": 31}
{"name": "Archimedean.ratLt'_bddAbove", "kind": "theorem", "module": "Mathlib.Data.Real.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Archimedean.ratLt'_nonempty", "kind": "theorem", "module": "Mathlib.Data.Real.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Archimedean.ratLt'_add", "kind": "theorem", "module": "Mathlib.Data.Real.Embedding", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Archimedean.embedRealFun_zero", "kind": "theorem", "module": "Mathlib.Data.Real.Embedding", "is_tactic_proof": true, "tactics": ["apply", "apply", "intro", "unfold", "suffices", "intro", "rw", "exact", "rw", "intro", "rw", "suffices", "intro", "have", "exact", "contrapose", "obtain", "exact"], "tactic_count": 18}
{"name": "Archimedean.embedRealFun_add", "kind": "theorem", "module": "Mathlib.Data.Real.Embedding", "is_tactic_proof": true, "tactics": ["rw", "csSup_add"], "tactic_count": 2}
{"name": "Archimedean.embedRealFun_strictMono", "kind": "theorem", "module": "Mathlib.Data.Real.Embedding", "is_tactic_proof": true, "tactics": ["intro", "have", "have", "apply", "rw", "obtain", "have", "simpa", "exact"], "tactic_count": 9}
{"name": "Archimedean.embedReal", "kind": "definition", "module": "Mathlib.Data.Real.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Archimedean.embedReal_apply", "kind": "theorem", "module": "Mathlib.Data.Real.Embedding", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "Archimedean.embedReal_injective", "kind": "theorem", "module": "Mathlib.Data.Real.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Archimedean.embedReal_one", "kind": "theorem", "module": "Mathlib.Data.Real.Embedding", "is_tactic_proof": true, "tactics": ["rw", "apply", "apply", "suffices", "intro", "suffices", "simpa", "rw", "simp_rw", "suffices", "intro", "have", "h", "contrapose", "obtain", "exact"], "tactic_count": 16}
{"name": "Archimedean.exists_orderAddMonoidHom_real_injective", "kind": "theorem", "module": "Mathlib.Data.Real.Embedding", "is_tactic_proof": true, "tactics": ["cases", "exact", "obtain", "let", "have", "have", "exact"], "tactic_count": 7}
{"name": "Real.sInf_smul_of_nonneg", "kind": "theorem", "module": "Mathlib.Data.Real.Pointwise", "is_tactic_proof": true, "tactics": ["obtain", "rw", "obtain", "rw", "exact", "by_cases", "exact", "rw"], "tactic_count": 8}
{"name": "Real.smul_iInf_of_nonneg", "kind": "theorem", "module": "Mathlib.Data.Real.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sSup_smul_of_nonneg", "kind": "theorem", "module": "Mathlib.Data.Real.Pointwise", "is_tactic_proof": true, "tactics": ["obtain", "rw", "obtain", "rw", "exact", "by_cases", "exact", "rw"], "tactic_count": 8}
{"name": "Real.smul_iSup_of_nonneg", "kind": "theorem", "module": "Mathlib.Data.Real.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sInf_smul_of_nonpos", "kind": "theorem", "module": "Mathlib.Data.Real.Pointwise", "is_tactic_proof": true, "tactics": ["obtain", "rw", "obtain", "rw", "exact", "by_cases", "exact", "rw"], "tactic_count": 8}
{"name": "Real.smul_iSup_of_nonpos", "kind": "theorem", "module": "Mathlib.Data.Real.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sSup_smul_of_nonpos", "kind": "theorem", "module": "Mathlib.Data.Real.Pointwise", "is_tactic_proof": true, "tactics": ["obtain", "rw", "obtain", "rw", "exact", "by_cases", "exact", "rw"], "tactic_count": 8}
{"name": "Real.smul_iInf_of_nonpos", "kind": "theorem", "module": "Mathlib.Data.Real.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.mul_iInf_of_nonneg", "kind": "theorem", "module": "Mathlib.Data.Real.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.mul_iSup_of_nonneg", "kind": "theorem", "module": "Mathlib.Data.Real.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.mul_iInf_of_nonpos", "kind": "theorem", "module": "Mathlib.Data.Real.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.mul_iSup_of_nonpos", "kind": "theorem", "module": "Mathlib.Data.Real.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.iInf_mul_of_nonneg", "kind": "theorem", "module": "Mathlib.Data.Real.Pointwise", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.iSup_mul_of_nonneg", "kind": "theorem", "module": "Mathlib.Data.Real.Pointwise", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.iInf_mul_of_nonpos", "kind": "theorem", "module": "Mathlib.Data.Real.Pointwise", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.iSup_mul_of_nonpos", "kind": "theorem", "module": "Mathlib.Data.Real.Pointwise", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.sign", "kind": "definition", "module": "Mathlib.Data.Real.Sign", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sign_of_neg", "kind": "theorem", "module": "Mathlib.Data.Real.Sign", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.sign_of_pos", "kind": "theorem", "module": "Mathlib.Data.Real.Sign", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.sign_zero", "kind": "theorem", "module": "Mathlib.Data.Real.Sign", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.sign_one", "kind": "theorem", "module": "Mathlib.Data.Real.Sign", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sign_apply_eq", "kind": "theorem", "module": "Mathlib.Data.Real.Sign", "is_tactic_proof": true, "tactics": ["obtain", "exact", "exact", "exact"], "tactic_count": 4}
{"name": "Real.sign_apply_eq_of_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Real.Sign", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sign_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Data.Real.Sign", "is_tactic_proof": true, "tactics": ["refine", "obtain", "rw", "exact", "rfl", "rw", "exact"], "tactic_count": 7}
{"name": "Real.sign_intCast", "kind": "theorem", "module": "Mathlib.Data.Real.Sign", "is_tactic_proof": true, "tactics": ["obtain", "rw", "rw", "rw"], "tactic_count": 4}
{"name": "Real.sign_neg", "kind": "theorem", "module": "Mathlib.Data.Real.Sign", "is_tactic_proof": true, "tactics": ["obtain", "rw", "rw", "rw"], "tactic_count": 4}
{"name": "Real.sign_mul_nonneg", "kind": "theorem", "module": "Mathlib.Data.Real.Sign", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact", "rw", "rw", "exact"], "tactic_count": 6}
{"name": "Real.sign_mul_pos_of_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Real.Sign", "is_tactic_proof": true, "tactics": ["refine", "have", "exact"], "tactic_count": 3}
{"name": "Real.inv_sign", "kind": "theorem", "module": "Mathlib.Data.Real.Sign", "is_tactic_proof": true, "tactics": ["obtain", "rw", "simp", "rw", "exact", "rw", "exact"], "tactic_count": 7}
{"name": "Real.sign_inv", "kind": "theorem", "module": "Mathlib.Data.Real.Sign", "is_tactic_proof": true, "tactics": ["obtain", "rw", "rw", "rw"], "tactic_count": 4}
{"name": "NNReal.sqrt", "kind": "definition", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.sq_sqrt", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.sqrt_sq", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.mul_self_sqrt", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NNReal.sqrt_mul_self", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NNReal.sqrt_le_sqrt", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.sqrt_lt_sqrt", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.sqrt_eq_iff_eq_sq", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.sqrt_le_iff_le_sq", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.le_sqrt_iff_sq_le", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.sqrt_eq_zero", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NNReal.sqrt_eq_one", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NNReal.sqrt_zero", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NNReal.sqrt_one", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NNReal.sqrt_le_one", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NNReal.one_le_sqrt", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NNReal.sqrt_mul", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NNReal.sqrtHom", "kind": "definition", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.sqrt_inv", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.sqrt_div", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.continuous_sqrt", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.sqrt_pos", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NNReal.isSquare", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sqrt", "kind": "definition", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.term√_", "kind": "definition", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real._aux_Mathlib_Data_Real_Sqrt___macroRules_Real_term√__1", "kind": "definition", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real._aux_Mathlib_Data_Real_Sqrt___unexpand_Real_sqrt_1", "kind": "definition", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.coe_sqrt", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.continuous_sqrt", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "Real.map_sqrt_atTop", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["unfold", "simp_rw", "simp"], "tactic_count": 3}
{"name": "Real.comap_sqrt_atTop", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["unfold", "simp_rw", "simp"], "tactic_count": 3}
{"name": "Real.tendsto_sqrt_atTop", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sqrt_eq_zero_of_nonpos", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.sqrt_nonneg", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["unfold", "exact"], "tactic_count": 2}
{"name": "Real.mul_self_sqrt", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.sqrt_mul_self", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sqrt_eq_cases", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "rcases", "exact", "exact", "rintro", "exacts"], "tactic_count": 7}
{"name": "Real.sqrt_eq_iff_mul_self_eq", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sqrt_eq_iff_mul_self_eq_of_pos", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.sqrt_eq_one", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sq_sqrt", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.sqrt_sq", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.sqrt_eq_iff_eq_sq", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.sqrt_mul_self_eq_abs", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.sqrt_sq_eq_abs", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.sqrt_zero", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.sqrt_one", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.sqrt_le_sqrt_iff", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.sqrt_lt_sqrt_iff", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sqrt_lt_sqrt_iff_of_pos", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.sqrt_le_sqrt", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Real.sqrt_monotone", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.strictMonoOn_sqrt", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sqrt_lt_sqrt", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sqrt_le_left", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.sqrt_le_iff", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Real.sqrt_lt", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.sqrt_lt'", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.le_sqrt", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.le_sqrt'", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.abs_le_sqrt", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.sq_le", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["constructor", "simpa", "rw", "exact"], "tactic_count": 4}
{"name": "Real.neg_sqrt_le_of_sq_le", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.le_sqrt_of_sq_le", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sqrt_inj", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.sqrt_eq_zero", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.sqrt_eq_zero'", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.sqrt_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.sqrt_ne_zero'", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.sq_sqrt'", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["rcases", "grind"], "tactic_count": 2}
{"name": "Real._example", "kind": "example", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Real.sqrt_pos", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sqrt_le_sqrt_iff'", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["obtain", "exact", "exact"], "tactic_count": 3}
{"name": "Real.one_le_sqrt", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.sqrt_le_one", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.isSquare_iff", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalNNRealSqrt", "kind": "definition", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalSqrt", "kind": "definition", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.one_lt_sqrt_two", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.sqrt_two_lt_three_halves", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["rw", "grind"], "tactic_count": 2}
{"name": "Real.inv_sqrt_two_sub_one", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Real.sqrt_mul", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Real.sqrt_mul'", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.sqrt_inv", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.sqrt_div", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.sqrt_div'", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.div_sqrt", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Real.sqrt_div_self'", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.sqrt_div_self", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.lt_sqrt", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.sq_lt", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.neg_sqrt_lt_of_sq_lt", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.lt_sqrt_of_sq_lt", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.lt_sq_of_sqrt_lt", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "Real.nat_sqrt_le_real_sqrt", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["rw", "norm_cast", "exact"], "tactic_count": 3}
{"name": "Real.real_sqrt_lt_nat_sqrt_succ", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["rw", "exact", "exact"], "tactic_count": 3}
{"name": "Real.real_sqrt_le_nat_sqrt_succ", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.floor_real_sqrt_eq_nat_sqrt", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Real.nat_floor_real_sqrt_eq_nat_sqrt", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Real.sqrt_one_add_le", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["refine", "calc"], "tactic_count": 2}
{"name": "Real.sqrt_prod", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "Filter.Tendsto.sqrt", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.sqrt", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.sqrt", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.sqrt", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.sqrt", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.sum_mul_le_sqrt_mul_sqrt", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.sum_sqrt_mul_sqrt_le", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.sum_mul_le_sqrt_mul_sqrt", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.sum_sqrt_mul_sqrt_le", "kind": "theorem", "module": "Mathlib.Data.Real.Sqrt", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "instStarRingReal", "kind": "instance", "module": "Mathlib.Data.Real.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instTrivialStarReal", "kind": "instance", "module": "Mathlib.Data.Real.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.instStarOrderedRing", "kind": "instance", "module": "Mathlib.Data.Real.StarOrdered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.instStarOrderedRing", "kind": "instance", "module": "Mathlib.Data.Real.StarOrdered", "is_tactic_proof": true, "tactics": ["refine", "obtain", "refine", "simp", "rintro", "exact"], "tactic_count": 6}
{"name": "SetRel", "kind": "abbrev", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.term_~[_]_", "kind": "definition", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel._aux_Mathlib_Data_Rel___macroRules_SetRel_term_~[_]__1", "kind": "definition", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.inv", "kind": "definition", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.mem_inv", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.inv_inv", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.inv_mono", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.inv_empty", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.inv_univ", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.dom", "kind": "definition", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.cod", "kind": "definition", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.mem_dom", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.mem_cod", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.dom_mono", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.cod_mono", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.dom_empty", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SetRel.cod_empty", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SetRel.dom_eq_empty_iff", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.cod_eq_empty_iff", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.dom_univ", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SetRel.cod_univ", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SetRel.cod_inv", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.dom_inv", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.id", "kind": "definition", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.mem_id", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.inv_id", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SetRel.comp", "kind": "definition", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.term_○_", "kind": "definition", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel._aux_Mathlib_Data_Rel___macroRules_SetRel_term_○__1", "kind": "definition", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel._aux_Mathlib_Data_Rel___unexpand_SetRel_comp_1", "kind": "definition", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.mem_comp", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.prodMk_mem_comp", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.comp_assoc", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SetRel.comp_id", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SetRel.id_comp", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SetRel.inv_comp", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SetRel.comp_empty", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SetRel.empty_comp", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SetRel.comp_univ", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SetRel.univ_comp", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SetRel.comp_iUnion", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SetRel.iUnion_comp", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SetRel.comp_sUnion", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SetRel.sUnion_comp", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SetRel.comp_subset_comp", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.comp_subset_comp_left", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.comp_subset_comp_right", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.relComp", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.prod_comp_prod_of_inter_nonempty", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SetRel.prod_comp_prod_of_disjoint", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.prod_comp_prod", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["split_ifs", "exact", "rw"], "tactic_count": 3}
{"name": "SetRel.image", "kind": "definition", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.preimage", "kind": "definition", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.mem_image", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.mem_preimage", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.image_subset_image", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.image_subset_image_left", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.preimage_subset_preimage", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.preimage_subset_preimage_left", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.image_inv", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.preimage_inv", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.image_mono", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.preimage_mono", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.image_empty_right", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SetRel.preimage_empty_right", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SetRel.image_univ_right", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SetRel.preimage_univ_right", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SetRel.image_inter_subset", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.preimage_inter_subset", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.image_union", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SetRel.image_iUnion", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SetRel.image_sUnion", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SetRel.preimage_union", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SetRel.preimage_iUnion", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SetRel.preimage_sUnion", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SetRel.image_id", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SetRel.preimage_id", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SetRel.image_comp", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SetRel.preimage_comp", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SetRel.image_empty_left", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SetRel.preimage_empty_left", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SetRel.image_univ_left", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SetRel.preimage_univ_left", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SetRel.image_eq_cod_of_dom_subset", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SetRel.preimage_eq_dom_of_cod_subset", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SetRel.image_inter_dom", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SetRel.preimage_inter_cod", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SetRel.inter_dom_subset_preimage_image", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SetRel.inter_cod_subset_image_preimage", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SetRel.image_eq_biUnion", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SetRel.preimage_eq_biUnion", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SetRel.core", "kind": "definition", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.mem_core", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.core_subset_core", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.core_mono", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.core_inter", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SetRel.core_union_subset", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.core_univ", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SetRel.core_id", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SetRel.core_comp", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SetRel.image_subset_iff", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SetRel.image_core_gc", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.restrictDomain", "kind": "definition", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.IsRefl", "kind": "abbrev", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.refl", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.rfl", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.id_subset", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "SetRel.id_subset_iff", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.isRefl_univ", "kind": "instance", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.isRefl_inter", "kind": "instance", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.IsRefl.comp", "kind": "instance", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.IsRefl.sInter", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.isRefl_iInter", "kind": "instance", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.isRefl_preimage", "kind": "instance", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.isRefl_mono", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.left_subset_comp", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "SetRel.right_subset_comp", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "SetRel.subset_iterate_comp", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.self_subset_image", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.self_subset_preimage", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.exists_eq_singleton_of_prod_subset_id", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "simp", "obtain", "simp", "exact"], "tactic_count": 6}
{"name": "SetRel.IsSymm", "kind": "abbrev", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.symm", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.comm", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.inv_eq_self", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "SetRel.inv_eq_self_iff", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.instIsSymmInv", "kind": "instance", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "SetRel.isSymm_empty", "kind": "instance", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.isSymm_univ", "kind": "instance", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.isSymm_inter", "kind": "instance", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.IsSymm.sInter", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.isSymm_iInter", "kind": "instance", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.isSymm_id", "kind": "instance", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.isSymm_preimage", "kind": "instance", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.isSymm_image", "kind": "instance", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.isSymm_comp_inv", "kind": "instance", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.isSymm_inv_comp", "kind": "instance", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.isSymm_comp_self", "kind": "instance", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "SetRel.prod_subset_comm", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SetRel.preimage_eq_image", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SetRel.symmetrize", "kind": "definition", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.isSymm_symmetrize", "kind": "instance", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.symmetrize_subset_self", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.symmetrize_subset_inv", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.subset_symmetrize", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.symmetrize_mono", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.IsTrans", "kind": "abbrev", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.trans", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.instIsTransSetOfProdMatch_1PropOfIsTrans", "kind": "instance", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.comp_subset_self", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.comp_eq_self", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.isTrans_iff_comp_subset_self", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.isTrans_empty", "kind": "instance", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.isTrans_univ", "kind": "instance", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.isTrans_singleton", "kind": "instance", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.isTrans_inter", "kind": "instance", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.IsTrans.sInter", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.isTrans_iInter", "kind": "instance", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.isTrans_id", "kind": "instance", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.isTrans_preimage", "kind": "instance", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.isTrans_symmetrize", "kind": "instance", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.IsIrrefl", "kind": "abbrev", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.irrefl", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.instIsIrreflSetOfProdMatch_1PropOfIrrefl", "kind": "instance", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.IsWellFounded", "kind": "abbrev", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.Hom", "kind": "abbrev", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.graph", "kind": "definition", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.mem_graph", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.graph_injective", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Function.graph_inj", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.graph_id", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Function.graph_comp", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Function.tupleGraph", "kind": "definition", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.graph_inv", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "SetRel.exists_graph_eq_iff", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "simp", "intro", "choose", "refine", "ext", "constructor", "aesop", "exact"], "tactic_count": 10}
{"name": "Set.image_eq", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "Set.preimage_eq", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.preimage_eq_core", "kind": "theorem", "module": "Mathlib.Data.Rel", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Rel", "kind": "abbrev", "module": "Mathlib.Data.Rel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.IsCover", "kind": "definition", "module": "Mathlib.Data.Rel.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.IsCover.empty", "kind": "theorem", "module": "Mathlib.Data.Rel.Cover", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SetRel.isCover_empty_right", "kind": "theorem", "module": "Mathlib.Data.Rel.Cover", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SetRel.IsCover.nonempty", "kind": "theorem", "module": "Mathlib.Data.Rel.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.IsCover.refl", "kind": "theorem", "module": "Mathlib.Data.Rel.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.IsCover.rfl", "kind": "theorem", "module": "Mathlib.Data.Rel.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.isCover_univ", "kind": "theorem", "module": "Mathlib.Data.Rel.Cover", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SetRel.IsCover.mono", "kind": "theorem", "module": "Mathlib.Data.Rel.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.IsCover.anti", "kind": "theorem", "module": "Mathlib.Data.Rel.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.IsCover.mono_entourage", "kind": "theorem", "module": "Mathlib.Data.Rel.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.IsCover.union", "kind": "theorem", "module": "Mathlib.Data.Rel.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.IsCover.of_maximal_isSeparated", "kind": "theorem", "module": "Mathlib.Data.Rel.Cover", "is_tactic_proof": true, "tactics": ["rintro", "by_contra", "simpa", "h", "hN.2"], "tactic_count": 5}
{"name": "SetRel.isCover_id", "kind": "theorem", "module": "Mathlib.Data.Rel.Cover", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SetRel.IsSeparated", "kind": "definition", "module": "Mathlib.Data.Rel.Separated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.IsSeparated.empty", "kind": "theorem", "module": "Mathlib.Data.Rel.Separated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.IsSeparated.singleton", "kind": "theorem", "module": "Mathlib.Data.Rel.Separated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.IsSeparated.of_subsingleton", "kind": "theorem", "module": "Mathlib.Data.Rel.Separated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.IsSeparated.mono_left", "kind": "theorem", "module": "Mathlib.Data.Rel.Separated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.IsSeparated.mono_right", "kind": "theorem", "module": "Mathlib.Data.Rel.Separated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.isSeparated_insert'", "kind": "theorem", "module": "Mathlib.Data.Rel.Separated", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SetRel.isSeparated_insert", "kind": "theorem", "module": "Mathlib.Data.Rel.Separated", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "SetRel.isSeparated_insert_of_notMem", "kind": "theorem", "module": "Mathlib.Data.Rel.Separated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.IsSeparated.insert'", "kind": "theorem", "module": "Mathlib.Data.Rel.Separated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.IsSeparated.insert", "kind": "theorem", "module": "Mathlib.Data.Rel.Separated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "term_×ˢ_", "kind": "definition", "module": "Mathlib.Data.SProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Data_SProd___macroRules_term_×ˢ__1", "kind": "definition", "module": "Mathlib.Data.SProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Data_SProd___unexpand_SProd_sprod_1", "kind": "definition", "module": "Mathlib.Data.SProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Data_SProd___macroRules_term_×ˢ__2", "kind": "definition", "module": "Mathlib.Data.SProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Semiquot.exists_mem", "kind": "theorem", "module": "Mathlib.Data.Semiquot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Semiquot.eq_mk_of_mem", "kind": "theorem", "module": "Mathlib.Data.Semiquot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Semiquot.nonempty", "kind": "theorem", "module": "Mathlib.Data.Semiquot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Semiquot.blur'", "kind": "definition", "module": "Mathlib.Data.Semiquot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Semiquot.blur_eq_blur'", "kind": "theorem", "module": "Mathlib.Data.Semiquot", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "Semiquot.mem_blur'", "kind": "theorem", "module": "Mathlib.Data.Semiquot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Semiquot.liftOn", "kind": "definition", "module": "Mathlib.Data.Semiquot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Semiquot.liftOn_ofMem", "kind": "theorem", "module": "Mathlib.Data.Semiquot", "is_tactic_proof": true, "tactics": ["revert"], "tactic_count": 1}
{"name": "Semiquot.map", "kind": "definition", "module": "Mathlib.Data.Semiquot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Semiquot.instMonad", "kind": "instance", "module": "Mathlib.Data.Semiquot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Semiquot.mem_pure_self", "kind": "theorem", "module": "Mathlib.Data.Semiquot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Semiquot.pure_inj", "kind": "theorem", "module": "Mathlib.Data.Semiquot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Semiquot.instLawfulMonad", "kind": "instance", "module": "Mathlib.Data.Semiquot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Semiquot.instLE", "kind": "instance", "module": "Mathlib.Data.Semiquot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Semiquot.partialOrder", "kind": "instance", "module": "Mathlib.Data.Semiquot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Semiquot.instSemilatticeSup", "kind": "instance", "module": "Mathlib.Data.Semiquot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Semiquot.pure_le", "kind": "theorem", "module": "Mathlib.Data.Semiquot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Semiquot.IsPure", "kind": "definition", "module": "Mathlib.Data.Semiquot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Semiquot.get", "kind": "definition", "module": "Mathlib.Data.Semiquot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Semiquot.get_mem", "kind": "theorem", "module": "Mathlib.Data.Semiquot", "is_tactic_proof": true, "tactics": ["let", "unfold"], "tactic_count": 2}
{"name": "Semiquot.eq_pure", "kind": "theorem", "module": "Mathlib.Data.Semiquot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Semiquot.pure_isPure", "kind": "theorem", "module": "Mathlib.Data.Semiquot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Semiquot.isPure_iff", "kind": "theorem", "module": "Mathlib.Data.Semiquot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Semiquot.IsPure.mono", "kind": "theorem", "module": "Mathlib.Data.Semiquot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Semiquot.IsPure.min", "kind": "theorem", "module": "Mathlib.Data.Semiquot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Semiquot.isPure_of_subsingleton", "kind": "theorem", "module": "Mathlib.Data.Semiquot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Semiquot.univ", "kind": "definition", "module": "Mathlib.Data.Semiquot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Semiquot.instInhabited", "kind": "instance", "module": "Mathlib.Data.Semiquot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Semiquot.mem_univ", "kind": "theorem", "module": "Mathlib.Data.Semiquot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Semiquot.univ_unique", "kind": "theorem", "module": "Mathlib.Data.Semiquot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Semiquot.isPure_univ", "kind": "theorem", "module": "Mathlib.Data.Semiquot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Semiquot.instOrderTopOfInhabited", "kind": "instance", "module": "Mathlib.Data.Semiquot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.length'_of_terminates", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Stream'.Seq.length'_of_not_terminates", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Stream'.Seq.length_nil", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Stream'.Seq.length'_nil", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Stream'.Seq.length_cons", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "Stream'.Seq.length'_cons", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "simp"], "tactic_count": 3}
{"name": "Stream'.Seq.length_eq_zero", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Stream'.Seq.length'_eq_zero_iff_nil", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Stream'.Seq.length'_ne_zero_iff_cons", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Stream'.Seq.length_le_iff'", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["simp", "refine", "rintro", "exact", "intro", "exact"], "tactic_count": 6}
{"name": "Stream'.Seq.length_le_iff", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Stream'.Seq.length'_le_iff", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simpa", "simpa"], "tactic_count": 3}
{"name": "Stream'.Seq.lt_length_iff'", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": false, "tactics": ["simp", "refine", "intro", "exact", "intro", "exact"], "tactic_count": 6}
{"name": "Stream'.Seq.lt_length_iff", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Stream'.Seq.lt_length'_iff", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simpa", "simp", "rw", "rw", "exact"], "tactic_count": 6}
{"name": "Stream'.Seq.ofStream_cons", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "Stream'.Seq.terminatedAt_ofList", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Stream'.Seq.terminates_ofList", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.take_nil", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Stream'.Seq.take_zero", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Stream'.Seq.take_succ_cons", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "Stream'.Seq.getElem?_take", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Stream'.Seq.ofList_toList", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Stream'.Seq.toList_ofList", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.toList_nil", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Stream'.Seq.getLast?_toList", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Stream'.Seq.cons_append", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.nil_append", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["apply", "dsimp", "dsimp", "cases", "trivial", "rw", "dsimp", "exact"], "tactic_count": 8}
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{"name": "Stream'.Seq.mem_append_left", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "Stream'.Seq.ofList_append", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "Stream'.Seq.ofStream_append", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "Stream'.Seq.map_get?", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.map_nil", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Stream'.Seq.map_tail", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.map_comp", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.terminatedAt_map_iff", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Stream'.Seq.terminates_map_iff", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Stream'.Seq.length_map", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["rw", "congr", "ext", "simp"], "tactic_count": 4}
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{"name": "Stream'.Seq.mem_map", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.exists_of_mem_map", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.map_append", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": false, "tactics": ["apply", "intro", "exact", "cases", "cases", "refine", "exact"], "tactic_count": 7}
{"name": "Stream'.Seq.join_nil", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.join_cons_nil", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.join_cons_cons", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.join_cons", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": false, "tactics": ["apply", "eq_of_bisim", "intro", "exact", "s,", "cases", "rw", "exact", "cases", "simp", "simpa"], "tactic_count": 11}
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{"name": "Stream'.Seq.drop_get?", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "simp", "convert", "lia"], "tactic_count": 6}
{"name": "Stream'.Seq.dropn_add", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.dropn_tail", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Stream'.Seq.head_dropn", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Stream'.Seq.drop_zero", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.drop_succ_cons", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Stream'.Seq.drop_nil", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Stream'.Seq.drop_length'", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["cases", "zero", "succ", "cases", "nil", "cons", "simp", "convert", "generalize", "enat_to_nat", "lia"], "tactic_count": 11}
{"name": "Stream'.Seq.take_drop", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["ext", "grind"], "tactic_count": 2}
{"name": "Stream'.Seq.get?_zipWith", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.get?_zip", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.nats_get?", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.get?_enum", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.zipWith_nil_left", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.zipWith_nil_right", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["ext1", "simp"], "tactic_count": 2}
{"name": "Stream'.Seq.zipWith_cons_cons", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["ext1", "cases"], "tactic_count": 2}
{"name": "Stream'.Seq.zip_nil_left", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.zip_nil_right", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.zip_cons_cons", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.enum_nil", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.enum_cons", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp", "simp", "congr"], "tactic_count": 4}
{"name": "Stream'.Seq.zipWith_map", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["ext1", "simp", "cases"], "tactic_count": 3}
{"name": "Stream'.Seq.zipWith_map_left", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "Stream'.Seq.zipWith_map_right", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "Stream'.Seq.zip_map", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["ext1", "simp", "cases"], "tactic_count": 3}
{"name": "Stream'.Seq.zip_map_left", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "Stream'.Seq.zip_map_right", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "Stream'.Seq.fold_nil", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["unfold", "simp"], "tactic_count": 2}
{"name": "Stream'.Seq.fold_cons", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["unfold", "dsimp", "congr", "rw", "simp"], "tactic_count": 5}
{"name": "Stream'.Seq.fold_head", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Stream'.Seq.get?_update", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["simp", "split_ifs", "simp", "rfl"], "tactic_count": 4}
{"name": "Stream'.Seq.update_nil", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["ext1", "simp"], "tactic_count": 2}
{"name": "Stream'.Seq.set_nil", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.update_cons_zero", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["ext1", "cases"], "tactic_count": 2}
{"name": "Stream'.Seq.set_cons_zero", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.update_cons_succ", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["ext1", "cases"], "tactic_count": 2}
{"name": "Stream'.Seq.set_cons_succ", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.get?_set_of_not_terminatedAt", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Stream'.Seq.get?_set_of_terminatedAt", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Stream'.Seq.get?_set_of_ne", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Stream'.Seq.drop_set_of_lt", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["ext1", "simp"], "tactic_count": 2}
{"name": "Stream'.Seq.all_cons", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Stream'.Seq.all_get", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "Stream'.Seq.all_of_get", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["simp", "grind"], "tactic_count": 2}
{"name": "_private.Mathlib.Data.Seq.Basic.0.Stream'.Seq.all_coind_drop_motive", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "simp", "generalize", "cases", "simpa", "exact"], "tactic_count": 8}
{"name": "Stream'.Seq.all_coind", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["apply", "intro", "have", "rw", "generalize", "cases", "nil", "cons"], "tactic_count": 8}
{"name": "Stream'.Seq.map_all_iff", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["refine", "solve_by_elim", "obtain", "rw", "solve_by_elim"], "tactic_count": 5}
{"name": "Stream'.Seq.take_all", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "cases", "nil", "cons", "simp", "rcases", "exacts"], "tactic_count": 9}
{"name": "Stream'.Seq.set_all", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["intro", "simp", "obtain", "rcases", "by_cases", "simp", "simp_all", "rw", "apply"], "tactic_count": 9}
{"name": "Stream'.Seq.Pairwise.nil", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Stream'.Seq.Pairwise.cons", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["simp", "intro", "cases", "zero", "succ", "simp", "cases", "zero", "simp", "exact", "succ"], "tactic_count": 11}
{"name": "Stream'.Seq.Pairwise.cons_elim", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["simp", "refine", "intro", "rw", "obtain", "simpa"], "tactic_count": 6}
{"name": "Stream'.Seq.Pairwise_cons_nil", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "Stream'.Seq.Pairwise_cons_cons_head", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["simp", "simpa"], "tactic_count": 2}
{"name": "Stream'.Seq.Pairwise.cons_cons_of_trans", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["apply", "simp", "exact"], "tactic_count": 3}
{"name": "Stream'.Seq.Pairwise.coind", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["simp", "intro", "obtain", "rw", "rw", "have", "generalize", "cases", "nil", "cons", "simp", "exact"], "tactic_count": 12}
{"name": "Stream'.Seq.Pairwise.coind_trans", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": false, "tactics": ["have", "rw", "have", "exact", "simp", "intro", "obtain", "clear", "induction", "zero", "succ", "obtain", "exact"], "tactic_count": 13}
{"name": "Stream'.Seq.Pairwise_tail", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["cases", "simp", "simp"], "tactic_count": 3}
{"name": "Stream'.Seq.Pairwise_drop", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Stream'.Seq.at_least_as_long_as_coind", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": false, "tactics": ["have", "induction", "zero", "succ", "simp", "generalize", "cases", "nil", "cons", "simp", "obtain", "simpa", "by_cases", "simp", "simp", "by_contra", "have", "intro", "simp", "contradiction", "specialize", "generalize", "cases", "nil", "cons", "obtain", "apply_fun", "simp", "generalize", "enat_to_nat", "lia"], "tactic_count": 31}
{"name": "Stream'.Seq.instFunctor", "kind": "instance", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.instLawfulFunctor", "kind": "instance", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq1.toSeq", "kind": "definition", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq1.coeSeq", "kind": "instance", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq1.map", "kind": "definition", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq1.map_pair", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq1.map_id", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq1.join", "kind": "definition", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq1.join_nil", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq1.join_cons", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["dsimp"], "tactic_count": 1}
{"name": "Stream'.Seq1.ret", "kind": "definition", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq1.instInhabited", "kind": "instance", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq1.bind", "kind": "definition", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq1.join_map_ret", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "Stream'.Seq1.bind_ret", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq1.ret_bind", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["simp", "obtain", "cases"], "tactic_count": 3}
{"name": "Stream'.Seq1.map_join'", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": false, "tactics": ["apply", "intro", "exact", "cases", "cases", "obtain", "simpa", "exact", "refine"], "tactic_count": 9}
{"name": "Stream'.Seq1.map_join", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq1.join_join", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": false, "tactics": ["apply", "intro", "exact", "cases", "cases", "obtain", "simp", "cases", "exact", "refine", "exact", "refine"], "tactic_count": 12}
{"name": "Stream'.Seq1.bind_assoc", "kind": "theorem", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": true, "tactics": ["obtain", "simp", "rw", "simp", "rw", "generalize", "rcases", "induction", "nil", "cons", "induction", "nil", "cons", "obtain", "cases", "obtain"], "tactic_count": 16}
{"name": "Stream'.Seq1.monad", "kind": "instance", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq1.lawfulMonad", "kind": "instance", "module": "Mathlib.Data.Seq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation", "kind": "definition", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.pure", "kind": "definition", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.instCoeTC", "kind": "instance", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.think", "kind": "definition", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.thinkN", "kind": "definition", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.head", "kind": "definition", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.tail", "kind": "definition", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.empty", "kind": "definition", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.instInhabited", "kind": "instance", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.runFor", "kind": "definition", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.destruct", "kind": "definition", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.run", "kind": "definition", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.destruct_eq_pure", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": true, "tactics": ["dsimp", "cases", "contradiction", "apply", "funext", "induction", "zero", "succ"], "tactic_count": 8}
{"name": "Computation.destruct_eq_think", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": true, "tactics": ["dsimp", "rcases", "injection", "rw", "obtain", "apply", "dsimp", "rw", "exact", "contradiction"], "tactic_count": 10}
{"name": "Computation.destruct_pure", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.destruct_think", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.destruct_empty", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.head_pure", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.head_think", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.head_empty", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.tail_pure", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.tail_think", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.tail_empty", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.think_empty", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.recOn", "kind": "definition", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.Corec.f", "kind": "definition", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.corec", "kind": "definition", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": true, "tactics": ["refine", "rw", "change", "revert", "induction", "zero", "change", "rcases", "exact", "unfold", "succ", "rw", "exact"], "tactic_count": 13}
{"name": "Computation.lmap", "kind": "definition", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.rmap", "kind": "definition", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.corec_eq", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "dsimp", "rcases", "dsimp", "apply", "dsimp", "rw", "dsimp"], "tactic_count": 9}
{"name": "_private.Mathlib.Data.Seq.Computation.0.Computation.term_~_", "kind": "definition", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.Seq.Computation.0.Computation._aux_Mathlib_Data_Seq_Computation___macroRules__private_Mathlib_Data_Seq_Computation_0_Computation_term_~__1", "kind": "definition", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.BisimO", "kind": "definition", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.IsBisimulation", "kind": "definition", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.eq_of_bisim", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": true, "tactics": ["apply", "apply", "dsimp", "intro", "r⟩", "suffices", "have", "refine", "constructor", "rw", "rw", "rw", "assumption", "rw", "exact", "rw", "exact", "simp_all", "exact"], "tactic_count": 19}
{"name": "Computation.Mem", "kind": "definition", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.instMembership", "kind": "instance", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.le_stable", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": true, "tactics": ["obtain", "induction", "refl", "step"], "tactic_count": 4}
{"name": "Computation.mem_unique", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.Mem.left_unique", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.terminates_iff", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.terminates_of_mem", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.terminates_def", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.ret_mem", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.eq_of_pure_mem", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.mem_pure_iff", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.ret_terminates", "kind": "instance", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.think_mem", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.think_terminates", "kind": "instance", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.of_think_mem", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.of_think_terminates", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.notMem_empty", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.not_terminates_empty", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.eq_empty_of_not_terminates", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": true, "tactics": ["apply", "rcases", "refine"], "tactic_count": 3}
{"name": "Computation.thinkN_mem", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.thinkN_terminates", "kind": "instance", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.of_thinkN_terminates", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.Promises", "kind": "definition", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.term_~>_", "kind": "definition", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation._aux_Mathlib_Data_Seq_Computation___macroRules_Computation_term_~>__1", "kind": "definition", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation._aux_Mathlib_Data_Seq_Computation___unexpand_Computation_Promises_1", "kind": "definition", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.mem_promises", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.empty_promises", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.length", "kind": "definition", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.get", "kind": "definition", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.get_mem", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.get_eq_of_mem", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.mem_of_get_eq", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": true, "tactics": ["intro"], "tactic_count": 1}
{"name": "Computation.get_think", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.get_thinkN", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.get_promises", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.mem_of_promises", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact"], "tactic_count": 3}
{"name": "Computation.get_eq_of_promises", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.Results", "kind": "definition", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.results_of_terminates", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.results_of_terminates'", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Computation.Results.mem", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.Results.terminates", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.Results.length", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.Results.val_unique", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.Results.len_unique", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": true, "tactics": ["haveI"], "tactic_count": 1}
{"name": "Computation.exists_results_of_mem", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.get_pure", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.length_pure", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.results_pure", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.length_think", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": true, "tactics": ["apply", "exact", "have", "revert", "simp", "apply", "apply", "apply"], "tactic_count": 8}
{"name": "Computation.results_think", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.of_results_think", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": true, "tactics": ["haveI", "have", "exact"], "tactic_count": 3}
{"name": "Computation.results_think_iff", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.results_thinkN", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.results_thinkN_pure", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": true, "tactics": ["have"], "tactic_count": 1}
{"name": "Computation.length_thinkN", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.eq_thinkN", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": ["induction", "zero", "succ", "induction", "pure", "think", "rw", "rfl", "obtain", "cases", "contradiction", "have", "contradiction", "rw", "rfl"], "tactic_count": 15}
{"name": "Computation.eq_thinkN'", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.memRecOn", "kind": "definition", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": true, "tactics": ["haveI", "rw", "generalize", "induction", "zero", "succ"], "tactic_count": 6}
{"name": "Computation.terminatesRecOn", "kind": "definition", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.map", "kind": "definition", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.Bind.g", "kind": "definition", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.Bind.f", "kind": "definition", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.bind", "kind": "definition", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.instBind", "kind": "instance", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.has_bind_eq_bind", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.join", "kind": "definition", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.map_pure", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.map_think", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.destruct_map", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "Computation.map_id", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.map_comp", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.ret_bind", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": true, "tactics": ["apply", "intro", "simp", "rcases", "simp", "rcases", "simp"], "tactic_count": 7}
{"name": "Computation.think_bind", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.bind_pure", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": true, "tactics": ["apply", "intro", "induction", "pure", "think", "exact"], "tactic_count": 6}
{"name": "Computation.bind_pure'", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Computation.bind_assoc", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": true, "tactics": ["apply", "intro", "induction", "pure", "simp", "induction", "pure", "think", "think", "exact"], "tactic_count": 10}
{"name": "Computation.results_bind", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": true, "tactics": ["have", "apply", "intro", "rw", "rw", "exact", "intro", "rw", "obtain", "obtain", "rw", "exact"], "tactic_count": 12}
{"name": "Computation.mem_bind", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.terminates_bind", "kind": "instance", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.get_bind", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.length_bind", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.of_results_bind", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": ["induction", "zero", "succ", "induction", "pure", "think", "simp", "exact", "have", "contradiction", "simp", "exact", "simp", "let", "rw", "exact"], "tactic_count": 16}
{"name": "Computation.exists_of_mem_bind", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.bind_promises", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.monad", "kind": "instance", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.instLawfulMonad", "kind": "instance", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.has_map_eq_map", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.pure_def", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.map_pure'", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.map_think'", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.mem_map", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Computation.exists_of_mem_map", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": true, "tactics": ["rw", "let", "exact"], "tactic_count": 3}
{"name": "Computation.terminates_map", "kind": "instance", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Computation.terminates_map_iff", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.orElse", "kind": "definition", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.instAlternativeComputation", "kind": "instance", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.ret_orElse", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.orElse_pure", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.orElse_think", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.empty_orElse", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": true, "tactics": ["apply", "intro", "induction", "pure", "think"], "tactic_count": 5}
{"name": "Computation.orElse_empty", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": true, "tactics": ["apply", "intro", "induction", "pure", "think"], "tactic_count": 5}
{"name": "Computation.Equiv", "kind": "definition", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.term_~__1", "kind": "definition", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation._aux_Mathlib_Data_Seq_Computation___macroRules_Computation_term_~__1_1", "kind": "definition", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation._aux_Mathlib_Data_Seq_Computation___unexpand_Computation_Equiv_1", "kind": "definition", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.Equiv.refl", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.Equiv.symm", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.Equiv.trans", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.Equiv.equivalence", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.equiv_of_mem", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.terminates_congr", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Computation.promises_congr", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.get_equiv", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.think_equiv", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.thinkN_equiv", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.bind_congr", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.equiv_pure_of_mem", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.LiftRel", "kind": "definition", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.LiftRel.swap", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.lift_eq_iff_equiv", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.LiftRel.refl", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.LiftRel.symm", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.LiftRel.trans", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.LiftRel.equiv", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.LiftRel.imp", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.terminates_of_liftRel", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.rel_of_liftRel", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.liftRel_of_mem", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.exists_of_liftRel_left", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.exists_of_liftRel_right", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.liftRel_def", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.liftRel_bind", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.liftRel_pure_left", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.liftRel_pure_right", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Computation.liftRel_pure", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Computation.liftRel_think_left", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.liftRel_think_right", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Computation.liftRel_mem_cases", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.liftRel_congr", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.liftRel_map", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Computation.map_congr", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Computation.LiftRelAux", "kind": "definition", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.liftRelAux_inl_inl", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.liftRelAux_inl_inr", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.liftRelAux_inr_inl", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.liftRelAux_inr_inr", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.LiftRelAux.ret_left", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": true, "tactics": ["induction", "pure", "think", "rw", "exact"], "tactic_count": 5}
{"name": "Computation.LiftRelAux.swap", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "Computation.LiftRelAux.ret_right", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Computation.LiftRelRec.lem", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": true, "tactics": ["revert", "refine", "intro", "have", "simp", "simp", "simp", "induction", "pure", "think"], "tactic_count": 10}
{"name": "Computation.liftRel_rec", "kind": "theorem", "module": "Mathlib.Data.Seq.Computation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Stream'.Seq.get?", "kind": "definition", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Stream'.Seq.get?_mk", "kind": "theorem", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.le_stable", "kind": "theorem", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": true, "tactics": ["obtain", "induction", "refl", "step"], "tactic_count": 4}
{"name": "Stream'.Seq.ge_stable", "kind": "theorem", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Stream'.Seq.nil", "kind": "definition", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.instInhabited", "kind": "instance", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.cons", "kind": "definition", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.val_cons", "kind": "theorem", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.get?_nil", "kind": "theorem", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.get?_zero_eq_none", "kind": "theorem", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": true, "tactics": ["refine", "ext1", "exact"], "tactic_count": 3}
{"name": "Stream'.Seq.get?_cons_zero", "kind": "theorem", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.get?_cons_succ", "kind": "theorem", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.cons_ne_nil", "kind": "theorem", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": true, "tactics": ["intro", "simpa"], "tactic_count": 2}
{"name": "Stream'.Seq.nil_ne_cons", "kind": "theorem", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.cons_injective2", "kind": "theorem", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.cons_left_injective", "kind": "theorem", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.cons_right_injective", "kind": "theorem", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.cons_eq_cons", "kind": "theorem", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": true, "tactics": ["constructor", "apply", "intro", "congr"], "tactic_count": 4}
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{"name": "Stream'.Seq.destruct", "kind": "definition", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.head_eq_destruct", "kind": "theorem", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "Stream'.Seq.get?_tail", "kind": "theorem", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.destruct_nil", "kind": "theorem", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.destruct_cons", "kind": "theorem", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.destruct_eq_none", "kind": "theorem", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": true, "tactics": ["dsimp", "rcases", "apply", "funext", "induction", "zero", "succ", "contradiction"], "tactic_count": 8}
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{"name": "Stream'.Seq.head_cons", "kind": "theorem", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Stream'.Seq.tail_nil", "kind": "theorem", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.tail_cons", "kind": "theorem", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.head_eq_some", "kind": "theorem", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": true, "tactics": ["ext1", "cases", "exact"], "tactic_count": 3}
{"name": "Stream'.Seq.head_eq_none", "kind": "theorem", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.head_eq_none_iff", "kind": "theorem", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": true, "tactics": ["constructor", "apply", "intro", "simp"], "tactic_count": 4}
{"name": "Stream'.Seq.recOn", "kind": "definition", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": true, "tactics": ["rcases", "rw", "apply", "obtain", "rw", "apply"], "tactic_count": 6}
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{"name": "Stream'.Seq.Corec.f", "kind": "definition", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "_private.Mathlib.Data.Seq.Defs.0.Stream'.Seq.term_~_", "kind": "definition", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Stream'.Seq.BisimO", "kind": "definition", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.IsBisimulation", "kind": "definition", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.eq_of_bisim", "kind": "theorem", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": true, "tactics": ["apply", "apply", "dsimp", "intro", "exact", "suffices", "this", "have", "cases", "intro", "constructor", "rfl", "assumption", "intro", "rw", "exact", "intro", "rw", "exact", "simp", "exact"], "tactic_count": 21}
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{"name": "Stream'.Seq.coinduction", "kind": "theorem", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.coinduction2", "kind": "theorem", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": true, "tactics": ["refine", "intro", "rw"], "tactic_count": 3}
{"name": "Stream'.Seq.TerminatedAt", "kind": "definition", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.terminatedAtDecidable", "kind": "instance", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.Terminates", "kind": "definition", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.length", "kind": "definition", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.length'", "kind": "definition", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.terminated_stable", "kind": "theorem", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.not_terminates_iff", "kind": "theorem", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Stream'.Seq.terminatedAt_nil", "kind": "theorem", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.cons_not_terminatedAt_zero", "kind": "theorem", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Stream'.Seq.cons_terminatedAt_succ_iff", "kind": "theorem", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Stream'.Seq.terminates_nil", "kind": "theorem", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.terminates_cons_iff", "kind": "theorem", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": true, "tactics": ["constructor", "exact", "exact"], "tactic_count": 3}
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{"name": "Stream'.Seq.Mem", "kind": "definition", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.instMembership", "kind": "instance", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.get?_mem", "kind": "theorem", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.mem_iff_exists_get?", "kind": "theorem", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.notMem_nil", "kind": "theorem", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.mem_cons", "kind": "theorem", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.mem_cons_of_mem", "kind": "theorem", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.eq_or_mem_of_mem_cons", "kind": "theorem", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Stream'.Seq.coeList", "kind": "instance", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.ofList_nil", "kind": "theorem", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.ofList_get?", "kind": "theorem", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.ofList_cons", "kind": "theorem", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": true, "tactics": ["ext1"], "tactic_count": 1}
{"name": "Stream'.Seq.ofList_injective", "kind": "theorem", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Stream'.Seq.coeMLList", "kind": "instance", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.toMLList", "kind": "definition", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.forceToList", "kind": "definition", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.take", "kind": "definition", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Stream'.Seq.toStream", "kind": "definition", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.toListOrStream", "kind": "definition", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Stream'.Seq.drop", "kind": "definition", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.splitAt", "kind": "definition", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.zipWith", "kind": "definition", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Stream'.Seq.unzip", "kind": "definition", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Stream'.Seq.fold", "kind": "definition", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Seq.update", "kind": "definition", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Stream'.Seq.Pairwise", "kind": "definition", "module": "Mathlib.Data.Seq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.Seq.Parallel.0.Computation.parallel.aux2", "kind": "definition", "module": "Mathlib.Data.Seq.Parallel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Computation.parallel_empty", "kind": "theorem", "module": "Mathlib.Data.Seq.Parallel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.parallelRec", "kind": "definition", "module": "Mathlib.Data.Seq.Parallel", "is_tactic_proof": true, "tactics": ["let", "have", "rw", "refine", "funext", "dsimp", "rw", "exact", "have", "rw", "have", "rw", "haveI", "rcases", "have", "rcases", "rw", "cases", "dsimp", "cases", "rcases", "rcases", "rw", "rcases", "injection", "constructor", "rwa", "rwa", "obtain", "apply"], "tactic_count": 30}
{"name": "Computation.parallel_promises", "kind": "theorem", "module": "Mathlib.Data.Seq.Parallel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.mem_parallel", "kind": "theorem", "module": "Mathlib.Data.Seq.Parallel", "is_tactic_proof": true, "tactics": ["haveI", "haveI", "exact"], "tactic_count": 3}
{"name": "Computation.parallel_congr_lem", "kind": "theorem", "module": "Mathlib.Data.Seq.Parallel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.parallel_congr_left", "kind": "theorem", "module": "Mathlib.Data.Seq.Parallel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Computation.parallel_congr_right", "kind": "theorem", "module": "Mathlib.Data.Seq.Parallel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.instCoeTCSet", "kind": "instance", "module": "Mathlib.Data.SetLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.instMembership", "kind": "instance", "module": "Mathlib.Data.SetLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.instCoeSortType", "kind": "instance", "module": "Mathlib.Data.SetLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.delabSubtypeSetLike", "kind": "definition", "module": "Mathlib.Data.SetLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.coe_sort_coe", "kind": "theorem", "module": "Mathlib.Data.SetLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.exists", "kind": "theorem", "module": "Mathlib.Data.SetLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.forall", "kind": "theorem", "module": "Mathlib.Data.SetLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.coe_injective", "kind": "theorem", "module": "Mathlib.Data.SetLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.coe_set_eq", "kind": "theorem", "module": "Mathlib.Data.SetLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.coe_ne_coe", "kind": "theorem", "module": "Mathlib.Data.SetLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.ext'", "kind": "theorem", "module": "Mathlib.Data.SetLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.ext'_iff", "kind": "theorem", "module": "Mathlib.Data.SetLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.ext", "kind": "theorem", "module": "Mathlib.Data.SetLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.ext_iff", "kind": "theorem", "module": "Mathlib.Data.SetLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.mem_coe", "kind": "theorem", "module": "Mathlib.Data.SetLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.coe_eq_coe", "kind": "theorem", "module": "Mathlib.Data.SetLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.coe_mem", "kind": "theorem", "module": "Mathlib.Data.SetLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.mem_of_subset", "kind": "theorem", "module": "Mathlib.Data.SetLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.eta", "kind": "theorem", "module": "Mathlib.Data.SetLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.setOf_mem_eq", "kind": "theorem", "module": "Mathlib.Data.SetLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.mem_of_subsingleton", "kind": "theorem", "module": "Mathlib.Data.SetLike.Basic", "is_tactic_proof": true, "tactics": ["obtain", "simpa"], "tactic_count": 2}
{"name": "LE.ofSetLike", "kind": "definition", "module": "Mathlib.Data.SetLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialOrder.ofSetLike", "kind": "definition", "module": "Mathlib.Data.SetLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsConcreteLE", "kind": "instance", "module": "Mathlib.Data.SetLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.coe_subset_coe", "kind": "theorem", "module": "Mathlib.Data.SetLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.le_def", "kind": "theorem", "module": "Mathlib.Data.SetLike.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SetLike.not_le_iff_exists", "kind": "theorem", "module": "Mathlib.Data.SetLike.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "SetLike.coe_mono", "kind": "theorem", "module": "Mathlib.Data.SetLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.coe_ssubset_coe", "kind": "theorem", "module": "Mathlib.Data.SetLike.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SetLike.coe_strictMono", "kind": "theorem", "module": "Mathlib.Data.SetLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.exists_of_lt", "kind": "theorem", "module": "Mathlib.Data.SetLike.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "SetLike.lt_iff_le_and_exists", "kind": "theorem", "module": "Mathlib.Data.SetLike.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SetLike.instSubtypeSet", "kind": "abbrev", "module": "Mathlib.Data.SetLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.instSubtype", "kind": "abbrev", "module": "Mathlib.Data.SetLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.mem_mk_set", "kind": "theorem", "module": "Mathlib.Data.SetLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.mem_mk", "kind": "theorem", "module": "Mathlib.Data.SetLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.instFintype", "kind": "instance", "module": "Mathlib.Data.SetLike.Fintype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.instFinite", "kind": "instance", "module": "Mathlib.Data.SetLike.Fintype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.accumulate", "kind": "definition", "module": "Mathlib.Data.Set.Accumulate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.accumulate_def", "kind": "theorem", "module": "Mathlib.Data.Set.Accumulate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_accumulate", "kind": "theorem", "module": "Mathlib.Data.Set.Accumulate", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.subset_accumulate", "kind": "theorem", "module": "Mathlib.Data.Set.Accumulate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.accumulate_subset_iUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Accumulate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.monotone_accumulate", "kind": "theorem", "module": "Mathlib.Data.Set.Accumulate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.accumulate_subset_accumulate", "kind": "theorem", "module": "Mathlib.Data.Set.Accumulate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.biUnion_accumulate", "kind": "theorem", "module": "Mathlib.Data.Set.Accumulate", "is_tactic_proof": true, "tactics": ["apply", "exact", "exact"], "tactic_count": 3}
{"name": "Set.iUnion_accumulate", "kind": "theorem", "module": "Mathlib.Data.Set.Accumulate", "is_tactic_proof": true, "tactics": ["apply", "simp", "intro", "exact", "exact"], "tactic_count": 5}
{"name": "Set.accumulate_bot", "kind": "theorem", "module": "Mathlib.Data.Set.Accumulate", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.accumulate_zero_nat", "kind": "theorem", "module": "Mathlib.Data.Set.Accumulate", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.disjoint_accumulate", "kind": "theorem", "module": "Mathlib.Data.Set.Accumulate", "is_tactic_proof": true, "tactics": ["apply", "simp", "rcases", "exact"], "tactic_count": 4}
{"name": "Set.accumulate_succ", "kind": "theorem", "module": "Mathlib.Data.Set.Accumulate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.partialSups_eq_accumulate", "kind": "theorem", "module": "Mathlib.Data.Set.Accumulate", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Set.instDistribLattice", "kind": "instance", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instBoundedOrder", "kind": "instance", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instHasSSubset", "kind": "instance", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.top_eq_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.bot_eq_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sup_eq_union", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inf_eq_inter", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.le_eq_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.lt_eq_ssubset", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.le_iff_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.lt_iff_ssubset", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.PiSetCoe.canLift", "kind": "instance", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.PiSetCoe.canLift'", "kind": "instance", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCoeTCElem", "kind": "instance", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.coe_eq_subtype", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.coe_setOf", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetCoe.forall", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetCoe.exists", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetCoe.exists'", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetCoe.forall'", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "set_coe_cast", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetCoe.ext", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetCoe.ext_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.mem", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Eq.subset", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instInhabited", "kind": "instance", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_of_mem_of_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.setOf_injective", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.setOf_inj", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.setOf_bijective", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subset_setOf", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.setOf_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.setOf_subset_setOf", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.setOf_and", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.setOf_or", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instReflSubset", "kind": "instance", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instIsTransSubset", "kind": "instance", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instTransSubset", "kind": "instance", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instAntisymmSubset", "kind": "instance", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instIrreflSSubset", "kind": "instance", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instIsTransSSubset", "kind": "instance", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instTransSSubset", "kind": "instance", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instTransSSubsetSubset", "kind": "instance", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instTransSubsetSSubset", "kind": "instance", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instAsymmSSubset", "kind": "instance", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instIsNonstrictStrictOrderSubsetSSubset", "kind": "instance", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subset_def", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ssubset_def", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Subset.refl", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Subset.rfl", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Subset.trans", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_of_eq_of_mem", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Subset.antisymm", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Subset.antisymm_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.eq_of_subset_of_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_of_subset_of_mem", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.notMem_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.not_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.not_top_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.eq_of_forall_subset_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.eq_or_ssubset_of_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.exists_of_ssubset", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ssubset_iff_subset_ne", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ssubset_iff_of_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ssubset_iff_exists", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ssubset_of_ssubset_of_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ssubset_of_subset_of_ssubset", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.notMem_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.not_notMem", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.nonempty_coe_sort", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.nonempty_def", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.nonempty_of_mem", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nonempty.not_subset_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nonempty.some", "kind": "definition", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nonempty.some_mem", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nonempty.mono", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.nonempty_of_not_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.nonempty_of_ssubset", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nonempty.of_diff", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.nonempty_of_ssubset'", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nonempty.inl", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nonempty.inr", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.union_nonempty", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nonempty.left", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nonempty.right", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inter_nonempty", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inter_nonempty_iff_exists_left", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.inter_nonempty_iff_exists_right", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.nonempty_iff_univ_nonempty", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.univ_nonempty", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nonempty.to_subtype", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nonempty.to_type", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.univ.nonempty", "kind": "instance", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instNonemptyTop", "kind": "instance", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nonempty.of_subtype", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.empty_def", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_empty_iff_false", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.setOf_false", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.setOf_bot", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.empty_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subset_empty_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.eq_empty_iff_forall_notMem", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.eq_empty_of_forall_notMem", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.eq_empty_of_subset_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.not_nonempty_iff_eq_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.nonempty_iff_ne_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.nonempty_iff_empty_ne", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.not_nonempty_iff_eq_empty'", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.nonempty_iff_ne_empty'", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.not_nonempty_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.isEmpty_coe_sort", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.eq_empty_of_isEmpty", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.uniqueEmpty", "kind": "instance", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.eq_empty_or_nonempty", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subset_eq_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.forall_mem_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instIsEmptyElemEmptyCollection", "kind": "instance", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.empty_ssubset", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.setOf_true", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.setOf_top", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.univ_eq_empty_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.empty_ne_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subset_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.univ_subset_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.eq_univ_iff_forall", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.eq_univ_of_forall", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nonempty.eq_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "Set.eq_univ_of_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.exists_mem_of_nonempty", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ne_univ_iff_exists_notMem", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.not_subset_iff_exists_mem_notMem", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.univ_unique", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ssubset_univ_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.nontrivial_of_nonempty", "kind": "instance", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.union_def", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_union_left", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_union_right", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_or_mem_of_mem_union", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.MemUnion.elim", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_union", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.union_self", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.union_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.empty_union", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.union_comm", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.union_assoc", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.union_isAssoc", "kind": "instance", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.union_isComm", "kind": "instance", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.union_left_comm", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.union_right_comm", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.union_eq_left", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.union_eq_right", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.union_eq_self_of_subset_left", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.union_eq_self_of_subset_right", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subset_union_left", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subset_union_right", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.union_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.union_subset_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.union_subset_union", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.union_subset_union_left", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.union_subset_union_right", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subset_union_of_subset_left", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subset_union_of_subset_right", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.union_congr_left", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.union_congr_right", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.union_eq_union_iff_left", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.union_eq_union_iff_right", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.union_empty_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Set.union_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.univ_union", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ssubset_union_left_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ssubset_union_right_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inter_def", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_inter_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_inter", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_of_mem_inter_left", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_of_mem_inter_right", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inter_self", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inter_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.empty_inter", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inter_comm", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inter_assoc", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inter_isAssoc", "kind": "instance", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inter_isComm", "kind": "instance", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inter_left_comm", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inter_right_comm", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inter_subset_left", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inter_subset_right", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subset_inter", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subset_inter_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inter_eq_left", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inter_eq_right", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.left_eq_inter", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.right_eq_inter", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inter_eq_self_of_subset_left", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inter_eq_self_of_subset_right", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inter_congr_left", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inter_congr_right", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inter_eq_inter_iff_left", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inter_eq_inter_iff_right", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inter_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.univ_inter", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inter_subset_inter", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inter_subset_inter_left", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inter_subset_inter_right", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.union_inter_cancel_left", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.union_inter_cancel_right", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inter_setOf_eq_sep", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.setOf_inter_eq_sep", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sep_eq_inter_sep", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.inter_ssubset_right_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inter_ssubset_left_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inter_union_distrib_left", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.union_inter_distrib_right", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.union_inter_distrib_left", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inter_union_distrib_right", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.union_union_distrib_left", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.union_union_distrib_right", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inter_inter_distrib_left", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inter_inter_distrib_right", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.union_union_union_comm", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inter_inter_inter_comm", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_sep", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sep_mem_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_sep_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sep_ext_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.sep_eq_of_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sep_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sep_subset_setOf", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sep_eq_self_iff_mem_true", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.sep_eq_empty_iff_mem_false", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.sep_true", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sep_false", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sep_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sep_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sep_union", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sep_inter", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sep_and", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sep_or", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sep_setOf", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_powerset", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subset_of_mem_powerset", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_powerset_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.powerset_inter", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.powerset_mono", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.monotone_powerset", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.powerset_nonempty", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.powerset_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.powerset_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_dite_univ_right", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.mem_ite_univ_right", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_dite_univ_left", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": true, "tactics": ["split_ifs"], "tactic_count": 1}
{"name": "Set.mem_ite_univ_left", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_dite_empty_right", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Set.mem_ite_empty_right", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_dite_empty_left", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Set.mem_ite_empty_left", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.nonempty_apply_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subsingleton.eq_univ_of_nonempty", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsingleton.set_cases", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsingleton.mem_iff_nonempty", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.decidableSdiff", "kind": "instance", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.decidableInter", "kind": "instance", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.decidableUnion", "kind": "instance", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.decidableCompl", "kind": "instance", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.decidableEmptyset", "kind": "instance", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.decidableUniv", "kind": "instance", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.decidableInsert", "kind": "instance", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.decidableSetOf", "kind": "instance", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": true, "tactics": ["assumption"], "tactic_count": 1}
{"name": "Equiv.setSubtypeComm", "kind": "definition", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.setSubtypeComm_apply", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.setSubtypeComm_symm_apply", "kind": "theorem", "module": "Mathlib.Data.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.boolIndicator", "kind": "definition", "module": "Mathlib.Data.Set.BoolIndicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_iff_boolIndicator", "kind": "theorem", "module": "Mathlib.Data.Set.BoolIndicator", "is_tactic_proof": true, "tactics": ["unfold", "split_ifs"], "tactic_count": 2}
{"name": "Set.notMem_iff_boolIndicator", "kind": "theorem", "module": "Mathlib.Data.Set.BoolIndicator", "is_tactic_proof": true, "tactics": ["unfold", "split_ifs"], "tactic_count": 2}
{"name": "Set.preimage_boolIndicator_true", "kind": "theorem", "module": "Mathlib.Data.Set.BoolIndicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.preimage_boolIndicator_false", "kind": "theorem", "module": "Mathlib.Data.Set.BoolIndicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.preimage_boolIndicator_eq_union", "kind": "theorem", "module": "Mathlib.Data.Set.BoolIndicator", "is_tactic_proof": true, "tactics": ["ext", "simp", "split_ifs"], "tactic_count": 3}
{"name": "Set.preimage_boolIndicator", "kind": "theorem", "module": "Mathlib.Data.Set.BoolIndicator", "is_tactic_proof": true, "tactics": ["simp", "split_ifs"], "tactic_count": 2}
{"name": "Set.instCompleteAtomicBooleanAlgebra", "kind": "instance", "module": "Mathlib.Data.Set.BooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instOrderTop", "kind": "instance", "module": "Mathlib.Data.Set.BooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.encard", "kind": "definition", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.encard_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENat.card_coe_set_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.encard_univ_coe", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.Finite.encard_eq_coe_toFinset_card", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "Set.encard_eq_coe_toFinset_card", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "Set.toENat_cardinalMk", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.toENat_cardinalMk_subtype", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.coe_fintypeCard", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.encard_coe_eq_coe_finsetCard", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.Infinite.encard_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "Set.encard_eq_zero", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.encard_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.nonempty_of_encard_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Set.encard_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.encard_pos", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.encard_ne_zero_of_mem", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.encard_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.encard_union_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["classical", "unfold", "simp"], "tactic_count": 3}
{"name": "Set.encard_ne_add_one", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["have", "replace", "have", "rwa"], "tactic_count": 4}
{"name": "Set.encard_insert_of_notMem", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.Finite.encard_lt_top", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["induction", "empty", "insert", "rw", "exact"], "tactic_count": 5}
{"name": "Set.Finite.encard_eq_coe", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.exists_encard_eq_coe", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.encard_lt_top_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.encard_eq_top_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["contrapose", "rw"], "tactic_count": 2}
{"name": "Set.encard_ne_top_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.finite_of_encard_le_coe", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.finite_of_encard_eq_coe", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.encard_le_coe_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.encard_prod", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["unfold", "simp"], "tactic_count": 2}
{"name": "Set.encard_pi_eq_prod_encard", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["unfold", "simp"], "tactic_count": 2}
{"name": "Set.encard_le_encard", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.encard_le_card", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.encard_mono", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.encard_diff_add_encard_of_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.encard_diff", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.one_le_encard_iff_nonempty", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.encard_diff_add_encard_inter", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.encard_union_add_encard_inter", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.encard_eq_encard_iff_encard_diff_eq_encard_diff", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.encard_le_encard_iff_encard_diff_le_encard_diff", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.encard_lt_encard_iff_encard_diff_lt_encard_diff", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.encard_union_le", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.finite_iff_finite_of_encard_eq_encard", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.infinite_iff_infinite_of_encard_eq_encard", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.Finite.finite_of_encard_le", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.eq_of_subset_of_encard_le'", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rw", "have", "rw", "exact"], "tactic_count": 4}
{"name": "Set.Finite.eq_of_subset_of_encard_le", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.encard_lt_encard", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.encard_strictMono", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.encard_strictMonoOn", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.encard_diff_add_encard", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.encard_le_encard_diff_add_encard", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.tsub_encard_le_encard_diff", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.encard_add_encard_compl", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.encard_insert_le", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.one_le_encard_insert", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.encard_singleton_inter", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.encard_diff_singleton_add_one", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.encard_diff_singleton_of_mem", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rw", "tsub_add_cancel_of_le"], "tactic_count": 2}
{"name": "Set.encard_tsub_one_le_encard_diff_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.encard_exchange", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rw", "simp_all"], "tactic_count": 2}
{"name": "Set.encard_exchange'", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.encard_eq_add_one_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["refine", "obtain", "refine", "rw", "rintro", "rw"], "tactic_count": 6}
{"name": "Set.eq_empty_or_encard_eq_top_or_encard_diff_singleton_lt", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": false, "tactics": ["refine", "s.eq_empty_or_nonempty.elim", "rw", "exact"], "tactic_count": 4}
{"name": "Set.encard_pair", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rw", "encard_singleton]"], "tactic_count": 2}
{"name": "Set.encard_eq_one", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact"], "tactic_count": 3}
{"name": "Set.encard_le_one_iff_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.encard_le_one_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rw", "refine", "obtain", "rw"], "tactic_count": 4}
{"name": "Set.encard_le_one_iff_subsingleton", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rw", "tauto"], "tactic_count": 2}
{"name": "Set.one_lt_encard_iff_nontrivial", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["contrapose"], "tactic_count": 1}
{"name": "Set.one_lt_encard_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["contrapose"], "tactic_count": 1}
{"name": "Set.exists_ne_of_one_lt_encard", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["by_contra", "obtain", "apply", "rw"], "tactic_count": 4}
{"name": "Set.encard_eq_two", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["refine", "obtain", "rw", "obtain", "refine", "rw"], "tactic_count": 6}
{"name": "Set.encard_eq_three", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["refine", "obtain", "rw", "obtain", "refine", "rintro", "rintro", "rw", "rw"], "tactic_count": 9}
{"name": "Set.encard_eq_four", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["refine", "obtain", "rw", "obtain", "refine", "rintro", "rintro", "rintro", "rw", "rw"], "tactic_count": 10}
{"name": "Set.Nat.encard_range", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["convert", "rw", "rw"], "tactic_count": 3}
{"name": "Set.Finite.eq_insert_of_subset_of_encard_eq_succ", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": false, "tactics": ["rw", "obtain"], "tactic_count": 2}
{"name": "Set.exists_subset_encard_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "obtain", "simp", "have", "obtain", "exact", "top"], "tactic_count": 9}
{"name": "Set.exists_superset_subset_encard_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["obtain", "rw", "obtain", "obtain", "have", "rw", "exact", "obtain", "refine", "rw"], "tactic_count": 10}
{"name": "Set.InjOn.encard_image", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.encard_congr", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.encard_image", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.encard_range", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Function.Embedding.encard_le", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.encard_image_le", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["obtain", "rw", "rw", "apply", "exact"], "tactic_count": 5}
{"name": "Set.Finite.injOn_of_encard_image_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["obtain", "simp", "rw", "rw", "exact"], "tactic_count": 5}
{"name": "Set.encard_preimage_of_injective_subset_range", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.encard_preimage_of_bijective", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.encard_le_encard_of_injOn", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.encard_preimage_val_le_encard_left", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.encard_preimage_val_le_encard_right", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.exists_injOn_of_encard_le", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["classical", "obtain", "simp", "exact", "obtain", "have", "rwa", "encard_diff_singleton_add_one", "obtain", "simp", "use", "rw", "simp", "not_forall,", "refine", "rintro", "assumption", "exact", "exact", "termination_by"], "tactic_count": 20}
{"name": "Set.Finite.exists_bijOn_of_encard_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["obtain", "convert", "rw"], "tactic_count": 3}
{"name": "Set.exists_ne_map_eq_of_encard_lt_of_maps_to", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["contrapose", "suffices", "let", "exact", "simpa"], "tactic_count": 5}
{"name": "Set.tacticToFinite_tac", "kind": "definition", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set._aux_Mathlib_Data_Set_Card___macroRules_Set_tacticToFinite_tac_1", "kind": "definition", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.tacticTo_encard_tac", "kind": "definition", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set._aux_Mathlib_Data_Set_Card___macroRules_Set_tacticTo_encard_tac_1", "kind": "definition", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ncard", "kind": "definition", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ncard_def", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.cast_ncard_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Set.ncard_le_encard", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.card_coe_set_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ncard_eq_toFinset_card'", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.cast_ncard", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.encard_le_coe_iff_finite_ncard_le", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.Infinite.ncard", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.ncard_mono", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ncard_coe_finset", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.ncard_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ncard_le_card", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ncard_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.finite_of_ncard_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.finite_of_ncard_pos", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.nonempty_of_ncard_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.ncard_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.ncard_singleton_inter", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "Set.ncard_prod", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.ncard_insert_of_mem", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.ncard_insert_le", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["obtain", "to_encard_tac", "rw", "exact"], "tactic_count": 4}
{"name": "Set.ncard_le_ncard_insert", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["classical", "refine", "rw"], "tactic_count": 3}
{"name": "Set.ncard_pair", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.ncard_diff_singleton_of_mem", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rcases", "simp_all", "exact"], "tactic_count": 3}
{"name": "Set.ncard_diff_singleton_le", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["obtain", "apply", "convert", "exact"], "tactic_count": 4}
{"name": "Set.pred_ncard_le_ncard_diff_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "rw", "apply"], "tactic_count": 4}
{"name": "Set.ncard_exchange", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ncard_exchange'", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rw", "diff_singleton_eq_self"], "tactic_count": 2}
{"name": "Set.InjOn.ncard_image", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ncard_image_of_injective", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ncard_preimage_of_injective_subset_range", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.ncard_map", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ncard_subtype", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["convert", "ext", "simp"], "tactic_count": 3}
{"name": "Set.ncard_lt_card", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ncard_strictMono", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.ncard_strictMonoOn", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ncard_eq_of_bijective", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["let", "suffices", "rw", "exact", "ext", "simp", "refine", "obtain", "use"], "tactic_count": 9}
{"name": "Set.ncard_congr", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["set", "have", "constructor", "rintro", "simp", "exact", "rintro", "obtain", "simp", "exact", "simp_rw", "exact"], "tactic_count": 12}
{"name": "Set.ncard_congr'", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ncard_range_of_injective", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.ncard_coe", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.ncard_graphOn", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.ncard_union_le", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["obtain", "to_encard_tac", "rw", "apply", "rw", "apply"], "tactic_count": 6}
{"name": "Set.cast_ncard_sdiff", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.eq_univ_iff_ncard", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.even_ncard_compl_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Set.odd_ncard_compl_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.nonempty_inter_of_lt_ncard_add_ncard", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rw", "replace", "rwa"], "tactic_count": 3}
{"name": "Set.nonempty_inter_of_le_ncard_add_ncard", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rw", "replace", "rwa"], "tactic_count": 3}
{"name": "Set.union_ne_univ_of_ncard_add_ncard_lt", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["contrapose", "rw", "exact"], "tactic_count": 3}
{"name": "Set.nonempty_inter_compl_of_ncard_add_ncard_lt", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.exists_subsuperset_card_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact", "lift", "lift", "obtain", "exact"], "tactic_count": 7}
{"name": "Set.exists_subset_card_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.Infinite.exists_subset_ncard_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["have", "obtain", "refine", "rw", "simp"], "tactic_count": 5}
{"name": "Set.Infinite.exists_superset_ncard_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["obtain", "refine", "rwa"], "tactic_count": 3}
{"name": "Set.exists_subset_or_subset_of_two_mul_lt_ncard", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["classical", "have", "rw", "obtain", "exact"], "tactic_count": 5}
{"name": "Finset.exists_not_mem_of_card_lt_enatCard", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["contrapose", "simp"], "tactic_count": 2}
{"name": "Set.ncard_eq_one", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["refine", "have", "simp_rw", "refine", "simp_rw", "simp", "exact"], "tactic_count": 7}
{"name": "Set.ncard_le_one_iff_subsingleton", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ncard_le_one_of_subsingleton", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.one_lt_ncard_iff_nontrivial", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.one_lt_ncard_iff_nontrivial_and_finite", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["refine", "have", "rw", "exact", "rw", "rwa"], "tactic_count": 6}
{"name": "Set.exists_ne_of_one_lt_ncard", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["have", "rw", "simpa"], "tactic_count": 3}
{"name": "Set.eq_insert_of_ncard_eq_succ", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["classical", "have", "rw", "obtain", "simp", "refine", "simp", "simp"], "tactic_count": 8}
{"name": "Set.ncard_eq_two", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Set.ncard_eq_three", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Set.ncard_eq_four", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Function.Surjective.card_le_card_add_one_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["rcases", "simp", "let", "rw", "add_le_add_iff_left]", "replace", "refine", "rw", "obtain", "simp", "suffices", "intro", "by_cases", "rw", "simp", "intro", "simpa", "congrArg"], "tactic_count": 18}
{"name": "Set.ncard_le_ncard_image_add_one_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Card", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.exists_disjoint_union_of_even_card", "kind": "theorem", "module": "Mathlib.Data.Set.Card.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.exists_disjoint_union_of_even_card_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Card.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finsum_one", "kind": "theorem", "module": "Mathlib.Data.Set.Card.Arithmetic", "is_tactic_proof": true, "tactics": ["obtain", "rw", "by_cases", "simp", "exact", "simp"], "tactic_count": 6}
{"name": "Finset.set_ncard_biUnion_le", "kind": "theorem", "module": "Mathlib.Data.Set.Card.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.set_encard_biUnion_le", "kind": "theorem", "module": "Mathlib.Data.Set.Card.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Infinite.exists_union_disjoint_cardinal_eq_of_infinite", "kind": "theorem", "module": "Mathlib.Data.Set.Card.Arithmetic", "is_tactic_proof": true, "tactics": ["have", "obtain", "refine", "simp", "exact", "simp"], "tactic_count": 6}
{"name": "Set.exists_union_disjoint_cardinal_eq_of_even", "kind": "theorem", "module": "Mathlib.Data.Set.Card.Arithmetic", "is_tactic_proof": true, "tactics": ["obtain", "exact", "classical", "rw", "obtain", "use", "simp"], "tactic_count": 7}
{"name": "Set.exists_union_disjoint_ncard_eq_of_even", "kind": "theorem", "module": "Mathlib.Data.Set.Card.Arithmetic", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Set.exists_union_disjoint_cardinal_eq_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Card.Arithmetic", "is_tactic_proof": true, "tactics": ["use", "rintro", "obtain", "rw", "have", "rw", "exact", "simp"], "tactic_count": 8}
{"name": "Set.Finite.ncard_biUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Card.Arithmetic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.ncard_iUnion_of_finite", "kind": "theorem", "module": "Mathlib.Data.Set.Card.Arithmetic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Set.Finite.encard_biUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Card.Arithmetic", "is_tactic_proof": true, "tactics": ["classical", "by_cases", "have", "rw", "obtain", "rw", "simp"], "tactic_count": 7}
{"name": "Set.encard_iUnion_of_finite", "kind": "theorem", "module": "Mathlib.Data.Set.Card.Arithmetic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Set.Finite.ncard_biUnion_le", "kind": "theorem", "module": "Mathlib.Data.Set.Card.Arithmetic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.Finite.encard_biUnion_le", "kind": "theorem", "module": "Mathlib.Data.Set.Card.Arithmetic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.ncard_iUnion_le_of_fintype", "kind": "theorem", "module": "Mathlib.Data.Set.Card.Arithmetic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.encard_iUnion_le_of_fintype", "kind": "theorem", "module": "Mathlib.Data.Set.Card.Arithmetic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.ncard_iUnion_le_of_finite", "kind": "theorem", "module": "Mathlib.Data.Set.Card.Arithmetic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.encard_iUnion_le_of_finite", "kind": "theorem", "module": "Mathlib.Data.Set.Card.Arithmetic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.Elem", "kind": "definition", "module": "Mathlib.Data.Set.CoeSort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instCoeSortType", "kind": "instance", "module": "Mathlib.Data.Set.CoeSort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.elem_mem", "kind": "theorem", "module": "Mathlib.Data.Set.CoeSort", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteInter.finiteInterClosure", "kind": "inductive", "module": "Mathlib.Data.Set.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteInter.finiteInterClosure_finiteInter", "kind": "theorem", "module": "Mathlib.Data.Set.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteInter.finiteInter_mem", "kind": "theorem", "module": "Mathlib.Data.Set.Constructions", "is_tactic_proof": true, "tactics": ["classical", "refine", "simp", "intro", "suffices", "exact"], "tactic_count": 6}
{"name": "FiniteInter.finiteInterClosure_insert", "kind": "theorem", "module": "Mathlib.Data.Set.Constructions", "is_tactic_proof": true, "tactics": ["induction", "basic", "cases", "exact", "exact", "univ", "h2", "rcases", "exact", "exact", "exact", "exact", "ext", "constructor"], "tactic_count": 14}
{"name": "FiniteInter.mk₂", "kind": "theorem", "module": "Mathlib.Data.Set.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.biUnion_empty_finset", "kind": "theorem", "module": "Mathlib.Data.Set.Constructions", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.Countable", "kind": "definition", "module": "Mathlib.Data.Set.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.countable_coe_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.to_countable", "kind": "theorem", "module": "Mathlib.Data.Set.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.countable_iff_exists_injective", "kind": "theorem", "module": "Mathlib.Data.Set.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.countable_iff_exists_injOn", "kind": "theorem", "module": "Mathlib.Data.Set.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.countable_iff_nonempty_encodable", "kind": "theorem", "module": "Mathlib.Data.Set.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Countable.toEncodable", "kind": "definition", "module": "Mathlib.Data.Set.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.enumerateCountable", "kind": "definition", "module": "Mathlib.Data.Set.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subset_range_enumerate", "kind": "theorem", "module": "Mathlib.Data.Set.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.range_enumerateCountable_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Countable", "is_tactic_proof": true, "tactics": ["refine", "rw", "none", "some"], "tactic_count": 4}
{"name": "Set.range_enumerateCountable_of_mem", "kind": "theorem", "module": "Mathlib.Data.Set.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.enumerateCountable_mem", "kind": "theorem", "module": "Mathlib.Data.Set.Countable", "is_tactic_proof": true, "tactics": ["convert", "exact"], "tactic_count": 2}
{"name": "Set.Countable.mono", "kind": "theorem", "module": "Mathlib.Data.Set.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.countable_range", "kind": "theorem", "module": "Mathlib.Data.Set.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.countable_iff_exists_subset_range", "kind": "theorem", "module": "Mathlib.Data.Set.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.countable_iff_exists_surjective", "kind": "theorem", "module": "Mathlib.Data.Set.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.countable_univ_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.countable_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.not_countable_univ_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Countable", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.not_countable_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Countable.exists_eq_range", "kind": "theorem", "module": "Mathlib.Data.Set.Countable", "is_tactic_proof": true, "tactics": ["rcases", "refine", "rw"], "tactic_count": 3}
{"name": "Set.countable_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.countable_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Countable.image", "kind": "theorem", "module": "Mathlib.Data.Set.Countable", "is_tactic_proof": true, "tactics": ["rw", "have", "apply"], "tactic_count": 3}
{"name": "Set.MapsTo.countable_of_injOn", "kind": "theorem", "module": "Mathlib.Data.Set.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Countable.preimage_of_injOn", "kind": "theorem", "module": "Mathlib.Data.Set.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Countable.preimage", "kind": "theorem", "module": "Mathlib.Data.Set.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.exists_seq_iSup_eq_top_iff_countable", "kind": "theorem", "module": "Mathlib.Data.Set.Countable", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "refine", "rwa", "rintro", "rcases", "rw", "haveI", "rcases", "exact", "rcases", "refine", "rwa"], "tactic_count": 13}
{"name": "Set.exists_seq_cover_iff_countable", "kind": "theorem", "module": "Mathlib.Data.Set.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.countable_of_injective_of_countable_image", "kind": "theorem", "module": "Mathlib.Data.Set.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.countable_iUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Countable", "is_tactic_proof": true, "tactics": ["have", "rw", "apply"], "tactic_count": 3}
{"name": "Set.countable_iUnion_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Countable.biUnion_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Countable", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "Set.Countable.sUnion_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Countable", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.countable_union", "kind": "theorem", "module": "Mathlib.Data.Set.Countable", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.Countable.union", "kind": "theorem", "module": "Mathlib.Data.Set.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Countable.of_diff", "kind": "theorem", "module": "Mathlib.Data.Set.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.countable_insert", "kind": "theorem", "module": "Mathlib.Data.Set.Countable", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.Countable.insert", "kind": "theorem", "module": "Mathlib.Data.Set.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.countable", "kind": "theorem", "module": "Mathlib.Data.Set.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Countable.of_subsingleton", "kind": "theorem", "module": "Mathlib.Data.Set.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Subsingleton.countable", "kind": "theorem", "module": "Mathlib.Data.Set.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.countable_isTop", "kind": "theorem", "module": "Mathlib.Data.Set.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.countable_isBot", "kind": "theorem", "module": "Mathlib.Data.Set.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.countable_setOf_finite_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Countable", "is_tactic_proof": true, "tactics": ["have", "refine", "rintro", "lift", "lift", "exact"], "tactic_count": 6}
{"name": "Set.Countable.setOf_finite", "kind": "theorem", "module": "Mathlib.Data.Set.Countable", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.Countable.of_preimage_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Countable", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.countable_univ_pi", "kind": "theorem", "module": "Mathlib.Data.Set.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.countable_pi", "kind": "theorem", "module": "Mathlib.Data.Set.Countable", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.Countable.prod", "kind": "theorem", "module": "Mathlib.Data.Set.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Countable.image2", "kind": "theorem", "module": "Mathlib.Data.Set.Countable", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.countable_setOf_nonempty_of_disjoint", "kind": "theorem", "module": "Mathlib.Data.Set.Countable", "is_tactic_proof": true, "tactics": ["rw", "have", "rintro", "exact", "choose", "have", "rintro", "have", "refine", "rw", "exact", "simp", "by_contra", "exact", "exact"], "tactic_count": 15}
{"name": "Finset.countable_toSet", "kind": "theorem", "module": "Mathlib.Data.Set.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set", "kind": "definition", "module": "Mathlib.Data.Set.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "setOf", "kind": "definition", "module": "Mathlib.Data.Set.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Mem", "kind": "definition", "module": "Mathlib.Data.Set.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instMembership", "kind": "instance", "module": "Mathlib.Data.Set.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ext", "kind": "theorem", "module": "Mathlib.Data.Set.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Subset", "kind": "definition", "module": "Mathlib.Data.Set.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instLE", "kind": "instance", "module": "Mathlib.Data.Set.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instHasSubset", "kind": "instance", "module": "Mathlib.Data.Set.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instEmptyCollection", "kind": "instance", "module": "Mathlib.Data.Set.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.setBuilder", "kind": "definition", "module": "Mathlib.Data.Set.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.elabSetBuilder", "kind": "definition", "module": "Mathlib.Data.Set.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.setOf.unexpander", "kind": "definition", "module": "Mathlib.Data.Set.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.term{_|_}", "kind": "definition", "module": "Mathlib.Data.Set.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta._aux_Mathlib_Data_Set_Defs___macroRules_Mathlib_Meta_term{_|_}_1", "kind": "definition", "module": "Mathlib.Data.Set.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.macroPattSetBuilder", "kind": "definition", "module": "Mathlib.Data.Set.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta._aux_Mathlib_Data_Set_Defs___macroRules_Mathlib_Meta_macroPattSetBuilder_1", "kind": "definition", "module": "Mathlib.Data.Set.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.term{_|_}_1", "kind": "definition", "module": "Mathlib.Data.Set.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta._aux_Mathlib_Data_Set_Defs___macroRules_Mathlib_Meta_term{_|_}_1_1", "kind": "definition", "module": "Mathlib.Data.Set.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.setOfPatternMatchUnexpander", "kind": "definition", "module": "Mathlib.Data.Set.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.univ", "kind": "definition", "module": "Mathlib.Data.Set.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.insert", "kind": "definition", "module": "Mathlib.Data.Set.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instInsert", "kind": "instance", "module": "Mathlib.Data.Set.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.singleton", "kind": "definition", "module": "Mathlib.Data.Set.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instSingletonSet", "kind": "instance", "module": "Mathlib.Data.Set.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.union", "kind": "definition", "module": "Mathlib.Data.Set.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instUnion", "kind": "instance", "module": "Mathlib.Data.Set.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inter", "kind": "definition", "module": "Mathlib.Data.Set.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instInter", "kind": "instance", "module": "Mathlib.Data.Set.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.compl", "kind": "definition", "module": "Mathlib.Data.Set.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.diff", "kind": "definition", "module": "Mathlib.Data.Set.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instSDiff", "kind": "instance", "module": "Mathlib.Data.Set.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.powerset", "kind": "definition", "module": "Mathlib.Data.Set.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.term𝒫_", "kind": "definition", "module": "Mathlib.Data.Set.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set._aux_Mathlib_Data_Set_Defs___macroRules_Set_term𝒫__1", "kind": "definition", "module": "Mathlib.Data.Set.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set._aux_Mathlib_Data_Set_Defs___unexpand_Set_powerset_1", "kind": "definition", "module": "Mathlib.Data.Set.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image", "kind": "definition", "module": "Mathlib.Data.Set.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instFunctor", "kind": "instance", "module": "Mathlib.Data.Set.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instLawfulFunctor", "kind": "instance", "module": "Mathlib.Data.Set.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nonempty", "kind": "definition", "module": "Mathlib.Data.Set.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.disjoint_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.disjoint_iff_inter_eq_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Disjoint.inter_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.disjoint_left", "kind": "theorem", "module": "Mathlib.Data.Set.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.disjoint_right", "kind": "theorem", "module": "Mathlib.Data.Set.Disjoint", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.not_disjoint_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Disjoint", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.not_disjoint_iff_nonempty_inter", "kind": "theorem", "module": "Mathlib.Data.Set.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.disjoint_or_nonempty_inter", "kind": "theorem", "module": "Mathlib.Data.Set.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.disjoint_iff_forall_ne", "kind": "theorem", "module": "Mathlib.Data.Set.Disjoint", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.disjoint_of_subset_left", "kind": "theorem", "module": "Mathlib.Data.Set.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.disjoint_of_subset_right", "kind": "theorem", "module": "Mathlib.Data.Set.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.disjoint_of_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.disjoint_union_left", "kind": "theorem", "module": "Mathlib.Data.Set.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.disjoint_union_right", "kind": "theorem", "module": "Mathlib.Data.Set.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.disjoint_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.empty_disjoint", "kind": "theorem", "module": "Mathlib.Data.Set.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.univ_disjoint", "kind": "theorem", "module": "Mathlib.Data.Set.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.disjoint_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.disjoint_range_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Disjoint", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Disjoint.union_left", "kind": "theorem", "module": "Mathlib.Data.Set.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Disjoint.union_right", "kind": "theorem", "module": "Mathlib.Data.Set.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Disjoint.inter_left", "kind": "theorem", "module": "Mathlib.Data.Set.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Disjoint.inter_left'", "kind": "theorem", "module": "Mathlib.Data.Set.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Disjoint.inter_right", "kind": "theorem", "module": "Mathlib.Data.Set.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Disjoint.inter_right'", "kind": "theorem", "module": "Mathlib.Data.Set.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Disjoint.subset_left_of_subset_union", "kind": "theorem", "module": "Mathlib.Data.Set.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Disjoint.subset_right_of_subset_union", "kind": "theorem", "module": "Mathlib.Data.Set.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_union_of_disjoint", "kind": "theorem", "module": "Mathlib.Data.Set.Disjoint", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.enumerate", "kind": "definition", "module": "Mathlib.Data.Set.Enumerate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.enumerate_eq_none_of_sel", "kind": "theorem", "module": "Mathlib.Data.Set.Enumerate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.enumerate_eq_none", "kind": "theorem", "module": "Mathlib.Data.Set.Enumerate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.enumerate_mem", "kind": "theorem", "module": "Mathlib.Data.Set.Enumerate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.enumerate_inj", "kind": "theorem", "module": "Mathlib.Data.Set.Enumerate", "is_tactic_proof": true, "tactics": ["wlog", "exact", "rcases", "clear", "induction", "zero", "cases", "zero", "succ", "m", "have", "have", "simp_all", "succ", "rw", "cases"], "tactic_count": 16}
{"name": "Set.EquitableOn", "kind": "definition", "module": "Mathlib.Data.Set.Equitable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.equitableOn_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Equitable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.equitableOn_iff_exists_le_le_add_one", "kind": "theorem", "module": "Mathlib.Data.Set.Equitable", "is_tactic_proof": true, "tactics": ["refine", "obtain", "simp", "intro", "by_cases", "exact", "obtain", "refine", "rw", "exact"], "tactic_count": 10}
{"name": "Set.equitableOn_iff_exists_image_subset_icc", "kind": "theorem", "module": "Mathlib.Data.Set.Equitable", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.equitableOn_iff_exists_eq_eq_add_one", "kind": "theorem", "module": "Mathlib.Data.Set.Equitable", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.not_equitableOn", "kind": "theorem", "module": "Mathlib.Data.Set.Equitable", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.Subsingleton.equitableOn", "kind": "theorem", "module": "Mathlib.Data.Set.Equitable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.equitableOn_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Equitable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.equitableOn_iff_le_le_add_one", "kind": "theorem", "module": "Mathlib.Data.Set.Equitable", "is_tactic_proof": true, "tactics": ["rw", "refine", "rintro", "by_cases", "intro", "rw", "exact", "obtain", "suffices", "simp_rw", "apply", "symm", "refine", "rw", "exact"], "tactic_count": 15}
{"name": "Finset.EquitableOn.le", "kind": "theorem", "module": "Mathlib.Data.Set.Equitable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.EquitableOn.le_add_one", "kind": "theorem", "module": "Mathlib.Data.Set.Equitable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.equitableOn_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Equitable", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.FiniteExhaustion.instFunLikeNat", "kind": "instance", "module": "Mathlib.Data.Set.FiniteExhaustion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.FiniteExhaustion.instRelHomClassNatLeSubset", "kind": "instance", "module": "Mathlib.Data.Set.FiniteExhaustion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.FiniteExhaustion.instFiniteElemCoeNat", "kind": "instance", "module": "Mathlib.Data.Set.FiniteExhaustion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.FiniteExhaustion.toFun_eq_coe", "kind": "theorem", "module": "Mathlib.Data.Set.FiniteExhaustion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.FiniteExhaustion.finite", "kind": "theorem", "module": "Mathlib.Data.Set.FiniteExhaustion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.FiniteExhaustion.subset_succ", "kind": "theorem", "module": "Mathlib.Data.Set.FiniteExhaustion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.FiniteExhaustion.mono", "kind": "theorem", "module": "Mathlib.Data.Set.FiniteExhaustion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.FiniteExhaustion.iUnion_eq", "kind": "theorem", "module": "Mathlib.Data.Set.FiniteExhaustion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Countable.finiteExhaustion", "kind": "definition", "module": "Mathlib.Data.Set.FiniteExhaustion", "is_tactic_proof": true, "tactics": ["apply", "by_cases", "obtain", "refine", "exact", "grind", "simp", "refine", "simp"], "tactic_count": 9}
{"name": "Set.FiniteExhaustion.Set.nonempty_finiteExhaustion_iff", "kind": "theorem", "module": "Mathlib.Data.Set.FiniteExhaustion", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "Set.FiniteExhaustion.prod", "kind": "definition", "module": "Mathlib.Data.Set.FiniteExhaustion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.FiniteExhaustion.prod_apply", "kind": "theorem", "module": "Mathlib.Data.Set.FiniteExhaustion", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "Set.finite_def", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.ofFinset", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.fintype", "kind": "definition", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.toFinset", "kind": "definition", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.toFinset_eq_toFinset", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.toFinite_toFinset", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.exists_finset", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": true, "tactics": ["cases", "exact"], "tactic_count": 2}
{"name": "Set.Finite.exists_finset_coe", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": true, "tactics": ["cases", "exact"], "tactic_count": 2}
{"name": "Set.instCanLiftFinsetCoeFinite", "kind": "instance", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.mem_toFinset", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.coe_toFinset", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.toFinset_nonempty", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.Finite.coeSort_toFinset", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.Finite.subtypeEquivToFinset", "kind": "definition", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.toFinset_inj", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.toFinset_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.Finite.toFinset_ssubset", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.Finite.subset_toFinset", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.Finite.ssubset_toFinset", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.Finite.toFinset_subset_toFinset", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.Finite.toFinset_ssubset_toFinset", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.Finite.toFinset_setOf", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.Finite.disjoint_toFinset", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.toFinset_inter", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Set.Finite.toFinset_union", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Set.Finite.toFinset_diff", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Set.Finite.toFinset_symmDiff", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Set.Finite.toFinset_compl", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Set.Finite.toFinset_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.Finite.toFinset_eq_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.toFinset_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.Finite.toFinset_eq_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.toFinset_image", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Set.Finite.toFinset_range", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Set.Finite.toFinset_nontrivial", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.fintypeUniv", "kind": "instance", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.fintypeTop", "kind": "instance", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.fintypeOfFiniteUniv", "kind": "definition", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.fintypeUnion", "kind": "instance", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.fintypeSep", "kind": "instance", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.fintypeInter", "kind": "instance", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.fintypeInterOfLeft", "kind": "instance", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.fintypeInterOfRight", "kind": "instance", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.fintypeSubset", "kind": "definition", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "Set.fintypeDiff", "kind": "instance", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.fintypeDiffLeft", "kind": "instance", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.fintypeEmpty", "kind": "instance", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.fintypeSingleton", "kind": "instance", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.fintypeInsert", "kind": "instance", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.fintypeInsertOfNotMem", "kind": "definition", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.fintypeInsertOfMem", "kind": "definition", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.fintypeInsert'", "kind": "instance", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.fintypeImage", "kind": "instance", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.fintypeOfFintypeImage", "kind": "definition", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.fintypeMap", "kind": "instance", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.fintypeLTNat", "kind": "instance", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.fintypeLENat", "kind": "instance", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.Nat.fintypeIio", "kind": "definition", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.fintypeMemFinset", "kind": "instance", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.finite_toSet", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.finite_toSet_toFinset", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.forall", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.exists", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.finite_toSet", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Multiset.finite_toSet_toFinset", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "List.finite_toSet", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.finsetSetFinite", "kind": "definition", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instWellFoundedLTSubtypeSetFinite", "kind": "instance", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finite.Set._example", "kind": "example", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finite.Set._example", "kind": "example", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finite.Set._example", "kind": "example", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finite.Set.finite_union", "kind": "instance", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": true, "tactics": ["cases", "cases", "classical"], "tactic_count": 3}
{"name": "Finite.Set.finite_sep", "kind": "instance", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": true, "tactics": ["cases", "classical"], "tactic_count": 2}
{"name": "Finite.Set.subset", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "Finite.Set.finite_inter_of_right", "kind": "instance", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finite.Set.finite_inter_of_left", "kind": "instance", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finite.Set.finite_diff", "kind": "instance", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finite.Set.finite_insert", "kind": "instance", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finite.Set.finite_image", "kind": "instance", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": true, "tactics": ["cases", "classical"], "tactic_count": 2}
{"name": "Set.Finite.of_subsingleton", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.finite_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.finite_univ_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.subset", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "Set.Finite.union", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "Set.Finite.finite_of_compl", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.Finite.sup", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.sep", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.inter_of_left", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.inter_of_right", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.inf_of_left", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.inf_of_right", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Infinite.mono", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.diff", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.of_diff", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.symmDiff", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.symmDiff_congr", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.finite_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Infinite.nonempty", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.finite_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.insert", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.finite_insert", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.image", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": true, "tactics": ["have", "apply"], "tactic_count": 2}
{"name": "Set.Finite.of_surjOn", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.map", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.of_finite_image", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.of_injOn", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.BijOn.finite_iff_finite", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.finite_of_finite_preimage", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.Finite.of_preimage", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.preimage", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Infinite.preimage", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Infinite.preimage'", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.preimage_embedding", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.finite_lt_nat", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.finite_le_nat", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.surjOn_iff_bijOn_of_mapsTo", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": true, "tactics": ["refine", "have", "exact"], "tactic_count": 3}
{"name": "Set.Finite.injOn_iff_bijOn_of_mapsTo", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": true, "tactics": ["refine", "have", "exact"], "tactic_count": 3}
{"name": "Set.finite_mem_finset", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Subsingleton.finite", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Infinite.nontrivial", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.finite_preimage_inl_and_inr", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.exists_finite_iff_finset", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.exists_subset_image_finite_and", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": true, "tactics": ["classical", "simp_rw", "aesop"], "tactic_count": 3}
{"name": "Set.finite_range_ite", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.finite_range_const", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.inhabited", "kind": "instance", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.finite_union", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.finite_image_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.finite_range_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.univ_finite_iff_nonempty_fintype", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.toFinset_insert", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.toFinset_insert'", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.finite_option", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.induction_on", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": true, "tactics": ["lift", "induction", "empty", "cons"], "tactic_count": 4}
{"name": "Set.Finite.induction_on_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": ["refine", "intro", "rw", "exact"], "tactic_count": 4}
{"name": "Set.seq_of_forall_finite_exists", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": true, "tactics": ["haveI", "choose", "set", "set", "refine", "convert", "rw", "exact"], "tactic_count": 8}
{"name": "Set.card_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.card_fintypeInsertOfNotMem", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.card_insert", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.card_image_of_inj_on", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.card_image_of_injective", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.card_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.card_lt_card", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.card_le_card", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.eq_of_subset_of_card_le", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.card_range_of_injective", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.card_toFinset", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.card_ne_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": true, "tactics": ["haveI", "rw"], "tactic_count": 2}
{"name": "Set.infinite_univ_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.infinite_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Infinite.exists_notMem_finite", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": true, "tactics": ["by_contra"], "tactic_count": 1}
{"name": "Set.Infinite.exists_notMem_finset", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.exists_notMem", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": true, "tactics": ["by_contra"], "tactic_count": 1}
{"name": "Finset.exists_notMem", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Infinite.natEmbedding", "kind": "definition", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Infinite.exists_subset_card_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.infinite_of_finite_compl", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.infinite_compl", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Infinite.diff", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.infinite_union", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.Infinite.of_image", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.infinite_image_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.infinite_range_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.infinite_of_injOn_mapsTo", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Infinite.exists_ne_map_eq_of_mapsTo", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": true, "tactics": ["contrapose", "exact"], "tactic_count": 2}
{"name": "Set.infinite_range_of_injective", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.infinite_of_injective_forall_mem", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.not_injOn_infinite_finite_image", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": true, "tactics": ["have", "have", "have", "contrapose", "rwa"], "tactic_count": 5}
{"name": "Set.finite_range_findGreatest", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.exists_card_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.exists_subset_injOn_image_eq_of_surjOn", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": true, "tactics": ["obtain", "refine", "simpa"], "tactic_count": 3}
{"name": "Finite.of_forall_not_lt_lt", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": true, "tactics": ["nontriviality", "rcases", "refine", "simpa"], "tactic_count": 4}
{"name": "Set.finite_of_forall_not_lt_lt", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.fintypeiUnion", "kind": "instance", "module": "Mathlib.Data.Set.Finite.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.fintypesUnion", "kind": "instance", "module": "Mathlib.Data.Set.Finite.Lattice", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.toFinset_iUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Lattice", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Set.fintypeBiUnion", "kind": "definition", "module": "Mathlib.Data.Set.Finite.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.fintypeBiUnion'", "kind": "instance", "module": "Mathlib.Data.Set.Finite.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finite.Set.finite_iUnion", "kind": "instance", "module": "Mathlib.Data.Set.Finite.Lattice", "is_tactic_proof": true, "tactics": ["have", "have", "classical"], "tactic_count": 3}
{"name": "Finite.Set.finite_sUnion", "kind": "instance", "module": "Mathlib.Data.Set.Finite.Lattice", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finite.Set.finite_biUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Lattice", "is_tactic_proof": true, "tactics": ["rw", "haveI", "infer_instance"], "tactic_count": 3}
{"name": "Finite.Set.finite_biUnion'", "kind": "instance", "module": "Mathlib.Data.Set.Finite.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finite.Set.finite_biUnion''", "kind": "instance", "module": "Mathlib.Data.Set.Finite.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finite.Set.finite_iInter", "kind": "instance", "module": "Mathlib.Data.Set.Finite.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.finite_iUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.biUnion'", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Lattice", "is_tactic_proof": true, "tactics": ["have", "rw", "apply"], "tactic_count": 3}
{"name": "Set.Finite.biUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.sUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Lattice", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.Finite.sInter", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.iUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Lattice", "is_tactic_proof": true, "tactics": ["suffices", "refine", "by_cases", "exact", "rw", "contradiction"], "tactic_count": 6}
{"name": "Set.finite_iUnion_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Infinite.iUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Infinite.iUnion₂", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.finite_iUnion_of_subsingleton", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Lattice", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Set.PairwiseDisjoint.finite_biUnion_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Lattice", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Set.Finite.preimage'", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Lattice", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.union_finset_finite_of_range_finite", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Lattice", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.Finite.of_finite_fibers", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.finite_subset_iUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Lattice", "is_tactic_proof": true, "tactics": ["have", "choose", "refine", "rw", "exact"], "tactic_count": 5}
{"name": "Set.eq_finite_iUnion_of_finite_subset_iUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.infinite_iUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Infinite.biUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Lattice", "is_tactic_proof": true, "tactics": ["rw", "have", "exact"], "tactic_count": 3}
{"name": "Set.Infinite.sUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Lattice", "is_tactic_proof": true, "tactics": ["rw", "have", "exact"], "tactic_count": 3}
{"name": "Set.map_finite_biSup", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Lattice", "is_tactic_proof": true, "tactics": ["have", "simp", "exact"], "tactic_count": 3}
{"name": "Set.map_finite_biInf", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Lattice", "is_tactic_proof": true, "tactics": ["have", "simp", "exact"], "tactic_count": 3}
{"name": "Set.map_finite_iSup", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Lattice", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.map_finite_iInf", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Lattice", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.Finite.iSup_biInf_of_monotone", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Lattice", "is_tactic_proof": true, "tactics": ["induction", "empty", "insert", "rw", "simp", "exact"], "tactic_count": 6}
{"name": "Set.Finite.iSup_biInf_of_antitone", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.iInf_biSup_of_monotone", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.iInf_biSup_of_antitone", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iSup_iInf_of_monotone", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Lattice", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.iSup_iInf_of_antitone", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iInf_iSup_of_monotone", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iInf_iSup_of_antitone", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_iInter_of_monotone", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_iInter_of_antitone", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iInter_iUnion_of_monotone", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iInter_iUnion_of_antitone", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_pi_of_monotone", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Lattice", "is_tactic_proof": true, "tactics": ["simp", "haveI", "refine", "exact"], "tactic_count": 4}
{"name": "Set.iUnion_univ_pi_of_monotone", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.bddAbove", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.bddAbove_biUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Lattice", "is_tactic_proof": true, "tactics": ["induction", "empty", "insert"], "tactic_count": 3}
{"name": "Set.infinite_of_not_bddAbove", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.bddBelow", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.bddBelow_biUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.infinite_of_not_bddBelow", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.bddAbove", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.bddBelow", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.finite_diff_iUnion_Ioo", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.finite_diff_iUnion_Ioo'", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Lattice", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Directed.exists_mem_subset_of_finset_subset_biUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Lattice", "is_tactic_proof": true, "tactics": ["induction", "empty", "cons", "simp", "rcases", "rcases", "exact"], "tactic_count": 7}
{"name": "DirectedOn.exists_mem_subset_of_finset_subset_biUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Lattice", "is_tactic_proof": true, "tactics": ["rw", "haveI", "simpa"], "tactic_count": 3}
{"name": "DirectedOn.exists_mem_subset_of_finite_of_subset_sUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Lattice", "is_tactic_proof": true, "tactics": ["rw", "have", "exact"], "tactic_count": 3}
{"name": "Set.Finite.fin_embedding", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.fin_param", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.induction_to", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Lemmas", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "rw", "refine", "obtain", "exact"], "tactic_count": 7}
{"name": "Set.Finite.induction_to_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sUnion_finite_eq_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.exists_min_image", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.exists_max_image", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.exists_lower_bound_image", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Lemmas", "is_tactic_proof": true, "tactics": ["rcases", "exact", "rcases", "exact"], "tactic_count": 4}
{"name": "Set.exists_upper_bound_image", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.finite_length_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.finite_length_lt", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.List", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "List.finite_length_le", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.List", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.fintypeBind", "kind": "definition", "module": "Mathlib.Data.Set.Finite.Monad", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.fintypeBind'", "kind": "instance", "module": "Mathlib.Data.Set.Finite.Monad", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.fintypePure", "kind": "instance", "module": "Mathlib.Data.Set.Finite.Monad", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.fintypeSeq", "kind": "instance", "module": "Mathlib.Data.Set.Finite.Monad", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "Set.fintypeSeq'", "kind": "instance", "module": "Mathlib.Data.Set.Finite.Monad", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finite.Set.finite_pure", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Monad", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finite.Set.finite_seq", "kind": "instance", "module": "Mathlib.Data.Set.Finite.Monad", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "Set.Finite.bind", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Monad", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.seq", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Monad", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.seq'", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Monad", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.finite_subsets", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Powerset", "is_tactic_proof": true, "tactics": ["convert", "ext", "simpa", "h.subset"], "tactic_count": 4}
{"name": "Set.Finite.powerset", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Powerset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.fintypeRange", "kind": "instance", "module": "Mathlib.Data.Set.Finite.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finite.Set.finite_range", "kind": "instance", "module": "Mathlib.Data.Set.Finite.Range", "is_tactic_proof": true, "tactics": ["classical", "haveI", "infer_instance"], "tactic_count": 3}
{"name": "Finite.Set.finite_replacement", "kind": "instance", "module": "Mathlib.Data.Set.Finite.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.finite_range", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Range", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.dependent_image", "kind": "theorem", "module": "Mathlib.Data.Set.Finite.Range", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "Set.EqOn.eq_of_mem", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.eqOn_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.eqOn_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.eqOn_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.EqOn.symm", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.eqOn_comm", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.eqOn_refl", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.EqOn.trans", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.EqOn.image_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.EqOn.image_eq_self", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.EqOn.inter_preimage_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.EqOn.mono", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.eqOn_union", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.EqOn.union", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.EqOn.comp_left", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.EqOn.comp_left₂", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.eqOn_range", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mapsTo_iff_image_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mapsTo_prodMap_diagonal", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.MapsTo.subset_preimage", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mapsTo_iff_subset_preimage", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mapsTo_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mapsTo_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mapsTo_empty_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.MapsTo.nonempty", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.MapsTo.image_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.MapsTo.congr", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.EqOn.comp_right", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.EqOn.mapsTo_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.MapsTo.comp", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mapsTo_id", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.MapsTo.iterate", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.MapsTo.iterate_restrict", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": true, "tactics": ["ext", "simpa"], "tactic_count": 2}
{"name": "Set.mapsTo_of_subsingleton'", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mapsTo_of_subsingleton", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.MapsTo.mono", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.MapsTo.mono_left", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.MapsTo.mono_right", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.MapsTo.union_union", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.MapsTo.union", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mapsTo_union", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.MapsTo.inter", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.MapsTo.insert", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.MapsTo.inter_inter", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mapsTo_inter", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mapsTo_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mapsTo_range", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mapsTo_image_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.MapsTo.comp_left", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.MapsTo.comp_right", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mapsTo_univ_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mapsTo_range_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.MapsTo.mem_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Subsingleton.injOn", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.injOn_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.injOn_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.injOn_pair", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "Set.injOn_of_eq_iff_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.InjOn.eq_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.InjOn.ne_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.InjOn.congr", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.EqOn.injOn_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.InjOn.mono", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.injOn_union", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": true, "tactics": ["refine", "intro", "obtain", "exact", "rintro", "rintro", "exacts"], "tactic_count": 7}
{"name": "Set.injOn_insert", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Set.injOn_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.injective_iff_injOn_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.injOn_of_injective", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.injOn_subtype_val", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.injOn_id", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.InjOn.comp", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.InjOn.of_comp", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.InjOn.image_of_comp", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.InjOn.comp_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.InjOn.iterate", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.injOn_of_subsingleton", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.injOn_range", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "Set.InjOn.injective_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.exists_injOn_iff_injective", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.injOn_preimage", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.InjOn.mem_of_mem_image", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.InjOn.mem_image_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.InjOn.preimage_image_inter", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.EqOn.cancel_left", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.InjOn.cancel_left", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.InjOn.image_inter", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": true, "tactics": ["apply", "intro", "have", "apply", "rwa", "rw", "exact"], "tactic_count": 7}
{"name": "Set.InjOn.image", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.InjOn.image_eq_image_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.InjOn.image_subset_image_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "Set.InjOn.image_ssubset_image_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Disjoint.image", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": true, "tactics": ["rw", "rw"], "tactic_count": 2}
{"name": "Set.InjOn.image_diff", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": ["refine", "subset_antisymm", "exact"], "tactic_count": 3}
{"name": "Set.InjOn.image_diff_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.InjOn.imageFactorization_injective", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.imageFactorization_injective_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.graphOn_univ_inj", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.graphOn_univ_injective", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.exists_eq_graphOn_image_fst", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": true, "tactics": ["refine", "rintro", "rw", "exact", "have", "choose", "rw", "use", "rw", "exact"], "tactic_count": 10}
{"name": "Set.exists_eq_graphOn", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.SurjOn.subset_range", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.surjOn_iff_exists_map_subtype", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.surjOn_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.surjOn_empty_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.surjOn_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.surjOn_univ_of_subsingleton_nonempty", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Set.surjOn_image", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.SurjOn.comap_nonempty", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.SurjOn.congr", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Set.EqOn.surjOn_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.SurjOn.mono", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.SurjOn.union", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.SurjOn.union_union", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.SurjOn.inter_inter", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": true, "tactics": ["intro", "rcases", "rcases", "obtain", "exact"], "tactic_count": 5}
{"name": "Set.SurjOn.inter", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.surjOn_id", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.SurjOn.comp", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.SurjOn.of_comp", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": true, "tactics": ["intro", "obtain", "exact"], "tactic_count": 3}
{"name": "Set.surjOn_comp_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.SurjOn.iterate", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.SurjOn.comp_left", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.SurjOn.comp_right", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Set.surjOn_of_subsingleton'", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.surjOn_of_subsingleton", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.surjOn_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Function.Surjective.surjOn", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.SurjOn.surjective", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.surjective_iff_surjOn_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.SurjOn.image_eq_of_mapsTo", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_eq_iff_surjOn_mapsTo", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": true, "tactics": ["refine", "rintro", "exact"], "tactic_count": 3}
{"name": "Set.SurjOn.image_preimage", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.SurjOn.mapsTo_compl", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.MapsTo.surjOn_compl", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.EqOn.cancel_right", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": true, "tactics": ["intro", "obtain", "exact"], "tactic_count": 3}
{"name": "Set.SurjOn.cancel_right", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.eqOn_comp_right_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.SurjOn.forall", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.coind_surjective", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.coind_bijective", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.BijOn.mapsTo", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.BijOn.injOn", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.BijOn.surjOn", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.BijOn.mk", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.bijOn_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.bijOn_empty_iff_left", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.bijOn_empty_iff_right", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.bijOn_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.BijOn.inter_mapsTo", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.MapsTo.inter_bijOn", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.BijOn.inter", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.BijOn.union", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.BijOn.subset_range", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.InjOn.bijOn_image", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.BijOn.congr", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.EqOn.bijOn_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.BijOn.image_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.BijOn.forall", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.BijOn.exists", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.image_eq_iff_bijOn", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.bijOn_id", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.BijOn.comp", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.bijOn_comp_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.bijOn_image_image", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": true, "tactics": ["obtain", "refine", "rintro", "exact", "rintro", "obtain", "grind"], "tactic_count": 7}
{"name": "Set.BijOn.iterate", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.bijOn_of_subsingleton'", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.bijOn_of_subsingleton", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.BijOn.bijective", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.bijOn_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.bijective_iff_bijOn_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.BijOn.compl", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.BijOn.subset_right", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact"], "tactic_count": 3}
{"name": "Set.BijOn.subset_left", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.BijOn.insert_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.BijOn.insert", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.BijOn.sdiff_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "Set.LeftInvOn.eqOn", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.LeftInvOn.eq", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.LeftInvOn.congr_left", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.LeftInvOn.congr_right", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.LeftInvOn.injOn", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.LeftInvOn.surjOn", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.LeftInvOn.mapsTo", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.leftInvOn_id", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.LeftInvOn.comp", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.LeftInvOn.mono", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.LeftInvOn.image_inter'", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": true, "tactics": ["apply", "rintro", "exact", "rintro", "exact"], "tactic_count": 5}
{"name": "Set.LeftInvOn.image_inter", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": true, "tactics": ["rw", "refine", "rintro"], "tactic_count": 3}
{"name": "Set.LeftInvOn.image_image", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.LeftInvOn.image_image'", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.RightInvOn.eqOn", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.RightInvOn.eq", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.LeftInvOn.rightInvOn_image", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.RightInvOn.congr_left", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.RightInvOn.congr_right", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.RightInvOn.surjOn", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.RightInvOn.mapsTo", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.rightInvOn_id", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.RightInvOn.comp", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.RightInvOn.mono", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.InjOn.rightInvOn_of_leftInvOn", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.eqOn_of_leftInvOn_of_rightInvOn", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.SurjOn.leftInvOn_of_rightInvOn", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.invOn_id", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.InvOn.comp", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.InvOn.symm", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.InvOn.mono", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.InvOn.bijOn", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.invFunOn", "kind": "definition", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.invFunOn_pos", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Function.invFunOn_mem", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.invFunOn_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.invFunOn_neg", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Function.invFunOn_apply_mem", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.invFunOn_apply_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.InjOn.leftInvOn_invFunOn", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.InjOn.invFunOn_image", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.leftInvOn_invFunOn_of_subset_image_image", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.injOn_iff_invFunOn_image_image_eq_self", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.invFunOn_injOn_image", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": true, "tactics": ["rintro", "rw"], "tactic_count": 2}
{"name": "Function.invFunOn_image_image_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "Set.SurjOn.rightInvOn_invFunOn", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.BijOn.invOn_invFunOn", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.SurjOn.invOn_invFunOn", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": true, "tactics": ["refine", "rintro", "rw"], "tactic_count": 3}
{"name": "Set.SurjOn.mapsTo_invFunOn", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.SurjOn.image_invFunOn_image_of_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.SurjOn.image_invFunOn_image", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.SurjOn.bijOn_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": true, "tactics": ["refine", "rintro", "rwa"], "tactic_count": 3}
{"name": "Set.surjOn_iff_exists_bijOn_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": true, "tactics": ["constructor", "rcases", "exact", "intro", "haveI", "exact", "rintro", "exact"], "tactic_count": 8}
{"name": "Set.exists_subset_bijOn", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.exists_image_eq_and_injOn", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.exists_image_eq_injOn_of_subset_range", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.BijOn.exists_extend_of_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": true, "tactics": ["obtain", "rw", "refine", "exact", "rw", "exact", "rw", "refine", "rw", "exact", "exact", "rw", "exact"], "tactic_count": 13}
{"name": "Set.BijOn.exists_extend", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.InjOn.exists_subset_injOn_subset_range_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Set.preimage_invFun_of_mem", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": true, "tactics": ["ext", "rcases", "simp", "hf.mem_set_image]", "simp"], "tactic_count": 5}
{"name": "Set.preimage_invFun_of_notMem", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": true, "tactics": ["ext", "rcases", "rw", "have", "simp"], "tactic_count": 5}
{"name": "Set.BijOn.symm", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.bijOn_comm", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.SurjOn.exists_subset_injOn_image_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": true, "tactics": ["choose", "exact"], "tactic_count": 2}
{"name": "Function.Injective.comp_injOn", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.LeftInverse.leftInvOn", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.RightInverse.rightInvOn", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.LeftInverse.rightInvOn_range", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Semiconj.mapsTo_image", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Semiconj.mapsTo_image_right", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Semiconj.mapsTo_range", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Semiconj.surjOn_image", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": true, "tactics": ["rintro", "rcases", "rw", "exact"], "tactic_count": 4}
{"name": "Function.Semiconj.surjOn_range", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Function.Semiconj.injOn_image", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": true, "tactics": ["rintro", "simp", "exact"], "tactic_count": 3}
{"name": "Function.Semiconj.injOn_range", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Function.Semiconj.bijOn_image", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Semiconj.bijOn_range", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Function.Semiconj.mapsTo_preimage", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Semiconj.injOn_preimage", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": true, "tactics": ["intro", "have", "rw", "exact"], "tactic_count": 4}
{"name": "Function.update_comp_eq_of_notMem_range'", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.update_comp_eq_of_notMem_range", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.insert_injOn", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.apply_eq_of_range_eq_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.MapsTo.extendDomain", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "Set.SurjOn.extendDomain", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": true, "tactics": ["rintro", "obtain", "exact"], "tactic_count": 3}
{"name": "Set.BijOn.extendDomain", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.LeftInvOn.extendDomain", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "Set.RightInvOn.extendDomain", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "Set.InvOn.extendDomain", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.InjOn.prodMap", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.SurjOn.prodMap", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": true, "tactics": ["rintro", "obtain", "obtain", "exact"], "tactic_count": 4}
{"name": "Set.MapsTo.prodMap", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.BijOn.prodMap", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.LeftInvOn.prodMap", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.RightInvOn.prodMap", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.InvOn.prodMap", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.bijOn'", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.bijOn", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.invOn", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.bijOn_image", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.bijOn_symm_image", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.bijOn_symm", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.bijOn_swap", "kind": "theorem", "module": "Mathlib.Data.Set.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instAlternative", "kind": "instance", "module": "Mathlib.Data.Set.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.fmap_eq_image", "kind": "theorem", "module": "Mathlib.Data.Set.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.seq_eq_set_seq", "kind": "theorem", "module": "Mathlib.Data.Set.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.seqLeft_def", "kind": "theorem", "module": "Mathlib.Data.Set.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.seqRight_def", "kind": "theorem", "module": "Mathlib.Data.Set.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.pure_def", "kind": "theorem", "module": "Mathlib.Data.Set.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.failure_def", "kind": "theorem", "module": "Mathlib.Data.Set.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.orElse_def", "kind": "theorem", "module": "Mathlib.Data.Set.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image2_def", "kind": "theorem", "module": "Mathlib.Data.Set.Functor", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Set.instLawfulAlternative", "kind": "instance", "module": "Mathlib.Data.Set.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instCommApplicative", "kind": "instance", "module": "Mathlib.Data.Set.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.monad", "kind": "definition", "module": "Mathlib.Data.Set.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.bind_def", "kind": "theorem", "module": "Mathlib.Data.Set.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instLawfulMonad", "kind": "instance", "module": "Mathlib.Data.Set.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_coe_of_mem", "kind": "theorem", "module": "Mathlib.Data.Set.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.coe_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Functor", "is_tactic_proof": true, "tactics": ["intro"], "tactic_count": 1}
{"name": "Set.mem_of_mem_coe", "kind": "theorem", "module": "Mathlib.Data.Set.Functor", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "Set.eq_univ_of_coe_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_coe_eq_restrict_image", "kind": "theorem", "module": "Mathlib.Data.Set.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.coe_eq_image_val", "kind": "theorem", "module": "Mathlib.Data.Set.Functor", "is_tactic_proof": true, "tactics": ["change", "ext", "simp"], "tactic_count": 3}
{"name": "Set.mem_image_val_of_mem", "kind": "theorem", "module": "Mathlib.Data.Set.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_val_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_of_mem_image_val", "kind": "theorem", "module": "Mathlib.Data.Set.Functor", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "Set.eq_univ_of_image_val_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_image_val_eq_restrict_image", "kind": "theorem", "module": "Mathlib.Data.Set.Functor", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "SetM", "kind": "definition", "module": "Mathlib.Data.Set.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instAlternativeMonadSetM", "kind": "instance", "module": "Mathlib.Data.Set.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instLawfulMonadSetM", "kind": "instance", "module": "Mathlib.Data.Set.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instLawfulAlternativeSetM", "kind": "instance", "module": "Mathlib.Data.Set.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetM.run", "kind": "definition", "module": "Mathlib.Data.Set.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.preimage_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.preimage_congr", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["congr", "simp"], "tactic_count": 2}
{"name": "Set.preimage_mono", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.preimage_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subset_preimage_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.preimage_inter", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.preimage_union", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.preimage_compl", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.preimage_diff", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.preimage_symmDiff", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.preimage_ite", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.preimage_setOf_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.preimage_id_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.preimage_id", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.preimage_id'", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.preimage_const_of_mem", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.preimage_const_of_notMem", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.preimage_const", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.exists_eq_const_of_preimage_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["rcases", "exact", "have", "exact"], "tactic_count": 4}
{"name": "Set.preimage_comp", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.preimage_comp_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.preimage_iterate_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Set.preimage_preimage", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.eq_preimage_subtype_val_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.nonempty_of_nonempty_preimage", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.preimage_singleton_true", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Set.preimage_singleton_false", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Set.preimage_subtype_coe_eq_compl", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["ext", "constructor", "intro", "exact", "grind"], "tactic_count": 5}
{"name": "Set.preimage_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["rintro", "obtain", "rwa", "simpa"], "tactic_count": 4}
{"name": "Set.image_eta", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.mem_set_image", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.preimage_subset_of_surjOn", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.forall_mem_image", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.exists_mem_image", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.image_congr", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Set.image_congr'", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.image_mono", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.monotone_image", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_comp", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Set.image_comp_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.image_image", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_comm", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Function.Semiconj.set_image", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Commute.set_image", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_union", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.image_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.image_inter_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_inter_on", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_inter", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_univ_of_surjective", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.Nonempty.image_const", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_eq_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Set.preimage_compl_eq_image_compl", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_compl_image", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.image_id_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Set.image_id'", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Set.image_id", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.image_iterate_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Set.compl_compl_image", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.image_insert_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.image_pair", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Function.LeftInverse.mem_preimage_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.image_subset_preimage_of_inverse", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.preimage_subset_image_of_inverse", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.range_inter_ssubset_iff_preimage_ssubset", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["simp", "apply", "constructor", "all_goals", "intro", "simp_all", "aesop"], "tactic_count": 7}
{"name": "Set.image_eq_preimage_of_inverse", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Involutive.image_eq_preimage_symm", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_image_iff_of_inverse", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.image_compl_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subset_image_compl", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_compl_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subset_image_diff", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.subset_image_symmDiff", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_diff", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_symmDiff", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.Nonempty.image", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nonempty.of_image", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_nonempty", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nonempty.preimage", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instNonemptyElemImage", "kind": "instance", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_subset_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_preimage_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subset_preimage_image", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.preimage_image_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.preimage_image_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_preimage_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nonempty.subset_preimage_const", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.preimage_injective", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.preimage_surjective", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.preimage_eq_preimage", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_inter_preimage", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.image_preimage_inter", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.image_inter_nonempty_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.disjoint_image_left", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.disjoint_image_right", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.image_diff_preimage", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.compl_image", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.compl_image_set_of", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inter_preimage_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.union_preimage_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subset_image_union", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.preimage_subset_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_eq_image", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subset_image_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["refine", "rwa"], "tactic_count": 2}
{"name": "Set.exists_subset_image_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.forall_subset_image_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.image_subset_image_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.prod_quotient_preimage_eq_image", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.exists_image_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.imageFactorization_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.imageFactorization_surjective", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_perm", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["ext", "obtain", "refine", "rintro", "rwa", "refine", "grind"], "tactic_count": 7}
{"name": "Set.powerset_insert", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["ext", "constructor", "intro", "by_cases", "right", "refine", "grind", "grind"], "tactic_count": 8}
{"name": "Set.disjoint_powerset_insert", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.powerset_insert_injOn", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.forall_mem_range", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.forall_subtype_range_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.exists_range_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.exists_subtype_range_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.range_eq_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subset_range_of_surjective", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.image_compl_eq_range_diff_image", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.range_diff_image", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.preimage_eq_univ_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.image_subset_range", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.mem_range_of_mem_image", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.mem_range_succ", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nonempty.preimage'", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.range_comp", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Set.range_comp'", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.range_subset_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.range_subset_range_iff_exists_comp", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.range_eq_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.range_comp_subset_range", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.range_nonempty_iff_nonempty", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.range_nonempty", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.range_eq_empty_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.range_eq_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.range_eq_singleton_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Set.range_eq_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instNonemptyRange", "kind": "instance", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_union_image_compl_eq_range", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.insert_image_compl_eq_range", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.image_preimage_eq_range_inter", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.image_preimage_eq_inter_range", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.image_preimage_eq_of_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.image_preimage_eq_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.subset_range_iff_exists_image_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.range_image", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.exists_subset_range_and_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.forall_subset_range_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.preimage_subset_preimage_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rcases", "exact", "intro"], "tactic_count": 5}
{"name": "Set.preimage_eq_preimage'", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["constructor", "intro", "apply", "rw", "rw", "rintro", "rfl"], "tactic_count": 7}
{"name": "Set.preimage_inter_range", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.preimage_range_inter", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.preimage_image_preimage", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.range_id", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.range_id'", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.range_fst", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.range_snd", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.range_eval", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.range_inl", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Set.range_inr", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Set.isCompl_range_inl_range_inr", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.range_inl_union_range_inr", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.range_inl_inter_range_inr", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.range_inr_union_range_inl", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.range_inr_inter_range_inl", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.preimage_inl_image_inr", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Set.preimage_inr_image_inl", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Set.preimage_inl_range_inr", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.preimage_inr_range_inl", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.compl_range_inl", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.compl_range_inr", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.preimage_sumElim", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Set.image_preimage_inl_union_image_preimage_inr", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.image_sumElim", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.range_quot_mk", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.range_quot_lift", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.range_quotient_mk", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.range_quotient_lift", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.range_quotient_mk'", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Quotient.range_mk''", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.range_quotient_lift_on'", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.canLift", "kind": "instance", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.range_const_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.range_const", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.range_subtype_map", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["ext", "simp_rw", "simp"], "tactic_count": 3}
{"name": "Set.image_swap_eq_preimage_swap", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.preimage_singleton_nonempty", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.preimage_singleton_eq_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.range_subset_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.image_compl_preimage", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.rangeFactorization_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.rangeFactorization_coe", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.coe_comp_rangeFactorization", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_eq_range", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["ext", "constructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 6}
{"name": "Sum.range_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Sum.elim_range", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.range_ite_subset'", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.range_ite_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.preimage_range", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.range_unique", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["ext", "rw", "constructor", "rintro", "rw", "grind", "grind"], "tactic_count": 7}
{"name": "Set.range_diff_image_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.range_inclusion", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Set.leftInverse_rangeSplitting", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.rangeSplitting_injective", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.rightInverse_rangeSplitting", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.preimage_rangeSplitting", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.isCompl_range_some_none", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.compl_range_some", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.range_some_inter_none", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.range_some_union_none", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.insert_none_range_some", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_of_range_union_range_eq_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["rw", "image_preimage_eq_inter_range,"], "tactic_count": 2}
{"name": "Set.Subsingleton.image", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Subsingleton.preimage", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subsingleton_of_image", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subsingleton_of_preimage", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subsingleton_range", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nontrivial.preimage", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "exact"], "tactic_count": 3}
{"name": "Set.Nontrivial.image", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nontrivial.image_of_injOn", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Set.nontrivial_of_image", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_nontrivial", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.InjOn.image_nontrivial_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.nontrivial_of_preimage", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.preimage_injective", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.preimage_image", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.preimage_surjective", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.subsingleton_image_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.image_preimage", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.image_surjective", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["intro", "use", "rw"], "tactic_count": 3}
{"name": "Function.Surjective.nonempty_preimage", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Function.Injective.image_injective", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["intro", "rw"], "tactic_count": 2}
{"name": "Function.Injective.image_strictMono", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.preimage_subset_preimage_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["apply", "rw", "apply"], "tactic_count": 3}
{"name": "Function.Surjective.range_comp", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.mem_range_iff_existsUnique", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.compl_image_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Function.LeftInverse.image_image", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Function.LeftInverse.preimage_preimage", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Function.Involutive.preimage", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.LeftInverse.image_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EquivLike.range_comp", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.coe_image", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.coe_image_of_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["ext", "rw", "exact"], "tactic_count": 3}
{"name": "Subtype.range_coe", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Subtype.range_val", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.range_coe_subtype", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.coe_preimage_self", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subtype.range_val_subtype", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.coe_image_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.coe_image_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.image_preimage_coe", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.image_preimage_val", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.preimage_coe_eq_preimage_coe_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subtype.preimage_coe_self_inter", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subtype.preimage_coe_inter_self", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subtype.preimage_val_eq_preimage_val_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.preimage_val_subset_preimage_val_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["constructor", "rw", "exact", "intro", "exact"], "tactic_count": 5}
{"name": "Subtype.exists_set_subtype", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subtype.forall_set_subtype", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subtype.preimage_coe_nonempty", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subtype.preimage_coe_eq_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Subtype.preimage_coe_compl", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.preimage_coe_compl'", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Option.injective_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["simp", "refine", "rintro", "exacts"], "tactic_count": 4}
{"name": "Option.range_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Option.range_elim", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Option.image_elim_range_some_eq_range", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Set.image_surjective", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["refine", "rcases", "have", "exact"], "tactic_count": 4}
{"name": "Set.image_injective", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["refine", "rw", "rw"], "tactic_count": 3}
{"name": "Set.preimage_eq_iff_eq_image", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.eq_preimage_iff_image_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Disjoint.preimage", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Codisjoint.preimage", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["simp", "rw"], "tactic_count": 2}
{"name": "IsCompl.preimage", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.disjoint_image_image", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.disjoint_image_of_injective", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Disjoint.of_image", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.disjoint_image_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Disjoint.of_preimage", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.disjoint_preimage_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.preimage_eq_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.preimage_eq_empty_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.disjoint_image_inl_image_inr", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.disjoint_range_inl_image_inr", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.disjoint_image_inl_range_inr", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "sigma_mk_preimage_image'", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "sigma_mk_preimage_image_eq_self", "kind": "theorem", "module": "Mathlib.Data.Set.Image", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.inclusion", "kind": "abbrev", "module": "Mathlib.Data.Set.Inclusion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inclusion_self", "kind": "theorem", "module": "Mathlib.Data.Set.Inclusion", "is_tactic_proof": true, "tactics": ["cases", "rfl"], "tactic_count": 2}
{"name": "Set.inclusion_eq_id", "kind": "theorem", "module": "Mathlib.Data.Set.Inclusion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inclusion_mk", "kind": "theorem", "module": "Mathlib.Data.Set.Inclusion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inclusion_right", "kind": "theorem", "module": "Mathlib.Data.Set.Inclusion", "is_tactic_proof": true, "tactics": ["cases", "rfl"], "tactic_count": 2}
{"name": "Set.inclusion_inclusion", "kind": "theorem", "module": "Mathlib.Data.Set.Inclusion", "is_tactic_proof": true, "tactics": ["cases", "rfl"], "tactic_count": 2}
{"name": "Set.inclusion_comp_inclusion", "kind": "theorem", "module": "Mathlib.Data.Set.Inclusion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.coe_inclusion", "kind": "theorem", "module": "Mathlib.Data.Set.Inclusion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.val_comp_inclusion", "kind": "theorem", "module": "Mathlib.Data.Set.Inclusion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inclusion_injective", "kind": "theorem", "module": "Mathlib.Data.Set.Inclusion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inclusion_inj", "kind": "theorem", "module": "Mathlib.Data.Set.Inclusion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.eq_of_inclusion_surjective", "kind": "theorem", "module": "Mathlib.Data.Set.Inclusion", "is_tactic_proof": true, "tactics": ["refine", "obtain", "grind"], "tactic_count": 3}
{"name": "Set.inclusion_le_inclusion", "kind": "theorem", "module": "Mathlib.Data.Set.Inclusion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inclusion_lt_inclusion", "kind": "theorem", "module": "Mathlib.Data.Set.Inclusion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.insert_def", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subset_insert", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_insert", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_insert_of_mem", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.eq_or_mem_of_mem_insert", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_of_mem_insert_of_ne", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.eq_of_mem_insert_of_notMem", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_insert_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.insert_eq_of_mem", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.ne_insert_of_notMem", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.insert_eq_self", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.insert_ne_self", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.insert_subset_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.insert_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.insert_subset_insert", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.insert_subset_insert_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.subset_insert_iff_of_notMem", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.ssubset_iff_insert", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "HasSubset.Subset.ssubset_of_mem_notMem", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.ssubset_insert", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.insert_comm", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.insert_idem", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.insert_union", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.union_insert", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.insert_nonempty", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instNonemptyElemInsert", "kind": "instance", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.insert_inter_distrib", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.insert_union_distrib", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.forall_of_forall_insert", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.forall_insert_of_forall", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.exists_mem_insert", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.forall_mem_insert", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.subtypeInsertEquivOption", "kind": "definition", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instLawfulSingleton", "kind": "instance", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.singleton_def", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_singleton_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.notMem_singleton_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.setOf_eq_eq_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.setOf_eq_eq_singleton'", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.eq_of_mem_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.singleton_eq_singleton_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.singleton_injective", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_singleton_of_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.insert_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.singleton_nonempty", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.singleton_ne_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.empty_ne_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.empty_ssubset_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.singleton_subset_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.singleton_subset_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.set_compr_eq_eq_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.singleton_union", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.union_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.singleton_inter_nonempty", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.inter_singleton_nonempty", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.singleton_inter_eq_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inter_singleton_eq_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.singleton_inter_of_mem", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.inter_singleton_of_mem", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.notMem_singleton_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.uniqueSingleton", "kind": "instance", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.eq_singleton_iff_unique_mem", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.eq_singleton_iff_nonempty_unique_mem", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.setOf_mem_list_eq_replicate", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.setOf_mem_list_eq_singleton_of_nodup", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": true, "tactics": ["constructor", "rw", "rintro", "simp", "simp", "rintro", "simp"], "tactic_count": 7}
{"name": "Set.default_coe_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subset_singleton_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subset_singleton_iff_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.Nonempty.subset_singleton_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ssubset_singleton_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": false, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.eq_empty_of_ssubset_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.eq_of_nonempty_of_subsingleton", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.eq_of_nonempty_of_subsingleton'", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nonempty.eq_zero", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nonempty.eq_one", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.disjoint_singleton_left", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.disjoint_singleton_right", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.disjoint_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.disjoint_insert_left", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.disjoint_insert_right", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.insert_inj", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.insert_diff_eq_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.inter_insert_of_mem", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.insert_inter_of_mem", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.inter_insert_of_notMem", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.insert_inter_of_notMem", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.pair_eq_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.pair_comm", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.pair_eq_pair_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.pair_subset_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.pair_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subset_pair_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.subset_pair_iff_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nonempty.subset_pair_iff_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.powerset_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.preimage_fst_singleton_eq_range", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.preimage_snd_singleton_eq_range", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.decidableSingleton", "kind": "instance", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prop.compl_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Insert", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_iUnion₂", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.mem_iInter₂", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.mem_iUnion_of_mem", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_iUnion₂_of_mem", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_iInter_of_mem", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_iInter₂_of_mem", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_congr_Prop", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iInter_congr_Prop", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_plift_up", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_plift_down", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iInter_plift_up", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iInter_plift_down", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_eq_if", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_eq_dif", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iInter_eq_if", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iInf_eq_dif", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.exists_set_mem_of_union_eq_top", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["have", "rw", "simpa"], "tactic_count": 3}
{"name": "Set.nonempty_of_union_eq_top_of_nonempty", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Set.nonempty_of_nonempty_iUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Set.nonempty_of_nonempty_iUnion_eq_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.setOf_exists", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.setOf_forall", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion₂_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subset_iInter", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subset_iInter₂", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_subset_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion₂_subset_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.subset_iInter_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subset_iInter₂_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.subset_iUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iInter_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iInter_subset_iUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subset_iUnion₂", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iInter₂_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subset_iUnion_of_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iInter_subset_of_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subset_iUnion₂_of_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iInter₂_subset_of_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_mono", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_mono''", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion₂_mono", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iInter_mono", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iInter_mono''", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iInter₂_mono", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_mono'", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion₂_mono'", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iInter_mono'", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iInter₂_mono'", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion₂_subset_iUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iInter_subset_iInter₂", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_setOf", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "Set.iInter_setOf", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "Set.iUnion_congr_of_surjective", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iInter_congr_of_surjective", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_congr", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iInter_congr", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion₂_congr", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iInter₂_congr", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.BijOn.iUnion_comp", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.BijOn.iInter_comp", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.BijOn.iUnion_congr", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.BijOn.iInter_congr", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_const", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iInter_const", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_eq_const", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iInter_eq_const", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.compl_iUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.compl_iUnion₂", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.compl_iInter", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.compl_iInter₂", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.iUnion_eq_compl_iInter_compl", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.iInter_eq_compl_iUnion_compl", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.inter_iUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_inter", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_union_distrib", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iInter_inter_distrib", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.union_iUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_union", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inter_iInter", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iInter_inter", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.insert_iUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.union_iInter", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iInter_union", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.insert_iInter", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.iUnion_diff", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.diff_iUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.diff_iInter", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.iUnion_inter_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_inter_of_monotone", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_inter_of_antitone", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iInter_union_of_monotone", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iInter_union_of_antitone", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_iInter_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_option", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iInter_option", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_dite", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_ite", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iInter_dite", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iInter_ite", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iInter_false", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_false", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iInter_true", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_true", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iInter_exists", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_exists", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iInter_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_eq_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iInter_eq_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.nonempty_iUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.nonempty_biUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.iUnion_nonempty_index", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iInter_iInter_eq_left", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iInter_iInter_eq_right", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_iUnion_eq_left", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_iUnion_eq_right", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iInter_or", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_or", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_and", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iInter_and", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_comm", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iInter_comm", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_sigma", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_sigma'", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iInter_sigma", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iInter_sigma'", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion₂_comm", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iInter₂_comm", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.biUnion_and", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.biUnion_and'", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.biInter_and", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.biInter_and'", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.iUnion_iUnion_eq_or_left", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.iInter_iInter_eq_or_left", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.iUnion_sum", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iInter_sum", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_psigma", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_psigma'", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iInter_psigma", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iInter_psigma'", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_biUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_biInter", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subset_biUnion_of_mem", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.biInter_subset_of_mem", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.biInter_subset_biUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.biUnion_subset_biUnion_left", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.biInter_subset_biInter_left", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.biUnion_mono", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.biInter_mono", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.biUnion_eq_iUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.biInter_eq_iInter", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.biUnion_const", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.biInter_const", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_subtype", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iInter_subtype", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.biInter_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.biInter_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.biUnion_self", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_nonempty_self", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.biInter_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.biInter_union", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.biInter_insert", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.biInter_pair", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.biInter_inter", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["haveI", "simp"], "tactic_count": 2}
{"name": "Set.inter_biInter", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Set.biUnion_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.biUnion_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.biUnion_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.biUnion_of_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.biUnion_union", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_coe_set", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iInter_coe_set", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.biUnion_insert", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.biUnion_pair", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.inter_iUnion₂", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.iUnion₂_inter", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.union_iInter₂", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.iInter₂_union", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.mem_sUnion_of_mem", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.notMem_of_notMem_sUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sInter_subset_of_mem", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subset_sUnion_of_mem", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subset_sUnion_of_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sUnion_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sUnion_subset_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sUnion_mono_subsets", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sUnion_mono_supsets", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subset_sInter", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subset_sInter_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sUnion_subset_sUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sInter_subset_sInter", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sUnion_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sInter_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sUnion_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sInter_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sUnion_eq_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sInter_eq_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subset_powerset_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sUnion_powerset_gc", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sUnionPowersetGI", "kind": "definition", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sUnion_mem_empty_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.nonempty_sUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.Nonempty.of_sUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nonempty.of_sUnion_eq_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sUnion_union", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sInter_union", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sUnion_insert", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sInter_insert", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sUnion_diff_singleton_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sInter_diff_singleton_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sUnion_pair", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sInter_pair", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sUnion_image", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sInter_image", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sUnion_image2", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sInter_image2", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sUnion_range", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sInter_range", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_eq_univ_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.iUnion₂_eq_univ_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.sUnion_eq_univ_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.iInter_eq_empty_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.iInter₂_eq_empty_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.sInter_eq_empty_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.nonempty_iInter", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.nonempty_iInter₂", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.nonempty_sInter", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.compl_sUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sUnion_eq_compl_sInter_compl", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.compl_sInter", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.sInter_eq_compl_sUnion_compl", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.inter_empty_of_inter_sUnion_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.range_sigma_eq_iUnion_range", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_eq_range_sigma", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.iUnion_eq_range_psigma", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.iUnion_image_preimage_sigma_mk_eq_self", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["ext", "simp", "grind"], "tactic_count": 3}
{"name": "Set.Sigma.univ", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_subset_iUnion_const", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_singleton_eq_range", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Set.iUnion_insert_eq_range_union_iUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.iUnion_of_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.iUnion_of_singleton_coe", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.sUnion_eq_biUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.sInter_eq_biInter", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.sUnion_eq_iUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.sInter_eq_iInter", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.iUnion_of_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iInter_of_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.union_eq_iUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inter_eq_iInter", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sInter_union_sInter", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sUnion_inter_sUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.biUnion_iUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.biInter_iUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.sUnion_iUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.sInter_iUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.iUnion_range_eq_sUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["ext", "rintro", "refine", "exact", "rintro", "obtain", "refine", "exact"], "tactic_count": 8}
{"name": "Set.iUnion_range_eq_iUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["ext", "rintro", "exact", "rintro", "obtain", "exact"], "tactic_count": 6}
{"name": "Set.union_distrib_iInter_left", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.union_distrib_iInter₂_left", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.union_distrib_iInter_right", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.union_distrib_iInter₂_right", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.biUnion_lt_eq_iUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.biUnion_le_eq_iUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.biInter_lt_eq_iInter", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.biInter_le_eq_iInter", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.biUnion_gt_eq_iUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.biUnion_ge_eq_iUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.biInter_gt_eq_iInf", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.biInter_ge_eq_iInf", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.biUnion_le", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.biInter_le", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.biUnion_ge", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.biInter_ge", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.pi_def", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Set.univ_pi_eq_iInter", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.pi_diff_pi_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["refine", "simp", "exact"], "tactic_count": 3}
{"name": "Set.iUnion_univ_pi", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Set.biUnion_univ_pi", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Set.pi_iUnion_eq_iInter_pi", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["ext", "simp", "grind"], "tactic_count": 3}
{"name": "Set.directedOn_iUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["simp", "exact", "let", "let"], "tactic_count": 4}
{"name": "Set.directedOn_sUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Function.Surjective.iUnion_comp", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.iInter_comp", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.disjoint_iUnion_left", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.disjoint_iUnion_right", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.disjoint_iUnion₂_left", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.disjoint_iUnion₂_right", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.disjoint_sUnion_left", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.disjoint_sUnion_right", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.biUnion_compl_eq_of_pairwise_disjoint_of_iUnion_eq_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["ext", "obtain", "have", "refine", "intro", "simp", "obtain", "rwa", "have", "simpa", "rw"], "tactic_count": 11}
{"name": "Set.nonempty_iInter_Iic_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["have", "simp"], "tactic_count": 2}
{"name": "Set.nonempty_iInter_Ici_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ici_iSup", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iic_iInf", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ici_iSup₂", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.Iic_iInf₂", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.Ici_sSup", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.Iic_sInf", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.biUnion_diff_biUnion_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["simp", "apply", "rw", "apply"], "tactic_count": 4}
{"name": "Set.sigmaToiUnion", "kind": "definition", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sigmaToiUnion_surjective", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sigmaToiUnion_injective", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sigmaToiUnion_bijective", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sigmaEquiv", "kind": "definition", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.unionEqSigmaOfDisjoint", "kind": "definition", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.coe_unionEqSigmaOfDisjoint_symm_apply", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "Set.coe_snd_unionEqSigmaOfDisjoint", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["conv", "rfl"], "tactic_count": 2}
{"name": "Set.iUnion_ge_eq_iUnion_nat_add", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iInter_ge_eq_iInter_nat_add", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.iUnion_nat_add", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.iInter_nat_add", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_iInter_ge_nat_add", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.union_iUnion_nat_succ", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inter_iInter_nat_succ", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_le_nat", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_iUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["rw", "simp_rw"], "tactic_count": 2}
{"name": "iInf_iUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sSup_iUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "sSup_sUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "sInf_sUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_sUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "iInf_sUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "forall_sUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "exists_sUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.image_preimage", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.preimage_kernImage", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.kernImage_mono", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.kernImage_eq_compl", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.kernImage_compl", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.kernImage_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.kernImage_preimage_eq_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.compl_range_subset_kernImage", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.kernImage_union_preimage", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["rw", "compl_compl]"], "tactic_count": 2}
{"name": "Set.kernImage_preimage_union", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.image_projection_prod", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["classical", "apply", "simp", "intro", "simp", "rcases", "refine", "rw", "exact"], "tactic_count": 9}
{"name": "Set.mapsTo_sUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mapsTo_iUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mapsTo_iUnion₂", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mapsTo_iUnion_iUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mapsTo_iUnion₂_iUnion₂", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mapsTo_sInter", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mapsTo_iInter", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mapsTo_iInter₂", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.mapsTo_iInter_iInter", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mapsTo_iInter₂_iInter₂", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_iInter_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_iInter₂_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_sInter_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "Set.image2_sInter_right_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Set.image2_sInter_left_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Set.injective_iff_injective_of_iUnion_eq_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["refine", "obtain", "injection"], "tactic_count": 3}
{"name": "Set.surjective_iff_surjective_of_iUnion_eq_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact"], "tactic_count": 3}
{"name": "Set.bijective_iff_bijective_of_iUnion_eq_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Set.InjOn.image_iInter_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["inhabit", "refine", "simp", "choose", "refine", "suffices", "rw", "apply", "replace", "apply", "simp"], "tactic_count": 11}
{"name": "Set.InjOn.image_biInter_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["simp", "haveI", "apply", "simpa"], "tactic_count": 4}
{"name": "Set.image_iInter", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["cases", "simp_rw", "exact"], "tactic_count": 3}
{"name": "Set.image_iInter₂", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.inj_on_iUnion_of_directed", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["intro", "rcases", "rcases", "rcases", "exact"], "tactic_count": 5}
{"name": "Set.surjOn_sUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.surjOn_iUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.surjOn_iUnion_iUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.surjOn_iUnion₂", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.surjOn_iUnion₂_iUnion₂", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.surjOn_iInter", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["intro", "rw", "exact"], "tactic_count": 3}
{"name": "Set.surjOn_iInter_iInter", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.bijOn_iUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.bijOn_iInter", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.bijOn_iUnion_of_directed", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.bijOn_iInter_of_directed", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_iUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["ext1", "simp"], "tactic_count": 2}
{"name": "Set.image_iUnion₂", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.univ_subtype", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.range_eq_iUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_eq_iUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.biUnion_range", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_iUnion_eq'", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.biInter_range", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iInter_iInter_eq'", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.biUnion_image", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.biInter_image", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.biUnion_image2", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.biInter_image2", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_inter_iUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.iInter_union_iInter", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.iUnion₂_inter_iUnion₂", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.iInter₂_union_iInter₂", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.biUnion_inter_of_pairwise_disjoint", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.biUnion_iInter_of_pairwise_disjoint", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.monotone_preimage", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.preimage_iUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.preimage_iUnion₂", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.image_sUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["ext", "simp", "grind"], "tactic_count": 3}
{"name": "Set.preimage_sUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.preimage_iInter", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Set.preimage_iInter₂", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.preimage_sInter", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.biUnion_preimage_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.biUnion_range_preimage_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.prod_iUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Set.prod_iUnion₂", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.prod_sUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.iUnion_prod_const", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Set.iUnion₂_prod_const", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.sUnion_prod_const", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.iUnion_prod", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Set.iUnion_prod'", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_prod_of_monotone", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["ext", "intro", "exact", "intro", "exact"], "tactic_count": 5}
{"name": "Set.biUnion_prod", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Set.biUnion_prod'", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sInter_prod_sInter_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sInter_prod_sInter", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "refine", "rw", "exact"], "tactic_count": 5}
{"name": "Set.sInter_prod", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["rw", "simp_rw"], "tactic_count": 2}
{"name": "Set.prod_sInter", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["rw", "simp_rw"], "tactic_count": 2}
{"name": "Set.prod_iInter", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["ext", "simp", "exact"], "tactic_count": 3}
{"name": "Set.image2_eq_iUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Set.iUnion_image_left", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.iUnion_image_right", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.image2_iUnion_left", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.image2_iUnion_right", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.image2_sUnion_left", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Set.image2_sUnion_right", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Set.image2_iUnion₂_left", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.image2_iUnion₂_right", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.image2_iInter_subset_left", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Set.image2_iInter_subset_right", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Set.image2_iInter₂_subset_left", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Set.image2_iInter₂_subset_right", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Set.image2_sInter_subset_left", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.image2_sInter_subset_right", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.prod_eq_biUnion_left", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.prod_eq_biUnion_right", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.seq_def", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.seq_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.seq_mono", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.singleton_seq", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.seq_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.seq_seq", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Set.image_seq", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.prod_eq_seq", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.prod_image_seq_comm", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.image2_eq_seq", "kind": "theorem", "module": "Mathlib.Data.Set.Lattice.Image", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.range_list_map", "kind": "theorem", "module": "Mathlib.Data.Set.List", "is_tactic_proof": true, "tactics": ["refine", "induction", "nil", "cons", "rcases", "rcases", "exact"], "tactic_count": 7}
{"name": "Set.range_list_map_coe", "kind": "theorem", "module": "Mathlib.Data.Set.List", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.range_list_get", "kind": "theorem", "module": "Mathlib.Data.Set.List", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "Set.range_list_getElem?", "kind": "theorem", "module": "Mathlib.Data.Set.List", "is_tactic_proof": true, "tactics": ["rw", "refine", "exact", "exact", "exact"], "tactic_count": 5}
{"name": "Set.range_list_getD", "kind": "theorem", "module": "Mathlib.Data.Set.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.range_list_getI", "kind": "theorem", "module": "Mathlib.Data.Set.List", "is_tactic_proof": true, "tactics": ["unfold", "simp"], "tactic_count": 2}
{"name": "List.canLift", "kind": "instance", "module": "Mathlib.Data.Set.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "memPartition", "kind": "definition", "module": "Mathlib.Data.Set.MemPartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "memPartition_zero", "kind": "theorem", "module": "Mathlib.Data.Set.MemPartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "memPartition_succ", "kind": "theorem", "module": "Mathlib.Data.Set.MemPartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "disjoint_memPartition", "kind": "theorem", "module": "Mathlib.Data.Set.MemPartition", "is_tactic_proof": true, "tactics": ["revert", "induction", "zero", "intro", "simp", "rw", "exact", "succ", "intro", "rw", "obtain", "obtain", "rcases", "refine", "exact", "exact", "exact", "refine", "exact"], "tactic_count": 19}
{"name": "sUnion_memPartition", "kind": "theorem", "module": "Mathlib.Data.Set.MemPartition", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "ext", "have", "simp", "obtain", "by_cases", "exact", "exact"], "tactic_count": 11}
{"name": "finite_memPartition", "kind": "theorem", "module": "Mathlib.Data.Set.MemPartition", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "have", "rw", "simp_rw", "refine", "rw", "simp"], "tactic_count": 10}
{"name": "instFinite_memPartition", "kind": "instance", "module": "Mathlib.Data.Set.MemPartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFintype_memPartition", "kind": "instance", "module": "Mathlib.Data.Set.MemPartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "memPartitionSet", "kind": "definition", "module": "Mathlib.Data.Set.MemPartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "memPartitionSet_zero", "kind": "theorem", "module": "Mathlib.Data.Set.MemPartition", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "memPartitionSet_succ", "kind": "theorem", "module": "Mathlib.Data.Set.MemPartition", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "memPartitionSet_mem", "kind": "theorem", "module": "Mathlib.Data.Set.MemPartition", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "classical", "rw", "refine", "split_ifs"], "tactic_count": 7}
{"name": "mem_memPartitionSet", "kind": "theorem", "module": "Mathlib.Data.Set.MemPartition", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "classical", "rw", "split_ifs"], "tactic_count": 6}
{"name": "memPartitionSet_eq_iff", "kind": "theorem", "module": "Mathlib.Data.Set.MemPartition", "is_tactic_proof": true, "tactics": ["refine", "by_contra", "have", "disjoint_memPartition", "refine", "rw", "exact"], "tactic_count": 7}
{"name": "memPartitionSet_of_mem", "kind": "theorem", "module": "Mathlib.Data.Set.MemPartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonotoneOn.congr", "kind": "theorem", "module": "Mathlib.Data.Set.Monotone", "is_tactic_proof": true, "tactics": ["intro", "rw", "exact"], "tactic_count": 3}
{"name": "AntitoneOn.congr", "kind": "theorem", "module": "Mathlib.Data.Set.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMonoOn.congr", "kind": "theorem", "module": "Mathlib.Data.Set.Monotone", "is_tactic_proof": true, "tactics": ["intro", "rw", "exact"], "tactic_count": 3}
{"name": "StrictAntiOn.congr", "kind": "theorem", "module": "Mathlib.Data.Set.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.EqOn.congr_monotoneOn", "kind": "theorem", "module": "Mathlib.Data.Set.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.EqOn.congr_antitoneOn", "kind": "theorem", "module": "Mathlib.Data.Set.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.EqOn.congr_strictMonoOn", "kind": "theorem", "module": "Mathlib.Data.Set.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.EqOn.congr_strictAntiOn", "kind": "theorem", "module": "Mathlib.Data.Set.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonotoneOn.mono", "kind": "theorem", "module": "Mathlib.Data.Set.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntitoneOn.mono", "kind": "theorem", "module": "Mathlib.Data.Set.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMonoOn.mono", "kind": "theorem", "module": "Mathlib.Data.Set.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictAntiOn.mono", "kind": "theorem", "module": "Mathlib.Data.Set.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonotoneOn.monotone", "kind": "theorem", "module": "Mathlib.Data.Set.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntitoneOn.monotone", "kind": "theorem", "module": "Mathlib.Data.Set.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMonoOn.strictMono", "kind": "theorem", "module": "Mathlib.Data.Set.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictAntiOn.strictAnti", "kind": "theorem", "module": "Mathlib.Data.Set.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.monotoneOn_insert_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Monotone", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.antitoneOn_insert_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.restrict", "kind": "theorem", "module": "Mathlib.Data.Set.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.codRestrict", "kind": "theorem", "module": "Mathlib.Data.Set.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.rangeFactorization", "kind": "theorem", "module": "Mathlib.Data.Set.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictMono_restrict", "kind": "theorem", "module": "Mathlib.Data.Set.Monotone", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "StrictMono.codRestrict", "kind": "theorem", "module": "Mathlib.Data.Set.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictMonoOn_insert_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Monotone", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "strictAntiOn_insert_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictMonoOn_insert_iff_of_forall_le", "kind": "theorem", "module": "Mathlib.Data.Set.Monotone", "is_tactic_proof": true, "tactics": ["rw", "have", "intro", "cases", "tauto"], "tactic_count": 5}
{"name": "strictMonoOn_insert_iff_of_forall_ge", "kind": "theorem", "module": "Mathlib.Data.Set.Monotone", "is_tactic_proof": true, "tactics": ["rw", "have", "intro", "cases", "tauto"], "tactic_count": 5}
{"name": "strictAntiOn_insert_iff_of_forall_le", "kind": "theorem", "module": "Mathlib.Data.Set.Monotone", "is_tactic_proof": true, "tactics": ["rw", "have", "intro", "cases", "tauto"], "tactic_count": 5}
{"name": "strictAntiOn_insert_iff_of_forall_ge", "kind": "theorem", "module": "Mathlib.Data.Set.Monotone", "is_tactic_proof": true, "tactics": ["rw", "have", "intro", "cases", "tauto"], "tactic_count": 5}
{"name": "Function.monotoneOn_of_rightInvOn_of_mapsTo", "kind": "theorem", "module": "Mathlib.Data.Set.Monotone", "is_tactic_proof": true, "tactics": ["rintro", "rcases", "exact", "have", "rw", "induction", "exact"], "tactic_count": 7}
{"name": "Function.antitoneOn_of_rightInvOn_of_mapsTo", "kind": "theorem", "module": "Mathlib.Data.Set.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mulAntidiagonal", "kind": "definition", "module": "Mathlib.Data.Set.MulAntidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_mulAntidiagonal", "kind": "theorem", "module": "Mathlib.Data.Set.MulAntidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mulAntidiagonal_mono_left", "kind": "theorem", "module": "Mathlib.Data.Set.MulAntidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mulAntidiagonal_mono_right", "kind": "theorem", "module": "Mathlib.Data.Set.MulAntidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.swap_mem_mulAntidiagonal", "kind": "theorem", "module": "Mathlib.Data.Set.MulAntidiagonal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.swap_mem_mulAntidiagonal_aux", "kind": "theorem", "module": "Mathlib.Data.Set.MulAntidiagonal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.MulAntidiagonal.fst_eq_fst_iff_snd_eq_snd", "kind": "theorem", "module": "Mathlib.Data.Set.MulAntidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.MulAntidiagonal.eq_of_fst_eq_fst", "kind": "theorem", "module": "Mathlib.Data.Set.MulAntidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.MulAntidiagonal.eq_of_snd_eq_snd", "kind": "theorem", "module": "Mathlib.Data.Set.MulAntidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.MulAntidiagonal.eq_of_fst_le_fst_of_snd_le_snd", "kind": "theorem", "module": "Mathlib.Data.Set.MulAntidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.MulAntidiagonal.finite_of_isPWO", "kind": "theorem", "module": "Mathlib.Data.Set.MulAntidiagonal", "is_tactic_proof": true, "tactics": ["by_contra", "have", "hs", "have", "ht", "obtain", "obtain", "refine", "exact"], "tactic_count": 9}
{"name": "Set.MulAntidiagonal.finite_of_isWF", "kind": "theorem", "module": "Mathlib.Data.Set.MulAntidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_image2_iff", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image2_subset", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "Set.image2_subset_left", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image2_subset_right", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_subset_image2_left", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_subset_image2_right", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.forall_mem_image2", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.exists_mem_image2", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.image2_subset_iff", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image2_subset_iff_left", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.image2_subset_iff_right", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.image_prod", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_uncurry_prod", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image2_mk_eq_prod", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image2_curry", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.image2_swap", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.image2_union_left", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.image2_union_right", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.image2_inter_left", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.image2_inter_right", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.image2_empty_left", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image2_empty_right", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nonempty.image2", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image2_nonempty_iff", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nonempty.of_image2_left", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nonempty.of_image2_right", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image2_eq_empty_iff", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Set.Subsingleton.image2", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "Set.image2_inter_subset_left", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image2_inter_subset_right", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subset_image2_diff_left", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "Set.subset_image2_diff_right", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "Set.image2_singleton_left", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image2_singleton_right", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image2_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.image2_insert_left", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.image2_insert_right", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.image2_congr", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.image2_congr'", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_image2", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.image2_image_left", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Set.image2_image_right", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Set.image2_left", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.image2_right", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.image2_range", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.image2_assoc", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image2_comm", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image2_left_comm", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.image2_right_comm", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.image2_image2_image2_comm", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.image_image2_distrib", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.image_image2_distrib_left", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_image2_distrib_right", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image2_image_left_comm", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_image2_right_comm", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image2_distrib_subset_left", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.image2_distrib_subset_right", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.image_image2_antidistrib", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.image_image2_antidistrib_left", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_image2_antidistrib_right", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image2_image_left_anticomm", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_image2_right_anticomm", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image2_left_identity", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.image2_right_identity", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.image2_inter_union_subset_union", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.image2_union_inter_subset_union", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.image2_inter_union_subset", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.image2_union_inter_subset", "kind": "theorem", "module": "Mathlib.Data.Set.NAry", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.Notation.term_↓∩_", "kind": "definition", "module": "Mathlib.Data.Set.Notation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Notation._aux_Mathlib_Data_Set_Notation___macroRules_Set_Notation_term_↓∩__1", "kind": "definition", "module": "Mathlib.Data.Set.Notation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Notation._aux_Mathlib_Data_Set_Notation___delab_app_Set_Notation_term_↓∩__1", "kind": "definition", "module": "Mathlib.Data.Set.Notation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Notation.instCoeHeadElem", "kind": "instance", "module": "Mathlib.Data.Set.Notation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Notation.delab_set_image_subtype", "kind": "definition", "module": "Mathlib.Data.Set.Notation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_setOf_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.eq_mem_setOf", "kind": "theorem", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_setOf", "kind": "theorem", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.notMem_setOf_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.setOf_mem_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instCompl", "kind": "instance", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_compl_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.diff_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_diff", "kind": "theorem", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_diff_of_mem", "kind": "theorem", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.preimage", "kind": "definition", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.term_⁻¹'_", "kind": "definition", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set._aux_Mathlib_Data_Set_Operations___macroRules_Set_term_⁻¹'__1", "kind": "definition", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set._aux_Mathlib_Data_Set_Operations___unexpand_Set_preimage_1", "kind": "definition", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_preimage", "kind": "theorem", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.term_''_", "kind": "definition", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set._aux_Mathlib_Data_Set_Operations___macroRules_Set_term_''__1", "kind": "definition", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set._aux_Mathlib_Data_Set_Operations___unexpand_Set_image_1", "kind": "definition", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_image", "kind": "theorem", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_image_of_mem", "kind": "theorem", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.imageFactorization", "kind": "definition", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.kernImage", "kind": "definition", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subset_kernImage_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.range", "kind": "definition", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_range", "kind": "theorem", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_range_self", "kind": "theorem", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.rangeFactorization", "kind": "definition", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.rangeFactorization_injective", "kind": "theorem", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.rangeFactorization_surjective", "kind": "theorem", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.rangeFactorization_bijective", "kind": "theorem", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.rangeFactorization_eq_rangeFactorization_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.rangeFactorization_eq_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.rangeSplitting", "kind": "definition", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.apply_rangeSplitting", "kind": "theorem", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.comp_rangeSplitting", "kind": "theorem", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": true, "tactics": ["ext", "simp", "apply"], "tactic_count": 3}
{"name": "Set.Subtype.range_coind", "kind": "theorem", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.prod", "kind": "definition", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instSProd", "kind": "instance", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.prod_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_prod_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_prod", "kind": "theorem", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.prodMk_mem_set_prod_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mk_mem_prod", "kind": "theorem", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.prod_image_left", "kind": "theorem", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Set.prod_image_right", "kind": "theorem", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Set.diagonal", "kind": "definition", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_diagonal", "kind": "theorem", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_diagonal_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.offDiag", "kind": "definition", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_offDiag", "kind": "theorem", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.pi", "kind": "definition", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_pi", "kind": "theorem", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_univ_pi", "kind": "theorem", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.EqOn", "kind": "definition", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.MapsTo", "kind": "definition", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mapsTo_image", "kind": "theorem", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mapsTo_preimage", "kind": "theorem", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.MapsTo.restrict", "kind": "definition", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.restrictPreimage", "kind": "definition", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.InjOn", "kind": "definition", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.graphOn", "kind": "definition", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.SurjOn", "kind": "definition", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.BijOn", "kind": "definition", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.LeftInvOn", "kind": "definition", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.RightInvOn", "kind": "abbrev", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.InvOn", "kind": "definition", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image2", "kind": "definition", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_image2", "kind": "theorem", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_image2_of_mem", "kind": "theorem", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.seq", "kind": "definition", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_seq_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.seq_eq_image2", "kind": "theorem", "module": "Mathlib.Data.Set.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.op", "kind": "definition", "module": "Mathlib.Data.Set.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.unop", "kind": "definition", "module": "Mathlib.Data.Set.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_op", "kind": "theorem", "module": "Mathlib.Data.Set.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.op_mem_op", "kind": "theorem", "module": "Mathlib.Data.Set.Opposite", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "Set.mem_unop", "kind": "theorem", "module": "Mathlib.Data.Set.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.unop_mem_unop", "kind": "theorem", "module": "Mathlib.Data.Set.Opposite", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "Set.op_unop", "kind": "theorem", "module": "Mathlib.Data.Set.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.unop_op", "kind": "theorem", "module": "Mathlib.Data.Set.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.opEquiv_self", "kind": "definition", "module": "Mathlib.Data.Set.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.opEquiv", "kind": "definition", "module": "Mathlib.Data.Set.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.singleton_op", "kind": "theorem", "module": "Mathlib.Data.Set.Opposite", "is_tactic_proof": true, "tactics": ["ext", "constructor", "apply", "apply"], "tactic_count": 4}
{"name": "Set.singleton_unop", "kind": "theorem", "module": "Mathlib.Data.Set.Opposite", "is_tactic_proof": true, "tactics": ["ext", "constructor", "apply", "apply"], "tactic_count": 4}
{"name": "Set.singleton_op_unop", "kind": "theorem", "module": "Mathlib.Data.Set.Opposite", "is_tactic_proof": true, "tactics": ["ext", "constructor", "apply", "apply"], "tactic_count": 4}
{"name": "Set.singleton_unop_op", "kind": "theorem", "module": "Mathlib.Data.Set.Opposite", "is_tactic_proof": true, "tactics": ["ext", "constructor", "apply", "apply"], "tactic_count": 4}
{"name": "Set.monotoneOn_iff_monotone", "kind": "theorem", "module": "Mathlib.Data.Set.Order", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.antitoneOn_iff_antitone", "kind": "theorem", "module": "Mathlib.Data.Set.Order", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.strictMonoOn_iff_strictMono", "kind": "theorem", "module": "Mathlib.Data.Set.Order", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.strictAntiOn_iff_strictAnti", "kind": "theorem", "module": "Mathlib.Data.Set.Order", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.not_monotoneOn_not_antitoneOn_iff_exists_le_le", "kind": "theorem", "module": "Mathlib.Data.Set.Order", "is_tactic_proof": true, "tactics": ["simp", "not_monotone_not_antitone_iff_exists_le_le,"], "tactic_count": 2}
{"name": "Set.not_monotoneOn_not_antitoneOn_iff_exists_lt_lt", "kind": "theorem", "module": "Mathlib.Data.Set.Order", "is_tactic_proof": true, "tactics": ["simp", "not_monotone_not_antitone_iff_exists_lt_lt,"], "tactic_count": 2}
{"name": "Monotone.inter", "kind": "theorem", "module": "Mathlib.Data.Set.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonotoneOn.inter", "kind": "theorem", "module": "Mathlib.Data.Set.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.inter", "kind": "theorem", "module": "Mathlib.Data.Set.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntitoneOn.inter", "kind": "theorem", "module": "Mathlib.Data.Set.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.union", "kind": "theorem", "module": "Mathlib.Data.Set.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonotoneOn.union", "kind": "theorem", "module": "Mathlib.Data.Set.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.union", "kind": "theorem", "module": "Mathlib.Data.Set.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntitoneOn.union", "kind": "theorem", "module": "Mathlib.Data.Set.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.monotone_setOf", "kind": "theorem", "module": "Mathlib.Data.Set.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.antitone_setOf", "kind": "theorem", "module": "Mathlib.Data.Set.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.antitone_bforall", "kind": "theorem", "module": "Mathlib.Data.Set.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pairwise_on_bool", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "pairwise_disjoint_on_bool", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Symmetric.pairwise_on", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pairwise_disjoint_on", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pairwise_disjoint_mono", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pairwise.disjoint_extend_bot", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": true, "tactics": ["intro", "rcases", "rcases", "simpa", "simpa", "simpa"], "tactic_count": 6}
{"name": "Set.Pairwise.mono", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Pairwise.mono'", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.pairwise_top", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Subsingleton.pairwise", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.pairwise_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.pairwise_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.pairwise_iff_of_refl", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nonempty.pairwise_iff_exists_forall", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": true, "tactics": ["constructor", "rcases", "refine", "rcases", "apply", "exact", "rintro", "exact"], "tactic_count": 8}
{"name": "Set.Nonempty.pairwise_eq_iff_exists_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.pairwise_iff_exists_forall", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simp", "exact"], "tactic_count": 3}
{"name": "Set.pairwise_eq_iff_exists_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.pairwise_union", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.pairwise_union_of_symmetric", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.pairwise_insert", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.pairwise_insert_of_notMem", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Pairwise.insert", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Pairwise.insert_of_notMem", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.pairwise_insert_of_symmetric", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.pairwise_insert_of_symmetric_of_notMem", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.Pairwise.insert_of_symmetric", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.pairwise_pair", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.pairwise_pair_of_symmetric", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.pairwise_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.pairwise_bot_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.injOn_iff_pairwise_ne", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.Pairwise.image", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.InjOn.pairwise_image", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Pairwise.range_pairwise", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pairwise_subtype_iff_pairwise_set", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.PairwiseDisjoint", "kind": "definition", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.PairwiseDisjoint.subset", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.PairwiseDisjoint.mono_on", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.PairwiseDisjoint.mono", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.pairwiseDisjoint_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.pairwiseDisjoint_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.pairwiseDisjoint_insert", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.pairwiseDisjoint_insert_of_notMem", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.PairwiseDisjoint.insert", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.PairwiseDisjoint.insert_of_notMem", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.PairwiseDisjoint.image_of_le", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "Set.InjOn.pairwiseDisjoint_image", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.PairwiseDisjoint.range", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "Set.pairwiseDisjoint_union", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.PairwiseDisjoint.union", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.PairwiseDisjoint.elim", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.PairwiseDisjoint.eq_or_disjoint", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.pairwiseDisjoint_range_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Pairwise.pairwiseDisjoint", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.PairwiseDisjoint.elim'", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.PairwiseDisjoint.eq_of_le", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.pairwiseDisjoint_range_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.pairwiseDisjoint_fiber", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.PairwiseDisjoint.elim_set", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.PairwiseDisjoint.prod", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.pairwiseDisjoint_pi", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.pairwiseDisjoint_image_right_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": true, "tactics": ["refine", "suffices", "refine", "rw", "exact", "refine", "rintro", "exact"], "tactic_count": 8}
{"name": "Set.pairwiseDisjoint_image_left_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": true, "tactics": ["refine", "suffices", "refine", "rw", "exact", "refine", "rintro", "exact"], "tactic_count": 8}
{"name": "Set.exists_ne_mem_inter_of_not_pairwiseDisjoint", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": true, "tactics": ["change", "simp", "obtain", "replace", "obtain", "exact"], "tactic_count": 6}
{"name": "Set.exists_lt_mem_inter_of_not_pairwiseDisjoint", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": true, "tactics": ["obtain", "rcases", "exact", "exact"], "tactic_count": 4}
{"name": "Set.pairwiseDisjoint_singleton_iff_injOn", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "exists_ne_mem_inter_of_not_pairwise_disjoint", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": true, "tactics": ["rw", "obtain", "exact"], "tactic_count": 3}
{"name": "exists_lt_mem_inter_of_not_pairwise_disjoint", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": true, "tactics": ["rw", "obtain", "exact"], "tactic_count": 3}
{"name": "pairwise_disjoint_fiber", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "subsingleton_setOf_mem_iff_pairwise_disjoint", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pairwise_not_eq_iff_injective", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "pairwise_ne_iff_injective", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsChain.pairwise_iUnion₂", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsChain.pairwiseDisjoint_iUnion₂", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsChain.pairwise_sUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsChain.pairwiseDisjoint_sUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.pairwise_iUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Lattice", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "intro", "rcases", "rcases", "rcases", "exact"], "tactic_count": 8}
{"name": "Set.pairwise_iUnion₂", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Lattice", "is_tactic_proof": true, "tactics": ["simp", "intro", "obtain", "exact"], "tactic_count": 4}
{"name": "Set.pairwise_iUnion₂_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.pairwise_sUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Lattice", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.pairwiseDisjoint_iUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.pairwiseDisjoint_sUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.PairwiseDisjoint.biUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Lattice", "is_tactic_proof": true, "tactics": ["rintro", "simp_rw", "obtain", "obtain", "obtain", "exact", "exact"], "tactic_count": 7}
{"name": "Set.PairwiseDisjoint.prod_left", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Lattice", "is_tactic_proof": true, "tactics": ["rintro", "rw", "obtain", "refine", "convert", "convert", "refine", "convert", "convert"], "tactic_count": 9}
{"name": "Set.pairwiseDisjoint_prod_left", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Lattice", "is_tactic_proof": false, "tactics": ["refine", "simp_rw", "intro", "exact", "exact"], "tactic_count": 5}
{"name": "Set.biUnion_diff_biUnion_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Lattice", "is_tactic_proof": false, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "Set.biUnionEqSigmaOfDisjoint", "kind": "definition", "module": "Mathlib.Data.Set.Pairwise.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.coe_biUnionEqSigmaOfDisjoint_symm_apply", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Lattice", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "Set.coe_snd_biUnionEqSigmaOfDisjoint", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Lattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.pairwiseDisjoint_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Lattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.pairwiseDisjoint_pair_insert", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Lattice", "is_tactic_proof": true, "tactics": ["rw", "rintro", "have", "aesop"], "tactic_count": 4}
{"name": "Set.PairwiseDisjoint.subset_of_biUnion_subset_biUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Lattice", "is_tactic_proof": true, "tactics": ["rintro", "obtain", "obtain", "rwa"], "tactic_count": 4}
{"name": "Pairwise.subset_of_biUnion_subset_biUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pairwise.biUnion_injective", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pairwiseDisjoint_unique", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.Lattice", "is_tactic_proof": true, "tactics": ["refine", "simpa", "rintro", "exact"], "tactic_count": 4}
{"name": "List.Nodup.pairwise_of_set_pairwise", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Nodup.pairwise_coe", "kind": "theorem", "module": "Mathlib.Data.Set.Pairwise.List", "is_tactic_proof": false, "tactics": ["induction", "nil", "cons", "rw", "have", "simp"], "tactic_count": 6}
{"name": "Set.piecewise_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Piecewise", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Set.piecewise_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Piecewise", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Set.piecewise_insert_self", "kind": "theorem", "module": "Mathlib.Data.Set.Piecewise", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.piecewise_insert", "kind": "theorem", "module": "Mathlib.Data.Set.Piecewise", "is_tactic_proof": true, "tactics": ["simp", "ext", "by_cases", "rw", "simp", "by_cases"], "tactic_count": 6}
{"name": "Set.piecewise_eq_of_mem", "kind": "theorem", "module": "Mathlib.Data.Set.Piecewise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.piecewise_eq_of_notMem", "kind": "theorem", "module": "Mathlib.Data.Set.Piecewise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.piecewise_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Piecewise", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "subst", "simp", "simp"], "tactic_count": 5}
{"name": "Set.piecewise_eqOn", "kind": "theorem", "module": "Mathlib.Data.Set.Piecewise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.piecewise_eqOn_compl", "kind": "theorem", "module": "Mathlib.Data.Set.Piecewise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.piecewise_le", "kind": "theorem", "module": "Mathlib.Data.Set.Piecewise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.le_piecewise", "kind": "theorem", "module": "Mathlib.Data.Set.Piecewise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.piecewise_mono", "kind": "theorem", "module": "Mathlib.Data.Set.Piecewise", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "Set.piecewise_insert_of_ne", "kind": "theorem", "module": "Mathlib.Data.Set.Piecewise", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.piecewise_compl", "kind": "theorem", "module": "Mathlib.Data.Set.Piecewise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.piecewise_range_comp", "kind": "theorem", "module": "Mathlib.Data.Set.Piecewise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.piecewise_comp", "kind": "theorem", "module": "Mathlib.Data.Set.Piecewise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.MapsTo.piecewise_ite", "kind": "theorem", "module": "Mathlib.Data.Set.Piecewise", "is_tactic_proof": true, "tactics": ["refine", "exacts"], "tactic_count": 2}
{"name": "Set.eqOn_piecewise", "kind": "theorem", "module": "Mathlib.Data.Set.Piecewise", "is_tactic_proof": true, "tactics": ["simp", "refine"], "tactic_count": 2}
{"name": "Set.EqOn.piecewise_ite'", "kind": "theorem", "module": "Mathlib.Data.Set.Piecewise", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.EqOn.piecewise_ite", "kind": "theorem", "module": "Mathlib.Data.Set.Piecewise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.piecewise_preimage", "kind": "theorem", "module": "Mathlib.Data.Set.Piecewise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.apply_piecewise", "kind": "theorem", "module": "Mathlib.Data.Set.Piecewise", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "Set.apply_piecewise₂", "kind": "theorem", "module": "Mathlib.Data.Set.Piecewise", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "Set.piecewise_op", "kind": "theorem", "module": "Mathlib.Data.Set.Piecewise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.piecewise_op₂", "kind": "theorem", "module": "Mathlib.Data.Set.Piecewise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.piecewise_same", "kind": "theorem", "module": "Mathlib.Data.Set.Piecewise", "is_tactic_proof": true, "tactics": ["ext", "by_cases"], "tactic_count": 2}
{"name": "Set.range_piecewise", "kind": "theorem", "module": "Mathlib.Data.Set.Piecewise", "is_tactic_proof": true, "tactics": ["ext", "rintro", "by_cases", "rintro"], "tactic_count": 4}
{"name": "Set.injective_piecewise_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Piecewise", "is_tactic_proof": false, "tactics": ["rw", "refine", "rw"], "tactic_count": 3}
{"name": "Set.piecewise_mem_pi", "kind": "theorem", "module": "Mathlib.Data.Set.Piecewise", "is_tactic_proof": true, "tactics": ["intro", "by_cases"], "tactic_count": 2}
{"name": "Set.pi_piecewise", "kind": "theorem", "module": "Mathlib.Data.Set.Piecewise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.univ_pi_piecewise", "kind": "theorem", "module": "Mathlib.Data.Set.Piecewise", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.univ_pi_piecewise_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Piecewise", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "mulSupport_comp_inv_smul", "kind": "theorem", "module": "Mathlib.Data.Set.Pointwise.Support", "is_tactic_proof": true, "tactics": ["ext", "simp", "manually."], "tactic_count": 3}
{"name": "support_comp_inv_smul", "kind": "theorem", "module": "Mathlib.Data.Set.Pointwise.Support", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "mulSupport_comp_inv_smul₀", "kind": "theorem", "module": "Mathlib.Data.Set.Pointwise.Support", "is_tactic_proof": true, "tactics": ["ext", "simp", "manually."], "tactic_count": 3}
{"name": "support_comp_inv_smul₀", "kind": "theorem", "module": "Mathlib.Data.Set.Pointwise.Support", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Set.Subsingleton.prod", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.decidableMemProd", "kind": "instance", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.prod_mono", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.prod_mono_left", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.prod_mono_right", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.prod_self_subset_prod_self", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.prod_self_ssubset_prod_self", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.prod_subset_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.forall_prod_set", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.exists_prod_set", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.prod_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "Set.empty_prod", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "Set.univ_prod_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "Set.univ_prod", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.prod_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.prod_eq_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.singleton_prod", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Set.prod_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Set.singleton_prod_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Set.union_prod", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Set.prod_union", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Set.inter_prod", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Set.prod_inter", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Set.prod_inter_prod", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Set.compl_prod_eq_union", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.disjoint_prod", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["simp_rw", "grind"], "tactic_count": 2}
{"name": "Set.Disjoint.set_prod_left", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Disjoint.set_prod_right", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.prodMap_image_prod", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["ext", "aesop"], "tactic_count": 2}
{"name": "Set.insert_prod", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.prod_insert", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.prod_preimage_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.prod_preimage_left", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.prod_preimage_right", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.preimage_prod_map_prod", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mk_preimage_prod", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mk_preimage_prod_left", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.mk_preimage_prod_right", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.mk_preimage_prod_left_eq_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.mk_preimage_prod_right_eq_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.mk_preimage_prod_left_eq_if", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.mk_preimage_prod_right_eq_if", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.mk_preimage_prod_left_fn_eq_if", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.mk_preimage_prod_right_fn_eq_if", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.preimage_swap_prod", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.image_swap_prod", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.mapsTo_swap_prod", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.prod_image_image_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.prod_range_range_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.range_prodMap", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.prod_range_univ_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.prod_univ_range_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.range_pair_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.Nonempty.prod", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nonempty.fst", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nonempty.snd", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.prod_nonempty_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.prod_eq_empty_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.prod_sub_preimage_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.image_prodMk_subset_prod", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.image_prodMk_subset_prod_left", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.image_prodMk_subset_prod_right", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.prod_subset_preimage_fst", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.fst_image_prod_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.fst_image_prod", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mapsTo_fst_prod", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.prod_subset_preimage_snd", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.snd_image_prod_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.snd_image_prod", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subset_fst_image_prod_snd_image", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mapsTo_snd_prod", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.prod_diff_prod", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.prod_subset_prod_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["rcases", "simp", "have", "refine", "have", "rwa", "have", "rwa", "intro", "simp", "exact"], "tactic_count": 11}
{"name": "Set.prod_subset_prod_iff'", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "Set.prod_subset_prod_iff_left", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.prod_subset_prod_iff_right", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.prod_eq_prod_iff_of_nonempty", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["constructor", "intro", "have", "rw", "rw", "snd_image_prod", "grind"], "tactic_count": 7}
{"name": "Set.prod_eq_prod_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["symm", "rcases", "simp_rw", "rintro", "exact", "rw", "rw", "simp_rw"], "tactic_count": 8}
{"name": "Set.prod_eq_iff_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["simp_rw", "rintro", "rfl"], "tactic_count": 3}
{"name": "Set.subset_prod", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.set_prod", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.set_prod", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonotoneOn.set_prod", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntitoneOn.set_prod", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.eqOn_prod_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.EqOn.left_of_eqOn_prodMap", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["obtain", "intro", "have", "grind"], "tactic_count": 4}
{"name": "Set.EqOn.right_of_eqOn_prodMap", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["obtain", "intro", "have", "grind"], "tactic_count": 4}
{"name": "Set.EqOn.prodMap", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.eqOn_prodMap_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.diagonal_nonempty", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.decidableMemDiagonal", "kind": "instance", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.preimage_coe_coe_diagonal", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Set.range_diag", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Set.diagonal_subset_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.prod_subset_compl_diagonal_iff_disjoint", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.diag_preimage_prod", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.diag_preimage_prod_self", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.diag_image", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.diagonal_eq_univ_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.diagonal_eq_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.range_const_eq_diagonal", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["refine", "rcases", "exact", "exact"], "tactic_count": 4}
{"name": "Function.Pullback", "kind": "abbrev", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.PullbackSelf", "kind": "abbrev", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Pullback.fst", "kind": "definition", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Pullback.snd", "kind": "definition", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.pullback_comm_sq", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toPullbackDiag", "kind": "definition", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.pullbackDiagonal", "kind": "definition", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.mapPullback", "kind": "definition", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.PullbackSelf.map_fst", "kind": "definition", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.PullbackSelf.map_snd", "kind": "definition", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "preimage_map_fst_pullbackDiagonal", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["ext", "simp_rw", "exact"], "tactic_count": 3}
{"name": "Function.Injective.preimage_pullbackDiagonal", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "image_toPullbackDiag", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["ext", "constructor", "rintro", "exact", "obtain", "rintro", "exact"], "tactic_count": 7}
{"name": "range_toPullbackDiag", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "injective_toPullbackDiag", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.offDiag_mono", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.offDiag_nonempty", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.offDiag_eq_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.offDiag_subset_prod", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.offDiag_eq_sep_prod", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.offDiag_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.offDiag_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.offDiag_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.prod_sdiff_diagonal", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.disjoint_diagonal_offDiag", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.offDiag_inter", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.offDiag_union", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["ext", "simp", "constructor", "rintro", "rintro", "rintro", "rw", "exact", "rintro", "rw", "exact"], "tactic_count": 11}
{"name": "Set.offDiag_insert", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.empty_pi", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.subsingleton_univ_pi", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.pi_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.pi_univ_ite", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.pi_mono'", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.pi_mono", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.pi_inter_distrib", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.pi_congr", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.pi_eq_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.univ_pi_eq_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.pi_nonempty_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.univ_pi_nonempty_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.pi_eq_empty_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["rw", "push_neg", "refine", "cases"], "tactic_count": 4}
{"name": "Set.univ_pi_eq_empty_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.univ_pi_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.disjoint_univ_pi", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.Disjoint.set_pi", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.uniqueElim_preimage", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Set.pi_eq_empty_iff'", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.disjoint_pi", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.insert_pi", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.singleton_pi", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.singleton_pi'", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.univ_pi_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.preimage_pi", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.pi_if", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["ext", "refine", "constructor", "rintro", "simpa", "rintro", "by_cases"], "tactic_count": 7}
{"name": "Set.union_pi", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.union_pi_inter", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.pi_inter_compl", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.pi_update_of_notMem", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.pi_update_of_mem", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.univ_pi_update", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.univ_pi_update_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.eval_image_pi_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.eval_image_univ_pi_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subset_eval_image_pi", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["classical", "obtain", "refine", "obtain"], "tactic_count": 4}
{"name": "Set.eval_image_pi", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.eval_image_pi_of_notMem", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["classical", "ext", "simp", "constructor", "rintro", "exact", "rintro", "refine", "simpa"], "tactic_count": 9}
{"name": "Set.eval_image_univ_pi", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.piMap_mapsTo_pi", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.piMap_image_pi_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.piMap_image_pi", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["refine", "have", "choose", "exact"], "tactic_count": 4}
{"name": "Set.piMap_image_univ_pi", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.range_piMap", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.subset_pi_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.update_mem_pi_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.update_mem_pi_iff_of_mem", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.univ_pi_eq_singleton_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["classical", "simp", "refine", "rw"], "tactic_count": 4}
{"name": "Set.pi_subset_pi_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["refine", "rw", "intro", "simpa"], "tactic_count": 4}
{"name": "Set.univ_pi_subset_univ_pi_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.eval_preimage", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Set.eval_preimage'", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Set.update_preimage_pi", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["ext", "refine", "convert", "simp", "obtain", "simpa", "rw", "exact"], "tactic_count": 8}
{"name": "Set.update_image", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["ext", "simp", "true_implies]", "rw", "simp"], "tactic_count": 5}
{"name": "Set.update_preimage_univ_pi", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subset_pi_eval_image", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.univ_pi_ite", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.uncurry_preimage_prod_pi", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Equiv.piCongrLeft_symm_preimage_pi", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Equiv.piCongrLeft_symm_preimage_univ_pi", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Equiv.piCongrLeft_preimage_pi", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["apply", "rw", "simp"], "tactic_count": 3}
{"name": "Equiv.piCongrLeft_preimage_univ_pi", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Equiv.sumPiEquivProdPi_symm_preimage_univ_pi", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Set.mem_graphOn", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Set.graphOn_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.graphOn_eq_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.graphOn_nonempty", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.graphOn_union", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.graphOn_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.graphOn_insert", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_fst_graphOn", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.image_snd_graphOn", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Set.fst_injOn_graph", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Set.graphOn_comp", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.graphOn_univ_eq_range", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.graphOn_inj", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.graphOn_prod_graphOn", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Set.graphOn_prod_prodMap", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Set.exists_range_eq_graphOn_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["refine", "ext", "simp", "refine", "rintro", "exact"], "tactic_count": 6}
{"name": "Set.exists_equiv_range_eq_graphOn_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "have", "rw", "aesop", "exact", "invFun", "left_inv", "right_inv"], "tactic_count": 9}
{"name": "Set.exists_eq_mgraphOn_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Prod", "is_tactic_proof": true, "tactics": ["simpa", "exists_range_eq_graphOn_univ", "congr_arg"], "tactic_count": 3}
{"name": "Set.restrict", "kind": "definition", "module": "Mathlib.Data.Set.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.restrict_def", "kind": "theorem", "module": "Mathlib.Data.Set.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.restrict_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.restrict_id", "kind": "theorem", "module": "Mathlib.Data.Set.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.restrict_apply", "kind": "theorem", "module": "Mathlib.Data.Set.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.restrict_eq_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.eq_restrict_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.range_restrict", "kind": "theorem", "module": "Mathlib.Data.Set.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_restrict", "kind": "theorem", "module": "Mathlib.Data.Set.Restrict", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.restrict_dite", "kind": "theorem", "module": "Mathlib.Data.Set.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.restrict_dite_compl", "kind": "theorem", "module": "Mathlib.Data.Set.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.restrict_ite", "kind": "theorem", "module": "Mathlib.Data.Set.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.restrict_ite_compl", "kind": "theorem", "module": "Mathlib.Data.Set.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.restrict_piecewise", "kind": "theorem", "module": "Mathlib.Data.Set.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.restrict_piecewise_compl", "kind": "theorem", "module": "Mathlib.Data.Set.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.restrict_extend_range", "kind": "theorem", "module": "Mathlib.Data.Set.Restrict", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Set.restrict_extend_compl_range", "kind": "theorem", "module": "Mathlib.Data.Set.Restrict", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Set.restrict₂", "kind": "definition", "module": "Mathlib.Data.Set.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.restrict₂_def", "kind": "theorem", "module": "Mathlib.Data.Set.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.restrict₂_comp_restrict", "kind": "theorem", "module": "Mathlib.Data.Set.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.restrict₂_comp_restrict₂", "kind": "theorem", "module": "Mathlib.Data.Set.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.range_extend_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Restrict", "is_tactic_proof": true, "tactics": ["classical", "rintro", "rw", "split_ifs", "exacts"], "tactic_count": 5}
{"name": "Set.range_extend", "kind": "theorem", "module": "Mathlib.Data.Set.Restrict", "is_tactic_proof": true, "tactics": ["refine", "rintro", "exacts"], "tactic_count": 3}
{"name": "Set.codRestrict", "kind": "definition", "module": "Mathlib.Data.Set.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.val_codRestrict_apply", "kind": "theorem", "module": "Mathlib.Data.Set.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.restrict_comp_codRestrict", "kind": "theorem", "module": "Mathlib.Data.Set.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.injective_codRestrict", "kind": "theorem", "module": "Mathlib.Data.Set.Restrict", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.range_codRestrict", "kind": "theorem", "module": "Mathlib.Data.Set.Restrict", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Set.surjective_codRestrict", "kind": "theorem", "module": "Mathlib.Data.Set.Restrict", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.codRestrict_range_surjective", "kind": "theorem", "module": "Mathlib.Data.Set.Restrict", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "Set.restrict_eq_restrict_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.MapsTo.restrict_commutes", "kind": "theorem", "module": "Mathlib.Data.Set.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.MapsTo.val_restrict_apply", "kind": "theorem", "module": "Mathlib.Data.Set.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.MapsTo.coe_iterate_restrict", "kind": "theorem", "module": "Mathlib.Data.Set.Restrict", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Set.codRestrict_restrict", "kind": "theorem", "module": "Mathlib.Data.Set.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.MapsTo.restrict_eq_codRestrict", "kind": "theorem", "module": "Mathlib.Data.Set.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.MapsTo.coe_restrict", "kind": "theorem", "module": "Mathlib.Data.Set.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.MapsTo.range_restrict", "kind": "theorem", "module": "Mathlib.Data.Set.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mapsTo_iff_exists_map_subtype", "kind": "theorem", "module": "Mathlib.Data.Set.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.surjective_mapsTo_image_restrict", "kind": "theorem", "module": "Mathlib.Data.Set.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_restrictPreimage", "kind": "theorem", "module": "Mathlib.Data.Set.Restrict", "is_tactic_proof": true, "tactics": ["delta", "rw"], "tactic_count": 2}
{"name": "Set.range_restrictPreimage", "kind": "theorem", "module": "Mathlib.Data.Set.Restrict", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.restrictPreimage_mk", "kind": "theorem", "module": "Mathlib.Data.Set.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_val_preimage_restrictPreimage", "kind": "theorem", "module": "Mathlib.Data.Set.Restrict", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Set.preimage_restrictPreimage", "kind": "theorem", "module": "Mathlib.Data.Set.Restrict", "is_tactic_proof": true, "tactics": ["rw", "preimage_image_eq"], "tactic_count": 2}
{"name": "Set.restrictPreimage_injective", "kind": "theorem", "module": "Mathlib.Data.Set.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.restrictPreimage_surjective", "kind": "theorem", "module": "Mathlib.Data.Set.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.restrictPreimage_bijective", "kind": "theorem", "module": "Mathlib.Data.Set.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.injOn_iff_injective", "kind": "theorem", "module": "Mathlib.Data.Set.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.MapsTo.restrict_inj", "kind": "theorem", "module": "Mathlib.Data.Set.Restrict", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.surjOn_iff_surjective", "kind": "theorem", "module": "Mathlib.Data.Set.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.MapsTo.restrict_surjective_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Restrict", "is_tactic_proof": true, "tactics": ["refine", "obtain", "replace", "rw", "exact", "obtain", "exact"], "tactic_count": 7}
{"name": "Set.smulAntidiagonal", "kind": "definition", "module": "Mathlib.Data.Set.SMulAntidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_smulAntidiagonal", "kind": "theorem", "module": "Mathlib.Data.Set.SMulAntidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smulAntidiagonal_mono_left", "kind": "theorem", "module": "Mathlib.Data.Set.SMulAntidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.smulAntidiagonal_mono_right", "kind": "theorem", "module": "Mathlib.Data.Set.SMulAntidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.SMulAntidiagonal.fst_eq_fst_iff_snd_eq_snd", "kind": "theorem", "module": "Mathlib.Data.Set.SMulAntidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.SMulAntidiagonal.eq_of_fst_eq_fst", "kind": "theorem", "module": "Mathlib.Data.Set.SMulAntidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.SMulAntidiagonal.eq_of_snd_eq_snd", "kind": "theorem", "module": "Mathlib.Data.Set.SMulAntidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.SMulAntidiagonal.eq_of_fst_le_fst_of_snd_le_snd", "kind": "theorem", "module": "Mathlib.Data.Set.SMulAntidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.SMulAntidiagonal.finite_of_isPWO", "kind": "theorem", "module": "Mathlib.Data.Set.SMulAntidiagonal", "is_tactic_proof": true, "tactics": ["by_contra", "have", "hs", "have", "ht", "obtain", "obtain", "refine", "exact"], "tactic_count": 9}
{"name": "SetSemiring", "kind": "definition", "module": "Mathlib.Data.Set.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.up", "kind": "definition", "module": "Mathlib.Data.Set.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetSemiring.down", "kind": "definition", "module": "Mathlib.Data.Set.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetSemiring.down_up", "kind": "theorem", "module": "Mathlib.Data.Set.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetSemiring.up_down", "kind": "theorem", "module": "Mathlib.Data.Set.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetSemiring.up_le_up", "kind": "theorem", "module": "Mathlib.Data.Set.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetSemiring.up_lt_up", "kind": "theorem", "module": "Mathlib.Data.Set.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetSemiring.down_subset_down", "kind": "theorem", "module": "Mathlib.Data.Set.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetSemiring.down_ssubset_down", "kind": "theorem", "module": "Mathlib.Data.Set.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetSemiring.instZero", "kind": "instance", "module": "Mathlib.Data.Set.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetSemiring.instAdd", "kind": "instance", "module": "Mathlib.Data.Set.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetSemiring.instAddCommMonoid", "kind": "instance", "module": "Mathlib.Data.Set.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetSemiring.zero_def", "kind": "theorem", "module": "Mathlib.Data.Set.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetSemiring.down_zero", "kind": "theorem", "module": "Mathlib.Data.Set.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.up_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetSemiring.add_def", "kind": "theorem", "module": "Mathlib.Data.Set.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetSemiring.down_add", "kind": "theorem", "module": "Mathlib.Data.Set.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.up_union", "kind": "theorem", "module": "Mathlib.Data.Set.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetSemiring.addLeftMono", "kind": "instance", "module": "Mathlib.Data.Set.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetSemiring.instNonUnitalNonAssocSemiring", "kind": "instance", "module": "Mathlib.Data.Set.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetSemiring.mul_def", "kind": "theorem", "module": "Mathlib.Data.Set.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetSemiring.down_mul", "kind": "theorem", "module": "Mathlib.Data.Set.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.up_mul", "kind": "theorem", "module": "Mathlib.Data.Set.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetSemiring.instNoZeroDivisors", "kind": "instance", "module": "Mathlib.Data.Set.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetSemiring.mulLeftMono", "kind": "instance", "module": "Mathlib.Data.Set.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetSemiring.mulRightMono", "kind": "instance", "module": "Mathlib.Data.Set.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetSemiring.instOne", "kind": "instance", "module": "Mathlib.Data.Set.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetSemiring.one_def", "kind": "theorem", "module": "Mathlib.Data.Set.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetSemiring.down_one", "kind": "theorem", "module": "Mathlib.Data.Set.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.up_one", "kind": "theorem", "module": "Mathlib.Data.Set.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetSemiring.instNonAssocSemiringOfMulOneClass", "kind": "instance", "module": "Mathlib.Data.Set.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetSemiring.instNonUnitalSemiringOfSemigroup", "kind": "instance", "module": "Mathlib.Data.Set.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetSemiring.instIdemSemiringOfMonoid", "kind": "instance", "module": "Mathlib.Data.Set.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetSemiring.instNonUnitalCommSemiringOfCommSemigroup", "kind": "instance", "module": "Mathlib.Data.Set.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetSemiring.instIdemCommSemiringOfCommMonoid", "kind": "instance", "module": "Mathlib.Data.Set.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetSemiring.instCommMonoid", "kind": "instance", "module": "Mathlib.Data.Set.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetSemiring.instCanonicallyOrderedAdd", "kind": "instance", "module": "Mathlib.Data.Set.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetSemiring.instIsOrderedRing", "kind": "instance", "module": "Mathlib.Data.Set.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetSemiring.singletonMonoidHom", "kind": "definition", "module": "Mathlib.Data.Set.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetSemiring.imageHom", "kind": "definition", "module": "Mathlib.Data.Set.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetSemiring.imageHom_def", "kind": "theorem", "module": "Mathlib.Data.Set.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetSemiring.down_imageHom", "kind": "theorem", "module": "Mathlib.Data.Set.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.up_image", "kind": "theorem", "module": "Mathlib.Data.Set.Semiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.range_sigmaMk", "kind": "theorem", "module": "Mathlib.Data.Set.Sigma", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.preimage_image_sigmaMk_of_ne", "kind": "theorem", "module": "Mathlib.Data.Set.Sigma", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.image_sigmaMk_preimage_sigmaMap_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_sigmaMk_preimage_sigmaMap", "kind": "theorem", "module": "Mathlib.Data.Set.Sigma", "is_tactic_proof": true, "tactics": ["refine", "rintro", "simp", "grind"], "tactic_count": 4}
{"name": "Set.sigma", "kind": "definition", "module": "Mathlib.Data.Set.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_sigma_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mk_sigma_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mk_mem_sigma", "kind": "theorem", "module": "Mathlib.Data.Set.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sigma_mono", "kind": "theorem", "module": "Mathlib.Data.Set.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sigma_subset_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Sigma", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.forall_sigma_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Sigma", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.exists_sigma_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Sigma", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.sigma_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Sigma", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.empty_sigma", "kind": "theorem", "module": "Mathlib.Data.Set.Sigma", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.univ_sigma_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Sigma", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.sigma_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Sigma", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.univ_sigma_preimage_mk", "kind": "theorem", "module": "Mathlib.Data.Set.Sigma", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.singleton_sigma", "kind": "theorem", "module": "Mathlib.Data.Set.Sigma", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.sigma_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Sigma", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.singleton_sigma_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Sigma", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.union_sigma", "kind": "theorem", "module": "Mathlib.Data.Set.Sigma", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.sigma_union", "kind": "theorem", "module": "Mathlib.Data.Set.Sigma", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.sigma_inter_sigma", "kind": "theorem", "module": "Mathlib.Data.Set.Sigma", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "biSup_sigma", "kind": "theorem", "module": "Mathlib.Data.Set.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "biSup_sigma'", "kind": "theorem", "module": "Mathlib.Data.Set.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "biInf_sigma", "kind": "theorem", "module": "Mathlib.Data.Set.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "biInf_sigma'", "kind": "theorem", "module": "Mathlib.Data.Set.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.biUnion_sigma", "kind": "theorem", "module": "Mathlib.Data.Set.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.biUnion_sigma'", "kind": "theorem", "module": "Mathlib.Data.Set.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.biInter_sigma", "kind": "theorem", "module": "Mathlib.Data.Set.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.biInter_sigma'", "kind": "theorem", "module": "Mathlib.Data.Set.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.insert_sigma", "kind": "theorem", "module": "Mathlib.Data.Set.Sigma", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.sigma_insert", "kind": "theorem", "module": "Mathlib.Data.Set.Sigma", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.sigma_preimage_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sigma_preimage_left", "kind": "theorem", "module": "Mathlib.Data.Set.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sigma_preimage_right", "kind": "theorem", "module": "Mathlib.Data.Set.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.preimage_sigmaMap_sigma", "kind": "theorem", "module": "Mathlib.Data.Set.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mk_preimage_sigma", "kind": "theorem", "module": "Mathlib.Data.Set.Sigma", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.mk_preimage_sigma_eq_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Sigma", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.mk_preimage_sigma_eq_if", "kind": "theorem", "module": "Mathlib.Data.Set.Sigma", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.mk_preimage_sigma_fn_eq_if", "kind": "theorem", "module": "Mathlib.Data.Set.Sigma", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.sigma_univ_range_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nonempty.sigma", "kind": "theorem", "module": "Mathlib.Data.Set.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nonempty.sigma_fst", "kind": "theorem", "module": "Mathlib.Data.Set.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nonempty.sigma_snd", "kind": "theorem", "module": "Mathlib.Data.Set.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sigma_nonempty_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sigma_eq_empty_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_sigmaMk_subset_sigma_left", "kind": "theorem", "module": "Mathlib.Data.Set.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_sigmaMk_subset_sigma_right", "kind": "theorem", "module": "Mathlib.Data.Set.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sigma_subset_preimage_fst", "kind": "theorem", "module": "Mathlib.Data.Set.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.fst_image_sigma_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_sigma_eq_iUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Sigma", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Set.fst_image_sigma", "kind": "theorem", "module": "Mathlib.Data.Set.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sigma_diff_sigma", "kind": "theorem", "module": "Mathlib.Data.Set.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sigma_eq_biUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Sigma", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Set.uncurry_preimage_sigma_pi", "kind": "theorem", "module": "Mathlib.Data.Set.Sigma", "is_tactic_proof": true, "tactics": ["ext", "simp", "exact"], "tactic_count": 3}
{"name": "Set.preimage_val_eq_univ_of_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Subset", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.preimage_val_sUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Subset", "is_tactic_proof": true, "tactics": ["rw", "simp_rw"], "tactic_count": 2}
{"name": "Set.preimage_val_iInter", "kind": "theorem", "module": "Mathlib.Data.Set.Subset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.preimage_val_sInter", "kind": "theorem", "module": "Mathlib.Data.Set.Subset", "is_tactic_proof": true, "tactics": ["rw", "simp_rw"], "tactic_count": 2}
{"name": "Set.preimage_val_sInter_eq_sInter", "kind": "theorem", "module": "Mathlib.Data.Set.Subset", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.eq_of_preimage_val_eq_of_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Subset", "is_tactic_proof": true, "tactics": ["simp", "simp", "exact"], "tactic_count": 3}
{"name": "Set.image_val_union", "kind": "theorem", "module": "Mathlib.Data.Set.Subset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_val_inter", "kind": "theorem", "module": "Mathlib.Data.Set.Subset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_val_diff", "kind": "theorem", "module": "Mathlib.Data.Set.Subset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_val_compl", "kind": "theorem", "module": "Mathlib.Data.Set.Subset", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.image_val_sUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Subset", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.image_val_iUnion", "kind": "theorem", "module": "Mathlib.Data.Set.Subset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_val_sInter", "kind": "theorem", "module": "Mathlib.Data.Set.Subset", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.image_val_iInter", "kind": "theorem", "module": "Mathlib.Data.Set.Subset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_val_union_self_right_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Subset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_val_union_self_left_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Subset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_val_inter_self_right_eq_coe", "kind": "theorem", "module": "Mathlib.Data.Set.Subset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_val_inter_self_left_eq_coe", "kind": "theorem", "module": "Mathlib.Data.Set.Subset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subset_preimage_val_image_val_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Subset", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.image_val_inj", "kind": "theorem", "module": "Mathlib.Data.Set.Subset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_val_injective", "kind": "theorem", "module": "Mathlib.Data.Set.Subset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subset_of_image_val_subset_image_val", "kind": "theorem", "module": "Mathlib.Data.Set.Subset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_val_mono", "kind": "theorem", "module": "Mathlib.Data.Set.Subset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_val_preimage_val_subset_self", "kind": "theorem", "module": "Mathlib.Data.Set.Subset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.preimage_val_image_val_eq_self", "kind": "theorem", "module": "Mathlib.Data.Set.Subset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Subsingleton", "kind": "definition", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Subsingleton.anti", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Subsingleton.eq_singleton_of_mem", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subsingleton_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subsingleton_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subsingleton_of_subset_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subsingleton_of_forall_eq", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subsingleton_iff_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Subsingleton.eq_empty_or_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Subsingleton.induction_on", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": true, "tactics": ["rcases", "exacts"], "tactic_count": 2}
{"name": "Set.subsingleton_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subsingleton_of_univ_subsingleton", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subsingleton_univ_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Subsingleton.inter_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Subsingleton.singleton_inter", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subsingleton_of_subsingleton_inter_left", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subsingleton_of_subsingleton_inter_right", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subsingleton_of_subsingleton", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subsingleton_isTop", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subsingleton_isBot", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.exists_eq_singleton_iff_nonempty_subsingleton", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": true, "tactics": ["refine", "rintro", "exact", "exact"], "tactic_count": 4}
{"name": "Set.subsingleton_coe", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": true, "tactics": ["constructor", "refine", "exact", "exact"], "tactic_count": 4}
{"name": "Set.Subsingleton.coe_sort", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subsingleton_coe_of_subsingleton", "kind": "instance", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.Subsingleton.denselyOrdered", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nontrivial", "kind": "definition", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.nontrivial_of_mem_mem_ne", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nontrivial.choose", "kind": "definition", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nontrivial.choose_fst_mem", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nontrivial.choose_snd_mem", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nontrivial.choose_fst_ne_choose_snd", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nontrivial.mono", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.nontrivial_pair", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.nontrivial_of_pair_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nontrivial.pair_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.nontrivial_iff_pair_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.nontrivial_of_exists_ne", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nontrivial.exists_ne", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": true, "tactics": ["by_contra", "rcases", "rw", "exact"], "tactic_count": 4}
{"name": "Set.nontrivial_iff_exists_ne", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.nontrivial_of_lt", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.nontrivial_of_exists_lt", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nontrivial.exists_lt", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.nontrivial_iff_exists_lt", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nontrivial.nonempty", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nontrivial.ne_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nontrivial.not_subset_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.not_nontrivial_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.not_nontrivial_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nontrivial.ne_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nontrivial.not_subset_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.nontrivial_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.nontrivial_of_univ_nontrivial", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.nontrivial_univ_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.singleton_ne_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.singleton_ssubset_univ", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.nontrivial_of_nontrivial", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.nontrivial_coe_sort", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.nontrivial_of_nontrivial_coe", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.nontrivial_mono", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.not_subsingleton_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.not_nontrivial_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subsingleton_or_nontrivial", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.eq_singleton_or_nontrivial", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.nontrivial_iff_ne_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nonempty.exists_eq_singleton_or_nontrivial", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.univ_eq_true_false", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.univ_set_of_isEmpty", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.univ_set_eq_singleton_empty_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": true, "tactics": ["refine", "suffices", "simp"], "tactic_count": 3}
{"name": "Set.Subsingleton.monotoneOn", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Subsingleton.antitoneOn", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Subsingleton.strictMonoOn", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Subsingleton.strictAntiOn", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.monotoneOn_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.antitoneOn_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.strictMonoOn_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.strictAntiOn_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "term_⊻_", "kind": "definition", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Data_Set_Sups___macroRules_term_⊻__1", "kind": "definition", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Data_Set_Sups___unexpand_HasSups_sups_1", "kind": "definition", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "term_⊼_", "kind": "definition", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Data_Set_Sups___macroRules_term_⊼__1", "kind": "definition", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Data_Set_Sups___unexpand_HasInfs_infs_1", "kind": "definition", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.hasSups", "kind": "definition", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_sups", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.sup_mem_sups", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sups_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sups_subset_left", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sups_subset_right", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_subset_sups_left", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_subset_sups_right", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.forall_sups_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sups_subset_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sups_nonempty", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nonempty.sups", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nonempty.of_sups_left", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nonempty.of_sups_right", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.empty_sups", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sups_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sups_eq_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.singleton_sups", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sups_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.singleton_sups_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sups_union_left", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sups_union_right", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sups_inter_subset_left", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sups_inter_subset_right", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_sups", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subset_sups_self", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sups_subset_self", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sups_eq_self", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sep_sups_le", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Set.iUnion_image_sup_left", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_image_sup_right", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_sup_prod", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sups_assoc", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sups_comm", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sups_left_comm", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sups_right_comm", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sups_sups_sups_comm", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.hasInfs", "kind": "definition", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_infs", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.inf_mem_infs", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.infs_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.infs_subset_left", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.infs_subset_right", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_subset_infs_left", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_subset_infs_right", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.forall_infs_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.infs_subset_iff", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.infs_nonempty", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nonempty.infs", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nonempty.of_infs_left", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nonempty.of_infs_right", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.empty_infs", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.infs_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.infs_eq_empty", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.singleton_infs", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.infs_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.singleton_infs_singleton", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.infs_union_left", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.infs_union_right", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.infs_inter_subset_left", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.infs_inter_subset_right", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_infs", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subset_infs_self", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.infs_self_subset", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.infs_self", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sep_infs_le", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Set.iUnion_image_inf_left", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_image_inf_right", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_inf_prod", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.infs_assoc", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.infs_comm", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.infs_left_comm", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.infs_right_comm", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.infs_infs_infs_comm", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sups_infs_subset_left", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sups_infs_subset_right", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.infs_sups_subset_left", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.infs_sups_subset_right", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "upperClosure_sups", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": true, "tactics": ["ext", "simp", "constructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 7}
{"name": "lowerClosure_infs", "kind": "theorem", "module": "Mathlib.Data.Set.Sups", "is_tactic_proof": true, "tactics": ["ext", "simp", "constructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 7}
{"name": "Set.mem_symmDiff", "kind": "theorem", "module": "Mathlib.Data.Set.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.symmDiff_def", "kind": "theorem", "module": "Mathlib.Data.Set.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.symmDiff_subset_union", "kind": "theorem", "module": "Mathlib.Data.Set.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.symmDiff_eq_empty", "kind": "theorem", "module": "Mathlib.Data.Set.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.symmDiff_nonempty", "kind": "theorem", "module": "Mathlib.Data.Set.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inter_symmDiff_distrib_left", "kind": "theorem", "module": "Mathlib.Data.Set.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inter_symmDiff_distrib_right", "kind": "theorem", "module": "Mathlib.Data.Set.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subset_symmDiff_union_symmDiff_left", "kind": "theorem", "module": "Mathlib.Data.Set.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subset_symmDiff_union_symmDiff_right", "kind": "theorem", "module": "Mathlib.Data.Set.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.union_symmDiff_subset", "kind": "theorem", "module": "Mathlib.Data.Set.SymmDiff", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.symmDiff_union_subset", "kind": "theorem", "module": "Mathlib.Data.Set.SymmDiff", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.union_symmDiff_union_subset", "kind": "theorem", "module": "Mathlib.Data.Set.SymmDiff", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.iUnionLift", "kind": "definition", "module": "Mathlib.Data.Set.UnionLift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnionLift_mk", "kind": "theorem", "module": "Mathlib.Data.Set.UnionLift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnionLift_inclusion", "kind": "theorem", "module": "Mathlib.Data.Set.UnionLift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnionLift_of_mem", "kind": "theorem", "module": "Mathlib.Data.Set.UnionLift", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "Set.preimage_iUnionLift", "kind": "theorem", "module": "Mathlib.Data.Set.UnionLift", "is_tactic_proof": true, "tactics": ["ext", "simp", "constructor", "rcases", "refine", "rwa", "rintro", "obtain", "rwa"], "tactic_count": 9}
{"name": "Set.iUnionLift_const", "kind": "theorem", "module": "Mathlib.Data.Set.UnionLift", "is_tactic_proof": true, "tactics": ["let", "have", "rw"], "tactic_count": 3}
{"name": "Set.iUnionLift_unary", "kind": "theorem", "module": "Mathlib.Data.Set.UnionLift", "is_tactic_proof": true, "tactics": ["subst", "obtain", "rw", "have", "cases", "rfl", "conv_lhs"], "tactic_count": 7}
{"name": "Set.iUnionLift_binary", "kind": "theorem", "module": "Mathlib.Data.Set.UnionLift", "is_tactic_proof": true, "tactics": ["subst", "obtain", "obtain", "rcases", "rw", "have", "cases", "rfl", "have", "cases", "rfl", "have", "conv_lhs"], "tactic_count": 13}
{"name": "Set.liftCover", "kind": "definition", "module": "Mathlib.Data.Set.UnionLift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.liftCover_coe", "kind": "theorem", "module": "Mathlib.Data.Set.UnionLift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.liftCover_of_mem", "kind": "theorem", "module": "Mathlib.Data.Set.UnionLift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.preimage_liftCover", "kind": "theorem", "module": "Mathlib.Data.Set.UnionLift", "is_tactic_proof": true, "tactics": ["change", "rw", "ext"], "tactic_count": 3}
{"name": "Setoid.eq_iff_rel_eq", "kind": "theorem", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.instLE_mathlib", "kind": "instance", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.le_def", "kind": "theorem", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.refl'", "kind": "theorem", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.symm'", "kind": "theorem", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.trans'", "kind": "theorem", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.comm'", "kind": "theorem", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.ker", "kind": "definition", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.ker_mk_eq", "kind": "theorem", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.ker_apply_mk_out", "kind": "theorem", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.ker_def", "kind": "theorem", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.prod", "kind": "definition", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.prod_apply", "kind": "theorem", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.piSetoid_apply", "kind": "theorem", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.prodQuotientEquiv", "kind": "definition", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.piQuotientEquiv", "kind": "definition", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.instMin_mathlib", "kind": "instance", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.inf_def", "kind": "theorem", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.inf_iff_and", "kind": "theorem", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.instInfSet", "kind": "instance", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.sInf_def", "kind": "theorem", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp", "rfl"], "tactic_count": 3}
{"name": "Setoid.instPartialOrder", "kind": "instance", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.completeLattice", "kind": "instance", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.top_def", "kind": "theorem", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.bot_def", "kind": "theorem", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.mk_eq_top", "kind": "theorem", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Setoid.mk_eq_bot", "kind": "theorem", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Setoid.eq_top_iff", "kind": "theorem", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Setoid.sInf_equiv", "kind": "theorem", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.sInf_iff", "kind": "theorem", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.quotient_mk_sInf_eq", "kind": "theorem", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Setoid.map_of_le", "kind": "definition", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.map_sInf", "kind": "definition", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.eqvGen_eq", "kind": "theorem", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.sup_eq_eqvGen", "kind": "theorem", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply", "simp"], "tactic_count": 3}
{"name": "Setoid.sup_def", "kind": "theorem", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Setoid.sSup_eq_eqvGen", "kind": "theorem", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply", "simp", "ext", "exact"], "tactic_count": 5}
{"name": "Setoid.sSup_def", "kind": "theorem", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": true, "tactics": ["rw", "congr", "simp"], "tactic_count": 3}
{"name": "Setoid.eqvGen_of_setoid", "kind": "theorem", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.eqvGen_idem", "kind": "theorem", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.eqvGen_le", "kind": "theorem", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Setoid.eqvGen_mono", "kind": "theorem", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.gi", "kind": "definition", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.injective_iff_ker_bot", "kind": "theorem", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.ker_iff_mem_preimage", "kind": "theorem", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.liftEquiv", "kind": "definition", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.lift_unique", "kind": "theorem", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "Setoid.kerLift", "kind": "definition", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.kerLift_mk", "kind": "theorem", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.kerLift_injective", "kind": "theorem", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.ker_eq_lift_of_injective", "kind": "theorem", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.lift_injective_iff_ker_eq_of_le", "kind": "theorem", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.range_kerLift_eq_range", "kind": "theorem", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.quotientKerEquivRangeKerLift", "kind": "definition", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.quotientKerEquivRange", "kind": "definition", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.quotientKerEquivOfRightInverse", "kind": "definition", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.quotientKerEquivOfSurjective", "kind": "definition", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.map", "kind": "definition", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.mapOfSurjective", "kind": "definition", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.mapOfSurjective_eq_map", "kind": "theorem", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Setoid.comap", "kind": "abbrev", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.comap_rel", "kind": "theorem", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.comap_eq", "kind": "theorem", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.comapQuotientEquiv", "kind": "definition", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.quotientQuotientEquivQuotient", "kind": "definition", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.correspondence", "kind": "definition", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.sigmaQuotientEquivOfLe", "kind": "definition", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quotient.subsingleton_iff", "kind": "theorem", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": true, "tactics": ["simp", "refine", "refine", "simp_rw"], "tactic_count": 4}
{"name": "Quot.subsingleton_iff", "kind": "theorem", "module": "Mathlib.Data.Setoid.Basic", "is_tactic_proof": true, "tactics": ["simp", "refine", "refine", "rw", "simp"], "tactic_count": 5}
{"name": "Setoid.eq_of_mem_eqv_class", "kind": "theorem", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.mkClasses", "kind": "definition", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.classes", "kind": "definition", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.mem_classes", "kind": "theorem", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.classes_ker_subset_fiber_set", "kind": "theorem", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": true, "tactics": ["rintro", "rw", "exact"], "tactic_count": 3}
{"name": "Setoid.finite_classes_ker", "kind": "theorem", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.card_classes_ker_le", "kind": "theorem", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Setoid.eq_iff_classes_eq", "kind": "theorem", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.rel_iff_exists_classes", "kind": "theorem", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.classes_inj", "kind": "theorem", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.empty_notMem_classes", "kind": "theorem", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.classes_eqv_classes", "kind": "theorem", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.eq_of_mem_classes", "kind": "theorem", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.eq_eqv_class_of_mem", "kind": "theorem", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": true, "tactics": ["ext", "constructor", "intro", "rwa", "intro", "obtain", "rwa"], "tactic_count": 7}
{"name": "Setoid.eqv_class_mem", "kind": "theorem", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.eqv_class_mem'", "kind": "theorem", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "Setoid.eqv_classes_disjoint", "kind": "theorem", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.eqv_classes_of_disjoint_union", "kind": "theorem", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.setoidOfDisjointUnion", "kind": "definition", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.mkClasses_classes", "kind": "theorem", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.sUnion_classes", "kind": "theorem", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.quotientEquivClasses", "kind": "definition", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": true, "tactics": ["let", "have", "rw", "exact", "apply", "constructor", "intro", "induction", "induction", "simp", "apply", "change", "rw", "exact", "rw", "intro", "exact"], "tactic_count": 17}
{"name": "Setoid.quotientEquivClasses_mk_eq", "kind": "theorem", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.IsPartition", "kind": "definition", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.nonempty_of_mem_partition", "kind": "theorem", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.isPartition_classes", "kind": "theorem", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.IsPartition.pairwiseDisjoint", "kind": "theorem", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.PairwiseDisjoint.isPartition_of_exists_of_ne_empty", "kind": "theorem", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": true, "tactics": ["refine", "intro", "apply", "simp", "exact"], "tactic_count": 5}
{"name": "Setoid.IsPartition.sUnion_eq_univ", "kind": "theorem", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.exists_of_mem_partition", "kind": "theorem", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.classes_mkClasses", "kind": "theorem", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": true, "tactics": ["ext", "constructor", "rintro", "obtain", "rwa", "exact"], "tactic_count": 6}
{"name": "Setoid.Partition.le", "kind": "instance", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.Partition.partialOrder", "kind": "instance", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.Partition.orderIso", "kind": "definition", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.Partition.completeLattice", "kind": "instance", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Setoid.IsPartition.finpartition", "kind": "definition", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.isPartition_parts", "kind": "theorem", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IndexedPartition.mk'", "kind": "definition", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IndexedPartition.instInhabitedUnivOfUnique", "kind": "instance", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IndexedPartition.exists_mem", "kind": "theorem", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IndexedPartition.iUnion", "kind": "theorem", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "IndexedPartition.disjoint", "kind": "theorem", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IndexedPartition.mem_iff_index_eq", "kind": "theorem", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IndexedPartition.eq", "kind": "theorem", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IndexedPartition.setoid", "kind": "abbrev", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IndexedPartition.index_some", "kind": "theorem", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IndexedPartition.some_index", "kind": "theorem", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IndexedPartition.Quotient", "kind": "definition", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IndexedPartition.proj", "kind": "definition", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IndexedPartition.instInhabitedQuotient", "kind": "instance", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IndexedPartition.proj_eq_iff", "kind": "theorem", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IndexedPartition.proj_some_index", "kind": "theorem", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IndexedPartition.equivQuotient", "kind": "definition", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IndexedPartition.equivQuotient_index_apply", "kind": "theorem", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IndexedPartition.equivQuotient_symm_proj_apply", "kind": "theorem", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IndexedPartition.equivQuotient_index", "kind": "theorem", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IndexedPartition.out", "kind": "definition", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IndexedPartition.out_proj", "kind": "theorem", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IndexedPartition.index_out", "kind": "theorem", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IndexedPartition.proj_out", "kind": "theorem", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IndexedPartition.class_of", "kind": "theorem", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IndexedPartition.proj_fiber", "kind": "theorem", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IndexedPartition.piecewise", "kind": "definition", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IndexedPartition.piecewise_apply", "kind": "theorem", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IndexedPartition.piecewise_inj", "kind": "theorem", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": true, "tactics": ["intro", "suffices", "apply", "simpa", "apply", "contrapose", "exact"], "tactic_count": 7}
{"name": "IndexedPartition.piecewise_bij", "kind": "theorem", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": true, "tactics": ["set", "have", "refine", "rw", "have", "refine", "simp", "rintro", "exact", "rw", "exact"], "tactic_count": 11}
{"name": "IndexedPartition.piecewise_preimage", "kind": "theorem", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact", "rw", "simp_all"], "tactic_count": 5}
{"name": "IndexedPartition.range_piecewise", "kind": "theorem", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": true, "tactics": ["refine", "rintro", "exact", "simp", "obtain", "refine", "simp", "simpa"], "tactic_count": 8}
{"name": "IndexedPartition.range_piecewise_subset", "kind": "theorem", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IndexedPartition.coarserPartition", "kind": "definition", "module": "Mathlib.Data.Setoid.Partition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.instInhabitedSigma", "kind": "instance", "module": "Mathlib.Data.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.instDecidableEqSigma", "kind": "instance", "module": "Mathlib.Data.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.mk.inj_iff", "kind": "theorem", "module": "Mathlib.Data.Sigma.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Sigma.eta", "kind": "theorem", "module": "Mathlib.Data.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.eq", "kind": "theorem", "module": "Mathlib.Data.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.eq_of_sigmaMk_comp", "kind": "theorem", "module": "Mathlib.Data.Sigma.Basic", "is_tactic_proof": true, "tactics": ["rcases", "obtain", "simpa"], "tactic_count": 3}
{"name": "Sigma.subtype_ext", "kind": "theorem", "module": "Mathlib.Data.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.forall", "kind": "theorem", "module": "Mathlib.Data.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.exists", "kind": "theorem", "module": "Mathlib.Data.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.exists'", "kind": "theorem", "module": "Mathlib.Data.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.forall'", "kind": "theorem", "module": "Mathlib.Data.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sigma_mk_injective", "kind": "theorem", "module": "Mathlib.Data.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.fst_surjective", "kind": "theorem", "module": "Mathlib.Data.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.fst_surjective_iff", "kind": "theorem", "module": "Mathlib.Data.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.fst_injective", "kind": "theorem", "module": "Mathlib.Data.Sigma.Basic", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "Sigma.fst_injective_iff", "kind": "theorem", "module": "Mathlib.Data.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.map", "kind": "definition", "module": "Mathlib.Data.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.map_mk", "kind": "theorem", "module": "Mathlib.Data.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.sigma_map", "kind": "theorem", "module": "Mathlib.Data.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.of_sigma_map", "kind": "theorem", "module": "Mathlib.Data.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.sigma_map_iff", "kind": "theorem", "module": "Mathlib.Data.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.sigma_map", "kind": "theorem", "module": "Mathlib.Data.Sigma.Basic", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Sigma.curry", "kind": "definition", "module": "Mathlib.Data.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.uncurry", "kind": "definition", "module": "Mathlib.Data.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.uncurry_curry", "kind": "theorem", "module": "Mathlib.Data.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.curry_uncurry", "kind": "theorem", "module": "Mathlib.Data.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.curry_update", "kind": "theorem", "module": "Mathlib.Data.Sigma.Basic", "is_tactic_proof": true, "tactics": ["obtain", "ext", "unfold", "obtain", "obtain", "simp", "simp", "rw", "rintro", "injection", "rw", "exact", "exact"], "tactic_count": 13}
{"name": "Prod.toSigma", "kind": "definition", "module": "Mathlib.Data.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.fst_comp_toSigma", "kind": "theorem", "module": "Mathlib.Data.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.fst_toSigma", "kind": "theorem", "module": "Mathlib.Data.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.snd_toSigma", "kind": "theorem", "module": "Mathlib.Data.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.toSigma_mk", "kind": "theorem", "module": "Mathlib.Data.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.toSigma_injective", "kind": "theorem", "module": "Mathlib.Data.Sigma.Basic", "is_tactic_proof": true, "tactics": ["rintro", "simp_all"], "tactic_count": 2}
{"name": "Prod.toSigma_inj", "kind": "theorem", "module": "Mathlib.Data.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSigma.elim", "kind": "definition", "module": "Mathlib.Data.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSigma.elim_val", "kind": "theorem", "module": "Mathlib.Data.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSigma.instInhabitedOfDefault_mathlib", "kind": "instance", "module": "Mathlib.Data.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSigma.decidableEq", "kind": "instance", "module": "Mathlib.Data.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSigma.mk.inj_iff", "kind": "theorem", "module": "Mathlib.Data.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSigma.forall", "kind": "theorem", "module": "Mathlib.Data.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSigma.exists", "kind": "theorem", "module": "Mathlib.Data.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSigma.subtype_ext", "kind": "theorem", "module": "Mathlib.Data.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSigma.map", "kind": "definition", "module": "Mathlib.Data.Sigma.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.instLocallyFiniteOrder", "kind": "instance", "module": "Mathlib.Data.Sigma.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.card_Icc", "kind": "theorem", "module": "Mathlib.Data.Sigma.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.card_Ico", "kind": "theorem", "module": "Mathlib.Data.Sigma.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.card_Ioc", "kind": "theorem", "module": "Mathlib.Data.Sigma.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.card_Ioo", "kind": "theorem", "module": "Mathlib.Data.Sigma.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.Icc_mk_mk", "kind": "theorem", "module": "Mathlib.Data.Sigma.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.Ico_mk_mk", "kind": "theorem", "module": "Mathlib.Data.Sigma.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.Ioc_mk_mk", "kind": "theorem", "module": "Mathlib.Data.Sigma.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.Ioo_mk_mk", "kind": "theorem", "module": "Mathlib.Data.Sigma.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.instLocallyFiniteOrderBot", "kind": "instance", "module": "Mathlib.Data.Sigma.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.Iic_mk", "kind": "theorem", "module": "Mathlib.Data.Sigma.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.Iio_mk", "kind": "theorem", "module": "Mathlib.Data.Sigma.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.instLocallyFiniteOrderTop", "kind": "instance", "module": "Mathlib.Data.Sigma.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.Ici_mk", "kind": "theorem", "module": "Mathlib.Data.Sigma.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.Ioi_mk", "kind": "theorem", "module": "Mathlib.Data.Sigma.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.Lex", "kind": "inductive", "module": "Mathlib.Data.Sigma.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.lex_iff", "kind": "theorem", "module": "Mathlib.Data.Sigma.Lex", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "exact", "exact", "obtain", "dsimp", "rintro", "exact", "exact"], "tactic_count": 9}
{"name": "Sigma.Lex.decidable", "kind": "instance", "module": "Mathlib.Data.Sigma.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.Lex.mono", "kind": "theorem", "module": "Mathlib.Data.Sigma.Lex", "is_tactic_proof": true, "tactics": ["obtain", "exact", "exact"], "tactic_count": 3}
{"name": "Sigma.Lex.mono_left", "kind": "theorem", "module": "Mathlib.Data.Sigma.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.Lex.mono_right", "kind": "theorem", "module": "Mathlib.Data.Sigma.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.lex_swap", "kind": "theorem", "module": "Mathlib.Data.Sigma.Lex", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "exact", "exact"], "tactic_count": 4}
{"name": "Sigma.instReflLex", "kind": "instance", "module": "Mathlib.Data.Sigma.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.instIrreflLex", "kind": "instance", "module": "Mathlib.Data.Sigma.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.instIsTransLex", "kind": "instance", "module": "Mathlib.Data.Sigma.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.instSymmLex", "kind": "instance", "module": "Mathlib.Data.Sigma.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.instAntisymmLexOfAsymm", "kind": "instance", "module": "Mathlib.Data.Sigma.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.instTotalLexOfIsTrichotomous", "kind": "instance", "module": "Mathlib.Data.Sigma.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.instIsTrichotomousLex", "kind": "instance", "module": "Mathlib.Data.Sigma.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSigma.lex_iff", "kind": "theorem", "module": "Mathlib.Data.Sigma.Lex", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "exact", "exact", "obtain", "dsimp", "rintro", "exact", "exact"], "tactic_count": 9}
{"name": "PSigma.Lex.decidable", "kind": "instance", "module": "Mathlib.Data.Sigma.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSigma.Lex.mono", "kind": "theorem", "module": "Mathlib.Data.Sigma.Lex", "is_tactic_proof": true, "tactics": ["obtain", "exact", "exact"], "tactic_count": 3}
{"name": "PSigma.Lex.mono_left", "kind": "theorem", "module": "Mathlib.Data.Sigma.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSigma.Lex.mono_right", "kind": "theorem", "module": "Mathlib.Data.Sigma.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.LE", "kind": "inductive", "module": "Mathlib.Data.Sigma.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.LT", "kind": "inductive", "module": "Mathlib.Data.Sigma.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.instLE_mathlib", "kind": "instance", "module": "Mathlib.Data.Sigma.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.instLT_mathlib", "kind": "instance", "module": "Mathlib.Data.Sigma.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.mk_le_mk_iff", "kind": "theorem", "module": "Mathlib.Data.Sigma.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.mk_lt_mk_iff", "kind": "theorem", "module": "Mathlib.Data.Sigma.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.le_def", "kind": "theorem", "module": "Mathlib.Data.Sigma.Order", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "exact", "obtain", "obtain", "rintro", "exact"], "tactic_count": 7}
{"name": "Sigma.lt_def", "kind": "theorem", "module": "Mathlib.Data.Sigma.Order", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "exact", "obtain", "obtain", "rintro", "exact"], "tactic_count": 7}
{"name": "Sigma.preorder", "kind": "instance", "module": "Mathlib.Data.Sigma.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.instPartialOrder", "kind": "instance", "module": "Mathlib.Data.Sigma.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.instDenselyOrdered", "kind": "instance", "module": "Mathlib.Data.Sigma.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.Lex.termΣₗ_,_", "kind": "definition", "module": "Mathlib.Data.Sigma.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.Lex._aux_Mathlib_Data_Sigma_Order___macroRules_Sigma_Lex_termΣₗ_,__1", "kind": "definition", "module": "Mathlib.Data.Sigma.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.Lex._aux_Mathlib_Data_Sigma_Order___delab_app_Sigma_Lex_termΣₗ_,__1", "kind": "definition", "module": "Mathlib.Data.Sigma.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.Lex.LE", "kind": "instance", "module": "Mathlib.Data.Sigma.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.Lex.LT", "kind": "instance", "module": "Mathlib.Data.Sigma.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.Lex.le_def", "kind": "theorem", "module": "Mathlib.Data.Sigma.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.Lex.lt_def", "kind": "theorem", "module": "Mathlib.Data.Sigma.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.Lex.preorder", "kind": "instance", "module": "Mathlib.Data.Sigma.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.Lex.partialOrder", "kind": "instance", "module": "Mathlib.Data.Sigma.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.Lex.linearOrder", "kind": "instance", "module": "Mathlib.Data.Sigma.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.Lex.orderBot", "kind": "instance", "module": "Mathlib.Data.Sigma.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.Lex.orderTop", "kind": "instance", "module": "Mathlib.Data.Sigma.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.Lex.boundedOrder", "kind": "instance", "module": "Mathlib.Data.Sigma.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.Lex.denselyOrdered", "kind": "instance", "module": "Mathlib.Data.Sigma.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.Lex.denselyOrdered_of_noMaxOrder", "kind": "instance", "module": "Mathlib.Data.Sigma.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.Lex.denselyOrdered_of_noMinOrder", "kind": "instance", "module": "Mathlib.Data.Sigma.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.Lex.noMaxOrder_of_nonempty", "kind": "instance", "module": "Mathlib.Data.Sigma.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.Lex.noMinOrder_of_nonempty", "kind": "instance", "module": "Mathlib.Data.Sigma.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.Lex.noMaxOrder", "kind": "instance", "module": "Mathlib.Data.Sigma.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.Lex.noMinOrder", "kind": "instance", "module": "Mathlib.Data.Sigma.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SignType.intCast_cast", "kind": "theorem", "module": "Mathlib.Data.Sign.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SignType.pow_odd", "kind": "theorem", "module": "Mathlib.Data.Sign.Basic", "is_tactic_proof": true, "tactics": ["obtain", "rw", "cases"], "tactic_count": 3}
{"name": "SignType.zpow_odd", "kind": "theorem", "module": "Mathlib.Data.Sign.Basic", "is_tactic_proof": true, "tactics": ["obtain", "rw", "rintro", "simp", "obtain", "rw", "cases"], "tactic_count": 7}
{"name": "SignType.pow_even", "kind": "theorem", "module": "Mathlib.Data.Sign.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "SignType.zpow_even", "kind": "theorem", "module": "Mathlib.Data.Sign.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "SignType.castHom", "kind": "definition", "module": "Mathlib.Data.Sign.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SignType.univ_eq", "kind": "theorem", "module": "Mathlib.Data.Sign.Basic", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "SignType.range_eq", "kind": "theorem", "module": "Mathlib.Data.Sign.Basic", "is_tactic_proof": true, "tactics": ["classical", "classical"], "tactic_count": 2}
{"name": "SignType.coe_mul", "kind": "theorem", "module": "Mathlib.Data.Sign.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SignType.coe_pow", "kind": "theorem", "module": "Mathlib.Data.Sign.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SignType.coe_zpow", "kind": "theorem", "module": "Mathlib.Data.Sign.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sign_intCast", "kind": "theorem", "module": "Mathlib.Data.Sign.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "sign_mul", "kind": "theorem", "module": "Mathlib.Data.Sign.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simp"], "tactic_count": 2}
{"name": "sign_mul_abs", "kind": "theorem", "module": "Mathlib.Data.Sign.Basic", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "abs_mul_sign", "kind": "theorem", "module": "Mathlib.Data.Sign.Basic", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "sign_mul_self", "kind": "theorem", "module": "Mathlib.Data.Sign.Basic", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "self_mul_sign", "kind": "theorem", "module": "Mathlib.Data.Sign.Basic", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "signHom", "kind": "definition", "module": "Mathlib.Data.Sign.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sign_pow", "kind": "theorem", "module": "Mathlib.Data.Sign.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sign_sum", "kind": "theorem", "module": "Mathlib.Data.Sign.Basic", "is_tactic_proof": true, "tactics": ["cases", "simp_rw", "exact", "simp_rw", "exact", "simp_rw", "exact"], "tactic_count": 7}
{"name": "_private.Mathlib.Data.Sign.Basic.0.exists_signed_sum_aux", "kind": "theorem", "module": "Mathlib.Data.Sign.Basic", "is_tactic_proof": false, "tactics": ["refine", "simp", "intro", "simp", "sum_attach"], "tactic_count": 5}
{"name": "exists_signed_sum", "kind": "theorem", "module": "Mathlib.Data.Sign.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_signed_sum'", "kind": "theorem", "module": "Mathlib.Data.Sign.Basic", "is_tactic_proof": true, "tactics": ["obtain", "refine", "rintro", "cases", "rfl"], "tactic_count": 5}
{"name": "SignType", "kind": "inductive", "module": "Mathlib.Data.Sign.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDecidableEqSignType", "kind": "instance", "module": "Mathlib.Data.Sign.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInhabitedSignType.default", "kind": "definition", "module": "Mathlib.Data.Sign.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInhabitedSignType", "kind": "instance", "module": "Mathlib.Data.Sign.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFintypeSignType", "kind": "instance", "module": "Mathlib.Data.Sign.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SignType.instZero", "kind": "instance", "module": "Mathlib.Data.Sign.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SignType.instOne", "kind": "instance", "module": "Mathlib.Data.Sign.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SignType.instNeg", "kind": "instance", "module": "Mathlib.Data.Sign.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SignType.zero_eq_zero", "kind": "theorem", "module": "Mathlib.Data.Sign.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SignType.neg_eq_neg_one", "kind": "theorem", "module": "Mathlib.Data.Sign.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SignType.pos_eq_one", "kind": "theorem", "module": "Mathlib.Data.Sign.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SignType.trichotomy", "kind": "theorem", "module": "Mathlib.Data.Sign.Defs", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "SignType.instMul", "kind": "instance", "module": "Mathlib.Data.Sign.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SignType.LE", "kind": "inductive", "module": "Mathlib.Data.Sign.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SignType.instLE", "kind": "instance", "module": "Mathlib.Data.Sign.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SignType.instDecidableLE", "kind": "instance", "module": "Mathlib.Data.Sign.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SignType.instCommGroupWithZero", "kind": "instance", "module": "Mathlib.Data.Sign.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SignType.instLinearOrder", "kind": "instance", "module": "Mathlib.Data.Sign.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SignType.instBoundedOrder", "kind": "instance", "module": "Mathlib.Data.Sign.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SignType.instHasDistribNeg", "kind": "instance", "module": "Mathlib.Data.Sign.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SignType.fin3Equiv", "kind": "definition", "module": "Mathlib.Data.Sign.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SignType.nonneg_iff", "kind": "theorem", "module": "Mathlib.Data.Sign.Defs", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "SignType.nonneg_iff_ne_neg_one", "kind": "theorem", "module": "Mathlib.Data.Sign.Defs", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "SignType.neg_one_lt_iff", "kind": "theorem", "module": "Mathlib.Data.Sign.Defs", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "SignType.nonpos_iff", "kind": "theorem", "module": "Mathlib.Data.Sign.Defs", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "SignType.nonpos_iff_ne_one", "kind": "theorem", "module": "Mathlib.Data.Sign.Defs", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "SignType.lt_one_iff", "kind": "theorem", "module": "Mathlib.Data.Sign.Defs", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "SignType.neg_iff", "kind": "theorem", "module": "Mathlib.Data.Sign.Defs", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "SignType.le_neg_one_iff", "kind": "theorem", "module": "Mathlib.Data.Sign.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SignType.pos_iff", "kind": "theorem", "module": "Mathlib.Data.Sign.Defs", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "SignType.one_le_iff", "kind": "theorem", "module": "Mathlib.Data.Sign.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SignType.neg_one_le", "kind": "theorem", "module": "Mathlib.Data.Sign.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SignType.le_one", "kind": "theorem", "module": "Mathlib.Data.Sign.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SignType.not_lt_neg_one", "kind": "theorem", "module": "Mathlib.Data.Sign.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SignType.not_one_lt", "kind": "theorem", "module": "Mathlib.Data.Sign.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SignType.self_eq_neg_iff", "kind": "theorem", "module": "Mathlib.Data.Sign.Defs", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "SignType.neg_eq_self_iff", "kind": "theorem", "module": "Mathlib.Data.Sign.Defs", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "SignType.neg_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Data.Sign.Defs", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "SignType.neg_one_lt_one", "kind": "theorem", "module": "Mathlib.Data.Sign.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SignType.neg_le_neg_iff", "kind": "theorem", "module": "Mathlib.Data.Sign.Defs", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "SignType.neg_lt_neg_iff", "kind": "theorem", "module": "Mathlib.Data.Sign.Defs", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "SignType.cast", "kind": "definition", "module": "Mathlib.Data.Sign.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SignType.instCoeDep", "kind": "instance", "module": "Mathlib.Data.Sign.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SignType.map_cast'", "kind": "theorem", "module": "Mathlib.Data.Sign.Defs", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "SignType.map_cast", "kind": "theorem", "module": "Mathlib.Data.Sign.Defs", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "SignType.coe_zero", "kind": "theorem", "module": "Mathlib.Data.Sign.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SignType.coe_one", "kind": "theorem", "module": "Mathlib.Data.Sign.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SignType.coe_neg_one", "kind": "theorem", "module": "Mathlib.Data.Sign.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SignType.coe_neg", "kind": "theorem", "module": "Mathlib.Data.Sign.Defs", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "SignType.sign", "kind": "definition", "module": "Mathlib.Data.Sign.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sign_apply", "kind": "theorem", "module": "Mathlib.Data.Sign.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sign_zero", "kind": "theorem", "module": "Mathlib.Data.Sign.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "sign_pos", "kind": "theorem", "module": "Mathlib.Data.Sign.Defs", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "sign_neg", "kind": "theorem", "module": "Mathlib.Data.Sign.Defs", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "sign_eq_one_iff", "kind": "theorem", "module": "Mathlib.Data.Sign.Defs", "is_tactic_proof": true, "tactics": ["refine", "by_contra", "rw", "split_ifs"], "tactic_count": 4}
{"name": "sign_eq_neg_one_iff", "kind": "theorem", "module": "Mathlib.Data.Sign.Defs", "is_tactic_proof": true, "tactics": ["refine", "rw", "split_ifs", "assumption"], "tactic_count": 4}
{"name": "StrictMono.sign_comp", "kind": "theorem", "module": "Mathlib.Data.Sign.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "sign_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Data.Sign.Defs", "is_tactic_proof": true, "tactics": ["refine", "rw", "split_ifs", "cases", "exact"], "tactic_count": 5}
{"name": "sign_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Sign.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sign_nonneg_iff", "kind": "theorem", "module": "Mathlib.Data.Sign.Defs", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simp", "simp"], "tactic_count": 4}
{"name": "sign_nonpos_iff", "kind": "theorem", "module": "Mathlib.Data.Sign.Defs", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simp", "simp"], "tactic_count": 4}
{"name": "sign_eq_sign_or_eq_neg", "kind": "theorem", "module": "Mathlib.Data.Sign.Defs", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "sign_one", "kind": "theorem", "module": "Mathlib.Data.Sign.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Left.sign_neg", "kind": "theorem", "module": "Mathlib.Data.Sign.Defs", "is_tactic_proof": true, "tactics": ["simp_rw", "split_ifs", "exact", "simp", "simp", "simp"], "tactic_count": 6}
{"name": "Right.sign_neg", "kind": "theorem", "module": "Mathlib.Data.Sign.Defs", "is_tactic_proof": true, "tactics": ["simp_rw", "split_ifs", "exact", "simp", "simp", "simp"], "tactic_count": 6}
{"name": "Int.sign_eq_sign", "kind": "theorem", "module": "Mathlib.Data.Sign.Defs", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "Stream'", "kind": "definition", "module": "Mathlib.Data.Stream.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.cons", "kind": "definition", "module": "Mathlib.Data.Stream.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.term_::_", "kind": "definition", "module": "Mathlib.Data.Stream.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'._aux_Mathlib_Data_Stream_Defs___macroRules_Stream'_term_::__1", "kind": "definition", "module": "Mathlib.Data.Stream.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'._aux_Mathlib_Data_Stream_Defs___unexpand_Stream'_cons_1", "kind": "definition", "module": "Mathlib.Data.Stream.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.get", "kind": "definition", "module": "Mathlib.Data.Stream.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.head", "kind": "abbrev", "module": "Mathlib.Data.Stream.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.tail", "kind": "definition", "module": "Mathlib.Data.Stream.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.drop", "kind": "definition", "module": "Mathlib.Data.Stream.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.All", "kind": "definition", "module": "Mathlib.Data.Stream.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.Any", "kind": "definition", "module": "Mathlib.Data.Stream.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.instMembership", "kind": "instance", "module": "Mathlib.Data.Stream.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.map", "kind": "definition", "module": "Mathlib.Data.Stream.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.zip", "kind": "definition", "module": "Mathlib.Data.Stream.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.enum", "kind": "definition", "module": "Mathlib.Data.Stream.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.const", "kind": "definition", "module": "Mathlib.Data.Stream.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.iterate", "kind": "definition", "module": "Mathlib.Data.Stream.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.corec", "kind": "definition", "module": "Mathlib.Data.Stream.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.corecOn", "kind": "definition", "module": "Mathlib.Data.Stream.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.corec'", "kind": "definition", "module": "Mathlib.Data.Stream.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.corecState", "kind": "definition", "module": "Mathlib.Data.Stream.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.unfolds", "kind": "abbrev", "module": "Mathlib.Data.Stream.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.interleave", "kind": "definition", "module": "Mathlib.Data.Stream.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.term_⋈_", "kind": "definition", "module": "Mathlib.Data.Stream.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'._aux_Mathlib_Data_Stream_Defs___macroRules_Stream'_term_⋈__1", "kind": "definition", "module": "Mathlib.Data.Stream.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'._aux_Mathlib_Data_Stream_Defs___unexpand_Stream'_interleave_1", "kind": "definition", "module": "Mathlib.Data.Stream.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.even", "kind": "definition", "module": "Mathlib.Data.Stream.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.odd", "kind": "definition", "module": "Mathlib.Data.Stream.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.appendStream'", "kind": "definition", "module": "Mathlib.Data.Stream.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.term_++ₛ_", "kind": "definition", "module": "Mathlib.Data.Stream.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'._aux_Mathlib_Data_Stream_Defs___macroRules_Stream'_term_++ₛ__1", "kind": "definition", "module": "Mathlib.Data.Stream.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'._aux_Mathlib_Data_Stream_Defs___unexpand_Stream'_appendStream'_1", "kind": "definition", "module": "Mathlib.Data.Stream.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.take", "kind": "definition", "module": "Mathlib.Data.Stream.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.cycleF", "kind": "definition", "module": "Mathlib.Data.Stream.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.cycleG", "kind": "definition", "module": "Mathlib.Data.Stream.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.cycle", "kind": "definition", "module": "Mathlib.Data.Stream.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.tails", "kind": "definition", "module": "Mathlib.Data.Stream.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.initsCore", "kind": "definition", "module": "Mathlib.Data.Stream.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.inits", "kind": "definition", "module": "Mathlib.Data.Stream.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.pure", "kind": "definition", "module": "Mathlib.Data.Stream.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.apply", "kind": "definition", "module": "Mathlib.Data.Stream.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.term_⊛_", "kind": "definition", "module": "Mathlib.Data.Stream.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'._aux_Mathlib_Data_Stream_Defs___macroRules_Stream'_term_⊛__1", "kind": "definition", "module": "Mathlib.Data.Stream.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'._aux_Mathlib_Data_Stream_Defs___unexpand_Stream'_apply_1", "kind": "definition", "module": "Mathlib.Data.Stream.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.nats", "kind": "definition", "module": "Mathlib.Data.Stream.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.instInhabited", "kind": "instance", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.eta", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.ext", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.get_zero_cons", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.head_cons", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.tail_cons", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.get_drop", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Stream'.tail_eq_drop", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.drop_drop", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Stream'.get_tail", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.tail_drop'", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Stream'.drop_tail'", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.tail_drop", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Stream'.get_succ", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.get_succ_cons", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.get_cons_append_zero", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.append_eq_cons", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.drop_zero", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.drop_succ", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.head_drop", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Stream'.cons_injective2", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.cons_injective_left", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.cons_injective_right", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.all_def", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.any_def", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.mem_cons", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.mem_cons_of_mem", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.eq_or_mem_of_mem_cons", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.mem_of_get_eq", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.mem_iff_exists_get_eq", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.drop_map", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.get_map", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.tail_map", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.head_map", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.map_eq", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Stream'.map_cons", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Stream'.map_id", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.map_map", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.map_tail", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.mem_map", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.exists_of_mem_map", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.drop_zip", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.get_zip", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.head_zip", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.tail_zip", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.zip_eq", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Stream'.get_enum", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.enum_eq_zip", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.mem_const", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.const_eq", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": true, "tactics": ["apply", "cases"], "tactic_count": 2}
{"name": "Stream'.tail_const", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.map_const", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.get_const", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.drop_const", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.head_iterate", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.get_succ_iterate'", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.tail_iterate", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": true, "tactics": ["ext", "rw", "induction", "zero", "succ"], "tactic_count": 5}
{"name": "Stream'.iterate_eq", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": true, "tactics": ["rw", "rw"], "tactic_count": 2}
{"name": "Stream'.get_zero_iterate", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.get_succ_iterate", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "_private.Mathlib.Data.Stream.Init.0.Stream'.term_~_", "kind": "definition", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.Stream.Init.0.Stream'._aux_Mathlib_Data_Stream_Init___macroRules__private_Mathlib_Data_Stream_Init_0_Stream'_term_~__1", "kind": "definition", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.IsBisimulation", "kind": "definition", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.get_of_bisim", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.eq_of_bisim", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.bisim_simple", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.coinduction", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.iterate_id", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.map_iterate", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": true, "tactics": ["funext", "induction", "zero", "succ", "unfold", "rw", "rw", "exact"], "tactic_count": 8}
{"name": "Stream'.corec_def", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.corec_eq", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Stream'.corec_id_id_eq_const", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Stream'.corec_id_f_eq_iterate", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.corec'_eq", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.unfolds_eq", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "Stream'.get_unfolds_head_tail", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Stream'.unfolds_head_eq", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.interleave_eq", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": true, "tactics": ["let", "change", "unfold"], "tactic_count": 3}
{"name": "Stream'.tail_interleave", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "Stream'.interleave_tail_tail", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Stream'.get_interleave_left", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.get_interleave_right", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.mem_interleave_left", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.mem_interleave_right", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.odd_eq", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.head_even", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.tail_even", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": true, "tactics": ["unfold", "rw", "rfl"], "tactic_count": 3}
{"name": "Stream'.even_cons_cons", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": true, "tactics": ["unfold", "rw"], "tactic_count": 2}
{"name": "Stream'.even_tail", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.even_interleave", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.interleave_even_odd", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.get_even", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.get_odd", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.mem_of_mem_even", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.mem_of_mem_odd", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.nil_append_stream", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.cons_append_stream", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.append_append_stream", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.get_append_left", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "rcases", "simp", "simp"], "tactic_count": 6}
{"name": "Stream'.get_append_right", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "Stream'.get_append_length", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.append_right_injective", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Stream'.append_right_inj", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.append_left_injective", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": true, "tactics": ["apply", "intros", "rw"], "tactic_count": 3}
{"name": "Stream'.map_append_stream", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.drop_append_stream", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.append_stream_head_tail", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Stream'.mem_append_stream_right", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.mem_append_stream_left", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.take_zero", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.take_succ", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.take_succ_cons", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.take_succ'", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.length_take", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "Stream'.take_take", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.concat_take_get", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.getElem?_take", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.getElem?_take_succ", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.dropLast_take", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": true, "tactics": ["cases", "zero", "succ"], "tactic_count": 3}
{"name": "Stream'.append_take_drop", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Stream'.append_take", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "Stream'.take_get", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": true, "tactics": ["nth_rw"], "tactic_count": 1}
{"name": "Stream'.take_append_of_le_length", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": true, "tactics": ["apply", "intro"], "tactic_count": 2}
{"name": "Stream'.take_add", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "Stream'.take_prefix_take_left", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "Stream'.take_prefix", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.map_take", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "Stream'.take_drop", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "Stream'.drop_append_of_le_length", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": true, "tactics": ["obtain", "ext", "rw", "obtain", "have", "simp_rw"], "tactic_count": 6}
{"name": "Stream'.take_theorem", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": true, "tactics": ["ext", "induction", "zero", "succ", "n", "have", "rw", "injection"], "tactic_count": 8}
{"name": "Stream'.cycle_g_cons", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.cycle_eq", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.mem_cycle", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.cycle_singleton", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.tails_eq", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "Stream'.get_tails", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Stream'.tails_eq_iterate", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.inits_core_eq", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": true, "tactics": ["unfold", "rw"], "tactic_count": 2}
{"name": "Stream'.tail_inits", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": true, "tactics": ["unfold", "rw"], "tactic_count": 2}
{"name": "Stream'.inits_tail", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.cons_get_inits_core", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "rfl"], "tactic_count": 5}
{"name": "Stream'.get_inits", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Stream'.inits_eq", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": true, "tactics": ["apply", "cases", "rfl", "rw", "rfl"], "tactic_count": 5}
{"name": "Stream'.zip_inits_tails", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Stream'.identity", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.composition", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.homomorphism", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.interchange", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.map_eq_apply", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.get_nats", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.nats_eq", "kind": "theorem", "module": "Mathlib.Data.Stream.Init", "is_tactic_proof": true, "tactics": ["apply", "cases", "rfl", "rw"], "tactic_count": 4}
{"name": "String.ltb", "kind": "definition", "module": "Mathlib.Data.String.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "String.LT'", "kind": "instance", "module": "Mathlib.Data.String.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "String.decidableLT'", "kind": "instance", "module": "Mathlib.Data.String.Basic", "is_tactic_proof": true, "tactics": ["simp", "infer_instance"], "tactic_count": 2}
{"name": "String.ltb.inductionOn", "kind": "definition", "module": "Mathlib.Data.String.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "String.ltb_cons_addChar'", "kind": "theorem", "module": "Mathlib.Data.String.Basic", "is_tactic_proof": true, "tactics": ["fun_induction", "case1", "ih", "rw", "if_pos", "simp", "congr", "simpa", "case2", "h", "rw", "if_pos", "simp", "simpa", "case3", "rw", "if_neg", "case4"], "tactic_count": 18}
{"name": "String.ltb_cons_addChar", "kind": "theorem", "module": "Mathlib.Data.String.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "String.lt_iff_toList_lt", "kind": "theorem", "module": "Mathlib.Data.String.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "String.LE", "kind": "instance", "module": "Mathlib.Data.String.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "String.decidableLE", "kind": "instance", "module": "Mathlib.Data.String.Basic", "is_tactic_proof": true, "tactics": ["simp", "infer_instance"], "tactic_count": 2}
{"name": "String.le_iff_toList_le", "kind": "theorem", "module": "Mathlib.Data.String.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "String.asString_nil", "kind": "theorem", "module": "Mathlib.Data.String.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "String.asString_toList", "kind": "theorem", "module": "Mathlib.Data.String.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "String.toList_nonempty", "kind": "theorem", "module": "Mathlib.Data.String.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "String.head_empty", "kind": "theorem", "module": "Mathlib.Data.String.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "String.instLinearOrder", "kind": "instance", "module": "Mathlib.Data.String.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "String.ofList_eq", "kind": "theorem", "module": "Mathlib.Data.String.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.toList_asString", "kind": "theorem", "module": "Mathlib.Data.String.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.asString_eq", "kind": "theorem", "module": "Mathlib.Data.String.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "String.replicate", "kind": "definition", "module": "Mathlib.Data.String.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "String.IsPrefix", "kind": "definition", "module": "Mathlib.Data.String.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "String.IsSuffix", "kind": "definition", "module": "Mathlib.Data.String.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "String.mapTokens", "kind": "definition", "module": "Mathlib.Data.String.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "String.head", "kind": "definition", "module": "Mathlib.Data.String.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "String.congr_append", "kind": "theorem", "module": "Mathlib.Data.String.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "String.length_replicate", "kind": "theorem", "module": "Mathlib.Data.String.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "String.length_eq_list_length", "kind": "theorem", "module": "Mathlib.Data.String.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "String.length_leftpad", "kind": "theorem", "module": "Mathlib.Data.String.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "String.leftpad_prefix", "kind": "theorem", "module": "Mathlib.Data.String.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "String.leftpad_suffix", "kind": "theorem", "module": "Mathlib.Data.String.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.prop", "kind": "theorem", "module": "Mathlib.Data.Subtype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.forall'", "kind": "theorem", "module": "Mathlib.Data.Subtype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.exists'", "kind": "theorem", "module": "Mathlib.Data.Subtype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.heq_iff_coe_eq", "kind": "theorem", "module": "Mathlib.Data.Subtype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.heq_iff_coe_heq", "kind": "theorem", "module": "Mathlib.Data.Subtype", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Subtype.ext_val", "kind": "theorem", "module": "Mathlib.Data.Subtype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.ext_iff_val", "kind": "theorem", "module": "Mathlib.Data.Subtype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.coe_eta", "kind": "theorem", "module": "Mathlib.Data.Subtype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.coe_mk", "kind": "theorem", "module": "Mathlib.Data.Subtype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.mk_eq_mk", "kind": "theorem", "module": "Mathlib.Data.Subtype", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Subtype.coe_eq_of_eq_mk", "kind": "theorem", "module": "Mathlib.Data.Subtype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.coe_eq_iff", "kind": "theorem", "module": "Mathlib.Data.Subtype", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Subtype.coe_injective", "kind": "theorem", "module": "Mathlib.Data.Subtype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.val_injective", "kind": "theorem", "module": "Mathlib.Data.Subtype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.coe_inj", "kind": "theorem", "module": "Mathlib.Data.Subtype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.val_inj", "kind": "theorem", "module": "Mathlib.Data.Subtype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.coe_ne_coe", "kind": "theorem", "module": "Mathlib.Data.Subtype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_eq_subtype_mk_iff", "kind": "theorem", "module": "Mathlib.Data.Subtype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_subtype_mk_eq_iff", "kind": "theorem", "module": "Mathlib.Data.Subtype", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Function.extend_val_apply", "kind": "theorem", "module": "Mathlib.Data.Subtype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.extend_val_apply'", "kind": "theorem", "module": "Mathlib.Data.Subtype", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Subtype.restrict", "kind": "definition", "module": "Mathlib.Data.Subtype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.restrict_apply", "kind": "theorem", "module": "Mathlib.Data.Subtype", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "Subtype.restrict_def", "kind": "theorem", "module": "Mathlib.Data.Subtype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.restrict_injective", "kind": "theorem", "module": "Mathlib.Data.Subtype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.surjective_restrict", "kind": "theorem", "module": "Mathlib.Data.Subtype", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Subtype.coind", "kind": "definition", "module": "Mathlib.Data.Subtype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.coind_injective", "kind": "theorem", "module": "Mathlib.Data.Subtype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.map", "kind": "definition", "module": "Mathlib.Data.Subtype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.map_def", "kind": "theorem", "module": "Mathlib.Data.Subtype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.map_comp", "kind": "theorem", "module": "Mathlib.Data.Subtype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.map_id", "kind": "theorem", "module": "Mathlib.Data.Subtype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.map_injective", "kind": "theorem", "module": "Mathlib.Data.Subtype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.map_involutive", "kind": "theorem", "module": "Mathlib.Data.Subtype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.map_eq", "kind": "theorem", "module": "Mathlib.Data.Subtype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.map_ne", "kind": "theorem", "module": "Mathlib.Data.Subtype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.instHasEquiv_mathlib", "kind": "instance", "module": "Mathlib.Data.Subtype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.equiv_iff", "kind": "theorem", "module": "Mathlib.Data.Subtype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.refl", "kind": "theorem", "module": "Mathlib.Data.Subtype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.symm", "kind": "theorem", "module": "Mathlib.Data.Subtype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.trans", "kind": "theorem", "module": "Mathlib.Data.Subtype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.equivalence", "kind": "theorem", "module": "Mathlib.Data.Subtype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.instSetoid_mathlib", "kind": "instance", "module": "Mathlib.Data.Subtype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.coe_prop", "kind": "theorem", "module": "Mathlib.Data.Subtype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.val_prop", "kind": "theorem", "module": "Mathlib.Data.Subtype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_isLeft_and_isRight", "kind": "theorem", "module": "Mathlib.Data.Sum.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Sum.elim_swap", "kind": "theorem", "module": "Mathlib.Data.Sum.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Sum.exists_sum", "kind": "theorem", "module": "Mathlib.Data.Sum.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Sum.inl_injective", "kind": "theorem", "module": "Mathlib.Data.Sum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.inr_injective", "kind": "theorem", "module": "Mathlib.Data.Sum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.sum_rec_congr", "kind": "theorem", "module": "Mathlib.Data.Sum.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Sum.eq_left_iff_getLeft_eq", "kind": "theorem", "module": "Mathlib.Data.Sum.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Sum.eq_right_iff_getRight_eq", "kind": "theorem", "module": "Mathlib.Data.Sum.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Sum.getLeft_eq_getLeft?", "kind": "theorem", "module": "Mathlib.Data.Sum.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Sum.getRight_eq_getRight?", "kind": "theorem", "module": "Mathlib.Data.Sum.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Sum.isSome_getLeft?_iff_isLeft", "kind": "theorem", "module": "Mathlib.Data.Sum.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Sum.isSome_getRight?_iff_isRight", "kind": "theorem", "module": "Mathlib.Data.Sum.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Sum.update_elim_inl", "kind": "theorem", "module": "Mathlib.Data.Sum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.update_elim_inr", "kind": "theorem", "module": "Mathlib.Data.Sum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.update_inl_comp_inl", "kind": "theorem", "module": "Mathlib.Data.Sum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.update_inl_apply_inl", "kind": "theorem", "module": "Mathlib.Data.Sum.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Sum.update_inl_comp_inr", "kind": "theorem", "module": "Mathlib.Data.Sum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.update_inl_apply_inr", "kind": "theorem", "module": "Mathlib.Data.Sum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.update_inr_comp_inl", "kind": "theorem", "module": "Mathlib.Data.Sum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.update_inr_apply_inl", "kind": "theorem", "module": "Mathlib.Data.Sum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.update_inr_comp_inr", "kind": "theorem", "module": "Mathlib.Data.Sum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.update_inr_apply_inr", "kind": "theorem", "module": "Mathlib.Data.Sum.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Sum.update_inl_apply_inl'", "kind": "theorem", "module": "Mathlib.Data.Sum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.update_inr_apply_inr'", "kind": "theorem", "module": "Mathlib.Data.Sum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.rec_update_left", "kind": "theorem", "module": "Mathlib.Data.Sum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.rec_update_right", "kind": "theorem", "module": "Mathlib.Data.Sum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.elim_update_left", "kind": "theorem", "module": "Mathlib.Data.Sum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.elim_update_right", "kind": "theorem", "module": "Mathlib.Data.Sum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.swap_leftInverse", "kind": "theorem", "module": "Mathlib.Data.Sum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.swap_rightInverse", "kind": "theorem", "module": "Mathlib.Data.Sum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.LiftRel.isLeft_congr", "kind": "theorem", "module": "Mathlib.Data.Sum.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Sum.LiftRel.isRight_congr", "kind": "theorem", "module": "Mathlib.Data.Sum.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Sum.LiftRel.isLeft_left", "kind": "theorem", "module": "Mathlib.Data.Sum.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Sum.LiftRel.isLeft_right", "kind": "theorem", "module": "Mathlib.Data.Sum.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Sum.LiftRel.isRight_left", "kind": "theorem", "module": "Mathlib.Data.Sum.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Sum.LiftRel.isRight_right", "kind": "theorem", "module": "Mathlib.Data.Sum.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Sum.LiftRel.exists_of_isLeft_left", "kind": "theorem", "module": "Mathlib.Data.Sum.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Sum.LiftRel.exists_of_isLeft_right", "kind": "theorem", "module": "Mathlib.Data.Sum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.LiftRel.exists_of_isRight_left", "kind": "theorem", "module": "Mathlib.Data.Sum.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Sum.LiftRel.exists_of_isRight_right", "kind": "theorem", "module": "Mathlib.Data.Sum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.sumElim", "kind": "theorem", "module": "Mathlib.Data.Sum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.sumMap", "kind": "theorem", "module": "Mathlib.Data.Sum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.sumMap", "kind": "theorem", "module": "Mathlib.Data.Sum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Bijective.sumMap", "kind": "theorem", "module": "Mathlib.Data.Sum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.elim_injective", "kind": "theorem", "module": "Mathlib.Data.Sum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.map_injective", "kind": "theorem", "module": "Mathlib.Data.Sum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.map_surjective", "kind": "theorem", "module": "Mathlib.Data.Sum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.map_bijective", "kind": "theorem", "module": "Mathlib.Data.Sum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum3.in₀", "kind": "definition", "module": "Mathlib.Data.Sum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum3.in₁", "kind": "definition", "module": "Mathlib.Data.Sum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum3.in₂", "kind": "definition", "module": "Mathlib.Data.Sum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSum.inl_injective", "kind": "theorem", "module": "Mathlib.Data.Sum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSum.inr_injective", "kind": "theorem", "module": "Mathlib.Data.Sum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sumLift₂", "kind": "definition", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_sumLift₂", "kind": "theorem", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": true, "tactics": ["constructor", "rcases", "rw", "rintro", "exact", "refine", "refine", "rw", "rintro", "exact", "rintro"], "tactic_count": 11}
{"name": "Finset.inl_mem_sumLift₂", "kind": "theorem", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": true, "tactics": ["rw", "simp", "rintro", "exact"], "tactic_count": 4}
{"name": "Finset.inr_mem_sumLift₂", "kind": "theorem", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": true, "tactics": ["rw", "simp", "rintro", "exact"], "tactic_count": 4}
{"name": "Finset.sumLift₂_eq_empty", "kind": "theorem", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": true, "tactics": ["refine", "constructor", "rintro", "exact", "cases", "exact", "rfl", "rfl", "exact"], "tactic_count": 9}
{"name": "Finset.sumLift₂_nonempty", "kind": "theorem", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.sumLift₂_mono", "kind": "theorem", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sumLexLift", "kind": "definition", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sumLexLift_inl_inl", "kind": "theorem", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sumLexLift_inl_inr", "kind": "theorem", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sumLexLift_inr_inl", "kind": "theorem", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sumLexLift_inr_inr", "kind": "theorem", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_sumLexLift", "kind": "theorem", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": true, "tactics": ["constructor", "obtain", "rw", "rintro", "exact", "refine", "rintro", "exact", "rintro", "exact", "exact", "rw", "rintro", "exact", "rintro", "exact", "exact", "exact", "exact"], "tactic_count": 19}
{"name": "Finset.inl_mem_sumLexLift", "kind": "theorem", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.inr_mem_sumLexLift", "kind": "theorem", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.sumLexLift_mono", "kind": "theorem", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": true, "tactics": ["cases", "exacts"], "tactic_count": 2}
{"name": "Finset.sumLexLift_eq_empty", "kind": "theorem", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": true, "tactics": ["refine", "any_goals", "rintro", "cases", "exact", "simp", "rfl", "exact"], "tactic_count": 8}
{"name": "Finset.sumLexLift_nonempty", "kind": "theorem", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Sum.instLocallyFiniteOrder", "kind": "instance", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Icc_inl_inl", "kind": "theorem", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Ico_inl_inl", "kind": "theorem", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Ioc_inl_inl", "kind": "theorem", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Ioo_inl_inl", "kind": "theorem", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Icc_inl_inr", "kind": "theorem", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Ico_inl_inr", "kind": "theorem", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Ioc_inl_inr", "kind": "theorem", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Ioo_inl_inr", "kind": "theorem", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Icc_inr_inl", "kind": "theorem", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Ico_inr_inl", "kind": "theorem", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Ioc_inr_inl", "kind": "theorem", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Ioo_inr_inl", "kind": "theorem", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Icc_inr_inr", "kind": "theorem", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Ico_inr_inr", "kind": "theorem", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Ioc_inr_inr", "kind": "theorem", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Ioo_inr_inr", "kind": "theorem", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.instLocallyFiniteOrderBot", "kind": "instance", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Iic_inl", "kind": "theorem", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Iic_inr", "kind": "theorem", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Iio_inl", "kind": "theorem", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Iio_inr", "kind": "theorem", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.instLocallyFiniteOrderTop", "kind": "instance", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Ici_inl", "kind": "theorem", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Ici_inr", "kind": "theorem", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Ioi_inl", "kind": "theorem", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Ioi_inr", "kind": "theorem", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Lex.locallyFiniteOrder", "kind": "instance", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Lex.Icc_inl_inl", "kind": "theorem", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Sum.Lex.Ico_inl_inl", "kind": "theorem", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Sum.Lex.Ioc_inl_inl", "kind": "theorem", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Sum.Lex.Ioo_inl_inl", "kind": "theorem", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Sum.Lex.Icc_inl_inr", "kind": "theorem", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Lex.Ico_inl_inr", "kind": "theorem", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Lex.Ioc_inl_inr", "kind": "theorem", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Lex.Ioo_inl_inr", "kind": "theorem", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Lex.Icc_inr_inl", "kind": "theorem", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Lex.Ico_inr_inl", "kind": "theorem", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Lex.Ioc_inr_inl", "kind": "theorem", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Lex.Ioo_inr_inl", "kind": "theorem", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Lex.Icc_inr_inr", "kind": "theorem", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Sum.Lex.Ico_inr_inr", "kind": "theorem", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Sum.Lex.Ioc_inr_inr", "kind": "theorem", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Sum.Lex.Ioo_inr_inr", "kind": "theorem", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Sum.Lex.instLocallyFiniteOrderBot", "kind": "instance", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Lex.Iic_inl", "kind": "theorem", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Lex.Iic_inr", "kind": "theorem", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Lex.Iio_inl", "kind": "theorem", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Lex.Iio_inr", "kind": "theorem", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Lex._example", "kind": "example", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": false, "tactics": ["try", "with_reducible_and_instances", "rfl", "try", "rfl", "exact"], "tactic_count": 6}
{"name": "Sum.Lex.instLocallyFiniteOrderTop", "kind": "instance", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Lex.Ici_inl", "kind": "theorem", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Lex.Ici_inr", "kind": "theorem", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Lex.Ioi_inl", "kind": "theorem", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Lex.Ioi_inr", "kind": "theorem", "module": "Mathlib.Data.Sum.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Lex.instSemilatticeSup", "kind": "instance", "module": "Mathlib.Data.Sum.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Lex.inl_sup", "kind": "theorem", "module": "Mathlib.Data.Sum.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Lex.inr_sup", "kind": "theorem", "module": "Mathlib.Data.Sum.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Lex.instSemilatticeInf", "kind": "instance", "module": "Mathlib.Data.Sum.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Lex.inl_inf", "kind": "theorem", "module": "Mathlib.Data.Sum.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Lex.inr_inf", "kind": "theorem", "module": "Mathlib.Data.Sum.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Lex.instLattice", "kind": "instance", "module": "Mathlib.Data.Sum.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Lex.inlLatticeHom", "kind": "definition", "module": "Mathlib.Data.Sum.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Lex.inrLatticeHom", "kind": "definition", "module": "Mathlib.Data.Sum.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Lex.instDistribLattice", "kind": "instance", "module": "Mathlib.Data.Sum.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.LiftRel.refl", "kind": "theorem", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.instReflLiftRel_mathlib", "kind": "instance", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.instIrreflLiftRel_mathlib", "kind": "instance", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.LiftRel.trans", "kind": "theorem", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.instIsTransLiftRel", "kind": "instance", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.instAntisymmLiftRel_mathlib", "kind": "instance", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.instReflLex_mathlib", "kind": "instance", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.instIrreflLex_mathlib", "kind": "instance", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.instIsTransLex", "kind": "instance", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.instAntisymmLex_mathlib", "kind": "instance", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.instTotalLex_mathlib", "kind": "instance", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.instIsTrichotomousLex", "kind": "instance", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.instIsWellOrderLex", "kind": "instance", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.instLESum", "kind": "instance", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.instLTSum", "kind": "instance", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.le_def", "kind": "theorem", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.lt_def", "kind": "theorem", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.inl_le_inl_iff", "kind": "theorem", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.inr_le_inr_iff", "kind": "theorem", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.inl_lt_inl_iff", "kind": "theorem", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.inr_lt_inr_iff", "kind": "theorem", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.not_inl_le_inr", "kind": "theorem", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.not_inl_lt_inr", "kind": "theorem", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.not_inr_le_inl", "kind": "theorem", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.not_inr_lt_inl", "kind": "theorem", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.instPreorderSum", "kind": "instance", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.inl_mono", "kind": "theorem", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.inr_mono", "kind": "theorem", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.inl_strictMono", "kind": "theorem", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.inr_strictMono", "kind": "theorem", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.instPartialOrder", "kind": "instance", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.noMinOrder", "kind": "instance", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.noMaxOrder", "kind": "instance", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.noMinOrder_iff", "kind": "theorem", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.noMaxOrder_iff", "kind": "theorem", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.denselyOrdered", "kind": "instance", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.denselyOrdered_iff", "kind": "theorem", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.swap_le_swap_iff", "kind": "theorem", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.swap_lt_swap_iff", "kind": "theorem", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Lex.term_⊕ₗ_", "kind": "definition", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Lex._aux_Mathlib_Data_Sum_Order___macroRules_Sum_Lex_term_⊕ₗ__1", "kind": "definition", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Lex._aux_Mathlib_Data_Sum_Order___unexpand_Lex_1", "kind": "definition", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.inlₗ", "kind": "abbrev", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.inrₗ", "kind": "abbrev", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Lex.LE", "kind": "instance", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Lex.LT", "kind": "instance", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Lex.toLex_le_toLex", "kind": "theorem", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Lex.toLex_lt_toLex", "kind": "theorem", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Lex.le_def", "kind": "theorem", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Lex.lt_def", "kind": "theorem", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Lex.inl_le_inl_iff", "kind": "theorem", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Lex.inr_le_inr_iff", "kind": "theorem", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Lex.inl_lt_inl_iff", "kind": "theorem", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Lex.inr_lt_inr_iff", "kind": "theorem", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Lex.inl_le_inr", "kind": "theorem", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Lex.inl_lt_inr", "kind": "theorem", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Lex.not_inr_le_inl", "kind": "theorem", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Lex.not_inr_lt_inl", "kind": "theorem", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Lex.toLexRelIsoLT", "kind": "definition", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Lex.toLexRelIsoLT_coe", "kind": "theorem", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Lex.toLexRelIsoLT_symm_coe", "kind": "theorem", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Lex.toLexRelIsoLE", "kind": "definition", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Lex.toLexRelIsoLE_coe", "kind": "theorem", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Lex.toLexRelIsoLE_symm_coe", "kind": "theorem", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Lex.preorder", "kind": "instance", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Lex.toLex_mono", "kind": "theorem", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Lex.toLex_strictMono", "kind": "theorem", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Lex.inl_mono", "kind": "theorem", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Lex.inr_mono", "kind": "theorem", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Lex.inl_strictMono", "kind": "theorem", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Lex.inr_strictMono", "kind": "theorem", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Lex.partialOrder", "kind": "instance", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Lex.linearOrder", "kind": "instance", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Lex.orderBot", "kind": "instance", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Lex.inl_bot", "kind": "theorem", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Sum.Lex.boundedOrder", "kind": "instance", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Sum.Lex.noMaxOrder", "kind": "instance", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Sum.Lex.noMaxOrder_of_nonempty", "kind": "instance", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.Lex.denselyOrdered_of_noMaxOrder", "kind": "instance", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "OrderIso.sumCongr", "kind": "definition", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.sumCongr_trans", "kind": "theorem", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
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{"name": "OrderIso.sumCongr_refl", "kind": "theorem", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
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{"name": "OrderIso.sumAssoc_symm_apply_inl", "kind": "theorem", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "OrderIso.sumDualDistrib", "kind": "definition", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.sumDualDistrib_inl", "kind": "theorem", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "OrderIso.sumDualDistrib_symm_inr", "kind": "theorem", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.sumLexCongr", "kind": "definition", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.sumLexCongr_trans", "kind": "theorem", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
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{"name": "OrderIso.sumLexAssoc", "kind": "definition", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.sumLexAssoc_apply_inl_inl", "kind": "theorem", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "OrderIso.sumLexAssoc_symm_apply_inl", "kind": "theorem", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "OrderIso.sumLexDualAntidistrib_inl", "kind": "theorem", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "OrderIso.sumLexEmpty", "kind": "definition", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.emptySumLex", "kind": "definition", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.sumLexEmpty_apply_inl", "kind": "theorem", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.emptySumLex_apply_inr", "kind": "theorem", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.orderIsoPUnitSumLex", "kind": "definition", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "WithBot.orderIsoPUnitSumLex_toLex", "kind": "theorem", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.orderIsoPUnitSumLex_symm_inl", "kind": "theorem", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.orderIsoPUnitSumLex_symm_inr", "kind": "theorem", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "WithTop.orderIsoSumLexPUnit_toLex", "kind": "theorem", "module": "Mathlib.Data.Sum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "instDecidableRelVectorEquivOfDecidableEq", "kind": "instance", "module": "Mathlib.Data.Sym.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Sym.map_zero", "kind": "theorem", "module": "Mathlib.Data.Sym.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym.map_cons", "kind": "theorem", "module": "Mathlib.Data.Sym.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym.map_congr", "kind": "theorem", "module": "Mathlib.Data.Sym.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym.map_mk", "kind": "theorem", "module": "Mathlib.Data.Sym.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym.coe_map", "kind": "theorem", "module": "Mathlib.Data.Sym.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym.map_injective", "kind": "theorem", "module": "Mathlib.Data.Sym.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym.equivCongr", "kind": "definition", "module": "Mathlib.Data.Sym.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym.attach", "kind": "definition", "module": "Mathlib.Data.Sym.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym.attach_mk", "kind": "theorem", "module": "Mathlib.Data.Sym.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym.coe_attach", "kind": "theorem", "module": "Mathlib.Data.Sym.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym.attach_map_coe", "kind": "theorem", "module": "Mathlib.Data.Sym.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym.mem_attach", "kind": "theorem", "module": "Mathlib.Data.Sym.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym.attach_nil", "kind": "theorem", "module": "Mathlib.Data.Sym.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym.attach_cons", "kind": "theorem", "module": "Mathlib.Data.Sym.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym.cast", "kind": "definition", "module": "Mathlib.Data.Sym.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym.cast_rfl", "kind": "theorem", "module": "Mathlib.Data.Sym.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym.cast_cast", "kind": "theorem", "module": "Mathlib.Data.Sym.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym.coe_cast", "kind": "theorem", "module": "Mathlib.Data.Sym.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym.mem_cast", "kind": "theorem", "module": "Mathlib.Data.Sym.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym.append", "kind": "definition", "module": "Mathlib.Data.Sym.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym.append_inj_right", "kind": "theorem", "module": "Mathlib.Data.Sym.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym.append_inj_left", "kind": "theorem", "module": "Mathlib.Data.Sym.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym.append_comm", "kind": "theorem", "module": "Mathlib.Data.Sym.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Sym.coe_append", "kind": "theorem", "module": "Mathlib.Data.Sym.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym.mem_append_iff", "kind": "theorem", "module": "Mathlib.Data.Sym.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym.oneEquiv", "kind": "definition", "module": "Mathlib.Data.Sym.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym.fill", "kind": "definition", "module": "Mathlib.Data.Sym.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym.coe_fill", "kind": "theorem", "module": "Mathlib.Data.Sym.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym.mem_fill_iff", "kind": "theorem", "module": "Mathlib.Data.Sym.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Sym.filterNe", "kind": "definition", "module": "Mathlib.Data.Sym.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym.sigma_sub_ext", "kind": "theorem", "module": "Mathlib.Data.Sym.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym.fill_filterNe", "kind": "theorem", "module": "Mathlib.Data.Sym.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym.filter_ne_fill", "kind": "theorem", "module": "Mathlib.Data.Sym.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym.count_coe_fill_self_of_notMem", "kind": "theorem", "module": "Mathlib.Data.Sym.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Sym.count_coe_fill_of_ne", "kind": "theorem", "module": "Mathlib.Data.Sym.Basic", "is_tactic_proof": true, "tactics": ["suffices", "simp"], "tactic_count": 2}
{"name": "SymOptionSuccEquiv.encode", "kind": "definition", "module": "Mathlib.Data.Sym.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SymOptionSuccEquiv.encode_of_none_mem", "kind": "theorem", "module": "Mathlib.Data.Sym.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SymOptionSuccEquiv.encode_of_none_notMem", "kind": "theorem", "module": "Mathlib.Data.Sym.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SymOptionSuccEquiv.decode", "kind": "definition", "module": "Mathlib.Data.Sym.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SymOptionSuccEquiv.decode_inl", "kind": "theorem", "module": "Mathlib.Data.Sym.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SymOptionSuccEquiv.decode_inr", "kind": "theorem", "module": "Mathlib.Data.Sym.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SymOptionSuccEquiv.decode_encode", "kind": "theorem", "module": "Mathlib.Data.Sym.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "simp", "convert"], "tactic_count": 4}
{"name": "SymOptionSuccEquiv.encode_decode", "kind": "theorem", "module": "Mathlib.Data.Sym.Basic", "is_tactic_proof": true, "tactics": ["obtain", "simp", "unfold", "split_ifs", "obtain", "exact", "refine", "refine", "refine"], "tactic_count": 9}
{"name": "symOptionSuccEquiv", "kind": "definition", "module": "Mathlib.Data.Sym.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym.e1", "kind": "definition", "module": "Mathlib.Data.Sym.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym.e2", "kind": "definition", "module": "Mathlib.Data.Sym.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym.card_sym_fin_eq_multichoose", "kind": "theorem", "module": "Mathlib.Data.Sym.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym.card_sym_eq_multichoose", "kind": "theorem", "module": "Mathlib.Data.Sym.Card", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Sym.card_sym_eq_choose", "kind": "theorem", "module": "Mathlib.Data.Sym.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Sym2.card_image_diag", "kind": "theorem", "module": "Mathlib.Data.Sym.Card", "is_tactic_proof": true, "tactics": ["rw", "rintro", "cases", "rfl", "simp", "rw"], "tactic_count": 6}
{"name": "Sym2.two_mul_card_image_offDiag", "kind": "theorem", "module": "Mathlib.Data.Sym.Card", "is_tactic_proof": true, "tactics": ["rw", "rintro", "simp_rw", "obtain", "replace", "obtain", "have", "have", "ext", "rw", "rintro", "rw", "simp", "exact"], "tactic_count": 14}
{"name": "Sym2.card_image_offDiag", "kind": "theorem", "module": "Mathlib.Data.Sym.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Sym2.card_subtype_diag", "kind": "theorem", "module": "Mathlib.Data.Sym.Card", "is_tactic_proof": true, "tactics": ["convert", "rw", "rintro", "rw", "obtain", "exact"], "tactic_count": 6}
{"name": "Sym2.card_subtype_not_diag", "kind": "theorem", "module": "Mathlib.Data.Sym.Card", "is_tactic_proof": true, "tactics": ["convert", "rw", "rintro", "rw", "obtain", "exact"], "tactic_count": 6}
{"name": "Sym2.card_diagSet_compl", "kind": "theorem", "module": "Mathlib.Data.Sym.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.card", "kind": "theorem", "module": "Mathlib.Data.Sym.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.Rel", "kind": "inductive", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.Rel.symm", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Sym2.Rel.trans", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Sym2.Rel.is_equivalence", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.Rel.setoid", "kind": "definition", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.rel_iff'", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Sym2.rel_iff", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Sym2", "kind": "abbrev", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.mk", "kind": "abbrev", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "termS(_,_)", "kind": "definition", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Data_Sym_Sym2___macroRules_termS(_,_)_1", "kind": "definition", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Data_Sym_Sym2___delab_app_termS(_,_)_1", "kind": "definition", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.sound", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.exact", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.eq", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.ind", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.inductionOn", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.inductionOn₂", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.rec", "kind": "definition", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.hrec", "kind": "definition", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.recOnSubsingleton", "kind": "abbrev", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.mk_surjective", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.exists", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.forall", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.eq_swap", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.mk_prod_swap_eq", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["cases", "exact"], "tactic_count": 2}
{"name": "Sym2.congr_right", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Sym2.congr_left", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Sym2.eq_iff", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Sym2.mk_eq_mk_iff", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Sym2.lift", "kind": "definition", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.lift_mk", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.coe_lift_symm_apply", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.lift₂", "kind": "definition", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.lift₂_mk", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.coe_lift₂_symm_apply", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.map", "kind": "definition", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.map_id", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "Sym2.map_comp", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "Sym2.map_map", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "Sym2.map_mk", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.map_pair_eq", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.map.injective", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["intro", "refine", "simp"], "tactic_count": 3}
{"name": "Sym2.mkEmbedding", "kind": "definition", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.sym2Map", "kind": "definition", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.lift_comp_map", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.lift_map_apply", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["conv_rhs"], "tactic_count": 1}
{"name": "Sym2.Mem", "kind": "definition", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.mem_iff'", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.instSetLike", "kind": "instance", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.instPartialOrder", "kind": "instance", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.mem_iff_mem", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.mem_iff_exists", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.ext", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.mem_mk_left", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.mem_mk_right", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.mem_iff", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.out_fst_mem", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.out_snd_mem", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.ball", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Sym2.coe_mk", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Sym2.Mem.other", "kind": "definition", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.other_spec", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.other_mem", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "Sym2.mem_and_mem_iff", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["constructor", "cases", "rw", "aesop", "rintro", "simp"], "tactic_count": 6}
{"name": "Sym2.eq_of_ne_mem", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.Mem.decidable", "kind": "instance", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.mem_map", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["cases", "simp", "aesop"], "tactic_count": 3}
{"name": "Sym2.map_congr", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["ext", "simp", "constructor", "rintro", "exact"], "tactic_count": 5}
{"name": "Sym2.map_id'", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.pmap", "kind": "definition", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.forall_mem_pair", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Sym2.pair_eq_pmap", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.pmap_pair", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.mem_pmap_iff", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["obtain", "rw", "aesop"], "tactic_count": 3}
{"name": "Sym2.pmap_eq_map", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Sym2.map_pmap", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Sym2.pmap_map", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Sym2.pmap_pmap", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Sym2.pmap_subtype_map_subtypeVal", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Sym2.attachWith", "kind": "definition", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.attachWith_map_subtypeVal", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Sym2.diag", "kind": "definition", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.diag_injective", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.IsDiag", "kind": "definition", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.mk_isDiag_iff", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.isDiag_iff_proj_eq", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.IsDiag.map", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.isDiag_map", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.diag_isDiag", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.isDiag_of_subsingleton", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.diagSet", "kind": "definition", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.mem_diagSet", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.mem_diagSet_iff_isDiag", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.range_diag", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Sym2.isDiag_iff_mem_range_diag", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Sym2.mem_diagSet_iff_eq", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Sym2.diagSet_eq_setOf_isDiag", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.diagSet_compl_eq_setOf_not_isDiag", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.diagSet_eq_univ_of_subsingleton", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Sym2.IsDiag.decidablePred", "kind": "instance", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.decidablePred_mem_diagSet", "kind": "instance", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.other_ne", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["contrapose", "have", "rw", "rw", "simp"], "tactic_count": 5}
{"name": "Sym2.fromRel", "kind": "definition", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.fromRel_proj_prop", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.fromRel_prop", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.fromRel_mono_iff", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.fromRelOrderEmbedding", "kind": "definition", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.fromRel_bot", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["apply", "apply", "simp"], "tactic_count": 3}
{"name": "Sym2.fromRel_top", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["apply", "apply", "simp"], "tactic_count": 3}
{"name": "Sym2.fromRel_ne", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Sym2.diagSet_eq_fromRel_eq", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Sym2.diagSet_compl_eq_fromRel_ne", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Sym2.diagSet_subset_fromRel", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Sym2.disjoint_diagSet_fromRel", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Sym2.fromRel_subset_compl_diagSet", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Sym2.reflexive_iff_diagSet_subset_fromRel", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Sym2.irreflexive_iff_fromRel_subset_diagSet_compl", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Sym2.fromRel_irreflexive", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.mem_fromRel_irrefl_other_ne", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.fromRel.decidablePred", "kind": "instance", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.fromRel_relationMap", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["ext", "simp", "exact"], "tactic_count": 3}
{"name": "Sym2.ToRel", "kind": "definition", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.toRel_prop", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.toRel_symmetric", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.toRel_fromRel", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.fromRel_toRel", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.toMultiset", "kind": "definition", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["refine", "use", "simp"], "tactic_count": 3}
{"name": "Sym2.card_toMultiset", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["induction", "simp"], "tactic_count": 2}
{"name": "Sym2.mem_toMultiset", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["induction", "simp"], "tactic_count": 2}
{"name": "Sym2.toFinset", "kind": "definition", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.mem_toFinset", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Sym2.toFinset_mk_eq", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Sym2.card_toFinset_of_isDiag", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["induction", "rw", "simp"], "tactic_count": 3}
{"name": "Sym2.card_toFinset_of_not_isDiag", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["induction", "rw", "simp"], "tactic_count": 3}
{"name": "Sym2.card_toFinset", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "simp"], "tactic_count": 3}
{"name": "_private.Mathlib.Data.Sym.Sym2.0.Sym2.fromVector", "kind": "definition", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.Sym.Sym2.0.Sym2.perm_card_two_iff", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.sym2EquivSym'", "kind": "definition", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.equivSym", "kind": "definition", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.equivMultiset", "kind": "definition", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.instDecidableRel", "kind": "instance", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.instDecidableRel'", "kind": "instance", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.instDecidableEq", "kind": "instance", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.Sym.Sym2.0.Sym2.pairOther", "kind": "definition", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.Mem.other'", "kind": "definition", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.other_spec'", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["induction", "aesop"], "tactic_count": 2}
{"name": "Sym2.other_eq_other'", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Sym2.other_mem'", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Sym2.other_invol'", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["induction", "aesop"], "tactic_count": 2}
{"name": "Sym2.other_invol", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["classical", "rw", "convert", "apply"], "tactic_count": 4}
{"name": "Sym2.filter_image_mk_isDiag", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["ext", "simp", "constructor", "rintro", "rw", "exact", "rintro", "rw", "exact"], "tactic_count": 9}
{"name": "Sym2.filter_image_mk_not_isDiag", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["ext", "induction", "simp", "constructor", "rintro", "rw", "exact", "rintro", "rw", "exact"], "tactic_count": 10}
{"name": "Sym2.instSubsingleton", "kind": "instance", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.instUnique", "kind": "instance", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.instIsEmpty", "kind": "instance", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.instNontrivial", "kind": "instance", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.instRepr", "kind": "instance", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.lift_smul_lift", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["ext", "simp_all"], "tactic_count": 2}
{"name": "Sym2.mul", "kind": "definition", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.mul_mk", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sym2", "kind": "definition", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mk'_mem_sym2_iff", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mk_mem_sym2_iff", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_sym2_iff_subset", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["induction", "simp"], "tactic_count": 2}
{"name": "Set.sym2_eq_mk_image", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Set.mk_preimage_sym2", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sym2_empty", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Set.sym2_univ", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Set.sym2_singleton", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Set.sym2_insert", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Set.sym2_preimage", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Set.sym2_image", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sym2_inter", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sym2_iInter", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finsupp.sym2_support_eq_preimage_support_mul", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2.Finsupp", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finsupp.mem_sym2_support_of_mul_ne_zero", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2.Finsupp", "is_tactic_proof": true, "tactics": ["obtain", "simp", "simpa"], "tactic_count": 3}
{"name": "Finsupp.sym2Mul", "kind": "definition", "module": "Mathlib.Data.Sym.Sym2.Finsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.support_sym2Mul_subset", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2.Finsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.coe_sym2Mul", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2.Finsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.sym2Mul_apply_mk", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2.Finsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "initFn._@.Mathlib.Data.Sym.Sym2.Init.444600000._hygCtx._hyg.3", "kind": "definition", "module": "Mathlib.Data.Sym.Sym2.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.sup", "kind": "definition", "module": "Mathlib.Data.Sym.Sym2.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.sup_mk", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.inf", "kind": "definition", "module": "Mathlib.Data.Sym.Sym2.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.inf_mk", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.inf_le_sup", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2.Order", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Sym2.sortEquiv", "kind": "definition", "module": "Mathlib.Data.Sym.Sym2.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.inf_eq_inf_and_sup_eq_sup", "kind": "theorem", "module": "Mathlib.Data.Sym.Sym2.Order", "is_tactic_proof": false, "tactics": ["induction", "induction", "obtain"], "tactic_count": 3}
{"name": "Tree", "kind": "inductive", "module": "Mathlib.Data.Tree.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDecidableEqTree", "kind": "instance", "module": "Mathlib.Data.Tree.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instReprTree", "kind": "instance", "module": "Mathlib.Data.Tree.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tree.instInhabited", "kind": "instance", "module": "Mathlib.Data.Tree.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tree.traverse", "kind": "definition", "module": "Mathlib.Data.Tree.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tree.map", "kind": "definition", "module": "Mathlib.Data.Tree.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tree.id_map", "kind": "theorem", "module": "Mathlib.Data.Tree.Basic", "is_tactic_proof": true, "tactics": ["induction", "nil", "node"], "tactic_count": 3}
{"name": "Tree.comp_map", "kind": "theorem", "module": "Mathlib.Data.Tree.Basic", "is_tactic_proof": true, "tactics": ["induction", "nil", "node"], "tactic_count": 3}
{"name": "Tree.traverse_pure", "kind": "theorem", "module": "Mathlib.Data.Tree.Basic", "is_tactic_proof": true, "tactics": ["induction", "nil", "node"], "tactic_count": 3}
{"name": "Tree.numNodes", "kind": "definition", "module": "Mathlib.Data.Tree.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tree.numLeaves", "kind": "definition", "module": "Mathlib.Data.Tree.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tree.height", "kind": "definition", "module": "Mathlib.Data.Tree.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tree.numLeaves_eq_numNodes_succ", "kind": "theorem", "module": "Mathlib.Data.Tree.Basic", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "Tree.numLeaves_pos", "kind": "theorem", "module": "Mathlib.Data.Tree.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Tree.height_le_numNodes", "kind": "theorem", "module": "Mathlib.Data.Tree.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tree.left", "kind": "definition", "module": "Mathlib.Data.Tree.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "TypeVec.prod.map", "kind": "definition", "module": "Mathlib.Data.TypeVec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvFunctor.term_⊗'_", "kind": "definition", "module": "Mathlib.Data.TypeVec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvFunctor._aux_Mathlib_Data_TypeVec___macroRules_MvFunctor_term_⊗'__1", "kind": "definition", "module": "Mathlib.Data.TypeVec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvFunctor._aux_Mathlib_Data_TypeVec___unexpand_TypeVec_prod_map_1", "kind": "definition", "module": "Mathlib.Data.TypeVec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TypeVec.fst_prod_mk", "kind": "theorem", "module": "Mathlib.Data.TypeVec", "is_tactic_proof": true, "tactics": ["funext", "induction", "fz", "fs"], "tactic_count": 4}
{"name": "TypeVec.snd_prod_mk", "kind": "theorem", "module": "Mathlib.Data.TypeVec", "is_tactic_proof": true, "tactics": ["funext", "induction", "fz", "fs"], "tactic_count": 4}
{"name": "TypeVec.fst_diag", "kind": "theorem", "module": "Mathlib.Data.TypeVec", "is_tactic_proof": true, "tactics": ["funext", "induction", "fz", "fs"], "tactic_count": 4}
{"name": "TypeVec.snd_diag", "kind": "theorem", "module": "Mathlib.Data.TypeVec", "is_tactic_proof": true, "tactics": ["funext", "induction", "fz", "fs"], "tactic_count": 4}
{"name": "TypeVec.repeatEq_iff_eq", "kind": "theorem", "module": "Mathlib.Data.TypeVec", "is_tactic_proof": true, "tactics": ["induction", "fz", "fs", "rw", "exact"], "tactic_count": 5}
{"name": "TypeVec.Subtype_", "kind": "definition", "module": "Mathlib.Data.TypeVec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TypeVec.subtypeVal", "kind": "definition", "module": "Mathlib.Data.TypeVec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TypeVec.toSubtype", "kind": "definition", "module": "Mathlib.Data.TypeVec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TypeVec.ofSubtype", "kind": "definition", "module": "Mathlib.Data.TypeVec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TypeVec.toSubtype'", "kind": "definition", "module": "Mathlib.Data.TypeVec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TypeVec.ofSubtype'", "kind": "definition", "module": "Mathlib.Data.TypeVec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TypeVec.diagSub", "kind": "definition", "module": "Mathlib.Data.TypeVec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TypeVec.subtypeVal_nil", "kind": "theorem", "module": "Mathlib.Data.TypeVec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TypeVec.diag_sub_val", "kind": "theorem", "module": "Mathlib.Data.TypeVec", "is_tactic_proof": true, "tactics": ["ext", "induction", "fz", "fs"], "tactic_count": 4}
{"name": "TypeVec.prod_id", "kind": "theorem", "module": "Mathlib.Data.TypeVec", "is_tactic_proof": true, "tactics": ["intros", "ext", "induction", "fz", "fs"], "tactic_count": 5}
{"name": "TypeVec.append_prod_appendFun", "kind": "theorem", "module": "Mathlib.Data.TypeVec", "is_tactic_proof": true, "tactics": ["ext", "cases", "cases", "rfl", "rfl"], "tactic_count": 5}
{"name": "TypeVec.dropFun_diag", "kind": "theorem", "module": "Mathlib.Data.TypeVec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TypeVec.dropFun_subtypeVal", "kind": "theorem", "module": "Mathlib.Data.TypeVec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TypeVec.lastFun_subtypeVal", "kind": "theorem", "module": "Mathlib.Data.TypeVec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TypeVec.dropFun_toSubtype", "kind": "theorem", "module": "Mathlib.Data.TypeVec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TypeVec.lastFun_toSubtype", "kind": "theorem", "module": "Mathlib.Data.TypeVec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TypeVec.dropFun_of_subtype", "kind": "theorem", "module": "Mathlib.Data.TypeVec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TypeVec.lastFun_of_subtype", "kind": "theorem", "module": "Mathlib.Data.TypeVec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TypeVec.dropFun_RelLast'", "kind": "theorem", "module": "Mathlib.Data.TypeVec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TypeVec.dropFun_prod", "kind": "theorem", "module": "Mathlib.Data.TypeVec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TypeVec.lastFun_prod", "kind": "theorem", "module": "Mathlib.Data.TypeVec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TypeVec.dropFun_from_append1_drop_last", "kind": "theorem", "module": "Mathlib.Data.TypeVec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TypeVec.lastFun_from_append1_drop_last", "kind": "theorem", "module": "Mathlib.Data.TypeVec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TypeVec.dropFun_id", "kind": "theorem", "module": "Mathlib.Data.TypeVec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TypeVec.prod_map_id", "kind": "theorem", "module": "Mathlib.Data.TypeVec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TypeVec.toSubtype_of_subtype", "kind": "theorem", "module": "Mathlib.Data.TypeVec", "is_tactic_proof": true, "tactics": ["ext", "induction", "simp"], "tactic_count": 3}
{"name": "TypeVec.subtypeVal_toSubtype", "kind": "theorem", "module": "Mathlib.Data.TypeVec", "is_tactic_proof": true, "tactics": ["ext", "induction", "simp"], "tactic_count": 3}
{"name": "TypeVec.toSubtype_of_subtype_assoc", "kind": "theorem", "module": "Mathlib.Data.TypeVec", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "TypeVec.toSubtype'_of_subtype'", "kind": "theorem", "module": "Mathlib.Data.TypeVec", "is_tactic_proof": true, "tactics": ["ext", "induction"], "tactic_count": 2}
{"name": "TypeVec.subtypeVal_toSubtype'", "kind": "theorem", "module": "Mathlib.Data.TypeVec", "is_tactic_proof": true, "tactics": ["ext", "induction", "simp"], "tactic_count": 3}
{"name": "UInt8.toBitVec_nsmul", "kind": "theorem", "module": "Mathlib.Data.UInt", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "UInt8.toBitVec_natCast", "kind": "theorem", "module": "Mathlib.Data.UInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UInt8.toBitVec_intCast", "kind": "theorem", "module": "Mathlib.Data.UInt", "is_tactic_proof": true, "tactics": ["obtain", "erw", "rw", "erw", "simp"], "tactic_count": 5}
{"name": "UInt8.toBitVec_zsmul", "kind": "theorem", "module": "Mathlib.Data.UInt", "is_tactic_proof": true, "tactics": ["change", "rw", "congr", "rw", "rfl"], "tactic_count": 5}
{"name": "UInt16.toBitVec_nsmul", "kind": "theorem", "module": "Mathlib.Data.UInt", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "UInt16.toBitVec_natCast", "kind": "theorem", "module": "Mathlib.Data.UInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UInt16.toBitVec_intCast", "kind": "theorem", "module": "Mathlib.Data.UInt", "is_tactic_proof": true, "tactics": ["obtain", "erw", "rw", "erw", "simp"], "tactic_count": 5}
{"name": "UInt16.toBitVec_zsmul", "kind": "theorem", "module": "Mathlib.Data.UInt", "is_tactic_proof": true, "tactics": ["change", "rw", "congr", "rw", "rfl"], "tactic_count": 5}
{"name": "UInt32.toBitVec_nsmul", "kind": "theorem", "module": "Mathlib.Data.UInt", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "UInt32.toBitVec_natCast", "kind": "theorem", "module": "Mathlib.Data.UInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UInt32.toBitVec_intCast", "kind": "theorem", "module": "Mathlib.Data.UInt", "is_tactic_proof": true, "tactics": ["obtain", "erw", "rw", "erw", "simp"], "tactic_count": 5}
{"name": "UInt32.toBitVec_zsmul", "kind": "theorem", "module": "Mathlib.Data.UInt", "is_tactic_proof": true, "tactics": ["change", "rw", "congr", "rw", "rfl"], "tactic_count": 5}
{"name": "UInt64.toBitVec_nsmul", "kind": "theorem", "module": "Mathlib.Data.UInt", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "UInt64.toBitVec_natCast", "kind": "theorem", "module": "Mathlib.Data.UInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UInt64.toBitVec_intCast", "kind": "theorem", "module": "Mathlib.Data.UInt", "is_tactic_proof": true, "tactics": ["obtain", "erw", "rw", "erw", "simp"], "tactic_count": 5}
{"name": "UInt64.toBitVec_zsmul", "kind": "theorem", "module": "Mathlib.Data.UInt", "is_tactic_proof": true, "tactics": ["change", "rw", "congr", "rw", "rfl"], "tactic_count": 5}
{"name": "USize.toBitVec_nsmul", "kind": "theorem", "module": "Mathlib.Data.UInt", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "USize.toBitVec_natCast", "kind": "theorem", "module": "Mathlib.Data.UInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "USize.toBitVec_intCast", "kind": "theorem", "module": "Mathlib.Data.UInt", "is_tactic_proof": true, "tactics": ["obtain", "erw", "rw", "erw", "simp"], "tactic_count": 5}
{"name": "USize.toBitVec_zsmul", "kind": "theorem", "module": "Mathlib.Data.UInt", "is_tactic_proof": true, "tactics": ["change", "rw", "congr", "rw", "rfl"], "tactic_count": 5}
{"name": "UInt8.toFin_injective", "kind": "theorem", "module": "Mathlib.Data.UInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UInt8.toBitVec_injective", "kind": "theorem", "module": "Mathlib.Data.UInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UInt8.instCommMonoid", "kind": "instance", "module": "Mathlib.Data.UInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UInt8.instNonUnitalCommRing", "kind": "instance", "module": "Mathlib.Data.UInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UInt8.instCommRing", "kind": "instance", "module": "Mathlib.Data.UInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UInt16.toFin_injective", "kind": "theorem", "module": "Mathlib.Data.UInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UInt16.toBitVec_injective", "kind": "theorem", "module": "Mathlib.Data.UInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UInt16.instCommMonoid", "kind": "instance", "module": "Mathlib.Data.UInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UInt16.instNonUnitalCommRing", "kind": "instance", "module": "Mathlib.Data.UInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UInt16.instCommRing", "kind": "instance", "module": "Mathlib.Data.UInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UInt32.toFin_injective", "kind": "theorem", "module": "Mathlib.Data.UInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UInt32.toBitVec_injective", "kind": "theorem", "module": "Mathlib.Data.UInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UInt32.instCommMonoid", "kind": "instance", "module": "Mathlib.Data.UInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UInt32.instNonUnitalCommRing", "kind": "instance", "module": "Mathlib.Data.UInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UInt32.instCommRing", "kind": "instance", "module": "Mathlib.Data.UInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UInt64.toFin_injective", "kind": "theorem", "module": "Mathlib.Data.UInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UInt64.toBitVec_injective", "kind": "theorem", "module": "Mathlib.Data.UInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UInt64.instCommMonoid", "kind": "instance", "module": "Mathlib.Data.UInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UInt64.instNonUnitalCommRing", "kind": "instance", "module": "Mathlib.Data.UInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UInt64.instCommRing", "kind": "instance", "module": "Mathlib.Data.UInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "USize.toFin_injective", "kind": "theorem", "module": "Mathlib.Data.UInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "USize.toBitVec_injective", "kind": "theorem", "module": "Mathlib.Data.UInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "USize.instCommMonoid", "kind": "instance", "module": "Mathlib.Data.UInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "USize.instNonUnitalCommRing", "kind": "instance", "module": "Mathlib.Data.UInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "USize.instCommRing", "kind": "instance", "module": "Mathlib.Data.UInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UInt8.isASCIIUpper", "kind": "definition", "module": "Mathlib.Data.UInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UInt8.isASCIILower", "kind": "definition", "module": "Mathlib.Data.UInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UInt8.isASCIIAlpha", "kind": "definition", "module": "Mathlib.Data.UInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UInt8.isASCIIDigit", "kind": "definition", "module": "Mathlib.Data.UInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UInt8.isASCIIAlphanum", "kind": "definition", "module": "Mathlib.Data.UInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UInt8.toChar", "kind": "definition", "module": "Mathlib.Data.UInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PLift.instNonempty_mathlib", "kind": "instance", "module": "Mathlib.Data.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PLift.instUnique", "kind": "instance", "module": "Mathlib.Data.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PLift.instDecidableEq_mathlib", "kind": "instance", "module": "Mathlib.Data.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PLift.instIsEmpty", "kind": "instance", "module": "Mathlib.Data.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PLift.up_injective", "kind": "theorem", "module": "Mathlib.Data.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PLift.up_surjective", "kind": "theorem", "module": "Mathlib.Data.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PLift.up_bijective", "kind": "theorem", "module": "Mathlib.Data.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PLift.up_inj", "kind": "theorem", "module": "Mathlib.Data.ULift", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PLift.down_surjective", "kind": "theorem", "module": "Mathlib.Data.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PLift.down_bijective", "kind": "theorem", "module": "Mathlib.Data.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PLift.forall", "kind": "theorem", "module": "Mathlib.Data.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PLift.exists", "kind": "theorem", "module": "Mathlib.Data.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PLift.map_injective", "kind": "theorem", "module": "Mathlib.Data.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PLift.map_surjective", "kind": "theorem", "module": "Mathlib.Data.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PLift.map_bijective", "kind": "theorem", "module": "Mathlib.Data.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.instNonempty_mathlib", "kind": "instance", "module": "Mathlib.Data.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.instUnique", "kind": "instance", "module": "Mathlib.Data.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.instDecidableEq_mathlib", "kind": "instance", "module": "Mathlib.Data.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.instIsEmpty", "kind": "instance", "module": "Mathlib.Data.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.up_injective", "kind": "theorem", "module": "Mathlib.Data.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.up_surjective", "kind": "theorem", "module": "Mathlib.Data.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.up_bijective", "kind": "theorem", "module": "Mathlib.Data.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.up_inj", "kind": "theorem", "module": "Mathlib.Data.ULift", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ULift.down_surjective", "kind": "theorem", "module": "Mathlib.Data.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.down_bijective", "kind": "theorem", "module": "Mathlib.Data.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.forall", "kind": "theorem", "module": "Mathlib.Data.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.exists", "kind": "theorem", "module": "Mathlib.Data.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.map_injective", "kind": "theorem", "module": "Mathlib.Data.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.map_surjective", "kind": "theorem", "module": "Mathlib.Data.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.map_bijective", "kind": "theorem", "module": "Mathlib.Data.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.ext", "kind": "theorem", "module": "Mathlib.Data.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.rec_update", "kind": "theorem", "module": "Mathlib.Data.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Vector3", "kind": "definition", "module": "Mathlib.Data.Vector3", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInhabitedVector3", "kind": "instance", "module": "Mathlib.Data.Vector3", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Vector3.nil", "kind": "definition", "module": "Mathlib.Data.Vector3", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Vector3.cons", "kind": "definition", "module": "Mathlib.Data.Vector3", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Vector3._aux_Mathlib_Data_Vector3___macroRules_term[_]_1", "kind": "definition", "module": "Mathlib.Data.Vector3", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Vector3.unexpandNil", "kind": "definition", "module": "Mathlib.Data.Vector3", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Vector3.unexpandCons", "kind": "definition", "module": "Mathlib.Data.Vector3", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Vector3.term_::_", "kind": "definition", "module": "Mathlib.Data.Vector3", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Vector3._aux_Mathlib_Data_Vector3___macroRules_Vector3_term_::__1", "kind": "definition", "module": "Mathlib.Data.Vector3", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Vector3._aux_Mathlib_Data_Vector3___unexpand_Vector3_cons_1", "kind": "definition", "module": "Mathlib.Data.Vector3", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Vector3.cons_fz", "kind": "theorem", "module": "Mathlib.Data.Vector3", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Vector3.cons_fs", "kind": "theorem", "module": "Mathlib.Data.Vector3", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Vector3.nth", "kind": "abbrev", "module": "Mathlib.Data.Vector3", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Vector3.ofFn", "kind": "abbrev", "module": "Mathlib.Data.Vector3", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Vector3.head", "kind": "definition", "module": "Mathlib.Data.Vector3", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Vector3.tail", "kind": "definition", "module": "Mathlib.Data.Vector3", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Vector3.eq_nil", "kind": "theorem", "module": "Mathlib.Data.Vector3", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Vector3.cons_head_tail", "kind": "theorem", "module": "Mathlib.Data.Vector3", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Vector3.nilElim", "kind": "definition", "module": "Mathlib.Data.Vector3", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Vector3.consElim", "kind": "definition", "module": "Mathlib.Data.Vector3", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Vector3.consElim_cons", "kind": "theorem", "module": "Mathlib.Data.Vector3", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Vector3.recOn", "kind": "definition", "module": "Mathlib.Data.Vector3", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Vector3.recOn_nil", "kind": "theorem", "module": "Mathlib.Data.Vector3", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Vector3.recOn_cons", "kind": "theorem", "module": "Mathlib.Data.Vector3", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Vector3.append", "kind": "definition", "module": "Mathlib.Data.Vector3", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.Vector3.0.Vector3.term_+-+_", "kind": "definition", "module": "Mathlib.Data.Vector3", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.Vector3.0.Vector3._aux_Mathlib_Data_Vector3___macroRules__private_Mathlib_Data_Vector3_0_Vector3_term_+-+__1", "kind": "definition", "module": "Mathlib.Data.Vector3", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.Vector3.0.Vector3._aux_Mathlib_Data_Vector3___unexpand_Vector3_append_1", "kind": "definition", "module": "Mathlib.Data.Vector3", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Vector3.append_nil", "kind": "theorem", "module": "Mathlib.Data.Vector3", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Vector3.append_cons", "kind": "theorem", "module": "Mathlib.Data.Vector3", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Vector3.append_left", "kind": "theorem", "module": "Mathlib.Data.Vector3", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Vector3.append_add", "kind": "theorem", "module": "Mathlib.Data.Vector3", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Vector3.insert", "kind": "definition", "module": "Mathlib.Data.Vector3", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Vector3.insert_fz", "kind": "theorem", "module": "Mathlib.Data.Vector3", "is_tactic_proof": true, "tactics": ["refine"], "tactic_count": 1}
{"name": "Vector3.insert_fs", "kind": "theorem", "module": "Mathlib.Data.Vector3", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Vector3.append_insert", "kind": "theorem", "module": "Mathlib.Data.Vector3", "is_tactic_proof": true, "tactics": ["refine", "rfl", "have", "change", "insert", "rw", "fs", "simpa"], "tactic_count": 8}
{"name": "VectorEx", "kind": "definition", "module": "Mathlib.Data.Vector3", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorAll", "kind": "definition", "module": "Mathlib.Data.Vector3", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_vector_zero", "kind": "theorem", "module": "Mathlib.Data.Vector3", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_vector_succ", "kind": "theorem", "module": "Mathlib.Data.Vector3", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "vectorEx_iff_exists", "kind": "theorem", "module": "Mathlib.Data.Vector3", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "vectorAll_iff_forall", "kind": "theorem", "module": "Mathlib.Data.Vector3", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorAllP", "kind": "definition", "module": "Mathlib.Data.Vector3", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "vectorAllP_nil", "kind": "theorem", "module": "Mathlib.Data.Vector3", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "vectorAllP_singleton", "kind": "theorem", "module": "Mathlib.Data.Vector3", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "vectorAllP_cons", "kind": "theorem", "module": "Mathlib.Data.Vector3", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "vectorAllP_iff_forall", "kind": "theorem", "module": "Mathlib.Data.Vector3", "is_tactic_proof": true, "tactics": ["refine", "exact", "simp", "refine", "refine", "exacts", "simpa", "simpa"], "tactic_count": 8}
{"name": "VectorAllP.imp", "kind": "theorem", "module": "Mathlib.Data.Vector3", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.term_::ᵥ_", "kind": "definition", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector._aux_Mathlib_Data_Vector_Basic___macroRules_List_Vector_term_::ᵥ__1", "kind": "definition", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector._aux_Mathlib_Data_Vector_Basic___unexpand_List_Vector_cons_1", "kind": "definition", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.instInhabited", "kind": "instance", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.toList_injective", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.ext", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.zero_subsingleton", "kind": "instance", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.cons_val", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.eq_cons_iff", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.ne_cons_iff", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.Vector.exists_eq_cons", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.toList_ofFn", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.mk_toList", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.length_val", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.pmap_cons", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.pmap_cons'", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.toList_map", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "List.Vector.head_map", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": true, "tactics": ["obtain", "rw"], "tactic_count": 2}
{"name": "List.Vector.tail_map", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": true, "tactics": ["obtain", "rw"], "tactic_count": 2}
{"name": "List.Vector.getElem_map", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.Vector.toList_pmap", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "List.Vector.head_pmap", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": true, "tactics": ["obtain", "simp_rw"], "tactic_count": 2}
{"name": "List.Vector.tail_pmap", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": true, "tactics": ["obtain", "simp_rw"], "tactic_count": 2}
{"name": "List.Vector.getElem_pmap", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.Vector.get_eq_get_toList", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.get_replicate", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "List.Vector.get_map", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "List.Vector.map₂_nil", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.map₂_cons", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.get_ofFn", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.Vector.ofFn_get", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": true, "tactics": ["ext", "apply"], "tactic_count": 2}
{"name": "Equiv.vectorEquivFin", "kind": "definition", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.get_tail", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": true, "tactics": ["obtain", "rcases", "rw", "rw", "contradiction"], "tactic_count": 5}
{"name": "List.Vector.get_tail_succ", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.tail_val", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.tail_nil", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.singleton_tail", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.tail_ofFn", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.toList_tail", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.toList_empty", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.toList_singleton", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "List.Vector.empty_toList_eq_ff", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.not_empty_toList", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.Vector.map_id", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.nodup_iff_injective_get", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": true, "tactics": ["obtain", "subst", "exact"], "tactic_count": 3}
{"name": "List.Vector.head?_toList", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.reverse", "kind": "definition", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.toList_reverse", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.reverse_reverse", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": true, "tactics": ["cases", "simp"], "tactic_count": 2}
{"name": "List.Vector.get_zero", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.head_ofFn", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.Vector.get_cons_zero", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.Vector.get_cons_nil", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.get_cons_succ", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.Vector.last", "kind": "definition", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.last_def", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.reverse_get_zero", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "rw", "congr", "simp", "simp"], "tactic_count": 6}
{"name": "List.Vector.scanl", "kind": "definition", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.scanl_nil", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.scanl_cons", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "List.Vector.scanl_val", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.toList_scanl", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.scanl_singleton", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "List.Vector.scanl_head", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": true, "tactics": ["cases", "have", "simp", "rw", "simp"], "tactic_count": 5}
{"name": "List.Vector.scanl_get", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": true, "tactics": ["rcases", "exact", "induction", "zero", "have", "simp", "succ", "rw", "refine", "simp", "intro", "simp"], "tactic_count": 12}
{"name": "List.Vector.mOfFn", "kind": "definition", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.mOfFn_pure", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.mmap", "kind": "definition", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.mmap_nil", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.mmap_cons", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.inductionOn", "kind": "definition", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "rcases", "exact", "succ", "rcases", "cases", "exact"], "tactic_count": 8}
{"name": "List.Vector.inductionOn_nil", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.inductionOn_cons", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.inductionOn₂", "kind": "definition", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "rcases", "rcases", "exact", "succ", "rcases", "cases", "rcases", "cases", "apply", "apply"], "tactic_count": 12}
{"name": "List.Vector.inductionOn₃", "kind": "definition", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "rcases", "rcases", "rcases", "exact", "succ", "rcases", "cases", "rcases", "cases", "rcases", "cases", "apply", "apply"], "tactic_count": 15}
{"name": "List.Vector.casesOn", "kind": "definition", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.casesOn₂", "kind": "definition", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.casesOn₃", "kind": "definition", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.toArray", "kind": "definition", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.insertIdx", "kind": "definition", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.insertIdx_val", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.eraseIdx_val", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.eraseIdx_insertIdx_self", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.eraseIdx_insertIdx'", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.insertIdx_comm", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.set", "kind": "definition", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.toList_set", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.get_set_same", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "List.Vector.get_set_of_ne", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": true, "tactics": ["cases", "simp", "rw", "simpa"], "tactic_count": 4}
{"name": "List.Vector.get_set_eq_if", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": true, "tactics": ["split_ifs"], "tactic_count": 1}
{"name": "List.Vector.prod_set", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": true, "tactics": ["refine", "simp_all"], "tactic_count": 2}
{"name": "List.Vector.prod_set'", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": true, "tactics": ["refine", "simp"], "tactic_count": 2}
{"name": "_private.Mathlib.Data.Vector.Basic.0.List.Vector.traverseAux", "kind": "definition", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.traverse", "kind": "definition", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.traverse_def", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "List.Vector.id_traverse", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": true, "tactics": ["rintro", "induction", "nil", "cons"], "tactic_count": 4}
{"name": "List.Vector.comp_traverse", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": true, "tactics": ["induction", "nil", "simp", "rfl", "cons", "rw", "simp"], "tactic_count": 7}
{"name": "List.Vector.traverse_eq_map_id", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": true, "tactics": ["rintro", "simp", "induction", "rfl"], "tactic_count": 4}
{"name": "List.Vector.naturality", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "rw", "rfl"], "tactic_count": 5}
{"name": "List.Vector.instTraversableFlipNat", "kind": "instance", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.instLawfulTraversableFlipNat", "kind": "instance", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.replicate_succ", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.get_append_cons_zero", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.get_append_cons_succ", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.append_nil", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "List.Vector.get_map₂", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": true, "tactics": ["clear", "induction", "nil", "cons", "rw", "cases", "simp", "simp"], "tactic_count": 8}
{"name": "List.Vector.mapAccumr_cons", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.mapAccumr₂_cons", "kind": "theorem", "module": "Mathlib.Data.Vector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector", "kind": "definition", "module": "Mathlib.Data.Vector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.instDecidableEq", "kind": "instance", "module": "Mathlib.Data.Vector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.nil", "kind": "definition", "module": "Mathlib.Data.Vector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.cons", "kind": "definition", "module": "Mathlib.Data.Vector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.length", "kind": "definition", "module": "Mathlib.Data.Vector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.head", "kind": "definition", "module": "Mathlib.Data.Vector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.head_cons", "kind": "theorem", "module": "Mathlib.Data.Vector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.tail", "kind": "definition", "module": "Mathlib.Data.Vector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.tail_cons", "kind": "theorem", "module": "Mathlib.Data.Vector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.cons_head_tail", "kind": "theorem", "module": "Mathlib.Data.Vector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.toList", "kind": "definition", "module": "Mathlib.Data.Vector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.get", "kind": "definition", "module": "Mathlib.Data.Vector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.instHAppendHAddNat", "kind": "instance", "module": "Mathlib.Data.Vector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.append_def", "kind": "theorem", "module": "Mathlib.Data.Vector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.elim", "kind": "definition", "module": "Mathlib.Data.Vector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.map", "kind": "definition", "module": "Mathlib.Data.Vector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.map_nil", "kind": "theorem", "module": "Mathlib.Data.Vector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.map_cons", "kind": "theorem", "module": "Mathlib.Data.Vector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.pmap", "kind": "definition", "module": "Mathlib.Data.Vector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.pmap_nil", "kind": "theorem", "module": "Mathlib.Data.Vector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.map₂", "kind": "definition", "module": "Mathlib.Data.Vector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.replicate", "kind": "definition", "module": "Mathlib.Data.Vector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.drop", "kind": "definition", "module": "Mathlib.Data.Vector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.take", "kind": "definition", "module": "Mathlib.Data.Vector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.eraseIdx", "kind": "definition", "module": "Mathlib.Data.Vector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.ofFn", "kind": "definition", "module": "Mathlib.Data.Vector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.congr", "kind": "definition", "module": "Mathlib.Data.Vector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.mapAccumr", "kind": "definition", "module": "Mathlib.Data.Vector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.mapAccumr₂", "kind": "definition", "module": "Mathlib.Data.Vector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.shiftLeftFill", "kind": "definition", "module": "Mathlib.Data.Vector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.shiftRightFill", "kind": "definition", "module": "Mathlib.Data.Vector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.eq", "kind": "theorem", "module": "Mathlib.Data.Vector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.eq_nil", "kind": "theorem", "module": "Mathlib.Data.Vector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.toList_mk", "kind": "theorem", "module": "Mathlib.Data.Vector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.toList_nil", "kind": "theorem", "module": "Mathlib.Data.Vector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.toList_length", "kind": "theorem", "module": "Mathlib.Data.Vector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.toList_cons", "kind": "theorem", "module": "Mathlib.Data.Vector.Defs", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "List.Vector.toList_append", "kind": "theorem", "module": "Mathlib.Data.Vector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.toList_drop", "kind": "theorem", "module": "Mathlib.Data.Vector.Defs", "is_tactic_proof": true, "tactics": ["cases", "rfl"], "tactic_count": 2}
{"name": "List.Vector.toList_take", "kind": "theorem", "module": "Mathlib.Data.Vector.Defs", "is_tactic_proof": true, "tactics": ["cases", "rfl"], "tactic_count": 2}
{"name": "List.Vector.instGetElemNatLt", "kind": "instance", "module": "Mathlib.Data.Vector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.getElem_def", "kind": "theorem", "module": "Mathlib.Data.Vector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.toList_getElem", "kind": "theorem", "module": "Mathlib.Data.Vector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.mapAccumr_mapAccumr", "kind": "theorem", "module": "Mathlib.Data.Vector.MapLemmas", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.Vector.mapAccumr_map", "kind": "theorem", "module": "Mathlib.Data.Vector.MapLemmas", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.Vector.map_mapAccumr", "kind": "theorem", "module": "Mathlib.Data.Vector.MapLemmas", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.Vector.map_map", "kind": "theorem", "module": "Mathlib.Data.Vector.MapLemmas", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.Vector.map_pmap", "kind": "theorem", "module": "Mathlib.Data.Vector.MapLemmas", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.Vector.pmap_map", "kind": "theorem", "module": "Mathlib.Data.Vector.MapLemmas", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.Vector.mapAccumr₂_mapAccumr_left", "kind": "theorem", "module": "Mathlib.Data.Vector.MapLemmas", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.Vector.map₂_map_left", "kind": "theorem", "module": "Mathlib.Data.Vector.MapLemmas", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.Vector.mapAccumr₂_mapAccumr_right", "kind": "theorem", "module": "Mathlib.Data.Vector.MapLemmas", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.Vector.map₂_map_right", "kind": "theorem", "module": "Mathlib.Data.Vector.MapLemmas", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.Vector.mapAccumr_mapAccumr₂", "kind": "theorem", "module": "Mathlib.Data.Vector.MapLemmas", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.Vector.map_map₂", "kind": "theorem", "module": "Mathlib.Data.Vector.MapLemmas", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.Vector.mapAccumr₂_mapAccumr₂_left_left", "kind": "theorem", "module": "Mathlib.Data.Vector.MapLemmas", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.Vector.mapAccumr₂_mapAccumr₂_left_right", "kind": "theorem", "module": "Mathlib.Data.Vector.MapLemmas", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.Vector.mapAccumr₂_mapAccumr₂_right_left", "kind": "theorem", "module": "Mathlib.Data.Vector.MapLemmas", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.Vector.mapAccumr₂_mapAccumr₂_right_right", "kind": "theorem", "module": "Mathlib.Data.Vector.MapLemmas", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.Vector.mapAccumr_bisim", "kind": "theorem", "module": "Mathlib.Data.Vector.MapLemmas", "is_tactic_proof": true, "tactics": ["induction", "exact", "rcases", "simp", "congr"], "tactic_count": 5}
{"name": "List.Vector.mapAccumr_bisim_tail", "kind": "theorem", "module": "Mathlib.Data.Vector.MapLemmas", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "List.Vector.mapAccumr₂_bisim", "kind": "theorem", "module": "Mathlib.Data.Vector.MapLemmas", "is_tactic_proof": true, "tactics": ["induction", "exact", "rcases", "simp", "congr"], "tactic_count": 5}
{"name": "List.Vector.mapAccumr₂_bisim_tail", "kind": "theorem", "module": "Mathlib.Data.Vector.MapLemmas", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "List.Vector.map_eq_mapAccumr", "kind": "theorem", "module": "Mathlib.Data.Vector.MapLemmas", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.Vector.mapAccumr_eq_map", "kind": "theorem", "module": "Mathlib.Data.Vector.MapLemmas", "is_tactic_proof": true, "tactics": ["rw", "apply", "use", "exact"], "tactic_count": 4}
{"name": "List.Vector.map₂_eq_mapAccumr₂", "kind": "theorem", "module": "Mathlib.Data.Vector.MapLemmas", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.Vector.mapAccumr₂_eq_map₂", "kind": "theorem", "module": "Mathlib.Data.Vector.MapLemmas", "is_tactic_proof": true, "tactics": ["rw", "apply", "use", "exact"], "tactic_count": 4}
{"name": "List.Vector.mapAccumr_eq_map_of_constant_state", "kind": "theorem", "module": "Mathlib.Data.Vector.MapLemmas", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.Vector.mapAccumr₂_eq_map₂_of_constant_state", "kind": "theorem", "module": "Mathlib.Data.Vector.MapLemmas", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.Vector.mapAccumr_eq_map_of_unused_state", "kind": "theorem", "module": "Mathlib.Data.Vector.MapLemmas", "is_tactic_proof": true, "tactics": ["rw", "simp_all"], "tactic_count": 2}
{"name": "List.Vector.mapAccumr₂_eq_map₂_of_unused_state", "kind": "theorem", "module": "Mathlib.Data.Vector.MapLemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.mapAccumr_redundant_pair", "kind": "theorem", "module": "Mathlib.Data.Vector.MapLemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.mapAccumr₂_redundant_pair", "kind": "theorem", "module": "Mathlib.Data.Vector.MapLemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.mapAccumr₂_unused_input_left", "kind": "theorem", "module": "Mathlib.Data.Vector.MapLemmas", "is_tactic_proof": true, "tactics": ["induction", "nil", "snoc"], "tactic_count": 3}
{"name": "List.Vector.mapAccumr₂_unused_input_right", "kind": "theorem", "module": "Mathlib.Data.Vector.MapLemmas", "is_tactic_proof": true, "tactics": ["induction", "nil", "snoc"], "tactic_count": 3}
{"name": "List.Vector.map₂_comm", "kind": "theorem", "module": "Mathlib.Data.Vector.MapLemmas", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.Vector.mapAccumr₂_comm", "kind": "theorem", "module": "Mathlib.Data.Vector.MapLemmas", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.Vector.map₂_flip", "kind": "theorem", "module": "Mathlib.Data.Vector.MapLemmas", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.Vector.mapAccumr₂_flip", "kind": "theorem", "module": "Mathlib.Data.Vector.MapLemmas", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.Vector.get_mem", "kind": "theorem", "module": "Mathlib.Data.Vector.Mem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.mem_iff_get", "kind": "theorem", "module": "Mathlib.Data.Vector.Mem", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "List.Vector.notMem_nil", "kind": "theorem", "module": "Mathlib.Data.Vector.Mem", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.Vector.notMem_zero", "kind": "theorem", "module": "Mathlib.Data.Vector.Mem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.mem_cons_iff", "kind": "theorem", "module": "Mathlib.Data.Vector.Mem", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.Vector.mem_succ_iff", "kind": "theorem", "module": "Mathlib.Data.Vector.Mem", "is_tactic_proof": true, "tactics": ["obtain", "simp_rw"], "tactic_count": 2}
{"name": "List.Vector.mem_cons_self", "kind": "theorem", "module": "Mathlib.Data.Vector.Mem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.head_mem", "kind": "theorem", "module": "Mathlib.Data.Vector.Mem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.mem_cons_of_mem", "kind": "theorem", "module": "Mathlib.Data.Vector.Mem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.mem_of_mem_tail", "kind": "theorem", "module": "Mathlib.Data.Vector.Mem", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "List.Vector.mem_map_iff", "kind": "theorem", "module": "Mathlib.Data.Vector.Mem", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.Vector.notMem_map_zero", "kind": "theorem", "module": "Mathlib.Data.Vector.Mem", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "List.Vector.mem_map_succ_iff", "kind": "theorem", "module": "Mathlib.Data.Vector.Mem", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.Vector.snoc", "kind": "definition", "module": "Mathlib.Data.Vector.Snoc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.snoc_cons", "kind": "theorem", "module": "Mathlib.Data.Vector.Snoc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.snoc_nil", "kind": "theorem", "module": "Mathlib.Data.Vector.Snoc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.reverse_cons", "kind": "theorem", "module": "Mathlib.Data.Vector.Snoc", "is_tactic_proof": true, "tactics": ["cases", "simp", "congr"], "tactic_count": 3}
{"name": "List.Vector.reverse_snoc", "kind": "theorem", "module": "Mathlib.Data.Vector.Snoc", "is_tactic_proof": true, "tactics": ["cases", "simp", "congr", "simp"], "tactic_count": 4}
{"name": "List.Vector.replicate_succ_to_snoc", "kind": "theorem", "module": "Mathlib.Data.Vector.Snoc", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "conv", "rw"], "tactic_count": 6}
{"name": "List.Vector.revInductionOn", "kind": "definition", "module": "Mathlib.Data.Vector.Snoc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.revInductionOn₂", "kind": "definition", "module": "Mathlib.Data.Vector.Snoc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.revCasesOn", "kind": "definition", "module": "Mathlib.Data.Vector.Snoc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.map_snoc", "kind": "theorem", "module": "Mathlib.Data.Vector.Snoc", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.Vector.mapAccumr_nil", "kind": "theorem", "module": "Mathlib.Data.Vector.Snoc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.mapAccumr_snoc", "kind": "theorem", "module": "Mathlib.Data.Vector.Snoc", "is_tactic_proof": true, "tactics": ["induction", "rfl", "simp"], "tactic_count": 3}
{"name": "List.Vector.map₂_snoc", "kind": "theorem", "module": "Mathlib.Data.Vector.Snoc", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.Vector.mapAccumr₂_nil", "kind": "theorem", "module": "Mathlib.Data.Vector.Snoc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.mapAccumr₂_snoc", "kind": "theorem", "module": "Mathlib.Data.Vector.Snoc", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.Vector.zipWith", "kind": "definition", "module": "Mathlib.Data.Vector.Zip", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.zipWith_toList", "kind": "theorem", "module": "Mathlib.Data.Vector.Zip", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.zipWith_get", "kind": "theorem", "module": "Mathlib.Data.Vector.Zip", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "List.Vector.zipWith_tail", "kind": "theorem", "module": "Mathlib.Data.Vector.Zip", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "List.Vector.prod_mul_prod_eq_prod_zipWith", "kind": "theorem", "module": "Mathlib.Data.Vector.Zip", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq", "kind": "definition", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.ofSeq", "kind": "definition", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.ofList", "kind": "definition", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.ofStream", "kind": "definition", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.coeSeq", "kind": "instance", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.coeList", "kind": "instance", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.coeStream", "kind": "instance", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.nil", "kind": "definition", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.inhabited", "kind": "instance", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.cons", "kind": "definition", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.think", "kind": "definition", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.destruct", "kind": "definition", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.recOn", "kind": "definition", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.Mem", "kind": "definition", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.membership", "kind": "instance", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.notMem_nil", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.head", "kind": "definition", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.flatten", "kind": "definition", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.tail", "kind": "definition", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.drop", "kind": "definition", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.get?", "kind": "definition", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.toList", "kind": "definition", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.append", "kind": "definition", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.join", "kind": "definition", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.map", "kind": "definition", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.ret", "kind": "definition", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.bind", "kind": "definition", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.monad", "kind": "instance", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.destruct_nil", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.destruct_cons", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.destruct_think", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.seq_destruct_nil", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.seq_destruct_cons", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.seq_destruct_think", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.head_nil", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Stream'.WSeq.head_cons", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Stream'.WSeq.head_think", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Stream'.WSeq.flatten_pure", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": true, "tactics": ["refine", "intro", "rw", "simp", "cases", "none", "some", "obtain", "simp"], "tactic_count": 9}
{"name": "Stream'.WSeq.flatten_think", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.destruct_flatten", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": ["refine", "intro", "exact", "c,", "induction", "pure", "think"], "tactic_count": 7}
{"name": "Stream'.WSeq.head_terminates_iff", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.tail_nil", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Stream'.WSeq.tail_cons", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Stream'.WSeq.tail_think", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Stream'.WSeq.dropn_nil", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "Stream'.WSeq.dropn_cons", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Stream'.WSeq.dropn_think", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "Stream'.WSeq.dropn_add", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.dropn_tail", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": true, "tactics": ["rw", "symm", "apply"], "tactic_count": 3}
{"name": "Stream'.WSeq.get?_add", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.get?_tail", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.join_nil", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.join_think", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": true, "tactics": ["simp", "dsimp", "simp"], "tactic_count": 3}
{"name": "Stream'.WSeq.join_cons", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": true, "tactics": ["simp", "dsimp", "simp"], "tactic_count": 3}
{"name": "Stream'.WSeq.nil_append", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.cons_append", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.think_append", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.append_nil", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.append_assoc", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.tail.aux", "kind": "definition", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.destruct_tail", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": true, "tactics": ["simp", "apply"], "tactic_count": 2}
{"name": "Stream'.WSeq.drop.aux", "kind": "definition", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.drop.aux_none", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.destruct_dropn", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.head_terminates_of_head_tail_terminates", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.destruct_some_of_destruct_tail_some", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": true, "tactics": ["unfold", "rcases", "rcases", "rcases", "have", "contradiction", "exact"], "tactic_count": 7}
{"name": "Stream'.WSeq.head_some_of_head_tail_some", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": true, "tactics": ["unfold", "rcases", "rcases", "obtain", "exact"], "tactic_count": 5}
{"name": "Stream'.WSeq.head_some_of_get?_some", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "let", "exact"], "tactic_count": 5}
{"name": "Stream'.WSeq.get?_terminates_le", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": true, "tactics": ["induction", "refl", "step"], "tactic_count": 3}
{"name": "Stream'.WSeq.head_terminates_of_get?_terminates", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.destruct_terminates_of_get?_terminates", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Stream'.WSeq.mem_of_mem_dropn", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Stream'.WSeq.head_terminates_of_mem", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.of_mem_append", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.mem_append_left", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.exists_of_mem_map", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.ofList_nil", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.ofList_cons", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.toList'_nil", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.toList'_cons", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.toList'_think", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Stream'.WSeq.toList_cons", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.toList_nil", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.toList_ofList", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "Stream'.WSeq.destruct_ofSeq", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.head_ofSeq", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": true, "tactics": ["simp", "cases"], "tactic_count": 2}
{"name": "Stream'.WSeq.tail_ofSeq", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": true, "tactics": ["simp", "induction", "simp", "rfl"], "tactic_count": 4}
{"name": "Stream'.WSeq.dropn_ofSeq", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.get?_ofSeq", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": true, "tactics": ["dsimp"], "tactic_count": 1}
{"name": "Stream'.WSeq.map_nil", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.map_cons", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.map_think", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.map_id", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Stream'.WSeq.map_ret", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Stream'.WSeq.map_append", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Stream'.WSeq.mem_map", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.exists_of_mem_join", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": ["suffices", "from", "intro", "induction", "have", "substs", "simp", "rcases", "simp", "rcases", "simp", "exact", "induction", "have", "apply", "simp", "exact", "apply", "replace", "rcases", "exact", "simp", "apply"], "tactic_count": 23}
{"name": "Stream'.WSeq.exists_of_mem_bind", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.destruct_map", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": ["apply", "intro", "obtain", "rw", "induction", "exact", "exact"], "tactic_count": 7}
{"name": "Stream'.WSeq.destruct_append.aux", "kind": "definition", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.destruct_append", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": ["apply", "intro", "induction", "induction", "refine", "exact"], "tactic_count": 6}
{"name": "Stream'.WSeq.destruct_join.aux", "kind": "definition", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.destruct_join", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": false, "tactics": ["apply", "intro", "exact", "c,", "induction", "refine"], "tactic_count": 6}
{"name": "Stream'.WSeq.map_join", "kind": "theorem", "module": "Mathlib.Data.WSeq.Basic", "is_tactic_proof": true, "tactics": ["apply", "intro", "exact", "induction", "induction", "exact", "refine", "exact", "exact", "refine"], "tactic_count": 10}
{"name": "Stream'.WSeq.length", "kind": "definition", "module": "Mathlib.Data.WSeq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.toList_terminates", "kind": "instance", "module": "Mathlib.Data.WSeq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.get", "kind": "definition", "module": "Mathlib.Data.WSeq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.updateNth", "kind": "definition", "module": "Mathlib.Data.WSeq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.removeNth", "kind": "definition", "module": "Mathlib.Data.WSeq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.filterMap", "kind": "definition", "module": "Mathlib.Data.WSeq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.filter", "kind": "definition", "module": "Mathlib.Data.WSeq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stream'.WSeq.find", "kind": "definition", "module": "Mathlib.Data.WSeq.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "WType.equivList", "kind": "definition", "module": "Mathlib.Data.W.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WType.ListαEquivPUnitSum", "kind": "definition", "module": "Mathlib.Data.W.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.AddAutEquivUnits", "kind": "definition", "module": "Mathlib.Data.ZMod.Aut", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.instIsDomainOfNatNat", "kind": "instance", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ZMod.val_le", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ZMod.val_one'", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ZMod.val_mul'", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.val_natCast", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["cases", "rw", "exact", "apply"], "tactic_count": 4}
{"name": "ZMod.val_natCast_of_lt", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "ZMod.val_ofNat", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.val_ofNat_of_lt", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.val_unit'", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["simp", "rw"], "tactic_count": 2}
{"name": "ZMod.eq_one_of_isUnit_natCast", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ZMod.charP", "kind": "instance", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod._example", "kind": "example", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.addOrderOf_one", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.addOrderOf_coe", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rw"], "tactic_count": 3}
{"name": "ZMod.addOrderOf_coe'", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ZMod.ringChar_zmod_n", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ZMod.natCast_self", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ZMod.natCast_pow_eq_zero_of_le", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["obtain", "rw", "simp"], "tactic_count": 3}
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{"name": "ZMod.cast_eq_val", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["cases", "cases", "rfl"], "tactic_count": 3}
{"name": "Prod.fst_zmod_cast", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["cases", "rfl", "simp"], "tactic_count": 3}
{"name": "Prod.snd_zmod_cast", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["cases", "rfl", "simp"], "tactic_count": 3}
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{"name": "ZMod.natCast_rightInverse", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ZMod.intCast_zmod_cast", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["cases", "simp", "dsimp", "rw"], "tactic_count": 4}
{"name": "ZMod.intCast_rightInverse", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.intCast_surjective", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.forall", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ZMod.intCast_cast", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.cast_add_eq_ite", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simp", "change", "change", "simp", "norm_cast", "split_ifs", "rw", "congr", "rfl"], "tactic_count": 10}
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{"name": "ZMod.ringEquivCongr_refl_apply", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
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{"name": "ZMod.val_eq_zero", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.intCast_eq_intCast_iff", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ZMod.val_intCast", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["have", "have", "refine", "rw"], "tactic_count": 4}
{"name": "ZMod.natCast_eq_natCast_iff", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ZMod.natCast_eq_natCast_iff'", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.intCast_zmod_eq_zero_iff_dvd", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ZMod.intCast_eq_intCast_iff_dvd_sub", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ZMod.natCast_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ZMod.coe_intCast", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["cases", "rw", "rw"], "tactic_count": 3}
{"name": "ZMod.intCast_cast_add", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ZMod.intCast_cast_mul", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "ZMod.intCast_cast_neg", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ZMod.val_neg_one", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "cases", "simp", "dsimp", "rw"], "tactic_count": 5}
{"name": "ZMod.cast_neg_one", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["rcases", "dsimp", "rw"], "tactic_count": 3}
{"name": "ZMod.cast_sub_one", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["split_ifs", "rw", "cases", "dsimp", "rw", "dsimp", "rw", "rw", "rwa", "exact"], "tactic_count": 10}
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{"name": "ZMod.intCast_eq_iff", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "refine", "rw", "rintro", "rw", "add_zero,"], "tactic_count": 7}
{"name": "ZMod.intCast_mod", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "ZMod.ker_intCastAddHom", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "ZMod.cast_injective_of_le", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["cases", "zero", "succ", "rintro", "simp", "apply", "exact"], "tactic_count": 7}
{"name": "ZMod.cast_zmod_eq_zero_iff_of_le", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ZMod.natCast_toNat", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.val_injective", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["cases", "cases", "intro", "dsimp", "ext", "exact"], "tactic_count": 6}
{"name": "ZMod.val_one_eq_one_mod", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ZMod.val_two_eq_two_mod", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ZMod.val_one", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ZMod.val_one''", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.val_add", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["cases", "cases", "apply"], "tactic_count": 3}
{"name": "ZMod.val_add_of_lt", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "ZMod.val_add_val_of_le", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["rw", "rwa"], "tactic_count": 2}
{"name": "ZMod.val_add_of_le", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ZMod.val_add_le", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["cases", "simpa", "simpa"], "tactic_count": 3}
{"name": "ZMod.val_mul", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["cases", "rw", "apply", "apply"], "tactic_count": 4}
{"name": "ZMod.val_mul_le", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "ZMod.val_mul_of_lt", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "ZMod.val_mul_iff_lt", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["constructor", "rw", "apply"], "tactic_count": 3}
{"name": "ZMod.nontrivial", "kind": "instance", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.nontrivial'", "kind": "instance", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["delta"], "tactic_count": 1}
{"name": "ZMod.one_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ZMod.inv", "kind": "definition", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.instInv", "kind": "instance", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.inv_zero", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.mul_inv_eq_gcd", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["rcases", "dsimp", "calc", "calc", "a", "push_cast", "rw", "rfl"], "tactic_count": 8}
{"name": "ZMod.inv_one", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["obtain", "exact", "simpa"], "tactic_count": 3}
{"name": "ZMod.natCast_mod", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.eq_iff_modEq_nat", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.intCast_eq_zero_iff_even", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.natCast_eq_zero_iff_even", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.intCast_eq_one_iff_odd", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "ZMod.natCast_eq_one_iff_odd", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.natCast_ne_zero_iff_odd", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ZMod.coe_mul_inv_eq_one", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["rw", "rw"], "tactic_count": 2}
{"name": "ZMod.mul_val_inv", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["obtain", "simp", "haveI", "rw"], "tactic_count": 4}
{"name": "ZMod.val_inv_mul", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ZMod.unitOfCoprime", "kind": "definition", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.coe_unitOfCoprime", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.val_coe_unit_coprime", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "apply", "have", "rw", "rw", "rw", "rw"], "tactic_count": 8}
{"name": "ZMod.isUnit_iff_coprime", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["refine", "have", "rw", "rw", "exact"], "tactic_count": 5}
{"name": "ZMod.coprime_mod_iff_coprime", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["suffices", "exact"], "tactic_count": 2}
{"name": "ZMod.isUnit_prime_iff_not_dvd", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ZMod.isUnit_prime_of_not_dvd", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.inv_coe_unit", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["have", "rw", "let", "have", "apply", "rfl", "rw", "rfl"], "tactic_count": 8}
{"name": "ZMod.mul_inv_of_unit", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["rcases", "rw"], "tactic_count": 2}
{"name": "ZMod.inv_mul_of_unit", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ZMod.inv_eq_of_mul_eq_one", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.inv_neg_one", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.inv_mul_eq_one_of_isUnit", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["refine", "apply_fun", "rwa"], "tactic_count": 3}
{"name": "ZMod.unitsEquivCoprime", "kind": "definition", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.chineseRemainder", "kind": "definition", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.subsingleton_iff", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["constructor", "obtain", "simpa", "simp", "simpa", "rintro", "infer_instance"], "tactic_count": 7}
{"name": "ZMod.nontrivial_iff", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ZMod.instSubsingletonUnits", "kind": "instance", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.add_self_eq_zero_iff_eq_zero", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["rw", "rw"], "tactic_count": 2}
{"name": "ZMod.ne_neg_self", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "ZMod.neg_one_ne_one", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.neg_eq_self_mod_two", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["fin_cases"], "tactic_count": 1}
{"name": "ZMod.intCast_abs_mod_two", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "ZMod.natAbs_mod_two", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ZMod.val_ne_zero", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.val_pos", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ZMod.val_eq_one", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.neg_eq_self_iff", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["rw", "cases", "rw", "exact", "conv_lhs", "constructor", "rintro", "rcases", "rw", "rcases", "exact", "cases", "right", "rwa", "refine", "rw", "apply", "simp", "rintro", "rw", "apply", "rw"], "tactic_count": 22}
{"name": "ZMod.val_cast_of_lt", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ZMod.val_cast_zmod_lt", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["obtain", "by_cases", "obtain", "rw", "apply", "apply", "apply"], "tactic_count": 7}
{"name": "ZMod.neg_val'", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.neg_val", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["rw", "by_cases", "rw", "apply", "exact"], "tactic_count": 5}
{"name": "ZMod.val_neg_of_ne_zero", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["simp_all"], "tactic_count": 1}
{"name": "ZMod.val_sub", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "cases", "have", "rw", "apply"], "tactic_count": 5}
{"name": "ZMod.val_cast_eq_val_of_lt", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "exact"], "tactic_count": 3}
{"name": "ZMod.cast_cast_zmod_of_le", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "ZMod.val_pow", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "ih", "have", "obtain", "by_cases", "cases", "simp", "exact", "rw"], "tactic_count": 11}
{"name": "ZMod.val_pow_le", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "apply", "apply"], "tactic_count": 6}
{"name": "ZMod.natAbs_min_of_le_div_two", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["rw", "obtain", "rw", "subst", "obtain", "rw", "apply", "rw", "refine", "rw", "refine", "rw"], "tactic_count": 12}
{"name": "RingHom.ext_zmod", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["ext", "obtain", "let", "let", "change", "rw"], "tactic_count": 6}
{"name": "ZMod.subsingleton_ringHom", "kind": "instance", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.subsingleton_ringEquiv", "kind": "instance", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.ringHom_map_cast", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["cases", "dsimp", "dsimp", "rw"], "tactic_count": 4}
{"name": "ZMod.ringHom_rightInverse", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.ringHom_surjective", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.castHom_self", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.castHom_comp", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.lift", "kind": "definition", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.lift_coe", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.lift_castAddHom", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.lift_comp_coe", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.lift_comp_castAddHom", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.lift_injective", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "zmod_smul_mem", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "smulMemClass", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroupClass.instZModSMul", "kind": "instance", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroupClass.coe_zmod_smul", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroupClass.instZModModule", "kind": "instance", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZModModule.char_nsmul_eq_zero", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ZModModule.char_ne_one", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["rintro", "obtain", "exact"], "tactic_count": 3}
{"name": "ZModModule.two_le_char", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["have", "have", "lia"], "tactic_count": 3}
{"name": "ZModModule.periodicPts_add_left", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZModModule.add_self", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ZModModule.neg_eq_self", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ZModModule.sub_eq_add", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ZModModule.add_add_add_cancel", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "pow_zmod_val_inv_pow", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["replace", "rw"], "tactic_count": 2}
{"name": "pow_pow_zmod_val_inv", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.range_mul_add", "kind": "theorem", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp", "conv", "refine", "simpa", "obtain", "simp", "obtain", "exact"], "tactic_count": 9}
{"name": "Nat.residueClassesEquiv", "kind": "definition", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.instSubsingletonModule", "kind": "instance", "module": "Mathlib.Data.ZMod.Basic", "is_tactic_proof": true, "tactics": ["obtain", "exact", "refine", "obtain", "rw"], "tactic_count": 5}
{"name": "ZMod.coe_int_isUnit_iff_isCoprime", "kind": "theorem", "module": "Mathlib.Data.ZMod.Coprime", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "ZMod.eq_zero_iff_gcd_ne_one", "kind": "theorem", "module": "Mathlib.Data.ZMod.Coprime", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ZMod.ne_zero_of_gcd_eq_one", "kind": "theorem", "module": "Mathlib.Data.ZMod.Coprime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.eq_zero_of_gcd_ne_one", "kind": "theorem", "module": "Mathlib.Data.ZMod.Coprime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.val_intCast", "kind": "theorem", "module": "Mathlib.Data.ZMod.Defs", "is_tactic_proof": true, "tactics": ["rw", "split", "simp", "simp", "split", "rw", "rw", "rw", "have", "lia"], "tactic_count": 10}
{"name": "Fin.instCommSemigroup", "kind": "instance", "module": "Mathlib.Data.ZMod.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Data.ZMod.Defs.0.Fin.left_distrib_aux", "kind": "theorem", "module": "Mathlib.Data.ZMod.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.instDistrib", "kind": "instance", "module": "Mathlib.Data.ZMod.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.instNonUnitalCommRing", "kind": "instance", "module": "Mathlib.Data.ZMod.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.instCommMonoid", "kind": "instance", "module": "Mathlib.Data.ZMod.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.instHasDistribNeg", "kind": "instance", "module": "Mathlib.Data.ZMod.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.instCommRing", "kind": "definition", "module": "Mathlib.Data.ZMod.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.instNeZeroHAddNatOfNat_mathlib_1", "kind": "instance", "module": "Mathlib.Data.ZMod.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod", "kind": "definition", "module": "Mathlib.Data.ZMod.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.decidableEq", "kind": "instance", "module": "Mathlib.Data.ZMod.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.repr", "kind": "instance", "module": "Mathlib.Data.ZMod.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.instUnique", "kind": "instance", "module": "Mathlib.Data.ZMod.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.fintype", "kind": "instance", "module": "Mathlib.Data.ZMod.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.infinite", "kind": "instance", "module": "Mathlib.Data.ZMod.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.card", "kind": "theorem", "module": "Mathlib.Data.ZMod.Defs", "is_tactic_proof": true, "tactics": ["cases", "zero", "succ"], "tactic_count": 3}
{"name": "ZMod.commRing", "kind": "instance", "module": "Mathlib.Data.ZMod.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.inhabited", "kind": "instance", "module": "Mathlib.Data.ZMod.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod._example", "kind": "example", "module": "Mathlib.Data.ZMod.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.cast_descFactorial", "kind": "theorem", "module": "Mathlib.Data.ZMod.Factorial", "is_tactic_proof": true, "tactics": ["rw", "simp", "nth_rw", "rw", "refine", "intro", "rw"], "tactic_count": 7}
{"name": "instSMulZModOfNatNatAdditiveUnitsInt", "kind": "instance", "module": "Mathlib.Data.ZMod.IntUnitsPower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.smul_units_def", "kind": "theorem", "module": "Mathlib.Data.ZMod.IntUnitsPower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.natCast_smul_units", "kind": "theorem", "module": "Mathlib.Data.ZMod.IntUnitsPower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instModuleZModOfNatNatAdditiveUnitsInt", "kind": "instance", "module": "Mathlib.Data.ZMod.IntUnitsPower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.instUnitsPow", "kind": "instance", "module": "Mathlib.Data.ZMod.IntUnitsPower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_example", "kind": "example", "module": "Mathlib.Data.ZMod.IntUnitsPower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_example", "kind": "example", "module": "Mathlib.Data.ZMod.IntUnitsPower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "birkhoffAverage_one'", "kind": "theorem", "module": "Mathlib.Dynamics.BirkhoffSum.Average", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "map_birkhoffAverage", "kind": "theorem", "module": "Mathlib.Dynamics.BirkhoffSum.Average", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "birkhoffAverage_congr_ring", "kind": "theorem", "module": "Mathlib.Dynamics.BirkhoffSum.Average", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "birkhoffAverage_congr_ring'", "kind": "theorem", "module": "Mathlib.Dynamics.BirkhoffSum.Average", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Function.IsFixedPt.birkhoffAverage_eq", "kind": "theorem", "module": "Mathlib.Dynamics.BirkhoffSum.Average", "is_tactic_proof": true, "tactics": ["rw", "rwa"], "tactic_count": 2}
{"name": "birkhoffAverage_add", "kind": "theorem", "module": "Mathlib.Dynamics.BirkhoffSum.Average", "is_tactic_proof": true, "tactics": ["funext", "simp"], "tactic_count": 2}
{"name": "birkhoffAverage_neg", "kind": "theorem", "module": "Mathlib.Dynamics.BirkhoffSum.Average", "is_tactic_proof": true, "tactics": ["funext", "simp"], "tactic_count": 2}
{"name": "birkhoffAverage_sub", "kind": "theorem", "module": "Mathlib.Dynamics.BirkhoffSum.Average", "is_tactic_proof": true, "tactics": ["funext", "simp"], "tactic_count": 2}
{"name": "birkhoffAverage_apply_sub_birkhoffAverage", "kind": "theorem", "module": "Mathlib.Dynamics.BirkhoffSum.Average", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "birkhoffAverage_of_comp_eq", "kind": "theorem", "module": "Mathlib.Dynamics.BirkhoffSum.Average", "is_tactic_proof": true, "tactics": ["funext", "suffices", "rw"], "tactic_count": 3}
{"name": "birkhoffSum", "kind": "definition", "module": "Mathlib.Dynamics.BirkhoffSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "birkhoffSum_zero", "kind": "theorem", "module": "Mathlib.Dynamics.BirkhoffSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "birkhoffSum_zero'", "kind": "theorem", "module": "Mathlib.Dynamics.BirkhoffSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "birkhoffSum_one", "kind": "theorem", "module": "Mathlib.Dynamics.BirkhoffSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "birkhoffSum_one'", "kind": "theorem", "module": "Mathlib.Dynamics.BirkhoffSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "birkhoffSum_succ", "kind": "theorem", "module": "Mathlib.Dynamics.BirkhoffSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "birkhoffSum_succ'", "kind": "theorem", "module": "Mathlib.Dynamics.BirkhoffSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "birkhoffSum_add", "kind": "theorem", "module": "Mathlib.Dynamics.BirkhoffSum.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "birkhoffSum_add'", "kind": "theorem", "module": "Mathlib.Dynamics.BirkhoffSum.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Function.IsFixedPt.birkhoffSum_eq", "kind": "theorem", "module": "Mathlib.Dynamics.BirkhoffSum.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "map_birkhoffSum", "kind": "theorem", "module": "Mathlib.Dynamics.BirkhoffSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "birkhoffSum_of_comp_eq", "kind": "theorem", "module": "Mathlib.Dynamics.BirkhoffSum.Basic", "is_tactic_proof": true, "tactics": ["funext", "suffices", "intro", "exact"], "tactic_count": 4}
{"name": "birkhoffSum_neg", "kind": "theorem", "module": "Mathlib.Dynamics.BirkhoffSum.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "birkhoffSum_sub", "kind": "theorem", "module": "Mathlib.Dynamics.BirkhoffSum.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "birkhoffSum_apply_sub_birkhoffSum", "kind": "theorem", "module": "Mathlib.Dynamics.BirkhoffSum.Basic", "is_tactic_proof": true, "tactics": ["rw", "sub_add,"], "tactic_count": 2}
{"name": "Function.IsFixedPt.tendsto_birkhoffAverage", "kind": "theorem", "module": "Mathlib.Dynamics.BirkhoffSum.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dist_birkhoffSum_apply_birkhoffSum", "kind": "theorem", "module": "Mathlib.Dynamics.BirkhoffSum.NormedSpace", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "dist_birkhoffSum_birkhoffSum_le", "kind": "theorem", "module": "Mathlib.Dynamics.BirkhoffSum.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dist_birkhoffAverage_birkhoffAverage", "kind": "theorem", "module": "Mathlib.Dynamics.BirkhoffSum.NormedSpace", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "dist_birkhoffAverage_birkhoffAverage_le", "kind": "theorem", "module": "Mathlib.Dynamics.BirkhoffSum.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dist_birkhoffAverage_apply_birkhoffAverage", "kind": "theorem", "module": "Mathlib.Dynamics.BirkhoffSum.NormedSpace", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "tendsto_birkhoffAverage_apply_sub_birkhoffAverage", "kind": "theorem", "module": "Mathlib.Dynamics.BirkhoffSum.NormedSpace", "is_tactic_proof": true, "tactics": ["rcases", "have", "refine", "rw", "gcongr", "exact"], "tactic_count": 6}
{"name": "tendsto_birkhoffAverage_apply_sub_birkhoffAverage'", "kind": "theorem", "module": "Mathlib.Dynamics.BirkhoffSum.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformEquicontinuous_birkhoffAverage", "kind": "theorem", "module": "Mathlib.Dynamics.BirkhoffSum.NormedSpace", "is_tactic_proof": true, "tactics": ["refine", "rcases", "refine", "calc", "dist", "dist_birkhoffAverage_birkhoffAverage_le", "gcongr", "refine", "simpa"], "tactic_count": 9}
{"name": "isClosed_setOf_tendsto_birkhoffAverage", "kind": "theorem", "module": "Mathlib.Dynamics.BirkhoffSum.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.QuasiMeasurePreserving.birkhoffSum_ae_eq_of_ae_eq", "kind": "theorem", "module": "Mathlib.Dynamics.BirkhoffSum.QuasiMeasurePreserving", "is_tactic_proof": true, "tactics": ["apply", "apply", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.QuasiMeasurePreserving.birkhoffAverage_ae_eq_of_ae_eq", "kind": "theorem", "module": "Mathlib.Dynamics.BirkhoffSum.QuasiMeasurePreserving", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.instFunLikeReal", "kind": "instance", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.instOrderHomClassReal", "kind": "instance", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.coe_mk", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.coe_toOrderHom", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.monotone", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.mono", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.strictMono_iff_injective", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.map_add_one", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.map_one_add", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CircleDeg1Lift.ext", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.instMonoid", "kind": "instance", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.instInhabited", "kind": "instance", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.coe_mul", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.mul_apply", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.coe_one", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.unitsHasCoeToFun", "kind": "instance", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.units_inv_apply_apply", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CircleDeg1Lift.units_apply_inv_apply", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CircleDeg1Lift.toOrderIso", "kind": "definition", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.coe_toOrderIso", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.coe_toOrderIso_symm", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.coe_toOrderIso_inv", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.isUnit_iff_bijective", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.coe_pow", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.semiconjBy_iff_semiconj", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.commute_iff_commute", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.translate", "kind": "definition", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.translate_apply", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.translate_inv_apply", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.translate_zpow", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CircleDeg1Lift.translate_pow", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.translate_iterate", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CircleDeg1Lift.commute_nat_add", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CircleDeg1Lift.commute_add_nat", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CircleDeg1Lift.commute_sub_nat", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CircleDeg1Lift.commute_add_int", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.commute_int_add", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CircleDeg1Lift.commute_sub_int", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CircleDeg1Lift.map_int_add", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.map_add_int", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.map_sub_int", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.map_add_nat", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.map_nat_add", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.map_sub_nat", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.map_int_of_map_zero", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CircleDeg1Lift.map_fract_sub_fract_eq", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CircleDeg1Lift.instLattice", "kind": "instance", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.sup_apply", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.inf_apply", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.iterate_monotone", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.iterate_mono", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.pow_mono", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.pow_monotone", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.map_le_of_map_zero", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.map_map_zero_le", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.floor_map_map_zero_le", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.ceil_map_map_zero_le", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.map_map_zero_lt", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.le_map_of_map_zero", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.le_map_map_zero", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.le_floor_map_map_zero", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.le_ceil_map_map_zero", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.lt_map_map_zero", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.dist_map_map_zero_lt", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CircleDeg1Lift.dist_map_zero_lt_of_semiconj", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.dist_map_zero_lt_of_semiconjBy", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.tendsto_atBot", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.tendsto_atTop", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.continuous_iff_surjective", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.iterate_le_of_map_le_add_int", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CircleDeg1Lift.le_iterate_of_add_int_le_map", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CircleDeg1Lift.iterate_eq_of_map_eq_add_int", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CircleDeg1Lift.iterate_pos_le_iff", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CircleDeg1Lift.iterate_pos_lt_iff", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CircleDeg1Lift.iterate_pos_eq_iff", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CircleDeg1Lift.le_iterate_pos_iff", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CircleDeg1Lift.lt_iterate_pos_iff", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CircleDeg1Lift.mul_floor_map_zero_le_floor_iterate_zero", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": true, "tactics": ["rw", "apply", "simp"], "tactic_count": 3}
{"name": "CircleDeg1Lift.transnumAuxSeq", "kind": "definition", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.translationNumber", "kind": "definition", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber.0.CircleDeg1Lift.termτ", "kind": "definition", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber.0.CircleDeg1Lift._aux_Mathlib_Dynamics_Circle_RotationNumber_TranslationNumber___macroRules__private_Mathlib_Dynamics_Circle_RotationNumber_TranslationNumber_0_CircleDeg1Lift_termτ_1", "kind": "definition", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber.0.CircleDeg1Lift._aux_Mathlib_Dynamics_Circle_RotationNumber_TranslationNumber___unexpand_CircleDeg1Lift_translationNumber_1", "kind": "definition", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.transnumAuxSeq_def", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.translationNumber_eq_of_tendsto_aux", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.translationNumber_eq_of_tendsto₀", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.translationNumber_eq_of_tendsto₀'", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.transnumAuxSeq_zero", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CircleDeg1Lift.transnumAuxSeq_dist_lt", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": true, "tactics": ["have", "rw", "calc", "simp_rw", "rw", "mul_apply]"], "tactic_count": 6}
{"name": "CircleDeg1Lift.tendsto_translationNumber_aux", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.dist_map_zero_translationNumber_le", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.tendsto_translationNumber_of_dist_bounded_aux", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": true, "tactics": ["apply", "exact", "intro", "have", "convert", "rw", "exact", "mul_zero"], "tactic_count": 8}
{"name": "CircleDeg1Lift.translationNumber_eq_of_dist_bounded", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.translationNumber_one", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.translationNumber_eq_of_semiconjBy", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.translationNumber_eq_of_semiconj", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.translationNumber_mul_of_commute", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": true, "tactics": ["refine", "simp", "refine", "rw", "exact"], "tactic_count": 5}
{"name": "CircleDeg1Lift.translationNumber_units_inv", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.translationNumber_pow", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.translationNumber_zpow", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.translationNumber_conj_eq", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.translationNumber_conj_eq'", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.dist_pow_map_zero_mul_translationNumber_le", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.tendsto_translation_number₀'", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": ["refine", "tendsto_iff_dist_tendsto_zero.2", "squeeze_zero", "dsimp", "have", "rw", "div_le_div_iff_of_pos_right", "apply"], "tactic_count": 8}
{"name": "CircleDeg1Lift.tendsto_translation_number₀", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.tendsto_translationNumber", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp"], "tactic_count": 3}
{"name": "CircleDeg1Lift.tendsto_translation_number'", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.translationNumber_mono", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.translationNumber_translate", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.translationNumber_le_of_le_add", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.le_translationNumber_of_add_le", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.translationNumber_le_of_le_add_int", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.translationNumber_le_of_le_add_nat", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.le_translationNumber_of_add_int_le", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.le_translationNumber_of_add_nat_le", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.translationNumber_of_eq_add_int", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.floor_sub_le_translationNumber", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.translationNumber_le_ceil_sub", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.map_lt_of_translationNumber_lt_int", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.map_lt_of_translationNumber_lt_nat", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.map_lt_add_floor_translationNumber_add_one", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": true, "tactics": ["rw", "norm_cast", "refine", "push_cast", "exact"], "tactic_count": 5}
{"name": "CircleDeg1Lift.map_lt_add_translationNumber_add_one", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.lt_map_of_int_lt_translationNumber", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.lt_map_of_nat_lt_translationNumber", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.translationNumber_of_map_pow_eq_add_int", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": true, "tactics": ["have", "rwa", "exact"], "tactic_count": 3}
{"name": "CircleDeg1Lift.forall_map_sub_of_Icc", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.translationNumber_lt_of_forall_lt_add", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": ["obtain", "isCompact_Icc.exists_isMaxOn", "refine", "apply", "simp", "exact"], "tactic_count": 6}
{"name": "CircleDeg1Lift.lt_translationNumber_of_forall_add_lt", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": ["obtain", "isCompact_Icc.exists_isMinOn", "refine", "apply", "simp", "exact"], "tactic_count": 6}
{"name": "CircleDeg1Lift.exists_eq_add_translationNumber", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": ["obtain", "by_contra", "exact", "obtain", "by_contra", "exact", "exact"], "tactic_count": 7}
{"name": "CircleDeg1Lift.translationNumber_eq_int_iff", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": true, "tactics": ["constructor", "intro", "simp", "exact", "rintro", "exact"], "tactic_count": 6}
{"name": "CircleDeg1Lift.continuous_pow", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CircleDeg1Lift.translationNumber_eq_rat_iff", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CircleDeg1Lift.semiconj_of_group_action_of_forall_translationNumber_eq", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": true, "tactics": ["have", "refine", "rintro", "have", "rw", "calc", "f₂", "simp", "set", "set", "have", "have", "refine", "simp", "exact", "simp", "exact", "exact"], "tactic_count": 18}
{"name": "CircleDeg1Lift.units_semiconj_of_translationNumber_eq", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CircleDeg1Lift.semiconj_of_isUnit_of_translationNumber_eq", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "CircleDeg1Lift.semiconj_of_bijective_of_translationNumber_eq", "kind": "theorem", "module": "Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.aeconst_of_forall_preimage_smul_ae_eq", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Action.Basic", "is_tactic_proof": true, "tactics": ["rcases", "refine", "refine", "refine", "exact"], "tactic_count": 5}
{"name": "MeasureTheory.aeconst_of_forall_smul_ae_eq", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.aeconst_of_aestabilizer_eq_top", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ErgodicSMul.of_aestabilizer", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Action.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.ergodicSMul_iterateMulAct", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Action.Basic", "is_tactic_proof": true, "tactics": ["simp", "refine", "intro", "refine", "nth_rewrite", "rfl", "intro", "exact"], "tactic_count": 8}
{"name": "aeconst_of_dense_setOf_preimage_smul_ae", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Action.OfMinimal", "is_tactic_proof": true, "tactics": ["borelize", "refine", "rwa", "let", "exact"], "tactic_count": 5}
{"name": "aeconst_of_dense_setOf_preimage_smul_eq", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Action.OfMinimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ergodic_smul_of_denseRange_pow", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Action.OfMinimal", "is_tactic_proof": true, "tactics": ["borelize", "refine", "refine", "refine", "rw"], "tactic_count": 5}
{"name": "ErgodicSMul.trans_isMinimal", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Action.OfMinimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "aeconst_of_dense_aestabilizer_smul", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Action.OfMinimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ergodic_smul_of_denseRange_zpow", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Action.OfMinimal", "is_tactic_proof": true, "tactics": ["borelize", "refine", "refine", "rw"], "tactic_count": 4}
{"name": "DenseRange.zpow_of_ergodic_mul_left", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Action.OfMinimal", "is_tactic_proof": true, "tactics": ["intro", "by_contra", "obtain", "rw", "have", "rw", "simpa", "set", "have", "have", "have", "simp_rw", "rintro", "apply", "simp_all", "have", "simp", "refine", "simp", "cases", "inl", "inr", "refine", "rwa"], "tactic_count": 24}
{"name": "ergodic_mul_left_of_denseRange_pow", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Action.OfMinimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ergodic_mul_left_of_denseRange_zpow", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Action.OfMinimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ergodic_mul_left_iff_denseRange_zpow", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Action.OfMinimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.preErgodic_of_dense_iUnion_preimage_one", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Action.OfMinimal", "is_tactic_proof": true, "tactics": ["refine", "refine", "have", "rw", "rw", "ext", "simp"], "tactic_count": 7}
{"name": "MonoidHom.ergodic_of_dense_iUnion_preimage_one", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Action.OfMinimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instErgodicSMulOfIsMulLeftInvariant", "kind": "instance", "module": "Mathlib.Dynamics.Ergodic.Action.Regular", "is_tactic_proof": true, "tactics": ["refine", "suffices", "simp", "exact", "intro", "obtain", "refine", "rw", "exact", "exact", "simpa"], "tactic_count": 11}
{"name": "instErgodicSMulMulOppositeOfIsMulRightInvariant", "kind": "instance", "module": "Mathlib.Dynamics.Ergodic.Action.Regular", "is_tactic_proof": true, "tactics": ["refine", "suffices", "simp", "exact", "intro", "obtain", "refine", "rw", "exact", "exact", "simpa"], "tactic_count": 11}
{"name": "AddCircle.ae_empty_or_univ_of_forall_vadd_ae_eq_self", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.AddCircle", "is_tactic_proof": true, "tactics": ["measure", "there", "of", "must", "set", "set", "have", "have", "rw", "rcases", "right", "obtain", "d", "exists_mem_of_measure_ne_zero_of_ae", "let", "replace", "let", "have", "have", "refine", "replace", "convert", "ext", "simp", "have", "hδ₀.mono", "simp", "apply", "exact", "suffices", "replace", "rwa", "refine", "have", "have", "have", "have", "have", "have", "rw", "exact", "rw", "volume_of_add_preimage_eq"], "tactic_count": 43}
{"name": "AddCircle.ergodic_zsmul", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.AddCircle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCircle.ergodic_nsmul", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.AddCircle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCircle.ergodic_zsmul_add", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.AddCircle", "is_tactic_proof": true, "tactics": ["set", "let", "have", "suffices", "replace", "have", "conv_rhs", "rw", "ext", "simp", "neg_smul,", "abel"], "tactic_count": 12}
{"name": "AddCircle.ergodic_nsmul_add", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.AddCircle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCircle.ergodic_add_left", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.AddCircleAdd", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AddCircle.ergodic_add_right", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.AddCircleAdd", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.MeasurePreserving.conservative", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Conservative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Conservative.id", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Conservative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Conservative.of_absolutelyContinuous", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Conservative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Conservative.measureRestrict", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Conservative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Conservative.congr_ae", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Conservative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.conservative_congr", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Conservative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Conservative.exists_mem_iterate_mem", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Conservative", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.Conservative.frequently_measure_inter_ne_zero", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Conservative", "is_tactic_proof": true, "tactics": ["set", "by_contra", "obtain", "rw", "convert", "rw", "have", "set", "have", "rwa", "exact", "have", "rcases", "refine", "simpa", "simpa"], "tactic_count": 16}
{"name": "MeasureTheory.Conservative.exists_gt_measure_inter_ne_zero", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Conservative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Conservative.measure_mem_forall_ge_image_notMem_eq_zero", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Conservative", "is_tactic_proof": true, "tactics": ["by_contra", "have", "simp", "exact", "rcases", "rcases", "exact"], "tactic_count": 7}
{"name": "MeasureTheory.Conservative.ae_mem_imp_frequently_image_mem", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Conservative", "is_tactic_proof": true, "tactics": ["simp", "intro", "filter_upwards", "simp"], "tactic_count": 4}
{"name": "MeasureTheory.Conservative.inter_frequently_image_mem_ae_eq", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Conservative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Conservative.measure_inter_frequently_image_mem_eq", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Conservative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Conservative.ae_forall_image_mem_imp_frequently_image_mem", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Conservative", "is_tactic_proof": true, "tactics": ["refine", "refine", "rw", "refine", "rwa"], "tactic_count": 5}
{"name": "MeasureTheory.Conservative.frequently_ae_mem_and_frequently_image_mem", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Conservative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Conservative.ae_frequently_mem_of_mem_nhds", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Conservative", "is_tactic_proof": false, "tactics": ["have", "h.ae_mem_imp_frequently_image_mem", "refine", "rcases", "exact"], "tactic_count": 5}
{"name": "MeasureTheory.Conservative.iterate", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Conservative", "is_tactic_proof": true, "tactics": ["rcases", "exact", "refine", "rcases", "rw", "rcases", "set", "have", "apply", "exact", "refine", "intro", "rw", "exact", "rwa", "exact"], "tactic_count": 16}
{"name": "PreErgodic.ae_empty_or_univ", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Ergodic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "PreErgodic.measure_self_or_compl_eq_zero", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Ergodic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "PreErgodic.ae_mem_or_ae_notMem", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Ergodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PreErgodic.prob_eq_zero_or_one", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Ergodic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "PreErgodic.of_iterate", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Ergodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PreErgodic.smul_measure", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Ergodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PreErgodic.zero_measure", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Ergodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MeasurePreserving.preErgodic_of_preErgodic_semiconj", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Ergodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MeasurePreserving.ergodic_of_ergodic_semiconj", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Ergodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MeasurePreserving.preErgodic_conjugate_iff", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Ergodic", "is_tactic_proof": false, "tactics": ["refine", "simp", "simp"], "tactic_count": 3}
{"name": "MeasureTheory.MeasurePreserving.ergodic_conjugate_iff", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Ergodic", "is_tactic_proof": false, "tactics": ["have", "rw", "replace", "exact"], "tactic_count": 4}
{"name": "QuasiErgodic.aeconst_set₀", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Ergodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuasiErgodic.ae_empty_or_univ₀", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Ergodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuasiErgodic.ae_mem_or_ae_notMem₀", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Ergodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuasiErgodic.smul_measure", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Ergodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuasiErgodic.zero_measure", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Ergodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ergodic.quasiErgodic", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Ergodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ergodic.ae_empty_or_univ_of_preimage_ae_le'", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Ergodic", "is_tactic_proof": true, "tactics": ["refine", "refine", "exact"], "tactic_count": 3}
{"name": "Ergodic.ae_empty_or_univ_of_ae_le_preimage'", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Ergodic", "is_tactic_proof": true, "tactics": ["replace", "refine", "exact"], "tactic_count": 3}
{"name": "Ergodic.ae_empty_or_univ_of_image_ae_le'", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Ergodic", "is_tactic_proof": false, "tactics": ["replace", "exact"], "tactic_count": 2}
{"name": "Ergodic.symm", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Ergodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ergodic.symm_iff", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Ergodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ergodic.smul_measure", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Ergodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ergodic.zero_measure", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Ergodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ergodic.ae_empty_or_univ_of_preimage_ae_le", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Ergodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ergodic.ae_empty_or_univ_of_ae_le_preimage", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Ergodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ergodic.ae_empty_or_univ_of_image_ae_le", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Ergodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ergodic.of_mem_extremePoints_measure_univ_eq", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Extreme", "is_tactic_proof": true, "tactics": ["have", "rcases", "convert", "rw", "refine", "have", "constructor", "rwa", "set", "have", "refine", "convert", "exact", "rw", "intro", "by_contra", "obtain", "have", "apply", "refine", "rw", "simp", "rw", "simp"], "tactic_count": 24}
{"name": "Ergodic.of_mem_extremePoints", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Extreme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ergodic.eq_smul_of_absolutelyContinuous", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Extreme", "is_tactic_proof": true, "tactics": ["have", "obtain", "use", "ext", "calc", "ν"], "tactic_count": 6}
{"name": "Ergodic.eq_of_absolutelyContinuous_measure_univ_eq", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Extreme", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "simp", "simp_all"], "tactic_count": 4}
{"name": "Ergodic.eq_of_absolutelyContinuous", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Extreme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ergodic.mem_extremePoints_measure_univ_eq", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Extreme", "is_tactic_proof": true, "tactics": ["rw", "refine", "rintro", "have", "apply", "apply"], "tactic_count": 6}
{"name": "Ergodic.mem_extremePoints", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Extreme", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Ergodic.iff_mem_extremePoints_measure_univ_eq", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Extreme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ergodic.iff_mem_extremePoints", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Extreme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuasiErgodic.ae_eq_const_of_ae_eq_comp_of_ae_range₀", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Function", "is_tactic_proof": true, "tactics": ["refine", "refine", "refine", "rw"], "tactic_count": 4}
{"name": "PreErgodic.ae_eq_const_of_ae_eq_comp", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuasiErgodic.ae_eq_const_of_ae_eq_comp₀", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ergodic.ae_eq_const_of_ae_eq_comp₀", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuasiErgodic.ae_eq_const_of_ae_eq_comp_ae", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Function", "is_tactic_proof": true, "tactics": ["borelize", "rcases", "haveI", "exact"], "tactic_count": 4}
{"name": "QuasiErgodic.eq_const_of_compQuasiMeasurePreserving_eq", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ergodic.ae_eq_const_of_ae_eq_comp_ae", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ergodic.eq_const_of_compMeasurePreserving_eq", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.Function", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.measurePreserving", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.MeasurePreserving", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MeasurePreserving.id", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.MeasurePreserving", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MeasurePreserving.aemeasurable", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.MeasurePreserving", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MeasurePreserving.of_isEmpty", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.MeasurePreserving", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MeasurePreserving.symm", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.MeasurePreserving", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MeasurePreserving.restrict_preimage", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.MeasurePreserving", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MeasurePreserving.restrict_preimage_emb", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.MeasurePreserving", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MeasurePreserving.restrict_image_emb", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.MeasurePreserving", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.MeasurePreserving.aemeasurable_comp_iff", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.MeasurePreserving", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.MeasurePreserving.quasiMeasurePreserving", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.MeasurePreserving", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MeasurePreserving.comp", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.MeasurePreserving", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MeasurePreserving.map_of_comp", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.MeasurePreserving", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MeasurePreserving.of_semiconj", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.MeasurePreserving", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "MeasureTheory.MeasurePreserving.trans", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.MeasurePreserving", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MeasurePreserving.comp_left_iff", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.MeasurePreserving", "is_tactic_proof": true, "tactics": ["refine", "convert", "simp"], "tactic_count": 3}
{"name": "MeasureTheory.MeasurePreserving.comp_right_iff", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.MeasurePreserving", "is_tactic_proof": true, "tactics": ["refine", "convert", "simp"], "tactic_count": 3}
{"name": "MeasureTheory.MeasurePreserving.sigmaFinite", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.MeasurePreserving", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MeasurePreserving.sfinite", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.MeasurePreserving", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "MeasureTheory.MeasurePreserving.measure_preimage", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.MeasurePreserving", "is_tactic_proof": true, "tactics": ["rw", "rw"], "tactic_count": 2}
{"name": "MeasureTheory.MeasurePreserving.measureReal_preimage", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.MeasurePreserving", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.MeasurePreserving.measure_preimage_emb", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.MeasurePreserving", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.MeasurePreserving.measure_preimage_equiv", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.MeasurePreserving", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MeasurePreserving.measure_preimage_le", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.MeasurePreserving", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.MeasurePreserving.preimage_null", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.MeasurePreserving", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MeasurePreserving.aeconst_comp", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.MeasurePreserving", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MeasurePreserving.aeconst_preimage", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.MeasurePreserving", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MeasurePreserving.add_measure", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.MeasurePreserving", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MeasurePreserving.smul_measure", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.MeasurePreserving", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MeasurePreserving.iterate", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.MeasurePreserving", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MeasurePreserving.measure_symmDiff_preimage_iterate_le", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.MeasurePreserving", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "simp", "grw", "replace", "rw"], "tactic_count": 7}
{"name": "MeasureTheory.MeasurePreserving.exists_mem_iterate_mem_of_measure_univ_lt_mul_measure", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.MeasurePreserving", "is_tactic_proof": true, "tactics": ["have", "have", "have", "obtain", "simpa", "wlog", "exact", "refine", "rwa"], "tactic_count": 9}
{"name": "MeasureTheory.MeasurePreserving.exists_mem_iterate_mem", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.MeasurePreserving", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.measurePreserving_subtype_coe", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.MeasurePreserving", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MeasurableEquiv.measurePreserving_symm", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.MeasurePreserving", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MeasurePreserving.singularPart", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.RadonNikodym", "is_tactic_proof": true, "tactics": ["rcases", "convert", "refine", "rw", "calc", "μ.singularPart", "rw", "rw", "rw", "exact"], "tactic_count": 10}
{"name": "MeasureTheory.MeasurePreserving.withDensity_rnDeriv", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.RadonNikodym", "is_tactic_proof": true, "tactics": ["use", "ext", "rw", "rnDeriv_add_singularPart,", "rnDeriv_add_singularPart,"], "tactic_count": 5}
{"name": "MeasureTheory.MeasurePreserving.rnDeriv_comp_aeEq", "kind": "theorem", "module": "Mathlib.Dynamics.Ergodic.RadonNikodym", "is_tactic_proof": true, "tactics": ["wlog", "specialize", "refine", "apply", "exact", "refine", "set", "have", "have", "measure_diff_symm", "have", "measure_diff_symm", "suffices", "suffices", "contrapose", "apply", "calc", "μ", "apply", "rw", "finiteness", "exact"], "tactic_count": 22}
{"name": "Function.isFixedPt_id", "kind": "theorem", "module": "Mathlib.Dynamics.FixedPoints.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.forall_isFixedPt_iff", "kind": "theorem", "module": "Mathlib.Dynamics.FixedPoints.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.IsFixedPt.decidable", "kind": "instance", "module": "Mathlib.Dynamics.FixedPoints.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.IsFixedPt.eq", "kind": "theorem", "module": "Mathlib.Dynamics.FixedPoints.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.IsFixedPt.comp", "kind": "theorem", "module": "Mathlib.Dynamics.FixedPoints.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.IsFixedPt.iterate", "kind": "theorem", "module": "Mathlib.Dynamics.FixedPoints.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.IsFixedPt.left_of_comp", "kind": "theorem", "module": "Mathlib.Dynamics.FixedPoints.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.IsFixedPt.to_leftInverse", "kind": "theorem", "module": "Mathlib.Dynamics.FixedPoints.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.IsFixedPt.map", "kind": "theorem", "module": "Mathlib.Dynamics.FixedPoints.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.IsFixedPt.apply", "kind": "theorem", "module": "Mathlib.Dynamics.FixedPoints.Basic", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "Function.IsFixedPt.preimage_iterate", "kind": "theorem", "module": "Mathlib.Dynamics.FixedPoints.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Function.IsFixedPt.image_iterate", "kind": "theorem", "module": "Mathlib.Dynamics.FixedPoints.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.IsFixedPt.equiv_symm", "kind": "theorem", "module": "Mathlib.Dynamics.FixedPoints.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.IsFixedPt.perm_inv", "kind": "theorem", "module": "Mathlib.Dynamics.FixedPoints.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.IsFixedPt.perm_pow", "kind": "theorem", "module": "Mathlib.Dynamics.FixedPoints.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.IsFixedPt.perm_zpow", "kind": "theorem", "module": "Mathlib.Dynamics.FixedPoints.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.isFixedPt_apply_iff", "kind": "theorem", "module": "Mathlib.Dynamics.FixedPoints.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.fixedPoints", "kind": "definition", "module": "Mathlib.Dynamics.FixedPoints.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.fixedPoints.decidable", "kind": "instance", "module": "Mathlib.Dynamics.FixedPoints.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.mem_fixedPoints", "kind": "theorem", "module": "Mathlib.Dynamics.FixedPoints.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.mem_fixedPoints_iff", "kind": "theorem", "module": "Mathlib.Dynamics.FixedPoints.Basic", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "Function.fixedPoints_id", "kind": "theorem", "module": "Mathlib.Dynamics.FixedPoints.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.fixedPoints_subset_range", "kind": "theorem", "module": "Mathlib.Dynamics.FixedPoints.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Semiconj.mapsTo_fixedPoints", "kind": "theorem", "module": "Mathlib.Dynamics.FixedPoints.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "isForwardInvariant_iff_isInvariant", "kind": "theorem", "module": "Mathlib.Dynamics.Flow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Flow.instCoeFunForallForall", "kind": "instance", "module": "Mathlib.Dynamics.Flow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MulAction.dense_orbit", "kind": "theorem", "module": "Mathlib.Dynamics.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "denseRange_smul", "kind": "theorem", "module": "Mathlib.Dynamics.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.isMinimal_of_pretransitive", "kind": "instance", "module": "Mathlib.Dynamics.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.exists_smul_mem", "kind": "theorem", "module": "Mathlib.Dynamics.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.iUnion_preimage_smul", "kind": "theorem", "module": "Mathlib.Dynamics.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Function.IsPeriodicPt.map", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.IsPeriodicPt.apply_iterate", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.IsPeriodicPt.apply", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.IsPeriodicPt.add", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Function.IsPeriodicPt.left_of_add", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Function.IsPeriodicPt.right_of_add", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Function.IsPeriodicPt.sub", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": true, "tactics": ["rcases", "refine", "rwa", "rw", "apply"], "tactic_count": 5}
{"name": "Function.IsPeriodicPt.mul_const", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Function.IsPeriodicPt.const_mul", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Function.IsPeriodicPt.trans_dvd", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.IsPeriodicPt.iterate", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Function.IsPeriodicPt.comp", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Function.IsPeriodicPt.comp_lcm", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.IsPeriodicPt.left_of_comp", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Function.IsPeriodicPt.iterate_mod_apply", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": true, "tactics": ["conv_rhs"], "tactic_count": 1}
{"name": "Function.IsPeriodicPt.mod", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.IsPeriodicPt.gcd", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": true, "tactics": ["revert", "refine", "rwa", "rw", "exact"], "tactic_count": 5}
{"name": "Function.IsPeriodicPt.eq_of_apply_eq_same", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Function.IsPeriodicPt.eq_of_apply_eq", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.ptsOfPeriod", "kind": "definition", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.mem_ptsOfPeriod", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Semiconj.mapsTo_ptsOfPeriod", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.bijOn_ptsOfPeriod", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.periodicPts", "kind": "definition", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.mk_mem_periodicPts", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.mem_periodicPts", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.periodicPts_subset_range", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": true, "tactics": ["intro", "rw", "rcases", "use", "nth_rw", "rw", "exact"], "tactic_count": 7}
{"name": "Function.isPeriodicPt_of_mem_periodicPts_of_isPeriodicPt_iterate", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": true, "tactics": ["rcases", "suffices", "unfold", "convert", "rw", "rw", "exact"], "tactic_count": 7}
{"name": "Function.bUnion_ptsOfPeriod", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.iUnion_pnat_ptsOfPeriod", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Semiconj.mapsTo_periodicPts", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.minimalPeriod", "kind": "definition", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.isPeriodicPt_minimalPeriod", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": true, "tactics": ["classical", "delta", "split_ifs", "exact", "exact"], "tactic_count": 5}
{"name": "Function.iterate_minimalPeriod", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.iterate_add_minimalPeriod_eq", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": true, "tactics": ["rw", "congr", "exact"], "tactic_count": 3}
{"name": "Function.iterate_mod_minimalPeriod_eq", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.minimalPeriod_pos_of_mem_periodicPts", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Function.minimalPeriod_eq_zero_of_notMem_periodicPts", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Function.IsPeriodicPt.minimalPeriod_pos", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.minimalPeriod_pos_iff_mem_periodicPts", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.minimalPeriod_eq_zero_iff_notMem_periodicPts", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Function.IsPeriodicPt.minimalPeriod_le", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": true, "tactics": ["classical", "rw", "exact"], "tactic_count": 3}
{"name": "Function.minimalPeriod_apply_iterate", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": false, "tactics": ["apply", "exact", "rcases", "exact"], "tactic_count": 4}
{"name": "Function.minimalPeriod_apply", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.le_of_lt_minimalPeriod_of_iterate_eq", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": true, "tactics": ["by_contra", "rw", "exact", "hm"], "tactic_count": 4}
{"name": "Function.iterate_injOn_Iio_minimalPeriod", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.iterate_eq_iterate_iff_of_lt_minimalPeriod", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.minimalPeriod_id", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.minimalPeriod_eq_one_iff_isFixedPt", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": true, "tactics": ["refine", "rw", "refine", "rw", "exact", "exact"], "tactic_count": 6}
{"name": "Function.minimalPeriod_eq_one_of_subsingleton", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Function.IsPeriodicPt.eq_zero_of_lt_minimalPeriod", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.not_isPeriodicPt_of_pos_of_lt_minimalPeriod", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.IsPeriodicPt.minimalPeriod_dvd", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.isPeriodicPt_iff_minimalPeriod_dvd", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.minimalPeriod_eq_minimalPeriod_iff", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Function.Commute.minimalPeriod_of_comp_dvd_lcm", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "_private.Mathlib.Dynamics.PeriodicPts.Defs.0.Function.minimalPeriod_iterate_eq_div_gcd_aux", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": true, "tactics": ["apply", "apply", "rw", "exact", "apply", "apply", "rw", "apply", "rw", "exact"], "tactic_count": 10}
{"name": "Function.minimalPeriod_iterate_eq_div_gcd", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.minimalPeriod_iterate_eq_div_gcd'", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.periodicOrbit", "kind": "definition", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.periodicOrbit_def", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.periodicOrbit_eq_cycle_map", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.periodicOrbit_length", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Function.periodicOrbit_eq_nil_iff_not_periodic_pt", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Function.periodicOrbit_eq_nil_of_not_periodic_pt", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.mem_periodicOrbit_iff", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": true, "tactics": ["simp", "use", "rintro", "use", "rw"], "tactic_count": 5}
{"name": "Function.iterate_mem_periodicOrbit", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Function.exists_iterate_apply_eq_of_mem_periodicPts", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Function.self_mem_periodicOrbit", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Function.nodup_periodicOrbit", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "rwa"], "tactic_count": 4}
{"name": "Function.periodicOrbit_apply_iterate_eq", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.periodicOrbit_apply_eq", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.periodicOrbit_chain", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": true, "tactics": ["by_cases", "have", "have", "rw", "refine", "rintro", "rcases", "rwa", "exact", "rw", "nth_rw", "nth_rw", "exact", "rw", "simp"], "tactic_count": 15}
{"name": "Function.periodicOrbit_chain'", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "minimalPeriod_apply", "exact"], "tactic_count": 5}
{"name": "Function.isFixedPt_prodMap", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.IsFixedPt.prodMap", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.isPeriodicPt_prodMap", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Function.IsPeriodicPt.prodMap", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.isFixedPt_piMap", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.IsFixedPt.piMap", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.isPeriodicPt_piMap", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Function.IsPeriodicPt.piMap", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.period", "kind": "definition", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.period_eq_minimalPeriod", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.pow_period_smul", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MulAction.isPeriodicPt_smul_iff", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MulAction.pow_smul_eq_iff_period_dvd", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MulAction.zpow_smul_eq_iff_period_dvd", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": true, "tactics": ["rw", "pow_smul_eq_iff_period_dvd]"], "tactic_count": 2}
{"name": "MulAction.pow_mod_period_smul", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": true, "tactics": ["conv_rhs", "rw"], "tactic_count": 2}
{"name": "MulAction.zpow_mod_period_smul", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": true, "tactics": ["conv_rhs", "rw"], "tactic_count": 2}
{"name": "MulAction.pow_add_period_smul", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MulAction.pow_period_add_smul", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MulAction.zpow_add_period_smul", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MulAction.zpow_period_add_smul", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MulAction.pow_smul_eq_iff_minimalPeriod_dvd", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MulAction.zpow_smul_eq_iff_minimalPeriod_dvd", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MulAction.pow_smul_mod_minimalPeriod", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MulAction.zpow_smul_mod_minimalPeriod", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Function.directed_ptsOfPeriod_pnat", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.bijOn_periodicPts", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.minimalPeriod_eq_prime_iff", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Lemmas", "is_tactic_proof": false, "tactics": ["rw", "or_and_right,", "exact"], "tactic_count": 3}
{"name": "Function.minimalPeriod_eq_sInf_n_pos_IsPeriodicPt", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Lemmas", "is_tactic_proof": true, "tactics": ["dsimp", "grind"], "tactic_count": 2}
{"name": "Function.minimalPeriod_eq_prime", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.minimalPeriod_eq_prime_pow", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Lemmas", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "Function.Commute.minimalPeriod_of_comp_dvd_mul", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Commute.minimalPeriod_of_comp_eq_mul_of_coprime", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Lemmas", "is_tactic_proof": true, "tactics": ["apply", "suffices", "from", "intro", "refine", "exact", "exact"], "tactic_count": 7}
{"name": "Function.minimalPeriod_le_card", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Function.isPeriodicPt_factorial_card_of_mem_periodicPts", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.mem_periodicPts_iff_isPeriodicPt_factorial_card", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.mem_periodicPts", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Lemmas", "is_tactic_proof": false, "tactics": ["obtain", "simpa", "rcases", "exact", "exact"], "tactic_count": 5}
{"name": "Function.injective_iff_periodicPts_eq_univ", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Lemmas", "is_tactic_proof": true, "tactics": ["refine", "rw", "apply"], "tactic_count": 3}
{"name": "Function.injective_iff_iterate_factorial_card_eq_id", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Lemmas", "is_tactic_proof": true, "tactics": ["simp", "eq_univ_iff_forall,"], "tactic_count": 2}
{"name": "Function.minimalPeriod_prodMap", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.minimalPeriod_fst_dvd", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Function.minimalPeriod_snd_dvd", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Function.minimalPeriod_piMap", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Lemmas", "is_tactic_proof": true, "tactics": ["conv_lhs", "simp"], "tactic_count": 2}
{"name": "Function.minimalPeriod_piMap_fintype", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.minimalPeriod_single_dvd_minimalPeriod_piMap", "kind": "theorem", "module": "Mathlib.Dynamics.PeriodicPts.Lemmas", "is_tactic_proof": true, "tactics": ["simp", "by_cases", "exact", "simp"], "tactic_count": 4}
{"name": "Dynamics.IsDynCoverOf", "kind": "definition", "module": "Mathlib.Dynamics.TopologicalEntropy.CoverEntropy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.IsDynCoverOf.of_le", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.CoverEntropy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.IsDynCoverOf.of_entourage_subset", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.CoverEntropy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.isDynCoverOf_empty", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.CoverEntropy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.isDynCoverOf_empty_right", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.CoverEntropy", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Dynamics.IsDynCoverOf.nonempty", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.CoverEntropy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.isDynCoverOf_zero", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.CoverEntropy", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Dynamics.isDynCoverOf_univ", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.CoverEntropy", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Dynamics.IsDynCoverOf.nonempty_inter", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.CoverEntropy", "is_tactic_proof": true, "tactics": ["classical", "use", "simp", "refine", "obtain", "exact"], "tactic_count": 6}
{"name": "Dynamics.IsDynCoverOf.iterate_le_pow", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.CoverEntropy", "is_tactic_proof": true, "tactics": ["classical", "rcases", "exact", "have", "have", "obtain", "rcases", "use", "simp", "exact", "one_le_pow_of_one_le", "have", "rcases", "inter_nemp", "exact", "obtain", "refine", "simp", "mem_comp]", "intro", "replace", "specialize", "specialize", "rw", "exact", "choose", "let", "refine", "rw", "have", "intro", "have", "intro", "have", "simp", "obtain", "exact", "choose", "simp", "refine", "rw", "apply", "simp"], "tactic_count": 43}
{"name": "Dynamics.exists_isDynCoverOf_of_isCompact_uniformContinuous", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.CoverEntropy", "is_tactic_proof": true, "tactics": ["obtain", "have", "let", "obtain", "exact"], "tactic_count": 5}
{"name": "Dynamics.exists_isDynCoverOf_of_isCompact_invariant", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.CoverEntropy", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "have", "obtain", "rw", "exact"], "tactic_count": 6}
{"name": "Dynamics.coverMincard", "kind": "definition", "module": "Mathlib.Dynamics.TopologicalEntropy.CoverEntropy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.IsDynCoverOf.coverMincard_le_card", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.CoverEntropy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.coverMincard_monotone_time", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.CoverEntropy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.coverMincard_antitone", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.CoverEntropy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.coverMincard_finite_iff", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.CoverEntropy", "is_tactic_proof": true, "tactics": ["refine", "obtain", "rw", "simp", "have", "by_contra", "apply", "rw", "simp", "rw", "exact", "have", "rw", "rw", "simp", "exact"], "tactic_count": 16}
{"name": "Dynamics.coverMincard_empty", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.CoverEntropy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.coverMincard_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.CoverEntropy", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Dynamics.one_le_coverMincard_iff", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.CoverEntropy", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Dynamics.coverMincard_zero", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.CoverEntropy", "is_tactic_proof": true, "tactics": ["apply", "obtain", "have", "rw", "apply", "rw"], "tactic_count": 6}
{"name": "Dynamics.coverMincard_univ", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.CoverEntropy", "is_tactic_proof": true, "tactics": ["apply", "obtain", "have", "rw", "apply", "rw"], "tactic_count": 6}
{"name": "Dynamics.coverMincard_mul_le_pow", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.CoverEntropy", "is_tactic_proof": true, "tactics": ["rcases", "rw", "obtain", "rw", "rcases", "simp", "obtain", "obtain", "rw", "exact"], "tactic_count": 10}
{"name": "Dynamics.coverMincard_le_pow", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.CoverEntropy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.coverMincard_finite_of_isCompact_uniformContinuous", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.CoverEntropy", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Dynamics.coverMincard_finite_of_isCompact_invariant", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.CoverEntropy", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Dynamics.nonempty_inter_of_coverMincard", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.CoverEntropy", "is_tactic_proof": true, "tactics": ["classical", "by_contra", "have", "intro", "specialize", "simp", "simp", "obtain", "refine", "rw", "rw", "exact", "apply", "rw", "exact_mod_cast"], "tactic_count": 15}
{"name": "Dynamics.coverEntropyEntourage", "kind": "definition", "module": "Mathlib.Dynamics.TopologicalEntropy.CoverEntropy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.coverEntropyInfEntourage", "kind": "definition", "module": "Mathlib.Dynamics.TopologicalEntropy.CoverEntropy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.coverEntropyInfEntourage_antitone", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.CoverEntropy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.coverEntropyEntourage_antitone", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.CoverEntropy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.coverEntropyInfEntourage_le_coverEntropyEntourage", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.CoverEntropy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.coverEntropyEntourage_empty", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.CoverEntropy", "is_tactic_proof": true, "tactics": ["simp", "rw"], "tactic_count": 2}
{"name": "Dynamics.coverEntropyInfEntourage_empty", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.CoverEntropy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.coverEntropyInfEntourage_nonneg", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.CoverEntropy", "is_tactic_proof": true, "tactics": ["apply", "exact", "rw", "use", "rw", "exact"], "tactic_count": 6}
{"name": "Dynamics.coverEntropyEntourage_nonneg", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.CoverEntropy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.coverEntropyEntourage_univ", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.CoverEntropy", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Dynamics.coverEntropyInfEntourage_univ", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.CoverEntropy", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Dynamics.coverEntropyEntourage_le_log_coverMincard_div", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.CoverEntropy", "is_tactic_proof": false, "tactics": ["have", "have", "rw", "rw", "apply", "rw", "refine", "rw", "exact"], "tactic_count": 9}
{"name": "Dynamics.IsDynCoverOf.coverEntropyEntourage_le_log_card_div", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.CoverEntropy", "is_tactic_proof": true, "tactics": ["apply", "apply", "exact_mod_cast"], "tactic_count": 3}
{"name": "Dynamics.coverEntropyEntourage_le_coverEntropyInfEntourage", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.CoverEntropy", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "Dynamics.coverEntropyEntourage_finite_of_isCompact_invariant", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.CoverEntropy", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "apply", "apply", "rw", "exact_mod_cast"], "tactic_count": 6}
{"name": "Dynamics.coverEntropy", "kind": "definition", "module": "Mathlib.Dynamics.TopologicalEntropy.CoverEntropy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.coverEntropyInf", "kind": "definition", "module": "Mathlib.Dynamics.TopologicalEntropy.CoverEntropy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.coverEntropyInf_antitone", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.CoverEntropy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.coverEntropy_antitone", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.CoverEntropy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.coverEntropyEntourage_le_coverEntropy", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.CoverEntropy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.coverEntropyInfEntourage_le_coverEntropyInf", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.CoverEntropy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.coverEntropy_eq_iSup_basis", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.CoverEntropy", "is_tactic_proof": false, "tactics": ["refine", "obtain", "exact"], "tactic_count": 3}
{"name": "Dynamics.coverEntropyInf_eq_iSup_basis", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.CoverEntropy", "is_tactic_proof": false, "tactics": ["refine", "obtain", "exact"], "tactic_count": 3}
{"name": "Dynamics.coverEntropyInf_le_coverEntropy", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.CoverEntropy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.coverEntropy_empty", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.CoverEntropy", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Dynamics.coverEntropyInf_empty", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.CoverEntropy", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Dynamics.coverEntropyInf_nonneg", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.CoverEntropy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.coverEntropy_nonneg", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.CoverEntropy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.coverEntropyInf_eq_coverEntropy", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.CoverEntropy", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact", "le_iSup₂_of_le"], "tactic_count": 4}
{"name": "Dynamics.dynEntourage", "kind": "definition", "module": "Mathlib.Dynamics.TopologicalEntropy.DynamicalEntourage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.dynEntourage_eq_inter_Ico", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.DynamicalEntourage", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Dynamics.mem_dynEntourage", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.DynamicalEntourage", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Dynamics.mem_ball_dynEntourage", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.DynamicalEntourage", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Dynamics.dynEntourage_mem_uniformity", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.DynamicalEntourage", "is_tactic_proof": true, "tactics": ["rw", "induction", "zero", "succ", "simp", "rw", "apply", "rw", "exact"], "tactic_count": 9}
{"name": "Dynamics.ball_dynEntourage_mem_nhds", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.DynamicalEntourage", "is_tactic_proof": true, "tactics": ["rw", "intro", "simp", "exact"], "tactic_count": 4}
{"name": "Dynamics.isRefl_dynEntourage", "kind": "instance", "module": "Mathlib.Dynamics.TopologicalEntropy.DynamicalEntourage", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Dynamics.isSymm_dynEntourage", "kind": "instance", "module": "Mathlib.Dynamics.TopologicalEntropy.DynamicalEntourage", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Dynamics.idRel_subset_dynEntourage", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.DynamicalEntourage", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "IsSymmetricRel.dynEntourage", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.DynamicalEntourage", "is_tactic_proof": true, "tactics": ["ext", "simp", "refine", "exact"], "tactic_count": 4}
{"name": "Dynamics.dynEntourage_comp_subset", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.DynamicalEntourage", "is_tactic_proof": true, "tactics": ["simp", "intro", "simp", "rcases", "exact"], "tactic_count": 5}
{"name": "isOpen.dynEntourage", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.DynamicalEntourage", "is_tactic_proof": true, "tactics": ["rw", "refine", "exact"], "tactic_count": 3}
{"name": "Dynamics.dynEntourage_monotone", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.DynamicalEntourage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.dynEntourage_antitone", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.DynamicalEntourage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.dynEntourage_mono", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.DynamicalEntourage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.dynEntourage_zero", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.DynamicalEntourage", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Dynamics.dynEntourage_one", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.DynamicalEntourage", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Dynamics.dynEntourage_univ", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.DynamicalEntourage", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Dynamics.mem_ball_dynEntourage_comp", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.DynamicalEntourage", "is_tactic_proof": true, "tactics": ["rcases", "rw", "exact"], "tactic_count": 3}
{"name": "Function.Semiconj.preimage_dynEntourage", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.DynamicalEntourage", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw"], "tactic_count": 3}
{"name": "Dynamics.IsDynNetIn", "kind": "definition", "module": "Mathlib.Dynamics.TopologicalEntropy.NetEntropy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.IsDynNetIn.of_le", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.NetEntropy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.IsDynNetIn.of_entourage_subset", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.NetEntropy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.isDynNetIn_empty", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.NetEntropy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.isDynNetIn_singleton", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.NetEntropy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.IsDynNetIn.card_le_card_of_isDynCoverOf", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.NetEntropy", "is_tactic_proof": true, "tactics": ["have", "choose", "apply", "exact"], "tactic_count": 4}
{"name": "Dynamics.netMaxcard", "kind": "definition", "module": "Mathlib.Dynamics.TopologicalEntropy.NetEntropy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.IsDynNetIn.card_le_netMaxcard", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.NetEntropy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.netMaxcard_monotone_time", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.NetEntropy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.netMaxcard_antitone", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.NetEntropy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.netMaxcard_finite_iff", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.NetEntropy", "is_tactic_proof": true, "tactics": ["apply", "obtain", "rw", "simp", "have", "rw", "simp", "rw", "have", "refine", "simp", "intro", "rw", "apply", "simp", "exact", "have", "refine", "simp", "exact", "rw", "have", "rw", "simp", "exact", "obtain", "rw", "exact"], "tactic_count": 28}
{"name": "Dynamics.netMaxcard_empty", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.NetEntropy", "is_tactic_proof": true, "tactics": ["rw", "intro", "replace", "norm_cast", "rw"], "tactic_count": 5}
{"name": "Dynamics.netMaxcard_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.NetEntropy", "is_tactic_proof": true, "tactics": ["refine", "rw", "intro", "have", "rw", "replace", "rw", "exact"], "tactic_count": 8}
{"name": "Dynamics.one_le_netMaxcard_iff", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.NetEntropy", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Dynamics.netMaxcard_zero", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.NetEntropy", "is_tactic_proof": true, "tactics": ["apply", "intro", "simp", "norm_cast", "refine", "exact"], "tactic_count": 6}
{"name": "Dynamics.netMaxcard_univ", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.NetEntropy", "is_tactic_proof": true, "tactics": ["apply", "intro", "simp", "norm_cast", "refine", "exact"], "tactic_count": 6}
{"name": "Dynamics.netMaxcard_infinite_iff", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.NetEntropy", "is_tactic_proof": true, "tactics": ["apply", "intro", "rw", "specialize", "simp", "obtain", "exact", "refine", "specialize", "obtain", "apply", "rw", "exact"], "tactic_count": 13}
{"name": "Dynamics.netMaxcard_le_coverMincard", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.NetEntropy", "is_tactic_proof": true, "tactics": ["rcases", "exact", "obtain", "rw", "exact"], "tactic_count": 5}
{"name": "Dynamics.coverMincard_le_netMaxcard", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.NetEntropy", "is_tactic_proof": true, "tactics": ["classical", "rcases", "exact", "obtain", "rw", "apply", "rw", "by_contra", "obtain", "simp", "have", "refine", "refine", "exact", "rw", "apply", "rw", "refine", "exact", "x_uncov"], "tactic_count": 20}
{"name": "Dynamics.netEntropyEntourage", "kind": "definition", "module": "Mathlib.Dynamics.TopologicalEntropy.NetEntropy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.netEntropyInfEntourage", "kind": "definition", "module": "Mathlib.Dynamics.TopologicalEntropy.NetEntropy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.netEntropyInfEntourage_antitone", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.NetEntropy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.netEntropyEntourage_antitone", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.NetEntropy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.netEntropyInfEntourage_le_netEntropyEntourage", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.NetEntropy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.netEntropyEntourage_empty", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.NetEntropy", "is_tactic_proof": true, "tactics": ["rw", "congr", "simp"], "tactic_count": 3}
{"name": "Dynamics.netEntropyInfEntourage_empty", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.NetEntropy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.netEntropyInfEntourage_nonneg", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.NetEntropy", "is_tactic_proof": true, "tactics": ["apply", "exact", "rw", "use", "rw", "exact"], "tactic_count": 6}
{"name": "Dynamics.netEntropyEntourage_nonneg", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.NetEntropy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.netEntropyInfEntourage_univ", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.NetEntropy", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Dynamics.netEntropyEntourage_univ", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.NetEntropy", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Dynamics.netEntropyInfEntourage_le_coverEntropyInfEntourage", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.NetEntropy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.coverEntropyInfEntourage_le_netEntropyInfEntourage", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.NetEntropy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.netEntropyEntourage_le_coverEntropyEntourage", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.NetEntropy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.coverEntropyEntourage_le_netEntropyEntourage", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.NetEntropy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.coverEntropyInf_eq_iSup_netEntropyInfEntourage", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.NetEntropy", "is_tactic_proof": true, "tactics": ["apply", "obtain", "have", "apply", "exact", "apply", "apply", "exact"], "tactic_count": 8}
{"name": "Dynamics.coverEntropy_eq_iSup_netEntropyEntourage", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.NetEntropy", "is_tactic_proof": true, "tactics": ["apply", "obtain", "apply", "have", "exact", "apply", "apply", "exact"], "tactic_count": 8}
{"name": "Dynamics.coverEntropyInf_eq_iSup_basis_netEntropyInfEntourage", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.NetEntropy", "is_tactic_proof": true, "tactics": ["rw", "apply", "refine", "obtain", "apply", "exact"], "tactic_count": 6}
{"name": "Dynamics.coverEntropy_eq_iSup_basis_netEntropyEntourage", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.NetEntropy", "is_tactic_proof": true, "tactics": ["rw", "apply", "refine", "obtain", "apply", "exact"], "tactic_count": 6}
{"name": "Dynamics.netEntropyInfEntourage_le_coverEntropyInf", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.NetEntropy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.netEntropyEntourage_le_coverEntropy", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.NetEntropy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.IsDynCoverOf.image", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.Semiconj", "is_tactic_proof": true, "tactics": ["rintro", "obtain", "refine", "rwa"], "tactic_count": 4}
{"name": "Dynamics.IsDynCoverOf.preimage", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.Semiconj", "is_tactic_proof": true, "tactics": ["classical", "rcases", "exact", "obtain", "choose", "choose", "refine", "simp", "map_apply,", "obtain", "refine", "rw", "exact"], "tactic_count": 13}
{"name": "Dynamics.le_coverMincard_image", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.Semiconj", "is_tactic_proof": true, "tactics": ["rcases", "exact", "obtain", "obtain", "rw", "exact"], "tactic_count": 6}
{"name": "Dynamics.coverMincard_image_le", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.Semiconj", "is_tactic_proof": true, "tactics": ["classical", "rcases", "exact", "obtain", "rw", "have", "rw", "exact"], "tactic_count": 8}
{"name": "Dynamics.le_coverEntropyEntourage_image", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.Semiconj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.le_coverEntropyInfEntourage_image", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.Semiconj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.coverEntropyEntourage_image_le", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.Semiconj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.coverEntropyInfEntourage_image_le", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.Semiconj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.coverEntropy_image_of_comap", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.Semiconj", "is_tactic_proof": true, "tactics": ["let", "apply", "refine", "iSup₂_le", "apply", "rw", "exact", "refine", "simp", "obtain", "obtain", "apply", "apply", "exact"], "tactic_count": 14}
{"name": "Dynamics.coverEntropyInf_image_of_comap", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.Semiconj", "is_tactic_proof": true, "tactics": ["let", "apply", "refine", "iSup₂_le", "apply", "rw", "exact", "refine", "simp", "obtain", "obtain", "apply", "apply", "exact"], "tactic_count": 14}
{"name": "Dynamics.coverEntropy_restrict_subset", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.Semiconj", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Dynamics.coverEntropyInf_restrict_subset", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.Semiconj", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Dynamics.coverEntropy_restrict", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.Semiconj", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Dynamics.coverEntropy_image_le_of_uniformContinuous", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.Semiconj", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Dynamics.coverEntropyInf_image_le_of_uniformContinuous", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.Semiconj", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Dynamics.coverEntropy_image_le_of_uniformContinuousOn_invariant", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.Semiconj", "is_tactic_proof": true, "tactics": ["rw", "have", "intro", "rw", "apply", "rw"], "tactic_count": 6}
{"name": "Dynamics.coverEntropyInf_image_le_of_uniformContinuousOn_invariant", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.Semiconj", "is_tactic_proof": true, "tactics": ["rw", "have", "intro", "rw", "apply", "rw"], "tactic_count": 6}
{"name": "Dynamics.IsDynCoverOf.monotone_subset", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.Subset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.IsDynNetIn.monotone_subset", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.Subset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.coverMincard_monotone_subset", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.Subset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.netMaxcard_monotone_subset", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.Subset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.coverEntropyInfEntourage_monotone", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.Subset", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "Dynamics.coverEntropyEntourage_monotone", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.Subset", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "Dynamics.netEntropyInfEntourage_monotone", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.Subset", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "Dynamics.netEntropyEntourage_monotone", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.Subset", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "Dynamics.coverEntropyInf_monotone", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.Subset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.coverEntropy_monotone", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.Subset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.IsDynCoverOf.closure", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.Subset", "is_tactic_proof": true, "tactics": ["rcases", "refine", "obtain", "obtain", "exact"], "tactic_count": 5}
{"name": "Dynamics.coverMincard_closure_le", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.Subset", "is_tactic_proof": true, "tactics": ["rcases", "exact", "obtain", "exact"], "tactic_count": 4}
{"name": "Dynamics.coverEntropyInfEntourage_closure", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.Subset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.coverEntropyEntourage_closure", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.Subset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.coverEntropyInf_closure", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.Subset", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact", "le_iSup₂_of_le"], "tactic_count": 4}
{"name": "Dynamics.coverEntropy_closure", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.Subset", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact", "le_iSup₂_of_le"], "tactic_count": 4}
{"name": "Dynamics.IsDynCoverOf.union", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.Subset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.coverMincard_union_le", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.Subset", "is_tactic_proof": true, "tactics": ["classical", "rcases", "rw", "rcases", "rw", "obtain", "obtain", "rw", "apply", "rw", "exact"], "tactic_count": 11}
{"name": "Dynamics.coverEntropyEntourage_union", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.Subset", "is_tactic_proof": true, "tactics": ["refine", "apply", "rw", "exact", "exact", "max_le"], "tactic_count": 6}
{"name": "Dynamics.coverEntropy_union", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.Subset", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Dynamics.coverEntropyInf_iUnion_le", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.Subset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.coverEntropy_iUnion_le", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.Subset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.coverEntropyInf_biUnion_le", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.Subset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.coverEntropy_biUnion_le", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.Subset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.coverEntropy_supBotHom", "kind": "definition", "module": "Mathlib.Dynamics.TopologicalEntropy.Subset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.coverEntropy_iUnion_of_finite", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.Subset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dynamics.coverEntropy_biUnion_finset", "kind": "theorem", "module": "Mathlib.Dynamics.TopologicalEntropy.Subset", "is_tactic_proof": true, "tactics": ["have", "rw", "rw", "congr"], "tactic_count": 4}
{"name": "MulAction.isTopologicallyTransitive_iff", "kind": "theorem", "module": "Mathlib.Dynamics.Transitive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.isTopologicallyTransitive_iff_dense_iUnion", "kind": "theorem", "module": "Mathlib.Dynamics.Transitive", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "MulAction.isTopologicallyTransitive_iff_dense_iUnion_preimage", "kind": "theorem", "module": "Mathlib.Dynamics.Transitive", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "IsOpen.dense_iUnion_smul", "kind": "theorem", "module": "Mathlib.Dynamics.Transitive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.dense_iUnion_preimage_smul", "kind": "theorem", "module": "Mathlib.Dynamics.Transitive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.dense_of_preimage_smul_invariant", "kind": "theorem", "module": "Mathlib.Dynamics.Transitive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.isTopologicallyTransitive_iff_dense_of_preimage_invariant", "kind": "theorem", "module": "Mathlib.Dynamics.Transitive", "is_tactic_proof": true, "tactics": ["refine", "refine", "refine", "exact", "simp", "exact"], "tactic_count": 6}
{"name": "MulAction.isTopologicallyTransitive_of_isMinimal", "kind": "instance", "module": "Mathlib.Dynamics.Transitive", "is_tactic_proof": true, "tactics": ["refine", "simp"], "tactic_count": 2}
{"name": "gal_zero_isSolvable", "kind": "theorem", "module": "Mathlib.FieldTheory.AbelRuffini", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "gal_one_isSolvable", "kind": "theorem", "module": "Mathlib.FieldTheory.AbelRuffini", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "gal_C_isSolvable", "kind": "theorem", "module": "Mathlib.FieldTheory.AbelRuffini", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "gal_X_isSolvable", "kind": "theorem", "module": "Mathlib.FieldTheory.AbelRuffini", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "gal_X_sub_C_isSolvable", "kind": "theorem", "module": "Mathlib.FieldTheory.AbelRuffini", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "gal_X_pow_isSolvable", "kind": "theorem", "module": "Mathlib.FieldTheory.AbelRuffini", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "gal_mul_isSolvable", "kind": "theorem", "module": "Mathlib.FieldTheory.AbelRuffini", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "gal_prod_isSolvable", "kind": "theorem", "module": "Mathlib.FieldTheory.AbelRuffini", "is_tactic_proof": true, "tactics": ["apply", "exact", "intro", "rw", "exact"], "tactic_count": 5}
{"name": "gal_isSolvable_of_splits", "kind": "theorem", "module": "Mathlib.FieldTheory.AbelRuffini", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "gal_isSolvable_tower", "kind": "theorem", "module": "Mathlib.FieldTheory.AbelRuffini", "is_tactic_proof": true, "tactics": ["let", "let", "haveI", "let", "have", "haveI", "haveI", "exact"], "tactic_count": 8}
{"name": "gal_X_pow_sub_one_isSolvable", "kind": "theorem", "module": "Mathlib.FieldTheory.AbelRuffini", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "exact", "have", "have", "apply", "intro", "ext", "simp", "have", "intro", "lift", "exact", "obtain", "obtain", "rw"], "tactic_count": 16}
{"name": "gal_X_pow_sub_C_isSolvable_aux", "kind": "theorem", "module": "Mathlib.FieldTheory.AbelRuffini", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "exact", "have", "mt", "by_cases", "rw", "exact", "have", "have", "have", "have", "apply", "intro", "ext", "rw", "have", "intro", "rw", "exact", "have", "intro", "have", "obtain", "use", "rw", "obtain", "obtain", "rw", "mul_right_inj"], "tactic_count": 30}
{"name": "splits_X_pow_sub_one_of_X_pow_sub_C", "kind": "theorem", "module": "Mathlib.FieldTheory.AbelRuffini", "is_tactic_proof": true, "tactics": ["have", "by_cases", "simp", "have", "have", "obtain", "rw", "have", "intro", "rw", "exact", "let", "have", "rw", "have", "rw", "use", "rw", "have", "have", "rw", "pow_comp,", "have", "ext1", "dsimp", "rw", "rw", "rfl"], "tactic_count": 28}
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{"name": "IsSolvableByRad", "kind": "inductive", "module": "Mathlib.FieldTheory.AbelRuffini", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "solvableByRad", "kind": "definition", "module": "Mathlib.FieldTheory.AbelRuffini", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "solvableByRad.isSolvable", "kind": "theorem", "module": "Mathlib.FieldTheory.AbelRuffini", "is_tactic_proof": true, "tactics": ["revert", "apply", "exact", "exact", "induction2", "exact", "exact", "induction2", "exact", "exact"], "tactic_count": 10}
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{"name": "Field.absoluteGaloisGroup", "kind": "definition", "module": "Mathlib.FieldTheory.AbsoluteGaloisGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.FieldTheory.AbsoluteGaloisGroup.0.Field.termG_K", "kind": "definition", "module": "Mathlib.FieldTheory.AbsoluteGaloisGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Field.instGroupAbsoluteGaloisGroup", "kind": "instance", "module": "Mathlib.FieldTheory.AbsoluteGaloisGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Field.instTopologicalSpaceAbsoluteGaloisGroup", "kind": "instance", "module": "Mathlib.FieldTheory.AbsoluteGaloisGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Field.absoluteGaloisGroupAbelianization", "kind": "abbrev", "module": "Mathlib.FieldTheory.AbsoluteGaloisGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "algebraicClosure_toSubalgebra", "kind": "theorem", "module": "Mathlib.FieldTheory.AlgebraicClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "algebraicClosure.isAlgebraic", "kind": "instance", "module": "Mathlib.FieldTheory.AlgebraicClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "algebraicClosure.isIntegralClosure", "kind": "instance", "module": "Mathlib.FieldTheory.AlgebraicClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Transcendental.algebraicClosure", "kind": "theorem", "module": "Mathlib.FieldTheory.AlgebraicClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_algebraicClosure'", "kind": "theorem", "module": "Mathlib.FieldTheory.AlgebraicClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "algebraicClosure.eq_top_iff", "kind": "theorem", "module": "Mathlib.FieldTheory.AlgebraicClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "algebraicClosure.le_restrictScalars", "kind": "theorem", "module": "Mathlib.FieldTheory.AlgebraicClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "algebraicClosure.eq_restrictScalars_of_isAlgebraic", "kind": "theorem", "module": "Mathlib.FieldTheory.AlgebraicClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Splits.algebraicClosure", "kind": "theorem", "module": "Mathlib.FieldTheory.AlgebraicClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "_private.Mathlib.FieldTheory.CardinalEmb.0.Field.Emb.Cardinal.termι", "kind": "definition", "module": "Mathlib.FieldTheory.CardinalEmb", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "_private.Mathlib.FieldTheory.CardinalEmb.0.Field.Emb.Cardinal.termB", "kind": "definition", "module": "Mathlib.FieldTheory.CardinalEmb", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Field.Emb.Cardinal.adjoin_basis_eq_top", "kind": "theorem", "module": "Mathlib.FieldTheory.CardinalEmb", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Field.Emb.Cardinal.noMaxOrder_rank_toType", "kind": "theorem", "module": "Mathlib.FieldTheory.CardinalEmb", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Field.Emb.Cardinal.isLeast_leastExt", "kind": "theorem", "module": "Mathlib.FieldTheory.CardinalEmb", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
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{"name": "Field.Emb.Cardinal.iSup_adjoin_eq_top", "kind": "theorem", "module": "Mathlib.FieldTheory.CardinalEmb", "is_tactic_proof": true, "tactics": ["simp_rw", "rintro", "refine", "exact"], "tactic_count": 4}
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{"name": "Field.Emb.Cardinal.succEquiv_coherence", "kind": "theorem", "module": "Mathlib.FieldTheory.CardinalEmb", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Field.Emb.Cardinal.instFiniteDimensionalSubtypeMemIntermediateFieldAdjoinImageToTypeOrdRankCompCoeBasisWellOrderedBasisLeastExtIioSingletonSet", "kind": "instance", "module": "Mathlib.FieldTheory.CardinalEmb", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Field.Emb.Cardinal.two_le_deg", "kind": "theorem", "module": "Mathlib.FieldTheory.CardinalEmb", "is_tactic_proof": false, "tactics": ["rw", "finSepDegree,", "by_contra", "obtain", "refine", "exact"], "tactic_count": 6}
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{"name": "Field.Emb.Cardinal.iSup_filtration", "kind": "theorem", "module": "Mathlib.FieldTheory.CardinalEmb", "is_tactic_proof": true, "tactics": ["cases", "rw", "refine", "rintro", "refine", "exacts"], "tactic_count": 6}
{"name": "Field.Emb.Cardinal.eq_bot_of_not_nonempty", "kind": "theorem", "module": "Mathlib.FieldTheory.CardinalEmb", "is_tactic_proof": true, "tactics": ["cases", "have", "rw", "exact"], "tactic_count": 4}
{"name": "Field.Emb.Cardinal.equivLim", "kind": "definition", "module": "Mathlib.FieldTheory.CardinalEmb", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Field.Emb.Cardinal.equivLim_coherence", "kind": "theorem", "module": "Mathlib.FieldTheory.CardinalEmb", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Field.Emb.Cardinal.embEquivPi", "kind": "definition", "module": "Mathlib.FieldTheory.CardinalEmb", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Field.Emb.cardinal_eq_two_pow_rank", "kind": "theorem", "module": "Mathlib.FieldTheory.CardinalEmb", "is_tactic_proof": true, "tactics": ["haveI", "rw", "apply", "rw", "conv_rhs", "exact", "conv_lhs", "exact"], "tactic_count": 8}
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{"name": "Field.Emb.cardinal_eq_two_pow_sepDegree", "kind": "theorem", "module": "Mathlib.FieldTheory.CardinalEmb", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
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{"name": "Fintype.isPrimePow_card_of_field", "kind": "theorem", "module": "Mathlib.FieldTheory.Cardinality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "mem_bot_iff_intCast", "kind": "theorem", "module": "Mathlib.FieldTheory.Finite.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "Subfield.fintypeBot", "kind": "definition", "module": "Mathlib.FieldTheory.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.roots_X_pow_char_sub_X_bot", "kind": "theorem", "module": "Mathlib.FieldTheory.Finite.Basic", "is_tactic_proof": true, "tactics": ["let", "conv_lhs", "exact"], "tactic_count": 3}
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{"name": "FiniteField.Extension", "kind": "definition", "module": "Mathlib.FieldTheory.Finite.Extension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "FiniteField.instAlgebraExtension", "kind": "instance", "module": "Mathlib.FieldTheory.Finite.Extension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "FiniteField.instIsScalarTowerZModExtension", "kind": "instance", "module": "Mathlib.FieldTheory.Finite.Extension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteField.natCard_extension", "kind": "theorem", "module": "Mathlib.FieldTheory.Finite.Extension", "is_tactic_proof": true, "tactics": ["letI", "rw"], "tactic_count": 2}
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{"name": "FiniteField._example", "kind": "example", "module": "Mathlib.FieldTheory.Finite.Extension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteField._example", "kind": "example", "module": "Mathlib.FieldTheory.Finite.Extension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "galois_poly_separable", "kind": "theorem", "module": "Mathlib.FieldTheory.Finite.GaloisField", "is_tactic_proof": true, "tactics": ["use", "rw", "rw", "ring"], "tactic_count": 4}
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{"name": "MvPolynomial.C_dvd_iff_zmod", "kind": "theorem", "module": "Mathlib.FieldTheory.Finite.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MvPolynomial.instInhabitedR", "kind": "instance", "module": "Mathlib.FieldTheory.Finite.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MvPolynomial.decidableRestrictDegree", "kind": "instance", "module": "Mathlib.FieldTheory.Finite.Polynomial", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MvPolynomial.rank_R", "kind": "theorem", "module": "Mathlib.FieldTheory.Finite.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.instFiniteDimensionalROfFinite", "kind": "instance", "module": "Mathlib.FieldTheory.Finite.Polynomial", "is_tactic_proof": true, "tactics": ["cases", "rw", "simpa"], "tactic_count": 3}
{"name": "MvPolynomial.finrank_R", "kind": "theorem", "module": "Mathlib.FieldTheory.Finite.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.range_evalᵢ", "kind": "theorem", "module": "Mathlib.FieldTheory.Finite.Polynomial", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
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{"name": "MvPolynomial.eq_zero_of_eval_eq_zero", "kind": "theorem", "module": "Mathlib.FieldTheory.Finite.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteField.trace_to_zmod_nondegenerate", "kind": "theorem", "module": "Mathlib.FieldTheory.Finite.Trace", "is_tactic_proof": true, "tactics": ["haveI", "have", "simp_rw", "by_contra", "exact"], "tactic_count": 5}
{"name": "FiniteField.algebraMap_trace_eq_sum_pow", "kind": "theorem", "module": "Mathlib.FieldTheory.Finite.Trace", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "exact", "sum_bijective", "rw"], "tactic_count": 6}
{"name": "FiniteField.algebraMap_norm_eq_prod_pow", "kind": "theorem", "module": "Mathlib.FieldTheory.Finite.Trace", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "exact", "prod_bijective", "rw"], "tactic_count": 6}
{"name": "FiniteField.algebraMap_norm_eq_pow_sum", "kind": "theorem", "module": "Mathlib.FieldTheory.Finite.Trace", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsNoetherian.iff_rank_lt_aleph0", "kind": "theorem", "module": "Mathlib.FieldTheory.Finiteness", "is_tactic_proof": true, "tactics": ["let", "rw", "constructor", "intro", "exact", "intro", "refine", "refine", "rw"], "tactic_count": 9}
{"name": "IsNoetherian.fintypeBasisIndex", "kind": "definition", "module": "Mathlib.FieldTheory.Finiteness", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsNoetherian.instFintypeElemOfVectorSpaceIndex", "kind": "instance", "module": "Mathlib.FieldTheory.Finiteness", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsNoetherian.finite_basis_index", "kind": "theorem", "module": "Mathlib.FieldTheory.Finiteness", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsNoetherian.finsetBasisIndex", "kind": "definition", "module": "Mathlib.FieldTheory.Finiteness", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsNoetherian.coe_finsetBasisIndex", "kind": "theorem", "module": "Mathlib.FieldTheory.Finiteness", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsNoetherian.coeSort_finsetBasisIndex", "kind": "theorem", "module": "Mathlib.FieldTheory.Finiteness", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsNoetherian.finsetBasis", "kind": "definition", "module": "Mathlib.FieldTheory.Finiteness", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsNoetherian.range_finsetBasis", "kind": "theorem", "module": "Mathlib.FieldTheory.Finiteness", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Module.card_eq_pow_finrank", "kind": "theorem", "module": "Mathlib.FieldTheory.Finiteness", "is_tactic_proof": true, "tactics": ["let", "rw"], "tactic_count": 2}
{"name": "Module.natCard_eq_pow_finrank", "kind": "theorem", "module": "Mathlib.FieldTheory.Finiteness", "is_tactic_proof": true, "tactics": ["let", "rw"], "tactic_count": 2}
{"name": "IsNoetherian.iff_fg", "kind": "theorem", "module": "Mathlib.FieldTheory.Finiteness", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "convert", "simp⟩⟩", "rintro", "rw", "exact"], "tactic_count": 8}
{"name": "FixedBy.subfield", "kind": "definition", "module": "Mathlib.FieldTheory.Fixed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FixedBy.subfield_mem_iff", "kind": "theorem", "module": "Mathlib.FieldTheory.Fixed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FixedBy.intermediateField", "kind": "definition", "module": "Mathlib.FieldTheory.Fixed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FixedBy.intermediateField_mem_iff", "kind": "theorem", "module": "Mathlib.FieldTheory.Fixed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsInvariantSubfield.toMulSemiringAction", "kind": "instance", "module": "Mathlib.FieldTheory.Fixed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsInvariantSubringOfIsInvariantSubfield", "kind": "instance", "module": "Mathlib.FieldTheory.Fixed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FixedPoints.subfield", "kind": "definition", "module": "Mathlib.FieldTheory.Fixed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FixedPoints.instIsInvariantSubfieldSubfield", "kind": "instance", "module": "Mathlib.FieldTheory.Fixed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FixedPoints.instSMulCommClassSubtypeMemSubfieldSubfield", "kind": "instance", "module": "Mathlib.FieldTheory.Fixed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FixedPoints.smulCommClass'", "kind": "instance", "module": "Mathlib.FieldTheory.Fixed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FixedPoints.smul", "kind": "theorem", "module": "Mathlib.FieldTheory.Fixed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FixedPoints.smul_polynomial", "kind": "theorem", "module": "Mathlib.FieldTheory.Fixed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FixedPoints.instAlgebraSubtypeMemSubfieldSubfield", "kind": "instance", "module": "Mathlib.FieldTheory.Fixed", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "FixedPoints.coe_algebraMap", "kind": "theorem", "module": "Mathlib.FieldTheory.Fixed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FixedPoints.linearIndependent_smul_of_linearIndependent", "kind": "theorem", "module": "Mathlib.FieldTheory.Fixed", "is_tactic_proof": true, "tactics": ["classical", "have", "refine", "rw", "rw", "rw", "rw", "rw", "suffices", "replace", "simp_rw", "refine", "change", "exact", "intro", "refine", "eq_of_sub_eq_zero", "refine", "ext", "conv_lhs", "rw", "congr", "skip", "ext", "rw", "rw", "conv_lhs", "congr", "skip", "ext", "rw", "change", "rw", "rw"], "tactic_count": 34}
{"name": "FixedPoints.minpoly", "kind": "definition", "module": "Mathlib.FieldTheory.Fixed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FixedPoints.minpoly.monic", "kind": "theorem", "module": "Mathlib.FieldTheory.Fixed", "is_tactic_proof": true, "tactics": ["simp", "rw", "exact"], "tactic_count": 3}
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{"name": "FixedPoints.minpoly.ne_one", "kind": "theorem", "module": "Mathlib.FieldTheory.Fixed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FixedPoints.minpoly.of_eval₂", "kind": "theorem", "module": "Mathlib.FieldTheory.Fixed", "is_tactic_proof": true, "tactics": ["classical", "rw", "refine", "rw", "map_smul,"], "tactic_count": 5}
{"name": "FixedPoints.minpoly.irreducible_aux", "kind": "theorem", "module": "Mathlib.FieldTheory.Fixed", "is_tactic_proof": true, "tactics": ["have", "have", "have", "rw", "rcases", "right", "have", "rwa", "left", "have", "rwa"], "tactic_count": 11}
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{"name": "FixedPoints.isIntegral", "kind": "theorem", "module": "Mathlib.FieldTheory.Fixed", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "FixedPoints.minpoly_eq_minpoly", "kind": "theorem", "module": "Mathlib.FieldTheory.Fixed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FixedPoints.rank_le_card", "kind": "theorem", "module": "Mathlib.FieldTheory.Fixed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FixedPoints.normal", "kind": "instance", "module": "Mathlib.FieldTheory.Fixed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FixedPoints.isSeparable", "kind": "instance", "module": "Mathlib.FieldTheory.Fixed", "is_tactic_proof": true, "tactics": ["classical", "exact", "cases", "rw", "exact"], "tactic_count": 5}
{"name": "FixedPoints.instFiniteDimensionalSubtypeMemSubfieldSubfield", "kind": "instance", "module": "Mathlib.FieldTheory.Fixed", "is_tactic_proof": true, "tactics": ["cases", "exact"], "tactic_count": 2}
{"name": "FixedPoints.finrank_le_card", "kind": "theorem", "module": "Mathlib.FieldTheory.Fixed", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "linearIndependent_toLinearMap", "kind": "theorem", "module": "Mathlib.FieldTheory.Fixed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cardinalMk_algHom", "kind": "theorem", "module": "Mathlib.FieldTheory.Fixed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.fintype", "kind": "instance", "module": "Mathlib.FieldTheory.Fixed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finrank_algHom", "kind": "theorem", "module": "Mathlib.FieldTheory.Fixed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.card_le", "kind": "theorem", "module": "Mathlib.FieldTheory.Fixed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.card_le", "kind": "theorem", "module": "Mathlib.FieldTheory.Fixed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FixedPoints.finrank_eq_card", "kind": "theorem", "module": "Mathlib.FieldTheory.Fixed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FixedPoints.toAlgHom_bijective", "kind": "theorem", "module": "Mathlib.FieldTheory.Fixed", "is_tactic_proof": true, "tactics": ["cases", "rw", "constructor", "exact", "apply", "exact", "rw", "exact"], "tactic_count": 8}
{"name": "FixedPoints.toAlgHomEquiv", "kind": "definition", "module": "Mathlib.FieldTheory.Fixed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FixedPoints.toAlgAut_bijective", "kind": "theorem", "module": "Mathlib.FieldTheory.Fixed", "is_tactic_proof": true, "tactics": ["refine", "rwa"], "tactic_count": 2}
{"name": "FixedPoints.toAlgAutMulEquiv", "kind": "definition", "module": "Mathlib.FieldTheory.Fixed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FixedPoints.toAlgAut_surjective", "kind": "theorem", "module": "Mathlib.FieldTheory.Fixed", "is_tactic_proof": true, "tactics": ["let", "let", "let", "have", "intro", "refine", "rwa", "intro", "obtain", "revert", "refine", "rwa"], "tactic_count": 12}
{"name": "IsAbelianGalois.tower_bot", "kind": "theorem", "module": "Mathlib.FieldTheory.Galois.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAbelianGalois.tower_top", "kind": "theorem", "module": "Mathlib.FieldTheory.Galois.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAbelianGalois.of_algHom", "kind": "theorem", "module": "Mathlib.FieldTheory.Galois.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsAbelianGaloisSubtypeMemIntermediateField", "kind": "instance", "module": "Mathlib.FieldTheory.Galois.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsAbelianGaloisSubtypeMemIntermediateField_1", "kind": "instance", "module": "Mathlib.FieldTheory.Galois.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsAbelianGalois", "kind": "instance", "module": "Mathlib.FieldTheory.Galois.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsAbelianGaloisSubtypeMemIntermediateFieldBot", "kind": "instance", "module": "Mathlib.FieldTheory.Galois.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAbelianGalois.of_isCyclic", "kind": "theorem", "module": "Mathlib.FieldTheory.Galois.Abelian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isGalois_iff", "kind": "theorem", "module": "Mathlib.FieldTheory.Galois.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGalois.self", "kind": "instance", "module": "Mathlib.FieldTheory.Galois.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGalois.integral", "kind": "theorem", "module": "Mathlib.FieldTheory.Galois.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGalois.separable", "kind": "theorem", "module": "Mathlib.FieldTheory.Galois.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGalois.splits", "kind": "theorem", "module": "Mathlib.FieldTheory.Galois.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGalois.of_fixed_field", "kind": "instance", "module": "Mathlib.FieldTheory.Galois.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGalois.IntermediateField.AdjoinSimple.card_aut_eq_finrank", "kind": "theorem", "module": "Mathlib.FieldTheory.Galois.Basic", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "IsGalois.card_aut_eq_finrank", "kind": "theorem", "module": "Mathlib.FieldTheory.Galois.Basic", "is_tactic_proof": true, "tactics": ["obtain", "let", "invFun", "map_mul", "map_add", "commutes", "have", "have", "have", "replace", "simpa", "rw", "rw", "apply", "exact"], "tactic_count": 15}
{"name": "IsGalois.finiteDimensional_of_finite", "kind": "theorem", "module": "Mathlib.FieldTheory.Galois.Basic", "is_tactic_proof": true, "tactics": ["by_contra", "obtain", "let", "have", "have", "rw", "exact"], "tactic_count": 7}
{"name": "IsGalois.tower_top_of_isGalois", "kind": "theorem", "module": "Mathlib.FieldTheory.Galois.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGalois.tower_top_intermediateField", "kind": "instance", "module": "Mathlib.FieldTheory.Galois.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isGalois_iff_isGalois_bot", "kind": "theorem", "module": "Mathlib.FieldTheory.Galois.Basic", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "intro"], "tactic_count": 4}
{"name": "IsGalois.of_algEquiv", "kind": "theorem", "module": "Mathlib.FieldTheory.Galois.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.transfer_galois", "kind": "theorem", "module": "Mathlib.FieldTheory.Galois.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isGalois_iff_isGalois_top", "kind": "theorem", "module": "Mathlib.FieldTheory.Galois.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isGalois_bot", "kind": "instance", "module": "Mathlib.FieldTheory.Galois.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGalois.of_equiv_equiv", "kind": "theorem", "module": "Mathlib.FieldTheory.Galois.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FixedPoints.intermediateField", "kind": "definition", "module": "Mathlib.FieldTheory.Galois.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FixedPoints.mem_intermediateField_iff", "kind": "theorem", "module": "Mathlib.FieldTheory.Galois.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.fixedField", "kind": "definition", "module": "Mathlib.FieldTheory.Galois.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.mem_fixedField_iff", "kind": "theorem", "module": "Mathlib.FieldTheory.Galois.Basic", "is_tactic_proof": true, "tactics": ["change", "simp"], "tactic_count": 2}
{"name": "IntermediateField.fixedField_bot", "kind": "theorem", "module": "Mathlib.FieldTheory.Galois.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "IntermediateField.finrank_fixedField_eq_card", "kind": "theorem", "module": "Mathlib.FieldTheory.Galois.Basic", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "IntermediateField.fixingSubgroup", "kind": "definition", "module": "Mathlib.FieldTheory.Galois.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.le_iff_le", "kind": "theorem", "module": "Mathlib.FieldTheory.Galois.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.fixingSubgroup_le", "kind": "theorem", "module": "Mathlib.FieldTheory.Galois.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.fixedField_le", "kind": "theorem", "module": "Mathlib.FieldTheory.Galois.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.fixingSubgroup_antitone", "kind": "theorem", "module": "Mathlib.FieldTheory.Galois.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.fixedField_antitone", "kind": "theorem", "module": "Mathlib.FieldTheory.Galois.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.mem_fixingSubgroup_iff", "kind": "theorem", "module": "Mathlib.FieldTheory.Galois.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.fixingSubgroup_top", "kind": "theorem", "module": "Mathlib.FieldTheory.Galois.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "IntermediateField.fixingSubgroup_bot", "kind": "theorem", "module": "Mathlib.FieldTheory.Galois.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "IntermediateField.fixingSubgroup_sup", "kind": "theorem", "module": "Mathlib.FieldTheory.Galois.Basic", "is_tactic_proof": true, "tactics": ["ext", "exact", "simp"], "tactic_count": 3}
{"name": "IntermediateField.fixingSubgroupEquiv", "kind": "definition", "module": "Mathlib.FieldTheory.Galois.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.fixingSubgroup_fixedField", "kind": "theorem", "module": "Mathlib.FieldTheory.Galois.Basic", "is_tactic_proof": true, "tactics": ["have", "classical", "suffices", "exact", "apply", "refine", "refine", "exact"], "tactic_count": 8}
{"name": "IntermediateField.subgroupEquivAlgEquiv", "kind": "definition", "module": "Mathlib.FieldTheory.Galois.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "IntermediateField.fixedField.algebra", "kind": "instance", "module": "Mathlib.FieldTheory.Galois.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.fixedField.isScalarTower", "kind": "instance", "module": "Mathlib.FieldTheory.Galois.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGalois.fixedField_fixingSubgroup", "kind": "theorem", "module": "Mathlib.FieldTheory.Galois.Basic", "is_tactic_proof": false, "tactics": ["have", "suffices", "exact", "classical", "rw", "exact"], "tactic_count": 6}
{"name": "IsGalois.fixedField_top", "kind": "theorem", "module": "Mathlib.FieldTheory.Galois.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsGalois.mem_bot_iff_fixed", "kind": "theorem", "module": "Mathlib.FieldTheory.Galois.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "IsGalois.mem_range_algebraMap_iff_fixed", "kind": "theorem", "module": "Mathlib.FieldTheory.Galois.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGalois.card_fixingSubgroup_eq_finrank", "kind": "theorem", "module": "Mathlib.FieldTheory.Galois.Basic", "is_tactic_proof": true, "tactics": ["conv_rhs"], "tactic_count": 1}
{"name": "IsGalois.intermediateFieldEquivSubgroup", "kind": "definition", "module": "Mathlib.FieldTheory.Galois.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGalois.ofDual_intermediateFieldEquivSubgroup_apply", "kind": "theorem", "module": "Mathlib.FieldTheory.Galois.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGalois.intermediateFieldEquivSubgroup_symm_apply", "kind": "theorem", "module": "Mathlib.FieldTheory.Galois.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGalois.intermediateFieldEquivSubgroup_symm_apply_toDual", "kind": "theorem", "module": "Mathlib.FieldTheory.Galois.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGalois.galoisInsertionIntermediateFieldSubgroup", "kind": "definition", "module": "Mathlib.FieldTheory.Galois.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGalois.galoisCoinsertionIntermediateFieldSubgroup", "kind": "definition", "module": "Mathlib.FieldTheory.Galois.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "IsGaloisGroup.ofDual_intermediateFieldEquivSubgroup_apply", "kind": "theorem", "module": "Mathlib.FieldTheory.Galois.IsGaloisGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGaloisGroup.intermediateFieldEquivSubgroup_symm_apply", "kind": "theorem", "module": "Mathlib.FieldTheory.Galois.IsGaloisGroup", "is_tactic_proof": true, "tactics": ["obtain", "simp"], "tactic_count": 2}
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{"name": "delabGal", "kind": "definition", "module": "Mathlib.FieldTheory.Galois.Notation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteGaloisIntermediateField.finGaloisGroup", "kind": "definition", "module": "Mathlib.FieldTheory.Galois.Profinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finGaloisGroupMap", "kind": "definition", "module": "Mathlib.FieldTheory.Galois.Profinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finGaloisGroupMap.map_id", "kind": "theorem", "module": "Mathlib.FieldTheory.Galois.Profinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "InfiniteGalois.asProfiniteGaloisGroupFunctor", "kind": "abbrev", "module": "Mathlib.FieldTheory.Galois.Profinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfiniteGalois.algEquivToLimit", "kind": "definition", "module": "Mathlib.FieldTheory.Galois.Profinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfiniteGalois.restrictNormalHom_continuous", "kind": "theorem", "module": "Mathlib.FieldTheory.Galois.Profinite", "is_tactic_proof": true, "tactics": ["apply", "intro", "rw", "obtain", "have", "apply", "use", "constructor", "intro", "apply", "simp", "intro", "have", "dsimp", "rw", "exact", "exact"], "tactic_count": 17}
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{"name": "InfiniteGalois.proj", "kind": "definition", "module": "Mathlib.FieldTheory.Galois.Profinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfiniteGalois.finGaloisGroupFunctor_map_proj_eq_proj", "kind": "theorem", "module": "Mathlib.FieldTheory.Galois.Profinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "InfiniteGalois.mk_toAlgEquivAux", "kind": "theorem", "module": "Mathlib.FieldTheory.Galois.Profinite", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "InfiniteGalois.toAlgEquivAux_eq_liftNormal", "kind": "theorem", "module": "Mathlib.FieldTheory.Galois.Profinite", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "InfiniteGalois.limitToAlgEquiv", "kind": "definition", "module": "Mathlib.FieldTheory.Galois.Profinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfiniteGalois.mulEquivToLimit", "kind": "definition", "module": "Mathlib.FieldTheory.Galois.Profinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfiniteGalois.krullTopology_mem_nhds_one_iff_of_isGalois", "kind": "theorem", "module": "Mathlib.FieldTheory.Galois.Profinite", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "InfiniteGalois.isOpen_mulEquivToLimit_image_fixingSubgroup", "kind": "theorem", "module": "Mathlib.FieldTheory.Galois.Profinite", "is_tactic_proof": true, "tactics": ["let", "suffices", "rw", "exact", "ext", "obtain", "simpa"], "tactic_count": 7}
{"name": "InfiniteGalois.mulEquivToLimit_symm_continuous", "kind": "theorem", "module": "Mathlib.FieldTheory.Galois.Profinite", "is_tactic_proof": true, "tactics": ["apply", "simp", "intro", "rw", "use", "simp", "simpa"], "tactic_count": 7}
{"name": "InfiniteGalois.continuousMulEquivToLimit", "kind": "definition", "module": "Mathlib.FieldTheory.Galois.Profinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfiniteGalois.instCompactSpaceAlgEquivOfIsGalois", "kind": "instance", "module": "Mathlib.FieldTheory.Galois.Profinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfiniteGalois.profiniteGalGrp", "kind": "definition", "module": "Mathlib.FieldTheory.Galois.Profinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfiniteGalois.profiniteGalGrpIsoLimit", "kind": "definition", "module": "Mathlib.FieldTheory.Galois.Profinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.algebra_adjoin_le_adjoin", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.algebraAdjoinAdjoin.instAlgebraSubtypeMemSubalgebraAdjoinAdjoin", "kind": "instance", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.algebraAdjoinAdjoin.instIsScalarTowerSubtypeMemSubalgebraAdjoinAdjoin", "kind": "instance", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.algebraAdjoinAdjoin.instIsScalarTowerSubtypeMemSubalgebraAdjoinAdjoin_1", "kind": "instance", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.algebraAdjoinAdjoin.instFaithfulSMulSubtypeMemSubalgebraAdjoinAdjoin", "kind": "instance", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.algebraAdjoinAdjoin.instIsFractionRingSubtypeMemSubalgebraAdjoinAdjoin", "kind": "instance", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.algebraAdjoinAdjoin.instIsAlgebraicSubtypeMemSubalgebraAdjoinAdjoin", "kind": "instance", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.adjoin_eq_algebra_adjoin", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.eq_adjoin_of_eq_algebra_adjoin", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Algebra", "is_tactic_proof": true, "tactics": ["apply", "rw", "refine", "rw", "exact"], "tactic_count": 5}
{"name": "IntermediateField.adjoin_eq_top_of_algebra", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.fg_top_iff", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Algebra", "is_tactic_proof": true, "tactics": ["constructor", "intro", "have", "have", "have", "rw", "exact", "intro", "use", "refine", "obtain", "have", "have", "rw", "exact", "div_mem"], "tactic_count": 16}
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{"name": "IntermediateField.essFiniteType_iff", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Algebra", "is_tactic_proof": false, "tactics": ["suffices", "simpa", "exact"], "tactic_count": 3}
{"name": "IntermediateField.AdjoinSimple.isIntegral_gen", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Algebra", "is_tactic_proof": true, "tactics": ["conv_rhs", "rw"], "tactic_count": 2}
{"name": "IntermediateField.adjoin_toSubalgebra_of_isAlgebraic", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.adjoin_simple_toSubalgebra_of_isAlgebraic", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.adjoin_simple_toSubalgebra_of_integral", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.adjoin_toSubalgebra", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.adjoin_eq_top_iff_of_isAlgebraic", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Algebra", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "Algebra.finite_of_essFiniteType_of_isAlgebraic", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Algebra", "is_tactic_proof": true, "tactics": ["obtain", "have", "use", "rw", "simpa", "exact"], "tactic_count": 6}
{"name": "IntermediateField.RingHom.adjoinAlgebraMapOfAlgebra", "kind": "definition", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.instAlgebraSubtypeMemSubalgebraAdjoinSingletonSetAdjoinCoeRingHomAlgebraMap", "kind": "instance", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.instIsScalarTowerSubtypeMemSubalgebraAdjoinSingletonSetAdjoinCoeRingHomAlgebraMap", "kind": "instance", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.le_sup_toSubalgebra", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "IntermediateField.fg_of_fg_toSubalgebra", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Algebra", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
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{"name": "IntermediateField.induction_on_adjoin", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractionRing.algHom_fieldRange_eq_of_comp_eq", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Algebra", "is_tactic_proof": true, "tactics": ["apply", "simp_rw", "convert", "exact"], "tactic_count": 4}
{"name": "IsFractionRing.algHom_fieldRange_eq_of_comp_eq_of_range_eq", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Algebra", "is_tactic_proof": true, "tactics": ["apply", "simp_rw", "refine", "rw"], "tactic_count": 4}
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{"name": "IsFractionRing.liftAlgHom_fieldRange_eq_of_range_eq", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.restrictScalars_le_iff", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.FG.of_restrictScalars", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": true, "tactics": ["obtain", "refine", "rw", "exact", "rw", "exact"], "tactic_count": 6}
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{"name": "IntermediateField.forall_mem_adjoin_smul_eq_self_iff", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": true, "tactics": ["change", "simp"], "tactic_count": 2}
{"name": "IntermediateField.finiteDimensional_sup", "kind": "instance", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": true, "tactics": ["let", "suffices", "have", "rwa", "rw"], "tactic_count": 5}
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{"name": "IntermediateField.coe_iSup_of_directed", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.toSubalgebra_iSup_of_directed", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": true, "tactics": ["cases", "simp_rw", "exact"], "tactic_count": 3}
{"name": "IntermediateField.finiteDimensional_iSup_of_finite", "kind": "instance", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": true, "tactics": ["rw", "induction", "empty", "rw", "exact", "insert", "rw", "exact"], "tactic_count": 8}
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{"name": "IntermediateField.finiteDimensional_iSup_of_finset'", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.isSplittingField_iSup", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": true, "tactics": ["let", "have", "simp", "refine", "simp", "exact"], "tactic_count": 6}
{"name": "IntermediateField.adjoin_rank_le_of_isAlgebraic", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": false, "tactics": ["have", "have", "rwa"], "tactic_count": 3}
{"name": "IntermediateField.adjoin_rank_le_of_isAlgebraic_left", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.adjoin_rank_le_of_isAlgebraic_right", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.adjoin_simple_isCompactElement", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "intro", "have", "rwa"], "tactic_count": 4}
{"name": "IntermediateField.adjoin_finset_isCompactElement", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "exact"], "tactic_count": 3}
{"name": "IntermediateField.adjoin_finite_isCompactElement", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.instIsCompactlyGenerated", "kind": "instance", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.exists_finset_of_mem_iSup", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": true, "tactics": ["have", "simp", "exact"], "tactic_count": 3}
{"name": "IntermediateField.exists_finset_of_mem_supr'", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "IntermediateField.exists_finset_of_mem_supr''", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": true, "tactics": ["refine", "refine", "rw", "rw", "exact"], "tactic_count": 5}
{"name": "IntermediateField.exists_finset_of_mem_adjoin", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "obtain", "classical", "refine", "simp_rw", "rintro", "exact"], "tactic_count": 7}
{"name": "IntermediateField.rank_eq_one_iff", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IntermediateField.finrank_eq_one_iff", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IntermediateField.rank_bot", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IntermediateField.finrank_bot", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IntermediateField.rank_bot'", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IntermediateField.finrank_bot'", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.rank_top", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.finrank_top", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.rank_top'", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.finrank_top'", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.finrank_eq_one_iff_eq_top", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "intro", "obtain", "exact"], "tactic_count": 5}
{"name": "IntermediateField.bot_eq_top_iff_finrank_eq_one", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IntermediateField.isSimpleOrder_of_finrank_prime", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": true, "tactics": ["refine", "exact", "intro", "simpa"], "tactic_count": 4}
{"name": "IntermediateField.rank_adjoin_eq_one_iff", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.rank_adjoin_simple_eq_one_iff", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IntermediateField.finrank_adjoin_eq_one_iff", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.finrank_adjoin_simple_eq_one_iff", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IntermediateField.bot_eq_top_of_rank_adjoin_eq_one", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": true, "tactics": ["ext", "rw", "exact"], "tactic_count": 3}
{"name": "IntermediateField.bot_eq_top_of_finrank_adjoin_eq_one", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": true, "tactics": ["ext", "rw", "exact"], "tactic_count": 3}
{"name": "IntermediateField.subsingleton_of_rank_adjoin_eq_one", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.subsingleton_of_finrank_adjoin_eq_one", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.bot_eq_top_of_finrank_adjoin_le_one", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": true, "tactics": ["apply", "exact"], "tactic_count": 2}
{"name": "IntermediateField.subsingleton_of_finrank_adjoin_le_one", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.minpoly_gen", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IntermediateField.aeval_gen_minpoly", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": true, "tactics": ["ext", "convert", "conv", "exact"], "tactic_count": 4}
{"name": "IntermediateField.adjoinRootEquivAdjoin", "kind": "definition", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.adjoinRootEquivAdjoin_apply_root", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.adjoinRootEquivAdjoin_symm_apply_gen", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IntermediateField.adjoin_root_eq_top", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.powerBasisAux", "kind": "definition", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.adjoin.powerBasis", "kind": "definition", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.adjoin.finiteDimensional", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.isAlgebraic_adjoin_simple", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.adjoin.finrank", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "IntermediateField.adjoin_eq_top_of_adjoin_eq_top", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.adjoin_minpoly_coeff_of_exists_primitive_element", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": true, "tactics": ["set", "set", "have", "refine", "rw", "rintro", "rw", "apply", "have", "apply", "rw", "erw", "rw", "exact", "have", "intro", "have", "rw", "simp_all", "refine", "simp_rw", "convert", "natDegree_le_of_dvd", "rw"], "tactic_count": 24}
{"name": "IntermediateField.instFiniteSubtypeMemBot", "kind": "instance", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.exists_lt_finrank_of_infinite_dimensional", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "obtain", "obtain", "contrapose", "rw", "exact", "let", "haveI", "refine", "have", "have", "exact"], "tactic_count": 14}
{"name": "minpoly.natDegree_le", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "minpoly.degree_le", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "minpoly.degree_dvd", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": true, "tactics": ["rw", "use", "rw"], "tactic_count": 3}
{"name": "IntermediateField.isAlgebraic_iSup", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "obtain", "rw", "haveI", "adjoin.finiteDimensional", "apply"], "tactic_count": 7}
{"name": "IntermediateField.isAlgebraic_adjoin", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IntermediateField.finiteDimensional_adjoin", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": true, "tactics": ["rw", "haveI", "exact"], "tactic_count": 3}
{"name": "IntermediateField.algHomAdjoinIntegralEquiv", "kind": "definition", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.algHomAdjoinIntegralEquiv_symm_apply_gen", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.fintypeOfAlgHomAdjoinIntegral", "kind": "definition", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.card_algHom_adjoin_integral", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": true, "tactics": ["let", "rw", "simp", "exact"], "tactic_count": 4}
{"name": "Polynomial.irreducible_comp", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": true, "tactics": ["have", "have", "have", "intro", "apply", "not_irreducible_C", "rw", "apply", "rw", "have", "have", "have", "suffices", "have", "let", "letI", "have", "refine", "rw", "exact", "have", "rw", "exact", "have", "g.map", "minpoly.eq_of_irreducible_of_monic", "have", "trans", "have", "apply", "rw", "restrictScalars_adjoin]", "simp", "rw", "exact", "simp", "have", "rwa"], "tactic_count": 38}
{"name": "minpoly.eq_of_root", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "minpoly.algEquiv", "kind": "definition", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "minpoly.algEquiv_apply", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "PowerBasis.equivAdjoinSimple", "kind": "definition", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerBasis.equivAdjoinSimple_aeval", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerBasis.equivAdjoinSimple_gen", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerBasis.equivAdjoinSimple_symm_aeval", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PowerBasis.equivAdjoinSimple_symm_gen", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IntermediateField.lift_cardinalMk_adjoin_le", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply", "rw", "refine", "simp_rw", "grw"], "tactic_count": 6}
{"name": "IntermediateField.cardinalMk_adjoin_le", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IntermediateField.isAlgebraic_adjoin_pair", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "IntermediateField.finiteDimensional_adjoin_pair", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "exact"], "tactic_count": 4}
{"name": "IntermediateField.mem_adjoin_pair_left", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.mem_adjoin_pair_right", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.AdjoinPair.gen₁", "kind": "definition", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.AdjoinPair.gen₂", "kind": "definition", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.AdjoinPair.algebraMap_gen₁", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.AdjoinPair.algebraMap_gen₂", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.adjoin", "kind": "definition", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.adjoin_toSubfield", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.mem_adjoin_iff_div", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "IntermediateField.adjoin_le_iff", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.gc", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.gi", "kind": "definition", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.instCompleteLattice", "kind": "instance", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.instAlgebraSubtypeMemMin", "kind": "instance", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.instAlgebraSubtypeMemMin_1", "kind": "instance", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.sup_def", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.sSup_def", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.instInhabited", "kind": "instance", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.instUnique", "kind": "instance", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.coe_bot", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.mem_bot", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.bot_toSubalgebra", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.bot_toSubfield", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.coe_top", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.mem_top", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.top_toSubalgebra", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.top_toSubfield", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.coe_inf", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.mem_inf", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.inf_toSubalgebra", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.inf_toSubfield", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.sup_toSubfield", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "congr", "rw", "rintro", "exact"], "tactic_count": 6}
{"name": "IntermediateField.coe_sInf", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.sInf_toSubalgebra", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.sInf_toSubfield", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.sSup_toSubfield", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": ["have", "rw", "congr", "exact", "rw", "congr", "rw", "rintro", "obtain", "simp", "exact"], "tactic_count": 11}
{"name": "IntermediateField.coe_iInf", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IntermediateField.iInf_toSubalgebra", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.iInf_toSubfield", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.iSup_toSubfield", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IntermediateField.botEquiv", "kind": "definition", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.botEquiv_def", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IntermediateField.botEquiv_symm", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.algebraOverBot", "kind": "instance", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.coe_algebraMap_over_bot", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.isScalarTower_over_bot", "kind": "instance", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.topEquiv", "kind": "definition", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.restrictScalars_bot_eq_self", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.restrictScalars_top", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.restrictScalars_eq_top_iff", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IntermediateField.restrictScalars_sup", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.restrictScalars_inf", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.map_bot", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.map_sup", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.map_iSup", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.map_inf", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.map_iInf", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": true, "tactics": ["apply", "simpa"], "tactic_count": 2}
{"name": "AlgHom.fieldRange_eq_map", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.map_fieldRange", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.fieldRange_eq_top", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.fieldRange_eq_top", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.adjoin_eq_range_algebraMap_adjoin", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.adjoin.algebraMap_mem", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.adjoin.range_algebraMap_subset", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.adjoin.fieldCoe", "kind": "instance", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.subset_adjoin", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.mem_adjoin_of_mem", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.notMem_of_notMem_adjoin", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.adjoin.setCoe", "kind": "instance", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.adjoin.mono", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.adjoin_contains_field_as_subfield", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.subset_adjoin_of_subset_left", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.subset_adjoin_of_subset_right", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.adjoin_empty", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.adjoin_univ", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.adjoin_le_subfield", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IntermediateField.adjoin_subset_adjoin_iff", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.adjoin_adjoin_left", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": true, "tactics": ["rw", "change", "apply", "rintro", "exact", "exact", "exact"], "tactic_count": 7}
{"name": "IntermediateField.adjoin_insert_adjoin", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.adjoin_adjoin_comm", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IntermediateField.adjoin_map", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.lift_adjoin", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.lift_adjoin_simple", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IntermediateField.lift_bot", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.lift_top", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IntermediateField.lift_sup", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IntermediateField.lift_inf", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IntermediateField.adjoin_self", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.restrictScalars_adjoin", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IntermediateField.extendScalars_adjoin", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.adjoin_union", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.restrictScalars_adjoin_eq_sup", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IntermediateField.adjoin_iUnion", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.iSup_eq_adjoin", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "IntermediateField.restrictScalars_adjoin_of_algEquiv", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": true, "tactics": ["apply_fun", "change", "congr", "ext", "exact"], "tactic_count": 5}
{"name": "IntermediateField.adjoin_induction", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.adjoin_algHom_ext", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.algHom_ext_of_eq_adjoin", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "_private.Mathlib.FieldTheory.IntermediateField.Adjoin.Defs.0.IntermediateField.mkInsertTerm", "kind": "definition", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.term_⟮_,,⟯", "kind": "definition", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField._aux_Mathlib_FieldTheory_IntermediateField_Adjoin_Defs___macroRules_IntermediateField_term_⟮_,,⟯_1", "kind": "definition", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.delabAdjoinNotation", "kind": "definition", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.mem_adjoin_simple_self", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.AdjoinSimple.gen", "kind": "definition", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.AdjoinSimple.coe_gen", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.AdjoinSimple.algebraMap_gen", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.adjoin_simple_adjoin_simple", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.adjoin_simple_comm", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.adjoin_simple_le_iff", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IntermediateField.biSup_adjoin_simple", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IntermediateField.RingHom.adjoinAlgebraMap", "kind": "definition", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.instAlgebraSubtypeMemAdjoinSingletonSetCoeRingHomAlgebraMap", "kind": "instance", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.instIsScalarTowerSubtypeMemAdjoinSingletonSetCoeRingHomAlgebraMap", "kind": "instance", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.adjoin_eq_bot_iff", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IntermediateField.adjoin_simple_eq_bot_iff", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IntermediateField.adjoin_zero", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.adjoin_one", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.adjoin_intCast", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "IntermediateField.adjoin_natCast", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.FG", "kind": "definition", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.fg_adjoin_finset", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.fg_def", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.fg_adjoin_of_finite", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.fg_bot", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.fg_sup", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": true, "tactics": ["obtain", "classical", "exact"], "tactic_count": 3}
{"name": "IntermediateField.fg_iSup", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": true, "tactics": ["choose", "simp_rw", "exact"], "tactic_count": 3}
{"name": "IntermediateField.induction_on_adjoin_finset", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": true, "tactics": ["classical", "refine", "simp", "rw", "exact"], "tactic_count": 5}
{"name": "IntermediateField.induction_on_adjoin_fg", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "IntermediateField.map_comap_eq", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.map_comap_eq_self", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IntermediateField.map_comap_eq_self_of_surjective", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.comap_map", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.extendScalars_self", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": true, "tactics": ["ext", "rw", "refine", "rintro", "exact"], "tactic_count": 5}
{"name": "Subfield.extendScalars_top", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.extendScalars_sup", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.extendScalars_inf", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.extendScalars_self", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.extendScalars_top", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.extendScalars_sup", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.extendScalars_inf", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Adjoin.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.coe_isIntegral_iff", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Algebraic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.IsAlgebraic.toIntermediateField", "kind": "definition", "module": "Mathlib.FieldTheory.IntermediateField.Algebraic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsAlgebraic.toIntermediateField", "kind": "abbrev", "module": "Mathlib.FieldTheory.IntermediateField.Algebraic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.isAlgebraic_tower_bot", "kind": "instance", "module": "Mathlib.FieldTheory.IntermediateField.Algebraic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.isAlgebraic_tower_top", "kind": "instance", "module": "Mathlib.FieldTheory.IntermediateField.Algebraic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.finiteDimensional_left", "kind": "instance", "module": "Mathlib.FieldTheory.IntermediateField.Algebraic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.finiteDimensional_right", "kind": "instance", "module": "Mathlib.FieldTheory.IntermediateField.Algebraic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.rank_eq_rank_subalgebra", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Algebraic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.finrank_eq_finrank_subalgebra", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Algebraic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.eq_of_le_of_finrank_le", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Algebraic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.eq_of_le_of_finrank_eq", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Algebraic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.FieldTheory.IntermediateField.Algebraic.0.IntermediateField.eq_of_le_of_finrank_le''", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Algebraic", "is_tactic_proof": true, "tactics": ["apply", "have", "have", "have", "nlinarith"], "tactic_count": 5}
{"name": "IntermediateField.eq_of_le_of_finrank_le'", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Algebraic", "is_tactic_proof": true, "tactics": ["refine", "rwa", "eq_of_le_of_finrank_le", "mem_extendScalars]"], "tactic_count": 4}
{"name": "IntermediateField.eq_of_le_of_finrank_eq'", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Algebraic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.finrank_lt_of_gt", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Algebraic", "is_tactic_proof": true, "tactics": ["letI", "have", "refine", "exact", "exact"], "tactic_count": 5}
{"name": "IntermediateField.finrank_dvd_of_le_left", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Algebraic", "is_tactic_proof": true, "tactics": ["let", "have", "exact"], "tactic_count": 3}
{"name": "IntermediateField.finrank_dvd_of_le_right", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Algebraic", "is_tactic_proof": true, "tactics": ["let", "exact"], "tactic_count": 2}
{"name": "IntermediateField.finrank_le_of_le_left", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Algebraic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.finrank_le_of_le_right", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Algebraic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.finiteDimensional_map", "kind": "instance", "module": "Mathlib.FieldTheory.IntermediateField.Algebraic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.isAlgebraic_iff", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Algebraic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.isIntegral_iff", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Algebraic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.minpoly_eq", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Algebraic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "subalgebraEquivIntermediateField", "kind": "definition", "module": "Mathlib.FieldTheory.IntermediateField.Algebraic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_subalgebraEquivIntermediateField", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Algebraic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_subalgebraEquivIntermediateField_symm", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Algebraic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.instSetLike", "kind": "instance", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.instPartialOrder", "kind": "instance", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.neg_mem", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": true, "tactics": ["change"], "tactic_count": 1}
{"name": "IntermediateField.toSubfield", "kind": "definition", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.instSubfieldClass", "kind": "instance", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.mem_carrier", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.ext", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.coe_toSubalgebra", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.coe_toSubfield", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.coe_type_toSubalgebra", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.coe_type_toSubfield", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.mem_mk", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.mem_toSubalgebra", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.mem_toSubfield", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.toSubalgebra_strictMono", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.copy", "kind": "definition", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.coe_copy", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.copy_eq", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.algebraMap_mem", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.smul_mem", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.one_mem", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.zero_mem", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.mul_mem", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.add_mem", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.sub_mem", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.inv_mem", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.div_mem", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.list_prod_mem", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.list_sum_mem", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.multiset_prod_mem", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.multiset_sum_mem", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.prod_mem", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.sum_mem", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.pow_mem", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.zsmul_mem", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.intCast_mem", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.coe_add", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.coe_neg", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.coe_mul", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.coe_inv", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.coe_zero", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.coe_one", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.coe_pow", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.natCast_mem", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IntermediateField.instSMulMemClass", "kind": "instance", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.toIntermediateField", "kind": "definition", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toSubalgebra_toIntermediateField", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "toIntermediateField_toSubalgebra", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "Subalgebra.toIntermediateField'", "kind": "definition", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toSubalgebra_toIntermediateField'", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "toIntermediateField'_toSubalgebra", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "Subfield.toIntermediateField", "kind": "definition", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.toIntermediateField_toSubfield", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.coe_toIntermediateField", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.toField", "kind": "instance", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.coe_sum", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.coe_prod", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.instSMulSubtypeMem", "kind": "instance", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.smul_def", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.smulCommClass_left", "kind": "instance", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.smulCommClass_right", "kind": "instance", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.instIsScalarTowerSubtypeMem", "kind": "instance", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.instFaithfulSMulSubtypeMem", "kind": "instance", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.instMulActionSubtypeMem", "kind": "instance", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.instDistribMulActionSubtypeMem", "kind": "instance", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.instMulDistribMulActionSubtypeMem", "kind": "instance", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.instSMulWithZeroSubtypeMem", "kind": "instance", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.instMulActionWithZeroSubtypeMem", "kind": "instance", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.instModuleSubtypeMem", "kind": "instance", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.instMulSemiringActionSubtypeMem", "kind": "instance", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.toAlgebra", "kind": "instance", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.module'", "kind": "instance", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.algebra'", "kind": "instance", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.isScalarTower", "kind": "instance", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.coe_smul", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.algebraMap_apply", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.coe_algebraMap_apply", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.isScalarTower_bot", "kind": "instance", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.isScalarTower_mid", "kind": "instance", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.isScalarTower_mid'", "kind": "instance", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.instAlgebraSubtypeMem", "kind": "instance", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.instAlgebraSubtypeMem_1", "kind": "instance", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.instModuleSubtypeMem_1", "kind": "instance", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.instSMulSubtypeMem_1", "kind": "instance", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.instIsScalarTowerSubtypeMem_1", "kind": "instance", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.comap", "kind": "definition", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.map", "kind": "definition", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.coe_map", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.toSubalgebra_map", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.toSubfield_map", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.map_id", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.map_map", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.map_mono", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.map_le_iff_le_comap", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.gc_map_comap", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.intermediateFieldMap", "kind": "definition", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.intermediateFieldMap_apply_coe", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.intermediateFieldMap_symm_apply_coe", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.fieldRange", "kind": "definition", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.coe_fieldRange", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.fieldRange_toSubfield", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.mem_fieldRange", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.val", "kind": "definition", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.coe_val", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.val_mk", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.range_val", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.fieldRange_val", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.AlgHom.inhabited", "kind": "instance", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.aeval_coe", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.inclusion", "kind": "definition", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.inclusion_injective", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.inclusion_self", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.inclusion_inclusion", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.coe_inclusion", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.toSubalgebra_injective", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": true, "tactics": ["intro", "ext", "simp_rw"], "tactic_count": 3}
{"name": "IntermediateField.toSubfield_injective", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": true, "tactics": ["intro", "ext", "simp_rw"], "tactic_count": 3}
{"name": "IntermediateField.toSubalgebra_inj", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.toSubfield_inj", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.map_injective", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": true, "tactics": ["intro", "rwa"], "tactic_count": 2}
{"name": "IntermediateField.set_range_subset", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.fieldRange_le", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.toSubalgebra_le_toSubalgebra", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.toSubalgebra_lt_toSubalgebra", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.lift", "kind": "definition", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.lift_injective", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.lift_inj", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.lift_le", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "IntermediateField.mem_lift", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.liftAlgEquiv", "kind": "definition", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.liftAlgEquiv_apply", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.restrictScalars", "kind": "definition", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.coe_restrictScalars", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.restrictScalars_toSubalgebra", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.restrictScalars_toSubfield", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.mem_restrictScalars", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.restrictScalars_injective", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.restrictScalars_inj", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField._example", "kind": "example", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "IntermediateField.equivOfEq", "kind": "definition", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.equivOfEq_symm", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.equivOfEq_rfl", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.equivOfEq_trans", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.fieldRange_comp_val", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.equivMap", "kind": "definition", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.coe_equivMap_apply", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.extendScalars", "kind": "definition", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.coe_extendScalars", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.extendScalars_toSubfield", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.mem_extendScalars", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.extendScalars_le_extendScalars_iff", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.extendScalars_le_iff", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.le_extendScalars_iff", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.extendScalars.orderIso", "kind": "definition", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.extendScalars_injective", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.extendScalars", "kind": "definition", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.coe_extendScalars", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.extendScalars_toSubfield", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.mem_extendScalars", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.extendScalars_restrictScalars", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.extendScalars_le_extendScalars_iff", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.extendScalars_le_iff", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.le_extendScalars_iff", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.extendScalars.orderIso", "kind": "definition", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.extendScalars_injective", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.restrict", "kind": "definition", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.mem_restrict", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.lift_restrict", "kind": "theorem", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": true, "tactics": ["ext", "refine", "let", "exact", "let", "exact"], "tactic_count": 6}
{"name": "IntermediateField.restrict_algEquiv", "kind": "definition", "module": "Mathlib.FieldTheory.IntermediateField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicClosure.Monics", "kind": "definition", "module": "Mathlib.FieldTheory.IsAlgClosed.AlgebraicClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicClosure.Vars", "kind": "definition", "module": "Mathlib.FieldTheory.IsAlgClosed.AlgebraicClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicClosure.subProdXSubC", "kind": "definition", "module": "Mathlib.FieldTheory.IsAlgClosed.AlgebraicClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicClosure.spanCoeffs", "kind": "definition", "module": "Mathlib.FieldTheory.IsAlgClosed.AlgebraicClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicClosure.finEquivRoots", "kind": "definition", "module": "Mathlib.FieldTheory.IsAlgClosed.AlgebraicClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicClosure.Monics.splits_finsetProd", "kind": "theorem", "module": "Mathlib.FieldTheory.IsAlgClosed.AlgebraicClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicClosure.toSplittingField", "kind": "definition", "module": "Mathlib.FieldTheory.IsAlgClosed.AlgebraicClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicClosure.toSplittingField_coeff", "kind": "theorem", "module": "Mathlib.FieldTheory.IsAlgClosed.AlgebraicClosure", "is_tactic_proof": true, "tactics": ["classical", "simp_rw", "rw", "conv", "rw"], "tactic_count": 5}
{"name": "AlgebraicClosure.spanCoeffs_ne_top", "kind": "theorem", "module": "Mathlib.FieldTheory.IsAlgClosed.AlgebraicClosure", "is_tactic_proof": false, "tactics": ["rw", "rintro", "classical", "replace", "rw", "exact", "intro", "rw"], "tactic_count": 8}
{"name": "AlgebraicClosure.maxIdeal", "kind": "definition", "module": "Mathlib.FieldTheory.IsAlgClosed.AlgebraicClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicClosure.maxIdeal.isMaximal", "kind": "instance", "module": "Mathlib.FieldTheory.IsAlgClosed.AlgebraicClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicClosure.le_maxIdeal", "kind": "theorem", "module": "Mathlib.FieldTheory.IsAlgClosed.AlgebraicClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicClosure", "kind": "definition", "module": "Mathlib.FieldTheory.IsAlgClosed.AlgebraicClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicClosure.instCommRing", "kind": "instance", "module": "Mathlib.FieldTheory.IsAlgClosed.AlgebraicClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicClosure.instInhabited", "kind": "instance", "module": "Mathlib.FieldTheory.IsAlgClosed.AlgebraicClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicClosure.instSMulOfIsScalarTower", "kind": "instance", "module": "Mathlib.FieldTheory.IsAlgClosed.AlgebraicClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicClosure.instAlgebra", "kind": "instance", "module": "Mathlib.FieldTheory.IsAlgClosed.AlgebraicClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicClosure.instIsScalarTower", "kind": "instance", "module": "Mathlib.FieldTheory.IsAlgClosed.AlgebraicClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicClosure.instGroupWithZero", "kind": "instance", "module": "Mathlib.FieldTheory.IsAlgClosed.AlgebraicClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicClosure.instField", "kind": "instance", "module": "Mathlib.FieldTheory.IsAlgClosed.AlgebraicClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicClosure.Monics.map_eq_prod", "kind": "theorem", "module": "Mathlib.FieldTheory.IsAlgClosed.AlgebraicClosure", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "rw", "refine"], "tactic_count": 4}
{"name": "AlgebraicClosure.isAlgebraic", "kind": "instance", "module": "Mathlib.FieldTheory.IsAlgClosed.AlgebraicClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicClosure.instIsAlgClosure", "kind": "instance", "module": "Mathlib.FieldTheory.IsAlgClosed.AlgebraicClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicClosure.isAlgClosed", "kind": "instance", "module": "Mathlib.FieldTheory.IsAlgClosed.AlgebraicClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicClosure.instCharZero", "kind": "instance", "module": "Mathlib.FieldTheory.IsAlgClosed.AlgebraicClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicClosure.instCharP", "kind": "instance", "module": "Mathlib.FieldTheory.IsAlgClosed.AlgebraicClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicClosure.instIsAlgClosureOfIsAlgebraic", "kind": "instance", "module": "Mathlib.FieldTheory.IsAlgClosed.AlgebraicClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.instIsAlgClosureAlgebraicClosureSubtypeMemOfIsAlgebraic", "kind": "instance", "module": "Mathlib.FieldTheory.IsAlgClosed.AlgebraicClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.AdjoinSimple.normal_algebraicClosure", "kind": "theorem", "module": "Mathlib.FieldTheory.IsAlgClosed.AlgebraicClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.AdjoinDouble.normal_algebraicClosure", "kind": "theorem", "module": "Mathlib.FieldTheory.IsAlgClosed.AlgebraicClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAlgClosed.splits_codomain", "kind": "theorem", "module": "Mathlib.FieldTheory.IsAlgClosed.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAlgClosed.splits_domain", "kind": "theorem", "module": "Mathlib.FieldTheory.IsAlgClosed.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAlgClosed.exists_root", "kind": "theorem", "module": "Mathlib.FieldTheory.IsAlgClosed.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAlgClosed.exists_pow_nat_eq", "kind": "theorem", "module": "Mathlib.FieldTheory.IsAlgClosed.Basic", "is_tactic_proof": false, "tactics": ["have", "rw", "exact", "obtain", "use", "simp", "exact"], "tactic_count": 7}
{"name": "IsAlgClosed.exists_eq_mul_self", "kind": "theorem", "module": "Mathlib.FieldTheory.IsAlgClosed.Basic", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "IsAlgClosed.roots_eq_zero_iff", "kind": "theorem", "module": "Mathlib.FieldTheory.IsAlgClosed.Basic", "is_tactic_proof": true, "tactics": ["refine", "rcases", "exact", "obtain", "rw", "simp"], "tactic_count": 6}
{"name": "IsAlgClosed.roots_eq_zero_iff_natDegree_eq_zero", "kind": "theorem", "module": "Mathlib.FieldTheory.IsAlgClosed.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAlgClosed.roots_eq_zero_iff_degree_nonpos", "kind": "theorem", "module": "Mathlib.FieldTheory.IsAlgClosed.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAlgClosed.card_roots_eq_natDegree", "kind": "theorem", "module": "Mathlib.FieldTheory.IsAlgClosed.Basic", "is_tactic_proof": true, "tactics": ["have", "simp"], "tactic_count": 2}
{"name": "IsAlgClosed.card_roots_map_eq_natDegree_of_leadingCoeff_ne_zero", "kind": "theorem", "module": "Mathlib.FieldTheory.IsAlgClosed.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAlgClosed.card_roots_map_eq_natDegree_of_isUnit_leadingCoeff", "kind": "theorem", "module": "Mathlib.FieldTheory.IsAlgClosed.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAlgClosed.card_roots_map_eq_natDegree_of_injective", "kind": "theorem", "module": "Mathlib.FieldTheory.IsAlgClosed.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAlgClosed.card_roots_map_eq_natDegree_from_simpleRing", "kind": "theorem", "module": "Mathlib.FieldTheory.IsAlgClosed.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAlgClosed.card_aroots_eq_natDegree_of_leadingCoeff_ne_zero", "kind": "theorem", "module": "Mathlib.FieldTheory.IsAlgClosed.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAlgClosed.card_aroots_eq_natDegree_of_isUnit_leadingCoeff", "kind": "theorem", "module": "Mathlib.FieldTheory.IsAlgClosed.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAlgClosed.card_aroots_eq_natDegree", "kind": "theorem", "module": "Mathlib.FieldTheory.IsAlgClosed.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAlgClosed.dvd_iff_roots_le_roots", "kind": "theorem", "module": "Mathlib.FieldTheory.IsAlgClosed.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAlgClosed.associated_iff_roots_eq_roots", "kind": "theorem", "module": "Mathlib.FieldTheory.IsAlgClosed.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAlgClosed.exists_eval₂_eq_zero_of_injective", "kind": "theorem", "module": "Mathlib.FieldTheory.IsAlgClosed.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAlgClosed.exists_eval₂_eq_zero", "kind": "theorem", "module": "Mathlib.FieldTheory.IsAlgClosed.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAlgClosed.exists_aeval_eq_zero_of_injective", "kind": "theorem", "module": "Mathlib.FieldTheory.IsAlgClosed.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAlgClosed.exists_aeval_eq_zero", "kind": "theorem", "module": "Mathlib.FieldTheory.IsAlgClosed.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAlgClosed.of_exists_root", "kind": "theorem", "module": "Mathlib.FieldTheory.IsAlgClosed.Basic", "is_tactic_proof": false, "tactics": ["replace", "obtain", "exact", "refine", "by_cases", "simp", "obtain", "rw", "refine", "let", "obtain", "exact"], "tactic_count": 12}
{"name": "IsAlgClosed.of_ringEquiv", "kind": "theorem", "module": "Mathlib.FieldTheory.IsAlgClosed.Basic", "is_tactic_proof": true, "tactics": ["apply", "intro", "have", "rw", "exact", "rcases", "use", "rw", "apply", "rw", "clear", "induction"], "tactic_count": 12}
{"name": "IsAlgClosed.degree_eq_one_of_irreducible", "kind": "theorem", "module": "Mathlib.FieldTheory.IsAlgClosed.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAlgClosed.algebraMap_bijective_of_isIntegral", "kind": "theorem", "module": "Mathlib.FieldTheory.IsAlgClosed.Basic", "is_tactic_proof": true, "tactics": ["refine", "have", "have", "degree_eq_one_of_irreducible", "have", "rw", "exact"], "tactic_count": 7}
{"name": "IsAlgClosed.ringHom_bijective_of_isIntegral", "kind": "theorem", "module": "Mathlib.FieldTheory.IsAlgClosed.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.eq_bot_of_isAlgClosed_of_isAlgebraic", "kind": "theorem", "module": "Mathlib.FieldTheory.IsAlgClosed.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.isCoprime_iff_aeval_ne_zero_of_isAlgClosed", "kind": "theorem", "module": "Mathlib.FieldTheory.IsAlgClosed.Basic", "is_tactic_proof": true, "tactics": ["refine", "replace", "contrapose", "rw", "rintro", "obtain", "simpa", "exact"], "tactic_count": 8}
{"name": "isAlgClosure_iff", "kind": "theorem", "module": "Mathlib.FieldTheory.IsAlgClosed.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAlgClosure.normal", "kind": "instance", "module": "Mathlib.FieldTheory.IsAlgClosed.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAlgClosure.separable", "kind": "instance", "module": "Mathlib.FieldTheory.IsAlgClosed.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAlgClosed.instIsAlgClosure", "kind": "instance", "module": "Mathlib.FieldTheory.IsAlgClosed.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAlgClosure.of_splits", "kind": "theorem", "module": "Mathlib.FieldTheory.IsAlgClosed.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAlgClosed.eval_surjective", "kind": "theorem", "module": "Mathlib.FieldTheory.IsAlgClosed.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAlgClosed.surjective_restrictDomain_of_isAlgebraic", "kind": "theorem", "module": "Mathlib.FieldTheory.IsAlgClosed.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.FieldTheory.IsAlgClosed.Basic.0.IsAlgClosed.liftAux", "kind": "definition", "module": "Mathlib.FieldTheory.IsAlgClosed.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "IsAlgClosed.lift", "kind": "definition", "module": "Mathlib.FieldTheory.IsAlgClosed.Basic", "is_tactic_proof": true, "tactics": ["letI", "letI", "letI", "have", "have", "let", "exact"], "tactic_count": 7}
{"name": "IsAlgClosed.nonempty_algEquiv_or_of_finrank_eq_two", "kind": "theorem", "module": "Mathlib.FieldTheory.IsAlgClosed.Basic", "is_tactic_proof": true, "tactics": ["have", "have", "have", "obtain", "exacts"], "tactic_count": 5}
{"name": "IsAlgClosed.perfectRing", "kind": "instance", "module": "Mathlib.FieldTheory.IsAlgClosed.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAlgClosed.perfectField", "kind": "instance", "module": "Mathlib.FieldTheory.IsAlgClosed.Basic", "is_tactic_proof": true, "tactics": ["obtain", "exacts"], "tactic_count": 2}
{"name": "IsAlgClosed.instInfinite", "kind": "instance", "module": "Mathlib.FieldTheory.IsAlgClosed.Basic", "is_tactic_proof": true, "tactics": ["apply", "intro", "set", "set", "have", "apply", "have", "rw", "unfold", "rw", "rw", "exact"], "tactic_count": 12}
{"name": "IsAlgClosure.equiv", "kind": "definition", "module": "Mathlib.FieldTheory.IsAlgClosed.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "IntermediateField.LinearDisjoint.of_isField'", "kind": "theorem", "module": "Mathlib.FieldTheory.LinearDisjoint", "is_tactic_proof": true, "tactics": ["rw", "apply", "exact"], "tactic_count": 3}
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{"name": "IntermediateField.LinearDisjoint.isField_of_isAlgebraic", "kind": "theorem", "module": "Mathlib.FieldTheory.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "IntermediateField.LinearDisjoint.trace_algebraMap", "kind": "theorem", "module": "Mathlib.FieldTheory.LinearDisjoint", "is_tactic_proof": true, "tactics": ["rw", "refine", "simpa"], "tactic_count": 3}
{"name": "IntermediateField.LinearDisjoint.norm_algebraMap", "kind": "theorem", "module": "Mathlib.FieldTheory.LinearDisjoint", "is_tactic_proof": true, "tactics": ["rw", "refine", "simpa"], "tactic_count": 3}
{"name": "minpoly", "kind": "definition", "module": "Mathlib.FieldTheory.Minpoly.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "minpoly.monic", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.Basic", "is_tactic_proof": true, "tactics": ["delta", "rw", "exact"], "tactic_count": 3}
{"name": "minpoly.ne_zero", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "minpoly.eq_zero", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "minpoly.ne_zero_iff", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "minpoly.algHom_eq", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.Basic", "is_tactic_proof": true, "tactics": ["classical", "simp_rw"], "tactic_count": 2}
{"name": "minpoly.algebraMap_eq", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "minpoly.algEquiv_eq", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "minpoly.aeval", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.Basic", "is_tactic_proof": true, "tactics": ["delta", "split_ifs", "exact", "exact"], "tactic_count": 4}
{"name": "minpoly.aeval_algHom", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "minpoly.ne_one", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.Basic", "is_tactic_proof": true, "tactics": ["intro", "refine", "simpa"], "tactic_count": 3}
{"name": "minpoly.map_ne_one", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "rw", "exact"], "tactic_count": 4}
{"name": "minpoly.not_isUnit", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.Basic", "is_tactic_proof": true, "tactics": ["haveI", "by_cases", "exact", "rw", "exact"], "tactic_count": 5}
{"name": "minpoly.mem_range_of_degree_eq_one", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.Basic", "is_tactic_proof": false, "tactics": ["have", "by_contra", "rw", "exact", "have", "rw", "eq_neg_iff_add_eq_zero,", "exact"], "tactic_count": 8}
{"name": "minpoly.min", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.Basic", "is_tactic_proof": true, "tactics": ["delta", "exact", "simp"], "tactic_count": 3}
{"name": "minpoly.unique'", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.Basic", "is_tactic_proof": true, "tactics": ["nontriviality", "have", "obtain", "swap", "exact", "obtain", "rw", "have", "rw", "have", "have", "rintro", "exact", "apply_fun", "rw", "apply", "rw", "exact", "rw"], "tactic_count": 19}
{"name": "minpoly.eq_of_linearIndependent", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "minpoly.subsingleton", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.Basic", "is_tactic_proof": true, "tactics": ["nontriviality", "have", "rw", "rcases", "rwa", "exact"], "tactic_count": 6}
{"name": "minpoly.natDegree_pos", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.Basic", "is_tactic_proof": true, "tactics": ["rw", "intro", "have", "rw", "convert", "simpa", "simpa"], "tactic_count": 7}
{"name": "minpoly.degree_pos", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "minpoly.degree_eq_one_iff", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.Basic", "is_tactic_proof": true, "tactics": ["refine", "rintro", "haveI", "exact"], "tactic_count": 4}
{"name": "minpoly.natDegree_eq_one_iff", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "minpoly.two_le_natDegree_iff", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "minpoly.two_le_natDegree_subalgebra", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "minpoly.eq_X_sub_C_of_algebraMap_inj", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.Basic", "is_tactic_proof": true, "tactics": ["nontriviality", "refine", "rw", "simp_rw", "intro", "rw", "rw", "rwa"], "tactic_count": 8}
{"name": "minpoly.aeval_ne_zero_of_dvdNotUnit_minpoly", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.Basic", "is_tactic_proof": true, "tactics": ["refine", "obtain", "have", "rw", "apply", "refine", "rw", "exact"], "tactic_count": 8}
{"name": "minpoly.irreducible", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "by_contra", "have", "rw", "rcases", "exact", "refine", "rw"], "tactic_count": 9}
{"name": "ConjRootClass", "kind": "definition", "module": "Mathlib.FieldTheory.Minpoly.ConjRootClass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjRootClass.mk", "kind": "definition", "module": "Mathlib.FieldTheory.Minpoly.ConjRootClass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjRootClass.mk_def", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.ConjRootClass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjRootClass.instZero", "kind": "instance", "module": "Mathlib.FieldTheory.Minpoly.ConjRootClass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjRootClass.ind", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.ConjRootClass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjRootClass.mk_eq_mk", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.ConjRootClass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjRootClass.mk_zero", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.ConjRootClass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjRootClass.mk_eq_zero_iff", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.ConjRootClass", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ConjRootClass.instDecidableEqOfNormalOfFintypeAlgEquiv", "kind": "instance", "module": "Mathlib.FieldTheory.Minpoly.ConjRootClass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjRootClass.carrier", "kind": "definition", "module": "Mathlib.FieldTheory.Minpoly.ConjRootClass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjRootClass.mem_carrier", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.ConjRootClass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjRootClass.carrier_zero", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.ConjRootClass", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "ConjRootClass.carrier_inj", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.ConjRootClass", "is_tactic_proof": true, "tactics": ["intro", "induction", "h", "induction", "h", "simp_rw", "rw"], "tactic_count": 7}
{"name": "ConjRootClass.instNeg", "kind": "instance", "module": "Mathlib.FieldTheory.Minpoly.ConjRootClass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjRootClass.mk_neg", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.ConjRootClass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjRootClass.instInvolutiveNeg", "kind": "instance", "module": "Mathlib.FieldTheory.Minpoly.ConjRootClass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjRootClass.carrier_neg", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.ConjRootClass", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "ConjRootClass.exists_mem_carrier_add_eq_zero", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.ConjRootClass", "is_tactic_proof": true, "tactics": ["simp_rw", "constructor", "rintro", "rw", "rintro", "induction", "h"], "tactic_count": 7}
{"name": "ConjRootClass.instDecidablePredMemSetCarrierOfNormalOfDecidableEqOfFintypeAlgEquiv", "kind": "instance", "module": "Mathlib.FieldTheory.Minpoly.ConjRootClass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjRootClass.instFintypeElemCarrierOfNormalOfDecidableEqOfAlgEquiv", "kind": "instance", "module": "Mathlib.FieldTheory.Minpoly.ConjRootClass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjRootClass.minpoly", "kind": "definition", "module": "Mathlib.FieldTheory.Minpoly.ConjRootClass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjRootClass.minpoly_mk", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.ConjRootClass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjRootClass.minpoly_inj", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.ConjRootClass", "is_tactic_proof": true, "tactics": ["induction", "induction", "simp"], "tactic_count": 3}
{"name": "ConjRootClass.minpoly_injective", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.ConjRootClass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjRootClass.splits_minpoly", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.ConjRootClass", "is_tactic_proof": true, "tactics": ["induction", "rw", "exact"], "tactic_count": 3}
{"name": "ConjRootClass.monic_minpoly", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.ConjRootClass", "is_tactic_proof": true, "tactics": ["induction", "rw", "exact"], "tactic_count": 3}
{"name": "ConjRootClass.minpoly_ne_zero", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.ConjRootClass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjRootClass.irreducible_minpoly", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.ConjRootClass", "is_tactic_proof": true, "tactics": ["induction", "rw", "exact"], "tactic_count": 3}
{"name": "ConjRootClass.aeval_minpoly_iff", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.ConjRootClass", "is_tactic_proof": true, "tactics": ["induction", "simpa"], "tactic_count": 2}
{"name": "ConjRootClass.rootSet_minpoly_eq_carrier", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.ConjRootClass", "is_tactic_proof": true, "tactics": ["ext", "rw", "simp"], "tactic_count": 3}
{"name": "ConjRootClass.separable_minpoly", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.ConjRootClass", "is_tactic_proof": true, "tactics": ["induction", "exact"], "tactic_count": 2}
{"name": "ConjRootClass.nodup_aroots_minpoly", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.ConjRootClass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjRootClass.aroots_minpoly_eq_carrier_val", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.ConjRootClass", "is_tactic_proof": true, "tactics": ["classical", "simp_rw", "c.nodup_aroots_minpoly.dedup]"], "tactic_count": 3}
{"name": "ConjRootClass.carrier_eq_mk_aroots_minpoly", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.ConjRootClass", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ConjRootClass.minpoly.map_eq_prod", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.ConjRootClass", "is_tactic_proof": true, "tactics": ["classical", "simp_rw", "rw", "prod_multiset_X_sub_C_of_monic_of_roots_card_eq", "rw", "exact"], "tactic_count": 6}
{"name": "minpoly.degree_le_of_ne_zero", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "minpoly.ne_zero_of_finite", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "minpoly.unique", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.Field", "is_tactic_proof": true, "tactics": ["have", "symm", "by_contra", "apply", "apply", "rw", "exact"], "tactic_count": 7}
{"name": "minpoly.unique_of_degree_le_degree_minpoly", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "minpoly.dvd", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.Field", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "have", "rw", "by_contra", "apply", "exact"], "tactic_count": 7}
{"name": "minpoly.dvd_iff", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "minpoly.isRadical", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "minpoly.dvd_map_of_isScalarTower", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.Field", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "minpoly.dvd_map_of_isScalarTower'", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.Field", "is_tactic_proof": true, "tactics": ["apply", "rw", "rw"], "tactic_count": 3}
{"name": "minpoly.aeval_of_isScalarTower", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "minpoly.map_algebraMap", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.Field", "is_tactic_proof": false, "tactics": ["refine", "eq_of_monic_of_dvd_of_natDegree_le", "obtain", "rw", "refine", "rw"], "tactic_count": 6}
{"name": "minpoly.ker_aeval_eq_span_minpoly", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.Field", "is_tactic_proof": true, "tactics": ["ext", "simp_rw", "eq_comm"], "tactic_count": 3}
{"name": "minpoly.eq_of_irreducible_of_monic", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "minpoly.eq_iff_aeval_eq_zero", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "minpoly.eq_iff_aeval_minpoly_eq_zero", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "minpoly.eq_of_irreducible", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.Field", "is_tactic_proof": true, "tactics": ["have", "apply", "exact", "rwa", "rfl⟩", "hp1", "rw", "rwa"], "tactic_count": 8}
{"name": "minpoly.add_algebraMap", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.Field", "is_tactic_proof": true, "tactics": ["by_cases", "refine", "simp", "have", "have", "rw", "natDegree_comp,", "rwa", "natDegree_X_add_C,", "rw", "refine", "simpa"], "tactic_count": 12}
{"name": "minpoly.sub_algebraMap", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.Field", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "minpoly.neg", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.Field", "is_tactic_proof": true, "tactics": ["by_cases", "refine", "simp", "have", "have", "have", "have", "rw", "natDegree_comp]", "rw", "degree_eq_natDegree", "natDegree_mul", "simpa", "rw", "simp", "exact"], "tactic_count": 16}
{"name": "minpoly.map_eq_of_equiv_equiv", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.Field", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact", "simpa", "exact"], "tactic_count": 5}
{"name": "minpoly.Fintype.subtypeProd", "kind": "definition", "module": "Mathlib.FieldTheory.Minpoly.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "minpoly.rootsOfMinPolyPiType", "kind": "definition", "module": "Mathlib.FieldTheory.Minpoly.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "minpoly.aux_inj_roots_of_min_poly", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.Field", "is_tactic_proof": true, "tactics": ["intro", "suffices", "rw", "exact"], "tactic_count": 4}
{"name": "minpoly.AlgHom.fintype", "kind": "instance", "module": "Mathlib.FieldTheory.Minpoly.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "minpoly.eq_X_sub_C", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "minpoly.eq_X_sub_C'", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "minpoly.zero", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.Field", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "minpoly.one", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.Field", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "minpoly.prime", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.Field", "is_tactic_proof": true, "tactics": ["refine", "rintro", "have", "replace", "exact"], "tactic_count": 5}
{"name": "minpoly.root", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.Field", "is_tactic_proof": false, "tactics": ["have", "eq_of_monic_of_associated", "have", "rwa"], "tactic_count": 4}
{"name": "minpoly.coeff_zero_eq_zero", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.Field", "is_tactic_proof": true, "tactics": ["constructor", "intro", "have", "rw", "exact", "rintro", "simp"], "tactic_count": 7}
{"name": "minpoly.coeff_zero_ne_zero", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.Field", "is_tactic_proof": true, "tactics": ["contrapose", "simpa"], "tactic_count": 2}
{"name": "minpoly_algEquiv_toLinearMap", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.Field", "is_tactic_proof": true, "tactics": ["refine", "simp", "intro", "rw", "intro", "rw", "simp_rw", "apply", "simpa"], "tactic_count": 9}
{"name": "minpoly_algHom_toLinearMap", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.Field", "is_tactic_proof": false, "tactics": ["have", "rw", "exact", "rw", "apply", "ext", "simp", "rwa"], "tactic_count": 8}
{"name": "IsConjRoot", "kind": "definition", "module": "Mathlib.FieldTheory.Minpoly.IsConjRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isConjRoot_def", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.IsConjRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsConjRoot.refl", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.IsConjRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsConjRoot.symm", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.IsConjRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsConjRoot.trans", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.IsConjRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsConjRoot.setoid", "kind": "definition", "module": "Mathlib.FieldTheory.Minpoly.IsConjRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsConjRoot.comm", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.IsConjRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsConjRoot.aeval_eq_zero", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.IsConjRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsConjRoot.add_algebraMap", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.IsConjRoot", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsConjRoot.sub_algebraMap", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.IsConjRoot", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsConjRoot.neg", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.IsConjRoot", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "isConjRoot_algHom_iff_of_injective", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.IsConjRoot", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "isConjRoot_algHom_iff", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.IsConjRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isConjRoot_of_aeval_eq_zero", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.IsConjRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isConjRoot_iff_aeval_eq_zero", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.IsConjRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isConjRoot_of_algEquiv", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.IsConjRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isConjRoot_of_algEquiv'", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.IsConjRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isConjRoot_of_algEquiv₂", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.IsConjRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsConjRoot.exists_algEquiv", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.IsConjRoot", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "isConjRoot_iff_exists_algEquiv", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.IsConjRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isConjRoot_iff_orbitRel", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.IsConjRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsConjRoot.of_isScalarTower", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.IsConjRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isConjRoot_iff_mem_minpoly_aroots", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.IsConjRoot", "is_tactic_proof": true, "tactics": ["rw", "simp", "exact"], "tactic_count": 3}
{"name": "isConjRoot_iff_mem_minpoly_rootSet", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.IsConjRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsConjRoot.decidable", "kind": "instance", "module": "Mathlib.FieldTheory.Minpoly.IsConjRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsConjRoot.instIsEquiv", "kind": "instance", "module": "Mathlib.FieldTheory.Minpoly.IsConjRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsConjRoot.isIntegral", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.IsConjRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsConjRoot.isIntegral_iff", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.IsConjRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsConjRoot.eq_algebraMap_of_injective", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.IsConjRoot", "is_tactic_proof": true, "tactics": ["rw", "have", "rw", "simp", "simpa"], "tactic_count": 5}
{"name": "IsConjRoot.eq_algebraMap", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.IsConjRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsConjRoot.eq_zero_of_injective", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.IsConjRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsConjRoot.eq_zero", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.IsConjRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isConjRoot_iff_eq_algebraMap_of_injective", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.IsConjRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isConjRoot_iff_eq_algebraMap", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.IsConjRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isConjRoot_iff_eq_algebraMap'", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.IsConjRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isConjRoot_zero_iff_eq_zero_of_injective", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.IsConjRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isConjRoot_zero_iff_eq_zero", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.IsConjRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isConjRoot_zero_iff_eq_zero'", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.IsConjRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsConjRoot.ne_zero_of_injective", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.IsConjRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsConjRoot.ne_zero", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.IsConjRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "notMem_iff_exists_ne_and_isConjRoot", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.IsConjRoot", "is_tactic_proof": true, "tactics": ["calc"], "tactic_count": 1}
{"name": "minpoly.isIntegrallyClosed_eq_field_fractions", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.IsIntegrallyClosed", "is_tactic_proof": true, "tactics": ["refine", "exact", "rw", "exact"], "tactic_count": 4}
{"name": "minpoly.isIntegrallyClosed_eq_field_fractions'", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.IsIntegrallyClosed", "is_tactic_proof": true, "tactics": ["let", "rw"], "tactic_count": 2}
{"name": "minpoly.isIntegrallyClosed_dvd", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.IsIntegrallyClosed", "is_tactic_proof": true, "tactics": ["let", "let", "let", "have", "rw", "refine", "rw", "rw", "apply", "rw", "exact", "rw", "map_dvd_map", "rw", "exact"], "tactic_count": 15}
{"name": "minpoly.isIntegrallyClosed_dvd_iff", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.IsIntegrallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "minpoly.ker_eval", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.IsIntegrallyClosed", "is_tactic_proof": true, "tactics": ["ext", "simp_rw"], "tactic_count": 2}
{"name": "minpoly.IsIntegrallyClosed.degree_le_of_ne_zero", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.IsIntegrallyClosed", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "rw", "norm_cast", "exact"], "tactic_count": 5}
{"name": "minpoly.IsIntegrallyClosed.isIntegral_iff_isUnit_leadingCoeff", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.IsIntegrallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegrallyClosed.minpoly.unique", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.IsIntegrallyClosed", "is_tactic_proof": true, "tactics": ["have", "symm", "by_contra", "refine", "refine", "exact", "rw"], "tactic_count": 7}
{"name": "minpoly.IsIntegrallyClosed.unique_of_degree_le_degree_minpoly", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.IsIntegrallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "minpoly.IsIntegrallyClosed.isIntegral_iff_leadingCoeff_dvd", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.IsIntegrallyClosed", "is_tactic_proof": true, "tactics": ["refine", "use", "have", "suffices", "apply", "convert", "rw", "rw", "convert", "refine", "have", "simp", "exact", "have", "simp", "false_or]", "exact", "exact"], "tactic_count": 18}
{"name": "minpoly.prime_of_isIntegrallyClosed", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.IsIntegrallyClosed", "is_tactic_proof": false, "tactics": ["refine", "or_iff_not_imp_left.mpr", "rw", "rw", "exact"], "tactic_count": 5}
{"name": "IsIntegrallyClosed.minpoly_smul", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.IsIntegrallyClosed", "is_tactic_proof": true, "tactics": ["let", "let", "let", "apply", "rw", "map_scaleRoots", "simp_rw", "refine", "refine", "simpa", "exact", "rw", "mul_inv_cancel₀", "refine", "nth_rw", "map_inv₀]", "exact"], "tactic_count": 17}
{"name": "minpoly.ToAdjoin.injective", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.IsIntegrallyClosed", "is_tactic_proof": true, "tactics": ["refine", "obtain", "simpa"], "tactic_count": 3}
{"name": "minpoly.equivAdjoin", "kind": "definition", "module": "Mathlib.FieldTheory.Minpoly.IsIntegrallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "minpoly.equivAdjoin_toAlgHom", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.IsIntegrallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "minpoly.coe_equivAdjoin", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.IsIntegrallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.adjoin.powerBasis'", "kind": "definition", "module": "Mathlib.FieldTheory.Minpoly.IsIntegrallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.adjoin.powerBasis'_dim", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.IsIntegrallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.adjoin.powerBasis'_gen", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.IsIntegrallyClosed", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PowerBasis.ofAdjoinEqTop'", "kind": "definition", "module": "Mathlib.FieldTheory.Minpoly.IsIntegrallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "minpoly._example", "kind": "example", "module": "Mathlib.FieldTheory.Minpoly.IsIntegrallyClosed", "is_tactic_proof": true, "tactics": ["apply", "exact"], "tactic_count": 2}
{"name": "PowerBasis.ofAdjoinEqTop'_dim", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.IsIntegrallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerBasis.ofAdjoinEqTop'_gen", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.IsIntegrallyClosed", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "minpoly.instAlgebraSubtypeMemSubringSubalgebraIntegralClosure", "kind": "instance", "module": "Mathlib.FieldTheory.Minpoly.IsIntegrallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "minpoly.instSMulSubtypeMemSubringSubalgebraIntegralClosure", "kind": "instance", "module": "Mathlib.FieldTheory.Minpoly.IsIntegrallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "minpoly.instIsScalarTowerSubtypeMemSubringSubalgebraIntegralClosure", "kind": "instance", "module": "Mathlib.FieldTheory.Minpoly.IsIntegrallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "minpoly.ofSubring", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.IsIntegrallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "minpolyDiv", "kind": "definition", "module": "Mathlib.FieldTheory.Minpoly.MinpolyDiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "minpolyDiv_spec", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.MinpolyDiv", "is_tactic_proof": true, "tactics": ["delta", "rw"], "tactic_count": 2}
{"name": "coeff_minpolyDiv", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.MinpolyDiv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "minpolyDiv_eq_zero", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.MinpolyDiv", "is_tactic_proof": true, "tactics": ["delta", "rw"], "tactic_count": 2}
{"name": "eval_minpolyDiv_self", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.MinpolyDiv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "minpolyDiv_eval_eq_zero_of_ne_of_aeval_eq_zero", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.MinpolyDiv", "is_tactic_proof": true, "tactics": ["rw", "simp", "exact"], "tactic_count": 3}
{"name": "eval₂_minpolyDiv_of_eval₂_eq_zero", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.MinpolyDiv", "is_tactic_proof": true, "tactics": ["split_ifs", "rw", "rw", "simpa"], "tactic_count": 4}
{"name": "eval₂_minpolyDiv_self", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.MinpolyDiv", "is_tactic_proof": true, "tactics": ["apply", "rw", "minpoly.aeval,"], "tactic_count": 3}
{"name": "eval_minpolyDiv_of_aeval_eq_zero", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.MinpolyDiv", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "coeff_minpolyDiv_mem_adjoin", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.MinpolyDiv", "is_tactic_proof": true, "tactics": ["by_contra", "have", "induction", "zero", "succ", "intro", "rw", "refine", "exact", "apply", "rw", "exact", "lia"], "tactic_count": 13}
{"name": "minpolyDiv_ne_zero", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.MinpolyDiv", "is_tactic_proof": true, "tactics": ["intro", "have", "rw", "exact"], "tactic_count": 4}
{"name": "minpolyDiv_monic", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.MinpolyDiv", "is_tactic_proof": true, "tactics": ["nontriviality", "have", "rw", "simpa", "simpa"], "tactic_count": 5}
{"name": "natDegree_minpolyDiv_succ", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.MinpolyDiv", "is_tactic_proof": true, "tactics": ["rw", "simp", "simpa"], "tactic_count": 3}
{"name": "natDegree_minpolyDiv_lt", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.MinpolyDiv", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "minpolyDiv_eq_of_isIntegrallyClosed", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.MinpolyDiv", "is_tactic_proof": true, "tactics": ["delta", "rw"], "tactic_count": 2}
{"name": "coeff_minpolyDiv_sub_pow_mem_span", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.MinpolyDiv", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "refine", "apply", "apply", "exact", "rw", "apply", "rw", "apply", "rintro", "rw", "exact"], "tactic_count": 15}
{"name": "span_coeff_minpolyDiv", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.MinpolyDiv", "is_tactic_proof": true, "tactics": ["nontriviality", "classical", "apply", "rw", "rintro", "apply", "rw", "simp", "intro", "induction", "ind", "intro", "have", "coeff", "rw", "refine", "rw", "intro", "exact", "rwa"], "tactic_count": 20}
{"name": "natDegree_minpolyDiv", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.MinpolyDiv", "is_tactic_proof": true, "tactics": ["nontriviality", "by_cases", "rw", "rw"], "tactic_count": 4}
{"name": "sum_smul_minpolyDiv_eq_X_pow", "kind": "theorem", "module": "Mathlib.FieldTheory.Minpoly.MinpolyDiv", "is_tactic_proof": true, "tactics": ["classical", "rw", "have", "apply", "intro", "simp", "eval₂_minpolyDiv_self,", "eval_X_pow]", "rw", "rw", "exact", "refine", "simp", "forall_true_left,", "refine", "intro", "exact", "rwa"], "tactic_count": 18}
{"name": "MvRatFunc.rank_eq_max_lift", "kind": "theorem", "module": "Mathlib.FieldTheory.MvRatFunc.Rank", "is_tactic_proof": true, "tactics": ["let", "let", "refine", "rw", "have", "have", "rw", "obtain", "have", "have", "rw", "exact"], "tactic_count": 12}
{"name": "Normal.exists_isSplittingField", "kind": "theorem", "module": "Mathlib.FieldTheory.Normal.Basic", "is_tactic_proof": true, "tactics": ["classical", "let", "refine", "rw", "refine", "exact", "rw", "exact"], "tactic_count": 8}
{"name": "Normal.of_isSplittingField", "kind": "theorem", "module": "Mathlib.FieldTheory.Normal.Basic", "is_tactic_proof": true, "tactics": ["rcases", "have", "rw", "exact", "refine", "haveI", "have", "let", "have", "rw", "obtain", "let", "rw", "refine", "rw", "letI", "let", "change", "rw", "exact", "rwa", "exact"], "tactic_count": 22}
{"name": "Polynomial.SplittingField.instNormal", "kind": "instance", "module": "Mathlib.FieldTheory.Normal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.normal_iSup", "kind": "instance", "module": "Mathlib.FieldTheory.Normal.Basic", "is_tactic_proof": true, "tactics": ["refine", "obtain", "let", "have", "haveI", "refine", "exact", "simpa", "apply", "have", "refine", "rw", "exact", "have", "rw", "have", "rwa"], "tactic_count": 17}
{"name": "IntermediateField.splits_of_mem_adjoin", "kind": "theorem", "module": "Mathlib.FieldTheory.Normal.Basic", "is_tactic_proof": true, "tactics": ["let", "have", "normal_iSup", "have", "splits_of_splits", "obtain", "convert", "simp"], "tactic_count": 8}
{"name": "IntermediateField.normal_sup", "kind": "instance", "module": "Mathlib.FieldTheory.Normal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.normal_iInf", "kind": "instance", "module": "Mathlib.FieldTheory.Normal.Basic", "is_tactic_proof": true, "tactics": ["refine", "let", "exact", "have", "intro", "rw", "exact", "simp", "rintro", "exact"], "tactic_count": 10}
{"name": "IntermediateField.normal_inf", "kind": "instance", "module": "Mathlib.FieldTheory.Normal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.fieldRange_of_normal", "kind": "theorem", "module": "Mathlib.FieldTheory.Normal.Basic", "is_tactic_proof": true, "tactics": ["let", "rw"], "tactic_count": 2}
{"name": "AlgHom.liftNormal", "kind": "definition", "module": "Mathlib.FieldTheory.Normal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.liftNormal_commutes", "kind": "theorem", "module": "Mathlib.FieldTheory.Normal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.restrict_liftNormal", "kind": "theorem", "module": "Mathlib.FieldTheory.Normal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.liftNormal", "kind": "definition", "module": "Mathlib.FieldTheory.Normal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.liftNormal_commutes", "kind": "theorem", "module": "Mathlib.FieldTheory.Normal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.restrict_liftNormal", "kind": "theorem", "module": "Mathlib.FieldTheory.Normal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.restrictNormalHom_surjective", "kind": "theorem", "module": "Mathlib.FieldTheory.Normal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Normal.minpoly_eq_iff_mem_orbit", "kind": "theorem", "module": "Mathlib.FieldTheory.Normal.Basic", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact"], "tactic_count": 3}
{"name": "isSolvable_of_isScalarTower", "kind": "theorem", "module": "Mathlib.FieldTheory.Normal.Basic", "is_tactic_proof": false, "tactics": ["let", "map_one", "map_mul", "refine", "solvable_of_ker_le_range", "exact"], "tactic_count": 6}
{"name": "minpoly.exists_algEquiv_of_root", "kind": "theorem", "module": "Mathlib.FieldTheory.Normal.Basic", "is_tactic_proof": true, "tactics": ["have", "set", "have", "rw", "exact"], "tactic_count": 5}
{"name": "minpoly.exists_algEquiv_of_root'", "kind": "theorem", "module": "Mathlib.FieldTheory.Normal.Basic", "is_tactic_proof": true, "tactics": ["obtain", "use", "rw"], "tactic_count": 3}
{"name": "Algebra.IsQuadraticExtension.normal", "kind": "instance", "module": "Mathlib.FieldTheory.Normal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.normalClosure", "kind": "definition", "module": "Mathlib.FieldTheory.Normal.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "normalClosure_def", "kind": "theorem", "module": "Mathlib.FieldTheory.Normal.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsNormalClosure.normal", "kind": "theorem", "module": "Mathlib.FieldTheory.Normal.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "normalClosure_le_iff", "kind": "theorem", "module": "Mathlib.FieldTheory.Normal.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.fieldRange_le_normalClosure", "kind": "theorem", "module": "Mathlib.FieldTheory.Normal.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsAlgebraic.normalClosure_le_iSup_adjoin", "kind": "theorem", "module": "Mathlib.FieldTheory.Normal.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsAlgebraic.normalClosure_eq_iSup_adjoin_of_splits", "kind": "theorem", "module": "Mathlib.FieldTheory.Normal.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsAlgebraic.isNormalClosure_iff", "kind": "theorem", "module": "Mathlib.FieldTheory.Normal.Closure", "is_tactic_proof": true, "tactics": ["refine", "simpa"], "tactic_count": 2}
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{"name": "Subfield.bot_eq_of_zMod_algebra", "kind": "theorem", "module": "Mathlib.FieldTheory.PrimeField", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "AlgHom.natCard_of_splits", "kind": "theorem", "module": "Mathlib.FieldTheory.PrimitiveElement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.card_of_splits", "kind": "theorem", "module": "Mathlib.FieldTheory.PrimitiveElement", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgHom.card", "kind": "theorem", "module": "Mathlib.FieldTheory.PrimitiveElement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "IsPurelyInseparable.isIntegral'", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPurelyInseparable.isAlgebraic", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPurelyInseparable.inseparable", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isPurelyInseparable_iff", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.isPurelyInseparable", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Basic", "is_tactic_proof": false, "tactics": ["refine", "rw", "simpa"], "tactic_count": 3}
{"name": "AlgEquiv.isPurelyInseparable_iff", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsAlgebraic.isPurelyInseparable_of_isSepClosed", "kind": "instance", "module": "Mathlib.FieldTheory.PurelyInseparable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPurelyInseparable.surjective_algebraMap_of_isSeparable", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPurelyInseparable.bijective_algebraMap_of_isSeparable", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.eq_bot_of_isPurelyInseparable_of_isSeparable", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.eq_bot_of_isPurelyInseparable_of_isSeparable", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "isPurelyInseparable_self", "kind": "instance", "module": "Mathlib.FieldTheory.PurelyInseparable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isPurelyInseparable_iff_pow_mem", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "obtain", "exact", "h1.of_dvd", "have", "have", "by_contra", "refine", "rwa"], "tactic_count": 10}
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{"name": "IsPurelyInseparable.tower_bot", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "obtain", "exact"], "tactic_count": 4}
{"name": "IsPurelyInseparable.tower_top", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Basic", "is_tactic_proof": true, "tactics": ["obtain", "haveI", "rw", "intro", "obtain", "exact"], "tactic_count": 6}
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{"name": "IntermediateField.isPurelyInseparable_tower_top", "kind": "instance", "module": "Mathlib.FieldTheory.PurelyInseparable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isPurelyInseparable_iff_natSepDegree_eq_one", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Basic", "is_tactic_proof": true, "tactics": ["obtain", "simp_rw"], "tactic_count": 2}
{"name": "IsPurelyInseparable.natSepDegree_eq_one", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "IsPurelyInseparable.injective_restrictDomain", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "IsPurelyInseparable.bijective_comp_algebraMap", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPurelyInseparable.bijective_restrictDomain", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instSubsingletonAlgHomOfIsPurelyInseparable", "kind": "instance", "module": "Mathlib.FieldTheory.PurelyInseparable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instUniqueAlgHomOfIsPurelyInseparable", "kind": "instance", "module": "Mathlib.FieldTheory.PurelyInseparable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instUniqueEmbOfIsPurelyInseparable", "kind": "instance", "module": "Mathlib.FieldTheory.PurelyInseparable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPurelyInseparable.finSepDegree_eq_one", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPurelyInseparable.sepDegree_eq_one", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsPurelyInseparable.insepDegree_eq", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsPurelyInseparable.finInsepDegree_eq", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isPurelyInseparable_iff_finSepDegree_eq_one", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isSeparable_iff_finInsepDegree_eq_one", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "isPurelyInseparable_iff_fd_isPurelyInseparable", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Basic", "is_tactic_proof": true, "tactics": ["refine", "have", "refine", "obtain", "show", "exact"], "tactic_count": 6}
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{"name": "Field.Emb.cardinal_separableClosure", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Basic", "is_tactic_proof": true, "tactics": ["rw", "mul_one,"], "tactic_count": 2}
{"name": "finInsepDegree_eq_pow", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "separableClosure_le", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "separableClosure_le_iff", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Basic", "is_tactic_proof": true, "tactics": ["refine", "letI", "letI", "haveI", "exact"], "tactic_count": 5}
{"name": "eq_separableClosure", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_separableClosure_iff", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPurelyInseparable.of_injective_comp_algebraMap", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Basic", "is_tactic_proof": true, "tactics": ["rw", "letI", "let", "exact", "j.injective.comp_left", "inferInstance⟩"], "tactic_count": 6}
{"name": "IntermediateField.isPurelyInseparable_bot", "kind": "instance", "module": "Mathlib.FieldTheory.PurelyInseparable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isSepClosed_iff_isPurelyInseparable_algebraicClosure", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsAlgebraic.isSepClosed", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Field.finSepDegree_eq", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Basic", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "Field.finSepDegree_mul_finInsepDegree", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "have", "rwa", "rw", "finrank_of_infinite_dimensional", "finrank_of_infinite_dimensional", "halg", "mul_zero]"], "tactic_count": 8}
{"name": "separableClosure.adjoin_eq_of_isAlgebraic_of_isSeparable", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "separableClosure.adjoin_eq_of_isAlgebraic", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Basic", "is_tactic_proof": true, "tactics": ["set", "have", "rw", "haveI", "rw", "simp"], "tactic_count": 6}
{"name": "Subalgebra.perfectClosure", "kind": "definition", "module": "Mathlib.FieldTheory.PurelyInseparable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.mem_perfectClosure_iff", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPurelyInseparable.exists_pow_pow_mem_range_tensorProduct_of_expChar", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Basic", "is_tactic_proof": true, "tactics": ["nontriviality", "obtain", "induction", "zero", "add", "h", "have", "simp_rw", "exact", "tmul", "obtain", "use", "have", "rw", "rw", "refine", "rw", "subst", "have", "exact"], "tactic_count": 20}
{"name": "IsPurelyInseparable.exists_pow_mem_range_tensorProduct", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Basic", "is_tactic_proof": true, "tactics": ["let", "obtain", "refine", "obtain"], "tactic_count": 4}
{"name": "IsPurelyInseparable.hasExponent_iff'", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Exponent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPurelyInseparable.exponent", "kind": "definition", "module": "Mathlib.FieldTheory.PurelyInseparable.Exponent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPurelyInseparable.exponent_def", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Exponent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPurelyInseparable.exponent_def'", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Exponent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPurelyInseparable.exponent_min", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Exponent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPurelyInseparable.exponent_min'", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Exponent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPurelyInseparable.instOfHasExponent", "kind": "instance", "module": "Mathlib.FieldTheory.PurelyInseparable.Exponent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPurelyInseparable.elemExponent", "kind": "definition", "module": "Mathlib.FieldTheory.PurelyInseparable.Exponent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPurelyInseparable.elemExponent_eq_zero_of_mem_range", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Exponent", "is_tactic_proof": true, "tactics": ["apply", "rw", "obtain", "exact"], "tactic_count": 4}
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{"name": "IsPurelyInseparable.elemReduct", "kind": "definition", "module": "Mathlib.FieldTheory.PurelyInseparable.Exponent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "IsPurelyInseparable.minpoly_eq'", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Exponent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPurelyInseparable.minpoly_natDegree_eq", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Exponent", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsPurelyInseparable.minpoly_natDegree_eq'", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Exponent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPurelyInseparable.algebraMap_elemReduct_eq", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Exponent", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "IsPurelyInseparable.algebraMap_elemReduct_eq'", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Exponent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPurelyInseparable.elemExponent_def", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Exponent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPurelyInseparable.elemExponent_def'", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Exponent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPurelyInseparable.elemExponent_le_of_pow_mem", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Exponent", "is_tactic_proof": true, "tactics": ["let", "rcases", "exact", "obtain", "let", "have", "have", "have", "exact", "ringExpChar.eq"], "tactic_count": 10}
{"name": "IsPurelyInseparable.elemExponent_le_of_pow_mem'", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Exponent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPurelyInseparable.elemExponent_min", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Exponent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPurelyInseparable.elemExponent_min'", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Exponent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPurelyInseparable.elemExponent_le_exponent", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Exponent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPurelyInseparable.hasExponent_of_finiteDimensional", "kind": "instance", "module": "Mathlib.FieldTheory.PurelyInseparable.Exponent", "is_tactic_proof": true, "tactics": ["let", "rcases", "exact", "let", "refine", "have", "rw"], "tactic_count": 7}
{"name": "_private.Mathlib.FieldTheory.PurelyInseparable.Exponent.0.IsPurelyInseparable.iterateFrobeniusAux", "kind": "definition", "module": "Mathlib.FieldTheory.PurelyInseparable.Exponent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.FieldTheory.PurelyInseparable.Exponent.0.IsPurelyInseparable.algebraMap_iterateFrobeniusAux", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Exponent", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsPurelyInseparable.iterateFrobenius", "kind": "definition", "module": "Mathlib.FieldTheory.PurelyInseparable.Exponent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPurelyInseparable.algebraMap_iterateFrobenius", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Exponent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPurelyInseparable.iterateFrobenius_algebraMap", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Exponent", "is_tactic_proof": true, "tactics": ["apply", "rw"], "tactic_count": 2}
{"name": "IsPurelyInseparable.iterateFrobeniusₛₗ", "kind": "definition", "module": "Mathlib.FieldTheory.PurelyInseparable.Exponent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPurelyInseparable.algebraMap_iterateFrobeniusₛₗ", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Exponent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPurelyInseparable.iterateFrobeniusₛₗ_algebraMap", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Exponent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPurelyInseparable.iterateFrobeniusₛₗ_algebraMap_base", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Exponent", "is_tactic_proof": true, "tactics": ["apply", "rw"], "tactic_count": 2}
{"name": "perfectClosure", "kind": "definition", "module": "Mathlib.FieldTheory.PurelyInseparable.PerfectClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_perfectClosure_iff", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.PerfectClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_perfectClosure_iff_pow_mem", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.PerfectClosure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mem_perfectClosure_iff_natSepDegree_eq_one", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.PerfectClosure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "perfectClosure.eq_bot_of_isSeparable", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.PerfectClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "map_mem_perfectClosure_iff", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.PerfectClosure", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "apply_fun", "rwa", "simpa"], "tactic_count": 5}
{"name": "perfectClosure.comap_eq_of_algHom", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.PerfectClosure", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "perfectClosure.map_le_of_algHom", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.PerfectClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "perfectClosure.map_eq_of_algEquiv", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.PerfectClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "perfectClosure.algEquivOfAlgEquiv", "kind": "definition", "module": "Mathlib.FieldTheory.PurelyInseparable.PerfectClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "perfectClosure.perfectRing", "kind": "instance", "module": "Mathlib.FieldTheory.PurelyInseparable.PerfectClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "perfectClosure.perfectField", "kind": "instance", "module": "Mathlib.FieldTheory.PurelyInseparable.PerfectClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.isPurelyInseparable_adjoin_simple_iff_natSepDegree_eq_one", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.PerfectClosure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "IntermediateField.isPurelyInseparable_sup", "kind": "instance", "module": "Mathlib.FieldTheory.PurelyInseparable.PerfectClosure", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IntermediateField.isPurelyInseparable_iSup", "kind": "instance", "module": "Mathlib.FieldTheory.PurelyInseparable.PerfectClosure", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "IntermediateField.adjoin_eq_adjoin_pow_expChar_pow_of_isSeparable", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.PerfectClosure", "is_tactic_proof": true, "tactics": ["set", "set", "have", "rw", "rintro", "exact", "letI", "haveI", "haveI", "rw", "exact", "simpa", "congr_arg"], "tactic_count": 13}
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{"name": "IntermediateField.adjoin_eq_adjoin_pow_expChar_of_isSeparable", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.PerfectClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.adjoin_eq_adjoin_pow_expChar_of_isSeparable'", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.PerfectClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.adjoin_simple_eq_adjoin_pow_expChar_pow_of_isSeparable", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.PerfectClosure", "is_tactic_proof": true, "tactics": ["haveI", "simpa"], "tactic_count": 2}
{"name": "IntermediateField.adjoin_simple_eq_adjoin_pow_expChar_pow_of_isSeparable'", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.PerfectClosure", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IntermediateField.adjoin_simple_eq_adjoin_pow_expChar_of_isSeparable", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.PerfectClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.adjoin_simple_eq_adjoin_pow_expChar_of_isSeparable'", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.PerfectClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Field.span_map_pow_expChar_pow_eq_top_of_isSeparable", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.PerfectClosure", "is_tactic_proof": false, "tactics": ["rw", "adjoin_eq_adjoin_pow_expChar_pow_of_isSeparable", "adjoin_toSubalgebra_of_isAlgebraic", "have", "simp", "rw", "refine", "rw", "haveI", "apply"], "tactic_count": 10}
{"name": "_private.Mathlib.FieldTheory.PurelyInseparable.PerfectClosure.0.LinearIndependent.map_pow_expChar_pow_of_fd_isSeparable", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.PerfectClosure", "is_tactic_proof": true, "tactics": ["have", "let", "let", "letI", "have", "linearIndependent_of_top_le_span_of_card_eq_finrank", "let", "convert", "simp_rw", "rw"], "tactic_count": 10}
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{"name": "LinearIndependent.map_pow_expChar_pow_of_isSeparable'", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.PerfectClosure", "is_tactic_proof": true, "tactics": ["let", "haveI", "let", "have", "exact"], "tactic_count": 5}
{"name": "Module.Basis.mapPowExpCharPowOfIsSeparable", "kind": "definition", "module": "Mathlib.FieldTheory.PurelyInseparable.PerfectClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "minpoly.iterateFrobenius_of_isSeparable", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.PerfectClosure", "is_tactic_proof": true, "tactics": ["have", "have", "symm", "refine", "simpa", "rw"], "tactic_count": 6}
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{"name": "perfectField_of_perfectClosure_eq_bot", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.PerfectClosure", "is_tactic_proof": true, "tactics": ["let", "haveI", "haveI", "obtain", "have", "obtain", "simp", "exact", "exact"], "tactic_count": 9}
{"name": "perfectField_of_isSeparable_of_perfectField_top", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.PerfectClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "perfectField_iff_isSeparable_algebraicClosure", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.PerfectClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIndependent.map_of_isPurelyInseparable_of_isSeparable", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Tower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.linearDisjoint_of_isPurelyInseparable_of_isSeparable", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Tower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Field.sepDegree_eq_of_isPurelyInseparable_of_isSeparable", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Tower", "is_tactic_proof": false, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "Field.lift_rank_mul_lift_sepDegree_of_isSeparable", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Tower", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Field.rank_mul_sepDegree_of_isSeparable", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Tower", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Field.insepDegree_eq_of_isSeparable", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Tower", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Field.sepDegree_eq_of_isPurelyInseparable", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Tower", "is_tactic_proof": true, "tactics": ["convert", "haveI", "rw", "exact"], "tactic_count": 4}
{"name": "Field.lift_rank_mul_lift_insepDegree_of_isPurelyInseparable", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Tower", "is_tactic_proof": false, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "Field.rank_mul_insepDegree_of_isPurelyInseparable", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Tower", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Field.lift_sepDegree_mul_lift_sepDegree_of_isAlgebraic", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Tower", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "Field.sepDegree_mul_sepDegree_of_isAlgebraic", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Tower", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Field.lift_insepDegree_mul_lift_insepDegree_of_isAlgebraic", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Tower", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "Field.insepDegree_mul_insepDegree_of_isAlgebraic", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Tower", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Field.finInsepDegree_mul_finInsepDegree_of_isAlgebraic", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Tower", "is_tactic_proof": true, "tactics": ["simpa", "congr"], "tactic_count": 2}
{"name": "IntermediateField.sepDegree_adjoin_eq_of_isAlgebraic_of_isPurelyInseparable", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Tower", "is_tactic_proof": true, "tactics": ["set", "set", "let", "let", "have", "rw", "exact", "let", "letI", "letI", "haveI", "haveI", "change", "obtain", "have", "restrictScalars_injective", "conv_lhs", "rw", "adjoin_adjoin_comm]", "rw", "rintro", "obtain", "refine", "rw", "have", "rw", "rw"], "tactic_count": 27}
{"name": "IntermediateField.sepDegree_adjoin_eq_of_isAlgebraic_of_isPurelyInseparable'", "kind": "theorem", "module": "Mathlib.FieldTheory.PurelyInseparable.Tower", "is_tactic_proof": true, "tactics": ["have", "have", "rwa"], "tactic_count": 3}
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{"name": "RatFunc.X", "kind": "definition", "module": "Mathlib.FieldTheory.RatFunc.AsPolynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "RatFunc.denom_X", "kind": "theorem", "module": "Mathlib.FieldTheory.RatFunc.AsPolynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RatFunc.X_ne_zero", "kind": "theorem", "module": "Mathlib.FieldTheory.RatFunc.AsPolynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RatFunc.eq_C_iff", "kind": "theorem", "module": "Mathlib.FieldTheory.RatFunc.AsPolynomial", "is_tactic_proof": true, "tactics": ["refine", "rw", "rintro", "use", "rw"], "tactic_count": 5}
{"name": "RatFunc.eval", "kind": "definition", "module": "Mathlib.FieldTheory.RatFunc.AsPolynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RatFunc.eval_eq_zero_of_eval₂_denom_eq_zero", "kind": "theorem", "module": "Mathlib.FieldTheory.RatFunc.AsPolynomial", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "RatFunc.eval_algebraMap", "kind": "theorem", "module": "Mathlib.FieldTheory.RatFunc.AsPolynomial", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "RatFunc.transcendental_X", "kind": "theorem", "module": "Mathlib.FieldTheory.RatFunc.AsPolynomial", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "RatFunc.transcendental", "kind": "instance", "module": "Mathlib.FieldTheory.RatFunc.AsPolynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.idealX", "kind": "definition", "module": "Mathlib.FieldTheory.RatFunc.AsPolynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.idealX_span", "kind": "theorem", "module": "Mathlib.FieldTheory.RatFunc.AsPolynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.valuation_X_eq_neg_one", "kind": "theorem", "module": "Mathlib.FieldTheory.RatFunc.AsPolynomial", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.valuation_of_mk", "kind": "theorem", "module": "Mathlib.FieldTheory.RatFunc.AsPolynomial", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.valuation_aeval_monomial_eq_valuation_pow", "kind": "theorem", "module": "Mathlib.FieldTheory.RatFunc.AsPolynomial", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "Polynomial.valuation_inv_monomial_eq_valuation_X_zpow", "kind": "theorem", "module": "Mathlib.FieldTheory.RatFunc.AsPolynomial", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "RatFunc.instValuedWithZeroMultiplicativeInt", "kind": "instance", "module": "Mathlib.FieldTheory.RatFunc.AsPolynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "RatFunc.ofFractionRing_zero", "kind": "theorem", "module": "Mathlib.FieldTheory.RatFunc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "RatFunc.ofFractionRing_add", "kind": "theorem", "module": "Mathlib.FieldTheory.RatFunc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "RatFunc.coe_mapRingHom_eq_coe_map", "kind": "theorem", "module": "Mathlib.FieldTheory.RatFunc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "RatFunc.liftMonoidWithZeroHom_apply_ofFractionRing_mk", "kind": "theorem", "module": "Mathlib.FieldTheory.RatFunc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "RatFunc.liftRingHom_comp_algebraMap", "kind": "theorem", "module": "Mathlib.FieldTheory.RatFunc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RatFunc.ofFractionRing_comp_algebraMap", "kind": "theorem", "module": "Mathlib.FieldTheory.RatFunc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "RatFunc.mapAlgHom", "kind": "definition", "module": "Mathlib.FieldTheory.RatFunc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RatFunc.coe_mapAlgHom_eq_coe_map", "kind": "theorem", "module": "Mathlib.FieldTheory.RatFunc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RatFunc.liftAlgHom", "kind": "definition", "module": "Mathlib.FieldTheory.RatFunc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RatFunc.liftAlgHom_apply_ofFractionRing_mk", "kind": "theorem", "module": "Mathlib.FieldTheory.RatFunc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "RatFunc.instIsFractionRingPolynomial", "kind": "instance", "module": "Mathlib.FieldTheory.RatFunc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RatFunc.algebraMap_ne_zero", "kind": "theorem", "module": "Mathlib.FieldTheory.RatFunc.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
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{"name": "RatFunc.ofFractionRing_mk'", "kind": "theorem", "module": "Mathlib.FieldTheory.RatFunc.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "RatFunc.ofFractionRing_eq", "kind": "theorem", "module": "Mathlib.FieldTheory.RatFunc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RatFunc.toFractionRing_eq", "kind": "theorem", "module": "Mathlib.FieldTheory.RatFunc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RatFunc.toFractionRingRingEquiv_symm_eq", "kind": "theorem", "module": "Mathlib.FieldTheory.RatFunc.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "RatFunc.liftAlgebra", "kind": "instance", "module": "Mathlib.FieldTheory.RatFunc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RatFunc.isScalarTower_liftAlgebra", "kind": "instance", "module": "Mathlib.FieldTheory.RatFunc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RatFunc.faithfulSMul", "kind": "instance", "module": "Mathlib.FieldTheory.RatFunc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RatFunc.rank_ratFunc_ratFunc", "kind": "theorem", "module": "Mathlib.FieldTheory.RatFunc.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RatFunc.finrank_ratFunc_ratFunc", "kind": "theorem", "module": "Mathlib.FieldTheory.RatFunc.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "have", "rw", "exact", "have", "rwa", "rw"], "tactic_count": 7}
{"name": "RatFunc.instIsScalarTowerOfIsDomainOfPolynomial", "kind": "instance", "module": "Mathlib.FieldTheory.RatFunc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RatFunc.instIsScalarTowerOfPolynomial", "kind": "instance", "module": "Mathlib.FieldTheory.RatFunc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RatFunc.instIsScalarTowerOfPolynomial_1", "kind": "instance", "module": "Mathlib.FieldTheory.RatFunc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "RatFunc.numDenom_div", "kind": "theorem", "module": "Mathlib.FieldTheory.RatFunc.Basic", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "simp"], "tactic_count": 4}
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{"name": "RatFunc.map_denom_ne_zero", "kind": "theorem", "module": "Mathlib.FieldTheory.RatFunc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RatFunc.map_apply", "kind": "theorem", "module": "Mathlib.FieldTheory.RatFunc.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "RatFunc.liftMonoidWithZeroHom_apply", "kind": "theorem", "module": "Mathlib.FieldTheory.RatFunc.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RatFunc.liftRingHom_apply", "kind": "theorem", "module": "Mathlib.FieldTheory.RatFunc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "RatFunc.num_mul_denom_add_denom_mul_num_ne_zero", "kind": "theorem", "module": "Mathlib.FieldTheory.RatFunc.Basic", "is_tactic_proof": true, "tactics": ["intro", "have", "rw", "exact"], "tactic_count": 4}
{"name": "RatFunc.instCharP", "kind": "instance", "module": "Mathlib.FieldTheory.RatFunc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RatFunc.instExpChar", "kind": "instance", "module": "Mathlib.FieldTheory.RatFunc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RatFunc.instCharZero", "kind": "instance", "module": "Mathlib.FieldTheory.RatFunc.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RatFunc.ofFractionRing_injective", "kind": "theorem", "module": "Mathlib.FieldTheory.RatFunc.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RatFunc.toFractionRing_injective", "kind": "theorem", "module": "Mathlib.FieldTheory.RatFunc.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RatFunc.toFractionRing_inj", "kind": "theorem", "module": "Mathlib.FieldTheory.RatFunc.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RatFunc.definition._@.Mathlib.FieldTheory.RatFunc.Defs.2008491285._hygCtx._hyg.2", "kind": "definition", "module": "Mathlib.FieldTheory.RatFunc.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "RatFunc.liftOn", "kind": "definition", "module": "Mathlib.FieldTheory.RatFunc.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RatFunc.liftOn_def", "kind": "theorem", "module": "Mathlib.FieldTheory.RatFunc.Defs", "is_tactic_proof": true, "tactics": ["intros", "delta", "rw", "rfl"], "tactic_count": 4}
{"name": "RatFunc.liftOn_ofFractionRing_mk", "kind": "theorem", "module": "Mathlib.FieldTheory.RatFunc.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "RatFunc.liftOn_condition_of_liftOn'_condition", "kind": "theorem", "module": "Mathlib.FieldTheory.RatFunc.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "RatFunc.mk_def", "kind": "theorem", "module": "Mathlib.FieldTheory.RatFunc.Defs", "is_tactic_proof": true, "tactics": ["intros", "delta", "rw", "rfl"], "tactic_count": 4}
{"name": "RatFunc.mk_eq_div'", "kind": "theorem", "module": "Mathlib.FieldTheory.RatFunc.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RatFunc.mk_zero", "kind": "theorem", "module": "Mathlib.FieldTheory.RatFunc.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RatFunc.mk_coe_def", "kind": "theorem", "module": "Mathlib.FieldTheory.RatFunc.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RatFunc.mk_def_of_mem", "kind": "theorem", "module": "Mathlib.FieldTheory.RatFunc.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RatFunc.mk_def_of_ne", "kind": "theorem", "module": "Mathlib.FieldTheory.RatFunc.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RatFunc.mk_eq_localization_mk", "kind": "theorem", "module": "Mathlib.FieldTheory.RatFunc.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RatFunc.mk_one'", "kind": "theorem", "module": "Mathlib.FieldTheory.RatFunc.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "RatFunc.liftOn'_mk", "kind": "theorem", "module": "Mathlib.FieldTheory.RatFunc.Defs", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "RatFunc.induction_on'", "kind": "theorem", "module": "Mathlib.FieldTheory.RatFunc.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RatFunc.intDegree", "kind": "definition", "module": "Mathlib.FieldTheory.RatFunc.Degree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RatFunc.intDegree_zero", "kind": "theorem", "module": "Mathlib.FieldTheory.RatFunc.Degree", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RatFunc.intDegree_one", "kind": "theorem", "module": "Mathlib.FieldTheory.RatFunc.Degree", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RatFunc.intDegree_C", "kind": "theorem", "module": "Mathlib.FieldTheory.RatFunc.Degree", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RatFunc.intDegree_X", "kind": "theorem", "module": "Mathlib.FieldTheory.RatFunc.Degree", "is_tactic_proof": true, "tactics": ["rw", "sub_zero]"], "tactic_count": 2}
{"name": "RatFunc.intDegree_polynomial", "kind": "theorem", "module": "Mathlib.FieldTheory.RatFunc.Degree", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RatFunc.intDegree_mul", "kind": "theorem", "module": "Mathlib.FieldTheory.RatFunc.Degree", "is_tactic_proof": true, "tactics": ["simp", "norm_cast", "rw"], "tactic_count": 3}
{"name": "RatFunc.intDegree_inv", "kind": "theorem", "module": "Mathlib.FieldTheory.RatFunc.Degree", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
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{"name": "Subfield.relrank_map_map", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
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{"name": "Subfield.relrank_comap", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
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{"name": "Subfield.lift_rank_comap", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Subfield.rank_comap", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Subfield.finrank_comap", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Subfield.relfinrank_map_map", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
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{"name": "Subfield.relrank_comap_comap_eq_relrank_inf", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Subfield.relfinrank_comap_comap_eq_relfinrank_inf", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Subfield.lift_relrank_comap_comap_eq_lift_relrank_of_le", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
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{"name": "Subfield.relfinrank_comap_comap_eq_relfinrank_of_le", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
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{"name": "Subfield.relrank_comap_comap_eq_relrank_of_surjective", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
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{"name": "Subfield.relfinrank_dvd_finrank_top_of_le", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Subfield.relfinrank_inf_mul_relfinrank", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Subfield.relrank_mul_relrank_eq_inf_relrank", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Subfield.relfinrank_mul_relfinrank_eq_inf_relfinrank", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Subfield.relrank_inf_mul_relrank_of_le", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Subfield.relfinrank_inf_mul_relfinrank_of_le", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Subfield.relrank_dvd_of_le_left", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.relfinrank_dvd_of_le_left", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.relrank", "kind": "definition", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.relfinrank", "kind": "definition", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.relfinrank_eq_toNat_relrank", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.relrank_eq_of_inf_eq", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.relfinrank_eq_of_inf_eq", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.relrank_eq_rank_of_le", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.relfinrank_eq_finrank_of_le", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.inf_relrank_right", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.inf_relfinrank_right", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.inf_relrank_left", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IntermediateField.inf_relfinrank_left", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.relrank_self", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.relfinrank_self", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.relrank_eq_one_of_le", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IntermediateField.relfinrank_eq_one_of_le", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IntermediateField.lift_rank_comap", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.rank_comap", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IntermediateField.finrank_comap", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IntermediateField.lift_relrank_comap", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.relrank_comap", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IntermediateField.relfinrank_comap", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IntermediateField.lift_relrank_map_map", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IntermediateField.relrank_map_map", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IntermediateField.relfinrank_map_map", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IntermediateField.lift_relrank_comap_comap_eq_lift_relrank_inf", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.relrank_comap_comap_eq_relrank_inf", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IntermediateField.relfinrank_comap_comap_eq_relfinrank_inf", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IntermediateField.lift_relrank_comap_comap_eq_lift_relrank_of_le", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IntermediateField.relrank_comap_comap_eq_relrank_of_le", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IntermediateField.relfinrank_comap_comap_eq_relfinrank_of_le", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IntermediateField.lift_relrank_comap_comap_eq_lift_relrank_of_surjective", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.relrank_comap_comap_eq_relrank_of_surjective", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IntermediateField.relfinrank_comap_comap_eq_relfinrank_of_surjective", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IntermediateField.relrank_mul_rank_top", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.relfinrank_mul_finrank_top", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IntermediateField.rank_bot_mul_relrank", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": true, "tactics": ["rw", "letI", "exact"], "tactic_count": 3}
{"name": "IntermediateField.finrank_bot_mul_relfinrank", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IntermediateField.relrank_dvd_rank_top_of_le", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.relfinrank_dvd_finrank_top_of_le", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.relrank_dvd_rank_bot", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.relfinrank_dvd_finrank_bot", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.relrank_mul_relrank", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.relfinrank_mul_relfinrank", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IntermediateField.relrank_inf_mul_relrank", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.relfinrank_inf_mul_relfinrank", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IntermediateField.relrank_mul_relrank_eq_inf_relrank", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IntermediateField.relfinrank_mul_relfinrank_eq_inf_relfinrank", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IntermediateField.relrank_inf_mul_relrank_of_le", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IntermediateField.relfinrank_inf_mul_relfinrank_of_le", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IntermediateField.relrank_top_left", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.relfinrank_top_left", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.relrank_top_right", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IntermediateField.relfinrank_top_right", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IntermediateField.relrank_bot_left", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IntermediateField.relfinrank_bot_left", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IntermediateField.relrank_bot_right", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.relfinrank_bot_right", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.relrank_dvd_of_le_left", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.relfinrank_dvd_of_le_left", "kind": "theorem", "module": "Mathlib.FieldTheory.Relrank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Separable", "kind": "definition", "module": "Mathlib.FieldTheory.Separable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.separable_def", "kind": "theorem", "module": "Mathlib.FieldTheory.Separable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.separable_def'", "kind": "theorem", "module": "Mathlib.FieldTheory.Separable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.not_separable_zero", "kind": "theorem", "module": "Mathlib.FieldTheory.Separable", "is_tactic_proof": true, "tactics": ["rintro", "simp"], "tactic_count": 2}
{"name": "Polynomial.Separable.ne_zero", "kind": "theorem", "module": "Mathlib.FieldTheory.Separable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.separable_one", "kind": "theorem", "module": "Mathlib.FieldTheory.Separable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.separable_of_subsingleton", "kind": "theorem", "module": "Mathlib.FieldTheory.Separable", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "Polynomial.separable_C", "kind": "theorem", "module": "Mathlib.FieldTheory.Separable", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.Separable.of_mul_left", "kind": "theorem", "module": "Mathlib.FieldTheory.Separable", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "Polynomial.Separable.of_mul_right", "kind": "theorem", "module": "Mathlib.FieldTheory.Separable", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
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{"name": "Polynomial.separable_gcd_right", "kind": "theorem", "module": "Mathlib.FieldTheory.Separable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Separable.isCoprime", "kind": "theorem", "module": "Mathlib.FieldTheory.Separable", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "Polynomial.Separable.of_pow'", "kind": "theorem", "module": "Mathlib.FieldTheory.Separable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Polynomial.Separable.map", "kind": "theorem", "module": "Mathlib.FieldTheory.Separable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Polynomial.Separable.unit_mul", "kind": "theorem", "module": "Mathlib.FieldTheory.Separable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Separable.eval₂_derivative_ne_zero", "kind": "theorem", "module": "Mathlib.FieldTheory.Separable", "is_tactic_proof": true, "tactics": ["intro", "obtain", "apply_fun", "simp"], "tactic_count": 4}
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{"name": "Polynomial.isUnit_of_self_mul_dvd_separable", "kind": "theorem", "module": "Mathlib.FieldTheory.Separable", "is_tactic_proof": true, "tactics": ["obtain", "apply", "have", "simp", "dsimp", "convert", "rw", "ring", "exact"], "tactic_count": 9}
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{"name": "Polynomial.Separable.mul", "kind": "theorem", "module": "Mathlib.FieldTheory.Separable", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
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{"name": "Polynomial.rootMultiplicity_le_one_of_separable", "kind": "theorem", "module": "Mathlib.FieldTheory.Separable", "is_tactic_proof": true, "tactics": ["classical", "by_cases", "simp", "rw", "apply"], "tactic_count": 5}
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{"name": "Polynomial.nodup_roots", "kind": "theorem", "module": "Mathlib.FieldTheory.Separable", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Polynomial.separable_iff_derivative_ne_zero", "kind": "theorem", "module": "Mathlib.FieldTheory.Separable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "IsSeparable", "kind": "definition", "module": "Mathlib.FieldTheory.Separable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsSeparable.isSeparable", "kind": "theorem", "module": "Mathlib.FieldTheory.Separable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Algebra.IsSeparable.isIntegral", "kind": "theorem", "module": "Mathlib.FieldTheory.Separable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsSeparable.isAlgebraic", "kind": "instance", "module": "Mathlib.FieldTheory.Separable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AlgEquiv.isSeparable_iff", "kind": "theorem", "module": "Mathlib.FieldTheory.Separable", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "IsSeparable.of_integral", "kind": "theorem", "module": "Mathlib.FieldTheory.Separable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "IntermediateField.isSeparable_tower_bot", "kind": "instance", "module": "Mathlib.FieldTheory.Separable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.isSeparable_tower_top", "kind": "instance", "module": "Mathlib.FieldTheory.Separable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSeparable.of_equiv_equiv", "kind": "theorem", "module": "Mathlib.FieldTheory.Separable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsSeparable.of_equiv_equiv", "kind": "theorem", "module": "Mathlib.FieldTheory.Separable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.natCard_of_powerBasis", "kind": "theorem", "module": "Mathlib.FieldTheory.Separable", "is_tactic_proof": true, "tactics": ["classical", "rw", "natDegree_map", "exact"], "tactic_count": 4}
{"name": "AlgHom.card_of_powerBasis", "kind": "theorem", "module": "Mathlib.FieldTheory.Separable", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "separableClosure", "kind": "definition", "module": "Mathlib.FieldTheory.SeparableClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_separableClosure_iff", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "separableClosure.comap_eq_of_algHom", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableClosure", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
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{"name": "separableClosure.isAlgebraic", "kind": "instance", "module": "Mathlib.FieldTheory.SeparableClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "separableClosure.isSeparable", "kind": "instance", "module": "Mathlib.FieldTheory.SeparableClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SeparableClosure", "kind": "abbrev", "module": "Mathlib.FieldTheory.SeparableClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "separableClosure.le_restrictScalars", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "separableClosure.eq_restrictScalars_of_isSeparable", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "separableClosureOperator", "kind": "abbrev", "module": "Mathlib.FieldTheory.SeparableClosure", "is_tactic_proof": false, "tactics": ["refine", "dsimp", "let", "have", "exact", "obtain", "exact"], "tactic_count": 7}
{"name": "isClosed_restrictScalars_separableClosure", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Field.sepDegree", "kind": "definition", "module": "Mathlib.FieldTheory.SeparableClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Field.finInsepDegree_def'", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Field.instNeZeroSepDegree", "kind": "instance", "module": "Mathlib.FieldTheory.SeparableClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Field.instNeZeroFinInsepDegree", "kind": "instance", "module": "Mathlib.FieldTheory.SeparableClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Field.lift_sepDegree_eq_of_equiv", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Field.sepDegree_eq_of_equiv", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Field.sepDegree_mul_insepDegree", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Field.sepDegree_le_rank", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Field.insepDegree_le_rank", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Field.lift_insepDegree_eq_of_equiv", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Field.sepDegree_self", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableClosure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Field.insepDegree_self", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableClosure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Field.finInsepDegree_self", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableClosure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IntermediateField.exists_finset_maximalFor_isTranscendenceBasis_separableClosure", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableClosure", "is_tactic_proof": true, "tactics": ["let", "have", "have", "have", "rw", "refine", "have", "lift", "exact", "let", "have", "refine", "have", "lift", "have", "apply", "exact", "convert", "have", "inferInstanceAs", "exact"], "tactic_count": 21}
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{"name": "IntermediateField.insepDegree_bot", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableClosure", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "IntermediateField.finInsepDegree_bot", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableClosure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IntermediateField.lift_sepDegree_bot'", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.lift_insepDegree_bot'", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.finInsepDegree_bot'", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableClosure", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IntermediateField.sepDegree_top", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "IntermediateField.finInsepDegree_top", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableClosure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IntermediateField.sepDegree_bot'", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.insepDegree_bot'", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Field.insepDegree_top_le_insepDegree_of_isScalarTower", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableClosure", "is_tactic_proof": true, "tactics": ["letI", "have", "exact"], "tactic_count": 3}
{"name": "Field.insepDegree_le_of_left_le", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableClosure", "is_tactic_proof": true, "tactics": ["letI", "have", "exact"], "tactic_count": 3}
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{"name": "IntermediateField.finInsepDegree_le_of_left_le", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableClosure", "is_tactic_proof": true, "tactics": ["letI", "have", "exact"], "tactic_count": 3}
{"name": "Algebra.IsSeparable.sepDegree_eq", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableClosure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Algebra.IsSeparable.insepDegree_eq", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableClosure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Algebra.IsSeparable.finInsepDegree_eq", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Field.Emb", "kind": "abbrev", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Field.finSepDegree", "kind": "definition", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Field.instInhabitedEmb", "kind": "instance", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Field.instNeZeroFinSepDegree", "kind": "instance", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Field.embEquivOfEquiv", "kind": "definition", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Field.finSepDegree_eq_of_equiv", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Field.finSepDegree_self", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": true, "tactics": ["rw", "constructor"], "tactic_count": 2}
{"name": "IntermediateField.finSepDegree_bot", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IntermediateField.finSepDegree_bot'", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.finSepDegree_top", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Field.embEquivOfAdjoinSplits", "kind": "definition", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Field.finSepDegree_eq_of_adjoin_splits", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Field.embEquivOfIsAlgClosed", "kind": "definition", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Field.finSepDegree_eq_of_isAlgClosed", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Field.embProdEmbOfIsAlgebraic", "kind": "definition", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Field.infinite_emb_of_transcendental", "kind": "instance", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Field.finSepDegree_eq_zero_of_transcendental", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Field.finSepDegree_mul_finSepDegree_of_isAlgebraic", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Polynomial.natSepDegree", "kind": "definition", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natSepDegree_le_natDegree", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": true, "tactics": ["have", "rw", "classical"], "tactic_count": 3}
{"name": "Polynomial.natSepDegree_X_sub_C", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.natSepDegree_X", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.natSepDegree_eq_zero", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": true, "tactics": ["linarith"], "tactic_count": 1}
{"name": "Polynomial.natSepDegree_C", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natSepDegree_zero", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.natSepDegree_one", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.natSepDegree_ne_zero", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": true, "tactics": ["rw", "use", "classical", "rw", "exact"], "tactic_count": 5}
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{"name": "Polynomial.natSepDegree_ne_zero_iff", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Polynomial.Separable.natSepDegree_eq_natDegree", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natSepDegree_eq_of_splits", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": true, "tactics": ["classical", "rw"], "tactic_count": 2}
{"name": "Polynomial.natSepDegree_eq_of_isAlgClosed", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natSepDegree_map", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": true, "tactics": ["classical", "let", "simp_rw"], "tactic_count": 3}
{"name": "Polynomial.natSepDegree_C_mul", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Polynomial.natSepDegree_smul_nonzero", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Polynomial.natSepDegree_pow", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": true, "tactics": ["classical", "simp", "by_cases", "simp", "simp"], "tactic_count": 5}
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{"name": "Polynomial.natSepDegree_X_pow", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.natSepDegree_X_sub_C_pow", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "Polynomial.natSepDegree_mul_of_isCoprime", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natSepDegree_le_of_dvd", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": true, "tactics": ["classical", "simp_rw", "exact"], "tactic_count": 3}
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{"name": "Polynomial.IsSeparableContraction.natSepDegree_eq", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": true, "tactics": ["obtain", "rw"], "tactic_count": 2}
{"name": "Polynomial.HasSeparableContraction.natSepDegree_eq", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Irreducible.natSepDegree_dvd_natDegree", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": true, "tactics": ["obtain", "have", "rw", "exact"], "tactic_count": 4}
{"name": "Irreducible.natSepDegree_eq_one_iff_of_monic'", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": true, "tactics": ["refine", "obtain", "have", "rw", "exact", "rw"], "tactic_count": 6}
{"name": "Irreducible.natSepDegree_eq_one_iff_of_monic", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Polynomial.Monic.eq_X_sub_C_pow_of_natSepDegree_eq_one_of_splits", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": true, "tactics": ["classical", "have", "have", "rw", "obtain", "exact", "rwa"], "tactic_count": 7}
{"name": "Polynomial.Monic.eq_X_pow_char_pow_sub_C_of_natSepDegree_eq_one_of_irreducible", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": true, "tactics": ["obtain", "cases", "zero", "simp_rw", "exact", "prime", "refine", "haveI", "rw", "exact"], "tactic_count": 10}
{"name": "Polynomial.Monic.eq_X_pow_char_pow_sub_C_pow_of_natSepDegree_eq_one", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": false, "tactics": ["obtain", "exists_monic_irreducible_factor", "not_isUnit_of_natDegree_pos", "have", "obtain", "have", "classical", "have", "refine", "obtain", "rw", "natSepDegree_pow_of_ne_zero", "simpa"], "tactic_count": 13}
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{"name": "minpoly.natSepDegree_eq_one_iff_pow_mem", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": true, "tactics": ["convert_to", "simp_rw", "refine", "obtain", "exact", "have", "refine", "natSepDegree_X_pow_char_pow_sub_C", "rw", "exact"], "tactic_count": 10}
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{"name": "IntermediateField.finSepDegree_adjoin_simple_eq_natSepDegree", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": false, "tactics": ["have", "classical", "rw", "simp_rw"], "tactic_count": 4}
{"name": "_private.Mathlib.FieldTheory.SeparableDegree.0.IntermediateField.finSepDegree_adjoin_simple_dvd_finrank", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "exact", "have", "finrank_of_infinite_dimensional", "halg", "rw", "exact"], "tactic_count": 8}
{"name": "IntermediateField.finSepDegree_adjoin_simple_le_finrank", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": true, "tactics": ["haveI", "exact"], "tactic_count": 2}
{"name": "IntermediateField.finSepDegree_adjoin_simple_eq_finrank_iff", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": true, "tactics": ["rw", "natSepDegree_eq_natDegree_iff"], "tactic_count": 2}
{"name": "Field.finSepDegree_dvd_finrank", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "refine", "induction_on_adjoin", "simp", "have", "set", "rwa", "rw", "exact"], "tactic_count": 10}
{"name": "Field.finSepDegree_le_finrank", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Field.finSepDegree_eq_finrank_of_isSeparable", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": true, "tactics": ["wlog", "rw", "obtain", "have", "rw", "by_cases", "rw", "linarith", "rw", "refine", "induction_on_adjoin", "simp", "have", "congr_arg₂", "set", "rwa"], "tactic_count": 16}
{"name": "Field.finSepDegree_eq_finrank_iff", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.isSeparable_of_mem_isSeparable", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IntermediateField.isSeparable_adjoin_simple_iff_isSeparable", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": true, "tactics": ["refine", "exact", "have", "haveI", "rwa"], "tactic_count": 5}
{"name": "IsSeparable.of_algebra_isSeparable_of_isSeparable", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": true, "tactics": ["set", "let", "haveI", "let", "have", "clear_value", "have", "have", "have", "simp", "replace", "haveI", "haveI", "haveI", "haveI", "have", "rw", "change", "exact"], "tactic_count": 19}
{"name": "Algebra.IsSeparable.trans", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.isSeparable_adjoin_pair_of_isSeparable", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": true, "tactics": ["rw", "replace", "rw", "exact"], "tactic_count": 4}
{"name": "Field.isSeparable_mul", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Field.isSeparable_add", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Field.isSeparable_neg", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Field.isSeparable_sub", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Field.isSeparable_inv", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "perfectField_iff_splits_of_natSepDegree_eq_one", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": true, "tactics": ["refine", "have", "obtain", "rw", "refine", "specialize", "have", "rw", "exact", "obtain", "haveI", "obtain", "exact", "exact"], "tactic_count": 14}
{"name": "PerfectField.splits_of_natSepDegree_eq_one", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparableDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.toPolynomialAdjoinImageCompl", "kind": "definition", "module": "Mathlib.FieldTheory.SeparablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.aeval_toPolynomialAdjoinImageCompl_eq_zero", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparablyGenerated", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "congr"], "tactic_count": 3}
{"name": "MvPolynomial.irreducible_toPolynomialAdjoinImageCompl", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparablyGenerated", "is_tactic_proof": true, "tactics": ["have", "delta", "convert", "hF.map", "rw", "congr", "aesop"], "tactic_count": 7}
{"name": "MvPolynomial.irreducible_of_forall_totalDegree_le", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparablyGenerated", "is_tactic_proof": true, "tactics": ["refine", "wlog", "exact", "have", "have", "rw", "refine", "rw", "simpa"], "tactic_count": 9}
{"name": "MvPolynomial.coeff_toPolynomialAdjoinImageCompl_ne_zero", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparablyGenerated", "is_tactic_proof": true, "tactics": ["classical", "intro", "let", "have", "have", "totalDegree_coeff_optionEquivLeft_add_le", "rw", "exact", "rw", "simpa", "refine", "let", "have", "optionEquivLeft_coeff_some_coeff_none", "dsimp", "rw", "eq_comm,", "exact", "apply_fun", "simp_rw", "map_zero]", "simp_rw", "congr"], "tactic_count": 23}
{"name": "MvPolynomial.isAlgebraic_of_mem_vars_of_forall_totalDegree_le", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparablyGenerated", "is_tactic_proof": true, "tactics": ["classical", "have", "refine", "coeff_toPolynomialAdjoinImageCompl_ne_zero", "aeval_toPolynomialAdjoinImageCompl_eq_zero", "rw"], "tactic_count": 6}
{"name": "MvPolynomial.exists_mem_support_not_dvd_of_forall_totalDegree_le", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparablyGenerated", "is_tactic_proof": true, "tactics": ["by_contra", "have", "choose", "exact", "choose", "have", "classical", "replace", "simpa", "have", "mt", "simp_rw", "refine", "simp", "rw", "simp", "obtain", "let", "have", "ne_of_ne_of_eq", "hF'0)", "have", "have", "simp", "suffices", "have", "contrapose", "rw", "rw", "replace", "exact", "rw", "intro", "obtain", "refine", "conv_rhs"], "tactic_count": 36}
{"name": "exists_isTranscendenceBasis_and_isSeparable_of_linearIndepOn_pow", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparablyGenerated", "is_tactic_proof": true, "tactics": ["have", "have", "have", "simpa", "let", "obtain", "replace", "have", "obtain", "have", "have", "have", "refine", "let", "have", "have", "have", "open", "algebraAdjoinAdjoin", "have", "coeff_ne", "h.trans_lt", "hF₁irr", "contrapose", "have", "hp.ne_one", "obtain", "replace", "rwa", "minpoly.eq_of_irreducible", "eq_mul_inv_iff_mul_eq₀", "map_eq_zero_iff"], "tactic_count": 32}
{"name": "exists_isTranscendenceBasis_and_isSeparable_of_linearIndepOn_pow'", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_isTranscendenceBasis_and_isSeparable_of_linearIndepOn_pow_of_adjoin_eq_top", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparablyGenerated", "is_tactic_proof": true, "tactics": ["have", "refine", "rw", "adjoin_le_iff]", "rintro", "obtain", "exact", "exact"], "tactic_count": 8}
{"name": "exists_isTranscendenceBasis_and_isSeparable_of_linearIndepOn_pow_of_essFiniteType", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparablyGenerated", "is_tactic_proof": true, "tactics": ["have", "refine", "have", "have", "rw", "refine", "rw", "intro", "obtain", "exacts", "obtain", "exacts"], "tactic_count": 12}
{"name": "exists_isTranscendenceBasis_and_isSeparable_of_perfectField", "kind": "theorem", "module": "Mathlib.FieldTheory.SeparablyGenerated", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "have", "rw", "exact", "obtain", "lift", "have", "exact", "have", "have", "refine", "apply", "simp"], "tactic_count": 14}
{"name": "Polynomial.factor", "kind": "definition", "module": "Mathlib.FieldTheory.SplittingField.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.irreducible_factor", "kind": "theorem", "module": "Mathlib.FieldTheory.SplittingField.Construction", "is_tactic_proof": true, "tactics": ["rw", "split_ifs", "exact", "exact"], "tactic_count": 4}
{"name": "Polynomial.fact_irreducible_factor", "kind": "theorem", "module": "Mathlib.FieldTheory.SplittingField.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.factor_dvd_of_not_isUnit", "kind": "theorem", "module": "Mathlib.FieldTheory.SplittingField.Construction", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "exact"], "tactic_count": 3}
{"name": "Polynomial.factor_dvd_of_degree_ne_zero", "kind": "theorem", "module": "Mathlib.FieldTheory.SplittingField.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.factor_dvd_of_natDegree_ne_zero", "kind": "theorem", "module": "Mathlib.FieldTheory.SplittingField.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.isCoprime_iff_aeval_ne_zero", "kind": "theorem", "module": "Mathlib.FieldTheory.SplittingField.Construction", "is_tactic_proof": true, "tactics": ["refine", "replace", "contrapose", "rw", "rintro", "replace", "simp", "not_true]"], "tactic_count": 8}
{"name": "Polynomial.removeFactor", "kind": "definition", "module": "Mathlib.FieldTheory.SplittingField.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.X_sub_C_mul_removeFactor", "kind": "theorem", "module": "Mathlib.FieldTheory.SplittingField.Construction", "is_tactic_proof": true, "tactics": ["let", "apply", "rw"], "tactic_count": 3}
{"name": "Polynomial.natDegree_removeFactor", "kind": "theorem", "module": "Mathlib.FieldTheory.SplittingField.Construction", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.natDegree_removeFactor'", "kind": "theorem", "module": "Mathlib.FieldTheory.SplittingField.Construction", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.SplittingFieldAuxAux", "kind": "definition", "module": "Mathlib.FieldTheory.SplittingField.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.SplittingFieldAux", "kind": "definition", "module": "Mathlib.FieldTheory.SplittingField.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.SplittingFieldAux.field", "kind": "instance", "module": "Mathlib.FieldTheory.SplittingField.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.instInhabitedSplittingFieldAux", "kind": "instance", "module": "Mathlib.FieldTheory.SplittingField.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.SplittingFieldAux.algebra", "kind": "instance", "module": "Mathlib.FieldTheory.SplittingField.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.SplittingFieldAux.succ", "kind": "theorem", "module": "Mathlib.FieldTheory.SplittingField.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.SplittingFieldAux.algebra'''", "kind": "instance", "module": "Mathlib.FieldTheory.SplittingField.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.SplittingFieldAux.algebra'", "kind": "instance", "module": "Mathlib.FieldTheory.SplittingField.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.SplittingFieldAux.algebra''", "kind": "instance", "module": "Mathlib.FieldTheory.SplittingField.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.SplittingFieldAux.scalar_tower'", "kind": "instance", "module": "Mathlib.FieldTheory.SplittingField.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.SplittingFieldAux.algebraMap_succ", "kind": "theorem", "module": "Mathlib.FieldTheory.SplittingField.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.SplittingFieldAux.splits", "kind": "theorem", "module": "Mathlib.FieldTheory.SplittingField.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.SplittingFieldAux.adjoin_rootSet", "kind": "theorem", "module": "Mathlib.FieldTheory.SplittingField.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.SplittingFieldAux.instIsSplittingFieldNatDegree", "kind": "instance", "module": "Mathlib.FieldTheory.SplittingField.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.SplittingField", "kind": "definition", "module": "Mathlib.FieldTheory.SplittingField.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.SplittingField.algEquivSplittingFieldAux", "kind": "definition", "module": "Mathlib.FieldTheory.SplittingField.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.SplittingField.instGroupWithZero", "kind": "instance", "module": "Mathlib.FieldTheory.SplittingField.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.SplittingField.instField", "kind": "instance", "module": "Mathlib.FieldTheory.SplittingField.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.SplittingField.instCharZero", "kind": "instance", "module": "Mathlib.FieldTheory.SplittingField.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.SplittingField.instCharP", "kind": "instance", "module": "Mathlib.FieldTheory.SplittingField.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.SplittingField.instExpChar", "kind": "instance", "module": "Mathlib.FieldTheory.SplittingField.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.IsSplittingField.splittingField", "kind": "instance", "module": "Mathlib.FieldTheory.SplittingField.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.SplittingField.splits", "kind": "theorem", "module": "Mathlib.FieldTheory.SplittingField.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.SplittingField.lift", "kind": "definition", "module": "Mathlib.FieldTheory.SplittingField.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.SplittingField.adjoin_rootSet", "kind": "theorem", "module": "Mathlib.FieldTheory.SplittingField.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.IsSplittingField.instFiniteDimensionalSplittingField", "kind": "instance", "module": "Mathlib.FieldTheory.SplittingField.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.IsSplittingField.instFiniteSplittingField", "kind": "instance", "module": "Mathlib.FieldTheory.SplittingField.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.IsSplittingField.instIsTorsionFreeSplittingField", "kind": "instance", "module": "Mathlib.FieldTheory.SplittingField.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.IsSplittingField.algEquiv", "kind": "definition", "module": "Mathlib.FieldTheory.SplittingField.Construction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.IsSplittingField.splits", "kind": "theorem", "module": "Mathlib.FieldTheory.SplittingField.IsSplittingField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.IsSplittingField.adjoin_rootSet", "kind": "theorem", "module": "Mathlib.FieldTheory.SplittingField.IsSplittingField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.IsSplittingField.map", "kind": "instance", "module": "Mathlib.FieldTheory.SplittingField.IsSplittingField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.IsSplittingField.splits_iff", "kind": "theorem", "module": "Mathlib.FieldTheory.SplittingField.IsSplittingField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.IsSplittingField.IsScalarTower.splits", "kind": "theorem", "module": "Mathlib.FieldTheory.SplittingField.IsSplittingField", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "Polynomial.IsSplittingField.mul", "kind": "theorem", "module": "Mathlib.FieldTheory.SplittingField.IsSplittingField", "is_tactic_proof": true, "tactics": ["constructor", "rw", "exact", "classical", "rw", "adjoin_rootSet,"], "tactic_count": 6}
{"name": "Polynomial.IsSplittingField.lift", "kind": "definition", "module": "Mathlib.FieldTheory.SplittingField.IsSplittingField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.IsSplittingField.finiteDimensional", "kind": "theorem", "module": "Mathlib.FieldTheory.SplittingField.IsSplittingField", "is_tactic_proof": true, "tactics": ["classical", "exact", "adjoin_rootSet", "fg_adjoin_of_finite"], "tactic_count": 4}
{"name": "Polynomial.IsSplittingField.IsScalarTower.isAlgebraic", "kind": "theorem", "module": "Mathlib.FieldTheory.SplittingField.IsSplittingField", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "Polynomial.IsSplittingField.of_algEquiv", "kind": "theorem", "module": "Mathlib.FieldTheory.SplittingField.IsSplittingField", "is_tactic_proof": true, "tactics": ["constructor", "rw", "exact", "rw"], "tactic_count": 4}
{"name": "Polynomial.IsSplittingField.adjoin_rootSet_eq_range", "kind": "theorem", "module": "Mathlib.FieldTheory.SplittingField.IsSplittingField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.splits_of_splits", "kind": "theorem", "module": "Mathlib.FieldTheory.SplittingField.IsSplittingField", "is_tactic_proof": true, "tactics": ["classical", "have", "rw", "exact"], "tactic_count": 4}
{"name": "IntermediateField.splits_iff_mem", "kind": "theorem", "module": "Mathlib.FieldTheory.SplittingField.IsSplittingField", "is_tactic_proof": true, "tactics": ["refine", "intro", "rw", "exact"], "tactic_count": 4}
{"name": "IsIntegral.mem_intermediateField_of_minpoly_splits", "kind": "theorem", "module": "Mathlib.FieldTheory.SplittingField.IsSplittingField", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "isSplittingField_iff_intermediateField", "kind": "theorem", "module": "Mathlib.FieldTheory.SplittingField.IsSplittingField", "is_tactic_proof": false, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IntermediateField.isSplittingField_iff", "kind": "theorem", "module": "Mathlib.FieldTheory.SplittingField.IsSplittingField", "is_tactic_proof": false, "tactics": ["suffices", "exact", "rw", "refine", "rw"], "tactic_count": 5}
{"name": "IntermediateField.adjoin_rootSet_isSplittingField", "kind": "theorem", "module": "Mathlib.FieldTheory.SplittingField.IsSplittingField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.isSplittingField_C", "kind": "theorem", "module": "Mathlib.FieldTheory.SplittingField.IsSplittingField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Finite.left", "kind": "theorem", "module": "Mathlib.FieldTheory.Tower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Finite.right", "kind": "theorem", "module": "Mathlib.FieldTheory.Tower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.instSetLike", "kind": "instance", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.instPartialOrder", "kind": "instance", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.coe_mk", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.mem_mk", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.ext", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.smul_mem", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.add_mem", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.instAddMemClass", "kind": "instance", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.copy", "kind": "definition", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.copy_eq", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.instInfSet", "kind": "instance", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.coe_sInf", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.mem_sInf", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.coe_iInf", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ConvexCone.mem_iInf", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.instCompleteSemilatticeInf", "kind": "instance", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.hull", "kind": "definition", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.subset_hull", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ConvexCone.hull_min", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.hull_le_iff", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.gc_hull_coe", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.gi", "kind": "definition", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.instBot", "kind": "instance", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.notMem_bot", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.coe_bot", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.coe_eq_empty", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ConvexCone.instCompleteLattice", "kind": "instance", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.coe_inf", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.mem_inf", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.mem_top", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.coe_top", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.disjoint_coe", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ConvexCone.instInhabited", "kind": "instance", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.convex", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.map", "kind": "definition", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.coe_map", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.mem_map", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.map_map", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.map_id", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.comap", "kind": "definition", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.coe_comap", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.comap_id", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.comap_comap", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.mem_comap", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.smul_mem_iff", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.Pointed", "kind": "definition", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.Blunt", "kind": "definition", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.blunt_iff_not_pointed", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.pointed_iff_not_blunt", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ConvexCone.Pointed.mono", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.Blunt.anti", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.Flat", "kind": "definition", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.Salient", "kind": "definition", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.salient_iff_not_flat", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ConvexCone.Flat.mono", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.Salient.anti", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.Flat.pointed", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact"], "tactic_count": 3}
{"name": "ConvexCone.Blunt.salient", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ConvexCone.toPreorder", "kind": "definition", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.toPartialOrder", "kind": "definition", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.to_isOrderedAddMonoid", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.instZero", "kind": "instance", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.mem_zero", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.coe_zero", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.pointed_zero", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ConvexCone.instAdd", "kind": "instance", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.coe_add", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.mem_add", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.instAddZeroClass", "kind": "instance", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.instAddCommSemigroup", "kind": "instance", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.IsGenerating", "kind": "definition", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.IsGenerating.of_top_le_span", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.IsGenerating.span_eq_top", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.IsGenerating.top_le_span", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.isGenerating_top", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ConvexCone.isGenerating_bot_iff", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": true, "tactics": ["simpa", "subsingleton_iff_bot_eq_top"], "tactic_count": 2}
{"name": "ConvexCone.isGenerating_bot", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.IsGenerating.mono", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ConvexCone.IsReproducing", "kind": "definition", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.IsReproducing.of_univ_subset", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.IsReproducing.sub_eq_univ", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.IsReproducing.isGenerating", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": true, "tactics": ["rw", "rintro", "rw", "obtain", "exact"], "tactic_count": 5}
{"name": "ConvexCone.IsGenerating.isReproducing", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": true, "tactics": ["rw", "intro", "have", "let", "add_mem", "rintro", "exact", "zero_mem", "obtain", "exact", "smul_mem", "rintro", "simp", "rcases", "refine", "rw", "simp", "obtain", "exact", "exact", "have", "let", "exact"], "tactic_count": 23}
{"name": "ConvexCone.isGenerating_iff_isReproducing", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.mem_hull_of_convex", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.coe_hull_of_convex", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "ConvexCone.disjoint_hull_left_of_convex", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.disjoint_hull_right_of_convex", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submodule.toConvexCone", "kind": "definition", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.coe_toConvexCone", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mem_toConvexCone", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.toConvexCone_le_toConvexCone", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.toConvexCone_bot", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.toConvexCone_top", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.toConvexCone_inf", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.pointed_toConvexCone", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.positive", "kind": "definition", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.mem_positive", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.coe_positive", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.salient_positive", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.pointed_positive", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.strictlyPositive", "kind": "definition", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.mem_strictlyPositive", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.coe_strictlyPositive", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.strictlyPositive_le_positive", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.salient_strictlyPositive", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.blunt_strictlyPositive", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Convex.toCone", "kind": "definition", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": true, "tactics": ["apply", "rintro", "exact", "rintro", "have", "refine", "simp"], "tactic_count": 7}
{"name": "Convex.mem_toCone", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Convex.mem_toCone'", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": true, "tactics": ["refine", "rintro", "exact", "rintro", "exact"], "tactic_count": 5}
{"name": "Convex.subset_toCone", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Convex.toCone_isLeast", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": true, "tactics": ["refine", "rcases", "exact"], "tactic_count": 3}
{"name": "Convex.toCone_eq_sInf", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "convexHull_toCone_isLeast", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": true, "tactics": ["convert", "ext", "exact"], "tactic_count": 3}
{"name": "convexHull_toCone_eq_sInf", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Geometry.Convex.Cone.Dual.0.PointedCone.termR≥0", "kind": "definition", "module": "Mathlib.Geometry.Convex.Cone.Dual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Geometry.Convex.Cone.Dual.0.PointedCone._aux_Mathlib_Geometry_Convex_Cone_Dual___macroRules__private_Mathlib_Geometry_Convex_Cone_Dual_0_PointedCone_termR≥0_1", "kind": "definition", "module": "Mathlib.Geometry.Convex.Cone.Dual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Geometry.Convex.Cone.Dual.0.PointedCone._aux_Mathlib_Geometry_Convex_Cone_Dual___delab_app__private_Mathlib_Geometry_Convex_Cone_Dual_0_PointedCone_termR≥0_1", "kind": "definition", "module": "Mathlib.Geometry.Convex.Cone.Dual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PointedCone.dual", "kind": "definition", "module": "Mathlib.Geometry.Convex.Cone.Dual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PointedCone.mem_dual", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Dual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PointedCone.dual_empty", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Dual", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "PointedCone.dual_zero", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Dual", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "PointedCone.dual_univ", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Dual", "is_tactic_proof": true, "tactics": ["refine", "ext", "exact"], "tactic_count": 3}
{"name": "PointedCone.dual_le_dual", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Dual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PointedCone.dual_singleton", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Dual", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "PointedCone.dual_union", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Dual", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "PointedCone.dual_insert", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Dual", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PointedCone.dual_iUnion", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Dual", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "PointedCone.dual_sUnion", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Dual", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "PointedCone.dual_eq_iInter_dual_singleton", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Dual", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "PointedCone.subset_dual_dual", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Dual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PointedCone.dual_dual_flip_dual", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Dual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PointedCone.dual_flip_dual_dual_flip", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Dual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PointedCone.dual_span", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Dual", "is_tactic_proof": true, "tactics": ["refine", "induction", "mem", "zero", "add", "smul"], "tactic_count": 6}
{"name": "_private.Mathlib.Geometry.Convex.Cone.Pointed.0.termR≥0", "kind": "definition", "module": "Mathlib.Geometry.Convex.Cone.Pointed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Geometry.Convex.Cone.Pointed.0._aux_Mathlib_Geometry_Convex_Cone_Pointed___macroRules__private_Mathlib_Geometry_Convex_Cone_Pointed_0_termR≥0_1", "kind": "definition", "module": "Mathlib.Geometry.Convex.Cone.Pointed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Geometry.Convex.Cone.Pointed.0._aux_Mathlib_Geometry_Convex_Cone_Pointed___delab_app__private_Mathlib_Geometry_Convex_Cone_Pointed_0_termR≥0_1", "kind": "definition", "module": "Mathlib.Geometry.Convex.Cone.Pointed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PointedCone", "kind": "abbrev", "module": "Mathlib.Geometry.Convex.Cone.Pointed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PointedCone.toConvexCone", "kind": "definition", "module": "Mathlib.Geometry.Convex.Cone.Pointed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PointedCone.instCoeConvexCone", "kind": "instance", "module": "Mathlib.Geometry.Convex.Cone.Pointed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PointedCone.toConvexCone_injective", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Pointed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PointedCone.pointed_toConvexCone", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Pointed", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PointedCone.mem_toConvexCone", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Pointed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PointedCone.ext", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Pointed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PointedCone.convex", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Pointed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PointedCone.instZero", "kind": "instance", "module": "Mathlib.Geometry.Convex.Cone.Pointed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PointedCone.smul_mem", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Pointed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.toPointedCone", "kind": "definition", "module": "Mathlib.Geometry.Convex.Cone.Pointed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.mem_toPointedCone", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Pointed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.coe_toPointedCone", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Pointed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConvexCone.toPointedCone_top", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Pointed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PointedCone.canLift", "kind": "instance", "module": "Mathlib.Geometry.Convex.Cone.Pointed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PointedCone.ofConeComb", "kind": "definition", "module": "Mathlib.Geometry.Convex.Cone.Pointed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PointedCone.span", "kind": "abbrev", "module": "Mathlib.Geometry.Convex.Cone.Pointed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PointedCone.subset_span", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Pointed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PointedCone.mem_span_set", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Pointed", "is_tactic_proof": true, "tactics": ["rw", "constructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 6}
{"name": "PointedCone.map", "kind": "definition", "module": "Mathlib.Geometry.Convex.Cone.Pointed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PointedCone.toConvexCone_map", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Pointed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PointedCone.coe_map", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Pointed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PointedCone.mem_map", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Pointed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PointedCone.map_map", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Pointed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PointedCone.map_id", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Pointed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PointedCone.comap", "kind": "definition", "module": "Mathlib.Geometry.Convex.Cone.Pointed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PointedCone.coe_comap", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Pointed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PointedCone.comap_id", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Pointed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PointedCone.comap_comap", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Pointed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PointedCone.mem_comap", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Pointed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PointedCone.positive", "kind": "definition", "module": "Mathlib.Geometry.Convex.Cone.Pointed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PointedCone.mem_positive", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Pointed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PointedCone.toConvexCone_positive", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Pointed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PointedCone.to_isOrderedModule", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Pointed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PointedCone.salient_iff_inter_neg_eq_singleton", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.Pointed", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PointedCone.minTensorProduct", "kind": "definition", "module": "Mathlib.Geometry.Convex.Cone.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PointedCone.maxTensorProduct", "kind": "definition", "module": "Mathlib.Geometry.Convex.Cone.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PointedCone.mem_maxTensorProduct", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.TensorProduct", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PointedCone.tmul_mem_maxTensorProduct", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.TensorProduct", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "PointedCone.tmul_mem_minTensorProduct", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PointedCone.tmul_subset_maxTensorProduct", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PointedCone.tmul_subset_minTensorProduct", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PointedCone.minTensorProduct_le_maxTensorProduct", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.TensorProduct", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "PointedCone.minTensorProduct_comm", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.TensorProduct", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PointedCone.maxTensorProduct_comm", "kind": "theorem", "module": "Mathlib.Geometry.Convex.Cone.TensorProduct", "is_tactic_proof": true, "tactics": ["ext", "simp", "refine", "rintro", "simpa", "intro", "simpa"], "tactic_count": 7}
{"name": "Affine.Simplex.altitude", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Altitude", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.altitude_def", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Altitude", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.altitude_reindex", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Altitude", "is_tactic_proof": true, "tactics": ["ext", "simp_rw", "simp"], "tactic_count": 3}
{"name": "Affine.Simplex.mem_altitude", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Altitude", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.direction_altitude", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Altitude", "is_tactic_proof": true, "tactics": ["rw", "direction_mk',"], "tactic_count": 2}
{"name": "Affine.Simplex.vectorSpan_isOrtho_altitude_direction", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Altitude", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Affine.Simplex.altitude_map", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Altitude", "is_tactic_proof": true, "tactics": ["refine", "exact", "exact", "have", "rw", "map_points,"], "tactic_count": 6}
{"name": "Affine.Simplex.map_altitude_restrict", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Altitude", "is_tactic_proof": true, "tactics": ["rw", "convert"], "tactic_count": 2}
{"name": "Affine.Simplex.altitude_restrict_eq_comap_subtype", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Altitude", "is_tactic_proof": true, "tactics": ["haveI", "rw"], "tactic_count": 2}
{"name": "Affine.Simplex.finiteDimensional_direction_altitude", "kind": "instance", "module": "Mathlib.Geometry.Euclidean.Altitude", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "Affine.Simplex.finrank_direction_altitude", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Altitude", "is_tactic_proof": true, "tactics": ["rw", "have", "have", "have", "cases", "have", "refine", "classical", "rw"], "tactic_count": 9}
{"name": "Affine.Simplex.affineSpan_pair_eq_altitude_iff", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Altitude", "is_tactic_proof": false, "tactics": ["rw", "direction_affineSpan,", "constructor", "intro", "constructor", "intro", "rw", "have", "simp", "rw", "exact", "rintro", "rw", "rw", "refine", "rw", "simpa", "rw", "simp", "exact"], "tactic_count": 20}
{"name": "Affine.Simplex.altitudeFoot", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Altitude", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.altitudeFoot_reindex", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Altitude", "is_tactic_proof": true, "tactics": ["ext", "simp", "exact"], "tactic_count": 3}
{"name": "Affine.Simplex.altitudeFoot_map", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Altitude", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Affine.Simplex.altitudeFoot_restrict", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Altitude", "is_tactic_proof": true, "tactics": ["rw", "convert"], "tactic_count": 2}
{"name": "Affine.Simplex.ne_altitudeFoot", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Altitude", "is_tactic_proof": true, "tactics": ["intro", "rw", "simp"], "tactic_count": 3}
{"name": "Affine.Simplex.altitudeFoot_mem_affineSpan_image_compl", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Altitude", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Affine.Simplex.altitudeFoot_mem_affineSpan_faceOpposite", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Altitude", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.altitudeFoot_mem_affineSpan", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Altitude", "is_tactic_proof": true, "tactics": ["refine", "simp"], "tactic_count": 2}
{"name": "Affine.Simplex.affineSpan_pair_altitudeFoot_eq_altitude", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Altitude", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "simp_rw", "exact"], "tactic_count": 5}
{"name": "Affine.Simplex.altitudeFoot_mem_altitude", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Altitude", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Affine.Simplex.height", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Altitude", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.height_reindex", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Altitude", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Affine.Simplex.height_map", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Altitude", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Affine.Simplex.height_restrict", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Altitude", "is_tactic_proof": true, "tactics": ["rw", "convert"], "tactic_count": 2}
{"name": "Affine.Simplex.height_pos", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Altitude", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Affine.Simplex.evalHeight", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Altitude", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex._example", "kind": "example", "module": "Mathlib.Geometry.Euclidean.Altitude", "is_tactic_proof": true, "tactics": ["positivity"], "tactic_count": 1}
{"name": "Affine.Simplex.inner_vsub_vsub_altitudeFoot_eq_height_sq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Altitude", "is_tactic_proof": false, "tactics": ["suffices", "rwa", "refine", "rw", "exact"], "tactic_count": 5}
{"name": "Affine.Simplex.abs_inner_vsub_altitudeFoot_lt_mul", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Altitude", "is_tactic_proof": true, "tactics": ["apply", "convert", "simp", "simp_rw", "rw", "rintro", "suffices", "rw", "refine", "refine", "simp", "rw", "have", "have", "vectorSpan", "vectorSpan", "rcases", "have", "rw", "exact", "have", "rw", "exact", "have", "simp", "simp_rw", "rw", "simpa", "convert", "rw", "refine", "rw", "exact", "rw", "exact"], "tactic_count": 35}
{"name": "Affine.Simplex.neg_mul_lt_inner_vsub_altitudeFoot", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Altitude", "is_tactic_proof": true, "tactics": ["obtain", "rw", "refine", "rw", "positivity", "positivity", "rw", "refine", "rw", "exact"], "tactic_count": 10}
{"name": "Affine.Simplex.abs_inner_vsub_altitudeFoot_div_lt_one", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Altitude", "is_tactic_proof": true, "tactics": ["rw", "nth_rw", "exact", "simp", "positivity"], "tactic_count": 5}
{"name": "Affine.Simplex.neg_one_lt_inner_vsub_altitudeFoot_div", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Altitude", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "_private.Mathlib.Geometry.Euclidean.Angle.Bisector.0.EuclideanGeometry.dist_orthogonalProjection_eq_iff_angle_eq_aux₁", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Bisector", "is_tactic_proof": true, "tactics": ["have", "have", "refine", "rw", "rw", "rw", "rw", "rw", "by_cases", "subst", "exact", "by_contra", "rw", "angle_eq_arcsin_of_angle_eq_pi_div_two", "div_eq_zero_iff]", "simp", "rw", "simp", "exact"], "tactic_count": 19}
{"name": "_private.Mathlib.Geometry.Euclidean.Angle.Bisector.0.EuclideanGeometry.dist_orthogonalProjection_eq_iff_angle_eq_aux", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Bisector", "is_tactic_proof": true, "tactics": ["have", "have", "rcases", "exact", "nth_rw", "nth_rw", "rw", "exact"], "tactic_count": 8}
{"name": "EuclideanGeometry.dist_orthogonalProjection_eq_iff_angle_eq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Bisector", "is_tactic_proof": true, "tactics": ["have", "have", "by_cases", "exact", "rw", "rw", "angle_eq_arcsin_of_angle_eq_pi_div_two", "angle_comm,", "angle_eq_arcsin_of_angle_eq_pi_div_two", "refine", "rw", "have", "rintro", "exact", "have", "rw", "rwa", "rw", "exact", "rw", "exact"], "tactic_count": 21}
{"name": "EuclideanGeometry.dist_orthogonalProjection_eq_of_oangle_eq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Bisector", "is_tactic_proof": true, "tactics": ["intro", "rw", "exact"], "tactic_count": 3}
{"name": "EuclideanGeometry.oangle_eq_of_dist_orthogonalProjection_eq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Bisector", "is_tactic_proof": true, "tactics": ["intro", "haveI", "haveI", "haveI", "have", "intro", "rw", "dist_sq_eq_dist_orthogonalProjection_sq_add_dist_orthogonalProjection_sq", "dist_eq_zero,", "grind", "have", "intro", "rw", "dist_sq_eq_dist_orthogonalProjection_sq_add_dist_orthogonalProjection_sq", "dist_eq_zero,", "grind", "have", "intro", "have", "hc.mem_affineSpan_of_mem_of_ne", "have", "have", "rw", "grind", "have", "hc.mem_affineSpan_of_mem_of_ne", "have", "orthogonalProjection_mem", "have", "rw", "grind", "apply", "rw", "rw", "rcases", "exact", "exfalso", "exact", "exfalso", "have", "rw", "exact"], "tactic_count": 42}
{"name": "EuclideanGeometry.dist_orthogonalProjection_eq_iff_oangle_eq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Bisector", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.o", "kind": "abbrev", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.oangle", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.term∡", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry._aux_Mathlib_Geometry_Euclidean_Angle_Oriented_Affine___macroRules_EuclideanGeometry_term∡_1", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry._aux_Mathlib_Geometry_Euclidean_Angle_Oriented_Affine___unexpand_EuclideanGeometry_oangle_1", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.continuousAt_oangle", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": true, "tactics": ["unfold", "fun_prop"], "tactic_count": 2}
{"name": "EuclideanGeometry.oangle_self_left", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "EuclideanGeometry.oangle_self_right", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "EuclideanGeometry.oangle_self_left_right", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.left_ne_of_oangle_ne_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EuclideanGeometry.right_ne_of_oangle_ne_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EuclideanGeometry.left_ne_right_of_oangle_ne_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EuclideanGeometry.left_ne_of_oangle_eq_pi", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.right_ne_of_oangle_eq_pi", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.left_ne_right_of_oangle_eq_pi", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.left_ne_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.right_ne_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.left_ne_right_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.left_ne_of_oangle_eq_neg_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.right_ne_of_oangle_eq_neg_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.left_ne_right_of_oangle_eq_neg_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.left_ne_of_oangle_sign_ne_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.right_ne_of_oangle_sign_ne_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.left_ne_right_of_oangle_sign_ne_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.left_ne_of_oangle_sign_eq_one", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.right_ne_of_oangle_sign_eq_one", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.left_ne_right_of_oangle_sign_eq_one", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.left_ne_of_oangle_sign_eq_neg_one", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.right_ne_of_oangle_sign_eq_neg_one", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.left_ne_right_of_oangle_sign_eq_neg_one", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.oangle_rev", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.oangle_add_oangle_rev", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.oangle_eq_zero_iff_oangle_rev_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.oangle_eq_pi_iff_oangle_rev_eq_pi", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.oangle_homothety", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": false, "tactics": ["simp_rw", "id_eq]", "rcases"], "tactic_count": 3}
{"name": "EuclideanGeometry.oangle_ne_zero_and_ne_pi_iff_affineIndependent", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": false, "tactics": ["rw", "affineIndependent_iff_linearIndependent_vsub", "linearIndependent_equiv", "convert", "ext", "fin_cases"], "tactic_count": 6}
{"name": "EuclideanGeometry.oangle_eq_zero_or_eq_pi_iff_collinear", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EuclideanGeometry.oangle_sign_eq_zero_iff_collinear", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EuclideanGeometry.oangle_ne_zero_and_ne_pi_iff_not_collinear", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EuclideanGeometry.affineIndependent_iff_of_two_zsmul_oangle_eq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "EuclideanGeometry.collinear_iff_of_two_zsmul_oangle_eq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "EuclideanGeometry.two_zsmul_oangle_of_vectorSpan_eq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "EuclideanGeometry.two_zsmul_oangle_of_parallel", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "EuclideanGeometry.oangle_eq_of_parallel", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": true, "tactics": ["rw", "have", "rw", "exact", "obtain", "exists_eq_smul_of_parallel", "rw", "rw", "rcases", "simp", "simp"], "tactic_count": 11}
{"name": "EuclideanGeometry.oangle_add", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.oangle_add_swap", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.oangle_sub_left", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.oangle_sub_right", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.oangle_add_cyc3", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "EuclideanGeometry.oangle_eq_oangle_of_dist_eq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": true, "tactics": ["simp_rw", "rw", "o.oangle_sub_eq_oangle_sub_rev_of_norm_eq"], "tactic_count": 3}
{"name": "EuclideanGeometry.oangle_eq_pi_sub_two_zsmul_oangle_of_dist_eq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": true, "tactics": ["simp_rw", "rw", "convert", "rw", "rw", "simpa"], "tactic_count": 6}
{"name": "EuclideanGeometry.abs_oangle_right_toReal_lt_pi_div_two_of_dist_eq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": true, "tactics": ["simp_rw", "rw", "exact"], "tactic_count": 3}
{"name": "EuclideanGeometry.abs_oangle_left_toReal_lt_pi_div_two_of_dist_eq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.cos_oangle_eq_cos_angle", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.oangle_eq_angle_or_eq_neg_angle", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.angle_eq_abs_oangle_toReal", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.eq_zero_or_angle_eq_zero_or_pi_of_sign_oangle_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "EuclideanGeometry.oangle_eq_of_angle_eq_of_sign_eq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.angle_eq_iff_oangle_eq_of_sign_eq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.oangle_eq_or_eq_neg_of_angle_eq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": true, "tactics": ["have", "have", "rcases", "left", "rw", "right", "rw", "right", "rw", "left", "rw"], "tactic_count": 11}
{"name": "EuclideanGeometry.oangle_eq_neg_of_angle_eq_of_sign_eq_neg", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.angle_eq_iff_oangle_eq_neg_of_sign_eq_neg", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.oangle_eq_angle_of_sign_eq_one", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.oangle_eq_neg_angle_of_sign_eq_neg_one", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.oangle_eq_zero_iff_angle_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.oangle_eq_pi_iff_angle_eq_pi", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.angle_eq_pi_div_two_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "EuclideanGeometry.angle_rev_eq_pi_div_two_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "EuclideanGeometry.angle_eq_pi_div_two_of_oangle_eq_neg_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "EuclideanGeometry.angle_rev_eq_pi_div_two_of_oangle_eq_neg_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "EuclideanGeometry.oangle_swap₁₂_sign", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": false, "tactics": ["rw", "vsub_sub_vsub_cancel_left", "add_comm,", "nth_rw", "rw", "simp"], "tactic_count": 6}
{"name": "EuclideanGeometry.oangle_swap₁₃_sign", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EuclideanGeometry.oangle_swap₂₃_sign", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EuclideanGeometry.oangle_rotate_sign", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EuclideanGeometry.oangle_eq_pi_iff_sbtw", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Sbtw.oangle₁₂₃_eq_pi", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sbtw.oangle₃₂₁_eq_pi", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Wbtw.oangle₂₁₃_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": true, "tactics": ["by_cases", "by_cases", "rw", "exact"], "tactic_count": 4}
{"name": "Sbtw.oangle₂₁₃_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Wbtw.oangle₃₁₂_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Sbtw.oangle₃₁₂_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Wbtw.oangle₂₃₁_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sbtw.oangle₂₃₁_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Wbtw.oangle₁₃₂_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sbtw.oangle₁₃₂_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.oangle_eq_zero_iff_wbtw", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": true, "tactics": ["by_cases", "by_cases", "rw", "simp"], "tactic_count": 4}
{"name": "Wbtw.oangle_eq_left", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": true, "tactics": ["by_cases", "by_cases", "rw"], "tactic_count": 3}
{"name": "Sbtw.oangle_eq_left", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Wbtw.oangle_eq_right", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Sbtw.oangle_eq_right", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.oangle_midpoint_left", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": true, "tactics": ["by_cases", "exact"], "tactic_count": 2}
{"name": "EuclideanGeometry.oangle_midpoint_rev_left", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EuclideanGeometry.oangle_midpoint_right", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": true, "tactics": ["by_cases", "exact"], "tactic_count": 2}
{"name": "EuclideanGeometry.oangle_midpoint_rev_right", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Sbtw.oangle_eq_add_pi_left", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Sbtw.oangle_eq_add_pi_right", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Sbtw.oangle_eq_left_right", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Collinear.two_zsmul_oangle_eq_left", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": true, "tactics": ["by_cases", "rcases", "have", "rw", "rw", "rw"], "tactic_count": 6}
{"name": "Collinear.two_zsmul_oangle_eq_right", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EuclideanGeometry.dist_eq_iff_eq_smul_rotation_pi_div_two_vadd_midpoint", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": true, "tactics": ["refine", "have", "rw", "real_inner_self_eq_norm_mul_norm,", "simp_rw", "hd,", "abel", "rw", "or_iff_right", "rcases", "rw", "exact", "rcases", "simp_rw", "neg_vsub_eq_vsub_rev", "inner_sub_sub_self]", "simp"], "tactic_count": 17}
{"name": "Collinear.oangle_sign_of_sameRay_vsub", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": true, "tactics": ["by_cases", "have", "have", "hc₅₁₂₃₄", "rw", "have", "have", "rw", "rw", "let", "have", "haveI", "have", "refine", "all_goals", "simp_rw", "obtain", "dsimp", "obtain", "dsimp", "obtain", "rintro", "refine", "exact", "refine", "rw", "obtain", "rw", "exact", "have", "intro", "simp_rw", "obtain", "dsimp", "obtain", "dsimp", "obtain", "rw", "obtain", "change", "rw", "refine", "affineIndependent_of_ne_of_mem_of_notMem_of_mem", "rwa", "refine", "rw", "exact", "have", "simp_rw", "refine", "simp", "have", "simp_rw", "refine", "hc.mem_affineSpan_of_mem_of_ne", "p₄", "simp", "convert"], "tactic_count": 58}
{"name": "Sbtw.oangle_sign_eq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Wbtw.oangle_sign_eq_of_ne_left", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sbtw.oangle_sign_eq_left", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Wbtw.oangle_sign_eq_of_ne_right", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Sbtw.oangle_sign_eq_right", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sbtw.oangle_sign_eq_of_sbtw", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Sbtw.oangle_sign_eq_of_sbtw_left", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AffineSubspace.SSameSide.oangle_sign_eq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": true, "tactics": ["by_cases", "let", "have", "have", "refine", "all_goals", "simp_rw", "obtain", "dsimp", "rintro", "exact", "exact", "have", "intro", "simp_rw", "obtain", "dsimp", "rw", "exact", "have", "have", "convert"], "tactic_count": 22}
{"name": "AffineSubspace.SOppSide.oangle_sign_eq_neg", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": true, "tactics": ["have", "rw", "oangle_rotate_sign"], "tactic_count": 3}
{"name": "EuclideanGeometry.angle_eq_iff_oangle_eq_or_wbtw", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Affine", "is_tactic_proof": true, "tactics": ["simp_rw", "apply", "refine", "obtain", "rw", "nth_rw", "exact", "rcases", "exact", "exact"], "tactic_count": 10}
{"name": "_private.Mathlib.Geometry.Euclidean.Angle.Oriented.Basic.0.Orientation.termω", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Geometry.Euclidean.Angle.Oriented.Basic.0.Orientation._aux_Mathlib_Geometry_Euclidean_Angle_Oriented_Basic___macroRules__private_Mathlib_Geometry_Euclidean_Angle_Oriented_Basic_0_Orientation_termω_1", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.oangle", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.continuousAt_oangle", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["refine", "exact", "exact"], "tactic_count": 3}
{"name": "Orientation.oangle_zero_left", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Orientation.oangle_zero_right", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Orientation.oangle_self", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["rw", "convert", "apply", "positivity"], "tactic_count": 4}
{"name": "Orientation.left_ne_zero_of_oangle_ne_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "Orientation.right_ne_zero_of_oangle_ne_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "Orientation.ne_of_oangle_ne_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "Orientation.left_ne_zero_of_oangle_eq_pi", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.right_ne_zero_of_oangle_eq_pi", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.ne_of_oangle_eq_pi", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.left_ne_zero_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.right_ne_zero_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.ne_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.left_ne_zero_of_oangle_eq_neg_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.right_ne_zero_of_oangle_eq_neg_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.ne_of_oangle_eq_neg_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.left_ne_zero_of_oangle_sign_ne_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.right_ne_zero_of_oangle_sign_ne_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.ne_of_oangle_sign_ne_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.left_ne_zero_of_oangle_sign_eq_one", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.right_ne_zero_of_oangle_sign_eq_one", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.ne_of_oangle_sign_eq_one", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.left_ne_zero_of_oangle_sign_eq_neg_one", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.right_ne_zero_of_oangle_sign_eq_neg_one", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.ne_of_oangle_sign_eq_neg_one", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.oangle_rev", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Orientation.oangle_add_oangle_rev", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Orientation.oangle_neg_left", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["simp", "convert", "exact"], "tactic_count": 3}
{"name": "Orientation.oangle_neg_right", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["simp", "convert", "exact"], "tactic_count": 3}
{"name": "Orientation.two_zsmul_oangle_neg_left", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "by_cases", "simp", "simp"], "tactic_count": 5}
{"name": "Orientation.two_zsmul_oangle_neg_right", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "by_cases", "simp", "simp"], "tactic_count": 5}
{"name": "Orientation.oangle_neg_neg", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Orientation.oangle_neg_left_eq_neg_right", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Orientation.oangle_neg_self_left", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Orientation.oangle_neg_self_right", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Orientation.two_zsmul_oangle_neg_self_left", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "Orientation.two_zsmul_oangle_neg_self_right", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "Orientation.oangle_add_oangle_rev_neg_left", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Orientation.oangle_add_oangle_rev_neg_right", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Orientation.oangle_smul_left_of_pos", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Orientation.oangle_smul_right_of_pos", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Orientation.oangle_smul_left_of_neg", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Orientation.oangle_smul_right_of_neg", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Orientation.oangle_smul_left_self_of_nonneg", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simp"], "tactic_count": 3}
{"name": "Orientation.oangle_smul_right_self_of_nonneg", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simp"], "tactic_count": 3}
{"name": "Orientation.oangle_smul_smul_self_of_nonneg", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simp"], "tactic_count": 3}
{"name": "Orientation.two_zsmul_oangle_smul_left_of_ne_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "Orientation.two_zsmul_oangle_smul_right_of_ne_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "Orientation.two_zsmul_oangle_smul_left_self", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "Orientation.two_zsmul_oangle_smul_right_self", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "Orientation.two_zsmul_oangle_smul_smul_self", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "Orientation.two_zsmul_oangle_left_of_span_eq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["rw", "rcases", "exact"], "tactic_count": 3}
{"name": "Orientation.two_zsmul_oangle_right_of_span_eq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["rw", "rcases", "exact"], "tactic_count": 3}
{"name": "Orientation.two_zsmul_oangle_of_span_eq_of_span_eq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Orientation.oangle_eq_zero_iff_oangle_rev_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Orientation.oangle_eq_zero_iff_sameRay", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": false, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "Orientation.oangle_eq_pi_iff_oangle_rev_eq_pi", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Orientation.oangle_eq_pi_iff_sameRay_neg", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["rw", "constructor", "intro", "by_cases", "by_cases", "refine", "rw", "rintro", "rwa"], "tactic_count": 9}
{"name": "Orientation.oangle_eq_zero_or_eq_pi_iff_not_linearIndependent", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["rw", "sameRay_or_ne_zero_and_sameRay_neg_iff_not_linearIndependent]"], "tactic_count": 2}
{"name": "Orientation.oangle_eq_zero_or_eq_pi_iff_right_eq_smul", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "rcases", "by_cases", "obtain", "exact", "by_cases", "obtain", "refine", "simp", "rcases", "by_cases", "rcases", "rw", "exact", "simp", "exact"], "tactic_count": 17}
{"name": "Orientation.oangle_ne_zero_and_ne_pi_iff_linearIndependent", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["contrapose"], "tactic_count": 1}
{"name": "Orientation.eq_iff_norm_eq_and_oangle_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["rw", "constructor", "rintro", "simp", "rcases", "simp", "rintro", "obtain", "have", "obtain", "apply", "simpa", "simp"], "tactic_count": 13}
{"name": "Orientation.eq_iff_oangle_eq_zero_of_norm_eq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.eq_iff_norm_eq_of_oangle_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.oangle_add", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "rw", "congr", "exact", "exact", "exact"], "tactic_count": 6}
{"name": "Orientation.oangle_add_swap", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Orientation.oangle_sub_left", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Orientation.oangle_sub_right", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Orientation.oangle_add_cyc3", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Orientation.oangle_add_cyc3_neg_left", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["rw", "show", "o.oangle", "o.oangle", "o.oangle_add_cyc3"], "tactic_count": 5}
{"name": "Orientation.oangle_add_cyc3_neg_right", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Orientation.oangle_sub_eq_oangle_sub_rev_of_norm_eq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Orientation.oangle_eq_pi_sub_two_zsmul_oangle_sub_of_norm_eq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["rw", "nth_rw", "rw", "have", "rintro", "rw", "exact", "have", "convert", "simp"], "tactic_count": 10}
{"name": "Orientation.oangle_map", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.oangle", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Orientation.oangle_map_complex", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["rw", "iterate"], "tactic_count": 2}
{"name": "Orientation.oangle_neg_orientation_eq_neg", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Orientation.inner_eq_norm_mul_norm_mul_cos_oangle", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "by_cases", "rw", "simp", "simp", "exact"], "tactic_count": 6}
{"name": "Orientation.cos_oangle_eq_inner_div_norm_mul_norm", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["rw", "field"], "tactic_count": 2}
{"name": "Orientation.cos_oangle_eq_cos_angle", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Orientation.oangle_eq_angle_or_eq_neg_angle", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.angle_eq_abs_oangle_toReal", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["have", "have", "rcases", "rw", "exact", "rw", "exact"], "tactic_count": 7}
{"name": "Orientation.eq_zero_or_angle_eq_zero_or_pi_of_sign_oangle_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "by_cases", "rw", "rw", "rcases"], "tactic_count": 5}
{"name": "Orientation.oangle_eq_of_angle_eq_of_sign_eq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "have", "rcases", "simpa", "simpa", "simpa", "simpa", "rcases", "have", "rcases", "simpa", "simpa", "simpa", "simpa", "rcases", "have", "intro", "rw", "exact", "exact", "have", "have", "simpa", "have", "have", "simpa", "rcases", "rw", "rwa"], "tactic_count": 29}
{"name": "Orientation.angle_eq_iff_oangle_eq_of_sign_eq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "Orientation.oangle_eq_neg_of_angle_eq_of_sign_eq_neg", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["rw", "rw", "nth_rw", "exact"], "tactic_count": 4}
{"name": "Orientation.angle_eq_iff_oangle_eq_neg_of_sign_eq_neg", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["rw", "rw", "nth_rw", "exact"], "tactic_count": 4}
{"name": "Orientation.oangle_eq_angle_of_sign_eq_one", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "by_cases", "refine", "intro", "rw", "exact", "h"], "tactic_count": 7}
{"name": "Orientation.oangle_eq_neg_angle_of_sign_eq_neg_one", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "by_cases", "refine", "intro", "rw", "exact", "h"], "tactic_count": 7}
{"name": "Orientation.oangle_eq_zero_iff_angle_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["refine", "simpa", "have", "rw", "simpa"], "tactic_count": 5}
{"name": "Orientation.oangle_eq_pi_iff_angle_eq_pi", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "by_cases", "simp", "refine", "rw", "simp", "have", "rw", "simpa"], "tactic_count": 10}
{"name": "Orientation.eq_zero_or_oangle_eq_iff_inner_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "by_cases", "rw", "refine", "rwa", "convert", "simp"], "tactic_count": 7}
{"name": "Orientation.inner_eq_zero_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.inner_rev_eq_zero_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Orientation.inner_eq_zero_of_oangle_eq_neg_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.inner_rev_eq_zero_of_oangle_eq_neg_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Orientation.oangle_sign_neg_left", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "by_cases", "rw"], "tactic_count": 3}
{"name": "Orientation.oangle_sign_neg_right", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "by_cases", "rw"], "tactic_count": 3}
{"name": "Orientation.oangle_sign_smul_left", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "Orientation.oangle_sign_smul_right", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "Orientation.oangle_smul_add_right_eq_zero_or_eq_pi_iff", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": false, "tactics": ["simp_rw", "refine", "rcases", "change", "refine", "change", "rw", "refine", "obtain", "rw", "rw", "simp", "rcases", "change", "refine", "change", "rw", "refine", "obtain", "rw", "rw", "simp"], "tactic_count": 22}
{"name": "Orientation.oangle_sign_smul_add_right", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "rwa", "have", "intro", "rwa", "let", "have", "have", "refine", "all_goals", "simp_rw", "obtain", "simp", "intro", "simpa", "simpa", "have", "have", "convert", "simp", "have", "convert"], "tactic_count": 22}
{"name": "Orientation.oangle_sign_add_smul_left", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Orientation.oangle_sign_sub_smul_right", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Orientation.oangle_sign_sub_smul_left", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Orientation.oangle_sign_add_right", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Orientation.oangle_sign_add_left", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Orientation.oangle_sign_sub_right", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Orientation.oangle_sign_sub_left", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Orientation.oangle_sign_smul_sub_right", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Orientation.oangle_sign_smul_sub_left", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Orientation.oangle_sign_sub_right_eq_neg", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Orientation.oangle_sign_sub_left_eq_neg", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Orientation.oangle_sign_sub_right_swap", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Orientation.oangle_sign_sub_left_swap", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Orientation.oangle_sign_smul_add_smul_right", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Orientation.oangle_sign_smul_add_smul_left", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Orientation.oangle_sign_smul_add_smul_smul_add_smul", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "oangle_sign_smul_add_smul_right,", "rw", "div_mul_cancel₀", "oangle_sign_smul_right,", "mul_comm"], "tactic_count": 7}
{"name": "Orientation.abs_oangle_sub_left_toReal_lt_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "have", "conv_rhs", "rw", "rw", "rcases", "rw", "rcases", "rw", "rcases", "rw", "nth_rw", "rw", "rw", "or_iff_left", "rw", "exact", "exact"], "tactic_count": 18}
{"name": "Orientation.abs_oangle_sub_right_toReal_lt_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.angle_eq_iff_oangle_eq_or_sameRay", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "by_cases", "obtain", "simp", "simp", "by_cases", "rw", "have", "simp", "intro", "apply", "by_cases", "rw", "rw", "simp", "have", "revert", "generalize", "generalize", "decide", "have", "rcases", "rcases", "rw", "obtain", "obtain", "simp_all", "rw", "obtain", "obtain", "simp_all"], "tactic_count": 32}
{"name": "EuclideanGeometry.oangle_self_orthogonalProjection", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Projection", "is_tactic_proof": true, "tactics": ["haveI", "have", "have", "rw", "rwa"], "tactic_count": 5}
{"name": "EuclideanGeometry.oangle_orthogonalProjection_self", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Projection", "is_tactic_proof": false, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "EuclideanGeometry.two_zsmul_oangle_self_orthogonalProjection", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Projection", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "EuclideanGeometry.two_zsmul_oangle_orthogonalProjection_self", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Projection", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Orientation.oangle_add_right_eq_arccos_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "Orientation.oangle_add_left_eq_arccos_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "Orientation.oangle_add_right_eq_arcsin_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "Orientation.oangle_add_left_eq_arcsin_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "Orientation.oangle_add_right_eq_arctan_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "Orientation.oangle_add_left_eq_arctan_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "Orientation.cos_oangle_add_right_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "Orientation.cos_oangle_add_left_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "Orientation.sin_oangle_add_right_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "Orientation.sin_oangle_add_left_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "Orientation.tan_oangle_add_right_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "Orientation.tan_oangle_add_left_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "Orientation.cos_oangle_add_right_mul_norm_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "Orientation.cos_oangle_add_left_mul_norm_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "Orientation.sin_oangle_add_right_mul_norm_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "Orientation.sin_oangle_add_left_mul_norm_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "Orientation.tan_oangle_add_right_mul_norm_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "Orientation.tan_oangle_add_left_mul_norm_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "Orientation.norm_div_cos_oangle_add_right_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "Orientation.norm_div_cos_oangle_add_left_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "Orientation.norm_div_sin_oangle_add_right_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "Orientation.norm_div_sin_oangle_add_left_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "Orientation.norm_div_tan_oangle_add_right_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "Orientation.norm_div_tan_oangle_add_left_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "Orientation.oangle_sub_right_eq_arccos_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": false, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "Orientation.oangle_sub_left_eq_arccos_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Orientation.oangle_sub_right_eq_arcsin_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": false, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "Orientation.oangle_sub_left_eq_arcsin_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Orientation.oangle_sub_right_eq_arctan_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": false, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "Orientation.oangle_sub_left_eq_arctan_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Orientation.cos_oangle_sub_right_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": false, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "Orientation.cos_oangle_sub_left_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Orientation.sin_oangle_sub_right_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": false, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "Orientation.sin_oangle_sub_left_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Orientation.tan_oangle_sub_right_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": false, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "Orientation.tan_oangle_sub_left_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Orientation.cos_oangle_sub_right_mul_norm_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": false, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "Orientation.cos_oangle_sub_left_mul_norm_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Orientation.sin_oangle_sub_right_mul_norm_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": false, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "Orientation.sin_oangle_sub_left_mul_norm_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Orientation.tan_oangle_sub_right_mul_norm_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": false, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "Orientation.tan_oangle_sub_left_mul_norm_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Orientation.norm_div_cos_oangle_sub_right_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": false, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "Orientation.norm_div_cos_oangle_sub_left_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Orientation.norm_div_sin_oangle_sub_right_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": false, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "Orientation.norm_div_sin_oangle_sub_left_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Orientation.norm_div_tan_oangle_sub_right_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": false, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "Orientation.norm_div_tan_oangle_sub_left_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Orientation.oangle_add_right_smul_rotation_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["rcases", "have", "rw", "add_comm,", "simpa", "rw", "rw", "mul_div_assoc,", "rw", "have", "rw", "rw", "div_self"], "tactic_count": 13}
{"name": "Orientation.oangle_add_left_smul_rotation_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "rotation_neg_orientation_eq_neg,", "have", "nth_rw", "refine", "simp"], "tactic_count": 7}
{"name": "Orientation.tan_oangle_add_right_smul_rotation_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Orientation.tan_oangle_add_left_smul_rotation_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Orientation.oangle_sub_right_smul_rotation_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["by_cases", "have", "rw", "simpa"], "tactic_count": 4}
{"name": "Orientation.oangle_sub_left_smul_rotation_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["by_cases", "have", "rw", "nth_rw", "nth_rw", "rw", "simpa"], "tactic_count": 7}
{"name": "EuclideanGeometry.oangle_right_eq_arccos_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["have", "rw", "angle_eq_arccos_of_angle_eq_pi_div_two"], "tactic_count": 3}
{"name": "EuclideanGeometry.oangle_left_eq_arccos_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["have", "rw", "angle_eq_arccos_of_angle_eq_pi_div_two"], "tactic_count": 3}
{"name": "EuclideanGeometry.oangle_right_eq_arcsin_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["have", "rw", "angle_eq_arcsin_of_angle_eq_pi_div_two"], "tactic_count": 3}
{"name": "EuclideanGeometry.oangle_left_eq_arcsin_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["have", "rw", "angle_eq_arcsin_of_angle_eq_pi_div_two", "dist_comm"], "tactic_count": 4}
{"name": "EuclideanGeometry.oangle_right_eq_arctan_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["have", "rw", "angle_eq_arctan_of_angle_eq_pi_div_two"], "tactic_count": 3}
{"name": "EuclideanGeometry.oangle_left_eq_arctan_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["have", "rw", "angle_eq_arctan_of_angle_eq_pi_div_two"], "tactic_count": 3}
{"name": "EuclideanGeometry.abs_oangle_toReal_lt_pi_div_two_of_angle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "by_cases", "simp", "rw", "exact"], "tactic_count": 6}
{"name": "EuclideanGeometry.oangle_eq_oangle_of_two_zsmul_eq_of_angle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "EuclideanGeometry.oangle_eq_oangle_rev_of_two_zsmul_eq_of_angle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": false, "tactics": ["refine", "h", "rw", "exact"], "tactic_count": 4}
{"name": "EuclideanGeometry.cos_oangle_right_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["have", "rw", "cos_angle_of_angle_eq_pi_div_two"], "tactic_count": 3}
{"name": "EuclideanGeometry.cos_oangle_left_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["have", "rw", "cos_angle_of_angle_eq_pi_div_two"], "tactic_count": 3}
{"name": "EuclideanGeometry.sin_oangle_right_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["have", "rw", "sin_angle_of_angle_eq_pi_div_two"], "tactic_count": 3}
{"name": "EuclideanGeometry.sin_oangle_left_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["have", "rw", "sin_angle_of_angle_eq_pi_div_two", "dist_comm"], "tactic_count": 4}
{"name": "EuclideanGeometry.tan_oangle_right_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["have", "rw", "tan_angle_of_angle_eq_pi_div_two"], "tactic_count": 3}
{"name": "EuclideanGeometry.tan_oangle_left_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["have", "rw", "tan_angle_of_angle_eq_pi_div_two"], "tactic_count": 3}
{"name": "EuclideanGeometry.cos_oangle_right_mul_dist_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["have", "rw", "cos_angle_mul_dist_of_angle_eq_pi_div_two"], "tactic_count": 3}
{"name": "EuclideanGeometry.cos_oangle_left_mul_dist_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["have", "rw", "cos_angle_mul_dist_of_angle_eq_pi_div_two"], "tactic_count": 3}
{"name": "EuclideanGeometry.sin_oangle_right_mul_dist_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["have", "rw", "sin_angle_mul_dist_of_angle_eq_pi_div_two"], "tactic_count": 3}
{"name": "EuclideanGeometry.sin_oangle_left_mul_dist_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["have", "rw", "sin_angle_mul_dist_of_angle_eq_pi_div_two"], "tactic_count": 3}
{"name": "EuclideanGeometry.tan_oangle_right_mul_dist_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["have", "rw", "tan_angle_mul_dist_of_angle_eq_pi_div_two"], "tactic_count": 3}
{"name": "EuclideanGeometry.tan_oangle_left_mul_dist_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["have", "rw", "tan_angle_mul_dist_of_angle_eq_pi_div_two"], "tactic_count": 3}
{"name": "EuclideanGeometry.dist_div_cos_oangle_right_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["have", "rw", "dist_div_cos_angle_of_angle_eq_pi_div_two"], "tactic_count": 3}
{"name": "EuclideanGeometry.dist_div_cos_oangle_left_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["have", "rw", "dist_div_cos_angle_of_angle_eq_pi_div_two"], "tactic_count": 3}
{"name": "EuclideanGeometry.dist_div_sin_oangle_right_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["have", "rw", "dist_div_sin_angle_of_angle_eq_pi_div_two"], "tactic_count": 3}
{"name": "EuclideanGeometry.dist_div_sin_oangle_left_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["have", "rw", "dist_div_sin_angle_of_angle_eq_pi_div_two"], "tactic_count": 3}
{"name": "EuclideanGeometry.dist_div_tan_oangle_right_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["have", "rw", "dist_div_tan_angle_of_angle_eq_pi_div_two"], "tactic_count": 3}
{"name": "EuclideanGeometry.dist_div_tan_oangle_left_of_oangle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle", "is_tactic_proof": true, "tactics": ["have", "rw", "dist_div_tan_angle_of_angle_eq_pi_div_two"], "tactic_count": 3}
{"name": "_private.Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation.0.Orientation.termJ", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation.0.Orientation._aux_Mathlib_Geometry_Euclidean_Angle_Oriented_Rotation___macroRules__private_Mathlib_Geometry_Euclidean_Angle_Oriented_Rotation_0_Orientation_termJ_1", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.rotationAux", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.rotationAux_apply", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.rotation", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.rotation_apply", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.rotation_symm_apply", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.rotation_eq_matrix_toLin", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation", "is_tactic_proof": true, "tactics": ["apply", "intro", "fin_cases", "rw", "simp", "rw", "simp"], "tactic_count": 7}
{"name": "Orientation.det_rotation", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation", "is_tactic_proof": true, "tactics": ["haveI", "obtain", "rw", "simpa"], "tactic_count": 4}
{"name": "Orientation.linearEquiv_det_rotation", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.rotation_symm", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Orientation.rotation_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Orientation.rotation_pi", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Orientation.rotation_pi_apply", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Orientation.rotation_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Orientation.rotation_rotation", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation", "is_tactic_proof": false, "tactics": ["simp", "rightAngleRotation_rightAngleRotation]", "module"], "tactic_count": 3}
{"name": "Orientation.rotation_trans", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.kahler_rotation_left", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation", "is_tactic_proof": false, "tactics": ["simp", "conj_I]", "ring"], "tactic_count": 3}
{"name": "Orientation.neg_rotation", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Orientation.neg_rotation_neg_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Orientation.neg_rotation_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.kahler_rotation_left'", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Orientation.kahler_rotation_right", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation", "is_tactic_proof": false, "tactics": ["simp", "ring"], "tactic_count": 2}
{"name": "Orientation.oangle_rotation_left", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation", "is_tactic_proof": true, "tactics": ["simp", "rw", "abel", "exact", "exact"], "tactic_count": 5}
{"name": "Orientation.oangle_rotation_right", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation", "is_tactic_proof": true, "tactics": ["simp", "rw", "abel", "exact", "exact"], "tactic_count": 5}
{"name": "Orientation.oangle_rotation_self_left", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Orientation.oangle_rotation_self_right", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Orientation.oangle_rotation_oangle_left", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "by_cases", "simp", "simp"], "tactic_count": 5}
{"name": "Orientation.oangle_rotation_oangle_right", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Orientation.oangle_rotation", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "Orientation.rotation_eq_self_iff_angle_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "simpa", "intro", "simp"], "tactic_count": 6}
{"name": "Orientation.eq_rotation_self_iff_angle_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Orientation.rotation_eq_self_iff", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "Orientation.eq_rotation_self_iff", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Orientation.rotation_oangle_eq_iff_norm_eq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "intro", "rw"], "tactic_count": 5}
{"name": "Orientation.oangle_eq_iff_eq_norm_div_norm_smul_rotation_of_ne_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation", "is_tactic_proof": true, "tactics": ["have", "constructor", "rintro", "rw", "intro", "rw"], "tactic_count": 6}
{"name": "Orientation.oangle_eq_iff_eq_pos_smul_rotation_of_ne_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "exact", "rintro", "rw"], "tactic_count": 6}
{"name": "Orientation.oangle_eq_iff_eq_norm_div_norm_smul_rotation_or_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "by_cases", "simp", "rw", "simp"], "tactic_count": 6}
{"name": "Orientation.oangle_eq_iff_eq_pos_smul_rotation_or_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "by_cases", "simp", "rw", "simp"], "tactic_count": 6}
{"name": "Orientation.exists_linearIsometryEquiv_eq_of_det_pos", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation", "is_tactic_proof": true, "tactics": ["haveI", "obtain", "use", "apply", "apply", "apply", "intro", "symm", "fin_cases", "simp", "have", "simp", "simp"], "tactic_count": 13}
{"name": "Orientation.rotation_map", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complex.rotation", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation", "is_tactic_proof": true, "tactics": ["simp", "ring"], "tactic_count": 2}
{"name": "Orientation.rotation_map_complex", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Orientation.rotation_neg_orientation_eq_neg", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.inner_rotation_pi_div_two_left", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Orientation.inner_rotation_pi_div_two_right", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Orientation.inner_smul_rotation_pi_div_two_left", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Orientation.inner_smul_rotation_pi_div_two_right", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Orientation.inner_rotation_pi_div_two_left_smul", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Orientation.inner_rotation_pi_div_two_right_smul", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Orientation.inner_smul_rotation_pi_div_two_smul_left", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Orientation.inner_smul_rotation_pi_div_two_smul_right", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Orientation.inner_eq_zero_iff_eq_zero_or_eq_smul_rotation_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation", "is_tactic_proof": true, "tactics": ["wlog", "rcases", "simp", "o.oangle_eq_iff_eq_pos_smul_rotation_of_ne_zero", "constructor", "grind", "rintro", "rcases", "grind", "simp_all", "right", "use", "simp_all"], "tactic_count": 13}
{"name": "Orientation.oangle_eq_two_zsmul_oangle_sub_of_norm_eq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Sphere", "is_tactic_proof": false, "tactics": ["have", "rintro", "rw", "exact", "have", "have", "calc", "o.oangle", "rw", "o.oangle_eq_pi_sub_two_zsmul_oangle_sub_of_norm_eq", "rw"], "tactic_count": 11}
{"name": "Orientation.oangle_eq_two_zsmul_oangle_sub_of_norm_eq_real", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Sphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.two_zsmul_oangle_sub_eq_two_zsmul_oangle_sub_of_norm_eq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Sphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.Sphere.angle_eq_pi_div_two_iff_mem_sphere_of_isDiameter", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Sphere", "is_tactic_proof": true, "tactics": ["rw", "let", "have", "rw", "have", "rw", "rw", "ring_nf", "rw", "sq_eq_sq₀", "exact"], "tactic_count": 11}
{"name": "EuclideanGeometry.Sphere.angle_eq_pi_div_two_iff_mem_sphere_ofDiameter", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Sphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.Sphere.isDiameter_of_angle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Sphere", "is_tactic_proof": true, "tactics": ["haveI", "have", "have", "have", "by_contra", "have", "eq_of_mem_sphere_of_mem_sphere_of_finrank_eq_two", "hd.right_mem", "exact", "exact"], "tactic_count": 10}
{"name": "EuclideanGeometry.Sphere.IsTangentAt.angle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Sphere", "is_tactic_proof": true, "tactics": ["have", "rw", "rw", "linarith"], "tactic_count": 4}
{"name": "EuclideanGeometry.Sphere.IsTangentAt_of_angle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Sphere", "is_tactic_proof": true, "tactics": ["have", "refine", "have", "rwa", "neg_eq_zero]", "have", "rw", "have", "simp_rw", "exact"], "tactic_count": 10}
{"name": "EuclideanGeometry.Sphere.IsTangentAt_iff_angle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Sphere", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "_private.Mathlib.Geometry.Euclidean.Angle.Sphere.0.EuclideanGeometry.termO", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Angle.Sphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Geometry.Euclidean.Angle.Sphere.0.EuclideanGeometry._aux_Mathlib_Geometry_Euclidean_Angle_Sphere___macroRules__private_Mathlib_Geometry_Euclidean_Angle_Sphere_0_EuclideanGeometry_termO_1", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Angle.Sphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Geometry.Euclidean.Angle.Sphere.0.EuclideanGeometry._aux_Mathlib_Geometry_Euclidean_Angle_Sphere___unexpand_Module_Oriented_positiveOrientation_1", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Angle.Sphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.Sphere.oangle_center_eq_two_zsmul_oangle", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Sphere", "is_tactic_proof": true, "tactics": ["rw", "rw"], "tactic_count": 2}
{"name": "EuclideanGeometry.Sphere.two_zsmul_oangle_eq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Sphere", "is_tactic_proof": true, "tactics": ["rw", "rw", "simp"], "tactic_count": 3}
{"name": "EuclideanGeometry.Cospherical.two_zsmul_oangle_eq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Sphere", "is_tactic_proof": true, "tactics": ["obtain", "simp_rw", "exact"], "tactic_count": 3}
{"name": "EuclideanGeometry.Sphere.oangle_eq_pi_sub_two_zsmul_oangle_center_left", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Sphere", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EuclideanGeometry.Sphere.oangle_eq_pi_sub_two_zsmul_oangle_center_right", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Sphere", "is_tactic_proof": true, "tactics": ["rw", "oangle_eq_oangle_of_dist_eq"], "tactic_count": 2}
{"name": "EuclideanGeometry.Sphere.two_zsmul_oangle_center_add_two_zsmul_oangle_eq_pi", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Sphere", "is_tactic_proof": true, "tactics": ["rw", "oangle_eq_pi_sub_two_zsmul_oangle_center_right"], "tactic_count": 2}
{"name": "EuclideanGeometry.Sphere.abs_oangle_center_left_toReal_lt_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Sphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.Sphere.abs_oangle_center_right_toReal_lt_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Sphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.Sphere.tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Sphere", "is_tactic_proof": false, "tactics": ["obtain", "rw", "nth_rw", "rw", "mul_div_cancel_right₀", "simpa"], "tactic_count": 6}
{"name": "EuclideanGeometry.Sphere.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Sphere", "is_tactic_proof": true, "tactics": ["convert", "convert", "rw"], "tactic_count": 3}
{"name": "EuclideanGeometry.Sphere.dist_div_cos_oangle_center_div_two_eq_radius", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Sphere", "is_tactic_proof": false, "tactics": ["rw", "show", "tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center", "vadd_vsub_assoc,", "div_mul_cancel₀", "norm_cast", "rw", "norm_add_sq_eq_norm_sq_add_norm_sq_real", "mul_comm", "conv_rhs", "ring", "simpa"], "tactic_count": 12}
{"name": "EuclideanGeometry.Sphere.dist_div_cos_oangle_center_eq_two_mul_radius", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Sphere", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EuclideanGeometry.Sphere.dist_div_sin_oangle_div_two_eq_radius", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Sphere", "is_tactic_proof": true, "tactics": ["convert", "rw", "abs_of_nonneg", "exact"], "tactic_count": 4}
{"name": "EuclideanGeometry.Sphere.dist_div_sin_oangle_eq_two_mul_radius", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Sphere", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "_private.Mathlib.Geometry.Euclidean.Angle.Sphere.0.Affine.Triangle.termO", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Angle.Sphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Geometry.Euclidean.Angle.Sphere.0.Affine.Triangle._aux_Mathlib_Geometry_Euclidean_Angle_Sphere___macroRules__private_Mathlib_Geometry_Euclidean_Angle_Sphere_0_Affine_Triangle_termO_1", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Angle.Sphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Geometry.Euclidean.Angle.Sphere.0.Affine.Triangle._aux_Mathlib_Geometry_Euclidean_Angle_Sphere___unexpand_Module_Oriented_positiveOrientation_1", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Angle.Sphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Triangle.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_circumcenter", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Sphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Triangle.dist_div_sin_oangle_div_two_eq_circumradius", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Sphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Triangle.dist_div_sin_oangle_eq_two_mul_circumradius", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Sphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Triangle.circumsphere_eq_of_dist_of_oangle", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Sphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Triangle.circumsphere_eq_circumsphere_of_eq_of_eq_of_two_zsmul_oangle_eq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Sphere", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Affine.Triangle.mem_circumsphere_of_two_zsmul_oangle_eq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Sphere", "is_tactic_proof": true, "tactics": ["let", "have", "have", "have", "have", "rw", "affineIndependent_iff_not_collinear_of_ne", "exact", "let", "have", "have", "have", "have", "rw", "exact"], "tactic_count": 15}
{"name": "Affine.Triangle.dist_div_sin_angle_div_two_eq_circumradius", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Sphere", "is_tactic_proof": true, "tactics": ["set", "let", "have", "rw", "simp⟩", "have", "convert", "rw", "angle_eq_abs_oangle_toReal", "congr", "simp"], "tactic_count": 11}
{"name": "Affine.Triangle.dist_div_sin_angle_eq_two_mul_circumradius", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Sphere", "is_tactic_proof": true, "tactics": ["rw", "ring"], "tactic_count": 2}
{"name": "_private.Mathlib.Geometry.Euclidean.Angle.Sphere.0.EuclideanGeometry.termO_1", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Angle.Sphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Geometry.Euclidean.Angle.Sphere.0.EuclideanGeometry._aux_Mathlib_Geometry_Euclidean_Angle_Sphere___macroRules__private_Mathlib_Geometry_Euclidean_Angle_Sphere_0_EuclideanGeometry_termO_1_1", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Angle.Sphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Geometry.Euclidean.Angle.Sphere.0.EuclideanGeometry._aux_Mathlib_Geometry_Euclidean_Angle_Sphere___unexpand_Module_Oriented_positiveOrientation_2", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Angle.Sphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.cospherical_of_two_zsmul_oangle_eq_of_not_collinear", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Sphere", "is_tactic_proof": true, "tactics": ["have", "let", "let", "rw", "refine", "simp_rw", "refine", "rw", "exact"], "tactic_count": 9}
{"name": "EuclideanGeometry.concyclic_of_two_zsmul_oangle_eq_of_not_collinear", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Sphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.cospherical_or_collinear_of_two_zsmul_oangle_eq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Sphere", "is_tactic_proof": true, "tactics": ["by_cases", "by_cases", "rw", "by_cases", "rw", "let", "rw", "refine", "simp_rw", "exact", "have", "refine", "rw", "rwa", "hc'.collinear_insert_iff_of_ne", "exact"], "tactic_count": 16}
{"name": "EuclideanGeometry.concyclic_or_collinear_of_two_zsmul_oangle_eq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Sphere", "is_tactic_proof": true, "tactics": ["rcases", "exact", "exact"], "tactic_count": 3}
{"name": "EuclideanGeometry.angle", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.term∠", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry._aux_Mathlib_Geometry_Euclidean_Angle_Unoriented_Affine___macroRules_EuclideanGeometry_term∠_1", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry._aux_Mathlib_Geometry_Euclidean_Angle_Unoriented_Affine___unexpand_EuclideanGeometry_angle_1", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.continuousAt_angle", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": true, "tactics": ["let", "have", "have", "exact"], "tactic_count": 4}
{"name": "AffineIsometry.angle_map", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "AffineSubspace.angle_coe", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.angle_homothety", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": false, "tactics": ["simp_rw", "rcases"], "tactic_count": 2}
{"name": "EuclideanGeometry.angle_const_vadd", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.angle_vadd_const", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.angle_const_vsub", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.angle_vsub_const", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.angle_add_const", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.angle_const_add", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.angle_sub_const", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "EuclideanGeometry.angle_const_sub", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "EuclideanGeometry.angle_neg", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "EuclideanGeometry.angle_comm", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.angle_nonneg", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.angle_le_pi", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.angle_self_left", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": true, "tactics": ["unfold", "rw", "exact"], "tactic_count": 3}
{"name": "EuclideanGeometry.angle_self_right", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EuclideanGeometry.angle_self_of_ne", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.angle_eq_zero_of_angle_eq_pi_left", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": true, "tactics": ["unfold", "rw", "rcases", "unfold", "rw", "rw", "use", "rw", "simp"], "tactic_count": 9}
{"name": "EuclideanGeometry.angle_eq_zero_of_angle_eq_pi_right", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "EuclideanGeometry.angle_eq_angle_of_angle_eq_pi", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": true, "tactics": ["unfold", "rcases", "rw", "convert", "rw", "simp"], "tactic_count": 6}
{"name": "EuclideanGeometry.angle_add_angle_eq_pi_of_angle_eq_pi", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": true, "tactics": ["unfold", "rw", "unfold", "exact"], "tactic_count": 4}
{"name": "EuclideanGeometry.angle_eq_angle_of_angle_eq_pi_of_angle_eq_pi", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": true, "tactics": ["linarith", "angle_add_angle_eq_pi_of_angle_eq_pi"], "tactic_count": 2}
{"name": "EuclideanGeometry.left_dist_ne_zero_of_angle_eq_pi", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": true, "tactics": ["by_contra", "rw", "rw", "exact"], "tactic_count": 4}
{"name": "EuclideanGeometry.right_dist_ne_zero_of_angle_eq_pi", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.dist_eq_add_dist_of_angle_eq_pi", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "EuclideanGeometry.dist_eq_add_dist_iff_angle_eq_pi", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": true, "tactics": ["rw", "exact", "norm_sub_eq_add_norm_iff_angle_eq_pi", "hp₃p₂"], "tactic_count": 4}
{"name": "EuclideanGeometry.dist_eq_abs_sub_dist_of_angle_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "EuclideanGeometry.dist_eq_abs_sub_dist_iff_angle_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": true, "tactics": ["rw", "exact", "norm_sub_eq_abs_sub_norm_iff_angle_eq_zero", "hp₃p₂"], "tactic_count": 4}
{"name": "EuclideanGeometry.angle_midpoint_eq_pi", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": false, "tactics": ["simp", "angle_smul_right_of_pos,", "rw", "apply", "simpa"], "tactic_count": 5}
{"name": "EuclideanGeometry.angle_left_midpoint_eq_pi_div_two_of_dist_eq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": true, "tactics": ["let", "have", "have", "rw", "exact"], "tactic_count": 5}
{"name": "EuclideanGeometry.angle_right_midpoint_eq_pi_div_two_of_dist_eq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Sbtw.angle₁₂₃_eq_pi", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": true, "tactics": ["rw", "rcases", "refine", "have", "rintro", "rw", "simp", "have", "rintro", "rw", "simp", "replace", "replace", "refine", "rw", "smul_smul,"], "tactic_count": 16}
{"name": "Sbtw.angle₃₂₁_eq_pi", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EuclideanGeometry.angle_eq_pi_iff_sbtw", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": true, "tactics": ["refine", "rw", "rintro", "refine", "rw", "rw", "smul_smul,", "convert", "field", "rw", "exact"], "tactic_count": 11}
{"name": "Wbtw.angle₂₁₃_eq_zero_of_ne", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": true, "tactics": ["rw", "rcases", "have", "rintro", "simp", "replace", "refine", "rw"], "tactic_count": 8}
{"name": "Sbtw.angle₂₁₃_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Wbtw.angle₃₁₂_eq_zero_of_ne", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Sbtw.angle₃₁₂_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Wbtw.angle₂₃₁_eq_zero_of_ne", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sbtw.angle₂₃₁_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Wbtw.angle₁₃₂_eq_zero_of_ne", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sbtw.angle₁₃₂_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.angle_eq_zero_iff_ne_and_wbtw", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": true, "tactics": ["constructor", "rw", "rintro", "rcases", "refine", "rw", "refine", "rw", "exact", "rw", "rintro", "exact", "exact"], "tactic_count": 13}
{"name": "EuclideanGeometry.angle_eq_zero_iff_eq_and_ne_or_sbtw", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": true, "tactics": ["rw", "by_cases", "by_cases", "by_cases", "simp"], "tactic_count": 5}
{"name": "Sbtw.angle_eq_right", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sbtw.angle_eq_left", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Wbtw.angle_eq_right", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": true, "tactics": ["by_cases", "exact"], "tactic_count": 2}
{"name": "Wbtw.angle_eq_left", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "EuclideanGeometry.collinear_iff_eq_or_eq_or_angle_eq_zero_or_angle_eq_pi", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": true, "tactics": ["refine", "replace", "by_cases", "exact", "by_cases", "exact", "rw", "rcases", "exact", "exact", "exact", "rcases", "simpa", "simpa", "rw", "rcases", "rw", "exact", "rw", "exact", "rw", "exact"], "tactic_count": 22}
{"name": "EuclideanGeometry.collinear_of_angle_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.collinear_of_angle_eq_pi", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.angle_ne_zero_of_not_collinear", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.angle_ne_pi_of_not_collinear", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.angle_pos_of_not_collinear", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.angle_lt_pi_of_not_collinear", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.cos_eq_one_iff_angle_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.cos_eq_zero_iff_angle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.cos_eq_neg_one_iff_angle_eq_pi", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.sin_eq_zero_iff_angle_eq_zero_or_angle_eq_pi", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.sin_eq_one_iff_angle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.collinear_iff_eq_or_eq_or_sin_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EuclideanGeometry.sin_pos_of_not_collinear", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.sin_ne_zero_of_not_collinear", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.collinear_of_sin_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine", "is_tactic_proof": true, "tactics": ["revert", "contrapose", "exact"], "tactic_count": 3}
{"name": "InnerProductGeometry.angle", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InnerProductGeometry.continuousAt_angle", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic", "is_tactic_proof": true, "tactics": ["unfold", "fun_prop"], "tactic_count": 2}
{"name": "InnerProductGeometry.angle_smul_smul", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic", "is_tactic_proof": true, "tactics": ["have", "rw", "mul_mul_mul_comm"], "tactic_count": 3}
{"name": "LinearIsometry.angle_map", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submodule.angle_coe", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InnerProductGeometry.cos_angle", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InnerProductGeometry.angle_comm", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic", "is_tactic_proof": true, "tactics": ["unfold", "rw"], "tactic_count": 2}
{"name": "InnerProductGeometry.angle_neg_neg", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic", "is_tactic_proof": true, "tactics": ["unfold", "rw"], "tactic_count": 2}
{"name": "InnerProductGeometry.angle_nonneg", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InnerProductGeometry.angle_le_pi", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InnerProductGeometry.sin_angle_nonneg", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InnerProductGeometry.angle_neg_right", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic", "is_tactic_proof": true, "tactics": ["unfold", "rw"], "tactic_count": 2}
{"name": "InnerProductGeometry.angle_neg_left", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "InnerProductGeometry.angle_zero_left", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic", "is_tactic_proof": true, "tactics": ["unfold", "rw"], "tactic_count": 2}
{"name": "InnerProductGeometry.angle_zero_right", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic", "is_tactic_proof": true, "tactics": ["unfold", "rw"], "tactic_count": 2}
{"name": "InnerProductGeometry.angle_self", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic", "is_tactic_proof": true, "tactics": ["unfold", "rw"], "tactic_count": 2}
{"name": "InnerProductGeometry.angle_self_neg_of_nonzero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "InnerProductGeometry.angle_neg_self_of_nonzero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "InnerProductGeometry.angle_smul_right_of_pos", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic", "is_tactic_proof": true, "tactics": ["unfold", "rw", "mul_div_mul_left"], "tactic_count": 3}
{"name": "InnerProductGeometry.angle_smul_left_of_pos", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "InnerProductGeometry.angle_smul_right_of_neg", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "InnerProductGeometry.angle_smul_left_of_neg", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "InnerProductGeometry.cos_angle_mul_norm_mul_norm", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "InnerProductGeometry.sin_angle_mul_norm_mul_norm", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic", "is_tactic_proof": true, "tactics": ["unfold", "rw", "nth_rw", "rw", "rcases", "rcases", "simp", "field_simp"], "tactic_count": 8}
{"name": "InnerProductGeometry.sin_angle", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic", "is_tactic_proof": true, "tactics": ["rw", "field"], "tactic_count": 2}
{"name": "InnerProductGeometry.sin_angle_add", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic", "is_tactic_proof": true, "tactics": ["rw", "field_simp", "simp", "ring_nf"], "tactic_count": 4}
{"name": "InnerProductGeometry.angle_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "InnerProductGeometry.angle_eq_pi_iff", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "InnerProductGeometry.angle_add_angle_eq_pi_of_angle_eq_pi", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic", "is_tactic_proof": true, "tactics": ["rcases", "rw"], "tactic_count": 2}
{"name": "InnerProductGeometry.inner_eq_zero_iff_angle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InnerProductGeometry.inner_eq_neg_mul_norm_of_angle_eq_pi", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "InnerProductGeometry.inner_eq_mul_norm_of_angle_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "InnerProductGeometry.inner_eq_neg_mul_norm_iff_angle_eq_pi", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic", "is_tactic_proof": true, "tactics": ["refine", "have", "rw"], "tactic_count": 3}
{"name": "InnerProductGeometry.inner_eq_mul_norm_iff_angle_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic", "is_tactic_proof": true, "tactics": ["refine", "have", "rw"], "tactic_count": 3}
{"name": "InnerProductGeometry.norm_sub_eq_add_norm_of_angle_eq_pi", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic", "is_tactic_proof": false, "tactics": ["rw", "inner_eq_neg_mul_norm_of_angle_eq_pi", "ring"], "tactic_count": 3}
{"name": "InnerProductGeometry.norm_add_eq_add_norm_of_angle_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic", "is_tactic_proof": false, "tactics": ["rw", "inner_eq_mul_norm_of_angle_eq_zero", "ring"], "tactic_count": 3}
{"name": "InnerProductGeometry.norm_sub_eq_abs_sub_norm_of_angle_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic", "is_tactic_proof": false, "tactics": ["rw", "inner_eq_mul_norm_of_angle_eq_zero", "ring"], "tactic_count": 3}
{"name": "InnerProductGeometry.norm_sub_eq_add_norm_iff_angle_eq_pi", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "obtain", "rw", "calc"], "tactic_count": 5}
{"name": "InnerProductGeometry.norm_add_eq_add_norm_iff_angle_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "obtain", "rw", "calc"], "tactic_count": 5}
{"name": "InnerProductGeometry.norm_sub_eq_abs_sub_norm_iff_angle_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "have", "rw", "exact", "rw", "calc"], "tactic_count": 7}
{"name": "InnerProductGeometry.norm_add_eq_norm_sub_iff_angle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic", "is_tactic_proof": false, "tactics": ["rw", "norm_add_pow_two_real,", "constructor"], "tactic_count": 3}
{"name": "InnerProductGeometry.cos_eq_one_iff_angle_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "InnerProductGeometry.cos_eq_zero_iff_angle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply", "constructor"], "tactic_count": 3}
{"name": "InnerProductGeometry.cos_eq_neg_one_iff_angle_eq_pi", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "InnerProductGeometry.sin_eq_zero_iff_angle_eq_zero_or_angle_eq_pi", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "InnerProductGeometry.sin_eq_one_iff_angle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "simp"], "tactic_count": 3}
{"name": "InnerProductGeometry.eq_of_angle_eq_zero_of_norm_eq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "InnerProductGeometry.angle_normalize_left", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "rw"], "tactic_count": 3}
{"name": "InnerProductGeometry.angle_normalize_right", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "InnerProductGeometry.inner_eq_cos_angle_of_norm_eq_one", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "InnerProductGeometry.IsConformalMap.preserves_angle", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Conformal", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "InnerProductGeometry.ConformalAt.preserves_angle", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Conformal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InnerProductGeometry.norm_ofLp_crossProduct", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.CrossProduct", "is_tactic_proof": true, "tactics": ["have", "refine", "trans", "simp_rw", "cross_dot_cross,", "linear_combination"], "tactic_count": 6}
{"name": "InnerProductGeometry.norm_toLp_symm_crossProduct", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.CrossProduct", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "EuclideanGeometry.angle_self_orthogonalProjection", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Projection", "is_tactic_proof": true, "tactics": ["haveI", "rw", "exact"], "tactic_count": 3}
{"name": "EuclideanGeometry.angle_orthogonalProjection_self", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.Projection", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "InnerProductGeometry.norm_add_sq_eq_norm_sq_add_norm_sq_iff_angle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "InnerProductGeometry.norm_add_sq_eq_norm_sq_add_norm_sq'", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InnerProductGeometry.norm_sub_sq_eq_norm_sq_add_norm_sq_iff_angle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "InnerProductGeometry.norm_sub_sq_eq_norm_sq_add_norm_sq'", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InnerProductGeometry.angle_add_eq_arccos_of_inner_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle", "is_tactic_proof": true, "tactics": ["rw", "by_cases", "rw"], "tactic_count": 3}
{"name": "InnerProductGeometry.angle_add_eq_arcsin_of_inner_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle", "is_tactic_proof": false, "tactics": ["have", "rw", "refine", "rcases", "exact", "exact", "rw", "div_pow,", "nth_rw", "rw"], "tactic_count": 10}
{"name": "InnerProductGeometry.angle_add_eq_arctan_of_inner_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle", "is_tactic_proof": false, "tactics": ["rw", "norm_add_eq_sqrt_iff_real_inner_eq_zero.2", "nth_rw", "rw_mod_cast", "mul_comm"], "tactic_count": 5}
{"name": "InnerProductGeometry.angle_add_pos_of_inner_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle", "is_tactic_proof": true, "tactics": ["rw", "by_cases", "rw", "simpa"], "tactic_count": 4}
{"name": "InnerProductGeometry.angle_add_le_pi_div_two_of_inner_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "InnerProductGeometry.angle_add_lt_pi_div_two_of_inner_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle", "is_tactic_proof": false, "tactics": ["rw", "exact", "div_pos"], "tactic_count": 3}
{"name": "InnerProductGeometry.cos_angle_add_of_inner_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle", "is_tactic_proof": false, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "InnerProductGeometry.sin_angle_add_of_inner_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle", "is_tactic_proof": false, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "InnerProductGeometry.tan_angle_add_of_inner_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle", "is_tactic_proof": true, "tactics": ["by_cases", "rw"], "tactic_count": 2}
{"name": "InnerProductGeometry.cos_angle_add_mul_norm_of_inner_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle", "is_tactic_proof": true, "tactics": ["rw", "by_cases", "have", "rw", "mul_self_eq_zero]", "simp", "exact"], "tactic_count": 7}
{"name": "InnerProductGeometry.sin_angle_add_mul_norm_of_inner_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "rw", "rw", "refine", "rcases", "exact", "exact"], "tactic_count": 8}
{"name": "InnerProductGeometry.tan_angle_add_mul_norm_of_inner_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle", "is_tactic_proof": true, "tactics": ["rw", "rcases"], "tactic_count": 2}
{"name": "InnerProductGeometry.norm_div_cos_angle_add_of_inner_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle", "is_tactic_proof": true, "tactics": ["rw", "rcases", "rw", "simp"], "tactic_count": 4}
{"name": "InnerProductGeometry.norm_div_sin_angle_add_of_inner_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle", "is_tactic_proof": true, "tactics": ["rcases", "rw", "mul_inv_cancel_right₀"], "tactic_count": 3}
{"name": "InnerProductGeometry.norm_div_tan_angle_add_of_inner_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle", "is_tactic_proof": true, "tactics": ["rw", "rcases", "simp", "rw"], "tactic_count": 4}
{"name": "InnerProductGeometry.angle_sub_eq_arccos_of_inner_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle", "is_tactic_proof": true, "tactics": ["rw", "rw"], "tactic_count": 2}
{"name": "InnerProductGeometry.angle_sub_eq_arcsin_of_inner_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle", "is_tactic_proof": true, "tactics": ["rw", "rw", "rw"], "tactic_count": 3}
{"name": "InnerProductGeometry.angle_sub_eq_arctan_of_inner_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle", "is_tactic_proof": true, "tactics": ["rw", "rw"], "tactic_count": 2}
{"name": "InnerProductGeometry.angle_sub_pos_of_inner_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle", "is_tactic_proof": true, "tactics": ["rw", "rw", "rw", "exact"], "tactic_count": 4}
{"name": "InnerProductGeometry.angle_sub_le_pi_div_two_of_inner_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "InnerProductGeometry.angle_sub_lt_pi_div_two_of_inner_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "InnerProductGeometry.cos_angle_sub_of_inner_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle", "is_tactic_proof": true, "tactics": ["rw", "rw"], "tactic_count": 2}
{"name": "InnerProductGeometry.sin_angle_sub_of_inner_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle", "is_tactic_proof": true, "tactics": ["rw", "rw", "rw"], "tactic_count": 3}
{"name": "InnerProductGeometry.tan_angle_sub_of_inner_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle", "is_tactic_proof": true, "tactics": ["rw", "rw"], "tactic_count": 2}
{"name": "InnerProductGeometry.cos_angle_sub_mul_norm_of_inner_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle", "is_tactic_proof": true, "tactics": ["rw", "rw"], "tactic_count": 2}
{"name": "InnerProductGeometry.sin_angle_sub_mul_norm_of_inner_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle", "is_tactic_proof": true, "tactics": ["rw", "rw"], "tactic_count": 2}
{"name": "InnerProductGeometry.tan_angle_sub_mul_norm_of_inner_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle", "is_tactic_proof": true, "tactics": ["rw", "rw", "rw"], "tactic_count": 3}
{"name": "InnerProductGeometry.norm_div_cos_angle_sub_of_inner_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle", "is_tactic_proof": true, "tactics": ["rw", "rw", "rw"], "tactic_count": 3}
{"name": "InnerProductGeometry.norm_div_sin_angle_sub_of_inner_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle", "is_tactic_proof": true, "tactics": ["rw", "rw", "rw"], "tactic_count": 3}
{"name": "InnerProductGeometry.norm_div_tan_angle_sub_of_inner_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle", "is_tactic_proof": true, "tactics": ["rw", "rw", "rw"], "tactic_count": 3}
{"name": "EuclideanGeometry.dist_sq_eq_dist_sq_add_dist_sq_iff_angle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle", "is_tactic_proof": true, "tactics": ["erw", "norm_sub_sq_eq_norm_sq_add_norm_sq_iff_angle_eq_pi_div_two,", "neg_vsub_eq_vsub_rev"], "tactic_count": 3}
{"name": "EuclideanGeometry.angle_eq_arccos_of_angle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle", "is_tactic_proof": false, "tactics": ["rw", "neg_vsub_eq_vsub_rev]", "rw", "angle_add_eq_arccos_of_inner_eq_zero"], "tactic_count": 4}
{"name": "EuclideanGeometry.angle_eq_arcsin_of_angle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle", "is_tactic_proof": false, "tactics": ["rw", "neg_vsub_eq_vsub_rev]", "rw", "rw", "angle_add_eq_arcsin_of_inner_eq_zero"], "tactic_count": 5}
{"name": "EuclideanGeometry.angle_eq_arctan_of_angle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle", "is_tactic_proof": false, "tactics": ["rw", "neg_vsub_eq_vsub_rev]", "rw", "rw", "angle_add_eq_arctan_of_inner_eq_zero"], "tactic_count": 5}
{"name": "EuclideanGeometry.angle_pos_of_angle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle", "is_tactic_proof": false, "tactics": ["rw", "neg_vsub_eq_vsub_rev]", "rw", "rw", "exact"], "tactic_count": 5}
{"name": "EuclideanGeometry.angle_le_pi_div_two_of_angle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle", "is_tactic_proof": false, "tactics": ["rw", "neg_vsub_eq_vsub_rev]", "rw", "exact"], "tactic_count": 4}
{"name": "EuclideanGeometry.angle_lt_pi_div_two_of_angle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle", "is_tactic_proof": false, "tactics": ["rw", "neg_vsub_eq_vsub_rev]", "rw", "rw", "exact"], "tactic_count": 5}
{"name": "EuclideanGeometry.cos_angle_of_angle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle", "is_tactic_proof": false, "tactics": ["rw", "neg_vsub_eq_vsub_rev]", "rw", "cos_angle_add_of_inner_eq_zero"], "tactic_count": 4}
{"name": "EuclideanGeometry.sin_angle_of_angle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle", "is_tactic_proof": false, "tactics": ["rw", "neg_vsub_eq_vsub_rev]", "rw", "rw", "sin_angle_add_of_inner_eq_zero"], "tactic_count": 5}
{"name": "EuclideanGeometry.tan_angle_of_angle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle", "is_tactic_proof": false, "tactics": ["rw", "neg_vsub_eq_vsub_rev]", "rw", "tan_angle_add_of_inner_eq_zero"], "tactic_count": 4}
{"name": "EuclideanGeometry.cos_angle_mul_dist_of_angle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle", "is_tactic_proof": false, "tactics": ["rw", "neg_vsub_eq_vsub_rev]", "rw", "cos_angle_add_mul_norm_of_inner_eq_zero"], "tactic_count": 4}
{"name": "EuclideanGeometry.sin_angle_mul_dist_of_angle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle", "is_tactic_proof": false, "tactics": ["rw", "neg_vsub_eq_vsub_rev]", "rw", "sin_angle_add_mul_norm_of_inner_eq_zero"], "tactic_count": 4}
{"name": "EuclideanGeometry.tan_angle_mul_dist_of_angle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle", "is_tactic_proof": false, "tactics": ["rw", "neg_vsub_eq_vsub_rev]", "rw", "rw", "tan_angle_add_mul_norm_of_inner_eq_zero"], "tactic_count": 5}
{"name": "EuclideanGeometry.dist_div_cos_angle_of_angle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle", "is_tactic_proof": false, "tactics": ["rw", "neg_vsub_eq_vsub_rev]", "rw", "rw", "norm_div_cos_angle_add_of_inner_eq_zero"], "tactic_count": 5}
{"name": "EuclideanGeometry.dist_div_sin_angle_of_angle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle", "is_tactic_proof": false, "tactics": ["rw", "neg_vsub_eq_vsub_rev]", "rw", "rw", "norm_div_sin_angle_add_of_inner_eq_zero"], "tactic_count": 5}
{"name": "EuclideanGeometry.dist_div_tan_angle_of_angle_eq_pi_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle", "is_tactic_proof": false, "tactics": ["rw", "neg_vsub_eq_vsub_rev]", "rw", "rw", "norm_div_tan_angle_add_of_inner_eq_zero"], "tactic_count": 5}
{"name": "InnerProductGeometry.ortho", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.TriangleInequality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InnerProductGeometry.ortho_eq_sub_inner", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.TriangleInequality", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "InnerProductGeometry.inner_ortho_nonneg", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.TriangleInequality", "is_tactic_proof": false, "tactics": ["rw", "real_inner_comm,", "grw"], "tactic_count": 3}
{"name": "InnerProductGeometry.inner_normalize_ortho", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.TriangleInequality", "is_tactic_proof": true, "tactics": ["simp", "right", "exact"], "tactic_count": 3}
{"name": "InnerProductGeometry.inner_normalized_ortho_sq_add_inner_sq_eq_one", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.TriangleInequality", "is_tactic_proof": false, "tactics": ["rw", "by_cases", "simp", "by_cases", "simp", "rw", "have", "simp", "intro", "rw", "apply", "rcases", "have", "rw", "real_inner_smul_left,", "real_inner_self_eq_norm_sq,", "ring", "field_simp"], "tactic_count": 18}
{"name": "InnerProductGeometry.inner_ortho_right_eq_sin_angle", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.TriangleInequality", "is_tactic_proof": false, "tactics": ["have", "simp", "rw", "have", "rw", "exact", "simp_all"], "tactic_count": 7}
{"name": "InnerProductGeometry.angle_le_angle_add_angle_aux", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.TriangleInequality", "is_tactic_proof": true, "tactics": ["rw", "by_cases", "simp", "rw", "hx,", "norm_num", "have", "rw", "constructor", "rw", "simp", "rw", "simp", "rw", "field_simp", "rw", "have", "rw", "sq,", "real_inner_comm", "ring", "rw", "simp"], "tactic_count": 23}
{"name": "InnerProductGeometry.angle_le_angle_add_angle_of_norm_eq_one", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.TriangleInequality", "is_tactic_proof": true, "tactics": ["rcases", "linarith", "suffices", "have", "rwa", "have", "nth_rw", "simp", "real_inner_comm", "norm_num", "rw", "rw", "have", "by_cases", "simp", "by_cases", "simp", "exact", "have", "grw", "apply", "ring"], "tactic_count": 22}
{"name": "InnerProductGeometry.ortho_ne_zero_of_not_collinear", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.TriangleInequality", "is_tactic_proof": true, "tactics": ["intro", "grind", "inner_eq_neg_mul_norm_iff_angle_eq_pi]"], "tactic_count": 3}
{"name": "InnerProductGeometry.eq_of_angle_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.TriangleInequality", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "InnerProductGeometry.angle_expression_of_angle_eq_angle_sum", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.TriangleInequality", "is_tactic_proof": true, "tactics": ["intros", "by_cases", "grind", "have", "by_cases", "grind", "by_cases", "grind", "by_cases", "grind", "by_cases", "grind", "have", "nth_rw", "simp", "real_inner_comm", "norm_num", "rw", "ring_nf", "have", "have", "have", "have", "have", "have", "rw", "nth_rw", "nth_rw", "rw"], "tactic_count": 29}
{"name": "InnerProductGeometry.angle_le_angle_add_angle", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.TriangleInequality", "is_tactic_proof": true, "tactics": ["by_cases", "simpa", "by_cases", "simpa", "by_cases", "simpa", "simpa", "angle_le_angle_add_angle_of_norm_eq_one"], "tactic_count": 8}
{"name": "InnerProductGeometry.angle_eq_angle_add_add_angle_add_of_mem_span", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.TriangleInequality", "is_tactic_proof": true, "tactics": ["rw", "obtain", "rcases", "simp", "simp_all", "simp_all", "rw", "by_cases", "simpa", "have", "rw", "simpa"], "tactic_count": 12}
{"name": "InnerProductGeometry.mem_span_of_linear_combination", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.TriangleInequality", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "InnerProductGeometry.angle_eq_angle_add_angle_iff", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.TriangleInequality", "is_tactic_proof": true, "tactics": ["constructor", "by_cases", "tauto", "right", "by_cases", "have", "rw", "obtain", "lift", "exact", "have", "by_cases", "subst", "rw", "obtain", "lift", "rw", "simp", "norm_cast", "grind", "by_cases", "subst", "rw", "obtain", "lift", "exact", "have", "grind", "have", "grind", "have", "grind", "have", "have", "angle_expression_of_angle_eq_angle_sum", "simp", "have", "have", "simp", "exact", "exact", "obtain", "grind", "exact"], "tactic_count": 44}
{"name": "EuclideanGeometry.angle_le_angle_add_angle", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Angle.Unoriented.TriangleInequality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.inner_weightedVSub", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "rcongr"], "tactic_count": 3}
{"name": "EuclideanGeometry.dist_affineCombination", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "have", "exact"], "tactic_count": 4}
{"name": "EuclideanGeometry.dist_smul_vadd_sq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Basic", "is_tactic_proof": false, "tactics": ["rw", "real_inner_smul_left,", "ring"], "tactic_count": 3}
{"name": "EuclideanGeometry.dist_smul_vadd_eq_dist", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Basic", "is_tactic_proof": false, "tactics": ["conv_lhs", "rw", "dist_eq_norm_vsub", "have", "have", "rw", "ring", "rw", "sub_eq_add_neg,", "simp"], "tactic_count": 10}
{"name": "EuclideanGeometry.eq_of_dist_eq_of_dist_eq_of_mem_of_finrank_eq_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Basic", "is_tactic_proof": false, "tactics": ["have", "inner_vsub_vsub_of_dist_eq_of_dist_eq", "have", "inner_vsub_vsub_of_dist_eq_of_dist_eq", "let", "have", "refine", "intro", "fin_cases", "intro", "fin_cases", "exact", "rw", "exact", "have", "refine", "rw", "intro", "fin_cases", "exact", "exact", "rw", "have", "intro", "have", "have", "classical", "rw", "simp", "rw", "rcases", "rw", "rcases", "exact", "rcases", "simp", "vsub_eq_zero_iff_eq,", "rw", "subst", "have", "have", "rw", "simp", "rw", "rcases"], "tactic_count": 45}
{"name": "EuclideanGeometry.eq_of_dist_eq_of_dist_eq_of_finrank_eq_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.existsUnique_dist_eq_of_insert", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Circumcenter", "is_tactic_proof": true, "tactics": ["haveI", "rcases", "simp", "let", "let", "have", "let", "let", "let", "use", "simp", "have", "constructor", "constructor", "refine", "rw", "exact", "intro", "rw", "rcases", "rw", "dist_sq_smul_orthogonal_vadd_smul_orthogonal_vadd", "simp", "field", "rw", "orthogonalProjection_vadd_smul_vsub_orthogonalProjection", "dist_of_mem_subset_mk_sphere", "rintro", "simp", "obtain", "rwa", "have", "rw", "orthogonalProjection_vadd_smul_vsub_orthogonalProjection", "obtain", "have", "simp", "replace", "cases", "have", "obtain", "have", "rw", "mul_self_inj_of_nonneg", "dist_sq_eq_dist_orthogonalProjection_sq_add_dist_orthogonalProjection_sq", "orthogonalProjection_vadd_smul_vsub_orthogonalProjection", "dist_eq_norm_vsub", "mul_comm", "ring", "replace", "rw", "dist_sq_smul_orthogonal_vadd_smul_orthogonal_vadd", "grind"], "tactic_count": 53}
{"name": "AffineIndependent.existsUnique_dist_eq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Circumcenter", "is_tactic_proof": true, "tactics": ["cases", "induction", "zero", "exfalso", "have", "lia", "succ", "rcases", "rw", "obtain", "haveI", "use", "simp", "constructor", "simp_rw", "exact", "rintro", "rintro", "replace", "rw", "have", "let", "classical", "have", "rw", "rw", "hn]", "simp", "simp", "haveI", "have", "replace", "have", "change", "rw", "congr", "simp", "rw", "refine", "convert", "change", "rw", "congr", "simp"], "tactic_count": 44}
{"name": "Affine.Simplex.circumsphere", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Circumcenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.circumsphere_unique_dist_eq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Circumcenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.circumcenter", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Circumcenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.circumradius", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Circumcenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.circumsphere_center", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Circumcenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.circumsphere_radius", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Circumcenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.circumcenter_mem_affineSpan", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Circumcenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.dist_circumcenter_eq_circumradius", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Circumcenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.mem_circumsphere", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Circumcenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.dist_circumcenter_eq_circumradius'", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Circumcenter", "is_tactic_proof": true, "tactics": ["intro", "rw", "exact"], "tactic_count": 3}
{"name": "Affine.Simplex.eq_circumcenter_of_dist_eq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Circumcenter", "is_tactic_proof": true, "tactics": ["have", "simp", "true_and]", "exact"], "tactic_count": 4}
{"name": "Affine.Simplex.eq_circumradius_of_dist_eq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Circumcenter", "is_tactic_proof": true, "tactics": ["have", "simp", "true_and]", "exact"], "tactic_count": 4}
{"name": "Affine.Simplex.circumradius_nonneg", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Circumcenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.circumradius_pos", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Circumcenter", "is_tactic_proof": true, "tactics": ["refine", "intro", "have", "simp_rw", "have", "simp"], "tactic_count": 6}
{"name": "Affine.Simplex.circumcenter_eq_point", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Circumcenter", "is_tactic_proof": true, "tactics": ["have", "have", "simp", "rw", "congr", "simp"], "tactic_count": 6}
{"name": "Affine.Simplex.circumcenter_ne_point", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Circumcenter", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Affine.Simplex.circumcenter_eq_centroid", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Circumcenter", "is_tactic_proof": false, "tactics": ["have", "dist", "intro", "rw", "vsub_vadd_eq_vsub_sub,", "one_smul", "fin_cases", "rw", "obtain", "exact", "hr"], "tactic_count": 11}
{"name": "Affine.Simplex.circumsphere_reindex", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Circumcenter", "is_tactic_proof": true, "tactics": ["refine", "exact", "exact"], "tactic_count": 3}
{"name": "Affine.Simplex.circumcenter_reindex", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Circumcenter", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Affine.Simplex.circumradius_reindex", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Circumcenter", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Affine.Simplex.circumcenter_map", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Circumcenter", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "Affine.Simplex.circumradius_map", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Circumcenter", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "Affine.Simplex.circumcenter_restrict", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Circumcenter", "is_tactic_proof": true, "tactics": ["rw", "have", "exact"], "tactic_count": 3}
{"name": "Affine.Simplex.circumradius_restrict", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Circumcenter", "is_tactic_proof": true, "tactics": ["rw", "have", "exact"], "tactic_count": 3}
{"name": "Affine.Simplex.dist_circumcenter_sq_eq_sq_sub_circumradius", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Circumcenter", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Affine.Simplex.orthogonalProjection_eq_circumcenter_of_exists_dist_eq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Circumcenter", "is_tactic_proof": true, "tactics": ["change", "have", "obtain", "use", "refine", "exact", "rw", "obtain", "exact"], "tactic_count": 9}
{"name": "Affine.Simplex.orthogonalProjection_eq_circumcenter_of_dist_eq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Circumcenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.orthogonalProjection_circumcenter", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Circumcenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.circumcenter_eq_of_range_eq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Circumcenter", "is_tactic_proof": true, "tactics": ["have", "have", "intro", "have", "rw", "rcases", "rw", "exact"], "tactic_count": 8}
{"name": "Affine.Simplex.PointsWithCircumcenterIndex", "kind": "inductive", "module": "Mathlib.Geometry.Euclidean.Circumcenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.instFintypePointsWithCircumcenterIndex", "kind": "instance", "module": "Mathlib.Geometry.Euclidean.Circumcenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.pointsWithCircumcenterIndexInhabited", "kind": "instance", "module": "Mathlib.Geometry.Euclidean.Circumcenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.pointIndexEmbedding", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Circumcenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.sum_pointsWithCircumcenter", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Circumcenter", "is_tactic_proof": true, "tactics": ["classical", "have", "ext", "refine", "obtain", "exact", "exact", "change", "rw", "simp_rw", "rintro", "injection"], "tactic_count": 12}
{"name": "Affine.Simplex.pointsWithCircumcenter", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Circumcenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.pointsWithCircumcenter_point", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Circumcenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.pointsWithCircumcenter_eq_circumcenter", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Circumcenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.pointWeightsWithCircumcenter", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Circumcenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.sum_pointWeightsWithCircumcenter", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Circumcenter", "is_tactic_proof": true, "tactics": ["classical", "convert", "cases", "simp"], "tactic_count": 4}
{"name": "Affine.Simplex.point_eq_affineCombination_of_pointsWithCircumcenter", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Circumcenter", "is_tactic_proof": true, "tactics": ["rw", "symm", "refine", "intro", "cases", "have", "simp", "rfl"], "tactic_count": 8}
{"name": "Affine.Simplex.centroidWeightsWithCircumcenter", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Circumcenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.sum_centroidWeightsWithCircumcenter", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Circumcenter", "is_tactic_proof": false, "tactics": ["simp_rw", "fs.sum_centroidWeights_eq_one_of_nonempty", "rcongr"], "tactic_count": 3}
{"name": "Affine.Simplex.centroid_eq_affineCombination_of_pointsWithCircumcenter", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Circumcenter", "is_tactic_proof": false, "tactics": ["simp_rw", "centroidWeightsWithCircumcenter,", "sum_indicator_subset_of_eq_zero", "congr"], "tactic_count": 4}
{"name": "Affine.Simplex.circumcenterWeightsWithCircumcenter", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Circumcenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.sum_circumcenterWeightsWithCircumcenter", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Circumcenter", "is_tactic_proof": true, "tactics": ["classical", "convert", "cases", "simp"], "tactic_count": 4}
{"name": "Affine.Simplex.circumcenter_eq_affineCombination_of_pointsWithCircumcenter", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Circumcenter", "is_tactic_proof": true, "tactics": ["rw", "symm", "refine", "rintro"], "tactic_count": 4}
{"name": "Affine.Simplex.reflectionCircumcenterWeightsWithCircumcenter", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Circumcenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.sum_reflectionCircumcenterWeightsWithCircumcenter", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Circumcenter", "is_tactic_proof": false, "tactics": ["simp_rw", "filter_eq']", "rw", "norm_num", "simpa"], "tactic_count": 5}
{"name": "Affine.Simplex.reflection_circumcenter_eq_affineCombination_of_pointsWithCircumcenter", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Circumcenter", "is_tactic_proof": false, "tactics": ["have", "simp", "set", "have", "apply", "simp", "rw", "s.face_centroid_eq_centroid", "circumcenter_eq_affineCombination_of_pointsWithCircumcenter,", "weightedVSub_vadd_affineCombination,", "simp_rw", "circumcenterWeightsWithCircumcenter,", "apply_ite₂", "convert", "norm_num"], "tactic_count": 15}
{"name": "EuclideanGeometry.cospherical_iff_exists_mem_of_complete", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Circumcenter", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "rw", "exact", "exact"], "tactic_count": 5}
{"name": "EuclideanGeometry.cospherical_iff_exists_mem_of_finiteDimensional", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Circumcenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.exists_circumradius_eq_of_cospherical_subset", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Circumcenter", "is_tactic_proof": true, "tactics": ["rw", "rcases", "use", "intro", "have", "refine", "sx.independent.affineSpan_eq_of_le_of_card_eq_finrank_add_one", "simp", "have", "exact"], "tactic_count": 10}
{"name": "EuclideanGeometry.circumradius_eq_of_cospherical_subset", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Circumcenter", "is_tactic_proof": true, "tactics": ["rcases", "rw"], "tactic_count": 2}
{"name": "EuclideanGeometry.exists_circumradius_eq_of_cospherical", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Circumcenter", "is_tactic_proof": true, "tactics": ["rw", "refine", "exact"], "tactic_count": 3}
{"name": "EuclideanGeometry.circumradius_eq_of_cospherical", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Circumcenter", "is_tactic_proof": true, "tactics": ["rcases", "rw"], "tactic_count": 2}
{"name": "EuclideanGeometry.exists_circumcenter_eq_of_cospherical_subset", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Circumcenter", "is_tactic_proof": true, "tactics": ["rw", "rcases", "use", "intro", "have", "refine", "sx.independent.affineSpan_eq_of_le_of_card_eq_finrank_add_one", "simp", "have", "exact"], "tactic_count": 10}
{"name": "EuclideanGeometry.circumcenter_eq_of_cospherical_subset", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Circumcenter", "is_tactic_proof": true, "tactics": ["rcases", "rw"], "tactic_count": 2}
{"name": "EuclideanGeometry.exists_circumcenter_eq_of_cospherical", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Circumcenter", "is_tactic_proof": true, "tactics": ["rw", "refine", "exact"], "tactic_count": 3}
{"name": "EuclideanGeometry.circumcenter_eq_of_cospherical", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Circumcenter", "is_tactic_proof": true, "tactics": ["rcases", "rw"], "tactic_count": 2}
{"name": "EuclideanGeometry.exists_circumsphere_eq_of_cospherical_subset", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Circumcenter", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "exact"], "tactic_count": 3}
{"name": "EuclideanGeometry.circumsphere_eq_of_cospherical_subset", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Circumcenter", "is_tactic_proof": true, "tactics": ["rcases", "rw"], "tactic_count": 2}
{"name": "EuclideanGeometry.exists_circumsphere_eq_of_cospherical", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Circumcenter", "is_tactic_proof": true, "tactics": ["rw", "refine", "exact"], "tactic_count": 3}
{"name": "EuclideanGeometry.circumsphere_eq_of_cospherical", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Circumcenter", "is_tactic_proof": true, "tactics": ["rcases", "rw"], "tactic_count": 2}
{"name": "EuclideanGeometry.eq_or_eq_reflection_of_dist_eq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Circumcenter", "is_tactic_proof": true, "tactics": ["set", "have", "have", "rw", "obtain", "obtain", "obtain", "subst", "exact", "rw", "obtain", "subst", "exact", "rw", "have", "have", "s.dist_circumcenter_sq_eq_sq_sub_circumradius", "have", "s.dist_circumcenter_sq_eq_sq_sub_circumradius", "rw", "real_inner_smul_right,", "by_cases", "rw", "rw", "simp", "have", "simpa", "rw", "rw", "rcases", "left", "rw", "right", "rw"], "tactic_count": 34}
{"name": "EuclideanGeometry.triangle_congruent_iff_dist_eq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Congruence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.side_side_side", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Congruence", "is_tactic_proof": true, "tactics": ["rw", "intro", "fin_cases"], "tactic_count": 3}
{"name": "EuclideanGeometry.side_angle_side", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Congruence", "is_tactic_proof": true, "tactics": ["apply", "rw", "simp"], "tactic_count": 3}
{"name": "EuclideanGeometry.angle_side_angle", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Congruence", "is_tactic_proof": false, "tactics": ["have", "grind", "have", "have", "simp", "have", "have", "have", "rw", "dist_eq_dist_mul_sin_angle_div_sin_angle", "angle_comm", "exact"], "tactic_count": 12}
{"name": "EuclideanGeometry.angle_angle_side", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Congruence", "is_tactic_proof": true, "tactics": ["have", "have", "grind", "have", "simp", "have", "have", "exact"], "tactic_count": 8}
{"name": "EuclideanGeometry.angle_eq_of_congruent", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Congruence", "is_tactic_proof": true, "tactics": ["unfold", "unfold", "simp_rw", "dist_eq_norm_vsub,"], "tactic_count": 4}
{"name": "Affine.Simplex.excenterWeightsUnnorm", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.excenterWeightsUnnorm_reindex", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Affine.Simplex.excenterWeightsUnnorm_map", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Affine.Simplex.excenterWeightsUnnorm_restrict", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Affine.Simplex.excenterWeightsUnnorm_empty_apply", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.excenterWeightsUnnorm_ne_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["rw", "refine", "grind", "simp"], "tactic_count": 4}
{"name": "Affine.Simplex.ExcenterExists", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.excenterExists_reindex", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Affine.Simplex.excenterExists_map", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Affine.Simplex.excenterExists_restrict", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Affine.Simplex.excenterWeights", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.excenterWeights_reindex", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Affine.Simplex.excenterWeights_map", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Affine.Simplex.excenterWeights_restrict", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Affine.Simplex.ExcenterExists.excenterWeights_ne_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "simp"], "tactic_count": 4}
{"name": "Affine.Simplex.excenterWeightsUnnorm_compl", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["ext", "by_cases"], "tactic_count": 2}
{"name": "Affine.Simplex.excenterWeights_compl", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Affine.Simplex.excenterExists_compl", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Affine.Simplex.sum_excenterWeights", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["simp_rw", "split_ifs", "simp", "simp", "simp"], "tactic_count": 5}
{"name": "Affine.Simplex.sum_excenterWeights_eq_one_iff", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Affine.Simplex.sum_excenterWeightsUnnorm_empty_pos", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["simp_rw", "positivity"], "tactic_count": 2}
{"name": "Affine.Simplex.excenterWeights_empty_pos", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["simp", "positivity"], "tactic_count": 2}
{"name": "Affine.Simplex.sign_excenterWeights_empty", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Affine.Simplex.excenterExists_empty", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.sum_inv_height_sq_smul_vsub_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": ["suffices", "rw", "refine", "vsub_mem_vectorSpan_of_mem_affineSpan_of_mem_affineSpan", "rw", "intro", "rcases", "simpa", "intro", "rw", "convert", "convert", "rw", "convert", "rw", "refine", "rw", "simp", "refine", "exact", "exact", "rw", "inner_neg_left,", "simp"], "tactic_count": 24}
{"name": "Affine.Simplex.inv_height_eq_sum_mul_inv_dist", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "rw", "real_inner_self_eq_norm_mul_norm,", "simp", "add_sub_cancel]", "have", "apply_fun", "rw", "simp", "convert", "ring"], "tactic_count": 12}
{"name": "Affine.Simplex.inv_height_lt_sum_inv_height", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "simp", "exact", "rintro", "refine", "simp", "rw", "exact"], "tactic_count": 10}
{"name": "Affine.Simplex.sum_excenterWeightsUnnorm_singleton_pos", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["rw", "nth_rw", "simp", "convert", "ext", "simp", "rw", "simp"], "tactic_count": 8}
{"name": "Affine.Simplex.sign_excenterWeights_singleton_neg", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["simp_rw", "convert", "rw", "exact", "simp"], "tactic_count": 5}
{"name": "Affine.Simplex.sign_excenterWeights_singleton_pos", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["simp_rw", "convert", "rw", "exact", "simp"], "tactic_count": 5}
{"name": "Affine.Simplex.excenterExists_singleton", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.excenterWeights_empty_lt_inv_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": ["have", "have", "rwa", "replace", "rwa", "replace", "rwa", "convert", "simp"], "tactic_count": 9}
{"name": "Affine.Simplex.exsphere", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.exsphere_reindex", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": ["simp_rw", "simp"], "tactic_count": 2}
{"name": "Affine.Simplex.insphere", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.insphere_reindex", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["simp_rw", "simp"], "tactic_count": 2}
{"name": "Affine.Simplex.excenter", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.excenter_reindex", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Affine.Simplex.ExcenterExists.excenter_map", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Affine.Simplex.ExcenterExists.excenter_restrict", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["rw", "haveI", "exact"], "tactic_count": 3}
{"name": "Affine.Simplex.incenter", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.incenter_reindex", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["simp_rw", "simp"], "tactic_count": 2}
{"name": "Affine.Simplex.incenter_map", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.incenter_restrict", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.exradius", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.exradius_reindex", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Affine.Simplex.exradius_map", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Affine.Simplex.exradius_restrict", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Affine.Simplex.inradius", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.inradius_reindex", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["simp_rw", "simp"], "tactic_count": 2}
{"name": "Affine.Simplex.inradius_map", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.inradius_restrict", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.exsphere_center", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.exsphere_radius", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.insphere_center", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.insphere_radius", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.exsphere_empty", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.excenter_empty", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.exradius_empty", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.exsphere_compl", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Affine.Simplex.excenter_compl", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Affine.Simplex.exradius_compl", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Affine.Simplex.exsphere_univ", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Affine.Simplex.excenter_univ", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Affine.Simplex.exradius_univ", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Affine.Simplex.excenter_eq_affineCombination", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.exradius_eq_abs_inv_sum", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.incenter_eq_affineCombination", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.inradius_eq_abs_inv_sum", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.exradius_nonneg", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.ExcenterExists.exradius_pos", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.inradius_pos", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.exradius_singleton_pos", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.ExcenterExists.excenter_mem_affineSpan_range", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.incenter_mem_affineSpan_range", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.incenter_mem_interior", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["have", "rw", "intro", "refine", "by_contra", "obtain", "rw", "revert", "apply", "nth_rw", "grw", "rw", "exact", "add_pos_of_pos_of_nonneg"], "tactic_count": 14}
{"name": "Affine.Simplex.excenter_singleton_mem_affineSpan_range", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.ExcenterExists.signedInfDist_excenter_eq_mul_sum_inv", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": ["simp_rw", "excenterWeights,", "rw", "simp"], "tactic_count": 4}
{"name": "Affine.Simplex.ExcenterExists.sign_signedInfDist_excenter", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["rw", "convert", "rw", "exact"], "tactic_count": 4}
{"name": "Affine.Simplex.sign_signedInfDist_incenter", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "Affine.Simplex.ExcenterExists.affineCombination_eq_excenter_iff", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["constructor", "simp_rw", "exact", "h.sum_excenterWeights_eq_one", "rintro", "rw"], "tactic_count": 6}
{"name": "Affine.Simplex.ExcenterExists.excenter_notMem_affineSpan_face", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["intro", "rw", "obtain", "simp", "have", "have", "grw", "simp", "lia", "obtain", "exact", "rw", "exact", "h.excenterWeights_ne_zero"], "tactic_count": 14}
{"name": "Affine.Simplex.incenter_notMem_affineSpan_face", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.ExcenterExists.excenter_notMem_affineSpan_faceOpposite", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.incenter_notMem_affineSpan_faceOpposite", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.ExcenterExists.excenter_ne_point", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "Affine.Simplex.incenter_ne_point", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.ExcenterExists.excenter_notMem_affineSpan_pair", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "exact", "convert", "simp"], "tactic_count": 5}
{"name": "Affine.Simplex.incenter_notMem_affineSpan_pair", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.ExcenterExists.excenterWeights_eq_excenterWeights_iff", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["refine", "have", "simp", "simp_rw", "have", "have", "rcases", "simp", "simp", "left", "ext", "replace", "split_ifs", "simp_rw", "simp", "simp", "right", "ext", "replace", "split_ifs", "rcases", "rfl", "simp"], "tactic_count": 23}
{"name": "Affine.Simplex.ExcenterExists.excenter_eq_excenter_iff", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Affine.Simplex.ExcenterExists.excenter_eq_incenter_iff", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Affine.Simplex.excenter_singleton_ne_incenter", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["intro", "rw", "simp"], "tactic_count": 3}
{"name": "Affine.Simplex.excenter_singleton_injective", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["intro", "dsimp", "rw", "rcases", "simpa", "have", "obtain", "rw", "replace", "simp_all"], "tactic_count": 10}
{"name": "Affine.Simplex.ExcenterExists.sSameSide_excenter_point_iff", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Affine.Simplex.ExcenterExists.sSameSide_point_excenter_iff", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Affine.Simplex.ExcenterExists.sOppSide_excenter_point_iff", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Affine.Simplex.ExcenterExists.sOppSide_point_excenter_iff", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Affine.Simplex.sSameSide_incenter_point", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.sSameSide_point_incenter", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.sOppSide_excenter_singleton_point", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["rw", "s.sign_excenterWeights_singleton_neg"], "tactic_count": 2}
{"name": "Affine.Simplex.sOppSide_point_excenter_singleton", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["rw", "s.sign_excenterWeights_singleton_neg"], "tactic_count": 2}
{"name": "Affine.Simplex.sSameSide_excenter_singleton_point", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["rw", "s.sign_excenterWeights_singleton_pos"], "tactic_count": 2}
{"name": "Affine.Simplex.sSameSide_point_excenter_singleton", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["rw", "s.sign_excenterWeights_singleton_pos"], "tactic_count": 2}
{"name": "Affine.Simplex.touchpoint", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.touchpoint_reindex", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.ExcenterExists.touchpoint_map", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Affine.Simplex.ExcenterExists.touchpoint_restrict", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["rw", "haveI", "exact"], "tactic_count": 3}
{"name": "Affine.Simplex.touchpoint_mem_affineSpan", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.touchpoint_mem_affineSpan_simplex", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["refine", "simp"], "tactic_count": 2}
{"name": "Affine.Simplex.touchpoint_eq_point_rev", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.ExcenterExists.signedInfDist_excenter", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["rw", "congr", "rw"], "tactic_count": 3}
{"name": "Affine.Simplex.signedInfDist_incenter", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Affine.Simplex.ExcenterExists.dist_excenter", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": ["rw", "h.signedInfDist_excenter,", "simp", "rcases", "simp", "simp", "simp"], "tactic_count": 7}
{"name": "Affine.Simplex.dist_incenter", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.ExcenterExists.dist_excenter_eq_dist_excenter", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Affine.Simplex.dist_incenter_eq_dist_incenter", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.ExcenterExists.touchpoint_mem_exsphere", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.touchpoint_mem_insphere", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.ExcenterExists.isTangentAt_touchpoint", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["rw", "excenter,"], "tactic_count": 2}
{"name": "Affine.Simplex.isTangentAt_insphere_touchpoint", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.eq_touchpoint_of_isTangentAt_exsphere", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Affine.Simplex.ExcenterExists.isTangentAt_exsphere_iff_eq_touchpoint", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["refine", "rintro", "exact"], "tactic_count": 3}
{"name": "Affine.Simplex.isTangentAt_insphere_iff_eq_touchpoint", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.ExcenterExists.affineSpan_faceOpposite_eq_orthRadius", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["refine", "rw", "have", "lia"], "tactic_count": 4}
{"name": "Affine.Simplex.affineSpan_faceOpposite_eq_orthRadius_insphere", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.exists_forall_signedInfDist_eq_iff_excenterExists_and_eq_excenter", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["refine", "rintro", "obtain", "have", "intro", "rw", "exact", "simp_rw", "have", "simp_rw", "intro", "replace", "rw", "rw", "have", "simp_rw", "ext", "rw", "simp", "subst", "exact", "rintro", "refine", "rw", "simp"], "tactic_count": 25}
{"name": "Affine.Simplex.exists_forall_signedInfDist_eq_iff_eq_incenter", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["convert", "simp", "simp"], "tactic_count": 3}
{"name": "Affine.Simplex.exists_forall_dist_eq_iff_exists_excenterExists_and_eq_excenter", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "rintro", "have", "refine", "apply", "refine", "grind", "rintro", "replace", "rcases", "refine", "simp"], "tactic_count": 13}
{"name": "Affine.Simplex.ExcenterExists.touchpoint_injective", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["intro", "by_contra", "by_cases", "subst", "rw", "apply", "convert", "suffices", "have", "rw", "exact", "have", "rw", "exact", "rw", "exact", "obtain", "have", "simp", "convert", "simp", "rw", "refine", "rw", "exact", "rw", "exact"], "tactic_count": 27}
{"name": "Affine.Simplex.touchpoint_empty_injective", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.ExcenterExists.touchpoint_notMem_affineSpan_of_ne", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.touchpoint_empty_notMem_affineSpan_of_ne", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.ExcenterExists.sign_signedInfDist_lineMap_excenter_touchpoint", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": ["have", "refine", "continuousOn_of_forall_continuousAt", "intro", "rw", "rw", "by_cases", "subst", "rw", "exact", "refine", "simp", "h.exradius_pos,", "rw", "rcases", "exact", "exact", "rw", "exact", "refine", "convert", "simp"], "tactic_count": 22}
{"name": "Affine.Simplex.sign_signedInfDist_lineMap_incenter_touchpoint", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.ExcenterExists.sign_signedInfDist_touchpoint", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Affine.Simplex.sign_signedInfDist_touchpoint_empty", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.touchpointWeights", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.sum_touchpointWeights", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.affineCombination_touchpointWeights", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.affineCombination_eq_touchpoint_iff", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["constructor", "rw", "exact", "rintro", "simp"], "tactic_count": 5}
{"name": "Affine.Simplex.touchpointWeights_reindex", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["rw", "rw", "dsimp", "rw", "simp", "rw", "simp"], "tactic_count": 7}
{"name": "Affine.Simplex.ExcenterExists.touchpointWeights_map", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["ext", "rw", "have", "rwa"], "tactic_count": 4}
{"name": "Affine.Simplex.ExcenterExists.touchpointWeights_restrict", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["rw", "haveI", "exact"], "tactic_count": 3}
{"name": "Affine.Simplex.ExcenterExists.sign_touchpointWeights", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["have", "rw", "s.signedInfDist_affineCombination", "rw", "convert", "rw", "exact"], "tactic_count": 7}
{"name": "Affine.Simplex.sign_touchpointWeights_empty", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Affine.Simplex.touchpointWeights_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": ["refine", "s.independent.eq_zero_of_affineCombination_mem_affineSpan", "rw", "convert", "simp"], "tactic_count": 5}
{"name": "Affine.Simplex.touchpointWeights_empty_pos", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Affine.Simplex.touchpoint_empty_mem_interior_faceOpposite", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": ["rw", "s.affineCombination_mem_interior_face_iff_pos", "simp", "intro", "exact"], "tactic_count": 5}
{"name": "Affine.Simplex.sign_touchpointWeights_singleton_pos", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Affine.Simplex.touchpointWeights_singleton_pos", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Affine.Simplex.touchpoint_singleton_mem_interior_faceOpposite", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": ["rw", "s.affineCombination_mem_interior_face_iff_pos", "simp", "intro", "exact"], "tactic_count": 5}
{"name": "Affine.Simplex.sign_touchpointWeights_singleton_neg", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Affine.Simplex.touchpointWeights_singleton_neg", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Affine.Simplex.ExcenterExists.touchpoint_ne_point", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["intro", "rw", "affineCombination_eq_touchpoint_iff", "have", "obtain", "have", "simp", "rw", "apply_fun", "rw", "have", "rw", "simp", "rw", "by_cases"], "tactic_count": 15}
{"name": "Affine.Simplex.touchpoint_empty_ne_point", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Triangle.excenterExists", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["have", "rcases", "exact", "rw", "exact", "exact", "rw", "exact"], "tactic_count": 8}
{"name": "Affine.Triangle.excenter_eq_incenter_or_excenter_singleton", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["have", "rcases", "exact", "exact", "exact", "refine", "rw"], "tactic_count": 7}
{"name": "Affine.Triangle.excenter_eq_incenter_or_excenter_singleton_of_ne", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["rcases", "exact", "refine", "rw", "have", "grind"], "tactic_count": 6}
{"name": "Affine.Triangle.sSameSide_affineSpan_pair_incenter_point", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["convert", "simp", "grind"], "tactic_count": 3}
{"name": "Affine.Triangle.sSameSide_affineSpan_pair_point_incenter", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["convert", "simp", "grind"], "tactic_count": 3}
{"name": "Affine.Triangle.sOppSide_affineSpan_pair_excenter_singleton_point", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["convert", "simp", "grind"], "tactic_count": 3}
{"name": "Affine.Triangle.sOppSide_affineSpan_pair_point_excenter_singleton", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["convert", "simp", "grind"], "tactic_count": 3}
{"name": "Affine.Triangle.sSameSide_affineSpan_pair_excenter_singleton_point", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["convert", "simp", "grind"], "tactic_count": 3}
{"name": "Affine.Triangle.sSameSide_affineSpan_pair_point_excenter_singleton", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["convert", "simp", "grind"], "tactic_count": 3}
{"name": "Affine.Triangle.affineSpan_pair_eq_orthRadius", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["convert", "have", "simp"], "tactic_count": 3}
{"name": "Affine.Triangle.affineSpan_pair_eq_orthRadius_insphere", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Triangle.sbtw_touchpoint_empty", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["rw", "convert", "rw", "convert", "decide"], "tactic_count": 5}
{"name": "Affine.Triangle.sbtw_touchpoint_singleton", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["rw", "convert", "rw", "convert", "decide"], "tactic_count": 5}
{"name": "Affine.Triangle.touchpoint_singleton_sbtw", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Incenter", "is_tactic_proof": true, "tactics": ["rw", "have", "rw", "simp", "have", "t.touchpointWeights", "ext", "have", "rcases", "rw", "simp", "simp", "simp", "rw", "sbtw_iff_right_ne_and_left_mem_image_Ioi]", "simp"], "tactic_count": 16}
{"name": "EuclideanGeometry.inversion", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Inversion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.inversion_def", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Inversion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.inversion_eq_lineMap", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Inversion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.inversion_vsub_center", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Inversion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.inversion_self", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Inversion.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "EuclideanGeometry.inversion_zero_radius", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Inversion.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "EuclideanGeometry.inversion_mul", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Inversion.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "EuclideanGeometry.inversion_dist_center", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Inversion.Basic", "is_tactic_proof": true, "tactics": ["rcases", "apply", "rw", "rwa"], "tactic_count": 4}
{"name": "EuclideanGeometry.inversion_dist_center'", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Inversion.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EuclideanGeometry.inversion_of_mem_sphere", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Inversion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.dist_inversion_center", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Inversion.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simp", "have", "simp", "field_simp", "simp", "field"], "tactic_count": 7}
{"name": "EuclideanGeometry.dist_center_inversion", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Inversion.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EuclideanGeometry.inversion_inversion", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Inversion.Basic", "is_tactic_proof": true, "tactics": ["rcases", "rw", "rw", "div_mul_cancel₀", "exact"], "tactic_count": 5}
{"name": "EuclideanGeometry.inversion_involutive", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Inversion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.inversion_surjective", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Inversion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.inversion_injective", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Inversion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.inversion_bijective", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Inversion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.inversion_eq_center", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Inversion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.inversion_eq_center'", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Inversion.Basic", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "EuclideanGeometry.center_eq_inversion", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Inversion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.center_eq_inversion'", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Inversion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.dist_inversion_inversion", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Inversion.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "simp_rw", "simpa"], "tactic_count": 3}
{"name": "EuclideanGeometry.dist_inversion_mul_dist_center_eq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Inversion.Basic", "is_tactic_proof": true, "tactics": ["rcases", "have", "conv", "rw", "field"], "tactic_count": 5}
{"name": "EuclideanGeometry.mul_dist_le_mul_dist_add_mul_dist", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Inversion.Basic", "is_tactic_proof": true, "tactics": ["rcases", "rw", "rcases", "rw", "positivity", "rcases", "rw", "have", "rw", "rw", "rw", "convert"], "tactic_count": 12}
{"name": "Filter.Tendsto.inversion", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Inversion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.inversion", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Inversion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.inversion", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Inversion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.inversion", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Inversion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.inversion", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Inversion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffWithinAt.inversion", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Inversion.Calculus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffOn.inversion", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Inversion.Calculus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffAt.inversion", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Inversion.Calculus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.inversion", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Inversion.Calculus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableWithinAt.inversion", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Inversion.Calculus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableOn.inversion", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Inversion.Calculus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableAt.inversion", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Inversion.Calculus", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Differentiable.inversion", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Inversion.Calculus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.hasFDerivAt_inversion", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Inversion.Calculus", "is_tactic_proof": true, "tactics": ["rcases", "have", "simp", "simp_rw", "have", "have", "exact", "refine", "this.congr_fderiv", "have", "simp", "mul_pow]", "simp", "div_eq_mul_inv,"], "tactic_count": 14}
{"name": "EuclideanGeometry.inversion_mem_perpBisector_inversion_iff", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Inversion.ImageHyperplane", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "EuclideanGeometry.inversion_mem_perpBisector_inversion_iff'", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Inversion.ImageHyperplane", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simp"], "tactic_count": 3}
{"name": "EuclideanGeometry.preimage_inversion_perpBisector_inversion", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Inversion.ImageHyperplane", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.preimage_inversion_perpBisector", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Inversion.ImageHyperplane", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EuclideanGeometry.image_inversion_perpBisector", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Inversion.ImageHyperplane", "is_tactic_proof": true, "tactics": ["rw", "preimage_inversion_perpBisector"], "tactic_count": 2}
{"name": "EuclideanGeometry.preimage_inversion_sphere_dist_center", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Inversion.ImageHyperplane", "is_tactic_proof": true, "tactics": ["ext", "rcases", "rw"], "tactic_count": 3}
{"name": "EuclideanGeometry.image_inversion_sphere_dist_center", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Inversion.ImageHyperplane", "is_tactic_proof": true, "tactics": ["rw", "preimage_inversion_sphere_dist_center"], "tactic_count": 2}
{"name": "EuclideanGeometry.mapsTo_inversion_affineSubspace_of_mem", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Inversion.ImageHyperplane", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.image_inversion_affineSubspace_of_mem", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Inversion.ImageHyperplane", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.mongePoint", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.MongePoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.mongePoint_eq_smul_vsub_vadd_circumcenter", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.MongePoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.mongePoint_reindex", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.MongePoint", "is_tactic_proof": true, "tactics": ["simp_rw", "have", "subst", "congr", "convert"], "tactic_count": 5}
{"name": "Affine.Simplex.mongePoint_map", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.MongePoint", "is_tactic_proof": true, "tactics": ["simp_rw", "rw", "simp"], "tactic_count": 3}
{"name": "Affine.Simplex.smul_mongePoint_vsub_circumcenter_eq_sum_vsub", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.MongePoint", "is_tactic_proof": true, "tactics": ["rw", "simp", "field_simp", "have", "rw", "rw", "rw", "simp", "invOf_eq_inv]"], "tactic_count": 9}
{"name": "Affine.Simplex.mongePoint_mem_affineSpan", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.MongePoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.mongePoint_restrict", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.MongePoint", "is_tactic_proof": true, "tactics": ["haveI", "simp_rw", "rw", "simp"], "tactic_count": 4}
{"name": "Affine.Simplex.mongePoint_eq_of_range_eq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.MongePoint", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Affine.Simplex.mongePointWeightsWithCircumcenter", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.MongePoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.sum_mongePointWeightsWithCircumcenter", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.MongePoint", "is_tactic_proof": true, "tactics": ["simp_rw", "simp", "ring"], "tactic_count": 3}
{"name": "Affine.Simplex.mongePoint_eq_affineCombination_of_pointsWithCircumcenter", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.MongePoint", "is_tactic_proof": false, "tactics": ["rw", "circumcenter_eq_affineCombination_of_pointsWithCircumcenter,", "weightedVSub_vadd_affineCombination]", "congr", "rw", "cases", "simp_rw", "mongePointWeightsWithCircumcenter]", "rw", "rw", "field", "simp", "ring"], "tactic_count": 13}
{"name": "Affine.Simplex.mongePointVSubFaceCentroidWeightsWithCircumcenter", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.MongePoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.mongePointVSubFaceCentroidWeightsWithCircumcenter_eq_sub", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.MongePoint", "is_tactic_proof": true, "tactics": ["ext", "obtain", "rw", "mongePointVSubFaceCentroidWeightsWithCircumcenter]", "have", "rw", "by_cases", "simp", "mongePointVSubFaceCentroidWeightsWithCircumcenter]"], "tactic_count": 9}
{"name": "Affine.Simplex.sum_mongePointVSubFaceCentroidWeightsWithCircumcenter", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.MongePoint", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "rw", "simp"], "tactic_count": 4}
{"name": "Affine.Simplex.mongePoint_vsub_face_centroid_eq_weightedVSub_of_pointsWithCircumcenter", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.MongePoint", "is_tactic_proof": true, "tactics": ["simp_rw", "centroid_eq_affineCombination_of_pointsWithCircumcenter,", "mongePointVSubFaceCentroidWeightsWithCircumcenter_eq_sub"], "tactic_count": 3}
{"name": "Affine.Simplex.inner_mongePoint_vsub_face_centroid_vsub", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.MongePoint", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "simp_rw", "point_eq_affineCombination_of_pointsWithCircumcenter,", "have", "rw", "pointsWithCircumcenter_eq_circumcenter]", "simp", "let", "have", "intro", "constructor", "rw", "simp_rw", "rw", "simp_rw", "repeat", "simp_rw", "simp", "all_goals", "intro", "simp", "intro", "simp"], "tactic_count": 24}
{"name": "Affine.Simplex.mongePlane", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.MongePoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.mongePlane_def", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.MongePoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.mongePlane_reindex", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.MongePoint", "is_tactic_proof": true, "tactics": ["have", "subst", "simp_rw", "congr", "convert", "ext", "simp", "simp", "simp_rw", "congr", "by_cases"], "tactic_count": 11}
{"name": "Affine.Simplex.mongePlane_comm", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.MongePoint", "is_tactic_proof": true, "tactics": ["simp_rw", "congr", "congr", "exact", "ext", "simp_rw", "constructor", "all_goals"], "tactic_count": 8}
{"name": "Affine.Simplex.mongePoint_mem_mongePlane", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.MongePoint", "is_tactic_proof": false, "tactics": ["rw", "refine", "intro", "rcases", "rw"], "tactic_count": 5}
{"name": "Affine.Simplex.direction_mongePlane", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.MongePoint", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Affine.Simplex.eq_mongePoint_of_forall_mem_mongePlane", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.MongePoint", "is_tactic_proof": true, "tactics": ["rw", "have", "intro", "rw", "exact", "have", "rw", "exact", "rw", "have", "rw", "ext", "simp_rw", "constructor", "rintro", "use", "rintro", "use", "rw", "have", "let", "obtain", "have", "exact", "exact"], "tactic_count": 25}
{"name": "Affine.Triangle.orthocenter", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.MongePoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Triangle.orthocenter_eq_mongePoint", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.MongePoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Triangle.orthocenter_reindex", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.MongePoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Triangle.orthocenter_eq_smul_vsub_vadd_circumcenter", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.MongePoint", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Affine.Triangle.orthocenter_vsub_circumcenter_eq_sum_vsub", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.MongePoint", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Affine.Triangle.orthocenter_mem_affineSpan", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.MongePoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Triangle.orthocenter_eq_of_range_eq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.MongePoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Triangle.altitude_eq_mongePlane", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.MongePoint", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "vectorSpan_image_eq_span_vsub_set_left_ne", "simp"], "tactic_count": 5}
{"name": "Affine.Triangle.orthocenter_mem_altitude", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.MongePoint", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact"], "tactic_count": 3}
{"name": "Affine.Triangle.eq_orthocenter_of_forall_mem_altitude", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.MongePoint", "is_tactic_proof": false, "tactics": ["obtain", "clear", "decide", "rw", "rw", "rw", "have", "intro", "obtain", "all_goals", "exact"], "tactic_count": 11}
{"name": "Affine.Triangle.dist_orthocenter_reflection_circumcenter", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.MongePoint", "is_tactic_proof": false, "tactics": ["rw", "t.reflection_circumcenter_eq_affineCombination_of_pointsWithCircumcenter", "mongePoint_eq_affineCombination_of_pointsWithCircumcenter,", "dist_affineCombination", "simp_rw", "reflectionCircumcenterWeightsWithCircumcenter]", "have", "obtain", "decide", "simp_rw", "norm_num"], "tactic_count": 11}
{"name": "Affine.Triangle.dist_orthocenter_reflection_circumcenter_finset", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.MongePoint", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Affine.Triangle.dist_circumcenter_reflection_orthocenter", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.MongePoint", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Affine.Triangle.dist_circumcenter_reflection_orthocenter_finset", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.MongePoint", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Affine.Triangle.affineSpan_orthocenter_point_le_altitude", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.MongePoint", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "Affine.Triangle.altitude_replace_orthocenter_eq_affineSpan", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.MongePoint", "is_tactic_proof": true, "tactics": ["symm", "rw", "rw", "use", "have", "refine", "refine", "have", "rw", "exact", "mem_affineSpan", "rw", "t₂.independent.finrank_vectorSpan", "rw", "use", "have", "rw", "have", "refine", "have", "rw", "exact"], "tactic_count": 22}
{"name": "Affine.Triangle.orthocenter_replace_orthocenter_eq_point", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.MongePoint", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact", "rw", "exact"], "tactic_count": 5}
{"name": "EuclideanGeometry.OrthocentricSystem", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.MongePoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.exists_of_range_subset_orthocentricSystem", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.MongePoint", "is_tactic_proof": true, "tactics": ["by_cases", "left", "rcases", "obtain", "clear", "decide", "have", "intro", "replace", "exact", "rcases", "rcases", "have", "intro", "rw", "exact", "exact", "right", "have", "rw", "classical", "refine", "rw"], "tactic_count": 23}
{"name": "EuclideanGeometry.exists_dist_eq_circumradius_of_subset_insert_orthocenter", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.MongePoint", "is_tactic_proof": false, "tactics": ["rcases", "use", "reflection_mem_of_le_of_mem", "intro", "rcases", "have", "repeat", "convert", "rw", "exact", "rw", "dist_reflection_eq_of_mem", "exact", "use", "intro", "rw", "rcases", "exact"], "tactic_count": 18}
{"name": "EuclideanGeometry.OrthocentricSystem.affineIndependent", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.MongePoint", "is_tactic_proof": true, "tactics": ["rcases", "rw", "rcases", "exact"], "tactic_count": 4}
{"name": "EuclideanGeometry.affineSpan_of_orthocentricSystem", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.MongePoint", "is_tactic_proof": true, "tactics": ["have", "rcases", "have", "rw", "refine", "ext_of_direction_eq", "have", "refine", "rw", "t.independent.finrank_vectorSpan"], "tactic_count": 10}
{"name": "EuclideanGeometry.OrthocentricSystem.exists_circumradius_eq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.MongePoint", "is_tactic_proof": true, "tactics": ["rcases", "use", "intro", "have", "rw", "rcases", "rw", "have", "rw", "exact", "rw", "affineSpan_of_orthocentricSystem", "exact"], "tactic_count": 13}
{"name": "EuclideanGeometry.OrthocentricSystem.eq_insert_orthocenter", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.MongePoint", "is_tactic_proof": true, "tactics": ["rcases", "rw", "rcases", "obtain", "clear", "decide", "suffices", "have", "have", "rw", "simp_rw", "rw", "exact", "rw", "convert", "exact"], "tactic_count": 16}
{"name": "Affine.Simplex.ninePointCircle", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.NinePointCircle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.ninePointCircle_center", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.NinePointCircle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.ninePointCircle_center_mem_affineSpan", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.NinePointCircle", "is_tactic_proof": true, "tactics": ["rw", "refine", "apply", "exact"], "tactic_count": 4}
{"name": "Affine.Simplex.ninePointCircle_radius", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.NinePointCircle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.ninePointCircle_reindex", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.NinePointCircle", "is_tactic_proof": true, "tactics": ["have", "ext", "simp", "simp"], "tactic_count": 4}
{"name": "Affine.Simplex.ninePointCircle_map", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.NinePointCircle", "is_tactic_proof": true, "tactics": ["ext", "simp", "simp"], "tactic_count": 3}
{"name": "Affine.Simplex.ninePointCircle_restrict", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.NinePointCircle", "is_tactic_proof": true, "tactics": ["ext", "simp", "simp"], "tactic_count": 3}
{"name": "Affine.Simplex.faceOppositeCentroid_mem_ninePointCircle", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.NinePointCircle", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "rw", "nth_rw", "rw", "one_smul,", "vsub_sub_vsub_cancel_left]"], "tactic_count": 7}
{"name": "Affine.Simplex.ninePointCircle_eq_circumsphere_medial", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.NinePointCircle", "is_tactic_proof": true, "tactics": ["apply", "constructor", "simpa", "rw", "simpa"], "tactic_count": 5}
{"name": "Affine.Simplex.eulerPoint", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.NinePointCircle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.eulerPoint_reindex", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.NinePointCircle", "is_tactic_proof": true, "tactics": ["have", "ext", "simp"], "tactic_count": 3}
{"name": "Affine.Simplex.eulerPoint_map", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.NinePointCircle", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Affine.Simplex.eulerPoint_restrict", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.NinePointCircle", "is_tactic_proof": true, "tactics": ["haveI", "simp"], "tactic_count": 2}
{"name": "Affine.Simplex.points_vsub_eulerPoint", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.NinePointCircle", "is_tactic_proof": true, "tactics": ["rw", "by_cases", "obtain", "have", "have", "have", "obtain", "rw", "simp", "have", "rw"], "tactic_count": 11}
{"name": "Affine.Simplex.midpoint_faceOppositeCentroid_eulerPoint", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.NinePointCircle", "is_tactic_proof": true, "tactics": ["apply", "rw", "centroid]", "by_cases", "obtain", "suffices", "simpa", "rw", "exact", "have", "have", "lia", "have", "push_cast", "rfl", "rw", "show", "div_mul_div_cancel₀", "faceOppositeCentroid_eq_smul_vsub_vadd_point,", "vsub_add_vsub_cancel,", "push_cast", "have", "rw", "norm_num"], "tactic_count": 24}
{"name": "Affine.Simplex.isDiameter_ninePointCircle", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.NinePointCircle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.eulerPoint_mem_ninePointCircle", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.NinePointCircle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.orthogonalProjectionSpan_eulerPoint_mem_ninePointCircle", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.NinePointCircle", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Affine.Triangle.eulerPoint_eq_midpoint", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.NinePointCircle", "is_tactic_proof": true, "tactics": ["apply", "rw", "norm_num"], "tactic_count": 3}
{"name": "Affine.Triangle.altitudeFoot_mem_ninePointCircle", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.NinePointCircle", "is_tactic_proof": true, "tactics": ["convert", "rw", "unfold", "congr", "rw", "refine", "exact"], "tactic_count": 7}
{"name": "AffineSubspace.perpBisector", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.PerpBisector", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.mem_perpBisector_iff_inner_eq_zero'", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.PerpBisector", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.mem_perpBisector_iff_inner_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.PerpBisector", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.mem_perpBisector_iff_inner_pointReflection_vsub_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.PerpBisector", "is_tactic_proof": false, "tactics": ["rw", "real_inner_smul_left,", "simp"], "tactic_count": 3}
{"name": "AffineSubspace.mem_perpBisector_pointReflection_iff_inner_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.PerpBisector", "is_tactic_proof": true, "tactics": ["rw", "inner_add_right,"], "tactic_count": 2}
{"name": "AffineSubspace.midpoint_mem_perpBisector", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.PerpBisector", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AffineSubspace.perpBisector_nonempty", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.PerpBisector", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.direction_perpBisector", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.PerpBisector", "is_tactic_proof": true, "tactics": ["rw", "ext", "exact"], "tactic_count": 3}
{"name": "AffineSubspace.mem_perpBisector_iff_inner_eq_inner", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.PerpBisector", "is_tactic_proof": true, "tactics": ["rw", "inner_add_left,", "simp"], "tactic_count": 3}
{"name": "AffineSubspace.mem_perpBisector_iff_inner_eq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.PerpBisector", "is_tactic_proof": true, "tactics": ["rw", "midpoint_vsub_left,", "div_eq_inv_mul]"], "tactic_count": 3}
{"name": "AffineSubspace.mem_perpBisector_iff_dist_eq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.PerpBisector", "is_tactic_proof": true, "tactics": ["rw", "inner_add_left,", "mem_perpBisector_iff_inner_eq_inner]"], "tactic_count": 3}
{"name": "AffineSubspace.mem_perpBisector_iff_dist_eq'", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.PerpBisector", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AffineSubspace.perpBisector_comm", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.PerpBisector", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "AffineSubspace.right_mem_perpBisector", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.PerpBisector", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "AffineSubspace.left_mem_perpBisector", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.PerpBisector", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AffineSubspace.perpBisector_self", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.PerpBisector", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.perpBisector_eq_top", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.PerpBisector", "is_tactic_proof": true, "tactics": ["refine", "rw", "trivial"], "tactic_count": 3}
{"name": "AffineSubspace.perpBisector_ne_bot", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.PerpBisector", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EuclideanGeometry.dist_lt_of_sbtw_of_inner_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.PerpBisector", "is_tactic_proof": true, "tactics": ["obtain", "have", "have", "have", "rw", "have", "have", "nlinarith", "simpa"], "tactic_count": 9}
{"name": "EuclideanGeometry.dist_le_of_wbtw_of_inner_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.PerpBisector", "is_tactic_proof": true, "tactics": ["obtain", "have", "rw", "have", "nlinarith", "simpa"], "tactic_count": 6}
{"name": "EuclideanGeometry.dist_lt_of_sbtw_of_mem_perpBisector", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.PerpBisector", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.dist_le_of_wbtw_of_mem_perpBisector", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.PerpBisector", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.inner_vsub_vsub_of_dist_eq_of_dist_eq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.PerpBisector", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "Isometry.preimage_perpBisector", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.PerpBisector", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Isometry.mapsTo_perpBisector", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.PerpBisector", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.orthogonalProjection", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Projection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.orthogonalProjection_apply", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Projection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.orthogonalProjection_apply'", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Projection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.orthogonalProjection_apply_mem", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Projection", "is_tactic_proof": false, "tactics": ["rw", "vsub_sub_vsub_cancel_left,", "exact"], "tactic_count": 3}
{"name": "EuclideanGeometry.orthogonalProjection_congr", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Projection", "is_tactic_proof": true, "tactics": ["subst", "rfl"], "tactic_count": 2}
{"name": "EuclideanGeometry.orthogonalProjection_linear", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Projection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.orthogonalProjection_contLinear", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Projection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.orthogonalProjection_mem", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Projection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.orthogonalProjection_mem_orthogonal", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Projection", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "EuclideanGeometry.inter_eq_singleton_orthogonalProjection", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Projection", "is_tactic_proof": false, "tactics": ["obtain", "inter_eq_singleton_of_nonempty_of_isCompl", "rw", "exact", "rwa"], "tactic_count": 5}
{"name": "EuclideanGeometry.orthogonalProjection_vsub_mem_direction", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Projection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.vsub_orthogonalProjection_mem_direction", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Projection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.orthogonalProjection_eq_self_iff", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Projection", "is_tactic_proof": true, "tactics": ["constructor", "exact", "intro", "have", "rw", "symm", "exact"], "tactic_count": 7}
{"name": "EuclideanGeometry.orthogonalProjection_mem_subspace_eq_self", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Projection", "is_tactic_proof": true, "tactics": ["ext", "rw", "exact"], "tactic_count": 3}
{"name": "EuclideanGeometry.orthogonalProjection_orthogonalProjection", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Projection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.eq_orthogonalProjection_of_eq_subspace", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Projection", "is_tactic_proof": true, "tactics": ["subst", "rfl"], "tactic_count": 2}
{"name": "EuclideanGeometry.orthogonalProjection_affineSpan_singleton", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Projection", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "EuclideanGeometry.dist_orthogonalProjection_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Projection", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EuclideanGeometry.dist_orthogonalProjection_ne_zero_of_notMem", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Projection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.orthogonalProjection_vsub_mem_direction_orthogonal", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Projection", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "EuclideanGeometry.vsub_orthogonalProjection_mem_direction_orthogonal", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Projection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.orthogonalProjection_vsub_orthogonalProjection", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Projection", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "EuclideanGeometry.coe_orthogonalProjection_eq_iff_mem", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Projection", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "exact", "rintro", "have", "suffices", "rw", "simp", "exact"], "tactic_count": 9}
{"name": "EuclideanGeometry.orthogonalProjection_eq_iff_mem", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Projection", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "EuclideanGeometry.orthogonalProjection_eq_orthogonalProjection_iff_vsub_mem", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Projection", "is_tactic_proof": false, "tactics": ["rw", "s.directionᗮ.add_mem_iff_left", "simp"], "tactic_count": 3}
{"name": "EuclideanGeometry.orthogonalProjection_sup_of_orthogonalProjection_eq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Projection", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "EuclideanGeometry.orthogonalProjection_vadd_eq_self", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Projection", "is_tactic_proof": true, "tactics": ["have", "rw", "refine", "ext", "refine", "exact"], "tactic_count": 6}
{"name": "EuclideanGeometry.orthogonalProjection_vadd_smul_vsub_orthogonalProjection", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Projection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.orthogonalProjection_orthogonalProjection_of_le", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Projection", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "EuclideanGeometry.dist_sq_eq_dist_orthogonalProjection_sq_add_dist_orthogonalProjection_sq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Projection", "is_tactic_proof": false, "tactics": ["rw", "vsub_add_vsub_cancel", "norm_add_sq_eq_norm_sq_add_norm_sq_of_inner_eq_zero", "exact"], "tactic_count": 4}
{"name": "EuclideanGeometry.dist_orthogonalProjection_eq_infDist", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Projection", "is_tactic_proof": true, "tactics": ["refine", "rw", "refine", "rw", "simp_rw", "simp"], "tactic_count": 6}
{"name": "EuclideanGeometry.dist_orthogonalProjection_eq_infNndist", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Projection", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "EuclideanGeometry.dist_sq_smul_orthogonal_vadd_smul_orthogonal_vadd", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Projection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.dist_eq_iff_dist_orthogonalProjection_eq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Projection", "is_tactic_proof": false, "tactics": ["rw", "dist_sq_eq_dist_orthogonalProjection_sq_add_dist_orthogonalProjection_sq", "dist_sq_eq_dist_orthogonalProjection_sq_add_dist_orthogonalProjection_sq", "simp"], "tactic_count": 4}
{"name": "EuclideanGeometry.dist_set_eq_iff_dist_orthogonalProjection_eq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Projection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.exists_dist_eq_iff_exists_dist_orthogonalProjection_eq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Projection", "is_tactic_proof": true, "tactics": ["have", "simp_rw", "exact"], "tactic_count": 3}
{"name": "EuclideanGeometry.reflection", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Projection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.reflection_apply", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Projection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.reflection_apply_of_mem", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Projection", "is_tactic_proof": false, "tactics": ["rw", "s.direction.reflection_eq_self_iff]", "exact"], "tactic_count": 3}
{"name": "EuclideanGeometry.reflection_apply'", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Projection", "is_tactic_proof": true, "tactics": ["rw", "set", "set", "rw", "vadd_vsub_assoc]"], "tactic_count": 5}
{"name": "EuclideanGeometry.eq_reflection_of_eq_subspace", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Projection", "is_tactic_proof": true, "tactics": ["subst", "rfl"], "tactic_count": 2}
{"name": "EuclideanGeometry.reflection_reflection", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Projection", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "EuclideanGeometry.reflection_symm", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Projection", "is_tactic_proof": true, "tactics": ["ext", "rw", "simp"], "tactic_count": 3}
{"name": "EuclideanGeometry.reflection_involutive", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Projection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.reflection_eq_self_iff", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Projection", "is_tactic_proof": false, "tactics": ["rw", "s.mem_direction_iff_eq_vsub_right", "simp"], "tactic_count": 3}
{"name": "EuclideanGeometry.reflection_eq_iff_orthogonalProjection_eq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Projection", "is_tactic_proof": true, "tactics": ["rw", "constructor", "intro", "rw", "vsub_sub_vsub_cancel_right,", "smul_eq_zero]", "norm_num", "exact", "intro", "rw"], "tactic_count": 10}
{"name": "EuclideanGeometry.dist_reflection", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Projection", "is_tactic_proof": true, "tactics": ["conv_lhs", "exact"], "tactic_count": 2}
{"name": "EuclideanGeometry.dist_reflection_eq_of_mem", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Projection", "is_tactic_proof": true, "tactics": ["rw", "convert", "rw"], "tactic_count": 3}
{"name": "EuclideanGeometry.reflection_mem_of_le_of_mem", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Projection", "is_tactic_proof": true, "tactics": ["rw", "have", "exact"], "tactic_count": 3}
{"name": "EuclideanGeometry.reflection_orthogonal_vadd", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Projection", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "EuclideanGeometry.reflection_vadd_smul_vsub_orthogonalProjection", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Projection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.orthogonalProjection_map", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Projection", "is_tactic_proof": true, "tactics": ["rw", "simp", "map_direction,", "rw", "intro", "rw", "obtain", "rw"], "tactic_count": 8}
{"name": "EuclideanGeometry.orthogonalProjection_subtype", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Projection", "is_tactic_proof": true, "tactics": ["rw", "have", "rw", "infer_instance", "convert"], "tactic_count": 5}
{"name": "EuclideanGeometry.reflection_map", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Projection", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "EuclideanGeometry.reflection_subtype", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Projection", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Affine.Simplex.orthogonalProjectionSpan", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Projection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.orthogonalProjectionSpan_congr", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Projection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.orthogonalProjectionSpan_reindex", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Projection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.orthogonalProjection_vadd_smul_vsub_orthogonalProjection", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Projection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.coe_orthogonalProjection_vadd_smul_vsub_orthogonalProjection", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Projection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.dist_sq_eq_dist_orthogonalProjection_sq_add_dist_orthogonalProjection_sq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Projection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.orthogonalProjectionSpan_eq_point", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Projection", "is_tactic_proof": true, "tactics": ["rw", "convert", "simp"], "tactic_count": 3}
{"name": "Affine.Simplex.orthogonalProjectionSpan_faceOpposite_eq_point_rev", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Projection", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Affine.Simplex.orthogonalProjectionSpan_map", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Projection", "is_tactic_proof": true, "tactics": ["simp_rw", "convert", "simp"], "tactic_count": 3}
{"name": "Affine.Simplex.orthogonalProjectionSpan_restrict", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Projection", "is_tactic_proof": true, "tactics": ["rw", "convert"], "tactic_count": 2}
{"name": "signedDist", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.SignedDist", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "signedDist_apply", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.SignedDist", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "signedDist_apply_apply", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.SignedDist", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "signedDist_apply_linear", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.SignedDist", "is_tactic_proof": true, "tactics": ["change", "simp"], "tactic_count": 2}
{"name": "signedDist_apply_linear_apply", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.SignedDist", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "signedDist_linear_apply", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.SignedDist", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "signedDist_linear_apply_apply", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.SignedDist", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "signedDist_smul", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.SignedDist", "is_tactic_proof": true, "tactics": ["simp", "rw"], "tactic_count": 2}
{"name": "signedDist_smul_of_pos", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.SignedDist", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "signedDist_smul_of_neg", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.SignedDist", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "signedDist_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.SignedDist", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "signedDist_neg", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.SignedDist", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "signedDist_congr", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.SignedDist", "is_tactic_proof": true, "tactics": ["obtain", "ext", "simpa"], "tactic_count": 3}
{"name": "signedDist_self", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.SignedDist", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "signedDist_anticomm", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.SignedDist", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "signedDist_triangle", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.SignedDist", "is_tactic_proof": true, "tactics": ["simp", "rw"], "tactic_count": 2}
{"name": "signedDist_triangle_left", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.SignedDist", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "signedDist_triangle_right", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.SignedDist", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "signedDist_vadd_left", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.SignedDist", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "signedDist_vadd_right", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.SignedDist", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "signedDist_vadd_left_swap", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.SignedDist", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "signedDist_vadd_right_swap", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.SignedDist", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "signedDist_vadd_vadd", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.SignedDist", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "signedDist_left_congr", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.SignedDist", "is_tactic_proof": true, "tactics": ["ext", "simpa"], "tactic_count": 2}
{"name": "signedDist_right_congr", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.SignedDist", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "signedDist_eq_zero_of_orthogonal", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.SignedDist", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "abs_signedDist_le_dist", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.SignedDist", "is_tactic_proof": true, "tactics": ["rw", "by_cases", "simp", "grw", "simp"], "tactic_count": 5}
{"name": "signedDist_le_dist", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.SignedDist", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "abs_signedDist_eq_dist_iff_vsub_mem_span", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.SignedDist", "is_tactic_proof": true, "tactics": ["rw", "rw", "abs_norm]", "by_cases", "simp", "rw", "rw", "simp"], "tactic_count": 8}
{"name": "signedDist_eq_dist_iff_vsub_mem_span", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.SignedDist", "is_tactic_proof": true, "tactics": ["rw", "rw", "by_cases", "simp", "rw", "rw", "simp", "refine", "simp", "use", "constructor", "positivity", "rw", "rw", "simp"], "tactic_count": 15}
{"name": "signedDist_vsub_self", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.SignedDist", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "signedDist_vsub_self_rev", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.SignedDist", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "signedDist_lineMap_lineMap", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.SignedDist", "is_tactic_proof": true, "tactics": ["trans", "simp", "rw"], "tactic_count": 3}
{"name": "signedDist_lineMap_left", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.SignedDist", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "signedDist_left_lineMap", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.SignedDist", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "signedDist_lineMap_right", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.SignedDist", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "signedDist_right_lineMap", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.SignedDist", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "AffineSubspace.signedInfDist", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.SignedDist", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.signedInfDist_def", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.SignedDist", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.signedInfDist_eq_signedDist_of_mem", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.SignedDist", "is_tactic_proof": true, "tactics": ["apply", "apply", "exact", "exact"], "tactic_count": 4}
{"name": "AffineSubspace.signedInfDist_eq_signedDist_orthogonalProjection", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.SignedDist", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AffineSubspace.signedInfDist_apply_self", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.SignedDist", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AffineSubspace.signedInfDist_apply_of_mem", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.SignedDist", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AffineSubspace.signedInfDist_eq_const_of_mem", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.SignedDist", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "AffineSubspace.abs_signedInfDist_eq_dist_of_mem_affineSpan_insert", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.SignedDist", "is_tactic_proof": true, "tactics": ["rw", "rcases", "simp", "norm_smul,"], "tactic_count": 4}
{"name": "AffineSubspace.signedInfDist_singleton", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.SignedDist", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Affine.Simplex.signedInfDist", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.SignedDist", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.signedInfDist_reindex", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.SignedDist", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Affine.Simplex.signedInfDist_apply_self", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.SignedDist", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.signedInfDist_apply_of_ne", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.SignedDist", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.signedInfDist_affineCombination", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.SignedDist", "is_tactic_proof": false, "tactics": ["rw", "simp", "simp", "simp", "intro", "exact"], "tactic_count": 6}
{"name": "Affine.Simplex.abs_signedInfDist_eq_dist_of_mem_affineSpan_range", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.SignedDist", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "rw", "convert", "exact"], "tactic_count": 5}
{"name": "EuclideanGeometry.similar_of_angle_angle", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Similarity", "is_tactic_proof": false, "tactics": ["have", "by_contra", "have", "grind", "have", "have", "grind", "have", "have", "have", "have", "have", "have", "have", "grind", "have", "grind", "have", "grind", "have", "have", "rw", "rw", "rw", "mul_comm]", "have", "have", "rw", "rw", "rw", "mul_comm]", "apply", "apply", "exact"], "tactic_count": 34}
{"name": "EuclideanGeometry.similar_of_side_angle_side", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Similarity", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "set", "have", "rw", "apply", "simp", "simp", "have", "have", "have", "rw", "rw", "field_simp", "rw", "have", "field_simp", "rw", "have", "have", "rw", "rw", "rw", "use", "refine", "intro", "fin_cases", "try", "all_goals"], "tactic_count": 30}
{"name": "Similar.angle_eq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Similarity", "is_tactic_proof": true, "tactics": ["rw", "rcases", "have", "have", "have", "have", "rw", "field_simp", "have", "field_simp", "rw", "by_cases", "rw", "rcases", "have", "rw", "simp_rw", "have", "rw", "simp_rw", "rw", "apply", "repeat"], "tactic_count": 23}
{"name": "Similar.angle_eq_all", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Similarity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.Equilateral.angle_eq_pi_div_three", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Simplex", "is_tactic_proof": true, "tactics": ["rcases", "rw", "refine", "simp", "have", "rintro", "replace", "rw", "exact", "field"], "tactic_count": 10}
{"name": "Affine.Simplex.AcuteAngled", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Simplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.acuteAngled_reindex_iff", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Simplex", "is_tactic_proof": true, "tactics": ["refine", "convert", "convert"], "tactic_count": 3}
{"name": "Affine.Simplex.Equilateral.acuteAngled", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Simplex", "is_tactic_proof": true, "tactics": ["intro", "rw", "linarith"], "tactic_count": 3}
{"name": "Affine.Simplex.dist_point_centroid", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Simplex", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Affine.Simplex.dist_point_faceOppositeCentroid", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Simplex", "is_tactic_proof": true, "tactics": ["simp_rw", "norm_cast"], "tactic_count": 2}
{"name": "Affine.Triangle.acuteAngled_iff_angle_lt", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Simplex", "is_tactic_proof": false, "tactics": ["refine", "h", "have", "have", "have", "intro", "fin_cases"], "tactic_count": 7}
{"name": "Affine.Triangle.dist_point_centroid", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Simplex", "is_tactic_proof": true, "tactics": ["rw", "norm_cast"], "tactic_count": 2}
{"name": "Affine.Triangle.dist_point_faceOppositeCentroid", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Simplex", "is_tactic_proof": true, "tactics": ["rw", "norm_cast"], "tactic_count": 2}
{"name": "EuclideanGeometry.instNonemptySphere", "kind": "instance", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.instCoeSphereSet", "kind": "instance", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.instMembershipSphere", "kind": "instance", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.Sphere.mk_center", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.Sphere.mk_radius", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.Sphere.mk_center_radius", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "EuclideanGeometry.Sphere.coe_mk", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.Sphere.mem_coe", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.Sphere.mem_coe'", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.mem_sphere", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.mem_sphere'", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.subset_sphere", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.dist_of_mem_subset_sphere", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.dist_of_mem_subset_mk_sphere", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.Sphere.ne_iff", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EuclideanGeometry.Sphere.center_eq_iff_eq_of_mem", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "rw"], "tactic_count": 3}
{"name": "EuclideanGeometry.Sphere.center_ne_iff_ne_of_mem", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.dist_center_eq_dist_center_of_mem_sphere", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EuclideanGeometry.dist_center_eq_dist_center_of_mem_sphere'", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EuclideanGeometry.Sphere.radius_nonneg_of_mem", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.Sphere.center_mem_iff", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "EuclideanGeometry.Cospherical", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.cospherical_def", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.cospherical_iff_exists_sphere", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": true, "tactics": ["refine", "rcases", "exact", "rcases", "exact"], "tactic_count": 5}
{"name": "EuclideanGeometry.Sphere.cospherical", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.Cospherical.subset", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "EuclideanGeometry.cospherical_empty", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.cospherical_singleton", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": true, "tactics": ["use", "simp"], "tactic_count": 2}
{"name": "EuclideanGeometry.Sphere.nonempty_iff", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": true, "tactics": ["refine", "obtain", "refine", "simpa"], "tactic_count": 4}
{"name": "EuclideanGeometry.cospherical_pair", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.Concyclic.subset", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.concyclic_empty", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.concyclic_singleton", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.concyclic_pair", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.Sphere.IsDiameter.right_mem", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EuclideanGeometry.Sphere.IsDiameter.symm", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.Sphere.isDiameter_comm", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.Sphere.isDiameter_iff_left_mem_and_midpoint_eq_center", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.Sphere.isDiameter_iff_right_mem_and_midpoint_eq_center", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.Sphere.IsDiameter.pointReflection_center_left", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EuclideanGeometry.Sphere.IsDiameter.pointReflection_center_right", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EuclideanGeometry.Sphere.isDiameter_iff_left_mem_and_pointReflection_center_left", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.Sphere.isDiameter_iff_right_mem_and_pointReflection_center_right", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EuclideanGeometry.Sphere.IsDiameter.right_eq_of_isDiameter", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EuclideanGeometry.Sphere.IsDiameter.left_eq_of_isDiameter", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EuclideanGeometry.Sphere.IsDiameter.dist_left_right", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "EuclideanGeometry.Sphere.IsDiameter.dist_left_right_div_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "EuclideanGeometry.Sphere.IsDiameter.left_eq_right_iff", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "EuclideanGeometry.Sphere.IsDiameter.left_ne_right_iff_radius_ne_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.Sphere.IsDiameter.left_ne_right_iff_radius_pos", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "EuclideanGeometry.Sphere.IsDiameter.wbtw", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "EuclideanGeometry.Sphere.IsDiameter.sbtw", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "EuclideanGeometry.Sphere.ofDiameter", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.Sphere.isDiameter_ofDiameter", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.Sphere.IsDiameter.ofDiameter_eq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp", "simp"], "tactic_count": 3}
{"name": "EuclideanGeometry.Sphere.isDiameter_iff_ofDiameter_eq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.Cospherical.affineIndependent", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "rcases", "rw", "have", "intro", "have", "exact", "rcases", "have", "choose", "have", "intro", "rw", "exact", "have", "have", "rw", "simpa", "have", "intro", "have", "rw", "exact", "simp_rw", "have", "have", "intro", "have", "simpa", "have", "exact"], "tactic_count": 33}
{"name": "EuclideanGeometry.Cospherical.affineIndependent_of_mem_of_ne", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": true, "tactics": ["refine", "simp", "erw", "simp"], "tactic_count": 4}
{"name": "EuclideanGeometry.Cospherical.affineIndependent_of_ne", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.inner_vsub_vsub_of_mem_sphere_of_mem_sphere", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.eq_of_mem_sphere_of_mem_sphere_of_mem_of_finrank_eq_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.eq_of_mem_sphere_of_mem_sphere_of_finrank_eq_two", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.inner_pos_or_eq_of_dist_le_radius", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "refine", "rw", "rw", "refine", "rwa", "rcases", "refine", "rwa", "rw", "rintro", "rw", "refine", "simpa", "rw", "nth_rw", "rw", "smul_ne_zero_iff,", "rintro", "refine", "simpa"], "tactic_count": 21}
{"name": "EuclideanGeometry.inner_nonneg_of_dist_le_radius", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": true, "tactics": ["rcases", "exact", "simp"], "tactic_count": 3}
{"name": "EuclideanGeometry.inner_pos_of_dist_lt_radius", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "exact", "exact"], "tactic_count": 4}
{"name": "EuclideanGeometry.wbtw_of_collinear_of_dist_center_le_radius", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.sbtw_of_collinear_of_dist_center_lt_radius", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.Sphere.isDiameter_iff_mem_and_mem_and_dist", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "apply", "simp_rw", "simp_rw", "rw"], "tactic_count": 6}
{"name": "EuclideanGeometry.Sphere.isDiameter_iff_mem_and_mem_and_wbtw", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "is_tactic_proof": true, "tactics": ["refine", "have", "rw", "exact"], "tactic_count": 4}
{"name": "EuclideanGeometry.Sphere.orthRadius", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Sphere.OrthRadius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.Sphere.self_mem_orthRadius", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.OrthRadius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.Sphere.mem_orthRadius_iff_inner_left", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.OrthRadius", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EuclideanGeometry.Sphere.mem_orthRadius_iff_inner_right", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.OrthRadius", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EuclideanGeometry.Sphere.direction_orthRadius", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.OrthRadius", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EuclideanGeometry.Sphere.orthRadius_center", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.OrthRadius", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "EuclideanGeometry.Sphere.center_mem_orthRadius_iff", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.OrthRadius", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "EuclideanGeometry.Sphere.orthRadius_le_orthRadius_iff", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.OrthRadius", "is_tactic_proof": true, "tactics": ["refine", "have", "simp", "have", "simp", "rcases", "have", "rw", "real_inner_smul_left,", "rcases", "nth_rw", "rw", "rcases", "rw", "rw", "exact", "rw", "exact", "simp", "rw", "exact", "rcases"], "tactic_count": 22}
{"name": "EuclideanGeometry.Sphere.orthRadius_eq_orthRadius_iff", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.OrthRadius", "is_tactic_proof": true, "tactics": ["refine", "have", "have", "grind"], "tactic_count": 4}
{"name": "EuclideanGeometry.Sphere.finrank_orthRadius", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.OrthRadius", "is_tactic_proof": true, "tactics": ["rw", "convert", "exact"], "tactic_count": 3}
{"name": "EuclideanGeometry.Sphere.orthRadius_map", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.OrthRadius", "is_tactic_proof": true, "tactics": ["rw", "convert", "convert", "simp"], "tactic_count": 4}
{"name": "EuclideanGeometry.Sphere.direction_orthRadius_le_iff", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.OrthRadius", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "EuclideanGeometry.Sphere.orthRadius_parallel_orthRadius_iff", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.OrthRadius", "is_tactic_proof": true, "tactics": ["simp_rw", "coe_eq_bot_iff,"], "tactic_count": 2}
{"name": "InnerProductGeometry.mul_norm_eq_abs_sub_sq_norm", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Power", "is_tactic_proof": true, "tactics": ["obtain", "have", "rwa", "have", "calc"], "tactic_count": 5}
{"name": "EuclideanGeometry.mul_dist_eq_abs_sub_sq_dist", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Power", "is_tactic_proof": true, "tactics": ["let", "have", "have", "have", "have", "have", "rw", "iterate", "rw", "rw", "refine", "rw", "rcases", "rw", "rw", "use", "match_scalars", "ring"], "tactic_count": 18}
{"name": "EuclideanGeometry.mul_dist_eq_mul_dist_of_cospherical", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Power", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "rw", "rw", "rw"], "tactic_count": 5}
{"name": "EuclideanGeometry.mul_dist_eq_mul_dist_of_cospherical_of_angle_eq_pi", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Power", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "EuclideanGeometry.mul_dist_eq_mul_dist_of_cospherical_of_angle_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Power", "is_tactic_proof": true, "tactics": ["apply", "apply", "exact", "mul_dist_eq_mul_dist_of_cospherical"], "tactic_count": 4}
{"name": "EuclideanGeometry.Sphere.power", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Sphere.Power", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.Sphere.power_eq_zero_iff_mem_sphere", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Power", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EuclideanGeometry.Sphere.power_pos_iff_radius_lt_dist_center", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Power", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EuclideanGeometry.Sphere.power_neg_iff_dist_center_lt_radius", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Power", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EuclideanGeometry.Sphere.power_nonneg_iff_radius_le_dist_center", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Power", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EuclideanGeometry.Sphere.power_nonpos_iff_dist_center_le_radius", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Power", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EuclideanGeometry.Sphere.mul_dist_eq_abs_power", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Power", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "EuclideanGeometry.Sphere.mul_dist_eq_zero_of_mem_sphere", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Power", "is_tactic_proof": true, "tactics": ["have", "rw", "abs_zero]"], "tactic_count": 3}
{"name": "EuclideanGeometry.Sphere.mul_dist_eq_power_of_radius_le_dist_center", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Power", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EuclideanGeometry.Sphere.mul_dist_eq_neg_power_of_dist_center_le_radius", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Power", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EuclideanGeometry.Sphere.dist_sq_eq_mul_dist_of_tangent_and_secant", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Power", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "h_tangent.dist_sq_eq_of_mem", "ring"], "tactic_count": 5}
{"name": "EuclideanGeometry.Sphere.IsTangentAt.power_eq_dist_sq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Power", "is_tactic_proof": true, "tactics": ["rw", "ring_nf"], "tactic_count": 2}
{"name": "EuclideanGeometry.Sphere.isTangentAt_iff_dist_sq_eq_power", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Power", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.mul_dist_add_mul_dist_eq_mul_dist_of_cospherical", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Ptolemy", "is_tactic_proof": true, "tactics": ["have", "have", "have", "have", "rw", "rw", "all_goals", "have", "rw", "rwa", "all_goals", "have", "have", "simp", "dist_sq_mul_dist_add_dist_sq_mul_dist"], "tactic_count": 15}
{"name": "EuclideanGeometry.Sphere.secondInter", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Sphere.SecondInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.Sphere.secondInter_map", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.SecondInter", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "EuclideanGeometry.Sphere.coe_secondInter", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.SecondInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.Sphere.secondInter_dist", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.SecondInter", "is_tactic_proof": true, "tactics": ["rw", "by_cases", "rw", "exact"], "tactic_count": 4}
{"name": "EuclideanGeometry.Sphere.secondInter_mem", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.SecondInter", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "EuclideanGeometry.Sphere.secondInter_zero", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.SecondInter", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "EuclideanGeometry.Sphere.secondInter_eq_self_iff", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.SecondInter", "is_tactic_proof": true, "tactics": ["refine", "by_cases", "simp", "rwa", "div_eq_zero_iff,", "rw"], "tactic_count": 6}
{"name": "EuclideanGeometry.Sphere.eq_or_eq_secondInter_of_mem_mk'_span_singleton_iff_mem", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.SecondInter", "is_tactic_proof": true, "tactics": ["refine", "rcases", "rwa", "rwa", "rw", "rcases", "rw", "subst", "by_cases", "simp", "rw", "rw", "rw", "rcases"], "tactic_count": 14}
{"name": "EuclideanGeometry.Sphere.eq_or_eq_secondInter_iff_mem_of_mem_affineSpan_pair", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.SecondInter", "is_tactic_proof": true, "tactics": ["convert", "convert", "rw", "simp"], "tactic_count": 4}
{"name": "EuclideanGeometry.Sphere.secondInter_smul", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.SecondInter", "is_tactic_proof": true, "tactics": ["simp_rw", "rw", "mul_div_cancel_left₀"], "tactic_count": 3}
{"name": "EuclideanGeometry.Sphere.secondInter_neg", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.SecondInter", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EuclideanGeometry.Sphere.secondInter_secondInter", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.SecondInter", "is_tactic_proof": true, "tactics": ["by_cases", "have", "simp", "rw", "convert", "convert", "ring"], "tactic_count": 7}
{"name": "EuclideanGeometry.Sphere.secondInter_eq_lineMap", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.SecondInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.Sphere.secondInter_vsub_mem_affineSpan", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.SecondInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.Sphere.secondInter_collinear", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.SecondInter", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "EuclideanGeometry.Sphere.wbtw_secondInter", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.SecondInter", "is_tactic_proof": true, "tactics": ["by_cases", "refine", "wbtw_of_collinear_of_dist_center_le_radius", "intro", "rw", "eq_comm]", "exact"], "tactic_count": 7}
{"name": "EuclideanGeometry.Sphere.sbtw_secondInter", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.SecondInter", "is_tactic_proof": true, "tactics": ["refine", "rintro", "rw", "simp", "rintro", "rw", "exact"], "tactic_count": 7}
{"name": "EuclideanGeometry.Sphere.sOppSide_faceOpposite_secondInter_of_mem_interior_faceOpposite", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.SecondInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.Sphere.sOppSide_faceOpposite_secondInter_of_mem_interior", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.SecondInter", "is_tactic_proof": true, "tactics": ["obtain", "let", "have", "let", "have", "suffices", "refine", "simp_rw", "rw", "simp", "refine", "simp", "simp"], "tactic_count": 13}
{"name": "EuclideanGeometry.Sphere.isTangentAt_orthRadius_iff_mem", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Tangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.Sphere.IsTangentAt.inner_left_eq_zero_of_mem", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Tangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.Sphere.IsTangentAt.inner_right_eq_zero_of_mem", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Tangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.Sphere.IsTangentAt.eq_of_isTangentAt", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Tangent", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "vsub_sub_vsub_cancel_right]", "simpa"], "tactic_count": 5}
{"name": "EuclideanGeometry.Sphere.isTangentAt_center_iff", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Tangent", "is_tactic_proof": true, "tactics": ["refine", "rintro", "rw", "exact", "rintro", "refine", "rw", "simp"], "tactic_count": 8}
{"name": "EuclideanGeometry.Sphere.IsTangentAt.dist_sq_eq_of_mem", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Tangent", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "rw", "conv_rhs", "rw", "exact"], "tactic_count": 6}
{"name": "EuclideanGeometry.Sphere.IsTangentAt.mem_and_mem_iff_eq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Tangent", "is_tactic_proof": true, "tactics": ["refine", "have", "rw", "simpa", "rintro", "exact"], "tactic_count": 6}
{"name": "EuclideanGeometry.Sphere.IsTangentAt.eq_of_mem_of_mem", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Tangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.Sphere.IsTangentAt.dist_eq_of_mem_of_mem", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Tangent", "is_tactic_proof": true, "tactics": ["have", "have", "rwa"], "tactic_count": 3}
{"name": "EuclideanGeometry.Sphere.IsTangentAt.radius_lt_dist_center", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Tangent", "is_tactic_proof": false, "tactics": ["suffices", "simpa", "rw", "simp"], "tactic_count": 4}
{"name": "EuclideanGeometry.Sphere.IsTangentAt.eq_orthRadius_of_finrank_add_one_eq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Tangent", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "exact", "eq_of_direction_eq_of_nonempty_of_le"], "tactic_count": 5}
{"name": "EuclideanGeometry.Sphere.IsTangent", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Sphere.Tangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.Sphere.IsTangentAt.isTangent", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Tangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.Sphere.isTangent_orthRadius_iff_mem", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Tangent", "is_tactic_proof": true, "tactics": ["refine", "rintro", "rw", "rcases", "exact", "rw", "rwa"], "tactic_count": 7}
{"name": "EuclideanGeometry.Sphere.IsTangent.radius_le_dist_center", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Tangent", "is_tactic_proof": true, "tactics": ["obtain", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "EuclideanGeometry.Sphere.IsTangent.notMem_of_dist_lt", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Tangent", "is_tactic_proof": true, "tactics": ["contrapose", "exact"], "tactic_count": 2}
{"name": "EuclideanGeometry.Sphere.IsTangent.infDist_eq_radius", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Tangent", "is_tactic_proof": true, "tactics": ["obtain", "refine", "convert", "rw", "rw", "have", "refine", "rw", "exact"], "tactic_count": 9}
{"name": "EuclideanGeometry.Sphere.dist_orthogonalProjection_eq_radius_iff_isTangentAt", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Tangent", "is_tactic_proof": true, "tactics": ["refine", "refine", "rwa", "rw", "exact", "orthogonalProjection_vsub_mem_direction_orthogonal", "rw"], "tactic_count": 7}
{"name": "EuclideanGeometry.Sphere.dist_orthogonalProjection_eq_radius_iff_isTangent", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Tangent", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "EuclideanGeometry.Sphere.infDist_eq_radius_iff_isTangent", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Tangent", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EuclideanGeometry.Sphere.isTangent_iff_isTangentAt_orthogonalProjection", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Tangent", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EuclideanGeometry.Sphere.IsTangent.eq_orthRadius_or_eq_orthRadius_pointReflection_of_parallel_orthRadius", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Tangent", "is_tactic_proof": true, "tactics": ["rcases", "have", "rw", "obtain", "rcases", "rw", "rw", "rw", "exact", "obtain", "refine", "rw", "congr", "rcases", "simp_all", "rw", "rcases", "simp_all", "have", "simp_rw", "right_eq_mul₀", "rcases", "simp_all", "right", "convert", "rw", "rw", "simp"], "tactic_count": 28}
{"name": "EuclideanGeometry.Sphere.IsTangentAt.eq_orthogonalProjection", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Tangent", "is_tactic_proof": true, "tactics": ["refine", "have", "rwa"], "tactic_count": 3}
{"name": "EuclideanGeometry.Sphere.tangentSet", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Sphere.Tangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.Sphere.mem_tangentSet_iff", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Tangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.Sphere.isTangent_of_mem_tangentSet", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Tangent", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "EuclideanGeometry.Sphere.tangentsFrom", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Sphere.Tangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.Sphere.mem_tangentsFrom_iff", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Tangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.Sphere.mem_tangentSet_of_mem_tangentsFrom", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Tangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.Sphere.mem_of_mem_tangentsFrom", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Tangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.Sphere.isTangent_of_mem_tangentsFrom", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Tangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.Sphere.commonTangents", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Sphere.Tangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.Sphere.mem_commonTangents_iff", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Tangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.Sphere.commonTangents_comm", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Tangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.Sphere.commonIntTangents", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Sphere.Tangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.Sphere.commonExtTangents", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Sphere.Tangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.Sphere.mem_commonIntTangents_iff", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Tangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.Sphere.mem_commonExtTangents_iff", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Tangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.Sphere.commonIntTangents_union_commonExtTangents", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Tangent", "is_tactic_proof": true, "tactics": ["ext", "rw", "rintro", "by_cases", "exact", "refine", "rintro", "exact"], "tactic_count": 8}
{"name": "EuclideanGeometry.Sphere.IsExtTangentAt.symm", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Tangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.Sphere.isExtTangentAt_comm", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Tangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.Sphere.isExtTangentAt_center_iff", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Tangent", "is_tactic_proof": true, "tactics": ["refine", "rintro", "rw", "exact", "rintro", "refine", "rw", "simp"], "tactic_count": 8}
{"name": "EuclideanGeometry.Sphere.isIntTangentAt_center_iff", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Tangent", "is_tactic_proof": true, "tactics": ["refine", "rintro", "rw", "exact", "rintro", "refine", "rw", "simp"], "tactic_count": 8}
{"name": "EuclideanGeometry.Sphere.isIntTangentAt_self_iff_mem", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Tangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.Sphere.IsExtTangent", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Sphere.Tangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.Sphere.IsExtTangent.symm", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Tangent", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "EuclideanGeometry.Sphere.isExtTangent_comm", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Tangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.Sphere.IsIntTangent", "kind": "definition", "module": "Mathlib.Geometry.Euclidean.Sphere.Tangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.Sphere.IsExtTangentAt.isExtTangent", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Tangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.Sphere.IsIntTangentAt.isIntTangent", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Tangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanGeometry.Sphere.isIntTangent_self_iff", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Tangent", "is_tactic_proof": true, "tactics": ["simp_rw", "rw", "simp"], "tactic_count": 3}
{"name": "EuclideanGeometry.Sphere.IsExtTangent.dist_center", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Tangent", "is_tactic_proof": true, "tactics": ["rcases", "rw", "rw"], "tactic_count": 3}
{"name": "EuclideanGeometry.Sphere.IsIntTangent.dist_center", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Tangent", "is_tactic_proof": true, "tactics": ["rcases", "rw", "simp"], "tactic_count": 3}
{"name": "EuclideanGeometry.Sphere.isExtTangent_iff_dist_center", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Tangent", "is_tactic_proof": true, "tactics": ["refine", "rcases", "exact", "rintro", "refine", "by_cases", "simp", "exact", "refine", "simp", "abs_of_nonneg", "field", "simp", "rw", "field", "simp", "refine", "positivity", "rw", "linarith"], "tactic_count": 20}
{"name": "EuclideanGeometry.Sphere.isIntTangent_iff_dist_center", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Sphere.Tangent", "is_tactic_proof": true, "tactics": ["refine", "rcases", "exact", "rintro", "by_cases", "rw", "have", "simp", "rw", "have", "refine", "rw", "exact", "have", "intro", "rw", "exact", "refine", "simp", "abs_neg,", "field", "simp", "field", "rw", "simp", "rw", "linarith", "rw", "simp"], "tactic_count": 29}
{"name": "InnerProductGeometry.norm_sub_sq_eq_norm_sq_add_norm_sq_sub_two_mul_norm_mul_norm_mul_cos_angle", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Triangle", "is_tactic_proof": true, "tactics": ["rw", "cos_angle_mul_norm_mul_norm,", "real_inner_self_eq_norm_mul_norm,"], "tactic_count": 3}
{"name": "InnerProductGeometry.sin_angle_mul_norm_eq_sin_angle_mul_norm", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Triangle", "is_tactic_proof": true, "tactics": ["obtain", "simp", "obtain", "simp", "obtain", "simp", "have", "simp", "rw", "simp", "have", "field_simp", "ring_nf"], "tactic_count": 13}
{"name": "InnerProductGeometry.sin_angle_div_norm_eq_sin_angle_div_norm", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Triangle", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "InnerProductGeometry.angle_sub_eq_angle_sub_rev_of_norm_eq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Triangle", "is_tactic_proof": true, "tactics": ["refine", "rw", "real_inner_self_eq_norm_mul_norm,"], "tactic_count": 3}
{"name": "InnerProductGeometry.norm_eq_of_angle_sub_eq_angle_sub_rev_of_angle_ne_pi", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Triangle", "is_tactic_proof": false, "tactics": ["replace", "by_cases", "rw", "rw", "mul_assoc,", "replace", "rw", "real_inner_self_eq_norm_mul_norm,", "mul_self_mul_inv,", "by_cases", "rw", "rw", "by_cases", "rw", "rw", "rw", "mul_div_assoc,", "symm", "by_contra", "replace", "rw", "exact"], "tactic_count": 22}
{"name": "_private.Mathlib.Geometry.Euclidean.Triangle.0.InnerProductGeometry.cos_angle_eq_cos_angle_add_add_angle_add", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Triangle", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rw", "mul_comm", "have", "simp", "rw", "simp", "ring"], "tactic_count": 9}
{"name": "_private.Mathlib.Geometry.Euclidean.Triangle.0.InnerProductGeometry.sin_angle_eq_sin_angle_add_add_angle_add", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Triangle", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rw", "add_comm", "have", "simp", "simp", "ring_nf"], "tactic_count": 8}
{"name": "InnerProductGeometry.angle_eq_angle_add_add_angle_add", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Triangle", "is_tactic_proof": true, "tactics": ["rcases", "simp", "have", "rw", "obtain", "simp", "have", "replace", "contrapose", "grw", "linear_combination", "have", "replace", "by_contra", "grw", "have", "grw", "rw", "obtain", "obtain", "have", "cases", "linarith", "contradiction", "obtain", "simpa"], "tactic_count": 26}
{"name": "InnerProductGeometry.angle_add_angle_sub_add_angle_sub_eq_pi", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Triangle", "is_tactic_proof": true, "tactics": ["have", "rw", "rw", "simp", "linear_combination"], "tactic_count": 5}
{"name": "Orientation.norm_eq_of_two_zsmul_oangle_sub_eq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Triangle", "is_tactic_proof": true, "tactics": ["have", "rw", "rcases", "rw", "o.angle_eq_iff_oangle_eq_of_sign_eq", "angle_comm", "refine", "rw", "exact", "rw", "simp"], "tactic_count": 11}
{"name": "EuclideanGeometry.dist_sq_eq_dist_sq_add_dist_sq_sub_two_mul_dist_mul_dist_mul_cos_angle", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Triangle", "is_tactic_proof": true, "tactics": ["rw", "unfold", "convert", "exact", "exact"], "tactic_count": 5}
{"name": "EuclideanGeometry.sin_angle_mul_dist_eq_sin_angle_mul_dist", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Triangle", "is_tactic_proof": true, "tactics": ["simp", "rw", "sin_angle_mul_norm_eq_sin_angle_mul_norm,", "left", "rw"], "tactic_count": 5}
{"name": "EuclideanGeometry.sin_angle_div_dist_eq_sin_angle_div_dist", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Triangle", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "EuclideanGeometry.dist_eq_dist_mul_sin_angle_div_sin_angle", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Triangle", "is_tactic_proof": true, "tactics": ["have", "field_simp", "rw"], "tactic_count": 3}
{"name": "EuclideanGeometry.angle_eq_angle_of_dist_eq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Triangle", "is_tactic_proof": true, "tactics": ["rw", "unfold", "convert", "exact", "exact"], "tactic_count": 5}
{"name": "EuclideanGeometry.dist_eq_of_angle_eq_angle_of_angle_ne_pi", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Triangle", "is_tactic_proof": true, "tactics": ["unfold", "rw", "rw", "rw", "exact"], "tactic_count": 5}
{"name": "EuclideanGeometry.dist_eq_of_two_zsmul_oangle_eq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Triangle", "is_tactic_proof": true, "tactics": ["convert", "rw", "rw", "rw", "nth_rw", "simp_rw", "simp_rw", "convert"], "tactic_count": 8}
{"name": "EuclideanGeometry.angle_add_angle_add_angle_eq_pi", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Triangle", "is_tactic_proof": true, "tactics": ["rw", "unfold", "rw", "neg_vsub_eq_vsub_rev,", "vsub_sub_vsub_cancel_right", "exact"], "tactic_count": 6}
{"name": "EuclideanGeometry.exterior_angle_eq_angle_add_angle", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Triangle", "is_tactic_proof": true, "tactics": ["linarith", "angle_add_angle_add_angle_eq_pi"], "tactic_count": 2}
{"name": "EuclideanGeometry.oangle_add_oangle_add_oangle_eq_pi", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Triangle", "is_tactic_proof": true, "tactics": ["simpa", "positiveOrientation.oangle_add_cyc3_neg_left"], "tactic_count": 2}
{"name": "EuclideanGeometry.angle_add_of_ne_of_ne", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Triangle", "is_tactic_proof": true, "tactics": ["by_cases", "by_cases", "have", "have", "have", "replace", "have", "rw", "rw", "have", "linarith"], "tactic_count": 11}
{"name": "EuclideanGeometry.dist_sq_mul_dist_add_dist_sq_mul_dist", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Triangle", "is_tactic_proof": false, "tactics": ["rw", "ring"], "tactic_count": 2}
{"name": "EuclideanGeometry.dist_sq_add_dist_sq_eq_two_mul_dist_midpoint_sq_add_half_dist_sq", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Triangle", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "let", "have", "have", "simp", "calc", "dist", "rw", "field"], "tactic_count": 10}
{"name": "EuclideanGeometry.dist_mul_of_eq_angle_of_dist_mul", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Triangle", "is_tactic_proof": false, "tactics": ["have", "calc", "dist", "simp", "ring", "by_cases", "have", "rw", "have", "have", "exact"], "tactic_count": 11}
{"name": "EuclideanGeometry.dist_lt_of_angle_lt", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Triangle", "is_tactic_proof": true, "tactics": ["have", "rw", "have", "have", "apply", "simp", "intro", "by_cases", "have", "exact", "by_contra", "have", "linarith", "by_contra", "have", "by_contra", "have", "linarith", "rw", "have", "have", "by_contra", "have", "linarith", "have", "rw", "have", "rw", "rw", "exact", "linarith"], "tactic_count": 31}
{"name": "EuclideanGeometry.angle_lt_iff_dist_lt", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Triangle", "is_tactic_proof": true, "tactics": ["constructor", "exact", "intro", "by_contra", "rcases", "have", "apply", "rw", "linarith", "linarith", "rw", "have", "linarith"], "tactic_count": 13}
{"name": "EuclideanGeometry.angle_le_iff_dist_le", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Triangle", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "EuclideanGeometry.pi_div_three_le_angle_of_le_of_le", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Triangle", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "linarith", "linarith"], "tactic_count": 4}
{"name": "EuclideanGeometry.pi_div_three_lt_angle_of_le_of_le_of_ne", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Triangle", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "linarith", "rcases", "linarith"], "tactic_count": 5}
{"name": "EuclideanGeometry.angle_le_pi_div_three_of_le_of_le", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Triangle", "is_tactic_proof": true, "tactics": ["by_cases", "subst", "simp_all", "linarith", "linarith"], "tactic_count": 5}
{"name": "EuclideanGeometry.angle_lt_pi_div_three_of_le_of_le_of_ne", "kind": "theorem", "module": "Mathlib.Geometry.Euclidean.Triangle", "is_tactic_proof": true, "tactics": ["by_cases", "subst", "by_cases", "subst", "simp", "simp_all", "linarith", "rcases", "linarith"], "tactic_count": 9}
{"name": "Finset.pow_ssubset_pow_succ_of_pow_ne_closure", "kind": "theorem", "module": "Mathlib.Geometry.Group.Growth.LinearLowerBound", "is_tactic_proof": true, "tactics": ["obtain", "simpa", "refine", "contrapose", "rw", "wlog", "simp", "replace", "induction", "zero", "succ", "rw", "rw", "exact", "subst", "simp", "let", "mul_mem", "norm_cast", "simpa", "one_mem", "inv_mem", "norm_cast", "have", "have", "rw", "rw", "simpa", "exact"], "tactic_count": 29}
{"name": "Finset.pow_right_strictMonoOn", "kind": "theorem", "module": "Mathlib.Geometry.Group.Growth.LinearLowerBound", "is_tactic_proof": true, "tactics": ["refine", "rintro", "apply", "obtain", "simp", "calc"], "tactic_count": 6}
{"name": "Finset.pow_right_strictMono", "kind": "theorem", "module": "Mathlib.Geometry.Group.Growth.LinearLowerBound", "is_tactic_proof": true, "tactics": ["obtain", "simp", "have", "simpa"], "tactic_count": 4}
{"name": "Finset.add_one_le_card_pow", "kind": "theorem", "module": "Mathlib.Geometry.Group.Growth.LinearLowerBound", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_pow_quotient_mul_pow_inter_subgroup_le", "kind": "theorem", "module": "Mathlib.Geometry.Group.Growth.QuotientInter", "is_tactic_proof": true, "tactics": ["set", "let", "have", "have", "have", "norm_cast", "simpa", "have", "calc", "rw", "rw", "simp", "rintro", "have", "have", "have", "simp_all", "gcongr", "simp", "forall_apply_eq_imp_iff₂,", "rintro", "exact"], "tactic_count": 22}
{"name": "Finset.le_card_quotient_mul_sq_inter_subgroup", "kind": "theorem", "module": "Mathlib.Geometry.Group.Growth.QuotientInter", "is_tactic_proof": true, "tactics": ["classical", "set", "rw", "refine", "calc", "gcongr", "simp", "rintro", "refine", "simp"], "tactic_count": 10}
{"name": "LeftInvariantDerivation.instCoeDerivationContMDiffMapModelWithCornersSelfSomeENatTop", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Algebra.LeftInvariantDerivation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LeftInvariantDerivation.toDerivation_injective", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.LeftInvariantDerivation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LeftInvariantDerivation.instFunLikeContMDiffMapModelWithCornersSelfSomeENatTop", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Algebra.LeftInvariantDerivation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LeftInvariantDerivation.instLinearMapClassContMDiffMapModelWithCornersSelfSomeENatTop", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Algebra.LeftInvariantDerivation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LeftInvariantDerivation.toFun_eq_coe", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.LeftInvariantDerivation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LeftInvariantDerivation.coe_injective", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.LeftInvariantDerivation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LeftInvariantDerivation.ext", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.LeftInvariantDerivation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LeftInvariantDerivation.coe_derivation", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.LeftInvariantDerivation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LeftInvariantDerivation.left_invariant'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.LeftInvariantDerivation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LeftInvariantDerivation.map_add", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.LeftInvariantDerivation", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LeftInvariantDerivation.map_zero", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.LeftInvariantDerivation", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LeftInvariantDerivation.map_neg", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.LeftInvariantDerivation", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LeftInvariantDerivation.map_sub", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.LeftInvariantDerivation", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LeftInvariantDerivation.map_smul", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.LeftInvariantDerivation", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LeftInvariantDerivation.leibniz", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.LeftInvariantDerivation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LeftInvariantDerivation.instZero", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Algebra.LeftInvariantDerivation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LeftInvariantDerivation.instInhabited", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Algebra.LeftInvariantDerivation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LeftInvariantDerivation.instAdd", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Algebra.LeftInvariantDerivation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LeftInvariantDerivation.instNeg", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Algebra.LeftInvariantDerivation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LeftInvariantDerivation.instSub", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Algebra.LeftInvariantDerivation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LeftInvariantDerivation.coe_add", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.LeftInvariantDerivation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LeftInvariantDerivation.coe_zero", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.LeftInvariantDerivation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LeftInvariantDerivation.coe_neg", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.LeftInvariantDerivation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LeftInvariantDerivation.coe_sub", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.LeftInvariantDerivation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LeftInvariantDerivation.lift_add", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.LeftInvariantDerivation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LeftInvariantDerivation.lift_zero", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.LeftInvariantDerivation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LeftInvariantDerivation.hasNatScalar", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Algebra.LeftInvariantDerivation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LeftInvariantDerivation.hasIntScalar", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Algebra.LeftInvariantDerivation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LeftInvariantDerivation.instAddCommGroup", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Algebra.LeftInvariantDerivation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LeftInvariantDerivation.instSMul", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Algebra.LeftInvariantDerivation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LeftInvariantDerivation.coe_smul", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.LeftInvariantDerivation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LeftInvariantDerivation.lift_smul", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.LeftInvariantDerivation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LeftInvariantDerivation.coeFnAddMonoidHom", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Algebra.LeftInvariantDerivation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LeftInvariantDerivation.instModule", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Algebra.LeftInvariantDerivation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LeftInvariantDerivation.evalAt", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Algebra.LeftInvariantDerivation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LeftInvariantDerivation.evalAt_apply", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.LeftInvariantDerivation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LeftInvariantDerivation.evalAt_coe", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.LeftInvariantDerivation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LeftInvariantDerivation.left_invariant", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.LeftInvariantDerivation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LeftInvariantDerivation.evalAt_mul", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.LeftInvariantDerivation", "is_tactic_proof": true, "tactics": ["ext", "rw", "simp", "rw"], "tactic_count": 4}
{"name": "LeftInvariantDerivation.comp_L", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.LeftInvariantDerivation", "is_tactic_proof": true, "tactics": ["ext", "rw", "evalAt_apply]"], "tactic_count": 3}
{"name": "LeftInvariantDerivation.instBracket", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Algebra.LeftInvariantDerivation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LeftInvariantDerivation.commutator_coe_derivation", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.LeftInvariantDerivation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LeftInvariantDerivation.commutator_apply", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.LeftInvariantDerivation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LeftInvariantDerivation.instLieRing", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Algebra.LeftInvariantDerivation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LeftInvariantDerivation.instLieAlgebra", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Algebra.LeftInvariantDerivation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieGroup.of_le", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.LieGroup", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "instLieGroupOfSomeENatTopOfLEInfty", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Algebra.LieGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instLieGroupOfTopWithTopENat", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Algebra.LieGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instLieGroupOfNatWithTopENatOfIsTopologicalGroup", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Algebra.LieGroup", "is_tactic_proof": true, "tactics": ["constructor", "rw", "exact"], "tactic_count": 3}
{"name": "instLieGroupOfNatWithTopENat", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Algebra.LieGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiff_inv", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.LieGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "topologicalGroup_of_lieGroup", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.LieGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffWithinAt.inv", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.LieGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffAt.inv", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.LieGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffOn.inv", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.LieGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiff.inv", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.LieGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffWithinAt.div", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.LieGroup", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "ContMDiffAt.div", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.LieGroup", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "ContMDiffOn.div", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.LieGroup", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "ContMDiff.div", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.LieGroup", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Prod.instLieGroup", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Algebra.LieGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instNormedSpaceLieAddGroup", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Algebra.LieGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instContMDiffInv₀ModelWithCornersSelf", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Algebra.LieGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffInv₀.of_le", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.LieGroup", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "instContMDiffInv₀OfSomeENatTopOfLEInfty", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Algebra.LieGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instContMDiffInv₀OfTopWithTopENat", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Algebra.LieGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instContMDiffInv₀OfNatWithTopENatOfContinuousInv₀", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Algebra.LieGroup", "is_tactic_proof": true, "tactics": ["have", "constructor", "have", "rw", "exact", "intro", "have", "apply", "exact"], "tactic_count": 9}
{"name": "instContMDiffInv₀OfNatWithTopENat", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Algebra.LieGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffAt_inv₀", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.LieGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousInv₀_of_contMDiffInv₀", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.LieGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffOn_inv₀", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.LieGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffWithinAt.inv₀", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.LieGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffAt.inv₀", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.LieGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiff.inv₀", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.LieGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffOn.inv₀", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.LieGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffWithinAt.div₀", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.LieGroup", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ContMDiffOn.div₀", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.LieGroup", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ContMDiffAt.div₀", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.LieGroup", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ContMDiff.div₀", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.LieGroup", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "LibraryNote.Design_choices_about_smooth_algebraic_structures", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffMul.of_le", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.Monoid", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "instContMDiffMulOfSomeENatTopOfLEInfty", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instContMDiffMulOfTopWithTopENat", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instContMDiffMulOfNatWithTopENatOfContinuousMul", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Algebra.Monoid", "is_tactic_proof": true, "tactics": ["constructor", "rw", "exact"], "tactic_count": 3}
{"name": "instContMDiffMulOfNatWithTopENat", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiff_mul", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousMul_of_contMDiffMul", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffWithinAt.mul", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffAt.mul", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffOn.mul", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiff.mul", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiff_mul_left", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffAt_mul_left", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiff_mul_right", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffAt_mul_right", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiable_mul_left", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiableAt_mul_left", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiable_mul_right", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiableAt_mul_right", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smoothLeftMul", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smoothRightMul", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieGroup.term𝑳", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieGroup._aux_Mathlib_Geometry_Manifold_Algebra_Monoid___macroRules_LieGroup_term𝑳_1", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieGroup._aux_Mathlib_Geometry_Manifold_Algebra_Monoid___unexpand_smoothLeftMul_1", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieGroup.term𝑹", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieGroup._aux_Mathlib_Geometry_Manifold_Algebra_Monoid___macroRules_LieGroup_term𝑹_1", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LieGroup._aux_Mathlib_Geometry_Manifold_Algebra_Monoid___unexpand_smoothRightMul_1", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "L_apply", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "R_apply", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "L_mul", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.Monoid", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "R_mul", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.Monoid", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "smoothLeftMul_one", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smoothRightMul_one", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffMul.prod", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiff_pow", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instOneContMDiffMonoidMorphism", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInhabitedContMDiffMonoidMorphism", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFunLikeContMDiffMonoidMorphism", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instMonoidHomClassContMDiffMonoidMorphism", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instContinuousMapClassContMDiffMonoidMorphism", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffWithinAt.prod", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.Monoid", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "insert", "simp", "exact"], "tactic_count": 6}
{"name": "contMDiffWithinAt_finprod", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffWithinAt_finset_prod'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffWithinAt_finset_prod", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.Monoid", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "ContMDiffAt.prod", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.Monoid", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "contMDiffAt_finprod", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffAt_finset_prod'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffAt_finset_prod", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffOn_finprod", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffOn_finset_prod'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffOn_finset_prod", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiff.prod", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiff_finset_prod'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiff_finset_prod", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiff_finprod", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiff_finprod_cond", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.Monoid", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "ContMDiffWithinAt.pow", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffAt.pow", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffOn.pow", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiff.pow", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instContMDiffAddSelf", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Algebra.Monoid", "is_tactic_proof": true, "tactics": ["constructor", "rw", "exact"], "tactic_count": 3}
{"name": "ContMDiffWithinAt.div_const", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.Monoid", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ContMDiffAt.div_const", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffOn.div_const", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiff.div_const", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffMap.instMul", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Algebra.SmoothFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffMap.coe_mul", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.SmoothFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffMap.mul_comp", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.SmoothFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffMap.instOne", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Algebra.SmoothFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffMap.coe_one", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.SmoothFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffMap.instNSMul", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Algebra.SmoothFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffMap.instPow", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Algebra.SmoothFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffMap.coe_pow", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.SmoothFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffMap.semigroup", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Algebra.SmoothFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffMap.monoid", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Algebra.SmoothFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffMap.coeFnMonoidHom", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Algebra.SmoothFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffMap.compLeftMonoidHom", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Algebra.SmoothFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffMap.restrictMonoidHom", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Algebra.SmoothFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffMap.commMonoid", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Algebra.SmoothFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffMap.group", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Algebra.SmoothFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffMap.coe_inv", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.SmoothFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffMap.coe_div", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.SmoothFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffMap.commGroup", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Algebra.SmoothFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffMap.semiring", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Algebra.SmoothFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffMap.ring", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Algebra.SmoothFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffMap.commRing", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Algebra.SmoothFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffMap.compLeftRingHom", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Algebra.SmoothFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffMap.restrictRingHom", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Algebra.SmoothFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffMap.coeFnRingHom", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Algebra.SmoothFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffMap.evalRingHom", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Algebra.SmoothFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffMap.instSMul", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Algebra.SmoothFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffMap.coe_smul", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.SmoothFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffMap.smul_comp", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.SmoothFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffMap.module", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Algebra.SmoothFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffMap.coeFnLinearMap", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Algebra.SmoothFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffMap.C", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Algebra.SmoothFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffMap.algebra", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Algebra.SmoothFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffMap.coeFnAlgHom", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Algebra.SmoothFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffMap.instSMul'", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Algebra.SmoothFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffMap.smul_comp'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.SmoothFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffMap.module'", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Algebra.SmoothFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffRing.toContMDiffMul", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Algebra.Structures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffRing.toLieAddGroup", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Algebra.Structures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFieldContMDiffRing", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Algebra.Structures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "topologicalSemiring_of_contMDiffRing", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Algebra.Structures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SingularManifold.map_f", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Bordism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SingularManifold.map_M", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Bordism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SingularManifold.map_comp", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Bordism", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SingularManifold.comap_M", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Bordism", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "SingularManifold.comap_f", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Bordism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SingularManifold.empty_M", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Bordism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SingularManifold.sum_M", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Bordism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SingularManifold.sum_f", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Bordism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SmoothBumpFunction.toFun", "kind": "definition", "module": "Mathlib.Geometry.Manifold.BumpFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SmoothBumpFunction.instCoeFunForallReal", "kind": "instance", "module": "Mathlib.Geometry.Manifold.BumpFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SmoothBumpFunction.coe_def", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.BumpFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SmoothBumpFunction.rOut_pos", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.BumpFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SmoothBumpFunction.ball_subset", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.BumpFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SmoothBumpFunction.ball_inter_range_eq_ball_inter_target", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.BumpFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SmoothBumpFunction.eqOn_source", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.BumpFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SmoothBumpFunction.eventuallyEq_of_mem_source", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.BumpFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SmoothBumpFunction.one_of_dist_le", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.BumpFunction", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SmoothBumpFunction.support_eq_inter_preimage", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.BumpFunction", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SmoothBumpFunction.isOpen_support", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.BumpFunction", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SmoothBumpFunction.support_eq_symm_image", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.BumpFunction", "is_tactic_proof": true, "tactics": ["rw", "ball_inter_range_eq_ball_inter_target]"], "tactic_count": 2}
{"name": "SmoothBumpFunction.support_subset_source", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.BumpFunction", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SmoothBumpFunction.image_eq_inter_preimage_of_subset_support", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.BumpFunction", "is_tactic_proof": true, "tactics": ["rw", "obtain", "apply", "refine", "rintro", "rw", "exact", "refine", "rw"], "tactic_count": 9}
{"name": "SmoothBumpFunction.mem_Icc", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.BumpFunction", "is_tactic_proof": true, "tactics": ["have", "rcases", "exacts"], "tactic_count": 3}
{"name": "SmoothBumpFunction.nonneg", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.BumpFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SmoothBumpFunction.le_one", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.BumpFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SmoothBumpFunction.eventuallyEq_one_of_dist_lt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.BumpFunction", "is_tactic_proof": true, "tactics": ["filter_upwards", "rintro", "exact"], "tactic_count": 3}
{"name": "SmoothBumpFunction.eventuallyEq_one", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.BumpFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SmoothBumpFunction.eq_one", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.BumpFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SmoothBumpFunction.support_mem_nhds", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.BumpFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SmoothBumpFunction.tsupport_mem_nhds", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.BumpFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SmoothBumpFunction.c_mem_support", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.BumpFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SmoothBumpFunction.nonempty_support", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.BumpFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SmoothBumpFunction.isCompact_symm_image_closedBall", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.BumpFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SmoothBumpFunction.nhdsWithin_range_basis", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.BumpFunction", "is_tactic_proof": false, "tactics": ["refine", "rintro", "exact", "exact"], "tactic_count": 4}
{"name": "SmoothBumpFunction.isClosed_image_of_isClosed", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.BumpFunction", "is_tactic_proof": true, "tactics": ["rw", "refine", "exact"], "tactic_count": 3}
{"name": "SmoothBumpFunction.exists_r_pos_lt_subset_ball", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.BumpFunction", "is_tactic_proof": true, "tactics": ["set", "have", "rw", "rcases", "exact"], "tactic_count": 5}
{"name": "SmoothBumpFunction.updateRIn", "kind": "definition", "module": "Mathlib.Geometry.Manifold.BumpFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SmoothBumpFunction.support_updateRIn", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.BumpFunction", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SmoothBumpFunction.instNonempty", "kind": "instance", "module": "Mathlib.Geometry.Manifold.BumpFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SmoothBumpFunction.isClosed_symm_image_closedBall", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.BumpFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SmoothBumpFunction.tsupport_subset_symm_image_closedBall", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.BumpFunction", "is_tactic_proof": true, "tactics": ["rw", "exact", "closure_minimal"], "tactic_count": 3}
{"name": "SmoothBumpFunction.tsupport_subset_extChartAt_source", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.BumpFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SmoothBumpFunction.tsupport_subset_chartAt_source", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.BumpFunction", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "SmoothBumpFunction.hasCompactSupport", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.BumpFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SmoothBumpFunction.nhds_basis_tsupport", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.BumpFunction", "is_tactic_proof": false, "tactics": ["have", "rw", "exact", "exact", "this.to_hasBasis"], "tactic_count": 5}
{"name": "SmoothBumpFunction.nhds_basis_support", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.BumpFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SmoothBumpFunction.contMDiff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.BumpFunction", "is_tactic_proof": true, "tactics": ["refine", "have", "refine", "exact"], "tactic_count": 4}
{"name": "SmoothBumpFunction.contMDiffAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.BumpFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SmoothBumpFunction.continuous", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.BumpFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SmoothBumpFunction.contMDiff_smul", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.BumpFunction", "is_tactic_proof": false, "tactics": ["refine", "contMDiff_of_tsupport", "have", "exact"], "tactic_count": 4}
{"name": "atlas", "kind": "abbrev", "module": "Mathlib.Geometry.Manifold.ChartedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "chartAt", "kind": "abbrev", "module": "Mathlib.Geometry.Manifold.ChartedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_chart_source", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ChartedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "chart_mem_atlas", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ChartedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nonempty_of_chartedSpace", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ChartedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isEmpty_of_chartedSpace", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ChartedSpace", "is_tactic_proof": true, "tactics": ["rcases", "exact", "exact"], "tactic_count": 3}
{"name": "mem_chart_target", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ChartedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "chart_source_mem_nhds", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ChartedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "chart_target_mem_nhds", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ChartedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iUnion_source_chartAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ChartedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ChartedSpace.isOpen_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ChartedSpace", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "achart", "kind": "definition", "module": "Mathlib.Geometry.Manifold.ChartedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "achart_def", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ChartedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "coe_achart", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ChartedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "achart_val", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ChartedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_achart_source", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ChartedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ChartedSpace.secondCountable_of_countable_cover", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ChartedSpace", "is_tactic_proof": false, "tactics": ["haveI", "haveI", "rw", "exact"], "tactic_count": 4}
{"name": "ChartedSpace.secondCountable_of_sigmaCompact", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ChartedSpace", "is_tactic_proof": false, "tactics": ["obtain", "countable_cover_nhds_of_sigmaCompact", "exact"], "tactic_count": 3}
{"name": "ChartedSpace.locallyCompactSpace", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ChartedSpace", "is_tactic_proof": false, "tactics": ["have", "rw", "exact", "refine", "rintro", "exact"], "tactic_count": 6}
{"name": "ChartedSpace.locallyConnectedSpace", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ChartedSpace", "is_tactic_proof": true, "tactics": ["let", "refine", "locallyConnectedSpace_of_connected_bases", "intro", "simpa", "rintro", "exact"], "tactic_count": 7}
{"name": "ChartedSpace.locPathConnectedSpace", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ChartedSpace", "is_tactic_proof": true, "tactics": ["refine", "let", "let", "have", "refine", "nth_rewrite", "apply", "exact", "refine", "refine", "exact", "exact"], "tactic_count": 12}
{"name": "ChartedSpace.comp", "kind": "definition", "module": "Mathlib.Geometry.Manifold.ChartedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "chartAt_comp", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ChartedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ChartedSpace.t1Space", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ChartedSpace", "is_tactic_proof": true, "tactics": ["apply", "by_cases", "refine", "exact", "simp", "true_and]", "exact", "exact"], "tactic_count": 8}
{"name": "ChartedSpace.discreteTopology", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ChartedSpace", "is_tactic_proof": true, "tactics": ["apply", "have", "isOpen_inter_preimage", "convert", "refine", "simp", "intro", "exact"], "tactic_count": 8}
{"name": "ChartedSpace.empty", "kind": "definition", "module": "Mathlib.Geometry.Manifold.ChartedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "chartedSpaceSelf", "kind": "instance", "module": "Mathlib.Geometry.Manifold.ChartedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "chartedSpaceSelf_atlas", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ChartedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "chartAt_self_eq", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ChartedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ChartedSpace.of_discreteTopology", "kind": "definition", "module": "Mathlib.Geometry.Manifold.ChartedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "chartedSpace_of_discreteTopology_chartAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ChartedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LibraryNote.Manifold_type_tags", "kind": "definition", "module": "Mathlib.Geometry.Manifold.ChartedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelProd", "kind": "definition", "module": "Mathlib.Geometry.Manifold.ChartedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelPi", "kind": "definition", "module": "Mathlib.Geometry.Manifold.ChartedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "modelProdInhabited", "kind": "instance", "module": "Mathlib.Geometry.Manifold.ChartedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instTopologicalSpaceModelProd", "kind": "instance", "module": "Mathlib.Geometry.Manifold.ChartedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "modelProd_range_prod_id", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ChartedSpace", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "modelPiInhabited", "kind": "instance", "module": "Mathlib.Geometry.Manifold.ChartedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instTopologicalSpaceModelPi", "kind": "instance", "module": "Mathlib.Geometry.Manifold.ChartedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "prodChartedSpace", "kind": "instance", "module": "Mathlib.Geometry.Manifold.ChartedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelProd.ext", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ChartedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "prodChartedSpace_chartAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ChartedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "chartedSpaceSelf_prod", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ChartedSpace", "is_tactic_proof": true, "tactics": ["ext1", "simp", "ext1", "simp", "rfl"], "tactic_count": 5}
{"name": "piChartedSpace", "kind": "instance", "module": "Mathlib.Geometry.Manifold.ChartedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "piChartedSpace_chartAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ChartedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ChartedSpace.sum_of_nonempty", "kind": "definition", "module": "Mathlib.Geometry.Manifold.ChartedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ChartedSpace.sum", "kind": "instance", "module": "Mathlib.Geometry.Manifold.ChartedSpace", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "have", "have", "exact"], "tactic_count": 5}
{"name": "ChartedSpace.sum_chartAt_inl", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ChartedSpace", "is_tactic_proof": true, "tactics": ["simp", "rfl"], "tactic_count": 2}
{"name": "ChartedSpace.sum_chartAt_inr", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ChartedSpace", "is_tactic_proof": true, "tactics": ["simp", "rfl"], "tactic_count": 2}
{"name": "sum_chartAt_inl_apply", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ChartedSpace", "is_tactic_proof": true, "tactics": ["haveI", "rw", "exact"], "tactic_count": 3}
{"name": "sum_chartAt_inr_apply", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ChartedSpace", "is_tactic_proof": true, "tactics": ["haveI", "rw", "exact"], "tactic_count": 3}
{"name": "ChartedSpace.mem_atlas_sum", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ChartedSpace", "is_tactic_proof": true, "tactics": ["simp", "obtain", "rw", "rw"], "tactic_count": 4}
{"name": "ChartedSpaceCore.toTopologicalSpace", "kind": "definition", "module": "Mathlib.Geometry.Manifold.ChartedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ChartedSpaceCore.open_source'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ChartedSpace", "is_tactic_proof": true, "tactics": ["apply", "simp", "refine", "simp"], "tactic_count": 4}
{"name": "ChartedSpaceCore.open_target", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ChartedSpace", "is_tactic_proof": false, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "ChartedSpaceCore.openPartialHomeomorph", "kind": "definition", "module": "Mathlib.Geometry.Manifold.ChartedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ChartedSpaceCore.toChartedSpace", "kind": "definition", "module": "Mathlib.Geometry.Manifold.ChartedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.norm_eventually_eq_of_mdifferentiableAt_of_isLocalMax", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Complex", "is_tactic_proof": true, "tactics": ["set", "have", "have", "have", "rw", "replace", "have", "filter_upwards", "have", "rw", "exact", "have", "rw", "exact", "convert", "exact", "simpa"], "tactic_count": 17}
{"name": "MDifferentiableOn.norm_eqOn_of_isPreconnected_of_isMaxOn", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Complex", "is_tactic_proof": true, "tactics": ["set", "suffices", "have", "refine", "replace", "replace", "exact", "have", "set", "have", "have", "have", "exact"], "tactic_count": 13}
{"name": "MDifferentiableOn.eqOn_of_isPreconnected_of_isMaxOn_norm", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableOn.apply_eq_of_isPreconnected_isCompact_isOpen", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Complex", "is_tactic_proof": false, "tactics": ["refine", "wlog", "have", "simpa", "rcases", "have", "rw"], "tactic_count": 7}
{"name": "MDifferentiable.isLocallyConstant", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiable.apply_eq_of_compactSpace", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiable.exists_eq_const_of_compactSpace", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "conformalPregroupoid", "kind": "definition", "module": "Mathlib.Geometry.Manifold.ConformalGroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "conformalGroupoid", "kind": "definition", "module": "Mathlib.Geometry.Manifold.ConformalGroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffWithinAt.mfderivWithin", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiffMFDeriv", "is_tactic_proof": true, "tactics": ["let", "have", "suffices", "apply", "apply", "exact", "hg.continuousWithinAt.preimage_mem_nhdsWithin", "have", "have", "change", "refine", "exact", "have", "have", "simp", "have", "have", "filter_upwards", "self_mem_nhdsWithin]", "apply", "exact", "have", "hg.continuousWithinAt.preimage_mem_nhdsWithin", "have", "fderivWithin", "have", "have", "rw", "simp_rw", "apply", "simp", "apply", "rw", "intro", "refine", "rw", "exact", "exact", "have", "range", "apply", "exact", "convert", "ext", "simp", "exact", "exact", "have", "fderivWithin", "t", "simp_rw", "exact", "apply", "apply", "filter_upwards", "have", "have", "apply", "apply", "refine", "rwa", "have", "mfderivWithin", "mfderivWithin", "apply", "apply", "exact", "exact", "rw", "exact", "exact", "apply", "convert", "exact", "apply", "exact", "exact", "exact", "simp", "exact", "apply", "exact", "exact", "exact", "exact", "exact", "simpa", "simpa"], "tactic_count": 88}
{"name": "ContMDiffWithinAt.mfderivWithin_const", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiffMFDeriv", "is_tactic_proof": false, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "ContMDiffWithinAt.mfderivWithin_apply", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiffMFDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffAt.mfderiv", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiffMFDeriv", "is_tactic_proof": true, "tactics": ["rw", "rw", "simp_rw", "exact"], "tactic_count": 4}
{"name": "ContMDiffAt.mfderiv_const", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiffMFDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffAt.mfderiv_apply", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiffMFDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffOn.contMDiffOn_tangentMapWithin", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiffMFDeriv", "is_tactic_proof": true, "tactics": ["intro", "let", "let", "let", "have", "let", "have", "let", "mfderivWithin", "have", "s", "have", "s", "exact", "exact"], "tactic_count": 15}
{"name": "ContMDiffOn.continuousOn_tangentMapWithin", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiffMFDeriv", "is_tactic_proof": false, "tactics": ["have", "hf.contMDiffOn_tangentMapWithin", "exact"], "tactic_count": 3}
{"name": "ContMDiff.contMDiff_tangentMap", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiffMFDeriv", "is_tactic_proof": true, "tactics": ["rw", "convert", "rw"], "tactic_count": 3}
{"name": "ContMDiff.continuous_tangentMap", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiffMFDeriv", "is_tactic_proof": true, "tactics": ["rw", "rw", "convert", "rw"], "tactic_count": 4}
{"name": "TangentBundle.tangentMap_tangentBundle_pure", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiffMFDeriv", "is_tactic_proof": true, "tactics": ["rcases", "have", "apply", "apply", "simp", "have", "haveI", "this.mdifferentiableAt", "have", "rw", "simp", "exact", "exact", "exact", "exact", "simp", "rw", "rw", "congr", "refine", "simp", "simp", "simp"], "tactic_count": 23}
{"name": "ContMDiffMap.mdifferentiable'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiffMFDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffMap.mdifferentiable", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiffMFDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffMap.mdifferentiableAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiffMFDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "equivTangentBundleProd", "kind": "definition", "module": "Mathlib.Geometry.Manifold.ContMDiffMFDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "equivTangentBundleProd_eq_tangentMap_prod_tangentMap", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiffMFDeriv", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "contMDiff_equivTangentBundleProd", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiffMFDeriv", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "contMDiff_equivTangentBundleProd_symm", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiffMFDeriv", "is_tactic_proof": true, "tactics": ["even", "functorial", "the", "is", "a", "to", "product", "rintro", "have", "simp", "apply", "exact", "exact", "rw", "simp", "refine", "exact", "the", "have", "apply", "filter_upwards", "simp", "let", "have", "apply", "apply", "simp", "have", "simp", "rw", "let", "have", "apply", "apply", "simp", "have", "exact", "simp", "change", "rw", "rw", "simp", "the", "have", "apply", "filter_upwards", "simp", "let", "have", "apply", "apply", "simp", "have", "simp", "rw", "let", "have", "apply", "apply", "simp", "have", "exact", "simp", "change", "rw", "rw", "simp"], "tactic_count": 67}
{"name": "ContMDiffMap", "kind": "definition", "module": "Mathlib.Geometry.Manifold.ContMDiffMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold.termC^_⟮_,_;_,_⟯", "kind": "definition", "module": "Mathlib.Geometry.Manifold.ContMDiffMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold._aux_Mathlib_Geometry_Manifold_ContMDiffMap___macroRules_Manifold_termC^_⟮_,_;_,_⟯_1", "kind": "definition", "module": "Mathlib.Geometry.Manifold.ContMDiffMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold._aux_Mathlib_Geometry_Manifold_ContMDiffMap___unexpand_ContMDiffMap_1", "kind": "definition", "module": "Mathlib.Geometry.Manifold.ContMDiffMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold.termC^_⟮_,_;_⟯", "kind": "definition", "module": "Mathlib.Geometry.Manifold.ContMDiffMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold._aux_Mathlib_Geometry_Manifold_ContMDiffMap___macroRules_Manifold_termC^_⟮_,_;_⟯_1", "kind": "definition", "module": "Mathlib.Geometry.Manifold.ContMDiffMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffMap.instFunLike", "kind": "instance", "module": "Mathlib.Geometry.Manifold.ContMDiffMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffMap.contMDiff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiffMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffMap.coeFn_mk", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiffMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffMap.coe_injective", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiffMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffMap.ext", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiffMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffMap.instContinuousMapClass", "kind": "instance", "module": "Mathlib.Geometry.Manifold.ContMDiffMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffMap.id", "kind": "definition", "module": "Mathlib.Geometry.Manifold.ContMDiffMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffMap.comp", "kind": "definition", "module": "Mathlib.Geometry.Manifold.ContMDiffMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffMap.comp_apply", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiffMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffMap.instInhabited", "kind": "instance", "module": "Mathlib.Geometry.Manifold.ContMDiffMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffMap.const", "kind": "definition", "module": "Mathlib.Geometry.Manifold.ContMDiffMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffMap.fst", "kind": "definition", "module": "Mathlib.Geometry.Manifold.ContMDiffMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffMap.snd", "kind": "definition", "module": "Mathlib.Geometry.Manifold.ContMDiffMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffMap.prodMk", "kind": "definition", "module": "Mathlib.Geometry.Manifold.ContMDiffMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.hasCoeToContMDiffMap", "kind": "instance", "module": "Mathlib.Geometry.Manifold.ContMDiffMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiff_model", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Atlas", "is_tactic_proof": true, "tactics": ["intro", "refine", "simp", "refine", "exact", "simp_rw"], "tactic_count": 6}
{"name": "contMDiffOn_model_symm", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Atlas", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp", "exact"], "tactic_count": 4}
{"name": "contMDiffOn_of_mem_maximalAtlas", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Atlas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffOn_symm_of_mem_maximalAtlas", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Atlas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffAt_of_mem_maximalAtlas", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Atlas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffAt_symm_of_mem_maximalAtlas", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Atlas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffOn_chart", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Atlas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffOn_chart_symm", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Atlas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffAt_extend", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Atlas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffAt_extChartAt'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Atlas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffAt_extChartAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Atlas", "is_tactic_proof": true, "tactics": ["rw", "apply", "filter_upwards", "exact"], "tactic_count": 4}
{"name": "contMDiffOn_extChartAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Atlas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffOn_extend_symm", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Atlas", "is_tactic_proof": false, "tactics": ["refine", "simp_rw", "preimage_id']", "rfl"], "tactic_count": 4}
{"name": "contMDiffOn_extChartAt_symm", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Atlas", "is_tactic_proof": true, "tactics": ["convert", "rw", "infer_instance", "infer_instance"], "tactic_count": 4}
{"name": "contMDiffWithinAt_extChartAt_symm_target", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Atlas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffWithinAt_extChartAt_symm_range", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Atlas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffWithinAt_extChartAt_symm_target_self", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Atlas", "is_tactic_proof": true, "tactics": ["rw", "constructor", "apply", "apply", "exact", "apply", "convert", "simp"], "tactic_count": 8}
{"name": "contMDiffWithinAt_extChartAt_symm_range_self", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Atlas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffOn_of_mem_contDiffGroupoid", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Atlas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLocalStructomorphOn_contDiffGroupoid_iff_aux", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Atlas", "is_tactic_proof": true, "tactics": ["apply", "intro", "let", "let", "obtain", "obtain", "hxf", "let", "refine", "simp", "rw", "simp", "have", "have", "have", "have", "refine", "dsimp", "mfld_set_tac", "have", "intro", "simp", "have", "have", "have", "calc", "f", "refine", "mfld_set_tac"], "tactic_count": 29}
{"name": "isLocalStructomorphOn_contDiffGroupoid_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Atlas", "is_tactic_proof": true, "tactics": ["constructor", "intro", "refine", "intro", "let", "have", "let", "let", "obtain", "refine", "obtain", "e", "e.source", "have", "have", "have", "rw", "rw", "exact", "dsimp", "apply", "simp", "have", "rw", "dsimp", "have", "rw", "have", "have", "apply", "refine", "rw", "rw", "have", "intro", "exact", "rw", "rwa", "refine", "mfld_set_tac", "refine", "rw", "rintro", "refine", "let", "let", "rintro", "refine", "intro", "simp", "have", "refine", "simp", "mfld_set_tac", "have", "have", "rw", "convert", "simp", "dsimp", "intro", "simp", "have", "refine", "simp", "mfld_set_tac", "have", "have", "rw", "convert", "simp", "dsimp", "mfld_set_tac", "simp", "simp"], "tactic_count": 75}
{"name": "ContMDiffWithinAt.comp", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "set", "set", "have", "rw", "have", "simp", "filter_upwards", "inter_mem_nhdsWithin", "rintro", "simp", "refine", "filter_upwards", "rintro", "simp", "exact", "filter_upwards", "rintro", "simp", "simp"], "tactic_count": 21}
{"name": "ContMDiffWithinAt.comp_of_eq", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Basic", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "ContMDiffOn.comp", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffOn.comp'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiff.comp", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ContMDiffWithinAt.comp'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffAt.comp_contMDiffWithinAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffAt.comp_contMDiffWithinAt_of_eq", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Basic", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "ContMDiffAt.comp", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffAt.comp_of_eq", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Basic", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "ContMDiff.comp_contMDiffOn", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffOn.comp_contMDiff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiff_id", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffOn_id", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffAt_id", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffWithinAt_id", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffOn.iterate", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "ContMDiff.iterate", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiff_const", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Basic", "is_tactic_proof": true, "tactics": ["intro", "refine", "simp", "exact"], "tactic_count": 4}
{"name": "contMDiff_one", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "contMDiffOn_const", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffOn_one", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffAt_const", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffAt_one", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffWithinAt_const", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffWithinAt_one", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiff_of_subsingleton", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Basic", "is_tactic_proof": true, "tactics": ["intro", "rw", "exact"], "tactic_count": 3}
{"name": "contMDiffAt_of_subsingleton", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffWithinAt_of_subsingleton", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffOn_of_subsingleton", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiff_of_discreteTopology", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Basic", "is_tactic_proof": true, "tactics": ["intro", "apply", "simp"], "tactic_count": 3}
{"name": "contMDiff_of_mulTSupport", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Basic", "is_tactic_proof": true, "tactics": ["intro", "by_cases", "exact", "exact"], "tactic_count": 4}
{"name": "contMDiffWithinAt_of_notMem_mulTSupport", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Basic", "is_tactic_proof": true, "tactics": ["apply", "contMDiffWithinAt_const.congr_of_eventuallyEq"], "tactic_count": 2}
{"name": "contMDiffAt_of_notMem_mulTSupport", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiff.piecewise", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Basic", "is_tactic_proof": true, "tactics": ["intro", "by_cases", "apply", "filter_upwards", "rw", "apply", "by_cases", "have", "apply", "filter_upwards", "simp", "apply", "filter_upwards", "rw", "contrapose", "simpa"], "tactic_count": 16}
{"name": "ContMDiff.piecewise_Iic", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffOn.union_of_isOpen", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Basic", "is_tactic_proof": true, "tactics": ["intro", "obtain", "exact", "exact"], "tactic_count": 4}
{"name": "contMDiffOn_union_iff_of_isOpen", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiff_of_contMDiffOn_union_of_isOpen", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ContMDiffOn.iUnion_of_isOpen", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Basic", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "contMDiffOn_iUnion_iff_of_isOpen", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiff_of_contMDiffOn_iUnion_of_isOpen", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "contMDiffAt_subtype_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiff_subtype_val", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiff.extend_one", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiff_inclusion", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Basic", "is_tactic_proof": true, "tactics": ["rintro", "apply", "intro", "dsimp", "rw", "exact"], "tactic_count": 6}
{"name": "contMDiff_isOpenEmbedding", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Basic", "is_tactic_proof": true, "tactics": ["haveI", "rw", "use", "intro", "apply", "intro", "simp", "rw", "rw", "apply", "exact", "letI", "extChartAt_target_subset_range", "have", "rw", "have", "rw", "exact"], "tactic_count": 18}
{"name": "contMDiffOn_isOpenEmbedding_symm", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Basic", "is_tactic_proof": true, "tactics": ["haveI", "rw", "constructor", "rw", "exact", "intro", "apply", "intro", "simp", "have", "rw", "exact", "rw", "apply", "exact"], "tactic_count": 15}
{"name": "ContMDiff.of_comp_isOpenEmbedding", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Basic", "is_tactic_proof": false, "tactics": ["have", "ext", "rw", "rw", "apply", "simp"], "tactic_count": 6}
{"name": "ContMDiffWithinAt.prodMk", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Constructions", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ContMDiffWithinAt.prodMk_space", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Constructions", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ContMDiffAt.prodMk", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffAt.prodMk_space", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffOn.prodMk", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffOn.prodMk_space", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiff.prodMk", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiff.prodMk_space", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffWithinAt_fst", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Constructions", "is_tactic_proof": true, "tactics": ["rw", "refine", "refine", "simp", "simp", "simp", "rw", "refine", "exact", "exact"], "tactic_count": 10}
{"name": "ContMDiffWithinAt.fst", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffAt_fst", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffOn_fst", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiff_fst", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffAt.fst", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiff.fst", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffWithinAt_snd", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Constructions", "is_tactic_proof": true, "tactics": ["rw", "refine", "refine", "simp", "simp", "simp", "rw", "refine", "exact", "exact"], "tactic_count": 10}
{"name": "ContMDiffWithinAt.snd", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffAt_snd", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffOn_snd", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiff_snd", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffAt.snd", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiff.snd", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffWithinAt_prod_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffWithinAt_prod_module_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Constructions", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "contMDiffAt_prod_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Constructions", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "contMDiffAt_prod_module_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Constructions", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "contMDiffOn_prod_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffOn_prod_module_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Constructions", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "contMDiff_prod_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiff_prod_module_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Constructions", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "contMDiff_prod_assoc", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffWithinAt.comp₂", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffWithinAt.comp₂_of_eq", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Constructions", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ContMDiffAt.comp₂", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffAt.comp₂_of_eq", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Constructions", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ContMDiffWithinAt.curry_left", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffWithinAt.curry_right", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffAt.curry_left", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffAt.curry_right", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffOn.curry_left", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffOn.curry_right", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiff.curry_left", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiff.curry_right", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffWithinAt.prodMap'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffWithinAt.prodMap", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffAt.prodMap", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Constructions", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "ContMDiffAt.prodMap'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffOn.prodMap", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiff.prodMap", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Constructions", "is_tactic_proof": true, "tactics": ["intro", "exact"], "tactic_count": 2}
{"name": "contMDiffWithinAt_pi_space", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Constructions", "is_tactic_proof": true, "tactics": ["simp", "extChartAt_model_space_eq_id,"], "tactic_count": 2}
{"name": "contMDiffOn_pi_space", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffAt_pi_space", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiff_pi_space", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiff.inl", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Constructions", "is_tactic_proof": true, "tactics": ["intro", "rw", "refine", "apply", "simp", "congr", "apply", "set", "have", "rw", "exact", "filter_upwards", "simp"], "tactic_count": 13}
{"name": "ContMDiff.inr", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Constructions", "is_tactic_proof": true, "tactics": ["intro", "rw", "refine", "apply", "simp", "congr", "apply", "set", "have", "rw", "exact", "filter_upwards", "simp"], "tactic_count": 13}
{"name": "extChartAt_inl_apply", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Constructions", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "extChartAt_inr_apply", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Constructions", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContMDiff.sumElim", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Constructions", "is_tactic_proof": true, "tactics": ["intro", "rw", "refine", "cases", "inl", "have", "let", "rw", "simpa", "apply", "simp", "filter_upwards", "congr", "simp", "congr", "inr", "have", "let", "rw", "simpa", "apply", "simp", "filter_upwards", "congr", "simp", "congr"], "tactic_count": 26}
{"name": "ContMDiff.sumMap", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiff_of_contMDiff_inl", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Constructions", "is_tactic_proof": true, "tactics": ["nontriviality", "inhabit", "let", "have", "rw", "rw", "apply", "intro", "rw", "use"], "tactic_count": 10}
{"name": "contMDiff_of_contMDiff_inr", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Constructions", "is_tactic_proof": true, "tactics": ["nontriviality", "inhabit", "let", "have", "rw", "rw", "apply", "intro", "rw", "use"], "tactic_count": 10}
{"name": "contMDiff_sum_map", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiff.swap", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffWithinAtProp", "kind": "definition", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiffWithinAtProp_self_source", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "contDiffWithinAtProp_self", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiffWithinAtProp_self_target", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiffWithinAt_localInvariantProp_of_le", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiffWithinAt_localInvariantProp", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiffWithinAtProp_mono_of_mem_nhdsWithin", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": true, "tactics": ["refine", "refine", "rwa"], "tactic_count": 3}
{"name": "contDiffWithinAtProp_id", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": true, "tactics": ["simp", "have", "refine", "simp", "simp"], "tactic_count": 5}
{"name": "ContMDiffWithinAt", "kind": "definition", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffAt", "kind": "definition", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffAt_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffOn", "kind": "definition", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiff", "kind": "definition", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffWithinAt.of_le", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "ContMDiffAt.of_le", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffOn.of_le", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiff.of_le", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiff.contMDiffAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffWithinAt_univ", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffOn_empty", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffOn_univ", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "contMDiffWithinAt_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "contMDiffWithinAt_iff'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "contMDiffWithinAt_iff_target", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": true, "tactics": ["simp_rw", "have", "and_iff_left_of_imp", "simp_rw", "rfl"], "tactic_count": 5}
{"name": "contMDiffAt_iff_target", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "contMDiffWithinAt_iff_source", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": true, "tactics": ["simp_rw", "have", "refine", "apply", "exact", "exact", "exact", "rw", "have", "apply", "intro", "have", "simpa", "apply", "intro", "have", "simp", "simp", "rw", "simp"], "tactic_count": 20}
{"name": "contMDiffAt_iff_source", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "contMDiffWithinAt_iff_source_of_mem_maximalAtlas", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": true, "tactics": ["have", "simp_rw", "contDiffWithinAtProp_self_source,", "rfl"], "tactic_count": 4}
{"name": "contMDiffWithinAt_iff_source_of_mem_source", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffAt_iff_source_of_mem_source", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "contMDiffWithinAt_iff_target_of_mem_source", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": true, "tactics": ["simp_rw", "rw", "and_congr_right]", "intro", "simp_rw", "simp_rw", "rw", "simp_rw", "rfl"], "tactic_count": 9}
{"name": "contMDiffAt_iff_target_of_mem_source", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "contMDiffWithinAt_iff_of_mem_maximalAtlas", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffWithinAt_iff_image", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp_rw"], "tactic_count": 3}
{"name": "contMDiffWithinAt_iff_of_mem_source", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffWithinAt_iff_of_mem_source'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": true, "tactics": ["refine", "rw", "rw", "rw", "set", "refine", "rw", "map_extChartAt_nhdsWithin", "exact"], "tactic_count": 9}
{"name": "contMDiffAt_iff_of_mem_source", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffOn_iff_of_mem_maximalAtlas", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "contMDiffOn_iff_of_mem_maximalAtlas'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffOn_iff_of_subset_source", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffOn_iff_of_subset_source'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "contMDiffOn_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": true, "tactics": ["constructor", "intro", "refine", "simp", "let", "have", "specialize", "have", "have", "convert", "simp", "mfld_set_tac", "rintro", "refine", "refine", "dsimp", "convert", "mfld_set_tac"], "tactic_count": 18}
{"name": "contMDiffOn_zero_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": true, "tactics": ["rw", "refine", "intro", "rw", "apply", "apply", "simp", "exact", "intro", "simp", "exact"], "tactic_count": 11}
{"name": "contMDiffOn_iff_target", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": false, "tactics": ["simp", "and_congr_right_iff]", "intro", "constructor", "refine", "have", "convert", "simp", "exact"], "tactic_count": 9}
{"name": "contMDiff_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "contMDiff_iff_target", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "contMDiff_zero_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ContMDiffWithinAt.of_succ", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffAt.of_succ", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffOn.of_succ", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiff.of_succ", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffWithinAt.continuousWithinAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffAt.continuousAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffOn.continuousOn", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiff.continuous", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffWithinAt_infty", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffAt_infty", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffOn_infty", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiff_infty", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffWithinAt_iff_nat", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact", "exact"], "tactic_count": 4}
{"name": "contMDiffAt_iff_nat", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "contMDiffWithinAt_iff_le_ne_infty", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": true, "tactics": ["refine", "cases", "top", "coe"], "tactic_count": 4}
{"name": "contMDiffAt_iff_le_ne_infty", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": true, "tactics": ["simp", "rw"], "tactic_count": 2}
{"name": "ContMDiffWithinAt.mono_of_mem_nhdsWithin", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffWithinAt.mono", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffWithinAt_congr_set", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffWithinAt.congr_set", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffWithinAt_insert_self", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": true, "tactics": ["simp", "refine", "simp"], "tactic_count": 3}
{"name": "ContMDiffWithinAt.insert", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffWithinAt_congr_set'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "ContMDiffAt.contMDiffWithinAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffOn.mono", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiff.contMDiffOn", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffWithinAt_inter'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffWithinAt_inter", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffWithinAt.contMDiffAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffOn.contMDiffAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffOn_iff_source_of_mem_maximalAtlas", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "rw", "apply", "simp_rw"], "tactic_count": 5}
{"name": "contMDiffWithinAt_iff_contMDiffOn_nhds", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": true, "tactics": ["wlog", "rw", "rw", "refine", "rcases", "have", "extChartAt", "apply", "rw", "refine", "rw", "h.1.nhdsWithin_extChartAt_symm_preimage_inter_range", "exact", "have", "image_subset_iff.2", "have", "rintro", "exact", "rwa", "exact"], "tactic_count": 20}
{"name": "ContMDiffWithinAt.contMDiffOn'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": true, "tactics": ["have", "have", "ω", "rcases", "rcases", "rw", "exact", "rcases", "rcases", "rw", "exact"], "tactic_count": 11}
{"name": "ContMDiffWithinAt.contMDiffOn", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": true, "tactics": ["let", "exact"], "tactic_count": 2}
{"name": "contMDiffAt_iff_contMDiffOn_nhds", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "contMDiffAt_iff_contMDiffAt_nhds", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": true, "tactics": ["refine", "rw", "rintro", "refine", "exact"], "tactic_count": 5}
{"name": "contMDiffWithinAt_iff_contMDiffWithinAt_nhdsWithin", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": true, "tactics": ["refine", "rw", "rintro", "filter_upwards", "apply", "exact"], "tactic_count": 6}
{"name": "ContMDiffWithinAt.congr", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffWithinAt.congr'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffWithinAt_congr", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffWithinAt.congr_of_mem", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffWithinAt_congr_of_mem", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffWithinAt.congr_of_eventuallyEq", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffWithinAt.congr_of_eventuallyEq_of_mem", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.contMDiffWithinAt_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffAt.congr_of_eventuallyEq", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.contMDiffAt_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffOn.congr", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffOn_congr", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.ContMDiff.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Diffeomorph.self_trans_symm", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Diffeomorph.symm_trans_self", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Diffeomorph.symm_trans'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Diffeomorph.symm_toEquiv", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Diffeomorph.toEquiv_coe_symm", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Diffeomorph.image_eq_preimage_symm", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Diffeomorph.symm_image_eq_preimage", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Diffeomorph.range_comp", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Diffeomorph.image_symm_image", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Diffeomorph.symm_image_image", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Diffeomorph.toHomeomorph", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Diffeomorph.toHomeomorph_toEquiv", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Diffeomorph.symm_toHomeomorph", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Diffeomorph.coe_toHomeomorph", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Diffeomorph.coe_toHomeomorph_symm", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Diffeomorph.contMDiffWithinAt_comp_diffeomorph_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "simpa", "rw", "exact"], "tactic_count": 6}
{"name": "Diffeomorph.contMDiffOn_comp_diffeomorph_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Diffeomorph.contMDiffAt_comp_diffeomorph_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Diffeomorph.contMDiff_comp_diffeomorph_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Diffeomorph.contMDiffWithinAt_diffeomorph_comp_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Diffeomorph.contMDiffAt_diffeomorph_comp_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Diffeomorph.contMDiffOn_diffeomorph_comp_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Diffeomorph.contMDiff_diffeomorph_comp_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Diffeomorph.toOpenPartialHomeomorph_mdifferentiable", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Diffeomorph.uniqueMDiffOn_image_aux", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "Diffeomorph.uniqueMDiffOn_image", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Diffeomorph.uniqueMDiffOn_preimage", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Diffeomorph.uniqueDiffOn_image", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Diffeomorph.uniqueDiffOn_preimage", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.toDiffeomorph", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.coe_toDiffeomorph", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.symm_toDiffeomorph", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.coe_toDiffeomorph_symm", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.transContinuousLinearEquiv", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.coe_transContinuousLinearEquiv", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.coe_transContinuousLinearEquiv_symm", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.transContinuousLinearEquiv_range", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.coe_extChartAt_transContinuousLinearEquiv", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.coe_extChartAt_transContinuousLinearEquiv_symm", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.extChartAt_transContinuousLinearEquiv_target", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousLinearEquiv.instIsManifoldtransContinuousLinearEquiv", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": true, "tactics": ["refine", "refine", "simp"], "tactic_count": 3}
{"name": "ContinuousLinearEquiv.toTransContinuousLinearEquiv", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.contMDiffWithinAt_transContinuousLinearEquiv_right", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.contMDiffAt_transContinuousLinearEquiv_right", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.contMDiffOn_transContinuousLinearEquiv_right", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.contMDiff_transContinuousLinearEquiv_right", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.contMDiffWithinAt_transContinuousLinearEquiv_left", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.contMDiffAt_transContinuousLinearEquiv_left", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.contMDiffOn_transContinuousLinearEquiv_left", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.contMDiff_transContinuousLinearEquiv_left", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Diffeomorph.prodCongr", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Diffeomorph.prodCongr_symm", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Diffeomorph.coe_prodCongr", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Diffeomorph.prodComm", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Diffeomorph.prodComm_symm", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Diffeomorph.coe_prodComm", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Diffeomorph.prodAssoc", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Diffeomorph.sumCongr", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Diffeomorph.sumCongr_symm_symm", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Diffeomorph.sumCongr_coe", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Diffeomorph.sumCongr_inl", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Diffeomorph.sumCongr_inr", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Diffeomorph.sumComm", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Diffeomorph.sumComm_coe", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Diffeomorph.sumComm_symm", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Diffeomorph.sumComm_inl", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "Diffeomorph.sumComm_inr", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "Diffeomorph.sumAssoc", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Diffeomorph.sumAssoc_coe", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Diffeomorph.sumEmpty", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Diffeomorph.sumEmpty_toEquiv", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Diffeomorph.sumEmpty_apply_inl", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Diffeomorph.empty", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Diffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupLieAlgebra", "kind": "abbrev", "module": "Mathlib.Geometry.Manifold.GroupLieAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mulInvariantVectorField", "kind": "definition", "module": "Mathlib.Geometry.Manifold.GroupLieAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mulInvariantVectorField_add", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.GroupLieAlgebra", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "addInvariantVectorField_smul", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.GroupLieAlgebra", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "mulInvariantVectorField_smul", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.GroupLieAlgebra", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "instBracketGroupLieAlgebra", "kind": "instance", "module": "Mathlib.Geometry.Manifold.GroupLieAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupLieAlgebra.bracket_def", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.GroupLieAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inverse_mfderiv_mul_left", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.GroupLieAlgebra", "is_tactic_proof": true, "tactics": ["have", "have", "have", "rw", "rw", "have", "have", "rw", "rw", "inv_mul_cancel_left", "exact"], "tactic_count": 11}
{"name": "mpullback_mulInvariantVectorField", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.GroupLieAlgebra", "is_tactic_proof": true, "tactics": ["have", "ext", "simp", "have", "rw", "congr", "simp", "exact", "exact"], "tactic_count": 9}
{"name": "mulInvariantVectorField_eq_mpullback", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.GroupLieAlgebra", "is_tactic_proof": true, "tactics": ["have", "simp", "congr", "simp"], "tactic_count": 4}
{"name": "contMDiff_mulInvariantVectorField", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.GroupLieAlgebra", "is_tactic_proof": true, "tactics": ["multiplication", "composition", "is", "smooth", "and", "which", "have", "have", "rw", "norm_num", "let", "have", "let", "have", "let", "have", "let", "have", "contMDiff_equivTangentBundleProd_symm", "let", "have", "apply", "rw", "exact", "let", "convert", "simp", "simp", "rw", "simp"], "tactic_count": 30}
{"name": "contMDiffAt_mulInvariantVectorField", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.GroupLieAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiable_mulInvariantVectorField", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.GroupLieAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiableAt_mulInvariantVectorField", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.GroupLieAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mulInvariantVector_mlieBracket", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.GroupLieAlgebra", "is_tactic_proof": true, "tactics": ["ext", "rw", "mpullback_mulInvariantVectorField,", "exact", "exact", "exact", "exact"], "tactic_count": 7}
{"name": "instLieRingGroupLieAlgebra", "kind": "instance", "module": "Mathlib.Geometry.Manifold.GroupLieAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instLieAlgebraAddGroupLieAlgebra", "kind": "instance", "module": "Mathlib.Geometry.Manifold.GroupLieAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instLieAlgebraGroupLieAlgebra", "kind": "instance", "module": "Mathlib.Geometry.Manifold.GroupLieAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StructureGroupoid.compatible", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.HasGroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasGroupoid_of_le", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.HasGroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasGroupoid_inf_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.HasGroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasGroupoid_of_pregroupoid", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.HasGroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasGroupoid_model_space", "kind": "instance", "module": "Mathlib.Geometry.Manifold.HasGroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasGroupoid_continuousGroupoid", "kind": "instance", "module": "Mathlib.Geometry.Manifold.HasGroupoid", "is_tactic_proof": true, "tactics": ["refine", "rw", "simp"], "tactic_count": 3}
{"name": "StructureGroupoid.trans_restricted", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.HasGroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StructureGroupoid.maximalAtlas", "kind": "definition", "module": "Mathlib.Geometry.Manifold.HasGroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StructureGroupoid.subset_maximalAtlas", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.HasGroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StructureGroupoid.chart_mem_maximalAtlas", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.HasGroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_maximalAtlas_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.HasGroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StructureGroupoid.compatible_of_mem_maximalAtlas", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.HasGroupoid", "is_tactic_proof": true, "tactics": ["refine", "set", "let", "have", "have", "simp", "exact", "refine", "have", "have", "have", "have", "calc", "exact"], "tactic_count": 14}
{"name": "StructureGroupoid.mem_maximalAtlas_of_eqOnSource", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.HasGroupoid", "is_tactic_proof": true, "tactics": ["intro", "obtain", "exact"], "tactic_count": 3}
{"name": "StructureGroupoid.id_mem_maximalAtlas", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.HasGroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StructureGroupoid.mem_maximalAtlas_of_mem_groupoid", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.HasGroupoid", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "StructureGroupoid.maximalAtlas_mono", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.HasGroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Geometry.Manifold.HasGroupoid.0.restr_mem_maximalAtlas_aux1", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.HasGroupoid", "is_tactic_proof": false, "tactics": ["have", "rw", "exact", "have", "apply", "exact", "refine", "exact"], "tactic_count": 8}
{"name": "_private.Mathlib.Geometry.Manifold.HasGroupoid.0.restr_mem_maximalAtlas_aux2", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.HasGroupoid", "is_tactic_proof": false, "tactics": ["have", "rw", "exact", "have", "rw", "exact", "exact"], "tactic_count": 7}
{"name": "restr_mem_maximalAtlas", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.HasGroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.singletonChartedSpace", "kind": "definition", "module": "Mathlib.Geometry.Manifold.HasGroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.singletonChartedSpace_chartAt_eq", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.HasGroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.singletonChartedSpace_chartAt_source", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.HasGroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.singletonChartedSpace_mem_atlas_eq", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.HasGroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.singleton_hasGroupoid", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.HasGroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsOpenEmbedding.singletonChartedSpace", "kind": "definition", "module": "Mathlib.Geometry.Manifold.HasGroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsOpenEmbedding.singletonChartedSpace_chartAt_eq", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.HasGroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsOpenEmbedding.singleton_hasGroupoid", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.HasGroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.instChartedSpace", "kind": "instance", "module": "Mathlib.Geometry.Manifold.HasGroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.chartAt_eq", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.HasGroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.chart_eq", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.HasGroupoid", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "TopologicalSpace.Opens.chart_eq'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.HasGroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.instHasGroupoid", "kind": "instance", "module": "Mathlib.Geometry.Manifold.HasGroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.chartAt_subtype_val_symm_eventuallyEq", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.HasGroupoid", "is_tactic_proof": true, "tactics": ["set", "have", "apply", "exact", "exact"], "tactic_count": 5}
{"name": "TopologicalSpace.Opens.chartAt_inclusion_symm_eventuallyEq", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.HasGroupoid", "is_tactic_proof": true, "tactics": ["set", "have", "apply", "exact", "exact"], "tactic_count": 5}
{"name": "StructureGroupoid.subtypeRestr_mem_maximalAtlas", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.HasGroupoid", "is_tactic_proof": true, "tactics": ["intro", "obtain", "rw", "exact"], "tactic_count": 4}
{"name": "Structomorph.refl", "kind": "definition", "module": "Mathlib.Geometry.Manifold.HasGroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Structomorph.symm", "kind": "definition", "module": "Mathlib.Geometry.Manifold.HasGroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Structomorph.trans", "kind": "definition", "module": "Mathlib.Geometry.Manifold.HasGroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StructureGroupoid.restriction_mem_maximalAtlas_subtype", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.HasGroupoid", "is_tactic_proof": true, "tactics": ["intro", "have", "obtain", "rw", "rw", "let", "have", "simp", "toFun_eq_coe,", "preimage_univ,", "exact", "exact"], "tactic_count": 12}
{"name": "OpenPartialHomeomorph.toStructomorph", "kind": "definition", "module": "Mathlib.Geometry.Manifold.HasGroupoid", "is_tactic_proof": true, "tactics": ["intro", "by_cases", "exact", "mem_groupoid", "have", "isEmpty_coe_sort.mpr", "exact", "mem_groupoid"], "tactic_count": 8}
{"name": "Manifold.ImmersionAtProp", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold.isLocalSourceTargetProperty_immersionAtProp", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold.definition._@.Mathlib.Geometry.Manifold.Immersion.4110262934._hygCtx._hyg.128", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold.wrapped._@.Mathlib.Geometry.Manifold.Immersion.4110262934._hygCtx._hyg.128", "kind": "opaque", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold.IsImmersionAtOfComplement", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold.IsImmersionAtOfComplement_def", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": true, "tactics": ["intros", "delta", "rw", "rfl"], "tactic_count": 4}
{"name": "Manifold.definition._@.Mathlib.Geometry.Manifold.Immersion.3457767310._hygCtx._hyg.128", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold.wrapped._@.Mathlib.Geometry.Manifold.Immersion.3457767310._hygCtx._hyg.128", "kind": "opaque", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold.IsImmersionAt", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold.IsImmersionAt_def", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": true, "tactics": ["intros", "delta", "rw", "rfl"], "tactic_count": 4}
{"name": "Manifold.IsImmersionAtOfComplement.mk_of_charts", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": true, "tactics": ["rw", "use", "use"], "tactic_count": 3}
{"name": "Manifold.IsImmersionAtOfComplement.mk_of_continuousAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": true, "tactics": ["rw", "exact", "hcodChart"], "tactic_count": 3}
{"name": "Manifold.IsImmersionAtOfComplement.domChart", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Manifold.IsImmersionAtOfComplement.codChart", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Manifold.IsImmersionAtOfComplement.mem_domChart_source", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Manifold.IsImmersionAtOfComplement.mem_codChart_source", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Manifold.IsImmersionAtOfComplement.domChart_mem_maximalAtlas", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Manifold.IsImmersionAtOfComplement.codChart_mem_maximalAtlas", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Manifold.IsImmersionAtOfComplement.source_subset_preimage_source", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
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{"name": "Manifold.IsImmersionAtOfComplement.writtenInCharts", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Manifold.IsImmersionAtOfComplement.property", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Manifold.IsImmersionAtOfComplement.map_target_subset_target", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": false, "tactics": ["rw", "have", "grw"], "tactic_count": 3}
{"name": "Manifold.IsImmersionAtOfComplement.target_subset_preimage_target", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold.IsImmersionAtOfComplement.congr_of_eventuallyEq", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Manifold.IsImmersionAtOfComplement.congr_iff_of_eventuallyEq", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Manifold.IsImmersionAtOfComplement.small", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold.IsImmersionAtOfComplement.smallComplement", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold.IsImmersionAtOfComplement.instNormedAddCommGroupSmallComplement", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": true, "tactics": ["haveI", "unfold", "infer_instance"], "tactic_count": 3}
{"name": "Manifold.IsImmersionAtOfComplement.instNormedSpaceSmallComplement", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": true, "tactics": ["haveI", "unfold", "infer_instance"], "tactic_count": 3}
{"name": "Manifold.IsImmersionAtOfComplement.smallEquiv", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold.IsImmersionAtOfComplement.trans_F", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": true, "tactics": ["rewrite", "refine", "h.codChart_mem_maximalAtlas,", "use", "apply", "intro", "simp"], "tactic_count": 7}
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{"name": "IsOpen.isImmersionAtOfComplement", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Manifold.IsImmersionAtOfComplement.prodMap", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": true, "tactics": ["rw", "apply", "rintro", "use", "rw", "exact"], "tactic_count": 6}
{"name": "Manifold.IsImmersionAtOfComplement.isImmersionAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": true, "tactics": ["rw", "use", "exact"], "tactic_count": 3}
{"name": "Manifold.IsImmersionAtOfComplement.of_opens", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": false, "tactics": ["apply", "intro", "suffices", "trans", "congr", "apply", "simp_all", "exact"], "tactic_count": 8}
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{"name": "Manifold.IsImmersionAt.mk_of_continuousAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": true, "tactics": ["rw", "have", "apply", "use", "rwa"], "tactic_count": 5}
{"name": "Manifold.IsImmersionAt.complement", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Manifold.IsImmersionAt.instNormedAddCommGroupComplement", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Manifold.IsImmersionAt.instNormedSpaceComplement", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Manifold.IsImmersionAt.isImmersionAtOfComplement_complement", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Manifold.IsImmersionAt.domChart", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold.IsImmersionAt.codChart", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold.IsImmersionAt.mem_domChart_source", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold.IsImmersionAt.mem_codChart_source", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold.IsImmersionAt.domChart_mem_maximalAtlas", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold.IsImmersionAt.codChart_mem_maximalAtlas", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold.IsImmersionAt.source_subset_preimage_source", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold.IsImmersionAt.equiv", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold.IsImmersionAt.writtenInCharts", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold.IsImmersionAt.property", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold.IsImmersionAt.map_target_subset_target", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold.IsImmersionAt.target_subset_preimage_target", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold.IsImmersionAt.congr_of_eventuallyEq", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": true, "tactics": ["rw", "use", "exact"], "tactic_count": 3}
{"name": "Manifold.IsImmersionAt.congr_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.isImmersionAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Manifold.IsImmersionAt.prodMap", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold.IsImmersionAt.of_opens", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": true, "tactics": ["rw", "use", "apply"], "tactic_count": 3}
{"name": "Manifold.IsImmersionOfComplement", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold.IsImmersion", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold.IsImmersionOfComplement.isImmersionAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold.IsImmersionOfComplement.congr", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold.IsImmersionOfComplement.trans_F", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold.IsImmersionOfComplement.congr_F", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold.IsImmersionOfComplement.prodMap", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold.IsImmersionOfComplement.isImmersion", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "use", "exact", "inhabit", "let", "use", "exact"], "tactic_count": 8}
{"name": "Manifold.IsImmersionOfComplement.id", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": true, "tactics": ["intro", "apply", "intro", "have", "rw", "simpa"], "tactic_count": 6}
{"name": "Manifold.IsImmersionOfComplement.of_opens", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold.IsImmersion.complement", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold.IsImmersion.instNormedAddCommGroupComplement", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold.IsImmersion.instNormedSpaceComplement", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold.IsImmersion.isImmersionOfComplement_complement", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold.IsImmersion.isImmersionAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": true, "tactics": ["rw", "use"], "tactic_count": 2}
{"name": "Manifold.IsImmersion.congr", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold.IsImmersion.prodMap", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold.IsImmersion.id", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold.IsImmersion.of_opens", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Immersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instOneTangentSpaceRealModelWithCornersSelf", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Instances.Icc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "definition._@.Mathlib.Geometry.Manifold.Instances.Icc.3024910664._hygCtx._hyg.2", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Instances.Icc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "wrapped._@.Mathlib.Geometry.Manifold.Instances.Icc.3024910664._hygCtx._hyg.2", "kind": "opaque", "module": "Mathlib.Geometry.Manifold.Instances.Icc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "oneTangentSpaceIcc_def", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Instances.Icc", "is_tactic_proof": true, "tactics": ["intros", "delta", "rw", "rfl"], "tactic_count": 4}
{"name": "instOneTangentSpaceRealEuclideanSpaceFinOfNatNatEuclideanHalfSpaceModelWithCornersEuclideanHalfSpaceElemIcc", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Instances.Icc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiff_subtype_coe_Icc", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Instances.Icc", "is_tactic_proof": true, "tactics": ["intro", "rw", "refine", "suffices", "split_ifs", "simp", "simp", "modelWithCornersEuclideanHalfSpace,", "rw", "have", "apply", "simpa", "have", "apply", "simpa", "filter_upwards", "rw", "linarith", "simp", "simp", "simp", "modelWithCornersEuclideanHalfSpace,", "rw", "have", "apply", "simpa", "have", "apply", "simpa", "filter_upwards", "rw", "linarith"], "tactic_count": 32}
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{"name": "instTopologicalSpaceEuclideanHalfSpace", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Instances.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instTopologicalSpaceEuclideanQuadrant", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Instances.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instZeroEuclideanHalfSpace", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Instances.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instZeroEuclideanQuadrant", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Instances.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInhabitedEuclideanHalfSpace", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Instances.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInhabitedEuclideanQuadrant", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Instances.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanQuadrant.ext", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Instances.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanHalfSpace.ext", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Instances.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanHalfSpace.convex", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Instances.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanQuadrant.convex", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Instances.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanHalfSpace.pathConnectedSpace", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Instances.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanQuadrant.pathConnectedSpace", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Instances.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instLocPathConnectedSpaceEuclideanHalfSpace", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Instances.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instLocPathConnectedSpaceEuclideanQuadrant", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Instances.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "range_euclideanHalfSpace", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Instances.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "interior_halfSpace", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Instances.Real", "is_tactic_proof": true, "tactics": ["let", "change", "rw", "fun_prop"], "tactic_count": 4}
{"name": "closure_halfSpace", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Instances.Real", "is_tactic_proof": true, "tactics": ["let", "change", "rw", "fun_prop"], "tactic_count": 4}
{"name": "closure_open_halfSpace", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Instances.Real", "is_tactic_proof": true, "tactics": ["let", "change", "rw", "fun_prop"], "tactic_count": 4}
{"name": "frontier_halfSpace", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Instances.Real", "is_tactic_proof": true, "tactics": ["rw", "ext", "simpa"], "tactic_count": 3}
{"name": "range_euclideanQuadrant", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Instances.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "interior_euclideanQuadrant", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Instances.Real", "is_tactic_proof": true, "tactics": ["let", "have", "have", "rw", "apply", "rw", "fun_prop"], "tactic_count": 7}
{"name": "modelWithCornersEuclideanHalfSpace", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Instances.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "modelWithCornersEuclideanQuadrant", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Instances.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold.term𝓡_", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Instances.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold._aux_Mathlib_Geometry_Manifold_Instances_Real___macroRules_Manifold_term𝓡__1", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Instances.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold._aux_Mathlib_Geometry_Manifold_Instances_Real___delab_app_Manifold_term𝓡__1", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Instances.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold.term𝓡∂_", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Instances.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold._aux_Mathlib_Geometry_Manifold_Instances_Real___macroRules_Manifold_term𝓡∂__1", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Instances.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold._aux_Mathlib_Geometry_Manifold_Instances_Real___delab_app_Manifold_term𝓡∂__1", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Instances.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "modelWithCornersEuclideanHalfSpace_zero", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Instances.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "range_modelWithCornersEuclideanHalfSpace", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Instances.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "interior_range_modelWithCornersEuclideanHalfSpace", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Instances.Real", "is_tactic_proof": true, "tactics": ["calc", "interior", "congr", "apply"], "tactic_count": 4}
{"name": "frontier_range_modelWithCornersEuclideanHalfSpace", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Instances.Real", "is_tactic_proof": true, "tactics": ["calc", "frontier", "congr", "apply"], "tactic_count": 4}
{"name": "IccLeftChart", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Instances.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fact.Manifold.instLeReal", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Instances.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IccLeftChart_extend_bot", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Instances.Real", "is_tactic_proof": true, "tactics": ["norm_num", "congr"], "tactic_count": 2}
{"name": "iccLeftChart_extend_zero", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Instances.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IccLeftChart_extend_interior_pos", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Instances.Real", "is_tactic_proof": true, "tactics": ["simp_rw", "norm_num"], "tactic_count": 2}
{"name": "IccLeftChart_extend_bot_mem_frontier", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Instances.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IccRightChart", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Instances.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IccRightChart_extend_top", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Instances.Real", "is_tactic_proof": true, "tactics": ["norm_num", "congr"], "tactic_count": 2}
{"name": "IccRightChart_extend_top_mem_frontier", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Instances.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "instIccChartedSpace", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Instances.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Icc_chartedSpaceChartAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Instances.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Icc_chartedSpaceChartAt_of_le_top", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Instances.Real", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Icc_chartedSpaceChartAt_of_top_le", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Instances.Real", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Icc_isBoundaryPoint_bot", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Instances.Real", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Icc_isBoundaryPoint_top", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Instances.Real", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Icc_isInteriorPoint_interior", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Instances.Real", "is_tactic_proof": false, "tactics": ["rw", "interior_range_modelWithCornersEuclideanHalfSpace]", "exact"], "tactic_count": 3}
{"name": "boundary_Icc", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Instances.Real", "is_tactic_proof": true, "tactics": ["ext", "rcases", "have", "rw", "apply", "have", "rw", "apply", "apply", "simpa", "rintro"], "tactic_count": 11}
{"name": "boundary_product", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Instances.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "instIsManifoldIcc", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Instances.Real", "is_tactic_proof": false, "tactics": ["have", "apply", "intro", "simp", "rcases", "exact", "apply", "rintro", "simp", "lt_sub_iff_add_lt,", "rw", "ext", "rw", "simp", "update_self,", "abel", "apply", "rintro", "simp", "max_eq_left", "rw", "ext", "rw", "simp", "mfld_simps]", "abel", "exact"], "tactic_count": 27}
{"name": "instChartedSpaceEuclideanHalfSpaceOfNatNatElemRealIcc", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Instances.Real", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "instIsManifoldRealEuclideanSpaceFinOfNatNatEuclideanHalfSpaceModelWithCornersEuclideanHalfSpaceElemIcc", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Instances.Real", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "stereoToFun", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Instances.Sphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "stereoToFun_apply", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Instances.Sphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiffOn_stereoToFun", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Instances.Sphere", "is_tactic_proof": true, "tactics": ["refine", "refine", "exact", "intro", "exact"], "tactic_count": 5}
{"name": "continuousOn_stereoToFun", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Instances.Sphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "stereoInvFunAux", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Instances.Sphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "stereoInvFunAux_apply", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Instances.Sphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "stereoInvFunAux_mem", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Instances.Sphere", "is_tactic_proof": true, "tactics": ["have", "suffices", "simp", "stereoInvFunAux_apply,", "suffices", "simpa", "rw", "simp", "ring"], "tactic_count": 9}
{"name": "hasFDerivAt_stereoInvFunAux", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Instances.Sphere", "is_tactic_proof": false, "tactics": ["have", "convert", "simp", "have", "convert", "have", "convert", "ext", "simp", "convert", "ext", "simp"], "tactic_count": 12}
{"name": "hasFDerivAt_stereoInvFunAux_comp_coe", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Instances.Sphere", "is_tactic_proof": false, "tactics": ["have", "hasFDerivAt_stereoInvFunAux", "refine"], "tactic_count": 3}
{"name": "contDiff_stereoInvFunAux", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Instances.Sphere", "is_tactic_proof": true, "tactics": ["have", "have", "refine", "intro", "nlinarith", "have", "refine", "exact", "exact"], "tactic_count": 9}
{"name": "stereoInvFun", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Instances.Sphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "stereoInvFun_apply", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Instances.Sphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "stereoInvFun_ne_north_pole", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Instances.Sphere", "is_tactic_proof": true, "tactics": ["refine", "rw", "have", "have", "rw", "linarith", "positivity", "simpa", "simpa"], "tactic_count": 9}
{"name": "continuous_stereoInvFun", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Instances.Sphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "stereo_left_inv", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Instances.Sphere", "is_tactic_proof": true, "tactics": ["ext", "simp", "set", "set", "have", "rw", "rfl", "have", "have", "have", "convert", "simp", "simp", "exact", "sq", "have", "have", "linarith", "rw", "simp", "match_scalars", "field_simp", "linear_combination", "field_simp", "linear_combination"], "tactic_count": 25}
{"name": "stereo_right_inv", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Instances.Sphere", "is_tactic_proof": false, "tactics": ["simp", "have", "have", "have", "rw", "match_scalars", "simp", "ring"], "tactic_count": 8}
{"name": "stereographic", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Instances.Sphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "stereographic_apply", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Instances.Sphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "stereographic_source", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Instances.Sphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "stereographic_target", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Instances.Sphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "stereographic_apply_neg", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Instances.Sphere", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "stereographic_neg_apply", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Instances.Sphere", "is_tactic_proof": true, "tactics": ["convert", "ext1", "simp"], "tactic_count": 3}
{"name": "surjective_stereographic", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Instances.Sphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpenEmbedding_stereographic_symm", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Instances.Sphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "stereographic'", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Instances.Sphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "stereographic'_source", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Instances.Sphere", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "stereographic'_target", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Instances.Sphere", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "EuclideanSpace.instChartedSpaceSphere", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Instances.Sphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instChartedSpaceEuclideanSpaceRealFinElemHAddNatOfNatSphere", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Instances.Sphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sphere_ext_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Instances.Sphere", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "stereographic'_symm_apply", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Instances.Sphere", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "EuclideanSpace.instIsManifoldSphere", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Instances.Sphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsManifoldRealEuclideanSpaceFinModelWithCornersSelfTopWithTopENatElemHAddNatOfNatSphere", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Instances.Sphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiff_coe_sphere", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Instances.Sphere", "is_tactic_proof": true, "tactics": ["rw", "constructor", "exact", "intro", "let", "exact"], "tactic_count": 6}
{"name": "ContMDiff.codRestrict_sphere", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Instances.Sphere", "is_tactic_proof": true, "tactics": ["rw", "refine", "intro", "let", "have", "have", "have", "convert", "ext", "have", "have", "rw", "exact", "simp"], "tactic_count": 14}
{"name": "contMDiff_neg_sphere", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Instances.Sphere", "is_tactic_proof": true, "tactics": ["apply", "apply", "exact"], "tactic_count": 3}
{"name": "_private.Mathlib.Geometry.Manifold.Instances.Sphere.0.stereographic'_neg", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Instances.Sphere", "is_tactic_proof": true, "tactics": ["dsimp", "simp", "apply"], "tactic_count": 3}
{"name": "range_mfderiv_coe_sphere", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Instances.Sphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mfderiv_coe_sphere_injective", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Instances.Sphere", "is_tactic_proof": true, "tactics": ["rw", "simp", "let", "suffices", "convert", "apply", "have", "convert", "simp", "have", "refine", "rw", "simpa"], "tactic_count": 13}
{"name": "finrank_real_complex_fact'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Instances.Sphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instChartedSpaceEuclideanSpaceRealFinOfNatNatCircle", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Instances.Sphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsManifoldRealEuclideanSpaceFinOfNatNatModelWithCornersSelfTopWithTopENatCircle", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Instances.Sphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instLieGroupRealEuclideanSpaceFinOfNatNatModelWithCornersSelfTopWithTopENatCircle", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Instances.Sphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiff_circleExp", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Instances.Sphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.instChartedSpace", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Instances.UnitsOfNormedAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.chartAt_apply", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Instances.UnitsOfNormedAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.chartAt_source", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Instances.UnitsOfNormedAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.instIsManifoldModelWithCornersSelf", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Instances.UnitsOfNormedAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.contMDiff_val", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Instances.UnitsOfNormedAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.instLieGroupModelWithCornersSelf", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Instances.UnitsOfNormedAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units._example", "kind": "example", "module": "Mathlib.Geometry.Manifold.Instances.UnitsOfNormedAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMIntegralCurveOn", "kind": "definition", "module": "Mathlib.Geometry.Manifold.IntegralCurve.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMIntegralCurveAt", "kind": "definition", "module": "Mathlib.Geometry.Manifold.IntegralCurve.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMIntegralCurve", "kind": "definition", "module": "Mathlib.Geometry.Manifold.IntegralCurve.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMIntegralCurve.isMIntegralCurveOn", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IntegralCurve.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isMIntegralCurve_iff_isMIntegralCurveOn", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IntegralCurve.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isMIntegralCurveAt_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IntegralCurve.Basic", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "obtain", "exact", "rintro", "rw", "obtain", "refine", "intro", "apply", "rw", "exact"], "tactic_count": 13}
{"name": "isMIntegralCurveAt_iff'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IntegralCurve.Basic", "is_tactic_proof": true, "tactics": ["rw", "constructor", "intro", "rw", "obtain", "refine", "intro", "exact"], "tactic_count": 8}
{"name": "IsMIntegralCurve.isMIntegralCurveAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IntegralCurve.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isMIntegralCurve_iff_isMIntegralCurveAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IntegralCurve.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMIntegralCurveOn.mono", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IntegralCurve.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMIntegralCurveAt.hasMFDerivAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IntegralCurve.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMIntegralCurveOn.isMIntegralCurveAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IntegralCurve.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMIntegralCurveAt.isMIntegralCurveOn", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IntegralCurve.Basic", "is_tactic_proof": true, "tactics": ["intro", "apply", "obtain", "exact"], "tactic_count": 4}
{"name": "isMIntegralCurveOn_iff_isMIntegralCurveAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IntegralCurve.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMIntegralCurveOn.continuousWithinAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IntegralCurve.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMIntegralCurveOn.continuousOn", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IntegralCurve.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMIntegralCurveAt.continuousAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IntegralCurve.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMIntegralCurve.continuous", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IntegralCurve.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMIntegralCurveOn.hasDerivWithinAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IntegralCurve.Basic", "is_tactic_proof": true, "tactics": ["replace", "rw", "apply", "rw", "intro", "rw", "mfderiv_chartAt_eq_tangentCoordChange", "rfl"], "tactic_count": 8}
{"name": "IsMIntegralCurveAt.eventually_hasDerivAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IntegralCurve.Basic", "is_tactic_proof": false, "tactics": ["apply", "eventually_mem_nhds_iff.mpr", "hγ", "rintro", "have", "rw", "rw", "apply", "rw", "intro", "rw", "mfderiv_chartAt_eq_tangentCoordChange", "rfl"], "tactic_count": 13}
{"name": "exists_isMIntegralCurveAt_of_contMDiffAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IntegralCurve.ExistUnique", "is_tactic_proof": true, "tactics": ["rw", "obtain", "obtain", "hv.contDiffAt", "t₀", "simp_rw", "have", "have", "rw", "have", "hcont", "rw", "obtain", "refine", "isMIntegralCurveAt_iff.mpr", "intro", "let", "have", "fderivWithin", "rw", "have", "have", "have", "have", "apply", "refine", "simp", "change", "rw", "tangentCoordChange_comp", "apply", "apply", "mem_nhds_iff.mpr", "isOpen_interior,", "rw", "exact"], "tactic_count": 36}
{"name": "exists_isMIntegralCurveAt_of_contMDiffAt_boundaryless", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IntegralCurve.ExistUnique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isMIntegralCurveAt_eventuallyEq_of_contMDiffAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IntegralCurve.ExistUnique", "is_tactic_proof": true, "tactics": ["set", "tangentCoordChange", "hv", "rw", "obtain", "obtain", "have", "have", "eventually_mem_nhds_iff.mpr", "have", "mem_preimage.mp", "have", "apply", "apply", "rintro", "rw", "apply", "congr", "apply", "rw", "exact", "have", "apply", "intro", "rw", "suffices", "exact"], "tactic_count": 27}
{"name": "isMIntegralCurveAt_eventuallyEq_of_contMDiffAt_boundaryless", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IntegralCurve.ExistUnique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isMIntegralCurveOn_Ioo_eqOn_of_contMDiff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IntegralCurve.ExistUnique", "is_tactic_proof": true, "tactics": ["set", "suffices", "apply", "rw", "image_subset_image_iff", "intro", "rw", "revert", "apply", "rw", "rintro", "apply", "rw", "exact", "rw", "rintro", "apply", "rw", "exact", "rw", "intro", "have", "have", "isMIntegralCurveAt_eventuallyEq_of_contMDiffAt", "apply", "exact"], "tactic_count": 26}
{"name": "isMIntegralCurveOn_Ioo_eqOn_of_contMDiff_boundaryless", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IntegralCurve.ExistUnique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isMIntegralCurve_eq_of_contMDiff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IntegralCurve.ExistUnique", "is_tactic_proof": true, "tactics": ["ext", "obtain", "obtain", "obtain", "obtain", "obtain", "exact", "exact", "isMIntegralCurveOn_Ioo_eqOn_of_contMDiff"], "tactic_count": 9}
{"name": "isMIntegralCurve_Ioo_eq_of_contMDiff_boundaryless", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IntegralCurve.ExistUnique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMIntegralCurve.periodic_of_eq", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IntegralCurve.ExistUnique", "is_tactic_proof": true, "tactics": ["apply", "rw"], "tactic_count": 2}
{"name": "IsMIntegralCurve.periodic_xor_injective", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IntegralCurve.ExistUnique", "is_tactic_proof": true, "tactics": ["rw", "refine", "intro", "rw", "push_neg", "obtain", "refine", "rw", "exact", "by_cases", "rw", "exact", "rw", "exact"], "tactic_count": 14}
{"name": "IsMIntegralCurveOn.comp_add", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IntegralCurve.Transform", "is_tactic_proof": true, "tactics": ["intro", "rw", "apply", "refine", "simp", "exact"], "tactic_count": 6}
{"name": "isMIntegralCurveOn_comp_add", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IntegralCurve.Transform", "is_tactic_proof": true, "tactics": ["refine", "convert", "ext", "simp", "simp"], "tactic_count": 5}
{"name": "isMIntegralCurveOn_comp_sub", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IntegralCurve.Transform", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsMIntegralCurveAt.comp_add", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IntegralCurve.Transform", "is_tactic_proof": true, "tactics": ["rw", "obtain", "refine", "convert", "rw", "simp_rw"], "tactic_count": 6}
{"name": "isMIntegralCurveAt_comp_add", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IntegralCurve.Transform", "is_tactic_proof": true, "tactics": ["refine", "convert", "ext", "simp", "simp"], "tactic_count": 5}
{"name": "isMIntegralCurveAt_comp_sub", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IntegralCurve.Transform", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsMIntegralCurve.comp_add", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IntegralCurve.Transform", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "isMIntegralCurve_comp_add", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IntegralCurve.Transform", "is_tactic_proof": true, "tactics": ["refine", "convert", "ext", "simp"], "tactic_count": 4}
{"name": "isMIntegralCurve_comp_sub", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IntegralCurve.Transform", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsMIntegralCurveOn.comp_mul", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IntegralCurve.Transform", "is_tactic_proof": true, "tactics": ["intro", "rw", "refine", "simp", "exact"], "tactic_count": 5}
{"name": "isMIntegralCurveOn_comp_mul_ne_zero", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IntegralCurve.Transform", "is_tactic_proof": true, "tactics": ["refine", "convert", "ext", "simp", "simp", "simp"], "tactic_count": 6}
{"name": "IsMIntegralCurveAt.comp_mul_ne_zero", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IntegralCurve.Transform", "is_tactic_proof": true, "tactics": ["rw", "obtain", "refine", "convert", "ext", "rw", "abs_mul,"], "tactic_count": 7}
{"name": "isMIntegralCurveAt_comp_mul_ne_zero", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IntegralCurve.Transform", "is_tactic_proof": true, "tactics": ["refine", "convert", "ext", "simp", "simp", "simp"], "tactic_count": 6}
{"name": "IsMIntegralCurve.comp_mul", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IntegralCurve.Transform", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "isMIntegralCurve_comp_mul_ne_zero", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IntegralCurve.Transform", "is_tactic_proof": true, "tactics": ["refine", "convert", "ext", "simp", "simp"], "tactic_count": 5}
{"name": "isMIntegralCurve_const", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IntegralCurve.Transform", "is_tactic_proof": true, "tactics": ["intro", "rw", "exact"], "tactic_count": 3}
{"name": "eqOn_of_isMIntegralCurveOn_Ioo", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IntegralCurve.UniformTime", "is_tactic_proof": false, "tactics": ["apply", "isMIntegralCurveOn_Ioo_eqOn_of_contMDiff_boundaryless", "rw", "exact", "apply"], "tactic_count": 5}
{"name": "eqOn_abs_add_one_of_isMIntegralCurveOn_Ioo", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IntegralCurve.UniformTime", "is_tactic_proof": true, "tactics": ["intro", "by_cases", "exact", "exact"], "tactic_count": 4}
{"name": "isMIntegralCurve_abs_add_one_of_isMIntegralCurveOn_Ioo", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IntegralCurve.UniformTime", "is_tactic_proof": true, "tactics": ["intro", "have", "rw", "exact", "apply", "exact", "rw", "refine", "have", "rw", "exact"], "tactic_count": 11}
{"name": "exists_isMIntegralCurve_iff_exists_isMIntegralCurveOn_Ioo", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IntegralCurve.UniformTime", "is_tactic_proof": true, "tactics": ["refine", "choose", "exact", "isMIntegralCurve_abs_add_one_of_isMIntegralCurveOn_Ioo"], "tactic_count": 4}
{"name": "eqOn_piecewise_of_isMIntegralCurveOn_Ioo", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IntegralCurve.UniformTime", "is_tactic_proof": true, "tactics": ["intro", "suffices", "by_cases", "rw", "apply", "simp", "rw", "apply", "isMIntegralCurveOn_Ioo_eqOn_of_contMDiff_boundaryless", "exact"], "tactic_count": 10}
{"name": "isMIntegralCurveOn_piecewise", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IntegralCurve.UniformTime", "is_tactic_proof": true, "tactics": ["intro", "by_cases", "rw", "apply", "hγ", "rw", "refine", "rw", "exact", "have", "rw", "rw", "apply", "hγ", "rw", "refine", "rw", "exact"], "tactic_count": 18}
{"name": "exists_isMIntegralCurve_of_isMIntegralCurveOn", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IntegralCurve.UniformTime", "is_tactic_proof": true, "tactics": ["let", "suffices", "rw", "rw", "intro", "obtain", "exact", "intro", "set", "obtain", "rw", "rw", "obtain", "obtain", "rw", "set", "have", "simp", "obtain", "rw", "set", "have", "simp", "simp_rw", "simp_rw", "have", "le_csSup", "set", "have", "rw", "suffices", "apply", "exact"], "tactic_count": 33}
{"name": "PartialEquiv.Continuous.invFun", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.range_eq_target", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ModelWithCorners.ofTargetUniv", "kind": "definition", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "modelWithCornersSelf", "kind": "definition", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold.term𝓘(_,_)", "kind": "definition", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold._aux_Mathlib_Geometry_Manifold_IsManifold_Basic___macroRules_Manifold_term𝓘(_,_)_1", "kind": "definition", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold._aux_Mathlib_Geometry_Manifold_IsManifold_Basic___unexpand_modelWithCornersSelf_1", "kind": "definition", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold.term𝓘(_)", "kind": "definition", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold._aux_Mathlib_Geometry_Manifold_IsManifold_Basic___macroRules_Manifold_term𝓘(_)_1", "kind": "definition", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.toFun'", "kind": "definition", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.instCoeFunForall", "kind": "instance", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.symm", "kind": "definition", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.Simps.apply", "kind": "definition", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.Simps.symm_apply", "kind": "definition", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.toPartialEquiv_coe", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.mk_coe", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.toPartialEquiv_coe_symm", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.mk_symm", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.continuous", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.continuousAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.continuousWithinAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.continuous_symm", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.continuousAt_symm", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.continuousWithinAt_symm", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.continuousOn_symm", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.target_eq", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ModelWithCorners.nonempty_interior", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.range_eq_univ_of_not_isRCLikeNormedField", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Convex.convex_isRCLikeNormedField", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": true, "tactics": ["letI", "letI", "simp", "intro", "convert", "rw", "rw"], "tactic_count": 7}
{"name": "ModelWithCorners.ofConvexRange", "kind": "definition", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.convex_range", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "letI", "have", "simp", "simp", "intro", "convert", "rw", "rfl", "rw", "rfl", "simp"], "tactic_count": 12}
{"name": "ModelWithCorners.uniqueDiffOn", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "letI", "letI", "apply", "simpa", "simp"], "tactic_count": 6}
{"name": "ModelWithCorners.range_subset_closure_interior", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "letI", "letI", "rw", "apply", "apply", "apply", "simp"], "tactic_count": 8}
{"name": "ModelWithCorners.left_inv", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": true, "tactics": ["refine"], "tactic_count": 1}
{"name": "ModelWithCorners.leftInverse", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.injective", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.symm_comp_self", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.rightInvOn", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.right_inv", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.preimage_image", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.image_eq", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "rw"], "tactic_count": 3}
{"name": "ModelWithCorners.isClosedEmbedding", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.isClosed_range", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.range_eq_closure_interior", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.map_nhds_eq", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.map_nhdsWithin_eq", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.image_mem_nhdsWithin", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.symm_map_nhdsWithin_image", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ModelWithCorners.symm_map_nhdsWithin_range", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ModelWithCorners.uniqueDiffOn_preimage", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ModelWithCorners.uniqueDiffOn_preimage_source", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.uniqueDiffWithinAt_image", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.symm_continuousWithinAt_comp_right_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": true, "tactics": ["refine", "have", "simp_rw", "rwa", "rw"], "tactic_count": 5}
{"name": "ModelWithCorners.locallyCompactSpace", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": ["have", "rw", "exact", "refine", "rintro", "exact"], "tactic_count": 6}
{"name": "ModelWithCorners.secondCountableTopology", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.t1Space", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "modelWithCornersSelf_partialEquiv", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "modelWithCornersSelf_coe", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "modelWithCornersSelf_coe_symm", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.prod", "kind": "definition", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.pi", "kind": "definition", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.tangent", "kind": "abbrev", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "modelWithCorners_prod_toPartialEquiv", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "modelWithCorners_prod_coe", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "modelWithCorners_prod_coe_symm", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "modelWithCornersSelf_prod", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": true, "tactics": ["ext1"], "tactic_count": 1}
{"name": "ModelWithCorners.range_prod", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "ModelWithCorners.range_eq_univ", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.toHomeomorph", "kind": "definition", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "modelWithCornersSelf_boundaryless", "kind": "instance", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.range_eq_univ_prod", "kind": "instance", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": true, "tactics": ["constructor", "dsimp", "rw", "univ_prod_univ]"], "tactic_count": 4}
{"name": "contDiffPregroupoid", "kind": "definition", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiffGroupoid", "kind": "definition", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiffGroupoid_le", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply", "intro", "exact"], "tactic_count": 4}
{"name": "contDiffGroupoid_zero_eq", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": true, "tactics": ["apply", "intro", "change", "rw", "simp", "constructor", "refine", "exact", "refine", "exact"], "tactic_count": 10}
{"name": "ContDiffGroupoid.mem_of_source_eq_empty", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "simp_all", "intro", "have", "simp_all"], "tactic_count": 7}
{"name": "ContinuousGroupoid.mem_of_source_eq_empty", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ofSet_mem_contDiffGroupoid", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": true, "tactics": ["rw", "suffices", "have", "exact"], "tactic_count": 4}
{"name": "symm_trans_mem_contDiffGroupoid", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiffGroupoid_prod", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "constructor", "have", "rw", "rw", "exact", "have", "rw", "rw", "exact"], "tactic_count": 11}
{"name": "instClosedUnderRestrictionContDiffGroupoid", "kind": "instance", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsManifold.mk'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isManifold_of_contDiffOn", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsManifoldModelSpace", "kind": "instance", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsManifold.of_le", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": ["have", "hasGroupoid_of_le", "exact"], "tactic_count": 3}
{"name": "IsManifold.instLEInftySomeENat", "kind": "instance", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsManifold.instLEInftyCastWithTopENat", "kind": "instance", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsManifold.instLEInftyOfNatWithTopENat", "kind": "instance", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsManifold.instLEInftyOfNatWithTopENat_1", "kind": "instance", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsManifold.instLEInftyOfNatWithTopENat_2", "kind": "instance", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsManifold.instOfSomeENatTopOfLEInfty", "kind": "instance", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsManifold.instOfTopWithTopENat", "kind": "instance", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsManifold.instOfNatWithTopENat", "kind": "instance", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": true, "tactics": ["suffices", "constructor", "intro", "rw", "trivial"], "tactic_count": 5}
{"name": "IsManifold.instOfNatWithTopENat_1", "kind": "instance", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsManifold.instOfNatWithTopENat_2", "kind": "instance", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsManifold.maximalAtlas", "kind": "definition", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsManifold.mem_maximalAtlas_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "IsManifold.subset_maximalAtlas", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsManifold.chart_mem_maximalAtlas", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsManifold.compatible_of_mem_maximalAtlas", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsManifold.maximalAtlas_subset_of_le", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsManifold.empty", "kind": "instance", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": true, "tactics": ["apply", "intro", "set", "have", "calc", "have", "calc", "t", "apply"], "tactic_count": 9}
{"name": "IsManifold.of_discreteTopology", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "IsManifold._example", "kind": "example", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsManifold.prod", "kind": "instance", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsManifold.mem_maximalAtlas_prod", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": true, "tactics": ["simp", "rintro", "rw", "constructor"], "tactic_count": 4}
{"name": "IsManifold.disjointUnion", "kind": "instance", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.isManifold_singleton", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsOpenEmbedding.isManifold_singleton", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.instIsManifoldSubtypeMem", "kind": "instance", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TangentSpace", "kind": "definition", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInhabitedTangentSpace", "kind": "instance", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TangentBundle", "kind": "abbrev", "module": "Mathlib.Geometry.Manifold.IsManifold.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.extend", "kind": "definition", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.extend_coe", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.extend_coe_symm", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.extend_source", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "OpenPartialHomeomorph.isOpen_extend_source", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "OpenPartialHomeomorph.extend_target", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "OpenPartialHomeomorph.extend_target'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "OpenPartialHomeomorph.isOpen_extend_target", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "OpenPartialHomeomorph.mapsTo_extend", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": ["rw", "f.image_eq_target_inter_inv_preimage", "exact"], "tactic_count": 3}
{"name": "OpenPartialHomeomorph.extend_left_inv", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.extend_left_inv'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.extend_source_mem_nhds", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.extend_source_mem_nhdsWithin", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.continuousOn_extend", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "OpenPartialHomeomorph.continuousAt_extend", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.map_extend_nhds", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "OpenPartialHomeomorph.map_extend_nhds_of_mem_interior_range", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "OpenPartialHomeomorph.map_extend_nhds_of_boundaryless", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "OpenPartialHomeomorph.extend_target_mem_nhdsWithin", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "OpenPartialHomeomorph.extend_image_target_mem_nhds", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "OpenPartialHomeomorph.extend_image_nhds_mem_nhds_of_boundaryless", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["rw", "filter_upwards"], "tactic_count": 2}
{"name": "OpenPartialHomeomorph.extend_image_nhds_mem_nhds_of_mem_interior_range", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["rw", "filter_upwards"], "tactic_count": 2}
{"name": "OpenPartialHomeomorph.extend_target_subset_range", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "OpenPartialHomeomorph.interior_extend_target_subset_interior_range", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "OpenPartialHomeomorph.mem_interior_extend_target", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": ["rw", "mem_preimage]", "exact"], "tactic_count": 3}
{"name": "OpenPartialHomeomorph.nhdsWithin_extend_target_eq", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.extend_target_eventuallyEq", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.continuousAt_extend_symm'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.continuousAt_extend_symm", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.continuousOn_extend_symm", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.extend_symm_continuousWithinAt_comp_right_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "OpenPartialHomeomorph.isOpen_extend_preimage'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.isOpen_extend_preimage", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "OpenPartialHomeomorph.map_extend_nhdsWithin_eq_image", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["set", "calc", "map", "congr_arg"], "tactic_count": 4}
{"name": "OpenPartialHomeomorph.map_extend_nhdsWithin_eq_image_of_subset", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["rw", "rwa"], "tactic_count": 2}
{"name": "OpenPartialHomeomorph.map_extend_nhdsWithin", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "OpenPartialHomeomorph.map_extend_symm_nhdsWithin", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "OpenPartialHomeomorph.map_extend_symm_nhdsWithin_range", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "OpenPartialHomeomorph.tendsto_extend_comp_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["refine", "have", "rw", "filter_upwards", "simpa"], "tactic_count": 5}
{"name": "OpenPartialHomeomorph.continuousWithinAt_writtenInExtend_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["unfold", "simp", "rw", "tendsto_map'_iff]", "rw", "filter_upwards", "rw", "exact", "hmaps", "hz.1"], "tactic_count": 10}
{"name": "OpenPartialHomeomorph.continuousOn_writtenInExtend_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["refine", "refine", "rw", "exacts"], "tactic_count": 4}
{"name": "OpenPartialHomeomorph.extend_preimage_mem_nhds_of_mem_nhdsWithin", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "OpenPartialHomeomorph.extend_preimage_mem_nhdsWithin", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "OpenPartialHomeomorph.extend_preimage_mem_nhds", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["apply", "rwa", "rwa"], "tactic_count": 3}
{"name": "OpenPartialHomeomorph.extend_preimage_inter_eq", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["mfld_set_tac"], "tactic_count": 1}
{"name": "OpenPartialHomeomorph.extend_symm_preimage_inter_range_eventuallyEq_aux", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["rw", "conv", "congr", "skip", "rw", "refine", "refine", "simp_rw"], "tactic_count": 8}
{"name": "OpenPartialHomeomorph.extend_symm_preimage_inter_range_eventuallyEq", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "OpenPartialHomeomorph.extend_prod", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "OpenPartialHomeomorph.extend_coord_change_source", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": ["simp_rw", "inter_right_comm", "rfl"], "tactic_count": 3}
{"name": "OpenPartialHomeomorph.extend_image_source_inter", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "OpenPartialHomeomorph.extend_coord_change_source_mem_nhdsWithin", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["rw", "obtain", "refine", "exact"], "tactic_count": 4}
{"name": "OpenPartialHomeomorph.extend_coord_change_source_mem_nhdsWithin'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["apply", "rw", "exact"], "tactic_count": 3}
{"name": "OpenPartialHomeomorph.contDiffOn_extend_coord_change", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "OpenPartialHomeomorph.contDiffWithinAt_extend_coord_change", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["apply", "rw", "obtain", "exact"], "tactic_count": 4}
{"name": "OpenPartialHomeomorph.contDiffWithinAt_extend_coord_change'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "extChartAt", "kind": "definition", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "extChartAt_coe", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "extChartAt_coe_symm", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "extChartAt_source", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpen_extChartAt_source", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_extChartAt_source", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "mem_extChartAt_target", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "extChartAt_target", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniqueDiffOn_extChartAt_target", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "uniqueDiffWithinAt_extChartAt_target", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "extChartAt_to_inv", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mapsTo_extChartAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "extChartAt_source_mem_nhds'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "extChartAt_source_mem_nhds", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "extChartAt_source_mem_nhdsWithin'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "extChartAt_source_mem_nhdsWithin", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousOn_extChartAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousAt_extChartAt'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousAt_extChartAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "map_extChartAt_nhds'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "map_extChartAt_nhds", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "map_extChartAt_nhds_of_boundaryless", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "extChartAt_image_nhds_mem_nhds_of_mem_interior_range", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "extChartAt_image_nhds_mem_nhds_of_boundaryless", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "extChartAt_target_mem_nhdsWithin'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "extChartAt_target_mem_nhdsWithin", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "extChartAt_target_mem_nhdsWithin_of_mem", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["rw", "apply", "exact"], "tactic_count": 3}
{"name": "extChartAt_target_union_compl_range_mem_nhds_of_mem", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "isOpen_extChartAt_target", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "extChartAt_target_mem_nhds", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "extChartAt_target_mem_nhds'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "extChartAt_target_subset_range", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "nhdsWithin_extChartAt_target_eq'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsWithin_extChartAt_target_eq_of_mem", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "nhdsWithin_extChartAt_target_eq", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "extChartAt_target_eventuallyEq'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "extChartAt_target_eventuallyEq_of_mem", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "extChartAt_target_eventuallyEq", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousAt_extChartAt_symm''", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousAt_extChartAt_symm'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousAt_extChartAt_symm", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousOn_extChartAt_symm", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "extChartAt_target_subset_closure_interior", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["intro", "rw", "intro", "have", "inter_mem", "have", "apply", "obtain", "mem_closure_iff_nhds.1", "refine", "have", "exact"], "tactic_count": 12}
{"name": "interior_extChartAt_target_nonempty", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["by_contra", "have", "simp"], "tactic_count": 3}
{"name": "extChartAt_mem_closure_interior", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["simp_rw", "intro", "obtain", "have", "apply", "refine", "apply", "have", "simp", "apply", "simp", "exact", "have", "apply", "exact", "exact"], "tactic_count": 16}
{"name": "isOpen_extChartAt_preimage'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpen_extChartAt_preimage", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "map_extChartAt_nhdsWithin_eq_image'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "map_extChartAt_nhdsWithin_eq_image", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "map_extChartAt_nhdsWithin'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "map_extChartAt_nhdsWithin", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "map_extChartAt_symm_nhdsWithin'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "map_extChartAt_symm_nhdsWithin_range'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "map_extChartAt_symm_nhdsWithin", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "map_extChartAt_symm_nhdsWithin_range", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "extChartAt_preimage_mem_nhds_of_mem_nhdsWithin", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "extChartAt_preimage_mem_nhdsWithin'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "extChartAt_preimage_mem_nhdsWithin", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "extChartAt_preimage_mem_nhds'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "extChartAt_preimage_mem_nhds", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["apply", "rwa"], "tactic_count": 2}
{"name": "extChartAt_preimage_inter_eq", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["mfld_set_tac"], "tactic_count": 1}
{"name": "ContinuousWithinAt.nhdsWithin_extChartAt_symm_preimage_inter_range", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": ["rw", "nhdsWithin_inter_of_mem']", "exact"], "tactic_count": 3}
{"name": "ContinuousWithinAt.extChartAt_symm_preimage_inter_range_eventuallyEq", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ext_coord_change_source", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiffOn_ext_coord_change", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiffWithinAt_ext_coord_change", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "writtenInExtChartAt", "kind": "definition", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "writtenInExtChartAt_chartAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["simp_all"], "tactic_count": 1}
{"name": "writtenInExtChartAt_chartAt_symm", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["simp_all"], "tactic_count": 1}
{"name": "writtenInExtChartAt_extChartAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["simp_all"], "tactic_count": 1}
{"name": "writtenInExtChartAt_extChartAt_symm", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["simp_all"], "tactic_count": 1}
{"name": "writtenInExtChart_prod", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "extChartAt_self_eq", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "extChartAt_self_apply", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "extChartAt_model_space_eq_id", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ext_chart_model_space_apply", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "extChartAt_prod", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["simp", "rw"], "tactic_count": 2}
{"name": "extChartAt_comp", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "writtenInExtChartAt_chartAt_comp", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["letI", "simp_all"], "tactic_count": 2}
{"name": "writtenInExtChartAt_chartAt_symm_comp", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["letI", "simp_all"], "tactic_count": 2}
{"name": "Manifold.locallyCompact_of_finiteDimensional", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["have", "have", "exact"], "tactic_count": 3}
{"name": "LocallyCompactSpace.of_locallyCompact_manifold", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["rcases", "obtain", "have", "obtain", "have", "apply", "rw", "apply", "simp", "exact"], "tactic_count": 10}
{"name": "FiniteDimensional.of_locallyCompact_manifold", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.ExtChartAt", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "ModelWithCorners.IsInteriorPoint", "kind": "definition", "module": "Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.IsBoundaryPoint", "kind": "definition", "module": "Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.interior", "kind": "definition", "module": "Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.isInteriorPoint_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.boundary", "kind": "definition", "module": "Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.isBoundaryPoint_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.isInteriorPoint_or_isBoundaryPoint", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary", "is_tactic_proof": false, "tactics": ["rw", "mem_diff]", "exact"], "tactic_count": 3}
{"name": "ModelWithCorners.interior_union_boundary_eq_univ", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.disjoint_interior_boundary", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary", "is_tactic_proof": true, "tactics": ["by_contra", "obtain", "rw", "mem_inter_iff]", "exact"], "tactic_count": 5}
{"name": "ModelWithCorners.isInteriorPoint_iff_not_isBoundaryPoint", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary", "is_tactic_proof": true, "tactics": ["refine", "by_contra", "rw", "mem_inter_iff]", "exact"], "tactic_count": 5}
{"name": "ModelWithCorners.compl_interior", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary", "is_tactic_proof": true, "tactics": ["apply", "exact"], "tactic_count": 2}
{"name": "ModelWithCorners.compl_boundary", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "range_mem_nhds_isInteriorPoint", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ModelWithCorners.instBoundarylessManifold", "kind": "instance", "module": "Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.BoundarylessManifold.of_empty", "kind": "instance", "module": "Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundarylessManifold.isInteriorPoint", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.interior_eq_univ", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.Boundaryless.boundary_eq_empty", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ModelWithCorners.instIsEmptyElemBoundaryOfBoundarylessManifold", "kind": "instance", "module": "Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.Boundaryless.iff_boundary_eq_empty", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary", "is_tactic_proof": true, "tactics": ["refine", "intro", "change", "rw", "rw", "trivial"], "tactic_count": 6}
{"name": "ModelWithCorners.Boundaryless.of_boundary_eq_empty", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.isInteriorPoint_iff_isInteriorPoint_val", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ModelWithCorners.isBoundaryPoint_iff_isBoundaryPoint_val", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ModelWithCorners.interior_open", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary", "is_tactic_proof": true, "tactics": ["ext1"], "tactic_count": 1}
{"name": "ModelWithCorners.boundary_open", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ModelWithCorners.BoundarylessManifold.open", "kind": "instance", "module": "Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.interior_prod", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary", "is_tactic_proof": true, "tactics": ["ext", "have", "rw", "constructor", "replace", "rw", "exact", "change", "rw", "obtain", "rw", "exact"], "tactic_count": 12}
{"name": "ModelWithCorners.boundary_prod", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary", "is_tactic_proof": false, "tactics": ["let", "calc", "rw", "rfl"], "tactic_count": 4}
{"name": "ModelWithCorners.boundary_of_boundaryless_left", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary", "is_tactic_proof": true, "tactics": ["rw", "have", "rw"], "tactic_count": 3}
{"name": "ModelWithCorners.boundary_of_boundaryless_right", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary", "is_tactic_proof": true, "tactics": ["rw", "have", "rw"], "tactic_count": 3}
{"name": "ModelWithCorners.BoundarylessManifold.prod", "kind": "instance", "module": "Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary", "is_tactic_proof": true, "tactics": ["apply", "simp", "exact"], "tactic_count": 3}
{"name": "ModelWithCorners.interiorPoint_inl", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary", "is_tactic_proof": true, "tactics": ["rw", "dsimp", "rw", "simpa"], "tactic_count": 4}
{"name": "ModelWithCorners.boundaryPoint_inl", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary", "is_tactic_proof": true, "tactics": ["rw", "dsimp", "rw", "simpa"], "tactic_count": 4}
{"name": "ModelWithCorners.interiorPoint_inr", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary", "is_tactic_proof": true, "tactics": ["rw", "dsimp", "rw", "simpa"], "tactic_count": 4}
{"name": "ModelWithCorners.boundaryPoint_inr", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary", "is_tactic_proof": true, "tactics": ["rw", "dsimp", "rw", "simpa"], "tactic_count": 4}
{"name": "ModelWithCorners.isInteriorPoint_disjointUnion_left", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary", "is_tactic_proof": true, "tactics": ["by_contra", "set", "rw", "rw", "have", "rw", "exact"], "tactic_count": 7}
{"name": "ModelWithCorners.isInteriorPoint_disjointUnion_right", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary", "is_tactic_proof": true, "tactics": ["by_contra", "set", "rw", "constructor", "rw", "rw", "have", "exact"], "tactic_count": 8}
{"name": "ModelWithCorners.interior_disjointUnion", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary", "is_tactic_proof": true, "tactics": ["grind", "isInteriorPoint_iff_not_isBoundaryPoint]"], "tactic_count": 2}
{"name": "ModelWithCorners.boundary_disjointUnion", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ModelWithCorners.boundaryless_disjointUnion", "kind": "instance", "module": "Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "instCoeFunPartialDiffeomorphForall", "kind": "instance", "module": "Mathlib.Geometry.Manifold.LocalDiffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Diffeomorph.toPartialDiffeomorph", "kind": "definition", "module": "Mathlib.Geometry.Manifold.LocalDiffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialDiffeomorph.toOpenPartialHomeomorph", "kind": "definition", "module": "Mathlib.Geometry.Manifold.LocalDiffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialDiffeomorph.symm", "kind": "definition", "module": "Mathlib.Geometry.Manifold.LocalDiffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialDiffeomorph.contMDiffOn", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalDiffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialDiffeomorph.mdifferentiableOn", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalDiffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialDiffeomorph.mdifferentiableAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalDiffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalDiffeomorphAt", "kind": "definition", "module": "Mathlib.Geometry.Manifold.LocalDiffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialDiffeomorph.isLocalDiffeomorphAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalDiffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalDiffeomorphAt.localInverse", "kind": "definition", "module": "Mathlib.Geometry.Manifold.LocalDiffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalDiffeomorphAt.localInverse_open_source", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalDiffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalDiffeomorphAt.localInverse_mem_source", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalDiffeomorph", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsLocalDiffeomorphAt.localInverse_mem_target", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalDiffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalDiffeomorphAt.contmdiffOn_localInverse", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalDiffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalDiffeomorphAt.localInverse_right_inv", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalDiffeomorph", "is_tactic_proof": false, "tactics": ["have", "rw", "exact", "rw", "exact"], "tactic_count": 5}
{"name": "IsLocalDiffeomorphAt.localInverse_eqOn_right", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalDiffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalDiffeomorphAt.localInverse_eventuallyEq_right", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalDiffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalDiffeomorphAt.localInverse_left_inv", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalDiffeomorph", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsLocalDiffeomorphAt.localInverse_eqOn_left", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalDiffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalDiffeomorphAt.localInverse_eventuallyEq_left", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalDiffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalDiffeomorphAt.localInverse_isLocalDiffeomorphAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalDiffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalDiffeomorphAt.localInverse_contMDiffOn", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalDiffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalDiffeomorphAt.localInverse_contMDiffAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalDiffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalDiffeomorphAt.localInverse_mdifferentiableAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalDiffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalDiffeomorphOn", "kind": "definition", "module": "Mathlib.Geometry.Manifold.LocalDiffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalDiffeomorph", "kind": "definition", "module": "Mathlib.Geometry.Manifold.LocalDiffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLocalDiffeomorphOn_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalDiffeomorph", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "isLocalDiffeomorph_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalDiffeomorph", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "isLocalDiffeomorph_iff_isLocalDiffeomorphOn_univ", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalDiffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalDiffeomorph.isLocalDiffeomorphOn", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalDiffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalDiffeomorphAt.contMDiffAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalDiffeomorph", "is_tactic_proof": true, "tactics": ["choose", "exact"], "tactic_count": 2}
{"name": "IsLocalDiffeomorphAt.mdifferentiableAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalDiffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalDiffeomorphOn.contMDiffOn", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalDiffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalDiffeomorphOn.mdifferentiableOn", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalDiffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalDiffeomorph.contMDiff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalDiffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalDiffeomorph.mdifferentiable", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalDiffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Diffeomorph.isLocalDiffeomorph", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalDiffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalDiffeomorphOn.isLocalHomeomorphOn", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalDiffeomorph", "is_tactic_proof": true, "tactics": ["apply", "intro", "choose", "exact"], "tactic_count": 4}
{"name": "IsLocalDiffeomorph.isLocalHomeomorph", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalDiffeomorph", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "IsLocalDiffeomorph.isOpenMap", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalDiffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalDiffeomorph.isOpen_range", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalDiffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalDiffeomorph.image", "kind": "definition", "module": "Mathlib.Geometry.Manifold.LocalDiffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalDiffeomorph.image_coe", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalDiffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalDiffeomorph.diffeomorphOfBijective", "kind": "definition", "module": "Mathlib.Geometry.Manifold.LocalDiffeomorph", "is_tactic_proof": true, "tactics": ["choose", "choose", "have", "eqOn_of_leftInvOn_of_rightInvOn", "exact", "invFun", "left_inv", "right_inv", "contMDiff_toFun", "contMDiff_invFun", "intro", "let", "obtain", "apply", "have", "exact"], "tactic_count": 16}
{"name": "IsLocalDiffeomorphAt.mfderivToContinuousLinearEquiv", "kind": "definition", "module": "Mathlib.Geometry.Manifold.LocalDiffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalDiffeomorphAt.mfderivToContinuousLinearEquiv_coe", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalDiffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Diffeomorph.mfderivToContinuousLinearEquiv", "kind": "definition", "module": "Mathlib.Geometry.Manifold.LocalDiffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Diffeomorph.mfderivToContinuousLinearEquiv_coe", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalDiffeomorph", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "IsLocalDiffeomorph.mfderivToContinuousLinearEquiv", "kind": "definition", "module": "Mathlib.Geometry.Manifold.LocalDiffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalDiffeomorph.mfderivToContinuousLinearEquiv_coe", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalDiffeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StructureGroupoid.LocalInvariantProp.congr_set", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": true, "tactics": ["obtain", "simp_rw", "rw"], "tactic_count": 3}
{"name": "StructureGroupoid.LocalInvariantProp.is_local_nhds", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StructureGroupoid.LocalInvariantProp.congr_iff_nhdsWithin", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "StructureGroupoid.LocalInvariantProp.congr_nhdsWithin", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StructureGroupoid.LocalInvariantProp.congr_nhdsWithin'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StructureGroupoid.LocalInvariantProp.congr_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StructureGroupoid.LocalInvariantProp.congr", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StructureGroupoid.LocalInvariantProp.congr'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StructureGroupoid.LocalInvariantProp.left_invariance", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": true, "tactics": ["have", "have", "e'.symm.open_source.mem_nhds", "constructor", "intro", "rw", "have", "rw", "refine", "exact", "simp_rw", "exact"], "tactic_count": 12}
{"name": "StructureGroupoid.LocalInvariantProp.right_invariance", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": true, "tactics": ["refine", "have", "rw", "refine", "refine", "simp_rw", "rw", "refine", "simp_rw"], "tactic_count": 9}
{"name": "ChartedSpace.LiftPropOn", "kind": "definition", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ChartedSpace.LiftPropAt", "kind": "definition", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ChartedSpace.liftPropAt_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ChartedSpace.LiftProp", "kind": "definition", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ChartedSpace.liftProp_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "StructureGroupoid.liftPropWithinAt_univ", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StructureGroupoid.liftPropOn_univ", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "StructureGroupoid.liftPropWithinAt_self", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StructureGroupoid.liftPropWithinAt_self_source", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StructureGroupoid.liftPropWithinAt_self_target", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StructureGroupoid.LocalInvariantProp.liftPropWithinAt_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": true, "tactics": ["rw", "refine", "exact"], "tactic_count": 3}
{"name": "StructureGroupoid.LocalInvariantProp.liftPropWithinAt_indep_chart_source_aux", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": true, "tactics": ["rw", "swap", "simp_rw", "rw", "refine", "refine", "refine", "simp_rw", "simp_rw", "e.left_inv", "refine", "simp", "rw"], "tactic_count": 13}
{"name": "StructureGroupoid.LocalInvariantProp.liftPropWithinAt_indep_chart_target_aux2", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": true, "tactics": ["have", "rw", "refine", "exact"], "tactic_count": 4}
{"name": "StructureGroupoid.LocalInvariantProp.liftPropWithinAt_indep_chart_target_aux", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": true, "tactics": ["rw", "refine", "exact"], "tactic_count": 3}
{"name": "StructureGroupoid.LocalInvariantProp.liftPropWithinAt_indep_chart_aux", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": true, "tactics": ["rw", "hG.liftPropWithinAt_indep_chart_target_aux"], "tactic_count": 2}
{"name": "StructureGroupoid.LocalInvariantProp.liftPropWithinAt_indep_chart", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": true, "tactics": ["simp", "exact", "and_congr_right", "hG.liftPropWithinAt_indep_chart_aux"], "tactic_count": 4}
{"name": "StructureGroupoid.LocalInvariantProp.liftPropWithinAt_indep_chart_source", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": false, "tactics": ["rw", "e.symm.continuousWithinAt_iff_continuousWithinAt_comp_right", "refine", "rw", "hG.liftPropWithinAt_indep_chart_source_aux", "he"], "tactic_count": 6}
{"name": "StructureGroupoid.LocalInvariantProp.liftPropWithinAt_indep_chart_target", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": true, "tactics": ["rw", "intro", "simp_rw", "exact", "hG.liftPropWithinAt_indep_chart_target_aux"], "tactic_count": 5}
{"name": "StructureGroupoid.LocalInvariantProp.liftPropWithinAt_indep_chart'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": false, "tactics": ["rw", "and_iff_right_iff_imp]", "intro", "have", "have", "exact"], "tactic_count": 6}
{"name": "StructureGroupoid.LocalInvariantProp.liftPropOn_indep_chart", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "StructureGroupoid.LocalInvariantProp.liftPropWithinAt_inter'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "exact"], "tactic_count": 3}
{"name": "StructureGroupoid.LocalInvariantProp.liftPropWithinAt_inter", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StructureGroupoid.LocalInvariantProp.liftPropWithinAt_congr_set", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": true, "tactics": ["rw", "congr", "aesop"], "tactic_count": 3}
{"name": "StructureGroupoid.LocalInvariantProp.liftPropAt_of_liftPropWithinAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "StructureGroupoid.LocalInvariantProp.liftPropWithinAt_of_liftPropAt_of_mem_nhds", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "StructureGroupoid.LocalInvariantProp.liftPropOn_of_locally_liftPropOn", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": true, "tactics": ["intro", "rcases", "have", "rwa", "exact"], "tactic_count": 5}
{"name": "StructureGroupoid.LocalInvariantProp.liftProp_of_locally_liftPropOn", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp"], "tactic_count": 3}
{"name": "StructureGroupoid.LocalInvariantProp.liftPropWithinAt_congr_of_eventuallyEq", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": true, "tactics": ["refine", "refine", "hG.congr_nhdsWithin", "simp_rw", "rw", "exact"], "tactic_count": 6}
{"name": "StructureGroupoid.LocalInvariantProp.liftPropWithinAt_congr_of_eventuallyEq_of_mem", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StructureGroupoid.LocalInvariantProp.liftPropWithinAt_congr_iff_of_eventuallyEq", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StructureGroupoid.LocalInvariantProp.liftPropWithinAt_congr_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StructureGroupoid.LocalInvariantProp.liftPropWithinAt_congr_iff_of_mem", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StructureGroupoid.LocalInvariantProp.liftPropWithinAt_congr", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StructureGroupoid.LocalInvariantProp.liftPropWithinAt_congr_of_mem", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StructureGroupoid.LocalInvariantProp.liftPropAt_congr_iff_of_eventuallyEq", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StructureGroupoid.LocalInvariantProp.liftPropAt_congr_of_eventuallyEq", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StructureGroupoid.LocalInvariantProp.liftPropOn_congr", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StructureGroupoid.LocalInvariantProp.liftPropOn_congr_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StructureGroupoid.LocalInvariantProp.liftPropWithinAt_mono_of_mem_nhdsWithin", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": true, "tactics": ["simp", "refine", "simp_rw"], "tactic_count": 3}
{"name": "StructureGroupoid.LocalInvariantProp.liftPropWithinAt_mono", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": true, "tactics": ["refine", "simp", "simp"], "tactic_count": 3}
{"name": "StructureGroupoid.LocalInvariantProp.liftPropWithinAt_of_liftPropAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "StructureGroupoid.LocalInvariantProp.liftPropOn_mono", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StructureGroupoid.LocalInvariantProp.liftPropOn_of_liftProp", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "StructureGroupoid.LocalInvariantProp.liftPropAt_of_mem_maximalAtlas", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": false, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "StructureGroupoid.LocalInvariantProp.liftPropOn_of_mem_maximalAtlas", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": true, "tactics": ["intro", "apply", "exact"], "tactic_count": 3}
{"name": "StructureGroupoid.LocalInvariantProp.liftPropAt_symm_of_mem_maximalAtlas", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": false, "tactics": ["suffices", "have", "rw", "refine", "simp", "exact"], "tactic_count": 6}
{"name": "StructureGroupoid.LocalInvariantProp.liftPropOn_symm_of_mem_maximalAtlas", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": true, "tactics": ["intro", "apply", "exact"], "tactic_count": 3}
{"name": "StructureGroupoid.LocalInvariantProp.liftPropAt_chart", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StructureGroupoid.LocalInvariantProp.liftPropOn_chart", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StructureGroupoid.LocalInvariantProp.liftPropAt_chart_symm", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StructureGroupoid.LocalInvariantProp.liftPropOn_chart_symm", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StructureGroupoid.LocalInvariantProp.liftPropAt_of_mem_groupoid", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StructureGroupoid.LocalInvariantProp.liftPropOn_of_mem_groupoid", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StructureGroupoid.LocalInvariantProp.liftProp_id", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "StructureGroupoid.LocalInvariantProp.liftPropAt_iff_comp_subtype_val", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": true, "tactics": ["simp", "congrm", "simp_rw", "apply", "exact"], "tactic_count": 5}
{"name": "StructureGroupoid.LocalInvariantProp.liftPropAt_iff_comp_inclusion", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": true, "tactics": ["simp", "congrm", "simp_rw", "apply", "exact"], "tactic_count": 5}
{"name": "StructureGroupoid.LocalInvariantProp.liftProp_subtype_val", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": true, "tactics": ["intro", "change", "rw", "apply"], "tactic_count": 4}
{"name": "StructureGroupoid.LocalInvariantProp.liftProp_inclusion", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": true, "tactics": ["intro", "change", "rw", "apply"], "tactic_count": 4}
{"name": "StructureGroupoid.IsLocalStructomorphWithinAt", "kind": "definition", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StructureGroupoid.isLocalStructomorphWithinAt_localInvariantProp", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.isLocalStructomorphWithinAt_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": true, "tactics": ["constructor", "intro", "obtain", "refine", "simp_rw", "exact", "intro", "exact", "rw", "exact", "intro", "obtain", "exact"], "tactic_count": 13}
{"name": "OpenPartialHomeomorph.isLocalStructomorphWithinAt_iff'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": true, "tactics": ["rw", "refine", "refine", "rw"], "tactic_count": 4}
{"name": "OpenPartialHomeomorph.isLocalStructomorphWithinAt_source_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StructureGroupoid.HasGroupoid.comp", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalInvariantProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold.LiftSourceTargetPropertyAt", "kind": "definition", "module": "Mathlib.Geometry.Manifold.LocalSourceTargetProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold.LiftSourceTargetPropertyAt.localPresentationAt", "kind": "definition", "module": "Mathlib.Geometry.Manifold.LocalSourceTargetProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold.LiftSourceTargetPropertyAt.domChart", "kind": "definition", "module": "Mathlib.Geometry.Manifold.LocalSourceTargetProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold.LiftSourceTargetPropertyAt.codChart", "kind": "definition", "module": "Mathlib.Geometry.Manifold.LocalSourceTargetProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold.LiftSourceTargetPropertyAt.mem_domChart_source", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalSourceTargetProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold.LiftSourceTargetPropertyAt.mem_codChart_source", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalSourceTargetProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold.LiftSourceTargetPropertyAt.domChart_mem_maximalAtlas", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalSourceTargetProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold.LiftSourceTargetPropertyAt.codChart_mem_maximalAtlas", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalSourceTargetProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold.LiftSourceTargetPropertyAt.source_subset_preimage_source", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalSourceTargetProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold.LiftSourceTargetPropertyAt.property", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalSourceTargetProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold.LiftSourceTargetPropertyAt.congr_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalSourceTargetProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold.LiftSourceTargetPropertyAt.mk_of_continuousAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalSourceTargetProperty", "is_tactic_proof": true, "tactics": ["obtain", "exact", "hcodChart,"], "tactic_count": 3}
{"name": "Manifold.LiftSourceTargetPropertyAt.congr_of_eventuallyEq", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalSourceTargetProperty", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "refine", "simpa", "exact", "exact", "trans", "apply", "exact", "exact", "rw", "exact"], "tactic_count": 12}
{"name": "Manifold.LiftSourceTargetPropertyAt.congr_iff_of_eventuallyEq", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalSourceTargetProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.liftSourceTargetPropertyAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalSourceTargetProperty", "is_tactic_proof": true, "tactics": ["rw", "intro", "refine", "exact", "hx.codChart_mem_maximalAtlas,"], "tactic_count": 5}
{"name": "Manifold.LiftSourceTargetPropertyAt.prodMap", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.LocalSourceTargetProperty", "is_tactic_proof": true, "tactics": ["use", "simp", "simp", "exact", "apply", "simp", "exact", "exact"], "tactic_count": 8}
{"name": "ModelWithCorners.hasMFDerivAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Atlas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.hasMFDerivWithinAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Atlas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.mdifferentiableWithinAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Atlas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.mdifferentiableAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Atlas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.mdifferentiableOn", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Atlas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.mdifferentiable", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Atlas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.hasMFDerivWithinAt_symm", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Atlas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.mdifferentiableOn_symm", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Atlas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModelWithCorners.mdifferentiableWithinAt_symm", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Atlas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiableAt_atlas", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Atlas", "is_tactic_proof": true, "tactics": ["rw", "refine", "have", "simp", "have", "have", "this.1", "have", "simp", "rw", "simpa", "apply"], "tactic_count": 12}
{"name": "mdifferentiableOn_atlas", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Atlas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiableAt_atlas_symm", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Atlas", "is_tactic_proof": true, "tactics": ["rw", "refine", "have", "have", "have", "this.1", "have", "simp", "rw", "simpa", "apply"], "tactic_count": 11}
{"name": "mdifferentiableOn_atlas_symm", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Atlas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiable_of_mem_atlas", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Atlas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiable_chart", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Atlas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.MDifferentiable.symm", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Atlas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.MDifferentiable.mdifferentiableAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Atlas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.MDifferentiable.mdifferentiableAt_symm", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Atlas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.MDifferentiable.symm_comp_deriv", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Atlas", "is_tactic_proof": false, "tactics": ["have", "mfderiv_comp", "rw", "have", "rw", "apply", "have", "exact"], "tactic_count": 8}
{"name": "OpenPartialHomeomorph.MDifferentiable.comp_symm_deriv", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Atlas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.MDifferentiable.mfderiv", "kind": "definition", "module": "Mathlib.Geometry.Manifold.MFDeriv.Atlas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.MDifferentiable.mfderiv_bijective", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Atlas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.MDifferentiable.mfderiv_injective", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Atlas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.MDifferentiable.mfderiv_surjective", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Atlas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.MDifferentiable.ker_mfderiv_eq_bot", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Atlas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.MDifferentiable.range_mfderiv_eq_top", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Atlas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.MDifferentiable.range_mfderiv_eq_univ", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Atlas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.MDifferentiable.trans", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Atlas", "is_tactic_proof": true, "tactics": ["constructor", "intro", "simp", "exact", "intro", "simp", "exact"], "tactic_count": 7}
{"name": "hasMFDerivAt_extChartAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Atlas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasMFDerivWithinAt_extChartAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Atlas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiableAt_extChartAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Atlas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiableOn_extChartAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Atlas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiableWithinAt_extChartAt_symm", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Atlas", "is_tactic_proof": true, "tactics": ["have", "apply", "apply", "simp", "exact"], "tactic_count": 5}
{"name": "mdifferentiableOn_extChartAt_symm", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Atlas", "is_tactic_proof": true, "tactics": ["intro", "exact"], "tactic_count": 2}
{"name": "mfderiv_extChartAt_comp_mfderivWithin_extChartAt_symm", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Atlas", "is_tactic_proof": false, "tactics": ["have", "apply", "exact", "have", "have", "rw", "apply", "exact", "exact", "rw", "apply", "filter_upwards", "simp", "simp"], "tactic_count": 14}
{"name": "mfderiv_extChartAt_comp_mfderivWithin_extChartAt_symm'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Atlas", "is_tactic_proof": true, "tactics": ["have", "convert"], "tactic_count": 2}
{"name": "mfderivWithin_extChartAt_symm_comp_mfderiv_extChartAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Atlas", "is_tactic_proof": true, "tactics": ["have", "have", "have", "have", "mfderiv", "mfderivWithin", "rw", "exact", "rw", "exact", "exact", "intro", "apply", "exact", "exact", "exact", "rw", "apply", "filter_upwards", "simp", "simp"], "tactic_count": 21}
{"name": "mfderivWithin_extChartAt_symm_comp_mfderiv_extChartAt'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Atlas", "is_tactic_proof": true, "tactics": ["have", "convert"], "tactic_count": 2}
{"name": "isInvertible_mfderivWithin_extChartAt_symm", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Atlas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isInvertible_mfderiv_extChartAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Atlas", "is_tactic_proof": true, "tactics": ["have", "have", "have", "rwa"], "tactic_count": 4}
{"name": "TangentBundle.continuousLinearMapAt_trivializationAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Atlas", "is_tactic_proof": true, "tactics": ["have", "simp", "simp"], "tactic_count": 3}
{"name": "TangentBundle.symmL_trivializationAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Atlas", "is_tactic_proof": false, "tactics": ["have", "simpa", "simp"], "tactic_count": 3}
{"name": "uniqueMDiffWithinAt_univ", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["unfold", "simp", "exact"], "tactic_count": 3}
{"name": "uniqueMDiffWithinAt_iff_inter_range", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniqueMDiffWithinAt_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["apply", "rw"], "tactic_count": 2}
{"name": "UniqueMDiffWithinAt.mono_nhds", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniqueMDiffWithinAt.mono_of_mem_nhdsWithin", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniqueMDiffWithinAt.mono", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniqueMDiffWithinAt.inter'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniqueMDiffWithinAt.inter", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.uniqueMDiffWithinAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniqueMDiffOn.inter", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.uniqueMDiffOn", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniqueMDiffOn_univ", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniqueMDiffWithinAt.prod", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "rfl"], "tactic_count": 3}
{"name": "UniqueMDiffOn.prod", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableWithinAt.mono", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiableWithinAt_univ", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "mdifferentiableWithinAt_inter", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["rw", "differentiableWithinAt_localInvariantProp.liftPropWithinAt_inter"], "tactic_count": 2}
{"name": "mdifferentiableWithinAt_inter'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["rw", "differentiableWithinAt_localInvariantProp.liftPropWithinAt_inter"], "tactic_count": 2}
{"name": "MDifferentiableAt.mdifferentiableWithinAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableWithinAt.mdifferentiableAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "MDifferentiableOn.mono", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiableOn_empty", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiableOn_univ", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MDifferentiableOn.mdifferentiableAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiable.mdifferentiableOn", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiableOn_of_locally_mdifferentiableOn", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["intro", "rcases", "exact"], "tactic_count": 3}
{"name": "MDifferentiable.mdifferentiableAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiableWithinAt_iff_target_inter", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "simp"], "tactic_count": 4}
{"name": "mdifferentiableWithinAt_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "mdifferentiableWithinAt_iff_target_inter'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["simp", "exact", "and_congr_right"], "tactic_count": 3}
{"name": "mdifferentiableWithinAt_iff_target", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "have", "and_iff_left_of_imp", "simp_rw", "rfl"], "tactic_count": 5}
{"name": "mdifferentiableAt_iff_target", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["rw", "continuousWithinAt_univ]"], "tactic_count": 2}
{"name": "mdifferentiableWithinAt_iff_source_of_mem_maximalAtlas", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["have", "simp_rw", "differentiableWithinAtProp_self_source,", "rfl"], "tactic_count": 4}
{"name": "mdifferentiableWithinAt_iff_source_of_mem_source", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiableAt_iff_source_of_mem_source", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "univ_inter]"], "tactic_count": 2}
{"name": "mdifferentiableWithinAt_iff_target_of_mem_source", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "rw", "and_congr_right]", "intro", "simp_rw", "simp_rw", "rw", "simp_rw", "rfl"], "tactic_count": 9}
{"name": "mdifferentiableAt_iff_target_of_mem_source", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["rw", "mdifferentiableWithinAt_univ]"], "tactic_count": 2}
{"name": "mdifferentiableWithinAt_iff_of_mem_maximalAtlas", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiableWithinAt_iff_image", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp_rw"], "tactic_count": 3}
{"name": "mdifferentiableWithinAt_iff_of_mem_source", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiableWithinAt_iff_of_mem_source'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "rw", "rw", "set", "refine", "rw", "nhdsWithin_inter_of_mem]", "exact"], "tactic_count": 9}
{"name": "mdifferentiableAt_iff_of_mem_source", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiableOn_iff_of_mem_maximalAtlas", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "mdifferentiableOn_iff_of_mem_maximalAtlas'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiableOn_iff_of_subset_source", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiableOn_iff_of_subset_source'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "mdifferentiableOn_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["constructor", "intro", "refine", "simp", "let", "have", "specialize", "have", "have", "convert", "simp", "mfld_set_tac", "rintro", "refine", "refine", "dsimp", "convert", "mfld_set_tac"], "tactic_count": 18}
{"name": "mdifferentiableOn_iff_target", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": ["simp", "intro", "constructor", "refine", "have", "convert", "simp", "exact"], "tactic_count": 8}
{"name": "mdifferentiable_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "mdifferentiable_iff_target", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "ContMDiffWithinAt.mdifferentiableWithinAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": ["suffices", "rwa", "apply", "exact", "rw", "exact"], "tactic_count": 6}
{"name": "ContMDiffAt.mdifferentiableAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiff.mdifferentiableAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiff.mdifferentiableWithinAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffOn.mdifferentiableOn", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiff.mdifferentiable", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableOn.continuousOn", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiable.continuous", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "writtenInExtChartAt_comp", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": ["apply", "mfld_set_tac"], "tactic_count": 2}
{"name": "UniqueMDiffWithinAt.eq", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "UniqueMDiffOn.eq", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mfderivWithin_univ", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp", "rw"], "tactic_count": 3}
{"name": "mfderivWithin_zero_of_not_mdifferentiableWithinAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "mfderiv_zero_of_not_mdifferentiableAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "mdifferentiable_of_subsingleton", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["intro", "have", "have", "simp", "exact"], "tactic_count": 5}
{"name": "mdifferentiableWithinAt_of_isInvertible_mfderivWithin", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["contrapose", "rw", "contrapose", "rcases", "have", "exact"], "tactic_count": 6}
{"name": "mdifferentiableAt_of_isInvertible_mfderiv", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "HasMFDerivWithinAt.mono", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasMFDerivAt.hasMFDerivWithinAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasMFDerivWithinAt.mdifferentiableWithinAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasMFDerivAt.mdifferentiableAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "hasMFDerivWithinAt_univ", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "hasMFDerivAt_unique", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "hasMFDerivWithinAt_inter'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": ["rw", "continuousWithinAt_inter", "exact"], "tactic_count": 3}
{"name": "hasMFDerivWithinAt_inter", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": ["rw", "continuousWithinAt_inter", "exact"], "tactic_count": 3}
{"name": "HasMFDerivWithinAt.union", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["constructor", "exact", "convert", "simp"], "tactic_count": 4}
{"name": "HasMFDerivWithinAt.mono_of_mem_nhdsWithin", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasMFDerivWithinAt.hasMFDerivAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "MDifferentiableWithinAt.hasMFDerivWithinAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["refine", "simp", "exact"], "tactic_count": 3}
{"name": "mdifferentiableWithinAt_iff_exists_hasMFDerivWithinAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["refine", "rintro", "exact"], "tactic_count": 3}
{"name": "MDifferentiableWithinAt.mono_of_mem_nhdsWithin", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableWithinAt.congr_nhds", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiableWithinAt_congr_nhds", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableWithinAt.mfderivWithin", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MDifferentiableAt.hasMFDerivAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["refine", "simp", "exact"], "tactic_count": 3}
{"name": "MDifferentiableAt.mfderiv", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HasMFDerivAt.mfderiv", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasMFDerivWithinAt.mfderivWithin", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "HasMFDerivWithinAt.mfderivWithin_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["simp", "simp", "rw", "exact"], "tactic_count": 4}
{"name": "MDifferentiable.mfderivWithin", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["apply", "exact"], "tactic_count": 2}
{"name": "mfderivWithin_subset", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mfderivWithin_inter", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["rw", "fderivWithin_inter"], "tactic_count": 2}
{"name": "mfderivWithin_of_mem_nhds", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mfderivWithin_of_isOpen", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasMFDerivWithinAt_insert", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["have", "refine", "rcases", "rw", "refine", "have", "nhdsWithin_mono", "rw", "apply", "rintro", "simp", "rcases", "left", "have", "exact", "exact", "apply", "simp_rw"], "tactic_count": 18}
{"name": "HasMFDerivWithinAt.insert", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasMFDerivWithinAt_diff_singleton", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mfderivWithin_eq_mfderiv", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "mdifferentiableWithinAt_insert_self", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiableWithinAt_insert", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["rcases", "exact", "have", "apply", "exact"], "tactic_count": 5}
{"name": "MDifferentiableWithinAt.insert", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableOn.union_of_isOpen", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["intro", "obtain", "exact", "exact"], "tactic_count": 4}
{"name": "mdifferentiableOn_union_iff_of_isOpen", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiable_of_mdifferentiableOn_union_of_isOpen", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MDifferentiableOn.iUnion_of_isOpen", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "mdifferentiableOn_iUnion_iff_of_isOpen", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiable_of_mdifferentiableOn_iUnion_of_isOpen", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "HasMFDerivWithinAt.continuousWithinAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasMFDerivAt.continuousAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tangentMapWithin_subset", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["simp", "rw"], "tactic_count": 2}
{"name": "tangentMapWithin_univ", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "tangentMapWithin_eq_tangentMap", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "tangentMapWithin_proj", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tangentMapWithin_snd", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tangentMap_proj", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tangentMap_snd", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "preimage_extChartAt_eventuallyEq_compl_singleton", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["have", "obtain", "mem_nhdsWithin_iff_exists_mem_nhds_inter.1", "rw", "have", "rw", "apply", "apply", "mem_nhdsWithin_iff_exists_mem_nhds_inter.2", "rintro", "simp", "change", "by_cases", "simp", "and_true]", "rw", "apply", "push", "rw", "exact", "simp"], "tactic_count": 21}
{"name": "hasMFDerivWithinAt_congr_set'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["have", "simp", "refine", "exact", "apply", "exact"], "tactic_count": 6}
{"name": "hasMFDerivWithinAt_congr_set", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiableWithinAt_congr_set'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "mdifferentiableWithinAt_congr_set", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "mfderivWithin_congr_set'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "apply", "exact", "simp"], "tactic_count": 5}
{"name": "mfderivWithin_congr_set", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mfderivWithin_eventually_congr_set'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mfderivWithin_eventually_congr_set", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasMFDerivAt.congr_mfderiv", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasMFDerivWithinAt.congr_mfderiv", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasMFDerivWithinAt.congr_of_eventuallyEq", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["refine", "apply", "have", "extChartAt_preimage_mem_nhdsWithin", "apply", "simp", "simp"], "tactic_count": 7}
{"name": "HasMFDerivWithinAt.congr_mono", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasMFDerivAt.congr_of_eventuallyEq", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply", "rwa"], "tactic_count": 3}
{"name": "mdifferentiableWithinAt_congr", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableWithinAt.congr_of_mem", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiableWithinAt_congr_of_mem", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.mdifferentiablefWithinAt_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableWithinAt.congr_of_eventuallyEq", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableWithinAt.congr_of_eventuallyEq_of_mem", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableWithinAt.congr_of_eventuallyEq_insert", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.mdifferentiableWithinAt_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableWithinAt.congr_mono", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableWithinAt.congr", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableWithinAt.congr'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.mdifferentiableAt_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableOn.congr", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiableOn_congr", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableOn.congr_mono", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableAt.congr_of_eventuallyEq", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableWithinAt.mfderivWithin_congr_mono", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableWithinAt.mfderivWithin_mono", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableWithinAt.mfderivWithin_mono_of_mem_nhdsWithin", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.mfderivWithin_eq", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "unfold", "simp", "apply", "simp", "filter_upwards", "simp", "simp", "unfold", "rw", "rwa"], "tactic_count": 11}
{"name": "Filter.EventuallyEq.mfderivWithin_eq_of_mem", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mfderivWithin_congr", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mfderivWithin_congr_of_mem", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tangentMapWithin_congr", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "Filter.EventuallyEq.mfderiv_eq", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["have", "rw", "rw", "exact"], "tactic_count": 4}
{"name": "mfderiv_congr_point", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "mfderiv_congr", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "HasMFDerivWithinAt.comp", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["refine", "have", "have", "extChartAt_preimage_mem_nhdsWithin", "unfold", "rw", "have", "rw", "apply", "intro", "simp", "have", "simp", "apply", "simp"], "tactic_count": 15}
{"name": "HasMFDerivAt.comp", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "HasMFDerivAt.comp_hasMFDerivWithinAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MDifferentiableWithinAt.comp", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["rcases", "have", "rcases", "have", "exact"], "tactic_count": 5}
{"name": "MDifferentiableWithinAt.comp_of_eq", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "MDifferentiableWithinAt.comp_of_preimage_mem_nhdsWithin", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableWithinAt.comp_of_preimage_mem_nhdsWithin_of_eq", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "MDifferentiableAt.comp", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableAt.comp_of_eq", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "MDifferentiableAt.comp_mdifferentiableWithinAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MDifferentiableAt.comp_mdifferentiableWithinAt_of_eq", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "mfderivWithin_comp", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["apply", "exact"], "tactic_count": 2}
{"name": "mfderivWithin_comp_of_eq", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "mfderivWithin_comp_of_preimage_mem_nhdsWithin", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["have", "have", "apply", "exact", "have", "rw", "exact"], "tactic_count": 7}
{"name": "mfderivWithin_comp_of_preimage_mem_nhdsWithin_of_eq", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "mfderiv_comp_mfderivWithin", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "mfderiv_comp_mfderivWithin_of_eq", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "mfderiv_comp", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["apply", "exact"], "tactic_count": 2}
{"name": "mfderiv_comp_of_eq", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "mfderiv_comp_apply", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "mfderiv_comp_apply_of_eq", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "MDifferentiableOn.comp", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiable.comp_mdifferentiableOn", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MDifferentiable.comp", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tangentMapWithin_comp_at", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["simp", "rw", "rfl"], "tactic_count": 3}
{"name": "tangentMap_comp_at", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["simp", "rw", "rfl"], "tactic_count": 3}
{"name": "tangentMap_comp", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "DifferentiableWithinAtProp", "kind": "definition", "module": "Mathlib.Geometry.Manifold.MFDeriv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableWithinAtProp_self_source", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Defs", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "DifferentiableWithinAtProp_self", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableWithinAtProp_self_target", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableWithinAt_localInvariantProp", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniqueMDiffWithinAt", "kind": "definition", "module": "Mathlib.Geometry.Manifold.MFDeriv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniqueMDiffOn", "kind": "definition", "module": "Mathlib.Geometry.Manifold.MFDeriv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableWithinAt", "kind": "definition", "module": "Mathlib.Geometry.Manifold.MFDeriv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiableWithinAt_iff'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MDifferentiableWithinAt.continuousWithinAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableWithinAt.differentiableWithinAt_writtenInExtChartAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableAt", "kind": "definition", "module": "Mathlib.Geometry.Manifold.MFDeriv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiableAt_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Defs", "is_tactic_proof": true, "tactics": ["rw", "congrm", "simp"], "tactic_count": 3}
{"name": "MDifferentiableAt.continuousAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableAt.differentiableWithinAt_writtenInExtChartAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableOn", "kind": "definition", "module": "Mathlib.Geometry.Manifold.MFDeriv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiable", "kind": "definition", "module": "Mathlib.Geometry.Manifold.MFDeriv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.MDifferentiable", "kind": "definition", "module": "Mathlib.Geometry.Manifold.MFDeriv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasMFDerivWithinAt", "kind": "definition", "module": "Mathlib.Geometry.Manifold.MFDeriv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasMFDerivAt", "kind": "definition", "module": "Mathlib.Geometry.Manifold.MFDeriv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mfderivWithin", "kind": "definition", "module": "Mathlib.Geometry.Manifold.MFDeriv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mfderiv", "kind": "definition", "module": "Mathlib.Geometry.Manifold.MFDeriv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tangentMapWithin", "kind": "definition", "module": "Mathlib.Geometry.Manifold.MFDeriv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tangentMap", "kind": "definition", "module": "Mathlib.Geometry.Manifold.MFDeriv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniqueMDiffWithinAt_iff_uniqueDiffWithinAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.FDeriv", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "uniqueMDiffOn_iff_uniqueDiffOn", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.FDeriv", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ModelWithCorners.uniqueMDiffOn", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.FDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "writtenInExtChartAt_model_space", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.FDeriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasMFDerivWithinAt_iff_hasFDerivWithinAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.FDeriv", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "hasMFDerivAt_iff_hasFDerivAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.FDeriv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mdifferentiableWithinAt_iff_differentiableWithinAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.FDeriv", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "mdifferentiableAt_iff_differentiableAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.FDeriv", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "mdifferentiableOn_iff_differentiableOn", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.FDeriv", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "mdifferentiable_iff_differentiable", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.FDeriv", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "mfderivWithin_eq_fderivWithin", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.FDeriv", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "simp", "rw", "exact"], "tactic_count": 5}
{"name": "mfderiv_eq_fderiv", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.FDeriv", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "DifferentiableWithinAt.comp_mdifferentiableWithinAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableAt.comp_mdifferentiableWithinAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentiableAt.comp_mdifferentiableAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Differentiable.comp_mdifferentiableWithinAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Differentiable.comp_mdifferentiableAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Differentiable.comp_mdifferentiable", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableWithinAt.clm_precomp", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableAt.clm_precomp", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableOn.clm_precomp", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiable.clm_precomp", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableWithinAt.clm_postcomp", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableAt.clm_postcomp", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableOn.clm_postcomp", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiable.clm_postcomp", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableWithinAt.clm_comp", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableAt.clm_comp", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableOn.clm_comp", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiable.clm_comp", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableWithinAt.clm_apply", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableAt.clm_apply", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableOn.clm_apply", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiable.clm_apply", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableWithinAt.cle_arrowCongr", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableAt.cle_arrowCongr", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableOn.cle_arrowCongr", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiable.cle_arrowCongr", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableWithinAt.clm_prodMap", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableAt.clm_prodMap", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableOn.clm_prodMap", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiable.clm_prodMap", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableWithinAt.smul", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableAt.smul", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableOn.smul", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiable.smul", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.hasMFDerivWithinAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.hasMFDerivAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.mdifferentiableWithinAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.mdifferentiableOn", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.mdifferentiableAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.mdifferentiable", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.mfderiv_eq", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.mfderivWithin_eq", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.hasMFDerivWithinAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.hasMFDerivAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.mdifferentiableWithinAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.mdifferentiableOn", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.mdifferentiableAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.mdifferentiable", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.mfderiv_eq", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.mfderivWithin_eq", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasMFDerivAt_id", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": true, "tactics": ["refine", "have", "apply", "mfld_set_tac", "apply", "simp"], "tactic_count": 6}
{"name": "hasMFDerivWithinAt_id", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiableAt_id", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiableWithinAt_id", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiable_id", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiableOn_id", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mfderiv_id", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mfderivWithin_id", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "tangentMap_id", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": true, "tactics": ["ext1"], "tactic_count": 1}
{"name": "tangentMapWithin_id", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": true, "tactics": ["simp", "rw", "rcases", "exact"], "tactic_count": 4}
{"name": "hasMFDerivAt_const", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasMFDerivWithinAt_const", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiableAt_const", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiableWithinAt_const", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiable_const", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiableOn_const", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mfderiv_const", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mfderivWithin_const", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableWithinAt.prodMk", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasMFDerivWithinAt.prodMk", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mfderivWithin_prodMk", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mfderiv_prodMk", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "MDifferentiableAt.prodMk", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasMFDerivAt.prodMk", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableWithinAt.prodMk_space", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableAt.prodMk_space", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableOn.prodMk", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiable.prodMk", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableOn.prodMk_space", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiable.prodMk_space", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasMFDerivAt_fst", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": true, "tactics": ["refine", "have", "apply", "mfld_set_tac", "filter_upwards", "rw", "exact", "apply", "exact"], "tactic_count": 9}
{"name": "hasMFDerivWithinAt_fst", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiableAt_fst", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiableWithinAt_fst", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiable_fst", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiableOn_fst", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mfderiv_fst", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mfderivWithin_fst", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "tangentMap_prodFst", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "tangentMapWithin_prodFst", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": true, "tactics": ["simp", "rw", "rcases", "exact"], "tactic_count": 4}
{"name": "hasMFDerivAt_snd", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": true, "tactics": ["refine", "have", "apply", "mfld_set_tac", "filter_upwards", "rw", "exact", "apply", "exact"], "tactic_count": 9}
{"name": "hasMFDerivWithinAt_snd", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiableAt_snd", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiableWithinAt_snd", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiable_snd", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiableOn_snd", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mfderiv_snd", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mfderivWithin_snd", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MDifferentiableWithinAt.fst", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableAt.fst", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiable.fst", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableWithinAt.snd", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableAt.snd", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiable.snd", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiableWithinAt_prod_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiableWithinAt_prod_module_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "mdifferentiableAt_prod_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "mdifferentiableAt_prod_module_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "mdifferentiableOn_prod_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiableOn_prod_module_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "mdifferentiable_prod_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiable_prod_module_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MDifferentiableWithinAt.prodMap'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableWithinAt.prodMap", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableAt.prodMap", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": true, "tactics": ["rw", "convert", "exact"], "tactic_count": 3}
{"name": "MDifferentiableAt.prodMap'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableOn.prodMap", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiable.prodMap", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasMFDerivWithinAt.prodMap", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": true, "tactics": ["refine", "have", "simp", "rw", "intro", "refine", "simp_all", "use", "simp_all", "use", "rw", "apply", "apply", "exacts"], "tactic_count": 14}
{"name": "HasMFDerivAt.prodMap", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": true, "tactics": ["simp_rw", "convert", "rw", "rw"], "tactic_count": 4}
{"name": "mfderivWithin_prodMap", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": ["have", "hf.hasMFDerivWithinAt.mono", "have", "hg.hasMFDerivWithinAt.mono", "exact"], "tactic_count": 5}
{"name": "mfderiv_prodMap", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": true, "tactics": ["simp_rw", "exact", "mfderivWithin_prodMap"], "tactic_count": 3}
{"name": "tangentMap_prodSnd", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "tangentMapWithin_prodSnd", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": true, "tactics": ["simp", "rw", "rcases", "rfl"], "tactic_count": 4}
{"name": "mfderiv_prod_left", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "tangentMap_prod_left", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": true, "tactics": ["simp", "rfl"], "tactic_count": 2}
{"name": "mfderiv_prod_right", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "tangentMap_prod_right", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": true, "tactics": ["simp", "rfl"], "tactic_count": 2}
{"name": "mfderiv_prod_eq_add", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": ["erw", "mfderiv_comp_of_eq", "mdifferentiableAt_fst.mfderiv_prod", "mdifferentiableAt_const.mfderiv_prod", "symm", "convert", "exact"], "tactic_count": 7}
{"name": "mfderiv_prod_eq_add_comp", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": true, "tactics": ["rw", "congr", "have", "rw", "simp", "rfl", "exact", "exact", "have", "rw", "simp", "rfl", "exact", "exact"], "tactic_count": 14}
{"name": "mfderiv_prod_eq_add_apply", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "writtenInExtChartAt_sumSwap_eventuallyEq_id", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": true, "tactics": ["cases", "inl", "let", "have", "intro", "simp", "dsimp", "rw", "exact", "apply", "rw", "refine", "exact", "inr", "let", "have", "intro", "simp", "dsimp", "rw", "exact", "apply", "rw", "refine", "exact"], "tactic_count": 25}
{"name": "hasMFDerivAt_sumSwap", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": true, "tactics": ["refine", "apply", "exact", "simp", "cases"], "tactic_count": 5}
{"name": "mfderivWithin_sumSwap", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mfderiv_sumSwap", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "writtenInExtChartAt_sumInl_eventuallyEq_id", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": ["have", "rw", "exact", "filter_upwards", "rcases", "simp"], "tactic_count": 6}
{"name": "writtenInExtChartAt_sumInr_eventuallyEq_id", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": ["have", "rw", "exact", "filter_upwards", "rcases", "simp"], "tactic_count": 6}
{"name": "hasMFDerivWithinAt_inl", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": true, "tactics": ["refine", "have", "id", "writtenInExtChartAt_sumInl_eventuallyEq_id.filter_mono", "exact"], "tactic_count": 5}
{"name": "hasMFDerivAt_inl", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "hasMFDerivWithinAt_inr", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": true, "tactics": ["refine", "have", "id", "writtenInExtChartAt_sumInr_eventuallyEq_id.filter_mono", "exact"], "tactic_count": 5}
{"name": "hasMFDerivAt_inr", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "mfderivWithin_sumInl", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mfderiv_sumInl", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "mfderivWithin_sumInr", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mfderiv_sumInr", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasMFDerivWithinAt.add", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasMFDerivAt.add", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableWithinAt.add", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableAt.add", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableOn.add", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiable.add", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mfderiv_add", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasMFDerivWithinAt.sum", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "insert"], "tactic_count": 4}
{"name": "HasMFDerivAt.sum", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": true, "tactics": ["simp_all", "exact"], "tactic_count": 2}
{"name": "MDifferentiableWithinAt.sum", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableAt.sum", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": true, "tactics": ["simp_all", "exact"], "tactic_count": 2}
{"name": "MDifferentiableOn.sum", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiable.sum", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasMFDerivAt.const_smul", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "HasMFDerivWithinAt.neg", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "mdifferentiableAt_neg", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "tangentMap_chart", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Tangent", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "rfl", "exact"], "tactic_count": 4}
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{"name": "mfderiv_chartAt_eq_tangentCoordChange", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Tangent", "is_tactic_proof": true, "tactics": ["have", "simp"], "tactic_count": 2}
{"name": "UniqueMDiffOn.tangentBundle_proj_preimage", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Tangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inTangentCoordinates_eq_mfderiv_comp", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.Tangent", "is_tactic_proof": true, "tactics": ["rw", "congr", "have", "simp_all", "simp", "rw", "simp", "apply", "apply", "simpa"], "tactic_count": 10}
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{"name": "UniqueMDiffWithinAt.image_denseRange", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.UniqueDifferential", "is_tactic_proof": true, "tactics": ["have", "refine", "simp", "mfld_set_tac", "rintro", "exact"], "tactic_count": 6}
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{"name": "UniqueMDiffWithinAt.preimage_openPartialHomeomorph", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.UniqueDifferential", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "UniqueMDiffOn.uniqueMDiffOn_preimage", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.UniqueDifferential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniqueMDiffOn.uniqueMDiffOn_target_inter", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.UniqueDifferential", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
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{"name": "UniqueMDiffOn.uniqueDiffWithinAt_range_inter", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.UniqueDifferential", "is_tactic_proof": true, "tactics": ["apply", "apply"], "tactic_count": 2}
{"name": "UniqueMDiffOn.uniqueDiffOn_inter_preimage", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.MFDeriv.UniqueDifferential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "normedSpaceTangentSpaceVectorSpace", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Riemannian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eventually_norm_mfderiv_extChartAt_lt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Riemannian.Basic", "is_tactic_proof": true, "tactics": ["rcases", "refine", "have", "filter_upwards", "rwa"], "tactic_count": 5}
{"name": "eventually_enorm_mfderiv_extChartAt_lt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Riemannian.Basic", "is_tactic_proof": true, "tactics": ["rcases", "lift", "simp", "refine", "filter_upwards", "simp", "exact_mod_cast"], "tactic_count": 7}
{"name": "eventually_norm_mfderivWithin_symm_extChartAt_comp_lt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Riemannian.Basic", "is_tactic_proof": true, "tactics": ["rcases", "refine", "have", "filter_upwards", "rw", "have", "convert"], "tactic_count": 7}
{"name": "eventually_norm_mfderivWithin_symm_extChartAt_lt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Riemannian.Basic", "is_tactic_proof": true, "tactics": ["rcases", "refine", "have", "rw", "have", "filter_upwards", "have", "simp", "convert"], "tactic_count": 9}
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{"name": "eventually_riemannianEDist_le_edist_extChartAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Riemannian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eventually_riemannianEDist_lt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Riemannian.Basic", "is_tactic_proof": true, "tactics": ["rcases", "have", "apply", "exact", "filter_upwards", "apply", "have", "rwa", "exact", "simp"], "tactic_count": 10}
{"name": "setOf_riemannianEDist_lt_subset_nhds", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Riemannian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "setOf_riemannianEDist_lt_subset_nhds'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Riemannian.Basic", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "PseudoEMetricSpace.ofRiemannianMetric", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Riemannian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsRiemannianManifold", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Riemannian.Basic", "is_tactic_proof": true, "tactics": ["letI", "exact"], "tactic_count": 2}
{"name": "EMetricSpace.ofRiemannianMetric", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Riemannian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold.definition._@.Mathlib.Geometry.Manifold.Riemannian.PathELength.3535955068._hygCtx._hyg.75", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Riemannian.PathELength", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Manifold.pathELength", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Riemannian.PathELength", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold.pathELength_def", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Riemannian.PathELength", "is_tactic_proof": true, "tactics": ["intros", "delta", "rw", "rfl"], "tactic_count": 4}
{"name": "Manifold.pathELength_eq_lintegral_mfderiv_Icc", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Riemannian.PathELength", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Manifold.pathELength_eq_lintegral_mfderiv_Ioo", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Riemannian.PathELength", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Manifold.pathELength_eq_lintegral_mfderivWithin_Icc", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Riemannian.PathELength", "is_tactic_proof": true, "tactics": ["rw", "apply", "rw", "exact"], "tactic_count": 4}
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{"name": "Manifold.pathELength_congr_Ioo", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Riemannian.PathELength", "is_tactic_proof": true, "tactics": ["simp", "apply", "have", "congr", "apply", "filter_upwards"], "tactic_count": 6}
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{"name": "Manifold.pathELength_mono", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Riemannian.PathELength", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Manifold.pathELength_add", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Riemannian.PathELength", "is_tactic_proof": true, "tactics": ["symm", "have", "rw", "exact", "simp"], "tactic_count": 5}
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{"name": "Manifold.riemannianEDist", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Riemannian.PathELength", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "smoothPresheafGroup", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Sheaf.Smooth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "instCommGroupObjOppositeOpensCarrierOfPresheafSmoothSheaf", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Sheaf.Smooth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "smoothSheafCommGroup", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Sheaf.Smooth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smoothSheafCommGroup.compLeft", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Sheaf.Smooth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instRingObjOppositeOpensCarrierOfPresheafSmoothSheaf", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Sheaf.Smooth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smoothPresheafRing", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Sheaf.Smooth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smoothSheafRing", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Sheaf.Smooth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "smoothPresheafCommRing", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Sheaf.Smooth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smoothSheafCommRing", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Sheaf.Smooth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_example", "kind": "example", "module": "Mathlib.Geometry.Manifold.Sheaf.Smooth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smoothSheafCommRing.coeFun", "kind": "instance", "module": "Mathlib.Geometry.Manifold.Sheaf.Smooth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smoothSheafCommRing.forgetStalk", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Sheaf.Smooth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smoothSheafCommRing.ι_forgetStalk_hom", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Sheaf.Smooth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smoothSheafCommRing.ι_forgetStalk_inv", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Sheaf.Smooth", "is_tactic_proof": true, "tactics": ["rw", "simp_rw"], "tactic_count": 2}
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{"name": "smoothSheafCommRing.evalHom", "kind": "definition", "module": "Mathlib.Geometry.Manifold.Sheaf.Smooth", "is_tactic_proof": true, "tactics": ["refine", "apply", "cat_disch"], "tactic_count": 3}
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{"name": "smoothSheafCommRing.forgetStalk_inv_comp_eval", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.Sheaf.Smooth", "is_tactic_proof": true, "tactics": ["apply", "intro", "change", "rw", "ext", "exact"], "tactic_count": 6}
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{"name": "Manifold.term_≫ₕ_", "kind": "definition", "module": "Mathlib.Geometry.Manifold.StructureGroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold._aux_Mathlib_Geometry_Manifold_StructureGroupoid___macroRules_Manifold_term_≫ₕ__1", "kind": "definition", "module": "Mathlib.Geometry.Manifold.StructureGroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold._aux_Mathlib_Geometry_Manifold_StructureGroupoid___unexpand_OpenPartialHomeomorph_trans_1", "kind": "definition", "module": "Mathlib.Geometry.Manifold.StructureGroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold.term_≫_", "kind": "definition", "module": "Mathlib.Geometry.Manifold.StructureGroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold._aux_Mathlib_Geometry_Manifold_StructureGroupoid___macroRules_Manifold_term_≫__1", "kind": "definition", "module": "Mathlib.Geometry.Manifold.StructureGroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold._aux_Mathlib_Geometry_Manifold_StructureGroupoid___unexpand_PartialEquiv_trans_1", "kind": "definition", "module": "Mathlib.Geometry.Manifold.StructureGroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instMembershipOpenPartialHomeomorphStructureGroupoid", "kind": "instance", "module": "Mathlib.Geometry.Manifold.StructureGroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instSetLikeStructureGroupoidOpenPartialHomeomorph", "kind": "instance", "module": "Mathlib.Geometry.Manifold.StructureGroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instMinStructureGroupoid", "kind": "instance", "module": "Mathlib.Geometry.Manifold.StructureGroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInfSetStructureGroupoid", "kind": "instance", "module": "Mathlib.Geometry.Manifold.StructureGroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StructureGroupoid.trans", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.StructureGroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StructureGroupoid.symm", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.StructureGroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StructureGroupoid.id_mem", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.StructureGroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StructureGroupoid.locality", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.StructureGroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StructureGroupoid.mem_of_eqOnSource", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.StructureGroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StructureGroupoid.mem_iff_of_eqOnSource", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.StructureGroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StructureGroupoid.partialOrder", "kind": "instance", "module": "Mathlib.Geometry.Manifold.StructureGroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StructureGroupoid.le_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.StructureGroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "idGroupoid", "kind": "definition", "module": "Mathlib.Geometry.Manifold.StructureGroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instStructureGroupoidOrderBot", "kind": "instance", "module": "Mathlib.Geometry.Manifold.StructureGroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInhabitedStructureGroupoid", "kind": "instance", "module": "Mathlib.Geometry.Manifold.StructureGroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pregroupoid.groupoid", "kind": "definition", "module": "Mathlib.Geometry.Manifold.StructureGroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_groupoid_of_pregroupoid", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.StructureGroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupoid_of_pregroupoid_le", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.StructureGroupoid", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "mem_pregroupoid_of_eqOnSource", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.StructureGroupoid", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "continuousPregroupoid", "kind": "abbrev", "module": "Mathlib.Geometry.Manifold.StructureGroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInhabitedPregroupoid", "kind": "instance", "module": "Mathlib.Geometry.Manifold.StructureGroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousGroupoid", "kind": "definition", "module": "Mathlib.Geometry.Manifold.StructureGroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instStructureGroupoidOrderTop", "kind": "instance", "module": "Mathlib.Geometry.Manifold.StructureGroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCompleteLatticeStructureGroupoid", "kind": "instance", "module": "Mathlib.Geometry.Manifold.StructureGroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "closedUnderRestriction'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.StructureGroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "idRestrGroupoid", "kind": "definition", "module": "Mathlib.Geometry.Manifold.StructureGroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "idRestrGroupoid_mem", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.StructureGroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "closedUnderRestriction_idRestrGroupoid", "kind": "instance", "module": "Mathlib.Geometry.Manifold.StructureGroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "closedUnderRestriction_iff_id_le", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.StructureGroupoid", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "rintro", "refine", "convert", "ext", "intro", "constructor", "intro", "rw", "refine", "apply", "exact"], "tactic_count": 14}
{"name": "instClosedUnderRestrictionContinuousGroupoid", "kind": "instance", "module": "Mathlib.Geometry.Manifold.StructureGroupoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiberBundle.chartedSpace'", "kind": "instance", "module": "Mathlib.Geometry.Manifold.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiberBundle.chartedSpace'_chartAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiberBundle.chartedSpace", "kind": "instance", "module": "Mathlib.Geometry.Manifold.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiberBundle.chartedSpace_chartAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "FiberBundle.chartedSpace_chartAt_symm_fst", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Basic", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "FiberBundle.extChartAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "simp", "rw"], "tactic_count": 3}
{"name": "FiberBundle.extChartAt_target", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Basic", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "FiberBundle.writtenInExtChartAt_trivializationAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiberBundle.writtenInExtChartAt_trivializationAt_symm", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bundle.contMDiffWithinAt_totalSpace", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Basic", "is_tactic_proof": true, "tactics": ["simp", "rw", "intro", "simp_rw", "chartedSpaceSelf_prod]", "refine", "have", "refine", "simp_rw", "rw", "exact", "simp"], "tactic_count": 12}
{"name": "Bundle.contMDiffAt_totalSpace", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Bundle.contMDiffWithinAt_section", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Bundle.contMDiffAt_section", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Bundle.contMDiff_proj", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bundle.contMDiffOn_proj", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bundle.contMDiffAt_proj", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bundle.contMDiffWithinAt_proj", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bundle.contMDiff_zeroSection", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Basic", "is_tactic_proof": true, "tactics": ["intro", "unfold", "rw", "apply", "filter_upwards", "congr_arg"], "tactic_count": 6}
{"name": "Bundle.contMDiffOn_zeroSection", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bundle.contMDiffAt_zeroSection", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bundle.contMDiffWithinAt_zeroSection", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffVectorBundle.of_le", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instContMDiffVectorBundleOfSomeENatTopOfLEInfty", "kind": "instance", "module": "Mathlib.Geometry.Manifold.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instContMDiffVectorBundleOfTopWithTopENat", "kind": "instance", "module": "Mathlib.Geometry.Manifold.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instContMDiffVectorBundleOfNatWithTopENat", "kind": "instance", "module": "Mathlib.Geometry.Manifold.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instContMDiffVectorBundleOfNatWithTopENat_1", "kind": "instance", "module": "Mathlib.Geometry.Manifold.VectorBundle.Basic", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "exact"], "tactic_count": 4}
{"name": "contMDiffOn_coordChangeL", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffOn_symm_coordChangeL", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw"], "tactic_count": 3}
{"name": "contMDiffAt_coordChangeL", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffWithinAt.coordChangeL", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffAt.coordChangeL", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffOn.coordChangeL", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiff.coordChangeL", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffWithinAt.coordChange", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Basic", "is_tactic_proof": true, "tactics": ["refine", "have", "filter_upwards", "exact", "exact"], "tactic_count": 5}
{"name": "ContMDiffAt.coordChange", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffOn.coordChange", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiff.coordChange", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.contMDiffOn_symm_trans", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Basic", "is_tactic_proof": false, "tactics": ["have", "rw", "refine", "rintro", "refine", "have", "simp_all", "exact"], "tactic_count": 8}
{"name": "ContMDiffWithinAt.change_section_trivialization", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "filter_upwards", "rw", "rw"], "tactic_count": 5}
{"name": "Trivialization.contMDiffWithinAt_snd_comp_iff₂", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffFiberwiseLinear.hasGroupoid", "kind": "instance", "module": "Mathlib.Geometry.Manifold.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bundle.TotalSpace.isManifold", "kind": "instance", "module": "Mathlib.Geometry.Manifold.VectorBundle.Basic", "is_tactic_proof": true, "tactics": ["refine", "intro", "rw", "obtain", "rw", "refine", "rw", "apply", "exact", "rw", "apply", "exact"], "tactic_count": 12}
{"name": "Trivialization.contMDiffWithinAt_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.contMDiffAt_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.contMDiffOn_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Basic", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Trivialization.contMDiff_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.contMDiffOn", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Basic", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "Trivialization.contMDiffOn_symm", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw"], "tactic_count": 3}
{"name": "Trivialization.contMDiffWithinAt_section", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Basic", "is_tactic_proof": true, "tactics": ["rw", "change", "simp", "rwa"], "tactic_count": 4}
{"name": "Trivialization.contMDiffAt_section_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Trivialization.contMDiffOn_section_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Basic", "is_tactic_proof": true, "tactics": ["refine", "exact", "exact"], "tactic_count": 3}
{"name": "Trivialization.contMDiffOn_section_baseSet_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorBundleCore.contMDiffOn_coordChange", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorBundleCore.instContMDiffVectorBundle", "kind": "instance", "module": "Mathlib.Geometry.Manifold.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bundle.Trivial.contMDiffVectorBundle", "kind": "instance", "module": "Mathlib.Geometry.Manifold.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bundle.Prod.contMDiffVectorBundle", "kind": "instance", "module": "Mathlib.Geometry.Manifold.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorPrebundle.contMDiffCoordChange", "kind": "definition", "module": "Mathlib.Geometry.Manifold.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorPrebundle.contMDiffOn_contMDiffCoordChange", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorPrebundle.contMDiffCoordChange_apply", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorPrebundle.mk_contMDiffCoordChange", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Basic", "is_tactic_proof": true, "tactics": ["ext", "rw", "rw", "exact"], "tactic_count": 4}
{"name": "VectorPrebundle.contMDiffVectorBundle", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiberwiseLinear.openPartialHomeomorph", "kind": "definition", "module": "Mathlib.Geometry.Manifold.VectorBundle.FiberwiseLinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiberwiseLinear.trans_openPartialHomeomorph_apply", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.FiberwiseLinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiberwiseLinear.source_trans_openPartialHomeomorph", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.FiberwiseLinear", "is_tactic_proof": true, "tactics": ["dsimp"], "tactic_count": 1}
{"name": "FiberwiseLinear.target_trans_openPartialHomeomorph", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.FiberwiseLinear", "is_tactic_proof": true, "tactics": ["dsimp"], "tactic_count": 1}
{"name": "ContMDiffFiberwiseLinear.locality_aux₁", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.FiberwiseLinear", "is_tactic_proof": true, "tactics": ["rw", "choose", "have", "intro", "rw", "exact", "have", "intro", "have", "simpa", "have", "intro", "have", "rw", "exact", "have", "apply", "intro", "exact", "rintro", "exact", "refine", "rintro", "refine", "intro", "rw"], "tactic_count": 26}
{"name": "ContMDiffFiberwiseLinear.locality_aux₂", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.FiberwiseLinear", "is_tactic_proof": true, "tactics": ["classical", "rw", "choose", "have", "refine", "rw", "exact", "have", "ext", "have", "have", "exact", "have", "ext", "rw", "refine", "rintro", "exact", "have", "rw", "apply", "let", "let", "have", "have", "intro", "refine", "exact", "have", "apply", "intro", "refine", "refine", "intro", "rw", "have", "apply", "intro", "refine", "refine", "intro", "rw", "refine", "rw", "rw", "congrm", "rw", "apply"], "tactic_count": 48}
{"name": "_private.Mathlib.Geometry.Manifold.VectorBundle.FiberwiseLinear.0.mem_aux", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.FiberwiseLinear", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "contMDiffFiberwiseLinear", "kind": "definition", "module": "Mathlib.Geometry.Manifold.VectorBundle.FiberwiseLinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_contMDiffFiberwiseLinear_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.FiberwiseLinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Geometry.Manifold.VectorBundle.Hom.0.termLE₁E₂", "kind": "definition", "module": "Mathlib.Geometry.Manifold.VectorBundle.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Geometry.Manifold.VectorBundle.Hom.0._aux_Mathlib_Geometry_Manifold_VectorBundle_Hom___macroRules__private_Mathlib_Geometry_Manifold_VectorBundle_Hom_0_termLE₁E₂_1", "kind": "definition", "module": "Mathlib.Geometry.Manifold.VectorBundle.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Geometry.Manifold.VectorBundle.Hom.0._aux_Mathlib_Geometry_Manifold_VectorBundle_Hom___unexpand_Bundle_TotalSpace_1", "kind": "definition", "module": "Mathlib.Geometry.Manifold.VectorBundle.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffOn_continuousLinearMapCoordChange", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Hom", "is_tactic_proof": true, "tactics": ["have", "have", "refine"], "tactic_count": 3}
{"name": "hom_chart", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Hom", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "contMDiffWithinAt_hom_bundle", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffAt_hom_bundle", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiableOn_continuousLinearMapCoordChange", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Hom", "is_tactic_proof": true, "tactics": ["have", "have", "refine"], "tactic_count": 3}
{"name": "mdifferentiableWithinAt_hom_bundle", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiableAt_hom_bundle", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bundle.ContinuousLinearMap.vectorPrebundle.isContMDiff", "kind": "instance", "module": "Mathlib.Geometry.Manifold.VectorBundle.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffVectorBundle.continuousLinearMap", "kind": "instance", "module": "Mathlib.Geometry.Manifold.VectorBundle.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffWithinAt.clm_apply_of_inCoordinates", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Hom", "is_tactic_proof": true, "tactics": ["rw", "rw", "refine", "apply", "have", "apply", "apply", "exact", "have", "apply", "apply", "exact", "filter_upwards", "rw", "simp", "congr", "rw"], "tactic_count": 17}
{"name": "ContMDiffAt.clm_apply_of_inCoordinates", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Hom", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ContMDiffWithinAt.clm_bundle_apply", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Hom", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "ContMDiffAt.clm_bundle_apply", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffOn.clm_bundle_apply", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiff.clm_bundle_apply", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableWithinAt.clm_bundle_apply", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Hom", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "MDifferentiableAt.clm_bundle_apply", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableOn.clm_bundle_apply", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiable.clm_bundle_apply", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffWithinAt.clm_bundle_apply₂", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffAt.clm_bundle_apply₂", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffOn.clm_bundle_apply₂", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiff.clm_bundle_apply₂", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableWithinAt.clm_bundle_apply₂", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableAt.clm_bundle_apply₂", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableOn.clm_bundle_apply₂", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiable.clm_bundle_apply₂", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalFrameOn.congr", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.LocalFrame", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalFrameOn.mono", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.LocalFrame", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalFrameOn.contMDiffAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.LocalFrame", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalFrameOn.toBasisAt", "kind": "definition", "module": "Mathlib.Geometry.Manifold.VectorBundle.LocalFrame", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalFrameOn.toBasisAt_coe", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.LocalFrame", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsLocalFrameOn.fintypeOfFiniteDimensional", "kind": "definition", "module": "Mathlib.Geometry.Manifold.VectorBundle.LocalFrame", "is_tactic_proof": false, "tactics": ["have", "let", "exact", "exact"], "tactic_count": 4}
{"name": "IsLocalFrameOn.coeff", "kind": "definition", "module": "Mathlib.Geometry.Manifold.VectorBundle.LocalFrame", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalFrameOn.coeff_apply_of_notMem", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.LocalFrame", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsLocalFrameOn.coeff_apply_of_mem", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.LocalFrame", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsLocalFrameOn.coeff_sum_eq", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.LocalFrame", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsLocalFrameOn.eventually_eq_sum_coeff_smul", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.LocalFrame", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalFrameOn.coeff_congr", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.LocalFrame", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "congr", "simp"], "tactic_count": 4}
{"name": "IsLocalFrameOn.coeff_eq_of_eq", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.LocalFrame", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "simp_all", "simp"], "tactic_count": 4}
{"name": "IsLocalFrameOn.eq_iff_coeff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.LocalFrame", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "IsLocalFrameOn.coeff_apply_zero_at", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.LocalFrame", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsLocalFrameOn.contMDiffOn_of_coeff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.LocalFrame", "is_tactic_proof": true, "tactics": ["rcases", "have", "have", "have", "apply", "intro", "simp"], "tactic_count": 7}
{"name": "IsLocalFrameOn.contMDiffAt_of_coeff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.LocalFrame", "is_tactic_proof": true, "tactics": ["have", "have", "exact"], "tactic_count": 3}
{"name": "IsLocalFrameOn.contMDiffAt_of_coeff_aux", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.LocalFrame", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "IsLocalFrameOn.mdifferentiableOn_of_coeff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.LocalFrame", "is_tactic_proof": true, "tactics": ["rcases", "have", "have", "have", "apply", "intro", "simp"], "tactic_count": 7}
{"name": "IsLocalFrameOn.mdifferentiableAt_of_coeff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.LocalFrame", "is_tactic_proof": true, "tactics": ["have", "have", "exact"], "tactic_count": 3}
{"name": "IsLocalFrameOn.mdifferentiableAt_of_coeff_aux", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.LocalFrame", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.basisAt", "kind": "definition", "module": "Mathlib.Geometry.Manifold.VectorBundle.LocalFrame", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.localFrame", "kind": "definition", "module": "Mathlib.Geometry.Manifold.VectorBundle.LocalFrame", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.localFrame_apply_of_mem_baseSet", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.LocalFrame", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Trivialization.localFrame_apply_of_notMem", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.LocalFrame", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Trivialization.contMDiffOn_localFrame_baseSet", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.LocalFrame", "is_tactic_proof": true, "tactics": ["rw", "apply", "intro", "simp"], "tactic_count": 4}
{"name": "Trivialization.isLocalFrameOn_localFrame_baseSet", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.LocalFrame", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiffAt_localFrame_of_mem", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.LocalFrame", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiableWithinAt_totalSpace", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": true, "tactics": ["simp", "rw", "intro", "simp_rw", "chartedSpaceSelf_prod]", "refine", "have", "refine", "simp_rw", "rw", "exact", "simp"], "tactic_count": 12}
{"name": "mdifferentiableAt_totalSpace", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "mdifferentiableWithinAt_section", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": true, "tactics": ["rw", "change", "simp"], "tactic_count": 3}
{"name": "mdifferentiableAt_section", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Bundle.mdifferentiable_proj", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bundle.mdifferentiableOn_proj", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bundle.mdifferentiableAt_proj", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bundle.mdifferentiableWithinAt_proj", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bundle.mdifferentiable_zeroSection", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": true, "tactics": ["intro", "unfold", "rw", "apply", "filter_upwards", "congr_arg"], "tactic_count": 6}
{"name": "Bundle.mdifferentiableOn_zeroSection", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bundle.mdifferentiableAt_zeroSection", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bundle.mdifferentiableWithinAt_zeroSection", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiableOn_coordChangeL", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiableOn_symm_coordChangeL", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiableAt_coordChangeL", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableWithinAt.coordChangeL", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableAt.coordChangeL", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableOn.coordChangeL", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiable.coordChangeL", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableWithinAt.coordChange", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": true, "tactics": ["refine", "have", "filter_upwards", "exact", "exact"], "tactic_count": 5}
{"name": "MDifferentiableAt.coordChange", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableOn.coordChange", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiable.coordChange", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableWithinAt.change_section_trivialization", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": true, "tactics": ["rw", "refine", "filter_upwards", "rw", "rw"], "tactic_count": 5}
{"name": "Trivialization.mdifferentiableWithinAt_snd_comp_iff₂", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.mdifferentiableAt_snd_comp_iff₂", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Trivialization.mdifferentiableWithinAt_totalSpace_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": true, "tactics": ["rw", "apply", "intro", "rw"], "tactic_count": 4}
{"name": "Trivialization.mdifferentiableAt_totalSpace_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": true, "tactics": ["rw", "apply", "intro", "rw"], "tactic_count": 4}
{"name": "Trivialization.mdifferentiableWithinAt_section_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": true, "tactics": ["rw", "change", "simp", "exact"], "tactic_count": 4}
{"name": "Trivialization.mdifferentiableAt_section_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Trivialization.mdifferentiableOn_section_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": true, "tactics": ["refine", "exact", "exact"], "tactic_count": 3}
{"name": "Trivialization.mdifferentiableOn_section_baseSet_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiableWithinAt_add_section", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": true, "tactics": ["rw", "set", "refine", "apply", "exact", "exact", "exact"], "tactic_count": 7}
{"name": "mdifferentiableAt_add_section", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "mdifferentiableOn_add_section", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiable_add_section", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiableWithinAt_neg_section", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": true, "tactics": ["rw", "set", "refine", "apply", "exact", "exact", "exact"], "tactic_count": 7}
{"name": "mdifferentiableAt_neg_section", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "mdifferentiableOn_neg_section", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiable_neg_section", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiableWithinAt_sub_section", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "mdifferentiableAt_sub_section", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "mDifferentiableOn_sub_section", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiable_sub_section", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableWithinAt.smul_section", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": true, "tactics": ["rw", "set", "refine", "apply", "exact", "exact", "apply"], "tactic_count": 7}
{"name": "MDifferentiableAt.smul_section", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MDifferentiableOn.smul_section", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiable_smul_section", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiableWithinAt_smul_const_section", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableAt.smul_const_section", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableOn.smul_const_section", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mdifferentiable_smul_const_section", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableWithinAt.sum_section", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "insert"], "tactic_count": 4}
{"name": "MDifferentiableAt.sum_section", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "MDifferentiableOn.sum_section", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiable.sum_section", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableOn.smul_section_of_tsupport", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": false, "tactics": ["apply", "mdifferentiable_of_mdifferentiableOn_union_of_isOpen", "apply", "intro", "simp", "exact"], "tactic_count": 6}
{"name": "MDifferentiableWithinAt.sum_section_of_locallyFinite", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": true, "tactics": ["obtain", "let", "have", "have", "apply", "apply", "rw", "refine", "by_contra", "have", "refine", "simp", "use", "simp", "exact"], "tactic_count": 15}
{"name": "MDifferentiableAt.sum_section_of_locallyFinite", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "MDifferentiableOn.sum_section_of_locallyFinite", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiable.sum_section_of_locallyFinite", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableWithinAt.finsum_section_of_locallyFinite", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": false, "tactics": ["apply", "trivial", "choose", "have", "intro", "rw", "use", "simpa", "rw"], "tactic_count": 9}
{"name": "MDifferentiableAt.finsum_section_of_locallyFinite", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "MDifferentiableOn.finsum_section_of_locallyFinite", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiable.finsum_section_of_locallyFinite", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableWithinAt.clm_apply_of_inCoordinates", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": true, "tactics": ["rw", "refine", "apply", "have", "apply", "apply", "exact", "have", "apply", "apply", "exact", "filter_upwards", "rw", "simp", "congr", "rw"], "tactic_count": 16}
{"name": "MDifferentiableAt.clm_apply_of_inCoordinates", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ContMDiffVectorBundle.pullback", "kind": "instance", "module": "Mathlib.Geometry.Manifold.VectorBundle.Pullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Geometry.Manifold.VectorBundle.Riemannian.0.term⟪_,_⟫", "kind": "definition", "module": "Mathlib.Geometry.Manifold.VectorBundle.Riemannian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Geometry.Manifold.VectorBundle.Riemannian.0._aux_Mathlib_Geometry_Manifold_VectorBundle_Riemannian___macroRules__private_Mathlib_Geometry_Manifold_VectorBundle_Riemannian_0_term⟪_,_⟫_1", "kind": "definition", "module": "Mathlib.Geometry.Manifold.VectorBundle.Riemannian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Geometry.Manifold.VectorBundle.Riemannian.0._aux_Mathlib_Geometry_Manifold_VectorBundle_Riemannian___unexpand_Inner_inner_1", "kind": "definition", "module": "Mathlib.Geometry.Manifold.VectorBundle.Riemannian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsContMDiffRiemannianBundle.of_le", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Riemannian", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "instIsContMDiffRiemannianBundleOfSomeENatTopOfLEInfty", "kind": "instance", "module": "Mathlib.Geometry.Manifold.VectorBundle.Riemannian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsContMDiffRiemannianBundleOfTopWithTopENat", "kind": "instance", "module": "Mathlib.Geometry.Manifold.VectorBundle.Riemannian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsContMDiffRiemannianBundleOfNatWithTopENat", "kind": "instance", "module": "Mathlib.Geometry.Manifold.VectorBundle.Riemannian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsContMDiffRiemannianBundleOfNatWithTopENat_1", "kind": "instance", "module": "Mathlib.Geometry.Manifold.VectorBundle.Riemannian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsContMDiffRiemannianBundleOfNatWithTopENat_2", "kind": "instance", "module": "Mathlib.Geometry.Manifold.VectorBundle.Riemannian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsContMDiffRiemannianBundleTrivial", "kind": "instance", "module": "Mathlib.Geometry.Manifold.VectorBundle.Riemannian", "is_tactic_proof": true, "tactics": ["refine", "simp", "convert", "ext", "simp"], "tactic_count": 5}
{"name": "ContMDiffWithinAt.inner_bundle", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Riemannian", "is_tactic_proof": true, "tactics": ["rcases", "have", "simp", "exact", "simp", "have", "apply", "exact", "exact", "exact", "simp", "exact"], "tactic_count": 12}
{"name": "ContMDiffAt.inner_bundle", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Riemannian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffOn.inner_bundle", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Riemannian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiff.inner_bundle", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Riemannian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableWithinAt.inner_bundle", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Riemannian", "is_tactic_proof": true, "tactics": ["rcases", "have", "simp", "exact", "simp", "have", "apply", "exact", "exact", "exact", "simp", "exact"], "tactic_count": 12}
{"name": "MDifferentiableAt.inner_bundle", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Riemannian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiableOn.inner_bundle", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Riemannian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MDifferentiable.inner_bundle", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Riemannian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bundle.ContMDiffRiemannianMetric.toContinuousRiemannianMetric", "kind": "definition", "module": "Mathlib.Geometry.Manifold.VectorBundle.Riemannian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bundle.ContMDiffRiemannianMetric.toRiemannianMetric", "kind": "definition", "module": "Mathlib.Geometry.Manifold.VectorBundle.Riemannian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bundle.instIsContMDiffRiemannianBundle", "kind": "instance", "module": "Mathlib.Geometry.Manifold.VectorBundle.Riemannian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffWithinAt.add_section", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.SmoothSection", "is_tactic_proof": true, "tactics": ["rw", "set", "refine", "apply", "exact", "intro", "apply", "apply"], "tactic_count": 8}
{"name": "ContMDiffAt.add_section", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.SmoothSection", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ContMDiffOn.add_section", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.SmoothSection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiff.add_section", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.SmoothSection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffWithinAt.neg_section", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.SmoothSection", "is_tactic_proof": true, "tactics": ["rw", "set", "refine", "apply", "exact", "intro", "apply", "apply"], "tactic_count": 8}
{"name": "ContMDiffAt.neg_section", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.SmoothSection", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ContMDiffOn.neg_section", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.SmoothSection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiff.neg_section", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.SmoothSection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffWithinAt.sub_section", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.SmoothSection", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ContMDiffAt.sub_section", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.SmoothSection", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "ContMDiffOn.sub_section", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.SmoothSection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiff.sub_section", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.SmoothSection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffWithinAt.smul_section", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.SmoothSection", "is_tactic_proof": true, "tactics": ["rw", "set", "refine", "apply", "exact", "intro", "apply", "apply"], "tactic_count": 8}
{"name": "ContMDiffAt.smul_section", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.SmoothSection", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ContMDiffOn.smul_section", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.SmoothSection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiff.smul_section", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.SmoothSection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffWithinAt.const_smul_section", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.SmoothSection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffAt.const_smul_section", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.SmoothSection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffOn.const_smul_section", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.SmoothSection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiff.const_smul_section", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.SmoothSection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffWithinAt.sum_section", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.SmoothSection", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "insert", "simp", "apply", "exact"], "tactic_count": 7}
{"name": "ContMDiffAt.sum_section", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.SmoothSection", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "ContMDiffOn.sum_section", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.SmoothSection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiff.sum_section", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.SmoothSection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffOn.smul_section_of_tsupport", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.SmoothSection", "is_tactic_proof": false, "tactics": ["apply", "contMDiff_of_contMDiffOn_union_of_isOpen", "apply", "intro", "simp", "exact"], "tactic_count": 6}
{"name": "ContMDiffWithinAt.sum_section_of_locallyFinite", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.SmoothSection", "is_tactic_proof": true, "tactics": ["obtain", "let", "have", "have", "apply", "apply", "rw", "refine", "by_contra", "have", "refine", "simp", "use", "simpa", "exact", "rw", "refine", "by_contra", "have", "refine", "simp", "use", "simpa", "exact"], "tactic_count": 24}
{"name": "ContMDiffAt.sum_section_of_locallyFinite", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.SmoothSection", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "ContMDiffOn.sum_section_of_locallyFinite", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.SmoothSection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiff.sum_section_of_locallyFinite", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.SmoothSection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffWithinAt.finsum_section_of_locallyFinite", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.SmoothSection", "is_tactic_proof": false, "tactics": ["apply", "rw", "choose", "have", "intro", "rw", "use", "simpa", "exact"], "tactic_count": 9}
{"name": "ContMDiffAt.finsum_section_of_locallyFinite", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.SmoothSection", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "ContMDiffOn.finsum_section_of_locallyFinite", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.SmoothSection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiff.finsum_section_of_locallyFinite", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.SmoothSection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold.termCₛ^_⟮_;_,_⟯", "kind": "definition", "module": "Mathlib.Geometry.Manifold.VectorBundle.SmoothSection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold._aux_Mathlib_Geometry_Manifold_VectorBundle_SmoothSection___macroRules_Manifold_termCₛ^_⟮_;_,_⟯_1", "kind": "definition", "module": "Mathlib.Geometry.Manifold.VectorBundle.SmoothSection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Manifold._aux_Mathlib_Geometry_Manifold_VectorBundle_SmoothSection___unexpand_ContMDiffSection_1", "kind": "definition", "module": "Mathlib.Geometry.Manifold.VectorBundle.SmoothSection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffSection.instDFunLike", "kind": "instance", "module": "Mathlib.Geometry.Manifold.VectorBundle.SmoothSection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffSection.coeFn_mk", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.SmoothSection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffSection.contMDiff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.SmoothSection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffSection.coe_inj", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.SmoothSection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffSection.coe_injective", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.SmoothSection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffSection.ext", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.SmoothSection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffSection.instAdd", "kind": "instance", "module": "Mathlib.Geometry.Manifold.VectorBundle.SmoothSection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffSection.coe_add", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.SmoothSection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffSection.instSub", "kind": "instance", "module": "Mathlib.Geometry.Manifold.VectorBundle.SmoothSection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffSection.coe_sub", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.SmoothSection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffSection.instZero", "kind": "instance", "module": "Mathlib.Geometry.Manifold.VectorBundle.SmoothSection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffSection.inhabited", "kind": "instance", "module": "Mathlib.Geometry.Manifold.VectorBundle.SmoothSection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffSection.coe_zero", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.SmoothSection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffSection.instNeg", "kind": "instance", "module": "Mathlib.Geometry.Manifold.VectorBundle.SmoothSection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffSection.coe_neg", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.SmoothSection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffSection.instNSMul", "kind": "instance", "module": "Mathlib.Geometry.Manifold.VectorBundle.SmoothSection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffSection.coe_nsmul", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.SmoothSection", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "ContMDiffSection.instZSMul", "kind": "instance", "module": "Mathlib.Geometry.Manifold.VectorBundle.SmoothSection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffSection.coe_zsmul", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.SmoothSection", "is_tactic_proof": true, "tactics": ["rcases", "refine", "simp", "refine", "simp"], "tactic_count": 5}
{"name": "ContMDiffSection.instAddCommGroup", "kind": "instance", "module": "Mathlib.Geometry.Manifold.VectorBundle.SmoothSection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffSection.instSMul", "kind": "instance", "module": "Mathlib.Geometry.Manifold.VectorBundle.SmoothSection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffSection.coe_smul", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.SmoothSection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffSection.coeAddHom", "kind": "definition", "module": "Mathlib.Geometry.Manifold.VectorBundle.SmoothSection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffSection.coeAddHom_apply", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.SmoothSection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffSection.instModule", "kind": "instance", "module": "Mathlib.Geometry.Manifold.VectorBundle.SmoothSection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffSection.mdifferentiable'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.SmoothSection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffSection.mdifferentiable", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.SmoothSection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContMDiffSection.mdifferentiableAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.SmoothSection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contDiffOn_fderiv_coord_change", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Tangent", "is_tactic_proof": false, "tactics": ["have", "apply", "intro", "refine", "refine", "hx).mono_of_mem_nhdsWithin", "exact"], "tactic_count": 7}
{"name": "tangentBundleCore", "kind": "definition", "module": "Mathlib.Geometry.Manifold.VectorBundle.Tangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tangentBundleCore_baseSet", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Tangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tangentBundleCore_localTriv_baseSet", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Tangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tangentBundleCore_coordChange_achart", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Tangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tangentCoordChange", "kind": "abbrev", "module": "Mathlib.Geometry.Manifold.VectorBundle.Tangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tangentCoordChange_def", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Tangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tangentCoordChange_self", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Tangent", "is_tactic_proof": true, "tactics": ["apply", "rw", "exact"], "tactic_count": 3}
{"name": "tangentCoordChange_comp", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Tangent", "is_tactic_proof": true, "tactics": ["apply", "simp", "exact"], "tactic_count": 3}
{"name": "hasFDerivWithinAt_tangentCoordChange", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Tangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousOn_tangentCoordChange", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Tangent", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "_private.Mathlib.Geometry.Manifold.VectorBundle.Tangent.0.termTM", "kind": "definition", "module": "Mathlib.Geometry.Manifold.VectorBundle.Tangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Geometry.Manifold.VectorBundle.Tangent.0._aux_Mathlib_Geometry_Manifold_VectorBundle_Tangent___macroRules__private_Mathlib_Geometry_Manifold_VectorBundle_Tangent_0_termTM_1", "kind": "definition", "module": "Mathlib.Geometry.Manifold.VectorBundle.Tangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Geometry.Manifold.VectorBundle.Tangent.0._aux_Mathlib_Geometry_Manifold_VectorBundle_Tangent___unexpand_TangentBundle_1", "kind": "definition", "module": "Mathlib.Geometry.Manifold.VectorBundle.Tangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instTopologicalSpaceTangentBundle", "kind": "instance", "module": "Mathlib.Geometry.Manifold.VectorBundle.Tangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TangentSpace.fiberBundle", "kind": "instance", "module": "Mathlib.Geometry.Manifold.VectorBundle.Tangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TangentSpace.vectorBundle", "kind": "instance", "module": "Mathlib.Geometry.Manifold.VectorBundle.Tangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TangentBundle.chartAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Tangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TangentBundle.chartAt_toPartialEquiv", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Tangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TangentBundle.trivializationAt_eq_localTriv", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Tangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TangentBundle.trivializationAt_source", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Tangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TangentBundle.trivializationAt_target", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Tangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TangentBundle.trivializationAt_baseSet", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Tangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TangentBundle.trivializationAt_apply", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Tangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TangentBundle.trivializationAt_fst", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Tangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TangentBundle.mem_chart_source_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Tangent", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "TangentBundle.mem_chart_target_iff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Tangent", "is_tactic_proof": true, "tactics": ["simp", "and_iff_left_iff_imp,", "simp", "rw", "simp"], "tactic_count": 5}
{"name": "TangentBundle.coe_chartAt_fst", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Tangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TangentBundle.coe_chartAt_symm_fst", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Tangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TangentBundle.continuousLinearMapAt_trivializationAt_eq_core", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Tangent", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "TangentBundle.symmL_trivializationAt_eq_core", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Tangent", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "TangentBundle.coordChange_model_space", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Tangent", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "TangentBundle.symmL_model_space", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Tangent", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "TangentBundle.continuousLinearMapAt_model_space", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Tangent", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "tangentBundleCore.isContMDiff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Tangent", "is_tactic_proof": true, "tactics": ["have", "refine", "rw", "refine", "rw", "simp_rw", "exact", "apply"], "tactic_count": 8}
{"name": "TangentBundle.contMDiffVectorBundle", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Tangent", "is_tactic_proof": true, "tactics": ["have", "have", "exact"], "tactic_count": 3}
{"name": "instContMDiffVectorBundleSomeENatTopTangentSpaceOfIsManifold", "kind": "instance", "module": "Mathlib.Geometry.Manifold.VectorBundle.Tangent", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "instContMDiffVectorBundleTopWithTopENatTangentSpaceOfIsManifold", "kind": "instance", "module": "Mathlib.Geometry.Manifold.VectorBundle.Tangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instContMDiffVectorBundleOfNatWithTopENatTangentSpaceOfIsManifold", "kind": "instance", "module": "Mathlib.Geometry.Manifold.VectorBundle.Tangent", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "trivializationAt_model_space_apply", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Tangent", "is_tactic_proof": true, "tactics": ["simp", "have", "fderivWithin_congr", "simp"], "tactic_count": 4}
{"name": "tangentBundle_model_space_chartAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Tangent", "is_tactic_proof": true, "tactics": ["ext", "ext", "exact", "ext", "apply", "exact", "simp_rw", "simp"], "tactic_count": 8}
{"name": "tangentBundle_model_space_coe_chartAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Tangent", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "tangentBundle_model_space_coe_chartAt_symm", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Tangent", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "tangentBundleCore_coordChange_model_space", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Tangent", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "tangentBundleModelSpaceHomeomorph", "kind": "definition", "module": "Mathlib.Geometry.Manifold.VectorBundle.Tangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tangentBundleModelSpaceHomeomorph_coe", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Tangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tangentBundleModelSpaceHomeomorph_coe_symm", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Tangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contMDiff_tangentBundleModelSpaceHomeomorph", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Tangent", "is_tactic_proof": true, "tactics": ["apply", "apply", "simp", "rintro", "simp"], "tactic_count": 5}
{"name": "contMDiff_tangentBundleModelSpaceHomeomorph_symm", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Tangent", "is_tactic_proof": true, "tactics": ["apply", "apply", "simp", "rintro", "simpa"], "tactic_count": 5}
{"name": "contMDiff_snd_tangentBundle_modelSpace", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Tangent", "is_tactic_proof": false, "tactics": ["change", "apply", "convert", "rw", "rfl", "exact"], "tactic_count": 6}
{"name": "contMDiffWithinAt_vectorSpace_iff_contDiffWithinAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Tangent", "is_tactic_proof": true, "tactics": ["refine", "exact", "apply", "refine", "convert", "simp"], "tactic_count": 6}
{"name": "contMDiffAt_vectorSpace_iff_contDiffAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Tangent", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "contMDiffOn_vectorSpace_iff_contDiffOn", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Tangent", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "contMDiff_vectorSpace_iff_contDiff", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Tangent", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "inCoordinates_tangent_bundle_core_model_space", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Tangent", "is_tactic_proof": true, "tactics": ["erw", "simp_rw"], "tactic_count": 2}
{"name": "inTangentCoordinates", "kind": "definition", "module": "Mathlib.Geometry.Manifold.VectorBundle.Tangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inTangentCoordinates_model_space", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Tangent", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "inTangentCoordinates_eq", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorBundle.Tangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorField.mlieBracketWithin", "kind": "definition", "module": "Mathlib.Geometry.Manifold.VectorField.LieBracket", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorField.mlieBracket", "kind": "definition", "module": "Mathlib.Geometry.Manifold.VectorField.LieBracket", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorField.mlieBracketWithin_def", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorField.LieBracket", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorField.mlieBracketWithin_apply", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorField.LieBracket", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorField.mlieBracketWithin_eq_lieBracketWithin", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorField.LieBracket", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "VectorField.mlieBracketWithin_univ", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorField.LieBracket", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorField.mlieBracketWithin_eq_zero_of_eq_zero", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorField.LieBracket", "is_tactic_proof": true, "tactics": ["simp", "rw", "simp", "simp", "have", "rw", "simp", "simp", "have", "rw", "simp"], "tactic_count": 11}
{"name": "VectorField.mlieBracketWithin_swap_apply", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorField.LieBracket", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "VectorField.mlieBracketWithin_swap", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorField.LieBracket", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "VectorField.mlieBracket_swap_apply", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorField.LieBracket", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorField.mlieBracket_swap", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorField.LieBracket", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorField.mlieBracketWithin_self", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorField.LieBracket", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "VectorField.mlieBracket_self", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorField.LieBracket", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "VectorField.mlieBracketWithin_zero_left", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorField.LieBracket", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "VectorField.mlieBracketWithin_zero_right", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorField.LieBracket", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "VectorField.mlieBracket_zero_left", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorField.LieBracket", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "VectorField.mlieBracket_zero_right", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorField.LieBracket", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "VectorField.mlieBracketWithin_congr_set'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorField.LieBracket", "is_tactic_proof": true, "tactics": ["simp", "congr", "suffices", "exact"], "tactic_count": 4}
{"name": "VectorField.mlieBracketWithin_congr_set", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorField.LieBracket", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorField.mlieBracketWithin_inter", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorField.LieBracket", "is_tactic_proof": true, "tactics": ["apply", "filter_upwards", "change", "simp_all"], "tactic_count": 4}
{"name": "VectorField.mlieBracketWithin_of_mem_nhds", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorField.LieBracket", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "VectorField.mlieBracketWithin_of_isOpen", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorField.LieBracket", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorField.mlieBracketWithin_eventually_congr_set'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorField.LieBracket", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorField.mlieBracketWithin_eventually_congr_set", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorField.LieBracket", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.mlieBracketWithin_vectorField_eq", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorField.LieBracket", "is_tactic_proof": true, "tactics": ["simp", "congr", "let", "let", "apply", "apply", "filter_upwards", "hy", "simp", "congr", "simp", "congr", "convert", "apply", "filter_upwards", "hy", "simp", "congr", "simp", "congr", "convert"], "tactic_count": 21}
{"name": "Filter.EventuallyEq.mlieBracketWithin_vectorField_eq_of_mem", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorField.LieBracket", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.mlieBracketWithin_vectorField'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorField.LieBracket", "is_tactic_proof": false, "tactics": ["filter_upwards", "hVy", "apply", "apply", "exact", "exact", "apply", "exact", "exact"], "tactic_count": 9}
{"name": "Filter.EventuallyEq.mlieBracketWithin_vectorField", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorField.LieBracket", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.mlieBracketWithin_vectorField_of_insert", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorField.LieBracket", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "Filter.EventuallyEq.mlieBracketWithin_vectorField_eq_nhds", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorField.LieBracket", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorField.mlieBracketWithin_congr", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorField.LieBracket", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorField.mlieBracketWithin_congr'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorField.LieBracket", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.mlieBracket_vectorField_eq", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorField.LieBracket", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.EventuallyEq.mlieBracket_vectorField", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorField.LieBracket", "is_tactic_proof": true, "tactics": ["filter_upwards", "exact"], "tactic_count": 2}
{"name": "MDifferentiableWithinAt.differentiableWithinAt_mpullbackWithin_vectorField", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorField.LieBracket", "is_tactic_proof": true, "tactics": ["apply", "have", "rw", "exact", "one_ne_zero).comp_mdifferentiableWithinAt"], "tactic_count": 5}
{"name": "VectorField.mlieBracketWithin_const_smul_left", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorField.LieBracket", "is_tactic_proof": true, "tactics": ["simp", "rw", "exact", "exact"], "tactic_count": 4}
{"name": "VectorField.mlieBracket_const_smul_left", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorField.LieBracket", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "VectorField.mlieBracketWithin_const_smul_right", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorField.LieBracket", "is_tactic_proof": true, "tactics": ["simp", "rw", "exact", "exact"], "tactic_count": 4}
{"name": "VectorField.mlieBracket_const_smul_right", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorField.LieBracket", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "VectorField.mlieBracketWithin_add_left", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorField.LieBracket", "is_tactic_proof": true, "tactics": ["simp", "rw", "exact", "exact", "exact"], "tactic_count": 5}
{"name": "VectorField.mlieBracket_add_left", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorField.LieBracket", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "VectorField.mlieBracketWithin_add_right", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorField.LieBracket", "is_tactic_proof": false, "tactics": ["rw", "mlieBracketWithin_swap", "abel"], "tactic_count": 3}
{"name": "VectorField.mlieBracket_add_right", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorField.LieBracket", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "VectorField.mlieBracketWithin_of_mem_nhdsWithin", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorField.LieBracket", "is_tactic_proof": true, "tactics": ["simp", "congr", "rw", "apply", "apply", "exact", "exact", "exact", "exact", "exact"], "tactic_count": 10}
{"name": "VectorField.mlieBracketWithin_subset", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorField.LieBracket", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorField.mlieBracketWithin_eq_mlieBracket", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorField.LieBracket", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "DifferentiableWithinAt.mlieBracketWithin_congr_mono", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorField.LieBracket", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "_private.Mathlib.Geometry.Manifold.VectorField.LieBracket.0.VectorField.mpullbackWithin_mlieBracketWithin_aux", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorField.LieBracket", "is_tactic_proof": true, "tactics": ["have", "have", "have", "simp", "rw", "rw", "mfderiv_comp_mfderivWithin", "rw", "have", "mfderiv", "apply", "convert", "mfderivWithin_extChartAt_symm_comp_mfderiv_extChartAt", "convert", "mfderiv_extChartAt_comp_mfderivWithin_extChartAt_symm", "rw", "exact", "have", "mfderivWithin", "mfderivWithin", "rw", "rw", "apply", "exact", "exact", "exact", "exact", "simp", "set", "set", "set", "have", "rw", "have", "mpullbackWithin", "have", "nhdsWithin_mono", "filter_upwards", "have", "have", "have", "apply", "rw", "apply", "exact", "simp", "rw", "apply", "exact", "exact", "exact", "exact", "rw", "exact", "exact", "exact", "rw", "exact", "rw", "exact", "have", "f", "congr", "have", "simp", "congr", "exact", "rw", "simp", "rw", "exact", "rw", "apply", "apply", "exact", "apply", "exact", "exact", "rw", "exact", "rw", "exact", "rw", "exact", "simp", "intro", "simp", "refine", "convert", "exact", "rw", "apply", "exact", "rw", "exact", "diffeomorphisms."], "tactic_count": 96}
{"name": "VectorField.mpullbackWithin_mlieBracketWithin_of_isSymmSndFDerivWithinAt", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorField.LieBracket", "is_tactic_proof": true, "tactics": ["have", "by_cases", "simp", "rw", "simp", "simp", "rw", "simp", "simp", "rw", "simp", "have", "rcases", "let", "exact", "obtain", "x₀", "obtain", "hf.contMDiffOn", "have", "hf.continuousWithinAt.preimage_mem_nhdsWithin", "rcases", "refine", "apply", "exact", "apply", "exact", "apply", "exact", "have", "set", "have", "filter_upwards", "change", "simp", "set", "calc", "mpullbackWithin", "simp", "simp", "apply", "mpullbackWithin_mlieBracketWithin_aux", "apply", "have", "apply", "apply", "filter_upwards", "change", "simp", "simp", "apply", "apply", "filter_upwards", "simp", "apply", "filter_upwards", "simp"], "tactic_count": 57}
{"name": "VectorField.mpullbackWithin_mlieBracketWithin'", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorField.LieBracket", "is_tactic_proof": false, "tactics": ["have", "apply", "exact", "apply", "mpullbackWithin_mlieBracketWithin_of_isSymmSndFDerivWithinAt", "have", "apply", "have", "apply", "rw", "exact", "apply", "simp", "exact", "apply", "apply", "exact", "rw", "exact", "rw", "exact", "simp"], "tactic_count": 22}
{"name": "VectorField.mpullbackWithin_mlieBracketWithin", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorField.LieBracket", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorField.mpullback_mlieBracketWithin", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorField.LieBracket", "is_tactic_proof": false, "tactics": ["have", "simp", "congr", "apply", "exact", "rw", "mpullbackWithin_mlieBracketWithin", "apply", "rw", "filter_upwards", "self_mem_nhdsWithin]", "simp", "congr", "apply", "exact", "rw", "filter_upwards", "self_mem_nhdsWithin]", "simp", "congr", "apply", "exact"], "tactic_count": 22}
{"name": "VectorField.mpullback_mlieBracket", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorField.LieBracket", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "ContMDiffWithinAt.mlieBracketWithin_vectorField", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorField.LieBracket", "is_tactic_proof": true, "tactics": ["different", "use", "in", "space", "locally", "under", "have", "grw", "exact", "apply", "have", "have", "have", "filter_upwards", "exact", "let", "let", "have", "have", "rw", "exact", "have", "s", "apply", "filter_upwards", "eventually_eventually_nhdsWithin.2", "eventually_eventually_nhdsWithin.2", "eventually_contMDiffWithinAt_mpullbackWithin_extChartAt_symm", "eventually_contMDiffWithinAt_mpullbackWithin_extChartAt_symm", "nhdsWithin_le_nhds", "simp", "rw", "exact"], "tactic_count": 33}
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{"name": "instIsManifoldOfNatWithTopENatOfMinSmoothness_1", "kind": "instance", "module": "Mathlib.Geometry.Manifold.VectorField.Pullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "VectorField.mpullbackWithin", "kind": "definition", "module": "Mathlib.Geometry.Manifold.VectorField.Pullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorField.mpullback", "kind": "definition", "module": "Mathlib.Geometry.Manifold.VectorField.Pullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorField.mpullbackWithin_apply", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorField.Pullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "VectorField.mpullbackWithin_add_apply", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorField.Pullback", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "VectorField.mpullbackWithin_add", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorField.Pullback", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "VectorField.mpullbackWithin_zero", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorField.Pullback", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "VectorField.mpullbackWithin_neg_apply", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorField.Pullback", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "VectorField.mpullbackWithin_id", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorField.Pullback", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "VectorField.mpullbackWithin_eq_pullbackWithin", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorField.Pullback", "is_tactic_proof": true, "tactics": ["ext", "simp", "rfl"], "tactic_count": 3}
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{"name": "VectorField.contMDiffWithinAt_mpullbackWithin_extChartAt_symm", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.VectorField.Pullback", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SmoothBumpCovering.embeddingPiTangent", "kind": "definition", "module": "Mathlib.Geometry.Manifold.WhitneyEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SmoothBumpCovering.embeddingPiTangent_coe", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.WhitneyEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SmoothBumpCovering.embeddingPiTangent_injOn", "kind": "theorem", "module": "Mathlib.Geometry.Manifold.WhitneyEmbedding", "is_tactic_proof": true, "tactics": ["intro", "simp", "obtain", "rw", "rw", "have", "exact"], "tactic_count": 7}
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{"name": "Polygon.instCoeFunForallFin", "kind": "instance", "module": "Mathlib.Geometry.Polygon.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polygon.edgePath", "kind": "definition", "module": "Mathlib.Geometry.Polygon.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AlgebraicGeometry.RingedSpace", "kind": "abbrev", "module": "Mathlib.Geometry.RingedSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.RingedSpace.res_zero", "kind": "theorem", "module": "Mathlib.Geometry.RingedSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AlgebraicGeometry.RingedSpace.zeroLocus_isClosed", "kind": "theorem", "module": "Mathlib.Geometry.RingedSpace.Basic", "is_tactic_proof": true, "tactics": ["apply", "intro", "simp", "exact"], "tactic_count": 4}
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{"name": "AlgebraicGeometry.RingedSpace.mem_zeroLocus_iff", "kind": "theorem", "module": "Mathlib.Geometry.RingedSpace.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "AlgebraicGeometry.LocallyRingedSpace.instIsLocalRingCarrierStalkCommRingCatPresheaf", "kind": "instance", "module": "Mathlib.Geometry.RingedSpace.LocallyRingedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AlgebraicGeometry.LocallyRingedSpace.Hom.toShHom", "kind": "abbrev", "module": "Mathlib.Geometry.RingedSpace.LocallyRingedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.LocallyRingedSpace.Hom.toShHom_mk", "kind": "theorem", "module": "Mathlib.Geometry.RingedSpace.LocallyRingedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AlgebraicGeometry.LocallyRingedSpace.Hom.ext'", "kind": "theorem", "module": "Mathlib.Geometry.RingedSpace.LocallyRingedSpace", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
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{"name": "AlgebraicGeometry.LocallyRingedSpace.isLocalHomStalkMap", "kind": "theorem", "module": "Mathlib.Geometry.RingedSpace.LocallyRingedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.LocallyRingedSpace.isLocalHomStalkMap'", "kind": "instance", "module": "Mathlib.Geometry.RingedSpace.LocallyRingedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AlgebraicGeometry.LocallyRingedSpace.instFaithfulSheafedSpaceCommRingCatForgetToSheafedSpace", "kind": "instance", "module": "Mathlib.Geometry.RingedSpace.LocallyRingedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AlgebraicGeometry.LocallyRingedSpace.id_toHom", "kind": "theorem", "module": "Mathlib.Geometry.RingedSpace.LocallyRingedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier", "kind": "instance", "module": "Mathlib.Geometry.RingedSpace.SheafedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.SheafedSpace.unit", "kind": "definition", "module": "Mathlib.Geometry.RingedSpace.SheafedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.SheafedSpace.instInhabitedDiscreteUnit", "kind": "instance", "module": "Mathlib.Geometry.RingedSpace.SheafedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.SheafedSpace.instCategory", "kind": "instance", "module": "Mathlib.Geometry.RingedSpace.SheafedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.SheafedSpace.ext", "kind": "theorem", "module": "Mathlib.Geometry.RingedSpace.SheafedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.SheafedSpace.isoMk", "kind": "definition", "module": "Mathlib.Geometry.RingedSpace.SheafedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.SheafedSpace.forgetToPresheafedSpace", "kind": "definition", "module": "Mathlib.Geometry.RingedSpace.SheafedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.SheafedSpace.fullyFaithfulForgetToPresheafedSpace", "kind": "definition", "module": "Mathlib.Geometry.RingedSpace.SheafedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.SheafedSpace.fullyFaithfulForgetToPresheafedSpace_preimage_hom", "kind": "theorem", "module": "Mathlib.Geometry.RingedSpace.SheafedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.SheafedSpace.forgetToPresheafedSpace_full", "kind": "instance", "module": "Mathlib.Geometry.RingedSpace.SheafedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.SheafedSpace.forgetToPresheafedSpace_faithful", "kind": "instance", "module": "Mathlib.Geometry.RingedSpace.SheafedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.SheafedSpace.is_presheafedSpace_iso", "kind": "instance", "module": "Mathlib.Geometry.RingedSpace.SheafedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.SheafedSpace.id_hom", "kind": "theorem", "module": "Mathlib.Geometry.RingedSpace.SheafedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.SheafedSpace.id_hom_base", "kind": "theorem", "module": "Mathlib.Geometry.RingedSpace.SheafedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.SheafedSpace.id_hom_c", "kind": "theorem", "module": "Mathlib.Geometry.RingedSpace.SheafedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.SheafedSpace.id_hom_c_app", "kind": "theorem", "module": "Mathlib.Geometry.RingedSpace.SheafedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.SheafedSpace.comp_hom_base", "kind": "theorem", "module": "Mathlib.Geometry.RingedSpace.SheafedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.SheafedSpace.comp_hom_c_app", "kind": "theorem", "module": "Mathlib.Geometry.RingedSpace.SheafedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.SheafedSpace.comp_hom_c_app'", "kind": "theorem", "module": "Mathlib.Geometry.RingedSpace.SheafedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.SheafedSpace.congr_hom_app", "kind": "theorem", "module": "Mathlib.Geometry.RingedSpace.SheafedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.SheafedSpace.forget", "kind": "definition", "module": "Mathlib.Geometry.RingedSpace.SheafedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.SheafedSpace.restrict", "kind": "definition", "module": "Mathlib.Geometry.RingedSpace.SheafedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.SheafedSpace.ofRestrict", "kind": "definition", "module": "Mathlib.Geometry.RingedSpace.SheafedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.SheafedSpace.restrictTopIso", "kind": "definition", "module": "Mathlib.Geometry.RingedSpace.SheafedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.SheafedSpace.Γ", "kind": "definition", "module": "Mathlib.Geometry.RingedSpace.SheafedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.SheafedSpace.Γ_def", "kind": "theorem", "module": "Mathlib.Geometry.RingedSpace.SheafedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.SheafedSpace.Γ_obj", "kind": "theorem", "module": "Mathlib.Geometry.RingedSpace.SheafedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.SheafedSpace.Γ_obj_op", "kind": "theorem", "module": "Mathlib.Geometry.RingedSpace.SheafedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.SheafedSpace.Γ_map", "kind": "theorem", "module": "Mathlib.Geometry.RingedSpace.SheafedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.SheafedSpace.Γ_map_op", "kind": "theorem", "module": "Mathlib.Geometry.RingedSpace.SheafedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.SheafedSpace.instCreatesColimitsOfShapePresheafedSpaceForgetToPresheafedSpaceOfSmallOfHasLimitsOfShapeOpposite", "kind": "instance", "module": "Mathlib.Geometry.RingedSpace.SheafedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.SheafedSpace.instCreatesColimitsPresheafedSpaceForgetToPresheafedSpaceOfHasLimits", "kind": "instance", "module": "Mathlib.Geometry.RingedSpace.SheafedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.SheafedSpace.instHasColimitsOfShapeOfSmallOfHasLimitsOfShapeOpposite", "kind": "instance", "module": "Mathlib.Geometry.RingedSpace.SheafedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.SheafedSpace.instHasColimitsOfHasLimits", "kind": "instance", "module": "Mathlib.Geometry.RingedSpace.SheafedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.SheafedSpace.instPreservesColimitsOfShapeTopCatForgetOfSmallOfHasLimitsOfShapeOpposite", "kind": "instance", "module": "Mathlib.Geometry.RingedSpace.SheafedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.SheafedSpace.instPreservesColimitsTopCatForgetOfHasLimits", "kind": "instance", "module": "Mathlib.Geometry.RingedSpace.SheafedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.SheafedSpace.hom_stalk_ext", "kind": "theorem", "module": "Mathlib.Geometry.RingedSpace.SheafedSpace", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "obtain", "congr", "ext", "refine", "erw", "simp"], "tactic_count": 8}
{"name": "AlgebraicGeometry.SheafedSpace.mono_of_base_injective_of_stalk_epi", "kind": "theorem", "module": "Mathlib.Geometry.RingedSpace.SheafedSpace", "is_tactic_proof": true, "tactics": ["constructor", "intro", "obtain", "refine", "rw", "replace", "congr"], "tactic_count": 7}
{"name": "AlgebraicGeometry.SheafedSpace.epi_of_base_surjective_of_stalk_mono", "kind": "theorem", "module": "Mathlib.Geometry.RingedSpace.SheafedSpace", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "obtain", "rw", "simpa", "refine", "rw", "congr"], "tactic_count": 9}
{"name": "AlgebraicGeometry.PresheafedSpace.Hom.stalkMap", "kind": "definition", "module": "Mathlib.Geometry.RingedSpace.Stalks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.PresheafedSpace.stalkMap_germ", "kind": "theorem", "module": "Mathlib.Geometry.RingedSpace.Stalks", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgebraicGeometry.PresheafedSpace.restrictStalkIso", "kind": "definition", "module": "Mathlib.Geometry.RingedSpace.Stalks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.PresheafedSpace.restrictStalkIso_hom_eq_germ", "kind": "theorem", "module": "Mathlib.Geometry.RingedSpace.Stalks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.PresheafedSpace.restrictStalkIso_inv_eq_germ", "kind": "theorem", "module": "Mathlib.Geometry.RingedSpace.Stalks", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgebraicGeometry.PresheafedSpace.restrictStalkIso_inv_eq_ofRestrict", "kind": "theorem", "module": "Mathlib.Geometry.RingedSpace.Stalks", "is_tactic_proof": true, "tactics": ["refine", "induction", "op", "let", "erw", "simp_rw", "erw", "erw", "exact"], "tactic_count": 9}
{"name": "AlgebraicGeometry.PresheafedSpace.ofRestrict_stalkMap_isIso", "kind": "instance", "module": "Mathlib.Geometry.RingedSpace.Stalks", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgebraicGeometry.PresheafedSpace.stalkMap.id", "kind": "theorem", "module": "Mathlib.Geometry.RingedSpace.Stalks", "is_tactic_proof": true, "tactics": ["dsimp", "simp", "rw", "convert", "ext", "simp", "rfl"], "tactic_count": 7}
{"name": "AlgebraicGeometry.PresheafedSpace.stalkMap.comp", "kind": "theorem", "module": "Mathlib.Geometry.RingedSpace.Stalks", "is_tactic_proof": false, "tactics": ["dsimp", "apply", "rintro", "simp"], "tactic_count": 4}
{"name": "AlgebraicGeometry.PresheafedSpace.stalkMap.congr", "kind": "theorem", "module": "Mathlib.Geometry.RingedSpace.Stalks", "is_tactic_proof": true, "tactics": ["ext", "substs", "simp"], "tactic_count": 3}
{"name": "AlgebraicGeometry.PresheafedSpace.stalkMap.congr_hom", "kind": "theorem", "module": "Mathlib.Geometry.RingedSpace.Stalks", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgebraicGeometry.PresheafedSpace.stalkMap.congr_point", "kind": "theorem", "module": "Mathlib.Geometry.RingedSpace.Stalks", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgebraicGeometry.PresheafedSpace.stalkMap.isIso", "kind": "instance", "module": "Mathlib.Geometry.RingedSpace.Stalks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.PresheafedSpace.stalkMap.stalkIso", "kind": "definition", "module": "Mathlib.Geometry.RingedSpace.Stalks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.PresheafedSpace.stalkMap.stalkSpecializes_stalkMap", "kind": "theorem", "module": "Mathlib.Geometry.RingedSpace.Stalks", "is_tactic_proof": true, "tactics": ["dsimp", "refine", "induction", "op", "dsimp", "simp", "assoc,", "tauto"], "tactic_count": 8}
{"name": "Abelianization", "kind": "definition", "module": "Mathlib.GroupTheory.Abelianization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Abelianization.commGroup", "kind": "instance", "module": "Mathlib.GroupTheory.Abelianization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Abelianization.instInhabited", "kind": "instance", "module": "Mathlib.GroupTheory.Abelianization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Abelianization.of", "kind": "definition", "module": "Mathlib.GroupTheory.Abelianization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Abelianization.mk_eq_of", "kind": "theorem", "module": "Mathlib.GroupTheory.Abelianization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Abelianization.ker_of", "kind": "theorem", "module": "Mathlib.GroupTheory.Abelianization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Abelianization.commutator_subset_ker", "kind": "theorem", "module": "Mathlib.GroupTheory.Abelianization.Defs", "is_tactic_proof": true, "tactics": ["rw", "rintro", "simp"], "tactic_count": 3}
{"name": "Abelianization.lift", "kind": "definition", "module": "Mathlib.GroupTheory.Abelianization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Abelianization.lift_apply_of", "kind": "theorem", "module": "Mathlib.GroupTheory.Abelianization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Abelianization.coe_lift_symm", "kind": "theorem", "module": "Mathlib.GroupTheory.Abelianization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Abelianization.lift_symm_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.Abelianization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Abelianization.lift_unique", "kind": "theorem", "module": "Mathlib.GroupTheory.Abelianization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Abelianization.lift_of", "kind": "theorem", "module": "Mathlib.GroupTheory.Abelianization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Abelianization.hom_ext", "kind": "theorem", "module": "Mathlib.GroupTheory.Abelianization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Abelianization.map", "kind": "definition", "module": "Mathlib.GroupTheory.Abelianization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Abelianization.lift_of_comp", "kind": "theorem", "module": "Mathlib.GroupTheory.Abelianization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Abelianization.map_of", "kind": "theorem", "module": "Mathlib.GroupTheory.Abelianization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Abelianization.map_id", "kind": "theorem", "module": "Mathlib.GroupTheory.Abelianization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Abelianization.map_comp", "kind": "theorem", "module": "Mathlib.GroupTheory.Abelianization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Abelianization.map_map_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.Abelianization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.abelianizationCongr", "kind": "definition", "module": "Mathlib.GroupTheory.Abelianization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "abelianizationCongr_of", "kind": "theorem", "module": "Mathlib.GroupTheory.Abelianization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "abelianizationCongr_refl", "kind": "theorem", "module": "Mathlib.GroupTheory.Abelianization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "abelianizationCongr_symm", "kind": "theorem", "module": "Mathlib.GroupTheory.Abelianization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "abelianizationCongr_trans", "kind": "theorem", "module": "Mathlib.GroupTheory.Abelianization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Abelianization.equivOfComm", "kind": "definition", "module": "Mathlib.GroupTheory.Abelianization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instUniqueAbelianization", "kind": "instance", "module": "Mathlib.GroupTheory.Abelianization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFintypeAbelianizationOfDecidablePredMemSubgroupCommutator", "kind": "instance", "module": "Mathlib.GroupTheory.Abelianization.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFiniteAbelianization", "kind": "instance", "module": "Mathlib.GroupTheory.Abelianization.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.cyclic_of_min", "kind": "theorem", "module": "Mathlib.GroupTheory.Archimedean", "is_tactic_proof": true, "tactics": ["obtain", "refine", "intro", "obtain", "have", "by_contra", "have", "refine", "exact", "exact", "have", "contradiction", "simp"], "tactic_count": 13}
{"name": "Subgroup.exists_isLeast_one_lt", "kind": "theorem", "module": "Mathlib.GroupTheory.Archimedean", "is_tactic_proof": true, "tactics": ["have", "rcases", "simp", "lift", "rw", "exact", "simp", "exact", "have", "rcases", "rcases", "exact", "classical", "by_contra", "simp", "rcases", "obtain", "rcases", "exact", "refine", "calc", "x"], "tactic_count": 22}
{"name": "Subgroup.cyclic_of_isolated_one", "kind": "theorem", "module": "Mathlib.GroupTheory.Archimedean", "is_tactic_proof": true, "tactics": ["rcases", "exact", "exact"], "tactic_count": 3}
{"name": "Int.subgroup_cyclic", "kind": "theorem", "module": "Mathlib.GroupTheory.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_pow_lt₀", "kind": "theorem", "module": "Mathlib.GroupTheory.ArchimedeanDensely", "is_tactic_proof": true, "tactics": ["rcases", "use", "simp", "lift", "simpa"], "tactic_count": 5}
{"name": "Subgroup.mem_closure_singleton_iff_existsUnique_zpow", "kind": "theorem", "module": "Mathlib.GroupTheory.ArchimedeanDensely", "is_tactic_proof": true, "tactics": ["rw", "constructor", "suffices", "rintro", "exact", "rcases", "exact", "exact", "exact"], "tactic_count": 9}
{"name": "Int.addEquiv_eq_refl_or_neg", "kind": "theorem", "module": "Mathlib.GroupTheory.ArchimedeanDensely", "is_tactic_proof": true, "tactics": ["suffices", "have", "not_isOfFinAddOrder_of_isAddTorsionFree", "rw", "simpa"], "tactic_count": 5}
{"name": "instFintypeAddEquivInt", "kind": "instance", "module": "Mathlib.GroupTheory.ArchimedeanDensely", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.univ_addEquiv", "kind": "theorem", "module": "Mathlib.GroupTheory.ArchimedeanDensely", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.card_fintype_addEquiv", "kind": "theorem", "module": "Mathlib.GroupTheory.ArchimedeanDensely", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instUniqueOrderAddMonoidIsoInt", "kind": "instance", "module": "Mathlib.GroupTheory.ArchimedeanDensely", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instUniqueOrderAddMonoidIsoIntOrderDual", "kind": "instance", "module": "Mathlib.GroupTheory.ArchimedeanDensely", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearOrderedCommGroup.closure_equiv_closure", "kind": "definition", "module": "Mathlib.GroupTheory.ArchimedeanDensely", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.isLeast_of_closure_iff_eq_mabs", "kind": "theorem", "module": "Mathlib.GroupTheory.ArchimedeanDensely", "is_tactic_proof": true, "tactics": ["constructor", "have", "have", "rw", "obtain", "have", "simp", "obtain", "have", "rw", "rw", "rcases", "wlog", "convert", "simp", "rwa", "rw", "rcases", "refine", "simp", "intro", "simp", "rintro", "rw", "contrapose", "rw", "exact"], "tactic_count": 27}
{"name": "LinearOrderedAddCommGroup.int_orderAddMonoidIso_of_isLeast_pos", "kind": "definition", "module": "Mathlib.GroupTheory.ArchimedeanDensely", "is_tactic_proof": true, "tactics": ["have", "replace", "let", "let", "let", "let", "let", "exact"], "tactic_count": 8}
{"name": "LinearOrderedCommGroup.multiplicative_int_orderMonoidIso_of_isLeast_one_lt", "kind": "definition", "module": "Mathlib.GroupTheory.ArchimedeanDensely", "is_tactic_proof": true, "tactics": ["have", "let", "exact"], "tactic_count": 3}
{"name": "Archimedean.of_locallyFiniteOrder", "kind": "theorem", "module": "Mathlib.GroupTheory.ArchimedeanDensely", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulArchimedean.of_locallyFiniteOrder", "kind": "theorem", "module": "Mathlib.GroupTheory.ArchimedeanDensely", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearOrderedAddCommGroup.discrete_or_denselyOrdered", "kind": "theorem", "module": "Mathlib.GroupTheory.ArchimedeanDensely", "is_tactic_proof": true, "tactics": ["by_cases", "obtain", "exact", "refine", "intro", "specialize", "obtain", "contrapose", "refine", "refine", "simp", "simpa"], "tactic_count": 12}
{"name": "LinearOrderedAddCommGroup.discrete_iff_not_denselyOrdered", "kind": "theorem", "module": "Mathlib.GroupTheory.ArchimedeanDensely", "is_tactic_proof": false, "tactics": ["suffices", "rcases", "simpa", "simp", "exact", "intro", "rw", "obtain", "lia"], "tactic_count": 9}
{"name": "LinearOrderedAddCommGroup.isAddCyclic_iff_not_denselyOrdered", "kind": "theorem", "module": "Mathlib.GroupTheory.ArchimedeanDensely", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LinearOrderedCommGroup.discrete_or_denselyOrdered", "kind": "theorem", "module": "Mathlib.GroupTheory.ArchimedeanDensely", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "LinearOrderedCommGroup.discrete_iff_not_denselyOrdered", "kind": "theorem", "module": "Mathlib.GroupTheory.ArchimedeanDensely", "is_tactic_proof": true, "tactics": ["let", "rw"], "tactic_count": 2}
{"name": "LinearOrderedCommGroup.isCyclic_iff_not_denselyOrdered", "kind": "theorem", "module": "Mathlib.GroupTheory.ArchimedeanDensely", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "LinearOrderedCommGroupWithZero.discrete_or_denselyOrdered", "kind": "theorem", "module": "Mathlib.GroupTheory.ArchimedeanDensely", "is_tactic_proof": true, "tactics": ["classical", "rw", "refine", "intro", "exact"], "tactic_count": 5}
{"name": "LinearOrderedCommGroupWithZero.discrete_iff_not_denselyOrdered", "kind": "theorem", "module": "Mathlib.GroupTheory.ArchimedeanDensely", "is_tactic_proof": true, "tactics": ["rw", "refine", "refine", "intros", "simp", "recZeroCoe_coe,", "map_eq_zero,", "rw", "refine", "intros", "simp", "split_ifs"], "tactic_count": 12}
{"name": "LinearOrderedAddCommGroup.wellFoundedOn_setOf_le_lt_iff_nonempty_discrete", "kind": "theorem", "module": "Mathlib.GroupTheory.ArchimedeanDensely", "is_tactic_proof": false, "tactics": ["suffices", "rw", "refine", "try", "simp", "constructor", "intro", "replace", "rw", "by_cases", "replace", "rw", "intro", "obtain", "wlog", "refine", "simp", "simp", "obtain", "obtain", "exact", "exfalso", "obtain", "obtain", "refine", "simp", "rintro", "have", "exact"], "tactic_count": 29}
{"name": "LinearOrderedAddCommGroup.wellFoundedOn_setOf_ge_gt_iff_nonempty_discrete", "kind": "theorem", "module": "Mathlib.GroupTheory.ArchimedeanDensely", "is_tactic_proof": true, "tactics": ["rw", "refine", "intro", "simp"], "tactic_count": 4}
{"name": "LinearOrderedCommGroup.wellFoundedOn_setOf_le_lt_iff_nonempty_discrete", "kind": "theorem", "module": "Mathlib.GroupTheory.ArchimedeanDensely", "is_tactic_proof": true, "tactics": ["let", "suffices", "rw", "refine", "simp"], "tactic_count": 5}
{"name": "LinearOrderedCommGroup.wellFoundedOn_setOf_ge_gt_iff_nonempty_discrete", "kind": "theorem", "module": "Mathlib.GroupTheory.ArchimedeanDensely", "is_tactic_proof": true, "tactics": ["rw", "refine", "intro", "simp"], "tactic_count": 4}
{"name": "LinearOrderedCommGroupWithZero.wellFoundedOn_setOf_le_lt_iff_nonempty_discrete_of_ne_zero", "kind": "theorem", "module": "Mathlib.GroupTheory.ArchimedeanDensely", "is_tactic_proof": false, "tactics": ["suffices", "rw", "refine", "exact", "intro", "rcases", "simp", "rcases", "simp", "simp", "exact", "intros", "rw", "simp", "rw", "refine", "intro", "simp", "simp", "exact", "simp", "simp", "intro", "simp"], "tactic_count": 24}
{"name": "LinearOrderedCommGroupWithZero.wellFoundedOn_setOf_ge_gt_iff_nonempty_discrete_of_ne_zero", "kind": "theorem", "module": "Mathlib.GroupTheory.ArchimedeanDensely", "is_tactic_proof": true, "tactics": ["have", "rw", "refine", "intro", "rcases", "simp", "simp", "refine", "simp", "intro", "refine", "contrapose", "simp", "simp", "intro", "simp", "intro", "refine", "simp", "simp", "intro", "refine", "simp"], "tactic_count": 23}
{"name": "instWellFoundedGTWithZeroMultiplicativeIntLeOne", "kind": "instance", "module": "Mathlib.GroupTheory.ArchimedeanDensely", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderMonoidIso.mulArchimedean", "kind": "theorem", "module": "Mathlib.GroupTheory.ArchimedeanDensely", "is_tactic_proof": true, "tactics": ["constructor", "intro", "replace", "refine", "simp"], "tactic_count": 5}
{"name": "WithZero.mulArchimedean_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.ArchimedeanDensely", "is_tactic_proof": true, "tactics": ["constructor", "exact", "infer_instance"], "tactic_count": 3}
{"name": "Units.mulArchimedean_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.ArchimedeanDensely", "is_tactic_proof": true, "tactics": ["constructor", "exact", "infer_instance"], "tactic_count": 3}
{"name": "instLocallyFiniteOrderMultiplicative", "kind": "instance", "module": "Mathlib.GroupTheory.ArchimedeanDensely", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instLocallyFiniteOrderAdditive", "kind": "instance", "module": "Mathlib.GroupTheory.ArchimedeanDensely", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instLocallyFiniteOrderUnits", "kind": "instance", "module": "Mathlib.GroupTheory.ArchimedeanDensely", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instLocallyFiniteOrderUnitsWithZero", "kind": "instance", "module": "Mathlib.GroupTheory.ArchimedeanDensely", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "denselyOrdered_additive_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.ArchimedeanDensely", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "denselyOrdered_multiplicative_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.ArchimedeanDensely", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDenselyOrderedMultiplicative", "kind": "instance", "module": "Mathlib.GroupTheory.ArchimedeanDensely", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDenselyOrderedAdditive", "kind": "instance", "module": "Mathlib.GroupTheory.ArchimedeanDensely", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.denselyOrdered_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.ArchimedeanDensely", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDenselyOrderedWithZeroOfNoMinOrder", "kind": "instance", "module": "Mathlib.GroupTheory.ArchimedeanDensely", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.not_denselyOrdered", "kind": "theorem", "module": "Mathlib.GroupTheory.ArchimedeanDensely", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_denselyOrdered_withZero_int", "kind": "theorem", "module": "Mathlib.GroupTheory.ArchimedeanDensely", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithZero.denselyOrdered_set_iff_subsingleton", "kind": "theorem", "module": "Mathlib.GroupTheory.ArchimedeanDensely", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sum_conjClasses_card_eq_card", "kind": "theorem", "module": "Mathlib.GroupTheory.ClassEquation", "is_tactic_proof": true, "tactics": ["suffices", "simpa"], "tactic_count": 2}
{"name": "Group.sum_card_conj_classes_eq_card", "kind": "theorem", "module": "Mathlib.GroupTheory.ClassEquation", "is_tactic_proof": true, "tactics": ["classical", "cases", "rw", "simp"], "tactic_count": 4}
{"name": "Group.nat_card_center_add_sum_card_noncenter_eq_card", "kind": "theorem", "module": "Mathlib.GroupTheory.ClassEquation", "is_tactic_proof": true, "tactics": ["classical", "cases", "rw", "simp", "congr", "swap", "convert", "simp", "calc", "rw", "rw", "refine", "rintro", "simp", "rw", "exact"], "tactic_count": 16}
{"name": "Group.card_center_add_sum_card_noncenter_eq_card", "kind": "theorem", "module": "Mathlib.GroupTheory.ClassEquation", "is_tactic_proof": true, "tactics": ["convert", "simp", "rw", "simp", "simp"], "tactic_count": 5}
{"name": "Subgroup.quotConjEquiv", "kind": "definition", "module": "Mathlib.GroupTheory.Commensurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.Commensurable", "kind": "definition", "module": "Mathlib.GroupTheory.Commensurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.Commensurable.refl", "kind": "theorem", "module": "Mathlib.GroupTheory.Commensurable", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Subgroup.Commensurable.comm", "kind": "theorem", "module": "Mathlib.GroupTheory.Commensurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.Commensurable.symm", "kind": "theorem", "module": "Mathlib.GroupTheory.Commensurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.Commensurable.trans", "kind": "theorem", "module": "Mathlib.GroupTheory.Commensurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.Commensurable.equivalence", "kind": "theorem", "module": "Mathlib.GroupTheory.Commensurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.Commensurable.commensurable_conj", "kind": "theorem", "module": "Mathlib.GroupTheory.Commensurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.Commensurable.conj", "kind": "theorem", "module": "Mathlib.GroupTheory.Commensurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.Commensurable.commensurable_inv", "kind": "theorem", "module": "Mathlib.GroupTheory.Commensurable", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subgroup.Commensurable.commensurator'", "kind": "definition", "module": "Mathlib.GroupTheory.Commensurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.Commensurable.commensurator", "kind": "definition", "module": "Mathlib.GroupTheory.Commensurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.Commensurable.commensurator'_mem_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Commensurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.Commensurable.commensurator_mem_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Commensurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.Commensurable.eq", "kind": "theorem", "module": "Mathlib.GroupTheory.Commensurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "commutatorElement_eq_one_iff_mul_comm", "kind": "theorem", "module": "Mathlib.GroupTheory.Commutator.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "commutatorElement_eq_one_iff_commute", "kind": "theorem", "module": "Mathlib.GroupTheory.Commutator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.commutator_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.Commutator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "commutatorElement_one_right", "kind": "theorem", "module": "Mathlib.GroupTheory.Commutator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "commutatorElement_one_left", "kind": "theorem", "module": "Mathlib.GroupTheory.Commutator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "commutatorElement_self", "kind": "theorem", "module": "Mathlib.GroupTheory.Commutator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "commutatorElement_inv", "kind": "theorem", "module": "Mathlib.GroupTheory.Commutator.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "map_commutatorElement", "kind": "theorem", "module": "Mathlib.GroupTheory.Commutator.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "conjugate_commutatorElement", "kind": "theorem", "module": "Mathlib.GroupTheory.Commutator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.commutator", "kind": "instance", "module": "Mathlib.GroupTheory.Commutator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.commutator_def", "kind": "theorem", "module": "Mathlib.GroupTheory.Commutator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.commutator_mem_commutator", "kind": "theorem", "module": "Mathlib.GroupTheory.Commutator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.commutator_le", "kind": "theorem", "module": "Mathlib.GroupTheory.Commutator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.commutator_mono", "kind": "theorem", "module": "Mathlib.GroupTheory.Commutator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.commutator_eq_bot_iff_le_centralizer", "kind": "theorem", "module": "Mathlib.GroupTheory.Commutator.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw"], "tactic_count": 3}
{"name": "Subgroup.commutator_commutator_eq_bot_of_rotate", "kind": "theorem", "module": "Mathlib.GroupTheory.Commutator.Basic", "is_tactic_proof": false, "tactics": ["simp_rw", "commutatorElement_def]", "intro", "trans", "x", "x⁻¹", "simp", "rw", "simp"], "tactic_count": 9}
{"name": "Subgroup.commutator_comm_le", "kind": "theorem", "module": "Mathlib.GroupTheory.Commutator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.commutator_comm", "kind": "theorem", "module": "Mathlib.GroupTheory.Commutator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.commutator_normal", "kind": "instance", "module": "Mathlib.GroupTheory.Commutator.Basic", "is_tactic_proof": true, "tactics": ["let", "change", "suffices", "rw", "exact", "refine", "simp_rw", "rcases", "exact"], "tactic_count": 9}
{"name": "Subgroup.commutator_def'", "kind": "theorem", "module": "Mathlib.GroupTheory.Commutator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.commutator_le_right", "kind": "theorem", "module": "Mathlib.GroupTheory.Commutator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.commutator_le_left", "kind": "theorem", "module": "Mathlib.GroupTheory.Commutator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.commutator_bot_left", "kind": "theorem", "module": "Mathlib.GroupTheory.Commutator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.commutator_bot_right", "kind": "theorem", "module": "Mathlib.GroupTheory.Commutator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.commutator_le_inf", "kind": "theorem", "module": "Mathlib.GroupTheory.Commutator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.map_commutator", "kind": "theorem", "module": "Mathlib.GroupTheory.Commutator.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "constructor", "intro", "exact", "rintro", "rw", "exact"], "tactic_count": 7}
{"name": "Subgroup.commutator_le_map_commutator", "kind": "theorem", "module": "Mathlib.GroupTheory.Commutator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.commutator_characteristic", "kind": "instance", "module": "Mathlib.GroupTheory.Commutator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.commutator_prod_prod", "kind": "theorem", "module": "Mathlib.GroupTheory.Commutator.Basic", "is_tactic_proof": true, "tactics": ["apply", "rw", "rintro", "exact", "rw", "constructor", "rw", "apply", "simp"], "tactic_count": 9}
{"name": "Subgroup.commutator_pi_pi_le", "kind": "theorem", "module": "Mathlib.GroupTheory.Commutator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "commutatorSet", "kind": "definition", "module": "Mathlib.GroupTheory.Commutator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "commutatorSet_def", "kind": "theorem", "module": "Mathlib.GroupTheory.Commutator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_mem_commutatorSet", "kind": "theorem", "module": "Mathlib.GroupTheory.Commutator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instNonemptyElemCommutatorSet", "kind": "instance", "module": "Mathlib.GroupTheory.Commutator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_commutatorSet_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Commutator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "commutator_mem_commutatorSet", "kind": "theorem", "module": "Mathlib.GroupTheory.Commutator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "commutator", "kind": "definition", "module": "Mathlib.GroupTheory.Commutator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "commutator_def", "kind": "theorem", "module": "Mathlib.GroupTheory.Commutator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "commutator_eq_closure", "kind": "theorem", "module": "Mathlib.GroupTheory.Commutator.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "commutator_eq_normalClosure", "kind": "theorem", "module": "Mathlib.GroupTheory.Commutator.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Subgroup.map_subtype_commutator", "kind": "theorem", "module": "Mathlib.GroupTheory.Commutator.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subgroup.commutator_le_self", "kind": "theorem", "module": "Mathlib.GroupTheory.Commutator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "commutator_eq_bot_iff_center_eq_top", "kind": "theorem", "module": "Mathlib.GroupTheory.Commutator.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "commutator_centralizer_commutator_le_center", "kind": "theorem", "module": "Mathlib.GroupTheory.Commutator.Basic", "is_tactic_proof": true, "tactics": ["rw", "suffices", "refine", "rwa", "rw", "exact"], "tactic_count": 6}
{"name": "mem_commutatorSet_of_isConj_sq", "kind": "theorem", "module": "Mathlib.GroupTheory.Commutator.Basic", "is_tactic_proof": true, "tactics": ["obtain", "use", "rw", "simp"], "tactic_count": 4}
{"name": "map_commutator_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.Commutator.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply", "rw", "rw"], "tactic_count": 4}
{"name": "commutatorRepresentatives", "kind": "definition", "module": "Mathlib.GroupTheory.Commutator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "closureCommutatorRepresentatives", "kind": "definition", "module": "Mathlib.GroupTheory.Commutator.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "image_commutatorSet_closureCommutatorRepresentatives", "kind": "theorem", "module": "Mathlib.GroupTheory.Commutator.Basic", "is_tactic_proof": true, "tactics": ["apply", "rintro", "exact", "exact", "rfl⟩,", "hg.choose_spec.choose_spec⟩"], "tactic_count": 6}
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{"name": "Subgroup.Normal.commutator_le_of_self_sup_commutative_eq_top", "kind": "theorem", "module": "Mathlib.GroupTheory.Commutator.Basic", "is_tactic_proof": true, "tactics": ["rw", "let", "apply", "rw", "simp", "have", "rw", "exact", "simp", "simp"], "tactic_count": 10}
{"name": "Subgroup.commutator_pi_pi_of_finite", "kind": "theorem", "module": "Mathlib.GroupTheory.Commutator.Finite", "is_tactic_proof": true, "tactics": ["classical", "apply", "rw", "intro", "rw", "apply", "rw", "intro", "rintro", "by_cases", "subst", "simpa", "simp"], "tactic_count": 13}
{"name": "Subgroup.instFGSubtypeMemCommutator", "kind": "instance", "module": "Mathlib.GroupTheory.Commutator.Finite", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subgroup.rank_commutator_le_card", "kind": "theorem", "module": "Mathlib.GroupTheory.Commutator.Finite", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "Subgroup.finiteIndex_center", "kind": "instance", "module": "Mathlib.GroupTheory.Commutator.Finite", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Subgroup.index_center_le_pow", "kind": "theorem", "module": "Mathlib.GroupTheory.Commutator.Finite", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact"], "tactic_count": 3}
{"name": "card_commutatorSet_closureCommutatorRepresentatives", "kind": "theorem", "module": "Mathlib.GroupTheory.Commutator.Finite", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "card_commutator_closureCommutatorRepresentatives", "kind": "theorem", "module": "Mathlib.GroupTheory.Commutator.Finite", "is_tactic_proof": false, "tactics": ["rw", "commutator_eq_closure]", "exact"], "tactic_count": 3}
{"name": "instFiniteElemProdCommutatorRepresentatives", "kind": "instance", "module": "Mathlib.GroupTheory.Commutator.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "closureCommutatorRepresentatives_fg", "kind": "instance", "module": "Mathlib.GroupTheory.Commutator.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "rank_closureCommutatorRepresentatives_le", "kind": "theorem", "module": "Mathlib.GroupTheory.Commutator.Finite", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "instFiniteElemSubtypeMemSubgroupClosureCommutatorRepresentativesCommutatorSet", "kind": "instance", "module": "Mathlib.GroupTheory.Commutator.Finite", "is_tactic_proof": true, "tactics": ["apply", "rw", "exact"], "tactic_count": 3}
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{"name": "commProb_def", "kind": "theorem", "module": "Mathlib.GroupTheory.CommutingProbability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "commProb_prod", "kind": "theorem", "module": "Mathlib.GroupTheory.CommutingProbability", "is_tactic_proof": false, "tactics": ["simp_rw", "congr", "exact"], "tactic_count": 3}
{"name": "commProb_pi", "kind": "theorem", "module": "Mathlib.GroupTheory.CommutingProbability", "is_tactic_proof": false, "tactics": ["simp_rw", "funext_iff]", "congr", "exact"], "tactic_count": 4}
{"name": "commProb_function", "kind": "theorem", "module": "Mathlib.GroupTheory.CommutingProbability", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "commProb_eq_zero_of_infinite", "kind": "theorem", "module": "Mathlib.GroupTheory.CommutingProbability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "commProb_pos", "kind": "theorem", "module": "Mathlib.GroupTheory.CommutingProbability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "commProb_le_one", "kind": "theorem", "module": "Mathlib.GroupTheory.CommutingProbability", "is_tactic_proof": true, "tactics": ["refine", "rw", "apply"], "tactic_count": 3}
{"name": "commProb_eq_one_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.CommutingProbability", "is_tactic_proof": true, "tactics": ["classical", "haveI", "rw", "rw", "exact", "exact"], "tactic_count": 6}
{"name": "commProb_def'", "kind": "theorem", "module": "Mathlib.GroupTheory.CommutingProbability", "is_tactic_proof": true, "tactics": ["rw", "by_cases", "rw", "exact"], "tactic_count": 4}
{"name": "Subgroup.commProb_subgroup_le", "kind": "theorem", "module": "Mathlib.GroupTheory.CommutingProbability", "is_tactic_proof": true, "tactics": ["commuting", "rw", "div_mul_cancel₀,", "refine", "exact", "exact", "exact"], "tactic_count": 7}
{"name": "Subgroup.commProb_quotient_le", "kind": "theorem", "module": "Mathlib.GroupTheory.CommutingProbability", "is_tactic_proof": true, "tactics": ["conjugacy", "rw", "div_mul_cancel₀,", "apply", "show", "exact", "exact", "exact"], "tactic_count": 8}
{"name": "inv_card_commutator_le_commProb", "kind": "theorem", "module": "Mathlib.GroupTheory.CommutingProbability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DihedralGroup.commProb_odd", "kind": "theorem", "module": "Mathlib.GroupTheory.CommutingProbability", "is_tactic_proof": true, "tactics": ["rw", "qify", "rw", "congr", "norm_num"], "tactic_count": 5}
{"name": "DihedralGroup.reciprocalFactors", "kind": "definition", "module": "Mathlib.GroupTheory.CommutingProbability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DihedralGroup.reciprocalFactors_zero", "kind": "theorem", "module": "Mathlib.GroupTheory.CommutingProbability", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "DihedralGroup.reciprocalFactors_one", "kind": "theorem", "module": "Mathlib.GroupTheory.CommutingProbability", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "DihedralGroup.reciprocalFactors_even", "kind": "theorem", "module": "Mathlib.GroupTheory.CommutingProbability", "is_tactic_proof": false, "tactics": ["have", "rintro", "norm_num", "rw"], "tactic_count": 4}
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{"name": "DihedralGroup.Product", "kind": "abbrev", "module": "Mathlib.GroupTheory.CommutingProbability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DihedralGroup.commProb_nil", "kind": "theorem", "module": "Mathlib.GroupTheory.CommutingProbability", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DihedralGroup.commProb_cons", "kind": "theorem", "module": "Mathlib.GroupTheory.CommutingProbability", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DihedralGroup.commProb_reciprocal", "kind": "theorem", "module": "Mathlib.GroupTheory.CommutingProbability", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "apply", "by_cases", "rw", "rcases", "rw", "simp", "norm_num", "rw", "have", "rw", "grind", "positivity"], "tactic_count": 14}
{"name": "Subgroup.IsComplement", "kind": "definition", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.IsComplement'", "kind": "abbrev", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.isComplement_iff_bijective", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.isComplement'_def", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.isComplement_iff_existsUnique", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.IsComplement.existsUnique", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.IsComplement'.symm", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": false, "tactics": ["let", "let", "suffices", "rwa", "exact"], "tactic_count": 5}
{"name": "Subgroup.isComplement'_comm", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.isComplement_univ_singleton", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.isComplement_singleton_univ", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.isComplement_singleton_left", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": true, "tactics": ["refine", "obtain", "rwa"], "tactic_count": 3}
{"name": "Subgroup.isComplement_singleton_right", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": true, "tactics": ["refine", "obtain", "conv_rhs", "rw", "exact"], "tactic_count": 5}
{"name": "Subgroup.isComplement_univ_left", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact", "have", "h.1", "exact", "rintro", "exact"], "tactic_count": 8}
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{"name": "Subgroup.IsComplement.mul_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.not_isComplement_empty_left", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.not_isComplement_empty_right", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.IsComplement.nonempty_left", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": true, "tactics": ["contrapose"], "tactic_count": 1}
{"name": "Subgroup.IsComplement.nonempty_right", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": true, "tactics": ["contrapose"], "tactic_count": 1}
{"name": "Subgroup.IsComplement.pairwiseDisjoint_smul", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.IsComplement.card_mul_card", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.isComplement'_top_bot", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.isComplement'_bot_top", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.isComplement'_bot_left", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.isComplement'_bot_right", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.isComplement'_top_left", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.isComplement'_top_right", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.isComplement_iff_existsUnique_inv_mul_mem", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": true, "tactics": ["convert", "constructor", "exact", "exact"], "tactic_count": 4}
{"name": "Subgroup.isComplement_iff_existsUnique_mul_inv_mem", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": true, "tactics": ["convert", "constructor", "exact", "exact"], "tactic_count": 4}
{"name": "Subgroup.isComplement_subgroup_right_iff_existsUnique_quotientGroupMk", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Subgroup.isComplement_subgroup_left_iff_existsUnique_quotientMk''", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Subgroup.isComplement_subgroup_right_iff_bijective", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.isComplement_subgroup_left_iff_bijective", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.IsComplement.card_left", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.IsComplement.ncard_left", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subgroup.IsComplement.card_right", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.IsComplement.ncard_right", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subgroup.isComplement_range_left", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": true, "tactics": ["rw", "refine", "rintro", "exact"], "tactic_count": 4}
{"name": "Subgroup.isComplement_range_right", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": true, "tactics": ["rw", "refine", "rintro", "exact"], "tactic_count": 4}
{"name": "Subgroup.exists_isComplement_left", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": true, "tactics": ["classical", "refine", "by_cases", "exact", "refine", "exact"], "tactic_count": 6}
{"name": "Subgroup.exists_isComplement_right", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": true, "tactics": ["classical", "refine", "by_cases", "exact", "refine", "exact"], "tactic_count": 6}
{"name": "Subgroup.exists_left_transversal_of_le", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": true, "tactics": ["let", "have", "rw", "obtain", "refine", "have", "rw", "simp", "rw", "refine"], "tactic_count": 10}
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{"name": "Subgroup.IsComplement.equiv", "kind": "definition", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.IsComplement.equiv_symm_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.IsComplement.equiv_fst_mul_equiv_snd", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.IsComplement.equiv_fst_eq_mul_inv", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.IsComplement.equiv_snd_eq_inv_mul", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.IsComplement.equiv_fst_eq_iff_leftCosetEquivalence", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": true, "tactics": ["rw", "constructor", "intro", "rw", "inv_mul_cancel_right,", "exact", "intro", "apply", "rw", "rw", "rw"], "tactic_count": 11}
{"name": "Subgroup.IsComplement.equiv_snd_eq_iff_rightCosetEquivalence", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": true, "tactics": ["rw", "constructor", "intro", "rw", "mul_inv_cancel_left,", "exact", "intro", "apply", "rw", "rw", "rw"], "tactic_count": 11}
{"name": "Subgroup.IsComplement.leftCosetEquivalence_equiv_fst", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subgroup.IsComplement.rightCosetEquivalence_equiv_snd", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subgroup.IsComplement.equiv_fst_eq_self_of_mem_of_one_mem", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": true, "tactics": ["have", "conv_lhs"], "tactic_count": 2}
{"name": "Subgroup.IsComplement.equiv_snd_eq_self_of_mem_of_one_mem", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": true, "tactics": ["have", "conv_lhs"], "tactic_count": 2}
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{"name": "Subgroup.IsComplement.equiv_mul_right_of_mem", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.IsComplement.equiv_mul_left", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": true, "tactics": ["have", "ext", "rw", "rw", "simp"], "tactic_count": 5}
{"name": "Subgroup.IsComplement.equiv_mul_left_of_mem", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.IsComplement.equiv_one", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subgroup.IsComplement.equiv_fst_eq_self_iff_mem", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "exact", "intro", "rw"], "tactic_count": 6}
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{"name": "Subgroup.IsComplement.coe_equiv_fst_eq_one_iff_mem", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subgroup.IsComplement.coe_equiv_snd_eq_one_iff_mem", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subgroup.IsComplement.leftQuotientEquiv", "kind": "definition", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.IsComplement.finite_left_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Subgroup.IsComplement.finite_left", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.IsComplement.quotientGroupMk_leftQuotientEquiv", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.IsComplement.leftQuotientEquiv_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "Subgroup.IsComplement.toLeftFun", "kind": "definition", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.IsComplement.inv_toLeftFun_mul_mem", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.IsComplement.inv_mul_toLeftFun_mem", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.IsComplement.rightQuotientEquiv", "kind": "definition", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.IsComplement.finite_right_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Subgroup.IsComplement.finite_right", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.IsComplement.mk''_rightQuotientEquiv", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.IsComplement.rightQuotientEquiv_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "Subgroup.IsComplement.toRightFun", "kind": "definition", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.IsComplement.mul_inv_toRightFun_mem", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.IsComplement.toRightFun_mul_inv_mem", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.IsComplement.encard_left", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subgroup.IsComplement.encard_right", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subgroup.LeftTransversal", "kind": "abbrev", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.RightTransversal", "kind": "abbrev", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.instMulActionLeftTransversal", "kind": "instance", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.smul_toLeftFun", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.smul_leftQuotientEquiv", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.smul_apply_eq_smul_apply_inv_smul", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subgroup.instInhabitedLeftTransversal", "kind": "instance", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.instInhabitedRightTransversal", "kind": "instance", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.IsComplement'.isCompl", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": false, "tactics": ["refine", "let", "let", "codisjoint_iff_le_sup.mpr", "obtain", "exact"], "tactic_count": 6}
{"name": "Subgroup.IsComplement'.sup_eq_top", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.IsComplement'.disjoint", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.IsComplement'.index_eq_card", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.IsComplement'.QuotientMulEquiv", "kind": "definition", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.IsComplement.card_mul", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.IsComplement'.card_mul", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.isComplement'_of_disjoint_and_mul_eq_univ", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact"], "tactic_count": 3}
{"name": "Subgroup.isComplement'_of_card_mul_and_disjoint", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.isComplement'_iff_card_mul_and_disjoint", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.isComplement'_of_coprime", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.isComplement'_stabilizer", "kind": "theorem", "module": "Mathlib.GroupTheory.Complement", "is_tactic_proof": true, "tactics": ["refine", "obtain", "have", "refine", "rintro", "specialize", "refine", "rwa"], "tactic_count": 8}
{"name": "Con.prod", "kind": "definition", "module": "Mathlib.GroupTheory.Congruence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.pi", "kind": "definition", "module": "Mathlib.GroupTheory.Congruence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.congr", "kind": "definition", "module": "Mathlib.GroupTheory.Congruence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.congr_mk", "kind": "theorem", "module": "Mathlib.GroupTheory.Congruence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.le_comap_conGen", "kind": "theorem", "module": "Mathlib.GroupTheory.Congruence.Basic", "is_tactic_proof": true, "tactics": ["intro", "simp", "exact", "h"], "tactic_count": 4}
{"name": "Con.comap_conGen_equiv", "kind": "theorem", "module": "Mathlib.GroupTheory.Congruence.Basic", "is_tactic_proof": true, "tactics": ["apply", "intro", "simp", "have", "intro", "induction", "of", "intro", "apply", "rwa", "refl", "intro", "rw", "exact", "symm", "trans", "exact", "mul", "rename_i", "intro", "rw", "rw", "exact", "exact"], "tactic_count": 24}
{"name": "Con.comap_conGen_of_bijective", "kind": "theorem", "module": "Mathlib.GroupTheory.Congruence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.submonoid", "kind": "definition", "module": "Mathlib.GroupTheory.Congruence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.ofSubmonoid", "kind": "definition", "module": "Mathlib.GroupTheory.Congruence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.toSubmonoid", "kind": "instance", "module": "Mathlib.GroupTheory.Congruence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.mem_coe", "kind": "theorem", "module": "Mathlib.GroupTheory.Congruence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.to_submonoid_inj", "kind": "theorem", "module": "Mathlib.GroupTheory.Congruence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.le_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Congruence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.mrange_mk'", "kind": "theorem", "module": "Mathlib.GroupTheory.Congruence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.lift_range", "kind": "theorem", "module": "Mathlib.GroupTheory.Congruence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.kerLift_range_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.Congruence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.quotientKerEquivRange", "kind": "definition", "module": "Mathlib.GroupTheory.Congruence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.quotientKerEquivOfRightInverse", "kind": "definition", "module": "Mathlib.GroupTheory.Congruence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.quotientKerEquivOfSurjective", "kind": "definition", "module": "Mathlib.GroupTheory.Congruence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.comapQuotientEquivOfSurj", "kind": "definition", "module": "Mathlib.GroupTheory.Congruence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.comapQuotientEquivOfSurj_mk", "kind": "theorem", "module": "Mathlib.GroupTheory.Congruence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.comapQuotientEquivOfSurj_symm_mk", "kind": "theorem", "module": "Mathlib.GroupTheory.Congruence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.comapQuotientEquivOfSurj_symm_mk'", "kind": "theorem", "module": "Mathlib.GroupTheory.Congruence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.comapQuotientEquiv", "kind": "definition", "module": "Mathlib.GroupTheory.Congruence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.quotientQuotientEquivQuotient", "kind": "definition", "module": "Mathlib.GroupTheory.Congruence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.smul", "kind": "theorem", "module": "Mathlib.GroupTheory.Congruence.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Con.instSMul", "kind": "instance", "module": "Mathlib.GroupTheory.Congruence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.coe_smul", "kind": "theorem", "module": "Mathlib.GroupTheory.Congruence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.instSMulCommClass", "kind": "instance", "module": "Mathlib.GroupTheory.Congruence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.instIsScalarTower", "kind": "instance", "module": "Mathlib.GroupTheory.Congruence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.instIsCentralScalar", "kind": "instance", "module": "Mathlib.GroupTheory.Congruence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.mulAction", "kind": "instance", "module": "Mathlib.GroupTheory.Congruence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.mulDistribMulAction", "kind": "instance", "module": "Mathlib.GroupTheory.Congruence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.list_prod", "kind": "theorem", "module": "Mathlib.GroupTheory.Congruence.BigOperators", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "rw", "exact"], "tactic_count": 5}
{"name": "Con.multiset_prod", "kind": "theorem", "module": "Mathlib.GroupTheory.Congruence.BigOperators", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "Con.finset_prod", "kind": "theorem", "module": "Mathlib.GroupTheory.Congruence.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddConGen.Rel", "kind": "inductive", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConGen.Rel", "kind": "inductive", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "conGen", "kind": "definition", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.instInhabited", "kind": "instance", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.toSetoid_injective", "kind": "theorem", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.toSetoid_inj", "kind": "theorem", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.instFunLikeForallProp", "kind": "instance", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.rel_eq_coe", "kind": "theorem", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.refl", "kind": "theorem", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.symm", "kind": "theorem", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.trans", "kind": "theorem", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.mul", "kind": "theorem", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.rel_mk", "kind": "theorem", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.instMembershipProd", "kind": "instance", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.ext'", "kind": "theorem", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.ext", "kind": "theorem", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.coe_inj", "kind": "theorem", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.Quotient", "kind": "definition", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.toQuotient", "kind": "definition", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.instCoeTCQuotient", "kind": "instance", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.instDecidableEqQuotientOfDecidableCoeForallProp", "kind": "instance", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.quot_mk_eq_coe", "kind": "theorem", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.liftOn", "kind": "definition", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.liftOn₂", "kind": "definition", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.hrecOn₂", "kind": "definition", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.hrec_on₂_coe", "kind": "theorem", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.induction_on", "kind": "theorem", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.induction_on₂", "kind": "theorem", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.eq", "kind": "theorem", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.hasMul", "kind": "instance", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.coe_mul", "kind": "theorem", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.liftOn_coe", "kind": "theorem", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.instLE", "kind": "instance", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.le_def", "kind": "theorem", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.instInfSet", "kind": "instance", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.sInf_toSetoid", "kind": "theorem", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.coe_sInf", "kind": "theorem", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": true, "tactics": ["ext", "simp", "rfl"], "tactic_count": 3}
{"name": "Con.coe_iInf", "kind": "theorem", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Con.instPartialOrder", "kind": "instance", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.instCompleteLattice", "kind": "instance", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.coe_inf", "kind": "theorem", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.toSetoid_top", "kind": "theorem", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.toSetoid_bot", "kind": "theorem", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.toSetoid_eq_top", "kind": "theorem", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Con.toSetoid_eq_bot", "kind": "theorem", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Con.inf_iff_and", "kind": "theorem", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.conGen_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.conGen_le", "kind": "theorem", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Con.conGen_mono", "kind": "theorem", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.conGen_of_con", "kind": "theorem", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.conGen_idem", "kind": "theorem", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Con.sup_eq_conGen", "kind": "theorem", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": true, "tactics": ["rw", "apply", "simp"], "tactic_count": 3}
{"name": "Con.sup_def", "kind": "theorem", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Con.sSup_eq_conGen", "kind": "theorem", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": true, "tactics": ["rw", "apply", "ext", "exact"], "tactic_count": 4}
{"name": "Con.sSup_def", "kind": "theorem", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": true, "tactics": ["rw", "congr", "simp"], "tactic_count": 3}
{"name": "Con.gi", "kind": "definition", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.comap", "kind": "definition", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.comap_rel", "kind": "theorem", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.mulOneClass", "kind": "instance", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.coe_one", "kind": "theorem", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.Quotient.inhabited", "kind": "instance", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.pow", "kind": "theorem", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.one", "kind": "instance", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCon.Quotient.nsmul", "kind": "instance", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.instPowQuotientNat", "kind": "instance", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.semigroup", "kind": "instance", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.commMagma", "kind": "instance", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.commSemigroup", "kind": "instance", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.monoid", "kind": "instance", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.commMonoid", "kind": "instance", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.map_of_mul_left_rel_one", "kind": "theorem", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": true, "tactics": ["simp", "have", "calc", "have", "exact"], "tactic_count": 5}
{"name": "Con.inv", "kind": "theorem", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.div", "kind": "theorem", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.zpow", "kind": "theorem", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.hasInv", "kind": "instance", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.hasDiv", "kind": "instance", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCon.Quotient.zsmul", "kind": "instance", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.zpowinst", "kind": "instance", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Con.commGroup", "kind": "instance", "module": "Mathlib.GroupTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Monoid.Coprod.snd_surjective", "kind": "theorem", "module": "Mathlib.GroupTheory.Coprod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monoid.Coprod.toProd_surjective", "kind": "theorem", "module": "Mathlib.GroupTheory.Coprod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monoid.Coprod.mk_of_inv_mul", "kind": "theorem", "module": "Mathlib.GroupTheory.Coprod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monoid.Coprod.con_inv_mul_cancel", "kind": "theorem", "module": "Mathlib.GroupTheory.Coprod.Basic", "is_tactic_proof": true, "tactics": ["rw", "induction", "one", "mul_of", "ihx", "simp", "rwa"], "tactic_count": 7}
{"name": "Monoid.Coprod.instInv", "kind": "instance", "module": "Mathlib.GroupTheory.Coprod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monoid.Coprod.inv_def", "kind": "theorem", "module": "Mathlib.GroupTheory.Coprod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monoid.Coprod.instGroup", "kind": "instance", "module": "Mathlib.GroupTheory.Coprod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monoid.Coprod.closure_range_inl_union_inr", "kind": "theorem", "module": "Mathlib.GroupTheory.Coprod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monoid.Coprod.range_inl_sup_range_inr", "kind": "theorem", "module": "Mathlib.GroupTheory.Coprod.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Monoid.Coprod.codisjoint_range_inl_range_inr", "kind": "theorem", "module": "Mathlib.GroupTheory.Coprod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monoid.Coprod.range_swap", "kind": "theorem", "module": "Mathlib.GroupTheory.Coprod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monoid.Coprod.range_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.Coprod.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Monoid.Coprod.range_lift", "kind": "theorem", "module": "Mathlib.GroupTheory.Coprod.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MulEquiv.coprodCongr", "kind": "definition", "module": "Mathlib.GroupTheory.Coprod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.coprodComm", "kind": "definition", "module": "Mathlib.GroupTheory.Coprod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.coprodAssoc", "kind": "definition", "module": "Mathlib.GroupTheory.Coprod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.coprodAssoc_apply_inl_inl", "kind": "theorem", "module": "Mathlib.GroupTheory.Coprod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.coprodAssoc_apply_inl_inr", "kind": "theorem", "module": "Mathlib.GroupTheory.Coprod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.coprodAssoc_apply_inr", "kind": "theorem", "module": "Mathlib.GroupTheory.Coprod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.coprodAssoc_symm_apply_inl", "kind": "theorem", "module": "Mathlib.GroupTheory.Coprod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.coprodAssoc_symm_apply_inr_inl", "kind": "theorem", "module": "Mathlib.GroupTheory.Coprod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.coprodAssoc_symm_apply_inr_inr", "kind": "theorem", "module": "Mathlib.GroupTheory.Coprod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.coprodPUnit", "kind": "definition", "module": "Mathlib.GroupTheory.Coprod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.punitCoprod", "kind": "definition", "module": "Mathlib.GroupTheory.Coprod.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.exists_leftTransversal_of_FiniteIndex", "kind": "theorem", "module": "Mathlib.GroupTheory.CosetCover", "is_tactic_proof": true, "tactics": ["have", "have", "refine", "ext", "suffices", "constructor", "rintro", "exact", "intro", "exact"], "tactic_count": 10}
{"name": "Subgroup.leftCoset_cover_const_iff_surjOn", "kind": "theorem", "module": "Mathlib.GroupTheory.CosetCover", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Subgroup.finiteIndex_of_leftCoset_cover_const", "kind": "theorem", "module": "Mathlib.GroupTheory.CosetCover", "is_tactic_proof": true, "tactics": ["simp_rw", "have", "exact"], "tactic_count": 3}
{"name": "Subgroup.index_le_of_leftCoset_cover_const", "kind": "theorem", "module": "Mathlib.GroupTheory.CosetCover", "is_tactic_proof": true, "tactics": ["cases", "inl", "inr", "rw", "exact"], "tactic_count": 5}
{"name": "Subgroup.pairwiseDisjoint_leftCoset_cover_const_of_index_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.CosetCover", "is_tactic_proof": false, "tactics": ["have", "fintypeOfIndexNeZero", "rw", "rw", "exact", "suffices", "intro", "specialize", "specialize", "rw", "rw", "exact", "rw", "constructor", "rwa", "simp"], "tactic_count": 16}
{"name": "Subgroup.exists_finiteIndex_of_leftCoset_cover_aux", "kind": "theorem", "module": "Mathlib.GroupTheory.CosetCover", "is_tactic_proof": true, "tactics": ["classical", "have", "induction", "ind", "have", "simpa", "replace", "intro", "simp_rw", "have", "simpa", "rw", "refine", "rwa", "simpa", "let", "let", "let", "have", "have", "exact", "have", "replace", "rw", "cases", "inl", "have", "have", "have", "exact", "inr", "have", "exact", "have", "not_isEmpty_iff.mp", "rw", "exact", "by_cases", "rw", "exact", "have", "hn", "refine", "rw", "exact", "have", "exact"], "tactic_count": 47}
{"name": "Subgroup.exists_finiteIndex_of_leftCoset_cover", "kind": "theorem", "module": "Mathlib.GroupTheory.CosetCover", "is_tactic_proof": true, "tactics": ["classical", "have", "by_contra", "rw", "exact", "by_cases", "rw", "exact", "have", "exact"], "tactic_count": 10}
{"name": "Subgroup.leftCoset_cover_filter_FiniteIndex_aux", "kind": "theorem", "module": "Mathlib.GroupTheory.CosetCover", "is_tactic_proof": true, "tactics": ["classical", "let", "have", "have", "iInf₂_le", "choose", "exists_leftTransversal_of_FiniteIndex", "let", "let", "let", "have", "rw", "rw", "apply", "by_cases", "simp", "by_cases", "simp", "have", "have", "have", "replace", "rw", "by_contra", "obtain", "by_cases", "have", "have", "rw", "refine", "by_cases", "rw", "mul_inv_cancel_right₀", "simpa", "rw", "simpa", "refine", "rw", "refine", "rw", "refine", "by_cases", "simp", "rw", "refine", "rw", "exact", "rw", "intro", "have", "rw", "have", "rw", "suffices", "have", "refine", "simpa", "simpa", "have", "have", "rw", "exact", "hdisjoint"], "tactic_count": 63}
{"name": "Subgroup.leftCoset_cover_filter_FiniteIndex", "kind": "theorem", "module": "Mathlib.GroupTheory.CosetCover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.one_le_sum_inv_index_of_leftCoset_cover", "kind": "theorem", "module": "Mathlib.GroupTheory.CosetCover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.pairwiseDisjoint_leftCoset_cover_of_sum_inv_index_eq_one", "kind": "theorem", "module": "Mathlib.GroupTheory.CosetCover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.exists_index_le_card_of_leftCoset_cover", "kind": "theorem", "module": "Mathlib.GroupTheory.CosetCover", "is_tactic_proof": true, "tactics": ["by_contra", "apply", "cases", "inl", "inr", "have", "have", "cases", "inl", "inr", "apply", "rw"], "tactic_count": 12}
{"name": "Submodule.exists_finiteIndex_of_cover", "kind": "theorem", "module": "Mathlib.GroupTheory.CosetCover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subspace.biUnion_ne_univ_of_top_notMem", "kind": "theorem", "module": "Mathlib.GroupTheory.CosetCover", "is_tactic_proof": true, "tactics": ["intro", "have", "have", "have", "have", "exact"], "tactic_count": 6}
{"name": "Subspace.top_mem_of_biUnion_eq_univ", "kind": "theorem", "module": "Mathlib.GroupTheory.CosetCover", "is_tactic_proof": true, "tactics": ["contrapose", "exact"], "tactic_count": 2}
{"name": "Subspace.exists_eq_top_of_iUnion_eq_univ", "kind": "theorem", "module": "Mathlib.GroupTheory.CosetCover", "is_tactic_proof": true, "tactics": ["have", "simp_rw", "apply"], "tactic_count": 3}
{"name": "mem_leftCoset", "kind": "theorem", "module": "Mathlib.GroupTheory.Coset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_rightCoset", "kind": "theorem", "module": "Mathlib.GroupTheory.Coset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LeftCosetEquivalence", "kind": "definition", "module": "Mathlib.GroupTheory.Coset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "leftCosetEquivalence_rel", "kind": "theorem", "module": "Mathlib.GroupTheory.Coset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RightCosetEquivalence", "kind": "definition", "module": "Mathlib.GroupTheory.Coset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "rightCosetEquivalence_rel", "kind": "theorem", "module": "Mathlib.GroupTheory.Coset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "leftCoset_assoc", "kind": "theorem", "module": "Mathlib.GroupTheory.Coset.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "rightCoset_assoc", "kind": "theorem", "module": "Mathlib.GroupTheory.Coset.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "leftCoset_rightCoset", "kind": "theorem", "module": "Mathlib.GroupTheory.Coset.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "one_leftCoset", "kind": "theorem", "module": "Mathlib.GroupTheory.Coset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "rightCoset_one", "kind": "theorem", "module": "Mathlib.GroupTheory.Coset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_own_leftCoset", "kind": "theorem", "module": "Mathlib.GroupTheory.Coset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_own_rightCoset", "kind": "theorem", "module": "Mathlib.GroupTheory.Coset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_leftCoset_leftCoset", "kind": "theorem", "module": "Mathlib.GroupTheory.Coset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mem_rightCoset_rightCoset", "kind": "theorem", "module": "Mathlib.GroupTheory.Coset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mem_leftCoset_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Coset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_rightCoset_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Coset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "leftCoset_mem_leftCoset", "kind": "theorem", "module": "Mathlib.GroupTheory.Coset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "rightCoset_mem_rightCoset", "kind": "theorem", "module": "Mathlib.GroupTheory.Coset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "orbit_subgroup_eq_rightCoset", "kind": "theorem", "module": "Mathlib.GroupTheory.Coset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "orbit_subgroup_eq_self_of_mem", "kind": "theorem", "module": "Mathlib.GroupTheory.Coset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "orbit_subgroup_one_eq_self", "kind": "theorem", "module": "Mathlib.GroupTheory.Coset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_cosets_of_normal", "kind": "theorem", "module": "Mathlib.GroupTheory.Coset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "normal_of_eq_cosets", "kind": "theorem", "module": "Mathlib.GroupTheory.Coset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "normal_iff_eq_cosets", "kind": "theorem", "module": "Mathlib.GroupTheory.Coset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "leftCoset_eq_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Coset.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "constructor", "intro", "apply", "rw", "exact", "intro", "rw", "rw", "exact"], "tactic_count": 11}
{"name": "rightCoset_eq_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Coset.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "constructor", "intro", "apply", "rw", "exact", "intro", "rw", "rw", "exact"], "tactic_count": 11}
{"name": "QuotientGroup.leftRel_r_eq_leftCosetEquivalence", "kind": "theorem", "module": "Mathlib.GroupTheory.Coset.Basic", "is_tactic_proof": true, "tactics": ["ext", "rw", "exact"], "tactic_count": 3}
{"name": "QuotientGroup.leftRel_prod", "kind": "theorem", "module": "Mathlib.GroupTheory.Coset.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "simp_rw", "rfl"], "tactic_count": 4}
{"name": "QuotientGroup.leftRel_pi", "kind": "theorem", "module": "Mathlib.GroupTheory.Coset.Basic", "is_tactic_proof": true, "tactics": ["refine", "simp"], "tactic_count": 2}
{"name": "QuotientGroup.rightRel_r_eq_rightCosetEquivalence", "kind": "theorem", "module": "Mathlib.GroupTheory.Coset.Basic", "is_tactic_proof": true, "tactics": ["ext", "rw", "exact"], "tactic_count": 3}
{"name": "QuotientGroup.rightRel_prod", "kind": "theorem", "module": "Mathlib.GroupTheory.Coset.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "simp_rw", "rfl"], "tactic_count": 4}
{"name": "QuotientGroup.rightRel_pi", "kind": "theorem", "module": "Mathlib.GroupTheory.Coset.Basic", "is_tactic_proof": true, "tactics": ["refine", "simp"], "tactic_count": 2}
{"name": "QuotientGroup.strictMono_comap_prod_image", "kind": "theorem", "module": "Mathlib.GroupTheory.Coset.Basic", "is_tactic_proof": true, "tactics": ["refine", "obtain", "convert", "apply"], "tactic_count": 4}
{"name": "QuotientGroup.eq_class_eq_leftCoset", "kind": "theorem", "module": "Mathlib.GroupTheory.Coset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.orbit_mk_eq_smul", "kind": "theorem", "module": "Mathlib.GroupTheory.Coset.Basic", "is_tactic_proof": true, "tactics": ["ext", "rw", "simpa"], "tactic_count": 3}
{"name": "QuotientGroup.orbit_eq_out_smul", "kind": "theorem", "module": "Mathlib.GroupTheory.Coset.Basic", "is_tactic_proof": true, "tactics": ["induction", "simp"], "tactic_count": 2}
{"name": "Subgroup.leftCosetEquivSubgroup", "kind": "definition", "module": "Mathlib.GroupTheory.Coset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.rightCosetEquivSubgroup", "kind": "definition", "module": "Mathlib.GroupTheory.Coset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.groupEquivQuotientProdSubgroup", "kind": "definition", "module": "Mathlib.GroupTheory.Coset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.quotientEquivProdOfLE'", "kind": "definition", "module": "Mathlib.GroupTheory.Coset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.quotientEquivProdOfLE", "kind": "definition", "module": "Mathlib.GroupTheory.Coset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.quotientSubgroupOfEmbeddingOfLE", "kind": "definition", "module": "Mathlib.GroupTheory.Coset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.quotientSubgroupOfEmbeddingOfLE_apply_mk", "kind": "theorem", "module": "Mathlib.GroupTheory.Coset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.quotientSubgroupOfMapOfLE", "kind": "definition", "module": "Mathlib.GroupTheory.Coset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.quotientSubgroupOfMapOfLE_apply_mk", "kind": "theorem", "module": "Mathlib.GroupTheory.Coset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.quotientMapOfLE", "kind": "definition", "module": "Mathlib.GroupTheory.Coset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.quotientMapOfLE_apply_mk", "kind": "theorem", "module": "Mathlib.GroupTheory.Coset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.quotientiInfSubgroupOfEmbedding", "kind": "definition", "module": "Mathlib.GroupTheory.Coset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.quotientiInfSubgroupOfEmbedding_apply_mk", "kind": "theorem", "module": "Mathlib.GroupTheory.Coset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.quotientiInfEmbedding", "kind": "definition", "module": "Mathlib.GroupTheory.Coset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.quotientiInfEmbedding_apply_mk", "kind": "theorem", "module": "Mathlib.GroupTheory.Coset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.fiberEquivKer", "kind": "definition", "module": "Mathlib.GroupTheory.Coset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.fiberEquivKer_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.Coset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.fiberEquivKer_symm_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.Coset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.fiberEquivKerOfSurjective", "kind": "definition", "module": "Mathlib.GroupTheory.Coset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.fiberEquiv", "kind": "definition", "module": "Mathlib.GroupTheory.Coset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.fiberEquiv_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.Coset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.fiberEquiv_symm_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.Coset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.fiberEquivOfSurjective", "kind": "definition", "module": "Mathlib.GroupTheory.Coset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.preimageMkEquivSubgroupProdSet", "kind": "definition", "module": "Mathlib.GroupTheory.Coset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.univ_eq_iUnion_smul", "kind": "theorem", "module": "Mathlib.GroupTheory.Coset.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "rfl"], "tactic_count": 2}
{"name": "QuotientGroup.quotientEquivSelf", "kind": "definition", "module": "Mathlib.GroupTheory.Coset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.fintype", "kind": "instance", "module": "Mathlib.GroupTheory.Coset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.finite", "kind": "instance", "module": "Mathlib.GroupTheory.Coset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.fintypeQuotientRightRel", "kind": "instance", "module": "Mathlib.GroupTheory.Coset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.card_quotient_rightRel", "kind": "theorem", "module": "Mathlib.GroupTheory.Coset.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.card_eq_card_quotient_mul_card_subgroup", "kind": "theorem", "module": "Mathlib.GroupTheory.Coset.Card", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subgroup.card_mul_eq_card_subgroup_mul_card_quotient", "kind": "theorem", "module": "Mathlib.GroupTheory.Coset.Card", "is_tactic_proof": true, "tactics": ["rw", "apply", "rw", "convert", "aesop"], "tactic_count": 5}
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{"name": "Subgroup.card_quotient_dvd_card", "kind": "theorem", "module": "Mathlib.GroupTheory.Coset.Card", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "CoxeterSystem.braidWord", "kind": "abbrev", "module": "Mathlib.GroupTheory.Coxeter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CoxeterSystem.IsReflection.conj", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Inversion", "is_tactic_proof": true, "tactics": ["obtain", "use", "group"], "tactic_count": 3}
{"name": "CoxeterSystem.isReflection_conj_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Inversion", "is_tactic_proof": true, "tactics": ["constructor", "intro", "simpa", "exact"], "tactic_count": 4}
{"name": "CoxeterSystem.IsRightInversion", "kind": "definition", "module": "Mathlib.GroupTheory.Coxeter.Inversion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoxeterSystem.IsLeftInversion", "kind": "definition", "module": "Mathlib.GroupTheory.Coxeter.Inversion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoxeterSystem.isRightInversion_inv_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Inversion", "is_tactic_proof": true, "tactics": ["apply", "intro", "rw"], "tactic_count": 3}
{"name": "CoxeterSystem.isLeftInversion_inv_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Inversion", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "CoxeterSystem.IsReflection.isRightInversion_mul_left_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Inversion", "is_tactic_proof": true, "tactics": ["unfold", "simp", "constructor", "exact", "exact"], "tactic_count": 5}
{"name": "CoxeterSystem.IsReflection.not_isRightInversion_mul_left_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Inversion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoxeterSystem.IsReflection.isLeftInversion_mul_right_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Inversion", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CoxeterSystem.IsReflection.not_isLeftInversion_mul_right_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Inversion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoxeterSystem.isRightInversion_simple_iff_isRightDescent", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Inversion", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CoxeterSystem.isLeftInversion_simple_iff_isLeftDescent", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Inversion", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CoxeterSystem.rightInvSeq", "kind": "definition", "module": "Mathlib.GroupTheory.Coxeter.Inversion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoxeterSystem.leftInvSeq", "kind": "definition", "module": "Mathlib.GroupTheory.Coxeter.Inversion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.GroupTheory.Coxeter.Inversion.0.CoxeterSystem.termRis_", "kind": "definition", "module": "Mathlib.GroupTheory.Coxeter.Inversion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.GroupTheory.Coxeter.Inversion.0.CoxeterSystem._aux_Mathlib_GroupTheory_Coxeter_Inversion___macroRules__private_Mathlib_GroupTheory_Coxeter_Inversion_0_CoxeterSystem_termRis__1", "kind": "definition", "module": "Mathlib.GroupTheory.Coxeter.Inversion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.GroupTheory.Coxeter.Inversion.0.CoxeterSystem.termLis_", "kind": "definition", "module": "Mathlib.GroupTheory.Coxeter.Inversion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.GroupTheory.Coxeter.Inversion.0.CoxeterSystem._aux_Mathlib_GroupTheory_Coxeter_Inversion___macroRules__private_Mathlib_GroupTheory_Coxeter_Inversion_0_CoxeterSystem_termLis__1", "kind": "definition", "module": "Mathlib.GroupTheory.Coxeter.Inversion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoxeterSystem.rightInvSeq_nil", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Inversion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoxeterSystem.leftInvSeq_nil", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Inversion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoxeterSystem.rightInvSeq_singleton", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Inversion", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CoxeterSystem.leftInvSeq_singleton", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Inversion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoxeterSystem.rightInvSeq_concat", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Inversion", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "dsimp", "rw", "simp", "cons.injEq,", "group"], "tactic_count": 8}
{"name": "_private.Mathlib.GroupTheory.Coxeter.Inversion.0.CoxeterSystem.leftInvSeq_eq_reverse_rightInvSeq_reverse", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Inversion", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "rw", "simp"], "tactic_count": 5}
{"name": "CoxeterSystem.leftInvSeq_concat", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Inversion", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CoxeterSystem.rightInvSeq_reverse", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Inversion", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CoxeterSystem.leftInvSeq_reverse", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Inversion", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CoxeterSystem.length_rightInvSeq", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Inversion", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "CoxeterSystem.length_leftInvSeq", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Inversion", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CoxeterSystem.getD_rightInvSeq", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Inversion", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "dsimp", "rcases", "simp", "simp", "simp"], "tactic_count": 8}
{"name": "CoxeterSystem.getElem_rightInvSeq", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Inversion", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CoxeterSystem.getD_leftInvSeq", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Inversion", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "dsimp", "rcases", "simp", "rw", "rw", "rw", "rw", "simp"], "tactic_count": 11}
{"name": "CoxeterSystem.getElem_leftInvSeq", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Inversion", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "CoxeterSystem.getD_rightInvSeq_mul_self", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Inversion", "is_tactic_proof": true, "tactics": ["simp_rw", "rcases", "rw", "simp", "rw", "simp"], "tactic_count": 6}
{"name": "CoxeterSystem.getD_leftInvSeq_mul_self", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Inversion", "is_tactic_proof": true, "tactics": ["simp_rw", "rcases", "rw", "simp", "rw", "simp"], "tactic_count": 6}
{"name": "CoxeterSystem.rightInvSeq_drop", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Inversion", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "induction", "nil", "cons"], "tactic_count": 6}
{"name": "CoxeterSystem.leftInvSeq_take", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Inversion", "is_tactic_proof": true, "tactics": ["simp", "rw", "nth_rw", "rw", "simp"], "tactic_count": 5}
{"name": "CoxeterSystem.isReflection_of_mem_rightInvSeq", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Inversion", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "dsimp", "rcases", "use", "group", "exact"], "tactic_count": 8}
{"name": "CoxeterSystem.isReflection_of_mem_leftInvSeq", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Inversion", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "CoxeterSystem.wordProd_mul_getD_rightInvSeq", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Inversion", "is_tactic_proof": true, "tactics": ["rw", "nth_rw", "rw", "obtain", "simp", "simp", "simp", "simp"], "tactic_count": 8}
{"name": "CoxeterSystem.getD_leftInvSeq_mul_wordProd", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Inversion", "is_tactic_proof": true, "tactics": ["rw", "nth_rw", "rw", "obtain", "simp", "simp", "simp", "simp"], "tactic_count": 8}
{"name": "CoxeterSystem.isRightInversion_of_mem_rightInvSeq", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Inversion", "is_tactic_proof": true, "tactics": ["constructor", "exact", "obtain", "rw", "rw", "calc", "ℓ"], "tactic_count": 7}
{"name": "CoxeterSystem.isLeftInversion_of_mem_leftInvSeq", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Inversion", "is_tactic_proof": true, "tactics": ["constructor", "exact", "obtain", "rw", "rw", "calc", "ℓ"], "tactic_count": 7}
{"name": "CoxeterSystem.prod_rightInvSeq", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Inversion", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "CoxeterSystem.prod_leftInvSeq", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Inversion", "is_tactic_proof": true, "tactics": ["simp", "have", "calc", "apply", "intro", "exact", "rw", "nth_rw", "rw", "exact"], "tactic_count": 10}
{"name": "CoxeterSystem.IsReduced.nodup_rightInvSeq", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Inversion", "is_tactic_proof": true, "tactics": ["apply", "intro", "show", "replace", "rw", "apply", "rw", "set", "set", "have", "have", "rw", "exact", "have", "calc", "π", "have", "calc", "ω.length", "grind"], "tactic_count": 20}
{"name": "CoxeterSystem.IsReduced.nodup_leftInvSeq", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Inversion", "is_tactic_proof": true, "tactics": ["simp", "apply", "rwa"], "tactic_count": 3}
{"name": "CoxeterSystem.getElem_succ_leftInvSeq_alternatingWord", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Inversion", "is_tactic_proof": false, "tactics": ["rw", "cs.getElem_leftInvSeq", "simp", "rw", "lia"], "tactic_count": 5}
{"name": "CoxeterSystem.getElem_leftInvSeq_alternatingWord", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Inversion", "is_tactic_proof": true, "tactics": ["induction", "zero", "simp", "wordProd_nil,", "simp", "succ", "hk", "simp", "alternatingWord_succ", "rw", "simp"], "tactic_count": 11}
{"name": "_private.Mathlib.GroupTheory.Coxeter.Length.0.CoxeterSystem.termS_", "kind": "definition", "module": "Mathlib.GroupTheory.Coxeter.Length", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.GroupTheory.Coxeter.Length.0.CoxeterSystem._aux_Mathlib_GroupTheory_Coxeter_Length___macroRules__private_Mathlib_GroupTheory_Coxeter_Length_0_CoxeterSystem_termS__1", "kind": "definition", "module": "Mathlib.GroupTheory.Coxeter.Length", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.GroupTheory.Coxeter.Length.0.CoxeterSystem.termπ_", "kind": "definition", "module": "Mathlib.GroupTheory.Coxeter.Length", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.GroupTheory.Coxeter.Length.0.CoxeterSystem._aux_Mathlib_GroupTheory_Coxeter_Length___macroRules__private_Mathlib_GroupTheory_Coxeter_Length_0_CoxeterSystem_termπ__1", "kind": "definition", "module": "Mathlib.GroupTheory.Coxeter.Length", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.GroupTheory.Coxeter.Length.0.CoxeterSystem.exists_word_with_prod", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Length", "is_tactic_proof": true, "tactics": ["rcases", "use"], "tactic_count": 2}
{"name": "CoxeterSystem.length", "kind": "definition", "module": "Mathlib.GroupTheory.Coxeter.Length", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.GroupTheory.Coxeter.Length.0.CoxeterSystem.termℓ_", "kind": "definition", "module": "Mathlib.GroupTheory.Coxeter.Length", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.GroupTheory.Coxeter.Length.0.CoxeterSystem._aux_Mathlib_GroupTheory_Coxeter_Length___macroRules__private_Mathlib_GroupTheory_Coxeter_Length_0_CoxeterSystem_termℓ__1", "kind": "definition", "module": "Mathlib.GroupTheory.Coxeter.Length", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoxeterSystem.exists_reduced_word", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Length", "is_tactic_proof": true, "tactics": ["classical", "have", "tauto"], "tactic_count": 3}
{"name": "CoxeterSystem.length_wordProd_le", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Length", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoxeterSystem.length_one", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Length", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoxeterSystem.length_eq_zero_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Length", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rcases", "have", "rw", "rintro", "exact"], "tactic_count": 7}
{"name": "CoxeterSystem.length_inv", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Length", "is_tactic_proof": true, "tactics": ["apply", "rcases", "have", "rwa", "rcases", "have", "rwa"], "tactic_count": 7}
{"name": "CoxeterSystem.length_mul_le", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Length", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "have", "simpa"], "tactic_count": 4}
{"name": "CoxeterSystem.length_mul_ge_length_sub_length", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Length", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CoxeterSystem.length_mul_ge_length_sub_length'", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Length", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CoxeterSystem.length_mul_ge_max", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Length", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoxeterSystem.lengthParity", "kind": "definition", "module": "Mathlib.GroupTheory.Coxeter.Length", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoxeterSystem.lengthParity_simple", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Length", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoxeterSystem.lengthParity_comp_simple", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Length", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoxeterSystem.lengthParity_eq_ofAdd_length", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Length", "is_tactic_proof": true, "tactics": ["rcases", "rw", "nsmul_one]"], "tactic_count": 3}
{"name": "CoxeterSystem.length_mul_mod_two", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Length", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "CoxeterSystem.length_simple", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Length", "is_tactic_proof": true, "tactics": ["apply", "simpa", "by_contra", "have", "rw", "have", "contradiction"], "tactic_count": 7}
{"name": "CoxeterSystem.length_eq_one_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Length", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rcases", "rcases", "exact", "rintro", "exact"], "tactic_count": 7}
{"name": "CoxeterSystem.length_mul_simple_ne", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Length", "is_tactic_proof": true, "tactics": ["intro", "have", "rw", "lia"], "tactic_count": 4}
{"name": "CoxeterSystem.length_simple_mul_ne", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Length", "is_tactic_proof": true, "tactics": ["convert", "convert", "simp", "simp"], "tactic_count": 4}
{"name": "CoxeterSystem.length_mul_simple", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Length", "is_tactic_proof": true, "tactics": ["rcases", "right", "have", "simp", "lia", "left", "have", "simp", "lia"], "tactic_count": 9}
{"name": "CoxeterSystem.length_simple_mul", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Length", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "CoxeterSystem.IsReduced", "kind": "definition", "module": "Mathlib.GroupTheory.Coxeter.Length", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoxeterSystem.isReduced_reverse_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Length", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CoxeterSystem.IsReduced.reverse", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Length", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoxeterSystem.exists_reduced_word'", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Length", "is_tactic_proof": true, "tactics": ["rcases", "use", "tauto"], "tactic_count": 3}
{"name": "_private.Mathlib.GroupTheory.Coxeter.Length.0.CoxeterSystem.isReduced_take_and_drop", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Length", "is_tactic_proof": true, "tactics": ["have", "have", "have", "calc", "unfold", "lia"], "tactic_count": 6}
{"name": "CoxeterSystem.IsReduced.take", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Length", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoxeterSystem.IsReduced.drop", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Length", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoxeterSystem.not_isReduced_alternatingWord", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Length", "is_tactic_proof": true, "tactics": ["induction", "refl", "suffices", "unfold", "rw", "lia", "have", "rw", "have", "rw", "calc", "ℓ", "step", "contrapose", "rw", "apply", "simpa"], "tactic_count": 17}
{"name": "CoxeterSystem.IsLeftDescent", "kind": "definition", "module": "Mathlib.GroupTheory.Coxeter.Length", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoxeterSystem.IsRightDescent", "kind": "definition", "module": "Mathlib.GroupTheory.Coxeter.Length", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoxeterSystem.not_isLeftDescent_one", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Length", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CoxeterSystem.not_isRightDescent_one", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Length", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CoxeterSystem.isLeftDescent_inv_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Length", "is_tactic_proof": true, "tactics": ["unfold", "nth_rw", "simp"], "tactic_count": 3}
{"name": "CoxeterSystem.isRightDescent_inv_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Length", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CoxeterSystem.exists_leftDescent_of_ne_one", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Length", "is_tactic_proof": true, "tactics": ["rcases", "have", "rcases", "use", "rw", "calc", "ℓ"], "tactic_count": 7}
{"name": "CoxeterSystem.exists_rightDescent_of_ne_one", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Length", "is_tactic_proof": true, "tactics": ["simp", "apply", "simpa"], "tactic_count": 3}
{"name": "CoxeterSystem.isLeftDescent_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Length", "is_tactic_proof": true, "tactics": ["unfold", "constructor", "intro", "exact", "lia"], "tactic_count": 5}
{"name": "CoxeterSystem.not_isLeftDescent_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Length", "is_tactic_proof": true, "tactics": ["unfold", "constructor", "intro", "exact", "lia"], "tactic_count": 5}
{"name": "CoxeterSystem.isRightDescent_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Length", "is_tactic_proof": true, "tactics": ["unfold", "constructor", "intro", "exact", "lia"], "tactic_count": 5}
{"name": "CoxeterSystem.not_isRightDescent_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Length", "is_tactic_proof": true, "tactics": ["unfold", "constructor", "intro", "exact", "lia"], "tactic_count": 5}
{"name": "CoxeterSystem.isLeftDescent_iff_not_isLeftDescent_mul", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Length", "is_tactic_proof": true, "tactics": ["rw", "tauto"], "tactic_count": 2}
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{"name": "CoxeterMatrix.symmetric", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoxeterMatrix.reindex", "kind": "definition", "module": "Mathlib.GroupTheory.Coxeter.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoxeterMatrix.reindex_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.Coxeter.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoxeterMatrix.Aₙ", "kind": "definition", "module": "Mathlib.GroupTheory.Coxeter.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoxeterMatrix.Bₙ", "kind": "definition", "module": "Mathlib.GroupTheory.Coxeter.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoxeterMatrix.Dₙ", "kind": "definition", "module": "Mathlib.GroupTheory.Coxeter.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoxeterMatrix.I₂ₘ", "kind": "definition", "module": "Mathlib.GroupTheory.Coxeter.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoxeterMatrix.E₆", "kind": "definition", "module": "Mathlib.GroupTheory.Coxeter.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoxeterMatrix.E₇", "kind": "definition", "module": "Mathlib.GroupTheory.Coxeter.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoxeterMatrix.E₈", "kind": "definition", "module": "Mathlib.GroupTheory.Coxeter.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoxeterMatrix.F₄", "kind": "definition", "module": "Mathlib.GroupTheory.Coxeter.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoxeterMatrix.G₂", "kind": "definition", "module": "Mathlib.GroupTheory.Coxeter.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoxeterMatrix.H₃", "kind": "definition", "module": "Mathlib.GroupTheory.Coxeter.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoxeterMatrix.H₄", "kind": "definition", "module": "Mathlib.GroupTheory.Coxeter.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsDedekindFiniteMonoidOfFinite", "kind": "instance", "module": "Mathlib.GroupTheory.DedekindFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pow_left_surj_of_rootableBy", "kind": "theorem", "module": "Mathlib.GroupTheory.Divisible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "rootableByOfPowLeftSurj", "kind": "definition", "module": "Mathlib.GroupTheory.Divisible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.rootableBy", "kind": "instance", "module": "Mathlib.GroupTheory.Divisible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ULift.instRootableBy", "kind": "instance", "module": "Mathlib.GroupTheory.Divisible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGroup.smul_top_eq_top_of_divisibleBy_int", "kind": "theorem", "module": "Mathlib.GroupTheory.Divisible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCommGroup.divisibleByIntOfSMulTopEqTop", "kind": "definition", "module": "Mathlib.GroupTheory.Divisible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "divisibleByIntOfCharZero", "kind": "instance", "module": "Mathlib.GroupTheory.Divisible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Group.rootableByIntOfRootableByNat", "kind": "definition", "module": "Mathlib.GroupTheory.Divisible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Group.rootableByNatOfRootableByInt", "kind": "definition", "module": "Mathlib.GroupTheory.Divisible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.rootableBy", "kind": "definition", "module": "Mathlib.GroupTheory.Divisible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootableBy.surjective_pow", "kind": "theorem", "module": "Mathlib.GroupTheory.Divisible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.rootableBy", "kind": "instance", "module": "Mathlib.GroupTheory.Divisible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.GroupTheory.DivisibleHull.0.term↑ⁿ", "kind": "definition", "module": "Mathlib.GroupTheory.DivisibleHull", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "DivisibleHull.mk", "kind": "definition", "module": "Mathlib.GroupTheory.DivisibleHull", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DivisibleHull.instModuleNNRat", "kind": "instance", "module": "Mathlib.GroupTheory.DivisibleHull", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DivisibleHull.coe", "kind": "abbrev", "module": "Mathlib.GroupTheory.DivisibleHull", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DivisibleHull.instCoe", "kind": "instance", "module": "Mathlib.GroupTheory.DivisibleHull", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DivisibleHull.mk_zero", "kind": "theorem", "module": "Mathlib.GroupTheory.DivisibleHull", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "DivisibleHull.liftOn", "kind": "definition", "module": "Mathlib.GroupTheory.DivisibleHull", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DivisibleHull.liftOn_mk", "kind": "theorem", "module": "Mathlib.GroupTheory.DivisibleHull", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DivisibleHull.liftOn₂", "kind": "definition", "module": "Mathlib.GroupTheory.DivisibleHull", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DivisibleHull.liftOn₂_mk", "kind": "theorem", "module": "Mathlib.GroupTheory.DivisibleHull", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DivisibleHull.mk_add_mk", "kind": "theorem", "module": "Mathlib.GroupTheory.DivisibleHull", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DivisibleHull.mk_add_mk_left", "kind": "theorem", "module": "Mathlib.GroupTheory.DivisibleHull", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
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{"name": "DivisibleHull.coeAddMonoidHom", "kind": "definition", "module": "Mathlib.GroupTheory.DivisibleHull", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DivisibleHull.nsmul_mk", "kind": "theorem", "module": "Mathlib.GroupTheory.DivisibleHull", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
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{"name": "DivisibleHull.instSMulRat", "kind": "instance", "module": "Mathlib.GroupTheory.DivisibleHull", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "DivisibleHull.zero_qsmul", "kind": "theorem", "module": "Mathlib.GroupTheory.DivisibleHull", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DivisibleHull.qsmul_of_nonneg", "kind": "theorem", "module": "Mathlib.GroupTheory.DivisibleHull", "is_tactic_proof": true, "tactics": ["have", "aesop"], "tactic_count": 2}
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{"name": "DivisibleHull.zsmul_mk", "kind": "theorem", "module": "Mathlib.GroupTheory.DivisibleHull", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "DivisibleHull.mk_le_mk", "kind": "theorem", "module": "Mathlib.GroupTheory.DivisibleHull", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "DivisibleHull.instLinearOrder", "kind": "instance", "module": "Mathlib.GroupTheory.DivisibleHull", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DivisibleHull.mk_lt_mk", "kind": "theorem", "module": "Mathlib.GroupTheory.DivisibleHull", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "DivisibleHull.instIsOrderedCancelAddMonoid", "kind": "instance", "module": "Mathlib.GroupTheory.DivisibleHull", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DivisibleHull.instIsStrictOrderedModuleNNRat", "kind": "instance", "module": "Mathlib.GroupTheory.DivisibleHull", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "DivisibleHull.coeOrderAddMonoidHom", "kind": "definition", "module": "Mathlib.GroupTheory.DivisibleHull", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DivisibleHull.archimedeanClassMk_mk_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.DivisibleHull", "is_tactic_proof": false, "tactics": ["suffices", "apply_fun", "rw", "rw", "exact", "simp_rw"], "tactic_count": 6}
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{"name": "_private.Mathlib.GroupTheory.DivisibleHull.0.DivisibleHull.archimedeanClassOrderHomInv", "kind": "definition", "module": "Mathlib.GroupTheory.DivisibleHull", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "DoubleCoset.doubleCoset", "kind": "definition", "module": "Mathlib.GroupTheory.DoubleCoset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "DoubleCoset.mem_doubleCoset", "kind": "theorem", "module": "Mathlib.GroupTheory.DoubleCoset", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DoubleCoset.mem_doubleCoset_self", "kind": "theorem", "module": "Mathlib.GroupTheory.DoubleCoset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "DoubleCoset.mem_doubleCoset_of_not_disjoint", "kind": "theorem", "module": "Mathlib.GroupTheory.DoubleCoset", "is_tactic_proof": true, "tactics": ["rw", "simp", "obtain", "refine", "rwa"], "tactic_count": 5}
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{"name": "DoubleCoset.setoid", "kind": "definition", "module": "Mathlib.GroupTheory.DoubleCoset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DoubleCoset.Quotient", "kind": "definition", "module": "Mathlib.GroupTheory.DoubleCoset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DoubleCoset.rel_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.DoubleCoset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DoubleCoset.bot_rel_eq_leftRel", "kind": "theorem", "module": "Mathlib.GroupTheory.DoubleCoset", "is_tactic_proof": true, "tactics": ["ext", "rw", "constructor", "rintro", "rwa", "rintro", "exact"], "tactic_count": 7}
{"name": "DoubleCoset.rel_bot_eq_right_group_rel", "kind": "theorem", "module": "Mathlib.GroupTheory.DoubleCoset", "is_tactic_proof": true, "tactics": ["ext", "rw", "constructor", "rintro", "rwa", "rintro", "exact"], "tactic_count": 7}
{"name": "DoubleCoset.quotToDoubleCoset", "kind": "definition", "module": "Mathlib.GroupTheory.DoubleCoset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DoubleCoset.mk", "kind": "abbrev", "module": "Mathlib.GroupTheory.DoubleCoset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DoubleCoset.instInhabitedQuotientCoeSubgroup", "kind": "instance", "module": "Mathlib.GroupTheory.DoubleCoset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DoubleCoset.eq", "kind": "theorem", "module": "Mathlib.GroupTheory.DoubleCoset", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "DoubleCoset.out_eq'", "kind": "theorem", "module": "Mathlib.GroupTheory.DoubleCoset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "DoubleCoset.union_quotToDoubleCoset", "kind": "theorem", "module": "Mathlib.GroupTheory.DoubleCoset", "is_tactic_proof": true, "tactics": ["ext", "simp", "use", "obtain", "refine", "simp"], "tactic_count": 6}
{"name": "DoubleCoset.doubleCoset_union_rightCoset", "kind": "theorem", "module": "Mathlib.GroupTheory.DoubleCoset", "is_tactic_proof": true, "tactics": ["ext", "simp", "constructor", "rintro", "refine", "simp", "rintro", "refine", "simp"], "tactic_count": 9}
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{"name": "EckmannHilton.MulOneClass.isUnital", "kind": "theorem", "module": "Mathlib.GroupTheory.EckmannHilton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EckmannHilton.one", "kind": "theorem", "module": "Mathlib.GroupTheory.EckmannHilton", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "EckmannHilton.mul", "kind": "theorem", "module": "Mathlib.GroupTheory.EckmannHilton", "is_tactic_proof": true, "tactics": ["funext", "calc", "m₁"], "tactic_count": 3}
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{"name": "EckmannHilton.mul_assoc", "kind": "theorem", "module": "Mathlib.GroupTheory.EckmannHilton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "FreeAbelianGroup.ring", "kind": "instance", "module": "Mathlib.GroupTheory.FreeAbelianGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeAbelianGroup.ofMulHom", "kind": "definition", "module": "Mathlib.GroupTheory.FreeAbelianGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeAbelianGroup.ofMulHom_coe", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeAbelianGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeAbelianGroup.liftMonoid", "kind": "definition", "module": "Mathlib.GroupTheory.FreeAbelianGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeAbelianGroup.liftMonoid_coe_addMonoidHom", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeAbelianGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeAbelianGroup.liftMonoid_coe", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeAbelianGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeAbelianGroup.liftMonoid_symm_coe", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeAbelianGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeAbelianGroup.instCommRingOfCommMonoid", "kind": "instance", "module": "Mathlib.GroupTheory.FreeAbelianGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeAbelianGroup.pemptyUnique", "kind": "instance", "module": "Mathlib.GroupTheory.FreeAbelianGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeAbelianGroup.uniqueEquiv", "kind": "definition", "module": "Mathlib.GroupTheory.FreeAbelianGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeAbelianGroup.equivOfEquiv", "kind": "definition", "module": "Mathlib.GroupTheory.FreeAbelianGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeAddGroup.Red.Step", "kind": "inductive", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.Red.Step", "kind": "inductive", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "FreeGroup.Red.refl", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.Red.trans", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.Red.Step.length", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.Red.Step.not_rev", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "FreeGroup.Red.Step.cons_not", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.Red.Step.cons_not_rev", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.Red.Step.append_left", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.Red.Step.cons", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.Red.Step.append_right", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.Red.not_step_nil", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": true, "tactics": ["generalize", "intro", "rcases", "simp"], "tactic_count": 4}
{"name": "FreeGroup.Red.Step.cons_left_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": true, "tactics": ["constructor", "generalize", "rintro", "rintro", "exact", "exact"], "tactic_count": 6}
{"name": "FreeGroup.Red.not_step_singleton", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.Red.Step.cons_cons_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "FreeGroup.Red.Step.diamond_aux", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.Red.Step.diamond", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.Red.Step.to_red", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.Red.church_rosser", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.Red.cons_cons", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.Red.cons_cons_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.Red.append_append_left_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.Red.append_append", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.Red.to_append_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.Red.nil_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.Red.singleton_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.Red.cons_nil_iff_singleton", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.Red.red_iff_irreducible", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": true, "tactics": ["apply", "generalize", "intro", "cases", "simp", "or_self,", "rcases", "simp"], "tactic_count": 8}
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{"name": "FreeGroup.Red.sizeof_of_step", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "FreeGroup.Red.antisymm", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.equivalence_join_red", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.join_red_of_step", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.eqvGen_step_iff_join_red", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.IsReduced", "kind": "definition", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.IsReduced.nil", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.IsReduced.singleton", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.isReduced_cons_cons", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "FreeGroup.IsReduced.of_forall_not_step", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "FreeGroup.IsReduced.append_overlap", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.IsReduced.infix", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "FreeGroup.quot_mk_eq_mk", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.quot_lift_mk", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.quot_liftOn_mk", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.quot_map_mk", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "FreeGroup.one_eq_mk", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.instInhabited", "kind": "instance", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.instUniqueOfIsEmpty", "kind": "instance", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "FreeGroup.instMul", "kind": "instance", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.mul_mk", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.invRev", "kind": "definition", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.invRev_length", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FreeGroup.invRev_invRev", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FreeGroup.invRev_empty", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.invRev_append", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FreeGroup.invRev_cons", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FreeGroup.invRev_involutive", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.invRev_injective", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.invRev_surjective", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.invRev_bijective", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.instInv", "kind": "instance", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.inv_mk", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.Red.Step.invRev", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": true, "tactics": ["obtain", "simp"], "tactic_count": 2}
{"name": "FreeGroup.Red.invRev", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.Red.step_invRev_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.red_invRev_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.instGroup", "kind": "instance", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.pow_mk", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.of", "kind": "definition", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.induction_on", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.ext_hom", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": true, "tactics": ["ext", "have", "trans", "simp_rw", "simp_rw", "induction"], "tactic_count": 6}
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{"name": "FreeGroup.of_injective", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.Lift.aux", "kind": "definition", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.Red.Step.lift", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "FreeGroup.lift", "kind": "definition", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.lift_mk", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.lift_apply_of", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FreeGroup.lift_unique", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.lift_of_eq_id", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.lift_of_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "FreeGroup.range_lift_eq_closure", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": true, "tactics": ["apply", "rw", "rintro", "exact"], "tactic_count": 4}
{"name": "FreeGroup.closure_eq_range", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "FreeGroup.map.unique", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": true, "tactics": ["rintro", "exact", "simp", "simp"], "tactic_count": 4}
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{"name": "FreeGroup.freeGroupCongr", "kind": "definition", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.freeGroupCongr_refl", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.freeGroupCongr_symm", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.freeGroupCongr_trans", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.prod", "kind": "definition", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.prod_mk", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.prod.of", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.prod.unique", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.lift_eq_prod_map", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "FreeGroup.reduce_invRev", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Reduce", "is_tactic_proof": true, "tactics": ["apply", "rw", "apply", "have", "rwa"], "tactic_count": 5}
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{"name": "FreeGroup.reduce_invRev_left_cancel", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Reduce", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FreeGroup.toWord_mul_sublist", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Reduce", "is_tactic_proof": true, "tactics": ["refine", "have", "rw", "rw", "exact"], "tactic_count": 5}
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{"name": "FreeGroup.instDecidableEq", "kind": "instance", "module": "Mathlib.GroupTheory.FreeGroup.Reduce", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.Red.decidableRel", "kind": "instance", "module": "Mathlib.GroupTheory.FreeGroup.Reduce", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "FreeGroup.Red.enum.complete", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Reduce", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.instFintypeSubtypeListProdBoolRed", "kind": "instance", "module": "Mathlib.GroupTheory.FreeGroup.Reduce", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.IsReduced.reduce_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Reduce", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
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{"name": "FreeGroup.instNontrivialOfNonempty", "kind": "instance", "module": "Mathlib.GroupTheory.FreeGroup.Reduce", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.norm", "kind": "definition", "module": "Mathlib.GroupTheory.FreeGroup.Reduce", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.norm_inv_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Reduce", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "FreeGroup.norm_mul_le", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Reduce", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeGroup.norm_of_pow", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Reduce", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "FreeGroup.norm_surjective", "kind": "theorem", "module": "Mathlib.GroupTheory.FreeGroup.Reduce", "is_tactic_proof": true, "tactics": ["let", "exact"], "tactic_count": 2}
{"name": "Subgroup.goursatFst", "kind": "definition", "module": "Mathlib.GroupTheory.Goursat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.goursatSnd", "kind": "definition", "module": "Mathlib.GroupTheory.Goursat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.mem_goursatFst", "kind": "theorem", "module": "Mathlib.GroupTheory.Goursat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Subgroup.mem_goursatSnd", "kind": "theorem", "module": "Mathlib.GroupTheory.Goursat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Subgroup.normal_goursatFst", "kind": "theorem", "module": "Mathlib.GroupTheory.Goursat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.normal_goursatSnd", "kind": "theorem", "module": "Mathlib.GroupTheory.Goursat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.mk_goursatFst_eq_iff_mk_goursatSnd_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.Goursat", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "simp", "constructor", "simpa", "simpa"], "tactic_count": 7}
{"name": "Subgroup.goursatFst_prod_goursatSnd_le", "kind": "theorem", "module": "Mathlib.GroupTheory.Goursat", "is_tactic_proof": true, "tactics": ["rintro", "simpa"], "tactic_count": 2}
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{"name": "MulAction.fst_mem_orbit_of_mem_orbit", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Basic", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "MulAction.snd_mem_orbit_of_mem_orbit", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Basic", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "Finite.finite_mulAction_orbit", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.orbit_eq_univ", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.subsingleton_orbit_iff_mem_fixedPoints", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Basic", "is_tactic_proof": true, "tactics": ["rw", "constructor", "exact", "rintro", "simp"], "tactic_count": 5}
{"name": "MulAction.mem_fixedPoints_iff_card_orbit_eq_one", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Basic", "is_tactic_proof": true, "tactics": ["simp", "implies_true]"], "tactic_count": 2}
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{"name": "MulAction.fixedPoints_of_subsingleton", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Basic", "is_tactic_proof": true, "tactics": ["apply", "simp", "intro", "apply"], "tactic_count": 4}
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{"name": "MulAction.instIsPretransitiveElemOrbit", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.orbitRel_subgroup_le", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.orbitRel_subgroupOf", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Basic", "is_tactic_proof": true, "tactics": ["rw", "ext", "simp_rw", "refine", "rcases", "simp", "refine", "simpa", "rcases", "simp", "simp", "refine", "exact", "simp", "exact"], "tactic_count": 15}
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{"name": "Finite.of_finite_mulAction_orbitRel_quotient", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Basic", "is_tactic_proof": true, "tactics": ["rw", "have", "intro", "induction", "simpa", "exact"], "tactic_count": 6}
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{"name": "isCancelSMul_iff_stabilizer_eq_bot", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "AddAction.stabilizerEquivStabilizer_symm", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "AddAction.stabilizerEquivStabilizer_neg", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "AddAction.stabilizerEquivStabilizerOfOrbitRel", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.swap_mem_stabilizer", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "exact"], "tactic_count": 3}
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{"name": "MulAction.orbit.pairwiseDisjoint", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Blocks", "is_tactic_proof": true, "tactics": ["rintro", "contrapose", "exact"], "tactic_count": 3}
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{"name": "MulAction.IsFixedBlock", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.Blocks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.IsInvariantBlock", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.Blocks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.IsTrivialBlock", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.Blocks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.IsTrivialBlock.image", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Blocks", "is_tactic_proof": true, "tactics": ["obtain", "apply", "apply", "simp"], "tactic_count": 4}
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{"name": "MulAction.IsBlock.not_smul_set_ssubset_smul_set", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Blocks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.IsBlock.disjoint_smul_set_smul", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Blocks", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MulAction.IsBlock.disjoint_smul_smul_set", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Blocks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.IsFixedBlock.isBlock", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Blocks", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MulAction.IsBlock.empty", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Blocks", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MulAction.IsBlock.singleton", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Blocks", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MulAction.IsBlock.of_subsingleton", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Blocks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.IsFixedBlock.isInvariantBlock", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Blocks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.IsBlock.disjoint_smul_right", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Blocks", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MulAction.IsBlock.disjoint_smul_left", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Blocks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.isBlock_iff_disjoint_smul_of_ne", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Blocks", "is_tactic_proof": true, "tactics": ["refine", "simp", "exact"], "tactic_count": 3}
{"name": "MulAction.isBlock_iff_smul_eq_of_nonempty", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Blocks", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MulAction.isBlock_iff_smul_eq_or_disjoint", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Blocks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.isBlock_iff_smul_eq_of_mem", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Blocks", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MulAction.IsBlock.subgroup", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Blocks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.isInvariantBlock_iff_isFixedBlock", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Blocks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.IsInvariantBlock.isBlock", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Blocks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.IsFixedBlock.univ", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Blocks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.IsBlock.univ", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Blocks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.IsBlock.inter", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Blocks", "is_tactic_proof": true, "tactics": ["simp", "rintro", "rw"], "tactic_count": 3}
{"name": "MulAction.IsBlock.iInter", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Blocks", "is_tactic_proof": true, "tactics": ["simp", "rintro", "simp_rw"], "tactic_count": 3}
{"name": "MulAction.IsTrivialBlock.isBlock", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Blocks", "is_tactic_proof": true, "tactics": ["obtain", "exact", "exact"], "tactic_count": 3}
{"name": "MulAction.IsFixedBlock.orbit", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Blocks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.IsBlock.orbit", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Blocks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.isBlock_top", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Blocks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.IsBlock.preimage", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Blocks", "is_tactic_proof": true, "tactics": ["rintro", "rw", "exact"], "tactic_count": 3}
{"name": "MulAction.IsBlock.image", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Blocks", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "MulAction.IsBlock.subtype_val_preimage", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Blocks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.isBlock_subtypeVal", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Blocks", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "AddAction.IsBlock.of_addSubgroup_of_conjugate", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Blocks", "is_tactic_proof": true, "tactics": ["rw", "intro", "obtain", "simp", "suffices", "simp", "apply", "intro", "exact", "suffices", "rw", "simp"], "tactic_count": 12}
{"name": "MulAction.IsBlock.of_subgroup_of_conjugate", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Blocks", "is_tactic_proof": true, "tactics": ["rw", "intro", "obtain", "simp", "suffices", "simp", "apply", "intro", "exact", "suffices", "rw"], "tactic_count": 11}
{"name": "AddAction.IsBlock.translate", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Blocks", "is_tactic_proof": true, "tactics": ["rw", "rw", "apply", "rwa", "exact"], "tactic_count": 5}
{"name": "MulAction.IsBlock.translate", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Blocks", "is_tactic_proof": true, "tactics": ["rw", "rw", "apply", "rwa"], "tactic_count": 4}
{"name": "MulAction.IsBlockSystem", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.Blocks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.IsBlock.isBlockSystem", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Blocks", "is_tactic_proof": true, "tactics": ["refine", "rintro", "simp", "intro", "apply", "simpa", "intro", "obtain", "obtain", "use", "simp", "forall_apply_eq_imp_iff,", "exact"], "tactic_count": 13}
{"name": "MulAction.smul_orbit_eq_orbit_smul", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Blocks", "is_tactic_proof": true, "tactics": ["simp", "ext", "simp", "constructor", "rintro", "use", "simp", "rw", "rintro", "use", "simp", "simp"], "tactic_count": 12}
{"name": "MulAction.IsBlock.orbit_of_normal", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Blocks", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "apply"], "tactic_count": 4}
{"name": "MulAction.IsBlockSystem.of_normal", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Blocks", "is_tactic_proof": true, "tactics": ["constructor", "apply", "intro", "exact"], "tactic_count": 4}
{"name": "MulAction.isBlock_subgroup", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Blocks", "is_tactic_proof": true, "tactics": ["simp", "rintro", "refine", "rw"], "tactic_count": 4}
{"name": "MulAction.isBlock_subgroup'", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Blocks", "is_tactic_proof": true, "tactics": ["simp", "rintro", "refine", "rw"], "tactic_count": 4}
{"name": "MulAction.IsBlock.of_orbit", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Blocks", "is_tactic_proof": true, "tactics": ["rw", "rintro", "suffices", "rw", "apply", "simpa"], "tactic_count": 6}
{"name": "MulAction.IsBlock.stabilizer_le", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Blocks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.IsBlock.orbit_stabilizer_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Blocks", "is_tactic_proof": true, "tactics": ["ext", "constructor", "rintro", "simp", "rw", "exact", "intro", "obtain", "exact"], "tactic_count": 9}
{"name": "MulAction.stabilizer_orbit_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Blocks", "is_tactic_proof": true, "tactics": ["ext", "constructor", "intro", "obtain", "simp_rw", "exact", "intro", "rw", "apply"], "tactic_count": 9}
{"name": "MulAction.block_stabilizerOrderIso", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.Blocks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.BlockMem", "kind": "abbrev", "module": "Mathlib.GroupTheory.GroupAction.Blocks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.BlockMem.instBoundedOrder", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.Blocks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.BlockMem.coe_top", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Blocks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.BlockMem.coe_bot", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Blocks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.BlockMem.instNontrivial", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.Blocks", "is_tactic_proof": true, "tactics": ["rw", "use", "intro", "rw", "simp", "obtain", "apply", "rw", "apply"], "tactic_count": 9}
{"name": "MulAction.IsBlock.ncard_block_eq_relIndex", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Blocks", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "MulAction.IsBlock.ncard_block_mul_ncard_orbit_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Blocks", "is_tactic_proof": true, "tactics": ["obtain", "rw", "index_stabilizer_of_transitive]"], "tactic_count": 3}
{"name": "MulAction.IsBlock.ncard_dvd_card", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Blocks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.IsBlock.eq_univ_of_card_lt", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Blocks", "is_tactic_proof": true, "tactics": ["rcases", "simp", "have", "rw", "interval_cases", "rw", "exact", "rw", "rw"], "tactic_count": 9}
{"name": "MulAction.IsBlock.subsingleton_of_card_lt", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Blocks", "is_tactic_proof": false, "tactics": ["suffices", "rw", "cases", "inl", "inr", "cases", "inl", "inr", "rw", "rw", "exact", "hB", "are"], "tactic_count": 13}
{"name": "MulAction.IsBlock.of_subset", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Blocks", "is_tactic_proof": true, "tactics": ["let", "rcases", "simp", "have", "intro", "exact", "have", "obtain", "obtain", "apply", "have", "intro", "simp", "exact", "have", "rw", "exact", "rw", "rintro", "obtain", "have", "refine", "simp", "have", "rw", "exact", "have", "have", "rw", "rw", "rw"], "tactic_count": 31}
{"name": "_private.Mathlib.GroupTheory.GroupAction.CardCommute.0.MulAction.termΩ", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.CardCommute", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.GroupTheory.GroupAction.CardCommute.0.MulAction._aux_Mathlib_GroupTheory_GroupAction_CardCommute___macroRules__private_Mathlib_GroupTheory_GroupAction_CardCommute_0_MulAction_termΩ_1", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.CardCommute", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.card_eq_sum_card_group_div_card_stabilizer'", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.CardCommute", "is_tactic_proof": true, "tactics": ["classical", "have", "intro", "rw", "exact", "simp_rw"], "tactic_count": 6}
{"name": "MulAction.card_eq_sum_card_group_div_card_stabilizer", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.CardCommute", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInfiniteProdSubtypeCommute", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.CardCommute", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "card_comm_eq_card_conjClasses_mul_card", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.CardCommute", "is_tactic_proof": true, "tactics": ["classical", "rcases", "rw", "simp", "calc", "card", "congr", "exact"], "tactic_count": 8}
{"name": "ConjAct", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.ConjAct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjAct.instGroup", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.ConjAct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjAct.instDivInvMonoid", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.ConjAct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjAct.instFintype", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.ConjAct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjAct.card", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.ConjAct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjAct.instInhabited", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.ConjAct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjAct.ofConjAct", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.ConjAct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjAct.toConjAct", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.ConjAct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjAct.rec", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.ConjAct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjAct.forall", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.ConjAct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjAct.of_mul_symm_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.ConjAct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjAct.to_mul_symm_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.ConjAct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjAct.toConjAct_ofConjAct", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.ConjAct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjAct.ofConjAct_toConjAct", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.ConjAct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjAct.ofConjAct_one", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.ConjAct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjAct.toConjAct_one", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.ConjAct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjAct.ofConjAct_inv", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.ConjAct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjAct.toConjAct_inv", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.ConjAct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjAct.ofConjAct_mul", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.ConjAct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjAct.toConjAct_mul", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.ConjAct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjAct.instSMul", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.ConjAct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjAct.smul_def", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.ConjAct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjAct.toConjAct_smul", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.ConjAct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjAct.unitsScalar", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.ConjAct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjAct.units_smul_def", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.ConjAct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjAct.unitsMulDistribMulAction", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.ConjAct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjAct.unitsSMulCommClass", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.ConjAct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjAct.unitsSMulCommClass'", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.ConjAct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjAct.instMulDistribMulAction", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.ConjAct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjAct.smulCommClass", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.ConjAct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjAct.smulCommClass'", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.ConjAct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjAct.smul_eq_mulAut_conj", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.ConjAct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjAct.fixedPoints_eq_center", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.ConjAct", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "ConjAct.mem_orbit_conjAct", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.ConjAct", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ConjAct.orbitRel_conjAct", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.ConjAct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjAct.orbit_eq_carrier_conjClasses", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.ConjAct", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "ConjAct.stabilizer_eq_centralizer", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.ConjAct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.centralizer_eq_comap_stabilizer", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.ConjAct", "is_tactic_proof": true, "tactics": ["ext", "simp", "rw", "exact"], "tactic_count": 4}
{"name": "ConjAct.Subgroup.conjAction", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.ConjAct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjAct.Subgroup.val_conj_smul", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.ConjAct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjAct.Subgroup.conjMulDistribMulAction", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.ConjAct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAut.conjNormal", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.ConjAct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAut.conjNormal_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.ConjAct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAut.conjNormal_symm_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.ConjAct", "is_tactic_proof": true, "tactics": ["change", "rw", "rfl"], "tactic_count": 3}
{"name": "MulAut.conjNormal_inv_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.ConjAct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAut.conjNormal_val", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.ConjAct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjAct.normal_of_characteristic_of_normal", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.ConjAct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitsCentralizerEquiv", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.ConjAct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.orbit", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.mem_orbit_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.mem_orbit", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.mem_orbit_of_mem_orbit", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Defs", "is_tactic_proof": true, "tactics": ["obtain", "simp"], "tactic_count": 2}
{"name": "MulAction.mem_orbit_self", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.nonempty_orbit", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.mapsTo_smul_orbit", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.smul_orbit_subset", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.orbit_smul_subset", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.instElemOrbit", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.orbit.coe_smul", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.orbit_submonoid_subset", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Defs", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "MulAction.mem_orbit_of_mem_orbit_submonoid", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.fixedPoints", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.fixedBy", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.fixed_eq_iInter_fixedBy", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.mem_fixedPoints", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.mem_fixedBy", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.mem_fixedPoints'", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.stabilizerSubmonoid", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.instDecidablePredMemSubmonoidStabilizerSubmonoidOfDecidableEq", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.mem_stabilizerSubmonoid_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FixedPoints.submonoid", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FixedPoints.mem_submonoid", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FixedPoints.subgroup", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FixedPoints.term_^*_", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FixedPoints._aux_Mathlib_GroupTheory_GroupAction_Defs___macroRules_FixedPoints_term_^*__1", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FixedPoints._aux_Mathlib_GroupTheory_GroupAction_Defs___unexpand_FixedPoints_subgroup_1", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FixedPoints.mem_subgroup", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FixedPoints.subgroup_toSubmonoid", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.orbit_smul", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.orbit_eq_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.mem_orbit_smul", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MulAction.smul_mem_orbit_smul", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MulAction.instMulAction", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.subgroup_smul_def", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.orbit_subgroup_subset", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.mem_orbit_of_mem_orbit_subgroup", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.mem_orbit_symm", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Defs", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MulAction.mem_subgroup_orbit_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Defs", "is_tactic_proof": true, "tactics": ["refine", "rcases", "exact", "rcases", "dsimp", "rw", "subst", "exact"], "tactic_count": 8}
{"name": "MulAction.orbitRel", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.orbitRel_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.quotient_preimage_image_eq_union_mul", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Defs", "is_tactic_proof": true, "tactics": ["letI", "set", "ext", "constructor", "rintro", "obtain", "rw", "exact", "intro", "rw", "obtain", "rw", "refine", "rw", "convert", "simp"], "tactic_count": 16}
{"name": "MulAction.disjoint_image_image_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Defs", "is_tactic_proof": true, "tactics": ["letI", "set", "refine", "simp", "intro", "rw", "rintro", "obtain", "exact"], "tactic_count": 9}
{"name": "MulAction.image_inter_image_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.orbitRel.Quotient", "kind": "abbrev", "module": "Mathlib.GroupTheory.GroupAction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.orbitRel.Quotient.orbit", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.orbitRel.Quotient.orbit_mk", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.orbitRel.Quotient.mem_orbit", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Defs", "is_tactic_proof": true, "tactics": ["induction", "rw", "rfl"], "tactic_count": 3}
{"name": "MulAction.orbitRel.Quotient.orbit_eq_orbit_out", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Defs", "is_tactic_proof": true, "tactics": ["conv_lhs", "rfl"], "tactic_count": 2}
{"name": "MulAction.orbitRel.Quotient.orbit_injective", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Defs", "is_tactic_proof": true, "tactics": ["intro", "simp_rw", "simpa"], "tactic_count": 3}
{"name": "MulAction.orbitRel.Quotient.orbit_inj", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.orbitRel.quotient_eq_of_quotient_subgroup_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MulAction.orbitRel.quotient_eq_of_quotient_subgroup_eq'", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.orbitRel.Quotient.nonempty_orbit", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MulAction.orbitRel.Quotient.mapsTo_smul_orbit", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MulAction.instElemOrbit_1", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.orbitRel.Quotient.orbit.coe_smul", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.orbitRel.Quotient.mem_subgroup_orbit_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Defs", "is_tactic_proof": true, "tactics": ["refine", "rcases", "dsimp", "rw", "subst", "exact", "rcases", "exact"], "tactic_count": 8}
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{"name": "MulAction.selfEquivSigmaOrbits'", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MulAction.univ_eq_iUnion_orbit", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Defs", "is_tactic_proof": true, "tactics": ["ext", "simp", "exact"], "tactic_count": 3}
{"name": "MulAction.stabilizer", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MulAction.le_stabilizer_smul_left", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Defs", "is_tactic_proof": true, "tactics": ["simp_rw", "rw"], "tactic_count": 2}
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{"name": "DomMulAct.mk_smul_mulActionHom_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.DomAct.ActionHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "DomMulAct.instSMulCommClassDistribMulActionHomId", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.DomAct.ActionHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "DomMulAct.mk_smul_mulDistribActionHom_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.DomAct.ActionHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.instMulActionDistribMulActionHomIdOfSMulCommClass", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.DomAct.ActionHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "DomMulAct.instInvOfMulOpposite", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.instSemigroupOfMulOpposite", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.instCommSemigroupOfMulOpposite", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.instLeftCancelSemigroupOfMulOpposite", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.instRightCancelSemigroupOfMulOpposite", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "DomMulAct.instDivInvMonoidOfMulOpposite", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "DomMulAct.instDivInvOneMonoidOfMulOpposite", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.instDivisionMonoidOfMulOpposite", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.instDivisionCommMonoidOfMulOpposite", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.instGroupOfMulOpposite", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.instCommGroupOfMulOpposite", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.instNonAssocSemiringOfMulOpposite", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.instNonUnitalSemiringOfMulOpposite", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.instSemiringOfMulOpposite", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.instRingOfMulOpposite", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.instCommRingOfMulOpposite", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.instIsLeftCancelMulOfMulOpposite", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.instIsRightCancelMulOfMulOpposite", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.instIsCancelMulOfMulOpposite", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.mk_one", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.symm_mk_one", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.mk_mul", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.symm_mk_mul", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.mk_inv", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.symm_mk_inv", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.mk_pow", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.symm_mk_pow", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.mk_zpow", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.symm_mk_zpow", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.instSMulForall", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.smul_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.instSMulCommClassForall", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.instSMulCommClassForall_1", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.instSMulCommClassForall_2", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.instFaithfulSMulForallOfNontrivial", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.instSMulZeroClassForallOfSMul", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.instDistribSMulForallOfSMul", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.instMulActionForall", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.instDistribMulActionForallOfMulAction", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.instMulDistribMulActionForallOfMulAction", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.instSMulMonoidHom", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.instSMulCommClassMonoidHom", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.smul_monoidHom_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.mk_smul_monoidHom_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.instMulActionMonoidHom", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.instSMulAddMonoidHom", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.instSMulCommClassAddMonoidHom", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.instSMulCommClassAddMonoidHom_1", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.smul_addMonoidHom_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.mk_smul_addMonoidHom_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.coe_smul_addMonoidHom", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.instMulActionAddMonoidHomOfDistribMulAction", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.instDistribMulActionAddMonoidHom", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.instMulDistribMulActionMonoidHom", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.smul", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.smul_def", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.smul_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.coe_smul", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.instIsScalarTower", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.instSMulCommClass", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.instIsCentralScalar", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.instMulAction", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.fixedBy_inv", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.FixedPoints", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "MulAction.smul_mem_fixedBy_iff_mem_fixedBy", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.FixedPoints", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "MulAction.smul_inv_mem_fixedBy_iff_mem_fixedBy", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.FixedPoints", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MulAction.minimalPeriod_eq_one_iff_fixedBy", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.FixedPoints", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.mem_fixedBy_zpow", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.FixedPoints", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MulAction.mem_fixedBy_zpowers_iff_mem_fixedBy", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.FixedPoints", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.fixedBy_subset_fixedBy_zpow", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.FixedPoints", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.fixedBy_one_eq_univ", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.FixedPoints", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.fixedBy_mul", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.FixedPoints", "is_tactic_proof": true, "tactics": ["intro", "rw"], "tactic_count": 2}
{"name": "MulAction.smul_fixedBy", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.FixedPoints", "is_tactic_proof": true, "tactics": ["ext", "simp_rw"], "tactic_count": 2}
{"name": "MulAction.set_mem_fixedBy_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.FixedPoints", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MulAction.smul_mem_of_set_mem_fixedBy", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.FixedPoints", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.set_mem_fixedBy_of_subset_fixedBy", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.FixedPoints", "is_tactic_proof": true, "tactics": ["rw", "ext", "rw", "refine", "rw", "rwa"], "tactic_count": 6}
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{"name": "MulAction.set_mem_fixedBy_of_movedBy_subset", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.FixedPoints", "is_tactic_proof": true, "tactics": ["rw", "ext", "rw", "by_cases", "rw", "constructor", "exact", "rwa"], "tactic_count": 8}
{"name": "MulAction.fixedBy_mem_fixedBy_of_commute", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.FixedPoints", "is_tactic_proof": true, "tactics": ["ext", "rw", "mem_fixedBy]"], "tactic_count": 3}
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{"name": "MulAction.movedBy_mem_fixedBy_of_commute", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.FixedPoints", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MulAction.smul_zpow_movedBy_eq_of_commute", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.FixedPoints", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.fixedBy_eq_univ_iff_eq_one", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.FixedPoints", "is_tactic_proof": true, "tactics": ["rw", "simp_rw"], "tactic_count": 2}
{"name": "MulAction.not_commute_of_disjoint_movedBy_preimage", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.FixedPoints", "is_tactic_proof": true, "tactics": ["contrapose", "rwa", "fixedBy_eq_univ_iff_eq_one]"], "tactic_count": 3}
{"name": "MulActionHom.map_mem_fixedPoints", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.FixedPoints", "is_tactic_proof": true, "tactics": ["intro", "simp_all"], "tactic_count": 2}
{"name": "MulActionHom.map_mem_fixedBy", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.FixedPoints", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "fixingSubmonoid", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.FixingSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_fixingSubmonoid_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.FixingSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fixingSubmonoid_fixedPoints_gc", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.FixingSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fixingSubmonoid_antitone", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.FixingSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fixedPoints_antitone", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.FixingSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fixingSubmonoid_union", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.FixingSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fixingSubmonoid_iUnion", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.FixingSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fixedPoints_submonoid_sup", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.FixingSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fixedPoints_submonoid_iSup", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.FixingSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fixingSubgroup", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.FixingSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_fixingSubgroup_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.FixingSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_fixingSubgroup_iff_subset_fixedBy", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.FixingSubgroup", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "mem_fixingSubgroup_compl_iff_movedBy_subset", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.FixingSubgroup", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "fixingSubgroup_fixedPoints_gc", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.FixingSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fixingSubgroup_empty", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.FixingSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fixingSubgroup_antitone", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.FixingSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fixedPoints_subgroup_antitone", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.FixingSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fixingSubgroup_union", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.FixingSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fixingSubgroup_iUnion", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.FixingSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fixedPoints_subgroup_sup", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.FixingSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "orbit_fixingSubgroup_compl_subset", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.FixingSubgroup", "is_tactic_proof": true, "tactics": ["intro", "let", "rw", "rw", "rwa"], "tactic_count": 5}
{"name": "MulActionHomLocal≺", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AddActionHomLocal≺", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MulActionHomClass", "kind": "abbrev", "module": "Mathlib.GroupTheory.GroupAction.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFunLikeMulActionHom", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "map_smul", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instMulActionSemiHomClassMulActionHom", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "IsScalarTower.smulHomClass", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulActionHom.map_smul", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulActionHom.ext", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulActionHom.congr_fun", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulActionHom.ofEq", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulActionHom.ofEq_coe", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulActionHom.ofEq_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FaithfulSMul.of_injective", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulActionHom.id", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulActionHom.id_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulActionHom.comp", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulActionHom.comp_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulActionHom.id_comp", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulActionHom.comp_id", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulActionHom.comp_assoc", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulActionHom.inverse", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MulActionHom.inverse'_inverse'", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MulActionHom.snd_comp_prod", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MulActionHom.prodMap", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MulActionHom.coe_smul", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "DistribMulActionHomLocal≺", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "DistribMulActionHom.zero_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "DistribMulActionHom.comp_assoc", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MulSemiringActionHomLocal≺", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MulSemiringActionHomClass.toMulSemiringActionHom", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulSemiringActionHom.instCoeTCOfMulSemiringActionSemiHomClassCoeMonoidHom", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MulSemiringActionHom.coe_fn_coe'", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MulSemiringActionHom.map_add", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MulSemiringActionHom.map_sub", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulSemiringActionHom.map_one", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulSemiringActionHom.map_mul", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulSemiringActionHom.map_smulₛₗ", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulSemiringActionHom.map_smul", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulSemiringActionHom.id", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulSemiringActionHom.id_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulSemiringActionHom.comp", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulSemiringActionHom.comp_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MulSemiringActionHom.comp_id", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulSemiringActionHom.inverse'", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulSemiringActionHom.inverse", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "IterateMulAct.instCommMonoid", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.IterateAct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IterateMulAct.instMulAction", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.IterateAct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IterateMulAct.mk_smul", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.IterateAct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MulAction.IwasawaStructure.isSimpleGroup", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Iwasawa", "is_tactic_proof": true, "tactics": ["apply", "intro", "cases", "inl", "refine", "apply", "intro", "rw", "exact", "inr"], "tactic_count": 10}
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{"name": "MulAction.IsPreprimitive.is_two_preprimitive", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Jordan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MulAction.IsPreprimitive.isMultiplyPreprimitive", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Jordan", "is_tactic_proof": false, "tactics": ["have", "induction", "zero", "succ", "hrec", "suffices", "obtain", "have", "intro", "apply", "have", "rw", "rw", "apply", "norm_num", "have", "have", "rw", "refine", "rw", "apply", "rw", "rw", "exact", "suffices", "obtain", "use", "ext", "by_cases", "rw"], "tactic_count": 30}
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{"name": "Equiv.Perm.isMultiplyPretransitive_of_nontrivial", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Jordan", "is_tactic_proof": false, "tactics": ["have", "have", "suffices", "by_cases", "apply", "simp", "suffices", "rwa", "hα]", "let", "let", "map_smul", "have", "suffices", "unfold", "rw", "apply", "rw", "apply", "apply", "simp", "by_contra", "simp", "apply", "apply", "intro", "suffices", "conv_rhs", "simp", "exact", "simpa"], "tactic_count": 31}
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{"name": "MulAction.isPreprimitive_of_fixingSubgroup_empty_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.MultiplePrimitivity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.isPreprimitive_ofFixingSubgroup_conj_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.MultiplePrimitivity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.isPreprimitive_fixingSubgroup_insert_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.MultiplePrimitivity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.instIsMultiplyPretransitiveOfIsMultiplyPreprimitive", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.MultiplePrimitivity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.is_zero_preprimitive", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.MultiplePrimitivity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.is_one_preprimitive_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.MultiplePrimitivity", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "apply", "intro", "rw", "constructor", "exact", "intro", "suffices", "rw", "suffices", "obtain", "rw", "simp", "exact"], "tactic_count": 16}
{"name": "MulAction.isMultiplyPreprimitive_ofStabilizer", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.MultiplePrimitivity", "is_tactic_proof": true, "tactics": ["rcases", "rw", "rw", "apply", "rw", "constructor", "rw", "exact", "intro", "have", "apply", "rw", "aesop", "exact"], "tactic_count": 14}
{"name": "MulAction.isMultiplyPreprimitive_succ_iff_ofStabilizer", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.MultiplePrimitivity", "is_tactic_proof": true, "tactics": ["constructor", "apply", "intro", "rw", "constructor", "exact", "intro", "have", "rw", "intro", "apply", "rw", "simp", "obtain", "obtain", "rw", "set", "let", "have", "ext", "constructor", "intro", "by_cases", "simp", "exact", "rw", "rintro", "simpa", "simpa", "rw", "apply", "apply", "simp", "rw", "apply", "rw", "rw", "exact"], "tactic_count": 38}
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{"name": "MulAction.IsMultiplyPreprimitive.of_bijective_map", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.MultiplePrimitivity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.isMultiplyPreprimitive_congr", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.MultiplePrimitivity", "is_tactic_proof": true, "tactics": ["refine", "intro", "rw", "constructor", "exact", "intro", "let", "let", "simp", "intro", "suffices", "obtain", "rwa", "obtain", "simpa", "let", "x", "simp", "exact", "map_smul", "rw", "apply", "simp", "rintro", "obtain", "suffices", "simp", "intro", "apply", "rw", "exact", "constructor", "rintro", "suffices", "simpa", "rintro", "obtain", "suffices", "simp", "exact"], "tactic_count": 40}
{"name": "MulAction.IsMultiplyPretransitive", "kind": "abbrev", "module": "Mathlib.GroupTheory.GroupAction.MultipleTransitivity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.isMultiplyPretransitive_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.MultipleTransitivity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.ofStabilizer.isPretransitive_iff_of_conj", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.MultipleTransitivity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.ofStabilizer.isPretransitive_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.MultipleTransitivity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.ofStabilizer.isMultiplyPretransitive_iff_of_conj", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.MultipleTransitivity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.ofStabilizer.isMultiplyPretransitive_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.MultipleTransitivity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SubMulAction.ofFixingSubgroup.isMultiplyPretransitive", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.MultipleTransitivity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.ofFixingSubgroup.isMultiplyPretransitive'", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.MultipleTransitivity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Equiv.Perm.isMultiplyPretransitive", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.MultipleTransitivity", "is_tactic_proof": true, "tactics": ["rw", "classical", "intro", "have", "have", "rw", "nth_rewrite", "rw", "simp", "rw", "obtain", "let", "set", "have", "constructor", "intro", "by_cases", "obtain", "by_cases", "obtain", "simp", "rw", "simp", "rw", "rw", "rw", "exfalso", "have", "rw", "exact", "rw", "apply", "exact", "by_cases", "obtain", "simp", "rw", "rw", "rw", "exfalso", "have", "rw", "exact", "rw", "apply", "exact", "simp", "rw", "rw", "rw", "rwa", "intro", "by_cases", "obtain", "use", "simp", "rw", "use", "simp", "rw", "simp", "set", "have", "rw", "simp", "rintro", "apply", "rw", "exact", "use", "ext", "simp"], "tactic_count": 72}
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{"name": "Equiv.Perm.eq_top_of_isMultiplyPretransitive", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.MultipleTransitivity", "is_tactic_proof": true, "tactics": ["have", "simp", "let", "rw", "intro", "let", "let", "obtain", "suffices", "have", "apply", "rw", "exact", "have", "have", "rcases", "exact", "obtain", "rcases", "suffices", "rw", "exact", "apply", "rw", "rw", "apply", "rw", "ext", "obtain", "specialize", "simp", "simp"], "tactic_count": 32}
{"name": "alternatingGroup.isMultiplyPretransitive", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.MultipleTransitivity", "is_tactic_proof": true, "tactics": ["rcases", "rw", "apply", "have", "have", "have", "refine", "obtain", "rcases", "exact", "have", "rw", "obtain", "refine", "ext", "have", "rw", "simp"], "tactic_count": 18}
{"name": "IsMultiplyPretransitive.alternatingGroup_le", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.MultipleTransitivity", "is_tactic_proof": true, "tactics": ["rcases", "rw", "rw", "exact", "apply", "obtain", "rw", "have", "rw", "rw", "rw", "refine"], "tactic_count": 12}
{"name": "alternatingGroup.isPretransitive_of_three_le_card", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.MultipleTransitivity", "is_tactic_proof": true, "tactics": ["rw", "letI", "apply", "rwa"], "tactic_count": 4}
{"name": "alternatingGroup.isTrivialBlock_of_isBlock", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.MultipleTransitivity", "is_tactic_proof": true, "tactics": ["rcases", "exact", "rcases", "replace", "have", "have", "exact", "suffices", "apply", "letI", "apply", "rwa"], "tactic_count": 12}
{"name": "alternatingGroup.isPreprimitive_of_three_le_card", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.MultipleTransitivity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.instQuotientSubgroupElemFixedPointsSubtypeMem", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.OfQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.coe_quotient_smul_fixedPoints", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.OfQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.quotient_out_smul_fixedPoints", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.OfQuotient", "is_tactic_proof": true, "tactics": ["conv_rhs", "rfl"], "tactic_count": 2}
{"name": "MulAction.le_period", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Period", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.period_le_of_fixed", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Period", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.period_pos_of_fixed", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Period", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.period_eq_one_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Period", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.pow_smul_ne_of_lt_period", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Period", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.period_one", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Period", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MulAction.period_dvd_orderOf", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Period", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MulAction.period_pos_of_orderOf_pos", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Period", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.period_le_orderOf", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Period", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.period_dvd_exponent", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Period", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MulAction.period_pos_of_exponent_pos", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Period", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.period_le_exponent", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Period", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.period_bounded_of_exponent_pos", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Period", "is_tactic_proof": true, "tactics": ["use", "simpa"], "tactic_count": 2}
{"name": "image_smul_setₛₗ", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.MapsTo.smul_setₛₗ", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smul_preimage_set_subsetₛₗ", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "preimage_smul_setₛₗ'", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Pointwise", "is_tactic_proof": true, "tactics": ["refine", "rw", "rintro", "rw", "subst", "exact"], "tactic_count": 6}
{"name": "preimage_smul_setₛₗ_of_isUnit_isUnit", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUnit.preimage_smul_setₛₗ", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.preimage_smul_setₛₗ", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Group.preimage_smul_setₛₗ", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "image_smul_set", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smul_preimage_set_subset", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.MapsTo.smul_set", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUnit.preimage_smul_set", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Group.preimage_smul_set", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.IsBlock.subsingleton_or_eq_univ", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Primitive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.IsPreprimitive.of_subsingleton", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Primitive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.isTrivialBlock_of_card_le_two", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Primitive", "is_tactic_proof": true, "tactics": ["rw", "have", "grind"], "tactic_count": 3}
{"name": "MulAction.IsPreprimitive.of_isTrivialBlock_base", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Primitive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.IsPreprimitive.of_isTrivialBlock_of_notMem_fixedPoints", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Primitive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.IsPreprimitive.mk'", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Primitive", "is_tactic_proof": true, "tactics": ["simp", "obtain", "exact"], "tactic_count": 3}
{"name": "MulAction.isSimpleOrder_blockMem_iff_isPreprimitive", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Primitive", "is_tactic_proof": true, "tactics": ["constructor", "intro", "apply", "intro", "rcases", "left", "right", "intro", "rintro", "simp", "cases", "inl", "inr"], "tactic_count": 13}
{"name": "MulAction.isCoatom_stabilizer_iff_preprimitive", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Primitive", "is_tactic_proof": true, "tactics": ["rw", "simp", "rw"], "tactic_count": 3}
{"name": "MulAction.IsPreprimitive.isCoatom_stabilizer_of_isPreprimitive", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Primitive", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "MulAction.IsPreprimitive.isQuasiPreprimitive", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.Primitive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.IsPreprimitive.of_prime_card", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Primitive", "is_tactic_proof": true, "tactics": ["refine", "have", "rw", "exact"], "tactic_count": 4}
{"name": "MulAction.left_quotientAction", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.right_quotientAction", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.right_quotientAction'", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.quotient", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.Quotient.smul_mk", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.Quotient.smul_coe", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.Quotient.mk_smul_out", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Quotient", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MulAction.Quotient.coe_smul_out", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Quotient", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "QuotientGroup.out_conj_pow_minimalPeriod_mem", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Quotient", "is_tactic_proof": true, "tactics": ["rw", "pow_smul_eq_iff_minimalPeriod_dvd]"], "tactic_count": 2}
{"name": "MulActionHom.toQuotient", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulActionHom.toQuotient_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.mulLeftCosetsCompSubtypeVal", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.ofQuotientStabilizer", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.ofQuotientStabilizer_mk", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.ofQuotientStabilizer_mem_orbit", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.ofQuotientStabilizer_smul", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.injective_ofQuotientStabilizer", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.orbitEquivQuotientStabilizer", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.orbitProdStabilizerEquivGroup", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.card_orbit_mul_card_stabilizer_eq_card_group", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Quotient", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MulAction.orbitEquivQuotientStabilizer_symm_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.stabilizer_quotient", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Quotient", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "_private.Mathlib.GroupTheory.GroupAction.Quotient.0.MulAction.termΩ", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.GroupTheory.GroupAction.Quotient.0.MulAction._aux_Mathlib_GroupTheory_GroupAction_Quotient___macroRules__private_Mathlib_GroupTheory_GroupAction_Quotient_0_MulAction_termΩ_1", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.selfEquivSigmaOrbitsQuotientStabilizer'", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.selfEquivSigmaOrbitsQuotientStabilizer", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.sigmaFixedByEquivOrbitsProdGroup", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.sum_card_fixedBy_eq_card_orbits_mul_card_group", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Quotient", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MulAction.isPretransitive_quotient", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.finite_quotient_of_pretransitive_of_finite_quotient", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.Quotient", "is_tactic_proof": true, "tactics": ["rcases", "exact", "have", "let", "replace", "rw", "simp", "exact", "exact"], "tactic_count": 9}
{"name": "MulAction.equivSubgroupOrbitsSetoidComap", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.equivSubgroupOrbits", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.finite_quotient_of_finite_quotient_of_finite_quotient", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.Quotient", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "MulAction.equivSubgroupOrbitsQuotientGroup", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.selfEquivOrbitsQuotientProd'", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.selfEquivOrbitsQuotientProd", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjClasses.card_carrier", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Quotient", "is_tactic_proof": true, "tactics": ["classical", "rw", "rw", "simp_rw", "exact"], "tactic_count": 5}
{"name": "Subgroup.normalCore_eq_ker", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Quotient", "is_tactic_proof": true, "tactics": ["apply", "intro", "apply", "refine", "refine", "rw", "exact", "refine", "rw", "exact"], "tactic_count": 10}
{"name": "Subgroup.quotientCentralizerEmbedding", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.quotientCentralizerEmbedding_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.quotientCenterEmbedding", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.quotientCenterEmbedding_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalNonAssocSemiring.toDistribSMul", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalNonAssocSemiring.nat_isScalarTower", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalNonAssocRing.int_isScalarTower", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoidClass.nsmulMemClass", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroupClass.zsmulMemClass", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.smul", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.instSMulCommClassSubtypeMem", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.instIsLeftCancelSMulSubtypeMem", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.instIsCancelSMulSubtypeMem", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SMulMemClass.ofIsScalarTower", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.instIsScalarTower", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.instSMulCommClass", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.val_smul", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.mk_smul_mk", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.smul_def", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.forall_smul_mem_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.smul'", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.instIsScalarTowerSubtypeMem", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.val_smul_of_tower", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.mk_smul_of_tower_mk", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.smul_of_tower_def", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.instSMulCommClassSubtypeMem_1", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.instSMulCommClassSubtypeMem_2", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.instSetLike", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.instPartialOrder", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.instSMulMemClass", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.mem_carrier", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.ext", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.copy", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.coe_copy", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.copy_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.instBot", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.instInhabited", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.instTop", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.instMax", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.instMin", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.instSupSet", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.instInfSet", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.instCompleteLattice", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.mem_iSup", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": true, "tactics": ["change", "simp"], "tactic_count": 2}
{"name": "SubMulAction.mem_iInf", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": true, "tactics": ["change", "simp"], "tactic_count": 2}
{"name": "SubMulAction.smul_mem", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.instSMulSubtypeMem", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.val_smul", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.subtype", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.subtype_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.subtype_injective", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.subtype_eq_val", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.SMulMemClass.toMulAction", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.SMulMemClass.subtype", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.SMulMemClass.subtype_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.SMulMemClass.subtype_injective", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.SMulMemClass.coe_subtype", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.smul_of_tower_mem", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SubMulAction.smul'", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.isScalarTower", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.isScalarTower'", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.val_smul_of_tower", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.smul_mem_iff'", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.isCentralScalar", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.mulAction'", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.mulAction", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.val_image_orbit", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.val_preimage_orbit", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SubMulAction.mem_orbit_subMul_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SubMulAction.stabilizer_of_subMul.submonoid", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "SubMulAction.orbitRel_of_subMul", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "SubMulAction.stabilizer_of_subMul", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SubMulAction.instCompl", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.compl_def", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.zero_mem", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.instZeroSubtypeMemOfNonempty", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.neg_mem", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SubMulAction.neg_mem_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.instNegSubtypeMem", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.val_neg", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.smul_mem_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.inclusion", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.inclusion.toFun_eq_coe", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.inclusion.coe_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.image_inclusion", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SubMulAction.inclusion_injective", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.nonZeroSubMul", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.instMulActionSubtypeNeOfNat", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.smul_coe", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.orbitRel_nonZero_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smul_mem_fixedPoints_of_normal", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": true, "tactics": ["intro", "rw", "exact"], "tactic_count": 3}
{"name": "fixedPointsSubMulOfNormal", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instMulActionElemFixedPointsSubtypeMemSubgroupOfNormal", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "coe_smul_fixedPoints_of_normal", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.closure", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.mem_closure", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.subset_closure", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.mem_closure_of_mem", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.closure_le", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.closure_mono", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.FG", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.fg_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.powersetCard", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.Combination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.powersetCard.mem_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.Combination", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.powersetCard.instSetLikeElemFinset", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.Combination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.powersetCard.instPartialOrderElemFinset", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.Combination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.powersetCard.coe_coe", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.Combination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.powersetCard.mem_coe_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.Combination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.powersetCard.card_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.Combination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.powersetCard.ncard_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.Combination", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.powersetCard.coe_nonempty_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.Combination", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.powersetCard.coe_nontrivial_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.Combination", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.powersetCard.eq_iff_subset", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.Combination", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.powersetCard.exists_mem_notMem", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.Combination", "is_tactic_proof": false, "tactics": ["have", "rwa", "obtain", "have", "exact", "simpa"], "tactic_count": 6}
{"name": "Set.powersetCard.subMulAction", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.Combination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.powersetCard.instMulActionElemFinset", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.Combination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.powersetCard.coe_smul", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.Combination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.powersetCard.stabilizer_coe", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.Combination", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Set.powersetCard.addAction_faithful", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.Combination", "is_tactic_proof": true, "tactics": ["refine", "contrapose", "have", "obtain", "obtain", "rw", "use", "contrapose", "simp", "rw", "simpa", "simp", "simp"], "tactic_count": 13}
{"name": "Set.powersetCard.faithfulVAdd", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.Combination", "is_tactic_proof": true, "tactics": ["rw", "intro", "apply", "rw", "exact"], "tactic_count": 5}
{"name": "Set.powersetCard.mulAction_faithful", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.Combination", "is_tactic_proof": true, "tactics": ["refine", "contrapose", "have", "obtain", "obtain", "rw", "use", "contrapose", "simp", "rw", "simpa", "simp", "simp"], "tactic_count": 13}
{"name": "Set.powersetCard.faithfulSMul", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.Combination", "is_tactic_proof": true, "tactics": ["rw", "intro", "apply", "rw", "exact"], "tactic_count": 5}
{"name": "Set.powersetCard.mulActionHom_of_embedding", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.Combination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.powersetCard.coe_mulActionHom_of_embedding", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.Combination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.powersetCard.mulActionHom_of_embedding_surjective", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.Combination", "is_tactic_proof": true, "tactics": ["intro", "obtain", "exact"], "tactic_count": 3}
{"name": "Set.powersetCard.coe_finset", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.Combination", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Set.powersetCard.instFiniteElemFinset", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.Combination", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "Set.powersetCard.card", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.Combination", "is_tactic_proof": true, "tactics": ["classical", "cases", "simp", "rcases", "simp", "rcases", "refine", "have", "exact", "simp"], "tactic_count": 10}
{"name": "Set.powersetCard.nontrivial", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.Combination", "is_tactic_proof": true, "tactics": ["classical", "have", "have", "have", "contrapose", "infer_instance"], "tactic_count": 6}
{"name": "Set.powersetCard.nontrivial'", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.Combination", "is_tactic_proof": true, "tactics": ["have", "apply", "simp"], "tactic_count": 3}
{"name": "Set.powersetCard.eq_empty_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.Combination", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.powersetCard.nontrivial_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.Combination", "is_tactic_proof": false, "tactics": ["rw", "grind"], "tactic_count": 2}
{"name": "Set.powersetCard.infinite", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.Combination", "is_tactic_proof": true, "tactics": ["apply", "rwa", "suffices", "apply", "simp"], "tactic_count": 5}
{"name": "Set.powersetCard.isPretransitive_of_isMultiplyPretransitive", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.Combination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.powersetCard.isPretransitive", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.Combination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.powersetCard.compl", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.Combination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.powersetCard.coe_compl", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.Combination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.powersetCard.mem_compl", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.Combination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.powersetCard.compl_compl", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.Combination", "is_tactic_proof": true, "tactics": ["ext", "change", "simp"], "tactic_count": 3}
{"name": "Set.powersetCard.compl_bijective", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.Combination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.powersetCard.mulActionHom_singleton", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.Combination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.powersetCard.mulActionHom_singleton_bijective", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.Combination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.powersetCard.isPreprimitive_perm", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.Combination", "is_tactic_proof": true, "tactics": ["have", "have", "have", "have", "obtain", "rw", "rw", "apply", "rwa", "rw", "exact", "rwa"], "tactic_count": 12}
{"name": "Set.powersetCard.isPretransitive_alternatingGroup", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.Combination", "is_tactic_proof": true, "tactics": ["wlog", "have", "apply", "grind", "by_cases", "apply", "aesop", "suffices", "rw", "rw", "simp", "apply", "rcases", "infer_instance", "rcases", "rw", "exact", "have", "apply"], "tactic_count": 19}
{"name": "Set.powersetCard.isPreprimitive_alternatingGroup", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.Combination", "is_tactic_proof": false, "tactics": ["have", "isPretransitive_alternatingGroup", "have", "obtain", "rw", "apply", "rw", "exact", "simp", "exact", "simpa"], "tactic_count": 11}
{"name": "SubMulAction.ofFixingSubgroup", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfFixingSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.ofFixingSubgroup_carrier", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfFixingSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.mem_ofFixingSubgroup_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfFixingSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.not_mem_of_mem_ofFixingSubgroup", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfFixingSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.disjoint_val_image", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfFixingSubgroup", "is_tactic_proof": true, "tactics": ["rw", "rintro"], "tactic_count": 2}
{"name": "SubMulAction.ofFixingSubgroup_equivariantMap", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfFixingSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.ofFixingSubgroup_equivariantMap_injective", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfFixingSubgroup", "is_tactic_proof": true, "tactics": ["rintro", "simpa"], "tactic_count": 2}
{"name": "SubMulAction.ofFixingSubgroupEmpty_equivariantMap_bijective", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfFixingSubgroup", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "SubMulAction.of_fixingSubgroupEmpty_mapScalars_surjective", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfFixingSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.mem_fixingSubgroup_insert_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfFixingSubgroup", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SubMulAction.fixingSubgroup_of_insert", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfFixingSubgroup", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "SubMulAction.mem_ofFixingSubgroup_insert_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfFixingSubgroup", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "SubMulAction.fixingSubgroupInsertEquiv", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfFixingSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.ofFixingSubgroup_insert_map", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfFixingSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.ofFixingSubgroup_insert_map_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfFixingSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.ofFixingSubgroup_insert_map_bijective", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfFixingSubgroup", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "simpa", "rintro", "exact"], "tactic_count": 5}
{"name": "Set.conj_mem_fixingSubgroup", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfFixingSubgroup", "is_tactic_proof": true, "tactics": ["simp", "intro", "rw", "apply", "rw", "exact"], "tactic_count": 6}
{"name": "SubMulAction.fixingSubgroup_map_conj_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfFixingSubgroup", "is_tactic_proof": true, "tactics": ["ext", "simp", "constructor", "rintro", "exact", "intro", "use", "constructor", "apply", "rw", "simp"], "tactic_count": 11}
{"name": "SubMulAction.fixingSubgroup_smul_eq_fixingSubgroup_map_conj", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfFixingSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.fixingSubgroupEquivFixingSubgroup", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfFixingSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.fixingSubgroupEquivFixingSubgroup_coe_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfFixingSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.conjMap_ofFixingSubgroup", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfFixingSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.conjMap_ofFixingSubgroup_coe_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfFixingSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.conjMap_ofFixingSubgroup_bijective", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfFixingSubgroup", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "simpa", "rintro", "rw", "use", "simp"], "tactic_count": 7}
{"name": "SubMulAction.mem_fixingSubgroup_union_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfFixingSubgroup", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SubMulAction.fixingSubgroup_union_to_fixingSubgroup_of_fixingSubgroup", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfFixingSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.map_ofFixingSubgroupUnion", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfFixingSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.map_ofFixingSubgroupUnion_def", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfFixingSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.map_ofFixingSubgroupUnion_bijective", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfFixingSubgroup", "is_tactic_proof": true, "tactics": ["constructor", "intro", "simpa", "rintro", "suffices", "intro", "rcases", "exact", "apply", "simpa"], "tactic_count": 10}
{"name": "SubMulAction.ofFixingSubgroup_of_inclusion", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfFixingSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.ofFixingSubgroup_of_inclusion_injective", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfFixingSubgroup", "is_tactic_proof": true, "tactics": ["rintro", "rw", "exact"], "tactic_count": 3}
{"name": "SubMulAction.ofFixingSubgroup_of_singleton", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfFixingSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.ofFixingSubgroup_of_singleton_bijective", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfFixingSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.ofFixingSubgroup_of_eq", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfFixingSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.ofFixingSubgroup_of_eq_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfFixingSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.ofFixingSubgroup_of_eq_bijective", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfFixingSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.ofFixingSubgroup.append", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfFixingSubgroup", "is_tactic_proof": true, "tactics": ["have", "let", "apply", "rw", "rintro", "apply", "simp", "simpa"], "tactic_count": 8}
{"name": "SubMulAction.ofFixingSubgroup.append_left", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfFixingSubgroup", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SubMulAction.ofFixingSubgroup.append_right", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfFixingSubgroup", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SubMulAction.IsPretransitive.isPretransitive_ofFixingSubgroup_inter", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfFixingSubgroup", "is_tactic_proof": true, "tactics": ["rw", "obtain", "rw", "have", "rw", "exact", "rw", "rintro", "rw", "rcases", "obtain", "use", "rwa", "have", "have", "obtain", "use", "simp", "rwa", "rw", "intro", "rw", "exact"], "tactic_count": 23}
{"name": "SubMulAction.IsPreprimitive.isPreprimitive_ofFixingSubgroup_inter", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfFixingSubgroup", "is_tactic_proof": true, "tactics": ["have", "apply", "rw", "show", "refine", "rwa", "rw"], "tactic_count": 7}
{"name": "MulAction.fixingSubgroup_le_stabilizer", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfFixingSubgroup", "is_tactic_proof": true, "tactics": ["intro", "rw", "conv_rhs", "apply", "simpa"], "tactic_count": 5}
{"name": "SubMulAction.ofStabilizer", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfStabilizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.ofStabilizer_carrier", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfStabilizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.mem_ofStabilizer_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfStabilizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.notMem_val_image", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfStabilizer", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "SubMulAction.neq_of_mem_ofStabilizer", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfStabilizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.ENat_card_ofStabilizer_add_one_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfStabilizer", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "congr", "simp"], "tactic_count": 4}
{"name": "SubMulAction.nat_card_ofStabilizer_add_one_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfStabilizer", "is_tactic_proof": true, "tactics": ["classical", "let", "rw", "simp"], "tactic_count": 4}
{"name": "SubMulAction.nat_card_ofStabilizer_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfStabilizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubAddAction.ofStabilizer.conjMap", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfStabilizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.ofStabilizer.conjMap", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfStabilizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.ofStabilizer.conjMap_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfStabilizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddAction.stabilizerEquivStabilizer_compTriple", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfStabilizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.stabilizerEquivStabilizer_compTriple", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfStabilizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.ofStabilizer.conjMap_comp_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfStabilizer", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SubMulAction.ofStabilizer.conjMap_comp_inv_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfStabilizer", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SubMulAction.ofStabilizer.inv_conjMap_comp_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfStabilizer", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SubMulAction.ofStabilizer.conjMap_comp", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfStabilizer", "is_tactic_proof": true, "tactics": ["ext", "simpa"], "tactic_count": 2}
{"name": "SubMulAction.ofStabilizer.conjMap_bijective", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfStabilizer", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "simp", "apply", "rwa", "intro", "exact"], "tactic_count": 7}
{"name": "SubMulAction.ofStabilizer.snoc", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfStabilizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.ofStabilizer.snoc_castSucc", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfStabilizer", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SubMulAction.ofStabilizer.snoc_last", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfStabilizer", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SubMulAction.exists_smul_of_last_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfStabilizer", "is_tactic_proof": true, "tactics": ["obtain", "have", "simp", "suffices", "simp", "use", "ext", "rcases", "simpa", "simpa"], "tactic_count": 10}
{"name": "SMul.ofStabilizer", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfStabilizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SMul.smul_stabilizer_def", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfStabilizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instMulActionSubtypeMemSubgroupStabilizerSetElem", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfStabilizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "stabilizer_empty_eq_top", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfStabilizer", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "stabilizer_univ_eq_top", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfStabilizer", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "stabilizer_compl", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.OfStabilizer", "is_tactic_proof": false, "tactics": ["have", "intro", "simp", "refine", "rw"], "tactic_count": 5}
{"name": "SubMulAction.instOne", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.coe_one", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.mem_one", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.subset_coe_one", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.instMul", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.coe_mul", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.mem_mul", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.instMulOneClass", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.instSemigroup", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.instMonoid", "kind": "instance", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.coe_pow", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubMulAction.subset_coe_pow", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.SubMulAction.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.Supports", "kind": "definition", "module": "Mathlib.GroupTheory.GroupAction.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.supports_of_mem", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.Supports.mono", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.Supports.smul", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Support", "is_tactic_proof": true, "tactics": ["rintro", "rw", "rintro", "have", "rwa"], "tactic_count": 5}
{"name": "MulAction.isPretransitive_iff_base", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Transitive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.isPretransitive_iff_orbit_eq_univ", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Transitive", "is_tactic_proof": true, "tactics": ["rw", "apply", "intro", "simp_rw"], "tactic_count": 4}
{"name": "MulAction.IsPretransitive.of_surjective_map", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Transitive", "is_tactic_proof": true, "tactics": ["apply", "intro", "obtain", "obtain", "obtain", "exact"], "tactic_count": 6}
{"name": "MulAction.isPretransitive_congr", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupAction.Transitive", "is_tactic_proof": true, "tactics": ["constructor", "apply", "intro", "apply", "intro", "obtain", "obtain", "use", "apply", "simp"], "tactic_count": 10}
{"name": "GroupExtension.quotientKerRightHomEquivRight", "kind": "definition", "module": "Mathlib.GroupTheory.GroupExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupExtension.quotientRangeInlEquivRight", "kind": "definition", "module": "Mathlib.GroupTheory.GroupExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupExtension.surjInvRightHom", "kind": "definition", "module": "Mathlib.GroupTheory.GroupExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupExtension.Section.mul_inv_mem_range_inl", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupExtension.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "GroupExtension.Section.inv_mul_mem_range_inl", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupExtension.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "GroupExtension.Section.exists_eq_inl_mul", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupExtension.Basic", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "GroupExtension.Section.exists_eq_mul_inl", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupExtension.Basic", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "GroupExtension.Section.mul_mul_mul_inv_mem_range_inl", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupExtension.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "GroupExtension.Section.mul_inv_mul_mul_mem_range_inl", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupExtension.Basic", "is_tactic_proof": true, "tactics": ["simp", "inv_mul_cancel]"], "tactic_count": 2}
{"name": "GroupExtension.Section.exists_mul_eq_inl_mul_mul", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupExtension.Basic", "is_tactic_proof": true, "tactics": ["obtain", "use", "rw"], "tactic_count": 3}
{"name": "GroupExtension.Section.exists_mul_eq_mul_mul_inl", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupExtension.Basic", "is_tactic_proof": true, "tactics": ["obtain", "use", "rw"], "tactic_count": 3}
{"name": "GroupExtension.Section.equivComp", "kind": "definition", "module": "Mathlib.GroupTheory.GroupExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupExtension.Equiv.ofMonoidHom", "kind": "definition", "module": "Mathlib.GroupTheory.GroupExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupExtension.Splitting.conjAct", "kind": "definition", "module": "Mathlib.GroupTheory.GroupExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupExtension.Splitting.semidirectProductToGroupExtensionEquiv", "kind": "definition", "module": "Mathlib.GroupTheory.GroupExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupExtension.Splitting.semidirectProductMulEquiv", "kind": "definition", "module": "Mathlib.GroupTheory.GroupExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupExtension.IsConj.refl", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupExtension.IsConj.symm", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupExtension.Basic", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "GroupExtension.IsConj.trans", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupExtension.Basic", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "exact"], "tactic_count": 3}
{"name": "GroupExtension.IsConj.setoid", "kind": "definition", "module": "Mathlib.GroupTheory.GroupExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupExtension.ConjClasses", "kind": "definition", "module": "Mathlib.GroupTheory.GroupExtension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemidirectProduct.right_splitting", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupExtension.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "GroupExtension.normal_inl_range", "kind": "instance", "module": "Mathlib.GroupTheory.GroupExtension.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupExtension.rightHom_inl", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupExtension.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "GroupExtension.rightHom_comp_inl", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupExtension.Defs", "is_tactic_proof": true, "tactics": ["ext", "rw", "exact"], "tactic_count": 3}
{"name": "GroupExtension.conjAct", "kind": "definition", "module": "Mathlib.GroupTheory.GroupExtension.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupExtension.inl_conjAct_comm", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupExtension.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "GroupExtension.Equiv.instEquivLike", "kind": "instance", "module": "Mathlib.GroupTheory.GroupExtension.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupExtension.Equiv.instMulEquivClass", "kind": "instance", "module": "Mathlib.GroupTheory.GroupExtension.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupExtension.Equiv.toMulEquiv_eq_coe", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupExtension.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupExtension.Equiv.coe_toMulEquiv", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupExtension.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupExtension.Equiv.map_inl", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupExtension.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupExtension.Equiv.rightHom_map", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupExtension.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupExtension.Equiv.symm", "kind": "definition", "module": "Mathlib.GroupTheory.GroupExtension.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupExtension.Equiv.Simps.symm_apply", "kind": "definition", "module": "Mathlib.GroupTheory.GroupExtension.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupExtension.Equiv.coe_symm", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupExtension.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupExtension.Equiv.trans", "kind": "definition", "module": "Mathlib.GroupTheory.GroupExtension.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupExtension.Equiv.refl", "kind": "definition", "module": "Mathlib.GroupTheory.GroupExtension.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupExtension.Section.instFunLike", "kind": "instance", "module": "Mathlib.GroupTheory.GroupExtension.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupExtension.Section.coe_mk", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupExtension.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupExtension.Section.rightHom_section", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupExtension.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupExtension.Section.rightHom_comp_section", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupExtension.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupExtension.Splitting.instFunLike", "kind": "instance", "module": "Mathlib.GroupTheory.GroupExtension.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupExtension.Splitting.instMonoidHomClass", "kind": "instance", "module": "Mathlib.GroupTheory.GroupExtension.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupExtension.Splitting.coe_mk", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupExtension.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupExtension.Splitting.coe_monoidHom_mk", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupExtension.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupExtension.Splitting.rightHom_splitting", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupExtension.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupExtension.Splitting.rightHom_comp_splitting", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupExtension.Defs", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "GroupExtension.IsConj", "kind": "definition", "module": "Mathlib.GroupTheory.GroupExtension.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemidirectProduct.toGroupExtension", "kind": "definition", "module": "Mathlib.GroupTheory.GroupExtension.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemidirectProduct.toGroupExtension_inl", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupExtension.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemidirectProduct.toGroupExtension_rightHom", "kind": "theorem", "module": "Mathlib.GroupTheory.GroupExtension.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemidirectProduct.inr_splitting", "kind": "definition", "module": "Mathlib.GroupTheory.GroupExtension.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HNNExtension.con", "kind": "definition", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HNNExtension", "kind": "definition", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instGroupHNNExtension", "kind": "instance", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": true, "tactics": ["delta"], "tactic_count": 1}
{"name": "HNNExtension.of", "kind": "definition", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HNNExtension.t", "kind": "definition", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HNNExtension.t_mul_of", "kind": "theorem", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HNNExtension.of_mul_t", "kind": "theorem", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HNNExtension.equiv_eq_conj", "kind": "theorem", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HNNExtension.equiv_symm_eq_conj", "kind": "theorem", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HNNExtension.inv_t_mul_of", "kind": "theorem", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HNNExtension.of_mul_inv_t", "kind": "theorem", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HNNExtension.lift", "kind": "definition", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HNNExtension.lift_t", "kind": "theorem", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": true, "tactics": ["delta"], "tactic_count": 1}
{"name": "HNNExtension.lift_of", "kind": "theorem", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": true, "tactics": ["delta"], "tactic_count": 1}
{"name": "HNNExtension.hom_ext", "kind": "theorem", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HNNExtension.induction_on", "kind": "theorem", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": false, "tactics": ["let", "one_mem", "mul_mem", "inv_mem", "let", "lift", "have", "change", "rw", "exact"], "tactic_count": 10}
{"name": "HNNExtension.toSubgroup", "kind": "definition", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HNNExtension.toSubgroup_one", "kind": "theorem", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HNNExtension.toSubgroup_neg_one", "kind": "theorem", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HNNExtension.toSubgroupEquiv", "kind": "definition", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HNNExtension.toSubgroupEquiv_one", "kind": "theorem", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HNNExtension.toSubgroupEquiv_neg_one", "kind": "theorem", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HNNExtension.toSubgroupEquiv_neg_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simp", "exact"], "tactic_count": 4}
{"name": "HNNExtension.NormalWord.TransversalPair.nonempty", "kind": "instance", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": true, "tactics": ["choose", "exact"], "tactic_count": 2}
{"name": "HNNExtension.NormalWord.ReducedWord.empty", "kind": "definition", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HNNExtension.NormalWord.ReducedWord.prod", "kind": "definition", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HNNExtension.NormalWord.ext", "kind": "theorem", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "HNNExtension.NormalWord.empty", "kind": "definition", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HNNExtension.NormalWord.ofGroup", "kind": "definition", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HNNExtension.NormalWord.instInhabited", "kind": "instance", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HNNExtension.NormalWord.instMulAction", "kind": "instance", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HNNExtension.NormalWord.group_smul_def", "kind": "theorem", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HNNExtension.NormalWord.group_smul_head", "kind": "theorem", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HNNExtension.NormalWord.group_smul_toList", "kind": "theorem", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HNNExtension.NormalWord.instFaithfulSMul", "kind": "instance", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HNNExtension.NormalWord.cons", "kind": "definition", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HNNExtension.NormalWord.consRecOn", "kind": "definition", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": true, "tactics": ["rcases", "induction", "nil", "cons", "exact", "cons", "toList", "mem_set"], "tactic_count": 8}
{"name": "HNNExtension.NormalWord.consRecOn_ofGroup", "kind": "theorem", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HNNExtension.NormalWord.consRecOn_cons", "kind": "theorem", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HNNExtension.NormalWord.smul_cons", "kind": "theorem", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HNNExtension.NormalWord.smul_ofGroup", "kind": "theorem", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HNNExtension.NormalWord.unitsSMulGroup", "kind": "definition", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HNNExtension.NormalWord.unitsSMulGroup_snd", "kind": "theorem", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "HNNExtension.NormalWord.Cancels", "kind": "definition", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HNNExtension.NormalWord.unitsSMulWithCancel", "kind": "definition", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HNNExtension.NormalWord.unitsSMul", "kind": "definition", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HNNExtension.NormalWord.not_cancels_of_cons_hyp", "kind": "theorem", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": false, "tactics": ["simp", "intro", "rw", "simpa"], "tactic_count": 4}
{"name": "HNNExtension.NormalWord.unitsSMul_cancels_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "induction", "ofGroup", "cons", "intro", "apply", "simp", "cases", "simpa", "simp", "simpa"], "tactic_count": 12}
{"name": "HNNExtension.NormalWord.unitsSMul_neg", "kind": "theorem", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": true, "tactics": ["rw", "split_ifs", "have", "unfold", "simp", "simp", "have", "unfold", "simp", "cases", "ofGroup", "cons", "clear", "simp", "mul_inv_rev]", "cases", "have", "apply", "dsimp", "conv_lhs", "rw", "simp", "dsimp", "conv_lhs", "simp"], "tactic_count": 25}
{"name": "HNNExtension.NormalWord.unitsSMulEquiv", "kind": "definition", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HNNExtension.NormalWord.unitsSMul_one_group_smul", "kind": "theorem", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": true, "tactics": ["unfold", "have", "by_cases", "simp", "mul_inv_rev,", "cases", "simp", "simp", "rw", "rfl", "rw", "simp", "group_smul_head,", "congr", "conv_lhs", "simp_rw", "simp", "conv_lhs", "rfl"], "tactic_count": 19}
{"name": "HNNExtension.NormalWord.instMulAction_1", "kind": "instance", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HNNExtension.NormalWord.prod_group_smul", "kind": "theorem", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HNNExtension.NormalWord.of_smul_eq_smul", "kind": "theorem", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HNNExtension.NormalWord.t_smul_eq_unitsSMul", "kind": "theorem", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HNNExtension.NormalWord.t_pow_smul_eq_unitsSMul", "kind": "theorem", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "HNNExtension.NormalWord.prod_cons", "kind": "theorem", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HNNExtension.NormalWord.prod_unitsSMul", "kind": "theorem", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": true, "tactics": ["rw", "split_ifs", "cases", "simp", "cases", "simp", "rcases", "simp", "simp", "zpow_one,", "grind", "simp", "rcases", "simp", "zpow_one,", "erw", "simp", "simp", "zpow_one,", "erw", "simp"], "tactic_count": 21}
{"name": "HNNExtension.NormalWord.prod_empty", "kind": "theorem", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HNNExtension.NormalWord.prod_smul", "kind": "theorem", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": true, "tactics": ["induction", "of", "t", "mul", "inv", "rw", "simp"], "tactic_count": 7}
{"name": "HNNExtension.NormalWord.prod_smul_empty", "kind": "theorem", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": true, "tactics": ["induction", "ofGroup", "cons", "ih", "rw", "rw", "simp", "ext", "rw", "simp"], "tactic_count": 10}
{"name": "HNNExtension.NormalWord.equiv", "kind": "definition", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HNNExtension.NormalWord.prod_injective", "kind": "theorem", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HNNExtension.NormalWord.instFaithfulSMul_1", "kind": "instance", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HNNExtension.of_injective", "kind": "theorem", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": true, "tactics": ["rcases", "refine", "intro", "exact"], "tactic_count": 4}
{"name": "HNNExtension.ReducedWord.exists_normalWord_prod_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": false, "tactics": ["suffices", "w.head", "w'.prod", "w'.toList.map", "by_cases", "simp", "exact", "rcases", "exact", "intro", "rcases", "dsimp", "induction", "nil", "exact", "toList", "mem_set", "chain", "cons", "rcases", "clear", "refine", "rw", "simp", "have", "simp", "exists_eq_right,", "intro", "have", "rw", "have", "rw", "have", "have", "have", "rwa", "simp", "rw", "erw", "rw", "simp"], "tactic_count": 41}
{"name": "HNNExtension.ReducedWord.map_fst_eq_and_of_prod_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "rcases", "have", "subst", "refine", "simp", "intro", "rw", "rwa"], "tactic_count": 10}
{"name": "HNNExtension.ReducedWord.toList_eq_nil_of_mem_of_range", "kind": "theorem", "module": "Mathlib.GroupTheory.HNNExtension", "is_tactic_proof": true, "tactics": ["rcases", "let", "have", "simpa"], "tactic_count": 4}
{"name": "Subgroup.index", "kind": "definition", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.relIndex", "kind": "definition", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.index_comap_of_surjective", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": false, "tactics": ["have", "simp", "exact", "refine", "simp_rw", "refine", "refine", "exact", "refine", "obtain", "exact"], "tactic_count": 11}
{"name": "Subgroup.index_comap", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.relIndex_comap", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subgroup.relIndex_map_map_of_injective", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subgroup.relIndex_map_map", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subgroup.relIndex_mul_index", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": true, "tactics": ["rw", "simp_rw"], "tactic_count": 2}
{"name": "Subgroup.index_dvd_of_le", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.relIndex_dvd_index_of_le", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.relIndex_subgroupOf", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.relIndex_mul_relIndex", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Subgroup.inf_relIndex_right", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subgroup.inf_relIndex_left", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subgroup.relIndex_inf_mul_relIndex", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": true, "tactics": ["rw", "relIndex_mul_relIndex"], "tactic_count": 2}
{"name": "Subgroup.relIndex_sup_right", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.relIndex_sup_left", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subgroup.relIndex_dvd_index_of_normal", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.relIndex_dvd_of_le_left", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.index_eq_two_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": false, "tactics": ["simp", "refine", "exact", "exact", "rw", "exact", "rwa"], "tactic_count": 7}
{"name": "Subgroup.index_eq_two_iff'", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp"], "tactic_count": 3}
{"name": "Subgroup.index_eq_two_iff_exists_notMem_and", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": true, "tactics": ["simp", "exact", "exists_congr"], "tactic_count": 3}
{"name": "Subgroup.index_eq_two_iff_exists_notMem_and'", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": true, "tactics": ["simp", "exact", "exists_congr"], "tactic_count": 3}
{"name": "Subgroup.relIndex_eq_two_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Subgroup.relIindex_eq_two_iff'", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Subgroup.relIndex_eq_two_iff_exists_notMem_and", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": true, "tactics": ["rw", "simp", "refine", "simp"], "tactic_count": 4}
{"name": "Subgroup.relIndex_eq_two_iff_exists_notMem_and'", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": true, "tactics": ["rw", "simp", "refine", "simp"], "tactic_count": 4}
{"name": "Subgroup.mul_mem_iff_of_index_two", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": true, "tactics": ["by_cases", "by_cases", "simp", "rcases", "refine", "rwa"], "tactic_count": 6}
{"name": "Subgroup.mul_self_mem_of_index_two", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subgroup.sq_mem_of_index_two", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.index_top", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.index_bot", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.relIndex_top_left", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.relIndex_top_right", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subgroup.relIndex_bot_left", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subgroup.relIndex_bot_right", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subgroup.relIndex_self", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subgroup.index_ker", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subgroup.relIndex_ker", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subgroup.card_mul_index", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Subgroup.card_dvd_of_surjective", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Subgroup.card_range_dvd", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.card_map_dvd", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.index_map", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subgroup.index_map_dvd", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Subgroup.dvd_index_map", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "Subgroup.index_map_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.index_map_of_bijective", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.index_map_equiv", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.index_map_of_injective", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subgroup.index_map_subtype", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subgroup.index_eq_card", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.index_mul_card", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subgroup.index_dvd_card", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.relIndex_dvd_card", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.relIndex_eq_zero_of_le_left", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.relIndex_eq_zero_of_le_right", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.relIndex_comap_ne_zero", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Subgroup.index_eq_zero_of_relIndex_eq_zero", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.relIndex_le_of_le_left", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.relIndex_le_of_le_right", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.relIndex_ne_zero_trans", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.relIndex_inf_ne_zero", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": true, "tactics": ["replace", "rw", "rw", "exact"], "tactic_count": 4}
{"name": "Subgroup.index_inf_ne_zero", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Subgroup.relIndex_inter_ne_zero", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": false, "tactics": ["rw", "comap_map_eq_self_of_injective", "exact"], "tactic_count": 3}
{"name": "Subgroup.relIndex_inf_le", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "rw", "inf_relIndex_right]", "grw"], "tactic_count": 5}
{"name": "Subgroup.index_inf_le", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Subgroup.relIndex_iInf_ne_zero", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.relIndex_iInf_le", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.index_iInf_ne_zero", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Subgroup.index_iInf_le", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Subgroup.index_eq_one", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.relIndex_eq_one", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.card_eq_one", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.index_dvd_two_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.index_dvd_two_iff'", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp"], "tactic_count": 3}
{"name": "Subgroup.relIndex_dvd_two_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Subgroup.relIindex_dvd_two_iff'", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Subgroup.inf_eq_bot_of_coprime", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.index_ne_zero_of_finite", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": true, "tactics": ["cases", "rw", "exact"], "tactic_count": 3}
{"name": "Subgroup.fintypeOfIndexNeZero", "kind": "definition", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.index_eq_zero_iff_infinite", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Subgroup.index_ne_zero_iff_finite", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Subgroup.one_lt_index_of_ne_top", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.finite_quotient_of_finite_quotient_of_index_ne_zero", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "Subgroup.finite_quotient_of_pretransitive_of_index_ne_zero", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "Subgroup.exists_pow_mem_of_index_ne_zero", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": false, "tactics": ["suffices", "rcases", "refine", "rw", "rw", "convert", "lia", "suffices", "rcases", "rcases", "exact", "exact", "by_contra", "simp_rw", "let", "have", "rintro", "have", "dsimp", "simpa", "have", "have", "simp"], "tactic_count": 23}
{"name": "Subgroup.exists_pow_mem_of_relIndex_ne_zero", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": true, "tactics": ["rcases", "refine", "simpa"], "tactic_count": 3}
{"name": "Subgroup.pow_mem_of_index_ne_zero_of_dvd", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "rw", "exact"], "tactic_count": 4}
{"name": "Subgroup.pow_mem_of_relIndex_ne_zero_of_dvd", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "Subgroup.index_prod", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "rw"], "tactic_count": 3}
{"name": "Subgroup.index_pi", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "rw"], "tactic_count": 3}
{"name": "Subgroup.index_toAddSubgroup", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroup.index_toSubgroup", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.relIndex_toAddSubgroup", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroup.relIndex_toSubgroup", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.relIndex_ne_zero", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.IsFiniteRelIndex.to_finiteIndex_subgroupOf", "kind": "instance", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.finiteIndex_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.not_finiteIndex_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Subgroup.fintypeQuotientOfFiniteIndex", "kind": "definition", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.finite_quotient_of_finiteIndex", "kind": "instance", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.finiteIndex_of_finite_quotient", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.finiteIndex_iff_finite_quotient", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.finiteIndex_of_finite", "kind": "instance", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.finite_iff_finite_and_finiteIndex", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.finite_iff_finite_ker_range", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": true, "tactics": ["rw", "finiteIndex_iff_finite_quotient]"], "tactic_count": 2}
{"name": "Subgroup.instFiniteIndexTop", "kind": "instance", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.instFiniteIndexMin", "kind": "instance", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.finiteIndex_iInf", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.finiteIndex_iInf'", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Subgroup.instFiniteIndex_subgroupOf", "kind": "instance", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.finiteIndex_of_le", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.index_antitone", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.index_strictAnti", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": true, "tactics": ["have", "apply", "rw", "exact"], "tactic_count": 4}
{"name": "Subgroup.finiteIndex_ker", "kind": "instance", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.finiteIndex_normalCore", "kind": "instance", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "Subgroup.index_range", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subgroup.relIndex_pointwise_smul", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AddSubgroup.relIndex_pointwise_smul", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MulAction.index_stabilizer", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.index_stabilizer_of_transitive", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MonoidHom.surjective_of_card_ker_le_div", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "MonoidHom.card_fiber_eq_of_mem_range", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "rcases", "conv_lhs", "congr", "simp", "let", "change", "rw"], "tactic_count": 9}
{"name": "AddSubgroup.index_smul", "kind": "theorem", "module": "Mathlib.GroupTheory.Index", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.normal_of_index_eq_one", "kind": "theorem", "module": "Mathlib.GroupTheory.IndexNormal", "is_tactic_proof": true, "tactics": ["rw", "rw", "infer_instance"], "tactic_count": 3}
{"name": "Subgroup.normal_of_index_eq_two", "kind": "theorem", "module": "Mathlib.GroupTheory.IndexNormal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.normal_of_index_eq_minFac_card", "kind": "theorem", "module": "Mathlib.GroupTheory.IndexNormal", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "exact", "by_cases", "rw", "exact", "suffices", "convert", "exact", "have", "have", "rw", "have", "have", "rw", "exact", "apply", "rwa", "have", "hp.ne_one", "rw", "exact", "lt_of_lt_of_le", "hHp", "minFac_le_of_dvd"], "tactic_count": 25}
{"name": "Subgroup.IsSubnormal", "kind": "inductive", "module": "Mathlib.GroupTheory.IsSubnormal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.Normal.isSubnormal", "kind": "theorem", "module": "Mathlib.GroupTheory.IsSubnormal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.IsSubnormal.bot", "kind": "theorem", "module": "Mathlib.GroupTheory.IsSubnormal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.IsSubnormal.normal_of_isSimpleGroup", "kind": "theorem", "module": "Mathlib.GroupTheory.IsSubnormal", "is_tactic_proof": true, "tactics": ["induction", "top", "step", "obtain", "grind", "grind"], "tactic_count": 6}
{"name": "Subgroup.IsSubnormal.eq_bot_or_top_of_isSimpleGroup", "kind": "theorem", "module": "Mathlib.GroupTheory.IsSubnormal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.IsSubnormal.iff_eq_top_or_exists", "kind": "theorem", "module": "Mathlib.GroupTheory.IsSubnormal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.IsSubnormal.exists_normal_and_le_and_lt_top_of_ne", "kind": "theorem", "module": "Mathlib.GroupTheory.IsSubnormal", "is_tactic_proof": true, "tactics": ["induction", "top", "step", "obtain", "rw", "exact", "grind"], "tactic_count": 7}
{"name": "Subgroup.IsSubnormal.lt_normal", "kind": "theorem", "module": "Mathlib.GroupTheory.IsSubnormal", "is_tactic_proof": true, "tactics": ["obtain", "simp", "grind"], "tactic_count": 3}
{"name": "Subgroup.IsSubnormal.isSubnormal_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.IsSubnormal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.IsSubnormal.trans'", "kind": "theorem", "module": "Mathlib.GroupTheory.IsSubnormal", "is_tactic_proof": true, "tactics": ["induction", "top", "step", "ih", "refine", "rw", "rw", "exact"], "tactic_count": 8}
{"name": "Subgroup.IsSubnormal.trans", "kind": "theorem", "module": "Mathlib.GroupTheory.IsSubnormal", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "Submonoid.LocalizationMap.AwayMap", "kind": "abbrev", "module": "Mathlib.GroupTheory.MonoidLocalization.Away", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.AwayMap.invSelf", "kind": "definition", "module": "Mathlib.GroupTheory.MonoidLocalization.Away", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.AwayMap.lift", "kind": "definition", "module": "Mathlib.GroupTheory.MonoidLocalization.Away", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.AwayMap.lift_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Away", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.AwayMap.lift_comp", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Away", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.awayToAwayRight", "kind": "definition", "module": "Mathlib.GroupTheory.MonoidLocalization.Away", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.LocalizationMap.AwayMap.negSelf", "kind": "definition", "module": "Mathlib.GroupTheory.MonoidLocalization.Away", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.LocalizationMap.AwayMap.lift", "kind": "definition", "module": "Mathlib.GroupTheory.MonoidLocalization.Away", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.LocalizationMap.AwayMap.lift_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Away", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.LocalizationMap.AwayMap.lift_comp", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Away", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.LocalizationMap.awayToAwayRight", "kind": "definition", "module": "Mathlib.GroupTheory.MonoidLocalization.Away", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.Away", "kind": "abbrev", "module": "Mathlib.GroupTheory.MonoidLocalization.Away", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.Away.invSelf", "kind": "definition", "module": "Mathlib.GroupTheory.MonoidLocalization.Away", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.Away.monoidOf", "kind": "abbrev", "module": "Mathlib.GroupTheory.MonoidLocalization.Away", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.Away.mk_eq_monoidOf_mk'", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Away", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Localization.Away.mulEquivOfQuotient", "kind": "definition", "module": "Mathlib.GroupTheory.MonoidLocalization.Away", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.r", "kind": "definition", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.r'", "kind": "definition", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": true, "tactics": ["refine", "iseqv", "mul", "rintro", "use", "simp", "calc", "rintro", "use", "calc"], "tactic_count": 10}
{"name": "Localization.r_eq_r'", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.r_iff_exists", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Localization.r_iff_oreEqv_r", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": true, "tactics": ["simp", "constructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 6}
{"name": "Localization", "kind": "abbrev", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.mk", "kind": "definition", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.mk_eq_mk_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Localization.rec", "kind": "definition", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.recOnSubsingleton₂", "kind": "definition", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.mk_mul", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.mk_one", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.mk_pow", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "Localization.mk_prod", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Localization.ndrec_mk", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.liftOn", "kind": "definition", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.liftOn_mk", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.ind", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.induction_on", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.liftOn₂", "kind": "definition", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.liftOn₂_mk", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.induction_on₂", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.induction_on₃", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.one_rel", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.r_of_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.mk_self", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": true, "tactics": ["symm", "rw", "exact"], "tactic_count": 3}
{"name": "Localization.mk_self_mk", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.mkHom", "kind": "definition", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.mkHom_surjective", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "Localization.smul_mk", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": true, "tactics": ["rw", "change", "rw"], "tactic_count": 3}
{"name": "Localization.instSMulCommClassOfIsScalarTower", "kind": "instance", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.toLocalizationMap", "kind": "definition", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.IsLocalizationMap.map_one", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Submonoid.IsLocalizationMap.mulEquiv_comp", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.toMonoidHom", "kind": "abbrev", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.toMap", "kind": "abbrev", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.toMonoidHom_injective", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.instFunLike", "kind": "instance", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.instMonoidHomClass", "kind": "instance", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.toMonoidHom_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.ext", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.map_units", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.surj", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.exists_of_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.surj₂", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": true, "tactics": ["let", "let", "refine", "simp_rw", "exact", "simp_rw", "exact"], "tactic_count": 7}
{"name": "Submonoid.LocalizationMap.eq_iff_exists", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.sec", "kind": "definition", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.sec_spec", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.sec_spec'", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submonoid.LocalizationMap.mul_inv_left", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Submonoid.LocalizationMap.mul_inv_right", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submonoid.LocalizationMap.mul_inv", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submonoid.LocalizationMap.inv_inj", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Submonoid.LocalizationMap.inv_unique", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Submonoid.LocalizationMap.map_right_cancel", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": true, "tactics": ["rw", "let", "rw", "exact"], "tactic_count": 4}
{"name": "Submonoid.LocalizationMap.map_left_cancel", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.mk'", "kind": "definition", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.mk'_mul", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": true, "tactics": ["refine", "simp", "rw", "simp"], "tactic_count": 4}
{"name": "Submonoid.LocalizationMap.mk'_one", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Submonoid.LocalizationMap.mk'_sec", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.mk'_surjective", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.mk'_spec", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.mk'_spec'", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submonoid.LocalizationMap.eq_mk'_iff_mul_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.mk'_eq_iff_eq_mul", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submonoid.LocalizationMap.mk'_eq_iff_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.mk'_eq_iff_eq'", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Submonoid.LocalizationMap.eq", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.eq'", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submonoid.LocalizationMap.eq_iff_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.mk'_eq_iff_mk'_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.exists_of_sec_mk'", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.mk'_eq_of_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.mk'_eq_of_eq'", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.mk'_cancel", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.mk'_eq_of_same", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Submonoid.LocalizationMap.mk'_self'", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.mk'_self", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.mul_mk'_eq_mk'_of_mul", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submonoid.LocalizationMap.mk'_mul_eq_mk'_of_mul", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submonoid.LocalizationMap.mul_mk'_one_eq_mk'", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submonoid.LocalizationMap.mk'_mul_cancel_right", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submonoid.LocalizationMap.mk'_mul_cancel_left", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submonoid.LocalizationMap.isUnit_comp", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.eq_of_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": true, "tactics": ["obtain", "rw", "change", "rw"], "tactic_count": 4}
{"name": "Submonoid.LocalizationMap.comp_eq_of_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.lift", "kind": "definition", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.lift_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.lift_mk'", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.lift_localizationMap_mk'", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.lift_spec", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.lift_spec_mul", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submonoid.LocalizationMap.lift_mk'_spec", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submonoid.LocalizationMap.lift_mul_right", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submonoid.LocalizationMap.lift_mul_left", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submonoid.LocalizationMap.lift_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submonoid.LocalizationMap.lift_eq_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submonoid.LocalizationMap.lift_comp", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Submonoid.LocalizationMap.lift_of_comp", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Submonoid.LocalizationMap.epic_of_localizationMap", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.lift_unique", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": true, "tactics": ["ext", "rw", "apply", "rw"], "tactic_count": 4}
{"name": "Submonoid.LocalizationMap.lift_id", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.lift_comp_lift", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.lift_comp_lift_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.lift_left_inverse", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.lift_surjective_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": true, "tactics": ["constructor", "intro", "obtain", "obtain", "use", "rw", "intro", "obtain", "use", "rw"], "tactic_count": 10}
{"name": "Submonoid.LocalizationMap.lift_injective_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": true, "tactics": ["constructor", "intro", "constructor", "exact", "intro", "rw", "exact", "intro", "obtain", "obtain", "rw", "exact"], "tactic_count": 12}
{"name": "Submonoid.LocalizationMap.map", "kind": "definition", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.map_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.map_comp", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.map_mk'", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": true, "tactics": ["rw", "change", "rw", "exact"], "tactic_count": 4}
{"name": "Submonoid.LocalizationMap.map_spec", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.map_mul_right", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.map_mul_left", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submonoid.LocalizationMap.map_id", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.map_comp_map", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": true, "tactics": ["ext", "change", "rw", "change", "rw", "refine", "rw"], "tactic_count": 7}
{"name": "Submonoid.LocalizationMap.map_map", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Submonoid.LocalizationMap.map_injective_of_surjOn_or_injective", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.map_surjective_of_surjOn", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.map_injective_of_injective", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.map_surjective_of_surjective", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.mulEquivOfLocalizations", "kind": "definition", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.mulEquivOfLocalizations_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.mulEquivOfLocalizations_symm_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.mulEquivOfLocalizations_symm_eq_mulEquivOfLocalizations", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.ofMulEquivOfLocalizations", "kind": "definition", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.ofMulEquivOfLocalizations_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.ofMulEquivOfLocalizations_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.symm_comp_ofMulEquivOfLocalizations_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.symm_comp_ofMulEquivOfLocalizations_apply'", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.ofMulEquivOfLocalizations_eq_iff_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.mulEquivOfLocalizations_right_inv", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.mulEquivOfLocalizations_right_inv_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Submonoid.LocalizationMap.mulEquivOfLocalizations_left_inv", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.mulEquivOfLocalizations_left_inv_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Submonoid.LocalizationMap.ofMulEquivOfLocalizations_id", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Submonoid.LocalizationMap.ofMulEquivOfLocalizations_comp", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Submonoid.LocalizationMap.ofMulEquivOfDom", "kind": "definition", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.ofMulEquivOfDom_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.ofMulEquivOfDom_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.ofMulEquivOfDom_comp_symm", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.ofMulEquivOfDom_comp", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.ofMulEquivOfDom_id", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Submonoid.LocalizationMap.mulEquivOfMulEquiv", "kind": "definition", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.mulEquivOfMulEquiv_eq_map_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.mulEquivOfMulEquiv_eq_map", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.mulEquivOfMulEquiv_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.mulEquivOfMulEquiv_mk'", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.of_mulEquivOfMulEquiv_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.of_mulEquivOfMulEquiv", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.monoidOf", "kind": "definition", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.mk_one_eq_monoidOf_mk", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.mk_eq_monoidOf_mk'_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.mk_eq_monoidOf_mk'", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.liftOn_mk'", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Localization.liftOn₂_mk'", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Localization.mulEquivOfQuotient", "kind": "definition", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.mulEquivOfQuotient_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.mulEquivOfQuotient_mk'", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.mulEquivOfQuotient_mk", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Localization.mulEquivOfQuotient_monoidOf", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Localization.mulEquivOfQuotient_symm_mk'", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.mulEquivOfQuotient_symm_mk", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Localization.mulEquivOfQuotient_symm_monoidOf", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.instIsMulTorsionFree", "kind": "instance", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.mk_left_injective", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.mk_eq_mk_iff'", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Localization.decidableEq", "kind": "instance", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OreLocalization.localizationMap", "kind": "definition", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OreLocalization.equivMonoidLocalization", "kind": "definition", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.isLocalizationMap_iff_bijective", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.isLocalizationMap_id", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.isLocalizationMap_of_group", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.isLocalizationMap_nat_int", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubmonoid.isLocalizationMap_top_nat_int", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.injective_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Submonoid.LocalizationMap.top_injective_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Submonoid.LocalizationMap.map_isRegular", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.isCancelMul", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": ["simp_rw", "intro", "have", "exact"], "tactic_count": 4}
{"name": "Submonoid.LocalizationMap.instIsCancelMulLocalization", "kind": "instance", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.instNontrivialLocalizationOfIsCancelMul", "kind": "instance", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.subsingleton_of_subsingleton", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.instSubsingletonLocalization", "kind": "instance", "module": "Mathlib.GroupTheory.MonoidLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.cardinalMk_le", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Cardinality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.divPairs", "kind": "definition", "module": "Mathlib.GroupTheory.MonoidLocalization.DivPairs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.mem_divPairs", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.DivPairs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.divPairs_comap", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.DivPairs", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Localization.fg", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Finite", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Algebra.GrothendieckGroup.instFG", "kind": "instance", "module": "Mathlib.GroupTheory.MonoidLocalization.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.GrothendieckGroup", "kind": "abbrev", "module": "Mathlib.GroupTheory.MonoidLocalization.GrothendieckGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.GrothendieckGroup.of", "kind": "abbrev", "module": "Mathlib.GroupTheory.MonoidLocalization.GrothendieckGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.GrothendieckGroup.of_injective", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.GrothendieckGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.GrothendieckGroup.instInv", "kind": "instance", "module": "Mathlib.GroupTheory.MonoidLocalization.GrothendieckGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.GrothendieckGroup.inv_mk", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.GrothendieckGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.GrothendieckGroup.instCommGroup", "kind": "instance", "module": "Mathlib.GroupTheory.MonoidLocalization.GrothendieckGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.GrothendieckGroup.mk_div_mk", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.GrothendieckGroup", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Algebra.GrothendieckGroup.lift", "kind": "definition", "module": "Mathlib.GroupTheory.MonoidLocalization.GrothendieckGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.GrothendieckGroup.lift_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.GrothendieckGroup", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Submonoid.IsLocalizationMap.surj_pi_of_finite", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Lemmas", "is_tactic_proof": true, "tactics": ["choose", "have", "classical", "refine", "rw"], "tactic_count": 5}
{"name": "Submonoid.IsLocalizationMap.pi", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.subsingleton", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.MonoidWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.subsingleton_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.MonoidWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.nontrivial", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.MonoidWithZero", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Submonoid.LocalizationMap.map_zero", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.MonoidWithZero", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "Submonoid.IsLocalizationMap.map_zero", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.MonoidWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.instMonoidWithZeroHomClassLocalizationMap", "kind": "instance", "module": "Mathlib.GroupTheory.MonoidLocalization.MonoidWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.mk_zero", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.MonoidWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.instCommMonoidWithZero", "kind": "instance", "module": "Mathlib.GroupTheory.MonoidLocalization.MonoidWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.liftOn_zero", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.MonoidWithZero", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submonoid.LocalizationMap.sec_zero_fst", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.MonoidWithZero", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submonoid.LocalizationMap.lift₀", "kind": "definition", "module": "Mathlib.GroupTheory.MonoidLocalization.MonoidWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.lift₀_def", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.MonoidWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.lift₀_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.MonoidWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.isCancelMulZero", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.MonoidWithZero", "is_tactic_proof": false, "tactics": ["simp_rw", "intro", "have", "refine", "refine", "rwa"], "tactic_count": 6}
{"name": "Submonoid.LocalizationMap.map_eq_zero_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.MonoidWithZero", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Submonoid.LocalizationMap.mk'_eq_zero_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.MonoidWithZero", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submonoid.LocalizationMap.mk'_zero", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.MonoidWithZero", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submonoid.LocalizationMap.nonZeroDivisors_le_comap", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.MonoidWithZero", "is_tactic_proof": true, "tactics": ["refine", "have", "rw", "simp_rw", "rwa"], "tactic_count": 5}
{"name": "Submonoid.LocalizationMap.map_nonZeroDivisors_le", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.MonoidWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.LocalizationMap.noZeroDivisors", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.MonoidWithZero", "is_tactic_proof": true, "tactics": ["refine", "have", "have", "exact"], "tactic_count": 4}
{"name": "Localization.le", "kind": "instance", "module": "Mathlib.GroupTheory.MonoidLocalization.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.lt", "kind": "instance", "module": "Mathlib.GroupTheory.MonoidLocalization.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.mk_le_mk", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.mk_lt_mk", "kind": "theorem", "module": "Mathlib.GroupTheory.MonoidLocalization.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.partialOrder", "kind": "instance", "module": "Mathlib.GroupTheory.MonoidLocalization.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.isOrderedCancelMonoid", "kind": "instance", "module": "Mathlib.GroupTheory.MonoidLocalization.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.decidableLE", "kind": "instance", "module": "Mathlib.GroupTheory.MonoidLocalization.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.decidableLT", "kind": "instance", "module": "Mathlib.GroupTheory.MonoidLocalization.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.mkOrderEmbedding", "kind": "definition", "module": "Mathlib.GroupTheory.MonoidLocalization.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.instLinearOrderOfIsOrderedCancelMonoid", "kind": "instance", "module": "Mathlib.GroupTheory.MonoidLocalization.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "upperCentralSeriesStep", "kind": "definition", "module": "Mathlib.GroupTheory.Nilpotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_upperCentralSeriesStep", "kind": "theorem", "module": "Mathlib.GroupTheory.Nilpotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "upperCentralSeriesStep_eq_comap_center", "kind": "theorem", "module": "Mathlib.GroupTheory.Nilpotent", "is_tactic_proof": true, "tactics": ["ext", "rw", "apply", "intro", "rw", "mul_assoc]"], "tactic_count": 6}
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{"name": "upperCentralSeriesAux", "kind": "definition", "module": "Mathlib.GroupTheory.Nilpotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "upperCentralSeries_one", "kind": "theorem", "module": "Mathlib.GroupTheory.Nilpotent", "is_tactic_proof": true, "tactics": ["ext", "simp", "exact"], "tactic_count": 3}
{"name": "mem_upperCentralSeries_succ_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Nilpotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "comap_upperCentralSeries", "kind": "theorem", "module": "Mathlib.GroupTheory.Nilpotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Group.IsNilpotent.nilpotent", "kind": "theorem", "module": "Mathlib.GroupTheory.Nilpotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Group.isNilpotent_congr", "kind": "theorem", "module": "Mathlib.GroupTheory.Nilpotent", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "simp", "simp"], "tactic_count": 4}
{"name": "Group.isNilpotent_top", "kind": "theorem", "module": "Mathlib.GroupTheory.Nilpotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Group.IsVirtuallyNilpotent", "kind": "definition", "module": "Mathlib.GroupTheory.Nilpotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Group.IsNilpotent.isVirtuallyNilpotent", "kind": "theorem", "module": "Mathlib.GroupTheory.Nilpotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAscendingCentralSeries", "kind": "definition", "module": "Mathlib.GroupTheory.Nilpotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDescendingCentralSeries", "kind": "definition", "module": "Mathlib.GroupTheory.Nilpotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ascending_central_series_le_upper", "kind": "theorem", "module": "Mathlib.GroupTheory.Nilpotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "upperCentralSeries_isAscendingCentralSeries", "kind": "theorem", "module": "Mathlib.GroupTheory.Nilpotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "upperCentralSeries_mono", "kind": "theorem", "module": "Mathlib.GroupTheory.Nilpotent", "is_tactic_proof": true, "tactics": ["refine", "intro", "rw", "exact"], "tactic_count": 4}
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{"name": "is_descending_rev_series_of_is_ascending", "kind": "theorem", "module": "Mathlib.GroupTheory.Nilpotent", "is_tactic_proof": true, "tactics": ["obtain", "refine", "dsimp", "by_cases", "rw", "subst", "rw", "exact", "apply", "convert", "rw"], "tactic_count": 11}
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{"name": "lowerCentralSeries_antitone", "kind": "theorem", "module": "Mathlib.GroupTheory.Nilpotent", "is_tactic_proof": true, "tactics": ["refine", "simp", "refine", "rintro", "rw", "exact"], "tactic_count": 6}
{"name": "lowerCentralSeries_isDescendingCentralSeries", "kind": "theorem", "module": "Mathlib.GroupTheory.Nilpotent", "is_tactic_proof": true, "tactics": ["constructor", "rfl", "intro", "exact"], "tactic_count": 4}
{"name": "descending_central_series_ge_lower", "kind": "theorem", "module": "Mathlib.GroupTheory.Nilpotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nilpotent_iff_lowerCentralSeries", "kind": "theorem", "module": "Mathlib.GroupTheory.Nilpotent", "is_tactic_proof": true, "tactics": ["rw", "constructor", "rintro", "use", "rw", "exact", "rintro", "exact"], "tactic_count": 8}
{"name": "Group.nilpotencyClass", "kind": "definition", "module": "Mathlib.GroupTheory.Nilpotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "upperCentralSeries_nilpotencyClass", "kind": "theorem", "module": "Mathlib.GroupTheory.Nilpotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "upperCentralSeries_eq_top_iff_nilpotencyClass_le", "kind": "theorem", "module": "Mathlib.GroupTheory.Nilpotent", "is_tactic_proof": true, "tactics": ["classical", "constructor", "intro", "exact", "intro", "rw", "exact"], "tactic_count": 7}
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{"name": "lowerCentralSeries_eq_bot_iff_nilpotencyClass_le", "kind": "theorem", "module": "Mathlib.GroupTheory.Nilpotent", "is_tactic_proof": true, "tactics": ["classical", "constructor", "intro", "rw", "exact", "intro", "rw", "exact"], "tactic_count": 8}
{"name": "lowerCentralSeries_map_subtype_le", "kind": "theorem", "module": "Mathlib.GroupTheory.Nilpotent", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "apply", "rintro", "exact"], "tactic_count": 7}
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{"name": "isNilpotent_of_ker_le_center", "kind": "theorem", "module": "Mathlib.GroupTheory.Nilpotent", "is_tactic_proof": true, "tactics": ["rw", "rcases", "use", "refine", "exact"], "tactic_count": 5}
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{"name": "nilpotent_quotient_of_nilpotent", "kind": "instance", "module": "Mathlib.GroupTheory.Nilpotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "commGroupOfNilpotencyClass", "kind": "definition", "module": "Mathlib.GroupTheory.Nilpotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "isNilpotent_pi_of_bounded_class", "kind": "theorem", "module": "Mathlib.GroupTheory.Nilpotent", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "apply", "rw", "intro", "apply"], "tactic_count": 7}
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{"name": "isNilpotent_pi", "kind": "instance", "module": "Mathlib.GroupTheory.Nilpotent", "is_tactic_proof": true, "tactics": ["cases", "rw", "refine", "rw", "intro", "rw", "exact"], "tactic_count": 7}
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{"name": "isNilpotent_of_product_of_sylow_group", "kind": "theorem", "module": "Mathlib.GroupTheory.Nilpotent", "is_tactic_proof": true, "tactics": ["classical", "let", "have", "intro", "haveI", "exact", "exact"], "tactic_count": 7}
{"name": "isNilpotent_of_finite_tfae", "kind": "theorem", "module": "Mathlib.GroupTheory.Nilpotent", "is_tactic_proof": true, "tactics": ["tfae_have", "tfae_have", "h,", "tfae_have", "h,", "tfae_have", "h", "tfae_have", "tfae_finish"], "tactic_count": 9}
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{"name": "orderOf", "kind": "definition", "module": "Mathlib.GroupTheory.OrderOfElement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsingleton.orderOf_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.OrderOfElement", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "addOrderOf_ofMul_eq_orderOf", "kind": "theorem", "module": "Mathlib.GroupTheory.OrderOfElement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "orderOf_ofAdd_eq_addOrderOf", "kind": "theorem", "module": "Mathlib.GroupTheory.OrderOfElement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOfFinOrder.orderOf_pos", "kind": "theorem", "module": "Mathlib.GroupTheory.OrderOfElement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "orderOf_ne_zero_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.OrderOfElement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "orderOf_zero", "kind": "theorem", "module": "Mathlib.GroupTheory.OrderOfElement", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
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{"name": "IsOfFinOrder.mono", "kind": "theorem", "module": "Mathlib.GroupTheory.OrderOfElement", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "pow_ne_one_of_lt_orderOf", "kind": "theorem", "module": "Mathlib.GroupTheory.OrderOfElement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "orderOf_le_of_pow_eq_one", "kind": "theorem", "module": "Mathlib.GroupTheory.OrderOfElement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "orderOf_map_dvd", "kind": "theorem", "module": "Mathlib.GroupTheory.OrderOfElement", "is_tactic_proof": true, "tactics": ["apply", "rw", "apply"], "tactic_count": 3}
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{"name": "orderOf_pow'", "kind": "theorem", "module": "Mathlib.GroupTheory.OrderOfElement", "is_tactic_proof": true, "tactics": ["unfold", "rw"], "tactic_count": 2}
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{"name": "orderOf_pow_orderOf_div", "kind": "theorem", "module": "Mathlib.GroupTheory.OrderOfElement", "is_tactic_proof": true, "tactics": ["rw", "rw"], "tactic_count": 2}
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{"name": "finEquivPowers", "kind": "definition", "module": "Mathlib.GroupTheory.OrderOfElement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "orderOf_dvd_iff_zpow_eq_one", "kind": "theorem", "module": "Mathlib.GroupTheory.OrderOfElement", "is_tactic_proof": true, "tactics": ["rcases", "rw", "rw"], "tactic_count": 3}
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{"name": "orderOf_dvd_sub_iff_zpow_eq_zpow", "kind": "theorem", "module": "Mathlib.GroupTheory.OrderOfElement", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "IsOfFinOrder.mem_powers_iff_mem_zpowers", "kind": "theorem", "module": "Mathlib.GroupTheory.OrderOfElement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Subgroup.closure_toSubmonoid_of_isOfFinOrder", "kind": "theorem", "module": "Mathlib.GroupTheory.OrderOfElement", "is_tactic_proof": true, "tactics": ["refine", "rw", "refine", "apply", "simp"], "tactic_count": 5}
{"name": "finEquivZPowers", "kind": "definition", "module": "Mathlib.GroupTheory.OrderOfElement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "isMulTorsionFree_iff_not_isOfFinOrder", "kind": "theorem", "module": "Mathlib.GroupTheory.OrderOfElement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_isMulTorsionFree_iff_isOfFinOrder", "kind": "theorem", "module": "Mathlib.GroupTheory.OrderOfElement", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "OreLocalization.mul_assoc", "kind": "theorem", "module": "Mathlib.GroupTheory.OreLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OreLocalization.npow", "kind": "abbrev", "module": "Mathlib.GroupTheory.OreLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OreLocalization.instMonoid", "kind": "instance", "module": "Mathlib.GroupTheory.OreLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OreLocalization.instMulActionOreLocalization", "kind": "instance", "module": "Mathlib.GroupTheory.OreLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OreLocalization.mul_inv", "kind": "theorem", "module": "Mathlib.GroupTheory.OreLocalization.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "OreLocalization.one_div_smul", "kind": "theorem", "module": "Mathlib.GroupTheory.OreLocalization.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "OreLocalization.one_div_mul", "kind": "theorem", "module": "Mathlib.GroupTheory.OreLocalization.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "OreLocalization.smul_cancel", "kind": "theorem", "module": "Mathlib.GroupTheory.OreLocalization.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "OreLocalization.mul_cancel", "kind": "theorem", "module": "Mathlib.GroupTheory.OreLocalization.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "OreLocalization.smul_cancel'", "kind": "theorem", "module": "Mathlib.GroupTheory.OreLocalization.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "OreLocalization.mul_cancel'", "kind": "theorem", "module": "Mathlib.GroupTheory.OreLocalization.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "OreLocalization.smul_div_one", "kind": "theorem", "module": "Mathlib.GroupTheory.OreLocalization.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "OreLocalization.mul_div_one", "kind": "theorem", "module": "Mathlib.GroupTheory.OreLocalization.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "OreLocalization.numeratorUnit", "kind": "definition", "module": "Mathlib.GroupTheory.OreLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OreLocalization.numeratorHom", "kind": "abbrev", "module": "Mathlib.GroupTheory.OreLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OreLocalization.numeratorHom_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.OreLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OreLocalization.numerator_isUnit", "kind": "theorem", "module": "Mathlib.GroupTheory.OreLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OreLocalization.universalMulHom", "kind": "definition", "module": "Mathlib.GroupTheory.OreLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OreLocalization.universalMulHom_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.OreLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OreLocalization.universalMulHom_commutes", "kind": "theorem", "module": "Mathlib.GroupTheory.OreLocalization.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "OreLocalization.universalMulHom_unique", "kind": "theorem", "module": "Mathlib.GroupTheory.OreLocalization.Basic", "is_tactic_proof": true, "tactics": ["ext", "cases", "rw", "inv_mul_cancel"], "tactic_count": 4}
{"name": "OreLocalization.hsmul", "kind": "definition", "module": "Mathlib.GroupTheory.OreLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OreLocalization.instSMulOfIsScalarTower", "kind": "instance", "module": "Mathlib.GroupTheory.OreLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OreLocalization.smul_oreDiv", "kind": "theorem", "module": "Mathlib.GroupTheory.OreLocalization.Basic", "is_tactic_proof": true, "tactics": ["with_unfolding_all"], "tactic_count": 1}
{"name": "OreLocalization.oreDiv_one_smul", "kind": "theorem", "module": "Mathlib.GroupTheory.OreLocalization.Basic", "is_tactic_proof": true, "tactics": ["cases", "rw"], "tactic_count": 2}
{"name": "OreLocalization.smul_one_smul", "kind": "theorem", "module": "Mathlib.GroupTheory.OreLocalization.Basic", "is_tactic_proof": true, "tactics": ["cases", "simp"], "tactic_count": 2}
{"name": "OreLocalization.smul_one_oreDiv_one_smul", "kind": "theorem", "module": "Mathlib.GroupTheory.OreLocalization.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "OreLocalization.instIsScalarTower", "kind": "instance", "module": "Mathlib.GroupTheory.OreLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OreLocalization.instSMulCommClass", "kind": "instance", "module": "Mathlib.GroupTheory.OreLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OreLocalization.instIsScalarTower_1", "kind": "instance", "module": "Mathlib.GroupTheory.OreLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OreLocalization.instSMulCommClass_1", "kind": "instance", "module": "Mathlib.GroupTheory.OreLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OreLocalization.instIsCentralScalar", "kind": "instance", "module": "Mathlib.GroupTheory.OreLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OreLocalization.instMulActionOfIsScalarTower", "kind": "instance", "module": "Mathlib.GroupTheory.OreLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OreLocalization.smul_oreDiv_one", "kind": "theorem", "module": "Mathlib.GroupTheory.OreLocalization.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "OreLocalization.oreDiv_mul_oreDiv_comm", "kind": "theorem", "module": "Mathlib.GroupTheory.OreLocalization.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "OreLocalization.instCommMonoid", "kind": "instance", "module": "Mathlib.GroupTheory.OreLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OreLocalization.zero", "kind": "definition", "module": "Mathlib.GroupTheory.OreLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OreLocalization.instZero", "kind": "instance", "module": "Mathlib.GroupTheory.OreLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OreLocalization.zero_def", "kind": "theorem", "module": "Mathlib.GroupTheory.OreLocalization.Basic", "is_tactic_proof": true, "tactics": ["with_unfolding_all"], "tactic_count": 1}
{"name": "OreLocalization.oreDiv_one_surjective_of_finite_left", "kind": "theorem", "module": "Mathlib.GroupTheory.OreLocalization.Cardinality", "is_tactic_proof": true, "tactics": ["refine", "obtain", "wlog", "exact", "use", "rw", "refine", "change", "rw", "simp_rw"], "tactic_count": 10}
{"name": "OreLocalization.oreDiv_one_surjective_of_finite_right", "kind": "theorem", "module": "Mathlib.GroupTheory.OreLocalization.Cardinality", "is_tactic_proof": true, "tactics": ["refine", "obtain", "wlog", "exact", "use", "rw", "refine", "change", "rw", "simp_rw"], "tactic_count": 10}
{"name": "OreLocalization.numeratorHom_surjective_of_finite", "kind": "theorem", "module": "Mathlib.GroupTheory.OreLocalization.Cardinality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OreLocalization.cardinalMk_le_max", "kind": "theorem", "module": "Mathlib.GroupTheory.OreLocalization.Cardinality", "is_tactic_proof": true, "tactics": ["rcases", "have", "rw", "exact", "rcases", "have", "rw", "exact", "convert", "rw", "refine"], "tactic_count": 11}
{"name": "OreLocalization.cardinalMk_le", "kind": "theorem", "module": "Mathlib.GroupTheory.OreLocalization.Cardinality", "is_tactic_proof": true, "tactics": ["convert", "simp_rw"], "tactic_count": 2}
{"name": "OreLocalization.cardinalMk_le_lift_cardinalMk_of_commute", "kind": "theorem", "module": "Mathlib.GroupTheory.OreLocalization.Cardinality", "is_tactic_proof": true, "tactics": ["rcases", "have", "rwa", "have", "rw", "refine", "exact_mod_cast", "let", "have", "have", "let", "suffices", "have", "rwa", "intro", "grind"], "tactic_count": 16}
{"name": "OreLocalization.ore_right_cancel", "kind": "theorem", "module": "Mathlib.GroupTheory.OreLocalization.OreSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OreLocalization.oreNum", "kind": "definition", "module": "Mathlib.GroupTheory.OreLocalization.OreSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OreLocalization.oreDenom", "kind": "definition", "module": "Mathlib.GroupTheory.OreLocalization.OreSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OreLocalization.ore_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.OreLocalization.OreSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OreLocalization.oreCondition", "kind": "definition", "module": "Mathlib.GroupTheory.OreLocalization.OreSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OreLocalization.oreSetBot", "kind": "instance", "module": "Mathlib.GroupTheory.OreLocalization.OreSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OreLocalization.oreSetComm", "kind": "instance", "module": "Mathlib.GroupTheory.OreLocalization.OreSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OreLocalization.oreSetComm_oreNum", "kind": "theorem", "module": "Mathlib.GroupTheory.OreLocalization.OreSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OreLocalization.oreSetComm_oreDenom", "kind": "theorem", "module": "Mathlib.GroupTheory.OreLocalization.OreSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPGroup", "kind": "definition", "module": "Mathlib.GroupTheory.PGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPGroup.iff_orderOf", "kind": "theorem", "module": "Mathlib.GroupTheory.PGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPGroup.of_card", "kind": "theorem", "module": "Mathlib.GroupTheory.PGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPGroup.of_bot", "kind": "theorem", "module": "Mathlib.GroupTheory.PGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPGroup.iff_card", "kind": "theorem", "module": "Mathlib.GroupTheory.PGroup", "is_tactic_proof": true, "tactics": ["have", "refine", "suffices", "use", "rw", "intro", "obtain", "haveI", "obtain", "obtain", "exact"], "tactic_count": 11}
{"name": "IsPGroup.of_injective", "kind": "theorem", "module": "Mathlib.GroupTheory.PGroup", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "IsPGroup.to_subgroup", "kind": "theorem", "module": "Mathlib.GroupTheory.PGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPGroup.of_surjective", "kind": "theorem", "module": "Mathlib.GroupTheory.PGroup", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "IsPGroup.to_quotient", "kind": "theorem", "module": "Mathlib.GroupTheory.PGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPGroup.of_equiv", "kind": "theorem", "module": "Mathlib.GroupTheory.PGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPGroup.orderOf_coprime", "kind": "theorem", "module": "Mathlib.GroupTheory.PGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPGroup.powEquiv", "kind": "definition", "module": "Mathlib.GroupTheory.PGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPGroup.powEquiv_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.PGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPGroup.powEquiv_symm_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.PGroup", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsPGroup.powEquiv'", "kind": "abbrev", "module": "Mathlib.GroupTheory.PGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPGroup.index", "kind": "theorem", "module": "Mathlib.GroupTheory.PGroup", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "exact"], "tactic_count": 3}
{"name": "IsPGroup.card_eq_or_dvd", "kind": "theorem", "module": "Mathlib.GroupTheory.PGroup", "is_tactic_proof": true, "tactics": ["cases", "obtain", "rw", "rcases", "exact", "exact", "rw", "exact"], "tactic_count": 8}
{"name": "IsPGroup.nontrivial_iff_card", "kind": "theorem", "module": "Mathlib.GroupTheory.PGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPGroup.card_orbit", "kind": "theorem", "module": "Mathlib.GroupTheory.PGroup", "is_tactic_proof": true, "tactics": ["let", "haveI", "haveI", "rw", "exact"], "tactic_count": 5}
{"name": "IsPGroup.card_modEq_card_fixedPoints", "kind": "theorem", "module": "Mathlib.GroupTheory.PGroup", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "classical", "calc", "card", "card_congr", "rw", "have", "refine", "rw", "obtain", "rw", "have", "contrapose", "simp", "exact", "ne_of_eq_of_ne"], "tactic_count": 18}
{"name": "IsPGroup.nonempty_fixed_point_of_prime_not_dvd_card", "kind": "theorem", "module": "Mathlib.GroupTheory.PGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPGroup.exists_fixed_point_of_prime_dvd_card_of_fixed_point", "kind": "theorem", "module": "Mathlib.GroupTheory.PGroup", "is_tactic_proof": false, "tactics": ["have", "have", "rw", "exact", "let"], "tactic_count": 5}
{"name": "IsPGroup.center_nontrivial", "kind": "theorem", "module": "Mathlib.GroupTheory.PGroup", "is_tactic_proof": true, "tactics": ["classical", "have", "rw", "have", "obtain", "exact", "obtain", "exact"], "tactic_count": 8}
{"name": "IsPGroup.bot_lt_center", "kind": "theorem", "module": "Mathlib.GroupTheory.PGroup", "is_tactic_proof": true, "tactics": ["haveI", "classical"], "tactic_count": 2}
{"name": "IsPGroup.to_le", "kind": "theorem", "module": "Mathlib.GroupTheory.PGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPGroup.to_inf_left", "kind": "theorem", "module": "Mathlib.GroupTheory.PGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPGroup.to_inf_right", "kind": "theorem", "module": "Mathlib.GroupTheory.PGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPGroup.map", "kind": "theorem", "module": "Mathlib.GroupTheory.PGroup", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsPGroup.comap_of_ker_isPGroup", "kind": "theorem", "module": "Mathlib.GroupTheory.PGroup", "is_tactic_proof": true, "tactics": ["intro", "obtain", "rw", "obtain", "rw", "exact"], "tactic_count": 6}
{"name": "IsPGroup.ker_isPGroup_of_injective", "kind": "theorem", "module": "Mathlib.GroupTheory.PGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPGroup.comap_of_injective", "kind": "theorem", "module": "Mathlib.GroupTheory.PGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPGroup.comap_subtype", "kind": "theorem", "module": "Mathlib.GroupTheory.PGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPGroup.to_sup_of_normal_right", "kind": "theorem", "module": "Mathlib.GroupTheory.PGroup", "is_tactic_proof": true, "tactics": ["rw", "apply", "rwa"], "tactic_count": 3}
{"name": "IsPGroup.to_sup_of_normal_left", "kind": "theorem", "module": "Mathlib.GroupTheory.PGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPGroup.to_sup_of_normal_right'", "kind": "theorem", "module": "Mathlib.GroupTheory.PGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPGroup.to_sup_of_normal_left'", "kind": "theorem", "module": "Mathlib.GroupTheory.PGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPGroup.coprime_card_of_ne", "kind": "theorem", "module": "Mathlib.GroupTheory.PGroup", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "exact"], "tactic_count": 3}
{"name": "IsPGroup.disjoint_of_ne", "kind": "theorem", "module": "Mathlib.GroupTheory.PGroup", "is_tactic_proof": true, "tactics": ["rw", "intro", "obtain", "obtain", "rw", "have", "rcases", "simpa", "exact"], "tactic_count": 9}
{"name": "IsPGroup.le_or_disjoint_of_coprime", "kind": "theorem", "module": "Mathlib.GroupTheory.PGroup", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "rw", "exact", "by_cases", "rw", "rw", "exact", "have", "apply", "rw", "exact", "have", "obtain", "refine", "contrapose", "exact", "refine", "rw", "exact", "exact"], "tactic_count": 21}
{"name": "IsPGroup.card_center_eq_prime_pow", "kind": "theorem", "module": "Mathlib.GroupTheory.PGroup", "is_tactic_proof": true, "tactics": ["have", "have", "rcases", "haveI", "exact"], "tactic_count": 5}
{"name": "IsPGroup.cyclic_center_quotient_of_card_eq_prime_sq", "kind": "theorem", "module": "Mathlib.GroupTheory.PGroup", "is_tactic_proof": true, "tactics": ["apply", "rw", "apply", "rcases", "rw", "exact"], "tactic_count": 6}
{"name": "IsPGroup.commGroupOfCardEqPrimeSq", "kind": "definition", "module": "Mathlib.GroupTheory.PGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPGroup.commutative_of_card_eq_prime_sq", "kind": "theorem", "module": "Mathlib.GroupTheory.PGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZModModule.isPGroup_multiplicative", "kind": "theorem", "module": "Mathlib.GroupTheory.PGroup", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Equiv.Perm.image_inv", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.preimage_inv", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.swap_smul_self_smul", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Equiv.swap_smul_involutive", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.BijOn.perm_inv", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.MapsTo.perm_pow", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.SurjOn.perm_pow", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.BijOn.perm_pow", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.BijOn.perm_zpow", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.OnCycleFactors.Subgroup.Centralizer.toConjAct_smul_mem_cycleFactorsFinset", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Centralizer", "is_tactic_proof": false, "tactics": ["suffices", "rw", "simp", "have", "rw", "simp", "conv_lhs", "simp"], "tactic_count": 8}
{"name": "Equiv.Perm.OnCycleFactors.Subgroup.Centralizer.cycleFactorsFinset_mulAction", "kind": "definition", "module": "Mathlib.GroupTheory.Perm.Centralizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.OnCycleFactors.instMulActionSubtypeMemSubgroupCentralizerSingletonSetFinsetCycleFactorsFinset", "kind": "instance", "module": "Mathlib.GroupTheory.Perm.Centralizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.OnCycleFactors.toPermHom", "kind": "definition", "module": "Mathlib.GroupTheory.Perm.Centralizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.OnCycleFactors.centralizer_smul_def", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Centralizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.OnCycleFactors.val_centralizer_smul", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Centralizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.OnCycleFactors.toPermHom_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Centralizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.OnCycleFactors.coe_toPermHom", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Centralizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.OnCycleFactors.range_toPermHom'", "kind": "definition", "module": "Mathlib.GroupTheory.Perm.Centralizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.OnCycleFactors.mem_range_toPermHom'_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Centralizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.OnCycleFactors.mem_ker_toPermHom_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Centralizer", "is_tactic_proof": true, "tactics": ["simp", "refine", "simp"], "tactic_count": 3}
{"name": "Equiv.Perm.instFunLikeBasisSubtypeMemFinsetCycleFactorsFinset", "kind": "instance", "module": "Mathlib.GroupTheory.Perm.Centralizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.Basis.nonempty", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Centralizer", "is_tactic_proof": false, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "Equiv.Perm.Basis.mem_support_self", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Centralizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.Basis.injective", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Centralizer", "is_tactic_proof": true, "tactics": ["intro", "rw", "apply", "simp", "use", "conv_rhs", "simp"], "tactic_count": 7}
{"name": "Equiv.Perm.Basis.cycleOf_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Centralizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.Basis.sameCycle", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Centralizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.Basis.ofPermHomFun", "kind": "definition", "module": "Mathlib.GroupTheory.Perm.Centralizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.Basis.mem_fixedPoints_or_exists_zpow_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Centralizer", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "refine", "rw", "simp"], "tactic_count": 6}
{"name": "Equiv.Perm.Basis.ofPermHomFun_apply_of_cycleOf_mem", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Centralizer", "is_tactic_proof": true, "tactics": ["have", "have", "set", "have", "rw", "congr", "rw", "suffices", "rw", "simp", "rw", "rw", "simp", "congr", "exact"], "tactic_count": 15}
{"name": "Equiv.Perm.Basis.ofPermHomFun_apply_of_mem_fixedPoints", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Centralizer", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "Equiv.Perm.Basis.ofPermHomFun_apply_mem_support_cycle_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Centralizer", "is_tactic_proof": true, "tactics": ["rcases", "simp", "suffices", "intro", "rw", "apply", "exact", "rw", "rw", "by_cases", "simp", "have", "have", "cycleFactorsFinset_pairwise_disjoint", "intro", "simpa", "rw", "simp"], "tactic_count": 18}
{"name": "Equiv.Perm.Basis.ofPermHomFun_commute_zpow_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Centralizer", "is_tactic_proof": true, "tactics": ["rcases", "rw", "rw", "simp", "conv_rhs", "obtain", "have", "rw", "zpow_add]", "exact"], "tactic_count": 10}
{"name": "Equiv.Perm.Basis.ofPermHomFun_mul", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Centralizer", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simp", "rw", "rfl", "rw", "apply"], "tactic_count": 7}
{"name": "Equiv.Perm.Basis.ofPermHomFun_one", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Centralizer", "is_tactic_proof": true, "tactics": ["rcases", "rw", "rw"], "tactic_count": 3}
{"name": "Equiv.Perm.Basis.ofPermHom", "kind": "definition", "module": "Mathlib.GroupTheory.Perm.Centralizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.Basis.ofPermHom_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Centralizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.Basis.ofPermHom_support", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Centralizer", "is_tactic_proof": true, "tactics": ["ext", "simp", "rcases", "simp", "rintro", "rw", "exact", "rw", "conv_lhs", "rw", "by_cases", "simp", "push_neg", "intro", "rw", "have", "rw", "exact", "simpa"], "tactic_count": 19}
{"name": "Equiv.Perm.Basis.card_ofPermHom_support", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Centralizer", "is_tactic_proof": true, "tactics": ["rw", "intro", "apply", "apply"], "tactic_count": 4}
{"name": "Equiv.Perm.Basis.ofPermHom_mem_centralizer", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Centralizer", "is_tactic_proof": true, "tactics": ["rw", "ext", "simp", "exact"], "tactic_count": 4}
{"name": "Equiv.Perm.Basis.toCentralizer", "kind": "definition", "module": "Mathlib.GroupTheory.Perm.Centralizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.Basis.toCentralizer_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Centralizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.Basis.toCentralizer_equivariant", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Centralizer", "is_tactic_proof": true, "tactics": ["simp", "ext", "simp", "by_cases", "rw", "have", "simp", "rw", "rw", "exact", "rw", "exact"], "tactic_count": 12}
{"name": "Equiv.Perm.Basis.toPermHom_apply_toCentralizer", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Centralizer", "is_tactic_proof": true, "tactics": ["apply", "intro", "rw"], "tactic_count": 3}
{"name": "Equiv.Perm.OnCycleFactors.mem_range_toPermHom_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Centralizer", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "rw", "apply", "obtain", "exact"], "tactic_count": 6}
{"name": "Equiv.Perm.OnCycleFactors.mem_range_toPermHom_iff'", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Centralizer", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Equiv.Perm.OnCycleFactors.range_toPermHom_eq_range_toPermHom'", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Centralizer", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "Equiv.Perm.OnCycleFactors.nat_card_range_toPermHom", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Centralizer", "is_tactic_proof": true, "tactics": ["classical", "set", "suffices", "simp", "simp_rw", "apply", "ext", "simp", "simp", "simp", "congr", "ext", "rw"], "tactic_count": 13}
{"name": "Equiv.Perm.OnCycleFactors.kerParam", "kind": "definition", "module": "Mathlib.GroupTheory.Perm.Centralizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.OnCycleFactors.kerParam_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Centralizer", "is_tactic_proof": true, "tactics": ["split_ifs", "have", "rw", "rw", "contrapose", "obtain", "simp", "have", "rw", "obtain", "replace", "obtain", "rwa", "rw", "rw", "contrapose", "obtain", "mem_support_of_mem_noncommProd_support", "g.pairwise_commute_of_mem_zpowers", "exact"], "tactic_count": 20}
{"name": "Equiv.Perm.OnCycleFactors.kerParam_injective", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Centralizer", "is_tactic_proof": true, "tactics": ["rw", "refine", "apply", "intro", "simp", "simp", "apply", "rintro", "rw", "apply", "simp", "exact", "exact", "rw", "simp", "apply", "rintro", "exact"], "tactic_count": 18}
{"name": "Equiv.Perm.OnCycleFactors.kerParam_range_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Centralizer", "is_tactic_proof": true, "tactics": ["apply", "rw", "simp", "constructor", "rintro", "refine", "rw", "exact", "exact", "intro", "refine", "exact", "rintro", "simp", "set", "subtypePerm", "simp", "set", "use", "ext", "rw", "split_ifs", "rw", "rw", "rwa", "rw", "rwa"], "tactic_count": 27}
{"name": "Equiv.Perm.OnCycleFactors.kerParam_range_le_centralizer", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Centralizer", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Equiv.Perm.OnCycleFactors.kerParam_range_card", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Centralizer", "is_tactic_proof": true, "tactics": ["rw", "rw", "apply", "rw", "refine", "rw"], "tactic_count": 6}
{"name": "Equiv.Perm.OnCycleFactors.sign_kerParam_apply_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Centralizer", "is_tactic_proof": false, "tactics": ["rw", "sign_ofSubtype,", "simp"], "tactic_count": 3}
{"name": "Equiv.Perm.OnCycleFactors.cycleType_kerParam_apply_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Centralizer", "is_tactic_proof": true, "tactics": ["let", "have", "obtain", "obtain", "simp", "apply", "apply", "exact", "rw", "exact"], "tactic_count": 10}
{"name": "Equiv.Perm.nat_card_centralizer", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Centralizer", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Equiv.Perm.card_isConj_mul_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Centralizer", "is_tactic_proof": true, "tactics": ["classical", "rw", "rw", "convert", "ext", "simp", "rw"], "tactic_count": 7}
{"name": "Equiv.Perm.card_isConj_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Centralizer", "is_tactic_proof": true, "tactics": ["rw", "rfl", "rw", "apply"], "tactic_count": 4}
{"name": "Equiv.Perm.card_of_cycleType_eq_zero_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Centralizer", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Equiv.Perm.card_of_cycleType_mul_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Centralizer", "is_tactic_proof": true, "tactics": ["split_ifs", "classical", "obtain", "convert", "simp_rw", "rw"], "tactic_count": 6}
{"name": "Equiv.Perm.card_of_cycleType", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Centralizer", "is_tactic_proof": true, "tactics": ["split_ifs", "apply", "apply", "have", "positivity", "rw", "exact"], "tactic_count": 7}
{"name": "Equiv.Perm.card_of_cycleType_singleton", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Centralizer", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "simpa"], "tactic_count": 4}
{"name": "Equiv.Perm.closure_isCycle", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Closure", "is_tactic_proof": true, "tactics": ["classical", "cases", "exact"], "tactic_count": 3}
{"name": "Equiv.Perm.closure_cycle_adjacent_swap", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Closure", "is_tactic_proof": true, "tactics": ["let", "have", "have", "have", "intro", "induction", "zero", "succ", "convert", "simp_rw", "have", "intro", "induction", "zero", "simp", "convert", "succ", "by_cases", "rw", "exact", "by_cases", "rw", "exact", "rw", "exact", "have", "intro", "have", "rw", "have", "rw", "obtain", "rw", "exact", "have", "intro", "by_cases", "rw", "exact", "by_cases", "rw", "exact", "rw", "exact", "rw", "rintro", "rw", "exact"], "tactic_count": 48}
{"name": "Equiv.Perm.closure_cycle_coprime_swap", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Closure", "is_tactic_proof": true, "tactics": ["rw", "obtain", "have", "have", "replace", "rw", "exact"], "tactic_count": 7}
{"name": "Equiv.Perm.closure_prime_cycle_swap", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Closure", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "h1.exists_pow_eq", "rw", "refine", "obtain", "rwa"], "tactic_count": 7}
{"name": "finite_compl_fixedBy_closure_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.ClosureSwap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_smul_notMem_of_subset_orbit_closure", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.ClosureSwap", "is_tactic_proof": false, "tactics": ["have", "have", "obtain", "contrapose", "exact", "contrapose", "refine", "simp_rw", "exact"], "tactic_count": 9}
{"name": "finite_compl_fixedBy_swap", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.ClosureSwap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.IsSwap.finite_compl_fixedBy", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.ClosureSwap", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "SubmonoidClass.swap_mem_trans", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.ClosureSwap", "is_tactic_proof": true, "tactics": ["obtain", "exact", "obtain", "exact", "rw", "exact"], "tactic_count": 6}
{"name": "swap_mem_closure_isSwap", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.ClosureSwap", "is_tactic_proof": true, "tactics": ["refine", "by_contra", "have", "exists_smul_notMem_of_subset_orbit_closure", "obtain", "obtain", "have", "rw", "refine", "obtain", "obtain", "exact", "rw"], "tactic_count": 13}
{"name": "mem_closure_isSwap", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.ClosureSwap", "is_tactic_proof": true, "tactics": ["refine", "exact", "rintro", "set", "suffices", "clear_value", "apply", "rintro", "rintro", "refine", "rw", "rw", "rw", "exact", "contrapose", "simp_rw", "by_cases", "rw", "simp"], "tactic_count": 19}
{"name": "mem_closure_isSwap'", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.ClosureSwap", "is_tactic_proof": false, "tactics": ["refine", "by_cases", "rw", "apply", "exact"], "tactic_count": 5}
{"name": "closure_of_isSwap_of_isPretransitive", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.ClosureSwap", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "surjective_of_isSwap_of_isPretransitive'", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.ClosureSwap", "is_tactic_proof": false, "tactics": ["have", "rw", "have", "rw", "rw", "rintro", "exact"], "tactic_count": 7}
{"name": "surjective_of_isSwap_of_isPretransitive", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.ClosureSwap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.mem_conj_support", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.ConjAct", "is_tactic_proof": true, "tactics": ["simp", "apply"], "tactic_count": 2}
{"name": "Equiv.Perm.cycleFactorsFinset_conj", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.ConjAct", "is_tactic_proof": true, "tactics": ["ext", "rw", "simp"], "tactic_count": 3}
{"name": "Equiv.Perm.mem_cycleFactorsFinset_conj'", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.ConjAct", "is_tactic_proof": true, "tactics": ["simp", "apply"], "tactic_count": 2}
{"name": "Equiv.Perm.cycleFactorsFinset_conj_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.ConjAct", "is_tactic_proof": true, "tactics": ["ext", "rw", "simp", "exact"], "tactic_count": 4}
{"name": "Equiv.Perm.SameCycle", "kind": "definition", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.SameCycle.refl", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.SameCycle.rfl", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Eq.sameCycle", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Equiv.Perm.SameCycle.symm", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.sameCycle_comm", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.SameCycle.trans", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.SameCycle.equivalence", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.SameCycle.setoid", "kind": "definition", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.sameCycle_one", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Equiv.Perm.sameCycle_inv", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.sameCycle_conj", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.SameCycle.conj", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Equiv.Perm.SameCycle.apply_eq_self_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.SameCycle.eq_of_left", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.SameCycle.eq_of_right", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.sameCycle_apply_left", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.sameCycle_apply_right", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Equiv.Perm.sameCycle_symm_apply_left", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Equiv.Perm.sameCycle_symm_apply_right", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Equiv.Perm.sameCycle_zpow_left", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.sameCycle_zpow_right", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Equiv.Perm.sameCycle_pow_left", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Equiv.Perm.sameCycle_pow_right", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Equiv.Perm.SameCycle.of_pow", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.SameCycle.of_zpow", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.sameCycle_subtypePerm", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.sameCycle_extendDomain", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.SameCycle.exists_pow_eq'", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": true, "tactics": ["rintro", "use", "have", "have", "rw", "refine", "rw", "exact"], "tactic_count": 8}
{"name": "Equiv.Perm.SameCycle.exists_pow_eq''", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": true, "tactics": ["obtain", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "Equiv.Perm.SameCycle.exists_fin_pow_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Equiv.Perm.SameCycle.exists_nat_pow_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Equiv.Perm.instDecidableRelSameCycleInv", "kind": "instance", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.instDecidableRelSameCycleOfNatOfDecidableEq", "kind": "instance", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.IsCycle", "kind": "definition", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.IsCycle.ne_one", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.not_isCycle_one", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.IsCycle.sameCycle", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.IsCycle.exists_zpow_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.IsCycle.inv", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.isCycle_inv", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.IsCycle.conj", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": true, "tactics": ["rintro", "refine", "simpa"], "tactic_count": 3}
{"name": "Equiv.Perm.IsCycle.extendDomain", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": true, "tactics": ["rintro", "refine", "rw", "exact", "have", "rw", "rw", "simp", "exact"], "tactic_count": 9}
{"name": "Equiv.Perm.isCycle_iff_sameCycle", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.IsCycle.exists_pow_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": true, "tactics": ["let", "classical", "exact", "have", "rwa"], "tactic_count": 5}
{"name": "Equiv.Perm.isCycle_swap", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.IsSwap.isCycle", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "Equiv.Perm.swap_isSwap_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": true, "tactics": ["constructor", "intro", "apply", "aesop", "intro"], "tactic_count": 5}
{"name": "Equiv.Perm.IsCycle.two_le_card_support", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.IsCycle.zpowersEquivSupport", "kind": "definition", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.IsCycle.zpowersEquivSupport_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.IsCycle.zpowersEquivSupport_symm_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.IsCycle.orderOf", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": true, "tactics": ["rw", "convert"], "tactic_count": 2}
{"name": "Equiv.Perm.isCycle_swap_mul_aux₁", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": true, "tactics": ["intro", "induction", "zero", "succ", "intro", "obtain", "exact", "have", "have", "simpa", "obtain", "refine", "rw", "swap_apply_of_ne_of_ne"], "tactic_count": 14}
{"name": "Equiv.Perm.isCycle_swap_mul_aux₂", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.IsCycle.eq_swap_of_apply_apply_eq_self", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.IsCycle.swap_mul", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": true, "tactics": ["refine", "simp", "obtain", "exact"], "tactic_count": 4}
{"name": "Equiv.Perm.IsCycle.sign", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.IsCycle.of_pow", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": false, "tactics": ["have", "simp_rw", "exact", "obtain", "refine", "obtain", "exact"], "tactic_count": 7}
{"name": "Equiv.Perm.IsCycle.of_zpow", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": true, "tactics": ["cases", "exact", "simp", "exact"], "tactic_count": 4}
{"name": "Equiv.Perm.nodup_of_pairwise_disjoint_cycles", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.IsCycle.support_congr", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": false, "tactics": ["have", "refine", "intro", "obtain", "have", "obtain", "have", "intro", "exact", "rwa", "pow_apply_mem_support,", "refine", "simpa"], "tactic_count": 13}
{"name": "Equiv.Perm.IsCycle.eq_on_support_inter_nonempty_congr", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": true, "tactics": ["have", "have", "intro", "obtain", "rwa", "rw", "exact"], "tactic_count": 7}
{"name": "Equiv.Perm.IsCycle.support_pow_eq_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": true, "tactics": ["rw", "constructor", "intro", "refine", "rw", "intro", "apply", "intro", "contrapose", "ext", "by_cases", "rw", "obtain", "apply", "rw", "simpa"], "tactic_count": 16}
{"name": "Equiv.Perm.IsCycle.support_pow_of_pos_of_lt_orderOf", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.IsCycle.pow_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": true, "tactics": ["classical", "cases", "constructor", "intro", "have", "rw", "rintro", "refine", "simp", "have", "rw", "rcases", "exact", "rwa", "intro", "obtain", "have", "refine", "rw", "exact"], "tactic_count": 20}
{"name": "Equiv.Perm.IsCycle.pow_eq_one_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": true, "tactics": ["classical", "cases", "constructor", "intro", "obtain", "exact", "rintro", "by_cases", "rw", "contradiction", "rw", "obtain", "rw"], "tactic_count": 13}
{"name": "Equiv.Perm.IsCycle.pow_eq_one_iff'", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.IsCycle.pow_eq_one_iff''", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.IsCycle.pow_eq_pow_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": true, "tactics": ["classical", "cases", "constructor", "intro", "obtain", "exact", "rintro", "wlog", "exact", "suffices", "rw", "rw", "rw", "by_cases", "refine", "simp", "have", "simp", "rw", "contradiction"], "tactic_count": 20}
{"name": "Equiv.Perm.IsCycle.isCycle_pow_pos_of_lt_prime_order", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": true, "tactics": ["classical", "cases", "have", "refine", "rw", "exact", "obtain", "have", "rw", "refine", "rw", "exact"], "tactic_count": 12}
{"name": "Int.addLeft_one_isCycle", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.addRight_one_isCycle", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.IsCycle.isConj", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": false, "tactics": ["refine", "isConj_of_support_equiv", "intro", "simp", "obtain", "simp"], "tactic_count": 6}
{"name": "Equiv.Perm.IsCycle.isConj_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.IsCycleOn", "kind": "definition", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.isCycleOn_empty", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Equiv.Perm.isCycleOn_one", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Equiv.Perm.isCycleOn_singleton", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Equiv.Perm.isCycleOn_of_subsingleton", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.isCycleOn_inv", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Equiv.Perm.IsCycleOn.conj", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.isCycleOn_swap", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.IsCycleOn.apply_ne", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "exact"], "tactic_count": 3}
{"name": "Equiv.Perm.IsCycle.isCycleOn", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.isCycle_iff_exists_isCycleOn", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact", "rintro", "obtain", "exact"], "tactic_count": 6}
{"name": "Equiv.Perm.IsCycleOn.apply_mem_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.IsCycleOn.isCycle_subtypePerm", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Equiv.Perm.IsCycleOn.subtypePerm", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": true, "tactics": ["obtain", "haveI", "exact", "convert", "rw", "exact", "ne_of_apply_ne"], "tactic_count": 7}
{"name": "Equiv.Perm.IsCycleOn.pow_apply_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": true, "tactics": ["obtain", "rw", "simpa", "classical", "have", "have", "simp", "implies_true,", "rw", "simp"], "tactic_count": 10}
{"name": "Equiv.Perm.IsCycleOn.zpow_apply_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.IsCycleOn.pow_apply_eq_pow_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Equiv.Perm.IsCycleOn.zpow_apply_eq_zpow_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Equiv.Perm.IsCycleOn.pow_card_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.IsCycleOn.exists_pow_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": true, "tactics": ["classical", "obtain", "obtain", "refine", "rw", "sub_eq_iff_eq_add'.1", "simp", "exact"], "tactic_count": 8}
{"name": "Equiv.Perm.IsCycleOn.exists_pow_eq'", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": true, "tactics": ["lift", "obtain", "exact"], "tactic_count": 3}
{"name": "Equiv.Perm.IsCycleOn.range_pow", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.IsCycleOn.range_zpow", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.IsCycleOn.of_pow", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.IsCycleOn.of_zpow", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.IsCycleOn.extendDomain", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.IsCycleOn.countable", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": true, "tactics": ["obtain", "exact", "exact"], "tactic_count": 3}
{"name": "List.Nodup.isCycleOn_formPerm", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "rw", "refine", "simp", "rw"], "tactic_count": 6}
{"name": "Finset.exists_cycleOn", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": false, "tactics": ["refine", "convert", "simp"], "tactic_count": 3}
{"name": "Set.Countable.exists_cycleOn", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": true, "tactics": ["classical", "obtain", "refine", "convert", "simp", "haveI", "haveI", "obtain", "refine", "of_not_not", "convert", "rw", "ext", "simp"], "tactic_count": 14}
{"name": "Set.prod_self_eq_iUnion_perm", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp", "refine", "obtain", "exact", "rintro", "exact"], "tactic_count": 7}
{"name": "Finset.product_self_eq_disjiUnion_perm_aux", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": true, "tactics": ["obtain", "refine", "simp_rw", "rwa", "classical", "rintro", "simp", "forall_exists_index,", "rintro", "rw", "rw", "exact"], "tactic_count": 12}
{"name": "Finset.product_self_eq_disjiUnion_perm", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp", "refine", "obtain", "exact", "rintro", "exact"], "tactic_count": 7}
{"name": "Finset.sum_smul_sum_eq_sum_perm", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp_rw"], "tactic_count": 2}
{"name": "Finset.sum_mul_sum_eq_sum_perm", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.subtypePerm_apply_pow_of_mem", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Equiv.Perm.subtypePerm_apply_zpow_of_mem", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Equiv.Perm.subtypePermOfSupport", "kind": "definition", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.subtypePerm_of_support_le", "kind": "definition", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.IsCycle.nonempty_support", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Equiv.Perm.IsCycle.commute_iff'", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": true, "tactics": ["constructor", "intro", "have", "use", "obtain", "obtain", "use", "ext", "simp", "rw", "obtain", "simp", "rw", "simp", "exact", "rintro", "ext", "simp", "by_cases", "suffices", "rw", "simp", "intro", "have", "simp", "exact", "rw", "contrapose", "exact"], "tactic_count": 29}
{"name": "Equiv.Perm.IsCycle.commute_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "rw", "simp", "apply", "intro", "by_cases", "rw", "rw", "exact", "exact"], "tactic_count": 11}
{"name": "Equiv.Perm.zpow_eq_ofSubtype_subtypePerm_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": true, "tactics": ["constructor", "intro", "ext", "simp", "rw", "simp", "exact", "intro", "rw", "by_cases", "rw", "rw", "exact"], "tactic_count": 13}
{"name": "Equiv.Perm.cycle_zpow_mem_support_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Basic", "is_tactic_proof": true, "tactics": ["set", "set", "have", "rw", "exact", "simp", "apply", "simp", "obtain", "simp", "rw", "simp", "id_eq]", "have", "constructor", "intro", "simp", "use", "intro", "simp", "rw", "by_cases", "simp", "simp", "exact"], "tactic_count": 25}
{"name": "List.formPerm_disjoint_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Concrete", "is_tactic_proof": true, "tactics": ["rw", "constructor", "rintro", "specialize", "rw", "lia", "intro", "by_cases", "on_goal", "exact", "all_goals"], "tactic_count": 11}
{"name": "List.isCycle_formPerm", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Concrete", "is_tactic_proof": true, "tactics": ["rcases", "norm_num", "induction", "nil", "cons", "use", "constructor", "rwa", "intro", "have", "obtain", "use", "simp"], "tactic_count": 13}
{"name": "List.pairwise_sameCycle_formPerm", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Concrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.cycleOf_formPerm", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Concrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.cycleType_formPerm", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Concrete", "is_tactic_proof": true, "tactics": ["rw", "rw", "rw", "simp", "rw", "simp", "intro", "simp", "simp", "simpa", "simp"], "tactic_count": 11}
{"name": "List.formPerm_apply_mem_eq_next", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Concrete", "is_tactic_proof": true, "tactics": ["obtain", "rw"], "tactic_count": 2}
{"name": "Cycle.formPerm", "kind": "definition", "module": "Mathlib.GroupTheory.Perm.Cycle.Concrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.formPerm_coe", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Concrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cycle.formPerm_subsingleton", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Concrete", "is_tactic_proof": true, "tactics": ["obtain", "simp", "simp", "obtain", "simp", "simp", "simp"], "tactic_count": 7}
{"name": "Cycle.isCycle_formPerm", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Concrete", "is_tactic_proof": true, "tactics": ["induction", "exact"], "tactic_count": 2}
{"name": "Cycle.support_formPerm", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Concrete", "is_tactic_proof": true, "tactics": ["obtain", "refine", "rintro", "simpa"], "tactic_count": 4}
{"name": "Cycle.formPerm_eq_self_of_notMem", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Concrete", "is_tactic_proof": true, "tactics": ["induction", "simpa"], "tactic_count": 2}
{"name": "Cycle.formPerm_apply_mem_eq_next", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Concrete", "is_tactic_proof": true, "tactics": ["induction", "simpa"], "tactic_count": 2}
{"name": "Cycle.formPerm_reverse", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Concrete", "is_tactic_proof": true, "tactics": ["induction", "simpa"], "tactic_count": 2}
{"name": "Cycle.formPerm_eq_formPerm_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Concrete", "is_tactic_proof": true, "tactics": ["rw", "revert", "intro", "apply", "intro", "simpa"], "tactic_count": 6}
{"name": "Equiv.Perm.toList", "kind": "definition", "module": "Mathlib.GroupTheory.Perm.Cycle.Concrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.toList_one", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Concrete", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Equiv.Perm.toList_eq_nil_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Concrete", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Equiv.Perm.length_toList", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Concrete", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Equiv.Perm.toList_ne_singleton", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Concrete", "is_tactic_proof": true, "tactics": ["intro", "simpa"], "tactic_count": 2}
{"name": "Equiv.Perm.two_le_length_toList_iff_mem_support", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Concrete", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Equiv.Perm.length_toList_pos_of_mem_support", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Concrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.getElem_toList", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Concrete", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Equiv.Perm.toList_getElem_zero", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Concrete", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Equiv.Perm.mem_toList_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Concrete", "is_tactic_proof": true, "tactics": ["simp", "constructor", "rintro", "refine", "contrapose", "rw", "simp", "rintro", "simpa"], "tactic_count": 9}
{"name": "Equiv.Perm.nodup_toList", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Concrete", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "simp", "have", "rw", "intro", "rw", "rw", "simp", "rw", "rcases", "simp", "rw", "simp", "rw", "simp", "intro", "have", "have", "rw", "rw", "refine", "rw", "rw", "intro", "obtain", "rw"], "tactic_count": 27}
{"name": "Equiv.Perm.next_toList_eq_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Concrete", "is_tactic_proof": true, "tactics": ["rw", "obtain", "rw", "simp_rw", "rw", "simp_rw", "rw", "exact"], "tactic_count": 8}
{"name": "Equiv.Perm.toList_pow_apply_eq_rotate", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Concrete", "is_tactic_proof": true, "tactics": ["apply", "simp", "intro", "rw", "mul_apply]"], "tactic_count": 5}
{"name": "Equiv.Perm.SameCycle.toList_isRotated", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Concrete", "is_tactic_proof": true, "tactics": ["by_cases", "obtain", "simp", "simp", "use", "rw", "rw", "rwa"], "tactic_count": 8}
{"name": "Equiv.Perm.pow_apply_mem_toList_iff_mem_support", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Concrete", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw"], "tactic_count": 3}
{"name": "Equiv.Perm.toList_formPerm_nil", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Concrete", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Equiv.Perm.toList_formPerm_singleton", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Concrete", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Equiv.Perm.toList_formPerm_nontrivial", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Concrete", "is_tactic_proof": true, "tactics": ["have", "have", "refine", "rintro", "simp", "rw", "refine", "simp", "simp"], "tactic_count": 9}
{"name": "Equiv.Perm.toList_formPerm_isRotated_self", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Concrete", "is_tactic_proof": true, "tactics": ["obtain", "have", "rw", "rw", "simp", "rw", "simp", "simpa", "simpa"], "tactic_count": 9}
{"name": "Equiv.Perm.formPerm_toList", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Concrete", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "ext", "by_cases", "obtain", "rw", "pow_succ',", "rw", "exact", "rw", "simp"], "tactic_count": 11}
{"name": "Equiv.Perm.toCycle", "kind": "definition", "module": "Mathlib.GroupTheory.Perm.Cycle.Concrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.toCycle_eq_toList", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Concrete", "is_tactic_proof": true, "tactics": ["have", "rw", "simp"], "tactic_count": 3}
{"name": "Equiv.Perm.exists_toCycle_toList", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Concrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.nodup_toCycle", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Concrete", "is_tactic_proof": true, "tactics": ["obtain", "simpa"], "tactic_count": 2}
{"name": "Equiv.Perm.nontrivial_toCycle", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Concrete", "is_tactic_proof": true, "tactics": ["obtain", "simp"], "tactic_count": 2}
{"name": "Equiv.Perm.mem_toCycle_iff_support", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Concrete", "is_tactic_proof": true, "tactics": ["constructor", "have", "simp", "intro", "have", "exact", "intro", "simp", "use", "exact"], "tactic_count": 10}
{"name": "Equiv.Perm.toCycle_next", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Concrete", "is_tactic_proof": true, "tactics": ["have", "simp", "exact"], "tactic_count": 3}
{"name": "Equiv.Perm.isoCycle", "kind": "definition", "module": "Mathlib.GroupTheory.Perm.Cycle.Concrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.IsCycle.existsUnique_cycle", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Concrete", "is_tactic_proof": true, "tactics": ["cases", "obtain", "refine", "simp", "rintro", "simp", "refine", "contrapose", "suffices", "rw", "exact", "rw", "refine", "simpa"], "tactic_count": 14}
{"name": "Equiv.Perm.IsCycle.existsUnique_cycle_subtype", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Concrete", "is_tactic_proof": true, "tactics": ["obtain", "refine", "rintro", "simpa"], "tactic_count": 4}
{"name": "Equiv.Perm.IsCycle.existsUnique_cycle_nontrivial_subtype", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Concrete", "is_tactic_proof": true, "tactics": ["obtain", "refine", "rw", "subst", "intro", "refine", "simpa", "simpa", "rintro", "simpa"], "tactic_count": 10}
{"name": "Equiv.Perm.isoCycle'", "kind": "definition", "module": "Mathlib.GroupTheory.Perm.Cycle.Concrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.termC[_,]", "kind": "definition", "module": "Mathlib.GroupTheory.Perm.Cycle.Concrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm._aux_Mathlib_GroupTheory_Perm_Cycle_Concrete___macroRules_Equiv_Perm_termC[_,]_1", "kind": "definition", "module": "Mathlib.GroupTheory.Perm.Cycle.Concrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.instRepr", "kind": "instance", "module": "Mathlib.GroupTheory.Perm.Cycle.Concrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.cycleOf", "kind": "definition", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.cycleOf_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": true, "tactics": ["dsimp", "split_ifs", "apply", "exact", "apply", "exact"], "tactic_count": 6}
{"name": "Equiv.Perm.cycleOf_inv", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.cycleOf_pow_apply_self", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": true, "tactics": ["intro", "induction", "zero", "succ", "rw", "exact"], "tactic_count": 6}
{"name": "Equiv.Perm.cycleOf_zpow_apply_self", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": true, "tactics": ["intro", "cases", "ofNat", "negSucc"], "tactic_count": 4}
{"name": "Equiv.Perm.SameCycle.cycleOf_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.cycleOf_apply_of_not_sameCycle", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.SameCycle.cycleOf_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": true, "tactics": ["ext", "rw", "split_ifs", "exact", "exact"], "tactic_count": 5}
{"name": "Equiv.Perm.cycleOf_apply_apply_zpow_self", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "Equiv.Perm.cycleOf_apply_apply_pow_self", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "Equiv.Perm.cycleOf_apply_apply_self", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "Equiv.Perm.cycleOf_apply_self", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.IsCycle.cycleOf_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.cycleOf_eq_one_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "by_cases", "rw", "exact"], "tactic_count": 5}
{"name": "Equiv.Perm.cycleOf_self_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.cycleOf_self_apply_pow", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.cycleOf_self_apply_zpow", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.IsCycle.cycleOf", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": true, "tactics": ["by_cases", "rwa", "rwa"], "tactic_count": 3}
{"name": "Equiv.Perm.cycleOf_one", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.isCycle_cycleOf", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.pow_mod_orderOf_cycleOf_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Equiv.Perm.cycleOf_mul_of_apply_right_eq_self", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "obtain", "rw", "simp", "rw", "contrapose", "obtain", "refine", "simp"], "tactic_count": 10}
{"name": "Equiv.Perm.Disjoint.cycleOf_mul_distrib", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": true, "tactics": ["classical", "rcases", "simp", "simp"], "tactic_count": 4}
{"name": "_private.Mathlib.GroupTheory.Perm.Cycle.Factors.0.Equiv.Perm.mem_support_cycleOf_iff_aux", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "simp", "rw", "split_ifs", "simp", "rcases", "rw", "simpa", "simpa"], "tactic_count": 10}
{"name": "_private.Mathlib.GroupTheory.Perm.Cycle.Factors.0.Equiv.Perm.mem_support_cycleOf_iff'_aux", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Equiv.Perm.isCycle_cycleOf_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "_private.Mathlib.GroupTheory.Perm.Cycle.Factors.0.Equiv.Perm.isCycleOn_support_cycleOf_aux", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.GroupTheory.Perm.Cycle.Factors.0.Equiv.Perm.SameCycle.exists_pow_eq_of_mem_support_aux", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Equiv.Perm.instDecidableRelSameCycle", "kind": "instance", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.two_le_card_support_cycleOf_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": true, "tactics": ["refine", "contrapose", "rw", "simp"], "tactic_count": 4}
{"name": "Equiv.Perm.support_cycleOf_nonempty", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Equiv.Perm.mem_support_cycleOf_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.mem_support_cycleOf_iff'", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.sameCycle_iff_cycleOf_eq_of_mem_support", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "Equiv.Perm.support_cycleOf_eq_nil_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Equiv.Perm.isCycleOn_support_cycleOf", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.SameCycle.exists_pow_eq_of_mem_support", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.support_cycleOf_le", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": true, "tactics": ["intro", "rw", "split_ifs", "exact", "exact"], "tactic_count": 5}
{"name": "Equiv.Perm.SameCycle.mem_support_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.pow_mod_card_support_cycleOf_self_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "rw"], "tactic_count": 3}
{"name": "Equiv.Perm.SameCycle.exists_pow_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": true, "tactics": ["by_cases", "obtain", "rcases", "refine", "simp", "subst", "rw", "exact", "refine", "obtain", "rw", "rw"], "tactic_count": 12}
{"name": "Equiv.Perm.zpow_eq_zpow_on_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": true, "tactics": ["rw", "conv_lhs", "simp", "rw", "rw", "rw", "exact", "simp"], "tactic_count": 8}
{"name": "Equiv.Perm.cycleFactorsAux", "kind": "definition", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.mem_list_cycles_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": false, "tactics": ["suffices", "exact", "intro", "classical", "cases", "constructor", "intro", "exact", "intro", "have", "intro", "rw", "rwa", "obtain", "rw", "obtain", "have", "have", "intro", "rw", "convert", "refine", "exact"], "tactic_count": 23}
{"name": "Equiv.Perm.list_cycles_perm_list_cycles", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": true, "tactics": ["classical", "refine", "by_cases", "obtain", "rw", "exact"], "tactic_count": 6}
{"name": "Equiv.Perm.cycleFactors", "kind": "definition", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.truncCycleFactors", "kind": "definition", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.cycleFactorsFinset", "kind": "definition", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.cycleFactorsFinset_eq_list_toFinset", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": true, "tactics": ["obtain", "have", "rw", "rw", "constructor", "intro", "have", "have", "refine", "exact", "have", "rwa", "rw", "refine", "exact", "rintro", "refine", "refine", "rw"], "tactic_count": 19}
{"name": "Equiv.Perm.cycleFactorsFinset_eq_finset", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": true, "tactics": ["obtain", "simp"], "tactic_count": 2}
{"name": "Equiv.Perm.cycleFactorsFinset_pairwise_disjoint", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.cycleFactorsFinset_mem_commute", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.cycleFactorsFinset_mem_commute'", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": true, "tactics": ["rcases", "apply", "exact"], "tactic_count": 3}
{"name": "Equiv.Perm.mem_cycleFactorsFinset_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": true, "tactics": ["obtain", "rw", "rw", "simpa"], "tactic_count": 4}
{"name": "Equiv.Perm.cycleOf_mem_cycleFactorsFinset_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": true, "tactics": ["rw", "constructor", "rintro", "contrapose", "rw", "simp", "intro", "refine", "intro", "rw", "rw", "split_ifs", "rfl", "rw", "contradiction"], "tactic_count": 15}
{"name": "Equiv.Perm.cycleOf_ne_one_iff_mem_cycleFactorsFinset", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Equiv.Perm.mem_cycleFactorsFinset_support_le", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": true, "tactics": ["rw", "intro", "rwa"], "tactic_count": 3}
{"name": "Equiv.Perm.support_zpowers_of_mem_cycleFactorsFinset_le", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": true, "tactics": ["obtain", "simp", "exact"], "tactic_count": 3}
{"name": "Equiv.Perm.pairwise_disjoint_of_mem_zpowers", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.pairwise_commute_of_mem_zpowers", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.disjoint_ofSubtype_noncommPiCoprod", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": true, "tactics": ["apply", "intro", "apply", "intro", "exact", "exact", "intro", "simp", "exact"], "tactic_count": 9}
{"name": "Equiv.Perm.commute_ofSubtype_noncommPiCoprod", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.mem_support_iff_mem_support_of_mem_cycleFactorsFinset", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": true, "tactics": ["constructor", "intro", "use", "rw", "exact", "rintro", "exact"], "tactic_count": 7}
{"name": "Equiv.Perm.cycleFactorsFinset_eq_empty_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Equiv.Perm.cycleFactorsFinset_one", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Equiv.Perm.cycleFactorsFinset_eq_singleton_self_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Equiv.Perm.IsCycle.cycleFactorsFinset_eq_singleton", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.cycleFactorsFinset_eq_singleton_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": false, "tactics": ["suffices", "rw", "simpa", "rintro", "exact"], "tactic_count": 5}
{"name": "Equiv.Perm.cycleFactorsFinset_injective", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": true, "tactics": ["intro", "rw", "simpa"], "tactic_count": 3}
{"name": "Equiv.Perm.Disjoint.disjoint_cycleFactorsFinset", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": true, "tactics": ["rw", "rw", "intro", "simp", "obtain", "have", "tauto"], "tactic_count": 7}
{"name": "Equiv.Perm.Disjoint.cycleFactorsFinset_mul_eq_union", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp", "rw", "exact", "h.mono", "rw", "rw"], "tactic_count": 8}
{"name": "Equiv.Perm.disjoint_mul_inv_of_mem_cycleFactorsFinset", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": true, "tactics": ["rw", "intro", "by_cases", "exact", "left", "rw", "simp"], "tactic_count": 7}
{"name": "Equiv.Perm.cycle_is_cycleOf", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": false, "tactics": ["suffices", "rw", "apply", "exact", "let", "let", "rw", "simp", "exact"], "tactic_count": 9}
{"name": "Equiv.Perm.isCycleOn_support_of_mem_cycleFactorsFinset", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact"], "tactic_count": 3}
{"name": "Equiv.Perm.eq_cycleOf_of_mem_cycleFactorsFinset_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": true, "tactics": ["refine", "rintro", "rw", "exact"], "tactic_count": 4}
{"name": "Equiv.Perm.zpow_apply_mem_support_of_mem_cycleFactorsFinset_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": true, "tactics": ["rw", "eq_cycleOf_of_mem_cycleFactorsFinset_iff"], "tactic_count": 2}
{"name": "Equiv.Perm.mem_cycleFactorsFinset_conj", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": false, "tactics": ["suffices", "refine", "have", "rw", "exact", "intro", "simp", "apply", "intro", "simp", "apply", "simp_all"], "tactic_count": 12}
{"name": "Equiv.Perm.commute_of_mem_cycleFactorsFinset_commute", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": true, "tactics": ["rw", "apply", "simpa"], "tactic_count": 3}
{"name": "Equiv.Perm.self_mem_cycle_factors_commute", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": true, "tactics": ["apply", "intro", "by_cases", "rw", "apply"], "tactic_count": 5}
{"name": "Equiv.Perm.mem_support_cycle_of_cycle", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": true, "tactics": ["intro", "simp", "by_cases", "rw", "rw"], "tactic_count": 5}
{"name": "Equiv.Perm.mem_cycleFactorsFinset_support", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.cycle_induction_on", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": true, "tactics": ["cases", "suffices", "classical", "let", "exact", "intro", "induction", "nil", "cons", "intro", "rw", "exact", "induction_disjoint"], "tactic_count": 13}
{"name": "Equiv.Perm.cycleFactorsFinset_mul_inv_mem_eq_sdiff", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": true, "tactics": ["revert", "refine", "cycle_induction_on", "simp", "intro", "simp", "simp", "intro", "simp_rw", "rintro", "rw", "rw", "intro", "rcases", "exact", "refine", "by_cases", "rw", "simpa", "rw", "rw", "contradiction", "exact", "rw", "rw", "intro", "rcases", "exact", "refine", "by_cases", "rw", "simpa", "rw", "rw", "contradiction", "exact"], "tactic_count": 36}
{"name": "Equiv.Perm.IsCycle.forall_commute_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": true, "tactics": ["apply", "intro", "apply", "intro", "exact"], "tactic_count": 5}
{"name": "Equiv.Perm.subtypePerm_on_cycleFactorsFinset", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": true, "tactics": ["ext", "simp", "exact"], "tactic_count": 3}
{"name": "Equiv.Perm.commute_iff_of_mem_cycleFactorsFinset", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "is_tactic_proof": true, "tactics": ["rw", "apply", "intro", "simp", "apply", "intro", "rw"], "tactic_count": 7}
{"name": "List.exists_pw_disjoint_with_card", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.PossibleTypes", "is_tactic_proof": true, "tactics": ["let", "let", "have", "intro", "apply", "rw", "exact", "let", "have", "intro", "conv_rhs", "rw", "simp", "use", "constructor", "rw", "simp", "constructor", "intro", "rw", "rintro", "apply", "obtain", "apply", "rw", "exact", "refine", "apply", "intro", "apply", "intro", "simpa", "exact"], "tactic_count": 33}
{"name": "Equiv.Perm.exists_with_cycleType_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.PossibleTypes", "is_tactic_proof": true, "tactics": ["constructor", "intro", "obtain", "constructor", "rw", "exact", "intro", "rw", "exact", "rintro", "have", "simp", "exact", "obtain", "use", "have", "intro", "apply", "rw", "exact", "rw", "rw", "apply", "rw", "apply", "intro", "rw", "rw", "grind", "simpa", "rw", "apply", "intro", "rw", "exact"], "tactic_count": 35}
{"name": "Equiv.Perm.cycleType", "kind": "definition", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.cycleType_def", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.cycleType_eq'", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": true, "tactics": ["rw", "congr", "rw", "exact"], "tactic_count": 4}
{"name": "Equiv.Perm.cycleType_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": true, "tactics": ["have", "rw", "simp", "simpa", "simpa", "simp"], "tactic_count": 6}
{"name": "Equiv.Perm.CycleType.count_def", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": true, "tactics": ["rw", "rw", "simp", "congr", "apply", "intro", "simp"], "tactic_count": 7}
{"name": "Equiv.Perm.cycleType_eq_zero", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Equiv.Perm.cycleType_one", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.card_cycleType_eq_zero", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Equiv.Perm.card_cycleType_pos", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.two_le_of_mem_cycleType", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": false, "tactics": ["simp", "obtain", "exact"], "tactic_count": 3}
{"name": "Equiv.Perm.one_lt_of_mem_cycleType", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.IsCycle.cycleType", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.card_cycleType_eq_one", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "cycleFactorsFinset_eq_singleton_iff]", "grind"], "tactic_count": 4}
{"name": "Equiv.Perm.Disjoint.cycleType_mul", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": false, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Equiv.Perm.cycleType_inv", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.cycleType_conj", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": true, "tactics": ["induction", "base_one", "base_cycles", "induction_disjoint"], "tactic_count": 4}
{"name": "Equiv.Perm.sum_cycleType", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": true, "tactics": ["induction", "base_one", "base_cycles", "induction_disjoint"], "tactic_count": 4}
{"name": "Equiv.Perm.sum_cycleType_le", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.card_fixedPoints", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": true, "tactics": ["rw", "congr"], "tactic_count": 2}
{"name": "Equiv.Perm.sign_of_cycleType'", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": true, "tactics": ["induction", "base_one", "base_cycles", "induction_disjoint"], "tactic_count": 4}
{"name": "Equiv.Perm.sign_of_cycleType", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": true, "tactics": ["rw", "induction", "empty", "cons", "rw", "simp"], "tactic_count": 6}
{"name": "Equiv.Perm.lcm_cycleType", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": true, "tactics": ["induction", "base_one", "base_cycles", "induction_disjoint"], "tactic_count": 4}
{"name": "Equiv.Perm.dvd_of_mem_cycleType", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Equiv.Perm.orderOf_cycleOf_dvd_orderOf", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "simp", "refine", "rw", "refine", "rwa", "simp"], "tactic_count": 8}
{"name": "Equiv.Perm.two_dvd_card_support", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.cycleType_prime_order", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": true, "tactics": ["refine", "rw", "rw", "exact", "exact"], "tactic_count": 5}
{"name": "Equiv.Perm.pow_prime_eq_one_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": true, "tactics": ["rw", "apply", "exact"], "tactic_count": 3}
{"name": "Equiv.Perm.cycleType_of_pow_prime_eq_one", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.isCycle_of_prime_order", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": true, "tactics": ["obtain", "rw", "rw"], "tactic_count": 3}
{"name": "Equiv.Perm.cycleType_le_of_mem_cycleFactorsFinset", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": true, "tactics": ["have", "rw", "refine", "simpa"], "tactic_count": 4}
{"name": "Equiv.Perm.cycleType_mul_inv_mem_cycleFactorsFinset_eq_sub", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.isConj_of_cycleType_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": true, "tactics": ["induction", "base_one", "rw", "rw", "base_cycles", "have", "rw", "apply", "rwa", "induction_disjoint", "rw", "have", "obtain", "have", "refine", "rw", "have", "rw", "rw", "refine", "rw", "rwa", "exact"], "tactic_count": 23}
{"name": "Equiv.Perm.isConj_iff_cycleType_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.cycleType_extendDomain", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": true, "tactics": ["induction", "base_one", "base_cycles", "induction_disjoint", "rw"], "tactic_count": 5}
{"name": "Equiv.Perm.cycleType_ofSubtype", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.mem_cycleType_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": true, "tactics": ["constructor", "intro", "obtain", "rw", "obtain", "rw", "refine", "rw", "exact", "rintro", "simp"], "tactic_count": 11}
{"name": "Equiv.Perm.le_card_support_of_mem_cycleType", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.cycleType_of_card_le_mem_cycleType_add_two", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": true, "tactics": ["obtain", "suffices", "contrapose", "grw"], "tactic_count": 4}
{"name": "Equiv.Perm.sign_of_cycleType_eq_replicate", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": true, "tactics": ["rw", "obtain", "rw", "show", "rw"], "tactic_count": 5}
{"name": "Equiv.Perm.sign_of_pow_two_eq_one", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Equiv.Perm.card_compl_support_modEq", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": true, "tactics": ["rw", "refine", "obtain", "obtain", "exact", "exact"], "tactic_count": 6}
{"name": "Equiv.Perm.card_fixedPoints_modEq", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": false, "tactics": ["let", "leftInverse_iff_comp.mpr", "have", "rw", "exact", "suffices", "suffices", "simp"], "tactic_count": 8}
{"name": "Equiv.Perm.exists_fixed_point_of_prime", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": true, "tactics": ["classical", "contrapose", "simp_rw", "exact"], "tactic_count": 4}
{"name": "Equiv.Perm.exists_fixed_point_of_prime'", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": true, "tactics": ["classical", "have", "obtain", "a", "exact"], "tactic_count": 5}
{"name": "Equiv.Perm.isCycle_of_prime_order'", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Equiv.Perm.isCycle_of_prime_order''", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.vectorsProdEqOne", "kind": "definition", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.VectorsProdEqOne.mem_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.VectorsProdEqOne.zero_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.VectorsProdEqOne.one_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": false, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Equiv.Perm.VectorsProdEqOne.zeroUnique", "kind": "instance", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Equiv.Perm.VectorsProdEqOne.oneUnique", "kind": "instance", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Equiv.Perm.VectorsProdEqOne.vectorEquiv", "kind": "definition", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.VectorsProdEqOne.equivVector", "kind": "definition", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.VectorsProdEqOne.instFintypeElemVectorVectorsProdEqOne", "kind": "instance", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.VectorsProdEqOne.card", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.VectorsProdEqOne.rotate", "kind": "definition", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.VectorsProdEqOne.rotate_zero", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.VectorsProdEqOne.rotate_rotate", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.VectorsProdEqOne.rotate_length", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_prime_orderOf_dvd_card", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": true, "tactics": ["have", "have", "calc", "p", "let", "have", "have", "have", "let", "rw", "have", "rw", "simp", "k", "replace", "let", "have", "obtain", "refine", "rw", "rw", "simp"], "tactic_count": 22}
{"name": "exists_prime_addOrderOf_dvd_card", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_prime_orderOf_dvd_card'", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "Equiv.Perm.subgroup_eq_top_of_swap_mem", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": true, "tactics": ["haveI", "obtain", "have", "have", "have", "have", "rw", "exact"], "tactic_count": 8}
{"name": "Equiv.Perm.partition", "kind": "definition", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.parts_partition", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.filter_parts_partition_eq_cycleType", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": false, "tactics": ["rw", "rw", "decide"], "tactic_count": 3}
{"name": "Equiv.Perm.partition_eq_of_isConj", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "rw"], "tactic_count": 4}
{"name": "Equiv.Perm.isSwap_iff_cycleType", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": true, "tactics": ["constructor", "intro", "simpa", "intro", "simp"], "tactic_count": 5}
{"name": "Equiv.Perm.IsSwap.orderOf", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "Equiv.Perm.IsThreeCycle", "kind": "definition", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.IsThreeCycle.cycleType", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.IsThreeCycle.card_support", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "card_support_eq_three_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": true, "tactics": ["refine", "by_cases", "rw", "exact", "obtain", "by_cases", "rw", "rw", "obtain", "rw", "have", "cases"], "tactic_count": 12}
{"name": "Equiv.Perm.IsThreeCycle.isCycle", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Equiv.Perm.IsThreeCycle.sign", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Equiv.Perm.IsThreeCycle.inv", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Equiv.Perm.IsThreeCycle.inv_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.IsThreeCycle.orderOf", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Equiv.Perm.IsThreeCycle.isThreeCycle_sq", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": true, "tactics": ["rw", "rw", "norm_num"], "tactic_count": 3}
{"name": "Equiv.Perm.isThreeCycle_swap_mul_swap_same", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": false, "tactics": ["suffices", "rw", "simp", "apply", "simp", "simp", "grind"], "tactic_count": 7}
{"name": "Equiv.Perm.IsThreeCycle.support_eq_iff_mem_support", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": true, "tactics": ["constructor", "intro", "intro", "symm", "apply", "apply", "apply", "rwa", "simpa", "rw", "simp", "rw", "rw", "simp", "simpa", "simp", "contrapose", "rcases", "exact", "suffices", "simp"], "tactic_count": 21}
{"name": "Equiv.Perm.IsThreeCycle.nodup_iff_mem_support", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "grind", "rw", "intro", "suffices", "exact"], "tactic_count": 8}
{"name": "Equiv.Perm.IsThreeCycle.eq_swap_mul_swap_iff_mem_support", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "intro", "apply", "simpa", "intro", "have", "have", "ext", "simp", "by_cases", "simp", "rcases", "rw", "simp", "rw", "simp", "suffices", "simp", "rw", "rw", "simpa"], "tactic_count": 23}
{"name": "Equiv.Perm.swap_mul_swap_same_mem_closure_three_cycles", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": true, "tactics": ["by_cases", "subst", "simp", "exact"], "tactic_count": 4}
{"name": "Equiv.Perm.IsSwap.mul_mem_closure_three_cycles", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "by_cases", "subst", "exact", "have", "rw", "exact", "mul_mem"], "tactic_count": 9}
{"name": "Equiv.Perm.cycleType_swap_mul_swap_of_nodup", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "is_tactic_proof": true, "tactics": ["rw", "rw", "simp", "rw", "rw"], "tactic_count": 5}
{"name": "DomMulAct.mem_stabilizer_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.DomMulAct", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DomMulAct.stabilizerEquiv_invFun", "kind": "definition", "module": "Mathlib.GroupTheory.Perm.DomMulAct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.stabilizerEquiv_invFun_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.DomMulAct", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "DomMulAct.comp_stabilizerEquiv_invFun", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.DomMulAct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.stabilizerEquiv_invFun_aux", "kind": "definition", "module": "Mathlib.GroupTheory.Perm.DomMulAct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.stabilizerMulEquiv", "kind": "definition", "module": "Mathlib.GroupTheory.Perm.DomMulAct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.stabilizerMulEquiv_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.DomMulAct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.stabilizer_card", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.DomMulAct", "is_tactic_proof": true, "tactics": ["rw", "exact", "rfl"], "tactic_count": 3}
{"name": "DomMulAct.stabilizer_ncard", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.DomMulAct", "is_tactic_proof": true, "tactics": ["classical", "cases", "simp", "exact"], "tactic_count": 4}
{"name": "DomMulAct.stabilizer_card'", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.DomMulAct", "is_tactic_proof": true, "tactics": ["set", "suffices", "simp", "apply", "exact", "exact", "simp", "intro", "apply", "apply", "apply", "intro", "rw", "simp", "intro", "simp", "apply", "intro", "simp"], "tactic_count": 19}
{"name": "Equiv.Perm.decomposeFin", "kind": "definition", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.decomposeFin_symm_of_refl", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Equiv.Perm.decomposeFin_symm_of_one", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.decomposeFin_symm_apply_zero", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Equiv.Perm.decomposeFin_symm_apply_succ", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": true, "tactics": ["refine", "simp", "intro", "by_cases", "simp", "simp"], "tactic_count": 6}
{"name": "Equiv.Perm.decomposeFin_symm_apply_one", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Equiv.Perm.decomposeFin.symm_sign", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": true, "tactics": ["refine"], "tactic_count": 1}
{"name": "Finset.univ_perm_fin_succ", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finRotate_succ_eq_decomposeFin", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": true, "tactics": ["ext", "cases", "refine", "simp", "rw", "split_ifs", "simp", "rw"], "tactic_count": 8}
{"name": "sign_finRotate", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "simp"], "tactic_count": 5}
{"name": "support_finRotate", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "support_finRotate_of_le", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": true, "tactics": ["obtain", "rw"], "tactic_count": 2}
{"name": "isCycle_finRotate", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": true, "tactics": ["refine", "clear", "obtain", "rw", "induction", "zero", "succ", "rw", "rw", "exact"], "tactic_count": 10}
{"name": "isCycle_finRotate_of_le", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact"], "tactic_count": 3}
{"name": "cycleType_finRotate", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "cycleType_finRotate_of_le", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": true, "tactics": ["obtain", "rw"], "tactic_count": 2}
{"name": "Fin.cycleRange", "kind": "definition", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.cycleRange_of_gt", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "Fin.cycleRange_of_le", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "split_ifs", "have", "simpa", "rw", "rfl", "have", "have", "val_add_one_of_lt", "exact"], "tactic_count": 12}
{"name": "Fin.coe_cycleRange_of_le", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": true, "tactics": ["rcases", "exact", "rw", "split_ifs", "rfl", "exact", "val_add_one_of_lt"], "tactic_count": 7}
{"name": "Fin.cycleRange_of_lt", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.coe_cycleRange_of_lt", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.cycleRange_of_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.cycleRange_self", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.cycleRange_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": true, "tactics": ["split_ifs", "exact", "exact", "exact"], "tactic_count": 4}
{"name": "Fin.cycleRange_zero", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": true, "tactics": ["ext", "rcases", "simp", "rw"], "tactic_count": 4}
{"name": "Fin.cycleRange_last", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "Fin.cycleRange_mk_zero", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.sign_cycleRange", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.succAbove_cycleRange", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": true, "tactics": ["cases", "rcases", "rcases", "have", "ext", "rw", "rw", "apply", "exact", "rw", "simpa", "rw", "rw", "apply", "rw", "apply", "apply", "simpa"], "tactic_count": 18}
{"name": "Fin.cycleRange_succAbove", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": true, "tactics": ["rcases", "rw", "rw"], "tactic_count": 3}
{"name": "Fin.cycleRange_symm_zero", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.cycleRange_symm_succ", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.insertNth_apply_cycleRange_symm", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Fin.insertNth_comp_cycleRange_symm", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Fin.cons_apply_cycleRange", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.cons_comp_cycleRange", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Fin.isCycle_cycleRange", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": true, "tactics": ["obtain", "cases", "exact", "exact"], "tactic_count": 4}
{"name": "Fin.cycleType_cycleRange", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": true, "tactics": ["obtain", "cases", "exact", "simp"], "tactic_count": 4}
{"name": "Fin.isThreeCycle_cycleRange_two", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Fin.instNeZeroNatHSubVal_mathlib", "kind": "instance", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.cycleIcc", "kind": "definition", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.cycleIcc_def_le", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.cycleIcc_def_gt", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.cycleIcc_def_gt'", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.cycleIcc_of_lt", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": true, "tactics": ["by_cases", "simpa", "simp"], "tactic_count": 3}
{"name": "Fin.cycleIcc_to_cycleRange", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.cycleIcc_of_gt", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": true, "tactics": ["by_cases", "have", "have", "subNat", "simp", "coe_toEmbedding,", "rw", "exact", "exact", "simp"], "tactic_count": 10}
{"name": "Fin.cycleIcc_of_le_of_le", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": true, "tactics": ["have", "have", "have", "subNat", "simp", "coe_toEmbedding,", "refine", "split_ifs", "have", "eq_of_val_eq", "simpa", "have", "simpa", "rw", "simp", "rw", "lia"], "tactic_count": 17}
{"name": "Fin.cycleIcc_of_ge_of_lt", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.cycleIcc_of_last", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.cycleIcc_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": true, "tactics": ["ext", "simp", "rcases", "simp", "simp", "simp"], "tactic_count": 6}
{"name": "Fin.cycleIcc_ge", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rw"], "tactic_count": 3}
{"name": "Fin.sign_cycleIcc_of_le", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.sign_cycleIcc_of_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.sign_cycleIcc_of_ge", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rw"], "tactic_count": 3}
{"name": "Fin.isCycle_cycleIcc", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Fin.cycleType_cycleIcc_of_lt", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Fin.cycleType_cycleIcc_of_ge", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Fin.cycleIcc_zero_eq_cycleRange", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": true, "tactics": ["ext", "rcases", "simp", "simp", "simp"], "tactic_count": 5}
{"name": "Fin.cycleIcc.trans", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": true, "tactics": ["ext", "rcases", "simp", "rcases", "simp", "rcases", "simp", "split_ifs", "repeat", "simp", "split_ifs", "exact", "simp"], "tactic_count": 13}
{"name": "Fin.cycleIcc.trans_left_one", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.cycleIcc.trans_right_one", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Equiv.Perm.sign_eq_prod_prod_Iio", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": false, "tactics": ["suffices", "rw", "convert", "simp", "simp", "refine", "rw"], "tactic_count": 7}
{"name": "Equiv.Perm.sign_eq_prod_prod_Ioi", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "Equiv.Perm.prod_Iio_comp_eq_sign_mul_prod", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": false, "tactics": ["simp_rw", "set", "have", "ext", "suffices", "refine", "rintro", "exact", "obtain", "exact", "exact", "nth_rw", "rw", "refine", "replace", "obtain", "simp", "simp"], "tactic_count": 18}
{"name": "Equiv.Perm.prod_Ioi_comp_eq_sign_mul_prod", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Fin", "is_tactic_proof": true, "tactics": ["convert", "apply", "convert", "apply"], "tactic_count": 4}
{"name": "Equiv.Perm.isConj_of_support_equiv", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Finite", "is_tactic_proof": true, "tactics": ["refine", "rw", "ext", "simp", "by_cases", "rw", "exact", "rwa"], "tactic_count": 8}
{"name": "Equiv.Perm.perm_symm_on_of_perm_on_finset", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Finite", "is_tactic_proof": false, "tactics": ["have", "obtain", "simpa"], "tactic_count": 3}
{"name": "Equiv.Perm.perm_symm_mapsTo_of_mapsTo", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Finite", "is_tactic_proof": true, "tactics": ["cases", "exact", "perm_symm_on_of_perm_on_finset"], "tactic_count": 3}
{"name": "Equiv.Perm.perm_symm_mapsTo_iff_mapsTo", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.perm_symm_on_of_perm_on_finite", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Finite", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "Equiv.Perm.subtypePermOfFintype", "kind": "abbrev", "module": "Mathlib.GroupTheory.Perm.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.subtypePermOfFintype_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.subtypePermOfFintype_one", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.perm_mapsTo_inl_iff_mapsTo_inr", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Finite", "is_tactic_proof": false, "tactics": ["constructor", "classical", "rw", "intro", "rcases", "rintro", "obtain", "grind", "rintro", "rintro", "rintro", "obtain", "grind"], "tactic_count": 13}
{"name": "Equiv.Perm.mem_sumCongrHom_range_of_perm_mapsTo_inl", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Finite", "is_tactic_proof": true, "tactics": ["classical", "have", "have", "exact", "let", "let", "let", "let", "rw", "use", "rw", "ext", "rw", "rw", "dsimp", "rw", "rw", "ofInjective_apply]", "dsimp", "rw"], "tactic_count": 20}
{"name": "Equiv.Perm.Disjoint.orderOf", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.Disjoint.extendDomain", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Finite", "is_tactic_proof": true, "tactics": ["intro", "by_cases", "refine", "intro", "rw", "left", "rw"], "tactic_count": 7}
{"name": "Equiv.Perm.Disjoint.isConj_mul", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Finite", "is_tactic_proof": true, "tactics": ["classical", "cases", "obtain", "obtain", "have", "have", "rw", "have", "have", "refine", "refine", "simp", "intro", "simp", "rw", "rcases", "rw", "rw", "simp", "apply_eq_iff_eq,", "have", "rw", "rw", "rwa", "rwa", "rwa", "rw", "rw", "simp", "have", "rw", "rw", "rwa", "rwa", "rwa"], "tactic_count": 35}
{"name": "Equiv.Perm.apply_mem_fixedPoints_iff_mem_of_mem_centralizer", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Finite", "is_tactic_proof": true, "tactics": ["simp", "simp", "rw"], "tactic_count": 3}
{"name": "Equiv.Perm.disjoint_ofSubtype_of_memFixedPoints_self", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Finite", "is_tactic_proof": true, "tactics": ["rw", "intro", "by_cases", "right", "left"], "tactic_count": 5}
{"name": "Equiv.Perm.support_pow_coprime", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Finite", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Equiv.Perm.ofSubtype_support_disjoint", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Finite", "is_tactic_proof": true, "tactics": ["rw", "rintro", "rw", "exact"], "tactic_count": 4}
{"name": "Equiv.Perm.disjoint_of_disjoint_support", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Finite", "is_tactic_proof": true, "tactics": ["rw", "intro", "specialize", "rwa"], "tactic_count": 4}
{"name": "Equiv.Perm.support_closure_subset_union", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Finite", "is_tactic_proof": true, "tactics": ["apply", "exact", "simp", "intro", "refine", "rw", "exact", "simp"], "tactic_count": 8}
{"name": "Equiv.Perm.disjoint_support_closure_of_disjoint_support", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Finite", "is_tactic_proof": true, "tactics": ["intro", "have", "have", "have", "simp_rw", "exact"], "tactic_count": 6}
{"name": "Equiv.Perm.disjoint_closure_of_disjoint_support", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Finite", "is_tactic_proof": true, "tactics": ["apply", "apply", "exact"], "tactic_count": 3}
{"name": "List.formPerm", "kind": "definition", "module": "Mathlib.GroupTheory.Perm.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.formPerm_nil", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.formPerm_singleton", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.formPerm_cons_cons", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.formPerm_pair", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.mem_or_mem_of_zipWith_swap_prod_ne", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.zipWith_swap_prod_support'", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.zipWith_swap_prod_support", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.List", "is_tactic_proof": true, "tactics": ["intro", "have", "simpa"], "tactic_count": 3}
{"name": "List.support_formPerm_le'", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.List", "is_tactic_proof": true, "tactics": ["refine", "simpa"], "tactic_count": 2}
{"name": "List.support_formPerm_le", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.List", "is_tactic_proof": true, "tactics": ["intro", "have", "simpa"], "tactic_count": 3}
{"name": "List.mem_of_formPerm_apply_ne", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.List", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "List.formPerm_apply_of_notMem", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.formPerm_apply_mem_of_mem", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.List", "is_tactic_proof": true, "tactics": ["rcases", "simp", "induction", "nil", "cons", "by_cases", "rw", "split_ifs", "simp", "simp", "simp", "replace", "simp"], "tactic_count": 13}
{"name": "List.mem_of_formPerm_apply_mem", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.List", "is_tactic_proof": true, "tactics": ["contrapose", "rwa"], "tactic_count": 2}
{"name": "List.formPerm_mem_iff_mem", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.formPerm_cons_concat_apply_last", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.List", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "List.formPerm_apply_getLast", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.List", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "List.formPerm_apply_getElem_length", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.List", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.formPerm_apply_head", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.List", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.formPerm_apply_getElem_zero", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.List", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simp", "rw"], "tactic_count": 4}
{"name": "List.formPerm_eq_head_iff_eq_getLast", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.formPerm_apply_lt_getElem", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.List", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rcases", "simp", "rw", "specialize", "simpa", "simp", "simp", "rw", "intro", "rw", "simp"], "tactic_count": 14}
{"name": "List.formPerm_apply_getElem", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.List", "is_tactic_proof": true, "tactics": ["rcases", "simp", "have", "refine", "simpa", "rcases", "simp", "rw", "congr", "rw"], "tactic_count": 10}
{"name": "List.support_formPerm_of_nodup'", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.List", "is_tactic_proof": true, "tactics": ["apply", "exact", "intro", "simp", "obtain", "rw", "intro", "rw", "specialize", "rcases", "simp", "refine", "rw", "simp"], "tactic_count": 14}
{"name": "List.support_formPerm_of_nodup", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.List", "is_tactic_proof": true, "tactics": ["rw", "convert", "simp"], "tactic_count": 3}
{"name": "List.formPerm_rotate_one", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.List", "is_tactic_proof": true, "tactics": ["have", "ext", "by_cases", "obtain", "rw", "simp", "rw", "simpa"], "tactic_count": 8}
{"name": "List.formPerm_rotate", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.List", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "rwa", "exact"], "tactic_count": 6}
{"name": "List.formPerm_eq_of_isRotated", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.List", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "List.formPerm_append_pair", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.formPerm_reverse", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.formPerm_pow_apply_getElem", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.List", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "List.formPerm_pow_apply_head", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.List", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "List.formPerm_ext_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.List", "is_tactic_proof": true, "tactics": ["refine", "rw", "have", "have", "rw", "simp", "push_neg", "exact", "simpa", "obtain", "have", "rw", "refine", "rw", "simp", "use", "apply", "rw", "intro", "rw", "induction", "zero", "refine", "congr", "simpa", "succ", "conv", "rw", "formPerm_apply_getElem", "congr", "rw", "apply"], "tactic_count": 32}
{"name": "List.formPerm_apply_mem_eq_self_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.List", "is_tactic_proof": true, "tactics": ["obtain", "rw", "cases", "exact", "rw", "rcases", "simp", "simpa"], "tactic_count": 8}
{"name": "List.formPerm_apply_mem_ne_self_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.List", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "List.formPerm_eq_one_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.List", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rw", "constructor", "simp", "intro", "simp", "nonpos_iff_eq_zero,", "simp"], "tactic_count": 9}
{"name": "List.formPerm_eq_formPerm_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.List", "is_tactic_proof": true, "tactics": ["rcases", "suffices", "simpa", "refine", "rintro", "simp", "exact", "suffices", "simpa", "refine", "rintro", "simp", "exact", "rcases", "simp", "simp", "simp"], "tactic_count": 17}
{"name": "List.form_perm_zpow_apply_mem_imp_mem", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.List", "is_tactic_proof": true, "tactics": ["by_cases", "simpa", "have", "rw", "replace", "simpa"], "tactic_count": 6}
{"name": "List.formPerm_pow_length_eq_one_of_nodup", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.List", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "obtain", "simp", "have", "intro", "refine", "replace", "simpa", "simpa"], "tactic_count": 10}
{"name": "MulAction.isPreprimitive_stabilizer_of_surjective", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.MaximalSubgroups", "is_tactic_proof": true, "tactics": ["let", "let", "map_smul", "have", "rw", "infer_instance"], "tactic_count": 6}
{"name": "MulAction.isPreprimitive_stabilizer_subgroup", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.MaximalSubgroups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.IsPretransitive.of_partition", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.MaximalSubgroups", "is_tactic_proof": false, "tactics": ["suffices", "obtain", "rw", "intro", "by_cases", "exact", "rw", "obtain", "use", "rw", "contrapose", "rw", "rintro", "by_contra", "exact"], "tactic_count": 15}
{"name": "Equiv.Perm.ofSubtype_mem_stabilizer", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.MaximalSubgroups", "is_tactic_proof": true, "tactics": ["rw", "ext", "simp_rw", "refine", "rintro", "simp", "use", "simp"], "tactic_count": 8}
{"name": "Equiv.Perm.swap_mem_stabilizer", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.MaximalSubgroups", "is_tactic_proof": false, "tactics": ["suffices", "rw", "apply", "exact", "rintro", "by_cases", "aesop", "have", "aesop"], "tactic_count": 9}
{"name": "Equiv.Perm.exists_mem_stabilizer_smul_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.MaximalSubgroups", "is_tactic_proof": true, "tactics": ["intro", "classical"], "tactic_count": 2}
{"name": "Equiv.Perm.stabilizer.surjective_toPerm", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.MaximalSubgroups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.stabilizer_isPreprimitive", "kind": "instance", "module": "Mathlib.GroupTheory.Perm.MaximalSubgroups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.stabilizer_ne_top_of_nonempty_of_nonempty_compl", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.MaximalSubgroups", "is_tactic_proof": true, "tactics": ["classical", "obtain", "obtain", "intro", "rw", "have", "rw", "rw", "aesop"], "tactic_count": 9}
{"name": "Equiv.Perm.has_swap_mem_of_lt_stabilizer", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.MaximalSubgroups", "is_tactic_proof": false, "tactics": ["have", "intro", "rw", "obtain", "use", "rcases", "obtain", "exact", "rcases", "obtain", "use", "rw", "exact", "have", "rw", "have", "convert", "apply", "assumption", "rw", "aesop", "have", "rw", "refine", "exact", "have", "rw", "exact", "have", "apply", "rw", "exact", "cases", "inl", "inr", "rw", "apply", "simp_all"], "tactic_count": 38}
{"name": "Subgroup.isPretransitive_of_stabilizer_lt", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.MaximalSubgroups", "is_tactic_proof": true, "tactics": ["apply", "intro", "obtain", "exact", "intro", "obtain", "rw", "exact", "contrapose", "apply", "have", "rw", "rw"], "tactic_count": 13}
{"name": "MulAction.IsBlock.subsingleton_of_ssubset_of_stabilizer_le", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.MaximalSubgroups", "is_tactic_proof": true, "tactics": ["rw", "apply", "suffices", "apply", "rw", "exact", "suffices", "apply", "let", "let", "map_smul", "exact", "let", "let", "map_smul", "have", "rw", "infer_instance"], "tactic_count": 18}
{"name": "MulAction.IsBlock.subsingleton_of_ssubset_of_stabilizer_Perm_le", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.MaximalSubgroups", "is_tactic_proof": true, "tactics": ["apply", "intro", "obtain", "let", "have", "exact"], "tactic_count": 6}
{"name": "MulAction.IsBlock.subsingleton_of_stabilizer_lt_of_subset", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.MaximalSubgroups", "is_tactic_proof": false, "tactics": ["suffices", "rcases", "rw", "apply", "have", "subst", "obtain", "have", "suffices", "apply", "exact", "suffices", "apply", "let", "let", "map_smul", "apply", "infer_instance"], "tactic_count": 18}
{"name": "MulAction.IsBlock.compl_subset_of_stabilizer_le_of_not_subset_of_not_subset_compl", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.MaximalSubgroups", "is_tactic_proof": true, "tactics": ["have", "obtain", "have", "obtain", "intro", "suffices", "obtain", "suffices", "this.le", "apply", "refine", "rw", "rw", "exact", "apply", "exact", "suffices", "obtain", "rw", "exact", "rw", "apply"], "tactic_count": 22}
{"name": "Equiv.Perm.isCoatom_stabilizer_of_ncard_lt_ncard_compl", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.MaximalSubgroups", "is_tactic_proof": true, "tactics": ["classical", "have", "have", "refine", "have", "rwa", "obtain", "apply", "have", "apply", "intro", "unfold", "rw", "intro", "suffices", "apply", "have", "rw", "lia", "it", "and", "of", "have", "rcases", "apply", "rw", "exact", "rw", "apply", "rwa", "have", "hB.subsingleton_of_ssubset_of_stabilizer_Perm_le", "have", "have", "hB.subsingleton_of_stabilizer_lt_of_subset", "have", "apply"], "tactic_count": 37}
{"name": "Equiv.Perm.isCoatom_stabilizer", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.MaximalSubgroups", "is_tactic_proof": true, "tactics": ["obtain", "exact", "contrapose", "rw", "rw", "apply", "rwa"], "tactic_count": 7}
{"name": "Equiv.optionCongr_one", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Option", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.optionCongr_swap", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Option", "is_tactic_proof": true, "tactics": ["ext", "simp", "by_cases", "simp", "by_cases"], "tactic_count": 5}
{"name": "Equiv.optionCongr_sign", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Option", "is_tactic_proof": true, "tactics": ["induction", "one", "swap_mul"], "tactic_count": 3}
{"name": "map_equiv_removeNone", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Option", "is_tactic_proof": true, "tactics": ["ext1", "have", "obtain", "simp", "cases", "simp", "have", "have", "simp", "simpa"], "tactic_count": 10}
{"name": "Equiv.Perm.decomposeOption", "kind": "definition", "module": "Mathlib.GroupTheory.Perm.Option", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.decomposeOption_symm_of_none_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Option", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Equiv.Perm.decomposeOption_symm_sign", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Option", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.univ_perm_option", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Option", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.modSwap", "kind": "definition", "module": "Mathlib.GroupTheory.Perm.Sign", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.instDecidableRelROfFintype", "kind": "instance", "module": "Mathlib.GroupTheory.Perm.Sign", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.swapFactorsAux", "kind": "definition", "module": "Mathlib.GroupTheory.Perm.Sign", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.swapFactors", "kind": "definition", "module": "Mathlib.GroupTheory.Perm.Sign", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.truncSwapFactors", "kind": "definition", "module": "Mathlib.GroupTheory.Perm.Sign", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.swap_induction_on", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Sign", "is_tactic_proof": true, "tactics": ["cases", "obtain", "induction", "nil", "cons", "rcases", "rw", "exact"], "tactic_count": 8}
{"name": "Equiv.Perm.mclosure_isSwap", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Sign", "is_tactic_proof": true, "tactics": ["cases", "refine", "obtain", "rw", "exact"], "tactic_count": 5}
{"name": "Equiv.Perm.closure_isSwap", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Sign", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.mclosure_swap_castSucc_succ", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Sign", "is_tactic_proof": true, "tactics": ["apply", "rw", "rintro", "wlog", "rw", "induction", "zero", "succ", "ih", "have", "obtain", "exact", "rw", "exact"], "tactic_count": 14}
{"name": "Equiv.Perm.swap_induction_on'", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Sign", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.isConj_swap", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Sign", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.finPairsLT", "kind": "definition", "module": "Mathlib.GroupTheory.Perm.Sign", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.mem_finPairsLT", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Sign", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Equiv.Perm.signAux", "kind": "definition", "module": "Mathlib.GroupTheory.Perm.Sign", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.signAux_one", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Sign", "is_tactic_proof": true, "tactics": ["unfold", "conv", "exact"], "tactic_count": 3}
{"name": "Equiv.Perm.signBijAux", "kind": "definition", "module": "Mathlib.GroupTheory.Perm.Sign", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.signBijAux_injOn", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Sign", "is_tactic_proof": true, "tactics": ["rintro", "dsimp", "rw", "have", "split_ifs", "exact", "exact"], "tactic_count": 7}
{"name": "Equiv.Perm.signBijAux_surj", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Sign", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.signBijAux_mem", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Sign", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.signAux_inv", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Sign", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.signAux_mul", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Sign", "is_tactic_proof": true, "tactics": ["rw", "unfold", "rw", "refine", "rintro", "dsimp", "rw", "rw", "by_cases", "simp", "obtain", "simp_all"], "tactic_count": 12}
{"name": "_private.Mathlib.GroupTheory.Perm.Sign.0.Equiv.Perm.signAux_swap_zero_one'", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Sign", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.GroupTheory.Perm.Sign.0.Equiv.Perm.signAux_swap_zero_one", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Sign", "is_tactic_proof": true, "tactics": ["rcases", "norm_num", "norm_num", "exact"], "tactic_count": 4}
{"name": "Equiv.Perm.signAux_swap", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Sign", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.signAux2", "kind": "definition", "module": "Mathlib.GroupTheory.Perm.Sign", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.signAux_eq_signAux2", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Sign", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.signAux3", "kind": "definition", "module": "Mathlib.GroupTheory.Perm.Sign", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.signAux3_mul_and_swap", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Sign", "is_tactic_proof": true, "tactics": ["obtain", "induction", "change", "have", "constructor", "rw", "signAux_eq_signAux2", "intro", "rw", "rw"], "tactic_count": 10}
{"name": "Equiv.Perm.signAux3_symm_trans_trans", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Sign", "is_tactic_proof": true, "tactics": ["induction", "change", "rcases", "rw", "exact"], "tactic_count": 5}
{"name": "Equiv.Perm.sign", "kind": "definition", "module": "Mathlib.GroupTheory.Perm.Sign", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.sign_mul", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Sign", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.sign_trans", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Sign", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Equiv.Perm.sign_one", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Sign", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.sign_refl", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Sign", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.sign_inv", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Sign", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Equiv.Perm.sign_symm", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Sign", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.sign_swap", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Sign", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.sign_swap'", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Sign", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.IsSwap.sign_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Sign", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.sign_symm_trans_trans", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Sign", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.sign_trans_trans_symm", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Sign", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.sign_prod_list_swap", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Sign", "is_tactic_proof": false, "tactics": ["have", "let", "hg.2", "rw"], "tactic_count": 4}
{"name": "Equiv.Perm.sign_abs", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Sign", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Equiv.Perm.sign_surjective", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Sign", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.eq_sign_of_surjective_hom", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Sign", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.sign_subtypePerm", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Sign", "is_tactic_proof": true, "tactics": ["let", "have", "let", "hg.2", "have", "conv", "congr", "rw", "simp_rw", "rw"], "tactic_count": 10}
{"name": "Equiv.Perm.sign_eq_sign_of_equiv", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Sign", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "Equiv.Perm.sign_bij", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Sign", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.prod_prodExtendRight", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Sign", "is_tactic_proof": false, "tactics": ["ext", "suffices", "a", "a", "obtain", "rw", "clear", "induction", "nil", "refine", "rw", "cons", "rw", "rcases", "refine", "rw", "by_cases", "rw", "refine", "rw", "refine", "rw"], "tactic_count": 22}
{"name": "Equiv.Perm.sign_prodExtendRight", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Sign", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.sign_prodCongrRight", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Sign", "is_tactic_proof": true, "tactics": ["obtain", "have", "apply", "intro", "exact", "rw", "simp_rw"], "tactic_count": 7}
{"name": "Equiv.Perm.sign_prodCongrLeft", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Sign", "is_tactic_proof": true, "tactics": ["refine", "rintro", "rfl"], "tactic_count": 3}
{"name": "Equiv.Perm.sign_permCongr", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Sign", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.sign_sumCongr", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Sign", "is_tactic_proof": false, "tactics": ["suffices", "rw", "constructor", "induction", "one", "swap_mul", "rw", "sign_swap", "induction", "one", "swap_mul", "rw", "sign_swap"], "tactic_count": 13}
{"name": "Equiv.Perm.sign_subtypeCongr", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Sign", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Equiv.Perm.sign_extendDomain", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Sign", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Equiv.Perm.sign_ofSubtype", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Sign", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.viaFintypeEmbedding_sign", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Sign", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Equiv.Perm.ofSign", "kind": "definition", "module": "Mathlib.GroupTheory.Perm.Sign", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.mem_ofSign", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Sign", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Equiv.Perm.ofSign_disjoint", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Sign", "is_tactic_proof": true, "tactics": ["rw", "rintro", "rw", "have", "contradiction"], "tactic_count": 5}
{"name": "Equiv.Perm.ofSign_disjUnion", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Sign", "is_tactic_proof": true, "tactics": ["ext", "simp_rw"], "tactic_count": 2}
{"name": "Equiv.Perm.sumCongrHom.decidableMemRange", "kind": "instance", "module": "Mathlib.GroupTheory.Perm.Subgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.sumCongrHom.card_range", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Subgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.sigmaCongrRightHom.decidableMemRange", "kind": "instance", "module": "Mathlib.GroupTheory.Perm.Subgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.sigmaCongrRightHom.card_range", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Subgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.subtypeCongrHom.decidableMemRange", "kind": "instance", "module": "Mathlib.GroupTheory.Perm.Subgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.subtypeCongrHom.card_range", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Subgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.subgroupOfMulAction", "kind": "definition", "module": "Mathlib.GroupTheory.Perm.Subgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.Disjoint", "kind": "definition", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.Disjoint.symm", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Equiv.Perm.Disjoint.symmetric", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.instSymmDisjoint", "kind": "instance", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.disjoint_comm", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.Disjoint.commute", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.disjoint_one_left", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.disjoint_one_right", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.disjoint_iff_eq_or_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.disjoint_refl_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": true, "tactics": ["refine", "ext", "rcases"], "tactic_count": 3}
{"name": "Equiv.Perm.Disjoint.inv_left", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": true, "tactics": ["intro", "rw", "exact"], "tactic_count": 3}
{"name": "Equiv.Perm.Disjoint.inv_right", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.disjoint_inv_left_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": true, "tactics": ["refine", "convert"], "tactic_count": 2}
{"name": "Equiv.Perm.disjoint_inv_right_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Equiv.Perm.Disjoint.mul_left", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.Disjoint.mul_right", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Equiv.Perm.disjoint_conj", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.Disjoint.conj", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.disjoint_prod_right", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "rw", "exact"], "tactic_count": 5}
{"name": "Equiv.Perm.disjoint_noncommProd_right", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.disjoint_prod_perm", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.nodup_of_pairwise_disjoint", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": true, "tactics": ["refine", "intro", "subst", "suffices", "rw", "exact", "exact"], "tactic_count": 7}
{"name": "Equiv.Perm.pow_apply_eq_self_of_apply_eq_self", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.zpow_apply_eq_self_of_apply_eq_self", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.pow_apply_eq_of_apply_apply_eq_self", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.zpow_apply_eq_of_apply_apply_eq_self", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.Disjoint.mul_apply_eq_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": true, "tactics": ["refine", "rcases", "exact", "exact"], "tactic_count": 4}
{"name": "Equiv.Perm.Disjoint.mul_eq_one_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Equiv.Perm.Disjoint.zpow_disjoint_zpow", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.Disjoint.pow_disjoint_pow", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.IsSwap", "kind": "definition", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.ofSubtype_swap_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.IsSwap.of_subtype_isSwap", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.ne_and_ne_of_swap_mul_apply_ne_self", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": true, "tactics": ["simp", "grind"], "tactic_count": 2}
{"name": "Equiv.Perm.set_support_symm_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Equiv.Perm.set_support_apply_mem", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Equiv.Perm.set_support_zpow_subset", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": true, "tactics": ["intro", "simp", "intro", "simp"], "tactic_count": 4}
{"name": "Equiv.Perm.set_support_mul_subset", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": true, "tactics": ["simp", "grind"], "tactic_count": 2}
{"name": "Equiv.Perm.apply_pow_apply_eq_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Equiv.Perm.apply_zpow_apply_eq_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Equiv.Perm.support", "kind": "definition", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.mem_support", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Equiv.Perm.notMem_support", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Equiv.Perm.coe_support_eq_set_support", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Equiv.Perm.support_eq_empty_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Equiv.Perm.support_one", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Equiv.Perm.support_refl", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.support_congr", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Equiv.Perm.mem_support_iff_of_commute", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": true, "tactics": ["simp", "rw"], "tactic_count": 2}
{"name": "Equiv.Perm.support_mul_le", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.exists_mem_support_of_mem_support_prod", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": true, "tactics": ["contrapose", "simp_rw", "induction", "nil", "cons", "rw", "simp", "grind"], "tactic_count": 8}
{"name": "Equiv.Perm.support_pow_le", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.support_inv", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Equiv.Perm.apply_mem_support", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Equiv.Perm.isInvariant_of_support_le", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "rw"], "tactic_count": 3}
{"name": "Equiv.Perm.ofSubtype_eq_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": true, "tactics": ["simp", "constructor", "intro", "constructor", "intro", "by_contra", "rw", "exact", "intro", "rw", "rintro", "specialize", "by_cases", "rw", "rw", "exact"], "tactic_count": 16}
{"name": "Equiv.Perm.support_ofSubtype", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": true, "tactics": ["ext", "simp", "exists_eq_right,", "by_cases", "simp", "simp"], "tactic_count": 6}
{"name": "Equiv.Perm.mem_support_of_mem_noncommProd_support", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": true, "tactics": ["contrapose", "classical", "revert", "apply", "simp", "intro", "rw", "apply", "rw", "exact"], "tactic_count": 10}
{"name": "Equiv.Perm.pow_apply_mem_support", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Equiv.Perm.zpow_apply_mem_support", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Equiv.Perm.pow_eq_on_of_mem_support", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "intro", "rw", "rwa"], "tactic_count": 6}
{"name": "Equiv.Perm.disjoint_iff_disjoint_support", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Equiv.Perm.Disjoint.disjoint_support", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.Disjoint.support_mul", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "Equiv.Perm.support_prod_of_pairwise_disjoint", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "rw", "have", "simp"], "tactic_count": 6}
{"name": "Equiv.Perm.support_noncommProd", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "insert", "hrec", "have", "hs.mono", "rw", "rw", "apply", "intro", "apply", "simp"], "tactic_count": 13}
{"name": "Equiv.Perm.support_prod_le", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "rw", "refine", "exact"], "tactic_count": 6}
{"name": "Equiv.Perm.support_zpow_le", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.support_swap", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "any_goals", "by_cases", "simpa", "simp"], "tactic_count": 6}
{"name": "Equiv.Perm.support_swap_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": true, "tactics": ["refine", "rintro", "simp"], "tactic_count": 3}
{"name": "Equiv.Perm.support_swap_mul_swap", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": false, "tactics": ["simp", "push_neg", "apply", "convert", "rw", "simp", "intro", "simp", "rintro", "simp", "h.right.left.symm]"], "tactic_count": 11}
{"name": "Equiv.Perm.support_swap_mul_ge_support_diff", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": true, "tactics": ["intro", "simp", "push_neg", "rintro", "rw", "exact"], "tactic_count": 6}
{"name": "Equiv.Perm.support_swap_mul_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "ext", "by_cases", "simp", "by_cases", "simp", "by_cases", "simp", "simp"], "tactic_count": 10}
{"name": "Equiv.Perm.mem_support_swap_mul_imp_mem_support_ne", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": true, "tactics": ["simp", "grind"], "tactic_count": 2}
{"name": "Equiv.Perm.disjoint_swap_swap", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": true, "tactics": ["intro"], "tactic_count": 1}
{"name": "Equiv.Perm.Disjoint.mem_imp", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.eq_on_support_mem_disjoint", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "intro", "rw", "rw", "rcases", "rw", "rw", "refine", "simpa"], "tactic_count": 11}
{"name": "Equiv.Perm.Disjoint.mono", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Equiv.Perm.support_le_prod_of_mem", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": true, "tactics": ["intro", "rwa"], "tactic_count": 2}
{"name": "Equiv.Perm.support_extend_domain", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": true, "tactics": ["ext", "simp", "by_cases", "rw", "grind", "rw", "simp", "rintro", "exact"], "tactic_count": 9}
{"name": "Equiv.Perm.card_support_extend_domain", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Equiv.Perm.card_support_eq_zero", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Equiv.Perm.one_lt_card_support_of_ne_one", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": true, "tactics": ["simp_rw", "contrapose", "ext", "specialize", "rwa"], "tactic_count": 5}
{"name": "Equiv.Perm.card_support_ne_one", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "exact"], "tactic_count": 3}
{"name": "Equiv.Perm.card_support_le_one", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": true, "tactics": ["rw", "imp_iff_right"], "tactic_count": 2}
{"name": "Equiv.Perm.two_le_card_support_of_ne_one", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.card_support_swap_mul", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.card_support_swap", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.card_support_eq_two", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": true, "tactics": ["constructor", "obtain", "obtain", "rw", "refine", "ext", "have", "by_cases", "have", "rw", "have", "obtain", "rw", "rw", "obtain", "exact"], "tactic_count": 16}
{"name": "Equiv.Perm.Disjoint.card_support_mul", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": true, "tactics": ["rw", "congr", "ext", "simp", "simpa"], "tactic_count": 5}
{"name": "Equiv.Perm.card_support_prod_list_of_pairwise_disjoint", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "obtain", "rw", "exact"], "tactic_count": 6}
{"name": "Equiv.Perm.support_subtypePerm", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Equiv.Perm.fixed_point_card_lt_of_ne_one", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Equiv.Perm.support_conj", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Equiv.Perm.card_support_conj", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.Support", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Equiv.Perm.viaEmbedding", "kind": "definition", "module": "Mathlib.GroupTheory.Perm.ViaEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.viaEmbedding_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.ViaEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.viaEmbedding_apply_of_notMem", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.ViaEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.viaEmbeddingHom", "kind": "definition", "module": "Mathlib.GroupTheory.Perm.ViaEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.viaEmbeddingHom_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.ViaEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.viaEmbeddingHom_injective", "kind": "theorem", "module": "Mathlib.GroupTheory.Perm.ViaEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresentedGroup", "kind": "definition", "module": "Mathlib.GroupTheory.PresentedGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresentedGroup.instGroup", "kind": "instance", "module": "Mathlib.GroupTheory.PresentedGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresentedGroup.mk", "kind": "definition", "module": "Mathlib.GroupTheory.PresentedGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresentedGroup.mk_surjective", "kind": "theorem", "module": "Mathlib.GroupTheory.PresentedGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresentedGroup.of", "kind": "definition", "module": "Mathlib.GroupTheory.PresentedGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresentedGroup.mk_eq_one_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.PresentedGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresentedGroup.one_of_mem", "kind": "theorem", "module": "Mathlib.GroupTheory.PresentedGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresentedGroup.mk_eq_mk_of_mul_inv_mem", "kind": "theorem", "module": "Mathlib.GroupTheory.PresentedGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresentedGroup.mk_eq_mk_of_inv_mul_mem", "kind": "theorem", "module": "Mathlib.GroupTheory.PresentedGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresentedGroup.closure_range_of", "kind": "theorem", "module": "Mathlib.GroupTheory.PresentedGroup", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "PresentedGroup.induction_on", "kind": "theorem", "module": "Mathlib.GroupTheory.PresentedGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresentedGroup.generated_by", "kind": "theorem", "module": "Mathlib.GroupTheory.PresentedGroup", "is_tactic_proof": true, "tactics": ["obtain", "induction", "exact", "exact", "exact", "rename_i", "change", "rw", "exact"], "tactic_count": 9}
{"name": "_private.Mathlib.GroupTheory.PresentedGroup.0.PresentedGroup.termF", "kind": "definition", "module": "Mathlib.GroupTheory.PresentedGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.GroupTheory.PresentedGroup.0.PresentedGroup._aux_Mathlib_GroupTheory_PresentedGroup___macroRules__private_Mathlib_GroupTheory_PresentedGroup_0_PresentedGroup_termF_1", "kind": "definition", "module": "Mathlib.GroupTheory.PresentedGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.GroupTheory.PresentedGroup.0.PresentedGroup._aux_Mathlib_GroupTheory_PresentedGroup___unexpand_FreeGroup_lift_1", "kind": "definition", "module": "Mathlib.GroupTheory.PresentedGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresentedGroup.closure_rels_subset_ker", "kind": "theorem", "module": "Mathlib.GroupTheory.PresentedGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresentedGroup.to_group_eq_one_of_mem_closure", "kind": "theorem", "module": "Mathlib.GroupTheory.PresentedGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresentedGroup.toGroup", "kind": "definition", "module": "Mathlib.GroupTheory.PresentedGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresentedGroup.toGroup.of", "kind": "theorem", "module": "Mathlib.GroupTheory.PresentedGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresentedGroup.toGroup.unique", "kind": "theorem", "module": "Mathlib.GroupTheory.PresentedGroup", "is_tactic_proof": true, "tactics": ["intro", "refine", "exact"], "tactic_count": 3}
{"name": "PresentedGroup.ext", "kind": "theorem", "module": "Mathlib.GroupTheory.PresentedGroup", "is_tactic_proof": true, "tactics": ["unfold", "ext", "apply"], "tactic_count": 3}
{"name": "PresentedGroup.equivPresentedGroup", "kind": "definition", "module": "Mathlib.GroupTheory.PresentedGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresentedGroup.equivPresentedGroup_apply_of", "kind": "theorem", "module": "Mathlib.GroupTheory.PresentedGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresentedGroup.equivPresentedGroup_symm_apply_of", "kind": "theorem", "module": "Mathlib.GroupTheory.PresentedGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PresentedGroup.instInhabited", "kind": "instance", "module": "Mathlib.GroupTheory.PresentedGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monoid.PushoutI.con", "kind": "definition", "module": "Mathlib.GroupTheory.PushoutI", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monoid.PushoutI", "kind": "definition", "module": "Mathlib.GroupTheory.PushoutI", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monoid.PushoutI.mul", "kind": "instance", "module": "Mathlib.GroupTheory.PushoutI", "is_tactic_proof": true, "tactics": ["delta"], "tactic_count": 1}
{"name": "Monoid.PushoutI.one", "kind": "instance", "module": "Mathlib.GroupTheory.PushoutI", "is_tactic_proof": true, "tactics": ["delta"], "tactic_count": 1}
{"name": "Monoid.PushoutI.monoid", "kind": "instance", "module": "Mathlib.GroupTheory.PushoutI", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monoid.PushoutI.of", "kind": "definition", "module": "Mathlib.GroupTheory.PushoutI", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monoid.PushoutI.base", "kind": "definition", "module": "Mathlib.GroupTheory.PushoutI", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monoid.PushoutI.of_comp_eq_base", "kind": "theorem", "module": "Mathlib.GroupTheory.PushoutI", "is_tactic_proof": true, "tactics": ["ext", "apply", "refine", "simp", "exact"], "tactic_count": 5}
{"name": "Monoid.PushoutI.of_apply_eq_base", "kind": "theorem", "module": "Mathlib.GroupTheory.PushoutI", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Monoid.PushoutI.lift", "kind": "definition", "module": "Mathlib.GroupTheory.PushoutI", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monoid.PushoutI.lift_of", "kind": "theorem", "module": "Mathlib.GroupTheory.PushoutI", "is_tactic_proof": true, "tactics": ["delta", "simp"], "tactic_count": 2}
{"name": "Monoid.PushoutI.lift_base", "kind": "theorem", "module": "Mathlib.GroupTheory.PushoutI", "is_tactic_proof": true, "tactics": ["delta", "simp"], "tactic_count": 2}
{"name": "Monoid.PushoutI.hom_ext", "kind": "theorem", "module": "Mathlib.GroupTheory.PushoutI", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monoid.PushoutI.hom_ext_nonempty", "kind": "theorem", "module": "Mathlib.GroupTheory.PushoutI", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monoid.PushoutI.homEquiv", "kind": "definition", "module": "Mathlib.GroupTheory.PushoutI", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monoid.PushoutI.ofCoprodI", "kind": "definition", "module": "Mathlib.GroupTheory.PushoutI", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monoid.PushoutI.ofCoprodI_of", "kind": "theorem", "module": "Mathlib.GroupTheory.PushoutI", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Monoid.PushoutI.induction_on", "kind": "theorem", "module": "Mathlib.GroupTheory.PushoutI", "is_tactic_proof": true, "tactics": ["delta", "induction", "induction", "inl", "induction", "of", "mul", "rw", "exact", "one", "inr", "mul"], "tactic_count": 12}
{"name": "Monoid.PushoutI.instGroup", "kind": "instance", "module": "Mathlib.GroupTheory.PushoutI", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monoid.PushoutI.NormalWord.transversal_nonempty", "kind": "theorem", "module": "Mathlib.GroupTheory.PushoutI", "is_tactic_proof": true, "tactics": ["choose", "apply", "exact", "set", "one_mem", "compl"], "tactic_count": 6}
{"name": "Monoid.PushoutI.NormalWord.empty", "kind": "definition", "module": "Mathlib.GroupTheory.PushoutI", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monoid.PushoutI.NormalWord.instInhabited", "kind": "instance", "module": "Mathlib.GroupTheory.PushoutI", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monoid.PushoutI.NormalWord.instInhabitedPair", "kind": "instance", "module": "Mathlib.GroupTheory.PushoutI", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monoid.PushoutI.NormalWord.ext", "kind": "theorem", "module": "Mathlib.GroupTheory.PushoutI", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "simp_all"], "tactic_count": 3}
{"name": "Monoid.PushoutI.NormalWord.baseAction", "kind": "instance", "module": "Mathlib.GroupTheory.PushoutI", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monoid.PushoutI.NormalWord.base_smul_def'", "kind": "theorem", "module": "Mathlib.GroupTheory.PushoutI", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monoid.PushoutI.NormalWord.prod", "kind": "definition", "module": "Mathlib.GroupTheory.PushoutI", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monoid.PushoutI.NormalWord.prod_base_smul", "kind": "theorem", "module": "Mathlib.GroupTheory.PushoutI", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Monoid.PushoutI.NormalWord.prod_empty", "kind": "theorem", "module": "Mathlib.GroupTheory.PushoutI", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Monoid.PushoutI.NormalWord.cons", "kind": "definition", "module": "Mathlib.GroupTheory.PushoutI", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monoid.PushoutI.NormalWord.prod_cons", "kind": "theorem", "module": "Mathlib.GroupTheory.PushoutI", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Monoid.PushoutI.NormalWord.eq_one_of_smul_normalized", "kind": "theorem", "module": "Mathlib.GroupTheory.PushoutI", "is_tactic_proof": true, "tactics": ["simp", "have", "rw", "split_ifs", "rcases", "exact", "rw", "by_contra", "have", "apply", "rw", "simpa", "simp", "mul_eq_left,", "constructor", "intro", "apply_fun", "simp", "equiv_mul_left_of_mem", "rcases", "rw", "erw", "simp", "contradiction", "rw", "dsimp", "split_ifs", "rcases", "rw", "simp_all", "push_neg", "by_cases", "simp", "simp"], "tactic_count": 34}
{"name": "Monoid.PushoutI.NormalWord.ext_smul", "kind": "theorem", "module": "Mathlib.GroupTheory.PushoutI", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "dsimp", "rw", "subst", "simp", "have", "rw", "simp"], "tactic_count": 9}
{"name": "Monoid.PushoutI.NormalWord.rcons", "kind": "definition", "module": "Mathlib.GroupTheory.PushoutI", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monoid.PushoutI.NormalWord.rcons_injective", "kind": "theorem", "module": "Mathlib.GroupTheory.PushoutI", "is_tactic_proof": true, "tactics": ["rintro", "simp", "intro", "subst", "rw", "simp"], "tactic_count": 6}
{"name": "Monoid.PushoutI.NormalWord.equivPair", "kind": "definition", "module": "Mathlib.GroupTheory.PushoutI", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monoid.PushoutI.NormalWord.summandAction", "kind": "instance", "module": "Mathlib.GroupTheory.PushoutI", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monoid.PushoutI.NormalWord.summand_smul_def'", "kind": "theorem", "module": "Mathlib.GroupTheory.PushoutI", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monoid.PushoutI.NormalWord.mulAction", "kind": "instance", "module": "Mathlib.GroupTheory.PushoutI", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monoid.PushoutI.NormalWord.base_smul_def", "kind": "theorem", "module": "Mathlib.GroupTheory.PushoutI", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monoid.PushoutI.NormalWord.summand_smul_def", "kind": "theorem", "module": "Mathlib.GroupTheory.PushoutI", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monoid.PushoutI.NormalWord.of_smul_eq_smul", "kind": "theorem", "module": "Mathlib.GroupTheory.PushoutI", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Monoid.PushoutI.NormalWord.base_smul_eq_smul", "kind": "theorem", "module": "Mathlib.GroupTheory.PushoutI", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Monoid.PushoutI.NormalWord.consRecOn", "kind": "definition", "module": "Mathlib.GroupTheory.PushoutI", "is_tactic_proof": true, "tactics": ["rcases", "convert", "simp", "induction", "empty", "cons", "ih", "convert", "cons", "simp", "apply", "simp", "mul_inv_cancel,", "rwa"], "tactic_count": 14}
{"name": "Monoid.PushoutI.NormalWord.cons_eq_smul", "kind": "theorem", "module": "Mathlib.GroupTheory.PushoutI", "is_tactic_proof": true, "tactics": ["apply", "simp", "map_inv,"], "tactic_count": 3}
{"name": "Monoid.PushoutI.NormalWord.prod_summand_smul", "kind": "theorem", "module": "Mathlib.GroupTheory.PushoutI", "is_tactic_proof": true, "tactics": ["simp", "inv_mul_cancel_left,"], "tactic_count": 2}
{"name": "Monoid.PushoutI.NormalWord.prod_smul", "kind": "theorem", "module": "Mathlib.GroupTheory.PushoutI", "is_tactic_proof": true, "tactics": ["induction", "of", "base", "mul"], "tactic_count": 4}
{"name": "Monoid.PushoutI.NormalWord.prod_smul_empty", "kind": "theorem", "module": "Mathlib.GroupTheory.PushoutI", "is_tactic_proof": true, "tactics": ["induction", "empty", "cons", "base"], "tactic_count": 4}
{"name": "Monoid.PushoutI.NormalWord.equiv", "kind": "definition", "module": "Mathlib.GroupTheory.PushoutI", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monoid.PushoutI.NormalWord.prod_injective", "kind": "theorem", "module": "Mathlib.GroupTheory.PushoutI", "is_tactic_proof": true, "tactics": ["letI", "letI", "classical"], "tactic_count": 3}
{"name": "Monoid.PushoutI.NormalWord.instFaithfulSMul", "kind": "instance", "module": "Mathlib.GroupTheory.PushoutI", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monoid.PushoutI.NormalWord.instFaithfulSMul_1", "kind": "instance", "module": "Mathlib.GroupTheory.PushoutI", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monoid.PushoutI.NormalWord.instFaithfulSMul_2", "kind": "instance", "module": "Mathlib.GroupTheory.PushoutI", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monoid.PushoutI.of_injective", "kind": "theorem", "module": "Mathlib.GroupTheory.PushoutI", "is_tactic_proof": true, "tactics": ["rcases", "let", "let", "refine", "intro", "exact"], "tactic_count": 6}
{"name": "Monoid.PushoutI.base_injective", "kind": "theorem", "module": "Mathlib.GroupTheory.PushoutI", "is_tactic_proof": true, "tactics": ["rcases", "let", "let", "refine", "intro", "exact"], "tactic_count": 6}
{"name": "Monoid.PushoutI.Reduced", "kind": "definition", "module": "Mathlib.GroupTheory.PushoutI", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monoid.PushoutI.Reduced.exists_normalWord_prod_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.PushoutI", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "cons", "ih", "rcases", "refine", "rwa", "exact", "simp"], "tactic_count": 10}
{"name": "Monoid.PushoutI.Reduced.eq_empty_of_mem_range", "kind": "theorem", "module": "Mathlib.GroupTheory.PushoutI", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "rcases", "have", "rw", "suffices", "simp", "ext", "simp", "rw"], "tactic_count": 10}
{"name": "Monoid.PushoutI.inf_of_range_eq_base_range", "kind": "theorem", "module": "Mathlib.GroupTheory.PushoutI", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.sound", "kind": "theorem", "module": "Mathlib.GroupTheory.QuotientGroup.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp", "congr", "exact"], "tactic_count": 4}
{"name": "_private.Mathlib.GroupTheory.QuotientGroup.Basic.0.QuotientGroup.termQ", "kind": "definition", "module": "Mathlib.GroupTheory.QuotientGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.GroupTheory.QuotientGroup.Basic.0.QuotientGroup._aux_Mathlib_GroupTheory_QuotientGroup_Basic___macroRules__private_Mathlib_GroupTheory_QuotientGroup_Basic_0_QuotientGroup_termQ_1", "kind": "definition", "module": "Mathlib.GroupTheory.QuotientGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.mk_prod", "kind": "theorem", "module": "Mathlib.GroupTheory.QuotientGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.strictMono_comap_prod_map", "kind": "theorem", "module": "Mathlib.GroupTheory.QuotientGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.kerLift", "kind": "definition", "module": "Mathlib.GroupTheory.QuotientGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.kerLift_mk", "kind": "theorem", "module": "Mathlib.GroupTheory.QuotientGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.kerLift_injective", "kind": "theorem", "module": "Mathlib.GroupTheory.QuotientGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.rangeKerLift", "kind": "definition", "module": "Mathlib.GroupTheory.QuotientGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.rangeKerLift_injective", "kind": "theorem", "module": "Mathlib.GroupTheory.QuotientGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.rangeKerLift_surjective", "kind": "theorem", "module": "Mathlib.GroupTheory.QuotientGroup.Basic", "is_tactic_proof": true, "tactics": ["rintro", "use", "rfl"], "tactic_count": 3}
{"name": "QuotientGroup.quotientKerEquivRange", "kind": "definition", "module": "Mathlib.GroupTheory.QuotientGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.quotientKerEquivOfRightInverse", "kind": "definition", "module": "Mathlib.GroupTheory.QuotientGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.quotientBot", "kind": "definition", "module": "Mathlib.GroupTheory.QuotientGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.quotientKerEquivOfSurjective", "kind": "definition", "module": "Mathlib.GroupTheory.QuotientGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.quotientMulEquivOfEq", "kind": "definition", "module": "Mathlib.GroupTheory.QuotientGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.quotientMulEquivOfEq_mk", "kind": "theorem", "module": "Mathlib.GroupTheory.QuotientGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.quotientMapSubgroupOfOfLe", "kind": "definition", "module": "Mathlib.GroupTheory.QuotientGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.quotientMapSubgroupOfOfLe_mk", "kind": "theorem", "module": "Mathlib.GroupTheory.QuotientGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.equivQuotientSubgroupOfOfEq", "kind": "definition", "module": "Mathlib.GroupTheory.QuotientGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.homQuotientZPowOfHom", "kind": "definition", "module": "Mathlib.GroupTheory.QuotientGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.homQuotientZPowOfHom_id", "kind": "theorem", "module": "Mathlib.GroupTheory.QuotientGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.homQuotientZPowOfHom_comp", "kind": "theorem", "module": "Mathlib.GroupTheory.QuotientGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.homQuotientZPowOfHom_comp_of_rightInverse", "kind": "theorem", "module": "Mathlib.GroupTheory.QuotientGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.equivQuotientZPowOfEquiv", "kind": "definition", "module": "Mathlib.GroupTheory.QuotientGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.equivQuotientZPowOfEquiv_refl", "kind": "theorem", "module": "Mathlib.GroupTheory.QuotientGroup.Basic", "is_tactic_proof": true, "tactics": ["ext", "rw", "rfl"], "tactic_count": 3}
{"name": "QuotientGroup.equivQuotientZPowOfEquiv_symm", "kind": "theorem", "module": "Mathlib.GroupTheory.QuotientGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.equivQuotientZPowOfEquiv_trans", "kind": "theorem", "module": "Mathlib.GroupTheory.QuotientGroup.Basic", "is_tactic_proof": true, "tactics": ["ext", "rw", "rfl"], "tactic_count": 3}
{"name": "QuotientGroup.quotientInfEquivProdNormalizerQuotient", "kind": "definition", "module": "Mathlib.GroupTheory.QuotientGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.quotientInfEquivProdNormalQuotient", "kind": "definition", "module": "Mathlib.GroupTheory.QuotientGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.map_normal", "kind": "instance", "module": "Mathlib.GroupTheory.QuotientGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.quotientQuotientEquivQuotientAux", "kind": "definition", "module": "Mathlib.GroupTheory.QuotientGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.quotientQuotientEquivQuotientAux_mk", "kind": "theorem", "module": "Mathlib.GroupTheory.QuotientGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.quotientQuotientEquivQuotientAux_mk_mk", "kind": "theorem", "module": "Mathlib.GroupTheory.QuotientGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.quotientQuotientEquivQuotient", "kind": "definition", "module": "Mathlib.GroupTheory.QuotientGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.le_comap_mk'", "kind": "theorem", "module": "Mathlib.GroupTheory.QuotientGroup.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "QuotientGroup.comap_map_mk'", "kind": "theorem", "module": "Mathlib.GroupTheory.QuotientGroup.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "QuotientGroup.comapMk'OrderIso", "kind": "definition", "module": "Mathlib.GroupTheory.QuotientGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.subsingleton_quotient_top", "kind": "theorem", "module": "Mathlib.GroupTheory.QuotientGroup.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "QuotientGroup.subgroup_eq_top_of_subsingleton", "kind": "theorem", "module": "Mathlib.GroupTheory.QuotientGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.comap_comap_center", "kind": "theorem", "module": "Mathlib.GroupTheory.QuotientGroup.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "QuotientAddGroup.mk_nat_mul", "kind": "theorem", "module": "Mathlib.GroupTheory.QuotientGroup.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "QuotientAddGroup.mk_int_mul", "kind": "theorem", "module": "Mathlib.GroupTheory.QuotientGroup.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "QuotientGroup.leftRel_eq_top", "kind": "theorem", "module": "Mathlib.GroupTheory.QuotientGroup.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "QuotientGroup.rightRel_eq_top", "kind": "theorem", "module": "Mathlib.GroupTheory.QuotientGroup.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "QuotientGroup.subsingleton_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.QuotientGroup.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "QuotientGroup.nontrivial_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.QuotientGroup.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "QuotientGroup.con", "kind": "definition", "module": "Mathlib.GroupTheory.QuotientGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.Quotient.group", "kind": "instance", "module": "Mathlib.GroupTheory.QuotientGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.con_ker_eq_conKer", "kind": "theorem", "module": "Mathlib.GroupTheory.QuotientGroup.Defs", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "QuotientGroup.mk'", "kind": "definition", "module": "Mathlib.GroupTheory.QuotientGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.coe_mk'", "kind": "theorem", "module": "Mathlib.GroupTheory.QuotientGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.mk'_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.QuotientGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.mk'_surjective", "kind": "theorem", "module": "Mathlib.GroupTheory.QuotientGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.mk'_eq_mk'", "kind": "theorem", "module": "Mathlib.GroupTheory.QuotientGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.monoidHom_ext", "kind": "theorem", "module": "Mathlib.GroupTheory.QuotientGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.eq_one_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.QuotientGroup.Defs", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "QuotientGroup.mk'_comp_subtype", "kind": "theorem", "module": "Mathlib.GroupTheory.QuotientGroup.Defs", "is_tactic_proof": true, "tactics": ["ext", "simp", "modified"], "tactic_count": 3}
{"name": "QuotientGroup.range_mk'", "kind": "theorem", "module": "Mathlib.GroupTheory.QuotientGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.ker_le_range_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.QuotientGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.ker_mk'", "kind": "theorem", "module": "Mathlib.GroupTheory.QuotientGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.eq_iff_div_mem", "kind": "theorem", "module": "Mathlib.GroupTheory.QuotientGroup.Defs", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "QuotientGroup.Quotient.commGroup", "kind": "instance", "module": "Mathlib.GroupTheory.QuotientGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.GroupTheory.QuotientGroup.Defs.0.QuotientGroup.termQ", "kind": "definition", "module": "Mathlib.GroupTheory.QuotientGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.GroupTheory.QuotientGroup.Defs.0.QuotientGroup._aux_Mathlib_GroupTheory_QuotientGroup_Defs___macroRules__private_Mathlib_GroupTheory_QuotientGroup_Defs_0_QuotientGroup_termQ_1", "kind": "definition", "module": "Mathlib.GroupTheory.QuotientGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.mk_one", "kind": "theorem", "module": "Mathlib.GroupTheory.QuotientGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.mk_mul", "kind": "theorem", "module": "Mathlib.GroupTheory.QuotientGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.mk_inv", "kind": "theorem", "module": "Mathlib.GroupTheory.QuotientGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.mk_div", "kind": "theorem", "module": "Mathlib.GroupTheory.QuotientGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.mk_pow", "kind": "theorem", "module": "Mathlib.GroupTheory.QuotientGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.mk_zpow", "kind": "theorem", "module": "Mathlib.GroupTheory.QuotientGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.map_mk'_self", "kind": "theorem", "module": "Mathlib.GroupTheory.QuotientGroup.Defs", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Con.subgroup", "kind": "definition", "module": "Mathlib.GroupTheory.QuotientGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.mem_subgroup_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.QuotientGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.instNormalSubgroup", "kind": "instance", "module": "Mathlib.GroupTheory.QuotientGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Con.subgroup_quotientGroupCon", "kind": "theorem", "module": "Mathlib.GroupTheory.QuotientGroup.Defs", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "QuotientGroup.con_subgroup", "kind": "theorem", "module": "Mathlib.GroupTheory.QuotientGroup.Defs", "is_tactic_proof": true, "tactics": ["ext", "rw", "exact"], "tactic_count": 3}
{"name": "Subgroup.orderIsoCon", "kind": "definition", "module": "Mathlib.GroupTheory.QuotientGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.con_le_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.QuotientGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.con_mono", "kind": "theorem", "module": "Mathlib.GroupTheory.QuotientGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.lift", "kind": "definition", "module": "Mathlib.GroupTheory.QuotientGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.lift_mk", "kind": "theorem", "module": "Mathlib.GroupTheory.QuotientGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.lift_mk'", "kind": "theorem", "module": "Mathlib.GroupTheory.QuotientGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.lift_comp_mk'", "kind": "theorem", "module": "Mathlib.GroupTheory.QuotientGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.lift_quot_mk", "kind": "theorem", "module": "Mathlib.GroupTheory.QuotientGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.lift_surjective_of_surjective", "kind": "theorem", "module": "Mathlib.GroupTheory.QuotientGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.ker_lift", "kind": "theorem", "module": "Mathlib.GroupTheory.QuotientGroup.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "QuotientGroup.map", "kind": "definition", "module": "Mathlib.GroupTheory.QuotientGroup.Defs", "is_tactic_proof": true, "tactics": ["refine", "intro", "refine", "rw", "exact"], "tactic_count": 5}
{"name": "QuotientGroup.map_mk", "kind": "theorem", "module": "Mathlib.GroupTheory.QuotientGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SemidirectProduct.mul_right", "kind": "theorem", "module": "Mathlib.GroupTheory.SemidirectProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemidirectProduct.instOne", "kind": "instance", "module": "Mathlib.GroupTheory.SemidirectProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemidirectProduct.one_left", "kind": "theorem", "module": "Mathlib.GroupTheory.SemidirectProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemidirectProduct.one_right", "kind": "theorem", "module": "Mathlib.GroupTheory.SemidirectProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemidirectProduct.instInv", "kind": "instance", "module": "Mathlib.GroupTheory.SemidirectProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemidirectProduct.inv_left", "kind": "theorem", "module": "Mathlib.GroupTheory.SemidirectProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemidirectProduct.inv_right", "kind": "theorem", "module": "Mathlib.GroupTheory.SemidirectProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemidirectProduct.instGroup", "kind": "instance", "module": "Mathlib.GroupTheory.SemidirectProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemidirectProduct.instInhabited", "kind": "instance", "module": "Mathlib.GroupTheory.SemidirectProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemidirectProduct.inl", "kind": "definition", "module": "Mathlib.GroupTheory.SemidirectProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemidirectProduct.left_inl", "kind": "theorem", "module": "Mathlib.GroupTheory.SemidirectProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemidirectProduct.right_inl", "kind": "theorem", "module": "Mathlib.GroupTheory.SemidirectProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemidirectProduct.inl_injective", "kind": "theorem", "module": "Mathlib.GroupTheory.SemidirectProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemidirectProduct.inl_inj", "kind": "theorem", "module": "Mathlib.GroupTheory.SemidirectProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemidirectProduct.inr", "kind": "definition", "module": "Mathlib.GroupTheory.SemidirectProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemidirectProduct.left_inr", "kind": "theorem", "module": "Mathlib.GroupTheory.SemidirectProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemidirectProduct.right_inr", "kind": "theorem", "module": "Mathlib.GroupTheory.SemidirectProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemidirectProduct.inr_injective", "kind": "theorem", "module": "Mathlib.GroupTheory.SemidirectProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemidirectProduct.inr_inj", "kind": "theorem", "module": "Mathlib.GroupTheory.SemidirectProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemidirectProduct.inl_aut", "kind": "theorem", "module": "Mathlib.GroupTheory.SemidirectProduct", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "SemidirectProduct.inl_aut_inv", "kind": "theorem", "module": "Mathlib.GroupTheory.SemidirectProduct", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SemidirectProduct.mk_eq_inl_mul_inr", "kind": "theorem", "module": "Mathlib.GroupTheory.SemidirectProduct", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "SemidirectProduct.inl_left_mul_inr_right", "kind": "theorem", "module": "Mathlib.GroupTheory.SemidirectProduct", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "SemidirectProduct.rightHom", "kind": "definition", "module": "Mathlib.GroupTheory.SemidirectProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemidirectProduct.rightHom_eq_right", "kind": "theorem", "module": "Mathlib.GroupTheory.SemidirectProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemidirectProduct.rightHom_comp_inl", "kind": "theorem", "module": "Mathlib.GroupTheory.SemidirectProduct", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "SemidirectProduct.rightHom_comp_inr", "kind": "theorem", "module": "Mathlib.GroupTheory.SemidirectProduct", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "SemidirectProduct.rightHom_inl", "kind": "theorem", "module": "Mathlib.GroupTheory.SemidirectProduct", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SemidirectProduct.rightHom_inr", "kind": "theorem", "module": "Mathlib.GroupTheory.SemidirectProduct", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SemidirectProduct.rightHom_surjective", "kind": "theorem", "module": "Mathlib.GroupTheory.SemidirectProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemidirectProduct.range_inl_eq_ker_rightHom", "kind": "theorem", "module": "Mathlib.GroupTheory.SemidirectProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemidirectProduct.equivProd", "kind": "definition", "module": "Mathlib.GroupTheory.SemidirectProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemidirectProduct.mulEquivProd", "kind": "definition", "module": "Mathlib.GroupTheory.SemidirectProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemidirectProduct.lift", "kind": "definition", "module": "Mathlib.GroupTheory.SemidirectProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemidirectProduct.lift_inl", "kind": "theorem", "module": "Mathlib.GroupTheory.SemidirectProduct", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SemidirectProduct.lift_comp_inl", "kind": "theorem", "module": "Mathlib.GroupTheory.SemidirectProduct", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "SemidirectProduct.lift_inr", "kind": "theorem", "module": "Mathlib.GroupTheory.SemidirectProduct", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SemidirectProduct.lift_comp_inr", "kind": "theorem", "module": "Mathlib.GroupTheory.SemidirectProduct", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "SemidirectProduct.lift_unique", "kind": "theorem", "module": "Mathlib.GroupTheory.SemidirectProduct", "is_tactic_proof": true, "tactics": ["rw", "simp", "forall_const]"], "tactic_count": 3}
{"name": "SemidirectProduct.hom_ext", "kind": "theorem", "module": "Mathlib.GroupTheory.SemidirectProduct", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "SemidirectProduct.monoidHomSubgroup", "kind": "definition", "module": "Mathlib.GroupTheory.SemidirectProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemidirectProduct.mulEquivSubgroup", "kind": "definition", "module": "Mathlib.GroupTheory.SemidirectProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemidirectProduct.map", "kind": "definition", "module": "Mathlib.GroupTheory.SemidirectProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemidirectProduct.map_left", "kind": "theorem", "module": "Mathlib.GroupTheory.SemidirectProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemidirectProduct.map_right", "kind": "theorem", "module": "Mathlib.GroupTheory.SemidirectProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemidirectProduct.rightHom_comp_map", "kind": "theorem", "module": "Mathlib.GroupTheory.SemidirectProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemidirectProduct.map_inl", "kind": "theorem", "module": "Mathlib.GroupTheory.SemidirectProduct", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SemidirectProduct.map_comp_inl", "kind": "theorem", "module": "Mathlib.GroupTheory.SemidirectProduct", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "SemidirectProduct.map_inr", "kind": "theorem", "module": "Mathlib.GroupTheory.SemidirectProduct", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SemidirectProduct.map_comp_inr", "kind": "theorem", "module": "Mathlib.GroupTheory.SemidirectProduct", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "SemidirectProduct.congr", "kind": "definition", "module": "Mathlib.GroupTheory.SemidirectProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemidirectProduct.congr'", "kind": "definition", "module": "Mathlib.GroupTheory.SemidirectProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemidirectProduct.card", "kind": "theorem", "module": "Mathlib.GroupTheory.SemidirectProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "derivedSeries", "kind": "definition", "module": "Mathlib.GroupTheory.Solvable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "derivedSeries_zero", "kind": "theorem", "module": "Mathlib.GroupTheory.Solvable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "derivedSeries_succ", "kind": "theorem", "module": "Mathlib.GroupTheory.Solvable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "derivedSeries_normal", "kind": "theorem", "module": "Mathlib.GroupTheory.Solvable", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "derivedSeries_one", "kind": "theorem", "module": "Mathlib.GroupTheory.Solvable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "derivedSeries_antitone", "kind": "theorem", "module": "Mathlib.GroupTheory.Solvable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "derivedSeries_characteristic", "kind": "instance", "module": "Mathlib.GroupTheory.Solvable", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "map_derivedSeries_le_derivedSeries", "kind": "theorem", "module": "Mathlib.GroupTheory.Solvable", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "derivedSeries_le_map_derivedSeries", "kind": "theorem", "module": "Mathlib.GroupTheory.Solvable", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "map_derivedSeries_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.Solvable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGroup.isSolvable", "kind": "instance", "module": "Mathlib.GroupTheory.Solvable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isSolvable_of_comm", "kind": "theorem", "module": "Mathlib.GroupTheory.Solvable", "is_tactic_proof": true, "tactics": ["letI", "cases", "exact"], "tactic_count": 3}
{"name": "isSolvable_of_top_eq_bot", "kind": "theorem", "module": "Mathlib.GroupTheory.Solvable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isSolvable_of_subsingleton", "kind": "instance", "module": "Mathlib.GroupTheory.Solvable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "solvable_of_ker_le_range", "kind": "theorem", "module": "Mathlib.GroupTheory.Solvable", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "refine", "clear", "induction", "zero", "exact", "f.range_eq_map", "hfg", "succ"], "tactic_count": 10}
{"name": "solvable_of_solvable_injective", "kind": "theorem", "module": "Mathlib.GroupTheory.Solvable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "subgroup_solvable_of_solvable", "kind": "instance", "module": "Mathlib.GroupTheory.Solvable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "solvable_of_surjective", "kind": "theorem", "module": "Mathlib.GroupTheory.Solvable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "solvable_quotient_of_solvable", "kind": "instance", "module": "Mathlib.GroupTheory.Solvable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "solvable_prod", "kind": "instance", "module": "Mathlib.GroupTheory.Solvable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSolvable.commutator_lt_top_of_nontrivial", "kind": "theorem", "module": "Mathlib.GroupTheory.Solvable", "is_tactic_proof": true, "tactics": ["rw", "obtain", "contrapose", "refine", "induction", "zero", "succ"], "tactic_count": 7}
{"name": "IsSolvable.commutator_lt_of_ne_bot", "kind": "theorem", "module": "Mathlib.GroupTheory.Solvable", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "isSolvable_iff_commutator_lt", "kind": "theorem", "module": "Mathlib.GroupTheory.Solvable", "is_tactic_proof": true, "tactics": ["refine", "suffices", "induction", "ind", "rcases", "infer_instance", "obtain", "use", "rw", "rw", "clear", "induction", "zero", "rw", "succ"], "tactic_count": 15}
{"name": "IsSimpleGroup.derivedSeries_succ", "kind": "theorem", "module": "Mathlib.GroupTheory.Solvable", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "rcases", "rw", "rwa"], "tactic_count": 7}
{"name": "IsSimpleGroup.comm_iff_isSolvable", "kind": "theorem", "module": "Mathlib.GroupTheory.Solvable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_solvable_of_mem_derivedSeries", "kind": "theorem", "module": "Mathlib.GroupTheory.Solvable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.fin_5_not_solvable", "kind": "theorem", "module": "Mathlib.GroupTheory.Solvable", "is_tactic_proof": true, "tactics": ["let", "let", "let", "have", "refine", "induction", "zero", "succ", "rw", "exact"], "tactic_count": 10}
{"name": "Equiv.Perm.not_solvable", "kind": "theorem", "module": "Mathlib.GroupTheory.Solvable", "is_tactic_proof": true, "tactics": ["intro", "have", "rwa", "exact"], "tactic_count": 4}
{"name": "_example", "kind": "example", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "alternatingGroup", "kind": "definition", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "alternatingGroup.instFintype", "kind": "instance", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instUniqueSubtypePermMemSubgroupAlternatingGroupOfSubsingleton", "kind": "instance", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "alternatingGroup_eq_sign_ker", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.mem_alternatingGroup", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.mul_mem_alternatingGroup_of_isSwap", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Equiv.Perm.prod_list_swap_mem_alternatingGroup_iff_even_length", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating", "is_tactic_proof": true, "tactics": ["rw", "decide"], "tactic_count": 2}
{"name": "Equiv.Perm.IsThreeCycle.mem_alternatingGroup", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.finRotate_bit1_mem_alternatingGroup", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "alternatingGroup.index_eq_two", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating", "is_tactic_proof": true, "tactics": ["rw", "simp_rw"], "tactic_count": 2}
{"name": "alternatingGroup.index_eq_one", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Equiv.altCongrHom", "kind": "definition", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "two_mul_nat_card_alternatingGroup", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "two_mul_card_alternatingGroup", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "card_alternatingGroup", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nat_card_alternatingGroup", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "alternatingGroup.normal", "kind": "instance", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "alternatingGroup.isConj_of", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "obtain", "rw", "rcases", "rw", "refine", "simpa", "have", "rw", "exact", "obtain", "refine", "rw", "simp", "have", "rw", "exact", "simp"], "tactic_count": 19}
{"name": "alternatingGroup.isThreeCycle_isConj", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.closure_three_cycles_eq_alternating", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.closure_cycleType_eq_2_2_eq_alternatingGroup", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating", "is_tactic_proof": true, "tactics": ["apply", "rw", "intro", "simp", "simp", "rw", "intro", "obtain", "have", "have", "have", "obtain", "have", "simp", "rw", "apply", "apply", "exact"], "tactic_count": 18}
{"name": "Equiv.Perm.IsThreeCycle.alternating_normalClosure", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.isThreeCycle_sq_of_three_mem_cycleType_five", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating", "is_tactic_proof": true, "tactics": ["obtain", "simp", "rw", "suffices", "rw", "exact", "rw", "intro", "rw", "apply", "rw", "exact"], "tactic_count": 12}
{"name": "alternatingGroup.eq_bot_of_card_le_two", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating", "is_tactic_proof": true, "tactics": ["nontriviality", "suffices", "rw", "two_mul_card_alternatingGroup,", "exact"], "tactic_count": 5}
{"name": "alternatingGroup.nontrivial_of_three_le_card", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating", "is_tactic_proof": true, "tactics": ["haveI", "rw", "refine", "rw", "exact"], "tactic_count": 5}
{"name": "alternatingGroup.instNontrivialSubtypePermFinHAddNatOfNatMemSubgroup", "kind": "instance", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "alternatingGroup.normalClosure_finRotate_five", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "alternatingGroup.normalClosure_swap_mul_swap_five", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating", "is_tactic_proof": true, "tactics": ["let", "let", "have", "rw", "simp", "decide", "rw", "refine", "rw", "have", "exact"], "tactic_count": 11}
{"name": "alternatingGroup.isConj_swap_mul_swap_of_cycleType_two", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating", "is_tactic_proof": true, "tactics": ["have", "rw", "rw", "have", "rw", "norm_num", "rw", "swap", "rw", "interval_cases", "exact", "simp", "have", "have", "rw", "card_support_swap", "simp", "rw", "decide", "contradiction"], "tactic_count": 20}
{"name": "alternatingGroup.isSimpleGroup_five", "kind": "instance", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "alternatingGroup.center_eq_bot", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating", "is_tactic_proof": true, "tactics": ["rw", "rintro", "simp", "simp", "intro", "have", "have", "rw", "rw", "rw", "exact", "rw", "obtain", "simp", "let", "have", "simp", "rw", "rw", "have", "simp", "rw", "suffices", "suffices", "exact", "rw", "suffices", "simp"], "tactic_count": 28}
{"name": "Equiv.Perm.eq_alternatingGroup_of_index_eq_two", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating", "is_tactic_proof": true, "tactics": ["nontriviality", "obtain", "by_contra", "suffices", "rwa", "ext", "refine", "rw", "refine", "contrapose", "rw", "exact"], "tactic_count": 12}
{"name": "Equiv.Perm.alternatingGroup_le_of_index_le_two", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating", "is_tactic_proof": true, "tactics": ["rcases", "exact", "rcases", "exact", "rw"], "tactic_count": 5}
{"name": "instCharacteristicPermAlternatingGroup", "kind": "instance", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.OnCycleFactors.odd_of_centralizer_le_alternatingGroup", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating.Centralizer", "is_tactic_proof": true, "tactics": ["rw", "obtain", "rw", "suffices", "rw", "rw", "exact", "rw", "exact", "apply", "rw", "exact"], "tactic_count": 12}
{"name": "AlternatingGroup.map_subtype_of_cycleType", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating.Centralizer", "is_tactic_proof": true, "tactics": ["split_ifs", "ext", "simp_rw", "exists_and_left,", "intro", "rw", "rw", "intro", "simp_rw", "exists_and_left,", "rcases", "rw", "contradiction"], "tactic_count": 13}
{"name": "AlternatingGroup.card_of_cycleType_mul_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating.Centralizer", "is_tactic_proof": true, "tactics": ["rw", "simp", "rw"], "tactic_count": 3}
{"name": "AlternatingGroup.card_of_cycleType", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating.Centralizer", "is_tactic_proof": true, "tactics": ["split_ifs", "rw", "mul_assoc]", "rw", "rw", "split_ifs", "rw", "obtain", "exact", "contradiction", "rfl"], "tactic_count": 11}
{"name": "AlternatingGroup.card_of_cycleType_singleton", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating.Centralizer", "is_tactic_proof": true, "tactics": ["rw", "simp", "simp_rw"], "tactic_count": 3}
{"name": "Equiv.Perm.card_le_of_centralizer_le_alternating", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating.Centralizer", "is_tactic_proof": true, "tactics": ["by_contra", "replace", "suffices", "obtain", "suffices", "simp", "rwa", "rw", "exact"], "tactic_count": 9}
{"name": "Equiv.Perm.count_le_one_of_centralizer_le_alternating", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating.Centralizer", "is_tactic_proof": true, "tactics": ["rw", "rw", "simp", "by_contra", "let", "obtain", "have", "by_cases", "rw", "by_cases", "rw", "rw", "set", "suffices", "apply", "rw", "we", "which", "but", "and", "have", "rw", "convert", "rw", "apply", "rw", "simp", "apply", "apply", "have", "rw", "simp", "have", "rw", "simp", "have", "simp", "rw", "rw", "simp", "exact"], "tactic_count": 41}
{"name": "Equiv.Perm.OnCycleFactors.kerParam_range_eq_centralizer_of_count_le_one", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating.Centralizer", "is_tactic_proof": true, "tactics": ["ext", "refine", "simp_rw", "exists_and_right,", "use", "ext", "rw", "exact"], "tactic_count": 8}
{"name": "Equiv.Perm.centralizer_le_alternating_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating.Centralizer", "is_tactic_proof": true, "tactics": ["rw", "constructor", "intro", "exact", "count_le_one_of_centralizer_le_alternating", "rintro", "rw", "obtain", "rw", "convert", "apply", "rintro", "obtain", "rw", "convert", "rw", "apply", "rw", "exact", "rw", "exact", "suffices", "have", "exact"], "tactic_count": 24}
{"name": "Equiv.Perm.IsThreeCycle.mem_commutatorSet_alternatingGroup", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating.Centralizer", "is_tactic_proof": true, "tactics": ["apply", "apply", "simpa"], "tactic_count": 3}
{"name": "Equiv.Perm.IsThreeCycle.mem_commutator_alternatingGroup", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating.Centralizer", "is_tactic_proof": true, "tactics": ["rw", "apply", "exact"], "tactic_count": 3}
{"name": "alternatingGroup.commutator_perm_le", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating.Centralizer", "is_tactic_proof": false, "tactics": ["simp", "mem_alternatingGroup,", "rintro", "simp"], "tactic_count": 4}
{"name": "commutator_alternatingGroup_eq_top", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating.Centralizer", "is_tactic_proof": false, "tactics": ["suffices", "rw", "intro", "exact", "rw", "exact"], "tactic_count": 6}
{"name": "commutator_alternatingGroup_eq_self", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating.Centralizer", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "alternatingGroup.commutator_perm_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating.Centralizer", "is_tactic_proof": true, "tactics": ["apply", "rw", "exact"], "tactic_count": 3}
{"name": "alternatingGroup.kleinFour", "kind": "definition", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating.KleinFour", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "alternatingGroup.mem_kleinFour_of_order_two_pow", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating.KleinFour", "is_tactic_proof": true, "tactics": ["rw", "have", "rw", "exact", "have", "intro", "have", "have", "interval_cases", "rfl", "rw", "exact", "contrapose", "obtain", "rw", "have", "replace", "simp", "rw", "rw", "interval_cases"], "tactic_count": 21}
{"name": "alternatingGroup.card_of_card_eq_four", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating.KleinFour", "is_tactic_proof": false, "tactics": ["have", "rw", "simp", "rw", "decide"], "tactic_count": 5}
{"name": "alternatingGroup.card_two_sylow_of_card_eq_four", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating.KleinFour", "is_tactic_proof": true, "tactics": ["rw", "have", "rw", "smul_eq_mul,", "simp"], "tactic_count": 5}
{"name": "alternatingGroup.coe_two_sylow_of_card_eq_four", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating.KleinFour", "is_tactic_proof": true, "tactics": ["classical", "refine", "obtain", "replace", "convert", "simp", "simp_rw", "refine", "rw", "apply", "rw", "decide"], "tactic_count": 12}
{"name": "alternatingGroup.two_sylow_eq_kleinFour_of_card_eq_four", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating.KleinFour", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "alternatingGroup.subsingleton_two_sylow", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating.KleinFour", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "alternatingGroup.characteristic_kleinFour", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating.KleinFour", "is_tactic_proof": true, "tactics": ["obtain", "have", "rw", "exact"], "tactic_count": 4}
{"name": "alternatingGroup.normal_kleinFour", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating.KleinFour", "is_tactic_proof": true, "tactics": ["have", "apply"], "tactic_count": 2}
{"name": "alternatingGroup.kleinFour_card_of_card_eq_four", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating.KleinFour", "is_tactic_proof": true, "tactics": ["obtain", "rw"], "tactic_count": 2}
{"name": "alternatingGroup.coe_kleinFour_of_card_eq_four", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating.KleinFour", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact"], "tactic_count": 3}
{"name": "alternatingGroup.exponent_kleinFour_of_card_eq_four", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating.KleinFour", "is_tactic_proof": false, "tactics": ["have", "rw", "rintro", "simp", "rw", "rcases", "convert", "simpa", "convert", "rw", "simp", "rw", "apply", "rw", "decide"], "tactic_count": 15}
{"name": "alternatingGroup.kleinFour_isKleinFour", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating.KleinFour", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "alternatingGroup.kleinFour_eq_commutator", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating.KleinFour", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "rw", "rw", "rw", "have", "rw", "exact", "have", "rw", "apply", "rw", "simp", "obtain", "suffices", "refine", "intro", "rw", "rcases", "exact", "rw", "obtain", "rw", "simp", "let", "suffices", "rw", "refine", "apply", "rw", "rw", "exact", "have", "rw", "exact"], "tactic_count": 36}
{"name": "Equiv.Perm.exists_mem_stabilizer_isThreeCycle_of_two_lt_ncard", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating.MaximalSubgroups", "is_tactic_proof": true, "tactics": ["rw", "obtain", "refine", "rw", "rintro", "aesop"], "tactic_count": 6}
{"name": "Equiv.Perm.exists_mem_stabilizer_isThreeCycle", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating.MaximalSubgroups", "is_tactic_proof": true, "tactics": ["rcases", "exact", "have", "rw", "exact"], "tactic_count": 5}
{"name": "Equiv.Perm.alternatingGroup_le_of_isPreprimitive", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating.MaximalSubgroups", "is_tactic_proof": true, "tactics": ["obtain", "apply", "exact"], "tactic_count": 3}
{"name": "alternatingGroup.stabilizer.surjective_toPerm", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating.MaximalSubgroups", "is_tactic_proof": true, "tactics": ["classical", "have", "obtain", "use", "rw", "obtain", "have", "rw", "intro", "simp", "rintro", "convert", "rw", "exact", "intro", "rcases", "use", "simp", "rw", "exact", "aesop", "use", "simp", "rw", "ext", "suffices", "rw", "rw", "exact"], "tactic_count": 29}
{"name": "alternatingGroup.stabilizer_isPreprimitive", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating.MaximalSubgroups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "alternatingGroup.stabilizer_subgroup_isPreprimitive", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating.MaximalSubgroups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "alternatingGroup.stabilizer_ne_top", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating.MaximalSubgroups", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "suffices", "use", "simp_rw", "grind", "so"], "tactic_count": 7}
{"name": "alternatingGroup.exists_mem_stabilizer_smul_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating.MaximalSubgroups", "is_tactic_proof": true, "tactics": ["intro", "by_cases", "use", "simpa", "by_cases", "rw", "replace", "obtain", "simp", "refine", "simp", "grind", "simp", "grind", "have", "obtain", "refine", "simp", "grind", "simp", "grind"], "tactic_count": 21}
{"name": "alternatingGroup.subgroup_eq_top_of_isPreprimitive", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating.MaximalSubgroups", "is_tactic_proof": true, "tactics": ["obtain", "rw", "apply", "use", "simpa", "let", "let", "map_smul", "rwa"], "tactic_count": 9}
{"name": "MulAction.IsBlock.subsingleton_of_ssubset_compl_of_stabilizer_alternatingGroup_le", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating.MaximalSubgroups", "is_tactic_proof": true, "tactics": ["apply", "intro", "obtain", "rw", "exact"], "tactic_count": 5}
{"name": "alternatingGroup.isCoatom_stabilizer_of_ncard_lt_ncard_compl", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating.MaximalSubgroups", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "exact", "have", "rw", "grind", "use", "intro", "suffices", "have", "apply", "intro", "rw", "intro", "suffices", "apply", "have", "grind", "in", "this", "of", "have", "apply", "apply", "grind", "have", "hG.le", "have", "have", "hB.subsingleton_of_stabilizer_lt_of_subset", "suffices", "apply", "have", "apply", "grind"], "tactic_count": 36}
{"name": "alternatingGroup.isCoatom_stabilizer_singleton", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating.MaximalSubgroups", "is_tactic_proof": false, "tactics": ["have", "rw", "grind", "obtain", "rw", "have", "apply"], "tactic_count": 7}
{"name": "alternatingGroup.isCoatom_stabilizer", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Alternating.MaximalSubgroups", "is_tactic_proof": true, "tactics": ["rw", "wlog", "rw", "apply", "by_cases", "apply", "simp", "apply", "rw", "rw", "grind"], "tactic_count": 11}
{"name": "IsCyclic.exists_generator", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCyclic_iff_exists_zpowers_eq_top", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Subgroup.isCyclic_iff_exists_zpowers_eq_top", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "exact"], "tactic_count": 3}
{"name": "Subgroup.isCyclic_zpowers", "kind": "instance", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCyclic_of_subsingleton", "kind": "instance", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCyclic_multiplicative_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCyclic_multiplicative", "kind": "instance", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isAddCyclic_additive_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isAddCyclic_additive", "kind": "instance", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCyclic.commutative", "kind": "instance", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCyclic.commGroup", "kind": "definition", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsMulCommutativeSubtypeMemSubgroupOfIsCyclic", "kind": "instance", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nontrivial.of_not_isCyclic", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": true, "tactics": ["contrapose", "exact"], "tactic_count": 2}
{"name": "MonoidHom.map_cyclic", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "refine", "obtain", "rw"], "tactic_count": 5}
{"name": "isCyclic_iff_exists_orderOf_eq_natCard", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "isCyclic_iff_exists_natCard_le_orderOf", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": true, "tactics": ["rw", "apply", "intro", "exact"], "tactic_count": 4}
{"name": "isCyclic_of_orderOf_eq_card", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCyclic_of_card_le_orderOf", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.eq_bot_or_eq_top_of_prime_card", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": true, "tactics": ["have", "have", "rwa"], "tactic_count": 3}
{"name": "zpowers_eq_top_of_prime_card", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": true, "tactics": ["subst", "have", "rwa"], "tactic_count": 3}
{"name": "mem_zpowers_of_prime_card", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "mem_powers_of_prime_card", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "powers_eq_top_of_prime_card", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "isCyclic_of_prime_card", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": true, "tactics": ["have", "have", "obtain", "exact"], "tactic_count": 4}
{"name": "isCyclic_of_card_dvd_prime", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": true, "tactics": ["rcases", "exact", "exact"], "tactic_count": 3}
{"name": "isCyclic_of_surjective", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": true, "tactics": ["obtain", "refine", "obtain", "obtain", "exact"], "tactic_count": 5}
{"name": "MulEquiv.isCyclic", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "orderOf_eq_card_of_forall_mem_zpowers", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "orderOf_eq_card_of_forall_mem_powers", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "orderOf_eq_card_of_zpowers_eq_top", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_pow_ne_one_of_isCyclic", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": true, "tactics": ["have", "rcases", "use", "contrapose", "convert", "rw", "exact"], "tactic_count": 7}
{"name": "Infinite.orderOf_eq_zero_of_forall_mem_zpowers", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Bot.isCyclic", "kind": "instance", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.isCyclic", "kind": "instance", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCyclic_of_injective", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.isCyclic_of_le", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.le_zpowers_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": true, "tactics": ["refine", "obtain", "obtain", "obtain", "exact", "exact", "rintro", "exact"], "tactic_count": 8}
{"name": "IsCyclic.card_pow_eq_one_le", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCyclic.exists_monoid_generator", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "IsCyclic.exists_ofOrder_eq_natCard", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": true, "tactics": ["obtain", "use", "rw", "exact"], "tactic_count": 4}
{"name": "MulDistribMulAction.toMonoidHomZModOfIsCyclic", "kind": "definition", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulDistribMulAction.toMonoidHomZModOfIsCyclic_apply", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": false, "tactics": ["rw", "zpow_eq_zpow_iff_modEq]", "apply", "rwa"], "tactic_count": 4}
{"name": "IsCyclic.unique_zpow_zmod", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": true, "tactics": ["obtain", "refine", "rw", "rw", "simp"], "tactic_count": 5}
{"name": "IsCyclic.image_range_orderOf", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsCyclic.image_range_card", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsCyclic.ext", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": true, "tactics": ["have", "obtain", "specialize", "subst", "rw", "simpa"], "tactic_count": 6}
{"name": "_private.Mathlib.GroupTheory.SpecificGroups.Cyclic.0.card_pow_eq_one_eq_orderOf_aux", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.GroupTheory.SpecificGroups.Cyclic.0.card_orderOf_eq_totient_aux₁", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": false, "tactics": ["induction", "rcases", "cases", "rcases", "have", "have", "refine", "simp", "refine", "rw", "have", "rw", "simpa"], "tactic_count": 13}
{"name": "card_orderOf_eq_totient_aux₂", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": true, "tactics": ["let", "have", "apply", "by_contra", "simp_rw", "apply", "calc", "c", "simp", "apply", "simp", "rw", "refine", "have", "contrapose", "exact", "simp", "refine", "have", "simp", "tauto", "obtain", "simp", "simp"], "tactic_count": 24}
{"name": "isCyclic_of_card_pow_eq_one_le", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCyclic.card_orderOf_eq_totient", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "isSimpleGroup_of_prime_card", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": true, "tactics": ["subst", "have", "have", "exact"], "tactic_count": 4}
{"name": "commutative_of_cyclic_center_quotient", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "commGroupOfCyclicCenterQuotient", "kind": "definition", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSimpleGroup.isCyclic", "kind": "instance", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": true, "tactics": ["nontriviality", "obtain", "have", "exact"], "tactic_count": 4}
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{"name": "IsSimpleGroup.finite", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Group.is_simple_iff_prime_card", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommGroup.is_simple_iff_prime_card", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsAddCyclicInt", "kind": "instance", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.instIsAddCyclic", "kind": "instance", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.instIsSimpleAddGroup", "kind": "instance", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearOrderedAddCommGroup.isAddCyclic_iff_nonempty_equiv_int", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": true, "tactics": ["refine", "rintro", "have", "obtain", "obtain", "aesop", "wlog", "exact", "have", "injective_zsmul_iff_not_isOfFinAddOrder.mpr", "exact", "map_add", "map_le_map_iff"], "tactic_count": 13}
{"name": "LinearOrderedCommGroup.isCyclic_iff_nonempty_equiv_int", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsCyclic.exponent_eq_card", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": true, "tactics": ["obtain", "apply", "rw", "exact"], "tactic_count": 4}
{"name": "IsCyclic.of_exponent_eq_card", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCyclic.iff_exponent_eq_card", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCyclic.exponent_eq_zero_of_infinite", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.exponent", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "not_isCyclic_iff_exponent_eq_prime", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": true, "tactics": ["have", "have", "immediately", "refine", "obtain", "exact", "exact", "orders", "the", "have", "have", "obtain", "interval_cases", "exact", "simp_all", "exact"], "tactic_count": 16}
{"name": "zmultiplesHom_ker_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": true, "tactics": ["ext", "simp_rw", "zsmul_eq_mul',"], "tactic_count": 3}
{"name": "zpowersHom_ker_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zmodAddCyclicAddEquiv", "kind": "definition", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": true, "tactics": ["let", "let", "have", "rw", "congr", "rw", "exact", "exact"], "tactic_count": 8}
{"name": "exists_prime_addEquiv_ZMod", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": true, "tactics": ["obtain", "use", "constructor", "exact", "exact"], "tactic_count": 5}
{"name": "zmodCyclicMulEquiv", "kind": "definition", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "addEquivOfAddCyclicCardEq", "kind": "definition", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mulEquivOfCyclicCardEq", "kind": "definition", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mulEquivOfPrimeCardEq", "kind": "definition", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": true, "tactics": ["have", "have", "apply", "exact"], "tactic_count": 4}
{"name": "IsCyclic.mulAutMulEquiv", "kind": "definition", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCyclic.card_mulAut", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "IsCyclic.card_powMonoidHom_range", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": true, "tactics": ["obtain", "rw", "orderOf_eq_card_of_zpowers_eq_top"], "tactic_count": 3}
{"name": "IsCyclic.index_powMonoidHom_ker", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsCyclic.card_powMonoidHom_ker", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "IsCyclic.index_powMonoidHom_range", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "monoidHomOfForallMemZpowers", "kind": "definition", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monoidHomOfForallMemZpowers_apply_gen", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": true, "tactics": ["simp", "nth_rw", "rw", "apply", "rw", "exact"], "tactic_count": 6}
{"name": "MonoidHom.eq_iff_eq_on_generator", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": true, "tactics": ["rw", "refine", "obtain", "rw"], "tactic_count": 4}
{"name": "MulEquiv.eq_iff_eq_on_generator", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mulEquivOfOrderOfEq", "kind": "definition", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": true, "tactics": ["refine", "refine", "simp"], "tactic_count": 3}
{"name": "mulEquivOfOrderOfEq_apply_gen", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mulEquivOfOrderOfEq_symm", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mulEquivOfOrderOfEq_symm_apply_gen", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Group.isCyclic_of_coprime_card_range_card_ker", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": true, "tactics": ["cases", "rw", "rw", "rwa", "cases", "rw", "rwa", "have", "rw", "apply", "rw", "apply", "exact", "exact"], "tactic_count": 14}
{"name": "Group.isCyclic_of_coprime_card_ker", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "isCyclic_left_of_prod", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCyclic_right_of_prod", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "coprime_card_of_isCyclic_prod", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": true, "tactics": ["have", "have", "let", "rw", "simpa"], "tactic_count": 5}
{"name": "not_isAddCyclic_prod_of_infinite_nontrivial", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_isCyclic_prod_of_infinite_nontrivial", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "Group.isCyclic_prod_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": true, "tactics": ["refine", "cases", "cases", "exact", "cases", "cases", "rw", "exact", "apply", "let", "let", "rw", "exact", "let", "rw", "rw", "exact"], "tactic_count": 17}
{"name": "instIsCyclicUnitsWithZero", "kind": "instance", "module": "Mathlib.GroupTheory.SpecificGroups.Cyclic", "is_tactic_proof": true, "tactics": ["apply", "apply"], "tactic_count": 2}
{"name": "DihedralGroup", "kind": "inductive", "module": "Mathlib.GroupTheory.SpecificGroups.Dihedral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDecidableEqDihedralGroup", "kind": "instance", "module": "Mathlib.GroupTheory.SpecificGroups.Dihedral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.GroupTheory.SpecificGroups.Dihedral.0.DihedralGroup.mul", "kind": "definition", "module": "Mathlib.GroupTheory.SpecificGroups.Dihedral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.GroupTheory.SpecificGroups.Dihedral.0.DihedralGroup.one", "kind": "definition", "module": "Mathlib.GroupTheory.SpecificGroups.Dihedral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DihedralGroup.instInhabited", "kind": "instance", "module": "Mathlib.GroupTheory.SpecificGroups.Dihedral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.GroupTheory.SpecificGroups.Dihedral.0.DihedralGroup.inv", "kind": "definition", "module": "Mathlib.GroupTheory.SpecificGroups.Dihedral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DihedralGroup.instGroup", "kind": "instance", "module": "Mathlib.GroupTheory.SpecificGroups.Dihedral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DihedralGroup.r_mul_r", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Dihedral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DihedralGroup.r_mul_sr", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Dihedral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DihedralGroup.sr_mul_r", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Dihedral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DihedralGroup.sr_mul_sr", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Dihedral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DihedralGroup.inv_r", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Dihedral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DihedralGroup.inv_sr", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Dihedral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DihedralGroup.r_zero", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Dihedral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DihedralGroup.one_def", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Dihedral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DihedralGroup.r_pow", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Dihedral", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "DihedralGroup.r_zpow", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Dihedral", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "_private.Mathlib.GroupTheory.SpecificGroups.Dihedral.0.DihedralGroup.fintypeHelper", "kind": "definition", "module": "Mathlib.GroupTheory.SpecificGroups.Dihedral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DihedralGroup.instFintypeOfNeZeroNat", "kind": "instance", "module": "Mathlib.GroupTheory.SpecificGroups.Dihedral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DihedralGroup.instInfiniteOfNatNat", "kind": "instance", "module": "Mathlib.GroupTheory.SpecificGroups.Dihedral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DihedralGroup.instNontrivial", "kind": "instance", "module": "Mathlib.GroupTheory.SpecificGroups.Dihedral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DihedralGroup.card", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Dihedral", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "DihedralGroup.nat_card", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Dihedral", "is_tactic_proof": true, "tactics": ["cases", "rw", "rw"], "tactic_count": 3}
{"name": "DihedralGroup.r_one_pow", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Dihedral", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DihedralGroup.r_one_zpow", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Dihedral", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DihedralGroup.r_one_pow_n", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Dihedral", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DihedralGroup.sr_mul_self", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Dihedral", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DihedralGroup.orderOf_sr", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Dihedral", "is_tactic_proof": true, "tactics": ["apply", "rw", "simp"], "tactic_count": 3}
{"name": "DihedralGroup.orderOf_r_one", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Dihedral", "is_tactic_proof": true, "tactics": ["rcases", "rw", "intro", "rw", "apply", "simpa", "apply", "intro", "have", "rw", "injection", "rw", "exact"], "tactic_count": 13}
{"name": "DihedralGroup.orderOf_r", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Dihedral", "is_tactic_proof": true, "tactics": ["conv_lhs", "rw"], "tactic_count": 2}
{"name": "DihedralGroup.exponent", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Dihedral", "is_tactic_proof": true, "tactics": ["rcases", "exact", "apply", "apply", "rintro", "rw", "refine", "exact", "rw", "exact", "apply", "convert", "exact", "convert", "exact"], "tactic_count": 15}
{"name": "DihedralGroup.not_commutative", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Dihedral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DihedralGroup.commutative_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Dihedral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DihedralGroup.not_isCyclic", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Dihedral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DihedralGroup.isCyclic_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Dihedral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DihedralGroup.instIsKleinFourOfNatNat", "kind": "instance", "module": "Mathlib.GroupTheory.SpecificGroups.Dihedral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DihedralGroup.oddCommuteEquiv", "kind": "definition", "module": "Mathlib.GroupTheory.SpecificGroups.Dihedral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DihedralGroup.card_commute_odd", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Dihedral", "is_tactic_proof": true, "tactics": ["have", "simp_rw", "ring"], "tactic_count": 3}
{"name": "DihedralGroup.card_conjClasses_odd", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Dihedral", "is_tactic_proof": true, "tactics": ["rw", "nat_card,"], "tactic_count": 2}
{"name": "DihedralGroup.center_eq_bot_of_odd_ne_one", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Dihedral", "is_tactic_proof": true, "tactics": ["simp", "rintro", "have", "simp_all", "have", "have", "simp"], "tactic_count": 7}
{"name": "instIsAddKleinFourProdZModOfNatNat", "kind": "instance", "module": "Mathlib.GroupTheory.SpecificGroups.KleinFour", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsAddKleinFourAdditiveOfIsKleinFour", "kind": "instance", "module": "Mathlib.GroupTheory.SpecificGroups.KleinFour", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsKleinFourMultiplicativeOfIsAddKleinFour", "kind": "instance", "module": "Mathlib.GroupTheory.SpecificGroups.KleinFour", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsKleinFour.instFinite", "kind": "instance", "module": "Mathlib.GroupTheory.SpecificGroups.KleinFour", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsKleinFour.card_four'", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.KleinFour", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsKleinFour.not_isCyclic", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.KleinFour", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsKleinFour.inv_eq_self", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.KleinFour", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsKleinFour.mul_self", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.KleinFour", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsKleinFour.eq_finset_univ", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.KleinFour", "is_tactic_proof": true, "tactics": ["apply", "rw", "repeat", "on_goal", "all_goals"], "tactic_count": 5}
{"name": "IsKleinFour.eq_mul_of_ne_all", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.KleinFour", "is_tactic_proof": true, "tactics": ["classical", "let", "apply", "simpa"], "tactic_count": 4}
{"name": "IsKleinFour.mulEquiv'", "kind": "definition", "module": "Mathlib.GroupTheory.SpecificGroups.KleinFour", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsKleinFour.mulEquiv", "kind": "abbrev", "module": "Mathlib.GroupTheory.SpecificGroups.KleinFour", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsKleinFour.nonempty_mulEquiv", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.KleinFour", "is_tactic_proof": true, "tactics": ["classical", "let", "let", "exact"], "tactic_count": 4}
{"name": "QuaternionGroup", "kind": "inductive", "module": "Mathlib.GroupTheory.SpecificGroups.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDecidableEqQuaternionGroup", "kind": "instance", "module": "Mathlib.GroupTheory.SpecificGroups.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.GroupTheory.SpecificGroups.Quaternion.0.QuaternionGroup.mul", "kind": "definition", "module": "Mathlib.GroupTheory.SpecificGroups.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.GroupTheory.SpecificGroups.Quaternion.0.QuaternionGroup.one", "kind": "definition", "module": "Mathlib.GroupTheory.SpecificGroups.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuaternionGroup.instInhabited", "kind": "instance", "module": "Mathlib.GroupTheory.SpecificGroups.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.GroupTheory.SpecificGroups.Quaternion.0.QuaternionGroup.inv", "kind": "definition", "module": "Mathlib.GroupTheory.SpecificGroups.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuaternionGroup.instGroup", "kind": "instance", "module": "Mathlib.GroupTheory.SpecificGroups.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuaternionGroup.a_mul_a", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuaternionGroup.a_mul_xa", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuaternionGroup.xa_mul_a", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuaternionGroup.xa_mul_xa", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuaternionGroup.a_zero", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Quaternion", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "QuaternionGroup.one_def", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.GroupTheory.SpecificGroups.Quaternion.0.QuaternionGroup.fintypeHelper", "kind": "definition", "module": "Mathlib.GroupTheory.SpecificGroups.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuaternionGroup.quaternionGroupZeroEquivDihedralGroupZero", "kind": "definition", "module": "Mathlib.GroupTheory.SpecificGroups.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuaternionGroup.instFintypeOfNeZeroNat", "kind": "instance", "module": "Mathlib.GroupTheory.SpecificGroups.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuaternionGroup.instNontrivial", "kind": "instance", "module": "Mathlib.GroupTheory.SpecificGroups.Quaternion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuaternionGroup.card", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Quaternion", "is_tactic_proof": true, "tactics": ["rw", "ring"], "tactic_count": 2}
{"name": "QuaternionGroup.a_one_pow", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Quaternion", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "congr", "norm_cast"], "tactic_count": 6}
{"name": "QuaternionGroup.a_one_pow_n", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Quaternion", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "QuaternionGroup.xa_sq", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Quaternion", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "QuaternionGroup.xa_pow_four", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Quaternion", "is_tactic_proof": true, "tactics": ["calc", "xa"], "tactic_count": 2}
{"name": "QuaternionGroup.orderOf_xa", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Quaternion", "is_tactic_proof": true, "tactics": ["change", "haveI", "apply", "intro", "simp", "injection", "apply_fun", "apply_fun", "simp", "reduceCtorEq]", "simp"], "tactic_count": 11}
{"name": "QuaternionGroup.quaternionGroup_one_isCyclic", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Quaternion", "is_tactic_proof": true, "tactics": ["apply", "rw", "exact"], "tactic_count": 3}
{"name": "QuaternionGroup.orderOf_a_one", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Quaternion", "is_tactic_proof": true, "tactics": ["rcases", "subst", "simp_rw", "intro", "rw", "apply", "haveI", "simpa", "apply", "intro", "have", "rw", "injection", "rw", "exact"], "tactic_count": 15}
{"name": "QuaternionGroup.orderOf_a", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Quaternion", "is_tactic_proof": true, "tactics": ["conv_lhs", "rw"], "tactic_count": 2}
{"name": "QuaternionGroup.exponent", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.Quaternion", "is_tactic_proof": true, "tactics": ["rw", "norm_num", "rcases", "subst", "simp", "exact", "apply", "apply", "rintro", "rw", "refine", "exact", "rw", "exact", "apply", "convert", "exact", "convert", "exact"], "tactic_count": 19}
{"name": "IsZGroup.instOfIsCyclic", "kind": "instance", "module": "Mathlib.GroupTheory.SpecificGroups.ZGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsZGroup.instIsCyclicSubtypeMemSubgroupOfFactPrime", "kind": "instance", "module": "Mathlib.GroupTheory.SpecificGroups.ZGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPGroup.isCyclic_of_isZGroup", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.ZGroup", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "IsZGroup.of_squarefree", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.ZGroup", "is_tactic_proof": true, "tactics": ["have", "refine", "have", "obtain", "exact"], "tactic_count": 5}
{"name": "IsZGroup.of_injective", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.ZGroup", "is_tactic_proof": true, "tactics": ["rw", "intro", "obtain", "specialize", "have", "have", "exact"], "tactic_count": 7}
{"name": "IsZGroup.instSubtypeMemSubgroup", "kind": "instance", "module": "Mathlib.GroupTheory.SpecificGroups.ZGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsZGroup.of_surjective", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.ZGroup", "is_tactic_proof": true, "tactics": ["rw", "intro", "have", "obtain", "specialize", "exact"], "tactic_count": 6}
{"name": "IsZGroup.instQuotientSubgroupOfFinite", "kind": "instance", "module": "Mathlib.GroupTheory.SpecificGroups.ZGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsZGroup.commutator_lt", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.ZGroup", "is_tactic_proof": true, "tactics": ["let", "have", "have", "let", "have", "let", "refine", "have", "contrapose", "rw", "exact"], "tactic_count": 11}
{"name": "IsZGroup.instIsSolvableOfFinite", "kind": "instance", "module": "Mathlib.GroupTheory.SpecificGroups.ZGroup", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "rw", "exact"], "tactic_count": 5}
{"name": "IsZGroup.exponent_eq_card", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.ZGroup", "is_tactic_proof": true, "tactics": ["refine", "rw", "intro", "have", "let", "rw", "exact"], "tactic_count": 7}
{"name": "IsZGroup.instIsCyclicOfFiniteOfIsNilpotent", "kind": "instance", "module": "Mathlib.GroupTheory.SpecificGroups.ZGroup", "is_tactic_proof": true, "tactics": ["have", "obtain", "let", "exact"], "tactic_count": 4}
{"name": "IsZGroup.isCyclic_abelianization", "kind": "instance", "module": "Mathlib.GroupTheory.SpecificGroups.ZGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsZGroup.isCyclic_commutator", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.ZGroup", "is_tactic_proof": true, "tactics": ["rw", "induction", "ind", "rcases", "rw", "infer_instance", "specialize", "replace", "let", "rw", "exact", "suffices", "let", "rw", "exact", "suffices", "rw", "let", "infer_instance", "suffices", "simpa", "rw", "let", "have", "rwa"], "tactic_count": 25}
{"name": "IsPGroup.smul_mul_inv_trivial_or_surjective", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.ZGroup", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "simp", "have", "let", "have", "rw", "rw", "replace", "obtain", "exact", "rcases", "exact", "obtain", "rw", "rw", "refine", "rw", "exact"], "tactic_count": 19}
{"name": "IsPGroup.commutator_eq_bot_or_commutator_eq_self", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.ZGroup", "is_tactic_proof": true, "tactics": ["let", "refine", "rw", "exact", "rw", "refine", "obtain", "rw", "exact"], "tactic_count": 9}
{"name": "Sylow.commutator_eq_bot_or_commutator_eq_self", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.ZGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sylow.le_center_or_le_commutator", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.ZGroup", "is_tactic_proof": true, "tactics": ["obtain", "refine", "replace", "rwa", "rw", "exact"], "tactic_count": 6}
{"name": "Sylow.normalizer_le_centralizer_or_le_commutator", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.ZGroup", "is_tactic_proof": true, "tactics": ["let", "have", "have", "refine", "rw", "replace", "rwa", "rw", "exact"], "tactic_count": 9}
{"name": "Sylow.not_dvd_card_commutator_or_not_dvd_index_commutator", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.ZGroup", "is_tactic_proof": false, "tactics": ["refine", "rw", "exact", "exact"], "tactic_count": 4}
{"name": "IsZGroup.coprime_commutator_index", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.ZGroup", "is_tactic_proof": false, "tactics": ["suffices", "contrapose", "exact", "intro", "have", "exact"], "tactic_count": 6}
{"name": "isZGroup_of_coprime", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.ZGroup", "is_tactic_proof": true, "tactics": ["refine", "have", "replace", "rcases", "replace", "suffices", "have", "exact", "obtain", "rw", "exact", "have", "apply", "rwa"], "tactic_count": 14}
{"name": "isZGroup_iff_exists_mulEquiv", "kind": "theorem", "module": "Mathlib.GroupTheory.SpecificGroups.ZGroup", "is_tactic_proof": true, "tactics": ["refine", "obtain", "have", "refine", "hG.isCyclic_commutator,", "exact", "rintro", "have", "exact"], "tactic_count": 9}
{"name": "Subgroup.center", "kind": "definition", "module": "Mathlib.GroupTheory.Subgroup.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.coe_center", "kind": "theorem", "module": "Mathlib.GroupTheory.Subgroup.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.center_toSubmonoid", "kind": "theorem", "module": "Mathlib.GroupTheory.Subgroup.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.center.isMulCommutative", "kind": "instance", "module": "Mathlib.GroupTheory.Subgroup.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.centerCongr", "kind": "definition", "module": "Mathlib.GroupTheory.Subgroup.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.centerToMulOpposite", "kind": "definition", "module": "Mathlib.GroupTheory.Subgroup.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.mem_center_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Subgroup.Center", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Subgroup.decidableMemCenter", "kind": "instance", "module": "Mathlib.GroupTheory.Subgroup.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.centerCharacteristic", "kind": "instance", "module": "Mathlib.GroupTheory.Subgroup.Center", "is_tactic_proof": true, "tactics": ["refine", "rw", "intro", "rw", "exact"], "tactic_count": 5}
{"name": "CommGroup.center_eq_top", "kind": "theorem", "module": "Mathlib.GroupTheory.Subgroup.Center", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "intro", "exact"], "tactic_count": 5}
{"name": "Group.commGroupOfCenterEqTop", "kind": "definition", "module": "Mathlib.GroupTheory.Subgroup.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.instNormalCenter", "kind": "instance", "module": "Mathlib.GroupTheory.Subgroup.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.center_le_normalizer", "kind": "theorem", "module": "Mathlib.GroupTheory.Subgroup.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsConj.eq_of_left_mem_center", "kind": "theorem", "module": "Mathlib.GroupTheory.Subgroup.Center", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "IsConj.eq_of_right_mem_center", "kind": "theorem", "module": "Mathlib.GroupTheory.Subgroup.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjClasses.mk_bijOn", "kind": "theorem", "module": "Mathlib.GroupTheory.Subgroup.Center", "is_tactic_proof": true, "tactics": ["refine", "simp", "intro", "simp", "rw", "rw", "exact", "rintro", "refine", "simp", "rw", "intro", "rw", "refine", "rw", "apply", "rw", "exact"], "tactic_count": 18}
{"name": "Subgroup.centralizer", "kind": "definition", "module": "Mathlib.GroupTheory.Subgroup.Centralizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.mem_centralizer_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Subgroup.Centralizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.mem_centralizer_iff_commutator_eq_one", "kind": "theorem", "module": "Mathlib.GroupTheory.Subgroup.Centralizer", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Subgroup.mem_centralizer_singleton_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Subgroup.Centralizer", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Subgroup.centralizer_univ", "kind": "theorem", "module": "Mathlib.GroupTheory.Subgroup.Centralizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.le_centralizer_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Subgroup.Centralizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.center_le_centralizer", "kind": "theorem", "module": "Mathlib.GroupTheory.Subgroup.Centralizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.centralizer_le", "kind": "theorem", "module": "Mathlib.GroupTheory.Subgroup.Centralizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.centralizer_eq_top_iff_subset", "kind": "theorem", "module": "Mathlib.GroupTheory.Subgroup.Centralizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.map_centralizer_le_centralizer_image", "kind": "theorem", "module": "Mathlib.GroupTheory.Subgroup.Centralizer", "is_tactic_proof": true, "tactics": ["rintro", "rw"], "tactic_count": 2}
{"name": "Subgroup.normal_centralizer", "kind": "instance", "module": "Mathlib.GroupTheory.Subgroup.Centralizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.characteristic_centralizer", "kind": "instance", "module": "Mathlib.GroupTheory.Subgroup.Centralizer", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "Subgroup.le_centralizer_iff_isMulCommutative", "kind": "theorem", "module": "Mathlib.GroupTheory.Subgroup.Centralizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.le_centralizer", "kind": "theorem", "module": "Mathlib.GroupTheory.Subgroup.Centralizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.closure_le_centralizer_centralizer", "kind": "theorem", "module": "Mathlib.GroupTheory.Subgroup.Centralizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.centralizer_closure", "kind": "theorem", "module": "Mathlib.GroupTheory.Subgroup.Centralizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.centralizer_eq_iInf", "kind": "theorem", "module": "Mathlib.GroupTheory.Subgroup.Centralizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.center_eq_iInf", "kind": "theorem", "module": "Mathlib.GroupTheory.Subgroup.Centralizer", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subgroup.center_eq_infi'", "kind": "theorem", "module": "Mathlib.GroupTheory.Subgroup.Centralizer", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subgroup.closureCommGroupOfComm", "kind": "abbrev", "module": "Mathlib.GroupTheory.Subgroup.Centralizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.instMulDistribMulActionSubtypeMemNormalizer", "kind": "instance", "module": "Mathlib.GroupTheory.Subgroup.Centralizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.normalizerMonoidHom", "kind": "definition", "module": "Mathlib.GroupTheory.Subgroup.Centralizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.normalizerMonoidHom_ker", "kind": "theorem", "module": "Mathlib.GroupTheory.Subgroup.Centralizer", "is_tactic_proof": true, "tactics": ["simp", "eq_comm]"], "tactic_count": 2}
{"name": "Subgroup.Saturated", "kind": "definition", "module": "Mathlib.GroupTheory.Subgroup.Saturated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.saturated_iff_npow", "kind": "theorem", "module": "Mathlib.GroupTheory.Subgroup.Saturated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.saturated_iff_zpow", "kind": "theorem", "module": "Mathlib.GroupTheory.Subgroup.Saturated", "is_tactic_proof": true, "tactics": ["constructor", "intro", "cases", "ofNat", "simp", "exact", "negSucc", "n", "suffices", "refine", "simp", "simpa", "intro", "specialize", "simp", "apply"], "tactic_count": 16}
{"name": "AddSubgroup.ker_saturated", "kind": "theorem", "module": "Mathlib.GroupTheory.Subgroup.Saturated", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Subgroup.Normal.eq_bot_or_eq_top", "kind": "theorem", "module": "Mathlib.GroupTheory.Subgroup.Simple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.isSimpleGroup_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Subgroup.Simple", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "IsSimpleGroup.instIsSimpleOrderSubgroup", "kind": "instance", "module": "Mathlib.GroupTheory.Subgroup.Simple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSimpleGroup.isSimpleGroup_of_surjective", "kind": "theorem", "module": "Mathlib.GroupTheory.Subgroup.Simple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.isSimpleGroup", "kind": "theorem", "module": "Mathlib.GroupTheory.Subgroup.Simple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.isSimpleGroup_congr", "kind": "theorem", "module": "Mathlib.GroupTheory.Subgroup.Simple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.center", "kind": "definition", "module": "Mathlib.GroupTheory.Submonoid.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.coe_center", "kind": "theorem", "module": "Mathlib.GroupTheory.Submonoid.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.center_toSubsemigroup", "kind": "theorem", "module": "Mathlib.GroupTheory.Submonoid.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.instSMulCommClassSubtypeMemCenter", "kind": "instance", "module": "Mathlib.GroupTheory.Submonoid.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.instSMulCommClassSubtypeMemCenter_1", "kind": "instance", "module": "Mathlib.GroupTheory.Submonoid.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.center.commMonoid'", "kind": "abbrev", "module": "Mathlib.GroupTheory.Submonoid.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.center.commMonoid", "kind": "instance", "module": "Mathlib.GroupTheory.Submonoid.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid._example", "kind": "example", "module": "Mathlib.GroupTheory.Submonoid.Center", "is_tactic_proof": true, "tactics": ["with_reducible_and_instances"], "tactic_count": 1}
{"name": "Submonoid.mem_center_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Submonoid.Center", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Submonoid.decidableMemCenter", "kind": "instance", "module": "Mathlib.GroupTheory.Submonoid.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.center.smulCommClass_left", "kind": "instance", "module": "Mathlib.GroupTheory.Submonoid.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.center.smulCommClass_right", "kind": "instance", "module": "Mathlib.GroupTheory.Submonoid.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid._example", "kind": "example", "module": "Mathlib.GroupTheory.Submonoid.Center", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Submonoid.center_eq_top", "kind": "theorem", "module": "Mathlib.GroupTheory.Submonoid.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitsCenterToCenterUnits", "kind": "definition", "module": "Mathlib.GroupTheory.Submonoid.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitsCenterToCenterUnits_injective", "kind": "theorem", "module": "Mathlib.GroupTheory.Submonoid.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquivClass.apply_mem_center", "kind": "theorem", "module": "Mathlib.GroupTheory.Submonoid.Center", "is_tactic_proof": true, "tactics": ["let", "change", "constructor", "simp"], "tactic_count": 4}
{"name": "MulEquivClass.apply_mem_center_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Submonoid.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.centerCongr", "kind": "definition", "module": "Mathlib.GroupTheory.Submonoid.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.centerCongr", "kind": "definition", "module": "Mathlib.GroupTheory.Submonoid.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.op_mem_center_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Submonoid.Center", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MulOpposite.unop_mem_center_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Submonoid.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.centerToMulOpposite", "kind": "definition", "module": "Mathlib.GroupTheory.Submonoid.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.centerToMulOpposite", "kind": "definition", "module": "Mathlib.GroupTheory.Submonoid.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.centralizer", "kind": "definition", "module": "Mathlib.GroupTheory.Submonoid.Centralizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.coe_centralizer", "kind": "theorem", "module": "Mathlib.GroupTheory.Submonoid.Centralizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.centralizer_toSubsemigroup", "kind": "theorem", "module": "Mathlib.GroupTheory.Submonoid.Centralizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.mem_centralizer_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Submonoid.Centralizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.center_le_centralizer", "kind": "theorem", "module": "Mathlib.GroupTheory.Submonoid.Centralizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.decidableMemCentralizer", "kind": "instance", "module": "Mathlib.GroupTheory.Submonoid.Centralizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.centralizer_le", "kind": "theorem", "module": "Mathlib.GroupTheory.Submonoid.Centralizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.centralizer_eq_top_iff_subset", "kind": "theorem", "module": "Mathlib.GroupTheory.Submonoid.Centralizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.centralizer_univ", "kind": "theorem", "module": "Mathlib.GroupTheory.Submonoid.Centralizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.le_centralizer_centralizer", "kind": "theorem", "module": "Mathlib.GroupTheory.Submonoid.Centralizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.centralizer_centralizer_centralizer", "kind": "theorem", "module": "Mathlib.GroupTheory.Submonoid.Centralizer", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "Submonoid.closure_le_centralizer_centralizer", "kind": "theorem", "module": "Mathlib.GroupTheory.Submonoid.Centralizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.closureCommMonoidOfComm", "kind": "abbrev", "module": "Mathlib.GroupTheory.Submonoid.Centralizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.instGroupSubtypeMemSubmonoid", "kind": "instance", "module": "Mathlib.GroupTheory.Submonoid.Inverses", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.instCommGroupSubtypeMemSubmonoid", "kind": "instance", "module": "Mathlib.GroupTheory.Submonoid.Inverses", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.IsUnit.Submonoid.coe_inv", "kind": "theorem", "module": "Mathlib.GroupTheory.Submonoid.Inverses", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.leftInv", "kind": "definition", "module": "Mathlib.GroupTheory.Submonoid.Inverses", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.leftInv_leftInv_le", "kind": "theorem", "module": "Mathlib.GroupTheory.Submonoid.Inverses", "is_tactic_proof": true, "tactics": ["rintro", "convert", "rw"], "tactic_count": 3}
{"name": "Submonoid.unit_mem_leftInv", "kind": "theorem", "module": "Mathlib.GroupTheory.Submonoid.Inverses", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.leftInv_leftInv_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.Submonoid.Inverses", "is_tactic_proof": true, "tactics": ["refine", "intro", "have", "rw", "rfl", "rw", "exact"], "tactic_count": 7}
{"name": "Submonoid.fromLeftInv", "kind": "definition", "module": "Mathlib.GroupTheory.Submonoid.Inverses", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.mul_fromLeftInv", "kind": "theorem", "module": "Mathlib.GroupTheory.Submonoid.Inverses", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.fromLeftInv_one", "kind": "theorem", "module": "Mathlib.GroupTheory.Submonoid.Inverses", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.fromLeftInv_mul", "kind": "theorem", "module": "Mathlib.GroupTheory.Submonoid.Inverses", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submonoid.leftInv_le_isUnit", "kind": "theorem", "module": "Mathlib.GroupTheory.Submonoid.Inverses", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.fromLeftInv_eq_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Submonoid.Inverses", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submonoid.fromCommLeftInv", "kind": "definition", "module": "Mathlib.GroupTheory.Submonoid.Inverses", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.leftInvEquiv", "kind": "definition", "module": "Mathlib.GroupTheory.Submonoid.Inverses", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.fromLeftInv_leftInvEquiv_symm", "kind": "theorem", "module": "Mathlib.GroupTheory.Submonoid.Inverses", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.leftInvEquiv_symm_fromLeftInv", "kind": "theorem", "module": "Mathlib.GroupTheory.Submonoid.Inverses", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.leftInvEquiv_mul", "kind": "theorem", "module": "Mathlib.GroupTheory.Submonoid.Inverses", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Submonoid.mul_leftInvEquiv", "kind": "theorem", "module": "Mathlib.GroupTheory.Submonoid.Inverses", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Submonoid.leftInvEquiv_symm_mul", "kind": "theorem", "module": "Mathlib.GroupTheory.Submonoid.Inverses", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "Submonoid.mul_leftInvEquiv_symm", "kind": "theorem", "module": "Mathlib.GroupTheory.Submonoid.Inverses", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "Submonoid.leftInv_eq_inv", "kind": "theorem", "module": "Mathlib.GroupTheory.Submonoid.Inverses", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.fromLeftInv_eq_inv", "kind": "theorem", "module": "Mathlib.GroupTheory.Submonoid.Inverses", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submonoid.leftInvEquiv_symm_eq_inv", "kind": "theorem", "module": "Mathlib.GroupTheory.Submonoid.Inverses", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subsemigroup.center", "kind": "definition", "module": "Mathlib.GroupTheory.Subsemigroup.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.center.commSemigroup", "kind": "instance", "module": "Mathlib.GroupTheory.Subsemigroup.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.mem_center_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Subsemigroup.Center", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Subsemigroup.decidableMemCenter", "kind": "instance", "module": "Mathlib.GroupTheory.Subsemigroup.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.center_eq_top", "kind": "theorem", "module": "Mathlib.GroupTheory.Subsemigroup.Center", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.centralizer", "kind": "definition", "module": "Mathlib.GroupTheory.Subsemigroup.Centralizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.coe_centralizer", "kind": "theorem", "module": "Mathlib.GroupTheory.Subsemigroup.Centralizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.mem_centralizer_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Subsemigroup.Centralizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.decidableMemCentralizer", "kind": "instance", "module": "Mathlib.GroupTheory.Subsemigroup.Centralizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.center_le_centralizer", "kind": "theorem", "module": "Mathlib.GroupTheory.Subsemigroup.Centralizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.centralizer_le", "kind": "theorem", "module": "Mathlib.GroupTheory.Subsemigroup.Centralizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.centralizer_eq_top_iff_subset", "kind": "theorem", "module": "Mathlib.GroupTheory.Subsemigroup.Centralizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.centralizer_univ", "kind": "theorem", "module": "Mathlib.GroupTheory.Subsemigroup.Centralizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.closure_le_centralizer_centralizer", "kind": "theorem", "module": "Mathlib.GroupTheory.Subsemigroup.Centralizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.closureCommSemigroupOfComm", "kind": "abbrev", "module": "Mathlib.GroupTheory.Subsemigroup.Centralizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sylow.instCoeOutSubgroup", "kind": "instance", "module": "Mathlib.GroupTheory.Sylow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sylow.ext", "kind": "theorem", "module": "Mathlib.GroupTheory.Sylow", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Sylow.instSetLike", "kind": "instance", "module": "Mathlib.GroupTheory.Sylow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sylow.instPartialOrder", "kind": "instance", "module": "Mathlib.GroupTheory.Sylow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sylow.instSubgroupClass", "kind": "instance", "module": "Mathlib.GroupTheory.Sylow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPGroup.toSylow", "kind": "definition", "module": "Mathlib.GroupTheory.Sylow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPGroup.toSylow_coe", "kind": "theorem", "module": "Mathlib.GroupTheory.Sylow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPGroup.mem_toSylow", "kind": "theorem", "module": "Mathlib.GroupTheory.Sylow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sylow.ofCard", "kind": "definition", "module": "Mathlib.GroupTheory.Sylow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sylow.coe_ofCard", "kind": "theorem", "module": "Mathlib.GroupTheory.Sylow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sylow.comapOfKerIsPGroup", "kind": "definition", "module": "Mathlib.GroupTheory.Sylow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sylow.coe_comapOfKerIsPGroup", "kind": "theorem", "module": "Mathlib.GroupTheory.Sylow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sylow.comapOfInjective", "kind": "definition", "module": "Mathlib.GroupTheory.Sylow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sylow.coe_comapOfInjective", "kind": "theorem", "module": "Mathlib.GroupTheory.Sylow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sylow.subtype", "kind": "definition", "module": "Mathlib.GroupTheory.Sylow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sylow.coe_subtype", "kind": "theorem", "module": "Mathlib.GroupTheory.Sylow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sylow.subtype_injective", "kind": "theorem", "module": "Mathlib.GroupTheory.Sylow", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsPGroup.exists_le_sylow", "kind": "theorem", "module": "Mathlib.GroupTheory.Sylow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sylow.nonempty", "kind": "instance", "module": "Mathlib.GroupTheory.Sylow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sylow.inhabited", "kind": "instance", "module": "Mathlib.GroupTheory.Sylow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sylow.exists_comap_eq_of_ker_isPGroup", "kind": "theorem", "module": "Mathlib.GroupTheory.Sylow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sylow.exists_comap_eq_of_injective", "kind": "theorem", "module": "Mathlib.GroupTheory.Sylow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sylow.exists_comap_subtype_eq", "kind": "theorem", "module": "Mathlib.GroupTheory.Sylow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sylow.finite_of_ker_is_pGroup", "kind": "theorem", "module": "Mathlib.GroupTheory.Sylow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sylow.finite_of_injective", "kind": "theorem", "module": "Mathlib.GroupTheory.Sylow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sylow.instFiniteSubtypeMemSubgroup", "kind": "instance", "module": "Mathlib.GroupTheory.Sylow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sylow.pointwiseMulAction", "kind": "instance", "module": "Mathlib.GroupTheory.Sylow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sylow.pointwise_smul_def", "kind": "theorem", "module": "Mathlib.GroupTheory.Sylow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sylow.mulAction", "kind": "instance", "module": "Mathlib.GroupTheory.Sylow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sylow.smul_def", "kind": "theorem", "module": "Mathlib.GroupTheory.Sylow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sylow.coe_subgroup_smul", "kind": "theorem", "module": "Mathlib.GroupTheory.Sylow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sylow.coe_smul", "kind": "theorem", "module": "Mathlib.GroupTheory.Sylow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sylow.smul_le", "kind": "theorem", "module": "Mathlib.GroupTheory.Sylow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sylow.smul_subtype", "kind": "theorem", "module": "Mathlib.GroupTheory.Sylow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sylow.smul_eq_iff_mem_normalizer", "kind": "theorem", "module": "Mathlib.GroupTheory.Sylow", "is_tactic_proof": false, "tactics": ["rw", "exact", "forall_congr", "iff_congr"], "tactic_count": 4}
{"name": "Sylow.smul_eq_of_normal", "kind": "theorem", "module": "Mathlib.GroupTheory.Sylow", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Subgroup.sylow_mem_fixedPoints_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Sylow", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "IsPGroup.inf_normalizer_sylow", "kind": "theorem", "module": "Mathlib.GroupTheory.Sylow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPGroup.sylow_mem_fixedPoints_iff", "kind": "theorem", "module": "Mathlib.GroupTheory.Sylow", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Sylow.isPretransitive_of_finite", "kind": "instance", "module": "Mathlib.GroupTheory.Sylow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "card_sylow_modEq_one", "kind": "theorem", "module": "Mathlib.GroupTheory.Sylow", "is_tactic_proof": true, "tactics": ["refine", "have", "calc", "have", "exact"], "tactic_count": 5}
{"name": "not_dvd_card_sylow", "kind": "theorem", "module": "Mathlib.GroupTheory.Sylow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sylow.equivSMul", "kind": "definition", "module": "Mathlib.GroupTheory.Sylow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sylow.equiv", "kind": "definition", "module": "Mathlib.GroupTheory.Sylow", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Sylow.orbit_eq_top", "kind": "theorem", "module": "Mathlib.GroupTheory.Sylow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sylow.stabilizer_eq_normalizer", "kind": "theorem", "module": "Mathlib.GroupTheory.Sylow", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Sylow.conj_eq_normalizer_conj_of_mem_centralizer", "kind": "theorem", "module": "Mathlib.GroupTheory.Sylow", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "rintro", "specialize", "rwa", "mul_assoc,", "obtain", "simp_rw", "refine", "rw"], "tactic_count": 11}
{"name": "Sylow.conj_eq_normalizer_conj_of_mem", "kind": "theorem", "module": "Mathlib.GroupTheory.Sylow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sylow.equivQuotientNormalizer", "kind": "definition", "module": "Mathlib.GroupTheory.Sylow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sylow.instFiniteQuotientSubgroupNormalizerOfFactPrime", "kind": "instance", "module": "Mathlib.GroupTheory.Sylow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sylow.card_eq_card_quotient_normalizer", "kind": "theorem", "module": "Mathlib.GroupTheory.Sylow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sylow.card_eq_index_normalizer", "kind": "theorem", "module": "Mathlib.GroupTheory.Sylow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sylow.card_dvd_index", "kind": "theorem", "module": "Mathlib.GroupTheory.Sylow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.GroupTheory.Sylow.0.Sylow.not_dvd_index_aux", "kind": "theorem", "module": "Mathlib.GroupTheory.Sylow", "is_tactic_proof": true, "tactics": ["intro", "rw", "obtain", "have", "let", "have", "apply", "rw", "exact", "replace", "rw", "exact"], "tactic_count": 12}
{"name": "Sylow.not_dvd_index'", "kind": "theorem", "module": "Mathlib.GroupTheory.Sylow", "is_tactic_proof": true, "tactics": ["rw", "haveI", "haveI", "replace", "exact"], "tactic_count": 5}
{"name": "Sylow.not_dvd_index", "kind": "theorem", "module": "Mathlib.GroupTheory.Sylow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sylow.mapSurjective", "kind": "definition", "module": "Mathlib.GroupTheory.Sylow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sylow.coe_mapSurjective", "kind": "theorem", "module": "Mathlib.GroupTheory.Sylow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sylow.mapSurjective_surjective", "kind": "theorem", "module": "Mathlib.GroupTheory.Sylow", "is_tactic_proof": true, "tactics": ["have", "intro", "let", "let", "have", "have", "have", "rw", "exact", "use", "rw", "exact"], "tactic_count": 12}
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{"name": "hammingNorm_comp_le_hammingNorm", "kind": "theorem", "module": "Mathlib.InformationTheory.Hamming", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
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{"name": "hammingNorm_smul_le_hammingNorm", "kind": "theorem", "module": "Mathlib.InformationTheory.Hamming", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hammingNorm_smul", "kind": "theorem", "module": "Mathlib.InformationTheory.Hamming", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hammingDist_eq_hammingNorm", "kind": "theorem", "module": "Mathlib.InformationTheory.Hamming", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Hamming", "kind": "definition", "module": "Mathlib.InformationTheory.Hamming", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Hamming.instNontrivialOfNonemptyOfDefault", "kind": "instance", "module": "Mathlib.InformationTheory.Hamming", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hamming.instDecidableEqOfFintype", "kind": "instance", "module": "Mathlib.InformationTheory.Hamming", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hamming.instZero", "kind": "instance", "module": "Mathlib.InformationTheory.Hamming", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hamming.instNeg", "kind": "instance", "module": "Mathlib.InformationTheory.Hamming", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hamming.instAdd", "kind": "instance", "module": "Mathlib.InformationTheory.Hamming", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Hamming.instSMulWithZero", "kind": "instance", "module": "Mathlib.InformationTheory.Hamming", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hamming.instAddMonoid", "kind": "instance", "module": "Mathlib.InformationTheory.Hamming", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Hamming.toHamming", "kind": "definition", "module": "Mathlib.InformationTheory.Hamming", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Hamming.toHamming_symm_eq", "kind": "theorem", "module": "Mathlib.InformationTheory.Hamming", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hamming.ofHamming_symm_eq", "kind": "theorem", "module": "Mathlib.InformationTheory.Hamming", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hamming.toHamming_ofHamming", "kind": "theorem", "module": "Mathlib.InformationTheory.Hamming", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Hamming.toHamming_zero", "kind": "theorem", "module": "Mathlib.InformationTheory.Hamming", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Hamming.ofHamming_smul", "kind": "theorem", "module": "Mathlib.InformationTheory.Hamming", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Hamming.instPseudoMetricSpace", "kind": "instance", "module": "Mathlib.InformationTheory.Hamming", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hamming.nndist_eq_hammingDist", "kind": "theorem", "module": "Mathlib.InformationTheory.Hamming", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hamming.instDiscreteTopology", "kind": "instance", "module": "Mathlib.InformationTheory.Hamming", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hamming.instMetricSpace", "kind": "instance", "module": "Mathlib.InformationTheory.Hamming", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hamming.instNormOfZero", "kind": "instance", "module": "Mathlib.InformationTheory.Hamming", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hamming.norm_eq_hammingNorm", "kind": "theorem", "module": "Mathlib.InformationTheory.Hamming", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hamming.instNormedAddGroupOfAddGroup", "kind": "instance", "module": "Mathlib.InformationTheory.Hamming", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Hamming.nnnorm_eq_hammingNorm", "kind": "theorem", "module": "Mathlib.InformationTheory.Hamming", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "InformationTheory.klFun_zero", "kind": "theorem", "module": "Mathlib.InformationTheory.KullbackLeibler.KLFun", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "InformationTheory.strictConvexOn_klFun", "kind": "theorem", "module": "Mathlib.InformationTheory.KullbackLeibler.KLFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InformationTheory.convexOn_klFun", "kind": "theorem", "module": "Mathlib.InformationTheory.KullbackLeibler.KLFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InformationTheory.convexOn_Ioi_klFun", "kind": "theorem", "module": "Mathlib.InformationTheory.KullbackLeibler.KLFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "InformationTheory.stronglyMeasurable_klFun", "kind": "theorem", "module": "Mathlib.InformationTheory.KullbackLeibler.KLFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InformationTheory.hasDerivAt_klFun", "kind": "theorem", "module": "Mathlib.InformationTheory.KullbackLeibler.KLFun", "is_tactic_proof": true, "tactics": ["convert", "ring"], "tactic_count": 2}
{"name": "InformationTheory.not_differentiableAt_klFun_zero", "kind": "theorem", "module": "Mathlib.InformationTheory.KullbackLeibler.KLFun", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
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{"name": "InformationTheory.rightDeriv_klFun", "kind": "theorem", "module": "Mathlib.InformationTheory.KullbackLeibler.KLFun", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "exact", "exact"], "tactic_count": 4}
{"name": "InformationTheory.leftDeriv_klFun", "kind": "theorem", "module": "Mathlib.InformationTheory.KullbackLeibler.KLFun", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "exact", "exact"], "tactic_count": 4}
{"name": "InformationTheory.rightDeriv_klFun_one", "kind": "theorem", "module": "Mathlib.InformationTheory.KullbackLeibler.KLFun", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "InformationTheory.tendsto_rightDeriv_klFun_atTop", "kind": "theorem", "module": "Mathlib.InformationTheory.KullbackLeibler.KLFun", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "InformationTheory.isMinOn_klFun", "kind": "theorem", "module": "Mathlib.InformationTheory.KullbackLeibler.KLFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AffineEquiv.bijective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AffineEquiv.group", "kind": "instance", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AffineEquiv.linearHom", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineEquiv.equivUnitsAffineMap", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AffineEquiv.prodComm", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AffineMap.instZero", "kind": "instance", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.instAdd", "kind": "instance", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.instSub", "kind": "instance", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.instNeg", "kind": "instance", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.coe_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.coe_add", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.coe_neg", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.coe_sub", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.zero_linear", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.add_linear", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.sub_linear", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.neg_linear", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.instAddCommGroup", "kind": "instance", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.instAddTorsor", "kind": "instance", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.vadd_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.vadd_linear", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.vsub_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.vsub_linear", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.fst", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.coe_fst", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.fst_linear", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.snd", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.coe_snd", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.snd_linear", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.id", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.coe_id", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.id_linear", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.id_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.instInhabited", "kind": "instance", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.comp", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.coe_comp", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.comp_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.comp_id", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.id_comp", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.comp_assoc", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.instMonoid", "kind": "instance", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.coe_mul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.coe_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.linearHom", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.linear_injective_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": true, "tactics": ["obtain", "have", "ext", "simp", "rw"], "tactic_count": 5}
{"name": "AffineMap.linear_surjective_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": true, "tactics": ["obtain", "have", "ext", "simp", "rw"], "tactic_count": 5}
{"name": "AffineMap.linear_bijective_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.image_vsub_image", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": true, "tactics": ["ext", "simp", "grind"], "tactic_count": 3}
{"name": "AffineMap.prod", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.coe_prod", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.prod_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.prodMap", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.coe_prodMap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.prodMap_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.lineMap", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.coe_lineMap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.lineMap_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.lineMap_apply_module'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.lineMap_apply_module", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AffineMap.lineMap_apply_ring'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.lineMap_apply_ring", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.lineMap_vadd_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AffineMap.lineMap_linear", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.lineMap_same_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AffineMap.lineMap_same", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.lineMap_apply_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AffineMap.lineMap_apply_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AffineMap.lineMap_eq_lineMap_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": true, "tactics": ["rw", "sub_eq_zero,"], "tactic_count": 2}
{"name": "AffineMap.lineMap_eq_left_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AffineMap.lineMap_eq_right_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AffineMap.lineMap_injective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.apply_lineMap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AffineMap.comp_lineMap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.fst_lineMap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.snd_lineMap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.lineMap_symm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AffineMap.lineMap_apply_one_sub", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": true, "tactics": ["rw", "congr", "simp"], "tactic_count": 3}
{"name": "AffineMap.lineMap_vsub_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.left_vsub_lineMap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AffineMap.lineMap_vsub_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AffineMap.right_vsub_lineMap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AffineMap.lineMap_vadd_lineMap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.lineMap_vsub_lineMap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.lineMap_lineMap_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AffineMap.lineMap_lineMap_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "AffineMap.lineMap_mono", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": true, "tactics": ["intro", "suffices", "gcongr", "simpa"], "tactic_count": 4}
{"name": "AffineMap.lineMap_anti", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": true, "tactics": ["intro", "suffices", "rw", "gcongr", "simpa"], "tactic_count": 5}
{"name": "AffineMap.decomp", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": true, "tactics": ["ext", "calc", "f"], "tactic_count": 3}
{"name": "AffineMap.decomp'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "AffineMap.image_uIcc", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": ["have", "ext", "change", "rw", "simp", "rw", "simp"], "tactic_count": 7}
{"name": "AffineMap.proj", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.proj_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.proj_linear", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.pi_lineMap_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.distribMulAction", "kind": "instance", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.instModule", "kind": "instance", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.toConstProdLinearMap", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.lineMap_apply'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AffineMap.pi", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.pi_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.pi_comp", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.pi_eq_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "AffineMap.pi_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "AffineMap.proj_pi", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.pi_ext_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": true, "tactics": ["apply", "apply", "intro", "have", "have", "have", "rw", "replace", "simp", "rwa", "exact"], "tactic_count": 11}
{"name": "AffineMap.pi_ext_nonempty", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": true, "tactics": ["apply", "inhabit", "rw", "apply"], "tactic_count": 4}
{"name": "AffineMap.pi_ext_nonempty'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": true, "tactics": ["refine", "convert"], "tactic_count": 2}
{"name": "AffineMap.homothety", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.homothety_def", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.coe_homothety", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.homothety_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.homothety_linear", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AffineMap.homothety_eq_lineMap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.homothety_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "AffineMap.homothety_apply_same", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.homothety_mul_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AffineMap.homothety_mul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.homothety_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "AffineMap.homothety_add", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AffineMap.homothetyHom", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.coe_homothetyHom", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.homothetyAffine", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.coe_homothetyAffine", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Convex.combo_affine_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineMap", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "vectorSpan_vadd", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AffineSubspace.vsub_right_mem_direction_iff_mem", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "AffineSubspace.vsub_left_mem_direction_iff_mem", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "AffineSubspace.toAddTorsor", "kind": "instance", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.coe_vsub", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.coe_vadd", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.subtype", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.subtype_linear", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.subtype_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.subtype_injective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.coe_subtype", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.lineMap_mem", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "AffineSubspace.coe_affineSpan_singleton", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": true, "tactics": ["ext", "rw", "simp"], "tactic_count": 3}
{"name": "AffineSubspace.mem_affineSpan_singleton", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AffineSubspace.unique_affineSpan_singleton", "kind": "instance", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.preimage_coe_affineSpan_singleton", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.topEquiv", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.subsingleton_of_subsingleton_span_eq_top", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": true, "tactics": ["obtain", "have", "rw", "subsingleton_iff_singleton", "exact"], "tactic_count": 5}
{"name": "AffineSubspace.eq_univ_of_subsingleton_span_eq_top", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": true, "tactics": ["obtain", "have", "rw", "exact"], "tactic_count": 4}
{"name": "AffineSubspace.direction_lt_of_nonempty", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": true, "tactics": ["obtain", "rw", "rcases", "rw", "use", "intro", "rw", "exact"], "tactic_count": 8}
{"name": "vectorSpan_eq_span_vsub_set_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "rintro", "simp_rw", "rw", "exact", "rintro", "exact"], "tactic_count": 9}
{"name": "vectorSpan_eq_span_vsub_set_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "rintro", "simp_rw", "rw", "exact", "rintro", "exact"], "tactic_count": 9}
{"name": "vectorSpan_eq_span_vsub_set_left_ne", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": false, "tactics": ["conv_lhs", "rw", "simp"], "tactic_count": 3}
{"name": "vectorSpan_eq_span_vsub_set_right_ne", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": false, "tactics": ["conv_lhs", "rw", "simp"], "tactic_count": 3}
{"name": "vectorSpan_eq_span_vsub_finset_right_ne", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "vectorSpan_image_eq_span_vsub_set_left_ne", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": false, "tactics": ["conv_lhs", "rw", "simp"], "tactic_count": 3}
{"name": "vectorSpan_image_eq_span_vsub_set_right_ne", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": false, "tactics": ["conv_lhs", "rw", "simp"], "tactic_count": 3}
{"name": "vectorSpan_range_eq_span_range_vsub_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": true, "tactics": ["rw", "congr"], "tactic_count": 2}
{"name": "vectorSpan_range_eq_span_range_vsub_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": true, "tactics": ["rw", "congr"], "tactic_count": 2}
{"name": "vectorSpan_range_eq_span_range_vsub_left_ne", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": true, "tactics": ["rw", "congr", "simp", "constructor", "rintro", "exact", "exact"], "tactic_count": 7}
{"name": "vectorSpan_range_eq_span_range_vsub_right_ne", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": true, "tactics": ["rw", "congr", "simp", "constructor", "rintro", "exact", "exact"], "tactic_count": 7}
{"name": "affineSpan_coe_preimage_eq_top", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": true, "tactics": ["rw", "rintro", "refine", "exact", "exact"], "tactic_count": 5}
{"name": "affineSpan_singleton_union_vadd_eq_top_of_span_eq_top", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": true, "tactics": ["convert", "rw", "vectorSpan_eq_span_vsub_set_right", "apply", "rintro", "use", "simp"], "tactic_count": 7}
{"name": "vectorSpan_pair", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "vectorSpan_pair_rev", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mem_vectorSpan_pair", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mem_vectorSpan_pair_rev", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AffineMap.lineMap_mem_affineSpan_pair", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.lineMap_rev_mem_affineSpan_pair", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smul_vsub_vadd_mem_affineSpan_pair", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smul_vsub_rev_vadd_mem_affineSpan_pair", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "vadd_left_mem_affineSpan_pair", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "vadd_right_mem_affineSpan_pair", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mem_affineSpan_pair_iff_exists_lineMap_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "obtain", "refine", "rw", "rintro", "exact"], "tactic_count": 8}
{"name": "mem_affineSpan_pair_iff_exists_lineMap_rev_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AffineSubspace.direction_sup", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": true, "tactics": ["refine", "change", "rw", "rw", "rintro", "rcases", "rw", "use", "rw", "rw", "use", "rw", "use", "rw", "use", "refine", "rw", "exact", "sInf_le_sInf", "hp"], "tactic_count": 20}
{"name": "AffineSubspace.direction_sup_eq_sup_direction", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "AffineSubspace.direction_affineSpan_insert", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": true, "tactics": ["rw", "change", "rw", "simp"], "tactic_count": 4}
{"name": "AffineSubspace.mem_affineSpan_insert_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": true, "tactics": ["rw", "rw", "direction_affineSpan_insert", "constructor", "rintro", "rw", "rcases", "use", "symm", "rw", "rw", "rintro", "use", "rw"], "tactic_count": 14}
{"name": "AffineSubspace.vectorSpan_union_of_mem_of_mem", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "direction_sup_eq_sup_direction"], "tactic_count": 2}
{"name": "AffineMap.map_vectorSpan", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AffineSubspace.map", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.coe_map", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.mem_map", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.mem_map_of_mem", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.mem_map_iff_mem_of_injective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.map_bot", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.map_eq_bot_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": true, "tactics": ["refine", "rwa", "rw"], "tactic_count": 3}
{"name": "AffineSubspace.map_id", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.map_map", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.map_direction", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AffineSubspace.map_span", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simp", "apply", "simp", "exact"], "tactic_count": 5}
{"name": "AffineSubspace.map_mono", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.map_inf_le", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.map_inf_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp", "grind"], "tactic_count": 3}
{"name": "AffineSubspace.map_mk'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp", "constructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 7}
{"name": "AffineSubspace.inclusion", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.coe_inclusion_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.inclusion_rfl", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.map_top_of_surjective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "AffineMap.span_eq_top_of_surjective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AffineMap.linear_eqOn_vectorSpan", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": true, "tactics": ["simp", "apply", "rintro", "simp"], "tactic_count": 4}
{"name": "AffineMap.eqOn_affineSpan", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": true, "tactics": ["rcases", "rintro", "simp"], "tactic_count": 3}
{"name": "AffineMap.ext_on", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "AffineEquiv.ext_on", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineEquiv.ofEq", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineEquiv.coe_ofEq_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineEquiv.ofEq_symm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "AffineEquiv.ofEq_rfl", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineEquiv.span_eq_top_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": true, "tactics": ["refine", "intro", "have", "rw", "exact"], "tactic_count": 5}
{"name": "AffineSubspace.comap", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.coe_comap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.mem_comap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.comap_mono", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.comap_top", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "AffineSubspace.comap_bot", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.comap_id", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.comap_comap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.map_le_iff_le_comap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.gc_map_comap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.map_comap_le", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.le_comap_map", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.map_sup", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.map_iSup", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.comap_inf", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.comap_supr", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.comap_symm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.map_symm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.comap_span", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AffineSubspace.gciMapComap", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.comap_map_eq_of_injective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.Parallel", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.term_∥_", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine._aux_Mathlib_LinearAlgebra_AffineSpace_AffineSubspace_Basic___macroRules_Affine_term_∥__1", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine._aux_Mathlib_LinearAlgebra_AffineSpace_AffineSubspace_Basic___unexpand_AffineSubspace_Parallel_1", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.Parallel.symm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": true, "tactics": ["rcases", "refine", "rw"], "tactic_count": 3}
{"name": "AffineSubspace.parallel_comm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.Parallel.refl", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.Parallel.trans", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "refine", "rw"], "tactic_count": 4}
{"name": "AffineSubspace.Parallel.direction_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simp"], "tactic_count": 2}
{"name": "AffineSubspace.parallel_bot_iff_eq_bot", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": true, "tactics": ["refine", "rcases", "rwa"], "tactic_count": 3}
{"name": "AffineSubspace.bot_parallel_iff_eq_bot", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AffineSubspace.parallel_iff_direction_eq_and_eq_bot_iff_eq_bot", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": true, "tactics": ["refine", "rintro", "exact", "rintro", "exact", "rcases", "by_cases", "rw", "exact", "have", "rcases", "rcases", "refine", "rw", "refine", "simp", "simpa"], "tactic_count": 17}
{"name": "AffineSubspace.Parallel.vectorSpan_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "AffineSubspace.affineSpan_parallel_iff_vectorSpan_eq_and_eq_empty_iff_eq_empty", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": true, "tactics": ["repeat", "exact"], "tactic_count": 2}
{"name": "AffineSubspace.affineSpan_pair_parallel_iff_vectorSpan_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AffineSubspace.affineSpan_pair_parallel_iff_exists_unit_smul'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AffineSubspace.affineSpan_pair_parallel_iff_exists_unit_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "AffineSubspace.direction_affineSpan_pair_le_iff_exists_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AffineSubspace.affineSpan_pair_comm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "affineSpan_pair_eq_of_mem_of_mem_of_ne", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "rcases", "rw", "rcases", "have", "rw", "rintro", "simp_all", "have", "rw", "refine", "convert", "simp", "convert", "simp"], "tactic_count": 16}
{"name": "affineSpan_pair_eq_of_left_mem_of_ne", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "affineSpan_pair_eq_of_right_mem_of_ne", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_eq_smul_of_parallel", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic", "is_tactic_proof": true, "tactics": ["rw", "rw", "obtain", "obtain", "obtain", "rw", "by_cases", "refine", "rw", "vsub_add_vsub_cancel", "exfalso", "have", "rw", "exact", "have", "rw", "exact", "have", "rw", "vsub_left_mem_direction_iff_mem", "exact"], "tactic_count": 21}
{"name": "vectorSpan", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "vectorSpan_def", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "vectorSpan_mono", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "vectorSpan_empty", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "vectorSpan_singleton", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "vsub_set_subset_vectorSpan", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "vsub_mem_vectorSpan", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "vectorSpan_of_subsingleton", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "vectorSpan_eq_bot_iff_subsingleton", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": true, "tactics": ["refine", "by_contra", "rw", "obtain", "have", "simp_all"], "tactic_count": 6}
{"name": "spanPoints", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_spanPoints", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "subset_spanPoints", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "spanPoints_nonempty", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": true, "tactics": ["constructor", "contrapose", "rw", "intro", "simp", "exact"], "tactic_count": 6}
{"name": "vadd_mem_spanPoints_of_mem_spanPoints_of_mem_vectorSpan", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": true, "tactics": ["rcases", "rw", "exact"], "tactic_count": 3}
{"name": "vsub_mem_vectorSpan_of_mem_spanPoints_of_mem_spanPoints", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "rw", "have", "refine", "exact"], "tactic_count": 6}
{"name": "Submodule.toAffineSubspace", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.instSetLike", "kind": "instance", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.instPartialOrder", "kind": "instance", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.mem_coe", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AffineSubspace.direction", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.direction_eq_vectorSpan", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.directionOfNonempty", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.directionOfNonempty_eq_direction", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "AffineSubspace.coe_direction_eq_vsub_set", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.mem_direction_iff_eq_vsub", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "AffineSubspace.vadd_mem_of_mem_direction", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": true, "tactics": ["rw", "rcases", "rw", "convert", "rw"], "tactic_count": 5}
{"name": "AffineSubspace.vsub_mem_direction", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.vadd_mem_iff_mem_direction", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.vadd_mem_iff_mem_of_mem_direction", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": true, "tactics": ["refine", "convert", "simp"], "tactic_count": 3}
{"name": "AffineSubspace.coe_direction_eq_vsub_set_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": true, "tactics": ["rw", "refine", "rintro", "exact", "rintro", "exact"], "tactic_count": 6}
{"name": "AffineSubspace.coe_direction_eq_vsub_set_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": true, "tactics": ["ext", "rw", "conv_lhs", "congr", "ext", "rw"], "tactic_count": 6}
{"name": "AffineSubspace.mem_direction_iff_eq_vsub_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "AffineSubspace.mem_direction_iff_eq_vsub_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "AffineSubspace.coe_injective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.ext", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.ext_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.ext_of_direction_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": true, "tactics": ["ext", "have", "have", "constructor", "intro", "rw", "refine", "rw", "exact", "intro", "rw", "refine", "rw", "exact"], "tactic_count": 14}
{"name": "AffineSubspace.eq_iff_direction_eq_of_mem", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.mk'", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.mem_mk'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.self_mem_mk'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AffineSubspace.vadd_mem_mk'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "AffineSubspace.mk'_nonempty", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.instNonemptySubtypeMemMk'", "kind": "instance", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.direction_mk'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": true, "tactics": ["ext", "rw", "constructor", "rintro", "simpa", "exact"], "tactic_count": 6}
{"name": "AffineSubspace.mk'_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.spanPoints_subset_coe_of_subset_coe", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": true, "tactics": ["rintro", "rw", "have", "refine", "have", "rw", "rw", "exact"], "tactic_count": 8}
{"name": "Submodule.mem_toAffineSubspace", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.toAffineSubspace_direction", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "affineSpan", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "coe_affineSpan", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_affineSpan_iff_exists", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "subset_affineSpan", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "direction_affineSpan", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": true, "tactics": ["apply", "refine", "rintro", "simp", "rw", "exact", "exact"], "tactic_count": 7}
{"name": "mem_affineSpan", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "vectorSpan_add_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": true, "tactics": ["ext", "simp", "grind"], "tactic_count": 3}
{"name": "vadd_mem_affineSpan_of_mem_affineSpan_of_mem_vectorSpan", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "vsub_mem_vectorSpan_of_mem_affineSpan_of_mem_affineSpan", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "affineSpan_le_of_subset_coe", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.instCompleteLattice", "kind": "instance", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.instInhabited", "kind": "instance", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.le_def", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.le_def'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.lt_def", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.not_le_iff_exists", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.exists_of_lt", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.lt_iff_le_and_exists", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AffineSubspace.eq_of_direction_eq_of_nonempty_of_le", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.nonempty_sup_left", "kind": "instance", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.nonempty_sup_right", "kind": "instance", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.affineSpan_eq_sInf", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.gi", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.span_empty", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.span_univ", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "affineSpan_le", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.span_union", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.span_iUnion", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.top_coe", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.mem_top", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.mk'_top", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "AffineSubspace.direction_top", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": true, "tactics": ["obtain", "ext", "refine", "have", "vsub_mem_direction", "rwa"], "tactic_count": 6}
{"name": "AffineSubspace.bot_coe", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.bot_ne_top", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": true, "tactics": ["intro", "rw", "exact"], "tactic_count": 3}
{"name": "AffineSubspace.instNontrivial", "kind": "instance", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.nonempty_of_affineSpan_eq_top", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": true, "tactics": ["rw", "rintro", "rw", "exact"], "tactic_count": 4}
{"name": "AffineSubspace.vectorSpan_eq_top_of_affineSpan_eq_top", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AffineSubspace.affineSpan_eq_top_iff_vectorSpan_eq_top_of_nonempty", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": true, "tactics": ["refine", "intro", "suffices", "obtain", "rw", "obtain", "exact"], "tactic_count": 7}
{"name": "AffineSubspace.affineSpan_eq_top_iff_vectorSpan_eq_top_of_nontrivial", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rw"], "tactic_count": 3}
{"name": "AffineSubspace.card_pos_of_affineSpan_eq_top", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "AffineSubspace.instNonemptySubtypeMemTop", "kind": "instance", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.notMem_bot", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.isEmpty_bot", "kind": "instance", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.direction_bot", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AffineSubspace.coe_eq_bot_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.coe_eq_univ_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.nonempty_iff_ne_bot", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "AffineSubspace.eq_bot_or_nonempty", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "AffineSubspace.instIsSimpleOrderOfSubsingleton", "kind": "instance", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.direction_eq_top_iff_of_nonempty", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "refine", "simp", "rintro", "simp"], "tactic_count": 7}
{"name": "AffineSubspace.coe_inf", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.mem_inf_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.direction_inf", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": true, "tactics": ["simp", "exact", "le_inf"], "tactic_count": 3}
{"name": "AffineSubspace.direction_inf_of_mem", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": true, "tactics": ["ext", "rw", "vadd_mem_iff_mem_direction"], "tactic_count": 3}
{"name": "AffineSubspace.direction_inf_of_mem_inf", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.coe_sInf", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.mem_sInf_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.direction_sInf", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "AffineSubspace.direction_sInf_of_mem", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": true, "tactics": ["apply", "intro", "rw", "intro", "rw", "simp", "exact"], "tactic_count": 7}
{"name": "AffineSubspace.direction_sInf_of_mem_sInf", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.coe_iInf", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AffineSubspace.mem_iInf_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AffineSubspace.direction_iInf", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": true, "tactics": ["apply", "rw"], "tactic_count": 2}
{"name": "AffineSubspace.direction_iInf_of_mem", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": true, "tactics": ["rw", "rwa"], "tactic_count": 2}
{"name": "AffineSubspace.direction_iInf_of_mem_iInf", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AffineSubspace.direction_le", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "AffineSubspace.sup_direction_le", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": true, "tactics": ["simp", "exact", "sup_le"], "tactic_count": 3}
{"name": "AffineSubspace.sup_direction_lt_of_nonempty_of_inter_empty", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "rw", "use", "vsub_mem_direction", "intro", "rw", "rcases", "rw", "add_comm,", "refine", "use", "rw", "exact"], "tactic_count": 14}
{"name": "AffineSubspace.inter_nonempty_of_nonempty_of_sup_direction_eq_top", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": true, "tactics": ["by_contra", "rw", "have", "rw", "exact"], "tactic_count": 5}
{"name": "AffineSubspace.inter_eq_singleton_of_nonempty_of_isCompl", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": true, "tactics": ["obtain", "use", "ext", "rw", "constructor", "rintro", "have", "rwa", "exact"], "tactic_count": 9}
{"name": "AffineSubspace.affineSpan_coe", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": true, "tactics": ["refine", "rintro", "exact"], "tactic_count": 3}
{"name": "affineSpan_nonempty", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instNonemptySubtypeMemAffineSubspaceAffineSpanOfElem", "kind": "instance", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "affineSpan_eq_bot", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "bot_lt_affineSpan", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "affineSpan_eq_top_iff_nonempty_of_subsingleton", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "affineSpan_induction", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "affineSpan_induction'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": true, "tactics": ["suffices", "refine", "exact", "exact", "hu.elim", "hv.elim", "hw.elim"], "tactic_count": 7}
{"name": "vsub_mem_vectorSpan_pair", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "vsub_rev_mem_vectorSpan_pair", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smul_vsub_mem_vectorSpan_pair", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smul_vsub_rev_mem_vectorSpan_pair", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "termLine[_,_,_]", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_LinearAlgebra_AffineSpace_AffineSubspace_Defs___macroRules_termLine[_,_,_]_1", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_LinearAlgebra_AffineSpace_AffineSubspace_Defs___unexpand_affineSpan_1", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "left_mem_affineSpan_pair", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "right_mem_affineSpan_pair", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "affineSpan_pair_le_of_mem_of_mem", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "affineSpan_pair_le_of_left_mem", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "affineSpan_pair_le_of_right_mem", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "affineSpan_mono", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "affineSpan_insert_affineSpan", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "affineSpan_insert_eq_affineSpan", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": true, "tactics": ["rw", "rw"], "tactic_count": 2}
{"name": "vectorSpan_insert_eq_vectorSpan", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "affineSpan_le_toAffineSubspace_span", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": true, "tactics": ["intro", "simp", "induction", "mem", "smul_vsub_vadd", "simp", "apply", "exact"], "tactic_count": 8}
{"name": "affineSpan_subset_span", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "affineSpan_insert_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "refine", "gcongr", "exact"], "tactic_count": 6}
{"name": "fintypeAffineCoords", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_fintypeAffineCoords_iff_sum", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Basis", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AffineIndependent.injOn_affineCombination_fintypeAffineCoords", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finsuppAffineCoords", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_finsuppAffineCoords_iff_linearCombination", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Basis", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AffineBasis.instInhabitedPUnit", "kind": "instance", "module": "Mathlib.LinearAlgebra.AffineSpace.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineBasis.instFunLike", "kind": "instance", "module": "Mathlib.LinearAlgebra.AffineSpace.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineBasis.ext", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineBasis.ind", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineBasis.tot", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineBasis.nonempty", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineBasis.reindex", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineBasis.coe_reindex", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineBasis.reindex_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineBasis.reindex_refl", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineBasis.basisOf", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineBasis.basisOf_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Basis", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AffineBasis.basisOf_reindex", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Basis", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "AffineBasis.coord", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineBasis.linear_eq_sumCoords", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineBasis.coord_reindex", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Basis", "is_tactic_proof": true, "tactics": ["ext", "classical"], "tactic_count": 2}
{"name": "AffineBasis.coord_apply_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Basis", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AffineBasis.coord_apply_ne", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Basis", "is_tactic_proof": true, "tactics": ["rw", "sub_self]"], "tactic_count": 2}
{"name": "AffineBasis.coord_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Basis", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "AffineBasis.coord_apply_combination_of_mem", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Basis", "is_tactic_proof": true, "tactics": ["classical", "simp"], "tactic_count": 2}
{"name": "AffineBasis.coord_apply_combination_of_notMem", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Basis", "is_tactic_proof": true, "tactics": ["classical", "simp"], "tactic_count": 2}
{"name": "AffineBasis.sum_coord_apply_eq_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Basis", "is_tactic_proof": false, "tactics": ["have", "rw", "exact", "obtain", "convert", "exact"], "tactic_count": 6}
{"name": "AffineBasis.affineCombination_coord_eq_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Basis", "is_tactic_proof": false, "tactics": ["have", "rw", "exact", "obtain", "congr", "ext", "exact"], "tactic_count": 7}
{"name": "AffineBasis.linear_combination_coord_eq_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Basis", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "AffineBasis.ext_elem", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Basis", "is_tactic_proof": true, "tactics": ["cases", "rw", "simp"], "tactic_count": 3}
{"name": "AffineBasis.coe_coord_of_subsingleton_eq_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Basis", "is_tactic_proof": true, "tactics": ["ext", "have", "rw", "apply", "apply", "haveI", "let", "have", "have", "have", "rw"], "tactic_count": 11}
{"name": "AffineBasis.surjective_coord", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Basis", "is_tactic_proof": true, "tactics": ["classical", "intro", "obtain", "let", "have", "let", "have", "simp", "use", "simp"], "tactic_count": 10}
{"name": "AffineBasis.coords", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineBasis.coords_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineBasis.instVAdd", "kind": "instance", "module": "Mathlib.LinearAlgebra.AffineSpace.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineBasis.coe_vadd", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineBasis.basisOf_vadd", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Basis", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "AffineBasis.instAddAction", "kind": "instance", "module": "Mathlib.LinearAlgebra.AffineSpace.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineBasis.coord_vadd", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Basis", "is_tactic_proof": true, "tactics": ["ext", "simp", "congr", "rw"], "tactic_count": 4}
{"name": "AffineBasis.instSMul", "kind": "instance", "module": "Mathlib.LinearAlgebra.AffineSpace.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineBasis.coe_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineBasis.instSMulCommClass", "kind": "instance", "module": "Mathlib.LinearAlgebra.AffineSpace.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineBasis.instIsScalarTower", "kind": "instance", "module": "Mathlib.LinearAlgebra.AffineSpace.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineBasis.basisOf_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Basis", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "AffineBasis.reindex_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineBasis.coord_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Basis", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "AffineBasis.instMulAction", "kind": "instance", "module": "Mathlib.LinearAlgebra.AffineSpace.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineBasis.coord_apply_centroid", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Basis", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AffineBasis.exists_affine_subbasis", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Basis", "is_tactic_proof": true, "tactics": ["obtain", "refine", "rw"], "tactic_count": 3}
{"name": "AffineBasis.exists_affineBasis", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.centroidWeights", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.Centroid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.centroidWeights_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Centroid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.centroidWeights_eq_const", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Centroid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sum_centroidWeights_eq_one_of_cast_card_ne_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Centroid", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.sum_centroidWeights_eq_one_of_card_ne_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Centroid", "is_tactic_proof": true, "tactics": ["simp_all"], "tactic_count": 1}
{"name": "Finset.sum_centroidWeights_eq_one_of_nonempty", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Centroid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sum_centroidWeights_eq_one_of_card_eq_add_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Centroid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.centroid", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.Centroid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.centroid_def", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Centroid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.centroid_univ", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Centroid", "is_tactic_proof": true, "tactics": ["rw", "congr", "ext", "simp"], "tactic_count": 4}
{"name": "Finset.centroid_singleton", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Centroid", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.centroid_pair", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Centroid", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "have", "rw", "norm_num", "exact", "rw", "affineCombination_eq_weightedVSubOfPoint_vadd_of_sum_eq_one", "simp"], "tactic_count": 9}
{"name": "Finset.centroid_pair_fin", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Centroid", "is_tactic_proof": true, "tactics": ["rw", "convert"], "tactic_count": 2}
{"name": "Finset.centroid_map", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Centroid", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.centroidWeightsIndicator", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.Centroid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.centroidWeightsIndicator_def", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Centroid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sum_centroidWeightsIndicator", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Centroid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sum_centroidWeightsIndicator_eq_one_of_card_ne_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Centroid", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finset.sum_centroidWeightsIndicator_eq_one_of_nonempty", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Centroid", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finset.sum_centroidWeightsIndicator_eq_one_of_card_eq_add_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Centroid", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finset.centroid_eq_affineCombination_fintype", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Centroid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.centroid_eq_centroid_image_of_inj_on", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Centroid", "is_tactic_proof": true, "tactics": ["let", "have", "let", "have", "have", "intro", "rw", "let", "have", "ext", "rw", "constructor", "rintro", "exact", "intro", "use", "refine", "rw", "rw", "congr", "change", "rw"], "tactic_count": 22}
{"name": "Finset.centroid_eq_of_inj_on_of_image_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Centroid", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finset.centroid_vsub_const", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Centroid", "is_tactic_proof": true, "tactics": ["have", "simp", "grind"], "tactic_count": 3}
{"name": "centroid_mem_affineSpan_of_cast_card_ne_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Centroid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "centroid_mem_affineSpan_of_card_ne_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Centroid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "centroid_mem_affineSpan_of_nonempty", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Centroid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "centroid_mem_affineSpan_of_card_eq_add_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Centroid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.LinearAlgebra.AffineSpace.Ceva.0.AffineIndependent.exists_affineCombination_eq_smul_eq_aux", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Ceva", "is_tactic_proof": true, "tactics": ["classical", "have", "p", "intro", "simp_rw", "obtain", "exact", "obtain", "obtain", "let", "refine", "simp", "simp", "intro", "obtain", "refine", "rw", "simp", "have", "intro", "by_cases", "simp", "replace", "convert", "simp", "simp", "simp", "simp"], "tactic_count": 28}
{"name": "AffineIndependent.exists_affineCombination_eq_smul_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Ceva", "is_tactic_proof": true, "tactics": ["classical", "let", "have", "let", "have", "intro", "simp_rw", "by_cases", "have", "intro", "convert", "simp_rw", "exact", "obtain", "refine", "obtain", "refine", "convert", "simp", "grind"], "tactic_count": 20}
{"name": "AffineIndependent.exists_affineCombination_eq_smul_eq_of_fintype", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Ceva", "is_tactic_proof": true, "tactics": ["classical", "obtain", "refine", "rw", "exact", "rw", "exact", "intro", "obtain", "refine", "convert", "simp", "by_cases"], "tactic_count": 13}
{"name": "Affine.Triangle.prod_eq_prod_one_sub_of_mem_line_point_lineMap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Ceva", "is_tactic_proof": true, "tactics": ["rcases", "exact", "let", "have", "have", "simpa", "obtain", "have", "intro", "obtain", "refine", "simpa", "simp", "let", "have", "have", "rw", "simp", "have", "rw", "simp", "have", "simp_rw", "suffices", "simp_rw", "simp", "by_cases", "rw", "obtain", "have", "have", "have", "rw", "fin_cases", "have", "have", "have", "suffices", "rw", "have", "have", "have", "have", "suffices", "rw", "have", "rw", "exact"], "tactic_count": 48}
{"name": "Affine.Triangle.prod_div_one_sub_eq_one_of_mem_line_point_lineMap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Ceva", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finset.univ_fin2", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.weightedVSubOfPoint", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.weightedVSubOfPoint_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.weightedVSubOfPoint_apply_const", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.weightedVSubOfPoint_vadd", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.weightedVSubOfPoint_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.weightedVSubOfPoint_congr", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "rw"], "tactic_count": 3}
{"name": "Finset.weightedVSubOfPoint_eq_of_weights_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["simp", "congr", "ext", "rcases", "simp", "simp"], "tactic_count": 6}
{"name": "Finset.weightedVSubOfPoint_eq_of_sum_eq_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["apply", "rw", "conv_lhs", "congr", "skip", "ext", "rw", "rw"], "tactic_count": 8}
{"name": "Finset.weightedVSubOfPoint_vadd_eq_of_sum_eq_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": false, "tactics": ["rw", "vsub_vadd_eq_vsub_sub,", "conv_lhs", "congr", "skip", "congr", "skip", "ext", "rw", "rw"], "tactic_count": 10}
{"name": "Finset.weightedVSubOfPoint_erase", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["rw", "apply", "rw"], "tactic_count": 3}
{"name": "Finset.weightedVSubOfPoint_insert", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["rw", "apply", "rw"], "tactic_count": 3}
{"name": "Finset.weightedVSubOfPoint_indicator_subset", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finset.weightedVSubOfPoint_map", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Finset.sum_smul_vsub_eq_weightedVSubOfPoint_sub", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Finset.sum_smul_vsub_const_eq_weightedVSubOfPoint_sub", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.sum_smul_const_vsub_eq_sub_weightedVSubOfPoint", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.weightedVSubOfPoint_sdiff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Finset.weightedVSubOfPoint_sdiff_sub", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.weightedVSubOfPoint_subtype_eq_filter", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.weightedVSubOfPoint_filter_of_ne", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["rw", "intro", "refine", "intro", "simp"], "tactic_count": 5}
{"name": "Finset.weightedVSubOfPoint_const_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Finset.weightedVSub", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.weightedVSub_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.weightedVSub_apply_const", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.weightedVSub_empty", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.weightedVSub_vadd", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.weightedVSub_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.weightedVSub_congr", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.weightedVSub_indicator_subset", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.weightedVSub_map", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sum_smul_vsub_eq_weightedVSub_sub", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sum_smul_vsub_const_eq_weightedVSub", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.sum_smul_const_vsub_eq_neg_weightedVSub", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.weightedVSub_sdiff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.weightedVSub_sdiff_sub", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.weightedVSub_subtype_eq_filter", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.weightedVSub_filter_of_ne", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.weightedVSub_const_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.instAddTorsorForall", "kind": "instance", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.affineCombination", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.affineCombination_linear", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.affineCombination_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.affineCombination_apply_const", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.affineCombination_congr", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Finset.affineCombination_eq_weightedVSubOfPoint_vadd_of_sum_eq_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.weightedVSub_vadd_affineCombination", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.affineCombination_vsub", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.attach_affineCombination_of_injective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.attach_affineCombination_coe", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["classical", "rw"], "tactic_count": 2}
{"name": "Finset.weightedVSub_eq_linear_combination", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.affineCombination_eq_linear_combination", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.affineCombination_of_eq_one_of_eq_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["have", "rw", "convert", "refine", "intro", "by_cases", "simp", "simp"], "tactic_count": 8}
{"name": "Finset.affineCombination_indicator_subset", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.affineCombination_map", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Finset.sum_smul_vsub_eq_affineCombination_vsub", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Finset.sum_smul_vsub_const_eq_affineCombination_vsub", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.sum_smul_const_vsub_eq_vsub_affineCombination", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.affineCombination_sdiff_sub", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Finset.affineCombination_eq_of_weightedVSub_eq_zero_of_eq_neg_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["classical", "rw", "sdiff_singleton_eq_erase,", "congr", "refine", "simp", "simp"], "tactic_count": 7}
{"name": "Finset.affineCombination_subtype_eq_filter", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.affineCombination_filter_of_ne", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.eq_weightedVSubOfPoint_subset_iff_eq_weightedVSubOfPoint_subtype", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["classical", "simp_rw", "constructor", "rintro", "exact", "rintro", "refine", "simp"], "tactic_count": 8}
{"name": "Finset.eq_weightedVSub_subset_iff_eq_weightedVSub_subtype", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.eq_affineCombination_subset_iff_eq_affineCombination_subtype", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Finset.map_affineCombination", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "s.affineCombination_eq_weightedVSubOfPoint_vadd_of_sum_eq_one", "s.weightedVSubOfPoint_vadd_eq_of_sum_eq_one", "simp", "map_sum,"], "tactic_count": 7}
{"name": "Finset.affineCombination_apply_eq_lineMap_sum", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": false, "tactics": ["rw", "s.sum_inter_add_sum_diff", "convert", "convert", "simp", "exact"], "tactic_count": 6}
{"name": "Finset.affineCombinationSingleWeights", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.affineCombinationSingleWeights_apply_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.affineCombinationSingleWeights_apply_of_ne", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sum_affineCombinationSingleWeights", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finset.weightedVSubVSubWeights", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.weightedVSubVSubWeights_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.weightedVSubVSubWeights_apply_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.weightedVSubVSubWeights_apply_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.weightedVSubVSubWeights_apply_of_ne", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.sum_weightedVSubVSubWeights", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["simp_rw", "simp"], "tactic_count": 2}
{"name": "Finset.affineCombinationLineMapWeights", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.affineCombinationLineMapWeights_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.affineCombinationLineMapWeights_apply_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.affineCombinationLineMapWeights_apply_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.affineCombinationLineMapWeights_apply_of_ne", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.sum_affineCombinationLineMapWeights", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["simp_rw", "simp"], "tactic_count": 2}
{"name": "Finset.affineCombination_affineCombinationSingleWeights", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["refine", "rintro", "simp"], "tactic_count": 3}
{"name": "Finset.weightedVSub_weightedVSubVSubWeights", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["rw", "s.affineCombination_affineCombinationSingleWeights"], "tactic_count": 2}
{"name": "Finset.affineCombination_affineCombinationLineMapWeights", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["rw", "s.affineCombination_affineCombinationSingleWeights"], "tactic_count": 2}
{"name": "weightedVSub_mem_vectorSpan", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["classical", "rcases", "simp", "rw", "let", "have", "use", "rw", "apply", "intro", "simp", "exact"], "tactic_count": 12}
{"name": "affineCombination_mem_affineSpan", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["classical", "have", "have", "obtain", "let", "have", "simp", "have", "s.affineCombination_of_eq_one_of_eq_zero", "have", "rw", "apply", "simp", "rw", "exact"], "tactic_count": 15}
{"name": "affineCombination_mem_affineSpan_of_nonempty", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["rcases", "have", "rw", "rw", "simp", "exact"], "tactic_count": 6}
{"name": "mem_vectorSpan_iff_eq_weightedVSub", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["classical", "constructor", "rcases", "swap", "rw", "rintro", "use", "set", "use", "have", "rw", "simp_rw", "simp", "use", "have", "change", "rw", "hv,", "change", "congr", "by_cases", "simp", "simp", "rw", "rintro", "use", "simp", "rintro", "exact"], "tactic_count": 29}
{"name": "eq_affineCombination_of_mem_affineSpan", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["classical", "have", "rw", "obtain", "have", "have", "rw", "rcases", "let", "let", "have", "have", "rw", "exact", "let", "have", "rw", "simp", "have", "s'.affineCombination_of_eq_one_of_eq_zero", "refine", "simp", "rw"], "tactic_count": 23}
{"name": "eq_affineCombination_of_mem_affineSpan_of_fintype", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["classical", "obtain", "refine", "simp", "rw"], "tactic_count": 5}
{"name": "eq_affineCombination_of_mem_affineSpan_image", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["classical", "rw", "obtain", "refine", "simp", "exact"], "tactic_count": 6}
{"name": "affineCombination_mem_affineSpan_image", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["classical", "rw", "let", "have", "rw", "refine", "intro", "simp", "exact", "rw", "convert", "rw", "refine", "simp_all"], "tactic_count": 14}
{"name": "mem_affineSpan_iff_eq_affineCombination", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["constructor", "exact", "rintro", "exact"], "tactic_count": 4}
{"name": "mem_affineSpan_iff_eq_weightedVSubOfPoint_vadd", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["constructor", "intro", "obtain", "exact", "rintro", "classical", "let", "have", "by_cases", "simp", "simp_rw", "have", "intro", "simp", "rw", "exact"], "tactic_count": 16}
{"name": "affineSpan_eq_affineSpan_lineMap_units", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": true, "tactics": ["have", "conv_rhs", "apply", "erw", "obtain", "use", "simp"], "tactic_count": 7}
{"name": "AffineMap.weightedVSubOfPoint", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.termAffineSpace", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine._aux_Mathlib_LinearAlgebra_AffineSpace_Defs___macroRules_Affine_termAffineSpace_1", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine._aux_Mathlib_LinearAlgebra_AffineSpace_Defs___unexpand_AddTorsor_1", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finiteDimensional_vectorSpan_of_finite", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finiteDimensional_vectorSpan_singleton", "kind": "instance", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finiteDimensional_vectorSpan_range", "kind": "instance", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finiteDimensional_vectorSpan_image_of_finite", "kind": "instance", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finiteDimensional_direction_affineSpan_of_finite", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finiteDimensional_direction_affineSpan_singleton", "kind": "instance", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "finiteDimensional_direction_affineSpan_range", "kind": "instance", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finiteDimensional_direction_affineSpan_image_of_finite", "kind": "instance", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finite_of_fin_dim_affineIndependent", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": true, "tactics": ["nontriviality", "rw", "letI", "exact"], "tactic_count": 4}
{"name": "finite_set_of_fin_dim_affineIndependent", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.finiteDimensional_sup", "kind": "instance", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": true, "tactics": ["rcases", "rwa", "rcases", "rwa", "rw", "infer_instance"], "tactic_count": 6}
{"name": "finiteDimensional_direction_map", "kind": "instance", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "AffineIndependent.finrank_vectorSpan_image_finset", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": true, "tactics": ["classical", "have", "have", "have", "rcases", "have", "rw", "have", "rw", "exact", "rwa"], "tactic_count": 11}
{"name": "AffineIndependent.finrank_vectorSpan", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": true, "tactics": ["classical", "rw", "rw", "exact"], "tactic_count": 4}
{"name": "AffineIndependent.finrank_vectorSpan_add_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AffineIndependent.vectorSpan_eq_top_of_card_eq_finrank_add_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finrank_vectorSpan_image_finset_le", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": true, "tactics": ["classical", "have", "rw", "apply", "rcases", "rw", "refine", "rw", "apply"], "tactic_count": 9}
{"name": "finrank_vectorSpan_range_le", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": true, "tactics": ["classical", "rw", "rw", "exact"], "tactic_count": 4}
{"name": "finrank_vectorSpan_range_add_one_le", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "affineIndependent_iff_finrank_vectorSpan_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": true, "tactics": ["classical", "have", "obtain", "rw", "vectorSpan_range_eq_span_range_vsub_right_ne", "rw", "rw", "simp"], "tactic_count": 8}
{"name": "affineIndependent_iff_le_finrank_vectorSpan", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": true, "tactics": ["rw", "constructor", "rintro", "rfl", "exact"], "tactic_count": 5}
{"name": "affineIndependent_iff_not_finrank_vectorSpan_le", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "finrank_vectorSpan_le_iff_not_affineIndependent", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIndependent.card_le_finrank_succ", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": true, "tactics": ["cases", "simp", "rw", "exact", "hp"], "tactic_count": 5}
{"name": "AffineIndependent.card_le_card_of_subset_affineSpan", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": true, "tactics": ["obtain", "simp", "obtain", "simpa", "have", "have", "have", "rw", "have", "add_le_add_left", "erw", "simpa"], "tactic_count": 12}
{"name": "AffineIndependent.card_lt_card_of_affineSpan_lt_affineSpan", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": true, "tactics": ["obtain", "simpa", "obtain", "simp", "have", "have", "have", "rw", "have", "add_lt_add_left", "erw", "simpa"], "tactic_count": 12}
{"name": "AffineIndependent.vectorSpan_image_finset_eq_of_le_of_card_eq_finrank_add_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIndependent.vectorSpan_eq_of_le_of_card_eq_finrank_add_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIndependent.affineSpan_image_finset_eq_of_le_of_card_eq_finrank_add_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": false, "tactics": ["have", "rw", "apply", "refine", "have", "rw", "exact"], "tactic_count": 7}
{"name": "AffineIndependent.affineSpan_eq_of_le_of_card_eq_finrank_add_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": true, "tactics": ["classical", "rw", "rw", "exact"], "tactic_count": 4}
{"name": "AffineIndependent.affineSpan_eq_top_iff_card_eq_finrank_add_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": true, "tactics": ["constructor", "intro", "let", "have", "rw", "intro", "rw", "exact"], "tactic_count": 8}
{"name": "Affine.Simplex.span_eq_top", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "finiteDimensional_vectorSpan_insert", "kind": "instance", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": true, "tactics": ["rw", "rcases", "rw", "rw", "convert", "rw", "infer_instance"], "tactic_count": 7}
{"name": "finiteDimensional_direction_affineSpan_insert", "kind": "instance", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finiteDimensional_vectorSpan_insert_set", "kind": "instance", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": true, "tactics": ["haveI", "rw", "exact"], "tactic_count": 3}
{"name": "finiteDimensional_direction_affineSpan_insert_set", "kind": "instance", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": true, "tactics": ["haveI", "rw", "infer_instance"], "tactic_count": 3}
{"name": "Collinear", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "collinear_iff_rank_le_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "collinear_iff_finrank_le_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "Collinear.subset", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Collinear.finiteDimensional_vectorSpan", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Collinear.finiteDimensional_direction_affineSpan", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "collinear_empty", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "collinear_singleton", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "collinear_iff_of_mem", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": true, "tactics": ["simp_rw", "constructor", "rintro", "use", "intro", "obtain", "use", "rw", "exact", "rintro", "use", "intro", "have", "rw", "intro", "rw", "rw", "rcases", "rcases", "use", "simp", "have", "rwa"], "tactic_count": 23}
{"name": "collinear_iff_exists_forall_eq_smul_vadd", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rw", "constructor", "exact", "rintro", "use", "intro", "rcases", "rcases", "use", "simp"], "tactic_count": 12}
{"name": "collinear_pair", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": true, "tactics": ["rw", "use", "intro", "rw", "rcases", "use", "simp", "use", "simp"], "tactic_count": 9}
{"name": "affineIndependent_iff_not_collinear", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "collinear_iff_not_affineIndependent", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "affineIndependent_iff_not_collinear_set", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": true, "tactics": ["rw", "simp_rw"], "tactic_count": 2}
{"name": "collinear_iff_not_affineIndependent_set", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "affineIndependent_iff_not_collinear_of_ne", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "collinear_iff_not_affineIndependent_of_ne", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ne₁₂_of_not_collinear", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": true, "tactics": ["rintro", "simp"], "tactic_count": 2}
{"name": "ne₁₃_of_not_collinear", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": true, "tactics": ["rintro", "simp"], "tactic_count": 2}
{"name": "ne₂₃_of_not_collinear", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": true, "tactics": ["rintro", "simp"], "tactic_count": 2}
{"name": "Collinear.mem_affineSpan_of_mem_of_ne", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": true, "tactics": ["rw", "rcases", "rcases", "rcases", "rw", "refine", "have", "rintro", "simp", "simp"], "tactic_count": 10}
{"name": "Collinear.affineSpan_eq_of_ne", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Collinear.collinear_insert_iff_of_ne", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": false, "tactics": ["have", "conv_rhs", "rw", "rw"], "tactic_count": 4}
{"name": "collinear_insert_iff_of_mem_affineSpan", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "collinear_insert_of_mem_affineSpan_pair", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "collinear_insert_insert_of_mem_affineSpan_pair", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": false, "tactics": ["rw", "collinear_insert_iff_of_mem_affineSpan", "exact"], "tactic_count": 3}
{"name": "collinear_insert_insert_insert_of_mem_affineSpan_pair", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": false, "tactics": ["rw", "collinear_insert_iff_of_mem_affineSpan", "collinear_insert_iff_of_mem_affineSpan", "exact"], "tactic_count": 4}
{"name": "collinear_insert_insert_insert_left_of_mem_affineSpan_pair", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": true, "tactics": ["refine", "gcongr"], "tactic_count": 2}
{"name": "collinear_triple_of_mem_affineSpan_pair", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": true, "tactics": ["refine", "gcongr"], "tactic_count": 2}
{"name": "affineIndependent_of_affineIndependent_collinear_ne", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": true, "tactics": ["rw", "by_contra", "have", "apply", "apply", "apply", "have", "rw", "exact"], "tactic_count": 9}
{"name": "Coplanar", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Coplanar.finiteDimensional_vectorSpan", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "Coplanar.finiteDimensional_direction_affineSpan", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "coplanar_iff_finrank_le_two", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "Coplanar.subset", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Collinear.coplanar", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "coplanar_empty", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "coplanar_singleton", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "coplanar_pair", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "coplanar_insert_iff_of_mem_affineSpan", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "finrank_vectorSpan_insert_le", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": true, "tactics": ["by_cases", "have", "intro", "have", "conv_lhs", "exact", "exact", "rw", "exact", "rw", "rcases", "rw", "rw", "convert", "rw", "convert", "rw", "refine", "gcongr", "refine", "have", "rw", "rcases", "refine", "ext", "exact"], "tactic_count": 26}
{"name": "finrank_vectorSpan_insert_le_set", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Collinear.coplanar_insert", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": true, "tactics": ["have", "grw"], "tactic_count": 2}
{"name": "coplanar_of_finrank_eq_two", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "coplanar_of_fact_finrank_eq_two", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "coplanar_triple", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.collinear_point_centroid_faceOppositeCentroid", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": true, "tactics": ["apply", "have", "rw", "rw", "exact"], "tactic_count": 5}
{"name": "AffineBasis.finiteDimensional", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineBasis.finite", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineBasis.finite_set", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineBasis.card_eq_finrank_add_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineBasis.exists_affineBasis_of_finiteDimensional", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "is_tactic_proof": true, "tactics": ["obtain", "lift", "refine", "rw"], "tactic_count": 4}
{"name": "AffineIndependent", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.Independent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "affineIndependent_def", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Independent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "affineIndependent_of_subsingleton", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Independent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "affineIndependent_iff_of_fintype", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Independent", "is_tactic_proof": true, "tactics": ["constructor", "exact", "intro", "rw", "rw", "replace", "simpa"], "tactic_count": 7}
{"name": "affineIndependent_vadd", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Independent", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "affineIndependent_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Independent", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "affineIndependent_iff_linearIndependent_vsub", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Independent", "is_tactic_proof": true, "tactics": ["classical", "constructor", "intro", "rw", "intro", "set", "let", "have", "rw", "have", "rw", "rw", "dsimp", "rw", "exact", "have", "set", "set", "have", "simp", "refine", "rw", "rw", "exact", "exact", "intro", "rw", "intro", "rw", "let", "have", "rw", "convert", "have", "simp_rw", "have", "exact"], "tactic_count": 37}
{"name": "affineIndependent_set_iff_linearIndependent_vsub", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Independent", "is_tactic_proof": true, "tactics": ["rw", "constructor", "intro", "have", "let", "convert", "ext", "exact", "intro", "let", "convert"], "tactic_count": 11}
{"name": "linearIndependent_set_iff_affineIndependent_vadd_union_singleton", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Independent", "is_tactic_proof": true, "tactics": ["rw", "have", "simp_rw", "vsub_self,", "exact", "rw"], "tactic_count": 6}
{"name": "affineIndependent_iff_indicator_eq_of_affineCombination_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Independent", "is_tactic_proof": true, "tactics": ["classical", "constructor", "intro", "ext", "by_cases", "rw", "rw", "rw", "have", "rw", "exact", "simp_all", "intro", "let", "have", "rw", "simp", "have", "s.affineCombination_of_eq_one_of_eq_zero", "let", "have", "have", "simp_all", "replace", "have", "rw", "rw", "simpa"], "tactic_count": 28}
{"name": "affineIndependent_iff_eq_of_fintype_affineCombination_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Independent", "is_tactic_proof": true, "tactics": ["rw", "constructor", "intro", "simpa", "intro", "have", "have", "rw", "exact"], "tactic_count": 9}
{"name": "AffineIndependent.units_lineMap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Independent", "is_tactic_proof": true, "tactics": ["rw", "simp", "exact"], "tactic_count": 3}
{"name": "AffineIndependent.indicator_eq_of_affineCombination_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Independent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIndependent.injective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Independent", "is_tactic_proof": true, "tactics": ["intro", "rw", "by_contra", "refine", "simp_all"], "tactic_count": 5}
{"name": "AffineIndependent.comp_embedding", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Independent", "is_tactic_proof": true, "tactics": ["classical", "intro", "let", "let", "have", "intro", "have", "have", "simp_rw", "have", "rw", "simp", "have", "rw", "congr", "simp_all", "rw"], "tactic_count": 17}
{"name": "AffineIndependent.subtype", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Independent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIndependent.range", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Independent", "is_tactic_proof": true, "tactics": ["let", "have", "let", "convert", "ext", "simp"], "tactic_count": 6}
{"name": "affineIndependent_equiv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Independent", "is_tactic_proof": true, "tactics": ["refine", "intro", "have", "ext", "simp", "rw", "exact"], "tactic_count": 7}
{"name": "AffineIndependent.comm_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Independent", "is_tactic_proof": true, "tactics": ["rw", "convert", "ext", "fin_cases"], "tactic_count": 4}
{"name": "AffineIndependent.comm_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Independent", "is_tactic_proof": true, "tactics": ["rw", "convert", "ext", "fin_cases"], "tactic_count": 4}
{"name": "AffineIndependent.reverse_of_three", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Independent", "is_tactic_proof": true, "tactics": ["rw", "convert", "ext", "fin_cases"], "tactic_count": 4}
{"name": "AffineIndependent.mono", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Independent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIndependent.of_set_of_injective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Independent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIndependent.eq_zero_of_affineCombination_mem_affineSpan", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Independent", "is_tactic_proof": true, "tactics": ["obtain", "have", "rw", "exact", "rw", "exact"], "tactic_count": 6}
{"name": "AffineIndependent.indicator_extend_eq_of_affineCombination_comp_embedding_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Independent", "is_tactic_proof": true, "tactics": ["have", "rw", "refine", "rw", "convert", "exact"], "tactic_count": 6}
{"name": "AffineIndependent.indicator_extend_eq_of_affineCombination_comp_embedding_eq_of_fintype", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Independent", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "AffineIndependent.of_comp", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Independent", "is_tactic_proof": true, "tactics": ["rcases", "apply", "obtain", "rw", "simp_rw", "exact"], "tactic_count": 6}
{"name": "AffineIndependent.map'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Independent", "is_tactic_proof": true, "tactics": ["rcases", "apply", "obtain", "rw", "simp_rw", "have", "exact"], "tactic_count": 7}
{"name": "AffineMap.affineIndependent_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Independent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineEquiv.affineIndependent_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Independent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineEquiv.affineIndependent_set_of_eq_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Independent", "is_tactic_proof": true, "tactics": ["have", "simp"], "tactic_count": 2}
{"name": "AffineIndependent.inf_affineSpan_eq_affineSpan_inter", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Independent", "is_tactic_proof": true, "tactics": ["classical", "ext", "simp_rw", "constructor", "rintro", "rw", "replace", "refine", "rw", "convert", "refine", "intro", "rw", "rw", "refine", "intro", "rw", "simp", "intro", "rw", "simp", "grind"], "tactic_count": 22}
{"name": "AffineIndependent.exists_mem_inter_of_exists_mem_inter_affineSpan", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Independent", "is_tactic_proof": true, "tactics": ["have", "rw", "rw", "by_contra", "rw", "simp"], "tactic_count": 6}
{"name": "AffineIndependent.affineSpan_disjoint_of_disjoint", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Independent", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact"], "tactic_count": 3}
{"name": "AffineIndependent.mem_affineSpan_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Independent", "is_tactic_proof": true, "tactics": ["constructor", "intro", "have", "rwa", "exact"], "tactic_count": 5}
{"name": "AffineIndependent.notMem_affineSpan_diff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Independent", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AffineIndependent.injective_affineSpan_image", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Independent", "is_tactic_proof": true, "tactics": ["by_contra", "rw", "obtain", "apply", "ext", "simp_rw"], "tactic_count": 6}
{"name": "_private.Mathlib.LinearAlgebra.AffineSpace.Independent.0.AffineIndependent.vectorSpan_image_ne_of_mem_of_notMem_of_not_subsingleton", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Independent", "is_tactic_proof": true, "tactics": ["classical", "rw", "obtain", "intro", "have", "vsub_mem_vectorSpan", "rw", "obtain", "let", "have", "simp", "exact", "have", "rw", "simp", "let", "have", "let", "have", "rw", "exact", "have", "rw", "exact", "let", "have", "have", "have", "have", "have", "simp"], "tactic_count": 31}
{"name": "AffineIndependent.vectorSpan_image_eq_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Independent", "is_tactic_proof": true, "tactics": ["constructor", "intro", "by_cases", "simp", "simp", "by_cases", "rw", "exact", "by_cases", "rw", "exact", "simp", "have", "rcases", "exact", "exact", "intro", "rcases", "rfl", "simp"], "tactic_count": 20}
{"name": "exists_nontrivial_relation_sum_zero_of_not_affine_ind", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Independent", "is_tactic_proof": true, "tactics": ["classical", "rw", "simp", "obtain", "simp", "let", "refine", "on_goal", "suffices", "convert", "rename", "by_cases", "all_goals"], "tactic_count": 13}
{"name": "affineIndependent_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Independent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIndependent.eq_zero_of_sum_eq_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Independent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineIndependent.eq_of_sum_eq_sum", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Independent", "is_tactic_proof": true, "tactics": ["refine", "simpa"], "tactic_count": 2}
{"name": "AffineIndependent.eq_zero_of_sum_eq_zero_subtype", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Independent", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "AffineIndependent.eq_of_sum_eq_sum_subtype", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Independent", "is_tactic_proof": true, "tactics": ["refine", "simpa"], "tactic_count": 2}
{"name": "weightedVSub_mem_vectorSpan_pair", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Independent", "is_tactic_proof": true, "tactics": ["rw", "refine", "rcases", "refine", "rw", "have", "simp_rw", "hw₂,", "have", "rw", "exact", "rcases", "refine", "let", "change", "rw", "congr"], "tactic_count": 17}
{"name": "affineCombination_mem_affineSpan_pair", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Independent", "is_tactic_proof": false, "tactics": ["rw", "s.affineCombination_vsub,", "simp", "simp_all"], "tactic_count": 4}
{"name": "exists_subset_affineIndependent_affineSpan_eq_top", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Independent", "is_tactic_proof": true, "tactics": ["rcases", "have", "let", "have", "have", "rw", "have", "intro", "simpa", "rw", "exact", "affineSpan_singleton_union_vadd_eq_top_of_span_eq_top", "rw", "let", "have", "have", "rw", "rw", "have", "have", "intro", "simpa", "rw", "linearIndependent_set_iff_affineIndependent_vadd_union_singleton", "refine", "refine", "simp", "use", "exact"], "tactic_count": 29}
{"name": "exists_affineIndependent", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Independent", "is_tactic_proof": true, "tactics": ["rcases", "exact", "obtain", "have", "rw", "refine", "apply", "rwa", "rw", "apply", "have", "simp", "vectorSpan_eq_span_vsub_set_right", "congr", "change", "rw", "simp", "use", "simp", "exact"], "tactic_count": 20}
{"name": "affineIndependent_of_ne", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Independent", "is_tactic_proof": true, "tactics": ["rw", "let", "have", "rintro", "ext", "fin_cases", "simp", "simp", "haveI", "refine", "rw", "simpa"], "tactic_count": 12}
{"name": "AffineIndependent.affineIndependent_of_notMem_span", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Independent", "is_tactic_proof": true, "tactics": ["classical", "intro", "let", "let", "by_cases", "refine", "let", "have", "have", "have", "let", "have", "simp_rw", "rw", "simpa", "rw", "exact", "rw", "let", "have", "simp_rw", "rw", "rintro", "exact", "have", "simp_rw", "rw", "rintro", "exact", "intro", "by_cases", "rw", "exact", "exact"], "tactic_count": 34}
{"name": "affineIndependent_of_ne_of_mem_of_mem_of_notMem", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Independent", "is_tactic_proof": false, "tactics": ["have", "rw", "convert", "ext", "fin_cases", "refine", "intro", "refine", "simp_rw", "intro", "fin_cases"], "tactic_count": 11}
{"name": "affineIndependent_of_ne_of_mem_of_notMem_of_mem", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Independent", "is_tactic_proof": true, "tactics": ["rw", "convert", "ext", "fin_cases"], "tactic_count": 4}
{"name": "affineIndependent_of_ne_of_notMem_of_mem_of_mem", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Independent", "is_tactic_proof": true, "tactics": ["rw", "convert", "ext", "fin_cases"], "tactic_count": 4}
{"name": "AffineIndependent.affineIndependent_update_of_notMem_affineSpan", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Independent", "is_tactic_proof": true, "tactics": ["set", "have", "have", "replace", "exact"], "tactic_count": 5}
{"name": "sign_eq_of_affineCombination_mem_affineSpan_pair", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Independent", "is_tactic_proof": true, "tactics": ["rw", "rcases", "rw"], "tactic_count": 3}
{"name": "sign_eq_of_affineCombination_mem_affineSpan_single_lineMap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Independent", "is_tactic_proof": true, "tactics": ["classical", "rw", "s.affineCombination_affineCombinationLineMapWeights", "refine", "sign_eq_of_affineCombination_mem_affineSpan_pair", "rw", "simp_all"], "tactic_count": 7}
{"name": "AffineBasis.toMatrix", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineBasis.toMatrix_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineBasis.toMatrix_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Matrix", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "AffineBasis.toMatrix_row_sum_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Matrix", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AffineBasis.affineIndependent_of_toMatrix_right_inv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Matrix", "is_tactic_proof": true, "tactics": ["cases", "rw", "intro", "have", "ext", "change", "rw", "replace", "simpa"], "tactic_count": 9}
{"name": "AffineBasis.affineSpan_eq_top_of_toMatrix_left_inv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Matrix", "is_tactic_proof": true, "tactics": ["cases", "suffices", "rw", "rintro", "exact", "intro", "have", "calc", "have", "apply", "intro", "rw", "change", "simp_rw", "rw", "exact"], "tactic_count": 16}
{"name": "AffineBasis.toMatrix_vecMul_coords", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Matrix", "is_tactic_proof": true, "tactics": ["ext", "change", "conv_rhs", "rw", "simp"], "tactic_count": 5}
{"name": "AffineBasis.toMatrix_mul_toMatrix", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Matrix", "is_tactic_proof": true, "tactics": ["ext", "change", "rw"], "tactic_count": 3}
{"name": "AffineBasis.isUnit_toMatrix", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineBasis.isUnit_toMatrix_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Matrix", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "exact", "rintro", "let", "change", "exact"], "tactic_count": 7}
{"name": "AffineBasis.toMatrix_inv_vecMul_toMatrix", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Matrix", "is_tactic_proof": true, "tactics": ["have", "rw", "rw"], "tactic_count": 3}
{"name": "AffineBasis.det_smul_coords_eq_cramer_coords", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Matrix", "is_tactic_proof": true, "tactics": ["have", "rw", "rw"], "tactic_count": 3}
{"name": "midpoint", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.Midpoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.map_midpoint", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Midpoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineEquiv.map_midpoint", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Midpoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineEquiv.pointReflection_midpoint_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Midpoint", "is_tactic_proof": true, "tactics": ["rw", "one_smul,"], "tactic_count": 2}
{"name": "Equiv.pointReflection_midpoint_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Midpoint", "is_tactic_proof": true, "tactics": ["rw", "one_smul,"], "tactic_count": 2}
{"name": "midpoint_comm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Midpoint", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AffineEquiv.pointReflection_midpoint_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Midpoint", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Equiv.pointReflection_midpoint_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Midpoint", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "midpoint_vsub_midpoint", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Midpoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "midpoint_vadd_midpoint", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Midpoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "midpoint_eq_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Midpoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "midpoint_pointReflection_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Midpoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "midpoint_pointReflection_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Midpoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineEquiv.midpoint_pointReflection_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Midpoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineEquiv.midpoint_pointReflection_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Midpoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "midpoint_vsub_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Midpoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "midpoint_vsub_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Midpoint", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "left_vsub_midpoint", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Midpoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "right_vsub_midpoint", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Midpoint", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "midpoint_vsub", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Midpoint", "is_tactic_proof": true, "tactics": ["rw", "invOf_two_smul_add_invOf_two_smul,"], "tactic_count": 2}
{"name": "vsub_midpoint", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Midpoint", "is_tactic_proof": true, "tactics": ["rw", "neg_vsub_eq_vsub_rev]"], "tactic_count": 2}
{"name": "midpoint_sub_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Midpoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "midpoint_sub_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Midpoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "left_sub_midpoint", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Midpoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "right_sub_midpoint", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Midpoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "midpoint_eq_left_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Midpoint", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "left_eq_midpoint_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Midpoint", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "midpoint_eq_right_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Midpoint", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "right_eq_midpoint_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Midpoint", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "midpoint_eq_midpoint_iff_vsub_eq_vsub", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Midpoint", "is_tactic_proof": true, "tactics": ["rw", "vadd_eq_add,"], "tactic_count": 2}
{"name": "midpoint_eq_iff'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Midpoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "midpoint_unique", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Midpoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "midpoint_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Midpoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "midpoint_add_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Midpoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "midpoint_zero_add", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Midpoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "midpoint_eq_smul_add", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Midpoint", "is_tactic_proof": true, "tactics": ["rw", "mul_invOf_self,"], "tactic_count": 2}
{"name": "midpoint_self_neg", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Midpoint", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "midpoint_neg_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Midpoint", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "midpoint_sub_add", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Midpoint", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "midpoint_add_sub", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Midpoint", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "midpoint_vsub_midpoint_same_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Midpoint", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "midpoint_vsub_midpoint_same_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Midpoint", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AddMonoidHom.ofMapMidpoint", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.Midpoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.coe_ofMapMidpoint", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Midpoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lineMap_inv_two", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.MidpointZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lineMap_one_half", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.MidpointZero", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "homothety_invOf_two", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.MidpointZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "homothety_inv_two", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.MidpointZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "homothety_one_half", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.MidpointZero", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "pi_midpoint_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.MidpointZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lineMap_mono_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Ordered", "is_tactic_proof": true, "tactics": ["simp", "gcongr", "exact"], "tactic_count": 3}
{"name": "lineMap_strict_mono_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Ordered", "is_tactic_proof": true, "tactics": ["simp", "gcongr", "exact"], "tactic_count": 3}
{"name": "lineMap_mono_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Ordered", "is_tactic_proof": true, "tactics": ["simp", "gcongr"], "tactic_count": 2}
{"name": "lineMap_strict_mono_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Ordered", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "lineMap_mono_endpoints", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Ordered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lineMap_strict_mono_endpoints", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Ordered", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "lineMap_lt_lineMap_iff_of_lt", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Ordered", "is_tactic_proof": true, "tactics": ["simp", "rw", "smul_lt_smul_iff_of_pos_left"], "tactic_count": 3}
{"name": "left_lt_lineMap_iff_lt", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Ordered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lineMap_lt_left_iff_lt", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Ordered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lineMap_lt_right_iff_lt", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Ordered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "right_lt_lineMap_iff_lt", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Ordered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lineMap_le_lineMap_iff_of_lt'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Ordered", "is_tactic_proof": true, "tactics": ["simp", "rw"], "tactic_count": 2}
{"name": "left_le_lineMap_iff_nonneg", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Ordered", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "lineMap_le_left_iff_nonpos", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Ordered", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "right_le_lineMap_iff_one_le", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Ordered", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "lineMap_le_right_iff_le_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Ordered", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "lineMap_lt_lineMap_iff_of_lt'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Ordered", "is_tactic_proof": true, "tactics": ["simp", "rw"], "tactic_count": 2}
{"name": "left_lt_lineMap_iff_pos", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Ordered", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "lineMap_lt_left_iff_neg", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Ordered", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "right_lt_lineMap_iff_one_lt", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Ordered", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "lineMap_lt_right_iff_lt_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Ordered", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "midpoint_le_midpoint", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Ordered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lineMap_le_lineMap_iff_of_lt", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Ordered", "is_tactic_proof": true, "tactics": ["simp", "rw", "smul_le_smul_iff_of_pos_left"], "tactic_count": 3}
{"name": "left_le_lineMap_iff_le", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Ordered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "left_le_midpoint", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Ordered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lineMap_le_left_iff_le", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Ordered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "midpoint_le_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Ordered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lineMap_le_right_iff_le", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Ordered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "midpoint_le_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Ordered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "right_le_lineMap_iff_le", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Ordered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "right_le_midpoint", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Ordered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.LinearAlgebra.AffineSpace.Ordered.0.termC", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.Ordered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.LinearAlgebra.AffineSpace.Ordered.0._aux_Mathlib_LinearAlgebra_AffineSpace_Ordered___macroRules__private_Mathlib_LinearAlgebra_AffineSpace_Ordered_0_termC_1", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.Ordered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.LinearAlgebra.AffineSpace.Ordered.0._aux_Mathlib_LinearAlgebra_AffineSpace_Ordered___unexpand_AffineMap_lineMap_1", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.Ordered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "map_le_lineMap_iff_slope_le_slope_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Ordered", "is_tactic_proof": true, "tactics": ["rw", "smul_eq_mul,", "mul_inv_cancel_right₀"], "tactic_count": 3}
{"name": "lineMap_le_map_iff_slope_le_slope_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Ordered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "map_lt_lineMap_iff_slope_lt_slope_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Ordered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lineMap_lt_map_iff_slope_lt_slope_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Ordered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "map_le_lineMap_iff_slope_le_slope_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Ordered", "is_tactic_proof": true, "tactics": ["rw", "revert", "simp_rw", "rw", "mul_inv_cancel_right₀,", "exact"], "tactic_count": 6}
{"name": "lineMap_le_map_iff_slope_le_slope_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Ordered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "map_lt_lineMap_iff_slope_lt_slope_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Ordered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lineMap_lt_map_iff_slope_lt_slope_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Ordered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "map_le_lineMap_iff_slope_le_slope", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Ordered", "is_tactic_proof": true, "tactics": ["rw", "lineMap_slope_lineMap_slope_lineMap"], "tactic_count": 2}
{"name": "lineMap_le_map_iff_slope_le_slope", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Ordered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "map_lt_lineMap_iff_slope_lt_slope", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Ordered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lineMap_lt_map_iff_slope_lt_slope", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Ordered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "slope_pos_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Ordered", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "slope_pos_iff_gt", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Ordered", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "pos_of_slope_pos", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Ordered", "is_tactic_proof": true, "tactics": ["simp_all"], "tactic_count": 1}
{"name": "neg_of_slope_pos", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Ordered", "is_tactic_proof": true, "tactics": ["rwa", "exact"], "tactic_count": 2}
{"name": "AffineSubspace.pointwiseVAdd", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.coe_pointwise_vadd", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.pointwiseAddAction", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.pointwise_vadd_eq_map", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.vadd_mem_pointwise_vadd_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.pointwise_vadd_bot", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Pointwise", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "AffineSubspace.pointwise_vadd_top", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Pointwise", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "AffineSubspace.pointwise_vadd_direction", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Pointwise", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "AffineSubspace.pointwise_vadd_span", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.map_pointwise_vadd", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Pointwise", "is_tactic_proof": true, "tactics": ["rw", "congr", "ext", "exact"], "tactic_count": 4}
{"name": "AffineSubspace.pointwiseSMul", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.coe_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.smul_eq_map", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.smul_mem_smul_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.smul_bot", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Pointwise", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "AffineSubspace.smul_span", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.mulAction", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.smul_mem_smul_iff_of_isUnit", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.smul_mem_smul_iff₀", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.smul_top", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Pointwise", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "AffineSubspace.direction_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Pointwise", "is_tactic_proof": true, "tactics": ["have", "simp"], "tactic_count": 2}
{"name": "AffineSubspace.nonempty_map", "kind": "instance", "module": "Mathlib.LinearAlgebra.AffineSpace.Restrict", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "AffineMap.restrict", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.Restrict", "is_tactic_proof": true, "tactics": ["refine", "exact", "refine", "rw", "exact", "intro", "simp", "apply"], "tactic_count": 8}
{"name": "AffineMap.restrict.coe_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.restrict.linear_aux", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Restrict", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "AffineMap.restrict.linear", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.restrict.injective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Restrict", "is_tactic_proof": true, "tactics": ["intro", "simp", "exact"], "tactic_count": 3}
{"name": "AffineMap.restrict.surjective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Restrict", "is_tactic_proof": true, "tactics": ["rintro", "rw", "obtain", "exact"], "tactic_count": 4}
{"name": "AffineMap.restrict.bijective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Triangle", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.mkOfPoint", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.mkOfPoint_points", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.instInhabitedOfNatNat", "kind": "instance", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.nonempty", "kind": "instance", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.range_mkOfPoint_points", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Affine.Simplex.ext", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic", "is_tactic_proof": true, "tactics": ["cases", "cases", "congr", "exact"], "tactic_count": 4}
{"name": "Affine.Simplex.face", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.face_points", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.face_points'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.face_eq_mkOfPoint", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Affine.Simplex.range_face_points", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Affine.Simplex.faceOpposite", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.range_faceOpposite_points", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Affine.Simplex.faceOpposite_point_eq_point_succAbove", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Affine.Simplex.faceOpposite_point_eq_point_rev", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic", "is_tactic_proof": true, "tactics": ["have", "simp"], "tactic_count": 2}
{"name": "Affine.Simplex.faceOpposite_point_eq_point_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.faceOpposite_point_eq_point_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.instNonemptyElemComplSetSingletonOfNontrivial", "kind": "instance", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.mem_affineSpan_image_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.affineCombination_mem_affineSpan_faceOpposite_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact", "rw", "rcases", "have", "have", "rw", "simp", "exact"], "tactic_count": 10}
{"name": "Affine.Simplex.map", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.map_id", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.map_comp", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.face_map", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.faceOpposite_map", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.map_mkOfPoint", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.reindex", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.reindex_refl", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.reindex_trans", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.reindex_reindex_symm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Affine.Simplex.reindex_symm_reindex", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Affine.Simplex.reindex_range_points", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Affine.Simplex.reindex_map", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.range_face_reindex", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic", "is_tactic_proof": true, "tactics": ["simp", "simp"], "tactic_count": 2}
{"name": "Affine.Simplex.range_faceOpposite_reindex", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Affine.Simplex.restrict", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.restrict_map_inclusion", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.map_subtype_restrict", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "Affine.Simplex.restrict_map_restrict", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "Affine.Simplex.restrict_map_subtype", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.restrict_reindex", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.setInterior", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.affineCombination_mem_setInterior_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic", "is_tactic_proof": true, "tactics": ["refine", "simp_rw", "exact"], "tactic_count": 3}
{"name": "Affine.Simplex.setInterior_reindex", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic", "is_tactic_proof": true, "tactics": ["ext", "refine", "subst", "simp_rw", "rw", "have", "rw", "exact", "subst", "rw", "change", "have", "rw", "exact"], "tactic_count": 14}
{"name": "Affine.Simplex.setInterior_mono", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.setInterior_subset_affineSpan", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "Affine.Simplex.interior", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.interior_reindex", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.affineCombination_mem_interior_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.closedInterior", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.closedInterior_reindex", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.affineCombination_mem_closedInterior_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.interior_subset_closedInterior", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.point_notMem_interior", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic", "is_tactic_proof": false, "tactics": ["rw", "affineCombination_mem_interior_iff", "exact"], "tactic_count": 3}
{"name": "Affine.Simplex.point_mem_closedInterior", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic", "is_tactic_proof": false, "tactics": ["rw", "affineCombination_mem_closedInterior_iff", "intro", "by_cases"], "tactic_count": 4}
{"name": "Affine.Simplex.interior_ssubset_closedInterior", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Affine.Simplex.closedInterior_subset_affineSpan", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "Affine.Simplex.interior_eq_empty", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp", "sum_singleton,", "intro", "simpa"], "tactic_count": 5}
{"name": "Affine.Simplex.closedInterior_eq_singleton", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp", "sum_singleton,", "constructor", "rintro", "simp", "rintro", "exact"], "tactic_count": 8}
{"name": "Affine.Simplex.affineCombination_mem_setInterior_face_iff_mem", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic", "is_tactic_proof": true, "tactics": ["refine", "obtain", "eq_affineCombination_of_mem_affineSpan_of_fintype", "rw", "have", "s.independent.indicator_extend_eq_of_affineCombination_comp_embedding_eq_of_fintype", "simp_rw", "refine", "simp", "rw", "obtain", "simp", "let", "have", "rw", "hw]", "have", "rw", "convert", "convert", "simp", "congr", "grind"], "tactic_count": 23}
{"name": "Affine.Simplex.affineCombination_mem_interior_face_iff_mem_Ioo", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.affineCombination_mem_closedInterior_face_iff_mem_Icc", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.affineCombination_mem_interior_face_iff_pos", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "obtain", "exact"], "tactic_count": 5}
{"name": "Affine.Simplex.affineCombination_mem_closedInterior_face_iff_nonneg", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "Affine.Simplex.centroid", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.univ_centroid_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.centroid_mem_affineSpan", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.centroid_eq_affineCombination", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "Affine.Simplex.centroid_notMem_affineSpan_of_ne_univ", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid", "is_tactic_proof": true, "tactics": ["intro", "have", "obtain", "rw", "set", "have", "have", "have", "simp", "simp", "norm_cast"], "tactic_count": 11}
{"name": "Affine.Simplex.centroid_vsub_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid", "is_tactic_proof": false, "tactics": ["rw", "affineCombination_eq_linear_combination", "simp"], "tactic_count": 3}
{"name": "Affine.Simplex.centroid_eq_smul_sum_vsub_vadd", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Affine.Simplex.smul_centroid_vsub_point_eq_sum_vsub", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid", "is_tactic_proof": true, "tactics": ["rw", "norm_cast"], "tactic_count": 2}
{"name": "Affine.Simplex.centroid_weighted_vsub_eq_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid", "is_tactic_proof": true, "tactics": ["have", "simp", "symm", "rw", "exact"], "tactic_count": 5}
{"name": "Affine.Simplex.eq_centroid_iff_sum_vsub_eq_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "intro", "rw", "have", "apply", "intro", "rw", "rw", "simp", "have", "rw", "exact"], "tactic_count": 14}
{"name": "Affine.Simplex.face_centroid_eq_centroid", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid", "is_tactic_proof": true, "tactics": ["convert", "rw", "simp"], "tactic_count": 3}
{"name": "Affine.Simplex.centroid_eq_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid", "is_tactic_proof": true, "tactics": ["refine", "rw", "have", "simp_rw", "h₁,", "ext", "specialize", "have", "constructor", "simp", "simpa"], "tactic_count": 11}
{"name": "Affine.Simplex.face_centroid_eq_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Affine.Simplex.centroid_eq_of_range_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Affine.Simplex.affineIndependent_points_update_centroid", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "Affine.Simplex.centroid_map", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid", "is_tactic_proof": true, "tactics": ["rw", "rw", "rw", "simp"], "tactic_count": 4}
{"name": "Affine.Simplex.centroid_reindex", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid", "is_tactic_proof": true, "tactics": ["rw", "simp", "simp", "have", "subst", "convert"], "tactic_count": 6}
{"name": "Affine.Simplex.centroid_restrict", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid", "is_tactic_proof": true, "tactics": ["rw", "haveI", "have", "exact"], "tactic_count": 4}
{"name": "Affine.Simplex.faceOppositeCentroid", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.faceOppositeCentroid_mem_affineSpan_face", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.faceOppositeCentroid_eq_affineCombination", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid", "is_tactic_proof": true, "tactics": ["unfold", "have", "rw", "unfold", "rw", "simp", "rfl"], "tactic_count": 7}
{"name": "Affine.Simplex.faceOppositeCentroid_vsub_point_eq_smul_sum_vsub", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid", "is_tactic_proof": false, "tactics": ["rw", "affineCombination_eq_weightedVSubOfPoint_vadd_of_sum_eq_one", "simp", "have", "rw", "simp", "rw", "simp", "rw"], "tactic_count": 9}
{"name": "Affine.Simplex.faceOppositeCentroid_eq_sum_vsub_vadd", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Affine.Simplex.point_vsub_faceOppositeCentroid_eq_smul_sum_vsub", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid", "is_tactic_proof": false, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Affine.Simplex.smul_faceOppositeCentroid_vsub_point_eq_sum_vsub", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Affine.Simplex.smul_centroid_vsub_point_eq_smul_faceOppositeCentroid_vsub_point", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Affine.Simplex.faceOppositeCentroid_vsub_faceOppositeCentroid", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid", "is_tactic_proof": false, "tactics": ["rw", "vadd_vsub_vadd_comm", "have", "apply", "simp", "simp_rw", "rw", "card_univ,", "have", "rw", "have", "norm_cast0", "congr", "rw"], "tactic_count": 14}
{"name": "Affine.Simplex.faceOppositeCentroid_vsub_point_eq_smul_vsub", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid", "is_tactic_proof": false, "tactics": ["rw", "centroid_vsub_eq,", "congr", "rw", "grind"], "tactic_count": 5}
{"name": "Affine.Simplex.point_vsub_faceOppositeCentroid_eq_smul_vsub", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid", "is_tactic_proof": true, "tactics": ["rw", "neg_vsub_eq_vsub_rev,"], "tactic_count": 2}
{"name": "Affine.Simplex.point_vsub_centroid_eq_smul_vsub", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid", "is_tactic_proof": true, "tactics": ["symm", "rw", "congr", "simp_rw", "symm", "rw", "have", "nth_rw", "rw"], "tactic_count": 9}
{"name": "Affine.Simplex.centroid_vsub_point_eq_smul_vsub", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid", "is_tactic_proof": true, "tactics": ["rw", "neg_neg]"], "tactic_count": 2}
{"name": "Affine.Simplex.faceOppositeCentroid_vsub_centroid_eq_smul_vsub", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Affine.Simplex.centroid_vsub_faceOppositeCentroid_eq_smul_vsub", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Affine.Simplex.centroid_eq_smul_vsub_vadd_point", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Affine.Simplex.faceOppositeCentroid_eq_smul_vsub_vadd_point", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Affine.Simplex.faceOppositeCentroid_map", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid", "is_tactic_proof": true, "tactics": ["simp", "rw", "rw", "simp"], "tactic_count": 4}
{"name": "Affine.Simplex.faceOppositeCentroid_restrict", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid", "is_tactic_proof": true, "tactics": ["rw", "haveI", "have", "exact"], "tactic_count": 4}
{"name": "Affine.Simplex.faceOppositeCentroid_reindex", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid", "is_tactic_proof": true, "tactics": ["ext", "rw", "obtain", "exact"], "tactic_count": 4}
{"name": "Affine.Simplex.median", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.median_reindex", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Affine.Simplex.median_map", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Affine.Simplex.median_restrict", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Affine.Simplex.faceOppositeCentroid_mem_median", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Affine.Simplex.point_mem_median", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Affine.Simplex.centroid_mem_median", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid", "is_tactic_proof": true, "tactics": ["rw", "have", "rw", "one_div,", "rw", "exact"], "tactic_count": 6}
{"name": "Affine.Simplex.median_eq_line_point_centroid", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid", "is_tactic_proof": false, "tactics": ["have", "unfold", "apply", "rw", "have", "rw", "have", "rw", "congr", "rw", "rw", "exact", "have", "rw", "apply", "exact", "exact"], "tactic_count": 17}
{"name": "Affine.Simplex.eq_centroid_of_forall_mem_median", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid", "is_tactic_proof": true, "tactics": ["rw", "set", "have", "let", "let", "have", "intro", "have", "grind", "have", "set", "have", "have", "unfold", "grind", "have", "simp_rw", "set", "have", "grind", "have", "have", "convert", "grind", "have", "simp", "have", "have", "rw", "tauto", "choose", "have", "have", "simp_rw", "exact"], "tactic_count": 35}
{"name": "Affine.Simplex.medial", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.medial_points", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Affine.Simplex.medial_reindex", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Affine.Simplex.medial_map", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Affine.Simplex.affineSpan_range_medial", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid", "is_tactic_proof": true, "tactics": ["have", "have", "apply", "exact", "rw", "simp_rw", "suffices", "rw", "simpa", "ext", "suffices", "simpa", "congrm", "simp"], "tactic_count": 14}
{"name": "Affine.Simplex.medial_restrict", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid", "is_tactic_proof": true, "tactics": ["haveI", "ext", "simp"], "tactic_count": 3}
{"name": "slope", "kind": "definition", "module": "Mathlib.LinearAlgebra.AffineSpace.Slope", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "slope_fun_def", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Slope", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "slope_def_field", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Slope", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "slope_fun_def_field", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Slope", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "slope_same", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Slope", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "slope_def_module", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Slope", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sub_smul_slope", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Slope", "is_tactic_proof": true, "tactics": ["rcases", "rw", "rw"], "tactic_count": 3}
{"name": "sub_smul_slope_vadd", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Slope", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "slope_vadd_const", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Slope", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "slope_sub_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Slope", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "eq_of_slope_eq_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Slope", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AffineMap.slope_comp", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Slope", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LinearMap.slope_comp", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Slope", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "slope_comm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Slope", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "slope_neg", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Slope", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "slope_neg_fun", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Slope", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "slope_eq_zero_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Slope", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "sub_div_sub_smul_slope_add_sub_div_sub_smul_slope", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Slope", "is_tactic_proof": true, "tactics": ["by_cases", "subst", "rw", "by_cases", "simp", "rw", "by_cases", "subst", "simp", "rw", "simp_rw", "smul_inv_smul₀"], "tactic_count": 12}
{"name": "lineMap_slope_slope_sub_div_sub", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Slope", "is_tactic_proof": true, "tactics": ["simp", "match_scalars", "field"], "tactic_count": 3}
{"name": "lineMap_slope_lineMap_slope_lineMap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Slope", "is_tactic_proof": true, "tactics": ["obtain", "rw", "convert", "rw"], "tactic_count": 4}
{"name": "slope_nonneg_iff_of_le", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Slope", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "refine", "have", "rwa", "sub_nonneg]", "rwa"], "tactic_count": 7}
{"name": "MonotoneOn.slope_nonneg", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Slope", "is_tactic_proof": true, "tactics": ["rcases", "exact", "exact"], "tactic_count": 3}
{"name": "slope_nonpos_iff_of_le", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Slope", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "AntitoneOn.slope_nonpos", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Slope", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "slope_pos_iff_of_le", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Slope", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "StrictMonoOn.slope_pos", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Slope", "is_tactic_proof": true, "tactics": ["rcases", "exact", "exact"], "tactic_count": 3}
{"name": "slope_neg_iff_of_le", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Slope", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "StrictAntiOn.slope_neg", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AffineSpace.Slope", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "term_[⋀^_]→ₗ[_]_", "kind": "definition", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_LinearAlgebra_Alternating_Basic___macroRules_term_[⋀^_]→ₗ[_]__1", "kind": "definition", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_LinearAlgebra_Alternating_Basic___unexpand_AlternatingMap_1", "kind": "definition", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.instFunLike", "kind": "instance", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.toFun_eq_coe", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.coe_mk", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.congr_fun", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.congr_arg", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.coe_injective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.coe_inj", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.ext", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.instCoe", "kind": "instance", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.coe_multilinearMap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.coe_multilinearMap_injective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.coe_multilinearMap_mk", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlternatingMap.map_update_add", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.map_update_sub", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.map_update_neg", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.map_update_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.map_eq_zero_of_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.map_coord_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.map_update_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.map_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.map_eq_zero_of_not_injective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": true, "tactics": ["rw", "push_neg", "rcases", "exact"], "tactic_count": 4}
{"name": "AlternatingMap.instSMul", "kind": "instance", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.smul_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.coe_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.coeFn_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.instSMulCommClass", "kind": "instance", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.instIsCentralScalar", "kind": "instance", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.prod", "kind": "definition", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.coe_prod", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.pi", "kind": "definition", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.coe_pi", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.smulRight", "kind": "definition", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.coe_smulRight", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.instAdd", "kind": "instance", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.add_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.coe_add", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.instZero", "kind": "instance", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.zero_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.coe_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.mk_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.instInhabited", "kind": "instance", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.instAddCommMonoid", "kind": "instance", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.instNeg", "kind": "instance", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.neg_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.coe_neg", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.instSub", "kind": "instance", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.sub_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.coe_sub", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.instAddCommGroup", "kind": "instance", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.instDistribMulAction", "kind": "instance", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.instModule", "kind": "instance", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.instIsTorsionFree", "kind": "instance", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.toMultilinearMapLM", "kind": "definition", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.ofSubsingleton", "kind": "definition", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.constOfIsEmpty", "kind": "definition", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.codRestrict", "kind": "definition", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.compAlternatingMap", "kind": "definition", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.coe_compAlternatingMap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.compAlternatingMap_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.compAlternatingMap_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.zero_compAlternatingMap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.compAlternatingMap_add", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.add_compAlternatingMap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.compAlternatingMap_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.smul_compAlternatingMap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.compAlternatingMapₗ", "kind": "definition", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.smulRight_eq_comp", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.subtype_compAlternatingMap_codRestrict", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.compAlternatingMap_codRestrict", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.compLinearMap", "kind": "definition", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.coe_compLinearMap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.compLinearMap_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.compLinearMap_assoc", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.zero_compLinearMap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "AlternatingMap.add_compLinearMap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "AlternatingMap.compLinearMap_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp_rw"], "tactic_count": 2}
{"name": "AlternatingMap.compLinearMap_id", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.compLinearMap_injective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.compLinearMap_inj", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.ext_ring", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.uniqueOfCommRing", "kind": "instance", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.domLCongr", "kind": "definition", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.domLCongr_refl", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.domLCongr_symm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.domLCongr_trans", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.compLinearEquiv_eq_zero_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.map_update_sum", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.map_update_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.map_update_update", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.map_swap_add", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": true, "tactics": ["rw", "convert", "simp"], "tactic_count": 3}
{"name": "AlternatingMap.map_add_swap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "AlternatingMap.map_swap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.map_perm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": true, "tactics": ["induction", "one", "mul_swap"], "tactic_count": 3}
{"name": "AlternatingMap.map_congr_perm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "AlternatingMap.domDomCongr", "kind": "definition", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.domDomCongr_refl", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.domDomCongr_trans", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.domDomCongr_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.domDomCongr_add", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.domDomCongr_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.domDomCongrEquiv", "kind": "definition", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.domDomCongrₗ", "kind": "definition", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.domDomCongrₗ_refl", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.domDomCongrₗ_toAddEquiv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.domDomCongr_eq_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.domDomCongr_eq_zero_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.domDomCongr_perm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.coe_domDomCongr", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.map_linearDependent", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": true, "tactics": ["obtain", "letI", "suffices", "rw", "exact", "rw", "rw", "apply", "intro", "obtain", "rw"], "tactic_count": 11}
{"name": "AlternatingMap.map_vecCons_add", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.map_vecCons_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.LinearAlgebra.Alternating.Basic.0.MultilinearMap.alternization_map_eq_zero_of_eq_aux", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact", "swap_mul_involutive"], "tactic_count": 3}
{"name": "MultilinearMap.alternatization", "kind": "definition", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.alternatization_def", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.alternatization_coe", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.alternatization_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlternatingMap.coe_alternatization", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": true, "tactics": ["apply", "simp_rw"], "tactic_count": 2}
{"name": "LinearMap.compMultilinearMap_alternatization", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Module.Basis.ext_alternating", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": true, "tactics": ["refine", "by_cases", "exact", "have", "rw", "g.map_eq_zero_of_not_injective"], "tactic_count": 6}
{"name": "LinearEquiv.alternatingMapCongrRight", "kind": "definition", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.constLinearEquivOfIsEmpty", "kind": "definition", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.curryLeft", "kind": "definition", "module": "Mathlib.LinearAlgebra.Alternating.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.curryLeft_apply_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.curryLeft_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.curryLeft_add", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.curryLeft_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.curryLeftLinearMap", "kind": "definition", "module": "Mathlib.LinearAlgebra.Alternating.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.curryLeft_same", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.curryLeft_compAlternatingMap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.curryLeft_compLinearMap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.ModSumCongr", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.Alternating.DomCoprod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.domCoprod.summand", "kind": "definition", "module": "Mathlib.LinearAlgebra.Alternating.DomCoprod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.domCoprod.summand_mk''", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.DomCoprod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.domCoprod.summand_add_swap_smul_eq_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.DomCoprod", "is_tactic_proof": true, "tactics": ["refine", "dsimp", "rw", "simp", "convert", "ext", "rw"], "tactic_count": 7}
{"name": "AlternatingMap.domCoprod.summand_eq_zero_of_smul_invariant", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.DomCoprod", "is_tactic_proof": true, "tactics": ["refine", "dsimp", "intro", "obtain", "rcases", "substs", "simpa", "simpa", "suffices", "exact", "suffices", "exact"], "tactic_count": 12}
{"name": "AlternatingMap.domCoprod", "kind": "definition", "module": "Mathlib.LinearAlgebra.Alternating.DomCoprod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.domCoprod_coe", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.DomCoprod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.domCoprod'", "kind": "definition", "module": "Mathlib.LinearAlgebra.Alternating.DomCoprod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.domCoprod'_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.DomCoprod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.domCoprod_alternization_coe", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.DomCoprod", "is_tactic_proof": true, "tactics": ["simp_rw", "simp_rw", "rfl"], "tactic_count": 3}
{"name": "MultilinearMap.domCoprod_alternization", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.DomCoprod", "is_tactic_proof": true, "tactics": ["apply", "rw", "congr", "ext1", "induction", "h", "set", "calc", "conv_lhs", "simp", "simp_rw", "sign", "simp"], "tactic_count": 13}
{"name": "MultilinearMap.domCoprod_alternization_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.DomCoprod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlternatingMap.map_insertNth", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Uncurry.Fin", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "AlternatingMap.neg_one_pow_smul_map_insertNth", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Uncurry.Fin", "is_tactic_proof": true, "tactics": ["rw", "use"], "tactic_count": 2}
{"name": "AlternatingMap.neg_one_pow_smul_map_removeNth_add_eq_zero_of_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Uncurry.Fin", "is_tactic_proof": true, "tactics": ["rcases", "obtain", "rw", "succAbove_succAbove_predAbove,", "update_eq_self_iff.2,", "smul_smul", "exact"], "tactic_count": 7}
{"name": "AlternatingMap.alternatizeUncurryFin", "kind": "definition", "module": "Mathlib.LinearAlgebra.Alternating.Uncurry.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.alternatizeUncurryFin_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Uncurry.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlternatingMap.alternatizeUncurryFin_add", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Uncurry.Fin", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "AlternatingMap.alternatizeUncurryFin_curryLeft", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Uncurry.Fin", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "AlternatingMap.alternatizeUncurryFin_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Uncurry.Fin", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "AlternatingMap.alternatizeUncurryFinLM", "kind": "definition", "module": "Mathlib.LinearAlgebra.Alternating.Uncurry.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.alternatizeUncurryFin_alternatizeUncurryFinLM_comp_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Uncurry.Fin", "is_tactic_proof": false, "tactics": ["simp", "refine", "rw", "have", "have", "simp", "smul_comm", "congr", "rw", "simp"], "tactic_count": 10}
{"name": "AlternatingMap.alternatizeUncurryFin_alternatizeUncurryFinLM_comp_of_symmetric", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Alternating.Uncurry.Fin", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Polynomial.annIdeal", "kind": "definition", "module": "Mathlib.LinearAlgebra.AnnihilatingPolynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.mem_annIdeal_iff_aeval_eq_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AnnihilatingPolynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.annIdealGenerator", "kind": "definition", "module": "Mathlib.LinearAlgebra.AnnihilatingPolynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.annIdealGenerator_eq_zero_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AnnihilatingPolynomial", "is_tactic_proof": true, "tactics": ["simp", "inv_eq_zero,"], "tactic_count": 2}
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{"name": "Polynomial.mem_iff_eq_smul_annIdealGenerator", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AnnihilatingPolynomial", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
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{"name": "Polynomial.annIdealGenerator_aeval_eq_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AnnihilatingPolynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Polynomial.degree_annIdealGenerator_le_of_mem", "kind": "theorem", "module": "Mathlib.LinearAlgebra.AnnihilatingPolynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Module.Basis.mem_span_repr_support", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Basis.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Module.Basis.self_mem_span_image", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Basis.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "Submodule.eq_top_iff_forall_basis_mem", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Basis.Basic", "is_tactic_proof": true, "tactics": ["refine", "replace", "simpa"], "tactic_count": 3}
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{"name": "Module.Basis.linearIndependent", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Basis.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.ne_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Basis.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.mk", "kind": "definition", "module": "Mathlib.LinearAlgebra.Basis.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.mk_repr", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Basis.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.mk_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Basis.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Module.Basis.singleton", "kind": "definition", "module": "Mathlib.LinearAlgebra.Basis.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Module.Basis.emptyUnique", "kind": "instance", "module": "Mathlib.LinearAlgebra.Basis.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.isTorsionFree", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Basis.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Module.Basis.extendLe_subset", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Basis.VectorSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Module.Basis.ofVectorSpaceIndex.linearIndependent", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Basis.VectorSpace", "is_tactic_proof": true, "tactics": ["convert", "ext", "rw"], "tactic_count": 3}
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{"name": "Submodule.exists_isCompl", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Basis.VectorSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.complementedLattice", "kind": "instance", "module": "Mathlib.LinearAlgebra.Basis.VectorSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LinearMap.BilinForm.zero_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LinearMap.BilinForm.restrict", "kind": "definition", "module": "Mathlib.LinearAlgebra.BilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LinearMap.BilinForm.compLeft", "kind": "definition", "module": "Mathlib.LinearAlgebra.BilinearForm.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LinearMap.BilinForm.linMulLin_compLeft", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.linMulLin_compRight", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.ext_basis", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.sum_repr_mul_repr_mul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Hom", "is_tactic_proof": true, "tactics": ["conv_rhs", "simp_rw"], "tactic_count": 2}
{"name": "LinearMap.BilinForm.IsOrtho", "kind": "definition", "module": "Mathlib.LinearAlgebra.BilinearForm.Orthogonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.isOrtho_def", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Orthogonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.isOrtho_zero_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Orthogonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.isOrtho_zero_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Orthogonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.ne_zero_of_not_isOrtho_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Orthogonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.IsRefl.ortho_comm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Orthogonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.IsAlt.ortho_comm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Orthogonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.IsSymm.ortho_comm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Orthogonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.iIsOrtho", "kind": "definition", "module": "Mathlib.LinearAlgebra.BilinearForm.Orthogonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.iIsOrtho_def", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Orthogonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.isOrtho_smul_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Orthogonal", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "simp", "exact"], "tactic_count": 4}
{"name": "LinearMap.BilinForm.isOrtho_smul_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Orthogonal", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "simp", "exact"], "tactic_count": 4}
{"name": "LinearMap.BilinForm.linearIndependent_of_iIsOrtho", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Orthogonal", "is_tactic_proof": true, "tactics": ["classical", "rw", "intro", "have", "have", "apply", "intro", "rw", "simp_rw", "exact"], "tactic_count": 10}
{"name": "LinearMap.BilinForm.orthogonal", "kind": "definition", "module": "Mathlib.LinearAlgebra.BilinearForm.Orthogonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.mem_orthogonal_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Orthogonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.orthogonal_bot", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Orthogonal", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "LinearMap.BilinForm.orthogonal_le", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Orthogonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.le_orthogonal_orthogonal", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Orthogonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.orthogonal_top_eq_ker", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Orthogonal", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "LinearMap.BilinForm.orthogonal_top_eq_bot", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Orthogonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.span_singleton_inf_orthogonal_eq_bot", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Orthogonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.orthogonal_span_singleton_eq_toLin_ker", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Orthogonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.span_singleton_sup_orthogonal_eq_top", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Orthogonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.isCompl_span_singleton_orthogonal", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Orthogonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.nondegenerate_restrict_of_disjoint_orthogonal", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Orthogonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.iIsOrtho.not_isOrtho_basis_self_of_nondegenerate", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Orthogonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.iIsOrtho.nondegenerate_iff_not_isOrtho_basis_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Orthogonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.toLin_restrict_ker_eq_inf_orthogonal", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Orthogonal", "is_tactic_proof": true, "tactics": ["ext", "rcases", "constructor", "simp", "intro", "rw", "change", "rw", "rfl", "simp_rw", "refine", "ext", "change", "rw", "exact"], "tactic_count": 15}
{"name": "LinearMap.BilinForm.toLin_restrict_range_dualCoannihilator_eq_orthogonal", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Orthogonal", "is_tactic_proof": true, "tactics": ["ext", "intro", "rw", "exact", "rw", "rintro", "exact"], "tactic_count": 7}
{"name": "LinearMap.BilinForm.ker_restrict_eq_of_codisjoint", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Orthogonal", "is_tactic_proof": true, "tactics": ["ext", "simp", "refine", "ext", "obtain", "simpa", "ext", "simpa"], "tactic_count": 8}
{"name": "LinearMap.BilinForm.inf_orthogonal_self_le_ker_restrict", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Orthogonal", "is_tactic_proof": true, "tactics": ["rintro", "simp", "exists_prop,", "refine", "ext", "exact"], "tactic_count": 6}
{"name": "LinearMap.BilinForm.finrank_add_finrank_orthogonal", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Orthogonal", "is_tactic_proof": false, "tactics": ["rw", "finrank_map_subtype_eq]", "conv_rhs", "rw"], "tactic_count": 4}
{"name": "LinearMap.BilinForm.finrank_orthogonal", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Orthogonal", "is_tactic_proof": true, "tactics": ["have", "rw", "lia"], "tactic_count": 3}
{"name": "LinearMap.BilinForm.orthogonal_orthogonal", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Orthogonal", "is_tactic_proof": true, "tactics": ["apply", "simp", "lia"], "tactic_count": 3}
{"name": "LinearMap.BilinForm.isCompl_orthogonal_iff_disjoint", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Orthogonal", "is_tactic_proof": true, "tactics": ["refine", "rw", "apply", "calc", "finrank", "rw"], "tactic_count": 6}
{"name": "LinearMap.BilinForm.isCompl_orthogonal_of_restrict_nondegenerate", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Orthogonal", "is_tactic_proof": false, "tactics": ["have", "rw", "intro", "obtain", "refine", "rintro", "simp", "exact", "refine", "conv_rhs", "rw", "exact"], "tactic_count": 12}
{"name": "LinearMap.BilinForm.restrict_nondegenerate_iff_isCompl_orthogonal", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Orthogonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.orthogonal_eq_top_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Orthogonal", "is_tactic_proof": true, "tactics": ["refine", "have", "rwa"], "tactic_count": 3}
{"name": "LinearMap.BilinForm.eq_top_of_restrict_nondegenerate_of_orthogonal_eq_bot", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Orthogonal", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "LinearMap.BilinForm.orthogonal_eq_bot_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Orthogonal", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "LinearMap.BilinForm.restrict_nondegenerate_orthogonal_spanSingleton", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Orthogonal", "is_tactic_proof": false, "tactics": ["have", "refine", "obtain", "rw", "rw"], "tactic_count": 5}
{"name": "LinearMap.BilinForm.IsRefl", "kind": "definition", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.IsRefl.eq_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.IsRefl.neg", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.IsRefl.smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.IsRefl.groupSMul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.isRefl_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.isRefl_neg", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.isSymm_def", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.isSymm_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LinearMap.BilinForm.IsSymm.isRefl", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.IsSymm.add", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.IsSymm.sub", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.IsSymm.neg", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.IsSymm.smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.IsSymm.restrict", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.isSymm_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.isSymm_neg", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.isSymm_iff_flip", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.IsSymm.polarization", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": true, "tactics": ["simp", "rw", "ring_nf", "rw"], "tactic_count": 4}
{"name": "LinearMap.BilinForm.ext_of_isSymm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": true, "tactics": ["ext", "rw", "simp_rw"], "tactic_count": 3}
{"name": "LinearMap.BilinForm.ext_iff_of_isSymm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.isSymm_iff_basis", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.isNonneg_def", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.isNonneg_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.isNonneg_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.IsNonneg.add", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.IsNonneg.smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.isPosSemidef_def", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.isPosSemidef_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.isPosSemidef_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.IsPosSemidef.add", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.IsPosSemidef.smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.IsAlt", "kind": "definition", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.IsAlt.self_eq_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.IsAlt.neg_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.IsAlt.isRefl", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.IsAlt.eq_of_add_add_eq_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.IsAlt.add", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.IsAlt.sub", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.IsAlt.neg", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.IsAlt.smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.isAlt_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.isAlt_neg", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.Nondegenerate", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.not_nondegenerate_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.Nondegenerate.ne_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.Nondegenerate.congr", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.nondegenerate_congr_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.Nondegenerate.ker_eq_bot", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.compLeft_injective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.isAdjointPair_unique_of_nondegenerate", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.Nondegenerate.flip", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.nondegenerate_flip_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.toDual", "kind": "definition", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.toDual_def", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.apply_toDual_symm_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": true, "tactics": ["change", "simp"], "tactic_count": 2}
{"name": "LinearMap.BilinForm.dualBasis", "kind": "definition", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.dualBasis_repr_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "LinearMap.BilinForm.apply_dualBasis_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "LinearMap.BilinForm.apply_dualBasis_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LinearMap.BilinForm.dualBasis_dualBasis_flip", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": true, "tactics": ["ext", "refine", "simp_rw"], "tactic_count": 3}
{"name": "LinearMap.BilinForm.dualBasis_flip_dualBasis", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.dualBasis_dualBasis", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": true, "tactics": ["convert", "rwa"], "tactic_count": 2}
{"name": "LinearMap.BilinForm.dualBasis_involutive", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.dualBasis_injective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.dualBasis_eq_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.symmCompOfNondegenerate", "kind": "definition", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.comp_symmCompOfNondegenerate_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": true, "tactics": ["rw", "simp", "erw"], "tactic_count": 3}
{"name": "LinearMap.BilinForm.symmCompOfNondegenerate_left_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": true, "tactics": ["conv_lhs"], "tactic_count": 1}
{"name": "LinearMap.BilinForm.leftAdjointOfNondegenerate", "kind": "definition", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.isAdjointPairLeftAdjointOfNondegenerate", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.isAdjointPair_iff_eq_of_nondegenerate", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.Properties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinMap.tensorDistrib", "kind": "definition", "module": "Mathlib.LinearAlgebra.BilinearForm.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinMap.tensorDistrib_tmul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinMap.tmul", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.BilinearForm.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinMap.tmul_isSymm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.TensorProduct", "is_tactic_proof": true, "tactics": ["revert", "rw", "aesop"], "tactic_count": 3}
{"name": "LinearMap.BilinMap.baseChange", "kind": "definition", "module": "Mathlib.LinearAlgebra.BilinearForm.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinMap.baseChange_tmul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinMap.baseChange_isSymm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.tensorDistrib", "kind": "definition", "module": "Mathlib.LinearAlgebra.BilinearForm.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.tensorDistrib_tmul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.tmul", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.BilinearForm.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsSymm.tmul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.TensorProduct", "is_tactic_proof": true, "tactics": ["rw", "ext", "exact"], "tactic_count": 3}
{"name": "LinearMap.BilinForm.baseChange", "kind": "definition", "module": "Mathlib.LinearAlgebra.BilinearForm.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.baseChange_tmul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.IsSymm.baseChange", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.tensorDistribEquiv", "kind": "definition", "module": "Mathlib.LinearAlgebra.BilinearForm.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.tensorDistribEquiv_tmul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.tensorDistribEquiv_toLinearMap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.TensorProduct", "is_tactic_proof": true, "tactics": ["ext", "ext", "exact"], "tactic_count": 3}
{"name": "LinearMap.BilinForm.tensorDistribEquiv_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearForm.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.mk₂'ₛₗ", "kind": "definition", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.mk₂'ₛₗ_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.mk₂'", "kind": "definition", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.mk₂'_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.ext₂", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.congr_fun₂", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.ext_iff₂", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.flip", "kind": "definition", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.flip_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.lcompₛₗ", "kind": "definition", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.lcompₛₗ_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.compl₂", "kind": "definition", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.compl₂_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.compl₂_id", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "LinearMap.lcomp", "kind": "definition", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.lcomp_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.lcomp_apply'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.lcomp_injective_of_surjective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.flip_flip", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.flip_inj", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.map_zero₂", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.map_neg₂", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.map_sub₂", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.map_add₂", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.map_smul₂", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.map_smulₛₗ₂", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.map_sum₂", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.domRestrict₂", "kind": "definition", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.domRestrict₂_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.domRestrict₁₂", "kind": "definition", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.domRestrict₁₂_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.restrictScalars₁₂", "kind": "definition", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.restrictScalars₁₂_injective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.restrictScalars₁₂_inj", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.lflip", "kind": "definition", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.lflip_symm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.lflip_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.mk₂", "kind": "definition", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.mk₂_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.compl₁₂", "kind": "definition", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.compl₁₂_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.compl₁₂_id_id", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": true, "tactics": ["ext", "simp_rw"], "tactic_count": 2}
{"name": "LinearMap.compl₁₂_inj", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": true, "tactics": ["constructor", "ext", "obtain", "subst", "obtain", "subst", "convert", "subst"], "tactic_count": 8}
{"name": "LinearMap.compr₂", "kind": "definition", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.compr₂_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.injective_compr₂_of_injective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.surjective_compr₂_of_exists_rightInverse", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.surjective_compr₂_of_equiv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.bijective_compr₂_of_equiv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.llcomp", "kind": "definition", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.llcomp_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.llcomp_apply'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.compr₂ₛₗ", "kind": "definition", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.compr₂ₛₗ_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.injective_compr₂ₛₗ_of_injective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.surjective_compr₂ₛₗ_of_exists_rightInverse", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.surjective_compr₂ₛₗ_of_equiv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.bijective_compr₂ₛₗ_of_equiv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.lsmul", "kind": "definition", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.lsmul_eq_distribSMultoLinearMap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.lsmul_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinMap", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.lsmul_injective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.ker_lsmul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.restrictScalarsRange", "kind": "definition", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.restrictScalarsRange_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "LinearMap.eq_restrictScalarsRange_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LinearMap.restrictScalarsRange_apply_eq_zero_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LinearMap.restrictScalarsRange₂", "kind": "definition", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.restrictScalarsRange₂_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LinearMap.eq_restrictScalarsRange₂_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LinearMap.restrictScalarsRange₂_apply_eq_zero_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.BilinearMap", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LinearMap.commute_transvections_iff_of_basis", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Center", "is_tactic_proof": true, "tactics": ["simp", "rcases", "refine", "ext", "simp", "simp", "replace", "have", "rw", "simpa", "have", "by_cases", "simp", "simpa", "replace", "obtain", "simpa", "let", "refine", "ext", "rw", "simp", "apply", "intro", "simp"], "tactic_count": 25}
{"name": "LinearMap.exists_mem_center_apply_eq_smul_of_forall_notLinearIndependent_of_basis", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Center", "is_tactic_proof": true, "tactics": ["have", "classical", "rw", "intro", "simp", "obtain", "simp", "split_ifs", "simp", "have", "rw", "simpa", "apply", "contrapose", "refine", "simp", "contrapose", "apply", "simpa", "have", "let", "specialize", "simp", "obtain", "simp", "smul_eq_mul,", "have", "simp", "rw", "have", "suffices", "rw", "rw", "simp", "simpa", "have", "suffices", "rw", "rw", "simp", "simpa", "rw", "rw", "symm", "apply", "contrapose", "simp", "replace", "by_cases", "rw", "have", "simp", "rw", "let", "have", "obtain", "rw", "simp", "refine", "simpa", "apply", "simpa"], "tactic_count": 62}
{"name": "LinearMap.exists_mem_center_apply_eq_smul_of_forall_notLinearIndependent", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Center", "is_tactic_proof": true, "tactics": ["rcases", "use", "ext", "apply", "let", "let", "rcases", "have", "have", "simp_all", "exact"], "tactic_count": 11}
{"name": "LinearMap.exists_eq_smul_id_of_forall_notLinearIndependent", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Center", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "let", "use", "apply", "intro", "nth_rewrite", "simp", "obtain", "refine"], "tactic_count": 10}
{"name": "LinearMap.charpoly_baseChange", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Charpoly.BaseChange", "is_tactic_proof": true, "tactics": ["nontriviality", "have", "let", "let", "rw", "congr", "ext", "simp"], "tactic_count": 8}
{"name": "LinearMap.det_eq_sign_charpoly_coeff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Charpoly.BaseChange", "is_tactic_proof": true, "tactics": ["nontriviality", "rw"], "tactic_count": 2}
{"name": "LinearMap.det_baseChange", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Charpoly.BaseChange", "is_tactic_proof": true, "tactics": ["nontriviality", "have", "rw", "simp"], "tactic_count": 4}
{"name": "LinearEquiv.det_baseChange", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Charpoly.BaseChange", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "LinearMap.charpoly", "kind": "definition", "module": "Mathlib.LinearAlgebra.Charpoly.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.charpoly_def", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Charpoly.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.eval_charpoly", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Charpoly.Basic", "is_tactic_proof": true, "tactics": ["rw", "toMatrix_algebraMap,"], "tactic_count": 2}
{"name": "LinearMap.charpoly_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Charpoly.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LinearMap.charpoly_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Charpoly.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LinearMap.charpoly_sub_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Charpoly.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "LinearMap.charpoly_monic", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Charpoly.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.charpoly_natDegree", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Charpoly.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LinearMap.aeval_self_charpoly", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Charpoly.Basic", "is_tactic_proof": true, "tactics": ["apply", "rw", "exact"], "tactic_count": 3}
{"name": "LinearMap.isIntegral", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Charpoly.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.minpoly_dvd_charpoly", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Charpoly.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "pinGroup.coe_star", "kind": "theorem", "module": "Mathlib.LinearAlgebra.CliffordAlgebra.SpinGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pinGroup.coe_star_mul_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.CliffordAlgebra.SpinGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "pinGroup.instGroupSubtypeCliffordAlgebraMemSubmonoid", "kind": "instance", "module": "Mathlib.LinearAlgebra.CliffordAlgebra.SpinGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "pinGroup.star_eq_inv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.CliffordAlgebra.SpinGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pinGroup.star_eq_inv'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.CliffordAlgebra.SpinGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pinGroup.toUnits", "kind": "definition", "module": "Mathlib.LinearAlgebra.CliffordAlgebra.SpinGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pinGroup.toUnits_injective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.CliffordAlgebra.SpinGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "spinGroup", "kind": "definition", "module": "Mathlib.LinearAlgebra.CliffordAlgebra.SpinGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "spinGroup.mem_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.CliffordAlgebra.SpinGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "spinGroup.mem_pin", "kind": "theorem", "module": "Mathlib.LinearAlgebra.CliffordAlgebra.SpinGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "spinGroup.mem_even", "kind": "theorem", "module": "Mathlib.LinearAlgebra.CliffordAlgebra.SpinGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "spinGroup.units_mem_lipschitzGroup", "kind": "theorem", "module": "Mathlib.LinearAlgebra.CliffordAlgebra.SpinGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "spinGroup.involute_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.CliffordAlgebra.SpinGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "spinGroup.units_involute_act_eq_conjAct", "kind": "theorem", "module": "Mathlib.LinearAlgebra.CliffordAlgebra.SpinGroup", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "spinGroup.coe_star", "kind": "theorem", "module": "Mathlib.LinearAlgebra.CliffordAlgebra.SpinGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "spinGroup.coe_star_mul_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.CliffordAlgebra.SpinGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "spinGroup.toUnits", "kind": "definition", "module": "Mathlib.LinearAlgebra.CliffordAlgebra.SpinGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Complex.equivRealProdLm_symm_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Complex.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "DFinsupp.range_mapRangeAddMonoidHom", "kind": "theorem", "module": "Mathlib.LinearAlgebra.DFinsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Submodule.dfinsuppSum_mem", "kind": "theorem", "module": "Mathlib.LinearAlgebra.DFinsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.dfinsuppSumAddHom_mem", "kind": "theorem", "module": "Mathlib.LinearAlgebra.DFinsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.iSup_eq_range_dfinsupp_lsum", "kind": "theorem", "module": "Mathlib.LinearAlgebra.DFinsupp", "is_tactic_proof": true, "tactics": ["apply", "apply", "intro", "simp", "exact", "rintro", "exact"], "tactic_count": 7}
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{"name": "iSupIndep_of_dfinsuppSumAddHom_injective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.DFinsupp", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
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{"name": "iSupIndep_of_dfinsuppSumAddHom_injective'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.DFinsupp", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
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{"name": "LinearMap.map_dfinsuppSumAddHom", "kind": "theorem", "module": "Mathlib.LinearAlgebra.DFinsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.map_dfinsuppSumAddHom", "kind": "theorem", "module": "Mathlib.LinearAlgebra.DFinsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "equivOfPiLEquivPi", "kind": "definition", "module": "Mathlib.LinearAlgebra.Determinant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.indexEquivOfInv", "kind": "definition", "module": "Mathlib.LinearAlgebra.Determinant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.det_comm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Determinant", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "LinearMap.det_eq_one_of_not_module_finite", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Determinant", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "LinearMap.det_eq_one_of_subsingleton", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Determinant", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
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{"name": "LinearMap.isUnit_iff_isUnit_det", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Determinant", "is_tactic_proof": true, "tactics": ["let", "rw"], "tactic_count": 2}
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{"name": "LinearMap.bot_lt_ker_of_det_eq_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Determinant", "is_tactic_proof": true, "tactics": ["have", "let", "suffices", "obtain", "refine", "rw", "simp_all"], "tactic_count": 7}
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{"name": "LinearMap.det_mulLeft", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Determinant", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LinearMap.det_mulRight", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Determinant", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "LinearEquiv.coe_det", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Determinant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LinearMap.det_map", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Determinant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.det_map", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Determinant", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
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{"name": "LinearEquiv.det_mul_det_symm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Determinant", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LinearEquiv.det_symm_mul_det", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Determinant", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "LinearEquiv.isUnit_det'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Determinant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.det_coe_symm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Determinant", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LinearEquiv.ofIsUnitDet", "kind": "definition", "module": "Mathlib.LinearAlgebra.Determinant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.coe_ofIsUnitDet", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Determinant", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "LinearMap.equivOfIsUnitDet", "kind": "definition", "module": "Mathlib.LinearAlgebra.Determinant", "is_tactic_proof": true, "tactics": ["by_cases", "let", "have", "have", "have", "exact", "exact"], "tactic_count": 7}
{"name": "LinearMap.equivOfIsUnitDet_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Determinant", "is_tactic_proof": true, "tactics": ["nontriviality", "simp"], "tactic_count": 2}
{"name": "LinearMap.coe_equivOfIsUnitDet", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Determinant", "is_tactic_proof": true, "tactics": ["ext", "apply"], "tactic_count": 2}
{"name": "LinearMap.equivOfDetNeZero", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.Determinant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.associated_det_of_eq_comp", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Determinant", "is_tactic_proof": false, "tactics": ["suffices", "convert", "ext", "exact", "rw", "exact"], "tactic_count": 6}
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{"name": "Module.Basis.det_map", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Determinant", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Module.Basis.det_map'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Determinant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.basisFun_det", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Determinant", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "Pi.basisFun_det_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Determinant", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
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{"name": "Module.Basis.det_isUnitSMul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Determinant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.det_dualMap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Determinant", "is_tactic_proof": true, "tactics": ["set", "have", "rw", "simp"], "tactic_count": 4}
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{"name": "definition._@.Mathlib.LinearAlgebra.Dimension.Basic.3070247278._hygCtx._hyg.2", "kind": "definition", "module": "Mathlib.LinearAlgebra.Dimension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "nonempty_linearIndependent_set", "kind": "instance", "module": "Mathlib.LinearAlgebra.Dimension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIndependent.cardinal_lift_le_rank", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "exact"], "tactic_count": 3}
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{"name": "LinearIndependent.cardinal_le_rank'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIndepOn.encard_le_toENat_rank", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
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{"name": "Module.rank_top_le_rank_of_isScalarTower", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact", "ciSup_le", "le_ciSup_of_le"], "tactic_count": 4}
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{"name": "subalgebra_top_rank_eq_submodule_top_rank", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.Constructions", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
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{"name": "DivisionRing.hasRankNullity", "kind": "instance", "module": "Mathlib.LinearAlgebra.Dimension.DivisionRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "finrank_eq_zero_of_basis_imp_false", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finrank_eq_zero_of_not_exists_basis", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finrank_eq_zero_of_not_exists_basis_finite", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finrank_eq_zero_of_not_exists_basis_finset", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "rank_eq_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.Finite", "is_tactic_proof": true, "tactics": ["haveI", "obtain", "rw"], "tactic_count": 3}
{"name": "finrank_eq_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "rank_le_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.Finite", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "finrank_le_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.Finite", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Module.finite_finsupp_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.finite_finsupp_self_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.Finite", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Module.finrank", "kind": "definition", "module": "Mathlib.LinearAlgebra.Dimension.Finrank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.finrank_subsingleton", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.Finrank", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Module.finrank_eq_of_rank_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.Finrank", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Module.rank_eq_one_iff_finrank_eq_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.Finrank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.rank_eq_ofNat_iff_finrank_eq_ofNat", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.Finrank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.finrank_le_of_rank_le", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.Finrank", "is_tactic_proof": true, "tactics": ["rwa", "exact", "exact"], "tactic_count": 3}
{"name": "Module.finrank_lt_of_rank_lt", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.Finrank", "is_tactic_proof": true, "tactics": ["rwa", "exact", "exact"], "tactic_count": 3}
{"name": "Module.lt_rank_of_lt_finrank", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.Finrank", "is_tactic_proof": true, "tactics": ["rwa", "exact", "contrapose", "rw", "exact"], "tactic_count": 5}
{"name": "Module.one_lt_rank_of_one_lt_finrank", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.Finrank", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Module.finrank_le_finrank_of_rank_le_rank", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.Finrank", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CommSemiring.finrank_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.Finrank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.finrank_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.Finrank", "is_tactic_proof": true, "tactics": ["unfold", "rw"], "tactic_count": 2}
{"name": "LinearEquiv.finrank_map_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.Finrank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.finrank_range_of_inj", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.Finrank", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submodule.finrank_map_subtype_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.Finrank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finrank_top", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.Finrank", "is_tactic_proof": true, "tactics": ["unfold", "simp"], "tactic_count": 2}
{"name": "Algebra.finrank_eq_of_equiv_equiv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.Finrank", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "lift_rank_mul_lift_rank", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.Free", "is_tactic_proof": true, "tactics": ["let", "let", "rw"], "tactic_count": 3}
{"name": "rank_mul_rank", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.Free", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "Module.finrank_mul_finrank", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.Free", "is_tactic_proof": true, "tactics": ["simp_rw", "rw", "toNat_lift]"], "tactic_count": 3}
{"name": "Module.Free.rank_eq_card_chooseBasisIndex", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.finrank_eq_card_chooseBasisIndex", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.Free", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Module.Free.rank_eq_mk_of_infinite_lt", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.Free", "is_tactic_proof": true, "tactics": ["have", "have", "simp", "refine", "exact"], "tactic_count": 5}
{"name": "nonempty_linearEquiv_of_lift_rank_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.Free", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "have", "exact"], "tactic_count": 4}
{"name": "nonempty_linearEquiv_of_rank_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.ofLiftRankEq", "kind": "definition", "module": "Mathlib.LinearAlgebra.Dimension.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.ofRankEq", "kind": "definition", "module": "Mathlib.LinearAlgebra.Dimension.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.nonempty_equiv_iff_lift_rank_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.nonempty_equiv_iff_rank_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteDimensional.nonempty_linearEquiv_of_finrank_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteDimensional.nonempty_linearEquiv_iff_finrank_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.ofFinrankEq", "kind": "definition", "module": "Mathlib.LinearAlgebra.Dimension.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.subsingleton_of_rank_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.Free", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Module.rank_lt_aleph0_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.Free", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Module.finrank_of_not_finite", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.Free", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Module.finite_of_finrank_pos", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.Free", "is_tactic_proof": true, "tactics": ["contrapose", "simp"], "tactic_count": 2}
{"name": "Module.finite_of_finrank_eq_succ", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.finite_iff_of_rank_eq_nsmul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.Free", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Module.finrank_top_le_finrank_of_isScalarTower_of_free", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.Free", "is_tactic_proof": true, "tactics": ["by_cases", "have", "exact", "rw", "exact", "rwa"], "tactic_count": 6}
{"name": "Module.finrank_bot_le_finrank_of_isScalarTower_of_free", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.Free", "is_tactic_proof": true, "tactics": ["by_cases", "have", "exact", "rw", "exact", "rwa"], "tactic_count": 6}
{"name": "Module.finBasis", "kind": "definition", "module": "Mathlib.LinearAlgebra.Dimension.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.finBasisOfFinrankEq", "kind": "definition", "module": "Mathlib.LinearAlgebra.Dimension.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.basisUnique", "kind": "definition", "module": "Mathlib.LinearAlgebra.Dimension.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.nonempty_unique_index_of_finrank_eq_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.Free", "is_tactic_proof": true, "tactics": ["have", "haveI", "have", "have", "rwa"], "tactic_count": 5}
{"name": "Module.nonempty_linearEquiv_of_finrank_eq_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.Free", "is_tactic_proof": true, "tactics": ["let", "have", "exact"], "tactic_count": 3}
{"name": "Module.basisUnique_repr_eq_zero_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.existsUnique_eq_smul_id_of_finrank_eq_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.Free", "is_tactic_proof": true, "tactics": ["let", "set", "suffices", "use", "simp", "intro", "rw", "simpa", "ext", "have", "rw", "simp", "rw"], "tactic_count": 13}
{"name": "LinearEquiv.smul_id_of_finrank_eq_one", "kind": "definition", "module": "Mathlib.LinearAlgebra.Dimension.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.instFiniteOfIsQuadraticExtension", "kind": "instance", "module": "Mathlib.LinearAlgebra.Dimension.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Basis.ofRankEqZero", "kind": "definition", "module": "Mathlib.LinearAlgebra.Dimension.FreeAndStrongRankCondition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Basis.ofRankEqZero_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.FreeAndStrongRankCondition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_rank_iff_exists_linearIndependent", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.FreeAndStrongRankCondition", "is_tactic_proof": true, "tactics": ["haveI", "constructor", "intro", "obtain", "let", "have", "convert", "ext", "simp", "rw", "rcases", "exact", "rintro", "exact"], "tactic_count": 14}
{"name": "le_rank_iff_exists_linearIndependent_finset", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.FreeAndStrongRankCondition", "is_tactic_proof": true, "tactics": ["simp", "constructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 6}
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{"name": "rank_submodule_le_one_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.FreeAndStrongRankCondition", "is_tactic_proof": true, "tactics": ["simp_rw", "simp"], "tactic_count": 2}
{"name": "rank_submodule_eq_one_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.FreeAndStrongRankCondition", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "obtain", "exact", "obtain", "exact"], "tactic_count": 6}
{"name": "rank_submodule_le_one_iff'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.FreeAndStrongRankCondition", "is_tactic_proof": true, "tactics": ["haveI", "constructor", "rw", "rintro", "exact", "rintro", "obtain", "simpa", "b.linearIndependent.map"], "tactic_count": 9}
{"name": "Submodule.rank_le_one_iff_isPrincipal", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.FreeAndStrongRankCondition", "is_tactic_proof": false, "tactics": ["simp", "span_singleton_le_iff_mem]", "constructor", "rintro", "choose", "exact", "rintro", "choose", "exact"], "tactic_count": 9}
{"name": "Module.rank_le_one_iff_top_isPrincipal", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.FreeAndStrongRankCondition", "is_tactic_proof": true, "tactics": ["haveI", "rw"], "tactic_count": 2}
{"name": "finrank_eq_one_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.FreeAndStrongRankCondition", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "rintro", "simpa"], "tactic_count": 5}
{"name": "finrank_eq_one_iff'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.FreeAndStrongRankCondition", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "finrank_le_one_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.FreeAndStrongRankCondition", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submodule.finrank_le_one_iff_isPrincipal", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.FreeAndStrongRankCondition", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Module.finrank_le_one_iff_top_isPrincipal", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.FreeAndStrongRankCondition", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "lift_cardinalMk_eq_lift_cardinalMk_field_pow_lift_rank", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.FreeAndStrongRankCondition", "is_tactic_proof": true, "tactics": ["haveI", "obtain", "haveI", "obtain", "exact", "have", "rwa", "lift_umax]"], "tactic_count": 8}
{"name": "cardinalMk_eq_cardinalMk_field_pow_rank", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.FreeAndStrongRankCondition", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "cardinal_lt_aleph0_of_finiteDimensional", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.FreeAndStrongRankCondition", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Subalgebra.eq_bot_of_rank_le_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.FreeAndStrongRankCondition", "is_tactic_proof": true, "tactics": ["nontriviality", "obtain", "by_cases", "refine", "rw", "obtain", "obtain", "exact", "haveI", "haveI", "exact"], "tactic_count": 11}
{"name": "Subalgebra.eq_bot_of_finrank_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.FreeAndStrongRankCondition", "is_tactic_proof": true, "tactics": ["refine", "rw", "rw"], "tactic_count": 3}
{"name": "Subalgebra.rank_eq_one_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.FreeAndStrongRankCondition", "is_tactic_proof": true, "tactics": ["refine", "rintro", "obtain", "refine", "have", "rwa", "by_contra", "rw", "haveI", "haveI", "exact"], "tactic_count": 11}
{"name": "Subalgebra.finrank_eq_one_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.FreeAndStrongRankCondition", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Subalgebra.bot_eq_top_iff_rank_eq_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.FreeAndStrongRankCondition", "is_tactic_proof": true, "tactics": ["haveI", "rw"], "tactic_count": 2}
{"name": "Subalgebra.bot_eq_top_iff_finrank_eq_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.FreeAndStrongRankCondition", "is_tactic_proof": true, "tactics": ["haveI", "rw"], "tactic_count": 2}
{"name": "LinearMap.rank", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.Dimension.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.rank_le_range", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.rank_le_domain", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.rank_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.LinearMap", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LinearMap.rank_comp_le_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.LinearMap", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "LinearMap.lift_rank_comp_le_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.LinearMap", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LinearMap.lift_rank_comp_le", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.rank_comp_le_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.LinearMap", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "LinearMap.rank_comp_le", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.LinearMap", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "LinearMap.rank_add_le", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.rank_finset_sum_le", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.le_rank_iff_exists_linearIndependent", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.LinearMap", "is_tactic_proof": true, "tactics": ["rcases", "have", "refine", "rcases", "refine", "replace", "intro", "convert", "replace", "exact", "rintro", "have", "convert", "rw", "exact"], "tactic_count": 15}
{"name": "LinearMap.le_rank_iff_exists_linearIndependent_finset", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.LinearMap", "is_tactic_proof": false, "tactics": ["simp", "constructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 6}
{"name": "IsLocalizedModule.lift_rank_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.Localization", "is_tactic_proof": true, "tactics": ["cases", "simp", "apply", "exacts", "hs.of_isLocalizedModule_of_isRegular"], "tactic_count": 5}
{"name": "IsLocalizedModule.finrank_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.Localization", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsLocalizedModule.rank_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.Localization", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsLocalization.rank_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.Localization", "is_tactic_proof": true, "tactics": ["cases", "have", "have", "apply", "have", "exact", "have", "exact"], "tactic_count": 8}
{"name": "exists_set_linearIndependent_of_isDomain", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.Localization", "is_tactic_proof": false, "tactics": ["obtain", "refine", "apply", "rw"], "tactic_count": 4}
{"name": "rank_quotient_add_rank_of_isDomain", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.Localization", "is_tactic_proof": true, "tactics": ["apply", "simp_rw"], "tactic_count": 2}
{"name": "IsDomain.hasRankNullity", "kind": "instance", "module": "Mathlib.LinearAlgebra.Dimension.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBaseChange.lift_rank_eq_of_le_nonZeroDivisors", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.Localization", "is_tactic_proof": true, "tactics": ["rw", "let", "conv_rhs", "rw", "lift_lift,", "lift_id'.", "let", "set", "rw", "lift_lift,", "exact"], "tactic_count": 11}
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{"name": "nontrivial_of_hasRankNullity", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.RankNullity", "is_tactic_proof": true, "tactics": ["refine", "have", "simp"], "tactic_count": 3}
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{"name": "Module.finrank_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.StrongRankCondition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LinearMap.finrank_le_of_isSMulRegular", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.StrongRankCondition", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
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{"name": "Submodule.exists_finset_span_eq_linearIndepOn", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dimension.StrongRankCondition", "is_tactic_proof": true, "tactics": ["rcases", "obtain", "rw", "exact"], "tactic_count": 4}
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{"name": "Subspace.dualAnnihilatorGci", "kind": "definition", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subspace.dualAnnihilator_le_dualAnnihilator_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subspace.dualAnnihilator_inj", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subspace.dualLift", "kind": "definition", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subspace.dualLift_of_subtype", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subspace.dualLift_of_mem", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subspace.dualRestrict_comp_dualLift", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Subspace.dualRestrict_leftInverse", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subspace.dualLift_rightInverse", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subspace.dualRestrict_surjective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subspace.dualLift_injective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subspace.quotAnnihilatorEquiv", "kind": "definition", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subspace.quotAnnihilatorEquiv_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "Subspace.dualEquivDual", "kind": "definition", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subspace.dualEquivDual_def", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subspace.dualEquivDual_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subspace.instModuleDualFiniteDimensional", "kind": "instance", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Subspace.dual_finrank_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": true, "tactics": ["by_cases", "classical", "rw", "exact", "exact"], "tactic_count": 5}
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{"name": "Subspace.quotDualEquivAnnihilator", "kind": "definition", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subspace.quotEquivAnnihilator", "kind": "definition", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subspace.finrank_add_finrank_dualAnnihilator_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subspace.finrank_dualCoannihilator_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Subspace.finrank_add_finrank_dualCoannihilator_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submodule.dualCopairing", "kind": "definition", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.instFunLikeSubtypeDualMemDualAnnihilator", "kind": "instance", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.dualCopairing_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.dualPairing", "kind": "definition", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.dualPairing_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.range_dualMap_mkQ_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": true, "tactics": ["ext", "rw", "constructor", "rintro", "have", "simpa", "intro", "exists"], "tactic_count": 8}
{"name": "Submodule.dualQuotEquivDualAnnihilator", "kind": "definition", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.dualQuotEquivDualAnnihilator_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.dualCopairing_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.dualQuotEquivDualAnnihilator_symm_apply_mk", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.finite_dualAnnihilator_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.dualAnnihilator_eq_bot_iff'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submodule.dualAnnihilator_eq_bot_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submodule.dualAnnihilator_eq_top_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": true, "tactics": ["refine", "refine", "refine", "simp"], "tactic_count": 4}
{"name": "Submodule.quotDualCoannihilatorToDual", "kind": "definition", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.quotDualCoannihilatorToDual_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.quotDualCoannihilatorToDual_injective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.flip_quotDualCoannihilatorToDual_injective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.quotDualCoannihilatorToDual_nondegenerate", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "exact"], "tactic_count": 3}
{"name": "LinearMap.range_dualMap_eq_dualAnnihilator_ker_of_surjective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.range_dualMap_eq_dualAnnihilator_ker_of_subtype_range_surjective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": true, "tactics": ["have", "have", "convert", "calc", "rw", "rwa", "apply", "exact"], "tactic_count": 8}
{"name": "Module.Dual.range_eq_top_of_ne_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Dual.finrank_ker_add_one_of_ne_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": false, "tactics": ["suffices", "rw", "rw"], "tactic_count": 3}
{"name": "Module.Dual.isCompl_ker_of_disjoint_of_ne_bot", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": true, "tactics": ["refine", "have", "simp", "rwa"], "tactic_count": 4}
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{"name": "LinearMap.dualPairing_nondegenerate", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.dualMap_surjective_of_injective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.range_dualMap_eq_dualAnnihilator_ker", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.dualMap_surjective_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subspace.dualPairing_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "Subspace.dualPairing_nondegenerate", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": true, "tactics": ["constructor", "rw", "apply", "intro", "rw", "intro", "simpa"], "tactic_count": 7}
{"name": "Subspace.dualCopairing_nondegenerate", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": true, "tactics": ["constructor", "rw", "apply", "rintro", "simp", "rw", "exact"], "tactic_count": 7}
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{"name": "Subspace.dualAnnihilator_iInf_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": true, "tactics": ["revert", "apply", "intro", "rw", "intro", "rw", "intro", "rw"], "tactic_count": 8}
{"name": "Subspace.isCompl_dualAnnihilator", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "Subspace.dualQuotDistrib", "kind": "definition", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.finrank_range_dualMap_eq_finrank_range", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": false, "tactics": ["rw", "range_eq_top.mpr", "finrank_range_of_inj,", "exact"], "tactic_count": 4}
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{"name": "LinearMap.dualMap_bijective_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "LinearMap.dualAnnihilator_ker_eq_range_flip", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": true, "tactics": ["change", "rw"], "tactic_count": 2}
{"name": "LinearMap.flip_injective_iff₁", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LinearMap.flip_injective_iff₂", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LinearMap.flip_surjective_iff₁", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.flip_surjective_iff₂", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.flip_bijective_iff₁", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "LinearMap.flip_bijective_iff₂", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subspace.quotDualCoannihilatorToDual_bijective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subspace.flip_quotDualCoannihilatorToDual_bijective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subspace.dualCoannihilator_dualAnnihilator_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subspace.finiteDimensional_quot_dualCoannihilator_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subspace.orderIsoFiniteCodimDim", "kind": "definition", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subspace.orderIsoFiniteDimensional", "kind": "definition", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subspace.dualAnnihilator_dualAnnihilator_eq_map", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": true, "tactics": ["let", "haveI", "let", "haveI", "rw", "rw", "exact"], "tactic_count": 7}
{"name": "Subspace.map_dualCoannihilator", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "span_flip_eq_top_iff_linearIndependent", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": false, "tactics": ["rw", "congr", "rw", "ext", "simp"], "tactic_count": 5}
{"name": "Module.exists_dual_forall_apply_eq_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": true, "tactics": ["replace", "let", "refine", "replace", "let", "have", "simp"], "tactic_count": 7}
{"name": "TensorProduct.dualDistrib", "kind": "definition", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.dualDistrib_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.dualDistrib_apply_comm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "TensorProduct.AlgebraTensorModule.dualDistrib", "kind": "definition", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.AlgebraTensorModule.dualDistrib_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.dualDistribInvOfBasis", "kind": "definition", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.dualDistribInvOfBasis_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "TensorProduct.dualDistrib_dualDistribInvOfBasis_left_inverse", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": true, "tactics": ["apply", "rintro", "apply", "rintro", "simp", "homTensorHomMap_apply,", "rw", "simpa", "all_goals"], "tactic_count": 9}
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{"name": "TensorProduct.dualDistribEquiv", "kind": "definition", "module": "Mathlib.LinearAlgebra.Dual.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.genEigenspace", "kind": "definition", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.mem_genEigenspace", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": true, "tactics": ["have", "have", "simp_rw"], "tactic_count": 3}
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{"name": "Module.End.mem_genEigenspace_nat", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": true, "tactics": ["rw", "constructor", "rintro", "simp", "exact", "intro", "exact"], "tactic_count": 7}
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{"name": "Module.End.genEigenspace_nat", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Module.End.genEigenspace_eq_iSup_genEigenspace_nat", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Module.End.genEigenspace_top", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
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{"name": "Module.End.genEigenspace_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
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{"name": "Module.End.HasUnifEigenvalue", "kind": "definition", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.UnifEigenvalues", "kind": "definition", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.UnifEigenvalues.val", "kind": "definition", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Module.End.HasUnifEigenvector.hasUnifEigenvalue", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": true, "tactics": ["rw", "use"], "tactic_count": 2}
{"name": "Module.End.HasUnifEigenvector.apply_eq_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.HasUnifEigenvector.pow_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "Module.End.HasUnifEigenvalue.exists_hasUnifEigenvector", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.HasUnifEigenvalue.pow", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": true, "tactics": ["rw", "obtain", "exact"], "tactic_count": 3}
{"name": "Module.End.HasUnifEigenvalue.isNilpotent_of_isNilpotent", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "exact"], "tactic_count": 3}
{"name": "Module.End.HasUnifEigenvalue.mem_spectrum", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": true, "tactics": ["refine", "set", "rcases", "refine", "rw"], "tactic_count": 5}
{"name": "Module.End.hasUnifEigenvalue_iff_mem_spectrum", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": false, "tactics": ["rw", "not_iff_not]", "simp"], "tactic_count": 3}
{"name": "Module.End.genEigenspace_div", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.genEigenrange", "kind": "definition", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.genEigenrange_nat", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp", "constructor", "intro", "exact", "rintro", "have", "rw", "exact"], "tactic_count": 9}
{"name": "Module.End.HasUnifEigenvalue.exp_ne_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": true, "tactics": ["rintro", "simp"], "tactic_count": 2}
{"name": "Module.End.maxUnifEigenspaceIndex", "kind": "definition", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.genEigenspace_top_eq_maxUnifEigenspaceIndex", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": false, "tactics": ["have", "convert", "simp", "rw", "congr", "aesop"], "tactic_count": 6}
{"name": "Module.End.genEigenspace_le_genEigenspace_maxUnifEigenspaceIndex", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Module.End.genEigenspace_eq_genEigenspace_maxUnifEigenspaceIndex_of_le", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.HasUnifEigenvalue.le", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": true, "tactics": ["unfold", "contrapose", "rw", "exact"], "tactic_count": 4}
{"name": "Module.End.HasUnifEigenvalue.lt", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": true, "tactics": ["apply", "intro", "rw", "rw", "intro", "rw", "rcases", "rwa", "rw", "exact"], "tactic_count": 10}
{"name": "Module.End.hasUnifEigenvalue_iff_hasUnifEigenvalue_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.maxUnifEigenspaceIndex_le_finrank", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": true, "tactics": ["apply", "intro", "apply", "exact", "change", "rw", "apply"], "tactic_count": 7}
{"name": "Module.End.genEigenspace_le_genEigenspace_finrank", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": true, "tactics": ["calc", "f.genEigenspace", "rw", "exact"], "tactic_count": 4}
{"name": "Module.End.genEigenspace_eq_genEigenspace_finrank_of_le", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.mapsTo_genEigenspace_of_comm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": true, "tactics": ["intro", "simp", "rcases", "replace", "use", "rw", "map_zero]"], "tactic_count": 7}
{"name": "Module.End.eigenspace", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.eigenspace_def", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Module.End.eigenspace_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Module.End.HasEigenvector", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.hasEigenvector_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.HasEigenvalue", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.hasEigenvalue_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.Eigenvalues", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.Eigenvalues.val", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.hasEigenvalue_of_hasEigenvector", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.mem_eigenspace_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.HasEigenvector.apply_eq_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.HasEigenvector.pow_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.HasEigenvalue.exists_hasEigenvector", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.HasEigenvalue.pow", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.HasEigenvalue.isNilpotent_of_isNilpotent", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.HasEigenvalue.mem_spectrum", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.hasEigenvalue_iff_mem_spectrum", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.eigenspace_div", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.HasGenEigenvector", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.hasGenEigenvector_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.HasGenEigenvalue", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.hasGenEigenvalue_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.exp_ne_zero_of_hasGenEigenvalue", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.maxGenEigenspace", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.iSup_genEigenspace_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Module.End.genEigenspace_le_maximal", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.mem_maxGenEigenspace", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.maxGenEigenspaceIndex", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.maxGenEigenspace_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.maxGenEigenspace_eq_maxGenEigenspace_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Module.End.hasGenEigenvalue_of_hasGenEigenvalue_of_le", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.eigenspace_le_genEigenspace", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.eigenspace_le_maxGenEigenspace", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.hasGenEigenvalue_of_hasEigenvalue", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.hasEigenvalue_of_hasGenEigenvalue", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.hasGenEigenvalue_iff_hasEigenvalue", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Module.End.maxGenEigenspace_eq_genEigenspace_finrank", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": true, "tactics": ["apply", "rw", "apply"], "tactic_count": 3}
{"name": "Module.End.mapsTo_maxGenEigenspace_of_comm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.disjoint_genEigenspace", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "rintro", "nontriviality", "rw", "set", "by_contra", "replace", "let", "let", "have", "apply", "ext", "apply", "apply", "apply", "apply", "have", "rw", "sub_eq_zero]", "contradiction"], "tactic_count": 21}
{"name": "Module.End.injOn_genEigenspace", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": true, "tactics": ["rintro", "by_contra", "apply", "simpa"], "tactic_count": 4}
{"name": "Module.End.injOn_maxGenEigenspace", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.independent_genEigenspace", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": true, "tactics": ["classical", "suffices", "simp_rw", "exact", "intro", "induction", "empty", "insert", "intro", "obtain", "specialize", "rw", "rintro", "simp", "suffices", "rw", "exact", "obtain", "let", "simp_rw", "peel", "simp", "have", "refine", "exact", "rw", "suffices", "exact", "simp_rw", "refine", "rintro", "refine", "exact", "rwa"], "tactic_count": 34}
{"name": "Module.End.independent_maxGenEigenspace", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "Module.End.eigenspaces_iSupIndep", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.eigenvectors_linearIndependent'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.eigenvectors_linearIndependent", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.genEigenspace_restrict", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": true, "tactics": ["ext", "suffices", "simp_rw", "mem_genEigenspace_nat]", "intro", "simp", "induction", "zero", "rw", "apply", "succ", "erw"], "tactic_count": 12}
{"name": "Submodule.inf_genEigenspace", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Module.End.mapsTo_restrict_maxGenEigenspace_restrict_of_mapsTo", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": true, "tactics": ["intro", "simp_rw", "exact"], "tactic_count": 3}
{"name": "Module.End.eigenspace_restrict_le_eigenspace", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": true, "tactics": ["rintro", "simp", "exact"], "tactic_count": 3}
{"name": "Module.End.generalized_eigenvec_disjoint_range_ker", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": false, "tactics": ["have", "calc", "rw", "genEigenspace_nat]", "apply"], "tactic_count": 5}
{"name": "Module.End.eigenspace_restrict_eq_bot", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": true, "tactics": ["rw", "intro", "simpa"], "tactic_count": 3}
{"name": "Module.End.pos_finrank_genEigenspace_of_hasEigenvalue", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.map_genEigenrange_le", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.genEigenspace_le_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": true, "tactics": ["intro", "simp_rw", "peel", "rw"], "tactic_count": 4}
{"name": "Module.End.genEigenspace_inf_le_add", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": true, "tactics": ["intro", "simp", "obtain", "use", "have", "exact", "replace", "rw", "constructor", "simpa", "refine", "suffices", "rw", "obtain", "rw", "rw"], "tactic_count": 16}
{"name": "Module.End.map_smul_of_iInf_genEigenspace_ne_bot", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": true, "tactics": ["by_contra", "let", "have", "refine", "apply", "simp", "exact"], "tactic_count": 7}
{"name": "Module.End.map_add_of_iInf_genEigenspace_ne_bot_of_commute", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Basic", "is_tactic_proof": true, "tactics": ["by_contra", "let", "have", "le_inf_iff.mpr", "refine", "apply", "simp", "exact"], "tactic_count": 8}
{"name": "Module.End.hasEigenvalue_iff_isRoot_charpoly", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Charpoly", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Module.End.mem_spectrum_iff_isRoot_charpoly", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Charpoly", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "hasEigenvector_toLin_diagonal", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasEigenvector_toLin'_diagonal", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasEigenvalue_toLin_diagonal_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Matrix", "is_tactic_proof": false, "tactics": ["have", "hasEigenvalue_of_hasEigenvector", "constructor", "contrapose", "intro", "have", "rw", "rintro", "simp", "apply", "apply", "rw", "exact", "have", "have", "rw", "exact", "rintro", "exact"], "tactic_count": 19}
{"name": "hasEigenvalue_toLin'_diagonal_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.iSup_eigenspace_toLin_diagonal_eq_top", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Matrix", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "Matrix.iSup_eigenspace_toLin'_diagonal_eq_top", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.maxGenEigenspace_toLin_diagonal_eq_eigenspace", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Matrix", "is_tactic_proof": true, "tactics": ["refine", "obtain", "replace", "have", "simp", "rw", "simpa", "have", "rcases", "simp", "rw", "simp"], "tactic_count": 12}
{"name": "Matrix.maxGenEigenspace_toLin'_diagonal_eq_eigenspace", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.spectrum_toMatrix", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.spectrum_toMatrix'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.spectrum_toLin", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.spectrum_toLin'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "spectrum_diagonal", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Matrix", "is_tactic_proof": true, "tactics": ["ext", "rw", "exact"], "tactic_count": 3}
{"name": "Module.End.ker_aeval_ring_hom'_unit_polynomial", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Minpoly", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.aeval_apply_of_hasEigenvector", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Minpoly", "is_tactic_proof": true, "tactics": ["refine", "intro", "intro", "intro", "rw", "simp"], "tactic_count": 6}
{"name": "Module.End.isRoot_of_hasEigenvalue", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Minpoly", "is_tactic_proof": true, "tactics": ["rcases", "refine", "rw", "simp"], "tactic_count": 4}
{"name": "Module.End.hasEigenvalue_of_isRoot", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Minpoly", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.hasEigenvalue_iff_isRoot", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Minpoly", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.finite_hasEigenvalue", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Eigenspace.Minpoly", "is_tactic_proof": true, "tactics": ["have", "convert", "ext", "change", "rw"], "tactic_count": 5}
{"name": "Module.End.instFintypeEigenvalues", "kind": "instance", "module": "Mathlib.LinearAlgebra.Eigenspace.Minpoly", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ExteriorAlgebra", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.ExteriorAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ExteriorAlgebra.ι", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.ExteriorAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ExteriorAlgebra.algebraMap_leftInverse", "kind": "theorem", "module": "Mathlib.LinearAlgebra.ExteriorAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Submodule.span_eq_iUnion_nat", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Finsupp.LinearCombination", "is_tactic_proof": true, "tactics": ["ext", "simp", "refine", "rintro", "exact", "rintro", "exact"], "tactic_count": 7}
{"name": "Finsupp.addSingleEquiv", "kind": "definition", "module": "Mathlib.LinearAlgebra.Finsupp.LinearCombination", "is_tactic_proof": false, "tactics": ["refine", "ext", "obtain", "simp", "simp", "simp", "simp"], "tactic_count": 7}
{"name": "Finsupp.linearCombination_comp_addSingleEquiv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Finsupp.LinearCombination", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finsupp.LinearEquiv.finsuppUnique", "kind": "definition", "module": "Mathlib.LinearAlgebra.Finsupp.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.LinearEquiv.finsuppUnique_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Finsupp.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.LinearEquiv.finsuppUnique_symm_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Finsupp.Pi", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finsupp.lcoeFun", "kind": "definition", "module": "Mathlib.LinearAlgebra.Finsupp.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.lcoeFun_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Finsupp.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.lcoeFun_comp_lsingle", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Finsupp.Pi", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "LinearMap.prodOfFinsuppNat", "kind": "definition", "module": "Mathlib.LinearAlgebra.Finsupp.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.fst_prodOfFinsuppNat", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Finsupp.Pi", "is_tactic_proof": true, "tactics": ["simp_rw", "rw", "simp", "obtain", "simp"], "tactic_count": 5}
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{"name": "LinearMap.splittingOfFunOnFintypeSurjective", "kind": "definition", "module": "Mathlib.LinearAlgebra.Finsupp.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.splittingOfFunOnFintypeSurjective_splits", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Finsupp.Pi", "is_tactic_proof": true, "tactics": ["classical", "ext", "dsimp", "rw", "rw"], "tactic_count": 5}
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{"name": "LinearMap.splittingOfFunOnFintypeSurjective_injective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Finsupp.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.submodule", "kind": "definition", "module": "Mathlib.LinearAlgebra.Finsupp.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.mem_submodule_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Finsupp.Pi", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "Finsupp.ker_mapRange", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Finsupp.Pi", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Finsupp.range_mapRange_linearMap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Finsupp.Pi", "is_tactic_proof": true, "tactics": ["ext", "constructor", "rintro", "simp", "intro", "choose", "refine", "constructor"], "tactic_count": 8}
{"name": "FunOnFinite.map", "kind": "definition", "module": "Mathlib.LinearAlgebra.Finsupp.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FunOnFinite.map_apply_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Finsupp.Pi", "is_tactic_proof": true, "tactics": ["obtain", "dsimp", "simp", "nth_rw", "rw", "simp", "congr", "aesop"], "tactic_count": 8}
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{"name": "FunOnFinite.map_id", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Finsupp.Pi", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
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{"name": "FunOnFinite.linearMap_apply_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Finsupp.Pi", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "FunOnFinite.linearMap_piSingle", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Finsupp.Pi", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
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{"name": "Finsupp.ker_lsingle", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Finsupp.Span", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.lsingle_range_le_ker_lapply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Finsupp.Span", "is_tactic_proof": true, "tactics": ["refine", "simp", "intro", "have", "exact"], "tactic_count": 5}
{"name": "Finsupp.iInf_ker_lapply_le_bot", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Finsupp.Span", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Finsupp.iSup_lsingle_range", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Finsupp.Span", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "Finsupp.disjoint_lsingle_lsingle", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Finsupp.Span", "is_tactic_proof": false, "tactics": ["refine", "rw", "refine", "classical", "by_cases", "by_cases", "exact", "exact", "exact"], "tactic_count": 9}
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{"name": "Finsupp.range_lmapDomain", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Finsupp.Span", "is_tactic_proof": true, "tactics": ["refine", "rintro", "induction", "single", "rw", "exact", "zero", "add", "rw", "exact", "rw", "intro", "exact"], "tactic_count": 13}
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{"name": "Submodule.mem_sSup_iff_exists_finset", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Finsupp.Span", "is_tactic_proof": true, "tactics": ["rw", "refine", "simpa", "suffices", "rwa", "have", "simpa"], "tactic_count": 7}
{"name": "Finsupp.sumFinsuppLEquivProdFinsupp", "kind": "definition", "module": "Mathlib.LinearAlgebra.Finsupp.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.fst_sumFinsuppLEquivProdFinsupp", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Finsupp.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Finsupp.supported", "kind": "definition", "module": "Mathlib.LinearAlgebra.Finsupp.Supported", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.mem_supported", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Finsupp.Supported", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Finsupp.span_le_supported_biUnion_support", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Finsupp.Supported", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.restrictDom", "kind": "definition", "module": "Mathlib.LinearAlgebra.Finsupp.Supported", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.restrictDom_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Finsupp.Supported", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.restrictDom_comp_subtype", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Finsupp.Supported", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "simp", "simpa"], "tactic_count": 4}
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{"name": "Finsupp.supported_mono", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Finsupp.Supported", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.supported_empty", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Finsupp.Supported", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.supported_univ", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Finsupp.Supported", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.supported_iUnion", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Finsupp.Supported", "is_tactic_proof": true, "tactics": ["refine", "haveI", "suffices", "rwa", "rw", "rintro", "induction", "zero", "single_add", "refine", "by_cases", "simp", "filter_single_of_pos]", "obtain", "exact", "simp"], "tactic_count": 16}
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{"name": "Finsupp.disjoint_supported_supported", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Finsupp.Supported", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.disjoint_supported_supported_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Finsupp.Supported", "is_tactic_proof": true, "tactics": ["refine", "rcases", "have", "rw", "exact"], "tactic_count": 5}
{"name": "Finsupp.codisjoint_supported_supported", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Finsupp.Supported", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "Finsupp.supportedEquivFinsupp_symm_apply_coe", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Finsupp.Supported", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "Finsupp.supportedEquivFinsupp_symm_single", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Finsupp.Supported", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
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{"name": "Module.Free.dfinsupp", "kind": "instance", "module": "Mathlib.LinearAlgebra.Finsupp.VectorSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DFinsupp.linearIndependent_single", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Finsupp.VectorSpace", "is_tactic_proof": true, "tactics": ["classical", "have", "linearCombination", "rw", "exact"], "tactic_count": 5}
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{"name": "Finsupp.basisSingleOne", "kind": "definition", "module": "Mathlib.LinearAlgebra.Finsupp.VectorSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.coe_basisSingleOne", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Finsupp.VectorSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AddMonoidAlgebra.instFree", "kind": "instance", "module": "Mathlib.LinearAlgebra.Finsupp.VectorSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "FreeAlgebra.basisFreeMonoid", "kind": "definition", "module": "Mathlib.LinearAlgebra.FreeAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Module.free_iff_set", "kind": "theorem", "module": "Mathlib.LinearAlgebra.FreeModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.free_def", "kind": "theorem", "module": "Mathlib.LinearAlgebra.FreeModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Free.of_basis", "kind": "theorem", "module": "Mathlib.LinearAlgebra.FreeModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Free.ChooseBasisIndex", "kind": "definition", "module": "Mathlib.LinearAlgebra.FreeModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Free.instDecidableEqChooseBasisIndex", "kind": "instance", "module": "Mathlib.LinearAlgebra.FreeModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Module.Free.constr", "kind": "definition", "module": "Mathlib.LinearAlgebra.FreeModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Free.instIsTorsionFree", "kind": "instance", "module": "Mathlib.LinearAlgebra.FreeModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Free.instNonemptyChooseBasisIndexOfNontrivial", "kind": "instance", "module": "Mathlib.LinearAlgebra.FreeModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Free.infinite", "kind": "theorem", "module": "Mathlib.LinearAlgebra.FreeModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Free.instFaithfulSMulOfNontrivial", "kind": "instance", "module": "Mathlib.LinearAlgebra.FreeModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Free.of_equiv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.FreeModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Free.of_equiv'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.FreeModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Free.Module.free_shrink", "kind": "instance", "module": "Mathlib.LinearAlgebra.FreeModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Free.of_ringEquiv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.FreeModule.Basic", "is_tactic_proof": true, "tactics": ["let", "obtain", "let", "have", "let", "exact"], "tactic_count": 6}
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{"name": "Module.Free.self", "kind": "instance", "module": "Mathlib.LinearAlgebra.FreeModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Free.ulift", "kind": "instance", "module": "Mathlib.LinearAlgebra.FreeModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Free.of_subsingleton", "kind": "instance", "module": "Mathlib.LinearAlgebra.FreeModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Free.of_subsingleton'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.FreeModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.repr_algebraMap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.FreeModule.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Module.End.mem_center_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.FreeModule.Basic", "is_tactic_proof": true, "tactics": ["simp", "refine", "by_cases", "exact", "let", "let", "have", "exact"], "tactic_count": 8}
{"name": "Module.End.mem_submonoidCenter_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.FreeModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.mem_subsemigroupCenter_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.FreeModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.det_zero''", "kind": "theorem", "module": "Mathlib.LinearAlgebra.FreeModule.Determinant", "is_tactic_proof": true, "tactics": ["letI", "nontriviality", "exact"], "tactic_count": 3}
{"name": "Module.Free.ChooseBasisIndex.fintype", "kind": "instance", "module": "Mathlib.LinearAlgebra.FreeModule.Finite.Basic", "is_tactic_proof": true, "tactics": ["refine", "cases", "have", "rw", "infer_instance", "exact"], "tactic_count": 6}
{"name": "Module.Finite.of_basis", "kind": "theorem", "module": "Mathlib.LinearAlgebra.FreeModule.Finite.Basic", "is_tactic_proof": true, "tactics": ["cases", "classical", "refine", "simp"], "tactic_count": 4}
{"name": "Module.Finite.matrix", "kind": "instance", "module": "Mathlib.LinearAlgebra.FreeModule.Finite.Basic", "is_tactic_proof": true, "tactics": ["cases", "cases", "exact"], "tactic_count": 3}
{"name": "_example", "kind": "example", "module": "Mathlib.LinearAlgebra.FreeModule.Finite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.natAbs_det_equiv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.FreeModule.Finite.CardQuotient", "is_tactic_proof": true, "tactics": ["let", "have", "let", "let", "let", "have", "let", "let", "let", "suffices", "calc", "have", "intro", "rw", "exact", "calc", "congr", "rw", "by_cases", "rw", "rw", "simp_rw"], "tactic_count": 22}
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{"name": "AddSubgroup.index_eq_natAbs_det", "kind": "theorem", "module": "Mathlib.LinearAlgebra.FreeModule.Finite.CardQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddSubgroup.relIndex_eq_natAbs_det", "kind": "theorem", "module": "Mathlib.LinearAlgebra.FreeModule.Finite.CardQuotient", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
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{"name": "_private.Mathlib.LinearAlgebra.FreeModule.Finite.Matrix.0.linearMapEquivFun", "kind": "definition", "module": "Mathlib.LinearAlgebra.FreeModule.Finite.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Free.linearMap", "kind": "instance", "module": "Mathlib.LinearAlgebra.FreeModule.Finite.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Finite.linearMap", "kind": "instance", "module": "Mathlib.LinearAlgebra.FreeModule.Finite.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.rank_linearMap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.FreeModule.Finite.Matrix", "is_tactic_proof": true, "tactics": ["rw", "finrank_eq_rank"], "tactic_count": 2}
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{"name": "Module.rank_linearMap_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.FreeModule.Finite.Matrix", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "Finite.algHom", "kind": "instance", "module": "Mathlib.LinearAlgebra.FreeModule.Finite.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cardinalMk_algHom_le_rank", "kind": "theorem", "module": "Mathlib.LinearAlgebra.FreeModule.Finite.Matrix", "is_tactic_proof": true, "tactics": ["convert", "rw", "have", "rw"], "tactic_count": 4}
{"name": "card_algHom_le_finrank", "kind": "theorem", "module": "Mathlib.LinearAlgebra.FreeModule.Finite.Matrix", "is_tactic_proof": true, "tactics": ["convert", "rw", "rw"], "tactic_count": 3}
{"name": "Module.Finite.addMonoidHom", "kind": "instance", "module": "Mathlib.LinearAlgebra.FreeModule.Finite.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Free.addMonoidHom", "kind": "instance", "module": "Mathlib.LinearAlgebra.FreeModule.Finite.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.quotientEquivPiSpan", "kind": "definition", "module": "Mathlib.LinearAlgebra.FreeModule.Finite.Quotient", "is_tactic_proof": true, "tactics": ["haveI", "let", "let", "let", "have", "have", "intro", "simp_rw", "have", "intro", "simp", "constructor", "rintro", "exact", "rintro", "choose", "exact", "let", "have", "ext", "simp", "forall_true_left,", "constructor", "rintro", "exact", "rintro", "refine", "exact", "refine", "classical"], "tactic_count": 30}
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{"name": "Submodule.finiteQuotientOfFreeOfRankEq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.FreeModule.Finite.Quotient", "is_tactic_proof": true, "tactics": ["let", "let", "let", "have", "exact"], "tactic_count": 5}
{"name": "Submodule.finiteQuotient_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.FreeModule.Finite.Quotient", "is_tactic_proof": false, "tactics": ["refine", "le_antisymm", "simpa", "refine", "exact"], "tactic_count": 5}
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{"name": "Ideal.quotientEquivPiSpan", "kind": "definition", "module": "Mathlib.LinearAlgebra.FreeModule.IdealQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Ideal.finiteQuotientOfFreeOfNeBot", "kind": "theorem", "module": "Mathlib.LinearAlgebra.FreeModule.IdealQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ModN.liftEquiv", "kind": "definition", "module": "Mathlib.LinearAlgebra.FreeModule.ModN", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ModN.mkQ", "kind": "definition", "module": "Mathlib.LinearAlgebra.FreeModule.ModN", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ModN.instModuleFinite", "kind": "instance", "module": "Mathlib.LinearAlgebra.FreeModule.ModN", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModN.instFinite", "kind": "instance", "module": "Mathlib.LinearAlgebra.FreeModule.ModN", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModN.natCard_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.FreeModule.ModN", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "finrank_quotient_span_eq_natDegree_norm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.FreeModule.Norm", "is_tactic_proof": true, "tactics": ["haveI", "have", "rw", "rw", "congr", "exact"], "tactic_count": 6}
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{"name": "Submodule.basisOfPidOfLESpan", "kind": "definition", "module": "Mathlib.LinearAlgebra.FreeModule.PID", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Module.free_iff_isTorsionFree", "kind": "theorem", "module": "Mathlib.LinearAlgebra.FreeModule.PID", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.SmithNormalForm.repr_eq_zero_of_notMem_range", "kind": "theorem", "module": "Mathlib.LinearAlgebra.FreeModule.PID", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "replace", "simp"], "tactic_count": 4}
{"name": "Module.Basis.SmithNormalForm.le_ker_coord_of_notMem_range", "kind": "theorem", "module": "Mathlib.LinearAlgebra.FreeModule.PID", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LinearMap.comap_leq_ker_subToSupQuotient", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Isomorphisms", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "LinearMap.quotientInfToSupQuotient", "kind": "definition", "module": "Mathlib.LinearAlgebra.Isomorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.quotientInfEquivSupQuotient_injective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Isomorphisms", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
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{"name": "LinearMap.coe_quotientInfToSupQuotient", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Isomorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.quotientInfEquivSupQuotient_apply_mk", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Isomorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.quotientInfEquivSupQuotient_symm_apply_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Isomorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.quotientInfEquivSupQuotient_symm_apply_eq_zero_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Isomorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.quotientInfEquivSupQuotient_symm_apply_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Isomorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.quotientQuotientEquivQuotientAux", "kind": "definition", "module": "Mathlib.LinearAlgebra.Isomorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.quotientQuotientEquivQuotientAux_mk", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Isomorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.quotientQuotientEquivQuotientAux_mk_mk", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Isomorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.quotientQuotientEquivQuotient", "kind": "definition", "module": "Mathlib.LinearAlgebra.Isomorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.quotientQuotientEquivQuotientSup", "kind": "definition", "module": "Mathlib.LinearAlgebra.Isomorphisms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.card_quotient_mul_card_quotient", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Isomorphisms", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Module.End.exists_isNilpotent_isSemisimple_of_separable_of_dvd_pow", "kind": "theorem", "module": "Mathlib.LinearAlgebra.JordanChevalley", "is_tactic_proof": true, "tactics": ["set", "set", "have", "use", "obtain", "rw", "simp", "have", "obtain", "replace", "simpa", "refine", "simpa", "obtain", "refine", "exact", "rw", "simpa", "replace", "exact"], "tactic_count": 20}
{"name": "Module.End.exists_isNilpotent_isSemisimple", "kind": "theorem", "module": "Mathlib.LinearAlgebra.JordanChevalley", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact"], "tactic_count": 3}
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{"name": "Lagrange.basisDivisor", "kind": "definition", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lagrange.basisDivisor_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Lagrange.basisDivisor_inj", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Lagrange.basisDivisor_eq_zero_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lagrange.basisDivisor_ne_zero_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Lagrange.degree_basisDivisor_of_ne", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Lagrange.degree_basisDivisor_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Lagrange.natDegree_basisDivisor_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Lagrange.natDegree_basisDivisor_of_ne", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lagrange.eval_basisDivisor_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Lagrange.eval_basisDivisor_left_of_ne", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Lagrange.basis", "kind": "definition", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lagrange.basis_empty", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lagrange.basis_singleton", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Lagrange.basis_pair_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": true, "tactics": ["simp", "prod_singleton]"], "tactic_count": 2}
{"name": "Lagrange.basis_pair_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Lagrange.basis_ne_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": true, "tactics": ["simp_rw", "rintro", "rw", "exact"], "tactic_count": 4}
{"name": "Lagrange.eval_basis_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "rcases", "exact"], "tactic_count": 5}
{"name": "Lagrange.eval_basis_of_ne", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Lagrange.natDegree_basis", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": false, "tactics": ["have", "simp_rw", "exact", "rw", "convert", "refine", "rw", "exact"], "tactic_count": 8}
{"name": "Lagrange.degree_basis", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Lagrange.sum_basis", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": true, "tactics": ["refine", "rw", "intro", "rw", "exact", "rw", "exact", "intro", "rw", "refine", "rcases", "rw"], "tactic_count": 12}
{"name": "Lagrange.basisDivisor_add_symm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": true, "tactics": ["classical", "rw", "sum_singleton,"], "tactic_count": 3}
{"name": "Lagrange.leadingCoeff_basis", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": false, "tactics": ["have", "simpa", "simp_rw", "simp"], "tactic_count": 4}
{"name": "Lagrange.interpolate", "kind": "definition", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lagrange.interpolate_empty", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Lagrange.interpolate_singleton", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Lagrange.interpolate_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Lagrange.eval_interpolate_at_node", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "refine", "rw"], "tactic_count": 4}
{"name": "Lagrange.degree_interpolate_le", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": true, "tactics": ["refine", "rw", "intro", "rw", "by_cases", "simpa", "rw"], "tactic_count": 7}
{"name": "Lagrange.degree_interpolate_lt", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": true, "tactics": ["rw", "rcases", "rw", "exact", "refine", "rw", "exact"], "tactic_count": 7}
{"name": "Lagrange.degree_interpolate_erase_lt", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Lagrange.values_eq_on_of_interpolate_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lagrange.interpolate_eq_of_values_eq_on", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lagrange.interpolate_eq_iff_values_eq_on", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lagrange.eq_interpolate", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lagrange.eq_interpolate_of_eval_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Lagrange.eq_interpolate_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": true, "tactics": ["constructor", "exact", "rw", "exact"], "tactic_count": 4}
{"name": "Lagrange.funEquivDegreeLT", "kind": "definition", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lagrange.interpolate_eq_sum_interpolate_insert_sdiff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": true, "tactics": ["symm", "refine", "simp_rw", "intro", "have", "have", "have", "rw", "zero_add]", "rw", "convert", "rw", "simp_rw", "by_cases", "rw", "eval_interpolate_at_node", "mul_one,", "refine", "rcases", "rw", "have", "rw", "rw", "refine", "congr", "exact", "eval_interpolate_at_node"], "tactic_count": 27}
{"name": "Lagrange.interpolate_eq_add_interpolate_erase", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": false, "tactics": ["rw", "sum_insert", "sdiff_insert_insert_of_mem_of_notMem", "sdiff_insert_insert_of_mem_of_notMem", "exact"], "tactic_count": 5}
{"name": "Lagrange.interpolate_eq_sum", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Lagrange.iterate_derivative_interpolate", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": true, "tactics": ["classical", "simp_rw", "mul_comm", "congr", "have", "calc", "derivative^", "rw", "grind", "rw", "congrm", "refine", "grind", "exact", "grind", "exact"], "tactic_count": 16}
{"name": "Lagrange.eval_iterate_derivative_eq_sum", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": true, "tactics": ["nth_rewrite", "simp"], "tactic_count": 2}
{"name": "Lagrange.interpolate_poly_eq_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lagrange.coeff_eq_sum", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": true, "tactics": ["nth_rewrite", "congr", "rw", "field_simp"], "tactic_count": 4}
{"name": "Lagrange.leadingCoeff_eq_sum", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": true, "tactics": ["lift", "rw", "replace", "have", "rw", "exact"], "tactic_count": 6}
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{"name": "Lagrange.nodal_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lagrange.nodal_empty", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "Lagrange.natDegree_nodal", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": true, "tactics": ["simp_rw", "smul_eq_mul,"], "tactic_count": 2}
{"name": "Lagrange.nodal_ne_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": true, "tactics": ["rcases", "exact", "apply", "simp"], "tactic_count": 4}
{"name": "Lagrange.degree_nodal", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Lagrange.nodal_monic", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lagrange.eval_nodal", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Lagrange.eval_nodal_at_node", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Lagrange.eval_nodal_not_at_node", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Lagrange.nodal_eq_mul_nodal_erase", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Lagrange.X_sub_C_dvd_nodal", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Lagrange.nodal_insert_eq_nodal", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Lagrange.derivative_nodal", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": true, "tactics": ["refine", "rw", "rw", "sum_insert", "refine", "rw"], "tactic_count": 6}
{"name": "Lagrange.eval_nodal_derivative_eval_node_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Lagrange.nodal_subgroup_eq_X_pow_card_sub_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": true, "tactics": ["have", "apply", "exact", "simp", "rw", "exact", "rw", "intro", "rw", "replace", "obtain", "simp"], "tactic_count": 12}
{"name": "Lagrange.nodalWeight", "kind": "definition", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lagrange.nodalWeight_eq_eval_nodal_erase_inv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Lagrange.nodal_erase_eq_nodal_div", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Lagrange.nodalWeight_eq_eval_derivative_nodal", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Lagrange.nodalWeight_ne_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": true, "tactics": ["rw", "intro", "rcases", "exact"], "tactic_count": 4}
{"name": "Lagrange.basis_eq_prod_sub_inv_mul_nodal_div", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Lagrange.eval_basis_not_at_node", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": true, "tactics": ["rw", "eval_nodal,", "one_mul]"], "tactic_count": 3}
{"name": "Lagrange.interpolate_eq_nodalWeight_mul_nodal_div_X_sub_C", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lagrange.eval_interpolate_not_at_node", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "rw"], "tactic_count": 3}
{"name": "Lagrange.sum_nodalWeight_mul_inv_sub_ne_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lagrange.eval_interpolate_not_at_node'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Lagrange", "is_tactic_proof": false, "tactics": ["rw", "eval_interpolate_not_at_node", "simp"], "tactic_count": 3}
{"name": "LinearMap.exact_lcomp_of_exact_of_surjective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LeftExact", "is_tactic_proof": true, "tactics": ["intro", "simp", "refine", "use", "ext", "simp", "rw"], "tactic_count": 7}
{"name": "Submodule.LinearDisjoint.mulMap", "kind": "definition", "module": "Mathlib.LinearAlgebra.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.LinearDisjoint.val_mulMap_tmul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.LinearDisjoint.of_subsingleton", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.LinearDisjoint.of_subsingleton_top", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.linearDisjoint_op", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearDisjoint", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Submodule.LinearDisjoint.symm_of_commute", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearDisjoint", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Submodule.linearDisjoint_comm_of_commute", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.LinearDisjoint.map", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearDisjoint", "is_tactic_proof": true, "tactics": ["rw", "have", "rw", "refine", "apply"], "tactic_count": 5}
{"name": "Submodule.LinearDisjoint.of_basis_left'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearDisjoint", "is_tactic_proof": false, "tactics": ["classical", "simp_rw", "exact"], "tactic_count": 3}
{"name": "Submodule.LinearDisjoint.of_basis_right'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearDisjoint", "is_tactic_proof": false, "tactics": ["classical", "simp_rw", "exact"], "tactic_count": 3}
{"name": "Submodule.LinearDisjoint.of_basis_mul'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearDisjoint", "is_tactic_proof": true, "tactics": ["let", "let", "let", "have", "ext", "simp", "simp_rw", "exact"], "tactic_count": 8}
{"name": "Submodule.LinearDisjoint.bot_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.LinearDisjoint.bot_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.LinearDisjoint.one_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearDisjoint", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Submodule.LinearDisjoint.one_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearDisjoint", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Submodule.LinearDisjoint.of_linearDisjoint_fg_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.LinearDisjoint.of_linearDisjoint_fg_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.LinearDisjoint.of_linearDisjoint_fg", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.LinearDisjoint.symm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.linearDisjoint_comm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.LinearDisjoint.linearIndependent_left_of_flat", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearDisjoint", "is_tactic_proof": true, "tactics": ["refine", "classical", "simp_rw", "rw", "exact"], "tactic_count": 5}
{"name": "Submodule.LinearDisjoint.of_basis_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.LinearDisjoint.linearIndependent_right_of_flat", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearDisjoint", "is_tactic_proof": true, "tactics": ["refine", "classical", "simp_rw", "rw", "exact"], "tactic_count": 5}
{"name": "Submodule.LinearDisjoint.of_basis_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.LinearDisjoint.linearIndependent_mul_of_flat_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearDisjoint", "is_tactic_proof": true, "tactics": ["rw", "let", "let", "let", "let", "have", "have", "have", "have", "ext", "simp", "rwa"], "tactic_count": 12}
{"name": "Submodule.LinearDisjoint.linearIndependent_mul_of_flat_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearDisjoint", "is_tactic_proof": true, "tactics": ["rw", "let", "let", "let", "let", "have", "have", "have", "have", "ext", "simp", "rwa"], "tactic_count": 12}
{"name": "Submodule.LinearDisjoint.linearIndependent_mul_of_flat", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearDisjoint", "is_tactic_proof": true, "tactics": ["rcases", "exact", "exact"], "tactic_count": 3}
{"name": "Submodule.LinearDisjoint.of_basis_mul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearDisjoint", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Submodule.LinearDisjoint.of_le_left_of_flat", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearDisjoint", "is_tactic_proof": true, "tactics": ["let", "have", "have", "exact"], "tactic_count": 4}
{"name": "Submodule.LinearDisjoint.of_le_right_of_flat", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearDisjoint", "is_tactic_proof": true, "tactics": ["let", "have", "have", "exact"], "tactic_count": 4}
{"name": "Submodule.LinearDisjoint.of_le_of_flat_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.LinearDisjoint.of_le_of_flat_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.LinearDisjoint.of_left_le_one_of_flat", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.LinearDisjoint.of_right_le_one_of_flat", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.LinearDisjoint.not_linearIndependent_pair_of_commute_of_flat_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.LinearDisjoint.not_linearIndependent_pair_of_commute_of_flat_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.LinearDisjoint.not_linearIndependent_pair_of_commute_of_flat", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearDisjoint", "is_tactic_proof": true, "tactics": ["rcases", "exact", "exact"], "tactic_count": 3}
{"name": "Submodule.LinearDisjoint.rank_inf_le_one_of_commute_of_flat", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearDisjoint", "is_tactic_proof": true, "tactics": ["nontriviality", "refine", "by_contra", "rw", "obtain", "refine", "have", "h.comp", "fin_cases", "rfl", "simp", "simp", "rfl", "convert", "ext", "fin_cases"], "tactic_count": 16}
{"name": "Submodule.LinearDisjoint.rank_inf_le_one_of_commute_of_flat_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.LinearDisjoint.rank_inf_le_one_of_commute_of_flat_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.LinearDisjoint.rank_le_one_of_commute_of_flat_of_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearDisjoint", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Submodule.LinearDisjoint.not_linearIndependent_pair_of_flat_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.LinearDisjoint.not_linearIndependent_pair_of_flat_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.LinearDisjoint.not_linearIndependent_pair_of_flat", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.LinearDisjoint.rank_inf_le_one_of_flat", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.LinearDisjoint.rank_inf_le_one_of_flat_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.LinearDisjoint.rank_inf_le_one_of_flat_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.LinearDisjoint.rank_le_one_of_flat_of_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIndependent.restrict_scalars", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIndependent.restrict_scalars'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.range_ker_disjoint", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Basic", "is_tactic_proof": true, "tactics": ["rw", "rw"], "tactic_count": 2}
{"name": "LinearIndependent.map_of_injective_injectiveₛ", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Basic", "is_tactic_proof": true, "tactics": ["rw", "intro", "simp_rw", "exact"], "tactic_count": 4}
{"name": "LinearIndependent.map_of_surjective_injectiveₛ", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Basic", "is_tactic_proof": true, "tactics": ["obtain", "refine", "apply_fun", "rwa", "rw"], "tactic_count": 5}
{"name": "LinearIndependent.map_injOn", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIndepOn.map_injOn", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIndepOn.comp_of_image", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIndepOn.image_of_comp", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Basic", "is_tactic_proof": true, "tactics": ["nontriviality", "have", "exact"], "tactic_count": 3}
{"name": "LinearIndepOn.id_image", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIndepOn_iff_linearIndepOn_image_injOn", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "linearIndepOn_congr", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Basic", "is_tactic_proof": true, "tactics": ["rw", "convert", "ext", "exact"], "tactic_count": 4}
{"name": "LinearIndepOn.congr", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIndependent.group_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Basic", "is_tactic_proof": true, "tactics": ["rw", "intro", "refine", "refine", "simp_rw", "simpa"], "tactic_count": 6}
{"name": "LinearIndependent.group_smul_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Basic", "is_tactic_proof": true, "tactics": ["refine", "convert", "simp"], "tactic_count": 3}
{"name": "LinearIndependent.units_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Basic", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "refine", "simp_rw", "simpa"], "tactic_count": 6}
{"name": "LinearIndependent.units_smul_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Basic", "is_tactic_proof": true, "tactics": ["refine", "convert", "simp"], "tactic_count": 3}
{"name": "linearIndependent_span", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "linearIndependent_finset_map_embedding_subtype", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "linearIndepOn_of_finite", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIndependent.eq_of_smul_apply_eq_smul_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Basic", "is_tactic_proof": false, "tactics": ["have", "rcases", "exact", "contradiction"], "tactic_count": 4}
{"name": "LinearIndependent.disjoint_span_image", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Basic", "is_tactic_proof": true, "tactics": ["simp", "rintro", "rw", "have", "simp"], "tactic_count": 5}
{"name": "LinearIndependent.notMem_span_image", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Basic", "is_tactic_proof": false, "tactics": ["have", "rw", "exact", "intro", "apply", "refine", "simpa"], "tactic_count": 7}
{"name": "LinearIndependent.linearCombination_ne_of_notMem_support", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Basic", "is_tactic_proof": true, "tactics": ["replace", "intro", "have", "simpa", "exact"], "tactic_count": 5}
{"name": "LinearIndepOn.id_imageₛ", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "surjective_of_linearIndependent_of_span", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Basic", "is_tactic_proof": true, "tactics": ["intro", "let", "let", "have", "dsimp", "rw", "rw", "have", "rw", "have", "dsimp", "rw", "rcases", "use", "exact"], "tactic_count": 15}
{"name": "eq_of_linearIndepOn_id_of_span_subtype", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Basic", "is_tactic_proof": true, "tactics": ["let", "have", "apply", "convert", "change", "apply", "intro", "rcases", "convert", "rw"], "tactic_count": 10}
{"name": "le_of_span_le_span", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Basic", "is_tactic_proof": false, "tactics": ["have", "eq_of_linearIndepOn_id_of_span_subtype", "rw"], "tactic_count": 3}
{"name": "span_le_span_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIndependent.eq_coords_of_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "exact"], "tactic_count": 3}
{"name": "LinearIndependent.map", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIndependent.map'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIndependent.map_of_injective_injective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Basic", "is_tactic_proof": true, "tactics": ["rw", "intro", "simp_rw", "exact"], "tactic_count": 4}
{"name": "LinearIndependent.map_of_surjective_injective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.linearIndependent_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIndependent.fin_cons'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Basic", "is_tactic_proof": true, "tactics": ["rw", "rintro", "simp_rw", "have", "refine", "exact", "rw", "exact"], "tactic_count": 8}
{"name": "linearIndependent_sum", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Basic", "is_tactic_proof": true, "tactics": ["classical", "rw", "refine", "intro", "refine", "exact", "rintro", "rw", "intro", "have", "rw", "simpa", "exact", "rw", "rw", "have", "refine", "exact", "exact", "rcases", "exact", "rw", "exact"], "tactic_count": 23}
{"name": "LinearIndependent.sum_type", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIndepOn.union", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Basic", "is_tactic_proof": true, "tactics": ["nontriviality", "classical", "have", "have", "rw", "convert", "rw", "rw"], "tactic_count": 8}
{"name": "LinearIndepOn.id_union", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "linearIndepOn_union_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Basic", "is_tactic_proof": true, "tactics": ["refine", "convert"], "tactic_count": 2}
{"name": "linearIndepOn_id_union_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LinearIndepOn.image", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "linearIndependent_monoidHom", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Basic", "is_tactic_proof": true, "tactics": ["letI", "letI", "apply", "intro", "induction", "empty", "insert", "intro", "have", "ext", "rw", "apply", "ext", "calc", "simp", "congrm", "rw", "rw", "simp", "simp", "have", "by_contra", "obtain", "contradiction", "have", "let", "have", "rw", "exact", "h.resolve_right", "have", "calc", "g", "rw", "simp", "rfl", "exact"], "tactic_count": 37}
{"name": "linearIndependent_unique_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Basic", "is_tactic_proof": true, "tactics": ["refine", "simpa"], "tactic_count": 2}
{"name": "linearIndepOn_singleton_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "linearIndependent_subsingleton_index_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Basic", "is_tactic_proof": true, "tactics": ["obtain", "simp", "obtain", "rw", "exact"], "tactic_count": 5}
{"name": "LinearIndependent", "kind": "definition", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "delabLinearIndependent", "kind": "definition", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIndepOn", "kind": "definition", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIndepOn.linearIndependent", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "linearIndependent_iff_injective_finsuppLinearCombination", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "linearIndependent_iff_injective_fintypeLinearCombination", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LinearIndependent.injective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "LinearIndepOn.injOn", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIndependent.smul_left_injective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "LinearIndependent.ne_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": true, "tactics": ["intro", "have", "simp"], "tactic_count": 3}
{"name": "LinearIndepOn.ne_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIndepOn.zero_notMem_image", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "linearIndependent_empty_type", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "linearIndependent_zero_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "linearIndepOn_zero_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "linearIndependent_subsingleton_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "linearIndependent_empty", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "linearIndepOn_empty", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "linearIndependent_set_coe_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "linearIndependent_subtype_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "linearIndependent_comp_subtype_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIndependent.comp", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "LinearIndepOn.mono", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "linearIndependent_iffₛ", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "linearIndependent_iff'ₛ", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "linearIndependent_iff''ₛ", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": true, "tactics": ["classical", "exact", "linearIndependent_iff'ₛ.trans", "convert", "exact"], "tactic_count": 5}
{"name": "not_linearIndependent_iffₛ", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Fintype.linearIndependent_iffₛ", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": true, "tactics": ["simp_rw", "funext_iff]"], "tactic_count": 2}
{"name": "Fintype.not_linearIndependent_iffₛ", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "linearIndepOn_finset_iffₛ", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": true, "tactics": ["classical", "simp_rw", "constructor", "rintro", "simp_rw", "exact", "rintro", "simpa", "hv"], "tactic_count": 9}
{"name": "not_linearIndepOn_finset_iffₛ", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "linearIndependent_iff_finset_linearIndependent", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "linearIndepOn_iff_linearIndepOn_finset", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIndependent.of_comp", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "LinearIndepOn.of_comp", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.linearIndependent_iff_of_injOn", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": true, "tactics": ["simp_rw", "rw", "rw"], "tactic_count": 3}
{"name": "LinearMap.linearIndepOn_iff_of_injOn", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "linearIndependent_of_subsingleton", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIndepOn.of_subsingleton", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "linearIndependent_equiv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "linearIndependent_equiv'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "linearIndepOn_equiv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "linearIndepOn_univ", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "linearIndepOn_iff_image", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "linearIndepOn_range_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "linearIndepOn_id_range_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIndependent.linearIndepOn_id", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "LinearIndependent.linearIndepOn_id'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "linearIndepOn_iffₛ", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": false, "tactics": ["simp", "refine", "h", "refine", "iterate", "simp_rw", "rwa"], "tactic_count": 7}
{"name": "linearDepOn_iff'ₛ", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "linearDepOn_iffₛ", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "linearIndependent_restrict_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIndepOn.linearIndependent_restrict", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "linearIndepOn_iff_linearCombinationOnₛ", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "LinearIndependent.linearCombinationEquiv", "kind": "definition", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": false, "tactics": ["refine", "simp_rw", "rw", "range_subtype,"], "tactic_count": 4}
{"name": "LinearIndependent.repr", "kind": "definition", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIndependent.linearCombination_repr", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIndependent.linearCombination_comp_repr", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIndependent.repr_ker", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LinearIndependent.repr_range", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LinearIndependent.repr_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": false, "tactics": ["have", "rfl", "have", "rw", "exact", "rw", "rw", "rfl"], "tactic_count": 8}
{"name": "LinearIndependent.repr_eq_single", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "LinearIndependent.span_repr_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": false, "tactics": ["have", "apply", "ext", "simp", "ext", "simp"], "tactic_count": 6}
{"name": "LinearIndependent.eq_zero_of_smul_mem_span", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": true, "tactics": ["rw", "rcases", "rw", "by_contra", "exact"], "tactic_count": 5}
{"name": "LinearIndepOn.eq_zero_of_smul_mem_span", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIndependent.notMem_span", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIndepOn.notMem_span", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIndepOn.notMem_span_of_insert", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "LinearIndependent.Maximal", "kind": "definition", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIndependent.maximal_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "specialize", "rw", "exact", "intro", "specialize", "p", "ext", "simp)", "have", "dsimp", "rw", "simpa"], "tactic_count": 14}
{"name": "linearIndependent_iffₒₛ", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": true, "tactics": ["classical", "letI", "haveI", "rw", "refine", "specialize", "simpa", "refine", "simpa", "simpa", "specialize", "simp_rw", "exact", "rw", "conv_lhs", "conv_rhs", "convert", "congr", "simp", "simp", "simp", "simp", "intro", "by_cases", "apply", "simpa", "apply", "simpa"], "tactic_count": 28}
{"name": "not_linearIndependent_iffₒₛ", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": true, "tactics": ["simp", "push_neg", "refine", "rcases", "exact", "exact"], "tactic_count": 6}
{"name": "Fintype.linearIndependent_iffₒₛ", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": true, "tactics": ["rw", "refine", "specialize", "by_cases", "exact", "exact", "specialize", "rw", "convert", "intro", "simp", "refine"], "tactic_count": 12}
{"name": "Fintype.not_linearIndependent_iffₒₛ", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": true, "tactics": ["simp", "refine", "by_cases", "exact", "refine", "simp"], "tactic_count": 6}
{"name": "linearIndepOn_finset_iffₒₛ", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp", "rw", "simpa", "specialize", "h", "i.2", "conv", "enter", "rw", "change", "rw", "simpa", "simpa"], "tactic_count": 15}
{"name": "not_linearIndepOn_finset_iffₒₛ", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": true, "tactics": ["simp", "refine", "by_cases", "exact", "refine", "simpa"], "tactic_count": 6}
{"name": "linearIndependent_iff_ker", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "linearIndependent_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "linearIndependent_iff'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": true, "tactics": ["rw", "refine", "convert", "rw", "convert"], "tactic_count": 5}
{"name": "linearIndependent_iff''", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": true, "tactics": ["classical", "exact", "linearIndependent_iff'.trans", "convert", "exact"], "tactic_count": 5}
{"name": "linearIndependent_add_smul_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "not_linearIndependent_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Fintype.linearIndependent_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": false, "tactics": ["refine", "linearIndependent_iff''.2", "rw", "refine", "rw"], "tactic_count": 5}
{"name": "Fintype.not_linearIndependent_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "linearIndepOn_finset_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": true, "tactics": ["classical", "simp_rw", "constructor", "rintro", "rw", "exact", "rintro", "simpa"], "tactic_count": 8}
{"name": "not_linearIndepOn_finset_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "LinearMap.linearIndependent_iff_of_disjoint", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "linearIndepOn_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "linearDepOn_iff'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "linearDepOn_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "linearIndepOn_iff_disjoint", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "linearIndepOn_iff_linearCombinationOn", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "linearIndepOn_iff'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": true, "tactics": ["classical", "rw", "refine", "refine", "rwa", "simp", "exact", "replace", "simpa", "apply"], "tactic_count": 10}
{"name": "linearIndepOn_iff''", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": true, "tactics": ["classical", "exact", "linearIndepOn_iff'.trans", "simpa"], "tactic_count": 4}
{"name": "linearIndependent_iff_eq_zero_of_smul_mem_span", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIndependent.of_subsingleton'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": true, "tactics": ["let", "simpa"], "tactic_count": 2}
{"name": "LinearIndepOn.singleton'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIndependent.of_subsingleton", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIndepOn.singleton", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LinearIndepOn.id_singleton", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "linearIndependent_iff_notMem_span", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": true, "tactics": ["apply", "constructor", "intro", "apply", "intro", "by_contra", "exact"], "tactic_count": 7}
{"name": "linearIndepOn_iff_notMem_span", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Defs", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "simp"], "tactic_count": 3}
{"name": "Fintype.linearIndependent_iff'ₛ", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LinearIndependent.pair_iffₛ", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LinearIndependent.eq_of_pair", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIndependent.eq_zero_of_pair'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Lemmas", "is_tactic_proof": true, "tactics": ["suffices", "exact"], "tactic_count": 2}
{"name": "LinearIndependent.eq_zero_of_pair", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "linearIndepOn_iUnion_of_directed", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Lemmas", "is_tactic_proof": true, "tactics": ["by_cases", "refine", "rcases", "rcases", "exact", "refine", "rintro", "exact"], "tactic_count": 8}
{"name": "linearIndepOn_sUnion_of_directed", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "linearIndepOn_biUnion_of_directed", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "iSupIndep_range_lsingle", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Lemmas", "is_tactic_proof": true, "tactics": ["refine", "rintro", "suffices", "have", "refine", "rintro", "simp"], "tactic_count": 7}
{"name": "LinearMap.iSupIndep_map", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Lemmas", "is_tactic_proof": true, "tactics": ["simp_rw", "rintro", "rw", "simp_rw", "have", "simpa"], "tactic_count": 6}
{"name": "LinearIndependent.iSupIndep_span_singleton", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Lemmas", "is_tactic_proof": true, "tactics": ["convert", "ext"], "tactic_count": 2}
{"name": "linearIndependent_inl_union_inr'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Lemmas", "is_tactic_proof": false, "tactics": ["have", "linearCombination", "rw", "simpa"], "tactic_count": 4}
{"name": "LinearIndependent.inl_union_inr", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Lemmas", "is_tactic_proof": true, "tactics": ["nontriviality", "let", "rintro", "refine", "ext"], "tactic_count": 5}
{"name": "exists_maximal_linearIndepOn'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Lemmas", "is_tactic_proof": true, "tactics": ["let", "let", "let", "have", "intro", "dsimp", "rw", "intro", "rcases", "rw", "haveI", "classical", "obtain", "f.support.coe_union", "simpa", "exact", "have", "obtain", "exists_maximal_of_chains_bounded", "exact"], "tactic_count": 20}
{"name": "Submodule.codisjoint_span_image_of_codisjoint", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "refine", "rwa"], "tactic_count": 3}
{"name": "LinearIndependent.isCompl_span_image", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.linearIndependent_iff'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LinearIndepOn.pair_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Lemmas", "is_tactic_proof": true, "tactics": ["classical", "rw", "refine", "specialize", "simpa", "have", "rw", "obtain", "exact", "simp"], "tactic_count": 10}
{"name": "LinearIndependent.pair_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Lemmas", "is_tactic_proof": false, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "LinearIndependent.pair_symm_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Lemmas", "is_tactic_proof": true, "tactics": ["suffices", "simp", "intro", "specialize", "rwa"], "tactic_count": 5}
{"name": "LinearIndependent.pair_neg_left_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "refine"], "tactic_count": 2}
{"name": "LinearIndependent.pair_neg_right_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LinearIndependent.pair_smul_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Lemmas", "is_tactic_proof": true, "tactics": ["simp", "refine", "exact", "specialize", "exact"], "tactic_count": 5}
{"name": "_private.Mathlib.LinearAlgebra.LinearIndependent.Lemmas.0.LinearIndependent.pair_add_smul_add_smul_iff_aux", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Lemmas", "is_tactic_proof": true, "tactics": ["simp", "intro", "specialize", "h", "abel)", "obtain", "constructor", "suffices", "calc", "rw", "suffices", "calc", "rw"], "tactic_count": 13}
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{"name": "LinearIndependent.of_pairwise_dual_eq_zero_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Lemmas", "is_tactic_proof": true, "tactics": ["refine", "have", "simpa"], "tactic_count": 3}
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{"name": "LinearIndepOn.id_insert", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LinearIndependent.option", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "linearIndependent_option", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "linearIndepOn_insert", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Lemmas", "is_tactic_proof": true, "tactics": ["classical", "rw", "linearIndependent_equiv", "simp", "rw", "simp"], "tactic_count": 6}
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{"name": "linearIndepOn_insert_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Lemmas", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "simp"], "tactic_count": 3}
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{"name": "LinearIndepOn.mem_span_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Lemmas", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "simp"], "tactic_count": 3}
{"name": "LinearIndepOn.notMem_span_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LinearIndepOn.mem_span_iff_id", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Lemmas", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "LinearIndepOn.notMem_span_iff_id", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "linearIndepOn_id_pair", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "linearIndependent_fin_succ", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "LinearIndepOn.extend_subset", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIndepOn.subset_extend", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearIndependent.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LinearPMap.toFun'", "kind": "definition", "module": "Mathlib.LinearAlgebra.LinearPMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LinearPMap.domain_mkSpanSingleton", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearPMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LinearPMap.mkSpanSingleton_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.LinearPMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LinearPMap.le", "kind": "instance", "module": "Mathlib.LinearAlgebra.LinearPMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LinearPMap.eqLocus", "kind": "definition", "module": "Mathlib.LinearAlgebra.LinearPMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearPMap.bot", "kind": "instance", "module": "Mathlib.LinearAlgebra.LinearPMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearPMap.inhabited", "kind": "instance", "module": "Mathlib.LinearAlgebra.LinearPMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LinearPMap.instInvolutiveNeg", "kind": "instance", "module": "Mathlib.LinearAlgebra.LinearPMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Matrix.det_adjugate", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Adjugate", "is_tactic_proof": true, "tactics": ["rcases", "haveI", "rw", "replace", "let", "suffices", "rw", "apply", "calc"], "tactic_count": 9}
{"name": "Matrix.adjugate_fin_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Adjugate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.adjugate_fin_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Adjugate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.adjugate_fin_succ_eq_det_submatrix", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Adjugate", "is_tactic_proof": true, "tactics": ["simp_rw", "rw", "rw"], "tactic_count": 3}
{"name": "Matrix.adjugate_fin_two", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Adjugate", "is_tactic_proof": true, "tactics": ["ext", "rw", "fin_cases"], "tactic_count": 3}
{"name": "Matrix.adjugate_fin_two_of", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Adjugate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.adjugate_fin_three", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Adjugate", "is_tactic_proof": true, "tactics": ["ext", "rw", "fin_cases"], "tactic_count": 3}
{"name": "Matrix.adjugate_fin_three_of", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Adjugate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.det_eq_sum_mul_adjugate_row", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Adjugate", "is_tactic_proof": true, "tactics": ["haveI", "obtain", "obtain", "let", "suffices", "simp_rw", "exact", "rw", "simp_rw"], "tactic_count": 9}
{"name": "Matrix.det_eq_sum_mul_adjugate_col", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Adjugate", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Matrix.adjugate_conjTranspose", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Adjugate", "is_tactic_proof": true, "tactics": ["dsimp", "have", "rw"], "tactic_count": 3}
{"name": "Matrix.isRegular_of_isLeftRegular_det", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Adjugate", "is_tactic_proof": true, "tactics": ["constructor", "intro", "refine", "simp", "rw", "intro", "refine", "simp", "rw"], "tactic_count": 9}
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{"name": "Matrix.det_smul_adjugate_adjugate", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Adjugate", "is_tactic_proof": false, "tactics": ["have", "rw", "rwa"], "tactic_count": 3}
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{"name": "Matrix.adjugate_adjugate'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Adjugate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.mem_subfield_of_mul_eq_one_of_mem_subfield_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BaseChange", "is_tactic_proof": true, "tactics": ["cases", "let", "have", "have", "have", "have", "simpa", "obtain", "suffices", "replace", "replace", "simp_rw", "rw", "simpa", "classical"], "tactic_count": 15}
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{"name": "Module.Basis.toMatrix", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.toMatrix_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.toMatrix_transpose_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.toMatrix_eq_toMatrix_constr", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Basis", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "Module.Basis.coePiBasisFun.toMatrix_eq_transpose", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Basis", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "Module.Basis.toMatrix_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Basis", "is_tactic_proof": true, "tactics": ["unfold", "ext", "simp"], "tactic_count": 3}
{"name": "Module.Basis.toMatrix_update", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Basis", "is_tactic_proof": true, "tactics": ["ext", "rw", "split_ifs", "rw", "rw"], "tactic_count": 5}
{"name": "Module.Basis.toMatrix_unitsSMul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Basis", "is_tactic_proof": true, "tactics": ["ext", "by_cases"], "tactic_count": 2}
{"name": "Module.Basis.toMatrix_isUnitSMul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.toMatrix_smul_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.sum_toMatrix_smul_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Basis", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Module.Basis.toMatrix_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Basis", "is_tactic_proof": true, "tactics": ["ext", "rw", "rfl"], "tactic_count": 3}
{"name": "Module.Basis.toMatrix_map_vecMul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Basis", "is_tactic_proof": true, "tactics": ["ext", "simp_rw"], "tactic_count": 2}
{"name": "Module.Basis.toLin_toMatrix", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.toMatrixEquiv", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.restrictScalars_toMatrix", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Basis", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "LinearMap.toMatrix_id_eq_basis_toMatrix", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Basis", "is_tactic_proof": true, "tactics": ["ext", "apply"], "tactic_count": 2}
{"name": "basis_toMatrix_mul_linearMap_toMatrix", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "basis_toMatrix_mul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Basis", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "linearMap_toMatrix_mul_basis_toMatrix", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "basis_toMatrix_mul_linearMap_toMatrix_mul_basis_toMatrix", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Basis", "is_tactic_proof": true, "tactics": ["cases", "rw"], "tactic_count": 2}
{"name": "mul_basis_toMatrix", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Basis", "is_tactic_proof": true, "tactics": ["cases", "have", "rwa"], "tactic_count": 3}
{"name": "basis_toMatrix_basisFun_mul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Basis", "is_tactic_proof": true, "tactics": ["classical", "simp", "ext", "rw"], "tactic_count": 4}
{"name": "Module.Basis.toMatrix_reindex'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Basis", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Module.Basis.toMatrix_mulVec_repr", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Basis", "is_tactic_proof": true, "tactics": ["classical", "cases", "simp"], "tactic_count": 3}
{"name": "Module.Basis.toMatrix_mul_toMatrix", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Basis", "is_tactic_proof": true, "tactics": ["haveI", "haveI", "haveI", "ext", "simp"], "tactic_count": 5}
{"name": "Module.Basis.toMatrix_mul_toMatrix_flip", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Basis", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Module.Basis.invertibleToMatrix", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.toMatrix_reindex", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Basis", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Module.Basis.toMatrix_map", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Basis", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Matrix.toBilin'Aux", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.toBilin'Aux_single", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.toMatrixAux", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.toMatrixAux_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.toBilin'Aux_toMatrixAux", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LinearMap.BilinForm.toMatrix'", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.toBilin'", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.toBilin'Aux_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.toBilin'_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.toBilin'_apply'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.toBilin'_single", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LinearMap.BilinForm.toMatrix'_symm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.toBilin'_symm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.toBilin'_toMatrix'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.toMatrix'_toBilin'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.toMatrix'_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.toMatrix'_comp", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.toMatrix'_compLeft", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.toMatrix'_compRight", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.mul_toMatrix'_mul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.mul_toMatrix'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.toMatrix'_mul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.toBilin'_comp", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.toMatrix", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.toBilin", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.toMatrix_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.dotProduct_toMatrix_mulVec", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.apply_eq_dotProduct_toMatrix_mulVec", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.toBilin_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.toMatrixAux_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.toMatrix_symm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.toBilin_symm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.toBilin_basisFun", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "LinearMap.BilinForm.toMatrix_basisFun", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matrix.toBilin_toMatrix", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.toMatrix_toBilin", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.toMatrix_comp", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.toMatrix_compLeft", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.toMatrix_compRight", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.toMatrix_mul_basis_toMatrix", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.mul_toMatrix_mul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.mul_toMatrix", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.toMatrix_mul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.toBilin_comp", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": true, "tactics": ["ext", "rw", "toMatrix₂_symm,", "simp"], "tactic_count": 4}
{"name": "Matrix.isAdjointPair_equiv'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_pairSelfAdjointMatricesSubmodule'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "selfAdjointMatricesSubmodule'", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_selfAdjointMatricesSubmodule'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "skewAdjointMatricesSubmodule'", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_skewAdjointMatricesSubmodule'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.nondegenerate_toBilin'_iff_nondegenerate_toBilin", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.Nondegenerate.toBilin'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.nondegenerate_toBilin'_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.Nondegenerate.toBilin", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.nondegenerate_toBilin_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.SeparatingLeft.toBilin'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.separatingLeft_toBilin'_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.SeparatingLeft.toBilin", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.separatingLeft_toBilin_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.SeparatingRight.toBilin'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.separatingRight_toBilin'_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.SeparatingRight.toBilin", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.separatingRight_toBilin_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.nondegenerate_toMatrix'_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.Nondegenerate.toMatrix'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.nondegenerate_toMatrix_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.Nondegenerate.toMatrix", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.separatingLeft_toMatrix'_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.SeparatingLeft.toMatrix'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.separatingLeft_toMatrix_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.SeparatingLeft.toMatrix", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.separatingRight_toMatrix'_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.SeparatingRight.toMatrix'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.separatingRight_toMatrix_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.SeparatingRight.toMatrix", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.nondegenerate_toBilin'_iff_det_ne_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LinearMap.BilinForm.nondegenerate_toBilin'_of_det_ne_zero'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.nondegenerate_iff_det_ne_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LinearMap.BilinForm.nondegenerate_of_det_ne_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.Nondegenerate.ofSeparatingLeft", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": true, "tactics": ["obtain", "have", "have", "have", "rwa"], "tactic_count": 5}
{"name": "LinearMap.BilinForm.Nondegenerate.ofSeparatingRight", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.nondegenerate_iff_ker_eq_bot", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.BilinearForm", "is_tactic_proof": true, "tactics": ["refine", "rwa"], "tactic_count": 2}
{"name": "Matrix.BlockTriangular", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.BlockTriangular.submatrix", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.blockTriangular_reindex_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Block", "is_tactic_proof": true, "tactics": ["refine", "convert", "simp", "convert", "simp"], "tactic_count": 5}
{"name": "Matrix.BlockTriangular.transpose", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.blockTriangular_transpose_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.blockTriangular_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.BlockTriangular.neg", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.BlockTriangular.add", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.BlockTriangular.sub", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.BlockTriangular.add_iff_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.BlockTriangular.add_iff_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.BlockTriangular.sub_iff_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.BlockTriangular.sub_iff_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.BlockTriangular.map", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.BlockTriangular.comp", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.blockTriangular_diagonal", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.blockTriangular_blockDiagonal'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Block", "is_tactic_proof": true, "tactics": ["rintro", "apply"], "tactic_count": 2}
{"name": "Matrix.blockTriangular_blockDiagonal", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Block", "is_tactic_proof": true, "tactics": ["rintro", "rw", "exact"], "tactic_count": 3}
{"name": "Matrix.blockTriangular_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.blockTriangular_single", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Block", "is_tactic_proof": true, "tactics": ["intro", "apply", "rintro", "exact"], "tactic_count": 4}
{"name": "Matrix.blockTriangular_single'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.blockTriangular_transvection", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.blockTriangular_transvection'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.BlockTriangular.mul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Block", "is_tactic_proof": true, "tactics": ["intro", "apply", "intro", "by_cases", "simp_rw", "simp_rw"], "tactic_count": 6}
{"name": "Matrix.upper_two_blockTriangular", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Block", "is_tactic_proof": true, "tactics": ["rintro", "first", "simp"], "tactic_count": 3}
{"name": "Matrix.equiv_block_det", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Block", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "Matrix.det_toSquareBlock_id", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.det_toBlock", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Block", "is_tactic_proof": true, "tactics": ["rw", "rw", "congr", "generalize", "cases", "simp", "fromBlocks_apply₁₁,"], "tactic_count": 7}
{"name": "Matrix.twoBlockTriangular_det", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Block", "is_tactic_proof": true, "tactics": ["rw", "convert", "ext", "exact"], "tactic_count": 4}
{"name": "Matrix.twoBlockTriangular_det'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Block", "is_tactic_proof": true, "tactics": ["rw", "congr", "exact", "simpa"], "tactic_count": 4}
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{"name": "Matrix.BlockTriangular.det_fintype", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Block", "is_tactic_proof": true, "tactics": ["refine", "have", "exact"], "tactic_count": 3}
{"name": "Matrix.det_of_upperTriangular", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Block", "is_tactic_proof": true, "tactics": ["haveI", "simp_rw"], "tactic_count": 2}
{"name": "Matrix.det_of_lowerTriangular", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Block", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Matrix.matrixOfPolynomials_blockTriangular", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.det_matrixOfPolynomials", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Block", "is_tactic_proof": false, "tactics": ["rw", "convert", "rw"], "tactic_count": 3}
{"name": "Matrix.BlockTriangular.toBlock_inverse_mul_toBlock_eq_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Block", "is_tactic_proof": true, "tactics": ["let", "have", "rw", "have", "ext", "simpa", "simpa"], "tactic_count": 7}
{"name": "Matrix.BlockTriangular.inv_toBlock", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.BlockTriangular.invertibleToBlock", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.Block", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.toBlock_inverse_eq_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Block", "is_tactic_proof": true, "tactics": ["let", "let", "have", "rw", "rw", "exact", "have", "ext", "simpa", "have", "haveI", "have", "ext", "exact", "rw"], "tactic_count": 15}
{"name": "Matrix.blockTriangular_inv_of_blockTriangular", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Block", "is_tactic_proof": true, "tactics": ["suffices", "intro", "induction", "subst", "intro", "haveI", "let", "let", "let", "obtain", "have", "simp", "simp", "haveI", "have", "have", "convert", "convert", "have", "simp"], "tactic_count": 20}
{"name": "Matrix.charP", "kind": "instance", "module": "Mathlib.LinearAlgebra.Matrix.CharP", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.charmatrix", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.charmatrix_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.charmatrix_apply_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.charmatrix_apply_ne", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.Basic", "is_tactic_proof": true, "tactics": ["simp", "sub_eq_neg_self]"], "tactic_count": 2}
{"name": "Matrix.charmatrix_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.charmatrix_diagonal", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matrix.charmatrix_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.charmatrix_natCast", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.charmatrix_ofNat", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.charmatrix_transpose", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.matPolyEquiv_charmatrix", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp", "by_cases", "subst", "rw", "simp", "split_ifs", "rw", "split_ifs"], "tactic_count": 9}
{"name": "Matrix.charmatrix_reindex", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.Basic", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "all_goals"], "tactic_count": 3}
{"name": "Matrix.charmatrix_map", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.Basic", "is_tactic_proof": true, "tactics": ["ext", "by_cases"], "tactic_count": 2}
{"name": "Matrix.charmatrix_fromBlocks", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.Basic", "is_tactic_proof": true, "tactics": ["simp", "ext", "simp"], "tactic_count": 3}
{"name": "Matrix.charmatrix_blockTriangular_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Matrix.charpoly", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.eval_charpoly", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.Basic", "is_tactic_proof": true, "tactics": ["rw", "congr", "ext", "obtain"], "tactic_count": 4}
{"name": "Matrix.charpoly_isEmpty", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.charpoly_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.charpoly_diagonal", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.charpoly_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.charpoly_natCast", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.charpoly_ofNat", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.charpoly_transpose", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.charpoly_reindex", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.Basic", "is_tactic_proof": true, "tactics": ["unfold", "rw"], "tactic_count": 2}
{"name": "Matrix.charpoly_map", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matrix.charpoly_fromBlocks_zero₁₂", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.charpoly_fromBlocks_zero₂₁", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.charmatrix_toSquareBlock", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Matrix.BlockTriangular.charpoly", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.charpoly_of_upperTriangular", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.aeval_self_charpoly", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.Basic", "is_tactic_proof": true, "tactics": ["have", "apply_fun", "simp", "apply_fun", "rw", "rw", "exact"], "tactic_count": 7}
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{"name": "Matrix.charpoly_mul_comm_of_le", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matrix.charpoly_mul_comm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.charpoly_vecMulVec", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.Basic", "is_tactic_proof": true, "tactics": ["cases", "simp", "have", "rw", "simp"], "tactic_count": 5}
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{"name": "Matrix.charpoly_units_conj'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.charpoly_sub_scalar", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "congr", "by_cases", "ring"], "tactic_count": 4}
{"name": "Matrix.charmatrix_apply_natDegree", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.Coeff", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "Matrix.charmatrix_apply_natDegree_le", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.Coeff", "is_tactic_proof": true, "tactics": ["split_ifs"], "tactic_count": 1}
{"name": "Matrix.charpoly_sub_diagonal_degree_lt", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.Coeff", "is_tactic_proof": false, "tactics": ["rw", "add_comm]", "simp", "rw", "apply", "intro", "apply", "rw", "apply", "rw", "apply", "apply", "rw", "intros", "apply"], "tactic_count": 15}
{"name": "Matrix.charpoly_coeff_eq_prod_coeff_of_le", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.Coeff", "is_tactic_proof": true, "tactics": ["apply", "apply", "apply", "rw"], "tactic_count": 4}
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{"name": "Matrix.charpolyRev", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.Coeff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Matrix.coeff_charpolyRev_eq_neg_trace", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.Coeff", "is_tactic_proof": true, "tactics": ["nontriviality", "cases", "simp", "simp"], "tactic_count": 4}
{"name": "Matrix.isUnit_charpolyRev_of_isNilpotent", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.Coeff", "is_tactic_proof": true, "tactics": ["obtain", "replace", "convert", "rw", "apply", "rw", "exact"], "tactic_count": 7}
{"name": "Matrix.isNilpotent_trace_of_isNilpotent", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.Coeff", "is_tactic_proof": true, "tactics": ["cases", "simp", "suffices", "exact"], "tactic_count": 4}
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{"name": "Matrix.discr", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.Disc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.discr_of_card_eq_two", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.Disc", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
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{"name": "Matrix.mem_spectrum_of_isRoot_charpoly", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.Eigs", "is_tactic_proof": true, "tactics": ["simp_all"], "tactic_count": 1}
{"name": "Matrix.mem_spectrum_iff_isRoot_charpoly", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.Eigs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "PiToModule.fromMatrix", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiToModule.fromMatrix_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiToModule.fromMatrix_apply_single_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap", "is_tactic_proof": true, "tactics": ["rw", "simp_rw"], "tactic_count": 2}
{"name": "PiToModule.fromEnd", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiToModule.fromEnd_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiToModule.fromEnd_apply_single_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "Matrix.Represents", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.Represents.congr_fun", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Matrix.isRepresentation", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.isRepresentation.toEnd", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.isRepresentation.toEnd_represents", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.isRepresentation.eq_toEnd_of_represents", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.isRepresentation.toEnd_exists_mem_ideal", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap", "is_tactic_proof": false, "tactics": ["have", "rw", "exact", "choose", "let", "have", "rw", "dsimp", "intro", "specialize", "rwa", "exact"], "tactic_count": 12}
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{"name": "Matrix.minpoly_toLin'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.Minpoly", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.minpoly_toLin", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.Minpoly", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.isIntegral", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.Minpoly", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.minpoly_dvd_charpoly", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.Minpoly", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.minpoly_toMatrix'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.Minpoly", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "charpoly_leftMulMatrix", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.Minpoly", "is_tactic_proof": true, "tactics": ["cases", "apply", "apply", "rw", "refine", "rw", "contrapose"], "tactic_count": 7}
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{"name": "Matrix.charpoly.univ_map_eval₂Hom", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.Univ", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
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{"name": "Matrix.charpoly.univ_coeff_eval₂Hom", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.Univ", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matrix.charpoly.univ_monic", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.Univ", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.charpoly.univ_natDegree", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.Univ", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.charpoly.univ_coeff_card", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.Univ", "is_tactic_proof": false, "tactics": ["suffices", "rw", "rw", "exact"], "tactic_count": 4}
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{"name": "Matrix.circulant", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.Circulant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.circulant_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Circulant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.circulant_col_zero_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Circulant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.circulant_injective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Circulant", "is_tactic_proof": true, "tactics": ["intro", "ext", "rw"], "tactic_count": 3}
{"name": "Matrix.Fin.circulant_injective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Circulant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.circulant_inj", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Circulant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.Fin.circulant_inj", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Circulant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.transpose_circulant", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Circulant", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Matrix.conjTranspose_circulant", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Circulant", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Matrix.Fin.transpose_circulant", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Circulant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.Fin.conjTranspose_circulant", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Circulant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.map_circulant", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Circulant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.circulant_neg", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Circulant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.circulant_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Circulant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.circulant_add", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Circulant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.circulant_sub", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Circulant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Matrix.circulant_mul_comm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Circulant", "is_tactic_proof": true, "tactics": ["ext", "simp", "refine", "intro", "simp", "congr", "abel"], "tactic_count": 7}
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{"name": "Matrix.circulant_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Circulant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.circulant_single_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Circulant", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Matrix.circulant_single", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Circulant", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
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{"name": "Matrix.circulant_isSymm_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Circulant", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matrix.Fin.circulant_isSymm_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Circulant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.circulant_isSymm_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Circulant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.Fin.circulant_isSymm_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Circulant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.conjTranspose", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.ConjTranspose", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.term_ᴴ", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.ConjTranspose", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix._aux_Mathlib_LinearAlgebra_Matrix_ConjTranspose___macroRules_Matrix_term_ᴴ_1", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.ConjTranspose", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Matrix.diagonal_conjTranspose", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.ConjTranspose", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
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{"name": "Matrix.subLeft", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.Matrix.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.subRight", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.Matrix.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Matrix.subDownRight", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.Matrix.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.subUpLeft", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.Matrix.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.subDownLeft", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.Matrix.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.row", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Matrix.row_eq_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.col_eq_transpose", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Matrix.row_submatrix_eq_comp", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Matrix.col_submatrix_eq_comp", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Matrix.row_transpose", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Set.matrix", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_matrix", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.matrix_eq_pi", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Defs", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Matrix.transpose_mem_matrix_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.submatrix_mem_matrix", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Defs", "is_tactic_proof": true, "tactics": ["simp_all"], "tactic_count": 1}
{"name": "Matrix.submatrix_mem_matrix_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.LinearAlgebra.Matrix.Determinant.Basic.0.Matrix.termε_", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.Determinant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Matrix.detRowAlternating", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.Determinant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Matrix.det_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Determinant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Matrix.det_eq_detp_sub_detp", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Determinant.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "refine", "rw", "simp"], "tactic_count": 5}
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{"name": "Matrix.det_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Determinant.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matrix.det_isEmpty", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Determinant.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.coe_det_isEmpty", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Determinant.Basic", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
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{"name": "Matrix.det_eq_elem_of_subsingleton", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Determinant.Basic", "is_tactic_proof": true, "tactics": ["have", "convert"], "tactic_count": 2}
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{"name": "Matrix.detMonoidHom", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.Determinant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.coe_detMonoidHom", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Determinant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Matrix.det_submatrix_equiv_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Determinant.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply", "intro", "rw", "congr", "apply", "intro", "rw"], "tactic_count": 8}
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{"name": "Matrix.det_reindex_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Determinant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Matrix.det_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Determinant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Matrix.det_mul_row", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Determinant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AlgEquiv.map_det", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Determinant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.cast_det", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Determinant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Matrix.det_conjTranspose", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Determinant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.det_eq_zero_of_row_eq_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Determinant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Matrix.det_fin_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Determinant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.det_fin_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Determinant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Matrix.reindex_isTotallyUnimodular", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Determinant.TotallyUnimodular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.emptyRows_isTotallyUnimodular", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Determinant.TotallyUnimodular", "is_tactic_proof": true, "tactics": ["intro", "cases", "zero", "succ"], "tactic_count": 4}
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{"name": "dotProduct_nonneg_of_nonneg", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.DotProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dotProduct_le_dotProduct_of_nonneg_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.DotProduct", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
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{"name": "dotProduct_self_eq_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.DotProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dotProduct_star_self_nonneg", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.DotProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "dotProduct_star_self_eq_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.DotProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dotProduct_self_star_eq_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.DotProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "FixedDetMatrices.reduceStep", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.FixedDetMatrices", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Matrix.GeneralLinearGroup", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Matrix.discr_conj", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.FinTwo", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "Matrix.isParabolic_iff_of_upperTriangular", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.FinTwo", "is_tactic_proof": true, "tactics": ["rw", "have", "suffices", "grind", "have", "constructor", "rintro", "simp", "intro", "use", "ext", "fin_cases", "tauto"], "tactic_count": 13}
{"name": "Matrix.sub_scalar_sq_eq_discr", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.FinTwo", "is_tactic_proof": false, "tactics": ["simp", "ext", "fin_cases", "simp", "field"], "tactic_count": 5}
{"name": "Matrix.parabolicEigenvalue", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.FinTwo", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.IsParabolic.sub_eigenvalue_sq_eq_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.FinTwo", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "Matrix.IsHyperbolic", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.FinTwo", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.IsElliptic", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.FinTwo", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.isHyperbolic_conj_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.FinTwo", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.isHyperbolic_conj'_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.FinTwo", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Matrix.isElliptic_conj_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.FinTwo", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.isElliptic_conj'_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.FinTwo", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Matrix.GeneralLinearGroup.upperRightHom", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.FinTwo", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.GeneralLinearGroup.injective_upperRightHom", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.FinTwo", "is_tactic_proof": true, "tactics": ["refine", "simp"], "tactic_count": 2}
{"name": "Matrix.GeneralLinearGroup.IsParabolic", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.FinTwo", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.GeneralLinearGroup.isParabolic_conj_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.FinTwo", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.GeneralLinearGroup.isParabolic_conj_iff'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.FinTwo", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.GeneralLinearGroup.IsElliptic", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.FinTwo", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.GeneralLinearGroup.IsHyperbolic", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.FinTwo", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.GeneralLinearGroup.fixpointPolynomial", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.FinTwo", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.GeneralLinearGroup.fixpointPolynomial_eq_zero_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.FinTwo", "is_tactic_proof": true, "tactics": ["rw", "constructor", "refine", "have", "have", "have", "ext", "fin_cases", "rintro", "simp"], "tactic_count": 10}
{"name": "Matrix.GeneralLinearGroup.parabolicEigenvalue_ne_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.FinTwo", "is_tactic_proof": true, "tactics": ["have", "rw", "show", "exact"], "tactic_count": 4}
{"name": "Matrix.GeneralLinearGroup.IsParabolic.pow", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.FinTwo", "is_tactic_proof": true, "tactics": ["rw", "obtain", "refine", "rw", "rw", "induction", "base", "succ", "simp", "simp", "rw", "ring_nf", "suffices", "refine", "rw", "rw", "rw"], "tactic_count": 17}
{"name": "Matrix.GeneralLinearGroup.isParabolic_iff_of_upperTriangular", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.FinTwo", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.GeneralLinearGroup.isParabolic_iff_of_upperTriangular_of_det", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.FinTwo", "is_tactic_proof": true, "tactics": ["rw", "constructor", "rintro", "have", "have", "simp", "exact", "apply", "refine", "rw", "simp_all", "refine", "rw", "simp_all", "rintro"], "tactic_count": 15}
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{"name": "det_ne_zero_of_sum_row_lt_diag", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Gershgorin", "is_tactic_proof": true, "tactics": ["contrapose", "suffices", "exact", "refine", "rw", "exact"], "tactic_count": 6}
{"name": "det_ne_zero_of_sum_col_lt_diag", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Gershgorin", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Matrix.hadamard", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.Hadamard", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.hadamard_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Hadamard", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.term_⊙_", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.Hadamard", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Matrix.hadamard_comm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Hadamard", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.hadamard_assoc", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Hadamard", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.hadamard_add", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Hadamard", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.add_hadamard", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Hadamard", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.smul_hadamard", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Hadamard", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.hadamard_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Hadamard", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.hadamard_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Hadamard", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.zero_hadamard", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Hadamard", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.hadamard_diagonal", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Hadamard", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Matrix.diagonal_hadamard", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Hadamard", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Matrix.diagonal_hadamard_diagonal", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Hadamard", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.diagonal_hadamard_eq_diagonal_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Hadamard", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.hadamard_diagonal_eq_diagonal_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Hadamard", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.hadamard_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Hadamard", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.one_hadamard", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Hadamard", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.one_hadamard_eq_diagonal_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Hadamard", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
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{"name": "Matrix.one_hadamard_eq_one_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Hadamard", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.hadamard_one_eq_one_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Hadamard", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.hadamard_of_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Hadamard", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Matrix.of_one_hadamard", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Hadamard", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Matrix.hadamard_self_eq_self_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Hadamard", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.single_hadamard_single_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Hadamard", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.single_hadamard_single_of_ne", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Hadamard", "is_tactic_proof": true, "tactics": ["rw", "cases"], "tactic_count": 2}
{"name": "Matrix.sum_hadamard_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Hadamard", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.dotProduct_vecMul_hadamard", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Hadamard", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Matrix.IsHermitian", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.Hermitian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.instDecidableIsHermitianOfEqConjTranspose", "kind": "instance", "module": "Mathlib.LinearAlgebra.Matrix.Hermitian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.IsHermitian.eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Hermitian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.isHermitian_iff_isSelfAdjoint", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Hermitian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.IsHermitian.ext", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Hermitian", "is_tactic_proof": true, "tactics": ["intro"], "tactic_count": 1}
{"name": "Matrix.IsHermitian.apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Hermitian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.IsHermitian.ext_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Hermitian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.IsHermitian.map", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Hermitian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.IsHermitian.of_subsingleton", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Hermitian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.IsHermitian.transpose", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Hermitian", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Matrix.isHermitian_transpose_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Hermitian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.IsHermitian.conjTranspose", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Hermitian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.IsHermitian.submatrix", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Hermitian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.isHermitian_submatrix_equiv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Hermitian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.isHermitian_conjTranspose_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Hermitian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.IsHermitian.fromBlocks", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Hermitian", "is_tactic_proof": true, "tactics": ["have", "unfold", "rw"], "tactic_count": 3}
{"name": "Matrix.isHermitian_fromBlocks_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Hermitian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.isHermitian_diagonal_of_self_adjoint", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Hermitian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.isHermitian_diagonal_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Hermitian", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.isHermitian_diagonal", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Hermitian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.isHermitian_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Hermitian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.IsHermitian.add", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Hermitian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.isHermitian_add_transpose_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Hermitian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.isHermitian_transpose_add_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Hermitian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.IsHermitian.neg", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Hermitian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.IsHermitian.sub", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Hermitian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.isHermitian_mul_conjTranspose_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Hermitian", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matrix.isHermitian_conjTranspose_mul_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Hermitian", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matrix.isHermitian_conjTranspose_mul_mul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Hermitian", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.isHermitian_mul_mul_conjTranspose", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Hermitian", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.IsHermitian.commute_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Hermitian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.isHermitian_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Hermitian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.isHermitian_natCast", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Hermitian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.IsHermitian.pow", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Hermitian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.isHermitian_intCast", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Hermitian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.IsHermitian.inv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Hermitian", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.isHermitian_inv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Hermitian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.IsHermitian.adjugate", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Hermitian", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.IsHermitian.zpow", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Hermitian", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matrix.term_⊕ᵥ_", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.Hermitian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix._aux_Mathlib_LinearAlgebra_Matrix_Hermitian___macroRules_Matrix_term_⊕ᵥ__1", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.Hermitian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Matrix.schur_complement_eq₁₁", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Hermitian", "is_tactic_proof": false, "tactics": ["simp", "conjTranspose_nonsing_inv,", "abel"], "tactic_count": 3}
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{"name": "Matrix.IsHermitian.fromBlocks₂₂", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Hermitian", "is_tactic_proof": false, "tactics": ["rw", "convert"], "tactic_count": 2}
{"name": "Ideal.matrix", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "RingCon.matrix", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.matrix_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "RingCon.matrix_strictMono_of_nonempty", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.matrix_bot", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "RingCon.ofMatrix", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.ofMatrix_rel", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.ofMatrix_matrix", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Ideal", "is_tactic_proof": true, "tactics": ["ext", "classical", "constructor", "intro", "inhabit", "simpa", "intro", "rwa"], "tactic_count": 8}
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{"name": "RingCon.coe_ofMatrix_eq_relationMap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Ideal", "is_tactic_proof": true, "tactics": ["ext", "constructor", "intro", "refine", "simp", "rintro", "simpa"], "tactic_count": 7}
{"name": "TwoSidedIdeal.matrix", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.mem_matrix", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.matrix_monotone", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.matrix_strictMono_of_nonempty", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "TwoSidedIdeal.matrix_top", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.equivMatrix", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.coe_equivMatrix_symm_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Ideal", "is_tactic_proof": true, "tactics": ["ext", "constructor", "intro", "exact", "rintro", "rw", "exact"], "tactic_count": 7}
{"name": "TwoSidedIdeal.orderIsoMatrix", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.asIdeal_matrix", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Ideal", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
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{"name": "Matrix.map_mul_natCast", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Integer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.map_mul_intCast", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Integer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.map_mul_ratCast", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Integer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.den", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.Integer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.num", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.Integer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.den_ne_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Integer", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.num_eq_zero_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Integer", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.den_dvd_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Integer", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "instIsStablyFiniteRingOfOrzechProperty", "kind": "instance", "module": "Mathlib.LinearAlgebra.Matrix.InvariantBasisNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instRankConditionOfIsStablyFiniteRingOfNontrivial", "kind": "instance", "module": "Mathlib.LinearAlgebra.Matrix.InvariantBasisNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "rankCondition_iff_le_of_comp_eq_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.InvariantBasisNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "rankCondition_iff_matrix", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.InvariantBasisNumber", "is_tactic_proof": true, "tactics": ["simp_rw", "toLinearMapRight'.injective.eq_iff]"], "tactic_count": 2}
{"name": "invariantBasisNumber_iff_matrix", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.InvariantBasisNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.rankCondition_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.InvariantBasisNumber", "is_tactic_proof": false, "tactics": ["simp_rw", "congr", "refine", "refine", "rw", "congrm", "ext", "simp"], "tactic_count": 8}
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{"name": "instInvariantBasisNumberMulOpposite", "kind": "instance", "module": "Mathlib.LinearAlgebra.Matrix.InvariantBasisNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "rankCondition_of_nontrivial_of_commSemiring", "kind": "instance", "module": "Mathlib.LinearAlgebra.Matrix.InvariantBasisNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.toQuiver", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.Irreducible.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.IsIrreducible.exists_pos", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Irreducible.Defs", "is_tactic_proof": true, "tactics": ["letI", "by_contra", "have", "obtain", "obtain", "have", "have", "have", "obtain", "obtain", "exact"], "tactic_count": 11}
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{"name": "Matrix.IsPrimitive.isIrreducible", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Irreducible.Defs", "is_tactic_proof": true, "tactics": ["obtain", "rw", "aesop"], "tactic_count": 3}
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{"name": "Matrix.IsDiag", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.IsDiag", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.isDiag_diagonal", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.IsDiag", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.IsDiag.diagonal_diag", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.IsDiag", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.isDiag_iff_diagonal_diag", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.IsDiag", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.isDiag_of_subsingleton", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.IsDiag", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.isDiag_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.IsDiag", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.isDiag_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.IsDiag", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Matrix.IsDiag.add", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.IsDiag", "is_tactic_proof": true, "tactics": ["intro", "simp"], "tactic_count": 2}
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{"name": "Matrix.IsDiag.smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.IsDiag", "is_tactic_proof": true, "tactics": ["intro", "simp"], "tactic_count": 2}
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{"name": "Matrix.IsDiag.transpose", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.IsDiag", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.isDiag_transpose_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.IsDiag", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.IsDiag.conjTranspose", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.IsDiag", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.isDiag_conjTranspose_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.IsDiag", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.IsDiag.submatrix", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.IsDiag", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.IsDiag.kronecker", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.IsDiag", "is_tactic_proof": true, "tactics": ["rintro", "simp", "rcases", "simp", "simp"], "tactic_count": 5}
{"name": "Matrix.IsDiag.isSymm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.IsDiag", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "simp"], "tactic_count": 3}
{"name": "Matrix.IsDiag.fromBlocks", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.IsDiag", "is_tactic_proof": true, "tactics": ["rintro", "exact", "rfl", "rfl", "exact"], "tactic_count": 5}
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{"name": "Matrix.transpose_mul_self_isDiag_iff_hasOrthogonalCols", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.IsDiag", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Matrix.kroneckerMap_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Kronecker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.kroneckerMap_transpose", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Kronecker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.kroneckerMap_map_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Kronecker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.kroneckerMap_map_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Kronecker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.kroneckerMap_map", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Kronecker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.kroneckerMap_zero_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Kronecker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Matrix.nonsing_inv_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matrix.invOf_eq_nonsing_inv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": true, "tactics": ["letI", "rw"], "tactic_count": 2}
{"name": "Matrix.coe_units_inv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": true, "tactics": ["letI", "rw"], "tactic_count": 2}
{"name": "Matrix.nonsing_inv_eq_ringInverse", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": true, "tactics": ["by_cases", "cases", "rw", "have", "rw"], "tactic_count": 5}
{"name": "Matrix.transpose_nonsing_inv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matrix.conjTranspose_nonsing_inv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matrix.mul_nonsing_inv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": true, "tactics": ["cases", "rw"], "tactic_count": 2}
{"name": "Matrix.nonsing_inv_mul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": true, "tactics": ["cases", "rw"], "tactic_count": 2}
{"name": "Matrix.instInvertibleInv", "kind": "instance", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "Matrix.inv_inv_of_invertible", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.mul_nonsing_inv_cancel_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.mul_nonsing_inv_cancel_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "Matrix.mul_inv_of_invertible", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.inv_mul_of_invertible", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.mul_inv_cancel_right_of_invertible", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.mul_inv_cancel_left_of_invertible", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.inv_mul_cancel_right_of_invertible", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.inv_mul_cancel_left_of_invertible", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.inv_mul_eq_iff_eq_mul_of_invertible", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.mul_inv_eq_iff_eq_mul_of_invertible", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.inv_mulVec_eq_vec", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matrix.mul_right_injective_of_invertible", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.mul_left_injective_of_invertible", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.mul_right_inj_of_invertible", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.mul_left_inj_of_invertible", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.IsSymm.inv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.mul_left_injective_of_inv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.mul_right_injective_of_inv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.vecMul_surjective_iff_exists_left_inverse", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": true, "tactics": ["cases", "refine", "choose", "refine", "rw", "rfl"], "tactic_count": 6}
{"name": "Matrix.mulVec_surjective_iff_exists_right_inverse", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": true, "tactics": ["cases", "refine", "choose", "refine", "rw", "rfl"], "tactic_count": 6}
{"name": "Matrix.vecMul_surjective_iff_isUnit", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matrix.mulVec_surjective_iff_isUnit", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "Matrix.linearIndependent_rows_iff_isUnit", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": true, "tactics": ["rw", "coe_vecMulLinear]"], "tactic_count": 2}
{"name": "Matrix.linearIndependent_cols_iff_isUnit", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matrix.vecMul_surjective_of_invertible", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.mulVec_surjective_of_invertible", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.vecMul_injective_of_invertible", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.mulVec_injective_of_invertible", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.linearIndependent_rows_of_invertible", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.linearIndependent_cols_of_invertible", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.nonsing_inv_cancel_or_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "exact"], "tactic_count": 3}
{"name": "Matrix.det_nonsing_inv_mul_det", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matrix.det_nonsing_inv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": true, "tactics": ["by_cases", "cases", "letI", "rw", "cases", "rw", "rw"], "tactic_count": 7}
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{"name": "Matrix.nonsing_inv_nonsing_inv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.isUnit_nonsing_inv_det_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matrix.isUnit_nonsing_inv_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Matrix.invertibleOfIsUnitDet", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.nonsingInvUnit", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.unitOfDetInvertible_eq_nonsingInvUnit", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "Matrix.inv_eq_left_inv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.inv_eq_right_inv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.left_inv_eq_left_inv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matrix.right_inv_eq_right_inv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matrix.right_inv_eq_left_inv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matrix.inv_inj", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": true, "tactics": ["refine", "rw", "refine", "rwa"], "tactic_count": 4}
{"name": "Matrix.inv_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rcases", "rw", "subsingleton", "have", "refine", "simp"], "tactic_count": 8}
{"name": "Matrix.instInvOneClass", "kind": "instance", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.inv_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.inv_smul'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.inv_adjugate", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "Matrix.diagonalInvertible", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.invOf_diagonal_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Matrix.invertibleOfDiagonalInvertible", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.diagonalInvertibleEquivInvertible", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.isUnit_diagonal", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.inv_diagonal", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": true, "tactics": ["rw", "by_cases", "have", "cases", "cases", "rw", "have", "rw"], "tactic_count": 8}
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{"name": "Matrix.add_mul_mul_inv_eq_sub", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "obtain", "simp", "letI", "simp", "apply"], "tactic_count": 7}
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{"name": "Matrix.inv_add_inv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Matrix.inv_sub_inv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Matrix.mul_inv_rev", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": true, "tactics": ["simp", "rw"], "tactic_count": 2}
{"name": "Matrix.list_prod_inv_reverse", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.det_smul_inv_mulVec_eq_cramer", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matrix.det_smul_inv_vecMul_eq_cramer_transpose", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matrix.submatrixEquivInvertible", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.invertibleOfSubmatrixEquivInvertible", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.invOf_submatrix_equiv_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Matrix.submatrixEquivInvertibleEquivInvertible", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.isUnit_submatrix_equiv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.inv_submatrix_equiv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": true, "tactics": ["by_cases", "cases", "letI", "rw", "have", "simp_rw"], "tactic_count": 6}
{"name": "Matrix.inv_reindex", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.inv_kronecker", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": true, "tactics": ["by_cases", "swap", "cases", "subsingleton", "have", "refine", "rw", "exact", "rw", "by_cases", "cases", "subsingleton", "have", "refine", "rw", "exact", "rw", "apply", "rw"], "tactic_count": 19}
{"name": "Matrix.det_conj", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matrix.det_conj'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matrix.trace_conj", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matrix.trace_conj'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.NonsingularInverse", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matrix.mkLiteralQ", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.Notation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.toExpr", "kind": "instance", "module": "Mathlib.LinearAlgebra.Matrix.Notation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.matrixNotation", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.Notation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.matrixNotationRx0", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.Notation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.matrixNotation0xC", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.Notation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix._aux_Mathlib_LinearAlgebra_Matrix_Notation___macroRules_Matrix_matrixNotation_1", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.Notation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Matrix.delabMatrixNotation", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.Notation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.repr", "kind": "instance", "module": "Mathlib.LinearAlgebra.Matrix.Notation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.cons_val'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Notation", "is_tactic_proof": true, "tactics": ["refine"], "tactic_count": 1}
{"name": "Matrix.head_val'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Notation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.tail_val'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Notation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.dotProduct_of_isEmpty", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Notation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.dotProduct_empty", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Notation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.cons_dotProduct", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Notation", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "Matrix.mul_val_succ", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Notation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Matrix.empty_vecMulVec", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Notation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.vecMulVec_empty", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Notation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.cons_vecMulVec", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Notation", "is_tactic_proof": true, "tactics": ["ext", "refine"], "tactic_count": 2}
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{"name": "Matrix.smul_mat_empty", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Notation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.submatrix_empty", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Notation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.submatrix_cons_row", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Notation", "is_tactic_proof": true, "tactics": ["ext", "refine"], "tactic_count": 2}
{"name": "Matrix.submatrix_updateRow_succAbove", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Notation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.submatrix_updateCol_succAbove", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Notation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.one_fin_two", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Notation", "is_tactic_proof": true, "tactics": ["ext", "fin_cases"], "tactic_count": 2}
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{"name": "Matrix.ofNat_fin_two", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Notation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.ofNat_fin_three", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Notation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.eta_fin_two", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Notation", "is_tactic_proof": true, "tactics": ["ext", "fin_cases"], "tactic_count": 2}
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{"name": "Matrix.vec2_dotProduct'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Notation", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.vec2_dotProduct", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Notation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Matrix.HasOrthogonalRows", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.Orthogonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.HasOrthogonalCols", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.Orthogonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.transpose_hasOrthogonalRows_iff_hasOrthogonalCols", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Orthogonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Matrix.permanent", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.Permanent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Equiv.Perm.permMatrix", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.Matrix.Permutation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.permMatrix_refl", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Permutation", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "Matrix.trace_permutation", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Permutation", "is_tactic_proof": true, "tactics": ["delta", "simp"], "tactic_count": 2}
{"name": "Matrix.permMatrix_mulVec", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Permutation", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Matrix.vecMul_permMatrix", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Permutation", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
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{"name": "Matrix.permMatrixHom", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.Permutation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.permMatrix_l2_opNorm_le", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Permutation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.permMatrix_l2_opNorm_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Permutation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natDegree_det_X_add_C_le", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Polynomial", "is_tactic_proof": true, "tactics": ["rw", "refine", "refine", "simp", "intro", "calc", "natDegree", "natDegree", "rcases", "rw", "rw", "dsimp", "compute_degree"], "tactic_count": 13}
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{"name": "Matrix.PosSemidef.diagonal", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.PosDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Matrix.PosSemidef.isHermitian", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.PosDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.PosSemidef.submatrix", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.PosDef", "is_tactic_proof": true, "tactics": ["refine", "simpa"], "tactic_count": 2}
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{"name": "Matrix.PosSemidef.conjTranspose", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.PosDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.posSemidef_conjTranspose_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.PosDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.PosSemidef.add", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.PosDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Matrix.PosSemidef.natCast", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.PosDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.PosSemidef.ofNat", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.PosDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.PosSemidef.intCast", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.PosDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.posSemidef_intCast_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.PosDef", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.PosSemidef.diag_nonneg", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.PosDef", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Matrix.posSemidef_submatrix_equiv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.PosDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Matrix.PosDef.isHermitian", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.PosDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.PosDef.posSemidef", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.PosDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Matrix.PosDef.ofNat", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.PosDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.PosDef.intCast", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.PosDef", "is_tactic_proof": true, "tactics": ["nontriviality", "exact"], "tactic_count": 2}
{"name": "Matrix.posDef_intCast_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.PosDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.PosDef.add_posSemidef", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.PosDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.PosDef.posSemidef_add", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.PosDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.PosDef.add", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.PosDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.posDef_sum", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.PosDef", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "insert", "rw", "by_cases", "simp_all", "exact"], "tactic_count": 8}
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{"name": "Matrix.PosDef.conjTranspose", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.PosDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.posDef_conjTranspose_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.PosDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.PosDef.diag_pos", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.PosDef", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Matrix.posSemidef_iff_dotProduct_mulVec", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.PosDef", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.PosSemidef.dotProduct_mulVec_nonneg", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.PosDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.PosSemidef.of_dotProduct_mulVec_nonneg", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.PosDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.PosSemidef.conjTranspose_mul_mul_same", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.PosDef", "is_tactic_proof": true, "tactics": ["have", "refine", "simpa"], "tactic_count": 3}
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{"name": "Matrix.PosSemidef.pow", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.PosDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.PosSemidef.inv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.PosDef", "is_tactic_proof": true, "tactics": ["by_cases", "have", "rwa", "rw", "exact"], "tactic_count": 5}
{"name": "Matrix.PosSemidef.zpow", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.PosDef", "is_tactic_proof": true, "tactics": ["obtain", "simpa", "simpa"], "tactic_count": 3}
{"name": "Matrix.PosSemidef.trace_nonneg", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.PosDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.posSemidef_conjTranspose_mul_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.PosDef", "is_tactic_proof": true, "tactics": ["have", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "Matrix.posSemidef_self_mul_conjTranspose", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.PosDef", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Matrix.trace_conjTranspose_mul_self_eq_zero_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.PosDef", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matrix.trace_mul_conjTranspose_self_eq_zero_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.PosDef", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Matrix.IsUnit.posSemidef_star_left_conjugate_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.PosDef", "is_tactic_proof": true, "tactics": ["refine", "lift", "have", "rwa", "one_mul]"], "tactic_count": 5}
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{"name": "Matrix.posSemidef_vecMulVec_self_star", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.PosDef", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.posSemidef_vecMulVec_star_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.PosDef", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.posDef_iff_dotProduct_mulVec", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.PosDef", "is_tactic_proof": false, "tactics": ["have", "simp", "mul_assoc,"], "tactic_count": 3}
{"name": "Matrix.PosDef.dotProduct_mulVec_pos", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.PosDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.PosDef.of_dotProduct_mulVec_pos", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.PosDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.PosDef.conjTranspose_mul_mul_same", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.PosDef", "is_tactic_proof": true, "tactics": ["refine", "have", "simpa"], "tactic_count": 3}
{"name": "Matrix.PosDef.mul_mul_conjTranspose_same", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.PosDef", "is_tactic_proof": true, "tactics": ["replace", "simp_rw", "simpa"], "tactic_count": 3}
{"name": "Matrix.PosDef.conjTranspose_mul_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.PosDef", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Matrix.PosDef.mul_conjTranspose_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.PosDef", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Matrix.PosDef.of_toQuadraticForm'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.PosDef", "is_tactic_proof": true, "tactics": ["refine", "simp", "apply"], "tactic_count": 3}
{"name": "Matrix.PosDef.toQuadraticForm'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.PosDef", "is_tactic_proof": true, "tactics": ["intro", "simp", "apply"], "tactic_count": 3}
{"name": "Matrix.PosDef.trace_pos", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.PosDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.PosDef.isUnit", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.PosDef", "is_tactic_proof": true, "tactics": ["by_contra", "obtain", "obtain", "exact", "simpa"], "tactic_count": 5}
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{"name": "Matrix.posDef_inv_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.PosDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.IsUnit.posDef_star_left_conjugate_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.PosDef", "is_tactic_proof": true, "tactics": ["refine", "lift", "have", "rwa", "one_mul]"], "tactic_count": 5}
{"name": "Matrix.IsUnit.posDef_star_right_conjugate_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.PosDef", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Matrix.PosDef.fromBlocks₁₁", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.PosDef", "is_tactic_proof": true, "tactics": ["have", "rw", "constructor", "refine", "have", "rwa", "dotProduct_mulVec]", "refine", "rw", "apply", "rw", "apply", "rw", "apply"], "tactic_count": 14}
{"name": "Matrix.PosDef.fromBlocks₂₂", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.PosDef", "is_tactic_proof": false, "tactics": ["rw", "convert"], "tactic_count": 2}
{"name": "QuadraticForm.posDef_of_toMatrix'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.PosDef", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "QuadraticForm.posDef_toMatrix'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.PosDef", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Matrix.ProjectiveSpecialLinearGroup", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.Matrix.ProjectiveSpecialLinearGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MatrixGroups.termPSL(_,_)", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.ProjectiveSpecialLinearGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MatrixGroups._aux_Mathlib_LinearAlgebra_Matrix_ProjectiveSpecialLinearGroup___macroRules_MatrixGroups_termPSL(_,_)_1", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.ProjectiveSpecialLinearGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MatrixGroups._aux_Mathlib_LinearAlgebra_Matrix_ProjectiveSpecialLinearGroup___unexpand_Matrix_ProjectiveSpecialLinearGroup_1", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.ProjectiveSpecialLinearGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.cRank", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.Rank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.cRank_subsingleton", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Rank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.cRank_toNat_eq_finrank", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Rank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.lift_cRank_submatrix_le", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Rank", "is_tactic_proof": false, "tactics": ["have", "refine", "let", "have", "rw", "aesop", "rw", "have", "simp_rw", "exact"], "tactic_count": 10}
{"name": "Matrix.cRank_submatrix_le", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Rank", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Matrix.cRank_le_card_height", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Rank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.cRank_le_card_width", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Rank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.eRank", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.Rank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.eRank_subsingleton", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Rank", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.eRank_toNat_eq_finrank", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Rank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.eRank_submatrix_le", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Rank", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Matrix.eRank_le_card_width", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Rank", "is_tactic_proof": true, "tactics": ["wlog", "simp", "have", "rw", "exact"], "tactic_count": 5}
{"name": "Matrix.eRank_le_card_height", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Rank", "is_tactic_proof": true, "tactics": ["classical", "wlog", "simp", "have", "rw", "exact"], "tactic_count": 6}
{"name": "Matrix.rank", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.Rank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.rank_subsingleton", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Rank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.cRank_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Rank", "is_tactic_proof": false, "tactics": ["have", "convert", "simp", "rw"], "tactic_count": 4}
{"name": "Matrix.eRank_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Rank", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matrix.rank_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Rank", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matrix.rank_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Rank", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matrix.cRank_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Rank", "is_tactic_proof": true, "tactics": ["obtain", "rw", "rw"], "tactic_count": 3}
{"name": "Matrix.eRank_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Rank", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.rank_le_card_width", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Rank", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "Matrix.rank_le_width", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Rank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.rank_mul_le_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Rank", "is_tactic_proof": true, "tactics": ["nontriviality", "rw", "exact"], "tactic_count": 3}
{"name": "Matrix.rank_mul_le_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Rank", "is_tactic_proof": true, "tactics": ["nontriviality", "rw", "exact"], "tactic_count": 3}
{"name": "Matrix.rank_mul_le", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Rank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.rank_vecMulVec_le", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Rank", "is_tactic_proof": true, "tactics": ["rw", "refine", "nontriviality", "exact"], "tactic_count": 4}
{"name": "Matrix.rank_unit", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Rank", "is_tactic_proof": true, "tactics": ["apply", "have", "rwa"], "tactic_count": 3}
{"name": "Matrix.rank_of_isUnit", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Rank", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Matrix.rank_mul_eq_left_of_isUnit_det", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Rank", "is_tactic_proof": false, "tactics": ["suffices", "rw", "intro", "exact"], "tactic_count": 4}
{"name": "Matrix.rank_mul_eq_right_of_isUnit_det", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Rank", "is_tactic_proof": true, "tactics": ["let", "replace", "have", "rw"], "tactic_count": 4}
{"name": "Matrix.rank_submatrix_le", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Rank", "is_tactic_proof": false, "tactics": ["rw", "show", "exact"], "tactic_count": 3}
{"name": "Matrix.rank_reindex", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Rank", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matrix.rank_submatrix", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Rank", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Matrix.lift_cRank_submatrix", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Rank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.cRank_submatrix", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Rank", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Matrix.lift_cRank_reindex", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Rank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.cRank_reindex", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Rank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.eRank_submatrix", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Rank", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Matrix.eRank_reindex", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Rank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.rank_eq_finrank_range_toLin", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Rank", "is_tactic_proof": true, "tactics": ["cases", "let", "let", "refine", "rw", "congr", "apply", "rintro", "apply", "have", "have", "rw", "rw", "simp", "toLin_self,"], "tactic_count": 15}
{"name": "Matrix.rank_le_card_height", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Rank", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "Matrix.rank_le_height", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Rank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.rank_eq_finrank_span_cols", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Rank", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matrix.cRank_toNat_eq_rank", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Rank", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matrix.eRank_toNat_eq_rank", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Rank", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matrix.rank_diagonal", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Rank", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matrix.cRank_diagonal", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Rank", "is_tactic_proof": true, "tactics": ["classical", "set", "have", "have", "convert", "ext", "simp", "have", "suffices", "simpa", "simp_rw", "simp", "rw"], "tactic_count": 13}
{"name": "Matrix.eRank_diagonal", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Rank", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.ker_mulVecLin_conjTranspose_mul_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Rank", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Matrix.rank_conjTranspose_mul_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Rank", "is_tactic_proof": true, "tactics": ["dsimp", "refine", "dsimp", "trans", "finrank", "finrank", "rw", "simp"], "tactic_count": 8}
{"name": "Matrix.rank_conjTranspose", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Rank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.rank_self_mul_conjTranspose", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Rank", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Matrix.ker_mulVecLin_transpose_mul_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Rank", "is_tactic_proof": true, "tactics": ["ext", "simp", "constructor", "intro", "replace", "rwa", "intro", "rw"], "tactic_count": 8}
{"name": "Matrix.rank_transpose_mul_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Rank", "is_tactic_proof": true, "tactics": ["dsimp", "refine", "dsimp", "trans", "finrank", "finrank", "rw", "simp"], "tactic_count": 8}
{"name": "Matrix.rank_transpose", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Rank", "is_tactic_proof": true, "tactics": ["classical", "rw"], "tactic_count": 2}
{"name": "Matrix.rank_self_mul_transpose", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Rank", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Matrix.rank_eq_finrank_span_row", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Rank", "is_tactic_proof": true, "tactics": ["cases", "rw"], "tactic_count": 2}
{"name": "LinearIndependent.rank_matrix", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Rank", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matrix.rank_add_rank_le_card_of_mul_eq_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Rank", "is_tactic_proof": true, "tactics": ["classical", "let", "let", "let", "rw", "add_le_add_iff_left]", "apply", "rw"], "tactic_count": 8}
{"name": "Matrix.rank_vecMulVec", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Rank", "is_tactic_proof": true, "tactics": ["nontriviality", "rw", "refine", "refine", "rw"], "tactic_count": 5}
{"name": "Matrix.reindexLinearEquiv", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.Reindex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.reindexLinearEquiv_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Reindex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.reindexLinearEquiv_symm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Reindex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.reindexLinearEquiv_refl_refl", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Reindex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.reindexLinearEquiv_trans", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Reindex", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "Matrix.reindexLinearEquiv_comp", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Reindex", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Matrix.reindexLinearEquiv_comp_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Reindex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.reindexLinearEquiv_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Reindex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.reindexLinearEquiv_mul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Reindex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.mul_reindexLinearEquiv_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Reindex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.reindexAlgEquiv", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.Reindex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.reindexAlgEquiv_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Reindex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.reindexAlgEquiv_symm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Reindex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.reindexAlgEquiv_refl", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Reindex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.reindexAlgEquiv_mul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Reindex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.det_reindexLinearEquiv_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Reindex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.det_reindexAlgEquiv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Reindex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.replicateCol", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.replicateCol_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.replicateRow", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.replicateRow_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.vecMulVec_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Matrix.one_vecMulVec", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Matrix.replicateCol_injective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": true, "tactics": ["inhabit", "exact"], "tactic_count": 2}
{"name": "Matrix.replicateCol_inj", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.replicateCol_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.replicateCol_eq_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.replicateCol_add", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "Matrix.replicateCol_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "Matrix.replicateRow_injective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": true, "tactics": ["inhabit", "exact"], "tactic_count": 2}
{"name": "Matrix.replicateRow_inj", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.replicateRow_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.replicateRow_eq_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.replicateRow_add", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "Matrix.replicateRow_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "Matrix.transpose_replicateCol", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "Matrix.transpose_replicateRow", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "Matrix.conjTranspose_replicateCol", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "Matrix.conjTranspose_replicateRow", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "Matrix.replicateRow_vecMul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "Matrix.replicateCol_vecMul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "Matrix.replicateCol_mulVec", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "Matrix.replicateRow_mulVec", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "Matrix.replicateRow_mulVec_eq_const", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.mulVec_replicateCol_eq_const", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.replicateRow_mul_replicateCol", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.replicateRow_mul_replicateCol_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.diag_replicateCol_mul_replicateRow", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Matrix.vecMulVec_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Matrix.updateRow", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.updateCol", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.updateRow_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.updateCol_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.updateRow_ne", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.updateCol_ne", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.updateRow_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "rw"], "tactic_count": 3}
{"name": "Matrix.updateCol_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "rw"], "tactic_count": 3}
{"name": "Matrix.updateCol_subsingleton", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Matrix.updateRow_subsingleton", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Matrix.map_updateRow", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": true, "tactics": ["ext", "rw", "exact"], "tactic_count": 3}
{"name": "Matrix.map_updateCol", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": true, "tactics": ["ext", "rw", "exact"], "tactic_count": 3}
{"name": "Matrix.updateRow_transpose", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": true, "tactics": ["ext", "rw", "rfl"], "tactic_count": 3}
{"name": "Matrix.updateCol_transpose", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": true, "tactics": ["ext", "rw", "rfl"], "tactic_count": 3}
{"name": "Matrix.updateRow_conjTranspose", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Matrix.updateCol_conjTranspose", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Matrix.updateRow_eq_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.updateCol_eq_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.updateRow_zero_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.updateCol_zero_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.diagonal_updateCol_single", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": true, "tactics": ["ext", "obtain", "rw", "obtain", "rw", "rw", "rw", "obtain", "rw", "rw"], "tactic_count": 10}
{"name": "Matrix.diagonal_updateRow_single", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matrix.updateRow_idem", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.updateRow_comm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.updateCol_idem", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Matrix.updateCol_comm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Matrix.updateRow_submatrix_equiv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Matrix.submatrix_updateRow_equiv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.updateCol_submatrix_equiv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": true, "tactics": ["simpa", "congr_arg"], "tactic_count": 2}
{"name": "Matrix.submatrix_updateCol_equiv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.updateRow_reindex", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.reindex_updateRow", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.updateCol_reindex", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.reindex_updateCol", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.single_eq_updateRow_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.single_eq_updateCol_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.updateRow_mulVec", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": true, "tactics": ["ext", "obtain", "simp", "simp"], "tactic_count": 4}
{"name": "Matrix.vecMul_updateCol", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": true, "tactics": ["ext", "obtain", "simp", "simp"], "tactic_count": 4}
{"name": "Matrix.update_vecMulVec", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": true, "tactics": ["ext", "obtain", "simp", "simp"], "tactic_count": 4}
{"name": "Matrix.vecMulVec_update", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": true, "tactics": ["ext", "obtain", "simp", "simp"], "tactic_count": 4}
{"name": "Matrix.updateRow_mul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": true, "tactics": ["ext", "obtain", "simp", "simp"], "tactic_count": 4}
{"name": "Matrix.mul_updateCol", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": true, "tactics": ["ext", "obtain", "simp", "simp"], "tactic_count": 4}
{"name": "Matrix.mul_single_eq_updateCol_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matrix.single_mul_eq_updateRow_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matrix.updateRow_zero_mul_updateCol_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.RowCol", "is_tactic_proof": true, "tactics": ["rw", "zero_mulVec,"], "tactic_count": 2}
{"name": "Matrix.fromBlocks_eq_of_invertible₁₁", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SchurComplement", "is_tactic_proof": true, "tactics": ["simp", "invOf_mul_self,"], "tactic_count": 2}
{"name": "Matrix.fromBlocks_eq_of_invertible₂₂", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SchurComplement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.fromBlocksZero₂₁Invertible", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.SchurComplement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.fromBlocksZero₁₂Invertible", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.SchurComplement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.invOf_fromBlocks_zero₂₁_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SchurComplement", "is_tactic_proof": true, "tactics": ["letI", "convert"], "tactic_count": 2}
{"name": "Matrix.invOf_fromBlocks_zero₁₂_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SchurComplement", "is_tactic_proof": true, "tactics": ["letI", "convert"], "tactic_count": 2}
{"name": "Matrix.invertibleOfFromBlocksZero₂₁Invertible", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.SchurComplement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.invertibleOfFromBlocksZero₁₂Invertible", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.SchurComplement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.fromBlocksZero₂₁InvertibleEquiv", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.SchurComplement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.fromBlocksZero₁₂InvertibleEquiv", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.SchurComplement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.isUnit_fromBlocks_zero₂₁", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SchurComplement", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.isUnit_fromBlocks_zero₁₂", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SchurComplement", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.inv_fromBlocks_zero₂₁_of_isUnit_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SchurComplement", "is_tactic_proof": true, "tactics": ["by_cases", "have", "cases", "cases", "letI", "simp_rw", "have", "have", "simp_rw"], "tactic_count": 9}
{"name": "Matrix.inv_fromBlocks_zero₁₂_of_isUnit_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SchurComplement", "is_tactic_proof": true, "tactics": ["by_cases", "have", "cases", "cases", "letI", "simp_rw", "have", "have", "simp_rw"], "tactic_count": 9}
{"name": "Matrix.fromBlocks₂₂Invertible", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.SchurComplement", "is_tactic_proof": true, "tactics": ["convert", "letI", "letI", "refine", "exact", "change", "fromBlocks", "fromBlocks", "simp", "zero_add,"], "tactic_count": 10}
{"name": "Matrix.fromBlocks₁₁Invertible", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.SchurComplement", "is_tactic_proof": true, "tactics": ["letI", "letI", "exact", "iDCBA.copy"], "tactic_count": 4}
{"name": "Matrix.invOf_fromBlocks₂₂_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SchurComplement", "is_tactic_proof": true, "tactics": ["letI", "convert"], "tactic_count": 2}
{"name": "Matrix.invOf_fromBlocks₁₁_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SchurComplement", "is_tactic_proof": true, "tactics": ["letI", "convert"], "tactic_count": 2}
{"name": "Matrix.invertibleOfFromBlocks₂₂Invertible", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.SchurComplement", "is_tactic_proof": false, "tactics": ["suffices", "exact", "letI", "letI", "letI", "letI", "letI", "refine", "exact"], "tactic_count": 9}
{"name": "Matrix.invertibleOfFromBlocks₁₁Invertible", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.SchurComplement", "is_tactic_proof": true, "tactics": ["letI", "letI", "exact"], "tactic_count": 3}
{"name": "Matrix.invertibleEquivFromBlocks₂₂Invertible", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.SchurComplement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.invertibleEquivFromBlocks₁₁Invertible", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.SchurComplement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.isUnit_fromBlocks_iff_of_invertible₂₂", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SchurComplement", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.isUnit_fromBlocks_iff_of_invertible₁₁", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SchurComplement", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.det_fromBlocks₁₁", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SchurComplement", "is_tactic_proof": true, "tactics": ["rw", "det_fromBlocks_zero₁₂,"], "tactic_count": 2}
{"name": "Matrix.det_fromBlocks_one₁₁", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SchurComplement", "is_tactic_proof": true, "tactics": ["haveI", "rw"], "tactic_count": 2}
{"name": "Matrix.det_fromBlocks₂₂", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SchurComplement", "is_tactic_proof": false, "tactics": ["have", "ext", "cases", "rw"], "tactic_count": 4}
{"name": "Matrix.det_fromBlocks_one₂₂", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SchurComplement", "is_tactic_proof": true, "tactics": ["haveI", "rw"], "tactic_count": 2}
{"name": "Matrix.det_one_add_mul_comm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SchurComplement", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.det_mul_add_one_comm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SchurComplement", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matrix.det_one_sub_mul_comm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SchurComplement", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matrix.det_one_add_replicateCol_mul_replicateRow", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SchurComplement", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matrix.det_add_replicateCol_mul_replicateRow", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SchurComplement", "is_tactic_proof": true, "tactics": ["nth_rewrite", "rwa"], "tactic_count": 2}
{"name": "Matrix.det_add_mul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SchurComplement", "is_tactic_proof": true, "tactics": ["nth_rewrite", "rwa", "det_one_add_mul_comm,"], "tactic_count": 3}
{"name": "Matrix.detp", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.SemiringInverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.detp_one_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SemiringInverse", "is_tactic_proof": true, "tactics": ["rw", "simp", "simp", "rintro", "obtain", "exact"], "tactic_count": 6}
{"name": "Matrix.detp_neg_one_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SemiringInverse", "is_tactic_proof": true, "tactics": ["rw", "intro", "have", "contrapose", "rw", "decide", "obtain", "exact"], "tactic_count": 8}
{"name": "Matrix.adjp", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.SemiringInverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.adjp_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SemiringInverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.detp_mul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SemiringInverse", "is_tactic_proof": false, "tactics": ["have", "ext", "simp_rw", "mul_inv_eq_iff_eq_mul,", "have", "simp_rw", "refine", "simp_rw", "exact", "let", "have", "let", "replace", "detp", "simp_rw", "rw", "simp_rw", "rw", "conv_rhs", "refine", "replace", "contrapose", "rw", "exact", "obtain", "replace", "rw", "split_ifs", "rw", "simp_rw", "refine", "rw", "simp"], "tactic_count": 33}
{"name": "Matrix.mul_adjp_apply_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SemiringInverse", "is_tactic_proof": true, "tactics": ["have", "simp_rw", "simp_rw", "refine", "rw"], "tactic_count": 5}
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{"name": "Matrix.mul_adjp_add_detp", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SemiringInverse", "is_tactic_proof": true, "tactics": ["ext", "rcases", "simp_rw", "simp_rw"], "tactic_count": 4}
{"name": "Matrix.isAddUnit_mul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SemiringInverse", "is_tactic_proof": true, "tactics": ["revert", "rw", "exact"], "tactic_count": 3}
{"name": "Matrix.isAddUnit_detp_mul_detp", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SemiringInverse", "is_tactic_proof": true, "tactics": ["suffices", "intro", "simp_rw", "intro", "rw", "rw", "replace", "rw", "simp_rw", "obtain", "rw", "exact"], "tactic_count": 12}
{"name": "Matrix.isAddUnit_detp_smul_mul_adjp", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SemiringInverse", "is_tactic_proof": true, "tactics": ["suffices", "intro", "rw", "intro", "simp_rw", "intro", "rw", "rw", "rw", "replace", "rw", "obtain", "rw", "rw", "rw", "apply", "have", "rw", "exact"], "tactic_count": 19}
{"name": "Matrix.detp_smul_add_adjp", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SemiringInverse", "is_tactic_proof": true, "tactics": ["have", "simp_rw", "rwa"], "tactic_count": 3}
{"name": "Matrix.detp_smul_adjp", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SemiringInverse", "is_tactic_proof": true, "tactics": ["have", "rw", "have", "replace", "simp", "rwa"], "tactic_count": 6}
{"name": "Matrix.instIsStablyFiniteRingOfCommSemiring", "kind": "instance", "module": "Mathlib.LinearAlgebra.Matrix.SemiringInverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.invertibleOfLeftInverse", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.SemiringInverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.invertibleOfRightInverse", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.SemiringInverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.isUnit_of_left_inverse", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SemiringInverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.exists_left_inverse_iff_isUnit", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SemiringInverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.isUnit_of_right_inverse", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SemiringInverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.exists_right_inverse_iff_isUnit", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SemiringInverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.toLinearMap₂'Aux", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.toLinearMap₂'Aux_single", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": true, "tactics": ["rw", "have", "simp_rw", "simp", "rw", "exact"], "tactic_count": 6}
{"name": "LinearMap.toMatrix₂Aux", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.toMatrix₂Aux_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.toLinearMap₂'Aux_toMatrix₂Aux", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": true, "tactics": ["refine", "simp_rw"], "tactic_count": 2}
{"name": "Matrix.toMatrix₂Aux_toLinearMap₂'Aux", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": true, "tactics": ["ext", "simp_rw"], "tactic_count": 2}
{"name": "LinearMap.toMatrixₛₗ₂'", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.toMatrix₂'", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.toLinearMapₛₗ₂'", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.toLinearMap₂'", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.toLinearMapₛₗ₂'_aux_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.toLinearMapₛₗ₂'_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "Matrix.toLinearMap₂'_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.toLinearMap₂'_apply'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "rw", "refine", "rw"], "tactic_count": 5}
{"name": "Matrix.toLinearMapₛₗ₂'_single", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.toLinearMap₂'_single", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.toMatrixₛₗ₂'_symm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.toLinearMapₛₗ₂'_symm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.toLinearMapₛₗ₂'_toMatrix'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.toLinearMap₂'_toMatrix'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.toMatrix'_toLinearMapₛₗ₂'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.toMatrix'_toLinearMap₂'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.toMatrixₛₗ₂'_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.toMatrix₂'_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.toMatrix₂'_compl₁₂", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": true, "tactics": ["ext", "simp", "rw", "conv_lhs", "rw", "apply", "rintro", "rw", "apply", "rintro", "simp", "intros", "simp", "intros", "simp"], "tactic_count": 15}
{"name": "LinearMap.toMatrix₂'_comp", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "LinearMap.toMatrix₂'_compl₂", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "LinearMap.mul_toMatrix₂'_mul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LinearMap.mul_toMatrix'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LinearMap.toMatrix₂'_mul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.toLinearMap₂'_comp", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.toMatrix₂", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.toLinearMapₛₗ₂", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.toLinearMap₂", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.toMatrix₂_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.toLinearMapₛₗ₂_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.toLinearMap₂_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.toLinearMapₛₗ₂_apply_basis", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": true, "tactics": ["simp", "rw", "simp"], "tactic_count": 3}
{"name": "Matrix.toLinearMap₂_apply_basis", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dotProduct_toMatrix₂_mulVec", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": false, "tactics": ["simp", "map_smulₛₗ,", "rw", "refine", "ring"], "tactic_count": 5}
{"name": "apply_eq_dotProduct_toMatrix₂_mulVec", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": true, "tactics": ["nth_rw", "suffices", "simp_rw", "exact"], "tactic_count": 4}
{"name": "LinearMap.toMatrix₂Aux_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.toMatrix₂_symm'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.toMatrix₂_symm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.toLinearMapₛₗ₂_symm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.toLinearMap₂_symm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.toLinearMap₂_basisFun", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "LinearMap.toMatrix₂_basisFun", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "Matrix.toLinearMapₛₗ₂_toMatrix₂", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.toLinearMap₂_toMatrix₂", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.toMatrix₂_toLinearMapₛₗ₂", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.toMatrix₂_toLinearMap₂", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.toMatrix₂_compl₁₂", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": true, "tactics": ["ext", "simp", "sum_mul]", "rw", "conv_lhs", "rw", "apply", "rintro", "rw", "apply", "rintro", "simp", "intros", "simp", "intros", "simp"], "tactic_count": 16}
{"name": "LinearMap.toMatrix₂_comp", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "LinearMap.toMatrix₂_compl₂", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "LinearMap.toMatrix₂_mul_basis_toMatrix", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": true, "tactics": ["simp_rw", "rw"], "tactic_count": 2}
{"name": "LinearMap.mul_toMatrix₂_mul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "LinearMap.mul_toMatrix₂", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LinearMap.toMatrix₂_mul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Matrix.toLinearMap₂_compl₁₂", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.IsAdjointPair", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.IsSelfAdjoint", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.IsSkewAdjoint", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isAdjointPair_toLinearMap₂'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": true, "tactics": ["rw", "have", "intro", "constructor", "rw", "exact", "simp_rw", "rfl"], "tactic_count": 8}
{"name": "isAdjointPair_toLinearMap₂", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": true, "tactics": ["rw", "have", "intro", "constructor", "rw", "exact", "simp_rw", "rfl"], "tactic_count": 8}
{"name": "Matrix.isAdjointPair_equiv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": true, "tactics": ["have", "let", "let", "let", "let", "suffices", "dsimp", "simp", "simp", "convert", "rw", "rfl", "rw", "rfl", "rw", "conv_rhs", "rw"], "tactic_count": 17}
{"name": "pairSelfAdjointMatricesSubmodule", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_pairSelfAdjointMatricesSubmodule", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "selfAdjointMatricesSubmodule", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_selfAdjointMatricesSubmodule", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "skewAdjointMatricesSubmodule", "kind": "definition", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_skewAdjointMatricesSubmodule", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Matrix.SeparatingLeft.toLinearMap₂'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Matrix.SeparatingRight.toLinearMap₂'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Matrix.Nondegenerate.toLinearMap₂'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.SesquilinearForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Matrix.kronecker_mulVec_vec_of_commute", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Vec", "is_tactic_proof": true, "tactics": ["ext", "simp_rw"], "tactic_count": 2}
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{"name": "Matrix.kronecker_mulVec_vec", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Vec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.vec_vecMul_kronecker", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Matrix.Vec", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Matrix.instDivInvMonoid", "kind": "instance", "module": "Mathlib.LinearAlgebra.Matrix.ZPow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MultilinearMap.instFunLikeForall", "kind": "instance", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MultilinearMap.map_piecewise_add", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": true, "tactics": ["revert", "refine", "intro", "have", "t.piecewise_insert", "have", "ext", "by_cases", "rw", "simp", "simp", "let", "have", "ext", "by_cases", "rw", "simp", "by_cases", "rw", "congr", "refine", "have", "ext", "by_cases", "rw", "simp", "by_cases", "rw"], "tactic_count": 28}
{"name": "MultilinearMap.map_add_univ", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MultilinearMap.map_sum_finset_aux", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": true, "tactics": ["letI", "induction", "h", "by_cases", "obtain", "have", "rw", "by_cases", "have", "intro", "have", "have", "exact", "have", "intro", "congr", "have", "intro", "congr", "apply", "exact", "simp", "simp", "obtain", "obtain", "let", "let", "have", "intro", "by_cases", "rw", "simp", "simp", "have", "intro", "by_cases", "rw", "simp", "simp", "have", "ext", "by_cases", "rw", "have", "simp", "symm", "simp", "rw", "refine", "have", "rw", "simp", "simp", "have", "ext", "by_cases", "rw", "simp", "simp", "have", "ext", "by_cases", "rw", "simp", "simp", "have", "have", "refine", "have", "simp", "exact", "rw", "exact", "have", "have", "rw", "exact", "have", "haveI", "piFinset_disjoint_of_disjoint", "have", "apply", "intro", "by_cases", "apply", "refine", "by_cases", "have", "rwa", "simp", "apply", "refine", "by_cases", "have", "rwa", "simp", "exact", "rw", "simp", "rw"], "tactic_count": 100}
{"name": "MultilinearMap.map_sum_finset", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.map_sum", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.map_update_sum", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "insert"], "tactic_count": 4}
{"name": "MultilinearMap.codRestrict", "kind": "definition", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.restrictScalars", "kind": "definition", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.coe_restrictScalars", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.domDomCongr", "kind": "definition", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.domDomCongr_trans", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.domDomCongr_mul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.domDomCongrEquiv", "kind": "definition", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.domDomCongr_eq_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.domDomRestrict_aux", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "MultilinearMap.domDomRestrict_aux_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MultilinearMap.domDomRestrict", "kind": "definition", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.domDomRestrict_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.linearDeriv", "kind": "definition", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.linearDeriv_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": true, "tactics": ["unfold", "simp"], "tactic_count": 2}
{"name": "LinearMap.compMultilinearMap", "kind": "definition", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.coe_compMultilinearMap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.compMultilinearMap_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.id_compMultilinearMap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.comp_compMultilinearMap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.compMultilinearMap_compLinearMap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.compMultilinearMap_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.zero_compMultilinearMap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.compMultilinearMap_add", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.add_compMultilinearMap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.compMultilinearMap_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.smul_compMultilinearMap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.subtype_compMultilinearMap_codRestrict", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.compMultilinearMap_codRestrict", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.compMultilinearMap_domDomCongr", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "MultilinearMap.instDistribMulActionOfSMulCommClass", "kind": "instance", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.instModule", "kind": "instance", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.instIsTorsionFree", "kind": "instance", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.compMultilinearMapₗ", "kind": "definition", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.multilinearMapCongrRight", "kind": "definition", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.ofSubsingletonₗ", "kind": "definition", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.domDomCongrLinearEquiv'", "kind": "definition", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.constLinearEquivOfIsEmpty", "kind": "definition", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.domDomCongrLinearEquiv", "kind": "definition", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.domDomRestrictₗ", "kind": "definition", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.iteratedFDeriv_aux", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": true, "tactics": ["ext", "rcases", "rw", "rw"], "tactic_count": 4}
{"name": "MultilinearMap.iteratedFDerivComponent", "kind": "definition", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.iteratedFDeriv", "kind": "definition", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.compLinearMapₗ", "kind": "definition", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.multilinearMapCongrLeft", "kind": "definition", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.compLinearMapMultilinear", "kind": "definition", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.piLinearMap", "kind": "definition", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.map_piecewise_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": true, "tactics": ["refine", "intro", "have", "ext", "by_cases", "rw", "simp", "simp", "rw", "simp"], "tactic_count": 10}
{"name": "MultilinearMap.map_smul_univ", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "MultilinearMap.map_update_smul_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": false, "tactics": ["have", "f", "map_piecewise_smul", "simpa"], "tactic_count": 4}
{"name": "MultilinearMap.ext_ring", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": true, "tactics": ["ext", "obtain", "have", "have", "simp_all"], "tactic_count": 5}
{"name": "MultilinearMap.mkPiAlgebra", "kind": "definition", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.mkPiAlgebra_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.mkPiAlgebraFin", "kind": "definition", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.mkPiAlgebraFin_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.mkPiAlgebraFin_apply_const", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MultilinearMap.smulRight", "kind": "definition", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.smulRight_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.mkPiRing", "kind": "definition", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.mkPiRing_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.mkPiRing_apply_one_eq_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "MultilinearMap.mkPiRing_eq_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "constructor", "simpa", "simp"], "tactic_count": 4}
{"name": "MultilinearMap.mkPiRing_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "MultilinearMap.mkPiRing_eq_zero_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MultilinearMap.instNeg", "kind": "instance", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.neg_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.instSub", "kind": "instance", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.sub_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.instAddCommGroup", "kind": "instance", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.map_update_neg", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.map_update_sub", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MultilinearMap.map_update", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MultilinearMap.map_sub_map_piecewise", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "rw", "simp_rw", "congr", "congr", "rw", "exact", "exact", "cases", "rw", "push_neg", "rw", "apply", "grind"], "tactic_count": 15}
{"name": "MultilinearMap.map_piecewise_sub_map_piecewise", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "by_cases", "rw", "rw", "rw", "obtain", "rw", "rw", "rw"], "tactic_count": 10}
{"name": "MultilinearMap.map_add_eq_map_add_linearDeriv_add", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "sum_union", "add_comm]"], "tactic_count": 4}
{"name": "MultilinearMap.map_add_sub_map_add_sub_linearDeriv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "add_sub_cancel_left,"], "tactic_count": 2}
{"name": "MultilinearMap.piRingEquiv", "kind": "definition", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.map", "kind": "definition", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.map_nonempty", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.range", "kind": "definition", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.ext_multilinear", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Basis", "is_tactic_proof": true, "tactics": ["cases", "classical", "ext", "rcases", "unfold", "simp_rw"], "tactic_count": 6}
{"name": "Basis.multilinearMap", "kind": "definition", "module": "Mathlib.LinearAlgebra.Multilinear.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Basis.multilinearMap_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Basis", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Basis.multilinearMap_apply_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Basis", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LinearMap.uncurryLeft", "kind": "definition", "module": "Mathlib.LinearAlgebra.Multilinear.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.uncurryLeft_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.curryLeft", "kind": "definition", "module": "Mathlib.LinearAlgebra.Multilinear.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.curryLeft_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.curry_uncurryLeft", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Curry", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "MultilinearMap.uncurry_curryLeft", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Curry", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "multilinearCurryLeftEquiv", "kind": "definition", "module": "Mathlib.LinearAlgebra.Multilinear.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.uncurryRight", "kind": "definition", "module": "Mathlib.LinearAlgebra.Multilinear.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.uncurryRight_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.curryRight", "kind": "definition", "module": "Mathlib.LinearAlgebra.Multilinear.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.curryRight_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.curry_uncurryRight", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Curry", "is_tactic_proof": true, "tactics": ["ext", "simp", "rw"], "tactic_count": 3}
{"name": "MultilinearMap.uncurry_curryRight", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Curry", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "multilinearCurryRightEquiv", "kind": "definition", "module": "Mathlib.LinearAlgebra.Multilinear.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.uncurryMid", "kind": "definition", "module": "Mathlib.LinearAlgebra.Multilinear.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.curryMid", "kind": "definition", "module": "Mathlib.LinearAlgebra.Multilinear.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.curryMid_uncurryMid", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Curry", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "MultilinearMap.uncurryMid_curryMid", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Curry", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "MultilinearMap.curryMidLinearEquiv", "kind": "definition", "module": "Mathlib.LinearAlgebra.Multilinear.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.currySum", "kind": "definition", "module": "Mathlib.LinearAlgebra.Multilinear.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.currySum_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.currySum_apply'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.currySum_add", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.currySum_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.uncurrySum", "kind": "definition", "module": "Mathlib.LinearAlgebra.Multilinear.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.uncurrySum_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.uncurrySum_add", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.uncurrySum_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.uncurrySum_currySum", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Curry", "is_tactic_proof": true, "tactics": ["ext", "simp", "congr", "ext"], "tactic_count": 4}
{"name": "MultilinearMap.currySum_uncurrySum", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.currySumEquiv", "kind": "definition", "module": "Mathlib.LinearAlgebra.Multilinear.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.coe_currySumEquiv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.coe_currySumEquiv_symm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.curryFinFinset", "kind": "definition", "module": "Mathlib.LinearAlgebra.Multilinear.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.curryFinFinset_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.curryFinFinset_symm_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.curryFinFinset_symm_apply_piecewise_const", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Curry", "is_tactic_proof": true, "tactics": ["rw", "ext", "rw", "apply", "ext", "rw", "exact"], "tactic_count": 7}
{"name": "MultilinearMap.curryFinFinset_symm_apply_const", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.curryFinFinset_apply_const", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Curry", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MultilinearMap.dfinsupp_ext", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.DFinsupp", "is_tactic_proof": true, "tactics": ["ext", "change", "classical", "cases", "rw", "simp_rw", "congr", "simp_rw", "exact"], "tactic_count": 9}
{"name": "MultilinearMap.dfinsuppFamily", "kind": "definition", "module": "Mathlib.LinearAlgebra.Multilinear.DFinsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.support_dfinsuppFamily_subset", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.DFinsupp", "is_tactic_proof": true, "tactics": ["intro", "simp", "intro", "exact"], "tactic_count": 4}
{"name": "MultilinearMap.dfinsuppFamily_single", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.DFinsupp", "is_tactic_proof": true, "tactics": ["ext", "obtain", "simp", "rw", "rw", "obtain", "apply", "simp_rw"], "tactic_count": 8}
{"name": "MultilinearMap.dfinsuppFamily_single_left_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.DFinsupp", "is_tactic_proof": true, "tactics": ["ext", "obtain", "simp", "simp"], "tactic_count": 4}
{"name": "MultilinearMap.dfinsuppFamily_single_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.DFinsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.dfinsuppFamily_compLinearMap_lsingle", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.DFinsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.dfinsuppFamily_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.DFinsupp", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "MultilinearMap.dfinsuppFamily_add", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.DFinsupp", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "MultilinearMap.dfinsuppFamily_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.DFinsupp", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "MultilinearMap.dfinsuppFamilyₗ", "kind": "definition", "module": "Mathlib.LinearAlgebra.Multilinear.DFinsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.fromDFinsuppEquiv", "kind": "definition", "module": "Mathlib.LinearAlgebra.Multilinear.DFinsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.fromDFinsuppEquiv_single", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.DFinsupp", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MultilinearMap.fromDFinsuppEquiv_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.DFinsupp", "is_tactic_proof": true, "tactics": ["classical", "refine", "refine", "simp"], "tactic_count": 4}
{"name": "MultilinearMap.fromDFinsuppEquiv_symm_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.DFinsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.freeDFinsuppEquiv", "kind": "definition", "module": "Mathlib.LinearAlgebra.Multilinear.DFinsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.freeDFinsuppEquiv_def", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.DFinsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.freeDFinsuppEquiv_single", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.DFinsupp", "is_tactic_proof": true, "tactics": ["classical", "conv_lhs", "congr", "ext", "obtain", "rcases", "suffices", "simpa", "exact", "simp"], "tactic_count": 10}
{"name": "MultilinearMap.freeDFinsuppEquiv_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.DFinsupp", "is_tactic_proof": true, "tactics": ["apply", "simp", "rintro", "simp"], "tactic_count": 4}
{"name": "MultilinearMap.directSum_ext", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.DirectSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.fromDirectSumEquiv", "kind": "definition", "module": "Mathlib.LinearAlgebra.Multilinear.DirectSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.fromDirectSumEquiv_lof", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.DirectSum", "is_tactic_proof": true, "tactics": ["haveI", "rw", "convert"], "tactic_count": 3}
{"name": "MultilinearMap.fromDirectSumEquiv_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.DirectSum", "is_tactic_proof": true, "tactics": ["rw", "convert"], "tactic_count": 2}
{"name": "MultilinearMap.fromDirectSumEquiv_symm_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.DirectSum", "is_tactic_proof": true, "tactics": ["haveI", "simp_rw", "convert"], "tactic_count": 3}
{"name": "_private.Mathlib.LinearAlgebra.Multilinear.FiniteDimensional.0.MultilinearMap.free_and_finite_fin", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.FiniteDimensional", "is_tactic_proof": true, "tactics": ["induction", "zero", "haveI", "exact", "succ", "ih", "suffices", "cases", "exact", "cases", "exact"], "tactic_count": 11}
{"name": "_private.Mathlib.LinearAlgebra.Multilinear.FiniteDimensional.0.MultilinearMap.free_and_finite", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.FiniteDimensional", "is_tactic_proof": true, "tactics": ["cases", "have", "obtain", "have", "exact"], "tactic_count": 5}
{"name": "Module.Finite.multilinearMap", "kind": "instance", "module": "Mathlib.LinearAlgebra.Multilinear.FiniteDimensional", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Free.multilinearMap", "kind": "instance", "module": "Mathlib.LinearAlgebra.Multilinear.FiniteDimensional", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.freeFinsuppEquiv", "kind": "definition", "module": "Mathlib.LinearAlgebra.Multilinear.Finsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.freeFinsuppEquiv_def", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Finsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.freeFinsuppEquiv_single", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Finsupp", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MultilinearMap.freeFinsuppEquiv_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Finsupp", "is_tactic_proof": true, "tactics": ["induction", "zero", "add", "single"], "tactic_count": 4}
{"name": "MultilinearMap.pi_ext", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Pi", "is_tactic_proof": true, "tactics": ["ext", "change", "obtain", "have", "have", "rw", "simp_rw", "congr", "simp_rw", "exact"], "tactic_count": 10}
{"name": "MultilinearMap.piFamily", "kind": "definition", "module": "Mathlib.LinearAlgebra.Multilinear.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.piFamily_single", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Pi", "is_tactic_proof": true, "tactics": ["ext", "obtain", "simp", "rw", "rw", "obtain", "apply", "simp_rw"], "tactic_count": 8}
{"name": "MultilinearMap.piFamily_single_left_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Pi", "is_tactic_proof": true, "tactics": ["ext", "obtain", "simp", "simp"], "tactic_count": 4}
{"name": "MultilinearMap.piFamily_single_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.piFamily_compLinearMap_lsingle", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.piFamily_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Pi", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "MultilinearMap.piFamily_add", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Pi", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "MultilinearMap.piFamily_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.Pi", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "MultilinearMap.piFamilyₗ", "kind": "definition", "module": "Mathlib.LinearAlgebra.Multilinear.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.domCoprodDep", "kind": "definition", "module": "Mathlib.LinearAlgebra.Multilinear.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.domCoprodDep'", "kind": "definition", "module": "Mathlib.LinearAlgebra.Multilinear.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.domCoprodDep'_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.TensorProduct", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "MultilinearMap.domCoprod", "kind": "definition", "module": "Mathlib.LinearAlgebra.Multilinear.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.domCoprod'", "kind": "definition", "module": "Mathlib.LinearAlgebra.Multilinear.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.domCoprod'_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultilinearMap.domCoprod_domDomCongr_sumCongr", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Multilinear.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.Orientation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.map", "kind": "definition", "module": "Mathlib.LinearAlgebra.Orientation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.map_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Orientation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.map_refl", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Orientation", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Orientation.map_symm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Orientation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.reindex", "kind": "definition", "module": "Mathlib.LinearAlgebra.Orientation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.reindex_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Orientation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.reindex_refl", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Orientation", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Orientation.reindex_symm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Orientation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsEmpty.oriented", "kind": "instance", "module": "Mathlib.LinearAlgebra.Orientation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.map_positiveOrientation_of_isEmpty", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Orientation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.map_of_isEmpty", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Orientation", "is_tactic_proof": true, "tactics": ["induction", "h", "rw", "congr", "ext", "rw", "congr", "simp"], "tactic_count": 8}
{"name": "Orientation.map_neg", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Orientation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.reindex_neg", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Orientation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.map_orientation_eq_det_inv_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Orientation", "is_tactic_proof": true, "tactics": ["cases", "letI", "induction", "h", "rw", "show"], "tactic_count": 6}
{"name": "Module.Basis.orientation", "kind": "definition", "module": "Mathlib.LinearAlgebra.Orientation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.orientation_map", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Orientation", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Module.Basis.orientation_reindex", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Orientation", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Module.Basis.orientation_unitsSMul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Orientation", "is_tactic_proof": false, "tactics": ["rw", "det_unitsSMul_self,", "norm_cast", "simp", "exact"], "tactic_count": 5}
{"name": "Module.Basis.orientation_isEmpty", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Orientation", "is_tactic_proof": true, "tactics": ["rw", "congr", "exact"], "tactic_count": 3}
{"name": "Orientation.eq_or_eq_neg_of_isEmpty", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Orientation", "is_tactic_proof": true, "tactics": ["induction", "h", "dsimp", "simp", "rw", "intro", "set", "have", "convert", "ext", "fin_cases", "rw", "simpa"], "tactic_count": 13}
{"name": "Module.Basis.orientation_eq_iff_det_pos", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Orientation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.orientation_eq_or_eq_neg", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Orientation", "is_tactic_proof": true, "tactics": ["induction", "h", "rw", "rwa", "sameRay_neg_smul_left_iff_of_ne", "ne_comm]"], "tactic_count": 6}
{"name": "Module.Basis.orientation_ne_iff_eq_neg", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Orientation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.orientation_comp_linearEquiv_eq_iff_det_pos", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Orientation", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Module.Basis.orientation_comp_linearEquiv_eq_neg_iff_det_neg", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Orientation", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Module.Basis.orientation_neg_single", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Orientation", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Module.Basis.adjustToOrientation", "kind": "definition", "module": "Mathlib.LinearAlgebra.Orientation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.orientation_adjustToOrientation", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Orientation", "is_tactic_proof": true, "tactics": ["rw", "split_ifs", "exact", "rw", "exact"], "tactic_count": 5}
{"name": "Module.Basis.adjustToOrientation_apply_eq_or_eq_neg", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Orientation", "is_tactic_proof": true, "tactics": ["rw", "split_ifs", "simp", "by_cases"], "tactic_count": 4}
{"name": "Module.Basis.det_adjustToOrientation", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Orientation", "is_tactic_proof": true, "tactics": ["dsimp", "split_ifs", "left", "rfl", "right", "simp", "mul_one,", "ext", "simp"], "tactic_count": 9}
{"name": "Module.Basis.abs_det_adjustToOrientation", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Orientation", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "Orientation.eq_or_eq_neg", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Orientation", "is_tactic_proof": true, "tactics": ["have", "letI", "rcases", "simp"], "tactic_count": 4}
{"name": "Orientation.ne_iff_eq_neg", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Orientation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.map_eq_det_inv_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Orientation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.map_eq_iff_det_pos", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Orientation", "is_tactic_proof": true, "tactics": ["cases", "have", "simp", "rw"], "tactic_count": 4}
{"name": "Orientation.map_eq_neg_iff_det_neg", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Orientation", "is_tactic_proof": true, "tactics": ["cases", "have", "simp", "have", "rw", "exact", "haveI", "rw"], "tactic_count": 8}
{"name": "Orientation.someBasis", "kind": "definition", "module": "Mathlib.LinearAlgebra.Orientation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.someBasis_orientation", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Orientation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsPerfPair.flip", "kind": "theorem", "module": "Mathlib.LinearAlgebra.PerfectPairing.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.flip.instIsPerfPair", "kind": "instance", "module": "Mathlib.LinearAlgebra.PerfectPairing.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.toPerfPair", "kind": "definition", "module": "Mathlib.LinearAlgebra.PerfectPairing.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.toLinearMap_toPerfPair", "kind": "theorem", "module": "Mathlib.LinearAlgebra.PerfectPairing.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.toPerfPair_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.PerfectPairing.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.apply_symm_toPerfPair_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.PerfectPairing.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.apply_toPerfPair_flip", "kind": "theorem", "module": "Mathlib.LinearAlgebra.PerfectPairing.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.IsReflexive.of_isPerfPair", "kind": "theorem", "module": "Mathlib.LinearAlgebra.PerfectPairing.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.finrank_of_isPerfPair", "kind": "theorem", "module": "Mathlib.LinearAlgebra.PerfectPairing.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsPerfPair.id", "kind": "instance", "module": "Mathlib.LinearAlgebra.PerfectPairing.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsPerfPair.dualEval", "kind": "instance", "module": "Mathlib.LinearAlgebra.PerfectPairing.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsPerfPair.compl₁₂", "kind": "instance", "module": "Mathlib.LinearAlgebra.PerfectPairing.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsPerfPair.congr", "kind": "theorem", "module": "Mathlib.LinearAlgebra.PerfectPairing.Basic", "is_tactic_proof": true, "tactics": ["obtain", "infer_instance"], "tactic_count": 2}
{"name": "LinearMap.IsPerfPair.of_bijective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.PerfectPairing.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsPerfPair.of_injective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.PerfectPairing.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsPerfPair.of_injective'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.PerfectPairing.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsPerfectCompl.flip", "kind": "theorem", "module": "Mathlib.LinearAlgebra.PerfectPairing.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsPerfectCompl.flip_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.PerfectPairing.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsPerfectCompl.left_top_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.PerfectPairing.Basic", "is_tactic_proof": true, "tactics": ["refine", "exact", "rw", "exact", "isCompl_right"], "tactic_count": 5}
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{"name": "LinearEquiv.flip", "kind": "definition", "module": "Mathlib.LinearAlgebra.PerfectPairing.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.coe_toLinearMap_flip", "kind": "theorem", "module": "Mathlib.LinearAlgebra.PerfectPairing.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.flip_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.PerfectPairing.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.symm_flip", "kind": "theorem", "module": "Mathlib.LinearAlgebra.PerfectPairing.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.trans_dualMap_symm_flip", "kind": "theorem", "module": "Mathlib.LinearAlgebra.PerfectPairing.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "LinearEquiv.isReflexive_of_equiv_dual_of_isReflexive", "kind": "theorem", "module": "Mathlib.LinearAlgebra.PerfectPairing.Basic", "is_tactic_proof": true, "tactics": ["constructor", "rw", "exact"], "tactic_count": 3}
{"name": "LinearEquiv.instIsPerfPair", "kind": "instance", "module": "Mathlib.LinearAlgebra.PerfectPairing.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.dualCoannihilator_map_linearEquiv_flip", "kind": "theorem", "module": "Mathlib.LinearAlgebra.PerfectPairing.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Submodule.map_dualAnnihilator_linearEquiv_flip_symm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.PerfectPairing.Basic", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "Submodule.map_dualCoannihilator_linearEquiv_flip", "kind": "theorem", "module": "Mathlib.LinearAlgebra.PerfectPairing.Basic", "is_tactic_proof": true, "tactics": ["have", "suffices", "from", "rw", "simp"], "tactic_count": 5}
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{"name": "Matrix.toPerfectPairing", "kind": "theorem", "module": "Mathlib.LinearAlgebra.PerfectPairing.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.toPerfectPairing_apply_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.PerfectPairing.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LinearMap.finrank_eq_of_isPerfPair", "kind": "theorem", "module": "Mathlib.LinearAlgebra.PerfectPairing.Restrict", "is_tactic_proof": true, "tactics": ["obtain", "rw"], "tactic_count": 2}
{"name": "_private.Mathlib.LinearAlgebra.PerfectPairing.Restrict.0.LinearMap.restrictScalars_field_aux", "kind": "theorem", "module": "Mathlib.LinearAlgebra.PerfectPairing.Restrict", "is_tactic_proof": false, "tactics": ["suffices", "obtain", "p.exists_basis_basis_of_span_eq_top_of_mem_algebraMap", "rintro", "exact", "have", "exact"], "tactic_count": 7}
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{"name": "LinearMap.pi_eq_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Pi", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
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{"name": "LinearMap.const_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LinearMap.toAddMonoidHom_proj", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LinearMap.iInf_ker_proj", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.CompatibleSMul.pi", "kind": "instance", "module": "Mathlib.LinearAlgebra.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LinearMap.sum_single_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Pi", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
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{"name": "LinearMap.proj_comp_single_same", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.proj_comp_single_ne", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LinearEquiv.piCongrRight", "kind": "definition", "module": "Mathlib.LinearAlgebra.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.piCongrRight_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LinearEquiv.piCongrRight_symm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.piCongrRight_trans", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LinearEquiv.fst_comp_prodAssoc", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Prod", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
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{"name": "LinearEquiv.prodProdProdComm", "kind": "definition", "module": "Mathlib.LinearAlgebra.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LinearEquiv.prodProdProdComm_toAddEquiv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LinearEquiv.coe_prodUnique", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Submodule.linearProjOfIsCompl_apply_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projection", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "Submodule.linearProjOfIsCompl_apply_eq_zero_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projection", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "Submodule.IsCompl.projection_isIdempotentElem", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.existsUnique_add_of_isCompl_prod", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Submodule.IsCompl.projection_add_projection_eq_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projection", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "exact"], "tactic_count": 3}
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{"name": "LinearMap.linearProjOfIsCompl", "kind": "definition", "module": "Mathlib.LinearAlgebra.Projection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.linearProjOfIsCompl_apply_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projection", "is_tactic_proof": true, "tactics": ["obtain", "simp"], "tactic_count": 2}
{"name": "LinearMap.linearProjOfIsCompl_apply_right'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projection", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
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{"name": "LinearMap.ofIsCompl_right_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projection", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LinearMap.ofIsCompl_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projection", "is_tactic_proof": true, "tactics": ["ext", "obtain", "simp"], "tactic_count": 3}
{"name": "LinearMap.ofIsCompl_eq'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.ofIsCompl_eq_add", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projection", "is_tactic_proof": true, "tactics": ["ext", "obtain", "simp"], "tactic_count": 3}
{"name": "LinearMap.ofIsCompl_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.ofIsCompl_add", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.ofIsCompl_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.surjective_comp_linearProjOfIsCompl", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.surjective_comp_subtype_of_isComplemented", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LinearMap.ofIsCompl_symm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projection", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LinearMap.ofIsComplProd", "kind": "definition", "module": "Mathlib.LinearAlgebra.Projection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.ofIsComplProd_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.ofIsComplProdEquiv", "kind": "definition", "module": "Mathlib.LinearAlgebra.Projection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.linearProjOfIsCompl_of_proj", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projection", "is_tactic_proof": true, "tactics": ["ext", "have", "rcases", "simp"], "tactic_count": 4}
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{"name": "LinearMap.coe_equivProdOfSurjectiveOfIsCompl", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.equivProdOfSurjectiveOfIsCompl_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.isComplEquivProj", "kind": "definition", "module": "Mathlib.LinearAlgebra.Projection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.coe_isComplEquivProj_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.coe_isComplEquivProj_symm_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.isIdempotentElemEquiv", "kind": "definition", "module": "Mathlib.LinearAlgebra.Projection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.isProj_range_iff_isIdempotentElem", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projection", "is_tactic_proof": false, "tactics": ["refine", "ext", "exact"], "tactic_count": 3}
{"name": "LinearMap.isProj_iff_isIdempotentElem", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projection", "is_tactic_proof": true, "tactics": ["refine", "ext", "exact"], "tactic_count": 3}
{"name": "LinearMap.IsProj.isIdempotentElem", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsProj.mem_iff_map_id", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsProj.codRestrict", "kind": "definition", "module": "Mathlib.LinearAlgebra.Projection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsProj.codRestrict_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsProj.codRestrict_apply_cod", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projection", "is_tactic_proof": true, "tactics": ["ext", "rw", "exact"], "tactic_count": 3}
{"name": "LinearMap.IsProj.codRestrict_ker", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsProj.isCompl", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projection", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "LinearMap.IsProj.eq_conj_prod_map'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projection", "is_tactic_proof": true, "tactics": ["rw", "ext", "simp", "h.map_id", "simp", "prodMap_apply,"], "tactic_count": 6}
{"name": "LinearMap.IsProj.submodule_unique", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projection", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "LinearMap.IsProj.range", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsProj.bot", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsProj.top", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsProj.subtype_comp_codRestrict", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsProj.submodule_eq_top_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projection", "is_tactic_proof": true, "tactics": ["constructor", "ext", "simp", "rw"], "tactic_count": 4}
{"name": "LinearMap.IsProj.submodule_eq_bot_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projection", "is_tactic_proof": true, "tactics": ["constructor", "ext", "simpa", "rw"], "tactic_count": 4}
{"name": "LinearMap.IsIdempotentElem.isCompl", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LinearMap.IsProj.mem_invtSubmodule_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsIdempotentElem.ker_mem_invtSubmodule_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projection", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "Projectivization.generalLinearGroup_smul_def", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projectivization.Action", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
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{"name": "LinearAlgebra.Projectivization.termℙ", "kind": "definition", "module": "Mathlib.LinearAlgebra.Projectivization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Projectivization.mk'", "kind": "definition", "module": "Mathlib.LinearAlgebra.Projectivization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Projectivization.mk'_eq_mk", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projectivization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Projectivization.instNonemptyOfNontrivial", "kind": "instance", "module": "Mathlib.LinearAlgebra.Projectivization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Projectivization.lift", "kind": "definition", "module": "Mathlib.LinearAlgebra.Projectivization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Projectivization.rep", "kind": "definition", "module": "Mathlib.LinearAlgebra.Projectivization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Projectivization.rep_nonzero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projectivization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Projectivization.mk_rep", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projectivization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Projectivization.mk_eq_mk_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projectivization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Projectivization.instFiniteDimensionalSubtypeMemSubmoduleSubmodule", "kind": "instance", "module": "Mathlib.LinearAlgebra.Projectivization.Basic", "is_tactic_proof": true, "tactics": ["rw", "change", "infer_instance"], "tactic_count": 3}
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{"name": "Projectivization.equivSubmodule", "kind": "definition", "module": "Mathlib.LinearAlgebra.Projectivization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Projectivization.mk''", "kind": "definition", "module": "Mathlib.LinearAlgebra.Projectivization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Projectivization.nonZeroEquivProjectivizationProdUnits", "kind": "definition", "module": "Mathlib.LinearAlgebra.Projectivization.Cardinality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Projectivization.isEmpty_of_subsingleton", "kind": "instance", "module": "Mathlib.LinearAlgebra.Projectivization.Cardinality", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
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{"name": "Projectivization.orthogonal_cross_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projectivization.Constructions", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Projectivization.orthogonal_cross_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projectivization.Constructions", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Projectivization.Independent", "kind": "inductive", "module": "Mathlib.LinearAlgebra.Projectivization.Independence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Projectivization.independent_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projectivization.Independence", "is_tactic_proof": true, "tactics": ["refine", "rintro", "choose", "convert", "ext", "exact", "convert", "simp", "intro", "apply"], "tactic_count": 10}
{"name": "Projectivization.independent_iff_iSupIndep", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projectivization.Independence", "is_tactic_proof": true, "tactics": ["refine", "rintro", "simp", "exact", "rw", "refine", "simpa", "exact"], "tactic_count": 8}
{"name": "Projectivization.Dependent", "kind": "inductive", "module": "Mathlib.LinearAlgebra.Projectivization.Independence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Projectivization.dependent_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projectivization.Independence", "is_tactic_proof": true, "tactics": ["refine", "rintro", "contrapose", "choose", "convert", "ext", "simp", "convert", "simp", "exact"], "tactic_count": 10}
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{"name": "Projectivization.dependent_pair_iff_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projectivization.Independence", "is_tactic_proof": true, "tactics": ["rw", "dsimp", "simp", "exact"], "tactic_count": 4}
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{"name": "Projectivization.Subspace.instSetLike", "kind": "instance", "module": "Mathlib.LinearAlgebra.Projectivization.Subspace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Projectivization.Subspace.instPartialOrder", "kind": "instance", "module": "Mathlib.LinearAlgebra.Projectivization.Subspace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Projectivization.Subspace.mem_carrier_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projectivization.Subspace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Projectivization.Subspace.mem_add", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projectivization.Subspace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Projectivization.Subspace.spanCarrier", "kind": "inductive", "module": "Mathlib.LinearAlgebra.Projectivization.Subspace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Projectivization.Subspace.span", "kind": "definition", "module": "Mathlib.LinearAlgebra.Projectivization.Subspace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Projectivization.Subspace.subset_span", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projectivization.Subspace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Projectivization.Subspace.gi", "kind": "definition", "module": "Mathlib.LinearAlgebra.Projectivization.Subspace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Projectivization.Subspace.span_coe", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projectivization.Subspace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Projectivization.Subspace.instInf", "kind": "instance", "module": "Mathlib.LinearAlgebra.Projectivization.Subspace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Projectivization.Subspace.instInfSet", "kind": "instance", "module": "Mathlib.LinearAlgebra.Projectivization.Subspace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Projectivization.Subspace.instCompleteLattice", "kind": "instance", "module": "Mathlib.LinearAlgebra.Projectivization.Subspace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Projectivization.Subspace.subspaceInhabited", "kind": "instance", "module": "Mathlib.LinearAlgebra.Projectivization.Subspace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Projectivization.Subspace.span_empty", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projectivization.Subspace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Projectivization.Subspace.span_univ", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projectivization.Subspace", "is_tactic_proof": true, "tactics": ["rw", "intro", "exact"], "tactic_count": 3}
{"name": "Projectivization.Subspace.span_le_subspace_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projectivization.Subspace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Projectivization.Subspace.monotone_span", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projectivization.Subspace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Projectivization.Subspace.span_le_span", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projectivization.Subspace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Projectivization.Subspace.subset_span_trans", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projectivization.Subspace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Projectivization.Subspace.span_union", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projectivization.Subspace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Projectivization.Subspace.span_iUnion", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projectivization.Subspace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Projectivization.Subspace.sup_span", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projectivization.Subspace", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Projectivization.Subspace.span_sup", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projectivization.Subspace", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "Projectivization.Subspace.mem_submodule_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projectivization.Subspace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.projectivization", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.Projectivization.Subspace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mk_mem_projectivization_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projectivization.Subspace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mem_projectivization_iff_submodule_le", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Projectivization.Subspace", "is_tactic_proof": true, "tactics": ["cases", "rw"], "tactic_count": 2}
{"name": "QuadraticMap.polar", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.map_add", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": true, "tactics": ["rw", "abel"], "tactic_count": 2}
{"name": "QuadraticMap.polar_add", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": true, "tactics": ["simp", "abel"], "tactic_count": 2}
{"name": "QuadraticMap.polar_neg", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "QuadraticMap.polar_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "QuadraticMap.polar_comm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "QuadraticMap.polar_add_left_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": true, "tactics": ["simp", "simp", "simp", "rw"], "tactic_count": 4}
{"name": "QuadraticMap.polar_comp", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "QuadraticMap.polarSym2", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.polarSym2_sym2Mk", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticForm", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.instFunLike", "kind": "instance", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.toFun_eq_coe", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.coe_mk", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.ext", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.congr_fun", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.copy", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.coe_copy", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.copy_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.map_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.exists_companion", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.map_add_add_add_map", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": true, "tactics": ["obtain", "rw", "simp", "abel"], "tactic_count": 4}
{"name": "QuadraticMap.map_add_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": true, "tactics": ["rw", "norm_num"], "tactic_count": 2}
{"name": "QuadraticMap.map_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "QuadraticMap.zeroHomClass", "kind": "instance", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.map_smul_of_tower", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "QuadraticMap.map_neg", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "QuadraticMap.map_sub", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "QuadraticMap.polar_zero_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "QuadraticMap.polar_add_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.polar_smul_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": true, "tactics": ["obtain", "simp_rw"], "tactic_count": 2}
{"name": "QuadraticMap.polar_neg_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "QuadraticMap.polar_sub_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "QuadraticMap.polar_zero_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "QuadraticMap.polar_add_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "QuadraticMap.polar_smul_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "QuadraticMap.polar_neg_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "QuadraticMap.polar_sub_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "QuadraticMap.polar_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "QuadraticMap.polarBilin", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.polarSym2_map_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "QuadraticMap.polar_smul_left_of_tower", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "QuadraticMap.polar_smul_right_of_tower", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "QuadraticMap.ofPolar", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.choose_exists_companion", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.map_sum", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": true, "tactics": ["induction", "empty", "cons", "ih", "simp_rw", "if_false,", "polarBilin_apply_apply]", "congr", "rw", "congr", "rw"], "tactic_count": 11}
{"name": "QuadraticMap.map_sum'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": true, "tactics": ["induction", "empty", "cons", "ih", "simp_rw", "polarBilin_apply_apply,", "abel_nf"], "tactic_count": 7}
{"name": "QuadraticMap.instSMul", "kind": "instance", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.coeFn_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.smul_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.instSMulCommClass", "kind": "instance", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.instIsScalarTower", "kind": "instance", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.instZero", "kind": "instance", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.coeFn_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.zero_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.instInhabited", "kind": "instance", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.instAdd", "kind": "instance", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.coeFn_add", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.add_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.instAddCommMonoid", "kind": "instance", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.coeFnAddMonoidHom", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.evalAddMonoidHom", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.coeFn_sum", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.sum_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.instDistribMulActionOfSMulCommClass", "kind": "instance", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.instModuleOfSMulCommClass", "kind": "instance", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.instNeg", "kind": "instance", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.coeFn_neg", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.neg_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.instSub", "kind": "instance", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.coeFn_sub", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.sub_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.instAddCommGroup", "kind": "instance", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.restrictScalars", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.comp", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.comp_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.compQuadraticMap", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.compQuadraticMap'", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.congrQuadraticMap", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.congrQuadraticMap_refl", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.congrQuadraticMap_symm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.linMulLin", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.linMulLin_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.add_linMulLin", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.linMulLin_add", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.linMulLin_comp", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.sq", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.proj", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.proj_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinMap.toQuadraticMap", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinMap.toQuadraticMap_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinMap.toQuadraticMap_comp_same", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinMap.toQuadraticMap_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinMap.toQuadraticMap_add", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinMap.toQuadraticMap_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinMap.toQuadraticMapAddMonoidHom", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinMap.toQuadraticMapLinearMap", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinMap.toQuadraticMap_list_sum", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinMap.toQuadraticMap_multiset_sum", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinMap.toQuadraticMap_sum", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinMap.toQuadraticMap_eq_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinMap.toQuadraticMap_neg", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinMap.toQuadraticMap_sub", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinMap.polar_toQuadraticMap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": true, "tactics": ["simp", "sub_eq_add_neg"], "tactic_count": 2}
{"name": "LinearMap.BilinMap.polarBilin_toQuadraticMap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.toQuadraticMap_polarBilin", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.polarBilin_injective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": true, "tactics": ["intro", "apply", "rw", "simp_rw", "exact"], "tactic_count": 5}
{"name": "QuadraticMap.polarBilin_comp", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.compQuadraticMap_polar", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LinearMap.compQuadraticMap_polarBilin", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "QuadraticMap.instInvertibleEndOfNat", "kind": "instance", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.half_moduleEnd_apply_eq_half_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.associatedHom", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.associated_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.two_nsmul_associated", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "rw"], "tactic_count": 3}
{"name": "QuadraticMap.associated_isSymm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "QuadraticForm.associated_isSymm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.associated_flip", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "QuadraticMap.associated_comp", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "QuadraticMap.associated_toQuadraticMap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": ["simp", "map_sub]", "abel_nf"], "tactic_count": 3}
{"name": "QuadraticMap.associated_left_inverse", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.associated_left_inverse'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "QuadraticMap.associated_eq_self_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": true, "tactics": ["rw", "add_sub_cancel_right,"], "tactic_count": 2}
{"name": "QuadraticMap.toQuadraticMap_associated", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.associated_rightInverse", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.associated'", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.canLift", "kind": "instance", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.canLift'", "kind": "instance", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.exists_quadraticMap_ne_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": true, "tactics": ["rw", "intro", "apply", "rw"], "tactic_count": 4}
{"name": "QuadraticMap.associated", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.coe_associatedHom", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.associated_linMulLin", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp", "compl₁₂_apply,", "simp", "ring_nf"], "tactic_count": 5}
{"name": "QuadraticMap.associated_sq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.IsOrtho", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.isOrtho_def", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.IsOrtho.all", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.IsOrtho.zero_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "QuadraticMap.IsOrtho.zero_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "QuadraticMap.ne_zero_of_not_isOrtho_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.isOrtho_comm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "LinearMap.BilinForm.toQuadraticMap_isOrtho", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": true, "tactics": ["letI", "simp_rw", "add_add_add_comm", "rw"], "tactic_count": 4}
{"name": "QuadraticMap.isOrtho_polarBilin", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "QuadraticMap.IsOrtho.polar_eq_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.associated_isOrtho", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "QuadraticMap.Anisotropic", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.not_anisotropic_iff_exists", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "QuadraticMap.Anisotropic.eq_zero_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.separatingLeft_of_anisotropic", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.PosDef", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.PosDef.smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.PosDef.nonneg", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.PosDef.anisotropic", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.PosDef.le_zero_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": true, "tactics": ["refine", "have", "rwa"], "tactic_count": 3}
{"name": "QuadraticMap.posDef_of_nonneg", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.posDef_iff_nonneg", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.PosDef.add", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.linMulLinSelfPosDef", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.toQuadraticMap'", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.toMatrix'", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.toMatrix'_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "QuadraticMap.isSymm_toMatrix'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "QuadraticMap.toMatrix'_comp", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "QuadraticMap.discr", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.discr_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "QuadraticMap.discr_comp", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LinearMap.BilinForm.separatingLeft_of_anisotropic", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.exists_bilinForm_self_ne_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": true, "tactics": ["lift", "obtain", "exact"], "tactic_count": 3}
{"name": "LinearMap.BilinForm.exists_orthogonal_basis", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": true, "tactics": ["suffices", "intro", "induction", "zero", "succ", "obtain", "let", "rw", "exact", "obtain", "rw", "finrank_span_singleton", "let", "obtain", "ih", "let", "rintro", "rw", "rw", "have", "rw", "have", "exact", "intro", "refine", "obtain", "rw", "add_neg_cancel,", "refine", "rw", "intro", "refine", "simp", "exact", "rw", "exact", "exact", "exact"], "tactic_count": 38}
{"name": "QuadraticMap.basisRepr", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.basisRepr_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "QuadraticMap.weightedSumSquares", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.weightedSumSquares_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.basisRepr_eq_of_iIsOrtho", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basic", "is_tactic_proof": true, "tactics": ["ext", "rw", "refine", "rw", "rw", "half_moduleEnd_apply_eq_half_smul]", "ring_nf", "intro", "rw", "module"], "tactic_count": 10}
{"name": "QuadraticMap.map_finsuppSum'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.apply_linearCombination'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basis", "is_tactic_proof": true, "tactics": ["simp_rw", "rw", "l.sym2Mul.sum_of_support_subset", "simp"], "tactic_count": 4}
{"name": "QuadraticMap.sum_polar_sub_repr_sq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basis", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "QuadraticMap.map_finsuppSum", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.apply_linearCombination", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basis", "is_tactic_proof": true, "tactics": ["simp_rw", "rw", "simp"], "tactic_count": 3}
{"name": "QuadraticMap.sum_repr_sq_add_sum_repr_mul_polar", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basis", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "QuadraticMap.toBilin", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.toBilin_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basis", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "QuadraticMap.toQuadraticMap_toBilin", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basis", "is_tactic_proof": true, "tactics": ["ext", "rw", "simp_rw", "rw", "simp_rw", "simp_rw", "rfl", "intro", "rw", "simpa"], "tactic_count": 10}
{"name": "LinearMap.BilinMap.toQuadraticMap_surjective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basis", "is_tactic_proof": true, "tactics": ["intro", "obtain", "letI", "exact"], "tactic_count": 4}
{"name": "QuadraticMap.add_toBilin", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basis", "is_tactic_proof": true, "tactics": ["refine", "obtain", "simp", "simp", "simp"], "tactic_count": 5}
{"name": "QuadraticMap.smul_toBilin", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basis", "is_tactic_proof": true, "tactics": ["refine", "obtain", "simp", "simp", "simp"], "tactic_count": 5}
{"name": "QuadraticMap.toBilinHom", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticForm.isometryEquivSumSquares", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.Complex", "is_tactic_proof": true, "tactics": ["let", "have", "intro", "exact", "convert", "ext1", "rw", "refine", "have", "classical", "rw", "intro", "rw", "mul_zero,", "intro", "simp_rw", "erw", "split_ifs", "simp", "have", "simp", "rw", "suffices", "rw", "inv_mul_cancel₀"], "tactic_count": 25}
{"name": "QuadraticForm.isometryEquivSumSquaresUnits", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.Complex", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "QuadraticForm.equivalent_sum_squares", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticForm.complex_equivalent", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.dualProd", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.Dual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.isSymm_dualProd", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Dual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.separatingLeft_dualProd", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Dual", "is_tactic_proof": true, "tactics": ["classical", "rw", "let", "let", "refine", "rw", "change", "have", "refine", "ext", "dsimp", "simp", "ext", "dsimp", "simp", "rw", "refine", "exact"], "tactic_count": 18}
{"name": "QuadraticForm.dualProd", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.Dual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.dualProd.toQuadraticForm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Dual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticForm.dualProdIsometry", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.Dual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticForm.dualProdProdIsometry", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.Dual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticForm.toDualProd", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.Dual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.linearIndependent_of_pairwise_le_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Dual", "is_tactic_proof": true, "tactics": ["refine", "set", "set", "replace", "classical", "simp_rw", "rw", "grind", "simp", "grind", "have", "suffices", "suffices", "simpa", "refine", "grind", "have", "have", "rw", "by_contra", "have", "grind", "replace", "replace", "grind"], "tactic_count": 25}
{"name": "QuadraticMap.Isometry.term_→qᵢ_", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.Isometry._aux_Mathlib_LinearAlgebra_QuadraticForm_Isometry___macroRules_QuadraticMap_Isometry_term_→qᵢ__1", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.Isometry._aux_Mathlib_LinearAlgebra_QuadraticForm_Isometry___unexpand_QuadraticMap_Isometry_1", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.Isometry.instFunLike", "kind": "instance", "module": "Mathlib.LinearAlgebra.QuadraticForm.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.Isometry.instLinearMapClass", "kind": "instance", "module": "Mathlib.LinearAlgebra.QuadraticForm.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.Isometry.toLinearMap_injective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.Isometry.ext", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.Isometry.Simps.apply", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.Isometry.map_app", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.Isometry.coe_toLinearMap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.Isometry.id", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.Isometry.ofEq", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.Isometry.ofEq_rfl", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.Isometry.comp", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.Isometry.toLinearMap_comp", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.Isometry.id_comp", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.Isometry.comp_id", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.Isometry.comp_assoc", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.Isometry.instZeroOfNat", "kind": "instance", "module": "Mathlib.LinearAlgebra.QuadraticForm.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.Isometry.hasZeroOfSubsingleton", "kind": "instance", "module": "Mathlib.LinearAlgebra.QuadraticForm.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.Isometry.instSubsingleton", "kind": "instance", "module": "Mathlib.LinearAlgebra.QuadraticForm.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.Equivalent", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.IsometryEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.IsometryEquiv.instEquivLike", "kind": "instance", "module": "Mathlib.LinearAlgebra.QuadraticForm.IsometryEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.IsometryEquiv.instLinearEquivClass", "kind": "instance", "module": "Mathlib.LinearAlgebra.QuadraticForm.IsometryEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.IsometryEquiv.instCoeOutLinearEquivId", "kind": "instance", "module": "Mathlib.LinearAlgebra.QuadraticForm.IsometryEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.IsometryEquiv.coe_toLinearEquiv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.IsometryEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.IsometryEquiv.map_app", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.IsometryEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.IsometryEquiv.refl", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.IsometryEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.IsometryEquiv.symm", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.IsometryEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.IsometryEquiv.trans", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.IsometryEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.IsometryEquiv.toIsometry", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.IsometryEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.Equivalent.refl", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.IsometryEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.Equivalent.symm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.IsometryEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.Equivalent.trans", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.IsometryEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.isometryEquivOfCompLinearEquiv", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.IsometryEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.isometryEquivBasisRepr", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.IsometryEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticForm.isometryEquivWeightedSumSquares", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.IsometryEquiv", "is_tactic_proof": true, "tactics": ["let", "refine", "convert", "rw"], "tactic_count": 4}
{"name": "QuadraticForm.equivalent_weightedSumSquares", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.IsometryEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticForm.equivalent_weightedSumSquares_units_of_nondegenerate'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.IsometryEquiv", "is_tactic_proof": true, "tactics": ["obtain", "have", "simp_rw", "exact"], "tactic_count": 4}
{"name": "QuadraticMap.prod", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.IsometryEquiv.prod", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.Isometry.inl", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.Isometry.inr", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.Isometry.fst", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.Isometry.snd", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.Isometry.fst_comp_inl", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.Isometry.snd_comp_inr", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.Isometry.snd_comp_inl", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.Isometry.fst_comp_inr", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.Equivalent.prod", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.IsometryEquiv.prodComm", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.IsometryEquiv.prodProdProdComm", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.anisotropic_of_prod", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Prod", "is_tactic_proof": true, "tactics": ["simp_rw", "constructor", "intro", "refine", "rw", "intro", "refine", "rw"], "tactic_count": 8}
{"name": "QuadraticMap.nonneg_prod_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Prod", "is_tactic_proof": true, "tactics": ["simp_rw", "constructor", "intro", "constructor", "intro", "intro", "rintro", "exact"], "tactic_count": 8}
{"name": "QuadraticMap.posDef_prod_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Prod", "is_tactic_proof": true, "tactics": ["simp_rw", "constructor", "rintro", "obtain", "exact", "rintro", "refine", "rintro", "rw", "rwa"], "tactic_count": 10}
{"name": "QuadraticMap.PosDef.prod", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.IsOrtho.prod", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.IsOrtho.inl_inr", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.IsOrtho.inr_inl", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.isOrtho_inl_inl_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "QuadraticMap.isOrtho_inr_inr_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "QuadraticMap.polar_prod", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Prod", "is_tactic_proof": true, "tactics": ["dsimp", "abel"], "tactic_count": 2}
{"name": "QuadraticMap.polarBilin_prod", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.associated_prod", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Prod", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "rfl"], "tactic_count": 3}
{"name": "QuadraticMap.pi", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.pi_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.pi_apply_single", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Prod", "is_tactic_proof": true, "tactics": ["rw", "rw"], "tactic_count": 2}
{"name": "QuadraticMap.IsometryEquiv.pi", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.Isometry.single", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.Isometry.proj", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.Isometry.proj_comp_single_of_same", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.Isometry.proj_comp_single_of_ne", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.Equivalent.pi", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.anisotropic_of_pi", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Prod", "is_tactic_proof": true, "tactics": ["simp_rw", "intro", "classical", "have", "rw", "exact", "apply", "intro", "by_cases", "subst", "rw"], "tactic_count": 11}
{"name": "QuadraticMap.nonneg_pi_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Prod", "is_tactic_proof": true, "tactics": ["simp_rw", "constructor", "intro", "classical", "convert", "rw", "rw", "rintro", "exact"], "tactic_count": 9}
{"name": "QuadraticMap.posDef_pi_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Prod", "is_tactic_proof": true, "tactics": ["simp_rw", "constructor", "rintro", "intro", "exact", "intro", "refine", "rw", "exact", "exact"], "tactic_count": 10}
{"name": "QuadraticMap.Ring.polar_pi", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Prod", "is_tactic_proof": true, "tactics": ["dsimp", "simp_rw"], "tactic_count": 2}
{"name": "QuadraticMap.Ring.polarBilin_pi", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.Ring.associated_pi", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Prod", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "rfl"], "tactic_count": 3}
{"name": "QuadraticModuleCat.instCoeSortType", "kind": "instance", "module": "Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticModuleCat.moduleCat_of_toModuleCat", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticModuleCat.of", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticModuleCat.category", "kind": "instance", "module": "Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticModuleCat.concreteCategory", "kind": "instance", "module": "Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticModuleCat.Hom.toIsometry", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticModuleCat.ofHom", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticModuleCat.Hom.toIsometry_injective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticModuleCat.hom_ext", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticModuleCat.toIsometry_comp", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticModuleCat.toIsometry_id", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticModuleCat.hasForgetToModule", "kind": "instance", "module": "Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticModuleCat.forget₂_obj", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticModuleCat.forget₂_map", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticModuleCat.ofIso", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticModuleCat.ofIso_refl", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticModuleCat.ofIso_symm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticModuleCat.ofIso_trans", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.toIsometryEquiv", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.toIsometryEquiv_refl", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.toIsometryEquiv_symm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.Iso.toIsometryEquiv_trans", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticModuleCat.instMonoidalCategory.tensorObj", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticModuleCat.instMonoidalCategory.tensorHom", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticModuleCat.instMonoidalCategoryStruct", "kind": "instance", "module": "Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticModuleCat.toIsometry_tensorHom", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticModuleCat.toIsometry_whiskerLeft", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticModuleCat.toIsometry_whiskerRight", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticModuleCat.toIsometry_hom_leftUnitor", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticModuleCat.toIsometry_inv_leftUnitor", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticModuleCat.toIsometry_hom_rightUnitor", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticModuleCat.toIsometry_inv_rightUnitor", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticModuleCat.hom_hom_associator", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticModuleCat.hom_inv_associator", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticModuleCat.toModuleCat_tensor", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticModuleCat.forget₂_map_associator_hom", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticModuleCat.forget₂_map_associator_inv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticModuleCat.instMonoidalCategory", "kind": "instance", "module": "Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticModuleCat._example", "kind": "example", "module": "Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat.Monoidal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticModuleCat.instBraidedCategory", "kind": "instance", "module": "Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat.Symmetric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticModuleCat.instBraidedModuleCatForget₂", "kind": "instance", "module": "Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat.Symmetric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticModuleCat.instSymmetricCategory", "kind": "instance", "module": "Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat.Symmetric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticForm.isometryEquivSignWeightedSumSquares", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.Real", "is_tactic_proof": true, "tactics": ["let", "have", "have", "have", "by_cases", "simp", "simp", "convert", "ext1", "classical", "suffices", "simpa", "exact"], "tactic_count": 13}
{"name": "QuadraticForm.equivalent_sign_ne_zero_weighted_sum_squared", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticForm.equivalent_one_neg_one_weighted_sum_squared", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticForm.equivalent_signType_weighted_sum_squared", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticForm.equivalent_one_zero_neg_one_weighted_sum_squared", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.tensorDistrib", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.tensorDistrib_tmul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.tmul", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.QuadraticForm.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.associated_tmul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.TensorProduct", "is_tactic_proof": true, "tactics": ["letI", "rw", "have", "convert", "associated_left_inverse"], "tactic_count": 5}
{"name": "QuadraticForm.tensorDistrib", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticForm.tensorDistrib_tmul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticForm.tmul", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.QuadraticForm.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticForm.associated_tmul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.TensorProduct", "is_tactic_proof": false, "tactics": ["rw", "aesop"], "tactic_count": 2}
{"name": "QuadraticForm.polarBilin_tmul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.TensorProduct", "is_tactic_proof": false, "tactics": ["simp_rw", "associated_tmul]", "rw"], "tactic_count": 3}
{"name": "QuadraticForm.baseChange", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticForm.baseChange_tmul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticForm.associated_baseChange", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.TensorProduct", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "exact"], "tactic_count": 3}
{"name": "QuadraticForm.polarBilin_baseChange", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.TensorProduct", "is_tactic_proof": true, "tactics": ["rw", "two_nsmul_associated", "invOf_two_add_invOf_two,"], "tactic_count": 3}
{"name": "baseChange_ext", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticForm.tmul_comp_tensorMap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.TensorProduct.Isometries", "is_tactic_proof": true, "tactics": ["have", "have", "refine", "ext", "simp"], "tactic_count": 5}
{"name": "QuadraticForm.tmul_tensorMap_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.TensorProduct.Isometries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.Isometry.tmul", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.TensorProduct.Isometries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticMap.Isometry.tmul_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.TensorProduct.Isometries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticForm.tmul_comp_tensorComm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.TensorProduct.Isometries", "is_tactic_proof": true, "tactics": ["refine", "ext", "dsimp", "simp", "exact"], "tactic_count": 5}
{"name": "QuadraticForm.tmul_tensorComm_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.TensorProduct.Isometries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticForm.tensorComm", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.TensorProduct.Isometries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticForm.tensorComm_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.TensorProduct.Isometries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticForm.tensorComm_symm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.TensorProduct.Isometries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticForm.tmul_comp_tensorAssoc", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.TensorProduct.Isometries", "is_tactic_proof": true, "tactics": ["refine", "ext", "dsimp", "simp", "exact"], "tactic_count": 5}
{"name": "QuadraticForm.tmul_tensorAssoc_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.TensorProduct.Isometries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticForm.tensorAssoc", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.TensorProduct.Isometries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticForm.tensorAssoc_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.TensorProduct.Isometries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticForm.tensorAssoc_symm_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.TensorProduct.Isometries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticForm.comp_tensorRId_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.TensorProduct.Isometries", "is_tactic_proof": true, "tactics": ["refine", "ext", "dsimp", "simp", "simp"], "tactic_count": 5}
{"name": "QuadraticForm.tmul_tensorRId_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.TensorProduct.Isometries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticForm.tensorRId", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.TensorProduct.Isometries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticForm.tensorRId_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.TensorProduct.Isometries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticForm.tensorRId_symm_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.TensorProduct.Isometries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticForm.comp_tensorLId_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.TensorProduct.Isometries", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "QuadraticForm.tmul_tensorLId_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.TensorProduct.Isometries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticForm.tensorLId", "kind": "definition", "module": "Mathlib.LinearAlgebra.QuadraticForm.TensorProduct.Isometries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticForm.tensorLId_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.TensorProduct.Isometries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuadraticForm.tensorLId_symm_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.QuadraticForm.TensorProduct.Isometries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.Quotient.restrictScalarsEquiv", "kind": "definition", "module": "Mathlib.LinearAlgebra.Quotient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.Quotient.restrictScalarsEquiv_mk", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.Quotient.restrictScalarsEquiv_symm_mk", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.Quotient.nontrivial_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.Quotient.subsingleton_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.Quotient.instSubsingletonQuotient", "kind": "instance", "module": "Mathlib.LinearAlgebra.Quotient.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Submodule.Quotient.nontrivial_of_lt_top", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.Quotient.nontrivial_of_ne_top", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.QuotientBot.infinite", "kind": "instance", "module": "Mathlib.LinearAlgebra.Quotient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.QuotientTop.unique", "kind": "instance", "module": "Mathlib.LinearAlgebra.Quotient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.QuotientTop.fintype", "kind": "instance", "module": "Mathlib.LinearAlgebra.Quotient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.unique_quotient_iff_eq_top", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.Quotient.fintype", "kind": "instance", "module": "Mathlib.LinearAlgebra.Quotient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.strictMono_comap_prod_map", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.liftQ", "kind": "definition", "module": "Mathlib.LinearAlgebra.Quotient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.liftQ_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.liftQ_mkQ", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Submodule.pi_liftQ_eq_liftQ_pi", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Submodule.liftQSpanSingleton", "kind": "definition", "module": "Mathlib.LinearAlgebra.Quotient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.liftQSpanSingleton_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.range_mkQ", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.ker_mkQ", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Submodule.le_comap_mkQ", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Submodule.mkQ_map_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submodule.comap_map_mkQ", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Submodule.map_mkQ_eq_top", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Submodule.mapQ", "kind": "definition", "module": "Mathlib.LinearAlgebra.Quotient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mapQ_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mapQ_mkQ", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Submodule.comap_liftQ", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.map_liftQ", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.ker_liftQ", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.range_liftQ", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Submodule.ker_liftQ_eq_bot", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submodule.ker_liftQ_eq_bot'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.factor", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.Quotient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.factor_mk", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.factor_comp_mk", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Basic", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "Submodule.factor_comp", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Submodule.factor_comp_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Submodule.factor_surjective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Basic", "is_tactic_proof": true, "tactics": ["intro", "use", "exact"], "tactic_count": 3}
{"name": "Submodule.comapMkQRelIso", "kind": "definition", "module": "Mathlib.LinearAlgebra.Quotient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.comapMkQOrderEmbedding", "kind": "definition", "module": "Mathlib.LinearAlgebra.Quotient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.comapMkQOrderEmbedding_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.span_preimage_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Basic", "is_tactic_proof": true, "tactics": ["suffices", "have", "let", "have", "rw", "use", "rw", "exact", "rw", "rw", "rw", "exact"], "tactic_count": 12}
{"name": "Submodule.Quotient.equiv", "kind": "definition", "module": "Mathlib.LinearAlgebra.Quotient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.Quotient.equiv_symm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.Quotient.equiv_trans", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Basic", "is_tactic_proof": false, "tactics": ["ext", "simp", "rw"], "tactic_count": 3}
{"name": "LinearMap.range_mkQ_comp", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.ker_le_range_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LinearMap.range_eq_top_of_cancel", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Basic", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "Submodule.quotEquivOfEqBot", "kind": "definition", "module": "Mathlib.LinearAlgebra.Quotient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.quotEquivOfEqBot_apply_mk", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.quotEquivOfEqBot_symm_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.coe_quotEquivOfEqBot_symm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.Quotient.equiv_refl", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mapQLinear", "kind": "definition", "module": "Mathlib.LinearAlgebra.Quotient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.liftQ₂", "kind": "definition", "module": "Mathlib.LinearAlgebra.Quotient.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.liftQ₂_mk", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsRefl.liftQ₂", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.Quotient.Bilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.card_eq_card_quotient_mul_card", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Card", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Submodule.quotientRel", "kind": "definition", "module": "Mathlib.LinearAlgebra.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.quotientRel_def", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.hasQuotient", "kind": "instance", "module": "Mathlib.LinearAlgebra.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.Quotient.mk", "kind": "definition", "module": "Mathlib.LinearAlgebra.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.Quotient.mk'_eq_mk'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.Quotient.mk''_eq_mk", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.Quotient.quot_mk_eq_mk", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.Quotient.quotientAddGroupMk_eq_mk", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.Quotient.eq'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.Quotient.eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.Quotient.instZeroQuotient", "kind": "instance", "module": "Mathlib.LinearAlgebra.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.Quotient.instInhabitedQuotient", "kind": "instance", "module": "Mathlib.LinearAlgebra.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.Quotient.mk_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.Quotient.mk_eq_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Submodule.Quotient.addCommGroup", "kind": "instance", "module": "Mathlib.LinearAlgebra.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.Quotient.mk_add", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.Quotient.mk_neg", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.Quotient.mk_sub", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.Quotient.mk_out", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.Quotient.forall", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.Quotient.instSMul'", "kind": "instance", "module": "Mathlib.LinearAlgebra.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.Quotient.instSMul", "kind": "instance", "module": "Mathlib.LinearAlgebra.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.Quotient.mk_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.Quotient.smulCommClass", "kind": "instance", "module": "Mathlib.LinearAlgebra.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.Quotient.isScalarTower", "kind": "instance", "module": "Mathlib.LinearAlgebra.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.Quotient.isCentralScalar", "kind": "instance", "module": "Mathlib.LinearAlgebra.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.Quotient.mulAction'", "kind": "instance", "module": "Mathlib.LinearAlgebra.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.Quotient.mulAction", "kind": "instance", "module": "Mathlib.LinearAlgebra.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.Quotient.smulZeroClass'", "kind": "instance", "module": "Mathlib.LinearAlgebra.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.Quotient.smulZeroClass", "kind": "instance", "module": "Mathlib.LinearAlgebra.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.Quotient.distribSMul'", "kind": "instance", "module": "Mathlib.LinearAlgebra.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.Quotient.distribSMul", "kind": "instance", "module": "Mathlib.LinearAlgebra.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.Quotient.distribMulAction'", "kind": "instance", "module": "Mathlib.LinearAlgebra.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.Quotient.distribMulAction", "kind": "instance", "module": "Mathlib.LinearAlgebra.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.Quotient.module'", "kind": "instance", "module": "Mathlib.LinearAlgebra.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.Quotient.module", "kind": "instance", "module": "Mathlib.LinearAlgebra.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.Quotient.induction_on", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.Quotient.mk_surjective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Defs", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "Submodule.Quotient.instSmallQuotient", "kind": "instance", "module": "Mathlib.LinearAlgebra.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.quot_hom_ext", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mkQ", "kind": "definition", "module": "Mathlib.LinearAlgebra.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mkQ_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mkQ_surjective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Defs", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "Submodule.linearMap_qext", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.quotEquivOfEq", "kind": "definition", "module": "Mathlib.LinearAlgebra.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.quotEquivOfEq_mk", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.piQuotientLift", "kind": "definition", "module": "Mathlib.LinearAlgebra.Quotient.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.piQuotientLift_mk", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Pi", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Submodule.piQuotientLift_single", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Pi", "is_tactic_proof": true, "tactics": ["simp_rw", "rw", "rw", "rintro", "rw", "intros", "have", "contradiction"], "tactic_count": 8}
{"name": "Submodule.quotientPiLift", "kind": "definition", "module": "Mathlib.LinearAlgebra.Quotient.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.quotientPiLift_mk", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.quotientPi_aux.toFun", "kind": "definition", "module": "Mathlib.LinearAlgebra.Quotient.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.quotientPi_aux.map_add", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.quotientPi_aux.map_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.quotientPi_aux.invFun", "kind": "definition", "module": "Mathlib.LinearAlgebra.Quotient.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.quotientPi_aux.left_inv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.quotientPi_aux.right_inv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Quotient.Pi", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "refine", "rw", "by_cases", "subst", "rw", "rw"], "tactic_count": 8}
{"name": "Submodule.quotientPi", "kind": "definition", "module": "Mathlib.LinearAlgebra.Quotient.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SameRay", "kind": "definition", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SameRay.zero_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SameRay.zero_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SameRay.of_subsingleton", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SameRay.of_subsingleton'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SameRay.refl", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SameRay.rfl", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SameRay.symm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SameRay.exists_pos", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SameRay.sameRay_comm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SameRay.trans", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "rcases", "exact", "rcases", "rcases", "refine", "rw"], "tactic_count": 8}
{"name": "SameRay.sameRay_nonneg_smul_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact", "refine", "module"], "tactic_count": 5}
{"name": "SameRay.sameRay_nonneg_smul_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SameRay.sameRay_pos_smul_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SameRay.sameRay_pos_smul_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SameRay.nonneg_smul_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SameRay.nonneg_smul_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SameRay.pos_smul_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SameRay.pos_smul_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SameRay.map", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.sameRay_map_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SameRay.sameRay_map_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SameRay.smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SameRay.add_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "rcases", "rcases", "rcases", "refine", "positivity", "convert"], "tactic_count": 8}
{"name": "SameRay.add_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RayVector", "kind": "definition", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RayVector.coe", "kind": "instance", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instNonemptyRayVectorOfNontrivial", "kind": "instance", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RayVector.Setoid", "kind": "instance", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Ray", "kind": "definition", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "equiv_iff_sameRay", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "rayOfNeZero", "kind": "definition", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Ray.ind", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instNonemptyRayOfNontrivial", "kind": "instance", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ray_eq_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ray_pos_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RayVector.mapLinearEquiv", "kind": "definition", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Ray.map", "kind": "definition", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Ray.map_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Ray.map_refl", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Ray.map_symm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instMulActionRayVector", "kind": "instance", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instMulActionRay", "kind": "instance", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Ray.linearEquiv_smul_eq_map", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smul_rayOfNeZero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Ray.units_smul_of_pos", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": true, "tactics": ["induction", "rw", "exact"], "tactic_count": 3}
{"name": "Module.Ray.someRayVector", "kind": "definition", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Ray.someRayVector_ray", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Ray.someVector", "kind": "definition", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Ray.someVector_ne_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Ray.someVector_ray", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sameRay_neg_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "sameRay_neg_swap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "eq_zero_of_sameRay_neg_smul_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": true, "tactics": ["rcases", "rfl", "simpa", "rw", "refine", "exact"], "tactic_count": 6}
{"name": "eq_zero_of_sameRay_self_neg", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": true, "tactics": ["refine", "rwa"], "tactic_count": 2}
{"name": "RayVector.instNeg", "kind": "instance", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RayVector.coe_neg", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RayVector.instInvolutiveNeg", "kind": "instance", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RayVector.equiv_neg_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instNegRay", "kind": "instance", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "neg_rayOfNeZero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Ray.instInvolutiveNeg", "kind": "instance", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Ray.ne_neg_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": true, "tactics": ["induction", "h", "rw", "exact"], "tactic_count": 4}
{"name": "Module.Ray.neg_units_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": true, "tactics": ["induction", "simp"], "tactic_count": 2}
{"name": "Module.Ray.units_smul_of_neg", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": true, "tactics": ["rw", "rwa"], "tactic_count": 2}
{"name": "Module.Ray.map_neg", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": true, "tactics": ["induction", "h"], "tactic_count": 2}
{"name": "sameRay_of_mem_orbit", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "units_inv_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sameRay_smul_right_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sameRay_smul_right_iff_of_ne", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "sameRay_smul_left_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sameRay_smul_left_iff_of_ne", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sameRay_neg_smul_right_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "sameRay_neg_smul_right_iff_of_ne", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "sameRay_neg_smul_left_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sameRay_neg_smul_left_iff_of_ne", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "units_smul_eq_self_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": true, "tactics": ["induction", "h"], "tactic_count": 2}
{"name": "units_smul_eq_neg_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "sameRay_or_sameRay_neg_iff_not_linearIndependent", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": true, "tactics": ["by_cases", "by_cases", "simp_rw", "refine", "rcases", "exact", "exact", "refine", "rw", "simp", "exact", "exact", "refine", "rw", "simp", "rcases", "rw", "dsimp", "rcases", "refine", "linear_combination", "exfalso", "simp", "refine", "linear_combination", "exfalso", "simp", "rw", "exact", "exfalso", "simp", "refine", "rwa", "exfalso", "simp", "refine", "rwa"], "tactic_count": 37}
{"name": "sameRay_or_ne_zero_and_sameRay_neg_iff_not_linearIndependent", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": true, "tactics": ["rw", "by_cases", "by_cases"], "tactic_count": 3}
{"name": "SameRay.exists_pos_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SameRay.exists_pos_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SameRay.exists_nonneg_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": true, "tactics": ["obtain", "exact", "exact"], "tactic_count": 3}
{"name": "SameRay.exists_nonneg_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SameRay.exists_eq_smul_add", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": true, "tactics": ["rcases", "use", "simp", "use", "simp", "have", "refine", "rw", "rw", "rw"], "tactic_count": 10}
{"name": "SameRay.exists_eq_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_pos_left_iff_sameRay", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": true, "tactics": ["refine", "rcases", "exact"], "tactic_count": 3}
{"name": "exists_pos_left_iff_sameRay_and_ne_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "simp", "rintro", "exact"], "tactic_count": 5}
{"name": "exists_nonneg_left_iff_sameRay", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": true, "tactics": ["refine", "rcases", "exact"], "tactic_count": 3}
{"name": "exists_pos_right_iff_sameRay", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "exact"], "tactic_count": 3}
{"name": "exists_pos_right_iff_sameRay_and_ne_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "exact"], "tactic_count": 3}
{"name": "exists_nonneg_right_iff_sameRay", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Ray", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "exact"], "tactic_count": 3}
{"name": "Module.preReflection", "kind": "definition", "module": "Mathlib.LinearAlgebra.Reflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.preReflection_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Reflection", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Module.preReflection_apply_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Reflection", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Module.involutive_preReflection", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Reflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.preReflection_preReflection", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Reflection", "is_tactic_proof": true, "tactics": ["ext", "simp", "map_smul,", "abel"], "tactic_count": 4}
{"name": "Module.reflection", "kind": "definition", "module": "Mathlib.LinearAlgebra.Reflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.reflection_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Reflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.reflection_apply_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Reflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.involutive_reflection", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Reflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.reflection_inv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Reflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.reflection_symm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Reflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.invOn_reflection_of_mapsTo", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Reflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.bijOn_reflection_of_mapsTo", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Reflection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mem_invtSubmodule_reflection_of_mem", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Reflection", "is_tactic_proof": true, "tactics": ["suffices", "intro", "simpa"], "tactic_count": 3}
{"name": "Submodule.mem_invtSubmodule_reflection_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Reflection", "is_tactic_proof": true, "tactics": ["refine", "have", "suffices", "have", "rw", "exact", "specialize", "simp", "simpa", "have", "simpa"], "tactic_count": 11}
{"name": "Module.Dual.eq_of_preReflection_mapsTo", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Reflection", "is_tactic_proof": true, "tactics": ["have", "let", "have", "ext", "simp", "abel", "replace", "intro", "induction", "zero", "succ", "ih", "have", "rw", "simp_rw", "add_smul,", "suffices", "obtain", "replace", "simpa", "exact"], "tactic_count": 21}
{"name": "Module.Dual.eq_of_preReflection_mapsTo'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Reflection", "is_tactic_proof": true, "tactics": ["set", "rw", "have", "have", "simp", "rw", "simp", "let", "have", "intro", "simp", "rw", "simp", "rw", "exact", "exact"], "tactic_count": 16}
{"name": "Module.reflection_reflection_iterate", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Reflection", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "ih", "have", "intro", "rw", "simp", "reflection_apply_self,", "abel"], "tactic_count": 10}
{"name": "Module.infinite_range_reflection_reflection_iterate_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Reflection", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Module.eq_of_mapsTo_reflection_of_mem", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Reflection", "is_tactic_proof": false, "tactics": ["suffices", "rw", "exact", "contrapose", "apply", "rw", "intro", "rw", "n]", "exact"], "tactic_count": 10}
{"name": "Module.injOn_dualMap_subtype_span_range_range", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Reflection", "is_tactic_proof": true, "tactics": ["rintro", "congr", "suffices", "rw", "exact", "eq_of_mapsTo_reflection_of_mem", "intro", "simpa"], "tactic_count": 8}
{"name": "RootPairing.Base.support_nonempty", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Base", "is_tactic_proof": true, "tactics": ["by_contra", "inhabit", "simpa"], "tactic_count": 3}
{"name": "RootPairing.Base.flip", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.Base", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Base.root_ne_neg_of_ne", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Base", "is_tactic_proof": true, "tactics": ["classical", "intro", "have", "linearIndepOn_iff'.mp", "simp_all"], "tactic_count": 5}
{"name": "RootPairing.Base.linearIndependent_pair_of_ne", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Base", "is_tactic_proof": true, "tactics": ["have", "rw", "simpa"], "tactic_count": 3}
{"name": "RootPairing.Base.root_mem_span_int", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Base", "is_tactic_proof": true, "tactics": ["have", "simp", "rw", "rcases", "exact", "rw", "exact"], "tactic_count": 7}
{"name": "RootPairing.Base.coroot_mem_span_int", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Base", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Base.span_int_root_support", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Base", "is_tactic_proof": true, "tactics": ["refine", "rintro", "exact"], "tactic_count": 3}
{"name": "RootPairing.Base.span_int_coroot_support", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Base", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Base.span_root_support", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Base", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RootPairing.Base.span_coroot_support", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Base", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Base.eq_one_or_neg_one_of_mem_support_of_smul_mem_aux", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Base", "is_tactic_proof": true, "tactics": ["classical", "obtain", "obtain", "have", "rw", "refine", "simp", "simp_rw", "use", "replace", "linearCombination", "rw", "simp_rw", "let", "have", "rw", "have", "simpa"], "tactic_count": 18}
{"name": "RootPairing.Base.eq_one_or_neg_one_of_mem_support_of_smul_mem", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Base", "is_tactic_proof": true, "tactics": ["obtain", "replace", "obtain", "simpa", "obtain", "have", "simpa", "suffices", "rcases", "left", "right", "norm_cast", "rw", "tauto"], "tactic_count": 14}
{"name": "RootPairing.Base.pos_or_neg_of_sum_smul_root_mem", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Base", "is_tactic_proof": false, "tactics": ["suffices", "obtain", "have", "rcases", "left", "right", "intro", "let", "replace", "suffices", "rw", "rw", "obtain", "replace", "have", "intro", "by_cases", "change", "simp", "replace", "simp_all", "refine", "by_contra", "replace", "contradiction"], "tactic_count": 25}
{"name": "RootPairing.Base.not_nonpos_iff_pos_of_sum_mem_range_root", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Base", "is_tactic_proof": true, "tactics": ["rw", "refine", "rcases", "exact", "exfalso", "exact", "contrapose"], "tactic_count": 7}
{"name": "RootPairing.Base.not_nonneg_iff_neg_of_sum_mem_range_root", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Base", "is_tactic_proof": true, "tactics": ["replace", "have", "simp_all"], "tactic_count": 3}
{"name": "RootPairing.Base.sub_notMem_range_root", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Base", "is_tactic_proof": true, "tactics": ["rcases", "simpa", "classical", "let", "have", "have", "rw", "simp", "intro", "rcases", "simpa", "simpa"], "tactic_count": 12}
{"name": "RootPairing.Base.sub_notMem_range_coroot", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Base", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Base.pairingIn_le_zero_of_ne", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Base", "is_tactic_proof": true, "tactics": ["by_contra", "exact"], "tactic_count": 2}
{"name": "RootPairing.Base.chainBotCoeff_eq_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Base", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Base.chainTopCoeff_eq_of_ne", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Base", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "RootPairing.Base.toWeightBasis", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.Base", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Base.toWeightBasis_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Base", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RootPairing.Base.toWeightBasis_repr_root", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Base", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RootPairing.Base.toCoweightBasis", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.Base", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Base.toCoweightBasis_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Base", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Base.toCoweightBasis_repr_coroot", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Base", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RootPairing.Base.exists_root_eq_sum_nat_or_neg", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Base", "is_tactic_proof": true, "tactics": ["classical", "simp_rw", "suffices", "rcases", "obtain", "exact", "obtain", "exact", "intro", "refine", "rintro", "exact", "intro", "refine", "exact"], "tactic_count": 15}
{"name": "RootPairing.Base.exists_root_eq_sum_int", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Base", "is_tactic_proof": true, "tactics": ["obtain", "refine", "by_contra", "replace", "exact", "refine", "by_contra", "replace", "exact"], "tactic_count": 9}
{"name": "RootPairing.Base.height", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.Base", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Base.height_eq_sum", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Base", "is_tactic_proof": true, "tactics": ["suffices", "intro", "obtain", "rw", "b.support.sum_subtype", "have", "simpa"], "tactic_count": 7}
{"name": "RootPairing.Base.height_ne_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Base", "is_tactic_proof": true, "tactics": ["obtain", "rw", "rcases", "refine", "by_contra", "replace", "by_cases", "exact", "simpa", "exact", "refine", "by_contra", "replace", "by_cases", "exact", "simpa", "exact"], "tactic_count": 17}
{"name": "RootPairing.Base.height_reflectionPerm_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Base", "is_tactic_proof": true, "tactics": ["letI", "obtain", "have", "simp"], "tactic_count": 4}
{"name": "RootPairing.Base.height_one_of_mem_support", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Base", "is_tactic_proof": true, "tactics": ["classical", "have", "rw", "simpa"], "tactic_count": 4}
{"name": "RootPairing.Base.height_add", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Base", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "have", "simp_rw", "simp_rw"], "tactic_count": 5}
{"name": "RootPairing.Base.height_sub", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Base", "is_tactic_proof": true, "tactics": ["letI", "replace", "rw"], "tactic_count": 3}
{"name": "RootPairing.Base.height_add_zsmul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Base", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "have", "simp_rw", "hk]", "simp_rw"], "tactic_count": 6}
{"name": "RootPairing.Base.IsPos", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.Base", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Base.isPos_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Base", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Base.isPos_iff'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Base", "is_tactic_proof": true, "tactics": ["rw", "have", "lia"], "tactic_count": 3}
{"name": "RootPairing.Base.IsPos.or_neg", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Base", "is_tactic_proof": true, "tactics": ["rw", "have", "lia"], "tactic_count": 3}
{"name": "RootPairing.Base.IsPos.neg_iff_not", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Base", "is_tactic_proof": true, "tactics": ["rw", "have", "lia"], "tactic_count": 3}
{"name": "RootPairing.Base.isPos_of_mem_support", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Base", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "RootPairing.Base.IsPos.add", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Base", "is_tactic_proof": true, "tactics": ["rw", "rw", "lia"], "tactic_count": 3}
{"name": "RootPairing.Base.IsPos.sub", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Base", "is_tactic_proof": true, "tactics": ["rw", "rw", "lia"], "tactic_count": 3}
{"name": "RootPairing.Base.IsPos.exists_mem_support_pos_pairingIn", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Base", "is_tactic_proof": true, "tactics": ["by_contra", "suffices", "obtain", "replace", "refine", "rw", "contrapose", "exact", "have", "algebraMap_injective", "simp_rw", "rw", "refine", "by_cases", "exact", "simp_all"], "tactic_count": 16}
{"name": "RootPairing.Base.exists_mem_support_pos_pairingIn_ne_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Base", "is_tactic_proof": true, "tactics": ["rcases", "obtain", "exact", "obtain", "exact"], "tactic_count": 5}
{"name": "RootPairing.Base.IsPos.add_zsmul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Base", "is_tactic_proof": false, "tactics": ["replace", "refine", "letI", "replace", "rw", "lia", "induction", "zero", "succ", "hw", "obtain", "replace", "simp", "lia", "replace", "exact", "pred", "hw", "obtain", "replace", "rw", "simp", "lia", "replace", "exact"], "tactic_count": 25}
{"name": "RootPairing.Base.IsPos.reflectionPerm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Base", "is_tactic_proof": false, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "RootPairing.Base.IsPos.induction_on_add", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Base", "is_tactic_proof": true, "tactics": ["generalize", "induction", "zero", "succ", "obtain", "rw", "rcases", "obtain", "have", "have", "exact", "pred", "rw", "lia"], "tactic_count": 14}
{"name": "RootPairing.Base.exists_eq_sum_and_forall_sum_mem_of_isPos", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Base", "is_tactic_proof": true, "tactics": ["apply", "intro", "refine", "simpa", "simp", "by_cases", "have", "rw", "simp", "replace", "replace", "simp"], "tactic_count": 12}
{"name": "RootPairing.Base.induction_add", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Base", "is_tactic_proof": true, "tactics": ["letI", "rcases", "exact", "suffices", "exact"], "tactic_count": 5}
{"name": "RootPairing.Base.IsPos.induction_on_reflect", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Base", "is_tactic_proof": true, "tactics": ["generalize", "induction", "ind", "obtain", "rw", "rcases", "have", "have", "suffices", "have", "lia", "have", "rw", "rw", "replace", "aesop", "simpa"], "tactic_count": 17}
{"name": "RootPairing.Base.induction_reflect", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Base", "is_tactic_proof": true, "tactics": ["letI", "rcases", "exact", "suffices", "exact"], "tactic_count": 5}
{"name": "RootPairing.Base.forall_mem_support_invtSubmodule_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Base", "is_tactic_proof": true, "tactics": ["refine", "letI", "have", "refine", "clear", "intro", "rw", "exact"], "tactic_count": 8}
{"name": "RootPairing.instIsBalancedOfIsRootSystem", "kind": "instance", "module": "Mathlib.LinearAlgebra.RootSystem.BaseChange", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.restrictScalars'", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.BaseChange", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.instIsRootSystemSubtypeMemSubmoduleSpanRangeCoeEmbeddingRootCorootRestrictScalars'", "kind": "instance", "module": "Mathlib.LinearAlgebra.RootSystem.BaseChange", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.restrictScalars_toLinearMap_apply_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.BaseChange", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RootPairing.restrictScalars_coe_root", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.BaseChange", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.restrictScalars_coe_coroot", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.BaseChange", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.restrictScalars_pairing", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.BaseChange", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RootPairing.restrictScalars", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.RootSystem.BaseChange", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.restrictScalarsRat", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.RootSystem.BaseChange", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.baseOf_pairwise_pairing_le_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.BaseExists", "is_tactic_proof": true, "tactics": ["letI", "intro", "have", "contrapose", "exact"], "tactic_count": 5}
{"name": "RootPairing.linearIndepOn_root_baseOf'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.BaseExists", "is_tactic_proof": true, "tactics": ["have", "have", "let", "let", "change", "suffices", "let", "obtain", "have", "have", "rintro", "rw", "simpa", "exact"], "tactic_count": 14}
{"name": "RootPairing.ncard_eq_finrank_of_linearIndepOn_of", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.BaseExists", "is_tactic_proof": false, "tactics": ["let", "rw", "rintro", "apply", "rcases", "simpa", "have", "rw", "simpa"], "tactic_count": 9}
{"name": "RootPairing.linearIndepOn_root_baseOf", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.BaseExists", "is_tactic_proof": true, "tactics": ["let", "let", "letI", "have", "let", "change", "have", "suffices", "rw", "simp", "apply", "rintro", "suffices", "rw", "image_comp]", "convert", "aesop", "rw", "exact", "have", "let", "replace", "exact", "rw", "replace", "rw", "simp", "rw"], "tactic_count": 28}
{"name": "RootPairing.eq_baseOf_of_linearIndepOn_of_mem_or_neg_mem_closure", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.BaseExists", "is_tactic_proof": true, "tactics": ["letI", "have", "have", "have", "rw", "suffices", "replace", "rcases", "exact", "suffices", "replace", "exact", "refine", "obtain", "obtain", "replace", "replace", "replace", "replace", "rwa", "lia"], "tactic_count": 21}
{"name": "RootPairing.eq_baseOf_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.BaseExists", "is_tactic_proof": true, "tactics": ["letI", "refine", "rintro", "exact"], "tactic_count": 4}
{"name": "_private.Mathlib.LinearAlgebra.RootSystem.BaseExists.0.RootPairing.baseOf_root_eq_baseOf_coroot_aux", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.BaseExists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.baseOf_root_eq_baseOf_coroot", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.BaseExists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.coroot_mem_or_neg_mem_closure_of_root", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.BaseExists", "is_tactic_proof": true, "tactics": ["letI", "letI", "let", "let", "obtain", "have", "have", "have", "refine", "simp", "exact", "simp", "let", "have", "obtain", "simp", "have", "obtain", "simp", "rw", "exact"], "tactic_count": 21}
{"name": "RootPairing.Base.mk'", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.BaseExists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.nonempty_base", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.BaseExists", "is_tactic_proof": true, "tactics": ["let", "let", "obtain", "exists_dual_forall_apply_ne_zero", "letI", "exact"], "tactic_count": 6}
{"name": "_private.Mathlib.LinearAlgebra.RootSystem.Basic.0.RootPairing.exist_eq_reflection_of_mapsTo", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.LinearAlgebra.RootSystem.Basic.0.RootPairing.choose_choose_eq_of_mapsTo", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "apply"], "tactic_count": 3}
{"name": "RootPairing.equiv_of_mapsTo", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.injOn_dualMap_subtype_span_root_coroot", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Basic", "is_tactic_proof": false, "tactics": ["have", "injOn_dualMap_subtype_span_range_range", "rintro", "exact"], "tactic_count": 4}
{"name": "RootPairing.ext", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Basic", "is_tactic_proof": false, "tactics": ["have", "ext", "refine", "conv_rhs", "simp", "simp", "suffices", "have", "ext", "apply", "simp", "apply", "exact", "exact", "exact", "exact", "exact"], "tactic_count": 17}
{"name": "_private.Mathlib.LinearAlgebra.RootSystem.Basic.0.RootPairing.coroot_eq_coreflection_of_root_eq'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Basic", "is_tactic_proof": true, "tactics": ["set", "set", "set", "set", "set", "set", "let", "have", "ext", "have", "simp", "obtain", "rw", "have", "simp", "rw", "abel", "suffices", "have", "have", "apply", "refine", "rw", "exact"], "tactic_count": 24}
{"name": "RootPairing.mk'", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.IsRootSystem.ext", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Basic", "is_tactic_proof": false, "tactics": ["suffices", "have", "have", "exact", "clear", "rintro", "use", "apply", "apply", "exact", "change", "simp_rw", "exact", "exact", "exact"], "tactic_count": 15}
{"name": "_private.Mathlib.LinearAlgebra.RootSystem.Basic.0.RootPairing.coroot_eq_coreflection_of_root_eq_of_span_eq_top", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Basic", "is_tactic_proof": true, "tactics": ["set", "set", "set", "set", "set", "set", "let", "have", "ext", "have", "simp", "apply", "apply", "simp", "ring", "rw", "exact"], "tactic_count": 17}
{"name": "RootPairing.mk''", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.isRootSystem_mk''", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Base.cartanMatrixIn", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.CartanMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Base.cartanMatrixIn_def", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.CartanMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Base.algebraMap_cartanMatrixIn_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.CartanMatrix", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RootPairing.Base.cartanMatrixIn_apply_same", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.CartanMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Base.cartanMatrixIn_mul_diagonal_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.CartanMatrix", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "RootPairing.Base.cartanMatrixIn_nondegenerate", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.CartanMatrix", "is_tactic_proof": true, "tactics": ["classical", "obtain", "replace", "rwa", "have", "rw", "aesop", "rw", "rwa"], "tactic_count": 9}
{"name": "RootPairing.Base.cartanMatrix", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.RootSystem.CartanMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Base.cartanMatrix_apply_same", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.CartanMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Base.cartanMatrix_apply_eq_zero_iff_pairing", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.CartanMatrix", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RootPairing.Base.cartanMatrix_apply_eq_zero_iff_symm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.CartanMatrix", "is_tactic_proof": true, "tactics": ["have", "simp"], "tactic_count": 2}
{"name": "RootPairing.Base.cartanMatrix_le_zero_of_ne", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.CartanMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Base.cartanMatrix_mem_of_ne", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.CartanMatrix", "is_tactic_proof": true, "tactics": ["have", "have", "simp", "have", "have", "suffices", "by_contra", "replace", "rw", "refine", "refine", "simp"], "tactic_count": 12}
{"name": "RootPairing.Base.cartanMatrix_eq_neg_chainTopCoeff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.CartanMatrix", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RootPairing.Base.cartanMatrix_apply_eq_zero_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.CartanMatrix", "is_tactic_proof": true, "tactics": ["rw", "replace", "tauto"], "tactic_count": 3}
{"name": "RootPairing.Base.abs_cartanMatrix_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.CartanMatrix", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simpa"], "tactic_count": 3}
{"name": "RootPairing.Base.cartanMatrix_map_abs", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.CartanMatrix", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "RootPairing.Base.cartanMatrix_nondegenerate", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.CartanMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Base.induction_on_cartanMatrix", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.CartanMatrix", "is_tactic_proof": true, "tactics": ["let", "have", "have", "refine", "contrapose", "exact", "have", "refine", "contrapose", "rw", "induction", "mem", "obtain", "replace", "rwa", "tauto", "zero", "add", "hy", "replace", "tauto", "smul", "have", "rw", "refine", "rw", "apply", "by_cases", "exact", "replace", "simp", "simp"], "tactic_count": 32}
{"name": "RootPairing.Base.injective_pairingIn", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.CartanMatrix", "is_tactic_proof": true, "tactics": ["classical", "intro", "obtain", "obtain", "let", "let", "suffices", "rw", "refine", "replace", "rw", "replace", "suffices", "simp", "refine", "simp_rw", "simp", "replace", "suffices", "simp", "refine", "simp_rw", "simp", "suffices", "rw", "apply", "rw", "exact"], "tactic_count": 28}
{"name": "RootPairing.Base.exists_mem_span_pairingIn_ne_zero_and_pairwise_ne", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.CartanMatrix", "is_tactic_proof": true, "tactics": ["set", "let", "suffices", "obtain", "refine", "simpa", "apply", "rintro", "obtain", "refine", "rw", "simpa", "obtain", "contrapose", "apply", "aesop", "simpa"], "tactic_count": 17}
{"name": "RootPairing.Base.apply_mem_range_root_of_cartanMatrixEq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.CartanMatrix", "is_tactic_proof": false, "tactics": ["have", "suffices", "rw", "exact", "intro", "suffices", "simpa", "obtain", "apply", "exact", "exact", "intro", "replace", "simpa", "rw", "exact"], "tactic_count": 16}
{"name": "RootPairing.Base.equivOfCartanMatrixEq", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.CartanMatrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.setOf_root_add_zsmul_eq_Icc_of_linearIndependent", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Chain", "is_tactic_proof": true, "tactics": ["replace", "set", "have", "have", "suffices", "intro", "have", "have", "have", "rwa", "exact", "have", "refine", "by_contra", "have", "replace", "replace", "simpa", "have", "rw", "contrapose", "replace", "exact", "have", "replace", "replace", "simpa", "have", "rw", "contrapose", "replace", "exact", "have", "have", "contrapose", "exact", "have", "apply", "rw", "simp", "have", "have", "contrapose", "exact", "have", "apply", "rw", "simp", "lia"], "tactic_count": 49}
{"name": "RootPairing.chainTopCoeff", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.chainBotCoeff", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.chainTopCoeff_of_not_linearIndependent", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Chain", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RootPairing.chainBotCoeff_of_not_linearIndependent", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Chain", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RootPairing.root_add_nsmul_mem_range_iff_le_chainTopCoeff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Chain", "is_tactic_proof": true, "tactics": ["set", "suffices", "have", "obtain", "rw", "have", "lia"], "tactic_count": 7}
{"name": "RootPairing.root_sub_nsmul_mem_range_iff_le_chainBotCoeff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Chain", "is_tactic_proof": true, "tactics": ["set", "suffices", "simpa", "have", "simp", "obtain", "rw", "lia"], "tactic_count": 8}
{"name": "RootPairing.Iic_chainTopCoeff_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Chain", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "RootPairing.Iic_chainBotCoeff_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Chain", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "RootPairing.one_le_chainTopCoeff_of_root_add_mem", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Chain", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "RootPairing.one_le_chainBotCoeff_of_root_add_mem", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Chain", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "RootPairing.root_add_zsmul_mem_range_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Chain", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simp"], "tactic_count": 3}
{"name": "RootPairing.root_sub_zsmul_mem_range_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Chain", "is_tactic_proof": true, "tactics": ["rw", "lia"], "tactic_count": 2}
{"name": "RootPairing.setOf_root_add_zsmul_mem_eq_Icc", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Chain", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "RootPairing.setOf_root_sub_zsmul_mem_eq_Icc", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Chain", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "RootPairing.chainTopCoeff_eq_sSup", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Chain", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RootPairing.chainBotCoeff_eq_sSup", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Chain", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RootPairing.coe_chainTopCoeff_eq_sSup", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Chain", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "RootPairing.coe_chainBotCoeff_eq_sSup", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Chain", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "_private.Mathlib.LinearAlgebra.RootSystem.Chain.0.RootPairing.chainCoeff_reflectionPerm_left_aux", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Chain", "is_tactic_proof": true, "tactics": ["letI", "by_cases", "have", "ext", "rw", "smul_neg,", "lia", "have", "simp", "chainBotCoeff_of_not_linearIndependent"], "tactic_count": 10}
{"name": "_private.Mathlib.LinearAlgebra.RootSystem.Chain.0.RootPairing.chainCoeff_reflectionPerm_right_aux", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Chain", "is_tactic_proof": true, "tactics": ["letI", "by_cases", "have", "ext", "rw", "sub_neg_eq_add,", "have", "simp", "chainBotCoeff_of_not_linearIndependent"], "tactic_count": 9}
{"name": "RootPairing.chainTopCoeff_reflectionPerm_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Chain", "is_tactic_proof": true, "tactics": ["letI", "have", "z", "z", "refine", "simpa", "simpa"], "tactic_count": 7}
{"name": "RootPairing.chainBotCoeff_reflectionPerm_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Chain", "is_tactic_proof": true, "tactics": ["letI", "have", "z", "z", "refine", "simpa", "simpa"], "tactic_count": 7}
{"name": "RootPairing.chainTopCoeff_reflectionPerm_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Chain", "is_tactic_proof": true, "tactics": ["letI", "have", "z", "z", "refine", "simpa", "simpa"], "tactic_count": 7}
{"name": "RootPairing.chainBotCoeff_reflectionPerm_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Chain", "is_tactic_proof": true, "tactics": ["letI", "have", "z", "z", "refine", "simpa", "simpa"], "tactic_count": 7}
{"name": "RootPairing.chainBotCoeff_eq_zero_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Chain", "is_tactic_proof": true, "tactics": ["by_cases", "swap", "have", "simpa", "simp", "refine", "replace", "rw", "rw", "lia"], "tactic_count": 10}
{"name": "RootPairing.chainTopCoeff_eq_zero_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Chain", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "RootPairing.chainBotCoeff_of_add", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Chain", "is_tactic_proof": true, "tactics": ["have", "apply", "rw", "have", "replace", "have", "rw", "exact", "rw"], "tactic_count": 9}
{"name": "RootPairing.chainTopCoeff_of_sub", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Chain", "is_tactic_proof": true, "tactics": ["letI", "replace", "simpa"], "tactic_count": 3}
{"name": "RootPairing.chainTopCoeff_of_add", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Chain", "is_tactic_proof": true, "tactics": ["replace", "replace", "exact"], "tactic_count": 3}
{"name": "RootPairing.chainTopIdx", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.chainBotIdx", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.root_chainTopIdx", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Chain", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "exact", "simp"], "tactic_count": 4}
{"name": "RootPairing.root_chainBotIdx", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Chain", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "exact", "simp"], "tactic_count": 4}
{"name": "RootPairing.chainBotCoeff_sub_chainTopCoeff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Chain", "is_tactic_proof": false, "tactics": ["suffices", "refine", "specialize", "simp", "pairingIn_reflectionPerm_self_right]", "lia", "intro", "have", "simp", "module", "have", "rw", "exact", "rw", "lia"], "tactic_count": 15}
{"name": "RootPairing.chainTopCoeff_sub_chainBotCoeff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Chain", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RootPairing.chainCoeff_chainTopIdx_aux", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Chain", "is_tactic_proof": false, "tactics": ["have", "by_cases", "swap", "have", "set", "set", "have", "simp", "have", "rw", "have", "rw", "rw", "neg_neg]", "norm_cast"], "tactic_count": 15}
{"name": "RootPairing.chainBotCoeff_chainTopIdx", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.chainTopCoeff_chainTopIdx", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.chainBotCoeff_add_chainTopCoeff_eq_pairingIn_chainTopIdx", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Chain", "is_tactic_proof": false, "tactics": ["replace", "rwa", "calc"], "tactic_count": 3}
{"name": "RootPairing.chainBotCoeff_add_chainTopCoeff_le_three", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Chain", "is_tactic_proof": true, "tactics": ["by_cases", "swap", "rw", "have", "aesop"], "tactic_count": 5}
{"name": "RootDatum", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.flip", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.flip_flip", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.flipEquiv", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.instIsRootSystemFlip", "kind": "instance", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.ne_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.ne_zero'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.zero_notMem_range_root", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "RootPairing.zero_notMem_range_coroot", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.exists_ne_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "RootPairing.exists_ne_zero'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.nontrivial", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "RootPairing.nontrivial'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.root'", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.coroot'", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.pairing", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.pairing_flip", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.root_coroot_eq_pairing", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.root'_coroot_eq_pairing", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.root_coroot'_eq_pairing", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.coroot_root_eq_pairing", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RootPairing.pairing_same", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.pairing_eq_add_of_root_eq_add", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RootPairing.pairing_eq_add_of_root_eq_smul_add_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RootPairing.coroot_root_two", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RootPairing.reflection", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.root_reflectionPerm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.mapsTo_reflection_root", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "RootPairing.reflection_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.reflection_apply_root", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.reflection_apply_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.reflection_same", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.reflection_inv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.reflection_sq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.reflectionPerm_sq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": true, "tactics": ["ext", "apply", "simp"], "tactic_count": 3}
{"name": "RootPairing.reflectionPerm_inv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.reflectionPerm_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "RootPairing.reflectionPerm_involutive", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.reflectionPerm_symm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.bijOn_reflection_root", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.reflection_image_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.coreflection", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.coroot_reflectionPerm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.mapsTo_coreflection_coroot", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "RootPairing.coreflection_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.coreflection_apply_coroot", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.coreflection_apply_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.coreflection_same", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.coreflection_inv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.coreflection_sq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.bijOn_coreflection_coroot", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.coreflection_image_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.coreflection_eq_flip_reflection", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.reflection_reflectionPerm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "RootPairing.reflection_dualMap_eq_coreflection", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "RootPairing.coroot_eq_coreflection_of_root_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": true, "tactics": ["rw", "rw"], "tactic_count": 2}
{"name": "RootPairing.coroot'_reflectionPerm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "RootPairing.coroot'_reflection", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.pairing_reflectionPerm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": true, "tactics": ["simp", "simp"], "tactic_count": 2}
{"name": "RootPairing.toPerfPair_conj_reflection", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "RootPairing.toPerfPair_flip_conj_coreflection", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.pairing_reflectionPerm_self_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RootPairing.pairing_reflectionPerm_self_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": true, "tactics": ["rw", "root_coroot_eq_pairing]"], "tactic_count": 2}
{"name": "RootPairing.indexNeg", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.ne_neg", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": true, "tactics": ["have", "intro", "replace", "simp"], "tactic_count": 4}
{"name": "RootPairing.root_eq_neg_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "RootPairing.coroot_eq_neg_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.neg_mem_range_root_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": ["suffices", "refine", "rw", "exact", "intro", "exact"], "tactic_count": 6}
{"name": "RootPairing.neg_mem_range_coroot_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.neg_root_mem", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.neg_coroot_mem", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.smul_coroot_eq_of_root_eq_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": true, "tactics": ["have", "refine", "convert", "ext", "replace", "simp"], "tactic_count": 6}
{"name": "RootPairing.coroot_eq_smul_coroot_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.mem_range_root_of_mem_range_reflection_of_mem_range_root", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "exact"], "tactic_count": 3}
{"name": "RootPairing.mem_range_coroot_of_mem_range_coreflection_of_mem_range_coroot", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "exact"], "tactic_count": 3}
{"name": "RootPairing.pairing_smul_root_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "RootPairing.pairing_smul_coroot_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "RootPairing.two_nsmul_reflection_eq_of_perm_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": true, "tactics": ["ext", "suffices", "simpa", "calc", "rw", "rw", "rw", "rw", "rw"], "tactic_count": 9}
{"name": "RootPairing.reflectionPerm_eq_reflectionPerm_iff_of_isSMulRegular", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": true, "tactics": ["refine", "suffices", "replace", "exact"], "tactic_count": 4}
{"name": "RootPairing.reflectionPerm_eq_reflectionPerm_iff_of_span", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": true, "tactics": ["refine", "induction", "mem", "obtain", "simp", "zero", "add", "smul", "ext", "apply", "simp"], "tactic_count": 11}
{"name": "RootPairing.reflectionPerm_eq_reflectionPerm_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": true, "tactics": ["refine", "ext", "exact"], "tactic_count": 3}
{"name": "RootPairing.toPerfPair_comp_root", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.toPerfPair_flip_comp_coroot", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.coxeterWeight", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.coxeterWeight_flip", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RootPairing.coxeterWeight_swap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RootPairing.IsOrthogonal", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.isOrthogonal_symm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RootPairing.isOrthogonal_comm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": true, "tactics": ["rw", "ext", "replace", "simp", "h,", "abel"], "tactic_count": 6}
{"name": "RootPairing.IsOrthogonal.flip", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.IsOrthogonal.symm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.IsOrthogonal.reflection_apply_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RootPairing.IsOrthogonal.reflection_apply_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.IsOrthogonal.coreflection_apply_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.IsOrthogonal.coreflection_apply_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.isFixedPt_reflection_of_isOrthogonal", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": true, "tactics": ["rw", "induction", "zero", "add", "smul", "mem", "obtain", "exact"], "tactic_count": 8}
{"name": "RootPairing.reflectionPerm_eq_of_pairing_eq_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.reflectionPerm_eq_of_pairing_eq_zero'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.reflectionPerm_eq_iff_smul_root", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.reflectionPerm_eq_iff_smul_coroot", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.pairing_eq_zero_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": true, "tactics": ["suffices", "intro", "simpa"], "tactic_count": 3}
{"name": "RootPairing.pairing_eq_zero_iff'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "RootPairing.coxeterWeight_zero_iff_isOrthogonal", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": true, "tactics": ["have", "simp"], "tactic_count": 2}
{"name": "RootPairing.isOrthogonal_iff_pairing_eq_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.isFixedPt_reflectionPerm_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RootPairing.map", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.instIsRootSystemMap", "kind": "instance", "module": "Mathlib.LinearAlgebra.RootSystem.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Polarization", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.CanonicalBilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Polarization_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.CanonicalBilinear", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RootPairing.CoPolarization", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.CanonicalBilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.CoPolarization_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.CanonicalBilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.CoPolarization_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.CanonicalBilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.RootForm", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.CanonicalBilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.CorootForm", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.CanonicalBilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.rootForm_apply_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.CanonicalBilinear", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RootPairing.corootForm_apply_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.CanonicalBilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.toLinearMap_apply_apply_Polarization", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.CanonicalBilinear", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RootPairing.toLinearMap_apply_CoPolarization", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.CanonicalBilinear", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "RootPairing.flip_comp_polarization_eq_rootForm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.CanonicalBilinear", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "RootPairing.self_comp_coPolarization_eq_corootForm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.CanonicalBilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.polarization_apply_eq_zero_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.CanonicalBilinear", "is_tactic_proof": true, "tactics": ["rw", "refine", "rintro", "simpa"], "tactic_count": 4}
{"name": "RootPairing.coPolarization_apply_eq_zero_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.CanonicalBilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.ker_polarization_eq_ker_rootForm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.CanonicalBilinear", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "RootPairing.ker_copolarization_eq_ker_corootForm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.CanonicalBilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.rootForm_symmetric", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.CanonicalBilinear", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RootPairing.rootForm_reflection_reflection_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.CanonicalBilinear", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "RootPairing.rootForm_self_sum_of_squares", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.CanonicalBilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.rootForm_root_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.CanonicalBilinear", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RootPairing.range_polarization_domRestrict_le_span_coroot", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.CanonicalBilinear", "is_tactic_proof": true, "tactics": ["intro", "obtain", "rw", "refine", "use", "simp"], "tactic_count": 6}
{"name": "RootPairing.corootSpan_dualAnnihilator_le_ker_rootForm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.CanonicalBilinear", "is_tactic_proof": true, "tactics": ["rw", "intro", "ext", "simp_all"], "tactic_count": 4}
{"name": "RootPairing.rootSpan_dualAnnihilator_le_ker_rootForm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.CanonicalBilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.PolarizationIn", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.CanonicalBilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.PolarizationIn_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.CanonicalBilinear", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RootPairing.PolarizationIn_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.CanonicalBilinear", "is_tactic_proof": false, "tactics": ["simp", "refine", "rw"], "tactic_count": 3}
{"name": "RootPairing.range_polarizationIn", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.CanonicalBilinear", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "RootPairing.CoPolarizationIn", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.CanonicalBilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.CoPolarizationIn_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.CanonicalBilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.CoPolarizationIn_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.CanonicalBilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.RootFormIn", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.CanonicalBilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.algebraMap_rootFormIn", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.CanonicalBilinear", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RootPairing.toLinearMap_apply_PolarizationIn", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.CanonicalBilinear", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "RootPairing.range_polarizationIn_le_span_coroot", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.CanonicalBilinear", "is_tactic_proof": true, "tactics": ["intro", "obtain", "rw", "exact"], "tactic_count": 4}
{"name": "RootPairing.rootFormIn_self_smul_coroot", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.CanonicalBilinear", "is_tactic_proof": false, "tactics": ["have", "simp_rw", "exact", "rw", "nth_rw", "rw", "simp", "rw", "simp", "sub_eq_zero]", "refine", "intro", "rw"], "tactic_count": 13}
{"name": "RootPairing.prod_rootFormIn_smul_coroot_mem_range_PolarizationIn", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.CanonicalBilinear", "is_tactic_proof": false, "tactics": ["obtain", "rw", "refine", "use", "rw"], "tactic_count": 5}
{"name": "RootPairing.rootForm_self_smul_coroot", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.CanonicalBilinear", "is_tactic_proof": false, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "RootPairing.corootForm_self_smul_root", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.CanonicalBilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.four_nsmul_coPolarization_compl_polarization_apply_root", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.CanonicalBilinear", "is_tactic_proof": true, "tactics": ["rw", "rootForm_self_smul_coroot,"], "tactic_count": 2}
{"name": "RootPairing.four_smul_rootForm_sq_eq_coxeterWeight_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.CanonicalBilinear", "is_tactic_proof": false, "tactics": ["have", "rw", "have", "rw", "rw", "mul_smul_comm,", "smul_eq_mul,", "ring"], "tactic_count": 8}
{"name": "RootPairing.prod_rootForm_smul_coroot_mem_range_domRestrict", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.CanonicalBilinear", "is_tactic_proof": true, "tactics": ["obtain", "rw", "refine", "use", "simp"], "tactic_count": 5}
{"name": "RootPairing.posRootForm", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.CanonicalBilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.algebraMap_posRootForm_posForm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.CanonicalBilinear", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RootPairing.posRootForm_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.CanonicalBilinear", "is_tactic_proof": true, "tactics": ["ext", "apply", "simp"], "tactic_count": 3}
{"name": "RootPairing.exists_ge_zero_eq_rootForm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.CanonicalBilinear", "is_tactic_proof": true, "tactics": ["refine", "choose", "suffices", "apply", "simp", "simp"], "tactic_count": 6}
{"name": "RootPairing.posRootForm_posForm_apply_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.CanonicalBilinear", "is_tactic_proof": true, "tactics": ["refine", "simp"], "tactic_count": 2}
{"name": "RootPairing.zero_le_posForm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.CanonicalBilinear", "is_tactic_proof": true, "tactics": ["obtain", "have", "rwa"], "tactic_count": 3}
{"name": "RootPairing.zero_lt_pairingIn_iff'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.CanonicalBilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.pairingIn_lt_zero_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.CanonicalBilinear", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "RootPairing.pairingIn_le_zero_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.CanonicalBilinear", "is_tactic_proof": true, "tactics": ["rcases", "rw", "rw", "rw", "rw", "exact"], "tactic_count": 6}
{"name": "RootPairing.IsG2.toEmbeddedG2", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.G2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.IsG2.nonempty", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.G2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.isG2_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.G2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.isNotG2_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.G2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.not_isG2_iff_isNotG2", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.G2", "is_tactic_proof": true, "tactics": ["simp", "refine", "have", "have", "aesop", "specialize", "lia"], "tactic_count": 7}
{"name": "RootPairing.IsG2.pairingIn_mem_zero_one_three", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.G2", "is_tactic_proof": false, "tactics": ["suffices", "have", "have", "simp", "lia", "obtain", "push_neg", "refine", "have", "simp", "omega"], "tactic_count": 11}
{"name": "RootPairing.chainBotCoeff_add_chainTopCoeff_le_two", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.G2", "is_tactic_proof": true, "tactics": ["by_cases", "swap", "rw", "have", "aesop"], "tactic_count": 5}
{"name": "RootPairing.pairingIn_le_zero_of_root_add_mem", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.G2", "is_tactic_proof": true, "tactics": ["have", "have", "have", "rw", "lia"], "tactic_count": 5}
{"name": "RootPairing.zero_le_pairingIn_of_root_sub_mem", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.G2", "is_tactic_proof": true, "tactics": ["replace", "simpa"], "tactic_count": 2}
{"name": "RootPairing.chainBotCoeff_if_one_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.G2", "is_tactic_proof": true, "tactics": ["have", "have", "have", "have", "rcases", "simp_rw", "lia"], "tactic_count": 7}
{"name": "RootPairing.chainTopCoeff_if_one_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.G2", "is_tactic_proof": true, "tactics": ["letI", "replace", "simpa"], "tactic_count": 3}
{"name": "RootPairing.EmbeddedG2.ofPairingInThree", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.G2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.EmbeddedG2.instIsG2OfIsIrreducible", "kind": "instance", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.G2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.EmbeddedG2.pairing_long_short", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.G2", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "RootPairing.EmbeddedG2.shortAddLong", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.G2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.EmbeddedG2.twoShortAddLong", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.G2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.EmbeddedG2.threeShortAddLong", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.G2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.EmbeddedG2.threeShortAddTwoLong", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.G2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.EmbeddedG2.shortRoot", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.G2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.EmbeddedG2.longRoot", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.G2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.EmbeddedG2.shortAddLongRoot", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.G2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.EmbeddedG2.twoShortAddLongRoot", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.G2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.EmbeddedG2.threeShortAddLongRoot", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.G2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.EmbeddedG2.threeShortAddTwoLongRoot", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.G2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.EmbeddedG2.allRoots", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.G2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.EmbeddedG2.allRoots_subset_range_root", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.G2", "is_tactic_proof": true, "tactics": ["intro", "simp", "mem_singleton_iff]", "rcases"], "tactic_count": 4}
{"name": "RootPairing.EmbeddedG2.pairingIn_short_long", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.G2", "is_tactic_proof": true, "tactics": ["have", "aesop"], "tactic_count": 2}
{"name": "RootPairing.EmbeddedG2.pairing_short_long", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.G2", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "RootPairing.EmbeddedG2.shortAddLongRoot_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.G2", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RootPairing.EmbeddedG2.twoShortAddLongRoot_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.G2", "is_tactic_proof": true, "tactics": ["simp", "module"], "tactic_count": 2}
{"name": "RootPairing.EmbeddedG2.threeShortAddLongRoot_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.G2", "is_tactic_proof": true, "tactics": ["simp", "module"], "tactic_count": 2}
{"name": "RootPairing.EmbeddedG2.threeShortAddTwoLongRoot_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.G2", "is_tactic_proof": true, "tactics": ["simp", "module"], "tactic_count": 2}
{"name": "RootPairing.EmbeddedG2.linearIndependent_short_long", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.G2", "is_tactic_proof": true, "tactics": ["have", "simp"], "tactic_count": 2}
{"name": "RootPairing.EmbeddedG2.allCoeffs", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.G2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.EmbeddedG2.allRoots_eq_map_allCoeffs", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.G2", "is_tactic_proof": true, "tactics": ["simp", "threeShortAddLongRoot_eq,"], "tactic_count": 2}
{"name": "RootPairing.EmbeddedG2.allRoots_nodup", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.G2", "is_tactic_proof": false, "tactics": ["have", "rw", "exact", "rw", "decide"], "tactic_count": 5}
{"name": "RootPairing.EmbeddedG2.mem_span_of_mem_allRoots", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.G2", "is_tactic_proof": true, "tactics": ["have", "simp_rw", "simp", "tauto"], "tactic_count": 4}
{"name": "RootPairing.EmbeddedG2.long_eq_three_mul_short", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.G2", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "RootPairing.EmbeddedG2.shortAddLongRoot_shortRoot", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.G2", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RootPairing.EmbeddedG2.twoShortAddLongRoot_shortRoot", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.G2", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RootPairing.EmbeddedG2.threeShortAddLongRoot_longRoot", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.G2", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RootPairing.EmbeddedG2.threeShortAddTwoLongRoot_longRoot", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.G2", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RootPairing.EmbeddedG2.pairingIn_shortAddLong_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.G2", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RootPairing.EmbeddedG2.pairingIn_shortAddLong_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.G2", "is_tactic_proof": false, "tactics": ["suffices", "algebraMap_injective", "have", "have", "apply", "calc", "rw", "rw", "rw", "rw"], "tactic_count": 10}
{"name": "RootPairing.EmbeddedG2.pairingIn_twoShortAddLong_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.G2", "is_tactic_proof": true, "tactics": ["rw", "simp", "simp", "norm_cast"], "tactic_count": 4}
{"name": "RootPairing.EmbeddedG2.pairingIn_twoShortAddLong_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.G2", "is_tactic_proof": false, "tactics": ["suffices", "algebraMap_injective", "have", "have", "apply", "calc", "rw", "rw", "rw", "rw"], "tactic_count": 10}
{"name": "RootPairing.EmbeddedG2.pairingIn_threeShortAddLong_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.G2", "is_tactic_proof": true, "tactics": ["rw", "simp", "simp", "norm_cast"], "tactic_count": 4}
{"name": "RootPairing.EmbeddedG2.pairingIn_threeShortAddLong_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.G2", "is_tactic_proof": false, "tactics": ["suffices", "algebraMap_injective", "have", "have", "apply", "calc", "rw", "rw", "rw", "rw"], "tactic_count": 10}
{"name": "RootPairing.EmbeddedG2.pairingIn_threeShortAddTwoLong_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.G2", "is_tactic_proof": true, "tactics": ["rw", "simp", "simp", "norm_cast"], "tactic_count": 4}
{"name": "RootPairing.EmbeddedG2.pairingIn_threeShortAddTwoLong_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.G2", "is_tactic_proof": false, "tactics": ["suffices", "algebraMap_injective", "have", "have", "apply", "calc", "rw", "simp", "rw", "rw"], "tactic_count": 10}
{"name": "_private.Mathlib.LinearAlgebra.RootSystem.Finite.G2.0.RootPairing.EmbeddedG2.isOrthogonal_short_and_long_aux", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.G2", "is_tactic_proof": true, "tactics": ["simp", "omega"], "tactic_count": 2}
{"name": "RootPairing.EmbeddedG2.isOrthogonal_short_and_long", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.G2", "is_tactic_proof": false, "tactics": ["suffices", "have", "simpa", "simp", "obtain", "have", "have", "have", "have", "have", "have", "apply"], "tactic_count": 12}
{"name": "RootPairing.EmbeddedG2.span_eq_top", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.G2", "is_tactic_proof": true, "tactics": ["have", "rw", "refine", "replace", "have", "rcases"], "tactic_count": 6}
{"name": "RootPairing.EmbeddedG2.basis", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.G2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.EmbeddedG2.mem_allRoots", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.G2", "is_tactic_proof": true, "tactics": ["by_contra", "obtain", "have", "have", "have", "rw", "have", "ext", "have", "simp", "induction", "zero", "mem", "add", "smul", "simpa"], "tactic_count": 16}
{"name": "RootPairing.EmbeddedG2.indexEquivAllRoots", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.G2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.EmbeddedG2.card_index_eq_twelve", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.G2", "is_tactic_proof": true, "tactics": ["classical", "have", "rw", "simp", "rw", "exact"], "tactic_count": 6}
{"name": "RootPairing.EmbeddedG2.setOf_index_eq_univ", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.G2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.IsG2.card_base_support_eq_two", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.G2", "is_tactic_proof": true, "tactics": ["have", "have", "rw"], "tactic_count": 3}
{"name": "RootPairing.IsG2.span_eq_rootSpan_int", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.G2", "is_tactic_proof": true, "tactics": ["classical", "have", "rw"], "tactic_count": 3}
{"name": "_private.Mathlib.LinearAlgebra.RootSystem.Finite.Lemmas.0.RootPairing.termΦ", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.LinearAlgebra.RootSystem.Finite.Lemmas.0.RootPairing._aux_Mathlib_LinearAlgebra_RootSystem_Finite_Lemmas___macroRules__private_Mathlib_LinearAlgebra_RootSystem_Finite_Lemmas_0_RootPairing_termΦ_1", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.LinearAlgebra.RootSystem.Finite.Lemmas.0.RootPairing._aux_Mathlib_LinearAlgebra_RootSystem_Finite_Lemmas___unexpand_Set_range_1", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.LinearAlgebra.RootSystem.Finite.Lemmas.0.RootPairing.termα", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.LinearAlgebra.RootSystem.Finite.Lemmas.0.RootPairing._aux_Mathlib_LinearAlgebra_RootSystem_Finite_Lemmas___macroRules__private_Mathlib_LinearAlgebra_RootSystem_Finite_Lemmas_0_RootPairing_termα_1", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.coxeterWeightIn_le_four", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Lemmas", "is_tactic_proof": true, "tactics": ["have", "let", "let", "set", "set", "set", "obtain", "obtain", "replace", "replace", "rw", "rw", "have", "rw", "refine", "intro", "obtain", "change", "rw", "rwa", "have", "apply", "simpa", "simp", "rwa"], "tactic_count": 25}
{"name": "RootPairing.coxeterWeightIn_mem_set_of_isCrystallographic", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Lemmas", "is_tactic_proof": true, "tactics": ["have", "obtain", "have", "simpa", "obtain", "exact", "have", "simp", "norm_cast", "lia"], "tactic_count": 10}
{"name": "RootPairing.pairingIn_pairingIn_mem_set_of_isCrystallographic", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Lemmas", "is_tactic_proof": true, "tactics": ["refine", "simpa"], "tactic_count": 2}
{"name": "RootPairing.pairingIn_pairingIn_mem_set_of_isCrystal_of_isRed", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Lemmas", "is_tactic_proof": true, "tactics": ["have", "rcases", "rcases", "have", "have", "aesop"], "tactic_count": 6}
{"name": "RootPairing.pairingIn_pairingIn_mem_set_of_isCrystal_of_isRed'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Lemmas", "is_tactic_proof": true, "tactics": ["have", "have", "simp_all"], "tactic_count": 3}
{"name": "RootPairing.RootPositiveForm.rootLength_le_of_pairingIn_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Lemmas", "is_tactic_proof": false, "tactics": ["have", "have", "aesop", "simp", "have", "have", "rcases"], "tactic_count": 7}
{"name": "RootPairing.RootPositiveForm.rootLength_lt_of_pairingIn_notMem", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Lemmas", "is_tactic_proof": false, "tactics": ["have", "have", "aesop", "have", "have", "have", "aesop", "have", "have", "rcases", "lia"], "tactic_count": 11}
{"name": "RootPairing.pairingIn_pairingIn_mem_set_of_length_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Lemmas", "is_tactic_proof": false, "tactics": ["replace", "simp", "exact", "have", "aesop"], "tactic_count": 5}
{"name": "RootPairing.pairingIn_pairingIn_mem_set_of_length_eq_of_ne", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Lemmas", "is_tactic_proof": true, "tactics": ["have", "have", "simp_all"], "tactic_count": 3}
{"name": "RootPairing.coxeterWeightIn_eq_zero_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Lemmas", "is_tactic_proof": true, "tactics": ["refine", "rwa"], "tactic_count": 2}
{"name": "RootPairing.root_sub_root_mem_of_pairingIn_pos", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Lemmas", "is_tactic_proof": true, "tactics": ["have", "have", "have", "by_cases", "suffices", "rcases", "replace", "exact", "replace", "rw", "exact", "have", "have", "have", "have", "simp_all", "simp_rw", "lia", "have", "have", "replace", "aesop", "simp", "rcases", "rw", "exact", "rw", "contradiction", "rw", "simp"], "tactic_count": 30}
{"name": "RootPairing.root_add_root_mem_of_pairingIn_neg", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Lemmas", "is_tactic_proof": true, "tactics": ["let", "replace", "replace", "simpa"], "tactic_count": 4}
{"name": "RootPairing.pairingIn_eq_zero_of_add_notMem_of_sub_notMem", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Lemmas", "is_tactic_proof": true, "tactics": ["apply", "contrapose", "exact", "contrapose", "exact"], "tactic_count": 5}
{"name": "RootPairing.pairing_eq_zero_of_add_notMem_of_sub_notMem", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RootPairing.root_mem_submodule_iff_of_add_mem_invtSubmodule", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Lemmas", "is_tactic_proof": true, "tactics": ["obtain", "rw", "suffices", "have", "rintro", "rcases", "have", "rw", "simpa", "suffices", "replace", "rwa", "replace", "rwa"], "tactic_count": 14}
{"name": "RootPairing.InvariantForm.apply_eq_or_aux", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Lemmas", "is_tactic_proof": true, "tactics": ["have", "have", "algebraMap", "aesop"], "tactic_count": 4}
{"name": "RootPairing.InvariantForm.apply_eq_or", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Lemmas", "is_tactic_proof": true, "tactics": ["obtain", "suffices", "contrapose", "replace", "exact"], "tactic_count": 5}
{"name": "RootPairing.InvariantForm.exists_apply_eq_or", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Lemmas", "is_tactic_proof": true, "tactics": ["obtain", "by_cases", "refine", "obtain", "refine", "by_contra", "have", "have", "have", "grind"], "tactic_count": 10}
{"name": "RootPairing.InvariantForm.apply_eq_or_of_apply_ne", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Lemmas", "is_tactic_proof": true, "tactics": ["have", "obtain", "rcases"], "tactic_count": 3}
{"name": "RootPairing.forall_pairing_eq_swap_or", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Lemmas", "is_tactic_proof": true, "tactics": ["have", "have", "by_cases", "refine", "have", "rwa", "obtain", "have", "set", "set", "have", "rcases", "refine", "have", "rcases", "simp", "aesop", "refine", "have", "rcases", "simp", "aesop"], "tactic_count": 22}
{"name": "RootPairing.forall_pairingIn_eq_swap_or", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Lemmas", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "RootPairing.instIsAnisotropicFlip", "kind": "instance", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Nondegenerate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.isAnisotropic_of_isValuedIn", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Nondegenerate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.instIsAnisotropicOfIsCrystallographic", "kind": "instance", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Nondegenerate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.toInvariantForm", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Nondegenerate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.smul_coroot_eq_of_root_add_root_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Nondegenerate", "is_tactic_proof": true, "tactics": ["let", "let", "have", "have", "simp", "rw", "have", "have", "simp", "ring", "have", "have", "replace", "rw", "replace", "simp", "convert", "module", "ring_nf", "simp", "apply", "simp", "convert", "module", "module"], "tactic_count": 25}
{"name": "RootPairing.finrank_range_polarization_eq_finrank_span_coroot", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Nondegenerate", "is_tactic_proof": true, "tactics": ["apply", "have", "have", "have", "refine", "have", "rw", "apply", "refine", "intro", "obtain", "rw", "simp_rw", "exact", "prod_rootFormIn_smul_coroot_mem_range_PolarizationIn"], "tactic_count": 15}
{"name": "_private.Mathlib.LinearAlgebra.RootSystem.Finite.Nondegenerate.0.RootPairing.finrank_corootSpan_le", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Nondegenerate", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "RootPairing.finrank_corootSpan_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Nondegenerate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.polarizationIn_Injective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Nondegenerate", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "refine", "rw", "exact"], "tactic_count": 6}
{"name": "RootPairing.exists_coroot_ne", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Nondegenerate", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "contrapose", "exact"], "tactic_count": 5}
{"name": "RootPairing.posRootForm_posForm_pos_of_ne_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Nondegenerate", "is_tactic_proof": true, "tactics": ["rw", "have", "have", "obtain", "use", "exact", "exact"], "tactic_count": 7}
{"name": "RootPairing.posRootForm_rootFormIn_posDef", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Nondegenerate", "is_tactic_proof": true, "tactics": ["intro", "simpa"], "tactic_count": 2}
{"name": "RootPairing.posRootForm_posForm_anisotropic", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Nondegenerate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.posRootForm_posForm_nondegenerate", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Nondegenerate", "is_tactic_proof": true, "tactics": ["constructor", "intro", "contrapose", "exact"], "tactic_count": 4}
{"name": "RootPairing.finrank_rootSpan_map_polarization_eq_finrank_corootSpan", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Nondegenerate", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "_private.Mathlib.LinearAlgebra.RootSystem.Finite.Nondegenerate.0.RootPairing.finrank_corootSpan_le'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Nondegenerate", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "RootPairing.finrank_corootSpan_eq'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Nondegenerate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.disjoint_rootSpan_ker_rootForm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Nondegenerate", "is_tactic_proof": true, "tactics": ["have", "rw", "refine", "rw"], "tactic_count": 4}
{"name": "RootPairing.disjoint_corootSpan_ker_corootForm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Nondegenerate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.rootForm_nondegenerate", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Nondegenerate", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "RootPairing.isCompl_rootSpan_ker_rootForm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Nondegenerate", "is_tactic_proof": true, "tactics": ["have", "have", "refine", "have", "rw", "rw", "convert", "exact"], "tactic_count": 8}
{"name": "RootPairing.isCompl_corootSpan_ker_corootForm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Nondegenerate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.ker_rootForm_eq_dualAnnihilator", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Nondegenerate", "is_tactic_proof": true, "tactics": ["have", "have", "suffices", "refine", "rw", "apply", "have", "have", "rw", "lia"], "tactic_count": 10}
{"name": "RootPairing.ker_corootForm_eq_dualAnnihilator", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Nondegenerate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.instIsBalanced", "kind": "instance", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Nondegenerate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.rootForm_restrict_nondegenerate_of_isAnisotropic", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Nondegenerate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.orthogonal_rootSpan_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Nondegenerate", "is_tactic_proof": true, "tactics": ["rw", "refine", "rintro", "simp", "obtain", "rw", "simp", "simp"], "tactic_count": 8}
{"name": "RootPairing.orthogonal_corootSpan_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Nondegenerate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.rootSpan_eq_top_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Nondegenerate", "is_tactic_proof": true, "tactics": ["have", "have", "refine", "rw", "rw"], "tactic_count": 5}
{"name": "RootPairing.PolarizationEquiv", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Nondegenerate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.polarizationEquiv_toLinearMap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Nondegenerate", "is_tactic_proof": false, "tactics": ["simp", "ext", "let", "change", "simp"], "tactic_count": 5}
{"name": "RootPairing.polarizationEquiv_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Nondegenerate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.coroot_eq_polarizationEquiv_apply_root", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Nondegenerate", "is_tactic_proof": true, "tactics": ["have", "rw", "mul_div_cancel₀", "norm_cast"], "tactic_count": 4}
{"name": "RootPairing.polarizationEquiv_symm_apply_coroot", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Nondegenerate", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "_private.Mathlib.LinearAlgebra.RootSystem.Finite.Nondegenerate.0.RootPairing.linearIndepOn_coroot_iff_aux", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Nondegenerate", "is_tactic_proof": false, "tactics": ["obtain", "have", "simp", "rw", "simpa"], "tactic_count": 5}
{"name": "RootPairing.linearIndepOn_coroot_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Nondegenerate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.instIsAnisotropicOfLinearOrderedCommRing", "kind": "instance", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Nondegenerate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.zero_le_rootForm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Nondegenerate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.rootForm_restrict_nondegenerate_of_ordered", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Nondegenerate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.rootForm_self_eq_zero_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Nondegenerate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.eq_zero_of_mem_rootSpan_of_rootForm_self_eq_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Nondegenerate", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "RootPairing.rootForm_pos_of_ne_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Nondegenerate", "is_tactic_proof": true, "tactics": ["apply", "contrapose", "exact"], "tactic_count": 3}
{"name": "RootPairing.rootForm_anisotropic", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Finite.Nondegenerate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.GeckConstruction.h", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.GeckConstruction.h_def", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "RootPairing.GeckConstruction.h_eq_diagonal", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "RootPairing.GeckConstruction.span_range_h_le_range_diagonal", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Basic", "is_tactic_proof": true, "tactics": ["rw", "rintro", "rw", "exact"], "tactic_count": 4}
{"name": "RootPairing.GeckConstruction.diagonal_elim_mem_span_h_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Basic", "is_tactic_proof": false, "tactics": ["let", "map_add", "map_smul", "have", "have", "have", "ext", "simp_rw", "exists_eq_right]"], "tactic_count": 9}
{"name": "RootPairing.GeckConstruction.apply_sum_inl_eq_zero_of_mem_span_h", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Basic", "is_tactic_proof": true, "tactics": ["induction", "mem", "zero", "add", "smul"], "tactic_count": 5}
{"name": "RootPairing.GeckConstruction.lie_h_h", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Basic", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "RootPairing.GeckConstruction.e", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.GeckConstruction.f", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.GeckConstruction.ω", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.GeckConstruction.lieAlgebra", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.GeckConstruction.cartanSubalgebra", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.GeckConstruction.cartanSubalgebra'", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.GeckConstruction.cartanSubalgebra_eq_lieSpan", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "RootPairing.GeckConstruction.h_mem_cartanSubalgebra", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.GeckConstruction.h_mem_cartanSubalgebra'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RootPairing.GeckConstruction.h_mem_lieAlgebra", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.GeckConstruction.e_mem_lieAlgebra", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.GeckConstruction.f_mem_lieAlgebra", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.GeckConstruction.h'", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.GeckConstruction.span_range_h'_eq_top", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Basic", "is_tactic_proof": true, "tactics": ["rw", "rintro", "let", "suffices", "rwa", "rwa"], "tactic_count": 6}
{"name": "RootPairing.GeckConstruction.ω_mul_ω", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "RootPairing.GeckConstruction.ω_mul_h", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Basic", "is_tactic_proof": true, "tactics": ["classical", "ext", "simp", "simp", "simp", "simp", "aesop"], "tactic_count": 7}
{"name": "RootPairing.GeckConstruction.ω_mul_e", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Basic", "is_tactic_proof": true, "tactics": ["letI", "classical", "ext", "simp", "simp", "rw", "simp", "simp", "simp", "rw", "simp"], "tactic_count": 11}
{"name": "RootPairing.GeckConstruction.ω_mul_f", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Basic", "is_tactic_proof": true, "tactics": ["classical", "have", "simp", "simpa"], "tactic_count": 4}
{"name": "RootPairing.GeckConstruction.lie_e_f_mul_ω", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Basic", "is_tactic_proof": true, "tactics": ["classical", "calc", "rw", "abel"], "tactic_count": 4}
{"name": "RootPairing.GeckConstruction.u", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.GeckConstruction.v", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.GeckConstruction.apply_inr_eq_zero_of_mem_span_range_u", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Basic", "is_tactic_proof": true, "tactics": ["induction", "mem", "zero", "add", "smul"], "tactic_count": 5}
{"name": "RootPairing.GeckConstruction.lie_e_lie_f_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp", "simp"], "tactic_count": 3}
{"name": "RootPairing.GeckConstruction.instIsLieAbelianSubtypeMatrixSumMemFinsetSupportLieSubalgebraCartanSubalgebra", "kind": "instance", "module": "Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Basic", "is_tactic_proof": true, "tactics": ["rw", "rintro", "exact"], "tactic_count": 3}
{"name": "RootPairing.GeckConstruction.instIsLieAbelianSubtypeMatrixSumMemFinsetSupportLieSubalgebraLieAlgebraCartanSubalgebra'", "kind": "instance", "module": "Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Basic", "is_tactic_proof": true, "tactics": ["refine", "let", "let", "suffices", "simp"], "tactic_count": 5}
{"name": "RootPairing.GeckConstruction.instIsTriangularizableSubtypeMatrixSumMemFinsetSupportLieSubalgebraLieAlgebraCartanSubalgebra'Forall", "kind": "instance", "module": "Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Basic", "is_tactic_proof": true, "tactics": ["refine", "obtain", "span_range_h_le_range_diagonal", "simp"], "tactic_count": 4}
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{"name": "RootPairing.GeckConstruction.e_lie_v_ne", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Basic", "is_tactic_proof": true, "tactics": ["letI", "ext", "replace", "simp", "simp"], "tactic_count": 5}
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{"name": "RootPairing.GeckConstruction.ωConj_mem_of_mem", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Basic", "is_tactic_proof": true, "tactics": ["induction", "mem", "hu", "obtain", "simpa", "rw", "exact", "exact", "exact", "zero", "add", "smul", "lie", "rw", "exact"], "tactic_count": 15}
{"name": "RootPairing.GeckConstruction.ωConjLieSubmodule", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.GeckConstruction.mem_ωConjLieSubmodule_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.GeckConstruction.ωConjLieSubmodule_eq_top_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Basic", "is_tactic_proof": true, "tactics": ["rw", "let", "change", "simp"], "tactic_count": 4}
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{"name": "RootPairing.GeckConstruction.isSl2Triple", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Relations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "_private.Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Semisimple.0.RootPairing.GeckConstruction.isNilpotent_e_aux", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Semisimple", "is_tactic_proof": true, "tactics": ["have", "have", "letI", "have", "rw", "induction", "zero", "succ", "rcases", "left", "rw", "have", "rintro", "replace", "simp", "one_smul]", "rw", "module", "rcases", "apply", "rw", "simp", "have", "exact", "by_cases", "obtain", "right", "refine", "ext", "simp", "rcases", "replace", "simp", "replace", "hml", "simp", "left", "ext", "simp", "replace", "simp"], "tactic_count": 41}
{"name": "RootPairing.GeckConstruction.isNilpotent_e", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Semisimple", "is_tactic_proof": true, "tactics": ["classical", "have", "have", "letI", "rw", "have", "ext", "simp", "have", "suffices", "exact", "simp", "rintro", "exact", "by_cases", "use", "replace", "ext", "simp", "have", "simp", "rw", "simp", "use", "rcases", "assumption", "exfalso", "replace", "have", "apply", "rintro", "apply", "convert", "module", "contrapose", "rw", "rw", "rw", "lia"], "tactic_count": 39}
{"name": "RootPairing.GeckConstruction.isNilpotent_f", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Semisimple", "is_tactic_proof": true, "tactics": ["obtain", "suffices", "suffices", "clear", "induction", "zero", "succ"], "tactic_count": 7}
{"name": "RootPairing.GeckConstruction.trace_h_eq_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Semisimple", "is_tactic_proof": true, "tactics": ["classical", "letI", "suffices", "simp", "norm_cast", "suffices", "let", "exact"], "tactic_count": 8}
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{"name": "_private.Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Semisimple.0.RootPairing.GeckConstruction.instIsIrreducible_aux₀", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Semisimple", "is_tactic_proof": false, "tactics": ["suffices", "obtain", "simpa", "replace", "obtain", "use", "rw", "exact", "clear", "intro", "have", "w", "set", "obtain", "replace", "have", "aesop", "simp", "obtain", "obtain", "replace", "exact", "let", "replace", "contrapose", "apply", "rintro", "simp", "contrapose", "suffices", "intro", "replace", "rw", "obtain", "simpa", "refine", "suffices", "obtain", "let", "replace", "rw", "obtain", "obtain", "simpa", "ext", "have", "simpa", "rcases", "simp", "suffices", "simpa", "rw", "exact", "simp_rw", "exact"], "tactic_count": 55}
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{"name": "RootPairing.Hom.root_weightMap_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Hom.coroot_coweightMap_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Hom.id", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Hom.comp", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Hom.id_comp", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
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{"name": "RootPairing.Hom.comp_assoc", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "RootPairing.Hom.instMonoid", "kind": "instance", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Hom.weightMap_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Hom.coweightMap_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "RootPairing.Hom.coweightMap_mul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "RootPairing.End", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Hom.weightHom", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "RootPairing.Hom.coweightHom", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Hom.coweightHom_injective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": true, "tactics": ["intro", "ext", "dsimp", "rw", "have", "rw", "have", "haveI", "refine", "exact", "dsimp", "simp_all", "dsimp", "rw", "set", "have", "exact", "rw", "rw", "rw"], "tactic_count": 20}
{"name": "RootPairing.Hom.indexHom", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Equiv.weightEquiv", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Equiv.weightEquiv_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Equiv.weightEquiv_symm_weightMap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Equiv.weightMap_weightEquiv_symm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "RootPairing.Equiv.coweightEquiv", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Equiv.coweightEquiv_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Equiv.coweightEquiv_symm_coweightMap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Equiv.coweightMap_coweightEquiv_symm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "RootPairing.Equiv.id", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Equiv.comp", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Equiv.toHom_comp", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "RootPairing.Equiv.id_comp", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "RootPairing.Equiv.comp_id", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "RootPairing.Equiv.comp_assoc", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "RootPairing.Equiv.instMonoid", "kind": "instance", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Equiv.weightEquiv_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Equiv.coweightEquiv_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Equiv.toHom_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Equiv.mul_eq_comp", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Equiv.weightEquiv_comp_toLin", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "RootPairing.Equiv.weightEquiv_mul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "RootPairing.Equiv.coweightEquiv_comp_toLin", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "RootPairing.Equiv.coweightEquiv_mul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "RootPairing.Equiv.symm", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Equiv.inv_weightMap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Equiv.inv_coweightMap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Equiv.inv_indexEquiv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Equiv.instGroup", "kind": "instance", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Equiv.mk'", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Aut", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Equiv.toEndUnit", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Equiv.toEndUnit_val", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Equiv.toEndUnit_inv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Equiv.weightHom", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Equiv.weightHom_toLinearMap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Equiv.weightHom_injective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": true, "tactics": ["refine", "let", "rw", "suffices", "exact"], "tactic_count": 5}
{"name": "RootPairing.Equiv.weightEquiv_inv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Equiv.coweightHom", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Equiv.coweightHom_toLinearMap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Equiv.coweightHom_injective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": true, "tactics": ["refine", "have", "simp_all", "rw", "suffices", "apply", "exact"], "tactic_count": 7}
{"name": "RootPairing.Equiv.coweightHom_op", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Equiv.coweightEquiv_inv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Equiv.indexHom", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Equiv.indexEquiv_inv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Equiv.reflection", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Equiv.reflection_weightEquiv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Equiv.reflection_coweightEquiv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Equiv.reflection_indexEquiv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Equiv.reflection_inv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": true, "tactics": ["refine", "exact", "exact", "exact"], "tactic_count": 4}
{"name": "RootPairing.Equiv.instDistribMulActionAut", "kind": "instance", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Equiv.reflection_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Equiv.root_indexEquiv_eq_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "RootPairing.Equiv.instDistribMulActionMulOppositeAut", "kind": "instance", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Equiv.instSMulCommClassAut", "kind": "instance", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Equiv.instSMulCommClassMulOppositeAut", "kind": "instance", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.Equiv.instMulActionAut", "kind": "instance", "module": "Mathlib.LinearAlgebra.RootSystem.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.invtRootSubmodule", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.mem_invtRootSubmodule_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Irreducible", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RootPairing.invtRootSubmodule.top_mem", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Irreducible", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RootPairing.invtRootSubmodule.bot_mem", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Irreducible", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RootPairing.instBoundedOrderSubtypeSubmoduleMemSublatticeInvtRootSubmodule", "kind": "instance", "module": "Mathlib.LinearAlgebra.RootSystem.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.instNontrivialSubtypeSubmoduleMemSublatticeInvtRootSubmodule", "kind": "instance", "module": "Mathlib.LinearAlgebra.RootSystem.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.coe_bot", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.coe_top", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.invtRootSubmodule.eq_bot_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Irreducible", "is_tactic_proof": true, "tactics": ["have", "refine", "rw", "intro", "by_contra", "obtain", "contrapose", "suffices", "exact", "replace", "specialize", "contrapose", "rw", "exact", "have", "contradiction"], "tactic_count": 16}
{"name": "RootPairing.invtRootSubmodule.eq_top_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.isSimpleModule_weylGroupRootRep_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Irreducible", "is_tactic_proof": true, "tactics": ["rw", "refine", "suffices", "let", "suffices", "apply", "simpa", "rintro", "induction", "mem", "one", "mul", "rcases", "suffices", "refine", "exact"], "tactic_count": 16}
{"name": "RootPairing.instIsIrreducibleFlip", "kind": "instance", "module": "Mathlib.LinearAlgebra.RootSystem.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.isSimpleModule_weylGroupRootRep", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.instIsRootSystemOfNonemptyOfNeZeroOfNatOfIsIrreducible", "kind": "instance", "module": "Mathlib.LinearAlgebra.RootSystem.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.invtSubmodule_reflection_of_invtSubmodule_coreflection", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Irreducible", "is_tactic_proof": false, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "RootPairing.IsIrreducible.mk'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.isIrreducible_iff_invtRootSubmodule", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Irreducible", "is_tactic_proof": true, "tactics": ["refine", "simp", "rw", "have", "tauto", "let", "replace", "suffices", "exact"], "tactic_count": 9}
{"name": "RootPairing.exist_set_root_not_disjoint_and_le_ker_coroot'_of_invtSubmodule", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Irreducible", "is_tactic_proof": true, "tactics": ["refine", "simp", "rw", "exact"], "tactic_count": 4}
{"name": "RootPairing.span_orbit_eq_top", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Irreducible", "is_tactic_proof": true, "tactics": ["refine", "let", "exact", "simpa"], "tactic_count": 4}
{"name": "RootPairing.exists_form_eq_form_and_form_ne_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Irreducible", "is_tactic_proof": true, "tactics": ["by_contra", "suffices", "refine", "obtain", "simp", "apply", "simp"], "tactic_count": 7}
{"name": "RootPairing.span_root_image_eq_top_of_forall_orthogonal", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Irreducible", "is_tactic_proof": false, "tactics": ["have", "by_cases", "exact", "refine", "rwa", "apply", "simpa"], "tactic_count": 7}
{"name": "RootPairing.eq_top_of_mem_invtSubmodule_of_forall_eq_univ", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Irreducible", "is_tactic_proof": true, "tactics": ["obtain", "rcases", "replace", "simp", "replace", "simpa"], "tactic_count": 6}
{"name": "RootPairing.IsCrystallographic", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.RootSystem.IsValuedIn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.instIsValuedIn", "kind": "instance", "module": "Mathlib.LinearAlgebra.RootSystem.IsValuedIn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.isValuedIn_iff_mem_range", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.IsValuedIn", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RootPairing.instIsValuedInFlip", "kind": "instance", "module": "Mathlib.LinearAlgebra.RootSystem.IsValuedIn", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "RootPairing.pairingIn", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.IsValuedIn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.algebraMap_pairingIn", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.IsValuedIn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.pairingIn_same", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.IsValuedIn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.pairingIn_eq_add_of_root_eq_add", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.IsValuedIn", "is_tactic_proof": true, "tactics": ["apply", "simpa"], "tactic_count": 2}
{"name": "RootPairing.pairingIn_eq_add_of_root_eq_smul_add_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.IsValuedIn", "is_tactic_proof": true, "tactics": ["apply", "replace", "simpa"], "tactic_count": 3}
{"name": "RootPairing.pairingIn_reflectionPerm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.IsValuedIn", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "RootPairing.pairingIn_reflectionPerm_self_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.IsValuedIn", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RootPairing.pairingIn_reflectionPerm_self_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.IsValuedIn", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RootPairing.IsValuedIn.trans", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.IsValuedIn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.instIsValuedInRatOfIsCrystallographic", "kind": "instance", "module": "Mathlib.LinearAlgebra.RootSystem.IsValuedIn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.algebraMap_pairingIn'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.IsValuedIn", "is_tactic_proof": true, "tactics": ["apply", "rw", "simp"], "tactic_count": 3}
{"name": "RootPairing.pairingIn_rat", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.IsValuedIn", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RootPairing.coroot'_apply_apply_mem_of_mem_span", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.IsValuedIn", "is_tactic_proof": true, "tactics": ["rw", "induction", "mem", "obtain", "simpa", "zero", "add", "smul"], "tactic_count": 8}
{"name": "RootPairing.root'_apply_apply_mem_of_mem_span", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.IsValuedIn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.rootSpan", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.RootSystem.IsValuedIn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.corootSpan", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.RootSystem.IsValuedIn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.instFiniteSubtypeMemSubmoduleRootSpanOfFinite", "kind": "instance", "module": "Mathlib.LinearAlgebra.RootSystem.IsValuedIn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.instFiniteSubtypeMemSubmoduleCorootSpanOfFinite", "kind": "instance", "module": "Mathlib.LinearAlgebra.RootSystem.IsValuedIn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.rootSpanMem", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.RootSystem.IsValuedIn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.corootSpanMem", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.RootSystem.IsValuedIn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.rootSpanMem_reflectionPerm_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.IsValuedIn", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "RootPairing.corootSpanMem_reflectionPerm_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.IsValuedIn", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "RootPairing.root'In", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.IsValuedIn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.algebraMap_root'In_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.IsValuedIn", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RootPairing.root'In_corootSpanMem_eq_pairingIn", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.IsValuedIn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.coroot'In", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.IsValuedIn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.algebraMap_coroot'In_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.IsValuedIn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.coroot'In_rootSpanMem_eq_pairingIn", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.IsValuedIn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.rootSpan_ne_bot", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.IsValuedIn", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "RootPairing.corootSpan_ne_bot", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.IsValuedIn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.rootSpan_mem_invtSubmodule_reflection", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.IsValuedIn", "is_tactic_proof": true, "tactics": ["rw", "intro", "induction", "mem", "obtain", "rw", "apply", "exact", "exact", "zero", "add", "smul"], "tactic_count": 12}
{"name": "RootPairing.corootSpan_mem_invtSubmodule_coreflection", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.IsValuedIn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.rootSpan_dualAnnihilator_map_eq_iInf_ker_root'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.IsValuedIn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.corootSpan_dualAnnihilator_map_eq_iInf_ker_coroot'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.IsValuedIn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.rootSpan_dualAnnihilator_map_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.IsValuedIn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.corootSpan_dualAnnihilator_map_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.IsValuedIn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.iInf_ker_root'_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.IsValuedIn", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RootPairing.iInf_ker_coroot'_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.IsValuedIn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.rootSpan_map_toPerfPair", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.IsValuedIn", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RootPairing.corootSpan_map_flip_toPerfPair", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.IsValuedIn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.span_root'_eq_top", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.IsValuedIn", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RootPairing.span_coroot'_eq_top", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.IsValuedIn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.pairingIn_eq_zero_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.IsValuedIn", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "RootPairing.reflection_apply_root'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.IsValuedIn", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RootPairing.coxeterWeightIn", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.IsValuedIn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.algebraMap_coxeterWeightIn", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.IsValuedIn", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RootPairing.toLinearMap_apply_apply_mem_range_algebraMap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.IsValuedIn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.finrank_rootSpanIn", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.IsValuedIn", "is_tactic_proof": true, "tactics": ["rw", "simp", "simp", "exact"], "tactic_count": 4}
{"name": "RootPairing.finrank_corootSpanIn", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.IsValuedIn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.finrank_rootSpanIn_int", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.IsValuedIn", "is_tactic_proof": true, "tactics": ["let", "let", "have", "rw"], "tactic_count": 4}
{"name": "RootPairing.finrank_corootSpanIn_int", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.IsValuedIn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsReflective.of_dvd_two", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.OfBilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsReflective.coroot", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.OfBilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsReflective.apply_self_mul_coroot_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.OfBilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsReflective.smul_coroot", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.OfBilinear", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "LinearMap.IsReflective.coroot_apply_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.OfBilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsReflective.isOrthogonal_reflection", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.OfBilinear", "is_tactic_proof": true, "tactics": ["intro", "simp", "refine", "simp", "rw", "apply_self_mul_coroot_apply]", "ring"], "tactic_count": 7}
{"name": "LinearMap.IsReflective.reflective_reflection", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.OfBilinear", "is_tactic_proof": true, "tactics": ["constructor", "rw", "exact", "intro", "have", "exact", "rw", "exact"], "tactic_count": 8}
{"name": "RootPairing.ofBilinear", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.OfBilinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.isReduced_iff'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Reduced", "is_tactic_proof": true, "tactics": ["rw", "refine", "specialize", "simp_all", "rcases", "tauto", "exact"], "tactic_count": 7}
{"name": "RootPairing.IsReduced.linearIndependent", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Reduced", "is_tactic_proof": true, "tactics": ["have", "simp_all"], "tactic_count": 2}
{"name": "RootPairing.IsReduced.linearIndependent_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Reduced", "is_tactic_proof": true, "tactics": ["refine", "rw", "contrapose", "rcases", "exact", "rw", "exact"], "tactic_count": 7}
{"name": "RootPairing.nsmul_notMem_range_root", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Reduced", "is_tactic_proof": false, "tactics": ["have", "simpa", "rintro", "replace", "simpa", "rcases", "replace", "rw", "have", "lia", "rw", "replace", "rw", "lia"], "tactic_count": 14}
{"name": "RootPairing.linearIndependent_of_add_mem_range_root", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Reduced", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact", "rwa"], "tactic_count": 4}
{"name": "RootPairing.linearIndependent_of_sub_mem_range_root", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Reduced", "is_tactic_proof": true, "tactics": ["suffices", "apply", "simpa"], "tactic_count": 3}
{"name": "RootPairing.linearIndependent_of_add_mem_range_root'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Reduced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.linearIndependent_of_sub_mem_range_root'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Reduced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.infinite_of_linearIndependent_coxeterWeight_four", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Reduced", "is_tactic_proof": false, "tactics": ["refine", "rw", "intro", "rw", "n]", "exact", "rw", "rw", "specialize", "simp", "rw", "exact"], "tactic_count": 12}
{"name": "RootPairing.pairing_smul_root_eq_of_not_linearIndependent", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Reduced", "is_tactic_proof": true, "tactics": ["rw", "push_neg", "obtain", "replace", "rcases", "exact", "assumption", "have", "rcases", "exact", "assumption", "replace", "have", "replace", "rw", "exact"], "tactic_count": 16}
{"name": "RootPairing.coxeterWeight_ne_four_of_linearIndependent", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Reduced", "is_tactic_proof": true, "tactics": ["intro", "have", "exact"], "tactic_count": 3}
{"name": "RootPairing.linearIndependent_iff_coxeterWeight_ne_four", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Reduced", "is_tactic_proof": true, "tactics": ["have", "refine", "contrapose", "have", "rw", "have", "suffices", "calc"], "tactic_count": 8}
{"name": "RootPairing.coxeterWeight_eq_four_iff_not_linearIndependent", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Reduced", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RootPairing.instFlipIsReduced", "kind": "instance", "module": "Mathlib.LinearAlgebra.RootSystem.Reduced", "is_tactic_proof": true, "tactics": ["refine", "rcases", "right", "rw", "coxeterWeight_eq_four_iff_not_linearIndependent,", "push_neg", "simp"], "tactic_count": 7}
{"name": "RootPairing.pairing_two_two_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Reduced", "is_tactic_proof": true, "tactics": ["refine", "have", "rw", "replace", "exact"], "tactic_count": 5}
{"name": "RootPairing.pairing_neg_two_neg_two_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Reduced", "is_tactic_proof": true, "tactics": ["simp", "simpa"], "tactic_count": 2}
{"name": "RootPairing.pairing_one_four_iff'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Reduced", "is_tactic_proof": true, "tactics": ["have", "have", "refine", "have", "rw", "replace", "rw", "exact", "rw", "rw", "norm_num", "suffices", "rw", "simp"], "tactic_count": 14}
{"name": "RootPairing.pairing_neg_one_neg_four_iff'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Reduced", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "RootPairing.pairing_one_four_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Reduced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.pairing_neg_one_neg_four_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Reduced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.linearIndependent_iff_coxeterWeightIn_ne_four", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Reduced", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RootPairing.coxeterWeightIn_eq_four_iff_not_linearIndependent", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Reduced", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RootPairing.coxeterWeightIn_ne_four", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Reduced", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "RootPairing.pairingIn_two_two_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Reduced", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RootPairing.pairingIn_neg_two_neg_two_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Reduced", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RootPairing.pairingIn_one_four_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Reduced", "is_tactic_proof": true, "tactics": ["rw", "map_ofNat"], "tactic_count": 2}
{"name": "RootPairing.pairingIn_neg_one_neg_four_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.Reduced", "is_tactic_proof": true, "tactics": ["rw", "map_one"], "tactic_count": 2}
{"name": "RootPairingCat.category", "kind": "instance", "module": "Mathlib.LinearAlgebra.RootSystem.RootPairingCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.InvariantForm.apply_root_ne_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.RootPositive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.InvariantForm.two_mul_apply_root_root", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.RootPositive", "is_tactic_proof": true, "tactics": ["rw", "nth_rw", "rw", "smul_eq_mul,"], "tactic_count": 4}
{"name": "RootPairing.InvariantForm.pairing_mul_eq_pairing_mul_swap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.RootPositive", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RootPairing.InvariantForm.apply_reflection_reflection", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.RootPositive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.InvariantForm.apply_root_root_zero_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.RootPositive", "is_tactic_proof": true, "tactics": ["calc"], "tactic_count": 1}
{"name": "RootPairing.RootPositiveForm.form_apply_root_ne_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.RootPositive", "is_tactic_proof": true, "tactics": ["obtain", "simpa"], "tactic_count": 2}
{"name": "RootPairing.RootPositiveForm.toInvariantForm", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.RootPositive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.RootPositiveForm.two_mul_apply_root_root", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.RootPositive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.RootPositiveForm.posForm", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.RootPositive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.RootPositiveForm.algebraMap_posForm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.RootPositive", "is_tactic_proof": true, "tactics": ["change", "simp"], "tactic_count": 2}
{"name": "RootPairing.RootPositiveForm.algebraMap_apply_eq_form_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.RootPositive", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RootPairing.RootPositiveForm.zero_lt_posForm_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.RootPositive", "is_tactic_proof": true, "tactics": ["refine", "rw", "rwa"], "tactic_count": 3}
{"name": "RootPairing.RootPositiveForm.isSymm_posForm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.RootPositive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.RootPositiveForm.rootLength", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.RootPositive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.RootPositiveForm.rootLength_pos", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.RootPositive", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "RootPairing.RootPositiveForm.rootLength_reflectionPerm_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.RootPositive", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RootPairing.RootPositiveForm.algebraMap_rootLength", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.RootPositive", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RootPairing.RootPositiveForm.pairingIn_mul_eq_pairingIn_mul_swap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.RootPositive", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "RootPairing.zero_lt_pairingIn_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.RootPositive", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RootPairing.coxeterWeight_nonneg", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.RootPositive", "is_tactic_proof": true, "tactics": ["dsimp", "rcases", "exact", "have", "exact"], "tactic_count": 5}
{"name": "RootPairing.weylGroup", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.WeylGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.reflection_mem_weylGroup", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.WeylGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.weylGroup.ofIdx", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.WeylGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.weylGroup.ofIdx_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.WeylGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.weylGroup_toSubmonoid", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.WeylGroup", "is_tactic_proof": false, "tactics": ["suffices", "rw", "ext"], "tactic_count": 3}
{"name": "RootPairing.weylGroup.induction", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.WeylGroup", "is_tactic_proof": false, "tactics": ["let", "pred", "have", "suffices", "apply", "rintro", "exact", "exact", "intro", "rw", "exact"], "tactic_count": 11}
{"name": "RootPairing.weylGroup.induction'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.WeylGroup", "is_tactic_proof": true, "tactics": ["refine", "obtain", "have", "simpa"], "tactic_count": 4}
{"name": "RootPairing.range_weylGroup_weightHom", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.WeylGroup", "is_tactic_proof": true, "tactics": ["refine", "rintro", "simp", "use", "exact", "rintro", "induction", "one", "change", "simp", "mem", "obtain", "simp", "simpa", "inv_mem", "obtain", "simp", "simpa", "mul", "simpa"], "tactic_count": 20}
{"name": "RootPairing.range_weylGroup_coweightHom", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.WeylGroup", "is_tactic_proof": true, "tactics": ["refine", "rintro", "simp", "use", "refine", "rintro", "induction", "one", "change", "simp", "mem", "obtain", "simp", "simpa", "inv_mem", "obtain", "simp", "simpa", "mul", "simpa"], "tactic_count": 20}
{"name": "RootPairing.weylGroupToPerm", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.RootSystem.WeylGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.range_weylGroupToPerm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.WeylGroup", "is_tactic_proof": true, "tactics": ["refine", "rintro", "simp", "use", "refine", "rintro", "induction", "one", "change", "simp", "mem", "obtain", "simp", "simpa", "inv_mem", "obtain", "simp", "simpa", "mul", "simpa"], "tactic_count": 20}
{"name": "RootPairing.weylGroupRootRep", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.WeylGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.weylGroupCorootRep", "kind": "definition", "module": "Mathlib.LinearAlgebra.RootSystem.WeylGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.weylGroup_apply_root", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.WeylGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RootPairing.InvariantForm.apply_weylGroup_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.RootSystem.WeylGroup", "is_tactic_proof": true, "tactics": ["revert", "obtain", "induction", "mem", "one", "mul", "intro", "rw"], "tactic_count": 8}
{"name": "SModEq", "kind": "definition", "module": "Mathlib.LinearAlgebra.SModEq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "term_≡_[SMOD_]", "kind": "definition", "module": "Mathlib.LinearAlgebra.SModEq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_LinearAlgebra_SModEq_Basic___macroRules_term_≡_[SMOD_]_1", "kind": "definition", "module": "Mathlib.LinearAlgebra.SModEq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_LinearAlgebra_SModEq_Basic___unexpand_SModEq_1", "kind": "definition", "module": "Mathlib.LinearAlgebra.SModEq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SModEq.def", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SModEq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SModEq.sub_mem", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SModEq.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SModEq.top", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SModEq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SModEq.bot", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SModEq.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SModEq.mono", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SModEq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SModEq.of_toAddSubgroup_le", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SModEq.Basic", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "SModEq.refl", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SModEq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SModEq.rfl", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SModEq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SModEq.instRefl", "kind": "instance", "module": "Mathlib.LinearAlgebra.SModEq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SModEq.symm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SModEq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SModEq.comm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SModEq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SModEq.trans", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SModEq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SModEq.instTrans", "kind": "instance", "module": "Mathlib.LinearAlgebra.SModEq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SModEq.add", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SModEq.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp_rw"], "tactic_count": 2}
{"name": "SModEq.sum", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SModEq.Basic", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "cons", "grw", "ih"], "tactic_count": 6}
{"name": "SModEq.smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SModEq.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp_rw"], "tactic_count": 2}
{"name": "SModEq.nsmul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SModEq.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp_rw"], "tactic_count": 2}
{"name": "SModEq.zsmul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SModEq.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp_rw"], "tactic_count": 2}
{"name": "SModEq.mul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SModEq.Basic", "is_tactic_proof": true, "tactics": ["simp", "rw"], "tactic_count": 2}
{"name": "SModEq.prod", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SModEq.Basic", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "cons", "grw", "ih"], "tactic_count": 6}
{"name": "SModEq.pow", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SModEq.Basic", "is_tactic_proof": true, "tactics": ["simp", "rw"], "tactic_count": 2}
{"name": "SModEq.neg", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SModEq.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "SModEq.sub", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SModEq.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp_rw"], "tactic_count": 2}
{"name": "SModEq.zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SModEq.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "sub_smodEq_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SModEq.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SModEq.map", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SModEq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SModEq.comap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SModEq.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SModEq.eval", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SModEq.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "gcongr"], "tactic_count": 2}
{"name": "SModEq.smul'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SModEq.Pointwise", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "Module.End.IsSemisimple", "kind": "definition", "module": "Mathlib.LinearAlgebra.Semisimple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.IsFinitelySemisimple", "kind": "definition", "module": "Mathlib.LinearAlgebra.Semisimple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.isSemisimple_iff'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Semisimple", "is_tactic_proof": false, "tactics": ["rw", "complementedLattice_iff]", "rfl"], "tactic_count": 3}
{"name": "Module.End.isSemisimple_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Semisimple", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Module.End.isSemisimple_restrict_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Semisimple", "is_tactic_proof": false, "tactics": ["let", "simp_rw", "invtSubmodule.mk_eq_bot_iff,", "rfl"], "tactic_count": 4}
{"name": "Module.End.isFinitelySemisimple_iff'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Semisimple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.isFinitelySemisimple_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Semisimple", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Module.End.isSemisimple_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Semisimple", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Module.End.isSemisimple_id", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Semisimple", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Module.End.isSemisimple_neg", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Semisimple", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LinearEquiv.isSemisimple_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Semisimple", "is_tactic_proof": false, "tactics": ["let", "simp_rw"], "tactic_count": 2}
{"name": "Module.End.eq_zero_of_isNilpotent_isSemisimple", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Semisimple", "is_tactic_proof": true, "tactics": ["have", "rw", "rw", "exact"], "tactic_count": 4}
{"name": "Module.End.eq_zero_of_isNilpotent_of_isFinitelySemisimple", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Semisimple", "is_tactic_proof": false, "tactics": ["have", "specialize", "replace", "exact", "ext", "obtain", "let", "have", "simp", "rintro", "apply", "rcases", "exact", "exact", "have", "let", "have", "exact", "simpa"], "tactic_count": 19}
{"name": "Module.End.isSemisimple_sub_algebraMap_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Semisimple", "is_tactic_proof": false, "tactics": ["suffices", "simp", "refine", "simpa"], "tactic_count": 4}
{"name": "Module.End.IsSemisimple.restrict", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Semisimple", "is_tactic_proof": true, "tactics": ["rw", "let", "exact"], "tactic_count": 3}
{"name": "Module.End.IsSemisimple.isFinitelySemisimple", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Semisimple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.isFinitelySemisimple_iff_isSemisimple", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Semisimple", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact"], "tactic_count": 3}
{"name": "Module.End.isFinitelySemisimple_sub_algebraMap_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Semisimple", "is_tactic_proof": false, "tactics": ["suffices", "simp_rw", "refine", "simpa"], "tactic_count": 4}
{"name": "Module.End.IsFinitelySemisimple.restrict", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Semisimple", "is_tactic_proof": true, "tactics": ["intro", "have", "let", "rw", "exact"], "tactic_count": 5}
{"name": "Module.End.IsSemisimple_smul_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Semisimple", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Module.End.IsSemisimple_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Semisimple", "is_tactic_proof": true, "tactics": ["wlog", "rwa"], "tactic_count": 2}
{"name": "Module.End.isSemisimple_of_squarefree_aeval_eq_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Semisimple", "is_tactic_proof": false, "tactics": ["rw", "isTorsionBySet_singleton_iff,", "let", "have", "have", "have", "have", "letI", "let", "exact"], "tactic_count": 10}
{"name": "Module.End.IsSemisimple.minpoly_squarefree", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Semisimple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.IsSemisimple.aeval", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Semisimple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.IsSemisimple.of_mem_adjoin_singleton", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Semisimple", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Module.End.IsSemisimple.pow", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Semisimple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.IsSemisimple.of_mem_adjoin_pair", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Semisimple", "is_tactic_proof": true, "tactics": ["let", "let", "have", "have", "have", "have", "have", "have", "simp_rw", "exact", "let", "rotate_left", "rw", "rintro", "exact", "p.induction_on", "simpa", "simpa", "have", "rintro", "exact", "exact", "obtain", "refine", "isSemisimple_of_squarefree_aeval_eq_zero", "rw"], "tactic_count": 26}
{"name": "Module.End.IsSemisimple.add_of_commute", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Semisimple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.IsSemisimple.sub_of_commute", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Semisimple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.IsSemisimple.mul_of_commute", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Semisimple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsOrtho", "kind": "definition", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.isOrtho_def", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.isOrtho_zero_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "LinearMap.isOrtho_zero_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.isOrtho_flip", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "LinearMap.IsOrthoᵢ", "kind": "definition", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.isOrthoᵢ_def", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.isOrthoᵢ_flip", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "constructor"], "tactic_count": 2}
{"name": "LinearMap.ortho_smul_left", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "constructor", "rw", "rw", "rcases", "rw", "trivial", "exact"], "tactic_count": 8}
{"name": "LinearMap.ortho_smul_right", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "constructor", "rw", "rw", "rcases", "simp", "exfalso", "exact", "exact"], "tactic_count": 9}
{"name": "LinearMap.linearIndependent_of_isOrthoᵢ", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": true, "tactics": ["classical", "rw", "intro", "have", "have", "apply", "intro", "rw", "simp_rw", "apply", "exact"], "tactic_count": 11}
{"name": "LinearMap.IsRefl", "kind": "definition", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsRefl.eq_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsRefl.eq_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsRefl.ortho_comm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsRefl.domRestrict", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsRefl.flip_isRefl_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsRefl.ker_flip", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "LinearMap.IsRefl.ker_flip_eq_bot", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "LinearMap.IsRefl.ker_eq_bot_iff_ker_flip_eq_bot", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "LinearMap.isSymm_def", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsSymm.isRefl", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsSymm.ortho_comm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsSymm.domRestrict", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.isSymm_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsSymm.add", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinMap.isSymm_iff_eq_flip", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LinearMap.isSymm_iff_eq_flip", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.isNonneg_def", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.isNonneg_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsNonneg.add", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsNonneg.smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.isPosSemidef_def", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.isPosSemidef_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsPosSemidef.add", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsAlt", "kind": "definition", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsAlt.self_eq_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsAlt.eq_of_add_add_eq_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": ["have", "simp_rw", "rw", "exact"], "tactic_count": 4}
{"name": "LinearMap.IsAlt.neg", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "LinearMap.IsAlt.isRefl", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": true, "tactics": ["intro", "rw"], "tactic_count": 2}
{"name": "LinearMap.IsAlt.ortho_comm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.isAlt_iff_eq_neg_flip", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": true, "tactics": ["constructor", "ext", "simp_rw", "exact", "intro", "let", "simp", "exact"], "tactic_count": 8}
{"name": "Submodule.orthogonalBilin", "kind": "definition", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mem_orthogonalBilin_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.orthogonalBilin_le", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.le_orthogonalBilin_orthogonalBilin", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.span_singleton_inf_orthogonal_eq_bot", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "obtain", "replace", "rw", "suffices", "rw", "exact"], "tactic_count": 8}
{"name": "LinearMap.orthogonal_span_singleton_eq_to_lin_ker", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp_rw", "constructor", "exact", "rintro", "rw", "exact"], "tactic_count": 7}
{"name": "LinearMap.span_singleton_sup_orthogonal_eq_top", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "LinearMap.isCompl_span_singleton_orthogonal", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsAdjointPair", "kind": "definition", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.isAdjointPair_iff_comp_eq_compl₂", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": true, "tactics": ["constructor", "ext", "rw", "exact", "intro", "rw"], "tactic_count": 6}
{"name": "LinearMap.isAdjointPair_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.isAdjointPair_id", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.isAdjointPair_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsAdjointPair.add", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsAdjointPair.comp", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsAdjointPair.mul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsAdjointPair.sub", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsAdjointPair.smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsOrthogonal", "kind": "definition", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.isAdjointPair_symm_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.isOrthogonal_of_forall_apply_same", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": true, "tactics": ["intro", "suffices", "have", "simp", "rw", "simp", "simp", "simpa"], "tactic_count": 8}
{"name": "LinearMap.IsPairSelfAdjoint", "kind": "definition", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsSelfAdjoint", "kind": "definition", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.isPairSelfAdjointSubmodule", "kind": "definition", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.IsSkewAdjoint", "kind": "definition", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.selfAdjointSubmodule", "kind": "definition", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.skewAdjointSubmodule", "kind": "definition", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.mem_isPairSelfAdjointSubmodule", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.isPairSelfAdjoint_equiv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": ["have", "ext", "simp", "have", "ext", "simp", "have", "simp_rw"], "tactic_count": 8}
{"name": "LinearMap.isSkewAdjoint_iff_neg_self_adjoint", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.mem_selfAdjointSubmodule", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.mem_skewAdjointSubmodule", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "LinearMap.SeparatingLeft", "kind": "definition", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.not_separatingLeft_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.SeparatingLeft.ne_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.SeparatingRight", "kind": "definition", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.Nondegenerate", "kind": "definition", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.SeparatingLeft.congr", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": true, "tactics": ["intro", "rw", "refine", "specialize", "simp", "exact"], "tactic_count": 6}
{"name": "LinearMap.SeparatingRight.congr", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.Nondegenerate.congr", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.separatingLeft_congr_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.separatingRight_congr_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.nondegenerate_congr_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.flip_separatingRight", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.flip_separatingLeft", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LinearMap.flip_nondegenerate", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.separatingLeft_iff_linear_nontrivial", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": true, "tactics": ["constructor", "simpa", "have", "ext", "rw", "exact", "exact"], "tactic_count": 7}
{"name": "LinearMap.separatingRight_iff_linear_flip_nontrivial", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LinearMap.separatingLeft_iff_ker_eq_bot", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.separatingRight_iff_flip_ker_eq_bot", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LinearMap.IsRefl.nondegenerate_iff_separatingLeft", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "rwa"], "tactic_count": 3}
{"name": "LinearMap.IsRefl.nondegenerate_iff_separatingRight", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "rwa"], "tactic_count": 3}
{"name": "LinearMap.disjoint_ker_of_nondegenerate_restrict", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": true, "tactics": ["refine", "let", "suffices", "apply", "simp_rw", "intro", "rw", "simp"], "tactic_count": 8}
{"name": "LinearMap.IsSymm.nondegenerate_restrict_of_isCompl_ker", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": true, "tactics": ["have", "rw", "intro", "simp", "replace", "replace", "refine", "ext", "obtain", "exact", "suffices", "exact", "simpa"], "tactic_count": 13}
{"name": "LinearMap.nondegenerate_restrict_of_disjoint_orthogonal", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": true, "tactics": ["rw", "rintro", "rw", "refine", "specialize", "simp_rw", "rw", "exact"], "tactic_count": 8}
{"name": "LinearMap.IsOrthoᵢ.not_isOrtho_basis_self_of_separatingLeft", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": true, "tactics": ["intro", "refine", "obtain", "rw", "apply", "rintro", "rw", "suffices", "obtain", "exact", "exact"], "tactic_count": 11}
{"name": "LinearMap.IsOrthoᵢ.not_isOrtho_basis_self_of_separatingRight", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "LinearMap.IsOrthoᵢ.separatingLeft_of_not_isOrtho_basis_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": true, "tactics": ["intro", "obtain", "rw", "ext", "rw", "specialize", "simp_rw", "rw", "exact", "intro", "replace", "rw", "intro", "replace", "rw"], "tactic_count": 15}
{"name": "LinearMap.IsOrthoᵢ.separatingRight_iff_not_isOrtho_basis_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": true, "tactics": ["rw", "rw", "refine", "rw", "exact"], "tactic_count": 5}
{"name": "LinearMap.IsOrthoᵢ.nondegenerate_of_not_isOrtho_basis_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.BilinForm.apply_smul_sub_smul_sub_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": ["simp", "mul_left_comm", "abel"], "tactic_count": 3}
{"name": "LinearMap.BilinForm.apply_mul_apply_le_of_forall_zero_le", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": ["have", "rw", "exact", "rcases", "exact", "replace", "rcases", "rw", "exact", "replace", "suffices", "rw", "apply", "simpa", "simpa"], "tactic_count": 15}
{"name": "LinearMap.BilinForm.apply_sq_le_of_symm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "LinearMap.BilinForm.not_linearIndependent_of_apply_mul_apply_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": ["have", "by_contra", "exact", "by_contra", "by_cases", "simpa", "have", "rw", "exact"], "tactic_count": 9}
{"name": "LinearMap.BilinForm.apply_apply_same_eq_zero_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "ext", "have", "simp", "exact"], "tactic_count": 6}
{"name": "LinearMap.BilinForm.nondegenerate_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": false, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "LinearMap.BilinForm.nondegenerate_iff'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": true, "tactics": ["rw", "contrapose", "exact"], "tactic_count": 3}
{"name": "LinearMap.BilinForm.nondegenerate_restrict_iff_disjoint_ker", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": true, "tactics": ["refine", "have", "rw", "intro", "simp_rw", "specialize", "rw", "have", "simpa"], "tactic_count": 9}
{"name": "LinearMap.BilinForm.apply_mul_apply_lt_iff_linearIndependent", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": true, "tactics": ["have", "constructor", "contrapose", "intro", "rw", "push_neg", "obtain", "by_cases", "by_cases", "suffices", "simp", "rw", "show", "have", "exact", "simp", "contrapose", "intro", "exact", "not_linearIndependent_of_apply_mul_apply_eq"], "tactic_count": 20}
{"name": "LinearMap.BilinForm.apply_sq_lt_iff_linearIndependent_of_symm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "LinearMap.isSymm_iff_basis", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.isSymm_iff_isHermitian_toMatrix", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Star", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "star_dotProduct_toMatrix₂_mulVec", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "apply_eq_star_dotProduct_toMatrix₂_mulVec", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.isPosSemidef_iff_posSemidef_toMatrix", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SesquilinearForm.Star", "is_tactic_proof": true, "tactics": ["rw", "apply", "rw", "refine", "rw", "exact", "rw", "exact"], "tactic_count": 8}
{"name": "AddSubmonoid.toNatSubmodule_closure", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.span_coe_eq_restrictScalars", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.image_span_subset", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.image_span_subset_span", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.map_span", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.map_span_le", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.span_preimage_le", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Submodule.mapsTo_span", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.linearMap_eq_iff_of_eq_span", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "rfl", "intro", "subst", "suffices", "ext", "exact", "intro", "induction", "mem", "zero", "add", "erw", "rw", "smul", "erw", "rw"], "tactic_count": 18}
{"name": "Submodule.linearMap_eq_iff_of_span_eq_top", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": true, "tactics": ["convert", "constructor", "rintro", "rfl", "intro", "ext", "exact"], "tactic_count": 7}
{"name": "Submodule.linearMap_eq_zero_iff_of_span_eq_top", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.linearMap_eq_zero_iff_of_eq_span", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.span_smul_eq_of_isUnit", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": true, "tactics": ["apply", "apply", "convert", "simp"], "tactic_count": 4}
{"name": "Submodule.coe_scott_continuous", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.inclusionSpan", "kind": "definition", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.injective_inclusionSpan", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": true, "tactics": ["intro", "rw", "simpa"], "tactic_count": 3}
{"name": "Submodule.span_range_inclusionSpan", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": false, "tactics": ["have", "simpa", "apply", "rw"], "tactic_count": 4}
{"name": "Submodule.span_le_restrictScalars", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.span_subset_span", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.span_span_of_tower", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.span_eq_top_of_span_eq_top", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.span_range_inclusion_eq_top", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": false, "tactics": ["suffices", "apply", "rw", "rw", "suffices", "refine", "simpa", "ext", "simpa"], "tactic_count": 9}
{"name": "Submodule.span_range_inclusion_restrictScalars_eq_top", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.span_singleton_eq_span_singleton", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": true, "tactics": ["constructor", "simp", "rintro", "rcases", "refine", "apply", "simpa", "rw", "apply", "simp", "rintro", "exact"], "tactic_count": 12}
{"name": "Submodule.span_image", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.span_image_linearEquiv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.apply_mem_span_image_of_mem_span", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Submodule.apply_mem_span_image_iff_mem_span", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submodule.map_subtype_span_singleton", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Submodule.notMem_span_of_apply_notMem_span_image", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.iSup_toAddSubmonoid", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": true, "tactics": ["refine", "simp_rw", "intro", "refine", "exact", "exact", "exact", "refine", "rintro", "apply", "exact", "rw", "exact", "intro", "rw", "exact"], "tactic_count": 16}
{"name": "Submodule.iSup_induction", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Submodule.iSup_induction'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": true, "tactics": ["refine", "refine", "iSup_induction", "exact", "exact", "rintro", "exact"], "tactic_count": 7}
{"name": "Submodule.singleton_span_isCompactElement", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": true, "tactics": ["rw", "intro", "have", "obtain", "exact"], "tactic_count": 5}
{"name": "Submodule.finset_span_isCompactElement", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp", "rw", "exact"], "tactic_count": 4}
{"name": "Submodule.finite_span_isCompactElement", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.instIsCompactlyGenerated", "kind": "instance", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.prod", "kind": "definition", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.prod_coe", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mem_prod", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.span_prod_le", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.prod_top", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Submodule.prod_bot", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Submodule.prod_mono", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.prod_inf_prod", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.prod_sup_prod", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": true, "tactics": ["refine", "simp", "rcases", "rcases", "exact"], "tactic_count": 5}
{"name": "LinearMap.BilinMap.apply_apply_mem_of_mem_span", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": true, "tactics": ["induction", "mem_mem", "zero_left", "zero_right", "add_left", "add_right", "smul_left", "smul_right"], "tactic_count": 8}
{"name": "Submodule.biSup_comap_subtype_eq_top", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": true, "tactics": ["refine", "suffices", "obtain", "exact", "suffices", "simpa", "intro", "rw", "exact"], "tactic_count": 9}
{"name": "LinearMap.exists_ne_zero_of_sSup_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.span_range_subtype_eq_top_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Submodule.comap_le_comap_iff_of_le_range", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submodule.comap_sup_of_injective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": true, "tactics": ["apply", "rw", "simp"], "tactic_count": 3}
{"name": "AddSubgroup.toIntSubmodule_closure", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.span_neg", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.instIsModularLattice", "kind": "instance", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.isCompl_comap_subtype_of_isCompl_of_le", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Submodule.comap_map_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": true, "tactics": ["refine", "rintro", "exact"], "tactic_count": 3}
{"name": "Submodule.map_lt_map_of_le_of_sup_lt_sup", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Submodule.comap_map_eq_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submodule.comap_map_sup_of_comap_le", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": true, "tactics": ["refine", "obtain", "rw", "simpa"], "tactic_count": 4}
{"name": "Submodule.isCoatom_comap_or_eq_top", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.isCoatom_comap_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": true, "tactics": ["have", "rw", "refine", "rw"], "tactic_count": 4}
{"name": "Submodule.isCoatom_map_of_ker_le", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.map_iInf_of_ker_le", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": true, "tactics": ["conv_rhs", "simp_rw"], "tactic_count": 2}
{"name": "Submodule.comap_covBy_of_surjective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": true, "tactics": ["refine", "intro", "refine", "rwa", "refine"], "tactic_count": 5}
{"name": "LinearMap.range_domRestrict_eq_range_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "intro", "have", "rw", "obtain", "have", "simpa", "refine", "rintro", "obtain", "exact"], "tactic_count": 12}
{"name": "LinearMap.surjective_domRestrict_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "Submodule.biSup_comap_eq_top_of_surjective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": true, "tactics": ["obtain", "suffices", "exact", "rw", "rw"], "tactic_count": 5}
{"name": "Submodule.biSup_comap_eq_top_of_range_eq_biSup", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": false, "tactics": ["suffices", "rw", "exact"], "tactic_count": 3}
{"name": "Submodule.map_strict_mono_or_ker_sup_lt_ker_sup", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": true, "tactics": ["obtain", "simpa", "apply"], "tactic_count": 3}
{"name": "LinearMap.ker_inf_lt_ker_inf_of_map_eq_of_lt", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.map_strict_mono_of_ker_inf_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.disjoint_span_singleton''", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submodule.wcovBy_span_singleton_sup", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": true, "tactics": ["refine", "rcases", "obtain", "rcases", "simp", "have", "simp"], "tactic_count": 7}
{"name": "Submodule.covBy_span_singleton_sup", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.disjoint_span_singleton", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Submodule.disjoint_span_singleton'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Submodule.disjoint_span_singleton_of_notMem", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Submodule.isCompl_span_singleton_of_isCoatom_of_notMem", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "simpa"], "tactic_count": 3}
{"name": "LinearMap.map_le_map_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LinearMap.map_le_map_iff'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LinearMap.map_injective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.map_eq_top_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "LinearMap.toSpanSingleton", "kind": "definition", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.smulRight_id", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.toSpanSingleton_apply_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.toSpanSingleton_injective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.toSpanSingleton_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "LinearMap.toSpanSingleton_eq_zero_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LinearMap.toSpanSingleton_add", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "LinearMap.toSpanSingleton_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "LinearMap.toSpanSingleton_isIdempotentElem_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": false, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "LinearMap.isIdempotentElem_map_one_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "exact"], "tactic_count": 3}
{"name": "LinearMap.range_toSpanSingleton", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.span_singleton_eq_range", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.comp_toSpanSingleton", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "LinearMap.submoduleOf_span_singleton_of_mem", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp_rw", "aesop"], "tactic_count": 3}
{"name": "LinearMap.ker_toSpanSingleton_eq_bot_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.eqOn_span_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LinearMap.eqOn_span'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.eqOn_span", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.ext_on", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.ext_on_range", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.ker_toSpanSingleton", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.span_singleton_sup_ker_eq_top", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.toSpanNonzeroSingleton", "kind": "definition", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.toSpanNonzeroSingleton_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "LinearEquiv.toSpanNonzeroSingleton_symm_apply_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.toSpanNonzeroSingleton_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LinearEquiv.coord", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.coord_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LinearEquiv.coord_apply_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.span", "kind": "definition", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.instIsPrincipalSpanSingletonSet", "kind": "instance", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.IsPrincipal.generator", "kind": "definition", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.IsPrincipal.span_singleton_generator", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mem_span", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.subset_span", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mem_span_of_mem", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.span_le", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.span_mono", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.span_monotone", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.span_eq_of_le", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.span_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.span_eq_span", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.coe_span_eq_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": true, "tactics": ["refine", "let", "add_mem", "zero_mem", "smul_mem", "exact"], "tactic_count": 6}
{"name": "Submodule.span_insert_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "Submodule.span_sdiff_singleton_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "simp"], "tactic_count": 3}
{"name": "Submodule.closure_subset_span", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.closure_le_toAddSubmonoid_span", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.span_closure", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.span_induction", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": false, "tactics": ["let", "add_mem", "zero_mem", "smul_mem", "exact"], "tactic_count": 5}
{"name": "Submodule.span_induction₂", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": true, "tactics": ["induction", "mem", "induction", "mem", "zero", "add", "smul", "zero", "add", "smul"], "tactic_count": 10}
{"name": "Submodule.span_eq_closure", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": true, "tactics": ["refine", "induction", "mem", "zero", "add", "smul", "clear", "induction", "mem", "obtain", "exact", "zero", "add", "refine", "rintro", "exact"], "tactic_count": 16}
{"name": "Submodule.closure_induction", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": true, "tactics": ["have", "refine", "rintro", "exact"], "tactic_count": 4}
{"name": "Submodule.span_span_coe_preimage", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.span_setOf_mem_eq_top", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.span_nat_eq_addSubmonoidClosure", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": true, "tactics": ["refine", "apply", "rw", "exact"], "tactic_count": 4}
{"name": "Submodule.span_nat_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submodule.span_int_eq_addSubgroupClosure", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.span_int_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Disjoint.of_span", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": true, "tactics": ["rw", "rintro", "exact"], "tactic_count": 3}
{"name": "Disjoint.of_span₀", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Submodule.gi", "kind": "definition", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.span_empty", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.span_univ", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.span_union", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.span_iUnion", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.span_iUnion₂", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.span_attach_biUnion", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Submodule.sup_span", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submodule.span_sup", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": true, "tactics": ["rw", "character"], "tactic_count": 2}
{"name": "Submodule.term_∙_", "kind": "definition", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule._aux_Mathlib_LinearAlgebra_Span_Defs___macroRules_Submodule_term_∙__1", "kind": "definition", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule._aux_Mathlib_LinearAlgebra_Span_Defs___unexpand_Submodule_span_1", "kind": "definition", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.span.unexpander", "kind": "definition", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.span_eq_iSup_of_singleton_spans", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Submodule.span_range_eq_iSup", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submodule.span_smul_le", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": true, "tactics": ["rw", "rintro", "exact"], "tactic_count": 3}
{"name": "Submodule.subset_span_trans", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.coe_iSup_of_directed", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mem_iSup_of_directed", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Submodule.mem_sSup_of_directed", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": true, "tactics": ["have", "simp"], "tactic_count": 2}
{"name": "Submodule.coe_iSup_of_chain", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mem_iSup_of_chain", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mem_sup", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mem_sup'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.codisjoint_iff_exists_add_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Submodule.coe_sup", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": true, "tactics": ["ext", "rw", "simp"], "tactic_count": 3}
{"name": "Submodule.sup_toAddSubmonoid", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": true, "tactics": ["ext", "rw", "rfl"], "tactic_count": 3}
{"name": "Submodule.sup_eq_top_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "tauto"], "tactic_count": 4}
{"name": "Submodule.forall_mem_sup", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": true, "tactics": ["simp", "aesop"], "tactic_count": 2}
{"name": "Submodule.exists_mem_sup", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Submodule.mem_span_singleton_self", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.nontrivial_span_singleton", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mem_span_singleton", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.le_span_singleton_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Submodule.eq_span_singleton_of_surjective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": true, "tactics": ["refine", "have", "exact"], "tactic_count": 3}
{"name": "Submodule.span_singleton_eq_top_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": true, "tactics": ["rw", "tauto"], "tactic_count": 2}
{"name": "Submodule.span_zero_singleton", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Submodule.span_singleton_eq_range", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.span_singleton_smul_le", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Submodule.span_singleton_group_smul_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": true, "tactics": ["refine", "convert", "exact"], "tactic_count": 3}
{"name": "Submodule.span_singleton_smul_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": true, "tactics": ["lift", "rw", "exact"], "tactic_count": 3}
{"name": "Submodule.mem_span_singleton_trans", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Submodule.span_insert", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submodule.span_insert_eq_span", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.span_span", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mem_span_insert", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Submodule.mem_span_pair", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Submodule.mem_span_triple", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "refine", "rintro", "exact", "rintro", "exact"], "tactic_count": 7}
{"name": "Submodule.span_eq_bot", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.span_singleton_eq_bot", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Submodule.span_zero", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submodule.span_singleton_le_iff_mem", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submodule.iSup_span", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.iSup_eq_span", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Submodule.iSup_eq_span'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Submodule.submodule_eq_sSup_le_nonzero_spans", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": true, "tactics": ["let", "apply", "intro", "by_cases", "rw", "simp", "exact", "rw", "rintro", "rwa"], "tactic_count": 10}
{"name": "Submodule.lt_sup_iff_notMem", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Submodule.mem_iSup", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Submodule.mem_sSup", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Submodule.mem_span_finite_of_mem_span", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": true, "tactics": ["classical", "refine", "refine", "rwa", "rw", "exact", "use", "simp", "rintro", "refine", "rw", "exact", "rw", "exact", "rintro", "exact"], "tactic_count": 16}
{"name": "Submodule.subset_span_finite_of_subset_span", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "insert", "obtain", "obtain", "refine", "simp", "exact"], "tactic_count": 9}
{"name": "Submodule.sup_toAddSubgroup", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": true, "tactics": ["ext", "rw", "rfl"], "tactic_count": 3}
{"name": "Submodule.mem_span_insert'", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": true, "tactics": ["rw", "rintro", "exact", "rintro", "exact"], "tactic_count": 5}
{"name": "Submodule.span_range_update_add_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": false, "tactics": ["refine", "obtain", "rw", "exact", "exact", "nth_rw", "exact", "exact"], "tactic_count": 8}
{"name": "Submodule.span_range_update_sub_smul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Module.IsPrincipal", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.isPrincipal_def", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.isPrincipal_submodule_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": true, "tactics": ["simp_rw", "constructor", "refine", "have", "exact", "refine", "have", "exact"], "tactic_count": 8}
{"name": "Module.IsPrincipal.of_surjective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.isPrincipal_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.tensorToSpan", "kind": "definition", "module": "Mathlib.LinearAlgebra.Span.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.tensorToSpan_apply_tmul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.surjective_tensorToSpan", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.TensorProduct", "is_tactic_proof": true, "tactics": ["intro", "obtain", "use", "rw", "simpa"], "tactic_count": 5}
{"name": "Submodule.injective_tensorToSpan", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.TensorProduct", "is_tactic_proof": false, "tactics": ["let", "let", "have", "have", "have", "rw", "exact"], "tactic_count": 7}
{"name": "Submodule.tensorEquivSpan", "kind": "definition", "module": "Mathlib.LinearAlgebra.Span.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.tensorEquivSpan_apply_tmul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.tensorSpanEquivSpan", "kind": "definition", "module": "Mathlib.LinearAlgebra.Span.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.coe_tensorSpanEquivSpan_apply_tmul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.finrank_span_eq_finrank", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.TensorProduct", "is_tactic_proof": true, "tactics": ["rcases", "let", "let", "let", "rw"], "tactic_count": 5}
{"name": "Submodule.finrank_span_eq_finrank_span", "kind": "theorem", "module": "Mathlib.LinearAlgebra.Span.TensorProduct", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SpecialLinearGroup", "kind": "abbrev", "module": "Mathlib.LinearAlgebra.SpecialLinearGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SpecialLinearGroup.det_eq_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SpecialLinearGroup", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SpecialLinearGroup.instCoeFunForall", "kind": "instance", "module": "Mathlib.LinearAlgebra.SpecialLinearGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SpecialLinearGroup.ext_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SpecialLinearGroup", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SpecialLinearGroup.ext", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SpecialLinearGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SpecialLinearGroup.subsingleton_of_finrank_eq_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SpecialLinearGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SpecialLinearGroup.instInv", "kind": "instance", "module": "Mathlib.LinearAlgebra.SpecialLinearGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SpecialLinearGroup.instMul", "kind": "instance", "module": "Mathlib.LinearAlgebra.SpecialLinearGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SpecialLinearGroup.instDiv", "kind": "instance", "module": "Mathlib.LinearAlgebra.SpecialLinearGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SpecialLinearGroup.instOne", "kind": "instance", "module": "Mathlib.LinearAlgebra.SpecialLinearGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SpecialLinearGroup.instPowNat", "kind": "instance", "module": "Mathlib.LinearAlgebra.SpecialLinearGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SpecialLinearGroup.instPowInt", "kind": "instance", "module": "Mathlib.LinearAlgebra.SpecialLinearGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SpecialLinearGroup.instInhabited", "kind": "instance", "module": "Mathlib.LinearAlgebra.SpecialLinearGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SpecialLinearGroup.dualMap", "kind": "definition", "module": "Mathlib.LinearAlgebra.SpecialLinearGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SpecialLinearGroup.term_ᵀ", "kind": "definition", "module": "Mathlib.LinearAlgebra.SpecialLinearGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SpecialLinearGroup._aux_Mathlib_LinearAlgebra_SpecialLinearGroup___macroRules_SpecialLinearGroup_term_ᵀ_1", "kind": "definition", "module": "Mathlib.LinearAlgebra.SpecialLinearGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SpecialLinearGroup._aux_Mathlib_LinearAlgebra_SpecialLinearGroup___unexpand_SpecialLinearGroup_dualMap_1", "kind": "definition", "module": "Mathlib.LinearAlgebra.SpecialLinearGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SpecialLinearGroup.coe_mk", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SpecialLinearGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SpecialLinearGroup.coe_mul", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SpecialLinearGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SpecialLinearGroup.coe_div", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SpecialLinearGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SpecialLinearGroup.coe_inv", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SpecialLinearGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SpecialLinearGroup.coe_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SpecialLinearGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SpecialLinearGroup.det_coe", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SpecialLinearGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SpecialLinearGroup.coe_pow", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SpecialLinearGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SpecialLinearGroup.coe_zpow", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SpecialLinearGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SpecialLinearGroup.coe_dualMap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SpecialLinearGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SpecialLinearGroup.instGroup", "kind": "instance", "module": "Mathlib.LinearAlgebra.SpecialLinearGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SpecialLinearGroup.toLinearEquiv", "kind": "definition", "module": "Mathlib.LinearAlgebra.SpecialLinearGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SpecialLinearGroup.toLinearEquiv_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SpecialLinearGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SpecialLinearGroup.toLinearEquiv_to_linearMap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SpecialLinearGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SpecialLinearGroup.toLinearEquiv_symm_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SpecialLinearGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SpecialLinearGroup.toLinearEquiv_symm_to_linearMap", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SpecialLinearGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SpecialLinearGroup.toLinearEquiv_injective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SpecialLinearGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SpecialLinearGroup.toGeneralLinearGroup", "kind": "definition", "module": "Mathlib.LinearAlgebra.SpecialLinearGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SpecialLinearGroup.toGeneralLinearGroup_toLinearEquiv_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SpecialLinearGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SpecialLinearGroup.coe_toGeneralLinearGroup_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SpecialLinearGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SpecialLinearGroup.toGeneralLinearGroup_injective", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SpecialLinearGroup", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SpecialLinearGroup.mem_range_toGeneralLinearGroup_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SpecialLinearGroup", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "rw", "exact", "intro", "refine"], "tactic_count": 6}
{"name": "SpecialLinearGroup.baseChange", "kind": "definition", "module": "Mathlib.LinearAlgebra.SpecialLinearGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SpecialLinearGroup.congr_linearEquiv", "kind": "definition", "module": "Mathlib.LinearAlgebra.SpecialLinearGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SpecialLinearGroup.congr_linearEquiv_coe_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SpecialLinearGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SpecialLinearGroup.congr_linearEquiv_apply_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SpecialLinearGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SpecialLinearGroup.congr_linearEquiv_symm", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SpecialLinearGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SpecialLinearGroup.congr_linearEquiv_trans", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SpecialLinearGroup", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "SpecialLinearGroup.congr_linearEquiv_refl", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SpecialLinearGroup", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "Matrix.SpecialLinearGroup.toLin'_equiv", "kind": "definition", "module": "Mathlib.LinearAlgebra.SpecialLinearGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.SpecialLinearGroup.toLin_equiv", "kind": "definition", "module": "Mathlib.LinearAlgebra.SpecialLinearGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.SpecialLinearGroup.toLin_equiv.toLinearMap_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SpecialLinearGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.SpecialLinearGroup.toLin_equiv.symm_toLinearMap_eq", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SpecialLinearGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SpecialLinearGroup.center_eq_bot_of_finrank_le_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SpecialLinearGroup", "is_tactic_proof": true, "tactics": ["nontriviality", "let", "have", "rwa", "have", "infer_instance", "rw", "exact"], "tactic_count": 8}
{"name": "SpecialLinearGroup.mem_center_iff", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SpecialLinearGroup", "is_tactic_proof": true, "tactics": ["rcases", "have", "simp", "let", "let", "rw", "let", "rw", "rw", "apply", "simp", "intro", "suffices", "simp", "rw", "simp", "apply", "intro", "simp", "ext", "simp"], "tactic_count": 21}
{"name": "SpecialLinearGroup.mem_center_iff_spec", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SpecialLinearGroup", "is_tactic_proof": true, "tactics": ["let", "rw", "simp", "and", "while"], "tactic_count": 5}
{"name": "SpecialLinearGroup.centerEquivRootsOfUnity_invFun", "kind": "definition", "module": "Mathlib.LinearAlgebra.SpecialLinearGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SpecialLinearGroup.centerEquivRootsOfUnity", "kind": "definition", "module": "Mathlib.LinearAlgebra.SpecialLinearGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SpecialLinearGroup.centerEquivRootsOfUnity_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SpecialLinearGroup", "is_tactic_proof": false, "tactics": ["simp", "split_ifs", "have", "apply", "apply", "rw", "rw"], "tactic_count": 7}
{"name": "SpecialLinearGroup.centerEquivRootsOfUnity_apply_apply", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SpecialLinearGroup", "is_tactic_proof": true, "tactics": ["simp", "rw", "simp"], "tactic_count": 3}
{"name": "rootsOfUnity.eq_one", "kind": "theorem", "module": "Mathlib.LinearAlgebra.SpecialLinearGroup", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
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{"name": "exists_and_exists_comm", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_forall_not", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "forall_or_exists_not", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "exists_or_forall_not", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "forall_imp_iff_exists_imp", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": true, "tactics": ["classical", "let", "refine", "exact"], "tactic_count": 4}
{"name": "forall_true_iff", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Ne.ne_or_ne", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_apply_eq_apply'", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_apply_eq_apply2", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_apply_eq_apply2'", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "exists_apply_eq_apply3'", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_apply_eq", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_exists_and_eq_and", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_exists_eq_and", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_exists_and_exists_and_eq_and", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_exists_exists_and_eq", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "forall_apply_eq_imp_iff'", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "forall_eq_apply_imp_iff'", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "exists₂_comm", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "And.exists", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "forall_or_of_or_forall", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Decidable.forall_or_left", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "forall_or_left", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Decidable.forall_or_right", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "forall_or_right", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "forall_and_index", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "forall_and_index'", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Exists.fst", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Exists.snd", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prop.exists_iff", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prop.forall_iff", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_iff_of_forall", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_prop_of_false", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "forall_prop_congr", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "forall_prop_congr'", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "imp_congr_eq", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "imp_congr_ctx_eq", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_true_intro", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_false_intro", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iff_eq_eq", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "forall_true_left", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Classical.dec", "kind": "definition", "module": "Mathlib.Logic.Basic", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Classical.decPred", "kind": "definition", "module": "Mathlib.Logic.Basic", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
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{"name": "Classical.existsCases", "kind": "definition", "module": "Mathlib.Logic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Classical.some_spec₂", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Classical.choose_eq", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "BEx.intro", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BAll.imp_right", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Ne.dite_eq_left_iff", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Ne.dite_ne_right_iff", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "dite_eq_or_eq", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "apply_dite₂", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "apply_ite₂", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ite_apply", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "apply_ite_left", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
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{"name": "ite_ite_comm", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ite_prop_iff_or", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "dite_prop_iff_or", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simp"], "tactic_count": 2}
{"name": "ite_prop_iff_and", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "dite_prop_iff_and", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "if_ctx_congr", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "if_congr", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_dite", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "dite_mem", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "mem_ite", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ite_mem", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_beq_of_ne", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "beq_eq_beq", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "beq_ext", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": true, "tactics": ["have", "congr", "funext", "exact"], "tactic_count": 4}
{"name": "lawful_beq_subsingleton", "kind": "theorem", "module": "Mathlib.Logic.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Denumerable.decode_isSome", "kind": "theorem", "module": "Mathlib.Logic.Denumerable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Denumerable.ofNat", "kind": "definition", "module": "Mathlib.Logic.Denumerable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Denumerable.decode_eq_ofNat", "kind": "theorem", "module": "Mathlib.Logic.Denumerable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Denumerable.ofNat_of_decode", "kind": "theorem", "module": "Mathlib.Logic.Denumerable", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Denumerable.encode_ofNat", "kind": "theorem", "module": "Mathlib.Logic.Denumerable", "is_tactic_proof": true, "tactics": ["obtain", "rwa"], "tactic_count": 2}
{"name": "Denumerable.ofNat_encode", "kind": "theorem", "module": "Mathlib.Logic.Denumerable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Denumerable.eqv", "kind": "definition", "module": "Mathlib.Logic.Denumerable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Denumerable.instInfinite", "kind": "instance", "module": "Mathlib.Logic.Denumerable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Denumerable.mk'", "kind": "definition", "module": "Mathlib.Logic.Denumerable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Denumerable.ofEquiv", "kind": "definition", "module": "Mathlib.Logic.Denumerable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Denumerable.ofEquiv_ofNat", "kind": "theorem", "module": "Mathlib.Logic.Denumerable", "is_tactic_proof": true, "tactics": ["letI", "refine", "rw", "simp"], "tactic_count": 4}
{"name": "Denumerable.equiv₂", "kind": "definition", "module": "Mathlib.Logic.Denumerable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Denumerable.nat", "kind": "instance", "module": "Mathlib.Logic.Denumerable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Denumerable.ofNat_nat", "kind": "theorem", "module": "Mathlib.Logic.Denumerable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Denumerable.sum", "kind": "instance", "module": "Mathlib.Logic.Denumerable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Denumerable.sigma", "kind": "instance", "module": "Mathlib.Logic.Denumerable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Denumerable.sigma_ofNat_val", "kind": "theorem", "module": "Mathlib.Logic.Denumerable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Denumerable.prod", "kind": "instance", "module": "Mathlib.Logic.Denumerable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Denumerable.prod_ofNat_val", "kind": "theorem", "module": "Mathlib.Logic.Denumerable", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Denumerable.prod_nat_ofNat", "kind": "theorem", "module": "Mathlib.Logic.Denumerable", "is_tactic_proof": true, "tactics": ["funext"], "tactic_count": 1}
{"name": "Denumerable.int", "kind": "instance", "module": "Mathlib.Logic.Denumerable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Denumerable.pnat", "kind": "instance", "module": "Mathlib.Logic.Denumerable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Denumerable.ulift", "kind": "instance", "module": "Mathlib.Logic.Denumerable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Denumerable.plift", "kind": "instance", "module": "Mathlib.Logic.Denumerable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Denumerable.pair", "kind": "definition", "module": "Mathlib.Logic.Denumerable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Subtype.exists_succ", "kind": "theorem", "module": "Mathlib.Logic.Denumerable", "is_tactic_proof": true, "tactics": ["by_contra", "have", "lt_of_not_ge", "classical", "exact"], "tactic_count": 5}
{"name": "Nat.Subtype.succ", "kind": "definition", "module": "Mathlib.Logic.Denumerable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Subtype.succ_le_of_lt", "kind": "theorem", "module": "Mathlib.Logic.Denumerable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Subtype.le_succ_of_forall_lt_le", "kind": "theorem", "module": "Mathlib.Logic.Denumerable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Subtype.lt_succ_self", "kind": "theorem", "module": "Mathlib.Logic.Denumerable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Subtype.lt_succ_iff_le", "kind": "theorem", "module": "Mathlib.Logic.Denumerable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Subtype.ofNat", "kind": "definition", "module": "Mathlib.Logic.Denumerable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Subtype.ofNat_surjective", "kind": "theorem", "module": "Mathlib.Logic.Denumerable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Subtype.ofNat_range", "kind": "theorem", "module": "Mathlib.Logic.Denumerable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Subtype.coe_comp_ofNat_range", "kind": "theorem", "module": "Mathlib.Logic.Denumerable", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "_private.Mathlib.Logic.Denumerable.0.Nat.Subtype.toFunAux", "kind": "definition", "module": "Mathlib.Logic.Denumerable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "_private.Mathlib.Logic.Denumerable.0.Nat.Subtype.right_inverse_aux", "kind": "theorem", "module": "Mathlib.Logic.Denumerable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Subtype.denumerable", "kind": "definition", "module": "Mathlib.Logic.Denumerable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Denumerable.ofEncodableOfInfinite", "kind": "definition", "module": "Mathlib.Logic.Denumerable", "is_tactic_proof": true, "tactics": ["letI", "letI", "letI", "exact"], "tactic_count": 4}
{"name": "nonempty_denumerable", "kind": "theorem", "module": "Mathlib.Logic.Denumerable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nonempty_denumerable_iff", "kind": "theorem", "module": "Mathlib.Logic.Denumerable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nonempty_equiv_of_countable", "kind": "instance", "module": "Mathlib.Logic.Denumerable", "is_tactic_proof": true, "tactics": ["cases", "cases", "exact"], "tactic_count": 3}
{"name": "Function.term_↪_", "kind": "definition", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function._aux_Mathlib_Logic_Embedding_Basic___macroRules_Function_term_↪__1", "kind": "definition", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function._aux_Mathlib_Logic_Embedding_Basic___unexpand_Function_Embedding_1", "kind": "definition", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.instFunLikeEmbedding", "kind": "instance", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.instEmbeddingLikeEmbedding", "kind": "instance", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.instCanLiftForallEmbeddingCoeInjective", "kind": "instance", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.exists_surjective_iff", "kind": "theorem", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.toEmbedding", "kind": "definition", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.coe_toEmbedding", "kind": "theorem", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.toEmbedding_apply", "kind": "theorem", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.toEmbedding_injective", "kind": "theorem", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.coeEmbedding", "kind": "instance", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.coeEmbedding", "kind": "abbrev", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.coe_injective", "kind": "theorem", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.ext", "kind": "theorem", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.instUniqueOfIsEmpty", "kind": "instance", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.toFun_eq_coe", "kind": "theorem", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.coeFn_mk", "kind": "theorem", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.mk_coe", "kind": "theorem", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.injective", "kind": "theorem", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.apply_eq_iff_eq", "kind": "theorem", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.refl", "kind": "definition", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.coe_refl", "kind": "theorem", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.trans", "kind": "definition", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.coe_trans", "kind": "theorem", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.instTrans", "kind": "instance", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.mk_id", "kind": "theorem", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.mk_trans_mk", "kind": "theorem", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.equiv_toEmbedding_trans_symm_toEmbedding", "kind": "theorem", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Function.Embedding.equiv_symm_toEmbedding_trans_toEmbedding", "kind": "theorem", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Function.Embedding.congr", "kind": "definition", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.ofSurjective", "kind": "definition", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.equivOfSurjective", "kind": "definition", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.ofIsEmpty", "kind": "definition", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.setValue", "kind": "definition", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.setValue_eq", "kind": "theorem", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Function.Embedding.setValue_eq_iff", "kind": "theorem", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.setValue_eq_of_ne", "kind": "theorem", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Function.Embedding.setValue_right_apply_eq", "kind": "theorem", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Function.Embedding.some", "kind": "definition", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.optionMap", "kind": "definition", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.subtype", "kind": "definition", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.subtype_apply", "kind": "theorem", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.subtype_injective", "kind": "theorem", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.coe_subtype", "kind": "theorem", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.quotientOut", "kind": "definition", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.coe_quotientOut", "kind": "theorem", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.punit", "kind": "definition", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.oneEmbeddingEquiv", "kind": "definition", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.sectL", "kind": "definition", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.sectR", "kind": "definition", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.prodMap", "kind": "definition", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.coe_prodMap", "kind": "theorem", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.pprodMap", "kind": "definition", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.sumMap", "kind": "definition", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.coe_sumMap", "kind": "theorem", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.inl", "kind": "definition", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.inr", "kind": "definition", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.sigmaMk", "kind": "definition", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.sigmaMap", "kind": "definition", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.piCongrRight", "kind": "definition", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.arrowCongrRight", "kind": "definition", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.arrowCongrRight_apply", "kind": "theorem", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.arrowCongrLeft", "kind": "definition", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.arrowCongrLeft_apply", "kind": "theorem", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.arrowCongrLeft_refl", "kind": "theorem", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Function.Embedding.trans_arrowCongrLeft", "kind": "theorem", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp", "rw"], "tactic_count": 3}
{"name": "Function.Embedding.subtypeMap", "kind": "definition", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.swap_apply", "kind": "theorem", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.swap_comp", "kind": "theorem", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.asEmbedding", "kind": "definition", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.subtypeInjectiveEquivEmbedding", "kind": "definition", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.embeddingCongr", "kind": "definition", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.embeddingCongr_refl", "kind": "theorem", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.embeddingCongr_trans", "kind": "theorem", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.embeddingCongr_symm", "kind": "theorem", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.embeddingCongr_apply_trans", "kind": "theorem", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Equiv.refl_toEmbedding", "kind": "theorem", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.trans_toEmbedding", "kind": "theorem", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "subtypeOrLeftEmbedding", "kind": "definition", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "subtypeOrLeftEmbedding_apply_left", "kind": "theorem", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "subtypeOrLeftEmbedding_apply_right", "kind": "theorem", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "subtypeOrLeftEmbedding_apply", "kind": "theorem", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.impEmbedding", "kind": "definition", "module": "Mathlib.Logic.Embedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.asEmbedding_range", "kind": "theorem", "module": "Mathlib.Logic.Embedding.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.optionElim", "kind": "definition", "module": "Mathlib.Logic.Embedding.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.optionEmbeddingEquiv", "kind": "definition", "module": "Mathlib.Logic.Embedding.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.codRestrict", "kind": "definition", "module": "Mathlib.Logic.Embedding.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.codRestrict_apply", "kind": "theorem", "module": "Mathlib.Logic.Embedding.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.image", "kind": "definition", "module": "Mathlib.Logic.Embedding.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.embeddingOfSubset", "kind": "definition", "module": "Mathlib.Logic.Embedding.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "subtypeOrEquiv", "kind": "definition", "module": "Mathlib.Logic.Embedding.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "subtypeOrEquiv_symm_inl", "kind": "theorem", "module": "Mathlib.Logic.Embedding.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "subtypeOrEquiv_symm_inr", "kind": "theorem", "module": "Mathlib.Logic.Embedding.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.sumSet", "kind": "definition", "module": "Mathlib.Logic.Embedding.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.coe_sumSet", "kind": "theorem", "module": "Mathlib.Logic.Embedding.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.sumSet_preimage_inl", "kind": "theorem", "module": "Mathlib.Logic.Embedding.Set", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Function.Embedding.sumSet_preimage_inr", "kind": "theorem", "module": "Mathlib.Logic.Embedding.Set", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Function.Embedding.sumSet_range", "kind": "theorem", "module": "Mathlib.Logic.Embedding.Set", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Function.Embedding.sigmaSet", "kind": "definition", "module": "Mathlib.Logic.Embedding.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.coe_sigmaSet", "kind": "theorem", "module": "Mathlib.Logic.Embedding.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.sigmaSet_preimage", "kind": "theorem", "module": "Mathlib.Logic.Embedding.Set", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Function.Embedding.sigmaSet_range", "kind": "theorem", "module": "Mathlib.Logic.Embedding.Set", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Encodable.encode_injective", "kind": "theorem", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.encode_inj", "kind": "theorem", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.countable", "kind": "instance", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.surjective_decode_getD", "kind": "theorem", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.surjective_decode_iget", "kind": "theorem", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.decidableEqOfEncodable", "kind": "definition", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.ofLeftInjection", "kind": "definition", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.ofLeftInverse", "kind": "definition", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.ofEquiv", "kind": "definition", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.encode_ofEquiv", "kind": "theorem", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.decode_ofEquiv", "kind": "theorem", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.encodable", "kind": "instance", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.encode_nat", "kind": "theorem", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.decode_nat", "kind": "theorem", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsEmpty.toEncodable", "kind": "instance", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PUnit.encodable", "kind": "instance", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.encode_star", "kind": "theorem", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.decode_unit_zero", "kind": "theorem", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.decode_unit_succ", "kind": "theorem", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Option.encodable", "kind": "instance", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.encode_none", "kind": "theorem", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.encode_some", "kind": "theorem", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.decode_option_zero", "kind": "theorem", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.decode_option_succ", "kind": "theorem", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.decode₂", "kind": "definition", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.mem_decode₂'", "kind": "theorem", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Encodable.mem_decode₂", "kind": "theorem", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.decode₂_eq_some", "kind": "theorem", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.decode₂_encode", "kind": "theorem", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Encodable.decode₂_ne_none_iff", "kind": "theorem", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "not_not]"], "tactic_count": 2}
{"name": "Encodable.decode₂_is_partial_inv", "kind": "theorem", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.decode₂_inj", "kind": "theorem", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.encodek₂", "kind": "theorem", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.decidableRangeEncode", "kind": "definition", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.equivRangeEncode", "kind": "definition", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unique.encodable", "kind": "definition", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.encodeSum", "kind": "definition", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.decodeSum", "kind": "definition", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.encodable", "kind": "instance", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.encode_inl", "kind": "theorem", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.encode_inr", "kind": "theorem", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.decode_sum_val", "kind": "theorem", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bool.encodable", "kind": "instance", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.encode_true", "kind": "theorem", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.encode_false", "kind": "theorem", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.decode_zero", "kind": "theorem", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.decode_one", "kind": "theorem", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.decode_ge_two", "kind": "theorem", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": ["suffices", "change", "rw", "rfl", "have", "rw", "exacts", "obtain", "simp"], "tactic_count": 9}
{"name": "Prop.encodable", "kind": "instance", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.encodeSigma", "kind": "definition", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.decodeSigma", "kind": "definition", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.encodable", "kind": "instance", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.decode_sigma_val", "kind": "theorem", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.encode_sigma_val", "kind": "theorem", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.Prod.encodable", "kind": "instance", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.decode_prod_val", "kind": "theorem", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": true, "tactics": ["simp", "cases"], "tactic_count": 2}
{"name": "Encodable.encode_prod_val", "kind": "theorem", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.encodeSubtype", "kind": "definition", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.decodeSubtype", "kind": "definition", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.encodable", "kind": "instance", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.Subtype.encode_eq", "kind": "theorem", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Fin.encodable", "kind": "instance", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.encodable", "kind": "instance", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.encodable", "kind": "instance", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.encodable", "kind": "instance", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PLift.encodable", "kind": "instance", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.ofInj", "kind": "definition", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.ofCountable", "kind": "definition", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.nonempty_encodable", "kind": "theorem", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nonempty_encodable", "kind": "theorem", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCountablePNat", "kind": "instance", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": true, "tactics": ["delta", "infer_instance"], "tactic_count": 2}
{"name": "ULower", "kind": "definition", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDecidableEqULower", "kind": "instance", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": true, "tactics": ["delta"], "tactic_count": 1}
{"name": "instEncodableULower", "kind": "instance", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": true, "tactics": ["delta"], "tactic_count": 1}
{"name": "ULower.equiv", "kind": "definition", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULower.down", "kind": "definition", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULower.instInhabited", "kind": "instance", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULower.up", "kind": "definition", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULower.down_up", "kind": "theorem", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULower.up_down", "kind": "theorem", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ULower.up_eq_up", "kind": "theorem", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULower.down_eq_down", "kind": "theorem", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULower.ext", "kind": "theorem", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Logic.Encodable.Basic.0.Encodable.good", "kind": "definition", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Logic.Encodable.Basic.0.Encodable.decidable_good", "kind": "definition", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.chooseX", "kind": "definition", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.choose", "kind": "definition", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.choose_spec", "kind": "theorem", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.axiom_of_choice", "kind": "theorem", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.skolem", "kind": "theorem", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.encode'", "kind": "definition", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.instAntisymmPreimageNatCoeEmbeddingEncode'Le", "kind": "instance", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.instTotalPreimageNatCoeEmbeddingEncode'Le", "kind": "instance", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Directed.sequence", "kind": "definition", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Directed.sequence_mono_nat", "kind": "theorem", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "generalize", "rcases", "exact", "exact"], "tactic_count": 5}
{"name": "Directed.rel_sequence", "kind": "theorem", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Directed.sequence_mono", "kind": "theorem", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Directed.le_sequence", "kind": "theorem", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Directed.sequence_anti", "kind": "theorem", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Directed.sequence_le", "kind": "theorem", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quotient.rep", "kind": "definition", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quotient.rep_spec", "kind": "theorem", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "encodableQuotient", "kind": "definition", "module": "Mathlib.Logic.Encodable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.iSup_decode₂", "kind": "theorem", "module": "Mathlib.Logic.Encodable.Lattice", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Encodable.iUnion_decode₂", "kind": "theorem", "module": "Mathlib.Logic.Encodable.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.iUnion_decode₂_cases", "kind": "theorem", "module": "Mathlib.Logic.Encodable.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.iUnion_decode₂_disjoint_on", "kind": "theorem", "module": "Mathlib.Logic.Encodable.Lattice", "is_tactic_proof": true, "tactics": ["rintro", "refine", "suffices", "rintro", "exact"], "tactic_count": 5}
{"name": "Encodable.List.Vector.encodable", "kind": "instance", "module": "Mathlib.Logic.Encodable.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.List.Vector.countable", "kind": "instance", "module": "Mathlib.Logic.Encodable.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.finArrow", "kind": "instance", "module": "Mathlib.Logic.Encodable.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.finPi", "kind": "instance", "module": "Mathlib.Logic.Encodable.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.fintypeArrow", "kind": "definition", "module": "Mathlib.Logic.Encodable.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.fintypePi", "kind": "definition", "module": "Mathlib.Logic.Encodable.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.fintypeArrowOfEncodable", "kind": "instance", "module": "Mathlib.Logic.Encodable.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.arrayEquivList", "kind": "definition", "module": "Mathlib.Logic.Equiv.Array", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Array.encodable", "kind": "instance", "module": "Mathlib.Logic.Equiv.Array", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Array.countable", "kind": "instance", "module": "Mathlib.Logic.Equiv.Array", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.piOptionEquivProd", "kind": "definition", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.subtypeCongr", "kind": "definition", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.subtypeCongr", "kind": "definition", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.subtypeCongr.apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "Equiv.Perm.subtypeCongr.left_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Equiv.Perm.subtypeCongr.left_apply_subtype", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.subtypeCongr.right_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Equiv.Perm.subtypeCongr.right_apply_subtype", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.subtypeCongr.refl", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": true, "tactics": ["ext", "by_cases"], "tactic_count": 2}
{"name": "Equiv.Perm.subtypeCongr.symm", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.subtypeCongr.trans", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Equiv.subtypePreimage", "kind": "definition", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.subtypePreimage_symm_apply_coe_pos", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.subtypePreimage_symm_apply_coe_neg", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.piCongrRight", "kind": "definition", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.piCongrRight_refl", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.piComm", "kind": "definition", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.piComm_symm", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.piCurry", "kind": "definition", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.piCurry_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.piCurry_symm_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.ofFiberEquiv", "kind": "definition", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.ofFiberEquiv_map", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.sigmaNatSucc", "kind": "definition", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.natEquivNatSumPUnit", "kind": "definition", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.natSumPUnitEquivNat", "kind": "definition", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.intEquivNatSumNat", "kind": "definition", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.uniqueCongr", "kind": "definition", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.isEmpty_congr", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.isEmpty", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.subtypeEquiv", "kind": "definition", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.coe_subtypeEquiv_eq_map", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.subtypeEquiv_symm", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.subtypeEquiv_trans", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.subtypeEquivRight", "kind": "definition", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.subtypeEquivRight_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.subtypeEquivRight_symm_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.subtypeEquivOfSubtype", "kind": "definition", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.subtypeEquivOfSubtype'", "kind": "definition", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.subtypeEquivProp", "kind": "definition", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.subtypeSubtypeEquivSubtypeExists", "kind": "definition", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.subtypeSubtypeEquivSubtypeInter", "kind": "definition", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.subtypeSubtypeEquivSubtype", "kind": "definition", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.subtypeUnivEquiv", "kind": "definition", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.subtypeSigmaEquiv", "kind": "definition", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.sigmaSubtypeEquivOfSubset", "kind": "definition", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.sigmaSubtypeFiberEquiv", "kind": "definition", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.sigmaSubtypeFiberEquivSubtype", "kind": "definition", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.sigmaOptionEquivOfSome", "kind": "definition", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.piEquivSubtypeSigma", "kind": "definition", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.subtypePiEquivPi", "kind": "definition", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.sigmaAssocProd", "kind": "definition", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.sigmaSubtype", "kind": "definition", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.sigmaSigmaSubtype", "kind": "definition", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.sigmaSigmaSubtype_symm_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Equiv.sigmaSigmaSubtypeEq", "kind": "definition", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.sigmaSigmaSubtypeEq_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Equiv.sigmaSigmaSubtypeEq_symm_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Equiv.subtypeEquivCodomain", "kind": "definition", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.coe_subtypeEquivCodomain", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.subtypeEquivCodomain_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.coe_subtypeEquivCodomain_symm", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.subtypeEquivCodomain_symm_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.subtypeEquivCodomain_symm_apply_eq", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.subtypeEquivCodomain_symm_apply_ne", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.instCanLiftForallCoeBijective", "kind": "instance", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.extendDomain", "kind": "definition", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.extendDomain_apply_image", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Equiv.Perm.extendDomain_apply_subtype", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Equiv.Perm.extendDomain_apply_not_subtype", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Equiv.Perm.extendDomain_refl", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Equiv.Perm.extendDomain_symm", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.extendDomain_trans", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Equiv.subtypeQuotientEquivQuotientSubtype", "kind": "definition", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.subtypeQuotientEquivQuotientSubtype_mk", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.subtypeQuotientEquivQuotientSubtype_symm_mk", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.swapCore", "kind": "definition", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.swapCore_self", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": true, "tactics": ["unfold", "split_ifs"], "tactic_count": 2}
{"name": "Equiv.swapCore_swapCore", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "Equiv.swapCore_comm", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "Equiv.swap", "kind": "definition", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.swap_self", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.swap_comm", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.swap_apply_def", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.swap_apply_left", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.swap_apply_right", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Equiv.swap_apply_of_ne_of_ne", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Equiv.eq_or_eq_of_swap_apply_ne_self", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": true, "tactics": ["contrapose", "exact"], "tactic_count": 2}
{"name": "Equiv.swap_swap", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.symm_swap", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.swap_eq_refl_iff", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.swap_comp_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": true, "tactics": ["cases", "rfl"], "tactic_count": 2}
{"name": "Equiv.swap_eq_update", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Equiv.comp_swap_eq_update", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Equiv.symm_trans_swap_trans", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Equiv.trans_swap_trans_symm", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.swap_apply_self", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Equiv.apply_swap_eq_self", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Equiv.swap_apply_eq_iff", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Equiv.swap_apply_ne_self_iff", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Equiv.swap_injective_of_left", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.swap_injective_of_right", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Equiv.instNontrivialPerm", "kind": "instance", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": true, "tactics": ["classical", "obtain", "exact"], "tactic_count": 3}
{"name": "Equiv.image_swap_of_mem_of_notMem", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.sumCongr_swap_refl", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Equiv.Perm.sumCongr_refl_swap", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Equiv.setValue", "kind": "definition", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.setValue_eq", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Function.Involutive.toPerm", "kind": "definition", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Involutive.coe_toPerm", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Involutive.toPerm_symm", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Involutive.toPerm_involutive", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Involutive.symm_eq_self_of_involutive", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PLift.eq_up_iff_down_eq", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.map_swap", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Equiv.piCongrLeft'", "kind": "definition", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.piCongrLeft'_symm", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Equiv.piCongrLeft'_symm_apply_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Equiv.piCongrLeft'_refl", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.piCongrLeft", "kind": "definition", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.piCongrLeft_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.piCongrLeft_symm_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.piCongrLeft_refl", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.piCongrLeft_apply_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.piCongrLeft_apply_eq_cast", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.piCongrLeft_sumInl", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Equiv.piCongrLeft_sumInr", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Equiv.piCongr", "kind": "definition", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.coe_piCongr_symm", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.piCongr_symm_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.piCongr_apply_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Equiv.piCongr'", "kind": "definition", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.coe_piCongr'", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.piCongr'_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.piCongr'_symm_apply_symm_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Equiv.piCongrSigmaFiber", "kind": "definition", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.piCongrSigmaFiber_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.piCongrSigmaFiber_symm_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.piCongrFiberwise", "kind": "definition", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.piCongrFiberwise_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.piCongrFiberwise_symm_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.piCongrSet", "kind": "definition", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.eq_conj", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Equiv.semiconj_conj", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.semiconj₂_conj", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.instAssociativeCoeForallForallArrowCongr", "kind": "instance", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.instIdempotentOpCoeForallForallArrowCongr", "kind": "instance", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.ulift_symm_down", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.swap_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.swap_comp", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "equivOfSubsingletonOfSubsingleton", "kind": "definition", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.punitOfNonemptyOfSubsingleton", "kind": "definition", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniqueUniqueEquiv", "kind": "definition", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniqueEquivEquivUnique", "kind": "definition", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.update_comp_equiv", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Function.update_apply_equiv_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.piCongrLeft'_update", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": true, "tactics": ["ext", "rcases"], "tactic_count": 2}
{"name": "Function.piCongrLeft'_symm_update", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Equiv.boolNot", "kind": "definition", "module": "Mathlib.Logic.Equiv.Bool", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bool.not_bijective", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Bool", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bool.not_injective", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Bool", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bool.not_surjective", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Bool", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bool.not_leftInverse", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Bool", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bool.not_rightInverse", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Bool", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bool.not_hasLeftInverse", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Bool", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bool.not_hasRightInverse", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Bool", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "term_≃_", "kind": "definition", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Logic_Equiv_Defs___macroRules_term_≃__1", "kind": "definition", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Logic_Equiv_Defs___unexpand_Equiv_1", "kind": "definition", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EquivLike.toEquiv", "kind": "definition", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCoeTCEquivOfEquivLike", "kind": "instance", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm", "kind": "abbrev", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.instEquivLike", "kind": "instance", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EquivLike.coe_coe", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.coe_fn_mk", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.coe_fn_injective", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.coe_inj", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.ext", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.congr_arg", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.congr_fun", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.ext", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.congr_arg", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.congr_fun", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.refl", "kind": "definition", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.inhabited'", "kind": "instance", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.symm", "kind": "definition", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Simps.symm_apply", "kind": "definition", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.left_inv'", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.right_inv'", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.trans", "kind": "definition", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.instTrans", "kind": "instance", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.symmEquiv", "kind": "definition", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.toFun_as_coe", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.invFun_as_coe", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.injective", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.surjective", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.bijective", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.subsingleton", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.subsingleton.symm", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.subsingleton_congr", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.equiv_subsingleton_cod", "kind": "instance", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.equiv_subsingleton_dom", "kind": "instance", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.permUnique", "kind": "instance", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.subsingleton_eq_refl", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.nontrivial", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.nontrivial_congr", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.decidableEq", "kind": "abbrev", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.nonempty_congr", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.nonempty", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.inhabited", "kind": "abbrev", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.unique", "kind": "abbrev", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.cast", "kind": "definition", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.coe_fn_symm_mk", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.coe_refl", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.coe_subsingleton", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Equiv.refl_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.coe_trans", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.trans_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.apply_symm_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.symm_apply_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.symm_comp_self", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.self_comp_symm", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EquivLike.apply_coe_symm_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EquivLike.coe_symm_apply_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EquivLike.coe_symm_comp_self", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EquivLike.self_comp_coe_symm", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.symm_trans_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.symm_symm_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.apply_eq_iff_eq", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.apply_eq_iff_eq_symm_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Equiv.cast_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.cast_symm", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.cast_trans", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.cast_eq_iff_heq", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "Equiv.symm_apply_eq", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Equiv.eq_symm_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Equiv.symm_symm", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.symm_bijective", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.trans_refl", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Equiv.refl_symm", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.refl_trans", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Equiv.symm_trans_self", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Equiv.self_trans_symm", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Equiv.trans_assoc", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Equiv.trans_cancel_left", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Equiv.trans_cancel_right", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Equiv.leftInverse_symm", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.rightInverse_symm", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.injective_comp", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.comp_injective", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.surjective_comp", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.comp_surjective", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.bijective_comp", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.comp_bijective", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.extend_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Equiv.equivCongr", "kind": "definition", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.equivCongr_apply_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.equivCongr_symm", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Equiv.equivCongr_refl", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Equiv.equivCongr_trans", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Equiv.equivCongr_refl_left", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.equivCongr_refl_right", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.permCongr", "kind": "definition", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.permCongr_def", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.permCongr_refl", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Equiv.permCongr_symm", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.permCongr_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.permCongr_symm_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.permCongr_trans", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Equiv.equivOfIsEmpty", "kind": "definition", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.equivEmpty", "kind": "definition", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.equivPEmpty", "kind": "definition", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.equivEmptyEquiv", "kind": "definition", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.propEquivPEmpty", "kind": "definition", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.ofUnique", "kind": "definition", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.equivPUnit", "kind": "definition", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.propEquivPUnit", "kind": "definition", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.ulift", "kind": "definition", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.plift", "kind": "definition", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.ofIff", "kind": "definition", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.arrowCongr", "kind": "definition", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.arrowCongr_comp", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Equiv.arrowCongr_refl", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.arrowCongr_trans", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.arrowCongr_symm", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.arrowCongr'", "kind": "definition", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.arrowCongr'_refl", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.arrowCongr'_trans", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.arrowCongr'_symm", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.conj", "kind": "definition", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.conj_refl", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.conj_symm", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.conj_trans", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.conj_comp", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "Equiv.eq_comp_symm", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.comp_symm_eq", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.eq_symm_comp", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.symm_comp_eq", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.trans_eq_refl_iff_eq_symm", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Equiv.trans_eq_refl_iff_symm_eq", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Equiv.eq_symm_iff_trans_eq_refl", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.symm_eq_iff_trans_eq_refl", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.punitEquivPUnit", "kind": "definition", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.propEquivBool", "kind": "definition", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.arrowPUnitEquivPUnit", "kind": "definition", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.piUnique", "kind": "definition", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.funUnique", "kind": "definition", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.punitArrowEquiv", "kind": "definition", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.trueArrowEquiv", "kind": "definition", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.arrowPUnitOfIsEmpty", "kind": "definition", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.emptyArrowEquivPUnit", "kind": "definition", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.pemptyArrowEquivPUnit", "kind": "definition", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.falseArrowEquivPUnit", "kind": "definition", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.psigmaEquivSigma", "kind": "definition", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.psigmaEquivSigmaPLift", "kind": "definition", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.psigmaCongrRight", "kind": "definition", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.psigmaCongrRight_trans", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.psigmaCongrRight_symm", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.psigmaCongrRight_refl", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.sigmaCongrRight", "kind": "definition", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.sigmaCongrRight_trans", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.sigmaCongrRight_symm", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.sigmaCongrRight_refl", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.psigmaEquivSubtype", "kind": "definition", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.sigmaPLiftEquivSubtype", "kind": "definition", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.sigmaULiftPLiftEquivSubtype", "kind": "definition", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.sigmaCongrRight", "kind": "abbrev", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.sigmaCongrRight_trans", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.sigmaCongrRight_symm", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.sigmaCongrRight_refl", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.functionSwap", "kind": "definition", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.swap_bijective", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.sigmaCongrLeft", "kind": "definition", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.sigmaCongrLeft'", "kind": "definition", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.sigmaCongr", "kind": "definition", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.sigmaEquivProd", "kind": "definition", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.sigmaEquivProdOfEquiv", "kind": "definition", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.sigmaAssoc", "kind": "definition", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.pSigmaAssoc", "kind": "definition", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.forall_congr_right", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.forall_congr_left", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.forall_congr", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.forall_congr'", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.exists_congr_right", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.exists_congr_left", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.exists_congr", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.exists_congr'", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.exists_subtype_congr", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Equiv.existsUnique_congr_right", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.existsUnique_congr_left", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.existsUnique_congr", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.existsUnique_congr'", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.existsUnique_subtype_congr", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Equiv.forall₂_congr", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.forall₂_congr'", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.forall₃_congr", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.forall₃_congr'", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.ofBijective", "kind": "definition", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.ofBijective_apply_symm_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.ofBijective_symm_apply_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quot.congr", "kind": "definition", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quot.congr_mk", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quot.congrRight", "kind": "definition", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quot.congrLeft", "kind": "definition", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quotient.congr", "kind": "definition", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quotient.congr_mk", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quotient.congrRight", "kind": "definition", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finZeroEquiv", "kind": "definition", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finZeroEquiv'", "kind": "definition", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finOneEquiv", "kind": "definition", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finTwoEquiv", "kind": "definition", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.sumIsLeft", "kind": "definition", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.sumIsRight", "kind": "definition", "module": "Mathlib.Logic.Equiv.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.sumEmbeddingEquivProdEmbeddingDisjoint", "kind": "definition", "module": "Mathlib.Logic.Equiv.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.codRestrict", "kind": "definition", "module": "Mathlib.Logic.Equiv.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.prodEmbeddingDisjointEquivSigmaEmbeddingRestricted", "kind": "definition", "module": "Mathlib.Logic.Equiv.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.sumEmbeddingEquivSigmaEmbeddingRestricted", "kind": "definition", "module": "Mathlib.Logic.Equiv.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.uniqueEmbeddingEquivResult", "kind": "definition", "module": "Mathlib.Logic.Equiv.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.preimage_apply_01_prod", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fin.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Fin.preimage_apply_01_prod'", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "prodEquivPiFinTwo", "kind": "definition", "module": "Mathlib.Logic.Equiv.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finTwoArrowEquiv", "kind": "definition", "module": "Mathlib.Logic.Equiv.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finSuccEquiv'", "kind": "definition", "module": "Mathlib.Logic.Equiv.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finSuccEquiv'_at", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fin.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "finSuccEquiv'_succAbove", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finSuccEquiv'_below", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fin.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "finSuccEquiv'_above", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fin.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "finSuccEquiv'_symm_none", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finSuccEquiv'_symm_some", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finSuccEquiv'_eq_some", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finSuccEquiv'_eq_none", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finSuccEquiv'_symm_some_below", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finSuccEquiv'_symm_some_above", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finSuccEquiv'_symm_coe_below", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finSuccEquiv'_symm_coe_above", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finSuccEquiv", "kind": "definition", "module": "Mathlib.Logic.Equiv.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finSuccEquiv_zero", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finSuccEquiv_succ", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finSuccEquiv_symm_none", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finSuccEquiv_symm_some", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "finSuccEquiv'_zero", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finSuccEquiv'_last_apply_castSucc", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fin.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "finSuccEquiv'_last_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fin.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "finSuccEquiv'_ne_last_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fin.Basic", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "simp"], "tactic_count": 3}
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{"name": "finSuccAboveEquiv_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "finSuccAboveEquiv_symm_apply_ne_last", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fin.Basic", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "finSuccEquivLast", "kind": "definition", "module": "Mathlib.Logic.Equiv.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finSuccEquivLast_castSucc", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "finSuccEquivLast_symm_some", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Equiv.embeddingFinSucc", "kind": "definition", "module": "Mathlib.Logic.Equiv.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.embeddingFinSucc_fst", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.embeddingFinSucc_snd", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.coe_embeddingFinSucc_symm", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fin.Basic", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "finSumFinEquiv", "kind": "definition", "module": "Mathlib.Logic.Equiv.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finSumFinEquiv_apply_left", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finSumFinEquiv_apply_right", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finSumFinEquiv_symm_apply_castAdd", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finSumFinEquiv_symm_apply_castSucc", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finSumFinEquiv_symm_apply_natAdd", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finSumFinEquiv_symm_last", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finSumNatEquiv", "kind": "definition", "module": "Mathlib.Logic.Equiv.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finSumNatEquiv_apply_left", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finSumNatEquiv_apply_right", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finSumNatEquiv_symm_apply_of_lt", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finSumNatEquiv_symm_apply_of_ge", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finSumNatEquiv_symm_apply_fin", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fin.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "finSumNatEquiv_symm_apply_add_left", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fin.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "finSumNatEquiv_symm_apply_add_right", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fin.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "isLeft_finSumNatEquiv_symm_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fin.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simp_rw", "simp_rw"], "tactic_count": 3}
{"name": "isRight_finSumNatEquiv_symm_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fin.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "cases"], "tactic_count": 2}
{"name": "finAddFlip", "kind": "definition", "module": "Mathlib.Logic.Equiv.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finAddFlip_apply_castAdd", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fin.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "finAddFlip_apply_natAdd", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fin.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "finAddFlip_apply_mk_right", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fin.Basic", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "finProdFinEquiv", "kind": "definition", "module": "Mathlib.Logic.Equiv.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.divModEquiv", "kind": "definition", "module": "Mathlib.Logic.Equiv.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.divModEquiv", "kind": "definition", "module": "Mathlib.Logic.Equiv.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.castLEquiv", "kind": "definition", "module": "Mathlib.Logic.Equiv.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.appendEquiv", "kind": "definition", "module": "Mathlib.Logic.Equiv.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.succFunEquiv", "kind": "definition", "module": "Mathlib.Logic.Equiv.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finRotate", "kind": "definition", "module": "Mathlib.Logic.Equiv.Fin.Rotate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finRotate_zero", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fin.Rotate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finRotate_succ", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fin.Rotate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finRotate_of_lt", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fin.Rotate", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "simp"], "tactic_count": 3}
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{"name": "finRotate_last", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fin.Rotate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.snoc_eq_cons_rotate", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fin.Rotate", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "rw", "rfl", "have", "simp", "exact", "subst", "rw", "rfl"], "tactic_count": 10}
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{"name": "finRotate_succ_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fin.Rotate", "is_tactic_proof": true, "tactics": ["cases", "exact", "obtain", "simp", "cases", "simp", "simp"], "tactic_count": 7}
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{"name": "coe_finRotate_of_ne_last", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fin.Rotate", "is_tactic_proof": true, "tactics": ["rw", "have", "exact"], "tactic_count": 3}
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{"name": "lt_finRotate_iff_ne_last", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fin.Rotate", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "lt_finRotate_iff_ne_neg_one", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fin.Rotate", "is_tactic_proof": true, "tactics": ["obtain", "rw"], "tactic_count": 2}
{"name": "finRotate_succ_symm_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fin.Rotate", "is_tactic_proof": true, "tactics": ["obtain", "apply", "rw"], "tactic_count": 3}
{"name": "coe_finRotate_symm_of_ne_zero", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fin.Rotate", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "finRotate_symm_lt_iff_ne_zero", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fin.Rotate", "is_tactic_proof": true, "tactics": ["obtain", "refine", "simp", "rw", "apply"], "tactic_count": 5}
{"name": "finCycle", "kind": "definition", "module": "Mathlib.Logic.Equiv.Fin.Rotate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finCycle_eq_finRotate_iterate", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fin.Rotate", "is_tactic_proof": true, "tactics": ["n", "induction", "zero", "succ", "rw", "rw", "finCycle_apply,"], "tactic_count": 7}
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{"name": "Encodable.sortedUniv", "kind": "definition", "module": "Mathlib.Logic.Equiv.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.mem_sortedUniv", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.length_sortedUniv", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.sortedUniv_nodup", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.sortedUniv_toFinset", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.fintypeEquivFin", "kind": "definition", "module": "Mathlib.Logic.Equiv.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Denumerable.lower'", "kind": "definition", "module": "Mathlib.Logic.Equiv.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Denumerable.raise'", "kind": "definition", "module": "Mathlib.Logic.Equiv.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Denumerable.lower_raise'", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Denumerable.raise_lower'", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Denumerable.isChain_raise'", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Denumerable.isChain_cons_raise'", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Denumerable.isChain_cons_raise'_of_lt", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Finset", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "Denumerable.raise'_sorted", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Denumerable.raise'Finset", "kind": "definition", "module": "Mathlib.Logic.Equiv.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Function.Embedding.toEquivRange", "kind": "definition", "module": "Mathlib.Logic.Equiv.Fintype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.toEquivRange_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fintype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.toEquivRange_symm_apply_self", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fintype", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Function.Embedding.toEquivRange_eq_ofInjective", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fintype", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Equiv.Perm.viaFintypeEmbedding", "kind": "definition", "module": "Mathlib.Logic.Equiv.Fintype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.viaFintypeEmbedding_apply_image", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fintype", "is_tactic_proof": true, "tactics": ["rw", "convert"], "tactic_count": 2}
{"name": "Equiv.Perm.viaFintypeEmbedding_apply_mem_range", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fintype", "is_tactic_proof": true, "tactics": ["simp", "rw", "congr"], "tactic_count": 3}
{"name": "Equiv.Perm.viaFintypeEmbedding_apply_notMem_range", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fintype", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
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{"name": "Equiv.extendSubtype", "kind": "abbrev", "module": "Mathlib.Logic.Equiv.Fintype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.extendSubtype_apply_of_mem", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fintype", "is_tactic_proof": true, "tactics": ["dsimp", "simp", "rw"], "tactic_count": 3}
{"name": "Equiv.extendSubtype_mem", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fintype", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "Equiv.extendSubtype_apply_of_not_mem", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fintype", "is_tactic_proof": true, "tactics": ["dsimp", "simp", "rw"], "tactic_count": 3}
{"name": "Equiv.extendSubtype_not_mem", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Fintype", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
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{"name": "Functor.mapEquiv_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Functor.mapEquiv_symm_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Functor.mapEquiv_refl", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Functor", "is_tactic_proof": true, "tactics": ["ext", "simp", "exact"], "tactic_count": 3}
{"name": "Bifunctor.mapEquiv", "kind": "definition", "module": "Mathlib.Logic.Equiv.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bifunctor.mapEquiv_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bifunctor.mapEquiv_symm_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Functor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bifunctor.mapEquiv_refl_refl", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Functor", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Equiv.listEquivOfEquiv", "kind": "definition", "module": "Mathlib.Logic.Equiv.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.encodeList", "kind": "definition", "module": "Mathlib.Logic.Equiv.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.decodeList", "kind": "definition", "module": "Mathlib.Logic.Equiv.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Encodable.decodeList_encodeList_eq_self", "kind": "theorem", "module": "Mathlib.Logic.Equiv.List", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
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{"name": "Encodable.encode_list_nil", "kind": "theorem", "module": "Mathlib.Logic.Equiv.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Encodable.decode_list_zero", "kind": "theorem", "module": "Mathlib.Logic.Equiv.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Encodable.length_le_encode", "kind": "theorem", "module": "Mathlib.Logic.Equiv.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Encodable.encodableOfList", "kind": "definition", "module": "Mathlib.Logic.Equiv.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.truncEncodable", "kind": "definition", "module": "Mathlib.Logic.Equiv.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Denumerable.denumerable_list_aux", "kind": "theorem", "module": "Mathlib.Logic.Equiv.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Denumerable.denumerableList", "kind": "instance", "module": "Mathlib.Logic.Equiv.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Denumerable.list_ofNat_zero", "kind": "theorem", "module": "Mathlib.Logic.Equiv.List", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Denumerable.list_ofNat_succ", "kind": "theorem", "module": "Mathlib.Logic.Equiv.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.listUniqueEquiv", "kind": "definition", "module": "Mathlib.Logic.Equiv.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.listNatEquivNat", "kind": "definition", "module": "Mathlib.Logic.Equiv.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.listEquivSelfOfEquivNat", "kind": "definition", "module": "Mathlib.Logic.Equiv.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Logic.Equiv.Multiset.0.enle", "kind": "definition", "module": "Mathlib.Logic.Equiv.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Logic.Equiv.Multiset.0.enle.isLinearOrder", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Logic.Equiv.Multiset.0.decidable_enle", "kind": "definition", "module": "Mathlib.Logic.Equiv.Multiset", "is_tactic_proof": true, "tactics": ["unfold", "infer_instance"], "tactic_count": 2}
{"name": "encodeMultiset", "kind": "definition", "module": "Mathlib.Logic.Equiv.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "decodeMultiset", "kind": "definition", "module": "Mathlib.Logic.Equiv.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.encodable", "kind": "instance", "module": "Mathlib.Logic.Equiv.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Denumerable.lower", "kind": "definition", "module": "Mathlib.Logic.Equiv.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Denumerable.raise", "kind": "definition", "module": "Mathlib.Logic.Equiv.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Denumerable.lower_raise", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Denumerable.raise_lower", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Denumerable.isChain_raise", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Denumerable.isChain_cons_raise", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Denumerable.raise_sorted", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Denumerable.multiset", "kind": "instance", "module": "Mathlib.Logic.Equiv.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.boolProdNatEquivNat", "kind": "definition", "module": "Mathlib.Logic.Equiv.Nat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.natSumNatEquivNat", "kind": "definition", "module": "Mathlib.Logic.Equiv.Nat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.natSumNatEquivNat_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Nat", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Equiv.intEquivNat", "kind": "definition", "module": "Mathlib.Logic.Equiv.Nat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.prodEquivOfEquivNat", "kind": "definition", "module": "Mathlib.Logic.Equiv.Nat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.optionCongr", "kind": "definition", "module": "Mathlib.Logic.Equiv.Option", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.optionCongr_refl", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Option", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.optionCongr_symm", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Option", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.optionCongr_trans", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Option", "is_tactic_proof": true, "tactics": ["ext", "symm", "apply"], "tactic_count": 3}
{"name": "Equiv.optionCongr_eq_equivFunctor_mapEquiv", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Option", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.removeNone_aux", "kind": "definition", "module": "Mathlib.Logic.Equiv.Option", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.removeNone_aux_some", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Option", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Equiv.removeNone_aux_none", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Option", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Equiv.removeNone_aux_inv", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Option", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.removeNone", "kind": "definition", "module": "Mathlib.Logic.Equiv.Option", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.removeNone_symm", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Option", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.removeNone_some", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Option", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.removeNone_none", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Option", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.option_symm_apply_none_iff", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Option", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.some_removeNone_iff", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Option", "is_tactic_proof": true, "tactics": ["rcases", "rw", "simpa", "rw", "have", "rw", "simp", "simp"], "tactic_count": 8}
{"name": "Equiv.removeNone_optionCongr", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Option", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.optionCongr_injective", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Option", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.optionSubtype", "kind": "definition", "module": "Mathlib.Logic.Equiv.Option", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.optionSubtype_apply_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Option", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.coe_optionSubtype_apply_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Option", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.optionSubtype_apply_symm_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Option", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "Equiv.optionSubtype_symm_apply_apply_coe", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Option", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.optionSubtype_symm_apply_apply_some", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Option", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.optionSubtype_symm_apply_apply_none", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Option", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.optionSubtype_symm_apply_symm_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Option", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Equiv.optionSubtypeNe", "kind": "definition", "module": "Mathlib.Logic.Equiv.Option", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.optionSubtypeNe_symm_self", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Option", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Equiv.optionSubtypeNe_symm_of_ne", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Option", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Equiv.optionSubtypeNe_none", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Option", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.optionSubtypeNe_some", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Option", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.optionEquivSumPUnit", "kind": "definition", "module": "Mathlib.Logic.Equiv.Option", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.optionEquivSumPUnit_none", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Option", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.optionEquivSumPUnit_some", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Option", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.optionEquivSumPUnit_coe", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Option", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.optionEquivSumPUnit_symm_inl", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Option", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.optionEquivSumPUnit_symm_inr", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Option", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.optionIsSomeEquiv", "kind": "definition", "module": "Mathlib.Logic.Equiv.Option", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EmbeddingLike.pairwise_comp", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Pairwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EquivLike.pairwise_comp_iff", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Pairwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mfld_cfg", "kind": "definition", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.MfldSetTac.mfldSetTac", "kind": "definition", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.MfldSetTac._aux_Mathlib_Logic_Equiv_PartialEquiv___elabRules_Tactic_MfldSetTac_mfldSetTac_1", "kind": "definition", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.instInhabited", "kind": "instance", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.symm", "kind": "definition", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.instCoeFunForall", "kind": "instance", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.Simps.symm_apply", "kind": "definition", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.coe_mk", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.coe_symm_mk", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.invFun_as_coe", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.map_source", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.map_source''", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.map_target", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.left_inv", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.right_inv", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.target_subset_range", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.eq_symm_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.mapsTo", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.symm_mapsTo", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.leftInvOn", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.rightInvOn", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.invOn", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.injOn", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.bijOn", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.surjOn", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.toPartialEquivOfImageEq", "kind": "definition", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.toPartialEquiv", "kind": "definition", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.inhabitedOfEmpty", "kind": "instance", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.copy", "kind": "definition", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.copy_eq", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": true, "tactics": ["substs", "cases", "rfl"], "tactic_count": 3}
{"name": "PartialEquiv.toEquiv", "kind": "definition", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.symm_source", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.symm_target", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.symm_symm", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.symm_bijective", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.image_source_eq_target", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.forall_mem_target", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PartialEquiv.exists_mem_target", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PartialEquiv.IsImage", "kind": "definition", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.IsImage.apply_mem_iff", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.IsImage.symm_apply_mem_iff", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.IsImage.symm", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.IsImage.symm_iff", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.IsImage.mapsTo", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.IsImage.symm_mapsTo", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.IsImage.restr", "kind": "definition", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.IsImage.image_eq", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.IsImage.symm_image_eq", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.IsImage.iff_preimage_eq", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PartialEquiv.IsImage.iff_symm_preimage_eq", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.IsImage.of_image_eq", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.IsImage.of_symm_image_eq", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.IsImage.compl", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.IsImage.inter", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.IsImage.union", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.IsImage.diff", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.IsImage.leftInvOn_piecewise", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": true, "tactics": ["rintro", "rw", "rw"], "tactic_count": 3}
{"name": "PartialEquiv.IsImage.inter_eq_of_inter_eq_of_eqOn", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PartialEquiv.IsImage.symm_eq_on_of_inter_eq_of_eqOn", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": true, "tactics": ["rw", "rintro", "have", "rw"], "tactic_count": 4}
{"name": "PartialEquiv.isImage_source_target", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.isImage_source_target_of_disjoint", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.image_source_inter_eq'", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PartialEquiv.image_source_inter_eq", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PartialEquiv.image_eq_target_inter_inv_preimage", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PartialEquiv.symm_image_eq_source_inter_preimage", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.symm_image_target_inter_eq", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.symm_image_target_inter_eq'", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.source_inter_preimage_inv_preimage", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.source_inter_preimage_target_inter", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.target_inter_inv_preimage_preimage", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.symm_image_image_of_subset_source", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.image_symm_image_of_subset_target", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.source_subset_preimage_target", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.symm_image_target_eq_source", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.target_subset_preimage_source", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.ext", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": ["have", "ext", "exact", "have", "ext", "exact", "have", "have", "rw", "cases", "simp_all"], "tactic_count": 11}
{"name": "PartialEquiv.restr", "kind": "definition", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.restr_coe", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.restr_coe_symm", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.restr_source", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.source_restr_subset_source", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.restr_target", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.restr_eq_of_source_subset", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.restr_univ", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.refl", "kind": "definition", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.refl_source", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.refl_target", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.refl_coe", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.refl_symm", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.refl_restr_source", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PartialEquiv.refl_restr_target", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PartialEquiv.ofSet", "kind": "definition", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.ofSet_source", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.ofSet_target", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.ofSet_coe", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.ofSet_symm", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.single", "kind": "definition", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.trans'", "kind": "definition", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.trans", "kind": "definition", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.coe_trans", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.coe_trans_symm", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.trans_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.trans_symm_eq_symm_trans_symm", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.trans_source", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.trans_source'", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": true, "tactics": ["mfld_set_tac"], "tactic_count": 1}
{"name": "PartialEquiv.trans_source''", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PartialEquiv.image_trans_source", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.trans_target", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.trans_target'", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.trans_target''", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.inv_image_trans_target", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.trans_assoc", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.trans_refl", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.refl_trans", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.trans_ofSet", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.trans_refl_restr", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.trans_refl_restr'", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.restr_trans", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.mem_symm_trans_source", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.EqOnSource", "kind": "definition", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.eqOnSourceSetoid", "kind": "instance", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.eqOnSource_refl", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.EqOnSource.source_eq", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.EqOnSource.eqOn", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.EqOnSource.target_eq", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PartialEquiv.EqOnSource.symm'", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": ["refine", "simp", "exact"], "tactic_count": 3}
{"name": "PartialEquiv.EqOnSource.symm_eqOn", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.EqOnSource.trans'", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": true, "tactics": ["constructor", "rw", "exact", "intro", "rw", "simp"], "tactic_count": 6}
{"name": "PartialEquiv.EqOnSource.restr", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": true, "tactics": ["constructor", "simp", "intro", "simp", "exact"], "tactic_count": 5}
{"name": "PartialEquiv.EqOnSource.source_inter_preimage_eq", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PartialEquiv.self_trans_symm", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": true, "tactics": ["have", "refine", "rw", "simp"], "tactic_count": 4}
{"name": "PartialEquiv.symm_trans_self", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.eq_of_eqOnSource_univ", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": true, "tactics": ["refine", "apply", "rw", "exact", "apply", "rw", "exact"], "tactic_count": 7}
{"name": "PartialEquiv.prod", "kind": "definition", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.prod_source", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.prod_target", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.prod_coe", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.prod_coe_symm", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.prod_symm", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "PartialEquiv.refl_prod_refl", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "PartialEquiv.prod_trans", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "PartialEquiv.piecewise", "kind": "definition", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.symm_piecewise", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.disjointUnion", "kind": "definition", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.disjointUnion_eq_piecewise", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.pi", "kind": "definition", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.pi_symm", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.pi_symm_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.pi_refl", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "PartialEquiv.pi_trans", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "PartialEquiv.surjective_of_target_eq_univ", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.injective_of_source_eq_univ", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "PartialEquiv.injective_symm_of_target_eq_univ", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.surjective_symm_of_source_eq_univ", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.BijOn.toPartialEquiv", "kind": "definition", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.InjOn.toPartialEquiv", "kind": "definition", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.refl_toPartialEquiv", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.symm_toPartialEquiv", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.trans_toPartialEquiv", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.transPartialEquiv", "kind": "definition", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.transPartialEquiv_eq_trans", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.transPartialEquiv_trans", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Equiv.trans_transPartialEquiv", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PartialEquiv.transEquiv", "kind": "definition", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.transEquiv_eq_trans", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialEquiv.transEquiv_transEquiv", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PartialEquiv.trans_transEquiv", "kind": "theorem", "module": "Mathlib.Logic.Equiv.PartialEquiv", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Equiv.pprodEquivProd", "kind": "definition", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.pprodCongr", "kind": "definition", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.pprodProd", "kind": "definition", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.prodPProd", "kind": "definition", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.pprodEquivProdPLift", "kind": "definition", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.prodCongr", "kind": "definition", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.prodCongr_symm", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.prodComm", "kind": "definition", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.coe_prodComm", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.prodComm_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.prodComm_symm", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.prodAssoc", "kind": "definition", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.prodProdProdComm", "kind": "definition", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.prodProdProdComm_symm", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.curry", "kind": "definition", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.prodPUnit", "kind": "definition", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.punitProd", "kind": "definition", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.sigmaPUnit", "kind": "definition", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.prodUnique", "kind": "definition", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.coe_prodUnique", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.prodUnique_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.prodUnique_symm_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.uniqueProd", "kind": "definition", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.coe_uniqueProd", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.uniqueProd_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.uniqueProd_symm_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.sigmaUnique", "kind": "definition", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.coe_sigmaUnique", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.sigmaUnique_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.sigmaUnique_symm_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.uniqueSigma", "kind": "definition", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.uniqueSigma_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.uniqueSigma_symm_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.prodEmpty", "kind": "definition", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.emptyProd", "kind": "definition", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.prodPEmpty", "kind": "definition", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.pemptyProd", "kind": "definition", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.prodCongrLeft", "kind": "definition", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.prodCongrLeft_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.prodCongr_refl_right", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.prodCongrLeft_symm", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.prodCongrRight", "kind": "definition", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.prodCongrRight_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.prodCongr_refl_left", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.prodCongrRight_symm", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.prodCongrLeft_trans_prodComm", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Equiv.prodCongrRight_trans_prodComm", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Equiv.sigmaCongrRight_sigmaEquivProd", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Equiv.sigmaEquivProd_sigmaCongrRight", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": true, "tactics": ["ext", "simp", "rfl"], "tactic_count": 3}
{"name": "Equiv.prodShear", "kind": "definition", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.prodExtendRight", "kind": "definition", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.prodExtendRight_apply_eq", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.prodExtendRight_apply_ne", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Perm.eq_of_prodExtendRight_ne", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": true, "tactics": ["contrapose", "exact"], "tactic_count": 2}
{"name": "Equiv.Perm.fst_prodExtendRight", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Equiv.arrowProdEquivProdArrow", "kind": "definition", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.sumPiEquivProdPi", "kind": "definition", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.prodPiEquivSumPi", "kind": "definition", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.sumArrowEquivProdArrow", "kind": "definition", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.sumArrowEquivProdArrow_apply_fst", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.sumArrowEquivProdArrow_apply_snd", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.sumArrowEquivProdArrow_symm_apply_inl", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.sumArrowEquivProdArrow_symm_apply_inr", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.sumProdDistrib", "kind": "definition", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.sumProdDistrib_apply_left", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.sumProdDistrib_apply_right", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.sumProdDistrib_symm_apply_left", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.sumProdDistrib_symm_apply_right", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.sigmaProdDistrib", "kind": "definition", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.boolProdEquivSum", "kind": "definition", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.boolArrowEquivProd", "kind": "definition", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.subtypeProdEquivProd", "kind": "definition", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.prodSubtypeFstEquivSubtypeProd", "kind": "definition", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.subtypeProdEquivSigmaSubtype", "kind": "definition", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.piEquivPiSubtypeProd", "kind": "definition", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.piSplitAt", "kind": "definition", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.funSplitAt", "kind": "definition", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "subsingletonProdSelfEquiv", "kind": "definition", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "optionProdEquiv", "kind": "definition", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "optionProdEquiv_mk_none", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "optionProdEquiv_mk_some", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "optionProdEquiv_symm_inl", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "optionProdEquiv_symm_inr", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EquivLike.range_eq_univ", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.range_eq_univ", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.image_symm_eq_preimage", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Equiv.image_eq_preimage_symm", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_image_equiv", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_equiv_eq_preimage_symm", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.preimage_equiv_eq_image_symm", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.symm_image_subset", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Equiv.subset_symm_image", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.symm_image_image", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.eq_image_iff_symm_image_eq", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.image_symm_image", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.image_preimage", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.preimage_image", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.image_compl", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.symm_preimage_preimage", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.preimage_symm_preimage", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.preimage_subset", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.image_subset", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.image_eq_iff_eq", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.preimage_eq_iff_eq_image", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.eq_preimage_iff_image_eq", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.setOf_apply_symm_eq_image_setOf", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Equiv.prod_assoc_preimage", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Equiv.prod_assoc_symm_preimage", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Equiv.prod_assoc_image", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Equiv.prod_assoc_symm_image", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Equiv.setProdEquivSigma", "kind": "definition", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.setCongr", "kind": "definition", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.image", "kind": "definition", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.image_monotone", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.image_antitone", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.image_strictMono", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.image_strictAnti", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Set.univ", "kind": "definition", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Set.empty", "kind": "definition", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Set.pempty", "kind": "definition", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Set.union'", "kind": "definition", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Set.union", "kind": "definition", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Set.union_apply_left", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Set.union_apply_right", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Set.union_symm_apply_left", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Set.union_symm_apply_right", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Set.singleton", "kind": "definition", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Set.Equiv.strictMono_setCongr", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Set.insert", "kind": "definition", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Set.insert_symm_apply_inl", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Set.insert_symm_apply_inr", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Set.insert_apply_left", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Set.insert_apply_right", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Set.sumCompl", "kind": "definition", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Set.sumCompl_apply_inl", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Set.sumCompl_apply_inr", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Set.sumCompl_symm_apply_of_mem", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Set.sumCompl_symm_apply_of_notMem", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Set.sumCompl_symm_apply", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Set.sumCompl_symm_apply_compl", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Set.sumDiffSubset", "kind": "definition", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Set.sumDiffSubset_apply_inl", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Set.sumDiffSubset_apply_inr", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Set.sumDiffSubset_symm_apply_of_mem", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "Equiv.Set.sumDiffSubset_symm_apply_of_notMem", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "Equiv.Set.unionSumInter", "kind": "definition", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Equiv.Set.univPi", "kind": "definition", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Set.imageOfInjOn", "kind": "definition", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Equiv.Set.sep", "kind": "definition", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Set.powerset", "kind": "definition", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Set.rangeSplittingImageEquiv", "kind": "definition", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.Set.rangeInl", "kind": "definition", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Equiv.sigmaPreimageEquiv", "kind": "definition", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Equiv.ofPreimageEquiv_map", "kind": "theorem", "module": "Mathlib.Logic.Equiv.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Function.Injective.piMap", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.comp_left", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.injective_comp_left_iff", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.injective_of_subsingleton", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.bijective_of_subsingleton", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.dite", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.of_comp", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.of_comp_iff", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.of_comp_left", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.bijective₂_of_surjective", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.of_comp_iff'", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.decidableEqPFun", "kind": "instance", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.forall", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.forall₂", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.forall₃", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.exists", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.exists₂", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.exists₃", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.injective_comp_right", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.injective_comp_right_iff_surjective", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": true, "tactics": ["refine", "have", "classical", "simpa", "ext"], "tactic_count": 5}
{"name": "Function.Surjective.right_cancellable", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.surjective_of_right_cancellable_Prop", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.bijective_iff_existsUnique", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Bijective.existsUnique", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Bijective.existsUnique_iff", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Bijective.of_comp_iff", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Bijective.of_comp_iff'", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.cantor_surjective", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.cantor_injective", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.not_surjective_Type", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": true, "tactics": ["intro", "let", "cases", "intro", "let", "have", "intro", "suffices", "simp", "assumption", "congr", "exact"], "tactic_count": 12}
{"name": "Function.IsPartialInv", "kind": "definition", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.isPartialInv_left", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.injective_of_isPartialInv", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.injective_of_isPartialInv_right", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.LeftInverse.eq", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.RightInverse.eq", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.LeftInverse.comp_eq_id", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.leftInverse_iff_comp", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.RightInverse.comp_eq_id", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.rightInverse_iff_comp", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.LeftInverse.comp", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.RightInverse.comp", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.LeftInverse.rightInverse", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.RightInverse.leftInverse", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.LeftInverse.surjective", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.RightInverse.injective", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.LeftInverse.rightInverse_of_injective", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.LeftInverse.rightInverse_of_surjective", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.RightInverse.leftInverse_of_surjective", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.RightInverse.leftInverse_of_injective", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.LeftInverse.eq_rightInverse", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.partialInv", "kind": "definition", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.partialInv_of_injective", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.partialInv_left", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.invFun", "kind": "definition", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.invFun_eq", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Function.apply_invFun_apply", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.invFun_neg", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.invFun_eq_of_injective_of_rightInverse", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.rightInverse_invFun", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.leftInverse_invFun", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.invFun_surjective", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.invFun_comp", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.hasLeftInverse", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.injective_iff_hasLeftInverse", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.surjInv", "kind": "definition", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.surjInv_eq", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.comp_surjInv", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.rightInverse_surjInv", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.leftInverse_surjInv", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.hasRightInverse", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.surjective_iff_hasRightInverse", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.bijective_iff_has_inverse", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.injective_surjInv", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.surjective_to_subsingleton", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.piMap", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.comp_left", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.surjective_comp_left_iff", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": true, "tactics": ["refine", "have", "exact"], "tactic_count": 3}
{"name": "Function.Bijective.piMap", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Bijective.comp_left", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.update", "kind": "definition", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.update_self", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.update_of_ne", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.update_apply", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "Function.update_eq_const_of_subsingleton", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.surjective_eval", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.update_injective", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.forall_update_iff", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Function.exists_update_iff", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Function.update_eq_iff", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.eq_update_iff", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.update_eq_self_iff", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Function.eq_update_self_iff", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Function.ne_update_self_iff", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.update_ne_self_iff", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.update_eq_self", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.update_comp_eq_of_forall_ne'", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.update_comp_eq_of_forall_ne", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.update_comp_eq_of_injective'", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.update_apply_of_injective", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.update_comp_eq_of_injective", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.rec_update", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Option.rec_update", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.apply_update", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Function.apply_update₂", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Function.pred_update", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Function.comp_update", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.update_comm", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Function.update_idem", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Pi.map_update", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": true, "tactics": ["ext", "obtain"], "tactic_count": 2}
{"name": "Pi.map_injective", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.extend", "kind": "definition", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.FactorsThrough", "kind": "definition", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.extend_def", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": true, "tactics": ["unfold", "congr"], "tactic_count": 2}
{"name": "Function.Injective.factorsThrough", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.FactorsThrough.extend_apply", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": true, "tactics": ["classical", "simp", "exact"], "tactic_count": 3}
{"name": "Function.Injective.extend_apply", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.extend_apply'", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Function.extend_id", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.extend_comp", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "obtain", "rw", "by_cases", "obtain", "rw", "exact", "rw", "exact", "rw", "exact"], "tactic_count": 12}
{"name": "Function.factorsThrough_iff", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.apply_extend", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.extend_injective", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": true, "tactics": ["intro", "refine", "have", "simp", "exact"], "tactic_count": 5}
{"name": "Function.FactorsThrough.extend_comp", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.extend_const", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.extend_comp", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.surjective_comp_right'", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.surjective_comp_right", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.surjective_comp_right_iff_injective", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": true, "tactics": ["classical", "refine", "simp", "have", "have", "have", "have", "simp", "rw"], "tactic_count": 9}
{"name": "Function.Bijective.comp_right", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.FactorsThrough.rfl", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.FactorsThrough.comp_left", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.FactorsThrough.comp_right", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.uncurry_def", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.uncurry_injective", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.curry_injective", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.uncurry_flip", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.flip_curry", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.curry_update", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": true, "tactics": ["ext", "let", "obtain"], "tactic_count": 3}
{"name": "Function.uncurry_update_update", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "Function.bicompl", "kind": "definition", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.bicompr", "kind": "definition", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Logic.Function.Basic.0.Function.term_∘₂_", "kind": "definition", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Logic.Function.Basic.0.Function._aux_Mathlib_Logic_Function_Basic___macroRules__private_Mathlib_Logic_Function_Basic_0_Function_term_∘₂__1", "kind": "definition", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Logic.Function.Basic.0.Function._aux_Mathlib_Logic_Function_Basic___unexpand_Function_bicompr_1", "kind": "definition", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.uncurry_bicompr", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.uncurry_bicompl", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.term↿_", "kind": "definition", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function._aux_Mathlib_Logic_Function_Basic___macroRules_Function_term↿__1", "kind": "definition", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function._aux_Mathlib_Logic_Function_Basic___unexpand_Function_HasUncurry_uncurry_1", "kind": "definition", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.hasUncurryBase", "kind": "instance", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.hasUncurryInduction", "kind": "instance", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Involutive", "kind": "definition", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bool.involutive_not", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Involutive.comp_self", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Involutive.leftInverse", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Involutive.leftInverse_iff", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Involutive.rightInverse", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Involutive.injective", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Involutive.surjective", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Involutive.bijective", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Involutive.ite_not", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Function.Involutive.eq_iff", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.not_involutive", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.not_injective", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.not_surjective", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.not_bijective", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.symmetric_apply_eq_iff", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Function.Injective2", "kind": "definition", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective2.left", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective2.right", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective2.uncurry", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective2.left'", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective2.right'", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective2.eq_iff", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.sometimes", "kind": "definition", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.sometimes_eq", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.sometimes_spec", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "forall_existsUnique_iff", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": true, "tactics": ["refine", "refine", "exacts", "rintro", "simp"], "tactic_count": 5}
{"name": "forall_existsUnique_iff'", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Symmetric.forall_existsUnique_iff'", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": true, "tactics": ["refine", "rcases", "exact"], "tactic_count": 3}
{"name": "Symmetric.forall_existsUnique_iff", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.piecewise", "kind": "definition", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_rec_on_bijective", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_mp_bijective", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": true, "tactics": ["cases", "exact"], "tactic_count": 2}
{"name": "eq_mpr_bijective", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": true, "tactics": ["cases", "exact"], "tactic_count": 2}
{"name": "cast_bijective", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": true, "tactics": ["cases", "exact"], "tactic_count": 2}
{"name": "eq_rec_inj", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cast_inj", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.LeftInverse.eq_rec_eq", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.LeftInverse.eq_rec_on_eq", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.LeftInverse.cast_eq", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.SeparatesPoints", "kind": "definition", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InvImage.equivalence", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDecidableUncurryOfFstSnd_mathlib", "kind": "instance", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDecidableCurryOfMk_mathlib", "kind": "instance", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.map_id", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.map_id'", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.map_comp_map", "kind": "theorem", "module": "Mathlib.Logic.Function.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Coequalizer.Rel", "kind": "inductive", "module": "Mathlib.Logic.Function.Coequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Coequalizer", "kind": "definition", "module": "Mathlib.Logic.Function.Coequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Coequalizer.mk", "kind": "definition", "module": "Mathlib.Logic.Function.Coequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Coequalizer.condition", "kind": "theorem", "module": "Mathlib.Logic.Function.Coequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Coequalizer.mk_surjective", "kind": "theorem", "module": "Mathlib.Logic.Function.Coequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Coequalizer.desc", "kind": "definition", "module": "Mathlib.Logic.Function.Coequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Coequalizer.desc_mk", "kind": "theorem", "module": "Mathlib.Logic.Function.Coequalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompTriple.instIsIdId", "kind": "instance", "module": "Mathlib.Logic.Function.CompTypeclasses", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompTriple.instComp_id", "kind": "instance", "module": "Mathlib.Logic.Function.CompTypeclasses", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompTriple.instId_comp", "kind": "instance", "module": "Mathlib.Logic.Function.CompTypeclasses", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompTriple.comp", "kind": "theorem", "module": "Mathlib.Logic.Function.CompTypeclasses", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompTriple.comp_inv", "kind": "theorem", "module": "Mathlib.Logic.Function.CompTypeclasses", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompTriple.comp_apply", "kind": "theorem", "module": "Mathlib.Logic.Function.CompTypeclasses", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Function.Semiconj", "kind": "definition", "module": "Mathlib.Logic.Function.Conjugate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.semiconj_iff_comp_eq", "kind": "theorem", "module": "Mathlib.Logic.Function.Conjugate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Semiconj.eq", "kind": "theorem", "module": "Mathlib.Logic.Function.Conjugate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Semiconj.comp_right", "kind": "theorem", "module": "Mathlib.Logic.Function.Conjugate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Semiconj.trans", "kind": "theorem", "module": "Mathlib.Logic.Function.Conjugate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Semiconj.comp_left", "kind": "theorem", "module": "Mathlib.Logic.Function.Conjugate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Semiconj.id_right", "kind": "theorem", "module": "Mathlib.Logic.Function.Conjugate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Semiconj.id_left", "kind": "theorem", "module": "Mathlib.Logic.Function.Conjugate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Semiconj.inverses_right", "kind": "theorem", "module": "Mathlib.Logic.Function.Conjugate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Semiconj.inverse_left", "kind": "theorem", "module": "Mathlib.Logic.Function.Conjugate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Semiconj.option_map", "kind": "theorem", "module": "Mathlib.Logic.Function.Conjugate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Commute", "kind": "definition", "module": "Mathlib.Logic.Function.Conjugate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Semiconj.commute", "kind": "theorem", "module": "Mathlib.Logic.Function.Conjugate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Commute.semiconj", "kind": "theorem", "module": "Mathlib.Logic.Function.Conjugate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Commute.refl", "kind": "theorem", "module": "Mathlib.Logic.Function.Conjugate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Commute.symm", "kind": "theorem", "module": "Mathlib.Logic.Function.Conjugate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Commute.comp_right", "kind": "theorem", "module": "Mathlib.Logic.Function.Conjugate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Commute.comp_left", "kind": "theorem", "module": "Mathlib.Logic.Function.Conjugate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Commute.id_right", "kind": "theorem", "module": "Mathlib.Logic.Function.Conjugate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Commute.id_left", "kind": "theorem", "module": "Mathlib.Logic.Function.Conjugate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Commute.option_map", "kind": "theorem", "module": "Mathlib.Logic.Function.Conjugate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Semiconj₂", "kind": "definition", "module": "Mathlib.Logic.Function.Conjugate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Semiconj₂.eq", "kind": "theorem", "module": "Mathlib.Logic.Function.Conjugate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Semiconj₂.comp_eq", "kind": "theorem", "module": "Mathlib.Logic.Function.Conjugate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Semiconj₂.id_left", "kind": "theorem", "module": "Mathlib.Logic.Function.Conjugate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Semiconj₂.comp", "kind": "theorem", "module": "Mathlib.Logic.Function.Conjugate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Semiconj₂.isAssociative_right", "kind": "theorem", "module": "Mathlib.Logic.Function.Conjugate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Semiconj₂.isAssociative_left", "kind": "theorem", "module": "Mathlib.Logic.Function.Conjugate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Semiconj₂.isIdempotent_right", "kind": "theorem", "module": "Mathlib.Logic.Function.Conjugate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Semiconj₂.isIdempotent_left", "kind": "theorem", "module": "Mathlib.Logic.Function.Conjugate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.flip_def", "kind": "theorem", "module": "Mathlib.Logic.Function.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.dcomp", "kind": "definition", "module": "Mathlib.Logic.Function.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.term_∘'_", "kind": "definition", "module": "Mathlib.Logic.Function.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function._aux_Mathlib_Logic_Function_Defs___macroRules_Function_term_∘'__1", "kind": "definition", "module": "Mathlib.Logic.Function.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function._aux_Mathlib_Logic_Function_Defs___unexpand_Function_dcomp_1", "kind": "definition", "module": "Mathlib.Logic.Function.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.onFun", "kind": "abbrev", "module": "Mathlib.Logic.Function.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.term_On_", "kind": "definition", "module": "Mathlib.Logic.Function.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function._aux_Mathlib_Logic_Function_Defs___macroRules_Function_term_On__1", "kind": "definition", "module": "Mathlib.Logic.Function.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function._aux_Mathlib_Logic_Function_Defs___unexpand_Function_onFun_1", "kind": "definition", "module": "Mathlib.Logic.Function.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.swap", "kind": "abbrev", "module": "Mathlib.Logic.Function.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.swap_def", "kind": "theorem", "module": "Mathlib.Logic.Function.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.comp_assoc", "kind": "theorem", "module": "Mathlib.Logic.Function.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Bijective", "kind": "definition", "module": "Mathlib.Logic.Function.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Bijective.comp", "kind": "theorem", "module": "Mathlib.Logic.Function.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.bijective_id", "kind": "theorem", "module": "Mathlib.Logic.Function.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.beq_eq", "kind": "theorem", "module": "Mathlib.Logic.Function.Defs", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "Function.IsFixedPt", "kind": "definition", "module": "Mathlib.Logic.Function.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.IsFixedPt.of_subsingleton", "kind": "theorem", "module": "Mathlib.Logic.Function.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.map", "kind": "definition", "module": "Mathlib.Logic.Function.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.map_apply", "kind": "theorem", "module": "Mathlib.Logic.Function.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DependsOn", "kind": "definition", "module": "Mathlib.Logic.Function.DependsOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dependsOn_iff_factorsThrough", "kind": "theorem", "module": "Mathlib.Logic.Function.DependsOn", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "dependsOn_iff_exists_comp", "kind": "theorem", "module": "Mathlib.Logic.Function.DependsOn", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "dependsOn_univ", "kind": "theorem", "module": "Mathlib.Logic.Function.DependsOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dependsOn_const", "kind": "theorem", "module": "Mathlib.Logic.Function.DependsOn", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DependsOn.mono", "kind": "theorem", "module": "Mathlib.Logic.Function.DependsOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DependsOn.empty", "kind": "theorem", "module": "Mathlib.Logic.Function.DependsOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.dependsOn_restrict", "kind": "theorem", "module": "Mathlib.Logic.Function.DependsOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Fiber", "kind": "definition", "module": "Mathlib.Logic.Function.FiberPartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Fiber.image", "kind": "definition", "module": "Mathlib.Logic.Function.FiberPartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Fiber.eq_fiber_image", "kind": "theorem", "module": "Mathlib.Logic.Function.FiberPartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Fiber.mk", "kind": "definition", "module": "Mathlib.Logic.Function.FiberPartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Fiber.mkSelf", "kind": "definition", "module": "Mathlib.Logic.Function.FiberPartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Fiber.map_eq_image", "kind": "theorem", "module": "Mathlib.Logic.Function.FiberPartition", "is_tactic_proof": true, "tactics": ["have", "rw", "convert"], "tactic_count": 3}
{"name": "Function.Fiber.mk_image", "kind": "theorem", "module": "Mathlib.Logic.Function.FiberPartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Fiber.mem_iff_eq_image", "kind": "theorem", "module": "Mathlib.Logic.Function.FiberPartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Fiber.preimage", "kind": "definition", "module": "Mathlib.Logic.Function.FiberPartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Fiber.map_preimage_eq_image", "kind": "theorem", "module": "Mathlib.Logic.Function.FiberPartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Fiber.fiber_nonempty", "kind": "theorem", "module": "Mathlib.Logic.Function.FiberPartition", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "Function.Fiber.map_preimage_eq_image_map", "kind": "theorem", "module": "Mathlib.Logic.Function.FiberPartition", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Function.Fiber.image_eq_image_mk", "kind": "theorem", "module": "Mathlib.Logic.Function.FiberPartition", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Function.FromTypes", "kind": "definition", "module": "Mathlib.Logic.Function.FromTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.fromTypes_zero", "kind": "theorem", "module": "Mathlib.Logic.Function.FromTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.fromTypes_nil", "kind": "theorem", "module": "Mathlib.Logic.Function.FromTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.fromTypes_succ", "kind": "theorem", "module": "Mathlib.Logic.Function.FromTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.fromTypes_cons", "kind": "theorem", "module": "Mathlib.Logic.Function.FromTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.fromTypes_zero_equiv", "kind": "definition", "module": "Mathlib.Logic.Function.FromTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.fromTypes_nil_equiv", "kind": "definition", "module": "Mathlib.Logic.Function.FromTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.fromTypes_succ_equiv", "kind": "definition", "module": "Mathlib.Logic.Function.FromTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.fromTypes_cons_equiv", "kind": "definition", "module": "Mathlib.Logic.Function.FromTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.FromTypes.const", "kind": "definition", "module": "Mathlib.Logic.Function.FromTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.FromTypes.const_zero", "kind": "theorem", "module": "Mathlib.Logic.Function.FromTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.FromTypes.const_succ", "kind": "theorem", "module": "Mathlib.Logic.Function.FromTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.FromTypes.const_succ_apply", "kind": "theorem", "module": "Mathlib.Logic.Function.FromTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.FromTypes.inhabited", "kind": "instance", "module": "Mathlib.Logic.Function.FromTypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.iterate", "kind": "definition", "module": "Mathlib.Logic.Function.Iterate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "term_^[_]", "kind": "definition", "module": "Mathlib.Logic.Function.Iterate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Logic_Function_Iterate___macroRules_term_^[_]_1", "kind": "definition", "module": "Mathlib.Logic.Function.Iterate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Logic_Function_Iterate___unexpand_Nat_iterate_1", "kind": "definition", "module": "Mathlib.Logic.Function.Iterate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.iterate_zero", "kind": "theorem", "module": "Mathlib.Logic.Function.Iterate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.iterate_zero_apply", "kind": "theorem", "module": "Mathlib.Logic.Function.Iterate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.iterate_succ", "kind": "theorem", "module": "Mathlib.Logic.Function.Iterate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.iterate_succ_apply", "kind": "theorem", "module": "Mathlib.Logic.Function.Iterate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.iterate_id", "kind": "theorem", "module": "Mathlib.Logic.Function.Iterate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.iterate_add", "kind": "theorem", "module": "Mathlib.Logic.Function.Iterate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.iterate_add_apply", "kind": "theorem", "module": "Mathlib.Logic.Function.Iterate", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Function.iterate_one", "kind": "theorem", "module": "Mathlib.Logic.Function.Iterate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.iterate_mul", "kind": "theorem", "module": "Mathlib.Logic.Function.Iterate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.iterate_fixed", "kind": "theorem", "module": "Mathlib.Logic.Function.Iterate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.iterate_invariant", "kind": "theorem", "module": "Mathlib.Logic.Function.Iterate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.iterate", "kind": "theorem", "module": "Mathlib.Logic.Function.Iterate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.iterate", "kind": "theorem", "module": "Mathlib.Logic.Function.Iterate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Bijective.iterate", "kind": "theorem", "module": "Mathlib.Logic.Function.Iterate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Semiconj.iterate_right", "kind": "theorem", "module": "Mathlib.Logic.Function.Iterate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Semiconj.iterate_left", "kind": "theorem", "module": "Mathlib.Logic.Function.Iterate", "is_tactic_proof": true, "tactics": ["induction", "zero", "rw", "exact", "succ", "rw", "exact"], "tactic_count": 7}
{"name": "Function.Commute.iterate_right", "kind": "theorem", "module": "Mathlib.Logic.Function.Iterate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Commute.iterate_left", "kind": "theorem", "module": "Mathlib.Logic.Function.Iterate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Commute.iterate_iterate", "kind": "theorem", "module": "Mathlib.Logic.Function.Iterate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Commute.iterate_eq_of_map_eq", "kind": "theorem", "module": "Mathlib.Logic.Function.Iterate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Commute.comp_iterate", "kind": "theorem", "module": "Mathlib.Logic.Function.Iterate", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "funext", "simp"], "tactic_count": 5}
{"name": "Function.Commute.iterate_self", "kind": "theorem", "module": "Mathlib.Logic.Function.Iterate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Commute.self_iterate", "kind": "theorem", "module": "Mathlib.Logic.Function.Iterate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Commute.iterate_iterate_self", "kind": "theorem", "module": "Mathlib.Logic.Function.Iterate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Semiconj₂.iterate", "kind": "theorem", "module": "Mathlib.Logic.Function.Iterate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.iterate_succ'", "kind": "theorem", "module": "Mathlib.Logic.Function.Iterate", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Function.iterate_succ_apply'", "kind": "theorem", "module": "Mathlib.Logic.Function.Iterate", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Function.iterate_pred_comp_of_pos", "kind": "theorem", "module": "Mathlib.Logic.Function.Iterate", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Function.comp_iterate_pred_of_pos", "kind": "theorem", "module": "Mathlib.Logic.Function.Iterate", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Function.Iterate.rec", "kind": "definition", "module": "Mathlib.Logic.Function.Iterate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Iterate.rec_zero", "kind": "theorem", "module": "Mathlib.Logic.Function.Iterate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.LeftInverse.iterate", "kind": "theorem", "module": "Mathlib.Logic.Function.Iterate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.RightInverse.iterate", "kind": "theorem", "module": "Mathlib.Logic.Function.Iterate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.iterate_comm", "kind": "theorem", "module": "Mathlib.Logic.Function.Iterate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.iterate_commute", "kind": "theorem", "module": "Mathlib.Logic.Function.Iterate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.iterate_add_eq_iterate", "kind": "theorem", "module": "Mathlib.Logic.Function.Iterate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.iterate_cancel", "kind": "theorem", "module": "Mathlib.Logic.Function.Iterate", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "Function.involutive_iff_iter_2_eq_id", "kind": "theorem", "module": "Mathlib.Logic.Function.Iterate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.foldl_const", "kind": "theorem", "module": "Mathlib.Logic.Function.Iterate", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "List.foldr_const", "kind": "theorem", "module": "Mathlib.Logic.Function.Iterate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.map_iterate", "kind": "theorem", "module": "Mathlib.Logic.Function.Iterate", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "Function.OfArity", "kind": "abbrev", "module": "Mathlib.Logic.Function.OfArity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.ofArity_zero", "kind": "theorem", "module": "Mathlib.Logic.Function.OfArity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.ofArity_succ", "kind": "theorem", "module": "Mathlib.Logic.Function.OfArity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.OfArity.const", "kind": "definition", "module": "Mathlib.Logic.Function.OfArity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.OfArity.const_zero", "kind": "theorem", "module": "Mathlib.Logic.Function.OfArity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.OfArity.const_succ", "kind": "theorem", "module": "Mathlib.Logic.Function.OfArity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.OfArity.const_succ_apply", "kind": "theorem", "module": "Mathlib.Logic.Function.OfArity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.OfArity.inhabited", "kind": "instance", "module": "Mathlib.Logic.Function.OfArity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.FromTypes.fromTypes_fin_const", "kind": "theorem", "module": "Mathlib.Logic.Function.OfArity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.FromTypes.fromTypes_fin_const_equiv", "kind": "definition", "module": "Mathlib.Logic.Function.OfArity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.down_injective", "kind": "theorem", "module": "Mathlib.Logic.Function.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.down_inj", "kind": "theorem", "module": "Mathlib.Logic.Function.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PLift.down_injective", "kind": "theorem", "module": "Mathlib.Logic.Function.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PLift.down_inj", "kind": "theorem", "module": "Mathlib.Logic.Function.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.coprime_mul_succ", "kind": "theorem", "module": "Mathlib.Logic.Godel.GodelBetaFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Logic.Godel.GodelBetaFunction.0.Nat.supOfSeq", "kind": "definition", "module": "Mathlib.Logic.Godel.GodelBetaFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Logic.Godel.GodelBetaFunction.0.Nat.coprimes", "kind": "definition", "module": "Mathlib.Logic.Godel.GodelBetaFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.coprimes_lt", "kind": "theorem", "module": "Mathlib.Logic.Godel.GodelBetaFunction", "is_tactic_proof": true, "tactics": ["have", "have", "le_trans", "simpa"], "tactic_count": 4}
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{"name": "Nat.unbeta", "kind": "definition", "module": "Mathlib.Logic.Godel.GodelBetaFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.beta_unbeta_coe", "kind": "theorem", "module": "Mathlib.Logic.Godel.GodelBetaFunction", "is_tactic_proof": true, "tactics": ["simpa", "mod_eq_of_modEq", "i"], "tactic_count": 3}
{"name": "Relation.CutExpand", "kind": "definition", "module": "Mathlib.Logic.Hydra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Relation.cutExpand_le_invImage_lex", "kind": "theorem", "module": "Mathlib.Logic.Hydra", "is_tactic_proof": true, "tactics": ["rintro", "replace", "classical", "refine", "apply_fun", "simpa", "apply_fun", "simp", "exact"], "tactic_count": 9}
{"name": "Relation.cutExpand_singleton", "kind": "theorem", "module": "Mathlib.Logic.Hydra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Relation.cutExpand_singleton_singleton", "kind": "theorem", "module": "Mathlib.Logic.Hydra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Relation.cutExpand_add_left", "kind": "theorem", "module": "Mathlib.Logic.Hydra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Relation.cutExpand_add_right", "kind": "theorem", "module": "Mathlib.Logic.Hydra", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "Relation.cutExpand_add_single", "kind": "theorem", "module": "Mathlib.Logic.Hydra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Relation.cutExpand_single_add", "kind": "theorem", "module": "Mathlib.Logic.Hydra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Relation.not_cutExpand_zero", "kind": "theorem", "module": "Mathlib.Logic.Hydra", "is_tactic_proof": true, "tactics": ["classical", "rw", "rintro"], "tactic_count": 3}
{"name": "Relation.cutExpand_zero", "kind": "theorem", "module": "Mathlib.Logic.Hydra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Relation.cutExpand_fibration", "kind": "theorem", "module": "Mathlib.Logic.Hydra", "is_tactic_proof": true, "tactics": ["rintro", "classical", "obtain", "rw", "obtain", "refine", "rw", "rw", "refine", "rw", "rw"], "tactic_count": 11}
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{"name": "Relation.cutExpand_double", "kind": "theorem", "module": "Mathlib.Logic.Hydra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Relation.cutExpand_pair_left", "kind": "theorem", "module": "Mathlib.Logic.Hydra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Relation.cutExpand_pair_right", "kind": "theorem", "module": "Mathlib.Logic.Hydra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Relation.cutExpand_double_left", "kind": "theorem", "module": "Mathlib.Logic.Hydra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Relation.acc_of_singleton", "kind": "theorem", "module": "Mathlib.Logic.Hydra", "is_tactic_proof": true, "tactics": ["induction", "empty", "cons", "rw", "rw", "exact"], "tactic_count": 6}
{"name": "Acc.cutExpand", "kind": "theorem", "module": "Mathlib.Logic.Hydra", "is_tactic_proof": false, "tactics": ["induction", "refine", "classical", "simp", "rintro", "refine", "rw", "exact"], "tactic_count": 8}
{"name": "WellFounded.cutExpand", "kind": "theorem", "module": "Mathlib.Logic.Hydra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Relation.instIsWellFoundedMultisetCutExpand", "kind": "instance", "module": "Mathlib.Logic.Hydra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Empty.instIsEmpty", "kind": "instance", "module": "Mathlib.Logic.IsEmpty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PEmpty.instIsEmpty", "kind": "instance", "module": "Mathlib.Logic.IsEmpty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsEmptyFalse", "kind": "instance", "module": "Mathlib.Logic.IsEmpty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.isEmpty", "kind": "instance", "module": "Mathlib.Logic.IsEmpty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.isEmpty'", "kind": "instance", "module": "Mathlib.Logic.IsEmpty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.isEmpty", "kind": "theorem", "module": "Mathlib.Logic.IsEmpty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.isEmpty", "kind": "theorem", "module": "Mathlib.Logic.IsEmpty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsEmptyForallOfNonempty", "kind": "instance", "module": "Mathlib.Logic.IsEmpty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PProd.isEmpty_left", "kind": "instance", "module": "Mathlib.Logic.IsEmpty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PProd.isEmpty_right", "kind": "instance", "module": "Mathlib.Logic.IsEmpty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.isEmpty_left", "kind": "instance", "module": "Mathlib.Logic.IsEmpty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.isEmpty_right", "kind": "instance", "module": "Mathlib.Logic.IsEmpty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quot.instIsEmpty", "kind": "instance", "module": "Mathlib.Logic.IsEmpty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quotient.instIsEmpty", "kind": "instance", "module": "Mathlib.Logic.IsEmpty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsEmptyPSum", "kind": "instance", "module": "Mathlib.Logic.IsEmpty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsEmptySum", "kind": "instance", "module": "Mathlib.Logic.IsEmpty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsEmptySubtype", "kind": "instance", "module": "Mathlib.Logic.IsEmpty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.isEmpty_of_false", "kind": "theorem", "module": "Mathlib.Logic.IsEmpty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.isEmpty_false", "kind": "instance", "module": "Mathlib.Logic.IsEmpty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.isEmpty_left", "kind": "instance", "module": "Mathlib.Logic.IsEmpty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_example", "kind": "example", "module": "Mathlib.Logic.IsEmpty", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "isEmptyElim", "kind": "definition", "module": "Mathlib.Logic.IsEmpty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isEmpty_iff", "kind": "theorem", "module": "Mathlib.Logic.IsEmpty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsEmpty.elim", "kind": "definition", "module": "Mathlib.Logic.IsEmpty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsEmpty.elim'", "kind": "definition", "module": "Mathlib.Logic.IsEmpty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsEmpty.prop_iff", "kind": "theorem", "module": "Mathlib.Logic.IsEmpty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsEmpty.forall_iff", "kind": "theorem", "module": "Mathlib.Logic.IsEmpty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsEmpty.exists_iff", "kind": "theorem", "module": "Mathlib.Logic.IsEmpty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsEmpty.instSubsingleton", "kind": "instance", "module": "Mathlib.Logic.IsEmpty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_nonempty_iff", "kind": "theorem", "module": "Mathlib.Logic.IsEmpty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_isEmpty_iff", "kind": "theorem", "module": "Mathlib.Logic.IsEmpty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isEmpty_Prop", "kind": "theorem", "module": "Mathlib.Logic.IsEmpty", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "isEmpty_pi", "kind": "theorem", "module": "Mathlib.Logic.IsEmpty", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "isEmpty_fun", "kind": "theorem", "module": "Mathlib.Logic.IsEmpty", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "nonempty_fun", "kind": "theorem", "module": "Mathlib.Logic.IsEmpty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isEmpty_sigma", "kind": "theorem", "module": "Mathlib.Logic.IsEmpty", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "isEmpty_psigma", "kind": "theorem", "module": "Mathlib.Logic.IsEmpty", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "isEmpty_subtype", "kind": "theorem", "module": "Mathlib.Logic.IsEmpty", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "isEmpty_prod", "kind": "theorem", "module": "Mathlib.Logic.IsEmpty", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "isEmpty_pprod", "kind": "theorem", "module": "Mathlib.Logic.IsEmpty", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "isEmpty_sum", "kind": "theorem", "module": "Mathlib.Logic.IsEmpty", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "isEmpty_psum", "kind": "theorem", "module": "Mathlib.Logic.IsEmpty", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "isEmpty_ulift", "kind": "theorem", "module": "Mathlib.Logic.IsEmpty", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "isEmpty_plift", "kind": "theorem", "module": "Mathlib.Logic.IsEmpty", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "wellFounded_of_isEmpty", "kind": "theorem", "module": "Mathlib.Logic.IsEmpty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isEmpty_or_nonempty", "kind": "theorem", "module": "Mathlib.Logic.IsEmpty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_isEmpty_of_nonempty", "kind": "theorem", "module": "Mathlib.Logic.IsEmpty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.extend_of_isEmpty", "kind": "theorem", "module": "Mathlib.Logic.IsEmpty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "leftTotal_empty", "kind": "theorem", "module": "Mathlib.Logic.IsEmpty", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "leftTotal_iff_isEmpty_left", "kind": "theorem", "module": "Mathlib.Logic.IsEmpty", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "rightTotal_empty", "kind": "theorem", "module": "Mathlib.Logic.IsEmpty", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "rightTotal_iff_isEmpty_right", "kind": "theorem", "module": "Mathlib.Logic.IsEmpty", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "biTotal_empty", "kind": "theorem", "module": "Mathlib.Logic.IsEmpty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "biTotal_iff_isEmpty_right", "kind": "theorem", "module": "Mathlib.Logic.IsEmpty", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "biTotal_iff_isEmpty_left", "kind": "theorem", "module": "Mathlib.Logic.IsEmpty", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Function.Surjective.of_isEmpty", "kind": "theorem", "module": "Mathlib.Logic.IsEmpty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.surjective_iff_isEmpty", "kind": "theorem", "module": "Mathlib.Logic.IsEmpty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Bijective.of_isEmpty", "kind": "theorem", "module": "Mathlib.Logic.IsEmpty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.not_surjective_of_isEmpty_of_nonempty", "kind": "theorem", "module": "Mathlib.Logic.IsEmpty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iff_assoc", "kind": "theorem", "module": "Mathlib.Logic.Lemmas", "is_tactic_proof": true, "tactics": ["tauto"], "tactic_count": 1}
{"name": "iff_left_comm", "kind": "theorem", "module": "Mathlib.Logic.Lemmas", "is_tactic_proof": true, "tactics": ["tauto"], "tactic_count": 1}
{"name": "iff_right_comm", "kind": "theorem", "module": "Mathlib.Logic.Lemmas", "is_tactic_proof": true, "tactics": ["tauto"], "tactic_count": 1}
{"name": "dite_dite_distrib_left", "kind": "theorem", "module": "Mathlib.Logic.Lemmas", "is_tactic_proof": true, "tactics": ["split_ifs"], "tactic_count": 1}
{"name": "dite_dite_distrib_right", "kind": "theorem", "module": "Mathlib.Logic.Lemmas", "is_tactic_proof": true, "tactics": ["split_ifs"], "tactic_count": 1}
{"name": "ite_dite_distrib_left", "kind": "theorem", "module": "Mathlib.Logic.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ite_dite_distrib_right", "kind": "theorem", "module": "Mathlib.Logic.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dite_ite_distrib_left", "kind": "theorem", "module": "Mathlib.Logic.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dite_ite_distrib_right", "kind": "theorem", "module": "Mathlib.Logic.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ite_ite_distrib_left", "kind": "theorem", "module": "Mathlib.Logic.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ite_ite_distrib_right", "kind": "theorem", "module": "Mathlib.Logic.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prop.forall", "kind": "theorem", "module": "Mathlib.Logic.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prop.exists", "kind": "theorem", "module": "Mathlib.Logic.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonempty.forall", "kind": "theorem", "module": "Mathlib.Logic.Nonempty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonempty.exists", "kind": "theorem", "module": "Mathlib.Logic.Nonempty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_const_iff", "kind": "theorem", "module": "Mathlib.Logic.Nonempty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_true_iff_nonempty", "kind": "theorem", "module": "Mathlib.Logic.Nonempty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonempty.imp", "kind": "theorem", "module": "Mathlib.Logic.Nonempty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_nonempty_iff_imp_false", "kind": "theorem", "module": "Mathlib.Logic.Nonempty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nonempty_psigma", "kind": "theorem", "module": "Mathlib.Logic.Nonempty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nonempty_subtype", "kind": "theorem", "module": "Mathlib.Logic.Nonempty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nonempty_pprod", "kind": "theorem", "module": "Mathlib.Logic.Nonempty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nonempty_psum", "kind": "theorem", "module": "Mathlib.Logic.Nonempty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nonempty_plift", "kind": "theorem", "module": "Mathlib.Logic.Nonempty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Classical.inhabited_of_nonempty'", "kind": "definition", "module": "Mathlib.Logic.Nonempty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonempty.some", "kind": "abbrev", "module": "Mathlib.Logic.Nonempty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Classical.arbitrary", "kind": "abbrev", "module": "Mathlib.Logic.Nonempty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonempty.map", "kind": "theorem", "module": "Mathlib.Logic.Nonempty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonempty.map2", "kind": "theorem", "module": "Mathlib.Logic.Nonempty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonempty.congr", "kind": "theorem", "module": "Mathlib.Logic.Nonempty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonempty.elim_to_inhabited", "kind": "theorem", "module": "Mathlib.Logic.Nonempty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Classical.nonempty_pi", "kind": "theorem", "module": "Mathlib.Logic.Nonempty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "subsingleton_of_not_nonempty", "kind": "theorem", "module": "Mathlib.Logic.Nonempty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.nonempty", "kind": "theorem", "module": "Mathlib.Logic.Nonempty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nonempty_sigma", "kind": "theorem", "module": "Mathlib.Logic.Nonempty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nonempty_sum", "kind": "theorem", "module": "Mathlib.Logic.Nonempty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nonempty_prod", "kind": "theorem", "module": "Mathlib.Logic.Nonempty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nonempty_ulift", "kind": "theorem", "module": "Mathlib.Logic.Nonempty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nontrivial_of_lt", "kind": "theorem", "module": "Mathlib.Logic.Nontrivial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_pair_lt", "kind": "theorem", "module": "Mathlib.Logic.Nontrivial.Basic", "is_tactic_proof": true, "tactics": ["rcases", "cases"], "tactic_count": 2}
{"name": "nontrivial_iff_lt", "kind": "theorem", "module": "Mathlib.Logic.Nontrivial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.nontrivial_iff_exists_ne", "kind": "theorem", "module": "Mathlib.Logic.Nontrivial.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "nontrivialPSumUnique", "kind": "definition", "module": "Mathlib.Logic.Nontrivial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Option.nontrivial", "kind": "instance", "module": "Mathlib.Logic.Nontrivial.Basic", "is_tactic_proof": true, "tactics": ["inhabit", "exact"], "tactic_count": 2}
{"name": "nontrivial_prod_right", "kind": "instance", "module": "Mathlib.Logic.Nontrivial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nontrivial_prod_left", "kind": "instance", "module": "Mathlib.Logic.Nontrivial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.nontrivial_at", "kind": "theorem", "module": "Mathlib.Logic.Nontrivial.Basic", "is_tactic_proof": true, "tactics": ["letI", "exact"], "tactic_count": 2}
{"name": "Pi.nontrivial", "kind": "instance", "module": "Mathlib.Logic.Nontrivial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.nontrivial", "kind": "instance", "module": "Mathlib.Logic.Nontrivial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsingleton.le", "kind": "theorem", "module": "Mathlib.Logic.Nontrivial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nontrivial_iff", "kind": "theorem", "module": "Mathlib.Logic.Nontrivial.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_pair_ne", "kind": "theorem", "module": "Mathlib.Logic.Nontrivial.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.nontrivial", "kind": "theorem", "module": "Mathlib.Logic.Nontrivial.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.exists_ne", "kind": "theorem", "module": "Mathlib.Logic.Nontrivial.Defs", "is_tactic_proof": true, "tactics": ["rcases", "by_cases", "exact", "exact"], "tactic_count": 4}
{"name": "Decidable.exists_ne", "kind": "theorem", "module": "Mathlib.Logic.Nontrivial.Defs", "is_tactic_proof": true, "tactics": ["rcases", "by_cases", "rw", "exact", "exact"], "tactic_count": 5}
{"name": "exists_ne", "kind": "theorem", "module": "Mathlib.Logic.Nontrivial.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nontrivial_of_ne", "kind": "theorem", "module": "Mathlib.Logic.Nontrivial.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nontrivial_iff_exists_ne", "kind": "theorem", "module": "Mathlib.Logic.Nontrivial.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.nontrivial_of_nontrivial", "kind": "theorem", "module": "Mathlib.Logic.Nontrivial.Defs", "is_tactic_proof": true, "tactics": ["obtain", "rw", "obtain", "exact"], "tactic_count": 4}
{"name": "instNontrivialProp", "kind": "instance", "module": "Mathlib.Logic.Nontrivial.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nontrivial.to_nonempty", "kind": "instance", "module": "Mathlib.Logic.Nontrivial.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "subsingleton_iff", "kind": "theorem", "module": "Mathlib.Logic.Nontrivial.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_nontrivial_iff_subsingleton", "kind": "theorem", "module": "Mathlib.Logic.Nontrivial.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "not_nontrivial", "kind": "theorem", "module": "Mathlib.Logic.Nontrivial.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_subsingleton", "kind": "theorem", "module": "Mathlib.Logic.Nontrivial.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_subsingleton_iff_nontrivial", "kind": "theorem", "module": "Mathlib.Logic.Nontrivial.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "subsingleton_or_nontrivial", "kind": "theorem", "module": "Mathlib.Logic.Nontrivial.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "false_of_nontrivial_of_subsingleton", "kind": "theorem", "module": "Mathlib.Logic.Nontrivial.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.nontrivial", "kind": "theorem", "module": "Mathlib.Logic.Nontrivial.Defs", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "rcases", "have", "refine", "rw", "exact"], "tactic_count": 7}
{"name": "Bool.instNontrivial", "kind": "instance", "module": "Mathlib.Logic.Nontrivial.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isSymmOp_of_isCommutative", "kind": "instance", "module": "Mathlib.Logic.OpClass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSymmOp.flip_eq", "kind": "theorem", "module": "Mathlib.Logic.OpClass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instRightCommutativeOfLeftCommutative", "kind": "instance", "module": "Mathlib.Logic.OpClass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instLeftCommutativeOfRightCommutative", "kind": "instance", "module": "Mathlib.Logic.OpClass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instLeftCommutativeOfCommutativeOfAssociative", "kind": "instance", "module": "Mathlib.Logic.OpClass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instRightCommutativeOfCommutativeOfAssociative", "kind": "instance", "module": "Mathlib.Logic.OpClass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pairwise", "kind": "definition", "module": "Mathlib.Logic.Pairwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pairwise.mono", "kind": "theorem", "module": "Mathlib.Logic.Pairwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pairwise.eq", "kind": "theorem", "module": "Mathlib.Logic.Pairwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsingleton.pairwise", "kind": "theorem", "module": "Mathlib.Logic.Pairwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.injective_iff_pairwise_ne", "kind": "theorem", "module": "Mathlib.Logic.Pairwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pairwise.comp_of_injective", "kind": "theorem", "module": "Mathlib.Logic.Pairwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pairwise.of_comp_of_surjective", "kind": "theorem", "module": "Mathlib.Logic.Pairwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Bijective.pairwise_comp_iff", "kind": "theorem", "module": "Mathlib.Logic.Pairwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pairwise_fin_succ_iff", "kind": "theorem", "module": "Mathlib.Logic.Pairwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pairwise_fin_succ_iff_of_isSymm", "kind": "theorem", "module": "Mathlib.Logic.Pairwise", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "Option.subsingleton_iff_isEmpty", "kind": "theorem", "module": "Mathlib.Logic.Unique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Option.instUniqueOfIsEmpty", "kind": "instance", "module": "Mathlib.Logic.Unique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unique.subtypeEq", "kind": "instance", "module": "Mathlib.Logic.Unique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unique.subtypeEq'", "kind": "instance", "module": "Mathlib.Logic.Unique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.instUnique", "kind": "instance", "module": "Mathlib.Logic.Unique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "univLE_max", "kind": "theorem", "module": "Mathlib.Logic.UnivLE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Small.trans_univLE", "kind": "theorem", "module": "Mathlib.Logic.UnivLE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UnivLE.trans", "kind": "theorem", "module": "Mathlib.Logic.UnivLE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UnivLE.self", "kind": "instance", "module": "Mathlib.Logic.UnivLE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UnivLE.zero", "kind": "instance", "module": "Mathlib.Logic.UnivLE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UnivLE.succ", "kind": "theorem", "module": "Mathlib.Logic.UnivLE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "univLE_of_max", "kind": "instance", "module": "Mathlib.Logic.UnivLE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_example", "kind": "example", "module": "Mathlib.Logic.UnivLE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_example", "kind": "example", "module": "Mathlib.Logic.UnivLE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_example", "kind": "example", "module": "Mathlib.Logic.UnivLE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_example", "kind": "example", "module": "Mathlib.Logic.UnivLE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_example", "kind": "example", "module": "Mathlib.Logic.UnivLE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_example", "kind": "example", "module": "Mathlib.Logic.UnivLE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_example", "kind": "example", "module": "Mathlib.Logic.UnivLE", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "MeasCat.instCoeSortType", "kind": "instance", "module": "Mathlib.MeasureTheory.Category.MeasCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasCat.coe_of", "kind": "theorem", "module": "Mathlib.MeasureTheory.Category.MeasCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasCat.instLargeCategory", "kind": "instance", "module": "Mathlib.MeasureTheory.Category.MeasCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasCat.instFunLikeSubtypeForallCarrierMeasurable", "kind": "instance", "module": "Mathlib.MeasureTheory.Category.MeasCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasCat.instConcreteCategorySubtypeForallCarrierMeasurable", "kind": "instance", "module": "Mathlib.MeasureTheory.Category.MeasCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasCat.instInhabited", "kind": "instance", "module": "Mathlib.MeasureTheory.Category.MeasCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasCat.Measure", "kind": "definition", "module": "Mathlib.MeasureTheory.Category.MeasCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasCat.Giry", "kind": "definition", "module": "Mathlib.MeasureTheory.Category.MeasCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasCat.Integral", "kind": "definition", "module": "Mathlib.MeasureTheory.Category.MeasCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.hasForgetToMeasCat", "kind": "instance", "module": "Mathlib.MeasureTheory.Category.MeasCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Borel", "kind": "abbrev", "module": "Mathlib.MeasureTheory.Category.MeasCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.instMeasurableSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.instDiscreteMeasurableSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "borel", "kind": "definition", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "borel_anti", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "borel_eq_top_of_discrete", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "borel_eq_generateFrom_of_subbasis", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.IsTopologicalBasis.borel_eq_generateFrom", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isPiSystem_isOpen", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isPiSystem_isClosed", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "borel_eq_generateFrom_isClosed", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "borel_comap", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.borel_measurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Borelize.tacticBorelize___", "kind": "definition", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Borelize.addBorelInstance", "kind": "definition", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Borelize.borelToRefl", "kind": "definition", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Borelize.borelize", "kind": "definition", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Borelize._aux_Mathlib_MeasureTheory_Constructions_BorelSpace_Basic___elabRules_Mathlib_Tactic_Borelize_tacticBorelize____1", "kind": "definition", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.opensMeasurableSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.borelSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BorelSpace.opensMeasurable", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.borelSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Countable.instBorelSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": true, "tactics": ["have", "have", "exact"], "tactic_count": 3}
{"name": "Subtype.opensMeasurableSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "opensMeasurableSpace_iff_forall_measurableSet", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "BorelSpace.countablyGenerated", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": true, "tactics": ["obtain", "refine", "borelize", "exact"], "tactic_count": 4}
{"name": "IsOpen.measurableSet", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.nullMeasurableSet", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSet.induction_on_open", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCountablySeparatedElemOfHasCountableSeparatingOnIsOpen", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "measurableSet_interior", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGδ.measurableSet", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "measurableSet_of_continuousAt", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.measurableSet", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.nullMeasurableSet", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.measurableSet", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.nullMeasurableSet", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Inseparable.mem_measurableSet_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.closure_subset_measurableSet", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsCompact.measure_closure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": true, "tactics": ["refine", "calc", "μ", "measure_mono"], "tactic_count": 4}
{"name": "measurableSet_closure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurableSet_frontier", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_of_isOpen", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "measurable_of_isClosed", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": true, "tactics": ["apply", "rw"], "tactic_count": 2}
{"name": "measurable_of_isClosed'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": true, "tactics": ["apply", "rcases", "simp", "by_cases", "simp", "exact"], "tactic_count": 6}
{"name": "nhds_isMeasurablyGenerated", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "exact"], "tactic_count": 3}
{"name": "MeasurableSet.nhdsWithin_isMeasurablyGenerated", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpensMeasurableSpace.separatesPoints", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": true, "tactics": ["rw", "intro", "apply", "rw", "exact"], "tactic_count": 5}
{"name": "borel_eq_top_of_countable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": true, "tactics": ["refine", "borelize", "exact"], "tactic_count": 3}
{"name": "OpensMeasurableSpace.toMeasurableSingletonClass", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.opensMeasurableSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": true, "tactics": ["constructor", "have", "rw", "apply", "rintro", "refine", "rw", "exact"], "tactic_count": 8}
{"name": "Pi.opensMeasurableSpace_of_subsingleton", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "secondCountableTopologyEither_of_left", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "secondCountableTopologyEither_of_right", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.opensMeasurableSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": true, "tactics": ["apply", "rcases", "let", "have", "intro", "apply", "rintro", "exact", "have", "apply", "rintro", "rcases", "obtain", "simp", "exact", "rintro", "simp", "rcases", "exact", "rw", "apply", "exact", "let", "have", "intro", "apply", "rintro", "exact", "have", "apply", "rintro", "rcases", "obtain", "simp", "exact", "rintro", "simp", "rcases", "exact", "rw", "apply", "exact"], "tactic_count": 42}
{"name": "interior_ae_eq_of_null_frontier", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measure_interior_of_null_frontier", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nullMeasurableSet_of_null_frontier", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "closure_ae_eq_of_null_frontier", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measure_closure_of_null_frontier", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "null_frontier_inter", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": true, "tactics": ["apply", "calc", "μ"], "tactic_count": 3}
{"name": "separatesPointsOfOpensMeasurableSpaceOfT0Space", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.measurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.aemeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosedEmbedding.measurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.measurable_piecewise", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "apply", "rcases", "rw", "exact", "rcases", "rw", "exact"], "tactic_count": 9}
{"name": "ContinuousMul.measurableMul", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousSub.measurableSub", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousInv.measurableInv", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousConstSMul.toMeasurableConstSMul", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousSMul.toMeasurableSMul", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.measurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.toMeasurableEquiv", "kind": "definition", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.measurableEmbedding", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.toMeasurableEquiv_coe", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.toMeasurableEquiv_symm_coe", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.measurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_of_continuousOn_compl_singleton", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.measurable2", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.aemeasurable2", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousInv₀.measurableInv", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMul.measurableMul₂", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousSub.measurableSub₂", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousSMul.measurableSMul₂", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instMeasurableEqOfSecondCountableTopologyOfT2Space", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pi_le_borel_pi", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "prod_le_borel_prod", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "exact", "exact"], "tactic_count": 4}
{"name": "Pi.borelSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.borelSpace_of_subsingleton", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.borelSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEmbedding.borelSpace", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": true, "tactics": ["constructor", "have", "rw"], "tactic_count": 3}
{"name": "ULift.instBorelSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteMeasurableSpace.toBorelSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": true, "tactics": ["constructor"], "tactic_count": 1}
{"name": "Topology.IsEmbedding.measurableEmbedding", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsClosedEmbedding.measurableEmbedding", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsOpenEmbedding.measurableEmbedding", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Empty.borelSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Unit.borelSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bool.borelSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.borelSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.borelSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.borelSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.measurableSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.borelSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.measurableSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.borelSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.measurableSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.borelSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.measurableSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.borelSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.IsFiniteMeasureOnCompacts.map", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.IsFiniteMeasureOnCompacts.comap", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.measurableSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.borelSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.measurableSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.borelSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.measurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.ContinuousLinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.measurable_comp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.ContinuousLinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.instMeasurableSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.ContinuousLinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.instBorelSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.ContinuousLinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.measurable_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.ContinuousLinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.measurable_apply'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.ContinuousLinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.measurable_coe", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.ContinuousLinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.apply_continuousLinearMap", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.ContinuousLinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.apply_continuousLinearMap", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.ContinuousLinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_smul_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.ContinuousLinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "aemeasurable_smul_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.ContinuousLinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurableSet_ball", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurableSet_closedBall", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_infDist", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.infDist", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_infNndist", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.infNndist", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_dist", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.dist", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.dist", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_nndist", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.nndist", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurableSet_eball", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_edist_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Metric", "is_tactic_proof": true, "tactics": ["fun_prop"], "tactic_count": 1}
{"name": "measurable_edist_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Metric", "is_tactic_proof": true, "tactics": ["fun_prop"], "tactic_count": 1}
{"name": "measurable_infEDist", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.infEDist", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_measure_cthickening", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Metric", "is_tactic_proof": false, "tactics": ["have", "rw", "exact", "tendsto_measure_biInter_gt", "have", "apply", "filter_upwards", "rw", "convert", "exact"], "tactic_count": 10}
{"name": "tendsto_measure_cthickening_of_isClosed", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Metric", "is_tactic_proof": true, "tactics": ["convert", "exact"], "tactic_count": 2}
{"name": "tendsto_measure_thickening", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Metric", "is_tactic_proof": true, "tactics": ["rw", "exact", "tendsto_measure_biInter_gt", "hs"], "tactic_count": 4}
{"name": "tendsto_measure_thickening_of_isClosed", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Metric", "is_tactic_proof": true, "tactics": ["convert", "exact"], "tactic_count": 2}
{"name": "measurable_edist", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.edist", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.edist", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_measure_cthickening_of_isCompact", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_borelSpace_of_countablyGenerated_of_separatesPoints", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Metric", "is_tactic_proof": true, "tactics": ["rcases", "letI", "let", "exact"], "tactic_count": 4}
{"name": "exists_opensMeasurableSpace_of_countablySeparated", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Metric", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "exact"], "tactic_count": 3}
{"name": "measurable_enorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.enorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.enorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_norm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.norm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.norm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_nnnorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.nnnorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.nnnorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Metric", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_of_tendsto_metrizable'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Metrizable", "is_tactic_proof": true, "tactics": ["letI", "apply", "intro", "have", "suffices", "rw", "intro", "exact", "have", "ext", "simp", "rw", "exact"], "tactic_count": 13}
{"name": "measurable_of_tendsto_metrizable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Metrizable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "aemeasurable_of_tendsto_metrizable_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Metrizable", "is_tactic_proof": true, "tactics": ["classical", "rcases", "have", "set", "have", "set", "refine", "simp_rw", "split_ifs", "simp_rw", "exact", "exact", "exact"], "tactic_count": 13}
{"name": "aemeasurable_of_tendsto_metrizable_ae'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Metrizable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "aemeasurable_of_unif_approx", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Metrizable", "is_tactic_proof": false, "tactics": ["obtain", "exists_seq_strictAnti_tendsto", "choose", "have", "have", "filter_upwards", "intro", "rw", "exact", "exact"], "tactic_count": 10}
{"name": "measurable_of_tendsto_metrizable_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Metrizable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_limit_of_tendsto_metrizable_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Metrizable", "is_tactic_proof": true, "tactics": ["classical", "inhabit", "rcases", "exact", "let", "have", "have", "set", "dite", "have", "intro", "simp", "split_ifs", "refine", "exact", "exact", "have", "h_ae_eq.mono", "have", "measurable_of_tendsto_metrizable", "exact"], "tactic_count": 21}
{"name": "measurableSet_of_tendsto_indicator", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Metrizable", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "nullMeasurableSet_of_tendsto_indicator", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Metrizable", "is_tactic_proof": true, "tactics": ["simp_rw", "apply", "simpa"], "tactic_count": 3}
{"name": "borel_eq_generateFrom_Iio", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Order", "is_tactic_proof": true, "tactics": ["refine", "rw", "letI", "have", "refine", "rintro", "rcases", "rw", "exact", "rcases", "have", "refine", "refine", "simpa", "simp", "exact", "apply", "rw", "intro", "exact"], "tactic_count": 20}
{"name": "borel_eq_generateFrom_Ioi", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "borel_eq_generateFrom_Iic", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Order", "is_tactic_proof": true, "tactics": ["rw", "refine", "refine", "obtain", "rw", "exact", "refine", "obtain", "rw", "exact"], "tactic_count": 10}
{"name": "borel_eq_generateFrom_Ici", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurableSet_Ici", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nullMeasurableSet_Ici", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurableSet_Iic", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nullMeasurableSet_Iic", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurableSet_Icc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nullMeasurableSet_Icc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsWithin_Ici_isMeasurablyGenerated", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsWithin_Iic_isMeasurablyGenerated", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsWithin_Icc_isMeasurablyGenerated", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Order", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "atTop_isMeasurablyGenerated", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "atBot_isMeasurablyGenerated", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsMeasurablyGeneratedCocompactOfR1Space", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurableSet_le'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurableSet_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.le'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Order", "is_tactic_proof": true, "tactics": ["fun_prop"], "tactic_count": 1}
{"name": "measurableSet_Iio", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nullMeasurableSet_Iio", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurableSet_Ioi", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nullMeasurableSet_Ioi", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurableSet_Ioo", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nullMeasurableSet_Ioo", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurableSet_Ioc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nullMeasurableSet_Ioc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurableSet_Ico", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nullMeasurableSet_Ico", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsWithin_Ioi_isMeasurablyGenerated", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsWithin_Iio_isMeasurablyGenerated", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsWithin_uIcc_isMeasurablyGenerated", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurableSet_lt'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_lt", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ContinuousInf.measurableInf₂", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Measurable.ennreal_ofReal", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.ennreal_ofReal", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_coe_nnreal_real_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "aemeasurable_coe_nnreal_real_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.ennrealEquivNNReal", "kind": "definition", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.measurable_of_measurable_nnreal", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.ennrealEquivSum", "kind": "definition", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.measurable_of_measurable_nnreal_prod", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.measurable_of_measurable_nnreal_nnreal", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.measurable_ofReal", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.measurable_toReal", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.measurable_toNNReal", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.instMeasurableMul₂", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Real", "is_tactic_proof": true, "tactics": ["refine", "simp", "simp", "exact", "simp", "exact"], "tactic_count": 6}
{"name": "ENNReal.instMeasurableSub₂", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.instMeasurableInv", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.instMeasurableSMulNNReal", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.measurable_of_tendsto'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Real", "is_tactic_proof": true, "tactics": ["rcases", "rw", "have", "ext1", "exact", "rw", "change", "exact"], "tactic_count": 8}
{"name": "ENNReal.measurable_of_tendsto", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.aemeasurable_of_tendsto'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Real", "is_tactic_proof": true, "tactics": ["rcases", "have", "set", "have", "classical", "set", "refine", "unfold", "simp_rw", "split_ifs", "simp_rw", "exact", "exact", "exact"], "tactic_count": 14}
{"name": "ENNReal.aemeasurable_of_tendsto", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.ennreal_toNNReal", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.ennreal_toNNReal", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_coe_nnreal_ennreal_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "aemeasurable_coe_nnreal_ennreal_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.ennreal_toReal", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.ennreal_toReal", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.ennreal_tsum", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Real", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Measurable.ennreal_tsum'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Real", "is_tactic_proof": true, "tactics": ["convert", "exact"], "tactic_count": 2}
{"name": "Measurable.nnreal_tsum", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Real", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "AEMeasurable.ennreal_tsum", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Real", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "AEMeasurable.nnreal_tsum", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Real", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "measurable_coe_real_ereal", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.coe_real_ereal", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.coe_real_ereal", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.erealEquivReal", "kind": "definition", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.measurable_of_measurable_real", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_ereal_toReal", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.ereal_toReal", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.ereal_toReal", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_coe_ennreal_ereal", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.coe_ereal_ennreal", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.coe_ereal_ennreal", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_ereal_toENNReal", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.ereal_toENNReal", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.ereal_toENNReal", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.instMeasurableSMul₂ENNReal", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.measurable_of_tendsto'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Real", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "NNReal.measurable_of_tendsto", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.measurableEmbedding_coe", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.instMeasurableAdd₂", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.measurable_of_real_prod", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.measurable_of_real_real", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Real", "is_tactic_proof": true, "tactics": ["refine", "refine", "exact", "exact", "exact"], "tactic_count": 5}
{"name": "_private.Mathlib.MeasureTheory.Constructions.BorelSpace.Real.0.EReal.measurable_const_mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Real", "is_tactic_proof": true, "tactics": ["refine", "have", "ext", "split_ifs", "simp", "rw", "rw", "exact", "have", "refine", "exact", "induction", "bot", "coe", "top", "simp_rw", "apply", "rwa"], "tactic_count": 18}
{"name": "EReal.instMeasurableMul₂", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Real", "is_tactic_proof": true, "tactics": ["refine", "exact", "exact", "exact", "simp_rw", "exact", "simp_rw", "exact"], "tactic_count": 8}
{"name": "exists_spanning_measurableSet_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Real", "is_tactic_proof": true, "tactics": ["let", "let", "have", "ext1", "simp", "exact", "let", "have", "refine", "exact", "exact", "have", "refine", "exact", "refine", "exact", "have", "refine", "simp", "refine", "exact", "rw"], "tactic_count": 22}
{"name": "tendsto_measure_Icc_nhdsWithin_right'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Real", "is_tactic_proof": true, "tactics": ["rw", "apply", "intro", "exact", "exact"], "tactic_count": 5}
{"name": "tendsto_measure_Icc_nhdsWithin_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Real", "is_tactic_proof": false, "tactics": ["simp", "tendsto_measure_Icc_nhdsWithin_right", "intro", "simpa"], "tactic_count": 4}
{"name": "tendsto_measure_Icc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.Real", "is_tactic_proof": true, "tactics": ["rw", "constructor", "apply", "filter_upwards", "rw", "simpa"], "tactic_count": 6}
{"name": "WithTop.instMeasurableSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.instBorelSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.MeasurableEquiv.neTopEquiv", "kind": "definition", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.measurable_of_measurable_comp_coe", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.measurable_untopD", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.measurable_untopA", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.measurable_coe", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.withTop_coe", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.untopD", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.untopA", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.measurableEquivSum", "kind": "definition", "module": "Mathlib.MeasureTheory.Constructions.BorelSpace.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.closedCompactCylinders", "kind": "definition", "module": "Mathlib.MeasureTheory.Constructions.ClosedCompactCylinders", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.empty_mem_closedCompactCylinders", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.ClosedCompactCylinders", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.mem_closedCompactCylinders", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.ClosedCompactCylinders", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MeasureTheory.closedCompactCylinders.finset", "kind": "definition", "module": "Mathlib.MeasureTheory.Constructions.ClosedCompactCylinders", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.closedCompactCylinders.set", "kind": "definition", "module": "Mathlib.MeasureTheory.Constructions.ClosedCompactCylinders", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.closedCompactCylinders.isClosed", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.ClosedCompactCylinders", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.closedCompactCylinders.isCompact", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.ClosedCompactCylinders", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.closedCompactCylinders.eq_cylinder", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.ClosedCompactCylinders", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.cylinder_mem_closedCompactCylinders", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.ClosedCompactCylinders", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.mem_measurableCylinders_of_mem_closedCompactCylinders", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.ClosedCompactCylinders", "is_tactic_proof": true, "tactics": ["rw", "refine", "exact", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.squareCylinders", "kind": "definition", "module": "Mathlib.MeasureTheory.Constructions.Cylinders", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.squareCylinders_eq_iUnion_image", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Cylinders", "is_tactic_proof": true, "tactics": ["ext1", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.isPiSystem_squareCylinders", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Cylinders", "is_tactic_proof": true, "tactics": ["rintro", "classical", "let", "let", "have", "have", "have", "have", "rw", "refine", "rw", "intro", "have", "obtain", "rw", "refine", "by_cases", "exact", "rw", "exact", "by_cases", "exact", "rw", "exact", "refine", "by_cases", "rw", "exact", "rw", "exact", "by_cases", "rw", "exact", "rw", "exact", "rw"], "tactic_count": 36}
{"name": "MeasureTheory.comap_eval_le_generateFrom_squareCylinders_singleton", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Cylinders", "is_tactic_proof": true, "tactics": ["simp", "rw", "refine", "simp", "intro", "classical", "refine", "by_cases", "simp", "convert", "simp", "simp", "grind"], "tactic_count": 13}
{"name": "MeasureTheory.generateFrom_squareCylinders", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Cylinders", "is_tactic_proof": true, "tactics": ["apply", "rw", "rintro", "simp", "exact", "refine", "refine", "refine", "rw", "exact", "subset_iUnion"], "tactic_count": 11}
{"name": "MeasureTheory.cylinder", "kind": "definition", "module": "Mathlib.MeasureTheory.Constructions.Cylinders", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.mem_cylinder", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Cylinders", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.cylinder_empty", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Cylinders", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.cylinder_univ", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Cylinders", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.cylinder_eq_empty_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Cylinders", "is_tactic_proof": true, "tactics": ["refine", "by_contra", "rw", "let", "have", "classical", "let", "have", "rw", "simpa", "rw", "exact"], "tactic_count": 12}
{"name": "MeasureTheory.inter_cylinder", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Cylinders", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.inter_cylinder_same", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Cylinders", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.union_cylinder", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Cylinders", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.union_cylinder_same", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Cylinders", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.compl_cylinder", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Cylinders", "is_tactic_proof": true, "tactics": ["ext1"], "tactic_count": 1}
{"name": "MeasureTheory.diff_cylinder_same", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Cylinders", "is_tactic_proof": true, "tactics": ["ext1"], "tactic_count": 1}
{"name": "MeasureTheory.eq_of_cylinder_eq_of_subset", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Cylinders", "is_tactic_proof": true, "tactics": ["rw", "simp", "ext1", "simp", "classical", "specialize", "have", "simpa"], "tactic_count": 8}
{"name": "MeasureTheory.cylinder_eq_cylinder_union", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Cylinders", "is_tactic_proof": true, "tactics": ["ext1"], "tactic_count": 1}
{"name": "MeasureTheory.disjoint_cylinder_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Cylinders", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MeasureTheory.IsClosed.cylinder", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Cylinders", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSet.cylinder", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Cylinders", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.dependsOn_cylinder_indicator_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Cylinders", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measurableCylinders", "kind": "definition", "module": "Mathlib.MeasureTheory.Constructions.Cylinders", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.empty_mem_measurableCylinders", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Cylinders", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.mem_measurableCylinders", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Cylinders", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MeasurableSet.of_mem_measurableCylinders", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Cylinders", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.measurableCylinders.finset", "kind": "definition", "module": "Mathlib.MeasureTheory.Constructions.Cylinders", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measurableCylinders.set", "kind": "definition", "module": "Mathlib.MeasureTheory.Constructions.Cylinders", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measurableCylinders.measurableSet", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Cylinders", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measurableCylinders.eq_cylinder", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Cylinders", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.cylinder_mem_measurableCylinders", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Cylinders", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.inter_mem_measurableCylinders", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Cylinders", "is_tactic_proof": true, "tactics": ["rw", "obtain", "obtain", "classical", "refine", "refine", "exact", "exact", "exact"], "tactic_count": 9}
{"name": "MeasureTheory.isPiSystem_measurableCylinders", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Cylinders", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.compl_mem_measurableCylinders", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Cylinders", "is_tactic_proof": true, "tactics": ["rw", "obtain", "refine", "rw"], "tactic_count": 4}
{"name": "MeasureTheory.univ_mem_measurableCylinders", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Cylinders", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.union_mem_measurableCylinders", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Cylinders", "is_tactic_proof": true, "tactics": ["rw", "exact", "compl_mem_measurableCylinders"], "tactic_count": 3}
{"name": "MeasureTheory.diff_mem_measurableCylinders", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Cylinders", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.generateFrom_measurableCylinders", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Cylinders", "is_tactic_proof": true, "tactics": ["apply", "refine", "obtain", "exact", "refine", "refine", "refine", "simp", "forall_exists_index,", "rintro", "refine", "ext1", "simp"], "tactic_count": 13}
{"name": "MeasureTheory.measurableCylinders_nat", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Cylinders", "is_tactic_proof": true, "tactics": ["ext", "simp", "refine", "rintro", "refine", "unfold", "rw", "exact"], "tactic_count": 8}
{"name": "MeasureTheory.cylinderEvents", "kind": "definition", "module": "Mathlib.MeasureTheory.Constructions.Cylinders", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.cylinderEvents_univ", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Cylinders", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.cylinderEvents_mono", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Cylinders", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.cylinderEvents_le_pi", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Cylinders", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.measurable_cylinderEvents_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Cylinders", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MeasureTheory.measurable_cylinderEvent_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Cylinders", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measurable.eval_cylinderEvents", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Cylinders", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measurable_cylinderEvents_lambda", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Cylinders", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measurable_update_cylinderEvents'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Cylinders", "is_tactic_proof": true, "tactics": ["rw", "intro", "dsimp", "split_ifs", "subst", "dsimp", "exact", "exact"], "tactic_count": 8}
{"name": "MeasureTheory.measurable_uniqueElim_cylinderEvents", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Cylinders", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MeasureTheory.measurable_update_cylinderEvents", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Cylinders", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measurable_update_cylinderEvents_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Cylinders", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measurable_restrict_cylinderEvents", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Cylinders", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "_private.Mathlib.MeasureTheory.Constructions.HaarToSphere.0.termDim", "kind": "definition", "module": "Mathlib.MeasureTheory.Constructions.HaarToSphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.MeasureTheory.Constructions.HaarToSphere.0._aux_Mathlib_MeasureTheory_Constructions_HaarToSphere___macroRules__private_Mathlib_MeasureTheory_Constructions_HaarToSphere_0_termDim_1", "kind": "definition", "module": "Mathlib.MeasureTheory.Constructions.HaarToSphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.MeasureTheory.Constructions.HaarToSphere.0._aux_Mathlib_MeasureTheory_Constructions_HaarToSphere___unexpand_Module_finrank_1", "kind": "definition", "module": "Mathlib.MeasureTheory.Constructions.HaarToSphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.toSphere", "kind": "definition", "module": "Mathlib.MeasureTheory.Constructions.HaarToSphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.toSphere_apply_aux", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.HaarToSphere", "is_tactic_proof": false, "tactics": ["rw", "image2_image_left,", "rfl"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.toSphere_apply'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.HaarToSphere", "is_tactic_proof": true, "tactics": ["rw", "image_comp,"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.toSphere_apply_univ'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.HaarToSphere", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.toSphere.instIsOpenPosMeasure", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.HaarToSphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.toSphere_apply_univ", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.HaarToSphere", "is_tactic_proof": true, "tactics": ["nontriviality", "rw"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.toSphere_real_apply_univ", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.HaarToSphere", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.toSphere_eq_zero_iff_finrank", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.HaarToSphere", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.toSphere_eq_zero_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.HaarToSphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.toSphere_ne_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.HaarToSphere", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.instIsFiniteMeasureElemSphereOfNatRealToSphere", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.HaarToSphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.volumeIoiPow", "kind": "definition", "module": "Mathlib.MeasureTheory.Constructions.HaarToSphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.volumeIoiPow_apply_Iio", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.HaarToSphere", "is_tactic_proof": true, "tactics": ["have", "rw", "setLIntegral_subtype", "restrict_congr_set", "integral_of_le", "simp", "filter_upwards", "exact"], "tactic_count": 8}
{"name": "MeasureTheory.Measure.finiteSpanningSetsIn_volumeIoiPow_range_Iio", "kind": "definition", "module": "Mathlib.MeasureTheory.Constructions.HaarToSphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.instSigmaFiniteElemRealIoiOfNatVolumeIoiPow", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.HaarToSphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.measurePreserving_homeomorphUnitSphereProd", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.HaarToSphere", "is_tactic_proof": true, "tactics": ["nontriviality", "refine", "refine", "prod_eq_generateFrom", "μ.toSphere.toFiniteSpanningSetsIn", "forall_mem_range.2", "have", "have", "rw", "comap_subtype_coe_apply", "μ.addHaar_smul_of_nonneg", "exacts"], "tactic_count": 12}
{"name": "_private.Mathlib.MeasureTheory.Constructions.HaarToSphere.0.MeasureTheory.Measure.ball_subset_sector_of_small_epsilon", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.HaarToSphere", "is_tactic_proof": true, "tactics": ["intro", "rw", "have", "abs_of_nonneg", "have", "rintro", "have", "linarith", "have", "calc", "simp", "set", "have", "refine", "rw", "have", "calc", "dist", "have", "have", "simpa", "linarith"], "tactic_count": 22}
{"name": "MeasureTheory.Measure.toSphereBallBound", "kind": "definition", "module": "Mathlib.MeasureTheory.Constructions.HaarToSphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.toSphereBallBound_pos", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.HaarToSphere", "is_tactic_proof": true, "tactics": ["unfold", "split_ifs", "cases", "positivity", "positivity"], "tactic_count": 5}
{"name": "MeasureTheory.Measure.toSphereBallBound_mul_measure_unitBall_le_toSphere_ball", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.HaarToSphere", "is_tactic_proof": true, "tactics": ["have", "wlog", "trans", "simpa", "gcongr", "simp", "rw", "grw", "have", "have", "simp", "mul_assoc,", "simp"], "tactic_count": 13}
{"name": "MeasureTheory.Measure.toSphereBallBound_mul_measureReal_unitBall_le_toSphere_ball", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.HaarToSphere", "is_tactic_proof": false, "tactics": ["grw", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.integrable_fun_norm_addHaar", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.HaarToSphere", "is_tactic_proof": false, "tactics": ["have", "μ.measurePreserving_homeomorphUnitSphereProd.integrable_comp_emb", "simp", "rw", "comp_def,", "comp_def,", "refine", "rintro", "simp", "fun_prop", "simp", "measurability", "simp"], "tactic_count": 13}
{"name": "MeasureTheory.integral_fun_norm_addHaar", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.HaarToSphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.piPremeasure", "kind": "definition", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.piPremeasure_pi", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.piPremeasure_pi'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": true, "tactics": ["cases", "simp", "rcases", "rcases", "have", "simpa", "piPremeasure]", "simp"], "tactic_count": 8}
{"name": "MeasureTheory.piPremeasure_pi_mono", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.piPremeasure_pi_eval", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.OuterMeasure.pi", "kind": "definition", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.pi_pi_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": true, "tactics": ["rcases", "simp", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.OuterMeasure.le_pi", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": true, "tactics": ["rw", "intro", "intro", "simp"], "tactic_count": 4}
{"name": "MeasureTheory.Measure.tprod", "kind": "definition", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.tprod_nil", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.tprod_cons", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.sigmaFinite_tprod", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.tprod_tprod", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "rw", "dsimp", "rw"], "tactic_count": 6}
{"name": "MeasureTheory.Measure.pi'", "kind": "definition", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.pi'_pi", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": true, "tactics": ["classical", "rw", "rw", "sortedUniv_toFinset]", "exact"], "tactic_count": 5}
{"name": "MeasureTheory.Measure.pi_caratheodory", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": true, "tactics": ["refine", "intro", "rw", "rcases", "apply", "intro", "simp_rw", "refine", "simp", "rintro", "rintro"], "tactic_count": 11}
{"name": "MeasureTheory.Measure.definition._@.Mathlib.MeasureTheory.Constructions.Pi.668077722._hygCtx._hyg.2", "kind": "definition", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.wrapped._@.Mathlib.MeasureTheory.Constructions.Pi.668077722._hygCtx._hyg.2", "kind": "opaque", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.pi", "kind": "definition", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.pi_def", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": true, "tactics": ["intros", "delta", "rw", "rfl"], "tactic_count": 4}
{"name": "MeasureTheory.MeasureSpace.pi", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.pi_pi_aux", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": true, "tactics": ["refine", "rw", "apply", "haveI", "simp_rw", "suffices", "clear", "rw", "intro", "exact"], "tactic_count": 10}
{"name": "MeasureTheory.Measure.FiniteSpanningSetsIn.pi", "kind": "definition", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": true, "tactics": ["haveI", "haveI", "refine", "let", "refine", "calc", "measure_mono", "simp_rw", "iUnion_univ_pi"], "tactic_count": 9}
{"name": "MeasureTheory.Measure.pi_eq_generateFrom", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": ["have", "exact", "refine", "rintro", "rw", "haveI", "simp_rw"], "tactic_count": 7}
{"name": "MeasureTheory.Measure.pi_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.pi'_eq_pi", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.pi_pi", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": true, "tactics": ["haveI", "rw"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.pi_univ", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.pi_singleton", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.pi.instIsFiniteMeasure", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.instIsFiniteMeasureForallVolume", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.pi.instIsProbabilityMeasure", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.instIsProbabilityMeasureForallVolume", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.pi_ball", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.pi_closedBall", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.pi.sigmaFinite", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.instSigmaFiniteForallVolume", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.pi_empty_univ", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.pi_eval_preimage_null", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": true, "tactics": ["classical", "rcases", "suffices", "rw", "apply", "simp"], "tactic_count": 6}
{"name": "MeasureTheory.Measure.quasiMeasurePreserving_eval", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": true, "tactics": ["classical", "refine", "rw"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.pi_map_eval", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": true, "tactics": ["ext", "classical", "rw", "smul_eq_mul,", "congrm", "swap", "refine", "simp"], "tactic_count": 8}
{"name": "MeasureTheory.Measure.pi_map_pi", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": true, "tactics": ["have", "refine", "rw", "swap", "exact", "have", "simp", "rw", "congr", "rw"], "tactic_count": 10}
{"name": "MeasureTheory.measurePreserving_eval", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": true, "tactics": ["refine", "classical", "rw", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.Measure.pi_hyperplane", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.ae_eval_ne", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.restrict_pi_pi", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": true, "tactics": ["refine", "simp_rw"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.tendsto_eval_ae_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.ae_pi_le_pi", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.ae_eq_pi", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.ae_le_pi", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.ae_le_set_pi", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.ae_eq_set_pi", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.pi_map_piCongrLeft", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": true, "tactics": ["let", "refine", "rw", "let", "have", "ext", "simp", "refine", "intro", "rw", "simpa"], "tactic_count": 11}
{"name": "MeasureTheory.Measure.pi_map_piOptionEquivProd", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": true, "tactics": ["refine", "let", "have", "have", "ext", "simp", "refine", "rcases", "simp"], "tactic_count": 9}
{"name": "MeasureTheory.Measure.pi_Iio_ae_eq_pi_Iic", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.pi_Ioi_ae_eq_pi_Ici", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.univ_pi_Iio_ae_eq_Iic", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.univ_pi_Ioi_ae_eq_Ici", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.pi_Ioo_ae_eq_pi_Icc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.pi_Ioo_ae_eq_pi_Ioc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.univ_pi_Ioo_ae_eq_Icc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.pi_Ioc_ae_eq_pi_Icc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.univ_pi_Ioc_ae_eq_Icc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.pi_Ico_ae_eq_pi_Icc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.univ_pi_Ico_ae_eq_Icc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.pi_noAtoms", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.pi_noAtoms'", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.instNoAtomsForallVolumeOfNonemptyOfSigmaFinite", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.pi.isLocallyFiniteMeasure", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": true, "tactics": ["refine", "choose", "refine", "rw", "exact"], "tactic_count": 5}
{"name": "MeasureTheory.Measure.instIsLocallyFiniteMeasureForallVolumeOfSigmaFinite", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUnifLocDoublingMeasure.pi", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": true, "tactics": ["use", "filter_upwards", "eventually_mem_nhdsWithin]", "simpa"], "tactic_count": 4}
{"name": "MeasureTheory.Measure.IsUnifLocDoublingMeasure.volume_pi", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.pi.isMulLeftInvariant", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": true, "tactics": ["refine", "rw", "show", "simp_rw"], "tactic_count": 4}
{"name": "MeasureTheory.Measure.instIsMulLeftInvariantForallVolumeOfMeasurableMulOfSigmaFinite", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.pi.isMulRightInvariant", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": true, "tactics": ["refine", "rw", "show", "simp_rw"], "tactic_count": 4}
{"name": "MeasureTheory.Measure.instIsMulRightInvariantForallVolumeOfMeasurableMulOfSigmaFinite", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.pi.isInvInvariant", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": true, "tactics": ["refine", "have", "simp_rw"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.instIsInvInvariantForallVolumeOfMeasurableInvOfSigmaFinite", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.pi.isOpenPosMeasure", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "obtain", "refine", "simp", "rw", "intro", "apply"], "tactic_count": 8}
{"name": "MeasureTheory.Measure.instIsOpenPosMeasureForallVolumeOfSigmaFinite", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.pi.isFiniteMeasureOnCompacts", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": true, "tactics": ["constructor", "intro", "suffices", "exact", "rw", "refine", "exact"], "tactic_count": 7}
{"name": "MeasureTheory.Measure.instIsFiniteMeasureOnCompactsForallVolumeOfSigmaFinite", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.pi.isHaarMeasure", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.instIsHaarMeasureForallVolumeOfMeasurableMulOfSigmaFinite", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.volume_pi", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.volume_pi_pi", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.volume_pi_ball", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.volume_pi_closedBall", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Pi.isMulLeftInvariant_volume", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Pi.isInvInvariant_volume", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measurePreserving_piEquivPiSubtypeProd", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": true, "tactics": ["set", "refine", "refine", "have", "rw", "exact"], "tactic_count": 6}
{"name": "MeasureTheory.volume_preserving_piEquivPiSubtypeProd", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measurePreserving_piCongrLeft", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.volume_measurePreserving_piCongrLeft", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measurePreserving_arrowProdEquivProdArrow", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.volume_measurePreserving_arrowProdEquivProdArrow", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measurePreserving_sumPiEquivProdPi_symm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.volume_measurePreserving_sumPiEquivProdPi_symm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measurePreserving_sumPiEquivProdPi", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.volume_measurePreserving_sumPiEquivProdPi", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measurePreserving_piFinSuccAbove", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": true, "tactics": ["set", "refine", "refine", "rw", "congr", "simp"], "tactic_count": 6}
{"name": "MeasureTheory.volume_preserving_piFinSuccAbove", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measurePreserving_piUnique", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.volume_preserving_piUnique", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measurePreserving_funUnique", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.volume_preserving_funUnique", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measurePreserving_piFinTwo", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": true, "tactics": ["refine", "rw", "rfl"], "tactic_count": 3}
{"name": "MeasureTheory.volume_preserving_piFinTwo", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measurePreserving_finTwoArrow_vec", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measurePreserving_finTwoArrow", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.volume_preserving_finTwoArrow", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measurePreserving_pi_empty", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": true, "tactics": ["set", "refine", "rw"], "tactic_count": 3}
{"name": "MeasureTheory.volume_preserving_pi_empty", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measurePreserving_piFinsetUnion", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.volume_preserving_piFinsetUnion", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measurePreserving_pi", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.volume_preserving_pi", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measurePreserving_arrowCongr'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": true, "tactics": ["classical", "convert", "simp"], "tactic_count": 3}
{"name": "MeasureTheory.volume_preserving_arrowCongr'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "upgradeStandardBorel", "kind": "definition", "module": "Mathlib.MeasureTheory.Constructions.Polish.Basic", "is_tactic_proof": true, "tactics": ["choose", "constructor"], "tactic_count": 2}
{"name": "eq_borel_upgradeStandardBorel", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Polish.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "standardBorel_of_polish", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.Polish.Basic", "is_tactic_proof": true, "tactics": ["exists"], "tactic_count": 1}
{"name": "standardBorelSpace_of_discreteMeasurableSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.Polish.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "countablyGenerated_of_standardBorel", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.Polish.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurableSingleton_of_standardBorel", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.Polish.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StandardBorelSpace.prod", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.Polish.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StandardBorelSpace.pi_countable", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.Polish.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.definition._@.Mathlib.MeasureTheory.Constructions.Polish.Basic.3011411360._hygCtx._hyg.2", "kind": "definition", "module": "Mathlib.MeasureTheory.Constructions.Polish.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.wrapped._@.Mathlib.MeasureTheory.Constructions.Polish.Basic.3011411360._hygCtx._hyg.2", "kind": "opaque", "module": "Mathlib.MeasureTheory.Constructions.Polish.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AnalyticSet", "kind": "definition", "module": "Mathlib.MeasureTheory.Constructions.Polish.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AnalyticSet_def", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Polish.Basic", "is_tactic_proof": true, "tactics": ["intros", "delta", "rw", "rfl"], "tactic_count": 4}
{"name": "MeasureTheory.analyticSet_empty", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Polish.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.analyticSet_range_of_polishSpace", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Polish.Basic", "is_tactic_proof": true, "tactics": ["cases", "rw", "exact", "rw", "obtain", "refine", "rw"], "tactic_count": 7}
{"name": "IsOpen.analyticSet_image", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Polish.Basic", "is_tactic_proof": true, "tactics": ["rw", "haveI", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.analyticSet_iff_exists_polishSpace_range", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Polish.Basic", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "rcases", "refine", "rw", "exact", "exact", "rintro", "rw", "exact"], "tactic_count": 11}
{"name": "MeasureTheory.AnalyticSet.image_of_continuousOn", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Polish.Basic", "is_tactic_proof": true, "tactics": ["rcases", "have", "rw", "apply", "apply", "rw", "exact"], "tactic_count": 7}
{"name": "MeasureTheory.AnalyticSet.image_of_continuous", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Polish.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AnalyticSet.iInter", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Polish.Basic", "is_tactic_proof": false, "tactics": ["rcases", "the", "choose", "let", "let", "have", "apply", "intro", "exact", "haveI", "let", "have", "have", "apply", "rintro", "refine", "have", "rw", "exact", "intro", "have", "intro", "rw", "exact", "choose", "have", "refine", "simp", "refine", "exact", "rw", "exact"], "tactic_count": 32}
{"name": "MeasureTheory.AnalyticSet.iUnion", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Polish.Basic", "is_tactic_proof": true, "tactics": ["coincides", "choose", "let", "let", "have", "have", "rw", "exact"], "tactic_count": 8}
{"name": "IsClosed.analyticSet", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Polish.Basic", "is_tactic_proof": true, "tactics": ["haveI", "rw", "exact"], "tactic_count": 3}
{"name": "MeasurableSet.isClopenable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Polish.Basic", "is_tactic_proof": true, "tactics": ["revert", "apply", "exact", "exact", "exact"], "tactic_count": 5}
{"name": "MeasurableSet.analyticSet", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Polish.Basic", "is_tactic_proof": true, "tactics": ["topology", "and", "obtain", "have", "convert", "simp"], "tactic_count": 6}
{"name": "Measurable.exists_continuous", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Polish.Basic", "is_tactic_proof": false, "tactics": ["obtain", "exists_countable_basis", "haveI", "have", "apply", "exact", "choose", "obtain", "exists_polishSpace_forall_le", "refine", "have", "exact"], "tactic_count": 12}
{"name": "MeasurableSet.analyticSet_image", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Polish.Basic", "is_tactic_proof": true, "tactics": ["letI", "rw", "rcases", "letI", "haveI", "have", "exact"], "tactic_count": 7}
{"name": "MeasureTheory.AnalyticSet.preimage", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Polish.Basic", "is_tactic_proof": true, "tactics": ["rcases", "have", "convert", "ext", "simp"], "tactic_count": 5}
{"name": "MeasureTheory.MeasurablySeparable", "kind": "definition", "module": "Mathlib.MeasureTheory.Constructions.Polish.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MeasurablySeparable.iUnion", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Polish.Basic", "is_tactic_proof": true, "tactics": ["choose", "refine", "refine", "exact", "simp_rw", "intro", "apply", "apply", "refine", "exact"], "tactic_count": 10}
{"name": "MeasureTheory.measurablySeparable_range_of_disjoint", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Polish.Basic", "is_tactic_proof": true, "tactics": ["images", "not", "points", "in", "and", "by_contra", "have", "x", "y", "intro", "contrapose", "intro", "rw", "refine", "exact", "let", "have", "rintro", "rcases", "exact", "choose", "let", "let", "have", "simp", "have", "induction", "zero", "succ", "simp", "have", "intro", "apply", "rfl", "intro", "have", "apply", "rw", "exact", "rw", "have", "intro", "apply", "rfl", "intro", "have", "apply", "rw", "exact", "rw", "set", "set", "have", "intro", "convert", "rw", "intro", "rw", "exact", "rw", "intro", "rw", "exact", "obtain", "apply", "exact", "letI", "obtain", "apply", "exact", "obtain", "apply", "exact", "obtain", "exists_pow_lt_of_lt_one", "have", "refine", "rw", "apply", "intro", "rw", "exact", "refine", "change", "rw", "apply", "intro", "rw", "exact", "hz.trans_lt", "exact"], "tactic_count": 91}
{"name": "MeasureTheory.AnalyticSet.measurablySeparable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Polish.Basic", "is_tactic_proof": true, "tactics": ["rw", "rcases", "refine", "rcases", "exact", "exact"], "tactic_count": 6}
{"name": "MeasureTheory.AnalyticSet.measurableSet_of_compl", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Polish.Basic", "is_tactic_proof": true, "tactics": ["rcases", "obtain", "exact"], "tactic_count": 3}
{"name": "Measurable.measurableSet_preimage_iff_of_surjective", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Polish.Basic", "is_tactic_proof": true, "tactics": ["refine", "rcases", "apply", "rw", "exact", "rw", "exact"], "tactic_count": 7}
{"name": "Measurable.map_measurableSpace_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Polish.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.map_measurableSpace_eq_borel", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Polish.Basic", "is_tactic_proof": true, "tactics": ["have", "letI", "exact"], "tactic_count": 3}
{"name": "Measurable.borelSpace_codomain", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Polish.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.measurableSet_preimage_iff_preimage_val", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Polish.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.measurableSet_preimage_iff_inter_range", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Polish.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Measurable.measurable_comp_iff_restrict", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Polish.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.measurable_comp_iff_of_surjective", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Polish.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.map_eq_borel", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Polish.Basic", "is_tactic_proof": true, "tactics": ["borelize", "exact"], "tactic_count": 2}
{"name": "Continuous.map_borel_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Polish.Basic", "is_tactic_proof": true, "tactics": ["borelize", "exact"], "tactic_count": 2}
{"name": "Quotient.borelSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.Polish.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CosetSpace.borelSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.Polish.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.borelSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.Polish.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measurableSet_range_of_continuous_injective", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Polish.Basic", "is_tactic_proof": true, "tactics": ["are", "measurable.", "is", "straightforward.", "to", "and", "separating", "the", "the", "contained", "contradiction", "letI", "obtain", "exists_countable_basis", "haveI", "let", "have", "intro", "apply", "exact", "choose", "let", "closure", "obtain", "exists_seq_strictAnti_tendsto", "let", "suffices", "have", "intro", "refine", "refine", "exact", "have", "intro", "refine", "exact", "rw", "exact", "apply", "rintro", "refine", "obtain", "apply", "exact", "have", "apply", "convert", "ring", "refine", "refine", "apply", "refine", "apply", "exact", "apply", "exact", "intro", "have", "simpa", "choose", "have", "intro", "rw", "grind", "choose", "have", "intro", "rw", "by_contra", "have", "haveI", "have", "haveI", "exact", "have", "have", "refine", "rcases", "calc", "dist", "haveI", "let", "have", "suffices", "rw", "exact", "mem_range_self", "by_contra", "obtain", "obtain", "apply", "exact", "obtain", "haveI", "simpa", "have", "rw", "apply", "intro", "calc", "dist", "have", "closure_mono", "exact"], "tactic_count": 104}
{"name": "IsClosed.measurableSet_image_of_continuousOn_injOn", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Polish.Basic", "is_tactic_proof": true, "tactics": ["rw", "haveI", "apply", "rwa", "rwa"], "tactic_count": 5}
{"name": "MeasurableSet.image_of_continuousOn_injOn", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Polish.Basic", "is_tactic_proof": false, "tactics": ["obtain", "exact", "f_inj"], "tactic_count": 3}
{"name": "MeasurableSet.image_of_measurable_injOn", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Polish.Basic", "is_tactic_proof": true, "tactics": ["letI", "let", "rcases", "obtain", "have", "exact"], "tactic_count": 6}
{"name": "Continuous.measurableEmbedding", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Polish.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.measurableEmbedding", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Polish.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.measurableEmbedding", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Polish.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.borel_eq_borel_of_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Polish.Basic", "is_tactic_proof": true, "tactics": ["refine", "intro", "have", "convert", "simp"], "tactic_count": 5}
{"name": "MeasureTheory.isClopenable_iff_measurableSet", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Polish.Basic", "is_tactic_proof": true, "tactics": ["refine", "borelize", "obtain", "rw", "exact", "infer_instance"], "tactic_count": 6}
{"name": "MeasurableSet.image_of_monotoneOn_of_continuousOn", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Polish.Basic", "is_tactic_proof": true, "tactics": ["many", "let", "have", "let", "have", "have", "rw", "apply", "obtain", "exact", "have", "rw", "apply", "apply", "intro", "contrapose", "wlog", "have", "exact", "intro", "exact", "exact"], "tactic_count": 22}
{"name": "MeasurableSet.image_of_monotoneOn", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Polish.Basic", "is_tactic_proof": true, "tactics": ["the", "let", "have", "have", "rw", "congr", "ext", "simp", "tauto", "rw", "apply", "apply", "intro", "simp", "exact"], "tactic_count": 15}
{"name": "MeasurableSet.image_of_antitoneOn", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Polish.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measurableSet_tendsto_fun", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Polish.Basic", "is_tactic_proof": true, "tactics": ["letI", "simp_rw", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.measurableSet_exists_tendsto", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Polish.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simp", "letI", "rcases", "simp_rw", "change", "have", "simp_rw", "refine", "simp_rw", "refine", "simp_rw", "exact", "measurableSet_lt"], "tactic_count": 14}
{"name": "MeasurableSet.isClopenable'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Polish.Basic", "is_tactic_proof": true, "tactics": ["letI", "obtain", "refine", "constructor", "rw", "infer_instance"], "tactic_count": 6}
{"name": "MeasurableSet.standardBorel", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Polish.Basic", "is_tactic_proof": true, "tactics": ["obtain", "haveI", "infer_instance"], "tactic_count": 3}
{"name": "PolishSpace.borelSchroederBernstein", "kind": "definition", "module": "Mathlib.MeasureTheory.Constructions.Polish.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PolishSpace.measurableEquivNatBoolOfNotCountable", "kind": "definition", "module": "Mathlib.MeasureTheory.Constructions.Polish.Basic", "is_tactic_proof": true, "tactics": ["apply", "letI", "obtain", "isClosed_univ.exists_nat_bool_injection_of_not_countable", "obtain", "exact"], "tactic_count": 6}
{"name": "PolishSpace.measurableEquivOfNotCountable", "kind": "definition", "module": "Mathlib.MeasureTheory.Constructions.Polish.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PolishSpace.Equiv.measurableEquiv", "kind": "definition", "module": "Mathlib.MeasureTheory.Constructions.Polish.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "letI", "refine", "refine", "rwa"], "tactic_count": 5}
{"name": "MeasureTheory.exists_nat_measurableEquiv_range_coe_fin_of_finite", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Polish.EmbeddingReal", "is_tactic_proof": true, "tactics": ["obtain", "refine", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.measurableEquiv_range_coe_nat_of_infinite_of_countable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Polish.EmbeddingReal", "is_tactic_proof": false, "tactics": ["have", "refine", "refine", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.exists_subset_real_measurableEquiv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Polish.EmbeddingReal", "is_tactic_proof": true, "tactics": ["by_cases", "cases", "obtain", "refine", "letI", "haveI", "apply", "exact", "refine", "apply", "exact", "refine", "rw", "exact"], "tactic_count": 14}
{"name": "MeasureTheory.exists_measurableEmbedding_real", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Polish.EmbeddingReal", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.embeddingReal", "kind": "definition", "module": "Mathlib.MeasureTheory.Constructions.Polish.EmbeddingReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measurableEmbedding_embeddingReal", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Polish.EmbeddingReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measurable_embeddingReal", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Polish.EmbeddingReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.StronglyMeasurable.measurableSet_exists_tendsto", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Polish.StronglyMeasurable", "is_tactic_proof": true, "tactics": ["obtain", "simp_all", "borelize", "letI", "let", "have", "toIsCompletelyMetrizableSpace", "let", "have", "convert", "refine", "exact"], "tactic_count": 12}
{"name": "MeasureTheory.StronglyMeasurable.limUnder", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Polish.StronglyMeasurable", "is_tactic_proof": true, "tactics": ["obtain", "simpa", "borelize", "let", "rw", "let", "have", "have", "ext", "by_cases", "rw", "rw", "rw", "refine", "measurable_const", "rwa", "let", "have", "refine", "rintro", "by_cases", "obtain", "simp_rw", "exact", "simp_rw", "exact"], "tactic_count": 26}
{"name": "MeasureTheory.IsProjectiveMeasureFamily", "kind": "definition", "module": "Mathlib.MeasureTheory.Constructions.Projective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IsProjectiveMeasureFamily.eq_zero_of_isEmpty", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Projective", "is_tactic_proof": true, "tactics": ["classical", "obtain", "rw", "have", "rw", "simp"], "tactic_count": 6}
{"name": "MeasureTheory.IsProjectiveMeasureFamily.measure_univ_eq_of_subset", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Projective", "is_tactic_proof": true, "tactics": ["classical", "have", "rw", "rw", "exact"], "tactic_count": 5}
{"name": "MeasureTheory.IsProjectiveMeasureFamily.measure_univ_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Projective", "is_tactic_proof": true, "tactics": ["classical", "rw", "hP.measure_univ_eq_of_subset"], "tactic_count": 3}
{"name": "MeasureTheory.IsProjectiveMeasureFamily.congr_cylinder_of_subset", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Projective", "is_tactic_proof": true, "tactics": ["cases", "inl", "h", "suffices", "simp", "simp", "intro", "simp", "obtain", "rw", "have", "simp", "inr", "have", "rw", "exact"], "tactic_count": 16}
{"name": "MeasureTheory.IsProjectiveMeasureFamily.congr_cylinder", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Projective", "is_tactic_proof": true, "tactics": ["classical", "let", "suffices", "constructor", "have", "exact", "have", "exact"], "tactic_count": 8}
{"name": "MeasureTheory.IsProjectiveLimit", "kind": "definition", "module": "Mathlib.MeasureTheory.Constructions.Projective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IsProjectiveLimit.measure_cylinder", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Projective", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.IsProjectiveLimit.measure_univ_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Projective", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.IsProjectiveLimit.isFiniteMeasure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Projective", "is_tactic_proof": true, "tactics": ["constructor", "rw", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.IsProjectiveLimit.isProbabilityMeasure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Projective", "is_tactic_proof": true, "tactics": ["constructor", "rw", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.IsProjectiveLimit.measure_univ_unique", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Projective", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.IsProjectiveLimit.unique", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.Projective", "is_tactic_proof": true, "tactics": ["haveI", "refine", "ext_of_generate_finite", "obtain", "rw"], "tactic_count": 5}
{"name": "MeasureTheory.isSetAlgebra_measurableCylinders", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.ProjectiveFamilyContent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.isSetRing_measurableCylinders", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.ProjectiveFamilyContent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.isSetSemiring_measurableCylinders", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.ProjectiveFamilyContent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.projectiveFamilyFun", "kind": "definition", "module": "Mathlib.MeasureTheory.Constructions.ProjectiveFamilyContent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.projectiveFamilyFun_congr", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.ProjectiveFamilyContent", "is_tactic_proof": true, "tactics": ["rw", "exact", "hP.congr_cylinder"], "tactic_count": 3}
{"name": "MeasureTheory.projectiveFamilyFun_empty", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.ProjectiveFamilyContent", "is_tactic_proof": true, "tactics": ["rw", "measure_empty]"], "tactic_count": 2}
{"name": "MeasureTheory.projectiveFamilyFun_union", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.ProjectiveFamilyContent", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "classical", "let", "let", "have", "have", "have", "have", "have", "rw", "projectiveFamilyFun_congr", "cases", "inl", "inr", "rw", "rwa"], "tactic_count": 17}
{"name": "MeasureTheory.projectiveFamilyContent", "kind": "definition", "module": "Mathlib.MeasureTheory.Constructions.ProjectiveFamilyContent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.projectiveFamilyContent_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.ProjectiveFamilyContent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.projectiveFamilyContent_congr", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.ProjectiveFamilyContent", "is_tactic_proof": true, "tactics": ["rw", "projectiveFamilyFun_congr"], "tactic_count": 2}
{"name": "MeasureTheory.projectiveFamilyContent_cylinder", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.ProjectiveFamilyContent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.projectiveFamilyContent_mono", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.ProjectiveFamilyContent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.projectiveFamilyContent_iUnion_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.ProjectiveFamilyContent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.projectiveFamilyContent_ne_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.ProjectiveFamilyContent", "is_tactic_proof": true, "tactics": ["rw", "finiteness"], "tactic_count": 2}
{"name": "MeasureTheory.projectiveFamilyContent_diff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.ProjectiveFamilyContent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.projectiveFamilyContent_diff_of_subset", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.ProjectiveFamilyContent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.Quotient.instMeasurableSpaceQuotient", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.SubmoduleQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.Quotient.instDiscreteMeasurableSpaceQuotient", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.SubmoduleQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.instMeasureSpaceElemReal", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.volume_def", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.instIsProbabilityMeasureElemRealVolume", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.measurableEmbedding_coe", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.volume_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.measurePreserving_coe", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.instNoAtomsElemRealVolume", "kind": "instance", "module": "Mathlib.MeasureTheory.Constructions.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.measurable_symm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.symmMeasurableEquiv", "kind": "definition", "module": "Mathlib.MeasureTheory.Constructions.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.symm_symmMeasurableEquiv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.coe_symmMeasurableEquiv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.measurePreserving_symm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.volume_Iic", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.UnitInterval", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "unitInterval.volume_Iio", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.UnitInterval", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "unitInterval.volume_Ici", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.UnitInterval", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "unitInterval.volume_Ioi", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.UnitInterval", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "unitInterval.volume_Icc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.UnitInterval", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "unitInterval.volume_uIcc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.UnitInterval", "is_tactic_proof": true, "tactics": ["simp", "edist_dist,"], "tactic_count": 2}
{"name": "unitInterval.volume_Ico", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.UnitInterval", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "unitInterval.volume_Ioc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.UnitInterval", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "unitInterval.volume_uIoc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.UnitInterval", "is_tactic_proof": true, "tactics": ["simp", "edist_dist,"], "tactic_count": 2}
{"name": "unitInterval.volume_Ioo", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.UnitInterval", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "unitInterval.volume_uIoo", "kind": "theorem", "module": "Mathlib.MeasureTheory.Constructions.UnitInterval", "is_tactic_proof": true, "tactics": ["simp", "edist_dist,"], "tactic_count": 2}
{"name": "Mathlib.Meta.Positivity.evalBesicovitchSatelliteConfigR", "kind": "definition", "module": "Mathlib.MeasureTheory.Covering.Besicovitch", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Besicovitch.SatelliteConfig.instInhabited", "kind": "instance", "module": "Mathlib.MeasureTheory.Covering.Besicovitch", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Besicovitch.SatelliteConfig.inter'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Covering.Besicovitch", "is_tactic_proof": true, "tactics": ["rcases", "exact", "have", "have", "simp"], "tactic_count": 5}
{"name": "Besicovitch.SatelliteConfig.hlast'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Covering.Besicovitch", "is_tactic_proof": true, "tactics": ["rcases", "exact", "have", "rw", "exact"], "tactic_count": 5}
{"name": "Besicovitch.unitBallPackage", "kind": "definition", "module": "Mathlib.MeasureTheory.Covering.Besicovitch", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Besicovitch.TauPackage.instInhabited", "kind": "instance", "module": "Mathlib.MeasureTheory.Covering.Besicovitch", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "VitaliFamily.limRatioMeas_measurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Covering.Differentiation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VitaliFamily.ae_tendsto_limRatioMeas", "kind": "theorem", "module": "Mathlib.MeasureTheory.Covering.Differentiation", "is_tactic_proof": true, "tactics": ["filter_upwards", "intro", "rwa"], "tactic_count": 3}
{"name": "VitaliFamily.measure_le_mul_of_subset_limRatioMeas_lt", "kind": "theorem", "module": "Mathlib.MeasureTheory.Covering.Differentiation", "is_tactic_proof": true, "tactics": ["let", "have", "suffices", "calc", "ρ", "refine", "have", "apply", "rw", "refine", "simp"], "tactic_count": 11}
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{"name": "VitaliFamily.measure_limRatioMeas_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Covering.Differentiation", "is_tactic_proof": true, "tactics": ["refine", "obtain", "let", "refine", "have", "have", "intro", "rw", "apply", "intro", "have", "simp", "simp", "have", "apply", "exact", "simp", "apply", "exact"], "tactic_count": 19}
{"name": "VitaliFamily.measure_limRatioMeas_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Covering.Differentiation", "is_tactic_proof": true, "tactics": ["refine", "obtain", "let", "refine", "have", "have", "intro", "apply", "intro", "have", "simp", "have", "apply", "rw", "exact", "simp", "apply", "filter_upwards"], "tactic_count": 18}
{"name": "VitaliFamily.withDensity_le_mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Covering.Differentiation", "is_tactic_proof": true, "tactics": ["show", "strict", "have", "have", "let", "let", "have", "have", "apply", "have", "simp", "apply", "exact", "have", "apply", "apply", "rw", "exact", "have", "ν", "intro", "let", "have", "simp", "calc", "lintegral_mono_ae", "simp", "rw", "congr", "abel", "gcongr", "rw", "apply", "intro", "apply", "rw", "conv_rhs", "gcongr", "rw", "exact", "calc", "ν", "measure_eq_measure_preimage_add_measure_tsum_Ico_zpow"], "tactic_count": 43}
{"name": "VitaliFamily.le_mul_withDensity", "kind": "theorem", "module": "Mathlib.MeasureTheory.Covering.Differentiation", "is_tactic_proof": true, "tactics": ["show", "have", "have", "let", "let", "have", "have", "refine", "exact", "have", "apply", "apply", "rw", "exact", "have", "ρ", "intro", "let", "have", "simp", "calc", "ρ", "rw", "apply", "intro", "apply", "rw", "simp", "apply", "grw", "calc", "ρ", "measure_eq_measure_preimage_add_measure_tsum_Ico_zpow"], "tactic_count": 33}
{"name": "VitaliFamily.withDensity_limRatioMeas_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Covering.Differentiation", "is_tactic_proof": true, "tactics": ["ext1", "refine", "have", "refine", "exact", "simp", "simp", "simp", "refine", "filter_upwards", "exact", "have", "refine", "simp", "simp", "refine", "filter_upwards", "exact"], "tactic_count": 18}
{"name": "VitaliFamily.ae_tendsto_rnDeriv_of_absolutelyContinuous", "kind": "theorem", "module": "Mathlib.MeasureTheory.Covering.Differentiation", "is_tactic_proof": false, "tactics": ["have", "rnDeriv_withDensity", "rw", "filter_upwards", "rwa"], "tactic_count": 5}
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{"name": "VitaliFamily.ae_tendsto_measure_inter_div_of_measurableSet", "kind": "theorem", "module": "Mathlib.MeasureTheory.Covering.Differentiation", "is_tactic_proof": true, "tactics": ["haveI", "filter_upwards", "intro", "simpa"], "tactic_count": 4}
{"name": "VitaliFamily.ae_tendsto_measure_inter_div", "kind": "theorem", "module": "Mathlib.MeasureTheory.Covering.Differentiation", "is_tactic_proof": true, "tactics": ["let", "have", "apply", "apply", "exact", "have", "refine", "filter_upwards", "simp", "filter_upwards", "rw", "apply", "filter_upwards", "congr", "exact"], "tactic_count": 15}
{"name": "VitaliFamily.ae_tendsto_lintegral_div'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Covering.Differentiation", "is_tactic_proof": true, "tactics": ["let", "have", "filter_upwards", "rw", "apply", "filter_upwards", "rw"], "tactic_count": 7}
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{"name": "VitaliFamily.ae_tendsto_lintegral_enorm_sub_div'_of_integrable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Covering.Differentiation", "is_tactic_proof": true, "tactics": ["desired", "lemmas", "above", "let", "rcases", "have", "simp_rw", "intro", "apply", "refine", "exact", "apply", "calc", "lintegral_mono", "haveI", "simp", "filter_upwards", "have", "obtain", "specialize", "simp", "apply", "filter_upwards", "v.eventually_filterAt_measurableSet", "congr", "apply", "simp", "apply", "obtain", "simp_rw", "have", "exact", "filter_upwards", "apply", "calc", "apply", "simpa", "gcongr", "rw", "exact", "simp", "gcongr"], "tactic_count": 42}
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{"name": "VitaliFamily.ae_tendsto_average_norm_sub", "kind": "theorem", "module": "Mathlib.MeasureTheory.Covering.Differentiation", "is_tactic_proof": true, "tactics": ["filter_upwards", "have", "simp", "apply", "filter_upwards", "simp", "have", "simp_rw", "exact", "dsimp", "rw", "simp"], "tactic_count": 12}
{"name": "VitaliFamily.ae_tendsto_average", "kind": "theorem", "module": "Mathlib.MeasureTheory.Covering.Differentiation", "is_tactic_proof": true, "tactics": ["filter_upwards", "rw", "refine", "filter_upwards", "nth_rw", "simp_rw", "rw", "exact", "exact", "exact"], "tactic_count": 10}
{"name": "blimsup_cthickening_ae_le_of_eventually_mul_le_aux", "kind": "theorem", "module": "Mathlib.MeasureTheory.Covering.LiminfLimsup", "is_tactic_proof": true, "tactics": ["showing", "density", "since", "is", "measure", "sets", "since", "the", "set", "set", "let", "suffices", "rwa", "intro", "set", "by_contra", "obtain", "d", "replace", "obtain", "simp", "obtain", "have", "tendsto_atTop_atTop.mpr", "replace", "replace", "replace", "intro", "specialize", "rw", "rcases", "specialize", "rw", "exact", "simpa", "mem_iUnion₂.mp", "choose", "let", "have", "suffices", "obtain", "replace", "simpa", "le_of_tendsto", "exact", "refine", "replace", "let", "let", "have", "have", "have", "apply", "rw", "refine", "change", "rw", "refine", "simp", "exact", "have", "hj", "refine", "change", "rcases", "apply", "rw", "replace", "obtain", "replace", "rw", "exact", "have", "grw", "rw", "grw", "replace", "rwa"], "tactic_count": 78}
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{"name": "Real.Icc_mem_vitaliFamily_at_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Covering.OneDim", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw"], "tactic_count": 3}
{"name": "Real.tendsto_Icc_vitaliFamily_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Covering.OneDim", "is_tactic_proof": true, "tactics": ["refine", "filter_upwards", "intro", "filter_upwards", "rw", "exact"], "tactic_count": 6}
{"name": "Real.Icc_mem_vitaliFamily_at_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Covering.OneDim", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw"], "tactic_count": 3}
{"name": "Real.tendsto_Icc_vitaliFamily_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Covering.OneDim", "is_tactic_proof": true, "tactics": ["refine", "filter_upwards", "intro", "filter_upwards", "rw", "exact"], "tactic_count": 6}
{"name": "Vitali.exists_disjoint_subfamily_covering_enlargement", "kind": "theorem", "module": "Mathlib.MeasureTheory.Covering.Vitali", "is_tactic_proof": true, "tactics": ["as", "the", "there", "intersects", "family", "intersect", "that", "intersects", "let", "u", "u.PairwiseDisjoint", "obtain", "refine", "refine", "simp", "refine", "obtain", "exact", "refine", "by_contra", "have", "intro", "by_contra", "rw", "obtain", "exact", "lt_irrefl", "let", "have", "let", "have", "refine", "rcases", "exact", "obtain", "have", "rcases", "refine", "simpa", "have", "rw", "conv_lhs", "gcongr", "rcases", "rcases", "exact", "clear", "have", "refine", "rw", "exact", "exact", "intro", "by_cases", "rcases", "rcases", "exact", "simp", "rcases", "refine", "calc", "δ", "rw", "exact"], "tactic_count": 64}
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{"name": "Vitali.vitaliFamily", "kind": "definition", "module": "Mathlib.MeasureTheory.Covering.Vitali", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VitaliFamily.mono", "kind": "definition", "module": "Mathlib.MeasureTheory.Covering.VitaliFamily", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VitaliFamily.FineSubfamilyOn", "kind": "definition", "module": "Mathlib.MeasureTheory.Covering.VitaliFamily", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VitaliFamily.FineSubfamilyOn.exists_disjoint_covering_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Covering.VitaliFamily", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "VitaliFamily.FineSubfamilyOn.covering", "kind": "definition", "module": "Mathlib.MeasureTheory.Covering.VitaliFamily", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VitaliFamily.FineSubfamilyOn.index_subset", "kind": "theorem", "module": "Mathlib.MeasureTheory.Covering.VitaliFamily", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VitaliFamily.FineSubfamilyOn.covering_disjoint", "kind": "theorem", "module": "Mathlib.MeasureTheory.Covering.VitaliFamily", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VitaliFamily.FineSubfamilyOn.covering_disjoint_subtype", "kind": "theorem", "module": "Mathlib.MeasureTheory.Covering.VitaliFamily", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VitaliFamily.FineSubfamilyOn.covering_mem", "kind": "theorem", "module": "Mathlib.MeasureTheory.Covering.VitaliFamily", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VitaliFamily.FineSubfamilyOn.covering_mem_family", "kind": "theorem", "module": "Mathlib.MeasureTheory.Covering.VitaliFamily", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VitaliFamily.FineSubfamilyOn.measure_diff_biUnion", "kind": "theorem", "module": "Mathlib.MeasureTheory.Covering.VitaliFamily", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VitaliFamily.FineSubfamilyOn.index_countable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Covering.VitaliFamily", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VitaliFamily.FineSubfamilyOn.measurableSet_u", "kind": "theorem", "module": "Mathlib.MeasureTheory.Covering.VitaliFamily", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VitaliFamily.FineSubfamilyOn.measure_le_tsum_of_absolutelyContinuous", "kind": "theorem", "module": "Mathlib.MeasureTheory.Covering.VitaliFamily", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VitaliFamily.FineSubfamilyOn.measure_le_tsum", "kind": "theorem", "module": "Mathlib.MeasureTheory.Covering.VitaliFamily", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VitaliFamily.enlarge", "kind": "definition", "module": "Mathlib.MeasureTheory.Covering.VitaliFamily", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VitaliFamily.filterAt", "kind": "definition", "module": "Mathlib.MeasureTheory.Covering.VitaliFamily", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.vitaliFamily", "kind": "theorem", "module": "Mathlib.MeasureTheory.Covering.VitaliFamily", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "VitaliFamily.filterAt_basis_closedBall", "kind": "theorem", "module": "Mathlib.MeasureTheory.Covering.VitaliFamily", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VitaliFamily.mem_filterAt_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Covering.VitaliFamily", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "VitaliFamily.filterAt_neBot", "kind": "instance", "module": "Mathlib.MeasureTheory.Covering.VitaliFamily", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VitaliFamily.eventually_filterAt_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Covering.VitaliFamily", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VitaliFamily.tendsto_filterAt_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Covering.VitaliFamily", "is_tactic_proof": true, "tactics": ["simp", "mem_powerset_iff]"], "tactic_count": 2}
{"name": "VitaliFamily.eventually_filterAt_mem_setsAt", "kind": "theorem", "module": "Mathlib.MeasureTheory.Covering.VitaliFamily", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VitaliFamily.eventually_filterAt_subset_closedBall", "kind": "theorem", "module": "Mathlib.MeasureTheory.Covering.VitaliFamily", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VitaliFamily.eventually_filterAt_measurableSet", "kind": "theorem", "module": "Mathlib.MeasureTheory.Covering.VitaliFamily", "is_tactic_proof": true, "tactics": ["filter_upwards"], "tactic_count": 1}
{"name": "VitaliFamily.frequently_filterAt_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Covering.VitaliFamily", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "VitaliFamily.eventually_filterAt_subset_of_nhds", "kind": "theorem", "module": "Mathlib.MeasureTheory.Covering.VitaliFamily", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VitaliFamily.filterAt_enlarge", "kind": "theorem", "module": "Mathlib.MeasureTheory.Covering.VitaliFamily", "is_tactic_proof": true, "tactics": ["ext1", "suffices", "simpa", "filter_upwards", "simp"], "tactic_count": 5}
{"name": "VitaliFamily.fineSubfamilyOn_iff_frequently", "kind": "theorem", "module": "Mathlib.MeasureTheory.Covering.VitaliFamily", "is_tactic_proof": true, "tactics": ["refine", "simp"], "tactic_count": 2}
{"name": "VitaliFamily.fineSubfamilyOn_of_frequently", "kind": "theorem", "module": "Mathlib.MeasureTheory.Covering.VitaliFamily", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.aeEqSetoid", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.AEEqFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEEqFun", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.AEEqFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.term_→ₘ[_]_", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.AEEqFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory._aux_Mathlib_MeasureTheory_Function_AEEqFun___macroRules_MeasureTheory_term_→ₘ[_]__1", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.AEEqFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory._aux_Mathlib_MeasureTheory_Function_AEEqFun___unexpand_MeasureTheory_AEEqFun_1", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.AEEqFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasureTheory.AEEqFun.cast", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.AEEqFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEEqFun.instCoeFun", "kind": "instance", "module": "Mathlib.MeasureTheory.Function.AEEqFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEEqFun.stronglyMeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.AEEqFun", "is_tactic_proof": true, "tactics": ["simp", "split_ifs", "exact", "apply"], "tactic_count": 4}
{"name": "MeasureTheory.AEEqFun.aestronglyMeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.AEEqFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ContinuousMap.toAEEqFunLinearMap", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.AEEqFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "DomMulAct.smul_aeeqFun_aeeq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.AEEqFun.DomAct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.mk_smul_mk_aeeqFun", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.AEEqFun.DomAct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.smul_aeeqFun_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.AEEqFun.DomAct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "aeSeq.aeSeq_eq_fun_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.AEMeasurableSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "aeSeq.aeSeq_n_eq_fun_n_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.AEMeasurableSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "aeSeq.iInf", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.AEMeasurableSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AbsolutelyContinuousOnInterval.totalLengthFilter", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.AbsolutelyContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AbsolutelyContinuousOnInterval.hasBasis_totalLengthFilter", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.AbsolutelyContinuous", "is_tactic_proof": true, "tactics": ["convert", "ext", "simp", "suffices", "exact"], "tactic_count": 5}
{"name": "AbsolutelyContinuousOnInterval.disjWithin", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.AbsolutelyContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AbsolutelyContinuousOnInterval.disjWithin_comm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.AbsolutelyContinuous", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AbsolutelyContinuousOnInterval.disjWithin_mono", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.AbsolutelyContinuous", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "AbsolutelyContinuousOnInterval.uIoc_subset_of_mem_disjWithin", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.AbsolutelyContinuous", "is_tactic_proof": true, "tactics": ["simp", "have", "dsimp", "simp", "simp"], "tactic_count": 5}
{"name": "AbsolutelyContinuousOnInterval.biUnion_uIoc_subset_of_mem_disjWithin", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.AbsolutelyContinuous", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "AbsolutelyContinuousOnInterval.tendsto_volume_totalLengthFilter_nhds_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.AbsolutelyContinuous", "is_tactic_proof": false, "tactics": ["apply", "tendsto_of_tendsto_of_tendsto_of_le_of_le", "convert", "simp", "intro", "intro", "simp", "grw", "rw", "apply", "apply", "simp"], "tactic_count": 12}
{"name": "AbsolutelyContinuousOnInterval.tendsto_volume_restrict_totalLengthFilter_disjWithin_nhds_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.AbsolutelyContinuous", "is_tactic_proof": false, "tactics": ["apply", "tendsto_of_tendsto_of_tendsto_of_le_of_le", "volume", "apply", "simp", "intro", "intro", "simp", "apply"], "tactic_count": 9}
{"name": "AbsolutelyContinuousOnInterval", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.AbsolutelyContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "absolutelyContinuousOnInterval_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.AbsolutelyContinuous", "is_tactic_proof": true, "tactics": ["simp", "abs_of_nonneg"], "tactic_count": 2}
{"name": "AbsolutelyContinuousOnInterval.symm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.AbsolutelyContinuous", "is_tactic_proof": true, "tactics": ["simp_all"], "tactic_count": 1}
{"name": "AbsolutelyContinuousOnInterval.mono", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.AbsolutelyContinuous", "is_tactic_proof": true, "tactics": ["simp", "refine", "gcongr"], "tactic_count": 3}
{"name": "AbsolutelyContinuousOnInterval.add", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.AbsolutelyContinuous", "is_tactic_proof": true, "tactics": ["apply", "exact", "rw", "gcongr", "exact"], "tactic_count": 5}
{"name": "AbsolutelyContinuousOnInterval.neg", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.AbsolutelyContinuous", "is_tactic_proof": true, "tactics": ["apply", "exact", "simp"], "tactic_count": 3}
{"name": "AbsolutelyContinuousOnInterval.sub", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.AbsolutelyContinuous", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "AbsolutelyContinuousOnInterval.const_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.AbsolutelyContinuous", "is_tactic_proof": true, "tactics": ["apply", "exact", "simp"], "tactic_count": 3}
{"name": "AbsolutelyContinuousOnInterval.const_mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.AbsolutelyContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AbsolutelyContinuousOnInterval.uniformity_eq_comap_totalLengthFilter", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.AbsolutelyContinuous", "is_tactic_proof": true, "tactics": ["refine", "convert", "simp"], "tactic_count": 3}
{"name": "AbsolutelyContinuousOnInterval.uniformlyContinuousOn", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.AbsolutelyContinuous", "is_tactic_proof": true, "tactics": ["simp", "simp", "convert", "simp", "congr", "ext", "simp", "simp", "simp"], "tactic_count": 9}
{"name": "AbsolutelyContinuousOnInterval.continuousOn", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.AbsolutelyContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AbsolutelyContinuousOnInterval.exists_bound", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.AbsolutelyContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AbsolutelyContinuousOnInterval.mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.AbsolutelyContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzOnWith.absolutelyContinuousOnInterval", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.AbsolutelyContinuous", "is_tactic_proof": true, "tactics": ["rw", "intro", "refine", "calc", "apply", "intro", "have", "apply", "rwa"], "tactic_count": 9}
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{"name": "AbsolutelyContinuousOnInterval.ae_differentiableAt", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.AbsolutelyContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntervalIntegrable.absolutelyContinuousOnInterval_intervalIntegral", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.AbsolutelyContinuous", "is_tactic_proof": true, "tactics": ["let", "have", "tendsto_setLIntegral_zero", "have", "refine", "filter_upwards", "exact", "simp", "have", "eventually_inf_principal.mpr", "filter_upwards", "obtain", "simp", "rw", "integral_biUnion_finset", "refine", "rw", "intervalIntegral.integral_interval_sub_left", "intervalIntegral.integral_symm,", "exact", "intro", "unfold", "have", "rw", "exact"], "tactic_count": 25}
{"name": "MeasureTheory.ae_eq_trim_iff_of_aestronglyMeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.AEMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEStronglyMeasurable.comp_ae_measurable'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.AEMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.lpMeasSubgroup", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.AEMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.lpMeas", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.AEMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.mem_lpMeasSubgroup_iff_aestronglyMeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.AEMeasurable", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.mem_lpMeas_iff_aestronglyMeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.AEMeasurable", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.lpMeas.aestronglyMeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.AEMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.mem_lpMeas_self", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.AEMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.mem_lpMeas_indicatorConstLp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.AEMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.memLp_trim_of_mem_lpMeasSubgroup", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.AEMeasurable", "is_tactic_proof": true, "tactics": ["have", "let", "obtain", "change", "refine", "have", "rw", "exact", "rw", "exact"], "tactic_count": 10}
{"name": "MeasureTheory.mem_lpMeasSubgroup_toLp_of_trim", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.AEMeasurable", "is_tactic_proof": true, "tactics": ["let", "rw", "refine", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.lpMeasSubgroupToLpTrim", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.AEMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.lpMeasToLpTrim", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.AEMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.lpTrimToLpMeasSubgroup", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.AEMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.lpTrimToLpMeas", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.AEMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.lpMeasSubgroupToLpTrim_ae_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.AEMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.lpTrimToLpMeasSubgroup_ae_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.AEMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.lpMeasToLpTrim_ae_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.AEMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.lpTrimToLpMeas_ae_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.AEMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.lpMeasSubgroupToLpTrim_right_inv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.AEMeasurable", "is_tactic_proof": true, "tactics": ["intro", "ext1", "refine", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.lpMeasSubgroupToLpTrim_left_inv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.AEMeasurable", "is_tactic_proof": true, "tactics": ["intro", "ext1", "ext1", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.lpMeasSubgroupToLpTrim_add", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.AEMeasurable", "is_tactic_proof": true, "tactics": ["ext1", "grw", "refine", "exact", "grw", "rfl"], "tactic_count": 6}
{"name": "MeasureTheory.lpMeasSubgroupToLpTrim_neg", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.AEMeasurable", "is_tactic_proof": true, "tactics": ["ext1", "grw", "refine", "grw", "rfl"], "tactic_count": 5}
{"name": "MeasureTheory.lpMeasSubgroupToLpTrim_sub", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.AEMeasurable", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "MeasureTheory.lpMeasSubgroupToLpTrim_norm_map", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.AEMeasurable", "is_tactic_proof": false, "tactics": ["rw", "congr"], "tactic_count": 2}
{"name": "MeasureTheory.isometry_lpMeasSubgroupToLpTrim", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.AEMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.lpMeasSubgroupToLpTrimIso", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.AEMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.lpMeasSubgroupToLpMeasIso", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.AEMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.lpMeasToLpTrimLie", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.AEMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.instCompleteSpaceSubtypeAEEqFunMemAddSubgroupLpLpMeasSubgroupOfFactLeMeasurableSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.AEMeasurable", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.instCompleteSpaceSubtypeAEEqFunMemAddSubgroupLpSubmoduleLpMeasOfFactLeMeasurableSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.AEMeasurable", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.isComplete_aestronglyMeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.AEMeasurable", "is_tactic_proof": true, "tactics": ["rw", "haveI", "change", "infer_instance"], "tactic_count": 4}
{"name": "MeasureTheory.isClosed_aestronglyMeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.AEMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.lpMeas.ae_fin_strongly_measurable'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.AEMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.lpMeasToLpTrimLie_symm_indicator", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.AEMeasurable", "is_tactic_proof": true, "tactics": ["ext1", "change", "grw"], "tactic_count": 3}
{"name": "MeasureTheory.lpMeasToLpTrimLie_symm_toLp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.AEMeasurable", "is_tactic_proof": true, "tactics": ["ext1", "change", "grw"], "tactic_count": 3}
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{"name": "MeasureTheory.MemLp.induction_stronglyMeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.AEMeasurable", "is_tactic_proof": true, "tactics": ["intro", "let", "have", "refine", "change", "refine", "intro", "rw", "refine", "exact", "intro", "have", "have", "specialize", "refine", "exact"], "tactic_count": 16}
{"name": "MeasureTheory.definition._@.Mathlib.MeasureTheory.Function.ConditionalExpectation.Basic.3112114093._hygCtx._hyg.47", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasureTheory.condExp", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.condExp_def", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.Basic", "is_tactic_proof": true, "tactics": ["intros", "delta", "rw", "rfl"], "tactic_count": 4}
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{"name": "MeasureTheory.condExpUnexpander", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.condExp_of_not_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.condExp_of_not_sigmaFinite", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.condExp_of_sigmaFinite", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.Basic", "is_tactic_proof": true, "tactics": ["rw", "grind"], "tactic_count": 2}
{"name": "MeasureTheory.condExp_of_stronglyMeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.condExp_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.condExp_ae_eq_condExpL1", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.Basic", "is_tactic_proof": true, "tactics": ["rw", "by_cases", "rw", "by_cases", "rw", "exact", "rw", "exact", "rw", "exact"], "tactic_count": 10}
{"name": "MeasureTheory.condExp_ae_eq_condExpL1CLM", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "MeasureTheory.condExp_of_not_integrable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "swap", "by_cases", "swap", "rw"], "tactic_count": 5}
{"name": "MeasureTheory.condExp_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "swap", "by_cases", "swap", "exact"], "tactic_count": 5}
{"name": "MeasureTheory.stronglyMeasurable_condExp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "swap", "by_cases", "swap", "rw", "split_ifs", "exact", "exact", "exact"], "tactic_count": 9}
{"name": "MeasureTheory.condExp_congr_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "swap", "by_cases", "swap", "exact"], "tactic_count": 5}
{"name": "MeasureTheory.condExp_congr_ae_trim", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.condExp_of_aestronglyMeasurable'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "MeasureTheory.integrable_condExp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "swap", "by_cases", "swap", "exact"], "tactic_count": 5}
{"name": "MeasureTheory.setIntegral_condExp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.integral_condExp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "suffices", "exact", "exact", "simp"], "tactic_count": 5}
{"name": "MeasureTheory.integral_condExp_indicator", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.ae_eq_condExp_of_forall_setIntegral_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.Basic", "is_tactic_proof": false, "tactics": ["refine", "ae_eq_of_forall_setIntegral_eq_of_sigmaFinite", "rw"], "tactic_count": 3}
{"name": "MeasureTheory.condExp_bot'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "swap", "have", "rw", "rw", "simp", "rfl", "have", "obtain", "rw", "have", "simp_rw", "rw", "rw", "exact"], "tactic_count": 15}
{"name": "MeasureTheory.condExp_bot_ae_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.Basic", "is_tactic_proof": true, "tactics": ["rcases", "rw", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.condExp_bot", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "MeasureTheory.condExp_add", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "swap", "by_cases", "swap", "refine", "rw", "exact"], "tactic_count": 7}
{"name": "MeasureTheory.condExp_finset_sum", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.Basic", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "insert", "rw", "exact"], "tactic_count": 6}
{"name": "MeasureTheory.condExp_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "swap", "by_cases", "swap", "refine", "rw", "refine", "refine", "simp"], "tactic_count": 9}
{"name": "MeasureTheory.condExp_neg", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.Basic", "is_tactic_proof": true, "tactics": ["calc", "μ"], "tactic_count": 2}
{"name": "MeasureTheory.condExp_sub", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.condExp_condExp_of_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "swap", "by_cases", "swap", "refine", "ae_eq_of_forall_setIntegral_eq_of_sigmaFinite", "stronglyMeasurable_condExp.aestronglyMeasurable", "intro", "rw", "rw"], "tactic_count": 10}
{"name": "ContinuousLinearMap.comp_condExp_comm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "by_cases", "refine", "exact", "exact", "calc", "exact", "simp", "simp"], "tactic_count": 9}
{"name": "ContinuousLinearMap.comp_condExp_add_const_comm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.Basic", "is_tactic_proof": false, "tactics": ["have", "filter_upwards", "simpa", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.MemLp.condExpL2_ae_eq_condExp'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.Basic", "is_tactic_proof": false, "tactics": ["refine", "ae_eq_condExp_of_forall_setIntegral_eq", "rw", "refine", "filter_upwards"], "tactic_count": 5}
{"name": "MeasureTheory.MemLp.condExpL2_ae_eq_condExp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.eLpNorm_condExp_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "by_cases", "rw", "simp", "by_cases", "rw", "simp", "obtain", "simp", "replace", "rw", "refine", "rw"], "tactic_count": 14}
{"name": "MeasureTheory.MemLp.condExp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "simp"], "tactic_count": 3}
{"name": "MeasureTheory.condExp_ofNat", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.tendsto_condExpL1_of_dominated_convergence", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.tendsto_condExp_unique", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "by_cases", "refine", "rw", "have", "intro", "ext1", "refine", "exact", "have", "tendsto_condExpL1_of_dominated_convergence", "have", "tendsto_condExpL1_of_dominated_convergence", "exact"], "tactic_count": 14}
{"name": "MeasureTheory.condExp_mono", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "swap", "by_cases", "swap", "exact"], "tactic_count": 5}
{"name": "MeasureTheory.condExp_nonneg", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "exact", "rw"], "tactic_count": 4}
{"name": "MeasureTheory.condExp_nonpos", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "exact", "rw"], "tactic_count": 4}
{"name": "MeasureTheory.condExpIndL1Fin", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.condExpIndL1Fin_ae_eq_condExpIndSMul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1.0.MeasureTheory.q", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.condExpIndL1Fin_add", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1", "is_tactic_proof": true, "tactics": ["ext1", "unfold", "grw"], "tactic_count": 3}
{"name": "MeasureTheory.condExpIndL1Fin_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1", "is_tactic_proof": true, "tactics": ["ext1", "grw"], "tactic_count": 2}
{"name": "MeasureTheory.condExpIndL1Fin_smul'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1", "is_tactic_proof": true, "tactics": ["ext1", "grw"], "tactic_count": 2}
{"name": "MeasureTheory.norm_condExpIndL1Fin_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1", "is_tactic_proof": false, "tactics": ["rw", "ofReal_integral_norm_eq_lintegral_enorm]", "swap", "have", "refine", "filter_upwards", "rw", "rw", "exact"], "tactic_count": 9}
{"name": "MeasureTheory.condExpIndL1Fin_disjoint_union", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1", "is_tactic_proof": true, "tactics": ["ext1", "grw", "condExpIndL1Fin_ae_eq_condExpIndSMul]", "rw", "rw", "rw", "push_cast", "rw", "grw", "rfl"], "tactic_count": 10}
{"name": "MeasureTheory.condExpIndL1", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.condExpIndL1_of_measurableSet_of_measure_ne_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.condExpIndL1_of_measure_eq_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.condExpIndL1_of_not_measurableSet", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.condExpIndL1_add", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1", "is_tactic_proof": true, "tactics": ["by_cases", "swap", "by_cases", "simp_rw", "simp_rw", "exact"], "tactic_count": 6}
{"name": "MeasureTheory.condExpIndL1_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1", "is_tactic_proof": true, "tactics": ["by_cases", "swap", "by_cases", "simp_rw", "simp_rw", "exact"], "tactic_count": 6}
{"name": "MeasureTheory.condExpIndL1_smul'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1", "is_tactic_proof": true, "tactics": ["by_cases", "swap", "by_cases", "simp_rw", "simp_rw", "exact"], "tactic_count": 6}
{"name": "MeasureTheory.norm_condExpIndL1_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1", "is_tactic_proof": true, "tactics": ["by_cases", "swap", "simp_rw", "exact", "by_cases", "rw", "exact", "rw", "exact"], "tactic_count": 9}
{"name": "MeasureTheory.continuous_condExpIndL1", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.condExpIndL1_disjoint_union", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1", "is_tactic_proof": false, "tactics": ["have", "rw", "condExpIndL1_of_measurableSet_of_measure_ne_top", "condExpIndL1_of_measurableSet_of_measure_ne_top", "exact"], "tactic_count": 5}
{"name": "MeasureTheory.condExpInd", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.condExpInd_ae_eq_condExpIndSMul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1", "is_tactic_proof": true, "tactics": ["grw", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.aestronglyMeasurable_condExpInd", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.condExpInd_empty", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1", "is_tactic_proof": true, "tactics": ["ext", "grw"], "tactic_count": 2}
{"name": "MeasureTheory.condExpInd_smul'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.norm_condExpInd_apply_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.norm_condExpInd_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.condExpInd_disjoint_union_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.condExpInd_disjoint_union", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1", "is_tactic_proof": true, "tactics": ["ext1"], "tactic_count": 1}
{"name": "MeasureTheory.dominatedFinMeasAdditive_condExpInd", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.setIntegral_condExpInd", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.condExpInd_of_measurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1", "is_tactic_proof": true, "tactics": ["ext1", "grw", "rw", "filter_upwards", "rw", "by_cases"], "tactic_count": 6}
{"name": "MeasureTheory.condExpInd_nonneg", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1", "is_tactic_proof": true, "tactics": ["rw", "refine", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.condExpL1CLM", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.condExpL1CLM_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.condExpL1CLM_indicatorConstLp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.condExpL1CLM_indicatorConst", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.setIntegral_condExpL1CLM_of_measure_ne_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1", "is_tactic_proof": false, "tactics": ["refine", "intro", "simp_rw", "rw", "exact", "intro", "simp_rw", "rw", "hx)]", "rw", "simp_rw", "rw", "integral_add", "exact", "exact"], "tactic_count": 15}
{"name": "MeasureTheory.setIntegral_condExpL1CLM", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1", "is_tactic_proof": true, "tactics": ["let", "have", "have", "have", "simp_rw", "rw", "have", "refine", "have", "rwa", "have", "intro", "simp_rw", "exact", "have", "funext", "setIntegral_condExpL1CLM_of_measure_ne_top", "have", "have", "tendsto_setIntegral_of_monotone", "rwa", "have", "have", "tendsto_setIntegral_of_monotone", "rwa", "rw", "exact"], "tactic_count": 27}
{"name": "MeasureTheory.aestronglyMeasurable_condExpL1CLM", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1", "is_tactic_proof": false, "tactics": ["refine", "intro", "rw", "exact", "intro", "rw", "exact", "have", "condExpL1CLM", "rfl", "rw", "refine", "exact"], "tactic_count": 13}
{"name": "MeasureTheory.condExpL1CLM_lpMeas", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1", "is_tactic_proof": true, "tactics": ["let", "have", "rw", "refine", "condExpL1CLM", "intro", "rw", "condExpL1CLM_indicatorConstLp]", "exact", "intro", "rw", "push_cast", "rw", "refine", "refine", "exact", "refine", "exact"], "tactic_count": 18}
{"name": "MeasureTheory.condExpL1CLM_of_aestronglyMeasurable'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.condExpL1", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.condExpL1_undef", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.condExpL1_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.condExpL1_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.condExpL1_measure_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.aestronglyMeasurable_condExpL1", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "exact", "rw", "exact"], "tactic_count": 5}
{"name": "MeasureTheory.condExpL1_congr_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integrable_condExpL1", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.setIntegral_condExpL1", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1", "is_tactic_proof": true, "tactics": ["simp_rw", "rw", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.condExpL1_add", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.condExpL1_neg", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.condExpL1_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.condExpL1_sub", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.condExpL1_of_aestronglyMeasurable'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.condExpL1_mono", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1", "is_tactic_proof": true, "tactics": ["rw", "have", "condExpInd_nonneg", "exact"], "tactic_count": 4}
{"name": "_private.Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL2.0.MeasureTheory.term⟪_,_⟫", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasureTheory.condExpL2", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.aestronglyMeasurable_condExpL2", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integrableOn_condExpL2_of_measure_ne_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integrable_condExpL2_of_isFiniteMeasure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.norm_condExpL2_le_one", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.norm_condExpL2_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.eLpNorm_condExpL2_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL2", "is_tactic_proof": false, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.norm_condExpL2_coe_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL2", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.inner_condExpL2_left_eq_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.condExpL2_indicator_of_measurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL2", "is_tactic_proof": true, "tactics": ["rw", "haveI", "have", "let", "have", "have", "rw"], "tactic_count": 7}
{"name": "MeasureTheory.inner_condExpL2_eq_inner_fun", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL2", "is_tactic_proof": true, "tactics": ["symm", "rw", "simp"], "tactic_count": 3}
{"name": "MeasureTheory.integral_condExpL2_eq_of_fin_meas_real", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL2", "is_tactic_proof": true, "tactics": ["rw", "have", "rw", "rw"], "tactic_count": 4}
{"name": "MeasureTheory.lintegral_nnnorm_condExpL2_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL2", "is_tactic_proof": true, "tactics": ["let", "let", "have", "have", "have", "have", "refine", "dsimp", "simp_rw", "rw", "refine", "exact", "exact", "rw", "exact", "intro", "rw", "exact"], "tactic_count": 18}
{"name": "MeasureTheory.condExpL2_ae_eq_zero_of_ae_eq_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL2", "is_tactic_proof": false, "tactics": ["suffices", "rw", "refine", "dsimp", "rw", "rwa", "refine", "exact", "refine", "refine", "rw", "refine", "dsimp", "rw", "simp", "exact"], "tactic_count": 16}
{"name": "MeasureTheory.lintegral_nnnorm_condExpL2_indicator_le_real", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL2", "is_tactic_proof": true, "tactics": ["refine", "have", "refine", "refine", "dsimp", "rw", "classical", "simp_rw", "split_ifs", "rw", "simp"], "tactic_count": 11}
{"name": "MeasureTheory.condExpL2_const_inner", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL2", "is_tactic_proof": false, "tactics": ["have", "exact", "have", "refine", "refine", "intro", "rw", "exact", "intro", "rw", "inner_condExpL2_left_eq_right,", "setIntegral_congr_ae", "exact", "refine", "exact"], "tactic_count": 15}
{"name": "MeasureTheory.integral_condExpL2_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL2", "is_tactic_proof": false, "tactics": ["rw", "integral_sub", "refine", "rw", "exact", "intro", "simp_rw", "rw", "have", "rw", "setIntegral_congr_ae", "exact"], "tactic_count": 12}
{"name": "MeasureTheory.condExpL2_comp_continuousLinearMap", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL2", "is_tactic_proof": false, "tactics": ["refine", "intro", "rw", "integral_condExpL2_eq", "exact", "have", "rw", "refine", "exact"], "tactic_count": 9}
{"name": "MeasureTheory.condExpL2_indicator_ae_eq_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL2", "is_tactic_proof": true, "tactics": ["rw", "have", "refine", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.condExpL2_indicator_eq_toSpanSingleton_comp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL2", "is_tactic_proof": true, "tactics": ["ext1", "refine", "have", "rw", "refine", "filter_upwards"], "tactic_count": 6}
{"name": "MeasureTheory.setLIntegral_nnnorm_condExpL2_indicator_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.lintegral_nnnorm_condExpL2_indicator_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL2", "is_tactic_proof": true, "tactics": ["refine", "refine", "gcongr", "apply"], "tactic_count": 4}
{"name": "MeasureTheory.integrable_condExpL2_indicator", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL2", "is_tactic_proof": false, "tactics": ["refine", "exact", "refine", "gcongr", "apply"], "tactic_count": 5}
{"name": "MeasureTheory.condExpIndSMul", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.aestronglyMeasurable_condExpIndSMul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL2", "is_tactic_proof": false, "tactics": ["have", "aestronglyMeasurable_condExpL2", "rw", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.condExpIndSMul_add", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL2", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MeasureTheory.condExpIndSMul_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL2", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MeasureTheory.condExpIndSMul_ae_eq_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.setLIntegral_nnnorm_condExpIndSMul_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.lintegral_nnnorm_condExpIndSMul_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL2", "is_tactic_proof": true, "tactics": ["refine", "refine", "gcongr", "apply"], "tactic_count": 4}
{"name": "MeasureTheory.integrable_condExpIndSMul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL2", "is_tactic_proof": false, "tactics": ["refine", "exact", "refine", "gcongr", "apply"], "tactic_count": 5}
{"name": "MeasureTheory.condExpIndSMul_empty", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL2", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.setIntegral_condExpL2_indicator", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.setIntegral_condExpIndSMul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.condExpL2_indicator_nonneg", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL2", "is_tactic_proof": false, "tactics": ["have", "aestronglyMeasurable_condExpL2", "refine", "refine", "refine", "rintro", "refine", "refine", "rw", "exact", "intro", "rw", "have", "filter_upwards", "rw", "exact"], "tactic_count": 16}
{"name": "MeasureTheory.condExpIndSMul_nonneg", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL2", "is_tactic_proof": true, "tactics": ["refine", "filter_upwards", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.condExp_ae_eq_restrict_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.Indicator", "is_tactic_proof": true, "tactics": ["by_cases", "swap", "by_cases", "swap", "haveI", "have", "rw", "exact", "by_cases", "swap", "refine", "exact", "exact", "intro", "rw", "refine", "filter_upwards", "exact", "exact"], "tactic_count": 19}
{"name": "MeasureTheory.condExp_indicator_aux", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.Indicator", "is_tactic_proof": true, "tactics": ["by_cases", "swap", "have", "indicator_ae_eq_of_restrict_compl_ae_eq_zero", "refine", "exact"], "tactic_count": 6}
{"name": "MeasureTheory.condExp_indicator", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.Indicator", "is_tactic_proof": true, "tactics": ["by_cases", "swap", "by_cases", "swap", "haveI", "have", "rw", "refine", "calc", "s.indicator", "s.indicator", "filter_upwards", "classical", "refine", "have", "refine", "exact", "rw", "filter_upwards", "by_cases", "simp", "simp", "rw", "refine", "exact", "rw"], "tactic_count": 26}
{"name": "MeasureTheory.condExp_restrict_ae_eq_restrict", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.Indicator", "is_tactic_proof": true, "tactics": ["have", "rw", "refine", "refine", "intro", "rw", "suffices", "rw", "exact", "exact", "intro", "calc", "rw", "rw", "exact"], "tactic_count": 15}
{"name": "MeasureTheory.condExp_ae_eq_restrict_of_measurableSpace_eq_on", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.Indicator", "is_tactic_proof": true, "tactics": ["rw", "have", "by_cases", "swap", "refine", "refine", "ae_eq_of_forall_setIntegral_eq_of_sigmaFinite", "swap", "have", "refine", "exact", "intro", "have", "rw", "suffices", "rw", "rw", "suffices", "rw", "calc", "refine", "filter_upwards", "refine", "exact", "have", "simp_rw", "setIntegral_condExp"], "tactic_count": 27}
{"name": "MeasureTheory.condExp_stronglyMeasurable_simpleFunc_bilin", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.PullOut", "is_tactic_proof": false, "tactics": ["have", "intro", "ext", "by_cases", "apply", "simp", "rw", "refine", "filter_upwards", "simp", "simp", "have", "calc", "μ", "simp_rw", "obtain", "obtain", "exact", "condExp_add", "hg)", "hg)", "m"], "tactic_count": 22}
{"name": "MeasureTheory.condExp_stronglyMeasurable_bilin_of_bound", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.PullOut", "is_tactic_proof": true, "tactics": ["let", "have", "by_cases", "simp", "have", "have", "rcases", "exact", "have", "have", "refine", "exact", "exact", "rw", "refine", "tendsto_condExp_unique", "exact", "exact", "filter_upwards", "exact", "filter_upwards", "exact", "exact", "fun_prop", "refine", "grw", "refine", "grw", "intro", "refine", "nth_rw", "exact", "exact"], "tactic_count": 33}
{"name": "MeasureTheory.condExp_aestronglyMeasurable_bilin_of_bound", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.PullOut", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.condExp_bilin_of_stronglyMeasurable_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.PullOut", "is_tactic_proof": true, "tactics": ["by_cases", "by_cases", "swap", "obtain", "simp_rw", "obtain", "suffices", "rw", "filter_upwards", "obtain", "have", "simpa", "exact", "refine", "suffices", "refine", "filter_upwards", "rw", "suffices", "refine", "filter_upwards", "rw", "filter_upwards", "rw", "have", "constructor", "rw", "exact", "refine", "filter_upwards", "by_cases"], "tactic_count": 31}
{"name": "MeasureTheory.condExp_bilin_of_stronglyMeasurable_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.PullOut", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.condExp_bilin_of_aestronglyMeasurable_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.PullOut", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.condExp_bilin_of_aestronglyMeasurable_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.PullOut", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.condExp_smul_of_aestronglyMeasurable_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.PullOut", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.condExp_smul_of_aestronglyMeasurable_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.PullOut", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.condExp_mul_of_aestronglyMeasurable_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.PullOut", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.condExp_mul_of_aestronglyMeasurable_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.PullOut", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.condExp_mul_of_stronglyMeasurable_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.PullOut", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.condExp_mul_of_stronglyMeasurable_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.PullOut", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.condExp_stronglyMeasurable_simpleFunc_mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.PullOut", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.condExp_stronglyMeasurable_mul_of_bound", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.PullOut", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.condExp_stronglyMeasurable_mul_of_bound₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.PullOut", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.rnDeriv_ae_eq_condExp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.Real", "is_tactic_proof": true, "tactics": ["refine", "exact", "intro", "conv_rhs", "rw", "rw", "setIntegral_trim", "exact", "exact"], "tactic_count": 9}
{"name": "MeasureTheory.eLpNorm_one_condExp_le_eLpNorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.Real", "is_tactic_proof": true, "tactics": ["by_cases", "swap", "by_cases", "swap", "by_cases", "swap", "calc", "eLpNorm", "refine", "filter_upwards", "x", "exact", "rw", "integral_norm_eq_lintegral_enorm", "simp_rw", "rw", "refine", "have", "rw", "exact", "filter_upwards", "exact"], "tactic_count": 22}
{"name": "MeasureTheory.integral_abs_condExp_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.Real", "is_tactic_proof": true, "tactics": ["by_cases", "swap", "simp_rw", "positivity", "by_cases", "swap", "simp", "positivity", "rw", "apply", "exact", "rw", "exact", "filter_upwards", "simp_rw", "exact", "filter_upwards", "simp_rw", "exact"], "tactic_count": 19}
{"name": "MeasureTheory.setIntegral_abs_condExp_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.Real", "is_tactic_proof": true, "tactics": ["by_cases", "swap", "simp_rw", "positivity", "by_cases", "swap", "simp", "positivity", "have", "rw", "refine", "have", "refine", "rw", "simp", "rw", "refine", "simp_rw"], "tactic_count": 18}
{"name": "MeasureTheory.ae_bdd_condExp_of_ae_bdd", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.Real", "is_tactic_proof": true, "tactics": ["by_cases", "swap", "simp_rw", "exact", "by_cases", "swap", "simp_rw", "filter_upwards", "rw", "exact", "by_contra", "change", "simp", "suffices", "refine", "exact", "refine", "simp_rw", "exact", "simp", "refine", "refine", "lt_of_le_of_lt", "refine", "rw", "exact"], "tactic_count": 26}
{"name": "MeasureTheory.Integrable.uniformIntegrable_condExp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.Real", "is_tactic_proof": true, "tactics": ["let", "have", "measurableSet_le", "have", "refine", "uniformIntegrable_of", "by_cases", "rw", "refine", "one_ne_zero).2", "filter_upwards", "simp", "obtain", "set", "have", "have", "intro", "have", "rw", "convert", "mul_meas_ge_le_pow_eLpNorm", "rw", "rw", "simp_rw", "refine", "rw", "exact", "refine", "have", "rw", "exact"], "tactic_count": 31}
{"name": "MeasureTheory.lpMeas.ae_eq_zero_of_forall_setIntegral_eq_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.Unique", "is_tactic_proof": true, "tactics": ["obtain", "refine", "refine", "intro", "have", "rw", "exact", "intro", "have", "rw", "exact"], "tactic_count": 11}
{"name": "MeasureTheory.Lp.ae_eq_zero_of_forall_setIntegral_eq_zero'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.Unique", "is_tactic_proof": true, "tactics": ["let", "have", "refine", "exact"], "tactic_count": 4}
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{"name": "MeasureTheory.ae_eq_of_forall_setIntegral_eq_of_sigmaFinite'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.Unique", "is_tactic_proof": true, "tactics": ["rw", "have", "intro", "rw", "rw", "refine", "exact", "have", "intro", "rw", "rw", "refine", "exact", "have", "intro", "rw", "rw", "integral_trim", "integral_congr_ae", "exact", "exact"], "tactic_count": 21}
{"name": "MeasureTheory.integral_norm_le_of_forall_fin_meas_integral_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.Unique", "is_tactic_proof": true, "tactics": ["rw", "have", "have", "have", "have", "refine", "rw", "hgf", "exact", "rw", "hgf", "exact"], "tactic_count": 12}
{"name": "MeasureTheory.lintegral_enorm_le_of_forall_fin_meas_integral_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalExpectation.Unique", "is_tactic_proof": false, "tactics": ["rw", "exact", "positivity"], "tactic_count": 3}
{"name": "MeasureTheory.definition._@.Mathlib.MeasureTheory.Function.ConditionalLExpectation.118845607._hygCtx._hyg.8", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.ConditionalLExpectation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.wrapped._@.Mathlib.MeasureTheory.Function.ConditionalLExpectation.118845607._hygCtx._hyg.8", "kind": "opaque", "module": "Mathlib.MeasureTheory.Function.ConditionalLExpectation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.condLExp", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.ConditionalLExpectation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.condLExp_def", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalLExpectation", "is_tactic_proof": true, "tactics": ["intros", "delta", "rw", "rfl"], "tactic_count": 4}
{"name": "MeasureTheory.term__⁻[_|_]", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.ConditionalLExpectation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasureTheory.condLExpUnexpander", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.ConditionalLExpectation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.condLExp_of_not_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalLExpectation", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.condLExp_of_not_sigmaFinite", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalLExpectation", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.condLExp_eq_self", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalLExpectation", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.condLExp_of_not_sub_sigma_measurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalLExpectation", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.measurable_condLExp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConditionalLExpectation", "is_tactic_proof": true, "tactics": ["by_cases", "by_cases", "by_cases", "simp", "simp", "simp", "simp"], "tactic_count": 7}
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{"name": "MeasureTheory.Lp.boundedContinuousFunction_topologicalClosure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ContinuousMapDense", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.toLp_denseRange", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ContinuousMapDense", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ContinuousMap.toLp_denseRange", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ContinuousMapDense", "is_tactic_proof": true, "tactics": ["refine", "refine", "exact"], "tactic_count": 3}
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{"name": "MeasureTheory.ExistsSeqTendstoAe.exists_nat_measure_lt_two_inv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConvergenceInMeasure", "is_tactic_proof": true, "tactics": ["specialize", "rw", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.ExistsSeqTendstoAe.seqTendstoAeSeqAux", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.ConvergenceInMeasure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasureTheory.ExistsSeqTendstoAe.seqTendstoAeSeq_strictMono", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConvergenceInMeasure", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
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{"name": "MeasureTheory.TendstoInMeasure.exists_seq_tendstoInMeasure_atTop", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.ConvergenceInMeasure", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
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{"name": "MeasureTheory.Egorov.mem_notConvergentSeq_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.Egorov", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MeasureTheory.Egorov.notConvergentSeq_antitone", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.Egorov", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Egorov.measure_inter_notConvergentSeq_eq_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.Egorov", "is_tactic_proof": true, "tactics": ["simp_rw", "rw", "refine", "simp", "push_neg", "rintro", "refine", "obtain", "exact"], "tactic_count": 9}
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{"name": "MeasureTheory.Egorov.exists_notConvergentSeq_lt", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.Egorov", "is_tactic_proof": false, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.Egorov.notConvergentSeqLTIndex", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.Egorov", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Egorov.notConvergentSeqLTIndex_spec", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.Egorov", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Egorov.iUnionNotConvergentSeq", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.Egorov", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Egorov.iUnionNotConvergentSeq_measurableSet", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.Egorov", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Egorov.measure_iUnionNotConvergentSeq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.Egorov", "is_tactic_proof": false, "tactics": ["refine", "le_trans", "simp_rw", "rw", "intro", "rw", "exact"], "tactic_count": 7}
{"name": "MeasureTheory.Egorov.iUnionNotConvergentSeq_subset", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.Egorov", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.Egorov.tendstoUniformlyOn_diff_iUnionNotConvergentSeq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.Egorov", "is_tactic_proof": true, "tactics": ["rw", "intro", "obtain", "rw", "refine", "simp", "exists_and_left]", "obtain", "specialize", "rw", "push_neg", "rw", "exact"], "tactic_count": 13}
{"name": "MeasureTheory.tendstoUniformlyOn_of_ae_tendsto_of_measurable_edist", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.Egorov", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.tendstoUniformlyOn_of_ae_tendsto", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.Egorov", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.tendstoUniformlyOn_of_ae_tendsto_of_measurable_edist'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.Egorov", "is_tactic_proof": false, "tactics": ["have", "tendstoUniformlyOn_of_ae_tendsto_of_measurable_edist", "refine", "rwa"], "tactic_count": 4}
{"name": "MeasureTheory.tendstoUniformlyOn_of_ae_tendsto'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.Egorov", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "essSup", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.EssSup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "essInf", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.EssSup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "essSup_congr_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.EssSup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "essInf_congr_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.EssSup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "essSup_const'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.EssSup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "essInf_const'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.EssSup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "essSup_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.EssSup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "essInf_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.EssSup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "essSup_smul_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.EssSup", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "essSup_ennreal_smul_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.EssSup", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "essSup_eq_ciSup", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.EssSup", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "essInf_eq_ciInf", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.EssSup", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "essSup_count_eq_ciSup", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.EssSup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "essInf_count_eq_ciInf", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.EssSup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "essSup_uniformOn_eq_ciSup", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.EssSup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "essInf_cond_count_eq_ciInf", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.EssSup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "essSup_eq_sInf", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.EssSup", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "essInf_eq_sSup", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.EssSup", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "essSup_measure_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.EssSup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "essInf_measure_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.EssSup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "essSup_mono_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.EssSup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "essInf_mono_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.EssSup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "essSup_le_of_ae_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.EssSup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_essInf_of_ae_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.EssSup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "essSup_const_bot", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.EssSup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "essInf_const_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.EssSup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.essSup_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.EssSup", "is_tactic_proof": true, "tactics": ["refine", "all_goals"], "tactic_count": 2}
{"name": "OrderIso.essInf_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.EssSup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "essSup_mono_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.EssSup", "is_tactic_proof": true, "tactics": ["refine", "all_goals"], "tactic_count": 2}
{"name": "essSup_mono_measure'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.EssSup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "essInf_antitone_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.EssSup", "is_tactic_proof": true, "tactics": ["refine", "all_goals"], "tactic_count": 2}
{"name": "essSup_eq_iSup", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.EssSup", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "essInf_eq_iInf", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.EssSup", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "essSup_count", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.EssSup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "essInf_count", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.EssSup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "essSup_comp_le_essSup_map_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.EssSup", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "MeasurableEmbedding.essSup_map_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.EssSup", "is_tactic_proof": true, "tactics": ["refine", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "essSup_map_measure_of_measurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.EssSup", "is_tactic_proof": true, "tactics": ["refine", "refine", "rw", "rw", "exact"], "tactic_count": 5}
{"name": "essSup_map_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.EssSup", "is_tactic_proof": true, "tactics": ["rw", "refine", "have", "rw", "exact"], "tactic_count": 5}
{"name": "ENNReal.essSup_piecewise", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.EssSup", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.essSup_indicator_eq_essSup_restrict", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.EssSup", "is_tactic_proof": true, "tactics": ["classical", "simp", "exact"], "tactic_count": 3}
{"name": "ENNReal.ae_le_essSup", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.EssSup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.essSup_eq_zero_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.EssSup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.essSup_const_mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.EssSup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.essSup_mul_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.EssSup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.essSup_add_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.EssSup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.essSup_liminf_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.EssSup", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "ENNReal.coe_essSup", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.EssSup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.essSup_restrict_eq_of_support_subset", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.EssSup", "is_tactic_proof": true, "tactics": ["apply", "apply", "obtain", "let", "have", "simp", "rw", "have", "exact", "have", "have", "apply", "apply", "intro", "exact", "exact", "apply", "rw", "apply", "contrapose", "exact"], "tactic_count": 21}
{"name": "Measurable.factorsThrough", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.FactorsThrough", "is_tactic_proof": true, "tactics": ["refine", "obtain", "rw"], "tactic_count": 3}
{"name": "MeasureTheory.StronglyMeasurable.factorsThrough", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.FactorsThrough", "is_tactic_proof": true, "tactics": ["borelize", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.StronglyMeasurable.exists_eq_measurable_comp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.FactorsThrough", "is_tactic_proof": true, "tactics": ["let", "induction", "const", "obtain", "obtain", "obtain", "classical", "choose", "refine", "ext", "rw", "simp_all"], "tactic_count": 12}
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{"name": "Measurable.dependsOn_of_piLE", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.FactorsThrough", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.StronglyMeasurable.dependsOn_of_piLE", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.FactorsThrough", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.dependsOn_of_piFinset", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.FactorsThrough", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.StronglyMeasurable.dependsOn_of_piFinset", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.FactorsThrough", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.measurable_floor", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.Floor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.floor", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.Floor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.measurable_ceil", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.Floor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.ceil", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.Floor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_fract", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.Floor", "is_tactic_proof": true, "tactics": ["intro", "rw", "exact"], "tactic_count": 3}
{"name": "Measurable.fract", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.Floor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSet.image_fract", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.Floor", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Nat.measurable_floor", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.Floor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.nat_floor", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.Floor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.measurable_ceil", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.Floor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.nat_ceil", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.Floor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.memLp_of_bilin", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.integrable_of_bilin_of_bdd_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.integrable_of_bilin_of_bdd_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.holder", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.coeFn_holder", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.Holder", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ContinuousLinearMap.nnnorm_holder_apply_apply_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.Holder", "is_tactic_proof": true, "tactics": ["simp_rw", "apply", "exact", "eLpNorm_le_eLpNorm_mul_eLpNorm_of_nnnorm"], "tactic_count": 4}
{"name": "ContinuousLinearMap.norm_holder_apply_apply_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.holder_add_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.Holder", "is_tactic_proof": true, "tactics": ["simp", "apply", "filter_upwards", "simp"], "tactic_count": 4}
{"name": "ContinuousLinearMap.holder_add_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.Holder", "is_tactic_proof": true, "tactics": ["simp", "apply", "filter_upwards", "simp"], "tactic_count": 4}
{"name": "ContinuousLinearMap.holder_smul_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.Holder", "is_tactic_proof": true, "tactics": ["simp", "apply", "filter_upwards", "simp"], "tactic_count": 4}
{"name": "ContinuousLinearMap.holder_smul_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.Holder", "is_tactic_proof": true, "tactics": ["simp", "apply", "filter_upwards", "simp"], "tactic_count": 4}
{"name": "ContinuousLinearMap.holderₗ", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.holderL", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.norm_holderL_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.lpPairing", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.lpPairing_eq_integral", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.Holder", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.Lp.instHSMulSubtypeAEEqFunMemAddSubgroup", "kind": "instance", "module": "Mathlib.MeasureTheory.Function.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.smul_def", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.coeFn_lpSMul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.Holder", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.Lp.norm_smul_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.Holder", "is_tactic_proof": true, "tactics": ["simp", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.Lp.smul_add", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.Holder", "is_tactic_proof": true, "tactics": ["simp", "apply", "filter_upwards", "simp"], "tactic_count": 4}
{"name": "MeasureTheory.Lp.add_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.Holder", "is_tactic_proof": true, "tactics": ["simp", "apply", "filter_upwards", "simp"], "tactic_count": 4}
{"name": "MeasureTheory.Lp.smul_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.Holder", "is_tactic_proof": true, "tactics": ["convert", "apply", "filter_upwards", "rw", "simp"], "tactic_count": 5}
{"name": "MeasureTheory.Lp.zero_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.Holder", "is_tactic_proof": true, "tactics": ["convert", "apply", "filter_upwards", "rw", "simp"], "tactic_count": 5}
{"name": "MeasureTheory.Lp.smul_neg", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.Holder", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.Lp.neg_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.Holder", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.Lp.neg_smul_neg", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.Holder", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.Lp.smul_assoc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.Holder", "is_tactic_proof": true, "tactics": ["simp", "apply", "filter_upwards", "simp"], "tactic_count": 4}
{"name": "MeasureTheory.Lp.smul_comm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.Holder", "is_tactic_proof": true, "tactics": ["simp", "apply", "filter_upwards", "simp"], "tactic_count": 4}
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{"name": "MeasureTheory.aemeasurable_ofReal_abs_det_fderivWithin", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.Jacobian", "is_tactic_proof": true, "tactics": ["apply", "refine", "refine", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.aemeasurable_toNNReal_abs_det_fderivWithin", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.Jacobian", "is_tactic_proof": true, "tactics": ["apply", "refine", "refine", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.measurable_image_of_fderivWithin", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.Jacobian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.nullMeasurable_image_of_fderivWithin", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.Jacobian", "is_tactic_proof": true, "tactics": ["rcases", "have", "have", "rw", "refine", "apply", "exact", "apply", "apply", "apply", "intro", "exact"], "tactic_count": 12}
{"name": "MeasureTheory.measurableEmbedding_of_fderivWithin", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.Jacobian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.addHaar_image_le_lintegral_abs_det_fderiv_aux1", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.Jacobian", "is_tactic_proof": true, "tactics": ["measure", "have", "intro", "let", "have", "simp", "rcases", "obtain", "refine", "exact", "let", "refine", "intro", "rw", "apply", "rw", "calc", "intro", "exact", "choose", "obtain", "exists_partition_approximatesLinearOn_of_hasFDerivWithinAt", "calc", "μ", "apply", "rw", "exact", "apply", "apply", "exact", "simp", "apply", "apply", "filter_upwards", "intro", "have", "calc", "calc", "simp", "have", "rw", "exact", "rw", "simp"], "tactic_count": 44}
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{"name": "MeasureTheory.lintegral_abs_det_fderiv_eq_addHaar_image", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.Jacobian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasureTheory.restrict_map_withDensity_abs_det_fderiv_eq_addHaar", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.Jacobian", "is_tactic_proof": false, "tactics": ["obtain", "classical", "refine", "refine", "have", "exact", "have", "set", "have", "rw", "exact", "rw", "have", "ext", "exact", "rwa"], "tactic_count": 16}
{"name": "MeasureTheory.lintegral_image_eq_lintegral_abs_det_fderiv_mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.Jacobian", "is_tactic_proof": false, "tactics": ["rw", "simp", "rw", "setLIntegral_withDensity_eq_setLIntegral_mul_non_measurable₀", "simp", "simp", "exact"], "tactic_count": 7}
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{"name": "MeasurableEmbedding.withDensity_ofReal_comap_apply_eq_integral_abs_det_fderiv_mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.Jacobian", "is_tactic_proof": false, "tactics": ["rw", "withDensity_apply", "ofReal_integral_eq_lintegral_ofReal", "integral_image_eq_integral_abs_det_fderiv_smul", "simp_rw"], "tactic_count": 5}
{"name": "MeasurableEquiv.withDensity_ofReal_map_symm_apply_eq_integral_abs_det_fderiv_mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.Jacobian", "is_tactic_proof": true, "tactics": ["rw", "hg_int"], "tactic_count": 2}
{"name": "MeasureTheory.lintegral_image_eq_lintegral_abs_deriv_mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.JacobianOneDim", "is_tactic_proof": true, "tactics": ["simpa", "lintegral_image_eq_lintegral_abs_det_fderiv_mul"], "tactic_count": 2}
{"name": "MeasureTheory.integrableOn_image_iff_integrableOn_abs_deriv_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.JacobianOneDim", "is_tactic_proof": true, "tactics": ["simpa", "integrableOn_image_iff_integrableOn_abs_det_fderiv_smul"], "tactic_count": 2}
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{"name": "MeasureTheory.lintegral_deriv_eq_volume_image_of_monotoneOn", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.JacobianOneDim", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
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{"name": "MeasureTheory.lintegral_image_eq_lintegral_deriv_mul_of_antitoneOn", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.JacobianOneDim", "is_tactic_proof": true, "tactics": ["let", "let", "have", "have", "rw", "have", "lintegral_image_eq_lintegral_abs_deriv_mul", "neg_injective.injOn", "simp", "rw", "convert"], "tactic_count": 11}
{"name": "MeasureTheory.lintegral_deriv_eq_volume_image_of_antitoneOn", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.JacobianOneDim", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.integrableOn_image_iff_integrableOn_deriv_smul_of_antitoneOn", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.JacobianOneDim", "is_tactic_proof": true, "tactics": ["let", "let", "have", "have", "rw", "have", "integrableOn_image_iff_integrableOn_abs_deriv_smul", "simp", "rw", "convert"], "tactic_count": 10}
{"name": "MeasureTheory.integral_image_eq_integral_deriv_smul_of_antitone", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.JacobianOneDim", "is_tactic_proof": true, "tactics": ["let", "let", "have", "have", "rw", "have", "integral_image_eq_integral_abs_deriv_smul", "neg_injective.injOn", "simp", "rw", "convert"], "tactic_count": 11}
{"name": "MeasurableEmbedding.withDensity_ofReal_comap_apply_eq_integral_abs_deriv_mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.JacobianOneDim", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "MeasurableEquiv.withDensity_ofReal_map_symm_apply_eq_integral_abs_deriv_mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.JacobianOneDim", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "MeasurableEmbedding.withDensity_ofReal_comap_apply_eq_integral_abs_deriv_mul'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.JacobianOneDim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.withDensity_ofReal_map_symm_apply_eq_integral_abs_deriv_mul'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.JacobianOneDim", "is_tactic_proof": false, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.AEEqFun.Integrable", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.L1Space.AEEqFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEEqFun.integrable_mk", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.AEEqFun", "is_tactic_proof": true, "tactics": ["simp", "apply", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.AEEqFun.integrable_coeFn", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.AEEqFun", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.AEEqFun.integrable_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.AEEqFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEEqFun.Integrable.neg", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.AEEqFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEEqFun.integrable_iff_mem_L1", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.AEEqFun", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.AEEqFun.Integrable.add", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.AEEqFun", "is_tactic_proof": true, "tactics": ["refine", "simp", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.AEEqFun.Integrable.sub", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.AEEqFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEEqFun.Integrable.smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.AEEqFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.L1.integrable_coeFn", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.AEEqFun", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.L1.hasFiniteIntegral_coeFn", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.AEEqFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.L1.stronglyMeasurable_coeFn", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.AEEqFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.L1.measurable_coeFn", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.AEEqFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.L1.aestronglyMeasurable_coeFn", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.AEEqFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.L1.aemeasurable_coeFn", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.AEEqFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.L1.edist_def", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.AEEqFun", "is_tactic_proof": false, "tactics": ["simp", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.L1.dist_def", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.AEEqFun", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MeasureTheory.L1.norm_def", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.AEEqFun", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.L1.norm_sub_eq_lintegral", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.AEEqFun", "is_tactic_proof": true, "tactics": ["rw", "congr", "rw", "filter_upwards", "simp"], "tactic_count": 5}
{"name": "MeasureTheory.L1.ofReal_norm_eq_lintegral", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.AEEqFun", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.L1.ofReal_norm_sub_eq_lintegral", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.AEEqFun", "is_tactic_proof": true, "tactics": ["simp_rw", "apply", "filter_upwards", "simp"], "tactic_count": 4}
{"name": "MeasureTheory.Integrable.toL1", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.L1Space.AEEqFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Integrable.toL1_coeFn", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.AEEqFun", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.Integrable.coeFn_toL1", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.AEEqFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Integrable.toL1_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.AEEqFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Integrable.toL1_eq_mk", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.AEEqFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Integrable.toL1_eq_toL1_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.AEEqFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Integrable.toL1_add", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.AEEqFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Integrable.toL1_neg", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.AEEqFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Integrable.toL1_sub", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.AEEqFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Integrable.norm_toL1", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.AEEqFun", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.Integrable.enorm_toL1", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.AEEqFun", "is_tactic_proof": true, "tactics": ["simp", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.Integrable.norm_toL1_eq_lintegral_norm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.AEEqFun", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Integrable.edist_toL1_toL1", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.AEEqFun", "is_tactic_proof": false, "tactics": ["simp", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.Integrable.edist_toL1_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.AEEqFun", "is_tactic_proof": true, "tactics": ["simp", "apply"], "tactic_count": 2}
{"name": "MeasureTheory.Integrable.toL1_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.AEEqFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Integrable.toL1_smul'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.AEEqFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.lintegral_enorm_eq_lintegral_edist", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.lintegral_norm_eq_lintegral_edist", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.lintegral_edist_triangle", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": true, "tactics": ["rw", "refine", "apply"], "tactic_count": 3}
{"name": "MeasureTheory.lintegral_enorm_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.lintegral_enorm_add_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.lintegral_enorm_add_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.lintegral_enorm_neg", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.hasFiniteIntegral_def", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.hasFiniteIntegral_iff_enorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.hasFiniteIntegral_iff_norm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.hasFiniteIntegral_iff_edist", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.hasFiniteIntegral_iff_ofReal", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.hasFiniteIntegral_iff_ofNNReal", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.HasFiniteIntegral.mono_enorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": true, "tactics": ["simp", "calc"], "tactic_count": 2}
{"name": "MeasureTheory.HasFiniteIntegral.mono", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.HasFiniteIntegral.mono'_enorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.HasFiniteIntegral.mono'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.HasFiniteIntegral.congr'_enorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.HasFiniteIntegral.congr'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.hasFiniteIntegral_congr'_enorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.hasFiniteIntegral_congr'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.HasFiniteIntegral.congr", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.hasFiniteIntegral_congr", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.hasFiniteIntegral_const_iff_enorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": true, "tactics": ["simpa", "isFiniteMeasure_iff]"], "tactic_count": 2}
{"name": "MeasureTheory.hasFiniteIntegral_const_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.hasFiniteIntegral_const_iff_isFiniteMeasure_enorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.hasFiniteIntegral_const_iff_isFiniteMeasure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.hasFiniteIntegral_const_enorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.hasFiniteIntegral_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.HasFiniteIntegral.of_mem_Icc_of_ne_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": true, "tactics": ["have", "apply", "filter_upwards"], "tactic_count": 3}
{"name": "MeasureTheory.HasFiniteIntegral.of_mem_Icc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": true, "tactics": ["apply", "filter_upwards"], "tactic_count": 2}
{"name": "MeasureTheory.HasFiniteIntegral.of_bounded", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.HasFiniteIntegral.of_finite", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.HasFiniteIntegral.mono_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.HasFiniteIntegral.add_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.HasFiniteIntegral.left_of_add_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.HasFiniteIntegral.right_of_add_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.hasFiniteIntegral_add_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.HasFiniteIntegral.smul_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.hasFiniteIntegral_zero_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.hasFiniteIntegral_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.HasFiniteIntegral.neg", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.hasFiniteIntegral_neg_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.HasFiniteIntegral.enorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.HasFiniteIntegral.norm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.hasFiniteIntegral_enorm_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.hasFiniteIntegral_norm_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.HasFiniteIntegral.of_subsingleton", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.HasFiniteIntegral.of_isEmpty", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.HasFiniteIntegral.of_subsingleton_codomain", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.hasFiniteIntegral_toReal_of_lintegral_ne_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": true, "tactics": ["have", "simp_rw", "refine", "by_cases", "simp", "lift", "simp"], "tactic_count": 7}
{"name": "MeasureTheory.hasFiniteIntegral_toReal_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": true, "tactics": ["have", "simp", "lt_top_iff_ne_top]"], "tactic_count": 3}
{"name": "MeasureTheory.isFiniteMeasure_withDensity_ofReal", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.all_ae_norm_ofReal_F_le_bound", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.ae_tendsto_enorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.ae_tendsto_ofReal_norm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "MeasureTheory.ae_norm_ofReal_f_le_bound", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": true, "tactics": ["have", "rw", "apply", "intro", "exact"], "tactic_count": 5}
{"name": "MeasureTheory.ae_enorm_le_bound", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": true, "tactics": ["rw", "apply", "intro", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.hasFiniteIntegral_of_dominated_convergence_enorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": true, "tactics": ["and", "rw", "calc"], "tactic_count": 3}
{"name": "MeasureTheory.hasFiniteIntegral_of_dominated_convergence", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": true, "tactics": ["and", "rw", "calc", "lintegral_mono_ae", "rw", "exact", "exact"], "tactic_count": 7}
{"name": "MeasureTheory.tendsto_lintegral_norm_of_dominated_convergence", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": true, "tactics": ["have", "let", "triangle", "have", "intro", "filter_upwards", "calc", "rw", "apply", "apply", "exact", "exact", "rw", "have", "rw", "refine", "rwa", "suffices", "rwa", "refine", "tendsto_lintegral_of_dominated_convergence", "exact", "rw", "calc", "rw", "finiteness", "filter_upwards", "exact"], "tactic_count": 28}
{"name": "MeasureTheory.HasFiniteIntegral.max_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.HasFiniteIntegral.min_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.HasFiniteIntegral.smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": true, "tactics": ["simp", "calc", "rw", "exacts"], "tactic_count": 4}
{"name": "MeasureTheory.HasFiniteIntegral.smul_enorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": true, "tactics": ["simp", "calc", "rw", "exacts"], "tactic_count": 4}
{"name": "MeasureTheory.hasFiniteIntegral_smul_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": true, "tactics": ["obtain", "constructor", "intro", "simpa", "exact"], "tactic_count": 5}
{"name": "MeasureTheory.HasFiniteIntegral.const_mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.HasFiniteIntegral.mul_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.hasFiniteIntegral_count_iff_enorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.hasFiniteIntegral_count_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.HasFiniteIntegral.restrict", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral", "is_tactic_proof": true, "tactics": ["refine", "simpa"], "tactic_count": 2}
{"name": "MeasureTheory.termIntegrable[_]", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory._aux_Mathlib_MeasureTheory_Function_L1Space_Integrable___macroRules_MeasureTheory_termIntegrable[_]_1", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.memLp_one_iff_integrable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MeasureTheory.Integrable.aestronglyMeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Integrable.aemeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Integrable.hasFiniteIntegral", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Integrable.mono_enorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Integrable.mono", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Integrable.mono'_enorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Integrable.mono'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Integrable.congr'_enorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Integrable.congr'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integrable_congr'_enorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integrable_congr'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Integrable.congr", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integrable_congr", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integrable_const_iff_enorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "MeasureTheory.integrable_const_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.integrable_const_iff_isFiniteMeasure_enorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.integrable_const_iff_isFiniteMeasure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.Integrable.of_mem_Icc_enorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Integrable.of_mem_Icc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integrable_const_enorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integrable_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Integrable.of_finite", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Integrable.of_isEmpty", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Integrable.of_subsingleton", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MemLp.integrable_enorm_rpow", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.MemLp.integrable_norm_rpow", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.MemLp.integrable_enorm_rpow'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "by_cases", "simp", "exact"], "tactic_count": 5}
{"name": "MeasureTheory.MemLp.integrable_norm_rpow'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "by_cases", "simp", "exact"], "tactic_count": 5}
{"name": "MeasureTheory.MemLp.integrable_enorm_pow", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.MemLp.integrable_norm_pow", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.MemLp.integrable_enorm_pow'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.MemLp.integrable_norm_pow'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.integrable_enorm_rpow_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.integrable_norm_rpow_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Integrable.mono_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Integrable.of_measure_le_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.Integrable.add_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.Integrable.left_of_add_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.Integrable.right_of_add_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.integrable_add_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integrable_zero_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["constructor"], "tactic_count": 1}
{"name": "MeasureTheory.integrable_dirac", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integrable_dirac'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integrable_finset_sum_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "MeasureTheory.Integrable.smul_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.Integrable.smul_measure_nnreal", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.integrable_smul_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integrable_inv_smul_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Integrable.to_average", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["rcases", "rwa", "apply", "simpa"], "tactic_count": 4}
{"name": "MeasureTheory.integrable_average", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integrable_map_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.Integrable.comp_aemeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Integrable.comp_measurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEmbedding.integrable_map_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.integrable_map_equiv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.MeasurePreserving.integrable_comp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.MeasurePreserving.integrable_comp_of_integrable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MeasurePreserving.integrable_comp_emb", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.lintegral_edist_lt_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integrable_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.Integrable.add'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Integrable.add", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Integrable.add''", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Integrable.of_subsingleton_codomain", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integrable_finset_sum'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integrable_finset_sum", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.Integrable.neg", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Integrable.neg'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integrable_neg_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integrable_add_iff_integrable_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integrable_add_iff_integrable_right'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integrable_add_iff_integrable_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.integrable_add_iff_integrable_left'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integrable_left_of_integrable_add_of_nonneg", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["refine", "filter_upwards", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.integrable_right_of_integrable_add_of_nonneg", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integrable_add_iff_of_nonneg", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integrable_add_iff_of_nonpos", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["rw", "exact", "integrable_add_iff_of_nonneg"], "tactic_count": 3}
{"name": "MeasureTheory.integrable_add_const_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integrable_const_add_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Integrable.sub", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.Integrable.sub'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.Integrable.enorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["constructor"], "tactic_count": 1}
{"name": "MeasureTheory.Integrable.norm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["constructor"], "tactic_count": 1}
{"name": "MeasureTheory.Integrable.inf", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.Integrable.sup", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.Integrable.abs", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.Integrable.essSup_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["rw", "refine", "have", "calc", "eLpNorm", "simpa"], "tactic_count": 6}
{"name": "MeasureTheory.Integrable.smul_essSup", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["rw", "refine", "have", "calc", "eLpNorm", "simpa"], "tactic_count": 6}
{"name": "MeasureTheory.integrable_enorm_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MeasureTheory.integrable_norm_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MeasureTheory.integrable_of_norm_sub_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integrable_of_le_of_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": ["have", "filter_upwards", "simp", "exact", "have", "filter_upwards", "refine", "conv_rhs", "exact", "exact"], "tactic_count": 10}
{"name": "MeasureTheory.Integrable.prodMk", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MemLp.integrable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Integrable.measure_enorm_ge_lt_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["refine", "apply", "simpa", "simpa"], "tactic_count": 4}
{"name": "MeasureTheory.Integrable.measure_norm_ge_lt_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "MeasureTheory.Integrable.measure_norm_gt_lt_top_enorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.Integrable.measure_norm_gt_lt_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Integrable.measure_ge_lt_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["refine", "intro", "simp", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.Integrable.measure_le_lt_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["refine", "intro", "simp", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.Integrable.measure_gt_lt_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Integrable.measure_lt_lt_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.LipschitzWith.integrable_comp_iff_of_antilipschitz", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.Integrable.real_toNNReal", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["refine", "rw", "refine", "apply", "intro", "simp"], "tactic_count": 6}
{"name": "MeasureTheory.ofReal_toReal_ae_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["filter_upwards", "intro", "simp"], "tactic_count": 3}
{"name": "MeasureTheory.coe_toNNReal_ae_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["filter_upwards", "intro", "simp"], "tactic_count": 3}
{"name": "MeasureTheory.integrable_count_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["rw", "intro", "have", "simpa", "letI", "haveI", "refine", "refine", "simpa", "refine", "suffices", "grind"], "tactic_count": 12}
{"name": "MeasureTheory.integrable_withDensity_iff_integrable_coe_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "rw", "simp", "simpa", "simp"], "tactic_count": 6}
{"name": "MeasureTheory.integrable_withDensity_iff_integrable_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integrable_withDensity_iff_integrable_smul'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.integrable_withDensity_iff_integrable_coe_smul₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integrable_withDensity_iff_integrable_smul₀'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["rw", "congr", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.integrable_withDensity_iff_integrable_smul₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integrable_withDensity_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.memL1_smul_of_L1_withDensity", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.withDensitySMulLI", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.withDensitySMulLI_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.mem_L1_toReal_of_lintegral_ne_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.integrable_toReal_of_lintegral_ne_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integrable_toReal_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.lintegral_ofReal_ne_top_iff_integrable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.Integrable.pos_part", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["constructor"], "tactic_count": 1}
{"name": "MeasureTheory.Integrable.neg_part", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Integrable.smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["constructor"], "tactic_count": 1}
{"name": "MeasureTheory.Integrable.smul_enorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["constructor"], "tactic_count": 1}
{"name": "IsUnit.integrable_smul_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integrable_smul_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integrable_fun_smul_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Integrable.smul_of_top_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.Integrable.bdd_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Integrable.smul_of_top_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.Integrable.smul_bdd", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Integrable.smul_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integrable_smul_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": ["simp_rw", "hasFiniteIntegral_iff_enorm,", "intro", "have", "simp"], "tactic_count": 5}
{"name": "MeasureTheory.Integrable.const_mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Integrable.const_mul'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Integrable.mul_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Integrable.mul_const'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integrable_const_mul_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integrable_mul_const_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Integrable.bdd_mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Integrable.mul_bdd", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Integrable.mul_of_top_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Integrable.mul_of_top_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MemLp.integrable_mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Integrable.div_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MeasureTheory.Integrable.ofReal", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.Integrable.re_im_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.Integrable.re", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.Integrable.im", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.Integrable.trim", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact", "fun_prop"], "tactic_count": 4}
{"name": "MeasureTheory.integrable_of_integrable_trim", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": true, "tactics": ["obtain", "refine", "simpa"], "tactic_count": 3}
{"name": "MeasureTheory.integrable_of_forall_fin_meas_le'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integrable_of_forall_fin_meas_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Integrable.restrict", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.integrable_comp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.integrable_comp_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.integrable_comp_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Integrable.apply_continuousLinearMap", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Integrable.fst", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Integrable.snd", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integrable_prod", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.lintegral_enorm_le_liminf_of_tendsto", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integrable_of_tendsto", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L1Space.Integrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MemLp.integrable_sq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L2Space", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.memLp_two_iff_integrable_sq_norm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L2Space", "is_tactic_proof": true, "tactics": ["rw", "convert", "simp", "rw"], "tactic_count": 4}
{"name": "MeasureTheory.memLp_two_iff_integrable_sq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L2Space", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "_private.Mathlib.MeasureTheory.Function.L2Space.0.MeasureTheory.term⟪_,_⟫", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.L2Space", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.MeasureTheory.Function.L2Space.0.MeasureTheory._aux_Mathlib_MeasureTheory_Function_L2Space___macroRules__private_Mathlib_MeasureTheory_Function_L2Space_0_MeasureTheory_term⟪_,_⟫_1", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.L2Space", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.MeasureTheory.Function.L2Space.0.MeasureTheory._aux_Mathlib_MeasureTheory_Function_L2Space___unexpand_Inner_inner_1", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.L2Space", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MemLp.const_inner", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L2Space", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MemLp.inner_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L2Space", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Integrable.const_inner", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L2Space", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Integrable.inner_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L2Space", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "integral_inner", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L2Space", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "integral_eq_zero_of_forall_integral_inner_eq_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L2Space", "is_tactic_proof": true, "tactics": ["specialize"], "tactic_count": 1}
{"name": "_private.Mathlib.MeasureTheory.Function.L2Space.0.MeasureTheory.L2.term⟪_,_⟫", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.L2Space", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.MeasureTheory.Function.L2Space.0.MeasureTheory.L2._aux_Mathlib_MeasureTheory_Function_L2Space___macroRules__private_Mathlib_MeasureTheory_Function_L2Space_0_MeasureTheory_L2_term⟪_,_⟫_1", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.L2Space", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.MeasureTheory.Function.L2Space.0.MeasureTheory.L2._aux_Mathlib_MeasureTheory_Function_L2Space___unexpand_Inner_inner_1", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.L2Space", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.L2.eLpNorm_rpow_two_norm_lt_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L2Space", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.L2.eLpNorm_inner_lt_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L2Space", "is_tactic_proof": false, "tactics": ["have", "intro", "rw", "calc", "refine", "exact", "exact", "rw", "exact"], "tactic_count": 9}
{"name": "MeasureTheory.L2.instInnerSubtypeAEEqFunMemAddSubgroupLpOfNatENNReal", "kind": "instance", "module": "Mathlib.MeasureTheory.Function.L2Space", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.L2.inner_def", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L2Space", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.L2.integral_inner_eq_sq_eLpNorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L2Space", "is_tactic_proof": true, "tactics": ["simp_rw", "norm_cast", "rw", "rotate_left", "exact", "exact", "congr", "ext1", "have", "rw", "ofReal_norm_eq_enorm]", "norm_cast"], "tactic_count": 12}
{"name": "_private.Mathlib.MeasureTheory.Function.L2Space.0.MeasureTheory.L2.norm_sq_eq_re_inner", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L2Space", "is_tactic_proof": true, "tactics": ["have", "rw", "rw", "one_div,", "simp", "refine", "rw", "finiteness"], "tactic_count": 8}
{"name": "MeasureTheory.L2.mem_L1_inner", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L2Space", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MeasureTheory.L2.integrable_inner", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L2Space", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.MeasureTheory.Function.L2Space.0.MeasureTheory.L2.add_left'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L2Space", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "simp"], "tactic_count": 3}
{"name": "_private.Mathlib.MeasureTheory.Function.L2Space.0.MeasureTheory.L2.smul_left'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L2Space", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp", "rw"], "tactic_count": 4}
{"name": "MeasureTheory.L2.innerProductSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.Function.L2Space", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.L2.inner_indicatorConstLp_eq_setIntegral_inner", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L2Space", "is_tactic_proof": true, "tactics": ["rw", "have", "suffices", "setIntegral_congr_ae", "have", "refine", "congr", "exact", "have", "suffices", "simp_rw", "suffices", "rw", "simp", "exact", "have", "refine", "rw", "exact", "rw"], "tactic_count": 20}
{"name": "MeasureTheory.L2.inner_indicatorConstLp_eq_inner_setIntegral", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L2Space", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.L2.inner_indicatorConstLp_one", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L2Space", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "_private.Mathlib.MeasureTheory.Function.L2Space.0.MeasureTheory.term⟪_,_⟫_1", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.L2Space", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.MeasureTheory.Function.L2Space.0.MeasureTheory._aux_Mathlib_MeasureTheory_Function_L2Space___macroRules__private_Mathlib_MeasureTheory_Function_L2Space_0_MeasureTheory_term⟪_,_⟫_1_1", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.L2Space", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.MeasureTheory.Function.L2Space.0.MeasureTheory._aux_Mathlib_MeasureTheory_Function_L2Space___unexpand_Inner_inner_2", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.L2Space", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.BoundedContinuousFunction.inner_toLp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L2Space", "is_tactic_proof": true, "tactics": ["apply", "have", "have", "filter_upwards", "rw", "simp"], "tactic_count": 6}
{"name": "MeasureTheory.ContinuousMap.inner_toLp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.L2Space", "is_tactic_proof": true, "tactics": ["apply", "have", "have", "filter_upwards", "rw", "simp"], "tactic_count": 6}
{"name": "MeasureTheory.LocallyIntegrableOn.mono_set", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LocallyIntegrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.LocallyIntegrableOn.enorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LocallyIntegrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.LocallyIntegrableOn.norm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LocallyIntegrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.LocallyIntegrableOn.mono_enorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LocallyIntegrable", "is_tactic_proof": true, "tactics": ["intro", "rcases", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.LocallyIntegrableOn.mono", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LocallyIntegrable", "is_tactic_proof": true, "tactics": ["intro", "rcases", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.IntegrableOn.locallyIntegrableOn", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LocallyIntegrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.LocallyIntegrableOn.integrableOn_isCompact", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LocallyIntegrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.LocallyIntegrableOn.integrableOn_compact_subset", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LocallyIntegrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.LocallyIntegrableOn.exists_countable_integrableOn", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LocallyIntegrable", "is_tactic_proof": false, "tactics": ["have", "rintro", "rcases", "rcases", "exact", "choose", "obtain", "have", "obtain", "exact", "refine", "rintro", "exact", "rintro", "exact"], "tactic_count": 15}
{"name": "MeasureTheory.LocallyIntegrableOn.exists_nat_integrableOn", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LocallyIntegrable", "is_tactic_proof": true, "tactics": ["rcases", "let", "have", "have", "rcases", "refine", "intro", "have", "rcases", "rw", "exact", "exact", "intro", "obtain", "have", "obtain", "exact", "intro", "have", "rcases", "simp", "exact"], "tactic_count": 22}
{"name": "MeasureTheory.LocallyIntegrableOn.aestronglyMeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LocallyIntegrable", "is_tactic_proof": true, "tactics": ["rcases", "have", "rw", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.locallyIntegrableOn_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LocallyIntegrable", "is_tactic_proof": true, "tactics": ["refine", "rcases", "rcases", "rw", "refine", "exact"], "tactic_count": 6}
{"name": "MeasureTheory.LocallyIntegrableOn.add", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LocallyIntegrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasureTheory.LocallyIntegrableOn.neg", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LocallyIntegrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.locallyIntegrable_comap", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LocallyIntegrable", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
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{"name": "MeasureTheory.locallyIntegrableOn_of_locallyIntegrable_restrict", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LocallyIntegrable", "is_tactic_proof": true, "tactics": ["intro", "obtain", "obtain", "refine", "simpa"], "tactic_count": 5}
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{"name": "MeasureTheory.LocallyIntegrable.integrableOn_nhds_isCompact", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LocallyIntegrable", "is_tactic_proof": true, "tactics": ["refine", "refine", "rintro", "exact", "rintro", "exact", "intro", "rcases", "rcases", "exact"], "tactic_count": 10}
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{"name": "MeasureTheory.LocallyIntegrable.aestronglyMeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LocallyIntegrable", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.LocallyIntegrable.exists_nat_integrableOn", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LocallyIntegrable", "is_tactic_proof": true, "tactics": ["rcases", "refine", "simpa"], "tactic_count": 3}
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{"name": "MeasureTheory.locallyIntegrable_const_enorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LocallyIntegrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.locallyIntegrable_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LocallyIntegrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.locallyIntegrableOn_const_enorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LocallyIntegrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasureTheory.locallyIntegrable_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LocallyIntegrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.locallyIntegrableOn_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LocallyIntegrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.LocallyIntegrable.indicator", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LocallyIntegrable", "is_tactic_proof": true, "tactics": ["intro", "rcases", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.locallyIntegrable_map_homeomorph", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LocallyIntegrable", "is_tactic_proof": true, "tactics": ["refine", "rcases", "refine", "exact", "rcases", "refine", "apply", "simp", "convert", "ext", "simp"], "tactic_count": 11}
{"name": "MeasureTheory.LocallyIntegrable.add", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LocallyIntegrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.LocallyIntegrable.sub", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LocallyIntegrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.LocallyIntegrable.neg", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LocallyIntegrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.LocallyIntegrable.smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LocallyIntegrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.locallyIntegrable_finset_sum'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LocallyIntegrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.locallyIntegrable_finset_sum", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LocallyIntegrable", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.LocallyIntegrable.integrable_smul_left_of_hasCompactSupport", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LocallyIntegrable", "is_tactic_proof": true, "tactics": ["let", "have", "have", "apply", "apply", "intro", "simp", "rw", "apply", "rw", "exact", "exact"], "tactic_count": 12}
{"name": "MeasureTheory.LocallyIntegrable.integrable_smul_right_of_hasCompactSupport", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LocallyIntegrable", "is_tactic_proof": true, "tactics": ["let", "have", "have", "apply", "apply", "intro", "simp", "rw", "apply", "rw", "exact", "exact"], "tactic_count": 12}
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{"name": "MeasureTheory.integrable_iff_integrableAtFilter_atBot_atTop", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LocallyIntegrable", "is_tactic_proof": true, "tactics": ["constructor", "exact", "refine", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.integrable_iff_integrableAtFilter_atBot", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LocallyIntegrable", "is_tactic_proof": true, "tactics": ["constructor", "exact", "refine", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.integrable_iff_integrableAtFilter_atTop", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LocallyIntegrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integrableOn_Iic_iff_integrableAtFilter_atBot", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LocallyIntegrable", "is_tactic_proof": true, "tactics": ["refine", "haveI", "obtain", "refine", "exact"], "tactic_count": 5}
{"name": "MeasureTheory.integrableOn_Ici_iff_integrableAtFilter_atTop", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LocallyIntegrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Continuous.locallyIntegrable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LocallyIntegrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.locallyIntegrableOn", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LocallyIntegrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.integrableOn_of_subset_isCompact", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LocallyIntegrable", "is_tactic_proof": true, "tactics": ["refine", "have", "obtain", "apply", "filter_upwards"], "tactic_count": 5}
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{"name": "ContinuousOn.integrableOn_compact", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LocallyIntegrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.integrableOn_Icc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LocallyIntegrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.integrableOn_Icc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LocallyIntegrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.integrableOn_Ioc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LocallyIntegrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.integrableOn_uIcc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LocallyIntegrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.integrableOn_uIcc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LocallyIntegrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.integrableOn_uIoc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LocallyIntegrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.integrable_of_hasCompactSupport", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LocallyIntegrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonotoneOn.memLp_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LocallyIntegrable", "is_tactic_proof": true, "tactics": ["borelize", "have", "have", "have", "rcases", "have", "apply", "apply", "apply", "exact"], "tactic_count": 10}
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{"name": "AntitoneOn.memLp_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LocallyIntegrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntitoneOn.memLp_of_measure_ne_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LocallyIntegrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AntitoneOn.integrableOn_of_measure_ne_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LocallyIntegrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Monotone.locallyIntegrable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LocallyIntegrable", "is_tactic_proof": true, "tactics": ["intro", "rcases", "obtain", "exists_Icc_mem_subset_of_mem_nhds", "have", "refine", "exact"], "tactic_count": 7}
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{"name": "MeasureTheory.IntegrableOn.continuousOn_mul_of_subset", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LocallyIntegrable", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
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{"name": "MeasureTheory.IntegrableOn.continuousOn_smul_of_subset", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LocallyIntegrable", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
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{"name": "MeasureTheory.LocallyIntegrableOn.continuousOn_mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LocallyIntegrable", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.LocallyIntegrableOn.mul_continuousOn", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LocallyIntegrable", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.LocallyIntegrableOn.continuousOn_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LocallyIntegrable", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.LocallyIntegrableOn.smul_continuousOn", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LocallyIntegrable", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
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{"name": "MeasureTheory.Lp.coeFn_nonneg", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpOrder", "is_tactic_proof": true, "tactics": ["rw", "have", "constructor", "rwa", "rwa"], "tactic_count": 5}
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{"name": "MeasureTheory.Lp.instIsOrderedAddMonoid", "kind": "instance", "module": "Mathlib.MeasureTheory.Function.LpOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.instOrderClosedTopologySubtypeAEEqFunMemAddSubgroupOfClosedIciTopology", "kind": "instance", "module": "Mathlib.MeasureTheory.Function.LpOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MemLp.sup", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MemLp.inf", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MemLp.abs", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.instLattice", "kind": "instance", "module": "Mathlib.MeasureTheory.Function.LpOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.coeFn_sup", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.coeFn_inf", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.coeFn_abs", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.instHasSolidNorm", "kind": "instance", "module": "Mathlib.MeasureTheory.Function.LpOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MemLp.eLpNorm_lt_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MemLp.eLpNorm_ne_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.lintegral_rpow_enorm_lt_top_of_eLpNorm'_lt_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.lintegral_rpow_enorm_lt_top_of_eLpNorm_lt_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": true, "tactics": ["apply", "exact", "simpa"], "tactic_count": 3}
{"name": "MeasureTheory.eLpNorm_lt_top_iff_lintegral_rpow_enorm_lt_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.eLpNorm'_exponent_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.eLpNorm_exponent_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "MeasureTheory.eLpNorm'_zero'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": true, "tactics": ["rcases", "exact", "simp"], "tactic_count": 3}
{"name": "MeasureTheory.eLpNormEssSup_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "MeasureTheory.eLpNorm'_measure_zero_of_pos", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "MeasureTheory.eLpNorm'_measure_zero_of_neg", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.eLpNormEssSup_measure_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.eLpNorm_measure_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "by_cases", "simp", "rw", "simp"], "tactic_count": 6}
{"name": "MeasureTheory.memLp_measure_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.eLpNorm'_neg", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.eLpNorm_neg", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "by_cases", "simp", "simp"], "tactic_count": 5}
{"name": "MeasureTheory.eLpNorm_sub_comm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.MemLp.neg", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.memLp_neg_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.eLpNorm'_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": false, "tactics": ["rw", "congr", "rw", "suffices", "rw"], "tactic_count": 5}
{"name": "MeasureTheory.eLpNorm'_const'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": true, "tactics": ["rw", "congr", "rw", "suffices", "rw", "finiteness"], "tactic_count": 6}
{"name": "MeasureTheory.eLpNormEssSup_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.eLpNorm'_const_of_isProbabilityMeasure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.eLpNorm_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "simp"], "tactic_count": 3}
{"name": "MeasureTheory.eLpNorm_const'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.eLpNorm_const_lt_top_iff_enorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": true, "tactics": ["have", "by_cases", "simp", "by_cases", "rw", "simp", "rw", "obtain", "simp", "rw", "simpa"], "tactic_count": 11}
{"name": "MeasureTheory.eLpNorm_const_lt_top_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.memLp_const_enorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": true, "tactics": ["refine", "by_cases", "simp", "by_cases", "simp", "rw", "finiteness"], "tactic_count": 7}
{"name": "MeasureTheory.memLp_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.memLp_top_const_enorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.memLp_top_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.memLp_const_iff_enorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": true, "tactics": ["simp_all"], "tactic_count": 1}
{"name": "MeasureTheory.memLp_const_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.eLpNorm'_mono_enorm_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": true, "tactics": ["simp", "gcongr", "refine", "gcongr"], "tactic_count": 4}
{"name": "MeasureTheory.eLpNorm'_mono_nnnorm_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": true, "tactics": ["simp", "gcongr", "refine", "dsimp", "gcongr"], "tactic_count": 5}
{"name": "MeasureTheory.eLpNorm'_mono_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.eLpNorm'_congr_enorm_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": true, "tactics": ["have", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.eLpNorm'_congr_nnnorm_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": true, "tactics": ["have", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.eLpNorm'_congr_norm_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.eLpNorm'_congr_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.eLpNormEssSup_congr_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.eLpNormEssSup_mono_enorm_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.eLpNormEssSup_mono_nnnorm_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.eLpNorm_mono_enorm_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": true, "tactics": ["simp", "split_ifs", "exact", "exact", "exact"], "tactic_count": 5}
{"name": "MeasureTheory.eLpNorm_mono_nnnorm_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": true, "tactics": ["simp", "split_ifs", "exact", "exact", "exact"], "tactic_count": 5}
{"name": "MeasureTheory.eLpNorm_mono_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.eLpNorm_mono_ae'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.eLpNorm_mono_ae_real", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.eLpNorm_mono_enorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.eLpNorm_mono_nnnorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.eLpNorm_mono", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.eLpNorm_mono_real", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.eLpNormEssSup_le_of_ae_enorm_bound", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.eLpNormEssSup_le_of_ae_nnnorm_bound", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.eLpNormEssSup_le_of_ae_bound", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.eLpNormEssSup_lt_top_of_ae_enorm_bound", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.eLpNormEssSup_lt_top_of_ae_nnnorm_bound", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.eLpNormEssSup_lt_top_of_ae_bound", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.eLpNorm_le_of_ae_enorm_bound", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simp", "by_cases", "simp", "have", "refine", "rw"], "tactic_count": 7}
{"name": "MeasureTheory.eLpNorm_le_of_ae_nnnorm_bound", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simp", "by_cases", "simp", "have", "refine", "rw"], "tactic_count": 7}
{"name": "MeasureTheory.eLpNorm_le_of_ae_bound", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.eLpNorm_congr_enorm_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.eLpNorm_congr_nnnorm_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.eLpNorm_congr_norm_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.eLpNorm_indicator_sub_indicator", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.eLpNorm'_norm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.eLpNorm'_enorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.eLpNorm_norm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.eLpNorm_enorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.eLpNorm'_enorm_rpow", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "mul_one,"], "tactic_count": 2}
{"name": "MeasureTheory.eLpNorm_ofReal", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.eLpNorm'_norm_rpow", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "mul_one,"], "tactic_count": 2}
{"name": "MeasureTheory.eLpNorm_enorm_rpow", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "by_cases", "simp", "eLpNorm_exponent_top,", "have", "rw", "have", "have", "let", "exact", "rw", "swap", "refine", "rwa", "rw", "exact"], "tactic_count": 17}
{"name": "MeasureTheory.eLpNorm_norm_rpow", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": true, "tactics": ["rw", "symm", "convert", "rw", "exact"], "tactic_count": 5}
{"name": "MeasureTheory.eLpNorm_congr_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.memLp_congr_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.MemLp.ae_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MemLp.of_le_enorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MemLp.of_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MemLp.mono'_enorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MemLp.mono'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MemLp.congr_enorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MemLp.congr_norm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.memLp_congr_enorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.memLp_congr_norm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.memLp_top_of_bound_enorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.memLp_top_of_bound", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MemLp.of_enorm_bound", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": true, "tactics": ["apply", "rw"], "tactic_count": 2}
{"name": "MeasureTheory.MemLp.of_bound", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.memLp_of_bounded", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.eLpNorm'_mono_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "gcongr"], "tactic_count": 2}
{"name": "MeasureTheory.eLpNormEssSup_mono_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.eLpNorm_mono_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "by_cases", "simp", "simp_rw", "exact"], "tactic_count": 6}
{"name": "MeasureTheory.MemLp.mono_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.eLpNorm_indicator_eq_eLpNorm_restrict", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "by_cases", "simp_rw", "simp_rw", "rw", "congr", "simp_rw", "rw", "simp"], "tactic_count": 10}
{"name": "MeasureTheory.eLpNormEssSup_indicator_eq_eLpNormEssSup_restrict", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MeasureTheory.eLpNorm_restrict_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.eLpNorm_indicator_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.eLpNormEssSup_indicator_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": true, "tactics": ["refine", "simp_rw", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.eLpNormEssSup_indicator_const_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "exact", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.eLpNormEssSup_indicator_const_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": true, "tactics": ["refine", "by_contra", "have", "push_neg", "refine", "rw"], "tactic_count": 6}
{"name": "MeasureTheory.eLpNorm_indicator_const₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.eLpNorm_indicator_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.eLpNorm_indicator_const'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.eLpNorm_indicator_const_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": true, "tactics": ["obtain", "simp", "obtain", "simp", "exact", "let", "calc", "eLpNorm", "eLpNorm_mono_enorm"], "tactic_count": 9}
{"name": "MeasureTheory.MemLp.indicator", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.memLp_indicator_iff_restrict", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.memLp_indicator_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": true, "tactics": ["rw", "obtain", "exact", "have", "apply"], "tactic_count": 5}
{"name": "MeasureTheory.eLpNormEssSup_piecewise", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": true, "tactics": ["simp", "congr", "by_cases"], "tactic_count": 3}
{"name": "MeasureTheory.eLpNorm_top_piecewise", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MemLp.piecewise", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "exact", "refine", "obtain", "rw", "exact", "rw", "constructor", "have", "rw", "exact", "have", "have", "simp", "rw", "exact"], "tactic_count": 17}
{"name": "MeasureTheory.eLpNorm_restrict_eq_of_support_subset", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "by_cases", "simp", "exact", "simp_rw", "congr", "apply", "have", "simpa"], "tactic_count": 10}
{"name": "MeasureTheory.MemLp.restrict", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasureTheory.eLpNorm_comp_measurePreserving", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEEqFun.eLpNorm_compMeasurePreserving", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
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{"name": "MeasureTheory.eLpNorm'_le_nnreal_smul_eLpNorm'_of_ae_le_mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "rw", "simp_rw", "apply", "simp_rw", "exact"], "tactic_count": 6}
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{"name": "MeasureTheory.mul_meas_ge_le_pow_eLpNorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.ChebyshevMarkov", "is_tactic_proof": false, "tactics": ["have", "refine", "rw", "exact", "rw", "gcongr", "exact"], "tactic_count": 7}
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{"name": "MeasureTheory.meas_ge_le_mul_pow_eLpNorm_enorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.ChebyshevMarkov", "is_tactic_proof": true, "tactics": ["by_cases", "have", "simp", "have", "have", "rw", "one_mul]", "exact"], "tactic_count": 8}
{"name": "MeasureTheory.MemLp.meas_ge_lt_top'_enorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.ChebyshevMarkov", "is_tactic_proof": false, "tactics": ["apply", "meas_ge_le_mul_pow_eLpNorm_enorm", "simp", "simp"], "tactic_count": 4}
{"name": "MeasureTheory.MemLp.meas_ge_lt_top'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.ChebyshevMarkov", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.MemLp.meas_ge_lt_top_enorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.ChebyshevMarkov", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MemLp.meas_ge_lt_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.ChebyshevMarkov", "is_tactic_proof": true, "tactics": ["simp_rw", "apply"], "tactic_count": 2}
{"name": "MeasureTheory.eLpNorm'_le_eLpNorm'_mul_rpow_measure_univ", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.CompareExp", "is_tactic_proof": true, "tactics": ["have", "by_cases", "rw", "have", "let", "have", "repeat", "rw", "let", "have", "calc"], "tactic_count": 11}
{"name": "MeasureTheory.eLpNorm'_le_eLpNormEssSup_mul_rpow_measure_univ", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.CompareExp", "is_tactic_proof": false, "tactics": ["have", "refine", "have", "exact", "rw", "nth_rw", "rw", "gcongr", "rwa"], "tactic_count": 9}
{"name": "MeasureTheory.eLpNorm_le_eLpNorm_mul_rpow_measure_univ", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.CompareExp", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "rw", "have", "have", "by_cases", "simp", "by_cases", "simp", "rw", "have", "refine", "congr", "exact", "have", "have", "rw", "have", "exact"], "tactic_count": 19}
{"name": "MeasureTheory.eLpNorm'_le_eLpNorm'_of_exponent_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.CompareExp", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "MeasureTheory.eLpNorm'_le_eLpNormEssSup", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.CompareExp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.eLpNorm_le_eLpNorm_of_exponent_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.CompareExp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.eLpNorm'_lt_top_of_eLpNorm'_lt_top_of_exponent_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.CompareExp", "is_tactic_proof": true, "tactics": ["rcases", "rw", "simp", "have", "calc", "eLpNorm", "eLpNorm'_le_eLpNorm'_mul_rpow_measure_univ", "rw", "refine", "rwa"], "tactic_count": 10}
{"name": "MeasureTheory.MemLp.mono_exponent", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.CompareExp", "is_tactic_proof": true, "tactics": ["obtain", "by_cases", "rwa", "rw", "refine", "by_cases", "have", "rw", "rwa", "have", "by_cases", "rw", "rw", "refine", "refine", "exact", "have", "by_contra", "have", "rw", "exact", "have", "rw", "rw", "exact"], "tactic_count": 25}
{"name": "MeasureTheory.MemLp.mono_exponent_of_measure_support_ne_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.CompareExp", "is_tactic_proof": false, "tactics": ["have", "apply", "apply", "contrapose", "exact", "rw", "have", "exact"], "tactic_count": 8}
{"name": "MeasureTheory.eLpNorm_le_eLpNorm_top_mul_eLpNorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.CompareExp", "is_tactic_proof": false, "tactics": ["calc", "eLpNorm", "simp", "rw", "gcongr", "obtain", "simp", "rw", "simp_rw", "exact", "obtain", "simp_rw", "rw", "simp", "apply", "filter_upwards", "gcongr", "exact"], "tactic_count": 18}
{"name": "MeasureTheory.eLpNorm_le_eLpNorm_mul_eLpNorm_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.CompareExp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.eLpNorm'_le_eLpNorm'_mul_eLpNorm'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.CompareExp", "is_tactic_proof": true, "tactics": ["calc", "eLpNorm", "simp", "gcongr", "refine", "gcongr", "simp", "simpa", "simp", "rw", "gcongr", "simpa"], "tactic_count": 12}
{"name": "MeasureTheory.eLpNorm_le_eLpNorm_mul_eLpNorm_of_nnnorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.CompareExp", "is_tactic_proof": true, "tactics": ["have", "obtain", "simp_all", "have", "exact", "obtain", "simp_all", "have", "exact", "obtain", "obtain", "have", "have", "rw", "simpa", "have", "obtain", "have", "rw", "exact", "all_goals", "first", "positivity", "finiteness"], "tactic_count": 24}
{"name": "MeasureTheory.eLpNorm_le_eLpNorm_mul_eLpNorm'_of_norm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.CompareExp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MemLp.of_bilin", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.CompareExp", "is_tactic_proof": true, "tactics": ["refine", "apply", "finiteness"], "tactic_count": 3}
{"name": "MeasureTheory.eLpNorm_smul_le_eLpNorm_top_mul_eLpNorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.CompareExp", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.eLpNorm_smul_le_eLpNorm_mul_eLpNorm_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.CompareExp", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.eLpNorm'_smul_le_mul_eLpNorm'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.CompareExp", "is_tactic_proof": true, "tactics": ["simpa", "eLpNorm'_le_eLpNorm'_mul_eLpNorm", "hpqr"], "tactic_count": 3}
{"name": "MeasureTheory.eLpNorm_smul_le_mul_eLpNorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.CompareExp", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.MemLp.smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.CompareExp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MemLp.mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.CompareExp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MemLp.mul'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.CompareExp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MemLp.prod", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.CompareExp", "is_tactic_proof": true, "tactics": ["induction", "empty", "cons", "rw", "exact"], "tactic_count": 5}
{"name": "MeasureTheory.MemLp.prod'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.CompareExp", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.eLpNorm'", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.eLpNorm'_eq_lintegral_enorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.eLpNormEssSup", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.eLpNormEssSup_eq_essSup_enorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.eLpNorm_eq_eLpNorm'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.eLpNorm_nnreal_eq_eLpNorm'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.eLpNorm_eq_lintegral_rpow_enorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.eLpNorm_nnreal_eq_lintegral", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.eLpNorm_one_eq_lintegral_enorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Defs", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MeasureTheory.eLpNorm_exponent_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.MemLp.aestronglyMeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MemLp.aemeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.lintegral_rpow_enorm_eq_rpow_eLpNorm'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.eLpNorm_nnreal_pow_eq_lintegral", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Defs", "is_tactic_proof": true, "tactics": ["simp", "lintegral_rpow_enorm_eq_rpow_eLpNorm"], "tactic_count": 2}
{"name": "MeasureTheory.MemLp.comp_fst", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Prod", "is_tactic_proof": true, "tactics": ["have", "change", "rw", "simpa", "simpa"], "tactic_count": 5}
{"name": "MeasureTheory.MemLp.comp_snd", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Prod", "is_tactic_proof": true, "tactics": ["have", "change", "rw", "simpa", "simpa"], "tactic_count": 5}
{"name": "MeasureTheory.eLpNorm'_add_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.TriangleInequality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.eLpNorm'_add_le_of_le_one", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.TriangleInequality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.eLpNormEssSup_add_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.TriangleInequality", "is_tactic_proof": true, "tactics": ["refine", "simp_rw", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.eLpNorm_add_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.TriangleInequality", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "by_cases", "simp", "have", "repeat", "exact"], "tactic_count": 7}
{"name": "MeasureTheory.LpAddConst", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.TriangleInequality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.LpAddConst_of_one_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.TriangleInequality", "is_tactic_proof": true, "tactics": ["rw", "intro", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.LpAddConst_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.TriangleInequality", "is_tactic_proof": true, "tactics": ["rw", "intro", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.LpAddConst_lt_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.TriangleInequality", "is_tactic_proof": true, "tactics": ["rw", "split_ifs", "apply", "rw", "exact", "exact"], "tactic_count": 6}
{"name": "MeasureTheory.eLpNorm_add_le'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.TriangleInequality", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rcases", "simp", "convert", "have", "simp", "simpa", "simpa"], "tactic_count": 9}
{"name": "MeasureTheory.exists_Lp_half", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.TriangleInequality", "is_tactic_proof": false, "tactics": ["have", "nhdsWithin_le_nhds", "simp", "rcases", "refine", "calc", "eLpNorm"], "tactic_count": 7}
{"name": "MeasureTheory.eLpNorm_sub_le'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.TriangleInequality", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.eLpNorm_sub_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.TriangleInequality", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.eLpNorm_add_lt_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.TriangleInequality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.eLpNorm'_sum_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.TriangleInequality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.eLpNorm_sum_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.TriangleInequality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MemLp.add", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.TriangleInequality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MemLp.sub", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.TriangleInequality", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.memLp_finset_sum", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.TriangleInequality", "is_tactic_proof": true, "tactics": ["haveI", "revert", "refine", "simp", "intro", "simp", "exact"], "tactic_count": 7}
{"name": "MeasureTheory.memLp_finset_sum'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.TriangleInequality", "is_tactic_proof": true, "tactics": ["convert", "ext", "simp"], "tactic_count": 3}
{"name": "MeasureTheory.eLpNorm'_trim", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Trim", "is_tactic_proof": true, "tactics": ["simp_rw", "congr", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.limsup_trim", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Trim", "is_tactic_proof": true, "tactics": ["simp_rw", "suffices", "ext1", "suffices", "refine", "exact"], "tactic_count": 6}
{"name": "MeasureTheory.essSup_trim", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Trim", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.eLpNormEssSup_trim", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Trim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.eLpNorm_trim", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Trim", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "by_cases", "simpa", "simpa"], "tactic_count": 5}
{"name": "MeasureTheory.eLpNorm_trim_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Trim", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.memLp_of_memLp_trim", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSeminorm.Trim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.eLpNorm_aeeqFun", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MemLp.eLpNorm_mk_lt_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.term_→₁[_]_", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory._aux_Mathlib_MeasureTheory_Function_LpSpace_Basic___macroRules_MeasureTheory_term_→₁[_]__1", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory._aux_Mathlib_MeasureTheory_Function_LpSpace_Basic___unexpand_MeasureTheory_Lp_1", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.term_→₂[_]_", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory._aux_Mathlib_MeasureTheory_Function_LpSpace_Basic___macroRules_MeasureTheory_term_→₂[_]__1", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory._aux_Mathlib_MeasureTheory_Function_LpSpace_Basic___unexpand_MeasureTheory_Lp_2", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MemLp.toLp", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MemLp.toLp_val", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MemLp.coeFn_toLp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MemLp.toLp_congr", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.MemLp.toLp_eq_toLp_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.MemLp.toLp_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MemLp.toLp_add", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MemLp.toLp_neg", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MemLp.toLp_sub", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.instCoeFun", "kind": "instance", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.ext", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.Lp.mem_Lp_iff_eLpNorm_lt_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.mem_Lp_iff_memLp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.Lp.antitone", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.coeFn_mk", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.coe_mk", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.toLp_coeFn", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.Lp.eLpNorm_lt_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.eLpNorm_ne_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.stronglyMeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.aestronglyMeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.memLp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.coeFn_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.coeFn_neg", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.coeFn_add", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.coeFn_sub", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.const_mem_Lp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.instNorm", "kind": "instance", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.instNNNorm", "kind": "instance", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.instDist", "kind": "instance", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.instEDist", "kind": "instance", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.norm_def", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.nnnorm_def", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.coe_nnnorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.enorm_def", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.norm_toLp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Lp.nnnorm_toLp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.enorm_toLp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.Lp.dist_def", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "apply"], "tactic_count": 3}
{"name": "MeasureTheory.Lp.edist_def", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.edist_dist", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Lp.dist_edist", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.dist_eq_norm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.edist_toLp_toLp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.Lp.edist_toLp_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.Lp.nnnorm_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": true, "tactics": ["rw", "change", "simp"], "tactic_count": 3}
{"name": "MeasureTheory.Lp.norm_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.norm_measure_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.Lp.norm_exponent_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.Lp.nnnorm_eq_zero_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "cases", "inl", "rw", "exact", "inr"], "tactic_count": 7}
{"name": "MeasureTheory.Lp.norm_eq_zero_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.eq_zero_iff_ae_eq_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Lp.nnnorm_neg", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Lp.norm_neg", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.nnnorm_le_mul_nnnorm_of_ae_le_mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": true, "tactics": ["simp", "have", "rwa", "finiteness", "exact"], "tactic_count": 5}
{"name": "MeasureTheory.Lp.norm_le_mul_norm_of_ae_le_mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": true, "tactics": ["rcases", "lift", "exact", "simp", "have", "simp"], "tactic_count": 6}
{"name": "MeasureTheory.Lp.norm_le_norm_of_ae_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.Lp.mem_Lp_of_nnnorm_ae_le_mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.mem_Lp_of_ae_le_mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.mem_Lp_of_nnnorm_ae_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.mem_Lp_of_ae_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.mem_Lp_of_ae_nnnorm_bound", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.mem_Lp_of_ae_bound", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.nnnorm_le_of_ae_bound", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "by_cases", "simp", "simp", "rw", "refine", "rw", "mul_comm,"], "tactic_count": 8}
{"name": "MeasureTheory.Lp.norm_le_of_ae_bound", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": true, "tactics": ["lift", "have", "rwa"], "tactic_count": 3}
{"name": "MeasureTheory.Lp.instNormedAddCommGroup", "kind": "instance", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp._example", "kind": "example", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": true, "tactics": ["with_reducible_and_instances"], "tactic_count": 1}
{"name": "MeasureTheory.Lp._example", "kind": "example", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": true, "tactics": ["with_reducible_and_instances"], "tactic_count": 1}
{"name": "MeasureTheory.Lp.const_smul_mem_Lp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.Lp.LpSubmodule", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.coe_LpSubmodule", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.instModule", "kind": "instance", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.coeFn_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.instIsCentralScalar", "kind": "instance", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.instSMulCommClass", "kind": "instance", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.instIsScalarTower", "kind": "instance", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.instIsBoundedSMul", "kind": "instance", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.instNormedSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MemLp.toLp_const_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MemLp.enorm_rpow_div", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": true, "tactics": ["refine", "by_cases", "simp", "by_cases", "simp", "by_cases", "simp", "rw", "simpa", "rw", "apply", "rw", "exact"], "tactic_count": 13}
{"name": "MeasureTheory.MemLp.norm_rpow_div", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": true, "tactics": ["refine", "by_cases", "simp", "by_cases", "simp", "by_cases", "simp", "rw", "exact", "rw", "apply", "rw", "exact"], "tactic_count": 13}
{"name": "MeasureTheory.memLp_enorm_rpow_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": true, "tactics": ["refine", "apply", "convert", "ext", "have", "simp", "rw"], "tactic_count": 7}
{"name": "MeasureTheory.memLp_norm_rpow_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": true, "tactics": ["refine", "apply", "convert", "ext", "rw", "mul_inv_cancel₀,", "simp", "rw"], "tactic_count": 8}
{"name": "MeasureTheory.MemLp.enorm_rpow", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "MeasureTheory.MemLp.norm_rpow", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "MeasureTheory.AEEqFun.compMeasurePreserving_mem_Lp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": true, "tactics": ["rw", "rwa"], "tactic_count": 2}
{"name": "MeasureTheory.Lp.compMeasurePreserving", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.compMeasurePreserving_val", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.coeFn_compMeasurePreserving", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.norm_compMeasurePreserving", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.isometry_compMeasurePreserving", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.toLp_compMeasurePreserving", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.compMeasurePreservingₗ", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.compMeasurePreservingₗᵢ", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzWith.comp_memLp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MemLp.of_comp_antilipschitzWith", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": ["have", "intro", "rw", "apply", "have", "exact"], "tactic_count": 6}
{"name": "MeasureTheory.MemLp.continuousLinearMap_comp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzWith.memLp_comp_iff_of_antilipschitz", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzWith.compLp", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzWith.coeFn_compLp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzWith.compLp_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply", "filter_upwards", "simp"], "tactic_count": 4}
{"name": "LipschitzWith.norm_compLp_sub_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": true, "tactics": ["apply", "filter_upwards", "simp", "exact"], "tactic_count": 4}
{"name": "LipschitzWith.norm_compLp_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "LipschitzWith.lipschitzWith_compLp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzWith.continuous_compLp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.compLp", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.coeFn_compLp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.coeFn_compLp'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.comp_memLp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.comp_memLp'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MemLp.ofReal", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.memLp_re_im_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": true, "tactics": ["refine", "rintro", "convert", "ext1", "rw"], "tactic_count": 5}
{"name": "ContinuousLinearMap.add_compLp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": true, "tactics": ["ext1", "grw", "refine", "filter_upwards", "rw"], "tactic_count": 5}
{"name": "ContinuousLinearMap.smul_compLp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": true, "tactics": ["ext1", "grw", "refine", "rw"], "tactic_count": 4}
{"name": "ContinuousLinearMap.norm_compLp_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.compLpₗ", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.compLpL", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.coeFn_compLpL", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.add_compLpL", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": true, "tactics": ["ext1"], "tactic_count": 1}
{"name": "ContinuousLinearMap.smul_compLpL", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": true, "tactics": ["ext1"], "tactic_count": 1}
{"name": "ContinuousLinearMap.norm_compLpL_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.lipschitzWith_pos_part", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MemLp.pos_part", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MemLp.neg_part", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.posPart", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.negPart", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.coe_posPart", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.coeFn_posPart", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.coeFn_negPart_eq_max", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": true, "tactics": ["rw", "filter_upwards", "rw"], "tactic_count": 3}
{"name": "MeasureTheory.Lp.coeFn_negPart", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.continuous_posPart", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.continuous_negPart", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": true, "tactics": ["unfold", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.Lp.pow_mul_meas_ge_le_enorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.mul_meas_ge_le_pow_enorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.mul_meas_ge_le_pow_enorm'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.meas_ge_le_mul_pow_enorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.instStarSubtypeAEEqFunMemAddSubgroup", "kind": "instance", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.coeFn_star", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.instInvolutiveStarSubtypeAEEqFunMemAddSubgroup", "kind": "instance", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.instTrivialStarSubtypeAEEqFunMemAddSubgroup", "kind": "instance", "module": "Mathlib.MeasureTheory.Function.LpSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.eLpNorm'_lim_eq_lintegral_liminf", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Complete", "is_tactic_proof": false, "tactics": ["suffices", "rw", "refine", "dsimp", "rw", "refine", "exact"], "tactic_count": 7}
{"name": "MeasureTheory.Lp.eLpNorm'_lim_le_liminf_eLpNorm'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Complete", "is_tactic_proof": true, "tactics": ["rw", "rw", "refine", "have", "have", "have", "refine", "all_goals", "rw", "simp_rw"], "tactic_count": 10}
{"name": "MeasureTheory.Lp.eLpNorm_exponent_top_lim_eq_essSup_liminf", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Complete", "is_tactic_proof": true, "tactics": ["rw", "refine", "dsimp", "apply", "exact"], "tactic_count": 5}
{"name": "MeasureTheory.Lp.eLpNorm_exponent_top_lim_le_liminf_eLpNorm_exponent_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Complete", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.Lp.eLpNorm_lim_le_liminf_eLpNorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Complete", "is_tactic_proof": true, "tactics": ["obtain", "simp", "by_cases", "simp_rw", "exact", "simp_rw", "have", "exact"], "tactic_count": 8}
{"name": "MeasureTheory.Lp.eLpNorm_le_of_ae_tendsto", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Complete", "is_tactic_proof": true, "tactics": ["obtain", "have", "filter_upwards", "exact", "calc", "refine", "obtain", "exact"], "tactic_count": 8}
{"name": "MeasureTheory.Lp.tendsto_Lp_iff_tendsto_eLpNorm'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Complete", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "rw", "rw", "exact"], "tactic_count": 5}
{"name": "MeasureTheory.Lp.tendsto_Lp_iff_tendsto_eLpNorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Complete", "is_tactic_proof": true, "tactics": ["rw", "suffices", "rw", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.Lp.tendsto_Lp_iff_tendsto_eLpNorm''", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Complete", "is_tactic_proof": true, "tactics": ["rw", "refine", "apply", "filter_upwards", "hx₁", "rw", "exact"], "tactic_count": 7}
{"name": "MeasureTheory.Lp.tendsto_Lp_of_tendsto_eLpNorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Complete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.cauchySeq_Lp_iff_cauchySeq_eLpNorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Complete", "is_tactic_proof": true, "tactics": ["simp_rw", "rw", "rw", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.Lp.completeSpace_lp_of_cauchy_complete_eLpNorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Complete", "is_tactic_proof": true, "tactics": ["let", "have", "refine", "rsuffices", "exact", "obtain", "let", "have", "have", "change", "rw", "exact", "have", "rwa", "have", "rw", "exact", "let", "refine", "specialize", "rw", "dsimp", "rwa", "rw", "exact"], "tactic_count": 25}
{"name": "_private.Mathlib.MeasureTheory.Function.LpSpace.Complete.0.MeasureTheory.Lp.eLpNorm'_sum_norm_sub_le_tsum_of_cauchy_eLpNorm'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Complete", "is_tactic_proof": true, "tactics": ["let", "have", "rw", "refine", "simp_rw", "refine", "exact"], "tactic_count": 7}
{"name": "_private.Mathlib.MeasureTheory.Function.LpSpace.Complete.0.MeasureTheory.Lp.lintegral_rpow_sum_enorm_sub_le_rpow_tsum", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Complete", "is_tactic_proof": true, "tactics": ["have", "rw", "simp_rw", "have", "ext1", "congr", "simp_rw", "rw", "rw", "exact", "exact", "rwa"], "tactic_count": 12}
{"name": "_private.Mathlib.MeasureTheory.Function.LpSpace.Complete.0.MeasureTheory.Lp.lintegral_rpow_tsum_coe_enorm_sub_le_tsum", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Complete", "is_tactic_proof": true, "tactics": ["have", "suffices", "rwa", "have", "intro", "rw", "simp_rw", "rw", "have", "refine", "have", "have", "refine", "all_goals", "rw", "refine", "exact"], "tactic_count": 17}
{"name": "_private.Mathlib.MeasureTheory.Function.LpSpace.Complete.0.MeasureTheory.Lp.tsum_enorm_sub_ae_lt_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Complete", "is_tactic_proof": true, "tactics": ["have", "have", "have", "refine", "rwa", "have", "refine", "exact", "refine", "rwa"], "tactic_count": 10}
{"name": "MeasureTheory.Lp.ae_tendsto_of_cauchy_eLpNorm'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Complete", "is_tactic_proof": false, "tactics": ["have", "have", "eLpNorm'_sum_norm_sub_le_tsum_of_cauchy_eLpNorm", "have", "lintegral_rpow_sum_enorm_sub_le_rpow_tsum", "have", "lintegral_rpow_tsum_coe_enorm_sub_le_tsum", "have", "exact", "have", "refine", "let", "exact", "refine", "obtain", "have", "ext1", "change", "rw", "rw", "have", "ext1", "abel", "rw", "exact"], "tactic_count": 25}
{"name": "MeasureTheory.Lp.ae_tendsto_of_cauchy_eLpNorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Complete", "is_tactic_proof": true, "tactics": ["by_cases", "simp_rw", "have", "simp_rw", "exact", "simp_rw", "refine", "refine", "intro", "specialize", "rw", "ofReal_norm_eq_enorm]", "exact", "rw", "exact", "have", "rw", "exact", "have", "intro", "specialize", "rwa", "exact"], "tactic_count": 23}
{"name": "MeasureTheory.Lp.cauchy_tendsto_of_tendsto", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Complete", "is_tactic_proof": true, "tactics": ["rw", "intro", "have", "suffices", "exact", "obtain", "refine", "have", "refine", "refine", "simp_rw", "exact", "refine", "refine", "refine", "exact"], "tactic_count": 16}
{"name": "MeasureTheory.Lp.memLp_of_cauchy_tendsto", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Complete", "is_tactic_proof": true, "tactics": ["refine", "rw", "obtain", "specialize", "have", "rw", "refine", "rw", "constructor", "refine", "have", "rwa", "exact"], "tactic_count": 13}
{"name": "MeasureTheory.Lp.cauchy_complete_eLpNorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Complete", "is_tactic_proof": false, "tactics": ["obtain", "exists_stronglyMeasurable_limit_of_tendsto_ae", "have", "cauchy_tendsto_of_tendsto", "have", "exact"], "tactic_count": 6}
{"name": "MeasureTheory.Lp.instCompleteSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.Function.LpSpace.Complete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.compMeasurePreserving_continuous", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.ContinuousCompMeasurePreserving", "is_tactic_proof": true, "tactics": ["have", "refine", "continuous_prod_of_dense_continuous_lipschitzWith", "intro", "lift", "induction", "add", "hνs", "dsimp", "refine", "apply", "exact"], "tactic_count": 12}
{"name": "Filter.Tendsto.compMeasurePreservingLp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.ContinuousCompMeasurePreserving", "is_tactic_proof": true, "tactics": ["have", "replace", "tendsto_subtype_rng.2", "convert"], "tactic_count": 4}
{"name": "ContinuousWithinAt.compMeasurePreservingLp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.ContinuousCompMeasurePreserving", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.compMeasurePreservingLp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.ContinuousCompMeasurePreserving", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.compMeasurePreservingLp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.ContinuousCompMeasurePreserving", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.compMeasurePreservingLp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.ContinuousCompMeasurePreserving", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.boundedContinuousFunction", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.LpSpace.ContinuousFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.mem_boundedContinuousFunction_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.ContinuousFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.memLp_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.ContinuousFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.mem_Lp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.ContinuousFunctions", "is_tactic_proof": true, "tactics": ["refine", "filter_upwards", "convert"], "tactic_count": 3}
{"name": "BoundedContinuousFunction.Lp_nnnorm_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.ContinuousFunctions", "is_tactic_proof": true, "tactics": ["apply", "refine", "intro", "rw", "convert"], "tactic_count": 5}
{"name": "BoundedContinuousFunction.Lp_norm_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.ContinuousFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.toLpHom", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.LpSpace.ContinuousFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.range_toLpHom", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.ContinuousFunctions", "is_tactic_proof": true, "tactics": ["symm", "exact"], "tactic_count": 2}
{"name": "BoundedContinuousFunction.toLp", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.LpSpace.ContinuousFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.coeFn_toLp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.ContinuousFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.range_toLp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.ContinuousFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.toLp_norm_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.ContinuousFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.toLp_inj", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.ContinuousFunctions", "is_tactic_proof": true, "tactics": ["refine", "rw", "refine", "rw"], "tactic_count": 4}
{"name": "BoundedContinuousFunction.toLp_injective", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.ContinuousFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.toLp", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.LpSpace.ContinuousFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.range_toLp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.ContinuousFunctions", "is_tactic_proof": true, "tactics": ["refine", "have", "convert", "rw"], "tactic_count": 4}
{"name": "ContinuousMap.coeFn_toLp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.ContinuousFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.toLp_def", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.ContinuousFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.toLp_comp_toContinuousMap", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.ContinuousFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.coe_toLp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.ContinuousFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.toLp_injective", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.ContinuousFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.toLp_inj", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.ContinuousFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.hasSum_of_hasSum_Lp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.ContinuousFunctions", "is_tactic_proof": true, "tactics": ["convert", "exact"], "tactic_count": 2}
{"name": "ContinuousMap.toLp_norm_eq_toLp_norm_coe", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.ContinuousFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.toLp_norm_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.ContinuousFunctions", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "DomMulAct.instSMulSubtypeAEEqFunMemAddSubgroupLp", "kind": "instance", "module": "Mathlib.MeasureTheory.Function.LpSpace.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.smul_Lp_val", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.smul_Lp_ae_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.mk_smul_toLp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.smul_Lp_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.mk_smul_indicatorConstLp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.instSMulCommClassSubtypeAEEqFunMemAddSubgroupLp", "kind": "instance", "module": "Mathlib.MeasureTheory.Function.LpSpace.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.instSMulCommClassSubtypeAEEqFunMemAddSubgroupLp_1", "kind": "instance", "module": "Mathlib.MeasureTheory.Function.LpSpace.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.instSMulCommClassSubtypeAEEqFunMemAddSubgroupLp_2", "kind": "instance", "module": "Mathlib.MeasureTheory.Function.LpSpace.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.smul_Lp_add", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.DomAct.Basic", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "DomMulAct.smul_Lp_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.smul_Lp_neg", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.DomAct.Basic", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "DomMulAct.smul_Lp_sub", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.DomAct.Basic", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "DomMulAct.instDistribSMulSubtypeAEEqFunMemAddSubgroupLp", "kind": "instance", "module": "Mathlib.MeasureTheory.Function.LpSpace.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.norm_smul_Lp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.nnnorm_smul_Lp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.dist_smul_Lp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.DomAct.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DomMulAct.edist_smul_Lp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.DomAct.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DomMulAct.instIsIsometricSMulSubtypeAEEqFunMemAddSubgroupLp", "kind": "instance", "module": "Mathlib.MeasureTheory.Function.LpSpace.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.instMulActionSubtypeAEEqFunMemAddSubgroupLp", "kind": "instance", "module": "Mathlib.MeasureTheory.Function.LpSpace.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DomMulAct.instDistribMulActionSubtypeAEEqFunMemAddSubgroupLp", "kind": "instance", "module": "Mathlib.MeasureTheory.Function.LpSpace.DomAct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.instContinuousSMulDomMulAct", "kind": "instance", "module": "Mathlib.MeasureTheory.Function.LpSpace.DomAct.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.exists_eLpNorm_indicator_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Indicator", "is_tactic_proof": true, "tactics": ["rcases", "exact", "have", "have", "have", "obtain", "have", "rw", "convert", "simp", "have", "obtain", "obtain", "refine", "simpa", "refine", "grw"], "tactic_count": 17}
{"name": "HasCompactSupport.memLp_of_bound", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Indicator", "is_tactic_proof": true, "tactics": ["have", "exact", "this.mono_exponent_of_measure_support_ne_top", "le_top"], "tactic_count": 4}
{"name": "Continuous.memLp_of_hasCompactSupport", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Indicator", "is_tactic_proof": true, "tactics": ["have", "exact", "this.mono_exponent_of_measure_support_ne_top", "le_top"], "tactic_count": 4}
{"name": "MeasureTheory.indicatorConstLp", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.LpSpace.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.indicatorConstLp_add", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Indicator", "is_tactic_proof": true, "tactics": ["simp_rw", "rfl"], "tactic_count": 2}
{"name": "MeasureTheory.indicatorConstLp_sub", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Indicator", "is_tactic_proof": true, "tactics": ["simp_rw", "rfl"], "tactic_count": 2}
{"name": "MeasureTheory.indicatorConstLp_coeFn", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.indicatorConstLp_coeFn_mem", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.indicatorConstLp_coeFn_notMem", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.norm_indicatorConstLp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Indicator", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.norm_indicatorConstLp_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Indicator", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.norm_indicatorConstLp'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Indicator", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "exact", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.norm_indicatorConstLp_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Indicator", "is_tactic_proof": true, "tactics": ["rw", "refine", "refine", "rw", "finiteness"], "tactic_count": 5}
{"name": "MeasureTheory.nnnorm_indicatorConstLp_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.enorm_indicatorConstLp_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Indicator", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.edist_indicatorConstLp_eq_enorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Indicator", "is_tactic_proof": true, "tactics": ["unfold", "rw"], "tactic_count": 2}
{"name": "MeasureTheory.dist_indicatorConstLp_eq_norm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Indicator", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.tendsto_indicatorConstLp_set", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Indicator", "is_tactic_proof": true, "tactics": ["rw", "have", "simp", "convert", "simp", "simp"], "tactic_count": 6}
{"name": "MeasureTheory.continuous_indicatorConstLp_set", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.indicatorConstLp_empty", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Indicator", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.indicatorConstLp_inj", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Indicator", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MeasureTheory.memLp_add_of_disjoint", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Indicator", "is_tactic_proof": true, "tactics": ["borelize", "refine", "rw", "rw"], "tactic_count": 4}
{"name": "MeasureTheory.indicatorConstLp_disjoint_union", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Indicator", "is_tactic_proof": true, "tactics": ["ext1", "grw", "refine", "rw"], "tactic_count": 4}
{"name": "MeasureTheory.Lp.const", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.LpSpace.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.coeFn_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.const_val", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MemLp.toLp_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.indicatorConstLp_univ", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Indicator", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.Lp.norm_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Indicator", "is_tactic_proof": true, "tactics": ["have", "rw", "rw"], "tactic_count": 3}
{"name": "MeasureTheory.Lp.norm_const'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Indicator", "is_tactic_proof": true, "tactics": ["rw", "rw"], "tactic_count": 2}
{"name": "MeasureTheory.Lp.norm_const_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Indicator", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.Lp.constₗ", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.LpSpace.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.constL", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.LpSpace.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.norm_constL_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.indicatorConstLp_compMeasurePreserving", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.indicatorConstLp_eq_toSpanSingleton_compLp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.LpSpace.Indicator", "is_tactic_proof": true, "tactics": ["ext1", "refine", "have", "rw", "refine", "refine", "dsimp", "rw", "simp_rw", "by_cases"], "tactic_count": 10}
{"name": "IndexedPartition.measurable_piecewise", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.Piecewise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IndexedPartition.aemeasurable_piecewise", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.Piecewise", "is_tactic_proof": true, "tactics": ["choose", "refine", "filter_upwards"], "tactic_count": 3}
{"name": "IndexedPartition.simpleFunc_piecewise", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.Piecewise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IndexedPartition.stronglyMeasurable_piecewise", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.Piecewise", "is_tactic_proof": true, "tactics": ["by_cases", "refine", "simp", "simp", "obtain", "classical", "let", "have", "intro", "unfold", "refine", "by_cases", "have", "simpa", "simp", "grind", "have", "refine", "exact", "simp", "have", "obtain", "refine", "have", "rw", "have", "simpa", "have", "filter_upwards", "exact"], "tactic_count": 30}
{"name": "IndexedPartition.aestronglyMeasurable_piecewise", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.Piecewise", "is_tactic_proof": true, "tactics": ["choose", "refine", "filter_upwards"], "tactic_count": 3}
{"name": "_private.Mathlib.MeasureTheory.Function.SimpleFunc.0.MeasureTheory.term_→ₛ_", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.MeasureTheory.Function.SimpleFunc.0.MeasureTheory._aux_Mathlib_MeasureTheory_Function_SimpleFunc___macroRules__private_Mathlib_MeasureTheory_Function_SimpleFunc_0_MeasureTheory_term_→ₛ__1", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.MeasureTheory.Function.SimpleFunc.0.MeasureTheory._aux_Mathlib_MeasureTheory_Function_SimpleFunc___unexpand_MeasureTheory_SimpleFunc_1", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.instFunLike", "kind": "instance", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.coe_injective", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.ext", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.finite_range", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.measurableSet_fiber", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.coe_mk", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.apply_mk", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.ofFinite", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.ofIsEmpty", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.range", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.mem_range", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.mem_range_self", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.coe_range", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.mem_range_of_measure_ne_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.forall_mem_range", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.SimpleFunc.exists_range_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.SimpleFunc.preimage_eq_empty_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.exists_forall_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.const", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.instInhabited", "kind": "instance", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.const_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.coe_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.range_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.range_const_subset", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.simpleFunc_bot", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": true, "tactics": ["have", "simp_rw", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.SimpleFunc.simpleFunc_bot'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.measurableSet_cut", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": false, "tactics": ["have", "ext", "suffices", "exact", "rw", "exact"], "tactic_count": 6}
{"name": "MeasureTheory.SimpleFunc.measurableSet_preimage", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.measurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.aemeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.sum_measure_preimage_singleton", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.sum_range_measure_preimage_singleton", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.SimpleFunc.piecewise", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.coe_piecewise", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.piecewise_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.piecewise_compl", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.piecewise_univ", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.piecewise_empty", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.piecewise_same", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.support_indicator", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.range_indicator", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.SimpleFunc.measurable_bind", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.bind", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.bind_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.map", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.map_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.map_map", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.coe_map", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.range_map", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.map_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.map_preimage", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": false, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.SimpleFunc.map_preimage_singleton", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.comp", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.coe_comp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.range_comp_subset_range", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.extend", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.extend_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.extend_apply'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.extend_comp_eq'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.extend_comp_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.seq", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.seq_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.pair", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.pair_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.pair_preimage", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.pair_preimage_singleton", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.SimpleFunc.map_fst_pair", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.map_snd_pair", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasureTheory.SimpleFunc.nearestPtInd_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDense", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasureTheory.SimpleFunc.nearestPtInd_succ", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDense", "is_tactic_proof": true, "tactics": ["simp", "congr", "simp"], "tactic_count": 3}
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{"name": "MeasureTheory.SimpleFunc.approxOn", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDense", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.approxOn_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDense", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.approxOn_mem", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDense", "is_tactic_proof": true, "tactics": ["haveI", "suffices", "rintro", "exacts"], "tactic_count": 4}
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{"name": "MeasureTheory.SimpleFunc.approxOn_comp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDense", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.tendsto_approxOn", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDense", "is_tactic_proof": true, "tactics": ["haveI", "rw", "simp", "refine", "simp", "exact"], "tactic_count": 6}
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{"name": "MeasureTheory.SimpleFunc.edist_approxOn_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDense", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.edist_approxOn_y0_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDense", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasCompactSupport.exists_simpleFunc_approx_of_prod", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDense", "is_tactic_proof": false, "tactics": ["have", "intro", "apply", "exact", "intro", "exact", "intro", "refine", "by_cases", "simpa", "simp", "apply", "simpa", "rintro", "obtain", "mem_nhds_prod_iff'.1", "refine", "exact", "obtain", "refine", "by_cases", "simpa", "have", "contrapose", "rw", "exact", "simp"], "tactic_count": 27}
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{"name": "MeasureTheory.SimpleFunc.norm_approxOn_zero_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.SimpleFunc.tendsto_approxOn_Lp_eLpNorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": true, "tactics": ["by_cases", "simpa", "have", "suffices", "simp", "convert", "simp", "have", "simpa", "have", "have", "have", "filter_upwards", "have", "convert", "simp", "simpa"], "tactic_count": 17}
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{"name": "MeasureTheory.SimpleFunc.tendsto_approxOn_range_Lp_eLpNorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": true, "tactics": ["refine", "filter_upwards", "simpa"], "tactic_count": 3}
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{"name": "MeasureTheory.SimpleFunc.eLpNorm'_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "MeasureTheory.SimpleFunc.measure_preimage_lt_top_of_memLp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "by_cases", "swap", "suffices", "ext1", "rw", "refine", "rw", "exact", "specialize", "rw", "cases", "inl", "inr", "cases", "inl", "refine", "simpa", "inr"], "tactic_count": 21}
{"name": "MeasureTheory.SimpleFunc.memLp_of_finite_measure_preimage", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "by_cases", "rw", "refine", "rw", "refine", "by_cases", "simp", "refine", "exact"], "tactic_count": 11}
{"name": "MeasureTheory.SimpleFunc.memLp_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.integrable_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.memLp_iff_integrable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.memLp_iff_finMeasSupp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.integrable_iff_finMeasSupp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.FinMeasSupp.integrable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.integrable_pair", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.SimpleFunc.memLp_of_isFiniteMeasure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.integrable_of_isFiniteMeasure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.measure_preimage_lt_top_of_integrable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.measure_support_lt_top_of_memLp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.measure_support_lt_top_of_integrable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.measure_lt_top_of_memLp_indicator", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": true, "tactics": ["have", "simpa", "this]"], "tactic_count": 3}
{"name": "MeasureTheory.Lp.simpleFunc", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.simpleFunc.eq'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.simpleFunc.smul", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.simpleFunc.coe_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.simpleFunc.module", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.simpleFunc.isBoundedSMul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.simpleFunc.normedSpace", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.simpleFunc.toLp", "kind": "abbrev", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.simpleFunc.toLp_eq_toLp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.simpleFunc.toLp_eq_mk", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.simpleFunc.toLp_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.simpleFunc.toLp_add", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.simpleFunc.toLp_neg", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.simpleFunc.toLp_sub", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.Lp.simpleFunc.toLp_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.simpleFunc.norm_toLp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.simpleFunc.toSimpleFunc", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.simpleFunc.measurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.simpleFunc.stronglyMeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.simpleFunc.aemeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.simpleFunc.aestronglyMeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.simpleFunc.toSimpleFunc_eq_toFun", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.simpleFunc.memLp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.simpleFunc.toLp_toSimpleFunc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.simpleFunc.toSimpleFunc_toLp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Lp.simpleFunc.zero_toSimpleFunc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": true, "tactics": ["filter_upwards", "rwa"], "tactic_count": 2}
{"name": "MeasureTheory.Lp.simpleFunc.add_toSimpleFunc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": false, "tactics": ["filter_upwards", "simp", "iterate"], "tactic_count": 3}
{"name": "MeasureTheory.Lp.simpleFunc.neg_toSimpleFunc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": true, "tactics": ["filter_upwards", "simp", "repeat"], "tactic_count": 3}
{"name": "MeasureTheory.Lp.simpleFunc.sub_toSimpleFunc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": false, "tactics": ["filter_upwards", "simp", "repeat"], "tactic_count": 3}
{"name": "MeasureTheory.Lp.simpleFunc.smul_toSimpleFunc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": true, "tactics": ["filter_upwards", "simp", "repeat"], "tactic_count": 3}
{"name": "MeasureTheory.Lp.simpleFunc.norm_toSimpleFunc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.Lp.simpleFunc.indicatorConst", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.simpleFunc.coe_indicatorConst", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.simpleFunc.toSimpleFunc_indicatorConst", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.simpleFunc.induction", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": false, "tactics": ["suffices", "rw", "apply", "clear", "apply", "intro", "by_cases", "convert", "ext1", "simp", "exact", "intro", "obtain", "exact"], "tactic_count": 14}
{"name": "MeasureTheory.Lp.simpleFunc.uniformContinuous", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.simpleFunc.isUniformEmbedding", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.simpleFunc.isUniformInducing", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.simpleFunc.isDenseEmbedding", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": true, "tactics": ["borelize", "apply", "intro", "rw", "have", "haveI", "refine", "toLp", "convert", "rw"], "tactic_count": 10}
{"name": "MeasureTheory.Lp.simpleFunc.isDenseInducing", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.simpleFunc.denseRange", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.simpleFunc.dense", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.Lp.simpleFunc.coeToLp", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.simpleFunc.coeFn_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Lp.simpleFunc.coeFn_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.simpleFunc.coeFn_nonneg", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Lp.simpleFunc.exists_simpleFunc_nonneg_ae_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": true, "tactics": ["rcases", "change", "classical", "refine", "simpa", "filter_upwards", "simpa"], "tactic_count": 7}
{"name": "MeasureTheory.Lp.simpleFunc.coeSimpleFuncNonnegToLpNonneg", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.simpleFunc.denseRange_coeSimpleFuncNonnegToLpNonneg", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.induction", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": true, "tactics": ["refine", "refine", "exact", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.MemLp.induction", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": false, "tactics": ["have", "apply", "intro", "by_cases", "subst", "have", "exact", "intro", "rw", "exact", "have", "intro", "exact", "ae", "have", "exact"], "tactic_count": 16}
{"name": "MeasureTheory.MemLp.induction_dense", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "exact", "suffices", "obtain", "rcases", "rcases", "refine", "convert", "hg).le", "simp", "apply", "intro", "rcases", "rcases", "rw", "refine", "convert", "ext", "simp", "indicator_zero',", "have", "rcases", "rw", "exact", "intro", "obtain", "rw", "rcases", "rcases", "refine", "convert", "rw", "abel"], "tactic_count": 34}
{"name": "MeasureTheory.term_→₁ₛ[_]_", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory._aux_Mathlib_MeasureTheory_Function_SimpleFuncDenseLp___macroRules_MeasureTheory_term_→₁ₛ[_]__1", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.L1.SimpleFunc.toLp_one_eq_toL1", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.L1.SimpleFunc.integrable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Integrable.induction", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SimpleFuncDenseLp", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Real.measurable_arctan", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SpecialFunctions.Arctan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.arctan", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SpecialFunctions.Arctan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.measurable_exp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SpecialFunctions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.measurable_log", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SpecialFunctions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.measurable_of_measurable_exp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SpecialFunctions.Basic", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "Real.aemeasurable_of_aemeasurable_exp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SpecialFunctions.Basic", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "Real.aemeasurable_of_aemeasurable_exp_mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SpecialFunctions.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.measurable_sin", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SpecialFunctions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.measurable_cos", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SpecialFunctions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.measurable_sinh", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SpecialFunctions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.measurable_cosh", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SpecialFunctions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.measurable_arcsin", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SpecialFunctions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.measurable_arccos", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SpecialFunctions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.measurable_re", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SpecialFunctions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.measurable_im", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SpecialFunctions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.measurable_ofReal", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SpecialFunctions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.measurable_exp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SpecialFunctions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.measurable_sin", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SpecialFunctions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.measurable_cos", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SpecialFunctions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.measurable_sinh", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SpecialFunctions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.measurable_cosh", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SpecialFunctions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.measurable_arg", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SpecialFunctions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.measurable_log", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SpecialFunctions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.exp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SpecialFunctions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.log", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SpecialFunctions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.cos", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SpecialFunctions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.sin", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SpecialFunctions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.cosh", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SpecialFunctions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.sinh", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SpecialFunctions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.sqrt", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SpecialFunctions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.exp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SpecialFunctions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.log", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SpecialFunctions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.cos", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SpecialFunctions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.sin", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SpecialFunctions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.cosh", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SpecialFunctions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.sinh", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SpecialFunctions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.sqrt", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SpecialFunctions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.cexp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SpecialFunctions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.ccos", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SpecialFunctions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.csin", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SpecialFunctions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Measurable.clog", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SpecialFunctions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Measurable.complex_ofReal", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SpecialFunctions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.complex_ofReal", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SpecialFunctions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.hasMeasurablePow", "kind": "instance", "module": "Mathlib.MeasureTheory.Function.SpecialFunctions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.hasMeasurablePow", "kind": "instance", "module": "Mathlib.MeasureTheory.Function.SpecialFunctions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.hasMeasurablePow", "kind": "instance", "module": "Mathlib.MeasureTheory.Function.SpecialFunctions.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "_private.Mathlib.MeasureTheory.Function.SpecialFunctions.Inner.0._aux_Mathlib_MeasureTheory_Function_SpecialFunctions_Inner___unexpand_Inner_inner_1", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.SpecialFunctions.Inner", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.inner", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SpecialFunctions.Inner", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.const_inner", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SpecialFunctions.Inner", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.inner_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SpecialFunctions.Inner", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.inner", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SpecialFunctions.Inner", "is_tactic_proof": true, "tactics": ["fun_prop"], "tactic_count": 1}
{"name": "AEMeasurable.const_inner", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SpecialFunctions.Inner", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "RCLike.measurable_re", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SpecialFunctions.RCLike", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.measurable_im", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SpecialFunctions.RCLike", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.re", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SpecialFunctions.RCLike", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.re", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SpecialFunctions.RCLike", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AEMeasurable.im", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SpecialFunctions.RCLike", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RCLike.measurable_ofReal", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SpecialFunctions.RCLike", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "aemeasurable_of_re_im", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SpecialFunctions.RCLike", "is_tactic_proof": false, "tactics": ["convert", "exact"], "tactic_count": 2}
{"name": "Real.measurable_sinc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SpecialFunctions.Sinc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.stronglyMeasurable_sinc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SpecialFunctions.Sinc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.integrable_sinc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SpecialFunctions.Sinc", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "Measurable.sinc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SpecialFunctions.Sinc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.sinc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SpecialFunctions.Sinc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.StronglyMeasurable.sinc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SpecialFunctions.Sinc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEStronglyMeasurable.sinc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.SpecialFunctions.Sinc", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "_private.Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable.0.MeasureTheory.term_→ₛ_", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "_private.Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable.0.MeasureTheory._aux_Mathlib_MeasureTheory_Function_StronglyMeasurable_AEStronglyMeasurable___unexpand_MeasureTheory_SimpleFunc_1", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.termAEStronglyMeasurable[_]", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasureTheory.FinStronglyMeasurable.aefinStronglyMeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.aefinStronglyMeasurable_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.StronglyMeasurable.aestronglyMeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.aestronglyMeasurable_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasureTheory.AEStronglyMeasurable.of_subsingleton_dom", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasureTheory.AEStronglyMeasurable.of_discrete", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasureTheory.AEStronglyMeasurable.aemeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasureTheory.AEStronglyMeasurable.mono_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasureTheory.AEStronglyMeasurable.mono_set", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasureTheory.AEStronglyMeasurable.of_trim", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "MeasureTheory.AEStronglyMeasurable.restrict", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEStronglyMeasurable.ae_mem_imp_eq_mk", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.comp_aestronglyMeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasureTheory.AEStronglyMeasurable.fst", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasureTheory.AEStronglyMeasurable.of_measurableSpace_le_on", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": false, "tactics": ["have", "refine", "filter_upwards", "by_cases", "simp", "simp", "suffices", "exact"], "tactic_count": 8}
{"name": "MeasureTheory.AEStronglyMeasurable.mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEStronglyMeasurable.mul_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEStronglyMeasurable.const_mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasureTheory.AEStronglyMeasurable.div", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEStronglyMeasurable.mul_iff_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEStronglyMeasurable.mul_iff_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasureTheory.AEStronglyMeasurable.pow", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasureTheory.AEStronglyMeasurable.sup", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasureTheory.AEStronglyMeasurable.dist", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEStronglyMeasurable.norm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEStronglyMeasurable.nnnorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEStronglyMeasurable.enorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEStronglyMeasurable.edist", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEStronglyMeasurable.real_toNNReal", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "aestronglyMeasurable_indicator_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "intro", "refine", "have", "have", "exact"], "tactic_count": 8}
{"name": "aestronglyMeasurable_indicator_iff₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": true, "tactics": ["rw", "aestronglyMeasurable_indicator_iff"], "tactic_count": 2}
{"name": "MeasureTheory.AEStronglyMeasurable.indicator", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEStronglyMeasurable.indicator₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEStronglyMeasurable.nullMeasurableSet_eq_fun", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": true, "tactics": ["apply", "filter_upwards", "change", "simp"], "tactic_count": 4}
{"name": "MeasureTheory.AEStronglyMeasurable.nullMeasurableSet_mulSupport", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEStronglyMeasurable.nullMeasurableSet_lt", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": true, "tactics": ["apply", "filter_upwards", "change", "simp"], "tactic_count": 4}
{"name": "MeasureTheory.AEStronglyMeasurable.nullMeasurableSet_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": true, "tactics": ["apply", "filter_upwards", "change", "simp"], "tactic_count": 4}
{"name": "aestronglyMeasurable_of_aestronglyMeasurable_trim", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEStronglyMeasurable.comp_aemeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEStronglyMeasurable.comp_measurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEStronglyMeasurable.comp_quasiMeasurePreserving", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEStronglyMeasurable.isSeparable_ae_range", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": true, "tactics": ["refine", "filter_upwards", "simp"], "tactic_count": 3}
{"name": "aestronglyMeasurable_iff_aemeasurable_separable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": true, "tactics": ["refine", "rintro", "rcases", "simp", "rw", "exact", "obtain", "refine", "exact"], "tactic_count": 9}
{"name": "aestronglyMeasurable_iff_nullMeasurable_separable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEmbedding.aestronglyMeasurable_map_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": true, "tactics": ["refine", "rintro", "rcases", "exact"], "tactic_count": 4}
{"name": "Topology.IsEmbedding.aestronglyMeasurable_comp_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": true, "tactics": ["letI", "borelize", "refine", "hg.continuous.comp_aestronglyMeasurable", "let", "have", "have", "exact", "rcases", "exact"], "tactic_count": 10}
{"name": "aestronglyMeasurable_of_tendsto_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": true, "tactics": ["borelize", "refine", "exact", "rcases", "have", "choose", "refine", "filter_upwards", "apply", "filter_upwards"], "tactic_count": 10}
{"name": "exists_stronglyMeasurable_limit_of_tendsto_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": true, "tactics": ["borelize", "obtain", "measurable_limit_of_tendsto_metrizable_ae", "have", "refine", "filter_upwards", "rwa"], "tactic_count": 7}
{"name": "MeasureTheory.AEStronglyMeasurable.exists_stronglyMeasurable_range_subset", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": true, "tactics": ["obtain", "classical", "refine", "exact", "rw", "simpa", "apply", "filter_upwards", "exact"], "tactic_count": 9}
{"name": "MeasureTheory.AEStronglyMeasurable.piecewise", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": false, "tactics": ["refine", "refine", "have", "rw", "rw", "filter_upwards", "intro", "simp", "have", "rw", "rw", "filter_upwards", "intro", "rw", "simp"], "tactic_count": 15}
{"name": "MeasureTheory.AEStronglyMeasurable.sum_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": true, "tactics": ["borelize", "refine", "have", "choose", "refine", "simp", "intro", "filter_upwards", "exact"], "tactic_count": 9}
{"name": "aestronglyMeasurable_sum_measure_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "aestronglyMeasurable_add_measure_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "MeasureTheory.AEStronglyMeasurable.add_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEStronglyMeasurable.iUnion", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "aestronglyMeasurable_iUnion_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "aestronglyMeasurable_union_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.AEStronglyMeasurable.aestronglyMeasurable_uIoc_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.AEStronglyMeasurable.smul_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "aestronglyMeasurable_const_smul_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUnit.aestronglyMeasurable_const_smul_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "aestronglyMeasurable_const_smul_iff₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEFinStronglyMeasurable.mk", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEFinStronglyMeasurable.finStronglyMeasurable_mk", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEFinStronglyMeasurable.ae_eq_mk", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEFinStronglyMeasurable.aemeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEFinStronglyMeasurable.mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEFinStronglyMeasurable.add", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEFinStronglyMeasurable.neg", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEFinStronglyMeasurable.sub", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEFinStronglyMeasurable.const_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEFinStronglyMeasurable.sup", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEFinStronglyMeasurable.inf", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEFinStronglyMeasurable.exists_set_sigmaFinite", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": true, "tactics": ["rcases", "obtain", "refine", "refine", "rw", "exact"], "tactic_count": 6}
{"name": "MeasureTheory.AEFinStronglyMeasurable.sigmaFiniteSet", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEFinStronglyMeasurable.measurableSet", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEFinStronglyMeasurable.ae_eq_zero_compl", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEFinStronglyMeasurable.sigmaFinite_restrict", "kind": "instance", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.aefinStronglyMeasurable_iff_aemeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MeasureTheory.aefinStronglyMeasurable_of_aemeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic.0.MeasureTheory.term_→ₛ_", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic.0.MeasureTheory._aux_Mathlib_MeasureTheory_Function_StronglyMeasurable_Basic___macroRules__private_Mathlib_MeasureTheory_Function_StronglyMeasurable_Basic_0_MeasureTheory_term_→ₛ__1", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic.0.MeasureTheory._aux_Mathlib_MeasureTheory_Function_StronglyMeasurable_Basic___unexpand_MeasureTheory_SimpleFunc_1", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.StronglyMeasurable", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.termStronglyMeasurable[_]", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory._aux_Mathlib_MeasureTheory_Function_StronglyMeasurable_Basic___macroRules_MeasureTheory_termStronglyMeasurable[_]_1", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.stronglyMeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.StronglyMeasurable.of_subsingleton_dom", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.StronglyMeasurable.of_subsingleton_cod", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": true, "tactics": ["let", "exact", "simp"], "tactic_count": 3}
{"name": "MeasureTheory.stronglyMeasurable_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.stronglyMeasurable_one", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.stronglyMeasurable_const'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": true, "tactics": ["nontriviality", "inhabit", "convert", "exact"], "tactic_count": 4}
{"name": "_private.Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic.0.MeasureTheory.simpleFuncAux", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic.0.MeasureTheory.simpleFuncAux_eq_of_lt", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic.0.MeasureTheory.simpleFuncAux_eventuallyEq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.StronglyMeasurable.of_discrete", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": true, "tactics": ["nontriviality", "obtain", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.StronglyMeasurable.approx", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.StronglyMeasurable.tendsto_approx", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.StronglyMeasurable.approxBounded", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.StronglyMeasurable.tendsto_approxBounded_of_norm_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": true, "tactics": ["have", "simp", "by_cases", "rw", "rw", "have", "convert", "rw", "refine", "calc", "refine", "rw", "exact", "exact", "rw", "refine", "have", "rw", "exact", "nth_rw", "refine", "exact"], "tactic_count": 22}
{"name": "MeasureTheory.StronglyMeasurable.tendsto_approxBounded_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": true, "tactics": ["filter_upwards"], "tactic_count": 1}
{"name": "MeasureTheory.StronglyMeasurable.norm_approxBounded_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": true, "tactics": ["simp", "refine", "by_cases", "simp", "exact", "rcases", "rw", "simpa", "rwa", "rw", "rw", "rwa"], "tactic_count": 12}
{"name": "stronglyMeasurable_bot_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simp", "refine", "refine", "let", "have", "have", "let", "have", "conv", "have", "ext1", "exact", "obtain", "exact"], "tactic_count": 15}
{"name": "MeasureTheory.StronglyMeasurable.finStronglyMeasurable_of_set_sigmaFinite", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": true, "tactics": ["haveI", "let", "have", "let", "let", "have", "intro", "rw", "refine", "simp", "refine", "simp_rw", "classical", "refine", "rw", "swap", "letI", "rw", "exact", "refine", "have", "rwa", "by_cases", "swap", "rw", "exact", "have", "obtain", "obtain", "rsuffices", "exact", "rsuffices", "exact", "rw", "trivial", "refine", "simp_rw", "rw", "intro", "obtain", "refine", "rw", "exact"], "tactic_count": 43}
{"name": "MeasureTheory.StronglyMeasurable.finStronglyMeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.StronglyMeasurable.measurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.StronglyMeasurable.aemeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.comp_stronglyMeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.StronglyMeasurable.measurableSet_mulSupport", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": true, "tactics": ["borelize", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.StronglyMeasurable.mono", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": ["let", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.StronglyMeasurable.fst", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.StronglyMeasurable.snd", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.StronglyMeasurable.prodMk", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.StronglyMeasurable.comp_measurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.StronglyMeasurable.of_uncurry_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.StronglyMeasurable.of_uncurry_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.StronglyMeasurable.prod_swap", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.StronglyMeasurable.comp_fst", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.StronglyMeasurable.comp_snd", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.StronglyMeasurable.mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.StronglyMeasurable.mul_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.StronglyMeasurable.const_mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.StronglyMeasurable.pow", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.StronglyMeasurable.inv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.StronglyMeasurable.div", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.StronglyMeasurable.mul_iff_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.StronglyMeasurable.mul_iff_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.StronglyMeasurable.smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.StronglyMeasurable.const_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.StronglyMeasurable.const_smul'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.StronglyMeasurable.smul_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.StronglyMeasurable.star", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.add_stronglyMeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": true, "tactics": ["rcases", "have", "apply", "exact"], "tactic_count": 4}
{"name": "Measurable.sub_stronglyMeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Measurable.stronglyMeasurable_add", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": true, "tactics": ["rcases", "have", "apply", "exact"], "tactic_count": 4}
{"name": "stronglyMeasurable_const_smul_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUnit.stronglyMeasurable_const_smul_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "stronglyMeasurable_const_smul_iff₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.StronglyMeasurable.sup", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.StronglyMeasurable.inf", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.stronglyMeasurable_prod", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "rw", "rw", "exact"], "tactic_count": 6}
{"name": "List.stronglyMeasurable_fun_prod", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Multiset.stronglyMeasurable_prod", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simpa"], "tactic_count": 2}
{"name": "Multiset.stronglyMeasurable_fun_prod", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.stronglyMeasurable_prod", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.stronglyMeasurable_fun_prod", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.StronglyMeasurable.Finset.stronglyMeasurable_prod_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.StronglyMeasurable.isSeparable_range", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": ["have", "apply", "rintro", "apply", "filter_upwards", "apply", "exact"], "tactic_count": 7}
{"name": "MeasureTheory.StronglyMeasurable.separableSpace_range_union_singleton", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.stronglyMeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": true, "tactics": ["letI", "nontriviality", "exact"], "tactic_count": 3}
{"name": "stronglyMeasurable_iff_measurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "stronglyMeasurable_id", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "stronglyMeasurable_iff_measurable_separable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": true, "tactics": ["refine", "have", "have", "exact"], "tactic_count": 4}
{"name": "Continuous.stronglyMeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": true, "tactics": ["borelize", "cases", "rw", "refine", "exact", "exact"], "tactic_count": 6}
{"name": "Continuous.stronglyMeasurable_of_mulSupport_subset_isCompact", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": true, "tactics": ["borelize", "letI", "rw", "exact"], "tactic_count": 4}
{"name": "Continuous.stronglyMeasurable_of_hasCompactMulSupport", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasCompactSupport.stronglyMeasurable_of_prod", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": true, "tactics": ["borelize", "apply", "letI", "exact"], "tactic_count": 4}
{"name": "Embedding.comp_stronglyMeasurable_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": true, "tactics": ["letI", "borelize", "refine", "let", "have", "isClosed_range", "rw", "exact", "have", "exact", "have", "rwa"], "tactic_count": 12}
{"name": "stronglyMeasurable_of_tendsto", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": true, "tactics": ["borelize", "refine", "exact", "rcases", "have", "apply", "rintro", "rw", "apply", "filter_upwards", "apply", "exact"], "tactic_count": 12}
{"name": "MeasureTheory.StronglyMeasurable.piecewise", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": true, "tactics": ["refine", "by_cases", "simpa", "simpa", "hg.tendsto_approx"], "tactic_count": 5}
{"name": "MeasureTheory.StronglyMeasurable.ite", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEmbedding.stronglyMeasurable_extend", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": true, "tactics": ["refine", "intro", "by_cases", "rcases", "simpa", "simpa"], "tactic_count": 6}
{"name": "MeasurableEmbedding.exists_stronglyMeasurable_extend", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "stronglyMeasurable_of_stronglyMeasurable_union_cover", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": true, "tactics": ["nontriviality", "suffices", "from", "this", "ext", "by_cases", "lift", "simp", "lift", "rw", "exact"], "tactic_count": 11}
{"name": "stronglyMeasurable_of_restrict_of_restrict_compl", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.StronglyMeasurable.indicator", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.StronglyMeasurable.induction", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": true, "tactics": ["let", "refine", "change", "induction", "const"], "tactic_count": 5}
{"name": "MeasureTheory.StronglyMeasurable.induction'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": true, "tactics": ["let", "refine", "change", "induction", "const", "simp_rw", "exact"], "tactic_count": 7}
{"name": "MeasureTheory.StronglyMeasurable.dist", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.StronglyMeasurable.edist", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.StronglyMeasurable.norm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.StronglyMeasurable.nnnorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.StronglyMeasurable.enorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.StronglyMeasurable.real_toNNReal", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.StronglyMeasurable.measurableSet_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": true, "tactics": ["borelize", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.StronglyMeasurable.measurableSet_lt", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.StronglyMeasurable.ae_le_trim_of_stronglyMeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": true, "tactics": ["rwa", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.StronglyMeasurable.ae_le_trim_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.StronglyMeasurable.measurableSet_eq_fun", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": true, "tactics": ["borelize", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.StronglyMeasurable.ae_eq_trim_of_stronglyMeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": true, "tactics": ["rwa", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.StronglyMeasurable.ae_eq_trim_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.StronglyMeasurable.stronglyMeasurable_in_set", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": true, "tactics": ["let", "have", "intro", "rw", "have", "intro", "rw", "refine", "by_cases", "simp_rw", "exact", "simp_rw", "exact"], "tactic_count": 13}
{"name": "MeasureTheory.StronglyMeasurable.stronglyMeasurable_of_measurableSpace_le_on", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": ["have", "rw", "refine", "rwa", "obtain", "let", "measurableSet_fiber", "rw", "refine", "exact", "by_cases", "suffices", "rw", "exact", "ext1", "rw", "exact", "suffices", "rw", "exact", "ext1", "simp", "not_and,", "refine", "rw", "exact", "finite_range", "exact"], "tactic_count": 28}
{"name": "MeasureTheory.StronglyMeasurable.exists_spanning_measurableSet_norm_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": true, "tactics": ["obtain", "refine", "have", "rw", "norm_cast"], "tactic_count": 5}
{"name": "MeasureTheory.finStronglyMeasurable_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.FinStronglyMeasurable.approx", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.FinStronglyMeasurable.fin_support_approx", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.FinStronglyMeasurable.tendsto_approx", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.FinStronglyMeasurable.stronglyMeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.FinStronglyMeasurable.exists_set_sigmaFinite", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": true, "tactics": ["rcases", "let", "have", "let", "refine", "have", "intro", "rw", "simpa", "refine", "rw", "exact", "refine", "rw", "exact", "rw", "exact"], "tactic_count": 17}
{"name": "MeasureTheory.FinStronglyMeasurable.measurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.FinStronglyMeasurable.mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": true, "tactics": ["refine", "intro", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.FinStronglyMeasurable.add", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.FinStronglyMeasurable.neg", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": true, "tactics": ["refine", "suffices", "rw", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.FinStronglyMeasurable.sub", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.FinStronglyMeasurable.const_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.FinStronglyMeasurable.sup", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": ["refine", "refine", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.FinStronglyMeasurable.inf", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": ["refine", "refine", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.finStronglyMeasurable_iff_stronglyMeasurable_and_exists_set_sigmaFinite", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.finStronglyMeasurable_iff_measurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.finStronglyMeasurable_of_measurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measurable_uncurry_of_continuous_of_measurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": false, "tactics": ["obtain", "have", "refine", "exact", "let", "have", "rw", "exact", "refine", "have", "have", "rfl", "rw", "exact", "have", "rfl", "simp_rw", "refine", "exact"], "tactic_count": 19}
{"name": "MeasureTheory.stronglyMeasurable_uncurry_of_continuous_of_stronglyMeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic", "is_tactic_proof": true, "tactics": ["borelize", "obtain", "have", "refine", "exact", "let", "have", "rw", "exact", "refine", "have", "refine", "have", "rfl", "rw", "exact", "have", "apply", "rintro", "simp", "exact", "have", "rfl", "simp_rw", "refine", "exact"], "tactic_count": 26}
{"name": "ENNReal.finStronglyMeasurable_of_measurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.ENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.aefinStronglyMeasurable_of_aemeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.ENNReal", "is_tactic_proof": true, "tactics": ["refine", "rwa"], "tactic_count": 2}
{"name": "_private.Mathlib.MeasureTheory.Function.StronglyMeasurable.Inner.0.MeasureTheory.term⟪_,_⟫", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Inner", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.MeasureTheory.Function.StronglyMeasurable.Inner.0.MeasureTheory._aux_Mathlib_MeasureTheory_Function_StronglyMeasurable_Inner___macroRules__private_Mathlib_MeasureTheory_Function_StronglyMeasurable_Inner_0_MeasureTheory_term⟪_,_⟫_1", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Inner", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.MeasureTheory.Function.StronglyMeasurable.Inner.0.MeasureTheory._aux_Mathlib_MeasureTheory_Function_StronglyMeasurable_Inner___unexpand_Inner_inner_1", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Inner", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.StronglyMeasurable.inner", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Inner", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEStronglyMeasurable.re", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Inner", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEStronglyMeasurable.im", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Inner", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEStronglyMeasurable.inner", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Inner", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEStronglyMeasurable.inner_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Inner", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEStronglyMeasurable.const_inner", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Inner", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "aestronglyMeasurable_dirac", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEStronglyMeasurable.comp_measurePreserving", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MeasurePreserving.aestronglyMeasurable_comp_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "aestronglyMeasurable_smul_const_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StronglyMeasurable.apply_continuousLinearMap", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEStronglyMeasurable.apply_continuousLinearMap", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.aestronglyMeasurable_comp₂", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "aestronglyMeasurable_withDensity_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Lemmas", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "have", "refine", "apply", "rw", "rw", "filter_upwards", "have", "rw", "filter_upwards", "simp", "simp", "rintro", "refine", "rw", "filter_upwards", "rw", "simp", "simpa"], "tactic_count": 20}
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{"name": "MeasureTheory.MemLp.finStronglyMeasurable_of_stronglyMeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Lp", "is_tactic_proof": true, "tactics": ["borelize", "haveI", "let", "refine", "have", "exact", "intro", "apply", "apply", "simp"], "tactic_count": 10}
{"name": "MeasureTheory.MemLp.aefinStronglyMeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Lp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Integrable.aefinStronglyMeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Lp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Lp.finStronglyMeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.StronglyMeasurable.Lp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.UnifTight", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.UnifTight", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.unifTight_iff_ennreal", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.UnifTight", "is_tactic_proof": true, "tactics": ["simp", "refine", "simp", "use"], "tactic_count": 4}
{"name": "MeasureTheory.unifTight_iff_real", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.UnifTight", "is_tactic_proof": true, "tactics": ["refine", "obtain", "use", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.UnifTight.eventually_cofinite_indicator", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.UnifTight", "is_tactic_proof": true, "tactics": ["by_cases", "subst", "rcases", "refine", "intro", "exact", "rwa"], "tactic_count": 7}
{"name": "MeasureTheory.UnifTight.exists_measurableSet_indicator", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.UnifTight", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.UnifTight.add", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.UnifTight", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.UnifTight.neg", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.UnifTight", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
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{"name": "MeasureTheory.UnifTight.aeeq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.UnifTight", "is_tactic_proof": true, "tactics": ["intro", "obtain", "refine", "filter_upwards", "simp"], "tactic_count": 5}
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{"name": "MeasureTheory.unifTight_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.UnifTight", "is_tactic_proof": true, "tactics": ["intro", "by_cases", "exact", "obtain", "exact"], "tactic_count": 5}
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{"name": "MeasureTheory.unifTight_finite", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.UnifTight", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.MeasureTheory.Function.UnifTight.0.MeasureTheory.unifTight_of_tendsto_Lp_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.UnifTight", "is_tactic_proof": true, "tactics": ["intro", "rw", "obtain", "let", "have", "obtain", "refine", "by_cases", "exact", "exact"], "tactic_count": 10}
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{"name": "MeasureTheory.tendsto_Lp_of_tendstoInMeasure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.UnifTight", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact", "tendsto_Lp_of_tendsto_ae", "let", "let", "hms'⟩"], "tactic_count": 7}
{"name": "MeasureTheory.tendstoInMeasure_iff_tendsto_Lp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.UnifTight", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.UnifIntegrable", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.UniformIntegrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.UniformIntegrable", "kind": "definition", "module": "Mathlib.MeasureTheory.Function.UniformIntegrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.UniformIntegrable.aestronglyMeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.UniformIntegrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.UniformIntegrable.unifIntegrable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.UniformIntegrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.UniformIntegrable.memLp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.UniformIntegrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.UnifIntegrable.add", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.UniformIntegrable", "is_tactic_proof": true, "tactics": ["intro", "have", "obtain", "obtain", "refine", "simp_rw", "refine", "have", "rw", "rw", "exact", "add_le_add"], "tactic_count": 12}
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{"name": "MeasureTheory.UnifIntegrable.ae_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.UniformIntegrable", "is_tactic_proof": true, "tactics": ["classical", "intro", "obtain", "refine", "filter_upwards", "simp_rw"], "tactic_count": 6}
{"name": "MeasureTheory.UnifIntegrable.indicator", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.UniformIntegrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.UnifIntegrable.restrict", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.UniformIntegrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.unifIntegrable_zero_meas", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.UniformIntegrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.unifIntegrable_congr_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.UniformIntegrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.tendsto_indicator_ge", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.UniformIntegrable", "is_tactic_proof": true, "tactics": ["refine", "rw", "simp", "refine", "refine", "norm_cast"], "tactic_count": 6}
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{"name": "MeasureTheory.eLpNorm_indicator_le_of_bound", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.UniformIntegrable", "is_tactic_proof": true, "tactics": ["by_cases", "refine", "rw", "simp", "ext", "rw", "exact", "refine", "by_cases", "simp", "rw", "have", "filter_upwards", "exact", "refine", "rw", "rw", "refine", "rw", "simpa"], "tactic_count": 20}
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{"name": "MeasureTheory.MemLp.eLpNorm_indicator_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.UniformIntegrable", "is_tactic_proof": true, "tactics": ["have", "obtain", "obtain", "refine", "convert", "rw", "exact"], "tactic_count": 7}
{"name": "MeasureTheory.unifIntegrable_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.UniformIntegrable", "is_tactic_proof": true, "tactics": ["intro", "obtain", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.unifIntegrable_subsingleton", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.UniformIntegrable", "is_tactic_proof": true, "tactics": ["intro", "by_cases", "obtain", "obtain", "refine", "convert", "exact"], "tactic_count": 7}
{"name": "MeasureTheory.unifIntegrable_fin", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.UniformIntegrable", "is_tactic_proof": true, "tactics": ["revert", "induction", "zero", "succ", "intro", "let", "have", "obtain", "obtain", "refine", "by_cases", "rw", "exact", "simp", "obtain", "exact"], "tactic_count": 16}
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{"name": "MeasureTheory.uniformIntegrable_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.UniformIntegrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.uniformIntegrable_of'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.UniformIntegrable", "is_tactic_proof": false, "tactics": ["refine", "obtain", "refine", "calc", "eLpNorm", "eLpNorm", "refine", "le_trans", "hp)", "rw", "split_ifs", "rw", "simpa", "rw", "simpa", "have", "filter_upwards", "simp_rw", "exact", "refine", "simp_rw", "exact"], "tactic_count": 22}
{"name": "MeasureTheory.uniformIntegrable_of", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.UniformIntegrable", "is_tactic_proof": true, "tactics": ["set", "have", "have", "refine", "obtain", "refine", "filter_upwards", "by_cases", "rw", "rwa", "rw", "rwa"], "tactic_count": 12}
{"name": "MeasureTheory.UniformIntegrable.spec'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.UniformIntegrable", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "obtain", "by_contra", "choose", "lift", "have", "intro", "calc", "rw", "simp_rw", "refine", "refine", "le_eLpNorm_of_bddBelow", "rwa", "specialize", "rw", "mul_assoc,", "refine", "rfl", "rw", "exact", "exact"], "tactic_count": 23}
{"name": "MeasureTheory.UniformIntegrable.spec", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.UniformIntegrable", "is_tactic_proof": true, "tactics": ["set", "have", "have", "obtain", "refine", "filter_upwards", "by_cases", "rw", "rwa", "rw", "rwa"], "tactic_count": 11}
{"name": "MeasureTheory.uniformIntegrable_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.UniformIntegrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.uniformIntegrable_average", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.UniformIntegrable", "is_tactic_proof": true, "tactics": ["obtain", "refine", "exact", "obtain", "refine", "simp_rw", "refine", "have", "obtain", "simp", "simp_rw", "rw", "refine", "simpa", "obtain", "simp_rw", "refine", "obtain", "simp", "simp_rw", "rw", "refine", "simpa"], "tactic_count": 23}
{"name": "MeasureTheory.uniformIntegrable_average_real", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.UniformIntegrable", "is_tactic_proof": true, "tactics": ["convert", "ext", "simp"], "tactic_count": 3}
{"name": "MeasureTheory.UniformIntegrable.uniformIntegrable_of_tendstoInMeasure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.UniformIntegrable", "is_tactic_proof": true, "tactics": ["refine", "exact", "obtain", "exact", "eLpNorm_le_of_tendstoInMeasure"], "tactic_count": 5}
{"name": "MeasureTheory.UniformIntegrable.memLp_of_tendstoInMeasure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.UniformIntegrable", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.UniformIntegrable.integrable_of_tendstoInMeasure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.UniformIntegrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.UniformIntegrable.uniformIntegrable_of_ae_tendsto", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.UniformIntegrable", "is_tactic_proof": true, "tactics": ["refine", "exact", "obtain", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.UniformIntegrable.memLp_of_ae_tendsto", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.UniformIntegrable", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.UniformIntegrable.integrable_of_ae_tendsto", "kind": "theorem", "module": "Mathlib.MeasureTheory.Function.UniformIntegrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.aestabilizer", "kind": "definition", "module": "Mathlib.MeasureTheory.Group.AEStabilizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.mem_aestabilizer", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.AEStabilizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.stabilizer_le_aestabilizer", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.AEStabilizer", "is_tactic_proof": true, "tactics": ["intro", "simp_all"], "tactic_count": 2}
{"name": "MulAction.aestabilizer_empty", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.AEStabilizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.aestabilizer_univ", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.AEStabilizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.aestabilizer_congr", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.AEStabilizer", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "MulAction.aestabilizer_of_aeconst", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.AEStabilizer", "is_tactic_proof": true, "tactics": ["refine", "cases", "inl", "inr"], "tactic_count": 4}
{"name": "MeasureTheory.smul_ae_eq_self_of_mem_zpowers", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.AEStabilizer", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.inv_smul_ae_eq_self", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.AEStabilizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SMulInvariantMeasure.zero", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SMulInvariantMeasure.add", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SMulInvariantMeasure.smul", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SMulInvariantMeasure.smul_nnreal", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_preimage_smul_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.tendsto_smul_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_preimage_smul_null", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_preimage_smul_of_nullMeasurableSet", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Action", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.measure_preimage_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Action", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.measure_inter_inv_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Action", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.measure_inv_smul_inter", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Action", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.measure_union_inv_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Action", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.measure_inv_smul_union", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Action", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.measure_sdiff_inv_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Action", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.measure_inv_smul_sdiff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Action", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.measure_symmDiff_inv_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Action", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.measure_inv_smul_symmDiff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Action", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.measure_smul_eq_zero_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Action", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.measure_smul_null", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.smul_mem_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Action", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.smul_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Action", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.eventuallyConst_smul_set_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Action", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.smul_set_ae_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Action", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.smul_set_ae_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Action", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.measurePreserving_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.map_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MeasurePreserving.smulInvariantMeasure_iterateMulAct", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.smulInvariantMeasure_iterateMulAct", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.smulInvariantMeasure_map", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.smulInvariantMeasure_map_smul", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.smulInvariantMeasure_tfae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Action", "is_tactic_proof": true, "tactics": ["tfae_have", "tfae_have", "tfae_have", "tfae_have", "tfae_have", "rw", "apply", "tfae_have", "tfae_have", "rw", "exact", "tfae_finish"], "tactic_count": 12}
{"name": "MeasureTheory.NullMeasurableSet.smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Action", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.measure_isOpen_pos_of_smulInvariant_of_compact_ne_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.isLocallyFiniteMeasure_of_smulInvariant", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_isOpen_pos_of_smulInvariant_of_ne_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_pos_iff_nonempty_of_smulInvariant", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Action", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_eq_zero_iff_eq_empty_of_smulInvariant", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Action", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AddCircle.closedBall_ae_eq_ball", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.AddCircle", "is_tactic_proof": true, "tactics": ["rcases", "rw", "exact", "suffices", "have", "simp_rw", "refine", "exact", "refine", "exact"], "tactic_count": 10}
{"name": "AddCircle.isAddFundamentalDomain_of_ae_ball", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.AddCircle", "is_tactic_proof": true, "tactics": ["set", "set", "set", "have", "refine", "exact", "rintro", "replace", "change", "refine", "hI", "have", "rw", "rw", "apply", "rw", "div_le_iff₀", "refine", "exact", "exact", "replace", "haveI", "have", "change", "rw", "simp_rw", "rw", "hG_card,", "exact"], "tactic_count": 29}
{"name": "AddCircle.volume_of_add_preimage_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.AddCircle", "is_tactic_proof": true, "tactics": ["let", "haveI", "have", "exact", "rw"], "tactic_count": 5}
{"name": "Measurable.const_mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.const_mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.mul_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.mul_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.mul'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": true, "tactics": ["dsimp"], "tactic_count": 1}
{"name": "AEMeasurable.mul'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableMul₂.toMeasurableMul", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.measurableMul", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.measurableMul₂", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_div_const'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Monoid.measurablePow", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.pow", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.pow", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.pow_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.pow_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.const_pow", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.const_pow", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.const_div", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.const_div", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.div_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.div_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.div", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.div'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": true, "tactics": ["dsimp"], "tactic_count": 1}
{"name": "AEMeasurable.div'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.div", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableDiv₂.toMeasurableDiv", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.measurableDiv", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.measurableDiv₂", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instMeasurableEqOfMeasurableSingletonClassOfMeasurableSub₂", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": true, "tactics": ["constructor", "simp_rw", "measurability"], "tactic_count": 3}
{"name": "instMeasurableEqOfCanonicallyOrderedAddOfOrderedSubOfMeasurableSub₂OfMeasurableSingletonClass", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": true, "tactics": ["constructor", "simp_rw", "measurability"], "tactic_count": 3}
{"name": "measurableDiv_of_mul_inv", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.inv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.inv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_inv_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "aemeasurable_inv_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.measurableInv", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSet.inv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurableEmbedding_inv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.mul_iff_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.mul_iff_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.mul_iff_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.mul_iff_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DivInvMonoid.measurableZPow", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurableDiv₂_of_mul_inv", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableDiv.toMeasurableInv", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurableSMul_of_mul", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurableSMul₂_of_mul", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.instMeasurableConstSMul", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.instMeasurableSMul", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.instMeasurableConstSMul", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.instMeasurableSMul", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.const_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.fun_const_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.fun_const_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.const_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instMeasurableConstSMul", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instMeasurableConstSMul", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.smul'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": true, "tactics": ["dsimp"], "tactic_count": 1}
{"name": "AEMeasurable.smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSMul₂.toMeasurableSMul", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.smul_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.smul_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": true, "tactics": ["fun_prop"], "tactic_count": 1}
{"name": "Pi.measurableSMul", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoid.measurableSMul_nat₂", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubNegMonoid.measurableSMul_int₂", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.measurableSMul₂_iterateMulAct", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurableSMul_iterateMulAct", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurableSMul₂_iterateMulAct", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_const_smul_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "aemeasurable_const_smul_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.instMeasurableConstSMul", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUnit.measurable_const_smul_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUnit.aemeasurable_const_smul_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.instMeasurableSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.measurableSMul", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_const_smul_iff₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "aemeasurable_const_smul_iff₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instMeasurableSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_mul_op", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_mul_unop", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instMeasurableMul", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instMeasurableMul₂", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSMul.op", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSMul₂.op", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurableSMul_opposite_of_mul", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurableSMul₂_opposite_of_mul", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.measurable_prod", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "rw", "rw", "exact"], "tactic_count": 6}
{"name": "List.aemeasurable_prod", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "rw", "rw", "exact"], "tactic_count": 6}
{"name": "List.measurable_fun_prod", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "List.aemeasurable_fun_prod", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Multiset.measurable_prod", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": true, "tactics": ["rcases", "simpa"], "tactic_count": 2}
{"name": "Multiset.aemeasurable_prod", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": true, "tactics": ["rcases", "simpa"], "tactic_count": 2}
{"name": "Multiset.measurable_fun_prod", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Multiset.aemeasurable_fun_prod", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.measurable_fun_prod", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Finset.measurable_prod", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Finset.measurable_prod_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.aemeasurable_prod", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.aemeasurable_fun_prod", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "DiscreteMeasurableSpace.toMeasurableMul", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteMeasurableSpace.toMeasurableMul₂", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteMeasurableSpace.toMeasurableInv", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteMeasurableSpace.toMeasurableDiv", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteMeasurableSpace.toMeasurableDiv₂", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.mconv", "kind": "definition", "module": "Mathlib.MeasureTheory.Group.Convolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.term_∗ₘ_", "kind": "definition", "module": "Mathlib.MeasureTheory.Group.Convolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory._aux_Mathlib_MeasureTheory_Group_Convolution___macroRules_MeasureTheory_term_∗ₘ__1", "kind": "definition", "module": "Mathlib.MeasureTheory.Group.Convolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory._aux_Mathlib_MeasureTheory_Group_Convolution___unexpand_MeasureTheory_Measure_mconv_1", "kind": "definition", "module": "Mathlib.MeasureTheory.Group.Convolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.term_∗_", "kind": "definition", "module": "Mathlib.MeasureTheory.Group.Convolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory._aux_Mathlib_MeasureTheory_Group_Convolution___macroRules_MeasureTheory_term_∗__1", "kind": "definition", "module": "Mathlib.MeasureTheory.Group.Convolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory._aux_Mathlib_MeasureTheory_Group_Convolution___unexpand_MeasureTheory_Measure_conv_1", "kind": "definition", "module": "Mathlib.MeasureTheory.Group.Convolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.lintegral_mconv_eq_lintegral_prod", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Convolution", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.lintegral_mconv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Convolution", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.dirac_mconv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Convolution", "is_tactic_proof": true, "tactics": ["unfold", "rw", "simp"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.mconv_dirac", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Convolution", "is_tactic_proof": true, "tactics": ["unfold", "rw", "simp"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.dirac_mconv_dirac", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Convolution", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.dirac_one_mconv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Convolution", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.mconv_dirac_one", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Convolution", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.zero_mconv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Convolution", "is_tactic_proof": true, "tactics": ["unfold", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.mconv_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Convolution", "is_tactic_proof": true, "tactics": ["unfold", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.mconv_smul_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Convolution", "is_tactic_proof": true, "tactics": ["unfold", "rw"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.mconv_add", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Convolution", "is_tactic_proof": true, "tactics": ["unfold", "rw", "fun_prop"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.add_mconv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Convolution", "is_tactic_proof": true, "tactics": ["unfold", "rw", "fun_prop"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.mconv_comm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Convolution", "is_tactic_proof": true, "tactics": ["unfold", "rw", "simp", "fun_prop"], "tactic_count": 4}
{"name": "MeasureTheory.Measure.sfinite_mconv_of_sfinite", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Convolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.finite_of_finite_mconv", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Convolution", "is_tactic_proof": false, "tactics": ["have", "unfold", "exact", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.Measure.mconv_assoc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Convolution", "is_tactic_proof": true, "tactics": ["refine", "repeat", "refine", "rw", "repeat", "simp"], "tactic_count": 6}
{"name": "MeasureTheory.Measure.probabilitymeasure_of_probabilitymeasures_mconv", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Convolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.mconv_absolutelyContinuous", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Convolution", "is_tactic_proof": true, "tactics": ["refine", "rw", "conv", "simp", "conv", "have", "apply", "rw", "simp"], "tactic_count": 9}
{"name": "MeasureTheory.Measure.map_mconv_monoidHom", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Convolution", "is_tactic_proof": true, "tactics": ["unfold", "rw", "have", "rw"], "tactic_count": 4}
{"name": "MeasureTheory.Measure.map_conv_continuousLinearMap", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Convolution", "is_tactic_proof": true, "tactics": ["suffices", "rw", "rw", "fun_prop"], "tactic_count": 4}
{"name": "MeasureTheory.Measure.IsMulLeftInvariant.smulInvariantMeasure", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.instSMulInvariantMeasureSubtypeMemSubmonoidOfIsMulLeftInvariant", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.IsMulRightInvariant.toSMulInvariantMeasure_op", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFoelner.univ_of_isFiniteMeasure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FoelnerFilter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFoelner.mono", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FoelnerFilter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFoelner.comp_tendsto", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FoelnerFilter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFoelner.mean", "kind": "definition", "module": "Mathlib.MeasureTheory.Group.FoelnerFilter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFoelner.tendsto_nhds_mean", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FoelnerFilter", "is_tactic_proof": false, "tactics": ["have", "filter_upwards", "simpa", "obtain", "exact"], "tactic_count": 5}
{"name": "IsFoelner.mean_univ_eq_one", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FoelnerFilter", "is_tactic_proof": true, "tactics": ["refine", "filter_upwards", "simp"], "tactic_count": 3}
{"name": "IsFoelner.mean_union_eq_add_of_disjoint", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FoelnerFilter", "is_tactic_proof": false, "tactics": ["refine", "tendsto_nhds_unique_of_eventuallyEq", "filter_upwards", "rw"], "tactic_count": 4}
{"name": "IsFoelner.tendsto_meas_smul_symmDiff_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FoelnerFilter", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsFoelner.mean_smul_eq_mean_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FoelnerFilter", "is_tactic_proof": true, "tactics": ["suffices", "intro", "rw", "refine", "le_of_tendsto_of_tendsto", "filter_upwards", "rw", "refine", "simpa"], "tactic_count": 9}
{"name": "IsFoelner.mean_smul_eq_mean", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FoelnerFilter", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsFoelner.amenable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FoelnerFilter", "is_tactic_proof": true, "tactics": ["use", "refine", "exact", "exact", "exact"], "tactic_count": 5}
{"name": "maxFoelner", "kind": "definition", "module": "Mathlib.MeasureTheory.Group.FoelnerFilter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isFoelner_iff_tendsto", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FoelnerFilter", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "isFoelner_maxFoelner", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FoelnerFilter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "amenable_of_maxFoelner_neBot", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FoelnerFilter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IsFundamentalDomain.mk'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IsFundamentalDomain.mk''", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IsFundamentalDomain.mk_of_measure_univ_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IsFundamentalDomain.iUnion_smul_ae_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IsFundamentalDomain.measure_ne_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": true, "tactics": ["have", "contrapose", "rw", "refine", "simp_rw"], "tactic_count": 5}
{"name": "MeasureTheory.IsFundamentalDomain.mono", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IsFundamentalDomain.preimage_of_equiv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IsFundamentalDomain.image_of_equiv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": true, "tactics": ["rw", "refine", "rcases", "rw"], "tactic_count": 4}
{"name": "MeasureTheory.IsFundamentalDomain.pairwise_aedisjoint_of_ac", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IsFundamentalDomain.smul_of_comm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IsFundamentalDomain.nullMeasurableSet_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IsFundamentalDomain.restrict_restrict", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IsFundamentalDomain.smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IsFundamentalDomain.sum_restrict_of_ac", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": true, "tactics": ["rw", "restrict_congr_set"], "tactic_count": 2}
{"name": "MeasureTheory.IsFundamentalDomain.lintegral_eq_tsum_of_ac", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.IsFundamentalDomain.sum_restrict", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasureTheory.IsFundamentalDomain.lintegral_eq_tsum''", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IsFundamentalDomain.setLIntegral_eq_tsum", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IsFundamentalDomain.setLIntegral_eq_tsum'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IsFundamentalDomain.measure_eq_tsum_of_ac", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": true, "tactics": ["have", "simpa", "inter_comm]"], "tactic_count": 3}
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{"name": "MeasureTheory.IsFundamentalDomain.measure_eq_tsum", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.IsFundamentalDomain.measure_zero_of_invariant", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.IsFundamentalDomain.measure_eq_card_smul_of_smul_ae_eq_self", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": true, "tactics": ["haveI", "rw", "replace", "simp_rw"], "tactic_count": 4}
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{"name": "MeasureTheory.IsFundamentalDomain.measure_set_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": false, "tactics": ["have", "refine", "convert", "rw", "simpa"], "tactic_count": 5}
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{"name": "MeasureTheory.IsFundamentalDomain.aestronglyMeasurable_on_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IsFundamentalDomain.hasFiniteIntegral_on_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "intro"], "tactic_count": 3}
{"name": "MeasureTheory.IsFundamentalDomain.integrableOn_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IsFundamentalDomain.integral_eq_tsum_of_ac", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
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{"name": "MeasureTheory.IsFundamentalDomain.integral_eq_tsum'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasureTheory.IsFundamentalDomain.setIntegral_eq_tsum", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IsFundamentalDomain.setIntegral_eq_tsum'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IsFundamentalDomain.setIntegral_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": true, "tactics": ["by_cases", "have", "calc", "rw", "rwa"], "tactic_count": 5}
{"name": "MeasureTheory.IsFundamentalDomain.measure_le_of_pairwise_disjoint", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IsFundamentalDomain.exists_ne_one_smul_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": true, "tactics": ["contrapose", "refine", "dsimp", "refine", "rw", "rintro", "refine", "rw"], "tactic_count": 8}
{"name": "MeasureTheory.IsFundamentalDomain.essSup_measure_restrict", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": true, "tactics": ["refine", "rw", "refine", "rintro", "rw", "refine", "intro", "ext", "rw", "simp"], "tactic_count": 10}
{"name": "MeasureTheory.fundamentalFrontier", "kind": "definition", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.fundamentalInterior", "kind": "definition", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.mem_fundamentalFrontier", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.mem_fundamentalInterior", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.fundamentalFrontier_subset", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.fundamentalInterior_subset", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.disjoint_fundamentalInterior_fundamentalFrontier", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.fundamentalInterior_union_fundamentalFrontier", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.fundamentalFrontier_union_fundamentalInterior", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.sdiff_fundamentalInterior", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.sdiff_fundamentalFrontier", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.fundamentalFrontier_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MeasureTheory.fundamentalInterior_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MeasureTheory.pairwise_disjoint_fundamentalInterior", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": true, "tactics": ["refine", "rintro", "rw", "refine", "rwa", "simpa"], "tactic_count": 6}
{"name": "MeasureTheory.NullMeasurableSet.fundamentalFrontier", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.NullMeasurableSet.fundamentalInterior", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IsFundamentalDomain.measure_fundamentalFrontier", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.IsFundamentalDomain.measure_fundamentalInterior", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IsFundamentalDomain.fundamentalInterior", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.MeasureTheory.Group.FundamentalDomain.0.MeasureTheory.termα_mod_G", "kind": "definition", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "_private.Mathlib.MeasureTheory.Group.FundamentalDomain.0.MeasureTheory.termπ", "kind": "definition", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasureTheory.measure_map_restrict_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.IsFundamentalDomain.quotientMeasure_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": true, "tactics": ["ext", "rw", "apply", "exact", "intro", "ext", "have", "apply", "use", "simp"], "tactic_count": 10}
{"name": "MeasureTheory.IsFundamentalDomain.hasFundamentalDomain", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IsFundamentalDomain.covolume_eq_volume", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": true, "tactics": ["dsimp", "simp", "rw", "exact"], "tactic_count": 4}
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{"name": "MeasureTheory.IsFundamentalDomain.projection_respects_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IsFundamentalDomain.projection_respects_measure_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.QuotientMeasureEqMeasurePreimage.unique", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": true, "tactics": ["obtain", "rw"], "tactic_count": 2}
{"name": "MeasureTheory.IsFundamentalDomain.measurePreserving_quotient_mk", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IsFundamentalDomain.quotientMeasureEqMeasurePreimage_quotientMeasure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IsFundamentalDomain.quotientMeasureEqMeasurePreimage", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.IsFundamentalDomain.quotientMeasureEqMeasurePreimage_of_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": true, "tactics": ["apply", "ext", "simp", "convert", "rw"], "tactic_count": 5}
{"name": "MeasureTheory.QuotientMeasureEqMeasurePreimage.sigmaFiniteQuotient", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": true, "tactics": ["rw", "obtain", "simp", "refine", "obtain", "have", "have", "let", "rw", "apply", "exact", "rw", "refine", "rw", "exact", "rw", "refine"], "tactic_count": 17}
{"name": "MeasureTheory.QuotientMeasureEqMeasurePreimage.isFiniteMeasure_quotient", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": true, "tactics": ["obtain", "rw", "have", "apply", "convert", "exact", "infer_instance"], "tactic_count": 7}
{"name": "MeasureTheory.QuotientMeasureEqMeasurePreimage.covolume_ne_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": true, "tactics": ["by_cases", "obtain", "have", "rw", "simpa", "simp"], "tactic_count": 6}
{"name": "_private.Mathlib.MeasureTheory.Group.FundamentalDomain.0.MeasureTheory.termα_mod_G_3", "kind": "definition", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasureTheory.instSigmaFiniteQuotientOrbitRelOfHasFundamentalDomainOfQuotientMeasureEqMeasurePreimageVolume", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.FundamentalDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.exists_pair_mem_lattice_not_disjoint_vadd", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.GeometryOfNumbers", "is_tactic_proof": true, "tactics": ["contrapose", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.exists_ne_zero_mem_lattice_of_measure_mul_two_pow_lt_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.GeometryOfNumbers", "is_tactic_proof": false, "tactics": ["have", "rw", "ofReal_pow", "norm_num", "rwa", "obtain", "obtain", "refine", "rw", "simp_rw", "rw", "refine"], "tactic_count": 12}
{"name": "MeasureTheory.exists_ne_zero_mem_lattice_of_measure_mul_two_pow_le_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.GeometryOfNumbers", "is_tactic_proof": true, "tactics": ["have", "have", "let", "let", "let", "let", "have", "suffices", "erw", "obtain", "exact", "exact", "have", "rsuffices", "rw", "exact", "exact", "refine", "refine", "refine", "rw", "exact", "suffices", "have", "rintro", "exact", "obtain", "exists_ne_zero_mem_lattice_of_measure_mul_two_pow_lt_measure", "exact", "refine", "rw", "rw", "dsimp", "gcongr", "exact", "rw", "refine", "simp"], "tactic_count": 38}
{"name": "MeasureTheory.Integrable.comp_inv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integral_inv_eq_self", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Integral", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "MeasureTheory.IntegrableOn.comp_inv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Integral", "is_tactic_proof": true, "tactics": ["apply", "have", "rw", "simpa"], "tactic_count": 4}
{"name": "MeasureTheory.IntegrableOn.comp_inv_Iic", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Integral", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.IntegrableOn.comp_inv_Ici", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Integral", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.IntegrableOn.comp_inv_Iio", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Integral", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.IntegrableOn.comp_inv_Ioi", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Integral", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
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{"name": "MeasureTheory.integral_mul_right_eq_self", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Integral", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "MeasureTheory.integral_div_right_eq_self", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Integral", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
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{"name": "MeasureTheory.Integrable.comp_mul_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Integrable.comp_mul_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Integrable.comp_div_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Integral", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.Integrable.comp_div_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integrable_comp_div_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Integral", "is_tactic_proof": true, "tactics": ["refine", "convert", "simp_rw"], "tactic_count": 3}
{"name": "MeasureTheory.integral_div_left_eq_self", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Integral", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MeasureTheory.integral_smul_eq_self", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Integral", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "MeasureTheory.integrable_mconv_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.IntegralConvolution", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.integral_mconv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.IntegralConvolution", "is_tactic_proof": true, "tactics": ["unfold", "rw", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.lintegral_inv_eq_self", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.LIntegral", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.lintegral_mul_left_eq_self", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.LIntegral", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.lintegral_mul_right_eq_self", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.LIntegral", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.lintegral_div_right_eq_self", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.LIntegral", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MeasureTheory.lintegral_div_left_eq_self", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.LIntegral", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MeasureTheory.lintegral_eq_zero_of_isMulLeftInvariant", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.LIntegral", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasurableEquiv.smul", "kind": "definition", "module": "Mathlib.MeasureTheory.Group.MeasurableEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurableEmbedding_const_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.MeasurableEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.symm_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.MeasurableEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.smul₀", "kind": "definition", "module": "Mathlib.MeasureTheory.Group.MeasurableEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.coe_smul₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.MeasurableEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.symm_smul₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.MeasurableEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurableEmbedding_const_smul₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.MeasurableEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.mulLeft", "kind": "definition", "module": "Mathlib.MeasureTheory.Group.MeasurableEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.coe_mulLeft", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.MeasurableEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.symm_mulLeft", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.MeasurableEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.toEquiv_mulLeft", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.MeasurableEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurableEmbedding_mulLeft", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.MeasurableEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.mulRight", "kind": "definition", "module": "Mathlib.MeasureTheory.Group.MeasurableEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurableEmbedding_mulRight", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.MeasurableEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.coe_mulRight", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.MeasurableEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.symm_mulRight", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.MeasurableEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.toEquiv_mulRight", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.MeasurableEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.mulLeft₀", "kind": "definition", "module": "Mathlib.MeasureTheory.Group.MeasurableEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurableEmbedding_mulLeft₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.MeasurableEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.coe_mulLeft₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.MeasurableEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.symm_mulLeft₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.MeasurableEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.toEquiv_mulLeft₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.MeasurableEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.mulRight₀", "kind": "definition", "module": "Mathlib.MeasureTheory.Group.MeasurableEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurableEmbedding_mulRight₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.MeasurableEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.coe_mulRight₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.MeasurableEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.symm_mulRight₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.MeasurableEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.toEquiv_mulRight₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.MeasurableEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.inv", "kind": "definition", "module": "Mathlib.MeasureTheory.Group.MeasurableEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.symm_inv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.MeasurableEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.divRight", "kind": "definition", "module": "Mathlib.MeasureTheory.Group.MeasurableEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurableEmbedding_divRight", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.MeasurableEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.divLeft", "kind": "definition", "module": "Mathlib.MeasureTheory.Group.MeasurableEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurableEmbedding_divLeft", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.MeasurableEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.instDistribMulActionDomMulAct", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.MeasurableEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.domSMul_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.MeasurableEquiv", "is_tactic_proof": true, "tactics": ["refine", "congr", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.instSMulCommClassNNRealDomMulAct", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.MeasurableEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.instSMulCommClassDomMulActNNReal", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.MeasurableEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.map_mul_left_eq_self", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.map_mul_right_eq_self", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.isMulLeftInvariant_smul", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.isMulRightInvariant_smul", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.isMulLeftInvariant_smul_nnreal", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.isMulRightInvariant_smul_nnreal", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measurePreserving_mul_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MeasurePreserving.mul_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measurePreserving_mul_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MeasurePreserving.mul_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Subgroup.smulInvariantMeasure", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.forall_measure_preimage_mul_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": true, "tactics": ["trans", "simp_rw", "refine", "rw", "exact"], "tactic_count": 5}
{"name": "MeasureTheory.forall_measure_preimage_mul_right_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": true, "tactics": ["trans", "simp_rw", "refine", "rw", "exact"], "tactic_count": 5}
{"name": "MeasureTheory.Measure.prod.instIsMulLeftInvariant", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "change", "rw", "map_mul_left_eq_self"], "tactic_count": 5}
{"name": "MeasureTheory.Measure.prod.instIsMulRightInvariant", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "change", "rw", "map_mul_right_eq_self"], "tactic_count": 5}
{"name": "MeasureTheory.isMulLeftInvariant_map", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": true, "tactics": ["refine", "rw", "obtain", "conv_rhs", "rw", "congr", "ext", "simp"], "tactic_count": 8}
{"name": "MeasureTheory.isMulLeftInvariant_map_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.isMulRightInvariant_map_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.isMulLeftInvariant_map_mul_right", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.isMulRightInvariant_map_mul_left", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.map_div_right_eq_self", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MeasureTheory.measurePreserving_div_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MeasureTheory.measure_preimage_mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_preimage_mul_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.map_mul_left_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.map_mul_right_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.map_div_right_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.eventually_mul_left_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": true, "tactics": ["conv_rhs", "rfl"], "tactic_count": 2}
{"name": "MeasureTheory.eventually_mul_right_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": true, "tactics": ["conv_rhs", "rfl"], "tactic_count": 2}
{"name": "MeasureTheory.eventually_div_right_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": true, "tactics": ["conv_rhs", "rfl"], "tactic_count": 2}
{"name": "MeasureTheory.Subgroup.index_mul_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": true, "tactics": ["obtain", "have", "calc", "rw", "simp", "exact"], "tactic_count": 6}
{"name": "MeasureTheory.Measure.inv", "kind": "definition", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.inv_def", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.inv_eq_self", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.map_inv_eq_self", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.measurePreserving_inv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.inv.instSFinite", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.inv_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.inv_inv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.measure_inv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.measure_preimage_inv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.inv.instSigmaFinite", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.inv.instIsMulRightInvariant", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": true, "tactics": ["constructor", "intro", "conv_rhs", "simp_rw", "map_map"], "tactic_count": 5}
{"name": "MeasureTheory.Measure.inv.instIsMulLeftInvariant", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": true, "tactics": ["constructor", "intro", "conv_rhs", "simp_rw", "map_map"], "tactic_count": 5}
{"name": "MeasureTheory.Measure.measurePreserving_div_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.map_div_left_eq_self", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.measurePreserving_mul_right_inv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.map_mul_right_inv_eq_self", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.instIsMulLeftInvariantCount", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.instIsMulRightInvariantCount", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.IsMulLeftInvariant.comap", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.IsMulRightInvariant.comap", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.instIsInvInvariantCount", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.map_div_left_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.IsFiniteMeasureOnCompacts.inv", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.IsOpenPosMeasure.inv", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.Regular.inv", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.InnerRegular.inv", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.innerRegular_map_smul", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.innerRegular_map_mul_left", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.innerRegular_map_mul_right", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.regular_inv_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.innerRegular_inv_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.eventually_nhds_one_measure_smul_diff_lt", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "filter_upwards", "calc", "μ", "gcongr", "exact"], "tactic_count": 7}
{"name": "MeasureTheory.tendsto_measure_smul_diff_isCompact_isClosed", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.isOpenPosMeasure_of_mulLeftInvariant_of_compact", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": true, "tactics": ["refine", "contrapose", "rw", "rw", "obtain", "compact_covered_by_mul_left_translates", "calc", "μ"], "tactic_count": 8}
{"name": "MeasureTheory.isOpenPosMeasure_of_mulLeftInvariant_of_regular", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.isOpenPosMeasure_of_mulLeftInvariant_of_innerRegular", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.null_iff_of_isMulLeftInvariant", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simp"], "tactic_count": 3}
{"name": "MeasureTheory.measure_ne_zero_iff_nonempty_of_isMulLeftInvariant", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.measure_pos_iff_nonempty_of_isMulLeftInvariant", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_lt_top_of_isCompact_of_isMulLeftInvariant", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": true, "tactics": ["rw", "obtain", "compact_covered_by_mul_left_translates", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.measure_lt_top_of_isCompact_of_isMulLeftInvariant'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_univ_of_isMulLeftInvariant", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": true, "tactics": ["find", "infinitely", "same", "obtain", "have", "have", "choose", "set", "have", "induction", "zero", "succ", "simp_rw", "apply", "have", "induction", "zero", "succ", "simp_rw", "apply", "have", "induction", "zero", "succ", "calc", "μ", "simp_rw", "exact", "have", "simp_rw", "apply", "exact", "simp", "apply", "exact"], "tactic_count": 35}
{"name": "MeasurableSet.mul_closure_one_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": true, "tactics": ["induction", "isOpen", "compl", "iUnion"], "tactic_count": 4}
{"name": "MeasureTheory.measure_mul_closure_one", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": true, "tactics": ["apply", "conv_rhs", "simp", "intro", "apply", "rw", "exact"], "tactic_count": 7}
{"name": "MeasureTheory.innerRegularWRT_isCompact_isClosed_measure_ne_top_of_group", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": true, "tactics": ["intro", "rcases", "refine", "exact", "rwa"], "tactic_count": 5}
{"name": "MeasureTheory.IsMulLeftInvariant.isMulRightInvariant", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.haar_singleton", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.IsHaarMeasure.smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.IsHaarMeasure.nnreal_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.isHaarMeasure_of_isCompact_nonempty_interior", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.isHaarMeasure_map", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.IsHaarMeasure.comap", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.isHaarMeasure_map_of_isFiniteMeasure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.isHaarMeasure_map_smul", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.isHaarMeasure_map_mul_right", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.isHaarMeasure_map", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMulEquiv.isHaarMeasure_map", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.isAddHaarMeasure_map", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.IsHaarMeasure.sigmaFinite", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.prod.instIsHaarMeasure", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.IsHaarMeasure.noAtoms", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": true, "tactics": ["cases", "inl", "inr", "obtain", "have", "exact"], "tactic_count": 6}
{"name": "MeasureTheory.Measure.IsAddHaarMeasure.domSMul", "kind": "instance", "module": "Mathlib.MeasureTheory.Group.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.modularCharacterFun", "kind": "definition", "module": "Mathlib.MeasureTheory.Group.ModularCharacter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.modularCharacterFun_eq_haarScalarFactor", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.ModularCharacter", "is_tactic_proof": true, "tactics": ["let", "obtain", "exists_continuous_nonneg_pos", "have", "ne_of_gt", "apply", "have", "refine", "exact", "have", "rw", "exact", "have", "refine", "rw", "apply", "calc", "rw", "rw", "rw", "rw"], "tactic_count": 21}
{"name": "MeasureTheory.Measure.map_right_mul_eq_modularCharacterFun_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.ModularCharacter", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.modularCharacterFun_pos", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.ModularCharacter", "is_tactic_proof": true, "tactics": ["borelize", "rw", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.modularCharacterFun_map_one", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.ModularCharacter", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.modularCharacterFun_map_mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.ModularCharacter", "is_tactic_proof": true, "tactics": ["borelize", "have", "have", "let", "symm", "calc", "modularCharacterFun", "rw", "simp"], "tactic_count": 9}
{"name": "MeasureTheory.Measure.modularCharacter", "kind": "definition", "module": "Mathlib.MeasureTheory.Group.ModularCharacter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSet.const_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Pointwise", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasurableSet.const_smul_of_ne_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Pointwise", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasurableSet.const_smul₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Pointwise", "is_tactic_proof": true, "tactics": ["rcases", "exacts"], "tactic_count": 2}
{"name": "MeasurableEquiv.shearMulRight", "kind": "definition", "module": "Mathlib.MeasureTheory.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.shearDivRight", "kind": "definition", "module": "Mathlib.MeasureTheory.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measurePreserving_prod_mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measurePreserving_prod_mul_swap", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measurable_measure_mul_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Prod", "is_tactic_proof": false, "tactics": ["suffices", "convert", "apply", "apply", "infer_instance"], "tactic_count": 5}
{"name": "MeasureTheory.measurePreserving_prod_inv_mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measurePreserving_prod_inv_mul_swap", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measurePreserving_mul_prod_inv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Prod", "is_tactic_proof": true, "tactics": ["convert", "ext1", "simp_rw"], "tactic_count": 3}
{"name": "MeasureTheory.quasiMeasurePreserving_inv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Prod", "is_tactic_proof": true, "tactics": ["refine", "rw", "have", "suffices", "simpa", "this", "have", "simp_rw", "inv_preimage,"], "tactic_count": 9}
{"name": "MeasureTheory.measure_inv_null", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Prod", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.inv_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Prod", "is_tactic_proof": true, "tactics": ["refine", "nth_rewrite", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.eventuallyConst_inv_set_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Prod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.inv_absolutelyContinuous", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.absolutelyContinuous_inv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Prod", "is_tactic_proof": true, "tactics": ["refine", "simp_rw"], "tactic_count": 2}
{"name": "MeasureTheory.lintegral_lintegral_mul_inv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Prod", "is_tactic_proof": false, "tactics": ["have", "have", "hf.comp_quasiMeasurePreserving", "simp_rw", "conv_rhs", "symm", "exact"], "tactic_count": 7}
{"name": "MeasureTheory.measure_mul_right_null", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_mul_right_ne_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.absolutelyContinuous_map_mul_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Prod", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "MeasureTheory.absolutelyContinuous_map_div_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Prod", "is_tactic_proof": true, "tactics": ["simp_rw", "have", "simp", "rw", "conv_lhs", "exact"], "tactic_count": 6}
{"name": "MeasureTheory.measure_mul_lintegral_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Prod", "is_tactic_proof": false, "tactics": ["rw", "lintegral_lintegral_mul", "lintegral_lintegral_mul_inv", "swap", "exact", "have", "measurable_const.indicator", "have", "simp_rw"], "tactic_count": 9}
{"name": "MeasureTheory.absolutelyContinuous_of_isMulLeftInvariant", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Prod", "is_tactic_proof": true, "tactics": ["refine", "have", "simp_rw", "mul_eq_zero", "exact"], "tactic_count": 5}
{"name": "MeasureTheory.ae_measure_preimage_mul_right_lt_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Prod", "is_tactic_proof": true, "tactics": ["wlog", "filter_upwards", "lt_of_le_of_lt", "refine", "intro", "simp", "apply", "have", "rw", "simp_rw", "indicator_mul_right", "rw", "finiteness"], "tactic_count": 13}
{"name": "MeasureTheory.ae_measure_preimage_mul_right_lt_top_of_ne_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Prod", "is_tactic_proof": true, "tactics": ["refine", "refine", "refine", "intro", "rw"], "tactic_count": 5}
{"name": "MeasureTheory.measure_lintegral_div_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Prod", "is_tactic_proof": true, "tactics": ["set", "have", "simp_rw", "refine", "refine", "simp_rw"], "tactic_count": 6}
{"name": "MeasureTheory.measure_mul_measure_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Prod", "is_tactic_proof": true, "tactics": ["wlog", "rcases", "rw", "wlog", "rcases", "rw", "have", "have", "rw", "rw"], "tactic_count": 10}
{"name": "MeasureTheory.measure_eq_div_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Prod", "is_tactic_proof": true, "tactics": ["ext1", "rw", "mul_div_assoc,"], "tactic_count": 3}
{"name": "MeasureTheory.measurePreserving_prod_mul_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measurePreserving_prod_mul_swap_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measurePreserving_mul_prod", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measurePreserving_prod_div", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measurePreserving_prod_div_swap", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measurePreserving_div_prod", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measurePreserving_mul_prod_inv_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Prod", "is_tactic_proof": true, "tactics": ["convert", "ext1", "simp_rw"], "tactic_count": 3}
{"name": "MeasureTheory.quasiMeasurePreserving_mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.quasiMeasurePreserving_mul_swap", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.quasiMeasurePreserving_inv_mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.quasiMeasurePreserving_inv_mul_swap", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.quasiMeasurePreserving_inv_of_right_invariant", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Prod", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.quasiMeasurePreserving_div_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Prod", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.quasiMeasurePreserving_div_left_of_right_invariant", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Prod", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.quasiMeasurePreserving_div_of_right_invariant", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Prod", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.quasiMeasurePreserving_div", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.quasiMeasurePreserving_mul_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Prod", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "MeasureTheory.quasiMeasurePreserving_mul_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Group.Prod", "is_tactic_proof": false, "tactics": ["have", "rw", "have", "simp_rw", "exact"], "tactic_count": 5}
{"name": "Asymptotics.IsBigO.integrableAtFilter", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Asymptotics", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "refine", "refine", "exact"], "tactic_count": 5}
{"name": "Asymptotics.IsBigO.integrable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Asymptotics", "is_tactic_proof": true, "tactics": ["rewrite", "exact"], "tactic_count": 2}
{"name": "Asymptotics.IsBigO.eventually_integrableOn", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Asymptotics", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "obtain", "obtain", "refine", "haveI", "refine", "filter_upwards", "intro", "exact"], "tactic_count": 10}
{"name": "Asymptotics.IsBigO.set_integral_isBigO", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Asymptotics", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "obtain", "refine", "rw", "smul_eq_mul,", "haveI", "refine", "integral_mono_of_nonneg", "filter_upwards", "intro", "rw", "exact"], "tactic_count": 13}
{"name": "MeasureTheory.LocallyIntegrable.integrable_of_isBigO_cocompact", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Asymptotics", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.LocallyIntegrable.integrable_of_isBigO_atBot_atTop", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Asymptotics", "is_tactic_proof": false, "tactics": ["refine", "integrable_iff_integrableAtFilter_atBot_atTop.mpr", "all_goals"], "tactic_count": 3}
{"name": "MeasureTheory.LocallyIntegrableOn.integrableOn_of_isBigO_atBot", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Asymptotics", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.LocallyIntegrableOn.integrableOn_of_isBigO_atTop", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Asymptotics", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.LocallyIntegrable.integrable_of_isBigO_atBot", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Asymptotics", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.LocallyIntegrable.integrable_of_isBigO_atTop", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Asymptotics", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.LocallyIntegrable.integrable_of_isBigO_atTop_of_norm_isNegInvariant", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Asymptotics", "is_tactic_proof": true, "tactics": ["have", "rw", "refine", "have", "conv", "simp", "rw", "refine", "refine", "exact"], "tactic_count": 10}
{"name": "MeasureTheory.laverage", "kind": "definition", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.term⨍⁻_,_∂_", "kind": "definition", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory._aux_Mathlib_MeasureTheory_Integral_Average___macroRules_MeasureTheory_term⨍⁻_,_∂__1", "kind": "definition", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory._aux_Mathlib_MeasureTheory_Integral_Average___delab_app_MeasureTheory_term⨍⁻_,_∂__1", "kind": "definition", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.term⨍⁻_,_", "kind": "definition", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory._aux_Mathlib_MeasureTheory_Integral_Average___macroRules_MeasureTheory_term⨍⁻_,__1", "kind": "definition", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory._aux_Mathlib_MeasureTheory_Integral_Average___delab_app_MeasureTheory_term⨍⁻_,__1", "kind": "definition", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.term⨍⁻_In_,_∂_", "kind": "definition", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory._aux_Mathlib_MeasureTheory_Integral_Average___macroRules_MeasureTheory_term⨍⁻_In_,_∂__1", "kind": "definition", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory._aux_Mathlib_MeasureTheory_Integral_Average___delab_app_MeasureTheory_term⨍⁻_In_,_∂__1", "kind": "definition", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.term⨍⁻_In_,_", "kind": "definition", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory._aux_Mathlib_MeasureTheory_Integral_Average___macroRules_MeasureTheory_term⨍⁻_In_,__1", "kind": "definition", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.laverage_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.laverage_zero_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.laverage_eq'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.laverage_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.laverage_eq_lintegral", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.measure_mul_laverage", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["rcases", "rw", "rw"], "tactic_count": 3}
{"name": "MeasureTheory.setLAverage_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.setLAverage_eq'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.laverage_congr", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.setLAverage_congr", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.setLAverage_congr_fun_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.setLAverage_congr_fun", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.laverage_lt_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["obtain", "simp", "rw", "finiteness"], "tactic_count": 4}
{"name": "MeasureTheory.setLAverage_lt_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.laverage_add_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "simp", "by_cases", "rw", "simp", "simp"], "tactic_count": 7}
{"name": "MeasureTheory.measure_mul_setLAverage", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "MeasureTheory.laverage_union", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.laverage_union_mem_openSegment", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": false, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "MeasureTheory.laverage_union_mem_segment", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "rw", "exact", "refine", "rw"], "tactic_count": 6}
{"name": "MeasureTheory.laverage_mem_openSegment_compl_self", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["simpa", "laverage_union_mem_openSegment"], "tactic_count": 2}
{"name": "MeasureTheory.laverage_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.setLAverage_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["simp", "mul_assoc,"], "tactic_count": 2}
{"name": "MeasureTheory.laverage_one", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.setLAverage_one", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.laverage_mul_measure_univ", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["obtain", "simp", "rw"], "tactic_count": 3}
{"name": "MeasureTheory.lintegral_laverage", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.setLIntegral_setLAverage", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.average", "kind": "definition", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.term⨍_,_∂_", "kind": "definition", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory._aux_Mathlib_MeasureTheory_Integral_Average___macroRules_MeasureTheory_term⨍_,_∂__1", "kind": "definition", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory._aux_Mathlib_MeasureTheory_Integral_Average___delab_app_MeasureTheory_term⨍_,_∂__1", "kind": "definition", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.term⨍_,_", "kind": "definition", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory._aux_Mathlib_MeasureTheory_Integral_Average___macroRules_MeasureTheory_term⨍_,__1", "kind": "definition", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory._aux_Mathlib_MeasureTheory_Integral_Average___delab_app_MeasureTheory_term⨍_,__1", "kind": "definition", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.term⨍_In_,_∂_", "kind": "definition", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory._aux_Mathlib_MeasureTheory_Integral_Average___macroRules_MeasureTheory_term⨍_In_,_∂__1", "kind": "definition", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory._aux_Mathlib_MeasureTheory_Integral_Average___delab_app_MeasureTheory_term⨍_In_,_∂__1", "kind": "definition", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.term⨍_In_,_", "kind": "definition", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory._aux_Mathlib_MeasureTheory_Integral_Average___macroRules_MeasureTheory_term⨍_In_,__1", "kind": "definition", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory._aux_Mathlib_MeasureTheory_Integral_Average___delab_app_MeasureTheory_term⨍_In_,__1", "kind": "definition", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.average_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.average_zero_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.average_neg", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.average_eq'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.average_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.average_eq_integral", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.measure_smul_average", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["rcases", "rw", "rw", "refine", "rwa"], "tactic_count": 5}
{"name": "MeasureTheory.setAverage_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.setAverage_eq'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.average_congr", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.setAverage_congr", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.setAverage_congr_fun", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.average_add_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["simp", "rw"], "tactic_count": 2}
{"name": "MeasureTheory.average_pair", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_smul_setAverage", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["haveI", "rw"], "tactic_count": 2}
{"name": "MeasureTheory.average_union", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["haveI", "rw", "measureReal_restrict_apply_univ]"], "tactic_count": 3}
{"name": "MeasureTheory.average_union_mem_openSegment", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["replace", "replace", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.average_union_mem_segment", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "rw", "exact", "refine", "mem_segment_iff_div.mpr", "calc"], "tactic_count": 7}
{"name": "MeasureTheory.average_mem_openSegment_compl_self", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["simpa", "average_union_mem_openSegment", "hfi.integrableOn"], "tactic_count": 3}
{"name": "MeasureTheory.average_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.setAverage_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integral_average", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.setIntegral_setAverage", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integral_sub_average", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "refine", "convert", "exact"], "tactic_count": 5}
{"name": "MeasureTheory.setAverage_sub_setAverage", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integral_average_sub", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.setIntegral_setAverage_sub", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.ofReal_average", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["obtain", "simp", "rw", "ofReal_toReal"], "tactic_count": 4}
{"name": "MeasureTheory.ofReal_setAverage", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.toReal_laverage", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["rw", "integral_toReal"], "tactic_count": 2}
{"name": "MeasureTheory.toReal_setLAverage", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.measure_le_setAverage_pos", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["refine", "replace", "rwa", "exact", "haveI", "refine", "refine", "refine", "simp", "exact", "exact", "rwa", "refine", "exact"], "tactic_count": 14}
{"name": "MeasureTheory.measure_setAverage_le_pos", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.exists_le_setAverage", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.exists_setAverage_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_le_average_pos", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.measure_average_le_pos", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.exists_le_average", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.exists_average_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.exists_notMem_null_le_average", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["have", "rw", "obtain", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.exists_notMem_null_average_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.measure_le_integral_pos", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.measure_integral_le_pos", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.exists_le_integral", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.exists_integral_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.exists_notMem_null_le_integral", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.exists_notMem_null_integral_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.measure_le_setLAverage_pos", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["obtain", "simpa", "have", "rw", "rw", "measure_diff_null", "refine", "rintro", "dsimp", "rwa", "simp_rw", "exact"], "tactic_count": 12}
{"name": "MeasureTheory.measure_setLAverage_le_pos", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["obtain", "simp", "obtain", "have", "rw", "have", "simp_rw", "rw", "measure_diff_null", "refine", "rintro", "dsimp", "rw", "exact", "simp_rw", "exact"], "tactic_count": 16}
{"name": "MeasureTheory.exists_le_setLAverage", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.exists_setLAverage_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_laverage_le_pos", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.exists_laverage_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.exists_notMem_null_laverage_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["have", "rw", "obtain", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.measure_le_laverage_pos", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.exists_le_laverage", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.exists_notMem_null_le_laverage", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["have", "rw", "obtain", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.measure_le_lintegral_pos", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.measure_lintegral_le_pos", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.exists_le_lintegral", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.exists_lintegral_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.exists_notMem_null_le_lintegral", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.exists_notMem_null_lintegral_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Average", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
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{"name": "MeasureTheory.integral_exp_pos", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Basic", "is_tactic_proof": true, "tactics": ["rw", "suffices", "ext1", "simp"], "tactic_count": 4}
{"name": "MeasureTheory.integral_tendsto_of_tendsto_of_monotone", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Basic", "is_tactic_proof": true, "tactics": ["let", "have", "filter_upwards", "simp", "have", "suffices", "simp_rw", "exact", "have", "filter_upwards", "simp", "exact", "rw", "simp_rw", "rw", "have", "swap", "rw", "finiteness", "refine", "h_cont.tendsto.comp", "refine", "exact", "filter_upwards", "refine", "simp", "exact", "filter_upwards", "refine", "simp", "exact"], "tactic_count": 31}
{"name": "MeasureTheory.integral_tendsto_of_tendsto_of_antitone", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Basic", "is_tactic_proof": false, "tactics": ["suffices", "suffices", "convert", "refine", "filter_upwards", "filter_upwards"], "tactic_count": 6}
{"name": "MeasureTheory.tendsto_of_integral_tendsto_of_monotone", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Basic", "is_tactic_proof": true, "tactics": ["let", "let", "have", "intro", "unfold", "rw", "exact", "filter_upwards", "simp", "have", "unfold", "rw", "exact", "filter_upwards", "simp", "have", "simp_rw", "refine", "rwa", "have", "filter_upwards", "refine", "simp", "have", "filter_upwards", "refine", "simp", "have", "rotate_left", "exact", "exact", "filter_upwards", "have", "unfold", "ext", "rw", "abel", "simp", "have", "unfold", "rw", "abel", "simp", "rw", "refine", "exact"], "tactic_count": 46}
{"name": "MeasureTheory.tendsto_of_integral_tendsto_of_antitone", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Basic", "is_tactic_proof": true, "tactics": ["let", "let", "suffices", "filter_upwards", "convert", "simp", "simp", "refine", "convert", "rw", "rw", "filter_upwards", "simp", "filter_upwards", "simp"], "tactic_count": 15}
{"name": "MeasureTheory.L1.norm_eq_integral_norm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Basic", "is_tactic_proof": false, "tactics": ["simp", "rw", "simp"], "tactic_count": 3}
{"name": "MeasureTheory.L1.dist_eq_integral_dist", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Basic", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.L1.norm_of_fun_eq_integral_norm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.MemLp.eLpNorm_eq_integral_rpow_norm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Basic", "is_tactic_proof": false, "tactics": ["have", "simp_rw", "simp", "rw", "exact", "exact", "rw", "exact"], "tactic_count": 8}
{"name": "MeasureTheory.norm_integral_le_integral_norm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Basic", "is_tactic_proof": true, "tactics": ["have", "by_cases", "calc", "rw", "exact"], "tactic_count": 5}
{"name": "MeasureTheory.abs_integral_le_integral_abs", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.norm_integral_le_of_norm_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integral_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "exact", "by_cases", "simp", "simp"], "tactic_count": 6}
{"name": "MeasureTheory.integral_eq_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.norm_integral_le_of_norm_le_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integral_add_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "have", "simp_rw", "have", "have", "rw", "setToFun_congr_measure_of_add_left", "refine", "rw", "rw"], "tactic_count": 11}
{"name": "MeasureTheory.integral_zero_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "exact", "simp"], "tactic_count": 4}
{"name": "MeasureTheory.setIntegral_measure_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integral_of_isEmpty", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integral_finset_sum_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Basic", "is_tactic_proof": true, "tactics": ["induction", "empty", "cons", "rw", "rw", "exact"], "tactic_count": 6}
{"name": "MeasureTheory.nndist_integral_add_measure_le_lintegral", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.hasSum_integral_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Basic", "is_tactic_proof": true, "tactics": ["have", "simp", "refine", "lift", "have", "have", "refine", "exacts", "refine", "obtain", "refine", "simpa", "rw", "rw", "refine", "rw", "exact"], "tactic_count": 17}
{"name": "MeasureTheory.integral_sum_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integral_smul_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "rcases", "rw", "simp_rw", "have", "mul_one", "have", "rw", "exact"], "tactic_count": 10}
{"name": "MeasureTheory.integral_smul_nnreal_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integral_map_of_stronglyMeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "by_cases", "rw", "exact", "borelize", "have", "refine", "tendsto_nhds_unique", "convert", "tendsto_integral_approxOn_of_measurable_of_range_subset", "ext1", "simp", "refine", "rw", "rw", "simp"], "tactic_count": 17}
{"name": "MeasureTheory.integral_map", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEmbedding.integral_map", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "rw", "exact"], "tactic_count": 4}
{"name": "Topology.IsClosedEmbedding.integral_map", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integral_map_equiv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integral_domSMul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MeasurePreserving.integral_comp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MeasurePreserving.integral_comp'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integral_subtype_comap", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.integral_subtype", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integral_dirac'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Basic", "is_tactic_proof": true, "tactics": ["borelize", "calc"], "tactic_count": 2}
{"name": "MeasureTheory.integral_dirac", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.setIntegral_dirac'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Basic", "is_tactic_proof": true, "tactics": ["rw", "split_ifs", "exact", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.setIntegral_dirac", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Basic", "is_tactic_proof": true, "tactics": ["rw", "split_ifs", "exact", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.mul_meas_ge_le_integral_of_nonneg", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simpa", "have", "calc", "ε", "ae_restrict_mem₀"], "tactic_count": 6}
{"name": "MeasureTheory.integral_mul_norm_le_Lp_mul_Lq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Basic", "is_tactic_proof": true, "tactics": ["rw", "rotate_left", "exact", "exact", "exact", "exact", "exact", "exact", "rw", "have", "simp_rw", "have", "refine", "rw", "have", "refine", "rw", "rw", "refine", "refine", "convert", "rw", "rw", "rw", "exact", "finiteness", "convert", "rw", "rw", "rw", "exact", "finiteness", "exact", "hg.1.nnnorm.aemeasurable.coe_nnreal_ennreal"], "tactic_count": 34}
{"name": "MeasureTheory.integral_mul_le_Lp_mul_Lq_of_nonneg", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Basic", "is_tactic_proof": false, "tactics": ["have", "refine", "filter_upwards", "rw", "have", "refine", "filter_upwards", "rw", "have", "refine", "filter_upwards", "rw", "rw", "exact"], "tactic_count": 14}
{"name": "MeasureTheory.integral_countable'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Basic", "is_tactic_proof": true, "tactics": ["rw", "rw", "congr", "rw"], "tactic_count": 4}
{"name": "MeasureTheory.integral_singleton'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.integral_singleton", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.integral_countable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Basic", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "apply", "exact", "exact", "exact", "rw", "congr", "rw", "simp"], "tactic_count": 11}
{"name": "MeasureTheory.integral_finset", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.integral_fintype", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.integral_unique", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integral_pos_of_integrable_nonneg_nonzero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integral_count", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.SimpleFunc.toLargerSpace", "kind": "definition", "module": "Mathlib.MeasureTheory.Integral.Bochner.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SimpleFunc.coe_toLargerSpace_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integral_simpleFunc_larger_space", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "rw", "congr"], "tactic_count": 3}
{"name": "MeasureTheory.integral_trim_simpleFunc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Basic", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "congr", "simp", "congr", "exact"], "tactic_count": 7}
{"name": "MeasureTheory.integral_trim", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "borelize", "by_cases", "swap", "have", "rw", "haveI", "let", "have", "have", "have", "have", "integral_trim_simpleFunc", "have", "refine", "exact", "have", "simp_rw", "refine", "exact", "exact"], "tactic_count": 22}
{"name": "MeasureTheory.integral_trim_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.eLpNorm_one_le_of_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "suffices", "rw", "norm_cast", "have", "rw", "exact", "have", "filter_upwards", "rwa", "filter_upwards", "rwa", "by_cases", "swap", "have", "by_contra", "exact", "rw", "exact", "simp", "simp", "haveI", "rw", "have", "rw", "refine", "filter_upwards", "rw", "simp_rw", "rw", "simp", "grw", "rwa", "exact"], "tactic_count": 34}
{"name": "MeasureTheory.eLpNorm_one_le_of_le'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Basic", "is_tactic_proof": true, "tactics": ["refine", "simp", "filter_upwards"], "tactic_count": 3}
{"name": "Mathlib.Meta.Positivity.evalIntegral", "kind": "definition", "module": "Mathlib.MeasureTheory.Integral.Bochner.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.integral_compLp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.ContinuousLinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.setIntegral_compLp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.ContinuousLinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.continuous_integral_comp_L1", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.ContinuousLinearMap", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ContinuousLinearMap.integral_comp_commSL", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.ContinuousLinearMap", "is_tactic_proof": true, "tactics": ["apply", "intro", "rw", "smul_assoc,", "congr", "rw", "intro", "simp", "integral_add", "exact", "intro", "convert", "exact", "rw"], "tactic_count": 14}
{"name": "ContinuousLinearMap.integral_comp_comm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.ContinuousLinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.integral_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.ContinuousLinearMap", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "rcases", "simp", "have", "simp"], "tactic_count": 6}
{"name": "ContinuousMultilinearMap.integral_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.ContinuousLinearMap", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "by_cases", "have", "rwa", "simp", "rcases", "simp"], "tactic_count": 8}
{"name": "ContinuousLinearMap.integral_comp_comm'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.ContinuousLinearMap", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "have", "rwa", "simp"], "tactic_count": 5}
{"name": "ContinuousLinearMap.integral_comp_L1_comm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.ContinuousLinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometry.integral_comp_comm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.ContinuousLinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.integral_comp_comm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.ContinuousLinearMap", "is_tactic_proof": true, "tactics": ["have", "obtain", "exact", "simp"], "tactic_count": 4}
{"name": "ContinuousMap.integral_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.ContinuousLinearMap", "is_tactic_proof": true, "tactics": ["calc"], "tactic_count": 1}
{"name": "ContinuousMapZero.integral_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.ContinuousLinearMap", "is_tactic_proof": true, "tactics": ["calc"], "tactic_count": 1}
{"name": "integral_ofReal", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.ContinuousLinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "integral_complex_ofReal", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.ContinuousLinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "integral_re", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.ContinuousLinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "integral_im", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.ContinuousLinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "integral_conj", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.ContinuousLinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "integral_coe_re_add_coe_im", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.ContinuousLinearMap", "is_tactic_proof": true, "tactics": ["rw", "congr", "ext1", "rw", "exact", "exact"], "tactic_count": 6}
{"name": "integral_re_add_im", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.ContinuousLinearMap", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "setIntegral_re_add_im", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.ContinuousLinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "swap_integral", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.ContinuousLinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fst_integral", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.ContinuousLinearMap", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "have", "simp"], "tactic_count": 4}
{"name": "snd_integral", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.ContinuousLinearMap", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "integral_pair", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.ContinuousLinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "integral_smul_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.ContinuousLinearMap", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "by_cases", "simp", "rw", "rw", "simp_rw"], "tactic_count": 7}
{"name": "integral_const_mul_of_integrable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.ContinuousLinearMap", "is_tactic_proof": true, "tactics": ["by_cases", "change", "rw", "simp"], "tactic_count": 4}
{"name": "integral_mul_const_of_integrable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.ContinuousLinearMap", "is_tactic_proof": true, "tactics": ["by_cases", "change", "rw", "simp"], "tactic_count": 4}
{"name": "integral_withDensity_eq_integral_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.ContinuousLinearMap", "is_tactic_proof": true, "tactics": ["by_cases", "by_cases", "rw", "rwa", "refine", "intro", "rw", "simp_rw", "simp", "rw", "rfl", "exact", "refine", "simpa", "intro", "change", "simp_rw", "rw", "exact", "exact", "have", "continuous_integral", "have", "have", "continuous_integral.comp", "convert", "simp", "exact", "exact", "intro", "rw", "apply", "filter_upwards", "rcases", "simp", "rw", "simpa"], "tactic_count": 37}
{"name": "integral_withDensity_eq_integral_smul₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.ContinuousLinearMap", "is_tactic_proof": true, "tactics": ["let", "calc", "congr", "apply", "filter_upwards", "rw", "apply", "filter_upwards", "rw"], "tactic_count": 9}
{"name": "integral_withDensity_eq_integral_toReal_smul₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.ContinuousLinearMap", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "withDensity_congr_ae"], "tactic_count": 3}
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{"name": "MeasureTheory.setIntegral_congr_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.setIntegral_congr_fun₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.setIntegral_congr_fun", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.setIntegral_congr_set", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.integral_union_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.setIntegral_union", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integral_diff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": true, "tactics": ["rw", "exacts"], "tactic_count": 2}
{"name": "MeasureTheory.integral_inter_add_diff₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": true, "tactics": ["rw", "exact", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.integral_inter_add_diff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integral_biUnion_finset", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "insert", "simp", "rw", "rw", "simp", "exact", "exact"], "tactic_count": 10}
{"name": "MeasureTheory.integral_iUnion_fintype", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": true, "tactics": ["convert", "simp", "simp"], "tactic_count": 3}
{"name": "MeasureTheory.setIntegral_empty", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.setIntegral_univ", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.integral_add_compl₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "MeasureTheory.integral_add_compl", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.setIntegral_compl₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.setIntegral_compl", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integral_indicator", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "rwa", "calc"], "tactic_count": 4}
{"name": "MeasureTheory.integral_indicator₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": true, "tactics": ["rw", "integral_indicator"], "tactic_count": 2}
{"name": "MeasureTheory.integral_integral_indicator", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MeasureTheory.setIntegral_indicator", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.integral_biUnion_eq_sum_powerset", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": true, "tactics": ["simp_rw", "have", "refine", "grind", "have", "apply", "rw", "rw", "intro", "rw", "apply", "simp", "rcases", "exact", "congr", "convert", "rw", "norm_cast"], "tactic_count": 18}
{"name": "MeasureTheory.ofReal_setIntegral_one", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.setIntegral_one_eq_measureReal", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.integral_piecewise", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": true, "tactics": ["rw", "integral_add", "integral_indicator"], "tactic_count": 3}
{"name": "MeasureTheory.tendsto_setIntegral_of_monotone", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": true, "tactics": ["refine", "have", "have", "set", "have", "have", "rw", "set", "refine", "lift", "have", "tendsto_measure_iUnion_atTop", "filter_upwards", "rw", "refine", "rw", "exacts"], "tactic_count": 17}
{"name": "MeasureTheory.tendsto_setIntegral_of_antitone", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": true, "tactics": ["refine", "have", "rcases", "suffices", "convert", "rw", "exact", "rw", "apply", "refine", "exact", "rw", "exact"], "tactic_count": 13}
{"name": "MeasureTheory.hasSum_integral_iUnion_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.hasSum_integral_iUnion", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integral_iUnion", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integral_iUnion_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.setIntegral_eq_zero_of_ae_eq_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "contrapose", "exact", "have", "refine", "rw", "filter_upwards", "rw", "exact", "rw", "exact"], "tactic_count": 12}
{"name": "MeasureTheory.setIntegral_eq_zero_of_forall_eq_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integral_union_eq_left_of_ae_aux", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": true, "tactics": ["let", "have", "have", "have", "rw", "union_comm]", "apply", "rw", "apply", "rw", "filter_upwards"], "tactic_count": 11}
{"name": "MeasureTheory.integral_union_eq_left_of_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": true, "tactics": ["have", "by_cases", "rw", "let", "calc", "apply", "filter_upwards", "rw", "integral_congr_ae"], "tactic_count": 9}
{"name": "MeasureTheory.integral_union_eq_left_of_forall₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integral_union_eq_left_of_forall", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.setIntegral_eq_of_subset_of_ae_diff_eq_zero_aux", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": true, "tactics": ["let", "have", "calc", "apply", "filter_upwards", "change", "simp", "intro", "by_cases", "simp", "simp", "intro", "exact", "have", "rw"], "tactic_count": 15}
{"name": "MeasureTheory.setIntegral_eq_of_subset_of_ae_diff_eq_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": true, "tactics": ["by_cases", "have", "rw", "let", "calc", "apply", "filter_upwards", "rw", "apply", "apply", "exact"], "tactic_count": 11}
{"name": "MeasureTheory.setIntegral_eq_of_subset_of_forall_diff_eq_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.setIntegral_eq_integral_of_ae_compl_eq_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": true, "tactics": ["symm", "nth_rw", "apply", "filter_upwards"], "tactic_count": 4}
{"name": "MeasureTheory.setIntegral_eq_integral_of_forall_compl_eq_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.setIntegral_neg_eq_setIntegral_nonpos", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": true, "tactics": ["have", "rw", "have", "symm", "refine", "filter_upwards"], "tactic_count": 6}
{"name": "MeasureTheory.integral_norm_eq_pos_sub_neg", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.setIntegral_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.integral_indicator_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.integral_indicator_one", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.setIntegral_indicatorConstLp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integral_indicatorConstLp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.setIntegral_map", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": false, "tactics": ["rw", "integral_map", "exact"], "tactic_count": 3}
{"name": "MeasurableEmbedding.setIntegral_map", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Topology.IsClosedEmbedding.setIntegral_map", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MeasurePreserving.setIntegral_preimage_emb", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MeasurePreserving.setIntegral_image_emb", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.setIntegral_map_equiv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.norm_setIntegral_le_of_norm_le_const_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": true, "tactics": ["rw", "haveI", "simpa"], "tactic_count": 3}
{"name": "MeasureTheory.norm_setIntegral_le_of_norm_le_const_ae'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": true, "tactics": ["by_cases", "apply", "have", "filter_upwards", "rw", "exact", "have", "filter_upwards", "rwa", "rw", "have", "apply", "contrapose", "simp", "rcases", "have", "simp", "positivity"], "tactic_count": 18}
{"name": "MeasureTheory.norm_setIntegral_le_of_norm_le_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.norm_integral_sub_setIntegral_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": false, "tactics": ["have", "rw", "have", "integral_mono_ae", "have", "rw", "exact"], "tactic_count": 7}
{"name": "MeasureTheory.setIntegral_eq_zero_iff_of_nonneg_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.setIntegral_pos_iff_support_of_nonneg_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.setIntegral_gt_gt", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": false, "tactics": ["have", "refine", "refine", "simp", "exact", "rw", "setIntegral_pos_iff_support_of_nonneg_ae]", "rw", "rwa", "exact", "rw", "exact", "exact", "exact"], "tactic_count": 14}
{"name": "MeasureTheory.setIntegral_trim", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "MeasureTheory.integral_Icc_eq_integral_Ioc'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integral_Icc_eq_integral_Ico'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integral_Ioc_eq_integral_Ioo'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integral_Ico_eq_integral_Ioo'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integral_Icc_eq_integral_Ioo'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integral_Iic_eq_integral_Iio'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integral_Ici_eq_integral_Ioi'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integral_Icc_eq_integral_Ioc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integral_Icc_eq_integral_Ico", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integral_Ioc_eq_integral_Ioo", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integral_Ico_eq_integral_Ioo", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integral_Icc_eq_integral_Ioo", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.integral_Iic_eq_integral_Iio", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integral_Ici_eq_integral_Ioi", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.setIntegral_mono_set", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.setIntegral_le_integral", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.setIntegral_mono_ae_restrict", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "simp"], "tactic_count": 3}
{"name": "MeasureTheory.setIntegral_mono_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.setIntegral_mono_on", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.setIntegral_mono_on_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": true, "tactics": ["refine"], "tactic_count": 1}
{"name": "MeasureTheory.setIntegral_mono_on_ae₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": true, "tactics": ["rw", "refine", "rwa", "rwa", "exact", "filter_upwards", "rwa"], "tactic_count": 7}
{"name": "MeasureTheory.setIntegral_mono_on₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.setIntegral_mono", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.setIntegral_ge_of_const_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.setIntegral_ge_of_const_le_real", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.setIntegral_nonneg_of_ae_restrict", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.setIntegral_nonneg_of_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.setIntegral_nonneg", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.setIntegral_nonneg_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.setIntegral_le_nonneg", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": true, "tactics": ["rw", "exact", "integral_mono"], "tactic_count": 3}
{"name": "MeasureTheory.setIntegral_nonpos_of_ae_restrict", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.setIntegral_nonpos_of_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.setIntegral_nonpos_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.setIntegral_nonpos", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.setIntegral_nonpos_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": true, "tactics": ["rw", "exact", "integral_mono"], "tactic_count": 3}
{"name": "MeasureTheory.Integrable.measure_le_integral", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": true, "tactics": ["rw", "apply", "exact", "intro", "simpa"], "tactic_count": 5}
{"name": "MeasureTheory.integral_le_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "let", "have", "have", "apply", "exact", "apply", "rw", "apply", "intro", "apply", "by_cases", "simpa", "apply", "simpa", "intro", "simpa"], "tactic_count": 18}
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{"name": "MeasureTheory.Lp_toLp_restrict_add", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": true, "tactics": ["ext1", "refine", "refine", "refine", "refine", "refine", "rw"], "tactic_count": 7}
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{"name": "MeasureTheory.LpToLpRestrictCLM", "kind": "definition", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.LpToLpRestrictCLM_coeFn", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.continuous_setIntegral", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": true, "tactics": ["haveI", "have", "ext1", "rw", "rw", "exact"], "tactic_count": 6}
{"name": "Continuous.integral_pos_of_hasCompactSupport_nonneg_nonzero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.setIntegral_support", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": true, "tactics": ["nth_rw", "rw", "exact"], "tactic_count": 3}
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{"name": "measure_le_lintegral_thickenedIndicatorAux", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": true, "tactics": ["convert_to", "rw", "simp", "apply", "apply"], "tactic_count": 5}
{"name": "measure_le_lintegral_thickenedIndicator", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": true, "tactics": ["convert", "dsimp", "simp"], "tactic_count": 3}
{"name": "MeasureTheory.Integrable.simpleFunc_mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": false, "tactics": ["refine", "simp", "have", "ext1", "by_cases", "simp", "simp", "rw", "exact"], "tactic_count": 9}
{"name": "MeasureTheory.Integrable.simpleFunc_mul'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "continuous_parametric_integral_of_continuous", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": true, "tactics": ["rw", "intro", "rcases", "rcases", "apply", "filter_upwards", "filter_upwards", "rw", "filter_upwards", "exact", "exact", "filter_upwards"], "tactic_count": 12}
{"name": "continuousOn_integral_bilinear_of_locally_integrable_of_compact_support", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.Set", "is_tactic_proof": false, "tactics": ["have", "refine", "simpa", "intro", "apply", "obtain", "simpa", "obtain", "hk.mem_uniformity_of_prod", "simp_rw", "have", "intro", "obtain", "have", "have", "exact", "rcases", "refine", "by_cases", "exact", "simp", "have", "apply", "borelize", "apply", "apply", "apply", "apply", "apply", "gcongr", "apply", "filter_upwards", "calc", "congr", "refine", "simp", "refine", "simp", "apply", "exact", "filter_upwards", "by_cases", "dsimp", "specialize", "calc", "simp", "positivity"], "tactic_count": 47}
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{"name": "_private.Mathlib.MeasureTheory.Integral.Bochner.VitaliCaratheodory.0.MeasureTheory.term_→ₛ_", "kind": "definition", "module": "Mathlib.MeasureTheory.Integral.Bochner.VitaliCaratheodory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasureTheory.SimpleFunc.exists_le_lowerSemicontinuous_lintegral_ge", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.VitaliCaratheodory", "is_tactic_proof": true, "tactics": ["induction", "let", "by_cases", "refine", "simp", "exact", "by_cases", "refine", "classical", "simp", "simp", "have", "classical", "simpa", "have", "have", "simpa", "obtain", "refine", "simp", "grw", "suffices", "classical", "simpa", "calc", "simp_rw", "rw", "simpa", "rcases", "rcases", "refine", "simp", "rw", "convert", "conv_lhs", "abel"], "tactic_count": 36}
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{"name": "MeasureTheory.exists_lt_lowerSemicontinuous_integral_lt", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.VitaliCaratheodory", "is_tactic_proof": true, "tactics": ["let", "have", "let", "have", "rcases", "let", "have", "rcases", "let", "have", "filter_upwards", "rw", "refine", "show", "rw", "convert", "simp", "show", "exact", "calc", "simp", "exact", "apply", "convert", "simp", "show", "filter_upwards", "simp", "show", "intro", "rw", "refine", "simp", "simp", "exact", "simp", "simp", "show", "apply", "exact", "continuous_coe_ennreal_ereal.comp_lowerSemicontinuous", "apply", "dsimp", "apply", "continuous_coe_ennreal_ereal.comp_upperSemicontinuous", "exact", "intro", "exact"], "tactic_count": 48}
{"name": "MeasureTheory.exists_upperSemicontinuous_lt_integral_gt", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Bochner.VitaliCaratheodory", "is_tactic_proof": false, "tactics": ["rcases", "refine", "exact", "exact", "convert", "simp", "simpa", "simp_rw", "rw", "simpa"], "tactic_count": 10}
{"name": "BoundedContinuousFunction.apply_le_nndist_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.BoundedContinuousFunction", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "BoundedContinuousFunction.lintegral_le_edist_mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.BoundedContinuousFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.measurable_coe_ennreal_comp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.BoundedContinuousFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.lintegral_lt_top_of_nnreal", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.BoundedContinuousFunction", "is_tactic_proof": true, "tactics": ["apply", "refine", "have", "rwa"], "tactic_count": 4}
{"name": "BoundedContinuousFunction.integrable_of_nnreal", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.BoundedContinuousFunction", "is_tactic_proof": true, "tactics": ["refine", "simp", "exact"], "tactic_count": 3}
{"name": "BoundedContinuousFunction.integral_eq_integral_nnrealPart_sub", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.BoundedContinuousFunction", "is_tactic_proof": true, "tactics": ["simp", "simp"], "tactic_count": 2}
{"name": "BoundedContinuousFunction.lintegral_of_real_lt_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.BoundedContinuousFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.toReal_lintegral_coe_eq_integral", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.BoundedContinuousFunction", "is_tactic_proof": false, "tactics": ["rw", "simp", "exact"], "tactic_count": 3}
{"name": "BoundedContinuousFunction.lintegral_nnnorm_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.BoundedContinuousFunction", "is_tactic_proof": true, "tactics": ["calc"], "tactic_count": 1}
{"name": "BoundedContinuousFunction.integrable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.BoundedContinuousFunction", "is_tactic_proof": true, "tactics": ["refine", "calc"], "tactic_count": 2}
{"name": "BoundedContinuousFunction.norm_integral_le_mul_norm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.BoundedContinuousFunction", "is_tactic_proof": false, "tactics": ["calc", "apply", "integral_mono", "exact"], "tactic_count": 4}
{"name": "BoundedContinuousFunction.norm_integral_le_norm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.BoundedContinuousFunction", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "BoundedContinuousFunction.isBounded_range_integral", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.BoundedContinuousFunction", "is_tactic_proof": true, "tactics": ["apply", "obtain", "rw", "apply"], "tactic_count": 4}
{"name": "BoundedContinuousFunction.integral_add_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.BoundedContinuousFunction", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "BoundedContinuousFunction.integral_const_sub", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.BoundedContinuousFunction", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "BoundedContinuousFunction.tendsto_integral_of_forall_limsup_integral_le_integral", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.BoundedContinuousFunction", "is_tactic_proof": true, "tactics": ["rcases", "simp", "have", "have", "have", "apply", "have", "simp_rw", "simp", "have", "rwa", "have", "simp_rw", "simp", "have", "rwa"], "tactic_count": 16}
{"name": "BoundedContinuousFunction.tendsto_integral_of_forall_integral_le_liminf_integral", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.BoundedContinuousFunction", "is_tactic_proof": true, "tactics": ["rcases", "simp", "have", "have", "have", "apply", "have", "simp_rw", "simp", "have", "rwa", "have", "simp_rw", "simp", "have", "rwa", "exact", "exact"], "tactic_count": 18}
{"name": "Real.circleAverage", "kind": "definition", "module": "Mathlib.MeasureTheory.Integral.CircleAverage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.circleAverage_def", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.CircleAverage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.circleAverage.integral_undef", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.CircleAverage", "is_tactic_proof": true, "tactics": ["simp_all"], "tactic_count": 1}
{"name": "Real.circleAverage_eq_intervalAverage", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.CircleAverage", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.circleAverage_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.CircleAverage", "is_tactic_proof": true, "tactics": ["rw", "simp", "smul_eq_mul,"], "tactic_count": 3}
{"name": "Real.circleAverage_map_add_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.CircleAverage", "is_tactic_proof": true, "tactics": ["unfold", "congr", "ext", "simp", "congr", "ring"], "tactic_count": 6}
{"name": "Real.circleAverage_eq_circleIntegral", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.CircleAverage", "is_tactic_proof": true, "tactics": ["calc", "circleAverage", "rw", "match_scalars", "field", "unfold", "congr", "simp", "field_simp"], "tactic_count": 9}
{"name": "Real.circleAverage_eq_integral_add", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.CircleAverage", "is_tactic_proof": true, "tactics": ["rw", "have", "have", "rw", "rw", "simp", "congr"], "tactic_count": 7}
{"name": "Real.circleAverage_neg_radius", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.CircleAverage", "is_tactic_proof": true, "tactics": ["unfold", "simp_rw"], "tactic_count": 2}
{"name": "Real.circleAverage_abs_radius", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.CircleAverage", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "rw"], "tactic_count": 3}
{"name": "Real.circleAverage_congr_codiscreteWithin", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.CircleAverage", "is_tactic_proof": true, "tactics": ["unfold", "congr", "apply", "apply", "apply"], "tactic_count": 5}
{"name": "Real.circleAverage_congr_sphere", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.CircleAverage", "is_tactic_proof": true, "tactics": ["unfold", "congr", "exact"], "tactic_count": 3}
{"name": "Real.circleAverage_eq_circleAverage_zero_one", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.CircleAverage", "is_tactic_proof": true, "tactics": ["unfold", "congr", "ring_nf", "simp"], "tactic_count": 4}
{"name": "Real.circleAverage_zero_one_congr_inv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.CircleAverage", "is_tactic_proof": true, "tactics": ["unfold", "congr", "calc", "rw", "have", "simpa"], "tactic_count": 6}
{"name": "Real.circleAverage_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.CircleAverage", "is_tactic_proof": true, "tactics": ["simp", "ring_nf", "simp"], "tactic_count": 3}
{"name": "Real.circleAverage_const_on_circle", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.CircleAverage", "is_tactic_proof": true, "tactics": ["rw", "conv", "left", "intro", "rw", "apply"], "tactic_count": 6}
{"name": "Real.circleAverage_mono", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.CircleAverage", "is_tactic_proof": true, "tactics": ["apply", "apply", "exact"], "tactic_count": 3}
{"name": "Real.circleAverage_mono_on_of_le_circle", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.CircleAverage", "is_tactic_proof": false, "tactics": ["rw", "mul_le_mul_iff_of_pos_left", "exact", "intervalIntegral.integral_mono_on_of_le_Ioo"], "tactic_count": 4}
{"name": "Real.abs_circleAverage_le_circleAverage_abs", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.CircleAverage", "is_tactic_proof": false, "tactics": ["rw", "mul_le_mul_iff_of_pos_left", "exact"], "tactic_count": 3}
{"name": "Real.circleAverage_nonneg_of_nonneg", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.CircleAverage", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "mul_le_mul_iff_of_pos_left", "apply", "intervalIntegral.integral_mono_on_of_le_Ioo", "rw"], "tactic_count": 6}
{"name": "ContinuousLinearMap.circleAverage_comp_comm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.CircleAverage", "is_tactic_proof": true, "tactics": ["unfold", "rw", "congr", "exact"], "tactic_count": 4}
{"name": "Real.circleAverage_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.CircleAverage", "is_tactic_proof": true, "tactics": ["unfold", "have", "rw", "simp"], "tactic_count": 4}
{"name": "Real.circleAverage_fun_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.CircleAverage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.circleAverage_add", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.CircleAverage", "is_tactic_proof": true, "tactics": ["rw", "congr", "apply"], "tactic_count": 3}
{"name": "Real.circleAverage_fun_add", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.CircleAverage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.circleAverage_sum", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.CircleAverage", "is_tactic_proof": true, "tactics": ["unfold", "simp"], "tactic_count": 2}
{"name": "Real.circleAverage_fun_sum", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.CircleAverage", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "Real.circleAverage_sub", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.CircleAverage", "is_tactic_proof": true, "tactics": ["rw", "congr", "apply"], "tactic_count": 3}
{"name": "Real.circleAverage_fun_sub", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.CircleAverage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "range_circleMap", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.CircleIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "image_circleMap_Ioc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.CircleIntegral", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "hasDerivAt_circleMap", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.CircleIntegral", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "differentiable_circleMap", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.CircleIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "analyticOnNhd_circleMap", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.CircleIntegral", "is_tactic_proof": true, "tactics": ["intro", "apply", "apply", "rw", "apply"], "tactic_count": 5}
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{"name": "continuous_circleMap_inv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.CircleIntegral", "is_tactic_proof": false, "tactics": ["have", "simp_rw", "exact", "exact"], "tactic_count": 4}
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{"name": "CircleIntegrable.finsum", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.CircleIntegral", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "exact", "rw", "apply"], "tactic_count": 5}
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{"name": "circleIntegrable_zero_radius", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.CircleIntegral", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CircleIntegrable.congr_codiscreteWithin", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.CircleIntegral", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "apply", "rw", "exact", "codiscreteWithin.mono"], "tactic_count": 6}
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{"name": "ContinuousOn.circleIntegrable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.CircleIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "circleIntegral.integral_radius_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.CircleIntegral", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "circleIntegral.integral_congr", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.CircleIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "circleIntegral.circleIntegral_congr_codiscreteWithin", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.CircleIntegral", "is_tactic_proof": true, "tactics": ["apply", "apply", "simp", "exact"], "tactic_count": 4}
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{"name": "circleIntegral.integral_undef", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.CircleIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "circleIntegral.norm_integral_le_of_norm_le_const'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.CircleIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "circleIntegral.integral_eq_zero_of_hasDerivWithinAt'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.CircleIntegral", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "refine", "exact", "exact"], "tactic_count": 5}
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{"name": "cauchyPowerSeries_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.CircleIntegral", "is_tactic_proof": false, "tactics": ["simp", "mul_smul,", "rw"], "tactic_count": 3}
{"name": "norm_cauchyPowerSeries_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.CircleIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_radius_cauchyPowerSeries", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.CircleIntegral", "is_tactic_proof": false, "tactics": ["refine", "refine", "rw", "rcases", "rw_mod_cast", "exact", "mul_nonneg", "rw", "have", "rw"], "tactic_count": 10}
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{"name": "hasSum_cauchyPowerSeries_integral", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.CircleIntegral", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "sum_cauchyPowerSeries_eq_integral", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.CircleIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasFPowerSeriesOn_cauchy_integral", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.CircleIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "circleIntegral.integral_sub_inv_of_mem_ball", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.CircleIntegral", "is_tactic_proof": true, "tactics": ["have", "suffices", "have", "refine", "simpa", "have", "refine", "have", "refine", "simp", "rw", "intro", "rw"], "tactic_count": 13}
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{"name": "Complex.circleTransformDeriv", "kind": "definition", "module": "Mathlib.MeasureTheory.Integral.CircleTransform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.circleTransformDeriv_periodic", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.CircleTransform", "is_tactic_proof": true, "tactics": ["have", "simp_rw", "intro", "simp_rw", "congr", "simp"], "tactic_count": 6}
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{"name": "Complex.continuous_circleTransformDeriv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.CircleTransform", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Complex.circleTransformBoundingFunction", "kind": "definition", "module": "Mathlib.MeasureTheory.Integral.CircleTransform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.continuousOn_prod_circle_transform_function", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.CircleTransform", "is_tactic_proof": true, "tactics": ["simp_rw", "apply_rules", "exact", "rintro", "have", "exact"], "tactic_count": 6}
{"name": "Complex.continuousOn_norm_circleTransformBoundingFunction", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.CircleTransform", "is_tactic_proof": false, "tactics": ["have", "apply_rules", "simp", "apply_rules", "simpa", "exact"], "tactic_count": 6}
{"name": "Complex.norm_circleTransformBoundingFunction_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.CircleTransform", "is_tactic_proof": true, "tactics": ["have", "have", "apply_rules", "have", "have", "simpa"], "tactic_count": 6}
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{"name": "CompactlySupportedContinuousMap.integrable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.CompactlySupported", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompactlySupportedContinuousMap.integralPositiveLinearMap", "kind": "definition", "module": "Mathlib.MeasureTheory.Integral.CompactlySupported", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompactlySupportedContinuousMap.integralLinearMap", "kind": "definition", "module": "Mathlib.MeasureTheory.Integral.CompactlySupported", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "definition._@.Mathlib.MeasureTheory.Integral.CurveIntegral.Basic.4195796962._hygCtx._hyg.2", "kind": "definition", "module": "Mathlib.MeasureTheory.Integral.CurveIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "curveIntegral_of_not_completeSpace", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.CurveIntegral.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "Antitone.tendsto_setIntegral", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.DominatedConvergence", "is_tactic_proof": true, "tactics": ["let", "have", "funext", "rw", "rw", "refine", "intro", "rw", "exact", "rw", "exact", "simp_rw", "refine", "grw", "filter_upwards"], "tactic_count": 15}
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{"name": "intervalIntegral.hasSum_intervalIntegral_of_summable_norm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.DominatedConvergence", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "apply", "hasSum_integral_of_dominated_convergence", "intro", "apply", "exact", "exact", "exact", "refine", "let", "have", "simpa"], "tactic_count": 13}
{"name": "intervalIntegral.tsum_intervalIntegral_eq_of_summable_norm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.DominatedConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.continuousWithinAt_of_dominated_interval", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.DominatedConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.continuousAt_of_dominated_interval", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.DominatedConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "intervalIntegral.continuousOn_primitive_interval_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.DominatedConvergence", "is_tactic_proof": true, "tactics": ["rw", "simp", "exact"], "tactic_count": 3}
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{"name": "MeasureTheory.Integrable.continuous_primitive", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.DominatedConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "intervalIntegral.continuous_parametric_intervalIntegral_of_continuous", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.DominatedConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.continuous_parametric_intervalIntegral_of_continuous'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.DominatedConvergence", "is_tactic_proof": true, "tactics": ["fun_prop"], "tactic_count": 1}
{"name": "exp_neg_integrableOn_Ioi", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.ExpDecay", "is_tactic_proof": false, "tactics": ["have", "refine", "exact", "refine", "simpa"], "tactic_count": 5}
{"name": "integrable_of_isBigO_exp_neg", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.ExpDecay", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.MeasureTheory.Integral.FinMeasAdditive.0.MeasureTheory.term_→ₛ_", "kind": "definition", "module": "Mathlib.MeasureTheory.Integral.FinMeasAdditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasureTheory.FinMeasAdditive", "kind": "definition", "module": "Mathlib.MeasureTheory.Integral.FinMeasAdditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasureTheory.FinMeasAdditive.of_eq_top_imp_eq_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.FinMeasAdditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.FinMeasAdditive.of_smul_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.FinMeasAdditive", "is_tactic_proof": true, "tactics": ["refine", "rw", "simp", "exact"], "tactic_count": 4}
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{"name": "MeasureTheory.DominatedFinMeasAdditive.add_measure_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.FinMeasAdditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.DominatedFinMeasAdditive.add_measure_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.FinMeasAdditive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "integral_rpow_mul_exp_neg_rpow", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Gamma", "is_tactic_proof": true, "tactics": ["calc", "rw", "refine", "rw", "simp_rw", "refine", "rw", "ring_nf", "rw", "simp_rw"], "tactic_count": 10}
{"name": "integral_rpow_mul_exp_neg_mul_rpow", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Gamma", "is_tactic_proof": true, "tactics": ["calc", "refine", "rw", "mul_assoc,", "all_goals", "rw", "all_goals", "rw", "rpow_add]", "congr", "all_goals"], "tactic_count": 11}
{"name": "integral_exp_neg_rpow", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Gamma", "is_tactic_proof": true, "tactics": ["convert", "simp_rw", "rw"], "tactic_count": 3}
{"name": "integral_exp_neg_mul_rpow", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Gamma", "is_tactic_proof": true, "tactics": ["convert", "simp_rw", "rw"], "tactic_count": 3}
{"name": "Complex.integral_rpow_mul_exp_neg_rpow", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Gamma", "is_tactic_proof": true, "tactics": ["calc", "rw", "simp_rw", "rw", "simp_rw", "congr", "simp_rw", "volume_real_Ioo_of_le", "mul_one,", "congr", "refine", "rw", "rw", "ring", "rw", "ring"], "tactic_count": 16}
{"name": "Complex.integral_rpow_mul_exp_neg_mul_rpow", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Gamma", "is_tactic_proof": true, "tactics": ["calc", "rw", "simp_rw", "rw", "simp_rw", "congr", "simp_rw", "volume_real_Ioo_of_le", "mul_one,", "congr", "refine", "rw", "rw", "ring", "rw", "ring"], "tactic_count": 16}
{"name": "Complex.integral_exp_neg_rpow", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Gamma", "is_tactic_proof": true, "tactics": ["convert", "simp_rw", "rw", "ring"], "tactic_count": 4}
{"name": "Complex.integral_exp_neg_mul_rpow", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Gamma", "is_tactic_proof": true, "tactics": ["convert", "simp_rw", "rw", "ring"], "tactic_count": 4}
{"name": "MeasureTheory.tendsto_measure_of_ae_tendsto_indicator", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Indicator", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "tendsto_lintegral_filter_of_dominated_convergence", "exact", "filter_upwards", "exact", "rwa", "simpa"], "tactic_count": 8}
{"name": "MeasureTheory.tendsto_measure_of_ae_tendsto_indicator_of_isFiniteMeasure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.tendsto_measure_of_tendsto_indicator", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Indicator", "is_tactic_proof": true, "tactics": ["rcases", "exact", "apply", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.tendsto_measure_of_tendsto_indicator_of_isFiniteMeasure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Indicator", "is_tactic_proof": true, "tactics": ["rcases", "exact", "apply", "exact"], "tactic_count": 4}
{"name": "stronglyMeasurableAt_bot", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StronglyMeasurableAtFilter.eventually", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StronglyMeasurableAtFilter.filter_mono", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEStronglyMeasurable.stronglyMeasurableAtFilter", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEStronglyMeasurable.stronglyMeasurableAtFilter_of_mem", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.StronglyMeasurable.stronglyMeasurableAtFilter", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.HasFiniteIntegral.restrict_of_bounded", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IntegrableOn.integrable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integrableOn_empty", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.integrableOn_univ", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.integrableOn_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IntegrableOn.of_measure_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.IntegrableOn.mono", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IntegrableOn.mono_set", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IntegrableOn.mono_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IntegrableOn.mono_set_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IntegrableOn.congr_set_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integrableOn_congr_set_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IntegrableOn.congr_fun_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integrableOn_congr_fun_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IntegrableOn.congr_fun", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integrableOn_congr_fun", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Integrable.integrableOn", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IntegrableOn.of_subsingleton_codomain", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Integrable.of_bound", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IntegrableOn.of_bound", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IntegrableOn.restrict", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": true, "tactics": ["dsimp", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.IntegrableOn.inter_of_restrict", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "MeasureTheory.Integrable.piecewise", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.IntegrableOn.left_of_union", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IntegrableOn.right_of_union", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IntegrableOn.union", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integrableOn_union", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integrableOn_finite_biUnion", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": true, "tactics": ["induction", "empty", "insert"], "tactic_count": 3}
{"name": "MeasureTheory.integrableOn_finset_iUnion", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integrableOn_finite_iUnion", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": true, "tactics": ["cases", "simpa", "integrableOn_finset_iUnion"], "tactic_count": 3}
{"name": "MeasureTheory.IntegrableOn.finset", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.IntegrableOn.of_finite", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.IntegrableOn.of_subsingleton", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IntegrableOn.add_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": true, "tactics": ["delta"], "tactic_count": 1}
{"name": "MeasureTheory.integrableOn_add_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEmbedding.integrableOn_map_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MeasurableEmbedding.integrableOn_iff_comap", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MeasurableEmbedding.integrableOn_range_iff_comap", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.integrableOn_iff_comap_subtypeVal", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.integrableOn_map_equiv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.MeasurePreserving.integrableOn_comp_preimage", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MeasurePreserving.integrableOn_image", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integrable_indicator_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": true, "tactics": ["simp_rw", "lintegral_indicator"], "tactic_count": 2}
{"name": "MeasureTheory.IntegrableOn.integrable_indicator", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IntegrableOn.integrable_indicator₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Integrable.indicator", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Integrable.indicator₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IntegrableOn.indicator", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integrable_indicatorConstLp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": false, "tactics": ["rw", "isFiniteMeasure_restrict]", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.IntegrableOn.restrict_toMeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": true, "tactics": ["rcases", "let", "have", "intro", "rw", "exact", "apply", "intro", "obtain", "exact", "mem_iUnion.2"], "tactic_count": 11}
{"name": "MeasureTheory.IntegrableOn.of_ae_diff_eq_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": true, "tactics": ["let", "have", "let", "have", "rw", "exact", "intro", "have", "apply", "filter_upwards", "ae_restrict_mem₀", "by_cases", "by_contra", "exact", "exact", "apply", "rw", "exact"], "tactic_count": 18}
{"name": "MeasureTheory.IntegrableOn.of_forall_diff_eq_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IntegrableOn.integrable_of_ae_notMem_eq_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": true, "tactics": ["rw", "apply", "filter_upwards"], "tactic_count": 3}
{"name": "MeasureTheory.IntegrableOn.integrable_of_forall_notMem_eq_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IntegrableOn.of_inter_support", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.integrableOn_iff_integrable_of_support_subset", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": true, "tactics": ["refine", "refine", "contrapose", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.integrableOn_Lp_of_measure_ne_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": true, "tactics": ["refine", "have", "simpa", "haveI", "exact"], "tactic_count": 5}
{"name": "MeasureTheory.Integrable.lintegral_lt_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IntegrableOn.setLIntegral_lt_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEmbedding.integrableAtFilter_map_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": true, "tactics": ["simp_rw", "constructor", "exact", "exact"], "tactic_count": 4}
{"name": "MeasurableEmbedding.integrableAtFilter_iff_comap", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": true, "tactics": ["simp_rw", "constructor", "exact", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.Integrable.integrableAtFilter", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IntegrableAtFilter.eventually", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integrableAtFilter_atBot_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.integrableAtFilter_atTop_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IntegrableAtFilter.add", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "refine", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.IntegrableAtFilter.neg", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.IntegrableAtFilter.sub", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.IntegrableAtFilter.smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.IntegrableAtFilter.enorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IntegrableAtFilter.norm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IntegrableAtFilter.filter_mono", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IntegrableAtFilter.inf_of_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IntegrableAtFilter.inf_of_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IntegrableAtFilter.inf_ae_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": true, "tactics": ["refine", "rintro", "refine", "filter_upwards"], "tactic_count": 4}
{"name": "MeasureTheory.integrableAtFilter_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.IntegrableAtFilter.sup_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": true, "tactics": ["constructor", "exact", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.FiniteAtFilter.integrableAtFilter", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": false, "tactics": ["obtain", "hf.imp", "rcases", "refine", "rw", "exact"], "tactic_count": 6}
{"name": "MeasureTheory.Measure.FiniteAtFilter.integrableAtFilter_of_tendsto_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.FiniteAtFilter.integrableAtFilter_of_tendsto", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.integrableOn_of_bounded", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integrable_add_of_disjoint", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": true, "tactics": ["refine", "rw", "rw"], "tactic_count": 3}
{"name": "MeasureTheory.IntegrableAtFilter.eq_zero_of_tendsto", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": true, "tactics": ["by_contra", "obtain", "rcases", "let", "have", "have", "have", "lt_of_le_of_lt", "have", "exact"], "tactic_count": 10}
{"name": "ContinuousOn.aemeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegrableOn", "is_tactic_proof": true, "tactics": ["classical", "nontriviality", "have", "refine", "apply", "intro", "obtain", "rw", "exact"], "tactic_count": 9}
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{"name": "MeasureTheory.tendsto_zero_of_hasDerivAt_of_integrableOn_Iic", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegralEqImproper", "is_tactic_proof": true, "tactics": ["let", "have", "have", "have", "have", "apply", "have", "have", "apply", "intro", "rcases", "apply", "rw", "exact", "rwa", "exact"], "tactic_count": 16}
{"name": "MeasureTheory.integral_Iic_of_hasDerivAt_of_tendsto", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegralEqImproper", "is_tactic_proof": false, "tactics": ["have", "intro", "rcases", "exact", "exact", "refine", "apply", "filter_upwards", "symm", "apply", "intervalIntegral.integral_eq_sub_of_hasDerivAt_of_le", "rw", "exact"], "tactic_count": 13}
{"name": "MeasureTheory.integral_Iic_of_hasDerivAt_of_tendsto'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegralEqImproper", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "HasCompactSupport.integral_Iic_deriv_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegralEqImproper", "is_tactic_proof": true, "tactics": ["have", "rw", "refine", "rw", "exact"], "tactic_count": 5}
{"name": "HasCompactSupport.enorm_le_lintegral_Ici_deriv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegralEqImproper", "is_tactic_proof": true, "tactics": ["let", "let", "have", "have", "have", "rw", "exact", "convert", "simp", "rw", "simp", "simp"], "tactic_count": 12}
{"name": "MeasureTheory.integral_of_hasDerivAt_of_tendsto", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegralEqImproper", "is_tactic_proof": false, "tactics": ["rw", "setIntegral_union", "integral_Iic_of_hasDerivAt_of_tendsto", "integral_Ioi_of_hasDerivAt_of_tendsto", "abel"], "tactic_count": 5}
{"name": "MeasureTheory.integral_eq_zero_of_hasDerivAt_of_integrable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegralEqImproper", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "have", "tendsto_zero_of_hasDerivAt_of_integrableOn_Iic", "have", "tendsto_zero_of_hasDerivAt_of_integrableOn_Ioi", "simpa"], "tactic_count": 7}
{"name": "MeasureTheory.integral_comp_smul_deriv_Ioi", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegralEqImproper", "is_tactic_proof": false, "tactics": ["have", "have", "rw", "exact", "have", "refine", "intervalIntegral.integral_comp_smul_deriv", "assumption", "rw", "have", "have", "hft", "have", "exact"], "tactic_count": 14}
{"name": "MeasureTheory.integral_comp_mul_deriv_Ioi", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegralEqImproper", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "MeasureTheory.integral_comp_rpow_Ioi", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegralEqImproper", "is_tactic_proof": true, "tactics": ["let", "have", "have", "rcases", "apply", "intro", "rw", "rpow_neg", "exact", "exact", "have", "ext1", "rintro", "intro", "rw", "have", "rw", "refine", "intro", "rw"], "tactic_count": 20}
{"name": "MeasureTheory.integral_comp_rpow_Ioi_of_pos", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegralEqImproper", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "MeasureTheory.integral_comp_mul_left_Ioi", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegralEqImproper", "is_tactic_proof": true, "tactics": ["have", "rw", "congr", "ext1", "rw"], "tactic_count": 5}
{"name": "MeasureTheory.integral_comp_mul_right_Ioi", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegralEqImproper", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.integrableOn_Ioi_comp_rpow_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegralEqImproper", "is_tactic_proof": true, "tactics": ["let", "have", "have", "rcases", "apply", "intro", "rw", "rpow_neg", "exact", "exact", "have", "ext1", "rintro", "intro", "rw", "have", "rw", "rw", "refine", "simp_rw"], "tactic_count": 20}
{"name": "MeasureTheory.integrableOn_Ioi_comp_rpow_iff'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegralEqImproper", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.integrableOn_Ioi_comp_mul_left_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegralEqImproper", "is_tactic_proof": true, "tactics": ["rw", "rw", "convert", "ext1", "rw"], "tactic_count": 5}
{"name": "MeasureTheory.integrableOn_Ioi_comp_mul_right_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegralEqImproper", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.integral_bilinear_hasDerivAt_eq_sub", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegralEqImproper", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integral_bilinear_hasDerivAt_right_eq_sub", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegralEqImproper", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.integral_bilinear_hasDerivAt_right_eq_neg_left_of_integrable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegralEqImproper", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "have", "tendsto_zero_of_hasDerivAt_of_integrableOn_Iic", "have", "tendsto_zero_of_hasDerivAt_of_integrableOn_Ioi", "simp"], "tactic_count": 7}
{"name": "MeasureTheory.integral_deriv_mul_eq_sub", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegralEqImproper", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integral_mul_deriv_eq_deriv_mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegralEqImproper", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integral_mul_deriv_eq_deriv_mul_of_integrable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegralEqImproper", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integral_Ioi_deriv_mul_eq_sub", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegralEqImproper", "is_tactic_proof": true, "tactics": ["rw", "let", "have", "intro", "apply", "filter_upwards", "exact", "have", "apply", "filter_upwards", "exact", "simpa"], "tactic_count": 12}
{"name": "MeasureTheory.integral_Ioi_mul_deriv_eq_deriv_mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegralEqImproper", "is_tactic_proof": true, "tactics": ["rw", "rw", "simpa"], "tactic_count": 3}
{"name": "MeasureTheory.integral_Iic_deriv_mul_eq_sub", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegralEqImproper", "is_tactic_proof": true, "tactics": ["rw", "let", "have", "intro", "apply", "filter_upwards", "exact", "have", "apply", "filter_upwards", "exact", "simpa"], "tactic_count": 12}
{"name": "MeasureTheory.integral_Iic_mul_deriv_eq_deriv_mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntegralEqImproper", "is_tactic_proof": true, "tactics": ["rw", "rw", "simpa"], "tactic_count": 3}
{"name": "term⨍_In_.._,_", "kind": "definition", "module": "Mathlib.MeasureTheory.Integral.IntervalAverage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_MeasureTheory_Integral_IntervalAverage___macroRules_term⨍_In_.._,__1", "kind": "definition", "module": "Mathlib.MeasureTheory.Integral.IntervalAverage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_MeasureTheory_Integral_IntervalAverage___delab_app_term⨍_In_.._,__1", "kind": "definition", "module": "Mathlib.MeasureTheory.Integral.IntervalAverage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "interval_average_symm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalAverage", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "interval_average_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalAverage", "is_tactic_proof": true, "tactics": ["rcases", "rw", "rw", "inv_neg,"], "tactic_count": 4}
{"name": "interval_average_eq_div", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalAverage", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "intervalAverage_congr_codiscreteWithin", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalAverage", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "exists_eq_interval_average_of_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalAverage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_eq_interval_average_of_noAtoms", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalAverage", "is_tactic_proof": false, "tactics": ["have", "hf.integrableOn_of_subset_isCompact", "have", "let", "have", "have", "have", "have", "rwa", "obtain", "exists_eq_setAverage", "exact"], "tactic_count": 12}
{"name": "exists_eq_interval_average", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalAverage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_dist_slope_lt_pairwiseDisjoint_hasSum", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.AbsolutelyContinuousFun", "is_tactic_proof": true, "tactics": ["rcases", "exact", "let", "let", "obtain", "apply", "grind", "intro", "simp", "rw", "linarith", "simp", "simp", "intro", "apply", "have", "obtain", "have", "rw", "exact", "have", "filter_upwards", "ε", "refine", "exact", "simp", "refine", "have", "have", "hu₃", "replace", "rw", "filter_upwards", "grind", "have", "convert", "simp", "rw", "simp_rw", "apply_fun", "rw", "convert", "grind"], "tactic_count": 43}
{"name": "AbsolutelyContinuousOnInterval.dist_le_of_pairwiseDisjoint_hasSum", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.AbsolutelyContinuousFun", "is_tactic_proof": true, "tactics": ["let", "replace", "replace", "let", "have", "have", "have", "have", "have", "intro", "grind", "have", "replace", "refine", "simp", "convert", "simp", "rw", "convert", "exact", "abel", "rw", "simp_rw", "have", "simp", "have", "dist", "rw", "add_right_comm,", "grw", "simp", "exact"], "tactic_count": 32}
{"name": "AbsolutelyContinuousOnInterval.const_of_ae_hasDerivAt_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.AbsolutelyContinuousFun", "is_tactic_proof": true, "tactics": ["wlog", "exact", "suffices", "rw", "intro", "suffices", "contrapose", "exact", "intro", "rw", "have", "rcases", "simp", "replace", "have", "have", "let", "have", "have", "have", "have", "have", "grw", "simp", "nth_rw", "simp", "field_simp", "rw", "grw", "rw", "have", "grw", "field_simp", "grind", "have", "have", "have", "hu₄", "linarith"], "tactic_count": 39}
{"name": "AbsolutelyContinuousOnInterval.integral_deriv_eq_sub", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.AbsolutelyContinuousFun", "is_tactic_proof": false, "tactics": ["have", "hf.intervalIntegrable_deriv.absolutelyContinuousOnInterval_intervalIntegral", "let", "have", "have", "filter_upwards", "convert", "abel", "obtain", "have", "have", "have", "grind"], "tactic_count": 13}
{"name": "AbsolutelyContinuousOnInterval.integral_deriv_mul_eq_sub", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.AbsolutelyContinuousFun", "is_tactic_proof": true, "tactics": ["rw", "apply", "filter_upwards", "have", "have", "exact"], "tactic_count": 6}
{"name": "AbsolutelyContinuousOnInterval.integral_mul_deriv_eq_deriv_mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.AbsolutelyContinuousFun", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "exact", "exact"], "tactic_count": 4}
{"name": "IntervalIntegrable", "kind": "definition", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegrable_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IntervalIntegrable.def'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegrable_congr_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IntervalIntegrable.congr_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "intervalIntegrable_congr", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntervalIntegrable.congr_codiscreteWithin", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegrable_congr_codiscreteWithin", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegrable_iff_integrableOn_Ioc_of_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Integrable.intervalIntegrable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IntegrableOn.intervalIntegrable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntervalIntegrable.zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntervalIntegrable.symm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntervalIntegrable.symm_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntervalIntegrable.refl", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["constructor"], "tactic_count": 1}
{"name": "IntervalIntegrable.trans", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntervalIntegrable.trans_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IntervalIntegrable.trans_iterate_Ico", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["revert", "refine", "simp", "intro", "exact"], "tactic_count": 5}
{"name": "IntervalIntegrable.trans_iterate", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntervalIntegrable.neg", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntervalIntegrable.enorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntervalIntegrable.norm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntervalIntegrable.intervalIntegrable_enorm_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "IntervalIntegrable.intervalIntegrable_norm_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "IntervalIntegrable.abs", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntervalIntegrable.mono", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntervalIntegrable.mono_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntervalIntegrable.mono_set", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntervalIntegrable.mono_set_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntervalIntegrable.mono_set'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntervalIntegrable.mono_fun_enorm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntervalIntegrable.mono_fun", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntervalIntegrable.mono_fun_enorm'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntervalIntegrable.mono_fun'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntervalIntegrable.aestronglyMeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntervalIntegrable.aestronglyMeasurable'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntervalIntegrable.aestronglyMeasurable_restrict_uIoc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "rw"], "tactic_count": 3}
{"name": "IntervalIntegrable.smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntervalIntegrable.add", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntervalIntegrable.sub", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntervalIntegrable.sum", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntervalIntegrable.finsum", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "rw", "apply", "tauto"], "tactic_count": 5}
{"name": "IntervalIntegrable.mul_continuousOn", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IntervalIntegrable.continuousOn_mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IntervalIntegrable.const_mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntervalIntegrable.mul_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntervalIntegrable.smul_continuousOn", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IntervalIntegrable.continuousOn_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IntervalIntegrable.div_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ContinuousOn.intervalIntegrable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.intervalIntegrable_of_Icc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.intervalIntegrable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonotoneOn.intervalIntegrable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "AntitoneOn.intervalIntegrable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.intervalIntegrable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.intervalIntegrable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.eventually_intervalIntegrable_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.eventually_intervalIntegrable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral", "kind": "definition", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "term∫_In_.._,_∂_", "kind": "definition", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_MeasureTheory_Integral_IntervalIntegral_Basic___macroRules_term∫_In_.._,_∂__1", "kind": "definition", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_MeasureTheory_Integral_IntervalIntegral_Basic___delab_app_term∫_In_.._,_∂__1", "kind": "definition", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "term∫_In_.._,_", "kind": "definition", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_MeasureTheory_Integral_IntervalIntegral_Basic___macroRules_term∫_In_.._,__1", "kind": "definition", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_MeasureTheory_Integral_IntervalIntegral_Basic___delab_app_term∫_In_.._,__1", "kind": "definition", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.integral_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "intervalIntegral.integral_of_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "intervalIntegral.integral_same", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.integral_symm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "intervalIntegral.integral_of_ge", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "intervalIntegral.intervalIntegral_eq_integral_uIoc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["split_ifs", "simp", "simp"], "tactic_count": 3}
{"name": "intervalIntegral.norm_intervalIntegral_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "split_ifs"], "tactic_count": 2}
{"name": "intervalIntegral.abs_intervalIntegral_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.integral_cases", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "intervalIntegral.integral_undef", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["rw", "rw"], "tactic_count": 2}
{"name": "intervalIntegral.intervalIntegrable_of_integral_ne_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.integral_non_aestronglyMeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "intervalIntegral.integral_non_aestronglyMeasurable_of_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.norm_integral_min_max", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "intervalIntegral.norm_integral_eq_norm_integral_uIoc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "intervalIntegral.abs_integral_eq_abs_integral_uIoc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.norm_integral_le_integral_norm_uIoc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.norm_integral_le_abs_integral_norm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "intervalIntegral.norm_integral_le_integral_norm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.norm_integral_le_abs_of_norm_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "intervalIntegral.norm_integral_le_of_norm_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "intervalIntegral.norm_integral_le_of_norm_le_const_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["rw", "convert", "rw", "simp"], "tactic_count": 4}
{"name": "intervalIntegral.norm_integral_le_of_norm_le_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.integral_add", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "intervalIntegral.integral_finset_sum", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "intervalIntegral.integral_neg", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "intervalIntegral.integral_sub", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "intervalIntegral.integral_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IntervalIntegrable.integral_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "intervalIntegral.integral_smul_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "intervalIntegral.integral_const_mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.integral_mul_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "intervalIntegral.integral_div", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "intervalIntegral.integral_const'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "intervalIntegral.integral_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["simp", "measureReal_def]"], "tactic_count": 2}
{"name": "intervalIntegral.integral_smul_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RCLike.intervalIntegral_ofReal", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "intervalIntegral.integral_ofReal", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.intervalIntegral_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "ContinuousLinearMap.intervalIntegral_comp_comm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "intervalIntegral.integral_comp_mul_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": ["have", "conv_rhs", "simp_rw", "rcases", "simp", "simp"], "tactic_count": 6}
{"name": "intervalIntegral.smul_integral_comp_mul_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "intervalIntegral.integral_comp_mul_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "intervalIntegral.smul_integral_comp_mul_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "intervalIntegral.integral_comp_div", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "intervalIntegral.inv_smul_integral_comp_div", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "intervalIntegral.integral_comp_add_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.integral_comp_add_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "intervalIntegral.integral_comp_mul_add", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "intervalIntegral.smul_integral_comp_mul_add", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "intervalIntegral.integral_comp_add_mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "intervalIntegral.smul_integral_comp_add_mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "intervalIntegral.integral_comp_div_add", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "intervalIntegral.inv_smul_integral_comp_div_add", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "intervalIntegral.integral_comp_add_div", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "intervalIntegral.inv_smul_integral_comp_add_div", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "intervalIntegral.integral_comp_mul_sub", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "intervalIntegral.smul_integral_comp_mul_sub", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "intervalIntegral.integral_comp_sub_mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["simp", "rw", "simp"], "tactic_count": 3}
{"name": "intervalIntegral.smul_integral_comp_sub_mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "intervalIntegral.integral_comp_div_sub", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "intervalIntegral.inv_smul_integral_comp_div_sub", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "intervalIntegral.integral_comp_sub_div", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "intervalIntegral.inv_smul_integral_comp_sub_div", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "intervalIntegral.integral_comp_sub_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "intervalIntegral.integral_comp_sub_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "intervalIntegral.integral_comp_neg", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "intervalIntegral.integral_congr", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simpa", "setIntegral_congr_fun"], "tactic_count": 3}
{"name": "intervalIntegral.integral_add_adjacent_intervals_cancel", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["have", "simp", "iterate", "suffices", "rw", "all_goals"], "tactic_count": 6}
{"name": "intervalIntegral.integral_add_adjacent_intervals", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "intervalIntegral.sum_integral_adjacent_intervals_Ico", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["revert", "refine", "simp", "intro", "rw", "refine", "exact", "apply", "simp", "intro", "exact"], "tactic_count": 11}
{"name": "intervalIntegral.sum_integral_adjacent_intervals", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "intervalIntegral.integral_interval_sub_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.integral_interval_add_interval_comm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["rw", "integral_add_adjacent_intervals"], "tactic_count": 2}
{"name": "intervalIntegral.integral_interval_sub_interval_comm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "intervalIntegral.integral_interval_sub_interval_comm'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["rw", "sub_eq_neg_add]"], "tactic_count": 2}
{"name": "intervalIntegral.integral_Iic_sub_Iic", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["wlog", "rw", "rw", "exacts"], "tactic_count": 4}
{"name": "intervalIntegral.integral_interval_add_Ioi", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["wlog", "rw", "rw", "setIntegral_union"], "tactic_count": 4}
{"name": "intervalIntegral.integral_interval_add_Ioi'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["rw", "by_cases", "exact", "exact"], "tactic_count": 4}
{"name": "intervalIntegral.integral_Iic_add_Ioi", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "intervalIntegral.integral_Iio_add_Ici", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "intervalIntegral.integral_const_of_cdf", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["simp", "refine"], "tactic_count": 2}
{"name": "intervalIntegral.integral_eq_integral_of_support_subset", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["rcases", "rw", "rw", "simp"], "tactic_count": 4}
{"name": "intervalIntegral.integral_congr_ae'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "intervalIntegral.integral_congr_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.integral_congr_ae_restrict", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.integral_congr_codiscreteWithin", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.integral_zero_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.integral_indicator", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["have", "rw", "exact", "all_goals"], "tactic_count": 4}
{"name": "intervalIntegral.integral_eq_zero_iff_of_le_of_nonneg_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "intervalIntegral.integral_eq_zero_iff_of_nonneg_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["rcases", "exact", "rw"], "tactic_count": 3}
{"name": "intervalIntegral.integral_pos_iff_support_of_nonneg_ae'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["rcases", "rw", "simp", "suffices", "rw", "rw", "exact"], "tactic_count": 7}
{"name": "intervalIntegral.integral_pos_iff_support_of_nonneg_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.intervalIntegral_pos_of_pos_on", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": ["have", "have", "rw", "refine", "rw", "filter_upwards", "rw", "exact"], "tactic_count": 8}
{"name": "intervalIntegral.intervalIntegral_pos_of_pos", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.integral_lt_integral_of_ae_le_of_measure_setOf_lt_ne_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "exact", "exacts"], "tactic_count": 4}
{"name": "intervalIntegral.integral_lt_integral_of_continuousOn_of_le_of_exists_lt", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": ["apply", "integral_lt_integral_of_ae_le_of_measure_setOf_lt_ne_zero", "simpa", "contrapose", "have", "simp", "exact", "rw", "exact"], "tactic_count": 9}
{"name": "intervalIntegral.integral_nonneg_of_ae_restrict", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["let", "simpa"], "tactic_count": 2}
{"name": "intervalIntegral.integral_nonneg_of_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.integral_nonneg_of_forall", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.integral_nonneg", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.abs_integral_le_integral_abs", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "intervalIntegral.integral_pos", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.integral_mono_interval", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "intervalIntegral.abs_integral_mono_interval", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.integral_mono_ae_restrict", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["let", "simpa"], "tactic_count": 2}
{"name": "intervalIntegral.integral_mono_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "intervalIntegral.integral_mono_on", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["let", "simpa"], "tactic_count": 2}
{"name": "intervalIntegral.integral_mono_on_of_le_Ioo", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["simp", "apply", "apply", "apply", "exact", "exact"], "tactic_count": 6}
{"name": "intervalIntegral.integral_mono", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Integrable.hasSum_intervalIntegral", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "rw", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.Integrable.hasSum_intervalIntegral_comp_add_int", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "intervalIntegral.integral_deriv_of_contDiffOn_Icc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.ContDiff", "is_tactic_proof": true, "tactics": ["rcases", "simp", "apply", "intro", "apply", "apply", "exact", "have", "apply", "simp", "rw", "filter_upwards", "exact"], "tactic_count": 13}
{"name": "intervalIntegral.integral_derivWithin_Icc_of_contDiffOn_Icc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.ContDiff", "is_tactic_proof": true, "tactics": ["rw", "rw", "apply", "rw", "filter_upwards", "exact"], "tactic_count": 6}
{"name": "intervalIntegral.integral_deriv_of_contDiffOn_uIcc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.ContDiff", "is_tactic_proof": true, "tactics": ["rcases", "simp", "exact", "simp", "rw", "abel"], "tactic_count": 6}
{"name": "intervalIntegral.integral_derivWithin_uIcc_of_contDiffOn_uIcc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.ContDiff", "is_tactic_proof": true, "tactics": ["rcases", "simp", "exact", "simp", "rw", "abel"], "tactic_count": 6}
{"name": "enorm_sub_le_lintegral_deriv_of_contDiffOn_Icc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.ContDiff", "is_tactic_proof": true, "tactics": ["norm", "true", "let", "have", "rw", "rw", "restrict_Ioc_eq_restrict_Icc]", "apply", "apply", "rw", "filter_upwards", "rw", "exact", "exact", "have", "simp"], "tactic_count": 16}
{"name": "enorm_sub_le_lintegral_derivWithin_Icc_of_contDiffOn_Icc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.ContDiff", "is_tactic_proof": true, "tactics": ["apply", "apply", "rw", "filter_upwards", "rw"], "tactic_count": 5}
{"name": "MonotoneOn.exists_tendsto_deriv_liminf_lintegral_enorm_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.DerivIntegrable", "is_tactic_proof": true, "tactics": ["from", "lemma.", "let", "have", "have", "replace", "have", "have", "let", "have", "have", "exact", "refine", "rw", "filter_upwards", "rw", "exact", "hx₁.hasDerivAt.tendsto_slope.comp", "tendsto_nhdsWithin_of_tendsto_nhds_of_eventually_within", "calc", "apply", "filter_upwards", "rw", "congr", "exact", "refine", "rw", "convert", "simp"], "tactic_count": 29}
{"name": "MonotoneOn.intervalIntegrable_deriv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.DerivIntegrable", "is_tactic_proof": true, "tactics": ["wlog", "exact", "rw", "obtain", "have", "lt_of_le_of_lt", "have", "exact"], "tactic_count": 8}
{"name": "MonotoneOn.intervalIntegral_deriv_mem_uIcc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.DerivIntegrable", "is_tactic_proof": true, "tactics": ["wlog", "specialize", "have", "rw", "refine", "simp", "rwa", "rw", "obtain", "have", "have", "have", "lt_of_le_of_lt", "have", "rw", "rw", "have", "rw", "have", "rw", "exact", "constructor", "apply", "rw", "filter_upwards", "exact", "have", "lintegral_enorm_le_liminf_of_tendsto", "grw", "rw", "intervalIntegral.integral_of_le", "convert", "refine", "rw", "filter_upwards", "exact"], "tactic_count": 36}
{"name": "BoundedVariationOn.intervalIntegrable_deriv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.DerivIntegrable", "is_tactic_proof": true, "tactics": ["obtain", "have", "apply", "rw", "filter_upwards", "have", "rw", "have", "replace", "replace", "exact"], "tactic_count": 11}
{"name": "AbsolutelyContinuousOnInterval.intervalIntegrable_deriv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.DerivIntegrable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.FTCFilter.pure", "kind": "instance", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.FTCFilter.nhdsWithinSingleton", "kind": "instance", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "intervalIntegral.FTCFilter.finiteAt_inner", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.FTCFilter.nhds", "kind": "instance", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.FTCFilter.nhdsUniv", "kind": "instance", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "intervalIntegral.FTCFilter.nhdsLeft", "kind": "instance", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.FTCFilter.nhdsRight", "kind": "instance", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.FTCFilter.nhdsIcc", "kind": "instance", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.FTCFilter.nhdsUIcc", "kind": "instance", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "have", "have", "simp_rw", "refine", "cases", "cases", "simp_rw", "abel"], "tactic_count": 10}
{"name": "intervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae_of_le'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae_of_ge'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae_of_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae_of_ge", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.measure_integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": true, "tactics": ["haveI", "refine", "have", "ha_lim.eventually_intervalIntegrable_ae", "have", "ha_lim.eventually_intervalIntegrable_ae", "have", "hb_lim.eventually_intervalIntegrable_ae", "have", "hb_lim.eventually_intervalIntegrable_ae", "filter_upwards", "rw", "abel", "exacts"], "tactic_count": 14}
{"name": "intervalIntegral.measure_integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": true, "tactics": ["simpa", "measure_integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae", "tendsto_const_pure"], "tactic_count": 3}
{"name": "intervalIntegral.measure_integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": true, "tactics": ["simpa", "measure_integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae", "tendsto_const_pure"], "tactic_count": 3}
{"name": "intervalIntegral.integral_sub_linear_isLittleO_of_tendsto_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "intervalIntegral.integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": true, "tactics": ["simpa", "measure_integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae"], "tactic_count": 2}
{"name": "intervalIntegral.integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": true, "tactics": ["simpa", "measure_integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae_right"], "tactic_count": 2}
{"name": "intervalIntegral.integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": true, "tactics": ["simpa", "measure_integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae_left"], "tactic_count": 2}
{"name": "intervalIntegral.integral_hasStrictFDerivAt_of_tendsto_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": false, "tactics": ["have", "integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae", "refine", "simp", "exact"], "tactic_count": 5}
{"name": "intervalIntegral.integral_hasStrictFDerivAt", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.integral_hasStrictDerivAt_of_tendsto_ae_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.integral_hasStrictDerivAt_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.integral_hasStrictDerivAt_of_tendsto_ae_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "intervalIntegral.integral_hasStrictDerivAt_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Continuous.integral_hasStrictDerivAt", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.deriv_integral", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.integral_hasFDerivAt_of_tendsto_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.integral_hasFDerivAt", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.fderiv_integral_of_tendsto_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.fderiv_integral", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.integral_hasDerivAt_of_tendsto_ae_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.integral_hasDerivAt_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.deriv_integral_of_tendsto_ae_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.deriv_integral_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.integral_hasDerivAt_of_tendsto_ae_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.integral_hasDerivAt_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.deriv_integral_of_tendsto_ae_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.deriv_integral_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.integral_hasFDerivWithinAt_of_tendsto_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": true, "tactics": ["rw", "have", "integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae", "refine", "simp", "exact"], "tactic_count": 6}
{"name": "intervalIntegral.integral_hasFDerivWithinAt", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.tacticUniqueDiffWithinAt_Ici_Iic_univ", "kind": "definition", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral._aux_Mathlib_MeasureTheory_Integral_IntervalIntegral_FundThmCalculus___macroRules_intervalIntegral_tacticUniqueDiffWithinAt_Ici_Iic_univ_1", "kind": "definition", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.integral_hasDerivWithinAt_of_tendsto_ae_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.integral_hasDerivWithinAt_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.integral_hasDerivWithinAt_of_tendsto_ae_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "intervalIntegral.integral_hasDerivWithinAt_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.differentiable_integral_of_continuous", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.differentiableOn_integral_of_continuous", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.sub_le_integral_of_hasDeriv_right_of_le_Ico", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": false, "tactics": ["refine", "le_of_forall_pos_le_add", "rcases", "set", "have", "have", "rw", "exact", "simp", "exact", "have", "refine", "s_closed.Icc_subset_of_forall_exists_gt", "obtain", "have", "have", "rcases", "have", "filter_upwards", "have", "calc", "simp", "hu.left.le,", "rw", "apply", "simp", "exact", "have", "have", "filter_upwards", "apply", "have", "simp", "and_self_iff]", "refine", "exact", "have", "have", "filter_upwards", "self_mem_nhdsWithin]", "have", "rwa", "have", "filter_upwards", "have", "lt_min", "ht.2.2", "rcases", "refine", "calc", "g", "apply", "rw", "exact", "rw", "apply", "exact", "calc", "g", "convert", "rw", "simp"], "tactic_count": 62}
{"name": "intervalIntegral.sub_le_integral_of_hasDeriv_right_of_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": true, "tactics": ["obtain", "simp", "set", "have", "have", "rw", "exact", "simp", "exact", "have", "apply", "intro", "refine", "exact", "sub_le_integral_of_hasDeriv_right_of_le_Ico", "hφg", "rw", "exact"], "tactic_count": 18}
{"name": "intervalIntegral.integral_le_sub_of_hasDeriv_right_of_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": true, "tactics": ["rw", "convert", "sub_le_integral_of_hasDeriv_right_of_le", "neg_le_neg", "abel", "simp"], "tactic_count": 6}
{"name": "intervalIntegral.integral_eq_sub_of_hasDeriv_right_of_le_real", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.integral_eq_sub_of_hasDeriv_right_of_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact", "integral_eq_sub_of_hasDeriv_right_of_le_real"], "tactic_count": 4}
{"name": "intervalIntegral.integral_eq_sub_of_hasDeriv_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": true, "tactics": ["rcases", "simp", "apply", "simp", "rw"], "tactic_count": 5}
{"name": "intervalIntegral.integral_eq_sub_of_hasDerivAt_of_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.integral_eq_sub_of_hasDerivAt", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.integral_eq_sub_of_hasDerivAt_of_tendsto", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": true, "tactics": ["set", "have", "refine", "filter_upwards", "unfold", "rw", "have", "rw", "refine", "exact", "rintro", "refine", "filter_upwards", "simpa"], "tactic_count": 14}
{"name": "intervalIntegral.integral_deriv_eq_sub", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.integral_deriv_eq_sub'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "intervalIntegral.integral_unitInterval_deriv_eq_sub", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": true, "tactics": ["let", "have", "have", "refine", "simp", "convert", "simp_rw", "simp"], "tactic_count": 8}
{"name": "intervalIntegral.integrableOn_deriv_right_of_nonneg", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "rw", "have", "apply", "refine", "exact", "suffices", "by_contra", "obtain", "exists_lt_lintegral_simpleFunc_of_lt_lintegral", "let", "have", "refine", "simpa", "have", "rw", "have", "rw", "refine", "rwa", "convert", "simp", "exact"], "tactic_count": 24}
{"name": "intervalIntegral.integrableOn_deriv_of_nonneg", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.intervalIntegrable_deriv_of_nonneg", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus", "is_tactic_proof": true, "tactics": ["rcases", "simp", "and_true]", "exact", "simp", "true_and]", "exact"], "tactic_count": 7}
{"name": "intervalIntegral.integral_deriv_mul_eq_sub_of_hasDeriv_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.IntegrationByParts", "is_tactic_proof": true, "tactics": ["apply", "exact"], "tactic_count": 2}
{"name": "intervalIntegral.integral_deriv_mul_eq_sub_of_hasDerivAt", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.IntegrationByParts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.integral_deriv_mul_eq_sub_of_hasDerivWithinAt", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.IntegrationByParts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.integral_deriv_mul_eq_sub", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.IntegrationByParts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.integral_mul_deriv_eq_deriv_mul_of_hasDeriv_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.IntegrationByParts", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "exact", "exact"], "tactic_count": 4}
{"name": "intervalIntegral.integral_mul_deriv_eq_deriv_mul_of_hasDerivAt", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.IntegrationByParts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.integral_mul_deriv_eq_deriv_mul_of_hasDerivWithinAt", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.IntegrationByParts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.integral_mul_deriv_eq_deriv_mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.IntegrationByParts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.integral_deriv_smul_eq_sub_of_hasDeriv_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.IntegrationByParts", "is_tactic_proof": true, "tactics": ["simp_rw", "apply", "exact"], "tactic_count": 3}
{"name": "intervalIntegral.integral_smul_deriv_eq_deriv_smul_of_hasDeriv_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.IntegrationByParts", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "exact", "exact"], "tactic_count": 4}
{"name": "intervalIntegral.integral_smul_deriv_eq_deriv_smul_of_hasDerivAt", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.IntegrationByParts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.integral_smul_deriv_eq_deriv_smul_of_hasDerivWithinAt", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.IntegrationByParts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.integral_smul_deriv_eq_deriv_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.IntegrationByParts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.integral_comp_smul_deriv'''", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.IntegrationByParts", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "rw", "have", "refine", "rw", "rw", "have", "intro", "obtain", "obtain", "have", "rw", "exact", "replace", "let", "have", "rw", "have", "have", "refine", "rw", "exact", "have", "hg_cont.stronglyMeasurableAtFilter_nhdsWithin", "haveI", "have", "intervalIntegral.integral_hasDerivWithinAt_right", "refine", "rw", "refine", "exact", "rw", "simp_rw"], "tactic_count": 34}
{"name": "intervalIntegral.integral_comp_smul_deriv''", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.IntegrationByParts", "is_tactic_proof": false, "tactics": ["refine", "integral_comp_smul_deriv", "rw", "exact"], "tactic_count": 4}
{"name": "intervalIntegral.integral_comp_smul_deriv'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.IntegrationByParts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.integral_comp_smul_deriv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.IntegrationByParts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.integral_deriv_comp_smul_deriv'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.IntegrationByParts", "is_tactic_proof": false, "tactics": ["rw", "integral_eq_sub_of_hasDeriv_right", "exacts"], "tactic_count": 3}
{"name": "intervalIntegral.integral_deriv_comp_smul_deriv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.IntegrationByParts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.integral_comp_mul_deriv'''", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.IntegrationByParts", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "intervalIntegral.integral_comp_mul_deriv''", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.IntegrationByParts", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "intervalIntegral.integral_comp_mul_deriv'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.IntegrationByParts", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "intervalIntegral.integral_comp_mul_deriv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.IntegrationByParts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intervalIntegral.integral_deriv_comp_mul_deriv'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.IntegrationByParts", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "intervalIntegral.integral_deriv_comp_mul_deriv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.IntegrationByParts", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "LocallyIntegrable.ae_hasDerivAt_integral", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.LebesgueDifferentiationThm", "is_tactic_proof": false, "tactics": ["have", "intervalIntegrable_iff.mpr", "have", "have", "integral_Icc_eq_integral_Ioc", "filter_upwards", "intro", "rw", "constructor", "refine", "filter_upwards", "replace", "simp", "grind", "refine", "filter_upwards", "replace", "simp"], "tactic_count": 18}
{"name": "IntervalIntegrable.ae_hasDerivAt_integral", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.LebesgueDifferentiationThm", "is_tactic_proof": true, "tactics": ["wlog", "exact", "rw", "have", "have", "let", "have", "integrableOn_congr_fun", "filter_upwards", "intro", "refine", "rw", "refine", "all_goals"], "tactic_count": 14}
{"name": "exists_eq_const_mul_intervalIntegral_of_ae_nonneg", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.MeanValue", "is_tactic_proof": true, "tactics": ["by_cases", "subst", "exact", "wlog", "simp", "obtain", "this", "exact", "let", "have", "have", "have", "have", "rw", "exact", "obtain", "exists_eq_const_mul_setIntegral_of_ae_nonneg", "have", "simpa", "exact"], "tactic_count": 20}
{"name": "exists_eq_const_mul_intervalIntegral_of_nonneg", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.MeanValue", "is_tactic_proof": false, "tactics": ["have", "rw", "exact", "exact"], "tactic_count": 4}
{"name": "AddCircle.measurable_mk'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCircle.measureSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCircle.measure_univ", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Periodic", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "simp"], "tactic_count": 3}
{"name": "AddCircle.instIsAddHaarMeasureRealVolume", "kind": "instance", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCircle.isFiniteMeasure", "kind": "instance", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCircle.instHasAddFundamentalDomainSubtypeAddOppositeRealMemAddSubgroupOpZmultiples", "kind": "instance", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCircle.instAddQuotientMeasureEqMeasurePreimageSubtypeAddOppositeRealMemAddSubgroupOpZmultiplesVolume", "kind": "instance", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Periodic", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "AddCircle.measurePreserving_mk", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCircle.add_projection_respects_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCircle.volume_closedBall", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Periodic", "is_tactic_proof": true, "tactics": ["have", "let", "have", "intro", "rw", "rintro", "have", "conv_rhs", "apply", "simpa", "rw", "by_cases", "simp", "simp"], "tactic_count": 14}
{"name": "AddCircle.instIsUnifLocDoublingMeasureRealVolume", "kind": "instance", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Periodic", "is_tactic_proof": true, "tactics": ["refine", "simp", "erw", "apply", "rw", "exact"], "tactic_count": 6}
{"name": "AddCircle.measurableEquivIoc", "kind": "definition", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCircle.measurableEquivIco", "kind": "definition", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCircle.measurePreserving_equivIoc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Periodic", "is_tactic_proof": true, "tactics": ["have", "refine", "ext", "rw", "map_apply", "congr", "ext", "simp", "rw", "congr", "rw"], "tactic_count": 11}
{"name": "AddCircle.lintegral_preimage", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Periodic", "is_tactic_proof": true, "tactics": ["have", "have", "simp", "rw", "convert", "rw", "exact", "congr", "have", "simp_rw", "rw", "rfl"], "tactic_count": 12}
{"name": "AddCircle.integral_preimage", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Periodic", "is_tactic_proof": true, "tactics": ["have", "have", "simp", "rw", "have", "simp_rw", "rw", "rfl"], "tactic_count": 8}
{"name": "AddCircle.intervalIntegral_preimage", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Periodic", "is_tactic_proof": true, "tactics": ["rw", "linarith"], "tactic_count": 2}
{"name": "AddCircle.integral_liftIoc_eq_intervalIntegral", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Periodic", "is_tactic_proof": true, "tactics": ["rw", "apply", "refine", "rw", "rw"], "tactic_count": 5}
{"name": "MeasureTheory.MemLp.memLp_liftIoc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Periodic", "is_tactic_proof": true, "tactics": ["simp", "apply", "refine", "exact"], "tactic_count": 4}
{"name": "UnitAddCircle.measure_univ", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Periodic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "UnitAddCircle.measurePreserving_mk", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UnitAddCircle.lintegral_preimage", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UnitAddCircle.integral_preimage", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UnitAddCircle.intervalIntegral_preimage", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Periodic.intervalIntegrable₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Periodic", "is_tactic_proof": true, "tactics": ["apply", "simpa"], "tactic_count": 2}
{"name": "Function.Periodic.intervalIntegral_add_eq_of_pos", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Periodic", "is_tactic_proof": true, "tactics": ["simp", "haveI", "apply", "exacts"], "tactic_count": 4}
{"name": "Function.Periodic.intervalIntegral_add_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Periodic", "is_tactic_proof": true, "tactics": ["rcases", "exact", "simp", "rw", "simpa", "hf.neg.intervalIntegral_add_eq_of_pos"], "tactic_count": 6}
{"name": "Function.Periodic.intervalIntegral_add_eq_add", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Periodic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Function.Periodic.intervalIntegral_add_zsmul_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Periodic", "is_tactic_proof": true, "tactics": ["suffices", "simp", "have", "induction", "zero", "succ", "simp", "rcases", "simp", "conv_rhs", "have", "rw", "simp_rw", "hf.intervalIntegral_add_eq"], "tactic_count": 14}
{"name": "Function.Periodic.sInf_add_zsmul_le_integral_of_pos", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Periodic", "is_tactic_proof": true, "tactics": ["let", "let", "conv_rhs", "rw", "integral_add_adjacent_intervals", "rw", "zero_add,", "exact", "mem_Icc_of_Ico"], "tactic_count": 9}
{"name": "Function.Periodic.integral_le_sSup_add_zsmul_of_pos", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Periodic", "is_tactic_proof": true, "tactics": ["let", "let", "conv_lhs", "rw", "integral_add_adjacent_intervals", "rw", "exact"], "tactic_count": 7}
{"name": "Function.Periodic.tendsto_atTop_intervalIntegral_of_pos", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Periodic", "is_tactic_proof": true, "tactics": ["have", "apply", "apply", "apply", "exact"], "tactic_count": 5}
{"name": "Function.Periodic.tendsto_atBot_intervalIntegral_of_pos", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Periodic", "is_tactic_proof": true, "tactics": ["have", "apply", "apply", "apply", "exact"], "tactic_count": 5}
{"name": "Function.Periodic.tendsto_atTop_intervalIntegral_of_pos'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Periodic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Periodic.tendsto_atBot_intervalIntegral_of_pos'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Periodic", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "IntervalIntegrable.intervalIntegrable_slope", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Slope", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "MonotoneOn.intervalIntegrable_slope", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Slope", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonotoneOn.intervalIntegral_slope_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.Slope", "is_tactic_proof": true, "tactics": ["rcases", "simp", "apply", "rw", "have", "simp", "rw", "intervalIntegral.integral_comp_add_right,", "intervalIntegral.integral_interval_sub_interval_comm", "have", "grw", "simp", "have", "grw", "intervalIntegral.integral_mono_on", "simp", "grw", "field_simp"], "tactic_count": 18}
{"name": "trapezoidal_integral", "kind": "definition", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.TrapezoidalRule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "trapezoidal_error", "kind": "definition", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.TrapezoidalRule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "trapezoidal_integral_symm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.TrapezoidalRule", "is_tactic_proof": true, "tactics": ["unfold", "rw", "congr", "apply", "intro", "norm_cast", "rw", "apply", "field"], "tactic_count": 9}
{"name": "trapezoidal_error_symm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.TrapezoidalRule", "is_tactic_proof": true, "tactics": ["unfold", "rw"], "tactic_count": 2}
{"name": "trapezoidal_integral_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.TrapezoidalRule", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "trapezoidal_error_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.TrapezoidalRule", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "trapezoidal_integral_one", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.TrapezoidalRule", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "sum_trapezoidal_integral_adjacent_intervals", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.TrapezoidalRule", "is_tactic_proof": false, "tactics": ["simp_rw", "one_mul,", "rw", "sum_add_distrib,", "simp_rw", "ring_nf"], "tactic_count": 6}
{"name": "trapezoidal_integral_ext", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.TrapezoidalRule", "is_tactic_proof": true, "tactics": ["rw", "sum_trapezoidal_integral_adjacent_intervals"], "tactic_count": 2}
{"name": "sum_trapezoidal_error_adjacent_intervals", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.IntervalIntegral.TrapezoidalRule", "is_tactic_proof": true, "tactics": ["unfold", "rw", "norm_cast", "rw", "simp", "intro", "suffices", "rcases", "simpa", "exact"], "tactic_count": 10}
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{"name": "MeasureTheory.lintegral_mono'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact", "iSup_mono", "iSup_mono"], "tactic_count": 4}
{"name": "MeasureTheory.lintegral_mono_fn'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.lintegral_mono", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.lintegral_mono_nnreal", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.iSup_lintegral_measurable_le_eq_lintegral", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["apply", "exact", "rw", "refine", "exact"], "tactic_count": 5}
{"name": "MeasureTheory.lintegral_mono_set", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.lintegral_mono_set'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.monotone_lintegral", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.lintegral_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "MeasureTheory.lintegral_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.lintegral_zero_fun", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.lintegral_one", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.setLIntegral_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.setLIntegral_one", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.iInf_mul_le_lintegral", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["calc"], "tactic_count": 1}
{"name": "MeasureTheory.lintegral_le_iSup_mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["calc"], "tactic_count": 1}
{"name": "MeasureTheory.exists_measurable_le_lintegral_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["rcases", "exact", "rcases", "have", "intro", "simpa", "choose", "refine", "refine", "exact", "exact"], "tactic_count": 11}
{"name": "MeasureTheory.lintegral_eq_nnreal", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "by_cases", "let", "replace", "have", "exact", "have", "refine", "obtain", "use", "simp", "map_coe_ennreal_restrict,", "refine", "simp", "simp"], "tactic_count": 16}
{"name": "MeasureTheory.exists_simpleFunc_forall_lintegral_sub_lt_of_pos", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["rw", "have", "erw", "simp_rw", "rcases", "refine", "have", "rw", "refine", "norm_cast", "simp", "rfl"], "tactic_count": 12}
{"name": "MeasureTheory.iSup_lintegral_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.iSup₂_lintegral_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.le_iInf_lintegral", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.le_iInf₂_lintegral", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.lintegral_mono_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["rcases", "have", "rw", "refine", "intro", "by_cases", "simp", "not_false_eq_true,", "exact", "exact"], "tactic_count": 10}
{"name": "MeasureTheory.setLIntegral_mono_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["rcases", "rw", "apply", "rw", "exact", "exact"], "tactic_count": 6}
{"name": "MeasureTheory.setLIntegral_mono", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.setLIntegral_mono_ae'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.setLIntegral_mono'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.setLIntegral_le_lintegral", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.iInf_mul_le_setLIntegral", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["calc"], "tactic_count": 1}
{"name": "MeasureTheory.setLIntegral_le_iSup_mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["calc"], "tactic_count": 1}
{"name": "MeasureTheory.lintegral_congr_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.lintegral_congr", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.setLIntegral_congr", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.setLIntegral_congr_fun_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["rw", "rw", "rwa"], "tactic_count": 3}
{"name": "MeasureTheory.setLIntegral_congr_fun", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.setLIntegral_eq_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.lintegral_eq_zero_of_ae_eq_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.lintegral_eq_zero_iff'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["refine", "have", "by_contra", "refine", "calc", "obtain", "have", "ext", "rw", "rw", "constructor", "obtain", "obtain", "have", "rwa"], "tactic_count": 15}
{"name": "MeasureTheory.lintegral_eq_zero_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.setLIntegral_eq_zero_iff'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.setLIntegral_eq_zero_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.lintegral_pos_iff_support", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.setLIntegral_pos_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.exists_pos_setLIntegral_lt_of_measure_lt", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "rcases", "rcases", "use", "refine", "simp", "intro", "calc", "rw", "refine", "simp", "gcongr", "refine", "exact", "gcongr", "exact", "simp"], "tactic_count": 18}
{"name": "MeasureTheory.tendsto_setLIntegral_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["simp", "intro", "rcases", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.lintegral_smul_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.setLIntegral_smul_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.lintegral_zero_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.lintegral_add_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["simp", "refine", "rintro", "refine", "gcongr", "exacts"], "tactic_count": 6}
{"name": "MeasureTheory.lintegral_finset_sum_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.lintegral_sum_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MeasureTheory.hasSum_lintegral_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.lintegral_of_isEmpty", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["have", "convert"], "tactic_count": 2}
{"name": "MeasureTheory.setLIntegral_empty", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.setLIntegral_univ", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.setLIntegral_measure_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["convert", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.lintegral_rw₁", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.lintegral_rw₂", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.lintegral_indicator_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["simp", "apply", "have", "refine", "rw", "congr", "by_cases", "simp", "congr", "simp", "rintro", "contrapose", "simpa"], "tactic_count": 13}
{"name": "MeasureTheory.lintegral_indicator", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["apply", "simp", "refine", "refine", "simp"], "tactic_count": 5}
{"name": "MeasureTheory.setLIntegral_indicator", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.lintegral_indicator₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["rw", "lintegral_indicator"], "tactic_count": 2}
{"name": "MeasureTheory.setLIntegral_indicator₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.lintegral_indicator_const_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.lintegral_indicator_const₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.lintegral_indicator_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.setLIntegral_eq_of_support_subset", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["apply", "apply", "congr", "simp", "split_ifs", "rfl", "exact"], "tactic_count": 7}
{"name": "MeasureTheory.setLIntegral_eq_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["have", "rw", "rw", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.lintegral_indicator_one_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.lintegral_indicator_one₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.lintegral_indicator_one", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.ext_iff_lintegral", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["refine", "intro", "ext", "simp", "exact"], "tactic_count": 5}
{"name": "MeasureTheory.Measure.ext_of_lintegral", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.lintegral_iUnion₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.lintegral_iUnion", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.lintegral_biUnion₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["haveI", "rw"], "tactic_count": 2}
{"name": "MeasureTheory.lintegral_biUnion", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.lintegral_biUnion_finset₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.lintegral_biUnion_finset", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.lintegral_iUnion_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.lintegral_union", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.lintegral_union_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.lintegral_inter_add_diff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.lintegral_add_compl", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.lintegral_piecewise", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["rw", "congr", "exact", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.setLIntegral_compl", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.setLIntegral_iUnion_of_directed", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.lintegral_max", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["have", "rw", "simp", "refine", "exacts"], "tactic_count": 5}
{"name": "MeasureTheory.setLIntegral_max", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["rw", "exacts"], "tactic_count": 2}
{"name": "MeasureTheory.setLIntegral_lt_top_of_le_nnreal", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["obtain", "refine", "simp"], "tactic_count": 3}
{"name": "MeasureTheory.setLIntegral_lt_top_of_bddAbove", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.setLIntegral_lt_top_of_isCompact", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.setLIntegral_const_lt_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Countable", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.lintegral_const_lt_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Countable", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.lintegral_eq_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Countable", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.lintegral_le_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.iInf_le_lintegral", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.lintegral_le_iSup", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Countable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFiniteMeasure.lintegral_lt_top_of_bounded_to_ennreal", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Countable", "is_tactic_proof": true, "tactics": ["rw", "refine", "simpa"], "tactic_count": 3}
{"name": "MeasureTheory.lintegral_dirac'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.Lebesgue.Countable", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "MeasureTheory.setToFun_smul_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.SetToL1", "is_tactic_proof": true, "tactics": ["by_cases", "simp_rw", "simp_rw"], "tactic_count": 3}
{"name": "MeasureTheory.setToFun_smul_left'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.SetToL1", "is_tactic_proof": true, "tactics": ["by_cases", "simp_rw", "simp_rw"], "tactic_count": 3}
{"name": "MeasureTheory.setToFun_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.SetToL1", "is_tactic_proof": true, "tactics": ["rw", "simp", "rw"], "tactic_count": 3}
{"name": "MeasureTheory.setToFun_zero_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.SetToL1", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.setToFun_zero_left'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.SetToL1", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.setToFun_add", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.SetToL1", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.setToFun_finset_sum'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.SetToL1", "is_tactic_proof": true, "tactics": ["classical", "revert", "refine", "intro", "simp", "intro", "simp", "rw", "rw", "convert", "simp"], "tactic_count": 11}
{"name": "MeasureTheory.setToFun_finset_sum", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.SetToL1", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "MeasureTheory.setToFun_neg", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.SetToL1", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "rw", "rwa"], "tactic_count": 4}
{"name": "MeasureTheory.setToFun_sub", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.SetToL1", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.setToFun_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.SetToL1", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "by_cases", "rw", "have", "rw"], "tactic_count": 6}
{"name": "MeasureTheory.setToFun_congr_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.SetToL1", "is_tactic_proof": true, "tactics": ["by_cases", "have", "rw", "have", "rw"], "tactic_count": 5}
{"name": "MeasureTheory.setToFun_measure_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.SetToL1", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "MeasureTheory.setToFun_measure_zero'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.SetToL1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.setToFun_toL1", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.SetToL1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.setToFun_indicator_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.SetToL1", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.setToFun_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.SetToL1", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.setToFun_mono_left'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.SetToL1", "is_tactic_proof": true, "tactics": ["by_cases", "simp_rw", "simp_rw"], "tactic_count": 3}
{"name": "MeasureTheory.setToFun_mono_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.SetToL1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.setToFun_nonneg", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.SetToL1", "is_tactic_proof": true, "tactics": ["by_cases", "simp_rw", "refine", "rw", "have", "have", "filter_upwards", "rw", "exact", "simp_rw"], "tactic_count": 10}
{"name": "MeasureTheory.setToFun_mono", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.SetToL1", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.continuous_setToFun", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.SetToL1", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MeasureTheory.tendsto_setToFun_of_L1", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.SetToL1", "is_tactic_proof": true, "tactics": ["classical", "let", "let", "have", "rw", "simp_rw", "refine", "filter_upwards", "refine", "filter_upwards", "simp_rw", "suffices", "refine", "filter_upwards", "suffices", "simp_rw", "exact", "rw", "exact"], "tactic_count": 19}
{"name": "MeasureTheory.tendsto_setToFun_approxOn_of_measurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.SetToL1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.tendsto_setToFun_approxOn_of_measurable_of_range_subset", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.SetToL1", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.continuous_L1_toL1", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.SetToL1", "is_tactic_proof": true, "tactics": ["by_cases", "have", "have", "ext1", "rw", "exact", "rw", "intro", "use", "refine", "intro", "rw", "let", "have", "eLpNorm_congr_ae", "rw", "have", "exact", "calc", "refine", "refine", "rw", "simp"], "tactic_count": 23}
{"name": "MeasureTheory.setToFun_congr_measure_of_integrable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.SetToL1", "is_tactic_proof": true, "tactics": ["have", "apply", "intro", "have", "refine", "rw", "exact", "rw", "intro", "rw", "refine", "have", "setToFun", "rw", "exact", "intro", "have", "rw"], "tactic_count": 18}
{"name": "MeasureTheory.setToFun_congr_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.SetToL1", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "have", "simp_rw"], "tactic_count": 4}
{"name": "MeasureTheory.setToFun_congr_measure_of_add_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.SetToL1", "is_tactic_proof": true, "tactics": ["refine", "rw", "nth_rw", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.setToFun_congr_measure_of_add_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.SetToL1", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.setToFun_top_smul_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.SetToL1", "is_tactic_proof": true, "tactics": ["refine", "rw", "simp", "simp"], "tactic_count": 4}
{"name": "MeasureTheory.setToFun_congr_smul_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.SetToL1", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "have", "rw", "simp", "refine", "simp", "rw"], "tactic_count": 8}
{"name": "MeasureTheory.norm_setToFun_le_mul_norm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.SetToL1", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.norm_setToFun_le_mul_norm'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.SetToL1", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.norm_setToFun_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.SetToL1", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.norm_setToFun_le'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.SetToL1", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.tendsto_setToFun_of_dominated_convergence", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.SetToL1", "is_tactic_proof": true, "tactics": ["have", "have", "have", "suffices", "convert", "exact", "exact", "refine", "rw", "have", "convert", "rw", "congr", "refine", "rw", "refine", "dsimp", "rw"], "tactic_count": 18}
{"name": "MeasureTheory.tendsto_setToFun_filter_of_dominated_convergence", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.SetToL1", "is_tactic_proof": true, "tactics": ["rw", "intro", "have", "have", "inter_mem", "obtain", "rw", "refine", "exact", "exact", "filter_upwards", "refine", "rwa"], "tactic_count": 13}
{"name": "MeasureTheory.continuousWithinAt_setToFun_of_dominated", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.SetToL1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.continuousAt_setToFun_of_dominated", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.SetToL1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.continuousOn_setToFun_of_dominated", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.SetToL1", "is_tactic_proof": true, "tactics": ["intro", "refine", "filter_upwards", "filter_upwards", "filter_upwards"], "tactic_count": 5}
{"name": "MeasureTheory.continuous_setToFun_of_dominated", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.SetToL1", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.MeasureTheory.Integral.TorusIntegral.0.term___", "kind": "definition", "module": "Mathlib.MeasureTheory.Integral.TorusIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.MeasureTheory.Integral.TorusIntegral.0._aux_Mathlib_MeasureTheory_Integral_TorusIntegral___macroRules__private_Mathlib_MeasureTheory_Integral_TorusIntegral_0_term____1", "kind": "definition", "module": "Mathlib.MeasureTheory.Integral.TorusIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "torusMap", "kind": "definition", "module": "Mathlib.MeasureTheory.Integral.TorusIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "torusMap_sub_center", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.TorusIntegral", "is_tactic_proof": true, "tactics": ["ext1"], "tactic_count": 1}
{"name": "torusMap_eq_center_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.TorusIntegral", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "torusMap_zero_radius", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.TorusIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TorusIntegrable", "kind": "definition", "module": "Mathlib.MeasureTheory.Integral.TorusIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TorusIntegrable.torusIntegrable_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.TorusIntegral", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "TorusIntegrable.neg", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.TorusIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TorusIntegrable.add", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.TorusIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TorusIntegrable.sub", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.TorusIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TorusIntegrable.torusIntegrable_zero_radius", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.TorusIntegral", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "TorusIntegrable.function_integrable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.TorusIntegral", "is_tactic_proof": true, "tactics": ["refine", "refine", "simp"], "tactic_count": 3}
{"name": "torusIntegral", "kind": "definition", "module": "Mathlib.MeasureTheory.Integral.TorusIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "term∯_InT(_,_),_", "kind": "definition", "module": "Mathlib.MeasureTheory.Integral.TorusIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_MeasureTheory_Integral_TorusIntegral___macroRules_term∯_InT(_,_),__1", "kind": "definition", "module": "Mathlib.MeasureTheory.Integral.TorusIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_MeasureTheory_Integral_TorusIntegral___delab_app_term∯_InT(_,_),__1", "kind": "definition", "module": "Mathlib.MeasureTheory.Integral.TorusIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "torusIntegral_radius_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.TorusIntegral", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "torusIntegral_neg", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.TorusIntegral", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "torusIntegral_add", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.TorusIntegral", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "torusIntegral_sub", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.TorusIntegral", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "torusIntegral_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.TorusIntegral", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "torusIntegral_const_mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.TorusIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "norm_torusIntegral_le_of_norm_le_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.TorusIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "torusIntegral_dim0", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.TorusIntegral", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "torusIntegral_dim1", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.TorusIntegral", "is_tactic_proof": false, "tactics": ["have", "have", "ext", "rw", "rw", "simp"], "tactic_count": 6}
{"name": "torusIntegral_succAbove", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.TorusIntegral", "is_tactic_proof": true, "tactics": ["set", "have", "have", "rw", "circleIntegral_def_Icc]", "refine", "simp", "torusMap,", "refine", "simp", "congr", "simp", "imp_true_iff,", "have", "rwa"], "tactic_count": 15}
{"name": "torusIntegral_succ", "kind": "theorem", "module": "Mathlib.MeasureTheory.Integral.TorusIntegral", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasurableSpace.map", "kind": "definition", "module": "Mathlib.MeasureTheory.MeasurableSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.map_def", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.map_id", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.map_comp", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.comap", "kind": "definition", "module": "Mathlib.MeasureTheory.MeasurableSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.measurableSet_comap", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.comap_eq_generateFrom", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.comap_id", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.comap_comp", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.comap_le_iff_le_map", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.gc_comap_map", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.map_mono", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.monotone_map", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.comap_mono", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.monotone_comap", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.comap_bot", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.comap_sup", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.comap_iSup", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.map_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.map_inf", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.map_iInf", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.comap_map_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.le_map_comap", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.map_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.comap_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.comap_generateFrom", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_iff_le_map", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_iff_comap_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "comap_measurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_comap_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Measurable.mono", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.iSup'", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.sup_of_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.sup_of_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_id''", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_from_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_generateFrom", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurableSet_generateFrom_of_mem_supClosure", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Basic", "is_tactic_proof": true, "tactics": ["rcases", "rw", "exact"], "tactic_count": 3}
{"name": "Subsingleton.measurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_of_subsingleton_codomain", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_one", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_of_empty", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_of_empty_codomain", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_const'", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Basic", "is_tactic_proof": true, "tactics": ["nontriviality", "inhabit", "convert", "apply"], "tactic_count": 4}
{"name": "measurable_natCast", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_intCast", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_of_countable", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_of_finite", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.iterate", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurableSet_preimage", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSet.preimage", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.piecewise", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.ite", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.indicator", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_indicator_const_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Basic", "is_tactic_proof": true, "tactics": ["constructor", "convert", "ext", "simp", "exact"], "tactic_count": 5}
{"name": "measurableSet_mulSupport", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.measurable_of_countable_ne", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Basic", "is_tactic_proof": true, "tactics": ["intro", "have", "rw", "refine", "have", "ext", "simp", "rw", "exact"], "tactic_count": 9}
{"name": "IsCountablySpanning", "kind": "definition", "module": "Mathlib.MeasureTheory.MeasurableSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCountablySpanning_measurableSet", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCountablySpanning.prod", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Basic", "is_tactic_proof": true, "tactics": ["rcases", "refine", "rw"], "tactic_count": 3}
{"name": "MeasurableSpace.generateMeasurableRec", "kind": "definition", "module": "Mathlib.MeasureTheory.MeasurableSpace.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.self_subset_generateMeasurableRec", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Card", "is_tactic_proof": true, "tactics": ["unfold", "apply_rules", "exact"], "tactic_count": 3}
{"name": "MeasurableSpace.empty_mem_generateMeasurableRec", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Card", "is_tactic_proof": true, "tactics": ["unfold", "exact"], "tactic_count": 2}
{"name": "MeasurableSpace.compl_mem_generateMeasurableRec", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Card", "is_tactic_proof": true, "tactics": ["unfold", "exact"], "tactic_count": 2}
{"name": "MeasurableSpace.iUnion_mem_generateMeasurableRec", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Card", "is_tactic_proof": true, "tactics": ["unfold", "exact", "mem_union_right", "let", "mem_iUnion₂.2", "rfl⟩"], "tactic_count": 6}
{"name": "MeasurableSpace.generateMeasurableRec_mono", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Card", "is_tactic_proof": true, "tactics": ["intro", "rcases", "exact", "convert", "exact"], "tactic_count": 5}
{"name": "MeasurableSpace.generateMeasurableRec_induction", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Card", "is_tactic_proof": true, "tactics": ["suffices", "intro", "apply", "intro", "replace", "unfold", "rintro", "exact", "exact", "simp_rw", "obtain", "exact", "apply", "intro", "obtain", "use"], "tactic_count": 16}
{"name": "MeasurableSpace.generateMeasurableRec_omega_one", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Card", "is_tactic_proof": true, "tactics": ["apply", "intro", "rw", "refine", "intro", "exact", "exact", "rintro", "exact", "intro", "choose", "simp_rw", "refine", "iUnion_mem_generateMeasurableRec", "rw", "exact"], "tactic_count": 16}
{"name": "MeasurableSpace.generateMeasurableRec_subset", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Card", "is_tactic_proof": true, "tactics": ["apply", "exact", "generateMeasurableRec_induction"], "tactic_count": 3}
{"name": "MeasurableSpace.generateMeasurable_eq_rec", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Card", "is_tactic_proof": true, "tactics": ["apply", "intro", "induction", "basic", "empty", "compl", "rw", "obtain", "exact", "generateMeasurableRec_mono", "iUnion", "simp_rw", "exact"], "tactic_count": 13}
{"name": "MeasurableSpace.generateMeasurableRec_of_omega_one_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Card", "is_tactic_proof": true, "tactics": ["apply", "rw", "exact"], "tactic_count": 3}
{"name": "MeasurableSpace.cardinal_generateMeasurableRec_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Card", "is_tactic_proof": false, "tactics": ["suffices", "obtain", "exact", "rw", "exact", "intro", "apply", "intro", "have", "have", "have", "apply", "intro", "exact", "rw", "rw", "have", "rw", "apply", "rw", "exact", "rw", "apply_rules", "exact", "rw", "exact", "apply", "simp", "have", "rwa"], "tactic_count": 30}
{"name": "MeasurableSpace.cardinal_generateMeasurable_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Card", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasurableSpace.cardinal_measurableSet_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.cardinal_generateMeasurable_le_continuum", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Card", "is_tactic_proof": true, "tactics": ["apply", "rw", "exact_mod_cast"], "tactic_count": 3}
{"name": "MeasurableSpace.cardinal_measurableSet_le_continuum", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Card", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_to_countable", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_to_countable'", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.measurable_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": true, "tactics": ["refine", "cases", "top", "rw", "exact", "coe"], "tactic_count": 6}
{"name": "measurable_unit", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.instMeasurableSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_down", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_up", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurableSet_preimage_down", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurableSet_preimage_up", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_from_nat", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_to_nat", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_to_bool", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": true, "tactics": ["apply", "rintro", "convert", "rw", "exact"], "tactic_count": 5}
{"name": "measurable_to_prop", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": true, "tactics": ["refine", "by_cases", "simpa", "simpa"], "tactic_count": 4}
{"name": "measurable_findGreatest'", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_findGreatest", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": true, "tactics": ["refine", "simp", "repeat", "apply_rules"], "tactic_count": 4}
{"name": "MeasurableSet.disjointed", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_find", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "Quot.instMeasurableSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quotient.instMeasurableSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.measurableSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurableSet_quotient", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_from_quotient", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_quotient_mk'", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_quotient_mk''", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_quot_mk", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.measurable_coe", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.measurable_from_quotient", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quotient.instDiscreteMeasurableSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.instDiscreteMeasurableSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.instMeasurableSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_subtype_coe", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.instMeasurableSingletonClass", "kind": "instance", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSet.of_subtype_image", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSet.subtype_image", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": true, "tactics": ["rintro", "rw", "exact"], "tactic_count": 3}
{"name": "Measurable.subtype_coe", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.subtype_mk", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.rangeFactorization", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.subtype_map", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_inclusion", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSet.image_inclusion'", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": true, "tactics": ["rcases", "convert", "ext", "simpa"], "tactic_count": 4}
{"name": "MeasurableSet.image_inclusion", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSet.of_union_cover", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "measurable_of_measurable_union_cover", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_of_restrict_of_restrict_compl", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.dite", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_of_measurable_on_compl_finite", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_of_measurable_on_compl_singleton", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurableAtom", "kind": "definition", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_measurableAtom_self", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "mem_of_mem_measurableAtom", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "measurableAtom_subset", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurableAtom_of_measurableSingletonClass", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSet.measurableAtom_of_countable", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": ["have", "simpa", "choose", "have", "apply", "intro", "simp", "intro", "exact", "apply", "intro", "simp", "exact", "rw", "exact"], "tactic_count": 15}
{"name": "measurableAtom_subset_of_mem", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": true, "tactics": ["intro", "simp", "exact"], "tactic_count": 3}
{"name": "measurableAtom_eq_of_mem", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": true, "tactics": ["refine", "by_cases", "exact", "exfalso", "simp", "obtain", "specialize", "exact"], "tactic_count": 8}
{"name": "disjoint_measurableAtom_of_notMem", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": true, "tactics": ["rw", "ext", "simp", "intro", "have", "have", "rw", "exact"], "tactic_count": 8}
{"name": "MeasurableSpace.prod", "kind": "definition", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instMeasurableSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_fst", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_snd", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.fst", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.snd", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.prod", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.prodMk", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.prodMap", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_prodMk_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_prodMk_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.of_uncurry_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.of_uncurry_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_fun_prod", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_swap", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_swap_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSet.prod", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurableSet_prod_of_nonempty", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": true, "tactics": ["rcases", "refine", "have", "have", "simp_all"], "tactic_count": 5}
{"name": "measurableSet_prod", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simp"], "tactic_count": 3}
{"name": "measurableSet_swap_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instMeasurableSingletonClass", "kind": "instance", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_from_prod_countable_left'", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_from_prod_countable_right'", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": true, "tactics": ["change", "exact"], "tactic_count": 2}
{"name": "measurable_from_prod_countable_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_from_prod_countable_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.find", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_iUnionLift", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_liftCover", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_measurable_piecewise", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": true, "tactics": ["inhabit", "set", "g", "have", "intro", "rcases", "rfl", "exact", "set", "have", "classical", "refine", "hfm.dite", "simp", "exact"], "tactic_count": 15}
{"name": "MeasurableSpace.pi", "kind": "instance", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_pi_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "measurable_pi_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.comap_le_comap_pi", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Measurable.eval", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_pi_lambda", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_update'", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": true, "tactics": ["rw", "intro", "dsimp", "split_ifs", "subst", "dsimp", "exact", "exact"], "tactic_count": 8}
{"name": "measurable_uniqueElim", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "measurable_updateFinset'", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": true, "tactics": ["simp", "intro", "by_cases"], "tactic_count": 3}
{"name": "measurable_updateFinset", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_updateFinset_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_update", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_update_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.measurable_restrict", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.measurable_restrict₂", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.measurable_restrict", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.measurable_restrict₂", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.measurable_restrict_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.measurable_restrict₂_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.measurable_restrict_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.measurable_restrict₂_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_eq_mp", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": true, "tactics": ["cases", "exact"], "tactic_count": 2}
{"name": "Measurable.eq_mp", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_piCongrLeft", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": true, "tactics": ["rw", "intro", "simp_rw", "exact"], "tactic_count": 4}
{"name": "MeasurableSet.pi", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasurableSet.univ_pi", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurableSet_pi_of_nonempty", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": true, "tactics": ["classical", "rcases", "refine", "convert", "rw", "exact"], "tactic_count": 6}
{"name": "measurableSet_pi", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simp"], "tactic_count": 3}
{"name": "Pi.instMeasurableSingletonClass", "kind": "instance", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_piEquivPiSubtypeProd_symm", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": true, "tactics": ["refine", "by_cases", "simp", "have", "measurable_pi_apply", "exact", "simp", "have", "measurable_pi_apply", "exact"], "tactic_count": 10}
{"name": "measurable_piEquivPiSubtypeProd", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TProd.instMeasurableSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_tProd_mk", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "measurable_tProd_elim", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_tProd_elim'", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSet.tProd", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "Sum.instMeasurableSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_inl", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_inr", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurableSet_sum_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_fun_sum", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.sumElim", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.sumMap", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurableSet_inl_image", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "measurableSet_inr_image", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "measurableSet_range_inl", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "measurableSet_range_inr", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Sigma.instMeasurableSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurableSet_setOf", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_mem", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.not", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.and", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.or", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.imp", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.forall", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.exists", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.eq_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.const_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": true, "tactics": ["conv", "exact"], "tactic_count": 2}
{"name": "Set.instMeasurableSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "Set.instMeasurableSingletonClass", "kind": "instance", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "measurable_setOf", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_set_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_set_mem", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_set_notMem", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurableSet_mem", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurableSet_notMem", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_compl", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSet.setOf_finite", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSet.setOf_infinite", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSet.sep_finite", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSet.sep_infinite", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.subset", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_curry", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_uncurry", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": true, "tactics": ["fun_prop"], "tactic_count": 1}
{"name": "measurable_equivCurry", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_equivCurry_symm", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_sigmaCurry", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_sigmaUncurry", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": true, "tactics": ["refine", "simp", "fun_prop"], "tactic_count": 3}
{"name": "measurable_piCurry", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_piCurry_symm", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurableSet_eq_fun", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instMeasurableSingletonClassOfMeasurableEq", "kind": "instance", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": true, "tactics": ["constructor", "simp_rw", "measurability"], "tactic_count": 3}
{"name": "instMeasurableEqOfMeasurableSingletonClassOfCountable", "kind": "instance", "module": "Mathlib.MeasureTheory.MeasurableSpace.Constructions", "is_tactic_proof": true, "tactics": ["constructor", "simp_rw", "measurability"], "tactic_count": 3}
{"name": "MeasurableSpace.countableGeneratingSet", "kind": "definition", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.countable_countableGeneratingSet", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.generateFrom_countableGeneratingSet", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.empty_mem_countableGeneratingSet", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.nonempty_countableGeneratingSet", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.measurableSet_countableGeneratingSet", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasurableSpace.natGeneratingSequence", "kind": "definition", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.generateFrom_natGeneratingSequence", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": true, "tactics": ["rw", "generateFrom_countableGeneratingSet]"], "tactic_count": 2}
{"name": "MeasurableSpace.measurableSet_natGeneratingSequence", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.CountablyGenerated.comap", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": true, "tactics": ["rcases", "rw", "letI", "exact"], "tactic_count": 4}
{"name": "MeasurableSpace.CountablyGenerated.sup", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "exact"], "tactic_count": 3}
{"name": "MeasurableSpace.instCountablyGeneratedOfCountable", "kind": "instance", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.instCountablyGeneratedSubtype", "kind": "instance", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.instCountablyGeneratedProd", "kind": "instance", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.separatesPoints_def", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.exists_measurableSet_of_ne", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": true, "tactics": ["contrapose", "exact"], "tactic_count": 2}
{"name": "MeasurableSpace.separatesPoints_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.separating_of_generateFrom", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": true, "tactics": ["letI", "intro", "rw", "exact"], "tactic_count": 4}
{"name": "MeasurableSpace.SeparatesPoints.mono", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_const_of_measurable_bot", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": false, "tactics": ["have", "by_contra", "obtain", "obtain", "absurd", "simp", "absurd", "simp", "obtain", "use", "use"], "tactic_count": 11}
{"name": "MeasurableSpace.countablySeparated_of_hasCountableSeparatingOn", "kind": "instance", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.hasCountableSeparatingOn_of_countablySeparated", "kind": "instance", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.countablySeparated_def", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.CountablySeparated.mono", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": true, "tactics": ["simp_rw", "rcases", "use"], "tactic_count": 3}
{"name": "MeasurableSpace.CountablySeparated.subtype_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasurableSpace.Subtype.separatesPoints", "kind": "instance", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.Subtype.countablySeparated", "kind": "instance", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasurableSpace.separatesPoints_of_measurableSingletonClass", "kind": "instance", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": true, "tactics": ["refine", "specialize", "simp_rw", "exact"], "tactic_count": 4}
{"name": "MeasurableSpace.MeasurableSingletonClass.of_separatesPoints", "kind": "instance", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.hasCountableSeparatingOn_of_countablySeparated_subtype", "kind": "instance", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.countablySeparated_subtype_of_hasCountableSeparatingOn", "kind": "instance", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.countablySeparated_of_separatesPoints", "kind": "instance", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": true, "tactics": ["rcases", "refine", "rw", "convert", "simp"], "tactic_count": 5}
{"name": "MeasurableSpace.exists_countablyGenerated_le_of_countablySeparated", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": true, "tactics": ["rcases", "refine", "use", "rw", "exact"], "tactic_count": 5}
{"name": "MeasurableSpace.mapNatBool", "kind": "definition", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.measurable_mapNatBool", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp", "apply"], "tactic_count": 4}
{"name": "MeasurableSpace.injective_mapNatBool", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": true, "tactics": ["intro", "rw", "apply", "rintro", "rw", "exact"], "tactic_count": 6}
{"name": "MeasurableSpace.measurableEquiv_nat_bool_of_countablyGenerated", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": false, "tactics": ["use", "simp_rw", "apply", "rintro", "rw", "refine", "rw", "simp"], "tactic_count": 8}
{"name": "MeasurableSpace.measurable_injection_nat_bool_of_countablySeparated", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": true, "tactics": ["rcases", "refine", "exact"], "tactic_count": 3}
{"name": "MeasurableSpace.measurableSingletonClass_of_countablySeparated", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": true, "tactics": ["rcases", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "MeasurableSpace.measurableSet_succ_memPartition", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": true, "tactics": ["rw", "refine", "refine", "rw", "exact"], "tactic_count": 5}
{"name": "MeasurableSpace.generateFrom_memPartition_le_succ", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.measurableSet_generateFrom_memPartition_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": true, "tactics": ["refine", "induction", "hC", "empty", "compl", "obtain", "classical", "refine", "simp", "exact", "simp", "refine", "refine", "refine", "refine", "exact", "rw", "simp", "rw", "iUnion", "choose", "have", "refine", "simp", "exact", "refine", "simp", "exact", "simp", "rw", "refine", "exact", "exact"], "tactic_count": 33}
{"name": "MeasurableSpace.measurableSet_generateFrom_memPartition", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": false, "tactics": ["have", "simp_rw", "rw", "refine", "refine", "rw", "exact"], "tactic_count": 7}
{"name": "MeasurableSpace.generateFrom_iUnion_memPartition", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": true, "tactics": ["refine", "simp", "obtain", "induction", "zero", "simp", "rw", "exact", "succ", "simp", "obtain", "rcases", "exact", "exact", "simp", "obtain", "exact"], "tactic_count": 17}
{"name": "MeasurableSpace.generateFrom_memPartition_le_range", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": true, "tactics": ["conv_rhs", "exact"], "tactic_count": 2}
{"name": "MeasurableSpace.generateFrom_iUnion_memPartition_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": true, "tactics": ["refine", "rintro", "exact"], "tactic_count": 3}
{"name": "MeasurableSpace.generateFrom_memPartition_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.measurableSet_memPartition", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.measurableSet_memPartitionSet", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.countablePartition", "kind": "definition", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.measurableSet_enumerateCountable_countableGeneratingSet", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.finite_countablePartition", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.instFinite_countablePartition", "kind": "instance", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.disjoint_countablePartition", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.sUnion_countablePartition", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.measurableSet_generateFrom_countablePartition_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.measurableSet_succ_countablePartition", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.generateFrom_countablePartition_le_succ", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.generateFrom_iUnion_countablePartition", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": true, "tactics": ["rw", "range_enumerateCountable_of_mem"], "tactic_count": 2}
{"name": "MeasurableSpace.generateFrom_countablePartition_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.measurableSet_countablePartition", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.countablePartitionSet", "kind": "definition", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.countablePartitionSet_mem", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.mem_countablePartitionSet", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.countablePartitionSet_eq_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.countablePartitionSet_of_mem", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.measurableSet_countablePartitionSet", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.instCountableOrCountablyGeneratedOfCountable", "kind": "instance", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.instCountableOrCountablyGeneratedOfCountablyGenerated", "kind": "instance", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.instCountableOrCountablyGeneratedProd", "kind": "instance", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "MeasurableSpace.countableOrCountablyGenerated_left_of_prod_left_of_nonempty", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": true, "tactics": ["rcases", "have", "infer_instance", "infer_instance"], "tactic_count": 4}
{"name": "MeasurableSpace.countableOrCountablyGenerated_right_of_prod_left_of_nonempty", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": true, "tactics": ["rcases", "have", "infer_instance", "infer_instance"], "tactic_count": 4}
{"name": "MeasurableSpace.countableOrCountablyGenerated_prod_left_swap", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated", "is_tactic_proof": true, "tactics": ["rcases", "refine", "exact"], "tactic_count": 3}
{"name": "instMeasurableSpaceOrderDual", "kind": "instance", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSet", "kind": "definition", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.termMeasurableSet[_]", "kind": "definition", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory._aux_Mathlib_MeasureTheory_MeasurableSpace_Defs___macroRules_MeasureTheory_termMeasurableSet[_]_1", "kind": "definition", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSet.empty", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSet.compl", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSet.of_compl", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSet.compl_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSet.univ", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsingleton.measurableSet", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSet.congr", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "MeasurableSet.iUnion", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": true, "tactics": ["cases", "simp", "rcases", "rw", "exact"], "tactic_count": 5}
{"name": "MeasurableSet.biUnion", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": true, "tactics": ["rw", "have", "exact"], "tactic_count": 3}
{"name": "Set.Finite.measurableSet_biUnion", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.measurableSet_biUnion", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSet.sUnion", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.Finite.measurableSet_sUnion", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSet.iInter", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSet.biInter", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.measurableSet_biInter", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.measurableSet_biInter", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSet.sInter", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.Finite.measurableSet_sInter", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSet.union", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasurableSet.inter", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasurableSet.diff", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSet.himp", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasurableSet.symmDiff", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSet.bihimp", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSet.ite", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSet.ite'", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": true, "tactics": ["split_ifs", "exacts"], "tactic_count": 2}
{"name": "MeasurableSet.cond", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": true, "tactics": ["cases", "exacts"], "tactic_count": 2}
{"name": "MeasurableSet.const", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "MeasurableSet.imp", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "MeasurableSet.iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "nonempty_measurable_superset", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.measurableSet_injective", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.ext", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSet.singleton", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurableSet_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSet.insert", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurableSet_insert", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": true, "tactics": ["classical", "exact"], "tactic_count": 2}
{"name": "Set.Subsingleton.measurableSet", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.measurableSet", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.measurableSet", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Countable.measurableSet", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasurableSpace.copy", "kind": "definition", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.measurableSet_copy", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.copy_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.instLE", "kind": "instance", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.le_def", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.instPartialOrder", "kind": "instance", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.GenerateMeasurable", "kind": "inductive", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.generateFrom", "kind": "definition", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.measurableSet_generateFrom", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.generateFrom_induction", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": true, "tactics": ["induction", "exacts"], "tactic_count": 2}
{"name": "MeasurableSpace.generateFrom_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.generateFrom_le_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.generateFrom_measurableSet", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.forall_generateFrom_mem_iff_mem_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": true, "tactics": ["refine", "apply", "exact", "rfl", "exact", "intro", "simp"], "tactic_count": 7}
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{"name": "MeasurableSpace.mkOfClosure_sets", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.giGenerateFrom", "kind": "definition", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.instCompleteLattice", "kind": "instance", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.instInhabited", "kind": "instance", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.generateFrom_mono", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.generateFrom_sup_generateFrom", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.iSup_generateFrom", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.generateFrom_empty", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasurableSpace.generateFrom_insert_empty", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasurableSpace.measurableSet_bot_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.measurableSet_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.measurableSet_inf", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.measurableSet_sInf", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.measurableSet_iInf", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasurableSpace.measurableSet_sup", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.measurableSet_sSup", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": true, "tactics": ["change", "simp"], "tactic_count": 2}
{"name": "MeasurableSpace.measurableSet_iSup", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasurableSpace.measurableSpace_iSup_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": true, "tactics": ["ext", "rw", "rfl"], "tactic_count": 3}
{"name": "MeasurableSpace.generateFrom_iUnion_measurableSet", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable", "kind": "definition", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.termMeasurable[_]", "kind": "definition", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "measurable_id", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_id'", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.comp", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.le", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDiscreteMeasurableSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSingletonClass.toDiscreteMeasurableSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSet.of_discrete", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.of_discrete", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteMeasurableSpace.toMeasurableSingletonClass", "kind": "instance", "module": "Mathlib.MeasureTheory.MeasurableSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEmbedding.measurableSet_image", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEmbedding.id", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEmbedding.comp", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEmbedding.subtype_coe", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEmbedding.measurableSet_range", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasurableEmbedding.measurableSet_preimage", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasurableEmbedding.measurable_rangeSplitting", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEmbedding.measurable_extend", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": true, "tactics": ["refine", "rw", "simpa", "rw", "exact"], "tactic_count": 5}
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{"name": "MeasurableSet.of_union₃_range_cover", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": ["convert", "simp"], "tactic_count": 2}
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{"name": "Measurable.of_union₃_range_cover", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "term_≃ᵐ_", "kind": "definition", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_MeasureTheory_MeasurableSpace_Embedding___macroRules_term_≃ᵐ__1", "kind": "definition", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_MeasureTheory_MeasurableSpace_Embedding___unexpand_MeasurableEquiv_1", "kind": "definition", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.toEquiv_injective", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": true, "tactics": ["rintro", "rfl"], "tactic_count": 2}
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{"name": "MeasurableEquiv.coe_toEquiv", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.measurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasurableEquiv.coe_toEquiv_symm", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasurableEquiv.self_comp_symm", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.apply_symm_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasurableEquiv.injective", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.symm_preimage_preimage", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.image_eq_preimage_symm", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.preimage_symm", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.image_symm", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.eq_image_iff_symm_image_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasurableEquiv.image_preimage", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasurableEquiv.preimage_image", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasurableEquiv.measurableSet_preimage", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasurableEquiv.measurableEmbedding", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasurableEquiv.ulift", "kind": "definition", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasurableEquiv.ofUniqueOfUnique", "kind": "definition", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.prodCongr", "kind": "definition", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.prodComm", "kind": "definition", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.prodAssoc", "kind": "definition", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.punitProd", "kind": "definition", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.prodPUnit", "kind": "definition", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.sumCongr", "kind": "definition", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.Set.prod", "kind": "definition", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.Set.univ", "kind": "definition", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.Set.singleton", "kind": "definition", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.Set.rangeInl", "kind": "definition", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.Set.rangeInr", "kind": "definition", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.sumProdDistrib", "kind": "definition", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.prodSumDistrib", "kind": "definition", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.sumProdSum", "kind": "definition", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.piCongrRight", "kind": "definition", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.piCongrLeft", "kind": "definition", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.coe_piCongrLeft", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "MeasurableEquiv.piCongrLeft_apply_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "MeasurableEquiv.arrowCongr'", "kind": "definition", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.piMeasurableEquivTProd", "kind": "definition", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.piUnique", "kind": "definition", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.funUnique", "kind": "definition", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.piFinTwo", "kind": "definition", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.finTwoArrow", "kind": "definition", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.piFinSuccAbove", "kind": "definition", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.piEquivPiSubtypeProd", "kind": "definition", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.sumPiEquivProdPi", "kind": "definition", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.coe_sumPiEquivProdPi", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "MeasurableEquiv.coe_sumPiEquivProdPi_symm", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "MeasurableEquiv.piOptionEquivProd", "kind": "definition", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.piFinsetUnion", "kind": "definition", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.sumCompl", "kind": "definition", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.ofInvolutive", "kind": "definition", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.ofInvolutive_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.ofInvolutive_symm", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.setOf", "kind": "definition", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.coe_setOf", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEmbedding.comap_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEmbedding.iff_comap_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEmbedding.equivImage", "kind": "definition", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEmbedding.equivRange", "kind": "definition", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEmbedding.of_measurable_inverse_on_range", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": ["set", "exact"], "tactic_count": 2}
{"name": "MeasurableEmbedding.of_measurable_inverse", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEmbedding.schroederBernstein", "kind": "definition", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": ["let", "suffices", "classical", "rcases", "let", "have", "refine", "apply", "have", "apply", "rw", "simp", "rw", "exact", "have", "compl_subset_compl.mpr", "let", "refine", "refine", "induction", "zero", "succ", "rw", "exact", "apply", "apply", "intro", "cases", "exact", "rw", "exact", "rintro", "rw", "apply", "rw", "rw", "intro", "specialize", "rw", "by_contra", "apply", "exact"], "tactic_count": 42}
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{"name": "MeasurableEmbedding.equivRange_symm_apply_mk", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": true, "tactics": ["nth_rw", "rw"], "tactic_count": 2}
{"name": "MeasurableEmbedding.invFun", "kind": "definition", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEmbedding.measurable_invFun", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEmbedding.leftInverse_invFun", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": true, "tactics": ["intro", "simp"], "tactic_count": 2}
{"name": "MeasurableSpace.comap_compl", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": true, "tactics": ["rw", "congr", "exact"], "tactic_count": 3}
{"name": "MeasurableSpace.comap_not", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.piCurry", "kind": "definition", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.coe_piCurry", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.coe_piCurry_symm", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.curry", "kind": "definition", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.coe_curry", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.coe_curry_symm", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Embedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eventuallyMeasurableSpace", "kind": "definition", "module": "Mathlib.MeasureTheory.MeasurableSpace.EventuallyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EventuallyMeasurableSet", "kind": "definition", "module": "Mathlib.MeasureTheory.MeasurableSpace.EventuallyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSet.eventuallyMeasurableSet", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.EventuallyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_eventuallyMeasurableSpace", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.EventuallyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eventuallyMeasurableSet_of_mem_filter", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.EventuallyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EventuallyMeasurableSet.congr", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.EventuallyMeasurable", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
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{"name": "EventuallyMeasurable", "kind": "definition", "module": "Mathlib.MeasureTheory.MeasurableSpace.EventuallyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.eventuallyMeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.EventuallyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.comp_eventuallyMeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.EventuallyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EventuallyMeasurable.congr", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.EventuallyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.eventuallyMeasurable_of_eventuallyEq", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.EventuallyMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Empty.instMeasurableSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.MeasurableSpace.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PUnit.instMeasurableSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.MeasurableSpace.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bool.instMeasurableSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.MeasurableSpace.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prop.instMeasurableSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.MeasurableSpace.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Subsingleton.measurableSingletonClass", "kind": "instance", "module": "Mathlib.MeasureTheory.MeasurableSpace.Instances", "is_tactic_proof": true, "tactics": ["refine", "convert", "simp"], "tactic_count": 3}
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{"name": "MeasurableSpace.invariants", "kind": "definition", "module": "Mathlib.MeasureTheory.MeasurableSpace.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.measurableSet_invariants", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.invariants_id", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasurableSpace.inf_le_invariants_comp", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasurableSpace.comp_eq_of_measurable_invariants", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Invariants", "is_tactic_proof": true, "tactics": ["funext", "suffices", "rw"], "tactic_count": 3}
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{"name": "Filter.Eventually.exists_measurable_mem", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.MeasurablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasurableSet.coe_inter", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.MeasurablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSet.Subtype.instInf", "kind": "instance", "module": "Mathlib.MeasureTheory.MeasurableSpace.MeasurablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSet.inf_eq_inter", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.MeasurablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSet.Subtype.instSDiff", "kind": "instance", "module": "Mathlib.MeasureTheory.MeasurableSpace.MeasurablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSet.Subtype.instHImp", "kind": "instance", "module": "Mathlib.MeasureTheory.MeasurableSpace.MeasurablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSet.coe_sdiff", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.MeasurablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSet.coe_himp", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.MeasurablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSet.Subtype.instBot", "kind": "instance", "module": "Mathlib.MeasureTheory.MeasurableSpace.MeasurablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSet.coe_bot", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.MeasurablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSet.Subtype.instTop", "kind": "instance", "module": "Mathlib.MeasureTheory.MeasurableSpace.MeasurablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSet.coe_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.MeasurablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSet.Subtype.instBooleanAlgebra", "kind": "instance", "module": "Mathlib.MeasureTheory.MeasurableSpace.MeasurablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSet.measurableSet_blimsup", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.MeasurablyGenerated", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "MeasurableSet.measurableSet_bliminf", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.MeasurablyGenerated", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "MeasurableSet.measurableSet_limsup", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.MeasurablyGenerated", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasurableSet.measurableSet_liminf", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.MeasurablyGenerated", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "measurable_encard", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.NCard", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_ncard", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.NCard", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.pi_eq_generateFrom_projections", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Pi", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsPiSystem.pi", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Pi", "is_tactic_proof": true, "tactics": ["rintro", "rw", "exact"], "tactic_count": 3}
{"name": "isPiSystem_pi", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCountablySpanning.pi", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Pi", "is_tactic_proof": true, "tactics": ["choose", "cases", "let", "refine", "simp_rw", "iUnion_univ_pi"], "tactic_count": 6}
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{"name": "generateFrom_eq_pi", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Pi", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "generateFrom_pi", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Preorder.measurable_restrictLe", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.PreorderRestrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Preorder.measurable_restrictLe₂", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.PreorderRestrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Preorder.measurable_frestrictLe", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.PreorderRestrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Preorder.measurable_frestrictLe₂", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.PreorderRestrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "generateFrom_prod_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Prod", "is_tactic_proof": true, "tactics": ["apply", "refine", "rcases", "rw", "apply", "intro", "apply", "exact", "rcases", "rw", "apply", "rintro", "apply", "exact", "apply", "rintro", "dsimp", "rw", "apply", "exact", "exact"], "tactic_count": 21}
{"name": "generateFrom_eq_prod", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Prod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "generateFrom_prod", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isPiSystem_prod", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.comap_prodMk", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Prod", "is_tactic_proof": true, "tactics": ["simp_rw", "rfl"], "tactic_count": 2}
{"name": "MeasurableSpace.comap_prodMap", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Prod", "is_tactic_proof": true, "tactics": ["simp_rw", "rfl"], "tactic_count": 2}
{"name": "MeasurableEmbedding.prodMap", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Prod", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "rw", "exact"], "tactic_count": 5}
{"name": "MeasurableEmbedding.prodMk_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurableEmbedding_prodMk_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEmbedding.prodMk_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurableEmbedding_prod_mk_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.MeasurableSpace.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEDisjoint", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.AEDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.exists_null_pairwise_disjoint_diff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEDisjoint", "is_tactic_proof": false, "tactics": ["refine", "simp", "exact", "simp", "intro", "replace", "simp", "exact"], "tactic_count": 8}
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{"name": "MeasureTheory.AEDisjoint.symm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEDisjoint", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "MeasureTheory.AEDisjoint.symmetric", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEDisjoint.comm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Disjoint.aedisjoint", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEDisjoint", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Pairwise.aedisjoint", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.PairwiseDisjoint.aedisjoint", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEDisjoint.mono_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEDisjoint.mono", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEDisjoint.congr", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEDisjoint.iUnion_left_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEDisjoint", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.AEDisjoint.iUnion_right_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEDisjoint", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.AEDisjoint.union_left_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEDisjoint", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.AEDisjoint.union_right_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEDisjoint", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.AEDisjoint.union_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEDisjoint.union_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEDisjoint.diff_ae_eq_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEDisjoint.diff_ae_eq_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEDisjoint.measure_diff_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEDisjoint.measure_diff_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEDisjoint.exists_disjoint_diff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEDisjoint.of_null_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEDisjoint.of_null_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.aedisjoint_compl_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.aedisjoint_compl_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsingleton.aemeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "aemeasurable_of_subsingleton_codomain", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "aemeasurable_zero_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEMeasurable", "is_tactic_proof": true, "tactics": ["nontriviality", "exact"], "tactic_count": 2}
{"name": "aemeasurable_id''", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "aemeasurable_of_map_neZero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEMeasurable", "is_tactic_proof": true, "tactics": ["by_contra", "simp"], "tactic_count": 2}
{"name": "AEMeasurable.mono_ac", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.mono_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.mono_set", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.mono'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.ae_mem_imp_eq_mk", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.ae_inf_principal_eq_mk", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.sum_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEMeasurable", "is_tactic_proof": true, "tactics": ["classical", "nontriviality", "inhabit", "set", "have", "intro", "rw", "exact", "have", "have", "intro", "contrapose", "exact", "set", "refine", "rw", "simp", "exact", "rw", "intro", "refine", "ext", "simp", "constructor", "rintro", "rwa", "rcases", "rw", "exact", "refine", "contrapose", "refine", "exact"], "tactic_count": 33}
{"name": "aemeasurable_sum_measure_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "aemeasurable_add_measure_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEMeasurable", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "AEMeasurable.add_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.iUnion", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "aemeasurable_iUnion_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "aemeasurable_union_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEMeasurable", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AEMeasurable.smul_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.comp_aemeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.comp_aemeasurable'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.comp_measurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.comp_quasiMeasurePreserving", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.map_map_of_aemeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEMeasurable", "is_tactic_proof": true, "tactics": ["ext1", "rw", "map_apply_of_aemeasurable"], "tactic_count": 3}
{"name": "AEMeasurable.fst", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.snd", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.prodMk", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nullMeasurableSet_eq_fun", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.exists_ae_eq_range_subset", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEMeasurable", "is_tactic_proof": true, "tactics": ["classical", "let", "let", "refine", "exact", "rintro", "by_cases", "simpa", "simp", "contrapose", "apply", "simp", "have", "rw", "exact", "filter_upwards", "rw", "simp", "contrapose", "apply", "simp"], "tactic_count": 21}
{"name": "AEMeasurable.exists_measurable_nonneg", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEMeasurable", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "AEMeasurable.subtype_mk", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEMeasurable", "is_tactic_proof": true, "tactics": ["nontriviality", "obtain", "h.exists_ae_eq_range_subset", "refine", "filter_upwards", "simpa"], "tactic_count": 6}
{"name": "aemeasurable_const'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEMeasurable", "is_tactic_proof": true, "tactics": ["rcases", "exact", "haveI", "rcases", "exact"], "tactic_count": 5}
{"name": "aemeasurable_uIoc_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEMeasurable", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "aemeasurable_iff_measurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEmbedding.aemeasurable_map_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEMeasurable", "is_tactic_proof": true, "tactics": ["refine", "rintro", "rcases", "exact"], "tactic_count": 4}
{"name": "MeasurableEmbedding.aemeasurable_comp_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEMeasurable", "is_tactic_proof": true, "tactics": ["refine", "suffices", "rwa", "exact"], "tactic_count": 4}
{"name": "aemeasurable_restrict_iff_comap_subtype", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEMeasurable", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "aemeasurable_one", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "aemeasurable_smul_measure_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "aemeasurable_of_aemeasurable_trim", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "aemeasurable_restrict_of_measurable_subtype", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "aemeasurable_map_equiv_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.restrict", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "aemeasurable_Ioi_of_forall_Ioc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEMeasurable", "is_tactic_proof": true, "tactics": ["haveI", "obtain", "have", "rw", "exact", "rw", "intro", "rcases", "exact", "rw", "exact"], "tactic_count": 11}
{"name": "aemeasurable_indicator_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEMeasurable", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "intro", "refine", "have", "have", "exact"], "tactic_count": 8}
{"name": "aemeasurable_indicator_iff₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEMeasurable", "is_tactic_proof": true, "tactics": ["rcases", "rw", "restrict_congr_set"], "tactic_count": 3}
{"name": "aemeasurable_indicator_const_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEMeasurable", "is_tactic_proof": true, "tactics": ["classical", "constructor", "convert", "rw", "simp", "exact"], "tactic_count": 6}
{"name": "AEMeasurable.indicator", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.indicator₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.restrict_map_of_aemeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.map_mono_of_aemeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.NullMeasurable.aemeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEMeasurable", "is_tactic_proof": true, "tactics": ["classical", "nontriviality", "rcases", "choose", "choose", "set", "have", "have", "refine", "measure_mono_null", "refine", "rw", "apply", "rw", "refine", "rw", "convert", "rw", "refine", "exact"], "tactic_count": 20}
{"name": "MeasureTheory.NullMeasurable.aemeasurable_of_aerange", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEMeasurable", "is_tactic_proof": true, "tactics": ["rcases", "obtain", "apply", "rw", "obtain", "h.measurable'.aemeasurable.exists_ae_eq_range_subset", "rw", "lift", "replace", "exact"], "tactic_count": 10}
{"name": "MeasureTheory.Measure.map_sum", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AEMeasurable", "is_tactic_proof": true, "tactics": ["ext", "rw", "have", "simp_rw"], "tactic_count": 4}
{"name": "MeasureTheory.Measure.instSFiniteMap", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.AEMeasurable", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "rw", "infer_instance", "rw", "infer_instance"], "tactic_count": 6}
{"name": "MeasureTheory.Measure.AbsolutelyContinuous", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.AbsolutelyContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.term_≪_", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.AbsolutelyContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory._aux_Mathlib_MeasureTheory_Measure_AbsolutelyContinuous___macroRules_MeasureTheory_term_≪__1", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.AbsolutelyContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory._aux_Mathlib_MeasureTheory_Measure_AbsolutelyContinuous___unexpand_MeasureTheory_Measure_AbsolutelyContinuous_1", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.AbsolutelyContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.absolutelyContinuous_of_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AbsolutelyContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.absolutelyContinuous_of_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AbsolutelyContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.AbsolutelyContinuous.mk", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AbsolutelyContinuous", "is_tactic_proof": true, "tactics": ["intro", "rcases", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.AbsolutelyContinuous.refl", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AbsolutelyContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.AbsolutelyContinuous.rfl", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AbsolutelyContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.AbsolutelyContinuous.instRefl", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.AbsolutelyContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.AbsolutelyContinuous.zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AbsolutelyContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.AbsolutelyContinuous.trans", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AbsolutelyContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.AbsolutelyContinuous.map", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AbsolutelyContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.AbsolutelyContinuous.smul_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AbsolutelyContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.AbsolutelyContinuous.smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AbsolutelyContinuous", "is_tactic_proof": true, "tactics": ["intro", "rw", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.AbsolutelyContinuous.add", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AbsolutelyContinuous", "is_tactic_proof": true, "tactics": ["intro", "simp", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.AbsolutelyContinuous.add_left_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AbsolutelyContinuous", "is_tactic_proof": true, "tactics": ["refine", "have", "exact", "rw", "exact"], "tactic_count": 5}
{"name": "MeasureTheory.Measure.AbsolutelyContinuous.add_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AbsolutelyContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.AbsolutelyContinuous.add_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AbsolutelyContinuous", "is_tactic_proof": true, "tactics": ["intro", "simp", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.AbsolutelyContinuous.null_mono", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AbsolutelyContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.AbsolutelyContinuous.pos_mono", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AbsolutelyContinuous", "is_tactic_proof": true, "tactics": ["contrapose", "simp_all"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.absolutelyContinuous_zero_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AbsolutelyContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.absolutelyContinuous_sum_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AbsolutelyContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.absolutelyContinuous_sum_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AbsolutelyContinuous", "is_tactic_proof": true, "tactics": ["refine", "simp", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.smul_absolutelyContinuous", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AbsolutelyContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.absolutelyContinuous_of_le_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AbsolutelyContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.absolutelyContinuous_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AbsolutelyContinuous", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.ae_le_iff_absolutelyContinuous", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AbsolutelyContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.AbsolutelyContinuous.ae_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AbsolutelyContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEDisjoint.of_absolutelyContinuous", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AbsolutelyContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AEDisjoint.of_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AbsolutelyContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.ae_mono", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AbsolutelyContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEmbedding.absolutelyContinuous_map", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AbsolutelyContinuous", "is_tactic_proof": true, "tactics": ["intro", "rw", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.instInhabitedAddContent", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.AddContent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.instFunLikeAddContentSet", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.AddContent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AddContent.ext", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AddContent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.addContent_empty", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AddContent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.addContent_sUnion", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AddContent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.addContent_biUnion", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AddContent", "is_tactic_proof": true, "tactics": ["classical", "have", "rw", "grind", "simpa", "rwa", "rw", "refine", "grind"], "tactic_count": 9}
{"name": "MeasureTheory.addContent_iUnion", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AddContent", "is_tactic_proof": true, "tactics": ["convert", "simp", "simpa", "simpa", "simpa"], "tactic_count": 5}
{"name": "MeasureTheory.addContent_union'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AddContent", "is_tactic_proof": true, "tactics": ["have", "convert", "simp", "fin_cases", "fin_cases", "rwa"], "tactic_count": 6}
{"name": "MeasureTheory.AddContent.IsSigmaSubadditive", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.AddContent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.addContent_eq_add_disjointOfDiffUnion_of_subset", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AddContent", "is_tactic_proof": true, "tactics": ["classical", "conv_lhs", "rw", "rw", "exact", "rw", "exact", "rw", "exact", "rwa"], "tactic_count": 10}
{"name": "MeasureTheory.eq_add_disjointOfDiff_of_subset", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AddContent", "is_tactic_proof": true, "tactics": ["classical", "conv_lhs", "rw", "rw", "exact", "rw", "exact", "rw", "exact", "rw", "rwa"], "tactic_count": 11}
{"name": "MeasureTheory.sum_addContent_eq_of_sUnion_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AddContent", "is_tactic_proof": true, "tactics": ["calc", "apply", "have", "simp_rw", "exact", "nth_rewrite", "apply", "exact", "exact", "rw", "exact", "apply", "have", "simp_rw", "exact", "nth_rewrite", "apply", "exact", "exact", "rw", "exact"], "tactic_count": 21}
{"name": "_private.Mathlib.MeasureTheory.Measure.AddContent.0.MeasureTheory.AddContent.supClosureFun", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.AddContent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.MeasureTheory.Measure.AddContent.0.MeasureTheory.AddContent.supClosureFun_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AddContent", "is_tactic_proof": false, "tactics": ["have", "simp", "apply", "rw", "exact"], "tactic_count": 5}
{"name": "_private.Mathlib.MeasureTheory.Measure.AddContent.0.MeasureTheory.AddContent.supClosureFun_apply_of_mem", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AddContent", "is_tactic_proof": true, "tactics": ["have", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.AddContent.supClosure", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.AddContent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AddContent.supClosure_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AddContent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AddContent.supClosure_apply_finpartition", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AddContent", "is_tactic_proof": true, "tactics": ["rw", "nth_rewrite", "rfl"], "tactic_count": 3}
{"name": "MeasureTheory.AddContent.supClosure_apply_of_mem", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AddContent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.sum_addContent_le_of_subset", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AddContent", "is_tactic_proof": true, "tactics": ["classical", "rw", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.addContent_mono", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AddContent", "is_tactic_proof": true, "tactics": ["have", "simpa", "rwa", "simp", "simp"], "tactic_count": 5}
{"name": "MeasureTheory.addContent_sUnion_le_sum", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AddContent", "is_tactic_proof": true, "tactics": ["classical", "have", "simp", "exact", "have", "id", "simp", "exact", "have", "simp", "exact", "rw", "gcongr", "refine", "sum_addContent_le_of_subset", "simp", "exact"], "tactic_count": 17}
{"name": "MeasureTheory.addContent_le_sum_of_subset_sUnion", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AddContent", "is_tactic_proof": true, "tactics": ["classical", "let", "have", "rw", "rwa", "rw", "refine", "intro", "simp", "rintro", "exact", "rwa", "refine", "exact"], "tactic_count": 14}
{"name": "MeasureTheory.addContent_iUnion_eq_tsum_of_disjoint_of_addContent_iUnion_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AddContent", "is_tactic_proof": true, "tactics": ["refine", "refine", "classical", "rw", "refine", "simp", "refine", "rintro", "exact", "simp", "intro", "rw", "obtain", "obtain", "have", "exact", "simp", "exact"], "tactic_count": 18}
{"name": "MeasureTheory.addContent_iUnion_eq_tsum_of_disjoint_of_IsSigmaSubadditive", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AddContent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AddContent.onIocAux", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.AddContent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AddContent.onIocAux_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AddContent", "is_tactic_proof": true, "tactics": ["have", "simp", "set", "set", "have", "rcases", "grind", "rw", "grind"], "tactic_count": 9}
{"name": "MeasureTheory.AddContent.onIocAux_empty", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AddContent", "is_tactic_proof": true, "tactics": ["classical", "rw", "grind"], "tactic_count": 3}
{"name": "MeasureTheory.AddContent.onIoc", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.AddContent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AddContent.onIoc_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AddContent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AddContent.extend", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.AddContent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AddContent.extend_eq_extend", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AddContent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AddContent.extend_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AddContent", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "MeasureTheory.AddContent.extend_eq_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AddContent", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "MeasureTheory.addContent_union", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AddContent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.addContent_biUnion_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AddContent", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "insert", "rw", "simp_rw", "simp", "simp", "rw", "refine", "rw", "exact"], "tactic_count": 12}
{"name": "MeasureTheory.addContent_accumulate", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AddContent", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "exact", "exact"], "tactic_count": 6}
{"name": "MeasureTheory.IsSetRing.addContent_of_union", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.AddContent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.addContent_union_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AddContent", "is_tactic_proof": true, "tactics": ["rw", "exact", "rw"], "tactic_count": 3}
{"name": "MeasureTheory.addContent_biUnion_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AddContent", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "insert", "rw", "simp_rw", "simp", "refine", "exact"], "tactic_count": 9}
{"name": "MeasureTheory.le_addContent_diff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AddContent", "is_tactic_proof": true, "tactics": ["conv_lhs", "rw", "refine", "rw"], "tactic_count": 4}
{"name": "MeasureTheory.addContent_diff_of_ne_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AddContent", "is_tactic_proof": false, "tactics": ["have", "simp_rw", "rw"], "tactic_count": 3}
{"name": "MeasureTheory.addContent_iUnion_eq_sum_of_tendsto_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AddContent", "is_tactic_proof": true, "tactics": ["let", "have", "have", "refine", "intro", "rw", "exact", "simp_rw", "rw", "exact", "have", "rw", "addContent_accumulate", "simp_rw", "refine", "refine", "rwa", "rw", "exact"], "tactic_count": 19}
{"name": "MeasureTheory.tendsto_atTop_addContent_iUnion_of_addContent_iUnion_eq_tsum", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AddContent", "is_tactic_proof": false, "tactics": ["rw", "have", "nth_rw", "partialSups_disjointed,", "rfl", "simp_rw", "refine", "exact"], "tactic_count": 8}
{"name": "MeasureTheory.isSigmaSubadditive_of_addContent_iUnion_eq_tsum", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.AddContent", "is_tactic_proof": true, "tactics": ["intro", "have", "rw", "refine", "tendsto_atTop_addContent_iUnion_of_addContent_iUnion_eq_tsum", "rwa", "have", "rw", "exact", "refine", "rw", "exact"], "tactic_count": 12}
{"name": "BoundedContinuousFunction.innerProbChar", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.CharacteristicFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.innerProbChar_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.CharacteristicFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.innerProbChar_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.CharacteristicFunction", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "BoundedContinuousFunction.probCharDual", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.CharacteristicFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.probCharDual_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.CharacteristicFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.probCharDual_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.CharacteristicFunction", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.ext_of_integral_char_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.CharacteristicFunction", "is_tactic_proof": false, "tactics": ["apply", "ext_of_forall_mem_subalgebra_integral_eq_of_pseudoEMetric_complete_countable", "intro", "simp", "obtain", "rw", "have", "integral_finset_sum", "rw", "apply", "simp", "exact"], "tactic_count": 12}
{"name": "MeasureTheory.charFun", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.CharacteristicFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.charFun_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.CharacteristicFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.charFun_apply_real", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.CharacteristicFunction", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.charFun_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.CharacteristicFunction", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.charFun_zero_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.CharacteristicFunction", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.charFun_neg", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.CharacteristicFunction", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.charFun_eq_integral_innerProbChar", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.CharacteristicFunction", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.charFun_eq_integral_probChar", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.CharacteristicFunction", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.charFun_eq_fourierIntegral", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.CharacteristicFunction", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.charFun_eq_fourierIntegral'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.CharacteristicFunction", "is_tactic_proof": false, "tactics": ["simp", "inner_smul_right,", "ofReal_ofNat,", "congr", "rw"], "tactic_count": 5}
{"name": "MeasureTheory.norm_charFun_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.CharacteristicFunction", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.norm_charFun_le_one", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.CharacteristicFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.norm_one_sub_charFun_le_two", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.CharacteristicFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.stronglyMeasurable_charFun", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.CharacteristicFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measurable_charFun", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.CharacteristicFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.intervalIntegrable_charFun", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.CharacteristicFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.charFun_map_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.CharacteristicFunction", "is_tactic_proof": true, "tactics": ["rw", "simp_rw"], "tactic_count": 2}
{"name": "MeasureTheory.charFun_map_mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.CharacteristicFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.charFun_dirac", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.CharacteristicFunction", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.charFun_map_add_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.CharacteristicFunction", "is_tactic_proof": true, "tactics": ["rw", "congr", "rw", "congr", "rw", "simp", "ring"], "tactic_count": 7}
{"name": "MeasureTheory.charFun_map_const_add", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.CharacteristicFunction", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.ext_of_charFun", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.CharacteristicFunction", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "exact", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.charFun_conv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.CharacteristicFunction", "is_tactic_proof": true, "tactics": ["simp_rw", "rw", "simp", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.charFun_prod", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.CharacteristicFunction", "is_tactic_proof": true, "tactics": ["simp_rw", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.charFun_eq_prod_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.CharacteristicFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.charFun_pi", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.CharacteristicFunction", "is_tactic_proof": false, "tactics": ["simp_rw", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.charFun_eq_pi_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.CharacteristicFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.charFunDual", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.CharacteristicFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.charFunDual_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.CharacteristicFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.charFunDual_eq_charFun_map_one", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.CharacteristicFunction", "is_tactic_proof": true, "tactics": ["rw", "have", "rw", "fun_prop", "exact", "rw", "simp"], "tactic_count": 7}
{"name": "MeasureTheory.charFun_map_eq_charFunDual_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.CharacteristicFunction", "is_tactic_proof": true, "tactics": ["rw", "have", "rw", "simp", "fun_prop", "exact", "rw", "simp"], "tactic_count": 8}
{"name": "MeasureTheory.charFun_eq_charFunDual_toDualMap", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.CharacteristicFunction", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.charFun_toDual_symm_eq_charFunDual", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.CharacteristicFunction", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.charFunDual_map", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.CharacteristicFunction", "is_tactic_proof": false, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.charFunDual_dirac", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.CharacteristicFunction", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.charFunDual_map_add_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.CharacteristicFunction", "is_tactic_proof": true, "tactics": ["rw", "congr", "rw", "congr", "simp", "ring"], "tactic_count": 6}
{"name": "MeasureTheory.charFunDual_map_const_add", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.CharacteristicFunction", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.charFunDual_prod", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.CharacteristicFunction", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MeasureTheory.charFunDual_prod'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.CharacteristicFunction", "is_tactic_proof": false, "tactics": ["simp_rw", "rw", "simp"], "tactic_count": 3}
{"name": "MeasureTheory.charFunDual_pi", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.CharacteristicFunction", "is_tactic_proof": true, "tactics": ["simp_rw", "integral_fintype_prod_eq_prod]"], "tactic_count": 2}
{"name": "MeasureTheory.charFunDual_pi'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.CharacteristicFunction", "is_tactic_proof": false, "tactics": ["simp_rw", "rw", "simp"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.ext_of_charFunDual", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.CharacteristicFunction", "is_tactic_proof": true, "tactics": ["refine", "intro", "rw", "simp", "change", "by_contra", "exact", "exact"], "tactic_count": 8}
{"name": "MeasureTheory.charFunDual_eq_prod_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.CharacteristicFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.charFunDual_eq_prod_iff'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.CharacteristicFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.charFunDual_eq_pi_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.CharacteristicFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.charFunDual_eq_pi_iff'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.CharacteristicFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.charFunDual_conv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.CharacteristicFunction", "is_tactic_proof": true, "tactics": ["simp_rw", "rw", "simp", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.Measure.comapₗ", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Comap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.comapₗ_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Comap", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.comap", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Comap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.comap_apply₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Comap", "is_tactic_proof": true, "tactics": ["rw", "rw"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.comap_undef", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Comap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.le_comap_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Comap", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.comap_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Comap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.comap_apply_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Comap", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "simp"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.comapₗ_eq_comap", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Comap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.measure_image_eq_zero_of_comap_eq_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Comap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.ae_eq_image_of_ae_eq_comap", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Comap", "is_tactic_proof": true, "tactics": ["rw", "have", "ext1", "simp", "tauto", "have", "ext1", "simp", "tauto", "rw", "rw", "rw", "exact"], "tactic_count": 13}
{"name": "MeasureTheory.Measure.NullMeasurableSet.image", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Comap", "is_tactic_proof": true, "tactics": ["refine", "refine", "swap", "exact", "have", "exact"], "tactic_count": 6}
{"name": "MeasureTheory.Measure.comap_preimage", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Comap", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.comap_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Comap", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "simp"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.comap_id", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Comap", "is_tactic_proof": true, "tactics": ["ext", "rw", "exact", "all_goals"], "tactic_count": 4}
{"name": "MeasureTheory.Measure.comap_comap", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Comap", "is_tactic_proof": true, "tactics": ["by_cases", "ext", "rw", "comap_apply", "rw"], "tactic_count": 5}
{"name": "MeasureTheory.Measure.comap_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Comap", "is_tactic_proof": true, "tactics": ["obtain", "simp", "by_cases", "ext", "rw", "comap_apply₀", "simpa", "have", "simpa", "simp"], "tactic_count": 10}
{"name": "MeasurableEmbedding.comap_add", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Comap", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "MeasurableEquiv.comap_symm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Comap", "is_tactic_proof": true, "tactics": ["ext", "rw", "exact"], "tactic_count": 3}
{"name": "MeasurableEquiv.map_symm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Comap", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.comap_swap", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Comap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.ComplexMeasure", "kind": "abbrev", "module": "Mathlib.MeasureTheory.Measure.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.ComplexMeasure.re", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.ComplexMeasure.im", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SignedMeasure.toComplexMeasure", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SignedMeasure.toComplexMeasure_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.ComplexMeasure.toComplexMeasure_to_signedMeasure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SignedMeasure.re_toComplexMeasure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SignedMeasure.im_toComplexMeasure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.ComplexMeasure.equivSignedMeasure", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.ComplexMeasure.equivSignedMeasureₗ", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.ComplexMeasure.absolutelyContinuous_ennreal_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Complex", "is_tactic_proof": true, "tactics": ["constructor", "constructor", "intro", "rw", "exacts"], "tactic_count": 5}
{"name": "MeasureTheory.instInhabitedContent", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Content", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Content.instFunLikeCompactsENNReal", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Content", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Content.toFun_eq_toNNReal_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Content", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Content.mk_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Content", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Content.apply_ne_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Content", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Content.mono", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Content", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.Content.sup_disjoint", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Content", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.Content.sup_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Content", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.Content.lt_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Content", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Content.empty", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Content", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.Content.innerContent", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Content", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Content.le_innerContent", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Content", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Content.innerContent_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Content", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Content.innerContent_of_isCompact", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Content", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Content.innerContent_bot", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Content", "is_tactic_proof": true, "tactics": ["refine", "rw", "refine", "have", "ext1", "rw", "rw"], "tactic_count": 7}
{"name": "MeasureTheory.Content.innerContent_mono", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Content", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Content.innerContent_exists_compact", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Content", "is_tactic_proof": true, "tactics": ["have", "rcases", "exact", "have", "conv", "simp", "rcases", "rw"], "tactic_count": 8}
{"name": "MeasureTheory.Content.innerContent_iSup_nat", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Content", "is_tactic_proof": false, "tactics": ["have", "intro", "refine", "simp", "intro", "grw", "refine", "obtain", "rcases", "let", "convert", "ext1", "rw", "exact", "refine", "intro", "refine", "refine", "rfl"], "tactic_count": 19}
{"name": "MeasureTheory.Content.innerContent_iUnion_nat", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Content", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "MeasureTheory.Content.innerContent_comap", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Content", "is_tactic_proof": true, "tactics": ["refine", "intro", "simp", "apply"], "tactic_count": 4}
{"name": "MeasureTheory.Content.is_mul_left_invariant_innerContent", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Content", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "MeasureTheory.Content.innerContent_pos_of_is_mul_left_invariant", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Content", "is_tactic_proof": true, "tactics": ["have", "rcases", "suffices", "have", "simpa", "refine", "refine", "simp"], "tactic_count": 8}
{"name": "MeasureTheory.Content.innerContent_mono'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Content", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Content.outerMeasure", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Content", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Content.outerMeasure_opens", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Content", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Content.outerMeasure_of_isOpen", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Content", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Content.outerMeasure_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Content", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Content.le_outerMeasure_compacts", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Content", "is_tactic_proof": true, "tactics": ["rw", "exact", "exact", "exact", "exact"], "tactic_count": 5}
{"name": "MeasureTheory.Content.outerMeasure_eq_iInf", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Content", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Content.outerMeasure_interior_compacts", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Content", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Content.outerMeasure_exists_compact", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Content", "is_tactic_proof": true, "tactics": ["rw", "rcases", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.Content.outerMeasure_exists_open", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Content", "is_tactic_proof": false, "tactics": ["rcases", "inducedOuterMeasure_exists_set", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.Content.outerMeasure_preimage", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Content", "is_tactic_proof": false, "tactics": ["refine", "intro", "convert"], "tactic_count": 3}
{"name": "MeasureTheory.Content.outerMeasure_lt_top_of_isCompact", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Content", "is_tactic_proof": true, "tactics": ["rcases", "calc", "μ.outerMeasure"], "tactic_count": 3}
{"name": "MeasureTheory.Content.is_mul_left_invariant_outerMeasure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Content", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "MeasureTheory.Content.outerMeasure_caratheodory", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Content", "is_tactic_proof": true, "tactics": ["rw", "apply", "apply", "apply"], "tactic_count": 4}
{"name": "MeasureTheory.Content.outerMeasure_pos_of_is_mul_left_invariant", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Content", "is_tactic_proof": true, "tactics": ["convert", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.Content.borel_le_caratheodory", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Content", "is_tactic_proof": true, "tactics": ["rw", "refine", "intro", "rw", "intro", "rw", "simp", "rw", "haveI", "rw", "refine", "rintro", "let", "dsimp", "grw", "simp", "have", "have", "have", "grw", "rw", "simp", "rw", "haveI", "rw", "refine", "rintro", "let", "dsimp", "grw", "have", "have", "simp", "exact", "rw", "refine", "exact"], "tactic_count": 37}
{"name": "MeasureTheory.Content.measure", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Content", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Content.measure_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Content", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Content.outerRegular", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Content", "is_tactic_proof": true, "tactics": ["refine", "rw", "simp", "rcases", "rw", "exact"], "tactic_count": 6}
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{"name": "MeasureTheory.Content.ContentRegular", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Content", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Content.contentRegular_exists_compact", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Content", "is_tactic_proof": true, "tactics": ["by_contra", "simp", "have", "μ", "le_iInf", "rw", "exact"], "tactic_count": 7}
{"name": "MeasureTheory.Content.measure_eq_content_of_regular", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Content", "is_tactic_proof": true, "tactics": ["refine", "apply", "intro", "obtain", "calc", "μ.measure", "rw", "exact", "calc", "μ", "rw", "exact"], "tactic_count": 12}
{"name": "MeasureTheory.tendsto_measure_symmDiff_preimage_nhds_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.ContinuousPreimage", "is_tactic_proof": false, "tactics": ["have", "rw", "exact", "rw", "intro", "wlog", "have", "rcases", "have", "replace", "filter_upwards", "calc", "μ", "μ", "refine", "gcongr", "apply", "gcongr", "rwa", "rwa", "simp", "have", "obtain", "have", "filter_upwards", "rw", "refine", "rw", "gcongr", "have", "rw", "measure_diff_le_iff_le_add", "exact"], "tactic_count": 33}
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{"name": "MeasureTheory.Measure.count_ne_zero''", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Count", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.le_count_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Count", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.count_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Count", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.count_apply_finset'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Count", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.count_apply_finset", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Count", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.count_apply_finite'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Count", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.count_apply_finite", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Count", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.count_apply_infinite", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Count", "is_tactic_proof": true, "tactics": ["refine", "rcases", "calc"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.count_apply_eq_top'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Count", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "change", "simp"], "tactic_count": 4}
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{"name": "MeasureTheory.Measure.count_ne_zero_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Count", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasureTheory.count_real_singleton'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Count", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "MeasureTheory.Measure.count_injective_image'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Count", "is_tactic_proof": true, "tactics": ["classical", "by_cases", "lift", "rw", "simpa", "rw", "rw", "rw"], "tactic_count": 8}
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{"name": "MeasureTheory.Measure.count.isFiniteMeasure", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Count", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.count_univ", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Count", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "MeasureTheory.Measure.haveLebesgueDecompositionSMulRight", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Decomposition.Lebesgue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.haveLebesgueDecomposition_withDensity", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Decomposition.Lebesgue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasureTheory.Measure.singularPart_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Decomposition.Lebesgue", "is_tactic_proof": true, "tactics": ["by_cases", "conv_rhs", "exact", "rw", "exact"], "tactic_count": 5}
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{"name": "MeasureTheory.Measure.singularPart_withDensity", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Decomposition.Lebesgue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasureTheory.Measure.singularPart.instSigmaFinite", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Decomposition.Lebesgue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.singularPart.instIsLocallyFiniteMeasure", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Decomposition.Lebesgue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasureTheory.Measure.eq_rnDeriv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Decomposition.Lebesgue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasureTheory.Measure.rnDeriv_add_of_mutuallySingular", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Decomposition.Lebesgue", "is_tactic_proof": true, "tactics": ["filter_upwards", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.withDensity_rnDeriv_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym", "is_tactic_proof": true, "tactics": ["suffices", "exact"], "tactic_count": 2}
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{"name": "MeasureTheory.Measure.rnDeriv_pos", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym", "is_tactic_proof": false, "tactics": ["rw", "exact"], "tactic_count": 2}
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{"name": "MeasureTheory.Measure.rnDeriv_withDensity_left_of_absolutelyContinuous", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym", "is_tactic_proof": true, "tactics": ["refine", "exact", "ext1", "rw", "conv_lhs", "rw", "congr", "rw", "simp", "refine", "exact", "exact"], "tactic_count": 12}
{"name": "MeasureTheory.Measure.rnDeriv_withDensity_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym", "is_tactic_proof": true, "tactics": ["let", "have", "have", "have", "have", "exact", "filter_upwards", "rw"], "tactic_count": 8}
{"name": "MeasureTheory.Measure.rnDeriv_withDensity_right_of_absolutelyContinuous", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym", "is_tactic_proof": true, "tactics": ["have", "refine", "refine", "exact", "ext1", "conv_lhs", "rw", "rw", "simp", "have", "filter_upwards", "simp", "rw", "refine", "filter_upwards", "exact"], "tactic_count": 16}
{"name": "MeasureTheory.Measure.rnDeriv_withDensity_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym", "is_tactic_proof": true, "tactics": ["let", "have", "rnDeriv_withDensity_withDensity_rnDeriv_right", "have", "have", "rnDeriv_withDensity_right_of_absolutelyContinuous", "hf_ne_top", "filter_upwards", "rw"], "tactic_count": 9}
{"name": "MeasureTheory.Measure.rnDeriv_eq_zero_of_mutuallySingular", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym", "is_tactic_proof": true, "tactics": ["let", "have", "refine", "change", "have", "have", "rw", "filter_upwards", "rw", "refine", "simp", "suffices", "have", "exact", "exact"], "tactic_count": 15}
{"name": "MeasureTheory.Measure.rnDeriv_add_right_of_absolutelyContinuous_of_mutuallySingular", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym", "is_tactic_proof": true, "tactics": ["let", "have", "refine", "change", "rw", "withDensity_eq_iff_of_sigmaFinite", "have", "rw"], "tactic_count": 8}
{"name": "MeasureTheory.Measure.rnDeriv_add_right_of_mutuallySingular'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym", "is_tactic_proof": true, "tactics": ["have", "rw", "have", "have", "refine", "have", "rnDeriv_add_right_of_absolutelyContinuous_of_mutuallySingular", "hνν", "have", "refine", "simp", "exact", "have", "filter_upwards", "simp", "rw"], "tactic_count": 16}
{"name": "MeasureTheory.Measure.rnDeriv_add_right_of_mutuallySingular", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym", "is_tactic_proof": true, "tactics": ["have", "rw", "have", "have", "refine", "have", "have", "refine", "exact", "have", "rw", "exact", "filter_upwards", "rw", "exact"], "tactic_count": 15}
{"name": "MeasureTheory.Measure.rnDeriv_withDensity_rnDeriv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym", "is_tactic_proof": true, "tactics": ["conv_rhs", "refine", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.inv_rnDeriv_aux", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym", "is_tactic_proof": false, "tactics": ["suffices", "calc", "rw", "conv", "change", "rw"], "tactic_count": 6}
{"name": "MeasureTheory.Measure.inv_rnDeriv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym", "is_tactic_proof": false, "tactics": ["suffices", "ν.rnDeriv", "refine", "exact", "constructor", "filter_upwards", "simp", "exact", "exact"], "tactic_count": 9}
{"name": "MeasureTheory.Measure.inv_rnDeriv'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym", "is_tactic_proof": true, "tactics": ["filter_upwards"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.setLIntegral_rnDeriv_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.lintegral_rnDeriv_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.setLIntegral_rnDeriv'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.setLIntegral_rnDeriv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.lintegral_rnDeriv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.integrableOn_toReal_rnDeriv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.setIntegral_toReal_rnDeriv_eq_withDensity'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym", "is_tactic_proof": true, "tactics": ["rw", "rw", "simp", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.Measure.setIntegral_toReal_rnDeriv_eq_withDensity", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym", "is_tactic_proof": true, "tactics": ["rw", "rw", "simp", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.Measure.setIntegral_toReal_rnDeriv_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym", "is_tactic_proof": true, "tactics": ["set", "have", "have", "calc", "refine", "exact", "exact", "simp", "gcongr", "exact", "apply"], "tactic_count": 11}
{"name": "MeasureTheory.Measure.setIntegral_toReal_rnDeriv'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.setIntegral_toReal_rnDeriv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.integral_toReal_rnDeriv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.integral_toReal_rnDeriv'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.rnDeriv_mul_rnDeriv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym", "is_tactic_proof": true, "tactics": ["refine", "exact", "exact", "rw"], "tactic_count": 4}
{"name": "MeasureTheory.Measure.rnDeriv_mul_rnDeriv'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym", "is_tactic_proof": true, "tactics": ["obtain", "filter_upwards", "hνκ", "nth_rw", "rw"], "tactic_count": 5}
{"name": "MeasureTheory.Measure.rnDeriv_le_one_of_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym", "is_tactic_proof": true, "tactics": ["refine", "simp", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.rnDeriv_le_one_iff_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.rnDeriv_eq_one_iff_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "MeasurableEmbedding.rnDeriv_map_aux", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym", "is_tactic_proof": true, "tactics": ["refine", "exact", "exact", "rw", "have", "have", "rw"], "tactic_count": 7}
{"name": "MeasurableEmbedding.rnDeriv_map", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym", "is_tactic_proof": true, "tactics": ["rw", "have", "have", "have", "have", "rw", "refine", "refine", "refine", "symm", "suffices", "rw", "exact", "refine", "exact", "exact"], "tactic_count": 16}
{"name": "MeasurableEmbedding.map_withDensity_rnDeriv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym", "is_tactic_proof": true, "tactics": ["ext", "rw", "setLIntegral_map", "refine", "filter_upwards"], "tactic_count": 5}
{"name": "MeasurableEmbedding.singularPart_map", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym", "is_tactic_proof": false, "tactics": ["have", "conv_lhs", "rw", "refine", "exact"], "tactic_count": 5}
{"name": "MeasureTheory.lintegral_rnDeriv_mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym", "is_tactic_proof": true, "tactics": ["nth_rw", "rw", "simp"], "tactic_count": 3}
{"name": "MeasureTheory.setLIntegral_rnDeriv_mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym", "is_tactic_proof": true, "tactics": ["nth_rw", "rw", "simp"], "tactic_count": 3}
{"name": "MeasureTheory.integrable_rnDeriv_smul_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym", "is_tactic_proof": true, "tactics": ["nth_rw", "rw"], "tactic_count": 2}
{"name": "MeasureTheory.integral_rnDeriv_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym", "is_tactic_proof": true, "tactics": ["rw", "withDensity_rnDeriv_eq"], "tactic_count": 2}
{"name": "MeasureTheory.setIntegral_rnDeriv_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym", "is_tactic_proof": true, "tactics": ["rw", "exacts"], "tactic_count": 2}
{"name": "MeasureTheory.setIntegral_rnDeriv_smul'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym", "is_tactic_proof": true, "tactics": ["rw", "exacts"], "tactic_count": 2}
{"name": "MeasureTheory.mconv_eq_withDensity_mlconvolution_rnDeriv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym", "is_tactic_proof": true, "tactics": ["rw", "withDensity_rnDeriv_eq"], "tactic_count": 2}
{"name": "MeasureTheory.HaveLebesgueDecomposition.mconv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.rnDeriv_mconv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym", "is_tactic_proof": true, "tactics": ["have", "rw", "mconv_eq_withDensity_mlconvolution_rnDeriv", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.rnDeriv_mconv'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym", "is_tactic_proof": true, "tactics": ["rw", "mconv_eq_withDensity_mlconvolution_rnDeriv"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.dirac", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Dirac", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.instMeasureSpacePUnit", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Dirac", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.le_dirac_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Dirac", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.dirac_apply'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Dirac", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.dirac_apply_eq_zero_or_one", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Dirac", "is_tactic_proof": true, "tactics": ["rw", "simp", "tauto"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.dirac_apply_ne_zero_iff_eq_one", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Dirac", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.dirac_apply_ne_one_iff_eq_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Dirac", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.dirac_apply_of_mem", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Dirac", "is_tactic_proof": true, "tactics": ["have", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.Measure.dirac_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Dirac", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "calc", "dirac"], "tactic_count": 4}
{"name": "MeasureTheory.Measure.dirac_ne_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Dirac", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.map_dirac", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Dirac", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.map_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Dirac", "is_tactic_proof": true, "tactics": ["ext", "simp", "classical", "rw", "by_cases", "rw", "rw"], "tactic_count": 7}
{"name": "MeasureTheory.Measure.restrict_singleton", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Dirac", "is_tactic_proof": true, "tactics": ["ext1", "by_cases", "have", "simp", "have", "simp"], "tactic_count": 6}
{"name": "MeasureTheory.Measure.ext_of_singleton", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Dirac", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.ext_iff_singleton", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Dirac", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.ext_iff_measureReal_singleton", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Dirac", "is_tactic_proof": true, "tactics": ["rw", "congr", "rw", "simp"], "tactic_count": 4}
{"name": "MeasureTheory.Measure.map_eq_sum", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Dirac", "is_tactic_proof": true, "tactics": ["ext", "have", "simp"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.sum_smul_dirac", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Dirac", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.exists_sum_smul_dirac", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Dirac", "is_tactic_proof": true, "tactics": ["let", "have", "obtain", "rw", "exact", "let", "have", "refine", "rw", "simp", "simp_rw", "rw", "rw", "simp", "congr", "refine", "convert", "simp", "convert", "simp", "simp", "refine", "rw", "congr", "have", "have", "specialize", "obtain", "simp", "rw", "refine", "convert", "rw"], "tactic_count": 33}
{"name": "MeasureTheory.Measure.tsum_indicator_apply_singleton", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Dirac", "is_tactic_proof": true, "tactics": ["classical", "calc", "simp", "mul_ite,"], "tactic_count": 4}
{"name": "MeasureTheory.mem_ae_dirac_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Dirac", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "MeasureTheory.ae_dirac_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Dirac", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.ae_dirac_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Dirac", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.ae_eq_dirac'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Dirac", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.ae_eq_dirac", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Dirac", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.aemeasurable_dirac", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Dirac", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.dirac.isProbabilityMeasure", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Dirac", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.instNonemptySubtypeMeasureIsProbabilityMeasure", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Dirac", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.dirac.instIsFiniteMeasure", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Dirac", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.dirac.instSigmaFinite", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Dirac", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.dirac_eq_one_iff_mem", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Dirac", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "MeasureTheory.dirac_eq_zero_iff_not_mem", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Dirac", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "MeasureTheory.restrict_dirac'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Dirac", "is_tactic_proof": true, "tactics": ["split_ifs", "apply", "rw", "rw"], "tactic_count": 4}
{"name": "MeasureTheory.restrict_dirac", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Dirac", "is_tactic_proof": true, "tactics": ["split_ifs", "apply", "rwa", "rw"], "tactic_count": 4}
{"name": "MeasureTheory.mutuallySingular_dirac", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Dirac", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.dirac_eq_dirac_iff_forall_mem_iff_mem", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Dirac", "is_tactic_proof": true, "tactics": ["constructor", "intro", "have", "simp", "by_cases", "simpa", "indicator_eq_one_iff_mem]", "simpa", "not_false_eq_true,", "intro", "ext", "by_cases", "simp", "have", "simp"], "tactic_count": 15}
{"name": "MeasureTheory.dirac_ne_dirac_iff_exists_measurableSet", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Dirac", "is_tactic_proof": true, "tactics": ["apply", "simp", "refine", "by_cases", "simp", "simpa"], "tactic_count": 6}
{"name": "MeasureTheory.dirac_ne_dirac", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Dirac", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.dirac_ne_dirac_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Dirac", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.dirac_eq_dirac_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Dirac", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.injective_dirac", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Dirac", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompletelyRegularSpace.exists_BCNN", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.DiracProba", "is_tactic_proof": true, "tactics": ["obtain", "have", "refine", "simpa", "set", "set", "refine"], "tactic_count": 7}
{"name": "MeasureTheory.diracProba", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.DiracProba", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.injective_diracProba", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.DiracProba", "is_tactic_proof": true, "tactics": ["intro", "rw", "rwa"], "tactic_count": 3}
{"name": "MeasureTheory.diracProba_toMeasure_apply'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.DiracProba", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.diracProba_toMeasure_apply_of_mem", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.DiracProba", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.diracProba_toMeasure_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.DiracProba", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.continuous_diracProba", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.DiracProba", "is_tactic_proof": true, "tactics": ["rw", "apply", "have", "simp", "exact"], "tactic_count": 5}
{"name": "MeasureTheory.not_tendsto_diracProba_of_not_tendsto", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.DiracProba", "is_tactic_proof": false, "tactics": ["obtain", "contrapose", "exact", "have", "obtain", "rw", "use", "simp", "lintegral_dirac", "apply", "refine", "intro", "rw", "simp"], "tactic_count": 14}
{"name": "MeasureTheory.tendsto_diracProba_iff_tendsto", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.DiracProba", "is_tactic_proof": true, "tactics": ["constructor", "contrapose", "exact", "intro", "have", "simp", "exact"], "tactic_count": 7}
{"name": "MeasureTheory.diracProbaInverse", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.DiracProba", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.diracProba_diracProbaInverse", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.DiracProba", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.diracProbaInverse_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.DiracProba", "is_tactic_proof": true, "tactics": ["apply", "simp", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.diracProbaEquiv", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.DiracProba", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.diracProba_comp_diracProbaEquiv_symm_eq_val", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.DiracProba", "is_tactic_proof": true, "tactics": ["funext"], "tactic_count": 1}
{"name": "MeasureTheory.tendsto_diracProbaEquivSymm_iff_tendsto", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.DiracProba", "is_tactic_proof": true, "tactics": ["have", "rw", "simp", "simp", "convert", "exact"], "tactic_count": 6}
{"name": "MeasureTheory.continuous_diracProbaEquiv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.DiracProba", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.continuous_diracProbaEquivSymm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.DiracProba", "is_tactic_proof": true, "tactics": ["apply", "intro", "apply", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.diracProbaHomeomorph", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.DiracProba", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.isEmbedding_diracProba", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.DiracProba", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUnifLocDoublingMeasure.exists_measure_closedBall_le_mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Doubling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUnifLocDoublingMeasure.doublingConstant", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Doubling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUnifLocDoublingMeasure.eventually_measure_le_doublingConstant_mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Doubling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "IsUnifLocDoublingMeasure.one_le_scalingConstantOf", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Doubling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "IsUnifLocDoublingMeasure.eventually_measure_le_scaling_constant_mul'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Doubling", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
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{"name": "IsUnifLocDoublingMeasure.scalingScaleOf_pos", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Doubling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUnifLocDoublingMeasure.measure_mul_le_scalingConstantOf_mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Doubling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.IsEverywherePos", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.EverywherePos", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.everywherePosSubset", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.EverywherePos", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.everywherePosSubset_subset", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.EverywherePos", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.exists_isOpen_everywherePosSubset_eq_diff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.EverywherePos", "is_tactic_proof": true, "tactics": ["refine", "rw", "intro", "rcases", "rcases", "have", "intro", "refine", "rw", "exact", "have", "exact"], "tactic_count": 12}
{"name": "MeasurableSet.everywherePosSubset", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.EverywherePos", "is_tactic_proof": true, "tactics": ["rcases", "rw", "exact"], "tactic_count": 3}
{"name": "IsClosed.everywherePosSubset", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.EverywherePos", "is_tactic_proof": true, "tactics": ["rcases", "rw", "exact"], "tactic_count": 3}
{"name": "IsCompact.everywherePosSubset", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.EverywherePos", "is_tactic_proof": true, "tactics": ["rcases", "rw", "exact"], "tactic_count": 3}
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{"name": "MeasureTheory.Measure.everywherePosSubset_ae_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.EverywherePos", "is_tactic_proof": false, "tactics": ["simp", "intro", "exact"], "tactic_count": 3}
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{"name": "MeasureTheory.Measure.isEverywherePos_everywherePosSubset", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.EverywherePos", "is_tactic_proof": true, "tactics": ["intro", "rcases", "have", "have", "exact", "have", "ae_eq_set_inter", "rw", "exact"], "tactic_count": 9}
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{"name": "MeasureTheory.Measure.IsEverywherePos.smul_measure_nnreal", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.EverywherePos", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "IsOpen.isEverywherePos", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.EverywherePos", "is_tactic_proof": true, "tactics": ["intro", "rcases", "apply", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.Measure.IsEverywherePos.IsGdelta_of_isMulLeftInvariant", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.EverywherePos", "is_tactic_proof": true, "tactics": ["has", "the", "positive", "obtain", "exists_seq_strictAnti_tendsto", "have", "exists_open_nhds_one_mul_subset", "choose", "let", "suffices", "replace", "apply", "exact", "rw", "refine", "exact", "intro", "choose", "obtain", "have", "apply", "have", "obtain", "refine", "have", "have", "exact", "have", "have", "have", "rw", "group", "simp", "by_contra", "have", "apply", "apply", "push", "contrapose", "simpa", "have", "exact"], "tactic_count": 42}
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{"name": "MeasureTheory.FiniteMeasure.toMeasure", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.FiniteMeasure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasureTheory.FiniteMeasure.isFiniteMeasure", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.FiniteMeasure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.FiniteMeasure.val_eq_toMeasure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.FiniteMeasure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasureTheory.FiniteMeasure.coeFn_def", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.FiniteMeasure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasureTheory.FiniteMeasure.tendsto_measure_iUnion_accumulate", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.FiniteMeasure", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.FiniteMeasure.mass", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.FiniteMeasure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasureTheory.FiniteMeasure.instAdd", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.FiniteMeasure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.FiniteMeasure.instSMul", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.FiniteMeasure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.FiniteMeasure.toMeasure_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.FiniteMeasure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.FiniteMeasure.toMeasure_add", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.FiniteMeasure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.FiniteMeasure.toMeasure_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.FiniteMeasure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasureTheory.FiniteMeasure.toMeasureAddMonoidHom", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.FiniteMeasure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasureTheory.FiniteMeasure.instModuleNNReal", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.FiniteMeasure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.FiniteMeasure.smul_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.FiniteMeasure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "MeasureTheory.FiniteMeasure.restrict_biUnion_finset", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.FiniteMeasure", "is_tactic_proof": true, "tactics": ["ext", "simp", "rw", "simp", "conv_rhs"], "tactic_count": 5}
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{"name": "MeasureTheory.FiniteMeasure.measurableSet_isFiniteMeasure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.FiniteMeasure", "is_tactic_proof": false, "tactics": ["suffices", "rw", "exact", "ext", "simp", "exact"], "tactic_count": 6}
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{"name": "MeasureTheory.Measure.join", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.GiryMonad", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.join_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.GiryMonad", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.le_join_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.GiryMonad", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.join_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.GiryMonad", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.join_sum", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.GiryMonad", "is_tactic_proof": true, "tactics": ["ext", "simp_rw"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.join_dirac", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.GiryMonad", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.le_ae_join", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.GiryMonad", "is_tactic_proof": true, "tactics": ["intro", "rcases", "rw", "rw", "exact"], "tactic_count": 5}
{"name": "MeasureTheory.Measure.ae_ae_of_ae_join", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.GiryMonad", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.ae_of_join", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.GiryMonad", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.aemeasurable_lintegral", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.GiryMonad", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.join_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.GiryMonad", "is_tactic_proof": true, "tactics": ["ext1", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.measurable_join", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.GiryMonad", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.lintegral_join", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.GiryMonad", "is_tactic_proof": true, "tactics": ["wlog", "rcases", "rw", "exact", "simp_rw", "join_apply", "clear", "suffices", "refine", "this", "exact", "exact", "intro", "rw", "swap", "fun_prop", "congr", "funext", "rw", "simp_rw", "exact"], "tactic_count": 21}
{"name": "MeasureTheory.Measure.lintegral_join_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.GiryMonad", "is_tactic_proof": true, "tactics": ["rcases", "rw", "gcongr", "apply"], "tactic_count": 4}
{"name": "MeasureTheory.Measure.bind", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.GiryMonad", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.bind_zero_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.GiryMonad", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.bind_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.GiryMonad", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.bind_apply_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.GiryMonad", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.ae_ae_of_ae_bind", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.GiryMonad", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.ae_of_bind", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.GiryMonad", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.bind_congr_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.GiryMonad", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.bind_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.GiryMonad", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.bind_zero_right'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.GiryMonad", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.bind_zero_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.GiryMonad", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.measurable_bind'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.GiryMonad", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.aemeasurable_bind", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.GiryMonad", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.bind_sum", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.GiryMonad", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.bind_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.GiryMonad", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.lintegral_bind", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.GiryMonad", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.lintegral_bind_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.GiryMonad", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.bind_bind", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.GiryMonad", "is_tactic_proof": true, "tactics": ["ext1", "rw", "exact", "exact", "exact"], "tactic_count": 5}
{"name": "MeasureTheory.Measure.dirac_bind", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.GiryMonad", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.bind_dirac", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.GiryMonad", "is_tactic_proof": true, "tactics": ["ext1", "simp", "lintegral_one,"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.bind_dirac_eq_map", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.GiryMonad", "is_tactic_proof": true, "tactics": ["rw", "exacts"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.join_eq_bind", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.GiryMonad", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.join_map_map", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.GiryMonad", "is_tactic_proof": true, "tactics": ["ext1", "rw", "simp_rw"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.join_map_join", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.GiryMonad", "is_tactic_proof": true, "tactics": ["change", "rw", "apply", "funext", "exact"], "tactic_count": 5}
{"name": "MeasureTheory.Measure.join_map_dirac", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.GiryMonad", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.haar.index", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Haar.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.haar.index_empty", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.haar.prehaar", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Haar.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.haar.prehaar_empty", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.haar.prehaar_nonneg", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.Basic", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.haar.haarProduct", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Haar.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.haar.mem_prehaar_empty", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.haar.clPrehaar", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Haar.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.haar.index_defined", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.Basic", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.haar.index_elim", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.Basic", "is_tactic_proof": true, "tactics": ["have"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.haar.le_index_mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.Basic", "is_tactic_proof": true, "tactics": ["classical", "obtain", "obtain", "rw", "refine", "apply", "apply", "have", "rcases", "exact"], "tactic_count": 10}
{"name": "MeasureTheory.Measure.haar.index_pos", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.Basic", "is_tactic_proof": true, "tactics": ["classical", "rw", "rintro", "obtain", "change", "convert", "simp", "exact"], "tactic_count": 8}
{"name": "MeasureTheory.Measure.haar.index_mono", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.Basic", "is_tactic_proof": true, "tactics": ["rcases", "apply"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.haar.index_union_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.Basic", "is_tactic_proof": true, "tactics": ["classical", "rcases", "rcases", "rw", "refine", "rw", "gcongr"], "tactic_count": 7}
{"name": "MeasureTheory.Measure.haar.index_union_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.Basic", "is_tactic_proof": true, "tactics": ["classical", "apply", "rcases", "have", "apply", "intro", "simp", "simp", "simp", "simp", "exact", "refine", "le_trans", "rw", "exact", "apply", "rintro", "simp", "refine", "constructor", "refine", "simp", "simp", "refine", "simp", "simp"], "tactic_count": 26}
{"name": "MeasureTheory.Measure.haar.mul_left_index_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.Basic", "is_tactic_proof": true, "tactics": ["rcases", "apply", "refine", "simp", "rintro", "simp", "simp", "refine"], "tactic_count": 8}
{"name": "MeasureTheory.Measure.haar.is_left_invariant_index", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.Basic", "is_tactic_proof": true, "tactics": ["refine", "convert", "rw"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.haar.prehaar_le_index", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.Basic", "is_tactic_proof": true, "tactics": ["unfold", "apply", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.haar.prehaar_pos", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.Basic", "is_tactic_proof": true, "tactics": ["apply", "apply", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.haar.prehaar_mono", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.Basic", "is_tactic_proof": true, "tactics": ["simp", "exact", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.haar.prehaar_self", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.haar.prehaar_sup_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.Basic", "is_tactic_proof": true, "tactics": ["simp", "exact", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.haar.prehaar_sup_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.Basic", "is_tactic_proof": true, "tactics": ["simp", "rw", "refine", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.Measure.haar.is_left_invariant_prehaar", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.haar.prehaar_mem_haarProduct", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.Basic", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.haar.nonempty_iInter_clPrehaar", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.Basic", "is_tactic_proof": true, "tactics": ["have", "refine", "let", "have", "have", "refine", "constructor", "apply", "simp", "apply", "exact"], "tactic_count": 11}
{"name": "MeasureTheory.Measure.haar.chaar", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Haar.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.haar.chaar_mem_haarProduct", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.haar.chaar_mem_clPrehaar", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.Basic", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.haar.chaar_nonneg", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.Basic", "is_tactic_proof": true, "tactics": ["have"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.haar.chaar_empty", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.Basic", "is_tactic_proof": true, "tactics": ["let", "have", "change", "apply", "unfold", "rintro", "apply"], "tactic_count": 7}
{"name": "MeasureTheory.Measure.haar.chaar_self", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.Basic", "is_tactic_proof": true, "tactics": ["let", "have", "change", "apply", "unfold", "rintro", "rw", "apply"], "tactic_count": 8}
{"name": "MeasureTheory.Measure.haar.chaar_mono", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.Basic", "is_tactic_proof": true, "tactics": ["let", "have", "rw", "apply", "unfold", "rintro", "apply", "apply"], "tactic_count": 8}
{"name": "MeasureTheory.Measure.haar.chaar_sup_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.Basic", "is_tactic_proof": true, "tactics": ["let", "have", "rw", "apply", "unfold", "rintro", "apply", "apply"], "tactic_count": 8}
{"name": "MeasureTheory.Measure.haar.chaar_sup_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.Basic", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "rcases", "replace", "rcases", "rcases", "replace", "let", "have", "rw", "let", "apply", "mem_of_subset_of_mem", "simp", "unfold", "rintro", "simp", "apply", "rw", "refine", "refine", "exact", "refine", "exact", "apply"], "tactic_count": 25}
{"name": "MeasureTheory.Measure.haar.is_left_invariant_chaar", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.Basic", "is_tactic_proof": true, "tactics": ["let", "have", "rw", "apply", "unfold", "rintro", "simp", "apply", "apply"], "tactic_count": 9}
{"name": "MeasureTheory.Measure.haar.haarContent", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Haar.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.haar.haarContent_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.haar.haarContent_self", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.haar.is_left_invariant_haarContent", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.haar.haarContent_outerMeasure_self_pos", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "refine", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.Measure.haar.haarContent_outerMeasure_closure_pos", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.haarMeasure", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Haar.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.haarMeasure_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.Basic", "is_tactic_proof": true, "tactics": ["change", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.isMulLeftInvariant_haarMeasure", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Haar.Basic", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "refine", "apply", "apply"], "tactic_count": 6}
{"name": "MeasureTheory.Measure.haarMeasure_self", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.Basic", "is_tactic_proof": true, "tactics": ["haveI", "simp", "rw", "exact", "exact"], "tactic_count": 5}
{"name": "MeasureTheory.Measure.regular_haarMeasure", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Haar.Basic", "is_tactic_proof": true, "tactics": ["haveI", "apply", "rw", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.Measure.haarMeasure_closure_self", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.sigmaFinite_haarMeasure", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Haar.Basic", "is_tactic_proof": true, "tactics": ["haveI"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.isHaarMeasure_haarMeasure", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Haar.Basic", "is_tactic_proof": true, "tactics": ["apply", "simp", "simp"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.haar", "kind": "abbrev", "module": "Mathlib.MeasureTheory.Measure.Haar.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.MeasureTheory.Measure.Haar.Basic.0.MeasureTheory.Measure.steinhaus_mul_aux", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.Basic", "is_tactic_proof": true, "tactics": ["a", "itself", "obtain", "obtain", "exact", "rwa", "filter_upwards", "obtain", "not_disjoint_iff.1", "simpa"], "tactic_count": 10}
{"name": "MeasureTheory.Measure.div_mem_nhds_one_of_haar_pos_ne_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.div_mem_nhds_one_of_haar_pos", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.haarMeasure_unique", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.Basic", "is_tactic_proof": false, "tactics": ["have", "have", "measure_eq_div_smul", "rwa"], "tactic_count": 4}
{"name": "MeasureTheory.Measure.haarMeasure_eq_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure._example", "kind": "example", "module": "Mathlib.MeasureTheory.Measure.Haar.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.regular_of_isMulLeftInvariant", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LinearMap.exists_map_addHaar_eq_smul_addHaar'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.Disintegration", "is_tactic_proof": true, "tactics": ["measure", "is", "follows", "projection", "have", "have", "rcases", "have", "infer_instance", "have", "have", "exact", "let", "obtain", "let", "have", "let", "have", "have", "let", "have", "have", "ext", "obtain", "have", "simp", "have", "rw", "rfl", "exact", "exact", "exact", "exact", "let", "let", "obtain", "have", "refine", "simpa", "have", "obtain", "have", "refine", "simpa", "refine", "simp", "rw"], "tactic_count": 47}
{"name": "LinearMap.exists_map_addHaar_eq_smul_addHaar", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.Disintegration", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.ae_comp_linearMap_mem_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.Disintegration", "is_tactic_proof": true, "tactics": ["have", "have", "apply", "rcases", "rw", "exact"], "tactic_count": 6}
{"name": "MeasureTheory.ae_ae_add_linearMap_mem_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.Disintegration", "is_tactic_proof": true, "tactics": ["have", "have", "have", "have", "let", "have", "have", "have", "simp_rw", "rw", "simp", "exact"], "tactic_count": 12}
{"name": "MeasureTheory.ae_mem_of_ae_add_linearMap_mem", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.Disintegration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.distribHaarChar", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Haar.DistribChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.distribHaarChar_pos", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.DistribChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.addHaarScalarFactor_smul_eq_distribHaarChar", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.DistribChar", "is_tactic_proof": true, "tactics": ["borelize", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.addHaarScalarFactor_smul_inv_eq_distribHaarChar", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.DistribChar", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.addHaarScalarFactor_smul_eq_distribHaarChar_inv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.DistribChar", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.distribHaarChar_mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.DistribChar", "is_tactic_proof": true, "tactics": ["have", "rw", "isAddLeftInvariant_eq_smul_of_regular]"], "tactic_count": 3}
{"name": "MeasureTheory.distribHaarChar_eq_div", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.DistribChar", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.distribHaarChar_eq_of_measure_smul_eq_mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.DistribChar", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "LinearIsometryEquiv.toMeasurableEquiv", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Haar.InnerProductSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.coe_toMeasurableEquiv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.InnerProductSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.toMeasurableEquiv_symm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.InnerProductSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIsometryEquiv.coe_symm_toMeasurableEquiv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.InnerProductSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Orientation.measure_orthonormalBasis", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.InnerProductSpace", "is_tactic_proof": false, "tactics": ["have", "refine", "rw", "have", "ext", "simp", "rw"], "tactic_count": 7}
{"name": "Orientation.measure_eq_volume", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.InnerProductSpace", "is_tactic_proof": false, "tactics": ["have", "rw", "simp"], "tactic_count": 3}
{"name": "OrthonormalBasis.volume_parallelepiped", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.InnerProductSpace", "is_tactic_proof": true, "tactics": ["haveI", "let", "rw", "exact"], "tactic_count": 4}
{"name": "OrthonormalBasis.addHaar_eq_volume", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.InnerProductSpace", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "OrthonormalBasis.measurableEquiv", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Haar.InnerProductSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrthonormalBasis.measurePreserving_measurableEquiv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.InnerProductSpace", "is_tactic_proof": true, "tactics": ["convert", "rw", "erw", "exact"], "tactic_count": 4}
{"name": "OrthonormalBasis.measurePreserving_repr", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.InnerProductSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrthonormalBasis.measurePreserving_repr_symm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.InnerProductSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanSpace.measurableEquiv", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Haar.InnerProductSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanSpace.measurableEquiv_toEquiv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.InnerProductSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanSpace.coe_measurableEquiv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.InnerProductSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanSpace.coe_measurableEquiv_symm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.InnerProductSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanSpace.volume_preserving_symm_measurableEquiv_toLp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.InnerProductSpace", "is_tactic_proof": false, "tactics": ["suffices", "convert", "rw", "exact"], "tactic_count": 4}
{"name": "PiLp.volume_preserving_ofLp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.InnerProductSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiLp.volume_preserving_toLp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.InnerProductSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "volume_euclideanSpace_eq_dirac", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.InnerProductSpace", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LinearIsometryEquiv.measurePreserving", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.InnerProductSpace", "is_tactic_proof": true, "tactics": ["refine", "rcases", "erw", "congr"], "tactic_count": 4}
{"name": "MeasureTheory.mulEquivHaarChar", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Haar.MulEquivHaarChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.mulEquivHaarChar_pos", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.MulEquivHaarChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.mulEquivHaarChar_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.MulEquivHaarChar", "is_tactic_proof": true, "tactics": ["have", "unfold", "conv", "enter", "rw", "conv", "enter", "rw", "simp_rw", "exact"], "tactic_count": 10}
{"name": "MeasureTheory.mulEquivHaarChar_smul_map", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.MulEquivHaarChar", "is_tactic_proof": true, "tactics": ["rw", "have", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.mulEquivHaarChar_smul_eq_comap", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.MulEquivHaarChar", "is_tactic_proof": true, "tactics": ["let", "rw", "have", "rw", "simp", "fun_prop", "fun_prop"], "tactic_count": 7}
{"name": "MeasureTheory.mulEquivHaarChar_smul_integral_map", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.MulEquivHaarChar", "is_tactic_proof": true, "tactics": ["nth_rw", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.integral_comap_eq_mulEquivHaarChar_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.MulEquivHaarChar", "is_tactic_proof": true, "tactics": ["let", "change", "have", "have", "rw", "map_map", "rw", "simp"], "tactic_count": 8}
{"name": "MeasureTheory.mulEquivHaarChar_smul_preimage", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.MulEquivHaarChar", "is_tactic_proof": true, "tactics": ["nth_rw", "simp", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.mulEquivHaarChar_refl", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.MulEquivHaarChar", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.mulEquivHaarChar_trans", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.MulEquivHaarChar", "is_tactic_proof": true, "tactics": ["rw", "have", "have", "simp_rw", "have", "rw"], "tactic_count": 6}
{"name": "MeasureTheory.mulEquivHaarChar_symm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.MulEquivHaarChar", "is_tactic_proof": true, "tactics": ["symm", "apply", "simp"], "tactic_count": 3}
{"name": "MeasureTheory.Measure._example", "kind": "example", "module": "Mathlib.MeasureTheory.Measure.Haar.NormedSpace", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.MapLinearEquiv.isAddHaarMeasure", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Haar.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.exists_nhds_isBounded", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.NormedSpace", "is_tactic_proof": true, "tactics": ["let", "obtain", "by_contra", "simp_rw", "preimage_univ,", "exact", "rw", "refine", "smul_mem_nhds_smul", "div_mem_nhds_one_of_haar_pos_ne_top", "mt", "have", "isBounded_ball.subset", "rw", "exact"], "tactic_count": 15}
{"name": "MeasureTheory.Measure.AddMonoidHom.continuous_of_measurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.integral_comp_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.NormedSpace", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "rcases", "simp", "rcases", "have", "have", "conv_rhs", "simp", "have", "simp", "calc", "simp"], "tactic_count": 13}
{"name": "MeasureTheory.Measure.integral_comp_smul_of_nonneg", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.NormedSpace", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.integral_comp_inv_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.NormedSpace", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.integral_comp_inv_smul_of_nonneg", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.NormedSpace", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.setIntegral_comp_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.NormedSpace", "is_tactic_proof": true, "tactics": ["let", "calc", "simp", "congr", "ext", "rw", "rfl"], "tactic_count": 7}
{"name": "MeasureTheory.Measure.setIntegral_comp_smul_of_pos", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.NormedSpace", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.integral_comp_mul_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.NormedSpace", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.integral_comp_inv_mul_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.NormedSpace", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.integral_comp_mul_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.NormedSpace", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.integral_comp_inv_mul_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.NormedSpace", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.integral_comp_div", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integrable_comp_smul_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.NormedSpace", "is_tactic_proof": true, "tactics": ["suffices", "refine", "convert", "rw", "intro", "let", "refine", "rwa", "simpa"], "tactic_count": 9}
{"name": "MeasureTheory.Integrable.comp_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integrable_comp_mul_left_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.NormedSpace", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.Integrable.comp_mul_left'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integrable_comp_mul_right_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.NormedSpace", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.Integrable.comp_mul_right'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integrable_comp_div_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Integrable.comp_div", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integrable_comp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integral_comp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.NormedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "parallelepiped", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Haar.OfBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_parallelepiped_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.OfBasis", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "parallelepiped_basis_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.OfBasis", "is_tactic_proof": true, "tactics": ["classical", "ext", "simp_rw", "aesop"], "tactic_count": 4}
{"name": "image_parallelepiped", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.OfBasis", "is_tactic_proof": true, "tactics": ["simp", "congr", "simp"], "tactic_count": 3}
{"name": "parallelepiped_comp_equiv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.OfBasis", "is_tactic_proof": true, "tactics": ["simp", "let", "have", "rw", "ext", "simp", "refine", "simpa", "simpa", "rw", "ext", "have", "simp_rw", "simp_rw"], "tactic_count": 14}
{"name": "parallelepiped_orthonormalBasis_one_dim", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.OfBasis", "is_tactic_proof": false, "tactics": ["have", "apply", "simp", "have", "convert", "ext", "simp", "rw", "let", "have", "apply", "intro", "refine", "ext", "simp", "rintro", "exact", "rcases", "left", "simp_rw", "simp", "image_id']", "right", "simp_rw", "simp"], "tactic_count": 25}
{"name": "parallelepiped_eq_sum_segment", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.OfBasis", "is_tactic_proof": true, "tactics": ["ext", "simp", "zero_add,", "constructor", "rintro", "exact", "rintro", "choose", "refine", "simp_rw"], "tactic_count": 10}
{"name": "convex_parallelepiped", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.OfBasis", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "parallelepiped_eq_convexHull", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.OfBasis", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "parallelepiped_single", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.OfBasis", "is_tactic_proof": true, "tactics": ["ext", "simp_rw", "constructor", "rintro", "specialize", "simp_rw", "rcases", "rw", "exact", "rw", "exact", "intro", "refine", "specialize", "rcases", "rw", "exact", "rw", "exact", "specialize", "simp", "rcases", "rw", "rw", "rw"], "tactic_count": 25}
{"name": "Module.Basis.parallelepiped", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Haar.OfBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.coe_parallelepiped", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.OfBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.parallelepiped_reindex", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.OfBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.parallelepiped_map", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.OfBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.prod_parallelepiped", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.OfBasis", "is_tactic_proof": true, "tactics": ["ext", "simp", "constructor", "intro", "rcases", "constructor", "use", "constructor", "exact", "simp", "use", "constructor", "exact", "simp", "intro", "rcases", "use", "constructor", "constructor", "change", "aesop", "change", "aesop", "ext", "simp", "simp"], "tactic_count": 26}
{"name": "Module.Basis.definition._@.Mathlib.MeasureTheory.Measure.Haar.OfBasis.29914027._hygCtx._hyg.2", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Haar.OfBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.wrapped._@.Mathlib.MeasureTheory.Measure.Haar.OfBasis.29914027._hygCtx._hyg.2", "kind": "opaque", "module": "Mathlib.MeasureTheory.Measure.Haar.OfBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.addHaar", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Haar.OfBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.addHaar_def", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.OfBasis", "is_tactic_proof": true, "tactics": ["intros", "delta", "rw", "rfl"], "tactic_count": 4}
{"name": "isAddHaarMeasure_basis_addHaar", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Haar.OfBasis", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Module.Basis.instSigmaFiniteAddHaar", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Haar.OfBasis", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "Module.Basis.addHaar_eq_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.OfBasis", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Module.Basis.addHaar_reindex", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.OfBasis", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Module.Basis.addHaar_self", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.OfBasis", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Module.Basis.prod_addHaar", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.OfBasis", "is_tactic_proof": true, "tactics": ["have", "have", "simp"], "tactic_count": 3}
{"name": "measureSpaceOfInnerProductSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Haar.OfBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsAddHaarMeasureVolume", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Haar.OfBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.measureSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Haar.OfBasis", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "QuotientGroup.measurableSMul", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Haar.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurePreserving_quotientGroup_mk_of_QuotientMeasureEqMeasurePreimage", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.MeasureTheory.Measure.Haar.Quotient.0.termπ", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Haar.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.MeasureTheory.Measure.Haar.Quotient.0._aux_Mathlib_MeasureTheory_Measure_Haar_Quotient___macroRules__private_Mathlib_MeasureTheory_Measure_Haar_Quotient_0_termπ_1", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Haar.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "essSup_comp_quotientGroup_mk", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Haar.Quotient", "is_tactic_proof": true, "tactics": ["have", "rw", "refine", "intro", "dsimp", "congr", "exact"], "tactic_count": 7}
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{"name": "MeasureTheory.instIsMulRightInvariantHausdorffMeasureOfIsIsometricSMulMulOpposite", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.hausdorffMeasure_pi_real", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Hausdorff", "is_tactic_proof": true, "tactics": ["classical", "refine", "simp", "intro", "choose", "obtain", "replace", "apply", "le_antisymm", "have", "refine", "rw", "exact", "rw", "exact", "have", "let", "let", "have", "simp", "have", "refine", "intro", "refine", "simp", "add_sub_add_left_eq_sub,", "have", "refine", "have", "intro", "simp", "simp", "let", "apply", "gcongr", "exact", "refine", "simpa", "refine", "calc", "gcongr", "exact", "calc", "x", "gcongr", "exact", "calc", "μH", "liminf", "hausdorffMeasure_le_liminf_sum", "refine", "filter_upwards", "apply", "simp", "intro", "exact", "isBoundedDefault", "simp", "simp", "apply", "refine", "apply", "apply", "intro", "simp", "simp"], "tactic_count": 66}
{"name": "MeasureTheory.isAddHaarMeasure_hausdorffMeasure", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.hausdorffMeasure_measurePreserving_funUnique", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.hausdorffMeasure_measurePreserving_piFinTwo", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.hausdorffMeasure_real", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Hausdorff", "is_tactic_proof": true, "tactics": ["rw", "hausdorffMeasure_pi_real,"], "tactic_count": 2}
{"name": "MeasureTheory.hausdorffMeasure_prod_real", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Hausdorff", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.hausdorffMeasure_smul_right_image", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Hausdorff", "is_tactic_proof": true, "tactics": ["obtain", "haveI", "obtain", "simp", "simp", "have", "suffices", "simpa", "have", "refine", "rw", "rw", "iso_smul.hausdorffMeasure_image"], "tactic_count": 13}
{"name": "MeasureTheory.hausdorffMeasure_homothety_image", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Hausdorff", "is_tactic_proof": false, "tactics": ["suffices", "μH", "simpa", "borelize", "rw"], "tactic_count": 5}
{"name": "MeasureTheory.hausdorffMeasure_homothety_preimage", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Hausdorff", "is_tactic_proof": true, "tactics": ["change", "rw", "hausdorffMeasure_homothety_image"], "tactic_count": 3}
{"name": "MeasureTheory.hausdorffMeasure_lineMap_image", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Hausdorff", "is_tactic_proof": false, "tactics": ["suffices", "simpa", "borelize", "rw"], "tactic_count": 4}
{"name": "MeasureTheory.hausdorffMeasure_affineSegment", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Hausdorff", "is_tactic_proof": false, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.hausdorffMeasure_segment", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Hausdorff", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.hausdorffMeasure_orthogonalProjection_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Hausdorff", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.integral_charFun_Icc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.IntegralCharFun", "is_tactic_proof": false, "tactics": ["have", "simp", "rw", "suffices", "rw", "fun_prop", "ext", "rw", "norm_cast", "simp", "calc", "congr", "by_cases", "simp", "simp", "have", "intervalIntegral.integral_comp_smul_deriv", "swap", "intro", "simp_rw", "exact", "simp", "rw", "norm_cast", "simp", "congr", "rw", "split_ifs", "simp", "have", "norm_cast", "field_simp", "norm_cast", "rw"], "tactic_count": 34}
{"name": "MeasureTheory.measureReal_abs_gt_le_integral_charFun", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.IntegralCharFun", "is_tactic_proof": false, "tactics": ["have", "calc", "μ.real", "congr", "simp", "rw", "inv_mul_cancel₀", "rw", "congr", "rw", "gcongr", "refine", "setIntegral_mono_on", "exact", "exact", "have", "intro", "simp", "linarith", "rw", "norm_num", "rw", "refine", "exact", "grw", "simp", "exact", "gcongr", "exact", "norm_cast", "rw", "congr", "ring_nf", "rw", "rw", "simp", "rw", "integral_charFun_Icc", "simp"], "tactic_count": 39}
{"name": "MeasureTheory.measureReal_abs_dual_gt_le_integral_charFunDual", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.IntegralCharFun", "is_tactic_proof": true, "tactics": ["have", "convert", "rw", "simp", "exact", "rw"], "tactic_count": 6}
{"name": "MeasureTheory.measureReal_abs_inner_gt_le_integral_charFun", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.IntegralCharFun", "is_tactic_proof": true, "tactics": ["have", "convert", "rw", "simp", "exact", "simp", "rw", "simp_rw"], "tactic_count": 8}
{"name": "Real.volume_eq_stieltjes_id", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": false, "tactics": ["haveI", "simp", "preimage_const_add_Ioo]⟩", "have", "change", "rcases", "simp", "conv_rhs", "rw", "simp"], "tactic_count": 10}
{"name": "Real.volume_val", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.volume_Ico", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.volume_real_Ico", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.volume_real_Ico_of_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.volume_Icc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.volume_real_Icc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.volume_real_Icc_of_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.volume_Ioo", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.volume_uIoo", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.volume_real_Ioo", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.volume_real_Ioo_of_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.volume_Ioc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.volume_uIoc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.volume_real_Ioc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.volume_real_Ioc_of_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.volume_singleton", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.volume_univ", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.volume_ball", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.volume_real_ball", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.volume_closedBall", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.volume_real_closedBall", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.volume_eball", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["rcases", "rw", "lift", "rw"], "tactic_count": 4}
{"name": "Real.volume_closedEBall", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["rcases", "rw", "lift", "rw"], "tactic_count": 4}
{"name": "Real.noAtoms_volume", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.volume_interval", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.volume_real_interval", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.volume_Ioi", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.volume_Ici", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.volume_Iio", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.volume_Iic", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.locallyFinite_volume", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.isFiniteMeasure_restrict_Icc", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.isFiniteMeasure_restrict_Ico", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.isFiniteMeasure_restrict_Ioc", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.isFiniteMeasure_restrict_Ioo", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.volume_le_diam", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "exact", "rw"], "tactic_count": 4}
{"name": "Filter.Eventually.volume_pos_of_nhds_real", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["rcases", "grw", "simpa"], "tactic_count": 3}
{"name": "Real.volume_Icc_pi", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Real.volume_Icc_pi_toReal", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.volume_pi_Ioo", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.volume_pi_Ioo_toReal", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.volume_pi_Ioc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.volume_pi_Ioc_toReal", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.volume_pi_Ico", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.volume_pi_Ico_toReal", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.volume_pi_ball", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Real.volume_pi_closedBall", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Real.volume_pi_le_prod_diam", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.volume_pi_le_diam_pow", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.smul_map_volume_mul_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["refine", "rcases", "simp", "preimage_const_mul_Ioo_of_neg", "simp", "mul_sub,"], "tactic_count": 6}
{"name": "Real.map_volume_mul_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["conv_rhs", "rw", "abs_one,"], "tactic_count": 3}
{"name": "Real.volume_preimage_mul_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.smul_map_volume_mul_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.map_volume_mul_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.volume_preimage_mul_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.smul_map_diagonal_volume_pi", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["refine", "simp", "rw", "swap", "have", "ext", "simp", "diagonal_toLin']", "have", "intro", "have", "simp", "exact", "rw", "abs_one,", "rw", "simp"], "tactic_count": 17}
{"name": "Real.volume_preserving_transvectionStruct", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["translation,", "have", "refine", "refine", "have", "simp_rw", "rw", "refine", "simp_rw", "ext", "cases", "mk", "simp", "lintegral_add_right_eq_self"], "tactic_count": 14}
{"name": "Real.map_matrix_volume_pi_eq_smul_volume_pi", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["apply", "intro", "conv_rhs", "rw", "one_smul]", "intro", "simp_rw", "intro", "rw", "apply", "apply", "apply", "apply"], "tactic_count": 13}
{"name": "Real.map_linearMap_volume_pi_eq_smul_volume_pi", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["classical", "let", "have", "have", "rw", "apply", "rwa"], "tactic_count": 7}
{"name": "regionBetween", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "regionBetween_subset", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "measurableSet_regionBetween", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "refine", "exact"], "tactic_count": 3}
{"name": "measurableSet_region_between_oc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "refine", "exact"], "tactic_count": 3}
{"name": "measurableSet_region_between_co", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "refine", "exact"], "tactic_count": 3}
{"name": "measurableSet_region_between_cc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "refine", "exact"], "tactic_count": 3}
{"name": "measurableSet_graph", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "volume_regionBetween_eq_lintegral'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["classical", "rw", "have", "funext", "rw", "split_ifs", "have", "simp", "have", "simp", "dsimp", "rw", "exact"], "tactic_count": 13}
{"name": "volume_regionBetween_eq_lintegral", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": false, "tactics": ["have", "have", "apply", "apply", "exact", "rw", "convert", "rw", "exact", "rw", "exact"], "tactic_count": 11}
{"name": "nullMeasurableSet_regionBetween", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["refine", "exact", "exact"], "tactic_count": 3}
{"name": "nullMeasurableSet_region_between_oc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["refine", "exact", "change", "rw", "ext", "simp", "exact"], "tactic_count": 7}
{"name": "nullMeasurableSet_region_between_co", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["refine", "change", "rw", "ext", "simp", "exact", "exact"], "tactic_count": 7}
{"name": "nullMeasurableSet_region_between_cc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["refine", "change", "rw", "ext", "simp", "exact", "change", "rw", "ext", "simp", "exact"], "tactic_count": 11}
{"name": "ae_restrict_of_ae_restrict_inter_Ioo", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["two", "let", "let", "have", "obtain", "isOpen_iUnion_countable", "have", "intro", "by_cases", "rw", "obtain", "simpa", "right", "exact", "exact", "apply", "rw", "constructor", "have", "simp", "rintro", "dsimp", "rcases", "simp", "exact"], "tactic_count": 25}
{"name": "ae_of_mem_of_ae_of_mem_inter_Ioo", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Basic", "is_tactic_proof": true, "tactics": ["two", "let", "let", "have", "obtain", "isOpen_iUnion_countable", "have", "have", "rw", "rintro", "change", "rcases", "simp", "exact", "filter_upwards", "intro", "by_cases", "rw", "obtain", "simpa", "apply", "exact"], "tactic_count": 22}
{"name": "Complex.measurableEquivPi", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.measurableEquivPi_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.measurableEquivPi_symm_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.measurableEquivRealProd", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.measurableEquivRealProd_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.measurableEquivRealProd_symm_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.volume_preserving_equiv_pi", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Complex", "is_tactic_proof": true, "tactics": ["convert", "rw", "exact"], "tactic_count": 3}
{"name": "Complex.volume_preserving_equiv_real_prod", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.PositiveCompacts.Icc01", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.PositiveCompacts.piIcc01", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.parallelepiped_basisFun", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.parallelepiped_eq_map", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar", "is_tactic_proof": true, "tactics": ["classical", "rw", "congr", "simp"], "tactic_count": 4}
{"name": "Module.Basis.map_addHaar", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar", "is_tactic_proof": false, "tactics": ["rw", "erw"], "tactic_count": 2}
{"name": "MeasureTheory.addHaarMeasure_eq_volume", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "MeasureTheory.addHaarMeasure_eq_volume_pi", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.isAddHaarMeasure_volume_pi", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.addHaar_eq_zero_of_disjoint_translates_aux", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar", "is_tactic_proof": true, "tactics": ["by_contra", "apply", "calc", "measure_iUnion"], "tactic_count": 4}
{"name": "MeasureTheory.Measure.addHaar_eq_zero_of_disjoint_translates", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar", "is_tactic_proof": false, "tactics": ["suffices", "apply", "calc", "μ", "conv_lhs", "exact", "intro", "apply", "addHaar_eq_zero_of_disjoint_translates_aux", "refine", "exact"], "tactic_count": 11}
{"name": "MeasureTheory.Measure.addHaar_submodule", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "have", "have", "isBounded_range_of_tendsto", "apply", "intro", "simp", "intro", "have", "convert", "simp", "have", "simpa", "have", "convert", "rw", "exact"], "tactic_count": 18}
{"name": "MeasureTheory.Measure.addHaar_affineSubspace", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar", "is_tactic_proof": true, "tactics": ["rcases", "rw", "rw", "rcases", "simpa", "measure_preimage_add_right]"], "tactic_count": 6}
{"name": "MeasureTheory.Measure.map_linearMap_addHaar_pi_eq_smul_addHaar", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar", "is_tactic_proof": true, "tactics": ["cases", "have", "rw"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.map_linearMap_addHaar_eq_smul_addHaar", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar", "is_tactic_proof": true, "tactics": ["let", "haveI", "have", "have", "obtain", "have", "rw", "have", "ext", "simp", "simp", "have", "have", "have", "rw", "haveI", "have", "rw", "ecomp,"], "tactic_count": 19}
{"name": "MeasureTheory.Measure.addHaar_preimage_linearMap", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.addHaar_preimage_continuousLinearMap", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.addHaar_preimage_linearEquiv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar", "is_tactic_proof": true, "tactics": ["have", "convert", "simp"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.addHaar_preimage_continuousLinearEquiv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.addHaar_image_linearMap", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar", "is_tactic_proof": true, "tactics": ["rcases", "let", "change", "rw", "congr", "simp", "have", "exact"], "tactic_count": 8}
{"name": "MeasureTheory.Measure.addHaar_image_continuousLinearMap", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.addHaar_image_continuousLinearEquiv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.LinearMap.quasiMeasurePreserving", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.ContinuousLinearMap.quasiMeasurePreserving", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.map_addHaar_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar", "is_tactic_proof": true, "tactics": ["let", "change", "have", "simp", "exact", "simp"], "tactic_count": 6}
{"name": "MeasureTheory.Measure.quasiMeasurePreserving_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.addHaar_preimage_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.addHaar_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar", "is_tactic_proof": true, "tactics": ["rcases", "rw", "rcases", "simp", "rw", "by_cases", "haveI", "simp", "haveI", "simp"], "tactic_count": 10}
{"name": "MeasureTheory.Measure.addHaar_smul_of_nonneg", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.addHaar_nnreal_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.NullMeasurableSet.const_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar", "is_tactic_proof": true, "tactics": ["obtain", "simp", "obtain", "simpa", "obtain", "refine", "rw", "rw"], "tactic_count": 8}
{"name": "MeasureTheory.Measure.addHaar_image_homothety", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.addHaar_ball_center", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.addHaar_real_ball_center", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.addHaar_closedBall_center", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.addHaar_real_closedBall_center", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.addHaar_ball_mul_of_pos", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar", "is_tactic_proof": false, "tactics": ["have", "simp", "simp"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.addHaar_ball_of_pos", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.addHaar_ball_mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar", "is_tactic_proof": true, "tactics": ["rcases", "simp", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.addHaar_ball", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.addHaar_closedBall_mul_of_pos", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar", "is_tactic_proof": false, "tactics": ["have", "simp", "simp"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.addHaar_closedBall_mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar", "is_tactic_proof": false, "tactics": ["have", "simp", "simp"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.addHaar_closedBall'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.addHaar_real_closedBall'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar", "is_tactic_proof": false, "tactics": ["simp", "left", "positivity"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.addHaar_unitClosedBall_eq_addHaar_unitBall", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar", "is_tactic_proof": true, "tactics": ["apply", "have", "refine", "exact", "simp", "refine", "filter_upwards", "rw", "exact"], "tactic_count": 9}
{"name": "MeasureTheory.Measure.addHaar_closedBall", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.addHaar_real_closedBall", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.addHaar_closedBall_eq_addHaar_ball", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "rw"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.addHaar_real_closedBall_eq_addHaar_real_ball", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.addHaar_sphere_of_ne_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rw", "measure_diff", "addHaar_ball_of_pos"], "tactic_count": 5}
{"name": "MeasureTheory.Measure.addHaar_sphere", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar", "is_tactic_proof": true, "tactics": ["rcases", "rw", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.addHaar_singleton_add_smul_div_singleton_add_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.isUnifLocDoublingMeasureOfIsAddHaarMeasure", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar", "is_tactic_proof": true, "tactics": ["refine", "filter_upwards", "rw", "simp"], "tactic_count": 4}
{"name": "MeasureTheory.Measure.addHaar_parallelepiped", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "exact", "rw"], "tactic_count": 5}
{"name": "MeasureTheory.Measure.definition._@.Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar.3071773250._hygCtx._hyg.2", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.wrapped._@.Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar.3071773250._hygCtx._hyg.2", "kind": "opaque", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.measure", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlternatingMap.measure_def", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar", "is_tactic_proof": true, "tactics": ["intros", "delta", "rw", "rfl"], "tactic_count": 4}
{"name": "AlternatingMap.measure_parallelepiped", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar", "is_tactic_proof": true, "tactics": ["conv_rhs", "simp", "smul_eq_mul,"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.instIsAddLeftInvariantMeasure", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.instIsLocallyFiniteMeasureMeasure", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.tendsto_addHaar_inter_smul_zero_of_density_zero_aux1", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar", "is_tactic_proof": false, "tactics": ["have", "apply", "filter_upwards", "rintro", "grw", "rw", "have", "apply", "filter_upwards", "rintro", "have", "simp", "singleton_add_closedBall,", "simp", "simp", "have", "apply", "simp", "simp", "apply", "filter_upwards", "rintro", "calc", "μ", "μ", "rw"], "tactic_count": 26}
{"name": "MeasureTheory.Measure.tendsto_addHaar_inter_smul_zero_of_density_zero_aux2", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar", "is_tactic_proof": true, "tactics": ["set", "set", "have", "apply", "simp", "inv_eq_zero,", "refine", "rw", "have", "apply", "exact", "filter_upwards", "intro", "rw", "exact", "rw", "apply", "filter_upwards", "rintro", "have", "have", "dsimp", "rw"], "tactic_count": 23}
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{"name": "MeasureTheory.Measure.tendsto_addHaar_inter_smul_one_of_density_one_aux", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar", "is_tactic_proof": false, "tactics": ["have", "intro", "simp_rw", "rw", "simp", "congr", "rw", "exact", "have", "have", "apply", "filter_upwards", "intro", "rw", "exact", "exact", "have", "simp", "apply", "filter_upwards", "rintro", "convert", "rw", "have", "tendsto_addHaar_inter_smul_zero_of_density_zero", "have", "apply", "filter_upwards", "rintro", "rw", "have", "simp", "apply", "filter_upwards", "rintro", "refine", "simp", "or_false,", "simp", "singleton_add]"], "tactic_count": 40}
{"name": "MeasureTheory.Measure.tendsto_addHaar_inter_smul_one_of_density_one", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar", "is_tactic_proof": false, "tactics": ["have", "apply", "apply", "refine", "gcongr", "apply", "filter_upwards", "rintro", "apply", "rw", "exact", "refine", "congr", "apply", "simp", "apply"], "tactic_count": 16}
{"name": "MeasureTheory.Measure.eventually_nonempty_inter_smul_of_density_one", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar", "is_tactic_proof": false, "tactics": ["obtain", "exists_subset_measure_lt_top", "filter_upwards", "intro", "have", "have", "apply", "exact"], "tactic_count": 8}
{"name": "volume_regionBetween_eq_integral'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Integral", "is_tactic_proof": false, "tactics": ["have", "hfg.mono", "rw", "lintegral_congr_ae,", "dsimp", "rfl"], "tactic_count": 6}
{"name": "volume_regionBetween_eq_integral", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.integrable_of_summable_norm_Icc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Integral", "is_tactic_proof": false, "tactics": ["refine", "integrable_of_summable_norm_restrict", "mul_nonneg", "simp", "mul_one,", "intro", "have", "simpa", "exact"], "tactic_count": 9}
{"name": "integral_comp_neg_Iic", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Integral", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "simp_rw"], "tactic_count": 4}
{"name": "integral_comp_neg_Ioi", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Integral", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "integral_comp_abs", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.Integral", "is_tactic_proof": false, "tactics": ["have", "refine", "rw", "by_cases", "have", "rw", "let", "rw", "simp_rw", "exact", "calc", "rw", "rw", "congr", "rw", "refine", "rw", "have", "contrapose", "exact", "rw"], "tactic_count": 21}
{"name": "MeasureTheory.measure_unitBall_eq_integral_div_gamma", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.VolumeOfBalls", "is_tactic_proof": true, "tactics": ["obtain", "rw", "integral_singleton,", "norm_zero,", "ofReal_toReal", "have", "have", "simp_rw", "rw", "field", "rw", "mul_div_assoc,", "exact"], "tactic_count": 13}
{"name": "MeasureTheory.measure_lt_one_eq_integral_div_gamma", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.VolumeOfBalls", "is_tactic_proof": true, "tactics": ["letI", "letI", "dist", "dist_self", "dist_comm", "dist_triangle", "edist", "edist_dist", "eq_of_dist_eq_zero", "letI", "letI", "letI", "have", "let", "let", "convert", "rw", "congr", "simp_rw", "rfl", "refine", "exact", "let", "have", "rw", "rfl"], "tactic_count": 26}
{"name": "MeasureTheory.measure_le_eq_lt", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.VolumeOfBalls", "is_tactic_proof": true, "tactics": ["letI", "letI", "dist", "dist_self", "dist_comm", "dist_triangle", "edist", "edist_dist", "eq_of_dist_eq_zero", "letI", "letI", "letI", "have", "let", "let", "convert", "rw", "congr", "simp_rw", "rfl", "refine", "exact", "rw", "congr", "simp_rw", "rfl", "refine", "exact"], "tactic_count": 28}
{"name": "MeasureTheory.volume_sum_rpow_lt_one", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Lebesgue.VolumeOfBalls", "is_tactic_proof": true, "tactics": ["have", "have", "have", "refine", "exact", "have", "simp", "have", "have", "have", "have", "have", "have", "norm_smul_le", "simp_rw", "convert", "nm_neg", "rw", "exact", "simp_rw", "rw", "integral_exp_neg_rpow", "rw"], "tactic_count": 23}
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{"name": "MeasureTheory.integral_llr_tilted_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.LogLikelihoodRatio", "is_tactic_proof": true, "tactics": ["calc", "integral_congr_ae", "rw", "swap", "rw", "swap", "simp"], "tactic_count": 7}
{"name": "MeasureTheory.Measure.liftLinear", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.liftLinear_apply₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.liftLinear_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.le_liftLinear_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.mapₗ", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.mapₗ_congr", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Map", "is_tactic_proof": true, "tactics": ["ext1", "simpa"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.definition._@.Mathlib.MeasureTheory.Measure.Map.2222372135._hygCtx._hyg.8", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.wrapped._@.Mathlib.MeasureTheory.Measure.Map.2222372135._hygCtx._hyg.8", "kind": "opaque", "module": "Mathlib.MeasureTheory.Measure.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.map", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.map_def", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Map", "is_tactic_proof": true, "tactics": ["intros", "delta", "rw", "rfl"], "tactic_count": 4}
{"name": "MeasureTheory.Measure.mapₗ_mk_apply_of_aemeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Map", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.mapₗ_apply_of_measurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Map", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.map_add", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Map", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.map_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Map", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.map_of_not_aemeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Map", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AEMeasurable.of_map_ne_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.map_congr", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Map", "is_tactic_proof": true, "tactics": ["by_cases", "have", "simp", "exact", "have", "simp"], "tactic_count": 6}
{"name": "MeasureTheory.Measure.map_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Map", "is_tactic_proof": true, "tactics": ["suffices", "clear", "rcases", "by_cases", "have", "simp", "congr", "apply", "exact", "have", "intro", "exact", "simp"], "tactic_count": 13}
{"name": "MeasureTheory.Measure.map_apply₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Map", "is_tactic_proof": true, "tactics": ["rw", "rw", "rfl"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.map_apply_of_aemeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.map_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.map_toOuterMeasure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Map", "is_tactic_proof": true, "tactics": ["rw", "intro", "simp"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.map_eq_zero_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Map", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.mapₗ_eq_zero_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Map", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.measure_preimage_of_map_eq_self", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Map", "is_tactic_proof": true, "tactics": ["rw", "rwa", "rw", "simp"], "tactic_count": 4}
{"name": "MeasureTheory.Measure.map_ne_zero_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.mapₗ_ne_zero_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.map_id", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.map_id'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.map_map", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.map_mono", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.le_map_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.le_map_apply_image", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.preimage_null_of_map_null", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.tendsto_ae_map", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.mem_ae_map_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Map", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.mem_ae_of_mem_ae_map", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.ae_map_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.ae_of_ae_map", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.ae_map_mem_range", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Map", "is_tactic_proof": true, "tactics": ["by_cases", "change", "rw", "filter_upwards", "simp"], "tactic_count": 5}
{"name": "MeasurableEmbedding.map_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Map", "is_tactic_proof": true, "tactics": ["refine", "set", "have", "have", "rw", "exact", "have", "rw", "calc", "μ.map"], "tactic_count": 10}
{"name": "MeasurableEmbedding.map_injective", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Map", "is_tactic_proof": true, "tactics": ["intro", "ext", "rw", "congr"], "tactic_count": 4}
{"name": "MeasurableEquiv.map_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.map_symm_map", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Map", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasurableEquiv.map_map_symm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Map", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasurableEquiv.map_measurableEquiv_injective", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Map", "is_tactic_proof": true, "tactics": ["intro", "apply_fun", "simpa"], "tactic_count": 3}
{"name": "MeasurableEquiv.map_apply_eq_iff_map_symm_apply_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Map", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasurableEquiv.map_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Map", "is_tactic_proof": true, "tactics": ["ext", "simp_rw"], "tactic_count": 2}
{"name": "MeasureTheory.ae_isMeasurablyGenerated", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.ae_uIoc_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.measure_union", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_union'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_inter_add_diff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_diff_add_inter", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_diff_eq_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["contrapose", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.measure_union_add_inter", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": ["rw", "measure_inter_add_diff", "ac_rfl"], "tactic_count": 3}
{"name": "MeasureTheory.measure_union_add_inter'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.measure_symmDiff_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.measure_symmDiff_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_symmDiff_eq_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_add_measure_compl", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_biUnion₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["haveI", "rw", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.measure_biUnion", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_sUnion₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.measure_sUnion", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.measure_biUnion_finset₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.measure_biUnion_finset", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.tsum_meas_le_meas_iUnion_of_disjoint₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["rw", "intro", "simp", "gcongr", "exact"], "tactic_count": 5}
{"name": "MeasureTheory.tsum_meas_le_meas_iUnion_of_disjoint", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.tsum_measure_preimage_singleton", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.measure_preimage_eq_zero_iff_of_countable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.sum_measure_preimage_singleton", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.sum_measure_singleton", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["trans", "simp", "rw", "simp", "simp"], "tactic_count": 5}
{"name": "MeasureTheory.measure_diff_null'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_add_diff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.measure_diff'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_diff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.le_measure_diff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.le_measure_symmDiff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_eq_top_iff_of_symmDiff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["suffices", "intro", "by_contra", "apply", "rw", "calc"], "tactic_count": 6}
{"name": "MeasureTheory.measure_ne_top_iff_of_symmDiff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_diff_lt_of_lt_add", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.measure_diff_le_iff_le_add", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.measure_eq_measure_of_null_diff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_eq_measure_of_between_null_diff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["have", "have", "have", "calc", "μ", "exact"], "tactic_count": 6}
{"name": "MeasureTheory.measure_eq_measure_smaller_of_between_null_diff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_eq_measure_larger_of_between_null_diff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_compl₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.measure_compl", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_inter_conull'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.measure_inter_conull", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.union_ae_eq_left_iff_ae_subset", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["rw", "refine", "eventuallyLE_antisymm_iff.mpr"], "tactic_count": 3}
{"name": "MeasureTheory.union_ae_eq_right_iff_ae_subset", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.ae_eq_of_ae_subset_of_measure_ge", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["refine", "replace", "replace", "rw"], "tactic_count": 4}
{"name": "MeasureTheory.ae_eq_of_subset_of_measure_ge", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_iUnion_congr_of_subset", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["refine", "by_cases", "rcases", "calc", "μ", "set", "have", "refine", "calc", "μ", "measure_mono", "subset_inter", "measurability", "rw", "exact", "calc", "μ"], "tactic_count": 17}
{"name": "MeasureTheory.measure_union_congr_of_subset", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.measure_iUnion_toMeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_biUnion_toMeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["haveI", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.measure_toMeasurable_union", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_union_toMeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.sum_measure_le_measure_univ", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.tsum_measure_le_measure_univ", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.exists_nonempty_inter_of_measure_univ_lt_tsum_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["contrapose", "apply", "intro", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.exists_nonempty_inter_of_measure_univ_lt_sum_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["contrapose", "apply", "intro", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.nonempty_inter_of_measure_lt_add", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["rw", "contrapose", "calc", "μ"], "tactic_count": 4}
{"name": "MeasureTheory.nonempty_inter_of_measure_lt_add'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "Directed.measure_iUnion", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["rcases", "generalize", "replace", "suffices", "simp", "bot_eq_empty,", "exact", "clear", "refine", "le_antisymm", "set", "set", "have", "calc", "μ", "iSup_le", "rcases", "calc"], "tactic_count": 18}
{"name": "Monotone.measure_iUnion", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["cases", "inl", "inr", "rcases", "rw", "exacts"], "tactic_count": 6}
{"name": "Antitone.measure_iUnion", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_iUnion_eq_iSup_accumulate", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.measure_biUnion_eq_iSup", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["haveI", "rw"], "tactic_count": 2}
{"name": "Directed.measure_iInter", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["rcases", "have", "rw", "measure_diff", "congr", "refine", "rcases", "use", "rw", "gcongr", "exact"], "tactic_count": 11}
{"name": "Monotone.measure_iInter", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["refine", "have", "rcases", "calc", "refine", "rcases", "rcases", "exact", "refine", "rcases", "exact"], "tactic_count": 11}
{"name": "Antitone.measure_iInter", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_iInter_eq_iInf_measure_iInter_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact", "exact", "exact", "refine", "rfl"], "tactic_count": 7}
{"name": "MeasureTheory.tendsto_measure_iUnion_atTop", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["refine", "have", "rw", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.tendsto_measure_iUnion_atBot", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.tendsto_measure_iUnion_accumulate", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["refine", "have", "rw", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.tendsto_measure_iInter_atTop", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["refine", "have", "rw", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.tendsto_measure_iInter_atBot", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.tendsto_measure_iInter_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["refine", "cases", "rw", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.exists_measure_iInter_lt", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["let", "have", "suffices", "let", "rw", "exact", "have", "rw", "exact"], "tactic_count": 9}
{"name": "MeasureTheory.tendsto_measure_biInter_gt", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["by_cases", "have", "rw", "infer_instance", "simp_rw", "apply", "rwa", "exact", "simpa", "rw", "rcases", "simp"], "tactic_count": 12}
{"name": "MeasureTheory.measure_if", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["split_ifs"], "tactic_count": 1}
{"name": "MeasureTheory.ext_of_measurableAtoms", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["ext", "have", "ext", "simp", "refine", "exact", "exact", "rw", "rw", "have", "have", "intro", "obtain", "obtain", "rw", "refine", "exact", "have", "obtain", "rw", "exact", "rw", "congr", "have", "obtain", "rw", "exact"], "tactic_count": 27}
{"name": "MeasureTheory.OuterMeasure.toMeasure", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.le_toOuterMeasure_caratheodory", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.toMeasure_toOuterMeasure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.toMeasure_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.le_toMeasure_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.toMeasure_apply₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["refine", "rcases", "calc", "m.toMeasure"], "tactic_count": 4}
{"name": "MeasureTheory.toOuterMeasure_toMeasure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.boundedBy_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.measure_inter_eq_of_measure_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["rw", "refine", "have", "calc", "μ", "have", "exact"], "tactic_count": 7}
{"name": "MeasureTheory.Measure.measure_inter_eq_of_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["refine", "apply", "filter_upwards"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.measure_toMeasurable_inter", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.instZero", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.zero_toOuterMeasure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.coe_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.toMeasure_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.OuterMeasure.toMeasure_eq_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.apply_eq_zero_of_isEmpty", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.instSubsingleton", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.eq_zero_of_isEmpty", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.instInhabited", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.instAdd", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.add_toOuterMeasure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.coe_add", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.add_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.instSMul", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.smul_toOuterMeasure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.coe_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.smul_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.instSMulCommClass", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.instIsScalarTower", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.instIsCentralScalar", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.instMulAction", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.instAddCommMonoid", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.coeAddHom", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.coeAddHom_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.coe_finset_sum", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.finset_sum_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.instDistribMulAction", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.instModule", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.instModuleIsTorsionFree", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.ennreal_smul_eq_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.coe_nnreal_smul_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.nnreal_smul_coe_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.ae_smul_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.ae_smul_measure_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.ae_smul_measure_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.ae_smul_measure_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.ae_ennreal_smul_measure_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.ae_ennreal_smul_measure_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.measure_eq_left_of_subset_of_measure_add_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["refine", "have", "calc", "μ", "apply", "exact"], "tactic_count": 6}
{"name": "MeasureTheory.Measure.measure_eq_right_of_subset_of_measure_add_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.measure_toMeasurable_add_inter_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["refine", "refine", "rwa", "simp", "exact"], "tactic_count": 5}
{"name": "MeasureTheory.Measure.measure_toMeasurable_add_inter_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.instPartialOrder", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.toOuterMeasure_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.le_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.le_intro", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.le_iff'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.lt_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.lt_iff'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.instIsOrderedAddMonoid", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.le_add_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.le_add_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.sInf_caratheodory", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp", "intro", "have", "intro", "rw", "exact", "rw", "exact"], "tactic_count": 10}
{"name": "MeasureTheory.Measure.instInfSet", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.sInf_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.MeasureTheory.Measure.MeasureSpace.0.MeasureTheory.Measure.measure_sInf_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.MeasureTheory.Measure.MeasureSpace.0.MeasureTheory.Measure.measure_le_sInf", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.instCompleteSemilatticeInf", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.instCompleteLattice", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.inf_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["rw", "refine", "subst", "set", "refine", "by_cases", "refine", "simp", "refine", "simp", "simp", "rw", "exact", "simp", "intro", "simp", "simp", "set", "suffices", "have", "have", "simp_rw", "refine", "obtain", "refine", "by_contra", "simp", "exact", "have", "refine", "have", "conv", "rw", "refine", "rw", "intro", "rw", "intro", "rw", "simp", "rw", "rintro", "rw", "exact"], "tactic_count": 44}
{"name": "MeasureTheory.OuterMeasure.toMeasure_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.toOuterMeasure_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.top_add", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.add_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.zero_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.nonpos_iff_eq_zero'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.measure_univ_eq_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.measure_univ_ne_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.instNeZeroENNRealCoeSetUniv", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.measure_univ_pos", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.nonempty_of_neZero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.sum", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.le_sum_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.sum_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.sum_apply₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["apply", "rcases", "calc", "sum"], "tactic_count": 4}
{"name": "MeasureTheory.Measure.sum_apply_of_countable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["apply", "rcases", "calc", "sum"], "tactic_count": 4}
{"name": "MeasureTheory.Measure.le_sum", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.sum_apply_eq_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.sum_apply_eq_zero'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.sum_eq_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.sum_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.sum_sum", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["ext1", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.sum_comm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["ext1", "simp_rw", "rw"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.ae_sum_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.ae_sum_iff'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.sum_fintype", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["ext1", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.sum_coe_finset", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.ae_sum_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.sum_bool", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.sum_cond", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.sum_of_isEmpty", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.sum_add_sum_compl", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["ext1", "simp", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.sum_congr", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.sum_add_sum", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["ext1", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.sum_comp_equiv", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["ext", "simpa"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.sum_extend_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.cofinite", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.mem_cofinite", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.compl_mem_cofinite", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.eventually_cofinite", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.cofinite.instIsMeasurablyGenerated", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.cofinite_le_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["intro", "simp_all"], "tactic_count": 2}
{"name": "AEMeasurable.nullMeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.nullMeasurableSet_preimage", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.ae_eq_bot", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.ae_neBot", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.ae.neBot", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.ae_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.biSup_measure_Iic", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["rw", "congr", "simp", "exact", "exact"], "tactic_count": 5}
{"name": "MeasureTheory.tendsto_measure_Ico_atTop", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.tendsto_measure_Ioc_atBot", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.tendsto_measure_Iic_atTop", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.tendsto_measure_Ici_atBot", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Iio_ae_eq_Iic'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Ioi_ae_eq_Ici'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Ioo_ae_eq_Ioc'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Ioc_ae_eq_Icc'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Ioo_ae_eq_Ico'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Ioo_ae_eq_Icc'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Ico_ae_eq_Icc'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Ico_ae_eq_Ioc'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.termMeasure[_]_", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory._aux_Mathlib_MeasureTheory_Measure_MeasureSpaceDef___macroRules_MeasureTheory_termMeasure[_]__1", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.toOuterMeasure_injective", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.instFunLike", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.instOuterMeasureClass", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.real", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measureReal_def", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.trimmed", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.ofMeasurable", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.ofMeasurable_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.ext", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.ext_iff'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.outerMeasure_le_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.mono_null", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.coe_toOuterMeasure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.toOuterMeasure_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_eq_trim", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.measure_eq_iInf", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.measure_eq_iInf'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MeasureTheory.measure_eq_inducedOuterMeasure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.toOuterMeasure_eq_inducedOuterMeasure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_eq_extend", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.nonempty_of_measure_ne_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_mono_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_le_measure_union_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_le_measure_union_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.exists_measurable_superset", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.exists_measurable_superset_forall_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.exists_measurable_superset₂", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.exists_measurable_superset_of_null", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.exists_measurable_superset_iff_measure_eq_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_biUnion_lt_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": true, "tactics": ["convert", "ext", "rw", "simpa"], "tactic_count": 4}
{"name": "MeasureTheory.measure_biUnion_ne_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_union_lt_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_union_lt_top_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": true, "tactics": ["refine", "exact", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.measure_union_ne_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_symmDiff_ne_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_union_eq_top_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.exists_measure_pos_of_not_measure_iUnion_null", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": true, "tactics": ["contrapose", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.measure_lt_top_of_subset", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_ne_top_of_subset", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_inter_ne_top_of_left_ne_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_inter_lt_top_of_left_ne_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": true, "tactics": ["finiteness"], "tactic_count": 1}
{"name": "MeasureTheory.measure_inter_ne_top_of_right_ne_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_inter_lt_top_of_right_ne_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": true, "tactics": ["finiteness"], "tactic_count": 1}
{"name": "MeasureTheory.measure_inter_null_of_null_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_inter_null_of_null_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.ae_induction_on_inter", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": true, "tactics": ["filter_upwards"], "tactic_count": 1}
{"name": "MeasureTheory.definition._@.Mathlib.MeasureTheory.Measure.MeasureSpaceDef.264985881._hygCtx._hyg.8", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.wrapped._@.Mathlib.MeasureTheory.Measure.MeasureSpaceDef.264985881._hygCtx._hyg.8", "kind": "opaque", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.toMeasurable", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.toMeasurable_def", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": true, "tactics": ["intros", "delta", "rw", "rfl"], "tactic_count": 4}
{"name": "MeasureTheory.subset_toMeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": true, "tactics": ["rw", "exacts"], "tactic_count": 2}
{"name": "MeasureTheory.ae_le_toMeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measurableSet_toMeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": true, "tactics": ["rw", "exacts"], "tactic_count": 2}
{"name": "MeasureTheory.measure_toMeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": true, "tactics": ["rw", "exact", "simpa", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.term∀ᵐ_,_", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory._aux_Mathlib_MeasureTheory_Measure_MeasureSpaceDef___macroRules_MeasureTheory_term∀ᵐ_,__1", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory._aux_Mathlib_MeasureTheory_Measure_MeasureSpaceDef___delab_app_MeasureTheory_term∀ᵐ_,__1", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.term∃ᵐ_,_", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory._aux_Mathlib_MeasureTheory_Measure_MeasureSpaceDef___macroRules_MeasureTheory_term∃ᵐ_,__1", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory._aux_Mathlib_MeasureTheory_Measure_MeasureSpaceDef___delab_app_MeasureTheory_term∃ᵐ_,__1", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.tacticVolume_tac", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory._aux_Mathlib_MeasureTheory_Measure_MeasureSpaceDef___macroRules_MeasureTheory_tacticVolume_tac_1", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.termAEMeasurable[_]", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory._aux_Mathlib_MeasureTheory_Measure_MeasureSpaceDef___macroRules_MeasureTheory_termAEMeasurable[_]_1", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.aemeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.of_discrete", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.mk", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.measurable_mk", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.ae_eq_mk", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.congr", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "aemeasurable_congr", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "aemeasurable_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "aemeasurable_id", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "aemeasurable_id'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.comp_aemeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.comp_aemeasurable'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.eval", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": true, "tactics": ["use", "exact"], "tactic_count": 2}
{"name": "aemeasurable_pi_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": true, "tactics": ["constructor", "exact", "intro", "use", "exact"], "tactic_count": 5}
{"name": "aemeasurable_pi_lambda", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasureSpaceDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MeasuredSets", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.MeasuredSets", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.instSetLikeMeasuredSets", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.MeasuredSets", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.instPseudoEMetricSpaceMeasuredSets", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.MeasuredSets", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MeasuredSets.edist_def", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasuredSets", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MeasuredSets.sub_le_edist", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasuredSets", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MeasuredSets.continuous_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasuredSets", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.instPseudoMetricSpaceMeasuredSetsOfIsFiniteMeasure", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.MeasuredSets", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MeasuredSets.dist_def", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasuredSets", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MeasuredSets.real_sub_real_le_dist", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasuredSets", "is_tactic_proof": true, "tactics": ["grw", "exacts"], "tactic_count": 2}
{"name": "MeasureTheory.MeasuredSets.lipschitzWith_measureReal", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasuredSets", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.exists_measure_symmDiff_lt_of_generateFrom_isSetRing", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasuredSets", "is_tactic_proof": true, "tactics": ["all", "apply", "hC.isSetSemiring.isPiSystem", "intro", "exact", "intro", "exact", "that", "approximates", "enough", "concludes", "intro", "obtain", "obtain", "obtain", "rcases", "refine", "simp", "simp", "obtain", "have", "have", "have", "rw", "rw", "apply", "tendsto_measure_iInter_atTop", "apply", "rw", "exact", "obtain", "exact", "refine", "calc", "μ", "well", "intro", "rcases", "have", "choose", "have", "tendsto_measure_biUnion_Ici_zero_of_pairwise_disjoint", "obtain", "refine", "calc", "μ", "gcongr", "intro", "simp", "mem_union]", "grind", "apply", "gcongr", "apply"], "tactic_count": 54}
{"name": "MeasureTheory.exists_measure_symmDiff_lt_of_generateFrom_isSetSemiring", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasuredSets", "is_tactic_proof": true, "tactics": ["apply", "rcases", "exact", "rw", "apply", "apply", "apply"], "tactic_count": 7}
{"name": "MeasureTheory.dense_of_generateFrom_isSetRing", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasuredSets", "is_tactic_proof": true, "tactics": ["rw", "rintro", "rcases", "have", "refine", "simpa"], "tactic_count": 6}
{"name": "MeasureTheory.dense_of_generateFrom_isSetSemiring", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MeasuredSets", "is_tactic_proof": true, "tactics": ["rw", "rintro", "rcases", "refine", "rw", "exact"], "tactic_count": 6}
{"name": "MeasureTheory.Measure.MutuallySingular", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.MutuallySingular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.term_⟂ₘ_", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.MutuallySingular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory._aux_Mathlib_MeasureTheory_Measure_MutuallySingular___macroRules_MeasureTheory_term_⟂ₘ__1", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.MutuallySingular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory._aux_Mathlib_MeasureTheory_Measure_MutuallySingular___unexpand_MeasureTheory_Measure_MutuallySingular_1", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.MutuallySingular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.MutuallySingular.mk", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MutuallySingular", "is_tactic_proof": true, "tactics": ["use", "refine", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.MutuallySingular.nullSet", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.MutuallySingular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.MutuallySingular.measurableSet_nullSet", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MutuallySingular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.MutuallySingular.measure_nullSet", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MutuallySingular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.MutuallySingular.measure_compl_nullSet", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MutuallySingular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.MutuallySingular.restrict_nullSet", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MutuallySingular", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.MutuallySingular.restrict_compl_nullSet", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MutuallySingular", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.MutuallySingular.zero_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MutuallySingular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.MutuallySingular.symm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MutuallySingular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.MutuallySingular.comm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MutuallySingular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.MutuallySingular.zero_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MutuallySingular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.MutuallySingular.mono_ac", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MutuallySingular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.MutuallySingular.congr_ac", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MutuallySingular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.MutuallySingular.mono", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MutuallySingular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.MutuallySingular.self_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MutuallySingular", "is_tactic_proof": true, "tactics": ["refine", "rintro", "suffices", "rw"], "tactic_count": 4}
{"name": "MeasureTheory.Measure.MutuallySingular.sum_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MutuallySingular", "is_tactic_proof": true, "tactics": ["refine", "choose", "refine", "rw", "exact", "rwa"], "tactic_count": 6}
{"name": "MeasureTheory.Measure.MutuallySingular.sum_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MutuallySingular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.MutuallySingular.add_left_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MutuallySingular", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.MutuallySingular.add_right_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MutuallySingular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.MutuallySingular.add_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MutuallySingular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.MutuallySingular.add_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MutuallySingular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.MutuallySingular.smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MutuallySingular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.MutuallySingular.smul_nnreal", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MutuallySingular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.MutuallySingular.restrict", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MutuallySingular", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.eq_zero_of_absolutelyContinuous_of_mutuallySingular", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MutuallySingular", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.absolutelyContinuous_of_add_of_mutuallySingular", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MutuallySingular", "is_tactic_proof": true, "tactics": ["refine", "let", "have", "have", "have", "have", "conv_lhs", "rw", "exact", "exact", "rw", "refine", "simp", "exact"], "tactic_count": 14}
{"name": "MeasurableEmbedding.mutuallySingular_map", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MutuallySingular", "is_tactic_proof": true, "tactics": ["refine", "rw", "rw"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.exists_null_set_measure_lt_of_disjoint", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MutuallySingular", "is_tactic_proof": true, "tactics": ["have", "simp_rw", "have", "intro", "obtain", "refine", "norm_cast", "exact", "exact", "choose", "refine", "refine", "eq_zero_of_le_mul_pow", "rw", "refine", "exact"], "tactic_count": 16}
{"name": "MeasureTheory.Measure.mutuallySingular_of_disjoint", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MutuallySingular", "is_tactic_proof": false, "tactics": ["have", "convert", "push_cast", "rw", "norm_cast", "rw", "push_cast", "simp", "simp", "choose", "refine", "rw", "refine", "rw", "exact", "rw"], "tactic_count": 16}
{"name": "MeasureTheory.Measure.MutuallySingular.disjoint", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MutuallySingular", "is_tactic_proof": false, "tactics": ["have", "rw", "rfl", "intro", "rw", "ext", "simp", "rw", "exact", "measure_inter_null_of_null_right", "exact", "exact"], "tactic_count": 12}
{"name": "MeasureTheory.Measure.MutuallySingular.disjoint_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MutuallySingular", "is_tactic_proof": true, "tactics": ["rw", "intro", "refine", "rw", "exact", "rw", "exact", "rw", "inter_union_compl,"], "tactic_count": 9}
{"name": "MeasureTheory.Measure.disjoint_of_disjoint_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MutuallySingular", "is_tactic_proof": true, "tactics": ["simp_rw", "obtain", "rw", "have", "refine", "simp", "refine", "simp"], "tactic_count": 8}
{"name": "MeasureTheory.Measure.mutuallySingular_tfae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MutuallySingular", "is_tactic_proof": false, "tactics": ["tfae_have", "h", "tfae_have", "h", "tfae_have", "h", "tfae_have", "h", "tfae_finish"], "tactic_count": 9}
{"name": "MeasureTheory.Measure.mutuallySingular_iff_disjoint", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MutuallySingular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.mutuallySingular_iff_disjoint_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.MutuallySingular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.NullMeasurableSpace.instInhabited", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.NullMeasurableSpace.instSubsingleton", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.NullMeasurableSpace.instMeasurableSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSet.nullMeasurableSet", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.nullMeasurableSet_empty", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.nullMeasurableSet_univ", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.NullMeasurableSet.of_null", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.NullMeasurableSet.compl", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.NullMeasurableSet.of_compl", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.NullMeasurableSet.compl_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.NullMeasurableSet.of_subsingleton", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.NullMeasurableSet.congr", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.NullMeasurableSet.iUnion", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.NullMeasurableSet.biUnion", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.NullMeasurableSet.sUnion", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.NullMeasurableSet.iInter", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.NullMeasurableSet.biInter", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.NullMeasurableSet.sInter", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.NullMeasurableSet.union", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.NullMeasurableSet.union_null", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.NullMeasurableSet.inter", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.NullMeasurableSet.diff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.NullMeasurableSet.symmDiff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.NullMeasurableSet.disjointed", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.NullMeasurableSet.const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.NullMeasurableSet.instMeasurableSingletonClass", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.NullMeasurableSet.insert", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.NullMeasurableSet.exists_measurable_superset_ae_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": true, "tactics": ["rcases", "refine", "exact", "have", "simpa"], "tactic_count": 5}
{"name": "MeasureTheory.NullMeasurableSet.toMeasurable_ae_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.NullMeasurableSet.compl_toMeasurable_compl_ae_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.NullMeasurableSet.exists_measurable_subset_ae_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.exists_subordinate_pairwise_disjoint", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": true, "tactics": ["choose", "rcases", "exact", "hud.mono"], "tactic_count": 4}
{"name": "MeasureTheory.measure_iUnion", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": false, "tactics": ["rw", "simp", "exact", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.measure_iUnion₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": true, "tactics": ["rcases", "calc", "μ"], "tactic_count": 3}
{"name": "MeasureTheory.measure_union₀_aux", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": true, "tactics": ["rw", "exacts"], "tactic_count": 2}
{"name": "MeasureTheory.measure_inter_add_diff₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": true, "tactics": ["refine", "rcases", "replace", "calc", "μ"], "tactic_count": 5}
{"name": "MeasureTheory.measure_diff_symm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.measure_union_add_inter₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": true, "tactics": ["rw", "add_comm,"], "tactic_count": 2}
{"name": "MeasureTheory.measure_union_add_inter₀'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.measure_union₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.measure_union₀'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.measure_add_measure_compl₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.measure_of_measure_compl_eq_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.nullMeasurableSet_singleton", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.nullMeasurableSet_insert", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.nullMeasurableSet_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.nullMeasurableSet", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.nullMeasurableSet", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "Set.Finite.nullMeasurableSet_biUnion", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.nullMeasurableSet_biUnion", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.nullMeasurableSet_sUnion", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.nullMeasurableSet_biInter", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.nullMeasurableSet_biInter", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.nullMeasurableSet_sInter", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.nullMeasurableSet_toMeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_preimage_fst_singleton_eq_tsum", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": true, "tactics": ["rw", "preimage_fst_singleton_eq_range]"], "tactic_count": 2}
{"name": "MeasureTheory.measure_preimage_snd_singleton_eq_tsum", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
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{"name": "Measurable.nullMeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.NullMeasurable.measurable'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measurable.comp_nullMeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.NullMeasurable.congr", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.isComplete_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.IsComplete.out", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measurableSet_of_null", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.NullMeasurableSet.measurable_of_complete", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.NullMeasurable.measurable_of_complete", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.congr_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.completion", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.completion.isComplete", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.coe_completion", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.completion_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.ae_completion", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.NullMeasurable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.measure_ne_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.OpenPos", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.measure_pos", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.OpenPos", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.instNeZeroOfNonempty", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.OpenPos", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.measure_pos_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.OpenPos", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.measure_eq_zero_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.OpenPos", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.measure_pos_of_nonempty_interior", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.OpenPos", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.measure_pos_of_mem_nhds", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.OpenPos", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasureTheory.Measure.AbsolutelyContinuous.isOpenPosMeasure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.OpenPos", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LE.le.isOpenPosMeasure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.OpenPos", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.measure_zero_iff_eq_empty", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.OpenPos", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.ae_eq_empty_iff_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.OpenPos", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "IsClosed.ae_eq_univ_iff_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.OpenPos", "is_tactic_proof": true, "tactics": ["refine", "rwa"], "tactic_count": 2}
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{"name": "MeasureTheory.Measure.eqOn_open_of_ae_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.OpenPos", "is_tactic_proof": true, "tactics": ["replace", "simp", "have", "refine", "rcases", "exact", "replace", "exact"], "tactic_count": 8}
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{"name": "Continuous.ae_eq_iff_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.OpenPos", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.isOpenPosMeasure_map", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.OpenPos", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
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{"name": "Metric.measure_ball_pos", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.OpenPos", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.measure_closedBall_pos", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.OpenPos", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Metric.measure_closedEBall_pos", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.OpenPos", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsNowhereDense.of_isClosed_null", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.OpenPos", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMeagre.of_isSigmaCompact_null", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.OpenPos", "is_tactic_proof": true, "tactics": ["rcases", "have", "have", "exact", "rw", "exact"], "tactic_count": 6}
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{"name": "MeasureTheory.Measure.prod.instIsFiniteMeasure", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": true, "tactics": ["constructor", "rw", "finiteness"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.instIsFiniteMeasureProdVolume", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.prod.instIsProbabilityMeasure", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.instIsProbabilityMeasureProdVolume", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.prod.instIsFiniteMeasureOnCompacts", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.instIsFiniteMeasureOnCompactsProdVolume", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUnifLocDoublingMeasure.prod", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": true, "tactics": ["constructor", "use", "filter_upwards", "hνr", "rw", "grw"], "tactic_count": 6}
{"name": "MeasureTheory.Measure.IsUnifLocDoublingMeasure.volume_prod", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.ae_measure_lt_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.measure_prod_null_of_ae_null", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": true, "tactics": ["rw", "calc", "μ.prod"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.measure_prod_null", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.measure_ae_null_of_prod_null", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": true, "tactics": ["obtain", "rw", "rw", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.Measure.AbsolutelyContinuous.prod", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": true, "tactics": ["refine", "apply", "rw", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.Measure.ae_ae_of_ae_prod", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.ae_ae_eq_curry_of_prod", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.ae_ae_eq_of_ae_eq_uncurry", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.ae_prod_iff_ae_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.ae_prod_mem_iff_ae_ae_mem", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.quasiMeasurePreserving_fst", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": true, "tactics": ["refine", "rw", "refine", "rw"], "tactic_count": 4}
{"name": "MeasureTheory.Measure.quasiMeasurePreserving_snd", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": true, "tactics": ["refine", "rw", "refine", "rw"], "tactic_count": 4}
{"name": "MeasureTheory.Measure.set_prod_ae_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.measure_prod_compl_eq_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.NullMeasurableSet.prod", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.NullMeasurableSet.right_of_prod", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": true, "tactics": ["rcases", "obtain", "refine", "rwa"], "tactic_count": 4}
{"name": "MeasureTheory.NullMeasurableSet.of_preimage_snd", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.nullMeasurableSet_preimage_snd", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.nullMeasurable_comp_snd", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.FiniteSpanningSetsIn.prod", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": true, "tactics": ["haveI", "refine", "rw", "exact", "simp_rw"], "tactic_count": 5}
{"name": "MeasureTheory.Measure.prod_sum_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.prod_sum_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": true, "tactics": ["ext", "simp", "have", "simp_rw", "rw"], "tactic_count": 5}
{"name": "MeasureTheory.Measure.prod_sum", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.prod.instSigmaFinite", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.prod.instSFinite", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": false, "tactics": ["have", "conv_lhs", "apply", "rw", "infer_instance"], "tactic_count": 5}
{"name": "MeasureTheory.Measure.instSigmaFiniteProdVolume", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.instSFiniteProdVolume", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.prod_eq_generateFrom", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": false, "tactics": ["refine", "rintro", "haveI", "rw", "and"], "tactic_count": 5}
{"name": "MeasureTheory.Measure.prod_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.ext_prod", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": true, "tactics": ["ext", "have", "rw", "exact", "have", "refine", "rintro", "exact", "intro", "simp_rw", "intro", "simp_rw"], "tactic_count": 12}
{"name": "MeasureTheory.Measure.ext_prod_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.ext_prod₃", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": true, "tactics": ["ext", "have", "simp_rw", "exact", "have", "let", "let", "refine", "refine", "isCountablySpanning_measurableSet", "exact", "exact", "rintro", "exact", "intro", "simp_rw", "intro", "simp_rw"], "tactic_count": 18}
{"name": "MeasureTheory.Measure.ext_prod₃_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.ext_prod₃_iff'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": true, "tactics": ["rw", "have", "ν.map", "rw", "congr", "simp", "refine", "rwa", "rwa"], "tactic_count": 9}
{"name": "MeasureTheory.Measure.prod_swap", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": false, "tactics": ["have", "sum", "sum", "ext", "rw", "exact", "rw", "congr", "ext1", "refine", "intro", "simp_rw"], "tactic_count": 12}
{"name": "MeasureTheory.Measure.measurePreserving_swap", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.prod_apply_symm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.ae_ae_comm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.NullMeasurableSet.left_of_prod", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.NullMeasurableSet.of_preimage_fst", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.nullMeasurableSet_preimage_fst", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.nullMeasurable_comp_fst", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.nullMeasurableSet_prod_of_ne_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.nullMeasurableSet_prod", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "simp"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.prodAssoc_prod", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": false, "tactics": ["have", "sum", "sum", "ext", "rw", "simp", "rw", "map_sum", "congr", "ext1", "refine", "rintro", "simp_rw"], "tactic_count": 13}
{"name": "MeasureTheory.Measure.prod_restrict", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": false, "tactics": ["rw", "restrict_sum_of_countable]", "congr", "ext1", "refine", "rw"], "tactic_count": 6}
{"name": "MeasureTheory.Measure.restrict_prod_eq_prod_univ", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.prod_dirac", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": true, "tactics": ["classical", "rw", "congr", "ext1", "refine", "simp_rw", "indicator_mul_right"], "tactic_count": 7}
{"name": "MeasureTheory.Measure.dirac_prod", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": true, "tactics": ["classical", "rw", "congr", "ext1", "refine", "simp_rw", "indicator_mul_left"], "tactic_count": 7}
{"name": "MeasureTheory.Measure.dirac_prod_dirac", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.prod_add", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": true, "tactics": ["simp_rw", "congr", "ext1", "refine", "simp_rw"], "tactic_count": 5}
{"name": "MeasureTheory.Measure.add_prod", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": true, "tactics": ["simp_rw", "congr", "ext1", "refine", "simp_rw"], "tactic_count": 5}
{"name": "MeasureTheory.Measure.zero_prod", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.prod_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.map_prod_map", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": false, "tactics": ["simp_rw", "map_sum", "congr", "ext1", "refine", "rw", "exact", "prod_prod"], "tactic_count": 8}
{"name": "MeasureTheory.Measure.prod_smul_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": true, "tactics": ["ext", "rw", "simp"], "tactic_count": 3}
{"name": "MeasureTheory.MeasurePreserving.skew_product", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": true, "tactics": ["have", "use", "rcases", "simp", "have", "obtain", "rw", "infer_instance", "ext", "rw", "apply", "filter_upwards", "rw"], "tactic_count": 13}
{"name": "MeasureTheory.MeasurePreserving.prod", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.QuasiMeasurePreserving.prod_of_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": true, "tactics": ["refine", "refine", "rw", "rw"], "tactic_count": 4}
{"name": "MeasureTheory.QuasiMeasurePreserving.prod_of_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": true, "tactics": ["rw", "convert"], "tactic_count": 2}
{"name": "MeasureTheory.QuasiMeasurePreserving.fst", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.QuasiMeasurePreserving.snd", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.QuasiMeasurePreserving.prodMap", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "AEMeasurable.prod_swap", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.NullMeasurable.comp_fst", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.comp_fst", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.NullMeasurable.comp_snd", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.comp_snd", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.lintegral_prod_right'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": true, "tactics": ["obtain", "refine", "exact"], "tactic_count": 3}
{"name": "AEMeasurable.lintegral_prod_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.lintegral_prod_left'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.lintegral_prod_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.lintegral_prod_swap", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.lintegral_prod", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": true, "tactics": ["rw", "rw", "apply", "filter_upwards", "exact"], "tactic_count": 5}
{"name": "MeasureTheory.lintegral_prod_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.setLIntegral_prod", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.lintegral_prod_symm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.lintegral_prod_symm'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.setLIntegral_prod_symm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": true, "tactics": ["rw", "rfl", "refine", "convert", "rw"], "tactic_count": 5}
{"name": "MeasureTheory.lintegral_lintegral", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.lintegral_lintegral_symm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.lintegral_lintegral_swap", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.lintegral_prod_mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.fst", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.fst_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.fst_univ", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.fst_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.instSFiniteFstOfProd", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.fst.instIsFiniteMeasure", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.fst.instIsProbabilityMeasure", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.fst.instIsZeroOrProbabilityMeasure", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": true, "tactics": ["rcases", "simp", "infer_instance", "infer_instance"], "tactic_count": 4}
{"name": "MeasureTheory.Measure.fst_prod", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": true, "tactics": ["ext1", "rw"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.fst_map_prodMk₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": true, "tactics": ["by_cases", "ext1", "rw", "have", "contrapose", "exact", "simp"], "tactic_count": 7}
{"name": "MeasureTheory.Measure.fst_map_prodMk", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.fst_add", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.fst_sum", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.fst_mono", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.snd", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.snd_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.snd_univ", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.snd_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "MeasureTheory.measureReal_iUnion_fintype_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Real", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
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{"name": "MeasureTheory.Measure.Regular.weaklyRegular", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.OuterRegular.zero", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.exists_isOpen_lt_of_lt", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Regular", "is_tactic_proof": false, "tactics": ["rcases", "exact"], "tactic_count": 2}
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{"name": "Set.exists_isOpen_lt_add", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.exists_isOpen_le_add", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Regular", "is_tactic_proof": true, "tactics": ["rcases", "exact", "rcases", "exact"], "tactic_count": 4}
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{"name": "MeasureTheory.Measure.OuterRegular.smul_nnreal", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasureTheory.Measure.OuterRegular.measure_closure_eq_of_isCompact", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Regular", "is_tactic_proof": true, "tactics": ["apply", "simp", "intro", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.Measure.OuterRegular.ext_isOpen", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Regular", "is_tactic_proof": true, "tactics": ["ext", "rw", "congr", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.Measure.FiniteSpanningSetsIn.outerRegular", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.InnerRegularWRT.of_restrict", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Regular", "is_tactic_proof": true, "tactics": ["intro", "have", "have", "rw", "rcases", "rw", "rcases", "exact"], "tactic_count": 8}
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{"name": "MeasureTheory.Measure.InnerRegularWRT.of_sigmaFinite", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Regular", "is_tactic_proof": true, "tactics": ["intro", "set", "have", "have", "rw", "rcases", "refine", "exact"], "tactic_count": 8}
{"name": "MeasureTheory.Measure.InnerRegularWRT.measurableSet_of_isOpen", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Regular", "is_tactic_proof": true, "tactics": ["rintro", "have", "have", "obtain", "simpa", "obtain", "use", "simp", "rcases", "rcases", "replace", "rcases", "refine", "calc", "μ"], "tactic_count": 15}
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{"name": "MeasureTheory.Measure.InnerRegularWRT.of_pseudoMetrizableSpace", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Regular", "is_tactic_proof": true, "tactics": ["let", "intro", "rcases", "rw", "rcases", "exact"], "tactic_count": 6}
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{"name": "MeasureTheory.Measure.InnerRegular.smul", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasureTheory.Measure.InnerRegular.instSum", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Regular", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "insert"], "tactic_count": 4}
{"name": "MeasureTheory.Measure.InnerRegular.instSum_1", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Regular", "is_tactic_proof": true, "tactics": ["constructor", "intro", "have", "simp", "exact", "obtain", "simp", "exact", "rcases", "refine", "simp", "exact"], "tactic_count": 12}
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{"name": "MeasureTheory.Measure.InnerRegularCompactLTTop.restrict", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.InnerRegularCompactLTTop.instInnerRegularOfIsFiniteMeasure", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Regular", "is_tactic_proof": true, "tactics": ["constructor", "convert", "simp"], "tactic_count": 3}
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{"name": "MeasurableSet.exists_isOpen_symmDiff_lt", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Regular", "is_tactic_proof": true, "tactics": ["have", "rcases", "rcases", "refine", "rw", "gcongr", "calc", "μ", "apply", "exact", "exact"], "tactic_count": 11}
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{"name": "MeasureTheory.Measure.InnerRegularCompactLTTop.instInnerRegularOfSigmaFinite", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasureTheory.Measure.WeaklyRegular.zero", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.exists_lt_isClosed", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasureTheory.Measure.WeaklyRegular.innerRegular_measurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasurableSet.exists_lt_isClosed_of_ne_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSet.measure_eq_iSup_isClosed_of_ne_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.WeaklyRegular.restrict_of_measure_ne_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Regular", "is_tactic_proof": true, "tactics": ["haveI", "refine", "have", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.Measure.WeaklyRegular.of_pseudoMetrizableSpace_of_isFiniteMeasure", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.WeaklyRegular.of_pseudoMetrizableSpace_secondCountable_of_locallyFinite", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.WeaklyRegular.smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Regular", "is_tactic_proof": true, "tactics": ["haveI", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.WeaklyRegular.smul_nnreal", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.Regular.zero", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.exists_lt_isCompact", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.measure_eq_iSup_isCompact", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.Regular.exists_isCompact_not_null", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Regular", "is_tactic_proof": true, "tactics": ["simp_rw", "exists_prop,"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.Regular.instInnerRegularCompactLTTop", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.Regular.map", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Regular", "is_tactic_proof": true, "tactics": ["haveI", "haveI", "exact"], "tactic_count": 3}
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{"name": "MeasureTheory.Measure.Regular.restrict_of_measure_ne_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Regular", "is_tactic_proof": true, "tactics": ["have", "constructor", "intro", "have", "rw", "exact", "exact"], "tactic_count": 7}
{"name": "MeasureTheory.Measure.Regular.domSMul", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.Regular.of_sigmaCompactSpace_of_isLocallyFiniteMeasure", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Regular", "is_tactic_proof": true, "tactics": ["let", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.instInnerRegularOfPseudoMetrizableSpaceOfSigmaCompactSpaceOfBorelSpaceOfSigmaFinite", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Regular", "is_tactic_proof": true, "tactics": ["refine", "refine", "have", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.innerRegularWRT_isCompact_closure_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.RegularityCompacts", "is_tactic_proof": true, "tactics": ["constructor", "rcases", "exact", "rcases", "refine", "simpa", "exact"], "tactic_count": 7}
{"name": "MeasureTheory.innerRegularWRT_isCompact_isClosed_iff_innerRegularWRT_isCompact_closure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.RegularityCompacts", "is_tactic_proof": true, "tactics": ["constructor", "obtain", "refine", "simp", "exact", "obtain", "refine", "simpa", "exact"], "tactic_count": 9}
{"name": "MeasureTheory.innerRegularWRT_isCompact_isClosed_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.RegularityCompacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.innerRegularWRT_of_exists_compl_lt", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.RegularityCompacts", "is_tactic_proof": true, "tactics": ["intro", "obtain", "obtain", "refine", "refine", "simp", "refine", "have", "exact"], "tactic_count": 9}
{"name": "MeasureTheory.innerRegularWRT_isCompact_closure_of_univ", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.RegularityCompacts", "is_tactic_proof": true, "tactics": ["refine", "have", "refine", "refine", "rw"], "tactic_count": 5}
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{"name": "MeasureTheory.innerRegularWRT_isCompact_isOpen", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.RegularityCompacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.instInnerRegularOfIsCompletelyPseudoMetrizableSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.RegularityCompacts", "is_tactic_proof": true, "tactics": ["suffices", "refine", "exact", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.instInnerRegularCompactLTTopOfIsCompletelyPseudoMetrizableSpace", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.RegularityCompacts", "is_tactic_proof": true, "tactics": ["constructor", "intro", "have", "have", "have", "obtain", "use", "rwa"], "tactic_count": 8}
{"name": "MeasureTheory.innerRegular_isCompact_isClosed_measurableSet_of_finite", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.RegularityCompacts", "is_tactic_proof": false, "tactics": ["suffices", "convert", "simp", "exact", "refine", "exact", "rintro", "rw", "exact"], "tactic_count": 9}
{"name": "MeasureTheory.Measure.restrictₗ", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.restrict", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.restrictₗ_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.restrict_toOuterMeasure_eq_toOuterMeasure_restrict", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.restrict_apply₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["rw", "rw"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.restrict_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.restrict_mono'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.restrict_mono", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.restrict_mono_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.restrict_mono_set", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.restrict_mono_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.restrict_congr_set", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.restrict_apply'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.restrict_apply₀'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["rw", "measure_congr"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.restrict_le_self", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.absolutelyContinuous_restrict", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.restrict_eq_self", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.restrict_apply_self", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.restrict_apply_univ", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.le_restrict_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.restrict_apply_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.restrict_apply_superset", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.restrict_add", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.restrict_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.restrict_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.restrict_restrict₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.restrict_restrict", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.restrict_restrict_of_subset", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["ext1", "rw", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.restrict_restrict₀'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.restrict_restrict'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.restrict_comm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.restrict_apply_eq_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.measure_inter_eq_zero_of_restrict", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.restrict_apply_eq_zero'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.restrict_eq_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.restrict.neZero", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.restrict_zero_set", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.restrict_empty", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.restrict_univ", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.restrict_inter_add_diff₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["ext1", "simp", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.restrict_inter_add_diff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.restrict_union_add_inter₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["rw", "restrict_inter_add_diff₀"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.restrict_union_add_inter", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.restrict_union_add_inter'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.restrict_union₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.restrict_union", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.restrict_union'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.restrict_add_restrict_compl", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.restrict_compl_add_restrict", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.restrict_union_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.restrict_iUnion_apply_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["simp", "exact", "measure_iUnion₀", "ht.nullMeasurableSet.inter"], "tactic_count": 4}
{"name": "MeasureTheory.Measure.restrict_iUnion_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.restrict_iUnion_apply_eq_iSup", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["simp", "rw", "exacts"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.restrict_map", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.restrict_inter_toMeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["ext", "rw", "measure_toMeasurable_inter", "congr", "grind"], "tactic_count": 5}
{"name": "MeasureTheory.Measure.restrict_toMeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.restrict_eq_self_of_ae_mem", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.restrict_congr_meas", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.restrict_congr_mono", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.restrict_union_congr", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["refine", "rintro", "ext1", "simp", "rcases", "calc", "μ", "simp"], "tactic_count": 8}
{"name": "MeasureTheory.Measure.restrict_biUnion_finset_congr", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "insert", "simp", "rw"], "tactic_count": 6}
{"name": "MeasureTheory.Measure.restrict_iUnion_congr", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["refine", "ext1", "have", "rw", "simp"], "tactic_count": 5}
{"name": "MeasureTheory.Measure.restrict_biUnion_congr", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["haveI", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.restrict_sUnion_congr", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.restrict_sInf_eq_sInf_restrict", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["ext1", "simp_rw", "restrict_toOuterMeasure_eq_toOuterMeasure_restrict"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.exists_mem_of_measure_ne_zero_of_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.QuasiMeasurePreserving.restrict", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.ext_iff_of_iUnion_eq_univ", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.ext_iff_of_biUnion_eq_univ", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.ext_iff_of_sUnion_eq_univ", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.ext_of_generateFrom_of_cover", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["refine", "ext1", "simp", "induction", "empty", "basic", "compl", "have", "rw", "rwa", "exact", "iUnion", "ihf", "simp", "simp"], "tactic_count": 15}
{"name": "MeasureTheory.Measure.ext_of_generateFrom_of_cover_subset", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["refine", "intro", "simp", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.Measure.ext_of_generateFrom_of_iUnion", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["refine", "rintro", "apply", "rintro", "apply"], "tactic_count": 5}
{"name": "MeasureTheory.Measure.restrict_sum", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.restrict_sum_of_countable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["ext", "simp_rw"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.AbsolutelyContinuous.restrict", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.restrict_iUnion_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.restrict_iUnion", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.restrict_biUnion", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.restrict_biUnion_finset", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.restrict_iUnion_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.restrict_biUnion_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.ae_restrict_iUnion_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.ae_restrict_union_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.ae_restrict_biUnion_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["haveI", "rw"], "tactic_count": 2}
{"name": "MeasureTheory.ae_restrict_biUnion_finset_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.ae_restrict_iUnion_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.ae_restrict_union_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.ae_restrict_biUnion_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MeasureTheory.ae_restrict_biUnion_finset_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MeasureTheory.ae_eq_restrict_iUnion_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MeasureTheory.ae_eq_restrict_biUnion_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MeasureTheory.ae_eq_restrict_biUnion_finset_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.ae_restrict_uIoc_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.ae_restrict_uIoc_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.ae_restrict_iff₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["simp", "rw"], "tactic_count": 2}
{"name": "MeasureTheory.ae_restrict_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.ae_imp_of_ae_restrict", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["simp", "simpa"], "tactic_count": 2}
{"name": "MeasureTheory.ae_restrict_iff'₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["simp", "rw"], "tactic_count": 2}
{"name": "MeasureTheory.ae_restrict_iff'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.restrict", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.ae_restrict_mem₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.ae_restrict_mem", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.ae_restrict_of_forall_mem", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.ae_restrict_of_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.ae_restrict_of_ae_restrict_of_subset", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.ae_of_ae_restrict_of_ae_restrict_compl", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.mem_map_restrict_ae_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.ae_add_measure_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.ae_eq_comp'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.QuasiMeasurePreserving.ae_eq_comp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.ae_eq_comp", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.div_ae_eq_one", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["refine", "rwa", "rwa"], "tactic_count": 3}
{"name": "MeasureTheory.one_le_div_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["refine", "rwa", "rwa"], "tactic_count": 3}
{"name": "MeasureTheory.le_ae_restrict", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.ae_restrict_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["ext", "simp", "rfl"], "tactic_count": 3}
{"name": "MeasureTheory.ae_restrict_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.ae_restrict_eq_bot", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.ae_restrict_neBot", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.self_mem_ae_restrict", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.ae_restrict_of_ae_eq_of_ae_restrict", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.ae_restrict_congr_set", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.NullMeasurable.measure_preimage_eq_measure_restrict_preimage_of_ae_compl_eq_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["rw", "rw", "apply", "apply", "apply", "have", "apply", "rw", "apply", "intro", "simp", "exact", "simp", "exact"], "tactic_count": 14}
{"name": "MeasureTheory.nullMeasurableSet_restrict", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["refine", "obtain", "have", "have", "filter_upwards", "change", "simpa", "obtain", "have", "exact", "have", "apply", "rw", "simp", "have", "simpa"], "tactic_count": 16}
{"name": "MeasureTheory.nullMeasurableSet_restrict_of_subset", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["refine", "obtain", "h.exists_measurable_subset_ae_eq", "have", "apply", "filter_upwards", "have", "filter_upwards", "change", "simp", "tauto", "exact"], "tactic_count": 12}
{"name": "MeasureTheory.Measure.MeasurableSet.nullMeasurableSet_subtype_coe", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["rw", "induction", "hC", "obtain", "rw", "exact", "empty", "compl", "ht", "simp", "exact", "iUnion", "dsimp", "rw", "exact"], "tactic_count": 15}
{"name": "MeasureTheory.Measure.NullMeasurableSet.subtype_coe", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.measure_subtype_coe_le_comap", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.measure_subtype_coe_eq_zero_of_comap_eq_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.Subtype.measureSpace", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.Subtype.volume_def", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.Subtype.volume_univ", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["rw", "simp", "exact", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.Measure.volume_subtype_coe_le_volume", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.volume_subtype_coe_eq_zero_of_volume_eq_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEmbedding.map_comap", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["ext1", "rw", "image_preimage_eq_inter_range,"], "tactic_count": 3}
{"name": "MeasurableEmbedding.comap_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEmbedding.comap_map", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "MeasurableEmbedding.ae_map_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasurableEmbedding.restrict_map", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEmbedding.comap_preimage", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasurableEmbedding.comap_restrict", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["ext", "rw", "image_inter_preimage]"], "tactic_count": 3}
{"name": "MeasurableEmbedding.restrict_comap", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasurableEquiv.restrict_map", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.comap_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.map_eq_comap", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["ext", "rw", "congr", "simp", "grind"], "tactic_count": 5}
{"name": "comap_subtype_coe_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "map_comap_subtype_coe", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ae_restrict_iff_subtype", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "volume_set_coe_def", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSet.map_coe_volume", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "volume_image_subtype_coe", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "volume_preimage_coe", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["rw", "comap_apply₀", "image_preimage_eq_inter_range,"], "tactic_count": 3}
{"name": "piecewise_ae_eq_restrict", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "piecewise_ae_eq_restrict_compl", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "piecewise_ae_eq_of_ae_eq_set", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_map_indicator_ae_iff_mem_map_restrict_ae_of_zero_mem", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["classical", "simp_rw", "rw", "simp_rw", "change", "simp", "simp_rw"], "tactic_count": 7}
{"name": "mem_map_indicator_ae_iff_of_zero_notMem", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["classical", "rw", "change", "simp"], "tactic_count": 4}
{"name": "map_restrict_ae_le_map_indicator_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["intro", "by_cases", "rw", "exact", "rw", "exact"], "tactic_count": 6}
{"name": "indicator_ae_eq_restrict", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "indicator_ae_eq_restrict_compl", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "indicator_ae_eq_of_restrict_compl_ae_eq_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["rw", "filter_upwards", "by_cases", "simp", "simp"], "tactic_count": 5}
{"name": "indicator_ae_eq_zero_of_restrict_ae_eq_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["rw", "filter_upwards", "by_cases", "simp", "simp"], "tactic_count": 5}
{"name": "indicator_ae_eq_of_ae_eq_set", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "indicator_meas_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ae_eq_restrict_iff_indicator_ae_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["rw", "refine", "by_cases", "simp", "simp", "intro", "simpa"], "tactic_count": 7}
{"name": "MeasureTheory.Measure.sum_restrict_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Restrict", "is_tactic_proof": true, "tactics": ["classical", "refine", "refine", "let", "let", "let", "have", "measurableSet_biInter", "have", "refine", "exact", "simp_rw", "have", "intro", "simp_rw", "have", "have", "exact", "have", "intro", "simp", "exact", "have", "rw", "exact", "have", "mem_C", "calc", "restrict_biUnion_le", "rw", "congr", "rw", "rw", "congr", "by_cases", "simp", "refine", "by_cases", "simp", "have", "have", "exact", "nsmul_le_nsmul_left", "calc", "rw", "refine", "exact", "rw", "exact"], "tactic_count": 49}
{"name": "MeasureTheory.Measure.MeasureDense.nonempty", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.SeparableMeasure", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.MeasureDense.nonempty'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.SeparableMeasure", "is_tactic_proof": true, "tactics": ["rcases", "refine", "convert", "rw"], "tactic_count": 4}
{"name": "MeasureTheory.measureDense_measurableSet", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.SeparableMeasure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.MeasureDense.completion", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.SeparableMeasure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.MeasureDense.fin_meas_approx", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.SeparableMeasure", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.MeasureDense.indicatorConstLp_subset_closure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.SeparableMeasure", "is_tactic_proof": true, "tactics": ["obtain", "refine", "rintro", "obtain", "refine", "simp_rw", "simp", "have", "rintro", "refine", "have", "obtain", "refine", "rw", "calc", "have", "rw", "gcongr", "exact", "rw", "mul_div_cancel₀"], "tactic_count": 21}
{"name": "MeasureTheory.Measure.MeasureDense.fin_meas", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.SeparableMeasure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.MeasureDense.of_generateFrom_isSetAlgebra_finite", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.SeparableMeasure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.MeasureDense.of_generateFrom_isSetAlgebra_sigmaFinite", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.SeparableMeasure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.exists_countable_measureDense", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.SeparableMeasure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.isSeparable_of_sigmaFinite", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.SeparableMeasure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.instIsSeparableOfCountablyGeneratedOfSFinite", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.SeparableMeasure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.instIsSeparableNullMeasurableSpaceCompletion", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.SeparableMeasure", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.Lp.SecondCountableTopology", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.SeparableMeasure", "is_tactic_proof": true, "tactics": ["refine", "rcases", "have", "set", "have", "have", "rcases", "let", "let", "refine", "let", "have", "have", "have", "rintro", "use", "exact", "refine", "intro", "apply", "rw", "intro", "have", "have", "have", "rcases", "have", "refine", "rw", "refine", "rw", "calc", "mul_le_mul_of_nonneg_right", "rw", "exact", "mul_le_mul_of_nonneg_left", "rintro", "rw", "intro", "rcases", "rcases", "let", "let", "sg", "refine", "simp", "calc", "congr"], "tactic_count": 48}
{"name": "Iotop", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Iotop_subset_Ioc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": true, "tactics": ["simp", "split_ifs"], "tactic_count": 2}
{"name": "Ioo_subset_Iotop", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": true, "tactics": ["simp", "split_ifs"], "tactic_count": 2}
{"name": "isOpen_Iotop", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": true, "tactics": ["simp", "split_ifs", "have", "simp", "simp"], "tactic_count": 5}
{"name": "botSet", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ioc_diff_botSet", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": true, "tactics": ["rw", "rintro", "exact"], "tactic_count": 3}
{"name": "notMem_botSet_of_lt", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": true, "tactics": ["contrapose", "exact"], "tactic_count": 2}
{"name": "subsingleton_botSet", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurableSet_botSet", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "botSet_eq_singleton_of_isBot", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StieltjesFunction.instCoeFun", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StieltjesFunction.ext", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "StieltjesFunction.mono", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StieltjesFunction.right_continuous", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StieltjesFunction.rightLim_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "StieltjesFunction.iInf_Ioi_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": true, "tactics": ["suffices", "rw", "rw", "infer_instance"], "tactic_count": 4}
{"name": "StieltjesFunction.iInf_rat_gt_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": true, "tactics": ["rw", "refine", "refine", "rintro", "exact"], "tactic_count": 5}
{"name": "StieltjesFunction.id", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StieltjesFunction.id_leftLim", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StieltjesFunction.const", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StieltjesFunction.instInhabited", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StieltjesFunction.const_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StieltjesFunction.add", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StieltjesFunction.instAddZeroClass", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StieltjesFunction.instAddCommMonoid", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StieltjesFunction.instModuleNNReal", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StieltjesFunction.zero_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StieltjesFunction.add_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.stieltjesFunction", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.stieltjesFunction_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StieltjesFunction.countable_leftLim_ne", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": true, "tactics": ["refine", "intro", "apply", "exact"], "tactic_count": 4}
{"name": "StieltjesFunction.length", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StieltjesFunction.length_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "StieltjesFunction.length_eq_of_isEmpty", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "StieltjesFunction.length_empty", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": true, "tactics": ["rcases", "simp", "inhabit", "rw", "exact"], "tactic_count": 5}
{"name": "StieltjesFunction.length_Ioc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": true, "tactics": ["have", "rw", "refine", "le_antisymm", "rcases", "rw", "apply", "simp", "obtain", "exact"], "tactic_count": 10}
{"name": "StieltjesFunction.length_mono", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simp", "exact"], "tactic_count": 4}
{"name": "StieltjesFunction.length_diff_botSet", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simp"], "tactic_count": 3}
{"name": "StieltjesFunction.outer", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StieltjesFunction.outer_le_length", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StieltjesFunction.length_subadditive_Icc_Ioo", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": false, "tactics": ["suffices", "rcases", "isCompact_Icc.elim_finite_subcover_image", "have", "simp", "rw", "refine", "exact", "clear", "refine", "rcases", "rw", "exact", "obtain", "simpa", "rw", "rw", "rw", "replace", "grw", "gcongr", "rw", "exact", "rintro", "apply", "order"], "tactic_count": 26}
{"name": "StieltjesFunction.outer_Ioc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": true, "tactics": ["intervals,", "compactness", "the", "still", "very", "slightly", "will", "of", "as", "not", "refine", "rw", "apply", "rcases", "have", "simp", "apply", "let", "have", "rcases", "obtain", "have", "refine", "exact", "have", "have", "exact", "have", "have", "intro", "have", "conv", "lhs", "rw", "simp", "rcases", "have", "rintro", "apply", "simp", "by_cases", "refine", "rintro", "simp", "exact", "have", "have", "apply", "refine", "exact", "rcases", "exact", "choose", "have", "calc", "calc", "ofReal"], "tactic_count": 57}
{"name": "StieltjesFunction.measurableSet_Ioi", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": true, "tactics": ["refine", "have", "simp", "refine", "simp", "rw", "refine", "le_trans", "rcases", "simp", "f.length_empty,", "simp", "f.mono", "simp", "le_sup_iff,", "simp", "max_eq_left,"], "tactic_count": 17}
{"name": "StieltjesFunction.outer_trim", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": true, "tactics": ["refine", "rw", "refine", "rcases", "grw", "rw", "choose", "show", "intro", "rcases", "refine", "simpa", "have", "conv", "lhs", "rw", "simp", "rcases", "rw", "rw", "refine", "calc", "f.outer", "simp", "simp", "simp", "apply", "apply", "apply", "exact"], "tactic_count": 30}
{"name": "StieltjesFunction.borel_le_measurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp"], "tactic_count": 3}
{"name": "StieltjesFunction.definition._@.Mathlib.MeasureTheory.Measure.Stieltjes.1973370438._hygCtx._hyg.2", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StieltjesFunction.wrapped._@.Mathlib.MeasureTheory.Measure.Stieltjes.1973370438._hygCtx._hyg.2", "kind": "opaque", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StieltjesFunction.measure", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StieltjesFunction.measure_def", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": true, "tactics": ["intros", "delta", "rw", "rfl"], "tactic_count": 4}
{"name": "StieltjesFunction.measure_Ioc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "StieltjesFunction.measure_singleton", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": true, "tactics": ["by_cases", "have", "apply", "simp", "simp", "apply", "rw", "apply", "rw", "simp", "obtain", "obtain", "exists_seq_strictMono_tendsto", "replace", "have", "refine", "replace", "have", "simp", "have", "rw", "refine", "exact", "exact", "have", "simp", "have", "apply", "exact", "exact", "exact"], "tactic_count": 31}
{"name": "StieltjesFunction.measure_Icc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": true, "tactics": ["rcases", "have", "simp", "measure_union", "simp", "symm", "simp"], "tactic_count": 7}
{"name": "StieltjesFunction.measure_Ioo", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": true, "tactics": ["rcases", "simp", "symm", "simp", "have", "have", "have", "simp", "rw", "simpa", "simp", "simp"], "tactic_count": 12}
{"name": "StieltjesFunction.measure_Ico", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": true, "tactics": ["rcases", "simp", "symm", "simp", "have", "simp", "f.mono.le_leftLim"], "tactic_count": 7}
{"name": "StieltjesFunction.measure_botSet", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "simp"], "tactic_count": 3}
{"name": "StieltjesFunction.measure_Iic", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": true, "tactics": ["have", "cases", "have", "rw", "rw", "have", "refine", "simp_rw", "exact"], "tactic_count": 9}
{"name": "StieltjesFunction.measure_Iio", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": true, "tactics": ["have", "rw", "ofReal_sub", "simp"], "tactic_count": 4}
{"name": "StieltjesFunction.measure_Ici", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": true, "tactics": ["have", "cases", "have", "rw", "rw", "have", "refine", "simp_rw", "refine", "apply", "obtain", "obtain", "simp", "refine", "apply", "exact", "filter_upwards", "exact"], "tactic_count": 18}
{"name": "StieltjesFunction.measure_Ioi", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": true, "tactics": ["rw", "ofReal_sub", "simp"], "tactic_count": 3}
{"name": "StieltjesFunction.measure_Ioi_of_tendsto_atTop_atTop", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": true, "tactics": ["have", "refine", "obtain", "exact"], "tactic_count": 4}
{"name": "StieltjesFunction.measure_Ici_of_tendsto_atTop_atTop", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "StieltjesFunction.measure_Iic_of_tendsto_atBot_atBot", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": true, "tactics": ["have", "refine", "obtain", "exact"], "tactic_count": 4}
{"name": "StieltjesFunction.measure_Iio_of_tendsto_atBot_atBot", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": true, "tactics": ["have", "cases", "rw", "simpa", "have", "obtain", "rw", "exact"], "tactic_count": 8}
{"name": "StieltjesFunction.measure_univ", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": true, "tactics": ["refine", "simp_rw", "exact"], "tactic_count": 3}
{"name": "StieltjesFunction.measure_univ_of_tendsto_atTop_atTop", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": true, "tactics": ["inhabit", "rw", "exact"], "tactic_count": 3}
{"name": "StieltjesFunction.measure_univ_of_tendsto_atBot_atBot", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": true, "tactics": ["inhabit", "rw", "exact"], "tactic_count": 3}
{"name": "StieltjesFunction.isFiniteMeasure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": true, "tactics": ["constructor", "cases", "simp", "simp"], "tactic_count": 4}
{"name": "StieltjesFunction.isFiniteMeasure_of_forall_abs_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": true, "tactics": ["cases", "infer_instance", "obtain", "rcases", "obtain", "grind", "exact", "obtain", "rcases", "obtain", "grind", "exact", "exact"], "tactic_count": 13}
{"name": "StieltjesFunction.isProbabilityMeasure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StieltjesFunction.instIsLocallyFiniteMeasure", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exists_Icc_mem_subset_of_mem_nhds", "exact"], "tactic_count": 4}
{"name": "StieltjesFunction.eq_of_measure_of_tendsto_atBot", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": true, "tactics": ["ext", "have", "rw", "simpa", "rw", "exact", "rw", "exact"], "tactic_count": 8}
{"name": "StieltjesFunction.eq_of_measure_of_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": true, "tactics": ["ext", "cases", "inl", "have", "rw", "simpa", "rw", "exact", "rw", "exact", "inr", "have", "rw", "simpa", "rw", "exact", "rw", "exact"], "tactic_count": 18}
{"name": "StieltjesFunction.measure_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": true, "tactics": ["apply", "simp", "rw", "simp", "exact"], "tactic_count": 5}
{"name": "StieltjesFunction.measure_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StieltjesFunction.measure_add", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": true, "tactics": ["refine", "have", "rcases", "simp", "exact", "tendsto_nhds_unique", "simp", "rw", "ring_nf"], "tactic_count": 9}
{"name": "StieltjesFunction.measure_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Stieltjes", "is_tactic_proof": true, "tactics": ["refine", "simp", "change", "have", "rcases", "simp", "rfl", "exact", "rw", "rfl"], "tactic_count": 10}
{"name": "MeasureTheory.Measure.instSub", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Sub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.sub_def", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Sub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.sub_le_of_le_add", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Sub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.sub_eq_zero_of_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Sub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.sub_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Sub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.sub_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Sub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.zero_sub", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Sub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.sub_self", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Sub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.sub_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Sub", "is_tactic_proof": true, "tactics": ["rw", "apply", "simp", "simp"], "tactic_count": 4}
{"name": "MeasureTheory.Measure.sub_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Sub", "is_tactic_proof": true, "tactics": ["let", "simp", "rw", "rw", "apply", "have", "ext1", "simp", "rw", "have", "rw", "apply", "apply", "simp", "apply", "intro", "rw", "apply", "rw", "apply"], "tactic_count": 20}
{"name": "MeasureTheory.Measure.sub_add_cancel_of_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Sub", "is_tactic_proof": true, "tactics": ["ext1", "rw"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.add_sub_cancel", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Sub", "is_tactic_proof": true, "tactics": ["ext1", "rw"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.restrict_sub_eq_restrict_sub_restrict", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Sub", "is_tactic_proof": true, "tactics": ["repeat", "have", "rw", "apply", "refine", "intro", "rw", "refine", "refine", "rw", "intro", "repeat", "refine", "rw", "apply", "rw", "apply", "rw", "have", "exact", "ext1", "simp", "refine", "refine", "rw", "exact"], "tactic_count": 26}
{"name": "MeasureTheory.Measure.sub_apply_eq_zero_of_restrict_le_restrict", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Sub", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.isFiniteMeasure_sub", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Sub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.support", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.mem_measureSupport", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.mem_support_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.mem_support_iff_forall", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.support_eq_univ", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Support", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.AbsolutelyContinuous.support_mono", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.support_mono", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.notMem_support_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Support", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.HasBasis.notMem_measureSupport", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Support", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.support_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Support", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.support_add", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Support", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.notMem_support_iff_exists", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Support", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.support_eq_forall_isOpen", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Support", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.isClosed_support", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Support", "is_tactic_proof": false, "tactics": ["simp_rw", "grind"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.isOpen_compl_support", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.subset_compl_support_of_isOpen", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.support_subset_of_isClosed", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.compl_support_eq_sUnion", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Support", "is_tactic_proof": true, "tactics": ["ext", "simp", "nhds_basis_opens"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.support_eq_sInter", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.support_mem_ae_of_isLindelof", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Support", "is_tactic_proof": true, "tactics": ["refine", "simpa"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.support_mem_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.measure_compl_support", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.nonempty_inter_support_of_pos", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Support", "is_tactic_proof": true, "tactics": ["rw", "contrapose", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.nullMeasurableSet_compl_support", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.nullMeasurableSet_support", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.nonempty_support", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.nonempty_support_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.mem_support_restrict", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Support", "is_tactic_proof": true, "tactics": ["rw", "grind"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.interior_inter_support", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Support", "is_tactic_proof": true, "tactics": ["rintro", "rw", "rw", "rintro", "apply", "gcongr", "exact"], "tactic_count": 7}
{"name": "MeasureTheory.Measure.support_restrict_subset", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Support", "is_tactic_proof": true, "tactics": ["refine", "rw", "convert", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.IsTightMeasureSet", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Tight", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.isTightMeasureSet_iff_exists_isCompact_measure_compl_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Tight", "is_tactic_proof": false, "tactics": ["simp", "tsub_le_iff_right,", "refine", "obtain", "exact", "obtain", "exact"], "tactic_count": 7}
{"name": "MeasureTheory.isTightMeasureSet_singleton_of_innerRegularWRT", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Tight", "is_tactic_proof": true, "tactics": ["rw", "intro", "let", "cases", "inl", "have", "obtain", "refine", "simp", "rw", "rw", "exact", "inr"], "tactic_count": 13}
{"name": "MeasureTheory.isTightMeasureSet_singleton_of_innerRegular", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Tight", "is_tactic_proof": true, "tactics": ["refine", "intro", "obtain", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.isTightMeasureSet_singleton", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Tight", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IsTightMeasureSet.of_compactSpace", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Tight", "is_tactic_proof": false, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.IsTightMeasureSet.subset", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Tight", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IsTightMeasureSet.union", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Tight", "is_tactic_proof": true, "tactics": ["rw", "convert", "simp"], "tactic_count": 3}
{"name": "MeasureTheory.IsTightMeasureSet.inter", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Tight", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IsTightMeasureSet.map", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Tight", "is_tactic_proof": true, "tactics": ["rw", "simp", "intro", "obtain", "refine", "by_cases", "swap", "rw", "refine", "simp", "exact"], "tactic_count": 11}
{"name": "MeasureTheory.exists_measure_iUnion_gt_of_isCompact_closure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Tight", "is_tactic_proof": true, "tactics": ["have", "lift", "obtain", "simp", "by_contra", "choose", "obtain", "have", "calc", "have", "have", "simp_rw", "rw", "exact", "use", "simpa", "apply", "simp", "use", "intro", "refine", "exact", "use", "use", "simpa", "apply", "use", "simp", "intro", "apply", "refine", "rw", "apply", "norm_cast", "have", "simp_rw", "rw", "have", "suffices", "filter_upwards", "linarith"], "tactic_count": 41}
{"name": "MeasureTheory.isTightMeasureSet_of_isCompact_closure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Tight", "is_tactic_proof": true, "tactics": ["rw", "rcases", "rw", "exact", "obtain", "obtain", "exists_seq_strictAnti_tendsto", "have", "rw", "ext", "exact", "intro", "rcases", "refine", "simp", "obtain", "rw", "exact", "have", "refine", "exists_measure_iUnion_gt_of_isCompact_closure", "simpa", "exact", "choose", "let", "have", "calc", "μ.toMeasure", "rw", "refine", "replace", "simp_all", "grw", "gcongr", "grw", "exact", "rw", "nth_rw", "congr", "ring_nf", "exact", "refine", "refine", "refine", "have", "refine", "simp", "calc", "gcongr", "exact", "simp_rw", "exact"], "tactic_count": 52}
{"name": "MeasureTheory.tendsto_measure_compl_closedBall_of_isTightMeasureSet", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.TightNormed", "is_tactic_proof": false, "tactics": ["suffices", "convert", "simp", "refine", "exact"], "tactic_count": 5}
{"name": "MeasureTheory.isTightMeasureSet_of_tendsto_measure_compl_closedBall", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.TightNormed", "is_tactic_proof": true, "tactics": ["refine", "rw", "obtain", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.isTightMeasureSet_iff_tendsto_measure_compl_closedBall", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.TightNormed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.tendsto_measure_norm_gt_of_isTightMeasureSet", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.TightNormed", "is_tactic_proof": true, "tactics": ["have", "convert", "ext", "simp"], "tactic_count": 4}
{"name": "MeasureTheory.isTightMeasureSet_of_tendsto_measure_norm_gt", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.TightNormed", "is_tactic_proof": true, "tactics": ["refine", "convert", "ext", "simp"], "tactic_count": 4}
{"name": "MeasureTheory.isTightMeasureSet_iff_tendsto_measure_norm_gt", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.TightNormed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.isTightMeasureSet_of_forall_basis_tendsto", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.TightNormed", "is_tactic_proof": true, "tactics": ["rcases", "simp", "convert", "simp", "have", "have", "have", "refine", "have", "intro", "calc", "gcongr", "intro", "simp", "have", "rw", "by_contra", "exact", "gcongr", "exact", "refine", "gcongr", "exact", "refine", "rw", "refine", "exact"], "tactic_count": 27}
{"name": "MeasureTheory.isTightMeasureSet_of_inner_tendsto", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.TightNormed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.isTightMeasureSet_iff_inner_tendsto", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.TightNormed", "is_tactic_proof": true, "tactics": ["refine", "have", "rw", "by_cases", "simp", "refine", "filter_upwards", "simp", "have", "h.comp", "refine", "intro", "have", "refine", "simp", "rw", "rw", "exact", "positivity", "refine", "exact"], "tactic_count": 21}
{"name": "MeasureTheory.Measure.tilted", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Tilted", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.tilted_of_not_integrable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Tilted", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.tilted_of_not_aemeasurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Tilted", "is_tactic_proof": true, "tactics": ["refine", "suffices", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.tilted_zero_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Tilted", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.tilted_const'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Tilted", "is_tactic_proof": true, "tactics": ["cases", "inl", "inr", "simp", "by_cases", "simp", "congr", "rw", "simp"], "tactic_count": 9}
{"name": "MeasureTheory.tilted_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Tilted", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.tilted_zero'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Tilted", "is_tactic_proof": true, "tactics": ["change", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.tilted_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Tilted", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.tilted_congr", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Tilted", "is_tactic_proof": false, "tactics": ["have", "refine", "filter_upwards", "rw", "refine", "filter_upwards", "rw"], "tactic_count": 7}
{"name": "MeasureTheory.tilted_eq_withDensity_nnreal", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Tilted", "is_tactic_proof": true, "tactics": ["rw", "congr", "rw"], "tactic_count": 3}
{"name": "MeasureTheory.tilted_apply'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Tilted", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.tilted_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Tilted", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.tilted_apply_eq_ofReal_integral'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Tilted", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "exact", "exact", "simp", "div_zero,"], "tactic_count": 6}
{"name": "MeasureTheory.tilted_apply_eq_ofReal_integral", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Tilted", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "exact", "exact", "simp"], "tactic_count": 5}
{"name": "MeasureTheory.isProbabilityMeasure_tilted", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Tilted", "is_tactic_proof": true, "tactics": ["constructor", "simp_rw", "div_eq_mul_inv]", "rw", "ofReal_integral_eq_lintegral_ofReal", "simp", "exact", "simp"], "tactic_count": 8}
{"name": "MeasureTheory.isZeroOrProbabilityMeasure_tilted", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Tilted", "is_tactic_proof": true, "tactics": ["rcases", "simp", "infer_instance", "by_cases", "have", "infer_instance", "simp", "infer_instance"], "tactic_count": 8}
{"name": "MeasureTheory.setLIntegral_tilted'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Tilted", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "simp", "refine", "exact", "exact", "filter_upwards", "simp", "have", "exact", "simp", "rw", "simp"], "tactic_count": 13}
{"name": "MeasureTheory.setLIntegral_tilted", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Tilted", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "simp", "refine", "exact", "filter_upwards", "simp", "have", "exact", "simp", "rw", "simp"], "tactic_count": 12}
{"name": "MeasureTheory.lintegral_tilted", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Tilted", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.setIntegral_tilted'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Tilted", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "congr", "suffices", "rw", "refine", "simpa", "exact", "have", "exact", "simp", "rw", "simp"], "tactic_count": 13}
{"name": "MeasureTheory.setIntegral_tilted", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Tilted", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "congr", "suffices", "rw", "refine", "simpa", "exact", "have", "exact", "simp", "rw", "simp"], "tactic_count": 13}
{"name": "MeasureTheory.integral_tilted", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Tilted", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.integral_exp_tilted", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Tilted", "is_tactic_proof": true, "tactics": ["cases", "inl", "inr", "rw", "simp_rw", "have", "intro", "rw", "ring", "simp_rw", "rw"], "tactic_count": 11}
{"name": "MeasureTheory.tilted_tilted", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Tilted", "is_tactic_proof": true, "tactics": ["cases", "inl", "inr", "ext1", "rw", "congr", "rw", "congr", "simp", "have", "simp"], "tactic_count": 11}
{"name": "MeasureTheory.tilted_comm", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Tilted", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.tilted_neg_same'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Tilted", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.tilted_neg_same", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Tilted", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.tilted_absolutelyContinuous", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Tilted", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.absolutelyContinuous_tilted", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Tilted", "is_tactic_proof": true, "tactics": ["cases", "inl", "inr", "refine", "exact", "filter_upwards", "simp", "exact"], "tactic_count": 8}
{"name": "MeasureTheory.integrable_tilted_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Tilted", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "have", "rw", "calc", "congr", "rw", "positivity", "congr", "rw", "rw", "simp", "have", "exact"], "tactic_count": 14}
{"name": "MeasureTheory.rnDeriv_tilted_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Tilted", "is_tactic_proof": true, "tactics": ["cases", "inl", "inr", "refine", "exact", "filter_upwards", "simp", "exact", "refine", "filter_upwards", "congr", "rw", "exact"], "tactic_count": 13}
{"name": "MeasureTheory.toReal_rnDeriv_tilted_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Tilted", "is_tactic_proof": true, "tactics": ["filter_upwards", "rw", "simp", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.rnDeriv_tilted_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Tilted", "is_tactic_proof": true, "tactics": ["let", "refine", "exact", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.toReal_rnDeriv_tilted_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Tilted", "is_tactic_proof": true, "tactics": ["filter_upwards", "rw", "simp", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.rnDeriv_tilted_left_self", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Tilted", "is_tactic_proof": true, "tactics": ["refine", "filter_upwards", "rw"], "tactic_count": 3}
{"name": "MeasureTheory.log_rnDeriv_tilted_left_self", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Tilted", "is_tactic_proof": true, "tactics": ["cases", "inl", "inr", "have", "filter_upwards", "rw", "exact"], "tactic_count": 7}
{"name": "MeasureTheory.Measure.trim", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Trim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.trim_eq_self", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Trim", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.toOuterMeasure_trim_eq_trim_toOuterMeasure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Trim", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.zero_trim", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Trim", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.trim_measurableSet_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Trim", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.le_trim", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Trim", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.trim_eq_map", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Trim", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "MeasureTheory.map_trim_comap", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Trim", "is_tactic_proof": true, "tactics": ["ext", "rw", "exact", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.trim_comap_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Trim", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.ae_map_iff_ae_trim", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Trim", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.trim_add", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Trim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_eq_zero_of_trim_eq_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Trim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_trim_toMeasurable_eq_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Trim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.ae_of_ae_trim", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Trim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.ae_eq_of_ae_eq_trim", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Trim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.ae_le_of_ae_le_trim", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Trim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.trim_trim", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Trim", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "MeasureTheory.restrict_trim", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Trim", "is_tactic_proof": true, "tactics": ["refine", "rw", "trim_measurableSet_eq"], "tactic_count": 3}
{"name": "MeasureTheory.isFiniteMeasure_trim", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Trim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.sigmaFiniteTrim_mono", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Trim", "is_tactic_proof": true, "tactics": ["refine", "refine", "set_mem", "finite", "spanning", "calc"], "tactic_count": 6}
{"name": "MeasureTheory.sigmaFinite_trim_bot_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Trim", "is_tactic_proof": true, "tactics": ["rw", "refine", "rwa", "rwa"], "tactic_count": 4}
{"name": "MeasureTheory.Measure.AbsolutelyContinuous.trim", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Trim", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "ae_eq_trim_of_measurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Trim", "is_tactic_proof": true, "tactics": ["rwa", "measurability"], "tactic_count": 2}
{"name": "MeasureTheory.not_isFiniteMeasure_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.isFiniteMeasure_restrict", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.Restrict.isFiniteMeasure", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_lt_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.isFiniteMeasureRestrict", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_ne_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_compl_le_add_of_le_add", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": true, "tactics": ["rw", "calc", "μ"], "tactic_count": 3}
{"name": "MeasureTheory.measure_compl_le_add_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.cofinite_eq_bot_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.cofinite_eq_bot", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measureUnivNNReal", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.coe_measureUnivNNReal", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.isFiniteMeasureZero", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.isFiniteMeasureOfIsEmpty", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "MeasureTheory.measureUnivNNReal_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.isFiniteMeasureAdd", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.isFiniteMeasureSMulNNReal", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IsFiniteMeasure.average", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.isFiniteMeasureSMulOfNNRealTower", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "MeasureTheory.isFiniteMeasure_of_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.isFiniteMeasure_map", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": true, "tactics": ["by_cases", "constructor", "rw", "exact", "rw", "exact"], "tactic_count": 6}
{"name": "MeasureTheory.Measure.isFiniteMeasure_of_map", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.isFiniteMeasure_map_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IsFiniteMeasure_comap", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measureUnivNNReal_eq_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": true, "tactics": ["rw", "norm_cast"], "tactic_count": 2}
{"name": "MeasureTheory.measureUnivNNReal_pos", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": true, "tactics": ["contrapose", "simpa"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.le_of_add_le_add_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.eq_of_le_of_measure_univ_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": true, "tactics": ["refine", "by_contra", "have", "rw", "exact"], "tactic_count": 5}
{"name": "MeasureTheory.summable_measure_toReal", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": true, "tactics": ["apply", "rw", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.ae_eq_univ_iff_measure_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.ae_iff_measure_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.ae_mem_iff_measure_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.tendsto_measure_biUnion_Ici_zero_of_pairwise_disjoint", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": ["have", "biUnion_mono", "have", "apply", "intro", "simp", "obtain", "obtain", "have", "contradiction", "have", "simp", "convert"], "tactic_count": 13}
{"name": "MeasureTheory.abs_measureReal_sub_le_measureReal_symmDiff'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": true, "tactics": ["simp", "have", "have", "suffices", "rw", "convert", "rw", "abel"], "tactic_count": 8}
{"name": "MeasureTheory.abs_measureReal_sub_le_measureReal_symmDiff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.instIsFiniteMeasureSumMeasure", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.instIsFiniteMeasureSumOfFinite", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.ite_ae_eq_of_measure_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": true, "tactics": ["have", "refine", "conv_rhs", "rwa"], "tactic_count": 4}
{"name": "MeasureTheory.ite_ae_eq_of_measure_compl_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": true, "tactics": ["rw", "filter_upwards", "intros", "split_ifs", "rfl"], "tactic_count": 5}
{"name": "MeasureTheory.Measure.FiniteAtFilter", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.finiteAtFilter_of_finite", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.FiniteAtFilter.exists_mem_basis", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.finiteAtBot", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IsFiniteMeasure.toIsLocallyFiniteMeasure", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.finiteAt_nhds", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.smul_finite", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": true, "tactics": ["lift", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.exists_isOpen_measure_lt_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.isLocallyFiniteMeasureSMulNNReal", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": true, "tactics": ["refine", "rcases", "refine", "apply", "simp"], "tactic_count": 5}
{"name": "MeasureTheory.Measure.isTopologicalBasis_isOpen_lt_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": true, "tactics": ["refine", "intro", "rcases", "refine", "exact"], "tactic_count": 5}
{"name": "IsCompact.measure_lt_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.measure_ne_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.IsBounded.measure_lt_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_closedBall_lt_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_ball_ne_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_ball_lt_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": true, "tactics": ["finiteness"], "tactic_count": 1}
{"name": "MeasureTheory.IsFiniteMeasureOnCompacts.smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IsFiniteMeasureOnCompacts.smul_nnreal", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.instIsFiniteMeasureOnCompactsRestrict", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IsFiniteMeasureOnCompacts.comap'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.CompactSpace.isFiniteMeasure", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.isLocallyFiniteMeasure_of_isFiniteMeasureOnCompacts", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.exists_pos_measure_of_cover", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": true, "tactics": ["contrapose", "rw", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.exists_pos_preimage_ball", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.exists_pos_ball", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.exists_ne_forall_mem_nhds_pos_measure_preimage", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": true, "tactics": ["set", "replace", "inhabit", "have", "rcases", "simp", "rcases", "simp", "exact"], "tactic_count": 9}
{"name": "MeasureTheory.ext_on_measurableSpace_of_generate_finite", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": ["haveI", "constructor", "rw", "apply", "induction", "empty", "basic", "compl", "rw", "iUnion"], "tactic_count": 10}
{"name": "MeasureTheory.ext_of_generate_finite", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.FiniteAtFilter.filter_mono", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.FiniteAtFilter.inf_of_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.FiniteAtFilter.inf_of_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.FiniteAtFilter.inf_ae_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": true, "tactics": ["refine", "rintro", "suffices", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.Measure.FiniteAtFilter.filter_mono_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.FiniteAtFilter.measure_mono", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.FiniteAtFilter.mono", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.FiniteAtFilter.eventually", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.FiniteAtFilter.filterSup", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.finiteAt_nhdsWithin", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.finiteAt_principal", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.isLocallyFiniteMeasure_of_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.exists_open_superset_measure_lt_top'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": true, "tactics": ["refine", "use", "simp", "rintro", "exact", "rintro", "refine", "intro", "rcases", "exact"], "tactic_count": 10}
{"name": "IsCompact.exists_open_superset_measure_lt_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.measure_lt_top_of_nhdsWithin", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.measure_zero_of_nhdsWithin", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "isFiniteMeasureOnCompacts_of_isLocallyFiniteMeasure", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isFiniteMeasure_iff_isFiniteMeasureOnCompacts_of_compactSpace", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": true, "tactics": ["constructor", "infer_instance", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.finiteSpanningSetsInCompact", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.finiteSpanningSetsInOpen", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "definition._@.Mathlib.MeasureTheory.Measure.Typeclasses.Finite.588747923._hygCtx._hyg.2", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": true, "tactics": ["suffices", "cases", "exact", "set_mem", "finite", "spanning", "inhabit", "let", "obtain", "isOpen_sUnion_countable", "rw", "have", "by_contra", "rw", "simpa", "obtain", "have", "intro", "apply", "rw", "exact", "refine", "set_mem", "finite", "spanning", "refine", "obtain", "have", "simpa", "obtain", "exact"], "tactic_count": 31}
{"name": "wrapped._@.Mathlib.MeasureTheory.Measure.Typeclasses.Finite.588747923._hygCtx._hyg.2", "kind": "opaque", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.finiteSpanningSetsInOpen'", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.finiteSpanningSetsInOpen'_def", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": true, "tactics": ["intros", "delta", "rw", "rfl"], "tactic_count": 4}
{"name": "measure_Icc_lt_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measure_Ico_lt_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measure_Ioc_lt_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measure_Ioo_lt_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Subsingleton.measure_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.NoAtoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.restrict_singleton'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.NoAtoms", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.restrict.instNoAtoms", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.NoAtoms", "is_tactic_proof": true, "tactics": ["refine", "obtain", "apply", "rw", "apply"], "tactic_count": 5}
{"name": "Set.Countable.measure_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.NoAtoms", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Set.Countable.ae_notMem", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.NoAtoms", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.ae_ne", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.NoAtoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Countable.measure_restrict_compl", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.NoAtoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.restrict_compl_singleton", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.NoAtoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.measure_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.NoAtoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.measure_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.NoAtoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.insert_ae_eq_self", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.NoAtoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.exists_accPt_of_noAtoms", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.NoAtoms", "is_tactic_proof": true, "tactics": ["by_contra", "haveI", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.Iio_ae_eq_Iic", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.NoAtoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Ioi_ae_eq_Ici", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.NoAtoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Ioo_ae_eq_Ioc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.NoAtoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Ioc_ae_eq_Icc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.NoAtoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Ioo_ae_eq_Ico", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.NoAtoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Ioo_ae_eq_Icc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.NoAtoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Ico_ae_eq_Icc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.NoAtoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Ico_ae_eq_Ioc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.NoAtoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.restrict_Iio_eq_restrict_Iic", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.NoAtoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.restrict_Ioi_eq_restrict_Ici", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.NoAtoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.restrict_Ioo_eq_restrict_Ioc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.NoAtoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.restrict_Ioc_eq_restrict_Icc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.NoAtoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.restrict_Ioo_eq_restrict_Ico", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.NoAtoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.restrict_Ioo_eq_restrict_Icc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.NoAtoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.restrict_Ico_eq_restrict_Icc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.NoAtoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.restrict_Ico_eq_restrict_Ioc", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.NoAtoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.uIoc_ae_eq_interval", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.NoAtoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.isZeroOrProbabilityMeasure_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Probability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.prob_le_one", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Probability", "is_tactic_proof": true, "tactics": ["apply", "rcases"], "tactic_count": 2}
{"name": "MeasureTheory.measureReal_le_one", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Probability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.one_le_prob_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Probability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IsZeroOrProbabilityMeasure.toIsFiniteMeasure", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Probability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.instIsZeroOrProbabilityMeasureOfNatMeasure", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Probability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.isProbabilityMeasure_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Probability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.instIsZeroOrProbabilityMeasureOfIsProbabilityMeasure", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Probability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.nonempty_of_isProbabilityMeasure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Probability", "is_tactic_proof": true, "tactics": ["by_contra", "have", "simp"], "tactic_count": 3}
{"name": "MeasureTheory.IsProbabilityMeasure.ne_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Probability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IsProbabilityMeasure.neZero", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Probability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IsProbabilityMeasure.ae_neBot", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Probability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.prob_add_prob_compl", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Probability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.probReal_add_probReal_compl", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Probability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.isProbabilityMeasureSMul", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Probability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.isProbabilityMeasure_dite", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Probability", "is_tactic_proof": true, "tactics": ["split"], "tactic_count": 1}
{"name": "MeasureTheory.isProbabilityMeasure_ite", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Probability", "is_tactic_proof": true, "tactics": ["split"], "tactic_count": 1}
{"name": "MeasureTheory.instIsProbabilityMeasureHAddMeasureHSMulNNRealToNNRealSymm", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Probability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.probReal_univ", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Probability", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.isProbabilityMeasure_iff_real", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Probability", "is_tactic_proof": true, "tactics": ["refine"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.isProbabilityMeasure_map", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Probability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.isProbabilityMeasure_of_map", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Probability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.isProbabilityMeasure_map_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Probability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IsProbabilityMeasure_comap_equiv", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Probability", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.prob_compl_eq_one_sub₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Probability", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.prob_compl_eq_one_sub", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Probability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.prob_compl_eq_zero_iff₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Probability", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.prob_compl_eq_zero_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Probability", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.prob_compl_eq_one_iff₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Probability", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.prob_compl_eq_one_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Probability", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.mem_ae_iff_prob_eq_one₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Probability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.mem_ae_iff_prob_eq_one", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Probability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.ae_iff_prob_eq_one", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Probability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.isProbabilityMeasure_comap", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Probability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEmbedding.isProbabilityMeasure_comap", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Probability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.isProbabilityMeasure_map_up", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Probability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.isProbabilityMeasure_comap_down", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Probability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.eq_of_le_of_isProbabilityMeasure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Probability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.isZeroOrProbabilityMeasureSMul", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Probability", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rcases", "simp", "have", "infer_instance"], "tactic_count": 6}
{"name": "MeasureTheory.eq_zero_or_isProbabilityMeasure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Probability", "is_tactic_proof": true, "tactics": ["rcases", "apply", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.instIsZeroOrProbabilityMeasureMap", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Probability", "is_tactic_proof": true, "tactics": ["by_cases", "simpa", "simp"], "tactic_count": 3}
{"name": "MeasureTheory.prob_compl_lt_one_sub_of_lt_prob", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Probability", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rw", "apply", "convert", "exact"], "tactic_count": 6}
{"name": "MeasureTheory.prob_compl_le_one_sub_of_le_prob", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Probability", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simpa"], "tactic_count": 3}
{"name": "MeasureTheory.inv_measure_univ_smul_eq_self", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.Probability", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "MeasureTheory.sfiniteSeq", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.isFiniteMeasure_sfiniteSeq", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.sum_sfiniteSeq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.sfiniteSeq_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.instSFiniteOfNatMeasure", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.sfiniteSeq_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.sfinite_sum_of_countable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": true, "tactics": ["classical", "obtain", "refine", "rcases", "rw", "infer_instance", "rw", "infer_instance"], "tactic_count": 8}
{"name": "MeasureTheory.instSFiniteSumOfCountable", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": true, "tactics": ["change", "simp_rw", "apply"], "tactic_count": 3}
{"name": "MeasureTheory.instSFiniteHAddMeasure", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "MeasureTheory.instSFiniteRestrict", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.exists_isFiniteMeasure_absolutelyContinuous", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": false, "tactics": ["rcases", "have", "conv_rhs", "simp", "refine", "simpa"], "tactic_count": 6}
{"name": "MeasureTheory.sigmaFinite_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SigmaFinite.out", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.toFiniteSpanningSetsIn", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.spanningSets", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.monotone_spanningSets", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.spanningSets_mono", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measurableSet_spanningSets", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_spanningSets_lt_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.iUnion_spanningSets", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MeasureTheory.isCountablySpanning_spanningSets", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.spanningSetsIndex", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measurableSet_spanningSetsIndex", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.preimage_spanningSetsIndex_singleton", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.spanningSetsIndex_eq_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "MeasureTheory.mem_disjointed_spanningSetsIndex", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.mem_spanningSetsIndex", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.mem_spanningSets_of_index_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.eventually_mem_spanningSets", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_singleton_lt_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.sum_restrict_disjointed_spanningSets", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": true, "tactics": ["rw", "iUnion_disjointed,"], "tactic_count": 2}
{"name": "MeasureTheory.instSFiniteOfSigmaFinite", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": false, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.forall_measure_inter_spanningSets_eq_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": true, "tactics": ["nth_rw", "rw"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.exists_measure_inter_spanningSets_pos", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": true, "tactics": ["contrapose", "simp", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.finite_const_le_meas_of_disjoint_iUnion₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.finite_const_le_meas_of_disjoint_iUnion", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Infinite.meas_eq_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.countable_meas_pos_of_disjoint_of_meas_iUnion_ne_top₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": true, "tactics": ["set", "rcases", "set", "have", "have", "simp", "rfl", "simpa", "iUnion_Ici_eq_Ioi_of_lt_of_tendsto", "rw", "refine", "exact"], "tactic_count": 12}
{"name": "MeasureTheory.Measure.countable_meas_pos_of_disjoint_of_meas_iUnion_ne_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.countable_meas_pos_of_disjoint_iUnion₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": true, "tactics": ["rw", "have", "intro", "by_contra", "simp", "rw", "simp_rw", "simp", "exact", "apply", "refine", "apply", "exact", "exact", "exact"], "tactic_count": 15}
{"name": "MeasureTheory.Measure.countable_meas_pos_of_disjoint_iUnion", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.countable_meas_level_set_pos₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": false, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.countable_meas_level_set_pos", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.MeasureTheory.Measure.Typeclasses.SFinite.0.MeasureTheory.Measure.exists_ae_subset_biUnion_countable_of_isFiniteMeasure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": true, "tactics": ["let", "obtain", "rcases", "exact", "obtain", "exists_seq_strictMono_tendsto", "have", "choose", "have", "refine", "apply", "apply", "exact", "refine", "symm", "apply", "rw", "apply", "simp", "exact", "simp"], "tactic_count": 21}
{"name": "MeasureTheory.Measure.exists_ae_subset_biUnion_countable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": false, "tactics": ["have", "exists_ae_subset_biUnion_countable_of_isFiniteMeasure", "choose", "refine", "rw", "apply", "exact"], "tactic_count": 7}
{"name": "MeasureTheory.Measure.measure_toMeasurable_inter_of_sum", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": true, "tactics": ["have", "let", "have", "have", "refine", "refine", "rw", "apply", "apply", "calc", "m", "measure_toMeasurable_inter", "rw", "split_ifs", "apply", "exact", "exact"], "tactic_count": 17}
{"name": "MeasureTheory.Measure.measure_toMeasurable_inter_of_cover", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": true, "tactics": ["have", "let", "have", "intro", "simp_rw", "exact", "set", "have", "calc", "t", "rw", "intro", "rcases", "refine", "have", "exact", "refine", "apply", "calc", "μ", "rw", "exact", "congr", "ext1", "apply", "apply", "calc", "μ", "gcongr", "exact", "congr", "ext1", "rw", "refine", "exact", "rw", "exact", "intro", "refine", "exact", "rw", "rw", "split_ifs", "apply", "exact", "exact"], "tactic_count": 46}
{"name": "MeasureTheory.Measure.restrict_toMeasurable_of_cover", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.measure_toMeasurable_inter_of_sFinite", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.restrict_toMeasurable_of_sFinite", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.iSup_restrict_spanningSets_of_measurableSet", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.iSup_restrict_spanningSets", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "restrict_apply", "restrict_apply"], "tactic_count": 4}
{"name": "MeasureTheory.Measure.exists_subset_measure_lt_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": true, "tactics": ["rw", "rcases", "simp", "refine", "exact"], "tactic_count": 5}
{"name": "MeasureTheory.Measure.FiniteSpanningSetsIn.mono'", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.FiniteSpanningSetsIn.mono", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.FiniteSpanningSetsIn.sigmaFinite", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.FiniteSpanningSetsIn.ext", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.FiniteSpanningSetsIn.isCountablySpanning", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.sigmaFinite_of_countable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": false, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.FiniteSpanningSetsIn.ofLE", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.sigmaFinite_of_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.add_right_inj", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": true, "tactics": ["refine", "rw", "intro", "ext", "rw", "simp", "simp"], "tactic_count": 7}
{"name": "MeasureTheory.Measure.add_left_inj", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.IsFiniteMeasure.toSigmaFinite", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.sigmaFinite_iff_measure_singleton_lt_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.sigmaFinite_bot_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": true, "tactics": ["refine", "haveI", "let", "have", "have", "simp_rw", "by_cases", "rw", "exact", "obtain", "by_contra", "have", "simp", "exact", "rw", "exact"], "tactic_count": 16}
{"name": "MeasureTheory.Restrict.sigmaFinite", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.sum.sigmaFinite", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": true, "tactics": ["cases", "have", "refine", "rw", "rintro", "exact", "rw", "simp_rw", "exact"], "tactic_count": 9}
{"name": "MeasureTheory.Add.sigmaFinite", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": true, "tactics": ["rw", "refine"], "tactic_count": 2}
{"name": "MeasureTheory.SMul.sigmaFinite", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.instSigmaFiniteRestrictUnionSet", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.instSigmaFiniteRestrictInterSet", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.instSigmaFiniteRestrictInterSet_1", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SigmaFinite.of_map", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEmbedding.sigmaFinite_map", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": true, "tactics": ["refine", "rw", "simp", "exact", "rw"], "tactic_count": 5}
{"name": "MeasurableEquiv.sigmaFinite_map", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.ae_of_forall_measure_lt_top_ae_restrict'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": false, "tactics": ["have", "intro", "have", "h", "exact", "filter_upwards"], "tactic_count": 6}
{"name": "MeasureTheory.ae_of_forall_measure_lt_top_ae_restrict", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SigmaFinite.of_isFiniteMeasureOnCompacts", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.sigmaFinite_of_locallyFinite", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": true, "tactics": ["choose", "rcases", "refine", "rwa"], "tactic_count": 4}
{"name": "MeasureTheory.Measure.FiniteSpanningSetsIn.disjointed", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.FiniteSpanningSetsIn.disjointed_set_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.exists_eq_disjoint_finiteSpanningSetsIn", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.Typeclasses.SFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.withDensity", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.withDensity_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.withDensity_apply_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": true, "tactics": ["let", "calc"], "tactic_count": 2}
{"name": "MeasureTheory.withDensity_apply'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": true, "tactics": ["apply", "let", "calc", "μ.withDensity"], "tactic_count": 4}
{"name": "MeasureTheory.withDensity_zero_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": true, "tactics": ["ext", "rw", "simp"], "tactic_count": 3}
{"name": "MeasureTheory.withDensity_congr_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.withDensity_mono", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": true, "tactics": ["refine", "rw", "refine", "filter_upwards"], "tactic_count": 4}
{"name": "MeasureTheory.withDensity_add_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": true, "tactics": ["refine", "rw", "lintegral_add_left", "simp"], "tactic_count": 4}
{"name": "MeasureTheory.withDensity_add_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.withDensity_add_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": true, "tactics": ["ext1", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.withDensity_sum", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": true, "tactics": ["ext1", "simp_rw"], "tactic_count": 2}
{"name": "MeasureTheory.withDensity_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": true, "tactics": ["refine", "rw", "lintegral_const_mul", "simp"], "tactic_count": 4}
{"name": "MeasureTheory.withDensity_smul'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": true, "tactics": ["refine", "rw", "lintegral_const_mul", "simp"], "tactic_count": 4}
{"name": "MeasureTheory.withDensity_smul_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.isFiniteMeasure_withDensity", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.withDensity_absolutelyContinuous", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.withDensity_apply₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": true, "tactics": ["let", "have", "have", "measure_congr", "rw", "exact"], "tactic_count": 6}
{"name": "MeasureTheory.noAtoms_withDensity", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.withDensity_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": true, "tactics": ["ext1", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.withDensity_one", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": true, "tactics": ["ext1", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.withDensity_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": true, "tactics": ["ext1", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.withDensity_tsum", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": true, "tactics": ["ext1", "simp_rw", "change", "rw", "exact"], "tactic_count": 5}
{"name": "MeasureTheory.withDensity_indicator", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": true, "tactics": ["ext1", "rw"], "tactic_count": 2}
{"name": "MeasureTheory.withDensity_indicator_one", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.withDensity_ofReal_mutuallySingular", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": true, "tactics": ["set", "have", "refine", "rw", "exact", "rw", "exact"], "tactic_count": 7}
{"name": "MeasureTheory.restrict_withDensity", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": true, "tactics": ["ext1", "rw"], "tactic_count": 2}
{"name": "MeasureTheory.restrict_withDensity'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": true, "tactics": ["ext1", "rw"], "tactic_count": 2}
{"name": "MeasureTheory.trim_withDensity", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": true, "tactics": ["refine", "rw", "withDensity_apply"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.MutuallySingular.withDensity", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.withDensity_eq_zero_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.withDensity_apply_eq_zero'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": true, "tactics": ["constructor", "intro", "let", "apply", "have", "rw", "swap", "simp", "simp", "convert", "ext", "simp", "intro", "let", "have", "intro", "rcases", "simp", "left", "apply", "exact", "apply", "apply", "rwa", "rcases", "have", "apply", "filter_upwards", "rw", "exact", "rw", "have", "rw", "filter_upwards", "simp"], "tactic_count": 35}
{"name": "MeasureTheory.withDensity_apply_eq_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.ae_withDensity_iff'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": true, "tactics": ["rw", "congr", "ext", "simp"], "tactic_count": 4}
{"name": "MeasureTheory.ae_withDensity_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.ae_withDensity_iff_ae_restrict'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": true, "tactics": ["rw", "simp", "rcases", "have", "filter_upwards", "simp", "exact", "exact"], "tactic_count": 8}
{"name": "MeasureTheory.ae_withDensity_iff_ae_restrict", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.aemeasurable_withDensity_ennreal_iff'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": true, "tactics": ["have", "rcases", "constructor", "rintro", "have", "refine", "apply", "rw", "rw", "filter_upwards", "have", "rw", "rw", "rw", "filter_upwards", "have", "rw", "rw", "simp", "rintro", "refine", "rw", "filter_upwards", "rw", "rw"], "tactic_count": 25}
{"name": "MeasureTheory.aemeasurable_withDensity_ennreal_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.dirac_withDensity'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": true, "tactics": ["ext", "classical"], "tactic_count": 2}
{"name": "MeasureTheory.dirac_withDensity", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": true, "tactics": ["ext", "classical"], "tactic_count": 2}
{"name": "MeasureTheory.count_withDensity'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.count_withDensity", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.lintegral_withDensity_eq_lintegral_mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": true, "tactics": ["apply", "intro", "simp", "intro", "simp", "intro", "have", "simp"], "tactic_count": 8}
{"name": "MeasureTheory.setLIntegral_withDensity_eq_setLIntegral_mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.lintegral_withDensity_eq_lintegral_mul₀'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": true, "tactics": ["let", "have", "rw", "let", "calc", "apply", "apply", "have", "rw", "filter_upwards", "intro", "simp", "have", "filter_upwards", "intro", "simp", "simp", "apply", "filter_upwards", "intro", "simp"], "tactic_count": 21}
{"name": "MeasureTheory.setLIntegral_withDensity_eq_lintegral_mul₀'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.lintegral_withDensity_eq_lintegral_mul₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.setLIntegral_withDensity_eq_lintegral_mul₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.lintegral_withDensity_le_lintegral_mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.lintegral_withDensity_eq_lintegral_mul_non_measurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": true, "tactics": ["refine", "rw", "refine", "have", "intro", "dsimp", "rw", "exact", "refine", "refine", "rw", "apply", "filter_upwards", "intro", "rcases", "have", "simp", "simp", "apply", "dsimp", "rw"], "tactic_count": 21}
{"name": "MeasureTheory.setLIntegral_withDensity_eq_setLIntegral_mul_non_measurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.lintegral_withDensity_eq_lintegral_mul_non_measurable₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": true, "tactics": ["let", "calc", "apply", "filter_upwards", "intro", "rwa", "apply", "filter_upwards", "intro", "simp"], "tactic_count": 10}
{"name": "MeasureTheory.setLIntegral_withDensity_eq_setLIntegral_mul_non_measurable₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.setLIntegral_withDensity_eq_setLIntegral_mul_non_measurable₀'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.withDensity_mul₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": true, "tactics": ["ext1", "rw", "lintegral_withDensity_eq_lintegral_mul₀"], "tactic_count": 3}
{"name": "MeasureTheory.withDensity_mul", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.withDensity_inv_same_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": true, "tactics": ["change", "rw", "suffices", "refine", "rw", "filter_upwards", "simp"], "tactic_count": 7}
{"name": "MeasureTheory.withDensity_inv_same₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": true, "tactics": ["rw", "suffices", "filter_upwards", "simp", "rw"], "tactic_count": 5}
{"name": "MeasureTheory.withDensity_inv_same", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.withDensity_absolutelyContinuous'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": true, "tactics": ["refine", "rw", "simp", "simp", "have", "exact", "measure_mono_null", "nonpos_iff_eq_zero.1"], "tactic_count": 8}
{"name": "MeasureTheory.withDensity_ae_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SigmaFinite.withDensity", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": true, "tactics": ["refine", "rw", "apply", "exact", "exact", "rw", "refine", "exact", "simp"], "tactic_count": 9}
{"name": "MeasureTheory.SigmaFinite.withDensity_of_ne_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": true, "tactics": ["have", "rw", "infer_instance"], "tactic_count": 3}
{"name": "MeasureTheory.SigmaFinite.withDensity_of_ne_top'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SigmaFinite.withDensity_ofReal", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.exists_measurable_le_withDensity_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": true, "tactics": ["obtain", "use", "ext", "simp"], "tactic_count": 4}
{"name": "MeasureTheory.Measure.withDensity.instSFinite", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": true, "tactics": ["wlog", "rcases", "exact", "wlog", "rw", "have", "infer_instance", "set", "have", "have", "calc", "μ.withDensity", "simp", "rw", "congr", "rw", "have", "refine", "simp", "have", "rw", "exact", "rw", "infer_instance"], "tactic_count": 24}
{"name": "MeasureTheory.instSFiniteHSMulENNRealMeasure", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "MeasureTheory.sFinite_of_absolutelyContinuous", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": false, "tactics": ["rw", "restrict_compl_sigmaFiniteSetWRT", "infer_instance"], "tactic_count": 3}
{"name": "MeasureTheory.instSFiniteOfCountable", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": true, "tactics": ["obtain", "rw", "infer_instance"], "tactic_count": 3}
{"name": "MeasureTheory.prod_withDensity_left₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": true, "tactics": ["refine", "rw", "lintegral_withDensity_eq_lintegral_mul₀", "refine", "rw", "simp", "all_goals"], "tactic_count": 7}
{"name": "MeasureTheory.prod_withDensity_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.prod_withDensity_right₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": true, "tactics": ["refine", "rw", "refine", "rw", "simp", "all_goals"], "tactic_count": 6}
{"name": "MeasureTheory.prod_withDensity_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.prod_withDensity₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": true, "tactics": ["rw", "rfl", "all_goals"], "tactic_count": 3}
{"name": "MeasureTheory.prod_withDensity", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.prod_smul_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": true, "tactics": ["ext", "simp_rw", "rw", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.IsLocallyFiniteMeasure.withDensity_coe", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": true, "tactics": ["refine", "rcases", "refine", "rw", "exact"], "tactic_count": 5}
{"name": "MeasureTheory.IsLocallyFiniteMeasure.withDensity_ofReal", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.mconv_smul_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": true, "tactics": ["unfold", "rw"], "tactic_count": 2}
{"name": "MeasureTheory.mconv_withDensity_eq_mlconvolution₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": true, "tactics": ["refine", "rw", "lintegral_withDensity_eq_lintegral_mul₀,", "lintegral_congr", "simp", "conv", "all_goals", "first", "fun_prop", "dsimp"], "tactic_count": 10}
{"name": "MeasureTheory.mconv_withDensity_eq_mlconvolution", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.toFiniteAux", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.WithDensityFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.toFinite", "kind": "definition", "module": "Mathlib.MeasureTheory.Measure.WithDensityFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.ae_toFiniteAux", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensityFinite", "is_tactic_proof": true, "tactics": ["rw", "split_ifs", "simp", "obtain", "exact"], "tactic_count": 5}
{"name": "MeasureTheory.isFiniteMeasure_toFiniteAux", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensityFinite", "is_tactic_proof": true, "tactics": ["rw", "split_ifs", "assumption", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.ae_toFinite", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensityFinite", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.toFinite_apply_eq_zero_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensityFinite", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.toFinite_eq_zero_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensityFinite", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MeasureTheory.toFinite_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensityFinite", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.toFinite_eq_self", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensityFinite", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "MeasureTheory.instIsFiniteMeasureToFinite", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.WithDensityFinite", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "MeasureTheory.instIsProbabilityMeasureToFiniteOfNeZeroMeasure", "kind": "instance", "module": "Mathlib.MeasureTheory.Measure.WithDensityFinite", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.absolutelyContinuous_toFinite", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensityFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.sfiniteSeq_absolutelyContinuous_toFinite", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensityFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.toFinite_absolutelyContinuous", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensityFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.restrict_compl_sigmaFiniteSet", "kind": "theorem", "module": "Mathlib.MeasureTheory.Measure.WithDensityFinite", "is_tactic_proof": true, "tactics": ["rw", "ext", "simp", "rw", "by_cases", "rw", "rw", "exact"], "tactic_count": 8}
{"name": "measurable_oneLePart", "kind": "theorem", "module": "Mathlib.MeasureTheory.Order.Group.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.oneLePart", "kind": "theorem", "module": "Mathlib.MeasureTheory.Order.Group.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_leOnePart", "kind": "theorem", "module": "Mathlib.MeasureTheory.Order.Group.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.leOnePart", "kind": "theorem", "module": "Mathlib.MeasureTheory.Order.Group.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_mabs", "kind": "theorem", "module": "Mathlib.MeasureTheory.Order.Group.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.mabs", "kind": "theorem", "module": "Mathlib.MeasureTheory.Order.Group.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.mabs", "kind": "theorem", "module": "Mathlib.MeasureTheory.Order.Group.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instMeasurableSup", "kind": "instance", "module": "Mathlib.MeasureTheory.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instMeasurableInf", "kind": "instance", "module": "Mathlib.MeasureTheory.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instMeasurableSup₂", "kind": "instance", "module": "Mathlib.MeasureTheory.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instMeasurableInf₂", "kind": "instance", "module": "Mathlib.MeasureTheory.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.const_sup", "kind": "theorem", "module": "Mathlib.MeasureTheory.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.const_sup", "kind": "theorem", "module": "Mathlib.MeasureTheory.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.sup_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.sup_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.sup'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.sup", "kind": "theorem", "module": "Mathlib.MeasureTheory.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.sup'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.sup", "kind": "theorem", "module": "Mathlib.MeasureTheory.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSup₂.toMeasurableSup", "kind": "instance", "module": "Mathlib.MeasureTheory.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.const_inf", "kind": "theorem", "module": "Mathlib.MeasureTheory.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.const_inf", "kind": "theorem", "module": "Mathlib.MeasureTheory.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.inf_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.inf_const", "kind": "theorem", "module": "Mathlib.MeasureTheory.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.inf'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Measurable.inf", "kind": "theorem", "module": "Mathlib.MeasureTheory.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.inf'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AEMeasurable.inf", "kind": "theorem", "module": "Mathlib.MeasureTheory.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableInf₂.to_hasMeasurableInf", "kind": "instance", "module": "Mathlib.MeasureTheory.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.measurable_sup'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.measurable_range_sup'", "kind": "theorem", "module": "Mathlib.MeasureTheory.Order.Lattice", "is_tactic_proof": true, "tactics": ["refine", "simpa"], "tactic_count": 2}
{"name": "Finset.measurable_range_sup''", "kind": "theorem", "module": "Mathlib.MeasureTheory.Order.Lattice", "is_tactic_proof": true, "tactics": ["convert", "ext", "simp"], "tactic_count": 3}
{"name": "_private.Mathlib.MeasureTheory.Order.UpperLower.0.aux₀", "kind": "theorem", "module": "Mathlib.MeasureTheory.Order.UpperLower", "is_tactic_proof": true, "tactics": ["choose", "intro", "obtain", "refine", "not_eventually.2", "on_goal", "calc", "volume", "gcongr", "exact", "have", "rw", "mul_div_mul_left", "all_goals"], "tactic_count": 14}
{"name": "_private.Mathlib.MeasureTheory.Order.UpperLower.0.aux₁", "kind": "theorem", "module": "Mathlib.MeasureTheory.Order.UpperLower", "is_tactic_proof": true, "tactics": ["choose", "intro", "obtain", "refine", "not_eventually.2", "on_goal", "calc", "volume", "volume", "gcongr", "rw", "refine", "rw", "exact", "dsimp", "have", "rw", "mul_div_mul_left", "all_goals", "simp_all", "exact"], "tactic_count": 21}
{"name": "IsUpperSet.null_frontier", "kind": "theorem", "module": "Mathlib.MeasureTheory.Order.UpperLower", "is_tactic_proof": false, "tactics": ["refine", "measure_mono_null", "by_cases", "simp", "refine", "rwa", "exact"], "tactic_count": 7}
{"name": "IsLowerSet.null_frontier", "kind": "theorem", "module": "Mathlib.MeasureTheory.Order.UpperLower", "is_tactic_proof": false, "tactics": ["refine", "measure_mono_null", "by_cases", "simp", "refine", "rwa", "exact"], "tactic_count": 7}
{"name": "Set.OrdConnected.null_frontier", "kind": "theorem", "module": "Mathlib.MeasureTheory.Order.UpperLower", "is_tactic_proof": true, "tactics": ["rw", "exact", "measure_mono_null", "measure_union_null"], "tactic_count": 4}
{"name": "Set.OrdConnected.nullMeasurableSet", "kind": "theorem", "module": "Mathlib.MeasureTheory.Order.UpperLower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAntichain.volume_eq_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.Order.UpperLower", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.ae", "kind": "definition", "module": "Mathlib.MeasureTheory.OuterMeasure.AE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.term∀ᵐ_∂_,_", "kind": "definition", "module": "Mathlib.MeasureTheory.OuterMeasure.AE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory._aux_Mathlib_MeasureTheory_OuterMeasure_AE___macroRules_MeasureTheory_term∀ᵐ_∂_,__1", "kind": "definition", "module": "Mathlib.MeasureTheory.OuterMeasure.AE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory._aux_Mathlib_MeasureTheory_OuterMeasure_AE___delab_app_MeasureTheory_term∀ᵐ_∂_,__1", "kind": "definition", "module": "Mathlib.MeasureTheory.OuterMeasure.AE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.term∃ᵐ_∂_,_", "kind": "definition", "module": "Mathlib.MeasureTheory.OuterMeasure.AE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory._aux_Mathlib_MeasureTheory_OuterMeasure_AE___macroRules_MeasureTheory_term∃ᵐ_∂_,__1", "kind": "definition", "module": "Mathlib.MeasureTheory.OuterMeasure.AE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory._aux_Mathlib_MeasureTheory_OuterMeasure_AE___delab_app_MeasureTheory_term∃ᵐ_∂_,__1", "kind": "definition", "module": "Mathlib.MeasureTheory.OuterMeasure.AE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.term_=ᵐ[_]_", "kind": "definition", "module": "Mathlib.MeasureTheory.OuterMeasure.AE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory._aux_Mathlib_MeasureTheory_OuterMeasure_AE___macroRules_MeasureTheory_term_=ᵐ[_]__1", "kind": "definition", "module": "Mathlib.MeasureTheory.OuterMeasure.AE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory._aux_Mathlib_MeasureTheory_OuterMeasure_AE___unexpand_Filter_EventuallyEq_1", "kind": "definition", "module": "Mathlib.MeasureTheory.OuterMeasure.AE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.term_≤ᵐ[_]_", "kind": "definition", "module": "Mathlib.MeasureTheory.OuterMeasure.AE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory._aux_Mathlib_MeasureTheory_OuterMeasure_AE___macroRules_MeasureTheory_term_≤ᵐ[_]__1", "kind": "definition", "module": "Mathlib.MeasureTheory.OuterMeasure.AE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory._aux_Mathlib_MeasureTheory_OuterMeasure_AE___unexpand_Filter_EventuallyLE_1", "kind": "definition", "module": "Mathlib.MeasureTheory.OuterMeasure.AE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.mem_ae_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.AE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.ae_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.AE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.compl_mem_ae_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.AE", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.frequently_ae_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.AE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.frequently_ae_mem_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.AE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_eq_zero_iff_ae_notMem", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.AE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.ae_of_all", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.AE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.instCountableInterFilter", "kind": "instance", "module": "Mathlib.MeasureTheory.OuterMeasure.AE", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "MeasureTheory.ae_all_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.AE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.all_ae_of", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.AE", "is_tactic_proof": true, "tactics": ["filter_upwards"], "tactic_count": 1}
{"name": "MeasureTheory.ae_iff_of_countable", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.AE", "is_tactic_proof": true, "tactics": ["rw", "exacts"], "tactic_count": 2}
{"name": "MeasureTheory.ae_ball_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.AE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.ae_eq_refl", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.AE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.ae_eq_rfl", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.AE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.ae_eq_comm", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.AE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.ae_eq_symm", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.AE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.ae_eq_trans", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.AE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.ae_eq_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.AE", "is_tactic_proof": true, "tactics": ["simp", "refine", "rw", "rintro", "exact", "rintro", "simp"], "tactic_count": 7}
{"name": "MeasureTheory.ae_le_of_ae_lt", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.AE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.ae_eq_empty", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.AE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.ae_eq_univ", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.AE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.ae_le_set", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.AE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.ae_le_set_inter", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.AE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.ae_le_set_union", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.AE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.union_ae_eq_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.AE", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.diff_ae_eq_self", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.AE", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.diff_null_ae_eq_self", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.AE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.ae_eq_set", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.AE", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.measure_symmDiff_eq_zero_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.AE", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.ae_eq_set_compl_compl", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.AE", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.ae_eq_set_compl", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.AE", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.ae_eq_set_inter", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.AE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.ae_eq_set_union", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.AE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.ae_eq_set_diff", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.AE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.ae_eq_set_symmDiff", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.AE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.union_ae_eq_univ_of_ae_eq_univ_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.AE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.union_ae_eq_univ_of_ae_eq_univ_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.AE", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "MeasureTheory.union_ae_eq_right_of_ae_eq_empty", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.AE", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "MeasureTheory.union_ae_eq_left_of_ae_eq_empty", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.AE", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "MeasureTheory.inter_ae_eq_right_of_ae_eq_univ", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.AE", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "MeasureTheory.inter_ae_eq_left_of_ae_eq_univ", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.AE", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "MeasureTheory.inter_ae_eq_empty_of_ae_eq_empty_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.AE", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "MeasureTheory.inter_ae_eq_empty_of_ae_eq_empty_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.AE", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "Set.mulIndicator_ae_eq_one", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.AE", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.measure_mono_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.AE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_congr", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.AE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_mono_null_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.AE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_empty", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_mono", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_mono_null", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.pos_mono", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_eq_top_mono", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_lt_top_mono", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_pos_of_superset", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_iUnion_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Basic", "is_tactic_proof": true, "tactics": ["refine", "calc", "μ"], "tactic_count": 3}
{"name": "MeasureTheory.measure_biUnion_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Basic", "is_tactic_proof": true, "tactics": ["have", "rw", "apply"], "tactic_count": 3}
{"name": "MeasureTheory.measure_biUnion_finset_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_iUnion_fintype_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.measure_union_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.measure_univ_le_add_compl", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_le_inter_add_diff", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.measure_diff_null", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_biUnion_null_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Basic", "is_tactic_proof": true, "tactics": ["refine", "have", "simpa"], "tactic_count": 3}
{"name": "MeasureTheory.measure_sUnion_null_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.measure_iUnion_null_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.measure_union_null_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.measure_union_null", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.measure_null_iff_singleton", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.measure_iUnion_of_tendsto_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Basic", "is_tactic_proof": true, "tactics": ["refine", "set", "set", "have", "calc", "μ", "have", "exact"], "tactic_count": 8}
{"name": "MeasureTheory.measure_null_of_locally_null", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Basic", "is_tactic_proof": true, "tactics": ["choose", "choose", "rcases", "apply", "exact"], "tactic_count": 5}
{"name": "MeasureTheory.exists_mem_forall_mem_nhdsWithin_pos_measure", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Basic", "is_tactic_proof": true, "tactics": ["contrapose", "simp", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.OuterMeasure.iUnion_of_tendsto_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.iUnion_nat_of_monotone_of_tsum_ne_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Basic", "is_tactic_proof": true, "tactics": ["classical", "refine", "refine", "refine", "have", "simp", "intro", "have", "rcases", "clear", "rcases", "exact", "have", "refine", "rwa", "rw"], "tactic_count": 16}
{"name": "MeasureTheory.OuterMeasure.coe_fn_injective", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.ext", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.ext_nonempty", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_limsup_cofinite_eq_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.BorelCantelli", "is_tactic_proof": true, "tactics": ["refine", "calc", "μ", "gcongr", "rw", "exact"], "tactic_count": 6}
{"name": "MeasureTheory.measure_limsup_atTop_eq_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.BorelCantelli", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.ae_finite_setOf_mem", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.BorelCantelli", "is_tactic_proof": true, "tactics": ["rw", "congr", "simp"], "tactic_count": 3}
{"name": "MeasureTheory.measure_setOf_frequently_eq_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.BorelCantelli", "is_tactic_proof": true, "tactics": ["simpa", "measure_limsup_atTop_eq_zero"], "tactic_count": 2}
{"name": "MeasureTheory.ae_eventually_notMem", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.BorelCantelli", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measure_liminf_cofinite_eq_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.BorelCantelli", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.measure_liminf_atTop_eq_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.BorelCantelli", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.limsup_ae_eq_of_forall_ae_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.BorelCantelli", "is_tactic_proof": true, "tactics": ["simp", "refine", "simp"], "tactic_count": 3}
{"name": "MeasureTheory.liminf_ae_eq_of_forall_ae_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.BorelCantelli", "is_tactic_proof": true, "tactics": ["simp", "refine", "simp"], "tactic_count": 3}
{"name": "MeasureTheory.OuterMeasure.IsCaratheodory", "kind": "definition", "module": "Mathlib.MeasureTheory.OuterMeasure.Caratheodory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.isCaratheodory_iff_le'", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Caratheodory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.isCaratheodory_empty", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Caratheodory", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.OuterMeasure.isCaratheodory_compl", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Caratheodory", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.OuterMeasure.isCaratheodory_compl_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Caratheodory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.isCaratheodory_union", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Caratheodory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.IsCaratheodory.biUnion_of_finite", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Caratheodory", "is_tactic_proof": true, "tactics": ["classical", "lift", "induction", "empty", "insert", "simp", "exact"], "tactic_count": 7}
{"name": "MeasureTheory.OuterMeasure.measure_inter_union", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Caratheodory", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.OuterMeasure.isCaratheodory_iUnion_lt", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Caratheodory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.isCaratheodory_inter", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Caratheodory", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.OuterMeasure.isCaratheodory_diff", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Caratheodory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.isCaratheodory_partialSups", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Caratheodory", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.OuterMeasure.isCaratheodory_disjointed", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Caratheodory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.isCaratheodory_sum", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Caratheodory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.isCaratheodory_iUnion_of_disjoint", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Caratheodory", "is_tactic_proof": true, "tactics": ["apply", "intro", "have", "convert", "simp", "simp", "grw", "refine", "rw", "gcongr", "exact"], "tactic_count": 11}
{"name": "MeasureTheory.OuterMeasure.isCaratheodory_iUnion", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Caratheodory", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.OuterMeasure.f_iUnion", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Caratheodory", "is_tactic_proof": true, "tactics": ["refine", "rw", "refine", "have", "simp", "exact"], "tactic_count": 6}
{"name": "MeasureTheory.OuterMeasure.caratheodoryDynkin", "kind": "definition", "module": "Mathlib.MeasureTheory.OuterMeasure.Caratheodory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.caratheodory", "kind": "definition", "module": "Mathlib.MeasureTheory.OuterMeasure.Caratheodory", "is_tactic_proof": true, "tactics": ["apply", "intro", "apply"], "tactic_count": 3}
{"name": "MeasureTheory.OuterMeasure.isCaratheodory_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Caratheodory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.isCaratheodory_iff_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Caratheodory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.iUnion_eq_of_caratheodory", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Caratheodory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.ofFunction_caratheodory", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Caratheodory", "is_tactic_proof": true, "tactics": ["apply", "refine", "refine", "le_trans", "rw", "exact", "rw", "exact", "rw", "exact"], "tactic_count": 10}
{"name": "MeasureTheory.OuterMeasure.boundedBy_caratheodory", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Caratheodory", "is_tactic_proof": true, "tactics": ["apply", "rcases", "simp", "convert", "simp", "exact"], "tactic_count": 6}
{"name": "MeasureTheory.OuterMeasure.zero_caratheodory", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Caratheodory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.top_caratheodory", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Caratheodory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.le_add_caratheodory", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Caratheodory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.le_sum_caratheodory", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Caratheodory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.le_smul_caratheodory", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Caratheodory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.dirac_caratheodory", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Caratheodory", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.instFunLikeSetENNReal", "kind": "instance", "module": "Mathlib.MeasureTheory.OuterMeasure.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.measureOf_eq_coe", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.instOuterMeasureClass", "kind": "instance", "module": "Mathlib.MeasureTheory.OuterMeasure.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.extend", "kind": "definition", "module": "Mathlib.MeasureTheory.OuterMeasure.Induced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.extend_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Induced", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.extend_eq_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Induced", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.smul_extend", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Induced", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "MeasureTheory.ennreal_smul_extend", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Induced", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "MeasureTheory.le_extend", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Induced", "is_tactic_proof": true, "tactics": ["simp", "intro", "rfl"], "tactic_count": 3}
{"name": "MeasureTheory.extend_congr", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Induced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.extend_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Induced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.extend_iUnion_nat", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Induced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.extend_empty", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Induced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.extend_iUnion_le_tsum_nat'", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Induced", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "apply", "funext", "apply", "obtain", "exact"], "tactic_count": 7}
{"name": "MeasureTheory.extend_mono'", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Induced", "is_tactic_proof": true, "tactics": ["refine", "intro", "rw", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.extend_iUnion", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Induced", "is_tactic_proof": true, "tactics": ["cases", "rw", "exact", "extend_iUnion_nat", "exact"], "tactic_count": 5}
{"name": "MeasureTheory.extend_union", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Induced", "is_tactic_proof": false, "tactics": ["rw", "tsum_fintype]", "simp"], "tactic_count": 3}
{"name": "MeasureTheory.inducedOuterMeasure", "kind": "definition", "module": "Mathlib.MeasureTheory.OuterMeasure.Induced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.le_inducedOuterMeasure", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Induced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.inducedOuterMeasure_union_of_false_of_nonempty_inter", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Induced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.inducedOuterMeasure_eq_extend'", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Induced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.inducedOuterMeasure_eq'", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Induced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.inducedOuterMeasure_eq_iInf", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Induced", "is_tactic_proof": true, "tactics": ["apply", "simp", "intro", "grw", "exact", "refine", "intro", "refine", "intro", "refine", "refine", "intro", "exact"], "tactic_count": 13}
{"name": "MeasureTheory.inducedOuterMeasure_preimage", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Induced", "is_tactic_proof": true, "tactics": ["rw", "refine", "refine", "refine", "intro"], "tactic_count": 5}
{"name": "MeasureTheory.inducedOuterMeasure_exists_set", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Induced", "is_tactic_proof": true, "tactics": ["have", "conv", "lhs", "rw", "simp", "rcases", "exact"], "tactic_count": 7}
{"name": "MeasureTheory.inducedOuterMeasure_caratheodory", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Induced", "is_tactic_proof": true, "tactics": ["rw", "constructor", "intro", "exact", "intro", "conv_rhs", "refine", "intro", "refine", "intro", "refine", "intro", "refine", "gcongr"], "tactic_count": 14}
{"name": "MeasureTheory.extend_mono", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Induced", "is_tactic_proof": true, "tactics": ["refine", "have", "rw", "rw", "exact"], "tactic_count": 5}
{"name": "MeasureTheory.extend_iUnion_le_tsum_nat", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Induced", "is_tactic_proof": true, "tactics": ["refine", "simp", "rw", "refine", "rw", "exact"], "tactic_count": 6}
{"name": "MeasureTheory.inducedOuterMeasure_eq_extend", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Induced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.inducedOuterMeasure_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Induced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.trim", "kind": "definition", "module": "Mathlib.MeasureTheory.OuterMeasure.Induced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.le_trim_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Induced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.le_trim", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Induced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.null_of_trim_null", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Induced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.trim_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Induced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.trim_congr", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Induced", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.OuterMeasure.trim_mono", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Induced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.trim_anti_measurableSpace", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Induced", "is_tactic_proof": true, "tactics": ["simp", "intro", "rw"], "tactic_count": 3}
{"name": "MeasureTheory.OuterMeasure.trim_le_trim_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Induced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.trim_eq_trim_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Induced", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.OuterMeasure.trim_eq_iInf", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Induced", "is_tactic_proof": true, "tactics": ["simp", "exact", "inducedOuterMeasure_eq_iInf", "s"], "tactic_count": 4}
{"name": "MeasureTheory.OuterMeasure.trim_eq_iInf'", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Induced", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.OuterMeasure.trim_trim", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Induced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.trim_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Induced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.trim_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Induced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.trim_sum_ge", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Induced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.exists_measurable_superset_eq_trim", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Induced", "is_tactic_proof": true, "tactics": ["simp", "by_cases", "simp", "simp", "exact", "have", "intro", "have", "rcases", "exists", "have", "intro", "refine", "simp", "choose", "refine", "have", "tendsto_const_nhds.add", "rw", "refine", "exact", "refine", "refine", "exact"], "tactic_count": 24}
{"name": "MeasureTheory.OuterMeasure.exists_measurable_superset_of_trim_eq_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Induced", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.OuterMeasure.exists_measurable_superset_forall_eq_trim", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Induced", "is_tactic_proof": true, "tactics": ["choose", "replace", "replace", "refine", "exacts"], "tactic_count": 5}
{"name": "MeasureTheory.OuterMeasure.trim_binop", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Induced", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rw"], "tactic_count": 3}
{"name": "MeasureTheory.OuterMeasure.trim_op", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Induced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.trim_add", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Induced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.trim_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Induced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.trim_sup", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Induced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.trim_iSup", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Induced", "is_tactic_proof": true, "tactics": ["simp_rw", "ext1", "obtain", "exists_measurable_superset_forall_eq_trim", "simp", "simp", "exact"], "tactic_count": 7}
{"name": "MeasureTheory.OuterMeasure.restrict_trim", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Induced", "is_tactic_proof": true, "tactics": ["refine", "rw", "rcases", "rw", "rw", "refine", "rw", "exact", "rw"], "tactic_count": 9}
{"name": "MeasureTheory.AddContent.ofFunction_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.OfAddContent", "is_tactic_proof": true, "tactics": ["refine", "rw", "refine", "calc", "m", "refine", "rwa", "refine", "exact"], "tactic_count": 9}
{"name": "MeasureTheory.AddContent.inducedOuterMeasure_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.OfAddContent", "is_tactic_proof": false, "tactics": ["suffices", "rwa", "refine", "congr", "intro", "rw", "refine", "congr", "rw", "exact"], "tactic_count": 10}
{"name": "MeasureTheory.AddContent.isCaratheodory_ofFunction_of_mem", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.OfAddContent", "is_tactic_proof": true, "tactics": ["rw", "intro", "conv_rhs", "refine", "let", "have", "classical", "have", "eq_add_disjointOfDiff_of_subset", "simp_rw", "rw", "refine", "refine", "rw", "exact", "apply", "le_trans", "simp", "apply", "apply", "intro", "simp_rw", "rw", "obtain", "simp", "exact"], "tactic_count": 26}
{"name": "MeasureTheory.AddContent.isCaratheodory_inducedOuterMeasure_of_mem", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.OfAddContent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AddContent.isCaratheodory_inducedOuterMeasure", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.OfAddContent", "is_tactic_proof": true, "tactics": ["induction", "basic", "empty", "compl", "iUnion"], "tactic_count": 5}
{"name": "MeasureTheory.AddContent.measureCaratheodory", "kind": "definition", "module": "Mathlib.MeasureTheory.OuterMeasure.OfAddContent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AddContent.measureCaratheodory_eq_inducedOuterMeasure", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.OfAddContent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AddContent.measureCaratheodory_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.OfAddContent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AddContent.measure", "kind": "definition", "module": "Mathlib.MeasureTheory.OuterMeasure.OfAddContent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.AddContent.measure_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.OfAddContent", "is_tactic_proof": true, "tactics": ["rw", "exact", "rw", "apply"], "tactic_count": 4}
{"name": "MeasureTheory.OuterMeasure.ofFunction", "kind": "definition", "module": "Mathlib.MeasureTheory.OuterMeasure.OfFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.ofFunction_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.OfFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.ofFunction_eq_iInf_mem", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.OfFunction", "is_tactic_proof": true, "tactics": ["rw", "apply", "exact", "simp_rw", "refine", "by_cases", "exact", "simp", "push_neg", "obtain", "have", "exact"], "tactic_count": 12}
{"name": "MeasureTheory.OuterMeasure.ofFunction_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.OfFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.ofFunction_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.OfFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.le_ofFunction", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.OfFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.isGreatest_ofFunction", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.OfFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.ofFunction_eq_sSup", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.OfFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.ofFunction_union_of_top_of_nonempty_inter", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.OfFunction", "is_tactic_proof": true, "tactics": ["refine", "set", "rcases", "calc", "μ", "set", "have", "have", "calc", "μ", "μ.mono", "let", "mem_iUnion.2", "calc", "μ", "add_le_add"], "tactic_count": 16}
{"name": "MeasureTheory.OuterMeasure.comap_ofFunction", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.OfFunction", "is_tactic_proof": true, "tactics": ["refine", "rw", "apply", "rw", "refine", "refine", "rw", "refine", "rcases", "exacts"], "tactic_count": 10}
{"name": "MeasureTheory.OuterMeasure.map_ofFunction_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.OfFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.map_ofFunction", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.OfFunction", "is_tactic_proof": true, "tactics": ["refine", "simp", "intro", "refine", "rw", "exact", "refine", "simp"], "tactic_count": 8}
{"name": "MeasureTheory.OuterMeasure.restrict_ofFunction", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.OfFunction", "is_tactic_proof": true, "tactics": ["rw", "simp", "rw", "simp"], "tactic_count": 4}
{"name": "MeasureTheory.OuterMeasure.smul_ofFunction", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.OfFunction", "is_tactic_proof": true, "tactics": ["ext1", "haveI", "simp", "rw"], "tactic_count": 4}
{"name": "MeasureTheory.OuterMeasure.boundedBy", "kind": "definition", "module": "Mathlib.MeasureTheory.OuterMeasure.OfFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.boundedBy_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.OfFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.boundedBy_eq_ofFunction", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.OfFunction", "is_tactic_proof": false, "tactics": ["have", "ext1", "rcases", "simp"], "tactic_count": 4}
{"name": "MeasureTheory.OuterMeasure.boundedBy_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.OfFunction", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.OuterMeasure.boundedBy_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.OfFunction", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.OuterMeasure.boundedBy_eq_self", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.OfFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.le_boundedBy", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.OfFunction", "is_tactic_proof": true, "tactics": ["rw", "rcases"], "tactic_count": 2}
{"name": "MeasureTheory.OuterMeasure.le_boundedBy'", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.OfFunction", "is_tactic_proof": true, "tactics": ["rw", "intro", "rcases"], "tactic_count": 3}
{"name": "MeasureTheory.OuterMeasure.boundedBy_top", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.OfFunction", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.OuterMeasure.boundedBy_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.OfFunction", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "MeasureTheory.OuterMeasure.smul_boundedBy", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.OfFunction", "is_tactic_proof": true, "tactics": ["simp", "congr", "rcases"], "tactic_count": 3}
{"name": "MeasureTheory.OuterMeasure.comap_boundedBy", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.OfFunction", "is_tactic_proof": true, "tactics": ["refine", "refine", "have", "exact", "dsimp", "congr", "rw"], "tactic_count": 7}
{"name": "MeasureTheory.OuterMeasure.boundedBy_union_of_top_of_nonempty_inter", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.OfFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.sInfGen", "kind": "definition", "module": "Mathlib.MeasureTheory.OuterMeasure.OfFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.sInfGen_def", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.OfFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.sInf_eq_boundedBy_sInfGen", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.OfFunction", "is_tactic_proof": true, "tactics": ["refine", "refine", "apply", "refine", "intro", "exact"], "tactic_count": 6}
{"name": "MeasureTheory.OuterMeasure.iSup_sInfGen_nonempty", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.OfFunction", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simp"], "tactic_count": 3}
{"name": "MeasureTheory.OuterMeasure.sInf_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.OfFunction", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MeasureTheory.OuterMeasure.sInf_apply'", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.OfFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.iInf_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.OfFunction", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.OuterMeasure.iInf_apply'", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.OfFunction", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.OuterMeasure.biInf_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.OfFunction", "is_tactic_proof": true, "tactics": ["haveI", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.OuterMeasure.biInf_apply'", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.OfFunction", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.OuterMeasure.map_iInf_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.OfFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.comap_iInf", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.OfFunction", "is_tactic_proof": true, "tactics": ["refine", "refine", "simp", "preimage_iUnion]", "refine", "exact"], "tactic_count": 6}
{"name": "MeasureTheory.OuterMeasure.map_iInf", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.OfFunction", "is_tactic_proof": true, "tactics": ["refine", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.OuterMeasure.map_iInf_comap", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.OfFunction", "is_tactic_proof": true, "tactics": ["refine", "simp", "refine", "rw", "exact", "refine", "simpa", "subset_rfl"], "tactic_count": 8}
{"name": "MeasureTheory.OuterMeasure.map_biInf_comap", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.OfFunction", "is_tactic_proof": true, "tactics": ["haveI", "rw", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.OuterMeasure.restrict_iInf_restrict", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.OfFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.restrict_iInf", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.OfFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.restrict_biInf", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.OfFunction", "is_tactic_proof": true, "tactics": ["haveI", "rw", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.OuterMeasure.restrict_sInf_eq_sInf_restrict", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.OfFunction", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.OuterMeasure.instZero", "kind": "instance", "module": "Mathlib.MeasureTheory.OuterMeasure.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.coe_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.instInhabited", "kind": "instance", "module": "Mathlib.MeasureTheory.OuterMeasure.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.instAdd", "kind": "instance", "module": "Mathlib.MeasureTheory.OuterMeasure.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.coe_add", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.add_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.instSMul", "kind": "instance", "module": "Mathlib.MeasureTheory.OuterMeasure.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.coe_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.smul_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.instSMulCommClass", "kind": "instance", "module": "Mathlib.MeasureTheory.OuterMeasure.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.instIsScalarTower", "kind": "instance", "module": "Mathlib.MeasureTheory.OuterMeasure.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.instIsCentralScalar", "kind": "instance", "module": "Mathlib.MeasureTheory.OuterMeasure.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.instMulAction", "kind": "instance", "module": "Mathlib.MeasureTheory.OuterMeasure.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.addCommMonoid", "kind": "instance", "module": "Mathlib.MeasureTheory.OuterMeasure.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.coeFnAddMonoidHom", "kind": "definition", "module": "Mathlib.MeasureTheory.OuterMeasure.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.instDistribMulAction", "kind": "instance", "module": "Mathlib.MeasureTheory.OuterMeasure.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.instModule", "kind": "instance", "module": "Mathlib.MeasureTheory.OuterMeasure.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.instBot", "kind": "instance", "module": "Mathlib.MeasureTheory.OuterMeasure.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.coe_bot", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.instPartialOrder", "kind": "instance", "module": "Mathlib.MeasureTheory.OuterMeasure.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.instIsOrderedAddMonoid", "kind": "instance", "module": "Mathlib.MeasureTheory.OuterMeasure.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.orderBot", "kind": "instance", "module": "Mathlib.MeasureTheory.OuterMeasure.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.univ_eq_zero_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.instSupSet", "kind": "instance", "module": "Mathlib.MeasureTheory.OuterMeasure.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.instCompleteLattice", "kind": "instance", "module": "Mathlib.MeasureTheory.OuterMeasure.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.sSup_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.iSup_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.OuterMeasure.coe_iSup", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.sup_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Operations", "is_tactic_proof": true, "tactics": ["have"], "tactic_count": 1}
{"name": "MeasureTheory.OuterMeasure.smul_iSup", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.mono''", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.map", "kind": "definition", "module": "Mathlib.MeasureTheory.OuterMeasure.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.OuterMeasure.map_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasureTheory.OuterMeasure.instLawfulFunctor", "kind": "instance", "module": "Mathlib.MeasureTheory.OuterMeasure.Operations", "is_tactic_proof": true, "tactics": ["constructor"], "tactic_count": 1}
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{"name": "MeasureTheory.OuterMeasure.map_le_restrict_range", "kind": "theorem", "module": "Mathlib.MeasureTheory.OuterMeasure.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "IsPiSystem", "kind": "definition", "module": "Mathlib.MeasureTheory.PiSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "isPiSystem_iUnion_of_directed_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.PiSystem", "is_tactic_proof": true, "tactics": ["intro", "rw", "obtain", "obtain", "obtain", "exact"], "tactic_count": 6}
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{"name": "generatePiSystem_subset_self", "kind": "theorem", "module": "Mathlib.MeasureTheory.PiSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "generateFrom_generatePiSystem_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.PiSystem", "is_tactic_proof": true, "tactics": ["apply", "exact", "exact"], "tactic_count": 3}
{"name": "mem_generatePiSystem_iUnion_elim", "kind": "theorem", "module": "Mathlib.MeasureTheory.PiSystem", "is_tactic_proof": true, "tactics": ["classical", "induction", "rcases", "refine", "simpa", "inter", "h_t", "rcases", "rcases", "use", "constructor", "ext", "simp_rw", "grind", "intro", "split_ifs", "refine", "exact", "exact", "exact", "rw", "apply"], "tactic_count": 22}
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{"name": "piiUnionInter", "kind": "definition", "module": "Mathlib.MeasureTheory.PiSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "generateFrom_piiUnionInter_singleton_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.PiSystem", "is_tactic_proof": true, "tactics": ["refine", "rintro", "refine", "exact", "rintro", "refine", "rw", "rwa", "exact", "simp"], "tactic_count": 10}
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{"name": "piiUnionInter_mono_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.PiSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "subset_piiUnionInter", "kind": "theorem", "module": "Mathlib.MeasureTheory.PiSystem", "is_tactic_proof": false, "tactics": ["have", "intro", "rw", "rwa", "refine", "rw", "exact"], "tactic_count": 7}
{"name": "mem_piiUnionInter_of_measurableSet", "kind": "theorem", "module": "Mathlib.MeasureTheory.PiSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_generateFrom_piiUnionInter", "kind": "theorem", "module": "Mathlib.MeasureTheory.PiSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurableSet_iSup_of_mem_piiUnionInter", "kind": "theorem", "module": "Mathlib.MeasureTheory.PiSystem", "is_tactic_proof": true, "tactics": ["rcases", "refine", "suffices", "have", "exact"], "tactic_count": 5}
{"name": "generateFrom_piiUnionInter_measurableSet", "kind": "theorem", "module": "Mathlib.MeasureTheory.PiSystem", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact", "refine", "rw", "exact"], "tactic_count": 6}
{"name": "MeasurableSpace.DynkinSystem.ext", "kind": "theorem", "module": "Mathlib.MeasureTheory.PiSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.DynkinSystem.has_compl_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.PiSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.DynkinSystem.has_univ", "kind": "theorem", "module": "Mathlib.MeasureTheory.PiSystem", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasurableSpace.DynkinSystem.has_iUnion", "kind": "theorem", "module": "Mathlib.MeasureTheory.PiSystem", "is_tactic_proof": true, "tactics": ["cases", "rw", "exact"], "tactic_count": 3}
{"name": "MeasurableSpace.DynkinSystem.has_union", "kind": "theorem", "module": "Mathlib.MeasureTheory.PiSystem", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasurableSpace.DynkinSystem.has_diff", "kind": "theorem", "module": "Mathlib.MeasureTheory.PiSystem", "is_tactic_proof": true, "tactics": ["apply", "simp", "exact"], "tactic_count": 3}
{"name": "MeasurableSpace.DynkinSystem.instLEDynkinSystem", "kind": "instance", "module": "Mathlib.MeasureTheory.PiSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.DynkinSystem.le_def", "kind": "theorem", "module": "Mathlib.MeasureTheory.PiSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.DynkinSystem.instPartialOrder", "kind": "instance", "module": "Mathlib.MeasureTheory.PiSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.DynkinSystem.ofMeasurableSpace", "kind": "definition", "module": "Mathlib.MeasureTheory.PiSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.DynkinSystem.ofMeasurableSpace_le_ofMeasurableSpace_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.PiSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.DynkinSystem.GenerateHas", "kind": "inductive", "module": "Mathlib.MeasureTheory.PiSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.DynkinSystem.generateHas_compl", "kind": "theorem", "module": "Mathlib.MeasureTheory.PiSystem", "is_tactic_proof": true, "tactics": ["refine", "intro", "convert", "simp"], "tactic_count": 4}
{"name": "MeasurableSpace.DynkinSystem.generate", "kind": "definition", "module": "Mathlib.MeasureTheory.PiSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.DynkinSystem.generateHas_def", "kind": "theorem", "module": "Mathlib.MeasureTheory.PiSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.DynkinSystem.instInhabited", "kind": "instance", "module": "Mathlib.MeasureTheory.PiSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.DynkinSystem.toMeasurableSpace", "kind": "definition", "module": "Mathlib.MeasureTheory.PiSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.DynkinSystem.ofMeasurableSpace_toMeasurableSpace", "kind": "theorem", "module": "Mathlib.MeasureTheory.PiSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.DynkinSystem.restrictOn", "kind": "definition", "module": "Mathlib.MeasureTheory.PiSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.DynkinSystem.generate_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.PiSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.DynkinSystem.generate_has_subset_generate_measurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.PiSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.DynkinSystem.generate_inter", "kind": "theorem", "module": "Mathlib.MeasureTheory.PiSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.DynkinSystem.generateFrom_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.PiSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableSpace.induction_on_inter", "kind": "theorem", "module": "Mathlib.MeasureTheory.PiSystem", "is_tactic_proof": false, "tactics": ["have", "rw", "rfl", "suffices", "intro", "induction", "basic", "empty"], "tactic_count": 8}
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{"name": "MeasureTheory.IsSetAlgebra.inter_mem", "kind": "theorem", "module": "Mathlib.MeasureTheory.SetAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IsSetAlgebra.diff_mem", "kind": "theorem", "module": "Mathlib.MeasureTheory.SetAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IsSetAlgebra.isSetRing", "kind": "theorem", "module": "Mathlib.MeasureTheory.SetAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasureTheory.IsSetAlgebra.biInter_mem", "kind": "theorem", "module": "Mathlib.MeasureTheory.SetAlgebra", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "exact", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.generateSetAlgebra", "kind": "inductive", "module": "Mathlib.MeasureTheory.SetAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.isSetAlgebra_generateSetAlgebra", "kind": "theorem", "module": "Mathlib.MeasureTheory.SetAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.self_subset_generateSetAlgebra", "kind": "theorem", "module": "Mathlib.MeasureTheory.SetAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.generateFrom_generateSetAlgebra_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.SetAlgebra", "is_tactic_proof": true, "tactics": ["refine", "induction", "hC", "clear", "induction", "base", "empty", "compl", "union", "empty", "compl", "iUnion"], "tactic_count": 12}
{"name": "MeasureTheory.generateSetAlgebra_mono", "kind": "theorem", "module": "Mathlib.MeasureTheory.SetAlgebra", "is_tactic_proof": true, "tactics": ["intro", "induction", "base", "empty", "compl", "union"], "tactic_count": 6}
{"name": "MeasureTheory.IsSetAlgebra.generateSetAlgebra_subset", "kind": "theorem", "module": "Mathlib.MeasureTheory.SetAlgebra", "is_tactic_proof": true, "tactics": ["intro", "induction", "base", "empty", "compl", "union"], "tactic_count": 6}
{"name": "MeasureTheory.IsSetAlgebra.generateSetAlgebra_subset_self", "kind": "theorem", "module": "Mathlib.MeasureTheory.SetAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IsSetAlgebra.generateSetAlgebra_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.SetAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.mem_generateSetAlgebra_elim", "kind": "theorem", "module": "Mathlib.MeasureTheory.SetAlgebra", "is_tactic_proof": true, "tactics": ["induction", "base", "u_mem", "refine", "simp⟩", "rw", "exact", "empty", "exact", "compl", "rcases", "have", "have", "refine", "hf", "rcases", "rcases", "rw", "exact", "ext", "simp", "mem_setOf_eq,", "constructor", "choose", "exact", "rcases", "exact", "union", "rcases", "rcases", "refine", "rintro", "exact", "exact", "rintro", "exact", "exact"], "tactic_count": 37}
{"name": "MeasureTheory.countable_generateSetAlgebra", "kind": "theorem", "module": "Mathlib.MeasureTheory.SetAlgebra", "is_tactic_proof": true, "tactics": ["let", "have", "apply", "have", "ext", "simpa", "exact", "let", "let", "have", "let", "have", "have", "intro", "rcases", "exact", "exact"], "tactic_count": 17}
{"name": "MeasureTheory.IsSetSemiring.isPiSystem", "kind": "theorem", "module": "Mathlib.MeasureTheory.SetSemiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IsSetSemiring.exists_finpartition_diff", "kind": "theorem", "module": "Mathlib.MeasureTheory.SetSemiring", "is_tactic_proof": true, "tactics": ["classical", "obtain", "refine", "rw", "grw"], "tactic_count": 5}
{"name": "MeasureTheory.IsSetSemiring.mem_supClosure_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.SetSemiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IsSetSemiring.diff_mem_supClosure", "kind": "theorem", "module": "Mathlib.MeasureTheory.SetSemiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IsSetSemiring.isSetRing_supClosure", "kind": "theorem", "module": "Mathlib.MeasureTheory.SetSemiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IsSetSemiring.disjointOfDiff", "kind": "definition", "module": "Mathlib.MeasureTheory.SetSemiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IsSetSemiring.empty_notMem_disjointOfDiff", "kind": "theorem", "module": "Mathlib.MeasureTheory.SetSemiring", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "MeasureTheory.IsSetSemiring.subset_disjointOfDiff", "kind": "theorem", "module": "Mathlib.MeasureTheory.SetSemiring", "is_tactic_proof": true, "tactics": ["classical", "simp", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.IsSetSemiring.pairwiseDisjoint_disjointOfDiff", "kind": "theorem", "module": "Mathlib.MeasureTheory.SetSemiring", "is_tactic_proof": true, "tactics": ["classical", "simp", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.IsSetSemiring.sUnion_disjointOfDiff", "kind": "theorem", "module": "Mathlib.MeasureTheory.SetSemiring", "is_tactic_proof": true, "tactics": ["classical", "rw", "simp", "rw"], "tactic_count": 4}
{"name": "MeasureTheory.IsSetSemiring.notMem_disjointOfDiff", "kind": "theorem", "module": "Mathlib.MeasureTheory.SetSemiring", "is_tactic_proof": true, "tactics": ["intro", "suffices", "have", "specialize", "simp", "refine", "rwa", "rw", "exact"], "tactic_count": 9}
{"name": "MeasureTheory.IsSetSemiring.sUnion_insert_disjointOfDiff", "kind": "theorem", "module": "Mathlib.MeasureTheory.SetSemiring", "is_tactic_proof": true, "tactics": ["conv_rhs", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.IsSetSemiring.disjoint_sUnion_disjointOfDiff", "kind": "theorem", "module": "Mathlib.MeasureTheory.SetSemiring", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.IsSetSemiring.pairwiseDisjoint_insert_disjointOfDiff", "kind": "theorem", "module": "Mathlib.MeasureTheory.SetSemiring", "is_tactic_proof": true, "tactics": ["have", "refine", "simp_rw", "refine", "simp", "exact"], "tactic_count": 6}
{"name": "MeasureTheory.IsSetSemiring.exists_disjoint_finset_diff_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.SetSemiring", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "simp", "refine", "simp", "insert", "rw", "have", "obtain", "let", "have", "intro", "exact", "have", "hC.pairwiseDisjoint_disjointOfDiff", "have", "have", "intro", "rw", "exact", "let", "have", "intro", "simp", "exists₂_imp]", "intro", "exact", "refine", "rw", "refine", "simp", "simp_rw", "intro", "have", "by_contra", "refine", "refine", "exact", "convert", "rw", "congr", "rw", "congr", "exact", "rw", "simp_rw", "simp", "rw", "refine", "by_cases", "simp", "rw", "simp", "simp"], "tactic_count": 55}
{"name": "MeasureTheory.IsSetSemiring.disjointOfDiffUnion", "kind": "definition", "module": "Mathlib.MeasureTheory.SetSemiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IsSetSemiring.empty_notMem_disjointOfDiffUnion", "kind": "theorem", "module": "Mathlib.MeasureTheory.SetSemiring", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "MeasureTheory.IsSetSemiring.disjointOfDiffUnion_subset", "kind": "theorem", "module": "Mathlib.MeasureTheory.SetSemiring", "is_tactic_proof": true, "tactics": ["classical", "simp", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.IsSetSemiring.pairwiseDisjoint_disjointOfDiffUnion", "kind": "theorem", "module": "Mathlib.MeasureTheory.SetSemiring", "is_tactic_proof": true, "tactics": ["classical", "simp", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.IsSetSemiring.diff_sUnion_eq_sUnion_disjointOfDiffUnion", "kind": "theorem", "module": "Mathlib.MeasureTheory.SetSemiring", "is_tactic_proof": true, "tactics": ["classical", "rw", "simp", "rw"], "tactic_count": 4}
{"name": "MeasureTheory.IsSetSemiring.sUnion_disjointOfDiffUnion_subset", "kind": "theorem", "module": "Mathlib.MeasureTheory.SetSemiring", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.IsSetSemiring.subset_of_diffUnion_disjointOfDiffUnion", "kind": "theorem", "module": "Mathlib.MeasureTheory.SetSemiring", "is_tactic_proof": true, "tactics": ["revert", "rw"], "tactic_count": 2}
{"name": "MeasureTheory.IsSetSemiring.subset_of_mem_disjointOfDiffUnion", "kind": "theorem", "module": "Mathlib.MeasureTheory.SetSemiring", "is_tactic_proof": true, "tactics": ["apply", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.IsSetSemiring.disjoint_sUnion_disjointOfDiffUnion", "kind": "theorem", "module": "Mathlib.MeasureTheory.SetSemiring", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.IsSetSemiring.disjoint_disjointOfDiffUnion", "kind": "theorem", "module": "Mathlib.MeasureTheory.SetSemiring", "is_tactic_proof": true, "tactics": ["by_contra", "rw", "obtain", "have", "hC.disjoint_sUnion_disjointOfDiffUnion", "simp", "refine", "rwa"], "tactic_count": 8}
{"name": "MeasureTheory.IsSetSemiring.pairwiseDisjoint_union_disjointOfDiffUnion", "kind": "theorem", "module": "Mathlib.MeasureTheory.SetSemiring", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp_rw", "exact", "disjoint_of_subset"], "tactic_count": 5}
{"name": "MeasureTheory.IsSetSemiring.sUnion_union_sUnion_disjointOfDiffUnion_of_subset", "kind": "theorem", "module": "Mathlib.MeasureTheory.SetSemiring", "is_tactic_proof": true, "tactics": ["conv_rhs", "rw"], "tactic_count": 2}
{"name": "MeasureTheory.IsSetSemiring.sUnion_union_disjointOfDiffUnion_of_subset", "kind": "theorem", "module": "Mathlib.MeasureTheory.SetSemiring", "is_tactic_proof": true, "tactics": ["conv_rhs", "simp_rw", "rw"], "tactic_count": 3}
{"name": "MeasureTheory.IsSetSemiring.disjointOfUnion_props", "kind": "theorem", "module": "Mathlib.MeasureTheory.SetSemiring", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "cons", "rw", "obtain", "let", "have", "have", "use", "simp", "sUnion_insert]", "have", "have", "apply", "intro", "exact_mod_cast", "simp", "refine", "apply", "intro", "rw", "exact", "intro", "have", "refine", "disjoint_of_sSup_disjoint_of_le_of_le", "simp", "apply", "exact", "have", "refine", "rw", "rw", "exact_mod_cast", "exact", "intro", "rw", "exact", "simp", "refine", "rw", "exact", "simpa", "simp", "intro", "obtain", "obtain", "obtain", "exact", "intro", "simp_rw", "change", "rw", "exact", "refine", "intro", "rw", "exact", "simp", "simp_rw", "simp"], "tactic_count": 62}
{"name": "MeasureTheory.IsSetSemiring.disjointOfUnion", "kind": "definition", "module": "Mathlib.MeasureTheory.SetSemiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IsSetSemiring.pairwiseDisjoint_disjointOfUnion", "kind": "theorem", "module": "Mathlib.MeasureTheory.SetSemiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IsSetSemiring.disjointOfUnion_subset", "kind": "theorem", "module": "Mathlib.MeasureTheory.SetSemiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IsSetSemiring.pairwiseDisjoint_biUnion_disjointOfUnion", "kind": "theorem", "module": "Mathlib.MeasureTheory.SetSemiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IsSetSemiring.pairwiseDisjoint_disjointOfUnion_of_mem", "kind": "theorem", "module": "Mathlib.MeasureTheory.SetSemiring", "is_tactic_proof": true, "tactics": ["apply", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.IsSetSemiring.disjointOfUnion_subset_of_mem", "kind": "theorem", "module": "Mathlib.MeasureTheory.SetSemiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IsSetSemiring.subset_of_mem_disjointOfUnion", "kind": "theorem", "module": "Mathlib.MeasureTheory.SetSemiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IsSetSemiring.empty_notMem_disjointOfUnion", "kind": "theorem", "module": "Mathlib.MeasureTheory.SetSemiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IsSetSemiring.sUnion_disjointOfUnion", "kind": "theorem", "module": "Mathlib.MeasureTheory.SetSemiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.MeasureTheory.SetSemiring.0.Set.Ioc_mem_setOf_Ioc_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.SetSemiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IsSetSemiring.Ioc", "kind": "theorem", "module": "Mathlib.MeasureTheory.SetSemiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IsSetRing.inter_mem", "kind": "theorem", "module": "Mathlib.MeasureTheory.SetSemiring", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.IsSetRing.isSetSemiring", "kind": "theorem", "module": "Mathlib.MeasureTheory.SetSemiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IsSetRing.biUnion_mem", "kind": "theorem", "module": "Mathlib.MeasureTheory.SetSemiring", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "insert", "simp_rw", "refine", "exact"], "tactic_count": 7}
{"name": "MeasureTheory.IsSetRing.biInter_mem", "kind": "theorem", "module": "Mathlib.MeasureTheory.SetSemiring", "is_tactic_proof": true, "tactics": ["classical", "induction", "singleton", "cons", "simp_rw", "simp", "refine", "exact"], "tactic_count": 8}
{"name": "MeasureTheory.IsSetRing.finsetSup_mem", "kind": "theorem", "module": "Mathlib.MeasureTheory.SetSemiring", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.IsSetRing.partialSups_mem", "kind": "theorem", "module": "Mathlib.MeasureTheory.SetSemiring", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.IsSetRing.disjointed_mem", "kind": "theorem", "module": "Mathlib.MeasureTheory.SetSemiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IsSetRing.iUnion_le_mem", "kind": "theorem", "module": "Mathlib.MeasureTheory.SetSemiring", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "MeasureTheory.IsSetRing.iInter_le_mem", "kind": "theorem", "module": "Mathlib.MeasureTheory.SetSemiring", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "MeasureTheory.IsSetRing.accumulate_mem", "kind": "theorem", "module": "Mathlib.MeasureTheory.SetSemiring", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "ContinuousMap.hasFiniteIntegral_of_bound", "kind": "theorem", "module": "Mathlib.MeasureTheory.SpecificCodomains.ContinuousMap", "is_tactic_proof": true, "tactics": ["rcases", "simp", "have", "filter_upwards", "refine", "filter_upwards", "exact"], "tactic_count": 7}
{"name": "ContinuousMap.hasFiniteIntegral_mkD_of_bound", "kind": "theorem", "module": "Mathlib.MeasureTheory.SpecificCodomains.ContinuousMap", "is_tactic_proof": true, "tactics": ["refine", "filter_upwards", "simpa"], "tactic_count": 3}
{"name": "ContinuousMap.hasFiniteIntegral_mkD_restrict_of_bound", "kind": "theorem", "module": "Mathlib.MeasureTheory.SpecificCodomains.ContinuousMap", "is_tactic_proof": true, "tactics": ["refine", "simpa", "simpa"], "tactic_count": 3}
{"name": "ContinuousMap.aeStronglyMeasurable_mkD_of_uncurry", "kind": "theorem", "module": "Mathlib.MeasureTheory.SpecificCodomains.ContinuousMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.aeStronglyMeasurable_restrict_mkD_of_uncurry", "kind": "theorem", "module": "Mathlib.MeasureTheory.SpecificCodomains.ContinuousMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.aeStronglyMeasurable_mkD_restrict_of_uncurry", "kind": "theorem", "module": "Mathlib.MeasureTheory.SpecificCodomains.ContinuousMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.aeStronglyMeasurable_restrict_mkD_restrict_of_uncurry", "kind": "theorem", "module": "Mathlib.MeasureTheory.SpecificCodomains.ContinuousMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.hasFiniteIntegral_of_bound", "kind": "theorem", "module": "Mathlib.MeasureTheory.SpecificCodomains.ContinuousMapZero", "is_tactic_proof": false, "tactics": ["have", "filter_upwards", "refine", "filter_upwards", "exact"], "tactic_count": 5}
{"name": "ContinuousMapZero.hasFiniteIntegral_mkD_of_bound", "kind": "theorem", "module": "Mathlib.MeasureTheory.SpecificCodomains.ContinuousMapZero", "is_tactic_proof": true, "tactics": ["refine", "filter_upwards", "simpa"], "tactic_count": 3}
{"name": "ContinuousMapZero.hasFiniteIntegral_mkD_restrict_of_bound", "kind": "theorem", "module": "Mathlib.MeasureTheory.SpecificCodomains.ContinuousMapZero", "is_tactic_proof": true, "tactics": ["refine", "simpa", "simpa"], "tactic_count": 3}
{"name": "ContinuousMapZero.aeStronglyMeasurable_mkD_of_uncurry", "kind": "theorem", "module": "Mathlib.MeasureTheory.SpecificCodomains.ContinuousMapZero", "is_tactic_proof": true, "tactics": ["rw", "refine", "filter_upwards", "rw"], "tactic_count": 4}
{"name": "ContinuousMapZero.aeStronglyMeasurable_restrict_mkD_of_uncurry", "kind": "theorem", "module": "Mathlib.MeasureTheory.SpecificCodomains.ContinuousMapZero", "is_tactic_proof": true, "tactics": ["rw", "refine", "filter_upwards", "rw"], "tactic_count": 4}
{"name": "ContinuousMapZero.aeStronglyMeasurable_mkD_restrict_of_uncurry", "kind": "theorem", "module": "Mathlib.MeasureTheory.SpecificCodomains.ContinuousMapZero", "is_tactic_proof": true, "tactics": ["rw", "refine", "filter_upwards", "rw"], "tactic_count": 4}
{"name": "ContinuousMapZero.aeStronglyMeasurable_restrict_mkD_restrict_of_uncurry", "kind": "theorem", "module": "Mathlib.MeasureTheory.SpecificCodomains.ContinuousMapZero", "is_tactic_proof": true, "tactics": ["rw", "refine", "aestronglyMeasurable_congr", "filter_upwards", "rw"], "tactic_count": 5}
{"name": "MeasureTheory.memLp_pi_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.SpecificCodomains.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integrable_pi_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.SpecificCodomains.Pi", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MeasureTheory.eval_integral", "kind": "theorem", "module": "Mathlib.MeasureTheory.SpecificCodomains.Pi", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.memLp_prod_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.SpecificCodomains.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MemLp.fst", "kind": "theorem", "module": "Mathlib.MeasureTheory.SpecificCodomains.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MemLp.snd", "kind": "theorem", "module": "Mathlib.MeasureTheory.SpecificCodomains.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.memLp_piLp_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.SpecificCodomains.WithLp", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.integrable_piLp_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.SpecificCodomains.WithLp", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MeasureTheory.eval_integral_piLp", "kind": "theorem", "module": "Mathlib.MeasureTheory.SpecificCodomains.WithLp", "is_tactic_proof": true, "tactics": ["rw", "simp", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.memLp_prodLp_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.SpecificCodomains.WithLp", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.MemLp.prodLp_fst", "kind": "theorem", "module": "Mathlib.MeasureTheory.SpecificCodomains.WithLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.MemLp.prodLp_snd", "kind": "theorem", "module": "Mathlib.MeasureTheory.SpecificCodomains.WithLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integrable_prodLp_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.SpecificCodomains.WithLp", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MeasureTheory.Integrable.prodLp_fst", "kind": "theorem", "module": "Mathlib.MeasureTheory.SpecificCodomains.WithLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Integrable.prodLp_snd", "kind": "theorem", "module": "Mathlib.MeasureTheory.SpecificCodomains.WithLp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.fst_integral_withLp", "kind": "theorem", "module": "Mathlib.MeasureTheory.SpecificCodomains.WithLp", "is_tactic_proof": true, "tactics": ["rw", "conv", "rw", "rfl", "exact"], "tactic_count": 5}
{"name": "MeasureTheory.snd_integral_withLp", "kind": "theorem", "module": "Mathlib.MeasureTheory.SpecificCodomains.WithLp", "is_tactic_proof": true, "tactics": ["rw", "conv", "rw", "rfl", "exact"], "tactic_count": 5}
{"name": "ae_restrict_le_codiscreteWithin", "kind": "theorem", "module": "Mathlib.MeasureTheory.Topology", "is_tactic_proof": true, "tactics": ["intro", "have", "isDiscrete_iff_discreteTopology.mp", "rw", "apply"], "tactic_count": 5}
{"name": "MeasureTheory.SignedMeasure", "kind": "abbrev", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.instCoeFun", "kind": "instance", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.empty", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.not_measurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.m_iUnion", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.coe_injective", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.ext_iff'", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.VectorMeasure.ext_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "rfl", "rw", "intro", "by_cases", "exact", "simp_rw"], "tactic_count": 8}
{"name": "MeasureTheory.VectorMeasure.ext", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.hasSum_of_disjoint_iUnion", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["rcases", "rw", "convert", "simp", "exact", "simp", "exact"], "tactic_count": 7}
{"name": "MeasureTheory.VectorMeasure.of_disjoint_iUnion", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.of_union", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["rw", "exacts"], "tactic_count": 2}
{"name": "MeasureTheory.VectorMeasure.of_add_of_diff", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.VectorMeasure.of_diff", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.VectorMeasure.of_compl", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MeasureTheory.VectorMeasure.of_diff_of_diff_eq_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["symm", "calc", "v", "rw", "rw", "exact", "exact", "exact", "rw", "exact", "exact", "exact"], "tactic_count": 12}
{"name": "MeasureTheory.VectorMeasure.of_iUnion_nonneg", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.of_iUnion_nonpos", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.of_nonneg_disjoint_union_eq_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["rw", "linarith"], "tactic_count": 2}
{"name": "MeasureTheory.VectorMeasure.of_nonpos_disjoint_union_eq_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["rw", "linarith"], "tactic_count": 2}
{"name": "MeasureTheory.VectorMeasure.of_biUnion_finset", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "insert", "ih", "simp", "rw", "exact", "grind", "simp", "exact", "apply", "apply"], "tactic_count": 13}
{"name": "MeasureTheory.VectorMeasure.tendsto_vectorMeasure_iUnion_atTop_nat", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["set", "have", "have", "rw", "apply", "convert", "dsimp", "rw", "rw", "exact", "exact"], "tactic_count": 11}
{"name": "MeasureTheory.VectorMeasure.tendsto_vectorMeasure_iInter_atTop_nat", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "simp", "simp_rw", "apply", "exact"], "tactic_count": 7}
{"name": "MeasureTheory.VectorMeasure.smul", "kind": "definition", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.instSMul", "kind": "instance", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.coe_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.smul_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.instZero", "kind": "instance", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.instInhabited", "kind": "instance", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.coe_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.zero_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.add", "kind": "definition", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.instAdd", "kind": "instance", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.coe_add", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.add_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.instAddCommMonoid", "kind": "instance", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.coeFnAddMonoidHom", "kind": "definition", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.neg", "kind": "definition", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.instNeg", "kind": "instance", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.coe_neg", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.neg_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.sub", "kind": "definition", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.instSub", "kind": "instance", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.coe_sub", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.sub_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.instAddCommGroup", "kind": "instance", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.instDistribMulAction", "kind": "instance", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.instModule", "kind": "instance", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.dirac", "kind": "definition", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.dirac_apply_of_mem", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.VectorMeasure.dirac_apply_of_notMem", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.toSignedMeasure", "kind": "definition", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.toSignedMeasure_apply_measurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.toSignedMeasure_congr", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["congr"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.toSignedMeasure_eq_toSignedMeasure_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["refine", "ext1", "have", "rwa", "measureReal_eq_measureReal_iff]", "congr"], "tactic_count": 6}
{"name": "MeasureTheory.Measure.toSignedMeasure_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.toSignedMeasure_add", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["ext", "rw", "toSignedMeasure_apply_measurable"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.toSignedMeasure_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["ext", "rw", "measureReal_nnreal_smul_apply]", "rfl"], "tactic_count": 4}
{"name": "MeasureTheory.Measure.toENNRealVectorMeasure", "kind": "definition", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.toENNRealVectorMeasure_apply_measurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.toENNRealVectorMeasure_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.toENNRealVectorMeasure_add", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "toENNRealVectorMeasure_apply_measurable"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.toSignedMeasure_sub_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.VectorMeasure.ennrealToMeasure", "kind": "definition", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.ennrealToMeasure_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.toENNRealVectorMeasure_ennrealToMeasure", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.ennrealToMeasure_toENNRealVectorMeasure", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.equivMeasure", "kind": "definition", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.map", "kind": "definition", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.map_not_measurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.map_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.VectorMeasure.map_id", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.map_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "ext", "rw", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.VectorMeasure.mapRange", "kind": "definition", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.mapRange_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.mapRange_id", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "MeasureTheory.VectorMeasure.mapRange_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.VectorMeasure.mapRange_add", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.VectorMeasure.mapRangeHom", "kind": "definition", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.mapRangeₗ", "kind": "definition", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.restrict", "kind": "definition", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.restrict_not_measurable", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.restrict_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.VectorMeasure.restrict_eq_self", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.VectorMeasure.restrict_empty", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.restrict_univ", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.restrict_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "ext", "rw", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.VectorMeasure.map_add", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "ext", "simp", "simp"], "tactic_count": 4}
{"name": "MeasureTheory.VectorMeasure.mapGm", "kind": "definition", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.restrict_add", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "ext", "simp", "simp"], "tactic_count": 4}
{"name": "MeasureTheory.VectorMeasure.restrictGm", "kind": "definition", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.restrict_add_restrict_compl", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["ext", "rw", "simp", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.VectorMeasure.restrict_neg", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "ext", "simp"], "tactic_count": 3}
{"name": "MeasureTheory.VectorMeasure.restrict_sub", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.VectorMeasure.map_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "ext", "simp", "simp", "ext", "simp"], "tactic_count": 6}
{"name": "MeasureTheory.VectorMeasure.restrict_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "ext", "simp", "simp", "ext", "simp"], "tactic_count": 6}
{"name": "MeasureTheory.VectorMeasure.mapₗ", "kind": "definition", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.restrictₗ", "kind": "definition", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.instPartialOrder", "kind": "instance", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.le_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.le_iff'", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["refine", "by_cases", "exact", "rw"], "tactic_count": 4}
{"name": "MeasureTheory.term_≤[_]_", "kind": "definition", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory._aux_Mathlib_MeasureTheory_VectorMeasure_Basic___macroRules_MeasureTheory_term_≤[_]__1", "kind": "definition", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory._aux_Mathlib_MeasureTheory_VectorMeasure_Basic___delab_app_MeasureTheory_term_≤[_]__1", "kind": "definition", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.restrict_le_restrict_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.subset_le_of_restrict_le_restrict", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "rw"], "tactic_count": 3}
{"name": "MeasureTheory.VectorMeasure.restrict_le_restrict_of_subset_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "rw"], "tactic_count": 3}
{"name": "MeasureTheory.VectorMeasure.restrict_le_restrict_subset", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.le_restrict_empty", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.VectorMeasure.le_restrict_univ_iff_le", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.VectorMeasure.neg_le_neg", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["intro", "rw", "refine", "rw", "exact"], "tactic_count": 5}
{"name": "MeasureTheory.VectorMeasure.neg_le_neg_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.restrict_le_restrict_iUnion", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["refine", "have", "have", "rw", "refine", "exact", "exact", "refine", "exact", "exact", "refine", "exact", "exact", "intro", "exact", "exact"], "tactic_count": 16}
{"name": "MeasureTheory.VectorMeasure.restrict_le_restrict_countable_iUnion", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["cases", "rw", "refine", "intro", "measurability", "intro", "rcases", "simp", "simp"], "tactic_count": 9}
{"name": "MeasureTheory.VectorMeasure.restrict_le_restrict_union", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "measurability", "rintro"], "tactic_count": 4}
{"name": "MeasureTheory.VectorMeasure.nonneg_of_zero_le_restrict", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "rw"], "tactic_count": 3}
{"name": "MeasureTheory.VectorMeasure.nonpos_of_restrict_le_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "rw"], "tactic_count": 3}
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{"name": "MeasureTheory.VectorMeasure.zero_le_restrict_subset", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasureTheory.VectorMeasure.AbsolutelyContinuous.add", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["intro", "rw"], "tactic_count": 2}
{"name": "MeasureTheory.VectorMeasure.AbsolutelyContinuous.sub", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["intro", "rw"], "tactic_count": 2}
{"name": "MeasureTheory.VectorMeasure.AbsolutelyContinuous.smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["intro", "rw"], "tactic_count": 2}
{"name": "MeasureTheory.VectorMeasure.AbsolutelyContinuous.map", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "refine", "rw", "exact", "intro", "rw"], "tactic_count": 6}
{"name": "MeasureTheory.VectorMeasure.AbsolutelyContinuous.ennrealToMeasure", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["constructor", "refine", "rw", "intro", "by_cases", "rw", "exact", "exact"], "tactic_count": 8}
{"name": "MeasureTheory.VectorMeasure.MutuallySingular", "kind": "definition", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.term_⟂ᵥ_", "kind": "definition", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasureTheory._aux_Mathlib_MeasureTheory_VectorMeasure_Basic___unexpand_MeasureTheory_VectorMeasure_MutuallySingular_1", "kind": "definition", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.MutuallySingular.mk", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["refine", "exact", "exact", "exact", "exact"], "tactic_count": 5}
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{"name": "MeasureTheory.VectorMeasure.MutuallySingular.zero_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.MutuallySingular.zero_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasureTheory.VectorMeasure.MutuallySingular.smul_right", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.MutuallySingular.smul_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.MutuallySingular.neg_left", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["obtain", "refine", "rw", "exact"], "tactic_count": 4}
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{"name": "MeasureTheory.VectorMeasure.MutuallySingular.neg_left_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.MutuallySingular.neg_right_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.trim", "kind": "definition", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.trim_eq_self", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.VectorMeasure.zero_trim", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.VectorMeasure.trim_measurableSet_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.VectorMeasure.restrict_trim", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["ext", "rw", "all_goals"], "tactic_count": 3}
{"name": "MeasureTheory.SignedMeasure.toMeasureOfZeroLE'", "kind": "definition", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasureTheory.SignedMeasure.toMeasureOfZeroLE_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MeasureTheory.SignedMeasure.toMeasureOfZeroLE_real_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.SignedMeasure.toMeasureOfLEZero", "kind": "definition", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SignedMeasure.toMeasureOfLEZero_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.SignedMeasure.toMeasureOfLEZero_real_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "MeasureTheory.SignedMeasure.toMeasureOfZeroLE_toSignedMeasure", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.SignedMeasure.toMeasureOfLEZero_toSignedMeasure", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.zero_le_toSignedMeasure", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.toSignedMeasure_toMeasureOfZeroLE", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Basic", "is_tactic_proof": true, "tactics": ["refine", "lift", "rw", "congr", "simp"], "tactic_count": 5}
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{"name": "_private.Mathlib.MeasureTheory.VectorMeasure.Decomposition.Hahn.0.MeasureTheory.SignedMeasure.someExistsOneDivLT", "kind": "definition", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Hahn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.MeasureTheory.VectorMeasure.Decomposition.Hahn.0.MeasureTheory.SignedMeasure.someExistsOneDivLT_spec", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Hahn", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "_private.Mathlib.MeasureTheory.VectorMeasure.Decomposition.Hahn.0.MeasureTheory.SignedMeasure.someExistsOneDivLT_subset", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Hahn", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "let", "h", "rw", "exact"], "tactic_count": 6}
{"name": "_private.Mathlib.MeasureTheory.VectorMeasure.Decomposition.Hahn.0.MeasureTheory.SignedMeasure.someExistsOneDivLT_subset'", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Hahn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.MeasureTheory.VectorMeasure.Decomposition.Hahn.0.MeasureTheory.SignedMeasure.someExistsOneDivLT_measurableSet", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Hahn", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "let", "h", "rw", "exact"], "tactic_count": 6}
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{"name": "_private.Mathlib.MeasureTheory.VectorMeasure.Decomposition.Hahn.0.MeasureTheory.SignedMeasure.restrictNonposSeq_succ", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Hahn", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "MeasureTheory.SignedMeasure.measureOfNegatives", "kind": "definition", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Hahn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SignedMeasure.zero_mem_measureOfNegatives", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Hahn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasureTheory.SignedMeasure.exists_isCompl_positive_negative", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Hahn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasureTheory.JordanDecomposition.instInhabited", "kind": "instance", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Jordan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.JordanDecomposition.instInvolutiveNeg", "kind": "instance", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Jordan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.JordanDecomposition.instSMul", "kind": "instance", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Jordan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.JordanDecomposition.instSMulReal", "kind": "instance", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Jordan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.JordanDecomposition.zero_posPart", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Jordan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.JordanDecomposition.zero_negPart", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Jordan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.JordanDecomposition.neg_posPart", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Jordan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.JordanDecomposition.neg_negPart", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Jordan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.JordanDecomposition.smul_posPart", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Jordan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.JordanDecomposition.smul_negPart", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Jordan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.JordanDecomposition.real_smul_def", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Jordan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.JordanDecomposition.coe_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Jordan", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.JordanDecomposition.real_smul_nonneg", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Jordan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.JordanDecomposition.real_smul_neg", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Jordan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.JordanDecomposition.real_smul_posPart_nonneg", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Jordan", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.JordanDecomposition.real_smul_negPart_nonneg", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Jordan", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.JordanDecomposition.real_smul_posPart_neg", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Jordan", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.JordanDecomposition.real_smul_negPart_neg", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Jordan", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.JordanDecomposition.toSignedMeasure", "kind": "definition", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Jordan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.JordanDecomposition.toSignedMeasure_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Jordan", "is_tactic_proof": true, "tactics": ["ext1", "rw"], "tactic_count": 2}
{"name": "MeasureTheory.JordanDecomposition.toSignedMeasure_neg", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Jordan", "is_tactic_proof": true, "tactics": ["ext1", "rw", "neg_posPart,"], "tactic_count": 3}
{"name": "MeasureTheory.JordanDecomposition.toSignedMeasure_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Jordan", "is_tactic_proof": true, "tactics": ["ext1", "rw", "toSignedMeasure_sub_apply", "measureReal_nnreal_smul_apply]", "rfl"], "tactic_count": 5}
{"name": "MeasureTheory.JordanDecomposition.exists_compl_positive_negative", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Jordan", "is_tactic_proof": true, "tactics": ["obtain", "refine", "refine", "rw", "show", "zero_apply,", "exact", "refine", "rw", "show", "exact"], "tactic_count": 11}
{"name": "MeasureTheory.SignedMeasure.toJordanDecomposition", "kind": "definition", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Jordan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SignedMeasure.toJordanDecomposition_spec", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Jordan", "is_tactic_proof": true, "tactics": ["set", "obtain", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.SignedMeasure.toSignedMeasure_toJordanDecomposition", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Jordan", "is_tactic_proof": true, "tactics": ["obtain", "simp", "ext", "rw", "toMeasureOfLEZero_real_apply", "simp", "rw", "exact"], "tactic_count": 8}
{"name": "MeasureTheory.SignedMeasure.subset_positive_null_set", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Jordan", "is_tactic_proof": false, "tactics": ["have", "rw", "have", "have", "nonneg_of_zero_le_restrict", "linarith"], "tactic_count": 6}
{"name": "MeasureTheory.SignedMeasure.subset_negative_null_set", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Jordan", "is_tactic_proof": true, "tactics": ["rw", "have", "simp", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.SignedMeasure.of_diff_eq_zero_of_symmDiff_eq_zero_positive", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Jordan", "is_tactic_proof": true, "tactics": ["rw", "on_goal", "have", "have", "rw", "of_union", "rw", "constructor", "linarith", "linarith", "assumption", "assumption"], "tactic_count": 12}
{"name": "MeasureTheory.SignedMeasure.of_diff_eq_zero_of_symmDiff_eq_zero_negative", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Jordan", "is_tactic_proof": true, "tactics": ["rw", "rw", "have", "simp", "exact"], "tactic_count": 5}
{"name": "MeasureTheory.SignedMeasure.of_inter_eq_of_symmDiff_eq_zero_positive", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Jordan", "is_tactic_proof": false, "tactics": ["have", "refine", "subset_positive_null_set", "rw", "exact", "obtain", "of_diff_eq_zero_of_symmDiff_eq_zero_positive", "rw"], "tactic_count": 8}
{"name": "MeasureTheory.SignedMeasure.of_inter_eq_of_symmDiff_eq_zero_negative", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Jordan", "is_tactic_proof": true, "tactics": ["rw", "rw", "have", "simp", "exact"], "tactic_count": 5}
{"name": "_private.Mathlib.MeasureTheory.VectorMeasure.Decomposition.Jordan.0.MeasureTheory.JordanDecomposition.eq_of_posPart_eq_posPart", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Jordan", "is_tactic_proof": true, "tactics": ["ext1", "exact", "rw", "unfold", "simp_rw", "exact"], "tactic_count": 6}
{"name": "MeasureTheory.JordanDecomposition.toSignedMeasure_injective", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Jordan", "is_tactic_proof": true, "tactics": ["the", "show", "intro", "obtain", "obtain", "rw", "obtain", "of_symmDiff_compl_positive_negative", "refine", "ext1", "have", "rw", "show", "conv_lhs", "rw", "show", "refine", "exact", "have", "rw", "show", "conv_lhs", "rw", "show", "exact", "exact", "rw", "exact"], "tactic_count": 28}
{"name": "MeasureTheory.JordanDecomposition.toJordanDecomposition_toSignedMeasure", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Jordan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SignedMeasure.toJordanDecompositionEquiv", "kind": "definition", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Jordan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SignedMeasure.toJordanDecomposition_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Jordan", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.SignedMeasure.toJordanDecomposition_neg", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Jordan", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.SignedMeasure.toJordanDecomposition_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Jordan", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "_private.Mathlib.MeasureTheory.VectorMeasure.Decomposition.Jordan.0.MeasureTheory.SignedMeasure.toJordanDecomposition_smul_real_nonneg", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Jordan", "is_tactic_proof": true, "tactics": ["lift", "rw", "rfl"], "tactic_count": 3}
{"name": "MeasureTheory.SignedMeasure.toJordanDecomposition_smul_real", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Jordan", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "ext1", "rw", "neg_posPart,", "all_goals", "rw", "neg_negPart,", "all_goals"], "tactic_count": 9}
{"name": "MeasureTheory.SignedMeasure.toJordanDecomposition_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Jordan", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.SignedMeasure.totalVariation", "kind": "definition", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Jordan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SignedMeasure.totalVariation_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Jordan", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.SignedMeasure.totalVariation_neg", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Jordan", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.SignedMeasure.null_of_totalVariation_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Jordan", "is_tactic_proof": true, "tactics": ["rw", "rw", "by_cases", "simp", "simp"], "tactic_count": 5}
{"name": "MeasureTheory.SignedMeasure.absolutelyContinuous_ennreal_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Jordan", "is_tactic_proof": true, "tactics": ["constructor", "refine", "obtain", "rw", "toMeasureOfLEZero_apply", "rw", "simp", "refine", "rw", "exact"], "tactic_count": 10}
{"name": "MeasureTheory.SignedMeasure.totalVariation_absolutelyContinuous_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Jordan", "is_tactic_proof": true, "tactics": ["constructor", "constructor", "all_goals", "refine", "have", "rw", "exacts", "refine", "rw"], "tactic_count": 9}
{"name": "MeasureTheory.SignedMeasure.mutuallySingular_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Jordan", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "obtain", "obtain", "refine", "rw", "toMeasureOfLEZero_apply", "simp", "rw", "toMeasureOfLEZero_apply", "simp", "rintro", "exact", "null_of_totalVariation_zero"], "tactic_count": 14}
{"name": "MeasureTheory.SignedMeasure.mutuallySingular_ennreal_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Jordan", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "obtain", "refine", "rw", "toMeasureOfLEZero_apply", "simp", "rw", "exact", "rintro", "refine", "rw", "exact"], "tactic_count": 13}
{"name": "MeasureTheory.SignedMeasure.totalVariation_mutuallySingular_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Jordan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.sub_apply_eq_zero_of_isHahnDecomposition", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.JordanSub", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.mutually_singular_measure_sub", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.JordanSub", "is_tactic_proof": true, "tactics": ["obtain", "exact", "sub_apply_eq_zero_of_isHahnDecomposition"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.toSignedMeasure_restrict_sub", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.JordanSub", "is_tactic_proof": true, "tactics": ["have", "rw", "simp", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.Measure.sub_toSignedMeasure_eq_toSignedMeasure_sub", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.JordanSub", "is_tactic_proof": true, "tactics": ["obtain", "have", "have", "have", "have", "have", "have", "have", "rw", "toSignedMeasure_restrict_eq_restrict_toSignedMeasure", "rw", "rw", "simp", "rw", "repeat", "abel"], "tactic_count": 16}
{"name": "MeasureTheory.Measure.jordanDecompositionOfToSignedMeasureSub", "kind": "definition", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.JordanSub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.jordanDecompositionOfToSignedMeasureSub_posPart", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.JordanSub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.jordanDecompositionOfToSignedMeasureSub_negPart", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.JordanSub", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.jordanDecompositionOfToSignedMeasureSub_toSignedMeasure", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.JordanSub", "is_tactic_proof": true, "tactics": ["simp_rw", "jordanDecompositionOfToSignedMeasureSub_negPart,"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.toJordanDecomposition_toSignedMeasure_sub", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.JordanSub", "is_tactic_proof": true, "tactics": ["apply", "rw"], "tactic_count": 2}
{"name": "MeasureTheory.SignedMeasure.not_haveLebesgueDecomposition_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Lebesgue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SignedMeasure.haveLebesgueDecomposition_of_sigmaFinite", "kind": "instance", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Lebesgue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SignedMeasure.haveLebesgueDecomposition_neg", "kind": "instance", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Lebesgue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SignedMeasure.haveLebesgueDecomposition_smul", "kind": "instance", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Lebesgue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SignedMeasure.haveLebesgueDecomposition_smul_real", "kind": "instance", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Lebesgue", "is_tactic_proof": true, "tactics": ["by_cases", "lift", "exact", "refine", "rw", "infer_instance", "negPart", "rw", "infer_instance"], "tactic_count": 9}
{"name": "MeasureTheory.SignedMeasure.singularPart", "kind": "definition", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Lebesgue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SignedMeasure.singularPart_mutuallySingular", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Lebesgue", "is_tactic_proof": true, "tactics": ["by_cases", "obtain", "rw", "rw", "rw", "exact", "rw", "rcases", "rw", "exact", "rw", "exact"], "tactic_count": 12}
{"name": "MeasureTheory.SignedMeasure.singularPart_totalVariation", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Lebesgue", "is_tactic_proof": false, "tactics": ["have", "singularPart_mutuallySingular", "refine", "rw", "rw"], "tactic_count": 5}
{"name": "MeasureTheory.SignedMeasure.mutuallySingular_singularPart", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Lebesgue", "is_tactic_proof": false, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.SignedMeasure.rnDeriv", "kind": "definition", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Lebesgue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SignedMeasure.rnDeriv_def", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Lebesgue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.SignedMeasure.measurable_rnDeriv", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Lebesgue", "is_tactic_proof": true, "tactics": ["rw", "fun_prop"], "tactic_count": 2}
{"name": "MeasureTheory.SignedMeasure.integrable_rnDeriv", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Lebesgue", "is_tactic_proof": true, "tactics": ["refine", "constructor", "apply", "fun_prop", "exact"], "tactic_count": 5}
{"name": "MeasureTheory.SignedMeasure.singularPart_add_withDensity_rnDeriv_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Lebesgue", "is_tactic_proof": true, "tactics": ["conv_rhs", "rw", "withDensityᵥ_sub", "withDensityᵥ_toReal,", "add_comm", "add_assoc", "add_assoc,", "convert", "exact", "rw", "exact", "all_goals", "first", "exact", "measurability"], "tactic_count": 15}
{"name": "MeasureTheory.SignedMeasure.jordanDecomposition_add_withDensity_mutuallySingular", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Lebesgue", "is_tactic_proof": false, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.SignedMeasure.toJordanDecomposition_eq_of_eq_add_withDensity", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Lebesgue", "is_tactic_proof": true, "tactics": ["haveI", "haveI", "refine", "simp_rw", "ext", "rw", "measureReal_add_apply,", "toSignedMeasure_apply_measurable", "toSignedMeasure_toJordanDecomposition,", "toSignedMeasure_apply_measurable"], "tactic_count": 10}
{"name": "_private.Mathlib.MeasureTheory.VectorMeasure.Decomposition.Lebesgue.0.MeasureTheory.SignedMeasure.haveLebesgueDecomposition_mk'", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Lebesgue", "is_tactic_proof": true, "tactics": ["have", "rw", "change", "rw", "refine", "use", "refine", "rw", "negPart", "use", "refine", "rw"], "tactic_count": 12}
{"name": "MeasureTheory.SignedMeasure.haveLebesgueDecomposition_mk", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Lebesgue", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "rw", "refine", "rwa"], "tactic_count": 5}
{"name": "_private.Mathlib.MeasureTheory.VectorMeasure.Decomposition.Lebesgue.0.MeasureTheory.SignedMeasure.eq_singularPart'", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Lebesgue", "is_tactic_proof": true, "tactics": ["have", "rw", "rw", "congr", "have", "refine", "rw", "have", "refine", "rw"], "tactic_count": 10}
{"name": "MeasureTheory.SignedMeasure.eq_singularPart", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Lebesgue", "is_tactic_proof": true, "tactics": ["by_cases", "refine", "convert", "exact", "rw", "refine", "rwa"], "tactic_count": 7}
{"name": "MeasureTheory.SignedMeasure.singularPart_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Lebesgue", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "MeasureTheory.SignedMeasure.singularPart_neg", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Lebesgue", "is_tactic_proof": false, "tactics": ["have", "refine", "rw", "have", "refine", "rw", "rw"], "tactic_count": 7}
{"name": "MeasureTheory.SignedMeasure.singularPart_smul_nnreal", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Lebesgue", "is_tactic_proof": true, "tactics": ["rw", "conv_lhs", "congr", "congr", "rw", "congr", "rw"], "tactic_count": 7}
{"name": "MeasureTheory.SignedMeasure.singularPart_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Lebesgue", "is_tactic_proof": true, "tactics": ["cases", "inl", "lift", "exact", "inr", "rw", "conv_lhs", "congr", "congr", "rw", "congr", "rw", "rw"], "tactic_count": 13}
{"name": "MeasureTheory.SignedMeasure.singularPart_add", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Lebesgue", "is_tactic_proof": false, "tactics": ["refine", "rw", "add_assoc,", "singularPart_add_withDensity_rnDeriv_eq]"], "tactic_count": 4}
{"name": "MeasureTheory.SignedMeasure.singularPart_sub", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Lebesgue", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.SignedMeasure.eq_rnDeriv", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Lebesgue", "is_tactic_proof": true, "tactics": ["set", "have", "convert", "exact", "have", "refine", "rw"], "tactic_count": 7}
{"name": "MeasureTheory.SignedMeasure.rnDeriv_neg", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Lebesgue", "is_tactic_proof": true, "tactics": ["refine", "rw", "singularPart_neg,"], "tactic_count": 3}
{"name": "MeasureTheory.SignedMeasure.rnDeriv_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Lebesgue", "is_tactic_proof": true, "tactics": ["refine", "rw", "singularPart_add_withDensity_rnDeriv_eq,"], "tactic_count": 3}
{"name": "MeasureTheory.SignedMeasure.rnDeriv_add", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Lebesgue", "is_tactic_proof": false, "tactics": ["refine", "rw", "withDensityᵥ_add", "add_comm", "add_assoc,"], "tactic_count": 5}
{"name": "MeasureTheory.SignedMeasure.rnDeriv_sub", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Lebesgue", "is_tactic_proof": true, "tactics": ["rw", "rw", "grw"], "tactic_count": 3}
{"name": "MeasureTheory.ComplexMeasure.singularPart", "kind": "definition", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Lebesgue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.ComplexMeasure.rnDeriv", "kind": "definition", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Lebesgue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.ComplexMeasure.integrable_rnDeriv", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Lebesgue", "is_tactic_proof": true, "tactics": ["rw", "exact", "memLp_one_iff_integrable.2"], "tactic_count": 3}
{"name": "MeasureTheory.ComplexMeasure.singularPart_add_withDensity_rnDeriv_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.Lebesgue", "is_tactic_proof": true, "tactics": ["conv_rhs", "ext", "rw", "apply", "rw", "integral_re", "change", "rw", "exact", "rw", "integral_im", "change", "rw", "exact"], "tactic_count": 14}
{"name": "MeasureTheory.SignedMeasure.withDensityᵥ_rnDeriv_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.RadonNikodym", "is_tactic_proof": false, "tactics": ["rw", "totalVariation_absolutelyContinuous_iff]", "ext1", "rw", "setIntegral_toReal_rnDeriv", "conv_rhs", "erw", "rw", "all_goals", "refine", "refine", "apply", "exact", "exact"], "tactic_count": 14}
{"name": "MeasureTheory.SignedMeasure.absolutelyContinuous_iff_withDensityᵥ_rnDeriv_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.RadonNikodym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.withDensityᵥ_rnDeriv_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.Decomposition.RadonNikodym", "is_tactic_proof": true, "tactics": ["rw", "withDensity_rnDeriv_eq"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.withDensityᵥ", "kind": "definition", "module": "Mathlib.MeasureTheory.VectorMeasure.WithDensity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.withDensityᵥ_apply", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.WithDensity", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.withDensityᵥ_zero", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.WithDensity", "is_tactic_proof": true, "tactics": ["ext1", "rw", "simp"], "tactic_count": 3}
{"name": "MeasureTheory.withDensityᵥ_neg", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.WithDensity", "is_tactic_proof": true, "tactics": ["by_cases", "ext1", "rw", "simp", "rw", "rwa"], "tactic_count": 6}
{"name": "MeasureTheory.withDensityᵥ_neg'", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.WithDensity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.withDensityᵥ_add", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.WithDensity", "is_tactic_proof": true, "tactics": ["ext1", "rw", "simp_rw", "rw", "exact", "exact"], "tactic_count": 6}
{"name": "MeasureTheory.withDensityᵥ_add'", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.WithDensity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.withDensityᵥ_sub", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.WithDensity", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.withDensityᵥ_sub'", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.WithDensity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.withDensityᵥ_smul", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.WithDensity", "is_tactic_proof": true, "tactics": ["by_cases", "ext1", "rw", "simp", "by_cases", "rw", "rw", "rwa"], "tactic_count": 8}
{"name": "MeasureTheory.withDensityᵥ_smul'", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.WithDensity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.withDensityᵥ_smul_eq_withDensityᵥ_withDensity", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.WithDensity", "is_tactic_proof": true, "tactics": ["ext", "rw", "setIntegral_withDensity_eq_setIntegral_smul₀", "simp"], "tactic_count": 4}
{"name": "MeasureTheory.withDensityᵥ_smul_eq_withDensityᵥ_withDensity'", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.WithDensity", "is_tactic_proof": false, "tactics": ["rw", "withDensityᵥ_smul_eq_withDensityᵥ_withDensity", "apply", "ext", "simp"], "tactic_count": 5}
{"name": "MeasureTheory.Measure.withDensityᵥ_absolutelyContinuous", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.WithDensity", "is_tactic_proof": true, "tactics": ["by_cases", "refine", "rw", "rw", "rw", "exact"], "tactic_count": 6}
{"name": "MeasureTheory.Integrable.ae_eq_of_withDensityᵥ_eq", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.WithDensity", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "MeasureTheory.WithDensityᵥEq.congr_ae", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.WithDensity", "is_tactic_proof": true, "tactics": ["by_cases", "ext", "rw", "exact", "have", "rw"], "tactic_count": 6}
{"name": "MeasureTheory.Integrable.withDensityᵥ_eq_iff", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.WithDensity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.withDensityᵥ_toReal", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.WithDensity", "is_tactic_proof": true, "tactics": ["have", "haveI", "ext", "rw", "integral_toReal", "refine", "conv_rhs", "exact"], "tactic_count": 8}
{"name": "MeasureTheory.withDensityᵥ_eq_withDensity_pos_part_sub_withDensity_neg_part", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.WithDensity", "is_tactic_proof": true, "tactics": ["haveI", "haveI", "ext", "rw", "measureReal_def,"], "tactic_count": 5}
{"name": "MeasureTheory.Integrable.withDensityᵥ_trim_eq_integral", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.WithDensity", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Integrable.withDensityᵥ_trim_absolutelyContinuous", "kind": "theorem", "module": "Mathlib.MeasureTheory.VectorMeasure.WithDensity", "is_tactic_proof": true, "tactics": ["refine", "rw", "rw", "simp"], "tactic_count": 4}
{"name": "FirstOrder.Field.FieldAxiom", "kind": "inductive", "module": "Mathlib.ModelTheory.Algebra.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Field.FieldAxiom.toSentence", "kind": "definition", "module": "Mathlib.ModelTheory.Algebra.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Field.FieldAxiom.toProp", "kind": "definition", "module": "Mathlib.ModelTheory.Algebra.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Theory.field", "kind": "definition", "module": "Mathlib.ModelTheory.Algebra.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Field.FieldAxiom.realize_toSentence_iff_toProp", "kind": "theorem", "module": "Mathlib.ModelTheory.Algebra.Field.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "FirstOrder.Field.FieldAxiom.toProp_of_model", "kind": "theorem", "module": "Mathlib.ModelTheory.Algebra.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Field.fieldOfModelField", "kind": "abbrev", "module": "Mathlib.ModelTheory.Algebra.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Field.compatibleRingOfModelField", "kind": "abbrev", "module": "Mathlib.ModelTheory.Algebra.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Field.instModelField", "kind": "instance", "module": "Mathlib.ModelTheory.Algebra.Field.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Field.eqZero", "kind": "definition", "module": "Mathlib.ModelTheory.Algebra.Field.CharP", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Field.realize_eqZero", "kind": "theorem", "module": "Mathlib.ModelTheory.Algebra.Field.CharP", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FirstOrder.Language.Theory.fieldOfChar", "kind": "definition", "module": "Mathlib.ModelTheory.Algebra.Field.CharP", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Field.model_hasChar_of_charP", "kind": "instance", "module": "Mathlib.ModelTheory.Algebra.Field.CharP", "is_tactic_proof": true, "tactics": ["refine", "cases", "inl", "inr", "subst", "simp", "and_imp,", "exact"], "tactic_count": 8}
{"name": "FirstOrder.Field.charP_iff_model_fieldOfChar", "kind": "theorem", "module": "Mathlib.ModelTheory.Algebra.Field.CharP", "is_tactic_proof": false, "tactics": ["simp", "split_ifs", "subst", "simp", "forall_apply_eq_imp_iff₂,", "exact", "simp", "simp", "intro", "cases"], "tactic_count": 10}
{"name": "FirstOrder.Field.model_fieldOfChar_of_charP", "kind": "instance", "module": "Mathlib.ModelTheory.Algebra.Field.CharP", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Field.charP_of_model_fieldOfChar", "kind": "theorem", "module": "Mathlib.ModelTheory.Algebra.Field.CharP", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Field.genericMonicPoly", "kind": "definition", "module": "Mathlib.ModelTheory.Algebra.Field.IsAlgClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Field.lift_genericMonicPoly", "kind": "theorem", "module": "Mathlib.ModelTheory.Algebra.Field.IsAlgClosed", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FirstOrder.Field.genericMonicPolyHasRoot", "kind": "definition", "module": "Mathlib.ModelTheory.Algebra.Field.IsAlgClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Field.realize_genericMonicPolyHasRoot", "kind": "theorem", "module": "Mathlib.ModelTheory.Algebra.Field.IsAlgClosed", "is_tactic_proof": true, "tactics": ["let", "rw", "simp"], "tactic_count": 3}
{"name": "FirstOrder.Language.Theory.ACF", "kind": "definition", "module": "Mathlib.ModelTheory.Algebra.Field.IsAlgClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Field.instModelFieldOfCharOfACF", "kind": "instance", "module": "Mathlib.ModelTheory.Algebra.Field.IsAlgClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Field.instModelACFOfCharPOfIsAlgClosed", "kind": "instance", "module": "Mathlib.ModelTheory.Algebra.Field.IsAlgClosed", "is_tactic_proof": true, "tactics": ["refine", "simp", "rintro", "simp", "rintro", "exact"], "tactic_count": 6}
{"name": "FirstOrder.Field.modelField_of_modelACF", "kind": "theorem", "module": "Mathlib.ModelTheory.Algebra.Field.IsAlgClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Field.fieldOfModelACF", "kind": "definition", "module": "Mathlib.ModelTheory.Algebra.Field.IsAlgClosed", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "FirstOrder.Field.isAlgClosed_of_model_ACF", "kind": "theorem", "module": "Mathlib.ModelTheory.Algebra.Field.IsAlgClosed", "is_tactic_proof": true, "tactics": ["refine", "intro", "have", "simp", "have", "rw", "exact"], "tactic_count": 7}
{"name": "FirstOrder.Field.ACF_isSatisfiable", "kind": "theorem", "module": "Mathlib.ModelTheory.Algebra.Field.IsAlgClosed", "is_tactic_proof": true, "tactics": ["cases", "inl", "have", "let", "exact", "inr", "subst", "let", "exact"], "tactic_count": 9}
{"name": "FirstOrder.Field.ACF_categorical", "kind": "theorem", "module": "Mathlib.ModelTheory.Algebra.Field.IsAlgClosed", "is_tactic_proof": true, "tactics": ["rintro", "let", "have", "let", "have", "have", "let", "have", "let", "have", "have", "constructor", "refine", "apply", "refine", "rw", "rw"], "tactic_count": 17}
{"name": "FirstOrder.Field.ACF_isComplete", "kind": "theorem", "module": "Mathlib.ModelTheory.Algebra.Field.IsAlgClosed", "is_tactic_proof": false, "tactics": ["apply", "simp", "exact", "exact", "rintro", "let", "have", "let", "have", "infer_instance"], "tactic_count": 10}
{"name": "FirstOrder.Field.finite_ACF_prime_not_realize_of_ACF_zero_realize", "kind": "theorem", "module": "Mathlib.ModelTheory.Algebra.Field.IsAlgClosed", "is_tactic_proof": true, "tactics": ["rw", "rcases", "have", "intro", "rw", "apply", "rcases", "refine", "intro", "exact", "refine", "rintro", "have", "let", "have", "let", "have", "simp", "intro", "exact", "let", "have", "intro", "simp", "exact", "refine", "intro", "exact"], "tactic_count": 28}
{"name": "FirstOrder.Field.ACF_zero_realize_iff_infinite_ACF_prime_realize", "kind": "theorem", "module": "Mathlib.ModelTheory.Algebra.Field.IsAlgClosed", "is_tactic_proof": false, "tactics": ["refine", "simpa", "finite_ACF_prime_not_realize_of_ACF_zero_realize"], "tactic_count": 3}
{"name": "FirstOrder.Field.ACF_zero_realize_iff_finite_ACF_prime_not_realize", "kind": "theorem", "module": "Mathlib.ModelTheory.Algebra.Field.IsAlgClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.ringFunc", "kind": "inductive", "module": "Mathlib.ModelTheory.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.instDecidableEqRingFunc", "kind": "instance", "module": "Mathlib.ModelTheory.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.ring", "kind": "definition", "module": "Mathlib.ModelTheory.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Ring._example", "kind": "example", "module": "Mathlib.ModelTheory.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Ring._example", "kind": "example", "module": "Mathlib.ModelTheory.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Ring.addFunc", "kind": "abbrev", "module": "Mathlib.ModelTheory.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Ring.mulFunc", "kind": "abbrev", "module": "Mathlib.ModelTheory.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Ring.negFunc", "kind": "abbrev", "module": "Mathlib.ModelTheory.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Ring.zeroFunc", "kind": "abbrev", "module": "Mathlib.ModelTheory.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Ring.oneFunc", "kind": "abbrev", "module": "Mathlib.ModelTheory.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Ring.instZeroTermRing", "kind": "instance", "module": "Mathlib.ModelTheory.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Ring.zero_def", "kind": "theorem", "module": "Mathlib.ModelTheory.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Ring.instOneTermRing", "kind": "instance", "module": "Mathlib.ModelTheory.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Ring.one_def", "kind": "theorem", "module": "Mathlib.ModelTheory.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Ring.instAddTermRing", "kind": "instance", "module": "Mathlib.ModelTheory.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Ring.add_def", "kind": "theorem", "module": "Mathlib.ModelTheory.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Ring.instMulTermRing", "kind": "instance", "module": "Mathlib.ModelTheory.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Ring.mul_def", "kind": "theorem", "module": "Mathlib.ModelTheory.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Ring.instNegTermRing", "kind": "instance", "module": "Mathlib.ModelTheory.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Ring.neg_def", "kind": "theorem", "module": "Mathlib.ModelTheory.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Ring.instFintypeSymbolsRing", "kind": "instance", "module": "Mathlib.ModelTheory.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Ring.card_ring", "kind": "theorem", "module": "Mathlib.ModelTheory.Algebra.Ring.Basic", "is_tactic_proof": true, "tactics": ["have", "simp"], "tactic_count": 2}
{"name": "FirstOrder.Ring.realize_add", "kind": "theorem", "module": "Mathlib.ModelTheory.Algebra.Ring.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FirstOrder.Ring.realize_mul", "kind": "theorem", "module": "Mathlib.ModelTheory.Algebra.Ring.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FirstOrder.Ring.realize_neg", "kind": "theorem", "module": "Mathlib.ModelTheory.Algebra.Ring.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FirstOrder.Ring.realize_zero", "kind": "theorem", "module": "Mathlib.ModelTheory.Algebra.Ring.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FirstOrder.Ring.realize_one", "kind": "theorem", "module": "Mathlib.ModelTheory.Algebra.Ring.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FirstOrder.Ring.compatibleRingOfRing", "kind": "definition", "module": "Mathlib.ModelTheory.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Ring.languageEquivEquivRingEquiv", "kind": "definition", "module": "Mathlib.ModelTheory.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Ring.addOfRingStructure", "kind": "abbrev", "module": "Mathlib.ModelTheory.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Ring.mulOfRingStructure", "kind": "abbrev", "module": "Mathlib.ModelTheory.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Ring.negOfRingStructure", "kind": "abbrev", "module": "Mathlib.ModelTheory.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Ring.zeroOfRingStructure", "kind": "abbrev", "module": "Mathlib.ModelTheory.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Ring.oneOfRingStructure", "kind": "abbrev", "module": "Mathlib.ModelTheory.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Ring.compatibleRingOfRingStructure", "kind": "abbrev", "module": "Mathlib.ModelTheory.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Ring.mvPolynomial_zeroLocus_definable", "kind": "theorem", "module": "Mathlib.ModelTheory.Algebra.Ring.Definability", "is_tactic_proof": true, "tactics": ["rw", "let", "letI", "letI", "rw", "refine", "simp", "exact", "id))", "simp"], "tactic_count": 10}
{"name": "_private.Mathlib.ModelTheory.Algebra.Ring.FreeCommRing.0.FirstOrder.Ring.exists_term_realize_eq_freeCommRing", "kind": "theorem", "module": "Mathlib.ModelTheory.Algebra.Ring.FreeCommRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Ring.termOfFreeCommRing", "kind": "definition", "module": "Mathlib.ModelTheory.Algebra.Ring.FreeCommRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Ring.realize_termOfFreeCommRing", "kind": "theorem", "module": "Mathlib.ModelTheory.Algebra.Ring.FreeCommRing", "is_tactic_proof": true, "tactics": ["rw", "conv_rhs", "induction", "var", "func"], "tactic_count": 5}
{"name": "FirstOrder.presburgerFunc", "kind": "inductive", "module": "Mathlib.ModelTheory.Arithmetic.Presburger.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.instDecidableEqPresburgerFunc", "kind": "instance", "module": "Mathlib.ModelTheory.Arithmetic.Presburger.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.presburger", "kind": "definition", "module": "Mathlib.ModelTheory.Arithmetic.Presburger.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.presburger.instZeroTerm", "kind": "instance", "module": "Mathlib.ModelTheory.Arithmetic.Presburger.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.presburger.instOneTerm", "kind": "instance", "module": "Mathlib.ModelTheory.Arithmetic.Presburger.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.presburger.instAddTerm", "kind": "instance", "module": "Mathlib.ModelTheory.Arithmetic.Presburger.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.presburger.instNatCastTerm", "kind": "instance", "module": "Mathlib.ModelTheory.Arithmetic.Presburger.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.presburger.natCast_zero", "kind": "theorem", "module": "Mathlib.ModelTheory.Arithmetic.Presburger.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.presburger.natCast_succ", "kind": "theorem", "module": "Mathlib.ModelTheory.Arithmetic.Presburger.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.presburger.instSMulNatTerm", "kind": "instance", "module": "Mathlib.ModelTheory.Arithmetic.Presburger.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.presburger.zero_nsmul", "kind": "theorem", "module": "Mathlib.ModelTheory.Arithmetic.Presburger.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.presburger.succ_nsmul", "kind": "theorem", "module": "Mathlib.ModelTheory.Arithmetic.Presburger.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.presburger.sum", "kind": "definition", "module": "Mathlib.ModelTheory.Arithmetic.Presburger.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.presburger.instStructure", "kind": "instance", "module": "Mathlib.ModelTheory.Arithmetic.Presburger.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.presburger.funMap_zero", "kind": "theorem", "module": "Mathlib.ModelTheory.Arithmetic.Presburger.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.presburger.funMap_one", "kind": "theorem", "module": "Mathlib.ModelTheory.Arithmetic.Presburger.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.presburger.funMap_add", "kind": "theorem", "module": "Mathlib.ModelTheory.Arithmetic.Presburger.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.presburger.realize_zero", "kind": "theorem", "module": "Mathlib.ModelTheory.Arithmetic.Presburger.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.presburger.realize_one", "kind": "theorem", "module": "Mathlib.ModelTheory.Arithmetic.Presburger.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.presburger.realize_add", "kind": "theorem", "module": "Mathlib.ModelTheory.Arithmetic.Presburger.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.presburger.realize_natCast", "kind": "theorem", "module": "Mathlib.ModelTheory.Arithmetic.Presburger.Basic", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "FirstOrder.Language.presburger.realize_nsmul", "kind": "theorem", "module": "Mathlib.ModelTheory.Arithmetic.Presburger.Basic", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "FirstOrder.Language.presburger.realize_sum", "kind": "theorem", "module": "Mathlib.ModelTheory.Arithmetic.Presburger.Basic", "is_tactic_proof": true, "tactics": ["classical", "simp", "conv", "generalize", "induction"], "tactic_count": 5}
{"name": "_private.Mathlib.ModelTheory.Arithmetic.Presburger.Semilinear.Basic.0.IsSlice", "kind": "definition", "module": "Mathlib.ModelTheory.Arithmetic.Presburger.Semilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "isSemilinearSet_setOf_eq", "kind": "theorem", "module": "Mathlib.ModelTheory.Arithmetic.Presburger.Semilinear.Basic", "is_tactic_proof": true, "tactics": ["rcases", "rw", "rw", "apply", "exact"], "tactic_count": 5}
{"name": "Nat.isSemilinearSet_setOf_mulVec_eq", "kind": "theorem", "module": "Mathlib.ModelTheory.Arithmetic.Presburger.Semilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLinearSet_iff_exists_fin_addMonoidHom", "kind": "theorem", "module": "Mathlib.ModelTheory.Arithmetic.Presburger.Semilinear.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "congr", "refine", "rw", "rw"], "tactic_count": 5}
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{"name": "IsSemilinearSet.biInter", "kind": "theorem", "module": "Mathlib.ModelTheory.Arithmetic.Presburger.Semilinear.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply", "simpa"], "tactic_count": 3}
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{"name": "_private.Mathlib.ModelTheory.Arithmetic.Presburger.Semilinear.Basic.0.toRatVec", "kind": "definition", "module": "Mathlib.ModelTheory.Arithmetic.Presburger.Semilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "FirstOrder.Language.Hom.comp_id", "kind": "theorem", "module": "Mathlib.ModelTheory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Hom.id_comp", "kind": "theorem", "module": "Mathlib.ModelTheory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "FirstOrder.Language.Embedding.embeddingLike", "kind": "instance", "module": "Mathlib.ModelTheory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Embedding.strongHomClass", "kind": "instance", "module": "Mathlib.ModelTheory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "FirstOrder.Language.Embedding.coe_toHom", "kind": "theorem", "module": "Mathlib.ModelTheory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "FirstOrder.Language.Embedding.ext", "kind": "theorem", "module": "Mathlib.ModelTheory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "FirstOrder.Language.Embedding.coeFn_ofInjective", "kind": "theorem", "module": "Mathlib.ModelTheory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Embedding.ofInjective_toHom", "kind": "theorem", "module": "Mathlib.ModelTheory.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "FirstOrder.Language.Embedding.refl", "kind": "definition", "module": "Mathlib.ModelTheory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "FirstOrder.Language.Embedding.refl_apply", "kind": "theorem", "module": "Mathlib.ModelTheory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Embedding.comp", "kind": "definition", "module": "Mathlib.ModelTheory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "FirstOrder.Language.Equiv.fg_iff", "kind": "theorem", "module": "Mathlib.ModelTheory.FinitelyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "FirstOrder.Language.age", "kind": "definition", "module": "Mathlib.ModelTheory.Fraisse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Hereditary", "kind": "definition", "module": "Mathlib.ModelTheory.Fraisse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.JointEmbedding", "kind": "definition", "module": "Mathlib.ModelTheory.Fraisse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Amalgamation", "kind": "definition", "module": "Mathlib.ModelTheory.Fraisse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.age.is_equiv_invariant", "kind": "theorem", "module": "Mathlib.ModelTheory.Fraisse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Embedding.age_subset_age", "kind": "theorem", "module": "Mathlib.ModelTheory.Fraisse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "FirstOrder.Language.Structure.FG.mem_age_of_equiv", "kind": "theorem", "module": "Mathlib.ModelTheory.Fraisse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "FirstOrder.Language.age.nonempty", "kind": "theorem", "module": "Mathlib.ModelTheory.Fraisse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.age.hereditary", "kind": "theorem", "module": "Mathlib.ModelTheory.Fraisse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.age.jointEmbedding", "kind": "theorem", "module": "Mathlib.ModelTheory.Fraisse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "FirstOrder.Language.IsUltrahomogeneous", "kind": "definition", "module": "Mathlib.ModelTheory.Fraisse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "FirstOrder.Language.LHom.id", "kind": "definition", "module": "Mathlib.ModelTheory.LanguageMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "FirstOrder.Language.LHom.sumInl", "kind": "definition", "module": "Mathlib.ModelTheory.LanguageMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "FirstOrder.Language.LHom.ofIsEmpty", "kind": "definition", "module": "Mathlib.ModelTheory.LanguageMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "FirstOrder.Language.LHom.sumElim", "kind": "definition", "module": "Mathlib.ModelTheory.LanguageMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "FirstOrder.Language.LHom.funMap_sumInl", "kind": "theorem", "module": "Mathlib.ModelTheory.LanguageMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.LHom.funMap_sumInr", "kind": "theorem", "module": "Mathlib.ModelTheory.LanguageMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.LHom.sumInl_injective", "kind": "theorem", "module": "Mathlib.ModelTheory.LanguageMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.LHom.sumInr_injective", "kind": "theorem", "module": "Mathlib.ModelTheory.LanguageMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.LHom.isExpansionOn_reduct", "kind": "instance", "module": "Mathlib.ModelTheory.LanguageMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "FirstOrder.Language.LEquiv.symm", "kind": "definition", "module": "Mathlib.ModelTheory.LanguageMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "FirstOrder.Language.constantsOnFunc", "kind": "definition", "module": "Mathlib.ModelTheory.LanguageMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "FirstOrder.Language.constantsOn_constants", "kind": "theorem", "module": "Mathlib.ModelTheory.LanguageMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.isAlgebraic_constantsOn", "kind": "instance", "module": "Mathlib.ModelTheory.LanguageMap", "is_tactic_proof": true, "tactics": ["unfold", "infer_instance"], "tactic_count": 2}
{"name": "FirstOrder.Language.isEmpty_functions_constantsOn_succ", "kind": "instance", "module": "Mathlib.ModelTheory.LanguageMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.isRelational_constantsOn", "kind": "instance", "module": "Mathlib.ModelTheory.LanguageMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.card_constantsOn", "kind": "theorem", "module": "Mathlib.ModelTheory.LanguageMap", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FirstOrder.Language.constantsOn.structure", "kind": "definition", "module": "Mathlib.ModelTheory.LanguageMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.LHom.constantsOnMap", "kind": "definition", "module": "Mathlib.ModelTheory.LanguageMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.constantsOnMap_isExpansionOn", "kind": "theorem", "module": "Mathlib.ModelTheory.LanguageMap", "is_tactic_proof": true, "tactics": ["letI", "letI", "exact"], "tactic_count": 3}
{"name": "FirstOrder.Language.withConstants", "kind": "definition", "module": "Mathlib.ModelTheory.LanguageMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.term_[[_]]", "kind": "definition", "module": "Mathlib.ModelTheory.LanguageMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder._aux_Mathlib_ModelTheory_LanguageMap___macroRules_FirstOrder_term_[[_]]_1", "kind": "definition", "module": "Mathlib.ModelTheory.LanguageMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder._aux_Mathlib_ModelTheory_LanguageMap___unexpand_FirstOrder_Language_withConstants_1", "kind": "definition", "module": "Mathlib.ModelTheory.LanguageMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.card_withConstants", "kind": "theorem", "module": "Mathlib.ModelTheory.LanguageMap", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "FirstOrder.Language.lhomWithConstants", "kind": "definition", "module": "Mathlib.ModelTheory.LanguageMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.lhomWithConstants_injective", "kind": "theorem", "module": "Mathlib.ModelTheory.LanguageMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.con", "kind": "definition", "module": "Mathlib.ModelTheory.LanguageMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.LHom.addConstants", "kind": "definition", "module": "Mathlib.ModelTheory.LanguageMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.paramsStructure", "kind": "instance", "module": "Mathlib.ModelTheory.LanguageMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.LEquiv.addEmptyConstants", "kind": "definition", "module": "Mathlib.ModelTheory.LanguageMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.withConstants_funMap_sumInl", "kind": "theorem", "module": "Mathlib.ModelTheory.LanguageMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.withConstants_relMap_sumInl", "kind": "theorem", "module": "Mathlib.ModelTheory.LanguageMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.lhomWithConstantsMap", "kind": "definition", "module": "Mathlib.ModelTheory.LanguageMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.LHom.map_constants_comp_sumInl", "kind": "theorem", "module": "Mathlib.ModelTheory.LanguageMap", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "FirstOrder.Language.constantsOnSelfStructure", "kind": "instance", "module": "Mathlib.ModelTheory.LanguageMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.withConstantsSelfStructure", "kind": "instance", "module": "Mathlib.ModelTheory.LanguageMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.withConstants_self_expansion", "kind": "instance", "module": "Mathlib.ModelTheory.LanguageMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.withConstantsStructure", "kind": "instance", "module": "Mathlib.ModelTheory.LanguageMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.withConstants_expansion", "kind": "instance", "module": "Mathlib.ModelTheory.LanguageMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.addEmptyConstants_is_expansion_on'", "kind": "instance", "module": "Mathlib.ModelTheory.LanguageMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.addEmptyConstants_symm_isExpansionOn", "kind": "instance", "module": "Mathlib.ModelTheory.LanguageMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.addConstants_expansion", "kind": "instance", "module": "Mathlib.ModelTheory.LanguageMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.withConstants_funMap_sumInr", "kind": "theorem", "module": "Mathlib.ModelTheory.LanguageMap", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "FirstOrder.Language.coe_con", "kind": "theorem", "module": "Mathlib.ModelTheory.LanguageMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.constantsOnMap_inclusion_isExpansionOn", "kind": "instance", "module": "Mathlib.ModelTheory.LanguageMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.map_constants_inclusion_isExpansionOn", "kind": "instance", "module": "Mathlib.ModelTheory.LanguageMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.orderRel", "kind": "inductive", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.instDecidableEqOrderRel", "kind": "instance", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.order", "kind": "definition", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.order.forall_relations", "kind": "theorem", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.order.instSubsingleton", "kind": "instance", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.order.instIsEmptyRelationsOfNatNat", "kind": "instance", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.order.instUniqueSigmaNatRelations", "kind": "instance", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.order.instUniqueSymbols", "kind": "instance", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.order.card_eq_one", "kind": "theorem", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FirstOrder.Language.instIsOrderedOrder", "kind": "instance", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.order.relation_eq_leSymb", "kind": "theorem", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Term.le", "kind": "definition", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Term.lt", "kind": "definition", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.orderLHom", "kind": "definition", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.orderLHom_leSymb", "kind": "theorem", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.orderLHom_order", "kind": "theorem", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.preorderTheory", "kind": "definition", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.instIsUniversalPreorderTheory", "kind": "instance", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.partialOrderTheory", "kind": "definition", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.instIsUniversalPartialOrderTheory", "kind": "instance", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.linearOrderTheory", "kind": "definition", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.instIsUniversalLinearOrderTheory", "kind": "instance", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language._example", "kind": "example", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.noTopOrderSentence", "kind": "definition", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.noBotOrderSentence", "kind": "definition", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.denselyOrderedSentence", "kind": "definition", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.dlo", "kind": "definition", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.instModelLinearOrderTheoryOfDlo", "kind": "instance", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.instModelPartialOrderTheoryOfLinearOrderTheory", "kind": "instance", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.instModelPreorderTheoryOfPartialOrderTheory", "kind": "instance", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.sum.instIsOrdered", "kind": "instance", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.orderStructure", "kind": "definition", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.instOrderedStructureOfOrderOfIsExpansionOnOrderLHom", "kind": "instance", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.instIsExpansionOnOrderLHomOfOrderedStructureOrder", "kind": "instance", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.instOrderedStructureSubtypeMemSubstructure", "kind": "instance", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Term.realize_le", "kind": "theorem", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FirstOrder.Language.realize_noTopOrder_iff", "kind": "theorem", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": false, "tactics": ["simp", "refine", "intro", "exact"], "tactic_count": 4}
{"name": "FirstOrder.Language.realize_noBotOrder_iff", "kind": "theorem", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": false, "tactics": ["simp", "refine", "intro", "exact"], "tactic_count": 4}
{"name": "FirstOrder.Language.realize_noTopOrder", "kind": "theorem", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.realize_noBotOrder", "kind": "theorem", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.noTopOrder_of_dlo", "kind": "theorem", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.noBotOrder_of_dlo", "kind": "theorem", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.orderedStructure_iff", "kind": "theorem", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.model_preorder", "kind": "instance", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": false, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "FirstOrder.Language.Term.realize_lt", "kind": "theorem", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FirstOrder.Language.realize_denselyOrdered_iff", "kind": "theorem", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": false, "tactics": ["simp", "refine", "intro", "exact"], "tactic_count": 4}
{"name": "FirstOrder.Language.realize_denselyOrdered", "kind": "theorem", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.denselyOrdered_of_dlo", "kind": "theorem", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.model_partialOrder", "kind": "instance", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": false, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "FirstOrder.Language.model_linearOrder", "kind": "instance", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": false, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "FirstOrder.Language.model_dlo", "kind": "instance", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FirstOrder.Language.leOfStructure", "kind": "definition", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.instOrderedStructure", "kind": "instance", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": true, "tactics": ["letI", "constructor", "simp", "intros", "rfl"], "tactic_count": 5}
{"name": "FirstOrder.Language.decidableLEOfStructure", "kind": "definition", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.preorderOfModels", "kind": "definition", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.partialOrderOfModels", "kind": "definition", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.linearOrderOfModels", "kind": "definition", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.order.instHomClassOfOrderHomClass", "kind": "instance", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.order.instStrongHomClassOrderEmbedding", "kind": "instance", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.order.instStrongHomClassOfOrderIsoClass", "kind": "instance", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.HomClass.monotone", "kind": "theorem", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.HomClass.strictMono", "kind": "theorem", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.StrongHomClass.toOrderIsoClass", "kind": "theorem", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.dlo_isExtensionPair", "kind": "theorem", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": true, "tactics": ["classical", "rw", "intro", "letI", "letI", "have", "have", "have", "have", "have", "have", "obtain", "m", "let", "convert", "simp", "g)", "use", "ext", "refine", "simp"], "tactic_count": 21}
{"name": "FirstOrder.Language.instInfiniteOfModelDloOrderOfNonempty", "kind": "instance", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": true, "tactics": ["letI", "obtain", "exact"], "tactic_count": 3}
{"name": "FirstOrder.Language.dlo_age", "kind": "theorem", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": true, "tactics": ["classical", "rw", "ext", "refine", "letI", "letI", "exact"], "tactic_count": 7}
{"name": "FirstOrder.Language.isFraisseLimit_of_countable_nonempty_dlo", "kind": "theorem", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.isFraisse_finite_linear_order", "kind": "theorem", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": true, "tactics": ["letI", "exact"], "tactic_count": 2}
{"name": "FirstOrder.Language.aleph0_categorical_dlo", "kind": "theorem", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.dlo_isComplete", "kind": "theorem", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order._example", "kind": "example", "module": "Mathlib.ModelTheory.Order", "is_tactic_proof": true, "tactics": ["letI", "letI", "letI", "exact"], "tactic_count": 4}
{"name": "FirstOrder.term_≃ₚ[_]_", "kind": "definition", "module": "Mathlib.ModelTheory.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder._aux_Mathlib_ModelTheory_PartialEquiv___macroRules_FirstOrder_term_≃ₚ[_]__1", "kind": "definition", "module": "Mathlib.ModelTheory.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder._aux_Mathlib_ModelTheory_PartialEquiv___unexpand_FirstOrder_Language_PartialEquiv_1", "kind": "definition", "module": "Mathlib.ModelTheory.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.PartialEquiv.instInhabited_self", "kind": "instance", "module": "Mathlib.ModelTheory.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.PartialEquiv.symm", "kind": "definition", "module": "Mathlib.ModelTheory.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.PartialEquiv.symm_symm", "kind": "theorem", "module": "Mathlib.ModelTheory.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.PartialEquiv.symm_bijective", "kind": "theorem", "module": "Mathlib.ModelTheory.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.PartialEquiv.symm_apply", "kind": "theorem", "module": "Mathlib.ModelTheory.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.PartialEquiv.instLE", "kind": "instance", "module": "Mathlib.ModelTheory.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.PartialEquiv.le_def", "kind": "theorem", "module": "Mathlib.ModelTheory.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.PartialEquiv.dom_le_dom", "kind": "theorem", "module": "Mathlib.ModelTheory.PartialEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.PartialEquiv.cod_le_cod", "kind": "theorem", "module": "Mathlib.ModelTheory.PartialEquiv", "is_tactic_proof": true, "tactics": ["rintro", "let", "have", "simp", "rw", "simp"], "tactic_count": 6}
{"name": "FirstOrder.Language.PartialEquiv.subtype_toEquiv_inclusion", "kind": "theorem", "module": "Mathlib.ModelTheory.PartialEquiv", "is_tactic_proof": true, "tactics": ["let"], "tactic_count": 1}
{"name": "FirstOrder.Language.PartialEquiv.toEquiv_inclusion", "kind": "theorem", "module": "Mathlib.ModelTheory.PartialEquiv", "is_tactic_proof": true, "tactics": ["rw", "ext", "simp"], "tactic_count": 3}
{"name": "FirstOrder.Language.PartialEquiv.toEquiv_inclusion_apply", "kind": "theorem", "module": "Mathlib.ModelTheory.PartialEquiv", "is_tactic_proof": true, "tactics": ["apply", "change", "rw", "simp"], "tactic_count": 4}
{"name": "FirstOrder.Language.PartialEquiv.le_iff", "kind": "theorem", "module": "Mathlib.ModelTheory.PartialEquiv", "is_tactic_proof": true, "tactics": ["constructor", "exact", "rintro", "rw", "exact"], "tactic_count": 5}
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{"name": "FirstOrder.Language.BoundedFormula.realize_iSup", "kind": "theorem", "module": "Mathlib.ModelTheory.Semantics", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FirstOrder.Language.BoundedFormula.realize_iInf", "kind": "theorem", "module": "Mathlib.ModelTheory.Semantics", "is_tactic_proof": true, "tactics": ["simp", "forall_apply_eq_imp_iff]"], "tactic_count": 2}
{"name": "FirstOrder.Language.Formula.realize_iSup", "kind": "theorem", "module": "Mathlib.ModelTheory.Semantics", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FirstOrder.Language.Formula.realize_iInf", "kind": "theorem", "module": "Mathlib.ModelTheory.Semantics", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FirstOrder.Language.Formula.realize_iExsUnique", "kind": "theorem", "module": "Mathlib.ModelTheory.Semantics", "is_tactic_proof": true, "tactics": ["rw", "simp", "simp", "refine", "rw", "cases"], "tactic_count": 6}
{"name": "FirstOrder.Language.BoundedFormula.realize_iExsUnique", "kind": "theorem", "module": "Mathlib.ModelTheory.Semantics", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "FirstOrder.Language.StrongHomClass.realize_boundedFormula", "kind": "theorem", "module": "Mathlib.ModelTheory.Semantics", "is_tactic_proof": true, "tactics": ["induction", "falsum", "equal", "rel", "simp", "exact", "imp", "all", "rw", "constructor", "intro", "have", "rw", "exact", "intro", "have", "rw", "exact"], "tactic_count": 18}
{"name": "FirstOrder.Language.StrongHomClass.realize_formula", "kind": "theorem", "module": "Mathlib.ModelTheory.Semantics", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "FirstOrder.Language.StrongHomClass.realize_sentence", "kind": "theorem", "module": "Mathlib.ModelTheory.Semantics", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "FirstOrder.Language.StrongHomClass.theory_model", "kind": "theorem", "module": "Mathlib.ModelTheory.Semantics", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.StrongHomClass.elementarilyEquivalent", "kind": "theorem", "module": "Mathlib.ModelTheory.Semantics", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Relations.realize_reflexive", "kind": "theorem", "module": "Mathlib.ModelTheory.Semantics", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Relations.realize_irreflexive", "kind": "theorem", "module": "Mathlib.ModelTheory.Semantics", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Relations.realize_symmetric", "kind": "theorem", "module": "Mathlib.ModelTheory.Semantics", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Relations.realize_antisymmetric", "kind": "theorem", "module": "Mathlib.ModelTheory.Semantics", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Relations.realize_transitive", "kind": "theorem", "module": "Mathlib.ModelTheory.Semantics", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Relations.realize_total", "kind": "theorem", "module": "Mathlib.ModelTheory.Semantics", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Sentence.realize_cardGe", "kind": "theorem", "module": "Mathlib.ModelTheory.Semantics", "is_tactic_proof": false, "tactics": ["rw", "simp_rw", "simp", "forall_exists_index,", "refine", "rintro", "refine", "contrapose", "have", "simp", "exact", "rintro", "simpa"], "tactic_count": 13}
{"name": "FirstOrder.Language.model_infiniteTheory_iff", "kind": "theorem", "module": "Mathlib.ModelTheory.Semantics", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FirstOrder.Language.model_infiniteTheory", "kind": "instance", "module": "Mathlib.ModelTheory.Semantics", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.model_nonemptyTheory_iff", "kind": "theorem", "module": "Mathlib.ModelTheory.Semantics", "is_tactic_proof": true, "tactics": ["simp", "one_le_iff_ne_zero,"], "tactic_count": 2}
{"name": "FirstOrder.Language.model_nonempty", "kind": "instance", "module": "Mathlib.ModelTheory.Semantics", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.model_distinctConstantsTheory", "kind": "theorem", "module": "Mathlib.ModelTheory.Semantics", "is_tactic_proof": true, "tactics": ["simp", "refine", "contrapose", "have", "simp", "exact", "rintro", "simp", "exact"], "tactic_count": 9}
{"name": "FirstOrder.Language.card_le_of_model_distinctConstantsTheory", "kind": "theorem", "module": "Mathlib.ModelTheory.Semantics", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.ElementarilyEquivalent.symm", "kind": "theorem", "module": "Mathlib.ModelTheory.Semantics", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.ElementarilyEquivalent.trans", "kind": "theorem", "module": "Mathlib.ModelTheory.Semantics", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.ElementarilyEquivalent.completeTheory_eq", "kind": "theorem", "module": "Mathlib.ModelTheory.Semantics", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.ElementarilyEquivalent.realize_sentence", "kind": "theorem", "module": "Mathlib.ModelTheory.Semantics", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.ElementarilyEquivalent.theory_model_iff", "kind": "theorem", "module": "Mathlib.ModelTheory.Semantics", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "FirstOrder.Language.ElementarilyEquivalent.theory_model", "kind": "theorem", "module": "Mathlib.ModelTheory.Semantics", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.ElementarilyEquivalent.nonempty_iff", "kind": "theorem", "module": "Mathlib.ModelTheory.Semantics", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.ElementarilyEquivalent.nonempty", "kind": "theorem", "module": "Mathlib.ModelTheory.Semantics", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.ElementarilyEquivalent.infinite_iff", "kind": "theorem", "module": "Mathlib.ModelTheory.Semantics", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.ElementarilyEquivalent.infinite", "kind": "theorem", "module": "Mathlib.ModelTheory.Semantics", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.skolem₁", "kind": "definition", "module": "Mathlib.ModelTheory.Skolem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.card_functions_sum_skolem₁", "kind": "theorem", "module": "Mathlib.ModelTheory.Skolem", "is_tactic_proof": true, "tactics": ["simp", "conv_lhs", "rw", "gcongr", "rw", "refine", "rcases", "rfl", "rw", "exact"], "tactic_count": 10}
{"name": "FirstOrder.Language.card_functions_sum_skolem₁_le", "kind": "theorem", "module": "Mathlib.ModelTheory.Skolem", "is_tactic_proof": true, "tactics": ["rw", "trans", "exact", "refine", "simp", "rfl"], "tactic_count": 6}
{"name": "FirstOrder.Language.skolem₁Structure", "kind": "instance", "module": "Mathlib.ModelTheory.Skolem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.skolem₁_reduct_isElementary", "kind": "theorem", "module": "Mathlib.ModelTheory.Skolem", "is_tactic_proof": true, "tactics": ["apply", "intro", "let", "use", "exact", "exact"], "tactic_count": 6}
{"name": "FirstOrder.Language.Substructure.elementarySkolem₁Reduct", "kind": "definition", "module": "Mathlib.ModelTheory.Skolem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.coeSort_elementarySkolem₁Reduct", "kind": "theorem", "module": "Mathlib.ModelTheory.Skolem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.elementarySkolem₁Reduct.instSmall", "kind": "instance", "module": "Mathlib.ModelTheory.Skolem", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "FirstOrder.Language.exists_small_elementarySubstructure", "kind": "theorem", "module": "Mathlib.ModelTheory.Skolem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.exists_elementarySubstructure_card_eq", "kind": "theorem", "module": "Mathlib.ModelTheory.Skolem", "is_tactic_proof": true, "tactics": ["obtain", "rw", "rw", "refine", "have", "rw", "rw", "refine", "le_antisymm", "rw", "refine", "rw", "exact", "rw", "aleph0_le_lift,", "refine", "rw", "refine", "rw", "refine", "rw", "exact"], "tactic_count": 22}
{"name": "FirstOrder.Language.ClosedUnder", "kind": "definition", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.closedUnder_univ", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.ClosedUnder.inter", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.ClosedUnder.inf", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.ClosedUnder.sInf", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.instSetLike", "kind": "instance", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.instPartialOrder", "kind": "instance", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.Simps.coe", "kind": "definition", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.mem_carrier", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.ext", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.copy", "kind": "definition", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Term.realize_mem", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": true, "tactics": ["induction", "var", "func"], "tactic_count": 3}
{"name": "FirstOrder.Language.Substructure.coe_copy", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.copy_eq", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.constants_mem", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.instTop", "kind": "instance", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.instInhabited", "kind": "instance", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.mem_top", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.coe_top", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.instInf", "kind": "instance", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.coe_inf", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.mem_inf", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.instInfSet", "kind": "instance", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.coe_sInf", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.mem_sInf", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.mem_iInf", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FirstOrder.Language.Substructure.coe_iInf", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FirstOrder.Language.Substructure.instCompleteLattice", "kind": "instance", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.closure", "kind": "definition", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.mem_closure", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.subset_closure", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.notMem_of_notMem_closure", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.closed", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.closure_le", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.closure_mono", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.closure_eq_of_le", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.coe_closure_eq_range_term_realize", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": ["let", "simp", "refine", "simp", "change", "rw", "refine", "rintro", "exact"], "tactic_count": 9}
{"name": "FirstOrder.Language.Substructure.small_closure", "kind": "instance", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "FirstOrder.Language.Substructure.mem_closure_iff_exists_term", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "FirstOrder.Language.Substructure.lift_card_closure_le_card_term", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "FirstOrder.Language.Substructure.lift_card_closure_le", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw"], "tactic_count": 3}
{"name": "FirstOrder.Language.Substructure.mem_closed_iff", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact", "have", "exact"], "tactic_count": 5}
{"name": "FirstOrder.Language.Substructure.mem_closed_of_isRelational", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.closure_eq_of_isRelational", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.mem_closure_iff_of_isRelational", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.Countable.substructure_closure", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": true, "tactics": ["haveI", "rw", "exact"], "tactic_count": 3}
{"name": "FirstOrder.Language.Substructure.closure_induction", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.dense_induction", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "FirstOrder.Language.Substructure.gi", "kind": "definition", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.closure_eq", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.closure_empty", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.closure_univ", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.closure_union", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.closure_iUnion", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.closure_insert", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.small_bot", "kind": "instance", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": true, "tactics": ["rw", "haveI", "exact"], "tactic_count": 3}
{"name": "FirstOrder.Language.Substructure.iSup_eq_closure", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "FirstOrder.Language.Substructure.mem_iSup_of_directed", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": true, "tactics": ["refine", "suffices", "refine", "simp_rw", "have", "refine"], "tactic_count": 6}
{"name": "FirstOrder.Language.Substructure.mem_sSup_of_directedOn", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": true, "tactics": ["haveI", "simp"], "tactic_count": 2}
{"name": "FirstOrder.Language.Substructure.instIsEmptySubtypeMemBotOfConstants", "kind": "instance", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": true, "tactics": ["refine", "have", "rw", "intro", "cases", "exact", "intro", "simp", "rw", "exact"], "tactic_count": 10}
{"name": "FirstOrder.Language.Substructure.comap", "kind": "definition", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.mem_comap", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.comap_comap", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.comap_id", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.map", "kind": "definition", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.mem_map", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.mem_map_of_mem", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.apply_coe_mem_map", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.map_map", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.map_le_iff_le_comap", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.gc_map_comap", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.map_le_of_le_comap", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.le_comap_of_map_le", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.le_comap_map", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.map_comap_le", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.monotone_map", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.monotone_comap", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.map_comap_map", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.comap_map_comap", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.map_sup", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.map_iSup", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.comap_inf", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.comap_iInf", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.map_bot", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.comap_top", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.map_id", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.map_closure", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.closure_image", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.gciMapComap", "kind": "definition", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.comap_map_eq_of_injective", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.comap_surjective_of_injective", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.map_injective_of_injective", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.comap_inf_map_of_injective", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.comap_iInf_map_of_injective", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.comap_sup_map_of_injective", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.comap_iSup_map_of_injective", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.map_le_map_iff_of_injective", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.map_strictMono_of_injective", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.giMapComap", "kind": "definition", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.map_comap_eq_of_surjective", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.map_surjective_of_surjective", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.comap_injective_of_surjective", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.map_inf_comap_of_surjective", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.map_iInf_comap_of_surjective", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.map_sup_comap_of_surjective", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.map_iSup_comap_of_surjective", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.comap_le_comap_iff_of_surjective", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.comap_strictMono_of_surjective", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.inducedStructure", "kind": "instance", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.subtype", "kind": "definition", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.subtype_apply", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.subtype_injective", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.coe_subtype", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.topEquiv", "kind": "definition", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.coe_topEquiv", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.realize_boundedFormula_top", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "FirstOrder.Language.Substructure.realize_formula_top", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "FirstOrder.Language.Substructure.closure_induction'", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "FirstOrder.Language.LHom.substructureReduct", "kind": "definition", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.LHom.mem_substructureReduct", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.LHom.coe_substructureReduct", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.withConstants", "kind": "definition", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.mem_withConstants", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.coe_withConstants", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.reduct_withConstants", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "FirstOrder.Language.Substructure.subset_closure_withConstants", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": true, "tactics": ["intro", "simp", "let", "exact"], "tactic_count": 4}
{"name": "FirstOrder.Language.Substructure.closure_withConstants_eq", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": true, "tactics": ["refine", "rw", "simp", "and_true]", "exact"], "tactic_count": 5}
{"name": "FirstOrder.Language.Hom.domRestrict", "kind": "definition", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Hom.codRestrict", "kind": "definition", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Hom.comp_codRestrict", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Hom.subtype_comp_codRestrict", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Hom.range", "kind": "definition", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Hom.range_coe", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Hom.mem_range", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Hom.range_eq_map", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "FirstOrder.Language.Hom.mem_range_self", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Hom.range_id", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Hom.range_comp", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Hom.range_comp_le_range", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Hom.range_eq_top", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "FirstOrder.Language.Hom.range_le_iff_comap", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "FirstOrder.Language.Hom.map_le_range", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Hom.eqLocus", "kind": "definition", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Hom.mem_eqLocus", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Hom.eqOn_closure", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Hom.eq_of_eqOn_top", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Hom.eq_of_eqOn_dense", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Embedding.domRestrict", "kind": "definition", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Embedding.domRestrict_apply", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Embedding.codRestrict", "kind": "definition", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Embedding.codRestrict_apply", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Embedding.codRestrict_apply'", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Embedding.comp_codRestrict", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Embedding.subtype_comp_codRestrict", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Embedding.substructureEquivMap", "kind": "definition", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Embedding.substructureEquivMap_apply", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Embedding.subtype_substructureEquivMap", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "FirstOrder.Language.Embedding.equivRange", "kind": "definition", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Embedding.equivRange_apply", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Embedding.subtype_equivRange", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "FirstOrder.Language.Equiv.toHom_range", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": true, "tactics": ["ext", "simp", "exact"], "tactic_count": 3}
{"name": "FirstOrder.Language.Substructure.inclusion", "kind": "definition", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.inclusion_self", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.coe_inclusion", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Substructure.range_subtype", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": true, "tactics": ["ext", "simp", "refine", "rintro", "exact"], "tactic_count": 5}
{"name": "FirstOrder.Language.Substructure.subtype_comp_inclusion", "kind": "theorem", "module": "Mathlib.ModelTheory.Substructures", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Term", "kind": "inductive", "module": "Mathlib.ModelTheory.Syntax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Term.instDecidableEq", "kind": "instance", "module": "Mathlib.ModelTheory.Syntax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Term.varFinset", "kind": "definition", "module": "Mathlib.ModelTheory.Syntax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Term.varFinsetLeft", "kind": "definition", "module": "Mathlib.ModelTheory.Syntax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Term.relabel", "kind": "definition", "module": "Mathlib.ModelTheory.Syntax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Term.relabel_id", "kind": "theorem", "module": "Mathlib.ModelTheory.Syntax", "is_tactic_proof": true, "tactics": ["induction", "var", "func"], "tactic_count": 3}
{"name": "FirstOrder.Language.Term.relabel_id_eq_id", "kind": "theorem", "module": "Mathlib.ModelTheory.Syntax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Term.relabel_relabel", "kind": "theorem", "module": "Mathlib.ModelTheory.Syntax", "is_tactic_proof": true, "tactics": ["induction", "var", "func"], "tactic_count": 3}
{"name": "FirstOrder.Language.Term.relabel_comp_relabel", "kind": "theorem", "module": "Mathlib.ModelTheory.Syntax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Term.relabelEquiv", "kind": "definition", "module": "Mathlib.ModelTheory.Syntax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Term.restrictVar", "kind": "definition", "module": "Mathlib.ModelTheory.Syntax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Term.restrictVarLeft", "kind": "definition", "module": "Mathlib.ModelTheory.Syntax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Constants.term", "kind": "definition", "module": "Mathlib.ModelTheory.Syntax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Functions.apply₁", "kind": "definition", "module": "Mathlib.ModelTheory.Syntax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Functions.apply₂", "kind": "definition", "module": "Mathlib.ModelTheory.Syntax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Functions.term", "kind": "definition", "module": "Mathlib.ModelTheory.Syntax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Term.constantsToVars", "kind": "definition", "module": "Mathlib.ModelTheory.Syntax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Term.varsToConstants", "kind": "definition", "module": "Mathlib.ModelTheory.Syntax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Term.constantsVarsEquiv", "kind": "definition", "module": "Mathlib.ModelTheory.Syntax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Term.constantsVarsEquivLeft", "kind": "definition", "module": "Mathlib.ModelTheory.Syntax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Term.constantsVarsEquivLeft_apply", "kind": "theorem", "module": "Mathlib.ModelTheory.Syntax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Term.constantsVarsEquivLeft_symm_apply", "kind": "theorem", "module": "Mathlib.ModelTheory.Syntax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Term.inhabitedOfVar", "kind": "instance", "module": "Mathlib.ModelTheory.Syntax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Term.inhabitedOfConstant", "kind": "instance", "module": "Mathlib.ModelTheory.Syntax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Term.liftAt", "kind": "definition", "module": "Mathlib.ModelTheory.Syntax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Term.subst", "kind": "definition", "module": "Mathlib.ModelTheory.Syntax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstOrder.Language.Term.substFunc", "kind": "definition", "module": "Mathlib.ModelTheory.Syntax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ArithmeticFunction.toFun_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.coe_mk", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.map_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.coe_inj", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.zero_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.ext", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.one", "kind": "instance", "module": "Mathlib.NumberTheory.ArithmeticFunction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.one_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.one_one", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.one_apply_ne", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.natToArithmeticFunction", "kind": "definition", "module": "Mathlib.NumberTheory.ArithmeticFunction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.natCoe", "kind": "instance", "module": "Mathlib.NumberTheory.ArithmeticFunction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ArithmeticFunction.intCoe", "kind": "instance", "module": "Mathlib.NumberTheory.ArithmeticFunction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ArithmeticFunction.intCoe_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ArithmeticFunction.natCoe_one", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Defs", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
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{"name": "ArithmeticFunction.add", "kind": "instance", "module": "Mathlib.NumberTheory.ArithmeticFunction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.add_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.instAddMonoid", "kind": "instance", "module": "Mathlib.NumberTheory.ArithmeticFunction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.instAddMonoidWithOne", "kind": "instance", "module": "Mathlib.NumberTheory.ArithmeticFunction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.instAddCommMonoid", "kind": "instance", "module": "Mathlib.NumberTheory.ArithmeticFunction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.instNeg", "kind": "instance", "module": "Mathlib.NumberTheory.ArithmeticFunction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.neg_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Defs", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "ArithmeticFunction.instAddGroup", "kind": "instance", "module": "Mathlib.NumberTheory.ArithmeticFunction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.instAddCommGroup", "kind": "instance", "module": "Mathlib.NumberTheory.ArithmeticFunction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.instSMul", "kind": "instance", "module": "Mathlib.NumberTheory.ArithmeticFunction.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ArithmeticFunction.bigproddvd", "kind": "definition", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ArithmeticFunction.prodPrimeFactors_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ArithmeticFunction.id", "kind": "definition", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.id_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.isMultiplicative_id", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.pow", "kind": "definition", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.pow_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "ArithmeticFunction.pow_zero_eq_zeta", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "ArithmeticFunction.pow_one_eq_id", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "ArithmeticFunction.isMultiplicative_pow", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.sigma", "kind": "definition", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ArithmeticFunction.sigma_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.sigma_eq_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simp", "aesop"], "tactic_count": 4}
{"name": "ArithmeticFunction.sigma_pos_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ArithmeticFunction.sigma_apply_prime_pow", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ArithmeticFunction.sigma_one_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ArithmeticFunction.sigma_one_apply_prime_pow", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ArithmeticFunction.sigma_eq_sum_div", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ArithmeticFunction.sigma_zero_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ArithmeticFunction.sigma_zero_apply_prime_pow", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ArithmeticFunction.sigma_one", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ArithmeticFunction.sigma_pos", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "ArithmeticFunction.sigma_mono", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": true, "tactics": ["simp_rw", "gcongr", "exact"], "tactic_count": 3}
{"name": "ArithmeticFunction.zeta_mul_pow_eq_sigma", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": true, "tactics": ["ext", "rw", "apply", "aesop"], "tactic_count": 4}
{"name": "ArithmeticFunction.isMultiplicative_sigma", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "ArithmeticFunction.sigma_eq_prod_primeFactors_sum_range_factorization_pow_mul", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Nat.card_divisors", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Nat.divisors_card_eq_one_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": true, "tactics": ["rcases", "simp", "refine", "exact"], "tactic_count": 4}
{"name": "_private.Mathlib.NumberTheory.ArithmeticFunction.Misc.0.ArithmeticFunction.sigma_zero_eq_one_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ArithmeticFunction.sigma_eq_one_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": true, "tactics": ["by_cases", "aesop", "constructor", "intro", "rw", "have", "have", "lia", "simp"], "tactic_count": 9}
{"name": "Nat.sum_divisors", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ArithmeticFunction.cardFactors", "kind": "definition", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.Omega.termΩ", "kind": "definition", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.Omega._aux_Mathlib_NumberTheory_ArithmeticFunction_Misc___macroRules_ArithmeticFunction_Omega_termΩ_1", "kind": "definition", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.Omega._aux_Mathlib_NumberTheory_ArithmeticFunction_Misc___unexpand_ArithmeticFunction_cardFactors_1", "kind": "definition", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.cardFactors_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.cardFactors_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ArithmeticFunction.cardFactors_one", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ArithmeticFunction.cardFactors_eq_zero_iff_eq_zero_or_one", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ArithmeticFunction.cardFactors_pos_iff_one_lt", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ArithmeticFunction.cardFactors_eq_one_iff_prime", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": true, "tactics": ["refine", "cases", "zero", "succ", "rcases", "rw", "apply", "rw"], "tactic_count": 8}
{"name": "ArithmeticFunction.cardFactors_mul", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ArithmeticFunction.cardFactors_multiset_prod", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": true, "tactics": ["induction", "empty", "cons"], "tactic_count": 3}
{"name": "ArithmeticFunction.cardFactors_apply_prime", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.cardFactors_pow", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": true, "tactics": ["by_cases", "cases", "induction", "zero", "succ", "rw", "ring"], "tactic_count": 7}
{"name": "ArithmeticFunction.cardFactors_apply_prime_pow", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ArithmeticFunction.cardFactors_eq_sum_factorization", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ArithmeticFunction.cardDistinctFactors", "kind": "definition", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.omega.termω", "kind": "definition", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.omega._aux_Mathlib_NumberTheory_ArithmeticFunction_Misc___macroRules_ArithmeticFunction_omega_termω_1", "kind": "definition", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.omega._aux_Mathlib_NumberTheory_ArithmeticFunction_Misc___unexpand_ArithmeticFunction_cardDistinctFactors_1", "kind": "definition", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.cardDistinctFactors_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ArithmeticFunction.cardDistinctFactors_one", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ArithmeticFunction.cardDistinctFactors_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.cardDistinctFactors_eq_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ArithmeticFunction.cardDistinctFactors_pos", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ArithmeticFunction.cardDistinctFactors_eq_cardFactors_iff_squarefree", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": true, "tactics": ["rw", "constructor", "rw", "apply", "simp"], "tactic_count": 5}
{"name": "ArithmeticFunction.cardDistinctFactors_eq_one_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ArithmeticFunction.cardDistinctFactors_apply_prime_pow", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.cardDistinctFactors_apply_prime", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ArithmeticFunction.cardDistinctFactors_mul", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": true, "tactics": ["simp", "coprime_primeFactorsList_disjoint"], "tactic_count": 2}
{"name": "ArithmeticFunction.cardDistinctFactors_prod", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": true, "tactics": ["induction", "empty", "cons", "rw", "exact", "exact"], "tactic_count": 6}
{"name": "ArithmeticFunction.sum_Ioc_zeta", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": true, "tactics": ["simp", "rw", "simp"], "tactic_count": 3}
{"name": "ArithmeticFunction.sum_Ioc_mul_eq_sum_prod_filter", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": true, "tactics": ["simp", "trans", "refine", "simp", "rw", "simp_rw", "rw", "exact"], "tactic_count": 8}
{"name": "ArithmeticFunction.sum_Ioc_mul_eq_sum_sum", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp", "congr", "ext", "simp", "intro", "constructor", "intro", "grw", "intro", "grw", "simp"], "tactic_count": 13}
{"name": "ArithmeticFunction.sum_Ioc_mul_zeta_eq_sum", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp_rw", "rw_mod_cast"], "tactic_count": 4}
{"name": "ArithmeticFunction.sum_Ioc_sigma0_eq_sum_div", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": true, "tactics": ["rw", "convert", "simpa"], "tactic_count": 3}
{"name": "Nat.Coprime.card_divisors_mul", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.Coprime.sum_divisors_mul", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Meta.Positivity.evalArithmeticFunctionSigma", "kind": "definition", "module": "Mathlib.NumberTheory.ArithmeticFunction.Misc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.moebius", "kind": "definition", "module": "Mathlib.NumberTheory.ArithmeticFunction.Moebius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.Moebius.termμ", "kind": "definition", "module": "Mathlib.NumberTheory.ArithmeticFunction.Moebius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.Moebius._aux_Mathlib_NumberTheory_ArithmeticFunction_Moebius___macroRules_ArithmeticFunction_Moebius_termμ_1", "kind": "definition", "module": "Mathlib.NumberTheory.ArithmeticFunction.Moebius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.Moebius._aux_Mathlib_NumberTheory_ArithmeticFunction_Moebius___unexpand_ArithmeticFunction_moebius_1", "kind": "definition", "module": "Mathlib.NumberTheory.ArithmeticFunction.Moebius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.moebius_apply_of_squarefree", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Moebius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.moebius_eq_zero_of_not_squarefree", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Moebius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.moebius_apply_one", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Moebius", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ArithmeticFunction.moebius_ne_zero_iff_squarefree", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Moebius", "is_tactic_proof": true, "tactics": ["constructor", "contrapose", "simp", "simp"], "tactic_count": 4}
{"name": "ArithmeticFunction.moebius_eq_or", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Moebius", "is_tactic_proof": true, "tactics": ["simp", "split_ifs", "right", "exact", "left", "rfl"], "tactic_count": 6}
{"name": "ArithmeticFunction.moebius_ne_zero_iff_eq_or", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Moebius", "is_tactic_proof": true, "tactics": ["have", "lia"], "tactic_count": 2}
{"name": "ArithmeticFunction.moebius_sq_eq_one_of_squarefree", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Moebius", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ArithmeticFunction.abs_moebius_eq_one_of_squarefree", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Moebius", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ArithmeticFunction.moebius_sq", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Moebius", "is_tactic_proof": true, "tactics": ["split_ifs", "exact", "simp"], "tactic_count": 3}
{"name": "ArithmeticFunction.abs_moebius", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Moebius", "is_tactic_proof": true, "tactics": ["split_ifs", "exact", "simp"], "tactic_count": 3}
{"name": "ArithmeticFunction.abs_moebius_le_one", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Moebius", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "ArithmeticFunction.moebius_apply_prime", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Moebius", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ArithmeticFunction.moebius_apply_prime_pow", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Moebius", "is_tactic_proof": true, "tactics": ["split_ifs", "rw", "rw", "rw", "exact"], "tactic_count": 5}
{"name": "ArithmeticFunction.moebius_apply_isPrimePow_not_prime", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Moebius", "is_tactic_proof": true, "tactics": ["obtain", "rw", "rintro", "exact"], "tactic_count": 4}
{"name": "ArithmeticFunction.isMultiplicative_moebius", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Moebius", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp"], "tactic_count": 3}
{"name": "ArithmeticFunction.IsMultiplicative.prodPrimeFactors_one_add_of_squarefree", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Moebius", "is_tactic_proof": true, "tactics": ["trans", "simp_rw", "apply", "rw", "rw"], "tactic_count": 5}
{"name": "ArithmeticFunction.IsMultiplicative.prodPrimeFactors_one_sub_of_squarefree", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Moebius", "is_tactic_proof": true, "tactics": ["trans", "apply", "rw", "ring", "rw", "simp_rw"], "tactic_count": 6}
{"name": "ArithmeticFunction.moebius_mul_coe_zeta", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Moebius", "is_tactic_proof": true, "tactics": ["ext", "induction", "zero", "one", "prime_pow", "rw", "simp", "coprime", "hb", "rw", "exact"], "tactic_count": 11}
{"name": "ArithmeticFunction.coe_zeta_mul_moebius", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Moebius", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ArithmeticFunction.coe_moebius_mul_coe_zeta", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Moebius", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ArithmeticFunction.coe_zeta_mul_coe_moebius", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Moebius", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ArithmeticFunction.instInvertibleNatToArithmeticFunctionZeta", "kind": "instance", "module": "Mathlib.NumberTheory.ArithmeticFunction.Moebius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.zetaUnit", "kind": "definition", "module": "Mathlib.NumberTheory.ArithmeticFunction.Moebius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.coe_zetaUnit", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Moebius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.inv_zetaUnit", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Moebius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.sum_eq_iff_sum_smul_moebius_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Moebius", "is_tactic_proof": true, "tactics": ["let", "let", "trans", "rw", "apply", "intro", "cases", "zero", "succ", "rw", "simp", "rw", "trans", "constructor", "rw", "apply", "intro", "cases", "zero", "succ", "simp", "rw", "rw"], "tactic_count": 23}
{"name": "ArithmeticFunction.sum_eq_iff_sum_mul_moebius_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Moebius", "is_tactic_proof": true, "tactics": ["rw", "apply", "refine", "rw"], "tactic_count": 4}
{"name": "ArithmeticFunction.prod_eq_iff_prod_pow_moebius_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Moebius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.prod_eq_iff_prod_pow_moebius_eq_of_nonzero", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Moebius", "is_tactic_proof": false, "tactics": ["refine", "refine", "dsimp", "rw", "intro", "rw", "dsimp", "rw", "intro", "rw"], "tactic_count": 10}
{"name": "ArithmeticFunction.sum_eq_iff_sum_smul_moebius_eq_on", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Moebius", "is_tactic_proof": true, "tactics": ["constructor", "intro", "let", "intro", "suffices", "rw", "intro", "rw", "rw", "apply", "intro", "intro", "let", "intro", "suffices", "rw", "intro", "rw", "apply", "intro"], "tactic_count": 20}
{"name": "ArithmeticFunction.sum_eq_iff_sum_smul_moebius_eq_on'", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Moebius", "is_tactic_proof": false, "tactics": ["have", "refine", "contrapose", "simpa", "simpa"], "tactic_count": 5}
{"name": "ArithmeticFunction.sum_eq_iff_sum_mul_moebius_eq_on", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Moebius", "is_tactic_proof": true, "tactics": ["rw", "apply", "intro", "refine", "rw"], "tactic_count": 5}
{"name": "ArithmeticFunction.prod_eq_iff_prod_pow_moebius_eq_on", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Moebius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.prod_eq_iff_prod_pow_moebius_eq_on_of_nonzero", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Moebius", "is_tactic_proof": false, "tactics": ["refine", "refine", "dsimp", "rw", "intro", "rw", "dsimp", "rw", "intro", "rw"], "tactic_count": 10}
{"name": "ArithmeticFunction.log", "kind": "definition", "module": "Mathlib.NumberTheory.ArithmeticFunction.VonMangoldt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.log_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.VonMangoldt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.vonMangoldt", "kind": "definition", "module": "Mathlib.NumberTheory.ArithmeticFunction.VonMangoldt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.termΛ", "kind": "definition", "module": "Mathlib.NumberTheory.ArithmeticFunction.VonMangoldt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction._aux_Mathlib_NumberTheory_ArithmeticFunction_VonMangoldt___macroRules_ArithmeticFunction_termΛ_1", "kind": "definition", "module": "Mathlib.NumberTheory.ArithmeticFunction.VonMangoldt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction._aux_Mathlib_NumberTheory_ArithmeticFunction_VonMangoldt___unexpand_ArithmeticFunction_vonMangoldt_1", "kind": "definition", "module": "Mathlib.NumberTheory.ArithmeticFunction.VonMangoldt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.vonMangoldt.termΛ", "kind": "definition", "module": "Mathlib.NumberTheory.ArithmeticFunction.VonMangoldt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.vonMangoldt._aux_Mathlib_NumberTheory_ArithmeticFunction_VonMangoldt___macroRules_ArithmeticFunction_vonMangoldt_termΛ_1", "kind": "definition", "module": "Mathlib.NumberTheory.ArithmeticFunction.VonMangoldt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.vonMangoldt._aux_Mathlib_NumberTheory_ArithmeticFunction_VonMangoldt___unexpand_ArithmeticFunction_vonMangoldt_1", "kind": "definition", "module": "Mathlib.NumberTheory.ArithmeticFunction.VonMangoldt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.vonMangoldt_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.VonMangoldt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.vonMangoldt_apply_one", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.VonMangoldt", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ArithmeticFunction.vonMangoldt_nonneg", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.VonMangoldt", "is_tactic_proof": true, "tactics": ["rw", "split_ifs", "exact", "rfl"], "tactic_count": 4}
{"name": "ArithmeticFunction.vonMangoldt_apply_pow", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.VonMangoldt", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ArithmeticFunction.vonMangoldt_apply_prime", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.VonMangoldt", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ArithmeticFunction.vonMangoldt_ne_zero_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.VonMangoldt", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "ArithmeticFunction.vonMangoldt_pos_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.VonMangoldt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.vonMangoldt_eq_zero_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.VonMangoldt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.vonMangoldt_sum", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.VonMangoldt", "is_tactic_proof": true, "tactics": ["refine", "simp", "intro", "rw", "simp", "intro", "simp", "rw"], "tactic_count": 8}
{"name": "ArithmeticFunction.vonMangoldt_mul_zeta", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.VonMangoldt", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "ArithmeticFunction.zeta_mul_vonMangoldt", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.VonMangoldt", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ArithmeticFunction.log_mul_moebius_eq_vonMangoldt", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.VonMangoldt", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ArithmeticFunction.moebius_mul_log_eq_vonMangoldt", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.VonMangoldt", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ArithmeticFunction.sum_moebius_mul_log_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.VonMangoldt", "is_tactic_proof": false, "tactics": ["simp", "rw", "have", "apply", "simp", "intro", "have", "rw", "rintro", "exact", "rw", "rw", "moebius_mul_coe_zeta]", "rcases"], "tactic_count": 14}
{"name": "ArithmeticFunction.vonMangoldt_le_log", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.VonMangoldt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.zeta", "kind": "definition", "module": "Mathlib.NumberTheory.ArithmeticFunction.Zeta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.zeta.termζ", "kind": "definition", "module": "Mathlib.NumberTheory.ArithmeticFunction.Zeta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.zeta._aux_Mathlib_NumberTheory_ArithmeticFunction_Zeta___macroRules_ArithmeticFunction_zeta_termζ_1", "kind": "definition", "module": "Mathlib.NumberTheory.ArithmeticFunction.Zeta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.zeta._aux_Mathlib_NumberTheory_ArithmeticFunction_Zeta___unexpand_ArithmeticFunction_zeta_1", "kind": "definition", "module": "Mathlib.NumberTheory.ArithmeticFunction.Zeta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.zeta_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Zeta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.zeta_apply_ne", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Zeta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.zeta_eq_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Zeta", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ArithmeticFunction.zeta_pos", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Zeta", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "ArithmeticFunction.sum_divisorsAntidiagonal_eq_sum_divisors", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Zeta", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ArithmeticFunction.coe_zeta_mul_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Zeta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.coe_mul_zeta_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Zeta", "is_tactic_proof": true, "tactics": ["rw", "trans", "refine", "rcases", "rw", "rw"], "tactic_count": 6}
{"name": "ArithmeticFunction.coe_zeta_mul_comm", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Zeta", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "ArithmeticFunction.zeta_mul_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Zeta", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ArithmeticFunction.mul_zeta_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Zeta", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ArithmeticFunction.zeta_mul_comm", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Zeta", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ArithmeticFunction.pmul", "kind": "definition", "module": "Mathlib.NumberTheory.ArithmeticFunction.Zeta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.pmul_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Zeta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.pmul_comm", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Zeta", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "ArithmeticFunction.pmul_assoc", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Zeta", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "ArithmeticFunction.pmul_zeta", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Zeta", "is_tactic_proof": true, "tactics": ["ext", "cases"], "tactic_count": 2}
{"name": "ArithmeticFunction.zeta_pmul", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Zeta", "is_tactic_proof": true, "tactics": ["ext", "cases"], "tactic_count": 2}
{"name": "ArithmeticFunction.ppow", "kind": "definition", "module": "Mathlib.NumberTheory.ArithmeticFunction.Zeta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.ppow_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Zeta", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ArithmeticFunction.ppow_one", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Zeta", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "ArithmeticFunction.ppow_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Zeta", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ArithmeticFunction.ppow_succ'", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Zeta", "is_tactic_proof": true, "tactics": ["ext", "rw", "induction"], "tactic_count": 3}
{"name": "ArithmeticFunction.ppow_succ", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Zeta", "is_tactic_proof": true, "tactics": ["ext", "rw", "induction"], "tactic_count": 3}
{"name": "ArithmeticFunction.pdiv", "kind": "definition", "module": "Mathlib.NumberTheory.ArithmeticFunction.Zeta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.pdiv_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Zeta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.pdiv_zeta", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Zeta", "is_tactic_proof": true, "tactics": ["ext", "cases"], "tactic_count": 2}
{"name": "ArithmeticFunction.isMultiplicative_zeta", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Zeta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.IsMultiplicative.pmul", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Zeta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.IsMultiplicative.pdiv", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Zeta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.IsMultiplicative.ppow", "kind": "theorem", "module": "Mathlib.NumberTheory.ArithmeticFunction.Zeta", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Mathlib.Meta.Positivity.evalArithmeticFunctionZeta", "kind": "definition", "module": "Mathlib.NumberTheory.ArithmeticFunction.Zeta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dvd_sub_pow_of_dvd_sub", "kind": "theorem", "module": "Mathlib.NumberTheory.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "refine", "let", "have", "rw", "rw", "rw"], "tactic_count": 10}
{"name": "bernoulli'", "kind": "definition", "module": "Mathlib.NumberTheory.Bernoulli", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bernoulli'_def'", "kind": "theorem", "module": "Mathlib.NumberTheory.Bernoulli", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "bernoulli'_def", "kind": "theorem", "module": "Mathlib.NumberTheory.Bernoulli", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "bernoulli'_spec", "kind": "theorem", "module": "Mathlib.NumberTheory.Bernoulli", "is_tactic_proof": false, "tactics": ["rw", "one_mul,", "exact"], "tactic_count": 3}
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{"name": "bernoulli'_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.Bernoulli", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "bernoulli'_one", "kind": "theorem", "module": "Mathlib.NumberTheory.Bernoulli", "is_tactic_proof": true, "tactics": ["rw", "norm_num"], "tactic_count": 2}
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{"name": "bernoulli'PowerSeries", "kind": "definition", "module": "Mathlib.NumberTheory.Bernoulli", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bernoulli'PowerSeries_mul_exp_sub_one", "kind": "theorem", "module": "Mathlib.NumberTheory.Bernoulli", "is_tactic_proof": true, "tactics": ["ext", "cases", "zero", "succ", "rw", "suffices", "simpa", "apply", "rw", "convert", "apply", "simp_rw", "rintro", "have", "simp"], "tactic_count": 15}
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{"name": "bernoulli'_eq_bernoulli", "kind": "theorem", "module": "Mathlib.NumberTheory.Bernoulli", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "Chebyshev.psi_eq_zero_of_lt_two", "kind": "theorem", "module": "Mathlib.NumberTheory.Chebyshev", "is_tactic_proof": true, "tactics": ["apply", "simp", "convert", "have", "norm_cast", "linarith"], "tactic_count": 6}
{"name": "Chebyshev.theta_eq_zero_of_lt_two", "kind": "theorem", "module": "Mathlib.NumberTheory.Chebyshev", "is_tactic_proof": true, "tactics": ["apply", "convert", "simp", "have", "norm_cast", "linarith"], "tactic_count": 6}
{"name": "Chebyshev.psi_eq_psi_coe_floor", "kind": "theorem", "module": "Mathlib.NumberTheory.Chebyshev", "is_tactic_proof": true, "tactics": ["unfold", "rw"], "tactic_count": 2}
{"name": "Chebyshev.theta_eq_theta_coe_floor", "kind": "theorem", "module": "Mathlib.NumberTheory.Chebyshev", "is_tactic_proof": true, "tactics": ["unfold", "rw"], "tactic_count": 2}
{"name": "Chebyshev.psi_mono", "kind": "theorem", "module": "Mathlib.NumberTheory.Chebyshev", "is_tactic_proof": true, "tactics": ["intro", "apply", "exact", "simp"], "tactic_count": 4}
{"name": "Chebyshev.theta_mono", "kind": "theorem", "module": "Mathlib.NumberTheory.Chebyshev", "is_tactic_proof": true, "tactics": ["intro", "apply", "exact", "simp", "exact"], "tactic_count": 5}
{"name": "Chebyshev.theta_eq_log_primorial", "kind": "theorem", "module": "Mathlib.NumberTheory.Chebyshev", "is_tactic_proof": true, "tactics": ["unfold", "rw", "congr", "simp_all"], "tactic_count": 4}
{"name": "Chebyshev.theta_le_log4_mul_x", "kind": "theorem", "module": "Mathlib.NumberTheory.Chebyshev", "is_tactic_proof": true, "tactics": ["rw", "trans", "apply", "exacts", "rw", "gcongr", "exact"], "tactic_count": 7}
{"name": "Chebyshev.sum_PrimePow_eq_sum_sum", "kind": "theorem", "module": "Mathlib.NumberTheory.Chebyshev", "is_tactic_proof": true, "tactics": ["trans", "refine", "simp", "le_rpow_inv_iff_of_pos,", "simp", "intro", "exact", "simp", "succ_le_iff,", "rintro", "rw", "refine", "rw", "refine", "exact", "exact", "simp_all", "simp", "rw", "refine", "simp", "congr", "ext", "simp", "refine", "simp_all", "grw", "apply", "have", "contrapose", "apply"], "tactic_count": 31}
{"name": "Chebyshev.psi_eq_sum_theta", "kind": "theorem", "module": "Mathlib.NumberTheory.Chebyshev", "is_tactic_proof": true, "tactics": ["simp_rw", "apply", "rw", "simp_all"], "tactic_count": 4}
{"name": "Chebyshev.psi_eq_theta_add_sum_theta", "kind": "theorem", "module": "Mathlib.NumberTheory.Chebyshev", "is_tactic_proof": true, "tactics": ["rw", "congr", "simp", "rw", "gcongr"], "tactic_count": 5}
{"name": "Chebyshev.theta_le_psi", "kind": "theorem", "module": "Mathlib.NumberTheory.Chebyshev", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "rw", "simp", "exact", "sum_nonneg", "theta_nonneg"], "tactic_count": 7}
{"name": "Chebyshev.abs_psi_sub_theta_le_sqrt_mul_log", "kind": "theorem", "module": "Mathlib.NumberTheory.Chebyshev", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "bound", "rw", "apply", "simp_rw", "trans", "apply", "apply", "rw", "gcongr", "simp", "calc", "gcongr", "rw", "trans", "linarith", "exact", "apply", "norm_cast", "apply", "congr", "rw", "field"], "tactic_count": 24}
{"name": "Chebyshev.psi_le", "kind": "theorem", "module": "Mathlib.NumberTheory.Chebyshev", "is_tactic_proof": true, "tactics": ["calc", "gcongr", "exact", "exact"], "tactic_count": 4}
{"name": "Chebyshev.psi_le_const_mul_self", "kind": "theorem", "module": "Mathlib.NumberTheory.Chebyshev", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "bound", "apply", "rw", "gcongr", "grw", "nth_rw", "rw", "norm_num", "linarith"], "tactic_count": 11}
{"name": "Chebyshev.psi_sub_theta_eq_sum_not_prime", "kind": "theorem", "module": "Mathlib.NumberTheory.Chebyshev", "is_tactic_proof": true, "tactics": ["rw", "refine", "split_ifs", "simp", "simp"], "tactic_count": 5}
{"name": "Chebyshev.integrableOn_theta_div_id_mul_log_sq", "kind": "theorem", "module": "Mathlib.NumberTheory.Chebyshev", "is_tactic_proof": true, "tactics": ["conv", "refine", "integrableOn_mul_sum_Icc", "have", "have", "fun_prop"], "tactic_count": 6}
{"name": "Chebyshev.primeCounting_eq_theta_div_log_add_integral", "kind": "theorem", "module": "Mathlib.NumberTheory.Chebyshev", "is_tactic_proof": true, "tactics": ["simp", "rw", "push_cast", "let", "trans", "refine", "split_ifs", "have", "simp", "simp", "rw", "intervalIntegral.integral_of_le", "have", "intervalIntegral.integral_congr", "simp", "grind", "intro", "have", "have", "fun_prop", "refine", "have", "have", "exact"], "tactic_count": 24}
{"name": "Chebyshev.intervalIntegrable_one_div_log_sq", "kind": "theorem", "module": "Mathlib.NumberTheory.Chebyshev", "is_tactic_proof": true, "tactics": ["refine", "rw", "have", "have", "fun_prop"], "tactic_count": 5}
{"name": "_private.Mathlib.NumberTheory.Chebyshev.0.Chebyshev.integral_1_div_log_sq_le", "kind": "theorem", "module": "Mathlib.NumberTheory.Chebyshev", "is_tactic_proof": true, "tactics": ["calc", "refine", "apply", "simp", "aren't"], "tactic_count": 5}
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{"name": "_private.Mathlib.NumberTheory.Chebyshev.0.Chebyshev.sqrt_isLittleO", "kind": "theorem", "module": "Mathlib.NumberTheory.Chebyshev", "is_tactic_proof": true, "tactics": ["apply", "conv", "apply", "simp_rw", "apply", "filter_upwards", "filter_upwards", "apply"], "tactic_count": 8}
{"name": "Chebyshev.integral_one_div_log_sq_isBigO", "kind": "theorem", "module": "Mathlib.NumberTheory.Chebyshev", "is_tactic_proof": true, "tactics": ["trans", "apply", "filter_upwards", "apply", "rw", "grw", "positivity", "intro", "simp", "refine", "simp_rw", "apply", "conv", "apply"], "tactic_count": 14}
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{"name": "Chebyshev.integral_theta_div_log_sq_isLittleO", "kind": "theorem", "module": "Mathlib.NumberTheory.Chebyshev", "is_tactic_proof": true, "tactics": ["refine", "refine", "refine", "filter_upwards", "field"], "tactic_count": 5}
{"name": "Chebyshev.primeCounting_sub_theta_div_log_isBigO", "kind": "theorem", "module": "Mathlib.NumberTheory.Chebyshev", "is_tactic_proof": true, "tactics": ["apply", "filter_upwards", "rw", "simp"], "tactic_count": 4}
{"name": "Chebyshev.eventually_primeCounting_le", "kind": "theorem", "module": "Mathlib.NumberTheory.Chebyshev", "is_tactic_proof": true, "tactics": ["have", "filter_upwards", "rw", "have", "rw", "grw", "grind"], "tactic_count": 7}
{"name": "AbsoluteValue.exists_partition_int", "kind": "theorem", "module": "Mathlib.NumberTheory.ClassNumber.AdmissibleAbs", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "exact", "have", "floor_nonneg.mpr", "refine", "rw", "apply", "gcongr", "rw", "exact", "intro", "have", "congr_arg", "rw", "have", "rw", "rwa"], "tactic_count": 19}
{"name": "AbsoluteValue.absIsAdmissible", "kind": "definition", "module": "Mathlib.NumberTheory.ClassNumber.AdmissibleAbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AbsoluteValue.instInhabitedIsAdmissibleIntAbs", "kind": "instance", "module": "Mathlib.NumberTheory.ClassNumber.AdmissibleAbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.ClassNumber.AdmissibleAbsoluteValue.0.term_≺_", "kind": "definition", "module": "Mathlib.NumberTheory.ClassNumber.AdmissibleAbsoluteValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "_private.Mathlib.NumberTheory.ClassNumber.AdmissibleAbsoluteValue.0._aux_Mathlib_NumberTheory_ClassNumber_AdmissibleAbsoluteValue___unexpand_EuclideanDomain_r_1", "kind": "definition", "module": "Mathlib.NumberTheory.ClassNumber.AdmissibleAbsoluteValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AbsoluteValue.IsAdmissible.exists_partition", "kind": "theorem", "module": "Mathlib.NumberTheory.ClassNumber.AdmissibleAbsoluteValue", "is_tactic_proof": true, "tactics": ["rcases", "obtain", "refine", "convert"], "tactic_count": 4}
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{"name": "AbsoluteValue.IsAdmissible.exists_approx", "kind": "theorem", "module": "Mathlib.NumberTheory.ClassNumber.AdmissibleAbsoluteValue", "is_tactic_proof": true, "tactics": ["let", "obtain", "refine", "convert"], "tactic_count": 4}
{"name": "Polynomial.exists_eq_polynomial", "kind": "theorem", "module": "Mathlib.NumberTheory.ClassNumber.AdmissibleCardPowDegree", "is_tactic_proof": true, "tactics": ["set", "have", "simpa", "lt_of_le_of_lt", "obtain", "use", "ext", "by_cases", "rw", "apply", "exact"], "tactic_count": 11}
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{"name": "Polynomial.cardPowDegree_anti_archimedean", "kind": "theorem", "module": "Mathlib.NumberTheory.ClassNumber.AdmissibleCardPowDegree", "is_tactic_proof": true, "tactics": ["have", "by_cases", "rwa", "by_cases", "rwa", "by_cases", "rwa", "rw", "refine", "rw", "have", "simp", "refine", "rw", "degree_eq_natDegree", "convert", "exact"], "tactic_count": 17}
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{"name": "Polynomial.cardPowDegreeIsAdmissible", "kind": "definition", "module": "Mathlib.NumberTheory.ClassNumber.AdmissibleCardPowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClassGroup.normBound", "kind": "definition", "module": "Mathlib.NumberTheory.ClassNumber.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClassGroup.normBound_pos", "kind": "theorem", "module": "Mathlib.NumberTheory.ClassNumber.Finite", "is_tactic_proof": false, "tactics": ["obtain", "by_contra", "obtain", "apply", "apply", "ext", "simp", "simp", "apply", "refine", "refine", "exact"], "tactic_count": 12}
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{"name": "ClassGroup.exists_min", "kind": "theorem", "module": "Mathlib.NumberTheory.ClassNumber.Finite", "is_tactic_proof": false, "tactics": ["obtain", "use", "rintro", "apply", "obtain", "exact", "refine", "intro", "contrapose", "exact"], "tactic_count": 10}
{"name": "ClassGroup.cardM", "kind": "definition", "module": "Mathlib.NumberTheory.ClassNumber.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClassGroup.distinctElems", "kind": "definition", "module": "Mathlib.NumberTheory.ClassNumber.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClassGroup.finsetApprox", "kind": "definition", "module": "Mathlib.NumberTheory.ClassNumber.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClassGroup.finsetApprox.zero_notMem", "kind": "theorem", "module": "Mathlib.NumberTheory.ClassNumber.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClassGroup.mem_finsetApprox", "kind": "theorem", "module": "Mathlib.NumberTheory.ClassNumber.Finite", "is_tactic_proof": true, "tactics": ["simp", "constructor", "rintro", "refine", "rintro", "simp", "rintro", "refine", "rw", "exact"], "tactic_count": 10}
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{"name": "ClassGroup.prod_finsetApprox_ne_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.ClassNumber.Finite", "is_tactic_proof": true, "tactics": ["refine", "simp", "rintro", "exact"], "tactic_count": 4}
{"name": "ClassGroup.ne_bot_of_prod_finsetApprox_mem", "kind": "theorem", "module": "Mathlib.NumberTheory.ClassNumber.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClassGroup.exists_mk0_eq_mk0", "kind": "theorem", "module": "Mathlib.NumberTheory.ClassNumber.Finite", "is_tactic_proof": true, "tactics": ["set", "have", "obtain", "suffices", "obtain", "refine", "rw", "rintro", "rw", "exact", "rw", "exact", "rw", "apply", "swap", "rw", "apply", "rw", "exact", "rw", "intro", "rw", "obtain", "apply", "simp", "rw", "refine", "exact"], "tactic_count": 28}
{"name": "ClassGroup.mkMMem", "kind": "definition", "module": "Mathlib.NumberTheory.ClassNumber.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClassGroup.mkMMem_surjective", "kind": "theorem", "module": "Mathlib.NumberTheory.ClassNumber.Finite", "is_tactic_proof": true, "tactics": ["intro", "obtain", "obtain", "exact"], "tactic_count": 4}
{"name": "ClassGroup.fintypeOfAdmissibleOfAlgebraic", "kind": "definition", "module": "Mathlib.NumberTheory.ClassNumber.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClassGroup.fintypeOfAdmissibleOfFinite", "kind": "definition", "module": "Mathlib.NumberTheory.ClassNumber.Finite", "is_tactic_proof": true, "tactics": ["letI", "letI", "letI", "choose", "have", "apply", "simp", "apply", "obtain", "let", "rw", "exact", "exact", "let", "have", "exact"], "tactic_count": 16}
{"name": "FunctionField.RingOfIntegers.instFintypeClassGroupSubtypeMemSubalgebraPolynomialRingOfIntegers", "kind": "instance", "module": "Mathlib.NumberTheory.ClassNumber.FunctionField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FunctionField.classNumber", "kind": "definition", "module": "Mathlib.NumberTheory.ClassNumber.FunctionField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FunctionField.classNumber_eq_one_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.ClassNumber.FunctionField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCyclotomicExtension.iff_adjoin_eq_top", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCyclotomicExtension.iff_singleton", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsCyclotomicExtension.instSubsingleton", "kind": "instance", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCyclotomicExtension.eq_self_sdiff_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsCyclotomicExtension.singleton_one", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCyclotomicExtension.singleton_zero_of_bot_eq_top", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCyclotomicExtension.isCyclotomicExtension_zero_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "IsCyclotomicExtension.trans", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["refine", "intro", "rcases", "obtain", "refine", "exact", "exact", "refine", "adjoin_induction", "let", "have", "rw", "refine", "obtain", "exact"], "tactic_count": 15}
{"name": "IsCyclotomicExtension.subsingleton_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["have", "refine", "refine", "obtain", "exact", "refine", "have", "exact"], "tactic_count": 8}
{"name": "IsCyclotomicExtension.union_right", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": ["have", "refine", "rintro", "left", "right", "rintro", "exact", "exact", "refine", "replace", "rwa"], "tactic_count": 11}
{"name": "IsCyclotomicExtension.union_left", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["refine", "obtain", "refine", "rwa", "convert", "rw", "norm_cast"], "tactic_count": 7}
{"name": "IsCyclotomicExtension.union_of_isPrimitiveRoot", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "rwa", "rw", "refine", "obtain", "exact", "use", "rw", "exact"], "tactic_count": 9}
{"name": "IsCyclotomicExtension.of_union_of_dvd", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "obtain", "exact", "obtain", "obtain", "refine", "have", "have", "rwa", "refine", "rw", "refine", "simp", "obtain", "exact"], "tactic_count": 16}
{"name": "IsCyclotomicExtension.iff_union_of_dvd", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["refine", "exact", "rw", "refine", "simp", "obtain", "obtain", "exact", "exact"], "tactic_count": 9}
{"name": "IsCyclotomicExtension.iff_union_singleton_one", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "rw", "empty_union,", "refine", "refine", "simpa", "refine", "simp"], "tactic_count": 9}
{"name": "IsCyclotomicExtension.singleton_one_of_bot_eq_top", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "IsCyclotomicExtension.singleton_one_of_algebraMap_bijective", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCyclotomicExtension.equiv", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["letI", "haveI", "haveI", "exact"], "tactic_count": 4}
{"name": "IsCyclotomicExtension.neZero_of_mem", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCyclotomicExtension.neZero_of_mem'", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCyclotomicExtension.neZero", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCyclotomicExtension.neZero'", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCyclotomicExtension.integral", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Algebra.isCyclotomicExtension_adjoin_of_exists_isPrimitiveRoot", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCyclotomicExtension.algEquiv_eq_of_apply_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["ext", "have", "induction", "mem", "obtain", "obtain", "have", "obtain", "simp", "algebraMap", "add", "mul"], "tactic_count": 12}
{"name": "IsCyclotomicExtension.isMulCommutative", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["refine", "obtain", "use", "simp", "have", "obtain", "obtain", "simp"], "tactic_count": 8}
{"name": "IsCyclotomicExtension.finite_of_singleton", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["classical", "rw", "refine", "simp", "have", "rw", "exact", "simp", "exact"], "tactic_count": 9}
{"name": "IsCyclotomicExtension.finite", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["rw", "induction", "empty", "refine", "simp", "by_cases", "have", "rw", "exact", "have", "union_left", "have", "have", "rw", "let", "have", "exact", "exact"], "tactic_count": 18}
{"name": "IsCyclotomicExtension.numberField", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCyclotomicExtension.finiteDimensional", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCyclotomicExtension.adjoin_roots_cyclotomic_eq_adjoin_nth_roots", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["simp", "refine", "rw", "simp", "rw", "refine", "rw", "exact", "simp", "obtain", "refine", "rw", "exact"], "tactic_count": 13}
{"name": "IsCyclotomicExtension.adjoin_roots_cyclotomic_eq_adjoin_root_cyclotomic", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["refine", "suffices", "obtain", "exact", "refine", "refine", "rw", "exact", "simp", "simpa"], "tactic_count": 10}
{"name": "IsCyclotomicExtension.adjoin_primitive_root_eq_top", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["classical", "rw", "rw", "exact"], "tactic_count": 4}
{"name": "IsPrimitiveRoot.adjoin_isCyclotomicExtension", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimitiveRoot.intermediateField_adjoin_isCyclotomicExtension", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["change", "rw", "exact"], "tactic_count": 3}
{"name": "IsCyclotomicExtension.splits_X_pow_sub_one", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["rw", "obtain", "exact"], "tactic_count": 3}
{"name": "IsCyclotomicExtension.splits_cyclotomic", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": ["refine", "use", "rw"], "tactic_count": 3}
{"name": "IntermediateField.isCyclotomicExtension_adjoin_of_exists_isPrimitiveRoot", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": ["have", "rintro", "exact", "change", "rw", "exact"], "tactic_count": 6}
{"name": "IsCyclotomicExtension.isSeparable", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "rw", "rintro", "have", "have", "exact"], "tactic_count": 8}
{"name": "IsCyclotomicExtension.nonempty_algEquiv_adjoin_of_isSepClosed", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["have", "let", "refine", "rintro", "let", "have", "ext", "simp", "constructor", "rintro", "rintro", "rw", "obtain", "induction", "mem", "obtain", "apply", "use", "rw", "congr", "apply_fun", "simpa", "algebraMap", "convert", "exact", "add", "convert", "exact", "mul", "convert", "exact", "rw", "rintro", "have", "obtain", "obtain", "exact"], "tactic_count": 37}
{"name": "IsCyclotomicExtension.isGalois", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["rw", "use", "obtain", "rw", "intro", "rw", "obtain", "rw", "induction", "mem", "obtain", "apply", "use", "rw", "algebraMap", "convert", "exact", "add", "rw", "exact", "mul", "rw", "exact", "inv", "rw", "exact"], "tactic_count": 26}
{"name": "IsCyclotomicExtension.isAbelianGalois", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCyclotomicExtension.algEquiv", "kind": "definition", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCyclotomicExtension.nonempty_algEquiv_adjoin_of_exists_isPrimitiveRoot", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCyclotomicExtension.isSplittingField_X_pow_sub_one", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCyclotomicExtension.splitting_field_cyclotomic", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CyclotomicField", "kind": "definition", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CyclotomicField.instField", "kind": "instance", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["delta"], "tactic_count": 1}
{"name": "CyclotomicField.algebra", "kind": "instance", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["delta"], "tactic_count": 1}
{"name": "CyclotomicField.instInhabited", "kind": "instance", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["delta"], "tactic_count": 1}
{"name": "CyclotomicField.instCharZero", "kind": "instance", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CyclotomicField.isCyclotomicExtension", "kind": "instance", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["have", "letI", "have", "obtain", "rw", "refine", "simp", "exact", "rw", "exact"], "tactic_count": 10}
{"name": "CyclotomicField.instIsCyclotomicExtensionSingletonNatSetOfNat", "kind": "instance", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CyclotomicField.instIsCyclotomicExtensionSingletonNatSetOfCharZero", "kind": "instance", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CyclotomicField.instNumberField", "kind": "instance", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CyclotomicField.algebraBase", "kind": "instance", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_example", "kind": "example", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsScalarTowerCyclotomicField", "kind": "instance", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsTorsionFreeCyclotomicFieldOfIsDomainOfIsFractionRing", "kind": "instance", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CyclotomicRing", "kind": "definition", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CyclotomicRing.instCommRing", "kind": "instance", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["delta"], "tactic_count": 1}
{"name": "CyclotomicRing.instIsDomain", "kind": "instance", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["delta"], "tactic_count": 1}
{"name": "CyclotomicRing.instInhabited", "kind": "instance", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["delta"], "tactic_count": 1}
{"name": "CyclotomicRing.algebraBase", "kind": "instance", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CyclotomicRing._example", "kind": "example", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CyclotomicRing.instIsTorsionFreeOfIsDomainOfIsFractionRing", "kind": "instance", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CyclotomicRing.algebraBase_injective", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CyclotomicRing.instAlgebraCyclotomicField", "kind": "instance", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CyclotomicRing.adjoin_algebra_injective", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CyclotomicRing.instIsTorsionFreeCyclotomicField", "kind": "instance", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CyclotomicRing.instIsScalarTowerCyclotomicField", "kind": "instance", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CyclotomicRing.isCyclotomicExtension", "kind": "instance", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CyclotomicRing.instIsFractionRingCyclotomicFieldOfIsDomainOfNeZeroCast", "kind": "instance", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CyclotomicRing.eq_adjoin_primitive_root", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "IsSepClosed.isCyclotomicExtension", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["refine", "have", "obtain", "exact"], "tactic_count": 4}
{"name": "IsSepClosedOfCharZero.isCyclotomicExtension", "kind": "instance", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCyclotomicExtension.mem_of_pow_eq_one", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["obtain", "replace", "have", "obtain", "rw", "exact"], "tactic_count": 6}
{"name": "isCyclotomicExtension_iff_eq_adjoin", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["refine", "have", "rw", "congr", "simp", "forall_exists_index,", "exact"], "tactic_count": 7}
{"name": "isCyclotomicExtension_singleton_iff_eq_adjoin", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp", "suffices", "apply", "refine", "obtain", "exact", "exact", "simpa"], "tactic_count": 9}
{"name": "IsCyclotomicExtension.eq", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": ["have", "obtain", "exact", "rw"], "tactic_count": 4}
{"name": "IsCyclotomicExtension.le_of_dvd", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": ["have", "constructor", "rintro", "exact", "obtain", "replace", "obtain", "have", "simpa", "adjoin_le"], "tactic_count": 10}
{"name": "IsCyclotomicExtension.lcm_sup", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "replace", "replace", "have", "rw", "hζ₁.adjoin_pair_eq", "have", "exact"], "tactic_count": 9}
{"name": "IntermediateField.isCyclotomicExtension_singleton_iff_eq_adjoin", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": ["rw", "adjoin_simple_toSubalgebra_of_isAlgebraic", "exact"], "tactic_count": 3}
{"name": "IntermediateField.isCyclotomicExtension_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.isCyclotomicExtension_le_of_dvd", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "IntermediateField.isCyclotomicExtension_lcm_sup", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["have", "have", "rwa"], "tactic_count": 3}
{"name": "rootsOfUnity.integer_power_of_ringEquiv", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.CyclotomicCharacter", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "rootsOfUnity.integer_power_of_ringEquiv'", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.CyclotomicCharacter", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "modularCyclotomicCharacter.aux", "kind": "definition", "module": "Mathlib.NumberTheory.Cyclotomic.CyclotomicCharacter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "modularCyclotomicCharacter.aux_spec", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.CyclotomicCharacter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "modularCyclotomicCharacter.pow_dvd_aux_pow_sub_aux_pow", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.CyclotomicCharacter", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "have", "have", "have", "have", "simp", "rw", "simp", "rw", "conv_lhs", "rwa"], "tactic_count": 12}
{"name": "modularCyclotomicCharacter.toFun", "kind": "definition", "module": "Mathlib.NumberTheory.Cyclotomic.CyclotomicCharacter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.Cyclotomic.CyclotomicCharacter.0.modularCyclotomicCharacter.termχ₀", "kind": "definition", "module": "Mathlib.NumberTheory.Cyclotomic.CyclotomicCharacter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.Cyclotomic.CyclotomicCharacter.0.modularCyclotomicCharacter._aux_Mathlib_NumberTheory_Cyclotomic_CyclotomicCharacter___macroRules__private_Mathlib_NumberTheory_Cyclotomic_CyclotomicCharacter_0_modularCyclotomicCharacter_termχ₀_1", "kind": "definition", "module": "Mathlib.NumberTheory.Cyclotomic.CyclotomicCharacter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.Cyclotomic.CyclotomicCharacter.0.modularCyclotomicCharacter._aux_Mathlib_NumberTheory_Cyclotomic_CyclotomicCharacter___unexpand_modularCyclotomicCharacter_toFun_1", "kind": "definition", "module": "Mathlib.NumberTheory.Cyclotomic.CyclotomicCharacter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "modularCyclotomicCharacter.toFun_spec", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.CyclotomicCharacter", "is_tactic_proof": false, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "modularCyclotomicCharacter.toFun_spec'", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.CyclotomicCharacter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "modularCyclotomicCharacter.toFun_spec''", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.CyclotomicCharacter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "modularCyclotomicCharacter.toFun_unique", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.CyclotomicCharacter", "is_tactic_proof": true, "tactics": ["apply", "specialize", "suffices", "rw"], "tactic_count": 4}
{"name": "modularCyclotomicCharacter.toFun_unique'", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.CyclotomicCharacter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "modularCyclotomicCharacter.id", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.CyclotomicCharacter", "is_tactic_proof": true, "tactics": ["refine", "have", "obtain", "have", "simp", "have", "obtain", "simp"], "tactic_count": 8}
{"name": "modularCyclotomicCharacter.comp", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.CyclotomicCharacter", "is_tactic_proof": true, "tactics": ["refine", "change", "rw", "congr", "norm_cast", "simp"], "tactic_count": 6}
{"name": "modularCyclotomicCharacter'", "kind": "definition", "module": "Mathlib.NumberTheory.Cyclotomic.CyclotomicCharacter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "modularCyclotomicCharacter'.spec'", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.CyclotomicCharacter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "modularCyclotomicCharacter'.unique'", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.CyclotomicCharacter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "modularCyclotomicCharacter", "kind": "definition", "module": "Mathlib.NumberTheory.Cyclotomic.CyclotomicCharacter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "modularCyclotomicCharacter.spec", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.CyclotomicCharacter", "is_tactic_proof": true, "tactics": ["rw", "congr", "exact"], "tactic_count": 3}
{"name": "modularCyclotomicCharacter.unique", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.CyclotomicCharacter", "is_tactic_proof": true, "tactics": ["change", "rw"], "tactic_count": 2}
{"name": "IsPrimitiveRoot.autToPow_eq_modularCyclotomicCharacter", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.CyclotomicCharacter", "is_tactic_proof": true, "tactics": ["ext", "apply", "apply", "simpa", "modularCyclotomicCharacter.toFun_spec"], "tactic_count": 5}
{"name": "cyclotomicCharacter.toFun", "kind": "definition", "module": "Mathlib.NumberTheory.Cyclotomic.CyclotomicCharacter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.Cyclotomic.CyclotomicCharacter.0.cyclotomicCharacter.termχ", "kind": "definition", "module": "Mathlib.NumberTheory.Cyclotomic.CyclotomicCharacter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.Cyclotomic.CyclotomicCharacter.0.cyclotomicCharacter._aux_Mathlib_NumberTheory_Cyclotomic_CyclotomicCharacter___macroRules__private_Mathlib_NumberTheory_Cyclotomic_CyclotomicCharacter_0_cyclotomicCharacter_termχ_1", "kind": "definition", "module": "Mathlib.NumberTheory.Cyclotomic.CyclotomicCharacter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.Cyclotomic.CyclotomicCharacter.0.cyclotomicCharacter._aux_Mathlib_NumberTheory_Cyclotomic_CyclotomicCharacter___unexpand_cyclotomicCharacter_toFun_1", "kind": "definition", "module": "Mathlib.NumberTheory.Cyclotomic.CyclotomicCharacter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cyclotomicCharacter.toFun_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.CyclotomicCharacter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cyclotomicCharacter.toZModPow_toFun", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.CyclotomicCharacter", "is_tactic_proof": true, "tactics": ["rw", "refine", "n).trans", "simp"], "tactic_count": 4}
{"name": "cyclotomicCharacter.toFun_spec", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.CyclotomicCharacter", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "cyclotomicCharacter", "kind": "definition", "module": "Mathlib.NumberTheory.Cyclotomic.CyclotomicCharacter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cyclotomicCharacter.spec", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.CyclotomicCharacter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cyclotomicCharacter.toZModPow", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.CyclotomicCharacter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cyclotomicCharacter.continuous", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.CyclotomicCharacter", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "exact", "haveI", "choose", "refine", "apply", "rw", "intro", "obtain", "obtain", "exact", "refine", "exact", "intro", "refine", "dsimp", "rw", "map_one,", "apply", "intro", "obtain", "rw", "exact", "exact"], "tactic_count": 25}
{"name": "IsPrimitiveRoot.discr_zeta_eq_discr_zeta_sub_one", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.Discriminant", "is_tactic_proof": true, "tactics": ["haveI", "have", "have", "refine", "discr_eq_discr_of_toMatrix_coeff_isIntegral", "toMatrix_isIntegral", "exact", "refine", "exact", "refine", "exact"], "tactic_count": 11}
{"name": "IsCyclotomicExtension.discr_prime_pow_ne_two", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.Discriminant", "is_tactic_proof": true, "tactics": ["haveI", "haveI", "haveI", "rw", "totient_prime_pow", "have", "rintro", "exact", "congr", "rcases", "rcases", "rw", "rw", "cases", "simp", "simp_rw", "have", "obtain", "rw", "mul_right_comm,", "refine", "rw", "exact", "have", "rw", "derivative_one,", "replace", "simp", "aeval_X_pow]", "replace", "have", "by_cases", "exact", "exact", "rw", "succ_eq_add_one,", "rw", "pow_mul,", "have", "rw", "replace", "simp", "have", "rw", "exact"], "tactic_count": 45}
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{"name": "IsCyclotomicExtension.autEquivPow", "kind": "definition", "module": "Mathlib.NumberTheory.Cyclotomic.Gal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCyclotomicExtension.fromZetaAut", "kind": "definition", "module": "Mathlib.NumberTheory.Cyclotomic.Gal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCyclotomicExtension.fromZetaAut_spec", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.Gal", "is_tactic_proof": true, "tactics": ["simp_rw", "generalize_proofs", "nth_rewrite", "rw", "convert", "exact"], "tactic_count": 6}
{"name": "galCyclotomicEquivUnitsZMod", "kind": "definition", "module": "Mathlib.NumberTheory.Cyclotomic.Gal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "galXPowEquivUnitsZMod", "kind": "definition", "module": "Mathlib.NumberTheory.Cyclotomic.Gal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCyclotomicExtension.zeta", "kind": "definition", "module": "Mathlib.NumberTheory.Cyclotomic.PrimitiveRoots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCyclotomicExtension.zeta_spec", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.PrimitiveRoots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "IsCyclotomicExtension.zeta_isRoot", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.PrimitiveRoots", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "IsCyclotomicExtension.zeta_pow", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.PrimitiveRoots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimitiveRoot.powerBasis", "kind": "definition", "module": "Mathlib.NumberTheory.Cyclotomic.PrimitiveRoots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimitiveRoot.powerBasis_gen_mem_adjoin_zeta_sub_one", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.PrimitiveRoots", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsPrimitiveRoot.subOnePowerBasis", "kind": "definition", "module": "Mathlib.NumberTheory.Cyclotomic.PrimitiveRoots", "is_tactic_proof": true, "tactics": ["apply", "exact"], "tactic_count": 2}
{"name": "IsPrimitiveRoot.embeddingsEquivPrimitiveRoots", "kind": "definition", "module": "Mathlib.NumberTheory.Cyclotomic.PrimitiveRoots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimitiveRoot.embeddingsEquivPrimitiveRoots_apply_coe", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.PrimitiveRoots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCyclotomicExtension.finrank", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.PrimitiveRoots", "is_tactic_proof": true, "tactics": ["haveI", "rw"], "tactic_count": 2}
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{"name": "IsPrimitiveRoot.dvd_of_isCyclotomicExtension", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.PrimitiveRoots", "is_tactic_proof": true, "tactics": ["have", "have", "have", "rw", "rcases", "have", "rw", "replace", "have", "refine", "simp", "replace", "rcases", "rw", "rw", "exact", "rw", "simpa"], "tactic_count": 18}
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{"name": "IsPrimitiveRoot.norm_of_cyclotomic_irreducible", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.PrimitiveRoots", "is_tactic_proof": true, "tactics": ["split_ifs", "subst", "rw", "norm_cast", "exact"], "tactic_count": 5}
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{"name": "IsPrimitiveRoot.sub_one_norm_isPrimePow", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.PrimitiveRoots", "is_tactic_proof": true, "tactics": ["have", "let", "rw", "nth_rw", "obtain", "exists_eq_succ_of_ne_zero", "mem_primeFactors_iff_mem_primeFactorsList.2", "simp"], "tactic_count": 8}
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{"name": "IsCyclotomicExtension.norm_zeta_sub_one_of_isPrimePow", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.PrimitiveRoots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCyclotomicExtension.norm_zeta_pow_sub_one_of_prime_pow_ne_two", "kind": "theorem", "module": "Mathlib.NumberTheory.Cyclotomic.PrimitiveRoots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "_private.Mathlib.NumberTheory.DiophantineApproximation.Basic.0.Real.aux₂", "kind": "theorem", "module": "Mathlib.NumberTheory.DiophantineApproximation.Basic", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "have", "rw", "mul_assoc,", "have", "refine", "rw", "replace", "rw", "exact", "mod_cast", "h.trans_le", "have", "refine", "replace", "rw", "add_comm", "have", "flip", "flip", "rw", "exact", "have", "refine", "rw", "simp", "rcases", "linarith"], "tactic_count": 29}
{"name": "_private.Mathlib.NumberTheory.DiophantineApproximation.Basic.0.Real.aux₃", "kind": "theorem", "module": "Mathlib.NumberTheory.DiophantineApproximation.Basic", "is_tactic_proof": true, "tactics": ["obtain", "have", "set", "have", "rw", "replace", "obtain", "obtain", "have", "replace", "have", "rwa", "have", "replace", "have", "rw", "mul_lt_mul_iff_right₀", "refine", "rw", "exact", "calc", "gcongr"], "tactic_count": 22}
{"name": "_private.Mathlib.NumberTheory.DiophantineApproximation.Basic.0.Real.invariant", "kind": "theorem", "module": "Mathlib.NumberTheory.DiophantineApproximation.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact", "obtain", "have", "have", "have", "rw", "rwa", "lt_inv_comm₀"], "tactic_count": 10}
{"name": "Real.exists_rat_eq_convergent'", "kind": "theorem", "module": "Mathlib.NumberTheory.DiophantineApproximation.Basic", "is_tactic_proof": false, "tactics": ["induction", "h", "rcases", "replace", "simp", "exact", "rw", "obtain", "rcases", "use", "rw", "convert", "replace", "have", "rw", "exact", "rcases", "rw", "exact", "have", "rw", "inv_lt_comm₀", "refine", "rw", "convert", "rw", "norm_num", "use", "simp", "obtain", "have", "have", "have", "obtain", "use", "rw", "cast_natCast,"], "tactic_count": 37}
{"name": "Real.exists_rat_eq_convergent", "kind": "theorem", "module": "Mathlib.NumberTheory.DiophantineApproximation.Basic", "is_tactic_proof": true, "tactics": ["refine", "exact", "rw", "simpa", "obtain", "replace", "have", "rw", "rw", "exact"], "tactic_count": 10}
{"name": "Real.convs_eq_convergent", "kind": "theorem", "module": "Mathlib.NumberTheory.DiophantineApproximation.ContinuedFractions", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Real.exists_convs_eq_rat", "kind": "theorem", "module": "Mathlib.NumberTheory.DiophantineApproximation.ContinuedFractions", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "DirichletCharacter", "kind": "abbrev", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirichletCharacter.toUnitHom_eq_char'", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DirichletCharacter.toUnitHom_inj", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DirichletCharacter.eval_modulus_sub", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DirichletCharacter.changeLevel", "kind": "definition", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirichletCharacter.changeLevel_def", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirichletCharacter.changeLevel_toUnitHom", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DirichletCharacter.changeLevel_injective", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": true, "tactics": ["intro", "ext1", "obtain", "rw", "simpa"], "tactic_count": 5}
{"name": "DirichletCharacter.changeLevel_eq_one_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirichletCharacter.changeLevel_self", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DirichletCharacter.changeLevel_self_toUnitHom", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "DirichletCharacter.changeLevel_trans", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DirichletCharacter.changeLevel_eq_cast_of_dvd", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DirichletCharacter.FactorsThrough", "kind": "definition", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirichletCharacter.changeLevel_factorsThrough", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirichletCharacter.FactorsThrough.dvd", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirichletCharacter.FactorsThrough.χ₀", "kind": "definition", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirichletCharacter.FactorsThrough.eq_changeLevel", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirichletCharacter.FactorsThrough.existsUnique", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "DirichletCharacter.FactorsThrough.same_level", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirichletCharacter.factorsThrough_iff_ker_unitsMap", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "let", "have", "refine", "simp_rw"], "tactic_count": 6}
{"name": "DirichletCharacter.factorsThrough_gcd", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "obtain", "suffices", "obtain", "refine", "simpa", "rwa", "rwa", "have", "refine", "exact", "exact", "have", "simp", "rw", "have", "simp", "rw"], "tactic_count": 19}
{"name": "DirichletCharacter.level_one", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "DirichletCharacter.level_one'", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": true, "tactics": ["subst", "exact"], "tactic_count": 2}
{"name": "DirichletCharacter.instSubsingletonOfNatNat", "kind": "instance", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": true, "tactics": ["refine", "simp"], "tactic_count": 2}
{"name": "DirichletCharacter.instUniqueOfNatNat", "kind": "instance", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirichletCharacter.map_zero'", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirichletCharacter.changeLevel_one", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DirichletCharacter.factorsThrough_one_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": true, "tactics": ["refine", "rwa"], "tactic_count": 2}
{"name": "DirichletCharacter.conductorSet", "kind": "definition", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirichletCharacter.mem_conductorSet_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirichletCharacter.level_mem_conductorSet", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirichletCharacter.mem_conductorSet_dvd", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirichletCharacter.zero_ne_mem_conductorSet", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirichletCharacter.conductor", "kind": "definition", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirichletCharacter.conductor_mem_conductorSet", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirichletCharacter.conductor_dvd_level", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirichletCharacter.factorsThrough_conductor", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirichletCharacter.conductor_ne_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirichletCharacter.conductor_one", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": false, "tactics": ["suffices", "have", "exact", "exact"], "tactic_count": 4}
{"name": "DirichletCharacter.eq_one_iff_conductor_eq_one", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact"], "tactic_count": 3}
{"name": "DirichletCharacter.conductor_eq_zero_iff_level_eq_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": true, "tactics": ["refine", "rintro", "exact"], "tactic_count": 3}
{"name": "DirichletCharacter.conductor_le_conductor_mem_conductorSet", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": false, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "DirichletCharacter.IsPrimitive", "kind": "definition", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirichletCharacter.isPrimitive_def", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirichletCharacter.isPrimitive_one_level_one", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirichletCharacter.isPrimitive_one_level_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirichletCharacter.conductor_one_dvd", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "DirichletCharacter.primitiveCharacter", "kind": "definition", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirichletCharacter.changeLevel_primitiveCharacter", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirichletCharacter.primitiveCharacter_isPrimitive", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "convert", "exact", "le_antisymm", "conductor_le_conductor_mem_conductorSet"], "tactic_count": 6}
{"name": "DirichletCharacter.primitiveCharacter_one", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "DirichletCharacter.conductor_dvd_of_mem_conductorSet", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": false, "tactics": ["have", "contrapose", "exact", "suffices", "have", "contrapose", "refine", "exact", "obtain", "suffices", "obtain", "refine", "rw", "have", "apply", "rw", "changeLevel_trans"], "tactic_count": 17}
{"name": "DirichletCharacter.mul", "kind": "definition", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirichletCharacter.primitive_mul", "kind": "definition", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirichletCharacter.mul_def", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirichletCharacter.primitive_mul_isPrimitive", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirichletCharacter.Odd", "kind": "definition", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirichletCharacter.Even", "kind": "definition", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirichletCharacter.even_or_odd", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": true, "tactics": ["suffices", "rw"], "tactic_count": 2}
{"name": "DirichletCharacter.not_even_and_odd", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": true, "tactics": ["rintro", "simp"], "tactic_count": 2}
{"name": "DirichletCharacter.Even.not_odd", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirichletCharacter.Odd.not_even", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirichletCharacter.Odd.toUnitHom_eval_neg_one", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "DirichletCharacter.Even.toUnitHom_eval_neg_one", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "DirichletCharacter.Odd.eval_neg", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": true, "tactics": ["rw", "rw", "simp"], "tactic_count": 3}
{"name": "DirichletCharacter.Even.eval_neg", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": true, "tactics": ["rw", "rw", "simp"], "tactic_count": 3}
{"name": "DirichletCharacter.Even.to_fun", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirichletCharacter.Odd.to_fun", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirichletCharacter.unit_norm_eq_one", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.Bounds", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "DirichletCharacter.norm_le_one", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.Bounds", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "rw", "exact"], "tactic_count": 4}
{"name": "gaussSum_aux_of_mulShift", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.GaussSum", "is_tactic_proof": true, "tactics": ["suffices", "rw", "rsuffices", "have", "simp", "rw", "ext1", "simpa", "rw", "have", "rwa"], "tactic_count": 11}
{"name": "factorsThrough_of_gaussSum_ne_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.GaussSum", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "simpa"], "tactic_count": 4}
{"name": "gaussSum_eq_zero_of_isPrimitive_of_not_isPrimitive", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.GaussSum", "is_tactic_proof": true, "tactics": ["contrapose", "rcases", "have", "exact"], "tactic_count": 4}
{"name": "gaussSum_mulShift_of_isPrimitive", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.GaussSum", "is_tactic_proof": true, "tactics": ["by_cases", "conv_rhs", "rw", "rw", "exact"], "tactic_count": 5}
{"name": "DirichletCharacter.fintype", "kind": "instance", "module": "Mathlib.NumberTheory.DirichletCharacter.Orthogonality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirichletCharacter.mulEquiv_units", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.Orthogonality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirichletCharacter.card_eq_totient_of_hasEnoughRootsOfUnity", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.Orthogonality", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "DirichletCharacter.exists_apply_ne_one_of_hasEnoughRootsOfUnity", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.Orthogonality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirichletCharacter.sum_characters_eq_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.Orthogonality", "is_tactic_proof": true, "tactics": ["obtain", "refine", "simp", "exact"], "tactic_count": 4}
{"name": "DirichletCharacter.sum_characters_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.Orthogonality", "is_tactic_proof": true, "tactics": ["split_ifs", "simpa", "exact"], "tactic_count": 3}
{"name": "DirichletCharacter.sum_char_inv_mul_char_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.DirichletCharacter.Orthogonality", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.divisors", "kind": "definition", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.properDivisors", "kind": "definition", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.divisorsAntidiagonal", "kind": "definition", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.divisorsAntidiagonalList", "kind": "definition", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.filter_dvd_eq_divisors", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["ext", "simp", "exact"], "tactic_count": 3}
{"name": "Nat.filter_dvd_eq_properDivisors", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["ext", "simp", "exact"], "tactic_count": 3}
{"name": "Nat.self_notMem_properDivisors", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.mem_properDivisors", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["rcases", "simp"], "tactic_count": 2}
{"name": "Nat.insert_self_properDivisors", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["rw", "if_pos"], "tactic_count": 2}
{"name": "Nat.cons_self_properDivisors", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.mem_divisors", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["rcases", "simp", "exact"], "tactic_count": 3}
{"name": "Nat.dvd_of_mem_divisors", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.ne_zero_of_mem_divisors", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.one_mem_divisors", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.mem_divisors_self", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.mem_divisorsAntidiagonal", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["obtain", "simp", "constructor", "rintro", "simp", "lia", "rintro", "rw", "simpa"], "tactic_count": 9}
{"name": "Nat.divisorsAntidiagonalList_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.divisorsAntidiagonalList_one", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.toFinset_divisorsAntidiagonalList", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.pairwise_divisorsAntidiagonalList_fst", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["refine", "rw", "simpa"], "tactic_count": 3}
{"name": "Nat.pairwise_divisorsAntidiagonalList_snd", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["obtain", "simp", "refine", "simp", "rintro", "rwa"], "tactic_count": 6}
{"name": "Nat.sortedLT_map_fst_divisorsAntidiagonalList", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.sortedGT_map_snd_divisorsAntidiagonalList", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.nodup_divisorsAntidiagonalList", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.val_divisorsAntidiagonal", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.mem_divisorsAntidiagonalList", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.swap_mem_divisorsAntidiagonalList", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.reverse_divisorsAntidiagonalList", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["have", "refine", "simp", "mul_comm]"], "tactic_count": 4}
{"name": "Nat.ne_zero_of_mem_divisorsAntidiagonal", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Nat.left_ne_zero_of_mem_divisorsAntidiagonal", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.right_ne_zero_of_mem_divisorsAntidiagonal", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.divisor_le", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simp", "exact"], "tactic_count": 4}
{"name": "Nat.divisors_subset_of_dvd", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.card_divisors_le_self", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.divisors_subset_properDivisors", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["apply", "intro", "exact", "lt_of_le_of_lt"], "tactic_count": 4}
{"name": "Nat.divisors_filter_dvd_of_dvd", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["ext", "simp_rw", "exact"], "tactic_count": 3}
{"name": "Nat.divisors_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Nat.properDivisors_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Nat.nonempty_divisors", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.divisors_eq_empty", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["contrapose"], "tactic_count": 1}
{"name": "Nat.properDivisors_subset_divisors", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.divisors_one", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Nat.properDivisors_one", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.pos_of_mem_divisors", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["cases", "rw", "cases", "apply"], "tactic_count": 4}
{"name": "Nat.pos_of_mem_properDivisors", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.one_mem_properDivisors_iff_one_lt", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.sup_divisors_id", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["refine", "rcases", "apply", "exact"], "tactic_count": 4}
{"name": "Nat.one_lt_of_mem_properDivisors", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.one_lt_div_of_mem_properDivisors", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["obtain", "rwa"], "tactic_count": 2}
{"name": "Nat.mem_properDivisors_iff_exists", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["refine", "exact", "rintro", "rw", "exact"], "tactic_count": 5}
{"name": "Nat.nonempty_properDivisors", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.properDivisors_eq_empty", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["contrapose"], "tactic_count": 1}
{"name": "Nat.divisorsAntidiagonal_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Nat.divisorsAntidiagonal_one", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Nat.swap_mem_divisorsAntidiagonal", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.prodMk_mem_divisorsAntidiag", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.fst_mem_divisors_of_mem_antidiagonal", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Nat.snd_mem_divisors_of_mem_antidiagonal", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Nat.map_swap_divisorsAntidiagonal", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["rw", "ext", "exact"], "tactic_count": 3}
{"name": "Nat.image_fst_divisorsAntidiagonal", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Nat.image_snd_divisorsAntidiagonal", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Nat.map_div_right_divisors", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["ext", "simp", "exists_eq_left]", "constructor", "rintro", "rw", "exact", "rintro", "exact"], "tactic_count": 9}
{"name": "Nat.map_div_left_divisors", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["apply", "ext", "rw", "simp"], "tactic_count": 4}
{"name": "Nat.sum_divisors_eq_sum_properDivisors_add_self", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rw"], "tactic_count": 3}
{"name": "Nat.Perfect", "kind": "definition", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.perfect_iff_sum_properDivisors", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.perfect_iff_sum_divisors_eq_two_mul", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["rw", "constructor", "rw", "apply"], "tactic_count": 4}
{"name": "Nat.mem_divisors_prime_pow", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.Prime.divisors", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "Nat.Prime.properDivisors", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["rw", "erase_insert"], "tactic_count": 2}
{"name": "Nat.divisors_prime_pow", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["ext", "rw", "simp"], "tactic_count": 3}
{"name": "Nat.divisors_injective", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.divisors_inj", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.eq_properDivisors_of_subset_of_sum_eq_sum", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["cases", "rw", "simp", "classical", "rw", "intro", "apply", "rw", "contrapose", "apply", "rw", "gcongr", "have", "simp", "apply"], "tactic_count": 15}
{"name": "Nat.sum_properDivisors_dvd", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rcases", "simp", "rw", "intro", "have", "lt_of_le_of_ne", "symm", "rw", "eq_properDivisors_of_subset_of_sum_eq_sum", "mem_properDivisors]", "exact"], "tactic_count": 13}
{"name": "Nat.Prime.prod_properDivisors", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.Prime.prod_divisors", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.properDivisors_eq_singleton_one_iff_prime", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["refine", "intro", "refine", "rw", "have", "simpa", "by_contra", "simp", "contradiction", "exact"], "tactic_count": 10}
{"name": "Nat.sum_properDivisors_eq_one_iff_prime", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["rcases", "simp", "cases", "simp", "rw", "refine", "rw", "apply", "eq_properDivisors_of_subset_of_sum_eq_sum"], "tactic_count": 9}
{"name": "Nat.mem_properDivisors_prime_pow", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["rw", "simp", "apply", "intro", "constructor", "rcases", "rw", "exact", "rcases", "rw", "simp"], "tactic_count": 11}
{"name": "Nat.properDivisors_prime_pow", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["ext", "simp", "have", "rw", "grind"], "tactic_count": 5}
{"name": "Nat.prod_properDivisors_prime_pow", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.prod_divisors_prime_pow", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.prod_divisorsAntidiagonal", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Nat.prod_divisorsAntidiagonal'", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Nat.primeFactors_eq_to_filter_divisors_prime", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Nat.primeFactors_filter_dvd_of_dvd", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Nat.image_div_divisors_eq_divisors", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "ext", "constructor", "rw", "rintro", "rw", "refine", "rw", "exact", "rw", "rintro", "exact"], "tactic_count": 13}
{"name": "Nat.prod_div_divisors", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "exact", "intro", "rw", "exact"], "tactic_count": 6}
{"name": "Nat.disjoint_divisors_filter_isPrimePow", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["simp", "rintro", "exact"], "tactic_count": 3}
{"name": "Nat.divisorsAntidiagonal_eq_prod_filter_of_le", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["ext", "rw", "simp", "constructor", "intro", "grw", "simp", "lia", "intro", "exact"], "tactic_count": 10}
{"name": "_private.Mathlib.NumberTheory.Divisors.0.Int.termNatCast", "kind": "definition", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.Divisors.0.Int._aux_Mathlib_NumberTheory_Divisors___macroRules__private_Mathlib_NumberTheory_Divisors_0_Int_termNatCast_1", "kind": "definition", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.Divisors.0.Int._aux_Mathlib_NumberTheory_Divisors___unexpand_Nat_castEmbedding_1", "kind": "definition", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.Divisors.0.Int.termNegNatCast", "kind": "definition", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.Divisors.0.Int._aux_Mathlib_NumberTheory_Divisors___macroRules__private_Mathlib_NumberTheory_Divisors_0_Int_termNegNatCast_1", "kind": "definition", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.Divisors.0.Int._aux_Mathlib_NumberTheory_Divisors___unexpand_Function_Embedding_trans_1", "kind": "definition", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.divisorsAntidiag", "kind": "definition", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.mem_divisorsAntidiag", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.divisorsAntidiag_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.divisorsAntidiagonal_one", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.divisorsAntidiagonal_two", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.divisorsAntidiagonal_three", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.divisorsAntidiagonal_four", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.prodMk_mem_divisorsAntidiag", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Int.swap_mem_divisorsAntidiag", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Int.neg_mem_divisorsAntidiag", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Int.map_prodComm_divisorsAntidiag", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Int.map_neg_divisorsAntidiag", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Int.divisorsAntidiag_neg", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Int.divisorsAntidiag_natCast", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.divisorsAntidiag_neg_natCast", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Int.divisorsAntidiag_ofNat", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.mul_mem_one_two_three_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": false, "tactics": ["simp", "not_false_eq_true,", "aesop"], "tactic_count": 3}
{"name": "Int.mul_mem_zero_one_two_three_four_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Divisors", "is_tactic_proof": false, "tactics": ["simp", "not_false_eq_true,", "aesop"], "tactic_count": 3}
{"name": "IsEllSequence", "kind": "definition", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDivSequence", "kind": "definition", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsEllDivSequence", "kind": "definition", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isEllSequence_id", "kind": "theorem", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isDivSequence_id", "kind": "theorem", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isEllDivSequence_id", "kind": "theorem", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsEllSequence.smul", "kind": "theorem", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDivSequence.smul", "kind": "theorem", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsEllDivSequence.smul", "kind": "theorem", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "preNormEDS'", "kind": "definition", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "preNormEDS'_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "preNormEDS'_one", "kind": "theorem", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "preNormEDS'_two", "kind": "theorem", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "preNormEDS'_three", "kind": "theorem", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "preNormEDS'_four", "kind": "theorem", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "preNormEDS'_even", "kind": "theorem", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "preNormEDS'_odd", "kind": "theorem", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "preNormEDS", "kind": "definition", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "preNormEDS_ofNat", "kind": "theorem", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "simp"], "tactic_count": 3}
{"name": "preNormEDS_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "preNormEDS_one", "kind": "theorem", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "preNormEDS_two", "kind": "theorem", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "preNormEDS_three", "kind": "theorem", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "preNormEDS_four", "kind": "theorem", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "preNormEDS_neg", "kind": "theorem", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "preNormEDS_even", "kind": "theorem", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": true, "tactics": ["induction", "nat", "rcases", "iterate", "simp_rw", "norm_cast", "simpa", "neg", "simp_rw", "ring1"], "tactic_count": 10}
{"name": "preNormEDS_odd", "kind": "theorem", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": true, "tactics": ["induction", "nat", "rcases", "iterate", "simp_rw", "norm_cast", "simpa", "neg", "rcases", "simp", "simp_rw", "show", "ring1"], "tactic_count": 13}
{"name": "complEDS₂", "kind": "definition", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "complEDS₂_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "complEDS₂_one", "kind": "theorem", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "complEDS₂_two", "kind": "theorem", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "complEDS₂_three", "kind": "theorem", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "complEDS₂_four", "kind": "theorem", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "complEDS₂_neg", "kind": "theorem", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": true, "tactics": ["simp_rw", "ring1"], "tactic_count": 2}
{"name": "preNormEDS_mul_complEDS₂", "kind": "theorem", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": true, "tactics": ["rw", "ring1"], "tactic_count": 2}
{"name": "normEDS", "kind": "definition", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "normEDS_ofNat", "kind": "theorem", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "normEDS_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "normEDS_one", "kind": "theorem", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "normEDS_two", "kind": "theorem", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "normEDS_three", "kind": "theorem", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "normEDS_four", "kind": "theorem", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "normEDS_neg", "kind": "theorem", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "normEDS_mul_complEDS₂", "kind": "theorem", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": true, "tactics": ["simp_rw", "if_pos"], "tactic_count": 2}
{"name": "normEDS_dvd_normEDS_two_mul", "kind": "theorem", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "complEDS₂_mul_b", "kind": "theorem", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": true, "tactics": ["induction", "nat", "k", "simp_rw", "split_ifs", "neg", "simp_rw", "ring1"], "tactic_count": 8}
{"name": "normEDS_even", "kind": "theorem", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": true, "tactics": ["rw", "ring1"], "tactic_count": 2}
{"name": "normEDS_odd", "kind": "theorem", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": false, "tactics": ["simp_rw", "split_ifs"], "tactic_count": 2}
{"name": "normEDSRec'", "kind": "definition", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "normEDSRec", "kind": "definition", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "complEDS'", "kind": "definition", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "complEDS'_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "complEDS'_one", "kind": "theorem", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "complEDS'_even", "kind": "theorem", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "complEDS'_odd", "kind": "theorem", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "complEDS", "kind": "definition", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "complEDS_ofNat", "kind": "theorem", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "simp"], "tactic_count": 3}
{"name": "complEDS_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "complEDS_one", "kind": "theorem", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "complEDS_neg", "kind": "theorem", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "complEDS_even", "kind": "theorem", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": true, "tactics": ["induction", "nat", "rcases", "simp", "norm_cast", "simpa", "neg"], "tactic_count": 7}
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{"name": "complEDSRec'", "kind": "definition", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "complEDSRec", "kind": "definition", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "map_preNormEDS'", "kind": "theorem", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": true, "tactics": ["induction", "zero", "one", "two", "three", "four", "simp", "repeat"], "tactic_count": 8}
{"name": "map_preNormEDS", "kind": "theorem", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "map_complEDS₂", "kind": "theorem", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "map_normEDS", "kind": "theorem", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "map_complEDS'", "kind": "theorem", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": true, "tactics": ["induction", "zero", "one", "simp", "repeat"], "tactic_count": 5}
{"name": "map_complEDS", "kind": "theorem", "module": "Mathlib.NumberTheory.EllipticDivisibilitySequence", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Summable.norm_lt_one", "kind": "theorem", "module": "Mathlib.NumberTheory.EulerProduct.Basic", "is_tactic_proof": true, "tactics": ["refine", "simp_rw", "exact"], "tactic_count": 3}
{"name": "_private.Mathlib.NumberTheory.EulerProduct.Basic.0.instT0Space", "kind": "theorem", "module": "Mathlib.NumberTheory.EulerProduct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EulerProduct.summable_and_hasSum_factoredNumbers_prod_filter_prime_tsum", "kind": "theorem", "module": "Mathlib.NumberTheory.EulerProduct.Basic", "is_tactic_proof": true, "tactics": ["induction", "empty", "rw", "simp", "exact", "insert", "rw", "split_ifs", "constructor", "simp", "equivProdNatFactoredNumbers_apply',", "refine", "apply", "have", "rw", "conv", "enter", "rw", "have", "apply", "ih.2", "apply", "rwa"], "tactic_count": 23}
{"name": "EulerProduct.prod_filter_prime_tsum_eq_tsum_factoredNumbers", "kind": "theorem", "module": "Mathlib.NumberTheory.EulerProduct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EulerProduct.norm_tsum_factoredNumbers_sub_tsum_lt", "kind": "theorem", "module": "Mathlib.NumberTheory.EulerProduct.Basic", "is_tactic_proof": true, "tactics": ["obtain", "simp_rw", "refine", "have", "rwa", "tsum_eq_tsum_diff_singleton"], "tactic_count": 6}
{"name": "EulerProduct.summable_and_hasSum_smoothNumbers_prod_primesBelow_tsum", "kind": "theorem", "module": "Mathlib.NumberTheory.EulerProduct.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "EulerProduct.prod_primesBelow_tsum_eq_tsum_smoothNumbers", "kind": "theorem", "module": "Mathlib.NumberTheory.EulerProduct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EulerProduct.norm_tsum_smoothNumbers_sub_tsum_lt", "kind": "theorem", "module": "Mathlib.NumberTheory.EulerProduct.Basic", "is_tactic_proof": true, "tactics": ["conv", "obtain", "refine", "exact"], "tactic_count": 4}
{"name": "EulerProduct.eulerProduct_hasProd", "kind": "theorem", "module": "Mathlib.NumberTheory.EulerProduct.Basic", "is_tactic_proof": true, "tactics": ["let", "change", "rw", "intro", "obtain", "refine", "have", "prod_mulIndicator_eq_prod_filter", "rw", "exact"], "tactic_count": 10}
{"name": "EulerProduct.eulerProduct_hasProd_mulIndicator", "kind": "theorem", "module": "Mathlib.NumberTheory.EulerProduct.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "EulerProduct.eulerProduct", "kind": "theorem", "module": "Mathlib.NumberTheory.EulerProduct.Basic", "is_tactic_proof": true, "tactics": ["have", "let", "have", "prod_mulIndicator_eq_prod_filter", "simpa"], "tactic_count": 5}
{"name": "EulerProduct.eulerProduct_tprod", "kind": "theorem", "module": "Mathlib.NumberTheory.EulerProduct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.IsMultiplicative.eulerProduct_hasProd", "kind": "theorem", "module": "Mathlib.NumberTheory.EulerProduct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.IsMultiplicative.eulerProduct", "kind": "theorem", "module": "Mathlib.NumberTheory.EulerProduct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.IsMultiplicative.eulerProduct_tprod", "kind": "theorem", "module": "Mathlib.NumberTheory.EulerProduct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EulerProduct.one_sub_inv_eq_geometric_of_summable_norm", "kind": "theorem", "module": "Mathlib.NumberTheory.EulerProduct.Basic", "is_tactic_proof": true, "tactics": ["simp", "refine", "refine", "simpa"], "tactic_count": 4}
{"name": "EulerProduct.summable_and_hasSum_factoredNumbers_prod_filter_prime_geometric", "kind": "theorem", "module": "Mathlib.NumberTheory.EulerProduct.Basic", "is_tactic_proof": true, "tactics": ["have", "have", "refine", "simp", "exact", "have", "intro", "simp", "refine", "exact", "exact"], "tactic_count": 11}
{"name": "EulerProduct.prod_filter_prime_geometric_eq_tsum_factoredNumbers", "kind": "theorem", "module": "Mathlib.NumberTheory.EulerProduct.Basic", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "EulerProduct.summable_and_hasSum_smoothNumbers_prod_primesBelow_geometric", "kind": "theorem", "module": "Mathlib.NumberTheory.EulerProduct.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "EulerProduct.prod_primesBelow_geometric_eq_tsum_smoothNumbers", "kind": "theorem", "module": "Mathlib.NumberTheory.EulerProduct.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "EulerProduct.eulerProduct_completely_multiplicative_hasProd", "kind": "theorem", "module": "Mathlib.NumberTheory.EulerProduct.Basic", "is_tactic_proof": false, "tactics": ["have", "funext", "simpa"], "tactic_count": 3}
{"name": "EulerProduct.eulerProduct_completely_multiplicative_tprod", "kind": "theorem", "module": "Mathlib.NumberTheory.EulerProduct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EulerProduct.eulerProduct_completely_multiplicative", "kind": "theorem", "module": "Mathlib.NumberTheory.EulerProduct.Basic", "is_tactic_proof": true, "tactics": ["have", "have", "have", "prod_mulIndicator_eq_prod_filter", "have", "simpa"], "tactic_count": 6}
{"name": "riemannZetaSummandHom", "kind": "definition", "module": "Mathlib.NumberTheory.EulerProduct.DirichletLSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dirichletSummandHom", "kind": "definition", "module": "Mathlib.NumberTheory.EulerProduct.DirichletLSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "summable_riemannZetaSummand", "kind": "theorem", "module": "Mathlib.NumberTheory.EulerProduct.DirichletLSeries", "is_tactic_proof": true, "tactics": ["simp", "convert", "rw"], "tactic_count": 3}
{"name": "tsum_riemannZetaSummand", "kind": "theorem", "module": "Mathlib.NumberTheory.EulerProduct.DirichletLSeries", "is_tactic_proof": true, "tactics": ["have", "rw", "simp", "one_div]"], "tactic_count": 4}
{"name": "summable_dirichletSummand", "kind": "theorem", "module": "Mathlib.NumberTheory.EulerProduct.DirichletLSeries", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "tsum_dirichletSummand", "kind": "theorem", "module": "Mathlib.NumberTheory.EulerProduct.DirichletLSeries", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "riemannZeta_eulerProduct_hasProd", "kind": "theorem", "module": "Mathlib.NumberTheory.EulerProduct.DirichletLSeries", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "riemannZeta_eulerProduct_tprod", "kind": "theorem", "module": "Mathlib.NumberTheory.EulerProduct.DirichletLSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "riemannZeta_eulerProduct", "kind": "theorem", "module": "Mathlib.NumberTheory.EulerProduct.DirichletLSeries", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "DirichletCharacter.LSeries_eulerProduct_hasProd", "kind": "theorem", "module": "Mathlib.NumberTheory.EulerProduct.DirichletLSeries", "is_tactic_proof": true, "tactics": ["rw", "convert"], "tactic_count": 2}
{"name": "DirichletCharacter.LSeries_eulerProduct_tprod", "kind": "theorem", "module": "Mathlib.NumberTheory.EulerProduct.DirichletLSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirichletCharacter.LSeries_eulerProduct", "kind": "theorem", "module": "Mathlib.NumberTheory.EulerProduct.DirichletLSeries", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "DirichletCharacter.LSeries_eulerProduct_exp_log", "kind": "theorem", "module": "Mathlib.NumberTheory.EulerProduct.DirichletLSeries", "is_tactic_proof": true, "tactics": ["let", "have", "rcases", "simp", "simp", "simpa"], "tactic_count": 6}
{"name": "ArithmeticFunction.LSeries_zeta_eulerProduct_exp_log", "kind": "theorem", "module": "Mathlib.NumberTheory.EulerProduct.DirichletLSeries", "is_tactic_proof": false, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "riemannZeta_eulerProduct_exp_log", "kind": "theorem", "module": "Mathlib.NumberTheory.EulerProduct.DirichletLSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirichletCharacter.LSeries_changeLevel", "kind": "theorem", "module": "Mathlib.NumberTheory.EulerProduct.DirichletLSeries", "is_tactic_proof": false, "tactics": ["rw", "have", "rw", "tprod_subtype", "rotate_left", "exact", "exact", "congr", "simp", "one_mul,", "by_cases", "simp", "simp", "by_cases", "simp", "have", "simp", "simp", "have", "rw", "refine", "rw", "apply_fun", "simp", "have", "have", "exact"], "tactic_count": 27}
{"name": "Summable.clog_one_sub", "kind": "theorem", "module": "Mathlib.NumberTheory.EulerProduct.ExpLog", "is_tactic_proof": false, "tactics": ["have", "have", "fun_prop", "have", "exact"], "tactic_count": 5}
{"name": "EulerProduct.exp_tsum_primes_log_eq_tsum", "kind": "theorem", "module": "Mathlib.NumberTheory.EulerProduct.ExpLog", "is_tactic_proof": true, "tactics": ["have", "have", "have", "simp", "exact"], "tactic_count": 5}
{"name": "FermatLastTheoremWith", "kind": "definition", "module": "Mathlib.NumberTheory.FLT.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FermatLastTheoremFor", "kind": "definition", "module": "Mathlib.NumberTheory.FLT.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FermatLastTheorem", "kind": "definition", "module": "Mathlib.NumberTheory.FLT.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fermatLastTheoremFor_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.FLT.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_fermatLastTheoremFor_one", "kind": "theorem", "module": "Mathlib.NumberTheory.FLT.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_fermatLastTheoremFor_two", "kind": "theorem", "module": "Mathlib.NumberTheory.FLT.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FermatLastTheoremWith.mono", "kind": "theorem", "module": "Mathlib.NumberTheory.FLT.Basic", "is_tactic_proof": true, "tactics": ["rintro", "obtain", "simp_rw", "refine"], "tactic_count": 4}
{"name": "FermatLastTheoremFor.mono", "kind": "theorem", "module": "Mathlib.NumberTheory.FLT.Basic", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "fermatLastTheoremWith_nat_int_rat_tfae", "kind": "theorem", "module": "Mathlib.NumberTheory.FLT.Basic", "is_tactic_proof": false, "tactics": ["tfae_have", "h,", "obtain", "refine", "push_cast", "simp", "obtain", "refine", "push_cast", "simp", "exact", "refine", "push_cast", "simp", "refine", "push_cast", "simp", "refine", "push_cast", "simp", "refine", "push_cast", "simp", "exact", "refine", "push_cast", "simp", "tfae_have", "h,", "rw", "refine", "h", "have", "refine", "push_cast", "simp", "div_self", "tfae_have", "h,", "tfae_finish"], "tactic_count": 40}
{"name": "fermatLastTheoremFor_iff_nat", "kind": "theorem", "module": "Mathlib.NumberTheory.FLT.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fermatLastTheoremFor_iff_int", "kind": "theorem", "module": "Mathlib.NumberTheory.FLT.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "FermatLastTheoremForThreeGen.Solution.Solution'_descent", "kind": "definition", "module": "Mathlib.NumberTheory.FLT.Three", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FermatLastTheoremForThreeGen.Solution.Solution'_descent_multiplicity", "kind": "theorem", "module": "Mathlib.NumberTheory.FLT.Three", "is_tactic_proof": true, "tactics": ["refine", "obtain", "rw", "simp", "simp"], "tactic_count": 5}
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{"name": "FermatLastTheoremForThreeGen.Solution.exists_Solution_multiplicity_lt", "kind": "theorem", "module": "Mathlib.NumberTheory.FLT.Three", "is_tactic_proof": true, "tactics": ["classical", "obtain", "exact"], "tactic_count": 3}
{"name": "fermatLastTheoremThree", "kind": "theorem", "module": "Mathlib.NumberTheory.FLT.Three", "is_tactic_proof": true, "tactics": ["classical", "let", "let", "have", "apply", "intro", "let", "b", "c", "u", "ha", "hb", "hc", "coprime", "hcdvd", "obtain", "obtain", "obtain", "linarith"], "tactic_count": 19}
{"name": "Nat.Abundant", "kind": "definition", "module": "Mathlib.NumberTheory.FactorisationProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Deficient", "kind": "definition", "module": "Mathlib.NumberTheory.FactorisationProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Pseudoperfect", "kind": "definition", "module": "Mathlib.NumberTheory.FactorisationProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Weird", "kind": "definition", "module": "Mathlib.NumberTheory.FactorisationProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.abundancyIndex", "kind": "definition", "module": "Mathlib.NumberTheory.FactorisationProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.not_pseudoperfect_iff_forall", "kind": "theorem", "module": "Mathlib.NumberTheory.FactorisationProperties", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Nat.deficient_one", "kind": "theorem", "module": "Mathlib.NumberTheory.FactorisationProperties", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "Nat.deficient_two", "kind": "theorem", "module": "Mathlib.NumberTheory.FactorisationProperties", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "Nat.deficient_three", "kind": "theorem", "module": "Mathlib.NumberTheory.FactorisationProperties", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "Nat.not_abundant_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.FactorisationProperties", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "Nat.abundant_twelve", "kind": "theorem", "module": "Mathlib.NumberTheory.FactorisationProperties", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "Nat.weird_seventy", "kind": "theorem", "module": "Mathlib.NumberTheory.FactorisationProperties", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "Nat.deficient_iff_not_abundant_and_not_perfect", "kind": "theorem", "module": "Mathlib.NumberTheory.FactorisationProperties", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Nat.perfect_iff_not_abundant_and_not_deficient", "kind": "theorem", "module": "Mathlib.NumberTheory.FactorisationProperties", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Nat.abundant_iff_not_perfect_and_not_deficient", "kind": "theorem", "module": "Mathlib.NumberTheory.FactorisationProperties", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Nat.deficient_or_perfect_or_abundant", "kind": "theorem", "module": "Mathlib.NumberTheory.FactorisationProperties", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Nat.Perfect.pseudoperfect", "kind": "theorem", "module": "Mathlib.NumberTheory.FactorisationProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Prime.not_abundant", "kind": "theorem", "module": "Mathlib.NumberTheory.FactorisationProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Prime.not_weird", "kind": "theorem", "module": "Mathlib.NumberTheory.FactorisationProperties", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Nat.Prime.not_pseudoperfect", "kind": "theorem", "module": "Mathlib.NumberTheory.FactorisationProperties", "is_tactic_proof": false, "tactics": ["simp_rw", "show", "refine", "fin_cases"], "tactic_count": 4}
{"name": "Nat.Prime.not_perfect", "kind": "theorem", "module": "Mathlib.NumberTheory.FactorisationProperties", "is_tactic_proof": true, "tactics": ["have", "revert", "exact"], "tactic_count": 3}
{"name": "Nat.Prime.deficient_pow", "kind": "theorem", "module": "Mathlib.NumberTheory.FactorisationProperties", "is_tactic_proof": true, "tactics": ["rcases", "simpa", "have", "apply", "simp", "rintro", "exact", "simp", "intro", "constructor", "rw", "exact", "rw", "exact", "have", "rw", "rintro", "apply", "rw", "calc"], "tactic_count": 20}
{"name": "IsPrimePow.deficient", "kind": "theorem", "module": "Mathlib.NumberTheory.FactorisationProperties", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Nat.Prime.deficient", "kind": "theorem", "module": "Mathlib.NumberTheory.FactorisationProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.infinite_deficient", "kind": "theorem", "module": "Mathlib.NumberTheory.FactorisationProperties", "is_tactic_proof": true, "tactics": ["rw", "intro", "obtain", "exact"], "tactic_count": 4}
{"name": "Nat.infinite_even_deficient", "kind": "theorem", "module": "Mathlib.NumberTheory.FactorisationProperties", "is_tactic_proof": true, "tactics": ["rw", "intro", "use", "constructor", "exact", "calc", "n"], "tactic_count": 7}
{"name": "Nat.infinite_odd_deficient", "kind": "theorem", "module": "Mathlib.NumberTheory.FactorisationProperties", "is_tactic_proof": true, "tactics": ["rw", "intro", "obtain", "exact"], "tactic_count": 4}
{"name": "Nat.abundant_iff_sum_divisors", "kind": "theorem", "module": "Mathlib.NumberTheory.FactorisationProperties", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Nat.abundant_iff_two_lt_abundancyIndex", "kind": "theorem", "module": "Mathlib.NumberTheory.FactorisationProperties", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "rw", "norm_cast"], "tactic_count": 4}
{"name": "Nat.abundancyIndex_le_of_dvd", "kind": "theorem", "module": "Mathlib.NumberTheory.FactorisationProperties", "is_tactic_proof": true, "tactics": ["obtain", "have", "rw", "refine", "rw", "exact"], "tactic_count": 6}
{"name": "Nat.Abundant.of_dvd", "kind": "theorem", "module": "Mathlib.NumberTheory.FactorisationProperties", "is_tactic_proof": true, "tactics": ["have", "grind"], "tactic_count": 2}
{"name": "Nat.Abundant.mul_left", "kind": "theorem", "module": "Mathlib.NumberTheory.FactorisationProperties", "is_tactic_proof": true, "tactics": ["have", "have", "exact"], "tactic_count": 3}
{"name": "Nat.infinite_even_abundant", "kind": "theorem", "module": "Mathlib.NumberTheory.FactorisationProperties", "is_tactic_proof": true, "tactics": ["rw", "intro", "have", "use", "grind"], "tactic_count": 5}
{"name": "Nat.infinite_odd_abundant", "kind": "theorem", "module": "Mathlib.NumberTheory.FactorisationProperties", "is_tactic_proof": true, "tactics": ["rw", "intro", "have", "use", "grind"], "tactic_count": 5}
{"name": "Nat.fermatNumber", "kind": "definition", "module": "Mathlib.NumberTheory.Fermat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.fermatNumber_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.Fermat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.fermatNumber_one", "kind": "theorem", "module": "Mathlib.NumberTheory.Fermat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.fermatNumber_two", "kind": "theorem", "module": "Mathlib.NumberTheory.Fermat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.fermatNumber_strictMono", "kind": "theorem", "module": "Mathlib.NumberTheory.Fermat", "is_tactic_proof": true, "tactics": ["intro", "simp"], "tactic_count": 2}
{"name": "Nat.fermatNumber_mono", "kind": "theorem", "module": "Mathlib.NumberTheory.Fermat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.fermatNumber_injective", "kind": "theorem", "module": "Mathlib.NumberTheory.Fermat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.three_le_fermatNumber", "kind": "theorem", "module": "Mathlib.NumberTheory.Fermat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.two_lt_fermatNumber", "kind": "theorem", "module": "Mathlib.NumberTheory.Fermat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.fermatNumber_ne_one", "kind": "theorem", "module": "Mathlib.NumberTheory.Fermat", "is_tactic_proof": true, "tactics": ["have"], "tactic_count": 1}
{"name": "Nat.odd_fermatNumber", "kind": "theorem", "module": "Mathlib.NumberTheory.Fermat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.prod_fermatNumber", "kind": "theorem", "module": "Mathlib.NumberTheory.Fermat", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "hn", "rw", "sq_sub_sq]", "ring_nf", "lia"], "tactic_count": 8}
{"name": "Nat.fermatNumber_eq_prod_add_two", "kind": "theorem", "module": "Mathlib.NumberTheory.Fermat", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Nat.fermatNumber_succ", "kind": "theorem", "module": "Mathlib.NumberTheory.Fermat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.two_mul_fermatNumber_sub_one_sq_le_fermatNumber_sq", "kind": "theorem", "module": "Mathlib.NumberTheory.Fermat", "is_tactic_proof": true, "tactics": ["simp", "have", "ring_nf", "lia"], "tactic_count": 4}
{"name": "Nat.fermatNumber_eq_fermatNumber_sq_sub_two_mul_fermatNumber_sub_one_sq", "kind": "theorem", "module": "Mathlib.NumberTheory.Fermat", "is_tactic_proof": true, "tactics": ["simp", "rw", "ring_nf"], "tactic_count": 3}
{"name": "Int.fermatNumber_eq_fermatNumber_sq_sub_two_mul_fermatNumber_sub_one_sq", "kind": "theorem", "module": "Mathlib.NumberTheory.Fermat", "is_tactic_proof": false, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Nat.coprime_fermatNumber_fermatNumber", "kind": "theorem", "module": "Mathlib.NumberTheory.Fermat", "is_tactic_proof": true, "tactics": ["wlog", "simpa", "let", "have", "have", "fermatNumber_eq_prod_add_two", "refine", "exact"], "tactic_count": 8}
{"name": "Nat.pairwise_coprime_fermatNumber", "kind": "theorem", "module": "Mathlib.NumberTheory.Fermat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.pow_of_pow_add_prime", "kind": "theorem", "module": "Mathlib.NumberTheory.Fermat", "is_tactic_proof": true, "tactics": ["obtain", "rw", "use", "replace", "let", "rw", "rw"], "tactic_count": 7}
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{"name": "Nat.pow_pow_add_primeFactors_one_lt", "kind": "theorem", "module": "Mathlib.NumberTheory.Fermat", "is_tactic_proof": true, "tactics": ["have", "have", "have", "rw", "exact_mod_cast", "have", "intro", "rw", "exact", "have", "apply", "rw", "exact", "rw", "simpa"], "tactic_count": 15}
{"name": "Nat.fermat_primeFactors_one_lt", "kind": "theorem", "module": "Mathlib.NumberTheory.Fermat", "is_tactic_proof": true, "tactics": ["have", "have", "have", "obtain", "obtain", "rw", "simp", "obtain", "suffices", "rw", "rw", "rwa"], "tactic_count": 12}
{"name": "Nat.prime_of_pow_sub_one_prime", "kind": "theorem", "module": "Mathlib.NumberTheory.Fermat", "is_tactic_proof": true, "tactics": ["have", "have", "have", "have", "have", "contrapose", "let", "rw", "exact", "subst", "refine", "have", "let", "rw", "exact"], "tactic_count": 15}
{"name": "Nat.ProbablePrime", "kind": "definition", "module": "Mathlib.NumberTheory.FermatPsp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.FermatPsp", "kind": "definition", "module": "Mathlib.NumberTheory.FermatPsp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.decidableProbablePrime", "kind": "instance", "module": "Mathlib.NumberTheory.FermatPsp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.decidablePsp", "kind": "instance", "module": "Mathlib.NumberTheory.FermatPsp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.coprime_of_probablePrime", "kind": "theorem", "module": "Mathlib.NumberTheory.FermatPsp", "is_tactic_proof": true, "tactics": ["by_cases", "apply", "rintro", "apply", "replace", "rw", "refine", "lia", "rw", "simp"], "tactic_count": 10}
{"name": "Nat.probablePrime_iff_modEq", "kind": "theorem", "module": "Mathlib.NumberTheory.FermatPsp", "is_tactic_proof": true, "tactics": ["have", "rw", "constructor", "intro", "apply", "exact", "intro", "exact"], "tactic_count": 8}
{"name": "Nat.coprime_of_fermatPsp", "kind": "theorem", "module": "Mathlib.NumberTheory.FermatPsp", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "Nat.fermatPsp_base_one", "kind": "theorem", "module": "Mathlib.NumberTheory.FermatPsp", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "_private.Mathlib.NumberTheory.FermatPsp.0.Nat.a_id_helper", "kind": "theorem", "module": "Mathlib.NumberTheory.FermatPsp", "is_tactic_proof": true, "tactics": ["change", "have", "rw", "exact"], "tactic_count": 4}
{"name": "_private.Mathlib.NumberTheory.FermatPsp.0.Nat.b_id_helper", "kind": "theorem", "module": "Mathlib.NumberTheory.FermatPsp", "is_tactic_proof": true, "tactics": ["rw", "apply", "calc"], "tactic_count": 3}
{"name": "_private.Mathlib.NumberTheory.FermatPsp.0.Nat.AB_id_helper", "kind": "theorem", "module": "Mathlib.NumberTheory.FermatPsp", "is_tactic_proof": true, "tactics": ["have", "have", "convert", "ring_nf"], "tactic_count": 4}
{"name": "_private.Mathlib.NumberTheory.FermatPsp.0.Nat.bp_helper", "kind": "theorem", "module": "Mathlib.NumberTheory.FermatPsp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.FermatPsp.0.Nat.psp_from_prime", "kind": "definition", "module": "Mathlib.NumberTheory.FermatPsp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.FermatPsp.0.Nat.psp_from_prime_psp", "kind": "theorem", "module": "Mathlib.NumberTheory.FermatPsp", "is_tactic_proof": true, "tactics": ["unfold", "set", "set", "have", "have", "have", "have", "have", "have", "have", "lia", "have", "have", "have", "have", "have", "have", "refine", "have", "apply_fun", "rw", "apply_fun", "nth_rw", "rw", "rw", "exact", "have", "rw", "have", "have", "have", "have", "have", "have", "exact", "have", "obtain", "have", "obtain", "have", "have", "rwa", "have", "suffices", "rwa", "have", "haveI", "rw", "exact", "have", "have", "have", "rwa", "have", "rw", "exact", "have", "use", "have", "congr_arg", "simpa", "obtain", "have", "simpa", "exact"], "tactic_count": 65}
{"name": "_private.Mathlib.NumberTheory.FermatPsp.0.Nat.psp_from_prime_gt_p", "kind": "theorem", "module": "Mathlib.NumberTheory.FermatPsp", "is_tactic_proof": true, "tactics": ["unfold", "set", "set", "rw", "have", "suffices", "have", "have", "linarith", "rwa", "rw", "conv_rhs", "rw", "suffices", "apply", "exact", "have", "exact", "suffices", "rw", "have", "have", "have", "exact"], "tactic_count": 24}
{"name": "Nat.exists_infinite_pseudoprimes", "kind": "theorem", "module": "Mathlib.NumberTheory.FermatPsp", "is_tactic_proof": true, "tactics": ["by_cases", "have", "obtain", "have", "have", "have", "have", "have", "have", "have", "have", "have", "have", "use", "constructor", "exact", "exact", "le_trans", "have", "rw", "use", "have", "exact"], "tactic_count": 23}
{"name": "Nat.frequently_atTop_fermatPsp", "kind": "theorem", "module": "Mathlib.NumberTheory.FermatPsp", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact"], "tactic_count": 3}
{"name": "Nat.infinite_setOf_pseudoprimes", "kind": "theorem", "module": "Mathlib.NumberTheory.FermatPsp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FrobeniusNumber", "kind": "definition", "module": "Mathlib.NumberTheory.FrobeniusNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "frobeniusNumber_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.FrobeniusNumber", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "frobeniusNumber_pair", "kind": "theorem", "module": "Mathlib.NumberTheory.FrobeniusNumber", "is_tactic_proof": true, "tactics": ["simp_rw", "have", "constructor", "push_neg", "intro", "apply", "simp", "zify", "rw", "rw", "ring", "intro", "dsimp", "contrapose", "let", "have", "suffices", "obtain", "obtain", "exact", "refine", "rw", "exact"], "tactic_count": 23}
{"name": "Nat.setGcd", "kind": "definition", "module": "Mathlib.NumberTheory.FrobeniusNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.setGcd_dvd_of_mem", "kind": "theorem", "module": "Mathlib.NumberTheory.FrobeniusNumber", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Nat.setGcd_dvd_of_mem_closure", "kind": "theorem", "module": "Mathlib.NumberTheory.FrobeniusNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.dvd_setGcd_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.FrobeniusNumber", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Nat.setGcd_mono", "kind": "theorem", "module": "Mathlib.NumberTheory.FrobeniusNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.dvdNotUnit_setGcd_insert", "kind": "theorem", "module": "Mathlib.NumberTheory.FrobeniusNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.setGcd_insert_of_dvd", "kind": "theorem", "module": "Mathlib.NumberTheory.FrobeniusNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.setGcd_eq_zero_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.FrobeniusNumber", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Nat.exists_ne_zero_of_setGcd_ne_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.FrobeniusNumber", "is_tactic_proof": true, "tactics": ["contrapose", "exact"], "tactic_count": 2}
{"name": "Nat.span_singleton_setGcd", "kind": "theorem", "module": "Mathlib.NumberTheory.FrobeniusNumber", "is_tactic_proof": true, "tactics": ["rw", "span_singleton_generator]"], "tactic_count": 2}
{"name": "Nat.subset_span_setGcd", "kind": "theorem", "module": "Mathlib.NumberTheory.FrobeniusNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.exists_mem_span_nat_finset_of_ge", "kind": "theorem", "module": "Mathlib.NumberTheory.FrobeniusNumber", "is_tactic_proof": true, "tactics": ["by_cases", "refine", "have", "have", "let", "refine", "obtain", "rw", "set", "set", "rw", "refine", "add_mem", "obtain", "dvd_mul_of_dvd_right", "dvd", "convert", "simp_rw", "smul_eq_mul,", "congr", "split_ifs", "rw", "rw", "mul_neg", "rw", "exact"], "tactic_count": 26}
{"name": "Nat.exists_mem_closure_of_ge", "kind": "theorem", "module": "Mathlib.NumberTheory.FrobeniusNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.finite_setOf_setGcd_dvd_and_mem_span", "kind": "theorem", "module": "Mathlib.NumberTheory.FrobeniusNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.instIsNoetherian", "kind": "instance", "module": "Mathlib.NumberTheory.FrobeniusNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.addSubmonoid_fg", "kind": "theorem", "module": "Mathlib.NumberTheory.FrobeniusNumber", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "exists_frobeniusNumber_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.FrobeniusNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FunctionField", "kind": "abbrev", "module": "Mathlib.NumberTheory.FunctionField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "functionField_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.FunctionField", "is_tactic_proof": true, "tactics": ["let", "have", "intro", "rw", "congr", "refine", "refine", "simp", "constructor", "let", "exact", "let", "refine", "intro"], "tactic_count": 14}
{"name": "FunctionField.algebraMap_injective", "kind": "theorem", "module": "Mathlib.NumberTheory.FunctionField", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "FunctionField.ringOfIntegers", "kind": "definition", "module": "Mathlib.NumberTheory.FunctionField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FunctionField.ringOfIntegers.instIsDomainSubtypeMemSubalgebraPolynomial", "kind": "instance", "module": "Mathlib.NumberTheory.FunctionField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FunctionField.ringOfIntegers.instIsIntegralClosureSubtypeMemSubalgebraPolynomial", "kind": "instance", "module": "Mathlib.NumberTheory.FunctionField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FunctionField.ringOfIntegers.algebraMap_injective", "kind": "theorem", "module": "Mathlib.NumberTheory.FunctionField", "is_tactic_proof": false, "tactics": ["have", "rw", "exact", "rw", "intro", "rw", "rw", "exact"], "tactic_count": 8}
{"name": "FunctionField.ringOfIntegers.not_isField", "kind": "theorem", "module": "Mathlib.NumberTheory.FunctionField", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "FunctionField.ringOfIntegers.instIsFractionRingSubtypeMemSubalgebraPolynomial", "kind": "instance", "module": "Mathlib.NumberTheory.FunctionField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FunctionField.ringOfIntegers.instIsIntegrallyClosedSubtypeMemSubalgebraPolynomial", "kind": "instance", "module": "Mathlib.NumberTheory.FunctionField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FunctionField.ringOfIntegers.instIsNoetherianPolynomialSubtypeMemSubalgebraOfIsSeparableRatFunc", "kind": "instance", "module": "Mathlib.NumberTheory.FunctionField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FunctionField.ringOfIntegers.instIsDedekindDomainSubtypeMemSubalgebraPolynomialOfIsSeparableRatFunc", "kind": "instance", "module": "Mathlib.NumberTheory.FunctionField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FunctionField.inftyValuationDef", "kind": "definition", "module": "Mathlib.NumberTheory.FunctionField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FunctionField.InftyValuation.map_zero'", "kind": "theorem", "module": "Mathlib.NumberTheory.FunctionField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FunctionField.InftyValuation.map_one'", "kind": "theorem", "module": "Mathlib.NumberTheory.FunctionField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FunctionField.InftyValuation.map_mul'", "kind": "theorem", "module": "Mathlib.NumberTheory.FunctionField", "is_tactic_proof": true, "tactics": ["rw", "by_cases", "rw", "by_cases", "rw", "simp_all"], "tactic_count": 6}
{"name": "FunctionField.InftyValuation.map_add_le_max'", "kind": "theorem", "module": "Mathlib.NumberTheory.FunctionField", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "conv_rhs", "rw", "by_cases", "rw", "conv_rhs", "rw", "by_cases", "rw", "rw", "simpa"], "tactic_count": 12}
{"name": "FunctionField.inftyValuation_of_nonzero", "kind": "theorem", "module": "Mathlib.NumberTheory.FunctionField", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "FunctionField.inftyValuation", "kind": "definition", "module": "Mathlib.NumberTheory.FunctionField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FunctionField.inftyValuation_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.FunctionField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FunctionField.inftyValuation.C", "kind": "theorem", "module": "Mathlib.NumberTheory.FunctionField", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FunctionField.inftyValuation.X", "kind": "theorem", "module": "Mathlib.NumberTheory.FunctionField", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FunctionField.inftyValuation.X_zpow", "kind": "theorem", "module": "Mathlib.NumberTheory.FunctionField", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FunctionField.inftyValuation.X_inv", "kind": "theorem", "module": "Mathlib.NumberTheory.FunctionField", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "FunctionField.inftyValuation.polynomial", "kind": "theorem", "module": "Mathlib.NumberTheory.FunctionField", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "FunctionField.instIsNontrivialRatFuncWithZeroMultiplicativeIntInftyValuation", "kind": "instance", "module": "Mathlib.NumberTheory.FunctionField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FunctionField.inftyValuedFqt", "kind": "definition", "module": "Mathlib.NumberTheory.FunctionField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FunctionField.inftyValuedFqt.def", "kind": "theorem", "module": "Mathlib.NumberTheory.FunctionField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FunctionField.FqtInfty", "kind": "definition", "module": "Mathlib.NumberTheory.FunctionField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FunctionField.instFieldFqtInfty", "kind": "instance", "module": "Mathlib.NumberTheory.FunctionField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FunctionField.instInhabitedFqtInfty", "kind": "instance", "module": "Mathlib.NumberTheory.FunctionField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FunctionField.valuedFqtInfty", "kind": "instance", "module": "Mathlib.NumberTheory.FunctionField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FunctionField.valuedFqtInfty.def", "kind": "theorem", "module": "Mathlib.NumberTheory.FunctionField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "gaussSum", "kind": "definition", "module": "Mathlib.NumberTheory.GaussSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "gaussSum_mulShift", "kind": "theorem", "module": "Mathlib.NumberTheory.GaussSum", "is_tactic_proof": true, "tactics": ["simp", "simp_rw", "exact"], "tactic_count": 3}
{"name": "gaussSum_mul", "kind": "theorem", "module": "Mathlib.NumberTheory.GaussSum", "is_tactic_proof": true, "tactics": ["rw", "conv", "simp", "have", "rw", "simp", "simp", "exact", "exact", "rw"], "tactic_count": 10}
{"name": "mul_gaussSum_inv_eq_gaussSum", "kind": "theorem", "module": "Mathlib.NumberTheory.GaussSum", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "_private.Mathlib.NumberTheory.GaussSum.0.gaussSum_mul_aux", "kind": "theorem", "module": "Mathlib.NumberTheory.GaussSum", "is_tactic_proof": true, "tactics": ["rcases", "simp", "χ.sum_eq_zero_of_ne_one", "refine", "rw"], "tactic_count": 5}
{"name": "gaussSum_mul_gaussSum_eq_card", "kind": "theorem", "module": "Mathlib.NumberTheory.GaussSum", "is_tactic_proof": true, "tactics": ["simp", "conv", "enter", "rw", "simp_rw", "rw", "classical", "simp_rw", "rw", "simp"], "tactic_count": 10}
{"name": "gaussSum_mul_gaussSum_pow_orderOf_sub_one", "kind": "theorem", "module": "Mathlib.NumberTheory.GaussSum", "is_tactic_proof": false, "tactics": ["have", "refine", "rw", "rw", "inv_neg_one]"], "tactic_count": 5}
{"name": "gaussSum_ne_zero_of_nontrivial", "kind": "theorem", "module": "Mathlib.NumberTheory.GaussSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "gaussSum_sq", "kind": "theorem", "module": "Mathlib.NumberTheory.GaussSum", "is_tactic_proof": true, "tactics": ["rw", "congr", "rw", "rfl"], "tactic_count": 4}
{"name": "gaussSum_frob", "kind": "theorem", "module": "Mathlib.NumberTheory.GaussSum", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "rfl"], "tactic_count": 3}
{"name": "MulChar.IsQuadratic.gaussSum_frob", "kind": "theorem", "module": "Mathlib.NumberTheory.GaussSum", "is_tactic_proof": true, "tactics": ["rw", "pow_two,"], "tactic_count": 2}
{"name": "MulChar.IsQuadratic.gaussSum_frob_iter", "kind": "theorem", "module": "Mathlib.NumberTheory.GaussSum", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "pow_apply"], "tactic_count": 5}
{"name": "Char.card_pow_char_pow", "kind": "theorem", "module": "Mathlib.NumberTheory.GaussSum", "is_tactic_proof": false, "tactics": ["have", "intro", "rw", "exact", "not_isUnit_prime_of_dvd_card", "rw", "apply", "rw"], "tactic_count": 8}
{"name": "Char.card_pow_card", "kind": "theorem", "module": "Mathlib.NumberTheory.GaussSum", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "let", "let", "have", "apply", "rw", "simp", "have", "have", "rw", "exact"], "tactic_count": 12}
{"name": "FiniteField.two_pow_card", "kind": "theorem", "module": "Mathlib.NumberTheory.GaussSum", "is_tactic_proof": true, "tactics": ["have", "obtain", "let", "have", "have", "have", "have", "have", "rw", "rw", "change", "exact", "let", "primitiveZModChar", "let", "let", "have", "rw", "refine", "rw", "decide", "rw", "decide", "let", "have", "have", "isQuadratic_χ₈.comp", "have", "have", "rw", "show", "show", "show", "simp", "linear_combination", "have", "rw", "linear_combination", "have", "rw", "convert_to", "rw", "apply", "simpa"], "tactic_count": 44}
{"name": "harmonic_eq_sum_Icc", "kind": "theorem", "module": "Mathlib.NumberTheory.Harmonic.Bounds", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "log_add_one_le_harmonic", "kind": "theorem", "module": "Mathlib.NumberTheory.Harmonic.Bounds", "is_tactic_proof": false, "tactics": ["calc", "rw", "exact", "simp"], "tactic_count": 4}
{"name": "harmonic_le_one_add_log", "kind": "theorem", "module": "Mathlib.NumberTheory.Harmonic.Bounds", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "have", "simp_rw", "rw", "gcongr", "simp", "calc", "simp_rw", "exact", "sub_inv_antitoneOn_Icc_right", "convert", "norm_num", "simp", "convert", "rw", "simp"], "tactic_count": 17}
{"name": "log_le_harmonic_floor", "kind": "theorem", "module": "Mathlib.NumberTheory.Harmonic.Bounds", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "calc", "gcongr", "apply", "norm_cast", "exact"], "tactic_count": 7}
{"name": "harmonic_floor_le_one_add_log", "kind": "theorem", "module": "Mathlib.NumberTheory.Harmonic.Bounds", "is_tactic_proof": true, "tactics": ["refine", "gcongr", "exact_mod_cast", "exact"], "tactic_count": 4}
{"name": "harmonic", "kind": "definition", "module": "Mathlib.NumberTheory.Harmonic.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "harmonic_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.Harmonic.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "harmonic_succ", "kind": "theorem", "module": "Mathlib.NumberTheory.Harmonic.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.eulerMascheroniSeq", "kind": "definition", "module": "Mathlib.NumberTheory.Harmonic.EulerMascheroni", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "_private.Mathlib.NumberTheory.Height.Basic.0.Height.mulSupport_max_nonarchAbsVal_finite", "kind": "theorem", "module": "Mathlib.NumberTheory.Height.Basic", "is_tactic_proof": true, "tactics": ["convert", "rw", "congr", "ext1", "fin_cases"], "tactic_count": 5}
{"name": "Height.mulHeight_smul_eq_mulHeight", "kind": "theorem", "module": "Mathlib.NumberTheory.Height.Basic", "is_tactic_proof": true, "tactics": ["rcases", "rw", "have", "have", "simp", "rw", "product_formula"], "tactic_count": 7}
{"name": "Height.one_le_mulHeight", "kind": "theorem", "module": "Mathlib.NumberTheory.Height.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simp", "obtain", "have", "rw", "refine", "simp", "obtain", "refine", "exact", "refine", "simp"], "tactic_count": 12}
{"name": "Height.mulHeight_pos", "kind": "theorem", "module": "Mathlib.NumberTheory.Height.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Height.mulHeight.ne_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.Height.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Height.zero_le_logHeight", "kind": "theorem", "module": "Mathlib.NumberTheory.Height.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalMulHeight", "kind": "definition", "module": "Mathlib.NumberTheory.Height.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalLogHeight", "kind": "definition", "module": "Mathlib.NumberTheory.Height.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Height.logHeight_smul_eq_logHeight", "kind": "theorem", "module": "Mathlib.NumberTheory.Height.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Height.mulHeight₁_eq_mulHeight", "kind": "theorem", "module": "Mathlib.NumberTheory.Height.Basic", "is_tactic_proof": false, "tactics": ["have", "have", "simpa", "have", "simp"], "tactic_count": 5}
{"name": "Height.logHeight₁_eq_logHeight", "kind": "theorem", "module": "Mathlib.NumberTheory.Height.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Height.mulHeight₁_div_eq_mulHeight", "kind": "theorem", "module": "Mathlib.NumberTheory.Height.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rcases", "rw", "simp", "have", "simp", "rw", "rw", "simp"], "tactic_count": 10}
{"name": "Height.logHeight₁_div_eq_logHeight", "kind": "theorem", "module": "Mathlib.NumberTheory.Height.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Height.mulHeight_pow", "kind": "theorem", "module": "Mathlib.NumberTheory.Height.Basic", "is_tactic_proof": true, "tactics": ["rcases", "cases", "have", "have", "simp", "simp", "norm_cast", "exact", "have", "simp"], "tactic_count": 10}
{"name": "Height.logHeight_pow", "kind": "theorem", "module": "Mathlib.NumberTheory.Height.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Height.mulHeight₁_inv", "kind": "theorem", "module": "Mathlib.NumberTheory.Height.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "rcases", "rw", "have", "rw"], "tactic_count": 5}
{"name": "Height.logHeight₁_inv", "kind": "theorem", "module": "Mathlib.NumberTheory.Height.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Height.mulHeight₁_pow", "kind": "theorem", "module": "Mathlib.NumberTheory.Height.Basic", "is_tactic_proof": true, "tactics": ["simp", "congr", "ext1", "fin_cases"], "tactic_count": 4}
{"name": "Height.logHeight₁_pow", "kind": "theorem", "module": "Mathlib.NumberTheory.Height.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Height.mulHeight₁_zpow", "kind": "theorem", "module": "Mathlib.NumberTheory.Height.Basic", "is_tactic_proof": true, "tactics": ["rcases", "lift", "rw", "nth_rewrite", "rw"], "tactic_count": 5}
{"name": "Height.logHeight₁_zpow", "kind": "theorem", "module": "Mathlib.NumberTheory.Height.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NumberField.multisetInfinitePlace", "kind": "definition", "module": "Mathlib.NumberTheory.Height.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mem_multisetInfinitePlace", "kind": "theorem", "module": "Mathlib.NumberTheory.Height.Instances", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NumberField.count_multisetInfinitePlace_eq_mult", "kind": "theorem", "module": "Mathlib.NumberTheory.Height.Instances", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "_private.Mathlib.NumberTheory.Height.Instances.0.NumberField.prod_multisetInfinitePlace_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.Height.Instances", "is_tactic_proof": true, "tactics": ["classical", "rw", "exact"], "tactic_count": 3}
{"name": "NumberField.instAdmissibleAbsValues", "kind": "instance", "module": "Mathlib.NumberTheory.Height.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.prod_archAbsVal_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.Height.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.prod_nonarchAbsVal_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.Height.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mulHeight₁_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.Height.Instances", "is_tactic_proof": true, "tactics": ["simp", "prod_nonarchAbsVal_eq"], "tactic_count": 2}
{"name": "NumberField.mulHeight_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.Height.Instances", "is_tactic_proof": true, "tactics": ["simp", "prod_nonarchAbsVal_eq"], "tactic_count": 2}
{"name": "jacobiSum", "kind": "definition", "module": "Mathlib.NumberTheory.JacobiSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "jacobiSum_comm", "kind": "theorem", "module": "Mathlib.NumberTheory.JacobiSum.Basic", "is_tactic_proof": true, "tactics": ["simp", "rw", "simp"], "tactic_count": 3}
{"name": "jacobiSum_ringHomComp", "kind": "theorem", "module": "Mathlib.NumberTheory.JacobiSum.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "jacobiSum_eq_sum_sdiff", "kind": "theorem", "module": "Mathlib.NumberTheory.JacobiSum.Basic", "is_tactic_proof": true, "tactics": ["simp", "apply", "simp", "add_neg_cancel,"], "tactic_count": 4}
{"name": "_private.Mathlib.NumberTheory.JacobiSum.Basic.0.jacobiSum_eq_aux", "kind": "theorem", "module": "Mathlib.NumberTheory.JacobiSum.Basic", "is_tactic_proof": true, "tactics": ["rw", "conv", "enter", "rw", "rw", "conv", "rw", "sum_sdiff_eq_sub", "congr", "rw"], "tactic_count": 10}
{"name": "jacobiSum_trivial_trivial", "kind": "theorem", "module": "Mathlib.NumberTheory.JacobiSum.Basic", "is_tactic_proof": true, "tactics": ["classical", "rw", "have", "intro", "rw", "simp", "simpa", "calc", "rw"], "tactic_count": 9}
{"name": "jacobiSum_one_one", "kind": "theorem", "module": "Mathlib.NumberTheory.JacobiSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "jacobiSum_one_nontrivial", "kind": "theorem", "module": "Mathlib.NumberTheory.JacobiSum.Basic", "is_tactic_proof": true, "tactics": ["classical", "have", "apply", "simp", "simp"], "tactic_count": 5}
{"name": "jacobiSum_nontrivial_inv", "kind": "theorem", "module": "Mathlib.NumberTheory.JacobiSum.Basic", "is_tactic_proof": true, "tactics": ["classical", "rw", "conv", "rw", "have", "refine", "sum_bij", "simp", "rw", "right_eq_add,", "exact", "simp", "rw", "exact", "simp", "rw", "simp", "simp", "rw", "simp", "rw", "exact"], "tactic_count": 22}
{"name": "jacobiSum_mul_nontrivial", "kind": "theorem", "module": "Mathlib.NumberTheory.JacobiSum.Basic", "is_tactic_proof": true, "tactics": ["classical", "rw", "conv", "enter", "rw", "mul_one]", "rw", "have", "intro", "simp", "exact", "simp_rw", "conv", "simp_rw", "rw", "add_zero]"], "tactic_count": 16}
{"name": "jacobiSum_eq_gaussSum_mul_gaussSum_div_gaussSum", "kind": "theorem", "module": "Mathlib.NumberTheory.JacobiSum.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "jacobiSum_mul_jacobiSum_inv", "kind": "theorem", "module": "Mathlib.NumberTheory.JacobiSum.Basic", "is_tactic_proof": false, "tactics": ["obtain", "let", "let", "let", "let", "have", "apply", "rw", "have", "rw", "exact", "have", "have", "have", "have", "intro", "simp", "exact", "have", "apply_fun", "simp", "rw", "jacobiSum_mul_nontrivial", "gaussSum_mul_gaussSum_eq_card"], "tactic_count": 24}
{"name": "_private.Mathlib.NumberTheory.JacobiSum.Basic.0.MulChar.exists_apply_sub_one_eq_mul_sub_one", "kind": "theorem", "module": "Mathlib.NumberTheory.JacobiSum.Basic", "is_tactic_proof": true, "tactics": ["obtain", "refine", "exact"], "tactic_count": 3}
{"name": "_private.Mathlib.NumberTheory.JacobiSum.Basic.0.MulChar.exists_apply_sub_one_mul_apply_sub_one", "kind": "theorem", "module": "Mathlib.NumberTheory.JacobiSum.Basic", "is_tactic_proof": true, "tactics": ["rcases", "exact", "rcases", "exact", "obtain", "obtain", "rewrite", "exact"], "tactic_count": 8}
{"name": "jacobiSum_mem_algebraAdjoin_of_pow_eq_one", "kind": "theorem", "module": "Mathlib.NumberTheory.JacobiSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_jacobiSum_eq_neg_one_add", "kind": "theorem", "module": "Mathlib.NumberTheory.JacobiSum.Basic", "is_tactic_proof": true, "tactics": ["obtain", "rw", "obtain", "by_cases", "rw", "refine", "rw", "ring", "refine", "rw", "refine", "rw", "classical", "rw", "have", "have", "have", "refine", "refine", "exact", "exact", "conv", "rw", "ring"], "tactic_count": 24}
{"name": "gaussSum_pow_eq_prod_jacobiSum_aux", "kind": "theorem", "module": "Mathlib.NumberTheory.JacobiSum.Basic", "is_tactic_proof": true, "tactics": ["induction", "base", "succ", "specialize", "have", "have", "rw", "apply_fun", "rw", "rw"], "tactic_count": 10}
{"name": "gaussSum_pow_eq_prod_jacobiSum", "kind": "theorem", "module": "Mathlib.NumberTheory.JacobiSum.Basic", "is_tactic_proof": true, "tactics": ["have", "apply_fun", "rw", "have", "rw"], "tactic_count": 5}
{"name": "KummerDedekind.quotMapEquivQuotQuotMap", "kind": "definition", "module": "Mathlib.NumberTheory.KummerDedekind", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "KummerDedekind.quotMapEquivQuotQuotMap_symm_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.KummerDedekind", "is_tactic_proof": true, "tactics": ["apply", "rw", "quotEquivOfEq_symm,", "congr", "convert", "apply", "simp"], "tactic_count": 7}
{"name": "KummerDedekind.normalizedFactorsMapEquivNormalizedFactorsMinPolyMk", "kind": "definition", "module": "Mathlib.NumberTheory.KummerDedekind", "is_tactic_proof": true, "tactics": ["refine", "rwa", "by_contra", "exact", "refine", "exact"], "tactic_count": 6}
{"name": "KummerDedekind.emultiplicity_factors_map_eq_emultiplicity", "kind": "theorem", "module": "Mathlib.NumberTheory.KummerDedekind", "is_tactic_proof": true, "tactics": ["rw", "emultiplicity_normalizedFactorsEquivSpanNormalizedFactors_symm_eq_emultiplicity,", "normalizedFactorsEquivOfQuotEquiv_emultiplicity_eq_emultiplicity]"], "tactic_count": 3}
{"name": "KummerDedekind.normalizedFactors_ideal_map_eq_normalizedFactors_min_poly_mk_map", "kind": "theorem", "module": "Mathlib.NumberTheory.KummerDedekind", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "swap", "rw", "simp", "rintro", "exact", "have", "rw", "refine", "this.trans", "generalize", "have", "rw", "subst", "rw", "exact", "exact", "exact", "exact", "exact", "rwa"], "tactic_count": 22}
{"name": "KummerDedekind.Ideal.irreducible_map_of_irreducible_minpoly", "kind": "theorem", "module": "Mathlib.NumberTheory.KummerDedekind", "is_tactic_proof": true, "tactics": ["classical", "have", "normalize", "normalizedFactors", "suffices", "obtain", "have", "prod_normalizedFactors", "rwa", "rw", "rw", "exact", "rw", "use", "rw", "use", "refine", "apply", "rw", "exact"], "tactic_count": 20}
{"name": "KummerDedekind.normalizedFactorsMapEquivNormalizedFactorsMinPolyMk_symm_apply_eq_span", "kind": "theorem", "module": "Mathlib.NumberTheory.KummerDedekind", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "dsimp", "simp", "refine", "le_antisymm", "rw", "obtain", "obtain", "rw", "rw", "exact"], "tactic_count": 12}
{"name": "WeakFEPair.h_feq'", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.AbstractFuncEq", "is_tactic_proof": true, "tactics": ["rw", "convert", "rw", "field"], "tactic_count": 4}
{"name": "WeakFEPair.symm", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.AbstractFuncEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrongFEPair.symm", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.AbstractFuncEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakFEPair.hf_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.AbstractFuncEq", "is_tactic_proof": true, "tactics": ["have", "simp_rw", "obtain", "use", "filter_upwards", "have", "have", "specialize", "simp_rw", "rw", "le_div_iff₀", "convert", "congr", "rw", "simp", "simp_rw", "norm_of_nonneg", "field"], "tactic_count": 18}
{"name": "WeakFEPair.hf_zero'", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.AbstractFuncEq", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "rw", "simp_rw", "apply", "refine", "filter_upwards", "apply", "rw", "exact"], "tactic_count": 10}
{"name": "StrongFEPair.hf_top'", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.AbstractFuncEq", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "StrongFEPair.hf_zero'", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.AbstractFuncEq", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "StrongFEPair.Λ", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.AbstractFuncEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrongFEPair.hasMellin", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.AbstractFuncEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrongFEPair.Λ_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.AbstractFuncEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrongFEPair.symm_Λ_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.AbstractFuncEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrongFEPair.differentiable_Λ", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.AbstractFuncEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrongFEPair.functional_equation", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.AbstractFuncEq", "is_tactic_proof": true, "tactics": ["rw", "have", "simp_rw", "one_div]", "have", "rw", "have", "rw", "rw", "refine", "simp_rw", "rw", "have", "field_simp"], "tactic_count": 14}
{"name": "WeakFEPair.f_modif", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.AbstractFuncEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakFEPair.g_modif", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.AbstractFuncEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakFEPair.hf_modif_int", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.AbstractFuncEq", "is_tactic_proof": false, "tactics": ["have", "refine", "refine", "have", "fun_prop", "refine", "obtain", "refine", "rw", "exact", "obtain", "refine", "rw", "exact"], "tactic_count": 14}
{"name": "WeakFEPair.hf_modif_FE", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.AbstractFuncEq", "is_tactic_proof": true, "tactics": ["rcases", "have", "rw", "indicator_of_mem", "indicator_of_mem", "smul_sub]", "simp_rw", "simp", "have", "rw", "g_modif,", "simp_rw", "match_scalars"], "tactic_count": 13}
{"name": "WeakFEPair.toStrongFEPair", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.AbstractFuncEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakFEPair.f_modif_aux1", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.AbstractFuncEq", "is_tactic_proof": true, "tactics": ["intro", "simp_rw", "rcases", "simp_rw", "indicator_of_notMem", "abel", "simp", "simp_rw", "indicator_of_notMem", "abel"], "tactic_count": 10}
{"name": "WeakFEPair.f_modif_aux2", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.AbstractFuncEq", "is_tactic_proof": true, "tactics": ["have", "have", "calc", "setIntegral_congr_fun", "refine", "setIntegral_congr_ae", "rw", "simp_rw", "integral_Ioc_eq_integral_Ioo]", "refine", "rw", "cpow_add", "rw", "apply", "rw", "exact", "refine", "rw", "exact", "simp_rw", "integral_cpow", "zero_cpow", "zero_cpow", "sub_eq_add_neg"], "tactic_count": 24}
{"name": "WeakFEPair.Λ₀", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.AbstractFuncEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakFEPair.Λ", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.AbstractFuncEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakFEPair.Λ₀_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.AbstractFuncEq", "is_tactic_proof": true, "tactics": ["unfold", "abel"], "tactic_count": 2}
{"name": "WeakFEPair.symm_Λ₀_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.AbstractFuncEq", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "WeakFEPair.differentiable_Λ₀", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.AbstractFuncEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakFEPair.differentiableAt_Λ", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.AbstractFuncEq", "is_tactic_proof": true, "tactics": ["refine", "rcases", "simpa", "simp", "rcases", "apply", "apply", "simpa", "simp"], "tactic_count": 9}
{"name": "WeakFEPair.hasMellin", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.AbstractFuncEq", "is_tactic_proof": false, "tactics": ["have", "let", "mellinConvergent_of_isBigO_rpow", "refine", "have", "have", "have", "simp_rw", "exact"], "tactic_count": 9}
{"name": "WeakFEPair.functional_equation₀", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.AbstractFuncEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakFEPair.functional_equation", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.AbstractFuncEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakFEPair.Λ_residue_k", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.AbstractFuncEq", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "rw", "apply", "rw", "refine", "have", "fun_prop", "refine", "refine", "match_scalars", "field"], "tactic_count": 12}
{"name": "WeakFEPair.Λ_residue_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.AbstractFuncEq", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "exact", "refine", "refine", "match_scalars", "field", "rw", "exact", "continuousAt_const)).mono_left", "nhdsWithin_le_nhds"], "tactic_count": 11}
{"name": "LSeries.term", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LSeries.term_def", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LSeries.term_def₀", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Basic", "is_tactic_proof": true, "tactics": ["rw", "split_ifs"], "tactic_count": 2}
{"name": "LSeries.term_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LSeries.term_of_ne_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LSeries.term_of_ne_zero'", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Basic", "is_tactic_proof": true, "tactics": ["rcases", "rw", "rw"], "tactic_count": 3}
{"name": "LSeries.term_congr", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Basic", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "LSeries.pow_mul_term_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LSeries.norm_term_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simp"], "tactic_count": 3}
{"name": "LSeries.norm_term_le", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Basic", "is_tactic_proof": true, "tactics": ["simp", "split", "rfl", "gcongr"], "tactic_count": 4}
{"name": "LSeries.norm_term_le_of_re_le_re", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Basic", "is_tactic_proof": true, "tactics": ["simp", "split", "rfl", "gcongr"], "tactic_count": 4}
{"name": "LSeries.term_nonneg", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Basic", "is_tactic_proof": true, "tactics": ["rw", "split_ifs", "exacts"], "tactic_count": 3}
{"name": "LSeries.term_pos", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "LSeries", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LSeries_congr", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LSeriesSummable", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LSeriesSummable_congr", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LSeriesSummable.congr'", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "have", "rw", "obtain", "refine", "rw", "simp", "exact"], "tactic_count": 9}
{"name": "LSeriesSummable_congr'", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LSeries.eq_zero_of_not_LSeriesSummable", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LSeriesSummable_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LSeriesHasSum", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LSeriesHasSum.LSeriesSummable", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LSeriesHasSum.LSeries_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LSeriesSummable.LSeriesHasSum", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LSeriesHasSum_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LSeriesHasSum_congr", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LSeriesSummable.of_re_le_re", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "LSeriesSummable_iff_of_re_eq_re", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LSeries.delta", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LSeries.notation.termL", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LSeries.notation._aux_Mathlib_NumberTheory_LSeries_Basic___macroRules_LSeries_notation_termL_1", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LSeries.notation._aux_Mathlib_NumberTheory_LSeries_Basic___unexpand_LSeries_1", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LSeries.notation.term↗_", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LSeries.notation._aux_Mathlib_NumberTheory_LSeries_Basic___macroRules_LSeries_notation_term↗__1", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LSeries.notation.termδ", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LSeries.notation._aux_Mathlib_NumberTheory_LSeries_Basic___macroRules_LSeries_notation_termδ_1", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LSeries.notation._aux_Mathlib_NumberTheory_LSeries_Basic___unexpand_LSeries_delta_1", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LSeries_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "LSeries.term_delta", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rcases"], "tactic_count": 3}
{"name": "LSeries.mul_delta_eq_smul_delta", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Basic", "is_tactic_proof": true, "tactics": ["ext", "by_cases"], "tactic_count": 2}
{"name": "LSeries.mul_delta", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LSeries.delta_mul_eq_smul_delta", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LSeries.delta_mul", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LSeries_delta", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "LSeriesSummable.le_const_mul_rpow", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Basic", "is_tactic_proof": true, "tactics": ["replace", "use", "by_contra", "have", "rw", "div_le_iff₀", "exact"], "tactic_count": 7}
{"name": "LSeriesSummable.isBigO_rpow", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Basic", "is_tactic_proof": true, "tactics": ["obtain", "refine", "convert", "rw"], "tactic_count": 4}
{"name": "LSeriesSummable_of_le_const_mul_rpow", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Basic", "is_tactic_proof": true, "tactics": ["obtain", "have", "have", "simp_rw", "have", "refine", "simpa", "simp", "refine", "simp", "ring_nf", "refine", "rcases", "simpa", "have", "simp_rw", "simpa"], "tactic_count": 17}
{"name": "LSeriesSummable_of_isBigO_rpow", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Basic", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "let", "have", "have", "refine", "rcases", "refine", "have", "gcongr", "rw", "have", "refine", "refine", "exact"], "tactic_count": 15}
{"name": "LSeriesSummable_of_bounded_of_one_lt_re", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LSeriesSummable_of_bounded_of_one_lt_real", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LSeries.abscissaOfAbsConv", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.Convergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LSeries.abscissaOfAbsConv_congr", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Convergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LSeries.abscissaOfAbsConv_congr'", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Convergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LSeriesSummable_of_abscissaOfAbsConv_lt_re", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Convergence", "is_tactic_proof": false, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "LSeriesSummable_lt_re_of_abscissaOfAbsConv_lt_re", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Convergence", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "LSeriesSummable.abscissaOfAbsConv_le", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Convergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LSeries.abscissaOfAbsConv_le_of_forall_lt_LSeriesSummable", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Convergence", "is_tactic_proof": true, "tactics": ["refine", "replace", "cases", "coe", "bot", "top"], "tactic_count": 6}
{"name": "LSeries.abscissaOfAbsConv_le_of_forall_lt_LSeriesSummable'", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Convergence", "is_tactic_proof": true, "tactics": ["cases", "coe", "top", "bot", "refine", "cases", "bot", "coe", "top"], "tactic_count": 9}
{"name": "LSeries.abscissaOfAbsConv_le_of_le_const_mul_rpow", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Convergence", "is_tactic_proof": true, "tactics": ["rw", "by_contra", "obtain", "exact", "hy₂).false"], "tactic_count": 5}
{"name": "LSeries.abscissaOfAbsConv_le_of_isBigO_rpow", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Convergence", "is_tactic_proof": true, "tactics": ["rw", "by_contra", "obtain", "exact"], "tactic_count": 4}
{"name": "LSeries.abscissaOfAbsConv_le_of_le_const", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Convergence", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "LSeries.abscissaOfAbsConv_le_one_of_isBigO_one", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Convergence", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "LSeries.summable_real_of_abscissaOfAbsConv_lt", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Convergence", "is_tactic_proof": false, "tactics": ["have", "ext", "simp", "have", "simp", "refine", "filter_upwards"], "tactic_count": 7}
{"name": "LSeries.abscissaOfAbsConv_binop_le", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Convergence", "is_tactic_proof": true, "tactics": ["refine", "exact", "exact"], "tactic_count": 3}
{"name": "toArithmeticFunction", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.Convolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toArithmeticFunction_congr", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Convolution", "is_tactic_proof": true, "tactics": ["ext", "simp_all"], "tactic_count": 2}
{"name": "ArithmeticFunction.toArithmeticFunction_eq_self", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Convolution", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "LSeries.convolution", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.Convolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LSeries.notation.term_⍟_", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.Convolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LSeries.notation._aux_Mathlib_NumberTheory_LSeries_Convolution___macroRules_LSeries_notation_term_⍟__1", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.Convolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LSeries.notation._aux_Mathlib_NumberTheory_LSeries_Convolution___unexpand_LSeries_convolution_1", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.Convolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LSeries.convolution_congr", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Convolution", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ArithmeticFunction.coe_mul", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Convolution", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LSeries.convolution_def", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Convolution", "is_tactic_proof": true, "tactics": ["ext", "simpa"], "tactic_count": 2}
{"name": "LSeries.convolution_map_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Convolution", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LSeries.term_convolution", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Convolution", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rw", "refine", "have", "rw", "cast_mul,"], "tactic_count": 7}
{"name": "LSeries.term_convolution'", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Convolution", "is_tactic_proof": true, "tactics": ["ext", "rcases", "refine", "have", "ext", "simp", "have", "rintro", "rcases", "simp", "rw"], "tactic_count": 11}
{"name": "LSeriesHasSum.convolution", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Convolution", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "LSeries_convolution'", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Convolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LSeries_convolution", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Convolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LSeriesSummable.convolution", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Convolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LSeries.abscissaOfAbsConv_convolution_le", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Convolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.LSeriesHasSum_mul", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Convolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.LSeries_mul'", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Convolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.LSeries_mul", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Convolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.LSeriesSummable_mul", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Convolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LSeries.logMul", "kind": "abbrev", "module": "Mathlib.NumberTheory.LSeries.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LSeries.hasDerivAt_term", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Deriv", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simp_rw", "exact", "simpa", "non-private"], "tactic_count": 6}
{"name": "_private.Mathlib.NumberTheory.LSeries.Deriv.0.LSeries.LSeriesSummable_logMul_and_hasDerivAt", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Deriv", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "let", "have", "have", "have", "have", "norm_term_le_of_re_le_re", "have", "simp_rw", "refine", "simpa"], "tactic_count": 12}
{"name": "LSeries_hasDerivAt", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LSeries_deriv", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LSeries_deriv_eqOn", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LSeriesSummable_logMul_of_lt_re", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LSeries.abscissaOfAbsConv_logMul", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Deriv", "is_tactic_proof": true, "tactics": ["apply", "exact", "refine", "filter_upwards", "simp", "refine", "simpa"], "tactic_count": 7}
{"name": "LSeries.absicssaOfAbsConv_logPowMul", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Deriv", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "LSeries_iteratedDeriv", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Deriv", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "ih", "have", "have", "simp_rw", "rw", "simp"], "tactic_count": 9}
{"name": "LSeries_differentiableOn", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LSeries_analyticOnNhd", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LSeries_analyticOn", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Deriv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.one_eq_delta", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Dirichlet", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "ArithmeticFunction.not_LSeriesSummable_moebius_at_one", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Dirichlet", "is_tactic_proof": true, "tactics": ["refine", "refine", "by_cases", "simp", "simp"], "tactic_count": 5}
{"name": "ArithmeticFunction.LSeriesSummable_moebius_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Dirichlet", "is_tactic_proof": true, "tactics": ["refine", "by_contra", "exact", "norm_cast", "exact"], "tactic_count": 5}
{"name": "ArithmeticFunction.abscissaOfAbsConv_moebius", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Dirichlet", "is_tactic_proof": true, "tactics": ["simpa", "csInf_Ioo"], "tactic_count": 2}
{"name": "ArithmeticFunction.const_one_eq_zeta", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Dirichlet", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LSeries.one_convolution_eq_zeta_convolution", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Dirichlet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LSeries.convolution_one_eq_convolution_zeta", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Dirichlet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.LSeries.Dirichlet.0.Dchar_one", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.Dirichlet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.LSeries.Dirichlet.0._aux_Mathlib_NumberTheory_LSeries_Dirichlet___macroRules__private_Mathlib_NumberTheory_LSeries_Dirichlet_0_Dchar_one_1", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.Dirichlet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirichletCharacter.isMultiplicative_toArithmeticFunction", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Dirichlet", "is_tactic_proof": true, "tactics": ["refine", "simp", "simp"], "tactic_count": 3}
{"name": "DirichletCharacter.apply_eq_toArithmeticFunction_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Dirichlet", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DirichletCharacter.mul_convolution_distrib", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Dirichlet", "is_tactic_proof": true, "tactics": ["ext", "simp", "refine", "rw", "exact"], "tactic_count": 5}
{"name": "DirichletCharacter.mul_delta", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Dirichlet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirichletCharacter.delta_mul", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Dirichlet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirichletCharacter.convolution_mul_moebius", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Dirichlet", "is_tactic_proof": false, "tactics": ["have", "rw", "simp_rw", "nth_rewrite", "simpa"], "tactic_count": 5}
{"name": "DirichletCharacter.modZero_eq_delta", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Dirichlet", "is_tactic_proof": true, "tactics": ["ext", "rcases", "simp_rw", "rcases", "simp", "have", "simp_all"], "tactic_count": 7}
{"name": "DirichletCharacter.modOne_eq_one", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Dirichlet", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "DirichletCharacter.LSeries_modOne_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Dirichlet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirichletCharacter.not_LSeriesSummable_at_one", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Dirichlet", "is_tactic_proof": true, "tactics": ["refine", "refine", "simp", "split_ifs", "simp", "simp", "all_goals"], "tactic_count": 7}
{"name": "DirichletCharacter.LSeriesSummable_of_one_lt_re", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Dirichlet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirichletCharacter.LSeriesSummable_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Dirichlet", "is_tactic_proof": true, "tactics": ["refine", "by_contra", "exact"], "tactic_count": 3}
{"name": "DirichletCharacter.absicssaOfAbsConv_eq_one", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Dirichlet", "is_tactic_proof": true, "tactics": ["simpa", "csInf_Ioo"], "tactic_count": 2}
{"name": "DirichletCharacter.LSeriesSummable_mul", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Dirichlet", "is_tactic_proof": true, "tactics": ["refine", "simpa"], "tactic_count": 2}
{"name": "DirichletCharacter.LSeries.mul_mu_eq_one", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Dirichlet", "is_tactic_proof": true, "tactics": ["rw", "convolution_mul_moebius,"], "tactic_count": 2}
{"name": "DirichletCharacter.LSeries_ne_zero_of_one_lt_re", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Dirichlet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LSeries.abscissaOfAbsConv_one", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Dirichlet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LSeriesSummable_one_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Dirichlet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.LSeries_zeta_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Dirichlet", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "ArithmeticFunction.LSeriesSummable_zeta_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Dirichlet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.abscissaOfAbsConv_zeta", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Dirichlet", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ArithmeticFunction.LSeries_zeta_eq_riemannZeta", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Dirichlet", "is_tactic_proof": false, "tactics": ["suffices", "simpa", "refine", "rcases"], "tactic_count": 4}
{"name": "ArithmeticFunction.LSeriesHasSum_zeta", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Dirichlet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.LSeries_zeta_mul_Lseries_moebius", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Dirichlet", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "ArithmeticFunction.LSeries_zeta_ne_zero_of_one_lt_re", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Dirichlet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LSeries_one_eq_riemannZeta", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Dirichlet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LSeriesHasSum_one", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Dirichlet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LSeries_one_mul_Lseries_moebius", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Dirichlet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LSeries_one_ne_zero_of_one_lt_re", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Dirichlet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "riemannZeta_ne_zero_of_one_lt_re", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Dirichlet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "riemannZeta_pos_of_one_lt", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Dirichlet", "is_tactic_proof": true, "tactics": ["have", "rw", "refine", "simpa"], "tactic_count": 4}
{"name": "riemannZeta_re_pos_of_one_lt", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Dirichlet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "riemannZeta_im_eq_zero_of_one_lt", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Dirichlet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.convolution_vonMangoldt_zeta", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Dirichlet", "is_tactic_proof": true, "tactics": ["ext", "simpa"], "tactic_count": 2}
{"name": "ArithmeticFunction.convolution_vonMangoldt_const_one", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Dirichlet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.LSeriesSummable_vonMangoldt", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Dirichlet", "is_tactic_proof": false, "tactics": ["have", "rw", "refine", "have", "simpa", "exact"], "tactic_count": 6}
{"name": "DirichletCharacter.convolution_twist_vonMangoldt", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Dirichlet", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "DirichletCharacter.LSeriesSummable_twist_vonMangoldt", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Dirichlet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirichletCharacter.LSeries_twist_vonMangoldt_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Dirichlet", "is_tactic_proof": true, "tactics": ["rcases", "simp", "have", "have", "have", "rw", "exact"], "tactic_count": 7}
{"name": "ArithmeticFunction.LSeries_vonMangoldt_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Dirichlet", "is_tactic_proof": true, "tactics": ["refine", "simp"], "tactic_count": 2}
{"name": "ArithmeticFunction.LSeries_vonMangoldt_eq_deriv_riemannZeta_div", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Dirichlet", "is_tactic_proof": false, "tactics": ["suffices", "refine", "exact"], "tactic_count": 3}
{"name": "DirichletCharacter.LFunction", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.DirichletContinuation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirichletCharacter.LFunction_modOne_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.DirichletContinuation", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "DirichletCharacter.LFunction_eq_LSeries", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.DirichletContinuation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirichletCharacter.deriv_LFunction_eq_deriv_LSeries", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.DirichletContinuation", "is_tactic_proof": true, "tactics": ["refine", "have", "filter_upwards", "exact"], "tactic_count": 4}
{"name": "DirichletCharacter.differentiableAt_LFunction", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.DirichletContinuation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirichletCharacter.differentiable_LFunction", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.DirichletContinuation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirichletCharacter.Even.LFunction_neg_two_mul_nat_add_one", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.DirichletContinuation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirichletCharacter.Even.LFunction_neg_two_mul_nat", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.DirichletContinuation", "is_tactic_proof": true, "tactics": ["obtain", "exact_mod_cast"], "tactic_count": 2}
{"name": "DirichletCharacter.Odd.LFunction_neg_two_mul_nat_sub_one", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.DirichletContinuation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.LSeries.DirichletContinuation.0.DirichletCharacter.LFunction_changeLevel_aux", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.DirichletContinuation", "is_tactic_proof": false, "tactics": ["have", "have", "refine", "refine", "exact", "refine", "refine", "refine", "have", "fun_prop", "refine", "exact", "simpa"], "tactic_count": 13}
{"name": "DirichletCharacter.LFunction_changeLevel", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.DirichletContinuation", "is_tactic_proof": true, "tactics": ["rcases", "have", "have", "continuous_finset_prod", "have", "fun_prop", "exact", "congrFun", "s", "exact"], "tactic_count": 10}
{"name": "DirichletCharacter.LFunctionTrivChar", "kind": "abbrev", "module": "Mathlib.NumberTheory.LSeries.DirichletContinuation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirichletCharacter.LFunctionTrivChar_eq_mul_riemannZeta", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.DirichletContinuation", "is_tactic_proof": true, "tactics": ["rw", "convert", "rw"], "tactic_count": 3}
{"name": "DirichletCharacter.LFunctionTrivChar_residue_one", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.DirichletContinuation", "is_tactic_proof": false, "tactics": ["have", "refine", "rw", "rw", "conv", "refine", "refine", "exact", "continuous_finset_prod", "have", "fun_prop"], "tactic_count": 11}
{"name": "DirichletCharacter.gammaFactor", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.DirichletContinuation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirichletCharacter.Even.gammaFactor_def", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.DirichletContinuation", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DirichletCharacter.Odd.gammaFactor_def", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.DirichletContinuation", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DirichletCharacter.completedLFunction", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.DirichletContinuation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirichletCharacter.completedLFunction_modOne_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.DirichletContinuation", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "DirichletCharacter.differentiableAt_completedLFunction", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.DirichletContinuation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirichletCharacter.differentiable_completedLFunction", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.DirichletContinuation", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "DirichletCharacter.LFunction_eq_completed_div_gammaFactor", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.DirichletContinuation", "is_tactic_proof": true, "tactics": ["rcases", "exact", "apply"], "tactic_count": 3}
{"name": "DirichletCharacter.rootNumber", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.DirichletContinuation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirichletCharacter.rootNumber_modOne", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.DirichletContinuation", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DirichletCharacter.IsPrimitive.completedLFunction_one_sub", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.DirichletContinuation", "is_tactic_proof": true, "tactics": ["classical", "rcases", "simp", "have", "refine", "rwa", "let", "rw", "calc", "completedLFunction", "simp", "split_ifs", "rw", "completedLFunction_one_sub_even", "replace", "rw", "neg_neg]", "congr", "rw", "rw", "ring", "rw"], "tactic_count": 22}
{"name": "DirichletCharacter.LFunctionTrivChar₁", "kind": "abbrev", "module": "Mathlib.NumberTheory.LSeries.DirichletContinuation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirichletCharacter.LFunctionTrivChar₁_apply_one_ne_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.DirichletContinuation", "is_tactic_proof": true, "tactics": ["simp", "refine", "simpa"], "tactic_count": 3}
{"name": "DirichletCharacter.differentiable_LFunctionTrivChar₁", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.DirichletContinuation", "is_tactic_proof": true, "tactics": ["rw", "refine", "continuousWithinAt_compl_self.mp", "simpa"], "tactic_count": 4}
{"name": "DirichletCharacter.deriv_LFunctionTrivChar₁_apply_of_ne_one", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.DirichletContinuation", "is_tactic_proof": false, "tactics": ["have", "refine", "exact", "rw", "add_comm]"], "tactic_count": 5}
{"name": "DirichletCharacter.continuousOn_neg_logDeriv_LFunctionTrivChar₁", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.DirichletContinuation", "is_tactic_proof": true, "tactics": ["simp_rw", "have", "refine", "rcases", "exact", "rw", "exact"], "tactic_count": 7}
{"name": "DirichletCharacter.continuousOn_neg_logDeriv_LFunction_of_nontriv", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.DirichletContinuation", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "HurwitzZeta.hurwitzZeta", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.HurwitzZeta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HurwitzZeta.hurwitzZetaEven_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZeta", "is_tactic_proof": true, "tactics": ["simp", "ring_nf"], "tactic_count": 2}
{"name": "HurwitzZeta.hurwitzZetaOdd_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZeta", "is_tactic_proof": true, "tactics": ["simp", "ring_nf"], "tactic_count": 2}
{"name": "HurwitzZeta.differentiableAt_hurwitzZeta", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZeta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HurwitzZeta.hasSum_hurwitzZeta_of_one_lt_re", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZeta", "is_tactic_proof": true, "tactics": ["convert", "ext1", "apply"], "tactic_count": 3}
{"name": "HurwitzZeta.hurwitzZeta_residue_one", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZeta", "is_tactic_proof": true, "tactics": ["simp", "refine", "exacts"], "tactic_count": 3}
{"name": "HurwitzZeta.differentiableAt_hurwitzZeta_sub_one_div", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZeta", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "HurwitzZeta.tendsto_hurwitzZeta_sub_one_div_nhds_one", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZeta", "is_tactic_proof": true, "tactics": ["simp", "refine"], "tactic_count": 2}
{"name": "HurwitzZeta.differentiable_hurwitzZeta_sub_hurwitzZeta", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZeta", "is_tactic_proof": true, "tactics": ["simp", "refine", "all_goals"], "tactic_count": 3}
{"name": "HurwitzZeta.expZeta", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.HurwitzZeta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HurwitzZeta.cosZeta_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZeta", "is_tactic_proof": true, "tactics": ["rw", "ring_nf"], "tactic_count": 2}
{"name": "HurwitzZeta.sinZeta_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZeta", "is_tactic_proof": true, "tactics": ["rw", "field"], "tactic_count": 2}
{"name": "HurwitzZeta.hasSum_expZeta_of_one_lt_re", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZeta", "is_tactic_proof": true, "tactics": ["convert", "ext1", "simp", "rw"], "tactic_count": 4}
{"name": "HurwitzZeta.differentiableAt_expZeta", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZeta", "is_tactic_proof": true, "tactics": ["apply", "exact", "apply"], "tactic_count": 3}
{"name": "HurwitzZeta.differentiable_expZeta_of_ne_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZeta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HurwitzZeta.LSeriesHasSum_exp", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZeta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HurwitzZeta.hurwitzZeta_one_sub", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZeta", "is_tactic_proof": false, "tactics": ["rw", "rw", "generalize", "generalize", "generalize", "ring_nf"], "tactic_count": 6}
{"name": "HurwitzZeta.expZeta_one_sub", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZeta", "is_tactic_proof": false, "tactics": ["have", "convert", "push_cast", "ring", "rw", "hurwitzZetaOdd_neg,", "rw", "generalize", "generalize", "generalize", "ring_nf", "rw", "ring_nf"], "tactic_count": 13}
{"name": "HurwitzZeta.evenKernel", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HurwitzZeta.evenKernel_def", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HurwitzZeta.evenKernel_undef", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "HurwitzZeta.cosKernel", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HurwitzZeta.cosKernel_def", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HurwitzZeta.cosKernel_undef", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "HurwitzZeta.evenKernel_eq_cosKernel_of_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": true, "tactics": ["ext1", "simp"], "tactic_count": 2}
{"name": "HurwitzZeta.evenKernel_neg", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "HurwitzZeta.cosKernel_neg", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "HurwitzZeta.continuousOn_evenKernel", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": true, "tactics": ["induction", "apply", "simp", "refine", "exact"], "tactic_count": 5}
{"name": "HurwitzZeta.continuousOn_cosKernel", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": true, "tactics": ["induction", "apply", "simp", "refine", "exact"], "tactic_count": 5}
{"name": "HurwitzZeta.evenKernel_functional_equation", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": true, "tactics": ["rcases", "rw", "exact", "induction", "rw", "have", "push_cast", "rw", "have", "have", "rw", "ring", "have", "rw", "have", "rw", "ring", "rw", "neg_add_cancel,"], "tactic_count": 19}
{"name": "HurwitzZeta.hasSum_int_evenKernel", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": true, "tactics": ["rw", "have", "rw", "ring_nf", "simp", "simpa"], "tactic_count": 6}
{"name": "HurwitzZeta.hasSum_int_cosKernel", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": true, "tactics": ["rw", "have", "rw", "ring_nf", "simp", "simpa"], "tactic_count": 6}
{"name": "HurwitzZeta.hasSum_int_evenKernel₀", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": true, "tactics": ["haveI", "simp_rw", "split_ifs", "obtain", "simpa", "suffices", "contrapose", "let", "exact"], "tactic_count": 9}
{"name": "HurwitzZeta.hasSum_int_cosKernel₀", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HurwitzZeta.hasSum_nat_cosKernel₀", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": true, "tactics": ["rw", "have", "rw", "simp_rw", "add_sub_assoc,", "refine", "push_cast", "rw", "congr"], "tactic_count": 9}
{"name": "HurwitzZeta.isBigO_atTop_evenKernel_sub", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": true, "tactics": ["induction", "obtain", "refine", "filter_upwards", "simp"], "tactic_count": 5}
{"name": "HurwitzZeta.isBigO_atTop_cosKernel_sub", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": true, "tactics": ["induction", "obtain", "refine", "filter_upwards", "simp", "apply", "intro", "rw", "exact"], "tactic_count": 9}
{"name": "HurwitzZeta.hurwitzEvenFEPair", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HurwitzZeta.hurwitzEvenFEPair_zero_symm", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": true, "tactics": ["unfold", "congr"], "tactic_count": 2}
{"name": "HurwitzZeta.hurwitzEvenFEPair_neg", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": true, "tactics": ["unfold", "congr"], "tactic_count": 2}
{"name": "HurwitzZeta.completedHurwitzZetaEven", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HurwitzZeta.completedHurwitzZetaEven₀", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HurwitzZeta.completedHurwitzZetaEven_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": true, "tactics": ["rw", "congr", "change", "completedHurwitzZetaEven₀", "completedHurwitzZetaEven₀", "rw", "change", "push_cast", "rw"], "tactic_count": 9}
{"name": "HurwitzZeta.completedCosZeta", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HurwitzZeta.completedCosZeta₀", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HurwitzZeta.completedCosZeta_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": true, "tactics": ["rw", "congr", "rw", "div_mul_cancel₀", "simp_rw", "mul_div_assoc,"], "tactic_count": 6}
{"name": "HurwitzZeta.completedHurwitzZetaEven_neg", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HurwitzZeta.completedHurwitzZetaEven₀_neg", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HurwitzZeta.completedCosZeta_neg", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HurwitzZeta.completedCosZeta₀_neg", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HurwitzZeta.completedHurwitzZetaEven_one_sub", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HurwitzZeta.completedHurwitzZetaEven₀_one_sub", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HurwitzZeta.completedCosZeta_one_sub", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HurwitzZeta.completedCosZeta₀_one_sub", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HurwitzZeta.differentiableAt_completedHurwitzZetaEven", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": false, "tactics": ["refine", "rcases", "change", "rw", "exact"], "tactic_count": 5}
{"name": "HurwitzZeta.differentiable_completedHurwitzZetaEven₀", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HurwitzZeta.differentiableAt_one_completedHurwitzZetaEven_sub_completedHurwitzZetaEven", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": false, "tactics": ["have", "completedHurwitzZetaEven", "completedHurwitzZetaEven₀", "simp_rw", "abel", "rw", "refine", "apply"], "tactic_count": 8}
{"name": "HurwitzZeta.differentiableAt_completedCosZeta", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": false, "tactics": ["refine", "exact", "change", "refine", "simpa", "simpa"], "tactic_count": 6}
{"name": "HurwitzZeta.differentiable_completedCosZeta₀", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.LSeries.HurwitzZetaEven.0.HurwitzZeta.tendsto_div_two_punctured_nhds", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HurwitzZeta.completedHurwitzZetaEven_residue_one", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": false, "tactics": ["have", "simp", "refine", "rw"], "tactic_count": 4}
{"name": "HurwitzZeta.completedHurwitzZetaEven_residue_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": false, "tactics": ["have", "have", "simp", "refine", "simp"], "tactic_count": 5}
{"name": "HurwitzZeta.completedCosZeta_residue_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": true, "tactics": ["have", "refine", "simp"], "tactic_count": 3}
{"name": "HurwitzZeta.hasSum_int_completedCosZeta", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": true, "tactics": ["let", "have", "refine", "split_ifs", "simp", "rw", "rw", "congr", "refine", "rwa", "refine", "apply", "intro", "simp", "norm_div,", "norm_of_nonneg", "simp"], "tactic_count": 17}
{"name": "HurwitzZeta.hasSum_nat_completedCosZeta", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "refine", "split_ifs", "simp", "simp", "show"], "tactic_count": 8}
{"name": "HurwitzZeta.hasSum_int_completedHurwitzZetaEven", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": false, "tactics": ["have", "refine", "split_ifs", "rw", "rw", "rw", "completedHurwitzZetaEven", "mellin", "simp_rw", "refine", "rwa", "refine", "simp_rw", "apply", "rwa", "rw"], "tactic_count": 16}
{"name": "HurwitzZeta.differentiableAt_update_of_residue", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": false, "tactics": ["have", "have", "refine", "filter_upwards", "rw", "rcases", "refine", "filter_upwards", "simp", "simp_rw", "have", "refine", "simp", "refine", "rw", "exact", "exact"], "tactic_count": 17}
{"name": "HurwitzZeta.hurwitzZetaEven", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HurwitzZeta.hurwitzZetaEven_def_of_ne_or_ne", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": true, "tactics": ["rw", "rcases", "rw", "simpa"], "tactic_count": 4}
{"name": "HurwitzZeta.hurwitzZetaEven_apply_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HurwitzZeta.hurwitzZetaEven_neg", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HurwitzZeta.hurwitzZetaEven_neg_two_mul_nat_add_one", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "HurwitzZeta.differentiableAt_hurwitzZetaEven", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": false, "tactics": ["have", "differentiableAt_update_of_residue", "simp_rw", "exact"], "tactic_count": 4}
{"name": "HurwitzZeta.hurwitzZetaEven_residue_one", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": false, "tactics": ["have", "simpa", "refine", "filter_upwards", "simp"], "tactic_count": 5}
{"name": "HurwitzZeta.differentiableAt_hurwitzZetaEven_sub_one_div", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": false, "tactics": ["suffices", "apply", "filter_upwards", "rw", "simp_rw", "refine", "simp_rw", "conv", "exact"], "tactic_count": 9}
{"name": "HurwitzZeta.tendsto_hurwitzZetaEven_sub_one_div_nhds_one", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HurwitzZeta.differentiable_hurwitzZetaEven_sub_hurwitzZetaEven", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": true, "tactics": ["intro", "rcases", "exact", "convert", "abel"], "tactic_count": 5}
{"name": "HurwitzZeta.hasSum_int_hurwitzZetaEven", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": true, "tactics": ["rw", "have", "exact", "this.congr_fun", "simp"], "tactic_count": 5}
{"name": "HurwitzZeta.hasSum_nat_hurwitzZetaEven", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": true, "tactics": ["refine", "simp"], "tactic_count": 2}
{"name": "HurwitzZeta.hasSum_nat_hurwitzZetaEven_of_mem_Icc", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": true, "tactics": ["refine", "congr"], "tactic_count": 2}
{"name": "HurwitzZeta.cosZeta", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HurwitzZeta.cosZeta_apply_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HurwitzZeta.cosZeta_neg", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HurwitzZeta.cosZeta_neg_two_mul_nat_add_one", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "HurwitzZeta.differentiableAt_cosZeta", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": true, "tactics": ["rcases", "exact", "differentiableAt_update_of_residue", "apply", "filter_upwards", "rw"], "tactic_count": 6}
{"name": "HurwitzZeta.differentiable_cosZeta_of_ne_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HurwitzZeta.hasSum_int_cosZeta", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "mul_div_cancel_left₀"], "tactic_count": 4}
{"name": "HurwitzZeta.hasSum_nat_cosZeta", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": true, "tactics": ["have", "simp_rw", "zero_cpow", "simp_rw", "exact"], "tactic_count": 5}
{"name": "HurwitzZeta.LSeriesHasSum_cos", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HurwitzZeta.hurwitzZetaEven_one_sub", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": false, "tactics": ["have", "rw", "simpa", "rw", "generalize", "ring_nf"], "tactic_count": 6}
{"name": "HurwitzZeta.cosZeta_one_sub", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaEven", "is_tactic_proof": true, "tactics": ["rw", "have", "rw", "simpa", "rw", "hurwitzZetaEven_def_of_ne_or_ne", "generalize", "ring_nf"], "tactic_count": 8}
{"name": "HurwitzZeta.jacobiTheta₂''", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaOdd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HurwitzZeta.jacobiTheta₂''_conj", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaOdd", "is_tactic_proof": true, "tactics": ["simp", "jacobiTheta₂'_neg_left]"], "tactic_count": 2}
{"name": "HurwitzZeta.jacobiTheta₂''_add_left", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaOdd", "is_tactic_proof": true, "tactics": ["simp", "generalize", "generalize", "simp_rw", "refine", "congr_arg", "rw", "congrm"], "tactic_count": 8}
{"name": "HurwitzZeta.jacobiTheta₂''_neg_left", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaOdd", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HurwitzZeta.jacobiTheta₂'_functional_equation'", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaOdd", "is_tactic_proof": true, "tactics": ["rcases", "rw", "have", "rw", "rw", "div_mul_div_comm,", "mul_comm", "congr", "rw", "div_mul_eq_mul_div", "jacobiTheta₂'_neg_left,", "congr", "rw"], "tactic_count": 13}
{"name": "HurwitzZeta.oddKernel", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaOdd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HurwitzZeta.oddKernel_def", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaOdd", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HurwitzZeta.oddKernel_def'", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaOdd", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HurwitzZeta.oddKernel_undef", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaOdd", "is_tactic_proof": true, "tactics": ["induction", "rw", "mul_zero]", "simpa"], "tactic_count": 4}
{"name": "HurwitzZeta.sinKernel", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaOdd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HurwitzZeta.sinKernel_def", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaOdd", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HurwitzZeta.sinKernel_undef", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaOdd", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "HurwitzZeta.oddKernel_neg", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaOdd", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "HurwitzZeta.oddKernel_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaOdd", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HurwitzZeta.sinKernel_neg", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaOdd", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "HurwitzZeta.sinKernel_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaOdd", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HurwitzZeta.continuousOn_oddKernel", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaOdd", "is_tactic_proof": true, "tactics": ["induction", "a", "suffices", "simp_rw", "refine", "fun_prop", "have", "apply", "exact", "exact", "continuousAt_const.mul"], "tactic_count": 11}
{"name": "HurwitzZeta.continuousOn_sinKernel", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaOdd", "is_tactic_proof": true, "tactics": ["induction", "a", "suffices", "simp_rw", "apply", "have", "fun_prop"], "tactic_count": 7}
{"name": "HurwitzZeta.oddKernel_functional_equation", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaOdd", "is_tactic_proof": true, "tactics": ["rcases", "rw", "induction", "a", "have", "rw", "neg_mul,", "have", "rw", "have", "simp", "have", "rw", "generalize", "rw", "ofReal_ofNat,", "eq_div_iff", "eq_div_iff"], "tactic_count": 18}
{"name": "HurwitzZeta.hasSum_int_oddKernel", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaOdd", "is_tactic_proof": true, "tactics": ["rw", "have", "have", "refine", "rw", "jacobiTheta₂_term,", "push_cast", "simp", "congrm", "simp", "ring_nf"], "tactic_count": 11}
{"name": "HurwitzZeta.hasSum_int_sinKernel", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaOdd", "is_tactic_proof": false, "tactics": ["have", "simp", "not_false_eq_true]", "rw", "refine", "rw", "ofReal_mul,", "congrm", "simp", "exact", "simp"], "tactic_count": 11}
{"name": "HurwitzZeta.hasSum_nat_sinKernel", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaOdd", "is_tactic_proof": true, "tactics": ["rw", "have", "simp", "refine", "simp_rw", "ofReal_sin,", "push_cast", "congr", "rw", "neg_neg,", "congr"], "tactic_count": 11}
{"name": "HurwitzZeta.isBigO_atTop_oddKernel", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaOdd", "is_tactic_proof": true, "tactics": ["induction", "obtain", "refine", "filter_upwards", "simpa", "abs_of_nonneg"], "tactic_count": 6}
{"name": "HurwitzZeta.isBigO_atTop_sinKernel", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaOdd", "is_tactic_proof": true, "tactics": ["induction", "obtain", "refine", "filter_upwards", "rw", "apply", "exact", "intro", "rw", "mul_assoc,", "exact"], "tactic_count": 11}
{"name": "HurwitzZeta.hurwitzOddFEPair", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaOdd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HurwitzZeta.completedHurwitzZetaOdd", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaOdd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HurwitzZeta.differentiable_completedHurwitzZetaOdd", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaOdd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HurwitzZeta.completedSinZeta", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaOdd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HurwitzZeta.differentiable_completedSinZeta", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaOdd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HurwitzZeta.completedHurwitzZetaOdd_neg", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaOdd", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HurwitzZeta.completedSinZeta_neg", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaOdd", "is_tactic_proof": true, "tactics": ["simp", "integral_neg,"], "tactic_count": 2}
{"name": "HurwitzZeta.completedHurwitzZetaOdd_one_sub", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaOdd", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HurwitzZeta.completedSinZeta_one_sub", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaOdd", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HurwitzZeta.hasSum_int_completedSinZeta", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaOdd", "is_tactic_proof": true, "tactics": ["let", "have", "simp_rw", "norm_div,", "have", "refine", "rw", "have", "simp_rw", "apply", "apply", "refine", "simp", "ring"], "tactic_count": 14}
{"name": "HurwitzZeta.hasSum_nat_completedSinZeta", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaOdd", "is_tactic_proof": true, "tactics": ["have", "simp_rw", "refine", "rw", "rcases", "simp", "simp_rw", "simp", "congr", "rw", "congr"], "tactic_count": 11}
{"name": "HurwitzZeta.hasSum_int_completedHurwitzZetaOdd", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaOdd", "is_tactic_proof": true, "tactics": ["let", "let", "have", "refine", "simp", "have", "simp_rw", "apply", "rwa", "have", "refine", "simp"], "tactic_count": 12}
{"name": "HurwitzZeta.hurwitzZetaOdd", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaOdd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HurwitzZeta.hurwitzZetaOdd_neg", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaOdd", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "HurwitzZeta.differentiable_hurwitzZetaOdd", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaOdd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HurwitzZeta.sinZeta", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaOdd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HurwitzZeta.sinZeta_neg", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaOdd", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "HurwitzZeta.differentiableAt_sinZeta", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaOdd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HurwitzZeta.hasSum_int_hurwitzZetaOdd", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaOdd", "is_tactic_proof": true, "tactics": ["refine", "have", "simp"], "tactic_count": 3}
{"name": "HurwitzZeta.hasSum_nat_hurwitzZetaOdd", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaOdd", "is_tactic_proof": true, "tactics": ["refine", "rw", "have", "rw"], "tactic_count": 4}
{"name": "HurwitzZeta.hasSum_nat_hurwitzZetaOdd_of_mem_Icc", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaOdd", "is_tactic_proof": true, "tactics": ["refine", "suffices", "simp", "intro", "rw", "rcases", "simp", "rw"], "tactic_count": 8}
{"name": "HurwitzZeta.hasSum_int_sinZeta", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaOdd", "is_tactic_proof": true, "tactics": ["rw", "refine", "have", "simp"], "tactic_count": 4}
{"name": "HurwitzZeta.hasSum_nat_sinZeta", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaOdd", "is_tactic_proof": true, "tactics": ["have", "simp_rw", "zero_cpow", "simp_rw", "refine", "rcases", "simp", "mul_comm", "congr", "simp"], "tactic_count": 10}
{"name": "HurwitzZeta.LSeriesHasSum_sin", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaOdd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HurwitzZeta.hurwitzZetaOdd_neg_two_mul_nat_sub_one", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaOdd", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HurwitzZeta.sinZeta_neg_two_mul_nat_sub_one", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaOdd", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HurwitzZeta.hurwitzZetaOdd_one_sub", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaOdd", "is_tactic_proof": true, "tactics": ["rw", "completedHurwitzZetaOdd_one_sub,"], "tactic_count": 2}
{"name": "HurwitzZeta.sinZeta_one_sub", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaOdd", "is_tactic_proof": true, "tactics": ["rw", "hurwitzZetaOdd,"], "tactic_count": 2}
{"name": "HurwitzZeta.cosZeta_two_mul_nat", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaValues", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "refine", "norm_cast", "ring_nf", "push_cast", "congr", "have", "rw", "apply", "norm_cast", "lia"], "tactic_count": 13}
{"name": "HurwitzZeta.sinZeta_two_mul_nat_add_one", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaValues", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "refine", "norm_cast", "ring_nf", "push_cast", "congr", "have", "rw", "apply", "norm_cast", "lia"], "tactic_count": 13}
{"name": "HurwitzZeta.cosZeta_two_mul_nat'", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaValues", "is_tactic_proof": true, "tactics": ["rw", "congr", "have", "rw", "simp_rw", "mul_right_comm", "norm_cast"], "tactic_count": 7}
{"name": "HurwitzZeta.sinZeta_two_mul_nat_add_one'", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaValues", "is_tactic_proof": true, "tactics": ["rw", "congr", "have", "rw", "simp_rw", "rw", "ring"], "tactic_count": 7}
{"name": "HurwitzZeta.hurwitzZetaEven_one_sub_two_mul_nat", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaValues", "is_tactic_proof": false, "tactics": ["have", "rw", "refine", "exact", "have", "have", "refine", "simp", "rw", "mul_assoc,", "congr", "rw", "sub_zero", "mul_neg_one,"], "tactic_count": 14}
{"name": "HurwitzZeta.hurwitzZetaOdd_neg_two_mul_nat", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaValues", "is_tactic_proof": false, "tactics": ["have", "rw", "refine", "positivity", "have", "refine", "simp", "rw", "sinZeta_two_mul_nat_add_one", "mul_div_assoc]", "congr", "rw", "ofReal_div,", "ofReal_one,"], "tactic_count": 14}
{"name": "_private.Mathlib.NumberTheory.LSeries.HurwitzZetaValues.0.HurwitzZeta.hurwitzZeta_one_sub_two_mul_nat", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaValues", "is_tactic_proof": false, "tactics": ["suffices", "rw", "obtain", "rw"], "tactic_count": 4}
{"name": "_private.Mathlib.NumberTheory.LSeries.HurwitzZetaValues.0.HurwitzZeta.hurwitzZeta_neg_two_mul_nat", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaValues", "is_tactic_proof": false, "tactics": ["suffices", "obtain", "simpa"], "tactic_count": 3}
{"name": "HurwitzZeta.hurwitzZeta_neg_nat", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaValues", "is_tactic_proof": true, "tactics": ["rcases", "exact_mod_cast", "exact_mod_cast"], "tactic_count": 3}
{"name": "riemannZeta_two_mul_nat", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaValues", "is_tactic_proof": true, "tactics": ["convert", "rw", "simp", "norm_cast"], "tactic_count": 4}
{"name": "riemannZeta_two", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaValues", "is_tactic_proof": true, "tactics": ["convert", "rw", "simp", "norm_cast"], "tactic_count": 4}
{"name": "riemannZeta_four", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaValues", "is_tactic_proof": true, "tactics": ["convert", "rw", "simp", "norm_cast"], "tactic_count": 4}
{"name": "riemannZeta_neg_nat_eq_bernoulli'", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaValues", "is_tactic_proof": true, "tactics": ["rcases", "rw", "rw", "ofReal_zero,"], "tactic_count": 4}
{"name": "riemannZeta_neg_nat_eq_bernoulli", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaValues", "is_tactic_proof": true, "tactics": ["rw", "neg_one_mul,"], "tactic_count": 2}
{"name": "LSeries.abscissaOfAbsConv_add_le", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Injectivity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LSeries.abscissaOfAbsConv_sub_le", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Injectivity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.LSeries.Injectivity.0.cpow_mul_div_cpow_eq_div_div_cpow", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Injectivity", "is_tactic_proof": true, "tactics": ["have", "rw", "congr", "simp_rw", "rw", "show", "congr", "rw"], "tactic_count": 8}
{"name": "LSeries.tendsto_cpow_mul_atTop", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Injectivity", "is_tactic_proof": true, "tactics": ["obtain", "lift", "let", "have", "have", "rcases", "simp", "exact", "simp", "have", "refine", "simpa", "have", "intro", "rw", "congr", "ext1", "rcases", "simp", "simp", "conv", "refine", "tendsto_const_nhds.add", "have", "refine", "by_cases", "simp", "simp", "have", "rcases", "have", "have", "have", "have", "simp", "conv", "enter", "rw", "conv", "exact", "simp", "rw", "refine", "filter_upwards", "rcases", "simp", "rw", "have", "gcongr", "assumption", "simp"], "tactic_count": 51}
{"name": "LSeries.tendsto_atTop", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Injectivity", "is_tactic_proof": true, "tactics": ["let", "have", "have", "have", "simp_rw", "convert", "simp"], "tactic_count": 7}
{"name": "LSeries_eq_zero_of_abscissaOfAbsConv_eq_top", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Injectivity", "is_tactic_proof": true, "tactics": ["ext1", "exact", "mt"], "tactic_count": 3}
{"name": "LSeries_eventually_eq_zero_iff'", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Injectivity", "is_tactic_proof": true, "tactics": ["by_cases", "simpa", "simp", "refine", "let", "have", "have", "suffices", "have", "have", "have", "simp", "rw", "obtain", "exact", "intro", "induction", "ind", "suffices", "replace", "simp", "exact", "cases", "zero", "succ", "simp"], "tactic_count": 26}
{"name": "LSeries_eq_zero_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Injectivity", "is_tactic_proof": true, "tactics": ["by_cases", "simpa", "simp", "refine", "convert", "refine", "ext", "simp", "simp", "simpa"], "tactic_count": 10}
{"name": "LSeries_sub_eventuallyEq_zero_of_LSeries_eventually_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Injectivity", "is_tactic_proof": true, "tactics": ["rw", "obtain", "obtain", "obtain", "lift", "lift", "refine", "have", "refine", "exact", "have", "refine", "exact", "rw"], "tactic_count": 14}
{"name": "LSeries.eq_of_LSeries_eventually_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Injectivity", "is_tactic_proof": false, "tactics": ["have", "have", "lt_top_iff_ne_top.mp", "simpa"], "tactic_count": 4}
{"name": "LSeries_eq_iff_of_abscissaOfAbsConv_lt_top", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Injectivity", "is_tactic_proof": true, "tactics": ["refine", "refine", "exact"], "tactic_count": 3}
{"name": "LSeries_injOn", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Injectivity", "is_tactic_proof": true, "tactics": ["intro", "push", "replace", "ext1", "cases", "zero", "succ"], "tactic_count": 7}
{"name": "LSeries.term_add", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Linearity", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "LSeries.term_add_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Linearity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LSeriesHasSum.add", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Linearity", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "LSeriesSummable.add", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Linearity", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "LSeries_add", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Linearity", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "LSeries.term_neg", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Linearity", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "LSeries.term_neg_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Linearity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LSeriesHasSum.neg", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Linearity", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "LSeriesSummable.neg", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Linearity", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "LSeriesSummable.neg_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Linearity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LSeries_neg", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Linearity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LSeries.term_sub", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Linearity", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "LSeries.term_sub_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Linearity", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LSeriesHasSum.sub", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Linearity", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "LSeriesSummable.sub", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Linearity", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "LSeries_sub", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Linearity", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "LSeries.term_smul", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Linearity", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "LSeries.term_smul_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Linearity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LSeriesHasSum.smul", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Linearity", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "LSeriesSummable.smul", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Linearity", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "LSeriesSummable.of_smul", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Linearity", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "LSeriesSummable.smul_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Linearity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LSeries_smul", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Linearity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LSeries.term_sum_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Linearity", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "LSeries.term_sum", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Linearity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LSeriesHasSum.sum", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Linearity", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "LSeriesSummable.sum", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Linearity", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "LSeries_sum", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Linearity", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "hasSum_mellin", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.MellinEqDirichlet", "is_tactic_proof": false, "tactics": ["simp_rw", "tsum_mul_left]", "convert", "hasSum_integral_of_summable_integral_norm", "simp_rw", "rcases", "rw", "have", "simp_rw", "rw", "rcases", "simp", "simp_rw", "have", "rw", "refine", "measurableSet_Ioi).const_mul", "simp_rw", "rw", "rw", "exact", "apply", "convert", "simp_rw", "rw", "rcases", "simp", "congr", "have", "simp_rw", "rw", "refine", "rw"], "tactic_count": 33}
{"name": "hasSum_mellin_pi_mul", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.MellinEqDirichlet", "is_tactic_proof": true, "tactics": ["have", "convert", "have", "rcases", "simp", "rw", "simp_rw", "ring_nf", "have", "rcases", "simp", "rw", "simpa"], "tactic_count": 13}
{"name": "hasSum_mellin_pi_mul₀", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.MellinEqDirichlet", "is_tactic_proof": true, "tactics": ["have", "let", "have", "simp", "split_ifs", "exact", "have", "simp_rw", "convert", "rcases", "refine", "simp", "split_ifs", "simp", "positivity", "have", "rw"], "tactic_count": 17}
{"name": "hasSum_mellin_pi_mul_sq", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.MellinEqDirichlet", "is_tactic_proof": true, "tactics": ["have", "simp_rw", "convert", "rw", "rw", "ring_nf", "all_goals", "convert", "rw"], "tactic_count": 9}
{"name": "hasSum_mellin_pi_mul_sq'", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.MellinEqDirichlet", "is_tactic_proof": true, "tactics": ["have", "have", "have", "have", "split_ifs", "conv", "convert", "rcases", "rw", "rw", "conv_rhs", "field", "convert", "rcases", "rw", "rw", "div_right_comm,"], "tactic_count": 17}
{"name": "DirichletCharacter.zetaMul", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.Nonvanishing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirichletCharacter.isMultiplicative_zetaMul", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Nonvanishing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirichletCharacter.LSeriesSummable_zetaMul", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Nonvanishing", "is_tactic_proof": false, "tactics": ["refine", "simpa"], "tactic_count": 2}
{"name": "DirichletCharacter.zetaMul_prime_pow_nonneg", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Nonvanishing", "is_tactic_proof": false, "tactics": ["simp", "hp.ne_zero,", "rcases", "refine", "simp", "refine", "simp", "simp", "split_ifs", "exacts"], "tactic_count": 10}
{"name": "DirichletCharacter.zetaMul_nonneg", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Nonvanishing", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simpa", "zetaMul_prime_pow_nonneg"], "tactic_count": 4}
{"name": "_private.Mathlib.NumberTheory.LSeries.Nonvanishing.0.DirichletCharacter.BadChar.F", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.Nonvanishing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.LSeries.Nonvanishing.0.DirichletCharacter.BadChar.F_differentiableAt_of_ne", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Nonvanishing", "is_tactic_proof": true, "tactics": ["apply", "exact", "filter_upwards"], "tactic_count": 3}
{"name": "_private.Mathlib.NumberTheory.LSeries.Nonvanishing.0.DirichletCharacter.BadChar.F_eq_LSeries", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Nonvanishing", "is_tactic_proof": true, "tactics": ["rw", "have", "simp", "congr", "simp_rw", "exact", "exact", "exact"], "tactic_count": 8}
{"name": "_private.Mathlib.NumberTheory.LSeries.Nonvanishing.0.DirichletCharacter.BadChar.F_differentiable", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Nonvanishing", "is_tactic_proof": true, "tactics": ["intro", "rcases", "exact", "refine", "filter_upwards", "exact", "let", "let", "have", "ext1", "rcases", "simp", "simp", "mul_div_cancel₀", "rw", "apply", "simpa", "exact"], "tactic_count": 18}
{"name": "_private.Mathlib.NumberTheory.LSeries.Nonvanishing.0.DirichletCharacter.BadChar.F_neg_two", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Nonvanishing", "is_tactic_proof": true, "tactics": ["have", "rw", "rw"], "tactic_count": 3}
{"name": "_private.Mathlib.NumberTheory.LSeries.Nonvanishing.0.DirichletCharacter.LFunction_apply_one_ne_zero_of_quadratic", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Nonvanishing", "is_tactic_proof": true, "tactics": ["intro", "let", "refine", "refine", "exact"], "tactic_count": 5}
{"name": "_private.Mathlib.NumberTheory.LSeries.Nonvanishing.0.DirichletCharacter.re_log_comb_nonneg'", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Nonvanishing", "is_tactic_proof": true, "tactics": ["have", "have", "have", "rw", "refine", "simp", "rcases", "simp", "simp", "refine", "rw", "convert", "ring"], "tactic_count": 13}
{"name": "_private.Mathlib.NumberTheory.LSeries.Nonvanishing.0.DirichletCharacter.re_log_comb_nonneg", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Nonvanishing", "is_tactic_proof": true, "tactics": ["by_cases", "have", "have", "rw", "exact", "have", "rw", "norm_cpow_eq_rpow_re_of_pos", "simp", "rw", "convert", "simp", "congr", "rw", "mul_left_comm]", "rw", "show", "simp", "add_zero,"], "tactic_count": 19}
{"name": "DirichletCharacter.summable_neg_log_one_sub_mul_prime_cpow", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Nonvanishing", "is_tactic_proof": false, "tactics": ["have", "simpa", "mul_le_of_le_one_left", "refine", "simp"], "tactic_count": 5}
{"name": "_private.Mathlib.NumberTheory.LSeries.Nonvanishing.0.DirichletCharacter.one_lt_re_one_add", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Nonvanishing", "is_tactic_proof": true, "tactics": ["simp", "sub_self,"], "tactic_count": 2}
{"name": "DirichletCharacter.norm_LSeries_product_ge_one", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Nonvanishing", "is_tactic_proof": true, "tactics": ["have", "have", "have", "have", "have", "have", "have", "rw", "simp", "rw", "simpa", "ofReal_one]"], "tactic_count": 12}
{"name": "DirichletCharacter.norm_LFunction_product_ge_one", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Nonvanishing", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "DirichletCharacter.LFunctionTrivChar_isBigO_near_one_horizontal", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Nonvanishing", "is_tactic_proof": false, "tactics": ["have", "have", "convert", "simp", "simpa", "exact", "exact"], "tactic_count": 7}
{"name": "_private.Mathlib.NumberTheory.LSeries.Nonvanishing.0.DirichletCharacter.one_add_I_mul_ne_one_or", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Nonvanishing", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "DirichletCharacter.LFunction_isBigO_horizontal", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Nonvanishing", "is_tactic_proof": true, "tactics": ["refine", "simp_rw", "have", "rw", "exact"], "tactic_count": 5}
{"name": "_private.Mathlib.NumberTheory.LSeries.Nonvanishing.0.DirichletCharacter.LFunction_isBigO_horizontal_of_eq_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Nonvanishing", "is_tactic_proof": true, "tactics": ["simp_rw", "have", "rw", "simpa"], "tactic_count": 4}
{"name": "_private.Mathlib.NumberTheory.LSeries.Nonvanishing.0.DirichletCharacter.LFunction_ne_zero_of_not_quadratic_or_ne_one", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Nonvanishing", "is_tactic_proof": true, "tactics": ["intro", "have", "refine", "simp", "have", "have", "rcases", "rw", "rw", "mul_one]", "have", "eventually_nhdsWithin_of_forall", "have", "simp", "replace", "simp", "exact", "isLittleO_irrefl"], "tactic_count": 18}
{"name": "DirichletCharacter.LFunction_ne_zero_of_re_eq_one", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Nonvanishing", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "have", "rw", "replace", "exact"], "tactic_count": 6}
{"name": "DirichletCharacter.LFunction_ne_zero_of_one_le_re", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Nonvanishing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirichletCharacter.LFunction_apply_one_ne_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Nonvanishing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "riemannZeta_ne_zero_of_one_le_re", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Nonvanishing", "is_tactic_proof": true, "tactics": ["rcases", "exact", "exact"], "tactic_count": 3}
{"name": "LSeries.iteratedDeriv_alternating", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Positivity", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "split", "exact", "refine", "induction", "zero", "succ", "rw", "refine", "simp"], "tactic_count": 12}
{"name": "LSeries.positive", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Positivity", "is_tactic_proof": true, "tactics": ["rw", "refine", "exact"], "tactic_count": 3}
{"name": "LSeries.positive_of_differentiable_of_eqOn", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Positivity", "is_tactic_proof": true, "tactics": ["have", "have", "have", "have", "refine", "have", "simpa", "exact_mod_cast"], "tactic_count": 8}
{"name": "ArithmeticFunction.iteratedDeriv_LSeries_alternating", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Positivity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.LSeries_positive", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Positivity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.LSeries_positive_of_differentiable_of_eqOn", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.Positivity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tprod_eq_tprod_primes_of_mulSupport_subset_prime_powers", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.PrimesInAP", "is_tactic_proof": false, "tactics": ["have", "prodNatEquiv.symm.multipliable_iff.mp", "simpa", "simp", "refine"], "tactic_count": 5}
{"name": "tprod_eq_tprod_primes_mul_tprod_primes_of_mulSupport_subset_prime_powers", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.PrimesInAP", "is_tactic_proof": true, "tactics": ["rw", "have", "hfm.comp_injective", "conv_lhs", "enter", "enter", "exact", "hfm.comp_injective"], "tactic_count": 8}
{"name": "ArithmeticFunction.vonMangoldt.residueClass", "kind": "abbrev", "module": "Mathlib.NumberTheory.LSeries.PrimesInAP", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.vonMangoldt.residueClass_nonneg", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.PrimesInAP", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.vonMangoldt.residueClass_le", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.PrimesInAP", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.vonMangoldt.residueClass_apply_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.PrimesInAP", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ArithmeticFunction.vonMangoldt.abscissaOfAbsConv_residueClass_le_one", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.PrimesInAP", "is_tactic_proof": true, "tactics": ["refine", "unfold", "have", "convert", "ext1", "by_cases", "simp", "simp", "zero_div,"], "tactic_count": 9}
{"name": "ArithmeticFunction.vonMangoldt.support_residueClass_prime_div", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.PrimesInAP", "is_tactic_proof": false, "tactics": ["simp", "ext1", "simp", "exact"], "tactic_count": 4}
{"name": "_private.Mathlib.NumberTheory.LSeries.PrimesInAP.0.ArithmeticFunction.vonMangoldt.F₀", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.PrimesInAP", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.LSeries.PrimesInAP.0.ArithmeticFunction.vonMangoldt.F'", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.PrimesInAP", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.LSeries.PrimesInAP.0.ArithmeticFunction.vonMangoldt.F''", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.PrimesInAP", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.LSeries.PrimesInAP.0.ArithmeticFunction.vonMangoldt.F''_le", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.PrimesInAP", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.LSeries.PrimesInAP.0.ArithmeticFunction.vonMangoldt.summable_F''", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.PrimesInAP", "is_tactic_proof": true, "tactics": ["have", "have", "suffices", "refine", "simp", "positivity", "conv", "refine", "dsimp", "exact", "dsimp", "conv", "refine", "positivity", "rw", "gcongr", "rw", "inv_le_inv₀", "exact"], "tactic_count": 19}
{"name": "ArithmeticFunction.vonMangoldt.summable_residueClass_non_primes_div", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.PrimesInAP", "is_tactic_proof": true, "tactics": ["have", "have", "refine", "split_ifs", "refine", "have", "refine", "swap", "simp", "implies_true,", "have", "refine", "ext1", "simp", "congr", "rw", "refine", "have", "have", "ext1", "simp", "refine", "exact", "simp", "true_and,", "rw"], "tactic_count": 26}
{"name": "ArithmeticFunction.vonMangoldt.residueClass_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.PrimesInAP", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "ArithmeticFunction.vonMangoldt.residueClass_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.PrimesInAP", "is_tactic_proof": true, "tactics": ["ext1", "simpa"], "tactic_count": 2}
{"name": "ArithmeticFunction.vonMangoldt.LSeries_residueClass_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.PrimesInAP", "is_tactic_proof": false, "tactics": ["simp", "rw", "simp_rw", "refine", "simp"], "tactic_count": 5}
{"name": "ArithmeticFunction.vonMangoldt.LFunctionResidueClassAux", "kind": "abbrev", "module": "Mathlib.NumberTheory.LSeries.PrimesInAP", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ArithmeticFunction.vonMangoldt.continuousOn_LFunctionResidueClassAux'", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.PrimesInAP", "is_tactic_proof": true, "tactics": ["rw", "simp", "refine", "refine", "simp", "tauto", "simp", "refine", "replace", "refine", "simp", "rcases", "simp", "not_false_eq_true]", "exact"], "tactic_count": 15}
{"name": "ArithmeticFunction.vonMangoldt.continuousOn_LFunctionResidueClassAux", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.PrimesInAP", "is_tactic_proof": true, "tactics": ["refine", "rcases", "simp", "simp", "exact"], "tactic_count": 5}
{"name": "ArithmeticFunction.vonMangoldt.eqOn_LFunctionResidueClassAux", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.PrimesInAP", "is_tactic_proof": true, "tactics": ["intro", "replace", "simp", "rw", "mul_add]", "congrm", "have", "classical", "rw", "simp", "congrm", "have", "rw", "add_div,", "conv_lhs", "rw"], "tactic_count": 16}
{"name": "ArithmeticFunction.vonMangoldt.LFunctionResidueClassAux_real", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.PrimesInAP", "is_tactic_proof": true, "tactics": ["rw", "simp", "congr", "rw", "re_tsum", "push_cast", "refine", "rcases", "simp", "simp", "rw"], "tactic_count": 11}
{"name": "ArithmeticFunction.vonMangoldt.LSeries_residueClass_lower_bound", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.PrimesInAP", "is_tactic_proof": false, "tactics": ["have", "refine", "simp", "ofReal_sub,", "simp_rw", "eqOn_LFunctionResidueClassAux", "refine", "split_ifs", "simp", "rfl", "have", "continuous_re.continuousOn.comp", "continuous_ofReal.continuousOn", "obtain", "replace", "hC", "refine", "rw", "exact"], "tactic_count": 19}
{"name": "ArithmeticFunction.vonMangoldt.not_summable_residueClass_prime_div", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.PrimesInAP", "is_tactic_proof": true, "tactics": ["intro", "have", "convert", "simp", "let", "have", "refine", "rcases", "simp", "refine", "conv_lhs", "exact", "exact", "obtain", "have", "have", "rcases", "have", "rw", "exact", "obtain", "refine", "simpa", "and_true]", "rw", "exact", "exact"], "tactic_count": 27}
{"name": "Nat.infinite_setOf_prime_and_eq_mod", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.PrimesInAP", "is_tactic_proof": true, "tactics": ["by_contra", "exact"], "tactic_count": 2}
{"name": "Nat.forall_exists_prime_gt_and_eq_mod", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.PrimesInAP", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Nat.forall_exists_prime_gt_and_zmodEq", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.PrimesInAP", "is_tactic_proof": true, "tactics": ["have", "have", "obtain", "refine", "simpa"], "tactic_count": 5}
{"name": "Nat.forall_exists_prime_gt_and_modEq", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.PrimesInAP", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Nat.frequently_atTop_prime_and_modEq", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.PrimesInAP", "is_tactic_proof": true, "tactics": ["rw", "intro", "obtain", "exact"], "tactic_count": 4}
{"name": "Nat.infinite_setOf_prime_and_modEq", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.PrimesInAP", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "completedRiemannZeta₀", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.RiemannZeta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "completedRiemannZeta", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.RiemannZeta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HurwitzZeta.completedHurwitzZetaEven_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.RiemannZeta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HurwitzZeta.completedHurwitzZetaEven₀_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.RiemannZeta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HurwitzZeta.completedCosZeta_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.RiemannZeta", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HurwitzZeta.completedCosZeta₀_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.RiemannZeta", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "completedRiemannZeta_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.RiemannZeta", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "differentiable_completedZeta₀", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.RiemannZeta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentiableAt_completedZeta", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.RiemannZeta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "completedRiemannZeta₀_one_sub", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.RiemannZeta", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "completedRiemannZeta_one_sub", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.RiemannZeta", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "completedRiemannZeta_residue_one", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.RiemannZeta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "riemannZeta", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.RiemannZeta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HurwitzZeta.hurwitzZetaEven_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.RiemannZeta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HurwitzZeta.cosZeta_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.RiemannZeta", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "HurwitzZeta.hurwitzZeta_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.RiemannZeta", "is_tactic_proof": true, "tactics": ["ext1", "simpa"], "tactic_count": 2}
{"name": "HurwitzZeta.expZeta_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.RiemannZeta", "is_tactic_proof": true, "tactics": ["ext1", "rw", "sinZeta_neg,"], "tactic_count": 3}
{"name": "differentiableAt_riemannZeta", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.RiemannZeta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "riemannZeta_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.RiemannZeta", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "riemannZeta_def_of_ne_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.RiemannZeta", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "riemannZeta_neg_two_mul_nat_add_one", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.RiemannZeta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "riemannZeta_one_sub", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.RiemannZeta", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RiemannHypothesis", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.RiemannZeta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "completedZeta_eq_tsum_of_one_lt_re", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.RiemannZeta", "is_tactic_proof": true, "tactics": ["have", "simp", "simp", "congr", "split_ifs", "simp", "rfl"], "tactic_count": 7}
{"name": "zeta_eq_tsum_one_div_nat_cpow", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.RiemannZeta", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "zeta_eq_tsum_one_div_nat_add_one_cpow", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.RiemannZeta", "is_tactic_proof": true, "tactics": ["have", "rw", "simpa", "rwa"], "tactic_count": 4}
{"name": "zeta_nat_eq_tsum_of_gt_one", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.RiemannZeta", "is_tactic_proof": true, "tactics": ["simp", "cpow_natCast]"], "tactic_count": 2}
{"name": "two_mul_riemannZeta_eq_tsum_int_inv_pow_of_even", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.RiemannZeta", "is_tactic_proof": true, "tactics": ["have", "rw", "have", "norm_cast", "simp", "tsum_pnat_eq_tsum_succ", "intro", "simp", "exact"], "tactic_count": 9}
{"name": "riemannZeta_residue_one", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.RiemannZeta", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "tendsto_sub_mul_tsum_nat_cpow", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.RiemannZeta", "is_tactic_proof": true, "tactics": ["refine", "simp", "filter_upwards"], "tactic_count": 3}
{"name": "tendsto_sub_mul_tsum_nat_rpow", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.RiemannZeta", "is_tactic_proof": true, "tactics": ["rw", "have", "continuous_ofReal.continuousWithinAt.tendsto_nhdsWithin", "apply", "simp", "ofReal_cpow"], "tactic_count": 6}
{"name": "_private.Mathlib.NumberTheory.LSeries.SumCoeff.0.LSeriesSummable_of_sum_norm_bigO_aux", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.SumCoeff", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "exact", "have", "have", "have", "filter_upwards", "rw", "simp_rw", "refine", "refine", "exact", "refine", "exact", "refine", "exact", "rwa"], "tactic_count": 18}
{"name": "LSeriesSummable_of_sum_norm_bigO", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.SumCoeff", "is_tactic_proof": false, "tactics": ["have", "filter_upwards", "refine", "refine", "rw"], "tactic_count": 5}
{"name": "LSeriesSummable_of_sum_norm_bigO_and_nonneg", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.SumCoeff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.LSeries.SumCoeff.0.LSeries_eq_mul_integral_aux", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.SumCoeff", "is_tactic_proof": false, "tactics": ["have", "rwa", "have", "have", "differentiableAt_id.ofReal_cpow_const", "have", "rw", "simp_rw", "rw", "refine", "simp_rw", "convert", "tendsto_sum_mul_atTop_nhds_one_sub_integral₀", "rw", "refine", "rw", "ring_nf", "exact", "refine", "integrableOn_Ioi_deriv_ofReal_cpow", "have", "refine", "exact", "linarith", "refine", "simpa", "exact"], "tactic_count": 27}
{"name": "LSeries_eq_mul_integral", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.SumCoeff", "is_tactic_proof": false, "tactics": ["rw", "have", "rw"], "tactic_count": 3}
{"name": "LSeries_eq_mul_integral'", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.SumCoeff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LSeries_eq_mul_integral_of_nonneg", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.SumCoeff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.LSeries.SumCoeff.0.lemma₁", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.SumCoeff", "is_tactic_proof": false, "tactics": ["have", "simp_rw", "refine", "refine", "exact", "have", "simp_rw", "refine", "have", "simpa", "refine", "refine", "exact", "rwa"], "tactic_count": 14}
{"name": "_private.Mathlib.NumberTheory.LSeries.SumCoeff.0.lemma₂", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.SumCoeff", "is_tactic_proof": false, "tactics": ["have", "refine", "exact", "refine", "filter_upwards", "simpa", "mul_le_mul_of_nonneg_right", "exact"], "tactic_count": 8}
{"name": "_private.Mathlib.NumberTheory.LSeries.SumCoeff.0.LSeries_tendsto_sub_mul_nhds_one_of_tendsto_sum_div_aux₁", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.SumCoeff", "is_tactic_proof": false, "tactics": ["have", "refine", "ofReal_one", "filter_upwards", "simp", "filter_upwards", "rwa", "div_lt_iff₀"], "tactic_count": 8}
{"name": "_private.Mathlib.NumberTheory.LSeries.SumCoeff.0.LSeries_tendsto_sub_mul_nhds_one_of_tendsto_sum_div_aux₂", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.SumCoeff", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "calc", "refine", "exact", "exact", "have", "rw", "exact", "rw", "refine", "mul_le_mul_of_nonneg_left", "exact", "exact", "rw", "field"], "tactic_count": 17}
{"name": "_private.Mathlib.NumberTheory.LSeries.SumCoeff.0.LSeries_tendsto_sub_mul_nhds_one_of_tendsto_sum_div_aux₃", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.SumCoeff", "is_tactic_proof": false, "tactics": ["obtain", "let", "let", "have", "refine", "exact", "refine", "filter_upwards", "rw", "have", "have", "refine", "simpa", "have", "have", "refine", "isCompact_Icc).mono_set", "exact", "have", "rw", "show", "exact", "let", "have", "refine", "exact", "gcongr", "exact", "calc", "l", "rw", "mul_assoc]", "exact", "rw", "congr", "exact", "exact", "congr", "refine", "replace", "rw", "rw", "exact", "congr", "refine", "replace", "rw", "rw", "exact", "exact", "rw", "gcongr", "gcongr", "exact"], "tactic_count": 54}
{"name": "LSeries_tendsto_sub_mul_nhds_one_of_tendsto_sum_div", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.SumCoeff", "is_tactic_proof": false, "tactics": ["have", "rw", "exact", "have", "obtain", "exact", "suffices", "rw", "have", "tendsto_nhdsWithin_of_tendsto_nhds", "exact", "refine", "exact", "refine", "rw", "obtain", "refine", "exact", "exact"], "tactic_count": 19}
{"name": "LSeries_tendsto_sub_mul_nhds_one_of_tendsto_sum_div_and_nonneg", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.SumCoeff", "is_tactic_proof": false, "tactics": ["refine", "simp", "refine", "exact"], "tactic_count": 4}
{"name": "ZMod.LSeriesSummable_of_one_lt_re", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.ZMod", "is_tactic_proof": true, "tactics": ["let", "refine", "exact"], "tactic_count": 3}
{"name": "ZMod.LFunction", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.ZMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.LFunction_modOne_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.ZMod", "is_tactic_proof": true, "tactics": ["simp", "hurwitzZeta_zero,"], "tactic_count": 2}
{"name": "ZMod.LFunction_eq_LSeries", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.ZMod", "is_tactic_proof": true, "tactics": ["rw", "congr", "have", "mem_Icc.mpr", "rw", "congr", "calc", "simp", "mul_div_cancel_left₀", "rw", "simp", "simp"], "tactic_count": 12}
{"name": "ZMod.differentiableAt_LFunction", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.ZMod", "is_tactic_proof": true, "tactics": ["refine", "rcases", "exact", "have", "simpa"], "tactic_count": 5}
{"name": "ZMod.differentiable_LFunction_of_sum_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.ZMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.LFunction_residue_one", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.ZMod", "is_tactic_proof": true, "tactics": ["simp", "refine", "rw", "simp", "refine", "exact"], "tactic_count": 6}
{"name": "_private.Mathlib.NumberTheory.LSeries.ZMod.0.ZMod.term𝕖", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.ZMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.LSeries.ZMod.0.ZMod._aux_Mathlib_NumberTheory_LSeries_ZMod___macroRules__private_Mathlib_NumberTheory_LSeries_ZMod_0_ZMod_term𝕖_1", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.ZMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.LSeries.ZMod.0.ZMod._aux_Mathlib_NumberTheory_LSeries_ZMod___unexpand_ZMod_stdAddChar_1", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.ZMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.LSeries.ZMod.0.ZMod.LFunction_stdAddChar_eq_expZeta_of_one_lt_re", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.ZMod", "is_tactic_proof": false, "tactics": ["rw", "congr", "rw", "div_mul_eq_mul_div,", "have", "conv_rhs", "rw"], "tactic_count": 7}
{"name": "ZMod.LFunction_stdAddChar_eq_expZeta", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.ZMod", "is_tactic_proof": true, "tactics": ["let", "let", "have", "by_cases", "simpa", "simp", "let", "let", "have", "tauto", "have", "refine", "refine", "simp", "have", "refine", "refine", "rwa", "have", "by_cases", "simpa", "simpa", "have", "have", "have", "refine", "filter_upwards"], "tactic_count": 27}
{"name": "ZMod.LFunction_dft", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.ZMod", "is_tactic_proof": false, "tactics": ["have", "by_cases", "rw", "simp", "rw", "simp", "rw", "simp", "congr", "congr", "rw"], "tactic_count": 11}
{"name": "ZMod.LFunction_one_sub", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.ZMod", "is_tactic_proof": true, "tactics": ["rw", "have", "rcases", "rcases", "simp", "rw", "rw", "simp", "generalize", "simp_rw", "congr", "rw", "conv_rhs", "simp_rw"], "tactic_count": 14}
{"name": "ZMod.LFunction_def_even", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.ZMod", "is_tactic_proof": true, "tactics": ["simp", "congr", "simp", "refine", "simp"], "tactic_count": 5}
{"name": "ZMod.LFunction_def_odd", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.ZMod", "is_tactic_proof": true, "tactics": ["simp", "congr", "simp", "refine", "simp"], "tactic_count": 5}
{"name": "ZMod.LFunction_apply_zero_of_even", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.ZMod", "is_tactic_proof": true, "tactics": ["simp", "mul_div,"], "tactic_count": 2}
{"name": "ZMod.LFunction_neg_two_mul_nat_add_one", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.ZMod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ZMod.LFunction_neg_two_mul_nat_sub_one", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.ZMod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ZMod.completedLFunction", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.ZMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.completedLFunction_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.ZMod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ZMod.completedLFunction_const_mul", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.ZMod", "is_tactic_proof": true, "tactics": ["simp", "congr"], "tactic_count": 2}
{"name": "ZMod.completedLFunction_def_even", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.ZMod", "is_tactic_proof": false, "tactics": ["suffices", "refine", "rw"], "tactic_count": 3}
{"name": "ZMod.completedLFunction_def_odd", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.ZMod", "is_tactic_proof": false, "tactics": ["suffices", "rw", "refine", "rw"], "tactic_count": 4}
{"name": "ZMod.completedLFunction_modOne_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.ZMod", "is_tactic_proof": true, "tactics": ["rw", "one_mul,"], "tactic_count": 2}
{"name": "ZMod.completedLFunction₀", "kind": "definition", "module": "Mathlib.NumberTheory.LSeries.ZMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.differentiable_completedLFunction₀", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.ZMod", "is_tactic_proof": true, "tactics": ["refine", "exacts"], "tactic_count": 2}
{"name": "ZMod.completedLFunction_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.ZMod", "is_tactic_proof": false, "tactics": ["simp", "zero_mul,", "mul_assoc]", "abel"], "tactic_count": 4}
{"name": "ZMod.differentiableAt_completedLFunction", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.ZMod", "is_tactic_proof": false, "tactics": ["simp", "refine", "refine", "exact", "exact", "refine", "exact", "exact"], "tactic_count": 8}
{"name": "ZMod.differentiable_completedLFunction", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.ZMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.LFunction_eq_completed_div_gammaFactor_even", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.ZMod", "is_tactic_proof": true, "tactics": ["simp", "congr", "rcases", "rw", "rcases", "rw", "simp"], "tactic_count": 7}
{"name": "ZMod.LFunction_eq_completed_div_gammaFactor_odd", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.ZMod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "_private.Mathlib.NumberTheory.LSeries.ZMod.0.ZMod.completedLFunction_one_sub_of_one_lt_even", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.ZMod", "is_tactic_proof": true, "tactics": ["have", "have", "suffices", "simp", "suffices", "simpa", "div_left_inj", "simp", "map_neg,", "exact"], "tactic_count": 10}
{"name": "_private.Mathlib.NumberTheory.LSeries.ZMod.0.ZMod.completedLFunction_one_sub_of_one_lt_odd", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.ZMod", "is_tactic_proof": true, "tactics": ["suffices", "simp", "suffices", "have", "simpa", "calc", "simp", "congrm", "exact", "simp", "ring"], "tactic_count": 11}
{"name": "ZMod.completedLFunction_one_sub_even", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.ZMod", "is_tactic_proof": true, "tactics": ["let", "let", "let", "have", "have", "have", "have", "let", "have", "convert", "ext", "by_cases", "simp", "have", "refine", "refine", "exacts", "have", "refine", "apply", "apply", "exact", "ht.2.imp_right", "have", "have", "eventually_of_mem", "simpa", "exact"], "tactic_count": 28}
{"name": "ZMod.completedLFunction_one_sub_odd", "kind": "theorem", "module": "Mathlib.NumberTheory.LSeries.ZMod", "is_tactic_proof": true, "tactics": ["let", "let", "have", "have", "apply", "rw", "exact", "have", "have", "rw", "exact"], "tactic_count": 11}
{"name": "AddChar.val_mem_rootsOfUnity", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.AddCharacter", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AddChar.IsPrimitive", "kind": "definition", "module": "Mathlib.NumberTheory.LegendreSymbol.AddCharacter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.IsPrimitive.compMulHom_of_isPrimitive", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.AddCharacter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.to_mulShift_inj_of_isPrimitive", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.AddCharacter", "is_tactic_proof": true, "tactics": ["intro", "apply_fun", "simp", "simpa"], "tactic_count": 4}
{"name": "AddChar.IsPrimitive.of_ne_one", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.AddCharacter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.not_isPrimitive_mulShift", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.AddCharacter", "is_tactic_proof": true, "tactics": ["simp", "simp", "rcases", "exact"], "tactic_count": 4}
{"name": "AddChar.exists_divisor_of_not_isPrimitive", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.AddCharacter", "is_tactic_proof": true, "tactics": ["simp_rw", "rcases", "obtain", "refine", "exact", "rw", "ext1", "rw"], "tactic_count": 8}
{"name": "AddChar.zmodChar", "kind": "definition", "module": "Mathlib.NumberTheory.LegendreSymbol.AddCharacter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.zmodChar_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.AddCharacter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.zmodChar_apply'", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.AddCharacter", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AddChar.zmod_char_ne_one_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.AddCharacter", "is_tactic_proof": true, "tactics": ["rw", "refine", "contrapose", "rintro", "have", "rw"], "tactic_count": 6}
{"name": "AddChar.IsPrimitive.zmod_char_eq_one_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.AddCharacter", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "AddChar.zmod_char_primitive_of_eq_one_only_at_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.AddCharacter", "is_tactic_proof": true, "tactics": ["refine", "have", "rw", "exact"], "tactic_count": 4}
{"name": "AddChar.zmodChar_primitive_of_primitive_root", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.AddCharacter", "is_tactic_proof": true, "tactics": ["apply", "intro", "rw", "exact"], "tactic_count": 4}
{"name": "AddChar.primitiveZModChar", "kind": "definition", "module": "Mathlib.NumberTheory.LegendreSymbol.AddCharacter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddChar.FiniteField.primitiveChar", "kind": "definition", "module": "Mathlib.NumberTheory.LegendreSymbol.AddCharacter", "is_tactic_proof": true, "tactics": ["let", "haveI", "let", "have", "rcases", "exact", "rw", "exact", "let", "letI", "let", "have", "obtain", "rw", "exact", "exact"], "tactic_count": 16}
{"name": "AddChar.sum_eq_zero_of_ne_one", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.AddCharacter", "is_tactic_proof": true, "tactics": ["rcases", "have", "simp_rw", "have", "rw", "exact"], "tactic_count": 6}
{"name": "AddChar.sum_eq_card_of_eq_one", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.AddCharacter", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AddChar.sum_mulShift", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.AddCharacter", "is_tactic_proof": true, "tactics": ["split_ifs", "simp", "rfl", "simp_rw", "exact"], "tactic_count": 5}
{"name": "AddChar.starComp_eq_inv", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.AddCharacter", "is_tactic_proof": true, "tactics": ["ext1", "simp", "have", "exact"], "tactic_count": 4}
{"name": "AddChar.starComp_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.AddCharacter", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "_private.Mathlib.NumberTheory.LegendreSymbol.AddCharacter.0.AddChar.ringChar_ne", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.AddCharacter", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "AddChar.FiniteField.primitiveChar_to_Complex", "kind": "definition", "module": "Mathlib.NumberTheory.LegendreSymbol.AddCharacter", "is_tactic_proof": true, "tactics": ["letI", "refine", "exact"], "tactic_count": 3}
{"name": "AddChar.FiniteField.primitiveChar_to_Complex_isPrimitive", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.AddCharacter", "is_tactic_proof": true, "tactics": ["refine", "let", "exact"], "tactic_count": 3}
{"name": "ZMod.euler_criterion_units", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "subst", "simp", "have", "have", "rw", "simp_rw", "rw", "rwa"], "tactic_count": 9}
{"name": "ZMod.euler_criterion", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.Basic", "is_tactic_proof": true, "tactics": ["apply", "simp", "constructor", "rintro", "rintro", "have", "rintro", "simp", "refine"], "tactic_count": 9}
{"name": "ZMod.pow_div_two_eq_neg_one_or_one", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.Basic", "is_tactic_proof": true, "tactics": ["rcases", "subst", "tauto", "simp", "rw", "exact"], "tactic_count": 6}
{"name": "legendreSym", "kind": "definition", "module": "Mathlib.NumberTheory.LegendreSymbol.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "legendreSym.eq_pow", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.Basic", "is_tactic_proof": true, "tactics": ["rcases", "by_cases", "rw", "norm_cast", "have", "subst", "rw", "revert", "push_cast", "generalize", "tauto", "simp", "convert", "exact"], "tactic_count": 14}
{"name": "legendreSym.eq_one_or_neg_one", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "legendreSym.eq_neg_one_iff_not_one", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "legendreSym.eq_zero_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "legendreSym.at_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "legendreSym.at_one", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "legendreSym.mul", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "legendreSym.hom", "kind": "definition", "module": "Mathlib.NumberTheory.LegendreSymbol.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "legendreSym.sq_one", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "legendreSym.sq_one'", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "exact"], "tactic_count": 3}
{"name": "legendreSym.mod", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "legendreSym.eq_one_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "legendreSym.eq_one_iff'", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.Basic", "is_tactic_proof": true, "tactics": ["rw", "norm_cast", "exact"], "tactic_count": 3}
{"name": "legendreSym.eq_neg_one_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "legendreSym.eq_neg_one_iff'", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "legendreSym.card_sqrts", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "legendreSym.eq_one_of_sq_sub_mul_sq_eq_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.Basic", "is_tactic_proof": true, "tactics": ["apply_fun", "simp", "rw", "mul_one,", "exact"], "tactic_count": 5}
{"name": "legendreSym.eq_one_of_sq_sub_mul_sq_eq_zero'", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.Basic", "is_tactic_proof": false, "tactics": ["haveI", "rintro", "rw", "exact", "exact"], "tactic_count": 5}
{"name": "legendreSym.eq_zero_mod_of_eq_neg_one", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.Basic", "is_tactic_proof": false, "tactics": ["have", "intro", "rw", "simp", "by_contra", "rcases", "rw", "exact", "rw", "exact"], "tactic_count": 10}
{"name": "legendreSym.prime_dvd_of_eq_neg_one", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "push_cast", "exact"], "tactic_count": 3}
{"name": "legendreSym.at_neg_one", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ZMod.exists_sq_eq_neg_one_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ZMod.mod_four_ne_three_of_sq_eq_neg_one", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.mod_four_ne_three_of_sq_eq_neg_sq'", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.mod_four_ne_three_of_sq_eq_neg_sq", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.Ico_map_valMinAbs_natAbs_eq_Ico_map_id", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.GaussEisensteinLemmas", "is_tactic_proof": true, "tactics": ["have", "have", "lt_of_le_of_lt", "have", "not_lt_of_ge", "have", "intro", "simp", "have", "intro", "refine", "apply", "simp", "inv_eq_zero,", "apply", "rw", "split_ifs", "rw", "rw", "if_pos", "exact"], "tactic_count": 21}
{"name": "_private.Mathlib.NumberTheory.LegendreSymbol.GaussEisensteinLemmas.0.ZMod.gauss_lemma_aux₁", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.GaussEisensteinLemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.gauss_lemma_aux", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.GaussEisensteinLemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.gauss_lemma", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.GaussEisensteinLemmas", "is_tactic_proof": true, "tactics": ["replace", "have", "cases", "cases", "simp_all"], "tactic_count": 5}
{"name": "_private.Mathlib.NumberTheory.LegendreSymbol.GaussEisensteinLemmas.0.ZMod.eisenstein_lemma_aux₁", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.GaussEisensteinLemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.eisenstein_lemma_aux", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.GaussEisensteinLemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.div_eq_filter_card", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.GaussEisensteinLemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.LegendreSymbol.GaussEisensteinLemmas.0.ZMod.sum_Ico_eq_card_lt", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.GaussEisensteinLemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.sum_mul_div_add_sum_mul_div_eq_mul", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.GaussEisensteinLemmas", "is_tactic_proof": false, "tactics": ["have", "card_equiv", "simp", "and_left_comm])", "have", "apply", "have", "have", "apply_fun", "rw", "simp", "have", "have", "simp", "tauto", "rw", "simp"], "tactic_count": 17}
{"name": "ZMod.eisenstein_lemma", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.GaussEisensteinLemmas", "is_tactic_proof": true, "tactics": ["haveI", "have", "rw"], "tactic_count": 3}
{"name": "jacobiSym", "kind": "definition", "module": "Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberTheorySymbols.termJ(_|_)", "kind": "definition", "module": "Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberTheorySymbols._aux_Mathlib_NumberTheory_LegendreSymbol_JacobiSymbol___macroRules_NumberTheorySymbols_termJ(_|_)_1", "kind": "definition", "module": "Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberTheorySymbols._aux_Mathlib_NumberTheory_LegendreSymbol_JacobiSymbol___unexpand_jacobiSym_1", "kind": "definition", "module": "Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "jacobiSym.zero_right", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "jacobiSym.one_right", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "jacobiSym.legendreSym.to_jacobiSym", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "jacobiSym.mul_right'", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol", "is_tactic_proof": true, "tactics": ["rw", "pick_goal", "exact", "rfl"], "tactic_count": 4}
{"name": "jacobiSym.mul_right", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "jacobiSym.trichotomy", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "jacobiSym.one_left", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "jacobiSym.mul_left", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "jacobiSym.eq_zero_iff_not_coprime", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "jacobiSym.ne_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol", "is_tactic_proof": true, "tactics": ["rcases", "rw", "exact", "contrapose"], "tactic_count": 4}
{"name": "jacobiSym.eq_zero_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "jacobiSym.zero_left", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "jacobiSym.eq_one_or_neg_one", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "jacobiSym.pow_left", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "jacobiSym.pow_right", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rcases", "rw", "rw"], "tactic_count": 6}
{"name": "jacobiSym.sq_one", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "jacobiSym.sq_one'", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "jacobiSym.mod_left", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "jacobiSym.mod_left'", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "jacobiSym.prime_dvd_of_eq_neg_one", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "jacobiSym.list_prod_left", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "jacobiSym.list_prod_right", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "have", "have", "have", "hl", "rw"], "tactic_count": 8}
{"name": "jacobiSym.eq_neg_one_at_prime_divisor_of_eq_neg_one", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol", "is_tactic_proof": false, "tactics": ["have", "rintro", "rw", "exact", "have", "rw", "obtain", "exact"], "tactic_count": 8}
{"name": "ZMod.nonsquare_of_jacobiSym_eq_neg_one", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.nonsquare_iff_jacobiSym_eq_neg_one", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ZMod.isSquare_of_jacobiSym_eq_one", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "jacobiSym.value_at", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol", "is_tactic_proof": true, "tactics": ["conv_rhs", "rw", "congr", "exact"], "tactic_count": 4}
{"name": "jacobiSym.at_neg_one", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "jacobiSym.neg", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "jacobiSym.at_two", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "jacobiSym.at_neg_two", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "jacobiSym.div_four_left", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol", "is_tactic_proof": true, "tactics": ["obtain", "have", "rw", "rw", "jacobiSym.sq_one"], "tactic_count": 5}
{"name": "jacobiSym.even_odd", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol", "is_tactic_proof": true, "tactics": ["obtain", "rw", "grind"], "tactic_count": 3}
{"name": "qrSign", "kind": "definition", "module": "Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "qrSign.neg_one_pow", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol", "is_tactic_proof": true, "tactics": ["rw", "rcases", "rw", "rw"], "tactic_count": 4}
{"name": "qrSign.sq_eq_one", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "qrSign.mul_left", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "qrSign.mul_right", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "qrSign.symm", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "qrSign.eq_iff_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol", "is_tactic_proof": true, "tactics": ["refine", "let", "rw"], "tactic_count": 3}
{"name": "jacobiSym.quadratic_reciprocity'", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol", "is_tactic_proof": true, "tactics": ["let", "map_one", "map_mul", "have", "refine", "have", "rw", "refine", "have", "rw"], "tactic_count": 10}
{"name": "jacobiSym.quadratic_reciprocity", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "jacobiSym.quadratic_reciprocity_one_mod_four", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol", "is_tactic_proof": true, "tactics": ["rw", "neg_one_pow_div_two_of_one_mod_four"], "tactic_count": 2}
{"name": "jacobiSym.quadratic_reciprocity_one_mod_four'", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "jacobiSym.quadratic_reciprocity_three_mod_four", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol", "is_tactic_proof": true, "tactics": ["let", "rw"], "tactic_count": 2}
{"name": "jacobiSym.quadratic_reciprocity_if", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol", "is_tactic_proof": true, "tactics": ["rcases", "simpa", "rcases", "simpa", "simpa"], "tactic_count": 5}
{"name": "jacobiSym.mod_right'", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol", "is_tactic_proof": true, "tactics": ["rcases", "rw", "have", "rcases", "have", "nth_rw", "rw", "pow_left,", "congr", "congr", "simp_rw", "rw", "rw", "simp", "apply", "rcases", "rw", "use"], "tactic_count": 18}
{"name": "jacobiSym.mod_right", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol", "is_tactic_proof": true, "tactics": ["rcases", "exact", "have", "rw", "mod_mod_of_dvd"], "tactic_count": 5}
{"name": "_private.Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol.0.fastJacobiSymAux", "kind": "definition", "module": "Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol.0.fastJacobiSymAux.eq_jacobiSym", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol", "is_tactic_proof": true, "tactics": ["induction", "ind", "unfold", "split", "rw", "simp", "split", "rw", "simp", "by_cases", "split", "subst", "split", "suffices", "refine", "rwa", "rw", "simp", "rw", "by_cases"], "tactic_count": 20}
{"name": "_private.Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol.0.fastJacobiSym", "kind": "definition", "module": "Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol.0.fastJacobiSym.eq", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol", "is_tactic_proof": true, "tactics": ["ext", "induction", "ind", "unfold", "split_ifs", "rw", "refine", "refine", "refine", "exact", "dsimp", "rw", "obtain", "rw", "mod_left", "rw", "rw", "rw", "exact", "exact"], "tactic_count": 20}
{"name": "_private.Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol.0.fastLegendreSym", "kind": "definition", "module": "Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol.0.fastLegendreSym.eq", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "quadraticCharFun", "kind": "definition", "module": "Mathlib.NumberTheory.LegendreSymbol.QuadraticChar.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "quadraticCharFun_eq_zero_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.QuadraticChar.Basic", "is_tactic_proof": true, "tactics": ["simp", "grind"], "tactic_count": 2}
{"name": "quadraticCharFun_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.QuadraticChar.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "quadraticCharFun_one", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.QuadraticChar.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "quadraticCharFun_eq_one_of_char_two", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.QuadraticChar.Basic", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "quadraticCharFun_eq_pow_of_char_ne_two", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.QuadraticChar.Basic", "is_tactic_proof": true, "tactics": ["simp", "simp_rw"], "tactic_count": 2}
{"name": "quadraticCharFun_mul", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.QuadraticChar.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "by_cases", "rw", "have", "by_cases", "rw", "quadraticCharFun_eq_one_of_char_two", "rw", "quadraticCharFun_eq_pow_of_char_ne_two", "rcases", "simp", "have", "simp", "rcases"], "tactic_count": 15}
{"name": "quadraticChar", "kind": "definition", "module": "Mathlib.NumberTheory.LegendreSymbol.QuadraticChar.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "quadraticChar_eq_zero_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.QuadraticChar.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "quadraticChar_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.QuadraticChar.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "quadraticChar_one_iff_isSquare", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.QuadraticChar.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "quadraticChar_sq_one'", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.QuadraticChar.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "quadraticChar_sq_one", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.QuadraticChar.Basic", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "quadraticChar_dichotomy", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.QuadraticChar.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "quadraticChar_eq_neg_one_iff_not_one", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.QuadraticChar.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "quadraticChar_neg_one_iff_not_isSquare", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.QuadraticChar.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "rw"], "tactic_count": 3}
{"name": "quadraticChar_exists_neg_one", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.QuadraticChar.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "quadraticChar_exists_neg_one'", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.QuadraticChar.Basic", "is_tactic_proof": true, "tactics": ["refine", "contrapose", "exact"], "tactic_count": 3}
{"name": "quadraticChar_eq_one_of_char_two", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.QuadraticChar.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "quadraticChar_eq_pow_of_char_ne_two", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.QuadraticChar.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "quadraticChar_eq_pow_of_char_ne_two'", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.QuadraticChar.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "have", "simp", "rw", "by_cases", "simp", "have", "simp", "exact"], "tactic_count": 9}
{"name": "quadraticChar_isQuadratic", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.QuadraticChar.Basic", "is_tactic_proof": true, "tactics": ["intro", "by_cases", "left", "right"], "tactic_count": 4}
{"name": "quadraticChar_ne_one", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.QuadraticChar.Basic", "is_tactic_proof": true, "tactics": ["rcases", "intro", "simp"], "tactic_count": 3}
{"name": "quadraticChar_card_sqrts", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.QuadraticChar.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "set", "by_cases", "rw", "rcases", "rw", "have", "ext1", "rw", "simp_rw", "mem_insert,", "exact", "norm_cast", "rw", "exact", "rw", "simp", "simpa"], "tactic_count": 19}
{"name": "quadraticChar_sum_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.QuadraticChar.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "quadraticChar_neg_one", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.QuadraticChar.Basic", "is_tactic_proof": true, "tactics": ["have", "rw", "generalize", "rcases", "simp", "simp"], "tactic_count": 6}
{"name": "FiniteField.isSquare_neg_one_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.QuadraticChar.Basic", "is_tactic_proof": true, "tactics": ["classical", "by_cases", "simp", "exact", "have", "rw", "χ₄_nat_eq_if_mod_four,", "lia"], "tactic_count": 8}
{"name": "quadraticChar_two", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.QuadraticChar.GaussSum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteField.isSquare_two_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.QuadraticChar.GaussSum", "is_tactic_proof": true, "tactics": ["classical", "by_cases", "have", "simp", "lia", "have", "rw", "lia"], "tactic_count": 8}
{"name": "quadraticChar_neg_two", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.QuadraticChar.GaussSum", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "FiniteField.isSquare_neg_two_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.QuadraticChar.GaussSum", "is_tactic_proof": true, "tactics": ["classical", "by_cases", "have", "simp", "lia", "have", "rw", "χ₈'_nat_eq_if_mod_eight]", "lia"], "tactic_count": 9}
{"name": "quadraticChar_card_card", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.QuadraticChar.GaussSum", "is_tactic_proof": true, "tactics": ["let", "have", "obtain", "refine", "simpa", "have", "rw", "exact"], "tactic_count": 8}
{"name": "quadraticChar_odd_prime", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.QuadraticChar.GaussSum", "is_tactic_proof": true, "tactics": ["rw", "have", "quadraticChar_card_card", "rwa"], "tactic_count": 4}
{"name": "FiniteField.isSquare_odd_prime_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.QuadraticChar.GaussSum", "is_tactic_proof": true, "tactics": ["classical", "rcases", "obtain", "simp", "rwa"], "tactic_count": 5}
{"name": "legendreSym.at_two", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.QuadraticReciprocity", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "legendreSym.at_neg_two", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.QuadraticReciprocity", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "ZMod.exists_sq_eq_two_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.QuadraticReciprocity", "is_tactic_proof": true, "tactics": ["rw", "have", "lia"], "tactic_count": 3}
{"name": "ZMod.exists_sq_eq_neg_two_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.QuadraticReciprocity", "is_tactic_proof": true, "tactics": ["rw", "have", "lia"], "tactic_count": 3}
{"name": "legendreSym.quadratic_reciprocity", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.QuadraticReciprocity", "is_tactic_proof": true, "tactics": ["have", "have", "have", "have", "rw", "have", "have", "rw", "quadraticChar_sq_one", "quadraticChar_neg_one"], "tactic_count": 10}
{"name": "legendreSym.quadratic_reciprocity'", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.QuadraticReciprocity", "is_tactic_proof": true, "tactics": ["rcases", "subst", "rw", "have", "have", "simpa"], "tactic_count": 6}
{"name": "legendreSym.quadratic_reciprocity_one_mod_four", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.QuadraticReciprocity", "is_tactic_proof": true, "tactics": ["rw", "neg_one_pow_div_two_of_one_mod_four"], "tactic_count": 2}
{"name": "legendreSym.quadratic_reciprocity_three_mod_four", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.QuadraticReciprocity", "is_tactic_proof": true, "tactics": ["let", "rw", "rwa"], "tactic_count": 3}
{"name": "ZMod.exists_sq_eq_prime_iff_of_mod_four_eq_one", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.QuadraticReciprocity", "is_tactic_proof": true, "tactics": ["rcases", "subst", "rw", "quadratic_reciprocity_one_mod_four"], "tactic_count": 4}
{"name": "ZMod.exists_sq_eq_prime_iff_of_mod_four_eq_three", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.QuadraticReciprocity", "is_tactic_proof": true, "tactics": ["rw", "neg_inj]"], "tactic_count": 2}
{"name": "ZMod.χ₄", "kind": "definition", "module": "Mathlib.NumberTheory.LegendreSymbol.ZModChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.isQuadratic_χ₄", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.ZModChar", "is_tactic_proof": true, "tactics": ["unfold", "decide"], "tactic_count": 2}
{"name": "ZMod.χ₄_nat_mod_four", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.ZModChar", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "ZMod.χ₄_int_mod_four", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.ZModChar", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ZMod.χ₄_int_eq_if_mod_four", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.ZModChar", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "ZMod.χ₄_nat_eq_if_mod_four", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.ZModChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.χ₄_eq_neg_one_pow", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.ZModChar", "is_tactic_proof": true, "tactics": ["rw", "simp", "nth_rewrite", "nth_rewrite", "rw", "have", "exact"], "tactic_count": 7}
{"name": "ZMod.χ₄_nat_one_mod_four", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.ZModChar", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "ZMod.χ₄_nat_three_mod_four", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.ZModChar", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "ZMod.χ₄_int_one_mod_four", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.ZModChar", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "ZMod.χ₄_int_three_mod_four", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.ZModChar", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "ZMod.neg_one_pow_div_two_of_one_mod_four", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.ZModChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.neg_one_pow_div_two_of_three_mod_four", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.ZModChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.χ₈", "kind": "definition", "module": "Mathlib.NumberTheory.LegendreSymbol.ZModChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.isQuadratic_χ₈", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.ZModChar", "is_tactic_proof": true, "tactics": ["unfold", "decide"], "tactic_count": 2}
{"name": "ZMod.χ₈_nat_mod_eight", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.ZModChar", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ZMod.χ₈_int_mod_eight", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.ZModChar", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ZMod.χ₈_int_eq_if_mod_eight", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.ZModChar", "is_tactic_proof": false, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "ZMod.χ₈_nat_eq_if_mod_eight", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.ZModChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.χ₈'", "kind": "definition", "module": "Mathlib.NumberTheory.LegendreSymbol.ZModChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.isQuadratic_χ₈'", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.ZModChar", "is_tactic_proof": true, "tactics": ["unfold", "decide"], "tactic_count": 2}
{"name": "ZMod.χ₈'_int_eq_if_mod_eight", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.ZModChar", "is_tactic_proof": false, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "ZMod.χ₈'_nat_eq_if_mod_eight", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.ZModChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.χ₈'_eq_χ₄_mul_χ₈", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.ZModChar", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "ZMod.χ₈'_int_eq_χ₄_mul_χ₈", "kind": "theorem", "module": "Mathlib.NumberTheory.LegendreSymbol.ZModChar", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsNonarchimedeanLocalField.instIsTopologicalDivisionRing", "kind": "instance", "module": "Mathlib.NumberTheory.LocalField.Basic", "is_tactic_proof": true, "tactics": ["letI", "haveI", "infer_instance"], "tactic_count": 3}
{"name": "IsNonarchimedeanLocalField.isCompact_closedBall", "kind": "theorem", "module": "Mathlib.NumberTheory.LocalField.Basic", "is_tactic_proof": true, "tactics": ["obtain", "by_cases", "simp", "letI", "letI", "obtain", "obtain", "obtain", "obtain", "simp", "obtain", "obtain", "simp", "refine", "simp", "exact", "refine", "intro", "dsimp", "exact", "convert", "refine", "ext", "simp"], "tactic_count": 24}
{"name": "IsNonarchimedeanLocalField.instCompactSpaceSubtypeMemSubringIntegerValueGroupWithZeroValuation", "kind": "instance", "module": "Mathlib.NumberTheory.LocalField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsNonarchimedeanLocalField.instCompatibleValueGroupWithZeroV", "kind": "instance", "module": "Mathlib.NumberTheory.LocalField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsNonarchimedeanLocalField.instIsDiscreteValuationRingSubtypeMemSubringIntegerValueGroupWithZeroValuation", "kind": "instance", "module": "Mathlib.NumberTheory.LocalField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsNonarchimedeanLocalField.valueGroupWithZeroIsoInt", "kind": "definition", "module": "Mathlib.NumberTheory.LocalField.Basic", "is_tactic_proof": true, "tactics": ["apply", "letI", "haveI", "obtain", "let", "have", "have", "exact"], "tactic_count": 8}
{"name": "IsNonarchimedeanLocalField.instIsDiscrete", "kind": "instance", "module": "Mathlib.NumberTheory.LocalField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsNonarchimedeanLocalField.instIsRankLeOne", "kind": "instance", "module": "Mathlib.NumberTheory.LocalField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsNonarchimedeanLocalField.instFiniteResidueFieldSubtypeMemSubringIntegerValueGroupWithZeroValuation", "kind": "instance", "module": "Mathlib.NumberTheory.LocalField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsNonarchimedeanLocalField.isAdicComplete", "kind": "proofWanted", "module": "Mathlib.NumberTheory.LocalField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsNonarchimedeanLocalField.instCompleteSpace", "kind": "instance", "module": "Mathlib.NumberTheory.LocalField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsNonarchimedeanLocalField.instCompleteSpaceSubtypeMemSubringIntegerValueGroupWithZeroValuation", "kind": "instance", "module": "Mathlib.NumberTheory.LocalField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mersenne", "kind": "definition", "module": "Mathlib.NumberTheory.LucasLehmer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictMono_mersenne", "kind": "theorem", "module": "Mathlib.NumberTheory.LucasLehmer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mersenne_lt_mersenne", "kind": "theorem", "module": "Mathlib.NumberTheory.LucasLehmer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mersenne_le_mersenne", "kind": "theorem", "module": "Mathlib.NumberTheory.LucasLehmer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mersenne_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.LucasLehmer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mersenne_odd", "kind": "theorem", "module": "Mathlib.NumberTheory.LucasLehmer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mersenne_pos", "kind": "theorem", "module": "Mathlib.NumberTheory.LucasLehmer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mersenne_succ", "kind": "theorem", "module": "Mathlib.NumberTheory.LucasLehmer", "is_tactic_proof": true, "tactics": ["dsimp", "have", "lia"], "tactic_count": 3}
{"name": "Nat.Prime.of_mersenne", "kind": "theorem", "module": "Mathlib.NumberTheory.LucasLehmer", "is_tactic_proof": true, "tactics": ["apply", "rintro", "apply"], "tactic_count": 3}
{"name": "Mathlib.Meta.Positivity.evalMersenne", "kind": "definition", "module": "Mathlib.NumberTheory.LucasLehmer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_lt_mersenne", "kind": "theorem", "module": "Mathlib.NumberTheory.LucasLehmer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "succ_mersenne", "kind": "theorem", "module": "Mathlib.NumberTheory.LucasLehmer", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "mersenne_mod_four", "kind": "theorem", "module": "Mathlib.NumberTheory.LucasLehmer", "is_tactic_proof": true, "tactics": ["induction", "base", "succ"], "tactic_count": 3}
{"name": "mersenne_mod_three", "kind": "theorem", "module": "Mathlib.NumberTheory.LucasLehmer", "is_tactic_proof": true, "tactics": ["obtain", "replace", "induction", "base", "succ", "rw", "lia"], "tactic_count": 7}
{"name": "mersenne_mod_eight", "kind": "theorem", "module": "Mathlib.NumberTheory.LucasLehmer", "is_tactic_proof": true, "tactics": ["induction", "base", "succ"], "tactic_count": 3}
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{"name": "legendreSym_mersenne_three", "kind": "theorem", "module": "Mathlib.NumberTheory.LucasLehmer", "is_tactic_proof": false, "tactics": ["rw", "legendreSym.quadratic_reciprocity_three_mod_four", "rw_mod_cast", "simp"], "tactic_count": 4}
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{"name": "LucasLehmer.sMod", "kind": "definition", "module": "Mathlib.NumberTheory.LucasLehmer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LucasLehmer.mersenne_int_pos", "kind": "theorem", "module": "Mathlib.NumberTheory.LucasLehmer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LucasLehmer.mersenne_int_ne_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.LucasLehmer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LucasLehmer.sMod_nonneg", "kind": "theorem", "module": "Mathlib.NumberTheory.LucasLehmer", "is_tactic_proof": true, "tactics": ["cases", "exact", "apply", "exact"], "tactic_count": 4}
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{"name": "LucasLehmer.sMod_lt", "kind": "theorem", "module": "Mathlib.NumberTheory.LucasLehmer", "is_tactic_proof": true, "tactics": ["rw", "refine", "exact"], "tactic_count": 3}
{"name": "LucasLehmer.sZMod_eq_s", "kind": "theorem", "module": "Mathlib.NumberTheory.LucasLehmer", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
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{"name": "LucasLehmer.q", "kind": "definition", "module": "Mathlib.NumberTheory.LucasLehmer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LucasLehmer.X.instAddCommGroup", "kind": "instance", "module": "Mathlib.NumberTheory.LucasLehmer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ModularForm.instModuleReal", "kind": "instance", "module": "Mathlib.NumberTheory.ModularForms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ModularForm.constℝ_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModularForm.instOneOfNatIntOfHasDetPlusMinusOneFinNatReal", "kind": "instance", "module": "Mathlib.NumberTheory.ModularForms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModularForm.one_coe_eq_one", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ModularForm.coe_natCast", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModularForm.toSlashInvariantForm_natCast", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ModularForm.coe_intCast", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModularForm.toSlashInvariantForm_intCast", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CuspForm.hasAdd", "kind": "instance", "module": "Mathlib.NumberTheory.ModularForms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CuspForm.instIsScalarTowerComplex", "kind": "instance", "module": "Mathlib.NumberTheory.ModularForms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CuspForm.instSMul", "kind": "instance", "module": "Mathlib.NumberTheory.ModularForms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CuspForm.smul_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CuspForm.instModuleReal", "kind": "instance", "module": "Mathlib.NumberTheory.ModularForms.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ModularForm.gradedMonoid_eq_of_cast", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.Basic", "is_tactic_proof": true, "tactics": ["obtain", "cases", "exact"], "tactic_count": 3}
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{"name": "CongruenceSubgroup.Gamma_one_top", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.CongruenceSubgroups", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "CongruenceSubgroup.mem_Gamma_one", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.CongruenceSubgroups", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CongruenceSubgroup.Gamma_zero_bot", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.CongruenceSubgroups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CongruenceSubgroup.ModularGroup_T_pow_mem_Gamma", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.CongruenceSubgroups", "is_tactic_proof": false, "tactics": ["simp", "cons_val_fin_one,", "refine", "simp"], "tactic_count": 4}
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{"name": "CongruenceSubgroup.Gamma0", "kind": "definition", "module": "Mathlib.NumberTheory.ModularForms.CongruenceSubgroups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CongruenceSubgroup.Gamma0_mem", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.CongruenceSubgroups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CongruenceSubgroup.Gamma0Map", "kind": "definition", "module": "Mathlib.NumberTheory.ModularForms.CongruenceSubgroups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CongruenceSubgroup.Gamma1'", "kind": "definition", "module": "Mathlib.NumberTheory.ModularForms.CongruenceSubgroups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CongruenceSubgroup.Gamma1_mem'", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.CongruenceSubgroups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CongruenceSubgroup.Gamma1_to_Gamma0_mem", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.CongruenceSubgroups", "is_tactic_proof": true, "tactics": ["constructor", "intro", "have", "rw", "simp", "simpa", "intro", "simp", "exact"], "tactic_count": 9}
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{"name": "CongruenceSubgroup.Gamma0_is_congruence", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.CongruenceSubgroups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CongruenceSubgroup.IsCongruenceSubgroup.finiteIndex", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.CongruenceSubgroups", "is_tactic_proof": true, "tactics": ["obtain", "have", "exact"], "tactic_count": 3}
{"name": "CongruenceSubgroup.instFiniteIndexGamma0", "kind": "instance", "module": "Mathlib.NumberTheory.ModularForms.CongruenceSubgroups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CongruenceSubgroup.instFiniteIndexGamma1", "kind": "instance", "module": "Mathlib.NumberTheory.ModularForms.CongruenceSubgroups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CongruenceSubgroup.conjGL", "kind": "definition", "module": "Mathlib.NumberTheory.ModularForms.CongruenceSubgroups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CongruenceSubgroup.mem_conjGL", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.CongruenceSubgroups", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CongruenceSubgroup.mem_conjGL'", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.CongruenceSubgroups", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw"], "tactic_count": 3}
{"name": "CongruenceSubgroup.conjGL_coe", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.CongruenceSubgroups", "is_tactic_proof": true, "tactics": ["ext", "simp_rw", "toConjAct_inv,"], "tactic_count": 3}
{"name": "CongruenceSubgroup.Gamma_cong_eq_self", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.CongruenceSubgroups", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "CongruenceSubgroup.conj_cong_is_cong", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.CongruenceSubgroups", "is_tactic_proof": true, "tactics": ["obtain", "refine", "rw", "exact"], "tactic_count": 4}
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{"name": "Subgroup.HasDetPlusMinusOne.isParabolic_iff_of_upperTriangular", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.Cusps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "EisensteinSeries.δ_eq_two", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.Transform", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "EisensteinSeries.δ_eventually_cofinite", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.Transform", "is_tactic_proof": true, "tactics": ["filter_upwards", "simp_all"], "tactic_count": 2}
{"name": "EisensteinSeries.G2Term", "kind": "abbrev", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.Transform", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EisensteinSeries.G2Term_summable", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.Transform", "is_tactic_proof": false, "tactics": ["have", "simp_rw", "apply", "simpa", "exact"], "tactic_count": 5}
{"name": "EisensteinSeries.G2Term_prod_summable", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.Transform", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "EisensteinSeries.aux_identity", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.Transform", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "simp", "by_cases", "by_cases", "simp", "ring", "have", "have", "simp", "grind", "have", "have", "simp", "grind"], "tactic_count": 15}
{"name": "EisensteinSeries.G2_eq_tsum_G2Term", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.Transform", "is_tactic_proof": true, "tactics": ["set", "rw", "rw", "congr", "rw", "exact", "simpa", "grind", "exact"], "tactic_count": 9}
{"name": "EisensteinSeries.G2_S_action_eq_tsum_G2Term", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.Transform", "is_tactic_proof": false, "tactics": ["rw", "tsum_eq_of_summable_unconditional", "apply", "rw", "apply", "simp", "mul_inv_rev]", "nth_rw", "ring", "simpa", "simpa", "apply", "rw", "apply", "rw", "simpa", "apply", "rw", "exact", "have", "rw", "exact"], "tactic_count": 22}
{"name": "EisensteinSeries.tsum_G2Term_eq_tsum", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.Transform", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "EisensteinSeries.tsum_G2Term_eq_tsum'", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.Transform", "is_tactic_proof": true, "tactics": ["rw", "exact", "exact", "have", "rw", "exact"], "tactic_count": 6}
{"name": "EisensteinSeries.G2_S_transform", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.Transform", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EisensteinSeries.G2_T_transform", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.Transform", "is_tactic_proof": true, "tactics": ["ext", "simp_rw", "simp", "grind"], "tactic_count": 4}
{"name": "EisensteinSeries.G2_slash_action", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.Transform", "is_tactic_proof": true, "tactics": ["have", "induction", "one", "mem", "simp", "rcases", "ext", "simp", "modular_S_smul]", "ring_nf", "aesop", "simpa", "mul", "ih", "rw", "grind", "inv", "have", "simp_rw", "nth_rw", "have", "simp", "rw"], "tactic_count": 23}
{"name": "EisensteinSeries.E2_slash_action", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.Transform", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "EisensteinSeries.summable_norm_eisSummand", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.IsBoundedAtImInfty", "is_tactic_proof": true, "tactics": ["have", "apply", "intro", "simp", "exact_mod_cast"], "tactic_count": 5}
{"name": "EisensteinSeries.norm_le_tsum_norm", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.IsBoundedAtImInfty", "is_tactic_proof": true, "tactics": ["simp_rw", "apply", "le_trans"], "tactic_count": 3}
{"name": "EisensteinSeries.isBoundedAtImInfty_eisensteinSeries_SIF", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.IsBoundedAtImInfty", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "intro", "obtain", "rw", "apply", "have", "apply", "exact_mod_cast", "intro", "simp_rw", "exact_mod_cast", "summand_bound_of_mem_verticalStrip"], "tactic_count": 13}
{"name": "EisensteinSeries.div_linear_zpow_differentiableOn", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.MDifferentiable", "is_tactic_proof": true, "tactics": ["rcases", "apply", "fun_prop", "left", "exact", "simp", "apply"], "tactic_count": 7}
{"name": "EisensteinSeries.eisSummand_extension_differentiableOn", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.MDifferentiable", "is_tactic_proof": true, "tactics": ["apply", "intro", "lift", "apply"], "tactic_count": 4}
{"name": "EisensteinSeries.eisensteinSeries_SIF_MDifferentiable", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.MDifferentiable", "is_tactic_proof": true, "tactics": ["intro", "suffices", "convert", "exact", "refine", "exact", "isOpen_upperHalfPlaneSet"], "tactic_count": 7}
{"name": "_private.Mathlib.NumberTheory.ModularForms.EisensteinSeries.QExpansion.0.termℍₒ", "kind": "definition", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.QExpansion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.ModularForms.EisensteinSeries.QExpansion.0._aux_Mathlib_NumberTheory_ModularForms_EisensteinSeries_QExpansion___macroRules__private_Mathlib_NumberTheory_ModularForms_EisensteinSeries_QExpansion_0_termℍₒ_1", "kind": "definition", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.QExpansion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.ModularForms.EisensteinSeries.QExpansion.0._aux_Mathlib_NumberTheory_ModularForms_EisensteinSeries_QExpansion___unexpand_UpperHalfPlane_upperHalfPlaneSet_1", "kind": "definition", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.QExpansion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.ModularForms.EisensteinSeries.QExpansion.0.iteratedDerivWithin_cexp_aux", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.QExpansion", "is_tactic_proof": true, "tactics": ["apply", "intro", "have", "ext", "ring_nf", "simp", "ring_nf"], "tactic_count": 7}
{"name": "_private.Mathlib.NumberTheory.ModularForms.EisensteinSeries.QExpansion.0.aux_IsBigO_mul", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.QExpansion", "is_tactic_proof": false, "tactics": ["have", "have", "ext", "ring", "simpa", "isBigO_ofReal_right.mp", "simp", "convert", "ring"], "tactic_count": 9}
{"name": "summableLocallyUniformlyOn_iteratedDerivWithin_smul_cexp", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.QExpansion", "is_tactic_proof": true, "tactics": ["apply", "intro", "have", "let", "let", "have", "simp", "intro", "have", "simpa", "refine", "simpa", "have", "simp", "iteratedDerivWithin_cexp_aux", "c]", "rw", "gcongr", "convert", "rw"], "tactic_count": 20}
{"name": "summableLocallyUniformlyOn_iteratedDerivWithin_cexp", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.QExpansion", "is_tactic_proof": false, "tactics": ["have", "simp", "exact", "simpa"], "tactic_count": 4}
{"name": "differentiableAt_iteratedDerivWithin_cexp", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.QExpansion", "is_tactic_proof": true, "tactics": ["apply", "suffices", "apply", "fun_prop"], "tactic_count": 4}
{"name": "iteratedDerivWithin_tsum_cexp_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.QExpansion", "is_tactic_proof": true, "tactics": ["rw", "exact", "exact", "exact"], "tactic_count": 4}
{"name": "contDiffOn_tsum_cexp", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.QExpansion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.ModularForms.EisensteinSeries.QExpansion.0.iteratedDerivWithin_tsum_exp_aux_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.QExpansion", "is_tactic_proof": false, "tactics": ["have", "iteratedDerivWithin", "rw", "iteratedDerivWithin_const_mul", "simp", "exact", "have", "simp_rw", "congr", "ext", "ring", "simp", "ofReal_eq_zero,", "congr", "ext", "have", "simp_rw", "simpa"], "tactic_count": 18}
{"name": "EisensteinSeries.qExpansion_identity", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.QExpansion", "is_tactic_proof": false, "tactics": ["have", "rw", "iteratedDerivWithin_cot_pi_mul_eq_mul_tsum_div_pow", "exact", "simp_rw", "congr", "ext", "rw", "field_simp", "ring_nf", "simp"], "tactic_count": 11}
{"name": "summable_pow_mul_cexp", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.QExpansion", "is_tactic_proof": true, "tactics": ["have", "apply", "he).congr", "grind"], "tactic_count": 4}
{"name": "EisensteinSeries.qExpansion_identity_pnat", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.QExpansion", "is_tactic_proof": true, "tactics": ["rw", "simp", "apply", "simp"], "tactic_count": 4}
{"name": "summable_eisSummand", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.QExpansion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "summable_prod_eisSummand", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.QExpansion", "is_tactic_proof": true, "tactics": ["refine", "simp"], "tactic_count": 2}
{"name": "tsum_eisSummand_eq_tsum_sigma_mul_cexp_pow", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.QExpansion", "is_tactic_proof": false, "tactics": ["rw", "tsum_int_eq_zero_add_two_mul_tsum_pnat", "nth_rewrite", "exact", "have", "simp_rw", "simp", "rw", "congr", "simp", "suffices", "simp_rw", "exact"], "tactic_count": 13}
{"name": "eisSummand_of_gammaSet_eq_divIntMap", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.QExpansion", "is_tactic_proof": true, "tactics": ["simp_rw", "nth_rw", "simp"], "tactic_count": 3}
{"name": "tsum_eisSummand_eq_riemannZeta_mul_eisensteinSeries", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.QExpansion", "is_tactic_proof": true, "tactics": ["have", "have", "simp_rw", "rw", "tsum_mul_tsum_of_summable_norm", "exact", "simp_rw", "rw", "exact", "summable_mul_of_summable_norm", "eisSummand", "simpa", "refine", "rcases", "simp", "have", "simpa"], "tactic_count": 17}
{"name": "EisensteinSeries.q_expansion_riemannZeta", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.QExpansion", "is_tactic_proof": true, "tactics": ["have", "rw", "have", "have", "have", "simp", "grind"], "tactic_count": 7}
{"name": "_private.Mathlib.NumberTheory.ModularForms.EisensteinSeries.QExpansion.0.eisensteinSeries_coeff_identity", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.QExpansion", "is_tactic_proof": true, "tactics": ["have", "set", "rw", "show", "show", "norm_cast", "simp", "grind"], "tactic_count": 8}
{"name": "EisensteinSeries.q_expansion_bernoulli", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.QExpansion", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "EisensteinSeries.norm_eq_max_natAbs", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.Summable", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp"], "tactic_count": 3}
{"name": "EisensteinSeries.norm_symm", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.Summable", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "EisensteinSeries.abs_le_left_of_norm", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.Summable", "is_tactic_proof": false, "tactics": ["simp", "left", "rw", "exact"], "tactic_count": 4}
{"name": "EisensteinSeries.abs_le_right_of_norm", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.Summable", "is_tactic_proof": false, "tactics": ["simp", "right", "rw", "exact"], "tactic_count": 4}
{"name": "EisensteinSeries.abs_norm_eq_max_natAbs", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.Summable", "is_tactic_proof": false, "tactics": ["simp", "norm_cast"], "tactic_count": 2}
{"name": "EisensteinSeries.abs_norm_eq_max_natAbs_neg", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.Summable", "is_tactic_proof": false, "tactics": ["simp", "norm_cast"], "tactic_count": 2}
{"name": "EisensteinSeries.r1", "kind": "definition", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EisensteinSeries.r1_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.Summable", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EisensteinSeries.r1_pos", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.Summable", "is_tactic_proof": true, "tactics": ["dsimp", "positivity"], "tactic_count": 2}
{"name": "EisensteinSeries.r1_aux_bound", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.Summable", "is_tactic_proof": false, "tactics": ["have", "have", "rw", "exact"], "tactic_count": 4}
{"name": "EisensteinSeries.r", "kind": "definition", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EisensteinSeries.r_pos", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.Summable", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "EisensteinSeries.r_lower_bound_on_verticalStrip", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.Summable", "is_tactic_proof": true, "tactics": ["apply", "rw", "simp", "rw", "gcongr", "exacts"], "tactic_count": 6}
{"name": "EisensteinSeries.auxbound1", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.Summable", "is_tactic_proof": true, "tactics": ["rcases", "have", "rw", "exact", "simpa", "zero_mul,"], "tactic_count": 6}
{"name": "EisensteinSeries.auxbound2", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.Summable", "is_tactic_proof": false, "tactics": ["have", "simpa", "coe_im,"], "tactic_count": 3}
{"name": "EisensteinSeries.div_max_sq_ge_one", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.Summable", "is_tactic_proof": true, "tactics": ["refine", "have", "simp", "not_false_eq_true,", "have", "simp", "not_false_eq_true,"], "tactic_count": 7}
{"name": "EisensteinSeries.r_mul_max_le", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.Summable", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "rw", "gcongr", "rcases", "simpa", "simpa"], "tactic_count": 8}
{"name": "EisensteinSeries.summand_bound", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.Summable", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "by_cases", "rw", "rw", "rw", "exact"], "tactic_count": 7}
{"name": "EisensteinSeries.summand_bound_of_mem_verticalStrip", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.Summable", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "EisensteinSeries.linear_isTheta_right_add", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.Summable", "is_tactic_proof": true, "tactics": ["apply", "skip]", "simpa"], "tactic_count": 3}
{"name": "EisensteinSeries.linear_isTheta_right", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.Summable", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "EisensteinSeries.linear_isTheta_left", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.Summable", "is_tactic_proof": true, "tactics": ["apply", "simp_rw", "apply", "simp", "tendsto_norm_comp_cofinite_atTop_of_isClosedEmbedding"], "tactic_count": 5}
{"name": "EisensteinSeries.linear_inv_isBigO_right_add", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EisensteinSeries.linear_inv_isBigO_right", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.Summable", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "EisensteinSeries.linear_inv_isBigO_left", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EisensteinSeries.tendsto_zero_inv_linear", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.Summable", "is_tactic_proof": true, "tactics": ["apply", "have", "simpa"], "tactic_count": 3}
{"name": "EisensteinSeries.tendsto_zero_inv_linear_sub", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.Summable", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "EisensteinSeries.summable_one_div_norm_rpow", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.Summable", "is_tactic_proof": true, "tactics": ["rw", "simp", "refine", "suffices", "refine", "simp", "simp", "apply", "filter_upwards", "rw", "exact"], "tactic_count": 11}
{"name": "EisensteinSeries.summable_inv_of_isBigO_rpow_inv", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EisensteinSeries.linear_right_summable", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.Summable", "is_tactic_proof": true, "tactics": ["apply", "lift", "grind"], "tactic_count": 3}
{"name": "EisensteinSeries.linear_left_summable", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.Summable", "is_tactic_proof": true, "tactics": ["apply", "lift", "simp", "apply"], "tactic_count": 4}
{"name": "EisensteinSeries.summable_linear_sub_mul_linear_add", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.Summable", "is_tactic_proof": true, "tactics": ["apply", "simpa"], "tactic_count": 2}
{"name": "EisensteinSeries.summable_linear_right_add_one_mul_linear_right", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.Summable", "is_tactic_proof": true, "tactics": ["apply", "simpa"], "tactic_count": 2}
{"name": "EisensteinSeries.summable_linear_left_mul_linear_left", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.Summable", "is_tactic_proof": true, "tactics": ["apply", "simp", "simpa"], "tactic_count": 3}
{"name": "_private.Mathlib.NumberTheory.ModularForms.EisensteinSeries.Summable.0.EisensteinSeries.aux_isBigO_linear", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.Summable", "is_tactic_proof": true, "tactics": ["rw", "have", "use", "filter_upwards", "apply", "le_trans", "simpa", "summand_bound_of_mem_verticalStrip", "simp", "aesop"], "tactic_count": 10}
{"name": "EisensteinSeries.isLittleO_const_left_of_properSpace_of_discreteTopology", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.Summable", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "EisensteinSeries.vec_add_const_isTheta", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.Summable", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "EisensteinSeries.isBigO_linear_add_const_vec", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EisensteinSeries.summable_of_isBigO_rpow_norm", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EisensteinSeries.eisensteinSeries_tendstoLocallyUniformly", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.UniformConvergence", "is_tactic_proof": true, "tactics": ["have", "have", "mod_cast", "simp", "intro", "obtain", "refine", "simpa", "summand_bound_of_mem_verticalStrip"], "tactic_count": 9}
{"name": "EisensteinSeries.eisensteinSeries_tendstoLocallyUniformlyOn", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.EisensteinSeries.UniformConvergence", "is_tactic_proof": true, "tactics": ["rw", "apply", "simp", "apply", "simp", "forall_const]"], "tactic_count": 6}
{"name": "SlashInvariantForm.vAdd_apply_of_mem_strictPeriods", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.Identities", "is_tactic_proof": true, "tactics": ["rw", "suffices", "simp_rw", "simp", "ext", "simp"], "tactic_count": 6}
{"name": "SlashInvariantForm.vAdd_width_periodic", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.Identities", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "SlashInvariantForm.T_zpow_width_invariant", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.Identities", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "SlashInvariantForm.slash_S_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.Identities", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "HurwitzKernelBounds.isBigO_exp_neg_mul_of_le", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.JacobiTheta.Bounds", "is_tactic_proof": true, "tactics": ["apply", "filter_upwards", "rw", "gcongr"], "tactic_count": 4}
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{"name": "HurwitzKernelBounds.F_nat_zero_zero_sub_le", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.JacobiTheta.Bounds", "is_tactic_proof": true, "tactics": ["convert", "rw", "mul_zero,", "simp_rw", "rw"], "tactic_count": 5}
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{"name": "HurwitzKernelBounds.f_int_ofNat", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.JacobiTheta.Bounds", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HurwitzKernelBounds.f_int_negSucc", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.JacobiTheta.Bounds", "is_tactic_proof": false, "tactics": ["have", "rw"], "tactic_count": 2}
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{"name": "jacobiTheta", "kind": "definition", "module": "Mathlib.NumberTheory.ModularForms.JacobiTheta.OneVariable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "jacobiTheta_eq_jacobiTheta₂", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.JacobiTheta.OneVariable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "jacobiTheta_two_add", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.JacobiTheta.OneVariable", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
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{"name": "norm_jacobiTheta_sub_one_le", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.JacobiTheta.OneVariable", "is_tactic_proof": false, "tactics": ["suffices", "calc", "rw", "have", "intro", "simpa", "have", "simp_rw", "exact", "hasSum_geometric_of_lt_one", "have", "exact"], "tactic_count": 12}
{"name": "isBigO_at_im_infty_jacobiTheta_sub_one", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.JacobiTheta.OneVariable", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "rw", "gcongr", "simp"], "tactic_count": 5}
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{"name": "jacobiTheta₂_term", "kind": "definition", "module": "Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "hasFDerivAt_jacobiTheta₂_term", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable", "is_tactic_proof": true, "tactics": ["let", "suffices", "from", "exact"], "tactic_count": 4}
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{"name": "norm_jacobiTheta₂_term_le", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable", "is_tactic_proof": false, "tactics": ["simp_rw", "mul_comm", "refine", "rw", "refine", "rw", "exact"], "tactic_count": 7}
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{"name": "ModularForm.is_invariant_const", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.SlashActions", "is_tactic_proof": true, "tactics": ["funext", "simp"], "tactic_count": 2}
{"name": "ModularForm.is_invariant_one", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.SlashActions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModularForm.is_invariant_one'", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.SlashActions", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ModularForm.slash_action_eq'_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.SlashActions", "is_tactic_proof": true, "tactics": ["simp", "convert", "simp", "rfl", "exact"], "tactic_count": 5}
{"name": "ModularForm.mul_slash", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.SlashActions", "is_tactic_proof": true, "tactics": ["ext1", "simp", "set", "have", "have", "rw", "ring_nf", "rw", "ring"], "tactic_count": 9}
{"name": "ModularForm.mul_slash_SL2", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.SlashActions", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ModularForm.prod_slash_sum_weights", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.SlashActions", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "simp", "ext", "simp", "insert", "rcases", "simp", "simp", "show", "congr", "nth_rw", "rw", "left", "exact"], "tactic_count": 16}
{"name": "ModularForm.prod_slash", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.SlashActions", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "ModularForm.prod_fintype_slash", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.SlashActions", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "SlashInvariantForm.funLike", "kind": "instance", "module": "Mathlib.NumberTheory.ModularForms.SlashInvariantForms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SlashInvariantForm.Simps.coe", "kind": "definition", "module": "Mathlib.NumberTheory.ModularForms.SlashInvariantForms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SlashInvariantFormClass.slashInvariantForm", "kind": "instance", "module": "Mathlib.NumberTheory.ModularForms.SlashInvariantForms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SlashInvariantForm.toFun_eq_coe", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.SlashInvariantForms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SlashInvariantForm.coe_mk", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.SlashInvariantForms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SlashInvariantForm.ext", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.SlashInvariantForms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SlashInvariantForm.copy", "kind": "definition", "module": "Mathlib.NumberTheory.ModularForms.SlashInvariantForms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SlashInvariantForm.slash_action_eqn", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.SlashInvariantForms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SlashInvariantForm.slash_action_eqn'", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.SlashInvariantForms", "is_tactic_proof": false, "tactics": ["have", "simpa", "rw"], "tactic_count": 3}
{"name": "SlashInvariantForm.slash_action_eqn''", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.SlashInvariantForms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SlashInvariantForm.slash_action_eqn_SL''", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.SlashInvariantForms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SlashInvariantForm.instCoeTCOfSlashInvariantFormClass", "kind": "instance", "module": "Mathlib.NumberTheory.ModularForms.SlashInvariantForms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SlashInvariantForm.instAdd", "kind": "instance", "module": "Mathlib.NumberTheory.ModularForms.SlashInvariantForms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SlashInvariantForm.coe_add", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.SlashInvariantForms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SlashInvariantForm.add_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.SlashInvariantForms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SlashInvariantForm.instZero", "kind": "instance", "module": "Mathlib.NumberTheory.ModularForms.SlashInvariantForms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SlashInvariantForm.coe_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.SlashInvariantForms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SlashInvariantForm.instSMul", "kind": "instance", "module": "Mathlib.NumberTheory.ModularForms.SlashInvariantForms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SlashInvariantForm.coe_smul", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.SlashInvariantForms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SlashInvariantForm.smul_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.SlashInvariantForms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SlashInvariantForm.instSMulℝ", "kind": "instance", "module": "Mathlib.NumberTheory.ModularForms.SlashInvariantForms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SlashInvariantForm.coe_smulℝ", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.SlashInvariantForms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SlashInvariantForm.smul_applyℝ", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.SlashInvariantForms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SlashInvariantForm.instNeg", "kind": "instance", "module": "Mathlib.NumberTheory.ModularForms.SlashInvariantForms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SlashInvariantForm.coe_neg", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.SlashInvariantForms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SlashInvariantForm.neg_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.SlashInvariantForms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SlashInvariantForm.instSub", "kind": "instance", "module": "Mathlib.NumberTheory.ModularForms.SlashInvariantForms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SlashInvariantForm.coe_sub", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.SlashInvariantForms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SlashInvariantForm.sub_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.SlashInvariantForms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SlashInvariantForm.instAddCommGroup", "kind": "instance", "module": "Mathlib.NumberTheory.ModularForms.SlashInvariantForms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SlashInvariantForm.coeHom", "kind": "definition", "module": "Mathlib.NumberTheory.ModularForms.SlashInvariantForms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SlashInvariantForm.coeHom_injective", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.SlashInvariantForms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SlashInvariantForm.instModuleComplex", "kind": "instance", "module": "Mathlib.NumberTheory.ModularForms.SlashInvariantForms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SlashInvariantForm.instModuleReal", "kind": "instance", "module": "Mathlib.NumberTheory.ModularForms.SlashInvariantForms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SlashInvariantForm.const", "kind": "definition", "module": "Mathlib.NumberTheory.ModularForms.SlashInvariantForms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SlashInvariantForm.constℝ", "kind": "definition", "module": "Mathlib.NumberTheory.ModularForms.SlashInvariantForms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SlashInvariantForm.instOneOfNatIntOfHasDetPlusMinusOneFinNatReal", "kind": "instance", "module": "Mathlib.NumberTheory.ModularForms.SlashInvariantForms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SlashInvariantForm.one_coe_eq_one", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.SlashInvariantForms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SlashInvariantForm.instInhabited", "kind": "instance", "module": "Mathlib.NumberTheory.ModularForms.SlashInvariantForms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SlashInvariantForm.mul", "kind": "definition", "module": "Mathlib.NumberTheory.ModularForms.SlashInvariantForms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SlashInvariantForm.coe_mul", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.SlashInvariantForms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SlashInvariantForm.prod", "kind": "definition", "module": "Mathlib.NumberTheory.ModularForms.SlashInvariantForms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SlashInvariantForm.prodEqualWeights", "kind": "definition", "module": "Mathlib.NumberTheory.ModularForms.SlashInvariantForms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SlashInvariantForm.instNatCastOfNatIntOfHasDetPlusMinusOneFinNatReal", "kind": "instance", "module": "Mathlib.NumberTheory.ModularForms.SlashInvariantForms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SlashInvariantForm.coe_natCast", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.SlashInvariantForms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SlashInvariantForm.instIntCastOfNatIntOfHasDetPlusMinusOneFinNatReal", "kind": "instance", "module": "Mathlib.NumberTheory.ModularForms.SlashInvariantForms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SlashInvariantForm.coe_intCast", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.SlashInvariantForms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SlashInvariantForm.translate", "kind": "definition", "module": "Mathlib.NumberTheory.ModularForms.SlashInvariantForms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SlashInvariantForm.coe_translate", "kind": "theorem", "module": "Mathlib.NumberTheory.ModularForms.SlashInvariantForms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulChar.instFunLike", "kind": "instance", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulChar.trivial", "kind": "definition", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulChar.coe_mk", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulChar.ext'", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulChar.instMulCharClass", "kind": "instance", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulChar.map_nonunit", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulChar.ext", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": true, "tactics": ["apply", "intro", "by_cases", "exact", "rw"], "tactic_count": 5}
{"name": "MulChar.toUnitHom", "kind": "definition", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulChar.coe_toUnitHom", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulChar.ofUnitHom", "kind": "definition", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulChar.ofUnitHom_coe", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MulChar.equivToUnitHom", "kind": "definition", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulChar.toUnitHom_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulChar.ofUnitHom_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulChar.coe_equivToUnitHom", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulChar.equivToUnitHom_symm_coe", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulChar.coe_toMonoidHom", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulChar.map_one", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulChar.map_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MulChar.toMonoidWithZeroHom", "kind": "definition", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulChar.map_ringChar", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MulChar.hasOne", "kind": "instance", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulChar.inhabited", "kind": "instance", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulChar.one_apply_coe", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "MulChar.one_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulChar.mul", "kind": "definition", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulChar.hasMul", "kind": "instance", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulChar.mul_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulChar.coeToFun_mul", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulChar.one_mul", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "MulChar.mul_one", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "MulChar.inv", "kind": "definition", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulChar.hasInv", "kind": "instance", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulChar.inv_apply_eq_inv", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulChar.inv_apply_eq_inv'", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulChar.inv_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "have", "apply_fun", "dsimp", "rw", "revert", "nontriviality", "intro", "rw"], "tactic_count": 10}
{"name": "MulChar.inv_apply'", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulChar.inv_mul", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": true, "tactics": ["ext", "rw", "simp", "rw"], "tactic_count": 4}
{"name": "MulChar.commGroup", "kind": "instance", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulChar.pow_apply_coe", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "MulChar.pow_apply'", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "rw"], "tactic_count": 3}
{"name": "MulChar.equivToUnitHom_mul_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": true, "tactics": ["apply_fun", "push_cast", "simp_rw"], "tactic_count": 3}
{"name": "MulChar.mulEquivToUnitHom", "kind": "definition", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulChar.eq_one_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MulChar.ne_one_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MulChar.IsQuadratic", "kind": "definition", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulChar.IsQuadratic.eq_of_eq_coe", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulChar.ringHomComp", "kind": "definition", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulChar.ringHomComp_one", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": true, "tactics": ["ext1", "simp"], "tactic_count": 2}
{"name": "MulChar.ringHomComp_inv", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": true, "tactics": ["ext1", "simp"], "tactic_count": 2}
{"name": "MulChar.ringHomComp_mul", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": true, "tactics": ["ext1", "simp"], "tactic_count": 2}
{"name": "MulChar.ringHomComp_pow", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "MulChar.injective_ringHomComp", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MulChar.ringHomComp_eq_one_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": true, "tactics": ["conv_lhs", "exact"], "tactic_count": 2}
{"name": "MulChar.ringHomComp_ne_one_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulChar.IsQuadratic.comp", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": true, "tactics": ["intro", "rcases"], "tactic_count": 2}
{"name": "MulChar.IsQuadratic.inv", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": true, "tactics": ["ext", "rw", "rcases", "rw", "rw", "have", "rw"], "tactic_count": 7}
{"name": "MulChar.IsQuadratic.sq_eq_one", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MulChar.IsQuadratic.pow_char", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": true, "tactics": ["ext", "rw", "rcases", "rw", "rw", "exact"], "tactic_count": 6}
{"name": "MulChar.IsQuadratic.pow_even", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": true, "tactics": ["obtain", "rw"], "tactic_count": 2}
{"name": "MulChar.IsQuadratic.pow_odd", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": true, "tactics": ["obtain", "rw"], "tactic_count": 2}
{"name": "MulChar.isQuadratic_iff_sq_eq_one", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "rcases", "exact", "simp", "simp", "by_cases", "refine", "rw", "exact"], "tactic_count": 10}
{"name": "MulChar.pow_card_eq_one", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": true, "tactics": ["ext1", "rw", "map_one]"], "tactic_count": 3}
{"name": "MulChar.orderOf_pos", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": true, "tactics": ["cases", "apply", "exact"], "tactic_count": 3}
{"name": "MulChar.sum_eq_zero_of_ne_one", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": true, "tactics": ["rcases", "refine", "simpa"], "tactic_count": 3}
{"name": "MulChar.sum_one_eq_card_units", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": false, "tactics": ["calc", "split_ifs", "exact", "exact", "congr", "ext", "simp"], "tactic_count": 7}
{"name": "MulChar.val_neg_one_eq_one_of_odd_order", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MulChar.finite", "kind": "instance", "module": "Mathlib.NumberTheory.MulChar.Duality", "is_tactic_proof": false, "tactics": ["have", "have", "let", "let", "have", "refine", "have", "refine", "simp", "exact"], "tactic_count": 10}
{"name": "MulChar.exists_apply_ne_one_iff_exists_monoidHom", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Duality", "is_tactic_proof": true, "tactics": ["refine", "contrapose", "rwa", "contrapose", "simpa"], "tactic_count": 5}
{"name": "MulChar.exists_apply_ne_one_of_hasEnoughRootsOfUnity", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Duality", "is_tactic_proof": true, "tactics": ["by_cases", "refine", "refine", "contrapose", "rw", "exact"], "tactic_count": 6}
{"name": "MulChar.mulEquiv_units", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Duality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulChar.card_eq_card_units_of_hasEnoughRootsOfUnity", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Duality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulChar.eq_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "coe_equivToUnitHom,"], "tactic_count": 2}
{"name": "MulChar.starComp", "kind": "definition", "module": "Mathlib.NumberTheory.MulChar.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulChar.instStarMul", "kind": "instance", "module": "Mathlib.NumberTheory.MulChar.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulChar.star_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulChar.apply_mem_rootsOfUnity", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MulChar.star_eq_inv", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Lemmas", "is_tactic_proof": true, "tactics": ["cases", "ext1", "simp", "exact"], "tactic_count": 4}
{"name": "MulChar.star_apply'", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MulChar.ofRootOfUnity", "kind": "definition", "module": "Mathlib.NumberTheory.MulChar.Lemmas", "is_tactic_proof": true, "tactics": ["have", "refine", "rw"], "tactic_count": 3}
{"name": "MulChar.ofRootOfUnity_spec", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MulChar.equiv_rootsOfUnity", "kind": "definition", "module": "Mathlib.NumberTheory.MulChar.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulChar.exists_mulChar_orderOf", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Lemmas", "is_tactic_proof": true, "tactics": ["classical", "have", "refine", "simp", "exact", "let", "let", "have", "use", "rw", "refine", "ext", "push_cast", "exact", "rw", "push_cast", "exact"], "tactic_count": 17}
{"name": "MulChar.orderOf_dvd_card_sub_one", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Lemmas", "is_tactic_proof": true, "tactics": ["classical", "rw", "exact"], "tactic_count": 3}
{"name": "MulChar.exists_mulChar_orderOf_eq_card_units", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulChar.apply_mem_rootsOfUnity_orderOf", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Lemmas", "is_tactic_proof": true, "tactics": ["have", "refine", "rw", "χ.pow_apply", "show"], "tactic_count": 5}
{"name": "MulChar.apply_mem_rootsOfUnity_of_pow_eq_one", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Lemmas", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "MulChar.exists_apply_eq_pow", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Lemmas", "is_tactic_proof": true, "tactics": ["obtain", "have", "obtain", "exact"], "tactic_count": 4}
{"name": "MulChar.apply_mem_algebraAdjoin_of_pow_eq_one", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Lemmas", "is_tactic_proof": true, "tactics": ["rcases", "exact", "obtain", "rw", "obtain", "exact"], "tactic_count": 6}
{"name": "MulChar.apply_mem_algebraAdjoin", "kind": "theorem", "module": "Mathlib.NumberTheory.MulChar.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dvd_geom_sum₂_iff_of_dvd_sub", "kind": "theorem", "module": "Mathlib.NumberTheory.Multiplicity", "is_tactic_proof": true, "tactics": ["rw", "simp", "map_natCast]"], "tactic_count": 3}
{"name": "dvd_geom_sum₂_iff_of_dvd_sub'", "kind": "theorem", "module": "Mathlib.NumberTheory.Multiplicity", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "dvd_geom_sum₂_self", "kind": "theorem", "module": "Mathlib.NumberTheory.Multiplicity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sq_dvd_add_pow_sub_sub", "kind": "theorem", "module": "Mathlib.NumberTheory.Multiplicity", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simp", "tsub_self,", "suffices", "apply", "intro", "calc", "p"], "tactic_count": 9}
{"name": "not_dvd_geom_sum₂", "kind": "theorem", "module": "Mathlib.NumberTheory.Multiplicity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "odd_sq_dvd_geom_sum₂_sub", "kind": "theorem", "module": "Mathlib.NumberTheory.Multiplicity", "is_tactic_proof": false, "tactics": ["have", "intro", "calc", "simp", "simp_rw", "let", "calc", "mk", "mk", "ring_nf", "simp_rw", "mk", "mk", "rw", "have", "intro", "rw", "exact", "rw", "mk", "mk", "simp", "rw", "rintro", "rw", "have", "rw", "exact", "rw", "ring1", "have", "simp", "simp", "norm_cast", "simp", "norm_cast", "simp", "ring_nf", "rw", "refine", "refine", "simp"], "tactic_count": 42}
{"name": "emultiplicity_pow_sub_pow_of_prime", "kind": "theorem", "module": "Mathlib.NumberTheory.Multiplicity", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "emultiplicity_geom_sum₂_eq_one", "kind": "theorem", "module": "Mathlib.NumberTheory.Multiplicity", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "exact", "rw", "obtain", "rw", "refine", "rw", "exact"], "tactic_count": 10}
{"name": "emultiplicity_pow_prime_sub_pow_prime", "kind": "theorem", "module": "Mathlib.NumberTheory.Multiplicity", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "emultiplicity_pow_prime_pow_sub_pow_prime_pow", "kind": "theorem", "module": "Mathlib.NumberTheory.Multiplicity", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "apply", "rw", "exact", "exact"], "tactic_count": 8}
{"name": "Int.emultiplicity_pow_sub_pow", "kind": "theorem", "module": "Mathlib.NumberTheory.Multiplicity", "is_tactic_proof": true, "tactics": ["rcases", "simp", "have", "simp", "rcases", "conv_lhs", "rw", "rw", "h.emultiplicity_eq_multiplicity]", "rw", "exact", "exact", "rw", "rintro", "refine", "rwa"], "tactic_count": 16}
{"name": "Int.emultiplicity_pow_add_pow", "kind": "theorem", "module": "Mathlib.NumberTheory.Multiplicity", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
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{"name": "pow_two_pow_sub_pow_two_pow", "kind": "theorem", "module": "Mathlib.NumberTheory.Multiplicity", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "hd", "suffices", "rw", "rw", "ring"], "tactic_count": 8}
{"name": "Int.sq_mod_four_eq_one_of_odd", "kind": "theorem", "module": "Mathlib.NumberTheory.Multiplicity", "is_tactic_proof": true, "tactics": ["intro", "unfold", "rcases", "ring_nf", "rw", "decide"], "tactic_count": 6}
{"name": "Int.eight_dvd_sq_sub_one_of_odd", "kind": "theorem", "module": "Mathlib.NumberTheory.Multiplicity", "is_tactic_proof": true, "tactics": ["rcases", "have", "simpa"], "tactic_count": 3}
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{"name": "padicValNat.pow_two_sub_pow", "kind": "theorem", "module": "Mathlib.NumberTheory.Multiplicity", "is_tactic_proof": true, "tactics": ["simp", "iterate", "exact", "exact", "exact", "lia", "simp"], "tactic_count": 7}
{"name": "padicValNat.pow_two_sub_one", "kind": "theorem", "module": "Mathlib.NumberTheory.Multiplicity", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "padicValNat.pow_two_sub_one_ge", "kind": "theorem", "module": "Mathlib.NumberTheory.Multiplicity", "is_tactic_proof": false, "tactics": ["have", "refine", "simpa", "have", "grind"], "tactic_count": 5}
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{"name": "IsIntegral.ratCast_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Niven", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegral.exists_int_iff_exists_rat", "kind": "theorem", "module": "Mathlib.NumberTheory.Niven", "is_tactic_proof": true, "tactics": ["refine", "rintro", "rw", "peel", "simp"], "tactic_count": 5}
{"name": "Complex.exp_rat_mul_pi_mul_I_pow_two_mul_den", "kind": "theorem", "module": "Mathlib.NumberTheory.Niven", "is_tactic_proof": true, "tactics": ["nth_rw", "push_cast", "rw"], "tactic_count": 3}
{"name": "Complex.isIntegral_exp_rat_mul_pi_mul_I", "kind": "theorem", "module": "Mathlib.NumberTheory.Niven", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
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{"name": "Complex.isAlgebraic_tan_rat_mul_pi", "kind": "theorem", "module": "Mathlib.NumberTheory.Niven", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Real.isIntegral_two_mul_cos_rat_mul_pi", "kind": "theorem", "module": "Mathlib.NumberTheory.Niven", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.isAlgebraic_sin_rat_mul_pi", "kind": "theorem", "module": "Mathlib.NumberTheory.Niven", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Real.isAlgebraic_tan_rat_mul_pi", "kind": "theorem", "module": "Mathlib.NumberTheory.Niven", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "niven_angle_div_pi_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.Niven", "is_tactic_proof": true, "tactics": ["apply", "replace", "constructor", "generalize", "have", "simp_all", "grind"], "tactic_count": 7}
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{"name": "NumberField.AdeleRing.principalSubgroup", "kind": "abbrev", "module": "Mathlib.NumberTheory.NumberField.AdeleRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.not_isField", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "NumberField.term𝓞", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "NumberField.RingOfIntegers.neg_mk", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.RingOfIntegers.mapRingHom", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.RingOfIntegers.mapRingHom_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.RingOfIntegers.mapRingEquiv", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.RingOfIntegers.mapRingEquiv_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.RingOfIntegers.mapRingEquiv_symm_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "NumberField.RingOfIntegers.inst_isScalarTower", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "NumberField.RingOfIntegers.coe_eq_zero_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "NumberField.RingOfIntegers.equiv", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.RingOfIntegers.instCharZero_1", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "NumberField.RingOfIntegers.instIsDedekindDomain", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.RingOfIntegers.instFreeInt", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.RingOfIntegers.instIsLocalizationAlgebraMapSubmonoidIntNonZeroDivisors", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.RingOfIntegers.basis", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.RingOfIntegers.restrict", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.RingOfIntegers.restrict_addMonoidHom", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.RingOfIntegers.restrict_monoidHom", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.RingOfIntegers.instIsScalarTower_1", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.RingOfIntegers.instIsIntegralClosure", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.RingOfIntegers.algEquiv", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.RingOfIntegers.extension_algebra_isIntegral", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.RingOfIntegers.extension_isNoetherian", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.RingOfIntegers.ker_algebraMap_eq_bot", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.RingOfIntegers.algebraMap.injective", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.RingOfIntegers.instIsTorsionFree_1", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.RingOfIntegers.instIsTorsionFree_2", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.integralBasis", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.integralBasis_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.integralBasis_repr_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mem_span_integralBasis", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NumberField.RingOfIntegers.rank", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.numberField", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.ringOfIntegersEquiv", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.ringOfIntegersEquiv_apply_coe", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Basic", "is_tactic_proof": true, "tactics": ["obtain", "simp"], "tactic_count": 2}
{"name": "Rat.ringOfIntegersEquiv_symm_apply_coe", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.instNumberFieldRat", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.NumberField.CMField.0.NumberField.IsCMField.termK⁺", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.CMField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "NumberField.IsCMField.isQuadraticExtension", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.CMField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.IsCMField.isTotallyComplex", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.CMField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.IsCMField.card_infinitePlace_eq_card_infinitePlace", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CMField", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NumberField.IsCMField.equivInfinitePlace", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.CMField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.IsCMField.equivInfinitePlace_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CMField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.IsCMField.equivInfinitePlace_symm_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CMField", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NumberField.IsCMField.units_rank_eq_units_rank", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CMField", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NumberField.IsCMField.exists_isConj", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CMField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.IsCMField.isConj_eq_isConj", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CMField", "is_tactic_proof": false, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "NumberField.IsCMField.complexConj", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.CMField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.IsCMField.isConj_complexConj", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CMField", "is_tactic_proof": true, "tactics": ["obtain", "have", "rwa"], "tactic_count": 3}
{"name": "NumberField.IsCMField.complexEmbedding_complexConj", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CMField", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NumberField.IsCMField.infinitePlace_complexConj", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CMField", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NumberField.IsCMField.complexConj_apply_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CMField", "is_tactic_proof": true, "tactics": ["let", "exact"], "tactic_count": 2}
{"name": "NumberField.IsCMField.complexConj_ne_one", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CMField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.IsCMField.complexConj_apply_eq_self", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CMField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.IsCMField.orderOf_complexConj", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CMField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.IsCMField.zpowers_complexConj_eq_top", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CMField", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "NumberField.IsCMField.complexConj_eq_self_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CMField", "is_tactic_proof": true, "tactics": ["convert", "rw", "exact", "rw", "aesop"], "tactic_count": 5}
{"name": "NumberField.IsCMField.RingOfIntegers.complexConj_eq_self_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CMField", "is_tactic_proof": true, "tactics": ["rw", "refine", "have", "refine", "rw", "rfl", "rw", "exact"], "tactic_count": 8}
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{"name": "NumberField.IsCMField.starRing", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.CMField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.IsCMField.ringOfIntegersComplexConj", "kind": "abbrev", "module": "Mathlib.NumberTheory.NumberField.CMField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.IsCMField.coe_ringOfIntegersComplexConj", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CMField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.IsCMField.ringOfIntegersComplexConj_eq_self_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CMField", "is_tactic_proof": true, "tactics": ["refine", "rw", "obtain", "exact", "rintro", "simp"], "tactic_count": 6}
{"name": "NumberField.IsCMField.unitsComplexConj", "kind": "abbrev", "module": "Mathlib.NumberTheory.NumberField.CMField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.IsCMField.realUnits", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.CMField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.IsCMField.mem_realUnits_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CMField", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NumberField.IsCMField.unitsComplexConj_eq_self_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CMField", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "NumberField.IsCMField.complexConj_torsion", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CMField", "is_tactic_proof": true, "tactics": ["let", "apply", "rw", "exact"], "tactic_count": 4}
{"name": "NumberField.IsCMField.unitsComplexConj_torsion", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CMField", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "NumberField.IsCMField.unitsMulComplexConjInv", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.CMField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.IsCMField.unitsMulComplexConjInv_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CMField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.IsCMField.unitsMulComplexConjInv_apply_torsion", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CMField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.IsCMField.map_unitsMulComplexConjInv_torsion", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CMField", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "NumberField.IsCMField.unitsMulComplexConjInv_ker", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CMField", "is_tactic_proof": true, "tactics": ["ext", "rw", "unitsComplexConj_eq_self_iff]"], "tactic_count": 3}
{"name": "NumberField.IsCMField.index_unitsMulComplexConjInv_range_dvd", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CMField", "is_tactic_proof": false, "tactics": ["suffices", "refine", "rintro", "exact", "rw", "exact"], "tactic_count": 6}
{"name": "NumberField.IsCMField.indexRealUnits", "kind": "abbrev", "module": "Mathlib.NumberTheory.NumberField.CMField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.IsCMField.indexRealUnits_mul_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CMField", "is_tactic_proof": true, "tactics": ["rw", "convert", "rw", "rw", "rw", "exact"], "tactic_count": 6}
{"name": "NumberField.IsCMField.indexRealUnits_eq_one_or_two", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CMField", "is_tactic_proof": true, "tactics": ["have", "obtain", "exact", "exact"], "tactic_count": 4}
{"name": "NumberField.IsCMField.indexRealUnits_eq_two_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CMField", "is_tactic_proof": false, "tactics": ["suffices", "rw", "have", "refine", "rwa", "rwa", "refine", "refine", "rw", "obtain", "rw", "obtain", "exact"], "tactic_count": 13}
{"name": "NumberField.IsCMField.realFundSystem", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.CMField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.IsCMField.closure_realFundSystem_sup_torsion", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CMField", "is_tactic_proof": false, "tactics": ["have", "rintro", "exact", "rw", "congr", "simp"], "tactic_count": 6}
{"name": "NumberField.IsCMField.regOfFamily_realFunSystem", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CMField", "is_tactic_proof": true, "tactics": ["classical", "let", "let", "let", "rw", "rw", "simp]", "rw", "congr", "rw", "show", "simp"], "tactic_count": 12}
{"name": "NumberField.IsCMField.regulator_div_regulator_eq_two_pow_mul_indexRealUnits_inv", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CMField", "is_tactic_proof": true, "tactics": ["rw", "regOfFamily_realFunSystem,"], "tactic_count": 2}
{"name": "NumberField.CMExtension.eq_maximalRealSubfield", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CMField", "is_tactic_proof": true, "tactics": ["refine", "by_contra", "have", "let", "have", "simpa", "contrapose", "rw", "rw", "aesop", "have", "have", "obtain", "exact"], "tactic_count": 14}
{"name": "NumberField.CMExtension.equivMaximalRealSubfield", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.CMField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.CMExtension.equivMaximalRealSubfield_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CMField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.CMExtension.algebraMap_equivMaximalRealSubfield_symm_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CMField", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "NumberField.IsCMField.ofCMExtension", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CMField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.IsCMField.of_forall_isConj", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CMField", "is_tactic_proof": true, "tactics": ["let", "have", "rw", "exact", "have", "let", "have", "obtain", "dsimp", "rw", "exact", "have", "exact"], "tactic_count": 13}
{"name": "NumberField.IsCMField.of_isAbelianGalois", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.CMField", "is_tactic_proof": true, "tactics": ["let", "obtain", "exists_isConj_of_isRamified", "have", "intro", "obtain", "rw", "exact", "exact"], "tactic_count": 9}
{"name": "IsCyclotomicExtension.Rat.isCMField", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CMField", "is_tactic_proof": true, "tactics": ["have", "obtain", "have", "obtain", "have", "have", "have", "exact", "have", "exact"], "tactic_count": 10}
{"name": "IsCyclotomicExtension.Rat.instIsCMFieldOfTopSetNatRat", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.CMField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.canonicalEmbedding", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.canonicalEmbedding_injective", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.canonicalEmbedding.apply_at", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.canonicalEmbedding.conj_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["refine", "rintro", "rw", "rw", "rw", "rw", "exact"], "tactic_count": 7}
{"name": "NumberField.canonicalEmbedding.nnnorm_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "NumberField.canonicalEmbedding.norm_le_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "refine", "exact", "exact", "lift", "simp_rw"], "tactic_count": 7}
{"name": "NumberField.canonicalEmbedding.integerLattice", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.canonicalEmbedding.integerLattice.inter_ball_finite", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["obtain", "simp", "have", "rw", "convert", "ext", "rintro", "exact", "rintro", "exact"], "tactic_count": 10}
{"name": "NumberField.canonicalEmbedding.latticeBasis", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["classical", "let", "let", "let", "suffices", "rw", "exact", "let", "rw", "rw", "convert", "rw", "exact"], "tactic_count": 13}
{"name": "NumberField.canonicalEmbedding.latticeBasis_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NumberField.canonicalEmbedding.mem_span_latticeBasis", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": false, "tactics": ["rw", "rw", "rw", "simp", "rfl"], "tactic_count": 5}
{"name": "NumberField.canonicalEmbedding.mem_rat_span_latticeBasis", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "refine", "rw", "exact"], "tactic_count": 5}
{"name": "NumberField.canonicalEmbedding.integralBasis_repr_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["rw", "let", "suffices", "refine", "have", "apply", "rw", "rfl", "simp_rw"], "tactic_count": 9}
{"name": "NumberField.mixedEmbedding.mixedSpace", "kind": "abbrev", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.mixedEmbedding_apply_isReal", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "NumberField.mixedEmbedding.mixedEmbedding_apply_isComplex", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "NumberField.mixedEmbedding.instNontrivialMixedSpace", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "have", "exact", "have", "exact"], "tactic_count": 6}
{"name": "NumberField.mixedEmbedding.finrank", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["classical", "rw", "nrRealPlaces,"], "tactic_count": 3}
{"name": "NumberField.mixedEmbedding_injective", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "NumberField.mixedEmbedding.instIsAddHaarMeasureMixedSpaceVolume", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.instNoAtomsMixedSpaceVolume", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["obtain", "by_cases", "have", "exact", "have", "pi_noAtoms", "exact"], "tactic_count": 7}
{"name": "NumberField.mixedEmbedding.volume_eq_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": false, "tactics": ["let", "convert", "simpa"], "tactic_count": 3}
{"name": "NumberField.mixedEmbedding.commMap", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.commMap_apply_of_isReal", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.commMap_apply_of_isComplex", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.commMap_canonical_eq_mixed", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": false, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "NumberField.mixedEmbedding.disjoint_span_commMap_ker", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["refine", "replace", "refine", "rintro", "exact", "ext1", "rw", "by_cases", "apply", "rw", "exact", "rw", "have", "cases", "inl", "inr", "apply", "rwa"], "tactic_count": 18}
{"name": "NumberField.mixedEmbedding.normAtPlace", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.normAtPlace_nonneg", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["rw", "split_ifs"], "tactic_count": 2}
{"name": "NumberField.mixedEmbedding.normAtPlace_neg", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["rw", "split_ifs"], "tactic_count": 2}
{"name": "NumberField.mixedEmbedding.normAtPlace_add_le", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["rw", "split_ifs"], "tactic_count": 2}
{"name": "NumberField.mixedEmbedding.normAtPlace_smul", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["rw", "split_ifs"], "tactic_count": 2}
{"name": "NumberField.mixedEmbedding.normAtPlace_real", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NumberField.mixedEmbedding.normAtPlace_apply_of_isReal", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NumberField.mixedEmbedding.normAtPlace_apply_of_isComplex", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NumberField.mixedEmbedding.normAtPlace_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "norm_embedding_of_isReal,"], "tactic_count": 2}
{"name": "NumberField.mixedEmbedding.forall_normAtPlace_eq_zero_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["refine", "ext", "exact", "exact", "simp_rw"], "tactic_count": 5}
{"name": "NumberField.mixedEmbedding.exists_normAtPlace_ne_zero_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NumberField.mixedEmbedding.continuous_normAtPlace", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "split_ifs"], "tactic_count": 2}
{"name": "NumberField.mixedEmbedding.nnnorm_eq_sup_normAtPlace", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": false, "tactics": ["have", "rw", "congr", "ext", "simp", "ext", "simp"], "tactic_count": 7}
{"name": "NumberField.mixedEmbedding.norm_eq_sup'_normAtPlace", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": false, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "NumberField.mixedEmbedding.norm", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.norm_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.norm_nonneg", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.norm_eq_zero_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "pow_eq_zero_iff"], "tactic_count": 2}
{"name": "NumberField.mixedEmbedding.norm_ne_zero_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp_rw"], "tactic_count": 2}
{"name": "NumberField.mixedEmbedding.norm_eq_of_normAtPlace_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "NumberField.mixedEmbedding.norm_smul", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "NumberField.mixedEmbedding.norm_real", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NumberField.mixedEmbedding.norm_eq_norm", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "NumberField.mixedEmbedding.norm_unit", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NumberField.mixedEmbedding.norm_eq_zero_iff'", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["obtain", "rw"], "tactic_count": 2}
{"name": "NumberField.mixedEmbedding.continuous_norm", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["refine", "simp_rw", "split_ifs"], "tactic_count": 3}
{"name": "NumberField.mixedEmbedding.index", "kind": "abbrev", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.stdBasis", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.stdBasis_apply_isReal", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.stdBasis_apply_isComplex_fst", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.stdBasis_apply_isComplex_snd", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.fundamentalDomain_stdBasis", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "NumberField.mixedEmbedding.volume_fundamentalDomain_stdBasis", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": false, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "NumberField.mixedEmbedding.indexEquiv", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["refine", "cases", "inl", "inr", "rcases", "exact", "intro", "by_cases", "exact", "by_cases", "exact", "exact", "rw"], "tactic_count": 13}
{"name": "NumberField.mixedEmbedding.indexEquiv_apply_isReal", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.indexEquiv_apply_isComplex_fst", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.indexEquiv_apply_isComplex_snd", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.matrixToStdBasis", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.det_matrixToStdBasis", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.stdBasis_repr_eq_matrixToStdBasis_mul", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": false, "tactics": ["simp_rw", "mul_one,", "cases", "inl", "simp_rw", "one_mul,", "hx", "inr", "rcases", "fin_cases", "simp", "zero_apply,", "blockDiagonal_apply,", "sum_add_distrib,", "ring", "simp", "zero_apply,", "blockDiagonal_apply,", "neg_mul,", "ring_nf"], "tactic_count": 20}
{"name": "NumberField.mixedEmbedding.integerLattice", "kind": "abbrev", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.latticeBasis", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["classical", "have", "refine", "rw", "smul_eq_mul,"], "tactic_count": 5}
{"name": "NumberField.mixedEmbedding.latticeBasis_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["simp", "canonicalEmbedding.latticeBasis_apply,"], "tactic_count": 2}
{"name": "NumberField.mixedEmbedding.mem_span_latticeBasis", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": false, "tactics": ["rw", "rw", "rw", "simp", "rfl"], "tactic_count": 5}
{"name": "NumberField.mixedEmbedding.span_latticeBasis", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.instDiscreteTopologySubtypeMixedSpaceMemSubmoduleIntIntegerLattice", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["classical", "rw", "infer_instance"], "tactic_count": 3}
{"name": "NumberField.mixedEmbedding.instIsZLatticeRealMixedSpaceIntegerLattice", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "infer_instance"], "tactic_count": 2}
{"name": "NumberField.mixedEmbedding.fundamentalDomain_integerLattice", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "NumberField.mixedEmbedding.mem_rat_span_latticeBasis", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "refine", "rw", "exact"], "tactic_count": 5}
{"name": "NumberField.mixedEmbedding.latticeBasis_repr_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["rw", "let", "suffices", "refine", "have", "apply", "rw", "rfl", "simp_rw"], "tactic_count": 9}
{"name": "NumberField.mixedEmbedding.idealLattice", "kind": "abbrev", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.mem_idealLattice", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NumberField.mixedEmbedding.det_basisOfFractionalIdeal_eq_norm", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": false, "tactics": ["suffices", "rw", "det_basisOfFractionalIdeal_eq_absNorm", "rw", "congr", "ext", "simp_rw", "exact"], "tactic_count": 8}
{"name": "NumberField.mixedEmbedding.fractionalIdealLatticeBasis", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": false, "tactics": ["let", "refine", "rw", "refine", "suffices", "rw", "exact", "rw", "exact"], "tactic_count": 9}
{"name": "NumberField.mixedEmbedding.fractionalIdealLatticeBasis_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NumberField.mixedEmbedding.mem_span_fractionalIdealLatticeBasis", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": false, "tactics": ["rw", "rw", "exact", "rw", "rw", "simp", "rfl"], "tactic_count": 7}
{"name": "NumberField.mixedEmbedding.span_idealLatticeBasis", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "NumberField.mixedEmbedding.instDiscreteTopologySubtypeMixedSpaceMemSubmoduleIntIdealLattice", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["classical", "rw", "infer_instance"], "tactic_count": 3}
{"name": "NumberField.mixedEmbedding.instIsZLatticeRealMixedSpaceIdealLattice", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "infer_instance"], "tactic_count": 2}
{"name": "NumberField.mixedEmbedding.fundamentalDomain_idealLattice", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "NumberField.mixedEmbedding.euclidean.mixedSpace", "kind": "abbrev", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.euclidean.instRingMixedSpace", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.euclidean.toMixed", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.euclidean.instNontrivialMixedSpace", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.euclidean.finrank", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NumberField.mixedEmbedding.euclidean.stdOrthonormalBasis", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.euclidean.stdOrthonormalBasis_map_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "NumberField.mixedEmbedding.euclidean.volumePreserving_toMixed", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.euclidean.volumePreserving_toMixed_symm", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "NumberField.mixedEmbedding.euclidean.integerLattice", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.euclidean.instDiscreteTopologySubtypeMixedSpaceMemSubmoduleIntIntegerLattice", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["classical", "rw", "infer_instance"], "tactic_count": 3}
{"name": "NumberField.mixedEmbedding.euclidean.instIsZLatticeRealMixedSpaceIntegerLattice", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "infer_instance"], "tactic_count": 2}
{"name": "NumberField.mixedEmbedding.negAt", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.negAt_apply_isReal_and_mem", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "NumberField.mixedEmbedding.negAt_apply_isReal_and_notMem", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "NumberField.mixedEmbedding.negAt_apply_isComplex", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.negAt_apply_snd", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.negAt_apply_norm_isReal", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "NumberField.mixedEmbedding.volume_preserving_negAt", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["refine", "by_cases", "simp_rw", "exact", "simp_rw", "exact"], "tactic_count": 6}
{"name": "NumberField.mixedEmbedding.normAtPlace_negAt", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["obtain", "simp_rw", "simp_rw"], "tactic_count": 3}
{"name": "NumberField.mixedEmbedding.norm_negAt", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.negAt_symm", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "simp_rw", "if_pos", "simp_rw", "if_neg", "rfl"], "tactic_count": 7}
{"name": "NumberField.mixedEmbedding.signSet", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.negAt_signSet_apply_isReal", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "rw"], "tactic_count": 3}
{"name": "NumberField.mixedEmbedding.negAt_signSet_apply_isComplex", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.negAt_preimage", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NumberField.mixedEmbedding.plusPart", "kind": "abbrev", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.neg_of_mem_negA_plusPart", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact"], "tactic_count": 3}
{"name": "NumberField.mixedEmbedding.pos_of_notMem_negAt_plusPart", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact"], "tactic_count": 3}
{"name": "NumberField.mixedEmbedding.disjoint_negAt_plusPart", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["intro", "refine", "obtain", "exact", "exact", "lt_irrefl"], "tactic_count": 6}
{"name": "NumberField.mixedEmbedding.mem_negAt_plusPart_of_mem", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": false, "tactics": ["refine", "ext", "by_cases", "simp", "simp", "rfl"], "tactic_count": 6}
{"name": "NumberField.mixedEmbedding.iUnion_negAt_plusPart_union", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["ext", "rw", "refine", "rintro", "simp_rw", "rwa", "exact", "obtain", "exact", "refine", "exact", "exact"], "tactic_count": 12}
{"name": "NumberField.mixedEmbedding.iUnion_negAt_plusPart_ae", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["nth_rewrite", "refine", "exact"], "tactic_count": 3}
{"name": "NumberField.mixedEmbedding.measurableSet_plusPart", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["convert_to", "ext", "refine", "exact"], "tactic_count": 4}
{"name": "NumberField.mixedEmbedding.measurableSet_negAt_plusPart", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.volume_negAt_plusPart", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["rw", "volume_preserving_negAt.measure_preimage"], "tactic_count": 2}
{"name": "NumberField.mixedEmbedding.volume_eq_two_pow_mul_volume_plusPart", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["simp", "measure_iUnion", "tsum_fintype,"], "tactic_count": 3}
{"name": "NumberField.mixedEmbedding.realSpace", "kind": "abbrev", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.realSpace.volume_eq_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": false, "tactics": ["let", "convert", "simpa"], "tactic_count": 3}
{"name": "NumberField.mixedEmbedding.mixedSpaceOfRealSpace", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.mixedSpaceOfRealSpace_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.injective_mixedSpaceOfRealSpace", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "ext", "obtain", "exact", "exact"], "tactic_count": 6}
{"name": "NumberField.mixedEmbedding.normAtPlace_mixedSpaceOfRealSpace", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["simp", "obtain", "rw", "rw"], "tactic_count": 4}
{"name": "NumberField.mixedEmbedding.normAtComplexPlaces", "kind": "abbrev", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.normAtComplexPlaces_apply_isReal", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NumberField.mixedEmbedding.normAtComplexPlaces_apply_isComplex", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NumberField.mixedEmbedding.normAtComplexPlaces_mixedSpaceOfRealSpace", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["ext", "obtain", "rw", "rw"], "tactic_count": 4}
{"name": "NumberField.mixedEmbedding.normAtAllPlaces", "kind": "abbrev", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.normAtAllPlaces_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.continuous_normAtAllPlaces", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["fun_prop"], "tactic_count": 1}
{"name": "NumberField.mixedEmbedding.normAtAllPlaces_nonneg", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.normAtAllPlaces_mixedSpaceOfRealSpace", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "NumberField.mixedEmbedding.normAtAllPlaces_mixedEmbedding", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NumberField.mixedEmbedding.normAtAllPlaces_normAtAllPlaces", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.normAtAllPlaces_norm_at_real_places", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["ext", "obtain", "simp_rw", "simp_rw"], "tactic_count": 4}
{"name": "NumberField.mixedEmbedding.normAtComplexPlaces_normAtAllPlaces", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.normAtAllPlaces_eq_of_normAtComplexPlaces_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["ext", "obtain", "simpa", "congr_arg", "simpa", "congr_fun"], "tactic_count": 6}
{"name": "NumberField.mixedEmbedding.normAtAllPlaces_image_preimage_of_nonneg", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic", "is_tactic_proof": true, "tactics": ["rw", "rintro", "refine", "rw"], "tactic_count": 4}
{"name": "NumberField.mixedEmbedding.convexBodyLT", "kind": "abbrev", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.convexBodyLT_mem", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody", "is_tactic_proof": true, "tactics": ["simp_rw", "mem_ball_zero_iff,", "forall₂_or_left,"], "tactic_count": 3}
{"name": "NumberField.mixedEmbedding.convexBodyLT_neg_mem", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody", "is_tactic_proof": false, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "NumberField.mixedEmbedding.convexBodyLT_convex", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.convexBodyLTFactor", "kind": "abbrev", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.convexBodyLTFactor_ne_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.one_le_convexBodyLTFactor", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.convexBodyLT_volume", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody", "is_tactic_proof": true, "tactics": ["calc", "simp_rw", "ofReal_ofNat,", "simp_rw", "ring", "simp_rw", "ofReal_coe_nnreal]"], "tactic_count": 7}
{"name": "NumberField.mixedEmbedding.adjust_f", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody", "is_tactic_proof": true, "tactics": ["classical", "let", "refine", "exact", "rw", "rw", "exact", "rw"], "tactic_count": 8}
{"name": "NumberField.mixedEmbedding.convexBodyLT'", "kind": "abbrev", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.convexBodyLT'_mem", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody", "is_tactic_proof": false, "tactics": ["simp_rw", "refine", "by_cases", "exact", "specialize", "rw", "rwa", "simpa", "exact", "by_cases", "simpa", "rw", "rw", "exact"], "tactic_count": 14}
{"name": "NumberField.mixedEmbedding.convexBodyLT'_neg_mem", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody", "is_tactic_proof": false, "tactics": ["simp", "convert", "split_ifs"], "tactic_count": 3}
{"name": "NumberField.mixedEmbedding.convexBodyLT'_convex", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody", "is_tactic_proof": true, "tactics": ["refine", "split_ifs", "simp_rw", "refine", "exact"], "tactic_count": 5}
{"name": "NumberField.mixedEmbedding.convexBodyLT'Factor", "kind": "abbrev", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.convexBodyLT'Factor_ne_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.one_le_convexBodyLT'Factor", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.convexBodyLT'_volume", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody", "is_tactic_proof": false, "tactics": ["have", "intro", "rw", "simp_rw", "rw", "ext", "simp_rw", "ofReal_mul", "show", "refine", "exact", "exact", "calc", "simp_rw", "rw", "congr", "refine", "rw", "simpa", "simp_rw", "convexBodyLT'Factor", "rw", "simp_rw", "ring", "simp_rw", "ofReal_coe_nnreal,"], "tactic_count": 26}
{"name": "NumberField.mixedEmbedding.convexBodySumFun", "kind": "abbrev", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.convexBodySumFun_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.convexBodySumFun_apply'", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "NumberField.mixedEmbedding.convexBodySumFun_nonneg", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.convexBodySumFun_neg", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "NumberField.mixedEmbedding.convexBodySumFun_add_le", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "NumberField.mixedEmbedding.convexBodySumFun_smul", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "NumberField.mixedEmbedding.convexBodySumFun_eq_zero_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody", "is_tactic_proof": false, "tactics": ["rw", "conv", "enter", "rw", "simp_rw"], "tactic_count": 5}
{"name": "NumberField.mixedEmbedding.norm_le_convexBodySumFun", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "refine", "exact", "exact"], "tactic_count": 6}
{"name": "NumberField.mixedEmbedding.convexBodySumFun_continuous", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody", "is_tactic_proof": true, "tactics": ["fun_prop"], "tactic_count": 1}
{"name": "NumberField.mixedEmbedding.convexBodySum", "kind": "abbrev", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.convexBodySum_volume_eq_zero_of_le_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody", "is_tactic_proof": true, "tactics": ["obtain", "suffices", "ext", "refine", "rw", "linarith", "suffices", "ext", "rw", "exact"], "tactic_count": 10}
{"name": "NumberField.mixedEmbedding.convexBodySum_mem", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody", "is_tactic_proof": true, "tactics": ["simp_rw", "rfl"], "tactic_count": 2}
{"name": "NumberField.mixedEmbedding.convexBodySum_neg_mem", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "NumberField.mixedEmbedding.convexBodySum_convex", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody", "is_tactic_proof": true, "tactics": ["refine", "convert", "exact"], "tactic_count": 3}
{"name": "NumberField.mixedEmbedding.convexBodySum_isBounded", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody", "is_tactic_proof": true, "tactics": ["classical", "refine", "refine", "exact", "exact"], "tactic_count": 5}
{"name": "NumberField.mixedEmbedding.convexBodySum_compact", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody", "is_tactic_proof": true, "tactics": ["classical", "rw", "refine", "convert", "ext", "simp"], "tactic_count": 6}
{"name": "NumberField.mixedEmbedding.convexBodySumFactor", "kind": "abbrev", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.convexBodySumFactor_ne_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "NumberField.mixedEmbedding.convexBodySum_volume", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact", "suffices", "rw", "convert", "simp_rw", "abs_inv,", "inv_mul_le_iff₀", "rw", "exact", "rw", "convexBodySumFun_add_le", "rw", "zero_lt_one]", "simp_rw", "ofReal_div_of_pos", "suffices", "rw", "ofReal_div_of_pos", "coe_div", "coe_div", "calc", "simp_rw", "exp_sum,", "rw", "integral_fintype_prod_volume_eq_pow", "simp_rw", "rw", "simp_rw", "simp_rw"], "tactic_count": 31}
{"name": "NumberField.mixedEmbedding.minkowskiBound", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.volume_fundamentalDomain_fractionalIdealLatticeBasis", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody", "is_tactic_proof": false, "tactics": ["let", "refine", "rw", "rw", "measure_fundamentalDomain", "rw", "ext1", "rw"], "tactic_count": 8}
{"name": "NumberField.mixedEmbedding.minkowskiBound_lt_top", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody", "is_tactic_proof": true, "tactics": ["classical", "exact"], "tactic_count": 2}
{"name": "NumberField.mixedEmbedding.minkowskiBound_pos", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.exists_ne_zero_mem_ideal_lt", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody", "is_tactic_proof": true, "tactics": ["have", "have", "change", "infer_instance", "obtain", "exists_ne_zero_mem_lattice_of_measure_mul_two_pow_lt_measure", "rw", "obtain", "exact"], "tactic_count": 9}
{"name": "NumberField.mixedEmbedding.exists_ne_zero_mem_ideal_lt'", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody", "is_tactic_proof": true, "tactics": ["have", "have", "change", "infer_instance", "obtain", "exists_ne_zero_mem_lattice_of_measure_mul_two_pow_lt_measure", "rw", "obtain", "exact"], "tactic_count": 9}
{"name": "NumberField.mixedEmbedding.exists_ne_zero_mem_ringOfIntegers_lt", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "exact"], "tactic_count": 3}
{"name": "NumberField.mixedEmbedding.exists_ne_zero_mem_ringOfIntegers_lt'", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "exact"], "tactic_count": 3}
{"name": "NumberField.mixedEmbedding.exists_primitive_element_lt_of_isReal", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody", "is_tactic_proof": true, "tactics": ["classical", "have", "rw", "simp_rw", "rw", "simp_rw", "exact", "obtain", "refine", "exact", "split_ifs"], "tactic_count": 11}
{"name": "NumberField.mixedEmbedding.exists_primitive_element_lt_of_isComplex", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody", "is_tactic_proof": true, "tactics": ["classical", "have", "rw", "simp_rw", "rw", "simp_rw", "exact", "obtain", "refine", "exact", "is_primitive_element_of_infinitePlace_lt", "by_cases", "rw", "dsimp", "rw", "refine", "rw", "exact", "rw", "exact", "refine", "rw", "norm_num"], "tactic_count": 23}
{"name": "NumberField.mixedEmbedding.exists_ne_zero_mem_ideal_of_norm_le", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody", "is_tactic_proof": false, "tactics": ["have", "contrapose", "rw", "exact", "have", "have", "have", "have", "change", "infer_instance", "obtain", "exists_ne_zero_mem_lattice_of_measure_mul_two_pow_le_measure", "rw", "obtain", "refine", "rw", "mul_inv_cancel₀", "le_div_iff₀", "refine", "rw", "refine", "le_trans", "simp_rw", "exact", "rw", "exact"], "tactic_count": 26}
{"name": "NumberField.mixedEmbedding.exists_ne_zero_mem_ringOfIntegers_of_norm_le", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "exact"], "tactic_count": 3}
{"name": "NumberField.mixedEmbedding.unitSMul", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.instMulActionUnitsRingOfIntegersMixedSpace", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.instSMulZeroClassUnitsRingOfIntegersMixedSpace", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.unit_smul_eq_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone", "is_tactic_proof": true, "tactics": ["refine", "contrapose", "obtain", "refine", "rw", "exact"], "tactic_count": 6}
{"name": "NumberField.mixedEmbedding.unit_smul_eq_iff_mul_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone", "is_tactic_proof": false, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "NumberField.mixedEmbedding.norm_unit_smul", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NumberField.mixedEmbedding.logMap", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.logMap_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.logMap_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "NumberField.mixedEmbedding.logMap_one", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "NumberField.mixedEmbedding.logMap_mul", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone", "is_tactic_proof": true, "tactics": ["ext", "simp_rw", "rw", "ring", "exact", "exact"], "tactic_count": 6}
{"name": "NumberField.mixedEmbedding.logMap_apply_of_norm_eq_one", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NumberField.mixedEmbedding.logMap_eq_logEmbedding", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "NumberField.mixedEmbedding.logMap_unit_smul", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NumberField.mixedEmbedding.logMap_torsion_smul", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone", "is_tactic_proof": true, "tactics": ["ext", "simp_rw"], "tactic_count": 2}
{"name": "NumberField.mixedEmbedding.logMap_real", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone", "is_tactic_proof": true, "tactics": ["ext", "rw", "mul_comm", "mul_zero,"], "tactic_count": 4}
{"name": "NumberField.mixedEmbedding.logMap_real_smul", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone", "is_tactic_proof": false, "tactics": ["have", "rw", "exact", "rw"], "tactic_count": 4}
{"name": "NumberField.mixedEmbedding.logMap_eq_of_normAtPlace_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone", "is_tactic_proof": true, "tactics": ["ext", "simp_rw"], "tactic_count": 2}
{"name": "NumberField.mixedEmbedding.fundamentalCone", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.measurableSet_fundamentalCone", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone", "is_tactic_proof": true, "tactics": ["classical", "refine", "unfold", "refine", "measurable_pi_iff.mpr", "exact", "exact"], "tactic_count": 7}
{"name": "NumberField.mixedEmbedding.fundamentalCone.norm_pos_of_mem", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.fundamentalCone.normAtPlace_pos_of_mem", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.fundamentalCone.mem_of_normAtPlace_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "NumberField.mixedEmbedding.fundamentalCone.smul_mem_of_mem", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact", "rw", "exact"], "tactic_count": 5}
{"name": "NumberField.mixedEmbedding.fundamentalCone.smul_mem_iff_mem", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone", "is_tactic_proof": true, "tactics": ["refine", "convert", "rw"], "tactic_count": 3}
{"name": "NumberField.mixedEmbedding.fundamentalCone.exists_unit_smul_mem", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone", "is_tactic_proof": true, "tactics": ["classical", "let", "rsuffices", "exact", "obtain", "exact"], "tactic_count": 6}
{"name": "NumberField.mixedEmbedding.fundamentalCone.torsion_smul_mem_of_mem", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone", "is_tactic_proof": true, "tactics": ["constructor", "rw", "exact", "rw", "exact"], "tactic_count": 5}
{"name": "NumberField.mixedEmbedding.fundamentalCone.unit_smul_mem_iff_mem_torsion", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone", "is_tactic_proof": true, "tactics": ["classical", "refine", "rw", "let", "refine", "rw", "exact", "rw", "exact", "rw", "exact"], "tactic_count": 11}
{"name": "NumberField.mixedEmbedding.fundamentalCone.integerSet", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.fundamentalCone.mem_integerSet", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NumberField.mixedEmbedding.fundamentalCone.existsUnique_preimage_of_mem_integerSet", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone", "is_tactic_proof": true, "tactics": ["obtain", "refine", "exact"], "tactic_count": 3}
{"name": "NumberField.mixedEmbedding.fundamentalCone.ne_zero_of_mem_integerSet", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone", "is_tactic_proof": true, "tactics": ["by_contra", "exact"], "tactic_count": 2}
{"name": "NumberField.mixedEmbedding.fundamentalCone.preimageOfMemIntegerSet", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.fundamentalCone.mixedEmbedding_preimageOfMemIntegerSet", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NumberField.mixedEmbedding.fundamentalCone.preimageOfMemIntegerSet_mixedEmbedding", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "NumberField.mixedEmbedding.fundamentalCone.exists_unitSMul_mem_integerSet", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone", "is_tactic_proof": false, "tactics": ["replace", "obtain", "obtain", "exact"], "tactic_count": 4}
{"name": "NumberField.mixedEmbedding.fundamentalCone.torsion_unitSMul_mem_integerSet", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone", "is_tactic_proof": true, "tactics": ["obtain", "refine"], "tactic_count": 2}
{"name": "NumberField.mixedEmbedding.fundamentalCone.integerSetTorsionSMul", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.fundamentalCone.instMulActionSubtypeUnitsRingOfIntegersMemSubgroupTorsionElemMixedSpaceIntegerSet", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.fundamentalCone.intNorm", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.fundamentalCone.intNorm_coe", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone", "is_tactic_proof": true, "tactics": ["rw", "mixedEmbedding_preimageOfMemIntegerSet]"], "tactic_count": 2}
{"name": "NumberField.mixedEmbedding.fundamentalCone.quotIntNorm", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.fundamentalCone.quotIntNorm_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.fundamentalCone.integerSetToAssociates", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.fundamentalCone.integerSetToAssociates_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.fundamentalCone.integerSetToAssociates_surjective", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone", "is_tactic_proof": true, "tactics": ["rintro", "obtain", "refine", "exact", "refine", "simp_rw", "mixedEmbedding_preimageOfMemIntegerSet,", "val_inv_unitsNonZeroDivisorsEquiv_symm_apply_coe,"], "tactic_count": 8}
{"name": "NumberField.mixedEmbedding.fundamentalCone.integerSetToAssociates_eq_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone", "is_tactic_proof": false, "tactics": ["simp_rw", "mul_comm,", "map_mul,", "refine", "exact"], "tactic_count": 5}
{"name": "NumberField.mixedEmbedding.fundamentalCone.integerSetQuotEquivAssociates", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.fundamentalCone.integerSetQuotEquivAssociates_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.fundamentalCone.integerSetTorsionSMul_stabilizer", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone", "is_tactic_proof": true, "tactics": ["refine", "rwa", "mixedEmbedding_preimageOfMemIntegerSet,", "exact"], "tactic_count": 4}
{"name": "NumberField.mixedEmbedding.fundamentalCone.integerSetEquiv", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.fundamentalCone.integerSetEquiv_apply_fst", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.fundamentalCone.integerSetEquivNorm", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.fundamentalCone.integerSetEquivNorm_apply_fst", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone", "is_tactic_proof": true, "tactics": ["simp_rw", "integerSetEquiv_apply_fst]"], "tactic_count": 2}
{"name": "NumberField.mixedEmbedding.fundamentalCone.card_isPrincipal_norm_eq_mul_torsion", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "NumberField.mixedEmbedding.fundamentalCone.idealSet", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.fundamentalCone.mem_idealSet", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone", "is_tactic_proof": true, "tactics": ["simp_rw", "nonempty_prop,"], "tactic_count": 2}
{"name": "NumberField.mixedEmbedding.fundamentalCone.idealSetMap", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.fundamentalCone.idealSetMap_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.fundamentalCone.preimage_of_IdealSetMap", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone", "is_tactic_proof": true, "tactics": ["obtain", "simp_rw", "exact"], "tactic_count": 3}
{"name": "NumberField.mixedEmbedding.fundamentalCone.idealSetEquiv", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.fundamentalCone.idealSetEquiv_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.fundamentalCone.idealSetEquiv_symm_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NumberField.mixedEmbedding.fundamentalCone.intNorm_idealSetEquiv_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NumberField.mixedEmbedding.fundamentalCone.idealSetEquivNorm", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.fundamentalCone.card_isPrincipal_dvd_norm_le", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone", "is_tactic_proof": true, "tactics": ["obtain", "simp_rw", "rw", "refine", "simp_rw", "calc", "simp_rw", "rfl", "intNorm", "simp_rw", "lt_iff_not_ge.mp"], "tactic_count": 11}
{"name": "NumberField.mixedEmbedding.fundamentalCone.logMap_normAtAllPlaces", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.fundamentalCone.norm_normAtAllPlaces", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_mem_fundamentalCone_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": true, "tactics": ["simp_rw", "norm_normAtAllPlaces]"], "tactic_count": 2}
{"name": "NumberField.mixedEmbedding.fundamentalCone.normLeOne", "kind": "abbrev", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.fundamentalCone.mem_normLeOne", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.fundamentalCone.measurableSet_normLeOne", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.fundamentalCone.normLeOne_eq_preimage_image", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": true, "tactics": ["refine", "rintro", "rw", "rwa"], "tactic_count": 4}
{"name": "NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_normLeOne", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": true, "tactics": ["ext", "refine", "rintro", "refine", "rwa", "exact", "rwa", "rwa", "exact"], "tactic_count": 9}
{"name": "NumberField.mixedEmbedding.fundamentalCone.expMap_single", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.fundamentalCone.deriv_expMap_single", "kind": "abbrev", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.fundamentalCone.hasDerivAt_expMap_single", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "NumberField.mixedEmbedding.fundamentalCone.expMap", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.fundamentalCone.expMap_source", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "NumberField.mixedEmbedding.fundamentalCone.expMap_target", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "NumberField.mixedEmbedding.fundamentalCone.injective_expMap", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.fundamentalCone.continuous_expMap", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.fundamentalCone.expMap_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.fundamentalCone.expMap_pos", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.fundamentalCone.expMap_smul", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "NumberField.mixedEmbedding.fundamentalCone.expMap_add", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "NumberField.mixedEmbedding.fundamentalCone.expMap_sum", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "NumberField.mixedEmbedding.fundamentalCone.expMap_symm_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.fundamentalCone.logMap_expMap", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": true, "tactics": ["ext", "rw", "mul_inv_cancel_left₀"], "tactic_count": 3}
{"name": "NumberField.mixedEmbedding.fundamentalCone.sum_expMap_symm_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": true, "tactics": ["simp_rw", "expMap_symm_apply,"], "tactic_count": 2}
{"name": "NumberField.mixedEmbedding.fundamentalCone.fderiv_expMap", "kind": "abbrev", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.fundamentalCone.hasFDerivAt_expMap", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "NumberField.mixedEmbedding.fundamentalCone.equivFinRank", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.fundamentalCone.completeFamily", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_expMap_symm", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": true, "tactics": ["ext", "simp_rw", "mul_assoc,"], "tactic_count": 3}
{"name": "NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_completeFamily_of_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": true, "tactics": ["ext", "rw", "mul_inv_cancel_right₀"], "tactic_count": 3}
{"name": "NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_completeFamily_of_ne", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": true, "tactics": ["ext", "rw", "exact"], "tactic_count": 3}
{"name": "NumberField.mixedEmbedding.fundamentalCone.sum_eq_zero_of_mem_span_completeFamily", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": true, "tactics": ["induction", "mem", "obtain", "simp_rw", "zero", "add", "smul"], "tactic_count": 7}
{"name": "NumberField.mixedEmbedding.fundamentalCone.linearIndependent_completeFamily", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": true, "tactics": ["classical", "have", "refine", "simp_rw", "convert", "simp", "have", "intro", "have", "rw", "exact", "rw", "exact"], "tactic_count": 13}
{"name": "NumberField.mixedEmbedding.fundamentalCone.completeBasis", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.fundamentalCone.completeBasis_apply_of_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NumberField.mixedEmbedding.fundamentalCone.completeBasis_apply_of_ne", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NumberField.mixedEmbedding.fundamentalCone.expMap_basis_of_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": true, "tactics": ["ext", "simp_rw"], "tactic_count": 2}
{"name": "NumberField.mixedEmbedding.fundamentalCone.expMap_basis_of_ne", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NumberField.mixedEmbedding.fundamentalCone.abs_det_completeBasis_equivFunL_symm", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": true, "tactics": ["classical", "rw", "regulator_eq_regOfFamily_fundSystem,", "congr", "rw", "split_ifs", "rw", "simp_rw"], "tactic_count": 8}
{"name": "NumberField.mixedEmbedding.fundamentalCone.expMapBasis", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.fundamentalCone.expMapBasis_source", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NumberField.mixedEmbedding.fundamentalCone.injective_expMapBasis", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.fundamentalCone.continuous_expMapBasis", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.fundamentalCone.expMapBasis_pos", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.fundamentalCone.expMapBasis_nonneg", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.fundamentalCone.expMapBasis_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.fundamentalCone.expMapBasis_apply'", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": true, "tactics": ["simp_rw", "expMap_smul,", "expMap_basis_of_ne,"], "tactic_count": 3}
{"name": "NumberField.mixedEmbedding.fundamentalCone.expMapBasis_apply''", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": true, "tactics": ["rw", "conv_rhs", "enter", "rw"], "tactic_count": 4}
{"name": "NumberField.mixedEmbedding.fundamentalCone.prod_expMapBasis_pow", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": false, "tactics": ["simp_rw", "prod_pow]", "rw", "simp_rw", "prod_eq_abs_norm,"], "tactic_count": 5}
{"name": "NumberField.mixedEmbedding.fundamentalCone.norm_expMapBasis", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": true, "tactics": ["simpa", "prod_expMapBasis_pow"], "tactic_count": 2}
{"name": "NumberField.mixedEmbedding.fundamentalCone.norm_expMapBasis_ne_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.fundamentalCone.logMap_expMapBasis", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": true, "tactics": ["classical", "simp_rw", "refine", "rw", "expMapBasis_apply,", "logMap_expMap", "conv_lhs", "enter", "rw", "simp_rw", "expMap_symm_apply,", "smul_ite,"], "tactic_count": 12}
{"name": "NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_image_preimage_expMapBasis", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": true, "tactics": ["apply", "rintro", "exact"], "tactic_count": 3}
{"name": "NumberField.mixedEmbedding.fundamentalCone.prod_deriv_expMap_single", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": true, "tactics": ["simp", "rw", "congr", "simp_rw", "mult_isComplex,", "mul_inv_cancel₀", "simp"], "tactic_count": 7}
{"name": "NumberField.mixedEmbedding.fundamentalCone.fderiv_expMapBasis", "kind": "abbrev", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.fundamentalCone.hasFDerivAt_expMapBasis", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": true, "tactics": ["change", "exact"], "tactic_count": 2}
{"name": "NumberField.mixedEmbedding.fundamentalCone.abs_det_fderiv_expMapBasis", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": false, "tactics": ["simp_rw", "abs_det_completeBasis_equivFunL_symm,", "simp_rw", "abs_of_nonneg", "ring"], "tactic_count": 5}
{"name": "NumberField.mixedEmbedding.fundamentalCone.setLIntegral_expMapBasis_image", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": false, "tactics": ["rw", "simp_rw", "have", "rw", "congr", "have", "inv_nonneg.mpr", "rw", "ofReal_pow", "ofReal_inv_of_pos", "ofReal_prod_of_nonneg", "ring"], "tactic_count": 12}
{"name": "NumberField.mixedEmbedding.fundamentalCone.paramSet", "kind": "abbrev", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.fundamentalCone.measurableSet_paramSet", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": true, "tactics": ["refine", "split_ifs", "exact", "exact"], "tactic_count": 4}
{"name": "NumberField.mixedEmbedding.fundamentalCone.interior_paramSet", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NumberField.mixedEmbedding.fundamentalCone.closure_paramSet", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_normLeOne_eq_image", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "rw", "simp", "logMap_expMapBasis,", "pow_le_one_iff_of_nonneg", "refine", "split_ifs", "exact", "exact", "refine", "rintro", "exact", "rintro", "exact"], "tactic_count": 15}
{"name": "NumberField.mixedEmbedding.fundamentalCone.normLeOne_eq_preimage", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NumberField.mixedEmbedding.fundamentalCone.subset_interior_normLeOne", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": true, "tactics": ["rw", "refine", "subset_trans", "have", "expMapBasis.isOpen_image_of_subset_source", "exact"], "tactic_count": 6}
{"name": "NumberField.mixedEmbedding.fundamentalCone.closure_paramSet_ae_interior", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": true, "tactics": ["rw", "refine", "split_ifs", "exact", "exact"], "tactic_count": 5}
{"name": "NumberField.mixedEmbedding.fundamentalCone.setLIntegral_paramSet_exp", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": true, "tactics": ["classical", "have", "rw", "lmarginal_erase", "simp_rw", "if_neg", "ofReal_one,", "rw", "filter_upwards"], "tactic_count": 9}
{"name": "NumberField.mixedEmbedding.fundamentalCone.compactSet", "kind": "abbrev", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.fundamentalCone.isCompact_compactSet", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": false, "tactics": ["refine", "isCompact_Icc.smul_set", "split_ifs", "exact", "exact"], "tactic_count": 5}
{"name": "NumberField.mixedEmbedding.fundamentalCone.zero_mem_compactSet", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "NumberField.mixedEmbedding.fundamentalCone.nonneg_of_mem_compactSet", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "NumberField.mixedEmbedding.fundamentalCone.compactSet_eq_union_aux₁", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": true, "tactics": ["classical", "obtain", "refine", "rw", "intro", "split_ifs", "refine", "simpa", "have", "contrapose", "rw", "rw", "congr", "split_ifs", "simpa", "rfl"], "tactic_count": 16}
{"name": "NumberField.mixedEmbedding.fundamentalCone.compactSet_eq_union_aux₂", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": true, "tactics": ["classical", "simp", "obtain", "refine", "rw", "exact", "split_ifs", "rfl", "simpa"], "tactic_count": 9}
{"name": "NumberField.mixedEmbedding.fundamentalCone.compactSet_eq_union", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": true, "tactics": ["classical", "ext", "by_cases", "simpa", "refine", "simp", "exact"], "tactic_count": 7}
{"name": "NumberField.mixedEmbedding.fundamentalCone.expMapBasis_closure_subset_compactSet", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "NumberField.mixedEmbedding.fundamentalCone.closure_normLeOne_subset", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": true, "tactics": ["rw", "refine", "refine", "exact"], "tactic_count": 4}
{"name": "NumberField.mixedEmbedding.fundamentalCone.compactSet_ae", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "NumberField.mixedEmbedding.fundamentalCone.isBounded_normLeOne", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": true, "tactics": ["classical", "rw", "suffices", "obtain", "refine", "rw", "refine", "simpa", "refine", "exact"], "tactic_count": 10}
{"name": "NumberField.mixedEmbedding.fundamentalCone.volume_normLeOne", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": false, "tactics": ["rw", "normLeOne_eq_preimage,", "setLIntegral_expMapBasis_image", "simp_rw", "rw"], "tactic_count": 5}
{"name": "NumberField.mixedEmbedding.fundamentalCone.volume_interior_eq_volume_closure", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": false, "tactics": ["have", "have", "refine", "refine", "exact", "refine", "refine", "refine", "rw", "normAtAllPlaces_image_preimage_of_nonneg", "volume_eq_two_pow_mul_two_pi_pow_mul_integral", "normAtAllPlaces_image_preimage_expMapBasis,", "setLIntegral_expMapBasis_image", "setLIntegral_expMapBasis_image", "setLIntegral_congr"], "tactic_count": 15}
{"name": "NumberField.mixedEmbedding.fundamentalCone.volume_frontier_normLeOne", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne", "is_tactic_proof": true, "tactics": ["rw", "exact", "exact", "refine", "rw", "exact"], "tactic_count": 6}
{"name": "NumberField.mixedEmbedding.realMixedSpace", "kind": "abbrev", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.PolarCoord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.mixedSpaceToRealMixedSpace", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.PolarCoord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.mixedSpaceToRealMixedSpace_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.PolarCoord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.volume_preserving_mixedSpaceToRealMixedSpace_symm", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.PolarCoord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.instIsAddHaarMeasureRealMixedSpaceVolume", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.PolarCoord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.polarCoordReal", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.PolarCoord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.measurable_polarCoordReal_symm", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.PolarCoord", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "NumberField.mixedEmbedding.polarCoordReal_source", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.PolarCoord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.NumberField.CanonicalEmbedding.PolarCoord.0.NumberField.mixedEmbedding.abs_of_mem_polarCoordReal_target", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.PolarCoord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.FDerivPolarCoordRealSymm", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.PolarCoord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.hasFDerivAt_polarCoordReal_symm", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.PolarCoord", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "NumberField.mixedEmbedding.det_fderivPolarCoordRealSymm", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.PolarCoord", "is_tactic_proof": false, "tactics": ["have", "rfl", "rw", "det_fderivPiPolarCoordSymm]"], "tactic_count": 4}
{"name": "NumberField.mixedEmbedding.polarCoordReal_symm_target_ae_eq_univ", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.PolarCoord", "is_tactic_proof": false, "tactics": ["rw", "polarCoord.symm_image_target_eq_source,", "exact"], "tactic_count": 3}
{"name": "NumberField.mixedEmbedding.integral_comp_polarCoordReal_symm", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.PolarCoord", "is_tactic_proof": false, "tactics": ["rw", "integral_image_eq_integral_abs_det_fderiv_smul", "refine", "simp_rw"], "tactic_count": 4}
{"name": "NumberField.mixedEmbedding.lintegral_comp_polarCoordReal_symm", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.PolarCoord", "is_tactic_proof": false, "tactics": ["rw", "lintegral_image_eq_lintegral_abs_det_fderiv_mul", "refine", "simp_rw", "abs_of_mem_polarCoordReal_target"], "tactic_count": 5}
{"name": "NumberField.mixedEmbedding.polarCoord", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.PolarCoord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.polarCoord_target_eq_polarCoordReal_target", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.PolarCoord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.polarCoord_symm_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.PolarCoord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.measurable_polarCoord_symm", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.PolarCoord", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "NumberField.mixedEmbedding.normAtPlace_polarCoord_symm_of_isReal", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.PolarCoord", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NumberField.mixedEmbedding.normAtPlace_polarCoord_symm_of_isComplex", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.PolarCoord", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NumberField.mixedEmbedding.integral_comp_polarCoord_symm", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.PolarCoord", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NumberField.mixedEmbedding.lintegral_comp_polarCoord_symm", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.PolarCoord", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NumberField.mixedEmbedding.polarSpace", "kind": "abbrev", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.PolarCoord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.measurableEquivRealMixedSpacePolarSpace", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.PolarCoord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.homeoRealMixedSpacePolarSpace", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.PolarCoord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.homeoRealMixedSpacePolarSpace_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.PolarCoord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.homeoRealMixedSpacePolarSpace_apply_fst_ofIsReal", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.PolarCoord", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "NumberField.mixedEmbedding.homeoRealMixedSpacePolarSpace_apply_fst_ofIsComplex", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.PolarCoord", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "NumberField.mixedEmbedding.homeoRealMixedSpacePolarSpace_apply_snd", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.PolarCoord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.homeoRealMixedSpacePolarSpace_symm_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.PolarCoord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.volume_preserving_homeoRealMixedSpacePolarSpace", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.PolarCoord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.polarSpaceCoord", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.PolarCoord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mixedEmbedding.measurable_polarSpaceCoord_symm", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.PolarCoord", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "NumberField.mixedEmbedding.polarSpaceCoord_target'", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.PolarCoord", "is_tactic_proof": true, "tactics": ["ext", "simp_rw"], "tactic_count": 2}
{"name": "NumberField.mixedEmbedding.integral_comp_polarSpaceCoord_symm", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.PolarCoord", "is_tactic_proof": false, "tactics": ["rw", "simp_rw", "homeoRealMixedSpacePolarSpace_apply_fst_ofIsReal,", "homeoRealMixedSpacePolarSpace_apply_snd]"], "tactic_count": 4}
{"name": "NumberField.mixedEmbedding.lintegral_comp_polarSpaceCoord_symm", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.PolarCoord", "is_tactic_proof": false, "tactics": ["rw", "simp_rw", "homeoRealMixedSpacePolarSpace_apply_fst_ofIsReal,", "homeoRealMixedSpacePolarSpace_apply_snd]"], "tactic_count": 4}
{"name": "NumberField.mixedEmbedding.normAtComplexPlaces_polarSpaceCoord_symm", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.PolarCoord", "is_tactic_proof": true, "tactics": ["ext", "obtain", "simp", "simp"], "tactic_count": 4}
{"name": "_private.Mathlib.NumberTheory.NumberField.CanonicalEmbedding.PolarCoord.0.NumberField.mixedEmbedding.volume_eq_two_pi_pow_mul_integral_aux", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.PolarCoord", "is_tactic_proof": false, "tactics": ["have", "intro", "rw", "exact", "ext", "refine", "rintro", "refine", "rw", "exact", "rwa", "intro", "simpa"], "tactic_count": 13}
{"name": "NumberField.mixedEmbedding.volume_eq_two_pi_pow_mul_integral", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.PolarCoord", "is_tactic_proof": false, "tactics": ["have", "simp_rw", "rw", "simp_rw", "rw", "erw", "rw", "congr", "refine", "split_ifs", "exacts", "exact", "measurable_const.indicator"], "tactic_count": 13}
{"name": "_private.Mathlib.NumberTheory.NumberField.CanonicalEmbedding.PolarCoord.0.NumberField.mixedEmbedding.volume_eq_two_pow_mul_two_pi_pow_mul_integral_aux", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.PolarCoord", "is_tactic_proof": true, "tactics": ["ext", "refine", "rintro", "refine", "rw", "exact", "intro", "refine", "rw", "rintro", "refine", "obtain", "simpa", "rw", "simpa"], "tactic_count": 15}
{"name": "NumberField.mixedEmbedding.volume_eq_two_pow_mul_two_pi_pow_mul_integral", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.CanonicalEmbedding.PolarCoord", "is_tactic_proof": false, "tactics": ["have", "rw", "simp_rw", "have", "refine", "rw", "exact", "have", "rw", "rw", "exact", "rw", "mul_assoc]", "refine", "rw", "refine", "rw", "exact"], "tactic_count": 18}
{"name": "_private.Mathlib.NumberTheory.NumberField.ClassNumber.0.termM_", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.ClassNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.NumberField.ClassNumber.0._aux_Mathlib_NumberTheory_NumberField_ClassNumber___macroRules__private_Mathlib_NumberTheory_NumberField_ClassNumber_0_termM__1", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.ClassNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.RingOfIntegers.instFintypeClassGroup", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.ClassNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.classNumber", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.ClassNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.classNumber_ne_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.ClassNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.classNumber_pos", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.ClassNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.classNumber_eq_one_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.ClassNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.exists_ideal_in_class_of_norm_le", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.ClassNumber", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "obtain", "have", "contrapose", "rw", "rw", "let", "refine", "suffices", "exact", "rw", "absNorm_apply,", "refine", "exact"], "tactic_count": 15}
{"name": "RingOfIntegers.isPrincipalIdealRing_of_isPrincipal_of_norm_le", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.ClassNumber", "is_tactic_proof": true, "tactics": ["rw", "refine", "obtain", "simpa"], "tactic_count": 4}
{"name": "RingOfIntegers.isPrincipalIdealRing_of_isPrincipal_of_norm_le_of_isPrime", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.ClassNumber", "is_tactic_proof": true, "tactics": ["refine", "rw", "refine", "by_cases", "simpa", "rw", "refine", "exact", "le_of_dvd", "absNorm_dvd_absNorm_of_le", "hI"], "tactic_count": 11}
{"name": "RingOfIntegers.isPrincipalIdealRing_of_isPrincipal_of_pow_le_of_mem_primesOver_of_mem_Icc", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.ClassNumber", "is_tactic_proof": true, "tactics": ["refine", "obtain", "have", "nonZeroDivisors.coe_ne_zero", "eq_bot_of_comap_eq_bot", "have", "simp", "have", "rcases", "have", "have", "refine", "simpa", "have", "refine", "suffices", "exact", "have", "simp", "exact", "exact"], "tactic_count": 21}
{"name": "RingOfIntegers.isPrincipalIdealRing_of_isPrincipal_of_lt_or_isPrincipal_of_mem_primesOver_of_mem_Icc", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.ClassNumber", "is_tactic_proof": false, "tactics": ["refine", "isPrincipalIdealRing_of_isPrincipal_of_pow_le_of_mem_primesOver_of_mem_Icc", "obtain", "have", "by_cases", "linarith", "rw", "obtain", "exact"], "tactic_count": 9}
{"name": "RingOfIntegers.isPrincipalIdealRing_of_abs_discr_lt", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.ClassNumber", "is_tactic_proof": true, "tactics": ["have", "rw", "inv_div,", "refine", "rw", "le_antisymm", "one_le_iff_ne_zero.mpr", "exact"], "tactic_count": 8}
{"name": "Rat.classNumber_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.ClassNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCyclotomicExtension.Rat.finrank", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCyclotomicExtension.Rat.discr_prime_pow_ne_two'", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsCyclotomicExtension.Rat.discr_odd_prime'", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsCyclotomicExtension.Rat.discr_prime_pow'", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsCyclotomicExtension.Rat.discr_prime_pow_eq_unit_mul_pow'", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsCyclotomicExtension.Rat.isIntegralClosure_adjoin_singleton_of_prime_pow", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["refine", "swap", "rintro", "exact", "let", "have", "letI", "have", "obtain", "rw", "replace", "rw", "one_mul,", "cases", "haveI", "have", "rw", "exact", "obtain", "replace", "obtain", "rw", "exact", "have", "have", "have", "rw", "rw", "show", "rw", "exact", "refine", "adjoin_le", "simp", "exact"], "tactic_count": 35}
{"name": "IsCyclotomicExtension.Rat.isIntegralClosure_adjoin_singleton_of_prime", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsCyclotomicExtension.Rat.cyclotomicRing_isIntegralClosure_of_prime_pow", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["have", "refine", "obtain", "refine", "simp", "exact", "rintro", "exact"], "tactic_count": 8}
{"name": "IsCyclotomicExtension.Rat.cyclotomicRing_isIntegralClosure_of_prime", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsPrimitiveRoot.adjoinEquivRingOfIntegersOfPrimePow", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimitiveRoot.IsCyclotomicExtension.ringOfIntegersOfPrimePow", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimitiveRoot.integralPowerBasisOfPrimePow", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimitiveRoot.toInteger", "kind": "abbrev", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimitiveRoot.coe_toInteger", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimitiveRoot.finite_quotient_toInteger_sub_one", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["refine", "simp", "exact"], "tactic_count": 3}
{"name": "IsPrimitiveRoot.card_quotient_toInteger_sub_one", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsPrimitiveRoot.toInteger_isPrimitiveRoot", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimitiveRoot.integralPowerBasisOfPrimePow_gen", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimitiveRoot.integralPowerBasisOfPrimePow_dim", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsPrimitiveRoot.subOneIntegralPowerBasisOfPrimePow", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimitiveRoot.subOneIntegralPowerBasisOfPrimePow_gen", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsPrimitiveRoot.zeta_sub_one_prime_of_ne_two", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["letI", "refine", "apply", "rw", "simpa", "rw", "convert", "apply", "rw", "simp", "exact"], "tactic_count": 11}
{"name": "IsPrimitiveRoot.zeta_sub_one_prime_of_two_pow", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["have", "refine", "apply", "rw", "simpa", "rw", "cases", "convert", "apply", "rw", "simp", "simpa", "hζ.norm_pow_sub_one_two", "convert", "apply", "rw", "exact"], "tactic_count": 17}
{"name": "IsPrimitiveRoot.zeta_sub_one_prime", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "subst", "apply", "apply"], "tactic_count": 4}
{"name": "IsPrimitiveRoot.zeta_sub_one_prime'", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["convert", "simpa"], "tactic_count": 2}
{"name": "IsPrimitiveRoot.subOneIntegralPowerBasisOfPrimePow_gen_prime", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsPrimitiveRoot.norm_toInteger_sub_one_eq_one", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["have", "have", "dsimp", "rw", "sub_one_norm_eq_eval_cyclotomic", "eval_one_cyclotomic_not_prime_pow"], "tactic_count": 6}
{"name": "IsPrimitiveRoot.norm_toInteger_pow_sub_one_of_prime_pow_ne_two", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["have", "rw", "simp"], "tactic_count": 3}
{"name": "IsPrimitiveRoot.norm_toInteger_pow_sub_one_of_two", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["have", "rw", "simp"], "tactic_count": 3}
{"name": "IsPrimitiveRoot.norm_toInteger_pow_sub_one_of_prime_ne_two", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["refine", "apply", "rwa"], "tactic_count": 3}
{"name": "IsPrimitiveRoot.norm_toInteger_sub_one_of_eq_two_pow", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["have", "rw", "hζ.norm_sub_one_two"], "tactic_count": 3}
{"name": "IsPrimitiveRoot.norm_toInteger_sub_one_of_prime_ne_two", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsPrimitiveRoot.norm_toInteger_sub_one_of_eq_two", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "IsPrimitiveRoot.norm_toInteger_sub_one_of_prime_ne_two'", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["have", "replace", "exact"], "tactic_count": 3}
{"name": "IsPrimitiveRoot.prime_norm_toInteger_sub_one_of_prime_pow_ne_two", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["have", "simp", "rw", "exact"], "tactic_count": 4}
{"name": "IsPrimitiveRoot.prime_norm_toInteger_sub_one_of_prime_ne_two", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["have", "simp", "rw", "exact"], "tactic_count": 4}
{"name": "IsPrimitiveRoot.prime_norm_toInteger_sub_one_of_prime_ne_two'", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["have", "replace", "exact"], "tactic_count": 3}
{"name": "IsPrimitiveRoot.not_exists_int_prime_dvd_sub_of_prime_pow_ne_two", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": ["intro", "let", "have", "simp", "replace", "rw", "refine", "simp", "ne_of_gt", "by_cases", "simp", "exact", "exact", "one_lt_mul_of_lt_of_le", "rw", "replace", "have", "rw", "simp", "rw", "pB.basis.repr_self_apply]", "simp", "rw", "map_smul,", "pB.basis.coord_apply,", "simp", "exact"], "tactic_count": 27}
{"name": "IsPrimitiveRoot.not_exists_int_prime_dvd_sub_of_prime_ne_two", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["refine", "simp_all"], "tactic_count": 2}
{"name": "IsPrimitiveRoot.not_exists_int_prime_dvd_sub_of_prime_ne_two'", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["have", "replace", "exact"], "tactic_count": 3}
{"name": "IsPrimitiveRoot.finite_quotient_span_sub_one", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["have", "refine", "simp", "exact"], "tactic_count": 4}
{"name": "IsPrimitiveRoot.finite_quotient_span_sub_one'", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["have", "replace", "exact"], "tactic_count": 3}
{"name": "IsPrimitiveRoot.toInteger_sub_one_dvd_prime", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "have", "simp", "have", "refine", "rwa", "replace", "ext", "exact", "rw", "exact", "suffices", "have", "have", "rw", "rw", "simp", "exact"], "tactic_count": 18}
{"name": "IsPrimitiveRoot.toInteger_sub_one_dvd_prime'", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["have", "replace", "exact"], "tactic_count": 3}
{"name": "IsPrimitiveRoot.toInteger_sub_one_not_dvd_two", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimitiveRoot.prime_dvd_of_dvd_norm_sub_one", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["have", "obtain", "refine", "coe_submonoidClass_iff.mp", "have", "rw", "show", "map_sub", "rw", "rsuffices", "obtain", "by_cases", "obtain", "have", "cases", "zero", "succ", "rw", "refine", "by_cases", "cases", "zero", "rw", "exact", "succ", "rw", "rwa", "rwa", "rw", "exact", "exact", "rw", "refine", "rwa", "have", "rw", "exact", "rw", "exact"], "tactic_count": 39}
{"name": "IsCyclotomicExtension.Rat.discr_prime_pow", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["have", "have", "let", "apply", "rw", "convert", "have", "rw", "exact", "rw", "congr", "ext", "simp_rw", "pB₁,", "convert", "simp_rw"], "tactic_count": 16}
{"name": "IsCyclotomicExtension.Rat.discr_prime_pow_succ", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsCyclotomicExtension.Rat.discr_prime", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": ["have", "rw", "infer_instance", "rw", "simp"], "tactic_count": 5}
{"name": "IsCyclotomicExtension.Rat.discr", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["haveI", "rw", "congr", "induction", "zero", "prime_pow", "have", "rw", "cases", "zero", "succ", "simpa", "coprime", "have", "have", "let", "have", "have", "have", "have", "replace", "have", "have", "have", "replace", "have", "have", "have", "have", "rw", "exact", "exact", "have", "rw", "refine", "refine", "exact", "have", "have", "have", "rw", "hK₁,", "primeFactors_mul", "have", "p.totient_prime", "simp_rw", "rw"], "tactic_count": 47}
{"name": "IsCyclotomicExtension.Rat.natAbs_discr", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["have", "rw", "rw", "exact"], "tactic_count": 4}
{"name": "_private.Mathlib.NumberTheory.NumberField.Cyclotomic.Basic.0.IsCyclotomicExtension.Rat.adjoin_singleton_eq_top_aux", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": ["have", "rw", "refine", "refine", "exact", "have", "have", "apply", "exact", "replace", "replace", "replace", "replace", "rw", "refine", "rw", "exact", "simp", "exact"], "tactic_count": 19}
{"name": "IsCyclotomicExtension.Rat.adjoin_singleton_eq_top", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["haveI", "induction", "zero", "prime_pow", "have", "rw", "coprime", "have", "have", "have", "have", "replace", "replace", "have", "have", "replace", "replace", "have", "have", "have", "rw", "exact", "exact", "exact"], "tactic_count": 24}
{"name": "IsCyclotomicExtension.Rat.isIntegralClosure_adjoin_singleton", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["constructor", "exact", "intro", "have", "simp", "simp"], "tactic_count": 6}
{"name": "IsCyclotomicExtension.Rat.cyclotomicRing_isIntegralClosure", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["have", "refine", "obtain", "refine", "simp", "exact", "rintro", "exact"], "tactic_count": 8}
{"name": "IsPrimitiveRoot.adjoinEquivRingOfIntegers", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCyclotomicExtension.ringOfIntegers", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimitiveRoot.integralPowerBasis", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimitiveRoot.integralPowerBasis_gen", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimitiveRoot.integralPowerBasis_dim", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsPrimitiveRoot.subOneIntegralPowerBasis", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimitiveRoot.subOneIntegralPowerBasis_gen", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NumberField.Units.dvd_torsionOrder_of_isPrimitiveRoot", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["rw", "replace", "convert", "rw", "exact", "refine", "rw", "exact"], "tactic_count": 8}
{"name": "IsCyclotomicExtension.Rat.torsionOrder_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["have", "obtain", "rw", "exact", "rw", "replace", "hμ.map_of_injective", "have", "have", "have", "have", "rwa", "exact", "have", "obtain", "rw", "apply", "have", "rwa", "exact", "rw", "have", "rw", "exact", "rw", "exact"], "tactic_count": 26}
{"name": "IsCyclotomicExtension.Rat.nrRealPlaces_eq_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Embeddings", "is_tactic_proof": true, "tactics": ["have", "apply"], "tactic_count": 2}
{"name": "IsCyclotomicExtension.Rat.isTotallyComplex", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Embeddings", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "IsCyclotomicExtension.Rat.nrComplexPlaces_eq_totient_div_two", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Embeddings", "is_tactic_proof": true, "tactics": ["have", "by_cases", "obtain", "have", "rw", "simp", "have", "by_cases", "convert", "exact", "convert", "exact", "rw", "apply", "rw"], "tactic_count": 15}
{"name": "_private.Mathlib.NumberTheory.NumberField.Cyclotomic.Ideal.0.IsCyclotomicExtension.Rat.term𝒑", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.NumberField.Cyclotomic.Ideal.0.IsCyclotomicExtension.Rat._aux_Mathlib_NumberTheory_NumberField_Cyclotomic_Ideal___macroRules__private_Mathlib_NumberTheory_NumberField_Cyclotomic_Ideal_0_IsCyclotomicExtension_Rat_term𝒑_1", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.NumberField.Cyclotomic.Ideal.0.IsCyclotomicExtension.Rat._aux_Mathlib_NumberTheory_NumberField_Cyclotomic_Ideal___delab_app__private_Mathlib_NumberTheory_NumberField_Cyclotomic_Ideal_0_IsCyclotomicExtension_Rat_term𝒑_1", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCyclotomicExtension.Rat.isPrime_span_zeta_sub_one", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Ideal", "is_tactic_proof": true, "tactics": ["rw", "exact", "exact"], "tactic_count": 3}
{"name": "IsCyclotomicExtension.Rat.associated_norm_zeta_sub_one", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Ideal", "is_tactic_proof": true, "tactics": ["by_cases", "cases", "zero", "rw", "rw", "succ", "rw", "rw", "rw"], "tactic_count": 9}
{"name": "IsCyclotomicExtension.Rat.absNorm_span_zeta_sub_one", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Ideal", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsCyclotomicExtension.Rat.p_mem_span_zeta_sub_one", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Ideal", "is_tactic_proof": true, "tactics": ["convert", "exact"], "tactic_count": 2}
{"name": "IsCyclotomicExtension.Rat.span_zeta_sub_one_ne_bot", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCyclotomicExtension.Rat.liesOver_span_zeta_sub_one", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Ideal", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "IsCyclotomicExtension.Rat.inertiaDeg_span_zeta_sub_one", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Ideal", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "IsCyclotomicExtension.Rat.map_eq_span_zeta_sub_one_pow", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Ideal", "is_tactic_proof": true, "tactics": ["have", "have", "refine", "rw", "span_singleton_eq_span_singleton.mpr", "conv_lhs", "enter", "rw", "rw"], "tactic_count": 9}
{"name": "IsCyclotomicExtension.Rat.ramificationIdx_span_zeta_sub_one", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Ideal", "is_tactic_proof": true, "tactics": ["have", "rw", "map_eq_span_zeta_sub_one_pow", "multiplicity_pow_self", "exact"], "tactic_count": 5}
{"name": "IsCyclotomicExtension.Rat.ncard_primesOver_of_prime_pow", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Ideal", "is_tactic_proof": true, "tactics": ["have", "have", "have", "have", "have", "rwa", "inertiaDegIn_eq_inertiaDeg", "ramificationIdx_span_zeta_sub_one,", "exact"], "tactic_count": 9}
{"name": "IsCyclotomicExtension.Rat.eq_span_zeta_sub_one_of_liesOver", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Ideal", "is_tactic_proof": true, "tactics": ["have", "have", "have", "aesop"], "tactic_count": 4}
{"name": "IsCyclotomicExtension.Rat.inertiaDeg_eq_of_prime_pow", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Ideal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsCyclotomicExtension.Rat.ramificationIdx_eq_of_prime_pow", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Ideal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsCyclotomicExtension.Rat.inertiaDegIn_eq_of_prime_pow", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Ideal", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "IsCyclotomicExtension.Rat.ramificationIdxIn_eq_of_prime_pow", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Ideal", "is_tactic_proof": true, "tactics": ["have", "rw", "ramificationIdx_span_zeta_sub_one]"], "tactic_count": 3}
{"name": "IsCyclotomicExtension.Rat.isPrime_span_zeta_sub_one'", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Ideal", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsCyclotomicExtension.Rat.inertiaDeg_span_zeta_sub_one'", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Ideal", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsCyclotomicExtension.Rat.ramificationIdx_span_zeta_sub_one'", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Ideal", "is_tactic_proof": true, "tactics": ["rw", "rw"], "tactic_count": 2}
{"name": "IsCyclotomicExtension.Rat.ncard_primesOver_of_prime", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Ideal", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsCyclotomicExtension.Rat.eq_span_zeta_sub_one_of_liesOver'", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Ideal", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsCyclotomicExtension.Rat.inertiaDeg_eq_of_prime", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Ideal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsCyclotomicExtension.Rat.ramificationIdx_eq_of_prime", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Ideal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsCyclotomicExtension.Rat.inertiaDegIn_eq_of_prime", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Ideal", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsCyclotomicExtension.Rat.ramificationIdxIn_eq_of_prime", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Ideal", "is_tactic_proof": true, "tactics": ["rw", "rw"], "tactic_count": 2}
{"name": "IsCyclotomicExtension.Rat.inertiaDeg_eq_of_not_dvd", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Ideal", "is_tactic_proof": true, "tactics": ["replace", "let", "have", "rw", "exact", "have", "have", "simp", "rw", "rw", "simpa", "refine", "rw", "simp"], "tactic_count": 14}
{"name": "IsCyclotomicExtension.Rat.ramificationIdx_eq_of_not_dvd", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Ideal", "is_tactic_proof": true, "tactics": ["let", "have", "rw", "exact", "have", "have", "simp", "rw", "rw", "refine", "apply", "exact", "exact", "rw", "exact"], "tactic_count": 15}
{"name": "IsCyclotomicExtension.Rat.inertiaDegIn_eq_of_not_dvd", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Ideal", "is_tactic_proof": true, "tactics": ["have", "obtain", "rw"], "tactic_count": 3}
{"name": "IsCyclotomicExtension.Rat.ramificationIdxIn_eq_of_not_dvd", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Ideal", "is_tactic_proof": true, "tactics": ["have", "obtain", "rw"], "tactic_count": 3}
{"name": "_private.Mathlib.NumberTheory.NumberField.Cyclotomic.Ideal.0.IsCyclotomicExtension.Rat.inertiaDegIn_ramificationIdxIn_aux", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Ideal", "is_tactic_proof": true, "tactics": ["have", "have", "have", "have", "let", "have", "let", "have", "let", "have", "obtain", "exists_maximal_ideal_liesOver_of_isIntegral", "let", "have", "let", "have", "obtain", "have", "map_ne_bot_of_ne_bot", "suffices", "replace", "rw", "ramificationIdxIn_mul_ramificationIdxIn", "inertiaDegIn_eq_of_not_dvd", "exact", "have", "rw", "exact", "rwa", "ncard_primesOver_mul_ramificationIdxIn_mul_inertiaDegIn", "ncard_primesOver_mul_ramificationIdxIn_mul_inertiaDegIn", "ncard_primesOver_mul_ramificationIdxIn_mul_inertiaDegIn", "ncard_primesOver_mul_ncard_primesOver", "ramificationIdxIn_eq_of_not_dvd", "one_mul,", "mul_rotate", "mul_assoc,", "ramificationIdxIn_mul_ramificationIdxIn", "hPp,", "eq_comm,"], "tactic_count": 40}
{"name": "IsCyclotomicExtension.Rat.inertiaDegIn_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCyclotomicExtension.Rat.ramificationIdxIn_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCyclotomicExtension.Rat.inertiaDeg_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Ideal", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "IsCyclotomicExtension.Rat.ramificationIdx_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Ideal", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "IsCyclotomicExtension.Rat.three_pid", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.PID", "is_tactic_proof": true, "tactics": ["apply", "rw", "nrComplexPlaces_eq_totient_div_two", "simp", "one_mul,", "suffices", "gcongr", "exact"], "tactic_count": 8}
{"name": "IsCyclotomicExtension.Rat.five_pid", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.PID", "is_tactic_proof": true, "tactics": ["have", "apply", "rw", "nrComplexPlaces_eq_totient_div_two", "simp", "show", "suffices", "lt_trans", "gcongr", "exact"], "tactic_count": 10}
{"name": "_private.Mathlib.NumberTheory.NumberField.Cyclotomic.Three.0.IsCyclotomicExtension.Rat.Three.termη", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Three", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.NumberField.Cyclotomic.Three.0.IsCyclotomicExtension.Rat.Three._aux_Mathlib_NumberTheory_NumberField_Cyclotomic_Three___macroRules__private_Mathlib_NumberTheory_NumberField_Cyclotomic_Three_0_IsCyclotomicExtension_Rat_Three_termη_1", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Three", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "_private.Mathlib.NumberTheory.NumberField.Cyclotomic.Three.0.IsCyclotomicExtension.Rat.Three._aux_Mathlib_NumberTheory_NumberField_Cyclotomic_Three___macroRules__private_Mathlib_NumberTheory_NumberField_Cyclotomic_Three_0_IsCyclotomicExtension_Rat_Three_termλ_1", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Three", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.NumberField.Cyclotomic.Three.0.IsCyclotomicExtension.Rat.Three._aux_Mathlib_NumberTheory_NumberField_Cyclotomic_Three___delab_app__private_Mathlib_NumberTheory_NumberField_Cyclotomic_Three_0_IsCyclotomicExtension_Rat_Three_termλ_1", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Three", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCyclotomicExtension.Rat.Three.coe_eta", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Three", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimitiveRoot.toInteger_cube_eq_one", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Three", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCyclotomicExtension.Rat.Three.Units.mem", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Three", "is_tactic_proof": false, "tactics": ["have", "dsimp", "rw", "nrComplexPlaces_eq_totient_div_two", "rfl", "obtain", "replace", "rw", "apply", "rw", "congr", "rw", "infer_instance", "obtain", "replace", "rw", "convert", "rw_mod_cast", "simp", "obtain", "hζ.exists_pow_or_neg_mul_pow_of_isOfFinOrder", "replace", "replace", "rcases", "left", "right", "fin_cases"], "tactic_count": 27}
{"name": "_private.Mathlib.NumberTheory.NumberField.Cyclotomic.Three.0.IsCyclotomicExtension.Rat.Three.lambda_sq", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Three", "is_tactic_proof": true, "tactics": ["ext", "calc"], "tactic_count": 2}
{"name": "IsCyclotomicExtension.Rat.Three.eta_sq", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Three", "is_tactic_proof": true, "tactics": ["rw", "ext"], "tactic_count": 2}
{"name": "IsCyclotomicExtension.Rat.Three.eq_one_or_neg_one_of_unit_of_congruent", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Three", "is_tactic_proof": false, "tactics": ["replace", "obtain", "exact", "have", "fin_cases", "left", "right", "all_goals", "exact", "apply", "obtain", "rw", "refine", "simp", "exact", "apply", "obtain", "refine", "have", "simp", "val_pow_eq_pow_val,"], "tactic_count": 21}
{"name": "IsCyclotomicExtension.Rat.Three.lambda_dvd_or_dvd_sub_one_or_dvd_add_one", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Three", "is_tactic_proof": true, "tactics": ["classical", "have", "let", "let", "let", "have", "have", "rw", "hζ.norm_toInteger_sub_one_of_prime_ne_two", "simp", "rw", "simp", "rcases", "left", "exact", "right", "refine", "rw", "right", "refine", "rw"], "tactic_count": 21}
{"name": "IsCyclotomicExtension.Rat.Three.eta_sq_add_eta_add_one", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Three", "is_tactic_proof": true, "tactics": ["rw", "ring"], "tactic_count": 2}
{"name": "IsCyclotomicExtension.Rat.Three.cube_sub_one_eq_mul", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Three", "is_tactic_proof": true, "tactics": ["symm", "calc"], "tactic_count": 2}
{"name": "IsCyclotomicExtension.Rat.Three.lambda_dvd_mul_sub_one_mul_sub_eta_add_one", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Three", "is_tactic_proof": true, "tactics": ["rcases", "exact", "exact", "refine", "rw", "exact"], "tactic_count": 6}
{"name": "IsCyclotomicExtension.Rat.Three.lambda_pow_four_dvd_cube_sub_one_of_dvd_sub_one", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Three", "is_tactic_proof": true, "tactics": ["obtain", "have", "calc", "rw", "exact"], "tactic_count": 5}
{"name": "IsCyclotomicExtension.Rat.Three.lambda_pow_four_dvd_cube_add_one_of_dvd_add_one", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Three", "is_tactic_proof": false, "tactics": ["replace", "convert", "exact", "convert", "ring"], "tactic_count": 5}
{"name": "IsCyclotomicExtension.Rat.Three.lambda_pow_four_dvd_cube_sub_one_or_add_one_of_lambda_not_dvd", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Cyclotomic.Three", "is_tactic_proof": true, "tactics": ["rcases", "contradiction", "left", "exact", "right", "exact"], "tactic_count": 6}
{"name": "NumberField.dedekindZeta", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.DedekindZeta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.dedekindZeta_residue", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.DedekindZeta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.dedekindZeta_residue_def", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.DedekindZeta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.dedekindZeta_residue_pos", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.DedekindZeta", "is_tactic_proof": true, "tactics": ["refine", "exact", "exact", "mul_pos"], "tactic_count": 4}
{"name": "NumberField.dedekindZeta_residue_ne_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.DedekindZeta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.tendsto_sub_one_mul_dedekindZeta_nhdsGT", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.DedekindZeta", "is_tactic_proof": true, "tactics": ["refine", "refine", "simp", "congr", "rw", "show", "show", "simp"], "tactic_count": 8}
{"name": "NumberField.discr_eq_basisMatrix_det_sq", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Discriminant.Basic", "is_tactic_proof": true, "tactics": ["rw", "eq_ratCast]"], "tactic_count": 2}
{"name": "NumberField.sign_discr", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Discriminant.Basic", "is_tactic_proof": true, "tactics": ["classical", "have", "rw", "conj_basisMatrix,", "mul_eq_right₀,", "simp", "rw", "exact", "obtain", "rw", "grind", "rw", "rwa"], "tactic_count": 13}
{"name": "NumberField.mixedEmbedding.volume_fundamentalDomain_latticeBasis", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Discriminant.Basic", "is_tactic_proof": false, "tactics": ["let", "let", "let", "let", "suffices", "calc", "volume", "rw", "measure_fundamentalDomain", "rfl", "rw", "det_reindex_self]", "have", "rw", "nnnorm_pow,", "rw", "ext", "dsimp", "rw", "latticeBasis_apply,", "stdBasis_repr_eq_matrixToStdBasis_mul", "rfl"], "tactic_count": 22}
{"name": "NumberField.mixedEmbedding.covolume_integerLattice", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Discriminant.Basic", "is_tactic_proof": true, "tactics": ["rw", "volume_fundamentalDomain_latticeBasis,"], "tactic_count": 2}
{"name": "NumberField.mixedEmbedding.covolume_idealLattice", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Discriminant.Basic", "is_tactic_proof": true, "tactics": ["rw", "volume_fundamentalDomain_fractionalIdealLatticeBasis,", "coe_nnnorm,", "mul_assoc]"], "tactic_count": 4}
{"name": "NumberField.exists_ne_zero_mem_ideal_of_norm_le_mul_sqrt_discr", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Discriminant.Basic", "is_tactic_proof": true, "tactics": ["classical", "let", "have", "refine", "rw", "div_mul_cancel₀,", "inv_mul_cancel₀", "exact", "exact", "convert", "rw", "div_mul_cancel₀", "congr", "rw", "calc", "simp_rw", "volume_fundamentalDomain_latticeBasis,", "mixedEmbedding.finrank,", "rw", "simp_rw", "π⁻¹", "simp_rw", "mul_neg_one,", "ring", "π⁻¹", "congr", "rw", "ring", "rw", "zpow_natCast]", "ring"], "tactic_count": 31}
{"name": "NumberField.exists_ne_zero_mem_ringOfIntegers_of_norm_le_mul_sqrt_discr", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Discriminant.Basic", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "refine", "simp_rw", "exact"], "tactic_count": 5}
{"name": "NumberField.abs_discr_ge'", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Discriminant.Basic", "is_tactic_proof": true, "tactics": ["obtain", "have", "rw", "exact", "replace", "rwa", "mul_pow,", "exact"], "tactic_count": 8}
{"name": "NumberField.abs_discr_ge_of_isTotallyComplex", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Discriminant.Basic", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "NumberField.abs_discr_rpow_ge_of_isTotallyComplex", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Discriminant.Basic", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "NumberField.abs_discr_ge", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Discriminant.Basic", "is_tactic_proof": false, "tactics": ["refine", "le_trans", "rw", "let", "suffices", "refine", "simp", "gcongr", "exact", "rw", "exact", "intro", "induction", "base", "succ", "h_m", "suffices", "convert_to", "simp_rw", "field_simp", "simp", "ring", "rw", "convert", "field", "refine", "exact"], "tactic_count": 27}
{"name": "NumberField.abs_discr_gt_two", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Discriminant.Basic", "is_tactic_proof": true, "tactics": ["rw", "rify", "calc", "gcongr", "linarith"], "tactic_count": 5}
{"name": "NumberField.hermiteTheorem.finite_of_finite_generating_set", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Discriminant.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "convert", "all_goals"], "tactic_count": 5}
{"name": "NumberField.hermiteTheorem.rankOfDiscrBdd", "kind": "abbrev", "module": "Mathlib.NumberTheory.NumberField.Discriminant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.hermiteTheorem.boundOfDiscBdd", "kind": "abbrev", "module": "Mathlib.NumberTheory.NumberField.Discriminant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.hermiteTheorem.rank_le_rankOfDiscrBdd", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Discriminant.Basic", "is_tactic_proof": false, "tactics": ["have", "refine", "rwa", "have", "rw", "linarith", "obtain", "apply", "rw", "have", "contrapose", "rw", "rw", "refine", "lt_of_le_of_lt", "rw", "inv_mul_cancel₀", "refine", "rw", "exact", "exact"], "tactic_count": 21}
{"name": "NumberField.hermiteTheorem.minkowskiBound_lt_boundOfDiscBdd", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Discriminant.Basic", "is_tactic_proof": false, "tactics": ["have", "simp_rw", "refine", "rw", "volume_fundamentalDomain_latticeBasis,", "show", "gcongr", "exact", "rwa", "exact", "exact"], "tactic_count": 11}
{"name": "NumberField.hermiteTheorem.natDegree_le_rankOfDiscrBdd", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Discriminant.Basic", "is_tactic_proof": false, "tactics": ["rw", "minpoly.isIntegrallyClosed_eq_field_fractions", "exact"], "tactic_count": 3}
{"name": "NumberField.hermiteTheorem.finite_of_discr_bdd_of_isReal", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Discriminant.Basic", "is_tactic_proof": true, "tactics": ["classical", "let", "let", "let", "refine", "finite_of_finite_generating_set", "simp_rw", "have", "haveI", "obtain", "suffices", "obtain", "have", "refine", "exact", "rw", "refine", "rw", "refine", "rw", "gcongr", "exact", "exact", "exact", "refine", "exact", "rw", "convert", "simp", "simp", "calc", "minkowskiBound"], "tactic_count": 32}
{"name": "NumberField.hermiteTheorem.finite_of_discr_bdd_of_isComplex", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Discriminant.Basic", "is_tactic_proof": true, "tactics": ["classical", "let", "let", "let", "refine", "finite_of_finite_generating_set", "simp_rw", "have", "haveI", "obtain", "suffices", "obtain", "have", "refine", "exact", "rw", "refine", "rw", "refine", "rw", "gcongr", "exact", "exact", "rw", "exact", "refine", "exact", "rw", "convert", "simp", "simp", "calc", "minkowskiBound"], "tactic_count": 33}
{"name": "NumberField.finite_of_discr_bdd", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Discriminant.Basic", "is_tactic_proof": false, "tactics": ["refine", "rintro", "have", "haveI", "obtain", "by_cases", "apply", "exact", "apply", "exact"], "tactic_count": 10}
{"name": "NumberField.discr", "kind": "abbrev", "module": "Mathlib.NumberTheory.NumberField.Discriminant.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.coe_discr", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Discriminant.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.discr_ne_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Discriminant.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "NumberField.discr_eq_discr", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Discriminant.Defs", "is_tactic_proof": true, "tactics": ["let", "rw"], "tactic_count": 2}
{"name": "NumberField.discr_eq_discr_of_algEquiv", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Discriminant.Defs", "is_tactic_proof": true, "tactics": ["let", "rw", "discr_eq_discr", "change", "rw", "congr", "ext", "simp", "rfl"], "tactic_count": 9}
{"name": "NumberField.discr_eq_discr_of_ringEquiv", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Discriminant.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.numberField_discr", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Discriminant.Defs", "is_tactic_proof": false, "tactics": ["let", "calc", "rw", "rw", "map_one,"], "tactic_count": 5}
{"name": "Algebra.discr_eq_discr_of_toMatrix_coeff_isIntegral", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Discriminant.Defs", "is_tactic_proof": false, "tactics": ["replace", "intro", "convert", "simp", "classical", "rw", "congr", "have", "obtain", "have", "have", "obtain", "refine", "suffices", "rw", "exact", "rw", "rw", "rcases", "simp", "simp"], "tactic_count": 21}
{"name": "NumberField.absNorm_differentIdeal", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Discriminant.Different", "is_tactic_proof": true, "tactics": ["refine", "rw", "refine", "have", "one_ne_zero", "have", "refine", "rw", "let", "let", "have", "ext", "let", "simpa", "qify", "refine", "rw", "exact", "apply", "rw", "apply", "rw", "simp", "simp", "rw", "congr", "ext", "simp"], "tactic_count": 28}
{"name": "NumberField.discr_mem_differentIdeal", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Discriminant.Different", "is_tactic_proof": true, "tactics": ["have", "cases", "inl", "inr", "rwa"], "tactic_count": 5}
{"name": "NumberField.natAbs_discr_eq_absNorm_differentIdeal_mul_natAbs_discr_pow", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Discriminant.Different", "is_tactic_proof": true, "tactics": ["have", "rwa", "ext", "exact"], "tactic_count": 4}
{"name": "NumberField.isCoprime_differentIdeal_of_isCoprime_discr", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Discriminant.Different", "is_tactic_proof": true, "tactics": ["obtain", "refine", "apply", "rw", "exact", "apply", "rw", "exact", "rw"], "tactic_count": 9}
{"name": "NumberField.discr_dvd_discr", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Discriminant.Different", "is_tactic_proof": false, "tactics": ["suffices", "dvd_trans", "rw", "exact"], "tactic_count": 4}
{"name": "NumberField.linearDisjoint_of_isGalois_isCoprime_discr", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Discriminant.Different", "is_tactic_proof": true, "tactics": ["apply", "suffices", "contrapose", "have", "refine", "rwa", "exact", "exact"], "tactic_count": 8}
{"name": "NumberField.natAbs_discr_eq_natAbs_discr_pow_mul_natAbs_discr_pow", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Discriminant.Different", "is_tactic_proof": true, "tactics": ["let", "have", "rwa", "h₁.finrank_left_eq_finrank", "ext", "exact"], "tactic_count": 6}
{"name": "NumberField.equivReindex", "kind": "abbrev", "module": "Mathlib.NumberTheory.NumberField.EquivReindex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.basisMatrix", "kind": "abbrev", "module": "Mathlib.NumberTheory.NumberField.EquivReindex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.basisMatrix_eq_embeddingsMatrixReindex", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.EquivReindex", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "NumberField.conj_basisMatrix", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.EquivReindex", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "NumberField.det_of_basisMatrix_non_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.EquivReindex", "is_tactic_proof": true, "tactics": ["rw", "convert", "rw", "exact"], "tactic_count": 4}
{"name": "NumberField.instInvertibleMatrixRingHomComplexBasisMatrix", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.EquivReindex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.canonicalEmbedding_eq_basisMatrix_mulVec", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.EquivReindex", "is_tactic_proof": true, "tactics": ["ext", "rw", "simp", "smul_eq_mul]"], "tactic_count": 4}
{"name": "NumberField.inverse_basisMatrix_mulVec_eq_repr", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.EquivReindex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsPrincipalIdealRingSubtypeMemSubringIntegerWithZeroMultiplicativeIntValuation", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.FinitePlaces", "is_tactic_proof": false, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "instIsDiscreteValuationRingSubtypeMemSubringIntegerWithZeroMultiplicativeIntValuation", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.FinitePlaces", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsPrincipalIdealRingSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegers", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.FinitePlaces", "is_tactic_proof": true, "tactics": ["unfold", "rw", "simpa"], "tactic_count": 3}
{"name": "instIsDiscreteValuationRingSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegers", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.FinitePlaces", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.RingOfIntegers.HeightOneSpectrum.one_lt_absNorm", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.FinitePlaces", "is_tactic_proof": true, "tactics": ["by_contra", "apply", "rw", "have", "rw", "exact", "lia"], "tactic_count": 7}
{"name": "NumberField.RingOfIntegers.HeightOneSpectrum.one_lt_absNorm_nnreal", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.FinitePlaces", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.RingOfIntegers.HeightOneSpectrum.absNorm_ne_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.FinitePlaces", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.FinitePlaces", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_def", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.FinitePlaces", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.RingOfIntegers.HeightOneSpectrum.isNonarchimedean_adicAbv", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.FinitePlaces", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.FinitePlace.embedding", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.FinitePlaces", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.FinitePlace.embedding_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.FinitePlaces", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.instRankOneWithZeroMultiplicativeIntValuationRingOfIntegers", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.FinitePlaces", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.instRankOneValuedAdicCompletion", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.FinitePlaces", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.instNormedFieldValuedAdicCompletion", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.FinitePlaces", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.FinitePlace", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.FinitePlaces", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.FinitePlace.mk", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.FinitePlaces", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.toNNReal_valued_eq_adicAbv", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.FinitePlaces", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.IsFinitePlace", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.FinitePlaces", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.FinitePlace.isFinitePlace", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.FinitePlaces", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NumberField.isFinitePlace_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.FinitePlaces", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.FinitePlace.norm_def", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.FinitePlaces", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NumberField.FinitePlace.norm_def'", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.FinitePlaces", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NumberField.FinitePlace.norm_def_int", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.FinitePlaces", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_add_le_max", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.FinitePlaces", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_natCast_le_one", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.FinitePlaces", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_intCast_le_one", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.FinitePlaces", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.FinitePlace.norm_le_one", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.FinitePlaces", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "NumberField.FinitePlace.norm_eq_one_iff_notMem", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.FinitePlaces", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "NumberField.FinitePlace.norm_lt_one_iff_mem", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.FinitePlaces", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "NumberField.FinitePlace.instFunLikeReal", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.FinitePlaces", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.FinitePlace.instMonoidWithZeroHomClassReal", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.FinitePlaces", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.FinitePlace.instNonnegHomClassReal", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.FinitePlaces", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.FinitePlace.mk_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.FinitePlaces", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.FinitePlace.coe_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.FinitePlaces", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.FinitePlace.maximalIdeal", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.FinitePlaces", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.FinitePlace.mk_maximalIdeal", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.FinitePlaces", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.FinitePlace.norm_embedding_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.FinitePlaces", "is_tactic_proof": true, "tactics": ["conv_rhs"], "tactic_count": 1}
{"name": "NumberField.FinitePlace.pos_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.FinitePlaces", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.FinitePlace.mk_eq_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.FinitePlaces", "is_tactic_proof": true, "tactics": ["refine", "contrapose", "intro", "rw", "have", "by_contra", "exact", "use", "simp", "rw", "rw", "linarith"], "tactic_count": 12}
{"name": "NumberField.FinitePlace.maximalIdeal_mk", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.FinitePlaces", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NumberField.FinitePlace.equivHeightOneSpectrum", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.FinitePlaces", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.FinitePlace.maximalIdeal_injective", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.FinitePlaces", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.FinitePlace.maximalIdeal_inj", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.FinitePlaces", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.FinitePlace.mulSupport_finite_int", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.FinitePlaces", "is_tactic_proof": false, "tactics": ["have", "ne_iff_lt_iff_le.mpr", "simp_rw", "have", "apply", "simp", "have", "refine", "simp"], "tactic_count": 9}
{"name": "NumberField.FinitePlace.mulSupport_finite", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.FinitePlaces", "is_tactic_proof": true, "tactics": ["rcases", "simp_all", "obtain", "simp_rw", "apply", "intro", "simp", "contrapose", "simp"], "tactic_count": 9}
{"name": "NumberField.FinitePlace.add_le", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.FinitePlaces", "is_tactic_proof": true, "tactics": ["obtain", "have", "rw", "grind", "simpa"], "tactic_count": 5}
{"name": "NumberField.FinitePlace.instNonarchimedeanHomClassReal", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.FinitePlaces", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.HeightOneSpectrum.equivHeightOneSpectrum_symm_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.FinitePlaces", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.HeightOneSpectrum.embedding_mul_absNorm", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.FinitePlaces", "is_tactic_proof": false, "tactics": ["rw", "push_cast", "rw", "norm_cast", "rw", "simp"], "tactic_count": 6}
{"name": "NumberField.instFreeIntSubtypeMemSubmoduleRingOfIntegersCoeToSubmodule", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.FractionalIdeal", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "NumberField.instFiniteIntSubtypeMemSubmoduleRingOfIntegersCoeToSubmodule", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.FractionalIdeal", "is_tactic_proof": false, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "NumberField.instIsLocalizedModuleIntSubtypeMemSubmoduleRingOfIntegersCoeToSubmoduleValFractionalIdealNonZeroDivisorsRestrictScalarsSubtype", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.FractionalIdeal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.fractionalIdealBasis", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.FractionalIdeal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.basisOfFractionalIdeal", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.FractionalIdeal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.basisOfFractionalIdeal_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.FractionalIdeal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mem_span_basisOfFractionalIdeal", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.FractionalIdeal", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "NumberField.fractionalIdeal_rank", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.FractionalIdeal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NumberField.det_basisOfFractionalIdeal_eq_absNorm", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.FractionalIdeal", "is_tactic_proof": false, "tactics": ["rw", "congr", "ext", "simpa"], "tactic_count": 4}
{"name": "NumberField.house", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.House", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.house_eq_sup'", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.House", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NumberField.house_sum_le_sum_house", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.House", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NumberField.house_nonneg", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.House", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.house_mul_le", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.House", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NumberField.house_prod_le", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.House", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "NumberField.house_add_le", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.House", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NumberField.house_pow_le", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.House", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "NumberField.house_nat_mul", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.House", "is_tactic_proof": true, "tactics": ["rw", "norm_cast", "simp"], "tactic_count": 3}
{"name": "NumberField.house_intCast", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.House", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NumberField.exists_conjugate_one_le_norm", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.House", "is_tactic_proof": false, "tactics": ["obtain", "by_contra", "let", "have", "exact", "use", "rwa"], "tactic_count": 7}
{"name": "NumberField.norm_embedding_le_house", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.House", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "NumberField.one_le_house_of_isIntegral", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.House", "is_tactic_proof": false, "tactics": ["have", "apply", "simpa", "apply"], "tactic_count": 4}
{"name": "NumberField.norm_norm_le_norm_mul_house_pow", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.House", "is_tactic_proof": true, "tactics": ["classical", "set", "calc", "rw", "rw", "gcongr", "exact"], "tactic_count": 7}
{"name": "_private.Mathlib.NumberTheory.NumberField.House.0.NumberField.house.c", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.House", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.NumberField.House.0.NumberField.house.c_nonneg", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.House", "is_tactic_proof": true, "tactics": ["rw", "positivity"], "tactic_count": 2}
{"name": "NumberField.house.basis_repr_norm_le_const_mul_house", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.House", "is_tactic_proof": true, "tactics": ["let", "calc", "rw", "exact", "gcongr", "exact", "gcongr", "exact", "simp"], "tactic_count": 9}
{"name": "_private.Mathlib.NumberTheory.NumberField.House.0.NumberField.house.newBasis", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.House", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.NumberField.House.0.NumberField.house.supOfBasis", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.House", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.NumberField.House.0.NumberField.house.supOfBasis_nonneg", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.House", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "_private.Mathlib.NumberTheory.NumberField.House.0.NumberField.house.a'", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.House", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.NumberField.House.0.NumberField.house.asiegel", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.House", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.NumberField.House.0.NumberField.house.asiegel_ne_0", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.House", "is_tactic_proof": true, "tactics": ["simp", "simp", "rw", "simp", "apply", "rw", "specialize", "let", "have", "ext", "specialize", "rw", "simp", "apply", "simp", "exact"], "tactic_count": 16}
{"name": "_private.Mathlib.NumberTheory.NumberField.House.0.NumberField.house.ξ", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.House", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.NumberField.House.0.NumberField.house.ξ_ne_0", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.House", "is_tactic_proof": true, "tactics": ["intro", "apply", "ext", "rw", "have", "simp", "exact"], "tactic_count": 7}
{"name": "_private.Mathlib.NumberTheory.NumberField.House.0.NumberField.house.lin_1", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.House", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "_private.Mathlib.NumberTheory.NumberField.House.0.NumberField.house.ξ_mulVec_eq_0", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.House", "is_tactic_proof": true, "tactics": ["funext", "have", "intro", "have", "rw", "rcases", "rw", "specialize", "simp", "rw", "exact", "have", "simp", "have", "conv", "rw", "rw", "conv", "rw", "rw", "ring", "rw", "rw", "rw", "rw"], "tactic_count": 25}
{"name": "_private.Mathlib.NumberTheory.NumberField.House.0.NumberField.house.c₂", "kind": "abbrev", "module": "Mathlib.NumberTheory.NumberField.House", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.NumberField.House.0.NumberField.house.c₂_nonneg", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.House", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.NumberField.House.0.NumberField.house.asiegel_remark", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.House", "is_tactic_proof": true, "tactics": ["have", "rw", "intro", "calc", "simp", "have", "simp", "exact", "simp", "gcongr", "apply", "rw", "gcongr", "apply", "exact", "gcongr", "simp", "rw", "gcongr", "exacts", "exact"], "tactic_count": 21}
{"name": "_private.Mathlib.NumberTheory.NumberField.House.0.NumberField.house.c₁", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.House", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.NumberField.House.0.NumberField.house.house_le_bound", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.House", "is_tactic_proof": true, "tactics": ["let", "intro", "have", "have", "calc", "simp_rw", "gcongr", "simp", "unfold", "gcongr", "simp", "gcongr", "exact", "simp", "rw", "gcongr", "exact", "exact", "rw"], "tactic_count": 19}
{"name": "NumberField.house.exists_ne_zero_int_vec_house_le", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.House", "is_tactic_proof": true, "tactics": ["classical", "let", "have", "have", "have", "have", "have", "simp", "rw", "have", "have", "have", "exact", "use"], "tactic_count": 14}
{"name": "_private.Mathlib.NumberTheory.NumberField.Ideal.Asymptotics.0.NumberField.Ideal.tendsto_norm_le_and_mk_eq_div_atTop_aux₁", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Ideal.Asymptotics", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "refine", "rw", "simp_rw", "mul_comm", "exact"], "tactic_count": 7}
{"name": "_private.Mathlib.NumberTheory.NumberField.Ideal.Asymptotics.0.NumberField.Ideal.tendsto_norm_le_and_mk_eq_div_atTop_aux₂", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.Ideal.Asymptotics", "is_tactic_proof": true, "tactics": ["rw", "refine", "ext", "simp_rw", "constructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 9}
{"name": "NumberField.Ideal.tendsto_norm_le_and_mk_eq_div_atTop", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Ideal.Asymptotics", "is_tactic_proof": true, "tactics": ["classical", "have", "toMixed", "have", "obtain", "have", "convert", "simp_rw", "mul_comm", "rw", "rw", "inv_pow,", "ring_nf", "rw", "rwa", "dsimp", "rw", "exact", "rw", "volume_frontier_normLeOne]"], "tactic_count": 20}
{"name": "NumberField.Ideal.tendsto_norm_le_div_atTop₀", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Ideal.Asymptotics", "is_tactic_proof": true, "tactics": ["classical", "convert", "rw", "ring", "filter_upwards", "have", "simp_rw", "refine", "let", "simp_rw", "rw"], "tactic_count": 11}
{"name": "NumberField.Ideal.tendsto_norm_le_div_atTop", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Ideal.Asymptotics", "is_tactic_proof": true, "tactics": ["have", "rw", "apply", "filter_upwards", "simp_rw", "rw"], "tactic_count": 6}
{"name": "IsPrimitiveRoot.not_coprime_norm_of_mk_eq_one", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Ideal.Basic", "is_tactic_proof": true, "tactics": ["intro", "rw", "obtain", "have", "refine", "exact", "hζ.prime_dvd_of_dvd_norm_sub_one"], "tactic_count": 7}
{"name": "Ideal.rootsOfUnityMapQuot", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.Ideal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.rootsOfUnityMapQuot_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Ideal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.torsionMapQuot", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.Ideal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.torsionMapQuot_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Ideal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.rootsOfUnityMapQuot_injective", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Ideal.Basic", "is_tactic_proof": true, "tactics": ["refine", "obtain", "suffices", "intro", "let", "have", "rw", "refine", "exact"], "tactic_count": 9}
{"name": "Ideal.torsionMapQuot_injective", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Ideal.Basic", "is_tactic_proof": true, "tactics": ["intro", "rw", "rw", "exact"], "tactic_count": 4}
{"name": "NumberField.torsionOrder_dvd_absNorm_sub_one", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Ideal.Basic", "is_tactic_proof": true, "tactics": ["have", "let", "have", "have", "rwa"], "tactic_count": 5}
{"name": "instFiniteQuotientRingOfIntegersIdealOfNumberFieldOfIsMaximal", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.Ideal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingOfIntegers.exponent", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.Ideal.KummerDedekind", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingOfIntegers.exponent_eq_one_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Ideal.KummerDedekind", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RingOfIntegers.not_dvd_exponent_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Ideal.KummerDedekind", "is_tactic_proof": false, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "RingOfIntegers.exponent_eq_sInf", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Ideal.KummerDedekind", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RingOfIntegers.ZModXQuotSpanEquivQuotSpan", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.Ideal.KummerDedekind", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingOfIntegers.ZModXQuotSpanEquivQuotSpan_mk_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Ideal.KummerDedekind", "is_tactic_proof": false, "tactics": ["simp", "mapEquiv_symm_apply,", "exact", "congr_arg", "quotMapEquivQuotQuotMap_symm_apply"], "tactic_count": 5}
{"name": "RingOfIntegers.monicFactorsMod", "kind": "abbrev", "module": "Mathlib.NumberTheory.NumberField.Ideal.KummerDedekind", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingOfIntegers.ZModXQuotSpanEquivQuotSpanPair", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.Ideal.KummerDedekind", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.NumberField.Ideal.KummerDedekind.0.NumberField.Ideal.primesOverSpanEquivMonicFactorsModAux", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.Ideal.KummerDedekind", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.NumberField.Ideal.KummerDedekind.0.NumberField.Ideal.primesOverSpanEquivMonicFactorsModAux_symm_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Ideal.KummerDedekind", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.Ideal.primesOverSpanEquivMonicFactorsMod", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.Ideal.KummerDedekind", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.Ideal.primesOverSpanEquivMonicFactorsMod_symm_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Ideal.KummerDedekind", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.Ideal.primesOverSpanEquivMonicFactorsMod_symm_apply_eq_span", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Ideal.KummerDedekind", "is_tactic_proof": false, "tactics": ["simp", "rw"], "tactic_count": 2}
{"name": "NumberField.Ideal.liesOver_primesOverSpanEquivMonicFactorsMod_symm", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Ideal.KummerDedekind", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "NumberField.Ideal.inertiaDeg_primesOverSpanEquivMonicFactorsMod_symm_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Ideal.KummerDedekind", "is_tactic_proof": true, "tactics": ["have", "rw", "finrank_quotient_span_eq_natDegree]", "refine", "exact"], "tactic_count": 5}
{"name": "NumberField.Ideal.inertiaDeg_primesOverSpanEquivMonicFactorsMod_symm_apply'", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Ideal.KummerDedekind", "is_tactic_proof": true, "tactics": ["obtain", "rw"], "tactic_count": 2}
{"name": "NumberField.Ideal.ramificationIdx_primesOverSpanEquivMonicFactorsMod_symm_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Ideal.KummerDedekind", "is_tactic_proof": true, "tactics": ["rw", "apply", "rw", "emultiplicity_factors_map_eq_emultiplicity", "simp", "rw", "exact"], "tactic_count": 7}
{"name": "NumberField.Ideal.ramificationIdx_primesOverSpanEquivMonicFactorsMod_symm_apply'", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Ideal.KummerDedekind", "is_tactic_proof": true, "tactics": ["obtain", "rw"], "tactic_count": 2}
{"name": "NumberField.InfiniteAdeleRing", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.InfiniteAdeleRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfiniteAdeleRing.instCommRing", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.InfiniteAdeleRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfiniteAdeleRing.instInhabited", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.InfiniteAdeleRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfiniteAdeleRing.instNontrivial", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.InfiniteAdeleRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfiniteAdeleRing.instTopologicalSpace", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.InfiniteAdeleRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfiniteAdeleRing.instIsTopologicalRing", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.InfiniteAdeleRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfiniteAdeleRing.instAlgebra", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.InfiniteAdeleRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfiniteAdeleRing.algebraMap_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfiniteAdeleRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfiniteAdeleRing.locallyCompactSpace", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.InfiniteAdeleRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfiniteAdeleRing.ringEquiv_mixedSpace", "kind": "abbrev", "module": "Mathlib.NumberTheory.NumberField.InfiniteAdeleRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfiniteAdeleRing.ringEquiv_mixedSpace_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfiniteAdeleRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfiniteAdeleRing.mixedEmbedding_eq_algebraMap_comp", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfiniteAdeleRing", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "NumberField.InfiniteAdeleRing.denseRange_algebraMap", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfiniteAdeleRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.instNonemptyInfinitePlaceOfRingHomComplex", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.mk", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.IsInfinitePlace", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.isInfinitePlace", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NumberField.isInfinitePlace_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.instFunLikeReal", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.coe_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.ext", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.instMonoidWithZeroHomClassReal", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.instNonnegHomClassReal", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.apply", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.embedding", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.mk_embedding", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.mk_conjugate_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "NumberField.InfinitePlace.norm_embedding_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": true, "tactics": ["nth_rewrite", "rfl"], "tactic_count": 2}
{"name": "NumberField.InfinitePlace.embedding_injective", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.embedding_inj", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.conjugate_embedding_injective", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.eq_of_embedding_eq_conjugate", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NumberField.InfinitePlace.eq_iff_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.le_iff_le", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.pos_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.mk_eq_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": true, "tactics": ["constructor", "intro", "obtain", "let", "have", "change", "apply", "intro", "rw", "apply", "suffices", "rw", "rfl", "exact", "cases", "inl", "left", "conv_rhs", "exact", "inr", "right", "conv_rhs", "exact", "rintro", "exact", "rw", "exact"], "tactic_count": 27}
{"name": "NumberField.InfinitePlace.IsReal", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.IsComplex", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.embedding_mk_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NumberField.InfinitePlace.embedding_mk_eq_of_isReal", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "NumberField.InfinitePlace.isReal_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": true, "tactics": ["refine", "rintro", "rwa"], "tactic_count": 3}
{"name": "NumberField.InfinitePlace.isComplex_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": true, "tactics": ["refine", "rintro", "contrapose", "cases", "inl", "inr"], "tactic_count": 6}
{"name": "NumberField.InfinitePlace.conjugate_embedding_eq_of_isReal", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.not_isReal_iff_isComplex", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NumberField.InfinitePlace.not_isComplex_iff_isReal", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NumberField.InfinitePlace.isReal_or_isComplex", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NumberField.InfinitePlace.ne_of_isReal_isComplex", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.disjoint_isReal_isComplex", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.embedding_of_isReal", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.embedding_of_isReal_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.norm_embedding_of_isReal", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NumberField.InfinitePlace.isReal_of_mk_isReal", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": true, "tactics": ["contrapose", "rw", "exact"], "tactic_count": 3}
{"name": "NumberField.InfinitePlace.isReal_mk_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.isComplex_mk_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.not_isReal_of_mk_isComplex", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "NumberField.InfinitePlace.mult", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.mult_isReal", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NumberField.InfinitePlace.mult_isComplex", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NumberField.InfinitePlace.mult_pos", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": true, "tactics": ["rw", "split_ifs"], "tactic_count": 2}
{"name": "NumberField.InfinitePlace.mult_ne_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.mult_coe_ne_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.one_le_mult", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "NumberField.InfinitePlace.card_filter_mk_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": false, "tactics": ["conv_lhs", "congr", "rw", "simp_rw", "split_ifs", "rw", "refine", "rwa"], "tactic_count": 8}
{"name": "NumberField.InfinitePlace.NumberField.InfinitePlace.fintype", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.prod_eq_prod_mul_prod", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "NumberField.InfinitePlace.sum_mult_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": true, "tactics": ["classical", "rw", "exact"], "tactic_count": 3}
{"name": "NumberField.InfinitePlace.mkReal", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": true, "tactics": ["refine", "exact", "rwa", "exact"], "tactic_count": 4}
{"name": "NumberField.InfinitePlace.mkComplex", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.mkReal_coe", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.mkComplex_coe", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.prod_eq_abs_norm", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": true, "tactics": ["classical", "convert", "rw", "simp", "rw", "have", "rw", "simp_rw", "rw"], "tactic_count": 9}
{"name": "NumberField.InfinitePlace.one_le_of_lt_one", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": false, "tactics": ["suffices", "contrapose", "rw", "refine", "exact", "refine", "by_cases", "rwa", "exact", "rw", "exact"], "tactic_count": 11}
{"name": "NumberField.is_primitive_element_of_infinitePlace_lt", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": true, "tactics": ["rw", "intro", "have", "have", "simp", "rw", "contrapose", "exact", "rw", "cases", "inl", "rw", "exact", "inr", "refine", "have", "rw", "have", "simp", "rw", "exact", "rwa", "exact"], "tactic_count": 23}
{"name": "NumberField.adjoin_eq_top_of_infinitePlace_lt", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "NumberField.InfinitePlace.nrRealPlaces", "kind": "abbrev", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.nrComplexPlaces", "kind": "abbrev", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.card_real_embeddings", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.card_eq_nrRealPlaces_add_nrComplexPlaces", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": true, "tactics": ["classical", "convert", "exact"], "tactic_count": 3}
{"name": "NumberField.InfinitePlace.card_complex_embeddings", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": false, "tactics": ["suffices", "rw", "simp_rw", "rintro", "convert", "rw", "refine", "exact", "rwa", "refine", "rwa", "simp_rw"], "tactic_count": 12}
{"name": "NumberField.InfinitePlace.card_add_two_mul_card_eq_rank", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": true, "tactics": ["classical", "rw", "exact"], "tactic_count": 3}
{"name": "NumberField.InfinitePlace.ComplexEmbedding.conjugate_sign", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": false, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "NumberField.InfinitePlace.nrComplexPlaces_eq_zero_of_finrank_eq_one", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": true, "tactics": ["linarith"], "tactic_count": 1}
{"name": "NumberField.InfinitePlace.nrRealPlaces_eq_one_of_finrank_eq_one", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "NumberField.InfinitePlace.nrRealPlaces_pos_of_odd_finrank", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": true, "tactics": ["refine", "by_contra", "refine", "rw", "exact"], "tactic_count": 5}
{"name": "NumberField.InfinitePlace.IsPrimitiveRoot.nrRealPlaces_eq_zero_of_two_lt", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "let", "have", "have", "rw", "congr", "have", "rw", "have", "rwa", "cases", "inl", "inr", "replace", "simp", "lia"], "tactic_count": 17}
{"name": "Rat.infinitePlace", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.infinitePlace_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": true, "tactics": ["rw", "obtain", "simp"], "tactic_count": 3}
{"name": "Rat.instSubsingletonInfinitePlace", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.isReal_infinitePlace", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.map_ratCast", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": true, "tactics": ["rcases", "aesop"], "tactic_count": 2}
{"name": "NumberField.InfinitePlace.map_natCast", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": true, "tactics": ["rcases", "aesop"], "tactic_count": 2}
{"name": "NumberField.InfinitePlace.map_intCast", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": true, "tactics": ["rcases", "aesop"], "tactic_count": 2}
{"name": "NumberField.InfinitePlace.eq_one_of_rpow_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "NumberField.InfinitePlace.eq_iff_isEquiv", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact"], "tactic_count": 3}
{"name": "NumberField.InfinitePlace.isNontrivial", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "NumberField.InfinitePlace.denseRange_algebraMap_pi", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Basic", "is_tactic_proof": true, "tactics": ["classical", "refine", "choose", "let", "have", "refine", "simp_rw", "refine", "by_cases", "rw", "have", "simpa", "simp", "have", "simpa", "simpa", "let", "exact"], "tactic_count": 18}
{"name": "NumberField.InfinitePlace.isometry_embedding", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.isometry_embedding_of_isReal", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.Completion", "kind": "abbrev", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.Completion.instNormedField", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.Completion.norm_coe", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.Completion.instAlgebra", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.Completion.WithAbs.ratCast_equiv", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.Completion.Rat.norm_infinitePlace_completion", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Completion", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NumberField.InfinitePlace.Completion.locallyCompactSpace", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.Completion.extensionEmbedding", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.Completion.extensionEmbeddingOfIsReal", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.Completion.extensionEmbedding_coe", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.Completion.extensionEmbeddingOfIsReal_coe", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.Completion.isometry_extensionEmbedding", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.Completion.isometry_extensionEmbeddingOfIsReal", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.Completion.isClosed_image_extensionEmbedding", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.Completion.isClosed_image_extensionEmbeddingOfIsReal", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.Completion.subfield_ne_real_of_isComplex", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Completion", "is_tactic_proof": true, "tactics": ["contrapose", "simp", "ext", "obtain", "simp"], "tactic_count": 5}
{"name": "NumberField.InfinitePlace.Completion.surjective_extensionEmbedding_of_isComplex", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Completion", "is_tactic_proof": true, "tactics": ["rw", "exact", "subfield_ne_real_of_isComplex"], "tactic_count": 3}
{"name": "NumberField.InfinitePlace.Completion.bijective_extensionEmbedding_of_isComplex", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.Completion.ringEquivComplexOfIsComplex", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.Completion.isometryEquivComplexOfIsComplex", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.Completion.surjective_extensionEmbeddingOfIsReal", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Completion", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "NumberField.InfinitePlace.Completion.bijective_extensionEmbeddingOfIsReal", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.Completion.ringEquivRealOfIsReal", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.Completion.isometryEquivRealOfIsReal", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.Embeddings.instNonemptyRingHomOfIsAlgebraicRatOfIsAlgClosed", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Embeddings", "is_tactic_proof": false, "tactics": ["obtain", "apply", "exact", "exact"], "tactic_count": 4}
{"name": "NumberField.Embeddings.instFintypeRingHom", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Embeddings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.Embeddings.card", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Embeddings", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NumberField.Embeddings.instNonemptyRingHom", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Embeddings", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "NumberField.Embeddings.range_eval_eq_rootSet_minpoly", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Embeddings", "is_tactic_proof": true, "tactics": ["convert", "ext", "exact"], "tactic_count": 3}
{"name": "NumberField.Embeddings.coeff_bdd_of_norm_le", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Embeddings", "is_tactic_proof": true, "tactics": ["have", "rw", "refine", "classical", "rw", "obtain", "exact"], "tactic_count": 7}
{"name": "NumberField.Embeddings.finite_of_norm_le", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Embeddings", "is_tactic_proof": true, "tactics": ["classical", "let", "have", "refine", "have", "refine", "rw", "exact", "rw", "refine", "rw"], "tactic_count": 11}
{"name": "NumberField.Embeddings.pow_eq_one_of_norm_le_one", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Embeddings", "is_tactic_proof": false, "tactics": ["obtain", "wlog", "exact", "refine", "rw", "refine"], "tactic_count": 6}
{"name": "NumberField.Embeddings.pow_eq_one_of_norm_eq_one", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Embeddings", "is_tactic_proof": true, "tactics": ["apply", "intro", "simp_rw", "exact"], "tactic_count": 4}
{"name": "NumberField.place", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Embeddings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.place_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Embeddings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.ComplexEmbedding.lift", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Embeddings", "is_tactic_proof": true, "tactics": ["letI", "exact"], "tactic_count": 2}
{"name": "NumberField.ComplexEmbedding.lift_comp_algebraMap", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Embeddings", "is_tactic_proof": true, "tactics": ["unfold", "letI", "rw"], "tactic_count": 3}
{"name": "NumberField.ComplexEmbedding.lift_algebraMap_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Embeddings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.ComplexEmbedding.conjugate", "kind": "abbrev", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Embeddings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.ComplexEmbedding.conjugate_comp", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Embeddings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.ComplexEmbedding.involutive_conjugate", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Embeddings", "is_tactic_proof": true, "tactics": ["intro"], "tactic_count": 1}
{"name": "NumberField.ComplexEmbedding.conjugate_coe_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Embeddings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.ComplexEmbedding.place_conjugate", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Embeddings", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "NumberField.ComplexEmbedding.IsReal", "kind": "abbrev", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Embeddings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.ComplexEmbedding.isReal_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Embeddings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.ComplexEmbedding.isReal_conjugate_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Embeddings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.ComplexEmbedding.IsReal.embedding", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Embeddings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.ComplexEmbedding.IsReal.coe_embedding_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Embeddings", "is_tactic_proof": true, "tactics": ["apply", "rfl", "rw", "exact"], "tactic_count": 4}
{"name": "NumberField.ComplexEmbedding.IsReal.comp", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Embeddings", "is_tactic_proof": true, "tactics": ["ext1"], "tactic_count": 1}
{"name": "NumberField.ComplexEmbedding.isReal_comp_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Embeddings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.ComplexEmbedding.exists_comp_symm_eq_of_comp_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Embeddings", "is_tactic_proof": true, "tactics": ["letI", "letI", "have", "let", "use", "ext1", "exact"], "tactic_count": 7}
{"name": "NumberField.ComplexEmbedding.IsConj", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Embeddings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.ComplexEmbedding.IsConj.eq", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Embeddings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.ComplexEmbedding.IsConj.ext", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Embeddings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.ComplexEmbedding.IsConj.ext_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Embeddings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.ComplexEmbedding.IsConj.isReal_comp", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Embeddings", "is_tactic_proof": true, "tactics": ["ext1", "simp"], "tactic_count": 2}
{"name": "NumberField.ComplexEmbedding.isConj_one_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Embeddings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.ComplexEmbedding.isConj_ne_one_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Embeddings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.ComplexEmbedding.IsConj.symm", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Embeddings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.ComplexEmbedding.isConj_symm", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Embeddings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.ComplexEmbedding.isConj_apply_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Embeddings", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NumberField.ComplexEmbedding.IsConj.comp", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Embeddings", "is_tactic_proof": true, "tactics": ["ext", "simpa"], "tactic_count": 2}
{"name": "NumberField.ComplexEmbedding.orderOf_isConj_two_of_ne_one", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Embeddings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.ComplexEmbedding.Extension", "kind": "abbrev", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Embeddings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.ComplexEmbedding.Extension.comp_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Embeddings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.ComplexEmbedding.Extension.conjugate_comp_ne", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Embeddings", "is_tactic_proof": true, "tactics": ["simp_all"], "tactic_count": 1}
{"name": "NumberField.ComplexEmbedding.Extension.not_isReal_of_not_isReal", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Embeddings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.ComplexEmbedding.IsMixed", "kind": "abbrev", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Embeddings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.ComplexEmbedding.IsUnmixed", "kind": "abbrev", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Embeddings", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.ComplexEmbedding.IsUnmixed.isReal_iff_isReal", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Embeddings", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "NumberField.InfinitePlace.comap", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.comap_mk", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.comap_id", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.comap_comp", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.comap_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.comp_of_comap_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NumberField.InfinitePlace.comap_mk_lift", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NumberField.InfinitePlace.IsReal.comap", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "NumberField.InfinitePlace.IsComplex.of_comap", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "NumberField.InfinitePlace.isReal_comap_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NumberField.InfinitePlace.comap_surjective", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.comap_embedding_of_isReal", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": true, "tactics": ["rw", "embedding_mk_eq_of_isReal"], "tactic_count": 2}
{"name": "NumberField.InfinitePlace.mult_comap_le", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": true, "tactics": ["rw", "split_ifs", "pick_goal", "exact", "all_goals"], "tactic_count": 5}
{"name": "NumberField.InfinitePlace.card_mono", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.instMulActionAlgEquiv", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.smul_eq_comap", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.smul_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.smul_mk", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.comap_smul", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.isReal_smul_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.isComplex_smul_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NumberField.InfinitePlace.ComplexEmbedding.exists_comp_symm_eq_of_comp_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.exists_smul_eq_of_comap_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": true, "tactics": ["rw", "cases", "inl", "obtain", "use", "rw", "inr", "h", "obtain", "use", "rw", "exact"], "tactic_count": 12}
{"name": "NumberField.InfinitePlace.mem_orbit_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": true, "tactics": ["refine", "rintro", "rw", "congr"], "tactic_count": 4}
{"name": "NumberField.InfinitePlace.orbitRelEquiv", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": false, "tactics": ["refine", "rintro", "exact", "intro", "obtain", "exact"], "tactic_count": 6}
{"name": "NumberField.InfinitePlace.orbitRelEquiv_apply_mk''", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.IsUnramified", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.IsRamified", "kind": "abbrev", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.isUnramified_self", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.IsUnramified.eq", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.isUnramified_iff_mult_le", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "NumberField.InfinitePlace.IsUnramified.comap_algHom", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "NumberField.InfinitePlace.IsUnramified.of_restrictScalars", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": false, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "NumberField.InfinitePlace.IsUnramified.comap", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.not_isUnramified_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": true, "tactics": ["rw", "split_ifs", "simp", "exact"], "tactic_count": 4}
{"name": "NumberField.InfinitePlace.isUnramified_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NumberField.InfinitePlace.isRamified_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.IsRamified.isComplex", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.IsRamified.isReal", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.IsRamified.ne_conjugate", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "exact", "contrapose", "rw"], "tactic_count": 5}
{"name": "NumberField.InfinitePlace.IsRamified.comap_embedding", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NumberField.InfinitePlace.IsRamified.comap_embedding_conjugate", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "NumberField.InfinitePlace.IsRamified.isMixed_embedding", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.IsRamified.isMixed_conjugate_embedding", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.isRamified_mk_iff_isMixed", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": true, "tactics": ["refine", "rcases", "exact", "rw", "rw", "exact"], "tactic_count": 6}
{"name": "NumberField.InfinitePlace.IsUnramified.isUnmixed", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": true, "tactics": ["intro", "rw", "exact"], "tactic_count": 3}
{"name": "NumberField.InfinitePlace.IsUnramified.isUnmixed_conjugate", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": true, "tactics": ["intro", "simp_rw", "simpa"], "tactic_count": 3}
{"name": "NumberField.InfinitePlace.isUnramified_mk_iff_isUnmixed", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": true, "tactics": ["refine", "rcases", "exact", "rw", "rw", "by_cases", "exact", "exact"], "tactic_count": 8}
{"name": "NumberField.InfinitePlace.IsReal.isUnramified", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.ComplexEmbedding.IsConj.isUnramified_mk_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": true, "tactics": ["rw", "comap_mk,"], "tactic_count": 2}
{"name": "NumberField.InfinitePlace.isUnramified_mk_iff_forall_isConj", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": true, "tactics": ["refine", "by_contra", "rw", "rw", "letI", "letI", "have", "let", "have", "exact"], "tactic_count": 10}
{"name": "_private.Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification.0.NumberField.InfinitePlace.termStab", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification.0.NumberField.InfinitePlace._aux_Mathlib_NumberTheory_NumberField_InfinitePlace_Ramification___macroRules__private_Mathlib_NumberTheory_NumberField_InfinitePlace_Ramification_0_NumberField_InfinitePlace_termStab_1", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification.0.NumberField.InfinitePlace._aux_Mathlib_NumberTheory_NumberField_InfinitePlace_Ramification___unexpand_MulAction_stabilizer_1", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.mem_stabilizer_mk_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": true, "tactics": ["simp", "rw", "refine", "exact"], "tactic_count": 4}
{"name": "NumberField.InfinitePlace.IsUnramified.stabilizer_eq_bot", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": true, "tactics": ["rw", "simp", "exact"], "tactic_count": 3}
{"name": "NumberField.ComplexEmbedding.IsConj.coe_stabilizer_mk", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "NumberField.InfinitePlace.nat_card_stabilizer_eq_one_or_two", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": true, "tactics": ["classical", "rw", "by_cases", "obtain", "simp", "by_cases", "left", "right", "left", "trans", "congr", "simp", "simp"], "tactic_count": 13}
{"name": "NumberField.InfinitePlace.isUnramified_iff_stabilizer_eq_bot", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "NumberField.InfinitePlace.isUnramified_iff_card_stabilizer_eq_one", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NumberField.InfinitePlace.not_isUnramified_iff_card_stabilizer_eq_two", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": true, "tactics": ["rw", "obtain"], "tactic_count": 2}
{"name": "NumberField.InfinitePlace.isRamified_iff_card_stabilizer_eq_two", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.exists_isConj_of_isRamified", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": true, "tactics": ["rw", "obtain", "rw", "grind"], "tactic_count": 4}
{"name": "NumberField.InfinitePlace.card_stabilizer", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": true, "tactics": ["split", "rwa", "rwa"], "tactic_count": 3}
{"name": "NumberField.InfinitePlace.even_nat_card_aut_of_not_isUnramified", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": true, "tactics": ["by_cases", "cases", "rw", "exact", "convert", "by_contra", "exact"], "tactic_count": 7}
{"name": "NumberField.InfinitePlace.even_card_aut_of_not_isUnramified", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.even_finrank_of_not_isUnramified", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "exact"], "tactic_count": 3}
{"name": "NumberField.InfinitePlace.isUnramified_smul_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NumberField.InfinitePlace.IsUnramifiedIn", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.isUnramifiedIn_comap", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": true, "tactics": ["refine", "obtain", "rwa"], "tactic_count": 3}
{"name": "NumberField.InfinitePlace.even_card_aut_of_not_isUnramifiedIn", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact"], "tactic_count": 3}
{"name": "NumberField.InfinitePlace.even_finrank_of_not_isUnramifiedIn", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact"], "tactic_count": 3}
{"name": "NumberField.InfinitePlace.card_isUnramified", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": false, "tactics": ["rw", "refine", "obtain", "rw", "trans", "congr", "rw", "intro", "rw", "rwa", "simp"], "tactic_count": 11}
{"name": "NumberField.InfinitePlace.card_isUnramified_compl", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": false, "tactics": ["rw", "refine", "obtain", "rw", "trans", "congr", "rw", "and_iff_right_iff_imp]", "intro", "rw", "rwa", "simp"], "tactic_count": 12}
{"name": "NumberField.InfinitePlace.card_eq_card_isUnramifiedIn", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsUnramifiedAtInfinitePlaces.id", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUnramifiedAtInfinitePlaces.trans", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUnramifiedAtInfinitePlaces.top", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUnramifiedAtInfinitePlaces.bot", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.isUnramified", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.InfinitePlace.isUnramifiedIn", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUnramifiedAtInfinitePlaces_of_odd_card_aut", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUnramifiedAtInfinitePlaces_of_odd_finrank", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUnramifiedAtInfinitePlaces.card_infinitePlace", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": true, "tactics": ["classical", "rw", "exact", "simp", "exact"], "tactic_count": 5}
{"name": "NumberField.InfinitePlace.LiesOver.comap_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": true, "tactics": ["ext", "simpa"], "tactic_count": 2}
{"name": "NumberField.InfinitePlace.LiesOver.mk_embedding_comp", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NumberField.InfinitePlace.LiesOver.embedding_comp_eq_or_conjugate_embedding_comp_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": true, "tactics": ["cases", "inl", "inr"], "tactic_count": 3}
{"name": "NumberField.InfinitePlace.LiesOver.isComplex_of_isComplex_under", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": true, "tactics": ["rw", "obtain", "use", "rw", "rcases"], "tactic_count": 5}
{"name": "NumberField.InfinitePlace.LiesOver.isReal_of_isReal_over", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "NumberField.nrComplexPlaces_eq_zero_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NumberField.IsTotallyReal.complexEmbedding_isReal", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.IsTotallyReal.mult_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.IsTotallyReal.ofRingEquiv", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.IsTotallyReal.of_algebra", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.isTotallyReal_iff_ofRingEquiv", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.isTotallyReal_top_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.instIsTotallyRealSubtypeMemIntermediateFieldRatOfIsAlgebraic", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.instIsTotallyRealSubtypeMemSubfieldOfIsAlgebraic", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.IsTotallyReal.nrComplexPlaces_eq_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.IsTotallyReal.finrank", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NumberField.instIsTotallyRealRat", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.instIsTotallyRealSubtypeMemSubfieldTop", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.isTotallyReal_bot", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.isTotallyReal_bot", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "NumberField.maximalRealSubfield", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.mem_maximalRealSubfield_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.IsTotallyReal.le_maximalRealSubfield", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex", "is_tactic_proof": true, "tactics": ["intro", "rw", "refine", "exact"], "tactic_count": 4}
{"name": "NumberField.IsTotallyReal.maximalRealSubfield_eq_top", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.instIsAlgebraicSubtypeMemSubfield", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.isTotallyReal_maximalRealSubfield", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.isTotallyReal_iff_le_maximalRealSubfield", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex", "is_tactic_proof": true, "tactics": ["refine", "let", "have", "have", "exact"], "tactic_count": 5}
{"name": "NumberField.isTotallyReal_sup", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex", "is_tactic_proof": false, "tactics": ["rw", "isTotallyReal_iff_le_maximalRealSubfield]", "exact"], "tactic_count": 3}
{"name": "NumberField.isTotallyReal_iSup", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex", "is_tactic_proof": true, "tactics": ["obtain", "rw", "infer_instance", "rw", "exact"], "tactic_count": 5}
{"name": "NumberField.maximalRealSubfield_eq_top_iff_isTotallyReal", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.nrRealPlaces_eq_zero_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NumberField.IsTotallyComplex.complexEmbedding_not_isReal", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.IsTotallyComplex.mult_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.isTotallyComplex_of_algebra", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.IsTotallyComplex.nrRealPlaces_eq_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.IsTotallyComplex.finrank", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Algebra.coe_norm_int", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Norm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.coe_trace_int", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Norm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingOfIntegers.norm", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.Norm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingOfIntegers.coe_norm", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Norm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingOfIntegers.coe_algebraMap_norm", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Norm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingOfIntegers.algebraMap_norm_algebraMap", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Norm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingOfIntegers.norm_algebraMap", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Norm", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RingOfIntegers.isUnit_norm_of_isGalois", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Norm", "is_tactic_proof": true, "tactics": ["classical", "refine", "replace", "refine", "convert", "ext", "convert_to", "rw", "rw"], "tactic_count": 9}
{"name": "RingOfIntegers.dvd_norm", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Norm", "is_tactic_proof": true, "tactics": ["classical", "have", "refine", "ext", "rw", "simp"], "tactic_count": 6}
{"name": "RingOfIntegers.norm_norm", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Norm", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RingOfIntegers.isUnit_norm", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Norm", "is_tactic_proof": true, "tactics": ["letI", "let", "haveI", "haveI", "calc", "rw"], "tactic_count": 6}
{"name": "NumberField.FinitePlace.prod_eq_inv_abs_norm_int", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.ProductFormula", "is_tactic_proof": true, "tactics": ["simp", "refine", "norm_cast", "have", "rw", "let", "have", "let", "let", "have", "have", "refine", "simp", "intro", "simp", "classical", "refine", "congr", "have", "rw", "exact"], "tactic_count": 21}
{"name": "NumberField.FinitePlace.prod_eq_inv_abs_norm", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.ProductFormula", "is_tactic_proof": true, "tactics": ["rcases", "apply", "have", "rintro", "simp", "simp_rw", "finprod_div_distrib", "prod_eq_inv_abs_norm_int", "rw", "congr", "have", "refine", "norm_cast", "rw"], "tactic_count": 14}
{"name": "NumberField.prod_abs_eq_one", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.ProductFormula", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Rat.RingOfIntegers.isUnit_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "rfl"], "tactic_count": 2}
{"name": "NumberField.isUnit_iff_norm", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.Basic", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "NumberField.Units.instCoeHTCUnitsRingOfIntegers", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.Units.coe_injective", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.Units.coe_coe", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.Units.coe_mul", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.Units.coe_pow", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NumberField.Units.coe_zpow", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.Basic", "is_tactic_proof": true, "tactics": ["change", "exact"], "tactic_count": 2}
{"name": "NumberField.Units.coe_one", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.Units.coe_neg_one", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.Units.coe_ne_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.Units.complexEmbedding", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.Units.complexEmbedding_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.Units.complexEmbedding_injective", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.Units.complexEmbedding_inj", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.Units.norm", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NumberField.Units.pos_at_place", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.Units.sum_mult_mul_log", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "NumberField.Units.torsion", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.Units.instNonemptySubtypeUnitsRingOfIntegersMemSubgroupTorsion", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.Units.mem_torsion", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "obtain", "exact", "rw", "coe_one]⟩"], "tactic_count": 6}
{"name": "NumberField.Units.instFintypeSubtypeUnitsRingOfIntegersMemSubgroupTorsion", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.Units.Basic", "is_tactic_proof": true, "tactics": ["refine", "refine", "refine", "rw", "exact", "rw", "exact"], "tactic_count": 7}
{"name": "NumberField.Units.instIsCyclicSubtypeUnitsRingOfIntegersMemSubgroupTorsion", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.Units.torsionOrder", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.Units.instNeZeroNatTorsionOrder", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.Units.torsionOrder_ne_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.Units.torsionOrder_pos", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.Units.rootsOfUnity_eq_one", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "refine", "exact", "have", "rw", "exact", "rw", "exact"], "tactic_count": 9}
{"name": "NumberField.Units.rootsOfUnity_eq_torsion", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.Basic", "is_tactic_proof": true, "tactics": ["ext", "rw", "refine", "rw", "exact", "exact"], "tactic_count": 6}
{"name": "NumberField.Units.map_complexEmbedding_torsion", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.Basic", "is_tactic_proof": true, "tactics": ["apply", "rw", "exact", "let", "rw"], "tactic_count": 5}
{"name": "NumberField.Units.even_torsionOrder", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.Basic", "is_tactic_proof": false, "tactics": ["suffices", "rw", "exact", "rw", "if_neg"], "tactic_count": 5}
{"name": "NumberField.Units.torsion_eq_one_or_neg_one_of_odd_finrank", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "linarith", "interval_cases", "linarith", "exact", "rw", "simp"], "tactic_count": 8}
{"name": "NumberField.Units.torsionOrder_eq_two_of_odd_finrank", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.Basic", "is_tactic_proof": true, "tactics": ["classical", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "NumberField.Units.dirichletUnitTheorem.w₀", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.Units.DirichletTheorem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.Units.dirichletUnitTheorem.logSpace", "kind": "abbrev", "module": "Mathlib.NumberTheory.NumberField.Units.DirichletTheorem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.Units.logEmbedding", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.Units.DirichletTheorem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.Units.dirichletUnitTheorem.logEmbedding_component", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.DirichletTheorem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.Units.dirichletUnitTheorem.sum_logEmbedding_component", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.DirichletTheorem", "is_tactic_proof": true, "tactics": ["have", "rw", "simpa"], "tactic_count": 3}
{"name": "NumberField.Units.dirichletUnitTheorem.mult_log_place_eq_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.DirichletTheorem", "is_tactic_proof": true, "tactics": ["rw", "linarith", "exact", "exact"], "tactic_count": 4}
{"name": "NumberField.Units.dirichletUnitTheorem.logEmbedding_eq_zero_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.DirichletTheorem", "is_tactic_proof": true, "tactics": ["rw", "refine", "by_cases", "suffices", "rw", "exact", "rw", "exact", "exact", "ext", "rw"], "tactic_count": 11}
{"name": "NumberField.Units.dirichletUnitTheorem.logEmbedding_ker", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.DirichletTheorem", "is_tactic_proof": true, "tactics": ["ext", "rw", "simp"], "tactic_count": 3}
{"name": "NumberField.Units.dirichletUnitTheorem.map_logEmbedding_sup_torsion", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.DirichletTheorem", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NumberField.Units.dirichletUnitTheorem.logEmbedding_component_le", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.DirichletTheorem", "is_tactic_proof": true, "tactics": ["lift", "simp_rw", "exact"], "tactic_count": 3}
{"name": "NumberField.Units.dirichletUnitTheorem.log_le_of_logEmbedding_le", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.DirichletTheorem", "is_tactic_proof": false, "tactics": ["have", "nth_rw", "refine", "all_goals", "by_cases", "have", "replace", "simp_rw", "refine", "rw", "exact", "refine", "rw", "refine", "simp", "have", "rw", "refine", "exact", "nth_rw", "exact"], "tactic_count": 21}
{"name": "NumberField.Units.unitLattice", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.Units.DirichletTheorem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.Units.dirichletUnitTheorem.unitLattice_inter_ball_finite", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.DirichletTheorem", "is_tactic_proof": true, "tactics": ["obtain", "convert", "rw", "exact", "suffices", "refine", "rintro", "refine", "exact", "rw", "exact", "refine", "refine", "rintro", "exact"], "tactic_count": 15}
{"name": "NumberField.Units.dirichletUnitTheorem.seq_next", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.DirichletTheorem", "is_tactic_proof": true, "tactics": ["have", "let", "suffices", "obtain", "obtain", "exists_ne_zero_mem_ringOfIntegers_lt", "refine", "rw", "calc", "simp_rw", "exact", "refine", "exact", "intro", "rw", "exact"], "tactic_count": 16}
{"name": "NumberField.Units.dirichletUnitTheorem.seq", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.Units.DirichletTheorem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.Units.dirichletUnitTheorem.seq_ne_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.DirichletTheorem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.Units.dirichletUnitTheorem.seq_decreasing", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.DirichletTheorem", "is_tactic_proof": true, "tactics": ["induction", "zero", "exfalso", "exact", "succ", "cases", "inl", "rw", "exact", "inr", "refine", "exact"], "tactic_count": 12}
{"name": "NumberField.Units.dirichletUnitTheorem.seq_norm_le", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.DirichletTheorem", "is_tactic_proof": true, "tactics": ["cases", "zero", "have", "contrapose", "simp", "simp", "succ", "rw", "exact"], "tactic_count": 9}
{"name": "NumberField.Units.dirichletUnitTheorem.exists_unit", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.DirichletTheorem", "is_tactic_proof": false, "tactics": ["obtain", "conv", "exact", "rsuffices", "have", "refine", "calc", "rw", "inv_mul_cancel₀", "rw", "exact", "refine", "rw", "exact"], "tactic_count": 14}
{"name": "NumberField.Units.dirichletUnitTheorem.unitLattice_span_eq_top", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.DirichletTheorem", "is_tactic_proof": true, "tactics": ["classical", "refine", "le_antisymm", "let", "let", "logEmbedding", "suffices", "rw", "rw", "refine", "rw", "refine", "simp_rw", "rw", "sum_erase_eq_sub", "refine", "rw", "exact", "rw", "refine", "rw", "refine", "rw", "exact"], "tactic_count": 24}
{"name": "NumberField.Units.rank", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.Units.DirichletTheorem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.Units.instDiscrete_unitLattice", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.Units.DirichletTheorem", "is_tactic_proof": true, "tactics": ["classical", "refine", "refine", "exact", "refine", "convert", "ext", "refine", "rintro", "exact"], "tactic_count": 10}
{"name": "NumberField.Units.instZLattice_unitLattice", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.Units.DirichletTheorem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.Units.finrank_eq_rank", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.DirichletTheorem", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "NumberField.Units.unitLattice_rank", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.DirichletTheorem", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "NumberField.Units.logEmbeddingQuot", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.Units.DirichletTheorem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.Units.logEmbeddingQuot_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.DirichletTheorem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.Units.logEmbeddingQuot_injective", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.DirichletTheorem", "is_tactic_proof": true, "tactics": ["unfold", "intro", "simp_rw", "exact"], "tactic_count": 4}
{"name": "NumberField.Units.logEmbeddingEquiv", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.Units.DirichletTheorem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.Units.logEmbeddingEquiv_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.DirichletTheorem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.Units.inst._@.Mathlib.NumberTheory.NumberField.Units.DirichletTheorem.873343626._hygCtx._hyg.37", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.Units.DirichletTheorem", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "NumberField.Units.inst._@.Mathlib.NumberTheory.NumberField.Units.DirichletTheorem.1302255403._hygCtx._hyg.37", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.Units.DirichletTheorem", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "NumberField.Units.instFiniteIntAdditiveUnitsRingOfIntegers", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.Units.DirichletTheorem", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "infer_instance", "rw", "have", "exact"], "tactic_count": 7}
{"name": "NumberField.Units.instFGUnitsRingOfIntegers", "kind": "instance", "module": "Mathlib.NumberTheory.NumberField.Units.DirichletTheorem", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "NumberField.Units.rank_modTorsion", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.DirichletTheorem", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NumberField.Units.basisModTorsion", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.Units.DirichletTheorem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.Units.basisUnitLattice", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.Units.DirichletTheorem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.Units.fundSystem", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.Units.DirichletTheorem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.Units.fundSystem_mk", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.DirichletTheorem", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "NumberField.Units.logEmbedding_fundSystem", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.DirichletTheorem", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NumberField.Units.fun_eq_repr", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.DirichletTheorem", "is_tactic_proof": false, "tactics": ["suffices", "calc", "rw"], "tactic_count": 3}
{"name": "NumberField.Units.exist_unique_eq_mul_prod", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.DirichletTheorem", "is_tactic_proof": true, "tactics": ["let", "have", "rw", "simp_rw", "rw", "exact", "refine", "simp", "rintro", "simp", "nth_rewrite", "rw"], "tactic_count": 12}
{"name": "NumberField.Units.closure_fundSystem_sup_torsion_eq_top", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.DirichletTheorem", "is_tactic_proof": true, "tactics": ["rw", "intro", "obtain", "exact"], "tactic_count": 4}
{"name": "NumberField.Units.equivFinRank", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.Units.Regulator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.Units.IsMaxRank", "kind": "abbrev", "module": "Mathlib.NumberTheory.NumberField.Units.Regulator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.Units.basisOfIsMaxRank", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.Units.Regulator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.Units.basisOfIsMaxRank_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.Regulator", "is_tactic_proof": true, "tactics": ["simp", "coe_basisOfPiSpaceOfLinearIndependent]"], "tactic_count": 2}
{"name": "NumberField.Units.span_basisOfIsMaxRank", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.Regulator", "is_tactic_proof": true, "tactics": ["rw", "congr"], "tactic_count": 2}
{"name": "NumberField.Units.finiteIndex_iff_sup_torsion_finiteIndex", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.Regulator", "is_tactic_proof": true, "tactics": ["refine", "rw", "refine", "rw", "exact"], "tactic_count": 5}
{"name": "NumberField.Units.isMaxRank_iff_closure_finiteIndex", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.Regulator", "is_tactic_proof": true, "tactics": ["classical", "have", "change", "rw", "have", "rw", "rw", "span_int_eq_addSubgroupClosure,", "rfl", "have", "rw", "refine", "rw", "rintro", "exact", "rw", "simp"], "tactic_count": 17}
{"name": "NumberField.Units.regOfFamily", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.Units.Regulator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.Units.regOfFamily_eq_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.Regulator", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NumberField.Units.regOfFamily_of_isMaxRank", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.Regulator", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NumberField.Units.regOfFamily_pos", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.Regulator", "is_tactic_proof": true, "tactics": ["classical", "rw", "exact"], "tactic_count": 3}
{"name": "NumberField.Units.regOfFamily_ne_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.Regulator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.Units.regOfFamily_ne_zero_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.Regulator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.Units.regOfFamily_eq_det'", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.Regulator", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "congr", "simp", "rw", "rwa"], "tactic_count": 6}
{"name": "NumberField.Units.abs_det_eq_abs_det", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.Regulator", "is_tactic_proof": true, "tactics": ["let", "let", "have", "congr_arg", "det_permute", "rw", "rw", "have", "congr_arg", "submatrix_succAbove_det_eq_negOnePow_submatrix_succAbove_det", "rw", "rw", "convert", "ext", "simp", "ext", "simp", "id_eq,", "rfl", "intro", "simp_rw", "rw", "exact"], "tactic_count": 23}
{"name": "NumberField.Units.regOfFamily_eq_det", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.Regulator", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NumberField.Units.finrank_mul_regOfFamily_eq_det", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.Regulator", "is_tactic_proof": true, "tactics": ["let", "let", "rw", "abs_mul,", "simp_rw", "rw", "congr", "rw", "rfl", "simp_rw", "f.apply_symm_apply,", "intro", "rw"], "tactic_count": 13}
{"name": "NumberField.Units.regulator", "kind": "definition", "module": "Mathlib.NumberTheory.NumberField.Units.Regulator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.Units.isMaxRank_fundSystem", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.Regulator", "is_tactic_proof": true, "tactics": ["classical", "convert", "rw"], "tactic_count": 3}
{"name": "NumberField.Units.basisOfIsMaxRank_fundSystem", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.Regulator", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "NumberField.Units.regulator_eq_regOfFamily_fundSystem", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.Regulator", "is_tactic_proof": true, "tactics": ["classical", "rw", "basisOfIsMaxRank_fundSystem]"], "tactic_count": 3}
{"name": "NumberField.Units.regulator_pos", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.Regulator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.Units.regulator_ne_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.Regulator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NumberField.Units.regulator_eq_det'", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.Regulator", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NumberField.Units.regulator_eq_det", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.Regulator", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NumberField.Units.finrank_mul_regulator_eq_det", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.Regulator", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NumberField.Units.regOfFamily_div_regOfFamily", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.Regulator", "is_tactic_proof": true, "tactics": ["classical", "by_cases", "have", "rw", "map_logEmbedding_sup_torsion", "map_logEmbedding_sup_torsion", "exact", "rw", "span_basisOfIsMaxRank", "rw", "have", "rw", "exact", "rwa", "finiteIndex_iff_sup_torsion_finiteIndex,"], "tactic_count": 15}
{"name": "NumberField.Units.regOfFamily_div_regulator", "kind": "theorem", "module": "Mathlib.NumberTheory.NumberField.Units.Regulator", "is_tactic_proof": true, "tactics": ["rw", "regOfFamily_div_regOfFamily", "closure_fundSystem_sup_torsion_eq_top,"], "tactic_count": 3}
{"name": "_private.Mathlib.NumberTheory.Ostrowski.0.tendsto_const_rpow_inv", "kind": "theorem", "module": "Mathlib.NumberTheory.Ostrowski", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.Ostrowski.0.tendsto_nat_rpow_inv", "kind": "theorem", "module": "Mathlib.NumberTheory.Ostrowski", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "_private.Mathlib.NumberTheory.Ostrowski.0.list_mul_sum", "kind": "theorem", "module": "Mathlib.NumberTheory.Ostrowski", "is_tactic_proof": true, "tactics": ["simp_rw", "congr", "simp"], "tactic_count": 3}
{"name": "_private.Mathlib.NumberTheory.Ostrowski.0.list_geom", "kind": "theorem", "module": "Mathlib.NumberTheory.Ostrowski", "is_tactic_proof": true, "tactics": ["rw", "simp", "let", "exact"], "tactic_count": 4}
{"name": "Rat.AbsoluteValue.eq_on_nat_iff_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.Ostrowski", "is_tactic_proof": true, "tactics": ["refine", "ext1", "rw"], "tactic_count": 3}
{"name": "Rat.AbsoluteValue.exists_nat_rpow_iff_isEquiv", "kind": "theorem", "module": "Mathlib.NumberTheory.Ostrowski", "is_tactic_proof": true, "tactics": ["rw", "refine", "ext1", "rw", "apply_natAbs_eq,"], "tactic_count": 5}
{"name": "Rat.AbsoluteValue.padic", "kind": "definition", "module": "Mathlib.NumberTheory.Ostrowski", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.AbsoluteValue.padic_eq_padicNorm", "kind": "theorem", "module": "Mathlib.NumberTheory.Ostrowski", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.AbsoluteValue.padic_le_one", "kind": "theorem", "module": "Mathlib.NumberTheory.Ostrowski", "is_tactic_proof": true, "tactics": ["simp", "exact_mod_cast"], "tactic_count": 2}
{"name": "Rat.AbsoluteValue.exists_minimal_nat_zero_lt_and_lt_one", "kind": "theorem", "module": "Mathlib.NumberTheory.Ostrowski", "is_tactic_proof": true, "tactics": ["obtain", "contrapose", "refine", "rcases", "simp", "simp", "set", "have", "exact"], "tactic_count": 9}
{"name": "Rat.AbsoluteValue.is_prime_of_minimal_nat_zero_lt_and_lt_one", "kind": "theorem", "module": "Mathlib.NumberTheory.Ostrowski", "is_tactic_proof": true, "tactics": ["rw", "constructor", "rw", "rintro", "simp", "rintro", "rw", "by_contra", "obtain", "refine", "rwa", "have", "have", "have", "have", "rw", "exact"], "tactic_count": 17}
{"name": "Rat.AbsoluteValue.eq_one_of_not_dvd", "kind": "theorem", "module": "Mathlib.NumberTheory.Ostrowski", "is_tactic_proof": true, "tactics": ["apply", "by_contra", "set", "set", "obtain", "is_prime_of_minimal_nat_zero_lt_and_lt_one", "have", "calc", "x", "apply", "rw", "push_cast", "exact", "apply", "simp", "gcongr", "simp", "exact", "apply", "calc", "simp", "gcongr", "all_goals", "have", "linarith"], "tactic_count": 25}
{"name": "Rat.AbsoluteValue.exists_pos_eq_pow_neg", "kind": "theorem", "module": "Mathlib.NumberTheory.Ostrowski", "is_tactic_proof": true, "tactics": ["have", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "Rat.AbsoluteValue.equiv_padic_of_bounded", "kind": "theorem", "module": "Mathlib.NumberTheory.Ostrowski", "is_tactic_proof": true, "tactics": ["obtain", "have", "have", "obtain", "simp_rw", "refine", "have", "rcases", "simp", "rcases", "simp", "padic_eq_padicNorm,", "rw", "simp", "field_simp", "by_contra", "apply", "rw", "rcases", "simpa"], "tactic_count": 20}
{"name": "Rat.AbsoluteValue.real", "kind": "definition", "module": "Mathlib.NumberTheory.Ostrowski", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.AbsoluteValue.real_eq_abs", "kind": "theorem", "module": "Mathlib.NumberTheory.Ostrowski", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.AbsoluteValue.apply_le_sum_digits", "kind": "theorem", "module": "Mathlib.NumberTheory.Ostrowski", "is_tactic_proof": true, "tactics": ["set", "set", "have", "lt_of_le_of_lt", "calc", "f", "simp", "refine", "dsimp", "replace", "push_cast", "rw", "refine", "simp", "exact"], "tactic_count": 15}
{"name": "Rat.AbsoluteValue.one_lt_of_not_bounded", "kind": "theorem", "module": "Mathlib.NumberTheory.Ostrowski", "is_tactic_proof": true, "tactics": ["contrapose", "intro", "have", "set", "calc", "f", "simp", "refine", "simp", "exact", "mul_le_of_le_one_right", "rw", "simp", "exact", "natLog_le_logb", "rcases", "simp", "have", "have", "calc", "f", "rw", "gcongr", "exact", "gcongr", "exact", "rw", "rcases", "simp", "refine", "nth_rw", "have", "exact"], "tactic_count": 33}
{"name": "_private.Mathlib.NumberTheory.Ostrowski.0.Rat.AbsoluteValue.expr_pos", "kind": "theorem", "module": "Mathlib.NumberTheory.Ostrowski", "is_tactic_proof": true, "tactics": ["apply", "linarith"], "tactic_count": 2}
{"name": "_private.Mathlib.NumberTheory.Ostrowski.0.Rat.AbsoluteValue.param_upperbound", "kind": "theorem", "module": "Mathlib.NumberTheory.Ostrowski", "is_tactic_proof": false, "tactics": ["have", "let", "calc", "f", "rw", "gcongr", "linarith", "simp", "gcongr", "exact", "rw", "exact", "apply", "le_of_pow_le_pow_left₀", "nth_rewrite", "rw", "rpow_mul", "mul_comm", "calc"], "tactic_count": 19}
{"name": "Rat.AbsoluteValue.le_pow_log", "kind": "theorem", "module": "Mathlib.NumberTheory.Ostrowski", "is_tactic_proof": false, "tactics": ["have", "nth_rw", "exact", "exact", "le_of_tendsto_of_tendsto", "eventually_atTop.mpr"], "tactic_count": 6}
{"name": "_private.Mathlib.NumberTheory.Ostrowski.0.Rat.AbsoluteValue.le_of_eq_pow", "kind": "theorem", "module": "Mathlib.NumberTheory.Ostrowski", "is_tactic_proof": true, "tactics": ["rw", "apply", "rw", "rpow_logb"], "tactic_count": 4}
{"name": "_private.Mathlib.NumberTheory.Ostrowski.0.Rat.AbsoluteValue.eq_of_eq_pow", "kind": "theorem", "module": "Mathlib.NumberTheory.Ostrowski", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.AbsoluteValue.equiv_real_of_unbounded", "kind": "theorem", "module": "Mathlib.NumberTheory.Ostrowski", "is_tactic_proof": true, "tactics": ["obtain", "have", "contrapose", "rcases", "rw", "set", "refine", "rcases", "obtain", "have", "simp", "exact", "linarith", "simp", "simp", "simp", "rw", "have", "rw", "have", "rw", "rwa"], "tactic_count": 22}
{"name": "Rat.AbsoluteValue.equiv_real_or_padic", "kind": "theorem", "module": "Mathlib.NumberTheory.Ostrowski", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "exact"], "tactic_count": 3}
{"name": "Rat.AbsoluteValue.not_real_isEquiv_padic", "kind": "theorem", "module": "Mathlib.NumberTheory.Ostrowski", "is_tactic_proof": true, "tactics": ["rw", "rintro", "apply_fun", "simp", "exact"], "tactic_count": 5}
{"name": "AddChar.tendsto_eval_one_sub_pow", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.AddChar", "is_tactic_proof": true, "tactics": ["refine", "simpa"], "tactic_count": 2}
{"name": "PadicInt.addChar_of_value_at_one", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.continuous_addChar_of_value_at_one", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.coe_addChar_of_value_at_one", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.addChar_of_value_at_one_def", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.AddChar", "is_tactic_proof": true, "tactics": ["change", "rw"], "tactic_count": 2}
{"name": "PadicInt.eq_addChar_of_value_at_one", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.continuousAddCharEquiv", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.continuousAddCharEquiv_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.continuousAddCharEquiv_symm_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.continuousAddCharEquiv_of_norm_mul", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.continuousAddCharEquiv_of_norm_mul_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.continuousAddCharEquiv_of_norm_mul_symm_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.AddChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicAlgCl", "kind": "abbrev", "module": "Mathlib.NumberTheory.Padics.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicAlgCl.isAlgebraic", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicAlgCl.instCoePadic", "kind": "instance", "module": "Mathlib.NumberTheory.Padics.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicAlgCl.coe_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicAlgCl.normedField", "kind": "instance", "module": "Mathlib.NumberTheory.Padics.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicAlgCl.isNonarchimedean", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicAlgCl.spectralNorm_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicAlgCl.norm_extends", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicAlgCl.instIsUltrametricDist", "kind": "instance", "module": "Mathlib.NumberTheory.Padics.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicAlgCl.valued", "kind": "instance", "module": "Mathlib.NumberTheory.Padics.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicAlgCl.valuation_def", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicAlgCl.valuation_coe", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicAlgCl.valuation_p", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.Complex", "is_tactic_proof": true, "tactics": ["rw", "ext", "rw"], "tactic_count": 3}
{"name": "PadicAlgCl.instRankOneNNRealV", "kind": "instance", "module": "Mathlib.NumberTheory.Padics.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicAlgCl.instUniformContinuousConstSMulPadic", "kind": "instance", "module": "Mathlib.NumberTheory.Padics.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicComplex", "kind": "abbrev", "module": "Mathlib.NumberTheory.Padics.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "termℂ_[_]", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_NumberTheory_Padics_Complex___macroRules_termℂ_[_]_1", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_NumberTheory_Padics_Complex___unexpand_PadicComplex_1", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicComplex.valued", "kind": "instance", "module": "Mathlib.NumberTheory.Padics.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicComplex.valuation_extends", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicComplex.coe_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicComplex.coe_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicComplex.instAlgebraPadic", "kind": "instance", "module": "Mathlib.NumberTheory.Padics.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicComplex.instIsScalarTowerPadicPadicAlgCl", "kind": "instance", "module": "Mathlib.NumberTheory.Padics.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicComplex.coe_natCast", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.Complex", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PadicComplex.valuation_p", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.Complex", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PadicComplex.instRankOneNNRealV", "kind": "instance", "module": "Mathlib.NumberTheory.Padics.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicComplex.rankOne_hom_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicComplex.instNormedField", "kind": "instance", "module": "Mathlib.NumberTheory.Padics.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicComplex.norm_def", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicComplex.norm_extends", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.Complex", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "PadicComplex.nnnorm_extends", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.Complex", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "PadicComplex.isNonarchimedean", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicComplexInt", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "term𝓞_ℂ_[_]", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_NumberTheory_Padics_Complex___macroRules_term𝓞_ℂ_[_]_1", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_NumberTheory_Padics_Complex___unexpand_PadicComplexInt_1", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicComplexInt.integers", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFactPrimeValNat", "kind": "instance", "module": "Mathlib.NumberTheory.Padics.HeightOneSpectrum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.int_algebraMap_injective", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.HeightOneSpectrum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.int_algebraMap_surjective", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.HeightOneSpectrum", "is_tactic_proof": true, "tactics": ["intro", "obtain", "exact"], "tactic_count": 3}
{"name": "Rat.IsIntegralClosure.intEquiv", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.HeightOneSpectrum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.IsIntegralClosure.intEquiv_apply_eq_ringOfIntegersEquiv", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.HeightOneSpectrum", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Rat.HeightOneSpectrum.natGenerator", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.HeightOneSpectrum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.HeightOneSpectrum.span_natGenerator", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.HeightOneSpectrum", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Rat.HeightOneSpectrum.natGenerator_dvd_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.HeightOneSpectrum", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
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{"name": "Rat.HeightOneSpectrum.valuation_equiv_padicValuation", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.HeightOneSpectrum", "is_tactic_proof": true, "tactics": ["simp", "natGenerator_dvd_iff,"], "tactic_count": 2}
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{"name": "Rat.HeightOneSpectrum.adicCompletionIntegers.coe_padicIntEquiv_symm_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.HeightOneSpectrum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "padic_polynomial_dist", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.Hensel", "is_tactic_proof": true, "tactics": ["let", "simp", "calc"], "tactic_count": 3}
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{"name": "_private.Mathlib.NumberTheory.Padics.Hensel.0.deriv_sq_norm_ne_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.Hensel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.Padics.Hensel.0.deriv_norm_ne_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.Hensel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "_private.Mathlib.NumberTheory.Padics.Hensel.0.T_lt_one", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.Hensel", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
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{"name": "_private.Mathlib.NumberTheory.Padics.Hensel.0.ih_gen", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.Hensel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "_private.Mathlib.NumberTheory.Padics.Hensel.0.calc_norm_le_one", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.Hensel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "_private.Mathlib.NumberTheory.Padics.Hensel.0.calc_eval_z'", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.Hensel", "is_tactic_proof": true, "tactics": ["have", "have", "obtain", "have", "simpa", "have", "calc", "exact"], "tactic_count": 8}
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{"name": "_private.Mathlib.NumberTheory.Padics.Hensel.0.ih_n", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.Hensel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.Padics.Hensel.0.newton_seq_aux", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.Hensel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.Padics.Hensel.0.newton_seq_gen", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.Hensel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.Padics.Hensel.0.termNewton_seq", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.Hensel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "_private.Mathlib.NumberTheory.Padics.Hensel.0.newton_seq_deriv_norm", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.Hensel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.Padics.Hensel.0.newton_seq_norm_le", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.Hensel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "_private.Mathlib.NumberTheory.Padics.Hensel.0.newton_seq_succ_dist", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.Hensel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.Padics.Hensel.0.newton_seq_dist_aux", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.Hensel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.Padics.Hensel.0.newton_seq_dist", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.Hensel", "is_tactic_proof": true, "tactics": ["have", "let", "rw"], "tactic_count": 3}
{"name": "_private.Mathlib.NumberTheory.Padics.Hensel.0.bound'", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.Hensel", "is_tactic_proof": true, "tactics": ["rw", "exact", "tendsto_const_nhds.mul"], "tactic_count": 3}
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{"name": "_private.Mathlib.NumberTheory.Padics.Hensel.0.bound'_sq", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.Hensel", "is_tactic_proof": true, "tactics": ["rw", "simp", "apply", "apply", "apply", "assumption"], "tactic_count": 6}
{"name": "_private.Mathlib.NumberTheory.Padics.Hensel.0.newton_seq_is_cauchy", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.Hensel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.Padics.Hensel.0.newton_cau_seq", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.Hensel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.Padics.Hensel.0.soln_gen", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.Hensel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.Padics.Hensel.0.termSoln", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.Hensel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.Padics.Hensel.0._aux_Mathlib_NumberTheory_Padics_Hensel___macroRules__private_Mathlib_NumberTheory_Padics_Hensel_0_termSoln_1", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.Hensel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.Padics.Hensel.0._aux_Mathlib_NumberTheory_Padics_Hensel___unexpand__private_Mathlib_NumberTheory_Padics_Hensel_0_soln_gen_1", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.Hensel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.Padics.Hensel.0.soln_spec", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.Hensel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.Padics.Hensel.0.soln_deriv_norm", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.Hensel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.Padics.Hensel.0.newton_seq_norm_tendsto_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.Hensel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.Padics.Hensel.0.newton_seq_dist_tendsto'", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.Hensel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.Padics.Hensel.0.eval_soln", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.Hensel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.Padics.Hensel.0.T_pos", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.Hensel", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "_private.Mathlib.NumberTheory.Padics.Hensel.0.newton_seq_succ_dist_weak", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.Hensel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.Padics.Hensel.0.newton_seq_dist_to_a", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.Hensel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.Padics.Hensel.0.newton_seq_dist_tendsto", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.Hensel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.Padics.Hensel.0.soln_dist_to_a", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.Hensel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.Padics.Hensel.0.soln_dist_to_a_lt_deriv", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.Hensel", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "_private.Mathlib.NumberTheory.Padics.Hensel.0.soln_unique", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.Hensel", "is_tactic_proof": false, "tactics": ["have", "calc", "let", "let", "simp", "have", "have", "by_contra", "have", "have", "lt_irrefl", "rw", "exact", "exact"], "tactic_count": 14}
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{"name": "_private.Mathlib.NumberTheory.Padics.Hensel.0.a_is_soln", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.Hensel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hensels_lemma", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.Hensel", "is_tactic_proof": true, "tactics": ["classical", "exact", "exact", "soln_unique"], "tactic_count": 4}
{"name": "PadicInt.norm_ascPochhammer_le", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.MahlerBasis", "is_tactic_proof": true, "tactics": ["let", "change", "have", "have", "obtain", "obtain", "obtain", "simpa", "refine", "sub_add_cancel", "simp_rw", "smul_eq_mul,", "exact"], "tactic_count": 13}
{"name": "PadicInt.instIsAddTorsionFree", "kind": "instance", "module": "Mathlib.NumberTheory.Padics.MahlerBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.instBinomialRing", "kind": "instance", "module": "Mathlib.NumberTheory.Padics.MahlerBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.continuous_multichoose", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.MahlerBasis", "is_tactic_proof": true, "tactics": ["simp", "fun_prop"], "tactic_count": 2}
{"name": "PadicInt.continuous_choose", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.MahlerBasis", "is_tactic_proof": true, "tactics": ["simp", "fun_prop"], "tactic_count": 2}
{"name": "mahler", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.MahlerBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mahler_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.MahlerBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mahler_natCast_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.MahlerBasis", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsUltrametricDist.norm_fwdDiff_iter_apply_le", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.MahlerBasis", "is_tactic_proof": true, "tactics": ["rw", "refine", "exact"], "tactic_count": 3}
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{"name": "PadicInt.mahlerTerm", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.MahlerBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.mahlerTerm_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.MahlerBasis", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PadicInt.norm_mahlerTerm", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.MahlerBasis", "is_tactic_proof": true, "tactics": ["apply", "rw", "refine", "refine", "simp"], "tactic_count": 5}
{"name": "PadicInt.mahlerTerm_one", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.MahlerBasis", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "PadicInt.norm_mahler_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.MahlerBasis", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PadicInt.mahlerSeries", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.MahlerBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.hasSum_mahlerSeries", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.MahlerBasis", "is_tactic_proof": true, "tactics": ["refine", "rw", "simpa"], "tactic_count": 3}
{"name": "PadicInt.mahlerSeries_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.MahlerBasis", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PadicInt.mahlerSeries_apply_nat", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.MahlerBasis", "is_tactic_proof": true, "tactics": ["have", "have", "simpa", "simp"], "tactic_count": 4}
{"name": "PadicInt.fwdDiff_mahlerSeries", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.MahlerBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.hasSum_mahler", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.MahlerBasis", "is_tactic_proof": true, "tactics": ["have", "hasSum_mahlerSeries", "convert", "refine", "simpa"], "tactic_count": 5}
{"name": "PadicInt.mahlerEquiv", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.MahlerBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.mahlerEquiv_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.MahlerBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.mahlerEquiv_symm_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.MahlerBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "termℤ_[_]", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_NumberTheory_Padics_PadicIntegers___macroRules_termℤ_[_]_1", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_NumberTheory_Padics_PadicIntegers___unexpand_PadicInt_1", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.instCoePadic", "kind": "instance", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.ext", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.subring", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.mem_subring_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.instCommRing", "kind": "instance", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.instInhabited", "kind": "instance", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.mk_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.coe_add", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.coe_mul", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.coe_neg", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.coe_sub", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.coe_one", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.coe_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.coe_eq_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PadicInt.coe_ne_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.coe_natCast", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.coe_intCast", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.Coe.ringHom", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.coe_pow", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.mk_coe", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PadicInt.coe_sum", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PadicInt.isOpenEmbedding_coe", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": true, "tactics": ["refine", "simpa"], "tactic_count": 2}
{"name": "PadicInt.inv", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.instCharZero", "kind": "instance", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.intCast_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PadicInt.ofIntSeq", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.instMetricSpace", "kind": "instance", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.instIsUltrametricDist", "kind": "instance", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.completeSpace", "kind": "instance", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.instNorm", "kind": "instance", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.norm_def", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.instNormedCommRing", "kind": "instance", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.instNormOneClass", "kind": "instance", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.instNormMulClass", "kind": "instance", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.instIsDomain", "kind": "instance", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.norm_le_one", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.nonarchimedean", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.norm_add_eq_max_of_ne", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.norm_eq_of_norm_add_lt_right", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.norm_eq_of_norm_add_lt_left", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.padic_norm_e_of_padicInt", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PadicInt.norm_intCast_eq_padic_norm", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PadicInt.norm_eq_padic_norm", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.norm_p", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.norm_p_pow", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PadicInt.one_le_norm_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PadicInt.norm_natCast_p_sub_one", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "_private.Mathlib.NumberTheory.Padics.PadicIntegers.0.PadicInt.cauSeq_to_rat_cauSeq", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.complete", "kind": "instance", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.exists_pow_neg_lt", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": true, "tactics": ["obtain", "use", "rw", "rw", "apply", "norm_cast", "apply", "convert", "exact", "exact"], "tactic_count": 10}
{"name": "PadicInt.exists_pow_neg_lt_rat", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": true, "tactics": ["obtain", "use", "rw", "exact"], "tactic_count": 4}
{"name": "PadicInt.norm_int_lt_one_iff_dvd", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.norm_int_le_pow_iff_dvd", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.norm_natCast_eq_one_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PadicInt.norm_natCast_lt_one_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PadicInt.norm_intCast_eq_one_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PadicInt.norm_intCast_lt_one_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PadicInt.valuation_coe_nonneg", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": true, "tactics": ["obtain", "simp", "have", "rwa", "exact"], "tactic_count": 5}
{"name": "PadicInt.valuation", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.valuation_coe", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PadicInt.valuation_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PadicInt.valuation_one", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PadicInt.valuation_p", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PadicInt.le_valuation_add", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": true, "tactics": ["zify"], "tactic_count": 1}
{"name": "PadicInt.valuation_mul", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": true, "tactics": ["zify"], "tactic_count": 1}
{"name": "PadicInt.valuation_pow", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": true, "tactics": ["zify"], "tactic_count": 1}
{"name": "PadicInt.norm_eq_zpow_neg_valuation", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PadicInt.valuation_p_pow_mul", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PadicInt.mul_inv", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.inv_mul", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PadicInt.isUnit_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.norm_lt_one_add", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.norm_lt_one_mul", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.mem_nonunits", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PadicInt.not_isUnit_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "PadicInt.mkUnits", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.val_mkUnits", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.mkUnits_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.norm_units", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.unitCoeff", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.unitCoeff_coe", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.unitCoeff_spec", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": true, "tactics": ["apply", "push_cast", "rw", "simp", "exact"], "tactic_count": 5}
{"name": "PadicInt.isUnit_den", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": true, "tactics": ["rw", "apply", "rw", "intro", "have", "congr", "rw_mod_cast", "rw", "have", "calc", "have", "simp", "exact", "apply", "rwa"], "tactic_count": 15}
{"name": "PadicInt.norm_le_pow_iff_le_valuation", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "PadicInt.mem_span_pow_iff_le_valuation", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": true, "tactics": ["rw", "constructor", "rintro", "suffices", "rw", "exact", "contrapose", "rw", "nth_rewrite", "simpa"], "tactic_count": 10}
{"name": "PadicInt.norm_le_pow_iff_mem_span_pow", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": true, "tactics": ["by_cases", "subst", "simp", "exact", "rw"], "tactic_count": 5}
{"name": "PadicInt.norm_le_pow_iff_norm_lt_pow_add_one", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PadicInt.norm_lt_pow_iff_norm_le_pow_sub_one", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PadicInt.norm_lt_one_iff_dvd", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": true, "tactics": ["have", "rw", "rw", "simp"], "tactic_count": 4}
{"name": "PadicInt.pow_p_dvd_int_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PadicInt.instIsLocalRing", "kind": "instance", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.p_nonunit", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "PadicInt.maximalIdeal_eq_span_p", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": true, "tactics": ["apply", "intro", "simp", "rwa", "rw", "exact"], "tactic_count": 6}
{"name": "PadicInt.prime_p", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": true, "tactics": ["rw", "infer_instance", "exact"], "tactic_count": 3}
{"name": "PadicInt.irreducible_p", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.instIsDiscreteValuationRing", "kind": "instance", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.ideal_eq_span_pow_p", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.instIsAdicCompleteMaximalIdeal", "kind": "instance", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.algebra", "kind": "instance", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.algebraMap_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.isFractionRing", "kind": "instance", "module": "Mathlib.NumberTheory.Padics.PadicIntegers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "padicNorm", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.PadicNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "padicNorm.eq_zpow_of_nonzero", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNorm", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "padicNorm.nonneg", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "padicNorm.zero", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNorm", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "padicNorm.one", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNorm", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "padicNorm.padicNorm_p", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNorm", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "padicNorm.padicNorm_p_of_prime", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "padicNorm.padicNorm_of_prime_of_ne", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNorm", "is_tactic_proof": true, "tactics": ["have", "rw", "simp"], "tactic_count": 3}
{"name": "padicNorm.padicNorm_p_lt_one", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNorm", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "padicNorm.padicNorm_p_lt_one_of_prime", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "padicNorm.values_discrete", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "padicNorm.neg", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "padicNorm.nonzero", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNorm", "is_tactic_proof": true, "tactics": ["rw", "apply", "exact"], "tactic_count": 3}
{"name": "padicNorm.zero_of_padicNorm_eq_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNorm", "is_tactic_proof": true, "tactics": ["apply", "unfold", "apply", "apply", "exact"], "tactic_count": 5}
{"name": "padicNorm.mul", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "padicNorm.div", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "padicNorm.of_int", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNorm", "is_tactic_proof": true, "tactics": ["obtain", "simp", "rw", "exact"], "tactic_count": 4}
{"name": "_private.Mathlib.NumberTheory.Padics.PadicNorm.0.padicNorm.nonarchimedean_aux", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "padicNorm.nonarchimedean", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNorm", "is_tactic_proof": true, "tactics": ["wlog", "rw", "exact", "exact"], "tactic_count": 4}
{"name": "padicNorm.triangle_ineq", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "padicNorm.sub", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNorm", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "padicNorm.add_eq_max_of_ne", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNorm", "is_tactic_proof": true, "tactics": ["wlog", "rw", "exact", "have", "calc", "padicNorm", "have", "apply", "intro", "rw", "exact", "have", "apply", "apply", "rwa"], "tactic_count": 15}
{"name": "padicNorm.instIsAbsoluteValueRat", "kind": "instance", "module": "Mathlib.NumberTheory.Padics.PadicNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "padicNorm.dvd_iff_norm_le", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNorm", "is_tactic_proof": true, "tactics": ["unfold", "norm_cast", "simp", "rw", "norm_cast", "rw", "norm_cast", "apply", "exact_mod_cast", "exact_mod_cast"], "tactic_count": 10}
{"name": "padicNorm.int_eq_one_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNorm", "is_tactic_proof": true, "tactics": ["nth_rw", "simp", "constructor", "intro", "rw", "exact", "exact", "simp", "split_ifs", "rw", "intro", "exact", "have", "rw", "have", "intro", "rw"], "tactic_count": 17}
{"name": "padicNorm.int_lt_one_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNorm", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "padicNorm.of_nat", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "padicNorm.nat_eq_one_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNorm", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "padicNorm.nat_lt_one_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNorm", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "padicNorm.not_int_of_not_padic_int", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNorm", "is_tactic_proof": true, "tactics": ["contrapose", "rw", "apply"], "tactic_count": 3}
{"name": "padicNorm.sum_lt", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNorm", "is_tactic_proof": true, "tactics": ["classical", "refine", "rintro", "by_cases", "rw", "exact", "lt_of_le_of_lt", "simp_all"], "tactic_count": 8}
{"name": "padicNorm.sum_le", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNorm", "is_tactic_proof": true, "tactics": ["classical", "refine", "rintro", "by_cases", "rw", "exact", "padicNorm.nonarchimedean.trans", "simp_all"], "tactic_count": 8}
{"name": "padicNorm.sum_lt'", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNorm", "is_tactic_proof": true, "tactics": ["obtain", "simp", "exact"], "tactic_count": 3}
{"name": "padicNorm.sum_le'", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNorm", "is_tactic_proof": true, "tactics": ["obtain", "simp", "exact"], "tactic_count": 3}
{"name": "Rat.padicValuation", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.padicValuation", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.padicValuation_cast", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.padicValuation_eq_zero_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Int.padicValuation_eq_zero_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Rat.padicValuation_self", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Int.padicValuation_self", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Int.padicValuation_le_one", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": ["simp", "split_ifs", "simp", "rw"], "tactic_count": 4}
{"name": "Int.padicValuation_eq_one_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": ["simp", "split_ifs", "simp_all", "rw", "simp_all"], "tactic_count": 5}
{"name": "Int.padicValuation_lt_one_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Rat.padicValuation_le_one_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": ["nth_rw", "rcases", "simp", "simp", "rcases", "simp", "rw", "exfalso", "rw", "rw", "exact", "simp"], "tactic_count": 12}
{"name": "Rat.surjective_padicValuation", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["intro", "induction", "zero", "coe", "x", "induction", "ofAdd", "simp_rw", "rcases", "exact", "exact"], "tactic_count": 11}
{"name": "PadicSeq", "kind": "abbrev", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicSeq.stationary", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicSeq.stationaryPoint", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicSeq.stationaryPoint_spec", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicSeq.norm", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicSeq.norm_zero_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["constructor", "intro", "by_contra", "unfold", "split_ifs", "apply", "intro", "exists", "intro", "have", "simpa", "intro", "simp"], "tactic_count": 13}
{"name": "PadicSeq.equiv_zero_of_val_eq_of_equiv_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicSeq.norm_nonzero_of_not_equiv_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicSeq.norm_eq_norm_app_of_nonzero", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicSeq.not_limZero_const_of_nonzero", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicSeq.not_equiv_zero_const_of_nonzero", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicSeq.norm_nonneg", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "PadicSeq.lift_index_left_left", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["apply", "apply", "exact"], "tactic_count": 3}
{"name": "PadicSeq.lift_index_left", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["apply", "apply", "apply", "apply", "exact"], "tactic_count": 5}
{"name": "PadicSeq.lift_index_right", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["apply", "apply", "apply", "apply", "exact"], "tactic_count": 5}
{"name": "PadicSeq.valuation", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicSeq.norm_eq_zpow_neg_valuation", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["rw", "intro", "apply", "intro", "use", "intro", "rw", "simpa"], "tactic_count": 8}
{"name": "PadicSeq.val_eq_iff_norm_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["rw", "exact", "exact"], "tactic_count": 3}
{"name": "PadicSeq.norm_mul", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["classical", "exact", "have", "simp", "have", "simp", "unfold", "have", "simp", "rw", "apply"], "tactic_count": 11}
{"name": "PadicSeq.eq_zero_iff_equiv_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicSeq.ne_zero_iff_nequiv_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicSeq.norm_const", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["obtain", "simp", "simp"], "tactic_count": 3}
{"name": "PadicSeq.norm_values_discrete", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["let", "simpa"], "tactic_count": 2}
{"name": "PadicSeq.norm_one", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["have", "simp"], "tactic_count": 2}
{"name": "_private.Mathlib.NumberTheory.Padics.PadicNumbers.0.PadicSeq.norm_eq_of_equiv_aux", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["have", "obtain", "let", "have", "have", "rw", "have", "rw", "have", "apply", "apply", "apply", "exact"], "tactic_count": 13}
{"name": "_private.Mathlib.NumberTheory.Padics.PadicNumbers.0.PadicSeq.norm_eq_of_equiv", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["by_contra", "cases", "inl", "inr", "apply", "exact"], "tactic_count": 6}
{"name": "PadicSeq.norm_equiv", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["classical", "exact", "have", "simp", "have", "unfold"], "tactic_count": 6}
{"name": "_private.Mathlib.NumberTheory.Padics.PadicNumbers.0.PadicSeq.norm_nonarchimedean_aux", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["unfold", "split_ifs", "rw", "apply"], "tactic_count": 4}
{"name": "PadicSeq.norm_nonarchimedean", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["classical", "exact", "have", "simpa", "have", "change", "change", "have", "have", "have", "rw", "have", "change", "change", "have", "have", "have", "rw"], "tactic_count": 18}
{"name": "PadicSeq.norm_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["classical", "exact", "have", "simp", "have", "simp", "let", "have", "apply", "apply", "exact", "have", "apply", "apply", "exact", "rw"], "tactic_count": 16}
{"name": "PadicSeq.norm_neg", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicSeq.norm_eq_of_add_equiv_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["have", "have", "have", "simpa"], "tactic_count": 4}
{"name": "PadicSeq.add_eq_max_of_ne", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["classical", "have", "exact", "have", "have", "have", "have", "rw", "have", "have", "have", "have", "rw", "unfold", "split_ifs", "rw", "rw", "exact"], "tactic_count": 18}
{"name": "Padic", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "termℚ_[_]", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_NumberTheory_Padics_PadicNumbers___macroRules_termℚ_[_]_1", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_NumberTheory_Padics_PadicNumbers___unexpand_Padic_1", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Padic.field", "kind": "instance", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Padic.instInhabited", "kind": "instance", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Padic.instCommRing", "kind": "instance", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Padic.instRing", "kind": "instance", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Padic.instZero", "kind": "instance", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Padic.instOne", "kind": "instance", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Padic.instAdd", "kind": "instance", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Padic.instMul", "kind": "instance", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Padic.instSub", "kind": "instance", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Padic.instNeg", "kind": "instance", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Padic.instDiv", "kind": "instance", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Padic.instAddCommGroup", "kind": "instance", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Padic.mk", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Padic.zero_def", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Padic.mk_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Padic.const_equiv", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Padic.coe_inj", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Padic.instCharZero", "kind": "instance", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Padic.coe_add", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Padic.coe_neg", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Padic.coe_mul", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Padic.coe_sub", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Padic.coe_div", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Padic.coe_one", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Padic.coe_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "padicNormE", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "padicNormE.defn", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": ["dsimp", "suffices", "by_contra", "obtain", "rcases", "have", "rw", "exact", "unfold", "apply", "cases", "inl", "inr", "have", "rw", "exact"], "tactic_count": 16}
{"name": "padicNormE.nonarchimedean'", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "padicNormE.add_eq_max_of_ne'", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "padicNormE.eq_padic_norm'", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "padicNormE.image'", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Padic.rat_dense'", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.Padics.PadicNumbers.0.Padic.div_nat_pos", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Padic.limSeq", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Padic.exi_rat_seq_conv", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["refine", "have", "refine", "rw", "apply", "exact", "apply", "simpa"], "tactic_count": 8}
{"name": "Padic.exi_rat_seq_conv_cauchy", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.Padics.PadicNumbers.0.Padic.lim'", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.Padics.PadicNumbers.0.Padic.lim", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Padic.complete'", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Padic.complete''", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["obtain", "refine", "obtain", "refine", "rw", "exact"], "tactic_count": 6}
{"name": "Padic.instDist", "kind": "instance", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Padic.instIsUltrametricDist", "kind": "instance", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Padic.metricSpace", "kind": "instance", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Padic.instNorm", "kind": "instance", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Padic.normedField", "kind": "instance", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Padic.isAbsoluteValue", "kind": "instance", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Padic.rat_dense", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Padic.denseRange_ratCast", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["intro", "rw", "exact"], "tactic_count": 3}
{"name": "Padic.padicNormE.mul", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Padic.padicNormE.is_norm", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Padic.nonarchimedean", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["dsimp", "exact"], "tactic_count": 2}
{"name": "Padic.add_eq_max_of_ne", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["dsimp", "have", "exact"], "tactic_count": 3}
{"name": "Padic.eq_padicNorm", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "Padic.norm_p", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["rw", "rw", "simp"], "tactic_count": 3}
{"name": "Padic.norm_p_lt_one", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Padic.norm_p_zpow", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Padic.norm_p_pow", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Padic.instNontriviallyNormedField", "kind": "instance", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Padic.padicNormE.image", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Padic.padicNormE.is_rat", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["classical", "exact", "let"], "tactic_count": 3}
{"name": "Padic.ratNorm", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Padic.eq_ratNorm", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Padic.norm_rat_le_one", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Padic.norm_int_le_one", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Padic.norm_intCast_lt_one_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["constructor", "intro", "contrapose", "apply", "rw", "calc", "rintro", "push_cast", "rw", "calc", "rw", "exact"], "tactic_count": 12}
{"name": "Padic.norm_natCast_lt_one_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Padic.norm_intCast_eq_one_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Padic.norm_natCast_eq_one_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Padic.norm_int_le_pow_iff_dvd", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["have", "rw", "norm_cast", "rw"], "tactic_count": 4}
{"name": "Padic.norm_eq_of_norm_add_lt_right", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Padic.norm_eq_of_norm_add_lt_left", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Padic.norm_eq_of_norm_sub_lt_right", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["rw", "apply", "simp"], "tactic_count": 3}
{"name": "Padic.norm_eq_of_norm_sub_lt_left", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["rw", "apply", "simpa"], "tactic_count": 3}
{"name": "Padic.norm_natCast_p_sub_one", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Padic.complete", "kind": "instance", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Padic.padicNormE_lim_le", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["obtain", "calc"], "tactic_count": 2}
{"name": "Padic.instCompleteSpace", "kind": "instance", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["apply", "intro", "let", "refine", "rcases", "have", "simp", "exact"], "tactic_count": 8}
{"name": "Padic.valuation", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Padic.valuation_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Padic.norm_eq_zpow_neg_valuation", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["refine", "change", "rw", "rw", "apply", "contrapose", "apply", "simpa"], "tactic_count": 8}
{"name": "Padic.valuation_ratCast", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["rcases", "simp", "refine", "neg_injective", "rw", "exact"], "tactic_count": 6}
{"name": "Padic.valuation_intCast", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Padic.valuation_natCast", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Padic.valuation_ofNat", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Padic.valuation_one", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Padic.valuation_p", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Padic.le_valuation_add", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["by_cases", "simpa", "by_cases", "simpa", "have", "simpa", "zpow_le_zpow_iff_right₀"], "tactic_count": 7}
{"name": "Padic.valuation_mul", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["have", "have", "have", "rwa", "zpow_add₀"], "tactic_count": 5}
{"name": "Padic.valuation_inv", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["obtain", "simp", "have", "have", "have", "rwa", "zpow_right_inj₀"], "tactic_count": 7}
{"name": "Padic.valuation_pow", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Padic.valuation_zpow", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Padic.addValuationDef", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Padic.AddValuation.map_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Padic.AddValuation.map_one", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Padic.AddValuation.map_mul", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["simp", "by_cases", "rw", "by_cases", "rw", "rw"], "tactic_count": 6}
{"name": "Padic.AddValuation.map_add", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["simp", "by_cases", "rw", "exact", "by_cases", "rw", "exact", "by_cases", "rw", "exact", "rw", "exact"], "tactic_count": 12}
{"name": "Padic.mulValuation", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Padic.comap_mulValuation_eq_padicValuation", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Padic.comap_mulValuation_eq_int_padicValuation", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Padic.norm_eq_zpow_log_mulValuation", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Padic.addValuation", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Padic.addValuation.apply", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Padic.norm_le_pow_iff_norm_lt_pow_add_one", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["have", "by_cases", "simp", "rw", "have", "have", "rw"], "tactic_count": 7}
{"name": "Padic.norm_lt_pow_iff_norm_le_pow_sub_one", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Padic.norm_le_one_iff_val_nonneg", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicNumbers", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "rw", "exact"], "tactic_count": 4}
{"name": "padicValNat.self", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "padicValNat.eq_zero_of_not_dvd", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "padicValNat.maxPowDiv_eq_emultiplicity", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["apply", "intro", "apply", "simp"], "tactic_count": 4}
{"name": "padicValNat.maxPowDiv_eq_multiplicity", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["exact_mod_cast"], "tactic_count": 1}
{"name": "padicValNat.padicValNat_eq_maxPowDiv", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "rw", "exact", "rcases", "interval_cases", "simp", "dsimp", "rw", "simp"], "tactic_count": 10}
{"name": "padicValInt", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "padicValInt.of_ne_one_ne_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "padicValInt.zero", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "padicValInt.one", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "padicValInt.of_nat", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "padicValInt.self", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "padicValInt.eq_zero_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "padicValInt.eq_zero_of_not_dvd", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "padicValRat", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "padicValRat_def", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "padicValRat.neg", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "padicValRat.zero", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "padicValRat.one", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "padicValRat.of_int", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "padicValRat.of_int_multiplicity", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "padicValRat.multiplicity_sub_multiplicity", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "padicValRat.of_nat", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "padicValRat.self", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "zero_le_padicValRat_of_nat", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "padicValRat_of_nat", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "padicValNat_self", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "one_le_padicValNat_of_dvd", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "dvd_iff_padicValNat_ne_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "padicValRat.finite_int_prime_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "padicValRat.defn", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["have", "let", "rw", "simp", "rw", "rw", "simp_rw", "ring", "simpa", "simpa"], "tactic_count": 10}
{"name": "padicValRat.mul", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": false, "tactics": ["have", "have", "have", "have", "rw", "conv_rhs", "rw", "ring", "simp", "simp"], "tactic_count": 10}
{"name": "padicValRat.pow", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "padicValRat.inv", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "rw"], "tactic_count": 3}
{"name": "padicValRat.div", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "padicValRat.padicValRat_le_padicValRat_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["have", "have", "conv", "lhs", "rw", "padicValRat.defn", "le_sub_iff_add_le]", "norm_cast", "rw", "multiplicity_mul"], "tactic_count": 10}
{"name": "padicValRat.le_padicValRat_add_of_le", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "padicValRat.min_le_padicValRat_add", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "padicValRat.add_eq_min", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["have", "have", "have", "rw", "rw", "omega"], "tactic_count": 6}
{"name": "padicValRat.add_eq_of_lt", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "padicValRat.lt_add_of_lt", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "padicValRat.self_pow_inv", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["rw", "mul_one]"], "tactic_count": 2}
{"name": "padicValRat.sum_pos_of_pos", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "by_cases", "rw", "exact", "refine", "refine", "exact"], "tactic_count": 10}
{"name": "padicValRat.lt_sum_of_lt", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["induction", "singleton", "rw", "exact", "cons", "rw", "exact", "padicValRat.lt_add_of_lt"], "tactic_count": 8}
{"name": "padicValNat.mul", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "padicValNat.div_of_dvd", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simp", "obtain", "obtain", "rw"], "tactic_count": 5}
{"name": "padicValNat.div", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "padicValNat.pow", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "padicValNat.prime_pow", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "padicValNat.div_pow", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "padicValNat.div'", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "dvd_of_one_le_padicValNat", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["by_contra", "rw", "exact"], "tactic_count": 3}
{"name": "pow_padicValNat_dvd", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "apply", "rw"], "tactic_count": 4}
{"name": "padicValNat_dvd_iff_le", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "padicValNat_dvd_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["rcases", "exact", "rw"], "tactic_count": 3}
{"name": "pow_succ_padicValNat_not_dvd", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "padicValNat_primes", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "padicValNat_prime_prime_pow", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "padicValNat_mul_pow_left", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["rw", "padicValNat_prime_prime_pow"], "tactic_count": 2}
{"name": "padicValNat_mul_pow_right", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "padicValNat_le_nat_log", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rcases", "simp", "simp", "exact"], "tactic_count": 6}
{"name": "padicValNat_add_le_self", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "rcases", "have", "calc", "rw", "calc", "rw", "lia"], "tactic_count": 8}
{"name": "nat_log_eq_padicValNat_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Nat.log_ne_padicValNat_succ", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["rw", "rintro", "rw", "rw", "refine", "exact"], "tactic_count": 6}
{"name": "Nat.max_log_padicValNat_succ_eq_log_succ", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": false, "tactics": ["apply", "rw", "intro", "replace", "rw"], "tactic_count": 5}
{"name": "range_pow_padicValNat_subset_divisors", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["intro", "simp", "obtain", "rw", "exact"], "tactic_count": 5}
{"name": "range_pow_padicValNat_subset_divisors'", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simp", "intro", "simp", "obtain", "rw", "refine", "exact"], "tactic_count": 8}
{"name": "padicValNat_factorial_mul", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["apply", "rw", "padicValNat_eq_emultiplicity", "exact"], "tactic_count": 4}
{"name": "padicValNat_eq_zero_of_mem_Ioo", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "padicValNat_factorial_mul_add", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "hn", "padicValNat_eq_zero_of_mem_Ioo", "zero_add]"], "tactic_count": 7}
{"name": "padicValNat_mul_div_factorial", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["nth_rw", "exact"], "tactic_count": 2}
{"name": "padicValNat_factorial", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["exact_mod_cast"], "tactic_count": 1}
{"name": "sub_one_mul_padicValNat_factorial", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["rw", "nth_rw", "rw", "sub_one_mul_sum_log_div_pow_eq_sub_sum_digits,"], "tactic_count": 4}
{"name": "sub_one_mul_padicValNat_factorial_lt_of_ne_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "have", "exact"], "tactic_count": 4}
{"name": "padicValNat_factorial_lt_of_ne_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["apply", "conv_lhs", "gcongr", "exact"], "tactic_count": 4}
{"name": "padicValNat_factorial_le", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "exact"], "tactic_count": 3}
{"name": "padicValNat_choose", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["exact_mod_cast"], "tactic_count": 1}
{"name": "padicValNat_choose'", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["exact_mod_cast"], "tactic_count": 1}
{"name": "sub_one_mul_padicValNat_choose_eq_sub_sum_digits'", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["have", "simp", "rw", "padicValNat.mul", "simp", "rw", "tsub_tsub_assoc"], "tactic_count": 7}
{"name": "sub_one_mul_padicValNat_choose_eq_sub_sum_digits", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["convert", "all_goals"], "tactic_count": 2}
{"name": "padicValInt_dvd_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "padicValInt_dvd", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "padicValInt_self", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "padicValInt.mul", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "rw"], "tactic_count": 2}
{"name": "padicValInt_mul_eq_succ", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "padicValNat", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.PadicVal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "padicValNat_def'", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Defs", "is_tactic_proof": false, "tactics": ["simp", "emultiplicity,", "convert"], "tactic_count": 3}
{"name": "padicValNat_def", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "padicValNat_eq_emultiplicity", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact_mod_cast"], "tactic_count": 2}
{"name": "padicValNat.zero", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "padicValNat.one", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "padicValNat.eq_zero_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "le_emultiplicity_iff_replicate_subperm_primeFactorsList", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_padicValNat_iff_replicate_subperm_primeFactorsList", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.PadicVal.Defs", "is_tactic_proof": true, "tactics": ["rw", "padicValNat_def"], "tactic_count": 2}
{"name": "PadicInt.totallyBounded_univ", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.ProperSpace", "is_tactic_proof": true, "tactics": ["refine", "obtain", "refine", "simp", "refine", "simpa", "exact"], "tactic_count": 7}
{"name": "PadicInt.compactSpace", "kind": "instance", "module": "Mathlib.NumberTheory.Padics.ProperSpace", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Padic.instProperSpace", "kind": "instance", "module": "Mathlib.NumberTheory.Padics.ProperSpace", "is_tactic_proof": true, "tactics": ["suffices", "have", "simp", "refine", "simpa"], "tactic_count": 5}
{"name": "PadicInt.modPart", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.modPart_lt_p", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": true, "tactics": ["convert", "simp", "exact"], "tactic_count": 3}
{"name": "PadicInt.modPart_nonneg", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.norm_sub_modPart_aux", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": true, "tactics": ["rw", "simp", "have", "simp", "add_zero]", "push_cast", "rw", "suffices", "rw", "simp", "apply", "apply", "rw", "apply", "rw", "exact"], "tactic_count": 16}
{"name": "PadicInt.norm_sub_modPart", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": true, "tactics": ["let", "rw", "suffices", "convert", "simp", "apply", "simp", "norm_cast", "simp", "exact"], "tactic_count": 10}
{"name": "PadicInt.exists_mem_range_of_norm_rat_le_one", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.zmod_congr_of_sub_mem_span_aux", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": true, "tactics": ["rw", "rw", "rw", "have", "rwa", "pow_p_dvd_int_iff]"], "tactic_count": 6}
{"name": "PadicInt.zmod_congr_of_sub_mem_span", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "PadicInt.zmod_congr_of_sub_mem_max_ideal", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": true, "tactics": ["rw", "have", "simp", "specialize", "apply_fun", "simp", "simpa"], "tactic_count": 7}
{"name": "PadicInt.exists_mem_range", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": true, "tactics": ["simp", "obtain", "have", "rw", "calc", "obtain", "lift", "use", "constructor", "exact", "simp", "rw", "apply", "apply", "simpa"], "tactic_count": 15}
{"name": "PadicInt.existsUnique_mem_range", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": true, "tactics": ["obtain", "use", "have", "rwa"], "tactic_count": 4}
{"name": "PadicInt.zmodRepr", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.zmodRepr_spec", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.zmodRepr_unique", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.zmodRepr_lt_p", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.sub_zmodRepr_mem", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.zmodRepr_eq_zero_of_dvd", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "PadicInt.zmodRepr_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.norm_sub_zmodRepr_lt_one", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "PadicInt.norm_natCast_zmodRepr_eq_one_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": true, "tactics": ["rcases", "rw", "have", "constructor", "exact", "exact"], "tactic_count": 6}
{"name": "PadicInt.zmodRepr_eq_zero_iff_dvd", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "PadicInt.norm_natCast_zmodRepr_eq_one_iff_ne", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "PadicInt.norm_natCast_zmodRepr_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "PadicInt.zmodRepr_natCast_zmodRepr", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "PadicInt.norm_natCast_zmodRepr_eq_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": true, "tactics": ["rcases", "simp_all", "rw", "simp"], "tactic_count": 4}
{"name": "PadicInt.zmodRepr_natCast", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": true, "tactics": ["nth_rw", "apply", "exact", "simp"], "tactic_count": 4}
{"name": "PadicInt.zmodRepr_natCast_of_lt", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PadicInt.zmodRepr_natCast_ofNat", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": true, "tactics": ["convert", "rcases"], "tactic_count": 2}
{"name": "PadicInt.zmodRepr_units_ne_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "PadicInt.toZModHom", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.toZMod", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.toZMod_spec", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": true, "tactics": ["convert", "dsimp", "rcases", "change", "rw", "apply", "simpa"], "tactic_count": 7}
{"name": "PadicInt.ker_toZMod", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": true, "tactics": ["ext", "rw", "constructor", "intro", "simpa", "intro", "rw", "dsimp", "convert", "norm_cast", "apply"], "tactic_count": 11}
{"name": "PadicInt.val_toZMod_eq_zmodRepr", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.zmodRepr_mul", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PadicInt.residueField", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.appr", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.appr_lt", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "simp", "have", "split_ifs", "apply", "calc", "apply", "apply", "apply", "apply", "rw", "apply"], "tactic_count": 14}
{"name": "PadicInt.appr_mono", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": true, "tactics": ["apply", "intro", "dsimp", "split_ifs", "apply"], "tactic_count": 5}
{"name": "PadicInt.dvd_appr_sub_appr", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": true, "tactics": ["obtain", "induction", "zero", "succ", "rw", "dsimp", "split_ifs", "exact", "rw", "apply", "apply", "apply"], "tactic_count": 12}
{"name": "PadicInt.appr_spec", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": true, "tactics": ["simp", "induction", "zero", "succ", "intro", "dsimp", "split_ifs", "rw", "apply", "push_cast", "rw", "obtain", "simp", "have", "rintro", "simp", "contradiction", "conv_rhs", "congr", "simp", "rw", "rw", "apply", "obtain", "simp", "rw", "suffices", "rw", "apply", "lift", "rw", "exact", "simp", "rw", "exact"], "tactic_count": 35}
{"name": "PadicInt.toZMod_eq_residueField_comp_residue", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.toZModPow", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.ker_toZModPow", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": true, "tactics": ["ext", "rw", "constructor", "intro", "suffices", "convert", "simp", "dsimp", "rw", "apply", "intro", "rw", "dsimp", "rw", "apply"], "tactic_count": 15}
{"name": "PadicInt.zmod_cast_comp_toZModPow", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": true, "tactics": ["apply", "ext", "rw", "simp", "simp", "dsimp", "rw", "rw", "apply", "rw", "rcases", "use", "rw"], "tactic_count": 13}
{"name": "PadicInt.cast_toZModPow", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "PadicInt.denseRange_natCast", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": true, "tactics": ["intro", "rw", "intro", "obtain", "use", "rw", "apply", "rw", "apply"], "tactic_count": 9}
{"name": "PadicInt.denseRange_intCast", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": true, "tactics": ["intro", "refine", "exact", "intro", "apply", "exact"], "tactic_count": 6}
{"name": "PadicInt.nthHom", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.nthHom_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PadicInt.pow_dvd_nthHom_sub", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": true, "tactics": ["specialize", "rw", "dsimp", "rw", "simp"], "tactic_count": 5}
{"name": "PadicInt.isCauSeq_nthHom", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": true, "tactics": ["intro", "obtain", "use", "intro", "refine", "beta_reduce", "norm_cast", "rw", "exact"], "tactic_count": 9}
{"name": "PadicInt.nthHomSeq", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.nthHomSeq_one", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": true, "tactics": ["intro", "change", "use", "intro", "haveI", "suffices", "rw"], "tactic_count": 7}
{"name": "PadicInt.nthHomSeq_add", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": true, "tactics": ["intro", "obtain", "use", "intro", "dsimp", "apply", "rw", "dsimp", "simp", "rw", "simp"], "tactic_count": 11}
{"name": "PadicInt.nthHomSeq_mul", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": true, "tactics": ["intro", "obtain", "use", "intro", "dsimp", "apply", "rw", "dsimp", "simp", "rw"], "tactic_count": 10}
{"name": "PadicInt.limNthHom", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.limNthHom_spec", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": true, "tactics": ["intro", "obtain", "norm_cast", "obtain", "use", "intro", "apply", "change", "norm_cast", "exact"], "tactic_count": 10}
{"name": "PadicInt.limNthHom_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PadicInt.limNthHom_one", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.limNthHom_add", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.limNthHom_mul", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.lift", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.lift_sub_val_mem_span", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": false, "tactics": ["obtain", "limNthHom_spec", "have", "rw", "dsimp", "rw", "apply", "rw", "convert", "simp", "simp"], "tactic_count": 11}
{"name": "PadicInt.lift_spec", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": true, "tactics": ["ext", "rw", "apply"], "tactic_count": 3}
{"name": "PadicInt.lift_unique", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": true, "tactics": ["ext1", "apply", "intro", "obtain", "apply", "rw"], "tactic_count": 6}
{"name": "PadicInt.lift_self", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": true, "tactics": ["change", "rw", "intro"], "tactic_count": 3}
{"name": "PadicInt.ext_of_toZModPow", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "simp", "rintro", "rfl"], "tactic_count": 6}
{"name": "PadicInt.toZModPow_eq_iff_ext", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": true, "tactics": ["constructor", "intro", "ext", "apply", "intro", "change", "rw", "rintro", "rfl"], "tactic_count": 9}
{"name": "PadicInt.isCauSeq_padicNorm_of_pow_dvd_sub", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": true, "tactics": ["intro", "obtain", "simp", "refine", "obtain", "clear", "induction", "zero", "succ", "have", "simpa"], "tactic_count": 11}
{"name": "PadicInt.toZModPow_ofIntSeq_of_pow_dvd_sub", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.RingHoms", "is_tactic_proof": true, "tactics": ["set", "let", "have", "obtain", "rw", "obtain", "padicNormE.defn", "replace", "rw", "push_cast", "simp", "have", "by_contra", "have", "refine", "simpa", "rw", "exact", "rw", "refine", "clear", "induction", "zero", "succ", "rw", "exact"], "tactic_count": 26}
{"name": "Padic.instValuativeRel", "kind": "instance", "module": "Mathlib.NumberTheory.Padics.ValuativeRel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Padic.instCompatibleWithZeroMultiplicativeIntMulValuation", "kind": "instance", "module": "Mathlib.NumberTheory.Padics.ValuativeRel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Padic.valuation_p_ne_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.ValuativeRel", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Padic.valuation_p_lt_one", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.ValuativeRel", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Padic.instIsNontrivial", "kind": "instance", "module": "Mathlib.NumberTheory.Padics.ValuativeRel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Padic.instIsRankLeOne", "kind": "instance", "module": "Mathlib.NumberTheory.Padics.ValuativeRel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Padic.isUniformInducing_cast_withVal", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.WithVal", "is_tactic_proof": true, "tactics": ["have", "have", "have", "have", "rw", "simp", "constructor", "intro", "use", "intro", "set", "set", "rw", "change", "rw", "rw", "simp", "split_ifs", "simp", "simp", "simpa", "zpow_right_mono₀", "simp", "intro", "use", "intro", "set", "set", "rw", "change", "rw", "change", "simp", "split_ifs", "simp", "rw", "simp_all", "simp"], "tactic_count": 38}
{"name": "Padic.isDenseInducing_cast_withVal", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.WithVal", "is_tactic_proof": true, "tactics": ["refine", "intro", "simpa"], "tactic_count": 3}
{"name": "Padic.withValRingEquiv", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.WithVal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Padic.coe_withValRingEquiv", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.WithVal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Padic.coe_withValRingEquiv_symm", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.WithVal", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "Padic.withValUniformEquiv", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.WithVal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Padic.toEquiv_withValUniformEquiv_eq_toEquiv_withValRingEquiv", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.WithVal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Padic.withValUniformEquiv_cast_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.WithVal", "is_tactic_proof": true, "tactics": ["simpa", "extension_coe"], "tactic_count": 2}
{"name": "Padic.norm_rat_le_one_iff_padicValuation_le_one", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.WithVal", "is_tactic_proof": true, "tactics": ["rw", "refine", "simpa"], "tactic_count": 3}
{"name": "Padic.withValUniformEquiv_norm_le_one_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Padics.WithVal", "is_tactic_proof": true, "tactics": ["induction", "hp", "rw", "apply", "withValUniformEquiv.toHomeomorph.isClosed_setOf_iff", "simpa", "ih", "rw", "exact"], "tactic_count": 9}
{"name": "PadicInt.withValIntegersRingEquiv", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.WithVal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PadicInt.withValIntegersUniformEquiv", "kind": "definition", "module": "Mathlib.NumberTheory.Padics.WithVal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pell.is_pell_solution_iff_mem_unitary", "kind": "theorem", "module": "Mathlib.NumberTheory.Pell", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Pell.Solution₁", "kind": "definition", "module": "Mathlib.NumberTheory.Pell", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pell.Solution₁.instCommGroup", "kind": "instance", "module": "Mathlib.NumberTheory.Pell", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pell.Solution₁.instHasDistribNeg", "kind": "instance", "module": "Mathlib.NumberTheory.Pell", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pell.Solution₁.instInhabited", "kind": "instance", "module": "Mathlib.NumberTheory.Pell", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pell.Solution₁.instCoeZsqrtd", "kind": "instance", "module": "Mathlib.NumberTheory.Pell", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pell.Solution₁.x", "kind": "definition", "module": "Mathlib.NumberTheory.Pell", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pell.Solution₁.y", "kind": "definition", "module": "Mathlib.NumberTheory.Pell", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pell.Solution₁.prop", "kind": "theorem", "module": "Mathlib.NumberTheory.Pell", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pell.Solution₁.prop_x", "kind": "theorem", "module": "Mathlib.NumberTheory.Pell", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Pell.Solution₁.prop_y", "kind": "theorem", "module": "Mathlib.NumberTheory.Pell", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Pell.Solution₁.ext", "kind": "theorem", "module": "Mathlib.NumberTheory.Pell", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pell.Solution₁.mk", "kind": "definition", "module": "Mathlib.NumberTheory.Pell", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pell.Solution₁.x_mk", "kind": "theorem", "module": "Mathlib.NumberTheory.Pell", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pell.Solution₁.y_mk", "kind": "theorem", "module": "Mathlib.NumberTheory.Pell", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pell.Solution₁.coe_mk", "kind": "theorem", "module": "Mathlib.NumberTheory.Pell", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pell.Solution₁.x_one", "kind": "theorem", "module": "Mathlib.NumberTheory.Pell", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pell.Solution₁.y_one", "kind": "theorem", "module": "Mathlib.NumberTheory.Pell", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pell.Solution₁.x_mul", "kind": "theorem", "module": "Mathlib.NumberTheory.Pell", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Pell.Solution₁.y_mul", "kind": "theorem", "module": "Mathlib.NumberTheory.Pell", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pell.Solution₁.x_inv", "kind": "theorem", "module": "Mathlib.NumberTheory.Pell", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pell.Solution₁.y_inv", "kind": "theorem", "module": "Mathlib.NumberTheory.Pell", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pell.Solution₁.x_neg", "kind": "theorem", "module": "Mathlib.NumberTheory.Pell", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pell.Solution₁.y_neg", "kind": "theorem", "module": "Mathlib.NumberTheory.Pell", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pell.Solution₁.eq_zero_of_d_neg", "kind": "theorem", "module": "Mathlib.NumberTheory.Pell", "is_tactic_proof": true, "tactics": ["have", "contrapose", "have", "have", "nlinarith"], "tactic_count": 5}
{"name": "Pell.Solution₁.x_ne_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.Pell", "is_tactic_proof": true, "tactics": ["intro", "have", "rw", "exact"], "tactic_count": 4}
{"name": "Pell.Solution₁.y_ne_zero_of_one_lt_x", "kind": "theorem", "module": "Mathlib.NumberTheory.Pell", "is_tactic_proof": true, "tactics": ["intro", "have", "rw", "exact"], "tactic_count": 4}
{"name": "Pell.Solution₁.d_pos_of_one_lt_x", "kind": "theorem", "module": "Mathlib.NumberTheory.Pell", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "Pell.Solution₁.d_nonsquare_of_one_lt_x", "kind": "theorem", "module": "Mathlib.NumberTheory.Pell", "is_tactic_proof": true, "tactics": ["have", "rintro", "simp_rw", "lia"], "tactic_count": 4}
{"name": "Pell.Solution₁.eq_one_of_x_eq_one", "kind": "theorem", "module": "Mathlib.NumberTheory.Pell", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "Pell.Solution₁.eq_one_or_neg_one_iff_y_eq_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.Pell", "is_tactic_proof": true, "tactics": ["refine", "have", "rw", "exact"], "tactic_count": 4}
{"name": "Pell.Solution₁.x_mul_pos", "kind": "theorem", "module": "Mathlib.NumberTheory.Pell", "is_tactic_proof": true, "tactics": ["simp", "refine", "rw", "ring_nf", "rcases", "positivity", "rw", "simp"], "tactic_count": 8}
{"name": "Pell.Solution₁.y_mul_pos", "kind": "theorem", "module": "Mathlib.NumberTheory.Pell", "is_tactic_proof": true, "tactics": ["simp", "positivity"], "tactic_count": 2}
{"name": "Pell.Solution₁.x_pow_pos", "kind": "theorem", "module": "Mathlib.NumberTheory.Pell", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Pell.Solution₁.y_pow_succ_pos", "kind": "theorem", "module": "Mathlib.NumberTheory.Pell", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Pell.Solution₁.y_zpow_pos", "kind": "theorem", "module": "Mathlib.NumberTheory.Pell", "is_tactic_proof": true, "tactics": ["lift", "norm_cast", "rw", "exact"], "tactic_count": 4}
{"name": "Pell.Solution₁.x_zpow_pos", "kind": "theorem", "module": "Mathlib.NumberTheory.Pell", "is_tactic_proof": true, "tactics": ["cases", "ofNat", "rw", "exact", "negSucc", "rw", "exact"], "tactic_count": 7}
{"name": "Pell.Solution₁.sign_y_zpow_eq_sign_of_x_pos_of_y_pos", "kind": "theorem", "module": "Mathlib.NumberTheory.Pell", "is_tactic_proof": true, "tactics": ["rcases", "rfl", "rw", "exact", "rw", "exact"], "tactic_count": 6}
{"name": "Pell.Solution₁.exists_pos_variant", "kind": "theorem", "module": "Mathlib.NumberTheory.Pell", "is_tactic_proof": true, "tactics": ["refine", "simp", "y_inv,", "assumption"], "tactic_count": 4}
{"name": "Pell.exists_of_not_isSquare", "kind": "theorem", "module": "Mathlib.NumberTheory.Pell", "is_tactic_proof": true, "tactics": ["let", "have", "refine", "rintro", "refine", "rw", "obtain", "have", "refine", "have", "have", "rw", "push_cast", "rw", "sq_sub_sq,", "refine", "rw", "rw", "refine", "rw", "exact", "obtain", "contrapose", "refine", "simp", "have", "rintro", "obtain", "rw", "obtain", "rw", "exact", "haveI", "let", "obtain", "hm.exists_ne_map_eq_of_mapsTo", "obtain", "have", "rw", "push_cast", "rw", "norm_cast", "rw", "have", "rw", "push_cast", "rw", "replace", "refine", "qify", "field_simp", "norm_cast", "grind", "qify", "refine", "exact"], "tactic_count": 56}
{"name": "Pell.exists_iff_not_isSquare", "kind": "theorem", "module": "Mathlib.NumberTheory.Pell", "is_tactic_proof": true, "tactics": ["refine", "rintro", "rw", "simpa"], "tactic_count": 4}
{"name": "Pell.Solution₁.exists_nontrivial_of_not_isSquare", "kind": "theorem", "module": "Mathlib.NumberTheory.Pell", "is_tactic_proof": true, "tactics": ["obtain", "refine"], "tactic_count": 2}
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{"name": "Pell.IsFundamental", "kind": "definition", "module": "Mathlib.NumberTheory.Pell", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pell.IsFundamental.x_pos", "kind": "theorem", "module": "Mathlib.NumberTheory.Pell", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pell.IsFundamental.d_pos", "kind": "theorem", "module": "Mathlib.NumberTheory.Pell", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pell.IsFundamental.d_nonsquare", "kind": "theorem", "module": "Mathlib.NumberTheory.Pell", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pell.IsFundamental.subsingleton", "kind": "theorem", "module": "Mathlib.NumberTheory.Pell", "is_tactic_proof": true, "tactics": ["have", "refine", "have", "exact"], "tactic_count": 4}
{"name": "Pell.IsFundamental.exists_of_not_isSquare", "kind": "theorem", "module": "Mathlib.NumberTheory.Pell", "is_tactic_proof": true, "tactics": ["obtain", "have", "have", "lift", "norm_cast", "exact", "classical", "let", "obtain", "refine", "rw", "have", "have", "rw", "norm_cast", "refine", "rw", "exact"], "tactic_count": 18}
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{"name": "Pell.IsFundamental.zpow_y_lt_iff_lt", "kind": "theorem", "module": "Mathlib.NumberTheory.Pell", "is_tactic_proof": true, "tactics": ["refine", "contrapose", "exact"], "tactic_count": 3}
{"name": "Pell.IsFundamental.zpow_eq_one_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Pell", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Pell.IsFundamental.zpow_ne_neg_zpow", "kind": "theorem", "module": "Mathlib.NumberTheory.Pell", "is_tactic_proof": true, "tactics": ["intro", "apply_fun", "have", "rw", "exact"], "tactic_count": 5}
{"name": "Pell.IsFundamental.x_le_x", "kind": "theorem", "module": "Mathlib.NumberTheory.Pell", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pell.IsFundamental.y_le_y", "kind": "theorem", "module": "Mathlib.NumberTheory.Pell", "is_tactic_proof": true, "tactics": ["have", "rw", "sub_nonpos,", "exact"], "tactic_count": 4}
{"name": "Pell.IsFundamental.x_mul_y_le_y_mul_x", "kind": "theorem", "module": "Mathlib.NumberTheory.Pell", "is_tactic_proof": false, "tactics": ["rw", "abs_mul,", "ring_nf", "rw", "exact"], "tactic_count": 5}
{"name": "Pell.IsFundamental.mul_inv_y_nonneg", "kind": "theorem", "module": "Mathlib.NumberTheory.Pell", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
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{"name": "Pell.IsFundamental.eq_zpow_or_neg_zpow", "kind": "theorem", "module": "Mathlib.NumberTheory.Pell", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "rcases", "exact", "exact", "exact", "rw", "rw", "exact"], "tactic_count": 9}
{"name": "Pell.existsUnique_pos_generator", "kind": "theorem", "module": "Mathlib.NumberTheory.Pell", "is_tactic_proof": true, "tactics": ["obtain", "refine", "obtain", "obtain", "obtain", "rcases", "rw", "zpow_add,", "rcases", "rcases", "rw", "rw", "exact", "rw", "exact", "rw", "have", "norm_num"], "tactic_count": 18}
{"name": "Pell.pos_generator_iff_fundamental", "kind": "theorem", "module": "Mathlib.NumberTheory.Pell", "is_tactic_proof": true, "tactics": ["refine", "have", "have", "obtain", "obtain", "rwa"], "tactic_count": 6}
{"name": "Pell.IsPell", "kind": "definition", "module": "Mathlib.NumberTheory.PellMatiyasevic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pell.isPell_norm", "kind": "theorem", "module": "Mathlib.NumberTheory.PellMatiyasevic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pell.isPell_iff_mem_unitary", "kind": "theorem", "module": "Mathlib.NumberTheory.PellMatiyasevic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pell.isPell_mul", "kind": "theorem", "module": "Mathlib.NumberTheory.PellMatiyasevic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pell.isPell_star", "kind": "theorem", "module": "Mathlib.NumberTheory.PellMatiyasevic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Pell.xn", "kind": "definition", "module": "Mathlib.NumberTheory.PellMatiyasevic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Pell.pell_val", "kind": "theorem", "module": "Mathlib.NumberTheory.PellMatiyasevic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pell.xn_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.PellMatiyasevic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Pell.re_pellZd", "kind": "theorem", "module": "Mathlib.NumberTheory.PellMatiyasevic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Pell.xn_ge_a_pow", "kind": "theorem", "module": "Mathlib.NumberTheory.PellMatiyasevic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Ideal.Quotient.algebraMap_quotient_pow_ramificationIdx", "kind": "theorem", "module": "Mathlib.NumberTheory.RamificationInertia.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Ideal.sum_ramification_inertia", "kind": "theorem", "module": "Mathlib.NumberTheory.RamificationInertia.Basic", "is_tactic_proof": true, "tactics": ["set", "set", "calc", "rw", "refine", "rw", "refine", "rwa", "exact"], "tactic_count": 9}
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{"name": "beattySeq'", "kind": "definition", "module": "Mathlib.NumberTheory.Rayleigh", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.Rayleigh.0.Beatty.no_collision", "kind": "theorem", "module": "Mathlib.NumberTheory.Rayleigh", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "rw", "div_lt_iff₀", "have", "have", "simp_rw", "rw", "simp_rw", "exact"], "tactic_count": 11}
{"name": "_private.Mathlib.NumberTheory.Rayleigh.0.Beatty.no_anticollision", "kind": "theorem", "module": "Mathlib.NumberTheory.Rayleigh", "is_tactic_proof": true, "tactics": ["intro", "have", "have", "simp_rw", "rw", "simp_rw", "exact"], "tactic_count": 7}
{"name": "_private.Mathlib.NumberTheory.Rayleigh.0.Beatty.hit_or_miss", "kind": "theorem", "module": "Mathlib.NumberTheory.Rayleigh", "is_tactic_proof": true, "tactics": ["cases", "refine", "rw", "exact", "refine", "rw", "exact"], "tactic_count": 7}
{"name": "_private.Mathlib.NumberTheory.Rayleigh.0.Beatty.hit_or_miss'", "kind": "theorem", "module": "Mathlib.NumberTheory.Rayleigh", "is_tactic_proof": true, "tactics": ["cases", "exact", "refine", "rw", "constructor", "rwa", "exact"], "tactic_count": 7}
{"name": "compl_beattySeq", "kind": "theorem", "module": "Mathlib.NumberTheory.Rayleigh", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "exact", "simp", "simp", "have", "have", "exact"], "tactic_count": 8}
{"name": "compl_beattySeq'", "kind": "theorem", "module": "Mathlib.NumberTheory.Rayleigh", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "beattySeq_symmDiff_beattySeq'_pos", "kind": "theorem", "module": "Mathlib.NumberTheory.Rayleigh", "is_tactic_proof": true, "tactics": ["apply", "rintro", "rw", "exact", "rw", "exact", "intro", "have", "intro", "refine", "rw", "exact_mod_cast", "have", "intro", "refine", "rw", "exact_mod_cast", "rw", "exact"], "tactic_count": 19}
{"name": "beattySeq'_symmDiff_beattySeq_pos", "kind": "theorem", "module": "Mathlib.NumberTheory.Rayleigh", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Irrational.beattySeq'_pos_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.Rayleigh", "is_tactic_proof": true, "tactics": ["dsimp", "congr", "rw", "refine", "exact"], "tactic_count": 5}
{"name": "Irrational.beattySeq_symmDiff_beattySeq_pos", "kind": "theorem", "module": "Mathlib.NumberTheory.Rayleigh", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.goldenRatio", "kind": "abbrev", "module": "Mathlib.NumberTheory.Real.GoldenRatio", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.goldenConj", "kind": "abbrev", "module": "Mathlib.NumberTheory.Real.GoldenRatio", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "goldenRatio.termφ", "kind": "definition", "module": "Mathlib.NumberTheory.Real.GoldenRatio", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "goldenRatio._aux_Mathlib_NumberTheory_Real_GoldenRatio___macroRules_goldenRatio_termφ_1", "kind": "definition", "module": "Mathlib.NumberTheory.Real.GoldenRatio", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "goldenRatio._aux_Mathlib_NumberTheory_Real_GoldenRatio___unexpand_Real_goldenRatio_1", "kind": "definition", "module": "Mathlib.NumberTheory.Real.GoldenRatio", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "goldenRatio.termψ", "kind": "definition", "module": "Mathlib.NumberTheory.Real.GoldenRatio", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "goldenRatio._aux_Mathlib_NumberTheory_Real_GoldenRatio___macroRules_goldenRatio_termψ_1", "kind": "definition", "module": "Mathlib.NumberTheory.Real.GoldenRatio", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "goldenRatio._aux_Mathlib_NumberTheory_Real_GoldenRatio___unexpand_Real_goldenConj_1", "kind": "definition", "module": "Mathlib.NumberTheory.Real.GoldenRatio", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.inv_goldenRatio", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.GoldenRatio", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Real.inv_goldenConj", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.GoldenRatio", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Real.goldenRatio_mul_goldenConj", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.GoldenRatio", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Real.goldenConj_mul_goldenRatio", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.GoldenRatio", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Real.goldenRatio_add_goldenConj", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.GoldenRatio", "is_tactic_proof": true, "tactics": ["rw", "ring"], "tactic_count": 2}
{"name": "Real.one_sub_goldenConj", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.GoldenRatio", "is_tactic_proof": true, "tactics": ["linarith"], "tactic_count": 1}
{"name": "Real.one_sub_goldenRatio", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.GoldenRatio", "is_tactic_proof": true, "tactics": ["linarith"], "tactic_count": 1}
{"name": "Real.goldenRatio_sub_goldenConj", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.GoldenRatio", "is_tactic_proof": true, "tactics": ["ring"], "tactic_count": 1}
{"name": "Real.goldenRatio_pow_sub_goldenRatio_pow", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.GoldenRatio", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Real.goldenRatio_sq", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.GoldenRatio", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Real.goldenConj_sq", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.GoldenRatio", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Real.goldenRatio_pos", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.GoldenRatio", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.goldenRatio_ne_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.GoldenRatio", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.one_lt_goldenRatio", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.GoldenRatio", "is_tactic_proof": true, "tactics": ["refine", "simp"], "tactic_count": 2}
{"name": "Real.goldenRatio_lt_two", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.GoldenRatio", "is_tactic_proof": true, "tactics": ["calc"], "tactic_count": 1}
{"name": "Real.goldenConj_neg", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.GoldenRatio", "is_tactic_proof": true, "tactics": ["linarith"], "tactic_count": 1}
{"name": "Real.goldenConj_ne_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.GoldenRatio", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.neg_one_lt_goldenConj", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.GoldenRatio", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Real.goldenRatio_irrational", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.GoldenRatio", "is_tactic_proof": true, "tactics": ["have", "have", "convert", "simp", "ring"], "tactic_count": 5}
{"name": "Real.goldenConj_irrational", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.GoldenRatio", "is_tactic_proof": true, "tactics": ["have", "have", "convert", "simp", "ring"], "tactic_count": 5}
{"name": "Real.fibRec", "kind": "definition", "module": "Mathlib.NumberTheory.Real.GoldenRatio", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.fibRec_charPoly_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.GoldenRatio", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Real.fib_isSol_fibRec", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.GoldenRatio", "is_tactic_proof": true, "tactics": ["rw", "intro", "simp", "rw", "simp"], "tactic_count": 5}
{"name": "Real.geom_goldenRatio_isSol_fibRec", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.GoldenRatio", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Real.geom_goldenConj_isSol_fibRec", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.GoldenRatio", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Real.coe_fib_eq'", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.GoldenRatio", "is_tactic_proof": true, "tactics": ["rw", "intro", "norm_cast", "fin_cases", "simp", "simp", "ring_nf", "rw", "exact", "suffices", "convert", "rw", "ring", "apply", "exact", "exact"], "tactic_count": 16}
{"name": "Real.coe_fib_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.GoldenRatio", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.coe_intFib_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.GoldenRatio", "is_tactic_proof": true, "tactics": ["obtain", "exact", "simp", "zpow_natCast,", "neg_one_pow_eq_ite]", "grind"], "tactic_count": 6}
{"name": "Real.fib_succ_sub_goldenRatio_mul_fib", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.GoldenRatio", "is_tactic_proof": true, "tactics": ["repeat", "rw", "ring_nf", "have", "rw"], "tactic_count": 5}
{"name": "Real.goldenConj_mul_fib_succ_add_fib", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.GoldenRatio", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Real.goldenRatio_mul_fib_succ_add_fib", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.GoldenRatio", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "calc", "simp", "goldenRatio_sq]", "ring"], "tactic_count": 7}
{"name": "Real.fib_succ_sub_goldenConj_mul_fib", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.GoldenRatio", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Irrational", "kind": "definition", "module": "Mathlib.NumberTheory.Real.Irrational", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "irrational_iff_ne_rational", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.Irrational", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Irrational.ne_rational", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.Irrational", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "exists_rat_of_not_irrational", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.Irrational", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Transcendental.irrational", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.Irrational", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "irrational_nrt_of_notint_nrt", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.Irrational", "is_tactic_proof": true, "tactics": ["rintro", "rw", "have", "rw", "exact", "have", "rw", "have", "rw", "obtain", "refine", "rw"], "tactic_count": 12}
{"name": "irrational_nrt_of_n_not_dvd_multiplicity", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.Irrational", "is_tactic_proof": true, "tactics": ["rcases", "rw", "simp", "multiplicity_of_one_right", "refine", "rintro", "rw", "subst", "have", "rw", "exact"], "tactic_count": 11}
{"name": "irrational_sqrt_of_multiplicity_odd", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.Irrational", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_irrational_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.Irrational", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_irrational_one", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.Irrational", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "irrational_sqrt_ratCast_iff_of_nonneg", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.Irrational", "is_tactic_proof": true, "tactics": ["refine", "constructor", "rintro", "refine", "rw", "rintro", "exact"], "tactic_count": 7}
{"name": "irrational_sqrt_ratCast_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.Irrational", "is_tactic_proof": true, "tactics": ["obtain", "simp_rw", "rw", "simp_rw"], "tactic_count": 4}
{"name": "irrational_sqrt_intCast_iff_of_nonneg", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.Irrational", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "irrational_sqrt_intCast_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.Irrational", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "irrational_sqrt_natCast_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.Irrational", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "irrational_sqrt_ofNat_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.Irrational", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Prime.irrational_sqrt", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.Irrational", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "irrational_sqrt_two", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.Irrational", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "instDecidableIrrationalSqrtOfNatReal", "kind": "instance", "module": "Mathlib.NumberTheory.Real.Irrational", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDecidableIrrationalSqrtCastReal", "kind": "instance", "module": "Mathlib.NumberTheory.Real.Irrational", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDecidableIrrationalSqrtCastReal_1", "kind": "instance", "module": "Mathlib.NumberTheory.Real.Irrational", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDecidableIrrationalSqrtCastReal_2", "kind": "instance", "module": "Mathlib.NumberTheory.Real.Irrational", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Irrational.ne_rat", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.Irrational", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Irrational.ne_int", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.Irrational", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Irrational.ne_nat", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.Irrational", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Irrational.ne_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.Irrational", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Irrational.ne_one", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.Irrational", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Irrational.ne_ofNat", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.Irrational", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.not_irrational", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.Irrational", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.not_irrational", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.Irrational", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.not_irrational", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.Irrational", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_irrational_ofNat", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.Irrational", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Irrational.add_cases", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.Irrational", "is_tactic_proof": true, "tactics": ["delta", "contrapose", "rintro", "exact"], "tactic_count": 4}
{"name": "Irrational.of_ratCast_add", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.Irrational", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Irrational.ratCast_add", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.Irrational", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Irrational.of_add_ratCast", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.Irrational", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Irrational.add_ratCast", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.Irrational", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Irrational.of_intCast_add", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.Irrational", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Irrational.of_add_intCast", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.Irrational", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Irrational.intCast_add", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.Irrational", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Irrational.add_intCast", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.Irrational", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Irrational.of_natCast_add", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.Irrational", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Irrational.of_add_natCast", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.Irrational", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Irrational.natCast_add", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.Irrational", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Irrational.add_natCast", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.Irrational", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Irrational.of_neg", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.Irrational", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Irrational.neg", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.Irrational", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Irrational.sub_ratCast", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.Irrational", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Irrational.ratCast_sub", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.Irrational", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Irrational.of_sub_ratCast", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.Irrational", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Irrational.of_ratCast_sub", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.Irrational", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Irrational.sub_intCast", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.Irrational", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Irrational.intCast_sub", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.Irrational", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Irrational.of_sub_intCast", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.Irrational", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Irrational.of_intCast_sub", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.Irrational", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Irrational.sub_natCast", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.Irrational", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Irrational.natCast_sub", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.Irrational", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Irrational.of_sub_natCast", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.Irrational", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Irrational.of_natCast_sub", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.Irrational", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Irrational.mul_cases", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.Irrational", "is_tactic_proof": true, "tactics": ["delta", "contrapose", "rintro", "exact"], "tactic_count": 4}
{"name": "Irrational.of_mul_ratCast", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.Irrational", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Irrational.mul_ratCast", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.Irrational", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Irrational.of_ratCast_mul", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.Irrational", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Irrational.ratCast_mul", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.Irrational", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Irrational.of_mul_intCast", "kind": "theorem", "module": "Mathlib.NumberTheory.Real.Irrational", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Int.Matrix.one_le_norm_A_of_ne_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.SiegelsLemma", "is_tactic_proof": true, "tactics": ["by_contra", "apply", "ext", "simp", "rw", "specialize", "rw", "norm_cast", "exact"], "tactic_count": 9}
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{"name": "Int.Matrix.exists_ne_zero_int_vec_norm_le", "kind": "theorem", "module": "Mathlib.NumberTheory.SiegelsLemma", "is_tactic_proof": true, "tactics": ["classical", "rcases", "refine", "have", "rw", "intro", "simp", "rw", "refine", "norm_cast", "rw", "rw", "constructor", "simp", "apply", "norm_cast", "simp", "exact", "simp", "apply", "norm_cast", "simp", "exact"], "tactic_count": 23}
{"name": "Int.Matrix.exists_ne_zero_int_vec_norm_le'", "kind": "theorem", "module": "Mathlib.NumberTheory.SiegelsLemma", "is_tactic_proof": true, "tactics": ["have", "rwa", "exact"], "tactic_count": 3}
{"name": "Nat.primesBelow", "kind": "definition", "module": "Mathlib.NumberTheory.SmoothNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.primesBelow_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.SmoothNumbers", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.mem_primesBelow", "kind": "theorem", "module": "Mathlib.NumberTheory.SmoothNumbers", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.prime_of_mem_primesBelow", "kind": "theorem", "module": "Mathlib.NumberTheory.SmoothNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.lt_of_mem_primesBelow", "kind": "theorem", "module": "Mathlib.NumberTheory.SmoothNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.primesBelow_succ", "kind": "theorem", "module": "Mathlib.NumberTheory.SmoothNumbers", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.notMem_primesBelow", "kind": "theorem", "module": "Mathlib.NumberTheory.SmoothNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.factoredNumbers", "kind": "definition", "module": "Mathlib.NumberTheory.SmoothNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.mem_factoredNumbers", "kind": "theorem", "module": "Mathlib.NumberTheory.SmoothNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.instDecidablePredMemSetFactoredNumbers", "kind": "instance", "module": "Mathlib.NumberTheory.SmoothNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.mem_factoredNumbers_of_dvd", "kind": "theorem", "module": "Mathlib.NumberTheory.SmoothNumbers", "is_tactic_proof": true, "tactics": ["obtain", "have", "refine", "rw", "exact"], "tactic_count": 5}
{"name": "Nat.mem_factoredNumbers_iff_forall_le", "kind": "theorem", "module": "Mathlib.NumberTheory.SmoothNumbers", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Nat.mem_factoredNumbers'", "kind": "theorem", "module": "Mathlib.NumberTheory.SmoothNumbers", "is_tactic_proof": true, "tactics": ["obtain", "rw", "refine", "calc", "p"], "tactic_count": 5}
{"name": "Nat.ne_zero_of_mem_factoredNumbers", "kind": "theorem", "module": "Mathlib.NumberTheory.SmoothNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.primeFactors_subset_of_mem_factoredNumbers", "kind": "theorem", "module": "Mathlib.NumberTheory.SmoothNumbers", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Nat.mem_factoredNumbers_of_primeFactors_subset", "kind": "theorem", "module": "Mathlib.NumberTheory.SmoothNumbers", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Nat.mem_factoredNumbers_iff_primeFactors_subset", "kind": "theorem", "module": "Mathlib.NumberTheory.SmoothNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.factoredNumbers_empty", "kind": "theorem", "module": "Mathlib.NumberTheory.SmoothNumbers", "is_tactic_proof": true, "tactics": ["ext", "simp", "and_or_left,"], "tactic_count": 3}
{"name": "Nat.mul_mem_factoredNumbers", "kind": "theorem", "module": "Mathlib.NumberTheory.SmoothNumbers", "is_tactic_proof": true, "tactics": ["have", "have", "exact", "mem_factoredNumbers_of_primeFactors_subset", "primeFactors_mul"], "tactic_count": 5}
{"name": "Nat.prod_mem_factoredNumbers", "kind": "theorem", "module": "Mathlib.NumberTheory.SmoothNumbers", "is_tactic_proof": false, "tactics": ["have", "refine", "obtain", "simpa", "mem_list_primes_of_dvd_prod"], "tactic_count": 5}
{"name": "Nat.factoredNumbers_insert", "kind": "theorem", "module": "Mathlib.NumberTheory.SmoothNumbers", "is_tactic_proof": true, "tactics": ["ext", "refine", "exact"], "tactic_count": 3}
{"name": "Nat.factoredNumbers_mono", "kind": "theorem", "module": "Mathlib.NumberTheory.SmoothNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.factoredNumbers_compl", "kind": "theorem", "module": "Mathlib.NumberTheory.SmoothNumbers", "is_tactic_proof": true, "tactics": ["intro", "simp", "simp", "obtain", "have", "contrapose", "exact", "exact"], "tactic_count": 8}
{"name": "Nat.pow_mul_mem_factoredNumbers", "kind": "theorem", "module": "Mathlib.NumberTheory.SmoothNumbers", "is_tactic_proof": true, "tactics": ["have", "refine", "rcases", "rw", "rw", "exact", "exact"], "tactic_count": 7}
{"name": "Nat.Prime.factoredNumbers_coprime", "kind": "theorem", "module": "Mathlib.NumberTheory.SmoothNumbers", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Nat.factoredNumbers.map_prime_pow_mul", "kind": "theorem", "module": "Mathlib.NumberTheory.SmoothNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.equivProdNatFactoredNumbers", "kind": "definition", "module": "Mathlib.NumberTheory.SmoothNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.equivProdNatFactoredNumbers_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.SmoothNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.equivProdNatFactoredNumbers_apply'", "kind": "theorem", "module": "Mathlib.NumberTheory.SmoothNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.smoothNumbers", "kind": "definition", "module": "Mathlib.NumberTheory.SmoothNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.mem_smoothNumbers", "kind": "theorem", "module": "Mathlib.NumberTheory.SmoothNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.smoothNumbers_eq_factoredNumbers", "kind": "theorem", "module": "Mathlib.NumberTheory.SmoothNumbers", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.smoothNumbers_eq_factoredNumbers_primesBelow", "kind": "theorem", "module": "Mathlib.NumberTheory.SmoothNumbers", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp_rw", "exact"], "tactic_count": 4}
{"name": "Nat.instDecidablePredMemSetSmoothNumbers", "kind": "instance", "module": "Mathlib.NumberTheory.SmoothNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.mem_smoothNumbers_of_dvd", "kind": "theorem", "module": "Mathlib.NumberTheory.SmoothNumbers", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Nat.mem_smoothNumbers_iff_forall_le", "kind": "theorem", "module": "Mathlib.NumberTheory.SmoothNumbers", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.mem_smoothNumbers'", "kind": "theorem", "module": "Mathlib.NumberTheory.SmoothNumbers", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.primeFactors_subset_of_mem_smoothNumbers", "kind": "theorem", "module": "Mathlib.NumberTheory.SmoothNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.mem_smoothNumbers_of_primeFactors_subset", "kind": "theorem", "module": "Mathlib.NumberTheory.SmoothNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.mem_smoothNumbers_iff_primeFactors_subset", "kind": "theorem", "module": "Mathlib.NumberTheory.SmoothNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.ne_zero_of_mem_smoothNumbers", "kind": "theorem", "module": "Mathlib.NumberTheory.SmoothNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.smoothNumbers_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.SmoothNumbers", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.mul_mem_smoothNumbers", "kind": "theorem", "module": "Mathlib.NumberTheory.SmoothNumbers", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Nat.prod_mem_smoothNumbers", "kind": "theorem", "module": "Mathlib.NumberTheory.SmoothNumbers", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.smoothNumbers_succ", "kind": "theorem", "module": "Mathlib.NumberTheory.SmoothNumbers", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.smoothNumbers_one", "kind": "theorem", "module": "Mathlib.NumberTheory.SmoothNumbers", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.smoothNumbers_mono", "kind": "theorem", "module": "Mathlib.NumberTheory.SmoothNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.mem_smoothNumbers_of_lt", "kind": "theorem", "module": "Mathlib.NumberTheory.SmoothNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.smoothNumbers_compl", "kind": "theorem", "module": "Mathlib.NumberTheory.SmoothNumbers", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Nat.pow_mul_mem_smoothNumbers", "kind": "theorem", "module": "Mathlib.NumberTheory.SmoothNumbers", "is_tactic_proof": true, "tactics": ["have", "have", "refine", "rcases", "rw", "exact", "exact"], "tactic_count": 7}
{"name": "Nat.Prime.smoothNumbers_coprime", "kind": "theorem", "module": "Mathlib.NumberTheory.SmoothNumbers", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Nat.map_prime_pow_mul", "kind": "theorem", "module": "Mathlib.NumberTheory.SmoothNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.equivProdNatSmoothNumbers", "kind": "definition", "module": "Mathlib.NumberTheory.SmoothNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.equivProdNatSmoothNumbers_apply", "kind": "theorem", "module": "Mathlib.NumberTheory.SmoothNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.equivProdNatSmoothNumbers_apply'", "kind": "theorem", "module": "Mathlib.NumberTheory.SmoothNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.smoothNumbersUpTo", "kind": "definition", "module": "Mathlib.NumberTheory.SmoothNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.mem_smoothNumbersUpTo", "kind": "theorem", "module": "Mathlib.NumberTheory.SmoothNumbers", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.roughNumbersUpTo", "kind": "definition", "module": "Mathlib.NumberTheory.SmoothNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.smoothNumbersUpTo_card_add_roughNumbersUpTo_card", "kind": "theorem", "module": "Mathlib.NumberTheory.SmoothNumbers", "is_tactic_proof": false, "tactics": ["rw", "suffices", "have", "have", "refine", "simp", "rwa", "rw", "simp"], "tactic_count": 9}
{"name": "Nat.eq_prod_primes_mul_sq_of_mem_smoothNumbers", "kind": "theorem", "module": "Mathlib.NumberTheory.SmoothNumbers", "is_tactic_proof": true, "tactics": ["obtain", "have", "refine", "simp", "refine", "rw", "exact", "rw", "congr", "simp", "exact"], "tactic_count": 11}
{"name": "Nat.smoothNumbersUpTo_subset_image", "kind": "theorem", "module": "Mathlib.NumberTheory.SmoothNumbers", "is_tactic_proof": true, "tactics": ["intro", "obtain", "obtain", "simp", "refine", "have", "simp", "exact", "rw", "refine", "nth_rw", "gcongr", "exact"], "tactic_count": 13}
{"name": "Nat.smoothNumbersUpTo_card_le", "kind": "theorem", "module": "Mathlib.NumberTheory.SmoothNumbers", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "Nat.roughNumbersUpTo_eq_biUnion", "kind": "theorem", "module": "Mathlib.NumberTheory.SmoothNumbers", "is_tactic_proof": true, "tactics": ["ext", "simp", "show", "simp_rw", "refine", "have", "grind"], "tactic_count": 7}
{"name": "Nat.roughNumbersUpTo_card_le", "kind": "theorem", "module": "Mathlib.NumberTheory.SmoothNumbers", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "euler_four_squares", "kind": "theorem", "module": "Mathlib.NumberTheory.SumFourSquares", "is_tactic_proof": true, "tactics": ["ring"], "tactic_count": 1}
{"name": "Nat.euler_four_squares", "kind": "theorem", "module": "Mathlib.NumberTheory.SumFourSquares", "is_tactic_proof": true, "tactics": ["rw", "push_cast", "simp"], "tactic_count": 3}
{"name": "Int.sq_add_sq_of_two_mul_sq_add_sq", "kind": "theorem", "module": "Mathlib.NumberTheory.SumFourSquares", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.lt_of_sum_four_squares_eq_mul", "kind": "theorem", "module": "Mathlib.NumberTheory.SumFourSquares", "is_tactic_proof": true, "tactics": ["nlinarith"], "tactic_count": 1}
{"name": "Int.exists_sq_add_sq_add_one_eq_mul", "kind": "theorem", "module": "Mathlib.NumberTheory.SumFourSquares", "is_tactic_proof": true, "tactics": ["rcases", "use", "rcases", "rcases", "rw", "have", "refine", "rw", "positivity", "lift", "refine", "replace", "refine", "exact", "exact", "exact", "exact"], "tactic_count": 17}
{"name": "_private.Mathlib.NumberTheory.SumFourSquares.0.Nat.sum_four_squares_of_two_mul_sum_four_squares", "kind": "theorem", "module": "Mathlib.NumberTheory.SumFourSquares", "is_tactic_proof": false, "tactics": ["have", "f", "set", "obtain", "this", "rw", "simp", "rfl", "set", "obtain", "simpa", "obtain", "refine", "rw", "mul_right_inj", "have", "simpa"], "tactic_count": 17}
{"name": "Nat.Prime.sum_four_squares", "kind": "theorem", "module": "Mathlib.NumberTheory.SumFourSquares", "is_tactic_proof": true, "tactics": ["classical", "have", "have", "a.natAbs", "rw", "have", "obtain", "refine", "simpa", "rcases", "rcases", "use", "exfalso", "have", "by_cases", "rcases", "rw", "have", "apply_fun", "push_cast", "obtain", "exact", "obtain", "refine", "exact", "obtain", "simp", "push_cast", "norm_cast", "simp", "rcases", "replace", "obtain", "simp", "have", "rw", "exact", "have", "rw", "apply", "rsuffices", "have", "refine", "conv_rhs", "simp", "rw", "exact", "hmin", "replace", "rw", "ac_rfl", "have", "simp", "refine", "simp", "suffices", "simpa", "norm_cast", "simp", "simp", "simp"], "tactic_count": 61}
{"name": "Nat.sum_four_squares", "kind": "theorem", "module": "Mathlib.NumberTheory.SumFourSquares", "is_tactic_proof": true, "tactics": ["induction", "zero", "one", "prime", "mul", "rcases", "rcases", "exact"], "tactic_count": 8}
{"name": "Nat.roughNumbersUpTo_card_le'", "kind": "theorem", "module": "Mathlib.NumberTheory.SumPrimeReciprocals", "is_tactic_proof": true, "tactics": ["simp_rw", "exact", "cast_sum"], "tactic_count": 3}
{"name": "one_half_le_sum_primes_ge_one_div", "kind": "theorem", "module": "Mathlib.NumberTheory.SumPrimeReciprocals", "is_tactic_proof": true, "tactics": ["set", "set", "let", "suffices", "convert", "rw", "ring", "suffices", "rwa", "cast_two,", "mul_le_mul_iff_right₀", "calc", "exact_mod_cast", "exact_mod_cast"], "tactic_count": 14}
{"name": "not_summable_one_div_on_primes", "kind": "theorem", "module": "Mathlib.NumberTheory.SumPrimeReciprocals", "is_tactic_proof": true, "tactics": ["intro", "obtain", "specialize", "rw", "have", "convert", "simp", "refine", "convert", "obtain", "have", "refine", "exact"], "tactic_count": 13}
{"name": "Nat.Primes.not_summable_one_div", "kind": "theorem", "module": "Mathlib.NumberTheory.SumPrimeReciprocals", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "Nat.Primes.summable_rpow", "kind": "theorem", "module": "Mathlib.NumberTheory.SumPrimeReciprocals", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "exact", "simp", "refine", "intro", "rw", "exact"], "tactic_count": 8}
{"name": "Nat.Prime.sq_add_sq", "kind": "theorem", "module": "Mathlib.NumberTheory.SumTwoSquares", "is_tactic_proof": true, "tactics": ["apply", "rwa"], "tactic_count": 2}
{"name": "sq_add_sq_mul", "kind": "theorem", "module": "Mathlib.NumberTheory.SumTwoSquares", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.sq_add_sq_mul", "kind": "theorem", "module": "Mathlib.NumberTheory.SumTwoSquares", "is_tactic_proof": true, "tactics": ["zify", "obtain", "refine", "simpa"], "tactic_count": 4}
{"name": "ZMod.isSquare_neg_one_of_dvd", "kind": "theorem", "module": "Mathlib.NumberTheory.SumTwoSquares", "is_tactic_proof": true, "tactics": ["let", "rw", "exact"], "tactic_count": 3}
{"name": "ZMod.isSquare_neg_one_mul", "kind": "theorem", "module": "Mathlib.NumberTheory.SumTwoSquares", "is_tactic_proof": false, "tactics": ["have", "rw", "obtain", "obtain", "rw", "exact", "simpa"], "tactic_count": 7}
{"name": "Nat.mod_four_ne_three_of_mem_primeFactors_of_isSquare_neg_one", "kind": "theorem", "module": "Mathlib.NumberTheory.SumTwoSquares", "is_tactic_proof": true, "tactics": ["obtain", "rw", "have", "exact"], "tactic_count": 4}
{"name": "ZMod.isSquare_neg_one_iff_forall_mem_primeFactors_mod_four_ne_three", "kind": "theorem", "module": "Mathlib.NumberTheory.SumTwoSquares", "is_tactic_proof": true, "tactics": ["refine", "induction", "zero", "one", "prime_mul", "have", "have", "by_contra", "exact", "have", "exact", "ih"], "tactic_count": 12}
{"name": "ZMod.isSquare_neg_one_iff'", "kind": "theorem", "module": "Mathlib.NumberTheory.SumTwoSquares", "is_tactic_proof": true, "tactics": ["have", "rw", "refine", "intro", "refine", "exact", "exact", "replace", "replace", "rw", "rw", "exact"], "tactic_count": 12}
{"name": "Nat.eq_sq_add_sq_of_isSquare_mod_neg_one", "kind": "theorem", "module": "Mathlib.NumberTheory.SumTwoSquares", "is_tactic_proof": true, "tactics": ["induction", "zero", "one", "prime_mul", "have", "have", "obtain", "obtain", "exact"], "tactic_count": 9}
{"name": "ZMod.isSquare_neg_one_of_eq_sq_add_sq_of_isCoprime", "kind": "theorem", "module": "Mathlib.NumberTheory.SumTwoSquares", "is_tactic_proof": false, "tactics": ["obtain", "have", "rw", "exact", "have", "linear_combination", "refine", "conv_rhs", "rw", "exact"], "tactic_count": 10}
{"name": "ZMod.isSquare_neg_one_of_eq_sq_add_sq_of_coprime", "kind": "theorem", "module": "Mathlib.NumberTheory.SumTwoSquares", "is_tactic_proof": true, "tactics": ["zify", "exact"], "tactic_count": 2}
{"name": "Nat.eq_sq_add_sq_iff_eq_sq_mul", "kind": "theorem", "module": "Mathlib.NumberTheory.SumTwoSquares", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "by_cases", "exact", "have", "obtain", "exact", "rintro", "obtain", "exact"], "tactic_count": 10}
{"name": "Nat.eq_sq_add_sq_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.SumTwoSquares", "is_tactic_proof": true, "tactics": ["rcases", "exact", "refine", "have", "have", "grind", "mod_four_ne_three_of_mem_primeFactors_of_isSquare_neg_one]", "obtain", "refine", "have", "have", "have", "grind", "dvd_of_mem_primeFactors]", "grind"], "tactic_count": 15}
{"name": "instDecidableExistsNatEqHAddHPowOfNat_mathlib", "kind": "instance", "module": "Mathlib.NumberTheory.SumTwoSquares", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LindemannWeierstrass.hasDerivAt_cexp_mul_sumIDeriv", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Lindemann.AnalyticalPart", "is_tactic_proof": true, "tactics": ["have", "have", "have", "convert", "nth_rw", "simp", "ring"], "tactic_count": 7}
{"name": "LindemannWeierstrass.integral_exp_mul_eval", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Lindemann.AnalyticalPart", "is_tactic_proof": false, "tactics": ["rw", "intervalIntegral.integral_eq_sub_of_hasDerivAt", "simp"], "tactic_count": 3}
{"name": "_private.Mathlib.NumberTheory.Transcendental.Lindemann.AnalyticalPart.0.LindemannWeierstrass.P", "kind": "definition", "module": "Mathlib.NumberTheory.Transcendental.Lindemann.AnalyticalPart", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.Transcendental.Lindemann.AnalyticalPart.0.LindemannWeierstrass.P_eq_integral_exp_mul_eval", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Lindemann.AnalyticalPart", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "_private.Mathlib.NumberTheory.Transcendental.Lindemann.AnalyticalPart.0.LindemannWeierstrass.P_le_aux", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Lindemann.AnalyticalPart", "is_tactic_proof": true, "tactics": ["refine", "rw", "gcongr", "rw", "convert", "rw", "rw", "intro", "rw", "gcongr", "simp", "apply", "rw", "exact", "rw", "exact"], "tactic_count": 16}
{"name": "_private.Mathlib.NumberTheory.Transcendental.Lindemann.AnalyticalPart.0.LindemannWeierstrass.P_le", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Lindemann.AnalyticalPart", "is_tactic_proof": true, "tactics": ["obtain", "let", "let", "let", "use", "intro", "refine", "simp_rw", "have", "gcongr"], "tactic_count": 10}
{"name": "_private.Mathlib.NumberTheory.Transcendental.Lindemann.AnalyticalPart.0.LindemannWeierstrass.exp_polynomial_approx_aux", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Lindemann.AnalyticalPart", "is_tactic_proof": false, "tactics": ["have", "have", "refine", "fun_prop", "obtain", "simp_rw", "refine", "specialize", "grw", "simp_rw", "real_smul,", "refine", "rw", "split_ifs", "rw", "exact", "push_neg", "exact"], "tactic_count": 18}
{"name": "LindemannWeierstrass.exp_polynomial_approx", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Lindemann.AnalyticalPart", "is_tactic_proof": true, "tactics": ["simp_rw", "choose", "use", "intro", "obtain", "specialize", "use", "constructor", "rw", "contrapose", "exact", "obtain", "refine", "refine", "rw", "intro", "specialize", "rw", "rw", "exact", "rw", "have", "rw", "have", "rw", "aeval_sumIDeriv_eq_eval,", "refine", "have", "simpa", "have", "simpa"], "tactic_count": 31}
{"name": "Liouville", "kind": "definition", "module": "Mathlib.NumberTheory.Transcendental.Liouville.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Liouville.irrational", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.Basic", "is_tactic_proof": true, "tactics": ["rintro", "rw", "rcases", "have", "have", "have", "replace", "rw", "one_mul]", "exact", "replace", "rw", "exact", "lift", "have", "lift", "norm_cast", "exact"], "tactic_count": 18}
{"name": "Liouville.exists_one_le_pow_mul_dist", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.Basic", "is_tactic_proof": true, "tactics": ["have", "lt_max_iff.mpr", "refine", "by_cases", "exact", "have", "refine", "exact", "refine", "gcongr", "exact", "refine", "gcongr", "apply"], "tactic_count": 14}
{"name": "Liouville.exists_pos_real_of_irrational_root", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.Basic", "is_tactic_proof": true, "tactics": ["set", "obtain", "have", "obtain", "obtain", "refine", "exact", "one_le_pow₀", "rw", "rw", "refine", "exact", "change", "rw", "rw", "refine", "one_le_pow_mul_abs_eval_div", "refine", "refine", "refine", "exact"], "tactic_count": 21}
{"name": "Liouville.transcendental", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.Basic", "is_tactic_proof": true, "tactics": ["rintro", "replace", "obtain", "exists_pos_real_of_irrational_root", "rcases", "obtain", "lx", "have", "zero_lt_one.trans", "refine", "lt_irrefl", "rw", "refine", "refine", "refine", "gcongr", "refine", "rw", "gcongr", "norm_cast", "lift", "specialize", "rwa", "exact"], "tactic_count": 24}
{"name": "liouvilleNumber", "kind": "definition", "module": "Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LiouvilleNumber.partialSum", "kind": "definition", "module": "Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LiouvilleNumber.remainder", "kind": "definition", "module": "Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LiouvilleNumber.summable", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LiouvilleNumber.remainder_summable", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleNumber", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "LiouvilleNumber.remainder_pos", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LiouvilleNumber.partialSum_succ", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LiouvilleNumber.partialSum_add_remainder", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LiouvilleNumber.remainder_lt'", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LiouvilleNumber.aux_calc", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LiouvilleNumber.remainder_lt", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LiouvilleNumber.partialSum_eq_rat", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleNumber", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rcases", "use", "rw", "norm_cast", "rw", "simp", "all_goals"], "tactic_count": 10}
{"name": "liouville_liouvilleNumber", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleNumber", "is_tactic_proof": true, "tactics": ["have", "have", "intro", "rcases", "refine", "push_cast", "rw", "rw", "have", "simpa"], "tactic_count": 10}
{"name": "transcendental_liouvilleNumber", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LiouvilleWith", "kind": "definition", "module": "Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleWith", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "liouvilleWith_one", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleWith", "is_tactic_proof": true, "tactics": ["use", "refine", "have", "have", "rw", "exact", "refine", "rw", "gcongr", "calc"], "tactic_count": 10}
{"name": "LiouvilleWith.exists_pos", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleWith", "is_tactic_proof": true, "tactics": ["rcases", "refine", "refine", "rintro", "refine", "gcongr", "apply"], "tactic_count": 7}
{"name": "LiouvilleWith.mono", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleWith", "is_tactic_proof": true, "tactics": ["rcases", "refine", "refine", "gcongr", "exact_mod_cast"], "tactic_count": 5}
{"name": "LiouvilleWith.frequently_lt_rpow_neg", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleWith", "is_tactic_proof": true, "tactics": ["rcases", "have", "simpa", "refine", "rintro", "replace", "refine", "rwa"], "tactic_count": 8}
{"name": "LiouvilleWith.mul_rat", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleWith", "is_tactic_proof": true, "tactics": ["rcases", "refine", "rintro", "have", "refine", "rw", "rw", "simp", "calc", "rw", "simp", "all_goals"], "tactic_count": 12}
{"name": "LiouvilleWith.mul_rat_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleWith", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LiouvilleWith.rat_mul_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleWith", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LiouvilleWith.rat_mul", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleWith", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LiouvilleWith.mul_int_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleWith", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LiouvilleWith.mul_int", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleWith", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LiouvilleWith.int_mul_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleWith", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LiouvilleWith.int_mul", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleWith", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LiouvilleWith.mul_nat_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleWith", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LiouvilleWith.mul_nat", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleWith", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LiouvilleWith.nat_mul_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleWith", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LiouvilleWith.nat_mul", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleWith", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LiouvilleWith.add_rat", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleWith", "is_tactic_proof": true, "tactics": ["rcases", "refine", "rintro", "have", "rw", "nth_rewrite", "push_cast", "rw", "refine", "refine", "have", "simp"], "tactic_count": 12}
{"name": "LiouvilleWith.add_rat_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleWith", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LiouvilleWith.rat_add_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleWith", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LiouvilleWith.rat_add", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleWith", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LiouvilleWith.add_int_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleWith", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LiouvilleWith.int_add_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleWith", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LiouvilleWith.add_nat_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleWith", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LiouvilleWith.nat_add_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleWith", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LiouvilleWith.add_int", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleWith", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LiouvilleWith.int_add", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleWith", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LiouvilleWith.add_nat", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleWith", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LiouvilleWith.nat_add", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleWith", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LiouvilleWith.neg", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleWith", "is_tactic_proof": true, "tactics": ["rcases", "refine", "rintro", "refine", "convert", "rw", "congr"], "tactic_count": 7}
{"name": "LiouvilleWith.neg_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleWith", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LiouvilleWith.sub_rat_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleWith", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LiouvilleWith.sub_rat", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleWith", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LiouvilleWith.sub_int_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleWith", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LiouvilleWith.sub_int", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleWith", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LiouvilleWith.sub_nat_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleWith", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LiouvilleWith.sub_nat", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleWith", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LiouvilleWith.rat_sub_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleWith", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LiouvilleWith.rat_sub", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleWith", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LiouvilleWith.int_sub_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleWith", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LiouvilleWith.int_sub", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleWith", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LiouvilleWith.nat_sub_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleWith", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LiouvilleWith.nat_sub", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleWith", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LiouvilleWith.ne_cast_int", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleWith", "is_tactic_proof": true, "tactics": ["rintro", "rcases", "refine", "have", "rw", "gcongr", "norm_cast", "rw", "rw", "exact"], "tactic_count": 10}
{"name": "LiouvilleWith.irrational", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleWith", "is_tactic_proof": true, "tactics": ["rintro", "rcases", "refine", "refine", "rw", "exacts"], "tactic_count": 6}
{"name": "Liouville.frequently_exists_num", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleWith", "is_tactic_proof": true, "tactics": ["by_contra", "simp", "rcases", "have", "intro", "replace", "have", "simp", "exact", "refine", "exact", "have", "rcases", "rcases", "lift", "rcases", "refine", "gcongr", "exact_mod_cast", "exact"], "tactic_count": 20}
{"name": "Liouville.liouvilleWith", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleWith", "is_tactic_proof": true, "tactics": ["suffices", "refine", "rintro", "refine", "rwa"], "tactic_count": 5}
{"name": "forall_liouvilleWith_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleWith", "is_tactic_proof": true, "tactics": ["refine", "rcases", "exact"], "tactic_count": 3}
{"name": "setOf_liouvilleWith_subset_aux", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.Measure", "is_tactic_proof": true, "tactics": ["rintro", "rcases", "rw", "suffices", "y", "simp", "have", "simp", "exact", "clear", "refine", "rintro", "rw", "refine", "replace", "have", "replace", "refine", "calc", "simpa", "rw", "sub_lt_iff_lt_add,", "rw", "push_cast", "refine", "simp", "rw", "exact"], "tactic_count": 28}
{"name": "volume_iUnion_setOf_liouvilleWith", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.Measure", "is_tactic_proof": true, "tactics": ["simp", "refine", "rw", "refine", "generalize", "replace", "clear", "refine", "simp", "set", "have", "rw", "have", "calc", "volume", "measure_biUnion_finset_le", "simp", "have", "rw", "simp", "refine", "refine"], "tactic_count": 22}
{"name": "ae_not_liouvilleWith", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.Measure", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ae_not_liouville", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "volume_setOf_liouville", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.Measure", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.disjoint_residual_ae", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.Measure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "setOf_liouville_eq_iInter_iUnion", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.Residual", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "IsGδ.setOf_liouville", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.Residual", "is_tactic_proof": true, "tactics": ["rw", "refine", "refine", "exact"], "tactic_count": 4}
{"name": "setOf_liouville_eq_irrational_inter_iInter_iUnion", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.Residual", "is_tactic_proof": true, "tactics": ["refine", "refine", "rw", "exact", "simp", "refine", "rw", "exact"], "tactic_count": 8}
{"name": "eventually_residual_liouville", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.Residual", "is_tactic_proof": true, "tactics": ["rw", "refine", "refine", "exact", "rintro", "simp", "refine", "have", "convert", "push_cast", "rw", "norm_cast", "simp", "refine", "exact"], "tactic_count": 15}
{"name": "dense_liouville", "kind": "theorem", "module": "Mathlib.NumberTheory.Transcendental.Liouville.Residual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "divisorsAntidiagonalFactors", "kind": "definition", "module": "Mathlib.NumberTheory.TsumDivisorsAntidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "divisorsAntidiagonalFactors_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.TsumDivisorsAntidiagonal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "divisorsAntidiagonalFactors_one", "kind": "theorem", "module": "Mathlib.NumberTheory.TsumDivisorsAntidiagonal", "is_tactic_proof": true, "tactics": ["have", "simp", "simp"], "tactic_count": 3}
{"name": "sigmaAntidiagonalEquivProd", "kind": "definition", "module": "Mathlib.NumberTheory.TsumDivisorsAntidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sigmaAntidiagonalEquivProd_symm_apply_fst", "kind": "theorem", "module": "Mathlib.NumberTheory.TsumDivisorsAntidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sigmaAntidiagonalEquivProd_symm_apply_snd", "kind": "theorem", "module": "Mathlib.NumberTheory.TsumDivisorsAntidiagonal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "summable_norm_pow_mul_geometric_div_one_sub", "kind": "theorem", "module": "Mathlib.NumberTheory.TsumDivisorsAntidiagonal", "is_tactic_proof": true, "tactics": ["simp", "apply", "simpa", "tendsto_const_nhds.div"], "tactic_count": 4}
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{"name": "Zsqrtd.instMul", "kind": "instance", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.re_mul", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.im_mul", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.addCommGroup", "kind": "instance", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": true, "tactics": ["refine", "nsmul", "zsmul", "add_assoc", "zero_add", "add_zero", "neg_add_cancel", "add_comm"], "tactic_count": 8}
{"name": "Zsqrtd.re_sub", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.im_sub", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.addGroupWithOne", "kind": "instance", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.commRing", "kind": "instance", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": true, "tactics": ["refine", "npow", "left_distrib", "right_distrib", "zero_mul", "mul_zero", "mul_assoc", "one_mul", "mul_one", "mul_comm", "intros", "ext", "simp", "ring"], "tactic_count": 14}
{"name": "Zsqrtd.instAddMonoid", "kind": "instance", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Zsqrtd.instMonoid", "kind": "instance", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Zsqrtd.instCommMonoid", "kind": "instance", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Zsqrtd.instCommSemigroup", "kind": "instance", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Zsqrtd.instSemigroup", "kind": "instance", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Zsqrtd.instAddCommSemigroup", "kind": "instance", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Zsqrtd.instAddSemigroup", "kind": "instance", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Zsqrtd.instCommSemiring", "kind": "instance", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Zsqrtd.instSemiring", "kind": "instance", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Zsqrtd.instRing", "kind": "instance", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Zsqrtd.instDistrib", "kind": "instance", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "Zsqrtd.instStar", "kind": "instance", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.star_mk", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.re_star", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.im_star", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.instStarRing", "kind": "instance", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.nontrivial", "kind": "instance", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.re_natCast", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.re_ofNat", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.im_natCast", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.im_ofNat", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.natCast_val", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.re_intCast", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Zsqrtd.im_intCast", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Zsqrtd.intCast_val", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Zsqrtd.instCharZero", "kind": "instance", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.ofInt_eq_intCast", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Zsqrtd.nsmul_val", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Zsqrtd.smul_val", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Zsqrtd.re_smul", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Zsqrtd.im_smul", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Zsqrtd.muld_val", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Zsqrtd.dmuld", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Zsqrtd.smuld_val", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Zsqrtd.decompose", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Zsqrtd.mul_star", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Zsqrtd.intCast_dvd", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "simp", "rintro", "use", "rw", "exact"], "tactic_count": 7}
{"name": "Zsqrtd.intCast_dvd_intCast", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": true, "tactics": ["rw", "constructor", "rintro", "rwa", "rw", "exact"], "tactic_count": 6}
{"name": "Zsqrtd.eq_of_smul_eq_smul_left", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "Zsqrtd.gcd_eq_zero_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Zsqrtd.gcd_pos_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.isCoprime_of_dvd_isCoprime", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": true, "tactics": ["apply", "rintro", "obtain", "rw", "simp", "rintro", "apply", "obtain", "rw", "apply", "rw", "exact", "exact"], "tactic_count": 13}
{"name": "Zsqrtd.exists_coprime_of_gcd_pos", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": true, "tactics": ["obtain", "rw", "refine", "rw", "rw"], "tactic_count": 5}
{"name": "Zsqrtd.SqLe", "kind": "definition", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.sqLe_of_le", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.sqLe_add_mixed", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.sqLe_add", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": true, "tactics": ["have", "simp", "simp"], "tactic_count": 3}
{"name": "Zsqrtd.sqLe_cancel", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": true, "tactics": ["apply", "intro", "refine", "simp", "have", "simp", "grw", "gcongr"], "tactic_count": 8}
{"name": "Zsqrtd.sqLe_smul", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Zsqrtd.sqLe_mul", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": true, "tactics": ["refine", "intro", "have", "refine", "convert", "simp", "ring"], "tactic_count": 7}
{"name": "Zsqrtd.Nonnegg", "kind": "definition", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.nonnegg_comm", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Zsqrtd.nonnegg_neg_pos", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.nonnegg_pos_neg", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Zsqrtd.nonnegg_cases_right", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.nonnegg_cases_left", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.norm", "kind": "definition", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.norm_def", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.norm_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Zsqrtd.norm_one", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Zsqrtd.norm_intCast", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Zsqrtd.norm_natCast", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.norm_mul", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": true, "tactics": ["simp", "ring"], "tactic_count": 2}
{"name": "Zsqrtd.normMonoidHom", "kind": "definition", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.norm_eq_mul_conj", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Zsqrtd.norm_neg", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.norm_conj", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.norm_nonneg", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.abs_norm", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.norm_eq_one_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.isUnit_iff_norm_isUnit", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Zsqrtd.norm_eq_one_iff'", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Zsqrtd.norm_eq_zero_iff", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "have", "have", "obtain", "ext", "exact", "rw", "exact", "rintro", "exact"], "tactic_count": 12}
{"name": "Zsqrtd.norm_eq_of_associated", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": true, "tactics": ["obtain", "rw"], "tactic_count": 2}
{"name": "Zsqrtd.Nonneg", "kind": "definition", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.instLECastInt", "kind": "instance", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.instLTCastInt", "kind": "instance", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.decidableNonnegg", "kind": "instance", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Zsqrtd.decidableNonneg", "kind": "instance", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.decidableLE", "kind": "instance", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.nonneg_cases", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.nonneg_add_lem", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": ["have", "let", "have", "absurd", "rw", "rwa"], "tactic_count": 6}
{"name": "Zsqrtd.Nonneg.add", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": true, "tactics": ["rcases", "trivial", "refine", "dsimp", "exact", "apply", "refine", "dsimp", "exact", "apply", "refine", "dsimp", "exact", "apply", "have", "rw", "rwa", "exact", "refine", "dsimp", "exact", "apply", "dsimp", "rw", "exact", "have", "rw", "rwa"], "tactic_count": 28}
{"name": "Zsqrtd.nonneg_iff_zero_le", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.le_of_le_le", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.nonneg_total", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.le_total", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "Zsqrtd.preorder", "kind": "instance", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.le_arch", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": ["obtain", "refine", "change", "rcases", "simp", "trivial", "have", "simpa", "rw", "exact"], "tactic_count": 10}
{"name": "Zsqrtd.add_le_add_left", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.le_of_add_le_add_left", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Zsqrtd.add_lt_add_left", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.nonneg_smul", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact", "simpa", "simpa"], "tactic_count": 4}
{"name": "Zsqrtd.nonneg_muld", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.nonneg_mul_lem", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": ["have", "rw", "rw", "exact"], "tactic_count": 4}
{"name": "Zsqrtd.nonneg_mul", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.mul_nonneg", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Zsqrtd.not_sqLe_succ", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.d_pos", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.divides_sq_eq_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.divides_sq_eq_zero_z", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact", "let"], "tactic_count": 3}
{"name": "Zsqrtd.not_divides_sq", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.nonneg_antisymm", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.le_antisymm", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.linearOrder", "kind": "instance", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.eq_zero_or_eq_zero_of_mul_eq_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.instNoZeroDivisorsCastInt", "kind": "instance", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.instIsDomainCastInt", "kind": "instance", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.mul_pos", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.instZeroLEOneClassCastInt", "kind": "instance", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.instIsOrderedAddMonoidCastInt", "kind": "instance", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.instIsStrictOrderedRingCastInt", "kind": "instance", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.norm_eq_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": true, "tactics": ["refine", "dsimp", "rw", "by_cases", "obtain", "haveI", "exact", "suffices", "rw", "simpa", "false_or,", "apply", "rw", "exact"], "tactic_count": 14}
{"name": "Zsqrtd.hom_ext", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Zsqrtd.lift", "kind": "definition", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.lift_injective", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.norm_eq_one_iff_mem_unitary", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": true, "tactics": ["rw", "norm_cast"], "tactic_count": 2}
{"name": "Zsqrtd.mker_norm_eq_unitary", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaussianInt", "kind": "abbrev", "module": "Mathlib.NumberTheory.Zsqrtd.GaussianInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.Zsqrtd.GaussianInt.0.termℤ[i]", "kind": "definition", "module": "Mathlib.NumberTheory.Zsqrtd.GaussianInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.Zsqrtd.GaussianInt.0._aux_Mathlib_NumberTheory_Zsqrtd_GaussianInt___macroRules__private_Mathlib_NumberTheory_Zsqrtd_GaussianInt_0_termℤ[i]_1", "kind": "definition", "module": "Mathlib.NumberTheory.Zsqrtd.GaussianInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.Zsqrtd.GaussianInt.0._aux_Mathlib_NumberTheory_Zsqrtd_GaussianInt___unexpand_GaussianInt_1", "kind": "definition", "module": "Mathlib.NumberTheory.Zsqrtd.GaussianInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaussianInt.instRepr", "kind": "instance", "module": "Mathlib.NumberTheory.Zsqrtd.GaussianInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaussianInt.instCommRing", "kind": "instance", "module": "Mathlib.NumberTheory.Zsqrtd.GaussianInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaussianInt.toComplex", "kind": "definition", "module": "Mathlib.NumberTheory.Zsqrtd.GaussianInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaussianInt.instCoeComplex", "kind": "instance", "module": "Mathlib.NumberTheory.Zsqrtd.GaussianInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaussianInt.toComplex_def", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.GaussianInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaussianInt.toComplex_def'", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.GaussianInt", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "GaussianInt.toComplex_def₂", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.GaussianInt", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "GaussianInt.intCast_re", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.GaussianInt", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "GaussianInt.intCast_im", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.GaussianInt", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "GaussianInt.re_toComplex", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.GaussianInt", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "GaussianInt.im_toComplex", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.GaussianInt", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "GaussianInt.toComplex_add", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.GaussianInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaussianInt.toComplex_mul", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.GaussianInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaussianInt.toComplex_one", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.GaussianInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaussianInt.toComplex_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.GaussianInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaussianInt.toComplex_neg", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.GaussianInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaussianInt.toComplex_sub", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.GaussianInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaussianInt.toComplex_star", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.GaussianInt", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "GaussianInt.toComplex_inj", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.GaussianInt", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "GaussianInt.toComplex_injective", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.GaussianInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaussianInt.toComplex_eq_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.GaussianInt", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "GaussianInt.intCast_real_norm", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.GaussianInt", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "GaussianInt.intCast_complex_norm", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.GaussianInt", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "GaussianInt.norm_nonneg", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.GaussianInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaussianInt.norm_eq_zero", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.GaussianInt", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "GaussianInt.norm_pos", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.GaussianInt", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "GaussianInt.abs_natCast_norm", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.GaussianInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaussianInt.natCast_natAbs_norm", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.GaussianInt", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "GaussianInt.natAbs_norm_eq", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.GaussianInt", "is_tactic_proof": true, "tactics": ["zify", "rw", "simp"], "tactic_count": 3}
{"name": "GaussianInt.instDiv", "kind": "instance", "module": "Mathlib.NumberTheory.Zsqrtd.GaussianInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaussianInt.div_def", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.GaussianInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaussianInt.toComplex_re_div", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.GaussianInt", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "GaussianInt.toComplex_im_div", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.GaussianInt", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "GaussianInt.normSq_le_normSq_of_re_le_of_im_le", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.GaussianInt", "is_tactic_proof": false, "tactics": ["rw", "gcongr"], "tactic_count": 2}
{"name": "GaussianInt.normSq_div_sub_div_lt_one", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.GaussianInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaussianInt.instMod", "kind": "instance", "module": "Mathlib.NumberTheory.Zsqrtd.GaussianInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaussianInt.mod_def", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.GaussianInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaussianInt.norm_mod_lt", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.GaussianInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaussianInt.natAbs_norm_mod_lt", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.GaussianInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaussianInt.norm_le_norm_mul_left", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.GaussianInt", "is_tactic_proof": true, "tactics": ["rw", "exact", "le_mul_of_one_le_right", "rw", "exact"], "tactic_count": 5}
{"name": "GaussianInt.instNontrivial", "kind": "instance", "module": "Mathlib.NumberTheory.Zsqrtd.GaussianInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaussianInt.instEuclideanDomain", "kind": "instance", "module": "Mathlib.NumberTheory.Zsqrtd.GaussianInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaussianInt.sq_add_sq_of_nat_prime_of_not_irreducible", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.GaussianInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.Zsqrtd.QuadraticReciprocity.0.termℤ[i]", "kind": "definition", "module": "Mathlib.NumberTheory.Zsqrtd.QuadraticReciprocity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.Zsqrtd.QuadraticReciprocity.0._aux_Mathlib_NumberTheory_Zsqrtd_QuadraticReciprocity___macroRules__private_Mathlib_NumberTheory_Zsqrtd_QuadraticReciprocity_0_termℤ[i]_1", "kind": "definition", "module": "Mathlib.NumberTheory.Zsqrtd.QuadraticReciprocity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.NumberTheory.Zsqrtd.QuadraticReciprocity.0._aux_Mathlib_NumberTheory_Zsqrtd_QuadraticReciprocity___unexpand_GaussianInt_1", "kind": "definition", "module": "Mathlib.NumberTheory.Zsqrtd.QuadraticReciprocity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaussianInt.mod_four_eq_three_of_nat_prime_of_prime", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.QuadraticReciprocity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaussianInt.prime_of_nat_prime_of_mod_four_eq_three", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.QuadraticReciprocity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaussianInt.prime_iff_mod_four_eq_three_of_nat_prime", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.QuadraticReciprocity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.toReal", "kind": "definition", "module": "Mathlib.NumberTheory.Zsqrtd.ToReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Zsqrtd.toReal_injective", "kind": "theorem", "module": "Mathlib.NumberTheory.Zsqrtd.ToReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Symmetric.compl", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAntichain", "kind": "definition", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAntichain.empty", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAntichain.singleton", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAntichain.subset", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAntichain.mono", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAntichain.mono_on", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAntichain.eq", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAntichain.eq'", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAntichain.antisymm", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAntichain.subsingleton", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": true, "tactics": ["rintro", "obtain", "exact", "exact", "exact"], "tactic_count": 5}
{"name": "IsAntichain.flip", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAntichain.swap", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAntichain.image", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "IsAntichain.preimage", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isAntichain_insert", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAntichain.insert", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isAntichain_insert_of_symmetric", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAntichain.insert_of_symmetric", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAntichain.image_relEmbedding", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": true, "tactics": ["intro", "rw", "obtain", "exact"], "tactic_count": 4}
{"name": "IsAntichain.preimage_relEmbedding", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAntichain.image_relIso", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAntichain.preimage_relIso", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAntichain.image_relEmbedding_iff", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAntichain.image_relIso_iff", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAntichain.image_embedding", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAntichain.preimage_embedding", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAntichain.image_embedding_iff", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAntichain.image_iso", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAntichain.image_iso_iff", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAntichain.preimage_iso", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAntichain.preimage_iso_iff", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAntichain.to_dual", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAntichain.to_dual_iff", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAntichain.image_compl", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAntichain.preimage_compl", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAntichain.diff", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isAntichain_preimage_subtypeVal", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "isAntichain_coe_univ_iff", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "isAntichain_union", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.Subsingleton.isAntichain", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "subsingleton_of_isChain_of_isAntichain", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": true, "tactics": ["intro", "by_contra", "cases", "inl", "inr"], "tactic_count": 5}
{"name": "isChain_and_isAntichain_iff_subsingleton", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inter_subsingleton_of_isChain_of_isAntichain", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inter_subsingleton_of_isAntichain_of_isChain", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAntichain.not_lt", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isAntichain_and_least_iff", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isAntichain_and_greatest_iff", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAntichain.least_iff", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAntichain.greatest_iff", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLeast.antichain_iff", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGreatest.antichain_iff", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAntichain.bot_mem_iff", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAntichain.top_mem_iff", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAntichain.minimal_mem_iff", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAntichain.maximal_mem_iff", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAntichain.eq_setOf_maximal", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": true, "tactics": ["refine", "obtain", "rwa"], "tactic_count": 3}
{"name": "IsAntichain.eq_setOf_minimal", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAntichain.of_strictMonoOn_antitoneOn", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAntichain.of_monotoneOn_strictAntiOn", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isAntichain_iff_forall_not_lt", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "setOf_maximal_antichain", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "setOf_minimal_antichain", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsStrongAntichain", "kind": "definition", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsStrongAntichain.subset", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsStrongAntichain.mono", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsStrongAntichain.eq", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsStrongAntichain.isAntichain", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsStrongAntichain.subsingleton", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsStrongAntichain.flip", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsStrongAntichain.swap", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsStrongAntichain.image", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": true, "tactics": ["rintro", "obtain", "exact"], "tactic_count": 3}
{"name": "IsStrongAntichain.preimage", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isStrongAntichain_insert", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsStrongAntichain.insert", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Subsingleton.isStrongAntichain", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMaxAntichain", "kind": "definition", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMaxAntichain.isAntichain", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMaxAntichain.image", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMaxAntichain.isEmpty_iff", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": true, "tactics": ["refine", "constructor", "intro", "simp", "exact"], "tactic_count": 5}
{"name": "IsMaxAntichain.nonempty_iff", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMaxAntichain.symm", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Order.Antichain.0.term_≺_", "kind": "definition", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Order.Antichain.0._aux_Mathlib_Order_Antichain___macroRules__private_Mathlib_Order_Antichain_0_term_≺__1", "kind": "definition", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Order.Antichain.0._aux_Mathlib_Order_Antichain___unexpand_StrongLT_1", "kind": "definition", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsWeakAntichain", "kind": "definition", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsWeakAntichain.subset", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsWeakAntichain.eq", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsWeakAntichain.insert", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isWeakAntichain_insert", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAntichain.isWeakAntichain", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Subsingleton.isWeakAntichain", "kind": "theorem", "module": "Mathlib.Order.Antichain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntisymmRel", "kind": "definition", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "antisymmRel_swap", "kind": "theorem", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "antisymmRel_swap_apply", "kind": "theorem", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntisymmRel.refl", "kind": "theorem", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntisymmRel.rfl", "kind": "theorem", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instReflAntisymmRel", "kind": "instance", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntisymmRel.of_eq", "kind": "theorem", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntisymmRel.symm", "kind": "theorem", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instSymmAntisymmRel", "kind": "instance", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "antisymmRel_comm", "kind": "theorem", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntisymmRel.trans", "kind": "theorem", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsTransAntisymmRel", "kind": "instance", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntisymmRel.decidableRel", "kind": "instance", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "antisymmRel_iff_eq", "kind": "theorem", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.GCongr.AntisymmRel.left", "kind": "theorem", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.GCongr.AntisymmRel.right", "kind": "theorem", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.GCongr.exactAntisymmRelLeft", "kind": "definition", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.GCongr.exactAntisymmRelRight", "kind": "definition", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntisymmRel.le", "kind": "theorem", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntisymmRel.ge", "kind": "theorem", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntisymmRel.setoid", "kind": "definition", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antisymmetrization", "kind": "definition", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toAntisymmetrization", "kind": "definition", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofAntisymmetrization", "kind": "definition", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInhabitedAntisymmetrization", "kind": "instance", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "instSubsingletonAntisymmetrization", "kind": "instance", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "Antisymmetrization.ind", "kind": "theorem", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antisymmetrization.induction_on", "kind": "theorem", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toAntisymmetrization_ofAntisymmetrization", "kind": "theorem", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_iff_lt_or_antisymmRel", "kind": "theorem", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": true, "tactics": ["rw", "tauto"], "tactic_count": 2}
{"name": "le_of_le_of_antisymmRel", "kind": "theorem", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_of_antisymmRel_of_le", "kind": "theorem", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lt_of_lt_of_antisymmRel", "kind": "theorem", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lt_of_antisymmRel_of_lt", "kind": "theorem", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_lt_of_antisymmRel", "kind": "theorem", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_gt_of_antisymmRel", "kind": "theorem", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_antisymmRel_of_lt", "kind": "theorem", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_antisymmRel_of_gt", "kind": "theorem", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instTransLeAntisymmRel", "kind": "instance", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instTransAntisymmRelLe", "kind": "instance", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instTransLtAntisymmRelLe", "kind": "instance", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instTransAntisymmRelLeLt", "kind": "instance", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntisymmRel.le_congr", "kind": "theorem", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntisymmRel.le_congr_left", "kind": "theorem", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntisymmRel.le_congr_right", "kind": "theorem", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntisymmRel.lt_congr", "kind": "theorem", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntisymmRel.lt_congr_left", "kind": "theorem", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntisymmRel.lt_congr_right", "kind": "theorem", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntisymmRel.antisymmRel_congr", "kind": "theorem", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntisymmRel.antisymmRel_congr_left", "kind": "theorem", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntisymmRel.antisymmRel_congr_right", "kind": "theorem", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntisymmRel.image", "kind": "theorem", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instPartialOrderAntisymmetrization", "kind": "instance", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "antisymmetrization_fibration", "kind": "theorem", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "acc_antisymmetrization_iff", "kind": "theorem", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "wellFounded_antisymmetrization_iff", "kind": "theorem", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "wellFoundedLT_antisymmetrization_iff", "kind": "theorem", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "wellFoundedGT_antisymmetrization_iff", "kind": "theorem", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": true, "tactics": ["simp_rw", "convert", "exact"], "tactic_count": 3}
{"name": "instWellFoundedLTAntisymmetrizationLe", "kind": "instance", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instWellFoundedGTAntisymmetrizationLe", "kind": "instance", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instLinearOrderAntisymmetrizationLeOfDecidableLEOfDecidableLTOfTotal", "kind": "instance", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toAntisymmetrization_le_toAntisymmetrization_iff", "kind": "theorem", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toAntisymmetrization_lt_toAntisymmetrization_iff", "kind": "theorem", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofAntisymmetrization_le_ofAntisymmetrization_iff", "kind": "theorem", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofAntisymmetrization_lt_ofAntisymmetrization_iff", "kind": "theorem", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toAntisymmetrization_mono", "kind": "theorem", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Order.Antisymmetrization.0.liftFun_antisymmRel", "kind": "theorem", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.antisymmetrization", "kind": "definition", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.coe_antisymmetrization", "kind": "theorem", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.antisymmetrization_apply", "kind": "theorem", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.antisymmetrization_apply_mk", "kind": "theorem", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderEmbedding.ofAntisymmetrization", "kind": "definition", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.dualAntisymmetrization", "kind": "definition", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.dualAntisymmetrization_apply", "kind": "theorem", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.dualAntisymmetrization_symm_apply", "kind": "theorem", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antisymmetrization.prodEquiv", "kind": "definition", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antisymmetrization.prodEquiv_apply_mk", "kind": "theorem", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antisymmetrization.prodEquiv_symm_apply_mk", "kind": "theorem", "module": "Mathlib.Order.Antisymmetrization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAtom", "kind": "definition", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAtom.Iic", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAtom.of_isAtom_coe_Iic", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isAtom_iff_le_of_ge", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAtom.ne_bot", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAtom.lt_iff", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAtom.le_iff", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsAtom.bot_lt", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAtom.le_iff_eq", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAtom.ne_iff_eq_bot", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAtom.ne_bot_iff_eq", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAtom.Iic_eq", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bot_covBy_iff", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsAtom.le_iSup", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": true, "tactics": ["refine", "change", "refine", "push_neg", "have", "disjoint_iSup_iff.2", "le_bot_iff.2", "of_not_not", "have", "hx", "obtain", "exact"], "tactic_count": 12}
{"name": "IsAtom.le_sSup", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsCoatom", "kind": "definition", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCoatom_dual_iff_isAtom", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isAtom_dual_iff_isCoatom", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCoatom.Ici", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCoatom.of_isCoatom_coe_Ici", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCoatom_iff_ge_of_le", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCoatom.ne_top", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCoatom.lt_iff", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCoatom.le_iff", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCoatom.lt_top", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCoatom.le_iff_eq", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCoatom.ne_iff_eq_top", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCoatom.ne_top_iff_eq", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCoatom.Ici_eq", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "covBy_top_iff", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.isAtom_iff", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": true, "tactics": ["simp_rw", "and_comm]"], "tactic_count": 2}
{"name": "SetLike.isCoatom_iff", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": true, "tactics": ["simp_rw", "and_comm]"], "tactic_count": 2}
{"name": "SetLike.covBy_iff", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": true, "tactics": ["refine", "contrapose", "rw", "simp_rw"], "tactic_count": 4}
{"name": "SetLike.covBy_iff'", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": true, "tactics": ["refine", "push_neg", "rw", "simp_rw"], "tactic_count": 4}
{"name": "IsCoatom.iInf_le", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCoatom.sInf_le", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.Ici.isAtom_iff", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": true, "tactics": ["rw", "refine", "simpa"], "tactic_count": 3}
{"name": "Set.Iic.isCoatom_iff", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": true, "tactics": ["rw", "refine", "simpa"], "tactic_count": 3}
{"name": "covBy_iff_atom_Ici", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "covBy_iff_coatom_Iic", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsAtom.not_disjoint_iff_le", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsAtom.not_le_iff_disjoint", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAtom.disjoint_of_ne", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsCoatom.not_codisjoint_iff_le", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsCoatom.not_le_iff_codisjoint", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCoatom.codisjoint_of_ne", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsCoatom.sup_eq_top_of_ne", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAtomic.exists_atom", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCoatomic.exists_coatom", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCoatomic_dual_iff_isAtomic", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isAtomic_dual_iff_isCoatomic", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instIsCoatomic", "kind": "instance", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAtomic.Set.Iic.isAtomic", "kind": "instance", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instIsAtomic", "kind": "instance", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCoatomic.Set.Ici.isCoatomic", "kind": "instance", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isAtomic_iff_forall_isAtomic_Iic", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCoatomic_iff_forall_isCoatomic_Ici", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_covBy_le_of_lt", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_le_covBy_of_lt", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isStronglyAtomic_dual_iff_is_stronglyCoatomic", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": true, "tactics": ["simpa", "isStronglyCoatomic_iff]"], "tactic_count": 2}
{"name": "isStronglyCoatomic_dual_iff_is_stronglyAtomic", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "OrderDual.instIsStronglyCoatomic", "kind": "instance", "module": "Mathlib.Order.Atoms", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "instIsStronglyAtomicOrderDualOfIsStronglyCoatomic", "kind": "instance", "module": "Mathlib.Order.Atoms", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "IsStronglyAtomic.isAtomic", "kind": "instance", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsStronglyCoatomic.toIsCoatomic", "kind": "instance", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.OrdConnected.isStronglyAtomic", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.OrdConnected.isStronglyCoatomic", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsStronglyAtomicElemOfOrdConnected", "kind": "instance", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsStronglyCoatomicElemOfOrdConnected", "kind": "instance", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SuccOrder.toIsStronglyAtomic", "kind": "instance", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsStronglyCoatomicOfPredOrder", "kind": "instance", "module": "Mathlib.Order.Atoms", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsStronglyAtomic.of_wellFounded_lt", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsStronglyCoatomic.of_wellFounded_gt", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsStronglyAtomicOfWellFoundedLT", "kind": "instance", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsStronglyCoatomicOfWellFoundedGT", "kind": "instance", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isAtomic_of_orderBot_wellFounded_lt", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCoatomic_of_orderTop_gt_wellFounded", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanAlgebra.le_iff_atom_le_imp", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": true, "tactics": ["refine", "have", "of_not_not", "have", "have", "have", "have", "ha.1", "exact"], "tactic_count": 9}
{"name": "BooleanAlgebra.eq_iff_atom_le_iff", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": true, "tactics": ["refine", "exact", "le_antisymm"], "tactic_count": 3}
{"name": "CompleteBooleanAlgebra.toCompleteAtomicBooleanAlgebra", "kind": "abbrev", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCoatomistic_dual_iff_isAtomistic", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isAtomistic_dual_iff_isCoatomistic", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instIsCoatomistic", "kind": "instance", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAtomistic.instIsAtomic", "kind": "instance", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLUB_atoms_le", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "isLUB_atoms_top", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "le_iff_atom_le_imp", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_iff_atom_le_iff", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": true, "tactics": ["refine", "rw", "simp_all"], "tactic_count": 3}
{"name": "OrderDual.instIsAtomistic", "kind": "instance", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCoatomistic.instIsCoatomic", "kind": "instance", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sSup_atoms_le_eq", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sSup_atoms_eq_top", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteLattice.isAtomistic_iff", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "eq_sSup_atoms", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteLattice.isCoatomistic_iff", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "eq_sInf_coatoms", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteAtomicBooleanAlgebra.instIsAtomistic", "kind": "instance", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteAtomicBooleanAlgebra.instIsCoatomistic", "kind": "instance", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteAtomicBooleanAlgebra.exists_mem_le_of_le_sSup_of_isAtom", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteAtomicBooleanAlgebra.eq_setOf_le_sSup_and_isAtom", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": true, "tactics": ["ext", "refine", "obtain", "obtain", "simpa", "assumption"], "tactic_count": 6}
{"name": "CompleteAtomicBooleanAlgebra.toSetOfIsAtom", "kind": "definition", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSimpleOrder.of_forall_eq_top", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isSimpleOrder_iff_isSimpleOrder_orderDual", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": true, "tactics": ["constructor", "exact", "exact", "eq_bot_or_eq_top"], "tactic_count": 4}
{"name": "IsSimpleOrder.bot_ne_top", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": true, "tactics": ["obtain", "rcases", "first", "simpa", "simpa"], "tactic_count": 5}
{"name": "OrderDual.instIsSimpleOrder", "kind": "instance", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSimpleOrder.preorder", "kind": "definition", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSimpleOrder.linearOrder", "kind": "definition", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isAtom_top", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isAtom_iff_eq_top", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCoatom_bot", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCoatom_iff_eq_bot", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bot_covBy_top", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSimpleOrder.eq_bot_of_lt", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSimpleOrder.eq_top_of_lt", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSimpleOrder.lattice", "kind": "definition", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSimpleOrder.distribLattice", "kind": "definition", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSimpleOrder.instIsAtomic", "kind": "instance", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSimpleOrder.instIsCoatomic", "kind": "instance", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSimpleOrder.equivBool", "kind": "definition", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSimpleOrder.orderIsoBool", "kind": "definition", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSimpleOrder.booleanAlgebra", "kind": "definition", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSimpleOrder.completeLattice", "kind": "definition", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSimpleOrder.completeBooleanAlgebra", "kind": "definition", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSimpleOrder.instComplementedLattice", "kind": "instance", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSimpleOrder.instIsAtomistic", "kind": "instance", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSimpleOrder.instIsCoatomistic", "kind": "instance", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSimpleOrder.bot_lt_iff_eq_top", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSimpleOrder.lt_top_iff_eq_bot", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isSimpleOrder_iff_isAtom_top", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isSimpleOrder_iff_isCoatom_bot", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.isSimpleOrder_Iic_iff_isAtom", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.isSimpleOrder_Ici_iff_isCoatom", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderEmbedding.isAtom_of_map_bot_of_image", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "OrderEmbedding.isCoatom_of_map_top_of_image", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisInsertion.isAtom_of_u_bot", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisInsertion.isAtom_iff", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": true, "tactics": ["refine", "obtain", "have", "ha'.1", "have", "exact"], "tactic_count": 6}
{"name": "GaloisInsertion.isAtom_iff'", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "GaloisInsertion.isCoatom_of_image", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisInsertion.isCoatom_iff", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": true, "tactics": ["refine", "obtain", "hb.1", "have", "ha.1", "exact"], "tactic_count": 6}
{"name": "GaloisCoinsertion.isCoatom_of_l_top", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisCoinsertion.isCoatom_iff", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisCoinsertion.isCoatom_iff'", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisCoinsertion.isAtom_of_image", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisCoinsertion.isAtom_iff", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.isAtom_iff", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.isCoatom_iff", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.isSimpleOrder_iff", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "OrderIso.isSimpleOrder", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.isAtomic_iff", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": true, "tactics": ["simp", "f.isAtom_iff]"], "tactic_count": 2}
{"name": "OrderIso.isCoatomic_iff", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Lattice.isStronglyAtomic", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lattice.isStronglyCoatomic", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsCompl.isAtom_iff_isCoatom", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompl.isCoatom_iff_isAtom", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCoatomic_of_isAtomic_of_complementedLattice_of_isModular", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isAtomic_of_isCoatomic_of_complementedLattice_of_isModular", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isAtomic_iff_isCoatomic", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplementedLattice.isStronglyAtomic", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplementedLattice.isStronglyCoatomic", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ComplementedLattice.isStronglyAtomic'", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ComplementedLattice.isStronglyCoatomic'", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Prop.instIsSimpleOrderProp", "kind": "instance", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prop.isAtom_iff", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Prop.isCoatom_iff", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Pi.eq_bot_iff", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.isAtom_iff", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Pi.isAtom_single", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.isAtom_iff_eq_single", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Pi.isAtomic", "kind": "instance", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.isCoatomic", "kind": "instance", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.isAtomistic", "kind": "instance", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.isCoatomistic", "kind": "instance", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isAtom_compl", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCoatom_compl", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.isAtom_singleton", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.isAtom_iff", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": ["refine", "rintro", "exact", "rw", "rintro", "exact", "eq_singleton_iff_unique_mem.2"], "tactic_count": 7}
{"name": "Set.isCoatom_iff", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": true, "tactics": ["rw", "simp_rw"], "tactic_count": 2}
{"name": "Set.isCoatom_singleton_compl", "kind": "theorem", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instIsAtomistic", "kind": "instance", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instIsCoatomistic", "kind": "instance", "module": "Mathlib.Order.Atoms", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSimpleOrder.instFintypeOfDecidableEq", "kind": "instance", "module": "Mathlib.Order.Atoms.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSimpleOrder.instFinite", "kind": "instance", "module": "Mathlib.Order.Atoms.Finite", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Fintype.IsSimpleOrder.univ", "kind": "theorem", "module": "Mathlib.Order.Atoms.Finite", "is_tactic_proof": true, "tactics": ["ext", "simpa"], "tactic_count": 2}
{"name": "Fintype.IsSimpleOrder.card", "kind": "theorem", "module": "Mathlib.Order.Atoms.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bool.instIsSimpleOrder", "kind": "instance", "module": "Mathlib.Order.Atoms.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finite.to_isCoatomic", "kind": "instance", "module": "Mathlib.Order.Atoms.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finite.to_isAtomic", "kind": "instance", "module": "Mathlib.Order.Atoms.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsStronglyAtomic", "kind": "instance", "module": "Mathlib.Order.Atoms.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsStronglyCoatomic", "kind": "instance", "module": "Mathlib.Order.Atoms.Finite", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "exists_covby_infinite_Ici_of_infinite_Ici", "kind": "theorem", "module": "Mathlib.Order.Atoms.Finite", "is_tactic_proof": true, "tactics": ["by_contra", "refine", "obtain", "exact"], "tactic_count": 4}
{"name": "exists_covby_infinite_Iic_of_infinite_Iic", "kind": "theorem", "module": "Mathlib.Order.Atoms.Finite", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "LE.le.ge", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GE.ge.le", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_of_le_of_eq'", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_of_eq_of_le'", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LT.lt.gt", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GT.gt.lt", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lt_of_lt_of_eq'", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lt_of_eq_of_lt'", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Preimage", "kind": "definition", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "term_⁻¹'o_", "kind": "definition", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Order_Basic___macroRules_term_⁻¹'o__1", "kind": "definition", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Order_Basic___unexpand_Order_Preimage_1", "kind": "definition", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Preimage.decidable", "kind": "instance", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_lt_iff_not_le_or_ge", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "not_lt_iff_le_imp_ge", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "lt_self_iff_false", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LT.lt.false", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Eq.not_lt", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ne_of_not_le", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_of_subsingleton", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_lt_of_subsingleton", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_of_forall_le", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "forall_le_iff_le", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_imp_le_of_le_of_le", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lt_imp_lt_of_le_of_le", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.GCongr.exactLeOfLt", "kind": "definition", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ne.lt_of_le", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LE.le.lt_iff_ne", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LE.le.not_lt_iff_eq", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LE.le.ge_iff_eq", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_imp_eq_iff_le_imp_ge", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Decidable.le_iff_eq_or_lt", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_iff_eq_or_lt", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lt_iff_le_and_ne", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Decidable.eq_iff_le_not_lt", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_iff_le_not_lt", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Decidable.eq_or_lt_of_le", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_or_lt_of_le", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_of_le_of_not_lt", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ne.le_iff_lt", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ne.not_le_or_not_ge", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Decidable.ne_iff_lt_iff_le", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ne_iff_lt_iff_le", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_of_forall_le_iff", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "commutative_of_le", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "associative_of_commutative_of_le", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LE.le.gt_or_le", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LE.le.ge_or_lt", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LE.le.ge_or_le", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LT.lt.gt_or_lt", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ne.lt_or_gt", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lt_or_lt_iff_ne", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_lt_iff_eq_or_lt", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_ge_of_linear", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_forall_ge_and", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_of_forall_lt", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "forall_lt_iff_le", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_of_forall_lt_imp_ne", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lt_of_forall_le_imp_ne", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "forall_lt_imp_ne_iff_le", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "forall_le_imp_ne_iff_lt", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_of_forall_lt_iff", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_iff_eq_of_lt_iff_lt_of_gt_iff_gt", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "min_rec", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "min_rec'", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "min_def_lt", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "max_def_lt", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "lt_imp_lt_of_le_imp_le", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_imp_le_iff_lt_imp_lt", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lt_iff_lt_of_le_iff_le'", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lt_iff_lt_of_le_iff_le", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_iff_le_iff_lt_iff_lt", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "rel_imp_eq_of_rel_imp_le", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Preorder.toLE_injective", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialOrder.toPreorder_injective", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "LinearOrder.toPartialOrder_injective", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Preorder.ext", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "PartialOrder.ext", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "PartialOrder.ext_lt", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "LinearOrder.ext", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "LinearOrder.ext_lt", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual", "kind": "definition", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "term_ᵒᵈ", "kind": "definition", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Order_Basic___macroRules_term_ᵒᵈ_1", "kind": "definition", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Order_Basic___unexpand_OrderDual_1", "kind": "definition", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instNonempty", "kind": "instance", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instSubsingleton", "kind": "instance", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instLE", "kind": "instance", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instLT", "kind": "instance", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instOrd", "kind": "instance", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instSup", "kind": "instance", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "OrderDual.instIsTransLT", "kind": "instance", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "OrderDual.Ord.dual_dual", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LinearOrder.ofSubsingleton", "kind": "abbrev", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instLinearOrderEmpty", "kind": "instance", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "PUnit.instDenselyOrdered", "kind": "instance", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "subrelation_iff_le", "kind": "theorem", "module": "Mathlib.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "OrderEmbedding.infIrredUpperSet", "kind": "definition", "module": "Mathlib.Order.Birkhoff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderEmbedding.supIrredLowerSet_apply", "kind": "theorem", "module": "Mathlib.Order.Birkhoff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderEmbedding.infIrredUpperSet_apply", "kind": "theorem", "module": "Mathlib.Order.Birkhoff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderEmbedding.supIrredLowerSet_surjective", "kind": "theorem", "module": "Mathlib.Order.Birkhoff", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "OrderEmbedding.infIrredUpperSet_surjective", "kind": "theorem", "module": "Mathlib.Order.Birkhoff", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "OrderIso.supIrredLowerSet", "kind": "definition", "module": "Mathlib.Order.Birkhoff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.infIrredUpperSet", "kind": "definition", "module": "Mathlib.Order.Birkhoff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.supIrredLowerSet_apply", "kind": "theorem", "module": "Mathlib.Order.Birkhoff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.infIrredUpperSet_apply", "kind": "theorem", "module": "Mathlib.Order.Birkhoff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.supIrredLowerSet_symm_apply", "kind": "theorem", "module": "Mathlib.Order.Birkhoff", "is_tactic_proof": true, "tactics": ["classical", "obtain", "obtain", "cases", "have", "simp"], "tactic_count": 6}
{"name": "OrderIso.infIrredUpperSet_symm_apply", "kind": "theorem", "module": "Mathlib.Order.Birkhoff", "is_tactic_proof": true, "tactics": ["classical", "obtain", "obtain", "cases", "have", "simp"], "tactic_count": 6}
{"name": "OrderIso.lowerSetSupIrred", "kind": "definition", "module": "Mathlib.Order.Birkhoff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderEmbedding.birkhoffSet", "kind": "definition", "module": "Mathlib.Order.Birkhoff", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "have", "exact"], "tactic_count": 4}
{"name": "OrderEmbedding.birkhoffFinset", "kind": "definition", "module": "Mathlib.Order.Birkhoff", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "OrderEmbedding.coe_birkhoffFinset", "kind": "theorem", "module": "Mathlib.Order.Birkhoff", "is_tactic_proof": true, "tactics": ["classical", "simp"], "tactic_count": 2}
{"name": "OrderEmbedding.birkhoffSet_sup", "kind": "theorem", "module": "Mathlib.Order.Birkhoff", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "OrderEmbedding.birkhoffSet_inf", "kind": "theorem", "module": "Mathlib.Order.Birkhoff", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "OrderEmbedding.birkhoffSet_apply", "kind": "theorem", "module": "Mathlib.Order.Birkhoff", "is_tactic_proof": true, "tactics": ["have", "simp"], "tactic_count": 2}
{"name": "OrderEmbedding.birkhoffFinset_sup", "kind": "theorem", "module": "Mathlib.Order.Birkhoff", "is_tactic_proof": true, "tactics": ["classical", "dsimp", "rw", "simp"], "tactic_count": 4}
{"name": "OrderEmbedding.birkhoffFinset_inf", "kind": "theorem", "module": "Mathlib.Order.Birkhoff", "is_tactic_proof": true, "tactics": ["classical", "dsimp", "rw", "simp"], "tactic_count": 4}
{"name": "LatticeHom.birkhoffSet", "kind": "definition", "module": "Mathlib.Order.Birkhoff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LatticeHom.birkhoffFinset", "kind": "definition", "module": "Mathlib.Order.Birkhoff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LatticeHom.birkhoffFinset_injective", "kind": "theorem", "module": "Mathlib.Order.Birkhoff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_birkhoff_representation", "kind": "theorem", "module": "Mathlib.Order.Birkhoff", "is_tactic_proof": true, "tactics": ["classical", "cases", "exact"], "tactic_count": 3}
{"name": "sup_inf_sdiff", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inf_inf_sdiff", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sup_sdiff_inf", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "inf_sdiff_inf", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "GeneralizedBooleanAlgebra.toOrderBot", "kind": "instance", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "disjoint_inf_sdiff", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sdiff_unique", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": true, "tactics": ["conv_rhs", "rw", "conv_rhs", "rw", "exact"], "tactic_count": 5}
{"name": "_private.Mathlib.Order.BooleanAlgebra.Basic.0.sdiff_le'", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Order.BooleanAlgebra.Basic.0.sdiff_sup_self'", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sdiff_inf_sdiff", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "disjoint_sdiff_sdiff", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inf_sdiff_self_right", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inf_sdiff_self_left", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra", "kind": "instance", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "disjoint_sdiff_self_left", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "disjoint_sdiff_self_right", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_sdiff", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sdiff_eq_left", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Disjoint.sdiff_eq_of_sup_eq", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Disjoint.sdiff_unique", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "disjoint_sdiff_iff_le", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_iff_disjoint_sdiff", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inf_sdiff_eq_bot_iff", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "le_iff_eq_sup_sdiff", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sdiff_sup", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sdiff_eq_sdiff_iff_inf_eq_inf", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sdiff_eq_self_iff_disjoint", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sdiff_lt", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "rw"], "tactic_count": 3}
{"name": "sdiff_lt_left", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "le_sdiff_right", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sdiff_eq_right", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "sdiff_ne_right", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sdiff_lt_sdiff_right", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sup_inf_inf_sdiff", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "sdiff_sdiff_right", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply", "calc", "x", "rw", "inf_sdiff_sup_right,", "calc", "x"], "tactic_count": 8}
{"name": "sdiff_sdiff_right'", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sdiff_sdiff_eq_sdiff_sup", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "sdiff_sdiff_right_self", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "sdiff_sdiff_eq_self", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "sdiff_eq_symm", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "sdiff_eq_comm", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_of_sdiff_eq_sdiff", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "sdiff_le_sdiff_iff_le", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "sdiff_sdiff_left'", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "sdiff_sdiff_sup_sdiff", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sdiff_sdiff_sup_sdiff'", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sdiff_sdiff_sdiff_cancel_left", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sdiff_sdiff_sdiff_cancel_right", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "inf_sdiff", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inf_sdiff_assoc", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sdiff_inf_right_comm", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "inf_sdiff_left_comm", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "inf_sdiff_distrib_left", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "inf_sdiff_distrib_right", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "disjoint_sdiff_comm", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "sup_eq_sdiff_sup_sdiff_sup_inf", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sup_lt_of_lt_sdiff_left", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "sup_lt_of_lt_sdiff_right", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "Prod.instGeneralizedBooleanAlgebra", "kind": "instance", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instGeneralizedBooleanAlgebra", "kind": "instance", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GeneralizedBooleanAlgebra.toBooleanAlgebra", "kind": "abbrev", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inf_compl_eq_bot'", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sup_compl_eq_top", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "compl_sup_eq_top", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "isCompl_compl", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sdiff_eq", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "himp_eq", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanAlgebra.toComplementedLattice", "kind": "instance", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanAlgebra.toGeneralizedBooleanAlgebra", "kind": "instance", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanAlgebra.toBiheytingAlgebra", "kind": "instance", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hnot_eq_compl", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "top_sdiff", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_compl_iff_isCompl", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "compl_eq_iff_isCompl", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "compl_eq_comm", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "eq_compl_comm", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "compl_compl", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "compl_comp_compl", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "compl_involutive", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "compl_bijective", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "compl_surjective", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "compl_injective", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "compl_inj_iff", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompl.compl_eq_iff", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "compl_eq_top", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "compl_eq_bot", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "compl_inf", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "compl_le_compl_iff_le", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "compl_lt_compl_iff_lt", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "compl_le_of_compl_le", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "compl_le_iff_compl_le", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "compl_le_self", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "compl_lt_self", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "sdiff_compl", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "OrderDual.instBooleanAlgebra", "kind": "instance", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sup_inf_inf_compl", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "compl_sdiff", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "compl_himp", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "compl_sdiff_compl", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "compl_himp_compl", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "disjoint_compl_left_iff", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "disjoint_compl_right_iff", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "codisjoint_himp_self_left", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "codisjoint_himp_self_right", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "himp_le", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "himp_le_left", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "himp_eq_left", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "himp_ne_right", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "codisjoint_iff_compl_le_left", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "codisjoint_iff_compl_le_right", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instBooleanAlgebra", "kind": "instance", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instBooleanAlgebra", "kind": "instance", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.generalizedBooleanAlgebra", "kind": "abbrev", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.booleanAlgebra", "kind": "abbrev", "module": "Mathlib.Order.BooleanAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanAlgebra.toBoundedOrder", "kind": "instance", "module": "Mathlib.Order.BooleanAlgebra.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prop.instBooleanAlgebra", "kind": "instance", "module": "Mathlib.Order.BooleanAlgebra.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bool.instBooleanAlgebra", "kind": "instance", "module": "Mathlib.Order.BooleanAlgebra.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bool.sup_eq_bor", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Defs", "is_tactic_proof": true, "tactics": ["dsimp"], "tactic_count": 1}
{"name": "Bool.inf_eq_band", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Defs", "is_tactic_proof": true, "tactics": ["dsimp"], "tactic_count": 1}
{"name": "Bool.compl_eq_bnot", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PUnit.instBooleanAlgebra", "kind": "instance", "module": "Mathlib.Order.BooleanAlgebra.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DistribLattice.booleanAlgebraOfComplemented", "kind": "definition", "module": "Mathlib.Order.BooleanAlgebra.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instBooleanAlgebra", "kind": "instance", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inter_diff_assoc", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sdiff_inter_right_comm", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inter_sdiff_left_comm", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.diff_union_diff_cancel", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.diff_union_diff_cancel'", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.diff_diff_eq_sdiff_union", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inter_diff_distrib_left", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inter_diff_distrib_right", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.diff_inter_distrib_right", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.compl_def", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_compl", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.compl_setOf", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.notMem_of_mem_compl", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.notMem_compl_iff", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inter_compl_self", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.compl_inter_self", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.compl_empty", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.compl_union", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.compl_inter", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.compl_univ", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.compl_empty_iff", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.compl_univ_iff", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.compl_ne_univ", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inl_compl_union_inr_compl", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.nonempty_compl", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.union_eq_compl_compl_inter_compl", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inter_eq_compl_compl_union_compl", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.union_compl_self", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.compl_union_self", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.compl_subset_comm", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subset_compl_comm", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.compl_subset_compl", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.compl_subset_compl_of_subset", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subset_union_compl_iff_inter_subset", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.compl_subset_iff_union", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inter_subset", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inter_compl_nonempty_iff", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subset_compl_iff_disjoint_left", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subset_compl_iff_disjoint_right", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.disjoint_compl_left_iff_subset", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.disjoint_compl_right_iff_subset", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.nonempty_compl_of_nontrivial", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_compl_singleton_iff", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.compl_singleton_eq", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.compl_ne_eq_singleton", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subset_compl_singleton_iff", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.notMem_diff_of_mem", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_of_mem_diff", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.notMem_of_mem_diff", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.diff_eq_compl_inter", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.diff_nonempty", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.diff_subset", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.diff_subset_compl", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.union_diff_cancel'", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.union_diff_cancel", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.union_diff_cancel_left", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.union_diff_cancel_right", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.union_diff_left", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.union_diff_right", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.union_diff_distrib", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inter_diff_self", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inter_union_diff", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.diff_union_inter", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.inter_union_compl", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subset_inter_union_compl_left", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.subset_inter_union_compl_right", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.union_inter_compl_left_subset", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.union_inter_compl_right_subset", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.diff_subset_diff", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.diff_subset_diff_left", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.diff_subset_diff_right", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.diff_subset_diff_iff_subset", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.compl_eq_univ_diff", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.empty_diff", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.diff_eq_empty", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.diff_empty", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.diff_univ", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.diff_diff", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.diff_diff_comm", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.diff_subset_iff", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subset_diff_union", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.diff_union_of_subset", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.diff_subset_comm", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.diff_inter", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.diff_inter_diff", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.diff_compl", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.compl_diff", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.diff_diff_right", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.inter_diff_right_comm", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.diff_inter_right_comm", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.union_diff_self", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.diff_union_self", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.diff_inter_self", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.diff_inter_self_eq_diff", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.diff_self_inter", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.diff_self", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.diff_diff_right_self", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.diff_diff_cancel_left", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.union_eq_diff_union_diff_union_inter", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sdiff_sep_self", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.disjoint_sdiff_left", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.disjoint_sdiff_right", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.disjoint_sdiff_inter", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subset_diff", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.disjoint_of_subset_iff_left_eq_empty", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.diff_ssubset_left_iff", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasSubset.Subset.diff_ssubset_of_nonempty", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.ssubset_iff_sdiff_singleton", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.diff_singleton_subset_iff", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "Set.subset_diff_singleton", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subset_insert_diff_singleton", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.diff_insert_of_notMem", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.insert_diff_of_mem", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.insert_diff_of_notMem", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.insert_diff_self_of_notMem", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Set.insert_diff_self_of_mem", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Set.insert_diff_subset", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "Set.insert_erase_invOn", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.diff_singleton_eq_self", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.diff_singleton_ssubset", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.insert_diff_singleton", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.insert_diff_singleton_comm", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.insert_diff_insert", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.mem_diff_singleton", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_diff_singleton_empty", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subset_insert_iff", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.pair_diff_left", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.pair_diff_right", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.ite", "kind": "definition", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ite_inter_self", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.ite_compl", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.ite_inter_compl_self", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.ite_diff_self", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ite_same", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Set.ite_univ", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "Set.inter_subset_ite", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ite_inter_inter", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": true, "tactics": ["ext", "unfold", "push", "tauto"], "tactic_count": 4}
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{"name": "Set.ite_inter_of_inter_eq", "kind": "theorem", "module": "Mathlib.Order.BooleanAlgebra.Set", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "IsCompactlyGenerated.BooleanGenerators.mono", "kind": "theorem", "module": "Mathlib.Order.BooleanGenerators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "BooleanSubalgebra.instSetLike", "kind": "instance", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanSubalgebra.instPartialOrder", "kind": "instance", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanSubalgebra.coe_inj", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanSubalgebra.supClosed", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanSubalgebra.infClosed", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanSubalgebra.compl_mem", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanSubalgebra.compl_mem_iff", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanSubalgebra.bot_mem", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanSubalgebra.top_mem", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "BooleanSubalgebra.sup_mem", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanSubalgebra.inf_mem", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanSubalgebra.sdiff_mem", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "BooleanSubalgebra.himp_mem", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "BooleanSubalgebra.mem_carrier", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanSubalgebra.mem_toSublattice", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanSubalgebra.mem_mk", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanSubalgebra.coe_mk", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanSubalgebra.mk_le_mk", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanSubalgebra.mk_lt_mk", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanSubalgebra.copy", "kind": "definition", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanSubalgebra.coe_copy", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanSubalgebra.copy_eq", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanSubalgebra.ext", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanSubalgebra.instBotCoe", "kind": "instance", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "BooleanSubalgebra.instInfCoe", "kind": "instance", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "BooleanSubalgebra.instSDiffCoe", "kind": "instance", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanSubalgebra.instHImpCoe", "kind": "instance", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanSubalgebra.val_bot", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanSubalgebra.val_top", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "BooleanSubalgebra.val_compl", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "BooleanSubalgebra.val_himp", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "BooleanSubalgebra.subtype", "kind": "definition", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "BooleanSubalgebra.subtype_apply", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "BooleanSubalgebra.inclusion_rfl", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanSubalgebra.subtype_comp_inclusion", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "BooleanSubalgebra.instInhabited", "kind": "instance", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanSubalgebra.topEquiv", "kind": "definition", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "BooleanSubalgebra.instCompleteLattice", "kind": "instance", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanSubalgebra.instSubsingletonOfIsEmpty", "kind": "instance", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanSubalgebra.instUniqueOfIsEmpty", "kind": "instance", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanSubalgebra.comap", "kind": "definition", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanSubalgebra.coe_comap", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "BooleanSubalgebra.comap_mono", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanSubalgebra.comap_id", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "BooleanSubalgebra.map", "kind": "definition", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanSubalgebra.coe_map", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanSubalgebra.mem_map", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanSubalgebra.mem_map_of_mem", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanSubalgebra.apply_coe_mem_map", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanSubalgebra.map_mono", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanSubalgebra.map_id", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanSubalgebra.map_map", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanSubalgebra.mem_map_equiv", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanSubalgebra.apply_mem_map_iff", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanSubalgebra.map_equiv_eq_comap_symm", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanSubalgebra.comap_equiv_eq_map_symm", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanSubalgebra.map_symm_eq_iff_eq_map", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "BooleanSubalgebra.map_le_iff_le_comap", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanSubalgebra.gc_map_comap", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanSubalgebra.map_bot", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanSubalgebra.map_sup", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanSubalgebra.map_iSup", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanSubalgebra.comap_top", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanSubalgebra.comap_inf", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanSubalgebra.comap_iInf", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "BooleanSubalgebra.le_comap_sup", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanSubalgebra.le_comap_iSup", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanSubalgebra.map_inf", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "BooleanSubalgebra.map_top", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanSubalgebra.closure", "kind": "definition", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanSubalgebra.mem_closure", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanSubalgebra.subset_closure", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanSubalgebra.mem_closure_of_mem", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanSubalgebra.closure_le", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanSubalgebra.closure_mono", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanSubalgebra.latticeClosure_subset_closure", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanSubalgebra.closure_latticeClosure", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanSubalgebra.closure_bot_sup_induction", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanSubalgebra.mem_closure_iff_sup_sdiff", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": true, "tactics": ["classical", "refine", "rintro", "exact", "t.sup_mem", "sdiff_mem", "rintro", "exact", "rintro", "refine", "simp_rw", "refine", "simp_rw", "use", "simp_rw", "compl_compl,"], "tactic_count": 16}
{"name": "BooleanSubalgebra.closure_sdiff_sup_induction", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": true, "tactics": ["obtain", "revert", "classical", "refine", "simp", "exact"], "tactic_count": 6}
{"name": "BooleanSubalgebra.iSup_mem", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanSubalgebra.iInf_mem", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanSubalgebra.sSup_mem", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanSubalgebra.sInf_mem", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanSubalgebra.biSup_mem", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BooleanSubalgebra.biInf_mem", "kind": "theorem", "module": "Mathlib.Order.BooleanSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Booleanisation", "kind": "definition", "module": "Mathlib.Order.Booleanisation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Booleanisation.instDecidableEq", "kind": "instance", "module": "Mathlib.Order.Booleanisation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Booleanisation.lift", "kind": "definition", "module": "Mathlib.Order.Booleanisation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Booleanisation.comp", "kind": "definition", "module": "Mathlib.Order.Booleanisation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Booleanisation.instCompl", "kind": "instance", "module": "Mathlib.Order.Booleanisation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Booleanisation.compl_lift", "kind": "theorem", "module": "Mathlib.Order.Booleanisation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Booleanisation.compl_comp", "kind": "theorem", "module": "Mathlib.Order.Booleanisation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Booleanisation.LE", "kind": "inductive", "module": "Mathlib.Order.Booleanisation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Booleanisation.LT", "kind": "inductive", "module": "Mathlib.Order.Booleanisation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Booleanisation.instLE", "kind": "instance", "module": "Mathlib.Order.Booleanisation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Booleanisation.instLT", "kind": "instance", "module": "Mathlib.Order.Booleanisation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Booleanisation.instSup", "kind": "instance", "module": "Mathlib.Order.Booleanisation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Booleanisation.instInf", "kind": "instance", "module": "Mathlib.Order.Booleanisation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Booleanisation.instBot", "kind": "instance", "module": "Mathlib.Order.Booleanisation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Booleanisation.instTop", "kind": "instance", "module": "Mathlib.Order.Booleanisation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Booleanisation.instSDiff", "kind": "instance", "module": "Mathlib.Order.Booleanisation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Booleanisation.lift_le_lift", "kind": "theorem", "module": "Mathlib.Order.Booleanisation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Booleanisation.comp_le_comp", "kind": "theorem", "module": "Mathlib.Order.Booleanisation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Booleanisation.lift_le_comp", "kind": "theorem", "module": "Mathlib.Order.Booleanisation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Booleanisation.not_comp_le_lift", "kind": "theorem", "module": "Mathlib.Order.Booleanisation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Booleanisation.lift_lt_lift", "kind": "theorem", "module": "Mathlib.Order.Booleanisation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Booleanisation.comp_lt_comp", "kind": "theorem", "module": "Mathlib.Order.Booleanisation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Booleanisation.lift_lt_comp", "kind": "theorem", "module": "Mathlib.Order.Booleanisation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Booleanisation.not_comp_lt_lift", "kind": "theorem", "module": "Mathlib.Order.Booleanisation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Booleanisation.lift_sup_lift", "kind": "theorem", "module": "Mathlib.Order.Booleanisation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Booleanisation.lift_sup_comp", "kind": "theorem", "module": "Mathlib.Order.Booleanisation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Booleanisation.comp_sup_lift", "kind": "theorem", "module": "Mathlib.Order.Booleanisation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Booleanisation.comp_sup_comp", "kind": "theorem", "module": "Mathlib.Order.Booleanisation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Booleanisation.lift_inf_lift", "kind": "theorem", "module": "Mathlib.Order.Booleanisation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Booleanisation.lift_inf_comp", "kind": "theorem", "module": "Mathlib.Order.Booleanisation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Booleanisation.comp_inf_lift", "kind": "theorem", "module": "Mathlib.Order.Booleanisation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Booleanisation.comp_inf_comp", "kind": "theorem", "module": "Mathlib.Order.Booleanisation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Booleanisation.lift_bot", "kind": "theorem", "module": "Mathlib.Order.Booleanisation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Booleanisation.comp_bot", "kind": "theorem", "module": "Mathlib.Order.Booleanisation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Booleanisation.lift_sdiff_lift", "kind": "theorem", "module": "Mathlib.Order.Booleanisation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Booleanisation.lift_sdiff_comp", "kind": "theorem", "module": "Mathlib.Order.Booleanisation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Booleanisation.comp_sdiff_lift", "kind": "theorem", "module": "Mathlib.Order.Booleanisation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Booleanisation.comp_sdiff_comp", "kind": "theorem", "module": "Mathlib.Order.Booleanisation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Booleanisation.instPreorder", "kind": "instance", "module": "Mathlib.Order.Booleanisation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Booleanisation.instPartialOrder", "kind": "instance", "module": "Mathlib.Order.Booleanisation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Booleanisation.instSemilatticeSup", "kind": "instance", "module": "Mathlib.Order.Booleanisation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Booleanisation.instSemilatticeInf", "kind": "instance", "module": "Mathlib.Order.Booleanisation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Booleanisation.instDistribLattice", "kind": "instance", "module": "Mathlib.Order.Booleanisation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Booleanisation.instBoundedOrder", "kind": "instance", "module": "Mathlib.Order.Booleanisation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Booleanisation.instBooleanAlgebra", "kind": "instance", "module": "Mathlib.Order.Booleanisation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Booleanisation.liftLatticeHom", "kind": "definition", "module": "Mathlib.Order.Booleanisation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Booleanisation.liftLatticeHom_injective", "kind": "theorem", "module": "Mathlib.Order.Booleanisation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Bounded.mono", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Unbounded.mono", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.unbounded_le_of_forall_exists_lt", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.unbounded_le_iff", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.unbounded_lt_of_forall_exists_le", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.unbounded_lt_iff", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.unbounded_ge_of_forall_exists_gt", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.unbounded_ge_iff", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.unbounded_gt_of_forall_exists_ge", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.unbounded_gt_iff", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Bounded.rel_mono", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.bounded_le_of_bounded_lt", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Unbounded.rel_mono", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.unbounded_lt_of_unbounded_le", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.bounded_le_iff_bounded_lt", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": true, "tactics": ["refine", "obtain", "obtain", "exact"], "tactic_count": 4}
{"name": "Set.unbounded_lt_iff_unbounded_le", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.bounded_ge_of_bounded_gt", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.unbounded_gt_of_unbounded_ge", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.bounded_ge_iff_bounded_gt", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.unbounded_gt_iff_unbounded_ge", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.unbounded_le_univ", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.unbounded_lt_univ", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.unbounded_ge_univ", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.unbounded_gt_univ", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.bounded_self", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.bounded_lt_Iio", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.bounded_le_Iio", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.bounded_le_Iic", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.bounded_lt_Iic", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.bounded_gt_Ioi", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.bounded_ge_Ioi", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.bounded_ge_Ici", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.bounded_gt_Ici", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.bounded_lt_Ioo", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.bounded_lt_Ico", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.bounded_lt_Ioc", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.bounded_lt_Icc", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.bounded_le_Ioo", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.bounded_le_Ico", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.bounded_le_Ioc", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.bounded_le_Icc", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.bounded_gt_Ioo", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.bounded_gt_Ioc", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.bounded_gt_Ico", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.bounded_gt_Icc", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.bounded_ge_Ioo", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.bounded_ge_Ioc", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.bounded_ge_Ico", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.bounded_ge_Icc", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.unbounded_le_Ioi", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.unbounded_le_Ici", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.unbounded_lt_Ioi", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.unbounded_lt_Ici", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.bounded_inter_not", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": true, "tactics": ["refine", "rintro", "obtain", "exact"], "tactic_count": 4}
{"name": "Set.unbounded_inter_not", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.bounded_le_inter_not_le", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.unbounded_le_inter_not_le", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.bounded_le_inter_lt", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.unbounded_le_inter_lt", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": true, "tactics": ["convert", "exact"], "tactic_count": 2}
{"name": "Set.bounded_le_inter_le", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "Set.unbounded_le_inter_le", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.bounded_lt_inter_not_lt", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.unbounded_lt_inter_not_lt", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.bounded_lt_inter_le", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": true, "tactics": ["convert", "exact"], "tactic_count": 2}
{"name": "Set.unbounded_lt_inter_le", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": true, "tactics": ["convert", "exact"], "tactic_count": 2}
{"name": "Set.bounded_lt_inter_lt", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.unbounded_lt_inter_lt", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.bounded_ge_inter_not_ge", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.unbounded_ge_inter_not_ge", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.bounded_ge_inter_gt", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.unbounded_ge_inter_gt", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.bounded_ge_inter_ge", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.unbounded_ge_iff_unbounded_inter_ge", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.bounded_gt_inter_not_gt", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.unbounded_gt_inter_not_gt", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.bounded_gt_inter_ge", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.unbounded_inter_ge", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.bounded_gt_inter_gt", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.unbounded_gt_inter_gt", "kind": "theorem", "module": "Mathlib.Order.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "topOrderOrNoTopOrder", "kind": "definition", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "letI", "exact"], "tactic_count": 4}
{"name": "dite_ne_top", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": true, "tactics": ["split"], "tactic_count": 1}
{"name": "ite_ne_top", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_top", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isTop_top", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsTop.rec", "kind": "definition", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": true, "tactics": ["letI", "apply"], "tactic_count": 2}
{"name": "isMax_top", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_top_lt", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ne_top_of_lt", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lt_top_of_lt", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isMax_iff_eq_top", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isTop_iff_eq_top", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_isMax_iff_ne_top", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_isTop_iff_ne_top", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "top_le_iff", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "top_unique", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_top_iff", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_top_mono", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lt_top_iff_ne_top", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_lt_top_iff", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_top_or_lt_top", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ne.lt_top", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ne.lt_top'", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ne_top_of_le_ne_top", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "top_notMem_iff", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_isMin_top", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderTop.ext_top", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": true, "tactics": ["cases", "apply", "exact"], "tactic_count": 3}
{"name": "OrderBot.ext_bot", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": true, "tactics": ["cases", "apply", "exact"], "tactic_count": 3}
{"name": "OrderDual.instTop", "kind": "instance", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instOrderTop", "kind": "instance", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.ofDual_top", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.toDual_top", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.ofDual_eq_top", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.toDual_eq_top", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_bot_of_minimal", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instBoundedOrder", "kind": "instance", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderBot.instSubsingleton", "kind": "instance", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedOrder.instSubsingleton", "kind": "instance", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instBotForall", "kind": "instance", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.bot_apply", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.bot_def", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.bot_comp", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "Pi.instOrderBot", "kind": "instance", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instBoundedOrder", "kind": "instance", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_bot_of_bot_eq_top", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_top_of_bot_eq_top", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "subsingleton_of_top_le_bot", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "subsingleton_of_bot_eq_top", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "subsingleton_iff_bot_eq_top", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderTop.lift", "kind": "abbrev", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderBot.lift", "kind": "abbrev", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedOrder.lift", "kind": "abbrev", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.orderBot", "kind": "abbrev", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.boundedOrder", "kind": "abbrev", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.mk_bot", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.coe_bot", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.coe_eq_bot_iff", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subtype.mk_eq_bot_iff", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instTop", "kind": "instance", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.fst_top", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.snd_top", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instOrderTop", "kind": "instance", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instBoundedOrder", "kind": "instance", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.instTop", "kind": "instance", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.up_top", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.down_top", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.instOrderBot", "kind": "instance", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.instOrderTop", "kind": "instance", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.instBoundedOrder", "kind": "instance", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bot_ne_top", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bot_lt_top", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bool.instBoundedOrder", "kind": "instance", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "top_eq_true", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bot_eq_false", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "top_sup_eq", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sup_top_eq", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bot_sup_eq", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sup_bot_eq", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sup_eq_bot_iff", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Lattice", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "min_bot_left", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "min_bot_right", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "max_bot_left", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "max_bot_right", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "max_eq_bot", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "min_eq_bot", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Lattice", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "min_ne_bot", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Lattice", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "WellFoundedGT.induction_top", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Lattice", "is_tactic_proof": true, "tactics": ["contrapose", "intro", "induction", "ind", "by_cases", "exact", "intro", "obtain", "exact"], "tactic_count": 9}
{"name": "StrictMono.apply_eq_top_iff", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictAnti.apply_eq_top_iff", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.maximal_preimage_top", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.apply_eq_bot_iff", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictAnti.apply_eq_bot_iff", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.minimal_preimage_bot", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monotone_and", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monotone_or", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monotone_le", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monotone_lt", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "antitone_le", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "antitone_lt", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.forall", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.forall", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.ball", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.ball", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.exists", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.exists", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "forall_ge_iff", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "forall_le_iff", "kind": "theorem", "module": "Mathlib.Order.BoundedOrder.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_upperBounds", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_upperBounds_iff_subset_Iic", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bddAbove_def", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "top_mem_upperBounds", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLeast_bot_iff", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_bddAbove_iff'", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "not_bddAbove_iff", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "bddAbove_preimage_ofDual", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bddAbove_preimage_toDual", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddAbove.dual", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLeast.dual", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLUB.dual", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLeast.orderBot", "kind": "abbrev", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLUB_congr", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsCofinalFor.of_subset", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCofinalFor.rfl", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCofinalFor.trans", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCofinalFor.mono_left", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCofinalFor.mono_right", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectedOn.isCofinalFor_fst_image_prod_snd_image", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": true, "tactics": ["rintro", "obtain", "exact"], "tactic_count": 3}
{"name": "upperBounds_mono_set", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "upperBounds_mono_of_isCofinalFor", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "upperBounds_mono_mem", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "upperBounds_mono", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddAbove.mono", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLUB.of_subset_of_superset", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLeast.mono", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLUB.mono", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "subset_lowerBounds_upperBounds", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nonempty.bddAbove_lowerBounds", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLeast.isGLB", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLUB.upperBounds_eq", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLeast.lowerBounds_eq", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGreatest.lt_iff", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLUB_le_iff", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "isLUB_iff_le_iff", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLUB.bddAbove", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGreatest.bddAbove", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLeast.nonempty", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "upperBounds_union", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "union_upperBounds_subset_upperBounds_inter", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLeast_union_iff", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "BddAbove.inter_of_left", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddAbove.inter_of_right", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddAbove.union", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": true, "tactics": ["rintro", "obtain", "rw", "exact"], "tactic_count": 4}
{"name": "bddAbove_union", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLUB.union", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLeast.union", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLUB.inter_Ici_of_mem", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bddAbove_iff_exists_ge", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "bddBelow_iff_exists_le", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddAbove.exists_ge", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLeast_Ici", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLUB_Iic", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "upperBounds_Iic", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bddAbove_Iic", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bddAbove_Iio", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_of_isLUB_Iio", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lub_Iio_eq_self_or_Iio_eq_Iic", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": true, "tactics": ["rcases", "exact", "right", "exact"], "tactic_count": 4}
{"name": "exists_lub_Iio", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "obtain", "exact", "refine", "rw", "exact"], "tactic_count": 6}
{"name": "isLUB_Iio", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "upperBounds_Iio", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isGreatest_singleton", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLUB_singleton", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bddAbove_singleton", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "upperBounds_singleton", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bddAbove_Icc", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bddBelow_Icc", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bddAbove_Ico", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bddBelow_Ico", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bddAbove_Ioc", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bddBelow_Ioc", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bddAbove_Ioo", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bddBelow_Ioo", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isGreatest_Icc", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLUB_Icc", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "upperBounds_Icc", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLeast_Icc", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isGLB_Icc", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lowerBounds_Icc", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isGreatest_Ioc", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLUB_Ioc", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "upperBounds_Ioc", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLeast_Ico", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isGLB_Ico", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lowerBounds_Ico", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isGLB_Ioo", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lowerBounds_Ioo", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isGLB_Ioc", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lowerBounds_Ioc", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLUB_Ioo", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "upperBounds_Ioo", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLUB_Ico", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "upperBounds_Ico", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bddBelow_iff_subset_Ici", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bddAbove_iff_subset_Iic", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bddBelow_bddAbove_iff_subset_Icc", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": true, "tactics": ["simp", "exists_and_right]"], "tactic_count": 2}
{"name": "isGreatest_univ_iff", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "isGreatest_univ", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderTop.upperBounds_univ", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "isLUB_univ", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderBot.lowerBounds_univ", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLeast_univ_iff", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLeast_univ", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isGLB_univ", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NoTopOrder.upperBounds_univ", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NoBotOrder.lowerBounds_univ", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_bddAbove_univ", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "not_bddBelow_univ", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "upperBounds_empty", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "lowerBounds_empty", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bddAbove_empty", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "bddBelow_empty", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "isGLB_empty_iff", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "isLUB_empty_iff", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isGLB_empty", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLUB_empty", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLUB.nonempty", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGLB.nonempty", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nonempty_of_not_bddAbove", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nonempty_of_not_bddBelow", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bddAbove_insert", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "BddAbove.insert", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bddBelow_insert", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "BddBelow.insert", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLUB.insert", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsGLB.insert", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsGreatest.insert", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsLeast.insert", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "upperBounds_insert", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "lowerBounds_insert", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "OrderTop.bddAbove", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderBot.bddBelow", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tacticBddDefault", "kind": "definition", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Order_Bounds_Basic___macroRules_tacticBddDefault_1", "kind": "definition", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLUB_pair", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isGLB_pair", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLeast_pair", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isGreatest_pair", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLUB_lowerBounds", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isGLB_upperBounds", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectedOn.le_of_minimal", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "DirectedOn.le_of_maximal", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "DirectedOn.minimal_iff_isLeast", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectedOn.maximal_iff_isGreatest", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "minimal_iff_isLeast", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "maximal_iff_isGreatest", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lowerBounds_le_upperBounds", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isGLB_le_isLUB", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLUB_lt_iff", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lt_isGLB_iff", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_of_isLUB_le_isGLB", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "upperBounds_prod", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "lowerBounds_prod", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "IsLUB.prod", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": true, "tactics": ["simp_all"], "tactic_count": 1}
{"name": "IsGLB.prod", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": true, "tactics": ["simp_all"], "tactic_count": 1}
{"name": "IsLeast.unique", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLeast.isLeast_iff_eq", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGreatest.unique", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGreatest.isGreatest_iff_eq", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLUB.unique", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGLB.unique", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subsingleton_of_isLUB_le_isGLB", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isGLB_lt_isLUB_of_ne", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lt_isLUB_iff", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "isGLB_lt_iff", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLUB.exists_between", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLUB.exists_between'", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGLB.exists_between", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGLB.exists_between'", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isGreatest_himp", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "isLeast_sdiff", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "isGreatest_compl", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "isLeast_hnot", "kind": "theorem", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Nat.instDecidableIsLeast", "kind": "instance", "module": "Mathlib.Order.Bounds.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "upperBounds", "kind": "definition", "module": "Mathlib.Order.Bounds.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddAbove", "kind": "definition", "module": "Mathlib.Order.Bounds.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLeast", "kind": "definition", "module": "Mathlib.Order.Bounds.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLUB", "kind": "definition", "module": "Mathlib.Order.Bounds.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCofinalFor", "kind": "definition", "module": "Mathlib.Order.Bounds.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCofinal", "kind": "definition", "module": "Mathlib.Order.Bounds.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonotoneOn.mem_upperBounds_image", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonotoneOn.mem_upperBounds_image_self", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonotoneOn.mem_lowerBounds_image", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonotoneOn.mem_lowerBounds_image_self", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonotoneOn.image_upperBounds_subset_upperBounds_image", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "MonotoneOn.image_lowerBounds_subset_lowerBounds_image", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonotoneOn.map_bddAbove", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonotoneOn.map_bddBelow", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonotoneOn.map_isLeast", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonotoneOn.map_isGreatest", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntitoneOn.mem_upperBounds_image", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntitoneOn.mem_upperBounds_image_self", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntitoneOn.mem_lowerBounds_image", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntitoneOn.mem_lowerBounds_image_self", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntitoneOn.image_lowerBounds_subset_upperBounds_image", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntitoneOn.image_upperBounds_subset_lowerBounds_image", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntitoneOn.map_bddAbove", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntitoneOn.map_bddBelow", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntitoneOn.map_isGreatest", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntitoneOn.map_isLeast", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.mem_upperBounds_image", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.mem_lowerBounds_image", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.image_upperBounds_subset_upperBounds_image", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "Monotone.image_lowerBounds_subset_lowerBounds_image", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.map_bddAbove", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.map_bddBelow", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.map_isLeast", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.map_isGreatest", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.mem_upperBounds_image", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.mem_lowerBounds_image", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.image_lowerBounds_subset_upperBounds_image", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.image_upperBounds_subset_lowerBounds_image", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.map_bddAbove", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.map_bddBelow", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.map_isGreatest", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.map_isLeast", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.mem_upperBounds_image", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "StrictMono.mem_lowerBounds_image", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "StrictMono.map_isLeast", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "StrictMono.map_isGreatest", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "StrictAnti.mem_upperBounds_image", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "StrictAnti.mem_lowerBounds_image", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "StrictAnti.map_isLeast", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "StrictAnti.map_isGreatest", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "mem_upperBounds_image2", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_lowerBounds_image2", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "image2_upperBounds_upperBounds_subset", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "image2_lowerBounds_lowerBounds_subset", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddAbove.image2", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "BddBelow.image2", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "IsGreatest.image2", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLeast.image2", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_upperBounds_image2_of_mem_upperBounds_of_mem_lowerBounds", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_lowerBounds_image2_of_mem_lowerBounds_of_mem_upperBounds", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "image2_upperBounds_lowerBounds_subset_upperBounds_image2", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "image2_lowerBounds_upperBounds_subset_lowerBounds_image2", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddAbove.bddAbove_image2_of_bddBelow", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "BddBelow.bddBelow_image2_of_bddAbove", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "IsGreatest.isGreatest_image2_of_isLeast", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLeast.isLeast_image2_of_isGreatest", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_upperBounds_image2_of_mem_lowerBounds", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_lowerBounds_image2_of_mem_upperBounds", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "image2_upperBounds_upperBounds_subset_upperBounds_image2", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "image2_lowerBounds_lowerBounds_subset_lowerBounds_image2", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddBelow.image2_bddAbove", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "BddAbove.image2_bddBelow", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "IsLeast.isGreatest_image2", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGreatest.isLeast_image2", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_upperBounds_image2_of_mem_upperBounds_of_mem_upperBounds", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_lowerBounds_image2_of_mem_lowerBounds_of_mem_lowerBounds", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "image2_lowerBounds_upperBounds_subset_upperBounds_image2", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "image2_upperBounds_lowerBounds_subset_lowerBounds_image2", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddBelow.bddAbove_image2_of_bddAbove", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "BddAbove.bddBelow_image2_of_bddAbove", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "IsLeast.isGreatest_image2_of_isGreatest", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGreatest.isLeast_image2_of_isLeast", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCofinalFor.image_of_monotone", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": true, "tactics": ["simp", "rintro", "obtain", "exact"], "tactic_count": 4}
{"name": "IsCofinalFor.image_of_antitone", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": true, "tactics": ["simp", "rintro", "obtain", "exact"], "tactic_count": 4}
{"name": "IsCoinitialFor.image_of_monotone", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": true, "tactics": ["simp", "rintro", "obtain", "exact"], "tactic_count": 4}
{"name": "IsCoinitialFor.image_of_antitone", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": true, "tactics": ["simp", "rintro", "obtain", "exact"], "tactic_count": 4}
{"name": "bddAbove_prod", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bddBelow_prod", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bddAbove_range_prod", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "bddBelow_range_prod", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLUB_prod", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": ["refine", "suffices", "exact", "suffices", "exact", "exact", "exact"], "tactic_count": 7}
{"name": "isGLB_prod", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.upperBounds_image_of_directedOn_prod", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bddAbove_pi", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bddBelow_pi", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bddAbove_range_pi", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": true, "tactics": ["simp", "rfl"], "tactic_count": 2}
{"name": "bddBelow_range_pi", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLUB_pi", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": true, "tactics": ["classical", "refine", "suffices", "exact", "exact", "exact"], "tactic_count": 6}
{"name": "isGLB_pi", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGLB.of_image", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLUB.of_image", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddAbove.range_mono", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": true, "tactics": ["obtain", "use", "rintro", "exact"], "tactic_count": 4}
{"name": "BddBelow.range_mono", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddAbove.range_comp", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": true, "tactics": ["change", "simpa"], "tactic_count": 2}
{"name": "BddBelow.range_comp", "kind": "theorem", "module": "Mathlib.Order.Bounds.Image", "is_tactic_proof": true, "tactics": ["change", "simpa"], "tactic_count": 2}
{"name": "gc_upperBounds_lowerBounds", "kind": "theorem", "module": "Mathlib.Order.Bounds.Lattice", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "upperBounds_iUnion", "kind": "theorem", "module": "Mathlib.Order.Bounds.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lowerBounds_iUnion", "kind": "theorem", "module": "Mathlib.Order.Bounds.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLUB_iUnion_iff_of_isLUB", "kind": "theorem", "module": "Mathlib.Order.Bounds.Lattice", "is_tactic_proof": true, "tactics": ["refine", "simp_rw"], "tactic_count": 2}
{"name": "isGLB_iUnion_iff_of_isLUB", "kind": "theorem", "module": "Mathlib.Order.Bounds.Lattice", "is_tactic_proof": true, "tactics": ["refine", "simp_rw"], "tactic_count": 2}
{"name": "OrderIso.upperBounds_image", "kind": "theorem", "module": "Mathlib.Order.Bounds.OrderIso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.lowerBounds_image", "kind": "theorem", "module": "Mathlib.Order.Bounds.OrderIso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.isLUB_image", "kind": "theorem", "module": "Mathlib.Order.Bounds.OrderIso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.isLUB_image'", "kind": "theorem", "module": "Mathlib.Order.Bounds.OrderIso", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "OrderIso.isGLB_image", "kind": "theorem", "module": "Mathlib.Order.Bounds.OrderIso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.isGLB_image'", "kind": "theorem", "module": "Mathlib.Order.Bounds.OrderIso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.isLUB_preimage", "kind": "theorem", "module": "Mathlib.Order.Bounds.OrderIso", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "OrderIso.isLUB_preimage'", "kind": "theorem", "module": "Mathlib.Order.Bounds.OrderIso", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "OrderIso.isGLB_preimage", "kind": "theorem", "module": "Mathlib.Order.Bounds.OrderIso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.isGLB_preimage'", "kind": "theorem", "module": "Mathlib.Order.Bounds.OrderIso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instSetLikeNonemptyChain", "kind": "instance", "module": "Mathlib.Order.BourbakiWitt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instPartialOrderNonemptyChain", "kind": "instance", "module": "Mathlib.Order.BourbakiWitt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ChainCompletePartialOrder.instOmegaCompletePartialOrder", "kind": "instance", "module": "Mathlib.Order.BourbakiWitt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ChainCompletePartialOrder.instOfCompleteLattice", "kind": "instance", "module": "Mathlib.Order.BourbakiWitt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ChainCompletePartialOrder.ici_isAdmissible", "kind": "theorem", "module": "Mathlib.Order.BourbakiWitt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ChainCompletePartialOrder.bot", "kind": "abbrev", "module": "Mathlib.Order.BourbakiWitt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ChainCompletePartialOrder.bot_isAdmissible", "kind": "theorem", "module": "Mathlib.Order.BourbakiWitt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ChainCompletePartialOrder.subset_bot_iff", "kind": "theorem", "module": "Mathlib.Order.BourbakiWitt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ChainCompletePartialOrder.map_mem_bot", "kind": "theorem", "module": "Mathlib.Order.BourbakiWitt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ChainCompletePartialOrder.IsExtremePt.bot_eq_of_le_or_map_le", "kind": "theorem", "module": "Mathlib.Order.BourbakiWitt", "is_tactic_proof": true, "tactics": ["rw", "apply", "apply", "constructor", "constructor", "exact", "exact", "exact", "rintro", "rcases", "left", "right", "right", "intro", "refine", "by_cases", "left", "rcases", "have", "right", "apply"], "tactic_count": 21}
{"name": "ChainCompletePartialOrder.IsExtremePt.setOf_isExtremePt_isAdmissible", "kind": "theorem", "module": "Mathlib.Order.BourbakiWitt", "is_tactic_proof": true, "tactics": ["apply", "constructor", "refine", "intro", "exfalso", "exact", "exact", "rintro", "refine", "intro", "have", "rw", "rcases", "rcases", "exact", "exact", "exfalso", "exact", "intro", "refine", "intro", "obtain", "by_contra", "apply", "apply", "intro", "exact", "have", "rw", "exact", "obtain", "exact", "have", "rw", "apply", "intro", "exact"], "tactic_count": 37}
{"name": "ChainCompletePartialOrder.IsExtremePt.setOf_isExtremePt_eq_bot", "kind": "theorem", "module": "Mathlib.Order.BourbakiWitt", "is_tactic_proof": true, "tactics": ["rw", "exact", "exact"], "tactic_count": 3}
{"name": "ChainCompletePartialOrder.IsExtremePt.mem_bot_iff_isExtremePt", "kind": "theorem", "module": "Mathlib.Order.BourbakiWitt", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ChainCompletePartialOrder.IsExtremePt.bot_isChain", "kind": "theorem", "module": "Mathlib.Order.BourbakiWitt", "is_tactic_proof": true, "tactics": ["intro", "rw", "rw", "obtain", "right", "left"], "tactic_count": 6}
{"name": "ChainCompletePartialOrder.nonempty_fixedPoints_of_inflationary", "kind": "theorem", "module": "Mathlib.Order.BourbakiWitt", "is_tactic_proof": true, "tactics": ["let", "let", "use", "apply", "apply", "use", "exact"], "tactic_count": 7}
{"name": "BddDistLat.instCoeSortType", "kind": "instance", "module": "Mathlib.Order.Category.BddDistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddDistLat.instDistribLatticeCarrier", "kind": "instance", "module": "Mathlib.Order.Category.BddDistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddDistLat.of", "kind": "abbrev", "module": "Mathlib.Order.Category.BddDistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddDistLat.coe_of", "kind": "theorem", "module": "Mathlib.Order.Category.BddDistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddDistLat.instCategory", "kind": "instance", "module": "Mathlib.Order.Category.BddDistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddDistLat.instConcreteCategoryBoundedLatticeHomCarrier", "kind": "instance", "module": "Mathlib.Order.Category.BddDistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddDistLat.Hom.hom", "kind": "abbrev", "module": "Mathlib.Order.Category.BddDistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddDistLat.ofHom", "kind": "abbrev", "module": "Mathlib.Order.Category.BddDistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddDistLat.Hom.Simps.hom", "kind": "definition", "module": "Mathlib.Order.Category.BddDistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddDistLat.coe_id", "kind": "theorem", "module": "Mathlib.Order.Category.BddDistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddDistLat.coe_comp", "kind": "theorem", "module": "Mathlib.Order.Category.BddDistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddDistLat.forget_map", "kind": "theorem", "module": "Mathlib.Order.Category.BddDistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddDistLat.ext", "kind": "theorem", "module": "Mathlib.Order.Category.BddDistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddDistLat.hom_id", "kind": "theorem", "module": "Mathlib.Order.Category.BddDistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddDistLat.id_apply", "kind": "theorem", "module": "Mathlib.Order.Category.BddDistLat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "BddDistLat.hom_comp", "kind": "theorem", "module": "Mathlib.Order.Category.BddDistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddDistLat.comp_apply", "kind": "theorem", "module": "Mathlib.Order.Category.BddDistLat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "BddDistLat.hom_ext", "kind": "theorem", "module": "Mathlib.Order.Category.BddDistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddDistLat.hom_ofHom", "kind": "theorem", "module": "Mathlib.Order.Category.BddDistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddDistLat.ofHom_hom", "kind": "theorem", "module": "Mathlib.Order.Category.BddDistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddDistLat.ofHom_id", "kind": "theorem", "module": "Mathlib.Order.Category.BddDistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddDistLat.ofHom_comp", "kind": "theorem", "module": "Mathlib.Order.Category.BddDistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddDistLat.ofHom_apply", "kind": "theorem", "module": "Mathlib.Order.Category.BddDistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddDistLat.inv_hom_apply", "kind": "theorem", "module": "Mathlib.Order.Category.BddDistLat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "BddDistLat.toBddLat", "kind": "definition", "module": "Mathlib.Order.Category.BddDistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddDistLat.coe_toBddLat", "kind": "theorem", "module": "Mathlib.Order.Category.BddDistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddDistLat.hasForgetToDistLat", "kind": "instance", "module": "Mathlib.Order.Category.BddDistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddDistLat.hasForgetToBddLat", "kind": "instance", "module": "Mathlib.Order.Category.BddDistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddDistLat.forget_bddLat_lat_eq_forget_distLat_lat", "kind": "theorem", "module": "Mathlib.Order.Category.BddDistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddDistLat.Iso.mk", "kind": "definition", "module": "Mathlib.Order.Category.BddDistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddDistLat.dual", "kind": "definition", "module": "Mathlib.Order.Category.BddDistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddDistLat.dualEquiv", "kind": "definition", "module": "Mathlib.Order.Category.BddDistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bddDistLat_dual_comp_forget_to_distLat", "kind": "theorem", "module": "Mathlib.Order.Category.BddDistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "BddLat.of", "kind": "abbrev", "module": "Mathlib.Order.Category.BddLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "BddLat.instLargeCategory", "kind": "instance", "module": "Mathlib.Order.Category.BddLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddLat.instConcreteCategoryBoundedLatticeHomCarrier", "kind": "instance", "module": "Mathlib.Order.Category.BddLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddLat.Hom.hom", "kind": "abbrev", "module": "Mathlib.Order.Category.BddLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddLat.ofHom", "kind": "abbrev", "module": "Mathlib.Order.Category.BddLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "BddLat.id_apply", "kind": "theorem", "module": "Mathlib.Order.Category.BddLat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "BddLat.hasForgetToBddOrd", "kind": "instance", "module": "Mathlib.Order.Category.BddLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddLat.hasForgetToLat", "kind": "instance", "module": "Mathlib.Order.Category.BddLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddLat.hasForgetToSemilatSup", "kind": "instance", "module": "Mathlib.Order.Category.BddLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddLat.hasForgetToSemilatInf", "kind": "instance", "module": "Mathlib.Order.Category.BddLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddLat.coe_forget_to_bddOrd", "kind": "theorem", "module": "Mathlib.Order.Category.BddLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddLat.coe_forget_to_lat", "kind": "theorem", "module": "Mathlib.Order.Category.BddLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddLat.coe_forget_to_semilatSup", "kind": "theorem", "module": "Mathlib.Order.Category.BddLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddLat.coe_forget_to_semilatInf", "kind": "theorem", "module": "Mathlib.Order.Category.BddLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddLat.forget_lat_partOrd_eq_forget_bddOrd_partOrd", "kind": "theorem", "module": "Mathlib.Order.Category.BddLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddLat.forget_semilatSup_partOrd_eq_forget_bddOrd_partOrd", "kind": "theorem", "module": "Mathlib.Order.Category.BddLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddLat.forget_semilatInf_partOrd_eq_forget_bddOrd_partOrd", "kind": "theorem", "module": "Mathlib.Order.Category.BddLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "bddLat_dual_comp_forget_to_bddOrd", "kind": "theorem", "module": "Mathlib.Order.Category.BddLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bddLat_dual_comp_forget_to_lat", "kind": "theorem", "module": "Mathlib.Order.Category.BddLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "bddLat_dual_comp_forget_to_semilatInfCat", "kind": "theorem", "module": "Mathlib.Order.Category.BddLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "latToBddLat", "kind": "definition", "module": "Mathlib.Order.Category.BddLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "latToBddLatForgetAdjunction", "kind": "definition", "module": "Mathlib.Order.Category.BddLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "latToBddLatCompDualIsoDualCompLatToBddLat", "kind": "definition", "module": "Mathlib.Order.Category.BddLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddOrd.instCoeSortType", "kind": "instance", "module": "Mathlib.Order.Category.BddOrd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddOrd.of", "kind": "abbrev", "module": "Mathlib.Order.Category.BddOrd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddOrd.instCategory", "kind": "instance", "module": "Mathlib.Order.Category.BddOrd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "BddOrd.Hom.hom", "kind": "abbrev", "module": "Mathlib.Order.Category.BddOrd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddOrd.ofHom", "kind": "abbrev", "module": "Mathlib.Order.Category.BddOrd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "BddOrd.forget_map", "kind": "theorem", "module": "Mathlib.Order.Category.BddOrd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "BddOrd.comp_apply", "kind": "theorem", "module": "Mathlib.Order.Category.BddOrd", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "BddOrd.hom_ofHom", "kind": "theorem", "module": "Mathlib.Order.Category.BddOrd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddOrd.ofHom_hom", "kind": "theorem", "module": "Mathlib.Order.Category.BddOrd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "BddOrd.ofHom_apply", "kind": "theorem", "module": "Mathlib.Order.Category.BddOrd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddOrd.inv_hom_apply", "kind": "theorem", "module": "Mathlib.Order.Category.BddOrd", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "BddOrd.dualEquiv", "kind": "definition", "module": "Mathlib.Order.Category.BddOrd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bddOrd_dual_comp_forget_to_partOrd", "kind": "theorem", "module": "Mathlib.Order.Category.BddOrd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bddOrd_dual_comp_forget_to_bipointed", "kind": "theorem", "module": "Mathlib.Order.Category.BddOrd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoolAlg.instCoeSortType", "kind": "instance", "module": "Mathlib.Order.Category.BoolAlg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoolAlg.instCategory", "kind": "instance", "module": "Mathlib.Order.Category.BoolAlg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoolAlg.instConcreteCategoryBoundedLatticeHomCarrier", "kind": "instance", "module": "Mathlib.Order.Category.BoolAlg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoolAlg.Hom.hom", "kind": "abbrev", "module": "Mathlib.Order.Category.BoolAlg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoolAlg.ofHom", "kind": "abbrev", "module": "Mathlib.Order.Category.BoolAlg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoolAlg.Hom.Simps.hom", "kind": "definition", "module": "Mathlib.Order.Category.BoolAlg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoolAlg.coe_id", "kind": "theorem", "module": "Mathlib.Order.Category.BoolAlg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoolAlg.coe_comp", "kind": "theorem", "module": "Mathlib.Order.Category.BoolAlg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoolAlg.forget_map", "kind": "theorem", "module": "Mathlib.Order.Category.BoolAlg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoolAlg.ext", "kind": "theorem", "module": "Mathlib.Order.Category.BoolAlg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoolAlg.coe_of", "kind": "theorem", "module": "Mathlib.Order.Category.BoolAlg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoolAlg.hom_id", "kind": "theorem", "module": "Mathlib.Order.Category.BoolAlg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoolAlg.id_apply", "kind": "theorem", "module": "Mathlib.Order.Category.BoolAlg", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "BoolAlg.hom_comp", "kind": "theorem", "module": "Mathlib.Order.Category.BoolAlg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoolAlg.comp_apply", "kind": "theorem", "module": "Mathlib.Order.Category.BoolAlg", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "BoolAlg.hom_ext", "kind": "theorem", "module": "Mathlib.Order.Category.BoolAlg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoolAlg.hom_ofHom", "kind": "theorem", "module": "Mathlib.Order.Category.BoolAlg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoolAlg.ofHom_hom", "kind": "theorem", "module": "Mathlib.Order.Category.BoolAlg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoolAlg.ofHom_id", "kind": "theorem", "module": "Mathlib.Order.Category.BoolAlg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoolAlg.ofHom_comp", "kind": "theorem", "module": "Mathlib.Order.Category.BoolAlg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoolAlg.ofHom_apply", "kind": "theorem", "module": "Mathlib.Order.Category.BoolAlg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoolAlg.inv_hom_apply", "kind": "theorem", "module": "Mathlib.Order.Category.BoolAlg", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "BoolAlg.hom_inv_apply", "kind": "theorem", "module": "Mathlib.Order.Category.BoolAlg", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "BoolAlg.instInhabited", "kind": "instance", "module": "Mathlib.Order.Category.BoolAlg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoolAlg.toBddDistLat", "kind": "definition", "module": "Mathlib.Order.Category.BoolAlg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoolAlg.coe_toBddDistLat", "kind": "theorem", "module": "Mathlib.Order.Category.BoolAlg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoolAlg.hasForgetToBddDistLat", "kind": "instance", "module": "Mathlib.Order.Category.BoolAlg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoolAlg.hasForgetToHeytAlg", "kind": "instance", "module": "Mathlib.Order.Category.BoolAlg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoolAlg.Iso.mk", "kind": "definition", "module": "Mathlib.Order.Category.BoolAlg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoolAlg.dual", "kind": "definition", "module": "Mathlib.Order.Category.BoolAlg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoolAlg.dualEquiv", "kind": "definition", "module": "Mathlib.Order.Category.BoolAlg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "boolAlg_dual_comp_forget_to_bddDistLat", "kind": "theorem", "module": "Mathlib.Order.Category.BoolAlg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "typeToBoolAlgOp", "kind": "definition", "module": "Mathlib.Order.Category.BoolAlg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteLat.instCoeSortType", "kind": "instance", "module": "Mathlib.Order.Category.CompleteLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteLat.coe_of", "kind": "theorem", "module": "Mathlib.Order.Category.CompleteLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteLat.instInhabited", "kind": "instance", "module": "Mathlib.Order.Category.CompleteLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteLat.instLargeCategory", "kind": "instance", "module": "Mathlib.Order.Category.CompleteLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteLat.instConcreteCategoryCompleteLatticeHomCarrier", "kind": "instance", "module": "Mathlib.Order.Category.CompleteLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteLat.hasForgetToBddLat", "kind": "instance", "module": "Mathlib.Order.Category.CompleteLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteLat.Iso.mk", "kind": "definition", "module": "Mathlib.Order.Category.CompleteLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteLat.dual", "kind": "definition", "module": "Mathlib.Order.Category.CompleteLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteLat.dualEquiv", "kind": "definition", "module": "Mathlib.Order.Category.CompleteLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "completeLat_dual_comp_forget_to_bddLat", "kind": "theorem", "module": "Mathlib.Order.Category.CompleteLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DistLat.instCoeSortType", "kind": "instance", "module": "Mathlib.Order.Category.DistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DistLat.of", "kind": "abbrev", "module": "Mathlib.Order.Category.DistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DistLat.instCategory", "kind": "instance", "module": "Mathlib.Order.Category.DistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DistLat.instConcreteCategoryLatticeHomCarrier", "kind": "instance", "module": "Mathlib.Order.Category.DistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DistLat.Hom.hom", "kind": "abbrev", "module": "Mathlib.Order.Category.DistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DistLat.ofHom", "kind": "abbrev", "module": "Mathlib.Order.Category.DistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DistLat.Hom.Simps.hom", "kind": "definition", "module": "Mathlib.Order.Category.DistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DistLat.coe_id", "kind": "theorem", "module": "Mathlib.Order.Category.DistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DistLat.coe_comp", "kind": "theorem", "module": "Mathlib.Order.Category.DistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DistLat.forget_map", "kind": "theorem", "module": "Mathlib.Order.Category.DistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DistLat.ext", "kind": "theorem", "module": "Mathlib.Order.Category.DistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DistLat.coe_of", "kind": "theorem", "module": "Mathlib.Order.Category.DistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DistLat.hom_id", "kind": "theorem", "module": "Mathlib.Order.Category.DistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DistLat.id_apply", "kind": "theorem", "module": "Mathlib.Order.Category.DistLat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DistLat.hom_comp", "kind": "theorem", "module": "Mathlib.Order.Category.DistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DistLat.comp_apply", "kind": "theorem", "module": "Mathlib.Order.Category.DistLat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DistLat.hom_ext", "kind": "theorem", "module": "Mathlib.Order.Category.DistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DistLat.hom_ofHom", "kind": "theorem", "module": "Mathlib.Order.Category.DistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DistLat.ofHom_hom", "kind": "theorem", "module": "Mathlib.Order.Category.DistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DistLat.ofHom_id", "kind": "theorem", "module": "Mathlib.Order.Category.DistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DistLat.ofHom_comp", "kind": "theorem", "module": "Mathlib.Order.Category.DistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DistLat.ofHom_apply", "kind": "theorem", "module": "Mathlib.Order.Category.DistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DistLat.inv_hom_apply", "kind": "theorem", "module": "Mathlib.Order.Category.DistLat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DistLat.hom_inv_apply", "kind": "theorem", "module": "Mathlib.Order.Category.DistLat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DistLat.hasForgetToLat", "kind": "instance", "module": "Mathlib.Order.Category.DistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DistLat.Iso.mk", "kind": "definition", "module": "Mathlib.Order.Category.DistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DistLat.dual", "kind": "definition", "module": "Mathlib.Order.Category.DistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DistLat.dualEquiv", "kind": "definition", "module": "Mathlib.Order.Category.DistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "distLat_dual_comp_forget_to_Lat", "kind": "theorem", "module": "Mathlib.Order.Category.DistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinBddDistLat.instCoeSortType", "kind": "instance", "module": "Mathlib.Order.Category.FinBddDistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinBddDistLat.instDistribLatticeCarrier", "kind": "instance", "module": "Mathlib.Order.Category.FinBddDistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinBddDistLat.instBoundedOrderCarrier", "kind": "instance", "module": "Mathlib.Order.Category.FinBddDistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinBddDistLat.of", "kind": "abbrev", "module": "Mathlib.Order.Category.FinBddDistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinBddDistLat.of'", "kind": "abbrev", "module": "Mathlib.Order.Category.FinBddDistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinBddDistLat.instCategory", "kind": "instance", "module": "Mathlib.Order.Category.FinBddDistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinBddDistLat.instConcreteCategoryBoundedLatticeHomCarrier", "kind": "instance", "module": "Mathlib.Order.Category.FinBddDistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinBddDistLat.Hom.hom", "kind": "abbrev", "module": "Mathlib.Order.Category.FinBddDistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinBddDistLat.ofHom", "kind": "abbrev", "module": "Mathlib.Order.Category.FinBddDistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinBddDistLat.Hom.Simps.hom", "kind": "definition", "module": "Mathlib.Order.Category.FinBddDistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinBddDistLat.coe_id", "kind": "theorem", "module": "Mathlib.Order.Category.FinBddDistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinBddDistLat.coe_comp", "kind": "theorem", "module": "Mathlib.Order.Category.FinBddDistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinBddDistLat.forget_map", "kind": "theorem", "module": "Mathlib.Order.Category.FinBddDistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinBddDistLat.ext", "kind": "theorem", "module": "Mathlib.Order.Category.FinBddDistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinBddDistLat.hom_id", "kind": "theorem", "module": "Mathlib.Order.Category.FinBddDistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinBddDistLat.id_apply", "kind": "theorem", "module": "Mathlib.Order.Category.FinBddDistLat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FinBddDistLat.hom_comp", "kind": "theorem", "module": "Mathlib.Order.Category.FinBddDistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinBddDistLat.comp_apply", "kind": "theorem", "module": "Mathlib.Order.Category.FinBddDistLat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FinBddDistLat.hom_ext", "kind": "theorem", "module": "Mathlib.Order.Category.FinBddDistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinBddDistLat.hom_ofHom", "kind": "theorem", "module": "Mathlib.Order.Category.FinBddDistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinBddDistLat.ofHom_hom", "kind": "theorem", "module": "Mathlib.Order.Category.FinBddDistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinBddDistLat.ofHom_id", "kind": "theorem", "module": "Mathlib.Order.Category.FinBddDistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinBddDistLat.ofHom_comp", "kind": "theorem", "module": "Mathlib.Order.Category.FinBddDistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinBddDistLat.ofHom_apply", "kind": "theorem", "module": "Mathlib.Order.Category.FinBddDistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinBddDistLat.inv_hom_apply", "kind": "theorem", "module": "Mathlib.Order.Category.FinBddDistLat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FinBddDistLat.hom_inv_apply", "kind": "theorem", "module": "Mathlib.Order.Category.FinBddDistLat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FinBddDistLat.instInhabited", "kind": "instance", "module": "Mathlib.Order.Category.FinBddDistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinBddDistLat.hasForgetToBddDistLat", "kind": "instance", "module": "Mathlib.Order.Category.FinBddDistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinBddDistLat.hasForgetToFinPartOrd", "kind": "instance", "module": "Mathlib.Order.Category.FinBddDistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinBddDistLat.Iso.mk", "kind": "definition", "module": "Mathlib.Order.Category.FinBddDistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinBddDistLat.dual", "kind": "definition", "module": "Mathlib.Order.Category.FinBddDistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinBddDistLat.dualEquiv", "kind": "definition", "module": "Mathlib.Order.Category.FinBddDistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finBddDistLat_dual_comp_forget_to_bddDistLat", "kind": "theorem", "module": "Mathlib.Order.Category.FinBddDistLat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinBoolAlg.instCoeSortType", "kind": "instance", "module": "Mathlib.Order.Category.FinBoolAlg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinBoolAlg.of", "kind": "abbrev", "module": "Mathlib.Order.Category.FinBoolAlg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinBoolAlg.coe_of", "kind": "theorem", "module": "Mathlib.Order.Category.FinBoolAlg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinBoolAlg.instInhabited", "kind": "instance", "module": "Mathlib.Order.Category.FinBoolAlg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinBoolAlg.largeCategory", "kind": "instance", "module": "Mathlib.Order.Category.FinBoolAlg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinBoolAlg.concreteCategory", "kind": "instance", "module": "Mathlib.Order.Category.FinBoolAlg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinBoolAlg.hasForgetToBoolAlg", "kind": "instance", "module": "Mathlib.Order.Category.FinBoolAlg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinBoolAlg.hasForgetToFinBddDistLat", "kind": "instance", "module": "Mathlib.Order.Category.FinBoolAlg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinBoolAlg.forgetToBoolAlg_full", "kind": "instance", "module": "Mathlib.Order.Category.FinBoolAlg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinBoolAlg.forgetToBoolAlgFaithful", "kind": "instance", "module": "Mathlib.Order.Category.FinBoolAlg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinBoolAlg.hasForgetToFinPartOrd", "kind": "instance", "module": "Mathlib.Order.Category.FinBoolAlg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinBoolAlg.forgetToFinPartOrdFaithful", "kind": "instance", "module": "Mathlib.Order.Category.FinBoolAlg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinBoolAlg.Iso.mk", "kind": "definition", "module": "Mathlib.Order.Category.FinBoolAlg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinBoolAlg.dual", "kind": "definition", "module": "Mathlib.Order.Category.FinBoolAlg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinBoolAlg.dualEquiv", "kind": "definition", "module": "Mathlib.Order.Category.FinBoolAlg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finBoolAlg_dual_comp_forget_to_finBddDistLat", "kind": "theorem", "module": "Mathlib.Order.Category.FinBoolAlg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fintypeToFinBoolAlgOp", "kind": "definition", "module": "Mathlib.Order.Category.FinBoolAlg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinPartOrd.instCoeSortType", "kind": "instance", "module": "Mathlib.Order.Category.FinPartOrd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinPartOrd.instPartialOrderCarrier", "kind": "instance", "module": "Mathlib.Order.Category.FinPartOrd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinPartOrd.of", "kind": "abbrev", "module": "Mathlib.Order.Category.FinPartOrd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinPartOrd.instInhabited", "kind": "instance", "module": "Mathlib.Order.Category.FinPartOrd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinPartOrd.largeCategory", "kind": "instance", "module": "Mathlib.Order.Category.FinPartOrd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinPartOrd.concreteCategory", "kind": "instance", "module": "Mathlib.Order.Category.FinPartOrd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinPartOrd.hasForgetToPartOrd", "kind": "instance", "module": "Mathlib.Order.Category.FinPartOrd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "NonemptyFinLinOrd.of", "kind": "abbrev", "module": "Mathlib.Order.Category.NonemptyFinLinOrd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyFinLinOrd.coe_of", "kind": "theorem", "module": "Mathlib.Order.Category.NonemptyFinLinOrd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyFinLinOrd.ofHom", "kind": "abbrev", "module": "Mathlib.Order.Category.NonemptyFinLinOrd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyFinLinOrd.hom_hom_id", "kind": "theorem", "module": "Mathlib.Order.Category.NonemptyFinLinOrd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "NonemptyFinLinOrd.hom_ext", "kind": "theorem", "module": "Mathlib.Order.Category.NonemptyFinLinOrd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyFinLinOrd.hom_hom_ofHom", "kind": "theorem", "module": "Mathlib.Order.Category.NonemptyFinLinOrd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyFinLinOrd.ofHom_hom", "kind": "theorem", "module": "Mathlib.Order.Category.NonemptyFinLinOrd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyFinLinOrd.instInhabited", "kind": "instance", "module": "Mathlib.Order.Category.NonemptyFinLinOrd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyFinLinOrd.hasForgetToLinOrd", "kind": "instance", "module": "Mathlib.Order.Category.NonemptyFinLinOrd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyFinLinOrd.hasForgetToFinPartOrd", "kind": "instance", "module": "Mathlib.Order.Category.NonemptyFinLinOrd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyFinLinOrd.Iso.mk", "kind": "definition", "module": "Mathlib.Order.Category.NonemptyFinLinOrd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyFinLinOrd.dual", "kind": "definition", "module": "Mathlib.Order.Category.NonemptyFinLinOrd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyFinLinOrd.dualEquiv", "kind": "definition", "module": "Mathlib.Order.Category.NonemptyFinLinOrd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyFinLinOrd.mono_iff_injective", "kind": "theorem", "module": "Mathlib.Order.Category.NonemptyFinLinOrd", "is_tactic_proof": true, "tactics": ["refine", "intro", "let", "let", "let", "change", "have", "ext", "exact", "rw", "rw"], "tactic_count": 11}
{"name": "NonemptyFinLinOrd.epi_iff_surjective", "kind": "theorem", "module": "Mathlib.Order.Category.NonemptyFinLinOrd", "is_tactic_proof": true, "tactics": ["constructor", "intro", "dsimp", "by_contra", "let", "let", "ofHom", "simp", "split_ifs", "any_goals", "exfalso", "exact", "rfl⟩", "let", "ofHom", "simp", "split_ifs", "any_goals", "exfalso", "exact", "rfl⟩", "have", "congr", "rw", "ext", "simp", "change", "split_ifs", "any_goals", "exfalso", "exact", "exfalso", "exact", "simp", "intro", "exact"], "tactic_count": 36}
{"name": "NonemptyFinLinOrd.instSplitEpiCategory", "kind": "instance", "module": "Mathlib.Order.Category.NonemptyFinLinOrd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyFinLinOrd.instHasStrongEpiMonoFactorisations", "kind": "instance", "module": "Mathlib.Order.Category.NonemptyFinLinOrd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nonemptyFinLinOrd_dual_comp_forget_to_linOrd", "kind": "theorem", "module": "Mathlib.Order.Category.NonemptyFinLinOrd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nonemptyFinLinOrdDualCompForgetToFinPartOrd", "kind": "definition", "module": "Mathlib.Order.Category.NonemptyFinLinOrd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.hom_succ", "kind": "definition", "module": "Mathlib.Order.Category.NonemptyFinLinOrd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ωCPO.instCoeSortType", "kind": "instance", "module": "Mathlib.Order.Category.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ωCPO.coe_of", "kind": "theorem", "module": "Mathlib.Order.Category.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ωCPO.instLargeCategory", "kind": "instance", "module": "Mathlib.Order.Category.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ωCPO.instConcreteCategoryContinuousHomCarrier", "kind": "instance", "module": "Mathlib.Order.Category.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ωCPO.instInhabited", "kind": "instance", "module": "Mathlib.Order.Category.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ωCPO.HasProducts.product", "kind": "definition", "module": "Mathlib.Order.Category.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ωCPO.HasProducts.isProduct", "kind": "definition", "module": "Mathlib.Order.Category.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ωCPO.HasProducts.instHasProduct", "kind": "instance", "module": "Mathlib.Order.Category.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ωCPO.omegaCompletePartialOrderEqualizer", "kind": "instance", "module": "Mathlib.Order.Category.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ωCPO.HasEqualizers.equalizerι", "kind": "definition", "module": "Mathlib.Order.Category.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ωCPO.HasEqualizers.equalizer", "kind": "definition", "module": "Mathlib.Order.Category.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ωCPO.HasEqualizers.isEqualizer", "kind": "definition", "module": "Mathlib.Order.Category.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ωCPO.instHasProducts", "kind": "instance", "module": "Mathlib.Order.Category.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ωCPO.instHasLimitWalkingParallelPairParallelPair", "kind": "instance", "module": "Mathlib.Order.Category.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ωCPO.instHasEqualizers", "kind": "instance", "module": "Mathlib.Order.Category.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ωCPO.instHasLimits", "kind": "instance", "module": "Mathlib.Order.Category.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartOrd.instCoeSortType", "kind": "instance", "module": "Mathlib.Order.Category.PartOrd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartOrd.instCategory", "kind": "instance", "module": "Mathlib.Order.Category.PartOrd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartOrd.instConcreteCategoryOrderHomCarrier", "kind": "instance", "module": "Mathlib.Order.Category.PartOrd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartOrd.Hom.hom", "kind": "abbrev", "module": "Mathlib.Order.Category.PartOrd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartOrd.ofHom", "kind": "abbrev", "module": "Mathlib.Order.Category.PartOrd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartOrd.Hom.Simps.hom", "kind": "definition", "module": "Mathlib.Order.Category.PartOrd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartOrd.coe_id", "kind": "theorem", "module": "Mathlib.Order.Category.PartOrd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartOrd.coe_comp", "kind": "theorem", "module": "Mathlib.Order.Category.PartOrd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartOrd.forget_map", "kind": "theorem", "module": "Mathlib.Order.Category.PartOrd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartOrd.ext", "kind": "theorem", "module": "Mathlib.Order.Category.PartOrd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartOrd.coe_of", "kind": "theorem", "module": "Mathlib.Order.Category.PartOrd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartOrd.hom_id", "kind": "theorem", "module": "Mathlib.Order.Category.PartOrd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartOrd.id_apply", "kind": "theorem", "module": "Mathlib.Order.Category.PartOrd", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PartOrd.hom_comp", "kind": "theorem", "module": "Mathlib.Order.Category.PartOrd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartOrd.comp_apply", "kind": "theorem", "module": "Mathlib.Order.Category.PartOrd", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PartOrd.hom_ext", "kind": "theorem", "module": "Mathlib.Order.Category.PartOrd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartOrd.hom_ofHom", "kind": "theorem", "module": "Mathlib.Order.Category.PartOrd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartOrd.ofHom_hom", "kind": "theorem", "module": "Mathlib.Order.Category.PartOrd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartOrd.ofHom_id", "kind": "theorem", "module": "Mathlib.Order.Category.PartOrd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartOrd.ofHom_comp", "kind": "theorem", "module": "Mathlib.Order.Category.PartOrd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartOrd.ofHom_apply", "kind": "theorem", "module": "Mathlib.Order.Category.PartOrd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartOrd.inv_hom_apply", "kind": "theorem", "module": "Mathlib.Order.Category.PartOrd", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PartOrd.hom_inv_apply", "kind": "theorem", "module": "Mathlib.Order.Category.PartOrd", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PartOrd.hasForgetToPreord", "kind": "instance", "module": "Mathlib.Order.Category.PartOrd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartOrd.Iso.mk", "kind": "definition", "module": "Mathlib.Order.Category.PartOrd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartOrd.dual", "kind": "definition", "module": "Mathlib.Order.Category.PartOrd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartOrd.dualEquiv", "kind": "definition", "module": "Mathlib.Order.Category.PartOrd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "partOrd_dual_comp_forget_to_preord", "kind": "theorem", "module": "Mathlib.Order.Category.PartOrd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "preordToPartOrd", "kind": "definition", "module": "Mathlib.Order.Category.PartOrd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "preordToPartOrdForgetAdjunction", "kind": "definition", "module": "Mathlib.Order.Category.PartOrd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "preordToPartOrdCompToDualIsoToDualCompPreordToPartOrd", "kind": "definition", "module": "Mathlib.Order.Category.PartOrd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "preordToPartOrdCompToDualIsoToDualCompPreordToPartOrd_inv_app_hom_coe'", "kind": "theorem", "module": "Mathlib.Order.Category.PartOrd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartOrdEmb.instCoeSortType", "kind": "instance", "module": "Mathlib.Order.Category.PartOrdEmb", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartOrdEmb.instCategory", "kind": "instance", "module": "Mathlib.Order.Category.PartOrdEmb", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartOrdEmb.instConcreteCategoryOrderEmbeddingCarrier", "kind": "instance", "module": "Mathlib.Order.Category.PartOrdEmb", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartOrdEmb.Hom.hom", "kind": "abbrev", "module": "Mathlib.Order.Category.PartOrdEmb", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartOrdEmb.ofHom", "kind": "abbrev", "module": "Mathlib.Order.Category.PartOrdEmb", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartOrdEmb.Hom.Simps.hom", "kind": "definition", "module": "Mathlib.Order.Category.PartOrdEmb", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartOrdEmb.coe_id", "kind": "theorem", "module": "Mathlib.Order.Category.PartOrdEmb", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartOrdEmb.coe_comp", "kind": "theorem", "module": "Mathlib.Order.Category.PartOrdEmb", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartOrdEmb.forget_map", "kind": "theorem", "module": "Mathlib.Order.Category.PartOrdEmb", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartOrdEmb.ext", "kind": "theorem", "module": "Mathlib.Order.Category.PartOrdEmb", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartOrdEmb.coe_of", "kind": "theorem", "module": "Mathlib.Order.Category.PartOrdEmb", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartOrdEmb.hom_id", "kind": "theorem", "module": "Mathlib.Order.Category.PartOrdEmb", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartOrdEmb.id_apply", "kind": "theorem", "module": "Mathlib.Order.Category.PartOrdEmb", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PartOrdEmb.hom_comp", "kind": "theorem", "module": "Mathlib.Order.Category.PartOrdEmb", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartOrdEmb.comp_apply", "kind": "theorem", "module": "Mathlib.Order.Category.PartOrdEmb", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PartOrdEmb.Hom.injective", "kind": "theorem", "module": "Mathlib.Order.Category.PartOrdEmb", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartOrdEmb.Hom.le_iff_le", "kind": "theorem", "module": "Mathlib.Order.Category.PartOrdEmb", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartOrdEmb.hom_ext", "kind": "theorem", "module": "Mathlib.Order.Category.PartOrdEmb", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartOrdEmb.hom_ofHom", "kind": "theorem", "module": "Mathlib.Order.Category.PartOrdEmb", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartOrdEmb.ofHom_hom", "kind": "theorem", "module": "Mathlib.Order.Category.PartOrdEmb", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartOrdEmb.ofHom_id", "kind": "theorem", "module": "Mathlib.Order.Category.PartOrdEmb", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartOrdEmb.ofHom_comp", "kind": "theorem", "module": "Mathlib.Order.Category.PartOrdEmb", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartOrdEmb.ofHom_apply", "kind": "theorem", "module": "Mathlib.Order.Category.PartOrdEmb", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartOrdEmb.inv_hom_apply", "kind": "theorem", "module": "Mathlib.Order.Category.PartOrdEmb", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PartOrdEmb.hom_inv_apply", "kind": "theorem", "module": "Mathlib.Order.Category.PartOrdEmb", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PartOrdEmb.hasForgetToPartOrd", "kind": "instance", "module": "Mathlib.Order.Category.PartOrdEmb", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartOrdEmb.Iso.mk", "kind": "definition", "module": "Mathlib.Order.Category.PartOrdEmb", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartOrdEmb.dual", "kind": "definition", "module": "Mathlib.Order.Category.PartOrdEmb", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartOrdEmb.dualEquiv", "kind": "definition", "module": "Mathlib.Order.Category.PartOrdEmb", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "partOrdEmb_dual_comp_forget_to_pardOrd", "kind": "theorem", "module": "Mathlib.Order.Category.PartOrdEmb", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartOrdEmb.Limits.CoconePt", "kind": "definition", "module": "Mathlib.Order.Category.PartOrdEmb", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartOrdEmb.Limits.instPartialOrderCoconePt", "kind": "instance", "module": "Mathlib.Order.Category.PartOrdEmb", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartOrdEmb.Limits.cocone", "kind": "definition", "module": "Mathlib.Order.Category.PartOrdEmb", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartOrdEmb.Limits.CoconePt.desc", "kind": "definition", "module": "Mathlib.Order.Category.PartOrdEmb", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartOrdEmb.Limits.CoconePt.fac_apply", "kind": "theorem", "module": "Mathlib.Order.Category.PartOrdEmb", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartOrdEmb.Limits.isColimitCocone", "kind": "definition", "module": "Mathlib.Order.Category.PartOrdEmb", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartOrdEmb.Limits.instHasColimit", "kind": "instance", "module": "Mathlib.Order.Category.PartOrdEmb", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartOrdEmb.Limits.instPreservesColimitForget", "kind": "instance", "module": "Mathlib.Order.Category.PartOrdEmb", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartOrdEmb.Limits.instHasColimitsOfShape", "kind": "instance", "module": "Mathlib.Order.Category.PartOrdEmb", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartOrdEmb.Limits.instPreservesColimitsOfShapeForget", "kind": "instance", "module": "Mathlib.Order.Category.PartOrdEmb", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartOrdEmb.Limits.instHasFilteredColimitsOfSize", "kind": "instance", "module": "Mathlib.Order.Category.PartOrdEmb", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartOrdEmb.Limits.instPreservesFilteredColimitsOfSizeForget", "kind": "instance", "module": "Mathlib.Order.Category.PartOrdEmb", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Preord.instCoeSortType", "kind": "instance", "module": "Mathlib.Order.Category.Preord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Preord.instCategory", "kind": "instance", "module": "Mathlib.Order.Category.Preord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Preord.instConcreteCategoryOrderHomCarrier", "kind": "instance", "module": "Mathlib.Order.Category.Preord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Preord.Hom.hom", "kind": "abbrev", "module": "Mathlib.Order.Category.Preord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Preord.ofHom", "kind": "abbrev", "module": "Mathlib.Order.Category.Preord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Preord.Hom.Simps.hom", "kind": "definition", "module": "Mathlib.Order.Category.Preord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Preord.coe_id", "kind": "theorem", "module": "Mathlib.Order.Category.Preord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Preord.coe_comp", "kind": "theorem", "module": "Mathlib.Order.Category.Preord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Preord.forget_map", "kind": "theorem", "module": "Mathlib.Order.Category.Preord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Preord.ext", "kind": "theorem", "module": "Mathlib.Order.Category.Preord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Preord.coe_of", "kind": "theorem", "module": "Mathlib.Order.Category.Preord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Preord.hom_id", "kind": "theorem", "module": "Mathlib.Order.Category.Preord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Preord.id_apply", "kind": "theorem", "module": "Mathlib.Order.Category.Preord", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Preord.hom_comp", "kind": "theorem", "module": "Mathlib.Order.Category.Preord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Preord.comp_apply", "kind": "theorem", "module": "Mathlib.Order.Category.Preord", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Preord.hom_ext", "kind": "theorem", "module": "Mathlib.Order.Category.Preord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Preord.hom_ofHom", "kind": "theorem", "module": "Mathlib.Order.Category.Preord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Preord.ofHom_hom", "kind": "theorem", "module": "Mathlib.Order.Category.Preord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Preord.ofHom_id", "kind": "theorem", "module": "Mathlib.Order.Category.Preord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Preord.ofHom_comp", "kind": "theorem", "module": "Mathlib.Order.Category.Preord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Preord.ofHom_apply", "kind": "theorem", "module": "Mathlib.Order.Category.Preord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Preord.inv_hom_apply", "kind": "theorem", "module": "Mathlib.Order.Category.Preord", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Preord.hom_inv_apply", "kind": "theorem", "module": "Mathlib.Order.Category.Preord", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Preord.instInhabited", "kind": "instance", "module": "Mathlib.Order.Category.Preord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Preord.Iso.mk", "kind": "definition", "module": "Mathlib.Order.Category.Preord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Preord.dual", "kind": "definition", "module": "Mathlib.Order.Category.Preord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Preord.dualEquiv", "kind": "definition", "module": "Mathlib.Order.Category.Preord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "preordToCat", "kind": "definition", "module": "Mathlib.Order.Category.Preord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFaithfulPreordCatPreordToCat", "kind": "instance", "module": "Mathlib.Order.Category.Preord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFullPreordCatPreordToCat", "kind": "instance", "module": "Mathlib.Order.Category.Preord", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemilatSupCat.instCoeSortType", "kind": "instance", "module": "Mathlib.Order.Category.Semilat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemilatSupCat.coe_of", "kind": "theorem", "module": "Mathlib.Order.Category.Semilat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemilatSupCat.instInhabited", "kind": "instance", "module": "Mathlib.Order.Category.Semilat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemilatSupCat.instLargeCategory", "kind": "instance", "module": "Mathlib.Order.Category.Semilat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemilatSupCat.instConcreteCategorySupBotHomX", "kind": "instance", "module": "Mathlib.Order.Category.Semilat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemilatSupCat.hasForgetToPartOrd", "kind": "instance", "module": "Mathlib.Order.Category.Semilat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemilatSupCat.coe_forget_to_partOrd", "kind": "theorem", "module": "Mathlib.Order.Category.Semilat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemilatInfCat.instCoeSortType", "kind": "instance", "module": "Mathlib.Order.Category.Semilat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemilatInfCat.coe_of", "kind": "theorem", "module": "Mathlib.Order.Category.Semilat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemilatInfCat.instInhabited", "kind": "instance", "module": "Mathlib.Order.Category.Semilat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemilatInfCat.instLargeCategory", "kind": "instance", "module": "Mathlib.Order.Category.Semilat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemilatInfCat.instConcreteCategoryInfTopHomX", "kind": "instance", "module": "Mathlib.Order.Category.Semilat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemilatInfCat.hasForgetToPartOrd", "kind": "instance", "module": "Mathlib.Order.Category.Semilat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemilatInfCat.coe_forget_to_partOrd", "kind": "theorem", "module": "Mathlib.Order.Category.Semilat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemilatSupCat.Iso.mk", "kind": "definition", "module": "Mathlib.Order.Category.Semilat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemilatSupCat.dual", "kind": "definition", "module": "Mathlib.Order.Category.Semilat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemilatInfCat.Iso.mk", "kind": "definition", "module": "Mathlib.Order.Category.Semilat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemilatInfCat.dual", "kind": "definition", "module": "Mathlib.Order.Category.Semilat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemilatSupCatEquivSemilatInfCat", "kind": "definition", "module": "Mathlib.Order.Category.Semilat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemilatSupCat_dual_comp_forget_to_partOrd", "kind": "theorem", "module": "Mathlib.Order.Category.Semilat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemilatInfCat_dual_comp_forget_to_partOrd", "kind": "theorem", "module": "Mathlib.Order.Category.Semilat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "btw_rfl", "kind": "theorem", "module": "Mathlib.Order.Circular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Btw.btw.cyclic_left", "kind": "theorem", "module": "Mathlib.Order.Circular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "btw_cyclic_right", "kind": "theorem", "module": "Mathlib.Order.Circular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "btw_cyclic", "kind": "theorem", "module": "Mathlib.Order.Circular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sbtw_iff_btw_not_btw", "kind": "theorem", "module": "Mathlib.Order.Circular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "btw_of_sbtw", "kind": "theorem", "module": "Mathlib.Order.Circular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_btw_of_sbtw", "kind": "theorem", "module": "Mathlib.Order.Circular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_sbtw_of_btw", "kind": "theorem", "module": "Mathlib.Order.Circular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sbtw_of_btw_not_btw", "kind": "theorem", "module": "Mathlib.Order.Circular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sbtw_cyclic_left", "kind": "theorem", "module": "Mathlib.Order.Circular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sbtw_cyclic_right", "kind": "theorem", "module": "Mathlib.Order.Circular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sbtw_cyclic", "kind": "theorem", "module": "Mathlib.Order.Circular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SBtw.sbtw.trans_left", "kind": "theorem", "module": "Mathlib.Order.Circular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sbtw_trans_right", "kind": "theorem", "module": "Mathlib.Order.Circular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sbtw_asymm", "kind": "theorem", "module": "Mathlib.Order.Circular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sbtw_irrefl_left_right", "kind": "theorem", "module": "Mathlib.Order.Circular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sbtw_irrefl_left", "kind": "theorem", "module": "Mathlib.Order.Circular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sbtw_irrefl_right", "kind": "theorem", "module": "Mathlib.Order.Circular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sbtw_irrefl", "kind": "theorem", "module": "Mathlib.Order.Circular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Btw.btw.antisymm", "kind": "theorem", "module": "Mathlib.Order.Circular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "btw_refl_left_right", "kind": "theorem", "module": "Mathlib.Order.Circular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "btw_rfl_left_right", "kind": "theorem", "module": "Mathlib.Order.Circular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "btw_refl_left", "kind": "theorem", "module": "Mathlib.Order.Circular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "btw_rfl_left", "kind": "theorem", "module": "Mathlib.Order.Circular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "btw_refl_right", "kind": "theorem", "module": "Mathlib.Order.Circular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "btw_rfl_right", "kind": "theorem", "module": "Mathlib.Order.Circular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sbtw_iff_not_btw", "kind": "theorem", "module": "Mathlib.Order.Circular", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "btw_iff_not_sbtw", "kind": "theorem", "module": "Mathlib.Order.Circular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.cIcc", "kind": "definition", "module": "Mathlib.Order.Circular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.cIoo", "kind": "definition", "module": "Mathlib.Order.Circular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_cIcc", "kind": "theorem", "module": "Mathlib.Order.Circular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_cIoo", "kind": "theorem", "module": "Mathlib.Order.Circular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.left_mem_cIcc", "kind": "theorem", "module": "Mathlib.Order.Circular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.right_mem_cIcc", "kind": "theorem", "module": "Mathlib.Order.Circular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.compl_cIcc", "kind": "theorem", "module": "Mathlib.Order.Circular", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "Set.compl_cIoo", "kind": "theorem", "module": "Mathlib.Order.Circular", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "LE.toBtw", "kind": "abbrev", "module": "Mathlib.Order.Circular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LT.toSBtw", "kind": "abbrev", "module": "Mathlib.Order.Circular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "btw_iff", "kind": "theorem", "module": "Mathlib.Order.Circular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sbtw_iff", "kind": "theorem", "module": "Mathlib.Order.Circular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Preorder.toCircularPreorder", "kind": "abbrev", "module": "Mathlib.Order.Circular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartialOrder.toCircularPartialOrder", "kind": "abbrev", "module": "Mathlib.Order.Circular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearOrder.toCircularOrder", "kind": "abbrev", "module": "Mathlib.Order.Circular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.btw", "kind": "instance", "module": "Mathlib.Order.Circular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.sbtw", "kind": "instance", "module": "Mathlib.Order.Circular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.circularPreorder", "kind": "instance", "module": "Mathlib.Order.Circular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.circularPartialOrder", "kind": "instance", "module": "Mathlib.Order.Circular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instCircularOrder", "kind": "instance", "module": "Mathlib.Order.Circular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCircularOrderInt", "kind": "instance", "module": "Mathlib.Order.Circular.ZMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.btw_iff", "kind": "theorem", "module": "Mathlib.Order.Circular.ZMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.sbtw_iff", "kind": "theorem", "module": "Mathlib.Order.Circular.ZMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCircularOrderFin", "kind": "instance", "module": "Mathlib.Order.Circular.ZMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.btw_iff", "kind": "theorem", "module": "Mathlib.Order.Circular.ZMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.sbtw_iff", "kind": "theorem", "module": "Mathlib.Order.Circular.ZMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCircularOrderZMod", "kind": "instance", "module": "Mathlib.Order.Circular.ZMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClosureOperator.instFunLike", "kind": "instance", "module": "Mathlib.Order.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClosureOperator.instOrderHomClass", "kind": "instance", "module": "Mathlib.Order.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClosureOperator.conjBy", "kind": "definition", "module": "Mathlib.Order.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClosureOperator.conjBy_refl", "kind": "theorem", "module": "Mathlib.Order.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClosureOperator.conjBy_trans", "kind": "theorem", "module": "Mathlib.Order.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClosureOperator.id", "kind": "definition", "module": "Mathlib.Order.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClosureOperator.instInhabited", "kind": "instance", "module": "Mathlib.Order.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClosureOperator.ext", "kind": "theorem", "module": "Mathlib.Order.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClosureOperator.mk'", "kind": "definition", "module": "Mathlib.Order.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClosureOperator.mk₂", "kind": "definition", "module": "Mathlib.Order.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClosureOperator.ofPred", "kind": "definition", "module": "Mathlib.Order.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClosureOperator.monotone", "kind": "theorem", "module": "Mathlib.Order.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClosureOperator.le_closure", "kind": "theorem", "module": "Mathlib.Order.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClosureOperator.idempotent", "kind": "theorem", "module": "Mathlib.Order.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClosureOperator.isClosed_closure", "kind": "theorem", "module": "Mathlib.Order.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClosureOperator.Closeds", "kind": "abbrev", "module": "Mathlib.Order.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClosureOperator.toCloseds", "kind": "definition", "module": "Mathlib.Order.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClosureOperator.IsClosed.closure_eq", "kind": "theorem", "module": "Mathlib.Order.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClosureOperator.isClosed_iff_closure_le", "kind": "theorem", "module": "Mathlib.Order.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClosureOperator.setOf_isClosed_eq_range_closure", "kind": "theorem", "module": "Mathlib.Order.Closure", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "ClosureOperator.le_closure_iff", "kind": "theorem", "module": "Mathlib.Order.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClosureOperator.IsClosed.closure_le_iff", "kind": "theorem", "module": "Mathlib.Order.Closure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ClosureOperator.closure_min", "kind": "theorem", "module": "Mathlib.Order.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClosureOperator.closure_isGLB", "kind": "theorem", "module": "Mathlib.Order.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClosureOperator.ext_isClosed", "kind": "theorem", "module": "Mathlib.Order.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClosureOperator.eq_ofPred_closed", "kind": "theorem", "module": "Mathlib.Order.Closure", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "ClosureOperator.closure_top", "kind": "theorem", "module": "Mathlib.Order.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClosureOperator.isClosed_top", "kind": "theorem", "module": "Mathlib.Order.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClosureOperator.closure_inf_le", "kind": "theorem", "module": "Mathlib.Order.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClosureOperator.closure_sup_closure_le", "kind": "theorem", "module": "Mathlib.Order.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClosureOperator.closure_sup_closure_left", "kind": "theorem", "module": "Mathlib.Order.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClosureOperator.closure_sup_closure_right", "kind": "theorem", "module": "Mathlib.Order.Closure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ClosureOperator.closure_sup_closure", "kind": "theorem", "module": "Mathlib.Order.Closure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ClosureOperator.ofCompletePred", "kind": "definition", "module": "Mathlib.Order.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClosureOperator.sInf_isClosed", "kind": "theorem", "module": "Mathlib.Order.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClosureOperator.closure_iSup_closure", "kind": "theorem", "module": "Mathlib.Order.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClosureOperator.closure_iSup₂_closure", "kind": "theorem", "module": "Mathlib.Order.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.equivClosureOperator", "kind": "definition", "module": "Mathlib.Order.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerAdjoint.id", "kind": "definition", "module": "Mathlib.Order.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerAdjoint.instInhabitedId", "kind": "instance", "module": "Mathlib.Order.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerAdjoint.instCoeFunForall", "kind": "instance", "module": "Mathlib.Order.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerAdjoint.gc", "kind": "theorem", "module": "Mathlib.Order.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerAdjoint.ext", "kind": "theorem", "module": "Mathlib.Order.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerAdjoint.monotone", "kind": "theorem", "module": "Mathlib.Order.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerAdjoint.le_closure", "kind": "theorem", "module": "Mathlib.Order.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerAdjoint.closureOperator", "kind": "definition", "module": "Mathlib.Order.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerAdjoint.idempotent", "kind": "theorem", "module": "Mathlib.Order.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerAdjoint.le_closure_iff", "kind": "theorem", "module": "Mathlib.Order.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerAdjoint.closed", "kind": "definition", "module": "Mathlib.Order.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerAdjoint.mem_closed_iff", "kind": "theorem", "module": "Mathlib.Order.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerAdjoint.closure_eq_self_of_mem_closed", "kind": "theorem", "module": "Mathlib.Order.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerAdjoint.mem_closed_iff_closure_le", "kind": "theorem", "module": "Mathlib.Order.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerAdjoint.closure_is_closed", "kind": "theorem", "module": "Mathlib.Order.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerAdjoint.closed_eq_range_close", "kind": "theorem", "module": "Mathlib.Order.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerAdjoint.toClosed", "kind": "definition", "module": "Mathlib.Order.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerAdjoint.closure_le_closed_iff_le", "kind": "theorem", "module": "Mathlib.Order.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CompRel.of_compRel_of_antisymmRel", "kind": "theorem", "module": "Mathlib.Order.Comparable", "is_tactic_proof": true, "tactics": ["obtain", "exact", "exact"], "tactic_count": 3}
{"name": "instTransCompRelLeAntisymmRel", "kind": "instance", "module": "Mathlib.Order.Comparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompRel.of_antisymmRel_of_compRel", "kind": "theorem", "module": "Mathlib.Order.Comparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instTransAntisymmRelLeCompRel", "kind": "instance", "module": "Mathlib.Order.Comparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntisymmRel.compRel_congr", "kind": "theorem", "module": "Mathlib.Order.Comparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntisymmRel.compRel_congr_left", "kind": "theorem", "module": "Mathlib.Order.Comparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "linearOrderOfComprel", "kind": "definition", "module": "Mathlib.Order.Comparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IncompRel", "kind": "definition", "module": "Mathlib.Order.Comparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "antisymmRel_compl", "kind": "theorem", "module": "Mathlib.Order.Comparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "antisymmRel_compl_apply", "kind": "theorem", "module": "Mathlib.Order.Comparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "incompRel_compl", "kind": "theorem", "module": "Mathlib.Order.Comparable", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "incompRel_compl_apply", "kind": "theorem", "module": "Mathlib.Order.Comparable", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "incompRel_swap", "kind": "theorem", "module": "Mathlib.Order.Comparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "incompRel_swap_apply", "kind": "theorem", "module": "Mathlib.Order.Comparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IncompRel.refl", "kind": "theorem", "module": "Mathlib.Order.Comparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IncompRel.rfl", "kind": "theorem", "module": "Mathlib.Order.Comparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instReflIncompRelOfIrrefl", "kind": "instance", "module": "Mathlib.Order.Comparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IncompRel.symm", "kind": "theorem", "module": "Mathlib.Order.Comparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instSymmIncompRel", "kind": "instance", "module": "Mathlib.Order.Comparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "incompRel_comm", "kind": "theorem", "module": "Mathlib.Order.Comparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IncompRel.decidableRel", "kind": "instance", "module": "Mathlib.Order.Comparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IncompRel.not_antisymmRel", "kind": "theorem", "module": "Mathlib.Order.Comparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntisymmRel.not_incompRel", "kind": "theorem", "module": "Mathlib.Order.Comparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_compRel_iff", "kind": "theorem", "module": "Mathlib.Order.Comparable", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "not_incompRel_iff", "kind": "theorem", "module": "Mathlib.Order.Comparable", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "not_incompRel_of_total", "kind": "theorem", "module": "Mathlib.Order.Comparable", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IncompRel.ne", "kind": "theorem", "module": "Mathlib.Order.Comparable", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
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{"name": "IncompRel.not_ge", "kind": "theorem", "module": "Mathlib.Order.Comparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LE.le.not_incompRel", "kind": "theorem", "module": "Mathlib.Order.Comparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IncompRel.not_lt", "kind": "theorem", "module": "Mathlib.Order.Comparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IncompRel.not_gt", "kind": "theorem", "module": "Mathlib.Order.Comparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LT.lt.not_incompRel", "kind": "theorem", "module": "Mathlib.Order.Comparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_le_iff_lt_or_incompRel", "kind": "theorem", "module": "Mathlib.Order.Comparable", "is_tactic_proof": true, "tactics": ["rw", "tauto"], "tactic_count": 2}
{"name": "lt_or_antisymmRel_or_gt_or_incompRel", "kind": "theorem", "module": "Mathlib.Order.Comparable", "is_tactic_proof": true, "tactics": ["simp_rw", "tauto"], "tactic_count": 2}
{"name": "incompRel_of_incompRel_of_antisymmRel", "kind": "theorem", "module": "Mathlib.Order.Comparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instTransIncompRelLeAntisymmRel", "kind": "instance", "module": "Mathlib.Order.Comparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "incompRel_of_antisymmRel_of_incompRel", "kind": "theorem", "module": "Mathlib.Order.Comparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instTransAntisymmRelLeIncompRel", "kind": "instance", "module": "Mathlib.Order.Comparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntisymmRel.incompRel_congr", "kind": "theorem", "module": "Mathlib.Order.Comparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntisymmRel.incompRel_congr_left", "kind": "theorem", "module": "Mathlib.Order.Comparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntisymmRel.incompRel_congr_right", "kind": "theorem", "module": "Mathlib.Order.Comparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lt_or_eq_or_gt_or_incompRel", "kind": "theorem", "module": "Mathlib.Order.Comparable", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "cmpLE", "kind": "definition", "module": "Mathlib.Order.Compare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cmpLE_swap", "kind": "theorem", "module": "Mathlib.Order.Compare", "is_tactic_proof": true, "tactics": ["by_cases", "cases"], "tactic_count": 2}
{"name": "cmpLE_eq_cmp", "kind": "theorem", "module": "Mathlib.Order.Compare", "is_tactic_proof": true, "tactics": ["by_cases", "cases"], "tactic_count": 2}
{"name": "Ordering.compares_swap", "kind": "theorem", "module": "Mathlib.Order.Compare", "is_tactic_proof": true, "tactics": ["cases", "exact", "exact", "exact"], "tactic_count": 4}
{"name": "Ordering.swap_eq_iff_eq_swap", "kind": "theorem", "module": "Mathlib.Order.Compare", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordering.Compares.eq_lt", "kind": "theorem", "module": "Mathlib.Order.Compare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordering.Compares.ne_lt", "kind": "theorem", "module": "Mathlib.Order.Compare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordering.Compares.eq_eq", "kind": "theorem", "module": "Mathlib.Order.Compare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordering.Compares.eq_gt", "kind": "theorem", "module": "Mathlib.Order.Compare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordering.Compares.ne_gt", "kind": "theorem", "module": "Mathlib.Order.Compare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordering.Compares.le_total", "kind": "theorem", "module": "Mathlib.Order.Compare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordering.Compares.le_antisymm", "kind": "theorem", "module": "Mathlib.Order.Compare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordering.Compares.inj", "kind": "theorem", "module": "Mathlib.Order.Compare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "toDual_compares_toDual", "kind": "theorem", "module": "Mathlib.Order.Compare", "is_tactic_proof": true, "tactics": ["cases", "exacts"], "tactic_count": 2}
{"name": "ofDual_compares_ofDual", "kind": "theorem", "module": "Mathlib.Order.Compare", "is_tactic_proof": true, "tactics": ["cases", "exacts"], "tactic_count": 2}
{"name": "cmp_compares", "kind": "theorem", "module": "Mathlib.Order.Compare", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
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{"name": "Eq.cmp_eq_eq", "kind": "theorem", "module": "Mathlib.Order.Compare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Order.Frame.MinimalAxioms.inf_sSup_eq", "kind": "theorem", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Order.Frame.MinimalAxioms.iSup_inf_eq", "kind": "theorem", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Order.Frame.MinimalAxioms.inf_iSup_eq", "kind": "theorem", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Order.Frame.MinimalAxioms.inf_iSup₂_eq", "kind": "theorem", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "Order.Coframe.MinimalAxioms.sup_sInf_eq", "kind": "theorem", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Coframe.MinimalAxioms.sInf_sup_eq", "kind": "theorem", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Order.Coframe.MinimalAxioms.iInf_sup_eq", "kind": "theorem", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Order.Coframe.MinimalAxioms.sup_iInf_eq", "kind": "theorem", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
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{"name": "Order.Coframe.ofMinimalAxioms", "kind": "abbrev", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteDistribLattice.MinimalAxioms.of", "kind": "definition", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteDistribLattice.MinimalAxioms.toFrame", "kind": "abbrev", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteDistribLattice.MinimalAxioms.toCoframe", "kind": "abbrev", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteDistribLattice.ofMinimalAxioms", "kind": "abbrev", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompletelyDistribLattice.MinimalAxioms.iInf_iSup_eq'", "kind": "theorem", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": true, "tactics": ["let", "refine", "calc", "iSup_le", "refine", "refine", "rw"], "tactic_count": 7}
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{"name": "CompletelyDistribLattice.MinimalAxioms.of", "kind": "definition", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompletelyDistribLattice.ofMinimalAxioms", "kind": "abbrev", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iInf_iSup_eq", "kind": "theorem", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_iInf_eq", "kind": "theorem", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CompleteLinearOrder.toCompletelyDistribLattice", "kind": "instance", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instCoframe", "kind": "instance", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sSup_inf_eq", "kind": "theorem", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "iSup_inf_eq", "kind": "theorem", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "inf_iSup_eq", "kind": "theorem", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "iSup₂_inf_eq", "kind": "theorem", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "inf_iSup₂_eq", "kind": "theorem", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "biSup_inf_biSup", "kind": "theorem", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
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{"name": "biSup_inter_of_pairwise_disjoint", "kind": "theorem", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": true, "tactics": ["rw", "refine", "le_antisymm", "by_cases", "exact", "simp"], "tactic_count": 6}
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{"name": "disjoint_iSup_iff", "kind": "theorem", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
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{"name": "disjoint_iSup₂_iff", "kind": "theorem", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "sSup_disjoint_iff", "kind": "theorem", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "disjoint_sSup_iff", "kind": "theorem", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "iSup_inf_of_monotone", "kind": "theorem", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": true, "tactics": ["refine", "rw", "refine", "rcases", "exact"], "tactic_count": 5}
{"name": "iSup_inf_of_antitone", "kind": "theorem", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "himp_eq_sSup", "kind": "theorem", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "compl_eq_sSup_disjoint", "kind": "theorem", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "himp_le_iff", "kind": "theorem", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Frame.toDistribLattice", "kind": "instance", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instFrame", "kind": "instance", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instFrame", "kind": "instance", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instFrame", "kind": "instance", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sInf_sup_eq", "kind": "theorem", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iInf_sup_eq", "kind": "theorem", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sup_iInf_eq", "kind": "theorem", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iInf₂_sup_eq", "kind": "theorem", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sup_iInf₂_eq", "kind": "theorem", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iInf_sup_iInf", "kind": "theorem", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "biInf_sup_biInf", "kind": "theorem", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sInf_sup_sInf", "kind": "theorem", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iInf_sup_of_monotone", "kind": "theorem", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iInf_sup_of_antitone", "kind": "theorem", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sdiff_eq_sInf", "kind": "theorem", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hnot_eq_sInf_codisjoint", "kind": "theorem", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_sdiff_iff", "kind": "theorem", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Coframe.toDistribLattice", "kind": "instance", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instCoframe", "kind": "instance", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instCoframe", "kind": "instance", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instCompleteDistribLattice", "kind": "instance", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instCompleteDistribLattice", "kind": "instance", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instCompleteDistribLattice", "kind": "instance", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instCompletelyDistribLattice", "kind": "instance", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instCompletelyDistribLattice", "kind": "instance", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instCompletelyDistribLattice", "kind": "instance", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteBooleanAlgebra.toCompleteDistribLattice", "kind": "instance", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instCompleteBooleanAlgebra", "kind": "instance", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instCompleteBooleanAlgebra", "kind": "instance", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instCompleteBooleanAlgebra", "kind": "instance", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "compl_iInf", "kind": "theorem", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "compl_iSup", "kind": "theorem", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "compl_sInf", "kind": "theorem", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "compl_sSup", "kind": "theorem", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "compl_sInf'", "kind": "theorem", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "compl_sSup'", "kind": "theorem", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_symmDiff_iSup_le", "kind": "theorem", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": true, "tactics": ["simp_rw", "exact", "iSup_mono"], "tactic_count": 3}
{"name": "biSup_symmDiff_biSup_le", "kind": "theorem", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteAtomicBooleanAlgebra.toCompletelyDistribLattice", "kind": "instance", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instCompleteAtomicBooleanAlgebra", "kind": "instance", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instCompleteAtomicBooleanAlgebra", "kind": "instance", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instCompleteAtomicBooleanAlgebra", "kind": "instance", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prop.instCompleteAtomicBooleanAlgebra", "kind": "instance", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prop.instCompleteBooleanAlgebra", "kind": "instance", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.frameMinimalAxioms", "kind": "abbrev", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.coframeMinimalAxioms", "kind": "abbrev", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.frame", "kind": "abbrev", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.coframe", "kind": "abbrev", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.completeDistribLatticeMinimalAxioms", "kind": "abbrev", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.completeDistribLattice", "kind": "abbrev", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.completelyDistribLatticeMinimalAxioms", "kind": "abbrev", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.completelyDistribLattice", "kind": "abbrev", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.completeBooleanAlgebra", "kind": "abbrev", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.completeAtomicBooleanAlgebra", "kind": "abbrev", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PUnit.instCompleteAtomicBooleanAlgebra", "kind": "instance", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PUnit.instCompleteBooleanAlgebra", "kind": "instance", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PUnit.sSup_eq", "kind": "theorem", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PUnit.sInf_eq", "kind": "theorem", "module": "Mathlib.Order.CompleteBooleanAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "subsetSupSet", "kind": "definition", "module": "Mathlib.Order.CompleteLatticeIntervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "subset_sSup_def", "kind": "theorem", "module": "Mathlib.Order.CompleteLatticeIntervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "subset_sSup_of_within", "kind": "theorem", "module": "Mathlib.Order.CompleteLatticeIntervals", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "subset_sSup_emptyset", "kind": "theorem", "module": "Mathlib.Order.CompleteLatticeIntervals", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "subset_sSup_of_not_bddAbove", "kind": "theorem", "module": "Mathlib.Order.CompleteLatticeIntervals", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "subsetInfSet", "kind": "definition", "module": "Mathlib.Order.CompleteLatticeIntervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "subset_sInf_def", "kind": "theorem", "module": "Mathlib.Order.CompleteLatticeIntervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "subset_sInf_of_within", "kind": "theorem", "module": "Mathlib.Order.CompleteLatticeIntervals", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "subset_sInf_emptyset", "kind": "theorem", "module": "Mathlib.Order.CompleteLatticeIntervals", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "subset_sInf_of_not_bddBelow", "kind": "theorem", "module": "Mathlib.Order.CompleteLatticeIntervals", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "subsetConditionallyCompleteLinearOrder", "kind": "abbrev", "module": "Mathlib.Order.CompleteLatticeIntervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sSup_within_of_ordConnected", "kind": "theorem", "module": "Mathlib.Order.CompleteLatticeIntervals", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "refine", "exact", "exact"], "tactic_count": 5}
{"name": "sInf_within_of_ordConnected", "kind": "theorem", "module": "Mathlib.Order.CompleteLatticeIntervals", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "refine", "exact", "exact"], "tactic_count": 5}
{"name": "ordConnectedSubsetConditionallyCompleteLinearOrder", "kind": "instance", "module": "Mathlib.Order.CompleteLatticeIntervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc.completeLattice", "kind": "instance", "module": "Mathlib.Order.CompleteLatticeIntervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCompleteLinearOrderElemIccOfFactLe", "kind": "instance", "module": "Mathlib.Order.CompleteLatticeIntervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc.coe_sSup", "kind": "theorem", "module": "Mathlib.Order.CompleteLatticeIntervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc.coe_sInf", "kind": "theorem", "module": "Mathlib.Order.CompleteLatticeIntervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc.coe_iSup", "kind": "theorem", "module": "Mathlib.Order.CompleteLatticeIntervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc.coe_iInf", "kind": "theorem", "module": "Mathlib.Order.CompleteLatticeIntervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iic.instCompleteLattice", "kind": "instance", "module": "Mathlib.Order.CompleteLatticeIntervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iic.coe_sSup", "kind": "theorem", "module": "Mathlib.Order.CompleteLatticeIntervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iic.coe_iSup", "kind": "theorem", "module": "Mathlib.Order.CompleteLatticeIntervals", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.Iic.coe_biSup", "kind": "theorem", "module": "Mathlib.Order.CompleteLatticeIntervals", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.Iic.coe_sInf", "kind": "theorem", "module": "Mathlib.Order.CompleteLatticeIntervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iic.coe_iInf", "kind": "theorem", "module": "Mathlib.Order.CompleteLatticeIntervals", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.Iic.coe_biInf", "kind": "theorem", "module": "Mathlib.Order.CompleteLatticeIntervals", "is_tactic_proof": true, "tactics": ["cases", "simp", "simp_rw"], "tactic_count": 3}
{"name": "iSup_ulift", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "iInf_ulift", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "sSup_le_sSup_of_isCofinalFor", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sSup_singleton", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sInf_le_sInf_of_isCoinitialFor", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sInf_singleton", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sInf_le_sSup", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sSup_union", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sInf_union", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sSup_inter_le", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_sInf_inter", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sSup_empty", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sInf_empty", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sSup_univ", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sInf_univ", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sSup_insert", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sInf_insert", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sSup_le_sSup_of_subset_insert_bot", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sInf_le_sInf_of_subset_insert_top", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sSup_diff_singleton_bot", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sInf_diff_singleton_top", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sSup_pair", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sInf_pair", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sSup_eq_bot", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sInf_eq_top", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sSup_eq_bot'", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "eq_singleton_bot_of_sSup_eq_bot_of_nonempty", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "eq_singleton_top_of_sInf_eq_top_of_nonempty", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sSup_eq_of_forall_le_of_forall_lt_exists_gt", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sInf_eq_of_forall_ge_of_forall_gt_exists_lt", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sSup_range", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sSup_eq_iSup'", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "iSup_congr", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "biSup_congr", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "biSup_congr'", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Function.Surjective.iSup_comp", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["simp", "congr", "exact"], "tactic_count": 3}
{"name": "Equiv.iSup_comp", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.iSup_congr", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["convert", "exact"], "tactic_count": 2}
{"name": "Equiv.iSup_congr", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_congr_Prop", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["obtain", "congr", "apply"], "tactic_count": 3}
{"name": "iSup_plift_up", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_plift_down", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_range'", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "sSup_image'", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "sInf_range", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sInf_eq_iInf'", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iInf_congr", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "biInf_congr", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "biInf_congr'", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Function.Surjective.iInf_comp", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.iInf_comp", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.iInf_congr", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.iInf_congr", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iInf_congr_Prop", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iInf_plift_up", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iInf_plift_down", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iInf_range'", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sInf_image'", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_iSup", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iInf_le", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iInf_le_iSup", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLUB_iSup", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isGLB_iInf", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLUB.iSup_eq", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGLB.iInf_eq", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_iSup_of_le", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iInf_le_of_le", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_iSup₂", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iInf₂_le", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_iSup₂_of_le", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iInf₂_le_of_le", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_le", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_iInf", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup₂_le", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_iInf₂", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup₂_le_iSup", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iInf_le_iInf₂", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_mono", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iInf_mono", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup₂_mono", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iInf₂_mono", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_mono'", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iInf_mono'", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup₂_mono'", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iInf₂_mono'", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_const_mono", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iInf_const_mono", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_iInf_le_iInf_iSup", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "biSup_mono", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "biInf_mono", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_le_iff", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_iInf_iff", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup₂_le_iff", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "le_iInf₂_iff", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "iSup_lt_iff", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lt_iInf_iff", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sSup_eq_iSup", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sInf_eq_iInf", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sSup_lowerBounds_eq_sInf", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sInf_upperBounds_eq_csSup", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.le_map_iSup", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.le_map_iInf", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.le_map_iSup₂", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.le_map_iInf₂", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.le_map_sSup", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Antitone.le_map_sInf", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.map_iSup", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.map_iSup₂", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.map_iInf", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.map_iInf₂", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.map_sSup", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "OrderIso.map_sInf", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_comp_le", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_iInf_comp", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.iSup_comp_eq", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.iInf_comp_eq", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.map_iSup_le", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.map_iInf_le", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.map_iSup₂_le", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.map_iInf₂_le", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.map_sSup_le", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Monotone.map_sInf_le", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_const_le", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_iInf_const", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_const", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "iInf_const", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_unique", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "iInf_unique", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "iSup_bot", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iInf_top", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_eq_bot", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iInf_eq_top", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bot_lt_iSup", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "iInf_lt_top", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "iSup₂_eq_bot", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "iInf₂_eq_top", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "iSup_pos", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iInf_pos", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_neg", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iInf_neg", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_eq_of_forall_le_of_forall_lt_exists_gt", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iInf_eq_of_forall_ge_of_forall_gt_exists_lt", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_eq_dif", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "iSup_eq_if", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iInf_eq_dif", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iInf_eq_if", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_comm", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iInf_comm", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup₂_comm", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "iInf₂_comm", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["simp", "but", "begin", "apply", "simp,", "begin", "ematch,", "trace_state,", "end", "end"], "tactic_count": 10}
{"name": "iSup_iSup_eq_left", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iInf_iInf_eq_left", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_iSup_eq_right", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iInf_iInf_eq_right", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_subtype", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iInf_subtype", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_subtype'", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iInf_subtype'", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_subtype''", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iInf_subtype''", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "biSup_const", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["haveI", "rw"], "tactic_count": 2}
{"name": "biInf_const", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_sup_eq", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iInf_inf_eq", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.biSup_comp", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Equiv.biInf_comp", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "biInf_le", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_biSup", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "biInf_le_biSup", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_sup", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "iInf_inf", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "sup_iSup", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "inf_iInf", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "biSup_sup", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": ["haveI", "let", "rw"], "tactic_count": 3}
{"name": "sup_biSup", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "biInf_inf", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inf_biInf", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "biSup_lt_eq_iSup", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["apply", "exact", "refine", "obtain", "exact"], "tactic_count": 5}
{"name": "biSup_le_eq_iSup", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["apply", "exact", "exact"], "tactic_count": 3}
{"name": "biInf_lt_eq_iInf", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "biInf_le_eq_iInf", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "biSup_gt_eq_iSup", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "biSup_ge_eq_iSup", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "biInf_gt_eq_iInf", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "biInf_ge_eq_iInf", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "biSup_le_eq_of_monotone", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "biInf_le_eq_of_antitone", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "biSup_ge_eq_of_antitone", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "biInf_ge_eq_of_monotone", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_false", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "iInf_false", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "iSup_true", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iInf_true", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_exists", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iInf_exists", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_and", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iInf_and", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_and'", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iInf_and'", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_or", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iInf_or", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_dite", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["rw", "congr", "split_ifs"], "tactic_count": 3}
{"name": "iInf_dite", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_ite", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iInf_ite", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_range", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "iInf_range", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sSup_image", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "sInf_image", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.map_sSup_eq_sSup_symm_preimage", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "OrderIso.map_sInf_eq_sInf_symm_preimage", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "iSup_emptyset", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "iInf_emptyset", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "iSup_univ", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "iInf_univ", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "iSup_union", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "iInf_union", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_split", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "iInf_split", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_split_single", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "iInf_split_single", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_le_iSup_of_subset", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iInf_le_iInf_of_subset", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_insert", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iInf_insert", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_singleton", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "iInf_singleton", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "iSup_pair", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "iInf_pair", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "iSup_image", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "iInf_image", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_extend_bot", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "iInf_extend_top", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.BijOn.iSup_comp", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.BijOn.iInf_comp", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.BijOn.iSup_congr", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.BijOn.iInf_congr", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "biSup_le_eq_sup", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "biInf_le_eq_inf", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "biSup_ge_eq_sup", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "biInf_ge_eq_inf", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_of_empty'", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iInf_of_isEmpty", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_of_empty", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iInf_of_empty", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isGLB_biInf", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "isLUB_biSup", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "iSup_sigma", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iInf_sigma", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_sigma'", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iInf_sigma'", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_psigma", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iInf_psigma", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_psigma'", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iInf_psigma'", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_prod", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iInf_prod", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_prod'", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iInf_prod'", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "biSup_prod", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "biSup_prod'", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "biInf_prod", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "biInf_prod'", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_image2", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "iInf_image2", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_sum", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iInf_sum", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_option", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iInf_option", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_option_elim", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "iInf_option_elim", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_ne_bot_subtype", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "refine", "by_cases", "rw", "obtain", "exact", "exact"], "tactic_count": 8}
{"name": "iInf_ne_top_subtype", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sSup_image2", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "sInf_image2", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "iSup_eq_top", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "iInf_eq_bot", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "iSup₂_eq_top", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "iInf₂_eq_bot", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Prop.instCompleteLattice", "kind": "instance", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prop.instCompleteLinearOrder", "kind": "instance", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sSup_Prop_eq", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sInf_Prop_eq", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_Prop_eq", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iInf_Prop_eq", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.supSet", "kind": "instance", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.infSet", "kind": "instance", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instCompleteLattice", "kind": "instance", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sSup_apply", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sInf_apply", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_apply", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "iInf_apply", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unary_relation_sSup_iff", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "unary_relation_sInf_iff", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "binary_relation_sSup_iff", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "binary_relation_sInf_iff", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Monotone.sSup", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.sInf", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.sSup", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.sInf", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.iSup", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.iInf", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.iSup", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.iInf", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.supSet", "kind": "instance", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.infSet", "kind": "instance", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.fst_sInf", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.snd_sInf", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.swap_sInf", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.fst_sSup", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.snd_sSup", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.swap_sSup", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.fst_iInf", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.snd_iInf", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.swap_iInf", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Prod.iInf_mk", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.fst_iSup", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.snd_iSup", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.swap_iSup", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Prod.iSup_mk", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instCompleteLattice", "kind": "instance", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sInf_prod", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sSup_prod", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.completeLattice", "kind": "abbrev", "module": "Mathlib.Order.CompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ChainClosure", "kind": "inductive", "module": "Mathlib.Order.CompleteLattice.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "maxChain", "kind": "definition", "module": "Mathlib.Order.CompleteLattice.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "chainClosure_empty", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Chain", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "chainClosure_maxChain", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Order.CompleteLattice.Chain.0.chainClosure_succ_total_aux", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Chain", "is_tactic_proof": true, "tactics": ["induction", "obtain", "exact", "exact", "union", "refine", "exact"], "tactic_count": 7}
{"name": "_private.Mathlib.Order.CompleteLattice.Chain.0.chainClosure_succ_total", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Chain", "is_tactic_proof": true, "tactics": ["induction", "succ", "refine", "obtain", "exact", "exact", "union", "apply", "apply", "simp", "intro", "obtain", "exact", "obtain", "exact", "exact"], "tactic_count": 16}
{"name": "ChainClosure.total", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ChainClosure.succ_fixpoint", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Chain", "is_tactic_proof": true, "tactics": ["induction", "succ", "union"], "tactic_count": 3}
{"name": "ChainClosure.succ_fixpoint_iff", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ChainClosure.isChain", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Chain", "is_tactic_proof": true, "tactics": ["induction", "succ", "union", "exact"], "tactic_count": 4}
{"name": "maxChain_spec", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Chain", "is_tactic_proof": false, "tactics": ["let"], "tactic_count": 1}
{"name": "OrderDual.supSet", "kind": "instance", "module": "Mathlib.Order.CompleteLattice.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.infSet", "kind": "instance", "module": "Mathlib.Order.CompleteLattice.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_sSup", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sSup_le", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLUB_sSup", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLUB_iff_sSup_eq", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_sSup_of_le", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sSup_le_sSup", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sSup_le_iff", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_sSup_iff", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_iSup_iff", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "sInf_le", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_sInf", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isGLB_sInf", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isGLB_iff_sInf_eq", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sInf_le_of_le", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sInf_le_sInf", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_sInf_iff", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sInf_le_iff", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iInf_le_iff", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "instCompleteSemilatticeSupOrderDualOfCompleteSemilatticeInf", "kind": "instance", "module": "Mathlib.Order.CompleteLattice.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCompleteSemilatticeInfOrderDualOfCompleteSemilatticeSup", "kind": "instance", "module": "Mathlib.Order.CompleteLattice.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteLattice.toPartialOrder'", "kind": "instance", "module": "Mathlib.Order.CompleteLattice.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "completeLatticeOfInf", "kind": "definition", "module": "Mathlib.Order.CompleteLattice.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "completeLatticeOfCompleteSemilatticeInf", "kind": "definition", "module": "Mathlib.Order.CompleteLattice.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "completeLatticeOfSup", "kind": "definition", "module": "Mathlib.Order.CompleteLattice.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "completeLatticeOfCompleteSemilatticeSup", "kind": "definition", "module": "Mathlib.Order.CompleteLattice.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteLinearOrder.toLinearOrder", "kind": "instance", "module": "Mathlib.Order.CompleteLattice.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instCompleteLattice", "kind": "instance", "module": "Mathlib.Order.CompleteLattice.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instCompleteLinearOrder", "kind": "instance", "module": "Mathlib.Order.CompleteLattice.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toDual_sSup", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toDual_sInf", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofDual_sSup", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofDual_sInf", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toDual_iSup", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toDual_iInf", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofDual_iSup", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofDual_iInf", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lt_sSup_iff", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sInf_lt_iff", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sSup_eq_top", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sInf_eq_bot", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lt_iSup_iff", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iInf_lt_iff", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lt_biSup_iff", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "biInf_lt_iff", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "iSup_eq_iSup_finset", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Finset", "is_tactic_proof": true, "tactics": ["classical", "refine", "exact", "exact"], "tactic_count": 4}
{"name": "iSup_eq_iSup_finset'", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Finset", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "iInf_eq_iInf_finset", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iInf_eq_iInf_finset'", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_eq_iUnion_finset", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_eq_iUnion_finset'", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iInter_eq_iInter_finset", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iInter_eq_iInter_finset'", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_finset_eq_set", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Finset", "is_tactic_proof": true, "tactics": ["ext", "simp", "exact"], "tactic_count": 3}
{"name": "Finset.maximal_iff_forall_insert", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Finset", "is_tactic_proof": true, "tactics": ["simp", "exact", "by_contra"], "tactic_count": 3}
{"name": "Finset.minimal_iff_forall_diff_singleton", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.iSup_coe", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.iInf_coe", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.iSup_singleton", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Finset", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.iInf_singleton", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Finset", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.iSup_option_toFinset", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Finset", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.iInf_option_toFinset", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.iSup_union", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Finset", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.iInf_union", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.iSup_insert", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Finset", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Finset.iInf_insert", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.iSup_finset_image", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Finset", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.iInf_finset_image", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Finset", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.iSup_insert_update", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Finset", "is_tactic_proof": true, "tactics": ["simp", "rcongr"], "tactic_count": 2}
{"name": "Finset.iInf_insert_update", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.iSup_biUnion", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Finset", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.iInf_biUnion", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.set_biUnion_coe", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.set_biInter_coe", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.set_biUnion_singleton", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.set_biInter_singleton", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.set_biUnion_preimage_singleton", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.set_biUnion_option_toFinset", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.set_biInter_option_toFinset", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.subset_set_biUnion_of_mem", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.set_biUnion_union", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.set_biInter_inter", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.set_biUnion_insert", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.set_biInter_insert", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.set_biUnion_finset_image", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.set_biInter_finset_image", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.set_biUnion_insert_update", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.set_biInter_insert_update", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.set_biUnion_biUnion", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.set_biInter_biUnion", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_mul_le", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_iInf_mul", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup₂_mul_le", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Group", "is_tactic_proof": true, "tactics": ["refine", "gcongr", "exact"], "tactic_count": 3}
{"name": "le_iInf₂_mul", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_bool_eq", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "iInf_bool_eq", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sup_eq_iSup", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "inf_eq_iInf", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_ge_eq_iSup_nat_add", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Lemmas", "is_tactic_proof": true, "tactics": ["apply", "refine", "dsimp", "rw", "exact"], "tactic_count": 5}
{"name": "iInf_ge_eq_iInf_nat_add", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.iSup_nat_add", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.iInf_nat_add", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_iInf_ge_nat_add", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Lemmas", "is_tactic_proof": true, "tactics": ["have", "rw", "simp_rw"], "tactic_count": 3}
{"name": "iInf_iSup_ge_nat_add", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sup_iSup_nat_succ", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inf_iInf_nat_succ", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iInf_nat_gt_zero_eq", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "iSup_nat_gt_zero_eq", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sup_sInf_le_iInf_sup", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_inf_le_inf_sSup", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sInf_sup_le_iInf_sup", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_inf_le_sSup_inf", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_iSup_inf_iSup", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iInf_sup_iInf_le", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "disjoint_sSup_left", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "disjoint_sSup_right", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "disjoint_of_sSup_disjoint_of_le_of_le", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Lemmas", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "disjoint_of_sSup_disjoint", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.supSet", "kind": "instance", "module": "Mathlib.Order.CompleteLattice.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.down_sSup", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.up_sSup", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.infSet", "kind": "instance", "module": "Mathlib.Order.CompleteLattice.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.down_sInf", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.up_sInf", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.down_iSup", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.up_iSup", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.down_iInf", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.up_iInf", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.instCompleteLattice", "kind": "instance", "module": "Mathlib.Order.CompleteLattice.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PUnit.instCompleteLinearOrder", "kind": "instance", "module": "Mathlib.Order.CompleteLattice.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lattice.BicartSq.le₁₂", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.MulticoequalizerDiagram", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Lattice.BicartSq.le₁₃", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.MulticoequalizerDiagram", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Lattice.BicartSq.le₂₄", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.MulticoequalizerDiagram", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Lattice.BicartSq.le₃₄", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.MulticoequalizerDiagram", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Lattice.BicartSq.commSq", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.MulticoequalizerDiagram", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteLattice.MulticoequalizerDiagram.multispanIndex", "kind": "definition", "module": "Mathlib.Order.CompleteLattice.MulticoequalizerDiagram", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteLattice.MulticoequalizerDiagram.multicofork", "kind": "definition", "module": "Mathlib.Order.CompleteLattice.MulticoequalizerDiagram", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lattice.BicartSq.multicoequalizerDiagram", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.MulticoequalizerDiagram", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Order.CompleteLattice.PiLex.0.Pi.Lex.inf", "kind": "definition", "module": "Mathlib.Order.CompleteLattice.PiLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.Lex.instInfSetLexForall", "kind": "instance", "module": "Mathlib.Order.CompleteLattice.PiLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.Lex.sInf_apply", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.PiLex", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Pi.Lex.sInf_apply_le", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.PiLex", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Pi.Lex.le_sInf_apply", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.PiLex", "is_tactic_proof": true, "tactics": ["rw", "apply", "grind"], "tactic_count": 3}
{"name": "_private.Mathlib.Order.CompleteLattice.PiLex.0.Pi.Lex.sInf_le", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.PiLex", "is_tactic_proof": true, "tactics": ["by_contra", "obtain", "exact"], "tactic_count": 3}
{"name": "_private.Mathlib.Order.CompleteLattice.PiLex.0.Pi.Lex.le_sInf", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.PiLex", "is_tactic_proof": true, "tactics": ["by_contra", "obtain", "refine", "simp_all"], "tactic_count": 4}
{"name": "Pi.Lex.instSupSetLexForall", "kind": "instance", "module": "Mathlib.Order.CompleteLattice.PiLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.Lex.sSup_apply", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.PiLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.Lex.le_sSup_apply", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.PiLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.Lex.sSup_apply_le", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.PiLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Order.CompleteLattice.PiLex.0.Pi.Lex.le_sSup", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.PiLex", "is_tactic_proof": true, "tactics": ["by_contra", "obtain", "exact"], "tactic_count": 3}
{"name": "_private.Mathlib.Order.CompleteLattice.PiLex.0.Pi.Lex.sSup_le", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.PiLex", "is_tactic_proof": true, "tactics": ["by_contra", "obtain", "refine", "simp_all"], "tactic_count": 4}
{"name": "Pi.Lex.completeLattice", "kind": "instance", "module": "Mathlib.Order.CompleteLattice.PiLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.Lex.instCompleteLinearOrderLexForall", "kind": "instance", "module": "Mathlib.Order.CompleteLattice.PiLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.Colex.instInfSetColexForall", "kind": "instance", "module": "Mathlib.Order.CompleteLattice.PiLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.Colex.sInf_apply", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.PiLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.Colex.sInf_apply_le", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.PiLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.Colex.le_sInf_apply", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.PiLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.Colex.instSupSetColexForall", "kind": "instance", "module": "Mathlib.Order.CompleteLattice.PiLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.Colex.sSup_apply", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.PiLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.Colex.le_sSup_apply", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.PiLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.Colex.sSup_apply_le", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.PiLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.Colex.completeLattice", "kind": "instance", "module": "Mathlib.Order.CompleteLattice.PiLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.Colex.instCompleteLinearOrderColexForall", "kind": "instance", "module": "Mathlib.Order.CompleteLattice.PiLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.ext_mem", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.SetLike", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.mem_subtype", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.SetLike", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.setLike_mem_inf", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.SetLike", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Sublattice.setLike_mem_sup", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.SetLike", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Sublattice.setLike_mem_coe", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.SetLike", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteSublattice.ext", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.SetLike", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteSublattice.mem_subtype", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.SetLike", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteSublattice.mem_inf", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.SetLike", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CompleteSublattice.mem_sInf", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.SetLike", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CompleteSublattice.mem_iInf", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.SetLike", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CompleteSublattice.mem_top", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.SetLike", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CompleteSublattice.mem_sup", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.SetLike", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CompleteSublattice.mem_sSup", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.SetLike", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CompleteSublattice.mem_iSup", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.SetLike", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CompleteSublattice.notMem_bot", "kind": "theorem", "module": "Mathlib.Order.CompleteLattice.SetLike", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DirectedOn.isLUB_sSup", "kind": "theorem", "module": "Mathlib.Order.CompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectedOn.le_sSup", "kind": "theorem", "module": "Mathlib.Order.CompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectedOn.sSup_le", "kind": "theorem", "module": "Mathlib.Order.CompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Directed.le_iSup", "kind": "theorem", "module": "Mathlib.Order.CompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Directed.iSup_le", "kind": "theorem", "module": "Mathlib.Order.CompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompletePartialOrder.scottContinuous", "kind": "theorem", "module": "Mathlib.Order.CompletePartialOrder", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "CompletePartialOrder.toOmegaCompletePartialOrder", "kind": "instance", "module": "Mathlib.Order.CompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteLattice.toCompletePartialOrder", "kind": "instance", "module": "Mathlib.Order.CompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteSublattice.mk'", "kind": "definition", "module": "Mathlib.Order.CompleteSublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteSublattice.instSetLike", "kind": "instance", "module": "Mathlib.Order.CompleteSublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteSublattice.instPartialOrder", "kind": "instance", "module": "Mathlib.Order.CompleteSublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteSublattice.top_mem", "kind": "theorem", "module": "Mathlib.Order.CompleteSublattice", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CompleteSublattice.bot_mem", "kind": "theorem", "module": "Mathlib.Order.CompleteSublattice", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CompleteSublattice.instBot", "kind": "instance", "module": "Mathlib.Order.CompleteSublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteSublattice.instTop", "kind": "instance", "module": "Mathlib.Order.CompleteSublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteSublattice.instSupSet", "kind": "instance", "module": "Mathlib.Order.CompleteSublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteSublattice.instInfSet", "kind": "instance", "module": "Mathlib.Order.CompleteSublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteSublattice.sSupClosed", "kind": "theorem", "module": "Mathlib.Order.CompleteSublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteSublattice.sInfClosed", "kind": "theorem", "module": "Mathlib.Order.CompleteSublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteSublattice.coe_bot", "kind": "theorem", "module": "Mathlib.Order.CompleteSublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteSublattice.coe_top", "kind": "theorem", "module": "Mathlib.Order.CompleteSublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteSublattice.coe_sSup", "kind": "theorem", "module": "Mathlib.Order.CompleteSublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteSublattice.coe_sSup'", "kind": "theorem", "module": "Mathlib.Order.CompleteSublattice", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CompleteSublattice.coe_sInf", "kind": "theorem", "module": "Mathlib.Order.CompleteSublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteSublattice.coe_sInf'", "kind": "theorem", "module": "Mathlib.Order.CompleteSublattice", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CompleteSublattice.coe_iSup", "kind": "theorem", "module": "Mathlib.Order.CompleteSublattice", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CompleteSublattice.coe_iInf", "kind": "theorem", "module": "Mathlib.Order.CompleteSublattice", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CompleteSublattice.instMaxSubtypeMem", "kind": "instance", "module": "Mathlib.Order.CompleteSublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteSublattice.instMinSubtypeMem", "kind": "instance", "module": "Mathlib.Order.CompleteSublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteSublattice.instCompleteLattice", "kind": "instance", "module": "Mathlib.Order.CompleteSublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteSublattice.subtype", "kind": "definition", "module": "Mathlib.Order.CompleteSublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteSublattice.coe_subtype", "kind": "theorem", "module": "Mathlib.Order.CompleteSublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteSublattice.subtype_apply", "kind": "theorem", "module": "Mathlib.Order.CompleteSublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteSublattice.subtype_injective", "kind": "theorem", "module": "Mathlib.Order.CompleteSublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteSublattice.map", "kind": "definition", "module": "Mathlib.Order.CompleteSublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteSublattice.mem_map", "kind": "theorem", "module": "Mathlib.Order.CompleteSublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteSublattice.comap", "kind": "definition", "module": "Mathlib.Order.CompleteSublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteSublattice.mem_comap", "kind": "theorem", "module": "Mathlib.Order.CompleteSublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteSublattice.disjoint_iff", "kind": "theorem", "module": "Mathlib.Order.CompleteSublattice", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CompleteSublattice.codisjoint_iff", "kind": "theorem", "module": "Mathlib.Order.CompleteSublattice", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CompleteSublattice.isCompl_iff", "kind": "theorem", "module": "Mathlib.Order.CompleteSublattice", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CompleteSublattice.isComplemented_iff", "kind": "theorem", "module": "Mathlib.Order.CompleteSublattice", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact", "obtain", "exact"], "tactic_count": 5}
{"name": "CompleteSublattice.instTop_1", "kind": "instance", "module": "Mathlib.Order.CompleteSublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteSublattice.copy", "kind": "definition", "module": "Mathlib.Order.CompleteSublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteSublattice.coe_copy", "kind": "theorem", "module": "Mathlib.Order.CompleteSublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteSublattice.copy_eq", "kind": "theorem", "module": "Mathlib.Order.CompleteSublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteLatticeHom.range", "kind": "definition", "module": "Mathlib.Order.CompleteSublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteLatticeHom.range_coe", "kind": "theorem", "module": "Mathlib.Order.CompleteSublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteLatticeHom.toOrderIsoRangeOfInjective", "kind": "definition", "module": "Mathlib.Order.CompleteSublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "upperPolar", "kind": "definition", "module": "Mathlib.Order.Concept", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lowerPolar", "kind": "definition", "module": "Mathlib.Order.Concept", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "subset_upperPolar_iff_subset_lowerPolar", "kind": "theorem", "module": "Mathlib.Order.Concept", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "gc_upperPolar_lowerPolar", "kind": "theorem", "module": "Mathlib.Order.Concept", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "upperPolar_swap", "kind": "theorem", "module": "Mathlib.Order.Concept", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lowerPolar_swap", "kind": "theorem", "module": "Mathlib.Order.Concept", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "upperPolar_empty", "kind": "theorem", "module": "Mathlib.Order.Concept", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lowerPolar_empty", "kind": "theorem", "module": "Mathlib.Order.Concept", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "upperPolar_union", "kind": "theorem", "module": "Mathlib.Order.Concept", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lowerPolar_union", "kind": "theorem", "module": "Mathlib.Order.Concept", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "upperPolar_iUnion", "kind": "theorem", "module": "Mathlib.Order.Concept", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lowerPolar_iUnion", "kind": "theorem", "module": "Mathlib.Order.Concept", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "upperPolar_iUnion₂", "kind": "theorem", "module": "Mathlib.Order.Concept", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lowerPolar_iUnion₂", "kind": "theorem", "module": "Mathlib.Order.Concept", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "subset_lowerPolar_upperPolar", "kind": "theorem", "module": "Mathlib.Order.Concept", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "subset_upperPolar_lowerPolar", "kind": "theorem", "module": "Mathlib.Order.Concept", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "upperPolar_lowerPolar_upperPolar", "kind": "theorem", "module": "Mathlib.Order.Concept", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lowerPolar_upperPolar_lowerPolar", "kind": "theorem", "module": "Mathlib.Order.Concept", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "upperPolar_anti", "kind": "theorem", "module": "Mathlib.Order.Concept", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lowerPolar_anti", "kind": "theorem", "module": "Mathlib.Order.Concept", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Concept.ext", "kind": "theorem", "module": "Mathlib.Order.Concept", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "substs", "rfl"], "tactic_count": 4}
{"name": "Concept.ext'", "kind": "theorem", "module": "Mathlib.Order.Concept", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "substs", "rfl"], "tactic_count": 4}
{"name": "Concept.extent_injective", "kind": "theorem", "module": "Mathlib.Order.Concept", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Concept.intent_injective", "kind": "theorem", "module": "Mathlib.Order.Concept", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Concept.copy", "kind": "definition", "module": "Mathlib.Order.Concept", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Concept.copy_eq", "kind": "theorem", "module": "Mathlib.Order.Concept", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Concept.rel_extent_intent", "kind": "theorem", "module": "Mathlib.Order.Concept", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Concept.disjoint_extent_intent", "kind": "theorem", "module": "Mathlib.Order.Concept", "is_tactic_proof": true, "tactics": ["rw", "rintro", "exact"], "tactic_count": 3}
{"name": "Concept.mem_extent_of_rel_extent", "kind": "theorem", "module": "Mathlib.Order.Concept", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Concept.mem_intent_of_intent_rel", "kind": "theorem", "module": "Mathlib.Order.Concept", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Concept.codisjoint_extent_intent", "kind": "theorem", "module": "Mathlib.Order.Concept", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "intro", "obtain", "cases", "contradiction", "assumption"], "tactic_count": 8}
{"name": "Concept.isCompl_extent_intent", "kind": "theorem", "module": "Mathlib.Order.Concept", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Concept.compl_extent", "kind": "theorem", "module": "Mathlib.Order.Concept", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Concept.compl_intent", "kind": "theorem", "module": "Mathlib.Order.Concept", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Concept.instSupConcept", "kind": "instance", "module": "Mathlib.Order.Concept", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Concept.instInfConcept", "kind": "instance", "module": "Mathlib.Order.Concept", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Concept.instSemilatticeInfConcept", "kind": "instance", "module": "Mathlib.Order.Concept", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Concept.extent_subset_extent_iff", "kind": "theorem", "module": "Mathlib.Order.Concept", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Concept.extent_ssubset_extent_iff", "kind": "theorem", "module": "Mathlib.Order.Concept", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Concept.intent_subset_intent_iff", "kind": "theorem", "module": "Mathlib.Order.Concept", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact", "rw", "exact"], "tactic_count": 5}
{"name": "Concept.intent_ssubset_intent_iff", "kind": "theorem", "module": "Mathlib.Order.Concept", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Concept.strictMono_extent", "kind": "theorem", "module": "Mathlib.Order.Concept", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Concept.strictAnti_intent", "kind": "theorem", "module": "Mathlib.Order.Concept", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Concept.instLatticeConcept", "kind": "instance", "module": "Mathlib.Order.Concept", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Concept.instBoundedOrderConcept", "kind": "instance", "module": "Mathlib.Order.Concept", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Concept.instSupSet", "kind": "instance", "module": "Mathlib.Order.Concept", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Concept.instInfSet", "kind": "instance", "module": "Mathlib.Order.Concept", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Concept.instCompleteLattice", "kind": "instance", "module": "Mathlib.Order.Concept", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Concept.extent_top", "kind": "theorem", "module": "Mathlib.Order.Concept", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Concept.intent_top", "kind": "theorem", "module": "Mathlib.Order.Concept", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Concept.extent_bot", "kind": "theorem", "module": "Mathlib.Order.Concept", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Concept.intent_bot", "kind": "theorem", "module": "Mathlib.Order.Concept", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Concept.extent_sup", "kind": "theorem", "module": "Mathlib.Order.Concept", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Concept.intent_sup", "kind": "theorem", "module": "Mathlib.Order.Concept", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Concept.extent_inf", "kind": "theorem", "module": "Mathlib.Order.Concept", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Concept.intent_inf", "kind": "theorem", "module": "Mathlib.Order.Concept", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Concept.extent_sSup", "kind": "theorem", "module": "Mathlib.Order.Concept", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Concept.intent_sSup", "kind": "theorem", "module": "Mathlib.Order.Concept", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Concept.extent_sInf", "kind": "theorem", "module": "Mathlib.Order.Concept", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Concept.intent_sInf", "kind": "theorem", "module": "Mathlib.Order.Concept", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Concept.instInhabited", "kind": "instance", "module": "Mathlib.Order.Concept", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Concept.swap", "kind": "definition", "module": "Mathlib.Order.Concept", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Concept.swap_swap", "kind": "theorem", "module": "Mathlib.Order.Concept", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Concept.swap_le_swap_iff", "kind": "theorem", "module": "Mathlib.Order.Concept", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Concept.swap_lt_swap_iff", "kind": "theorem", "module": "Mathlib.Order.Concept", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Concept.swapEquiv", "kind": "definition", "module": "Mathlib.Order.Concept", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.instSupSet", "kind": "instance", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.instInfSet", "kind": "instance", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.instSupSet", "kind": "instance", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.instInfSet", "kind": "instance", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.sSup_eq", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.sInf_eq", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.sInf_eq", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.sSup_eq", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.sInf_empty", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.coe_sInf'", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["classical", "obtain", "change", "split_ifs", "rcases", "cases", "exact", "rw", "exact"], "tactic_count": 9}
{"name": "WithTop.coe_sSup'", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["classical", "change", "rw", "exact", "rintro"], "tactic_count": 5}
{"name": "WithBot.sSup_empty", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.sInf_empty", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "WithBot.coe_sSup'", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.coe_sInf'", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConditionallyCompleteLinearOrder.toLinearOrder", "kind": "instance", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteLattice.toConditionallyCompleteLattice", "kind": "instance", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteLinearOrder.toConditionallyCompleteLinearOrderBot", "kind": "instance", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instConditionallyCompleteLattice", "kind": "instance", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instConditionallyCompleteLinearOrder", "kind": "instance", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_csSup", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csSup_le", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csInf_le", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_csInf", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_csSup_of_le", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csInf_le_of_le", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csSup_le_csSup", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csInf_le_csInf", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_csSup_iff", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csInf_le_iff", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLUB_csSup", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isGLB_csInf", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLUB.csSup_eq", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGreatest.csSup_eq", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGreatest.csSup_mem", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGLB.csInf_eq", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLeast.csInf_eq", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLeast.csInf_mem", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "subset_Icc_csInf_csSup", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csSup_le_iff", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_csInf_iff", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csSup_lowerBounds_eq_csInf", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csInf_upperBounds_eq_csSup", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csSup_lowerBounds_range", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csInf_upperBounds_range", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "notMem_of_lt_csInf", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "notMem_of_csSup_lt", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csSup_eq_of_forall_le_of_forall_lt_exists_gt", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csInf_eq_of_forall_ge_of_forall_gt_exists_lt", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lt_csSup_of_lt", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csInf_lt_of_lt", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_between_of_forall_le", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csSup_singleton", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csInf_singleton", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csSup_pair", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csInf_pair", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csInf_le_csSup", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csSup_union", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csInf_union", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csSup_inter_le", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_csInf_inter", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csSup_insert", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csInf_insert", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csInf_Icc", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csInf_Ici", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csInf_Ico", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csInf_Ioc", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csInf_Ioi", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csInf_Ioo", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csSup_Icc", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csSup_Ico", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csSup_Iic", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csSup_Iio", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csSup_Ioc", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csSup_Ioo", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csSup_eq_of_is_forall_le_of_forall_le_imp_ge", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sup_eq_top_of_top_mem", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inf_eq_bot_of_bot_mem", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.conditionallyCompleteLattice", "kind": "instance", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_lt_of_lt_csSup", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["contrapose", "exact"], "tactic_count": 2}
{"name": "exists_lt_of_csInf_lt", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lt_csSup_iff", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csInf_lt_iff", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csSup_of_not_bddAbove", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ciSup_of_not_bddAbove", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csSup_eq_univ_of_not_bddAbove", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["rw", "contrapose", "exact"], "tactic_count": 3}
{"name": "ciSup_eq_univ_of_not_bddAbove", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csInf_of_not_bddBelow", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ciInf_of_not_bddBelow", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csInf_eq_univ_of_not_bddBelow", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ciInf_eq_univ_of_not_bddBelow", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csSup_eq_csSup_of_forall_exists_le", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["rcases", "have", "rw", "rcases", "have", "rw", "by_cases", "have", "rcases", "exact", "refine", "rcases", "exact", "have", "rcases", "refine", "rcases", "exact", "exact", "apply", "apply", "rcases", "exact", "apply", "rcases", "exact", "simp"], "tactic_count": 27}
{"name": "csInf_eq_csInf_of_forall_exists_le", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sSup_iUnion_Iic", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["apply", "rintro", "exact", "rintro", "exact"], "tactic_count": 5}
{"name": "sInf_iUnion_Ici", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csInf_eq_bot_of_bot_mem", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csSup_eq_top_of_top_mem", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sInf_eq_argmin_on", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLeast_csInf", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "le_csInf_iff'", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csInf_mem", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonotoneOn.map_csInf", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.map_csInf", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csInf_univ", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csSup_empty", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLUB_csSup'", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simp", "exact"], "tactic_count": 3}
{"name": "csSup_le_iff'", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csSup_le'", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lt_csSup_iff'", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "le_csSup_iff'", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_csInf_iff''", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csInf_le'", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_lt_of_lt_csSup'", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["contrapose", "exact"], "tactic_count": 2}
{"name": "notMem_of_lt_csInf'", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csInf_le_csInf'", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csSup_le_csSup'", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["rcases", "rw", "exact", "exact"], "tactic_count": 4}
{"name": "WithTop.isLUB_sSup'", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["classical", "constructor", "change", "split_ifs", "intro", "exact", "rintro", "contradiction", "apply", "exact", "intro", "exact", "change", "split_ifs", "rintro", "exact", "exact", "rintro", "exact", "refine", "rcases", "exact", "exact", "intro", "exact", "rintro", "exact", "exfalso", "apply", "use", "intro", "exact"], "tactic_count": 32}
{"name": "WithTop.isLUB_sSup", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simp", "exact"], "tactic_count": 3}
{"name": "WithTop.isGLB_sInf'", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["classical", "constructor", "change", "simp", "split_ifs", "intro", "exact", "rintro", "exact", "refine", "rcases", "exfalso", "apply", "intro", "rw", "exact", "use", "intro", "exact", "change", "simp", "split_ifs", "intro", "exact", "rintro", "exfalso", "apply", "intro", "exact", "refine", "classical", "contrapose", "rintro", "exact", "exact", "intro", "rw", "exact"], "tactic_count": 38}
{"name": "WithTop.isGLB_sInf", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "exfalso", "apply", "use", "intro", "exact"], "tactic_count": 7}
{"name": "WithTop.instCompleteLinearOrder", "kind": "instance", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.coe_sSup", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "WithTop.coe_sInf", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Monotone.le_csSup_image", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.csSup_image_le", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.csInf_image_le", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["let", "exact"], "tactic_count": 2}
{"name": "Monotone.le_csInf_image", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["let", "exact"], "tactic_count": 2}
{"name": "MonotoneOn.csInf_eq_of_subset_of_forall_exists_le", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "rfl", "refine", "refine", "simp", "intro", "obtain", "exact"], "tactic_count": 9}
{"name": "MonotoneOn.csSup_eq_of_subset_of_forall_exists_le", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonotoneOn.sInf_image_Icc", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["refine", "refine", "intro", "rintro", "exact", "exact"], "tactic_count": 6}
{"name": "MonotoneOn.sSup_image_Icc", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "AntitoneOn.sInf_image_Icc", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "AntitoneOn.sSup_image_Icc", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csSup_image2_eq_csSup_csSup", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csSup_image2_eq_csSup_csInf", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csSup_image2_eq_csInf_csSup", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csSup_image2_eq_csInf_csInf", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csInf_image2_eq_csInf_csInf", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csInf_image2_eq_csInf_csSup", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csInf_image2_eq_csSup_csInf", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csInf_image2_eq_csSup_csSup", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.conditionallyCompleteLattice", "kind": "instance", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.conditionallyCompleteLattice", "kind": "instance", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCompleteLatticeWithBot", "kind": "instance", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.WithBot.completeLattice", "kind": "instance", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.WithBot.completeLinearOrder", "kind": "instance", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.WithTop.completeLattice", "kind": "instance", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.WithTop.completeLinearOrder", "kind": "instance", "module": "Mathlib.Order.ConditionallyCompleteLattice.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WellFoundedLT.conditionallyCompleteLinearOrderBot", "kind": "abbrev", "module": "Mathlib.Order.ConditionallyCompleteLattice.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "conditionallyCompleteLatticeOfsSup", "kind": "definition", "module": "Mathlib.Order.ConditionallyCompleteLattice.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "conditionallyCompleteLatticeOfsInf", "kind": "definition", "module": "Mathlib.Order.ConditionallyCompleteLattice.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "conditionallyCompleteLatticeOfLatticeOfsSup", "kind": "definition", "module": "Mathlib.Order.ConditionallyCompleteLattice.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "conditionallyCompleteLatticeOfLatticeOfsInf", "kind": "definition", "module": "Mathlib.Order.ConditionallyCompleteLattice.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Nonempty.csSup_eq_max'", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Nonempty.csInf_eq_min'", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Nonempty.csSup_mem", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Finset", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finset.Nonempty.csInf_mem", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nonempty.csSup_mem", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Finset", "is_tactic_proof": true, "tactics": ["lift", "exact"], "tactic_count": 2}
{"name": "Set.Nonempty.csInf_mem", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.csSup_lt_iff", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.lt_csInf_iff", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.ciSup_mem_image", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Finset", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finset.ciInf_mem_image", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Finset", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.Finite.ciSup_mem_image", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Finset", "is_tactic_proof": true, "tactics": ["lift", "simp", "simpa"], "tactic_count": 3}
{"name": "Set.Finite.ciInf_mem_image", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Finset", "is_tactic_proof": true, "tactics": ["lift", "simp", "simpa"], "tactic_count": 3}
{"name": "Set.Finite.ciSup_lt_iff", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Finset", "is_tactic_proof": true, "tactics": ["constructor", "intro", "refine", "classical", "refine", "intro", "simp", "grind", "simp", "refine", "simp", "have", "grind"], "tactic_count": 13}
{"name": "Set.Finite.lt_ciInf_iff", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Finset", "is_tactic_proof": true, "tactics": ["constructor", "intro", "refine", "classical", "refine", "intro", "simp", "grind", "simp", "refine", "simp", "intro", "have", "simp", "obtain", "rw", "exact"], "tactic_count": 17}
{"name": "List.iSup_mem_map_of_exists_sSup_empty_le", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Finset", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "List.iInf_mem_map_of_exists_le_sInf_empty", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Finset", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Multiset.iSup_mem_map_of_exists_sSup_empty_le", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Finset", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Multiset.iInf_mem_map_of_exists_le_sInf_empty", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Finset", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "exists_eq_ciSup_of_finite", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_eq_ciInf_of_finite", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finite.le_ciSup", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Finset", "is_tactic_proof": true, "tactics": ["suffices", "let", "use", "simp", "exact"], "tactic_count": 5}
{"name": "Finite.ciInf_le", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sup'_eq_csSup_image", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inf'_eq_csInf_image", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sup'_id_eq_csSup", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Finset", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.inf'_id_eq_csInf", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sup'_univ_eq_ciSup", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Finset", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.inf'_univ_eq_ciInf", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Finset", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.sup_univ_eq_ciSup", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Nonempty.ciSup_mem_image", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nonempty.ciSup_mem_image", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nonempty.ciSup_lt_iff", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.iSup_mem_map_of_ne_nil", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.iSup_mem_map_of_ne_zero", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ciSup_mul_le_ciSup_mul_ciSup", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ciInf_mul_ciInf_le_ciInf_mul", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_mul_ciInf", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_ciSup_le", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_ciInf_mul", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ciSup_mul_le", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_ciInf_mul_ciInf", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ciSup_mul_ciSup_le", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.iInf_empty", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "WithTop.coe_iInf", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "WithTop.coe_iSup", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "WithBot.ciSup_empty", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.coe_iSup", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.coe_biSup", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": true, "tactics": ["rcases", "have", "refine", "le_antisymm", "iSup_le_iff.mpr", "by_cases", "simpa", "simpa"], "tactic_count": 8}
{"name": "WithBot.coe_iInf", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.coe_biInf", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": ["refine", "le_antisymm", "by_cases", "simpa", "simp"], "tactic_count": 5}
{"name": "isLUB_ciSup", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLUB_ciSup_set", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "isGLB_ciInf", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isGLB_ciInf_set", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ciSup_le_iff", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_ciInf_iff", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ciSup_set_le_iff", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_ciInf_set_iff", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLUB.ciSup_eq", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLUB.ciSup_set_eq", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGLB.ciInf_eq", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGLB.ciInf_set_eq", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ciSup_le", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_ciSup", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_ciSup_of_le", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ciSup_mono", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": true, "tactics": ["cases", "rw", "exact"], "tactic_count": 3}
{"name": "le_ciSup_set", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ciInf_mono", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_ciInf", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ciInf_le", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ciInf_le_of_le", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ciInf_set_le", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ciInf_le_ciSup", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ciSup_const", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ciInf_const", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ciSup_unique", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": true, "tactics": ["have", "simp"], "tactic_count": 2}
{"name": "ciInf_unique", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ciSup_subsingleton", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ciInf_subsingleton", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ciSup_pos", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ciInf_pos", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ciSup_neg", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": true, "tactics": ["rw", "congr", "rwa"], "tactic_count": 3}
{"name": "ciInf_neg", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ciSup_eq_ite", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "ciInf_eq_ite", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cbiSup_eq_of_forall", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": true, "tactics": ["simp", "simp", "congr", "apply", "rintro", "simp", "rintro", "simp"], "tactic_count": 8}
{"name": "cbiInf_eq_of_forall", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ciSup_eq_of_forall_le_of_forall_lt_exists_gt", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ciInf_eq_of_forall_ge_of_forall_gt_exists_lt", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.ciSup_mem_iInter_Icc_of_antitone", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": true, "tactics": ["refine", "haveI", "have", "exact"], "tactic_count": 4}
{"name": "ciSup_mem_iInter_Icc_of_antitone_Icc", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iic_ciInf", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": true, "tactics": ["ext", "simpa"], "tactic_count": 2}
{"name": "Set.Ici_ciSup", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ciSup_Iic", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": true, "tactics": ["have", "apply", "rw", "rintro", "exact"], "tactic_count": 5}
{"name": "ciInf_Ici", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": true, "tactics": ["have", "apply", "rw", "rintro", "exact"], "tactic_count": 5}
{"name": "ciSup_subtype", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": true, "tactics": ["classical", "refine", "intro", "have", "rw", "refine", "simp_rw", "refine", "intro", "simp", "intro", "split_ifs", "exact", "simp_all", "refine", "simp_rw", "split_ifs", "exact", "exact"], "tactic_count": 19}
{"name": "ciInf_subtype", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ciSup_subtype'", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ciInf_subtype'", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ciSup_subtype''", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ciInf_subtype''", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csSup_image", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "csInf_image", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ciSup_image", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": true, "tactics": ["have", "have", "refine", "have", "refine", "intro", "obtain", "have", "exact", "rw", "refine", "simpa", "rw"], "tactic_count": 13}
{"name": "ciInf_image", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_lt_of_lt_ciSup", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_lt_of_ciInf_lt", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lt_ciSup_iff", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ciInf_lt_iff", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "cbiSup_eq_of_not_forall", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": true, "tactics": ["classical", "rcases", "have", "simp", "by_cases", "have", "rcases", "refine", "rintro", "by_cases", "simp", "simp", "apply", "apply", "by_cases", "simp", "left", "exact", "simp", "apply", "rcases", "rw", "convert", "simp", "apply", "rintro", "convert", "simp", "convert", "simp", "have", "simp", "apply", "contrapose", "apply", "rintro", "convert", "simp"], "tactic_count": 38}
{"name": "cbiInf_eq_of_not_forall", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ciInf_eq_bot_of_bot_mem", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ciInf_eq_top_of_top_mem", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ciInf_mem", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ciSup_of_empty", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ciSup_false", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_ciSup_iff'", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "le_ciInf_iff'", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ciInf_le'", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ciInf_le_of_le'", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ciSup_le_iff'", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ciSup_le'", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lt_ciSup_iff'", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "exists_lt_of_lt_ciSup'", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": true, "tactics": ["contrapose", "exact"], "tactic_count": 2}
{"name": "ciSup_mono'", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ciSup_or'", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "GaloisConnection.l_csSup", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisConnection.l_csSup'", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "GaloisConnection.l_ciSup", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "GaloisConnection.l_ciSup_set", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": true, "tactics": ["haveI", "rw", "exact"], "tactic_count": 3}
{"name": "GaloisConnection.u_csInf", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisConnection.u_csInf'", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisConnection.u_ciInf", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisConnection.u_ciInf_set", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.map_csSup", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.map_csSup'", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.map_ciSup", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.map_ciSup_set", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.map_csInf", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.map_csInf'", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.map_ciInf", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.map_ciInf_set", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.map_ciSup'", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": true, "tactics": ["cases", "simp", "by_cases", "exact", "have", "simpa", "simp"], "tactic_count": 7}
{"name": "WithTop.iSup_coe_eq_top", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": true, "tactics": ["rw", "refine", "rcases", "exact", "rcases", "exact"], "tactic_count": 6}
{"name": "WithTop.iSup_coe_lt_top", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.iInf_coe_eq_top", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WithTop.iInf_coe_lt_top", "kind": "theorem", "module": "Mathlib.Order.ConditionallyCompleteLattice.Indexed", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "OrderTop.copy", "kind": "definition", "module": "Mathlib.Order.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderBot.copy", "kind": "definition", "module": "Mathlib.Order.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedOrder.copy", "kind": "definition", "module": "Mathlib.Order.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lattice.copy", "kind": "definition", "module": "Mathlib.Order.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DistribLattice.copy", "kind": "definition", "module": "Mathlib.Order.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GeneralizedHeytingAlgebra.copy", "kind": "definition", "module": "Mathlib.Order.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GeneralizedCoheytingAlgebra.copy", "kind": "definition", "module": "Mathlib.Order.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HeytingAlgebra.copy", "kind": "definition", "module": "Mathlib.Order.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoheytingAlgebra.copy", "kind": "definition", "module": "Mathlib.Order.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BiheytingAlgebra.copy", "kind": "definition", "module": "Mathlib.Order.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteLattice.copy", "kind": "definition", "module": "Mathlib.Order.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Frame.copy", "kind": "definition", "module": "Mathlib.Order.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Coframe.copy", "kind": "definition", "module": "Mathlib.Order.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteDistribLattice.copy", "kind": "definition", "module": "Mathlib.Order.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConditionallyCompleteLattice.copy", "kind": "definition", "module": "Mathlib.Order.Copy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.exists_between_finsets", "kind": "theorem", "module": "Mathlib.Order.CountableDenseLinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.exists_orderEmbedding_insert", "kind": "theorem", "module": "Mathlib.Order.CountableDenseLinearOrder", "is_tactic_proof": true, "tactics": ["let", "let", "obtain", "simp", "obtain", "obtain", "exact", "refine", "rintro", "obtain", "simp", "exact", "obtain", "simp", "exact", "ext", "simp"], "tactic_count": 17}
{"name": "Order.PartialIso", "kind": "definition", "module": "Mathlib.Order.CountableDenseLinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.PartialIso.instInhabited", "kind": "instance", "module": "Mathlib.Order.CountableDenseLinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.PartialIso.instPreorder", "kind": "instance", "module": "Mathlib.Order.CountableDenseLinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.PartialIso.exists_across", "kind": "theorem", "module": "Mathlib.Order.CountableDenseLinearOrder", "is_tactic_proof": true, "tactics": ["by_cases", "obtain", "exact", "have", "intro", "rw", "rcases", "rcases", "rw", "rw", "exact", "obtain", "use", "rintro", "have", "rcases", "have", "rw", "exact", "have", "rw", "exact"], "tactic_count": 22}
{"name": "Order.PartialIso.comm", "kind": "definition", "module": "Mathlib.Order.CountableDenseLinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.PartialIso.definedAtLeft", "kind": "definition", "module": "Mathlib.Order.CountableDenseLinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.PartialIso.definedAtRight", "kind": "definition", "module": "Mathlib.Order.CountableDenseLinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.PartialIso.funOfIdeal", "kind": "definition", "module": "Mathlib.Order.CountableDenseLinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.PartialIso.invOfIdeal", "kind": "definition", "module": "Mathlib.Order.CountableDenseLinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.embedding_from_countable_to_dense", "kind": "theorem", "module": "Mathlib.Order.CountableDenseLinearOrder", "is_tactic_proof": true, "tactics": ["cases", "rcases", "obtain", "haveI", "let", "let", "refine", "rcases", "rcases", "rcases", "exact"], "tactic_count": 11}
{"name": "Order.iso_of_countable_dense", "kind": "theorem", "module": "Mathlib.Order.CountableDenseLinearOrder", "is_tactic_proof": true, "tactics": ["cases", "cases", "let", "let", "let", "let", "exact", "rcases", "rcases", "rcases", "exact"], "tactic_count": 11}
{"name": "WCovBy.le", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WCovBy.refl", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WCovBy.rfl", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Eq.wcovBy", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "wcovBy_of_le_of_le", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntisymmRel.wcovBy", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WCovBy.wcovBy_iff_le", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "wcovBy_of_eq_or_eq", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntisymmRel.trans_wcovBy", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "wcovBy_congr_left", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WCovBy.trans_antisymm_rel", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "wcovBy_congr_right", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_wcovBy_iff", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "WCovBy.stdRefl", "kind": "instance", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WCovBy.Ioo_eq", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "wcovBy_iff_Ioo_eq", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WCovBy.of_le_of_le", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WCovBy.of_le_of_le'", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WCovBy.of_image", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WCovBy.image", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": true, "tactics": ["refine", "obtain", "rw", "exact"], "tactic_count": 4}
{"name": "Set.OrdConnected.apply_wcovBy_apply_iff", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "apply_wcovBy_apply_iff", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toDual_wcovBy_toDual_iff", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofDual_wcovBy_ofDual_iff", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WCovBy.eq_or_eq", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "exact"], "tactic_count": 3}
{"name": "wcovBy_iff_le_and_eq_or_eq", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WCovBy.le_and_le_iff", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": true, "tactics": ["refine", "exacts"], "tactic_count": 2}
{"name": "WCovBy.Icc_eq", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "WCovBy.Ico_subset", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "WCovBy.Ioc_subset", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "WCovBy.sup_eq", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WCovBy.inf_eq", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CovBy.lt", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_covBy_iff", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "not_covBy", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "denselyOrdered_iff_forall_not_covBy", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toDual_covBy_toDual_iff", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofDual_covBy_ofDual_iff", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CovBy.le", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CovBy.ne", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CovBy.ne'", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CovBy.wcovBy", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WCovBy.covBy_of_not_le", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WCovBy.covBy_of_lt", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CovBy.of_le_of_lt", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CovBy.of_lt_of_le", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_covBy_of_lt_of_lt", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "covBy_iff_wcovBy_and_lt", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "covBy_iff_wcovBy_and_not_le", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "wcovBy_iff_covBy_or_le_and_le", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntisymmRel.trans_covBy", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "covBy_congr_left", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CovBy.trans_antisymmRel", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "covBy_congr_right", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsNonstrictStrictOrderWCovByCovBy", "kind": "instance", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CovBy.irrefl", "kind": "instance", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CovBy.Ioo_eq", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "covBy_iff_Ioo_eq", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CovBy.of_image", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CovBy.image", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.OrdConnected.apply_covBy_apply_iff", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "apply_covBy_apply_iff", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "covBy_of_eq_or_eq", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WCovBy.covBy_of_ne", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "covBy_iff_wcovBy_and_ne", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "wcovBy_iff_covBy_or_eq", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "wcovBy_iff_eq_or_covBy", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CovBy.eq_or_eq", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "covBy_iff_lt_and_eq_or_eq", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CovBy.Ico_eq", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CovBy.Ioc_eq", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CovBy.Icc_eq", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CovBy.Ioi_eq", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CovBy.Iio_eq", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "WCovBy.le_of_lt", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WCovBy.ge_of_gt", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CovBy.le_of_lt", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CovBy.ge_of_gt", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CovBy.unique_left", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CovBy.unique_right", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CovBy.eq_of_between", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "covBy_iff_lt_iff_le_left", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "covBy_iff_le_iff_lt_left", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "covBy_iff_lt_iff_le_right", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": true, "tactics": ["trans", "simp_rw", "simp"], "tactic_count": 3}
{"name": "covBy_iff_le_iff_lt_right", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "LT.lt.exists_disjoint_Iio_Ioi", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Bool.wcovBy_iff", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "Bool.covBy_iff", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "Bool.instDecidableRelWCovBy", "kind": "instance", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bool.instDecidableRelCovBy", "kind": "instance", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.wcovBy_insert", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": true, "tactics": ["refine", "by_cases", "exact", "refine", "rwa"], "tactic_count": 5}
{"name": "Set.sdiff_singleton_wcovBy", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": true, "tactics": ["by_cases", "convert", "ext", "simp", "simp"], "tactic_count": 5}
{"name": "Set.covBy_insert", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.empty_covBy_singleton", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sdiff_singleton_covBy", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CovBy.exists_set_insert", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CovBy.exists_set_sdiff_singleton", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.covBy_iff_exists_insert", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.covBy_iff_exists_sdiff_singleton", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "wcovBy_eq_reflGen_covBy", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "transGen_wcovBy_eq_reflTransGen_covBy", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "reflTransGen_wcovBy_eq_reflTransGen_covBy", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Prod.swap_wcovBy_swap", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.swap_covBy_swap", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.fst_eq_or_snd_eq_of_wcovBy", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": true, "tactics": ["refine", "push_neg", "exact"], "tactic_count": 3}
{"name": "WCovBy.fst", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WCovBy.snd", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.mk_wcovBy_mk_iff_left", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": true, "tactics": ["refine", "have", "rw", "exact"], "tactic_count": 4}
{"name": "Prod.mk_wcovBy_mk_iff_right", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Prod.mk_covBy_mk_iff_right", "kind": "theorem", "module": "Mathlib.Order.Cover", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
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{"name": "DirectLimit.setoid", "kind": "definition", "module": "Mathlib.Order.DirectedInverseSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectLimit.r_of_le", "kind": "theorem", "module": "Mathlib.Order.DirectedInverseSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectLimit", "kind": "abbrev", "module": "Mathlib.Order.DirectedInverseSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectLimit.eq_of_le", "kind": "theorem", "module": "Mathlib.Order.DirectedInverseSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectLimit.induction", "kind": "theorem", "module": "Mathlib.Order.DirectedInverseSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectLimit.exists_eq_mk", "kind": "theorem", "module": "Mathlib.Order.DirectedInverseSystem", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "DirectLimit.exists_eq_mk₂", "kind": "theorem", "module": "Mathlib.Order.DirectedInverseSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectLimit.exists_eq_mk₃", "kind": "theorem", "module": "Mathlib.Order.DirectedInverseSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectLimit.induction₂", "kind": "theorem", "module": "Mathlib.Order.DirectedInverseSystem", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "DirectLimit.induction₃", "kind": "theorem", "module": "Mathlib.Order.DirectedInverseSystem", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "DirectLimit.mk_injective", "kind": "theorem", "module": "Mathlib.Order.DirectedInverseSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectLimit.map₀", "kind": "definition", "module": "Mathlib.Order.DirectedInverseSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectLimit.map₀_def", "kind": "theorem", "module": "Mathlib.Order.DirectedInverseSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectLimit.lift", "kind": "definition", "module": "Mathlib.Order.DirectedInverseSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectLimit.lift_def", "kind": "theorem", "module": "Mathlib.Order.DirectedInverseSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectLimit.lift_injective", "kind": "theorem", "module": "Mathlib.Order.DirectedInverseSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectLimit.map", "kind": "definition", "module": "Mathlib.Order.DirectedInverseSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectLimit.map_def", "kind": "theorem", "module": "Mathlib.Order.DirectedInverseSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Order.DirectedInverseSystem.0.DirectLimit.lift₂Aux", "kind": "definition", "module": "Mathlib.Order.DirectedInverseSystem", "is_tactic_proof": true, "tactics": ["choose", "refine", "have", "simp_rw"], "tactic_count": 4}
{"name": "DirectLimit.lift₂", "kind": "definition", "module": "Mathlib.Order.DirectedInverseSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectLimit.lift₂_def₂", "kind": "theorem", "module": "Mathlib.Order.DirectedInverseSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectLimit.lift₂_def", "kind": "theorem", "module": "Mathlib.Order.DirectedInverseSystem", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "DirectLimit.map₂", "kind": "definition", "module": "Mathlib.Order.DirectedInverseSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectLimit.map₂_def₂", "kind": "theorem", "module": "Mathlib.Order.DirectedInverseSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectLimit.map₂_def", "kind": "theorem", "module": "Mathlib.Order.DirectedInverseSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InverseSystem.limit", "kind": "definition", "module": "Mathlib.Order.DirectedInverseSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InverseSystem.piLT", "kind": "abbrev", "module": "Mathlib.Order.DirectedInverseSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InverseSystem.piLTProj", "kind": "abbrev", "module": "Mathlib.Order.DirectedInverseSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InverseSystem.piLTProj_intro", "kind": "theorem", "module": "Mathlib.Order.DirectedInverseSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InverseSystem.IsNatEquiv", "kind": "definition", "module": "Mathlib.Order.DirectedInverseSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InverseSystem.piLTLim", "kind": "definition", "module": "Mathlib.Order.DirectedInverseSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InverseSystem.piLTLim_symm_apply", "kind": "theorem", "module": "Mathlib.Order.DirectedInverseSystem", "is_tactic_proof": true, "tactics": ["conv_rhs", "rfl"], "tactic_count": 2}
{"name": "InverseSystem.piSplitLE", "kind": "definition", "module": "Mathlib.Order.DirectedInverseSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InverseSystem.piSplitLE_eq", "kind": "theorem", "module": "Mathlib.Order.DirectedInverseSystem", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "InverseSystem.piSplitLE_lt", "kind": "theorem", "module": "Mathlib.Order.DirectedInverseSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Order.DirectedInverseSystem.0.InverseSystem.term_⁺", "kind": "definition", "module": "Mathlib.Order.DirectedInverseSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Order.DirectedInverseSystem.0.InverseSystem._aux_Mathlib_Order_DirectedInverseSystem___macroRules__private_Mathlib_Order_DirectedInverseSystem_0_InverseSystem_term_⁺_1", "kind": "definition", "module": "Mathlib.Order.DirectedInverseSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Order.DirectedInverseSystem.0.InverseSystem._aux_Mathlib_Order_DirectedInverseSystem___unexpand_Order_succ_1", "kind": "definition", "module": "Mathlib.Order.DirectedInverseSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InverseSystem.piEquivSucc", "kind": "definition", "module": "Mathlib.Order.DirectedInverseSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InverseSystem.piEquivSucc_self", "kind": "theorem", "module": "Mathlib.Order.DirectedInverseSystem", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "InverseSystem.isNatEquiv_piEquivSucc", "kind": "theorem", "module": "Mathlib.Order.DirectedInverseSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InverseSystem.invLimEquiv", "kind": "definition", "module": "Mathlib.Order.DirectedInverseSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InverseSystem.piEquivLim", "kind": "definition", "module": "Mathlib.Order.DirectedInverseSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InverseSystem.isNatEquiv_piEquivLim", "kind": "theorem", "module": "Mathlib.Order.DirectedInverseSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InverseSystem.PEquivOn.restrict", "kind": "definition", "module": "Mathlib.Order.DirectedInverseSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InverseSystem.unique_pEquivOn", "kind": "theorem", "module": "Mathlib.Order.DirectedInverseSystem", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "ext1", "refine", "ext", "obtain", "exact", "have", "rw", "nat₂", "ext", "have", "have", "rw", "ih"], "tactic_count": 15}
{"name": "InverseSystem.pEquivOn_apply_eq", "kind": "theorem", "module": "Mathlib.Order.DirectedInverseSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InverseSystem.pEquivOnSucc", "kind": "definition", "module": "Mathlib.Order.DirectedInverseSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InverseSystem.pEquivOnGlue", "kind": "definition", "module": "Mathlib.Order.DirectedInverseSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InverseSystem.pEquivOnLim", "kind": "definition", "module": "Mathlib.Order.DirectedInverseSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Order.DirectedInverseSystem.0.InverseSystem.globalEquivAux", "kind": "definition", "module": "Mathlib.Order.DirectedInverseSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InverseSystem.globalEquiv", "kind": "definition", "module": "Mathlib.Order.DirectedInverseSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InverseSystem.globalEquiv_naturality", "kind": "theorem", "module": "Mathlib.Order.DirectedInverseSystem", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "InverseSystem.globalEquiv_compatibility", "kind": "theorem", "module": "Mathlib.Order.DirectedInverseSystem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Disjoint", "kind": "definition", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "disjoint_of_subsingleton", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "disjoint_comm", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Disjoint.symm", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "symmetric_disjoint", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "disjoint_bot_left", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "disjoint_bot_right", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Disjoint.mono", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Disjoint.mono_left", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Disjoint.mono_right", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Disjoint.out", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "disjoint_self", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Disjoint.ne", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Disjoint.eq_bot_of_le", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Disjoint.eq_bot_of_ge", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Disjoint.eq_iff", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Disjoint.ne_iff", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "disjoint_of_le_iff_left_eq_bot", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "disjoint_top", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "top_disjoint", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Disjoint.ne_top_of_ne_bot", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Codisjoint.ne_bot_of_ne_top'", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "disjoint_iff_inf_le", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "disjoint_iff", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Disjoint.le_bot", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Disjoint.eq_bot", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "disjoint_assoc", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "disjoint_left_comm", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "disjoint_right_comm", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Disjoint.inf_left", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Disjoint.inf_left'", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Disjoint.inf_right", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Disjoint.inf_right'", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Disjoint.of_disjoint_inf_of_le", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Disjoint.of_disjoint_inf_of_le'", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Disjoint.right_lt_sup_of_left_ne_bot", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "disjoint_sup_left", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "disjoint_sup_right", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Disjoint.sup_left", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Disjoint.sup_right", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Disjoint.left_le_of_le_sup_right", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Disjoint.left_le_of_le_sup_left", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "codisjoint_inf_left", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "codisjoint_inf_right", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Codisjoint.inf_left", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Codisjoint.inf_right", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Codisjoint.left_le_of_le_inf_right", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Codisjoint.left_le_of_le_inf_left", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Disjoint.dual", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "disjoint_toDual_iff", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "disjoint_ofDual_iff", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Disjoint.le_of_codisjoint", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "isCompl_iff", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompl.symm", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCompl_comm", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompl.dual", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompl.ofDual", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompl.of_le", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompl.of_eq", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompl.inf_eq_bot", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompl.inf_left_le_of_le_sup_right", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompl.le_sup_right_iff_inf_left_le", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompl.inf_left_eq_bot_iff", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsCompl.inf_right_eq_bot_iff", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompl.disjoint_left_iff", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsCompl.disjoint_right_iff", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompl.le_left_iff", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompl.le_right_iff", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompl.left_le_iff", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompl.right_le_iff", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompl.Antitone", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompl.right_unique", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompl.left_unique", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompl.sup_inf", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompl.inf_sup", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.disjoint_iff", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": true, "tactics": ["constructor", "intro", "refine", "all_goals", "rintro", "exact"], "tactic_count": 6}
{"name": "Prod.codisjoint_iff", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.isCompl_iff", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "isCompl_toDual_iff", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCompl_ofDual_iff", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCompl_bot_top", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCompl_top_bot", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_top_of_isCompl_bot", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "eq_top_of_bot_isCompl", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_bot_of_isCompl_top", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_bot_of_top_isCompl", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsComplemented", "kind": "definition", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isComplemented_bot", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isComplemented_top", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsComplemented.sup", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsComplemented.inf", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "complementedLattice_iff", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsingleton.instComplementedLattice", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "ComplementedLattice.instOrderDual", "kind": "instance", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complementeds", "kind": "abbrev", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complementeds.hasCoeT", "kind": "instance", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complementeds.coe_injective", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complementeds.coe_inj", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complementeds.coe_le_coe", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complementeds.coe_lt_coe", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complementeds.instBoundedOrder", "kind": "instance", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complementeds.coe_bot", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complementeds.coe_top", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complementeds.mk_bot", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complementeds.mk_top", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Complementeds.instInhabited", "kind": "instance", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complementeds.instMax", "kind": "instance", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complementeds.instMin", "kind": "instance", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complementeds.coe_sup", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complementeds.coe_inf", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complementeds.mk_sup_mk", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complementeds.mk_inf_mk", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complementeds.instDistribLattice", "kind": "instance", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complementeds.disjoint_coe", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complementeds.codisjoint_coe", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Complementeds.isCompl_coe", "kind": "theorem", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Complementeds.instComplementedLattice", "kind": "instance", "module": "Mathlib.Order.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "disjointed", "kind": "definition", "module": "Mathlib.Order.Disjointed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "disjointed_apply", "kind": "theorem", "module": "Mathlib.Order.Disjointed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "disjointed_of_isMin", "kind": "theorem", "module": "Mathlib.Order.Disjointed", "is_tactic_proof": true, "tactics": ["have", "simp"], "tactic_count": 2}
{"name": "disjointed_bot", "kind": "theorem", "module": "Mathlib.Order.Disjointed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "disjointed_le_id", "kind": "theorem", "module": "Mathlib.Order.Disjointed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "disjointed_le", "kind": "theorem", "module": "Mathlib.Order.Disjointed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "disjoint_disjointed_of_lt", "kind": "theorem", "module": "Mathlib.Order.Disjointed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "disjointed_eq_self", "kind": "theorem", "module": "Mathlib.Order.Disjointed", "is_tactic_proof": false, "tactics": ["rw", "sup_congr", "exact", "sup_bot", "prove", "for"], "tactic_count": 6}
{"name": "disjointedRec", "kind": "theorem", "module": "Mathlib.Order.Disjointed", "is_tactic_proof": true, "tactics": ["classical", "intro", "rw", "suffices", "intro", "induction", "empty", "insert", "rw", "exact"], "tactic_count": 10}
{"name": "partialSups_disjointed", "kind": "theorem", "module": "Mathlib.Order.Disjointed", "is_tactic_proof": true, "tactics": ["classical", "suffices", "intro", "induction", "zero", "simp", "simp", "succ", "rcases", "exact", "simp", "have", "simpa", "rw", "simp", "simp", "simp", "refine", "ih", "rw", "apply", "simpa", "refine", "simp", "exact"], "tactic_count": 25}
{"name": "Fintype.sup_disjointed", "kind": "theorem", "module": "Mathlib.Order.Disjointed", "is_tactic_proof": true, "tactics": ["classical", "have", "simpa", "rw", "rw", "partialSups_disjointed]"], "tactic_count": 6}
{"name": "disjointed_partialSups", "kind": "theorem", "module": "Mathlib.Order.Disjointed", "is_tactic_proof": true, "tactics": ["classical", "ext", "have", "rw", "simp", "rw", "simp", "simp", "congr", "simpa"], "tactic_count": 10}
{"name": "disjointed_unique", "kind": "theorem", "module": "Mathlib.Order.Disjointed", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "biUnion_Iic_disjointed", "kind": "theorem", "module": "Mathlib.Order.Disjointed", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "biUnion_range_succ_disjointed", "kind": "theorem", "module": "Mathlib.Order.Disjointed", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "disjoint_disjointed", "kind": "theorem", "module": "Mathlib.Order.Disjointed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "disjointed_unique'", "kind": "theorem", "module": "Mathlib.Order.Disjointed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.disjiUnion_Iic_disjointed", "kind": "theorem", "module": "Mathlib.Order.Disjointed", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "disjointed_succ", "kind": "theorem", "module": "Mathlib.Order.Disjointed", "is_tactic_proof": true, "tactics": ["rw", "congr", "simpa"], "tactic_count": 3}
{"name": "Monotone.disjointed_succ", "kind": "theorem", "module": "Mathlib.Order.Disjointed", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Monotone.disjointed_succ_sup", "kind": "theorem", "module": "Mathlib.Order.Disjointed", "is_tactic_proof": true, "tactics": ["by_cases", "simpa", "rw", "have", "ext", "simp", "rw"], "tactic_count": 7}
{"name": "sup_Ioc_disjointed_of_monotone", "kind": "theorem", "module": "Mathlib.Order.Disjointed", "is_tactic_proof": true, "tactics": ["let", "induction", "rfl", "succ", "by_cases", "simpa", "rw", "simp", "exact"], "tactic_count": 9}
{"name": "biUnion_Ioc_disjointed_of_monotone", "kind": "theorem", "module": "Mathlib.Order.Disjointed", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fintype.exists_disjointed_le", "kind": "theorem", "module": "Mathlib.Order.Disjointed", "is_tactic_proof": true, "tactics": ["rcases", "exact", "let", "let", "have", "refine", "intro", "simpa", "simpa", "exact"], "tactic_count": 10}
{"name": "iSup_disjointed", "kind": "theorem", "module": "Mathlib.Order.Disjointed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "disjointed_eq_inf_compl", "kind": "theorem", "module": "Mathlib.Order.Disjointed", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "disjointed_subset", "kind": "theorem", "module": "Mathlib.Order.Disjointed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iUnion_disjointed", "kind": "theorem", "module": "Mathlib.Order.Disjointed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "disjointed_eq_inter_compl", "kind": "theorem", "module": "Mathlib.Order.Disjointed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "preimage_find_eq_disjointed", "kind": "theorem", "module": "Mathlib.Order.Disjointed", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "disjointed_zero", "kind": "theorem", "module": "Mathlib.Order.Disjointed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "extend_partialOrder", "kind": "theorem", "module": "Mathlib.Order.Extension.Linear", "is_tactic_proof": true, "tactics": ["let", "have", "rintro", "haveI", "refine", "refine", "trans", "antisymm", "simp_rw", "intro", "exact", "rintro", "haveI", "haveI", "rcases", "exact", "exact", "rintro", "haveI", "haveI", "rcases", "exact", "apply", "obtain", "haveI", "refine", "intro", "by_contra", "let", "rw", "apply", "refine", "trans", "antisymm", "rintro", "exact", "exact", "exact", "exact", "rintro", "exact", "exact", "exact", "exact"], "tactic_count": 44}
{"name": "LinearExtension", "kind": "definition", "module": "Mathlib.Order.Extension.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instLinearOrderLinearExtensionOfPartialOrder", "kind": "instance", "module": "Mathlib.Order.Extension.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toLinearExtension", "kind": "definition", "module": "Mathlib.Order.Extension.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInhabitedLinearExtension", "kind": "instance", "module": "Mathlib.Order.Extension.Linear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsWellFounded.wellOrderExtension", "kind": "definition", "module": "Mathlib.Order.Extension.Well", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsWellFounded.wellOrderExtension.isWellFounded_lt", "kind": "instance", "module": "Mathlib.Order.Extension.Well", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsWellFounded.wellOrderExtension.isWellOrder_lt", "kind": "instance", "module": "Mathlib.Order.Extension.Well", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsWellFounded.exists_well_order_ge", "kind": "theorem", "module": "Mathlib.Order.Extension.Well", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WellOrderExtension", "kind": "definition", "module": "Mathlib.Order.Extension.Well", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInhabitedWellOrderExtension", "kind": "instance", "module": "Mathlib.Order.Extension.Well", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toWellOrderExtension", "kind": "definition", "module": "Mathlib.Order.Extension.Well", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instLinearOrderWellOrderExtensionOfWellFoundedLT", "kind": "instance", "module": "Mathlib.Order.Extension.Well", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WellOrderExtension.wellFoundedLT", "kind": "instance", "module": "Mathlib.Order.Extension.Well", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toWellOrderExtension_strictMono", "kind": "theorem", "module": "Mathlib.Order.Extension.Well", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.comap_cast_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_natCast_atTop_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.tendsto_comp_val_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Archimedean", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "tendsto_natCast_atTop_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_PNat_val_atTop_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Eventually.natCast_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.comap_cast_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.comap_cast_atBot", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_intCast_atTop_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Archimedean", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "tendsto_intCast_atBot_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Archimedean", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "tendsto_intCast_atTop_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Eventually.intCast_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Archimedean", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.Eventually.intCast_atBot", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Archimedean", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Rat.comap_cast_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.comap_cast_atBot", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_ratCast_atTop_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Archimedean", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "tendsto_ratCast_atBot_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Archimedean", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.Eventually.ratCast_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Archimedean", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.Eventually.ratCast_atBot", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Archimedean", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "atTop_hasAntitoneBasis_of_archimedean", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "atTop_hasCountableBasis_of_archimedean", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "atBot_hasCountableBasis_of_archimedean", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "atTop_isCountablyGenerated_of_archimedean", "kind": "instance", "module": "Mathlib.Order.Filter.AtTopBot.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "atBot_isCountablyGenerated_of_archimedean", "kind": "instance", "module": "Mathlib.Order.Filter.AtTopBot.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map_add_atTop_eq", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map_sub_atTop_eq", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Archimedean", "is_tactic_proof": true, "tactics": ["simp_rw", "apply"], "tactic_count": 2}
{"name": "Filter.Tendsto.const_mul_atTop'", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Archimedean", "is_tactic_proof": true, "tactics": ["refine", "obtain", "rw", "filter_upwards", "calc", "b", "rw", "exact"], "tactic_count": 8}
{"name": "Filter.Tendsto.atTop_mul_const'", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Archimedean", "is_tactic_proof": true, "tactics": ["refine", "obtain", "have", "filter_upwards", "calc", "b", "rw", "exact"], "tactic_count": 8}
{"name": "Filter.Tendsto.atTop_mul_const_of_neg'", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Archimedean", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Filter.Tendsto.atBot_mul_const'", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Archimedean", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Filter.Tendsto.atBot_mul_const_of_neg'", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Archimedean", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Filter.Tendsto.atTop_nsmul_const", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Archimedean", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact"], "tactic_count": 3}
{"name": "Filter.Tendsto.atTop_nsmul_neg_const", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Archimedean", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Filter.Tendsto.atTop_zsmul_const", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Archimedean", "is_tactic_proof": true, "tactics": ["refine", "obtain", "replace", "exact"], "tactic_count": 4}
{"name": "Filter.Tendsto.atTop_zsmul_neg_const", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Archimedean", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Filter.Tendsto.atBot_zsmul_const", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Archimedean", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Filter.Tendsto.atBot_zsmul_neg_const", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Archimedean", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Filter.hasAntitoneBasis_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.atTop_basis", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.atTop_basis_Ioi", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.atTop_basis_Ioi'", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": true, "tactics": ["have", "refine", "obtain", "obtain", "exact"], "tactic_count": 5}
{"name": "Filter.atTop_basis'", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": true, "tactics": ["have", "refine", "obtain", "exact"], "tactic_count": 4}
{"name": "Filter.atTop_neBot", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.atTop_neBot_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "Filter.atBot_neBot_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_atTop_sets", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventually_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.frequently_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.exists_eventually_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Filter.map_atTop_eq", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.frequently_atTop'", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.atBot_basis_Iio", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.atBot_basis_Iio'", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.atBot_basis'", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.atBot_basis", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.atBot_neBot", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_atBot_sets", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventually_atBot", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.frequently_atBot", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.exists_eventually_atBot", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map_atBot_eq", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.frequently_atBot'", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.extraction_of_frequently_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Filter.extraction_of_eventually_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.extraction_forall_of_frequently", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": true, "tactics": ["simp", "choose", "use", "constructor", "apply", "intro", "apply", "intro", "cases"], "tactic_count": 9}
{"name": "Filter.extraction_forall_of_eventually", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.extraction_forall_of_eventually'", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.inf_map_atTop_neBot_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Filter.exists_le_of_tendsto_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": true, "tactics": ["have", "have", "exact"], "tactic_count": 3}
{"name": "Filter.exists_le_of_tendsto_atBot", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.exists_lt_of_tendsto_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": true, "tactics": ["obtain", "rcases", "exact"], "tactic_count": 3}
{"name": "Filter.exists_lt_of_tendsto_atBot", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.inf_map_atBot_neBot_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_atTop'", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.tendsto_atTop_principal", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Filter.tendsto_atTop_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_atTop_atBot", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_atTop_atTop_iff_of_monotone", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_atTop_atBot_iff_of_antitone", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_atBot'", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_atBot_principal", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_atBot_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_atBot_atBot", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_atBot_atBot_iff_of_monotone", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_atBot_atTop_iff_of_antitone", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.subseq_mem", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map_atTop_eq_of_gc_preorder", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": true, "tactics": ["have", "choose", "refine", "rcases", "exact", "have", "rw", "intro", "filter_upwards", "exact"], "tactic_count": 10}
{"name": "Filter.map_atTop_eq_of_gc", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map_atBot_eq_of_gc_preorder", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map_atBot_eq_of_gc", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map_val_atTop_of_Ici_subset", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": true, "tactics": ["choose", "have", "have", "rw", "rwa", "refine", "exact"], "tactic_count": 7}
{"name": "Nat.map_cast_int_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": true, "tactics": ["refine", "lift", "exact"], "tactic_count": 3}
{"name": "Filter.map_val_Ici_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map_val_Ioi_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.atTop_Ioi_eq", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": true, "tactics": ["rcases", "subsingleton", "rw"], "tactic_count": 3}
{"name": "Filter.atTop_Ici_eq", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.map_val_Iio_atBot", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.atBot_Iio_eq", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map_val_Iic_atBot", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.atBot_Iic_eq", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_Ioi_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.tendsto_Iio_atBot", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_Ici_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.tendsto_Iic_atBot", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_comp_val_Ioi_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.tendsto_comp_val_Ici_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.tendsto_comp_val_Iio_atBot", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_comp_val_Iic_atBot", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map_add_atTop_eq_nat", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map_sub_atTop_eq_nat", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_add_atTop_nat", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_sub_atTop_nat", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_add_atTop_iff_nat", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map_div_atTop_eq_nat", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.not_bddAbove_of_tendsto_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": true, "tactics": ["rintro", "have", "have", "apply", "aesop"], "tactic_count": 5}
{"name": "Filter.not_bddBelow_of_tendsto_atBot", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasAntitoneBasis.eventually_subset", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasAntitoneBasis.tendsto", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasAntitoneBasis.comp_mono", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasAntitoneBasis.comp_strictMono", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.subseq_forall_of_frequently", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Basic", "is_tactic_proof": true, "tactics": ["choose", "exact"], "tactic_count": 2}
{"name": "Filter.map_atTop_finset_prod_le_of_prod_eq", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.BigOperators", "is_tactic_proof": true, "tactics": ["classical", "refine", "let", "refine", "simpa"], "tactic_count": 5}
{"name": "Function.Injective.map_atTop_finset_prod_eq", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.BigOperators", "is_tactic_proof": true, "tactics": ["haveI", "apply", "refine", "refine", "rw", "refine", "simp", "refine", "rintro", "exact", "refine", "simp", "exact"], "tactic_count": 13}
{"name": "Filter.Subsingleton.atTop_eq", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.CompleteLattice", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "Filter.Subsingleton.atBot_eq", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.ciSup_comp_tendsto_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.CompleteLattice", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "exacts"], "tactic_count": 4}
{"name": "Monotone.ciInf_comp_tendsto_atBot", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.ciSup_comp_tendsto_atBot", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.ciInf_comp_tendsto_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.ciSup_comp_tendsto_atTop_of_linearOrder", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.CompleteLattice", "is_tactic_proof": true, "tactics": ["rw", "rwa"], "tactic_count": 2}
{"name": "Monotone.ciInf_comp_tendsto_atBot_of_linearOrder", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.ciInf_comp_tendsto_atTop_of_linearOrder", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.ciSup_comp_tendsto_atBot_of_linearOrder", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.iSup_comp_tendsto_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.iInf_comp_tendsto_atBot", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.iSup_comp_tendsto_atBot", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.iInf_comp_tendsto_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.iUnion_comp_tendsto_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.iInter_comp_tendsto_atBot", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.iInter_comp_tendsto_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.iUnion_comp_tendsto_atBot", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.atTop.isCountablyGenerated", "kind": "instance", "module": "Mathlib.Order.Filter.AtTopBot.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.atBot.isCountablyGenerated", "kind": "instance", "module": "Mathlib.Order.Filter.AtTopBot.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.instIsCountablyGeneratedAtTopProd", "kind": "instance", "module": "Mathlib.Order.Filter.AtTopBot.CountablyGenerated", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "Filter.instIsCountablyGeneratedAtBotProd", "kind": "instance", "module": "Mathlib.Order.Filter.AtTopBot.CountablyGenerated", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "OrderDual.instIsCountablyGeneratedAtTop", "kind": "instance", "module": "Mathlib.Order.Filter.AtTopBot.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instIsCountablyGeneratedAtBot", "kind": "instance", "module": "Mathlib.Order.Filter.AtTopBot.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.atTop_countable_basis", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.atBot_countable_basis", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.exists_seq_tendsto", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.CountablyGenerated", "is_tactic_proof": true, "tactics": ["obtain", "choose", "exact"], "tactic_count": 3}
{"name": "Filter.exists_seq_monotone_tendsto_atTop_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.CountablyGenerated", "is_tactic_proof": true, "tactics": ["obtain", "choose", "set", "have", "refine", "refine", "rw", "apply", "refine", "rw", "apply"], "tactic_count": 11}
{"name": "Filter.exists_seq_antitone_tendsto_atTop_atBot", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_iff_seq_tendsto", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.CountablyGenerated", "is_tactic_proof": true, "tactics": ["refine", "contrapose", "have", "rcases", "rw", "refine", "rcases", "exact"], "tactic_count": 8}
{"name": "Filter.tendsto_of_seq_tendsto", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventually_iff_seq_eventually", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.CountablyGenerated", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Filter.frequently_iff_seq_frequently", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.CountablyGenerated", "is_tactic_proof": true, "tactics": ["simp", "push_neg"], "tactic_count": 2}
{"name": "Filter.exists_seq_forall_of_frequently", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.CountablyGenerated", "is_tactic_proof": true, "tactics": ["rw", "obtain", "obtain", "exact"], "tactic_count": 4}
{"name": "Filter.frequently_iff_seq_forall", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_of_subseq_tendsto", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.CountablyGenerated", "is_tactic_proof": true, "tactics": ["contrapose", "obtain", "obtain", "refine", "rcases", "exact"], "tactic_count": 6}
{"name": "Filter.subseq_tendsto_of_neBot", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.CountablyGenerated", "is_tactic_proof": true, "tactics": ["rw", "rcases", "rw", "obtain", "exact"], "tactic_count": 5}
{"name": "Filter.atTop", "kind": "definition", "module": "Mathlib.Order.Filter.AtTopBot.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.atBot", "kind": "definition", "module": "Mathlib.Order.Filter.AtTopBot.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Ici_mem_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Ioi_mem_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_atBot", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Iic_mem_atBot", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Iio_mem_atBot", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventually_ge_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventually_le_atBot", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventually_gt_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventually_ne_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventually_lt_atBot", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventually_ne_atBot", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsTop.atTop_eq", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBot.atBot_eq", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.atTop_eq_generate_Ici", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.Frequently.forall_exists_of_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Defs", "is_tactic_proof": true, "tactics": ["rw", "contrapose", "exact"], "tactic_count": 3}
{"name": "Filter.Frequently.forall_exists_of_atBot", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.atTop_eq_generate_of_forall_exists_le", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Defs", "is_tactic_proof": true, "tactics": ["rw", "apply", "rw", "rintro", "exact", "rw", "rintro", "rcases", "have", "have", "exact"], "tactic_count": 11}
{"name": "Filter.atTop_eq_generate_of_not_bddAbove", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Defs", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact"], "tactic_count": 3}
{"name": "Monotone.piecewise_eventually_eq_iUnion", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Defs", "is_tactic_proof": true, "tactics": ["rcases", "refine", "simp", "filter_upwards", "simp"], "tactic_count": 5}
{"name": "Antitone.piecewise_eventually_eq_iInter", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Defs", "is_tactic_proof": true, "tactics": ["classical", "convert", "convert", "simp"], "tactic_count": 4}
{"name": "Filter.disjoint_atBot_principal_Ioi", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.disjoint_atTop_principal_Iio", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.disjoint_atTop_principal_Iic", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.disjoint_atBot_principal_Ici", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.disjoint_pure_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.disjoint_pure_atBot", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.disjoint_atBot_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Disjoint", "is_tactic_proof": true, "tactics": ["rcases", "by_cases", "refine", "exact", "refine", "exact"], "tactic_count": 6}
{"name": "Filter.disjoint_atTop_atBot", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_const_mul_atTop_of_pos", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_mul_const_atTop_of_pos", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Field", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Filter.tendsto_div_const_atTop_of_pos", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Field", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Filter.tendsto_const_mul_atTop_iff_pos", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Field", "is_tactic_proof": true, "tactics": ["refine", "rcases", "exact"], "tactic_count": 3}
{"name": "Filter.tendsto_mul_const_atTop_iff_pos", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Field", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.tendsto_div_const_atTop_iff_pos", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Field", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.Tendsto.const_mul_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.atTop_mul_const", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.atTop_div_const", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Field", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Filter.tendsto_const_mul_pow_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_const_mul_pow_atTop_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Field", "is_tactic_proof": true, "tactics": ["refine", "rintro", "simp", "rcases", "exact"], "tactic_count": 5}
{"name": "Filter.tendsto_zpow_atTop_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Field", "is_tactic_proof": true, "tactics": ["lift"], "tactic_count": 1}
{"name": "Filter.map_div_atTop_eq", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_const_mul_atBot_of_pos", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Field", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Filter.tendsto_mul_const_atBot_of_pos", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Field", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Filter.tendsto_div_const_atBot_of_pos", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Field", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.tendsto_const_mul_atTop_of_neg", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Field", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Filter.tendsto_mul_const_atTop_of_neg", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Field", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Filter.tendsto_div_const_atTop_of_neg", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Field", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.tendsto_const_mul_atBot_of_neg", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Field", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Filter.tendsto_mul_const_atBot_of_neg", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Field", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Filter.tendsto_div_const_atBot_of_neg", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Field", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.tendsto_const_mul_atTop_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Field", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simp", "simp"], "tactic_count": 4}
{"name": "Filter.tendsto_mul_const_atTop_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Field", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.tendsto_div_const_atTop_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Field", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.tendsto_const_mul_atBot_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Field", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.tendsto_mul_const_atBot_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Field", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.tendsto_div_const_atBot_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Field", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.tendsto_const_mul_atTop_iff_neg", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Field", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.tendsto_mul_const_atTop_iff_neg", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Field", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.tendsto_div_const_atTop_iff_neg", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Field", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.tendsto_const_mul_atBot_iff_pos", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Field", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.tendsto_mul_const_atBot_iff_pos", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Field", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.tendsto_div_const_atBot_iff_pos", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Field", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.tendsto_const_mul_atBot_iff_neg", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Field", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.tendsto_mul_const_atBot_iff_neg", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Field", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.tendsto_div_const_atBot_iff_neg", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Field", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.Tendsto.const_mul_atTop_of_neg", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.atTop_mul_const_of_neg", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.atTop_div_const_of_neg", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.const_mul_atBot", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.atBot_mul_const", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.atBot_div_const", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.const_mul_atBot_of_neg", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.atBot_mul_const_of_neg", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_neg_const_mul_pow_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_const_mul_pow_atBot_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Field", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.eventually_forall_ge_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Finite", "is_tactic_proof": true, "tactics": ["refine", "rcases", "refine", "simp", "exact"], "tactic_count": 5}
{"name": "Filter.eventually_forall_le_atBot", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.eventually_forall_ge_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Finite", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.Tendsto.eventually_forall_le_atBot", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Finite", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.high_scores", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Finite", "is_tactic_proof": true, "tactics": ["intro", "obtain", "exists_max_image", "have", "obtain", "rcases", "push_neg", "exact", "use", "rintro", "have", "rcases", "exact", "exact", "calc", "u"], "tactic_count": 16}
{"name": "Filter.low_scores", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.frequently_high_scores", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Finite", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Filter.frequently_low_scores", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.strictMono_subseq_of_tendsto_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.strictMono_subseq_of_id_le", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Eventually.atTop_of_arithmetic", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Finite", "is_tactic_proof": true, "tactics": ["simp", "choose", "refine", "rw", "have", "refine", "rw", "exact"], "tactic_count": 8}
{"name": "Filter.HasAntitoneBasis.subbasis_with_rel", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Finite", "is_tactic_proof": true, "tactics": ["rsuffices", "exact", "have", "rcases", "simp", "exact"], "tactic_count": 6}
{"name": "Nat.eventually_pow_lt_factorial_sub", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Finite", "is_tactic_proof": true, "tactics": ["rw", "refine", "intro", "obtain", "obtain", "simp", "refine", "convert_to", "rw", "congr", "lia", "congr", "lia", "refine", "rw", "apply", "exact", "exact", "exact"], "tactic_count": 19}
{"name": "Nat.eventually_mul_pow_lt_factorial_sub", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Finite", "is_tactic_proof": true, "tactics": ["filter_upwards", "rw", "exact"], "tactic_count": 3}
{"name": "Filter.tendsto_finset_range", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.atTop_finset_eq_iInf", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Finset", "is_tactic_proof": true, "tactics": ["refine", "refine", "simp", "exact"], "tactic_count": 4}
{"name": "Filter.tendsto_atTop_finset_of_monotone", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Finset", "is_tactic_proof": true, "tactics": ["simp", "intro", "rcases", "exact"], "tactic_count": 4}
{"name": "Filter.tendsto_finset_image_atTop_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_finset_preimage_atTop_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_toLeft_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Finset", "is_tactic_proof": true, "tactics": ["intro", "simp", "obtain", "exact"], "tactic_count": 4}
{"name": "Filter.tendsto_toRight_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Finset", "is_tactic_proof": true, "tactics": ["intro", "simp", "obtain", "exact"], "tactic_count": 4}
{"name": "Filter.tendsto_finset_powerset_atTop_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Finset", "is_tactic_proof": true, "tactics": ["classical", "refine", "exact"], "tactic_count": 3}
{"name": "Filter.tendsto_finset_Iic_atTop_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Finset", "is_tactic_proof": true, "tactics": ["rcases", "exact", "by_cases", "refine", "obtain", "exact", "obtain", "simp"], "tactic_count": 8}
{"name": "Filter.tendsto_finset_Ici_atBot_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FloorSemiring.eventually_mul_pow_lt_factorial_sub", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Floor", "is_tactic_proof": true, "tactics": ["filter_upwards", "calc", "a", "rw", "gcongr", "try", "first", "positivity", "apply", "simp_rw"], "tactic_count": 10}
{"name": "Filter.tendsto_atTop_mul_left_of_le'", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_atBot_mul_left_of_ge'", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_atTop_mul_left_of_le", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_atBot_mul_left_of_ge", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_atTop_mul_right_of_le'", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_atBot_mul_right_of_ge'", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_atTop_mul_right_of_le", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_atBot_mul_right_of_ge", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_atTop_mul_const_left", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_atBot_mul_const_left", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_atTop_mul_const_right", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_atBot_mul_const_right", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map_inv_atBot", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map_inv_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.comap_inv_atBot", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.comap_inv_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_inv_atTop_atBot", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_inv_atBot_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_inv_atTop_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_inv_atBot_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_mabs_atTop_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_mabs_atBot_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.comap_mabs_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Group", "is_tactic_proof": false, "tactics": ["refine", "le_antisymm", "rintro", "refine", "rw", "exact"], "tactic_count": 6}
{"name": "Finset.tendsto_Icc_atBot_prod_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Interval", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.tendsto_Ioc_atBot_prod_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Interval", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.tendsto_Ico_atBot_prod_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Interval", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.tendsto_Ioo_atBot_prod_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Interval", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.tendsto_Icc_neg_atTop_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.tendsto_Ioc_neg_atTop_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.tendsto_Ico_neg_atTop_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.tendsto_Ioo_neg_atTop_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.tendsto_Icc_neg", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.tendsto_Ioc_neg", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.tendsto_Ico_neg", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.tendsto_Ioo_neg", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.comap_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Map", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "OrderIso.comap_atBot", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.map_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Map", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "OrderIso.map_atBot", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.tendsto_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.tendsto_atBot", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.tendsto_atTop_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Map", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "OrderIso.tendsto_atBot_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.frequently_modEq", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.frequently_mod_eq", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.ModEq", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Nat.frequently_even", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.ModEq", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Nat.frequently_odd", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.ModEq", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Filter.nonneg_of_eventually_pow_nonneg", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.one_eventuallyLE_mul_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.eventuallyLE_one_mul_atBot", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.one_le_mul_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.le_one_mul_atBot", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.atTop_mul_one_eventuallyLE", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.atBot_mul_eventuallyLE_one", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.atTop_mul_one_le", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.atBot_mul_le_one", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.atTop_mul_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.atBot_mul_atBot", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.atTop_pow", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Monoid", "is_tactic_proof": true, "tactics": ["refine", "simpa"], "tactic_count": 2}
{"name": "Filter.Tendsto.atBot_pow", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.atTop_of_const_mul", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.atBot_of_const_mul", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.atTop_of_mul_const", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.atBot_of_mul_const", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.atTop_of_isBoundedUnder_le_mul", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Monoid", "is_tactic_proof": true, "tactics": ["obtain", "refine", "exact"], "tactic_count": 3}
{"name": "Filter.Tendsto.atBot_of_isBoundedUnder_ge_mul", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.atTop_of_le_const_mul", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.atBot_of_const_le_mul", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.atTop_of_mul_isBoundedUnder_le", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Monoid", "is_tactic_proof": true, "tactics": ["obtain", "refine", "exact"], "tactic_count": 3}
{"name": "Filter.Tendsto.atBot_of_mul_isBoundedUnder_ge", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.atTop_of_mul_le_const", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.atBot_of_mul_const_le", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.prod_atTop_atTop_eq", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Prod", "is_tactic_proof": true, "tactics": ["cases", "subsingleton", "cases", "subsingleton", "simpa"], "tactic_count": 5}
{"name": "Filter.tendsto_finset_prod_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Prod", "is_tactic_proof": true, "tactics": ["classical", "apply", "intro", "simpa", "intro", "use", "exact"], "tactic_count": 7}
{"name": "Filter.prod_atBot_atBot_eq", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.prod_map_atTop_eq", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Prod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.prod_map_atBot_eq", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_atBot_diagonal", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Prod", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Filter.tendsto_atTop_diagonal", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Prod", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Filter.Tendsto.prod_map_prod_atBot", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Prod", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Filter.Tendsto.prod_map_prod_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Prod", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Filter.Tendsto.prod_atBot", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Prod", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Filter.Tendsto.prod_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Prod", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Filter.eventually_atBot_prod_self", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.eventually_atTop_prod_self", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventually_atBot_prod_self'", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.eventually_atTop_prod_self'", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.eventually_atTop_curry", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Prod", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Filter.eventually_atBot_curry", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.atTop_mul_atTop₀", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Ring", "is_tactic_proof": true, "tactics": ["refine", "filter_upwards", "le_mul_of_one_le_left"], "tactic_count": 3}
{"name": "Filter.tendsto_mul_self_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_pow_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.zero_pow_eventuallyEq", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.atTop_mul_atBot₀", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Ring", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "Filter.Tendsto.atBot_mul_atTop₀", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Ring", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "Filter.Tendsto.atBot_mul_atBot₀", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Ring", "is_tactic_proof": false, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "Filter.Tendsto.atTop_of_const_mul₀", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.atTop_of_mul_const₀", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_pow_atTop_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.not_tendsto_pow_atTop_atBot", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_lt_mul_self", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_le_mul_self", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.not_tendsto_const_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.not_tendsto_const_atBot", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.eventually_gt_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.eventually_ge_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.eventually_ne_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.eventually_ne_atTop'", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.eventually_lt_atBot", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.eventually_le_atBot", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.eventually_ne_atBot", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.OrderTop.atTop_eq", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Tendsto", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.OrderBot.atBot_eq", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_atTop_pure", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_atBot_pure", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Tendsto", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.tendsto_atBot", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_atTop_mono'", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_atBot_mono'", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_atTop_mono", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_atBot_mono", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.tendsto_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.upperBounds_range_comp_tendsto_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Tendsto", "is_tactic_proof": true, "tactics": ["refine", "rintro", "obtain", "exact"], "tactic_count": 4}
{"name": "Monotone.lowerBounds_range_comp_tendsto_atBot", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.lowerBounds_range_comp_tendsto_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.upperBounds_range_comp_tendsto_atBot", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_atTop_atTop_of_monotone", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_atTop_atBot_of_antitone", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_atBot_atBot_of_monotone", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_atBot_atTop_of_antitone", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.comap_embedding_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.comap_embedding_atBot", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_atTop_embedding", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Tendsto", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.tendsto_atBot_embedding", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_atTop_atTop_of_monotone'", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Tendsto", "is_tactic_proof": true, "tactics": ["apply", "intro", "rcases", "exact"], "tactic_count": 4}
{"name": "Filter.tendsto_atBot_atBot_of_monotone'", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_atTop_of_monotone_of_filter", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_atBot_of_monotone_of_filter", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_atTop_of_monotone_of_subseq", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_atBot_of_monotone_of_subseq", "kind": "theorem", "module": "Mathlib.Order.Filter.AtTopBot.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FilterBasis.nonempty_sets", "kind": "instance", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instMembershipSetFilterBasis", "kind": "instance", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FilterBasis.mem_sets", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInhabitedFilterBasisNat", "kind": "instance", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.asBasis", "kind": "definition", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.IsBasis.filterBasis", "kind": "definition", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.IsBasis.mem_filterBasis_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FilterBasis.filter", "kind": "definition", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FilterBasis.mem_filter_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FilterBasis.mem_filter_of_mem", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FilterBasis.eq_iInf_principal", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": ["have", "rintro", "rcases", "use", "simp", "exact", "ext", "simp"], "tactic_count": 8}
{"name": "FilterBasis.generate", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": true, "tactics": ["apply", "intro", "rcases", "exact", "rw", "apply"], "tactic_count": 6}
{"name": "FilterBasis.ker_filter", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Filter.IsBasis.filter", "kind": "definition", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.IsBasis.mem_filter_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.IsBasis.filter_eq_generate", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.HasBasis.mem_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.eq_of_same_basis", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "Filter.hasBasis_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.ex_mem", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.nonempty", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.IsBasis.hasBasis", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.mem_of_superset", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.mem_of_mem", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.index", "kind": "definition", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.property_index", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.set_index_mem", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.set_index_subset", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.isBasis", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.filter_eq", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Filter.HasBasis.eq_generate", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "FilterBasis.hasBasis", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.to_hasBasis'", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": true, "tactics": ["refine", "rcases", "rcases", "exact"], "tactic_count": 4}
{"name": "Filter.HasBasis.to_hasBasis", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.congr", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.to_subset", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.eventually_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Filter.HasBasis.frequently_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.HasBasis.exists_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.forall_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.neBot_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.eq_bot_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.basis_sets", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.asBasis_filter", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.hasBasis_self", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Filter.HasBasis.comp_surjective", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.comp_equiv", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.to_image_id'", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.to_image_id", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.restrict", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": true, "tactics": ["refine", "rcases", "rcases", "exact"], "tactic_count": 4}
{"name": "Filter.HasBasis.restrict_subset", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.hasBasis_self_subset", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Filter.HasBasis.ge_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.le_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.HasBasis.le_basis_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.HasBasis.eq_top_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.HasBasis.ext", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": true, "tactics": ["apply", "rw", "simpa", "rw", "simpa"], "tactic_count": 5}
{"name": "Filter.HasBasis.inf'", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.inf", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.hasBasis_iInf_of_directed'", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "Filter.hasBasis_iInf_of_directed", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "Filter.hasBasis_biInf_of_directed'", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "refine", "rintro", "rcases", "exact", "rintro", "exact"], "tactic_count": 8}
{"name": "Filter.hasBasis_biInf_of_directed", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "refine", "rintro", "rcases", "exact", "rintro", "exact"], "tactic_count": 8}
{"name": "Filter.hasBasis_top", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.hasBasis_principal", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.hasBasis_pure", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.HasBasis.sup'", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.sup", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.hasBasis_iSup", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.sup_principal", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.sup_pure", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.HasBasis.inf_principal", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.principal_inf", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Filter.HasBasis.inf_basis_neBot_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.inf_neBot_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.inf_principal_neBot_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.disjoint_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Disjoint.exists_mem_filter_basis", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.inf_neBot_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.inf_principal_neBot_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_iff_inf_principal_compl", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": true, "tactics": ["refine", "exact", "inter_compl_nonempty_iff.2"], "tactic_count": 3}
{"name": "Filter.notMem_iff_inf_principal_compl", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.disjoint_principal_right", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.disjoint_principal_left", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.disjoint_principal_principal", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.disjoint_pure_pure", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.HasBasis.disjoint_iff_left", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.HasBasis.disjoint_iff_right", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.le_iff_forall_inf_principal_compl", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.inf_neBot_iff_frequently_left", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.inf_neBot_iff_frequently_right", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Filter.HasBasis.eq_biInf", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.eq_iInf", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Filter.hasBasis_iInf_principal", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.hasBasis_biInf_principal", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.hasBasis_biInf_principal'", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.map", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.comap", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.comap_hasBasis", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.forall_mem_mem", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Filter.HasBasis.biInf_mem", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.biInter_mem", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.ker", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasAntitoneBasis.map", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasAntitoneBasis.comap", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasAntitoneBasis.iInf_principal", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.tendsto_left_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": true, "tactics": ["simp", "rfl"], "tactic_count": 2}
{"name": "Filter.HasBasis.tendsto_right_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.HasBasis.tendsto_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.Tendsto.basis_left", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.basis_right", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.basis_both", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.prod_pprod", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.prod", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.principal_prod", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Filter.HasBasis.prod_principal", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Filter.HasBasis.top_prod", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Filter.HasBasis.prod_top", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Filter.HasBasis.prod_same_index", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": true, "tactics": ["simp", "refine", "rintro", "rcases", "exact", "rintro", "exact"], "tactic_count": 7}
{"name": "Filter.HasBasis.prod_same_index_mono", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.prod_same_index_anti", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.prod_self", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_prod_self_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventually_prod_self_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventually_prod_self_iff'", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasAntitoneBasis.prod", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.coprod", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map_sigma_mk_comap", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Basic", "is_tactic_proof": true, "tactics": ["refine", "convert", "apply"], "tactic_count": 3}
{"name": "Filter.hasBasis_generate", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.FilterBasis.ofSets", "kind": "definition", "module": "Mathlib.Order.Filter.Bases.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.FilterBasis.ofSets_sets", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.generate_eq_generate_inter", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Finite", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.ofSets_filter_eq_generate", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Finite", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.generate_neBot_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.iInf'", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.iInf", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Finite", "is_tactic_proof": true, "tactics": ["refine", "rcases", "exact", "rintro", "refine", "cases", "exact"], "tactic_count": 7}
{"name": "Pairwise.exists_mem_filter_basis_of_disjoint", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Finite", "is_tactic_proof": true, "tactics": ["rcases", "choose", "exact"], "tactic_count": 3}
{"name": "Set.PairwiseDisjoint.exists_mem_filter_basis", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Finite", "is_tactic_proof": true, "tactics": ["rcases", "choose", "exact"], "tactic_count": 3}
{"name": "Filter.hasBasis_iInf_principal_finite", "kind": "theorem", "module": "Mathlib.Order.Filter.Bases.Finite", "is_tactic_proof": true, "tactics": ["refine", "simp"], "tactic_count": 2}
{"name": "Filter.inhabitedMem", "kind": "instance", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.filter_eq_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.sets_subset_sets", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.sets_ssubset_sets", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.coext", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.instTransSetSupersetMem", "kind": "instance", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.instTransSetMemSubset", "kind": "instance", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.inter_mem_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.diff_mem", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.congr_sets", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.copy_eq", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.biInter_mem'", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "Filter.iInter_mem'", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.exists_mem_subset_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.monotone_mem", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.exists_mem_and_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 5}
{"name": "Filter.mem_principal_self", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventually_mem_principal", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.not_le", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Filter.GenerateSets", "kind": "inductive", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.generate", "kind": "definition", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_generate_of_mem", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.le_generate_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.generate_singleton", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mkOfClosure", "kind": "definition", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mkOfClosure_sets", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.giGenerate", "kind": "definition", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_inf_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_inf_of_left", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_inf_of_right", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.inter_mem_inf", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_inf_of_inter", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_inf_iff_superset", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_sdiff_iff_union", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.instCompleteLatticeFilter", "kind": "instance", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.instInhabited", "kind": "instance", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.NeBot.ne", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.not_neBot", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.NeBot.mono", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.neBot_of_le", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.sup_neBot", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.not_disjoint_self_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.bot_sets_eq", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eq_or_neBot", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.sup_sets_eq", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.sSup_sets_eq", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.iSup_sets_eq", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.generate_empty", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.generate_univ", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.generate_union", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.generate_iUnion", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_sup", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.union_mem_sup", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_iSup", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.iSup_neBot", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.iInf_eq_generate", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_iInf_of_mem", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.iInf_sets_induct", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": true, "tactics": ["have", "let", "have", "have", "use", "intro", "have", "rw", "exact", "have", "let", "univ_sets", "sets_of_superset", "inter_sets", "exact", "have", "let", "univ_sets", "sets_of_superset", "inter_sets", "have", "exact"], "tactic_count": 22}
{"name": "Filter.le_principal_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Iic_principal", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.principal_mono", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.monotone_principal", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.principal_eq_iff_eq", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.join_principal_eq_sSup", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.principal_univ", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.principal_empty", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.generate_eq_biInf", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.empty_mem_iff_bot", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.nonempty_of_mem", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.NeBot.nonempty_of_mem", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.empty_notMem", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.nonempty_of_neBot", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.compl_notMem", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.filter_eq_bot_of_isEmpty", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.disjoint_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.disjoint_of_disjoint_of_mem", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.NeBot.not_disjoint", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.inf_eq_bot_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.unique", "kind": "instance", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.NeBot.nonempty", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eq_top_of_neBot", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact"], "tactic_count": 3}
{"name": "Filter.forall_mem_nonempty_iff_neBot", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.instNeBotTop", "kind": "instance", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.instNontrivialFilter", "kind": "instance", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.nontrivial_iff_nonempty", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eq_sInf_of_mem_iff_exists_mem", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eq_iInf_of_mem_iff_exists_mem", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eq_biInf_of_mem_iff_exists_mem", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Filter.iInf_sets_eq", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_iInf_of_directed", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.mem_biInf_of_directed", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": true, "tactics": ["haveI", "simp_rw"], "tactic_count": 2}
{"name": "Filter.biInf_sets_eq", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.sup_join", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.iSup_join", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.instCoframe", "kind": "instance", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.instDistribLattice", "kind": "instance", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.iInf_neBot_of_directed'", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.iInf_neBot_of_directed", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": true, "tactics": ["cases", "constructor", "simp", "exact"], "tactic_count": 4}
{"name": "Filter.sInf_neBot_of_directed'", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.sInf_neBot_of_directed", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.iInf_neBot_iff_of_directed'", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.iInf_neBot_iff_of_directed", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.inf_principal", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.sup_principal", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.iSup_principal", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.principal_eq_bot_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.principal_neBot_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.isCompl_principal", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_inf_principal'", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.mem_inf_principal", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.iSup_inf_principal", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Filter.inf_principal_eq_bot", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Filter.mem_of_eq_bot", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Filter.diff_mem_inf_principal_compl", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.principal_le_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Filter.join_mono", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventually_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventually_mem_set", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.ext'", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Eventually.filter_mono", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventually_of_mem", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Eventually.and", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventually_true", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Eventually.of_forall", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventually_false_iff_eq_bot", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventually_const", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "Filter.eventually_iff_exists_mem", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Eventually.exists_mem", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Eventually.mp", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Eventually.mono", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.GCongr.eventually_mono", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.forall_eventually_of_eventually_forall", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventually_and", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Eventually.congr", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventually_congr", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventually_or_distrib_left", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventually_or_distrib_right", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.eventually_imp_distrib_left", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.eventually_bot", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventually_top", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventually_sup", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventually_sSup", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventually_iSup", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventually_principal", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Eventually.forall_mem", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventually_inf", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventually_inf_principal", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventually_iff_all_subsets", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Eventually.frequently", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Frequently.of_forall", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Frequently.mp", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.frequently_congr", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Frequently.filter_mono", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Frequently.mono", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.GCongr.frequently_mono", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Frequently.and_eventually", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "Filter.Eventually.and_frequently", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Filter.Frequently.exists", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": true, "tactics": ["by_contra", "replace", "exact"], "tactic_count": 3}
{"name": "Filter.Eventually.exists", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.frequently_iff_neBot", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.frequently_mem_iff_neBot", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.frequently_iff_forall_eventually_exists_and", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.frequently_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": true, "tactics": ["simp", "rfl"], "tactic_count": 2}
{"name": "Filter.not_eventually", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.not_frequently", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.frequently_true_iff_neBot", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.frequently_false", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.frequently_const", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "Filter.frequently_or_distrib", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.frequently_or_distrib_left", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.frequently_or_distrib_right", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.frequently_imp_distrib", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.frequently_imp_distrib_left", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.frequently_imp_distrib_right", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.eventually_imp_distrib_right", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.frequently_and_distrib_left", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.frequently_and_distrib_right", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.frequently_bot", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.frequently_top", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.frequently_principal", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.frequently_inf_principal", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.frequently_sup", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.frequently_sSup", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.frequently_iSup", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.Eventually.choice", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": ["haveI", "let", "hx.nonempty", "choose", "exact"], "tactic_count": 5}
{"name": "Filter.skolem", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": true, "tactics": ["classical", "refine", "refine", "filter_upwards", "exact"], "tactic_count": 5}
{"name": "Filter.EventuallyEq.eventually", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventuallyEq_top", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.EventuallyEq.rw", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventuallyEq_set", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventuallyEq_univ", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.EventuallyEq.exists_mem", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventuallyEq_of_mem", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventuallyEq_iff_exists_mem", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.filter_mono", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.refl", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.rfl", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.of_eq", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.symm", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventuallyEq_comm", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.trans", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.congr_left", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.congr_right", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.instTransForallEventuallyEq", "kind": "instance", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.prodMk", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.fun_comp", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.comp₂", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.mul", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.fun_mul", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.mul_left", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.mul_right", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.pow_const", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.fun_pow_const", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.inv", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.fun_inv", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.div", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.fun_div", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.smul", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.fun_star", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.star", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.sup", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.inf", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.preimage", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.inter", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.union", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.compl", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.diff", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.symmDiff", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventuallyEq_empty", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.inter_eventuallyEq_left", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.inter_eventuallyEq_right", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.eventuallyEq_principal", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventuallyEq_inf_principal_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.sub_eq", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Filter.eventuallyEq_iff_sub", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventuallyEq_iff_all_subsets", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyLE.congr", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventuallyLE_congr", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventuallyLE_iff_all_subsets", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.le", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyLE.refl", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyLE.rfl", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyLE.trans", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.instTransForallEventuallyLE", "kind": "instance", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.trans_le", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.instTransForallEventuallyEqEventuallyLE", "kind": "instance", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyLE.trans_eq", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.instTransForallEventuallyLEEventuallyEq", "kind": "instance", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyLE.antisymm", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventuallyLE_antisymm_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.EventuallyLE.ge_iff_eq'", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Eventually.ne_of_lt", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Eventually.ne_top_of_lt", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Eventually.lt_top_of_ne", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Eventually.lt_top_iff_ne_top", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyLE.inter", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyLE.union", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyLE.compl", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyLE.diff", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.set_eventuallyLE_iff_mem_inf_principal", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.set_eventuallyLE_iff_inf_principal_le", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.set_eventuallyEq_iff_inf_principal", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.EventuallyLE.sup", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": true, "tactics": ["filter_upwards"], "tactic_count": 1}
{"name": "Filter.EventuallyLE.sup_le", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": true, "tactics": ["filter_upwards"], "tactic_count": 1}
{"name": "Filter.EventuallyLE.le_sup_of_le_left", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyLE.le_sup_of_le_right", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.join_le", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.EqOn.eventuallyEq", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.EqOn.eventuallyEq_of_mem", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasSubset.Subset.eventuallyLE", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.compl_mem_comk", "kind": "theorem", "module": "Mathlib.Order.Filter.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "cardinal_sInter_mem", "kind": "theorem", "module": "Mathlib.Order.Filter.CardinalInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.cardinalInterFilter_aleph0", "kind": "theorem", "module": "Mathlib.Order.Filter.CardinalInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CardinalInterFilter.toCountableInterFilter", "kind": "theorem", "module": "Mathlib.Order.Filter.CardinalInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CountableInterFilter.toCardinalInterFilter", "kind": "instance", "module": "Mathlib.Order.Filter.CardinalInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cardinalInterFilter_aleph_one_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.CardinalInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CardinalInterFilter.of_cardinalInterFilter_of_le", "kind": "theorem", "module": "Mathlib.Order.Filter.CardinalInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CardinalInterFilter.of_cardinalInterFilter_of_lt", "kind": "theorem", "module": "Mathlib.Order.Filter.CardinalInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.cardinal_iInter_mem", "kind": "theorem", "module": "Mathlib.Order.Filter.CardinalInter", "is_tactic_proof": true, "tactics": ["rw", "apply", "exact"], "tactic_count": 3}
{"name": "Filter.cardinal_bInter_mem", "kind": "theorem", "module": "Mathlib.Order.Filter.CardinalInter", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Filter.eventually_cardinal_forall", "kind": "theorem", "module": "Mathlib.Order.Filter.CardinalInter", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Filter.eventually_cardinal_ball", "kind": "theorem", "module": "Mathlib.Order.Filter.CardinalInter", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Filter.EventuallyLE.cardinal_iUnion", "kind": "theorem", "module": "Mathlib.Order.Filter.CardinalInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.cardinal_iUnion", "kind": "theorem", "module": "Mathlib.Order.Filter.CardinalInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyLE.cardinal_bUnion", "kind": "theorem", "module": "Mathlib.Order.Filter.CardinalInter", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Filter.EventuallyEq.cardinal_bUnion", "kind": "theorem", "module": "Mathlib.Order.Filter.CardinalInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyLE.cardinal_iInter", "kind": "theorem", "module": "Mathlib.Order.Filter.CardinalInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.cardinal_iInter", "kind": "theorem", "module": "Mathlib.Order.Filter.CardinalInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyLE.cardinal_bInter", "kind": "theorem", "module": "Mathlib.Order.Filter.CardinalInter", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Filter.EventuallyEq.cardinal_bInter", "kind": "theorem", "module": "Mathlib.Order.Filter.CardinalInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.ofCardinalInter", "kind": "definition", "module": "Mathlib.Order.Filter.CardinalInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.cardinalInter_ofCardinalInter", "kind": "instance", "module": "Mathlib.Order.Filter.CardinalInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_ofCardinalInter", "kind": "theorem", "module": "Mathlib.Order.Filter.CardinalInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.ofCardinalUnion", "kind": "definition", "module": "Mathlib.Order.Filter.CardinalInter", "is_tactic_proof": true, "tactics": ["refine", "rw", "apply", "intro", "rw", "rcases", "apply", "rw", "rw", "exact"], "tactic_count": 10}
{"name": "Filter.cardinalInter_ofCardinalUnion", "kind": "instance", "module": "Mathlib.Order.Filter.CardinalInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_ofCardinalUnion", "kind": "theorem", "module": "Mathlib.Order.Filter.CardinalInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.cardinalInterFilter_principal", "kind": "instance", "module": "Mathlib.Order.Filter.CardinalInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.cardinalInterFilter_bot", "kind": "instance", "module": "Mathlib.Order.Filter.CardinalInter", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "Filter.cardinalInterFilter_top", "kind": "instance", "module": "Mathlib.Order.Filter.CardinalInter", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "Filter.instCardinalInterFilterComap", "kind": "instance", "module": "Mathlib.Order.Filter.CardinalInter", "is_tactic_proof": true, "tactics": ["refine", "choose", "refine", "simpa"], "tactic_count": 4}
{"name": "Filter.instCardinalInterFilterMap", "kind": "instance", "module": "Mathlib.Order.Filter.CardinalInter", "is_tactic_proof": true, "tactics": ["refine", "simp", "exact"], "tactic_count": 3}
{"name": "Filter.cardinalInterFilter_inf_eq", "kind": "instance", "module": "Mathlib.Order.Filter.CardinalInter", "is_tactic_proof": true, "tactics": ["refine", "choose", "replace", "replace", "refine", "rw", "apply"], "tactic_count": 7}
{"name": "Filter.cardinalInterFilter_inf", "kind": "instance", "module": "Mathlib.Order.Filter.CardinalInter", "is_tactic_proof": true, "tactics": ["have", "have", "exact"], "tactic_count": 3}
{"name": "Filter.cardinalInterFilter_sup_eq", "kind": "instance", "module": "Mathlib.Order.Filter.CardinalInter", "is_tactic_proof": true, "tactics": ["refine", "exacts"], "tactic_count": 2}
{"name": "Filter.cardinalInterFilter_sup", "kind": "instance", "module": "Mathlib.Order.Filter.CardinalInter", "is_tactic_proof": true, "tactics": ["have", "have", "exact"], "tactic_count": 3}
{"name": "Filter.CardinalGenerateSets", "kind": "inductive", "module": "Mathlib.Order.Filter.CardinalInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.cardinalGenerate", "kind": "definition", "module": "Mathlib.Order.Filter.CardinalInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.cardinalInter_ofCardinalGenerate", "kind": "theorem", "module": "Mathlib.Order.Filter.CardinalInter", "is_tactic_proof": true, "tactics": ["delta", "apply"], "tactic_count": 2}
{"name": "Filter.mem_cardinalGenerate_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.CardinalInter", "is_tactic_proof": true, "tactics": ["constructor", "induction", "refine", "simpa", "univ", "superset", "choose", "refine", "apply", "apply", "rcases", "have", "exact"], "tactic_count": 13}
{"name": "Filter.le_cardinalGenerate_iff_of_cardinalInterFilter", "kind": "theorem", "module": "Mathlib.Order.Filter.CardinalInter", "is_tactic_proof": true, "tactics": ["constructor", "exact", "intro", "induction", "basic", "univ", "superset", "sInter"], "tactic_count": 8}
{"name": "Filter.cardinalGenerate_isGreatest", "kind": "theorem", "module": "Mathlib.Order.Filter.CardinalInter", "is_tactic_proof": true, "tactics": ["refine", "rintro", "rwa"], "tactic_count": 3}
{"name": "Filter.cocardinal", "kind": "definition", "module": "Mathlib.Order.Filter.Cocardinal", "is_tactic_proof": true, "tactics": ["apply", "refine", "exact", "exact"], "tactic_count": 4}
{"name": "Filter.mem_cocardinal", "kind": "theorem", "module": "Mathlib.Order.Filter.Cocardinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.cocardinal_aleph0_eq_cofinite", "kind": "theorem", "module": "Mathlib.Order.Filter.Cocardinal", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Filter.instCardinalInterFilter_cocardinal", "kind": "instance", "module": "Mathlib.Order.Filter.Cocardinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventually_cocardinal", "kind": "theorem", "module": "Mathlib.Order.Filter.Cocardinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.hasBasis_cocardinal", "kind": "theorem", "module": "Mathlib.Order.Filter.Cocardinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.frequently_cocardinal", "kind": "theorem", "module": "Mathlib.Order.Filter.Cocardinal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.frequently_cocardinal_mem", "kind": "theorem", "module": "Mathlib.Order.Filter.Cocardinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.cocardinal_inf_principal_neBot_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Cocardinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.compl_mem_cocardinal_of_card_lt", "kind": "theorem", "module": "Mathlib.Order.Filter.Cocardinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.compl_mem_cocardinal", "kind": "theorem", "module": "Mathlib.Order.Filter.Cocardinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventually_cocardinal_notMem_of_card_lt", "kind": "theorem", "module": "Mathlib.Order.Filter.Cocardinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.eventually_cocardinal_notMem", "kind": "theorem", "module": "Mathlib.Order.Filter.Cocardinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventually_cocardinal_ne", "kind": "theorem", "module": "Mathlib.Order.Filter.Cocardinal", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Filter.cocountable", "kind": "abbrev", "module": "Mathlib.Order.Filter.Cocardinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_cocountable", "kind": "theorem", "module": "Mathlib.Order.Filter.Cocardinal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.cofinite", "kind": "definition", "module": "Mathlib.Order.Filter.Cofinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_cofinite", "kind": "theorem", "module": "Mathlib.Order.Filter.Cofinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventually_cofinite", "kind": "theorem", "module": "Mathlib.Order.Filter.Cofinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.hasBasis_cofinite", "kind": "theorem", "module": "Mathlib.Order.Filter.Cofinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.cofinite_neBot", "kind": "instance", "module": "Mathlib.Order.Filter.Cofinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.cofinite_eq_bot_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Cofinite", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.cofinite_eq_bot", "kind": "theorem", "module": "Mathlib.Order.Filter.Cofinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.frequently_cofinite_iff_infinite", "kind": "theorem", "module": "Mathlib.Order.Filter.Cofinite", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.frequently_cofinite_mem_iff_infinite", "kind": "theorem", "module": "Mathlib.Order.Filter.Cofinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.cofinite_inf_principal_neBot_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Cofinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.compl_mem_cofinite", "kind": "theorem", "module": "Mathlib.Order.Filter.Cofinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.eventually_cofinite_notMem", "kind": "theorem", "module": "Mathlib.Order.Filter.Cofinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.eventually_cofinite_notMem", "kind": "theorem", "module": "Mathlib.Order.Filter.Cofinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.infinite_iff_frequently_cofinite", "kind": "theorem", "module": "Mathlib.Order.Filter.Cofinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventually_cofinite_ne", "kind": "theorem", "module": "Mathlib.Order.Filter.Cofinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.le_cofinite_iff_compl_singleton_mem", "kind": "theorem", "module": "Mathlib.Order.Filter.Cofinite", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "Filter.le_cofinite_iff_eventually_ne", "kind": "theorem", "module": "Mathlib.Order.Filter.Cofinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.atTop_le_cofinite", "kind": "theorem", "module": "Mathlib.Order.Filter.Cofinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.atBot_le_cofinite", "kind": "theorem", "module": "Mathlib.Order.Filter.Cofinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.comap_cofinite_le", "kind": "theorem", "module": "Mathlib.Order.Filter.Cofinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.coprod_cofinite", "kind": "theorem", "module": "Mathlib.Order.Filter.Cofinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.coprodᵢ_cofinite", "kind": "theorem", "module": "Mathlib.Order.Filter.Cofinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.disjoint_cofinite_left", "kind": "theorem", "module": "Mathlib.Order.Filter.Cofinite", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.disjoint_cofinite_right", "kind": "theorem", "module": "Mathlib.Order.Filter.Cofinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.countable_compl_ker", "kind": "theorem", "module": "Mathlib.Order.Filter.Cofinite", "is_tactic_proof": true, "tactics": ["rcases", "simp", "exact"], "tactic_count": 3}
{"name": "Filter.Tendsto.countable_compl_preimage_ker", "kind": "theorem", "module": "Mathlib.Order.Filter.Cofinite", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.univ_pi_mem_pi", "kind": "theorem", "module": "Mathlib.Order.Filter.Cofinite", "is_tactic_proof": true, "tactics": ["filter_upwards"], "tactic_count": 1}
{"name": "Filter.map_piMap_pi", "kind": "theorem", "module": "Mathlib.Order.Filter.Cofinite", "is_tactic_proof": true, "tactics": ["refine", "refine", "rintro", "classical", "rw", "refine", "by_cases", "simpa", "simp", "filter_upwards", "simp"], "tactic_count": 11}
{"name": "Filter.map_piMap_pi_finite", "kind": "theorem", "module": "Mathlib.Order.Filter.Cofinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.cofinite_inf_principal_compl", "kind": "theorem", "module": "Mathlib.Order.Filter.Cofinite", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.Finite.cofinite_inf_principal_diff", "kind": "theorem", "module": "Mathlib.Order.Filter.Cofinite", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.cofinite_eq_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.Cofinite", "is_tactic_proof": true, "tactics": ["refine", "refine", "simpa"], "tactic_count": 3}
{"name": "Nat.frequently_atTop_iff_infinite", "kind": "theorem", "module": "Mathlib.Order.Filter.Cofinite", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.eventually_pos", "kind": "theorem", "module": "Mathlib.Order.Filter.Cofinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.exists_within_forall_le", "kind": "theorem", "module": "Mathlib.Order.Filter.Cofinite", "is_tactic_proof": true, "tactics": ["by_cases", "rcases", "have", "simp", "obtain", "refine", "exact", "obtain", "exact"], "tactic_count": 9}
{"name": "Filter.Tendsto.exists_forall_le", "kind": "theorem", "module": "Mathlib.Order.Filter.Cofinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.exists_within_forall_ge", "kind": "theorem", "module": "Mathlib.Order.Filter.Cofinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.exists_forall_ge", "kind": "theorem", "module": "Mathlib.Order.Filter.Cofinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.le_map_cofinite", "kind": "theorem", "module": "Mathlib.Order.Filter.Cofinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.tendsto_cofinite", "kind": "theorem", "module": "Mathlib.Order.Filter.Cofinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.cofinite_of_finite_preimage_singleton", "kind": "theorem", "module": "Mathlib.Order.Filter.Cofinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.comap_cofinite_eq", "kind": "theorem", "module": "Mathlib.Order.Filter.Cofinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.nat_tendsto_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.Cofinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.update_eventuallyEq", "kind": "theorem", "module": "Mathlib.Order.Filter.Cofinite", "is_tactic_proof": true, "tactics": ["filter_upwards"], "tactic_count": 1}
{"name": "Function.update_eventuallyEq_cofinite", "kind": "theorem", "module": "Mathlib.Order.Filter.Cofinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "countable_sInter_mem", "kind": "theorem", "module": "Mathlib.Order.Filter.CountableInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "countable_iInter_mem", "kind": "theorem", "module": "Mathlib.Order.Filter.CountableInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "countable_bInter_mem", "kind": "theorem", "module": "Mathlib.Order.Filter.CountableInter", "is_tactic_proof": true, "tactics": ["rw", "haveI", "exact"], "tactic_count": 3}
{"name": "eventually_countable_forall", "kind": "theorem", "module": "Mathlib.Order.Filter.CountableInter", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "eventually_countable_ball", "kind": "theorem", "module": "Mathlib.Order.Filter.CountableInter", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "EventuallyLE.countable_iUnion", "kind": "theorem", "module": "Mathlib.Order.Filter.CountableInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EventuallyEq.countable_iUnion", "kind": "theorem", "module": "Mathlib.Order.Filter.CountableInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EventuallyLE.countable_bUnion", "kind": "theorem", "module": "Mathlib.Order.Filter.CountableInter", "is_tactic_proof": true, "tactics": ["simp", "haveI", "exact"], "tactic_count": 3}
{"name": "EventuallyEq.countable_bUnion", "kind": "theorem", "module": "Mathlib.Order.Filter.CountableInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EventuallyLE.countable_iInter", "kind": "theorem", "module": "Mathlib.Order.Filter.CountableInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EventuallyEq.countable_iInter", "kind": "theorem", "module": "Mathlib.Order.Filter.CountableInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EventuallyLE.countable_bInter", "kind": "theorem", "module": "Mathlib.Order.Filter.CountableInter", "is_tactic_proof": true, "tactics": ["simp", "haveI", "exact"], "tactic_count": 3}
{"name": "EventuallyEq.countable_bInter", "kind": "theorem", "module": "Mathlib.Order.Filter.CountableInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.ofCountableInter", "kind": "definition", "module": "Mathlib.Order.Filter.CountableInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.countableInter_ofCountableInter", "kind": "instance", "module": "Mathlib.Order.Filter.CountableInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_ofCountableInter", "kind": "theorem", "module": "Mathlib.Order.Filter.CountableInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.ofCountableUnion", "kind": "definition", "module": "Mathlib.Order.Filter.CountableInter", "is_tactic_proof": true, "tactics": ["refine", "rw", "apply", "intro", "rw", "rcases", "apply", "rw", "rw", "exact"], "tactic_count": 10}
{"name": "Filter.countableInter_ofCountableUnion", "kind": "instance", "module": "Mathlib.Order.Filter.CountableInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_ofCountableUnion", "kind": "theorem", "module": "Mathlib.Order.Filter.CountableInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "countableInterFilter_principal", "kind": "instance", "module": "Mathlib.Order.Filter.CountableInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "countableInterFilter_bot", "kind": "instance", "module": "Mathlib.Order.Filter.CountableInter", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "countableInterFilter_top", "kind": "instance", "module": "Mathlib.Order.Filter.CountableInter", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "instCountableInterFilterComap", "kind": "instance", "module": "Mathlib.Order.Filter.CountableInter", "is_tactic_proof": true, "tactics": ["refine", "choose", "have", "refine", "simpa"], "tactic_count": 5}
{"name": "instCountableInterFilterMap", "kind": "instance", "module": "Mathlib.Order.Filter.CountableInter", "is_tactic_proof": true, "tactics": ["refine", "simp", "exact"], "tactic_count": 3}
{"name": "countableInterFilter_inf", "kind": "instance", "module": "Mathlib.Order.Filter.CountableInter", "is_tactic_proof": true, "tactics": ["refine", "choose", "replace", "replace", "refine", "rw", "apply"], "tactic_count": 7}
{"name": "countableInterFilter_sup", "kind": "instance", "module": "Mathlib.Order.Filter.CountableInter", "is_tactic_proof": true, "tactics": ["refine", "exacts"], "tactic_count": 2}
{"name": "CountableInterFilter.curry", "kind": "instance", "module": "Mathlib.Order.Filter.CountableInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.CountableGenerateSets", "kind": "inductive", "module": "Mathlib.Order.Filter.CountableInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.countableGenerate", "kind": "definition", "module": "Mathlib.Order.Filter.CountableInter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_countableGenerate_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.CountableInter", "is_tactic_proof": true, "tactics": ["constructor", "induction", "univ", "superset", "choose", "refine", "apply", "intro", "exact", "rcases", "refine", "intro", "exact"], "tactic_count": 13}
{"name": "Filter.le_countableGenerate_iff_of_countableInterFilter", "kind": "theorem", "module": "Mathlib.Order.Filter.CountableInter", "is_tactic_proof": true, "tactics": ["constructor", "exact", "intro", "induction", "basic", "univ", "superset", "sInter"], "tactic_count": 8}
{"name": "Filter.countableGenerate_isGreatest", "kind": "theorem", "module": "Mathlib.Order.Filter.CountableInter", "is_tactic_proof": true, "tactics": ["refine", "rintro", "rwa"], "tactic_count": 3}
{"name": "exists_countable_separating", "kind": "theorem", "module": "Mathlib.Order.Filter.CountableSeparatingOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_nonempty_countable_separating", "kind": "theorem", "module": "Mathlib.Order.Filter.CountableSeparatingOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_seq_separating", "kind": "theorem", "module": "Mathlib.Order.Filter.CountableSeparatingOn", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "use", "simpa"], "tactic_count": 4}
{"name": "HasCountableSeparatingOn.mono", "kind": "theorem", "module": "Mathlib.Order.Filter.CountableSeparatingOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasCountableSeparatingOn.of_subtype", "kind": "theorem", "module": "Mathlib.Order.Filter.CountableSeparatingOn", "is_tactic_proof": true, "tactics": ["rcases", "choose", "refine", "refine", "rw", "exact"], "tactic_count": 6}
{"name": "HasCountableSeparatingOn.subtype_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.CountableSeparatingOn", "is_tactic_proof": true, "tactics": ["constructor", "exact", "rcases", "use", "rintro", "exact", "rintro", "exact", "hS"], "tactic_count": 9}
{"name": "Filter.exists_subset_subsingleton_mem_of_forall_separating", "kind": "theorem", "module": "Mathlib.Order.Filter.CountableSeparatingOn", "is_tactic_proof": true, "tactics": ["rcases", "refine", "exact", "intro", "simp", "refine", "cases", "inl", "inr", "exact", "inter_mem"], "tactic_count": 11}
{"name": "Filter.exists_mem_singleton_mem_of_mem_of_nonempty_of_forall_separating", "kind": "theorem", "module": "Mathlib.Order.Filter.CountableSeparatingOn", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "exact", "exact"], "tactic_count": 4}
{"name": "Filter.exists_singleton_mem_of_mem_of_forall_separating", "kind": "theorem", "module": "Mathlib.Order.Filter.CountableSeparatingOn", "is_tactic_proof": true, "tactics": ["rcases", "exact", "exact"], "tactic_count": 3}
{"name": "Filter.exists_subsingleton_mem_of_forall_separating", "kind": "theorem", "module": "Mathlib.Order.Filter.CountableSeparatingOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.exists_singleton_mem_of_forall_separating", "kind": "theorem", "module": "Mathlib.Order.Filter.CountableSeparatingOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.exists_mem_eventuallyEq_const_of_eventually_mem_of_forall_separating", "kind": "theorem", "module": "Mathlib.Order.Filter.CountableSeparatingOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.exists_eventuallyEq_const_of_eventually_mem_of_forall_separating", "kind": "theorem", "module": "Mathlib.Order.Filter.CountableSeparatingOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.exists_eventuallyEq_const_of_forall_separating", "kind": "theorem", "module": "Mathlib.Order.Filter.CountableSeparatingOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.of_eventually_mem_of_forall_separating_mem_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.CountableSeparatingOn", "is_tactic_proof": true, "tactics": ["rcases", "have", "filter_upwards"], "tactic_count": 3}
{"name": "Filter.EventuallyEq.of_forall_separating_mem_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.CountableSeparatingOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.of_eventually_mem_of_forall_separating_preimage", "kind": "theorem", "module": "Mathlib.Order.Filter.CountableSeparatingOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.of_forall_separating_preimage", "kind": "theorem", "module": "Mathlib.Order.Filter.CountableSeparatingOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Nat.inhabitedCountableFilterBasis", "kind": "instance", "module": "Mathlib.Order.Filter.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasCountableBasis.isCountablyGenerated", "kind": "theorem", "module": "Mathlib.Order.Filter.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.isCountablyGenerated", "kind": "theorem", "module": "Mathlib.Order.Filter.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.antitone_seq_of_seq", "kind": "theorem", "module": "Mathlib.Order.Filter.CountablyGenerated", "is_tactic_proof": true, "tactics": ["use", "exact", "apply", "rw", "refine", "exact", "refine", "rfl"], "tactic_count": 8}
{"name": "Filter.countable_biInf_eq_iInf_seq", "kind": "theorem", "module": "Mathlib.Order.Filter.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.countable_biInf_eq_iInf_seq'", "kind": "theorem", "module": "Mathlib.Order.Filter.CountablyGenerated", "is_tactic_proof": true, "tactics": ["rcases", "rw", "use", "simp", "exact"], "tactic_count": 5}
{"name": "Filter.countable_biInf_principal_eq_seq_iInf", "kind": "theorem", "module": "Mathlib.Order.Filter.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasAntitoneBasis.mem_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasAntitoneBasis.mem", "kind": "theorem", "module": "Mathlib.Order.Filter.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasAntitoneBasis.hasBasis_ge", "kind": "theorem", "module": "Mathlib.Order.Filter.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.exists_antitone_subbasis", "kind": "theorem", "module": "Mathlib.Order.Filter.CountablyGenerated", "is_tactic_proof": false, "tactics": ["obtain", "rcases", "rw", "exact", "have", "let", "have", "antitone_nat_of_succ_le", "have", "rintro", "exacts", "refine", "have", "convert", "exact", "le_antisymm"], "tactic_count": 16}
{"name": "Filter.exists_antitone_basis", "kind": "theorem", "module": "Mathlib.Order.Filter.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.exists_antitone_seq", "kind": "theorem", "module": "Mathlib.Order.Filter.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Inf.isCountablyGenerated", "kind": "instance", "module": "Mathlib.Order.Filter.CountablyGenerated", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "exact"], "tactic_count": 3}
{"name": "Filter.map.isCountablyGenerated", "kind": "instance", "module": "Mathlib.Order.Filter.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.comap.isCountablyGenerated", "kind": "instance", "module": "Mathlib.Order.Filter.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Sup.isCountablyGenerated", "kind": "instance", "module": "Mathlib.Order.Filter.CountablyGenerated", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "exact"], "tactic_count": 3}
{"name": "Filter.prod.isCountablyGenerated", "kind": "instance", "module": "Mathlib.Order.Filter.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.coprod.isCountablyGenerated", "kind": "instance", "module": "Mathlib.Order.Filter.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.isCountablyGenerated_seq", "kind": "theorem", "module": "Mathlib.Order.Filter.CountablyGenerated", "is_tactic_proof": true, "tactics": ["use", "rw"], "tactic_count": 2}
{"name": "Filter.isCountablyGenerated_of_seq", "kind": "theorem", "module": "Mathlib.Order.Filter.CountablyGenerated", "is_tactic_proof": true, "tactics": ["rcases", "apply"], "tactic_count": 2}
{"name": "Filter.isCountablyGenerated_biInf_principal", "kind": "theorem", "module": "Mathlib.Order.Filter.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.isCountablyGenerated_iff_exists_antitone_basis", "kind": "theorem", "module": "Mathlib.Order.Filter.CountablyGenerated", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "rintro", "rw", "exact"], "tactic_count": 6}
{"name": "Filter.isCountablyGenerated_principal", "kind": "theorem", "module": "Mathlib.Order.Filter.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.isCountablyGenerated_pure", "kind": "theorem", "module": "Mathlib.Order.Filter.CountablyGenerated", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Filter.isCountablyGenerated_bot", "kind": "theorem", "module": "Mathlib.Order.Filter.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.isCountablyGenerated_top", "kind": "theorem", "module": "Mathlib.Order.Filter.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.iInf.isCountablyGenerated", "kind": "instance", "module": "Mathlib.Order.Filter.CountablyGenerated", "is_tactic_proof": true, "tactics": ["choose", "rw", "refine", "refine", "rintro", "lift", "exact"], "tactic_count": 7}
{"name": "Filter.pi.isCountablyGenerated", "kind": "instance", "module": "Mathlib.Order.Filter.CountablyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventually_curry_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.frequently_curry_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Curry", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Filter.mem_curry_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.curry_le_prod", "kind": "theorem", "module": "Mathlib.Order.Filter.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.curry", "kind": "theorem", "module": "Mathlib.Order.Filter.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.frequently_curry_prod_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Curry", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.eventually_curry_prod_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Curry", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.prod_mem_curry", "kind": "theorem", "module": "Mathlib.Order.Filter.Curry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.filter_eq", "kind": "theorem", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.instMembership", "kind": "instance", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.ext", "kind": "theorem", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_mk", "kind": "theorem", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_sets", "kind": "theorem", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.univ_mem", "kind": "theorem", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_of_superset", "kind": "theorem", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.univ_mem'", "kind": "theorem", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.inter_mem", "kind": "theorem", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mp_mem", "kind": "theorem", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.copy", "kind": "definition", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_copy", "kind": "theorem", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.comk", "kind": "definition", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_comk", "kind": "theorem", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.principal", "kind": "definition", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.term𝓟", "kind": "definition", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter._aux_Mathlib_Order_Filter_Defs___macroRules_Filter_term𝓟_1", "kind": "definition", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter._aux_Mathlib_Order_Filter_Defs___unexpand_Filter_principal_1", "kind": "definition", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_principal", "kind": "theorem", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.instPure", "kind": "instance", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_pure", "kind": "theorem", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.ker", "kind": "definition", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.join", "kind": "definition", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_join", "kind": "theorem", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.instPartialOrder", "kind": "instance", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.le_def", "kind": "theorem", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.instSupSet", "kind": "instance", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_sSup", "kind": "theorem", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.sInf", "kind": "definition", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.instInfSet", "kind": "instance", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.sSup_lowerBounds", "kind": "theorem", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.instTop", "kind": "instance", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_top_iff_forall", "kind": "theorem", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_top", "kind": "theorem", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.instBot", "kind": "instance", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_bot", "kind": "theorem", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.instInf", "kind": "instance", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.instSup", "kind": "instance", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.instSDiff", "kind": "instance", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.instHNot", "kind": "instance", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_sdiff", "kind": "theorem", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.hnot_def", "kind": "theorem", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.neBot_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Eventually", "kind": "definition", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.term∀ᶠ_In_,_", "kind": "definition", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter._aux_Mathlib_Order_Filter_Defs___macroRules_Filter_term∀ᶠ_In_,__1", "kind": "definition", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter._aux_Mathlib_Order_Filter_Defs___delab_app_Filter_term∀ᶠ_In_,__1", "kind": "definition", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Frequently", "kind": "definition", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.term∃ᶠ_In_,_", "kind": "definition", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter._aux_Mathlib_Order_Filter_Defs___macroRules_Filter_term∃ᶠ_In_,__1", "kind": "definition", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter._aux_Mathlib_Order_Filter_Defs___delab_app_Filter_term∃ᶠ_In_,__1", "kind": "definition", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq", "kind": "definition", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.term_=ᶠ[_]_", "kind": "definition", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter._aux_Mathlib_Order_Filter_Defs___macroRules_Filter_term_=ᶠ[_]__1", "kind": "definition", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter._aux_Mathlib_Order_Filter_Defs___unexpand_Filter_EventuallyEq_1", "kind": "definition", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyLE", "kind": "definition", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.term_≤ᶠ[_]_", "kind": "definition", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter._aux_Mathlib_Order_Filter_Defs___macroRules_Filter_term_≤ᶠ[_]__1", "kind": "definition", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter._aux_Mathlib_Order_Filter_Defs___unexpand_Filter_EventuallyLE_1", "kind": "definition", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map", "kind": "definition", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto", "kind": "definition", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.comap", "kind": "definition", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.coprod", "kind": "definition", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.instSProd", "kind": "instance", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.prod_eq_inf", "kind": "theorem", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.pi", "kind": "definition", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.bind", "kind": "definition", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.seq", "kind": "definition", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.curry", "kind": "definition", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.instBind", "kind": "instance", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.instFunctor", "kind": "instance", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.lift", "kind": "definition", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.lift'", "kind": "definition", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.IsBounded", "kind": "definition", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.IsBoundedUnder", "kind": "definition", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.IsCobounded", "kind": "definition", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.IsCoboundedUnder", "kind": "definition", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.filterUpwards", "kind": "definition", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic._aux_Mathlib_Order_Filter_Defs___elabRules_Mathlib_Tactic_filterUpwards_1", "kind": "definition", "module": "Mathlib.Order.Filter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.limsSup_of_not_isCobounded", "kind": "theorem", "module": "Mathlib.Order.Filter.ENNReal", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Real.limsSup_of_not_isBounded", "kind": "theorem", "module": "Mathlib.Order.Filter.ENNReal", "is_tactic_proof": true, "tactics": ["rw", "convert", "simpa"], "tactic_count": 3}
{"name": "Real.limsInf_of_not_isCobounded", "kind": "theorem", "module": "Mathlib.Order.Filter.ENNReal", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Real.limsInf_of_not_isBounded", "kind": "theorem", "module": "Mathlib.Order.Filter.ENNReal", "is_tactic_proof": true, "tactics": ["rw", "convert", "simpa"], "tactic_count": 3}
{"name": "Real.limsup_of_not_isCoboundedUnder", "kind": "theorem", "module": "Mathlib.Order.Filter.ENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.limsup_of_not_isBoundedUnder", "kind": "theorem", "module": "Mathlib.Order.Filter.ENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.liminf_of_not_isCoboundedUnder", "kind": "theorem", "module": "Mathlib.Order.Filter.ENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.liminf_of_not_isBoundedUnder", "kind": "theorem", "module": "Mathlib.Order.Filter.ENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.isBoundedUnder_le_toReal", "kind": "theorem", "module": "Mathlib.Order.Filter.ENNReal", "is_tactic_proof": true, "tactics": ["simp", "constructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 6}
{"name": "NNReal.isBoundedUnder_ge_toReal", "kind": "theorem", "module": "Mathlib.Order.Filter.ENNReal", "is_tactic_proof": true, "tactics": ["simp", "constructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 6}
{"name": "NNReal.isCoboundedUnder_le_toReal", "kind": "theorem", "module": "Mathlib.Order.Filter.ENNReal", "is_tactic_proof": true, "tactics": ["simp", "constructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 6}
{"name": "NNReal.isCoboundedUnder_ge_toReal", "kind": "theorem", "module": "Mathlib.Order.Filter.ENNReal", "is_tactic_proof": true, "tactics": ["simp", "constructor", "rintro", "exact", "rintro", "refine", "obtain", "exact", "exact"], "tactic_count": 9}
{"name": "NNReal.limsSup_of_not_isBounded", "kind": "theorem", "module": "Mathlib.Order.Filter.ENNReal", "is_tactic_proof": true, "tactics": ["rw", "convert", "simpa"], "tactic_count": 3}
{"name": "NNReal.limsInf_of_not_isCobounded", "kind": "theorem", "module": "Mathlib.Order.Filter.ENNReal", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "NNReal.limsup_of_not_isBoundedUnder", "kind": "theorem", "module": "Mathlib.Order.Filter.ENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.liminf_of_not_isCoboundedUnder", "kind": "theorem", "module": "Mathlib.Order.Filter.ENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.toReal_liminf", "kind": "theorem", "module": "Mathlib.Order.Filter.ENNReal", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "refine", "rw", "simp", "refine", "simpa"], "tactic_count": 7}
{"name": "NNReal.toReal_limsup", "kind": "theorem", "module": "Mathlib.Order.Filter.ENNReal", "is_tactic_proof": true, "tactics": ["obtain", "simp", "by_cases", "simp", "have", "refine", "rw", "simp", "refine", "simpa"], "tactic_count": 10}
{"name": "ENNReal.eventually_le_limsup", "kind": "theorem", "module": "Mathlib.Order.Filter.ENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.limsup_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.ENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.limsup_const_mul_of_ne_top", "kind": "theorem", "module": "Mathlib.Order.Filter.ENNReal", "is_tactic_proof": true, "tactics": ["by_cases", "simp_rw", "exact", "let", "exact"], "tactic_count": 5}
{"name": "ENNReal.limsup_const_mul", "kind": "theorem", "module": "Mathlib.Order.Filter.ENNReal", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "by_cases", "have", "simp", "simp", "have", "rw", "refine", "rw", "simp", "have", "eq_top_iff.mpr", "have", "simp"], "tactic_count": 15}
{"name": "ENNReal.limsup_mul_le", "kind": "theorem", "module": "Mathlib.Order.Filter.ENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.limsup_add_le", "kind": "theorem", "module": "Mathlib.Order.Filter.ENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.limsup_liminf_le_liminf_limsup", "kind": "theorem", "module": "Mathlib.Order.Filter.ENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyConst", "kind": "definition", "module": "Mathlib.Order.Filter.EventuallyConst", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.eventuallyConst_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.EventuallyConst", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.eventuallyConst_iff'", "kind": "theorem", "module": "Mathlib.Order.Filter.EventuallyConst", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventuallyConst_iff_tendsto", "kind": "theorem", "module": "Mathlib.Order.Filter.EventuallyConst", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyConst.of_tendsto", "kind": "theorem", "module": "Mathlib.Order.Filter.EventuallyConst", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventuallyConst_iff_exists_eventuallyEq", "kind": "theorem", "module": "Mathlib.Order.Filter.EventuallyConst", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventuallyConst_pred'", "kind": "theorem", "module": "Mathlib.Order.Filter.EventuallyConst", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.eventuallyConst_pred", "kind": "theorem", "module": "Mathlib.Order.Filter.EventuallyConst", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.eventuallyConst_set'", "kind": "theorem", "module": "Mathlib.Order.Filter.EventuallyConst", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventuallyConst_set", "kind": "theorem", "module": "Mathlib.Order.Filter.EventuallyConst", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventuallyConst_preimage", "kind": "theorem", "module": "Mathlib.Order.Filter.EventuallyConst", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.eventuallyConst_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.EventuallyConst", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.eventuallyConst_id", "kind": "theorem", "module": "Mathlib.Order.Filter.EventuallyConst", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyConst.bot", "kind": "theorem", "module": "Mathlib.Order.Filter.EventuallyConst", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyConst.const", "kind": "theorem", "module": "Mathlib.Order.Filter.EventuallyConst", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyConst.congr", "kind": "theorem", "module": "Mathlib.Order.Filter.EventuallyConst", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyConst.of_subsingleton_right", "kind": "theorem", "module": "Mathlib.Order.Filter.EventuallyConst", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyConst.anti", "kind": "theorem", "module": "Mathlib.Order.Filter.EventuallyConst", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyConst.of_subsingleton_left", "kind": "theorem", "module": "Mathlib.Order.Filter.EventuallyConst", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyConst.comp", "kind": "theorem", "module": "Mathlib.Order.Filter.EventuallyConst", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyConst.inv", "kind": "theorem", "module": "Mathlib.Order.Filter.EventuallyConst", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyConst.comp_tendsto", "kind": "theorem", "module": "Mathlib.Order.Filter.EventuallyConst", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyConst.apply", "kind": "theorem", "module": "Mathlib.Order.Filter.EventuallyConst", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyConst.comp₂", "kind": "theorem", "module": "Mathlib.Order.Filter.EventuallyConst", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyConst.prodMk", "kind": "theorem", "module": "Mathlib.Order.Filter.EventuallyConst", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyConst.mul", "kind": "theorem", "module": "Mathlib.Order.Filter.EventuallyConst", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyConst.of_mulIndicator_const", "kind": "theorem", "module": "Mathlib.Order.Filter.EventuallyConst", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Filter.EventuallyConst.mulIndicator_const", "kind": "theorem", "module": "Mathlib.Order.Filter.EventuallyConst", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Filter.EventuallyConst.mulIndicator_const_iff_of_ne", "kind": "theorem", "module": "Mathlib.Order.Filter.EventuallyConst", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyConst.mulIndicator_const_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.EventuallyConst", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "Filter.eventuallyConst_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.EventuallyConst", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventuallyConst_atTop_nat", "kind": "theorem", "module": "Mathlib.Order.Filter.EventuallyConst", "is_tactic_proof": true, "tactics": ["rw", "refine", "exact", "induction", "base", "succ"], "tactic_count": 6}
{"name": "IsMinFilter", "kind": "definition", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMaxFilter", "kind": "definition", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsExtrFilter", "kind": "definition", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMinOn", "kind": "definition", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMaxOn", "kind": "definition", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsExtrOn", "kind": "definition", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsExtrOn.elim", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isMinOn_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isMaxOn_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isMinOn_univ_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isMaxOn_univ_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMinOn.bddBelow", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMinOn.isGLB", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": true, "tactics": ["rw", "intro", "simp", "exact"], "tactic_count": 4}
{"name": "IsMaxOn.isLUB", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMaxOn.bddAbove", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMinFilter.tendsto_principal_Ici", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMaxFilter.tendsto_principal_Iic", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMinFilter.isExtr", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMaxFilter.isExtr", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMinOn.isExtr", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMaxOn.isExtr", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isMinFilter_const", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isMaxFilter_const", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isExtrFilter_const", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isMinOn_const", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isMaxOn_const", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isExtrOn_const", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eventuallyEq_of_isMinFilter_of_isMaxFilter", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": true, "tactics": ["filter_upwards"], "tactic_count": 1}
{"name": "isMinFilter_dual_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isMaxFilter_dual_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isExtrFilter_dual_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isMinOn_dual_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isMaxOn_dual_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isExtrOn_dual_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMinFilter.filter_mono", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMaxFilter.filter_mono", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsExtrFilter.filter_mono", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMinFilter.filter_inf", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMaxFilter.filter_inf", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsExtrFilter.filter_inf", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMinOn.on_subset", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMaxOn.on_subset", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsExtrOn.on_subset", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMinOn.inter", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMaxOn.inter", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsExtrOn.inter", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMinFilter.comp_mono", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMaxFilter.comp_mono", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsExtrFilter.comp_mono", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMinFilter.comp_antitone", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMaxFilter.comp_antitone", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsExtrFilter.comp_antitone", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMinOn.comp_mono", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMaxOn.comp_mono", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsExtrOn.comp_mono", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMinOn.comp_antitone", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMaxOn.comp_antitone", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsExtrOn.comp_antitone", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMinFilter.bicomp_mono", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMaxFilter.bicomp_mono", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMinOn.bicomp_mono", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMaxOn.bicomp_mono", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMinFilter.comp_tendsto", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMaxFilter.comp_tendsto", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsExtrFilter.comp_tendsto", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMinOn.on_preimage", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMaxOn.on_preimage", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsExtrOn.on_preimage", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMinOn.comp_mapsTo", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMaxOn.comp_mapsTo", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsExtrOn.comp_mapsTo", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMinFilter.add", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMaxFilter.add", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMinOn.add", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMaxOn.add", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMinFilter.neg", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMaxFilter.neg", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsExtrFilter.neg", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMinOn.neg", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMaxOn.neg", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsExtrOn.neg", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMinFilter.sub", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsMaxFilter.sub", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsMinOn.sub", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsMaxOn.sub", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsMinFilter.sup", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMaxFilter.sup", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMinOn.sup", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMaxOn.sup", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMinFilter.inf", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMaxFilter.inf", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMinOn.inf", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMaxOn.inf", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMinFilter.min", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMaxFilter.min", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMinOn.min", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMaxOn.min", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMinFilter.max", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMaxFilter.max", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMinOn.max", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMaxOn.max", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyLE.isMaxFilter", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "IsMaxFilter.congr", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.isMaxFilter_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyLE.isMinFilter", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMinFilter.congr", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.isMinFilter_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsExtrFilter.congr", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": true, "tactics": ["rw", "rwa"], "tactic_count": 2}
{"name": "Filter.EventuallyEq.isExtrFilter_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMaxOn.iSup_eq", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMinOn.iInf_eq", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sup_eq_of_isMaxOn", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sup_eq_of_max", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": true, "tactics": ["obtain", "rw", "apply", "rw"], "tactic_count": 4}
{"name": "inf_eq_of_isMinOn", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inf_eq_of_min", "kind": "theorem", "module": "Mathlib.Order.Filter.Extr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Order.Filter.FilterProduct.0.Filter.term∀*_,_", "kind": "definition", "module": "Mathlib.Order.Filter.FilterProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Order.Filter.FilterProduct.0.Filter._aux_Mathlib_Order_Filter_FilterProduct___macroRules__private_Mathlib_Order_Filter_FilterProduct_0_Filter_term∀*_,__1", "kind": "definition", "module": "Mathlib.Order.Filter.FilterProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Order.Filter.FilterProduct.0.Filter._aux_Mathlib_Order_Filter_FilterProduct___delab_app__private_Mathlib_Order_Filter_FilterProduct_0_Filter_term∀*_,__1", "kind": "definition", "module": "Mathlib.Order.Filter.FilterProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Order.Filter.FilterProduct.0.Filter.Germ.termβ*", "kind": "definition", "module": "Mathlib.Order.Filter.FilterProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Order.Filter.FilterProduct.0.Filter.Germ._aux_Mathlib_Order_Filter_FilterProduct___macroRules__private_Mathlib_Order_Filter_FilterProduct_0_Filter_Germ_termβ*_1", "kind": "definition", "module": "Mathlib.Order.Filter.FilterProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Order.Filter.FilterProduct.0.Filter.Germ._aux_Mathlib_Order_Filter_FilterProduct___unexpand_Filter_Germ_1", "kind": "definition", "module": "Mathlib.Order.Filter.FilterProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instGroupWithZero", "kind": "instance", "module": "Mathlib.Order.Filter.FilterProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instDivisionSemiring", "kind": "instance", "module": "Mathlib.Order.Filter.FilterProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instDivisionRing", "kind": "instance", "module": "Mathlib.Order.Filter.FilterProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instSemifield", "kind": "instance", "module": "Mathlib.Order.Filter.FilterProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instField", "kind": "instance", "module": "Mathlib.Order.Filter.FilterProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.coe_lt", "kind": "theorem", "module": "Mathlib.Order.Filter.FilterProduct", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.Germ.coe_pos", "kind": "theorem", "module": "Mathlib.Order.Filter.FilterProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.const_lt", "kind": "theorem", "module": "Mathlib.Order.Filter.FilterProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.const_lt_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.FilterProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.lt_def", "kind": "theorem", "module": "Mathlib.Order.Filter.FilterProduct", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "Filter.Germ.total", "kind": "instance", "module": "Mathlib.Order.Filter.FilterProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instLinearOrder", "kind": "instance", "module": "Mathlib.Order.Filter.FilterProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instIsStrictOrderedRing", "kind": "instance", "module": "Mathlib.Order.Filter.FilterProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.max_def", "kind": "theorem", "module": "Mathlib.Order.Filter.FilterProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.min_def", "kind": "theorem", "module": "Mathlib.Order.Filter.FilterProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.abs_def", "kind": "theorem", "module": "Mathlib.Order.Filter.FilterProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.const_max", "kind": "theorem", "module": "Mathlib.Order.Filter.FilterProduct", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.Germ.const_min", "kind": "theorem", "module": "Mathlib.Order.Filter.FilterProduct", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.Germ.const_abs", "kind": "theorem", "module": "Mathlib.Order.Filter.FilterProduct", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.biInter_mem", "kind": "theorem", "module": "Mathlib.Order.Filter.Finite", "is_tactic_proof": true, "tactics": ["induction", "empty", "insert"], "tactic_count": 3}
{"name": "Filter.biInter_finset_mem", "kind": "theorem", "module": "Mathlib.Order.Filter.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.sInter_mem", "kind": "theorem", "module": "Mathlib.Order.Filter.Finite", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.iInter_mem", "kind": "theorem", "module": "Mathlib.Order.Filter.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_generate_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Finite", "is_tactic_proof": true, "tactics": ["constructor", "induction", "univ", "superset", "rcases", "exact", "inter", "rcases", "exact", "rcases", "exact"], "tactic_count": 11}
{"name": "Filter.mem_iInf_of_iInter", "kind": "theorem", "module": "Mathlib.Order.Filter.Finite", "is_tactic_proof": true, "tactics": ["haveI", "refine", "exact"], "tactic_count": 3}
{"name": "Filter.mem_iInf", "kind": "theorem", "module": "Mathlib.Order.Filter.Finite", "is_tactic_proof": true, "tactics": ["constructor", "rw", "rintro", "rcases", "rw", "set", "have", "rintro", "have", "rw", "apply", "exact", "refine", "rwa", "rintro", "exact"], "tactic_count": 16}
{"name": "Filter.mem_iInf'", "kind": "theorem", "module": "Mathlib.Order.Filter.Finite", "is_tactic_proof": true, "tactics": ["classical", "simp", "refine", "rintro", "refine", "dsimp", "split_ifs", "exacts", "exact", "simp", "true_and]"], "tactic_count": 11}
{"name": "Filter.exists_iInter_of_mem_iInf", "kind": "theorem", "module": "Mathlib.Order.Filter.Finite", "is_tactic_proof": true, "tactics": ["rw", "let", "use", "rw"], "tactic_count": 4}
{"name": "Filter.mem_iInf_of_finite", "kind": "theorem", "module": "Mathlib.Order.Filter.Finite", "is_tactic_proof": true, "tactics": ["refine", "rintro", "exact"], "tactic_count": 3}
{"name": "Filter.mem_biInf_principal", "kind": "theorem", "module": "Mathlib.Order.Filter.Finite", "is_tactic_proof": true, "tactics": ["constructor", "simp", "rintro", "choose", "refine", "simp", "gcongr", "exact", "rintro", "rw", "refine", "simp"], "tactic_count": 12}
{"name": "Pairwise.exists_mem_filter_of_disjoint", "kind": "theorem", "module": "Mathlib.Order.Filter.Finite", "is_tactic_proof": false, "tactics": ["have", "simpa", "choose", "refine", "exacts"], "tactic_count": 5}
{"name": "Set.PairwiseDisjoint.exists_mem_filter", "kind": "theorem", "module": "Mathlib.Order.Filter.Finite", "is_tactic_proof": true, "tactics": ["haveI", "rcases", "lift", "rcases", "exact"], "tactic_count": 5}
{"name": "Filter.iInf_sets_eq_finite", "kind": "theorem", "module": "Mathlib.Order.Filter.Finite", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Filter.iInf_sets_eq_finite'", "kind": "theorem", "module": "Mathlib.Order.Filter.Finite", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.mem_iInf_finite", "kind": "theorem", "module": "Mathlib.Order.Filter.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_iInf_finite'", "kind": "theorem", "module": "Mathlib.Order.Filter.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_iInf_finset", "kind": "theorem", "module": "Mathlib.Order.Filter.Finite", "is_tactic_proof": true, "tactics": ["classical", "simp", "refine", "rcases", "refine", "refine", "rintro", "simp", "rintro", "exact"], "tactic_count": 10}
{"name": "Filter.iInf_principal_finset", "kind": "theorem", "module": "Mathlib.Order.Filter.Finite", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "insert"], "tactic_count": 4}
{"name": "Filter.iInf_principal", "kind": "theorem", "module": "Mathlib.Order.Filter.Finite", "is_tactic_proof": true, "tactics": ["cases", "rw", "simpa"], "tactic_count": 3}
{"name": "Filter.iInf_principal'", "kind": "theorem", "module": "Mathlib.Order.Filter.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.iInf_principal_finite", "kind": "theorem", "module": "Mathlib.Order.Filter.Finite", "is_tactic_proof": true, "tactics": ["lift", "exact"], "tactic_count": 2}
{"name": "Filter.eventually_all", "kind": "theorem", "module": "Mathlib.Order.Filter.Finite", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Filter.eventually_all_finite", "kind": "theorem", "module": "Mathlib.Order.Filter.Finite", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Filter.eventually_all_finset", "kind": "theorem", "module": "Mathlib.Order.Filter.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.frequently_exists", "kind": "theorem", "module": "Mathlib.Order.Filter.Finite", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Filter.frequently_exists_finite", "kind": "theorem", "module": "Mathlib.Order.Filter.Finite", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Filter.frequently_exists_finset", "kind": "theorem", "module": "Mathlib.Order.Filter.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventually_subset_of_finite", "kind": "theorem", "module": "Mathlib.Order.Filter.Finite", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Filter.EventuallyLE.iUnion", "kind": "theorem", "module": "Mathlib.Order.Filter.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.iUnion", "kind": "theorem", "module": "Mathlib.Order.Filter.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyLE.iInter", "kind": "theorem", "module": "Mathlib.Order.Filter.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.iInter", "kind": "theorem", "module": "Mathlib.Order.Filter.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.eventuallyLE_iUnion", "kind": "theorem", "module": "Mathlib.Order.Filter.Finite", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "Set.Finite.eventuallyEq_iUnion", "kind": "theorem", "module": "Mathlib.Order.Filter.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.eventuallyLE_iInter", "kind": "theorem", "module": "Mathlib.Order.Filter.Finite", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "Set.Finite.eventuallyEq_iInter", "kind": "theorem", "module": "Mathlib.Order.Filter.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.eventuallyLE_iUnion", "kind": "theorem", "module": "Mathlib.Order.Filter.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.eventuallyEq_iUnion", "kind": "theorem", "module": "Mathlib.Order.Filter.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.eventuallyLE_iInter", "kind": "theorem", "module": "Mathlib.Order.Filter.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.eventuallyEq_iInter", "kind": "theorem", "module": "Mathlib.Order.Filter.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.const_eventuallyEq'", "kind": "theorem", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.const_eventuallyEq", "kind": "theorem", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.germSetoid", "kind": "definition", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ", "kind": "definition", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.productSetoid", "kind": "definition", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Product", "kind": "definition", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Product.coeTC", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Product.instInhabited", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.ofFun", "kind": "definition", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instCoeTCForall", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.const", "kind": "definition", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.coeTail", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.IsConstant", "kind": "definition", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.isConstant_coe", "kind": "theorem", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.isConstant_coe_const", "kind": "theorem", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": true, "tactics": ["use"], "tactic_count": 1}
{"name": "Filter.Germ.isConstant_comp", "kind": "theorem", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Filter.Germ.quot_mk_eq_coe", "kind": "theorem", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.mk'_eq_coe", "kind": "theorem", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.inductionOn", "kind": "theorem", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.inductionOn₂", "kind": "theorem", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.inductionOn₃", "kind": "theorem", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.map'", "kind": "definition", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.liftOn", "kind": "definition", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.map'_coe", "kind": "theorem", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.coe_eq", "kind": "theorem", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.map", "kind": "definition", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.map_coe", "kind": "theorem", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.map_id", "kind": "theorem", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "Filter.Germ.map_map", "kind": "theorem", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.map₂", "kind": "definition", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.map₂_coe", "kind": "theorem", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.Tendsto", "kind": "definition", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.coe_tendsto", "kind": "theorem", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.compTendsto'", "kind": "definition", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.coe_compTendsto'", "kind": "theorem", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.compTendsto", "kind": "definition", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.coe_compTendsto", "kind": "theorem", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.compTendsto'_coe", "kind": "theorem", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.Filter.Tendsto.congr_germ", "kind": "theorem", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.isConstant_comp_tendsto", "kind": "theorem", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "Filter.Germ.isConstant_compTendsto", "kind": "theorem", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": ["induction", "exact"], "tactic_count": 2}
{"name": "Filter.Germ.const_inj", "kind": "theorem", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.map_const", "kind": "theorem", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.map₂_const", "kind": "theorem", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.const_compTendsto", "kind": "theorem", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.const_compTendsto'", "kind": "theorem", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.LiftPred", "kind": "definition", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.liftPred_coe", "kind": "theorem", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.liftPred_const", "kind": "theorem", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.liftPred_const_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.LiftRel", "kind": "definition", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.liftRel_coe", "kind": "theorem", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.liftRel_const", "kind": "theorem", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.liftRel_const_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instInhabited", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instMul", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.coe_mul", "kind": "theorem", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instOne", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.coe_one", "kind": "theorem", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instSemigroup", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instCommSemigroup", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instIsLeftCancelMul", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instIsRightCancelMul", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instIsCancelMul", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instLeftCancelSemigroup", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instRightCancelSemigroup", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instMulOneClass", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instSMul", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instPow", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.coe_smul", "kind": "theorem", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.const_smul", "kind": "theorem", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.coe_pow", "kind": "theorem", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.const_pow", "kind": "theorem", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instMonoid", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.coeMulHom", "kind": "definition", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.coe_coeMulHom", "kind": "theorem", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instCommMonoid", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instNatCast", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.natCast_def", "kind": "theorem", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.const_nat", "kind": "theorem", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.coe_ofNat", "kind": "theorem", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.const_ofNat", "kind": "theorem", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instIntCast", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.intCast_def", "kind": "theorem", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instAddMonoidWithOne", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instAddCommMonoidWithOne", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instInv", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.coe_inv", "kind": "theorem", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.const_inv", "kind": "theorem", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instDiv", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.coe_div", "kind": "theorem", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.const_div", "kind": "theorem", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instInvolutiveInv", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instHasDistribNeg", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instInvOneClass", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instDivInvMonoid", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instDivisionMonoid", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instGroup", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instCommGroup", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instAddGroupWithOne", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instNontrivial", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instMulZeroClass", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instMulZeroOneClass", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instMonoidWithZero", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instDistrib", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instNonUnitalNonAssocSemiring", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instNonUnitalSemiring", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instNonAssocSemiring", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instNonUnitalNonAssocRing", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instNonUnitalRing", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instNonAssocRing", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instSemiring", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instRing", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instNonUnitalCommSemiring", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instCommSemiring", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instNonUnitalCommRing", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instCommRing", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.coeRingHom", "kind": "definition", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.coe_coeRingHom", "kind": "theorem", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instSMul'", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.coe_smul'", "kind": "theorem", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instMulAction", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instMulAction'", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instDistribMulAction", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instDistribMulAction'", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instModule", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instModule'", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instLE", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.le_def", "kind": "theorem", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.coe_le", "kind": "theorem", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.coe_nonneg", "kind": "theorem", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.const_le", "kind": "theorem", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.const_le_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instPreorder", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instPartialOrder", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instBot", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instTop", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.const_bot", "kind": "theorem", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.const_top", "kind": "theorem", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instOrderBot", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instOrderTop", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instBoundedOrder", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instSup", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instInf", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.const_sup", "kind": "theorem", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.const_inf", "kind": "theorem", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instSemilatticeSup", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instSemilatticeInf", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instLattice", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instDistribLattice", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instExistsMulOfLE", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instIsOrderedMonoid", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.OrderedMonoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instIsOrderedCancelMonoid", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.OrderedMonoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instCanonicallyOrderedMul", "kind": "instance", "module": "Mathlib.Order.Filter.Germ.OrderedMonoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mulIndicator_eventuallyEq", "kind": "theorem", "module": "Mathlib.Order.Filter.IndicatorFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mulIndicator_union_eventuallyEq", "kind": "theorem", "module": "Mathlib.Order.Filter.IndicatorFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mulIndicator_eventuallyLE_mulIndicator", "kind": "theorem", "module": "Mathlib.Order.Filter.IndicatorFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.mulIndicator_eventuallyEq_iUnion", "kind": "theorem", "module": "Mathlib.Order.Filter.IndicatorFunction", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Monotone.tendsto_mulIndicator", "kind": "theorem", "module": "Mathlib.Order.Filter.IndicatorFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.mulIndicator_eventuallyEq_iInter", "kind": "theorem", "module": "Mathlib.Order.Filter.IndicatorFunction", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Antitone.tendsto_mulIndicator", "kind": "theorem", "module": "Mathlib.Order.Filter.IndicatorFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mulIndicator_biUnion_finset_eventuallyEq", "kind": "theorem", "module": "Mathlib.Order.Filter.IndicatorFunction", "is_tactic_proof": true, "tactics": ["rw", "apply", "exact"], "tactic_count": 3}
{"name": "tendsto_mulIndicator_biUnion_finset", "kind": "theorem", "module": "Mathlib.Order.Filter.IndicatorFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.mulSupport", "kind": "theorem", "module": "Mathlib.Order.Filter.IndicatorFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.mulIndicator", "kind": "theorem", "module": "Mathlib.Order.Filter.IndicatorFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.mulIndicator_one", "kind": "theorem", "module": "Mathlib.Order.Filter.IndicatorFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.of_mulIndicator", "kind": "theorem", "module": "Mathlib.Order.Filter.IndicatorFunction", "is_tactic_proof": false, "tactics": ["have", "rw", "exact", "exact"], "tactic_count": 4}
{"name": "Filter.EventuallyEq.of_mulIndicator_const", "kind": "theorem", "module": "Mathlib.Order.Filter.IndicatorFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mulIndicator_const_eventuallyEq", "kind": "theorem", "module": "Mathlib.Order.Filter.IndicatorFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendstoIxxClass_principal", "kind": "theorem", "module": "Mathlib.Order.Filter.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendstoIxxClass_inf", "kind": "theorem", "module": "Mathlib.Order.Filter.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendstoIxxClass_of_subset", "kind": "theorem", "module": "Mathlib.Order.Filter.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.tendstoIxxClass", "kind": "theorem", "module": "Mathlib.Order.Filter.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.Icc", "kind": "theorem", "module": "Mathlib.Order.Filter.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.Ioc", "kind": "theorem", "module": "Mathlib.Order.Filter.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.Ico", "kind": "theorem", "module": "Mathlib.Order.Filter.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.Ioo", "kind": "theorem", "module": "Mathlib.Order.Filter.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_Icc_atTop_atTop", "kind": "instance", "module": "Mathlib.Order.Filter.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_Ico_atTop_atTop", "kind": "instance", "module": "Mathlib.Order.Filter.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_Ioc_atTop_atTop", "kind": "instance", "module": "Mathlib.Order.Filter.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_Ioo_atTop_atTop", "kind": "instance", "module": "Mathlib.Order.Filter.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_Icc_atBot_atBot", "kind": "instance", "module": "Mathlib.Order.Filter.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_Ico_atBot_atBot", "kind": "instance", "module": "Mathlib.Order.Filter.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_Ioc_atBot_atBot", "kind": "instance", "module": "Mathlib.Order.Filter.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_Ioo_atBot_atBot", "kind": "instance", "module": "Mathlib.Order.Filter.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.OrdConnected.tendsto_Icc", "kind": "instance", "module": "Mathlib.Order.Filter.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_Ico_Ici_Ici", "kind": "instance", "module": "Mathlib.Order.Filter.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_Ico_Ioi_Ioi", "kind": "instance", "module": "Mathlib.Order.Filter.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_Ico_Iic_Iio", "kind": "instance", "module": "Mathlib.Order.Filter.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_Ico_Iio_Iio", "kind": "instance", "module": "Mathlib.Order.Filter.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_Ioc_Ici_Ioi", "kind": "instance", "module": "Mathlib.Order.Filter.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_Ioc_Iic_Iic", "kind": "instance", "module": "Mathlib.Order.Filter.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_Ioc_Iio_Iio", "kind": "instance", "module": "Mathlib.Order.Filter.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_Ioc_Ioi_Ioi", "kind": "instance", "module": "Mathlib.Order.Filter.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_Ioo_Ici_Ioi", "kind": "instance", "module": "Mathlib.Order.Filter.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_Ioo_Iic_Iio", "kind": "instance", "module": "Mathlib.Order.Filter.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_Ioo_Ioi_Ioi", "kind": "instance", "module": "Mathlib.Order.Filter.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_Ioo_Iio_Iio", "kind": "instance", "module": "Mathlib.Order.Filter.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_Icc_Icc_Icc", "kind": "instance", "module": "Mathlib.Order.Filter.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_Ioc_Icc_Icc", "kind": "instance", "module": "Mathlib.Order.Filter.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_Icc_pure_pure", "kind": "instance", "module": "Mathlib.Order.Filter.Interval", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Filter.tendsto_Ico_pure_bot", "kind": "instance", "module": "Mathlib.Order.Filter.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_Ioc_pure_bot", "kind": "instance", "module": "Mathlib.Order.Filter.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_Ioo_pure_bot", "kind": "instance", "module": "Mathlib.Order.Filter.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_Icc_uIcc_uIcc", "kind": "instance", "module": "Mathlib.Order.Filter.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_Ioc_uIcc_uIcc", "kind": "instance", "module": "Mathlib.Order.Filter.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_uIcc_of_Icc", "kind": "instance", "module": "Mathlib.Order.Filter.Interval", "is_tactic_proof": true, "tactics": ["refine", "obtain", "mem_prod_self_iff.1", "refine", "rcases", "rw", "exact", "rw", "exact"], "tactic_count": 9}
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{"name": "Filter.isBounded_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.IsBounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Filter.isBounded_top", "kind": "theorem", "module": "Mathlib.Order.Filter.IsBounded", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.isBounded_principal", "kind": "theorem", "module": "Mathlib.Order.Filter.IsBounded", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.isBounded_sup", "kind": "theorem", "module": "Mathlib.Order.Filter.IsBounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Filter.isBoundedUnder_const", "kind": "theorem", "module": "Mathlib.Order.Filter.IsBounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.IsBounded.isBoundedUnder", "kind": "theorem", "module": "Mathlib.Order.Filter.IsBounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.IsBoundedUnder.comp", "kind": "theorem", "module": "Mathlib.Order.Filter.IsBounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Filter.Tendsto.isBoundedUnder_comp", "kind": "theorem", "module": "Mathlib.Order.Filter.IsBounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.IsBoundedUnder.eventually_le", "kind": "theorem", "module": "Mathlib.Order.Filter.IsBounded", "is_tactic_proof": true, "tactics": ["tauto"], "tactic_count": 1}
{"name": "Filter.IsBoundedUnder.eventually_ge", "kind": "theorem", "module": "Mathlib.Order.Filter.IsBounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.isBoundedUnder_of_eventually_le", "kind": "theorem", "module": "Mathlib.Order.Filter.IsBounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.isBoundedUnder_of_eventually_ge", "kind": "theorem", "module": "Mathlib.Order.Filter.IsBounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.isBoundedUnder_iff_eventually_bddAbove", "kind": "theorem", "module": "Mathlib.Order.Filter.IsBounded", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 5}
{"name": "Filter.isBoundedUnder_iff_eventually_bddBelow", "kind": "theorem", "module": "Mathlib.Order.Filter.IsBounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddAbove.isBoundedUnder", "kind": "theorem", "module": "Mathlib.Order.Filter.IsBounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddAbove.isBoundedUnder_of_range", "kind": "theorem", "module": "Mathlib.Order.Filter.IsBounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddBelow.isBoundedUnder", "kind": "theorem", "module": "Mathlib.Order.Filter.IsBounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddBelow.isBoundedUnder_of_range", "kind": "theorem", "module": "Mathlib.Order.Filter.IsBounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.IsBoundedUnder.le_of_finite", "kind": "theorem", "module": "Mathlib.Order.Filter.IsBounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.IsBoundedUnder.ge_of_finite", "kind": "theorem", "module": "Mathlib.Order.Filter.IsBounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.isBoundedUnder_le_comp", "kind": "theorem", "module": "Mathlib.Order.Filter.IsBounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Filter.not_isBoundedUnder_of_tendsto_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.IsBounded", "is_tactic_proof": true, "tactics": ["rintro", "rw", "obtain", "have", "have", "eq_empty_of_subset_empty", "exact"], "tactic_count": 7}
{"name": "Filter.not_isBoundedUnder_of_tendsto_atBot", "kind": "theorem", "module": "Mathlib.Order.Filter.IsBounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.IsBoundedUnder.bddAbove_range_of_cofinite", "kind": "theorem", "module": "Mathlib.Order.Filter.IsBounded", "is_tactic_proof": true, "tactics": ["rcases", "haveI", "rw", "exact"], "tactic_count": 4}
{"name": "Filter.IsBoundedUnder.bddBelow_range_of_cofinite", "kind": "theorem", "module": "Mathlib.Order.Filter.IsBounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Filter.IsBounded.isCobounded_le", "kind": "theorem", "module": "Mathlib.Order.Filter.IsBounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Filter.IsBoundedUnder.isCoboundedUnder_le", "kind": "theorem", "module": "Mathlib.Order.Filter.IsBounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Filter.bddAbove_range_of_tendsto_atTop_atBot", "kind": "theorem", "module": "Mathlib.Order.Filter.IsBounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.bddBelow_range_of_tendsto_atTop_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.IsBounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Filter.isBoundedUnder_le_inv", "kind": "theorem", "module": "Mathlib.Order.Filter.IsBounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Monotone.isCoboundedUnder_le_of_isCobounded", "kind": "theorem", "module": "Mathlib.Order.Filter.IsBounded", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
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{"name": "Antitone.isCoboundedUnder_ge_of_isCobounded", "kind": "theorem", "module": "Mathlib.Order.Filter.IsBounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Filter.subset_ker", "kind": "theorem", "module": "Mathlib.Order.Filter.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Filter.ker_surjective", "kind": "theorem", "module": "Mathlib.Order.Filter.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.ker_bot", "kind": "theorem", "module": "Mathlib.Order.Filter.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Filter.ker_eq_univ", "kind": "theorem", "module": "Mathlib.Order.Filter.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.ker_inf", "kind": "theorem", "module": "Mathlib.Order.Filter.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.ker_iInf", "kind": "theorem", "module": "Mathlib.Order.Filter.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.ker_sInf", "kind": "theorem", "module": "Mathlib.Order.Filter.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.ker_principal", "kind": "theorem", "module": "Mathlib.Order.Filter.Ker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.ker_pure", "kind": "theorem", "module": "Mathlib.Order.Filter.Ker", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.ker_comap", "kind": "theorem", "module": "Mathlib.Order.Filter.Ker", "is_tactic_proof": true, "tactics": ["ext", "simp", "exact"], "tactic_count": 3}
{"name": "Filter.ker_iSup", "kind": "theorem", "module": "Mathlib.Order.Filter.Ker", "is_tactic_proof": true, "tactics": ["refine", "simp", "contrapose", "choose", "refine", "exact"], "tactic_count": 6}
{"name": "Filter.ker_sSup", "kind": "theorem", "module": "Mathlib.Order.Filter.Ker", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.ker_sup", "kind": "theorem", "module": "Mathlib.Order.Filter.Ker", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.ker_prod", "kind": "theorem", "module": "Mathlib.Order.Filter.Ker", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.ker_pi", "kind": "theorem", "module": "Mathlib.Order.Filter.Ker", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.lift_top", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.HasBasis.mem_lift_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": true, "tactics": ["refine", "intro", "exact", "simp", "exact"], "tactic_count": 5}
{"name": "Filter.HasBasis.lift", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": true, "tactics": ["refine", "simp"], "tactic_count": 2}
{"name": "Filter.mem_lift_sets", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.sInter_lift_sets", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.mem_lift", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.lift_le", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.le_lift", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.lift_mono", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.lift_mono'", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_lift", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.map_lift_eq", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.comap_lift_eq", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.comap_lift_eq2", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.lift_map_le", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map_lift_eq2", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.lift_comm", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.lift_assoc", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.lift_lift_same_le_lift", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.lift_lift_same_eq_lift", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.lift_principal", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.monotone_lift", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.lift_neBot_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.lift_const", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.lift_inf", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.lift_principal2", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.lift_iInf_le", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.lift_iInf", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": true, "tactics": ["refine", "have", "intro", "refine", "inhabit", "exact", "rw", "exact", "simp", "exact"], "tactic_count": 10}
{"name": "Filter.lift_iInf_of_directed", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.lift_iInf_of_map_univ", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": true, "tactics": ["cases", "simp", "exact"], "tactic_count": 3}
{"name": "Filter.lift'_top", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_lift'", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_lift'", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.HasBasis.lift'", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_lift'_sets", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventually_lift'_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.sInter_lift'_sets", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.lift'_le", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.lift'_mono", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.lift'_mono'", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.lift'_cong", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map_lift'_eq", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.lift'_map_le", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map_lift'_eq2", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.comap_lift'_eq", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.comap_lift'_eq2", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.lift'_principal", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.lift'_pure", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.lift'_bot", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.le_lift'", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.principal_le_lift'", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.monotone_lift'", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.lift_lift'_assoc", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.lift'_lift'_assoc", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.lift'_lift_assoc", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.lift_lift'_same_le_lift'", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.lift_lift'_same_eq_lift'", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.lift'_inf_principal_eq", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.lift'_neBot_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.lift'_id", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.lift'_iInf", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.lift'_iInf_of_map_univ", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.lift'_inf", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": true, "tactics": ["rw", "refine", "rintro"], "tactic_count": 3}
{"name": "Filter.lift'_inf_le", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.comap_eq_lift'", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.prod_def", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": true, "tactics": ["simpa", "iInf_congr"], "tactic_count": 2}
{"name": "Filter.prod_same_eq", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_prod_self_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.prod_lift_lift", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": true, "tactics": ["simp", "apply", "rw", "apply", "apply"], "tactic_count": 5}
{"name": "Filter.prod_lift'_lift'", "kind": "theorem", "module": "Mathlib.Order.Filter.Lift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.sequence_mono", "kind": "theorem", "module": "Mathlib.Order.Filter.ListTraverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_traverse", "kind": "theorem", "module": "Mathlib.Order.Filter.ListTraverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_traverse_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.ListTraverse", "is_tactic_proof": true, "tactics": ["constructor", "induction", "nil", "simp", "traverse_nil]", "cons", "intro", "rcases", "rcases", "rcases", "exact", "rintro", "exact"], "tactic_count": 13}
{"name": "Filter.map_principal", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventually_map", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.frequently_map", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventuallyEq_map", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventuallyLE_map", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_map", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_map'", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.image_mem_map", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.image_mem_map_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.range_mem_map", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Filter.mem_map_iff_exists_image", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map_id", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map_id'", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map_compose", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map_map", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map_congr", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_comap'", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_comap''", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_comap_prodMk", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Filter.eventually_comap", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.frequently_comap", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.mem_comap_iff_compl", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.compl_mem_comap", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.instLawfulFunctor", "kind": "instance", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.pure_sets", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventually_pure", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.principal_singleton", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.biSup_pure_eq_principal", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.iSup_pure_eq_top", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.map_pure", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.pure_le_principal", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.join_pure", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.pure_bind", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.map_bind", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.bind_map", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.monad", "kind": "definition", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.lawfulMonad", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.instAlternative", "kind": "instance", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map_def", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.bind_def", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_comap", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.preimage_mem_comap", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Eventually.comap", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.comap_id", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.comap_id'", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.comap_const_of_notMem", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.comap_const_of_mem", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map_const", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["ext", "by_cases"], "tactic_count": 2}
{"name": "Filter.comap_comap", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map_comm", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.comap_comm", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Function.Semiconj.filter_map", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Commute.filter_map", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Semiconj.filter_comap", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Commute.filter_comap", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.LeftInverse.filter_map", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.LeftInverse.filter_comap", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.RightInverse.filter_map", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.RightInverse.filter_comap", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.LeftInvOn.filter_map_Iic", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.RightInvOn.filter_map_Iic", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.kernMap", "kind": "definition", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_kernMap", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_kernMap_iff_compl", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw"], "tactic_count": 3}
{"name": "Filter.compl_mem_kernMap", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Filter.comap_le_iff_le_kernMap", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.gc_comap_kernMap", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.kernMap_principal", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "Filter.comap_principal", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.principal_subtype", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.comap_pure", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.map_le_iff_le_comap", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.gc_map_comap", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map_mono", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.comap_mono", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map_bot", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map_sup", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map_iSup", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map_top", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.comap_top", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.comap_inf", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.comap_iInf", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.le_comap_top", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Filter.map_comap_le", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.le_comap_map", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.comap_bot", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.neBot_of_comap", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["rw", "contrapose", "rw", "exact"], "tactic_count": 4}
{"name": "Filter.comap_inf_principal_range", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.disjoint_comap", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.comap_iSup", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.comap_sSup", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.comap_sup", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.map_comap", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["refine", "rintro", "refine", "rintro", "exact"], "tactic_count": 5}
{"name": "Filter.map_comap_setCoe_val", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.map_comap_of_mem", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.canLift", "kind": "instance", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.comap_le_comap_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map_comap_of_surjective", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.comap_injective", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.filter_map_top", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.subtype_coe_map_comap", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.image_mem_of_mem_comap", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Filter.image_coe_mem_of_mem_comap", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.comap_map", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_comap_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.map_le_map_iff_of_injOn", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map_le_map_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.map_eq_map_iff_of_injOn", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.map_inj", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map_injective", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.comap_neBot_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Filter.comap_neBot", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.comap_neBot_iff_frequently", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.comap_neBot_iff_compl_range", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.comap_eq_bot_iff_compl_range", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.comap_surjective_eq_bot", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.disjoint_comap_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.NeBot.comap_of_range_mem", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.comap_inl_map_inr", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["ext", "rw", "simp"], "tactic_count": 3}
{"name": "Filter.comap_inr_map_inl", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["ext", "rw", "simp"], "tactic_count": 3}
{"name": "Filter.map_inl_inf_map_inr", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["apply", "trans", "apply", "simp"], "tactic_count": 4}
{"name": "Filter.map_inr_inf_map_inl", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.comap_sumElim_eq", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["ext", "simp_rw", "simp"], "tactic_count": 3}
{"name": "Filter.map_comap_inl_sup_map_comap_inr", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.map_sumElim_eq", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Filter.comap_fst_neBot_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["cases", "rw", "simp"], "tactic_count": 3}
{"name": "Filter.comap_fst_neBot", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.comap_snd_neBot_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["rcases", "rw", "simp"], "tactic_count": 3}
{"name": "Filter.comap_snd_neBot", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.comap_eval_neBot_iff'", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["rcases", "rw", "simp", "have", "simp"], "tactic_count": 5}
{"name": "Filter.comap_eval_neBot_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.comap_eval_neBot", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.comap_coe_neBot_of_le_principal", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.NeBot.comap_of_surj", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.NeBot.comap_of_image_mem", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map_eq_bot_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map_neBot_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.NeBot.map", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.NeBot.of_map", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map_neBot", "kind": "instance", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.sInter_comap_sets", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["ext", "suffices", "simp", "constructor", "intro", "simpa", "intro", "exact"], "tactic_count": 8}
{"name": "Filter.map_iInf_le", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map_iInf_eq", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map_biInf_eq", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["haveI", "simp", "exact"], "tactic_count": 3}
{"name": "Filter.map_inf_le", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map_inf", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["refine", "rintro", "refine", "rw"], "tactic_count": 4}
{"name": "Filter.map_inf'", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["lift", "replace", "simp"], "tactic_count": 3}
{"name": "Filter.disjoint_of_map", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.disjoint_map", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.map_equiv_symm", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map_eq_comap_of_inverse", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.comap_equiv_symm", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map_swap_eq_comap_swap", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map_swap4_eq_comap", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.le_map", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.le_map_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.push_pull", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["apply", "calc", "map", "rintro", "apply", "calc", "f"], "tactic_count": 7}
{"name": "Filter.push_pull'", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.disjoint_comap_iff_map", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.disjoint_comap_iff_map'", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.neBot_inf_comap_iff_map", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.neBot_inf_comap_iff_map'", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.comap_inf_principal_neBot_of_image_mem", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Filter.principal_eq_map_coe_top", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.inf_principal_eq_bot_iff_comap", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.map_generate_le_generate_preimage_preimage", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Filter.generate_image_preimage_le_comap", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Filter.singleton_mem_pure", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.pure_injective", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.pure_neBot", "kind": "instance", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.le_pure_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.mem_seq_def", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_seq_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.mem_map_seq_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.seq_mem_seq", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.le_seq", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.seq_mono", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.pure_seq_eq_map", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["refine", "rw", "apply", "exact", "refine", "rintro", "exact"], "tactic_count": 7}
{"name": "Filter.seq_pure", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact", "refine", "rintro", "exact"], "tactic_count": 6}
{"name": "Filter.seq_assoc", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["refine", "rcases", "rcases", "refine", "rw", "exact", "rcases", "refine", "rw", "exact"], "tactic_count": 10}
{"name": "Filter.prod_map_seq_comm", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["refine", "rcases", "refine", "rw", "exact", "rcases", "refine", "rw", "exact"], "tactic_count": 9}
{"name": "Filter.seq_eq_filter_seq", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.instLawfulApplicative", "kind": "instance", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.instCommApplicative", "kind": "instance", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventually_bind", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.frequently_bind", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Filter.eventuallyEq_bind", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventuallyLE_bind", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_bind'", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_bind", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.bind_le", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.bind_mono", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["refine", "simp", "filter_upwards"], "tactic_count": 3}
{"name": "Filter.bind_inf_principal", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.sup_bind", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.principal_bind", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map_surjOn_Iic_iff_le_map", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["refine", "rcases", "exact", "have", "simpa", "exact"], "tactic_count": 6}
{"name": "Filter.map_surjOn_Iic_iff_surjOn", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.filter_injOn_Iic_iff_injOn", "kind": "theorem", "module": "Mathlib.Order.Filter.Map", "is_tactic_proof": true, "tactics": ["refine", "rwa", "rwa", "simp"], "tactic_count": 4}
{"name": "Filter.map₂", "kind": "definition", "module": "Mathlib.Order.Filter.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_map₂_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.image2_mem_map₂", "kind": "theorem", "module": "Mathlib.Order.Filter.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map_prod_eq_map₂", "kind": "theorem", "module": "Mathlib.Order.Filter.NAry", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.map_prod_eq_map₂'", "kind": "theorem", "module": "Mathlib.Order.Filter.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map₂_mk_eq_prod", "kind": "theorem", "module": "Mathlib.Order.Filter.NAry", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.HasBasis.map₂", "kind": "theorem", "module": "Mathlib.Order.Filter.NAry", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Filter.map₂_mono", "kind": "theorem", "module": "Mathlib.Order.Filter.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map₂_mono_left", "kind": "theorem", "module": "Mathlib.Order.Filter.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map₂_mono_right", "kind": "theorem", "module": "Mathlib.Order.Filter.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.le_map₂_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map₂_eq_bot_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.NAry", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.map₂_bot_left", "kind": "theorem", "module": "Mathlib.Order.Filter.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map₂_bot_right", "kind": "theorem", "module": "Mathlib.Order.Filter.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map₂_neBot_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.NAry", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.NeBot.map₂", "kind": "theorem", "module": "Mathlib.Order.Filter.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map₂.neBot", "kind": "instance", "module": "Mathlib.Order.Filter.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.NeBot.of_map₂_left", "kind": "theorem", "module": "Mathlib.Order.Filter.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.NeBot.of_map₂_right", "kind": "theorem", "module": "Mathlib.Order.Filter.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map₂_sup_left", "kind": "theorem", "module": "Mathlib.Order.Filter.NAry", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Filter.map₂_sup_right", "kind": "theorem", "module": "Mathlib.Order.Filter.NAry", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Filter.map₂_inf_subset_left", "kind": "theorem", "module": "Mathlib.Order.Filter.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map₂_inf_subset_right", "kind": "theorem", "module": "Mathlib.Order.Filter.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map₂_pure_left", "kind": "theorem", "module": "Mathlib.Order.Filter.NAry", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.map₂_pure_right", "kind": "theorem", "module": "Mathlib.Order.Filter.NAry", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.map₂_pure", "kind": "theorem", "module": "Mathlib.Order.Filter.NAry", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.map₂_swap", "kind": "theorem", "module": "Mathlib.Order.Filter.NAry", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Filter.map₂_left", "kind": "theorem", "module": "Mathlib.Order.Filter.NAry", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.map₂_right", "kind": "theorem", "module": "Mathlib.Order.Filter.NAry", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.map_map₂", "kind": "theorem", "module": "Mathlib.Order.Filter.NAry", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.map₂_map_left", "kind": "theorem", "module": "Mathlib.Order.Filter.NAry", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.map₂_map_right", "kind": "theorem", "module": "Mathlib.Order.Filter.NAry", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.map₂_curry", "kind": "theorem", "module": "Mathlib.Order.Filter.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map_uncurry_prod", "kind": "theorem", "module": "Mathlib.Order.Filter.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map₂_assoc", "kind": "theorem", "module": "Mathlib.Order.Filter.NAry", "is_tactic_proof": false, "tactics": ["rw", "map_prod_eq_map₂,", "simp"], "tactic_count": 3}
{"name": "Filter.map₂_comm", "kind": "theorem", "module": "Mathlib.Order.Filter.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map₂_left_comm", "kind": "theorem", "module": "Mathlib.Order.Filter.NAry", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Filter.map₂_right_comm", "kind": "theorem", "module": "Mathlib.Order.Filter.NAry", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Filter.map_map₂_distrib", "kind": "theorem", "module": "Mathlib.Order.Filter.NAry", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Filter.map_map₂_distrib_left", "kind": "theorem", "module": "Mathlib.Order.Filter.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map_map₂_distrib_right", "kind": "theorem", "module": "Mathlib.Order.Filter.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map₂_map_left_comm", "kind": "theorem", "module": "Mathlib.Order.Filter.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map_map₂_right_comm", "kind": "theorem", "module": "Mathlib.Order.Filter.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map₂_distrib_le_left", "kind": "theorem", "module": "Mathlib.Order.Filter.NAry", "is_tactic_proof": true, "tactics": ["rintro", "refine", "refine", "exact", "exact"], "tactic_count": 5}
{"name": "Filter.map₂_distrib_le_right", "kind": "theorem", "module": "Mathlib.Order.Filter.NAry", "is_tactic_proof": true, "tactics": ["rintro", "refine", "refine", "exact", "exact"], "tactic_count": 5}
{"name": "Filter.map_map₂_antidistrib", "kind": "theorem", "module": "Mathlib.Order.Filter.NAry", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Filter.map_map₂_antidistrib_left", "kind": "theorem", "module": "Mathlib.Order.Filter.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map_map₂_antidistrib_right", "kind": "theorem", "module": "Mathlib.Order.Filter.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map₂_map_left_anticomm", "kind": "theorem", "module": "Mathlib.Order.Filter.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map_map₂_right_anticomm", "kind": "theorem", "module": "Mathlib.Order.Filter.NAry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map₂_left_identity", "kind": "theorem", "module": "Mathlib.Order.Filter.NAry", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.map₂_right_identity", "kind": "theorem", "module": "Mathlib.Order.Filter.NAry", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.rmap", "kind": "definition", "module": "Mathlib.Order.Filter.Partial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.rmap_sets", "kind": "theorem", "module": "Mathlib.Order.Filter.Partial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_rmap", "kind": "theorem", "module": "Mathlib.Order.Filter.Partial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.rmap_rmap", "kind": "theorem", "module": "Mathlib.Order.Filter.Partial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.rmap_compose", "kind": "theorem", "module": "Mathlib.Order.Filter.Partial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.RTendsto", "kind": "definition", "module": "Mathlib.Order.Filter.Partial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.rtendsto_def", "kind": "theorem", "module": "Mathlib.Order.Filter.Partial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.rcomap", "kind": "definition", "module": "Mathlib.Order.Filter.Partial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.rcomap_sets", "kind": "theorem", "module": "Mathlib.Order.Filter.Partial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.rcomap_rcomap", "kind": "theorem", "module": "Mathlib.Order.Filter.Partial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.rcomap_compose", "kind": "theorem", "module": "Mathlib.Order.Filter.Partial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.rtendsto_iff_le_rcomap", "kind": "theorem", "module": "Mathlib.Order.Filter.Partial", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "constructor", "simpa", "simpa"], "tactic_count": 5}
{"name": "Filter.rcomap'", "kind": "definition", "module": "Mathlib.Order.Filter.Partial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_rcomap'", "kind": "theorem", "module": "Mathlib.Order.Filter.Partial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.rcomap'_sets", "kind": "theorem", "module": "Mathlib.Order.Filter.Partial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.rcomap'_rcomap'", "kind": "theorem", "module": "Mathlib.Order.Filter.Partial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.rcomap'_compose", "kind": "theorem", "module": "Mathlib.Order.Filter.Partial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.RTendsto'", "kind": "definition", "module": "Mathlib.Order.Filter.Partial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.rtendsto'_def", "kind": "theorem", "module": "Mathlib.Order.Filter.Partial", "is_tactic_proof": true, "tactics": ["unfold", "simpa", "simpa"], "tactic_count": 3}
{"name": "Filter.tendsto_iff_rtendsto", "kind": "theorem", "module": "Mathlib.Order.Filter.Partial", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.tendsto_iff_rtendsto'", "kind": "theorem", "module": "Mathlib.Order.Filter.Partial", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.pmap", "kind": "definition", "module": "Mathlib.Order.Filter.Partial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_pmap", "kind": "theorem", "module": "Mathlib.Order.Filter.Partial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.PTendsto", "kind": "definition", "module": "Mathlib.Order.Filter.Partial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.ptendsto_def", "kind": "theorem", "module": "Mathlib.Order.Filter.Partial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.ptendsto_iff_rtendsto", "kind": "theorem", "module": "Mathlib.Order.Filter.Partial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.pmap_res", "kind": "theorem", "module": "Mathlib.Order.Filter.Partial", "is_tactic_proof": true, "tactics": ["ext", "simp", "rfl"], "tactic_count": 3}
{"name": "Filter.tendsto_iff_ptendsto", "kind": "theorem", "module": "Mathlib.Order.Filter.Partial", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.tendsto_iff_ptendsto_univ", "kind": "theorem", "module": "Mathlib.Order.Filter.Partial", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Filter.pcomap'", "kind": "definition", "module": "Mathlib.Order.Filter.Partial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.PTendsto'", "kind": "definition", "module": "Mathlib.Order.Filter.Partial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.ptendsto'_def", "kind": "theorem", "module": "Mathlib.Order.Filter.Partial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.ptendsto_of_ptendsto'", "kind": "theorem", "module": "Mathlib.Order.Filter.Partial", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Filter.ptendsto'_of_ptendsto", "kind": "theorem", "module": "Mathlib.Order.Filter.Partial", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "exact"], "tactic_count": 4}
{"name": "Filter.tendsto_eval_pi", "kind": "theorem", "module": "Mathlib.Order.Filter.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_pi", "kind": "theorem", "module": "Mathlib.Order.Filter.Pi", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.le_pi", "kind": "theorem", "module": "Mathlib.Order.Filter.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.pi_mono", "kind": "theorem", "module": "Mathlib.Order.Filter.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_pi_of_mem", "kind": "theorem", "module": "Mathlib.Order.Filter.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.pi_mem_pi", "kind": "theorem", "module": "Mathlib.Order.Filter.Pi", "is_tactic_proof": true, "tactics": ["rw", "refine", "exact"], "tactic_count": 3}
{"name": "Filter.mem_pi", "kind": "theorem", "module": "Mathlib.Order.Filter.Pi", "is_tactic_proof": true, "tactics": ["constructor", "simp", "rintro", "choose", "exact", "rintro", "exact"], "tactic_count": 7}
{"name": "Filter.mem_pi'", "kind": "theorem", "module": "Mathlib.Order.Filter.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_of_pi_mem_pi", "kind": "theorem", "module": "Mathlib.Order.Filter.Pi", "is_tactic_proof": true, "tactics": ["classical", "rcases", "refine", "have", "choose", "have", "simpa"], "tactic_count": 7}
{"name": "Filter.pi_mem_pi_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Eventually.eval_pi", "kind": "theorem", "module": "Mathlib.Order.Filter.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventually_pi", "kind": "theorem", "module": "Mathlib.Order.Filter.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.hasBasis_pi", "kind": "theorem", "module": "Mathlib.Order.Filter.Pi", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Filter.hasBasis_pi_same_index", "kind": "theorem", "module": "Mathlib.Order.Filter.Pi", "is_tactic_proof": true, "tactics": ["refine", "rintro", "rcases", "exact", "rintro", "exact"], "tactic_count": 6}
{"name": "Filter.HasBasis.pi_self", "kind": "theorem", "module": "Mathlib.Order.Filter.Pi", "is_tactic_proof": true, "tactics": ["refine", "rcases", "exact"], "tactic_count": 3}
{"name": "Filter.le_pi_principal", "kind": "theorem", "module": "Mathlib.Order.Filter.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.pi_principal", "kind": "theorem", "module": "Mathlib.Order.Filter.Pi", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.mem_pi_principal", "kind": "theorem", "module": "Mathlib.Order.Filter.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.hasBasis_pi_principal", "kind": "theorem", "module": "Mathlib.Order.Filter.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.pi_pure", "kind": "theorem", "module": "Mathlib.Order.Filter.Pi", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.mem_pi_pure", "kind": "theorem", "module": "Mathlib.Order.Filter.Pi", "is_tactic_proof": true, "tactics": ["simp", "simp"], "tactic_count": 2}
{"name": "Filter.hasBasis_pi_pure", "kind": "theorem", "module": "Mathlib.Order.Filter.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.pi_inf_principal_univ_pi_eq_bot", "kind": "theorem", "module": "Mathlib.Order.Filter.Pi", "is_tactic_proof": true, "tactics": ["constructor", "simp", "contrapose", "rintro", "have", "choose", "exact", "simp", "rintro", "filter_upwards"], "tactic_count": 10}
{"name": "Filter.pi_inf_principal_pi_eq_bot", "kind": "theorem", "module": "Mathlib.Order.Filter.Pi", "is_tactic_proof": true, "tactics": ["classical", "rw", "refine", "by_cases"], "tactic_count": 4}
{"name": "Filter.pi_inf_principal_univ_pi_neBot", "kind": "theorem", "module": "Mathlib.Order.Filter.Pi", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.pi_inf_principal_pi_neBot", "kind": "theorem", "module": "Mathlib.Order.Filter.Pi", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.PiInfPrincipalPi.neBot", "kind": "instance", "module": "Mathlib.Order.Filter.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.pi_eq_bot", "kind": "theorem", "module": "Mathlib.Order.Filter.Pi", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Filter.pi_neBot", "kind": "theorem", "module": "Mathlib.Order.Filter.Pi", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.instNeBotForallPi", "kind": "instance", "module": "Mathlib.Order.Filter.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map_eval_pi", "kind": "theorem", "module": "Mathlib.Order.Filter.Pi", "is_tactic_proof": true, "tactics": ["refine", "rcases", "rw", "refine", "exact"], "tactic_count": 5}
{"name": "Filter.pi_le_pi", "kind": "theorem", "module": "Mathlib.Order.Filter.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.pi_inj", "kind": "theorem", "module": "Mathlib.Order.Filter.Pi", "is_tactic_proof": true, "tactics": ["refine", "have", "haveI", "exact"], "tactic_count": 4}
{"name": "Filter.tendsto_piMap_pi", "kind": "theorem", "module": "Mathlib.Order.Filter.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.pi_comap", "kind": "theorem", "module": "Mathlib.Order.Filter.Pi", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.coprodᵢ", "kind": "definition", "module": "Mathlib.Order.Filter.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_coprodᵢ_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Pi", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.compl_mem_coprodᵢ", "kind": "theorem", "module": "Mathlib.Order.Filter.Pi", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.coprodᵢ_neBot_iff'", "kind": "theorem", "module": "Mathlib.Order.Filter.Pi", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.coprodᵢ_neBot_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Pi", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.coprodᵢ_eq_bot_iff'", "kind": "theorem", "module": "Mathlib.Order.Filter.Pi", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Filter.coprodᵢ_eq_bot_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Pi", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Filter.coprodᵢ_bot'", "kind": "theorem", "module": "Mathlib.Order.Filter.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.coprodᵢ_bot", "kind": "theorem", "module": "Mathlib.Order.Filter.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.NeBot.coprodᵢ", "kind": "theorem", "module": "Mathlib.Order.Filter.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.coprodᵢ_neBot", "kind": "theorem", "module": "Mathlib.Order.Filter.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.coprodᵢ_mono", "kind": "theorem", "module": "Mathlib.Order.Filter.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map_pi_map_coprodᵢ_le", "kind": "theorem", "module": "Mathlib.Order.Filter.Pi", "is_tactic_proof": true, "tactics": ["simp", "intro", "obtain", "exact"], "tactic_count": 4}
{"name": "Filter.Tendsto.pi_map_coprodᵢ", "kind": "theorem", "module": "Mathlib.Order.Filter.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.instOne", "kind": "definition", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_one", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.one_mem_one", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.pure_one", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.one_prod", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.prod_one", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.principal_one", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.one_neBot", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map_one'", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.le_one_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.NeBot.le_one_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventually_one", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_one", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.one_prod_one", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.pureOneHom", "kind": "definition", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.coe_pureOneHom", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.pureOneHom_apply", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map_one", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.instInv", "kind": "definition", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map_inv", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_inv", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.inv_le_inv", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.inv_pure", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.inv_eq_bot_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.neBot_inv_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.NeBot.inv", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.inv.instNeBot", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.comap_inv", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.inv_mem_inv", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Filter.HasBasis.inv", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Filter.instInvolutiveInv", "kind": "definition", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.inv_le_inv_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.inv_le_iff_le_inv", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.inv_le_self", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.inv_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.instMul", "kind": "definition", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.mul", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map₂_mul", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_mul", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mul_mem_mul", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.bot_mul", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mul_bot", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mul_eq_bot_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mul_neBot_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.NeBot.mul", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.NeBot.of_mul_left", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.NeBot.of_mul_right", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mul.instNeBot", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.pure_mul", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mul_pure", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.pure_mul_pure", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.le_mul_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mulLeftMono", "kind": "instance", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mulRightMono", "kind": "instance", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map_mul", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.pureMulHom", "kind": "definition", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.coe_pureMulHom", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.pureMulHom_apply", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.instDiv", "kind": "definition", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.div", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map₂_div", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_div", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.div_mem_div", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.bot_div", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.div_bot", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.div_eq_bot_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.div_neBot_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.NeBot.div", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.NeBot.of_div_left", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.NeBot.of_div_right", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.div.instNeBot", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.pure_div", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.div_pure", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.pure_div_pure", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.div_le_div", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.div_le_div_left", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.div_le_div_right", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.le_div_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.covariant_div", "kind": "instance", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.covariant_swap_div", "kind": "instance", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.instNSMul", "kind": "definition", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.instNPow", "kind": "definition", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.instZSMul", "kind": "definition", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.instZPow", "kind": "definition", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.semigroup", "kind": "definition", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.commSemigroup", "kind": "definition", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mulOneClass", "kind": "definition", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mapMonoidHom", "kind": "definition", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.comap_mul_comap_le", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.mul_mul", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.pureMonoidHom", "kind": "definition", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.coe_pureMonoidHom", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.pureMonoidHom_apply", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.monoid", "kind": "definition", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.pow_mem_pow", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.bot_pow", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.mul_top_of_one_le", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": true, "tactics": ["refine", "simp", "rintro", "rwa"], "tactic_count": 4}
{"name": "Filter.top_mul_of_one_le", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": true, "tactics": ["refine", "simp", "rintro", "rwa"], "tactic_count": 4}
{"name": "Filter.top_mul_top", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.top_pow", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUnit.filter", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.commMonoid", "kind": "definition", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mul_eq_one_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": true, "tactics": ["refine", "obtain", "have", "rw", "obtain", "refine", "rwa", "rwa", "rintro", "rw"], "tactic_count": 10}
{"name": "Filter.divisionMonoid", "kind": "definition", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.isUnit_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "obtain", "refine", "rw", "exact", "rintro", "exact"], "tactic_count": 8}
{"name": "Filter.divisionCommMonoid", "kind": "definition", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.instDistribNeg", "kind": "definition", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mul_add_subset", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.add_mul_subset", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.NeBot.mul_zero_nonneg", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.NeBot.zero_mul_nonneg", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.one_le_div_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact", "rintro", "exact"], "tactic_count": 5}
{"name": "Filter.not_one_le_div_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.NeBot.one_le_div", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Filter.isUnit_pure", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.isUnit_iff_singleton", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.map_inv'", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.inv_inv", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map_div", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.div_div", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.NeBot.div_zero_nonneg", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.NeBot.zero_div_nonneg", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.instSMul", "kind": "definition", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.smul", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map₂_smul", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_smul", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.smul_mem_smul", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.bot_smul", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.smul_bot", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.smul_eq_bot_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.smul_neBot_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.NeBot.smul", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.NeBot.of_smul_left", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.NeBot.of_smul_right", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.smul.instNeBot", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.pure_smul", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.smul_pure", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.pure_smul_pure", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.smul_le_smul", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.smul_le_smul_left", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.smul_le_smul_right", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.le_smul_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.covariant_smul", "kind": "instance", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.instVSub", "kind": "definition", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map₂_vsub", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_vsub", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.vsub_mem_vsub", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.bot_vsub", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.vsub_bot", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.vsub_eq_bot_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.vsub_neBot_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.NeBot.vsub", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.NeBot.of_vsub_left", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.NeBot.of_vsub_right", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.vsub.instNeBot", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.pure_vsub", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.vsub_pure", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.pure_vsub_pure", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.vsub_le_vsub", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.vsub_le_vsub_left", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.vsub_le_vsub_right", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.le_vsub_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.instSMulFilter", "kind": "definition", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map_smul", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_smul_filter", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.smul_set_mem_smul_filter", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.smul_filter_bot", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.smul_filter_eq_bot_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.smul_filter_neBot_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.NeBot.smul_filter", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.NeBot.of_smul_filter", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.smul_filter.instNeBot", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.smul_filter_le_smul_filter", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.covariant_smul_filter", "kind": "instance", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.smulCommClass_filter", "kind": "instance", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.smulCommClass_filter'", "kind": "instance", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.smulCommClass_filter''", "kind": "instance", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.smulCommClass", "kind": "instance", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.isScalarTower", "kind": "instance", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.isScalarTower'", "kind": "instance", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.isScalarTower''", "kind": "instance", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.isCentralScalar", "kind": "instance", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mulAction", "kind": "definition", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mulActionFilter", "kind": "definition", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.distribMulActionFilter", "kind": "definition", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mulDistribMulActionFilter", "kind": "definition", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.NeBot.smul_zero_nonneg", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.NeBot.zero_smul_nonneg", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.zero_smul_filter_nonpos", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": true, "tactics": ["refine", "convert", "refine", "rwa"], "tactic_count": 4}
{"name": "Filter.zero_smul_filter", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUnit.smul_tendsto_smul_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": true, "tactics": ["rcases", "refine", "simpa"], "tactic_count": 3}
{"name": "Filter.smul_tendsto_smul_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.smul_tendsto_smul_iff₀", "kind": "theorem", "module": "Mathlib.Order.Filter.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.prod_mem_prod", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_prod_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 5}
{"name": "Filter.compl_diagonal_mem_prod", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.prod_mem_prod_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_prod_principal", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": true, "tactics": ["rw", "refine", "rintro", "exact", "rintro", "exact"], "tactic_count": 6}
{"name": "Filter.mem_prod_top", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Filter.eventually_prod_principal_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Filter.comap_prod", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.comap_prodMap_prod", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.prod_top", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.top_prod", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.sup_prod", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.prod_sup", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.eventually_prod_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Filter.tendsto_fst", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_snd", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.fst", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.snd", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.prodMk", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_prod_swap", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Eventually.prod_inl", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Eventually.prod_inr", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Eventually.prod_mk", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.prodMap", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyLE.prodMap", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Eventually.curry", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "Filter.Frequently.uncurry", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": true, "tactics": ["contrapose", "exact"], "tactic_count": 2}
{"name": "Filter.Frequently.of_curry", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Eventually.image_of_prod", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": true, "tactics": ["obtain", "filter_upwards"], "tactic_count": 2}
{"name": "Filter.Eventually.diag_of_prod", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Eventually.diag_of_prod_left", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": true, "tactics": ["intro", "obtain", "exact"], "tactic_count": 3}
{"name": "Filter.Eventually.diag_of_prod_right", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": true, "tactics": ["intro", "obtain", "exact"], "tactic_count": 3}
{"name": "Filter.tendsto_diag", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.prod_iInf_left", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.prod_iInf_right", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.prod_mono", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.prod_mono_left", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.prod_mono_right", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.prod_comap_comap_eq", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.prod_comm'", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.prod_comm", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.mem_prod_iff_left", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": true, "tactics": ["simp", "refine", "exact"], "tactic_count": 3}
{"name": "Filter.mem_prod_iff_right", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.map_fst_prod", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Filter.map_snd_prod", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.prod_le_prod", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.prod_inj", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": true, "tactics": ["refine", "have", "haveI", "exact"], "tactic_count": 4}
{"name": "Filter.eventually_swap_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.Eventually.eventually_prod_of_eventually_swap", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": true, "tactics": ["refine", "rcases", "exact"], "tactic_count": 3}
{"name": "Filter.Eventually.trans_prod", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.prod_assoc", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Filter.prod_assoc_symm", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Filter.tendsto_prodAssoc", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_prodAssoc_symm", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map_swap4_prod", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Filter.tendsto_swap4_prod", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.prod_map_map_eq", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.prod_map_map_eq'", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.prod_map_left", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.prod_map_right", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.le_prod_map_fst_snd", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.prodMap", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Filter.map_prod", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": true, "tactics": ["simp", "intro", "constructor", "exact", "exact"], "tactic_count": 5}
{"name": "Filter.prod_eq", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.prod_inf_prod", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.inf_prod", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.prod_inf", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.prod_principal_principal", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.pure_prod", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.map_pure_prod", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.prod_pure", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.prod_pure_pure", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.prod_eq_bot", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": true, "tactics": ["simp_rw", "exists_or,"], "tactic_count": 2}
{"name": "Filter.prod_bot", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.bot_prod", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.prod_neBot", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.NeBot.prod", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.prod.instNeBot", "kind": "instance", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.disjoint_prod", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.frequently_prod_and", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": true, "tactics": ["simp", "rfl"], "tactic_count": 2}
{"name": "Filter.tendsto_prod_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.tendsto_prod_iff'", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.le_prod", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.coprod_eq_prod_top_sup_top_prod", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Filter.mem_coprod_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.bot_coprod", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.coprod_bot", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.bot_coprod_bot", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.compl_mem_coprod", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.coprod_mono", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.coprod_neBot_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.coprod_neBot_left", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.coprod_neBot_right", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.coprod_inf_prod_le", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.principal_coprod_principal", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": true, "tactics": ["rw", "preimage_compl,"], "tactic_count": 2}
{"name": "Filter.map_prodMap_coprod_le", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": true, "tactics": ["intro", "simp", "rintro", "refine"], "tactic_count": 4}
{"name": "Filter.map_const_principal_coprod_map_id_principal", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.map_prodMap_const_id_principal_coprod_principal", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": true, "tactics": ["rw", "congr", "ext", "constructor", "rintro", "simp", "rintro", "use", "simpa"], "tactic_count": 9}
{"name": "Filter.Tendsto.prodMap_coprod", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.coprod_of_prod_top_right", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": true, "tactics": ["simp_all", "grind"], "tactic_count": 2}
{"name": "Filter.Tendsto.coprod_of_prod_top_left", "kind": "theorem", "module": "Mathlib.Order.Filter.Prod", "is_tactic_proof": true, "tactics": ["simp_all", "grind"], "tactic_count": 2}
{"name": "Filter.EventuallyLE.mul_le_mul", "kind": "theorem", "module": "Mathlib.Order.Filter.Ring", "is_tactic_proof": true, "tactics": ["filter_upwards"], "tactic_count": 1}
{"name": "Filter.EventuallyLE.mul_le_mul'", "kind": "theorem", "module": "Mathlib.Order.Filter.Ring", "is_tactic_proof": true, "tactics": ["filter_upwards"], "tactic_count": 1}
{"name": "Filter.EventuallyLE.mul_nonneg", "kind": "theorem", "module": "Mathlib.Order.Filter.Ring", "is_tactic_proof": true, "tactics": ["filter_upwards"], "tactic_count": 1}
{"name": "Filter.eventually_sub_nonneg", "kind": "theorem", "module": "Mathlib.Order.Filter.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.instIsOrderedRing", "kind": "instance", "module": "Mathlib.Order.Filter.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.smallSets", "kind": "definition", "module": "Mathlib.Order.Filter.SmallSets", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.smallSets_eq_generate", "kind": "theorem", "module": "Mathlib.Order.Filter.SmallSets", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Filter.bind_smallSets_gc", "kind": "theorem", "module": "Mathlib.Order.Filter.SmallSets", "is_tactic_proof": true, "tactics": ["intro", "simp_rw", "rfl"], "tactic_count": 3}
{"name": "Filter.HasBasis.smallSets", "kind": "theorem", "module": "Mathlib.Order.Filter.SmallSets", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.hasBasis_smallSets", "kind": "theorem", "module": "Mathlib.Order.Filter.SmallSets", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Eventually.exists_mem_basis_of_smallSets", "kind": "theorem", "module": "Mathlib.Order.Filter.SmallSets", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Frequently.smallSets_of_forall_mem_basis", "kind": "theorem", "module": "Mathlib.Order.Filter.SmallSets", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Eventually.exists_mem_of_smallSets", "kind": "theorem", "module": "Mathlib.Order.Filter.SmallSets", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_smallSets_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.SmallSets", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventually_smallSets", "kind": "theorem", "module": "Mathlib.Order.Filter.SmallSets", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventually_smallSets'", "kind": "theorem", "module": "Mathlib.Order.Filter.SmallSets", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.eventually_smallSets", "kind": "theorem", "module": "Mathlib.Order.Filter.SmallSets", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.frequently_smallSets", "kind": "theorem", "module": "Mathlib.Order.Filter.SmallSets", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.frequently_smallSets_mem", "kind": "theorem", "module": "Mathlib.Order.Filter.SmallSets", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.frequently_smallSets'", "kind": "theorem", "module": "Mathlib.Order.Filter.SmallSets", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "Filter.HasBasis.frequently_smallSets", "kind": "theorem", "module": "Mathlib.Order.Filter.SmallSets", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.tendsto_image_smallSets", "kind": "theorem", "module": "Mathlib.Order.Filter.SmallSets", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "simp"], "tactic_count": 4}
{"name": "Filter.HasAntitoneBasis.tendsto_smallSets", "kind": "theorem", "module": "Mathlib.Order.Filter.SmallSets", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.monotone_smallSets", "kind": "theorem", "module": "Mathlib.Order.Filter.SmallSets", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.smallSets_bot", "kind": "theorem", "module": "Mathlib.Order.Filter.SmallSets", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Filter.smallSets_top", "kind": "theorem", "module": "Mathlib.Order.Filter.SmallSets", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.smallSets_principal", "kind": "theorem", "module": "Mathlib.Order.Filter.SmallSets", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.smallSets_comap_eq_comap_image", "kind": "theorem", "module": "Mathlib.Order.Filter.SmallSets", "is_tactic_proof": true, "tactics": ["refine", "simp"], "tactic_count": 2}
{"name": "Filter.smallSets_comap", "kind": "theorem", "module": "Mathlib.Order.Filter.SmallSets", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.comap_smallSets", "kind": "theorem", "module": "Mathlib.Order.Filter.SmallSets", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.smallSets_iInf", "kind": "theorem", "module": "Mathlib.Order.Filter.SmallSets", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.smallSets_inf", "kind": "theorem", "module": "Mathlib.Order.Filter.SmallSets", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.smallSets_neBot", "kind": "instance", "module": "Mathlib.Order.Filter.SmallSets", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "Filter.Tendsto.smallSets_mono", "kind": "theorem", "module": "Mathlib.Order.Filter.SmallSets", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Filter.Tendsto.of_smallSets", "kind": "theorem", "module": "Mathlib.Order.Filter.SmallSets", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventually_smallSets_eventually", "kind": "theorem", "module": "Mathlib.Order.Filter.SmallSets", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventually_smallSets_forall", "kind": "theorem", "module": "Mathlib.Order.Filter.SmallSets", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Filter.eventually_smallSets_subset", "kind": "theorem", "module": "Mathlib.Order.Filter.SmallSets", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Subsingleton", "kind": "definition", "module": "Mathlib.Order.Filter.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.subsingleton_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Subsingleton.anti", "kind": "theorem", "module": "Mathlib.Order.Filter.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Subsingleton.of_subsingleton", "kind": "theorem", "module": "Mathlib.Order.Filter.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Subsingleton.map", "kind": "theorem", "module": "Mathlib.Order.Filter.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Subsingleton.prod", "kind": "theorem", "module": "Mathlib.Order.Filter.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.subsingleton_pure", "kind": "theorem", "module": "Mathlib.Order.Filter.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.subsingleton_bot", "kind": "theorem", "module": "Mathlib.Order.Filter.Subsingleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Subsingleton.exists_eq_pure", "kind": "theorem", "module": "Mathlib.Order.Filter.Subsingleton", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "refine", "rwa"], "tactic_count": 4}
{"name": "Filter.subsingleton_iff_bot_or_pure", "kind": "theorem", "module": "Mathlib.Order.Filter.Subsingleton", "is_tactic_proof": true, "tactics": ["refine", "exact", "rintro"], "tactic_count": 3}
{"name": "Filter.subsingleton_iff_exists_le_pure", "kind": "theorem", "module": "Mathlib.Order.Filter.Subsingleton", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simp"], "tactic_count": 3}
{"name": "Filter.subsingleton_iff_exists_singleton_mem", "kind": "theorem", "module": "Mathlib.Order.Filter.Subsingleton", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.Subsingleton.isCountablyGenerated", "kind": "theorem", "module": "Mathlib.Order.Filter.Subsingleton", "is_tactic_proof": true, "tactics": ["rcases", "exact", "exact"], "tactic_count": 3}
{"name": "Filter.tendsto_def", "kind": "theorem", "module": "Mathlib.Order.Filter.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_iff_eventually", "kind": "theorem", "module": "Mathlib.Order.Filter.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_iff_forall_eventually_mem", "kind": "theorem", "module": "Mathlib.Order.Filter.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.eventually_mem", "kind": "theorem", "module": "Mathlib.Order.Filter.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.eventually", "kind": "theorem", "module": "Mathlib.Order.Filter.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.not_tendsto_iff_exists_frequently_notMem", "kind": "theorem", "module": "Mathlib.Order.Filter.Tendsto", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.Tendsto.frequently", "kind": "theorem", "module": "Mathlib.Order.Filter.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.frequently_map", "kind": "theorem", "module": "Mathlib.Order.Filter.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_bot", "kind": "theorem", "module": "Mathlib.Order.Filter.Tendsto", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.Tendsto.of_neBot_imp", "kind": "theorem", "module": "Mathlib.Order.Filter.Tendsto", "is_tactic_proof": true, "tactics": ["rcases", "exact", "exact"], "tactic_count": 3}
{"name": "Filter.tendsto_top", "kind": "theorem", "module": "Mathlib.Order.Filter.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.le_map_of_right_inverse", "kind": "theorem", "module": "Mathlib.Order.Filter.Tendsto", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Filter.tendsto_of_isEmpty", "kind": "theorem", "module": "Mathlib.Order.Filter.Tendsto", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.eventuallyEq_of_left_inv_of_right_inv", "kind": "theorem", "module": "Mathlib.Order.Filter.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_iff_comap", "kind": "theorem", "module": "Mathlib.Order.Filter.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.disjoint", "kind": "theorem", "module": "Mathlib.Order.Filter.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_congr'", "kind": "theorem", "module": "Mathlib.Order.Filter.Tendsto", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.Tendsto.congr'", "kind": "theorem", "module": "Mathlib.Order.Filter.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_congr", "kind": "theorem", "module": "Mathlib.Order.Filter.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.congr", "kind": "theorem", "module": "Mathlib.Order.Filter.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_id'", "kind": "theorem", "module": "Mathlib.Order.Filter.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_id", "kind": "theorem", "module": "Mathlib.Order.Filter.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.comp", "kind": "theorem", "module": "Mathlib.Order.Filter.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.iterate", "kind": "theorem", "module": "Mathlib.Order.Filter.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.mono_left", "kind": "theorem", "module": "Mathlib.Order.Filter.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.mono_right", "kind": "theorem", "module": "Mathlib.Order.Filter.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.neBot", "kind": "theorem", "module": "Mathlib.Order.Filter.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_map", "kind": "theorem", "module": "Mathlib.Order.Filter.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_map'_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Tendsto", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.tendsto_comap", "kind": "theorem", "module": "Mathlib.Order.Filter.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_comap_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_comap'_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Tendsto", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Filter.Tendsto.of_tendsto_comp", "kind": "theorem", "module": "Mathlib.Order.Filter.Tendsto", "is_tactic_proof": true, "tactics": ["rw", "calc", "a"], "tactic_count": 3}
{"name": "Filter.comap_eq_of_inverse", "kind": "theorem", "module": "Mathlib.Order.Filter.Tendsto", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "Filter.map_eq_of_inverse", "kind": "theorem", "module": "Mathlib.Order.Filter.Tendsto", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "Filter.tendsto_inf", "kind": "theorem", "module": "Mathlib.Order.Filter.Tendsto", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.tendsto_inf_left", "kind": "theorem", "module": "Mathlib.Order.Filter.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_inf_right", "kind": "theorem", "module": "Mathlib.Order.Filter.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.inf", "kind": "theorem", "module": "Mathlib.Order.Filter.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_iInf", "kind": "theorem", "module": "Mathlib.Order.Filter.Tendsto", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.tendsto_iInf'", "kind": "theorem", "module": "Mathlib.Order.Filter.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_iInf_iInf", "kind": "theorem", "module": "Mathlib.Order.Filter.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_sup", "kind": "theorem", "module": "Mathlib.Order.Filter.Tendsto", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.Tendsto.sup", "kind": "theorem", "module": "Mathlib.Order.Filter.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.sup_sup", "kind": "theorem", "module": "Mathlib.Order.Filter.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_iSup", "kind": "theorem", "module": "Mathlib.Order.Filter.Tendsto", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.tendsto_iSup_iSup", "kind": "theorem", "module": "Mathlib.Order.Filter.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_principal", "kind": "theorem", "module": "Mathlib.Order.Filter.Tendsto", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.tendsto_principal_principal", "kind": "theorem", "module": "Mathlib.Order.Filter.Tendsto", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.tendsto_pure", "kind": "theorem", "module": "Mathlib.Order.Filter.Tendsto", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.tendsto_pure_pure", "kind": "theorem", "module": "Mathlib.Order.Filter.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_const_pure", "kind": "theorem", "module": "Mathlib.Order.Filter.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.pure_le_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_pure_left", "kind": "theorem", "module": "Mathlib.Order.Filter.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map_inf_principal_preimage", "kind": "theorem", "module": "Mathlib.Order.Filter.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.not_tendsto", "kind": "theorem", "module": "Mathlib.Order.Filter.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.if", "kind": "theorem", "module": "Mathlib.Order.Filter.Tendsto", "is_tactic_proof": true, "tactics": ["simp", "intro", "filter_upwards", "rw", "split_ifs", "exacts"], "tactic_count": 6}
{"name": "Filter.Tendsto.if'", "kind": "theorem", "module": "Mathlib.Order.Filter.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.piecewise", "kind": "theorem", "module": "Mathlib.Order.Filter.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.MapsTo.tendsto", "kind": "theorem", "module": "Mathlib.Order.Filter.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.comp_tendsto", "kind": "theorem", "module": "Mathlib.Order.Filter.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map_mapsTo_Iic_iff_tendsto", "kind": "theorem", "module": "Mathlib.Order.Filter.Tendsto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.map_mapsTo_Iic_iff_mapsTo", "kind": "theorem", "module": "Mathlib.Order.Filter.Tendsto", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ultrafilter.finite_sUnion_mem_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Basic", "is_tactic_proof": true, "tactics": ["induction", "empty", "insert"], "tactic_count": 3}
{"name": "Ultrafilter.finite_biUnion_mem_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Ultrafilter.eventually_exists_mem_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Basic", "is_tactic_proof": true, "tactics": ["simp", "convert", "aesop"], "tactic_count": 3}
{"name": "Ultrafilter.eventually_exists_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Ultrafilter.eq_pure_of_finite_mem", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Basic", "is_tactic_proof": true, "tactics": ["rw", "rcases", "exact"], "tactic_count": 3}
{"name": "Ultrafilter.eq_pure_of_finite", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ultrafilter.le_cofinite_or_eq_pure", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ultrafilter.exists_ultrafilter_of_finite_inter_nonempty", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.atTop_eq_pure_of_isTop", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.atBot_eq_pure_of_isBot", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_iff_ultrafilter", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Filter.hyperfilter", "kind": "definition", "module": "Mathlib.Order.Filter.Ultrafilter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.hyperfilter_le_cofinite", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.hyperfilter_le_atTop", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.bot_ne_hyperfilter", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.notMem_hyperfilter_of_finite", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.compl_mem_hyperfilter_of_finite", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_hyperfilter_of_finite_compl", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsAtomicFilter", "kind": "instance", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ultrafilter.instCoeTCFilter", "kind": "instance", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ultrafilter.instMembershipSet", "kind": "instance", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ultrafilter.neBot", "kind": "instance", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ultrafilter.isAtom", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ultrafilter.mem_coe", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ultrafilter.coe_injective", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ultrafilter.eq_of_le", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ultrafilter.coe_le_coe", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ultrafilter.coe_inj", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ultrafilter.ext", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ultrafilter.le_of_inf_neBot", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ultrafilter.le_of_inf_neBot'", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ultrafilter.inf_neBot_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ultrafilter.disjoint_iff_not_le", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ultrafilter.compl_notMem_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ultrafilter.frequently_iff_eventually", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ultrafilter.compl_mem_iff_notMem", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ultrafilter.diff_mem_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ultrafilter.ofComplNotMemIff", "kind": "definition", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ultrafilter.ofAtom", "kind": "definition", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ultrafilter.nonempty_of_mem", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ultrafilter.ne_empty_of_mem", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ultrafilter.empty_notMem", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ultrafilter.le_sup_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ultrafilter.union_mem_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Ultrafilter.mem_or_compl_mem", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ultrafilter.em", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ultrafilter.eventually_or", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ultrafilter.eventually_not", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ultrafilter.eventually_imp", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Ultrafilter.map", "kind": "definition", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ultrafilter.coe_map", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ultrafilter.mem_map", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ultrafilter.map_id", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ultrafilter.map_id'", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ultrafilter.map_map", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ultrafilter.comap", "kind": "definition", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ultrafilter.mem_comap", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ultrafilter.coe_comap", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ultrafilter.instPure", "kind": "instance", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ultrafilter.mem_pure", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ultrafilter.coe_pure", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ultrafilter.map_pure", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ultrafilter.comap_pure", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ultrafilter.pure_injective", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ultrafilter.instInhabited", "kind": "instance", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ultrafilter.instNonempty", "kind": "instance", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ultrafilter.bind", "kind": "definition", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ultrafilter.instBind", "kind": "instance", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ultrafilter.functor", "kind": "instance", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ultrafilter.monad", "kind": "instance", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ultrafilter.lawfulMonad", "kind": "instance", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ultrafilter.exists_le", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ultrafilter.of", "kind": "definition", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ultrafilter.of_le", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ultrafilter.of_coe", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.isAtom_pure", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.NeBot.le_pure_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.NeBot.eq_pure_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.lt_pure_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.le_pure_iff'", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Iic_pure", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_iff_ultrafilter", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": true, "tactics": ["refine", "set", "haveI", "simpa"], "tactic_count": 4}
{"name": "Filter.le_iff_ultrafilter", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.iSup_ultrafilter_le_eq", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.exists_ultrafilter_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.forall_neBot_le_iff", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": true, "tactics": ["refine", "intro", "exact"], "tactic_count": 3}
{"name": "Ultrafilter.comap_inf_principal_neBot_of_image_mem", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ultrafilter.ofComapInfPrincipal", "kind": "definition", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ultrafilter.ofComapInfPrincipal_mem", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": true, "tactics": ["let", "haveI", "have", "exact"], "tactic_count": 4}
{"name": "Ultrafilter.ofComapInfPrincipal_eq_of_map", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": true, "tactics": ["let", "haveI", "apply", "calc"], "tactic_count": 4}
{"name": "Ultrafilter.eq_of_le_pure", "kind": "theorem", "module": "Mathlib.Order.Filter.Ultrafilter.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.ZeroAtFilter", "kind": "definition", "module": "Mathlib.Order.Filter.ZeroAndBoundedAtFilter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.zero_zeroAtFilter", "kind": "theorem", "module": "Mathlib.Order.Filter.ZeroAndBoundedAtFilter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.ZeroAtFilter.add", "kind": "theorem", "module": "Mathlib.Order.Filter.ZeroAndBoundedAtFilter", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Filter.ZeroAtFilter.neg", "kind": "theorem", "module": "Mathlib.Order.Filter.ZeroAndBoundedAtFilter", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Filter.ZeroAtFilter.smul", "kind": "theorem", "module": "Mathlib.Order.Filter.ZeroAndBoundedAtFilter", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Filter.zeroAtFilterSubmodule", "kind": "definition", "module": "Mathlib.Order.Filter.ZeroAndBoundedAtFilter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.zeroAtFilterAddSubmonoid", "kind": "definition", "module": "Mathlib.Order.Filter.ZeroAndBoundedAtFilter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.BoundedAtFilter", "kind": "definition", "module": "Mathlib.Order.Filter.ZeroAndBoundedAtFilter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.ZeroAtFilter.boundedAtFilter", "kind": "theorem", "module": "Mathlib.Order.Filter.ZeroAndBoundedAtFilter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.const_boundedAtFilter", "kind": "theorem", "module": "Mathlib.Order.Filter.ZeroAndBoundedAtFilter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.BoundedAtFilter.add", "kind": "theorem", "module": "Mathlib.Order.Filter.ZeroAndBoundedAtFilter", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Filter.BoundedAtFilter.neg", "kind": "theorem", "module": "Mathlib.Order.Filter.ZeroAndBoundedAtFilter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.BoundedAtFilter.smul", "kind": "theorem", "module": "Mathlib.Order.Filter.ZeroAndBoundedAtFilter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.BoundedAtFilter.mul", "kind": "theorem", "module": "Mathlib.Order.Filter.ZeroAndBoundedAtFilter", "is_tactic_proof": true, "tactics": ["refine", "convert", "simp"], "tactic_count": 3}
{"name": "Filter.boundedFilterSubmodule", "kind": "definition", "module": "Mathlib.Order.Filter.ZeroAndBoundedAtFilter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.boundedFilterSubalgebra", "kind": "definition", "module": "Mathlib.Order.Filter.ZeroAndBoundedAtFilter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.BoundedAtFilter.prod", "kind": "theorem", "module": "Mathlib.Order.Filter.ZeroAndBoundedAtFilter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.instMax_mathlib", "kind": "instance", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.instMin_mathlib", "kind": "instance", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.coe_max", "kind": "theorem", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.coe_min", "kind": "theorem", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.compare_eq_compare_val", "kind": "theorem", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.instLinearOrder", "kind": "instance", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.instBoundedOrder", "kind": "instance", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.instBiheytingAlgebra", "kind": "instance", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.instPartialOrder", "kind": "instance", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.instLattice", "kind": "instance", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.instHeytingAlgebra", "kind": "instance", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.instCoheytingAlgebra", "kind": "instance", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.top_eq_last", "kind": "theorem", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.bot_eq_zero", "kind": "theorem", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.rev_bot", "kind": "theorem", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.rev_top", "kind": "theorem", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.rev_zero_eq_top", "kind": "theorem", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.rev_last_eq_bot", "kind": "theorem", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.succ_top", "kind": "theorem", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.val_top", "kind": "theorem", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.zero_eq_top", "kind": "theorem", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": true, "tactics": ["rw", "or_iff_right"], "tactic_count": 2}
{"name": "Fin.top_eq_zero", "kind": "theorem", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.cast_top", "kind": "theorem", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.strictMono_pred_comp", "kind": "theorem", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.monotone_pred_comp", "kind": "theorem", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.strictMono_castPred_comp", "kind": "theorem", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.monotone_castPred_comp", "kind": "theorem", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.strictMono_iff_lt_succ", "kind": "theorem", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.monotone_iff_le_succ", "kind": "theorem", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.strictAnti_iff_succ_lt", "kind": "theorem", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.antitone_iff_succ_le", "kind": "theorem", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.orderHom_injective_iff", "kind": "theorem", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": true, "tactics": ["constructor", "intro", "have", "simp", "intro", "refine", "exact"], "tactic_count": 7}
{"name": "Fin.val_strictMono", "kind": "theorem", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.cast_strictMono", "kind": "theorem", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.strictMono_succ", "kind": "theorem", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.strictMono_castLE", "kind": "theorem", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.strictMono_castAdd", "kind": "theorem", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.strictMono_castSucc", "kind": "theorem", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.strictMono_natAdd", "kind": "theorem", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.strictMono_addNat", "kind": "theorem", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.strictMono_succAbove", "kind": "theorem", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.succAbove_inj", "kind": "theorem", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.succAbove_le_succAbove_iff", "kind": "theorem", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.succAbove_lt_succAbove_iff", "kind": "theorem", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.natAdd_inj", "kind": "theorem", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.natAdd_injective", "kind": "theorem", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.natAdd_le_natAdd_iff", "kind": "theorem", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.natAdd_lt_natAdd_iff", "kind": "theorem", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.addNat_inj", "kind": "theorem", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.addNat_le_addNat_iff", "kind": "theorem", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.addNat_lt_addNat_iff", "kind": "theorem", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.castLE_le_castLE_iff", "kind": "theorem", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.castLE_lt_castLE_iff", "kind": "theorem", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.predAbove_right_monotone", "kind": "theorem", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.predAbove_left_monotone", "kind": "theorem", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.predAbove_le_predAbove", "kind": "theorem", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.predAboveOrderHom", "kind": "definition", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.predAbove_left_injective", "kind": "theorem", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": true, "tactics": ["intro", "obtain", "wlog", "obtain", "exact", "rfl", "replace", "rw", "exact"], "tactic_count": 9}
{"name": "Fin.predAbove_left_inj", "kind": "theorem", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.orderIsoSubtype", "kind": "definition", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.castOrderIso", "kind": "definition", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.symm_castOrderIso", "kind": "theorem", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "Fin.castOrderIso_toEquiv", "kind": "theorem", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "Fin.revOrderIso", "kind": "definition", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.revOrderIso_symm_apply", "kind": "theorem", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.rev_strictAnti", "kind": "theorem", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.rev_anti", "kind": "theorem", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.valOrderEmb", "kind": "definition", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.OrderEmbedding.instInhabitedOrderEmbeddingNat", "kind": "instance", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.Lt.isWellOrder", "kind": "instance", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.succOrderEmb", "kind": "definition", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.coe_succOrderEmb", "kind": "theorem", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.succOrderEmb_toEmbedding", "kind": "theorem", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.castLEOrderEmb", "kind": "definition", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.castAddOrderEmb", "kind": "definition", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.castSuccOrderEmb", "kind": "definition", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.addNatOrderEmb", "kind": "definition", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.natAddOrderEmb", "kind": "definition", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.succAboveOrderEmb", "kind": "definition", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.coe_orderIso_apply", "kind": "theorem", "module": "Mathlib.Order.Fin.Basic", "is_tactic_proof": true, "tactics": ["rcases", "dsimp", "induction", "refine", "have", "specialize", "simp", "rwa", "rwa"], "tactic_count": 9}
{"name": "Fin.orderIsoSingleton", "kind": "definition", "module": "Mathlib.Order.Fin.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.orderIsoSingleton_apply", "kind": "theorem", "module": "Mathlib.Order.Fin.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.orderIsoPair", "kind": "definition", "module": "Mathlib.Order.Fin.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.orderIsoPair_zero", "kind": "theorem", "module": "Mathlib.Order.Fin.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.orderIsoPair_one", "kind": "theorem", "module": "Mathlib.Order.Fin.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.orderIsoTriple", "kind": "definition", "module": "Mathlib.Order.Fin.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.orderIsoTriple_zero", "kind": "theorem", "module": "Mathlib.Order.Fin.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.orderIsoTriple_one", "kind": "theorem", "module": "Mathlib.Order.Fin.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.orderIsoTriple_two", "kind": "theorem", "module": "Mathlib.Order.Fin.Finset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.succAboveOrderIso", "kind": "definition", "module": "Mathlib.Order.Fin.SuccAboveOrderIso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.pi_lex_lt_cons_cons", "kind": "theorem", "module": "Mathlib.Order.Fin.Tuple", "is_tactic_proof": true, "tactics": ["simp_rw", "simp"], "tactic_count": 2}
{"name": "Fin.insertNth_mem_Icc", "kind": "theorem", "module": "Mathlib.Order.Fin.Tuple", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.preimage_insertNth_Icc_of_mem", "kind": "theorem", "module": "Mathlib.Order.Fin.Tuple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.preimage_insertNth_Icc_of_notMem", "kind": "theorem", "module": "Mathlib.Order.Fin.Tuple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "liftFun_vecCons", "kind": "theorem", "module": "Mathlib.Order.Fin.Tuple", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "strictMono_vecCons", "kind": "theorem", "module": "Mathlib.Order.Fin.Tuple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monotone_vecCons", "kind": "theorem", "module": "Mathlib.Order.Fin.Tuple", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "monotone_vecEmpty", "kind": "theorem", "module": "Mathlib.Order.Fin.Tuple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictMono_vecEmpty", "kind": "theorem", "module": "Mathlib.Order.Fin.Tuple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictAnti_vecCons", "kind": "theorem", "module": "Mathlib.Order.Fin.Tuple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "antitone_vecCons", "kind": "theorem", "module": "Mathlib.Order.Fin.Tuple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "antitone_vecEmpty", "kind": "theorem", "module": "Mathlib.Order.Fin.Tuple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictAnti_vecEmpty", "kind": "theorem", "module": "Mathlib.Order.Fin.Tuple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.vecCons", "kind": "theorem", "module": "Mathlib.Order.Fin.Tuple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictAnti.vecCons", "kind": "theorem", "module": "Mathlib.Order.Fin.Tuple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.vecCons", "kind": "theorem", "module": "Mathlib.Order.Fin.Tuple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.vecCons", "kind": "theorem", "module": "Mathlib.Order.Fin.Tuple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_example", "kind": "example", "module": "Mathlib.Order.Fin.Tuple", "is_tactic_proof": true, "tactics": ["decide"], "tactic_count": 1}
{"name": "OrderIso.piFinTwoIso", "kind": "definition", "module": "Mathlib.Order.Fin.Tuple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.finTwoArrowIso", "kind": "definition", "module": "Mathlib.Order.Fin.Tuple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.consOrderIso", "kind": "definition", "module": "Mathlib.Order.Fin.Tuple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.snocOrderIso", "kind": "definition", "module": "Mathlib.Order.Fin.Tuple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.insertNthOrderIso", "kind": "definition", "module": "Mathlib.Order.Fin.Tuple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.insertNthOrderIso_zero", "kind": "theorem", "module": "Mathlib.Order.Fin.Tuple", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Fin.insertNthOrderIso_last", "kind": "theorem", "module": "Mathlib.Order.Fin.Tuple", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "finSuccAboveOrderIso", "kind": "definition", "module": "Mathlib.Order.Fin.Tuple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finSuccAboveOrderIso_apply", "kind": "theorem", "module": "Mathlib.Order.Fin.Tuple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finSuccAboveOrderIso_symm_apply_last", "kind": "theorem", "module": "Mathlib.Order.Fin.Tuple", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "finSuccAboveOrderIso_symm_apply_ne_last", "kind": "theorem", "module": "Mathlib.Order.Fin.Tuple", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "Fin.castLEOrderIso", "kind": "definition", "module": "Mathlib.Order.Fin.Tuple", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.lfp", "kind": "definition", "module": "Mathlib.Order.FixedPoints", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.gfp", "kind": "definition", "module": "Mathlib.Order.FixedPoints", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.lfp_le", "kind": "theorem", "module": "Mathlib.Order.FixedPoints", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.lfp_le_fixed", "kind": "theorem", "module": "Mathlib.Order.FixedPoints", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.le_lfp", "kind": "theorem", "module": "Mathlib.Order.FixedPoints", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.map_le_lfp", "kind": "theorem", "module": "Mathlib.Order.FixedPoints", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.map_lfp", "kind": "theorem", "module": "Mathlib.Order.FixedPoints", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.isFixedPt_lfp", "kind": "theorem", "module": "Mathlib.Order.FixedPoints", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.lfp_le_map", "kind": "theorem", "module": "Mathlib.Order.FixedPoints", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.isLeast_lfp_le", "kind": "theorem", "module": "Mathlib.Order.FixedPoints", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.isLeast_lfp", "kind": "theorem", "module": "Mathlib.Order.FixedPoints", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.lfp_induction", "kind": "theorem", "module": "Mathlib.Order.FixedPoints", "is_tactic_proof": true, "tactics": ["set", "specialize", "suffices", "have", "have", "exact"], "tactic_count": 6}
{"name": "OrderHom.le_gfp", "kind": "theorem", "module": "Mathlib.Order.FixedPoints", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.gfp_le", "kind": "theorem", "module": "Mathlib.Order.FixedPoints", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.isFixedPt_gfp", "kind": "theorem", "module": "Mathlib.Order.FixedPoints", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.map_gfp", "kind": "theorem", "module": "Mathlib.Order.FixedPoints", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.map_le_gfp", "kind": "theorem", "module": "Mathlib.Order.FixedPoints", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.gfp_le_map", "kind": "theorem", "module": "Mathlib.Order.FixedPoints", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.isGreatest_gfp_le", "kind": "theorem", "module": "Mathlib.Order.FixedPoints", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.isGreatest_gfp", "kind": "theorem", "module": "Mathlib.Order.FixedPoints", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.gfp_induction", "kind": "theorem", "module": "Mathlib.Order.FixedPoints", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.lfp_le_gfp", "kind": "theorem", "module": "Mathlib.Order.FixedPoints", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.map_lfp_comp", "kind": "theorem", "module": "Mathlib.Order.FixedPoints", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.map_gfp_comp", "kind": "theorem", "module": "Mathlib.Order.FixedPoints", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.lfp_lfp", "kind": "theorem", "module": "Mathlib.Order.FixedPoints", "is_tactic_proof": true, "tactics": ["let", "refine", "exact", "have", "calc", "h"], "tactic_count": 6}
{"name": "OrderHom.gfp_gfp", "kind": "theorem", "module": "Mathlib.Order.FixedPoints", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.gfp_const_inf_le", "kind": "theorem", "module": "Mathlib.Order.FixedPoints", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.prevFixed", "kind": "definition", "module": "Mathlib.Order.FixedPoints", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.nextFixed", "kind": "definition", "module": "Mathlib.Order.FixedPoints", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.prevFixed_le", "kind": "theorem", "module": "Mathlib.Order.FixedPoints", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.le_nextFixed", "kind": "theorem", "module": "Mathlib.Order.FixedPoints", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.nextFixed_le", "kind": "theorem", "module": "Mathlib.Order.FixedPoints", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.nextFixed_le_iff", "kind": "theorem", "module": "Mathlib.Order.FixedPoints", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.le_prevFixed_iff", "kind": "theorem", "module": "Mathlib.Order.FixedPoints", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.le_prevFixed", "kind": "theorem", "module": "Mathlib.Order.FixedPoints", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.le_map_sup_fixedPoints", "kind": "theorem", "module": "Mathlib.Order.FixedPoints", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.map_inf_fixedPoints_le", "kind": "theorem", "module": "Mathlib.Order.FixedPoints", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.le_map_sSup_subset_fixedPoints", "kind": "theorem", "module": "Mathlib.Order.FixedPoints", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.map_sInf_subset_fixedPoints_le", "kind": "theorem", "module": "Mathlib.Order.FixedPoints", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fixedPoints.instBoundedOrderElemFixedPointsCoeOrderHom", "kind": "instance", "module": "Mathlib.Order.FixedPoints", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fixedPoints.instSemilatticeSupElemFixedPointsCoeOrderHom", "kind": "instance", "module": "Mathlib.Order.FixedPoints", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fixedPoints.instSemilatticeInfElemFixedPointsCoeOrderHom", "kind": "instance", "module": "Mathlib.Order.FixedPoints", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fixedPoints.completeLattice", "kind": "instance", "module": "Mathlib.Order.FixedPoints", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fixedPoints.lfp_eq_sSup_iterate", "kind": "theorem", "module": "Mathlib.Order.FixedPoints", "is_tactic_proof": true, "tactics": ["apply", "apply", "exact", "apply", "intro", "exact"], "tactic_count": 6}
{"name": "fixedPoints.gfp_eq_sInf_iterate", "kind": "theorem", "module": "Mathlib.Order.FixedPoints", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisConnection.upperBounds_l_image", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisConnection.lowerBounds_u_image", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisConnection.bddAbove_l_image", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisConnection.bddBelow_u_image", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisConnection.isLUB_l_image", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisConnection.isGLB_u_image", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisConnection.isLeast_l", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisConnection.isGreatest_u", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisConnection.isGLB_l", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisConnection.isLUB_u", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisConnection.l_sup", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisConnection.u_inf", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisConnection.l_iSup", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisConnection.l_iSup₂", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "GaloisConnection.u_iInf", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisConnection.u_iInf₂", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisConnection.l_sSup", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "GaloisConnection.u_sInf", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisConnection.compl", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "gc_sSup_Iic", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "gc_Ici_sInf", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLUB_image2_of_isLUB_isLUB", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "simp_rw"], "tactic_count": 2}
{"name": "isLUB_image2_of_isLUB_isGLB", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLUB_image2_of_isGLB_isLUB", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLUB_image2_of_isGLB_isGLB", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isGLB_image2_of_isGLB_isGLB", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isGLB_image2_of_isGLB_isLUB", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isGLB_image2_of_isLUB_isGLB", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isGLB_image2_of_isLUB_isLUB", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sSup_image2_eq_sSup_sSup", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sSup_image2_eq_sSup_sInf", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sSup_image2_eq_sInf_sSup", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sSup_image2_eq_sInf_sInf", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sInf_image2_eq_sInf_sInf", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sInf_image2_eq_sInf_sSup", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sInf_image2_eq_sSup_sInf", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sInf_image2_eq_sSup_sSup", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.to_galoisConnection", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.toGaloisInsertion", "kind": "definition", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.toGaloisCoinsertion", "kind": "definition", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.bddAbove_image", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.bddBelow_image", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.bddAbove_preimage", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "OrderIso.bddBelow_preimage", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.galoisConnection_mul_div", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisInsertion.l_sup_u", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisInsertion.l_iSup_u", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisInsertion.l_biSup_u", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "GaloisInsertion.l_sSup_u_image", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "GaloisInsertion.l_inf_u", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisInsertion.l_iInf_u", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisInsertion.l_biInf_u", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "GaloisInsertion.l_sInf_u_image", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "GaloisInsertion.l_iInf_of_ul_eq_self", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisInsertion.l_biInf_of_ul_eq_self", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "GaloisInsertion.isLUB_of_u_image", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisInsertion.isGLB_of_u_image", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisInsertion.liftSemilatticeSup", "kind": "abbrev", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisInsertion.liftSemilatticeInf", "kind": "abbrev", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisInsertion.liftLattice", "kind": "abbrev", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisInsertion.liftOrderTop", "kind": "abbrev", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisInsertion.liftBoundedOrder", "kind": "abbrev", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisInsertion.liftCompleteLattice", "kind": "abbrev", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisCoinsertion.u_inf_l", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisCoinsertion.u_iInf_l", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisCoinsertion.u_sInf_l_image", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisCoinsertion.u_sup_l", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisCoinsertion.u_iSup_l", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisCoinsertion.u_biSup_l", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisCoinsertion.u_sSup_l_image", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisCoinsertion.u_iSup_of_lu_eq_self", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisCoinsertion.u_biSup_of_lu_eq_self", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisCoinsertion.isGLB_of_l_image", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisCoinsertion.isLUB_of_l_image", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisCoinsertion.liftSemilatticeInf", "kind": "abbrev", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisCoinsertion.liftSemilatticeSup", "kind": "abbrev", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisCoinsertion.liftLattice", "kind": "abbrev", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisCoinsertion.liftOrderBot", "kind": "abbrev", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisCoinsertion.liftBoundedOrder", "kind": "abbrev", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisCoinsertion.liftCompleteLattice", "kind": "abbrev", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "gi_sSup_Iic", "kind": "definition", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "gci_Ici_sInf", "kind": "definition", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.giUnbotDBot", "kind": "definition", "module": "Mathlib.Order.GaloisConnection.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisConnection", "kind": "definition", "module": "Mathlib.Order.GaloisConnection.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisConnection.monotone_intro", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisConnection.dual", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisConnection.le_iff_le", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisConnection.l_le", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisConnection.le_u", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisConnection.le_u_l", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisConnection.l_u_le", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisConnection.monotone_u", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisConnection.monotone_l", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisConnection.le_u_l_trans", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisConnection.l_u_le_trans", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisConnection.u_l_u_eq_u", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisConnection.u_l_u_eq_u'", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisConnection.u_unique", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisConnection.exists_eq_u", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisConnection.u_eq", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Defs", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "exact", "intro", "exact"], "tactic_count": 5}
{"name": "GaloisConnection.l_u_l_eq_l", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisConnection.l_u_l_eq_l'", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisConnection.l_unique", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisConnection.exists_eq_l", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisConnection.l_eq", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisConnection.u_eq_top", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisConnection.u_top", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisConnection.u_l_top", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisConnection.l_eq_bot", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisConnection.l_bot", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisConnection.l_u_bot", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisConnection.lt_iff_lt", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisConnection.id", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisConnection.compose", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisConnection.dfun", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisConnection.l_comm_of_u_comm", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisConnection.u_comm_of_l_comm", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisConnection.l_comm_iff_u_comm", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisInsertion.monotoneIntro", "kind": "definition", "module": "Mathlib.Order.GaloisConnection.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisConnection.toGaloisInsertion", "kind": "definition", "module": "Mathlib.Order.GaloisConnection.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisConnection.liftOrderBot", "kind": "definition", "module": "Mathlib.Order.GaloisConnection.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisInsertion.l_u_eq", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisInsertion.leftInverse_l_u", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisInsertion.l_top", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisInsertion.l_surjective", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisInsertion.u_injective", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisInsertion.u_le_u_iff", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisInsertion.strictMono_u", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisCoinsertion.dual", "kind": "definition", "module": "Mathlib.Order.GaloisConnection.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisInsertion.dual", "kind": "definition", "module": "Mathlib.Order.GaloisConnection.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisCoinsertion.ofDual", "kind": "definition", "module": "Mathlib.Order.GaloisConnection.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisInsertion.ofDual", "kind": "definition", "module": "Mathlib.Order.GaloisConnection.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisCoinsertion.monotoneIntro", "kind": "definition", "module": "Mathlib.Order.GaloisConnection.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisConnection.toGaloisCoinsertion", "kind": "definition", "module": "Mathlib.Order.GaloisConnection.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisConnection.liftOrderTop", "kind": "definition", "module": "Mathlib.Order.GaloisConnection.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisCoinsertion.u_l_eq", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisCoinsertion.u_l_leftInverse", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisCoinsertion.u_bot", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisCoinsertion.u_surjective", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisCoinsertion.l_injective", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisCoinsertion.l_le_l_iff", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisCoinsertion.strictMono_l", "kind": "theorem", "module": "Mathlib.Order.GaloisConnection.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.GameAdd", "kind": "inductive", "module": "Mathlib.Order.GameAdd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.gameAdd_iff", "kind": "theorem", "module": "Mathlib.Order.GameAdd", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "exacts", "revert", "rintro", "exacts"], "tactic_count": 6}
{"name": "Prod.gameAdd_mk_iff", "kind": "theorem", "module": "Mathlib.Order.GameAdd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.gameAdd_swap_swap", "kind": "theorem", "module": "Mathlib.Order.GameAdd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.gameAdd_swap_swap_mk", "kind": "theorem", "module": "Mathlib.Order.GameAdd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.gameAdd_le_lex", "kind": "theorem", "module": "Mathlib.Order.GameAdd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.rprod_le_transGen_gameAdd", "kind": "theorem", "module": "Mathlib.Order.GameAdd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Acc.prod_gameAdd", "kind": "theorem", "module": "Mathlib.Order.GameAdd", "is_tactic_proof": false, "tactics": ["induction", "induction", "refine", "rintro", "exacts"], "tactic_count": 5}
{"name": "WellFounded.prod_gameAdd", "kind": "theorem", "module": "Mathlib.Order.GameAdd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.GameAdd.fix", "kind": "definition", "module": "Mathlib.Order.GameAdd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.GameAdd.fix_eq", "kind": "theorem", "module": "Mathlib.Order.GameAdd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.GameAdd.induction", "kind": "theorem", "module": "Mathlib.Order.GameAdd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.GameAdd", "kind": "definition", "module": "Mathlib.Order.GameAdd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.gameAdd_iff", "kind": "theorem", "module": "Mathlib.Order.GameAdd", "is_tactic_proof": true, "tactics": ["rintro", "rfl"], "tactic_count": 2}
{"name": "Sym2.gameAdd_mk'_iff", "kind": "theorem", "module": "Mathlib.Order.GameAdd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.GameAdd.to_sym2", "kind": "theorem", "module": "Mathlib.Order.GameAdd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.GameAdd.fst", "kind": "theorem", "module": "Mathlib.Order.GameAdd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.GameAdd.snd", "kind": "theorem", "module": "Mathlib.Order.GameAdd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.GameAdd.fst_snd", "kind": "theorem", "module": "Mathlib.Order.GameAdd", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Sym2.GameAdd.snd_fst", "kind": "theorem", "module": "Mathlib.Order.GameAdd", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Acc.sym2_gameAdd", "kind": "theorem", "module": "Mathlib.Order.GameAdd", "is_tactic_proof": false, "tactics": ["induction", "induction", "refine", "induction", "rw", "dsimp", "rintro", "exact", "exact", "rw", "exact", "rw", "exact"], "tactic_count": 13}
{"name": "WellFounded.sym2_gameAdd", "kind": "theorem", "module": "Mathlib.Order.GameAdd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.GameAdd.fix", "kind": "definition", "module": "Mathlib.Order.GameAdd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.GameAdd.fix_eq", "kind": "theorem", "module": "Mathlib.Order.GameAdd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sym2.GameAdd.induction", "kind": "theorem", "module": "Mathlib.Order.GameAdd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "grade", "kind": "definition", "module": "Mathlib.Order.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CovBy.grade", "kind": "theorem", "module": "Mathlib.Order.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "grade_strictMono", "kind": "theorem", "module": "Mathlib.Order.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "covBy_iff_lt_covBy_grade", "kind": "theorem", "module": "Mathlib.Order.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMin.grade", "kind": "theorem", "module": "Mathlib.Order.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isMin_grade_iff", "kind": "theorem", "module": "Mathlib.Order.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMax.grade", "kind": "theorem", "module": "Mathlib.Order.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isMax_grade_iff", "kind": "theorem", "module": "Mathlib.Order.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "grade_mono", "kind": "theorem", "module": "Mathlib.Order.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "grade_injective", "kind": "theorem", "module": "Mathlib.Order.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "grade_le_grade_iff", "kind": "theorem", "module": "Mathlib.Order.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "grade_lt_grade_iff", "kind": "theorem", "module": "Mathlib.Order.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "grade_eq_grade_iff", "kind": "theorem", "module": "Mathlib.Order.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "grade_ne_grade_iff", "kind": "theorem", "module": "Mathlib.Order.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "grade_covBy_grade_iff", "kind": "theorem", "module": "Mathlib.Order.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "grade_bot", "kind": "theorem", "module": "Mathlib.Order.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "grade_top", "kind": "theorem", "module": "Mathlib.Order.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Preorder.toGradeBoundedOrder", "kind": "instance", "module": "Mathlib.Order.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "grade_self", "kind": "theorem", "module": "Mathlib.Order.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.gradeOrder", "kind": "instance", "module": "Mathlib.Order.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.gradeMinOrder", "kind": "instance", "module": "Mathlib.Order.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.gradeMaxOrder", "kind": "instance", "module": "Mathlib.Order.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instGradeBoundedOrderOrderDual", "kind": "instance", "module": "Mathlib.Order.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "grade_toDual", "kind": "theorem", "module": "Mathlib.Order.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "grade_ofDual", "kind": "theorem", "module": "Mathlib.Order.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GradeOrder.liftLeft", "kind": "abbrev", "module": "Mathlib.Order.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GradeMinOrder.liftLeft", "kind": "abbrev", "module": "Mathlib.Order.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GradeMaxOrder.liftLeft", "kind": "abbrev", "module": "Mathlib.Order.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GradeBoundedOrder.liftLeft", "kind": "abbrev", "module": "Mathlib.Order.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GradeOrder.liftRight", "kind": "abbrev", "module": "Mathlib.Order.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GradeMinOrder.liftRight", "kind": "abbrev", "module": "Mathlib.Order.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GradeMaxOrder.liftRight", "kind": "abbrev", "module": "Mathlib.Order.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GradeBoundedOrder.liftRight", "kind": "abbrev", "module": "Mathlib.Order.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GradeOrder.finToNat", "kind": "abbrev", "module": "Mathlib.Order.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GradeMinOrder.finToNat", "kind": "abbrev", "module": "Mathlib.Order.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GradeOrder.natToInt", "kind": "instance", "module": "Mathlib.Order.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GradeOrder.wellFoundedLT", "kind": "theorem", "module": "Mathlib.Order.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GradeOrder.wellFoundedGT", "kind": "theorem", "module": "Mathlib.Order.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instWellFoundedLTOfGradeOrderNat", "kind": "instance", "module": "Mathlib.Order.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instWellFoundedGTOfGradeOrderOrderDualNat", "kind": "instance", "module": "Mathlib.Order.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Flag.coe_wcovBy_coe", "kind": "theorem", "module": "Mathlib.Order.Grade", "is_tactic_proof": false, "tactics": ["refine", "and_congr_right", "classical", "obtain", "exact", "obtain", "exact", "cases"], "tactic_count": 8}
{"name": "Flag.coe_covBy_coe", "kind": "theorem", "module": "Mathlib.Order.Grade", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Flag.isMax_coe", "kind": "theorem", "module": "Mathlib.Order.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Flag.isMin_coe", "kind": "theorem", "module": "Mathlib.Order.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Flag.instGradeOrderSubtypeMem", "kind": "instance", "module": "Mathlib.Order.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Flag.instGradeMinOrderSubtypeMem", "kind": "instance", "module": "Mathlib.Order.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Flag.instGradeMaxOrderSubtypeMem", "kind": "instance", "module": "Mathlib.Order.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Flag.instGradeBoundedOrderSubtypeMem", "kind": "instance", "module": "Mathlib.Order.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Flag.grade_coe", "kind": "theorem", "module": "Mathlib.Order.Grade", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.chainHeight", "kind": "definition", "module": "Mathlib.Order.Height", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.chainHeight_eq_iSup", "kind": "theorem", "module": "Mathlib.Order.Height", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.chainHeight_le_encard", "kind": "theorem", "module": "Mathlib.Order.Height", "is_tactic_proof": true, "tactics": ["simp_all"], "tactic_count": 1}
{"name": "Set.chainHeight_ne_top_of_finite", "kind": "theorem", "module": "Mathlib.Order.Height", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.exists_isChain_of_le_chainHeight", "kind": "theorem", "module": "Mathlib.Order.Height", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "obtain", "contrapose", "refine", "exact_mod_cast", "obtain", "exact"], "tactic_count": 8}
{"name": "Set.exists_eq_chainHeight_of_chainHeight_ne_top", "kind": "theorem", "module": "Mathlib.Order.Height", "is_tactic_proof": true, "tactics": ["have", "obtain", "exact"], "tactic_count": 3}
{"name": "Set.exists_eq_chainHeight_of_finite", "kind": "theorem", "module": "Mathlib.Order.Height", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.encard_le_chainHeight_of_isChain", "kind": "theorem", "module": "Mathlib.Order.Height", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.encard_eq_chainHeight_of_isChain", "kind": "theorem", "module": "Mathlib.Order.Height", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.finite_of_chainHeight_ne_top", "kind": "theorem", "module": "Mathlib.Order.Height", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.not_isChain_of_chainHeight_lt_encard", "kind": "theorem", "module": "Mathlib.Order.Height", "is_tactic_proof": true, "tactics": ["by_contra", "grw", "exact"], "tactic_count": 3}
{"name": "Set.chainHeight_eq_top_iff", "kind": "theorem", "module": "Mathlib.Order.Height", "is_tactic_proof": true, "tactics": ["refine", "contrapose", "obtain", "refine", "rw", "exact"], "tactic_count": 6}
{"name": "Set.chainHeight_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Order.Height", "is_tactic_proof": true, "tactics": ["refine", "simp", "ext", "simpa", "simp_all"], "tactic_count": 5}
{"name": "Set.chainHeight_empty", "kind": "theorem", "module": "Mathlib.Order.Height", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.one_le_chainHeight_iff", "kind": "theorem", "module": "Mathlib.Order.Height", "is_tactic_proof": true, "tactics": ["constructor", "all_goals", "intros", "by_contra", "simp_all"], "tactic_count": 5}
{"name": "Set.chainHeight_of_isEmpty", "kind": "theorem", "module": "Mathlib.Order.Height", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.chainHeight_mono", "kind": "theorem", "module": "Mathlib.Order.Height", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact"], "tactic_count": 3}
{"name": "Set.chainHeight_flip", "kind": "theorem", "module": "Mathlib.Order.Height", "is_tactic_proof": true, "tactics": ["refine", "all_goals", "obtain", "exact", "ha₂", "simpa"], "tactic_count": 6}
{"name": "Set.chainHeight_eq_of_relEmbedding", "kind": "theorem", "module": "Mathlib.Order.Height", "is_tactic_proof": true, "tactics": ["refine", "obtain", "rw", "exact", "obtain", "rw", "exact"], "tactic_count": 7}
{"name": "Set.chainHeight_eq_of_relIso", "kind": "theorem", "module": "Mathlib.Order.Height", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.chainHeight_coe_univ", "kind": "theorem", "module": "Mathlib.Order.Height", "is_tactic_proof": true, "tactics": ["have", "have", "simpa"], "tactic_count": 3}
{"name": "Set.chainHeight_coe_univ_le", "kind": "theorem", "module": "Mathlib.Order.Height", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.chainHeight_coe_univ_lt", "kind": "theorem", "module": "Mathlib.Order.Height", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Prod.instHImp", "kind": "instance", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instHNot", "kind": "instance", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instSDiff", "kind": "instance", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instCompl", "kind": "instance", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fst_himp", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "snd_himp", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fst_hnot", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "snd_hnot", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fst_sdiff", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "snd_sdiff", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fst_compl", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "snd_compl", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instHImpForall", "kind": "instance", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instHNotForall", "kind": "instance", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.himp_def", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.hnot_def", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.himp_apply", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.hnot_apply", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HeytingAlgebra.toBoundedOrder", "kind": "instance", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoheytingAlgebra.toBoundedOrder", "kind": "instance", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BiheytingAlgebra.toCoheytingAlgebra", "kind": "instance", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HeytingAlgebra.ofHImp", "kind": "abbrev", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HeytingAlgebra.ofCompl", "kind": "abbrev", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoheytingAlgebra.ofSDiff", "kind": "abbrev", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoheytingAlgebra.ofHNot", "kind": "abbrev", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_himp_iff", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_himp_iff'", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "le_himp_comm", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "le_himp", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_himp_iff_left", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "himp_self", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "himp_inf_le", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inf_himp_le", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "inf_himp", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "himp_inf_self", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "himp_eq_top_iff", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "himp_top", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "top_himp", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "himp_himp", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "himp_le_himp_himp_himp", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "himp_inf_himp_inf_le", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "himp_left_comm", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "himp_idem", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "himp_inf_distrib", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sup_himp_distrib", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "himp_le_himp_left", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "himp_le_himp_right", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "himp_le_himp", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sup_himp_self_left", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "sup_himp_self_right", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Codisjoint.himp_eq_right", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": true, "tactics": ["conv_rhs", "rw"], "tactic_count": 2}
{"name": "Codisjoint.himp_eq_left", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Codisjoint.himp_inf_cancel_right", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Codisjoint.himp_inf_cancel_left", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Codisjoint.himp_le_of_right_le", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_himp_himp", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "himp_eq_himp_iff", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "himp_ne_himp_iff", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "himp_triangle", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "himp_inf_himp_cancel", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "gc_inf_himp", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GeneralizedHeytingAlgebra.toDistribLattice", "kind": "instance", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instGeneralizedCoheytingAlgebra", "kind": "instance", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instGeneralizedHeytingAlgebra", "kind": "instance", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instGeneralizedHeytingAlgebra", "kind": "instance", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sdiff_le_iff", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sdiff_le_iff'", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "sdiff_le_comm", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "sdiff_le", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Disjoint.disjoint_sdiff_left", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Disjoint.disjoint_sdiff_right", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sdiff_le_iff_left", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "sdiff_self", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_sup_sdiff", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_sdiff_sup", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "sup_sdiff_left", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sup_sdiff_right", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inf_sdiff_left", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inf_sdiff_right", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sup_sdiff_self", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sdiff_sup_self", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "sup_sdiff_eq_sup", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sup_sdiff_cancel'", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "sup_sdiff_cancel_right", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sdiff_sup_cancel", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "sup_le_of_le_sdiff_left", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sup_le_of_le_sdiff_right", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sdiff_eq_bot_iff", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "sdiff_bot", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bot_sdiff", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sdiff_sdiff_sdiff_le_sdiff", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "le_sup_sdiff_sup_sdiff", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "sdiff_sdiff", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sdiff_sdiff_left", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sdiff_right_comm", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "sdiff_sdiff_comm", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sdiff_idem", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "sdiff_sdiff_self", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "sup_sdiff_distrib", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sdiff_inf_distrib", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sup_sdiff", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sup_sdiff_right_self", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "sup_sdiff_left_self", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "sdiff_le_sdiff_right", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sdiff_le_sdiff_left", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sdiff_le_sdiff", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sdiff_inf", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sdiff_inf_self_left", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "sdiff_inf_self_right", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Disjoint.sdiff_eq_left", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": true, "tactics": ["conv_rhs", "rw"], "tactic_count": 2}
{"name": "Disjoint.sdiff_eq_right", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Disjoint.sup_sdiff_cancel_left", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Disjoint.sup_sdiff_cancel_right", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Disjoint.le_sdiff_of_le_left", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sdiff_sdiff_le", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sdiff_eq_sdiff_iff", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "sdiff_ne_sdiff_iff", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sdiff_triangle", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "sdiff_sup_sdiff_cancel", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sdiff_sup_sdiff_cancel'", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "sdiff_le_sdiff_of_sup_le_sup_left", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "sdiff_le_sdiff_of_sup_le_sup_right", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "inf_sdiff_sup_left", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inf_sdiff_sup_right", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "gc_sdiff_sup", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GeneralizedCoheytingAlgebra.toDistribLattice", "kind": "instance", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instGeneralizedHeytingAlgebra", "kind": "instance", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instGeneralizedCoheytingAlgebra", "kind": "instance", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instGeneralizedCoheytingAlgebra", "kind": "instance", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "himp_bot", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bot_himp", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "compl_sup_distrib", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "compl_sup", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "compl_le_himp", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "compl_sup_le_himp", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sup_compl_le_himp", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "himp_compl", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "himp_compl_comm", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "le_compl_iff_disjoint_right", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "le_compl_iff_disjoint_left", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_compl_comm", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "disjoint_compl_left", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "disjoint_compl_right", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LE.le.disjoint_compl_left", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LE.le.disjoint_compl_right", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompl.compl_eq", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompl.eq_compl", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "compl_unique", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inf_compl_self", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "compl_inf_self", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inf_compl_eq_bot", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "compl_inf_eq_bot", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "compl_top", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "compl_bot", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "le_compl_self", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ne_compl_self", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": true, "tactics": ["intro", "cases", "simp"], "tactic_count": 3}
{"name": "compl_ne_self", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lt_compl_self", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "le_compl_compl", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "compl_anti", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "compl_le_compl", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "compl_compl_compl", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "disjoint_compl_compl_left_iff", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "disjoint_compl_compl_right_iff", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "compl_sup_compl_le", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "compl_compl_inf_distrib", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "disjoint_compl_compl_left_iff,", "exact"], "tactic_count": 4}
{"name": "compl_compl_himp_distrib", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": true, "tactics": ["apply", "rw", "exact", "refine", "rw", "exact"], "tactic_count": 6}
{"name": "OrderDual.instCoheytingAlgebra", "kind": "instance", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofDual_hnot", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toDual_compl", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instHeytingAlgebra", "kind": "instance", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instHeytingAlgebra", "kind": "instance", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "top_sdiff'", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sdiff_top", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hnot_inf_distrib", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "sdiff_le_hnot", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sdiff_le_inf_hnot", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoheytingAlgebra.toDistribLattice", "kind": "instance", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hnot_sdiff", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "hnot_sdiff_comm", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "hnot_le_iff_codisjoint_right", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "hnot_le_iff_codisjoint_left", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hnot_le_comm", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "codisjoint_hnot_right", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "codisjoint_hnot_left", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LE.le.codisjoint_hnot_left", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LE.le.codisjoint_hnot_right", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompl.hnot_eq", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompl.eq_hnot", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sup_hnot_self", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hnot_sup_self", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hnot_bot", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hnot_top", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "hnot_hnot_le", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hnot_anti", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hnot_le_hnot", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hnot_hnot_hnot", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "codisjoint_hnot_hnot_left_iff", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "codisjoint_hnot_hnot_right_iff", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "le_hnot_inf_hnot", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hnot_hnot_sup_distrib", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "codisjoint_hnot_hnot_left_iff,", "exact"], "tactic_count": 4}
{"name": "hnot_hnot_sdiff_distrib", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": true, "tactics": ["apply", "refine", "rw", "exact", "rw", "exact"], "tactic_count": 6}
{"name": "OrderDual.instHeytingAlgebra", "kind": "instance", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofDual_compl", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofDual_himp", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toDual_hnot", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toDual_sdiff", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instCoheytingAlgebra", "kind": "instance", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instCoheytingAlgebra", "kind": "instance", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "compl_le_hnot", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prop.instHeytingAlgebra", "kind": "instance", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "himp_iff_imp", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "compl_iff_not", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearOrder.toBiheytingAlgebra", "kind": "abbrev", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instBiheytingAlgebra", "kind": "instance", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instBiheytingAlgebra", "kind": "instance", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instBiheytingAlgebra", "kind": "instance", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.generalizedHeytingAlgebra", "kind": "abbrev", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.generalizedCoheytingAlgebra", "kind": "abbrev", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.heytingAlgebra", "kind": "abbrev", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.coheytingAlgebra", "kind": "abbrev", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.biheytingAlgebra", "kind": "abbrev", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PUnit.instBiheytingAlgebra", "kind": "instance", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PUnit.top_eq", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PUnit.bot_eq", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PUnit.sup_eq", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PUnit.inf_eq", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PUnit.compl_eq", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PUnit.sdiff_eq", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PUnit.hnot_eq", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PUnit.himp_eq", "kind": "theorem", "module": "Mathlib.Order.Heyting.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Coheyting.boundary", "kind": "definition", "module": "Mathlib.Order.Heyting.Boundary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Heyting.term∂_", "kind": "definition", "module": "Mathlib.Order.Heyting.Boundary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Heyting._aux_Mathlib_Order_Heyting_Boundary___macroRules_Heyting_term∂__1", "kind": "definition", "module": "Mathlib.Order.Heyting.Boundary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Heyting._aux_Mathlib_Order_Heyting_Boundary___unexpand_Coheyting_boundary_1", "kind": "definition", "module": "Mathlib.Order.Heyting.Boundary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Coheyting.inf_hnot_self", "kind": "theorem", "module": "Mathlib.Order.Heyting.Boundary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Coheyting.boundary_le", "kind": "theorem", "module": "Mathlib.Order.Heyting.Boundary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Coheyting.boundary_le_hnot", "kind": "theorem", "module": "Mathlib.Order.Heyting.Boundary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Coheyting.boundary_bot", "kind": "theorem", "module": "Mathlib.Order.Heyting.Boundary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Coheyting.boundary_top", "kind": "theorem", "module": "Mathlib.Order.Heyting.Boundary", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Coheyting.boundary_hnot_le", "kind": "theorem", "module": "Mathlib.Order.Heyting.Boundary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Coheyting.boundary_hnot_hnot", "kind": "theorem", "module": "Mathlib.Order.Heyting.Boundary", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Coheyting.hnot_boundary", "kind": "theorem", "module": "Mathlib.Order.Heyting.Boundary", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Coheyting.boundary_inf", "kind": "theorem", "module": "Mathlib.Order.Heyting.Boundary", "is_tactic_proof": true, "tactics": ["unfold", "rw"], "tactic_count": 2}
{"name": "Coheyting.boundary_inf_le", "kind": "theorem", "module": "Mathlib.Order.Heyting.Boundary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Coheyting.boundary_sup_le", "kind": "theorem", "module": "Mathlib.Order.Heyting.Boundary", "is_tactic_proof": true, "tactics": ["rw", "exact", "sup_le_sup", "proof", "logic", "intuitionistic."], "tactic_count": 6}
{"name": "Coheyting._example", "kind": "example", "module": "Mathlib.Order.Heyting.Boundary", "is_tactic_proof": true, "tactics": ["rintro", "exact", "exact"], "tactic_count": 3}
{"name": "Coheyting.boundary_le_boundary_sup_sup_boundary_inf_left", "kind": "theorem", "module": "Mathlib.Order.Heyting.Boundary", "is_tactic_proof": true, "tactics": ["simp", "refine", "try", "refine", "rw", "exact", "refine", "rw", "exact"], "tactic_count": 9}
{"name": "Coheyting.boundary_le_boundary_sup_sup_boundary_inf_right", "kind": "theorem", "module": "Mathlib.Order.Heyting.Boundary", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Coheyting.boundary_sup_sup_boundary_inf", "kind": "theorem", "module": "Mathlib.Order.Heyting.Boundary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Coheyting.boundary_idem", "kind": "theorem", "module": "Mathlib.Order.Heyting.Boundary", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Coheyting.hnot_hnot_sup_boundary", "kind": "theorem", "module": "Mathlib.Order.Heyting.Boundary", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Coheyting.hnot_eq_top_iff_exists_boundary", "kind": "theorem", "module": "Mathlib.Order.Heyting.Boundary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Coheyting.boundary_eq_bot", "kind": "theorem", "module": "Mathlib.Order.Heyting.Boundary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HeytingHomClass.toBoundedLatticeHomClass", "kind": "instance", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoheytingHomClass.toBoundedLatticeHomClass", "kind": "instance", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BiheytingHomClass.toHeytingHomClass", "kind": "instance", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BiheytingHomClass.toCoheytingHomClass", "kind": "instance", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIsoClass.toHeytingHomClass", "kind": "instance", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIsoClass.toCoheytingHomClass", "kind": "instance", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIsoClass.toBiheytingHomClass", "kind": "instance", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedLatticeHomClass.toBiheytingHomClass", "kind": "instance", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "map_compl", "kind": "theorem", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "map_bihimp", "kind": "theorem", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "map_hnot", "kind": "theorem", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "map_symmDiff", "kind": "theorem", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "instCoeTCHeytingHomOfHeytingHomClass", "kind": "instance", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCoeTCCoheytingHomOfCoheytingHomClass", "kind": "instance", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCoeTCBiheytingHomOfBiheytingHomClass", "kind": "instance", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HeytingHom.instFunLike", "kind": "instance", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HeytingHom.instHeytingHomClass", "kind": "instance", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HeytingHom.toFun_eq_coe", "kind": "theorem", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HeytingHom.toFun_eq_coe_aux", "kind": "theorem", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HeytingHom.ext", "kind": "theorem", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HeytingHom.copy", "kind": "definition", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HeytingHom.coe_copy", "kind": "theorem", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HeytingHom.copy_eq", "kind": "theorem", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HeytingHom.id", "kind": "definition", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HeytingHom.coe_id", "kind": "theorem", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HeytingHom.id_apply", "kind": "theorem", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HeytingHom.instInhabited", "kind": "instance", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HeytingHom.instPartialOrder", "kind": "instance", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HeytingHom.comp", "kind": "definition", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HeytingHom.coe_comp", "kind": "theorem", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HeytingHom.comp_apply", "kind": "theorem", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HeytingHom.comp_assoc", "kind": "theorem", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HeytingHom.comp_id", "kind": "theorem", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HeytingHom.id_comp", "kind": "theorem", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HeytingHom.cancel_right", "kind": "theorem", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HeytingHom.cancel_left", "kind": "theorem", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoheytingHom.instFunLike", "kind": "instance", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoheytingHom.instCoheytingHomClass", "kind": "instance", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoheytingHom.toFun_eq_coe", "kind": "theorem", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoheytingHom.toFun_eq_coe_aux", "kind": "theorem", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoheytingHom.ext", "kind": "theorem", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoheytingHom.copy", "kind": "definition", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoheytingHom.coe_copy", "kind": "theorem", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoheytingHom.copy_eq", "kind": "theorem", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoheytingHom.id", "kind": "definition", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoheytingHom.coe_id", "kind": "theorem", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoheytingHom.id_apply", "kind": "theorem", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoheytingHom.instInhabited", "kind": "instance", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoheytingHom.instPartialOrder", "kind": "instance", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoheytingHom.comp", "kind": "definition", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoheytingHom.coe_comp", "kind": "theorem", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoheytingHom.comp_apply", "kind": "theorem", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoheytingHom.comp_assoc", "kind": "theorem", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoheytingHom.comp_id", "kind": "theorem", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoheytingHom.id_comp", "kind": "theorem", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoheytingHom.cancel_right", "kind": "theorem", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoheytingHom.cancel_left", "kind": "theorem", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BiheytingHom.instFunLike", "kind": "instance", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BiheytingHom.instBiheytingHomClass", "kind": "instance", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BiheytingHom.toFun_eq_coe", "kind": "theorem", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BiheytingHom.toFun_eq_coe_aux", "kind": "theorem", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BiheytingHom.ext", "kind": "theorem", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BiheytingHom.copy", "kind": "definition", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BiheytingHom.coe_copy", "kind": "theorem", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BiheytingHom.copy_eq", "kind": "theorem", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BiheytingHom.id", "kind": "definition", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BiheytingHom.coe_id", "kind": "theorem", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BiheytingHom.id_apply", "kind": "theorem", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BiheytingHom.instInhabited", "kind": "instance", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BiheytingHom.instPartialOrder", "kind": "instance", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BiheytingHom.comp", "kind": "definition", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BiheytingHom.coe_comp", "kind": "theorem", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BiheytingHom.comp_apply", "kind": "theorem", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BiheytingHom.comp_assoc", "kind": "theorem", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BiheytingHom.comp_id", "kind": "theorem", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BiheytingHom.id_comp", "kind": "theorem", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BiheytingHom.cancel_right", "kind": "theorem", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BiheytingHom.cancel_left", "kind": "theorem", "module": "Mathlib.Order.Heyting.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Heyting.IsRegular", "kind": "definition", "module": "Mathlib.Order.Heyting.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Heyting.IsRegular.eq", "kind": "theorem", "module": "Mathlib.Order.Heyting.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Heyting.IsRegular.decidablePred", "kind": "instance", "module": "Mathlib.Order.Heyting.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Heyting.isRegular_bot", "kind": "theorem", "module": "Mathlib.Order.Heyting.Regular", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Heyting.isRegular_top", "kind": "theorem", "module": "Mathlib.Order.Heyting.Regular", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Heyting.IsRegular.inf", "kind": "theorem", "module": "Mathlib.Order.Heyting.Regular", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Heyting.IsRegular.himp", "kind": "theorem", "module": "Mathlib.Order.Heyting.Regular", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Heyting.isRegular_compl", "kind": "theorem", "module": "Mathlib.Order.Heyting.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Heyting.IsRegular.disjoint_compl_left_iff", "kind": "theorem", "module": "Mathlib.Order.Heyting.Regular", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Heyting.IsRegular.disjoint_compl_right_iff", "kind": "theorem", "module": "Mathlib.Order.Heyting.Regular", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "BooleanAlgebra.ofRegular", "kind": "abbrev", "module": "Mathlib.Order.Heyting.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Heyting.Regular", "kind": "definition", "module": "Mathlib.Order.Heyting.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Heyting.Regular.val", "kind": "definition", "module": "Mathlib.Order.Heyting.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Heyting.Regular.prop", "kind": "theorem", "module": "Mathlib.Order.Heyting.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Heyting.Regular.instCoeOut", "kind": "instance", "module": "Mathlib.Order.Heyting.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Heyting.Regular.coe_injective", "kind": "theorem", "module": "Mathlib.Order.Heyting.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Heyting.Regular.coe_inj", "kind": "theorem", "module": "Mathlib.Order.Heyting.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Heyting.Regular.top", "kind": "instance", "module": "Mathlib.Order.Heyting.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Heyting.Regular.bot", "kind": "instance", "module": "Mathlib.Order.Heyting.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Heyting.Regular.inf", "kind": "instance", "module": "Mathlib.Order.Heyting.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Heyting.Regular.himp", "kind": "instance", "module": "Mathlib.Order.Heyting.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Heyting.Regular.instCompl", "kind": "instance", "module": "Mathlib.Order.Heyting.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Heyting.Regular.coe_top", "kind": "theorem", "module": "Mathlib.Order.Heyting.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Heyting.Regular.coe_bot", "kind": "theorem", "module": "Mathlib.Order.Heyting.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Heyting.Regular.coe_inf", "kind": "theorem", "module": "Mathlib.Order.Heyting.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Heyting.Regular.coe_himp", "kind": "theorem", "module": "Mathlib.Order.Heyting.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Heyting.Regular.coe_compl", "kind": "theorem", "module": "Mathlib.Order.Heyting.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Heyting.Regular.instInhabited", "kind": "instance", "module": "Mathlib.Order.Heyting.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Heyting.Regular.instSemilatticeInf", "kind": "instance", "module": "Mathlib.Order.Heyting.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Heyting.Regular.boundedOrder", "kind": "instance", "module": "Mathlib.Order.Heyting.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Heyting.Regular.coe_le_coe", "kind": "theorem", "module": "Mathlib.Order.Heyting.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Heyting.Regular.coe_lt_coe", "kind": "theorem", "module": "Mathlib.Order.Heyting.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Heyting.Regular.toRegular", "kind": "definition", "module": "Mathlib.Order.Heyting.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Heyting.Regular.coe_toRegular", "kind": "theorem", "module": "Mathlib.Order.Heyting.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Heyting.Regular.toRegular_coe", "kind": "theorem", "module": "Mathlib.Order.Heyting.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Heyting.Regular.gi", "kind": "definition", "module": "Mathlib.Order.Heyting.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Heyting.Regular.lattice", "kind": "instance", "module": "Mathlib.Order.Heyting.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Heyting.Regular.coe_sup", "kind": "theorem", "module": "Mathlib.Order.Heyting.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Heyting.Regular.instBooleanAlgebra", "kind": "instance", "module": "Mathlib.Order.Heyting.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Heyting.Regular.coe_sdiff", "kind": "theorem", "module": "Mathlib.Order.Heyting.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Heyting.isRegular_of_boolean", "kind": "theorem", "module": "Mathlib.Order.Heyting.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Heyting.isRegular_of_decidable", "kind": "theorem", "module": "Mathlib.Order.Heyting.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "term_→o_", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Order_Hom_Basic___macroRules_term_→o__1", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Order_Hom_Basic___unexpand_OrderHom_1", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderEmbedding", "kind": "abbrev", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "term_↪o_", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Order_Hom_Basic___macroRules_term_↪o__1", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Order_Hom_Basic___unexpand_OrderEmbedding_1", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso", "kind": "abbrev", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "term_≃o_", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Order_Hom_Basic___macroRules_term_≃o__1", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Order_Hom_Basic___unexpand_OrderIso_1", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFunLikeOrderEmbedding", "kind": "instance", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFunLikeOrderIso", "kind": "instance", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHomClass", "kind": "abbrev", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIsoClass.toOrderIso", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCoeTCOrderIsoOfOrderIsoClass", "kind": "instance", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIsoClass.toOrderHomClass", "kind": "instance", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHomClass.monotone", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHomClass.mono", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHomClass.toOrderHom", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHomClass.instCoeTCOrderHom", "kind": "instance", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "map_inv_le_iff", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": true, "tactics": ["convert", "exact"], "tactic_count": 2}
{"name": "map_inv_le_map_inv_iff", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "map_lt_map_iff", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "map_inv_lt_iff", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "map_inv_lt_map_inv_iff", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "OrderHom.instFunLike", "kind": "instance", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.instOrderHomClass", "kind": "instance", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.coe_mk", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.monotone", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.mono", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.Simps.coe", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.toFun_eq_coe", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.ext", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.coe_eq", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHomClass.coe_coe", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.canLift", "kind": "instance", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.copy", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.coe_copy", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.copy_eq", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.instDecidableEqOfForall", "kind": "instance", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.id", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.instInhabited", "kind": "instance", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.instPreorder", "kind": "instance", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.instPartialOrder", "kind": "instance", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.le_def", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.coe_le_coe", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.mk_le_mk", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.apply_mono", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.curry", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.curry_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.curry_symm_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.comp", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.comp_mono", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.mk_comp_mk", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.compₘ", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.comp_id", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "OrderHom.id_comp", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "OrderHom.const", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.const_comp", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.comp_const", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.prod", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.prod_mono", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.comp_prod_comp_same", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.prodₘ", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.diag", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.onDiag", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.fst", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.snd", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.fst_prod_snd", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "OrderHom.fst_comp_prod", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.snd_comp_prod", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.prodIso", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.prodMap", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.evalOrderHom", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.coeFnHom", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.apply", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.pi", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.piIso", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.Subtype.val", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.orderEmbedding", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.unique", "kind": "instance", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.orderHom_eq_id", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.dual", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.dual_id", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.dual_comp", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.symm_dual_id", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.symm_dual_comp", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.dualIso", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.uliftMap", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.uliftRightMap", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.uliftLeftMap", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.uliftLeftMap_uliftRightMap_eq", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.uliftRightMap_uliftLeftMap_eq", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHomClass.toOrderHomClassOrderDual", "kind": "instance", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelEmbedding.orderEmbeddingOfLTEmbedding", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelEmbedding.orderEmbeddingOfLTEmbedding_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderEmbedding.ltEmbedding", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderEmbedding.ltEmbedding_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderEmbedding.le_iff_le", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderEmbedding.lt_iff_lt", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderEmbedding.eq_iff_eq", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderEmbedding.monotone", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderEmbedding.strictMono", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderEmbedding.acc", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderEmbedding.wellFounded", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderEmbedding.isWellOrder", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderEmbedding.dual", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderEmbedding.wellFoundedLT", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderEmbedding.wellFoundedGT", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderEmbedding.ofMapLEIff", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderEmbedding.coe_ofMapLEIff", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderEmbedding.ofStrictMono", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderEmbedding.coe_ofStrictMono", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderEmbedding.subtype", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderEmbedding.subtype_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderEmbedding.subtype_injective", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderEmbedding.coe_subtype", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderEmbedding.toOrderHom", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderEmbedding.ofIsEmpty", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderEmbedding.coe_ofIsEmpty", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Disjoint.of_orderEmbedding", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": true, "tactics": ["intro", "rw", "calc", "f"], "tactic_count": 4}
{"name": "Codisjoint.of_orderEmbedding", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompl.of_orderEmbedding", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelHom.toOrderHom", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelEmbedding.toOrderHom_injective", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.instEquivLike", "kind": "instance", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.instOrderIsoClass", "kind": "instance", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.toFun_eq_coe", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.ext", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.toOrderEmbedding", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.coe_toOrderEmbedding", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.bijective", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.injective", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.surjective", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.apply_eq_iff_eq", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.refl", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.coe_refl", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.refl_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.refl_toEquiv", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.symm", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.symm_mk", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.apply_symm_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.symm_apply_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.symm_refl", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.apply_eq_iff_eq_symm_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.symm_apply_eq", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.symm_symm", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.symm_bijective", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.symm_injective", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.toEquiv_symm", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.coe_toEquiv", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.coe_symm_toEquiv", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.trans", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.coe_trans", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.trans_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.refl_trans", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "OrderIso.trans_refl", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "OrderIso.symm_trans_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.symm_trans", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.self_trans_symm", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.symm_trans_self", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.arrowCongr", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.conj", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.prodComm", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.prodAssoc", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.coe_prodComm", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.prodComm_symm", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.dualDual", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.coe_dualDual", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.coe_dualDual_symm", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.dualDual_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.dualDual_symm_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.le_iff_le", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.le_symm_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.symm_apply_le", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.monotone", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.strictMono", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.lt_iff_lt", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.lt_symm_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "OrderIso.symm_apply_lt", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "OrderIso.toRelIsoLT", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.toRelIsoLT_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.toRelIsoLT_symm", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.coe_toRelIsoLT", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.coe_symm_toRelIsoLT", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.ofRelIsoLT", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.ofRelIsoLT_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.ofRelIsoLT_symm", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.ofRelIsoLT_toRelIsoLT", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "OrderIso.toRelIsoLT_ofRelIsoLT", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "OrderIso.ofCmpEqCmp", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.ofHomInv", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.ofHomInv_symm_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.funUnique", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.funUnique_symm_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.ofUnique", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.ofIsEmpty", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.toOrderIso", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.coe_toOrderIso", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.toOrderIso_toEquiv", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.orderIsoOfRightInverse", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.dual", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.dual_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.dual_symm_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.symm_dual", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.map_bot'", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "apply"], "tactic_count": 3}
{"name": "OrderIso.map_bot", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderEmbedding.map_inf_le", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.map_inf", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": true, "tactics": ["refine", "apply", "simpa"], "tactic_count": 3}
{"name": "OrderIso.isMax_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": true, "tactics": ["refine", "conv_lhs", "exact"], "tactic_count": 3}
{"name": "Disjoint.map_orderIso", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Codisjoint.map_orderIso", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "disjoint_map_orderIso_iff", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.isCompl", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.isCompl_iff", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.complementedLattice", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.complementedLattice_iff", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIsoClass.toOrderIsoClassOrderDual", "kind": "instance", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.denselyOrdered_range", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": true, "tactics": ["constructor", "simpa"], "tactic_count": 2}
{"name": "denselyOrdered_iff_of_orderIsoClass", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": true, "tactics": ["constructor", "intro", "refine", "obtain", "exact", "intro", "refine", "obtain", "exact"], "tactic_count": 9}
{"name": "denselyOrdered_iff_of_strictAnti", "kind": "theorem", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": true, "tactics": ["rw", "let", "exact", "simp", "intro", "rw"], "tactic_count": 6}
{"name": "ULift.orderIso", "kind": "definition", "module": "Mathlib.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedOrderHomClass.toTopHomClass", "kind": "instance", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedOrderHomClass.toBotHomClass", "kind": "instance", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIsoClass.toTopHomClass", "kind": "instance", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIsoClass.toBotHomClass", "kind": "instance", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIsoClass.toBoundedOrderHomClass", "kind": "instance", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "map_eq_top_iff", "kind": "theorem", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "map_eq_bot_iff", "kind": "theorem", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "TopHomClass.toTopHom", "kind": "definition", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCoeTCTopHomOfTopHomClass", "kind": "instance", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BotHomClass.toBotHom", "kind": "definition", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCoeTCBotHomOfBotHomClass", "kind": "instance", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedOrderHomClass.toBoundedOrderHom", "kind": "definition", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCoeTCBoundedOrderHomOfBoundedOrderHomClass", "kind": "instance", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopHom.instFunLike", "kind": "instance", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopHom.instTopHomClass", "kind": "instance", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopHom.ext", "kind": "theorem", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopHom.copy", "kind": "definition", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopHom.coe_copy", "kind": "theorem", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopHom.copy_eq", "kind": "theorem", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopHom.instInhabited", "kind": "instance", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopHom.id", "kind": "definition", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopHom.coe_id", "kind": "theorem", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopHom.id_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopHom.comp", "kind": "definition", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopHom.coe_comp", "kind": "theorem", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopHom.comp_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopHom.comp_assoc", "kind": "theorem", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopHom.comp_id", "kind": "theorem", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopHom.id_comp", "kind": "theorem", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopHom.cancel_right", "kind": "theorem", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopHom.cancel_left", "kind": "theorem", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopHom.instLE", "kind": "instance", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopHom.instPreorder", "kind": "instance", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopHom.instPartialOrder", "kind": "instance", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopHom.instOrderTop", "kind": "instance", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopHom.coe_top", "kind": "theorem", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopHom.top_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopHom.instMin", "kind": "instance", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopHom.instSemilatticeInf", "kind": "instance", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopHom.coe_inf", "kind": "theorem", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopHom.inf_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopHom.instMax", "kind": "instance", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopHom.instSemilatticeSup", "kind": "instance", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopHom.coe_sup", "kind": "theorem", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopHom.sup_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopHom.instLattice", "kind": "instance", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopHom.instDistribLattice", "kind": "instance", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BotHom.instFunLike", "kind": "instance", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BotHom.instBotHomClass", "kind": "instance", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BotHom.ext", "kind": "theorem", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BotHom.copy", "kind": "definition", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BotHom.coe_copy", "kind": "theorem", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BotHom.copy_eq", "kind": "theorem", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BotHom.instInhabited", "kind": "instance", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BotHom.id", "kind": "definition", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BotHom.coe_id", "kind": "theorem", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BotHom.id_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BotHom.comp", "kind": "definition", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BotHom.coe_comp", "kind": "theorem", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BotHom.comp_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BotHom.comp_assoc", "kind": "theorem", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BotHom.comp_id", "kind": "theorem", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BotHom.id_comp", "kind": "theorem", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BotHom.cancel_right", "kind": "theorem", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BotHom.cancel_left", "kind": "theorem", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BotHom.instLE", "kind": "instance", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BotHom.instPreorder", "kind": "instance", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BotHom.instPartialOrder", "kind": "instance", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BotHom.instOrderBot", "kind": "instance", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BotHom.coe_bot", "kind": "theorem", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BotHom.bot_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BotHom.instMin", "kind": "instance", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BotHom.instSemilatticeInf", "kind": "instance", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BotHom.coe_inf", "kind": "theorem", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BotHom.inf_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BotHom.instMax", "kind": "instance", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BotHom.instSemilatticeSup", "kind": "instance", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BotHom.coe_sup", "kind": "theorem", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BotHom.sup_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BotHom.instLattice", "kind": "instance", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BotHom.instDistribLattice", "kind": "instance", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedOrderHom.toTopHom", "kind": "definition", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedOrderHom.toBotHom", "kind": "definition", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedOrderHom.instFunLike", "kind": "instance", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedOrderHom.instBoundedOrderHomClass", "kind": "instance", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedOrderHom.ext", "kind": "theorem", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedOrderHom.copy", "kind": "definition", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedOrderHom.coe_copy", "kind": "theorem", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedOrderHom.copy_eq", "kind": "theorem", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedOrderHom.id", "kind": "definition", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedOrderHom.instInhabited", "kind": "instance", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedOrderHom.coe_id", "kind": "theorem", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedOrderHom.id_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedOrderHom.comp", "kind": "definition", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedOrderHom.coe_comp", "kind": "theorem", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedOrderHom.comp_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedOrderHom.coe_comp_orderHom", "kind": "theorem", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedOrderHom.coe_comp_topHom", "kind": "theorem", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedOrderHom.coe_comp_botHom", "kind": "theorem", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedOrderHom.comp_assoc", "kind": "theorem", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedOrderHom.comp_id", "kind": "theorem", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedOrderHom.id_comp", "kind": "theorem", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedOrderHom.cancel_right", "kind": "theorem", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedOrderHom.cancel_left", "kind": "theorem", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopHom.dual", "kind": "definition", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopHom.dual_id", "kind": "theorem", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopHom.dual_comp", "kind": "theorem", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopHom.symm_dual_id", "kind": "theorem", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopHom.symm_dual_comp", "kind": "theorem", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BotHom.dual", "kind": "definition", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BotHom.dual_id", "kind": "theorem", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BotHom.dual_comp", "kind": "theorem", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BotHom.symm_dual_id", "kind": "theorem", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BotHom.symm_dual_comp", "kind": "theorem", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedOrderHom.dual", "kind": "definition", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedOrderHom.dual_id", "kind": "theorem", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedOrderHom.dual_comp", "kind": "theorem", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedOrderHom.symm_dual_id", "kind": "theorem", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedOrderHom.symm_dual_comp", "kind": "theorem", "module": "Mathlib.Order.Hom.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupBotHomClass.toBotHomClass", "kind": "instance", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfTopHomClass.toTopHomClass", "kind": "instance", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedLatticeHomClass.toSupBotHomClass", "kind": "instance", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedLatticeHomClass.toInfTopHomClass", "kind": "instance", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedLatticeHomClass.toBoundedOrderHomClass", "kind": "instance", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIsoClass.toSupBotHomClass", "kind": "instance", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIsoClass.toInfTopHomClass", "kind": "instance", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIsoClass.toBoundedLatticeHomClass", "kind": "instance", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Disjoint.map", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Codisjoint.map", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsCompl.map", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "map_compl'", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "map_sdiff'", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "map_symmDiff'", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "instCoeTCSupBotHomOfSupBotHomClass", "kind": "instance", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCoeTCInfTopHomOfInfTopHomClass", "kind": "instance", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCoeTCBoundedLatticeHomOfBoundedLatticeHomClass", "kind": "instance", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupBotHom.toBotHom", "kind": "definition", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupBotHom.instFunLike", "kind": "instance", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupBotHom.instSupBotHomClass", "kind": "instance", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupBotHom.toFun_eq_coe", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupBotHom.coe_toSupHom", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupBotHom.coe_toBotHom", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupBotHom.coe_mk", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupBotHom.ext", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupBotHom.copy", "kind": "definition", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupBotHom.coe_copy", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupBotHom.copy_eq", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupBotHom.id", "kind": "definition", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupBotHom.instInhabited", "kind": "instance", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupBotHom.coe_id", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupBotHom.id_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupBotHom.comp", "kind": "definition", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupBotHom.coe_comp", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupBotHom.comp_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupBotHom.comp_assoc", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupBotHom.comp_id", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupBotHom.id_comp", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupBotHom.cancel_right", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupBotHom.cancel_left", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupBotHom.instMax", "kind": "instance", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupBotHom.instSemilatticeSup", "kind": "instance", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupBotHom.instOrderBot", "kind": "instance", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupBotHom.coe_sup", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupBotHom.coe_bot", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupBotHom.sup_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupBotHom.bot_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupBotHom.subtypeVal", "kind": "definition", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupBotHom.subtypeVal_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupBotHom.subtypeVal_coe", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfTopHom.toTopHom", "kind": "definition", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfTopHom.instFunLike", "kind": "instance", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfTopHom.instInfTopHomClass", "kind": "instance", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfTopHom.toFun_eq_coe", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfTopHom.coe_toInfHom", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfTopHom.coe_toTopHom", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfTopHom.coe_mk", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfTopHom.ext", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfTopHom.copy", "kind": "definition", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfTopHom.coe_copy", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfTopHom.copy_eq", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfTopHom.id", "kind": "definition", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "InfTopHom.coe_id", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfTopHom.id_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfTopHom.comp", "kind": "definition", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfTopHom.coe_comp", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfTopHom.comp_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfTopHom.comp_assoc", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfTopHom.comp_id", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfTopHom.id_comp", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfTopHom.cancel_right", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfTopHom.cancel_left", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfTopHom.instMin", "kind": "instance", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfTopHom.instSemilatticeInf", "kind": "instance", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfTopHom.instOrderTop", "kind": "instance", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfTopHom.coe_inf", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfTopHom.coe_top", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfTopHom.inf_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfTopHom.top_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfTopHom.subtypeVal", "kind": "definition", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfTopHom.subtypeVal_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfTopHom.subtypeVal_coe", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedLatticeHom.toSupBotHom", "kind": "definition", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedLatticeHom.toInfTopHom", "kind": "definition", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedLatticeHom.toBoundedOrderHom", "kind": "definition", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedLatticeHom.instFunLike", "kind": "instance", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedLatticeHom.instBoundedLatticeHomClass", "kind": "instance", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedLatticeHom.toFun_eq_coe", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedLatticeHom.coe_toLatticeHom", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedLatticeHom.coe_toSupBotHom", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedLatticeHom.coe_toInfTopHom", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedLatticeHom.coe_toBoundedOrderHom", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedLatticeHom.coe_mk", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedLatticeHom.ext", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedLatticeHom.copy", "kind": "definition", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedLatticeHom.coe_copy", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedLatticeHom.copy_eq", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedLatticeHom.id", "kind": "definition", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedLatticeHom.instInhabited", "kind": "instance", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedLatticeHom.coe_id", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedLatticeHom.id_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedLatticeHom.comp", "kind": "definition", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "BoundedLatticeHom.comp_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedLatticeHom.coe_comp_lattice_hom'", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedLatticeHom.coe_comp_lattice_hom", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedLatticeHom.coe_comp_sup_hom'", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedLatticeHom.coe_comp_sup_hom", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedLatticeHom.coe_comp_inf_hom'", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "BoundedLatticeHom.comp_assoc", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedLatticeHom.comp_id", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedLatticeHom.id_comp", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedLatticeHom.cancel_right", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedLatticeHom.cancel_left", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedLatticeHom.subtypeVal", "kind": "definition", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedLatticeHom.subtypeVal_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedLatticeHom.subtypeVal_coe", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupBotHom.dual", "kind": "definition", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupBotHom.dual_id", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupBotHom.dual_comp", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupBotHom.symm_dual_id", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupBotHom.symm_dual_comp", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfTopHom.dual", "kind": "definition", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfTopHom.dual_id", "kind": "theorem", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "BoundedLatticeHom.dual", "kind": "definition", "module": "Mathlib.Order.Hom.BoundedLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "sSupHomClass.toSupBotHomClass", "kind": "instance", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sInfHomClass.toInfTopHomClass", "kind": "instance", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CompleteLatticeHomClass.toFrameHomClass", "kind": "instance", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteLatticeHomClass.toBoundedLatticeHomClass", "kind": "instance", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "instCoeTCSInfHomOfSInfHomClass", "kind": "instance", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCoeTCFrameHomOfFrameHomClass", "kind": "instance", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCoeTCCompleteLatticeHomOfCompleteLatticeHomClass", "kind": "instance", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "sSupHom.instSSupHomClass", "kind": "instance", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "sSupHom.instOrderBot", "kind": "instance", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "sInfHom.cancel_right", "kind": "theorem", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sInfHom.cancel_left", "kind": "theorem", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sInfHom.instPartialOrder", "kind": "instance", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sInfHom.instTop", "kind": "instance", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sInfHom.instOrderTop", "kind": "instance", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sInfHom.coe_top", "kind": "theorem", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sInfHom.top_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FrameHom.instFunLike", "kind": "instance", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FrameHom.instFrameHomClass", "kind": "instance", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FrameHom.toLatticeHom", "kind": "definition", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FrameHom.toFun_eq_coe", "kind": "theorem", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FrameHom.coe_toInfTopHom", "kind": "theorem", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FrameHom.coe_toLatticeHom", "kind": "theorem", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FrameHom.coe_mk", "kind": "theorem", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FrameHom.ext", "kind": "theorem", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FrameHom.copy", "kind": "definition", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FrameHom.coe_copy", "kind": "theorem", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FrameHom.copy_eq", "kind": "theorem", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FrameHom.id", "kind": "definition", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FrameHom.instInhabited", "kind": "instance", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FrameHom.coe_id", "kind": "theorem", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FrameHom.id_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FrameHom.comp", "kind": "definition", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FrameHom.coe_comp", "kind": "theorem", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FrameHom.comp_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FrameHom.comp_assoc", "kind": "theorem", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FrameHom.comp_id", "kind": "theorem", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FrameHom.id_comp", "kind": "theorem", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FrameHom.cancel_right", "kind": "theorem", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FrameHom.cancel_left", "kind": "theorem", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FrameHom.instPartialOrder", "kind": "instance", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteLatticeHom.instFunLike", "kind": "instance", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteLatticeHom.instCompleteLatticeHomClass", "kind": "instance", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteLatticeHom.tosSupHom", "kind": "definition", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteLatticeHom.toBoundedLatticeHom", "kind": "definition", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteLatticeHom.toFun_eq_coe", "kind": "theorem", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteLatticeHom.coe_tosInfHom", "kind": "theorem", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteLatticeHom.coe_tosSupHom", "kind": "theorem", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteLatticeHom.coe_toBoundedLatticeHom", "kind": "theorem", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteLatticeHom.coe_mk", "kind": "theorem", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteLatticeHom.ext", "kind": "theorem", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteLatticeHom.copy", "kind": "definition", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteLatticeHom.coe_copy", "kind": "theorem", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteLatticeHom.copy_eq", "kind": "theorem", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteLatticeHom.id", "kind": "definition", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteLatticeHom.instInhabited", "kind": "instance", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteLatticeHom.coe_id", "kind": "theorem", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteLatticeHom.id_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteLatticeHom.comp", "kind": "definition", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteLatticeHom.coe_comp", "kind": "theorem", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteLatticeHom.comp_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteLatticeHom.comp_assoc", "kind": "theorem", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteLatticeHom.comp_id", "kind": "theorem", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteLatticeHom.id_comp", "kind": "theorem", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteLatticeHom.cancel_right", "kind": "theorem", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteLatticeHom.cancel_left", "kind": "theorem", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sSupHom.dual", "kind": "definition", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sSupHom.dual_id", "kind": "theorem", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sSupHom.dual_comp", "kind": "theorem", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sSupHom.symm_dual_id", "kind": "theorem", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sSupHom.symm_dual_comp", "kind": "theorem", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sInfHom.dual", "kind": "definition", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sInfHom.dual_id", "kind": "theorem", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sInfHom.dual_comp", "kind": "theorem", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sInfHom.symm_dual_id", "kind": "theorem", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sInfHom.symm_dual_comp", "kind": "theorem", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteLatticeHom.dual", "kind": "definition", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteLatticeHom.dual_id", "kind": "theorem", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteLatticeHom.dual_comp", "kind": "theorem", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteLatticeHom.symm_dual_id", "kind": "theorem", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteLatticeHom.symm_dual_comp", "kind": "theorem", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteLatticeHom.setPreimage", "kind": "definition", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteLatticeHom.coe_setPreimage", "kind": "theorem", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteLatticeHom.setPreimage_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteLatticeHom.setPreimage_id", "kind": "theorem", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteLatticeHom.setPreimage_comp", "kind": "theorem", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_sSup", "kind": "theorem", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sSupHom.setImage", "kind": "definition", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.toOrderIsoSet", "kind": "definition", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "supsSupHom", "kind": "definition", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "infsInfHom", "kind": "definition", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "supsSupHom_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "infsInfHom_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupHomClass.toOrderHomClass", "kind": "instance", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfHomClass.toOrderHomClass", "kind": "instance", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LatticeHomClass.toInfHomClass", "kind": "instance", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIsoClass.toSupHomClass", "kind": "instance", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIsoClass.toInfHomClass", "kind": "instance", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIsoClass.toLatticeHomClass", "kind": "instance", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "orderEmbeddingOfInjective", "kind": "definition", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCoeTCSupHomOfSupHomClass", "kind": "instance", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCoeTCInfHomOfInfHomClass", "kind": "instance", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCoeTCLatticeHomOfLatticeHomClass", "kind": "instance", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupHom.instFunLike", "kind": "instance", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupHom.instSupHomClass", "kind": "instance", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupHom.toFun_eq_coe", "kind": "theorem", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupHom.coe_mk", "kind": "theorem", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupHom.ext", "kind": "theorem", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupHom.copy", "kind": "definition", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupHom.coe_copy", "kind": "theorem", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupHom.copy_eq", "kind": "theorem", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupHom.id", "kind": "definition", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupHom.instInhabited", "kind": "instance", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupHom.coe_id", "kind": "theorem", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupHom.id_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupHom.comp", "kind": "definition", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupHom.coe_comp", "kind": "theorem", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupHom.comp_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupHom.comp_assoc", "kind": "theorem", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupHom.comp_id", "kind": "theorem", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupHom.id_comp", "kind": "theorem", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupHom.cancel_right", "kind": "theorem", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupHom.cancel_left", "kind": "theorem", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupHom.const", "kind": "definition", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupHom.coe_const", "kind": "theorem", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupHom.const_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupHom.instMax", "kind": "instance", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupHom.instSemilatticeSup", "kind": "instance", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupHom.instBot", "kind": "instance", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupHom.instTop", "kind": "instance", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupHom.instOrderBot", "kind": "instance", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupHom.instOrderTop", "kind": "instance", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupHom.instBoundedOrder", "kind": "instance", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupHom.coe_sup", "kind": "theorem", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupHom.coe_bot", "kind": "theorem", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupHom.coe_top", "kind": "theorem", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupHom.sup_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupHom.bot_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupHom.top_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupHom.mk_le_mk", "kind": "theorem", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupHom.subtypeVal", "kind": "definition", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupHom.subtypeVal_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupHom.subtypeVal_coe", "kind": "theorem", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfHom.instFunLike", "kind": "instance", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfHom.instInfHomClass", "kind": "instance", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfHom.toFun_eq_coe", "kind": "theorem", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "InfHom.ext", "kind": "theorem", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "InfHom.comp_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfHom.comp_assoc", "kind": "theorem", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "InfHom.coe_const", "kind": "theorem", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfHom.const_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "InfHom.instSemilatticeInf", "kind": "instance", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "InfHom.instOrderBot", "kind": "instance", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "InfHom.instBoundedOrder", "kind": "instance", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "InfHom.coe_bot", "kind": "theorem", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfHom.coe_top", "kind": "theorem", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "InfHom.bot_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfHom.top_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfHom.mk_le_mk", "kind": "theorem", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfHom.subtypeVal", "kind": "definition", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfHom.subtypeVal_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfHom.subtypeVal_coe", "kind": "theorem", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LatticeHom.toInfHom", "kind": "definition", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LatticeHom.instFunLike", "kind": "instance", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LatticeHom.instLatticeHomClass", "kind": "instance", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LatticeHom.toFun_eq_coe", "kind": "theorem", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LatticeHom.coe_toSupHom", "kind": "theorem", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LatticeHom.coe_toInfHom", "kind": "theorem", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LatticeHom.coe_mk", "kind": "theorem", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LatticeHom.ext", "kind": "theorem", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LatticeHom.copy_eq", "kind": "theorem", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LatticeHom.id", "kind": "definition", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LatticeHom.instInhabited", "kind": "instance", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LatticeHom.coe_id", "kind": "theorem", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LatticeHom.id_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LatticeHom.comp", "kind": "definition", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LatticeHom.coe_comp", "kind": "theorem", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LatticeHom.comp_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LatticeHom.coe_comp_sup_hom'", "kind": "theorem", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LatticeHom.coe_comp_sup_hom", "kind": "theorem", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LatticeHom.coe_comp_inf_hom'", "kind": "theorem", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LatticeHom.coe_comp_inf_hom", "kind": "theorem", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LatticeHom.comp_assoc", "kind": "theorem", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LatticeHom.comp_id", "kind": "theorem", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LatticeHom.id_comp", "kind": "theorem", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LatticeHom.cancel_right", "kind": "theorem", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LatticeHom.cancel_left", "kind": "theorem", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LatticeHom.subtypeVal", "kind": "definition", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LatticeHom.subtypeVal_coe", "kind": "theorem", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHomClass.toLatticeHomClass", "kind": "instance", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHomClass.toLatticeHom", "kind": "definition", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "OrderHomClass.to_lattice_hom_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupHom.dual", "kind": "definition", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LatticeHom.snd_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Pi.evalLatticeHom_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelIso.sumLexComplLeft", "kind": "definition", "module": "Mathlib.Order.Hom.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "OrderIso.sumLexIioIci", "kind": "definition", "module": "Mathlib.Order.Hom.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "OrderIso.sumLexIioIci_symm_apply_Iio", "kind": "theorem", "module": "Mathlib.Order.Hom.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "OrderIso.sumLexIicIoi_apply_inl", "kind": "theorem", "module": "Mathlib.Order.Hom.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Prod.Lex.prodUnique", "kind": "definition", "module": "Mathlib.Order.Hom.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.Lex.prodUnique_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.Lex.uniqueProd", "kind": "definition", "module": "Mathlib.Order.Hom.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Prod.Lex.sumLexProdLexDistrib", "kind": "definition", "module": "Mathlib.Order.Hom.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.Lex.prodLexCongr", "kind": "definition", "module": "Mathlib.Order.Hom.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "OrderHom.instBotOfOrderBot", "kind": "instance", "module": "Mathlib.Order.Hom.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "OrderHom.instTopOrderHom", "kind": "instance", "module": "Mathlib.Order.Hom.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.orderTop", "kind": "instance", "module": "Mathlib.Order.Hom.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "OrderHom.instSupSet", "kind": "instance", "module": "Mathlib.Order.Hom.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.sSup_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.iSup_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.coe_iSup", "kind": "theorem", "module": "Mathlib.Order.Hom.Order", "is_tactic_proof": true, "tactics": ["funext"], "tactic_count": 1}
{"name": "OrderHom.instCompleteLattice", "kind": "instance", "module": "Mathlib.Order.Hom.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.iterate_sup_le_sup_iff", "kind": "theorem", "module": "Mathlib.Order.Hom.Order", "is_tactic_proof": true, "tactics": ["constructor", "exact", "intro", "have", "intro", "induction", "zero", "succ", "intro", "calc", "f^", "calc", "f^"], "tactic_count": 13}
{"name": "Set.sumEquiv", "kind": "definition", "module": "Mathlib.Order.Hom.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.range_eq", "kind": "theorem", "module": "Mathlib.Order.Hom.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.symm_image_image", "kind": "theorem", "module": "Mathlib.Order.Hom.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.image_symm_image", "kind": "theorem", "module": "Mathlib.Order.Hom.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.image_eq_preimage_symm", "kind": "theorem", "module": "Mathlib.Order.Hom.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.preimage_symm_preimage", "kind": "theorem", "module": "Mathlib.Order.Hom.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.symm_preimage_preimage", "kind": "theorem", "module": "Mathlib.Order.Hom.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.image_preimage", "kind": "theorem", "module": "Mathlib.Order.Hom.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.preimage_image", "kind": "theorem", "module": "Mathlib.Order.Hom.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.setCongr", "kind": "definition", "module": "Mathlib.Order.Hom.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.Set.univ", "kind": "definition", "module": "Mathlib.Order.Hom.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderEmbedding.orderIso", "kind": "definition", "module": "Mathlib.Order.Hom.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMonoOn.orderIso", "kind": "definition", "module": "Mathlib.Order.Hom.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.orderIso", "kind": "definition", "module": "Mathlib.Order.Hom.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.orderIsoOfSurjective", "kind": "definition", "module": "Mathlib.Order.Hom.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.coe_orderIsoOfSurjective", "kind": "theorem", "module": "Mathlib.Order.Hom.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.orderIsoOfSurjective_symm_apply_self", "kind": "theorem", "module": "Mathlib.Order.Hom.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.orderIsoOfSurjective_self_symm_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderEmbedding.range_inj", "kind": "theorem", "module": "Mathlib.Order.Hom.Set", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "OrderIso.subsingleton_of_wellFoundedLT", "kind": "instance", "module": "Mathlib.Order.Hom.Set", "is_tactic_proof": true, "tactics": ["refine", "rw", "coe_toOrderEmbedding,"], "tactic_count": 3}
{"name": "OrderIso.subsingleton_of_wellFoundedLT'", "kind": "instance", "module": "Mathlib.Order.Hom.Set", "is_tactic_proof": true, "tactics": ["refine", "change", "rw"], "tactic_count": 3}
{"name": "OrderIso.unique_of_wellFoundedLT", "kind": "instance", "module": "Mathlib.Order.Hom.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.subsingleton_of_wellFoundedGT", "kind": "instance", "module": "Mathlib.Order.Hom.Set", "is_tactic_proof": true, "tactics": ["refine", "change", "rw"], "tactic_count": 3}
{"name": "OrderIso.subsingleton_of_wellFoundedGT'", "kind": "instance", "module": "Mathlib.Order.Hom.Set", "is_tactic_proof": true, "tactics": ["refine", "change", "rw"], "tactic_count": 3}
{"name": "OrderIso.unique_of_wellFoundedGT", "kind": "instance", "module": "Mathlib.Order.Hom.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.Iic", "kind": "definition", "module": "Mathlib.Order.Hom.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.Ici", "kind": "definition", "module": "Mathlib.Order.Hom.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.Icc", "kind": "definition", "module": "Mathlib.Order.Hom.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.compl", "kind": "definition", "module": "Mathlib.Order.Hom.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "compl_strictAnti", "kind": "theorem", "module": "Mathlib.Order.Hom.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "compl_antitone", "kind": "theorem", "module": "Mathlib.Order.Hom.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.toDualBotEquiv", "kind": "definition", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.toDualBotEquiv_coe", "kind": "theorem", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.toDualBotEquiv_symm_coe", "kind": "theorem", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.toDualBotEquiv_top", "kind": "theorem", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.toDualBotEquiv_symm_top", "kind": "theorem", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.coe_toDualBotEquiv", "kind": "theorem", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.coeWithTop", "kind": "definition", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.coeOrderHom", "kind": "definition", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.subtypeOrderIso", "kind": "definition", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.subtypeOrderIso_apply_coe", "kind": "theorem", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.subtypeOrderIso_symm_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "WithBot.toDualTopEquiv", "kind": "definition", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.toDualTopEquiv_coe", "kind": "theorem", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.toDualTopEquiv_symm_coe", "kind": "theorem", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.toDualTopEquiv_bot", "kind": "theorem", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.toDualTopEquiv_symm_bot", "kind": "theorem", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.coe_toDualTopEquiv_eq", "kind": "theorem", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.coeWithBot", "kind": "definition", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.coeOrderHom", "kind": "definition", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.subtypeOrderIso", "kind": "definition", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.subtypeOrderIso_apply_coe", "kind": "theorem", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.subtypeOrderIso_symm_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "OrderHom.withBotMap", "kind": "definition", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderHom.withTopMap", "kind": "definition", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderEmbedding.withBotMap", "kind": "definition", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderEmbedding.withTopMap", "kind": "definition", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.withTopCongr", "kind": "definition", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.withTopCongr_refl", "kind": "theorem", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.withTopCongr_symm", "kind": "theorem", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.withTopCongr_trans", "kind": "theorem", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.withBotCongr", "kind": "definition", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.withBotCongr_refl", "kind": "theorem", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.withBotCongr_symm", "kind": "theorem", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.withBotCongr_trans", "kind": "theorem", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupHom.withTop", "kind": "definition", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupHom.withTop_id", "kind": "theorem", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupHom.withTop_comp", "kind": "theorem", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupHom.withBot", "kind": "definition", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupHom.withBot_id", "kind": "theorem", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupHom.withBot_comp", "kind": "theorem", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupHom.withTop'", "kind": "definition", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupHom.withBot'", "kind": "definition", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfHom.withTop", "kind": "definition", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfHom.withTop_id", "kind": "theorem", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfHom.withTop_comp", "kind": "theorem", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfHom.withBot", "kind": "definition", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfHom.withBot_id", "kind": "theorem", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfHom.withBot_comp", "kind": "theorem", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfHom.withTop'", "kind": "definition", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfHom.withBot'", "kind": "definition", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LatticeHom.withTop", "kind": "definition", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LatticeHom.coe_withTop", "kind": "theorem", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LatticeHom.withTop_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LatticeHom.withTop_id", "kind": "theorem", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LatticeHom.withTop_comp", "kind": "theorem", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LatticeHom.withBot", "kind": "definition", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LatticeHom.coe_withBot", "kind": "theorem", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LatticeHom.withBot_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LatticeHom.withBot_id", "kind": "theorem", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LatticeHom.withBot_comp", "kind": "theorem", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LatticeHom.withTopWithBot", "kind": "definition", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LatticeHom.coe_withTopWithBot", "kind": "theorem", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LatticeHom.withTopWithBot_apply", "kind": "theorem", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LatticeHom.withTopWithBot_id", "kind": "theorem", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LatticeHom.withTopWithBot_comp", "kind": "theorem", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "LatticeHom.withTop'", "kind": "definition", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LatticeHom.withBot'", "kind": "definition", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LatticeHom.withTopWithBot'", "kind": "definition", "module": "Mathlib.Order.Hom.WithTopBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.IsIdeal.toIdeal", "kind": "definition", "module": "Mathlib.Order.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ideal.toLowerSet_injective", "kind": "theorem", "module": "Mathlib.Order.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ideal.instSetLike", "kind": "instance", "module": "Mathlib.Order.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ideal.instPartialOrder", "kind": "instance", "module": "Mathlib.Order.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ideal.ext", "kind": "theorem", "module": "Mathlib.Order.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ideal.carrier_eq_coe", "kind": "theorem", "module": "Mathlib.Order.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ideal.coe_toLowerSet", "kind": "theorem", "module": "Mathlib.Order.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ideal.lower", "kind": "theorem", "module": "Mathlib.Order.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ideal.nonempty", "kind": "theorem", "module": "Mathlib.Order.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ideal.directed", "kind": "theorem", "module": "Mathlib.Order.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ideal.isIdeal", "kind": "theorem", "module": "Mathlib.Order.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ideal.mem_compl_of_ge", "kind": "theorem", "module": "Mathlib.Order.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ideal.instPartialOrderIdeal", "kind": "instance", "module": "Mathlib.Order.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ideal.coe_subset_coe", "kind": "theorem", "module": "Mathlib.Order.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ideal.coe_ssubset_coe", "kind": "theorem", "module": "Mathlib.Order.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ideal.mem_of_mem_of_le", "kind": "theorem", "module": "Mathlib.Order.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ideal.isProper_of_notMem", "kind": "theorem", "module": "Mathlib.Order.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ideal.inter_nonempty", "kind": "theorem", "module": "Mathlib.Order.Ideal", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "obtain", "exact"], "tactic_count": 4}
{"name": "Order.Ideal.instOrderTop", "kind": "instance", "module": "Mathlib.Order.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ideal.top_toLowerSet", "kind": "theorem", "module": "Mathlib.Order.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ideal.coe_top", "kind": "theorem", "module": "Mathlib.Order.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ideal.isProper_of_ne_top", "kind": "theorem", "module": "Mathlib.Order.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ideal.IsProper.ne_top", "kind": "theorem", "module": "Mathlib.Order.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCoatom.isProper", "kind": "theorem", "module": "Mathlib.Order.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ideal.isProper_iff_ne_top", "kind": "theorem", "module": "Mathlib.Order.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ideal.IsMaximal.isCoatom", "kind": "theorem", "module": "Mathlib.Order.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ideal.IsMaximal.isCoatom'", "kind": "theorem", "module": "Mathlib.Order.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCoatom.isMaximal", "kind": "theorem", "module": "Mathlib.Order.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ideal.isMaximal_iff_isCoatom", "kind": "theorem", "module": "Mathlib.Order.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ideal.bot_mem", "kind": "theorem", "module": "Mathlib.Order.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ideal.top_of_top_mem", "kind": "theorem", "module": "Mathlib.Order.Ideal", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "Order.Ideal.IsProper.top_notMem", "kind": "theorem", "module": "Mathlib.Order.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ideal.principal", "kind": "definition", "module": "Mathlib.Order.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ideal.instInhabited", "kind": "instance", "module": "Mathlib.Order.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ideal.principal_le_iff", "kind": "theorem", "module": "Mathlib.Order.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ideal.mem_principal", "kind": "theorem", "module": "Mathlib.Order.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ideal.mem_principal_self", "kind": "theorem", "module": "Mathlib.Order.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ideal.instOrderBot", "kind": "instance", "module": "Mathlib.Order.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ideal.principal_bot", "kind": "theorem", "module": "Mathlib.Order.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ideal.principal_top", "kind": "theorem", "module": "Mathlib.Order.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ideal.sup_mem", "kind": "theorem", "module": "Mathlib.Order.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ideal.sup_mem_iff", "kind": "theorem", "module": "Mathlib.Order.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ideal.finsetSup_mem_iff", "kind": "theorem", "module": "Mathlib.Order.Ideal", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Order.Ideal.instMin", "kind": "instance", "module": "Mathlib.Order.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ideal.instMax", "kind": "instance", "module": "Mathlib.Order.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ideal.instLattice", "kind": "instance", "module": "Mathlib.Order.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ideal.coe_sup", "kind": "theorem", "module": "Mathlib.Order.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ideal.coe_inf", "kind": "theorem", "module": "Mathlib.Order.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ideal.mem_inf", "kind": "theorem", "module": "Mathlib.Order.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ideal.mem_sup", "kind": "theorem", "module": "Mathlib.Order.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ideal.lt_sup_principal_of_notMem", "kind": "theorem", "module": "Mathlib.Order.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ideal.instInfSet", "kind": "instance", "module": "Mathlib.Order.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ideal.coe_sInf", "kind": "theorem", "module": "Mathlib.Order.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ideal.mem_sInf", "kind": "theorem", "module": "Mathlib.Order.Ideal", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Order.Ideal.instCompleteLattice", "kind": "instance", "module": "Mathlib.Order.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ideal.eq_sup_of_le_sup", "kind": "theorem", "module": "Mathlib.Order.Ideal", "is_tactic_proof": true, "tactics": ["refine", "calc", "x"], "tactic_count": 3}
{"name": "Order.Ideal.coe_sup_eq", "kind": "theorem", "module": "Mathlib.Order.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ideal.IsProper.notMem_of_compl_mem", "kind": "theorem", "module": "Mathlib.Order.Ideal", "is_tactic_proof": true, "tactics": ["intro", "apply", "have", "rwa"], "tactic_count": 4}
{"name": "Order.Ideal.IsProper.notMem_or_compl_notMem", "kind": "theorem", "module": "Mathlib.Order.Ideal", "is_tactic_proof": true, "tactics": ["have", "tauto"], "tactic_count": 2}
{"name": "Order.Cofinal.instInhabited", "kind": "instance", "module": "Mathlib.Order.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Cofinal.instMembership", "kind": "instance", "module": "Mathlib.Order.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Cofinal.above", "kind": "definition", "module": "Mathlib.Order.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Cofinal.above_mem", "kind": "theorem", "module": "Mathlib.Order.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Cofinal.le_above", "kind": "theorem", "module": "Mathlib.Order.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.sequenceOfCofinals", "kind": "definition", "module": "Mathlib.Order.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.sequenceOfCofinals.monotone", "kind": "theorem", "module": "Mathlib.Order.Ideal", "is_tactic_proof": true, "tactics": ["apply", "intro", "dsimp", "cases", "rfl", "apply"], "tactic_count": 6}
{"name": "Order.sequenceOfCofinals.encode_mem", "kind": "theorem", "module": "Mathlib.Order.Ideal", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "apply"], "tactic_count": 3}
{"name": "Order.idealOfCofinals", "kind": "definition", "module": "Mathlib.Order.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.mem_idealOfCofinals", "kind": "theorem", "module": "Mathlib.Order.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.cofinal_meets_idealOfCofinals", "kind": "theorem", "module": "Mathlib.Order.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.isIdeal_sUnion_of_directedOn", "kind": "theorem", "module": "Mathlib.Order.Ideal", "is_tactic_proof": false, "tactics": ["refine", "directedOn_sUnion", "let", "exact"], "tactic_count": 4}
{"name": "Order.isIdeal_sUnion_of_isChain", "kind": "theorem", "module": "Mathlib.Order.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InitialSeg.term_≼i_", "kind": "definition", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InitialSeg._aux_Mathlib_Order_InitialSeg___macroRules_InitialSeg_term_≼i__1", "kind": "definition", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InitialSeg._aux_Mathlib_Order_InitialSeg___unexpand_InitialSeg_1", "kind": "definition", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "term_≤i_", "kind": "definition", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Order_InitialSeg___macroRules_term_≤i__1", "kind": "definition", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InitialSeg.instCoeRelEmbedding", "kind": "instance", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InitialSeg.instFunLike", "kind": "instance", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InitialSeg.instEmbeddingLike", "kind": "instance", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InitialSeg.instRelHomClass", "kind": "instance", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InitialSeg.toOrderEmbedding", "kind": "definition", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InitialSeg.toOrderEmbedding_apply", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InitialSeg.coe_toOrderEmbedding", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InitialSeg.instOrderHomClassLt", "kind": "instance", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InitialSeg.ext", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InitialSeg.coe_coe_fn", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InitialSeg.mem_range_of_rel", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InitialSeg.map_rel_iff", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InitialSeg.inj", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InitialSeg.exists_eq_iff_rel", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelIso.toInitialSeg", "kind": "definition", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InitialSeg.refl", "kind": "definition", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InitialSeg.instInhabited", "kind": "instance", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InitialSeg.trans", "kind": "definition", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InitialSeg.refl_apply", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InitialSeg.trans_apply", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InitialSeg.subsingleton_of_trichotomous_of_irrefl", "kind": "instance", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InitialSeg.instSubsingletonOfIsWellOrder", "kind": "instance", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InitialSeg.eq", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "InitialSeg.eq_relIso", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Order.InitialSeg.0.InitialSeg.antisymm_aux", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InitialSeg.antisymm", "kind": "definition", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InitialSeg.antisymm_toFun", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InitialSeg.antisymm_symm", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InitialSeg.eq_or_principal", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": true, "tactics": ["apply", "intro", "push_neg", "apply", "intro", "obtain", "obtain", "exact", "obtain", "exact", "obtain", "cases"], "tactic_count": 12}
{"name": "InitialSeg.codRestrict", "kind": "definition", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InitialSeg.codRestrict_apply", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InitialSeg.ofIsEmpty", "kind": "definition", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InitialSeg.leAdd", "kind": "definition", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InitialSeg.leAdd_apply", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InitialSeg.acc", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InitialSeg.term_≺i_", "kind": "definition", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InitialSeg._aux_Mathlib_Order_InitialSeg___macroRules_InitialSeg_term_≺i__1", "kind": "definition", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InitialSeg._aux_Mathlib_Order_InitialSeg___unexpand_PrincipalSeg_1", "kind": "definition", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "term_<i_", "kind": "definition", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Order_InitialSeg___macroRules_term_<i__1", "kind": "definition", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrincipalSeg.instCoeOutRelEmbedding", "kind": "instance", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrincipalSeg.instCoeFunForall", "kind": "instance", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrincipalSeg.toRelEmbedding_injective", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": true, "tactics": ["rintro", "congr", "refine", "rw"], "tactic_count": 4}
{"name": "PrincipalSeg.toRelEmbedding_inj", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrincipalSeg.ext", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": true, "tactics": ["rw", "ext", "exact"], "tactic_count": 3}
{"name": "PrincipalSeg.coe_fn_mk", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrincipalSeg.mem_range_iff_rel", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrincipalSeg.lt_top", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrincipalSeg.mem_range_of_rel_top", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrincipalSeg.mem_range_of_rel", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrincipalSeg.surjOn", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": true, "tactics": ["intro", "simpa"], "tactic_count": 2}
{"name": "PrincipalSeg.hasCoeInitialSeg", "kind": "instance", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrincipalSeg.coe_coe_fn'", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InitialSeg.eq_principalSeg", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrincipalSeg.exists_eq_iff_rel", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InitialSeg.toPrincipalSeg", "kind": "definition", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InitialSeg.toPrincipalSeg_apply", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrincipalSeg.irrefl", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "PrincipalSeg.instIsEmptyOfIsWellOrder", "kind": "instance", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrincipalSeg.transInitial", "kind": "definition", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrincipalSeg.transInitial_apply", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrincipalSeg.transInitial_top", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrincipalSeg.trans", "kind": "definition", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrincipalSeg.trans_apply", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrincipalSeg.trans_top", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrincipalSeg.relIsoTrans", "kind": "definition", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrincipalSeg.relIsoTrans_apply", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrincipalSeg.relIsoTrans_top", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrincipalSeg.transRelIso", "kind": "definition", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrincipalSeg.transRelIso_apply", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrincipalSeg.transRelIso_top", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrincipalSeg.instSubsingletonOfIsWellOrder", "kind": "instance", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrincipalSeg.eq", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PrincipalSeg.top_eq", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PrincipalSeg.top_rel_top", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "PrincipalSeg.ofElement", "kind": "definition", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrincipalSeg.ofElement_apply", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrincipalSeg.subrelIso", "kind": "definition", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrincipalSeg.apply_subrelIso", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrincipalSeg.subrelIso_apply", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrincipalSeg.codRestrict", "kind": "definition", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrincipalSeg.codRestrict_apply", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrincipalSeg.codRestrict_top", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrincipalSeg.ofIsEmpty", "kind": "definition", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrincipalSeg.ofIsEmpty_top", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrincipalSeg.pemptyToPunit", "kind": "abbrev", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrincipalSeg.acc", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "wellFounded_iff_principalSeg", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InitialSeg.principalSumRelIso", "kind": "definition", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InitialSeg.transPrincipal", "kind": "definition", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InitialSeg.transPrincipal_apply", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": true, "tactics": ["rw", "obtain", "rw", "rw"], "tactic_count": 4}
{"name": "InitialSeg.exists_sum_relIso", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": true, "tactics": ["classical", "obtain", "exact", "exact"], "tactic_count": 4}
{"name": "_private.Mathlib.Order.InitialSeg.0.collapseF", "kind": "definition", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Order.InitialSeg.0.collapseF_lt", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": true, "tactics": ["change", "rw", "dsimp", "exact"], "tactic_count": 4}
{"name": "_private.Mathlib.Order.InitialSeg.0.collapseF_not_lt", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": true, "tactics": ["rw", "dsimp", "exact"], "tactic_count": 3}
{"name": "RelEmbedding.collapse", "kind": "definition", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InitialSeg.total", "kind": "definition", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.toInitialSeg", "kind": "definition", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InitialSeg.mem_range_of_le", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": true, "tactics": ["obtain", "exacts"], "tactic_count": 2}
{"name": "InitialSeg.isLowerSet_range", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "InitialSeg.le_iff_le", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InitialSeg.lt_iff_lt", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InitialSeg.monotone", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InitialSeg.strictMono", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InitialSeg.isMin_apply_iff", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": true, "tactics": ["refine", "obtain", "rw", "exact"], "tactic_count": 4}
{"name": "InitialSeg.map_bot", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InitialSeg.image_Iio", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InitialSeg.le_apply_iff", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": true, "tactics": ["constructor", "intro", "obtain", "refine", "rwa", "rintro", "exact"], "tactic_count": 7}
{"name": "InitialSeg.lt_apply_iff", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": true, "tactics": ["constructor", "intro", "obtain", "refine", "rwa", "rintro", "exact"], "tactic_count": 7}
{"name": "PrincipalSeg.mem_range_of_le", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrincipalSeg.isLowerSet_range", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrincipalSeg.le_iff_le", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrincipalSeg.lt_iff_lt", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrincipalSeg.monotone", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrincipalSeg.strictMono", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrincipalSeg.isMin_apply_iff", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrincipalSeg.map_bot", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrincipalSeg.image_Iio", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrincipalSeg.le_apply_iff", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrincipalSeg.lt_apply_iff", "kind": "theorem", "module": "Mathlib.Order.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.toProd_injective", "kind": "theorem", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.instCanLift", "kind": "instance", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.toDualProd", "kind": "definition", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.toDualProd_apply", "kind": "theorem", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.toDualProd_injective", "kind": "theorem", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.instIsEmpty", "kind": "instance", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.instSubsingleton", "kind": "instance", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.instDecidableEq", "kind": "instance", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.le", "kind": "instance", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.le_def", "kind": "theorem", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.instDecidableLE", "kind": "instance", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.toDualProdHom", "kind": "definition", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.dual", "kind": "definition", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.fst_dual", "kind": "theorem", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.snd_dual", "kind": "theorem", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.instPreorder", "kind": "instance", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.toDualProd_mono", "kind": "theorem", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.toDualProd_strictMono", "kind": "theorem", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.instCoeSet", "kind": "instance", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.instMembership", "kind": "instance", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.mem_mk", "kind": "theorem", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.mem_def", "kind": "theorem", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.coe_nonempty", "kind": "theorem", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.pure", "kind": "definition", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.mem_pure_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.pure_injective", "kind": "theorem", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.dual_pure", "kind": "theorem", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.instInhabited", "kind": "instance", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.instNonempty", "kind": "instance", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.instNontrivial", "kind": "instance", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.map", "kind": "definition", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.map_pure", "kind": "theorem", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.map_map", "kind": "theorem", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.dual_map", "kind": "theorem", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.map₂", "kind": "definition", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.map₂_pure", "kind": "theorem", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.dual_map₂", "kind": "theorem", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.instOrderTop", "kind": "instance", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.dual_top", "kind": "theorem", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.instPartialOrder", "kind": "instance", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.instDecidableLE_1", "kind": "instance", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.coeHom", "kind": "definition", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.setLike", "kind": "instance", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.coe_subset_coe", "kind": "theorem", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.coe_ssubset_coe", "kind": "theorem", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.coe_coeHom", "kind": "theorem", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.coe_def", "kind": "theorem", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.coe_pure", "kind": "theorem", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.mem_pure", "kind": "theorem", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NonemptyInterval.coe_top", "kind": "theorem", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.coe_dual", "kind": "theorem", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.subset_coe_map", "kind": "theorem", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.instMax", "kind": "instance", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.instSemilatticeSup", "kind": "instance", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.fst_sup", "kind": "theorem", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.snd_sup", "kind": "theorem", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval", "kind": "abbrev", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.instInhabited", "kind": "instance", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.instLE", "kind": "instance", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.instOrderBot", "kind": "instance", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.instCoeNonemptyInterval", "kind": "instance", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.canLift", "kind": "instance", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.recBotCoe", "kind": "definition", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.coe_injective", "kind": "theorem", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.coe_inj", "kind": "theorem", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.forall", "kind": "theorem", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.exists", "kind": "theorem", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.instUniqueOfIsEmpty", "kind": "instance", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.dual", "kind": "definition", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.instPreorder", "kind": "instance", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.pure", "kind": "definition", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.pure_injective", "kind": "theorem", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.dual_pure", "kind": "theorem", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.dual_bot", "kind": "theorem", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.pure_ne_bot", "kind": "theorem", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.bot_ne_pure", "kind": "theorem", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.instNontrivialOfNonempty", "kind": "instance", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.map", "kind": "definition", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.map_pure", "kind": "theorem", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.map_map", "kind": "theorem", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.dual_map", "kind": "theorem", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": true, "tactics": ["cases", "rfl", "exact"], "tactic_count": 3}
{"name": "Interval.boundedOrder", "kind": "instance", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.dual_top", "kind": "theorem", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.partialOrder", "kind": "instance", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.coeHom", "kind": "definition", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.setLike", "kind": "instance", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.coe_subset_coe", "kind": "theorem", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.coe_sSubset_coe", "kind": "theorem", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.coe_pure", "kind": "theorem", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.coe_coe", "kind": "theorem", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.coe_bot", "kind": "theorem", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.coe_top", "kind": "theorem", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.coe_dual", "kind": "theorem", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": true, "tactics": ["cases", "bot", "coe"], "tactic_count": 3}
{"name": "Interval.subset_coe_map", "kind": "theorem", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.mem_pure", "kind": "theorem", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Interval.mem_pure_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.semilatticeSup", "kind": "instance", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.lattice", "kind": "instance", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.coe_inf", "kind": "theorem", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.disjoint_coe", "kind": "theorem", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": true, "tactics": ["classical", "rw", "rfl"], "tactic_count": 3}
{"name": "NonemptyInterval.coe_pure_interval", "kind": "theorem", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.coe_eq_pure", "kind": "theorem", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NonemptyInterval.coe_top_interval", "kind": "theorem", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.mem_coe_interval", "kind": "theorem", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.coe_sup_interval", "kind": "theorem", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.completeLattice", "kind": "instance", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": true, "tactics": ["classical", "exact", "sSup", "obtain", "lift", "exact", "le_sSup", "split_ifs", "exact", "cases", "exact", "apply", "constructor", "apply", "exact", "exact", "sSup_le", "split_ifs", "exact", "obtain", "lift", "exact", "iSup₂_le", "sInf", "iSup₂_le", "sInf_le", "split_ifs", "lift", "ne_of_mem_of_not_mem", "h.1", "let", "exact", "exact", "le_sInf", "intro", "cases", "bot", "coe", "split_ifs", "exact", "le_iInf₂", "rw", "rcases", "exact", "exfalso", "apply", "intro", "have", "repeat", "rw", "exact"], "tactic_count": 51}
{"name": "Interval.coe_sInf", "kind": "theorem", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": true, "tactics": ["classical", "change", "split_ifs", "ext", "simp", "simp_rw", "rcases", "refine", "exact", "refine", "rintro", "rw", "exact"], "tactic_count": 13}
{"name": "Interval.coe_iInf", "kind": "theorem", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Interval.coe_iInf₂", "kind": "theorem", "module": "Mathlib.Order.Interval.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Finset.nonempty_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.nonempty_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.nonempty_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.nonempty_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.Icc_eq_empty_iff", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.Ico_eq_empty_iff", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.Ioc_eq_empty_iff", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.Ioo_eq_empty_iff", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.Ioo_eq_empty", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Icc_eq_empty_of_lt", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ico_eq_empty_of_le", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ioc_eq_empty_of_le", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ioo_eq_empty_of_le", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.left_mem_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.left_mem_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.right_mem_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.right_mem_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.left_notMem_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.left_notMem_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.right_notMem_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.right_notMem_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Icc_subset_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.Ico_subset_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.Ioc_subset_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.Ioo_subset_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.Icc_subset_Icc_left", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ico_subset_Ico_left", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ioc_subset_Ioc_left", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ioo_subset_Ioo_left", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Icc_subset_Icc_right", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ico_subset_Ico_right", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ioc_subset_Ioc_right", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ioo_subset_Ioo_right", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ico_subset_Ioo_left", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finset.Ioc_subset_Ioo_right", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finset.Icc_subset_Ico_right", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finset.Ioo_subset_Ico_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finset.Ioo_subset_Ioc_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finset.Ico_subset_Icc_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finset.Ioc_subset_Icc_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finset.Ioo_subset_Icc_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Icc_subset_Icc_iff", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.Icc_subset_Ioo_iff", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.Icc_subset_Ico_iff", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.Icc_subset_Ioc_iff", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Icc_ssubset_Icc_left", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finset.Icc_ssubset_Icc_right", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finset.Ioc_disjoint_Ioc_of_le", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_lt_of_denselyOrdered_of_locallyFinite", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["intro", "induction", "subst", "obtain", "refine", "exact"], "tactic_count": 6}
{"name": "Finset.Ico_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ioc_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ioo_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.fintypeOfMemBounds", "kind": "definition", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ico_filter_lt_of_le_left", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ico_filter_lt_of_right_le", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ico_filter_lt_of_le_right", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.Ico_filter_le_of_le_left", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ico_filter_le_of_right_le", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ico_filter_le_of_left_le", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.Icc_filter_lt_of_lt_right", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ioc_filter_lt_of_lt_right", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Iic_filter_lt_of_lt_right", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.filter_lt_lt_eq_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finset.filter_lt_le_eq_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finset.filter_le_lt_eq_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finset.filter_le_le_eq_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finset.Ioi_eq_empty", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.Ioi_nonempty", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["contrapose"], "tactic_count": 1}
{"name": "Finset.Ioi_top", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ici_bot", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finset.nonempty_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.nonempty_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.Ici_subset_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.Ici_ssubset_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.Ioi_subset_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.Ioi_ssubset_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.Icc_subset_Ici_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.Ico_subset_Ici_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.Ioc_subset_Ioi_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.Ioo_subset_Ioi_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.Ioc_subset_Ici_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ioo_subset_Ici_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Iio_eq_empty", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Iio_nonempty", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["contrapose"], "tactic_count": 1}
{"name": "Finset.Iio_bot", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Iic_top", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finset.nonempty_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.nonempty_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.Iic_subset_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.Iic_ssubset_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.Iio_subset_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.Iio_ssubset_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.Icc_subset_Iic_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.Ioc_subset_Iic_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.Ico_subset_Iio_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.Ioo_subset_Iio_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.Ico_subset_Iic_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ioo_subset_Iic_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Iic_disjoint_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.IicFinsetSet", "kind": "definition", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ioi_subset_Ici_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "BddBelow.finite", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Infinite.not_bddBelow", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.filter_lt_eq_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finset.filter_le_eq_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finset.Iio_subset_Iic_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "BddAbove.finite", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Infinite.not_bddAbove", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.filter_gt_eq_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finset.filter_ge_eq_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Finset.Icc_bot", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Icc_top", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ico_bot", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ioc_top", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Icc_bot_top", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.disjoint_Ioi_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Icc_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.Icc_eq_singleton_iff", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.Ico_disjoint_Ico_consecutive", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ici_top", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Iic_bot", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.instUniqueSubtypeMemIicBot", "kind": "instance", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "Finset.Icc_erase_left", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.Icc_erase_right", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.Ico_erase_left", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.Ioc_erase_right", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.Icc_diff_both", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.Ico_insert_right", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.Ioc_insert_left", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.Ioo_insert_left", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.Ioo_insert_right", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.Icc_diff_Ico_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.Icc_diff_Ioc_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.Icc_diff_Ioo_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.Ico_diff_Ioo_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.Ioc_diff_Ioo_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.Ico_inter_Ico_consecutive", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Icc_eq_cons_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finset.Icc_eq_cons_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finset.Ioc_eq_cons_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finset.Ico_eq_cons_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finset.Ico_filter_le_left", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.card_Ico_eq_card_Icc_sub_one", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["classical", "by_cases", "rw", "exact", "rw"], "tactic_count": 5}
{"name": "Finset.card_Ioc_eq_card_Icc_sub_one", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_Ioo_eq_card_Ico_sub_one", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["classical", "by_cases", "rw", "exact", "rw"], "tactic_count": 5}
{"name": "Finset.card_Ioo_eq_card_Ioc_sub_one", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_Ioo_eq_card_Icc_sub_two", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Finset.uIcc_map_sectL", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Finset.Icc_map_sectL", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Finset.Ioc_map_sectL", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Finset.Ico_map_sectL", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Finset.Ioo_map_sectL", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Finset.uIcc_map_sectR", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Finset.Icc_map_sectR", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Finset.Ioc_map_sectR", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Finset.Ico_map_sectR", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Finset.Ioo_map_sectR", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Finset.Ici_erase", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp_rw"], "tactic_count": 2}
{"name": "Finset.Ioi_insert", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp_rw"], "tactic_count": 2}
{"name": "Finset.notMem_Ioi_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ici_eq_cons_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finset.card_Ioi_eq_card_Ici_sub_one", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.Iic_erase", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp_rw"], "tactic_count": 2}
{"name": "Finset.Iio_insert", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp_rw"], "tactic_count": 2}
{"name": "Finset.notMem_Iio_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Iic_eq_cons_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finset.card_Iio_eq_card_Iic_sub_one", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.sup'_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.sup_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.image_subset_Iic_sup", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact"], "tactic_count": 3}
{"name": "Finset.subset_Iic_sup_id", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inf'_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.inf_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ico_subset_Ico_iff", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.Ico_union_Ico_eq_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.Ioc_union_Ioc_eq_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.Ico_subset_Ico_union_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finset.Ico_union_Ico'", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.Ico_union_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.Ico_inter_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.Ioc_inter_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.Ico_filter_lt", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.Ico_filter_le", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.Ioo_filter_lt", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.Iio_filter_lt", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.Ico_diff_Ico_left", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.Ico_diff_Ico_right", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.Ioc_disjoint_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Finset.Iic_diff_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.Iic_diff_Ioc_self_of_le", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.Iic_union_Ioc_eq_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.Infinite.exists_gt", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.infinite_iff_exists_gt", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Infinite.exists_lt", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.infinite_iff_exists_lt", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ioi_disjUnion_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Finset.uIcc_toDual", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.uIcc_of_le", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.uIcc_of_ge", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.uIcc_comm", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.uIcc_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.nonempty_uIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Icc_subset_uIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Icc_subset_uIcc'", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.left_mem_uIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.right_mem_uIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_uIcc_of_le", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_uIcc_of_ge", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.uIcc_subset_uIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finset.uIcc_subset_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finset.uIcc_subset_uIcc_iff_mem", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.uIcc_subset_uIcc_iff_le'", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.uIcc_subset_uIcc_right", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.uIcc_subset_uIcc_left", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.eq_of_mem_uIcc_of_mem_uIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Finset.eq_of_mem_uIcc_of_mem_uIcc'", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Finset.uIcc_injective_right", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.uIcc_injective_left", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Finset.Icc_min_max", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.uIcc_of_not_le", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.uIcc_of_not_ge", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.uIcc_eq_union", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_uIcc'", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.notMem_uIcc_of_lt", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finset.notMem_uIcc_of_gt", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finset.uIcc_subset_uIcc_iff_le", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.uIcc_subset_uIcc_union_uIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "transGen_wcovBy_of_le", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["have", "card_lt_card", "by_cases", "exact", "obtain", "have", "calc", "have", "have", "exact", "termination_by"], "tactic_count": 11}
{"name": "le_iff_transGen_wcovBy", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["refine", "induction", "single", "tail"], "tactic_count": 4}
{"name": "le_iff_reflTransGen_covBy", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "transGen_covBy_of_lt", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["obtain", "have", "card_lt_card", "ssubset_iff_of_subset", "have", "by_cases", "exact", "simp", "exact", "termination_by"], "tactic_count": 10}
{"name": "lt_iff_transGen_covBy", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["refine", "induction", "single", "tail"], "tactic_count": 4}
{"name": "monotone_iff_forall_wcovBy", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["refine", "simpa"], "tactic_count": 2}
{"name": "monotone_iff_forall_covBy", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["refine", "simpa"], "tactic_count": 2}
{"name": "strictMono_iff_forall_covBy", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": true, "tactics": ["refine", "have", "rw", "exact"], "tactic_count": 4}
{"name": "antitone_iff_forall_wcovBy", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "antitone_iff_forall_covBy", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictAnti_iff_forall_covBy", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Order.Interval.Finset.Box.0.Finset.Icc_neg_mono", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Box", "is_tactic_proof": true, "tactics": ["refine"], "tactic_count": 1}
{"name": "Finset.box", "kind": "definition", "module": "Mathlib.Order.Interval.Finset.Box", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.box_zero", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Box", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.box_succ_eq_sdiff", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Box", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Finset.disjoint_box_succ_prod", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Box", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.box_succ_union_prod", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Box", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.box_succ_disjUnion", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Box", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.zero_mem_box", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Box", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Finset.eq_zero_iff_eq_zero_of_mem_box", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Box", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.card_box_succ", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Box", "is_tactic_proof": false, "tactics": ["rw", "simp_rw", "snd_add,"], "tactic_count": 3}
{"name": "Int.card_box", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Box", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.mem_box", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Box", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.existsUnique_mem_box", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Box", "is_tactic_proof": true, "tactics": ["use"], "tactic_count": 1}
{"name": "LocallyFiniteOrder.ofIcc'", "kind": "definition", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyFiniteOrder.ofIcc", "kind": "definition", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyFiniteOrderTop.ofIci'", "kind": "definition", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyFiniteOrderTop.ofIci", "kind": "definition", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyFiniteOrderBot.ofIic'", "kind": "definition", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyFiniteOrderBot.ofIic", "kind": "definition", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsEmpty.toLocallyFiniteOrder", "kind": "abbrev", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsEmpty.toLocallyFiniteOrderTop", "kind": "abbrev", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsEmpty.toLocallyFiniteOrderBot", "kind": "abbrev", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Icc", "kind": "definition", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ico", "kind": "definition", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ioc", "kind": "definition", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ioo", "kind": "definition", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.coe_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.coe_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.coe_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.coe_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ici", "kind": "definition", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ioi", "kind": "definition", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.coe_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.coe_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Iic", "kind": "definition", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Iio", "kind": "definition", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.coe_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.coe_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyFiniteOrder.toLocallyFiniteOrderTop", "kind": "instance", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ici_eq_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ioi_eq_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyFiniteOrder.toLocallyFiniteOrderBot", "kind": "instance", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Iic_eq_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Iio_eq_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.uIcc", "kind": "definition", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinsetInterval.term[[_,_]]", "kind": "definition", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinsetInterval._aux_Mathlib_Order_Interval_Finset_Defs___macroRules_FinsetInterval_term[[_,_]]_1", "kind": "definition", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FinsetInterval._aux_Mathlib_Order_Interval_Finset_Defs___unexpand_Finset_uIcc_1", "kind": "definition", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.mem_uIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.coe_uIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_uIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.elabFinsetBuilderIxx", "kind": "definition", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instFintypeIcc", "kind": "instance", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instFintypeIco", "kind": "instance", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instFintypeIoc", "kind": "instance", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instFintypeIoo", "kind": "instance", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.finite_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.finite_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.finite_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.finite_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instFintypeIci", "kind": "instance", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instFintypeIoi", "kind": "instance", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.finite_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.finite_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instFintypeIic", "kind": "instance", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instFintypeIio", "kind": "instance", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.finite_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.finite_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.fintypeUIcc", "kind": "instance", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.finite_interval", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyFiniteOrder.ofFiniteIcc", "kind": "definition", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.toLocallyFiniteOrder", "kind": "abbrev", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instSubsingletonLocallyFiniteOrder", "kind": "instance", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instSubsingletonLocallyFiniteOrderTop", "kind": "instance", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instSubsingletonLocallyFiniteOrderBot", "kind": "instance", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderEmbedding.locallyFiniteOrder", "kind": "definition", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instLocallyFiniteOrder", "kind": "instance", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Icc_orderDual_def", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ico_orderDual_def", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ioc_orderDual_def", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ioo_orderDual_def", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Icc_toDual", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ico_toDual", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ioc_toDual", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ioo_toDual", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Icc_ofDual", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ico_ofDual", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ioc_ofDual", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ioo_ofDual", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instLocallyFiniteOrderBot", "kind": "instance", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Iic_orderDual_def", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Iio_orderDual_def", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Iic_toDual", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Iio_toDual", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ici_ofDual", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ioi_ofDual", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instLocallyFiniteOrderTop", "kind": "instance", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ici_orderDual_def", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ioi_orderDual_def", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ici_toDual", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ioi_toDual", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Iic_ofDual", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Iio_ofDual", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instLocallyFiniteOrder", "kind": "instance", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Icc_prod_def", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Icc_product_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_Icc_prod", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instLocallyFiniteOrderTop", "kind": "instance", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ici_prod_def", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ici_product_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_Ici_prod", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instLocallyFiniteOrderBot", "kind": "instance", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Iic_prod_def", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Iic_product_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_Iic_prod", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.uIcc_prod_def", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.uIcc_product_uIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.card_uIcc_prod", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.insertTop", "kind": "definition", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.some_mem_insertTop", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WithTop.top_mem_insertTop", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WithTop.locallyFiniteOrder", "kind": "instance", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.Icc_coe_top", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.Icc_coe_coe", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.Ico_coe_top", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.Ico_coe_coe", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.Ioc_coe_top", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.Ioc_coe_coe", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.Ioo_coe_top", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.Ioo_coe_coe", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.insertBot", "kind": "definition", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.some_mem_insertBot", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WithBot.bot_mem_insertBot", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WithBot.instLocallyFiniteOrder", "kind": "instance", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.Icc_bot_coe", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.Icc_coe_coe", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.Ico_bot_coe", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.Ico_coe_coe", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.Ioc_bot_coe", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.Ioc_coe_coe", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.Ioo_bot_coe", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.Ioo_coe_coe", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.locallyFiniteOrder", "kind": "abbrev", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.locallyFiniteOrderTop", "kind": "abbrev", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.locallyFiniteOrderBot", "kind": "abbrev", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.instLocallyFiniteOrder", "kind": "instance", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.instLocallyFiniteOrderTop", "kind": "instance", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.instLocallyFiniteOrderBot", "kind": "instance", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.subtype_Icc_eq", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.subtype_Ico_eq", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.subtype_Ioc_eq", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.subtype_Ioo_eq", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.map_subtype_embedding_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "Finset.map_subtype_embedding_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "Finset.map_subtype_embedding_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "Finset.map_subtype_embedding_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "Finset.subtype_Ici_eq", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.subtype_Ioi_eq", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.map_subtype_embedding_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finset.map_subtype_embedding_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finset.subtype_Iic_eq", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.subtype_Iio_eq", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.map_subtype_embedding_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finset.map_subtype_embedding_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "BddBelow.finite_of_bddAbove", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.finite_iff_bddAbove", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.finite_iff_bddBelow", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.finite_iff_bddBelow_bddAbove", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": true, "tactics": ["obtain", "simp", "exact"], "tactic_count": 3}
{"name": "instLocallyFiniteOrderTopSubtypeLeOfDecidableLEOfLocallyFiniteOrder", "kind": "instance", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instLocallyFiniteOrderTopSubtypeLtOfDecidableLTOfLocallyFiniteOrder", "kind": "instance", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instLocallyFiniteOrderBotSubtypeLeOfDecidableLEOfLocallyFiniteOrder", "kind": "instance", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instLocallyFiniteOrderBotSubtypeLtOfDecidableLTOfLocallyFiniteOrder", "kind": "instance", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFiniteSubtypeLeOfLocallyFiniteOrderBot", "kind": "instance", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "instFiniteSubtypeLtOfLocallyFiniteOrderBot", "kind": "instance", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "instFiniteSubtypeLeOfLocallyFiniteOrderTop", "kind": "instance", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "instFiniteSubtypeLtOfLocallyFiniteOrderTop", "kind": "instance", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.toFinset_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Set.toFinset_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Set.toFinset_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Set.toFinset_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Set.toFinset_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Set.toFinset_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Set.toFinset_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Set.toFinset_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "LocallyFiniteOrder.ofOrderIsoClass", "kind": "abbrev", "module": "Mathlib.Order.Interval.Finset.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyFiniteOrder.denselyOrdered_iff_subsingleton", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.DenselyOrdered", "is_tactic_proof": true, "tactics": ["refine", "rw", "rintro", "exact"], "tactic_count": 4}
{"name": "denselyOrdered_set_iff_subsingleton", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.DenselyOrdered", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "WithBot.denselyOrdered_set_iff_subsingleton", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.DenselyOrdered", "is_tactic_proof": true, "tactics": ["refine", "rw", "suffices", "rintro", "rw", "obtain", "have", "replace", "rwa", "refine", "constructor", "simp", "intro", "have", "obtain", "simp", "refine", "simp", "rw", "simp", "rw", "simp"], "tactic_count": 22}
{"name": "WithTop.denselyOrdered_set_iff_subsingleton", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.DenselyOrdered", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "Fin.instLocallyFiniteOrder", "kind": "instance", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.instLocallyFiniteOrderBot", "kind": "instance", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.instLocallyFiniteOrderTop", "kind": "instance", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.attachFin_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.attachFin_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.attachFin_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.attachFin_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.attachFin_uIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.attachFin_Ico_eq_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Fin.attachFin_Ioo_eq_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Fin.attachFin_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Fin.attachFin_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Fin.finsetImage_val_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.finsetImage_val_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.finsetImage_val_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.finsetImage_val_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.finsetImage_val_uIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.finsetImage_val_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.finsetImage_val_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.finsetImage_val_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.finsetImage_val_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.map_valEmbedding_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.map_valEmbedding_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.map_valEmbedding_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.map_valEmbedding_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.map_valEmbedding_uIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.map_valEmbedding_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.map_valEmbedding_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.map_valEmbedding_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.map_valEmbedding_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.finsetImage_castLE_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.finsetImage_castLE_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.finsetImage_castLE_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.finsetImage_castLE_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.finsetImage_castLE_uIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.finsetImage_castLE_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.finsetImage_castLE_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.map_castLEEmb_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.map_castLEEmb_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.map_castLEEmb_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.map_castLEEmb_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.map_castLEEmb_uIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.map_castLEEmb_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.map_castLEEmb_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.finsetImage_castAdd_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.finsetImage_castAdd_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.finsetImage_castAdd_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.finsetImage_castAdd_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.finsetImage_castAdd_uIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.finsetImage_castAdd_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.finsetImage_castAdd_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.finsetImage_castAdd_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.finsetImage_castAdd_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.map_castAddEmb_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.map_castAddEmb_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.map_castAddEmb_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.map_castAddEmb_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.map_castAddEmb_uIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.map_castAddEmb_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.map_castAddEmb_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.map_castAddEmb_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.map_castAddEmb_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.finsetImage_cast_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.finsetImage_cast_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.finsetImage_cast_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.finsetImage_cast_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.finsetImage_cast_uIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.finsetImage_cast_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.finsetImage_cast_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.finsetImage_cast_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.finsetImage_cast_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.map_finCongr_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.map_finCongr_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.map_finCongr_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.map_finCongr_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.map_finCongr_uIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.map_finCongr_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.map_finCongr_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.map_finCongr_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.map_finCongr_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.finsetImage_castSucc_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.finsetImage_castSucc_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Fin.finsetImage_castSucc_uIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.finsetImage_castSucc_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.finsetImage_castSucc_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.finsetImage_castSucc_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.finsetImage_castSucc_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.map_castSuccEmb_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.map_castSuccEmb_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.map_castSuccEmb_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.map_castSuccEmb_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.map_castSuccEmb_uIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.map_castSuccEmb_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.map_castSuccEmb_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.map_castSuccEmb_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.map_castSuccEmb_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.finsetImage_natAdd_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.finsetImage_natAdd_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.finsetImage_natAdd_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.finsetImage_natAdd_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.finsetImage_natAdd_uIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.finsetImage_natAdd_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.finsetImage_natAdd_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.map_natAddEmb_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.map_natAddEmb_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.map_natAddEmb_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.map_natAddEmb_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.map_natAddEmb_uIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.map_natAddEmb_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.map_natAddEmb_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.finsetImage_addNat_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.finsetImage_addNat_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.finsetImage_addNat_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "Fin.finsetImage_addNat_uIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.finsetImage_addNat_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.finsetImage_addNat_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.map_addNatEmb_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.map_addNatEmb_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.map_addNatEmb_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.map_addNatEmb_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.map_addNatEmb_uIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.map_addNatEmb_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.map_addNatEmb_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.finsetImage_succ_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.finsetImage_succ_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.finsetImage_succ_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.finsetImage_succ_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.finsetImage_succ_uIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.finsetImage_succ_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.finsetImage_succ_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.finsetImage_succ_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.finsetImage_succ_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.map_succEmb_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.map_succEmb_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.map_succEmb_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.map_succEmb_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.map_succEmb_uIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.map_succEmb_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.map_succEmb_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.map_succEmb_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "Fin.finsetImage_rev_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.finsetImage_rev_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.finsetImage_rev_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.finsetImage_rev_uIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.finsetImage_rev_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.finsetImage_rev_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.finsetImage_rev_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.finsetImage_rev_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.map_revPerm_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.map_revPerm_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.map_revPerm_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.map_revPerm_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.map_revPerm_uIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.map_revPerm_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.map_revPerm_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.map_revPerm_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.map_revPerm_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.card_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.card_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.card_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.card_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.card_uIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.card_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.card_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.card_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.card_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.Iio_add_one_eq_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Fin.Iic_sub_one_eq_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Fin.Ici_add_one_eq_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Fin.Ioi_sub_one_eq_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Fin.Ioc_sub_one_eq_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Fin.Icc_add_one_eq_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Fin.Ioo_sub_one_eq_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Fin.Ico_add_one_eq_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Fin.Icc_sub_one_eq_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Fin.Ico_add_one_eq_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Fin.Ioc_sub_one_eq_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Fin.Ioo_add_one_eq_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Fin", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.intervalGapsWithin", "kind": "definition", "module": "Mathlib.Order.Interval.Finset.Gaps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.intervalGapsWithin_zero_fst", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Gaps", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.intervalGapsWithin_succ_fst_of_lt", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Gaps", "is_tactic_proof": true, "tactics": ["have", "grind"], "tactic_count": 2}
{"name": "Finset.intervalGapsWithin_fst_of_lt_lt", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Gaps", "is_tactic_proof": true, "tactics": ["convert", "omega"], "tactic_count": 2}
{"name": "Finset.intervalGapsWithin_last_snd", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Gaps", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finset.intervalGapsWithin_snd_of_lt", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Gaps", "is_tactic_proof": true, "tactics": ["have", "simp", "congr", "ext", "simp", "omega"], "tactic_count": 6}
{"name": "Finset.intervalGapsWithin_mapsTo", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Gaps", "is_tactic_proof": true, "tactics": ["intro", "rw", "simp", "convert"], "tactic_count": 4}
{"name": "Finset.intervalGapsWithin_injOn", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Gaps", "is_tactic_proof": true, "tactics": ["intro", "rw", "simp", "grind"], "tactic_count": 4}
{"name": "Finset.intervalGapsWithin_surjOn", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Gaps", "is_tactic_proof": true, "tactics": ["intro", "rw", "obtain", "use", "simp"], "tactic_count": 5}
{"name": "Finset.intervalGapsWithin_le_fst", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Gaps", "is_tactic_proof": true, "tactics": ["wlog", "convert", "by_cases", "simp", "have", "have", "simp", "grind"], "tactic_count": 8}
{"name": "Finset.intervalGapsWithin_snd_le", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Gaps", "is_tactic_proof": true, "tactics": ["wlog", "convert", "by_cases", "simp", "have", "grind"], "tactic_count": 6}
{"name": "Finset.intervalGapsWithin_fst_le_snd", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Gaps", "is_tactic_proof": true, "tactics": ["wlog", "convert", "by_cases", "simp", "by_cases", "simp", "simp", "exact", "have", "by_cases", "simp", "convert", "simp", "rw", "intervalGapsWithin_snd_of_lt", "have", "set", "have", "hF", "contrapose", "simp", "use", "have", "have", "simp"], "tactic_count": 25}
{"name": "Finset.intervalGapsWithin_pairwiseDisjoint_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Gaps", "is_tactic_proof": true, "tactics": ["intro", "rw", "wlog", "exact", "rw", "suffices", "have", "have", "simp", "grw", "rw", "exact"], "tactic_count": 12}
{"name": "Nat.instLocallyFiniteOrder", "kind": "instance", "module": "Mathlib.Order.Interval.Finset.Nat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.instUniqueSubtypeMemFinsetIicOfNat", "kind": "instance", "module": "Mathlib.Order.Interval.Finset.Nat", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "Nat.Icc_eq_range'", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Nat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Ico_eq_range'", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Nat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Ioc_eq_range'", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Nat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Ioo_eq_range'", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Nat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.uIcc_eq_range'", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Nat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Iio_eq_range", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Nat", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Nat.Ico_zero_eq_range", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Nat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.range_eq_Icc_zero_sub_one", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Nat", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Finset.range_eq_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Nat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.range_succ_eq_Icc_zero", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Nat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.range_succ_eq_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Nat", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Nat.card_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Nat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.card_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Nat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.card_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Nat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.card_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Nat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.card_uIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Nat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.card_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Nat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.card_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Nat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.Ico_succ_singleton", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Nat", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Nat.Ico_pred_singleton", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Nat", "is_tactic_proof": true, "tactics": ["ext", "rw", "lia"], "tactic_count": 3}
{"name": "Nat.Ioc_succ_singleton", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Nat", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Nat.mem_Ioc_succ", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Nat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.mem_Ioc_succ'", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Nat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.image_sub_const_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Nat", "is_tactic_proof": true, "tactics": ["ext", "simp_rw", "refine", "rintro", "lia"], "tactic_count": 5}
{"name": "Nat.Ico_image_const_sub_eq_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Nat", "is_tactic_proof": true, "tactics": ["ext", "simp_rw", "refine", "rintro", "lia"], "tactic_count": 5}
{"name": "Nat.Ico_succ_left_eq_erase_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Nat", "is_tactic_proof": true, "tactics": ["ext", "simp_rw", "lia"], "tactic_count": 3}
{"name": "Nat.Ico_succ_right_eq_insert_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Nat", "is_tactic_proof": true, "tactics": ["ext", "simp_rw", "lia"], "tactic_count": 3}
{"name": "Nat.mod_injOn_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Nat", "is_tactic_proof": true, "tactics": ["induction", "zero", "simp", "rintro", "simp", "rwa", "succ", "ih", "rw", "rintro", "have", "simp", "rcases", "rfl", "rw", "refine", "simpa", "rw", "suffices", "refine", "simpa", "refine"], "tactic_count": 22}
{"name": "Nat.image_Ico_mod", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Nat", "is_tactic_proof": true, "tactics": ["obtain", "rw", "ext", "simp", "constructor", "rintro", "exact", "intro", "have", "obtain", "refine", "rw", "refine", "simpa", "refine", "rw", "rw", "refine", "lia", "lia", "rw"], "tactic_count": 21}
{"name": "Nat.multiset_Ico_map_mod", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Nat", "is_tactic_proof": true, "tactics": ["convert", "refine", "exact"], "tactic_count": 3}
{"name": "List.toFinset_range'_1", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Nat", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "List.toFinset_range'_1_1", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Nat", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "List.toFinset_range", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Nat", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "Finset.range_image_pred_top_sub", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Nat", "is_tactic_proof": true, "tactics": ["cases", "rw", "rw", "simp_rw"], "tactic_count": 4}
{"name": "Finset.range_add_eq_union", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Nat", "is_tactic_proof": true, "tactics": ["rw", "convert", "ext", "simp", "constructor", "lia", "rintro", "exact"], "tactic_count": 8}
{"name": "Nat.decreasing_induction_of_not_bddAbove", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Nat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.strong_decreasing_induction", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Nat", "is_tactic_proof": true, "tactics": ["apply", "intro", "rcases", "exact", "exact", "rintro", "rcases", "specialize", "all_goals"], "tactic_count": 9}
{"name": "Nat.decreasing_induction_of_infinite", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Nat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.cauchy_induction'", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Nat", "is_tactic_proof": true, "tactics": ["apply", "intro", "obtain", "obtain", "exact"], "tactic_count": 5}
{"name": "Nat.cauchy_induction", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Nat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.cauchy_induction_mul", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Nat", "is_tactic_proof": true, "tactics": ["apply", "intro", "convert", "rw"], "tactic_count": 4}
{"name": "Nat.cauchy_induction_two_mul", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Nat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.pow_imp_self_of_one_lt", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.Nat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ico_succ_left_eq_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Icc_succ_left_eq_Ioc_of_not_isMax", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ico_succ_right_eq_Icc_of_not_isMax", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ioo_succ_right_eq_Ioc_of_not_isMax", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ico_succ_succ_eq_Ioc_of_not_isMax", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.insert_Icc_succ_left_eq_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.insert_Icc_right_eq_Icc_succ", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.insert_Ico_right_eq_Ico_succ_of_not_isMax", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.insert_Ico_succ_left_eq_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.insert_Ioc_right_eq_Ioc_succ_of_not_isMax", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.insert_Ioc_succ_left_eq_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Icc_succ_left_eq_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ico_succ_right_eq_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ioo_succ_right_eq_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ico_succ_succ_eq_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.insert_Ico_right_eq_Ico_succ", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.insert_Ioc_right_eq_Ioc_succ", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ioc_pred_right_eq_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Icc_pred_right_eq_Ico_of_not_isMin", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ioc_pred_left_eq_Icc_of_not_isMin", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ioo_pred_left_eq_Ioc_of_not_isMin", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ioc_pred_pred_eq_Ico_of_not_isMin", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.insert_Icc_pred_right_eq_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.insert_Icc_left_eq_Icc_pred", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.insert_Ioc_left_eq_Ioc_pred_of_not_isMin", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.insert_Ioc_pred_right_eq_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.insert_Ico_left_eq_Ico_pred_of_not_isMin", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.insert_Ico_pred_right_eq_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Icc_pred_right_eq_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ioc_pred_left_eq_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ioo_pred_left_eq_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ioc_pred_pred_eq_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.insert_Ioc_left_eq_Ioc_pred", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.insert_Ico_left_eq_Ico_pred", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Icc_succ_pred_eq_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Iio_succ_eq_Iic_of_not_isMax", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Iio_succ_eq_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Iic_pred_eq_Iio_of_not_isMin", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Iic_pred_eq_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ici_succ_eq_Ioi_of_not_isMax", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ici_succ_eq_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ioi_pred_eq_Ici_of_not_isMin", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.Ioi_pred_eq_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Finset.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.instLELex", "kind": "instance", "module": "Mathlib.Order.Interval.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.instLTLex", "kind": "instance", "module": "Mathlib.Order.Interval.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.toLex_le_toLex", "kind": "theorem", "module": "Mathlib.Order.Interval.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.toLex_lt_toLex", "kind": "theorem", "module": "Mathlib.Order.Interval.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.instDecidableLELexOfDecidableEqOfDecidableLT", "kind": "instance", "module": "Mathlib.Order.Interval.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.instDecidableLTLexOfDecidableEq", "kind": "instance", "module": "Mathlib.Order.Interval.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.instPreorderLex", "kind": "instance", "module": "Mathlib.Order.Interval.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.toLex_mono", "kind": "theorem", "module": "Mathlib.Order.Interval.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.toLex_strictMono", "kind": "theorem", "module": "Mathlib.Order.Interval.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.instPartialOrderLex", "kind": "instance", "module": "Mathlib.Order.Interval.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyInterval.instLinearOrderLex", "kind": "instance", "module": "Mathlib.Order.Interval.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Icc", "kind": "definition", "module": "Mathlib.Order.Interval.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Ico", "kind": "definition", "module": "Mathlib.Order.Interval.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Ioc", "kind": "definition", "module": "Mathlib.Order.Interval.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Ioo", "kind": "definition", "module": "Mathlib.Order.Interval.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.mem_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Multiset", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.mem_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Multiset", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.mem_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Multiset", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.mem_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Multiset", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.Ici", "kind": "definition", "module": "Mathlib.Order.Interval.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Ioi", "kind": "definition", "module": "Mathlib.Order.Interval.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.mem_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Multiset", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.mem_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Multiset", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.Iic", "kind": "definition", "module": "Mathlib.Order.Interval.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Iio", "kind": "definition", "module": "Mathlib.Order.Interval.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.mem_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Multiset", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.mem_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Multiset", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.nodup_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.nodup_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.nodup_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.nodup_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Icc_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Order.Interval.Multiset", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.Ico_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Order.Interval.Multiset", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.Ioc_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Order.Interval.Multiset", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.Ioo_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Order.Interval.Multiset", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.Ioo_eq_zero", "kind": "theorem", "module": "Mathlib.Order.Interval.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Icc_eq_zero_of_lt", "kind": "theorem", "module": "Mathlib.Order.Interval.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Ico_eq_zero_of_le", "kind": "theorem", "module": "Mathlib.Order.Interval.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Ioc_eq_zero_of_le", "kind": "theorem", "module": "Mathlib.Order.Interval.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Ioo_eq_zero_of_le", "kind": "theorem", "module": "Mathlib.Order.Interval.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Ico_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Multiset", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.Ioc_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Multiset", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.Ioo_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Multiset", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.left_mem_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.left_mem_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.right_mem_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.right_mem_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.left_notMem_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.left_notMem_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.right_notMem_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.right_notMem_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Ico_filter_lt_of_le_left", "kind": "theorem", "module": "Mathlib.Order.Interval.Multiset", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Multiset.Ico_filter_lt_of_right_le", "kind": "theorem", "module": "Mathlib.Order.Interval.Multiset", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.Ico_filter_lt_of_le_right", "kind": "theorem", "module": "Mathlib.Order.Interval.Multiset", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Multiset.Ico_filter_le_of_le_left", "kind": "theorem", "module": "Mathlib.Order.Interval.Multiset", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.Ico_filter_le_of_right_le", "kind": "theorem", "module": "Mathlib.Order.Interval.Multiset", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Multiset.Ico_filter_le_of_left_le", "kind": "theorem", "module": "Mathlib.Order.Interval.Multiset", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Multiset.Icc_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Multiset", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.Ico_cons_right", "kind": "theorem", "module": "Mathlib.Order.Interval.Multiset", "is_tactic_proof": true, "tactics": ["classical", "rw", "rfl"], "tactic_count": 3}
{"name": "Multiset.Ioo_cons_left", "kind": "theorem", "module": "Mathlib.Order.Interval.Multiset", "is_tactic_proof": true, "tactics": ["classical", "rw", "rfl"], "tactic_count": 3}
{"name": "Multiset.Ico_disjoint_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Ico_inter_Ico_of_le", "kind": "theorem", "module": "Mathlib.Order.Interval.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Ico_filter_le_left", "kind": "theorem", "module": "Mathlib.Order.Interval.Multiset", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Multiset.card_Ico_eq_card_Icc_sub_one", "kind": "theorem", "module": "Mathlib.Order.Interval.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.card_Ioc_eq_card_Icc_sub_one", "kind": "theorem", "module": "Mathlib.Order.Interval.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.card_Ioo_eq_card_Ico_sub_one", "kind": "theorem", "module": "Mathlib.Order.Interval.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.card_Ioo_eq_card_Icc_sub_two", "kind": "theorem", "module": "Mathlib.Order.Interval.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Ico_subset_Ico_iff", "kind": "theorem", "module": "Mathlib.Order.Interval.Multiset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiset.Ico_add_Ico_eq_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Multiset", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.Ico_inter_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Multiset", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.Ico_filter_lt", "kind": "theorem", "module": "Mathlib.Order.Interval.Multiset", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.Ico_filter_le", "kind": "theorem", "module": "Mathlib.Order.Interval.Multiset", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.Ico_sub_Ico_left", "kind": "theorem", "module": "Mathlib.Order.Interval.Multiset", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multiset.Ico_sub_Ico_right", "kind": "theorem", "module": "Mathlib.Order.Interval.Multiset", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.decidableMemIoo", "kind": "instance", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["assumption"], "tactic_count": 1}
{"name": "Set.decidableMemIco", "kind": "instance", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["assumption"], "tactic_count": 1}
{"name": "Set.decidableMemIio", "kind": "instance", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["assumption"], "tactic_count": 1}
{"name": "Set.decidableMemIcc", "kind": "instance", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["assumption"], "tactic_count": 1}
{"name": "Set.decidableMemIic", "kind": "instance", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["assumption"], "tactic_count": 1}
{"name": "Set.decidableMemIoc", "kind": "instance", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["assumption"], "tactic_count": 1}
{"name": "Set.decidableMemIci", "kind": "instance", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["assumption"], "tactic_count": 1}
{"name": "Set.decidableMemIoi", "kind": "instance", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["assumption"], "tactic_count": 1}
{"name": "Set.left_notMem_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.left_notMem_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.left_mem_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.left_mem_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.left_mem_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.left_mem_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.self_notMem_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.self_mem_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.right_notMem_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.right_notMem_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.right_mem_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.right_mem_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.right_mem_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.right_mem_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.self_notMem_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.self_mem_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.Ici_toDual", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iic_toDual", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioi_toDual", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iio_toDual", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc_toDual", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioc_toDual", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ico_toDual", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioo_toDual", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ici_ofDual", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iic_ofDual", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioi_ofDual", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iio_ofDual", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc_ofDual", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ico_ofDual", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioc_ofDual", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioo_ofDual", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.nonempty_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.nonempty_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.nonempty_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.nonempty_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.nonempty_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.nonempty_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.nonempty_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.nonempty_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.nonempty_Icc_subtype", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.nonempty_Ico_subtype", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.nonempty_Ioc_subtype", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.nonempty_Ici_subtype", "kind": "instance", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.nonempty_Iic_subtype", "kind": "instance", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.nonempty_Ioo_subtype", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.nonempty_Ioi_subtype", "kind": "instance", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.nonempty_Iio_subtype", "kind": "instance", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instNoMinOrderElemIio", "kind": "instance", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instNoMinOrderElemIic", "kind": "instance", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instNoMaxOrderElemIoi", "kind": "instance", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instNoMaxOrderElemIci", "kind": "instance", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc_eq_empty", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ico_eq_empty", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioc_eq_empty", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioo_eq_empty", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc_eq_empty_of_lt", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ico_eq_empty_of_le", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioc_eq_empty_of_le", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioo_eq_empty_of_le", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ico_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioc_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioo_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ici_subset_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ici_ssubset_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iic_subset_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iic_ssubset_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ici_subset_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iic_subset_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioo_subset_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioo_subset_Ioo_left", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioo_subset_Ioo_right", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ico_subset_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ico_subset_Ico_left", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ico_subset_Ico_right", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc_subset_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc_subset_Icc_left", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc_subset_Icc_right", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc_subset_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc_subset_Ici_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc_subset_Iic_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioc_subset_Iic_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioc_subset_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioc_subset_Ioc_left", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioc_subset_Ioc_right", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ico_subset_Ioo_left", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioc_subset_Ioo_right", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc_subset_Ico_right", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioo_subset_Ico_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioo_subset_Ioc_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ico_subset_Icc_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioc_subset_Icc_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioo_subset_Icc_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ico_subset_Iio_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioo_subset_Iio_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioc_subset_Ioi_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioo_subset_Ioi_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioi_subset_Ici_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iio_subset_Iic_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ico_subset_Ici_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioi_ssubset_Ici_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iio_ssubset_Iic_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc_subset_Icc_iff", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc_subset_Ioo_iff", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc_subset_Ico_iff", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc_subset_Ioc_iff", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc_subset_Iio_iff", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc_subset_Ioi_iff", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc_subset_Iic_iff", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc_subset_Ici_iff", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc_ssubset_Icc_left", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc_ssubset_Icc_right", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioi_subset_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioi_ssubset_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioi_subset_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iio_subset_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iio_ssubset_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iio_subset_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ici_inter_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ici_inter_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioi_inter_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioi_inter_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iic_inter_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iio_inter_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iic_inter_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iio_inter_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_Icc_of_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_Ico_of_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_Ioc_of_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_Icc_of_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_Icc_of_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_Ici_of_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_Iic_of_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc_eq_empty_iff", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.Ico_eq_empty_iff", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.Ioc_eq_empty_iff", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.Ioo_eq_empty_iff", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsTop.Iic_eq", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBot.Ici_eq", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioi_eq_empty_iff", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.Iio_eq_empty_iff", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iio_nonempty", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.Ioi_nonempty", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.Iic_inter_Ioc_of_le", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.notMem_Icc_of_lt", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.notMem_Icc_of_gt", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.notMem_Ico_of_lt", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.notMem_Ioc_of_gt", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.notMem_Ioi_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.notMem_Iio_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.notMem_Ioc_of_le", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.notMem_Ico_of_ge", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.notMem_Ioo_of_le", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.notMem_Ioo_of_ge", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc_eq_Ioc_same_iff", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc_eq_Ico_same_iff", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc_eq_Ioo_same_iff", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioc_eq_Ico_same_iff", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioo_eq_Ioc_same_iff", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioo_eq_Ico_same_iff", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioc_eq_Icc_same_iff", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ico_eq_Icc_same_iff", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioo_eq_Icc_same_iff", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ico_eq_Ioc_same_iff", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioc_eq_Ioo_same_iff", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ico_eq_Ioo_same_iff", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instIccUnique", "kind": "instance", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc_eq_singleton_iff", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["refine", "have", "exact", "rintro", "exact"], "tactic_count": 5}
{"name": "Set.subsingleton_Icc_of_ge", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subsingleton_Icc_iff", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["refine", "contrapose", "exact"], "tactic_count": 3}
{"name": "Set.Icc_diff_left", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc_diff_right", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ico_diff_left", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioc_diff_right", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc_diff_both", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.Ici_diff_left", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iic_diff_right", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ico_diff_Ioo_same", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.Ioc_diff_Ioo_same", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.Icc_diff_Ico_same", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.Icc_diff_Ioc_same", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.Icc_diff_Ioo_same", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Set.Ici_diff_Ioi_same", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.Iic_diff_Iio_same", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.Ioi_union_left", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iio_union_right", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioo_union_left", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.Ioo_union_right", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.Ioo_union_both", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": ["have", "diff_union_of_subset", "x,", "x,", "rw"], "tactic_count": 5}
{"name": "Set.Ioc_union_left", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.Ico_union_right", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.Ico_insert_right", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.Ioc_insert_left", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.Ioo_insert_left", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.Ioo_insert_right", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.Iio_insert", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioi_insert", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_Ici_Ioi_of_subset_of_subset", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_Iic_Iio_of_subset_of_subset", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_Icc_Ico_Ioc_Ioo_of_subset_of_subset", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["classical", "by_cases", "refine", "rwa", "insert_eq_of_mem", "refine", "rw", "exact", "rwa", "refine", "rw", "exact", "rwa", "refine", "rw", "apply_rules"], "tactic_count": 16}
{"name": "Set.eq_left_or_mem_Ioo_of_mem_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.eq_right_or_mem_Ioo_of_mem_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.eq_endpoints_or_mem_Ioo_of_mem_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMax.Ici_eq", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMin.Iic_eq", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ici_injective", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iic_injective", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ici_inj", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iic_inj", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc_inter_Icc_eq_singleton", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Set.Icc_eq_Icc_iff", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["refine", "have", "simp", "obtain", "obtain", "obtain", "obtain", "exact"], "tactic_count": 8}
{"name": "Set.Ici_top", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iio_top", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioi_top", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iic_top", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc_top", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.Ioc_top", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.Iic_bot", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioi_bot", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iio_bot", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ici_bot", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc_bot", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.Ico_bot", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.Icc_bot_top", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.Iic_inter_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Set.Ioc_inter_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.Ici_inter_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Set.Ico_inter_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.Icc_inter_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.Iic_prod_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ici_prod_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ici_prod_eq", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iic_prod_eq", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc_prod_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Set.Icc_prod_eq", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "instNoMinOrderElemIoo", "kind": "instance", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instNoMinOrderElemIoc", "kind": "instance", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instNoMinOrderElemIoi", "kind": "instance", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instNoMaxOrderElemIoo", "kind": "instance", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instNoMaxOrderElemIco", "kind": "instance", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instNoMaxOrderElemIio", "kind": "instance", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iic_False", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Set.Iic_True", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Set.Ici_False", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Set.Ici_True", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Set.Iio_False", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Set.Iio_True", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Set.Ioi_False", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Set.Ioi_True", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Basic", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Set.Iio", "kind": "definition", "module": "Mathlib.Order.Interval.Set.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iio_def", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iic", "kind": "definition", "module": "Mathlib.Order.Interval.Set.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iic_def", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioo", "kind": "definition", "module": "Mathlib.Order.Interval.Set.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioo_def", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ico", "kind": "definition", "module": "Mathlib.Order.Interval.Set.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ico_def", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc", "kind": "definition", "module": "Mathlib.Order.Interval.Set.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc_def", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioc", "kind": "definition", "module": "Mathlib.Order.Interval.Set.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioc_def", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iic_disjoint_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iio_disjoint_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iic_disjoint_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioc_disjoint_Ioc_of_le", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ico_disjoint_Ico_same", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ici_disjoint_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Disjoint", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.Iic_disjoint_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioc_disjoint_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioc_disjoint_Ioi_same", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioi_disjoint_Iio_of_not_lt", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioi_disjoint_Iio_of_le", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioi_disjoint_Iio_same", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioi_disjoint_Iio_iff", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iio_disjoint_Ioi_of_not_lt", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iio_disjoint_Ioi_of_le", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iio_disjoint_Ioi_same", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iio_disjoint_Ioi_iff", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_Icc_right", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Disjoint", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.iUnion_Ioc_right", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Disjoint", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.iUnion_Icc_left", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Disjoint", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.iUnion_Ico_left", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Disjoint", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.iUnion_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.iUnion_Ico_right", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Disjoint", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.iUnion_Ioo_right", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Disjoint", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.iUnion_Ioc_left", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Disjoint", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.iUnion_Ioo_left", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Disjoint", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.Ico_disjoint_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Disjoint", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.Ioc_disjoint_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Disjoint", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "Set.Ioo_disjoint_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Disjoint", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.eq_of_Ico_disjoint", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Disjoint", "is_tactic_proof": true, "tactics": ["rw", "apply", "exact"], "tactic_count": 3}
{"name": "Set.iUnion_Ico_eq_Iio_self_iff", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Disjoint", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.iUnion_Ioc_eq_Ioi_self_iff", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Disjoint", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.biUnion_Ico_eq_Iio_self_iff", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Disjoint", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.biUnion_Ioc_eq_Ioi_self_iff", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Disjoint", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsGLB.biUnion_Ioi_eq", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Disjoint", "is_tactic_proof": true, "tactics": ["refine", "exact", "rcases", "exact"], "tactic_count": 4}
{"name": "IsGLB.iUnion_Ioi_eq", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLUB.biUnion_Iio_eq", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLUB.iUnion_Iio_eq", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGLB.biUnion_Ici_eq_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Disjoint", "is_tactic_proof": true, "tactics": ["refine", "exact", "rcases", "rw", "exact"], "tactic_count": 5}
{"name": "IsGLB.biUnion_Ici_eq_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Disjoint", "is_tactic_proof": true, "tactics": ["refine", "exact", "exact"], "tactic_count": 3}
{"name": "IsLUB.biUnion_Iic_eq_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLUB.biUnion_Iic_eq_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iUnion_Ici_eq_Ioi_iInf", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Disjoint", "is_tactic_proof": true, "tactics": ["simp", "iUnion_iUnion_eq']"], "tactic_count": 2}
{"name": "iUnion_Iic_eq_Iio_iSup", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iUnion_Ici_eq_Ici_iInf", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Disjoint", "is_tactic_proof": true, "tactics": ["simp", "iUnion_iUnion_eq']"], "tactic_count": 2}
{"name": "iUnion_Iic_eq_Iic_iSup", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Disjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iUnion_Iio_eq_univ_iff", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Disjoint", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "iUnion_Iic_of_not_bddAbove_range", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Disjoint", "is_tactic_proof": true, "tactics": ["refine", "gcongr", "exact"], "tactic_count": 3}
{"name": "iInter_Iic_eq_empty_iff", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Disjoint", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "iInter_Iio_of_not_bddBelow_range", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Disjoint", "is_tactic_proof": true, "tactics": ["refine", "rw", "gcongr", "exact"], "tactic_count": 4}
{"name": "Fin.range_val", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Fin.preimage_val_Ici_val", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.preimage_val_Ioi_val", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.preimage_val_Iic_val", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.preimage_val_Iio_val", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.preimage_val_Icc_val", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.preimage_val_Ico_val", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.preimage_val_Ioc_val", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.preimage_val_Ioo_val", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.preimage_val_uIcc_val", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.preimage_val_uIoc_val", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.preimage_val_uIoo_val", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.image_val_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.image_val_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Fin.image_val_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Fin.image_val_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Fin.image_val_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Fin.image_val_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Fin.image_val_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Fin.image_val_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Fin.image_val_uIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.image_val_uIoc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.image_val_uIoo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.preimage_castLE_Ici_castLE", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.preimage_castLE_Ioi_castLE", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.preimage_castLE_Iic_castLE", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.preimage_castLE_Iio_castLE", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.preimage_castLE_Icc_castLE", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.preimage_castLE_Ico_castLE", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.preimage_castLE_Ioc_castLE", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.preimage_castLE_Ioo_castLE", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.preimage_castLE_uIcc_castLE", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.preimage_castLE_uIoc_castLE", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.preimage_castLE_uIoo_castLE", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.image_castLE_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.image_castLE_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.image_castLE_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.image_castLE_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.image_castLE_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.image_castLE_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.image_castLE_uIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.image_castLE_uIoc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.image_castLE_uIoo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.range_castAdd", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.preimage_castAdd_Ici_castAdd", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.preimage_castAdd_Ioi_castAdd", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.preimage_castAdd_Iic_castAdd", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.preimage_castAdd_Iio_castAdd", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.preimage_castAdd_Icc_castAdd", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.preimage_castAdd_Ico_castAdd", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.preimage_castAdd_Ioc_castAdd", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.preimage_castAdd_Ioo_castAdd", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.preimage_castAdd_uIcc_castAdd", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.preimage_castAdd_uIoc_castAdd", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.preimage_castAdd_uIoo_castAdd", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.image_castAdd_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.image_castAdd_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.image_castAdd_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.image_castAdd_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.image_castAdd_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.image_castAdd_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.image_castAdd_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.image_castAdd_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.image_castAdd_uIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.image_castAdd_uIoc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.image_castAdd_uIoo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.image_cast", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.image_cast_fun", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.preimage_cast_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.preimage_cast_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.preimage_cast_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.preimage_cast_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.preimage_cast_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.preimage_cast_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.preimage_cast_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.preimage_cast_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.preimage_cast_uIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.preimage_cast_uIoc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.preimage_cast_uIoo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.preimage_castSucc_Ici_castSucc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.preimage_castSucc_Ioi_castSucc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.preimage_castSucc_Iic_castSucc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.preimage_castSucc_Iio_castSucc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.preimage_castSucc_Icc_castSucc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.preimage_castSucc_Ico_castSucc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.preimage_castSucc_Ioc_castSucc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.preimage_castSucc_Ioo_castSucc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.preimage_castSucc_uIcc_castSucc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.preimage_castSucc_uIoc_castSucc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.preimage_castSucc_uIoo_castSucc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.image_castSucc_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.image_castSucc_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.image_castSucc_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.image_castSucc_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.image_castSucc_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.image_castSucc_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.image_castSucc_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.image_castSucc_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.image_castSucc_uIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.image_castSucc_uIoc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.image_castSucc_uIoo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.range_natAdd", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": true, "tactics": ["ext", "constructor", "rintro", "apply", "refine", "ext", "simp"], "tactic_count": 7}
{"name": "Fin.range_natAdd_eq_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.range_natAdd_eq_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Fin.preimage_natAdd_Ici_natAdd", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Fin.preimage_natAdd_Ioi_natAdd", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Fin.preimage_natAdd_Iic_natAdd", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Fin.preimage_natAdd_Iio_natAdd", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Fin.preimage_natAdd_Icc_natAdd", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Fin.preimage_natAdd_Ico_natAdd", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Fin.preimage_natAdd_Ioc_natAdd", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Fin.preimage_natAdd_Ioo_natAdd", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Fin.preimage_natAdd_uIcc_natAdd", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.preimage_natAdd_uIoc_natAdd", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.preimage_natAdd_uIoo_natAdd", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.image_natAdd_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "Fin.image_natAdd_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Fin.image_natAdd_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Fin.image_natAdd_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Fin.image_natAdd_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Fin.image_natAdd_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Fin.image_natAdd_uIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.image_natAdd_uIoc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.image_natAdd_uIoo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.preimage_addNat_Ici_addNat", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Fin.preimage_addNat_Ioi_addNat", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Fin.preimage_addNat_Iic_addNat", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Fin.preimage_addNat_Iio_addNat", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Fin.preimage_addNat_Icc_addNat", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Fin.preimage_addNat_Ico_addNat", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Fin.preimage_addNat_Ioc_addNat", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Fin.preimage_addNat_Ioo_addNat", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Fin.preimage_addNat_uIcc_addNat", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.preimage_addNat_uIoc_addNat", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.preimage_addNat_uIoo_addNat", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.image_addNat_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": true, "tactics": ["rw", "intro", "have", "refine", "simp"], "tactic_count": 5}
{"name": "Fin.image_addNat_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Fin.image_addNat_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Fin.image_addNat_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Fin.image_addNat_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Fin.image_addNat_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Fin.image_addNat_uIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.image_addNat_uIoc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.image_addNat_uIoo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.preimage_succ_Ici_succ", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.preimage_succ_Ioi_succ", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.preimage_succ_Iic_succ", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.preimage_succ_Iio_succ", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.preimage_succ_Icc_succ", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.preimage_succ_Ico_succ", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.preimage_succ_Ioc_succ", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.preimage_succ_Ioo_succ", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.preimage_succ_uIcc_succ", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.preimage_succ_uIoc_succ", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.preimage_succ_uIoo_succ", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.image_succ_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.image_succ_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.image_succ_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": true, "tactics": ["refine", "rintro", "rcases", "exact"], "tactic_count": 4}
{"name": "Fin.image_succ_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": true, "tactics": ["refine", "rintro", "rcases", "exact"], "tactic_count": 4}
{"name": "Fin.image_succ_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.image_succ_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.image_succ_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.image_succ_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.image_succ_uIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.image_succ_uIoc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.image_succ_uIoo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.range_rev", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.image_rev", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.image_rev_fun", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.preimage_rev_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Fin.preimage_rev_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Fin.preimage_rev_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Fin.preimage_rev_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Fin.preimage_rev_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Fin.preimage_rev_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Fin.preimage_rev_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Fin.preimage_rev_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Fin.preimage_rev_uIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.preimage_rev_uIoo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Fin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.Ici.subtype_functor_final", "kind": "instance", "module": "Mathlib.Order.Interval.Set.Final", "is_tactic_proof": true, "tactics": ["rw", "intro", "exact"], "tactic_count": 3}
{"name": "MonotoneOn.mapsTo_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonotoneOn.mapsTo_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonotoneOn.mapsTo_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntitoneOn.mapsTo_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntitoneOn.mapsTo_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntitoneOn.mapsTo_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMonoOn.mapsTo_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMonoOn.mapsTo_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMonoOn.mapsTo_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictAntiOn.mapsTo_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictAntiOn.mapsTo_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictAntiOn.mapsTo_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.mapsTo_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.mapsTo_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.mapsTo_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.mapsTo_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.mapsTo_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.mapsTo_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.mapsTo_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.mapsTo_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.mapsTo_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictAnti.mapsTo_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictAnti.mapsTo_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictAnti.mapsTo_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonotoneOn.image_Ici_subset", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonotoneOn.image_Iic_subset", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonotoneOn.image_Icc_subset", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntitoneOn.image_Ici_subset", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntitoneOn.image_Iic_subset", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntitoneOn.image_Icc_subset", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMonoOn.image_Ioi_subset", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMonoOn.image_Iio_subset", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMonoOn.image_Ioo_subset", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictAntiOn.image_Ioi_subset", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictAntiOn.image_Iio_subset", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictAntiOn.image_Ioo_subset", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.image_Ici_subset", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.image_Iic_subset", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.image_Icc_subset", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.image_Ici_subset", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.image_Iic_subset", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.image_Icc_subset", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.image_Ioi_subset", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.image_Iio_subset", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.image_Ioo_subset", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictAnti.image_Ioi_subset", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictAnti.image_Iio_subset", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictAnti.image_Ioo_subset", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMonoOn.mapsTo_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMonoOn.mapsTo_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictAntiOn.mapsTo_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictAntiOn.mapsTo_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.mapsTo_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.mapsTo_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictAnti.mapsTo_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictAnti.mapsTo_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMonoOn.image_Ico_subset", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMonoOn.image_Ioc_subset", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictAntiOn.image_Ico_subset", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictAntiOn.image_Ioc_subset", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.image_Ico_subset", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.image_Ioc_subset", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictAnti.image_Ico_subset", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictAnti.image_Ioc_subset", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Order.Interval.Set.Image.0.Set.image_subtype_val_Ixx_Ixi", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Order.Interval.Set.Image.0.Set.image_subtype_val_Ixx_Iix", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.preimage_subtype_val_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.preimage_subtype_val_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.preimage_subtype_val_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.preimage_subtype_val_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.preimage_subtype_val_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.preimage_subtype_val_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.preimage_subtype_val_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.preimage_subtype_val_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_subtype_val_Icc_subset", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_subtype_val_Ico_subset", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_subtype_val_Ioc_subset", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_subtype_val_Ioo_subset", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_subtype_val_Iic_subset", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_subtype_val_Iio_subset", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_subtype_val_Ici_subset", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_subtype_val_Ioi_subset", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_subtype_val_Ici_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_subtype_val_Ici_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_subtype_val_Ici_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_subtype_val_Ici_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_subtype_val_Iic_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_subtype_val_Iic_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_subtype_val_Iic_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_subtype_val_Iic_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_subtype_val_Ioi_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_subtype_val_Ioi_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_subtype_val_Ioi_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_subtype_val_Ioi_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_subtype_val_Iio_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_subtype_val_Iio_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_subtype_val_Iio_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_subtype_val_Iio_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_subtype_val_Icc_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_subtype_val_Icc_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_subtype_val_Icc_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_subtype_val_Icc_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_subtype_val_Ico_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_subtype_val_Ico_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_subtype_val_Ico_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_subtype_val_Ico_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_subtype_val_Ioc_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_subtype_val_Ioc_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_subtype_val_Ioc_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_subtype_val_Ioc_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_subtype_val_Ioo_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_subtype_val_Ioo_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_subtype_val_Ioo_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_subtype_val_Ioo_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "directedOn_le_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "directedOn_le_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "directedOn_le_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "directedOn_ge_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "directedOn_ge_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "directedOn_ge_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Image", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NoMaxOrder.infinite", "kind": "instance", "module": "Mathlib.Order.Interval.Set.Infinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NoMinOrder.infinite", "kind": "instance", "module": "Mathlib.Order.Interval.Set.Infinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioo.infinite", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Infinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioo_infinite", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Infinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ico_infinite", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Infinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ico.infinite", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Infinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioc_infinite", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Infinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioc.infinite", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Infinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc_infinite", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Infinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc.infinite", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Infinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instInfiniteElemIioOfNoMinOrder", "kind": "instance", "module": "Mathlib.Order.Interval.Set.Infinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iio_infinite", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Infinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instInfiniteElemIicOfNoMinOrder", "kind": "instance", "module": "Mathlib.Order.Interval.Set.Infinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iic_infinite", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Infinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instInfiniteElemIoiOfNoMaxOrder", "kind": "instance", "module": "Mathlib.Order.Interval.Set.Infinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioi_infinite", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Infinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instInfiniteElemIciOfNoMaxOrder", "kind": "instance", "module": "Mathlib.Order.Interval.Set.Infinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ici_infinite", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Infinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.initialSegIic", "kind": "definition", "module": "Mathlib.Order.Interval.Set.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.principalSegIio", "kind": "definition", "module": "Mathlib.Order.Interval.Set.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.principalSegIio_toRelEmbedding", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.initialSegIicIicOfLE", "kind": "definition", "module": "Mathlib.Order.Interval.Set.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.principalSegIioIicOfLE", "kind": "definition", "module": "Mathlib.Order.Interval.Set.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.principalSegIioIicOfLE_toRelEmbedding", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrincipalSeg.orderIsoIio", "kind": "definition", "module": "Mathlib.Order.Interval.Set.InitialSeg", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "orderIsoIooNegOneOne", "kind": "definition", "module": "Mathlib.Order.Interval.Set.IsoIoo", "is_tactic_proof": true, "tactics": ["refine", "refine", "have", "calc", "x", "refine", "intro", "simp", "rintro", "simp", "hy.trans_lt", "refine", "have", "simp"], "tactic_count": 14}
{"name": "Set.Ici.isSuccLimit_coe", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Limit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.notMem_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.notMem_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.notMem_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.notMem_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.compl_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.compl_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.compl_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.compl_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ici_diff_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.Ici_diff_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.Ioi_diff_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.Ioi_diff_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.Iic_diff_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.Iio_diff_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.Iic_diff_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.Iio_diff_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.Ioi_injective", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iio_injective", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioi_inj", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iio_inj", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ico_subset_Ico_iff", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioc_subset_Ioc_iff", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "Set.Ico_eq_Ico_iff", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": true, "tactics": ["refine", "have", "have", "grind"], "tactic_count": 4}
{"name": "Set.Ioc_eq_Ioc_iff", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": true, "tactics": ["refine", "have", "have", "grind"], "tactic_count": 4}
{"name": "Set.Ioo_subset_Ioo_iff", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ici_eq_singleton_iff_isTop", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": true, "tactics": ["refine", "by_contra", "have", "rw", "exact"], "tactic_count": 5}
{"name": "Set.Ioi_subset_Ioi_iff", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": true, "tactics": ["refine", "by_contra", "exact"], "tactic_count": 3}
{"name": "Set.Ioi_ssubset_Ioi_iff", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact"], "tactic_count": 3}
{"name": "Set.Ioi_subset_Ici_iff", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": true, "tactics": ["refine", "by_contra", "obtain", "exact"], "tactic_count": 4}
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{"name": "Set.Iio_ssubset_Iio_iff", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact"], "tactic_count": 3}
{"name": "Set.Iio_subset_Iic_iff", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.Iic_union_Ioi_of_le", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iio_union_Ici_of_le", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iic_union_Ici_of_le", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iio_union_Ioi_of_lt", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iic_union_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iio_union_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iic_union_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iio_union_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioo_union_Ioi'", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.Ioo_union_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.Ioi_subset_Ioo_union_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioo_union_Ici_eq_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ici_subset_Ico_union_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ico_union_Ici_eq_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ico_union_Ici'", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.Ico_union_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.Ioi_subset_Ioc_union_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioc_union_Ioi_eq_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioc_union_Ioi'", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.Ioc_union_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.Ici_subset_Icc_union_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc_union_Ioi_eq_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioi_subset_Ioc_union_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioc_union_Ici_eq_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ici_subset_Icc_union_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc_union_Ici_eq_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc_union_Ici'", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.Icc_union_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.Iic_subset_Iio_union_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iio_union_Icc_eq_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iio_subset_Iio_union_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iio_union_Ico_eq_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iio_union_Ico'", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.Iio_union_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.Iic_subset_Iic_union_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iic_union_Ioc_eq_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iic_union_Ioc'", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.Iic_union_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.Iio_subset_Iic_union_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iic_union_Ioo_eq_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iio_union_Ioo'", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
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{"name": "Set.Iic_subset_Iic_union_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iic_union_Icc_eq_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iic_union_Icc'", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
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{"name": "Set.Iio_subset_Iic_union_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iic_union_Ico_eq_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioo_subset_Ioo_union_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioo_union_Ico_eq_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ico_subset_Ico_union_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ico_union_Ico_eq_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ico_union_Ico'", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
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{"name": "Set.Icc_subset_Ico_union_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ico_union_Icc_eq_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioc_subset_Ioo_union_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioo_union_Icc_eq_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioo_subset_Ioc_union_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioc_union_Ioo_eq_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ico_subset_Icc_union_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc_union_Ioo_eq_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc_subset_Icc_union_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc_union_Ioc_eq_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioc_subset_Ioc_union_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioc_union_Ioc_eq_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioc_union_Ioc'", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
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{"name": "Set.Ioc_union_Ico_eq_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ico_subset_Icc_union_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc_union_Ico_eq_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc_subset_Icc_union_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc_union_Icc_eq_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc_union_Icc'", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.Icc_union_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.Ioc_subset_Ioc_union_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioc_union_Icc_eq_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioo_union_Ioo'", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
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{"name": "Set.Ioo_subset_Ioo_union_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioi_inter_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iio_inter_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ico_inter_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.Ioc_inter_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.Ioo_inter_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.Ioo_inter_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.Iio_inter_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.Ioo_inter_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.Ioi_inter_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.Ioc_inter_Ioo_of_left_lt", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.Ioc_inter_Ioo_of_right_le", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.Ioo_inter_Ioc_of_left_le", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.Ioo_inter_Ioc_of_right_lt", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
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{"name": "Set.Ioc_inter_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
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{"name": "Set.Iic_diff_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.Iic_diff_Ioc_self_of_le", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.Ioc_union_Ioc_right", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.Ioc_union_Ioc_left", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.Ioc_union_Ioc_symm", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.Ioc_union_Ioc_union_Ioc_cycle", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.LinearOrder", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "antitone_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monotone_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "antitone_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monotone_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonotoneOn.Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntitoneOn.Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonotoneOn.Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntitoneOn.Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonotoneOn.Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntitoneOn.Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonotoneOn.Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntitoneOn.Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonotoneOn.Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntitoneOn.Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonotoneOn.Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntitoneOn.Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonotoneOn.Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntitoneOn.Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonotoneOn.Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntitoneOn.Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iUnion_Ioo_of_mono_of_isGLB_of_isLUB", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictMonoOn_Iic_of_lt_succ", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictAntiOn_Iic_of_succ_lt", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictMonoOn_Ici_of_pred_lt", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictAntiOn_Ici_of_lt_pred", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMonoOn.Iic_id_le", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Monotone", "is_tactic_proof": true, "tactics": ["revert", "refine", "rintro", "by_cases", "rw", "exact", "obtain", "specialize", "nth_grw", "refine", "exact", "exact"], "tactic_count": 12}
{"name": "StrictMonoOn.Ici_le_id", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ncard_Icc_nat", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Nat", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.ncard_Ico_nat", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Nat", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.ncard_Ioc_nat", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Nat", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.ncard_Ioo_nat", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Nat", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.ncard_uIcc_nat", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Nat", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.ncard_Iic_nat", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Nat", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.ncard_Iio_nat", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Nat", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.OrdConnected.out", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ordConnected_def", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ordConnected_iff", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ordConnected_of_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnected", "is_tactic_proof": true, "tactics": ["rw", "intro", "rcases", "rw", "exact"], "tactic_count": 5}
{"name": "Set.OrdConnected.preimage_mono", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.OrdConnected.preimage_anti", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc_subset", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderEmbedding.image_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnected", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "OrderEmbedding.image_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnected", "is_tactic_proof": true, "tactics": ["rw", "inter_eq_left.2"], "tactic_count": 2}
{"name": "OrderEmbedding.image_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnected", "is_tactic_proof": true, "tactics": ["rw", "inter_eq_left.2"], "tactic_count": 2}
{"name": "OrderEmbedding.image_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnected", "is_tactic_proof": true, "tactics": ["rw", "inter_eq_left.2"], "tactic_count": 2}
{"name": "Set.image_subtype_val_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_subtype_val_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_subtype_val_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_subtype_val_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.OrdConnected.inter", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.OrdConnected.inter'", "kind": "instance", "module": "Mathlib.Order.Interval.Set.OrdConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.OrdConnected.dual", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.dual_ordConnected", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ordConnected_dual", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ordConnected_sInter", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ordConnected_iInter", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ordConnected_iInter'", "kind": "instance", "module": "Mathlib.Order.Interval.Set.OrdConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ordConnected_biInter", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ordConnected_pi", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ordConnected_pi'", "kind": "instance", "module": "Mathlib.Order.Interval.Set.OrdConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ordConnected_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ordConnected_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ordConnected_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ordConnected_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ordConnected_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ordConnected_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ordConnected_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ordConnected_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ordConnected_singleton", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnected", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.ordConnected_empty", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ordConnected_univ", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instDenselyOrdered", "kind": "instance", "module": "Mathlib.Order.Interval.Set.OrdConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ordConnected_preimage", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ordConnected_image", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnected", "is_tactic_proof": true, "tactics": ["erw", "apply"], "tactic_count": 2}
{"name": "Set.ordConnected_range", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnected", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Set.OrdConnected.preimage_monotoneOn", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnected", "is_tactic_proof": true, "tactics": ["let", "refine", "rintro", "exact", "rintro", "exact", "rintro", "refine", "apply", "exact"], "tactic_count": 10}
{"name": "Set.OrdConnected.preimage_antitoneOn", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAntichain.ordConnected", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ordConnected_inter_Icc_of_subset", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ordConnected_inter_Icc_iff", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnected", "is_tactic_proof": true, "tactics": ["refine", "have", "exact"], "tactic_count": 3}
{"name": "Set.not_ordConnected_inter_Icc_iff", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnected", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.ordConnected_uIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ordConnected_uIoc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.OrdConnected.uIcc_subset", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.OrdConnected.uIoc_subset", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ordConnected_iff_uIcc_subset", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ordConnected_of_uIcc_subset_left", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ordConnected_iff_uIcc_subset_left", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ordConnected_iff_uIcc_subset_right", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnected", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.image_subtype_val_uIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnected", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.image_subtype_val_uIoc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnected", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.image_subtype_val_uIoo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnected", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.ordConnectedComponent", "kind": "definition", "module": "Mathlib.Order.Interval.Set.OrdConnectedComponent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_ordConnectedComponent", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnectedComponent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.dual_ordConnectedComponent", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnectedComponent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ordConnectedComponent_subset", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnectedComponent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.subset_ordConnectedComponent", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnectedComponent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.self_mem_ordConnectedComponent", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnectedComponent", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.nonempty_ordConnectedComponent", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnectedComponent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ordConnectedComponent_eq_empty", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnectedComponent", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.ordConnectedComponent_empty", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnectedComponent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ordConnectedComponent_univ", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnectedComponent", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.ordConnectedComponent_inter", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnectedComponent", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.mem_ordConnectedComponent_comm", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnectedComponent", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.mem_ordConnectedComponent_trans", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnectedComponent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ordConnectedComponent_eq", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnectedComponent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.instOrdConnectedOrdConnectedComponent", "kind": "instance", "module": "Mathlib.Order.Interval.Set.OrdConnectedComponent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ordConnectedProj", "kind": "definition", "module": "Mathlib.Order.Interval.Set.OrdConnectedComponent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ordConnectedProj_mem_ordConnectedComponent", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnectedComponent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_ordConnectedComponent_ordConnectedProj", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnectedComponent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ordConnectedComponent_ordConnectedProj", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnectedComponent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ordConnectedProj_eq", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnectedComponent", "is_tactic_proof": true, "tactics": ["constructor", "rw", "ordConnectedComponent_ordConnectedProj,", "exact", "simp"], "tactic_count": 5}
{"name": "Set.ordConnectedSection", "kind": "definition", "module": "Mathlib.Order.Interval.Set.OrdConnectedComponent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.dual_ordConnectedSection", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnectedComponent", "is_tactic_proof": true, "tactics": ["simp", "simp", "ext", "simp", "tauto"], "tactic_count": 5}
{"name": "Set.ordConnectedSection_subset", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnectedComponent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.eq_of_mem_ordConnectedSection_of_uIcc_subset", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnectedComponent", "is_tactic_proof": true, "tactics": ["rcases", "exact", "ordConnectedProj_eq.2"], "tactic_count": 3}
{"name": "Set.ordSeparatingSet", "kind": "definition", "module": "Mathlib.Order.Interval.Set.OrdConnectedComponent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ordSeparatingSet_comm", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnectedComponent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.disjoint_left_ordSeparatingSet", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnectedComponent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.disjoint_right_ordSeparatingSet", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnectedComponent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.dual_ordSeparatingSet", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnectedComponent", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.ordT5Nhd", "kind": "definition", "module": "Mathlib.Order.Interval.Set.OrdConnectedComponent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.disjoint_ordT5Nhd", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnectedComponent", "is_tactic_proof": true, "tactics": ["rw", "rintro", "rcases", "clear", "rcases", "clear", "rw", "wlog", "exact", "obtain", "obtain", "have", "rw", "calc", "clear", "rcases", "exact", "rcases", "exact", "have", "lift", "suffices", "hsub", "rintro", "rw", "have", "have", "exact"], "tactic_count": 28}
{"name": "Set.Nonempty.ordConnected_iff_of_bdd", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnectedLinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nonempty.ordConnected_iff_of_bdd'", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnectedLinear", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ordConnected_iff_disjoint_Ioo_empty", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnectedLinear", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "suffices", "intro", "suffices", "exact", "by_contra", "obtain", "have", "obtain", "have", "have", "have", "have", "exact"], "tactic_count": 15}
{"name": "Set.Nonempty.eq_Icc_iff_nat", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnectedLinear", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.Nonempty.eq_Icc_iff_int", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrdConnectedLinear", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "OrderEmbedding.preimage_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrderEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderEmbedding.preimage_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrderEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderEmbedding.preimage_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrderEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderEmbedding.preimage_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrderEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderEmbedding.preimage_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrderEmbedding", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "OrderEmbedding.preimage_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrderEmbedding", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "OrderEmbedding.preimage_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrderEmbedding", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "OrderEmbedding.preimage_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrderEmbedding", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "OrderEmbedding.preimage_uIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrderEmbedding", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "OrderEmbedding.preimage_uIoc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrderEmbedding", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "OrderIso.preimage_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrderIso", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "OrderIso.preimage_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrderIso", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "OrderIso.preimage_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrderIso", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "OrderIso.preimage_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrderIso", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "OrderIso.preimage_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrderIso", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "OrderIso.preimage_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrderIso", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "OrderIso.preimage_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrderIso", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "OrderIso.preimage_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrderIso", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "OrderIso.image_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrderIso", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "OrderIso.image_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrderIso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.image_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrderIso", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "OrderIso.image_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrderIso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.image_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrderIso", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "OrderIso.image_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrderIso", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "OrderIso.image_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrderIso", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "OrderIso.image_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.OrderIso", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "OrderIso.IicTop", "kind": "definition", "module": "Mathlib.Order.Interval.Set.OrderIso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.IciBot", "kind": "definition", "module": "Mathlib.Order.Interval.Set.OrderIso", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.pi_univ_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.pi_univ_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.pi_univ_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.piecewise_mem_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.piecewise_mem_Icc'", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.pi_univ_Ioi_subset", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.pi_univ_Iio_subset", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.pi_univ_Ioo_subset", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.pi_univ_Ioc_subset", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.pi_univ_Ico_subset", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.pi_univ_Ioc_update_left", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Pi", "is_tactic_proof": false, "tactics": ["have", "rw", "simp_rw", "this]", "rfl"], "tactic_count": 5}
{"name": "Set.pi_univ_Ioc_update_right", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Pi", "is_tactic_proof": false, "tactics": ["have", "rw", "simp_rw", "this]", "rfl"], "tactic_count": 5}
{"name": "Set.disjoint_pi_univ_Ioc_update_left_right", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Pi", "is_tactic_proof": true, "tactics": ["rw", "rintro", "refine", "simpa"], "tactic_count": 4}
{"name": "Set.image_update_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Pi", "is_tactic_proof": true, "tactics": ["ext", "rw", "refine", "rintro", "simpa", "simpa", "ext", "obtain", "exact", "simpa"], "tactic_count": 10}
{"name": "Set.image_update_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Pi", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.image_update_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Pi", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.image_update_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Pi", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.image_update_Icc_left", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Pi", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.image_update_Ico_left", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Pi", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.image_update_Ioc_left", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Pi", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.image_update_Ioo_left", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Pi", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.image_update_Icc_right", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Pi", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.image_update_Ico_right", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Pi", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.image_update_Ioc_right", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Pi", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.image_update_Ioo_right", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Pi", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.image_mulSingle_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_mulSingle_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_mulSingle_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_mulSingle_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_mulSingle_Icc_left", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_mulSingle_Ico_left", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_mulSingle_Ioc_left", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_mulSingle_Ioo_left", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_mulSingle_Icc_right", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_mulSingle_Ico_right", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_mulSingle_Ioc_right", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_mulSingle_Ioo_right", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.pi_univ_uIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_update_uIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_update_uIcc_left", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Pi", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.image_update_uIcc_right", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Pi", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.image_mulSingle_uIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_mulSingle_uIcc_left", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.image_mulSingle_uIcc_right", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.pi_univ_Ioc_update_union", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Pi", "is_tactic_proof": true, "tactics": ["simp_rw", "le_or_gt,"], "tactic_count": 2}
{"name": "Set.Icc_diff_pi_univ_Ioo_subset", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Pi", "is_tactic_proof": true, "tactics": ["rintro", "simp", "simp", "rcases", "apply", "cases"], "tactic_count": 6}
{"name": "Set.Icc_diff_pi_univ_Ioc_subset", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Pi", "is_tactic_proof": true, "tactics": ["rintro", "simpa"], "tactic_count": 2}
{"name": "Set.projIci", "kind": "definition", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.projIic", "kind": "definition", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.projIcc", "kind": "definition", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.coe_projIci", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.coe_projIic", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.coe_projIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.projIci_of_le", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.projIic_of_le", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.projIcc_of_le_left", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.projIcc_of_right_le", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.projIci_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.projIic_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.projIcc_left", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.projIcc_right", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.projIci_eq_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.projIic_eq_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.projIcc_eq_left", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.projIcc_eq_right", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.projIci_of_mem", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.projIic_of_mem", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.projIcc_of_mem", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.projIci_coe", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Set.projIic_coe", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Set.projIcc_val", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": true, "tactics": ["cases", "apply"], "tactic_count": 2}
{"name": "Set.projIci_surjOn", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.projIic_surjOn", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.projIcc_surjOn", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.projIci_surjective", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.projIic_surjective", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.projIcc_surjective", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.range_projIci", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.range_projIic", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.range_projIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.monotone_projIci", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.monotone_projIic", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.monotone_projIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.strictMonoOn_projIci", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.strictMonoOn_projIic", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.strictMonoOn_projIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.IciExtend", "kind": "definition", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.IicExtend", "kind": "definition", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.IccExtend", "kind": "definition", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.IciExtend_apply", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.IicExtend_apply", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.IccExtend_apply", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.range_IciExtend", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.range_IicExtend", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.IccExtend_range", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.IciExtend_of_le", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.IicExtend_of_le", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.IccExtend_of_le_left", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.IccExtend_of_right_le", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.IciExtend_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.IicExtend_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.IccExtend_left", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.IccExtend_right", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.IciExtend_of_mem", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.IicExtend_of_mem", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.IccExtend_of_mem", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.IciExtend_coe", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.IicExtend_coe", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.IccExtend_val", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.IccExtend_eq_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": true, "tactics": ["ext", "rcases", "simp", "rcases", "lift", "rw", "simp"], "tactic_count": 7}
{"name": "Monotone.IciExtend", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.IicExtend", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.IccExtend", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.strictMonoOn_IciExtend", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.strictMonoOn_IicExtend", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.strictMonoOn_IccExtend", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.OrdConnected.IciExtend", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.OrdConnected.IicExtend", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.OrdConnected.restrict", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.ProjIcc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iic.coe_succ_of_not_isMax", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.SuccOrder", "is_tactic_proof": true, "tactics": ["rw", "apply", "exact"], "tactic_count": 3}
{"name": "Set.Iic.succ_eq_of_not_isMax", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.SuccOrder", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Set.Ici.coe_pred_of_not_isMin", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.SuccOrder", "is_tactic_proof": true, "tactics": ["rw", "apply", "exact"], "tactic_count": 3}
{"name": "Set.Ici.pred_eq_of_not_isMin", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.SuccOrder", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Set.Ico_succ_left_eq_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.SuccPred", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "ext", "rw"], "tactic_count": 4}
{"name": "Set.Icc_succ_left_eq_Ioc_of_not_isMax", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.SuccPred", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Set.Ico_succ_right_eq_Icc_of_not_isMax", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.SuccPred", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Set.Ioo_succ_right_eq_Ioc_of_not_isMax", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.SuccPred", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Set.Ico_succ_succ_eq_Ioc_of_not_isMax", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.SuccPred", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.insert_Icc_succ_left_eq_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.SuccPred", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Set.insert_Icc_right_eq_Icc_succ", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.SuccPred", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Set.insert_Ico_right_eq_Ico_succ_of_not_isMax", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.SuccPred", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.insert_Ico_succ_left_eq_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.SuccPred", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.insert_Ioc_right_eq_Ioc_succ_of_not_isMax", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.SuccPred", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Set.insert_Ioc_succ_left_eq_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.SuccPred", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.Icc_succ_left_eq_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ico_succ_right_eq_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioo_succ_right_eq_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ico_succ_succ_eq_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.insert_Ico_right_eq_Ico_succ", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.insert_Ioc_right_eq_Ioc_succ", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioc_pred_right_eq_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.SuccPred", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "ext", "rw"], "tactic_count": 4}
{"name": "Set.Icc_pred_right_eq_Ico_of_not_isMin", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.SuccPred", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Set.Ioc_pred_left_eq_Icc_of_not_isMin", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.SuccPred", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Set.Ioo_pred_left_eq_Ioc_of_not_isMin", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.SuccPred", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Set.Ioc_pred_pred_eq_Ico_of_not_isMin", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.SuccPred", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.insert_Icc_pred_right_eq_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.SuccPred", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Set.insert_Icc_left_eq_Icc_pred", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.SuccPred", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Set.insert_Ioc_left_eq_Ioc_pred_of_not_isMin", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.SuccPred", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.insert_Ioc_pred_right_eq_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.SuccPred", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.insert_Ico_left_eq_Ico_pred_of_not_isMin", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.SuccPred", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Set.insert_Ico_pred_right_eq_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.SuccPred", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.Icc_pred_right_eq_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioc_pred_left_eq_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioo_pred_left_eq_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioc_pred_pred_eq_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.insert_Ioc_left_eq_Ioc_pred", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.insert_Ico_left_eq_Ico_pred", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc_succ_pred_eq_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.SuccPred", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "exact", "rw"], "tactic_count": 4}
{"name": "Set.Iio_succ_eq_Iic_of_not_isMax", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.SuccPred", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Set.Iio_succ_eq_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iic_pred_eq_Iio_of_not_isMin", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.SuccPred", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Set.Iic_pred_eq_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ici_succ_eq_Ioi_of_not_isMax", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.SuccPred", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Set.Ici_succ_eq_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioi_pred_eq_Ici_of_not_isMin", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.SuccPred", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Set.Ioi_pred_eq_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.SuccPred", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "surjOn_Ioo_of_monotone_surjective", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.SurjOn", "is_tactic_proof": true, "tactics": ["intro", "rcases", "refine", "contrapose", "exact"], "tactic_count": 5}
{"name": "surjOn_Ico_of_monotone_surjective", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.SurjOn", "is_tactic_proof": true, "tactics": ["obtain", "intro", "rcases", "exact", "exact", "rw", "exact"], "tactic_count": 7}
{"name": "surjOn_Ioc_of_monotone_surjective", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.SurjOn", "is_tactic_proof": true, "tactics": ["simpa", "surjOn_Ico_of_monotone_surjective"], "tactic_count": 2}
{"name": "surjOn_Icc_of_monotone_surjective", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.SurjOn", "is_tactic_proof": true, "tactics": ["intro", "rcases", "exact", "exact", "exact"], "tactic_count": 5}
{"name": "surjOn_Ioi_of_monotone_surjective", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.SurjOn", "is_tactic_proof": true, "tactics": ["rw", "refine", "exact"], "tactic_count": 3}
{"name": "surjOn_Iio_of_monotone_surjective", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.SurjOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "surjOn_Ici_of_monotone_surjective", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.SurjOn", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "surjOn_Iic_of_monotone_surjective", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.SurjOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ioc_subset_biUnion_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Union", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "calc"], "tactic_count": 4}
{"name": "Ico_subset_biUnion_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.Union", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "calc"], "tactic_count": 4}
{"name": "Set.uIcc", "kind": "definition", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.term[[_,_]]", "kind": "definition", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval._aux_Mathlib_Order_Interval_Set_UnorderedInterval___macroRules_Interval_term[[_,_]]_1", "kind": "definition", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval._aux_Mathlib_Order_Interval_Set_UnorderedInterval___unexpand_Set_uIcc_1", "kind": "definition", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.uIcc_toDual", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.uIcc_ofDual", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.uIcc_of_le", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.uIcc_of_ge", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.uIcc_comm", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.uIcc_of_lt", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.uIcc_of_gt", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.uIcc_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.nonempty_uIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc_subset_uIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc_subset_uIcc'", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.left_mem_uIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.right_mem_uIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_uIcc_of_le", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_uIcc_of_ge", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.uIcc_subset_uIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.uIcc_subset_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.uIcc_subset_uIcc_iff_mem", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.uIcc_subset_uIcc_iff_le'", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.uIcc_subset_uIcc_right", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.uIcc_subset_uIcc_left", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.bdd_below_bdd_above_iff_subset_uIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.uIcc_prod_uIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.uIcc_prod_eq", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.eq_of_mem_uIcc_of_mem_uIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.eq_of_mem_uIcc_of_mem_uIcc'", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.uIcc_injective_right", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.uIcc_injective_left", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MonotoneOn.mapsTo_uIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AntitoneOn.mapsTo_uIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Monotone.mapsTo_uIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.mapsTo_uIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonotoneOn.image_uIcc_subset", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntitoneOn.image_uIcc_subset", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.image_uIcc_subset", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.image_uIcc_subset", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc_min_max", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.uIcc_of_not_le", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.uIcc_of_not_ge", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.uIcc_eq_union", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.mem_uIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.notMem_uIcc_of_lt", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.notMem_uIcc_of_gt", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.uIcc_subset_uIcc_iff_le", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.uIcc_subset_uIcc_union_uIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.monotone_or_antitone_iff_uIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "exacts", "contrapose", "rw", "rintro", "exact", "exact"], "tactic_count": 8}
{"name": "Set.monotoneOn_or_antitoneOn_iff_uIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.uIoc", "kind": "definition", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval.termΙ", "kind": "definition", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval._aux_Mathlib_Order_Interval_Set_UnorderedInterval___macroRules_Interval_termΙ_1", "kind": "definition", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Interval._aux_Mathlib_Order_Interval_Set_UnorderedInterval___unexpand_Set_uIoc_1", "kind": "definition", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.uIoc_of_le", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.uIoc_of_ge", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.uIoc_eq_union", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Set.mem_uIoc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.notMem_uIoc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": true, "tactics": ["simp", "tauto"], "tactic_count": 2}
{"name": "Set.left_mem_uIoc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.right_mem_uIoc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.forall_uIoc_iff", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.uIoc_subset_uIoc_of_uIcc_subset_uIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.uIoc_comm", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.Ioc_subset_uIoc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioc_subset_uIoc'", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.uIoc_subset_uIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.eq_of_mem_uIoc_of_mem_uIoc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": true, "tactics": ["simp_rw", "rintro", "first", "assumption", "exact", "exact"], "tactic_count": 6}
{"name": "Set.eq_of_mem_uIoc_of_mem_uIoc'", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.eq_of_notMem_uIoc_of_notMem_uIoc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Set.uIoc_injective_right", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": true, "tactics": ["rintro", "rw", "obtain", "have", "simp", "or_false]", "refine", "simpa", "refine", "simpa"], "tactic_count": 10}
{"name": "Set.uIoc_injective_left", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.uIoc_union_uIoc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": true, "tactics": ["wlog", "rw", "rwa", "rw", "rw"], "tactic_count": 5}
{"name": "Set.uIoo", "kind": "definition", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.uIoo_toDual", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.uIoo_ofDual", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.uIoo_of_le", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.uIoo_of_ge", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.uIoo_comm", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.uIoo_of_lt", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.uIoo_of_gt", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.uIoo_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.left_notMem_uIoo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.right_notMem_uIoo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.Ioo_subset_uIoo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioo_subset_uIoo'", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_uIoo_of_lt", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_uIoo_of_gt", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioo_min_max", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.uIoo_of_not_le", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.uIoo_of_not_ge", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.uIoo_subset_uIcc_self", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.uIoo_subset_uIcc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.uIoo_subset_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.nonempty_uIoo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.nonempty_uIoc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.uIoo_eq_union", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simp"], "tactic_count": 3}
{"name": "WithTop.preimage_coe_top", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.WithBotTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.range_coe", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.WithBotTop", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "WithTop.preimage_coe_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.WithBotTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.preimage_coe_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.WithBotTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.preimage_coe_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.WithBotTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.preimage_coe_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.WithBotTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.preimage_coe_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.WithBotTop", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WithTop.preimage_coe_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.WithBotTop", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WithTop.preimage_coe_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.WithBotTop", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WithTop.preimage_coe_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.WithBotTop", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WithTop.preimage_coe_Iio_top", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.WithBotTop", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "WithTop.preimage_coe_Ico_top", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.WithBotTop", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WithTop.preimage_coe_Ioo_top", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.WithBotTop", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WithTop.image_coe_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.WithBotTop", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "WithTop.image_coe_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.WithBotTop", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "WithTop.image_coe_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.WithBotTop", "is_tactic_proof": true, "tactics": ["rw", "inter_eq_self_of_subset_left"], "tactic_count": 2}
{"name": "WithTop.image_coe_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.WithBotTop", "is_tactic_proof": true, "tactics": ["rw", "inter_eq_self_of_subset_left"], "tactic_count": 2}
{"name": "WithTop.image_coe_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.WithBotTop", "is_tactic_proof": true, "tactics": ["rw", "inter_eq_self_of_subset_left"], "tactic_count": 2}
{"name": "WithTop.image_coe_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.WithBotTop", "is_tactic_proof": true, "tactics": ["rw", "inter_eq_self_of_subset_left"], "tactic_count": 2}
{"name": "WithTop.image_coe_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.WithBotTop", "is_tactic_proof": true, "tactics": ["rw", "inter_eq_self_of_subset_left"], "tactic_count": 2}
{"name": "WithTop.image_coe_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.WithBotTop", "is_tactic_proof": true, "tactics": ["rw", "inter_eq_self_of_subset_left"], "tactic_count": 2}
{"name": "WithTop.Ioi_coe", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.WithBotTop", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "WithTop.Ici_coe", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.WithBotTop", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "WithTop.Iio_coe", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.WithBotTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.Iic_coe", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.WithBotTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.Icc_coe", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.WithBotTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.Ico_coe", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.WithBotTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.Ioc_coe", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.WithBotTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.Ioo_coe", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.WithBotTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.preimage_coe_bot", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.WithBotTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.range_coe", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.WithBotTop", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "WithBot.preimage_coe_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.WithBotTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.preimage_coe_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.WithBotTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.preimage_coe_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.WithBotTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.preimage_coe_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.WithBotTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.preimage_coe_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.WithBotTop", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WithBot.preimage_coe_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.WithBotTop", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WithBot.preimage_coe_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.WithBotTop", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WithBot.preimage_coe_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.WithBotTop", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WithBot.preimage_coe_Ioi_bot", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.WithBotTop", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "WithBot.preimage_coe_Ioc_bot", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.WithBotTop", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WithBot.preimage_coe_Ioo_bot", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.WithBotTop", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WithBot.image_coe_Iio", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.WithBotTop", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "WithBot.image_coe_Iic", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.WithBotTop", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "WithBot.image_coe_Ioi", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.WithBotTop", "is_tactic_proof": true, "tactics": ["rw", "inter_eq_self_of_subset_left"], "tactic_count": 2}
{"name": "WithBot.image_coe_Ici", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.WithBotTop", "is_tactic_proof": true, "tactics": ["rw", "inter_eq_self_of_subset_left"], "tactic_count": 2}
{"name": "WithBot.image_coe_Icc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.WithBotTop", "is_tactic_proof": true, "tactics": ["rw", "inter_eq_self_of_subset_left"], "tactic_count": 2}
{"name": "WithBot.image_coe_Ioc", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.WithBotTop", "is_tactic_proof": true, "tactics": ["rw", "inter_eq_self_of_subset_left"], "tactic_count": 2}
{"name": "WithBot.image_coe_Ico", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.WithBotTop", "is_tactic_proof": true, "tactics": ["rw", "inter_eq_self_of_subset_left"], "tactic_count": 2}
{"name": "WithBot.image_coe_Ioo", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.WithBotTop", "is_tactic_proof": true, "tactics": ["rw", "inter_eq_self_of_subset_left"], "tactic_count": 2}
{"name": "WithBot.Ioi_coe", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.WithBotTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.Ici_coe", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.WithBotTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.Iio_coe", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.WithBotTop", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "WithBot.Iic_coe", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.WithBotTop", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "WithBot.Icc_coe", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.WithBotTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.Ico_coe", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.WithBotTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.Ioc_coe", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.WithBotTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.Ioo_coe", "kind": "theorem", "module": "Mathlib.Order.Interval.Set.WithBotTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupIrred", "kind": "definition", "module": "Mathlib.Order.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupPrime", "kind": "definition", "module": "Mathlib.Order.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupIrred.not_isMin", "kind": "theorem", "module": "Mathlib.Order.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupPrime.not_isMin", "kind": "theorem", "module": "Mathlib.Order.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMin.not_supIrred", "kind": "theorem", "module": "Mathlib.Order.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMin.not_supPrime", "kind": "theorem", "module": "Mathlib.Order.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_supIrred", "kind": "theorem", "module": "Mathlib.Order.Irreducible", "is_tactic_proof": true, "tactics": ["rw", "push_neg", "rw", "simp"], "tactic_count": 4}
{"name": "not_supPrime", "kind": "theorem", "module": "Mathlib.Order.Irreducible", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SupPrime.supIrred", "kind": "theorem", "module": "Mathlib.Order.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupPrime.le_sup", "kind": "theorem", "module": "Mathlib.Order.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_supIrred_bot", "kind": "theorem", "module": "Mathlib.Order.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_supPrime_bot", "kind": "theorem", "module": "Mathlib.Order.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SupIrred.ne_bot", "kind": "theorem", "module": "Mathlib.Order.Irreducible", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "SupPrime.ne_bot", "kind": "theorem", "module": "Mathlib.Order.Irreducible", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "SupIrred.finset_sup_eq", "kind": "theorem", "module": "Mathlib.Order.Irreducible", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "insert", "simp", "rw", "exact"], "tactic_count": 7}
{"name": "SupPrime.le_finset_sup", "kind": "theorem", "module": "Mathlib.Order.Irreducible", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "insert"], "tactic_count": 4}
{"name": "exists_supIrred_decomposition", "kind": "theorem", "module": "Mathlib.Order.Irreducible", "is_tactic_proof": true, "tactics": ["classical", "apply", "clear", "rintro", "by_cases", "exact", "rw", "obtain", "exact", "obtain", "obtain", "exact"], "tactic_count": 12}
{"name": "InfIrred", "kind": "definition", "module": "Mathlib.Order.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfPrime", "kind": "definition", "module": "Mathlib.Order.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMax.not_infIrred", "kind": "theorem", "module": "Mathlib.Order.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMax.not_infPrime", "kind": "theorem", "module": "Mathlib.Order.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_infIrred", "kind": "theorem", "module": "Mathlib.Order.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_infPrime", "kind": "theorem", "module": "Mathlib.Order.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfPrime.infIrred", "kind": "theorem", "module": "Mathlib.Order.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfPrime.inf_le", "kind": "theorem", "module": "Mathlib.Order.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_infIrred_top", "kind": "theorem", "module": "Mathlib.Order.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_infPrime_top", "kind": "theorem", "module": "Mathlib.Order.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfIrred.ne_top", "kind": "theorem", "module": "Mathlib.Order.Irreducible", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "InfPrime.ne_top", "kind": "theorem", "module": "Mathlib.Order.Irreducible", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "InfIrred.finset_inf_eq", "kind": "theorem", "module": "Mathlib.Order.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfPrime.finset_inf_le", "kind": "theorem", "module": "Mathlib.Order.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_infIrred_decomposition", "kind": "theorem", "module": "Mathlib.Order.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "infIrred_toDual", "kind": "theorem", "module": "Mathlib.Order.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "infPrime_toDual", "kind": "theorem", "module": "Mathlib.Order.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "supIrred_ofDual", "kind": "theorem", "module": "Mathlib.Order.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "supPrime_ofDual", "kind": "theorem", "module": "Mathlib.Order.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "supIrred_toDual", "kind": "theorem", "module": "Mathlib.Order.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "supPrime_toDual", "kind": "theorem", "module": "Mathlib.Order.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "infIrred_ofDual", "kind": "theorem", "module": "Mathlib.Order.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "infPrime_ofDual", "kind": "theorem", "module": "Mathlib.Order.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "supPrime_iff_supIrred", "kind": "theorem", "module": "Mathlib.Order.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "infPrime_iff_infIrred", "kind": "theorem", "module": "Mathlib.Order.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "supPrime_iff_not_isMin", "kind": "theorem", "module": "Mathlib.Order.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "infPrime_iff_not_isMax", "kind": "theorem", "module": "Mathlib.Order.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "supIrred_iff_not_isMin", "kind": "theorem", "module": "Mathlib.Order.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "infIrred_iff_not_isMax", "kind": "theorem", "module": "Mathlib.Order.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.isNormal_iff", "kind": "theorem", "module": "Mathlib.Order.IsNormal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Order.IsNormal.monotone", "kind": "theorem", "module": "Mathlib.Order.IsNormal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.IsNormal.isLUB_image_Iio_of_isSuccLimit", "kind": "theorem", "module": "Mathlib.Order.IsNormal", "is_tactic_proof": true, "tactics": ["refine", "rintro", "exact"], "tactic_count": 3}
{"name": "Order.IsNormal.le_iff_forall_le", "kind": "theorem", "module": "Mathlib.Order.IsNormal", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Order.IsNormal.lt_iff_exists_lt", "kind": "theorem", "module": "Mathlib.Order.IsNormal", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Order.IsNormal.map_isSuccLimit", "kind": "theorem", "module": "Mathlib.Order.IsNormal", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact", "obtain", "have", "rw", "exact"], "tactic_count": 7}
{"name": "Order.IsNormal.map_isLUB", "kind": "theorem", "module": "Mathlib.Order.IsNormal", "is_tactic_proof": true, "tactics": ["refine", "simpa", "by_cases", "simp_all", "have", "rw", "intro", "obtain", "simp_rw", "exact"], "tactic_count": 10}
{"name": "InitialSeg.isNormal", "kind": "theorem", "module": "Mathlib.Order.IsNormal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrincipalSeg.isNormal", "kind": "theorem", "module": "Mathlib.Order.IsNormal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.isNormal", "kind": "theorem", "module": "Mathlib.Order.IsNormal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.IsNormal.id", "kind": "theorem", "module": "Mathlib.Order.IsNormal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.IsNormal.comp", "kind": "theorem", "module": "Mathlib.Order.IsNormal", "is_tactic_proof": true, "tactics": ["refine", "simp_rw", "simpa"], "tactic_count": 3}
{"name": "Order.IsNormal.of_succ_lt", "kind": "theorem", "module": "Mathlib.Order.IsNormal", "is_tactic_proof": true, "tactics": ["refine", "induction", "isMin", "succ", "intro", "obtain", "exact", "exact", "isSuccLimit", "intro", "have", "exact"], "tactic_count": 12}
{"name": "Order.IsNormal.ext", "kind": "theorem", "module": "Mathlib.Order.IsNormal", "is_tactic_proof": true, "tactics": ["constructor", "simp_all", "rintro", "ext", "induction", "isMin", "succ", "isSuccLimit", "apply", "convert", "aesop"], "tactic_count": 11}
{"name": "Order.IsNormal.map_sSup", "kind": "theorem", "module": "Mathlib.Order.IsNormal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.IsNormal.map_iSup", "kind": "theorem", "module": "Mathlib.Order.IsNormal", "is_tactic_proof": true, "tactics": ["unfold", "convert", "ext", "simp"], "tactic_count": 4}
{"name": "Order.IsNormal.preimage_Iic", "kind": "theorem", "module": "Mathlib.Order.IsNormal", "is_tactic_proof": true, "tactics": ["refine", "obtain", "rw", "obtain", "exact", "rw", "apply", "rw", "simpa"], "tactic_count": 9}
{"name": "Order.IsNormal.apply_of_isSuccLimit", "kind": "theorem", "module": "Mathlib.Order.IsNormal", "is_tactic_proof": true, "tactics": ["convert", "exact", "exact", "use", "rintro", "exact"], "tactic_count": 6}
{"name": "Monotone.seq_le_seq", "kind": "theorem", "module": "Mathlib.Order.Iterate", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "refine", "exact", "exact"], "tactic_count": 6}
{"name": "Monotone.seq_pos_lt_seq_of_lt_of_le", "kind": "theorem", "module": "Mathlib.Order.Iterate", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "ihn", "suffices", "cases", "zero", "succ", "refine"], "tactic_count": 9}
{"name": "Monotone.seq_pos_lt_seq_of_le_of_lt", "kind": "theorem", "module": "Mathlib.Order.Iterate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.seq_lt_seq_of_lt_of_le", "kind": "theorem", "module": "Mathlib.Order.Iterate", "is_tactic_proof": true, "tactics": ["cases", "exacts"], "tactic_count": 2}
{"name": "Monotone.seq_lt_seq_of_le_of_lt", "kind": "theorem", "module": "Mathlib.Order.Iterate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.le_iterate_comp_of_le", "kind": "theorem", "module": "Mathlib.Order.Iterate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.iterate_le_of_le", "kind": "theorem", "module": "Mathlib.Order.Iterate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.id_le_iterate_of_id_le", "kind": "theorem", "module": "Mathlib.Order.Iterate", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Function.monotone_iterate_of_id_le", "kind": "theorem", "module": "Mathlib.Order.Iterate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.antitone_iterate_of_le_id", "kind": "theorem", "module": "Mathlib.Order.Iterate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Commute.iterate_le_of_map_le", "kind": "theorem", "module": "Mathlib.Order.Iterate", "is_tactic_proof": true, "tactics": ["apply", "rfl", "intros", "simp"], "tactic_count": 4}
{"name": "Function.Commute.iterate_pos_lt_of_map_lt", "kind": "theorem", "module": "Mathlib.Order.Iterate", "is_tactic_proof": true, "tactics": ["apply", "rfl", "intros", "simp"], "tactic_count": 4}
{"name": "Function.Commute.iterate_pos_lt_of_map_lt'", "kind": "theorem", "module": "Mathlib.Order.Iterate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Commute.iterate_pos_lt_iff_map_lt", "kind": "theorem", "module": "Mathlib.Order.Iterate", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simp", "simp"], "tactic_count": 4}
{"name": "Function.Commute.iterate_pos_lt_iff_map_lt'", "kind": "theorem", "module": "Mathlib.Order.Iterate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Commute.iterate_pos_le_iff_map_le", "kind": "theorem", "module": "Mathlib.Order.Iterate", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Function.Commute.iterate_pos_le_iff_map_le'", "kind": "theorem", "module": "Mathlib.Order.Iterate", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Function.Commute.iterate_pos_eq_iff_map_eq", "kind": "theorem", "module": "Mathlib.Order.Iterate", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Monotone.monotone_iterate_of_le_map", "kind": "theorem", "module": "Mathlib.Order.Iterate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.antitone_iterate_of_map_le", "kind": "theorem", "module": "Mathlib.Order.Iterate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.strictMono_iterate_of_lt_map", "kind": "theorem", "module": "Mathlib.Order.Iterate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.strictAnti_iterate_of_map_lt", "kind": "theorem", "module": "Mathlib.Order.Iterate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "JordanHolderLattice.isMaximal_inf_right_of_isMaximal_sup", "kind": "theorem", "module": "Mathlib.Order.JordanHolder", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "JordanHolderLattice.isMaximal_of_eq_inf", "kind": "theorem", "module": "Mathlib.Order.JordanHolder", "is_tactic_proof": true, "tactics": ["have", "substs", "exact"], "tactic_count": 3}
{"name": "JordanHolderLattice.second_iso_of_eq", "kind": "theorem", "module": "Mathlib.Order.JordanHolder", "is_tactic_proof": true, "tactics": ["substs"], "tactic_count": 1}
{"name": "JordanHolderLattice.IsMaximal.iso_refl", "kind": "theorem", "module": "Mathlib.Order.JordanHolder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompositionSeries", "kind": "abbrev", "module": "Mathlib.Order.JordanHolder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompositionSeries.lt_succ", "kind": "theorem", "module": "Mathlib.Order.JordanHolder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompositionSeries.strictMono", "kind": "theorem", "module": "Mathlib.Order.JordanHolder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompositionSeries.injective", "kind": "theorem", "module": "Mathlib.Order.JordanHolder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompositionSeries.inj", "kind": "theorem", "module": "Mathlib.Order.JordanHolder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompositionSeries.total", "kind": "theorem", "module": "Mathlib.Order.JordanHolder", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "rw", "exact"], "tactic_count": 4}
{"name": "CompositionSeries.toList_sorted", "kind": "theorem", "module": "Mathlib.Order.JordanHolder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CompositionSeries.head_le", "kind": "theorem", "module": "Mathlib.Order.JordanHolder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CompositionSeries.last_eraseLast_le", "kind": "theorem", "module": "Mathlib.Order.JordanHolder", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CompositionSeries.mem_eraseLast_of_ne_of_mem", "kind": "theorem", "module": "Mathlib.Order.JordanHolder", "is_tactic_proof": true, "tactics": ["rcases", "have", "conv_rhs", "exact", "exact"], "tactic_count": 5}
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{"name": "CompositionSeries.lt_last_of_mem_eraseLast", "kind": "theorem", "module": "Mathlib.Order.JordanHolder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompositionSeries.isMaximal_eraseLast_last", "kind": "theorem", "module": "Mathlib.Order.JordanHolder", "is_tactic_proof": true, "tactics": ["rw", "have", "simp", "convert", "exact"], "tactic_count": 5}
{"name": "CompositionSeries.eq_snoc_eraseLast", "kind": "theorem", "module": "Mathlib.Order.JordanHolder", "is_tactic_proof": true, "tactics": ["ext", "simp", "by_cases"], "tactic_count": 3}
{"name": "CompositionSeries.snoc_eraseLast_last", "kind": "theorem", "module": "Mathlib.Order.JordanHolder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompositionSeries.Equivalent", "kind": "definition", "module": "Mathlib.Order.JordanHolder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompositionSeries.Equivalent.refl", "kind": "theorem", "module": "Mathlib.Order.JordanHolder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompositionSeries.Equivalent.symm", "kind": "theorem", "module": "Mathlib.Order.JordanHolder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompositionSeries.Equivalent.trans", "kind": "theorem", "module": "Mathlib.Order.JordanHolder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompositionSeries.Equivalent.smash", "kind": "theorem", "module": "Mathlib.Order.JordanHolder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompositionSeries.Equivalent.snoc", "kind": "theorem", "module": "Mathlib.Order.JordanHolder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompositionSeries.Equivalent.length_eq", "kind": "theorem", "module": "Mathlib.Order.JordanHolder", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CompositionSeries.Equivalent.snoc_snoc_swap", "kind": "theorem", "module": "Mathlib.Order.JordanHolder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompositionSeries.length_eq_zero_of_head_eq_head_of_last_eq_last_of_length_eq_zero", "kind": "theorem", "module": "Mathlib.Order.JordanHolder", "is_tactic_proof": false, "tactics": ["have", "s₂.injective", "simpa"], "tactic_count": 3}
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{"name": "exists_seq_covby_of_forall_covby_finite", "kind": "theorem", "module": "Mathlib.Order.KonigLemma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_orderEmbedding_covby_of_forall_covby_finite", "kind": "theorem", "module": "Mathlib.Order.KonigLemma", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "exists_orderEmbedding_covby_of_forall_covby_finite_of_bot", "kind": "theorem", "module": "Mathlib.Order.KonigLemma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GradeMinOrder.exists_nat_orderEmbedding_of_forall_covby_finite", "kind": "theorem", "module": "Mathlib.Order.KonigLemma", "is_tactic_proof": true, "tactics": ["obtain", "refine", "induction", "zero", "succ"], "tactic_count": 5}
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{"name": "Order.krullDim", "kind": "definition", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.height", "kind": "definition", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.coheight", "kind": "definition", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.height_toDual", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.height_ofDual", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.coheight_toDual", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.coheight_ofDual", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.coheight_eq", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": false, "tactics": ["apply", "congr"], "tactic_count": 2}
{"name": "Order.height_le_iff", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Order.coheight_le_iff", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Order.height_le", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": true, "tactics": ["apply", "intro", "wlog", "simp_all", "let", "rw", "apply", "simp"], "tactic_count": 8}
{"name": "Order.height_le_iff'", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": true, "tactics": ["constructor", "rw", "exact", "exact"], "tactic_count": 4}
{"name": "Order.height_eq_iSup_last_eq", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": true, "tactics": ["apply", "intro", "rw"], "tactic_count": 3}
{"name": "Order.coheight_eq_iSup_head_eq", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": true, "tactics": ["change", "rw", "apply", "simp"], "tactic_count": 4}
{"name": "Order.coheight_le_iff'", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Order.coheight_le", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.length_le_height", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": true, "tactics": ["by_cases", "let", "p.eraseLast.snoc", "apply", "apply", "convert", "simp", "congr", "suffices", "simp", "p']", "convert", "norm_cast", "lia", "refine", "simp", "simp_all"], "tactic_count": 17}
{"name": "Order.length_le_coheight", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.length_le_height_last", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.length_le_coheight_head", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.index_le_height", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.rev_index_le_coheight", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Order.height_eq_index_of_length_eq_height_last", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": true, "tactics": ["refine", "intro", "have", "simp", "norm_cast", "lia"], "tactic_count": 6}
{"name": "Order.coheight_eq_index_of_length_eq_head_coheight", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Order.height_mono", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.coheight_anti", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Order.KrullDimension.0.Order.height_add_const", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "Order.height_strictMono", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": true, "tactics": ["rw", "intro", "have", "simpa"], "tactic_count": 4}
{"name": "Order.height_add_one_le", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": true, "tactics": ["cases", "top", "have", "rw", "gcongr", "simp", "coe", "apply", "rw", "gcongr", "simp"], "tactic_count": 11}
{"name": "Order.coheight_strictAnti", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.coheight_add_one_le", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": true, "tactics": ["cases", "top", "have", "rw", "gcongr", "simp", "coe", "apply", "rw", "gcongr", "simp"], "tactic_count": 11}
{"name": "Order.height_le_height_apply_of_strictMono", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": true, "tactics": ["simp", "apply", "intro", "apply"], "tactic_count": 4}
{"name": "Order.coheight_le_coheight_apply_of_strictMono", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": true, "tactics": ["apply", "exact"], "tactic_count": 2}
{"name": "Order.height_orderIso", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": true, "tactics": ["apply", "simpa", "exact"], "tactic_count": 3}
{"name": "Order.coheight_orderIso", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Order.KrullDimension.0.Order.exists_eq_iSup_of_iSup_eq_coe", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": true, "tactics": ["obtain", "use", "simpa"], "tactic_count": 3}
{"name": "Order.exists_series_of_le_height", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": true, "tactics": ["have", "cases", "top", "clear", "rw", "contrapose", "use", "rintro", "simp", "by_contra", "apply", "coe", "rw", "rw", "obtain", "simp", "use", "constructor", "simp", "simp"], "tactic_count": 20}
{"name": "Order.exists_series_of_le_coheight", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Order.exists_series_of_height_eq_coe", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.exists_series_of_coheight_eq_coe", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.height_eq_iSup_lt_height", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": true, "tactics": ["apply", "apply", "intro", "cases", "zero", "succ", "apply", "apply", "rw", "apply", "apply", "rw", "apply", "apply"], "tactic_count": 14}
{"name": "Order.coheight_eq_iSup_gt_coheight", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.height_le_coe_iff", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": true, "tactics": ["conv_lhs", "congr", "cases", "simp", "norm_cast"], "tactic_count": 5}
{"name": "Order.coheight_le_coe_iff", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.height_eq_top_iff", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.coheight_eq_top_iff", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": true, "tactics": ["convert", "constructor"], "tactic_count": 2}
{"name": "Order.height_eq_zero", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Order.coheight_eq_zero", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.height_ne_zero", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.height_pos", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Order.coheight_ne_zero", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.coheight_pos", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Order.height_bot", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Order.coheight_top", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Order.height_pos_of_bot_lt", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": true, "tactics": ["rw", "grind"], "tactic_count": 2}
{"name": "Order.coheight_pos_of_lt_top", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": true, "tactics": ["rw", "grind"], "tactic_count": 2}
{"name": "Order.coe_lt_height_iff", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.coe_lt_coheight_iff", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.height_eq_coe_add_one_iff", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": true, "tactics": ["wlog", "simp_all", "simp", "trans", "rw", "simp", "congr", "exact", "simpa"], "tactic_count": 9}
{"name": "Order.coheight_eq_coe_add_one_iff", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.height_eq_coe_iff", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": true, "tactics": ["wlog", "simp_all", "simp", "cases", "simp", "simp", "rw", "simp", "congr", "rename_i", "cases"], "tactic_count": 11}
{"name": "Order.coheight_eq_coe_iff", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.height_eq_coe_iff_minimal_le_height", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": true, "tactics": ["by_cases", "cases", "zero", "succ", "suffices", "simp", "obtain", "use", "simpa"], "tactic_count": 9}
{"name": "Order.coheight_eq_coe_iff_maximal_le_coheight", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.one_lt_height_iff", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": true, "tactics": ["rw", "refine", "obtain", "refine", "rintro", "let", "have", "exact"], "tactic_count": 8}
{"name": "Order.LTSeries.length_le_krullDim", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.krullDim_eq_bot_iff", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": true, "tactics": ["rw", "simp", "exact"], "tactic_count": 3}
{"name": "Order.krullDim_nonneg_iff", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": true, "tactics": ["contrapose", "rw"], "tactic_count": 2}
{"name": "Order.krullDim_eq_bot", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.krullDim_nonneg", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.krullDim_ne_bot_iff", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Order.bot_lt_krullDim_iff", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Order.bot_lt_krullDim", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.krullDim_nonpos_iff_forall_isMax", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": true, "tactics": ["simp", "refine", "rintro", "simp", "cases"], "tactic_count": 5}
{"name": "Order.krullDim_nonpos_iff_forall_isMin", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Order.krullDim_le_one_iff", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": true, "tactics": ["simp_rw", "contrapose", "constructor", "rintro", "iterate", "exact", "rintro", "exact"], "tactic_count": 8}
{"name": "Order.krullDim_pos_iff", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": true, "tactics": ["contrapose", "simp_rw"], "tactic_count": 2}
{"name": "Order.one_le_krullDim_iff", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Order.krullDim_nonpos_of_subsingleton", "kind": "theorem", "module": "Mathlib.Order.KrullDimension", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
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{"name": "sup_inf_le", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inf_sup_self", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "sup_eq_iff_inf_eq", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Lattice.ext", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": true, "tactics": ["cases", "cases", "cases", "cases", "congr"], "tactic_count": 5}
{"name": "le_sup_inf", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sup_inf_left", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sup_inf_right", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "inf_sup_left", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inf_sup_le", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "OrderDual.instDistribLattice", "kind": "instance", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inf_sup_right", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "le_of_inf_le_sup_le", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_of_inf_eq_sup_eq", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DistribLattice.ofInfSupLe", "kind": "abbrev", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearOrder.toLattice", "kind": "instance", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sup_ind", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_sup_iff", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "lt_sup_iff", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "sup_lt_iff", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "max_max_max_comm", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sup_eq_maxDefault", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": true, "tactics": ["ext", "unfold", "split_ifs", "exacts"], "tactic_count": 4}
{"name": "inf_eq_minDefault", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": true, "tactics": ["ext", "unfold", "split_ifs", "exacts"], "tactic_count": 4}
{"name": "Lattice.toLinearOrder", "kind": "abbrev", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDistribLatticeOfLinearOrder", "kind": "instance", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDistribLatticeNat", "kind": "instance", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instLatticeInt", "kind": "instance", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofDual_sup", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toDual_sup", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofDual_max", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toDual_max", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instMaxForall_mathlib", "kind": "instance", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.sup_apply", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.sup_def", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instSemilatticeSup", "kind": "instance", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instSemilatticeInf", "kind": "instance", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instLattice", "kind": "instance", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instDistribLattice", "kind": "instance", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.update_sup", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.sup", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.inf", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.max", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.min", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.le_map_sup", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.map_inf_le", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.of_map_inf_le_left", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": true, "tactics": ["intro", "rw", "apply"], "tactic_count": 3}
{"name": "Monotone.of_map_inf_le", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.of_map_inf", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.of_left_le_map_sup", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.of_le_map_sup", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.of_map_sup", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.map_sup", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.map_inf", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_ge_and_iff_exists", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_and_iff_of_monotone", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonotoneOn.sup", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonotoneOn.inf", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonotoneOn.max", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonotoneOn.min", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonotoneOn.of_map_inf", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonotoneOn.of_map_sup", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonotoneOn.map_sup", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": true, "tactics": ["cases", "first", "assumption", "simp"], "tactic_count": 4}
{"name": "MonotoneOn.map_inf", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.sup", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.inf", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.max", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.min", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.map_sup_le", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.le_map_inf", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.map_sup", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.map_inf", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_le_and_iff_exists", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_and_iff_of_antitone", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntitoneOn.sup", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntitoneOn.inf", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AntitoneOn.min", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntitoneOn.of_map_inf", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntitoneOn.of_map_sup", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Prod.fst_sup", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.snd_sup", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.swap_sup", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Prod.instSemilatticeInf", "kind": "instance", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Prod.instDistribLattice", "kind": "instance", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.semilatticeSup", "kind": "abbrev", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.semilatticeInf", "kind": "abbrev", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.lattice", "kind": "abbrev", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.coe_sup", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.mk_sup_mk", "kind": "theorem", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.semilatticeSup", "kind": "abbrev", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.semilatticeInf", "kind": "abbrev", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.lattice", "kind": "abbrev", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.distribLattice", "kind": "abbrev", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.instSemilatticeSup", "kind": "instance", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.instLattice", "kind": "instance", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.instDistribLattice", "kind": "instance", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.instLinearOrder", "kind": "instance", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bool.instPartialOrder", "kind": "instance", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bool.instDistribLattice", "kind": "instance", "module": "Mathlib.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ico.semilatticeInf", "kind": "instance", "module": "Mathlib.Order.LatticeIntervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ico.coe_inf", "kind": "theorem", "module": "Mathlib.Order.LatticeIntervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ico.orderBot", "kind": "instance", "module": "Mathlib.Order.LatticeIntervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ico.coe_bot", "kind": "theorem", "module": "Mathlib.Order.LatticeIntervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ico.disjoint_iff", "kind": "theorem", "module": "Mathlib.Order.LatticeIntervals", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.Iio.semilatticeInf", "kind": "instance", "module": "Mathlib.Order.LatticeIntervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iio.coe_inf", "kind": "theorem", "module": "Mathlib.Order.LatticeIntervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioc.semilatticeSup", "kind": "instance", "module": "Mathlib.Order.LatticeIntervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioc.coe_sup", "kind": "theorem", "module": "Mathlib.Order.LatticeIntervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioc.orderTop", "kind": "instance", "module": "Mathlib.Order.LatticeIntervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioc.coe_top", "kind": "theorem", "module": "Mathlib.Order.LatticeIntervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioc.codisjoint_iff", "kind": "theorem", "module": "Mathlib.Order.LatticeIntervals", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.Ioi.semilatticeSup", "kind": "instance", "module": "Mathlib.Order.LatticeIntervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ioi.coe_sup", "kind": "theorem", "module": "Mathlib.Order.LatticeIntervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iic.semilatticeInf", "kind": "instance", "module": "Mathlib.Order.LatticeIntervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iic.coe_inf", "kind": "theorem", "module": "Mathlib.Order.LatticeIntervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iic.semilatticeSup", "kind": "instance", "module": "Mathlib.Order.LatticeIntervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iic.coe_sup", "kind": "theorem", "module": "Mathlib.Order.LatticeIntervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iic.instLatticeElem", "kind": "instance", "module": "Mathlib.Order.LatticeIntervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iic.orderTop", "kind": "instance", "module": "Mathlib.Order.LatticeIntervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iic.coe_top", "kind": "theorem", "module": "Mathlib.Order.LatticeIntervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iic.eq_top_iff", "kind": "theorem", "module": "Mathlib.Order.LatticeIntervals", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.Iic.orderBot", "kind": "instance", "module": "Mathlib.Order.LatticeIntervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iic.coe_bot", "kind": "theorem", "module": "Mathlib.Order.LatticeIntervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iic.instBoundedOrderElemOfOrderBot", "kind": "instance", "module": "Mathlib.Order.LatticeIntervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iic.disjoint_iff", "kind": "theorem", "module": "Mathlib.Order.LatticeIntervals", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.Iic.codisjoint_iff", "kind": "theorem", "module": "Mathlib.Order.LatticeIntervals", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.Iic.isCompl_iff", "kind": "theorem", "module": "Mathlib.Order.LatticeIntervals", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.Iic.complementedLattice_iff", "kind": "theorem", "module": "Mathlib.Order.LatticeIntervals", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.Ici.semilatticeInf", "kind": "instance", "module": "Mathlib.Order.LatticeIntervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ici.coe_inf", "kind": "theorem", "module": "Mathlib.Order.LatticeIntervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ici.semilatticeSup", "kind": "instance", "module": "Mathlib.Order.LatticeIntervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Set.Ici.lattice", "kind": "instance", "module": "Mathlib.Order.LatticeIntervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ici.distribLattice", "kind": "instance", "module": "Mathlib.Order.LatticeIntervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ici.orderBot", "kind": "instance", "module": "Mathlib.Order.LatticeIntervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Set.Ici.orderTop", "kind": "instance", "module": "Mathlib.Order.LatticeIntervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ici.coe_top", "kind": "theorem", "module": "Mathlib.Order.LatticeIntervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ici.boundedOrder", "kind": "instance", "module": "Mathlib.Order.LatticeIntervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Ici.disjoint_iff", "kind": "theorem", "module": "Mathlib.Order.LatticeIntervals", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.Ici.codisjoint_iff", "kind": "theorem", "module": "Mathlib.Order.LatticeIntervals", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.Ici.isCompl_iff", "kind": "theorem", "module": "Mathlib.Order.LatticeIntervals", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.Icc.semilatticeInf", "kind": "instance", "module": "Mathlib.Order.LatticeIntervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc.coe_inf", "kind": "theorem", "module": "Mathlib.Order.LatticeIntervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc.semilatticeSup", "kind": "instance", "module": "Mathlib.Order.LatticeIntervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Set.Icc.lattice", "kind": "instance", "module": "Mathlib.Order.LatticeIntervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc.instOrderBotElemOfFactLe", "kind": "instance", "module": "Mathlib.Order.LatticeIntervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc.coe_bot", "kind": "theorem", "module": "Mathlib.Order.LatticeIntervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc.instOrderTopElemOfFactLe", "kind": "instance", "module": "Mathlib.Order.LatticeIntervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc.coe_top", "kind": "theorem", "module": "Mathlib.Order.LatticeIntervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc.instBoundedOrderElemOfFactLe", "kind": "instance", "module": "Mathlib.Order.LatticeIntervals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc.disjoint_iff", "kind": "theorem", "module": "Mathlib.Order.LatticeIntervals", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.Icc.codisjoint_iff", "kind": "theorem", "module": "Mathlib.Order.LatticeIntervals", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.Icc.isCompl_iff", "kind": "theorem", "module": "Mathlib.Order.LatticeIntervals", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LatticeCon.r_inf_sup_iff", "kind": "theorem", "module": "Mathlib.Order.Lattice.Congruence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Order.Lattice.Congruence.0.LatticeCon.closed_interval", "kind": "theorem", "module": "Mathlib.Order.Lattice.Congruence", "is_tactic_proof": true, "tactics": ["suffices", "apply", "simpa"], "tactic_count": 3}
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{"name": "LatticeCon.mk'", "kind": "definition", "module": "Mathlib.Order.Lattice.Congruence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LatticeCon.ker", "kind": "definition", "module": "Mathlib.Order.Lattice.Congruence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.limsSup", "kind": "definition", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.limsInf", "kind": "definition", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Filter.blimsup", "kind": "definition", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.bliminf", "kind": "definition", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.limsup_eq", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.liminf_eq", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Filter.blimsup_eq_limsup", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.bliminf_eq_liminf", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Filter.bliminf_eq_liminf_subtype", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.limsSup_principal_eq_csSup", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.limsInf_principal_eq_csSup", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.limsup_top_eq_ciSup", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.liminf_top_eq_ciInf", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.limsup_congr", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": true, "tactics": ["rw", "congr", "exact"], "tactic_count": 3}
{"name": "Filter.blimsup_congr", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
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{"name": "Filter.limsup_const", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
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{"name": "Filter.HasBasis.liminf_eq_sSup_iUnion_iInter", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": true, "tactics": ["simp_rw", "congr", "ext", "simp"], "tactic_count": 4}
{"name": "Filter.HasBasis.liminf_eq_sSup_univ_of_empty", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.HasBasis.limsup_eq_sInf_iUnion_iInter", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.limsup_eq_sInf_univ_of_empty", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.liminf_nat_add", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.limsup_nat_add", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Filter.bliminf_false", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "Filter.HasBasis.limsInf_eq_iSup_sInf", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.limsSup_eq_iInf_sSup", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Filter.limsup_eq_iInf_iSup_of_nat", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.limsup_eq_iInf_iSup_of_nat'", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.HasBasis.limsup_eq_iInf_iSup", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Filter.limsInf_principal_eq_sInf", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Filter.limsup_top_eq_iSup", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.liminf_top_eq_iInf", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.blimsup_congr'", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": true, "tactics": ["simp", "congr", "refine", "rcases", "rw"], "tactic_count": 5}
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{"name": "Filter.HasBasis.blimsup_eq_iInf_iSup", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "Filter.blimsup_eq_iInf_biSup_of_nat", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.liminf_eq_iSup_iInf", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.liminf_eq_iSup_iInf_of_nat", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.liminf_eq_iSup_iInf_of_nat'", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.liminf_eq_iSup_iInf", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.bliminf_eq_iSup_biInf", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.bliminf_eq_iSup_biInf_of_nat", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.limsup_eq_sInf_sSup", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": true, "tactics": ["apply", "rw", "refine", "rcases", "filter_upwards", "exact", "refine", "rintro", "exact"], "tactic_count": 9}
{"name": "Filter.liminf_eq_sSup_sInf", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.liminf_le_of_frequently_le'", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": true, "tactics": ["rw", "refine", "have", "contrapose", "exact", "exact"], "tactic_count": 6}
{"name": "Filter.le_limsup_of_frequently_le'", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteLatticeHom.apply_limsup_iterate", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "conv_rhs", "simp", "refine", "simp", "exact"], "tactic_count": 7}
{"name": "CompleteLatticeHom.apply_liminf_iterate", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.blimsup_mono", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.bliminf_antitone", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mono_blimsup'", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mono_blimsup", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mono_bliminf'", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Filter.bliminf_antitone_filter", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.blimsup_monotone_filter", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.blimsup_and_le_inf", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.bliminf_sup_le_inf_aux_left", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.bliminf_sup_le_inf_aux_right", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.bliminf_sup_le_and", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.bliminf_sup_le_and_aux_left", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.bliminf_sup_le_and_aux_right", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.blimsup_sup_le_or", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.bliminf_sup_le_or_aux_left", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.bliminf_sup_le_or_aux_right", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.bliminf_or_le_inf", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.bliminf_or_le_inf_aux_left", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.bliminf_or_le_inf_aux_right", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.apply_blimsup", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": true, "tactics": ["simp", "e.le_symm_apply]"], "tactic_count": 2}
{"name": "OrderIso.apply_bliminf", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sSupHom.apply_blimsup_le", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": true, "tactics": ["simp", "refine", "simp"], "tactic_count": 3}
{"name": "sInfHom.le_apply_bliminf", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Filter.bliminf_inf_not", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Filter.bliminf_not_inf", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.limsup_piecewise", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": true, "tactics": ["rw", "refine"], "tactic_count": 2}
{"name": "Filter.liminf_piecewise", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.sup_limsup", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": true, "tactics": ["simp", "congr", "exact"], "tactic_count": 3}
{"name": "Filter.inf_liminf", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.sup_liminf", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": true, "tactics": ["simp", "rw", "simp_rw"], "tactic_count": 3}
{"name": "Filter.inf_limsup", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.limsup_compl", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.liminf_compl", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.limsup_sdiff", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": true, "tactics": ["simp", "rw", "simp_rw"], "tactic_count": 3}
{"name": "Filter.liminf_sdiff", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.sdiff_limsup", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Filter.sdiff_liminf", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Filter.mem_liminf_iff_eventually_mem", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Filter.mem_limsup_iff_frequently_mem", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.cofinite.blimsup_set_eq", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": true, "tactics": ["simp", "ext", "refine", "simp", "exact", "exact"], "tactic_count": 6}
{"name": "Filter.cofinite.bliminf_set_eq", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": true, "tactics": ["rw", "simp", "rfl"], "tactic_count": 3}
{"name": "Filter.cofinite.limsup_set_eq", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.cofinite.liminf_set_eq", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.exists_forall_mem_of_hasBasis_mem_blimsup", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": true, "tactics": ["rw", "simp", "choose", "refine", "exact", "exact"], "tactic_count": 6}
{"name": "Filter.exists_forall_mem_of_hasBasis_mem_blimsup'", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Filter.eventually_lt_add_pos_of_limsup_le", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventually_add_neg_lt_of_le_liminf", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.exists_lt_of_limsup_le", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": true, "tactics": ["have", "simp", "obtain", "exact"], "tactic_count": 4}
{"name": "Filter.exists_lt_of_le_liminf", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": true, "tactics": ["have", "simp", "obtain", "exact"], "tactic_count": 4}
{"name": "Filter.lt_mem_sets_of_limsSup_lt", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.gt_mem_sets_of_limsInf_gt", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.liminf_reparam", "kind": "definition", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.liminf_eq_ciSup_ciInf", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": true, "tactics": ["classical", "rcases", "let", "have", "have", "apply", "apply", "by_cases", "have", "conv_lhs", "apply", "simp", "simp", "apply", "exact", "have", "intro", "apply", "change", "by_cases", "simpa", "simp", "have", "rcases", "exact", "rcases", "exact", "exact", "simp_rw"], "tactic_count": 29}
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{"name": "Filter.HasBasis.limsup_eq_ciInf_ciSup", "kind": "theorem", "module": "Mathlib.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "nonempty_lt", "kind": "instance", "module": "Mathlib.Order.Max", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsEmpty.toNoMinOrder", "kind": "instance", "module": "Mathlib.Order.Max", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.noBotOrder", "kind": "instance", "module": "Mathlib.Order.Max", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.noMinOrder", "kind": "instance", "module": "Mathlib.Order.Max", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instNoBotOrderOfNoMinOrder", "kind": "instance", "module": "Mathlib.Order.Max", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "noMinOrder_of_left", "kind": "instance", "module": "Mathlib.Order.Max", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "noMinOrder_of_right", "kind": "instance", "module": "Mathlib.Order.Max", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instNoMinOrderForallOfNonempty", "kind": "instance", "module": "Mathlib.Order.Max", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NoBotOrder.to_noMinOrder", "kind": "theorem", "module": "Mathlib.Order.Max", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "noBotOrder_iff_noMinOrder", "kind": "theorem", "module": "Mathlib.Order.Max", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NoMinOrder.not_acc", "kind": "theorem", "module": "Mathlib.Order.Max", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBot", "kind": "definition", "module": "Mathlib.Order.Max", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMin", "kind": "definition", "module": "Mathlib.Order.Max", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_isBot", "kind": "theorem", "module": "Mathlib.Order.Max", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBot.isMin", "kind": "theorem", "module": "Mathlib.Order.Max", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBot.isMin_iff", "kind": "theorem", "module": "Mathlib.Order.Max", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "isBot_toDual_iff", "kind": "theorem", "module": "Mathlib.Order.Max", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isMin_toDual_iff", "kind": "theorem", "module": "Mathlib.Order.Max", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isBot_ofDual_iff", "kind": "theorem", "module": "Mathlib.Order.Max", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isMin_ofDual_iff", "kind": "theorem", "module": "Mathlib.Order.Max", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBot.mono", "kind": "theorem", "module": "Mathlib.Order.Max", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMin.mono", "kind": "theorem", "module": "Mathlib.Order.Max", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMin.not_lt", "kind": "theorem", "module": "Mathlib.Order.Max", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_isMin_of_lt", "kind": "theorem", "module": "Mathlib.Order.Max", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isMin_iff_forall_not_lt", "kind": "theorem", "module": "Mathlib.Order.Max", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_isMin_iff", "kind": "theorem", "module": "Mathlib.Order.Max", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "not_isMin", "kind": "theorem", "module": "Mathlib.Order.Max", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsingleton.isBot", "kind": "theorem", "module": "Mathlib.Order.Max", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsingleton.isMin", "kind": "theorem", "module": "Mathlib.Order.Max", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMin.eq_of_le", "kind": "theorem", "module": "Mathlib.Order.Max", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMin.eq_of_ge", "kind": "theorem", "module": "Mathlib.Order.Max", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBot.lt_of_ne", "kind": "theorem", "module": "Mathlib.Order.Max", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsTop.lt_of_ne", "kind": "theorem", "module": "Mathlib.Order.Max", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBot.not_isMax", "kind": "theorem", "module": "Mathlib.Order.Max", "is_tactic_proof": true, "tactics": ["intro", "obtain", "exact"], "tactic_count": 3}
{"name": "IsBot.not_isTop", "kind": "theorem", "module": "Mathlib.Order.Max", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBot.prodMk", "kind": "theorem", "module": "Mathlib.Order.Max", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMin.prodMk", "kind": "theorem", "module": "Mathlib.Order.Max", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBot.fst", "kind": "theorem", "module": "Mathlib.Order.Max", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBot.snd", "kind": "theorem", "module": "Mathlib.Order.Max", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMin.fst", "kind": "theorem", "module": "Mathlib.Order.Max", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Prod.isBot_iff", "kind": "theorem", "module": "Mathlib.Order.Max", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.isMin_iff", "kind": "theorem", "module": "Mathlib.Order.Max", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_min_iff", "kind": "theorem", "module": "Mathlib.Order.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "max_le_iff", "kind": "theorem", "module": "Mathlib.Order.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lt_min_iff", "kind": "theorem", "module": "Mathlib.Order.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "max_le_max", "kind": "theorem", "module": "Mathlib.Order.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "max_le_max_right", "kind": "theorem", "module": "Mathlib.Order.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "min_le_min", "kind": "theorem", "module": "Mathlib.Order.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "min_le_min_left", "kind": "theorem", "module": "Mathlib.Order.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "min_le_min_right", "kind": "theorem", "module": "Mathlib.Order.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_max_of_le_left", "kind": "theorem", "module": "Mathlib.Order.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_max_of_le_right", "kind": "theorem", "module": "Mathlib.Order.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lt_max_of_lt_left", "kind": "theorem", "module": "Mathlib.Order.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lt_max_of_lt_right", "kind": "theorem", "module": "Mathlib.Order.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "min_le_of_left_le", "kind": "theorem", "module": "Mathlib.Order.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "min_le_of_right_le", "kind": "theorem", "module": "Mathlib.Order.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "min_lt_of_left_lt", "kind": "theorem", "module": "Mathlib.Order.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "min_lt_of_right_lt", "kind": "theorem", "module": "Mathlib.Order.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "max_min_distrib_left", "kind": "theorem", "module": "Mathlib.Order.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "max_min_distrib_right", "kind": "theorem", "module": "Mathlib.Order.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "min_max_distrib_left", "kind": "theorem", "module": "Mathlib.Order.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "min_max_distrib_right", "kind": "theorem", "module": "Mathlib.Order.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "min_le_max", "kind": "theorem", "module": "Mathlib.Order.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "min_eq_left_iff", "kind": "theorem", "module": "Mathlib.Order.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "min_eq_right_iff", "kind": "theorem", "module": "Mathlib.Order.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "max_eq_right_iff", "kind": "theorem", "module": "Mathlib.Order.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "min_cases", "kind": "theorem", "module": "Mathlib.Order.MinMax", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "max_cases", "kind": "theorem", "module": "Mathlib.Order.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "min_eq_iff", "kind": "theorem", "module": "Mathlib.Order.MinMax", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "max_eq_iff", "kind": "theorem", "module": "Mathlib.Order.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "min_lt_min_left_iff", "kind": "theorem", "module": "Mathlib.Order.MinMax", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "min_lt_min_right_iff", "kind": "theorem", "module": "Mathlib.Order.MinMax", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "max_lt_max_left_iff", "kind": "theorem", "module": "Mathlib.Order.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "max_lt_max_right_iff", "kind": "theorem", "module": "Mathlib.Order.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "max_idem", "kind": "instance", "module": "Mathlib.Order.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "min_idem", "kind": "instance", "module": "Mathlib.Order.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "min_lt_max", "kind": "theorem", "module": "Mathlib.Order.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "max_lt_max", "kind": "theorem", "module": "Mathlib.Order.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "min_lt_min", "kind": "theorem", "module": "Mathlib.Order.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "min_right_comm", "kind": "theorem", "module": "Mathlib.Order.MinMax", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Max.left_comm", "kind": "theorem", "module": "Mathlib.Order.MinMax", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Max.right_comm", "kind": "theorem", "module": "Mathlib.Order.MinMax", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "MonotoneOn.map_max", "kind": "theorem", "module": "Mathlib.Order.MinMax", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "MonotoneOn.map_min", "kind": "theorem", "module": "Mathlib.Order.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntitoneOn.map_max", "kind": "theorem", "module": "Mathlib.Order.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntitoneOn.map_min", "kind": "theorem", "module": "Mathlib.Order.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.map_max", "kind": "theorem", "module": "Mathlib.Order.MinMax", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "Monotone.map_min", "kind": "theorem", "module": "Mathlib.Order.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.map_max", "kind": "theorem", "module": "Mathlib.Order.MinMax", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "Antitone.map_min", "kind": "theorem", "module": "Mathlib.Order.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "min_choice", "kind": "theorem", "module": "Mathlib.Order.MinMax", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "max_choice", "kind": "theorem", "module": "Mathlib.Order.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_of_max_le_left", "kind": "theorem", "module": "Mathlib.Order.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_of_max_le_right", "kind": "theorem", "module": "Mathlib.Order.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCommutativeMax", "kind": "instance", "module": "Mathlib.Order.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instAssociativeMax", "kind": "instance", "module": "Mathlib.Order.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCommutativeMin", "kind": "instance", "module": "Mathlib.Order.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instAssociativeMin", "kind": "instance", "module": "Mathlib.Order.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "max_left_commutative", "kind": "theorem", "module": "Mathlib.Order.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "min_left_commutative", "kind": "theorem", "module": "Mathlib.Order.MinMax", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "minimalFor_eq_iff", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "maximalFor_eq_iff", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "minimalFor_id", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "maximalFor_id", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "minimal_toDual", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "maximal_toDual", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "minimal_false", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "maximal_false", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "minimal_true", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "maximal_true", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "minimal_subtype", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": true, "tactics": ["obtain", "simp", "tauto"], "tactic_count": 3}
{"name": "maximal_subtype", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "maximal_true_subtype", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": true, "tactics": ["obtain", "simp"], "tactic_count": 2}
{"name": "minimal_true_subtype", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": true, "tactics": ["obtain", "simp"], "tactic_count": 2}
{"name": "minimal_minimal", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "maximal_maximal", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "minimal_iff_isMin", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "maximal_iff_isMax", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Minimal.mono", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Maximal.mono", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Minimal.and_right", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Minimal.and_left", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Maximal.and_right", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Maximal.and_left", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "minimal_eq_iff", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "maximal_eq_iff", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "not_minimal_iff", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "not_maximal_iff", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Minimal.or", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": true, "tactics": ["obtain", "exact", "exact"], "tactic_count": 3}
{"name": "Maximal.or", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "minimal_and_iff_right_of_imp", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "minimal_and_iff_left_of_imp", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "maximal_and_iff_right_of_imp", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "maximal_and_iff_left_of_imp", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "minimal_iff_forall_lt", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "maximal_iff_forall_gt", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "minimalFor_iff_forall_lt", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "maximalFor_iff_forall_gt", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Minimal.not_prop_of_lt", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Maximal.not_prop_of_gt", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MinimalFor.not_prop_of_lt", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MaximalFor.not_prop_of_gt", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Minimal.not_lt", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Maximal.not_gt", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MinimalFor.not_lt", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MaximalFor.not_gt", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "minimal_le_iff", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "maximal_ge_iff", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "minimal_lt_iff", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "maximal_gt_iff", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_minimal_iff_exists_lt", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "not_maximal_iff_exists_gt", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MinimalFor.of_strictMonoOn_comp", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": true, "tactics": ["refine", "by_contra", "exact"], "tactic_count": 3}
{"name": "MaximalFor.of_strictMonoOn_comp", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": true, "tactics": ["refine", "by_contra", "exact"], "tactic_count": 3}
{"name": "MinimalFor.minimal_of_strictMonoOn", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MaximalFor.maximal_of_strictMonoOn", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MinimalFor.maximalFor_of_strictAntiOn_comp", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": true, "tactics": ["refine", "by_contra", "exact"], "tactic_count": 3}
{"name": "MaximalFor.minimalFor_of_strictAntiOn_comp", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": true, "tactics": ["refine", "by_contra", "exact"], "tactic_count": 3}
{"name": "MinimalFor.maximal_of_strictAntiOn", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MaximalFor.minimal_of_strictAntiOn", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_minimalFor_of_wellFoundedLT", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "exists_minimal_of_wellFoundedLT", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_minimal_le_of_wellFoundedLT", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "exists_maximalFor_of_wellFoundedGT", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_maximal_of_wellFoundedGT", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_maximal_ge_of_wellFoundedGT", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Minimal.eq_of_ge", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Minimal.eq_of_le", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Maximal.eq_of_le", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Maximal.eq_of_ge", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "minimal_iff", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "maximal_iff", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "minimal_mem_iff", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "maximal_mem_iff", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "minimal_iff_eq", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "maximal_iff_eq", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "minimal_ge_iff", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "maximal_le_iff", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "minimal_iff_minimal_of_imp_of_forall", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": true, "tactics": ["refine", "obtain", "rwa", "obtain", "exact"], "tactic_count": 5}
{"name": "maximal_iff_maximal_of_imp_of_forall", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Minimal.le", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Maximal.le", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MinimalFor.le", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MaximalFor.le", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Minimal.eq_of_superset", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Maximal.eq_of_subset", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Minimal.eq_of_subset", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Maximal.eq_of_superset", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "minimal_subset_iff", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "maximal_subset_iff", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "minimal_subset_iff'", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "maximal_subset_iff'", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_minimal_subset_iff", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_maximal_subset_iff", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.minimal_iff_forall_ssubset", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Minimal.not_prop_of_ssubset", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Minimal.not_ssubset", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Maximal.mem_of_prop_insert", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Minimal.notMem_of_prop_diff_singleton", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.minimal_iff_forall_diff_singleton", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.exists_diff_singleton_of_not_minimal", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.maximal_iff_forall_ssuperset", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Maximal.not_prop_of_ssuperset", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Maximal.not_ssuperset", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.maximal_iff_forall_insert", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Set.exists_insert_of_not_maximal", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "setOf_minimal_subset", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "setOf_maximal_subset", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Subsingleton.maximal_mem_iff", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "Set.Subsingleton.minimal_mem_iff", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "IsLeast.minimal", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGreatest.maximal", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLeast.minimal_iff", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGreatest.maximal_iff", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "minimal_mem_image_monotone", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": true, "tactics": ["refine", "rintro", "rw", "exact"], "tactic_count": 4}
{"name": "maximal_mem_image_monotone", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "minimal_mem_image_monotone_iff", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "maximal_mem_image_monotone_iff", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "minimal_mem_image_antitone", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "maximal_mem_image_antitone", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "minimal_mem_image_antitone_iff", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "maximal_mem_image_antitone_iff", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "image_monotone_setOf_minimal", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": true, "tactics": ["refine", "rintro", "exact", "obtain", "exact"], "tactic_count": 5}
{"name": "image_monotone_setOf_maximal", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "image_antitone_setOf_minimal", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "image_antitone_setOf_maximal", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "image_monotone_setOf_minimal_mem", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "image_monotone_setOf_maximal_mem", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "image_antitone_setOf_minimal_mem", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "image_antitone_setOf_maximal_mem", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderEmbedding.minimal_mem_image", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderEmbedding.maximal_mem_image", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderEmbedding.minimal_mem_image_iff", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderEmbedding.maximal_mem_image_iff", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderEmbedding.minimal_apply_mem_inter_range_iff", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact", "rintro", "simp_rw", "exact"], "tactic_count": 6}
{"name": "OrderEmbedding.maximal_apply_mem_inter_range_iff", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderEmbedding.minimal_apply_mem_iff", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "OrderEmbedding.maximal_apply_iff", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderEmbedding.image_setOf_minimal", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderEmbedding.image_setOf_maximal", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderEmbedding.inter_preimage_setOf_minimal_eq_of_subset", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": true, "tactics": ["simp_rw", "f.minimal_apply_mem_iff", "minimal_and_iff_left_of_imp"], "tactic_count": 3}
{"name": "OrderEmbedding.inter_preimage_setOf_maximal_eq_of_subset", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.image_setOf_minimal", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": true, "tactics": ["convert", "aesop"], "tactic_count": 2}
{"name": "OrderIso.image_setOf_maximal", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": true, "tactics": ["convert", "aesop"], "tactic_count": 2}
{"name": "OrderIso.map_minimal_mem", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": true, "tactics": ["simpa", "image_univ]"], "tactic_count": 2}
{"name": "OrderIso.map_maximal_mem", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": true, "tactics": ["simpa", "image_univ]"], "tactic_count": 2}
{"name": "OrderIso.mapSetOfMinimal", "kind": "definition", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.mapSetOfMaximal", "kind": "definition", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.setOfMinimalIsoSetOfMaximal", "kind": "definition", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.setOfMaximalIsoSetOfMinimal", "kind": "definition", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "minimal_mem_Icc", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "maximal_mem_Icc", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "minimal_mem_Ico", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "maximal_mem_Ioc", "kind": "theorem", "module": "Mathlib.Order.Minimal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "covBy_sup_of_inf_covBy_of_inf_covBy_left", "kind": "theorem", "module": "Mathlib.Order.ModularLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "covBy_sup_of_inf_covBy_of_inf_covBy_right", "kind": "theorem", "module": "Mathlib.Order.ModularLattice", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "instIsWeakLowerModularLatticeOrderDual", "kind": "instance", "module": "Mathlib.Order.ModularLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "covBy_sup_of_inf_covBy_left", "kind": "theorem", "module": "Mathlib.Order.ModularLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "covBy_sup_of_inf_covBy_right", "kind": "theorem", "module": "Mathlib.Order.ModularLattice", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsUpperModularLattice.to_isWeakUpperModularLattice", "kind": "instance", "module": "Mathlib.Order.ModularLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsLowerModularLatticeOrderDual", "kind": "instance", "module": "Mathlib.Order.ModularLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sup_inf_le_assoc_of_le", "kind": "theorem", "module": "Mathlib.Order.ModularLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inf_sup_le_assoc_of_le", "kind": "theorem", "module": "Mathlib.Order.ModularLattice", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "sup_inf_assoc_of_le", "kind": "theorem", "module": "Mathlib.Order.ModularLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsModularLattice.inf_sup_inf_assoc", "kind": "theorem", "module": "Mathlib.Order.ModularLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsModularLatticeOrderDual", "kind": "instance", "module": "Mathlib.Order.ModularLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_of_le_of_inf_le_of_le_sup", "kind": "theorem", "module": "Mathlib.Order.ModularLattice", "is_tactic_proof": true, "tactics": ["refine", "rw", "rwa"], "tactic_count": 3}
{"name": "eq_of_le_of_inf_le_of_sup_le", "kind": "theorem", "module": "Mathlib.Order.ModularLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sup_lt_sup_of_lt_of_inf_le_inf", "kind": "theorem", "module": "Mathlib.Order.ModularLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictMono_inf_prod_sup", "kind": "theorem", "module": "Mathlib.Order.ModularLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "wellFounded_lt_exact_sequence", "kind": "theorem", "module": "Mathlib.Order.ModularLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "wellFounded_gt_exact_sequence", "kind": "theorem", "module": "Mathlib.Order.ModularLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "infIccOrderIsoIccSup", "kind": "definition", "module": "Mathlib.Order.ModularLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inf_strictMonoOn_Icc_sup", "kind": "theorem", "module": "Mathlib.Order.ModularLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sup_strictMonoOn_Icc_inf", "kind": "theorem", "module": "Mathlib.Order.ModularLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "infIooOrderIsoIooSup", "kind": "definition", "module": "Mathlib.Order.ModularLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsModularLattice.to_isLowerModularLattice", "kind": "instance", "module": "Mathlib.Order.ModularLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsModularLattice.to_isUpperModularLattice", "kind": "instance", "module": "Mathlib.Order.ModularLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompl.IicOrderIsoIci", "kind": "definition", "module": "Mathlib.Order.ModularLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isModularLattice_iff_inf_sup_inf_assoc", "kind": "theorem", "module": "Mathlib.Order.ModularLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DistribLattice.instIsModularLattice", "kind": "instance", "module": "Mathlib.Order.ModularLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Disjoint.disjoint_sup_right_of_disjoint_sup_left", "kind": "theorem", "module": "Mathlib.Order.ModularLattice", "is_tactic_proof": true, "tactics": ["rw", "apply", "apply", "rw"], "tactic_count": 4}
{"name": "Disjoint.disjoint_sup_left_of_disjoint_sup_right", "kind": "theorem", "module": "Mathlib.Order.ModularLattice", "is_tactic_proof": true, "tactics": ["rw", "apply", "rwa"], "tactic_count": 3}
{"name": "Disjoint.isCompl_sup_right_of_isCompl_sup_left", "kind": "theorem", "module": "Mathlib.Order.ModularLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Disjoint.isCompl_sup_left_of_isCompl_sup_right", "kind": "theorem", "module": "Mathlib.Order.ModularLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Iic.isCompl_inf_inf_of_isCompl_of_le", "kind": "theorem", "module": "Mathlib.Order.ModularLattice", "is_tactic_proof": true, "tactics": ["constructor", "simp", "simp", "simp"], "tactic_count": 4}
{"name": "IsModularLattice.isModularLattice_Iic", "kind": "instance", "module": "Mathlib.Order.ModularLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsModularLattice.isModularLattice_Ici", "kind": "instance", "module": "Mathlib.Order.ModularLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsModularLattice.exists_inf_eq_and_sup_eq", "kind": "theorem", "module": "Mathlib.Order.ModularLattice", "is_tactic_proof": true, "tactics": ["obtain", "refine", "simpa", "simp"], "tactic_count": 4}
{"name": "IsModularLattice.exists_disjoint_and_sup_eq", "kind": "theorem", "module": "Mathlib.Order.ModularLattice", "is_tactic_proof": true, "tactics": ["simp_rw", "apply"], "tactic_count": 2}
{"name": "IsModularLattice.exists_inf_eq_and_codisjoint", "kind": "theorem", "module": "Mathlib.Order.ModularLattice", "is_tactic_proof": true, "tactics": ["simp_rw", "apply"], "tactic_count": 2}
{"name": "IsModularLattice.complementedLattice_Icc", "kind": "instance", "module": "Mathlib.Order.ModularLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsModularLattice.complementedLattice_Iic", "kind": "instance", "module": "Mathlib.Order.ModularLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsModularLattice.complementedLattice_Ici", "kind": "instance", "module": "Mathlib.Order.ModularLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Disjoint.exists_isCompl", "kind": "theorem", "module": "Mathlib.Order.ModularLattice", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "monotone_comp_ofDual_iff", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "antitone_comp_ofDual_iff", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monotone_toDual_comp_iff", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "antitone_toDual_comp_iff", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monotoneOn_comp_ofDual_iff", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "antitoneOn_comp_ofDual_iff", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monotoneOn_toDual_comp_iff", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "antitoneOn_toDual_comp_iff", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictMono_comp_ofDual_iff", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictAnti_comp_ofDual_iff", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictMono_toDual_comp_iff", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictAnti_toDual_comp_iff", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictMonoOn_comp_ofDual_iff", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictAntiOn_comp_ofDual_iff", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictMonoOn_toDual_comp_iff", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictAntiOn_toDual_comp_iff", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monotone_dual_iff", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "antitone_dual_iff", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "monotoneOn_dual_iff", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "antitoneOn_dual_iff", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "strictMono_dual_iff", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "strictAnti_dual_iff", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "strictMonoOn_dual_iff", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "strictAntiOn_dual_iff", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "StrictMono.wellFoundedLT", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictAnti.wellFoundedLT", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.wellFoundedGT", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictAnti.wellFoundedGT", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.isMax_of_apply", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.isMin_of_apply", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictAnti.isMax_of_apply", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictAnti.isMin_of_apply", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.add_le_nat", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": true, "tactics": ["rw", "induction", "zero", "succ", "rw", "exact"], "tactic_count": 6}
{"name": "StrictMono.ite'", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": true, "tactics": ["intro", "by_cases", "have", "simpa", "by_cases", "simpa", "simpa"], "tactic_count": 7}
{"name": "StrictMono.ite", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictAnti.ite'", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictAnti.ite", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.foldl_monotone", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.foldr_monotone", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.foldl_strictMono", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.foldr_strictMono", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMonoOn.le_iff_le", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictAntiOn.le_iff_ge", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMonoOn.eq_iff_eq", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictAntiOn.eq_iff_eq", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMonoOn.lt_iff_lt", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "StrictAntiOn.lt_iff_gt", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.le_iff_le", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictAnti.le_iff_ge", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.lt_iff_lt", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictAnti.lt_iff_gt", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMonoOn.compares", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictAntiOn.compares", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.compares", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictAnti.compares", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.injective", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictAnti.injective", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMonoOn.injOn", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictAntiOn.injOn", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.maximal_of_maximal_image", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.minimal_of_minimal_image", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictAnti.minimal_of_maximal_image", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictAnti.maximal_of_minimal_image", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.strictMono_iff_injective", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.strictAnti_iff_injective", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.eq_of_ge_of_le", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": true, "tactics": ["apply", "rw", "exact"], "tactic_count": 3}
{"name": "Antitone.eq_of_ge_of_le", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": true, "tactics": ["apply", "exact", "rw"], "tactic_count": 3}
{"name": "not_monotone_not_antitone_iff_exists_le_le", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": true, "tactics": ["simp", "grind"], "tactic_count": 2}
{"name": "not_monotone_not_antitone_iff_exists_lt_lt", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "refine"], "tactic_count": 2}
{"name": "StrictMonoOn.cmp_map_eq", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.cmp_map_eq", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictAntiOn.cmp_map_eq", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictAnti.cmp_map_eq", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.rel_of_forall_rel_succ_of_le_of_lt", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": true, "tactics": ["induction", "refl", "step"], "tactic_count": 3}
{"name": "Nat.rel_of_forall_rel_succ_of_le_of_le", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.rel_of_forall_rel_succ_of_lt", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.rel_of_forall_rel_succ_of_le", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monotone_nat_of_le_succ", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monotone_add_nat_of_le_succ", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monotoneOn_nat_Ici_of_le_succ", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monotone_add_nat_iff_monotoneOn_nat_Ici", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "rw", "exact", "rw", "exact"], "tactic_count": 6}
{"name": "antitone_nat_of_succ_le", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "antitone_add_nat_of_succ_le", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "antitoneOn_nat_Ici_of_succ_le", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "antitone_add_nat_iff_antitoneOn_nat_Ici", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictMono_nat_of_lt_succ", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictAnti_nat_of_succ_lt", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.exists_strictMono'", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": true, "tactics": ["choose", "exact"], "tactic_count": 2}
{"name": "Nat.exists_strictAnti'", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.exists_strictMono_subsequence", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": ["have", "obtain", "exact"], "tactic_count": 3}
{"name": "Nat.exists_strictMono", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.exists_strictAnti", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.pow_self_mono", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "Nat.pow_monotoneOn", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.pow_self_strictMonoOn", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.rel_of_forall_rel_succ_of_lt", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": true, "tactics": ["rcases", "clear", "induction", "zero", "succ"], "tactic_count": 5}
{"name": "Int.rel_of_forall_rel_succ_of_le", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monotone_int_of_le_succ", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "antitone_int_of_succ_le", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictMono_int_of_lt_succ", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictAnti_int_of_succ_lt", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.exists_strictMono", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": true, "tactics": ["inhabit", "rcases", "rcases", "refine", "rintro", "exact", "change", "rw", "exact", "exact"], "tactic_count": 10}
{"name": "Int.exists_strictAnti", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.ne_of_lt_of_lt_nat", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "Antitone.ne_of_lt_of_lt_nat", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "Monotone.ne_of_lt_of_lt_int", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "Antitone.ne_of_lt_of_lt_int", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "Nat.stabilises_of_monotone", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": false, "tactics": ["obtain", "contrapose", "let", "m", "exact", "replace", "replace", "exact"], "tactic_count": 8}
{"name": "converges_of_monotone_of_bounded", "kind": "theorem", "module": "Mathlib.Order.Monotone.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "by_cases", "exact", "obtain", "replace", "use", "specialize"], "tactic_count": 9}
{"name": "Monotone", "kind": "definition", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone", "kind": "definition", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonotoneOn", "kind": "definition", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntitoneOn", "kind": "definition", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono", "kind": "definition", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictAnti", "kind": "definition", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMonoOn", "kind": "definition", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictAntiOn", "kind": "definition", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDecidableMonotoneOfForallForallForallLe", "kind": "instance", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDecidableAntitoneOfForallForallForallLe", "kind": "instance", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDecidableMonotoneOnOfForallForallMemSetForallForallForallLe", "kind": "instance", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDecidableAntitoneOnOfForallForallMemSetForallForallForallLe", "kind": "instance", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDecidableStrictMonoOfForallForallForallLt", "kind": "instance", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDecidableStrictAntiOfForallForallForallLt", "kind": "instance", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDecidableStrictMonoOnOfForallForallMemSetForallForallForallLt", "kind": "instance", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDecidableStrictAntiOnOfForallForallMemSetForallForallForallLt", "kind": "instance", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.comp_le_comp_left", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monotone_lam", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monotone_app", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "antitone_lam", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "antitone_app", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.monotone_eval", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.imp", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.imp", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.imp", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictAnti.imp", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.monotoneOn", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.antitoneOn", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monotoneOn_univ", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "antitoneOn_univ", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.strictMonoOn", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictAnti.strictAntiOn", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictMonoOn_univ", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictAntiOn_univ", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.strictMono_of_injective", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.strictAnti_of_injective", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monotone_iff_forall_lt", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "antitone_iff_forall_lt", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monotoneOn_iff_forall_lt", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "antitoneOn_iff_forall_lt", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMonoOn.monotoneOn", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictAntiOn.antitoneOn", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.monotone", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictAnti.antitone", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsingleton.monotone", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsingleton.antitone", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsingleton.monotone'", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsingleton.antitone'", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsingleton.strictMono", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsingleton.strictAnti", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monotone_id", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monotoneOn_id", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictMono_id", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictMonoOn_id", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monotone_const", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monotoneOn_const", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "antitone_const", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "antitoneOn_const", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictMono_of_le_iff_le", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictAnti_of_le_iff_le", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.of_lt_imp_ne", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Function.Injective.of_eq_imp_le", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "injective_of_le_imp_le", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.comp", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.comp_antitone", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.comp", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.comp_monotone", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.iterate", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.comp_monotoneOn", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.comp_antitoneOn", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.comp_antitoneOn", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.comp_monotoneOn", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.comp", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.comp_strictAnti", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictAnti.comp", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictAnti.comp_strictMono", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.iterate", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.comp_strictMonoOn", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.comp_strictAntiOn", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictAnti.comp_strictAntiOn", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictAnti.comp_strictMonoOn", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonotoneOn.comp", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonotoneOn.comp_AntitoneOn", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntitoneOn.comp", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntitoneOn.comp_MonotoneOn", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMonoOn.comp", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMonoOn.comp_strictAntiOn", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictAntiOn.comp", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictAntiOn.comp_strictMonoOn", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.reflect_lt", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.reflect_lt", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonotoneOn.reflect_lt", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntitoneOn.reflect_lt", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.mono_coe", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.strictMono_coe", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monotone_fst", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monotone_snd", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monotone_prodMk_iff", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Monotone.prodMk", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.prodMap", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.prodMap", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monotone_prod_iff", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "antitone_prod_iff", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.prodMap", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictAnti.prodMap", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.update_mono", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.update_strictMono", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.const_mono", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.const_strictMono", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monotone_iff_apply₂", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "antitone_iff_apply₂", "kind": "theorem", "module": "Mathlib.Order.Monotone.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MonotoneOn.exists_monotone_extension", "kind": "theorem", "module": "Mathlib.Order.Monotone.Extension", "is_tactic_proof": true, "tactics": ["classical", "of", "rcases", "have", "let", "have", "intro", "simp", "have", "rw", "refine", "by_cases", "simp", "rcases", "exact", "exact", "rw", "gcongr"], "tactic_count": 18}
{"name": "AntitoneOn.exists_antitone_extension", "kind": "theorem", "module": "Mathlib.Order.Monotone.Extension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monovary", "kind": "definition", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antivary", "kind": "definition", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonovaryOn", "kind": "definition", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntivaryOn", "kind": "definition", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monovary.monovaryOn", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antivary.antivaryOn", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonovaryOn.empty", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntivaryOn.empty", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monovaryOn_univ", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "antivaryOn_univ", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monovaryOn_iff_monovary", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "antivaryOn_iff_antivary", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MonovaryOn.subset", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntivaryOn.subset", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monovary_const_left", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "antivary_const_left", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monovary_const_right", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "antivary_const_right", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monovary_self", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monovaryOn_self", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsingleton.monovary", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsingleton.antivary", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsingleton.monovaryOn", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsingleton.antivaryOn", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monovaryOn_const_left", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "antivaryOn_const_left", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monovaryOn_const_right", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "antivaryOn_const_right", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monovary.comp_right", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antivary.comp_right", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonovaryOn.comp_right", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntivaryOn.comp_right", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monovary.comp_monotone_left", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monovary.comp_antitone_left", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antivary.comp_monotone_left", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antivary.comp_antitone_left", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonovaryOn.comp_monotone_on_left", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonovaryOn.comp_antitone_on_left", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntivaryOn.comp_monotone_on_left", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntivaryOn.comp_antitone_on_left", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monovary.dual", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antivary.dual", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monovary.dual_left", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antivary.dual_left", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monovary.dual_right", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antivary.dual_right", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonovaryOn.dual", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntivaryOn.dual", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonovaryOn.dual_left", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntivaryOn.dual_left", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonovaryOn.dual_right", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntivaryOn.dual_right", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monovary_toDual_left", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monovary_toDual_right", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "antivary_toDual_left", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "antivary_toDual_right", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monovaryOn_toDual_left", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monovaryOn_toDual_right", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "antivaryOn_toDual_left", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "antivaryOn_toDual_right", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monovary_id_iff", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "antivary_id_iff", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monovaryOn_id_iff", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "antivaryOn_id_iff", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.trans_monovary", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.trans_antivary", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictAnti.trans_monovary", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictAnti.trans_antivary", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMonoOn.trans_monovaryOn", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMonoOn.trans_antivaryOn", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictAntiOn.trans_monovaryOn", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictAntiOn.trans_antivaryOn", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.monovary", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.antivary", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.monovary", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.antivary", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonotoneOn.monovaryOn", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonotoneOn.antivaryOn", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntitoneOn.monovaryOn", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntitoneOn.antivaryOn", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonovaryOn.comp_monotoneOn_right", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonovaryOn.comp_antitoneOn_right", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntivaryOn.comp_monotoneOn_right", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntivaryOn.comp_antitoneOn_right", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monovary.symm", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MonovaryOn.symm", "kind": "theorem", "module": "Mathlib.Order.Monotone.Monovary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "_private.Mathlib.Order.Nucleus.0.Nucleus.giAux", "kind": "definition", "module": "Mathlib.Order.Nucleus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nucleus.instCompleteLatticeElemRangeCoe", "kind": "instance", "module": "Mathlib.Order.Nucleus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nucleus.range.instFrameMinimalAxioms", "kind": "instance", "module": "Mathlib.Order.Nucleus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "OmegaCompletePartialOrder.Chain", "kind": "definition", "module": "Mathlib.Order.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OmegaCompletePartialOrder.Chain.instFunLikeNat", "kind": "instance", "module": "Mathlib.Order.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OmegaCompletePartialOrder.Chain.instOrderHomClassNat", "kind": "instance", "module": "Mathlib.Order.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OmegaCompletePartialOrder.Chain.ext", "kind": "theorem", "module": "Mathlib.Order.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OmegaCompletePartialOrder.Chain.instInhabited", "kind": "instance", "module": "Mathlib.Order.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OmegaCompletePartialOrder.Chain.instMembership", "kind": "instance", "module": "Mathlib.Order.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OmegaCompletePartialOrder.Chain.instLE", "kind": "instance", "module": "Mathlib.Order.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OmegaCompletePartialOrder.Chain.isChain_range", "kind": "theorem", "module": "Mathlib.Order.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OmegaCompletePartialOrder.Chain.directed", "kind": "theorem", "module": "Mathlib.Order.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OmegaCompletePartialOrder.Chain.map", "kind": "definition", "module": "Mathlib.Order.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OmegaCompletePartialOrder.Chain.map_coe", "kind": "theorem", "module": "Mathlib.Order.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OmegaCompletePartialOrder.Chain.mem_map", "kind": "theorem", "module": "Mathlib.Order.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OmegaCompletePartialOrder.Chain.exists_of_mem_map", "kind": "theorem", "module": "Mathlib.Order.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OmegaCompletePartialOrder.Chain.mem_map_iff", "kind": "theorem", "module": "Mathlib.Order.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OmegaCompletePartialOrder.Chain.map_id", "kind": "theorem", "module": "Mathlib.Order.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "OmegaCompletePartialOrder.Chain.zip", "kind": "definition", "module": "Mathlib.Order.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OmegaCompletePartialOrder.Chain.zip_coe", "kind": "theorem", "module": "Mathlib.Order.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OmegaCompletePartialOrder.Chain.pair", "kind": "definition", "module": "Mathlib.Order.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "OmegaCompletePartialOrder.Chain.pair_zip_pair", "kind": "theorem", "module": "Mathlib.Order.OmegaCompletePartialOrder", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "OmegaCompletePartialOrder.lift", "kind": "abbrev", "module": "Mathlib.Order.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OmegaCompletePartialOrder.le_ωSup_of_le", "kind": "theorem", "module": "Mathlib.Order.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OmegaCompletePartialOrder.ωSup_total", "kind": "theorem", "module": "Mathlib.Order.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": ["have", "let", "have"], "tactic_count": 3}
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{"name": "ScottContinuous.ωScottContinuous", "kind": "theorem", "module": "Mathlib.Order.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "OmegaCompletePartialOrder.ωScottContinuous.isLUB", "kind": "theorem", "module": "Mathlib.Order.OmegaCompletePartialOrder", "is_tactic_proof": true, "tactics": ["simpa", "hf"], "tactic_count": 2}
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{"name": "OmegaCompletePartialOrder.ωScottContinuous_iff_monotone_map_ωSup", "kind": "theorem", "module": "Mathlib.Order.OmegaCompletePartialOrder", "is_tactic_proof": true, "tactics": ["refine", "intro", "convert", "rw", "rw", "rw"], "tactic_count": 6}
{"name": "OmegaCompletePartialOrder.ωScottContinuous_iff_map_ωSup_of_orderHom", "kind": "theorem", "module": "Mathlib.Order.OmegaCompletePartialOrder", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
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{"name": "Part.mem_chain_of_mem_ωSup", "kind": "theorem", "module": "Mathlib.Order.OmegaCompletePartialOrder", "is_tactic_proof": true, "tactics": ["simp", "have", "rw", "rw", "exact", "rcases"], "tactic_count": 6}
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{"name": "Part.mem_ωSup", "kind": "theorem", "module": "Mathlib.Order.OmegaCompletePartialOrder", "is_tactic_proof": true, "tactics": ["simp", "constructor", "split_ifs", "swap", "rintro", "intro", "have", "simp", "subst", "exact", "intro", "have", "rw", "have", "rw", "simp"], "tactic_count": 16}
{"name": "instOmegaCompletePartialOrderForall", "kind": "instance", "module": "Mathlib.Order.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OmegaCompletePartialOrder.ωScottContinuous.apply₂", "kind": "theorem", "module": "Mathlib.Order.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OmegaCompletePartialOrder.ωScottContinuous.of_apply₂", "kind": "theorem", "module": "Mathlib.Order.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OmegaCompletePartialOrder.ωScottContinuous_iff_apply₂", "kind": "theorem", "module": "Mathlib.Order.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CompleteLattice.ωScottContinuous.prodMk", "kind": "theorem", "module": "Mathlib.Order.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteLattice.ωScottContinuous.iSup", "kind": "theorem", "module": "Mathlib.Order.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": ["refine", "ωScottContinuous.of_monotone_map_ωSup", "simp"], "tactic_count": 3}
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{"name": "CompleteLattice.ωScottContinuous.sup", "kind": "theorem", "module": "Mathlib.Order.OmegaCompletePartialOrder", "is_tactic_proof": true, "tactics": ["rw", "apply", "rintro"], "tactic_count": 3}
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{"name": "OmegaCompletePartialOrder.OrderHom.ωSup", "kind": "definition", "module": "Mathlib.Order.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "OmegaCompletePartialOrder._aux_Mathlib_Order_OmegaCompletePartialOrder___unexpand_OmegaCompletePartialOrder_ContinuousHom_1", "kind": "definition", "module": "Mathlib.Order.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OmegaCompletePartialOrder.instFunLikeContinuousHom", "kind": "instance", "module": "Mathlib.Order.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OmegaCompletePartialOrder.instOrderHomClassContinuousHom", "kind": "instance", "module": "Mathlib.Order.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OmegaCompletePartialOrder.instPartialOrderContinuousHom", "kind": "instance", "module": "Mathlib.Order.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OmegaCompletePartialOrder.ContinuousHom.ωScottContinuous", "kind": "theorem", "module": "Mathlib.Order.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OmegaCompletePartialOrder.ContinuousHom.toOrderHom_eq_coe", "kind": "theorem", "module": "Mathlib.Order.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "OmegaCompletePartialOrder.ContinuousHom.coe_toOrderHom", "kind": "theorem", "module": "Mathlib.Order.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OmegaCompletePartialOrder.ContinuousHom.Simps.apply", "kind": "definition", "module": "Mathlib.Order.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OmegaCompletePartialOrder.ContinuousHom.congr_fun", "kind": "theorem", "module": "Mathlib.Order.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "OmegaCompletePartialOrder.ContinuousHom.monotone", "kind": "theorem", "module": "Mathlib.Order.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OmegaCompletePartialOrder.ContinuousHom.apply_mono", "kind": "theorem", "module": "Mathlib.Order.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "OmegaCompletePartialOrder.ContinuousHom.continuous", "kind": "theorem", "module": "Mathlib.Order.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "OmegaCompletePartialOrder.ContinuousHom.toMono", "kind": "definition", "module": "Mathlib.Order.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OmegaCompletePartialOrder.ContinuousHom.forall_forall_merge", "kind": "theorem", "module": "Mathlib.Order.OmegaCompletePartialOrder", "is_tactic_proof": true, "tactics": ["constructor", "apply", "apply", "trans", "apply", "apply", "apply", "apply", "apply"], "tactic_count": 9}
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{"name": "OmegaCompletePartialOrder.ContinuousHom.ωSup", "kind": "definition", "module": "Mathlib.Order.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "OmegaCompletePartialOrder.ContinuousHom.ωSup_apply_ωSup", "kind": "theorem", "module": "Mathlib.Order.OmegaCompletePartialOrder", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "OmegaCompletePartialOrder.ContinuousHom.flip", "kind": "definition", "module": "Mathlib.Order.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "OmegaCompletePartialOrder.ContinuousHom.map", "kind": "definition", "module": "Mathlib.Order.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OmegaCompletePartialOrder.ContinuousHom.seq", "kind": "definition", "module": "Mathlib.Order.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OmegaCompletePartialOrder.fixedPoints.iterateChain", "kind": "definition", "module": "Mathlib.Order.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OmegaCompletePartialOrder.fixedPoints.ωSup_iterate_mem_fixedPoint", "kind": "theorem", "module": "Mathlib.Order.OmegaCompletePartialOrder", "is_tactic_proof": true, "tactics": ["rw", "apply", "apply", "intro", "simp", "have", "rw", "apply", "apply", "rintro", "apply", "change", "apply", "have", "rw", "apply"], "tactic_count": 16}
{"name": "OmegaCompletePartialOrder.fixedPoints.ωSup_iterate_le_prefixedPoint", "kind": "theorem", "module": "Mathlib.Order.OmegaCompletePartialOrder", "is_tactic_proof": true, "tactics": ["apply", "intro", "induction", "zero", "succ", "h_ind", "have", "rw", "exact"], "tactic_count": 9}
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{"name": "LeftOrdContinuous", "kind": "definition", "module": "Mathlib.Order.OrdContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RightOrdContinuous", "kind": "definition", "module": "Mathlib.Order.OrdContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LeftOrdContinuous.rightOrdContinuous_dual", "kind": "theorem", "module": "Mathlib.Order.OrdContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LeftOrdContinuous.map_isGreatest", "kind": "theorem", "module": "Mathlib.Order.OrdContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LeftOrdContinuous.coe_toOrderEmbedding", "kind": "theorem", "module": "Mathlib.Order.OrdContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LeftOrdContinuous.map_sSup'", "kind": "theorem", "module": "Mathlib.Order.OrdContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LeftOrdContinuous.map_csSup", "kind": "theorem", "module": "Mathlib.Order.OrdContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "RightOrdContinuous.map_iInf", "kind": "theorem", "module": "Mathlib.Order.OrdContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RightOrdContinuous.map_csInf", "kind": "theorem", "module": "Mathlib.Order.OrdContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RightOrdContinuous.map_ciInf", "kind": "theorem", "module": "Mathlib.Order.OrdContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisConnection.leftOrdContinuous", "kind": "theorem", "module": "Mathlib.Order.OrdContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GaloisConnection.rightOrdContinuous", "kind": "theorem", "module": "Mathlib.Order.OrdContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.leftOrdContinuous", "kind": "theorem", "module": "Mathlib.Order.OrdContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.rightOrdContinuous", "kind": "theorem", "module": "Mathlib.Order.OrdContinuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelEmbedding.natLT", "kind": "definition", "module": "Mathlib.Order.OrderIsoNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelEmbedding.coe_natLT", "kind": "theorem", "module": "Mathlib.Order.OrderIsoNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelEmbedding.natGT", "kind": "definition", "module": "Mathlib.Order.OrderIsoNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelEmbedding.coe_natGT", "kind": "theorem", "module": "Mathlib.Order.OrderIsoNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelEmbedding.acc_iff_isEmpty_subtype_mem_range", "kind": "theorem", "module": "Mathlib.Order.OrderIsoNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelEmbedding.not_acc", "kind": "theorem", "module": "Mathlib.Order.OrderIsoNat", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "RelEmbedding.wellFounded_iff_isEmpty", "kind": "theorem", "module": "Mathlib.Order.OrderIsoNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelEmbedding.not_wellFounded", "kind": "theorem", "module": "Mathlib.Order.OrderIsoNat", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "not_strictAnti_of_wellFoundedLT", "kind": "theorem", "module": "Mathlib.Order.OrderIsoNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_strictMono_of_wellFoundedGT", "kind": "theorem", "module": "Mathlib.Order.OrderIsoNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.orderEmbeddingOfSet", "kind": "definition", "module": "Mathlib.Order.OrderIsoNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Subtype.orderIsoOfNat", "kind": "definition", "module": "Mathlib.Order.OrderIsoNat", "is_tactic_proof": true, "tactics": ["classical", "exact"], "tactic_count": 2}
{"name": "Nat.coe_orderEmbeddingOfSet", "kind": "theorem", "module": "Mathlib.Order.OrderIsoNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.orderEmbeddingOfSet_apply", "kind": "theorem", "module": "Mathlib.Order.OrderIsoNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.Subtype.orderIsoOfNat_apply", "kind": "theorem", "module": "Mathlib.Order.OrderIsoNat", "is_tactic_proof": false, "tactics": ["simp", "congr"], "tactic_count": 2}
{"name": "Nat.orderEmbeddingOfSet_range", "kind": "theorem", "module": "Mathlib.Order.OrderIsoNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.exists_subseq_of_forall_mem_union", "kind": "theorem", "module": "Mathlib.Order.OrderIsoNat", "is_tactic_proof": true, "tactics": ["classical", "have", "simp", "cases", "exacts"], "tactic_count": 5}
{"name": "exists_increasing_or_nonincreasing_subseq'", "kind": "theorem", "module": "Mathlib.Order.OrderIsoNat", "is_tactic_proof": true, "tactics": ["classical", "let", "by_cases", "refine", "have", "rw", "exact", "rw", "obtain", "by_cases", "refine", "exact", "have", "intro", "have", "simp", "obtain", "refine", "convert", "lia", "let", "exact"], "tactic_count": 22}
{"name": "exists_increasing_or_nonincreasing_subseq", "kind": "theorem", "module": "Mathlib.Order.OrderIsoNat", "is_tactic_proof": true, "tactics": ["obtain", "refine", "obtain", "induction", "zero", "succ", "apply", "exact", "exact"], "tactic_count": 9}
{"name": "wellFoundedGT_iff_monotone_chain_condition'", "kind": "theorem", "module": "Mathlib.Order.OrderIsoNat", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact", "rw", "refine", "obtain", "exact"], "tactic_count": 7}
{"name": "WellFoundedGT.monotone_chain_condition'", "kind": "theorem", "module": "Mathlib.Order.OrderIsoNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "wellFoundedGT_iff_monotone_chain_condition", "kind": "theorem", "module": "Mathlib.Order.OrderIsoNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WellFoundedGT.monotone_chain_condition", "kind": "theorem", "module": "Mathlib.Order.OrderIsoNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monotonicSequenceLimitIndex", "kind": "definition", "module": "Mathlib.Order.OrderIsoNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monotonicSequenceLimit", "kind": "definition", "module": "Mathlib.Order.OrderIsoNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_monotonicSequenceLimit", "kind": "theorem", "module": "Mathlib.Order.OrderIsoNat", "is_tactic_proof": true, "tactics": ["rcases", "exact", "obtain", "exact"], "tactic_count": 4}
{"name": "WellFoundedGT.iSup_eq_monotonicSequenceLimit", "kind": "theorem", "module": "Mathlib.Order.OrderIsoNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WellFoundedGT.ciSup_eq_monotonicSequenceLimit", "kind": "theorem", "module": "Mathlib.Order.OrderIsoNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_covBy_seq_of_wellFoundedLT_wellFoundedGT", "kind": "theorem", "module": "Mathlib.Order.OrderIsoNat", "is_tactic_proof": true, "tactics": ["choose", "have", "classical", "let", "refine", "have", "change", "rw", "exact", "have", "by_contra", "exact", "exact"], "tactic_count": 13}
{"name": "exists_covBy_seq_of_wellFoundedLT_wellFoundedGT_of_le", "kind": "theorem", "module": "Mathlib.Order.OrderIsoNat", "is_tactic_proof": true, "tactics": ["let", "let", "obtain", "simp", "exact"], "tactic_count": 5}
{"name": "Order.IsPFilter", "kind": "definition", "module": "Mathlib.Order.PFilter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.IsPFilter.of_def", "kind": "theorem", "module": "Mathlib.Order.PFilter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.IsPFilter.toPFilter", "kind": "definition", "module": "Mathlib.Order.PFilter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.PFilter.instInhabited", "kind": "instance", "module": "Mathlib.Order.PFilter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.PFilter.instSetLike", "kind": "instance", "module": "Mathlib.Order.PFilter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.PFilter.instPartialOrder", "kind": "instance", "module": "Mathlib.Order.PFilter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.PFilter.isPFilter", "kind": "theorem", "module": "Mathlib.Order.PFilter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.PFilter.nonempty", "kind": "theorem", "module": "Mathlib.Order.PFilter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.PFilter.directed", "kind": "theorem", "module": "Mathlib.Order.PFilter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.PFilter.mem_of_le", "kind": "theorem", "module": "Mathlib.Order.PFilter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.PFilter.ext", "kind": "theorem", "module": "Mathlib.Order.PFilter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.PFilter.mem_of_mem_of_le", "kind": "theorem", "module": "Mathlib.Order.PFilter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.PFilter.principal", "kind": "definition", "module": "Mathlib.Order.PFilter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.PFilter.mem_mk", "kind": "theorem", "module": "Mathlib.Order.PFilter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.PFilter.principal_le_iff", "kind": "theorem", "module": "Mathlib.Order.PFilter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.PFilter.mem_principal", "kind": "theorem", "module": "Mathlib.Order.PFilter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.PFilter.principal_le_principal_iff", "kind": "theorem", "module": "Mathlib.Order.PFilter", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Order.PFilter.antitone_principal", "kind": "theorem", "module": "Mathlib.Order.PFilter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.PFilter.top_mem", "kind": "theorem", "module": "Mathlib.Order.PFilter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.PFilter.instOrderBot", "kind": "instance", "module": "Mathlib.Order.PFilter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.PFilter.instOrderTopOfOrderBot", "kind": "instance", "module": "Mathlib.Order.PFilter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.PFilter.inf_mem", "kind": "theorem", "module": "Mathlib.Order.PFilter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.PFilter.inf_mem_iff", "kind": "theorem", "module": "Mathlib.Order.PFilter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.PFilter.sInf_gc", "kind": "theorem", "module": "Mathlib.Order.PFilter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.PFilter.infGi", "kind": "definition", "module": "Mathlib.Order.PFilter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.partBind", "kind": "theorem", "module": "Mathlib.Order.Part", "is_tactic_proof": true, "tactics": ["rintro", "simp", "exact"], "tactic_count": 3}
{"name": "Antitone.partBind", "kind": "theorem", "module": "Mathlib.Order.Part", "is_tactic_proof": true, "tactics": ["rintro", "simp", "exact"], "tactic_count": 3}
{"name": "Monotone.partMap", "kind": "theorem", "module": "Mathlib.Order.Part", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Antitone.partMap", "kind": "theorem", "module": "Mathlib.Order.Part", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Monotone.partSeq", "kind": "theorem", "module": "Mathlib.Order.Part", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Antitone.partSeq", "kind": "theorem", "module": "Mathlib.Order.Part", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "OrderHom.partBind", "kind": "definition", "module": "Mathlib.Order.Part", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "partialSups", "kind": "definition", "module": "Mathlib.Order.PartialSups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "partialSups_apply", "kind": "theorem", "module": "Mathlib.Order.PartialSups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "partialSups_iff_forall", "kind": "theorem", "module": "Mathlib.Order.PartialSups", "is_tactic_proof": true, "tactics": ["classical", "rw", "change", "simp", "intro", "rw", "rfl"], "tactic_count": 7}
{"name": "partialSups_le_iff", "kind": "theorem", "module": "Mathlib.Order.PartialSups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_partialSups_of_le", "kind": "theorem", "module": "Mathlib.Order.PartialSups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_partialSups", "kind": "theorem", "module": "Mathlib.Order.PartialSups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "partialSups_le", "kind": "theorem", "module": "Mathlib.Order.PartialSups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "upperBounds_range_partialSups", "kind": "theorem", "module": "Mathlib.Order.PartialSups", "is_tactic_proof": true, "tactics": ["ext", "simp", "exact"], "tactic_count": 3}
{"name": "bddAbove_range_partialSups", "kind": "theorem", "module": "Mathlib.Order.PartialSups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.partialSups_eq", "kind": "theorem", "module": "Mathlib.Order.PartialSups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "partialSups_mono", "kind": "theorem", "module": "Mathlib.Order.PartialSups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "partialSups_monotone", "kind": "theorem", "module": "Mathlib.Order.PartialSups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "partialSups.gi", "kind": "definition", "module": "Mathlib.Order.PartialSups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.partialSups_apply", "kind": "theorem", "module": "Mathlib.Order.PartialSups", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "comp_partialSups", "kind": "theorem", "module": "Mathlib.Order.PartialSups", "is_tactic_proof": true, "tactics": ["funext"], "tactic_count": 1}
{"name": "map_partialSups", "kind": "theorem", "module": "Mathlib.Order.PartialSups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "partialSups_succ", "kind": "theorem", "module": "Mathlib.Order.PartialSups", "is_tactic_proof": false, "tactics": ["suffices", "simp", "ext", "simp", "constructor", "exact", "exact"], "tactic_count": 7}
{"name": "partialSups_bot", "kind": "theorem", "module": "Mathlib.Order.PartialSups", "is_tactic_proof": false, "tactics": ["simp", "suffices", "simp"], "tactic_count": 3}
{"name": "partialSups_zero", "kind": "theorem", "module": "Mathlib.Order.PartialSups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "partialSups_eq_sup'_range", "kind": "theorem", "module": "Mathlib.Order.PartialSups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "partialSups_eq_sup_range", "kind": "theorem", "module": "Mathlib.Order.PartialSups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "disjoint_partialSups_left", "kind": "theorem", "module": "Mathlib.Order.PartialSups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "disjoint_partialSups_right", "kind": "theorem", "module": "Mathlib.Order.PartialSups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "partialSups_disjoint_of_disjoint", "kind": "theorem", "module": "Mathlib.Order.PartialSups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "partialSups_eq_ciSup_Iic", "kind": "theorem", "module": "Mathlib.Order.PartialSups", "is_tactic_proof": true, "tactics": ["simp", "apply", "exact", "sup'_le", "le_ciSup_of_le", "exact"], "tactic_count": 6}
{"name": "ciSup_partialSups_eq", "kind": "theorem", "module": "Mathlib.Order.PartialSups", "is_tactic_proof": true, "tactics": ["by_cases", "refine", "simpa", "rwa", "exact"], "tactic_count": 5}
{"name": "ciSup_partialSups_eq'", "kind": "theorem", "module": "Mathlib.Order.PartialSups", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "rw"], "tactic_count": 3}
{"name": "iSup_partialSups_eq", "kind": "theorem", "module": "Mathlib.Order.PartialSups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "partialSups_eq_biSup", "kind": "theorem", "module": "Mathlib.Order.PartialSups", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "iSup_le_iSup_of_partialSups_le_partialSups", "kind": "theorem", "module": "Mathlib.Order.PartialSups", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "iSup_eq_iSup_of_partialSups_eq_partialSups", "kind": "theorem", "module": "Mathlib.Order.PartialSups", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "partialSups_eq_sUnion_image", "kind": "theorem", "module": "Mathlib.Order.PartialSups", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "partialSups_eq_biUnion_range", "kind": "theorem", "module": "Mathlib.Order.PartialSups", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Partition.instSetLike", "kind": "instance", "module": "Mathlib.Order.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Partition.instPartialOrder", "kind": "instance", "module": "Mathlib.Order.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Partition.Simps.coe", "kind": "definition", "module": "Mathlib.Order.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Partition.coe_parts", "kind": "theorem", "module": "Mathlib.Order.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Partition.ext", "kind": "theorem", "module": "Mathlib.Order.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Partition.sSupIndep", "kind": "theorem", "module": "Mathlib.Order.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Partition.disjoint", "kind": "theorem", "module": "Mathlib.Order.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Partition.pairwiseDisjoint", "kind": "theorem", "module": "Mathlib.Order.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Partition.sSup_eq", "kind": "theorem", "module": "Mathlib.Order.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Partition.iSup_eq", "kind": "theorem", "module": "Mathlib.Order.Partition.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "rfl"], "tactic_count": 2}
{"name": "Partition.le_of_mem", "kind": "theorem", "module": "Mathlib.Order.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Partition.parts_nonempty", "kind": "theorem", "module": "Mathlib.Order.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Partition.bot_notMem", "kind": "theorem", "module": "Mathlib.Order.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Partition.ne_bot_of_mem", "kind": "theorem", "module": "Mathlib.Order.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Partition.bot_lt_of_mem", "kind": "theorem", "module": "Mathlib.Order.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Partition.copy", "kind": "definition", "module": "Mathlib.Order.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Partition.mem_copy_iff", "kind": "theorem", "module": "Mathlib.Order.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Partition.partscopyEquiv", "kind": "definition", "module": "Mathlib.Order.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Partition.removeBot", "kind": "definition", "module": "Mathlib.Order.Partition.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.IsEquipartition", "kind": "definition", "module": "Mathlib.Order.Partition.Equipartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.isEquipartition_iff_card_parts_eq_average", "kind": "theorem", "module": "Mathlib.Order.Partition.Equipartition", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Finpartition.not_isEquipartition", "kind": "theorem", "module": "Mathlib.Order.Partition.Equipartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Subsingleton.isEquipartition", "kind": "theorem", "module": "Mathlib.Order.Partition.Equipartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.IsEquipartition.card_parts_eq_average", "kind": "theorem", "module": "Mathlib.Order.Partition.Equipartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.IsEquipartition.card_part_eq_average_iff", "kind": "theorem", "module": "Mathlib.Order.Partition.Equipartition", "is_tactic_proof": true, "tactics": ["have", "lia"], "tactic_count": 2}
{"name": "Finpartition.IsEquipartition.average_le_card_part", "kind": "theorem", "module": "Mathlib.Order.Partition.Equipartition", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finpartition.IsEquipartition.card_part_le_average_add_one", "kind": "theorem", "module": "Mathlib.Order.Partition.Equipartition", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finpartition.IsEquipartition.filter_ne_average_add_one_eq_average", "kind": "theorem", "module": "Mathlib.Order.Partition.Equipartition", "is_tactic_proof": true, "tactics": ["ext", "simp", "exact"], "tactic_count": 3}
{"name": "Finpartition.IsEquipartition.card_large_parts_eq_mod", "kind": "theorem", "module": "Mathlib.Order.Partition.Equipartition", "is_tactic_proof": true, "tactics": ["have", "rw", "hP.filter_ne_average_add_one_eq_average,", "sum_const_nat", "add_assoc,", "rw"], "tactic_count": 6}
{"name": "Finpartition.IsEquipartition.card_small_parts_eq_mod", "kind": "theorem", "module": "Mathlib.Order.Partition.Equipartition", "is_tactic_proof": false, "tactics": ["conv_rhs", "arg", "rw", "rw"], "tactic_count": 4}
{"name": "Finpartition.IsEquipartition.exists_partsEquiv", "kind": "theorem", "module": "Mathlib.Order.Partition.Equipartition", "is_tactic_proof": true, "tactics": ["let", "let", "simp_rw", "simp_rw", "let", "apply", "simp", "exact", "replace", "replace", "let", "use", "intro", "simp_rw", "by_cases"], "tactic_count": 15}
{"name": "Finpartition.IsEquipartition.exists_partPreservingEquiv", "kind": "theorem", "module": "Mathlib.Order.Partition.Equipartition", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "let", "have", "have", "rcases", "calc", "rw", "exact", "let", "have", "refine", "simp_rw", "haveI", "change", "simp", "apply_fun", "exact", "use", "intro", "simp_rw"], "tactic_count": 21}
{"name": "Finpartition.bot_isEquipartition", "kind": "theorem", "module": "Mathlib.Order.Partition.Equipartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.top_isEquipartition", "kind": "theorem", "module": "Mathlib.Order.Partition.Equipartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.indiscrete_isEquipartition", "kind": "theorem", "module": "Mathlib.Order.Partition.Equipartition", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "instDecidableEqFinpartition", "kind": "instance", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.ofErase", "kind": "definition", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.ofSubset", "kind": "definition", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.copy", "kind": "definition", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.map", "kind": "definition", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.parts_map", "kind": "theorem", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.empty", "kind": "definition", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.instInhabitedBot", "kind": "instance", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.default_eq_empty", "kind": "theorem", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.indiscrete", "kind": "definition", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.le", "kind": "theorem", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.ne_bot", "kind": "theorem", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": true, "tactics": ["intro", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "Finpartition.disjoint", "kind": "theorem", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.parts_eq_empty_iff", "kind": "theorem", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "rw", "exact", "rwa"], "tactic_count": 5}
{"name": "Finpartition.parts_nonempty_iff", "kind": "theorem", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": true, "tactics": ["contrapose"], "tactic_count": 1}
{"name": "Finpartition.parts_nonempty", "kind": "theorem", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.instUniqueBot", "kind": "instance", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAtom.uniqueFinpartition", "kind": "abbrev", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.instFintypeOfDecidableEq", "kind": "instance", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.instLE", "kind": "instance", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.instPartialOrder", "kind": "instance", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.instOrderTopOfDecidableEqBot", "kind": "instance", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.parts_top_subset", "kind": "theorem", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": true, "tactics": ["intro", "have", "split_ifs", "simp", "exact"], "tactic_count": 5}
{"name": "Finpartition.parts_top_subsingleton", "kind": "theorem", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.instFintypeFinset", "kind": "instance", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.instMin", "kind": "instance", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.parts_inf", "kind": "theorem", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.instSemilatticeInf", "kind": "instance", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.exists_le_of_le", "kind": "theorem", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": true, "tactics": ["by_contra", "refine", "rw", "rintro", "obtain", "refine", "rintro", "simp", "exact"], "tactic_count": 9}
{"name": "Finpartition.card_mono", "kind": "theorem", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": true, "tactics": ["classical", "have", "choose", "rw", "refine", "exact"], "tactic_count": 6}
{"name": "Finpartition.bind", "kind": "definition", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.mem_bind", "kind": "theorem", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": true, "tactics": ["rw", "constructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 6}
{"name": "Finpartition.card_bind", "kind": "theorem", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": true, "tactics": ["apply", "rintro", "rw", "rintro", "rw", "exact"], "tactic_count": 6}
{"name": "Finpartition.extend", "kind": "definition", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.card_extend", "kind": "theorem", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.avoid", "kind": "definition", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.mem_avoid", "kind": "theorem", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": true, "tactics": ["simp", "refine", "rintro", "rw"], "tactic_count": 4}
{"name": "Finpartition.subset", "kind": "theorem", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.nonempty_of_mem_parts", "kind": "theorem", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.empty_notMem_parts", "kind": "theorem", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.ne_empty", "kind": "theorem", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.eq_of_mem_parts", "kind": "theorem", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.exists_mem", "kind": "theorem", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Finpartition.biUnion_parts", "kind": "theorem", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.existsUnique_mem", "kind": "theorem", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": true, "tactics": ["obtain", "refine", "rintro", "exact"], "tactic_count": 4}
{"name": "Finpartition.ofExistsUnique", "kind": "definition", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.part", "kind": "definition", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.part_mem", "kind": "theorem", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "Finpartition.part_eq_empty", "kind": "theorem", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.part_nonempty", "kind": "theorem", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": true, "tactics": ["contrapose"], "tactic_count": 1}
{"name": "Finpartition.part_subset", "kind": "theorem", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "simp"], "tactic_count": 3}
{"name": "Finpartition.mem_part_self", "kind": "theorem", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "simp"], "tactic_count": 3}
{"name": "Finpartition.part_eq_iff_mem", "kind": "theorem", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "simp_all", "intro", "apply"], "tactic_count": 5}
{"name": "Finpartition.part_eq_of_mem", "kind": "theorem", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.mem_part_iff_part_eq_part", "kind": "theorem", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.part_surjOn", "kind": "theorem", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.exists_subset_part_bijOn", "kind": "theorem", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": true, "tactics": ["obtain", "lift", "exact"], "tactic_count": 3}
{"name": "Finpartition.mem_part_iff_exists", "kind": "theorem", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": true, "tactics": ["constructor", "intro", "have", "refine", "rintro", "obtain", "exact"], "tactic_count": 7}
{"name": "Finpartition.equivSigmaParts", "kind": "definition", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.exists_enumeration", "kind": "theorem", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": true, "tactics": ["use", "simp"], "tactic_count": 2}
{"name": "Finpartition.sum_card_parts", "kind": "theorem", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": true, "tactics": ["convert", "rw", "rfl"], "tactic_count": 3}
{"name": "Finpartition.instBotFinset", "kind": "instance", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.parts_bot", "kind": "theorem", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.card_bot", "kind": "theorem", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.mem_bot_iff", "kind": "theorem", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.instOrderBotFinset", "kind": "instance", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.card_parts_le_card", "kind": "theorem", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Finpartition.card_mod_card_parts_le", "kind": "theorem", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": true, "tactics": ["obtain", "rw", "rw", "rw", "exact"], "tactic_count": 5}
{"name": "Finpartition.ofSetSetoid", "kind": "definition", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.mem_part_ofSetSetoid_iff_rel", "kind": "theorem", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": false, "tactics": ["suffices", "simpa", "exact"], "tactic_count": 3}
{"name": "Finpartition.ofSetoid", "kind": "definition", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.mem_part_ofSetoid_iff_rel", "kind": "theorem", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": true, "tactics": ["suffices", "exact"], "tactic_count": 2}
{"name": "Finpartition.atomise", "kind": "definition", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.mem_atomise", "kind": "theorem", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Finpartition.atomise_empty", "kind": "theorem", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": false, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Finpartition.card_atomise_le", "kind": "theorem", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finpartition.biUnion_filter_atomise", "kind": "theorem", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": true, "tactics": ["ext", "refine", "obtain", "refine", "obtain", "rw", "rwa"], "tactic_count": 7}
{"name": "Finpartition.card_filter_atomise_le_two_pow", "kind": "theorem", "module": "Mathlib.Order.Partition.Finpartition", "is_tactic_proof": false, "tactics": ["suffices", "refine", "rw", "rw", "simp_rw", "rintro", "refine", "simp"], "tactic_count": 8}
{"name": "Pi.Lex", "kind": "definition", "module": "Mathlib.Order.PiLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.termΠₗ_,_", "kind": "definition", "module": "Mathlib.Order.PiLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi._aux_Mathlib_Order_PiLex___macroRules_Pi_termΠₗ_,__1", "kind": "definition", "module": "Mathlib.Order.PiLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.lex_lt_of_lt_of_preorder", "kind": "theorem", "module": "Mathlib.Order.PiLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.lex_lt_of_lt", "kind": "theorem", "module": "Mathlib.Order.PiLex", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Pi.lex_iff_of_unique", "kind": "theorem", "module": "Mathlib.Order.PiLex", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Pi.isTrichotomous_lex", "kind": "theorem", "module": "Mathlib.Order.PiLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instLTLexForall", "kind": "instance", "module": "Mathlib.Order.PiLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instLTColexForall", "kind": "instance", "module": "Mathlib.Order.PiLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.toLex_apply", "kind": "theorem", "module": "Mathlib.Order.PiLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.ofLex_apply", "kind": "theorem", "module": "Mathlib.Order.PiLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.toColex_apply", "kind": "theorem", "module": "Mathlib.Order.PiLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.ofColex_apply", "kind": "theorem", "module": "Mathlib.Order.PiLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.Lex.lt_iff_of_unique", "kind": "theorem", "module": "Mathlib.Order.PiLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.Colex.lt_iff_of_unique", "kind": "theorem", "module": "Mathlib.Order.PiLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.Lex.isStrictOrder", "kind": "instance", "module": "Mathlib.Order.PiLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.Colex.isStrictOrder", "kind": "instance", "module": "Mathlib.Order.PiLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instPartialOrderLexForallOfLinearOrder", "kind": "instance", "module": "Mathlib.Order.PiLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instPartialOrderColexForallOfLinearOrder", "kind": "instance", "module": "Mathlib.Order.PiLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.Lex.linearOrder", "kind": "instance", "module": "Mathlib.Order.PiLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.Colex.linearOrder", "kind": "instance", "module": "Mathlib.Order.PiLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.lex_le_iff_of_unique", "kind": "theorem", "module": "Mathlib.Order.PiLex", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Pi.colex_le_iff_of_unique", "kind": "theorem", "module": "Mathlib.Order.PiLex", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Pi.toLex_monotone", "kind": "theorem", "module": "Mathlib.Order.PiLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.toLex_strictMono", "kind": "theorem", "module": "Mathlib.Order.PiLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.lt_toLex_update_self_iff", "kind": "theorem", "module": "Mathlib.Order.PiLex", "is_tactic_proof": true, "tactics": ["refine", "rintro", "dsimp", "obtain", "by_contra", "rw", "exact", "rwa"], "tactic_count": 8}
{"name": "Pi.toLex_update_lt_self_iff", "kind": "theorem", "module": "Mathlib.Order.PiLex", "is_tactic_proof": true, "tactics": ["refine", "rintro", "dsimp", "obtain", "by_contra", "rw", "exact", "rwa"], "tactic_count": 8}
{"name": "Pi.le_toLex_update_self_iff", "kind": "theorem", "module": "Mathlib.Order.PiLex", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Pi.toLex_update_le_self_iff", "kind": "theorem", "module": "Mathlib.Order.PiLex", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Pi.toColex_monotone", "kind": "theorem", "module": "Mathlib.Order.PiLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.toColex_strictMono", "kind": "theorem", "module": "Mathlib.Order.PiLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.lt_toColex_update_self_iff", "kind": "theorem", "module": "Mathlib.Order.PiLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.toColex_update_lt_self_iff", "kind": "theorem", "module": "Mathlib.Order.PiLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.le_toColex_update_self_iff", "kind": "theorem", "module": "Mathlib.Order.PiLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.toColex_update_le_self_iff", "kind": "theorem", "module": "Mathlib.Order.PiLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.apply_le_of_toLex", "kind": "theorem", "module": "Mathlib.Order.PiLex", "is_tactic_proof": true, "tactics": ["contrapose", "apply", "use", "aesop"], "tactic_count": 4}
{"name": "Pi.apply_le_of_toColex", "kind": "theorem", "module": "Mathlib.Order.PiLex", "is_tactic_proof": true, "tactics": ["contrapose", "apply", "use", "aesop"], "tactic_count": 4}
{"name": "Pi.instOrderBotLexForallOfWellFoundedLT", "kind": "instance", "module": "Mathlib.Order.PiLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instOrderBotColexForallOfWellFoundedGT", "kind": "instance", "module": "Mathlib.Order.PiLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instOrderTopLexForallOfWellFoundedLT", "kind": "instance", "module": "Mathlib.Order.PiLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instOrderTopColexForallOfWellFoundedGT", "kind": "instance", "module": "Mathlib.Order.PiLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instBoundedOrderLexForallOfWellFoundedLT", "kind": "instance", "module": "Mathlib.Order.PiLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instBoundedOrderColexForallOfWellFoundedGT", "kind": "instance", "module": "Mathlib.Order.PiLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instDenselyOrderedLexForall", "kind": "instance", "module": "Mathlib.Order.PiLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instDenselyOrderedColexForall", "kind": "instance", "module": "Mathlib.Order.PiLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.Lex.noMaxOrder'", "kind": "theorem", "module": "Mathlib.Order.PiLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.Colex.noMaxOrder'", "kind": "theorem", "module": "Mathlib.Order.PiLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instNoMaxOrderLexForallOfWellFoundedLTOfNonempty", "kind": "instance", "module": "Mathlib.Order.PiLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instNoMaxOrderColexForallOfWellFoundedGTOfNonempty", "kind": "instance", "module": "Mathlib.Order.PiLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instNoMinOrderLexForallOfWellFoundedLTOfNonempty", "kind": "instance", "module": "Mathlib.Order.PiLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instNoMinOrderColexForallOfWellFoundedGTOfNonempty", "kind": "instance", "module": "Mathlib.Order.PiLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.lex_desc", "kind": "theorem", "module": "Mathlib.Order.PiLex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.colex_asc", "kind": "theorem", "module": "Mathlib.Order.PiLex", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "_private.Mathlib.Order.Preorder.Chain.0.term_≺_", "kind": "definition", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Order.Preorder.Chain.0._aux_Mathlib_Order_Preorder_Chain___macroRules__private_Mathlib_Order_Preorder_Chain_0_term_≺__1", "kind": "definition", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsChain", "kind": "definition", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SuperChain", "kind": "definition", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMaxChain", "kind": "definition", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsChain.empty", "kind": "theorem", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsChain.singleton", "kind": "theorem", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Subsingleton.isChain", "kind": "theorem", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsChain.mono", "kind": "theorem", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsChain.mono_rel", "kind": "theorem", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsChain.symm", "kind": "theorem", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isChain_of_trichotomous", "kind": "theorem", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsChain.insert", "kind": "theorem", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsChain.pair", "kind": "theorem", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isChain_univ_iff", "kind": "theorem", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "IsChain.image", "kind": "theorem", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsChain.preimage", "kind": "theorem", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": true, "tactics": ["intro", "have", "grind"], "tactic_count": 3}
{"name": "isChain_union", "kind": "theorem", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Monotone.isChain_image", "kind": "theorem", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.isChain_range", "kind": "theorem", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsChain.lt_of_le", "kind": "theorem", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsChain.diff", "kind": "theorem", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isChain_preimage_subtypeVal", "kind": "theorem", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "isChain_coe_univ_iff", "kind": "theorem", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsChain.image_relEmbedding", "kind": "theorem", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": true, "tactics": ["intro", "rw", "obtain", "have", "grind"], "tactic_count": 5}
{"name": "IsChain.preimage_relEmbedding", "kind": "theorem", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsChain.image_relIso", "kind": "theorem", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsChain.preimage_relIso", "kind": "theorem", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsChain.image_relEmbedding_iff", "kind": "theorem", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsChain.image_relIso_iff", "kind": "theorem", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsChain.image_embedding", "kind": "theorem", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsChain.preimage_embedding", "kind": "theorem", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsChain.image_embedding_iff", "kind": "theorem", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsChain.image_iso", "kind": "theorem", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsChain.image_iso_iff", "kind": "theorem", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsChain.preimage_iso", "kind": "theorem", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsChain.preimage_iso_iff", "kind": "theorem", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsChain.total", "kind": "theorem", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsChain.directedOn", "kind": "theorem", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsChain.directed", "kind": "theorem", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsChain.exists3", "kind": "theorem", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "exact"], "tactic_count": 3}
{"name": "IsChain.le_of_not_gt", "kind": "theorem", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": true, "tactics": ["cases", "inr", "inl"], "tactic_count": 3}
{"name": "IsChain.not_lt", "kind": "theorem", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsChain.lt_of_not_ge", "kind": "theorem", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsChain.not_le", "kind": "theorem", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMaxChain.isChain", "kind": "theorem", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMaxChain.not_superChain", "kind": "theorem", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMaxChain.bot_mem", "kind": "theorem", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMaxChain.top_mem", "kind": "theorem", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMaxChain.image", "kind": "theorem", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMaxChain.isEmpty_iff", "kind": "theorem", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": true, "tactics": ["refine", "constructor", "intro", "simp", "exact"], "tactic_count": 5}
{"name": "IsMaxChain.nonempty_iff", "kind": "theorem", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMaxChain.symm", "kind": "theorem", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SuccChain", "kind": "definition", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "succChain_spec", "kind": "theorem", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "IsChain.succ", "kind": "theorem", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsChain.superChain_succChain", "kind": "theorem", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": true, "tactics": ["simp", "obtain", "exact"], "tactic_count": 3}
{"name": "subset_succChain", "kind": "theorem", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Flag.instSetLike", "kind": "instance", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Flag.instPartialOrder", "kind": "instance", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Flag.ext", "kind": "theorem", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Flag.mem_coe_iff", "kind": "theorem", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Flag.coe_mk", "kind": "theorem", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Flag.mk_coe", "kind": "theorem", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Flag.chain_le", "kind": "theorem", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Flag.maxChain", "kind": "theorem", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Flag.top_mem", "kind": "theorem", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Flag.bot_mem", "kind": "theorem", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Flag.ofIsMaxChain", "kind": "definition", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Flag.coe_ofIsMaxChain", "kind": "theorem", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Flag.le_or_le", "kind": "theorem", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Flag.instOrderTopSubtypeMem", "kind": "instance", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Flag.instOrderBotSubtypeMem", "kind": "instance", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Flag.instBoundedOrderSubtypeMem", "kind": "instance", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Flag.mem_iff_forall_le_or_ge", "kind": "theorem", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Flag.map", "kind": "definition", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Flag.coe_map", "kind": "theorem", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Flag.symm_map", "kind": "theorem", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Flag.chain_lt", "kind": "theorem", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Flag.instLinearOrderSubtypeMemOfDecidableLEOfDecidableLTOfDecidableEq", "kind": "instance", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Flag.instUnique", "kind": "instance", "module": "Mathlib.Order.Preorder.Chain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.exists_maximalFor", "kind": "theorem", "module": "Mathlib.Order.Preorder.Finite", "is_tactic_proof": true, "tactics": ["induction", "singleton", "obtain", "by_cases", "refine", "simp", "exact", "exact"], "tactic_count": 8}
{"name": "Finset.exists_minimalFor", "kind": "theorem", "module": "Mathlib.Order.Preorder.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.exists_maximal", "kind": "theorem", "module": "Mathlib.Order.Preorder.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.exists_minimal", "kind": "theorem", "module": "Mathlib.Order.Preorder.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.exists_le_maximal", "kind": "theorem", "module": "Mathlib.Order.Preorder.Finite", "is_tactic_proof": true, "tactics": ["classical", "obtain", "simpa", "exact"], "tactic_count": 4}
{"name": "Finset.exists_le_minimal", "kind": "theorem", "module": "Mathlib.Order.Preorder.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.exists_maximalFor", "kind": "theorem", "module": "Mathlib.Order.Preorder.Finite", "is_tactic_proof": true, "tactics": ["lift"], "tactic_count": 1}
{"name": "Set.Finite.exists_minimalFor", "kind": "theorem", "module": "Mathlib.Order.Preorder.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.exists_maximal", "kind": "theorem", "module": "Mathlib.Order.Preorder.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.exists_minimal", "kind": "theorem", "module": "Mathlib.Order.Preorder.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.exists_maximalFor'", "kind": "theorem", "module": "Mathlib.Order.Preorder.Finite", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Set.Finite.exists_minimalFor'", "kind": "theorem", "module": "Mathlib.Order.Preorder.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.exists_le_maximal", "kind": "theorem", "module": "Mathlib.Order.Preorder.Finite", "is_tactic_proof": true, "tactics": ["lift"], "tactic_count": 1}
{"name": "Set.Finite.exists_le_minimal", "kind": "theorem", "module": "Mathlib.Order.Preorder.Finite", "is_tactic_proof": true, "tactics": ["lift"], "tactic_count": 1}
{"name": "Set.infinite_of_forall_exists_gt", "kind": "theorem", "module": "Mathlib.Order.Preorder.Finite", "is_tactic_proof": true, "tactics": ["inhabit", "let", "have", "exact"], "tactic_count": 4}
{"name": "Set.infinite_of_forall_exists_lt", "kind": "theorem", "module": "Mathlib.Order.Preorder.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.finite_isTop", "kind": "theorem", "module": "Mathlib.Order.Preorder.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.finite_isBot", "kind": "theorem", "module": "Mathlib.Order.Preorder.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Infinite.exists_lt_map_eq_of_mapsTo", "kind": "theorem", "module": "Mathlib.Order.Preorder.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.exists_lt_map_eq_of_forall_mem", "kind": "theorem", "module": "Mathlib.Order.Preorder.Finite", "is_tactic_proof": true, "tactics": ["rw", "obtain", "exact"], "tactic_count": 3}
{"name": "Finite.exists_le_maximal", "kind": "theorem", "module": "Mathlib.Order.Preorder.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finite.exists_le_minimal", "kind": "theorem", "module": "Mathlib.Order.Preorder.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.instLE", "kind": "instance", "module": "Mathlib.Order.Preorder.Finsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.le_def", "kind": "theorem", "module": "Mathlib.Order.Preorder.Finsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.coe_le_coe", "kind": "theorem", "module": "Mathlib.Order.Preorder.Finsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.orderEmbeddingToFun", "kind": "definition", "module": "Mathlib.Order.Preorder.Finsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.orderIsoFunOnFinite", "kind": "definition", "module": "Mathlib.Order.Preorder.Finsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.preorder", "kind": "instance", "module": "Mathlib.Order.Preorder.Finsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.lt_def", "kind": "theorem", "module": "Mathlib.Order.Preorder.Finsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.coe_lt_coe", "kind": "theorem", "module": "Mathlib.Order.Preorder.Finsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.coe_mono", "kind": "theorem", "module": "Mathlib.Order.Preorder.Finsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.coe_strictMono", "kind": "theorem", "module": "Mathlib.Order.Preorder.Finsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.partialorder", "kind": "instance", "module": "Mathlib.Order.Preorder.Finsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.semilatticeInf", "kind": "instance", "module": "Mathlib.Order.Preorder.Finsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.inf_apply", "kind": "theorem", "module": "Mathlib.Order.Preorder.Finsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.semilatticeSup", "kind": "instance", "module": "Mathlib.Order.Preorder.Finsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.sup_apply", "kind": "theorem", "module": "Mathlib.Order.Preorder.Finsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.lattice", "kind": "instance", "module": "Mathlib.Order.Preorder.Finsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.support_inf_union_support_sup", "kind": "theorem", "module": "Mathlib.Order.Preorder.Finsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsupp.support_sup_union_support_inf", "kind": "theorem", "module": "Mathlib.Order.Preorder.Finsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ideal.PrimePair.compl_I_eq_F", "kind": "theorem", "module": "Mathlib.Order.PrimeIdeal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ideal.PrimePair.compl_F_eq_I", "kind": "theorem", "module": "Mathlib.Order.PrimeIdeal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ideal.PrimePair.I_isProper", "kind": "theorem", "module": "Mathlib.Order.PrimeIdeal", "is_tactic_proof": true, "tactics": ["obtain", "apply", "rwa"], "tactic_count": 3}
{"name": "Order.Ideal.PrimePair.disjoint", "kind": "theorem", "module": "Mathlib.Order.PrimeIdeal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ideal.PrimePair.I_union_F", "kind": "theorem", "module": "Mathlib.Order.PrimeIdeal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ideal.PrimePair.F_union_I", "kind": "theorem", "module": "Mathlib.Order.PrimeIdeal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ideal.IsPrime.toPrimePair", "kind": "definition", "module": "Mathlib.Order.PrimeIdeal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ideal.PrimePair.I_isPrime", "kind": "theorem", "module": "Mathlib.Order.PrimeIdeal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ideal.IsPrime.mem_or_mem", "kind": "theorem", "module": "Mathlib.Order.PrimeIdeal", "is_tactic_proof": true, "tactics": ["contrapose", "let", "change", "exact"], "tactic_count": 4}
{"name": "Order.Ideal.IsPrime.of_mem_or_mem", "kind": "theorem", "module": "Mathlib.Order.PrimeIdeal", "is_tactic_proof": true, "tactics": ["rw", "use", "refine", "exact", "intro", "exact", "exact"], "tactic_count": 7}
{"name": "Order.Ideal.isPrime_iff_mem_or_mem", "kind": "theorem", "module": "Mathlib.Order.PrimeIdeal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ideal.IsMaximal.isPrime", "kind": "instance", "module": "Mathlib.Order.PrimeIdeal", "is_tactic_proof": true, "tactics": ["rw", "intro", "contrapose", "rintro", "apply", "let", "have", "have", "rw", "rcases", "rw", "refine", "rw", "exact"], "tactic_count": 14}
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{"name": "Order.Ideal.IsPrime.compl_mem_of_notMem", "kind": "theorem", "module": "Mathlib.Order.PrimeIdeal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ideal.isPrime_of_mem_or_compl_mem", "kind": "theorem", "module": "Mathlib.Order.PrimeIdeal", "is_tactic_proof": true, "tactics": ["simp", "intro", "have", "have", "rwa"], "tactic_count": 5}
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{"name": "Order.Ideal.IsPrime.isMaximal", "kind": "instance", "module": "Mathlib.Order.PrimeIdeal", "is_tactic_proof": true, "tactics": ["simp", "intro", "rcases", "suffices", "exact"], "tactic_count": 5}
{"name": "Order.PFilter.IsPrime.toPrimePair", "kind": "definition", "module": "Mathlib.Order.PrimeIdeal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ideal.PrimePair.F_isPrime", "kind": "theorem", "module": "Mathlib.Order.PrimeIdeal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DistribLattice.mem_ideal_sup_principal", "kind": "theorem", "module": "Mathlib.Order.PrimeSeparator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DistribLattice.prime_ideal_of_disjoint_filter_ideal", "kind": "theorem", "module": "Mathlib.Order.PrimeSeparator", "is_tactic_proof": true, "tactics": ["set", "have", "refine", "have", "intro", "use", "refine", "simp", "let", "refine", "obtain", "obtain", "set", "use", "have", "clear", "refine", "have", "isProper_of_notMem", "rw", "intro", "contrapose", "intro", "let", "let", "have", "have", "have", "have", "have", "have", "have", "intro", "apply", "simp", "exact", "have", "intro", "apply", "simp", "exact", "let", "let", "let", "let", "let", "have", "have", "calc", "c₁", "have", "contrapose", "rw", "use", "exact"], "tactic_count": 55}
{"name": "Prod.Lex.toLexOrderHom", "kind": "definition", "module": "Mathlib.Order.Prod.Lex.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prop.instDistribLattice", "kind": "instance", "module": "Mathlib.Order.PropInstances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prop.instBoundedOrder", "kind": "instance", "module": "Mathlib.Order.PropInstances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prop.bot_eq_false", "kind": "theorem", "module": "Mathlib.Order.PropInstances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prop.top_eq_true", "kind": "theorem", "module": "Mathlib.Order.PropInstances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prop.le_total", "kind": "instance", "module": "Mathlib.Order.PropInstances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prop.linearOrder", "kind": "instance", "module": "Mathlib.Order.PropInstances", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "sup_Prop_eq", "kind": "theorem", "module": "Mathlib.Order.PropInstances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inf_Prop_eq", "kind": "theorem", "module": "Mathlib.Order.PropInstances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.disjoint_iff", "kind": "theorem", "module": "Mathlib.Order.PropInstances", "is_tactic_proof": true, "tactics": ["classical", "constructor", "intro", "exact", "intro", "apply"], "tactic_count": 6}
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{"name": "Pi.isCompl_iff", "kind": "theorem", "module": "Mathlib.Order.PropInstances", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
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{"name": "Prop.isCompl_iff", "kind": "theorem", "module": "Mathlib.Order.PropInstances", "is_tactic_proof": true, "tactics": ["rw", "by_cases"], "tactic_count": 2}
{"name": "Prop.decidablePredBot", "kind": "instance", "module": "Mathlib.Order.PropInstances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Quotient.instLE_mathlib", "kind": "instance", "module": "Mathlib.Order.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quotient.le_def", "kind": "theorem", "module": "Mathlib.Order.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quotient.instReflLe_mathlib", "kind": "instance", "module": "Mathlib.Order.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quotient.instIsTransLe", "kind": "instance", "module": "Mathlib.Order.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quotient.instTotalLe_mathlib", "kind": "instance", "module": "Mathlib.Order.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quotient.instPreorder", "kind": "instance", "module": "Mathlib.Order.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quotient.mk_monotone", "kind": "theorem", "module": "Mathlib.Order.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Order.radical", "kind": "definition", "module": "Mathlib.Order.Radical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "OrderIso.map_radical", "kind": "theorem", "module": "Mathlib.Order.Radical", "is_tactic_proof": true, "tactics": ["unfold", "simp", "fapply", "exact", "simp"], "tactic_count": 5}
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{"name": "IsStrictOrder.swap", "kind": "theorem", "module": "Mathlib.Order.RelClasses", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPartialOrder.swap", "kind": "theorem", "module": "Mathlib.Order.RelClasses", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_empty_relation", "kind": "theorem", "module": "Mathlib.Order.RelClasses", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "partialOrderOfSO", "kind": "abbrev", "module": "Mathlib.Order.RelClasses", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "linearOrderOfSTO", "kind": "abbrev", "module": "Mathlib.Order.RelClasses", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsStrictTotalOrder.swap", "kind": "theorem", "module": "Mathlib.Order.RelClasses", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOrderConnected.neg_trans", "kind": "theorem", "module": "Mathlib.Order.RelClasses", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isStrictWeakOrder_of_isOrderConnected", "kind": "theorem", "module": "Mathlib.Order.RelClasses", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isStrictOrderConnected_of_isStrictTotalOrder", "kind": "instance", "module": "Mathlib.Order.RelClasses", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InvImage.isTrichotomous", "kind": "theorem", "module": "Mathlib.Order.RelClasses", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "WellFoundedRelation.isWellFounded", "kind": "instance", "module": "Mathlib.Order.RelClasses", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "WellFounded.psigma_skipLeft", "kind": "theorem", "module": "Mathlib.Order.RelClasses", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsWellFounded.induction", "kind": "theorem", "module": "Mathlib.Order.RelClasses", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "WellFoundedLT", "kind": "abbrev", "module": "Mathlib.Order.RelClasses", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "instIsWellFoundedInvImageNatLt", "kind": "instance", "module": "Mathlib.Order.RelClasses", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Quotient.outRelEmbedding", "kind": "definition", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "acc_lift₂_iff", "kind": "theorem", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": true, "tactics": ["constructor", "exact", "intro", "induction", "intro", "refine", "obtain", "exact"], "tactic_count": 8}
{"name": "acc_liftOn₂'_iff", "kind": "theorem", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "wellFounded_lift₂_iff", "kind": "theorem", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": true, "tactics": ["constructor", "exact", "refine", "obtain", "exact"], "tactic_count": 5}
{"name": "wellFounded_liftOn₂'_iff", "kind": "theorem", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelEmbedding.ofMapRelIff", "kind": "definition", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelEmbedding.ofMapRelIff_coe", "kind": "theorem", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelEmbedding.ofMonotone", "kind": "definition", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": true, "tactics": ["haveI", "refine", "refine", "exact", "exact", "refine", "subst", "exact", "exact"], "tactic_count": 9}
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{"name": "RelEmbedding.ofIsEmpty", "kind": "definition", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelEmbedding.sumLiftRelInl", "kind": "definition", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelEmbedding.sumLiftRelInr", "kind": "definition", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelEmbedding.sumLiftRelMap", "kind": "definition", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelEmbedding.sumLexInl", "kind": "definition", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelEmbedding.sumLexInr", "kind": "definition", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelEmbedding.sumLexMap", "kind": "definition", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelEmbedding.prodLexMkLeft", "kind": "definition", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelEmbedding.prodLexMkRight", "kind": "definition", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelEmbedding.prodLexMap", "kind": "definition", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "term_≃r_", "kind": "definition", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Order_RelIso_Basic___macroRules_term_≃r__1", "kind": "definition", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Order_RelIso_Basic___unexpand_RelIso_1", "kind": "definition", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelIso.toRelEmbedding", "kind": "definition", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelIso.toEquiv_injective", "kind": "theorem", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelIso.instCoeOutRelEmbedding", "kind": "instance", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelIso.instFunLike", "kind": "instance", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelIso.instRelHomClass", "kind": "instance", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelIso.instEquivLike", "kind": "instance", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelIso.coe_toRelEmbedding", "kind": "theorem", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelIso.coe_toEmbedding", "kind": "theorem", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelIso.map_rel_iff", "kind": "theorem", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelIso.coe_fn_mk", "kind": "theorem", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelIso.coe_fn_toEquiv", "kind": "theorem", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelIso.coe_fn_injective", "kind": "theorem", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelIso.ext", "kind": "theorem", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelIso.symm", "kind": "definition", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelIso.Simps.apply", "kind": "definition", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelIso.Simps.symm_apply", "kind": "definition", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelIso.refl", "kind": "definition", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelIso.trans", "kind": "definition", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelIso.instInhabited", "kind": "instance", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelIso.default_def", "kind": "theorem", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelIso.apply_symm_apply", "kind": "theorem", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelIso.symm_apply_apply", "kind": "theorem", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelIso.symm_comp_self", "kind": "theorem", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelIso.self_comp_symm", "kind": "theorem", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelIso.symm_trans_apply", "kind": "theorem", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "RelIso.apply_eq_iff_eq_symm_apply", "kind": "theorem", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": true, "tactics": ["conv_lhs", "rw"], "tactic_count": 2}
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{"name": "RelIso.eq_symm_apply", "kind": "theorem", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "RelIso.symm_bijective", "kind": "theorem", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelIso.refl_symm", "kind": "theorem", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelIso.trans_refl", "kind": "theorem", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "RelIso.symm_trans_self", "kind": "theorem", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "RelIso.trans_assoc", "kind": "theorem", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelIso.cast", "kind": "definition", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelIso.cast_symm", "kind": "theorem", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "RelIso.swap", "kind": "definition", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "RelIso.coe_fn_symm_mk", "kind": "theorem", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "RelIso.symm_apply_rel", "kind": "theorem", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "RelIso.IsWellOrder.ulift", "kind": "instance", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelIso.ofSurjective", "kind": "definition", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelIso.relHomCongr", "kind": "definition", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelIso.sumLexCongr", "kind": "definition", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelIso.prodLexCongr", "kind": "definition", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelIso.relIsoOfIsEmpty", "kind": "definition", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelIso.sumLexEmpty", "kind": "definition", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelIso.emptySumLex", "kind": "definition", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelIso.ofUniqueOfIrrefl", "kind": "definition", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelIso.ofUniqueOfRefl", "kind": "definition", "module": "Mathlib.Order.RelIso.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelHomClass.map_inf", "kind": "theorem", "module": "Mathlib.Order.RelIso.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelHomClass.map_sup", "kind": "theorem", "module": "Mathlib.Order.RelIso.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "RelHomClass.directedOn", "kind": "theorem", "module": "Mathlib.Order.RelIso.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "subrel_val", "kind": "theorem", "module": "Mathlib.Order.RelIso.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subrel.relEmbedding", "kind": "definition", "module": "Mathlib.Order.RelIso.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subrel.relEmbedding_apply", "kind": "theorem", "module": "Mathlib.Order.RelIso.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subrel.inclusionEmbedding", "kind": "definition", "module": "Mathlib.Order.RelIso.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subrel.coe_inclusionEmbedding", "kind": "theorem", "module": "Mathlib.Order.RelIso.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subrel.instReflSubtype", "kind": "instance", "module": "Mathlib.Order.RelIso.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subrel.instSymmSubtype", "kind": "instance", "module": "Mathlib.Order.RelIso.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subrel.instAsymmSubtype", "kind": "instance", "module": "Mathlib.Order.RelIso.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subrel.instIsTransSubtype", "kind": "instance", "module": "Mathlib.Order.RelIso.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subrel.instIrreflSubtype", "kind": "instance", "module": "Mathlib.Order.RelIso.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subrel.instIsTrichotomousSubtype", "kind": "instance", "module": "Mathlib.Order.RelIso.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subrel.instIsWellFoundedSubtype", "kind": "instance", "module": "Mathlib.Order.RelIso.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subrel.instIsPreorderSubtype", "kind": "instance", "module": "Mathlib.Order.RelIso.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subrel.instIsStrictOrderSubtype", "kind": "instance", "module": "Mathlib.Order.RelIso.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subrel.instIsWellOrderSubtype", "kind": "instance", "module": "Mathlib.Order.RelIso.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelIso.subrelUnivIso", "kind": "definition", "module": "Mathlib.Order.RelIso.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelEmbedding.codRestrict", "kind": "definition", "module": "Mathlib.Order.RelIso.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelEmbedding.codRestrict_apply", "kind": "theorem", "module": "Mathlib.Order.RelIso.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelIso.image_eq_preimage_symm", "kind": "theorem", "module": "Mathlib.Order.RelIso.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelIso.preimage_eq_image_symm", "kind": "theorem", "module": "Mathlib.Order.RelIso.Set", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Acc.of_subrel", "kind": "theorem", "module": "Mathlib.Order.RelIso.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "wellFounded_iff_wellFounded_subrel", "kind": "theorem", "module": "Mathlib.Order.RelIso.Set", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelSeries.instCoeFunForallFinHAddNatLengthOfNat", "kind": "instance", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelSeries.singleton", "kind": "definition", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelSeries.instIsEmpty", "kind": "instance", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelSeries.instInhabited", "kind": "instance", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelSeries.instNonempty", "kind": "instance", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "RelSeries.rel_of_lt", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelSeries.rel_or_eq_of_le", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelSeries.ofLE", "kind": "definition", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelSeries.coe_ofLE", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelSeries.toList", "kind": "definition", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelSeries.length_toList", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "RelSeries.isChain_toList", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": true, "tactics": ["simp_rw", "intro", "convert"], "tactic_count": 3}
{"name": "RelSeries.toList_ne_nil", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelSeries.fromListIsChain", "kind": "definition", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelSeries.Equiv", "kind": "definition", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelSeries.toList_injective", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelSeries.longestOf", "kind": "definition", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelSeries.length_le_length_longestOf", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelSeries.withLength", "kind": "definition", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelSeries.length_withLength", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelSeries.nonempty_of_infiniteDimensional", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelSeries.nonempty_of_finiteDimensional", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "RelSeries.membership", "kind": "instance", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelSeries.mem_def", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelSeries.mem_toList", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RelSeries.subsingleton_of_length_eq_zero", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": true, "tactics": ["rintro", "congr", "exact"], "tactic_count": 3}
{"name": "RelSeries.length_ne_zero_of_nontrivial", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelSeries.length_pos_of_nontrivial", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelSeries.length_ne_zero", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": ["refine", "length_ne_zero_of_nontrivial⟩", "nth_rw", "convert", "ext", "simpa"], "tactic_count": 6}
{"name": "RelSeries.length_pos", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelSeries.length_eq_zero", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RelSeries.head", "kind": "definition", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelSeries.last", "kind": "definition", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelSeries.apply_zero", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelSeries.apply_last", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelSeries.head_mem", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelSeries.last_mem", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelSeries.head_singleton", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RelSeries.last_singleton", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RelSeries.head_toList", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RelSeries.toList_getElem", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RelSeries.toList_getElem_eq_apply", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelSeries.toList_getElem_eq_apply_of_lt_length", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelSeries.toList_getElem_zero_eq_head", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelSeries.toList_fromListIsChain", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelSeries.head_fromListIsChain", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RelSeries.getLast_toList", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "RelSeries.append", "kind": "definition", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelSeries.append_apply_left", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": true, "tactics": ["delta", "simp", "convert"], "tactic_count": 3}
{"name": "RelSeries.append_apply_right", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelSeries.head_append", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelSeries.last_append", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": true, "tactics": ["delta", "convert", "ext1", "dsimp", "lia"], "tactic_count": 5}
{"name": "RelSeries.append_assoc", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": true, "tactics": ["ext", "simp", "lia", "simp"], "tactic_count": 4}
{"name": "RelSeries.toList_append", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": true, "tactics": ["apply", "simp", "simp"], "tactic_count": 3}
{"name": "RelSeries.map", "kind": "definition", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelSeries.map_apply", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelSeries.head_map", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelSeries.last_map", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelSeries.insertNth", "kind": "definition", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelSeries.reverse", "kind": "definition", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelSeries.reverse_apply", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelSeries.last_reverse", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RelSeries.head_reverse", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RelSeries.reverse_reverse", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "RelSeries.cons", "kind": "definition", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelSeries.head_cons", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelSeries.last_cons", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": true, "tactics": ["delta", "rw"], "tactic_count": 2}
{"name": "RelSeries.cons_cast_succ", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RelSeries.append_singleton_left", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelSeries.toList_cons", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "RelSeries.fromListIsChain_cons", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "RelSeries.append_cons", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": true, "tactics": ["simp", "rw"], "tactic_count": 2}
{"name": "RelSeries.snoc", "kind": "definition", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelSeries.head_snoc", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": true, "tactics": ["delta"], "tactic_count": 1}
{"name": "RelSeries.last_snoc", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelSeries.snoc_cast_castSucc", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelSeries.last_snoc'", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelSeries.snoc_castSucc", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelSeries.mem_snoc", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": ["simp", "constructor", "rintro", "exact", "intro", "rcases", "exact", "exact"], "tactic_count": 8}
{"name": "RelSeries.tail", "kind": "definition", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelSeries.head_tail", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": true, "tactics": ["change", "congr", "ext", "change", "rw", "simpa"], "tactic_count": 6}
{"name": "RelSeries.last_tail", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": true, "tactics": ["change", "congr", "ext", "simp", "exact"], "tactic_count": 5}
{"name": "RelSeries.toList_tail", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": true, "tactics": ["refine", "simp", "lia", "simp"], "tactic_count": 4}
{"name": "RelSeries.tail_cons", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "RelSeries.cons_self_tail", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "RelSeries.inductionOn", "kind": "definition", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": ["let", "induction", "zero", "convert", "ext", "exact", "simp", "succ", "have", "nth_rw", "convert", "exact", "exact"], "tactic_count": 13}
{"name": "RelSeries.toList_snoc", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RelSeries.eraseLast", "kind": "definition", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelSeries.head_eraseLast", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelSeries.last_eraseLast", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelSeries.eraseLast_last_rel_last", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": true, "tactics": ["simp", "convert", "simp"], "tactic_count": 3}
{"name": "RelSeries.toList_eraseLast", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": true, "tactics": ["apply", "simpa", "intro", "simp"], "tactic_count": 4}
{"name": "RelSeries.snoc_self_eraseLast", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": true, "tactics": ["apply", "rw"], "tactic_count": 2}
{"name": "RelSeries.inductionOn'", "kind": "definition", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": ["let", "induction", "zero", "convert", "ext", "exact", "simp", "succ", "have", "have", "convert", "exact", "exact"], "tactic_count": 13}
{"name": "RelSeries.smash", "kind": "definition", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelSeries.smash_castLE", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": true, "tactics": ["refine", "change", "simpa"], "tactic_count": 3}
{"name": "RelSeries.smash_castAdd", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelSeries.smash_succ_castAdd", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelSeries.smash_natAdd", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": true, "tactics": ["dsimp", "apply"], "tactic_count": 2}
{"name": "RelSeries.smash_succ_natAdd", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": true, "tactics": ["dsimp", "apply"], "tactic_count": 2}
{"name": "RelSeries.head_smash", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": true, "tactics": ["obtain", "simpa", "dsimp", "exact"], "tactic_count": 4}
{"name": "RelSeries.last_smash", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "RelSeries.take", "kind": "definition", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelSeries.head_take", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RelSeries.last_take", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RelSeries.drop", "kind": "definition", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelSeries.head_drop", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RelSeries.last_drop", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": true, "tactics": ["simp", "congr", "lia"], "tactic_count": 3}
{"name": "SetRel.not_finiteDimensional_iff", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": true, "tactics": ["rw", "push_neg", "constructor", "intro", "induction", "zero", "succ", "obtain", "obtain", "exact", "intro", "obtain", "exact"], "tactic_count": 13}
{"name": "SetRel.not_infiniteDimensional_iff", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SetRel.finiteDimensional_or_infiniteDimensional", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SetRel.FiniteDimensional.inv", "kind": "instance", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.finiteDimensional_inv", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.InfiniteDimensional.inv", "kind": "instance", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.infiniteDimensional_inv", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.IsWellFounded.inv_of_finiteDimensional", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": true, "tactics": ["rw", "refine", "let", "exact"], "tactic_count": 4}
{"name": "SetRel.IsWellFounded.of_finiteDimensional", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteDimensionalOrder", "kind": "abbrev", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteDimensionalOrder.ofUnique", "kind": "instance", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InfiniteDimensionalOrder", "kind": "abbrev", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LTSeries", "kind": "abbrev", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LTSeries.longestOf", "kind": "definition", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LTSeries.withLength", "kind": "definition", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LTSeries.length_withLength", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LTSeries.nonempty_of_infiniteDimensionalOrder", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LTSeries.nonempty_of_finiteDimensionalOrder", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "LTSeries.longestOf_is_longest", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LTSeries.longestOf_len_unique", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LTSeries.strictMono", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LTSeries.monotone", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LTSeries.head_le", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LTSeries.head_le_last", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LTSeries.mk", "kind": "definition", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LTSeries.injStrictMono", "kind": "definition", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LTSeries.map", "kind": "definition", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LTSeries.head_map", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LTSeries.last_map", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LTSeries.comap", "kind": "definition", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LTSeries.range", "kind": "definition", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LTSeries.length_range", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LTSeries.range_apply", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LTSeries.head_range", "kind": "theorem", "module": "Mathlib.Order.RelSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "equivShrink_bot", "kind": "theorem", "module": "Mathlib.Order.Shrink", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "equivShrink_symm_bot", "kind": "theorem", "module": "Mathlib.Order.Shrink", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instOrderBotShrink", "kind": "instance", "module": "Mathlib.Order.Shrink", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instSuccOrderShrink", "kind": "instance", "module": "Mathlib.Order.Shrink", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instWellFoundedLTShrink", "kind": "instance", "module": "Mathlib.Order.Shrink", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instWellFoundedGTShrink", "kind": "instance", "module": "Mathlib.Order.Shrink", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.instSetLike", "kind": "instance", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.instPartialOrder", "kind": "instance", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.Simps.coe", "kind": "definition", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.ofIsSublattice", "kind": "abbrev", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.coe_inj", "kind": "theorem", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.supClosed", "kind": "theorem", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.infClosed", "kind": "theorem", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.sup_mem", "kind": "theorem", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.inf_mem", "kind": "theorem", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.isSublattice", "kind": "theorem", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.mem_carrier", "kind": "theorem", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.mem_mk", "kind": "theorem", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.coe_mk", "kind": "theorem", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.mk_le_mk", "kind": "theorem", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.mk_lt_mk", "kind": "theorem", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.copy", "kind": "definition", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.coe_copy", "kind": "theorem", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.copy_eq", "kind": "theorem", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.ext", "kind": "theorem", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.instSupCoe", "kind": "instance", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.instInfCoe", "kind": "instance", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.coe_sup", "kind": "theorem", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.coe_inf", "kind": "theorem", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.mk_sup_mk", "kind": "theorem", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.mk_inf_mk", "kind": "theorem", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.instLatticeCoe", "kind": "instance", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.instDistribLatticeCoe", "kind": "instance", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.subtype", "kind": "definition", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.coe_subtype", "kind": "theorem", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.subtype_apply", "kind": "theorem", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.subtype_injective", "kind": "theorem", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.inclusion", "kind": "definition", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.coe_inclusion", "kind": "theorem", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.inclusion_apply", "kind": "theorem", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.inclusion_injective", "kind": "theorem", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.inclusion_rfl", "kind": "theorem", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.subtype_comp_inclusion", "kind": "theorem", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.instTop", "kind": "instance", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.instBot", "kind": "instance", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.instInf", "kind": "instance", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.instInfSet", "kind": "instance", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.instInhabited", "kind": "instance", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.topEquiv", "kind": "definition", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.coe_top", "kind": "theorem", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.coe_bot", "kind": "theorem", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.coe_inf'", "kind": "theorem", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.coe_sInf", "kind": "theorem", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.coe_iInf", "kind": "theorem", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Sublattice.coe_eq_univ", "kind": "theorem", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Sublattice.coe_eq_empty", "kind": "theorem", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Sublattice.notMem_bot", "kind": "theorem", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.mem_top", "kind": "theorem", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.mem_inf", "kind": "theorem", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.mem_sInf", "kind": "theorem", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Sublattice.mem_iInf", "kind": "theorem", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Sublattice.instCompleteLattice", "kind": "instance", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.subsingleton_iff", "kind": "theorem", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.instUniqueOfIsEmpty", "kind": "instance", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.comap", "kind": "definition", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.coe_comap", "kind": "theorem", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Sublattice.comap_mono", "kind": "theorem", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Sublattice.map", "kind": "definition", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.coe_map", "kind": "theorem", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Sublattice.apply_coe_mem_map", "kind": "theorem", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.map_mono", "kind": "theorem", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.map_id", "kind": "theorem", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Sublattice.apply_mem_map_iff", "kind": "theorem", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.map_equiv_eq_comap_symm", "kind": "theorem", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Sublattice.gc_map_comap", "kind": "theorem", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.map_bot", "kind": "theorem", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.map_sup", "kind": "theorem", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.map_iSup", "kind": "theorem", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.comap_top", "kind": "theorem", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Sublattice.map_inf_le", "kind": "theorem", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.le_comap_sup", "kind": "theorem", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Sublattice.prod_mono", "kind": "theorem", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.prod_mono_left", "kind": "theorem", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.prod_mono_right", "kind": "theorem", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Sublattice.pi", "kind": "definition", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Sublattice.pi_empty", "kind": "theorem", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublattice.pi_top", "kind": "theorem", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Sublattice.pi_univ_eq_bot_iff", "kind": "theorem", "module": "Mathlib.Order.Sublattice", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
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{"name": "Sublocale.instPartialOrder", "kind": "instance", "module": "Mathlib.Order.Sublocale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Sublocale.iInf_mem", "kind": "theorem", "module": "Mathlib.Order.Sublocale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublocale.infClosed", "kind": "theorem", "module": "Mathlib.Order.Sublocale", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
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{"name": "Sublocale.carrier.instOrderTop", "kind": "instance", "module": "Mathlib.Order.Sublocale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Sublocale.coe_inf", "kind": "theorem", "module": "Mathlib.Order.Sublocale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublocale.coe_sInf", "kind": "theorem", "module": "Mathlib.Order.Sublocale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Sublocale.carrier.instCompleteLattice", "kind": "instance", "module": "Mathlib.Order.Sublocale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Sublocale.carrier.instHeytingAlgebra", "kind": "instance", "module": "Mathlib.Order.Sublocale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublocale.carrier.instFrame", "kind": "instance", "module": "Mathlib.Order.Sublocale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Sublocale.toNucleus", "kind": "definition", "module": "Mathlib.Order.Sublocale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublocale.range_toNucleus", "kind": "theorem", "module": "Mathlib.Order.Sublocale", "is_tactic_proof": true, "tactics": ["ext", "constructor", "simp", "intro", "exact"], "tactic_count": 5}
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{"name": "Sublocale.instCoframeMinimalAxioms", "kind": "instance", "module": "Mathlib.Order.Sublocale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sublocale.instCoframe", "kind": "instance", "module": "Mathlib.Order.Sublocale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsPredArchimedeanOrderDual", "kind": "instance", "module": "Mathlib.Order.SuccPred.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "exists_pred_iterate_iff_le", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "lt_or_le_of_codirected", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Archimedean", "is_tactic_proof": true, "tactics": ["rw", "intro", "rcases", "apply", "contradiction"], "tactic_count": 5}
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{"name": "exists_succ_iterate_or", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Succ.rec_linear", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Pred.rec_linear", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "instPredOrderOrderDualOfSuccOrder", "kind": "instance", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instSuccOrderOrderDualOfPredOrder", "kind": "instance", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SuccOrder.ofCore", "kind": "definition", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SuccOrder.ofLinearWellFoundedLT", "kind": "definition", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PredOrder.ofLinearWellFoundedGT", "kind": "definition", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.succ", "kind": "definition", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Order.succ_le_iff_isMax", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Order.wcovBy_succ", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Order.le_succ_of_wcovBy", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": true, "tactics": ["obtain", "by_contra", "exact", "exact"], "tactic_count": 4}
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{"name": "Order.isMax_iterate_succ_of_eq_of_lt", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "have", "exact"], "tactic_count": 4}
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{"name": "Order.Icc_subset_Ico_succ_right_of_not_isMax", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": true, "tactics": ["rw", "gcongr", "intro", "apply"], "tactic_count": 4}
{"name": "Order.Ioc_subset_Ioo_succ_right_of_not_isMax", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": true, "tactics": ["rw", "gcongr", "intro", "apply"], "tactic_count": 4}
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{"name": "Order.lt_succ", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.lt_succ_of_le", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.succ_le_iff", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.succ_lt_succ", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Order.succ_strictMono", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.covBy_succ", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Iic_subset_Iio_succ", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Order.Ici_succ", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Icc_subset_Ico_succ_right", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ioc_subset_Ioo_succ_right", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Icc_succ_left", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ico_succ_left", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.succ_eq_iff_isMax", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.le_iff_eq_or_succ_le", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simpa", "rw"], "tactic_count": 3}
{"name": "Order.le_iff_eq_or_succ_le'", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Order.le_and_le_succ_iff", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": ["refine", "rintro", "exact", "exact"], "tactic_count": 4}
{"name": "Order.le_succ_and_le_iff", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Order.succ_eq_of_covBy", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.map_succ", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "exact"], "tactic_count": 3}
{"name": "Order.succ_eq_iff_covBy", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.succ_top", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Order.succ_le_iff_eq_top", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.lt_succ_iff_ne_top", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.bot_lt_succ", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.succ_ne_bot", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.le_of_lt_succ", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.lt_succ_iff_of_not_isMax", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.succ_lt_succ_iff_of_not_isMax", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Order.succ_le_succ_iff_of_not_isMax", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Order.Iio_succ_of_not_isMax", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ico_succ_right_of_not_isMax", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Order.Ioo_succ_right_of_not_isMax", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Order.succ_eq_succ_iff_of_not_isMax", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Order.le_succ_iff_eq_or_le", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "rw"], "tactic_count": 3}
{"name": "Order.lt_succ_iff_eq_or_lt_of_not_isMax", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.not_isMin_succ", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": true, "tactics": ["obtain", "exact", "exact"], "tactic_count": 3}
{"name": "Order.Iic_succ", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Icc_succ_right", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Order.Ioc_succ_right", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Order.Iio_succ_eq_insert_of_not_isMax", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ico_succ_right_eq_insert_of_not_isMax", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Order.Ioo_succ_right_eq_insert_of_not_isMax", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Order.lt_succ_iff", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.succ_le_succ_iff", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Order.succ_lt_succ_iff", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Order.Iio_succ", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ico_succ_right", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ioo_succ_right", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.succ_eq_succ_iff", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.succ_injective", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.succ_ne_succ_iff", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.lt_succ_iff_eq_or_lt", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.lt_succ_iff_eq_or_gt", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Order.Iio_succ_eq_insert", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ico_succ_right_eq_insert", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ioo_succ_right_eq_insert", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ioo_eq_empty_iff_le_succ", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": true, "tactics": ["refine", "contrapose", "exact", "ext", "suffices", "exact"], "tactic_count": 6}
{"name": "Order.lt_succ_bot_iff", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Order.le_succ_bot_iff", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Order.instSubsingletonSuccOrder", "kind": "instance", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.succ_eq_sInf", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": true, "tactics": ["apply", "obtain", "rw", "exact", "exact"], "tactic_count": 5}
{"name": "Order.succ_eq_iInf", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Order.succ_eq_csInf", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": true, "tactics": ["apply", "exact"], "tactic_count": 2}
{"name": "Order.pred_wcovBy", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.pred_covBy_of_not_isMin", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.pred_lt_of_not_isMin_of_le", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.pred_mono", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.pred_le_of_wcovBy", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": true, "tactics": ["obtain", "by_contra", "exact", "exact"], "tactic_count": 4}
{"name": "Order.isMin_iterate_pred_of_eq_of_lt", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.isMin_iterate_pred_of_eq_of_ne", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ici_subset_Ioi_pred_of_not_isMin", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Iic_pred_of_not_isMin", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Icc_subset_Ioc_pred_left_of_not_isMin", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": true, "tactics": ["rw", "gcongr", "apply"], "tactic_count": 3}
{"name": "Order.Ico_subset_Ioo_pred_left_of_not_isMin", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": true, "tactics": ["rw", "gcongr", "apply"], "tactic_count": 3}
{"name": "Order.Icc_pred_right_of_not_isMin", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Order.Ioc_pred_right_of_not_isMin", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Order.pred_strictMono", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.pred_covBy", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ici_subset_Ioi_pred", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Order.Iic_pred", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Icc_subset_Ioc_pred_left", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ico_subset_Ioo_pred_left", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Icc_pred_right", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ioc_pred_right", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.pred_eq_of_covBy", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.map_pred", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.pred_eq_iff_covBy", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ioi_pred_of_not_isMin", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ioc_pred_left_of_not_isMin", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Order.Ioo_pred_left_of_not_isMin", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Order.not_isMax_pred", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ici_pred", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ioi_pred_eq_insert_of_not_isMin", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Order.Icc_pred_left", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Order.Ico_pred_left", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Order.Ioi_pred", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ioc_pred_left", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ioo_pred_left", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ioi_pred_eq_insert", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.Ico_pred_right_eq_insert", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Order.Ioo_pred_right_eq_insert", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Order.Ioo_eq_empty_iff_pred_le", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": true, "tactics": ["refine", "contrapose", "exact", "ext", "suffices", "exact"], "tactic_count": 6}
{"name": "Order.instSubsingletonPredOrder", "kind": "instance", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.pred_eq_sSup", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.pred_eq_iSup", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.pred_eq_csSup", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.le_succ_pred", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.pred_le_iff_le_succ", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.gc_pred_succ", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.succ_pred_of_not_isMin", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.pred_succ_of_not_isMax", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.succ_pred", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.pred_succ", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.pred_succ_iterate_of_not_isMax", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "have", "rcases", "simpa", "rw", "have", "rw", "exact", "refine", "have", "exact", "rw", "simp", "rw", "exact"], "tactic_count": 18}
{"name": "Order.succ_pred_iterate_of_not_isMin", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.instSuccOrder", "kind": "instance", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.succ_coe_of_isMax", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.succ_coe_of_not_isMax", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.succ_coe", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.instPredOrder", "kind": "instance", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.orderPred_top", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.orderPred_coe", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.pred_untop", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.instIsEmptyPredOrderOfNonempty", "kind": "instance", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.instSuccOrder", "kind": "instance", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.orderSucc_bot", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.orderSucc_coe", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.succ_unbot", "kind": "theorem", "module": "Mathlib.Order.SuccPred.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "bihimp_self", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "bihimp_top", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "top_bihimp", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "bihimp_eq_top", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bihimp_of_le", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "bihimp_of_ge", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "le_bihimp", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_bihimp_iff", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "inf_le_bihimp", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bihimp_eq_sup_himp_inf", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Codisjoint.bihimp_eq_inf", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "himp_bihimp", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "sup_himp_bihimp", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "bihimp_himp_eq_inf", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "himp_bihimp_eq_inf", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bihimp_inf_sup", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sup_inf_bihimp", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bihimp_bihimp_sup", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sup_bihimp_bihimp", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bihimp_triangle", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "symmDiff_top'", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "top_symmDiff'", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "hnot_symmDiff_self", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "symmDiff_hnot_self", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsCompl.symmDiff_eq_top", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "bihimp_bot", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "bot_bihimp", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "compl_bihimp_self", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bihimp_hnot_self", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompl.bihimp_eq_bot", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "sup_sdiff_symmDiff", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "disjoint_symmDiff_inf", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "inf_symmDiff_distrib_left", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "inf_symmDiff_distrib_right", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "sdiff_symmDiff", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "sdiff_symmDiff'", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "symmDiff_sdiff_left", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "symmDiff_sdiff_right", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "sdiff_symmDiff_left", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "sdiff_symmDiff_right", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "symmDiff_eq_sup", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "le_symmDiff_iff_left", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "le_symmDiff_iff_right", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "symmDiff_symmDiff_left", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "symmDiff_symmDiff_right", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "symmDiff_assoc", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "symmDiff_isAssociative", "kind": "instance", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "symmDiff_left_comm", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "symmDiff_right_comm", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "symmDiff_symmDiff_symmDiff_comm", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "symmDiff_symmDiff_cancel_left", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "symmDiff_symmDiff_cancel_right", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "symmDiff_symmDiff_self'", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "symmDiff_left_involutive", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "symmDiff_right_involutive", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "symmDiff_left_injective", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "symmDiff_right_injective", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "symmDiff_left_surjective", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "symmDiff_right_surjective", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "symmDiff_left_inj", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "symmDiff_right_inj", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "symmDiff_eq_left", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "symmDiff_eq_right", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Disjoint.symmDiff_left", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Disjoint.symmDiff_right", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "symmDiff_eq_iff_sdiff_eq", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "inf_himp_bihimp", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "codisjoint_bihimp_sup", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "himp_bihimp_left", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "himp_bihimp_right", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bihimp_himp_left", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bihimp_himp_right", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bihimp_eq_inf", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bihimp_le_iff_left", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bihimp_le_iff_right", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bihimp_assoc", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bihimp_isAssociative", "kind": "instance", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bihimp_left_comm", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "bihimp_right_comm", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "bihimp_bihimp_bihimp_comm", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "bihimp_bihimp_cancel_left", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "bihimp_bihimp_cancel_right", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "bihimp_bihimp_self", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "bihimp_left_involutive", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bihimp_right_involutive", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bihimp_left_injective", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bihimp_right_injective", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bihimp_left_surjective", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bihimp_right_surjective", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bihimp_left_inj", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bihimp_right_inj", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bihimp_eq_left", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bihimp_eq_right", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Codisjoint.bihimp_left", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Codisjoint.bihimp_right", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "symmDiff_eq", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "bihimp_eq", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "symmDiff_eq'", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "bihimp_eq'", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "symmDiff_top", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "top_symmDiff", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "compl_symmDiff", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "compl_bihimp", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "compl_symmDiff_compl", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "compl_bihimp_compl", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "symmDiff_eq_top", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "bihimp_eq_bot", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "compl_symmDiff_self", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "symmDiff_compl_self", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "symmDiff_symmDiff_right'", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Disjoint.le_symmDiff_sup_symmDiff_left", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": true, "tactics": ["trans", "rw", "rw", "exact"], "tactic_count": 4}
{"name": "Disjoint.le_symmDiff_sup_symmDiff_right", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Codisjoint.bihimp_inf_bihimp_le_left", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Codisjoint.bihimp_inf_bihimp_le_right", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "symmDiff_fst", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "symmDiff_snd", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bihimp_fst", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bihimp_snd", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.symmDiff_def", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.bihimp_def", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.symmDiff_apply", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.bihimp_apply", "kind": "theorem", "module": "Mathlib.Order.SymmDiff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instNontrivial", "kind": "instance", "module": "Mathlib.Order.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instUnique", "kind": "instance", "module": "Mathlib.Order.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.toDual", "kind": "definition", "module": "Mathlib.Order.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.ofDual", "kind": "definition", "module": "Mathlib.Order.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.toDual_symm_eq", "kind": "theorem", "module": "Mathlib.Order.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.ofDual_symm_eq", "kind": "theorem", "module": "Mathlib.Order.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.toDual_ofDual", "kind": "theorem", "module": "Mathlib.Order.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.ofDual_toDual", "kind": "theorem", "module": "Mathlib.Order.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.toDual_trans_ofDual", "kind": "theorem", "module": "Mathlib.Order.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.ofDual_trans_toDual", "kind": "theorem", "module": "Mathlib.Order.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.toDual_comp_ofDual", "kind": "theorem", "module": "Mathlib.Order.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.ofDual_comp_toDual", "kind": "theorem", "module": "Mathlib.Order.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.toDual_inj", "kind": "theorem", "module": "Mathlib.Order.Synonym", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "OrderDual.ofDual_inj", "kind": "theorem", "module": "Mathlib.Order.Synonym", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "OrderDual.ext", "kind": "theorem", "module": "Mathlib.Order.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.toDual_le_toDual", "kind": "theorem", "module": "Mathlib.Order.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.toDual_lt_toDual", "kind": "theorem", "module": "Mathlib.Order.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.ofDual_le_ofDual", "kind": "theorem", "module": "Mathlib.Order.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.ofDual_lt_ofDual", "kind": "theorem", "module": "Mathlib.Order.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.le_toDual", "kind": "theorem", "module": "Mathlib.Order.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.lt_toDual", "kind": "theorem", "module": "Mathlib.Order.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.rec", "kind": "definition", "module": "Mathlib.Order.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.forall", "kind": "theorem", "module": "Mathlib.Order.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.exists", "kind": "theorem", "module": "Mathlib.Order.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lex", "kind": "definition", "module": "Mathlib.Order.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toLex", "kind": "definition", "module": "Mathlib.Order.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofLex", "kind": "definition", "module": "Mathlib.Order.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toLex_symm_eq", "kind": "theorem", "module": "Mathlib.Order.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofLex_symm_eq", "kind": "theorem", "module": "Mathlib.Order.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toLex_ofLex", "kind": "theorem", "module": "Mathlib.Order.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofLex_toLex", "kind": "theorem", "module": "Mathlib.Order.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toLex_inj", "kind": "theorem", "module": "Mathlib.Order.Synonym", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ofLex_inj", "kind": "theorem", "module": "Mathlib.Order.Synonym", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "instBEqLex", "kind": "instance", "module": "Mathlib.Order.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instLawfulBEqLex", "kind": "instance", "module": "Mathlib.Order.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDecidableEqLex", "kind": "instance", "module": "Mathlib.Order.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInhabitedLex", "kind": "instance", "module": "Mathlib.Order.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instNonemptyLex", "kind": "instance", "module": "Mathlib.Order.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instNontrivialLex", "kind": "instance", "module": "Mathlib.Order.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instUniqueLex", "kind": "instance", "module": "Mathlib.Order.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCoeFunLex", "kind": "instance", "module": "Mathlib.Order.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lex.rec", "kind": "definition", "module": "Mathlib.Order.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lex.forall", "kind": "theorem", "module": "Mathlib.Order.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Colex", "kind": "definition", "module": "Mathlib.Order.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toColex", "kind": "definition", "module": "Mathlib.Order.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofColex", "kind": "definition", "module": "Mathlib.Order.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toColex_symm_eq", "kind": "theorem", "module": "Mathlib.Order.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofColex_symm_eq", "kind": "theorem", "module": "Mathlib.Order.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toColex_ofColex", "kind": "theorem", "module": "Mathlib.Order.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofColex_toColex", "kind": "theorem", "module": "Mathlib.Order.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toColex_inj", "kind": "theorem", "module": "Mathlib.Order.Synonym", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ofColex_inj", "kind": "theorem", "module": "Mathlib.Order.Synonym", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "instBEqColex", "kind": "instance", "module": "Mathlib.Order.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instLawfulBEqColex", "kind": "instance", "module": "Mathlib.Order.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDecidableEqColex", "kind": "instance", "module": "Mathlib.Order.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInhabitedColex", "kind": "instance", "module": "Mathlib.Order.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instNonemptyColex", "kind": "instance", "module": "Mathlib.Order.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "instUniqueColex", "kind": "instance", "module": "Mathlib.Order.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCoeFunColex", "kind": "instance", "module": "Mathlib.Order.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Colex.rec", "kind": "definition", "module": "Mathlib.Order.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Colex.forall", "kind": "theorem", "module": "Mathlib.Order.Synonym", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Order.IsOfFiniteCharacter", "kind": "definition", "module": "Mathlib.Order.TeichmullerTukey", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.IsOfFiniteCharacter.exists_maximal", "kind": "theorem", "module": "Mathlib.Order.TeichmullerTukey", "is_tactic_proof": true, "tactics": ["refine", "refine", "subset", "obtain", "exact"], "tactic_count": 5}
{"name": "transfiniteIterate", "kind": "definition", "module": "Mathlib.Order.TransfiniteIteration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "transfiniteIterate_bot", "kind": "theorem", "module": "Mathlib.Order.TransfiniteIteration", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "transfiniteIterate_succ", "kind": "theorem", "module": "Mathlib.Order.TransfiniteIteration", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "rfl"], "tactic_count": 3}
{"name": "transfiniteIterate_limit", "kind": "theorem", "module": "Mathlib.Order.TransfiniteIteration", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "simp"], "tactic_count": 3}
{"name": "monotone_transfiniteIterate", "kind": "theorem", "module": "Mathlib.Order.TransfiniteIteration", "is_tactic_proof": true, "tactics": ["intro", "induction", "isMin", "obtain", "obtain", "rfl", "succ", "obtain", "refine", "dsimp", "rw", "apply", "rfl", "isSuccLimit", "obtain", "dsimp", "rw", "exact", "rfl"], "tactic_count": 19}
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{"name": "WithBot", "kind": "definition", "module": "Mathlib.Order.TypeTags", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "WithTop.instRepr", "kind": "instance", "module": "Mathlib.Order.TypeTags", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.some", "kind": "definition", "module": "Mathlib.Order.TypeTags", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "WithBot.bot", "kind": "instance", "module": "Mathlib.Order.TypeTags", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "WithBot.recBotCoe", "kind": "definition", "module": "Mathlib.Order.TypeTags", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.recBotCoe_bot", "kind": "theorem", "module": "Mathlib.Order.TypeTags", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.recBotCoe_coe", "kind": "theorem", "module": "Mathlib.Order.TypeTags", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderType.instSetoid", "kind": "definition", "module": "Mathlib.Order.Types.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderType", "kind": "definition", "module": "Mathlib.Order.Types.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderType.ToType", "kind": "definition", "module": "Mathlib.Order.Types.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderType.instLinearOrderToType", "kind": "instance", "module": "Mathlib.Order.Types.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderType.type", "kind": "definition", "module": "Mathlib.Order.Types.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "OrderType.instOne", "kind": "instance", "module": "Mathlib.Order.Types.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderType.type_toType", "kind": "theorem", "module": "Mathlib.Order.Types.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderType.type_eq_type", "kind": "theorem", "module": "Mathlib.Order.Types.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderType.type_congr", "kind": "theorem", "module": "Mathlib.Order.Types.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderType.type_of_isEmpty", "kind": "theorem", "module": "Mathlib.Order.Types.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderType.type_eq_zero", "kind": "theorem", "module": "Mathlib.Order.Types.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderType.type_ne_zero_iff", "kind": "theorem", "module": "Mathlib.Order.Types.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "OrderType.type_eq_one", "kind": "theorem", "module": "Mathlib.Order.Types.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "OrderType.inductionOn", "kind": "theorem", "module": "Mathlib.Order.Types.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "OrderType.inductionOn₃", "kind": "theorem", "module": "Mathlib.Order.Types.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderType.liftOn", "kind": "definition", "module": "Mathlib.Order.Types.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderType.liftOn_type", "kind": "theorem", "module": "Mathlib.Order.Types.Defs", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
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{"name": "OrderType.type_le_type", "kind": "theorem", "module": "Mathlib.Order.Types.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "OrderType.zero_le", "kind": "theorem", "module": "Mathlib.Order.Types.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderType.instOrderBot", "kind": "instance", "module": "Mathlib.Order.Types.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderType.bot_eq_zero", "kind": "theorem", "module": "Mathlib.Order.Types.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderType.not_lt_zero", "kind": "theorem", "module": "Mathlib.Order.Types.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderType.pos_iff_ne_zero", "kind": "theorem", "module": "Mathlib.Order.Types.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderType.omega0", "kind": "definition", "module": "Mathlib.Order.Types.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderType.termω", "kind": "definition", "module": "Mathlib.Order.Types.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderType._aux_Mathlib_Order_Types_Defs___macroRules_OrderType_termω_1", "kind": "definition", "module": "Mathlib.Order.Types.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "OrderType.type_nat", "kind": "theorem", "module": "Mathlib.Order.Types.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ULift.up_sup", "kind": "theorem", "module": "Mathlib.Order.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ULift.instTransOrd_mathlib", "kind": "instance", "module": "Mathlib.Order.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.instLawfulBEqOrd_mathlib", "kind": "instance", "module": "Mathlib.Order.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.instLawfulLTOrd_mathlib", "kind": "instance", "module": "Mathlib.Order.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.instLawfulLEOrd_mathlib", "kind": "instance", "module": "Mathlib.Order.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.instLawfulBOrd_mathlib", "kind": "instance", "module": "Mathlib.Order.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ULift.instPartialOrder", "kind": "instance", "module": "Mathlib.Order.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isUpperSet_empty", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isUpperSet_univ", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUpperSet.compl", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isUpperSet_compl", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUpperSet.union", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUpperSet.inter", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isUpperSet_sUnion", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isUpperSet_iUnion", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isUpperSet_iUnion₂", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isUpperSet_sInter", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isUpperSet_iInter", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isUpperSet_iInter₂", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isUpperSet_preimage_ofDual_iff", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isUpperSet_preimage_toDual_iff", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUpperSet.isLowerSet_preimage_coe", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Basic", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "IsUpperSet.sdiff", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUpperSet.sdiff_of_isLowerSet", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUpperSet.erase", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isUpperSet_Ici", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLowerSet_Iic", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isUpperSet_Ioi", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLowerSet_Iio", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isUpperSet_iff_Ici_subset", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "isLowerSet_iff_Iic_subset", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsUpperSet.Ioi_subset", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLowerSet.Iio_subset", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUpperSet.ordConnected", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLowerSet.ordConnected", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUpperSet.preimage", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLowerSet.preimage", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUpperSet.image", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Basic", "is_tactic_proof": true, "tactics": ["change", "rw", "exact"], "tactic_count": 3}
{"name": "OrderEmbedding.image_Ici", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "OrderEmbedding.image_Iic", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderEmbedding.image_Ioi", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "OrderEmbedding.image_Iio", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.monotone_mem", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.antitone_mem", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isUpperSet_setOf", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLowerSet_setOf", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUpperSet.upperBounds_subset", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLowerSet.lowerBounds_subset", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLowerSet.top_mem", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUpperSet.top_mem", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUpperSet.top_notMem", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUpperSet.not_bddAbove", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Basic", "is_tactic_proof": true, "tactics": ["rintro", "obtain", "exact"], "tactic_count": 3}
{"name": "not_bddAbove_Ici", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_bddAbove_Ioi", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLowerSet.not_bddBelow", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Basic", "is_tactic_proof": true, "tactics": ["rintro", "obtain", "exact"], "tactic_count": 3}
{"name": "not_bddBelow_Iic", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_bddBelow_Iio", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isUpperSet_iff_forall_lt", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isUpperSet_iff_Ioi_subset", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "isLowerSet_iff_Iio_subset", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsUpperSet.total", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Basic", "is_tactic_proof": true, "tactics": ["by_contra", "simp_rw", "obtain", "obtain", "exact", "exact"], "tactic_count": 6}
{"name": "IsUpperSet.eq_empty_or_Ici", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Basic", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact"], "tactic_count": 3}
{"name": "IsLowerSet.eq_empty_or_Iic", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLowerSet.eq_univ_or_Iio", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "simpa"], "tactic_count": 2}
{"name": "IsUpperSet.eq_univ_or_Ioi", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "upperClosure", "kind": "definition", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lowerClosure", "kind": "definition", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_upperClosure", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_lowerClosure", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "coe_upperClosure", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "coe_lowerClosure", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "instDecidablePredMemUpperClosure", "kind": "instance", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDecidablePredMemLowerClosure", "kind": "instance", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "subset_upperClosure", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "subset_lowerClosure", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "upperClosure_min", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lowerClosure_min", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUpperSet.upperClosure", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLowerSet.lowerClosure", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.upperClosure", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.lowerClosure", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "upperClosure_image", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": true, "tactics": ["rw", "ext", "simp"], "tactic_count": 3}
{"name": "lowerClosure_image", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": true, "tactics": ["rw", "ext", "simp"], "tactic_count": 3}
{"name": "UpperSet.iInf_Ici", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "LowerSet.iSup_Iic", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "lowerClosure_le", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_upperClosure", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "gc_upperClosure_coe", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "gc_lowerClosure_coe", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "giUpperClosureCoe", "kind": "definition", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "giLowerClosureCoe", "kind": "definition", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "upperClosure_anti", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lowerClosure_mono", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "upperClosure_empty", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lowerClosure_empty", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "upperClosure_singleton", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "lowerClosure_singleton", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "upperClosure_univ", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lowerClosure_univ", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "upperClosure_eq_top_iff", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lowerClosure_eq_bot_iff", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "upperClosure_union", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lowerClosure_union", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "upperClosure_iUnion", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lowerClosure_iUnion", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "upperClosure_sUnion", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "lowerClosure_sUnion", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.OrdConnected.upperClosure_inter_lowerClosure", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ordConnected_iff_upperClosure_inter_lowerClosure", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "upperBounds_lowerClosure", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lowerBounds_upperClosure", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bddAbove_lowerClosure", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "bddBelow_upperClosure", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "IsLowerSet.disjoint_upperClosure_left", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": true, "tactics": ["refine", "simp", "exact"], "tactic_count": 3}
{"name": "IsLowerSet.disjoint_upperClosure_right", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsUpperSet.disjoint_lowerClosure_left", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUpperSet.disjoint_lowerClosure_right", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "upperClosure_eq", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lowerClosure_eq", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAntichain.minimal_mem_upperClosure_iff_mem", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": true, "tactics": ["simp", "refine", "obtain", "rwa", "rwa"], "tactic_count": 5}
{"name": "IsAntichain.maximal_mem_lowerClosure_iff_mem", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "upperClosure_eq_bot", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "upperClosure_eq_bot_iff", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lowerClosure_eq_top", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lowerClosure_eq_top_iff", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.sdiff", "kind": "definition", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.erase", "kind": "definition", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.coe_sdiff", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.coe_erase", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.sdiff_singleton", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LowerSet.sdiff_le_left", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.erase_le", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.sdiff_eq_left", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LowerSet.erase_eq", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LowerSet.sdiff_lt_left", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.erase_lt", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.sdiff_idem", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.erase_idem", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.sdiff_sup_lowerClosure", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact", "refine", "rintro", "exact"], "tactic_count": 6}
{"name": "LowerSet.lowerClosure_sup_sdiff", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LowerSet.erase_sup_Iic", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LowerSet.Iic_sup_erase", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "UpperSet.sdiff", "kind": "definition", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.erase", "kind": "definition", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.coe_sdiff", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.coe_erase", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.sdiff_singleton", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "UpperSet.le_sdiff_left", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.le_erase", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.sdiff_eq_left", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "UpperSet.erase_eq", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "UpperSet.lt_sdiff_left", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.lt_erase", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.sdiff_idem", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.erase_idem", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.sdiff_inf_upperClosure", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact", "refine", "rintro", "exact"], "tactic_count": 6}
{"name": "UpperSet.upperClosure_inf_sdiff", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "UpperSet.erase_inf_Ici", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "UpperSet.Ici_inf_erase", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Closure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "UpperSet.instSetLike", "kind": "instance", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.Simps.coe", "kind": "definition", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.ext", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.carrier_eq_coe", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.upper", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.coe_mk", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.mem_mk", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.instSetLike", "kind": "instance", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.Simps.coe", "kind": "definition", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.ext", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.carrier_eq_coe", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.lower", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.coe_mk", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.mem_mk", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.instMax", "kind": "instance", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.instMin", "kind": "instance", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.instTop", "kind": "instance", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.instBot", "kind": "instance", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.instSupSet", "kind": "instance", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.instInfSet", "kind": "instance", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.completeLattice", "kind": "instance", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.completelyDistribLattice", "kind": "instance", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.instInhabited", "kind": "instance", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.coe_subset_coe", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.coe_ssubset_coe", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.coe_top", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.coe_bot", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.coe_eq_univ", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "UpperSet.coe_eq_empty", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "UpperSet.coe_nonempty", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.coe_sup", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.coe_inf", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.coe_sSup", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.coe_sInf", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.coe_iSup", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "UpperSet.coe_iInf", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "UpperSet.coe_iSup₂", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "UpperSet.coe_iInf₂", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "UpperSet.notMem_top", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.mem_bot", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.mem_sup_iff", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.mem_inf_iff", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.mem_sSup_iff", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.mem_sInf_iff", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.mem_iSup_iff", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "UpperSet.mem_iInf_iff", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "UpperSet.mem_iSup₂_iff", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "UpperSet.mem_iInf₂_iff", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "UpperSet.codisjoint_coe", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LowerSet.instMax", "kind": "instance", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.instMin", "kind": "instance", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.instTop", "kind": "instance", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.instBot", "kind": "instance", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.instSupSet", "kind": "instance", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.instInfSet", "kind": "instance", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.completeLattice", "kind": "instance", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.completelyDistribLattice", "kind": "instance", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.instInhabited", "kind": "instance", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.instIsConcreteLE", "kind": "instance", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.coe_subset_coe", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.coe_ssubset_coe", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.coe_top", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.coe_bot", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.coe_eq_univ", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LowerSet.coe_eq_empty", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LowerSet.coe_nonempty", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.coe_sup", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.coe_inf", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.coe_sSup", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.coe_sInf", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.coe_iSup", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "LowerSet.coe_iInf", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "LowerSet.coe_iSup₂", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LowerSet.coe_iInf₂", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LowerSet.mem_top", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.notMem_bot", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.mem_sup_iff", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.mem_inf_iff", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.mem_sSup_iff", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.mem_sInf_iff", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.mem_iSup_iff", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "LowerSet.mem_iInf_iff", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "LowerSet.mem_iSup₂_iff", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LowerSet.mem_iInf₂_iff", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LowerSet.disjoint_coe", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "UpperSet.compl", "kind": "definition", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.compl", "kind": "definition", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.coe_compl", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.mem_compl_iff", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.compl_compl", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.compl_le_compl", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.compl_sup", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.compl_inf", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.compl_top", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.compl_bot", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.compl_sSup", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.compl_sInf", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.compl_iSup", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.compl_iInf", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.compl_iSup₂", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "UpperSet.compl_iInf₂", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LowerSet.coe_compl", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.mem_compl_iff", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.compl_compl", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.compl_le_compl", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.compl_sup", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.compl_inf", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.compl_top", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.compl_bot", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.compl_sSup", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.compl_sInf", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.compl_iSup", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.compl_iInf", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.compl_iSup₂", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "LowerSet.compl_iInf₂", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "upperSetIsoLowerSet", "kind": "definition", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.total_le", "kind": "instance", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.total_le", "kind": "instance", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.instLinearOrder", "kind": "instance", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "LowerSet.instLinearOrder", "kind": "instance", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "UpperSet.instCompleteLinearOrder", "kind": "instance", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.instCompleteLinearOrder", "kind": "instance", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.map", "kind": "definition", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.symm_map", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "UpperSet.mem_map", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "UpperSet.map_refl", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "UpperSet.map_map", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "UpperSet.coe_map", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.map", "kind": "definition", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.symm_map", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "LowerSet.mem_map", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "LowerSet.map_refl", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "LowerSet.map_map", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "LowerSet.coe_map", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.compl_map", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.compl_map", "kind": "theorem", "module": "Mathlib.Order.UpperLower.CompleteLattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Relation.Fibration.isLowerSet_image", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Fibration", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "Relation.fibration_iff_isLowerSet_image_Iic", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Fibration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Relation.fibration_iff_isLowerSet_image", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Fibration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Relation.fibration_iff_image_Iic", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Fibration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Relation.Fibration.isUpperSet_image", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Fibration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Relation.fibration_iff_isUpperSet_image_Ici", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Fibration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Relation.fibration_iff_isUpperSet_image", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Fibration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Relation.fibration_iff_image_Ici", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Fibration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.iciSupHom", "kind": "definition", "module": "Mathlib.Order.UpperLower.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.coe_iciSupHom", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.iciSupHom_apply", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.icisSupHom", "kind": "definition", "module": "Mathlib.Order.UpperLower.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.coe_icisSupHom", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.icisSupHom_apply", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.iicInfHom", "kind": "definition", "module": "Mathlib.Order.UpperLower.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.coe_iicInfHom", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.iicInfHom_apply", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.iicsInfHom", "kind": "definition", "module": "Mathlib.Order.UpperLower.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.coe_iicsInfHom", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.iicsInfHom_apply", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.upperClosure", "kind": "theorem", "module": "Mathlib.Order.UpperLower.LocallyFinite", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.Finite.lowerClosure", "kind": "theorem", "module": "Mathlib.Order.UpperLower.LocallyFinite", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "UpperSet.Ici", "kind": "definition", "module": "Mathlib.Order.UpperLower.Principal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.Ioi", "kind": "definition", "module": "Mathlib.Order.UpperLower.Principal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.coe_Ici", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Principal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.coe_Ioi", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Principal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.mem_Ici_iff", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Principal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.mem_Ioi_iff", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Principal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.map_Ici", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Principal", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "UpperSet.map_Ioi", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Principal", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "UpperSet.Ici_le_Ioi", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Principal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.Ici_bot", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Principal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.Ioi_top", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Principal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.Ici_ne_top", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Principal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.Ici_lt_top", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Principal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.le_Ici", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Principal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.Ici_strictMono", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Principal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.Ioi_strictMono", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Principal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.Ici_injective", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Principal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.Ici_inj", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Principal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.Ici_ne_Ici", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Principal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.Ioi_eq_top", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Principal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "UpperSet.Ici_sup", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Principal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.Ici_sSup", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Principal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.Ici_iSup", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Principal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.Ici_iSup₂", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Principal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LowerSet.Iic", "kind": "definition", "module": "Mathlib.Order.UpperLower.Principal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.Iio", "kind": "definition", "module": "Mathlib.Order.UpperLower.Principal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.coe_Iic", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Principal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.coe_Iio", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Principal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.mem_Iic_iff", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Principal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.mem_Iio_iff", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Principal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.map_Iic", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Principal", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "LowerSet.map_Iio", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Principal", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "LowerSet.Ioi_le_Ici", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Principal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.Iic_top", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Principal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.Iio_bot", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Principal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.Iic_ne_bot", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Principal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.bot_lt_Iic", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Principal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.Iic_le", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Principal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.Iic_strictMono", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Principal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.Iio_strictMono", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Principal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.Iic_injective", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Principal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.Iic_inj", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Principal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.Iic_ne_Iic", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Principal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.Iio_eq_bot", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Principal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LowerSet.Iic_inf", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Principal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.Iic_sInf", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Principal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.Iic_iInf", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Principal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.Iic_iInf₂", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Principal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsUpperSet.prod", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLowerSet.prod", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.prod", "kind": "definition", "module": "Mathlib.Order.UpperLower.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.instSProd", "kind": "instance", "module": "Mathlib.Order.UpperLower.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.coe_prod", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.mem_prod", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.Ici_prod", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.Ici_prod_Ici", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.prod_top", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.top_prod", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.bot_prod_bot", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.sup_prod", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.prod_sup", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.inf_prod", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.prod_inf", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.prod_sup_prod", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.prod_mono", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.prod_mono_left", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.prod_mono_right", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.prod_self_le_prod_self", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.prod_self_lt_prod_self", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.prod_le_prod_iff", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSet.prod_eq_top", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Prod", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "UpperSet.codisjoint_prod", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Prod", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "LowerSet.prod", "kind": "definition", "module": "Mathlib.Order.UpperLower.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.instSProd", "kind": "instance", "module": "Mathlib.Order.UpperLower.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.coe_prod", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.mem_prod", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.Iic_prod", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.Ici_prod_Ici", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.prod_bot", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.bot_prod", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.top_prod_top", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.inf_prod", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.prod_inf", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.sup_prod", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.prod_sup", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.prod_inf_prod", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.prod_mono", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.prod_mono_left", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.prod_mono_right", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.prod_self_le_prod_self", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.prod_self_lt_prod_self", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.prod_le_prod_iff", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSet.prod_eq_bot", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Prod", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "LowerSet.disjoint_prod", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Prod", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "upperClosure_prod", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Prod", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "lowerClosure_prod", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Prod", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "IsRelUpperSet.prop_of_mem", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Relative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRelLowerSet.prop_of_mem", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Relative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isRelUpperSet_empty", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Relative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isRelLowerSet_empty", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Relative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isRelUpperSet_self", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Relative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isRelLowerSet_self", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Relative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRelUpperSet.union", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Relative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRelLowerSet.union", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Relative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRelUpperSet.inter", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Relative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRelLowerSet.inter", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Relative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRelUpperSet.sUnion", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Relative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRelLowerSet.sUnion", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Relative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRelUpperSet.iUnion", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Relative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRelLowerSet.iUnion", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Relative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRelUpperSet.iUnion₂", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Relative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRelLowerSet.iUnion₂", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Relative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRelUpperSet.sInter", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Relative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRelLowerSet.sInter", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Relative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRelUpperSet.iInter", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Relative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRelLowerSet.iInter", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Relative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRelUpperSet.iInter₂", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Relative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRelLowerSet.iInter₂", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Relative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isUpperSet_subtype_iff_isRelUpperSet", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Relative", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact", "have", "simpa"], "tactic_count": 5}
{"name": "isLowerSet_subtype_iff_isRelLowerSet", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Relative", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact", "have", "simpa"], "tactic_count": 5}
{"name": "instSetLikeRelUpperSet", "kind": "instance", "module": "Mathlib.Order.UpperLower.Relative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instPartialOrderRelUpperSet", "kind": "instance", "module": "Mathlib.Order.UpperLower.Relative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instSetLikeRelLowerSet", "kind": "instance", "module": "Mathlib.Order.UpperLower.Relative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelUpperSet.isRelUpperSet", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Relative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelLowerSet.isRelLowerSet", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Relative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isRelUpperSet_Icc_le", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Relative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isRelLowerSet_Icc_ge", "kind": "theorem", "module": "Mathlib.Order.UpperLower.Relative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "acc_def", "kind": "theorem", "module": "Mathlib.Order.WellFounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_not_acc_lt_of_not_acc", "kind": "theorem", "module": "Mathlib.Order.WellFounded", "is_tactic_proof": true, "tactics": ["rw", "push_neg", "simpa"], "tactic_count": 3}
{"name": "not_acc_iff_exists_descending_chain", "kind": "theorem", "module": "Mathlib.Order.WellFounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "acc_iff_isEmpty_descending_chain", "kind": "theorem", "module": "Mathlib.Order.WellFounded", "is_tactic_proof": true, "tactics": ["contrapose", "rw", "exact"], "tactic_count": 3}
{"name": "wellFounded_iff_isEmpty_descending_chain", "kind": "theorem", "module": "Mathlib.Order.WellFounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WellFounded.asymm", "kind": "theorem", "module": "Mathlib.Order.WellFounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WellFounded.irrefl", "kind": "theorem", "module": "Mathlib.Order.WellFounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WellFounded.instAsymmRel_mathlib", "kind": "instance", "module": "Mathlib.Order.WellFounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WellFounded.mono", "kind": "theorem", "module": "Mathlib.Order.WellFounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WellFounded.onFun", "kind": "theorem", "module": "Mathlib.Order.WellFounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WellFounded.has_min", "kind": "theorem", "module": "Mathlib.Order.WellFounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WellFounded.min", "kind": "definition", "module": "Mathlib.Order.WellFounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WellFounded.min_mem", "kind": "theorem", "module": "Mathlib.Order.WellFounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WellFounded.not_lt_min", "kind": "theorem", "module": "Mathlib.Order.WellFounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WellFounded.wellFounded_iff_has_min", "kind": "theorem", "module": "Mathlib.Order.WellFounded", "is_tactic_proof": true, "tactics": ["refine", "by_contra", "obtain", "refine", "by_contra", "exact"], "tactic_count": 6}
{"name": "WellFounded.not_rel_apply_succ", "kind": "theorem", "module": "Mathlib.Order.WellFounded", "is_tactic_proof": true, "tactics": ["by_contra", "exact"], "tactic_count": 2}
{"name": "WellFounded.sup", "kind": "definition", "module": "Mathlib.Order.WellFounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WellFounded.lt_sup", "kind": "theorem", "module": "Mathlib.Order.WellFounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.range_injOn_strictMono", "kind": "theorem", "module": "Mathlib.Order.WellFounded", "is_tactic_proof": true, "tactics": ["intro", "ext", "apply", "intro", "obtain", "obtain", "rw", "cases", "rw", "obtain", "have", "rw", "rw", "cases"], "tactic_count": 14}
{"name": "Set.range_injOn_strictAnti", "kind": "theorem", "module": "Mathlib.Order.WellFounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.range_inj", "kind": "theorem", "module": "Mathlib.Order.WellFounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictAnti.range_inj", "kind": "theorem", "module": "Mathlib.Order.WellFounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.id_le", "kind": "theorem", "module": "Mathlib.Order.WellFounded", "is_tactic_proof": true, "tactics": ["rw", "by_contra", "obtain", "exact"], "tactic_count": 4}
{"name": "StrictMono.le_apply", "kind": "theorem", "module": "Mathlib.Order.WellFounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.le_id", "kind": "theorem", "module": "Mathlib.Order.WellFounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.apply_le", "kind": "theorem", "module": "Mathlib.Order.WellFounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.not_bddAbove_range_of_wellFoundedLT", "kind": "theorem", "module": "Mathlib.Order.WellFounded", "is_tactic_proof": true, "tactics": ["rintro", "obtain", "exact"], "tactic_count": 3}
{"name": "StrictMono.not_bddBelow_range_of_wellFoundedGT", "kind": "theorem", "module": "Mathlib.Order.WellFounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.argmin", "kind": "definition", "module": "Mathlib.Order.WellFounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.not_lt_argmin", "kind": "theorem", "module": "Mathlib.Order.WellFounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.argminOn", "kind": "definition", "module": "Mathlib.Order.WellFounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.argminOn_mem", "kind": "theorem", "module": "Mathlib.Order.WellFounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.argmin_le", "kind": "theorem", "module": "Mathlib.Order.WellFounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.isMinimalFor_argmin", "kind": "theorem", "module": "Mathlib.Order.WellFounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.isMinimalFor_argminOn", "kind": "theorem", "module": "Mathlib.Order.WellFounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Acc.induction_bot'", "kind": "theorem", "module": "Mathlib.Order.WellFounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Acc.induction_bot", "kind": "theorem", "module": "Mathlib.Order.WellFounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WellFounded.induction_bot'", "kind": "theorem", "module": "Mathlib.Order.WellFounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WellFounded.induction_bot", "kind": "theorem", "module": "Mathlib.Order.WellFounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WellFoundedLT.toOrderBot", "kind": "definition", "module": "Mathlib.Order.WellFounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WellFoundedGT.toOrderTop", "kind": "definition", "module": "Mathlib.Order.WellFounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.instWellFoundedLT", "kind": "instance", "module": "Mathlib.Order.WellFounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.instWellFoundedGT", "kind": "instance", "module": "Mathlib.Order.WellFounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.WellFoundedOn", "kind": "definition", "module": "Mathlib.Order.WellFoundedSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.wellFoundedOn_empty", "kind": "theorem", "module": "Mathlib.Order.WellFoundedSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.wellFoundedOn_iff", "kind": "theorem", "module": "Mathlib.Order.WellFoundedSet", "is_tactic_proof": false, "tactics": ["have", "refine", "rw", "intro", "by_cases", "rw", "rcases", "exact", "rcases", "exact"], "tactic_count": 10}
{"name": "Set.wellFoundedOn_univ", "kind": "theorem", "module": "Mathlib.Order.WellFoundedSet", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WellFounded.wellFoundedOn", "kind": "theorem", "module": "Mathlib.Order.WellFoundedSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.wellFoundedOn_range", "kind": "theorem", "module": "Mathlib.Order.WellFoundedSet", "is_tactic_proof": true, "tactics": ["let", "refine", "rintro", "refine", "rintro", "exact", "exact"], "tactic_count": 7}
{"name": "Set.wellFoundedOn_image", "kind": "theorem", "module": "Mathlib.Order.WellFoundedSet", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.WellFoundedOn.induction", "kind": "theorem", "module": "Mathlib.Order.WellFoundedSet", "is_tactic_proof": true, "tactics": ["let", "change", "refine", "simpa"], "tactic_count": 4}
{"name": "Set.WellFoundedOn.mono", "kind": "theorem", "module": "Mathlib.Order.WellFoundedSet", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.WellFoundedOn.mono'", "kind": "theorem", "module": "Mathlib.Order.WellFoundedSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.WellFoundedOn.subset", "kind": "theorem", "module": "Mathlib.Order.WellFoundedSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.WellFoundedOn.acc_iff_wellFoundedOn", "kind": "theorem", "module": "Mathlib.Order.WellFoundedSet", "is_tactic_proof": false, "tactics": ["tfae_have", "refine", "rw", "obtain", "rwa", "exact", "tfae_have", "tfae_have", "refine", "exact", "tfae_finish"], "tactic_count": 11}
{"name": "Set.IsStrictOrder.subset", "kind": "instance", "module": "Mathlib.Order.WellFoundedSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.wellFoundedOn_iff_no_descending_seq", "kind": "theorem", "module": "Mathlib.Order.WellFoundedSet", "is_tactic_proof": false, "tactics": ["simp", "constructor", "rintro", "have", "refine", "simpa", "rintro", "refine", "simpa"], "tactic_count": 9}
{"name": "Set.WellFoundedOn.union", "kind": "theorem", "module": "Mathlib.Order.WellFoundedSet", "is_tactic_proof": true, "tactics": ["rw", "rintro", "rcases", "exacts"], "tactic_count": 4}
{"name": "Set.wellFoundedOn_union", "kind": "theorem", "module": "Mathlib.Order.WellFoundedSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.IsWF", "kind": "definition", "module": "Mathlib.Order.WellFoundedSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.isWF_empty", "kind": "theorem", "module": "Mathlib.Order.WellFoundedSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.IsWF.mono", "kind": "theorem", "module": "Mathlib.Order.WellFoundedSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.isWF_univ_iff", "kind": "theorem", "module": "Mathlib.Order.WellFoundedSet", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.IsWF.of_wellFoundedLT", "kind": "theorem", "module": "Mathlib.Order.WellFoundedSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.IsWF.union", "kind": "theorem", "module": "Mathlib.Order.WellFoundedSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.isWF_union", "kind": "theorem", "module": "Mathlib.Order.WellFoundedSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.isWF_iff_no_descending_seq", "kind": "theorem", "module": "Mathlib.Order.WellFoundedSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.PartiallyWellOrderedOn", "kind": "definition", "module": "Mathlib.Order.WellFoundedSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.PartiallyWellOrderedOn.exists_lt", "kind": "theorem", "module": "Mathlib.Order.WellFoundedSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.partiallyWellOrderedOn_iff_exists_lt", "kind": "theorem", "module": "Mathlib.Order.WellFoundedSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.partiallyWellOrderedOn_univ_iff", "kind": "theorem", "module": "Mathlib.Order.WellFoundedSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.PartiallyWellOrderedOn.mono", "kind": "theorem", "module": "Mathlib.Order.WellFoundedSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.partiallyWellOrderedOn_of_wellQuasiOrdered", "kind": "theorem", "module": "Mathlib.Order.WellFoundedSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.partiallyWellOrderedOn_empty", "kind": "theorem", "module": "Mathlib.Order.WellFoundedSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.PartiallyWellOrderedOn.union", "kind": "theorem", "module": "Mathlib.Order.WellFoundedSet", "is_tactic_proof": true, "tactics": ["intro", "obtain", "rcases", "exact", "rcases", "exact"], "tactic_count": 6}
{"name": "Set.partiallyWellOrderedOn_union", "kind": "theorem", "module": "Mathlib.Order.WellFoundedSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.PartiallyWellOrderedOn.image_of_monotone_on", "kind": "theorem", "module": "Mathlib.Order.WellFoundedSet", "is_tactic_proof": true, "tactics": ["rw", "intro", "choose", "obtain", "obtain", "exact"], "tactic_count": 6}
{"name": "IsAntichain.finite_of_partiallyWellOrderedOn", "kind": "theorem", "module": "Mathlib.Order.WellFoundedSet", "is_tactic_proof": true, "tactics": ["by_contra", "obtain", "exact", "hmn.ne"], "tactic_count": 4}
{"name": "Set.Finite.partiallyWellOrderedOn", "kind": "theorem", "module": "Mathlib.Order.WellFoundedSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAntichain.partiallyWellOrderedOn_iff", "kind": "theorem", "module": "Mathlib.Order.WellFoundedSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.partiallyWellOrderedOn_singleton", "kind": "theorem", "module": "Mathlib.Order.WellFoundedSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Subsingleton.partiallyWellOrderedOn", "kind": "theorem", "module": "Mathlib.Order.WellFoundedSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.partiallyWellOrderedOn_insert", "kind": "theorem", "module": "Mathlib.Order.WellFoundedSet", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.PartiallyWellOrderedOn.insert", "kind": "theorem", "module": "Mathlib.Order.WellFoundedSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Set.isPWO_of_finite", "kind": "theorem", "module": "Mathlib.Order.WellFoundedSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "WithBot.bot_ne_coe", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.coe_ne_bot", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.unbotD", "kind": "definition", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.unbotD_bot", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.unbotD_coe", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.coe_eq_coe", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.unbotD_eq_iff", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "WithBot.unbotD_eq_self_iff", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WithBot.unbotD_eq_unbotD_iff", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "WithBot.map", "kind": "definition", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.map_bot", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.map_coe", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.map_eq_bot_iff", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.map_eq_some_iff", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.some_eq_map_iff", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "WithBot.map_id", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.map_map", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.comp_map", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.map_comp_map", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.map_comm", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.map_injective", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.map₂", "kind": "definition", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.map₂_coe_coe", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.map₂_bot_left", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.map₂_bot_right", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "WithBot.map₂_coe_left", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.map₂_coe_right", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "WithBot.map₂_eq_bot_iff", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.ne_bot_iff_exists", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.eq_bot_iff_forall_ne", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.forall_ne_bot", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WithBot.exists_ne_bot", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WithBot.unbot", "kind": "definition", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.coe_unbot", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.canLift", "kind": "instance", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.instTop", "kind": "instance", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.coe_top", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.coe_eq_top", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.top_eq_coe", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.unbot_eq_iff", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": true, "tactics": ["induction", "simpa", "simp"], "tactic_count": 3}
{"name": "WithBot.eq_unbot_iff", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": true, "tactics": ["induction", "simpa", "simp"], "tactic_count": 3}
{"name": "Equiv.withBotSubtypeNe", "kind": "definition", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.unbotA", "kind": "abbrev", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.unbotA_eq_unbot", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": true, "tactics": ["cases", "bot", "coe"], "tactic_count": 3}
{"name": "Equiv.withBotCongr", "kind": "definition", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.withBotCongr_refl", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.withBotCongr_symm", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.withBotCongr_trans", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "WithBot.LE", "kind": "inductive", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.instLE", "kind": "instance", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.instLE", "kind": "instance", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.le_def", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.le_def'", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.le_def", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "WithBot.LT", "kind": "inductive", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.instLT", "kind": "instance", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.instLT", "kind": "instance", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.lt_def", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.lt_def'", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.lt_def", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "WithBot.le_iff_forall", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "WithBot.coe_le_coe", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WithBot.not_coe_le_bot", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WithBot.instOrderBot", "kind": "instance", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.instOrderTop", "kind": "instance", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.instBoundedOrder", "kind": "instance", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.le_bot_iff", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.coe_le", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.coe_le_iff", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WithBot.le_coe_iff", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsMax.withBot", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.le_unbot_iff", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": true, "tactics": ["lift"], "tactic_count": 1}
{"name": "WithBot.unbot_le_iff", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": true, "tactics": ["lift"], "tactic_count": 1}
{"name": "WithBot.unbot_le_unbot_iff", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WithBot.le_unbotD_iff", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": true, "tactics": ["lift"], "tactic_count": 1}
{"name": "WithBot.unbotD_le_iff", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "WithBot.unbotD_mono", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": true, "tactics": ["lift", "cases"], "tactic_count": 2}
{"name": "WithBot.le_unbotA_iff", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.unbotA_le_iff", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": true, "tactics": ["lift"], "tactic_count": 1}
{"name": "WithBot.unbotA_mono", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.lt_iff_exists", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "WithBot.coe_lt_coe", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WithBot.bot_lt_coe", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WithBot.not_lt_bot", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WithBot.lt_iff_exists_coe", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "WithBot.lt_coe_iff", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WithBot.bot_lt_iff_ne_bot", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "WithBot.lt_unbot_iff", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": true, "tactics": ["lift"], "tactic_count": 1}
{"name": "WithBot.unbot_lt_iff", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": true, "tactics": ["lift"], "tactic_count": 1}
{"name": "WithBot.unbot_lt_unbot_iff", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WithBot.lt_unbotD_iff", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": true, "tactics": ["lift"], "tactic_count": 1}
{"name": "WithBot.unbotD_lt_iff", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "WithBot.lt_unbotA_iff", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.unbotA_lt_iff", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": true, "tactics": ["lift"], "tactic_count": 1}
{"name": "WithBot.instPreorder", "kind": "instance", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.coe_strictMono", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.coe_strictMono", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.coe_mono", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.coe_mono", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.monotone_iff", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.monotone_iff", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.monotone_map_iff", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.monotone_map_iff", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.strictMono_iff", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.strictMono_iff", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.strictAnti_iff", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.strictAnti_iff", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.strictMono_map_iff", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.strictMono_map_iff", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.map_le_iff", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "WithBot.le_coe_unbotD", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "WithBot.lt_coe_bot", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "WithBot.eq_bot_iff_forall_lt", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "WithBot.eq_bot_iff_forall_le", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": true, "tactics": ["refine", "rintro", "exact"], "tactic_count": 3}
{"name": "WithBot.forall_coe_le_iff_le", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": true, "tactics": ["obtain", "simpa", "exact"], "tactic_count": 3}
{"name": "WithBot.forall_le_coe_iff_le", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": true, "tactics": ["obtain", "simp", "exact"], "tactic_count": 3}
{"name": "WithBot.forall_coe_lt", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WithBot.exists_coe_lt", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WithBot.forall_coe_le", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WithBot.exists_coe_le", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WithBot.instPartialOrder", "kind": "instance", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.le_unbotD", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": true, "tactics": ["rwa", "exact"], "tactic_count": 2}
{"name": "WithBot.le_unbotA", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.eq_top_iff_forall_ge", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": true, "tactics": ["refine", "induction", "simp", "simpa"], "tactic_count": 4}
{"name": "WithBot.eq_of_forall_coe_le_iff", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.eq_of_forall_le_coe_iff", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.semilatticeSup", "kind": "instance", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.semilatticeInf", "kind": "instance", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.semilatticeInf", "kind": "instance", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.semilatticeSup", "kind": "instance", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.coe_sup", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.coe_inf", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.lattice", "kind": "instance", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.lattice", "kind": "instance", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.distribLattice", "kind": "instance", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.distribLattice", "kind": "instance", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.decidableEq", "kind": "instance", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.decidableLE", "kind": "instance", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.decidableLT", "kind": "instance", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "WithTop.total_le", "kind": "instance", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "WithBot.instWellFoundedLT", "kind": "instance", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.instWellFoundedGT", "kind": "instance", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.denselyOrdered_iff", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": true, "tactics": ["constructor", "intro", "obtain", "induction", "bot", "coe", "simpa"], "tactic_count": 7}
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{"name": "WithBot.le_of_forall_lt_iff_le", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
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{"name": "WithBot.noTopOrder", "kind": "instance", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "WithBot.toDual", "kind": "definition", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "WithBot.toDual_symm_apply", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.ofDual_symm", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.ofDual_symm_apply", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.toDual_bot", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "WithBot.ofDual_apply_coe", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.map_toDual", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.map_ofDual", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.toDual_map", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.ofDual_map", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBot.toDual_le_iff", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "WithBot.le_toDual_iff", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "WithBot.toDual_le_toDual_iff", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "WithBot.ofDual_le_iff", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "WithBot.le_ofDual_iff", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
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{"name": "WithBot.toDual_lt_iff", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "WithBot.lt_toDual_iff", "kind": "theorem", "module": "Mathlib.Order.WithBot", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
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{"name": "WithBotTop", "kind": "abbrev", "module": "Mathlib.Order.WithBotTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBotTop.coe", "kind": "definition", "module": "Mathlib.Order.WithBotTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBotTop.instCoe", "kind": "instance", "module": "Mathlib.Order.WithBotTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBotTop.coe_injective", "kind": "theorem", "module": "Mathlib.Order.WithBotTop", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "WithBotTop.coe_ne_bot", "kind": "theorem", "module": "Mathlib.Order.WithBotTop", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "WithBotTop.coe_ne_top", "kind": "theorem", "module": "Mathlib.Order.WithBotTop", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "WithBotTop.top_ne_bot", "kind": "theorem", "module": "Mathlib.Order.WithBotTop", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "WithBotTop.rec", "kind": "definition", "module": "Mathlib.Order.WithBotTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBotTop.rec_bot", "kind": "theorem", "module": "Mathlib.Order.WithBotTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBotTop.rec_coe", "kind": "theorem", "module": "Mathlib.Order.WithBotTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBotTop.rec_top", "kind": "theorem", "module": "Mathlib.Order.WithBotTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBotTop.coe_le_coe", "kind": "theorem", "module": "Mathlib.Order.WithBotTop", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
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{"name": "WithBotTop.coe_strictMono", "kind": "theorem", "module": "Mathlib.Order.WithBotTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithBotTop.coe_monotone", "kind": "theorem", "module": "Mathlib.Order.WithBotTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EInt", "kind": "abbrev", "module": "Mathlib.Order.WithBotTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Order.Zorn.0.term_≺_", "kind": "definition", "module": "Mathlib.Order.Zorn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "exists_maximal_of_chains_bounded", "kind": "theorem", "module": "Mathlib.Order.Zorn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_maximal_of_nonempty_chains_bounded", "kind": "theorem", "module": "Mathlib.Order.Zorn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zorn_le", "kind": "theorem", "module": "Mathlib.Order.Zorn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zorn_le_nonempty", "kind": "theorem", "module": "Mathlib.Order.Zorn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zorn_le₀", "kind": "theorem", "module": "Mathlib.Order.Zorn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zorn_le_nonempty₀", "kind": "theorem", "module": "Mathlib.Order.Zorn", "is_tactic_proof": true, "tactics": ["have", "rcases", "exact", "rcases", "exact", "rcases", "exact"], "tactic_count": 7}
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{"name": "IsChain.exists_maxChain", "kind": "theorem", "module": "Mathlib.Order.Zorn", "is_tactic_proof": true, "tactics": ["have", "obtain", "exact", "rintro", "refine", "rintro", "obtain", "exact", "rcases", "exact", "exact"], "tactic_count": 11}
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{"name": "Flag.instNonempty", "kind": "instance", "module": "Mathlib.Order.Zorn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCoatomic.of_isChain_bounded", "kind": "theorem", "module": "Mathlib.Order.ZornAtoms", "is_tactic_proof": true, "tactics": ["refine", "have", "obtain", "refine", "exact", "rcases", "exact"], "tactic_count": 7}
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{"name": "ProbabilityTheory.iIndepFun.indep_comap_natural_of_lt", "kind": "theorem", "module": "Mathlib.Probability.BorelCantelli", "is_tactic_proof": false, "tactics": ["suffices", "exact"], "tactic_count": 2}
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{"name": "ProbabilityTheory.cdf_nonneg", "kind": "theorem", "module": "Mathlib.Probability.CDF", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.cdf_le_one", "kind": "theorem", "module": "Mathlib.Probability.CDF", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.monotone_cdf", "kind": "theorem", "module": "Mathlib.Probability.CDF", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.tendsto_cdf_atBot", "kind": "theorem", "module": "Mathlib.Probability.CDF", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.tendsto_cdf_atTop", "kind": "theorem", "module": "Mathlib.Probability.CDF", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.ofReal_cdf", "kind": "theorem", "module": "Mathlib.Probability.CDF", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "ProbabilityTheory.cdf_eq_real", "kind": "theorem", "module": "Mathlib.Probability.CDF", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ProbabilityTheory.instIsProbabilityMeasurecdf", "kind": "instance", "module": "Mathlib.Probability.CDF", "is_tactic_proof": true, "tactics": ["constructor", "simp"], "tactic_count": 2}
{"name": "ProbabilityTheory.measure_cdf", "kind": "theorem", "module": "Mathlib.Probability.CDF", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "ProbabilityTheory.cdf_measure_stieltjesFunction", "kind": "theorem", "module": "Mathlib.Probability.CDF", "is_tactic_proof": true, "tactics": ["refine", "have", "exact"], "tactic_count": 3}
{"name": "ProbabilityTheory.unitInterval.cdf_eq_real", "kind": "theorem", "module": "Mathlib.Probability.CDF", "is_tactic_proof": true, "tactics": ["haveI", "rw"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.eq_of_cdf", "kind": "theorem", "module": "Mathlib.Probability.CDF", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.cdf_eq_iff", "kind": "theorem", "module": "Mathlib.Probability.CDF", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.condVar", "kind": "definition", "module": "Mathlib.Probability.CondVar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ProbabilityTheory.condVar_of_not_sigmaFinite", "kind": "theorem", "module": "Mathlib.Probability.CondVar", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ProbabilityTheory.condVar_of_sigmaFinite", "kind": "theorem", "module": "Mathlib.Probability.CondVar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.condVar_of_stronglyMeasurable", "kind": "theorem", "module": "Mathlib.Probability.CondVar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.condVar_of_not_integrable", "kind": "theorem", "module": "Mathlib.Probability.CondVar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.condVar_zero", "kind": "theorem", "module": "Mathlib.Probability.CondVar", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ProbabilityTheory.condVar_const", "kind": "theorem", "module": "Mathlib.Probability.CondVar", "is_tactic_proof": true, "tactics": ["obtain", "simp", "by_cases", "simp", "simp", "integrable_const_iff_isFiniteMeasure"], "tactic_count": 6}
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{"name": "ProbabilityTheory.condVar_congr_ae", "kind": "theorem", "module": "Mathlib.Probability.CondVar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.condVar_of_aestronglyMeasurable", "kind": "theorem", "module": "Mathlib.Probability.CondVar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.integrable_condVar", "kind": "theorem", "module": "Mathlib.Probability.CondVar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.setIntegral_condVar", "kind": "theorem", "module": "Mathlib.Probability.CondVar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ProbabilityTheory.isProbabilityMeasure_gammaMeasure", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gamma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.gammaCDFReal", "kind": "definition", "module": "Mathlib.Probability.Distributions.Gamma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.cdf_gammaMeasure_eq_integral", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gamma", "is_tactic_proof": true, "tactics": ["have", "rw", "refine", "exact", "fun_prop"], "tactic_count": 5}
{"name": "ProbabilityTheory.cdf_gammaMeasure_eq_lintegral", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gamma", "is_tactic_proof": true, "tactics": ["have", "simp", "simp"], "tactic_count": 3}
{"name": "ProbabilityTheory.IsGaussian.toIsProbabilityMeasure", "kind": "instance", "module": "Mathlib.Probability.Distributions.Gaussian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.isGaussian_gaussianReal", "kind": "instance", "module": "Mathlib.Probability.Distributions.Gaussian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IsGaussian.eq_gaussianReal", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.isGaussian_of_isGaussian_map", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "simp", "all_goals"], "tactic_count": 4}
{"name": "ProbabilityTheory.isGaussian_of_map_eq_gaussianReal", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Basic", "is_tactic_proof": true, "tactics": ["refine", "obtain", "rw", "infer_instance"], "tactic_count": 4}
{"name": "ProbabilityTheory.isGaussian_map_of_measurable", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "ProbabilityTheory.instIsGaussianDirac", "kind": "instance", "module": "Mathlib.Probability.Distributions.Gaussian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IsGaussian.memLp_dual", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Basic", "is_tactic_proof": true, "tactics": ["suffices", "rw", "convert", "simp"], "tactic_count": 4}
{"name": "ProbabilityTheory.IsGaussian.integrable_dual", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ProbabilityTheory.isGaussian_map", "kind": "instance", "module": "Mathlib.Probability.Distributions.Gaussian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.isGaussian_map_equiv", "kind": "instance", "module": "Mathlib.Probability.Distributions.Gaussian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.isGaussian_map_equiv_iff", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Basic", "is_tactic_proof": true, "tactics": ["refine", "suffices", "rw", "simp"], "tactic_count": 4}
{"name": "ProbabilityTheory.IsGaussian.charFunDual_eq", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Basic", "is_tactic_proof": true, "tactics": ["calc", "charFunDual", "rw", "simp", "congr", "rw", "simp", "exact"], "tactic_count": 8}
{"name": "ProbabilityTheory.isGaussian_iff_charFunDual_eq", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Basic", "is_tactic_proof": true, "tactics": ["refine", "ext", "rw", "simp", "congr", "rw", "rw", "congr"], "tactic_count": 8}
{"name": "ProbabilityTheory.IsGaussian.charFun_eq", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "ProbabilityTheory.isGaussian_iff_charFun_eq", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "simp"], "tactic_count": 2}
{"name": "ProbabilityTheory.isGaussian_conv", "kind": "instance", "module": "Mathlib.Probability.Distributions.Gaussian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.instIsGaussianMapHAdd", "kind": "instance", "module": "Mathlib.Probability.Distributions.Gaussian.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "have", "rw", "variance_add_const", "simp", "rw", "congr", "simp", "ring"], "tactic_count": 10}
{"name": "ProbabilityTheory.instIsGaussianMapHAdd_1", "kind": "instance", "module": "Mathlib.Probability.Distributions.Gaussian.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "ProbabilityTheory.instIsGaussianMapHSub", "kind": "instance", "module": "Mathlib.Probability.Distributions.Gaussian.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "ProbabilityTheory.instIsGaussianMapNeg", "kind": "instance", "module": "Mathlib.Probability.Distributions.Gaussian.Basic", "is_tactic_proof": true, "tactics": ["change", "infer_instance"], "tactic_count": 2}
{"name": "ProbabilityTheory.instIsGaussianMapHSub_1", "kind": "instance", "module": "Mathlib.Probability.Distributions.Gaussian.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "suffices", "rwa", "infer_instance"], "tactic_count": 4}
{"name": "ProbabilityTheory.instIsGaussianProdProdOfSecondCountableTopologyEither", "kind": "instance", "module": "Mathlib.Probability.Distributions.Gaussian.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "congr", "let", "let", "rw", "congr", "simp_rw", "rw", "norm_cast", "field_simp", "rw", "norm_cast"], "tactic_count": 13}
{"name": "ProbabilityTheory.IsGaussian.charFunDual_eq'", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.CharFun", "is_tactic_proof": false, "tactics": ["rw", "exact", "exact"], "tactic_count": 3}
{"name": "ProbabilityTheory.isGaussian_iff_gaussian_charFunDual", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.CharFun", "is_tactic_proof": false, "tactics": ["refine", "isGaussian_of_map_eq_gaussianReal", "apply", "ext", "simp_rw", "norm_cast", "congrm", "rw", "ring", "exact"], "tactic_count": 10}
{"name": "ProbabilityTheory.gaussian_charFunDual_congr", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.CharFun", "is_tactic_proof": true, "tactics": ["have", "simp_rw", "choose", "have", "rw", "field_simp", "ring", "have", "rw", "change", "simp_rw", "fun_prop", "have", "have", "rw", "simp", "simp", "ofReal_im,", "div_left_inj',", "constructor", "rw", "simp", "rw", "apply", "intro", "simp"], "tactic_count": 26}
{"name": "ProbabilityTheory.IsGaussian.ext_covarianceBilinDual", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.CharFun", "is_tactic_proof": true, "tactics": ["apply", "ext", "simp_rw"], "tactic_count": 3}
{"name": "ProbabilityTheory.IsGaussian.ext_iff_covarianceBilinDual", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.CharFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IsGaussian.charFun_eq'", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.CharFun", "is_tactic_proof": true, "tactics": ["rw", "rfl", "exact", "exact"], "tactic_count": 4}
{"name": "ProbabilityTheory.isGaussian_iff_gaussian_charFun", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.CharFun", "is_tactic_proof": true, "tactics": ["rw", "refine", "f.bilinearComp", "f.bilinearComp", "any_goals", "any_goals", "simp", "simp"], "tactic_count": 8}
{"name": "ProbabilityTheory.gaussian_charFun_congr", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.CharFun", "is_tactic_proof": false, "tactics": ["let", "f.bilinearComp", "have", "simp", "have", "have", "refine", "ext", "simp"], "tactic_count": 9}
{"name": "ProbabilityTheory.IsGaussian.ext", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.CharFun", "is_tactic_proof": true, "tactics": ["apply", "ext", "simp_rw"], "tactic_count": 3}
{"name": "ProbabilityTheory.IsGaussian.ext_iff", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.CharFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IsGaussian.charFunDual_eq_of_forall_strongDual_eq_zero", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Fernique", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ProbabilityTheory.IsGaussian.map_rotation_eq_self_of_forall_strongDual_eq_zero", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Fernique", "is_tactic_proof": true, "tactics": ["refine", "ext", "simp_rw", "rw", "congr", "norm_cast", "have", "ext", "simp", "rw", "simp", "have", "ext", "simp", "rw", "simp", "rw", "simp", "rw", "covariance_smul_right,", "have", "grind", "all_goals"], "tactic_count": 23}
{"name": "ProbabilityTheory.IsGaussian.integral_dual_conv_map_neg_eq_zero", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Fernique", "is_tactic_proof": true, "tactics": ["rw", "simp", "calc", "congr", "rw", "simp", "rw", "simp", "rw", "simp"], "tactic_count": 10}
{"name": "ProbabilityTheory.IsGaussian.integrable_exp_sq_of_conv_neg", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Fernique", "is_tactic_proof": false, "tactics": ["have", "rw", "replace", "simp", "filter_upwards", "rw", "convert", "simp", "left", "simp_rw", "obtain", "let", "have", "suffices", "refine", "integrable_of_le_of_le", "exact", "exact", "intro", "rw", "gcongr", "have", "calc", "simp_rw", "gcongr", "exact", "calc"], "tactic_count": 27}
{"name": "ProbabilityTheory.IsGaussian.exists_integrable_exp_sq", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Fernique", "is_tactic_proof": true, "tactics": ["obtain", "exists_integrable_exp_sq_of_map_rotation_eq_self", "refine", "exact"], "tactic_count": 4}
{"name": "ProbabilityTheory.IsGaussian.memLp_id", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Fernique", "is_tactic_proof": false, "tactics": ["suffices", "rw", "simpa", "lift", "convert", "simp", "obtain", "have", "refine", "integrable_of_le_of_le", "filter_upwards", "simp", "positivity", "have", "rw", "exact", "exact"], "tactic_count": 17}
{"name": "ProbabilityTheory.IsGaussian.integrable_id", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Fernique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IsGaussian.integrable_fun_id", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Fernique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IsGaussian.memLp_two_id", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Fernique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IsGaussian.memLp_two_fun_id", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Fernique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IsGaussian.integral_dual", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Fernique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IsGaussian.eq_dirac_of_variance_eq_zero", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Fernique", "is_tactic_proof": true, "tactics": ["refine", "ext", "rw", "simp"], "tactic_count": 4}
{"name": "ProbabilityTheory.IsGaussian.noAtoms", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Fernique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IsGaussian.charFunDual_eq_of_integral_eq_zero", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Fernique", "is_tactic_proof": true, "tactics": ["refine", "simp", "simp"], "tactic_count": 3}
{"name": "ProbabilityTheory.IsGaussian.map_rotation_eq_self", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Fernique", "is_tactic_proof": true, "tactics": ["refine", "simp", "simp"], "tactic_count": 3}
{"name": "ProbabilityTheory.HasGaussianLaw.congr", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IsGaussian.hasGaussianLaw", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IsGaussian.hasGaussianLaw_id", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.HasGaussianLaw.aemeasurable", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.HasGaussianLaw.isProbabilityMeasure", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.HasLaw.hasGaussianLaw", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.HasGaussianLaw.map_of_measurable", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.HasGaussianLaw.charFun_map_eq", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Basic", "is_tactic_proof": false, "tactics": ["rw", "variance_map", "rfl"], "tactic_count": 3}
{"name": "ProbabilityTheory.hasGaussianLaw_iff_charFun_map_eq", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.HasGaussianLaw.charFunDual_map_eq", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Basic", "is_tactic_proof": false, "tactics": ["rw", "variance_map", "rfl"], "tactic_count": 3}
{"name": "ProbabilityTheory.hasGaussianLaw_iff_charFunDual_map_eq", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.HasGaussianLaw.charFunDual_map_eq_fun", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Basic", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "ProbabilityTheory.HasGaussianLaw.memLp", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact", "all_goals"], "tactic_count": 3}
{"name": "ProbabilityTheory.HasGaussianLaw.memLp_two", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.HasGaussianLaw.integrable", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.HasGaussianLaw.map", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.HasGaussianLaw.map_fun", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.HasGaussianLaw.map_equiv", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.HasGaussianLaw.map_equiv_fun", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.HasGaussianLaw.smul", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.HasGaussianLaw.fun_smul", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.HasGaussianLaw.neg", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ProbabilityTheory.HasGaussianLaw.fun_neg", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.HasGaussianLaw.toLp_prodMk", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.HasGaussianLaw.fst", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.HasGaussianLaw.snd", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.HasGaussianLaw.add", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.HasGaussianLaw.fun_add", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.HasGaussianLaw.sub", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.HasGaussianLaw.fun_sub", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.HasGaussianLaw.eval", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.HasGaussianLaw.prodMk", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.HasGaussianLaw.toLp_pi", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.HasGaussianLaw.sum", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Basic", "is_tactic_proof": true, "tactics": ["convert", "ext"], "tactic_count": 2}
{"name": "ProbabilityTheory.HasGaussianLaw.fun_sum", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Basic", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "ContinuousLinearMap.diagonalStrongDualPi", "kind": "definition", "module": "Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Independence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.diagonalStrongDualPi_apply", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Independence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.toBilinForm_diagonalStrongDualPi_apply", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Independence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.isPosSemidef_diagonalStrongDualPi", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Independence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.diagonalStrongDualProd", "kind": "definition", "module": "Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Independence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.diagonalStrongDualProd_apply", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Independence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.toBilinForm_diagonalStrongDualProd_apply", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Independence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.isPosSemidef_diagonalStrongDualProd", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Independence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndepFun.hasGaussianLaw", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Independence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.HasGaussianLaw.iIndepFun_of_covariance_strongDual", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Independence", "is_tactic_proof": true, "tactics": ["simp_rw", "have", "classical", "let", "rw", "intro", "have", "simp_rw", "sum_mul,", "congr", "simp_rw", "rw", "rw", "simp", "congr", "rw", "covariance_self"], "tactic_count": 17}
{"name": "ProbabilityTheory.HasGaussianLaw.iIndepFun_of_covariance_inner", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Independence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.HasGaussianLaw.iIndepFun_of_covariance_eval", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Independence", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "let", "let", "refine", "exact", "rw", "simp_rw", "rw", "simp", "refine", "rw", "simpa", "simpa"], "tactic_count": 15}
{"name": "ProbabilityTheory.HasGaussianLaw.iIndepFun_of_covariance_eq_zero", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Independence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IndepFun.hasGaussianLaw", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Independence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.HasGaussianLaw.indepFun_of_covariance_strongDual", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Independence", "is_tactic_proof": true, "tactics": ["have", "rw", "intro", "have", "simp", "rw", "add_mul,", "rfl", "exact", "exact", "exact", "exact"], "tactic_count": 12}
{"name": "ProbabilityTheory.HasGaussianLaw.indepFun_of_covariance_inner", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Independence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.HasGaussianLaw.indepFun_of_covariance_eval", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Independence", "is_tactic_proof": true, "tactics": ["have", "have", "have", "rw", "let", "let", "refine", "exact", "hXY.map_equiv", "rw", "simp_rw", "rw", "simp", "refine", "rw", "simp", "exact", "simp", "exact"], "tactic_count": 19}
{"name": "ProbabilityTheory.HasGaussianLaw.indepFun_of_covariance_eq_zero", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Independence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndepFun.hasGaussianLaw_sum", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Independence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndepFun.hasGaussianLaw_fun_sum", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Independence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndepFun.hasGaussianLaw_add", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Independence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndepFun.hasGaussianLaw_fun_add", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Independence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndepFun.hasGaussianLaw_sub", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Independence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndepFun.hasGaussianLaw_fun_sub", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Independence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IndepFun.hasGaussianLaw_sub_of_sub", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Independence", "is_tactic_proof": true, "tactics": ["have", "rw", "intro", "apply", "simp", "rw", "sub_add_sub_comm,", "hY.charFunDual_map_eq]", "congr", "any_goals", "exact", "rw", "exact", "exact", "exact", "rw", "exact"], "tactic_count": 17}
{"name": "ProbabilityTheory.IsGaussianProcess.isProbabilityMeasure", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.IsGaussianProcess.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IsGaussianProcess.aemeasurable", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.IsGaussianProcess.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IsGaussianProcess.congr", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.IsGaussianProcess.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IsGaussianProcess.hasGaussianLaw_eval", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.IsGaussianProcess.Basic", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "ProbabilityTheory.IsGaussianProcess.hasGaussianLaw_prodMk", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.IsGaussianProcess.Basic", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "ProbabilityTheory.IsGaussianProcess.hasGaussianLaw_add", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.IsGaussianProcess.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IsGaussianProcess.hasGaussianLaw_fun_add", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.IsGaussianProcess.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IsGaussianProcess.hasGaussianLaw_sub", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.IsGaussianProcess.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IsGaussianProcess.hasGaussianLaw_fun_sub", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.IsGaussianProcess.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IsGaussianProcess.hasGaussianLaw_sum", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.IsGaussianProcess.Basic", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "ProbabilityTheory.IsGaussianProcess.hasGaussianLaw_fun_sum", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.IsGaussianProcess.Basic", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "ProbabilityTheory.IsGaussianProcess.hasGaussianLaw_increments", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.IsGaussianProcess.Basic", "is_tactic_proof": true, "tactics": ["classical", "let", "map_add", "map_smul", "cont", "exact"], "tactic_count": 6}
{"name": "ProbabilityTheory.IsGaussianProcess.of_isGaussianProcess", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.IsGaussianProcess.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IsGaussianProcess.comp_right", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.IsGaussianProcess.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IsGaussianProcess.comp_left", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.IsGaussianProcess.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IsGaussianProcess.smul", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.IsGaussianProcess.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IsGaussianProcess.shift", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.IsGaussianProcess.Basic", "is_tactic_proof": true, "tactics": ["classical", "exact", "h.of_isGaussianProcess", "map_add", "map_smul"], "tactic_count": 5}
{"name": "ProbabilityTheory.IsGaussianProcess.restrict", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.IsGaussianProcess.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.gaussianPDFReal", "kind": "definition", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.gaussianPDFReal_def", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.gaussianPDFReal_zero_var", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": true, "tactics": ["ext1", "simp"], "tactic_count": 2}
{"name": "ProbabilityTheory.gaussianPDFReal_pos", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": true, "tactics": ["rw", "positivity"], "tactic_count": 2}
{"name": "ProbabilityTheory.gaussianPDFReal_nonneg", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": true, "tactics": ["rw", "positivity"], "tactic_count": 2}
{"name": "ProbabilityTheory.measurable_gaussianPDFReal", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.stronglyMeasurable_gaussianPDFReal", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.integrable_gaussianPDFReal", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": true, "tactics": ["rw", "by_cases", "simp", "let", "have", "suffices", "rw", "refine", "simp", "ext", "simp", "neg_mul,", "hv,", "rw", "left", "field", "exact"], "tactic_count": 17}
{"name": "ProbabilityTheory.lintegral_gaussianPDFReal_eq_one", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": true, "tactics": ["rw", "have", "have", "rw", "simp", "rw", "simp", "simp_rw", "rw", "simp", "positivity"], "tactic_count": 11}
{"name": "ProbabilityTheory.integral_gaussianPDFReal_eq_one", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": true, "tactics": ["have", "rw", "rwa"], "tactic_count": 3}
{"name": "ProbabilityTheory.gaussianPDFReal_sub", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": true, "tactics": ["simp", "rw"], "tactic_count": 2}
{"name": "ProbabilityTheory.gaussianPDFReal_add", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ProbabilityTheory.gaussianPDFReal_inv_mul", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": false, "tactics": ["simp", "rw", "refine", "simp", "rw", "congr", "field"], "tactic_count": 7}
{"name": "ProbabilityTheory.gaussianPDFReal_mul", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": true, "tactics": ["conv_lhs", "simp"], "tactic_count": 2}
{"name": "ProbabilityTheory.gaussianPDF", "kind": "definition", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.gaussianPDF_def", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.gaussianPDF_zero_var", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "ProbabilityTheory.toReal_gaussianPDF", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ProbabilityTheory.gaussianPDF_pos", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ProbabilityTheory.gaussianPDF_lt_top", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ProbabilityTheory.gaussianPDF_ne_top", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ProbabilityTheory.support_gaussianPDF", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": true, "tactics": ["ext", "simp", "exact"], "tactic_count": 3}
{"name": "ProbabilityTheory.measurable_gaussianPDF", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.lintegral_gaussianPDF_eq_one", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.gaussianReal", "kind": "definition", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.gaussianReal_of_var_ne_zero", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.gaussianReal_zero_var", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.instIsProbabilityMeasureGaussianReal", "kind": "instance", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.noAtoms_gaussianReal", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "ProbabilityTheory.gaussianReal_apply", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ProbabilityTheory.gaussianReal_apply_eq_integral", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": true, "tactics": ["rw", "rfl", "exact", "exact"], "tactic_count": 4}
{"name": "ProbabilityTheory.gaussianReal_absolutelyContinuous", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ProbabilityTheory.gaussianReal_absolutelyContinuous'", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": true, "tactics": ["rw", "refine", "exact", "exact"], "tactic_count": 4}
{"name": "ProbabilityTheory.rnDeriv_gaussianReal", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "refine", "rw", "rw", "exact"], "tactic_count": 6}
{"name": "ProbabilityTheory.integral_gaussianReal_eq_integral_smul", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": true, "tactics": ["simp", "integral_withDensity_eq_integral_toReal_smul"], "tactic_count": 2}
{"name": "MeasurableEmbedding.gaussianReal_comap_apply", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": true, "tactics": ["rw", "exact", "hf.withDensity_ofReal_comap_apply_eq_integral_abs_deriv_mul"], "tactic_count": 3}
{"name": "MeasurableEquiv.gaussianReal_map_symm_apply", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": true, "tactics": ["rw", "exact", "f.withDensity_ofReal_map_symm_apply_eq_integral_abs_deriv_mul"], "tactic_count": 3}
{"name": "ProbabilityTheory.gaussianReal_map_add_const", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "exact", "let", "have", "change", "ext", "rw", "simp", "rw", "simp"], "tactic_count": 11}
{"name": "ProbabilityTheory.gaussianReal_map_const_add", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "ProbabilityTheory.gaussianReal_map_const_mul", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "exact", "by_cases", "simp", "rw", "simp", "convert", "simp", "let", "have", "suffices", "exact", "change", "ext", "rw", "swap", "simp", "rw", "simp", "simp", "congr", "suffices", "rw", "rwa"], "tactic_count": 25}
{"name": "ProbabilityTheory.gaussianReal_map_mul_const", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "ProbabilityTheory.gaussianReal_map_neg", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ProbabilityTheory.gaussianReal_map_sub_const", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "ProbabilityTheory.gaussianReal_map_const_sub", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": true, "tactics": ["simp_rw", "have", "rw"], "tactic_count": 3}
{"name": "ProbabilityTheory.gaussianReal_add_const", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.gaussianReal_const_add", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.gaussianReal_sub_const", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.gaussianReal_const_mul", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.gaussianReal_mul_const", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.gaussianReal_neg", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ProbabilityTheory.gaussianReal_const_sub", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.complexMGF_id_gaussianReal", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "calc", "simp_rw", "unfold", "push_cast", "simp_rw", "congr", "congr", "ring", "cexp", "congr", "simp", "ofReal_ofNat,", "rw", "push_cast", "ring_nf", "rw", "congr", "have", "simp", "ring"], "tactic_count": 22}
{"name": "ProbabilityTheory.complexMGF_gaussianReal", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "ProbabilityTheory.charFun_gaussianReal", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": true, "tactics": ["rw", "congr", "simp", "ring_nf"], "tactic_count": 4}
{"name": "ProbabilityTheory.mgf_gaussianReal", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": true, "tactics": ["suffices", "have", "rw", "norm_cast"], "tactic_count": 4}
{"name": "ProbabilityTheory.mgf_fun_id_gaussianReal", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": true, "tactics": ["ext", "rw", "simp"], "tactic_count": 3}
{"name": "ProbabilityTheory.mgf_id_gaussianReal", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.cgf_gaussianReal", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ProbabilityTheory.integrable_exp_mul_gaussianReal", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ProbabilityTheory.integrableExpSet_id_gaussianReal", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": true, "tactics": ["ext", "simpa"], "tactic_count": 2}
{"name": "ProbabilityTheory.integrableExpSet_fun_id_gaussianReal", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.integral_id_gaussianReal", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": true, "tactics": ["rw", "simp", "one_mul]", "rw", "simp"], "tactic_count": 5}
{"name": "ProbabilityTheory.variance_fun_id_gaussianReal", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": true, "tactics": ["rw", "simp", "calc", "rw", "simp", "have", "ext", "rw", "simp", "deriv_id'',", "ring", "rw", "simp"], "tactic_count": 13}
{"name": "ProbabilityTheory.variance_id_gaussianReal", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.memLp_id_gaussianReal", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.memLp_id_gaussianReal'", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": true, "tactics": ["lift", "exact"], "tactic_count": 2}
{"name": "ProbabilityTheory.gaussianReal_ext_iff", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": true, "tactics": ["refine", "rw", "simp", "suffices", "rw"], "tactic_count": 5}
{"name": "ProbabilityTheory.gaussianReal_map_linearMap", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": false, "tactics": ["have", "ext", "have", "conv_lhs", "rw", "congr", "simp", "positivity"], "tactic_count": 8}
{"name": "ProbabilityTheory.gaussianReal_map_continuousLinearMap", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.integral_linearMap_gaussianReal", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Gaussian.Real", "is_tactic_proof": false, "tactics": ["have", "rw", "simp"], "tactic_count": 3}
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{"name": "ProbabilityTheory.poissonPMFRealSum", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Poisson", "is_tactic_proof": true, "tactics": ["let", "unfold", "apply", "simp", "have", "ext", "rw", "rw", "exact"], "tactic_count": 9}
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{"name": "PMF.mem_support_ofMultiset_iff", "kind": "theorem", "module": "Mathlib.Probability.Distributions.Uniform", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "ProbabilityTheory.IdentDistrib.refl", "kind": "theorem", "module": "Mathlib.Probability.IdentDistrib", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IdentDistrib.symm", "kind": "theorem", "module": "Mathlib.Probability.IdentDistrib", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ProbabilityTheory.IdentDistrib.comp_of_aemeasurable", "kind": "theorem", "module": "Mathlib.Probability.IdentDistrib", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IdentDistrib.comp", "kind": "theorem", "module": "Mathlib.Probability.IdentDistrib", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ProbabilityTheory.IdentDistrib.measure_mem_eq", "kind": "theorem", "module": "Mathlib.Probability.IdentDistrib", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ProbabilityTheory.IdentDistrib.ae_snd", "kind": "theorem", "module": "Mathlib.Probability.IdentDistrib", "is_tactic_proof": true, "tactics": ["apply", "rw", "exact"], "tactic_count": 3}
{"name": "ProbabilityTheory.IdentDistrib.ae_mem_snd", "kind": "theorem", "module": "Mathlib.Probability.IdentDistrib", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IdentDistrib.aestronglyMeasurable_fst", "kind": "theorem", "module": "Mathlib.Probability.IdentDistrib", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IdentDistrib.aestronglyMeasurable_snd", "kind": "theorem", "module": "Mathlib.Probability.IdentDistrib", "is_tactic_proof": true, "tactics": ["refine", "rcases", "refine", "apply", "filter_upwards"], "tactic_count": 5}
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{"name": "ProbabilityTheory.IdentDistrib.essSup_eq", "kind": "theorem", "module": "Mathlib.Probability.IdentDistrib", "is_tactic_proof": true, "tactics": ["have", "simp_rw"], "tactic_count": 2}
{"name": "ProbabilityTheory.IdentDistrib.lintegral_eq", "kind": "theorem", "module": "Mathlib.Probability.IdentDistrib", "is_tactic_proof": true, "tactics": ["change", "rw", "h.map_eq]"], "tactic_count": 3}
{"name": "ProbabilityTheory.IdentDistrib.integral_eq", "kind": "theorem", "module": "Mathlib.Probability.IdentDistrib", "is_tactic_proof": true, "tactics": ["by_cases", "have", "rw", "rcases", "refine", "rw", "filter_upwards", "exact", "change", "rw", "rw", "rw", "rw", "rw", "rw"], "tactic_count": 15}
{"name": "ProbabilityTheory.IdentDistrib.eLpNorm_eq", "kind": "theorem", "module": "Mathlib.Probability.IdentDistrib", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "by_cases", "simp", "apply", "exact", "simp", "congr", "apply", "exact"], "tactic_count": 10}
{"name": "ProbabilityTheory.IdentDistrib.memLp_snd", "kind": "theorem", "module": "Mathlib.Probability.IdentDistrib", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "ProbabilityTheory.IdentDistrib.memLp_iff", "kind": "theorem", "module": "Mathlib.Probability.IdentDistrib", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IdentDistrib.integrable_snd", "kind": "theorem", "module": "Mathlib.Probability.IdentDistrib", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ProbabilityTheory.IdentDistrib.integrable_iff", "kind": "theorem", "module": "Mathlib.Probability.IdentDistrib", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IdentDistrib.norm", "kind": "theorem", "module": "Mathlib.Probability.IdentDistrib", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IdentDistrib.nnnorm", "kind": "theorem", "module": "Mathlib.Probability.IdentDistrib", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IdentDistrib.pow", "kind": "theorem", "module": "Mathlib.Probability.IdentDistrib", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IdentDistrib.sq", "kind": "theorem", "module": "Mathlib.Probability.IdentDistrib", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IdentDistrib.coe_nnreal_ennreal", "kind": "theorem", "module": "Mathlib.Probability.IdentDistrib", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IdentDistrib.mul_const", "kind": "theorem", "module": "Mathlib.Probability.IdentDistrib", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IdentDistrib.const_mul", "kind": "theorem", "module": "Mathlib.Probability.IdentDistrib", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IdentDistrib.div_const", "kind": "theorem", "module": "Mathlib.Probability.IdentDistrib", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IdentDistrib.const_div", "kind": "theorem", "module": "Mathlib.Probability.IdentDistrib", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IdentDistrib.inv", "kind": "theorem", "module": "Mathlib.Probability.IdentDistrib", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IdentDistrib.evariance_eq", "kind": "theorem", "module": "Mathlib.Probability.IdentDistrib", "is_tactic_proof": true, "tactics": ["convert", "rw", "rfl"], "tactic_count": 3}
{"name": "ProbabilityTheory.IdentDistrib.variance_eq", "kind": "theorem", "module": "Mathlib.Probability.IdentDistrib", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ProbabilityTheory.MemLp.uniformIntegrable_of_identDistrib_aux", "kind": "theorem", "module": "Mathlib.Probability.IdentDistrib", "is_tactic_proof": true, "tactics": ["refine", "by_cases", "swap", "obtain", "refine", "have", "ext", "simp_rw", "exact", "rw", "simp_rw", "let", "have", "have", "intro", "ext", "simp", "rw", "eLpNorm_map_measure"], "tactic_count": 19}
{"name": "ProbabilityTheory.MemLp.uniformIntegrable_of_identDistrib", "kind": "theorem", "module": "Mathlib.Probability.IdentDistrib", "is_tactic_proof": true, "tactics": ["have", "set", "have", "have", "have", "exact", "hgeq"], "tactic_count": 7}
{"name": "ProbabilityTheory.indepFun_of_identDistrib_pair", "kind": "theorem", "module": "Mathlib.Probability.IdentDistrib", "is_tactic_proof": false, "tactics": ["rw", "exact", "exact", "exact", "exact", "exact"], "tactic_count": 6}
{"name": "ProbabilityTheory.IdentDistrib.prodMk", "kind": "theorem", "module": "Mathlib.Probability.IdentDistribIndep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IdentDistrib.pi", "kind": "theorem", "module": "Mathlib.Probability.IdentDistribIndep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.term_⟂ᵢ[_]_", "kind": "definition", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory._aux_Mathlib_Probability_Independence_Basic___macroRules_ProbabilityTheory_term_⟂ᵢ[_]__1", "kind": "definition", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory._aux_Mathlib_Probability_Independence_Basic___delab_app_ProbabilityTheory_term_⟂ᵢ[_]__1", "kind": "definition", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ProbabilityTheory._aux_Mathlib_Probability_Independence_Basic___macroRules_ProbabilityTheory_term_⟂ᵢ__1", "kind": "definition", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory._aux_Mathlib_Probability_Independence_Basic___delab_app_ProbabilityTheory_term_⟂ᵢ__1", "kind": "definition", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndepSets_iff", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ProbabilityTheory.iIndepSets.meas_biInter", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndepSets.isProbabilityMeasure", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndepSets.meas_iInter", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ProbabilityTheory.IndepSets_iff", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ProbabilityTheory.iIndep_iff_iIndepSets", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ProbabilityTheory.iIndep.iIndepSets'", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndep.isProbabilityMeasure", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ProbabilityTheory.iIndep.meas_biInter", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndep.meas_iInter", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ProbabilityTheory.Indep_iff_IndepSets", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ProbabilityTheory.Indep_iff", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ProbabilityTheory.iIndepSet_iff_iIndep", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ProbabilityTheory.iIndepSet.isProbabilityMeasure", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndepSet_iff", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ProbabilityTheory.IndepSet_iff_Indep", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ProbabilityTheory.IndepSet_iff", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ProbabilityTheory.iIndepFun_iff_iIndep", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ProbabilityTheory.iIndepSets.of_subsingleton", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndep.of_subsingleton", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndepFun.of_subsingleton", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndepFun.iIndep", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndepFun_iff", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ProbabilityTheory.iIndepFun.meas_biInter", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndepFun.meas_iInter", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IndepFun_iff_Indep", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ProbabilityTheory.IndepFun_iff", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ProbabilityTheory.IndepFun.meas_inter", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndepSets.precomp", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndepSets.of_precomp", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndepSets_precomp_of_bijective", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndep.precomp", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndep.of_precomp", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndep_precomp_of_bijective", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndepSet.precomp", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndepSet.of_precomp", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndepSet_precomp_of_bijective", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndepFun.precomp", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndepFun.of_precomp", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndepFun_precomp_of_bijective", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IndepSets.symm", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.Indep.symm", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.indep_bot_right", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.indep_bot_left", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.indepSet_empty_right", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.indepSet_empty_left", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.indepSets_of_indepSets_of_le_left", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.indepSets_of_indepSets_of_le_right", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.indep_of_indep_of_le_left", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.indep_of_indep_of_le_right", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndep_of_iIndep_of_le", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IndepSets.union", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IndepSets.union_iff", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IndepSets.iUnion", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IndepSets.biUnion", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IndepSets.inter", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IndepSets.iInter", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IndepSets.bInter", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.indepSets_singleton_iff", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ProbabilityTheory.indepSets_iff_singleton_indepSets", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndepSets.indepSets", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndep.indep", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndepFun.indepFun", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndep.iIndepSets", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.Indep.indepSets", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IndepSets.indep", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IndepSets.indep'", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.indepSets_piiUnionInter_of_disjoint", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndepSet.indep_generateFrom_of_disjoint", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.indep_iSup_of_disjoint", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.indep_iSup_of_directed_le", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndepSet.indep_generateFrom_lt", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndepSet.indep_generateFrom_le", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndepSet.indep_generateFrom_le_nat", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.indep_iSup_of_monotone", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.indep_iSup_of_antitone", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndepSets.piiUnionInter_of_notMem", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndepSets.iIndep", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IndepSet.measure_inter_eq_mul", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ProbabilityTheory.Indep.indepSet_of_measurableSet", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.indep_iff_forall_indepSet", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndep_comap_mem_iff", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndepSets_singleton_iff", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "ProbabilityTheory.iIndepSet.meas_biInter", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ProbabilityTheory.iIndepSet_iff_iIndepSets_singleton", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndepSet_iff_meas_biInter", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "ProbabilityTheory.iIndepSets.iIndepSet_of_mem", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.indepFun_iff_measure_inter_preimage_eq_mul", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ProbabilityTheory.iIndepFun_iff_measure_inter_preimage_eq_mul", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ProbabilityTheory.iIndepFun_congr", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndepFun.comp", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndepFun.comp₀", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.indepFun_iff_indepSet_preimage", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ProbabilityTheory.indepFun_iff_map_prod_eq_prod_map_map'", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": true, "tactics": ["rw", "have", "μ", "constructor", "refine", "rw", "intro", "rw"], "tactic_count": 8}
{"name": "ProbabilityTheory.indepFun_iff_map_prod_eq_prod_map_map", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "ProbabilityTheory.iIndepFun_iff_map_fun_eq_pi_map", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": true, "tactics": ["classical", "rw", "have", "μ", "constructor", "congr", "rw", "rw", "congr", "simp", "constructor", "refine", "rw", "simpa", "intro", "specialize", "h₀", "simp", "rw"], "tactic_count": 19}
{"name": "ProbabilityTheory.IndepFun.symm", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IndepFun.congr", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": true, "tactics": ["refine"], "tactic_count": 1}
{"name": "ProbabilityTheory.indepFun_prod", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": true, "tactics": ["refine", "convert", "rw", "rw"], "tactic_count": 4}
{"name": "ProbabilityTheory.indepFun_prod₀", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": ["have", "refine", "rw", "apply", "exact", "rw", "exact", "rw", "apply", "exact", "rw", "exact"], "tactic_count": 12}
{"name": "ProbabilityTheory.iIndepFun_pi", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": true, "tactics": ["refine", "exact", "rw", "congr", "ext", "rw", "rw", "exact", "exact"], "tactic_count": 9}
{"name": "ProbabilityTheory.IndepFun.comp", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IndepFun.comp₀", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.indepFun_const_left", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.indepFun_const_right", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IndepFun.neg_right", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IndepFun.neg_left", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndepFun.isProbabilityMeasure", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndepFun.indepFun_finset", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndepFun.indepFun_finset₀", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndepFun.indepFun_prodMk", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndepFun.indepFun_prodMk₀", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndepFun.indepFun_prodMk_prodMk", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndepFun.indepFun_prodMk_prodMk₀", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndepFun_iff_finset", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndepFun.indepFun_mul_left", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndepFun.indepFun_mul_left₀", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndepFun.indepFun_mul_right", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndepFun.indepFun_mul_right₀", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndepFun.indepFun_mul_mul", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndepFun.indepFun_mul_mul₀", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndepFun.indepFun_div_left", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndepFun.indepFun_div_left₀", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndepFun.indepFun_div_right", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndepFun.indepFun_div_right₀", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndepFun.indepFun_div_div", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndepFun.indepFun_div_div₀", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndepFun.indepFun_finset_prod_of_notMem", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndepFun.indepFun_finset_prod_of_notMem₀", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndepFun.indepFun_prod_range_succ", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndepFun.indepFun_prod_range_succ₀", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iIndepSet.iIndepFun_indicator", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.cond_iInter", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": true, "tactics": ["have", "classical", "cases", "let", "calc", "exact", "congr", "calc", "simp", "rw", "exact", "rw", "intro", "by_cases", "obtain", "exact", "exact", "rw", "exact", "refine", "by_cases", "simp", "simp"], "tactic_count": 23}
{"name": "ProbabilityTheory.iIndepFun.cond", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": true, "tactics": ["rw", "intro", "convert", "simpa"], "tactic_count": 4}
{"name": "ProbabilityTheory.IndepFun.map_mul_eq_map_mconv_map₀'", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": true, "tactics": ["conv", "rw"], "tactic_count": 2}
{"name": "ProbabilityTheory.IndepFun.map_mul_eq_map_mconv_map'", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IndepFun.map_mul_eq_map_mconv_map₀", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "ProbabilityTheory.IndepFun.map_mul_eq_map_mconv_map", "kind": "theorem", "module": "Mathlib.Probability.Independence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IndepFun.singleton_indepSets_of_indicator", "kind": "theorem", "module": "Mathlib.Probability.Independence.BoundedContinuousFunction", "is_tactic_proof": true, "tactics": ["rw", "rintro", "rw", "have", "rw", "exact"], "tactic_count": 6}
{"name": "pi_indepFun_pi_of_prod_bcf", "kind": "theorem", "module": "Mathlib.Probability.Independence.BoundedContinuousFunction", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "convert", "any_goals", "all_goals"], "tactic_count": 6}
{"name": "pi_indepFun_pi_of_bcf", "kind": "theorem", "module": "Mathlib.Probability.Independence.BoundedContinuousFunction", "is_tactic_proof": true, "tactics": ["have", "refine", "convert", "h", "simp"], "tactic_count": 5}
{"name": "indepFun_pi_of_prod_bcf", "kind": "theorem", "module": "Mathlib.Probability.Independence.BoundedContinuousFunction", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "convert", "any_goals", "all_goals"], "tactic_count": 6}
{"name": "indepFun_pi_of_bcf", "kind": "theorem", "module": "Mathlib.Probability.Independence.BoundedContinuousFunction", "is_tactic_proof": true, "tactics": ["have", "refine", "convert"], "tactic_count": 3}
{"name": "pi_indepFun_of_prod_bcf", "kind": "theorem", "module": "Mathlib.Probability.Independence.BoundedContinuousFunction", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "convert", "any_goals", "all_goals"], "tactic_count": 6}
{"name": "pi_indepFun_of_bcf", "kind": "theorem", "module": "Mathlib.Probability.Independence.BoundedContinuousFunction", "is_tactic_proof": true, "tactics": ["have", "refine", "convert"], "tactic_count": 3}
{"name": "indepFun_of_bcf", "kind": "theorem", "module": "Mathlib.Probability.Independence.BoundedContinuousFunction", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "exact", "any_goals", "exact"], "tactic_count": 6}
{"name": "indicator_indepFun_pi_of_prod_bcf", "kind": "theorem", "module": "Mathlib.Probability.Independence.BoundedContinuousFunction", "is_tactic_proof": true, "tactics": ["refine", "have", "f", "classical", "rw", "split_ifs", "have", "classical", "rw", "split_ifs", "have", "refine", "exact", "rw", "gcongr", "exact", "simp_rw", "rw", "integral_const_mul,", "integral_const,", "simp", "ring", "exact", "exact", "exact", "exact", "exact", "exact"], "tactic_count": 28}
{"name": "indicator_indepFun_pi_of_bcf", "kind": "theorem", "module": "Mathlib.Probability.Independence.BoundedContinuousFunction", "is_tactic_proof": true, "tactics": ["have", "refine", "convert"], "tactic_count": 3}
{"name": "indicator_indepFun_of_bcf", "kind": "theorem", "module": "Mathlib.Probability.Independence.BoundedContinuousFunction", "is_tactic_proof": false, "tactics": ["suffices", "this.comp", "refine", "convert"], "tactic_count": 4}
{"name": "indepSets_comap_pi_of_prod_bcf", "kind": "theorem", "module": "Mathlib.Probability.Independence.BoundedContinuousFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "indepSets_comap_pi_of_bcf", "kind": "theorem", "module": "Mathlib.Probability.Independence.BoundedContinuousFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "indepSets_comap_of_bcf", "kind": "theorem", "module": "Mathlib.Probability.Independence.BoundedContinuousFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "indep_comap_pi_of_prod_bcf", "kind": "theorem", "module": "Mathlib.Probability.Independence.BoundedContinuousFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "indep_comap_pi_of_bcf", "kind": "theorem", "module": "Mathlib.Probability.Independence.BoundedContinuousFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "indep_comap_of_bcf", "kind": "theorem", "module": "Mathlib.Probability.Independence.BoundedContinuousFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "process_indepFun_process_of_prod_bcf", "kind": "theorem", "module": "Mathlib.Probability.Independence.BoundedContinuousFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "process_indepFun_process_of_bcf", "kind": "theorem", "module": "Mathlib.Probability.Independence.BoundedContinuousFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "indepFun_process_of_prod_bcf", "kind": "theorem", "module": "Mathlib.Probability.Independence.BoundedContinuousFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "indepFun_process_of_bcf", "kind": "theorem", "module": "Mathlib.Probability.Independence.BoundedContinuousFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "process_indepFun_of_prod_bcf", "kind": "theorem", "module": "Mathlib.Probability.Independence.BoundedContinuousFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "process_indepFun_of_bcf", "kind": "theorem", "module": "Mathlib.Probability.Independence.BoundedContinuousFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "indicator_indepFun_process_of_prod_bcf", "kind": "theorem", "module": "Mathlib.Probability.Independence.BoundedContinuousFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "indicator_indepFun_process_of_bcf", "kind": "theorem", "module": "Mathlib.Probability.Independence.BoundedContinuousFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "indepSets_comap_process_of_prod_bcf", "kind": "theorem", "module": "Mathlib.Probability.Independence.BoundedContinuousFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "indepSets_comap_process_of_bcf", "kind": "theorem", "module": "Mathlib.Probability.Independence.BoundedContinuousFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "indep_comap_process_of_prod_bcf", "kind": "theorem", "module": "Mathlib.Probability.Independence.BoundedContinuousFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "indep_comap_process_of_bcf", "kind": "theorem", "module": "Mathlib.Probability.Independence.BoundedContinuousFunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IndepFun.charFun_map_add_eq_mul", "kind": "theorem", "module": "Mathlib.Probability.Independence.CharacteristicFunction", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "ProbabilityTheory.indepFun_iff_charFun_prod", "kind": "theorem", "module": "Mathlib.Probability.Independence.CharacteristicFunction", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ProbabilityTheory.IndepFun.charFunDual_map_add_eq_mul", "kind": "theorem", "module": "Mathlib.Probability.Independence.CharacteristicFunction", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "ProbabilityTheory.indepFun_iff_charFunDual_prod", "kind": "theorem", "module": "Mathlib.Probability.Independence.CharacteristicFunction", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ProbabilityTheory.indepFun_iff_charFunDual_prod'", "kind": "theorem", "module": "Mathlib.Probability.Independence.CharacteristicFunction", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ProbabilityTheory.iIndepFun_iff_charFun_pi", "kind": "theorem", "module": "Mathlib.Probability.Independence.CharacteristicFunction", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ProbabilityTheory.iIndepFun_iff_charFunDual_pi", "kind": "theorem", "module": "Mathlib.Probability.Independence.CharacteristicFunction", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ProbabilityTheory.iIndepFun_iff_charFunDual_pi'", "kind": "theorem", "module": "Mathlib.Probability.Independence.CharacteristicFunction", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ProbabilityTheory.term_⟂ᵢ[_,_;_]_", "kind": "definition", "module": "Mathlib.Probability.Independence.Conditional", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory._aux_Mathlib_Probability_Independence_Conditional___macroRules_ProbabilityTheory_term_⟂ᵢ[_,_;_]__1", "kind": "definition", "module": "Mathlib.Probability.Independence.Conditional", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ProbabilityTheory.iCondIndepFun_iff_iCondIndep", "kind": "theorem", "module": "Mathlib.Probability.Independence.Conditional", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "ProbabilityTheory.condIndepFun_iff_condIndep", "kind": "theorem", "module": "Mathlib.Probability.Independence.Conditional", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "ProbabilityTheory.CondIndepSets.union", "kind": "theorem", "module": "Mathlib.Probability.Independence.Conditional", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ProbabilityTheory.CondIndepSets.iUnion", "kind": "theorem", "module": "Mathlib.Probability.Independence.Conditional", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ProbabilityTheory.CondIndepSets.inter", "kind": "theorem", "module": "Mathlib.Probability.Independence.Conditional", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ProbabilityTheory.condIndep_bot_right", "kind": "theorem", "module": "Mathlib.Probability.Independence.Conditional", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ProbabilityTheory.condIndep_of_condIndep_of_le_right", "kind": "theorem", "module": "Mathlib.Probability.Independence.Conditional", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ProbabilityTheory.iCondIndepFun.condIndepFun", "kind": "theorem", "module": "Mathlib.Probability.Independence.Conditional", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ProbabilityTheory.condIndep_iSup_of_disjoint", "kind": "theorem", "module": "Mathlib.Probability.Independence.Conditional", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.condIndep_iSup_of_directed_le", "kind": "theorem", "module": "Mathlib.Probability.Independence.Conditional", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iCondIndepSet.condIndep_generateFrom_lt", "kind": "theorem", "module": "Mathlib.Probability.Independence.Conditional", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ProbabilityTheory.condIndep_iSup_of_antitone", "kind": "theorem", "module": "Mathlib.Probability.Independence.Conditional", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iCondIndepSets.piiUnionInter_of_notMem", "kind": "theorem", "module": "Mathlib.Probability.Independence.Conditional", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ProbabilityTheory.iCondIndepFun.condIndepFun_finset", "kind": "theorem", "module": "Mathlib.Probability.Independence.Conditional", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iCondIndepFun.condIndepFun_prodMk", "kind": "theorem", "module": "Mathlib.Probability.Independence.Conditional", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ProbabilityTheory.iCondIndepFun.indepFun_mul_left", "kind": "theorem", "module": "Mathlib.Probability.Independence.Conditional", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iCondIndepFun.indepFun_mul_right", "kind": "theorem", "module": "Mathlib.Probability.Independence.Conditional", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ProbabilityTheory.iCondIndepFun.indepFun_div_left", "kind": "theorem", "module": "Mathlib.Probability.Independence.Conditional", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iCondIndepFun.indepFun_div_right", "kind": "theorem", "module": "Mathlib.Probability.Independence.Conditional", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iCondIndepFun.indepFun_div_div", "kind": "theorem", "module": "Mathlib.Probability.Independence.Conditional", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iCondIndepFun.condIndepFun_finset_prod_of_notMem", "kind": "theorem", "module": "Mathlib.Probability.Independence.Conditional", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iCondIndepFun.condIndepFun_prod_range_succ", "kind": "theorem", "module": "Mathlib.Probability.Independence.Conditional", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iCondIndepSet.iCondIndepFun_indicator", "kind": "theorem", "module": "Mathlib.Probability.Independence.Conditional", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ProbabilityTheory.Kernel.IndepSet.measure_inter_eq_mul", "kind": "theorem", "module": "Mathlib.Probability.Independence.Kernel.Indep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ProbabilityTheory.Kernel.indepFun_zero_left", "kind": "theorem", "module": "Mathlib.Probability.Independence.Kernel.IndepFun", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "ProbabilityTheory.Kernel.iIndepFun.of_subsingleton", "kind": "theorem", "module": "Mathlib.Probability.Independence.Kernel.IndepFun", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ProbabilityTheory.Kernel.iIndepFun.iIndep", "kind": "theorem", "module": "Mathlib.Probability.Independence.Kernel.IndepFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.Kernel.iIndepFun.ae_isProbabilityMeasure", "kind": "theorem", "module": "Mathlib.Probability.Independence.Kernel.IndepFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.Kernel.iIndepFun.meas_biInter", "kind": "theorem", "module": "Mathlib.Probability.Independence.Kernel.IndepFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ProbabilityTheory.Kernel.iIndepFun.precomp", "kind": "theorem", "module": "Mathlib.Probability.Independence.Kernel.IndepFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.Kernel.iIndepFun.of_precomp", "kind": "theorem", "module": "Mathlib.Probability.Independence.Kernel.IndepFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.Kernel.iIndepFun_precomp_of_bijective", "kind": "theorem", "module": "Mathlib.Probability.Independence.Kernel.IndepFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.Kernel.iIndepFun.indepFun", "kind": "theorem", "module": "Mathlib.Probability.Independence.Kernel.IndepFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.Kernel.indepFun_iff_measure_inter_preimage_eq_mul", "kind": "theorem", "module": "Mathlib.Probability.Independence.Kernel.IndepFun", "is_tactic_proof": true, "tactics": ["constructor", "refine", "rintro"], "tactic_count": 3}
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{"name": "ProbabilityTheory.Kernel.IndepFun.symm", "kind": "theorem", "module": "Mathlib.Probability.Independence.Kernel.IndepFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ProbabilityTheory.Kernel.indepFun_const_right", "kind": "theorem", "module": "Mathlib.Probability.Independence.Kernel.IndepFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.Kernel.IndepFun.neg_right", "kind": "theorem", "module": "Mathlib.Probability.Independence.Kernel.IndepFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.Kernel.IndepFun.neg_left", "kind": "theorem", "module": "Mathlib.Probability.Independence.Kernel.IndepFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.Kernel.indepFun_iff_compProd_map_prod_eq_compProd_prod_map_map", "kind": "theorem", "module": "Mathlib.Probability.Independence.Kernel.IndepFun", "is_tactic_proof": true, "tactics": ["classical", "rw", "refine", "rw", "intro", "rw", "refine", "have", "simp_rw", "filter_upwards", "by_cases", "swap", "simp", "rw", "map_apply", "exacts", "intro", "rw", "refine", "exact", "exact", "intro", "specialize", "rw", "convert", "rw", "rw"], "tactic_count": 27}
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{"name": "ProbabilityTheory.Kernel.iIndepFun.indepFun_div_div₀", "kind": "theorem", "module": "Mathlib.Probability.Independence.Kernel.IndepFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ProbabilityTheory.Kernel.iIndepSet.iIndepFun_indicator", "kind": "theorem", "module": "Mathlib.Probability.Independence.Kernel.IndepFun", "is_tactic_proof": true, "tactics": ["classical", "rw", "rintro", "simp_rw", "apply", "have", "refine", "exact", "exact"], "tactic_count": 9}
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{"name": "ProbabilityTheory.Kernel.IndepFun.process_indepFun_process", "kind": "theorem", "module": "Mathlib.Probability.Independence.Process", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
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{"name": "ProbabilityTheory.indep_biSup_compl", "kind": "theorem", "module": "Mathlib.Probability.Independence.ZeroOne", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ProbabilityTheory.Kernel.isSFiniteKernel_prodMkLeft_iff", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MapComap", "is_tactic_proof": true, "tactics": ["inhabit", "refine", "rw", "infer_instance"], "tactic_count": 4}
{"name": "ProbabilityTheory.Kernel.isSFiniteKernel_prodMkRight_iff", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MapComap", "is_tactic_proof": true, "tactics": ["inhabit", "refine", "rw", "infer_instance"], "tactic_count": 4}
{"name": "MeasureTheory.Measure.comp_assoc", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureComp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.comp_eq_comp_const_apply", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureComp", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.comp_eq_sum_of_countable", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureComp", "is_tactic_proof": true, "tactics": ["ext", "rw", "simp"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.snd_compProd", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureComp", "is_tactic_proof": true, "tactics": ["ext", "rw", "rfl", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.Measure.comp_congr", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureComp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.ae_ae_of_ae_comp", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureComp", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.ae_comp_of_ae_ae", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureComp", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.ae_comp_iff", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureComp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.instSFiniteBindCoeKernelOfIsSFiniteKernel", "kind": "instance", "module": "Mathlib.Probability.Kernel.Composition.MeasureComp", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.instIsFiniteMeasureBindCoeKernelOfIsFiniteKernel", "kind": "instance", "module": "Mathlib.Probability.Kernel.Composition.MeasureComp", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.instIsProbabilityMeasureBindCoeKernelOfIsMarkovKernel", "kind": "instance", "module": "Mathlib.Probability.Kernel.Composition.MeasureComp", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.instIsZeroOrProbabilityMeasureBindCoeKernelOfIsZeroOrMarkovKernel", "kind": "instance", "module": "Mathlib.Probability.Kernel.Composition.MeasureComp", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ProbabilityTheory.Kernel.comp_const", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureComp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.map_comp", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureComp", "is_tactic_proof": true, "tactics": ["ext", "rw", "simp_rw"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.discard_comp", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureComp", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.copy_comp_map", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureComp", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.compProd_eq_comp_prod", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureComp", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.compProd_id_eq_copy_comp", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureComp", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.comp_compProd_comm", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureComp", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "ext", "rw", "swap", "congr", "rw", "rfl", "exact"], "tactic_count": 9}
{"name": "MeasureTheory.Measure.prodMkLeft_comp_compProd", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureComp", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.compProd_deterministic", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureComp", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.comp_add", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureComp", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.add_comp", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureComp", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.add_comp'", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureComp", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.comp_smul", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureComp", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.AbsolutelyContinuous.comp_right", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureComp", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.AbsolutelyContinuous.comp_left", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureComp", "is_tactic_proof": true, "tactics": ["refine", "rw", "filter_upwards"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.AbsolutelyContinuous.comp", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureComp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.absolutelyContinuous_comp_of_countable", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureComp", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ProbabilityTheory.Kernel.comp_boolKernel", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureComp", "is_tactic_proof": true, "tactics": ["ext", "rw", "cases"], "tactic_count": 3}
{"name": "ProbabilityTheory.boolKernel_comp_measure", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureComp", "is_tactic_proof": true, "tactics": ["ext", "rw", "simp"], "tactic_count": 3}
{"name": "ProbabilityTheory.absolutelyContinuous_boolKernel_comp_left", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureComp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.absolutelyContinuous_boolKernel_comp_right", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureComp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.compProd", "kind": "definition", "module": "Mathlib.Probability.Kernel.Composition.MeasureCompProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.term_⊗ₘ_", "kind": "definition", "module": "Mathlib.Probability.Kernel.Composition.MeasureCompProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory._aux_Mathlib_Probability_Kernel_Composition_MeasureCompProd___macroRules_ProbabilityTheory_term_⊗ₘ__1", "kind": "definition", "module": "Mathlib.Probability.Kernel.Composition.MeasureCompProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory._aux_Mathlib_Probability_Kernel_Composition_MeasureCompProd___unexpand_MeasureTheory_Measure_compProd_1", "kind": "definition", "module": "Mathlib.Probability.Kernel.Composition.MeasureCompProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.compProd_of_not_sfinite", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureCompProd", "is_tactic_proof": true, "tactics": ["rw", "rwa"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.compProd_of_not_isSFiniteKernel", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureCompProd", "is_tactic_proof": true, "tactics": ["rw", "rwa"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.compProd_apply", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureCompProd", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.compProd_apply_univ", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureCompProd", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.compProd_apply_prod", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureCompProd", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.compProd_congr", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureCompProd", "is_tactic_proof": true, "tactics": ["rw", "congr", "refine", "simpa"], "tactic_count": 4}
{"name": "MeasureTheory.Measure.compProd_zero_left", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureCompProd", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.compProd_zero_right", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureCompProd", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.compProd_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureCompProd", "is_tactic_proof": true, "tactics": ["refine", "simp_rw", "refine", "rw", "simp", "rw", "exact"], "tactic_count": 7}
{"name": "ProbabilityTheory.Kernel.compProd_apply_eq_compProd_sectR", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureCompProd", "is_tactic_proof": true, "tactics": ["ext", "simp_rw"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.compProd_id", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureCompProd", "is_tactic_proof": true, "tactics": ["ext", "rw", "have", "simp_rw", "calc", "rw", "exact"], "tactic_count": 7}
{"name": "MeasureTheory.Measure.ae_compProd_of_ae_ae", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureCompProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.ae_ae_of_ae_compProd", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureCompProd", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.ae_compProd_iff", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureCompProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.compProd_const", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureCompProd", "is_tactic_proof": true, "tactics": ["ext", "simp_rw"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.compProd_add_left", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureCompProd", "is_tactic_proof": true, "tactics": ["by_cases", "simp_rw", "simp"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.compProd_add_right", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureCompProd", "is_tactic_proof": true, "tactics": ["by_cases", "simp_rw", "simp"], "tactic_count": 3}
{"name": "MeasureTheory.Measure.compProd_sum_left", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureCompProd", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.compProd_sum_right", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureCompProd", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.fst_compProd", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureCompProd", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.compProd_smul_left", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureCompProd", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.lintegral_compProd", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureCompProd", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.setLIntegral_compProd", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureCompProd", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.dirac_compProd_apply", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureCompProd", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.dirac_unit_compProd", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureCompProd", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.dirac_unit_compProd_const", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureCompProd", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.snd_dirac_unit_compProd_const", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureCompProd", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.instSFiniteProdCompProd", "kind": "instance", "module": "Mathlib.Probability.Kernel.Composition.MeasureCompProd", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.instIsFiniteMeasureProdCompProdOfIsFiniteKernel", "kind": "instance", "module": "Mathlib.Probability.Kernel.Composition.MeasureCompProd", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.instIsProbabilityMeasureProdCompProdOfIsMarkovKernel", "kind": "instance", "module": "Mathlib.Probability.Kernel.Composition.MeasureCompProd", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.instIsZeroOrProbabilityMeasureProdCompProdOfIsZeroOrMarkovKernel", "kind": "instance", "module": "Mathlib.Probability.Kernel.Composition.MeasureCompProd", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.compProd_assoc", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureCompProd", "is_tactic_proof": true, "tactics": ["by_cases", "swap", "by_cases", "swap", "by_cases", "swap", "ext", "rw", "swap", "congr", "rw", "congr", "exact"], "tactic_count": 13}
{"name": "MeasureTheory.Measure.compProd_assoc'", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureCompProd", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.AbsolutelyContinuous.compProd_left", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureCompProd", "is_tactic_proof": true, "tactics": ["by_cases", "have", "refine", "rw", "exact", "simp"], "tactic_count": 6}
{"name": "MeasureTheory.Measure.AbsolutelyContinuous.compProd_right", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureCompProd", "is_tactic_proof": true, "tactics": ["by_cases", "refine", "rw", "filter_upwards", "simp"], "tactic_count": 5}
{"name": "MeasureTheory.Measure.AbsolutelyContinuous.compProd", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureCompProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.absolutelyContinuous_of_compProd", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureCompProd", "is_tactic_proof": true, "tactics": ["refine", "have", "by_cases", "swap", "by_cases", "swap", "rw", "exact", "have", "rw", "swap", "by_contra", "have", "obtain", "refine", "simp", "exact"], "tactic_count": 17}
{"name": "MeasureTheory.Measure.absolutelyContinuous_compProd_left_iff", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureCompProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.AbsolutelyContinuous.compProd_of_compProd", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureCompProd", "is_tactic_proof": true, "tactics": ["by_cases", "swap", "refine", "suffices", "rw", "exact"], "tactic_count": 6}
{"name": "MeasureTheory.Measure.MutuallySingular.compProd_of_left", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureCompProd", "is_tactic_proof": true, "tactics": ["by_cases", "swap", "by_cases", "swap", "by_cases", "swap", "by_cases", "swap", "refine", "rw", "simp", "rw", "simp"], "tactic_count": 13}
{"name": "MeasureTheory.Measure.mutuallySingular_of_mutuallySingular_compProd", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureCompProd", "is_tactic_proof": true, "tactics": ["have", "have", "have", "rw", "filter_upwards", "exact", "exact", "exact", "exact", "exact"], "tactic_count": 10}
{"name": "MeasureTheory.Measure.mutuallySingular_compProd_left_iff", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureCompProd", "is_tactic_proof": true, "tactics": ["refine", "rw", "have", "rotate_left", "exact", "exact", "simp_rw", "exact"], "tactic_count": 8}
{"name": "MeasureTheory.Measure.AbsolutelyContinuous.mutuallySingular_compProd_iff", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureCompProd", "is_tactic_proof": true, "tactics": ["conv_lhs", "rw", "simp", "refine", "exact", "exact"], "tactic_count": 6}
{"name": "MeasureTheory.Measure.mutuallySingular_compProd_iff", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureCompProd", "is_tactic_proof": true, "tactics": ["conv_lhs", "rw", "simp", "rw", "refine", "exact", "refine", "infer_instance", "exact", "exact"], "tactic_count": 10}
{"name": "MeasureTheory.Measure.absolutelyContinuous_compProd_of_compProd", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureCompProd", "is_tactic_proof": true, "tactics": ["rw", "have", "absolutelyContinuous_of_add_of_mutuallySingular", "refine", "exact"], "tactic_count": 5}
{"name": "MeasureTheory.Measure.absolutelyContinuous_compProd_iff", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.MeasureCompProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.Kernel.definition._@.Mathlib.Probability.Kernel.Composition.ParallelComp.2743311029._hygCtx._hyg.8", "kind": "definition", "module": "Mathlib.Probability.Kernel.Composition.ParallelComp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.Kernel.wrapped._@.Mathlib.Probability.Kernel.Composition.ParallelComp.2743311029._hygCtx._hyg.8", "kind": "opaque", "module": "Mathlib.Probability.Kernel.Composition.ParallelComp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.Kernel.parallelComp", "kind": "definition", "module": "Mathlib.Probability.Kernel.Composition.ParallelComp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.Kernel.parallelComp_def", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.ParallelComp", "is_tactic_proof": true, "tactics": ["intros", "delta", "rw", "rfl"], "tactic_count": 4}
{"name": "ProbabilityTheory.term_∥ₖ_", "kind": "definition", "module": "Mathlib.Probability.Kernel.Composition.ParallelComp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ProbabilityTheory.Kernel.parallelComp_of_not_isSFiniteKernel_left", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.ParallelComp", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ProbabilityTheory.Kernel.parallelComp_of_not_isSFiniteKernel_right", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Composition.ParallelComp", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "ProbabilityTheory.Kernel.instIsCondKernel_zero", "kind": "instance", "module": "Mathlib.Probability.Kernel.Disintegration.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.Kernel.disintegrate", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Disintegration.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ProbabilityTheory.Kernel.condKernelCountable", "kind": "definition", "module": "Mathlib.Probability.Kernel.Disintegration.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.Kernel.condKernelCountable_apply", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Disintegration.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.Kernel.condKernelCountable.instIsMarkovKernel", "kind": "instance", "module": "Mathlib.Probability.Kernel.Disintegration.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.Kernel.condKernelCountable.instIsCondKernel", "kind": "instance", "module": "Mathlib.Probability.Kernel.Disintegration.Basic", "is_tactic_proof": true, "tactics": ["constructor", "ext", "conv_rhs", "simp_rw", "congr"], "tactic_count": 5}
{"name": "ProbabilityTheory.IsRatCondKernelCDF.mono", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Disintegration.CDFToKernel", "is_tactic_proof": true, "tactics": ["filter_upwards"], "tactic_count": 1}
{"name": "ProbabilityTheory.IsRatCondKernelCDF.tendsto_atTop_one", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Disintegration.CDFToKernel", "is_tactic_proof": true, "tactics": ["filter_upwards"], "tactic_count": 1}
{"name": "ProbabilityTheory.IsRatCondKernelCDF.tendsto_atBot_zero", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Disintegration.CDFToKernel", "is_tactic_proof": true, "tactics": ["filter_upwards"], "tactic_count": 1}
{"name": "ProbabilityTheory.IsRatCondKernelCDF.iInf_rat_gt_eq", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Disintegration.CDFToKernel", "is_tactic_proof": true, "tactics": ["filter_upwards"], "tactic_count": 1}
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{"name": "ProbabilityTheory.setIntegral_stieltjesOfMeasurableRat_rat", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Disintegration.CDFToKernel", "is_tactic_proof": true, "tactics": ["rw", "filter_upwards"], "tactic_count": 2}
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{"name": "ProbabilityTheory.IsRatCondKernelCDFAux.measurable_right", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Disintegration.CDFToKernel", "is_tactic_proof": true, "tactics": ["let", "rw", "exact"], "tactic_count": 3}
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{"name": "ProbabilityTheory.IsRatCondKernelCDFAux.le_one", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Disintegration.CDFToKernel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ProbabilityTheory.IsRatCondKernelCDFAux.bddBelow_range", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Disintegration.CDFToKernel", "is_tactic_proof": true, "tactics": ["filter_upwards", "refine", "simp"], "tactic_count": 3}
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{"name": "ProbabilityTheory.IsRatCondKernelCDFAux.isRatStieltjesPoint_ae", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Disintegration.CDFToKernel", "is_tactic_proof": false, "tactics": ["filter_upwards", "ht_iInf", "exact"], "tactic_count": 3}
{"name": "ProbabilityTheory.IsRatCondKernelCDFAux.isRatCondKernelCDF", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Disintegration.CDFToKernel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ProbabilityTheory.IsCondKernelCDF.le_one", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Disintegration.CDFToKernel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ProbabilityTheory.IsCondKernelCDF.setLIntegral", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Disintegration.CDFToKernel", "is_tactic_proof": true, "tactics": ["rw", "hf.setIntegral"], "tactic_count": 2}
{"name": "ProbabilityTheory.IsCondKernelCDF.lintegral", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Disintegration.CDFToKernel", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ProbabilityTheory.isCondKernelCDF_stieltjesOfMeasurableRat", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Disintegration.CDFToKernel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ProbabilityTheory.IsCondKernelCDF.toKernel_apply", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Disintegration.CDFToKernel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.instIsMarkovKernel_toKernel", "kind": "instance", "module": "Mathlib.Probability.Kernel.Disintegration.CDFToKernel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IsCondKernelCDF.toKernel_Iic", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Disintegration.CDFToKernel", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "ProbabilityTheory.setLIntegral_toKernel_Iic", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Disintegration.CDFToKernel", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
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{"name": "ProbabilityTheory.setLIntegral_toKernel_prod", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Disintegration.CDFToKernel", "is_tactic_proof": true, "tactics": ["induction", "empty", "basic", "obtain", "exact", "compl", "calc", "rw", "exact", "rw", "exact", "exact", "rw", "rw", "simp", "rw", "exact", "iUnion", "simp_rw", "rw", "simp_rw", "exact", "exact", "exact"], "tactic_count": 24}
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{"name": "ProbabilityTheory.compProd_toKernel", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Disintegration.CDFToKernel", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "MeasureTheory.Measure.IicSnd", "kind": "definition", "module": "Mathlib.Probability.Kernel.Disintegration.CondCDF", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.IicSnd_apply", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Disintegration.CondCDF", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "MeasureTheory.Measure.IicSnd_mono", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Disintegration.CondCDF", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.IicSnd_le_fst", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Disintegration.CondCDF", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.IicSnd_ac_fst", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Disintegration.CondCDF", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.IsFiniteMeasure.IicSnd", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Disintegration.CondCDF", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.iInf_IicSnd_gt", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Disintegration.CondCDF", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MeasureTheory.Measure.tendsto_IicSnd_atTop", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Disintegration.CondCDF", "is_tactic_proof": true, "tactics": ["simp_rw", "rw", "apply", "exact"], "tactic_count": 4}
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{"name": "ProbabilityTheory.preCDF", "kind": "definition", "module": "Mathlib.Probability.Kernel.Disintegration.CondCDF", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.measurable_preCDF", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Disintegration.CondCDF", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.measurable_preCDF'", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Disintegration.CondCDF", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ProbabilityTheory.withDensity_preCDF", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Disintegration.CondCDF", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.setLIntegral_preCDF_fst", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Disintegration.CondCDF", "is_tactic_proof": false, "tactics": ["have", "simp", "rw", "simp", "univ_inter]", "rw", "exact"], "tactic_count": 7}
{"name": "ProbabilityTheory.lintegral_preCDF_fst", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Disintegration.CondCDF", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ProbabilityTheory.monotone_preCDF", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Disintegration.CondCDF", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "ProbabilityTheory.preCDF_le_one", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Disintegration.CondCDF", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "simp", "exact"], "tactic_count": 5}
{"name": "ProbabilityTheory.setIntegral_preCDF_fst", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Disintegration.CondCDF", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact", "refine", "filter_upwards", "exact"], "tactic_count": 6}
{"name": "ProbabilityTheory.integral_preCDF_fst", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Disintegration.CondCDF", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ProbabilityTheory.integrable_preCDF", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Disintegration.CondCDF", "is_tactic_proof": true, "tactics": ["refine", "exact", "simp_rw", "rw", "refine", "filter_upwards"], "tactic_count": 6}
{"name": "ProbabilityTheory.isRatCondKernelCDFAux_preCDF", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Disintegration.CondCDF", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.isRatCondKernelCDF_preCDF", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Disintegration.CondCDF", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.condCDF", "kind": "definition", "module": "Mathlib.Probability.Kernel.Disintegration.CondCDF", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.condCDF_eq_stieltjesOfMeasurableRat_unit_prod", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Disintegration.CondCDF", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "ProbabilityTheory.isCondKernelCDF_condCDF", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Disintegration.CondCDF", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
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{"name": "ProbabilityTheory.condCDF_le_one", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Disintegration.CondCDF", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.tendsto_condCDF_atBot", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Disintegration.CondCDF", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.tendsto_condCDF_atTop", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Disintegration.CondCDF", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.condCDF_ae_eq", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Disintegration.CondCDF", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "ProbabilityTheory.ofReal_condCDF_ae_eq", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Disintegration.CondCDF", "is_tactic_proof": true, "tactics": ["filter_upwards", "rw", "exact"], "tactic_count": 3}
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{"name": "ProbabilityTheory.stronglyMeasurable_condCDF", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Disintegration.CondCDF", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.setLIntegral_condCDF", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Disintegration.CondCDF", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.lintegral_condCDF", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Disintegration.CondCDF", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.integrable_condCDF", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Disintegration.CondCDF", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.setIntegral_condCDF", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Disintegration.CondCDF", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ProbabilityTheory.measure_condCDF_Iic", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Disintegration.CondCDF", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
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{"name": "ProbabilityTheory.Kernel.setIntegral_density_of_measurableSet", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Disintegration.Density", "is_tactic_proof": false, "tactics": ["suffices", "exact", "suffices", "rw", "simp", "refine", "rw", "have", "rw"], "tactic_count": 9}
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{"name": "ProbabilityTheory.condKernel_compProd", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Disintegration.Unique", "is_tactic_proof": true, "tactics": ["suffices", "refine", "rw"], "tactic_count": 3}
{"name": "ProbabilityTheory.Kernel.apply_eq_measure_condKernel_of_compProd_eq", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Disintegration.Unique", "is_tactic_proof": false, "tactics": ["have", "ext", "conv_lhs", "rw", "rfl", "have", "rw", "filter_upwards", "rw"], "tactic_count": 9}
{"name": "ProbabilityTheory.Kernel.condKernel_apply_eq_condKernel", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Disintegration.Unique", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.condKernel_const", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Disintegration.Unique", "is_tactic_proof": true, "tactics": ["have", "simp_rw", "filter_upwards"], "tactic_count": 3}
{"name": "ProbabilityTheory.eq_condKernel_of_kernel_eq_compProd", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Disintegration.Unique", "is_tactic_proof": false, "tactics": ["filter_upwards", "rw"], "tactic_count": 2}
{"name": "ProbabilityTheory.Kernel.IsFiniteKernel.integrable", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Integral", "is_tactic_proof": false, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "ProbabilityTheory.Kernel.IsMarkovKernel.integrable", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.Kernel.integral_congr_ae₂", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Integral", "is_tactic_proof": true, "tactics": ["apply", "filter_upwards", "apply", "filter_upwards"], "tactic_count": 4}
{"name": "ProbabilityTheory.Kernel.integral_indicator₂", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Integral", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "ProbabilityTheory.Kernel.integral_deterministic'", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Integral", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ProbabilityTheory.Kernel.integral_deterministic", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Integral", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ProbabilityTheory.Kernel.setIntegral_deterministic'", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Integral", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ProbabilityTheory.Kernel.setIntegral_deterministic", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Integral", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ProbabilityTheory.Kernel.integral_const", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Integral", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ProbabilityTheory.Kernel.setIntegral_const", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Integral", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ProbabilityTheory.Kernel.integral_restrict", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Integral", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ProbabilityTheory.Kernel.setIntegral_restrict", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Integral", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ProbabilityTheory.Kernel.integral_piecewise", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Integral", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "ProbabilityTheory.Kernel.setIntegral_piecewise", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Integral", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "ProbabilityTheory.Kernel.const_bind_eq_comp_const", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Invariance", "is_tactic_proof": true, "tactics": ["ext", "simp_rw"], "tactic_count": 2}
{"name": "ProbabilityTheory.Kernel.comp_const_apply_eq_bind", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Invariance", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ProbabilityTheory.Kernel.Invariant", "kind": "definition", "module": "Mathlib.Probability.Kernel.Invariance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.Kernel.Invariant.def", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Invariance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.Kernel.Invariant.comp_const", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Invariance", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ProbabilityTheory.Kernel.Invariant.comp", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Invariance", "is_tactic_proof": true, "tactics": ["rcases", "exact", "rw"], "tactic_count": 3}
{"name": "ProbabilityTheory.Kernel.IsReversible", "kind": "definition", "module": "Mathlib.Probability.Kernel.Invariance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.Kernel.IsReversible.invariant", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Invariance", "is_tactic_proof": true, "tactics": ["ext", "calc"], "tactic_count": 2}
{"name": "IocProdIoc", "kind": "definition", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "measurable_IocProdIoc", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Maps", "is_tactic_proof": true, "tactics": ["refine", "by_cases", "simpa", "simpa"], "tactic_count": 4}
{"name": "IicProdIoc", "kind": "definition", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IicProdIoc_def", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "frestrictLe₂_comp_IicProdIoc", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Maps", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "restrict₂_comp_IicProdIoc", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Maps", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "IicProdIoc_self", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Maps", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "IicProdIoc_le", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Maps", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "IicProdIoc_comp_restrict₂", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Maps", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "measurable_IicProdIoc", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Maps", "is_tactic_proof": true, "tactics": ["refine", "by_cases", "simpa", "simpa"], "tactic_count": 4}
{"name": "MeasurableEquiv.IicProdIoc", "kind": "definition", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.coe_IicProdIoc", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.coe_IicProdIoc_symm", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.IicProdIoi", "kind": "definition", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasurableEquiv.piSingleton", "kind": "definition", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IocProdIoc_preimage", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Maps", "is_tactic_proof": true, "tactics": ["ext", "simp", "refine", "convert", "rw", "convert", "rw", "split_ifs", "exact", "exact"], "tactic_count": 10}
{"name": "IicProdIoc_preimage", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Maps", "is_tactic_proof": true, "tactics": ["ext", "simp", "refine", "convert", "rw", "convert", "rw", "split_ifs", "exact", "exact"], "tactic_count": 10}
{"name": "ProbabilityTheory.Kernel.partialTraj", "kind": "definition", "module": "Mathlib.Probability.Kernel.IonescuTulcea.PartialTraj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.Kernel.partialTraj_le", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.PartialTraj", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ProbabilityTheory.Kernel.partialTraj_self", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.PartialTraj", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ProbabilityTheory.Kernel.partialTraj_zero", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.PartialTraj", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ProbabilityTheory.Kernel.partialTraj_le_def", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.PartialTraj", "is_tactic_proof": true, "tactics": ["obtain", "simp", "rw"], "tactic_count": 3}
{"name": "ProbabilityTheory.Kernel.partialTraj_succ_of_le", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.PartialTraj", "is_tactic_proof": true, "tactics": ["rw", "induction", "base", "succ"], "tactic_count": 4}
{"name": "ProbabilityTheory.Kernel.instIsSFiniteKernelForallValNatMemFinsetIicPartialTraj", "kind": "instance", "module": "Mathlib.Probability.Kernel.IonescuTulcea.PartialTraj", "is_tactic_proof": true, "tactics": ["obtain", "induction", "base", "succ", "rw"], "tactic_count": 5}
{"name": "ProbabilityTheory.Kernel.instIsFiniteKernelForallValNatMemFinsetIicPartialTrajOfHAddOfNat", "kind": "instance", "module": "Mathlib.Probability.Kernel.IonescuTulcea.PartialTraj", "is_tactic_proof": true, "tactics": ["obtain", "induction", "base", "succ", "rw"], "tactic_count": 5}
{"name": "ProbabilityTheory.Kernel.instIsZeroOrMarkovKernelForallValNatMemFinsetIicPartialTrajOfHAddOfNat", "kind": "instance", "module": "Mathlib.Probability.Kernel.IonescuTulcea.PartialTraj", "is_tactic_proof": true, "tactics": ["obtain", "induction", "base", "succ", "rw"], "tactic_count": 5}
{"name": "ProbabilityTheory.Kernel.instIsMarkovKernelForallValNatMemFinsetIicPartialTrajOfHAddOfNat", "kind": "instance", "module": "Mathlib.Probability.Kernel.IonescuTulcea.PartialTraj", "is_tactic_proof": true, "tactics": ["obtain", "induction", "base", "succ", "rw", "have", "exact", "rw"], "tactic_count": 8}
{"name": "ProbabilityTheory.Kernel.partialTraj_succ_self", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.PartialTraj", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ProbabilityTheory.Kernel.partialTraj_succ_eq_comp", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.PartialTraj", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ProbabilityTheory.Kernel.partialTraj_comp_partialTraj", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.PartialTraj", "is_tactic_proof": true, "tactics": ["induction", "base", "succ"], "tactic_count": 3}
{"name": "_private.Mathlib.Probability.Kernel.IonescuTulcea.PartialTraj.0.ProbabilityTheory.Kernel.fst_prod_comp_id_prod", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.PartialTraj", "is_tactic_proof": true, "tactics": ["ext", "simp_rw", "id_prod_apply", "lintegral_id_prod"], "tactic_count": 4}
{"name": "ProbabilityTheory.Kernel.partialTraj_eq_prod", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.PartialTraj", "is_tactic_proof": true, "tactics": ["obtain", "rw", "all_goals", "induction", "base", "ext1", "rw", "all_goals", "succ", "hk", "have", "ext", "simp", "split_ifs", "lia", "nth_rw", "comap_prod,", "map_comp_right,", "map_comp_right,", "deterministic_congr", "comp_deterministic_eq_comap,", "partialTraj_comp_partialTraj", "map_prod_eq,", "rfl", "all_goals"], "tactic_count": 25}
{"name": "ProbabilityTheory.Kernel.map_partialTraj_succ_self", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.PartialTraj", "is_tactic_proof": false, "tactics": ["have", "ext", "simp", "rw", "map_comp_right", "symm_comp_self,"], "tactic_count": 6}
{"name": "ProbabilityTheory.Kernel.partialTraj_succ_map_frestrictLe₂", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.PartialTraj", "is_tactic_proof": true, "tactics": ["obtain", "have", "rw", "fst_eq,", "all_goals", "rw", "rfl", "fun_prop"], "tactic_count": 8}
{"name": "ProbabilityTheory.Kernel.partialTraj_map_frestrictLe₂", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.PartialTraj", "is_tactic_proof": true, "tactics": ["induction", "base", "succ", "hk", "rw", "all_goals"], "tactic_count": 6}
{"name": "ProbabilityTheory.Kernel.partialTraj_map_frestrictLe₂_apply", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.PartialTraj", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ProbabilityTheory.Kernel.partialTraj_comp_partialTraj'", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.PartialTraj", "is_tactic_proof": true, "tactics": ["obtain", "rw", "rw"], "tactic_count": 3}
{"name": "ProbabilityTheory.Kernel.partialTraj_comp_partialTraj''", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.PartialTraj", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ProbabilityTheory.Kernel.lmarginalPartialTraj", "kind": "definition", "module": "Mathlib.Probability.Kernel.IonescuTulcea.PartialTraj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.Kernel.lmarginalPartialTraj_le", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.PartialTraj", "is_tactic_proof": true, "tactics": ["ext", "rw", "congr", "simp", "exact"], "tactic_count": 5}
{"name": "ProbabilityTheory.Kernel.lmarginalPartialTraj_mono", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.PartialTraj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.Kernel.lmarginalPartialTraj_eq_lintegral_map", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.PartialTraj", "is_tactic_proof": true, "tactics": ["nth_rw", "congrm", "simp", "split_ifs", "all_goals", "all_goals"], "tactic_count": 6}
{"name": "ProbabilityTheory.Kernel.lmarginalPartialTraj_succ", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.PartialTraj", "is_tactic_proof": true, "tactics": ["rw", "congrm", "simp", "split_ifs", "all_goals", "all_goals"], "tactic_count": 6}
{"name": "ProbabilityTheory.Kernel.measurable_lmarginalPartialTraj", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.PartialTraj", "is_tactic_proof": true, "tactics": ["unfold", "let", "let", "change", "refine", "simp", "intro", "by_cases"], "tactic_count": 8}
{"name": "ProbabilityTheory.Kernel.lmarginalPartialTraj_self", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.PartialTraj", "is_tactic_proof": true, "tactics": ["ext", "obtain", "rw", "rw", "rw", "simp_rw", "updateFinset_updateFinset_of_subset", "rw", "fun_prop"], "tactic_count": 9}
{"name": "DependsOn.lmarginalPartialTraj_of_le", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.PartialTraj", "is_tactic_proof": true, "tactics": ["ext", "rw", "refine", "refine", "exact", "simp_all", "lia"], "tactic_count": 7}
{"name": "DependsOn.lmarginalPartialTraj_const_right", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.PartialTraj", "is_tactic_proof": true, "tactics": ["wlog", "rw", "obtain", "rw", "rw"], "tactic_count": 5}
{"name": "DependsOn.dependsOn_lmarginalPartialTraj", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.PartialTraj", "is_tactic_proof": true, "tactics": ["intro", "obtain", "rw", "exact", "rw", "congrm", "exact", "refine", "rwa"], "tactic_count": 9}
{"name": "_private.Mathlib.Probability.Kernel.IonescuTulcea.Traj.0.Iic_pi_eq", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Traj", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "_private.Mathlib.Probability.Kernel.IonescuTulcea.Traj.0.cast_pi", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Traj", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "_private.Mathlib.Probability.Kernel.IonescuTulcea.Traj.0.measure_cast", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Traj", "is_tactic_proof": true, "tactics": ["cases", "exact"], "tactic_count": 2}
{"name": "_private.Mathlib.Probability.Kernel.IonescuTulcea.Traj.0.heq_measurableSpace_Iic_pi", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Traj", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "iterateInduction", "kind": "definition", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Traj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "frestrictLe_iterateInduction", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Traj", "is_tactic_proof": true, "tactics": ["ext", "simp", "obtain", "rw"], "tactic_count": 4}
{"name": "MeasureTheory.isProjectiveLimit_nat_iff'", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Traj", "is_tactic_proof": true, "tactics": ["refine", "have", "rw", "all_goals"], "tactic_count": 4}
{"name": "MeasureTheory.isProjectiveLimit_nat_iff", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Traj", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "MeasureTheory.inducedFamily", "kind": "definition", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Traj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.instSFiniteForallValNatMemFinsetInducedFamilyOfForallIic", "kind": "instance", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Traj", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.instIsFiniteMeasureForallValNatMemFinsetInducedFamilyOfForallIic", "kind": "instance", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Traj", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.instIsZeroOrProbabilityMeasureForallValNatMemFinsetInducedFamilyOfForallIic", "kind": "instance", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Traj", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.instIsProbabilityMeasureForallValNatMemFinsetInducedFamilyOfForallIic", "kind": "instance", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Traj", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.inducedFamily_Iic", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Traj", "is_tactic_proof": true, "tactics": ["rw", "congr", "rw"], "tactic_count": 3}
{"name": "MeasureTheory.isProjectiveMeasureFamily_inducedFamily", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Traj", "is_tactic_proof": true, "tactics": ["intro", "have", "simp", "rw", "all_goals"], "tactic_count": 5}
{"name": "ProbabilityTheory.Kernel.isProjectiveMeasureFamily_partialTraj", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Traj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.Kernel.trajContent", "kind": "definition", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Traj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.Kernel.trajContent_cylinder", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Traj", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ProbabilityTheory.Kernel.trajContent_eq_lmarginalPartialTraj", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Traj", "is_tactic_proof": true, "tactics": ["rw", "congr", "apply", "rw", "congrm", "simp"], "tactic_count": 6}
{"name": "ProbabilityTheory.Kernel.trajContent_ne_top", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Traj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.Kernel.le_lmarginalPartialTraj_succ", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Traj", "is_tactic_proof": false, "tactics": ["have", "induction", "hz", "hi", "hm", "have", "exact", "nonempty_of_isProbabilityMeasure", "let", "lmarginalPartialTraj", "have", "have", "simp_rw", "obtain", "rw", "rw", "rw", "all_goals", "lia", "have", "simpa", "lintegral_le_const", "have", "simp_rw", "exact", "tendsto_lintegral_of_dominated_convergence", "have", "ge_of_tendsto", "let", "obtain", "have", "ne_top_of_le_ne_top", "lintegral_le_const", "obtain", "refine", "rwa", "exact", "refine", "have", "le_trans", "convert", "refine", "simp", "split_ifs", "rw", "lia"], "tactic_count": 46}
{"name": "ProbabilityTheory.Kernel.trajContent_tendsto_zero", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Traj", "is_tactic_proof": false, "tactics": ["have", "induction", "hz", "hi", "hm", "have", "exact", "nonempty_of_isProbabilityMeasure", "have", "choose", "let", "have", "simp_rw", "exact", "have", "simp_rw", "exact", "dependsOn_cylinder_indicator_const", "have", "lmarginalPartialTraj", "lmarginalPartialTraj", "refine", "rw", "simp", "have", "apply", "simp", "have", "have", "intro", "simp", "rw", "exact", "lmarginalPartialTraj_mono", "have", "obtain", "rw", "exact", "exact", "choose", "have", "have", "simp_rw", "exact", "obtain", "have", "hε", "have", "apply", "simp", "choose", "le_lmarginalPartialTraj_succ", "let", "have", "induction", "base", "succ", "intro", "convert", "ext", "simp", "split_ifs", "any_goals", "cases", "rw", "have", "simp_rw", "nth_rw", "exact", "simp_rw", "convert", "rw", "by_contra", "have", "have", "rw", "simpa", "exact", "exact"], "tactic_count": 79}
{"name": "ProbabilityTheory.Kernel.isSigmaSubadditive_trajContent", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Traj", "is_tactic_proof": false, "tactics": ["refine", "refine", "addContent_iUnion_eq_sum_of_tendsto_zero", "exact"], "tactic_count": 4}
{"name": "ProbabilityTheory.Kernel.trajFun", "kind": "definition", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Traj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.Kernel.isProbabilityMeasure_trajFun", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Traj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.Kernel.isProjectiveLimit_trajFun", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Traj", "is_tactic_proof": true, "tactics": ["refine", "ext", "rw", "projectiveFamilyContent_congr", "exact", "exact"], "tactic_count": 6}
{"name": "ProbabilityTheory.Kernel.measurable_trajFun", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Traj", "is_tactic_proof": true, "tactics": ["apply", "refine", "measurableCylinders", "obtain", "simpa", "simp_rw", "projectiveFamilyContent_congr", "refine", "exact", "have", "simpa", "simpa"], "tactic_count": 12}
{"name": "ProbabilityTheory.Kernel.traj", "kind": "definition", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Traj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.Kernel.traj_apply", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Traj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.Kernel.instIsMarkovKernelForallValNatMemFinsetIicForallTraj", "kind": "instance", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Traj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.Kernel.traj_map_frestrictLe", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Traj", "is_tactic_proof": true, "tactics": ["ext", "rw", "fun_prop"], "tactic_count": 3}
{"name": "ProbabilityTheory.Kernel.traj_map_frestrictLe_apply", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Traj", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ProbabilityTheory.Kernel.traj_map_frestrictLe_of_le", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Traj", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ProbabilityTheory.Kernel.map_traj_succ_self", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Traj", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "ProbabilityTheory.Kernel.eq_traj'", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Traj", "is_tactic_proof": true, "tactics": ["ext", "refine", "rw", "intro", "rw", "exact"], "tactic_count": 6}
{"name": "ProbabilityTheory.Kernel.eq_traj", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Traj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.Kernel.traj_comp_partialTraj", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Traj", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "ProbabilityTheory.Kernel.traj_eq_prod", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Traj", "is_tactic_proof": true, "tactics": ["refine", "rw", "conv_lhs", "rw", "conv_lhs", "rw", "partialTraj_eq_prod]", "all_goals", "all_goals", "all_goals"], "tactic_count": 10}
{"name": "ProbabilityTheory.Kernel.traj_map_updateFinset", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Traj", "is_tactic_proof": true, "tactics": ["nth_rw", "have", "simp", "rw", "all_goals"], "tactic_count": 5}
{"name": "ProbabilityTheory.Kernel.lintegral_traj₀", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Traj", "is_tactic_proof": true, "tactics": ["nth_rw", "convert", "exact", "exact"], "tactic_count": 4}
{"name": "ProbabilityTheory.Kernel.lintegral_traj", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Traj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.Kernel.integrable_traj", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Traj", "is_tactic_proof": true, "tactics": ["rw", "apply", "fun_prop", "convert", "rw", "exact"], "tactic_count": 6}
{"name": "ProbabilityTheory.Kernel.aestronglyMeasurable_traj", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Traj", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ProbabilityTheory.Kernel.integral_traj", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Traj", "is_tactic_proof": true, "tactics": ["nth_rw", "exact", "convert", "rw"], "tactic_count": 4}
{"name": "ProbabilityTheory.Kernel.partialTraj_compProd_traj", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Traj", "is_tactic_proof": true, "tactics": ["ext", "rw", "congr", "rw", "congr", "simp", "congrm", "any_goals", "all_goals", "any_goals", "fun_prop"], "tactic_count": 11}
{"name": "ProbabilityTheory.Kernel.partialTraj_compProd_eq_map_traj", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Traj", "is_tactic_proof": false, "tactics": ["have", "rfl", "rw"], "tactic_count": 3}
{"name": "ProbabilityTheory.Kernel.integral_traj_partialTraj'", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Traj", "is_tactic_proof": true, "tactics": ["have", "rw", "simp_rw", "integral_map"], "tactic_count": 4}
{"name": "ProbabilityTheory.Kernel.integral_traj_partialTraj", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Traj", "is_tactic_proof": true, "tactics": ["apply", "rw", "exact"], "tactic_count": 3}
{"name": "ProbabilityTheory.Kernel.setIntegral_traj_partialTraj'", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Traj", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "rfl", "convert", "ext", "by_cases"], "tactic_count": 6}
{"name": "ProbabilityTheory.Kernel.setIntegral_traj_partialTraj", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Traj", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "ProbabilityTheory.Kernel.condExp_traj", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Traj", "is_tactic_proof": false, "tactics": ["have", "rw", "rw", "exact", "refine", "ae_eq_condExp_of_forall_setIntegral_eq", "rw", "rintro", "simp_rw", "rw", "all_goals", "exact"], "tactic_count": 12}
{"name": "ProbabilityTheory.Kernel.condExp_traj'", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Traj", "is_tactic_proof": true, "tactics": ["have", "have", "filter_upwards", "rw", "congr", "apply", "simp", "exact", "any_goals", "exact"], "tactic_count": 10}
{"name": "ProbabilityTheory.Kernel.trajMeasure", "kind": "definition", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Traj", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.Kernel.instIsProbabilityMeasureForallTrajMeasure", "kind": "instance", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Traj", "is_tactic_proof": true, "tactics": ["rw", "have", "infer_instance"], "tactic_count": 3}
{"name": "ProbabilityTheory.Kernel.map_frestrictLe_trajMeasure_compProd_eq_map_trajMeasure", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Traj", "is_tactic_proof": false, "tactics": ["rw", "congr", "rw"], "tactic_count": 3}
{"name": "ProbabilityTheory.Kernel.condDistrib_trajMeasure", "kind": "theorem", "module": "Mathlib.Probability.Kernel.IonescuTulcea.Traj", "is_tactic_proof": true, "tactics": ["apply", "exact"], "tactic_count": 2}
{"name": "ProbabilityTheory.Kernel.instIsIrreducibleIdOfSubsingleton", "kind": "instance", "module": "Mathlib.Probability.Kernel.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.Kernel.instIsIrreducibleHSMulENNRealMeasure", "kind": "instance", "module": "Mathlib.Probability.Kernel.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.Kernel.isIrreducible_of_le_measure", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.measurableSet_integrable", "kind": "theorem", "module": "Mathlib.Probability.Kernel.MeasurableIntegral", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "ProbabilityTheory.measurableSet_kernel_integrable", "kind": "theorem", "module": "Mathlib.Probability.Kernel.MeasurableIntegral", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.StronglyMeasurable.integral_kernel", "kind": "theorem", "module": "Mathlib.Probability.Kernel.MeasurableIntegral", "is_tactic_proof": true, "tactics": ["classical", "by_cases", "simp", "borelize", "have", "let", "let", "refine", "refine", "simp_rw", "refine", "refine", "exact", "rw", "by_cases", "simp", "apply", "exact", "simp"], "tactic_count": 19}
{"name": "MeasureTheory.StronglyMeasurable.integral_kernel_prod_right", "kind": "theorem", "module": "Mathlib.Probability.Kernel.MeasurableIntegral", "is_tactic_proof": true, "tactics": ["classical", "by_cases", "simp", "borelize", "haveI", "let", "let", "let", "have", "intro", "have", "intro", "simp_rw", "simp", "refine", "refine", "simp", "apply", "exact", "have", "rw", "by_cases", "have", "apply", "filter_upwards", "simp_rw", "simp", "refine", "tendsto_integral_of_dominated_convergence", "exact", "refine", "apply", "simp", "simp", "exact"], "tactic_count": 35}
{"name": "MeasureTheory.StronglyMeasurable.integral_kernel_prod_right'", "kind": "theorem", "module": "Mathlib.Probability.Kernel.MeasurableIntegral", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.StronglyMeasurable.integral_kernel_prod_right''", "kind": "theorem", "module": "Mathlib.Probability.Kernel.MeasurableIntegral", "is_tactic_proof": false, "tactics": ["change", "apply", "have", "simpa"], "tactic_count": 4}
{"name": "MeasureTheory.StronglyMeasurable.integral_kernel_prod_left", "kind": "theorem", "module": "Mathlib.Probability.Kernel.MeasurableIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.StronglyMeasurable.integral_kernel_prod_left'", "kind": "theorem", "module": "Mathlib.Probability.Kernel.MeasurableIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.StronglyMeasurable.integral_kernel_prod_left''", "kind": "theorem", "module": "Mathlib.Probability.Kernel.MeasurableIntegral", "is_tactic_proof": true, "tactics": ["change", "apply", "have", "simpa"], "tactic_count": 4}
{"name": "ProbabilityTheory.Kernel.measurable_kernel_prodMk_left_of_finite", "kind": "theorem", "module": "Mathlib.Probability.Kernel.MeasurableLIntegral", "is_tactic_proof": true, "tactics": ["induction", "empty", "basic", "simp", "obtain", "classical", "simp_rw", "have", "ext1", "split_ifs", "exacts", "rw", "exact", "compl", "iht", "have", "intro", "ext1", "simp", "simp_rw", "have", "ext1", "rw", "exact", "exact", "rw", "exact", "iUnion", "hf", "have", "rw", "exact", "exact", "simpa"], "tactic_count": 34}
{"name": "ProbabilityTheory.Kernel.measurable_kernel_prodMk_left", "kind": "theorem", "module": "Mathlib.Probability.Kernel.MeasurableLIntegral", "is_tactic_proof": true, "tactics": ["rw", "have", "simp_rw", "refine", "exact"], "tactic_count": 5}
{"name": "ProbabilityTheory.Kernel.measurable_kernel_prodMk_left'", "kind": "theorem", "module": "Mathlib.Probability.Kernel.MeasurableLIntegral", "is_tactic_proof": true, "tactics": ["have", "simp_rw", "refine", "exact"], "tactic_count": 4}
{"name": "ProbabilityTheory.Kernel.measurable_kernel_prodMk_right", "kind": "theorem", "module": "Mathlib.Probability.Kernel.MeasurableLIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.Kernel.measurable_lintegral_indicator_const", "kind": "theorem", "module": "Mathlib.Probability.Kernel.MeasurableLIntegral", "is_tactic_proof": true, "tactics": ["unfold", "simp_rw", "exact"], "tactic_count": 3}
{"name": "Measurable.lintegral_kernel_prod_right", "kind": "theorem", "module": "Mathlib.Probability.Kernel.MeasurableLIntegral", "is_tactic_proof": true, "tactics": ["let", "have", "simp", "simp_rw", "have", "intro", "rw", "exact", "exact", "simp_rw", "refine", "refine", "intro", "simp", "exact", "intro", "simp", "have", "ext1", "rw", "rw", "exact"], "tactic_count": 22}
{"name": "Measurable.lintegral_kernel_prod_right'", "kind": "theorem", "module": "Mathlib.Probability.Kernel.MeasurableLIntegral", "is_tactic_proof": true, "tactics": ["fun_prop"], "tactic_count": 1}
{"name": "Measurable.lintegral_kernel_prod_right''", "kind": "theorem", "module": "Mathlib.Probability.Kernel.MeasurableLIntegral", "is_tactic_proof": false, "tactics": ["change", "refine", "measurable_prodMk_left", "fun_prop"], "tactic_count": 4}
{"name": "Measurable.setLIntegral_kernel_prod_right", "kind": "theorem", "module": "Mathlib.Probability.Kernel.MeasurableLIntegral", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Measurable.lintegral_kernel_prod_left'", "kind": "theorem", "module": "Mathlib.Probability.Kernel.MeasurableLIntegral", "is_tactic_proof": true, "tactics": ["fun_prop"], "tactic_count": 1}
{"name": "Measurable.lintegral_kernel_prod_left", "kind": "theorem", "module": "Mathlib.Probability.Kernel.MeasurableLIntegral", "is_tactic_proof": true, "tactics": ["fun_prop"], "tactic_count": 1}
{"name": "Measurable.setLIntegral_kernel_prod_left", "kind": "theorem", "module": "Mathlib.Probability.Kernel.MeasurableLIntegral", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Measurable.lintegral_kernel", "kind": "theorem", "module": "Mathlib.Probability.Kernel.MeasurableLIntegral", "is_tactic_proof": true, "tactics": ["fun_prop"], "tactic_count": 1}
{"name": "Measurable.setLIntegral_kernel", "kind": "theorem", "module": "Mathlib.Probability.Kernel.MeasurableLIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.posterior", "kind": "definition", "module": "Mathlib.Probability.Kernel.Posterior", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.term_†_", "kind": "definition", "module": "Mathlib.Probability.Kernel.Posterior", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory._aux_Mathlib_Probability_Kernel_Posterior___macroRules_ProbabilityTheory_term_†__1", "kind": "definition", "module": "Mathlib.Probability.Kernel.Posterior", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory._aux_Mathlib_Probability_Kernel_Posterior___unexpand_ProbabilityTheory_posterior_1", "kind": "definition", "module": "Mathlib.Probability.Kernel.Posterior", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.instIsMarkovKernelPosterior", "kind": "instance", "module": "Mathlib.Probability.Kernel.Posterior", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ProbabilityTheory.compProd_posterior_eq_map_swap", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Posterior", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ProbabilityTheory.compProd_posterior_eq_swap_comp", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Posterior", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ProbabilityTheory.swap_compProd_posterior", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Posterior", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ProbabilityTheory.parallelProd_posterior_comp_copy_comp", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Posterior", "is_tactic_proof": true, "tactics": ["calc", "rw", "rw"], "tactic_count": 3}
{"name": "ProbabilityTheory.posterior_prod_id_comp", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Posterior", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ProbabilityTheory.ae_eq_posterior_of_compProd_eq", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Posterior", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.ae_eq_posterior_of_compProd_eq_swap_comp", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Posterior", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.posterior_comp_self", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Posterior", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ProbabilityTheory.posterior_id", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Posterior", "is_tactic_proof": false, "tactics": ["suffices", "rw", "filter_upwards", "refine", "rw"], "tactic_count": 5}
{"name": "ProbabilityTheory.deterministic_comp_posterior", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Posterior", "is_tactic_proof": true, "tactics": ["refine", "calc", "μ.map", "rw", "rw", "rw", "rw", "rw", "rw"], "tactic_count": 9}
{"name": "ProbabilityTheory.absolutelyContinuous_posterior", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Posterior", "is_tactic_proof": false, "tactics": ["suffices", "rw", "simpa", "suffices", "rw", "exact", "rw", "refine", "simpa"], "tactic_count": 9}
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{"name": "ProbabilityTheory.posterior_comp", "kind": "theorem", "module": "Mathlib.Probability.Kernel.Posterior", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp_rw", "calc", "rw", "rw", "simp_rw", "conv_rhs", "rw"], "tactic_count": 9}
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{"name": "MeasureTheory.BorelCantelli.predictablePart_process_ae_eq", "kind": "theorem", "module": "Mathlib.Probability.Martingale.BorelCantelli", "is_tactic_proof": true, "tactics": ["have", "simp_rw", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.BorelCantelli.process_difference_le", "kind": "theorem", "module": "Mathlib.Probability.Martingale.BorelCantelli", "is_tactic_proof": true, "tactics": ["norm_cast", "rw", "norm_indicator_eq_indicator_norm]", "refine", "rw"], "tactic_count": 5}
{"name": "MeasureTheory.BorelCantelli.integrable_process", "kind": "theorem", "module": "Mathlib.Probability.Martingale.BorelCantelli", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.tendsto_sum_indicator_atTop_iff", "kind": "theorem", "module": "Mathlib.Probability.Martingale.BorelCantelli", "is_tactic_proof": false, "tactics": ["have", "have", "have", "refine", "filter_upwards", "filter_upwards", "constructor", "refine", "intro", "simp", "exact", "rintro", "rw", "simp", "exact", "refine", "rintro", "exact"], "tactic_count": 18}
{"name": "MeasureTheory.tendsto_sum_indicator_atTop_iff'", "kind": "theorem", "module": "Mathlib.Probability.Martingale.BorelCantelli", "is_tactic_proof": false, "tactics": ["have", "tendsto_sum_indicator_atTop_iff", "swap", "rw", "exact", "simp_rw", "simpa"], "tactic_count": 7}
{"name": "MeasureTheory.ae_mem_limsup_atTop_iff", "kind": "theorem", "module": "Mathlib.Probability.Martingale.BorelCantelli", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.predictablePart", "kind": "definition", "module": "Mathlib.Probability.Martingale.Centering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.predictablePart_zero", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Centering", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MeasureTheory.stronglyAdapted_predictablePart", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Centering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.stronglyAdapted_predictablePart'", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Centering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.martingalePart", "kind": "definition", "module": "Mathlib.Probability.Martingale.Centering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.martingalePart_add_predictablePart", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Centering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.martingalePart_eq_sum", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Centering", "is_tactic_proof": true, "tactics": ["unfold", "ext1", "rw"], "tactic_count": 3}
{"name": "MeasureTheory.stronglyAdapted_martingalePart", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Centering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.integrable_martingalePart", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Centering", "is_tactic_proof": true, "tactics": ["rw", "fun_prop"], "tactic_count": 2}
{"name": "MeasureTheory.martingale_martingalePart", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Centering", "is_tactic_proof": false, "tactics": ["refine", "have", "μ", "f", "rw", "refine", "refine", "refine", "rw", "exact", "exact", "refine", "have", "intro", "have", "condExp_condExp_of_le", "filter_upwards", "rw", "have", "k", "μ", "refine", "rw", "exact", "exact", "rw", "exact", "exact", "rw", "refine", "rw", "add_zero", "refine", "refine", "simp", "rfl"], "tactic_count": 36}
{"name": "MeasureTheory.martingalePart_add_ae_eq", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Centering", "is_tactic_proof": true, "tactics": ["set", "have", "rw", "have", "rw", "exact", "have", "hf.sub", "refine", "filter_upwards", "unfold", "rw", "rw", "simp"], "tactic_count": 14}
{"name": "MeasureTheory.predictablePart_add_ae_eq", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Centering", "is_tactic_proof": true, "tactics": ["filter_upwards", "rw", "conv_rhs", "rw"], "tactic_count": 4}
{"name": "MeasureTheory.predictablePart_bdd_difference", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Centering", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.martingalePart_bdd_difference", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Centering", "is_tactic_proof": true, "tactics": ["filter_upwards", "simp", "have", "f", "f", "ring_nf", "rw", "exact"], "tactic_count": 8}
{"name": "MeasureTheory.not_frequently_of_upcrossings_lt_top", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Convergence", "is_tactic_proof": true, "tactics": ["rw", "replace", "obtain", "exact", "rintro", "rw", "refine", "push_neg", "intro", "induction", "zero", "succ", "obtain", "obtain", "obtain", "exact"], "tactic_count": 16}
{"name": "MeasureTheory.upcrossings_eq_top_of_frequently_lt", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Convergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.tendsto_of_uncrossing_lt_top", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Convergence", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "refine", "rintro", "exact", "obtain", "exact"], "tactic_count": 7}
{"name": "MeasureTheory.Submartingale.upcrossings_ae_lt_top'", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Convergence", "is_tactic_proof": true, "tactics": ["refine", "have", "rw", "refine", "have", "simp_rw", "intro", "refine", "intro", "simp_rw", "exact", "simp_rw", "exact", "refine", "ne_of_lt", "le_trans", "refine", "rw", "by_cases", "rw", "rw", "exact", "finiteness", "simp", "left", "left"], "tactic_count": 26}
{"name": "MeasureTheory.Submartingale.upcrossings_ae_lt_top", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Convergence", "is_tactic_proof": true, "tactics": ["simp", "rintro", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.Submartingale.exists_ae_tendsto_of_bdd", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Convergence", "is_tactic_proof": false, "tactics": ["filter_upwards", "ae_bdd_liminf_atTop_of_eLpNorm_bdd", "hbdd]", "ω", "exact"], "tactic_count": 5}
{"name": "MeasureTheory.Submartingale.exists_ae_trim_tendsto_of_bdd", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Convergence", "is_tactic_proof": true, "tactics": ["letI", "rw", "exact", "exact", "measurableSet_exists_tendsto"], "tactic_count": 5}
{"name": "MeasureTheory.Submartingale.ae_tendsto_limitProcess", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Convergence", "is_tactic_proof": true, "tactics": ["classical", "suffices", "rw", "exact", "set", "have", "have", "filter_upwards", "simp_rw", "exact", "have", "hg').aestronglyMeasurable", "obtain", "have", "filter_upwards", "exact", "exact"], "tactic_count": 17}
{"name": "MeasureTheory.Submartingale.memLp_limitProcess", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Convergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Submartingale.tendsto_eLpNorm_one_limitProcess", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Convergence", "is_tactic_proof": true, "tactics": ["obtain", "have", "exact", "tendsto_Lp_finite_of_tendstoInMeasure", "hunif.2.1"], "tactic_count": 5}
{"name": "MeasureTheory.Submartingale.ae_tendsto_limitProcess_of_uniformIntegrable", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Convergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Martingale.eq_condExp_of_tendsto_eLpNorm", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Convergence", "is_tactic_proof": false, "tactics": ["rw", "eLpNorm_eq_zero_iff", "one_ne_zero]", "have", "haveI", "tendsto_of_tendsto_of_tendsto_of_le_of_le", "eLpNorm_one_condExp_le_eLpNorm", "have", "refine", "filter_upwards", "simp", "exact"], "tactic_count": 12}
{"name": "MeasureTheory.Martingale.ae_eq_condExp_limitProcess", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Convergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Integrable.tendsto_ae_condExp", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Convergence", "is_tactic_proof": true, "tactics": ["have", "have", "obtain", "have", "suffices", "filter_upwards", "rwa", "have", "intro", "rw", "refine", "filter_upwards", "rw", "refine", "ae_eq_of_forall_setIntegral_eq_of_sigmaFinite", "stronglyMeasurable_limitProcess.aestronglyMeasurable", "have", "rw", "exact", "induction", "empty", "basic", "rcases", "exact", "compl", "ht", "have", "have", "rw", "hgeq,", "integral_trim", "this", "iUnion", "heq", "rw", "integral_iUnion", "exact"], "tactic_count": 37}
{"name": "MeasureTheory.Integrable.tendsto_eLpNorm_condExp", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Convergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.tendsto_ae_condExp", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Convergence", "is_tactic_proof": false, "tactics": ["have", "integrable_condExp.tendsto_ae_condExp", "have", "condExp_condExp_of_le", "rw", "filter_upwards", "exact"], "tactic_count": 7}
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{"name": "MeasureTheory.Martingale.condExp_stopping_time_ae_eq_restrict_eq_const", "kind": "theorem", "module": "Mathlib.Probability.Martingale.OptionalSampling", "is_tactic_proof": true, "tactics": ["refine", "refine", "condExp_ae_eq_restrict_of_measurableSpace_eq_on", "rw"], "tactic_count": 4}
{"name": "MeasureTheory.Martingale.condExp_stopping_time_ae_eq_restrict_eq_const_of_le_const", "kind": "theorem", "module": "Mathlib.Probability.Martingale.OptionalSampling", "is_tactic_proof": true, "tactics": ["by_cases", "refine", "refine", "condExp_ae_eq_restrict_of_measurableSpace_eq_on", "rw", "suffices", "ext1", "simp", "contrapose", "exact_mod_cast"], "tactic_count": 10}
{"name": "MeasureTheory.Martingale.stoppedValue_ae_eq_restrict_eq", "kind": "theorem", "module": "Mathlib.Probability.Martingale.OptionalSampling", "is_tactic_proof": false, "tactics": ["refine", "rw", "refine", "rw", "simp"], "tactic_count": 5}
{"name": "MeasureTheory.Martingale.stoppedValue_ae_eq_condExp_of_le_const_of_countable_range", "kind": "theorem", "module": "Mathlib.Probability.Martingale.OptionalSampling", "is_tactic_proof": false, "tactics": ["have", "ext1", "simp", "exists_apply_eq_apply']", "nth_rw", "rw", "intro", "have", "simp", "obtain", "specialize", "simp", "lift", "exact"], "tactic_count": 14}
{"name": "MeasureTheory.Martingale.stoppedValue_ae_eq_condExp_of_le_const", "kind": "theorem", "module": "Mathlib.Probability.Martingale.OptionalSampling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Martingale.stoppedValue_ae_eq_condExp_of_le_of_countable_range", "kind": "theorem", "module": "Mathlib.Probability.Martingale.OptionalSampling", "is_tactic_proof": false, "tactics": ["have", "sigmaFiniteTrim_mono", "have", "condExp_congr_ae", "refine", "exact", "h.stoppedValue_ae_eq_condExp_of_le_const_of_countable_range", "hσ_countable_range", "exact"], "tactic_count": 9}
{"name": "MeasureTheory.Martingale.stoppedValue_ae_eq_condExp_of_le", "kind": "theorem", "module": "Mathlib.Probability.Martingale.OptionalSampling", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Martingale.condExp_stoppedValue_stopping_time_ae_eq_restrict_le", "kind": "theorem", "module": "Mathlib.Probability.Martingale.OptionalSampling", "is_tactic_proof": true, "tactics": ["rw", "refine", "have", "refine", "exact", "have", "refine", "refine", "intro", "rw", "rw", "exact", "refine", "refine", "exact", "intro", "simp", "exact"], "tactic_count": 18}
{"name": "MeasureTheory.Martingale.stoppedValue_min_ae_eq_condExp", "kind": "theorem", "module": "Mathlib.Probability.Martingale.OptionalSampling", "is_tactic_proof": true, "tactics": ["refine", "refine", "exact", "suffices", "μ", "μ", "rw", "rw", "swap", "filter_upwards", "simp", "exact", "apply", "exact", "rw", "have", "apply", "exact", "exact", "rw", "exact"], "tactic_count": 21}
{"name": "MeasureTheory.Submartingale.expected_stoppedValue_mono", "kind": "theorem", "module": "Mathlib.Probability.Martingale.OptionalStopping", "is_tactic_proof": true, "tactics": ["rw", "simp", "have", "intro", "refine", "convert", "ext", "simp", "rw", "refine", "rw", "exact", "exact", "exact", "intro", "exact", "exact", "exact"], "tactic_count": 18}
{"name": "MeasureTheory.submartingale_of_expected_stoppedValue_mono", "kind": "theorem", "module": "Mathlib.Probability.Martingale.OptionalStopping", "is_tactic_proof": true, "tactics": ["refine", "classical", "specialize", "hf", "intro", "simp", "split_ifs", "exact", "norm_cast", "rwa", "integral_piecewise", "integral_add_compl"], "tactic_count": 12}
{"name": "MeasureTheory.submartingale_iff_expected_stoppedValue_mono", "kind": "theorem", "module": "Mathlib.Probability.Martingale.OptionalStopping", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Submartingale.stoppedProcess", "kind": "theorem", "module": "Mathlib.Probability.Martingale.OptionalStopping", "is_tactic_proof": true, "tactics": ["rw", "intro", "simp_rw", "obtain", "have", "have", "simp", "exact", "h.expected_stoppedValue_mono", "exact", "exact"], "tactic_count": 11}
{"name": "MeasureTheory.smul_le_stoppedValue_hittingBtwn", "kind": "theorem", "module": "Mathlib.Probability.Martingale.OptionalStopping", "is_tactic_proof": true, "tactics": ["have", "have", "intro", "simp_rw", "refine", "simp", "exact", "let", "have", "setIntegral_ge_of_const_le_real", "rw", "exact", "exact", "exact"], "tactic_count": 14}
{"name": "MeasureTheory.maximal_ineq", "kind": "theorem", "module": "Mathlib.Probability.Martingale.OptionalStopping", "is_tactic_proof": false, "tactics": ["suffices", "ε", "have", "rw", "rw", "convert", "ext", "change", "simp", "rw", "rintro", "change", "change", "exact", "exact", "measurableSet_lt", "measurable_const", "exacts", "integral_nonneg", "rwa", "calc", "ε", "stoppedValue", "stoppedValue", "gcongr", "exact", "exact", "refine", "refine", "exact", "exact", "nullMeasurableSet_lt", "aemeasurable_const", "rw", "have", "classical", "intro", "exact", "simp", "refine", "congr", "rw", "rw", "convert", "ext", "change", "simp", "rw", "rintro", "change", "change", "exact", "exact", "measurableSet_lt", "measurable_const", "exact", "exact", "exacts", "refine", "rw", "refine", "hsub.expected_stoppedValue_mono", "simp"], "tactic_count": 63}
{"name": "MeasureTheory.lowerCrossingTimeAux", "kind": "definition", "module": "Mathlib.Probability.Martingale.Upcrossing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.upperCrossingTime", "kind": "definition", "module": "Mathlib.Probability.Martingale.Upcrossing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.lowerCrossingTime", "kind": "definition", "module": "Mathlib.Probability.Martingale.Upcrossing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.upperCrossingTime_zero", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Upcrossing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.lowerCrossingTime_zero", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Upcrossing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.upperCrossingTime_succ", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Upcrossing", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MeasureTheory.upperCrossingTime_succ_eq", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Upcrossing", "is_tactic_proof": true, "tactics": ["simp", "rfl"], "tactic_count": 2}
{"name": "MeasureTheory.upperCrossingTime_le", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Upcrossing", "is_tactic_proof": true, "tactics": ["cases", "simp", "simp"], "tactic_count": 3}
{"name": "MeasureTheory.upperCrossingTime_zero'", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Upcrossing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.lowerCrossingTime_le", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Upcrossing", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.upperCrossingTime_le_lowerCrossingTime", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Upcrossing", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.lowerCrossingTime_le_upperCrossingTime_succ", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Upcrossing", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.lowerCrossingTime_mono", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Upcrossing", "is_tactic_proof": true, "tactics": ["suffices", "exact", "monotone_nat_of_le_succ", "le_trans"], "tactic_count": 4}
{"name": "MeasureTheory.upperCrossingTime_mono", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Upcrossing", "is_tactic_proof": true, "tactics": ["suffices", "exact", "monotone_nat_of_le_succ", "le_trans"], "tactic_count": 4}
{"name": "MeasureTheory.stoppedValue_lowerCrossingTime", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Upcrossing", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.stoppedValue_upperCrossingTime", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Upcrossing", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.upperCrossingTime_lt_lowerCrossingTime", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Upcrossing", "is_tactic_proof": false, "tactics": ["refine", "lt_of_le_of_ne", "not_le.2", "simp", "rw", "exact"], "tactic_count": 6}
{"name": "MeasureTheory.lowerCrossingTime_lt_upperCrossingTime", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Upcrossing", "is_tactic_proof": false, "tactics": ["refine", "lt_of_le_of_ne", "not_le.2", "simp", "rw", "exact"], "tactic_count": 6}
{"name": "MeasureTheory.upperCrossingTime_lt_succ", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Upcrossing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.lowerCrossingTime_stabilize", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Upcrossing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.upperCrossingTime_stabilize", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Upcrossing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.lowerCrossingTime_stabilize'", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Upcrossing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.upperCrossingTime_stabilize'", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Upcrossing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.exists_upperCrossingTime_eq", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Upcrossing", "is_tactic_proof": true, "tactics": ["by_contra", "have", "strictMono_nat_of_lt_succ", "obtain", "exact"], "tactic_count": 5}
{"name": "MeasureTheory.upperCrossingTime_lt_bddAbove", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Upcrossing", "is_tactic_proof": true, "tactics": ["obtain", "refine", "by_contra", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.upperCrossingTime_lt_nonempty", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Upcrossing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.upperCrossingTime_bound_eq", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Upcrossing", "is_tactic_proof": true, "tactics": ["by_cases", "refine", "have", "refine", "rw", "convert", "convert", "rw", "exact"], "tactic_count": 9}
{"name": "MeasureTheory.upperCrossingTime_eq_of_bound_le", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Upcrossing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.StronglyAdapted.isStoppingTime_crossing", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Upcrossing", "is_tactic_proof": true, "tactics": ["induction", "zero", "refine", "simp", "exact", "succ", "ih", "have", "intro", "simp_rw", "refine", "simp", "refine", "refine", "simp"], "tactic_count": 15}
{"name": "MeasureTheory.StronglyAdapted.isStoppingTime_upperCrossingTime", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Upcrossing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.StronglyAdapted.isStoppingTime_lowerCrossingTime", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Upcrossing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.upcrossingStrat", "kind": "definition", "module": "Mathlib.Probability.Martingale.Upcrossing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.upcrossingStrat_nonneg", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Upcrossing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.upcrossingStrat_le_one", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Upcrossing", "is_tactic_proof": true, "tactics": ["rw", "exact", "intro", "simp", "obtain", "rw", "upperCrossingTime", "max_eq_right", "refine", "rw", "upperCrossingTime", "max_eq_left", "refine"], "tactic_count": 13}
{"name": "MeasureTheory.StronglyAdapted.upcrossingStrat", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Upcrossing", "is_tactic_proof": true, "tactics": ["intro", "change", "refine", "have", "have", "simp", "simp_rw", "exact"], "tactic_count": 8}
{"name": "MeasureTheory.Submartingale.sum_upcrossingStrat_mul", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Upcrossing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Submartingale.sum_sub_upcrossingStrat_mul", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Upcrossing", "is_tactic_proof": false, "tactics": ["refine", "hf.sum_mul_sub", "exact", "intro", "simp"], "tactic_count": 5}
{"name": "MeasureTheory.Submartingale.sum_mul_upcrossingStrat_le", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Upcrossing", "is_tactic_proof": false, "tactics": ["have", "have", "rw", "refine", "simp", "have", "μ", "μ", "μ", "simp", "refine", "integral_sub", "convert", "ext", "rw", "refine", "simp_rw"], "tactic_count": 17}
{"name": "MeasureTheory.upcrossingsBefore", "kind": "definition", "module": "Mathlib.Probability.Martingale.Upcrossing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.upcrossingsBefore_bot", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Upcrossing", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.upcrossingsBefore_zero", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Upcrossing", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.upcrossingsBefore_zero'", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Upcrossing", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "MeasureTheory.upperCrossingTime_lt_of_le_upcrossingsBefore", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Upcrossing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.upperCrossingTime_eq_of_upcrossingsBefore_lt", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Upcrossing", "is_tactic_proof": true, "tactics": ["refine", "convert"], "tactic_count": 2}
{"name": "MeasureTheory.upcrossingsBefore_le", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Upcrossing", "is_tactic_proof": true, "tactics": ["by_cases", "subst", "rw", "refine", "by_contra", "exact"], "tactic_count": 6}
{"name": "MeasureTheory.crossing_eq_crossing_of_lowerCrossingTime_lt", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Upcrossing", "is_tactic_proof": true, "tactics": ["have", "induction", "zero", "simp", "refine", "rw", "obtain", "exact", "exact", "succ", "ih", "specialize", "ih", "have", "rw", "simp", "obtain", "rw", "exact", "exact", "refine", "simp", "refine", "rw", "obtain", "exact"], "tactic_count": 26}
{"name": "MeasureTheory.crossing_eq_crossing_of_upperCrossingTime_lt", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Upcrossing", "is_tactic_proof": false, "tactics": ["have", "refine", "rw", "refine", "rw", "obtain", "exact", "exact"], "tactic_count": 8}
{"name": "MeasureTheory.upperCrossingTime_eq_upperCrossingTime_of_lt", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Upcrossing", "is_tactic_proof": true, "tactics": ["cases", "simp", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.upcrossingsBefore_mono", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Upcrossing", "is_tactic_proof": true, "tactics": ["intro", "simp", "gcongr", "exact", "intro", "rw", "exact"], "tactic_count": 7}
{"name": "MeasureTheory.upcrossingsBefore_lt_of_exists_upcrossing", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Upcrossing", "is_tactic_proof": true, "tactics": ["refine", "rw", "refine", "rw", "refine", "by_cases", "have", "rw", "exact", "rw", "rw"], "tactic_count": 11}
{"name": "MeasureTheory.lowerCrossingTime_lt_of_lt_upcrossingsBefore", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Upcrossing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.le_sub_of_le_upcrossingsBefore", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Upcrossing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.sub_eq_zero_of_upcrossingsBefore_lt", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Upcrossing", "is_tactic_proof": false, "tactics": ["have", "rw", "rw", "exact", "simp", "lowerCrossingTime_stabilize"], "tactic_count": 6}
{"name": "MeasureTheory.mul_upcrossingsBefore_le", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Upcrossing", "is_tactic_proof": true, "tactics": ["classical", "by_cases", "simp", "simp_rw", "rw", "have", "stoppedValue", "stoppedValue", "intro", "rw", "rfl", "ext", "simp", "exact", "simp_rw", "have", "stoppedValue", "calc", "stoppedValue", "gcongr", "refine", "rwa", "stoppedValue", "refine", "by_cases", "subst", "simp", "rw", "by_cases", "rw", "rw", "exact", "rw", "rw", "exact", "refine", "rw"], "tactic_count": 37}
{"name": "MeasureTheory.integral_mul_upcrossingsBefore_le_integral", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Upcrossing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.crossing_pos_eq", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Upcrossing", "is_tactic_proof": true, "tactics": ["have", "have", "intro", "refine", "rwa", "rw", "rwa", "have", "induction", "zero", "refine", "simp", "simp_all", "succ", "ih", "have", "ext", "simp", "split_ifs", "simp_rw", "refine", "simp_all", "refine", "simp_all", "rfl", "refine", "ext", "simp", "split_ifs", "simp_rw", "refine", "simp_all", "refine", "simp_all", "rfl"], "tactic_count": 35}
{"name": "MeasureTheory.upcrossingsBefore_pos_eq", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Upcrossing", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MeasureTheory.mul_integral_upcrossingsBefore_le_integral_pos_part_aux", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Upcrossing", "is_tactic_proof": false, "tactics": ["refine", "le_trans", "simp_rw", "rfl"], "tactic_count": 4}
{"name": "MeasureTheory.Submartingale.mul_integral_upcrossingsBefore_le_integral_pos_part", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Upcrossing", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "rw", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.upcrossingsBefore_eq_sum", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Upcrossing", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "rw", "have", "rintro", "rw", "rw", "rfl", "exact", "have", "rintro", "rw", "rw", "simp", "exact", "rw", "smul_eq_mul,"], "tactic_count": 17}
{"name": "MeasureTheory.StronglyAdapted.measurable_upcrossingsBefore", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Upcrossing", "is_tactic_proof": false, "tactics": ["have", "upcrossingsBefore", "ext", "exact", "rw", "refine", "simpa"], "tactic_count": 7}
{"name": "MeasureTheory.StronglyAdapted.integrable_upcrossingsBefore", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Upcrossing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.upcrossings", "kind": "definition", "module": "Mathlib.Probability.Martingale.Upcrossing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.StronglyAdapted.measurable_upcrossings", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Upcrossing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.upcrossings_lt_top_iff", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Upcrossing", "is_tactic_proof": false, "tactics": ["have", "constructor", "intro", "lift", "exact", "rintro", "exact", "simp_rw", "constructor", "obtain", "refine", "rwa", "refine", "simp"], "tactic_count": 14}
{"name": "MeasureTheory.Submartingale.mul_lintegral_upcrossings_le_lintegral_pos_part", "kind": "theorem", "module": "Mathlib.Probability.Martingale.Upcrossing", "is_tactic_proof": true, "tactics": ["by_cases", "simp_rw", "have", "intro", "rw", "exact", "exact", "rw", "simp_rw", "intro", "rw", "lintegral_coe_eq_integral,", "simp_rw", "exact", "simp", "exact", "measurable_from_top.comp_aemeasurable", "filter_upwards", "rw", "exact", "rw", "rw", "exact"], "tactic_count": 23}
{"name": "ProbabilityTheory.moment", "kind": "definition", "module": "Mathlib.Probability.Moments.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.moment_def", "kind": "theorem", "module": "Mathlib.Probability.Moments.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.centralMoment", "kind": "definition", "module": "Mathlib.Probability.Moments.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.moment_zero", "kind": "theorem", "module": "Mathlib.Probability.Moments.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ProbabilityTheory.moment_zero_measure", "kind": "theorem", "module": "Mathlib.Probability.Moments.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ProbabilityTheory.centralMoment_zero", "kind": "theorem", "module": "Mathlib.Probability.Moments.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ProbabilityTheory.moment_one", "kind": "theorem", "module": "Mathlib.Probability.Moments.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ProbabilityTheory.centralMoment_zero_measure", "kind": "theorem", "module": "Mathlib.Probability.Moments.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ProbabilityTheory.centralMoment_one'", "kind": "theorem", "module": "Mathlib.Probability.Moments.Basic", "is_tactic_proof": true, "tactics": ["simp", "rw", "simp"], "tactic_count": 3}
{"name": "ProbabilityTheory.centralMoment_one", "kind": "theorem", "module": "Mathlib.Probability.Moments.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simp", "by_cases", "rw", "simp", "simp", "have", "refine", "have", "rw", "fun_prop", "rw"], "tactic_count": 12}
{"name": "ProbabilityTheory.centralMoment_two_eq_variance", "kind": "theorem", "module": "Mathlib.Probability.Moments.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.centralMoment_congr_ae", "kind": "theorem", "module": "Mathlib.Probability.Moments.Basic", "is_tactic_proof": true, "tactics": ["simp", "refine", "filter_upwards"], "tactic_count": 3}
{"name": "ProbabilityTheory.mgf", "kind": "definition", "module": "Mathlib.Probability.Moments.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.cgf", "kind": "definition", "module": "Mathlib.Probability.Moments.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.mgf_zero_fun", "kind": "theorem", "module": "Mathlib.Probability.Moments.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ProbabilityTheory.cgf_zero_fun", "kind": "theorem", "module": "Mathlib.Probability.Moments.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ProbabilityTheory.mgf_zero_measure", "kind": "theorem", "module": "Mathlib.Probability.Moments.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "ProbabilityTheory.cgf_zero_measure", "kind": "theorem", "module": "Mathlib.Probability.Moments.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "ProbabilityTheory.mgf_const'", "kind": "theorem", "module": "Mathlib.Probability.Moments.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ProbabilityTheory.mgf_const", "kind": "theorem", "module": "Mathlib.Probability.Moments.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ProbabilityTheory.cgf_const'", "kind": "theorem", "module": "Mathlib.Probability.Moments.Basic", "is_tactic_proof": true, "tactics": ["simp", "rw", "rw", "rw", "simp"], "tactic_count": 5}
{"name": "ProbabilityTheory.cgf_const", "kind": "theorem", "module": "Mathlib.Probability.Moments.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ProbabilityTheory.mgf_zero'", "kind": "theorem", "module": "Mathlib.Probability.Moments.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ProbabilityTheory.mgf_zero", "kind": "theorem", "module": "Mathlib.Probability.Moments.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ProbabilityTheory.cgf_zero'", "kind": "theorem", "module": "Mathlib.Probability.Moments.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ProbabilityTheory.cgf_zero", "kind": "theorem", "module": "Mathlib.Probability.Moments.Basic", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "ProbabilityTheory.mgf_undef", "kind": "theorem", "module": "Mathlib.Probability.Moments.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ProbabilityTheory.cgf_undef", "kind": "theorem", "module": "Mathlib.Probability.Moments.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ProbabilityTheory.mgf_nonneg", "kind": "theorem", "module": "Mathlib.Probability.Moments.Basic", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "ProbabilityTheory.mgf_pos'", "kind": "theorem", "module": "Mathlib.Probability.Moments.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "have", "rw", "have", "ext1", "simp", "exact", "rw", "refine", "simp", "filter_upwards", "rw", "exact", "rwa"], "tactic_count": 14}
{"name": "ProbabilityTheory.mgf_pos", "kind": "theorem", "module": "Mathlib.Probability.Moments.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.mgf_pos_iff", "kind": "theorem", "module": "Mathlib.Probability.Moments.Basic", "is_tactic_proof": true, "tactics": ["refine", "contrapose", "simp"], "tactic_count": 3}
{"name": "ProbabilityTheory.exp_cgf", "kind": "theorem", "module": "Mathlib.Probability.Moments.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ProbabilityTheory.mgf_map", "kind": "theorem", "module": "Mathlib.Probability.Moments.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "ProbabilityTheory.mgf_id_map", "kind": "theorem", "module": "Mathlib.Probability.Moments.Basic", "is_tactic_proof": true, "tactics": ["ext", "rw", "exact"], "tactic_count": 3}
{"name": "ProbabilityTheory.mgf_congr", "kind": "theorem", "module": "Mathlib.Probability.Moments.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.mgf_congr_identDistrib", "kind": "theorem", "module": "Mathlib.Probability.Moments.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ProbabilityTheory.mgf_neg", "kind": "theorem", "module": "Mathlib.Probability.Moments.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "ProbabilityTheory.cgf_neg", "kind": "theorem", "module": "Mathlib.Probability.Moments.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "ProbabilityTheory.mgf_smul_left", "kind": "theorem", "module": "Mathlib.Probability.Moments.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "ProbabilityTheory.mgf_const_mul", "kind": "theorem", "module": "Mathlib.Probability.Moments.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.mgf_const_add", "kind": "theorem", "module": "Mathlib.Probability.Moments.Basic", "is_tactic_proof": true, "tactics": ["rw", "congr", "dsimp", "rw"], "tactic_count": 4}
{"name": "ProbabilityTheory.mgf_add_const", "kind": "theorem", "module": "Mathlib.Probability.Moments.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ProbabilityTheory.mgf_add_measure", "kind": "theorem", "module": "Mathlib.Probability.Moments.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ProbabilityTheory.mgf_sum_measure", "kind": "theorem", "module": "Mathlib.Probability.Moments.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "ProbabilityTheory.mgf_smul_measure", "kind": "theorem", "module": "Mathlib.Probability.Moments.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ProbabilityTheory.mgf_mono_of_nonneg", "kind": "theorem", "module": "Mathlib.Probability.Moments.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "refine", "filter_upwards", "rw", "exact"], "tactic_count": 5}
{"name": "ProbabilityTheory.mgf_anti_of_nonpos", "kind": "theorem", "module": "Mathlib.Probability.Moments.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "refine", "filter_upwards", "rw", "exact"], "tactic_count": 5}
{"name": "ProbabilityTheory.IndepFun.exp_mul", "kind": "theorem", "module": "Mathlib.Probability.Moments.Basic", "is_tactic_proof": true, "tactics": ["have", "change", "exact"], "tactic_count": 3}
{"name": "ProbabilityTheory.IndepFun.mgf_add", "kind": "theorem", "module": "Mathlib.Probability.Moments.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "ProbabilityTheory.IndepFun.mgf_add'", "kind": "theorem", "module": "Mathlib.Probability.Moments.Basic", "is_tactic_proof": true, "tactics": ["have", "have", "have", "exact"], "tactic_count": 4}
{"name": "ProbabilityTheory.IndepFun.cgf_add", "kind": "theorem", "module": "Mathlib.Probability.Moments.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "simp", "exact"], "tactic_count": 4}
{"name": "ProbabilityTheory.aestronglyMeasurable_exp_mul_add", "kind": "theorem", "module": "Mathlib.Probability.Moments.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "ProbabilityTheory.aestronglyMeasurable_exp_mul_sum", "kind": "theorem", "module": "Mathlib.Probability.Moments.Basic", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "simp", "exact", "insert", "h_rec", "have", "h_int", "specialize", "rw", "apply"], "tactic_count": 12}
{"name": "ProbabilityTheory.IndepFun.integrable_exp_mul_add", "kind": "theorem", "module": "Mathlib.Probability.Moments.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "ProbabilityTheory.iIndepFun.integrable_exp_mul_sum", "kind": "theorem", "module": "Mathlib.Probability.Moments.Basic", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "simp", "exact", "insert", "h_rec", "have", "specialize", "rw", "refine", "exact"], "tactic_count": 12}
{"name": "ProbabilityTheory.iIndepFun.mgf_sum", "kind": "theorem", "module": "Mathlib.Probability.Moments.Basic", "is_tactic_proof": true, "tactics": ["have", "classical", "induction", "empty", "insert", "h_rec", "have", "rw", "h_rec,"], "tactic_count": 9}
{"name": "ProbabilityTheory.iIndepFun.cgf_sum", "kind": "theorem", "module": "Mathlib.Probability.Moments.Basic", "is_tactic_proof": true, "tactics": ["have", "simp_rw", "rw", "rw", "exact"], "tactic_count": 5}
{"name": "ProbabilityTheory.mgf_congr_of_identDistrib", "kind": "theorem", "module": "Mathlib.Probability.Moments.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.mgf_sum_of_identDistrib", "kind": "theorem", "module": "Mathlib.Probability.Moments.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ProbabilityTheory.measure_ge_le_exp_mul_mgf", "kind": "theorem", "module": "Mathlib.Probability.Moments.Basic", "is_tactic_proof": true, "tactics": ["rcases", "rw", "simp", "gcongr", "exacts", "calc", "μ.real", "congr", "simp", "exact", "have", "mul_meas_ge_le_integral_of_nonneg", "rwa"], "tactic_count": 13}
{"name": "ProbabilityTheory.measure_le_le_exp_mul_mgf", "kind": "theorem", "module": "Mathlib.Probability.Moments.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp", "simp_rw", "exact"], "tactic_count": 5}
{"name": "ProbabilityTheory.measure_ge_le_exp_cgf", "kind": "theorem", "module": "Mathlib.Probability.Moments.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
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{"name": "ProbabilityTheory.HasSubgaussianMGF.const_mul", "kind": "theorem", "module": "Mathlib.Probability.Moments.SubGaussian", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ProbabilityTheory.HasSubgaussianMGF.integrableExpSet_eq_univ", "kind": "theorem", "module": "Mathlib.Probability.Moments.SubGaussian", "is_tactic_proof": true, "tactics": ["ext", "simpa"], "tactic_count": 2}
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{"name": "ProbabilityTheory.HasSubgaussianMGF.integrable", "kind": "theorem", "module": "Mathlib.Probability.Moments.SubGaussian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.HasSubgaussianMGF.measure_ge_le", "kind": "theorem", "module": "Mathlib.Probability.Moments.SubGaussian", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
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{"name": "PMF.support_nonempty", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.support_countable", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.apply_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PMF.apply_pos_iff", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.apply_eq_one_iff", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Basic", "is_tactic_proof": false, "tactics": ["refine", "ha'.symm", "suffices", "classical", "have", "rw", "exact", "calc", "congr", "exact"], "tactic_count": 10}
{"name": "PMF.coe_le_one", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Basic", "is_tactic_proof": true, "tactics": ["classical", "refine", "split_ifs"], "tactic_count": 3}
{"name": "PMF.apply_ne_top", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.apply_lt_top", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.toOuterMeasure", "kind": "definition", "module": "Mathlib.Probability.ProbabilityMassFunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.toOuterMeasure_apply", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.toOuterMeasure_caratheodory", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Basic", "is_tactic_proof": true, "tactics": ["refine", "have", "exact"], "tactic_count": 3}
{"name": "PMF.toOuterMeasure_apply_finset", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Basic", "is_tactic_proof": true, "tactics": ["refine", "exact", "exact"], "tactic_count": 3}
{"name": "PMF.toOuterMeasure_apply_singleton", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Basic", "is_tactic_proof": true, "tactics": ["refine", "classical", "classical"], "tactic_count": 3}
{"name": "PMF.toOuterMeasure_injective", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.toOuterMeasure_inj", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.toOuterMeasure_apply_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "PMF.toOuterMeasure_apply_eq_one_iff", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Basic", "is_tactic_proof": true, "tactics": ["refine", "refine", "have", "have", "exact", "classical", "suffices", "p.tsum_coe", "exact"], "tactic_count": 9}
{"name": "PMF.toOuterMeasure_apply_inter_support", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PMF.toOuterMeasure_mono", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.toOuterMeasure_apply_eq_of_inter_support_eq", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.toOuterMeasure_apply_fintype", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.toMeasure", "kind": "definition", "module": "Mathlib.Probability.ProbabilityMassFunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.toOuterMeasure_apply_le_toMeasure_apply", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.toMeasure_apply_eq_toOuterMeasure_apply", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.toMeasure_apply", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.toMeasure_apply_singleton", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PMF.toMeasure_apply_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PMF.toMeasure_apply_eq_one_iff", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.toMeasure_mono", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "PMF.toMeasure_apply_inter_support", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.restrict_toMeasure_support", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Basic", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "PMF.toMeasure_apply_eq_of_inter_support_eq", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "PMF.toMeasure_injective", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Basic", "is_tactic_proof": true, "tactics": ["intro", "ext", "rw", "q.toMeasure_apply_singleton"], "tactic_count": 4}
{"name": "PMF.toMeasure_inj", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.toMeasure_apply_eq_toOuterMeasure", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Basic", "is_tactic_proof": true, "tactics": ["have", "rw", "p.toMeasure_apply_eq_toOuterMeasure_apply"], "tactic_count": 3}
{"name": "PMF.toMeasure_apply_finset", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.toMeasure_apply_eq_tsum", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.toMeasure_apply_fintype", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.toPMF", "kind": "definition", "module": "Mathlib.Probability.ProbabilityMassFunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.toPMF_apply", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Measure.toPMF_toMeasure", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.toMeasure.isProbabilityMeasure", "kind": "instance", "module": "Mathlib.Probability.ProbabilityMassFunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.toMeasure_toPMF", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.toMeasure_eq_iff_eq_toPMF", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PMF.toPMF_eq_iff_toMeasure_eq", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PMF.binomial", "kind": "definition", "module": "Mathlib.Probability.ProbabilityMassFunction.Binomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.binomial_apply", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Binomial", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PMF.binomial_apply_zero", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Binomial", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PMF.binomial_apply_last", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Binomial", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PMF.binomial_apply_self", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Binomial", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PMF.binomial_one_eq_bernoulli", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Binomial", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "PMF.map", "kind": "definition", "module": "Mathlib.Probability.ProbabilityMassFunction.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.monad_map_eq_map", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.map_apply", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Constructions", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PMF.support_map", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.mem_support_map_iff", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Constructions", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PMF.bind_pure_comp", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.map_id", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.map_comp", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Constructions", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PMF.pure_map", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.map_bind", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.bind_map", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.map_const", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Constructions", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PMF.toOuterMeasure_map_apply", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Constructions", "is_tactic_proof": true, "tactics": ["simp", "rfl"], "tactic_count": 2}
{"name": "PMF.toMeasure_map_apply", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Constructions", "is_tactic_proof": false, "tactics": ["rw", "toMeasure_apply_eq_toOuterMeasure_apply", "exact"], "tactic_count": 3}
{"name": "PMF.toMeasure_map", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Constructions", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "PMF.seq", "kind": "definition", "module": "Mathlib.Probability.ProbabilityMassFunction.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.monad_seq_eq_seq", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.seq_apply", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Constructions", "is_tactic_proof": true, "tactics": ["simp", "refine", "simpa"], "tactic_count": 3}
{"name": "PMF.support_seq", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.mem_support_seq_iff", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Constructions", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PMF.instLawfulFunctor", "kind": "instance", "module": "Mathlib.Probability.ProbabilityMassFunction.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.instLawfulMonad", "kind": "instance", "module": "Mathlib.Probability.ProbabilityMassFunction.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.instULiftable", "kind": "instance", "module": "Mathlib.Probability.ProbabilityMassFunction.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.ofFinset", "kind": "definition", "module": "Mathlib.Probability.ProbabilityMassFunction.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.ofFinset_apply", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.support_ofFinset", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.mem_support_ofFinset_iff", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Constructions", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PMF.ofFinset_apply_of_notMem", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.toOuterMeasure_ofFinset_apply", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.toMeasure_ofFinset_apply", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.ofFintype", "kind": "definition", "module": "Mathlib.Probability.ProbabilityMassFunction.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.ofFintype_apply", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.support_ofFintype", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.mem_support_ofFintype_iff", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.map_ofFintype", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Constructions", "is_tactic_proof": true, "tactics": ["ext", "simp", "exact"], "tactic_count": 3}
{"name": "PMF.toOuterMeasure_ofFintype_apply", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.toMeasure_ofFintype_apply", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.normalize", "kind": "definition", "module": "Mathlib.Probability.ProbabilityMassFunction.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.normalize_apply", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.support_normalize", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.mem_support_normalize_iff", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Constructions", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PMF.filter", "kind": "definition", "module": "Mathlib.Probability.ProbabilityMassFunction.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.filter_apply", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Constructions", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PMF.filter_apply_eq_zero_of_notMem", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Constructions", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PMF.mem_support_filter_iff", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.support_filter", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.filter_apply_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Constructions", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PMF.filter_apply_ne_zero_iff", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Constructions", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PMF.bernoulli", "kind": "definition", "module": "Mathlib.Probability.ProbabilityMassFunction.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.bernoulli_apply", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Constructions", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "PMF.support_bernoulli", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Constructions", "is_tactic_proof": true, "tactics": ["refine", "induction", "simp_rw", "constructor", "intro", "simp", "exact", "intro", "simp", "simp"], "tactic_count": 10}
{"name": "PMF.mem_support_bernoulli_iff", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Constructions", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PMF.integral_eq_tsum", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Integrals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.integral_eq_sum", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Integrals", "is_tactic_proof": true, "tactics": ["rw", "congr", "rw", "congr", "exact"], "tactic_count": 5}
{"name": "PMF.bernoulli_expectation", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Integrals", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PMF.pure", "kind": "definition", "module": "Mathlib.Probability.ProbabilityMassFunction.Monad", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.pure_apply", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Monad", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.support_pure", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Monad", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.mem_support_pure_iff", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Monad", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PMF.pure_apply_self", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Monad", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.pure_apply_of_ne", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Monad", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.instInhabited", "kind": "instance", "module": "Mathlib.Probability.ProbabilityMassFunction.Monad", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.toOuterMeasure_pure_apply", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Monad", "is_tactic_proof": true, "tactics": ["refine", "split_ifs", "refine", "exact", "refine", "exact"], "tactic_count": 6}
{"name": "PMF.toMeasure_pure_apply", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Monad", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.toMeasure_pure", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Monad", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.toPMF_dirac", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Monad", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PMF.bind", "kind": "definition", "module": "Mathlib.Probability.ProbabilityMassFunction.Monad", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.bind_apply", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Monad", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.support_bind", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Monad", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "PMF.bindOnSupport", "kind": "definition", "module": "Mathlib.Probability.ProbabilityMassFunction.Monad", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PMF.bindOnSupport_apply", "kind": "theorem", "module": "Mathlib.Probability.ProbabilityMassFunction.Monad", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasureTheory.Adapted", "kind": "definition", "module": "Mathlib.Probability.Process.Adapted", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasureTheory.StronglyAdapted.div", "kind": "theorem", "module": "Mathlib.Probability.Process.Adapted", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasureTheory.measurableSet_of_filtration", "kind": "theorem", "module": "Mathlib.Probability.Process.Filtration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.sigmaFinite_of_sigmaFiniteFiltration", "kind": "instance", "module": "Mathlib.Probability.Process.Filtration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasureTheory.Integrable.uniformIntegrable_condExp_filtration", "kind": "theorem", "module": "Mathlib.Probability.Process.Filtration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasureTheory.filtrationOfSet", "kind": "definition", "module": "Mathlib.Probability.Process.Filtration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measurableSet_filtrationOfSet", "kind": "theorem", "module": "Mathlib.Probability.Process.Filtration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MeasureTheory.Filtration.piLE_eq_comap_frestrictLe", "kind": "theorem", "module": "Mathlib.Probability.Process.Filtration", "is_tactic_proof": true, "tactics": ["apply", "simp_rw", "exact", "rw", "exact"], "tactic_count": 5}
{"name": "MeasureTheory.Filtration.piFinset", "kind": "definition", "module": "Mathlib.Probability.Process.Filtration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Filtration.piFinset_eq_comap_restrict", "kind": "theorem", "module": "Mathlib.Probability.Process.Filtration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Filtration.cylinderEventsCompl", "kind": "definition", "module": "Mathlib.Probability.Process.Filtration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.isProjectiveMeasureFamily_map_restrict", "kind": "theorem", "module": "Mathlib.Probability.Process.FiniteDimensionalLaws", "is_tactic_proof": true, "tactics": ["intro", "rw", "simp", "exact"], "tactic_count": 4}
{"name": "ProbabilityTheory.isProjectiveLimit_map", "kind": "theorem", "module": "Mathlib.Probability.Process.FiniteDimensionalLaws", "is_tactic_proof": true, "tactics": ["intro", "rw"], "tactic_count": 2}
{"name": "ProbabilityTheory.map_eq_iff_forall_finset_map_restrict_eq", "kind": "theorem", "module": "Mathlib.Probability.Process.FiniteDimensionalLaws", "is_tactic_proof": true, "tactics": ["refine", "have", "rw", "have", "rw", "rw", "have", "simp_rw", "exact"], "tactic_count": 9}
{"name": "ProbabilityTheory.identDistrib_iff_forall_finset_identDistrib", "kind": "theorem", "module": "Mathlib.Probability.Process.FiniteDimensionalLaws", "is_tactic_proof": true, "tactics": ["refine", "exact", "exact", "exact", "exact"], "tactic_count": 5}
{"name": "ProbabilityTheory.map_restrict_eq_of_forall_ae_eq", "kind": "theorem", "module": "Mathlib.Probability.Process.FiniteDimensionalLaws", "is_tactic_proof": false, "tactics": ["have", "rw", "exact", "refine", "filter_upwards"], "tactic_count": 5}
{"name": "ProbabilityTheory.map_eq_of_forall_ae_eq", "kind": "theorem", "module": "Mathlib.Probability.Process.FiniteDimensionalLaws", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MeasureTheory.hittingBtwn", "kind": "definition", "module": "Mathlib.Probability.Process.HittingTime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.hittingAfter", "kind": "definition", "module": "Mathlib.Probability.Process.HittingTime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.hittingBtwn_def", "kind": "theorem", "module": "Mathlib.Probability.Process.HittingTime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.hittingAfter_def", "kind": "theorem", "module": "Mathlib.Probability.Process.HittingTime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.hittingBtwn_empty", "kind": "theorem", "module": "Mathlib.Probability.Process.HittingTime", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "MeasureTheory.hittingAfter_empty", "kind": "theorem", "module": "Mathlib.Probability.Process.HittingTime", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "MeasureTheory.hittingBtwn_univ", "kind": "theorem", "module": "Mathlib.Probability.Process.HittingTime", "is_tactic_proof": true, "tactics": ["ext", "classical", "simp", "by_cases"], "tactic_count": 4}
{"name": "MeasureTheory.hittingAfter_univ", "kind": "theorem", "module": "Mathlib.Probability.Process.HittingTime", "is_tactic_proof": true, "tactics": ["ext", "classical", "simp", "rw", "exact_mod_cast"], "tactic_count": 5}
{"name": "MeasureTheory.hittingBtwn_of_lt", "kind": "theorem", "module": "Mathlib.Probability.Process.HittingTime", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "MeasureTheory.hittingBtwn_le", "kind": "theorem", "module": "Mathlib.Probability.Process.HittingTime", "is_tactic_proof": true, "tactics": ["simp", "split_ifs", "obtain", "change", "exact", "exact"], "tactic_count": 6}
{"name": "MeasureTheory.notMem_of_lt_hittingBtwn", "kind": "theorem", "module": "Mathlib.Probability.Process.HittingTime", "is_tactic_proof": true, "tactics": ["classical", "intro", "have", "refine", "simp_rw", "exact"], "tactic_count": 6}
{"name": "MeasureTheory.notMem_of_lt_hittingAfter", "kind": "theorem", "module": "Mathlib.Probability.Process.HittingTime", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact_mod_cast"], "tactic_count": 3}
{"name": "MeasureTheory.hittingBtwn_eq_end_iff", "kind": "theorem", "module": "Mathlib.Probability.Process.HittingTime", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "MeasureTheory.hittingAfter_eq_top_iff", "kind": "theorem", "module": "Mathlib.Probability.Process.HittingTime", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.hittingBtwn_of_le", "kind": "theorem", "module": "Mathlib.Probability.Process.HittingTime", "is_tactic_proof": true, "tactics": ["obtain", "classical", "rw", "conv", "intro", "rw", "exact", "exact"], "tactic_count": 8}
{"name": "MeasureTheory.le_hittingBtwn", "kind": "theorem", "module": "Mathlib.Probability.Process.HittingTime", "is_tactic_proof": true, "tactics": ["simp", "split_ifs", "refine", "obtain", "exact", "rw", "exact", "exact"], "tactic_count": 8}
{"name": "MeasureTheory.le_hittingAfter", "kind": "theorem", "module": "Mathlib.Probability.Process.HittingTime", "is_tactic_proof": true, "tactics": ["simp", "split_ifs", "exact_mod_cast", "simp"], "tactic_count": 4}
{"name": "MeasureTheory.le_hittingBtwn_of_exists", "kind": "theorem", "module": "Mathlib.Probability.Process.HittingTime", "is_tactic_proof": true, "tactics": ["refine", "by_contra", "rw", "simp"], "tactic_count": 4}
{"name": "MeasureTheory.hittingBtwn_mem_Icc", "kind": "theorem", "module": "Mathlib.Probability.Process.HittingTime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.hittingBtwn_mem_set", "kind": "theorem", "module": "Mathlib.Probability.Process.HittingTime", "is_tactic_proof": true, "tactics": ["simp_rw", "have", "obtain", "exact", "have", "rw", "exact"], "tactic_count": 7}
{"name": "MeasureTheory.hittingAfter_mem_set", "kind": "theorem", "module": "Mathlib.Probability.Process.HittingTime", "is_tactic_proof": true, "tactics": ["rw", "have", "obtain", "exact", "exact"], "tactic_count": 5}
{"name": "MeasureTheory.hittingBtwn_mem_set_of_hittingBtwn_lt", "kind": "theorem", "module": "Mathlib.Probability.Process.HittingTime", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "simp_rw", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.hittingAfter_mem_set_of_ne_top", "kind": "theorem", "module": "Mathlib.Probability.Process.HittingTime", "is_tactic_proof": true, "tactics": ["simp", "obtain", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.hittingBtwn_le_of_mem", "kind": "theorem", "module": "Mathlib.Probability.Process.HittingTime", "is_tactic_proof": true, "tactics": ["have", "simp_rw", "exact"], "tactic_count": 3}
{"name": "MeasureTheory.hittingAfter_le_of_mem", "kind": "theorem", "module": "Mathlib.Probability.Process.HittingTime", "is_tactic_proof": true, "tactics": ["have", "rw", "exact_mod_cast"], "tactic_count": 3}
{"name": "MeasureTheory.hittingBtwn_le_iff_of_exists", "kind": "theorem", "module": "Mathlib.Probability.Process.HittingTime", "is_tactic_proof": true, "tactics": ["constructor", "exact", "have", "obtain", "obtain", "refine", "exact", "obtain", "refine", "exact"], "tactic_count": 10}
{"name": "MeasureTheory.hittingAfter_le_iff", "kind": "theorem", "module": "Mathlib.Probability.Process.HittingTime", "is_tactic_proof": true, "tactics": ["constructor", "have", "have", "refine", "lift", "norm_cast", "obtain", "refine", "exact"], "tactic_count": 9}
{"name": "MeasureTheory.hittingBtwn_le_iff_of_lt", "kind": "theorem", "module": "Mathlib.Probability.Process.HittingTime", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "simp_rw", "push_neg", "simp", "exact"], "tactic_count": 6}
{"name": "MeasureTheory.hittingBtwn_lt_iff", "kind": "theorem", "module": "Mathlib.Probability.Process.HittingTime", "is_tactic_proof": true, "tactics": ["constructor", "have", "by_contra", "simp_rw", "exact", "exact", "obtain", "refine", "exact"], "tactic_count": 9}
{"name": "MeasureTheory.hittingAfter_lt_iff", "kind": "theorem", "module": "Mathlib.Probability.Process.HittingTime", "is_tactic_proof": true, "tactics": ["constructor", "have", "have", "refine", "lift", "norm_cast", "obtain", "refine", "exact"], "tactic_count": 9}
{"name": "MeasureTheory.hittingBtwn_eq_hittingBtwn_of_exists", "kind": "theorem", "module": "Mathlib.Probability.Process.HittingTime", "is_tactic_proof": true, "tactics": ["simp", "obtain", "rw", "refine", "refine", "by_cases", "exact", "change", "exact", "exact"], "tactic_count": 10}
{"name": "MeasureTheory.hittingBtwn_anti", "kind": "theorem", "module": "Mathlib.Probability.Process.HittingTime", "is_tactic_proof": true, "tactics": ["intro", "simp", "split_ifs", "gcongr", "exacts", "obtain", "exact", "obtain", "exact", "simp"], "tactic_count": 10}
{"name": "MeasureTheory.hittingAfter_anti", "kind": "theorem", "module": "Mathlib.Probability.Process.HittingTime", "is_tactic_proof": true, "tactics": ["intro", "simp", "split_ifs", "norm_cast", "gcongr", "exacts", "simp", "obtain", "exact", "simp"], "tactic_count": 10}
{"name": "MeasureTheory.hittingBtwn_apply_anti", "kind": "theorem", "module": "Mathlib.Probability.Process.HittingTime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.hittingAfter_apply_anti", "kind": "theorem", "module": "Mathlib.Probability.Process.HittingTime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.hittingBtwn_mono_right", "kind": "theorem", "module": "Mathlib.Probability.Process.HittingTime", "is_tactic_proof": true, "tactics": ["intro", "by_cases", "exact", "simp_rw", "split_ifs", "obtain", "refine", "by_contra", "exact", "exact"], "tactic_count": 10}
{"name": "MeasureTheory.hittingBtwn_mono_left", "kind": "theorem", "module": "Mathlib.Probability.Process.HittingTime", "is_tactic_proof": true, "tactics": ["intro", "simp", "split_ifs", "gcongr", "exacts", "obtain", "exact", "have", "exact", "simp"], "tactic_count": 10}
{"name": "MeasureTheory.hittingAfter_mono", "kind": "theorem", "module": "Mathlib.Probability.Process.HittingTime", "is_tactic_proof": true, "tactics": ["intro", "simp", "split_ifs", "norm_cast", "gcongr", "exacts", "simp", "have", "exact", "simp"], "tactic_count": 10}
{"name": "MeasureTheory.hittingBtwn_apply_mono_right", "kind": "theorem", "module": "Mathlib.Probability.Process.HittingTime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.hittingBtwn_apply_mono_left", "kind": "theorem", "module": "Mathlib.Probability.Process.HittingTime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.hittingAfter_apply_mono", "kind": "theorem", "module": "Mathlib.Probability.Process.HittingTime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.Adapted.isStoppingTime_hittingBtwn", "kind": "theorem", "module": "Mathlib.Probability.Process.HittingTime", "is_tactic_proof": true, "tactics": ["intro", "rcases", "have", "simp", "have", "simp", "simpa"], "tactic_count": 7}
{"name": "MeasureTheory.Adapted.isStoppingTime_hittingAfter", "kind": "theorem", "module": "Mathlib.Probability.Process.HittingTime", "is_tactic_proof": true, "tactics": ["intro", "have", "simp", "simpa"], "tactic_count": 4}
{"name": "MeasureTheory.stoppedValue_hittingBtwn_mem", "kind": "theorem", "module": "Mathlib.Probability.Process.HittingTime", "is_tactic_proof": true, "tactics": ["simp", "obtain", "have", "csInf_mem", "exact"], "tactic_count": 5}
{"name": "MeasureTheory.Adapted.isStoppingTime_hittingBtwn_isStoppingTime", "kind": "theorem", "module": "Mathlib.Probability.Process.HittingTime", "is_tactic_proof": true, "tactics": ["intro", "have", "ext", "simp", "exists_prop]", "specialize", "have", "lift", "simp", "have", "ext", "simp", "iff_false,", "refine", "specialize", "have", "lift", "rw", "exact", "simp", "refine", "simpa"], "tactic_count": 22}
{"name": "MeasureTheory.hittingBtwn_eq_sInf", "kind": "theorem", "module": "Mathlib.Probability.Process.HittingTime", "is_tactic_proof": true, "tactics": ["simp", "intro", "symm", "rw", "simp", "exact"], "tactic_count": 6}
{"name": "MeasureTheory.hittingAfter_eq_sInf", "kind": "theorem", "module": "Mathlib.Probability.Process.HittingTime", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MeasureTheory.hittingBtwn_bot_le_iff", "kind": "theorem", "module": "Mathlib.Probability.Process.HittingTime", "is_tactic_proof": true, "tactics": ["rcases", "rw", "simp", "simp", "obtain", "exact"], "tactic_count": 6}
{"name": "MeasureTheory.hittingAfter_bot_le_iff", "kind": "theorem", "module": "Mathlib.Probability.Process.HittingTime", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ProbabilityTheory.IsAEKolmogorovProcess", "kind": "definition", "module": "Mathlib.Probability.Process.Kolmogorov", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IsKolmogorovProcess.IsAEKolmogorovProcess", "kind": "theorem", "module": "Mathlib.Probability.Process.Kolmogorov", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IsAEKolmogorovProcess.mk", "kind": "definition", "module": "Mathlib.Probability.Process.Kolmogorov", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IsAEKolmogorovProcess.IsKolmogorovProcess_mk", "kind": "theorem", "module": "Mathlib.Probability.Process.Kolmogorov", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IsAEKolmogorovProcess.ae_eq_mk", "kind": "theorem", "module": "Mathlib.Probability.Process.Kolmogorov", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IsAEKolmogorovProcess.kolmogorovCondition", "kind": "theorem", "module": "Mathlib.Probability.Process.Kolmogorov", "is_tactic_proof": true, "tactics": ["convert", "refine", "filter_upwards", "simp_rw"], "tactic_count": 4}
{"name": "ProbabilityTheory.IsAEKolmogorovProcess.p_pos", "kind": "theorem", "module": "Mathlib.Probability.Process.Kolmogorov", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IsAEKolmogorovProcess.q_pos", "kind": "theorem", "module": "Mathlib.Probability.Process.Kolmogorov", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IsAEKolmogorovProcess.congr", "kind": "theorem", "module": "Mathlib.Probability.Process.Kolmogorov", "is_tactic_proof": true, "tactics": ["refine", "filter_upwards"], "tactic_count": 2}
{"name": "ProbabilityTheory.IsKolmogorovProcess.stronglyMeasurable_edist", "kind": "theorem", "module": "Mathlib.Probability.Process.Kolmogorov", "is_tactic_proof": true, "tactics": ["borelize", "exact"], "tactic_count": 2}
{"name": "ProbabilityTheory.IsAEKolmogorovProcess.aestronglyMeasurable_edist", "kind": "theorem", "module": "Mathlib.Probability.Process.Kolmogorov", "is_tactic_proof": true, "tactics": ["refine", "filter_upwards"], "tactic_count": 2}
{"name": "ProbabilityTheory.IsKolmogorovProcess.measurable_edist", "kind": "theorem", "module": "Mathlib.Probability.Process.Kolmogorov", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IsAEKolmogorovProcess.aemeasurable_edist", "kind": "theorem", "module": "Mathlib.Probability.Process.Kolmogorov", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IsKolmogorovProcess.measurable", "kind": "theorem", "module": "Mathlib.Probability.Process.Kolmogorov", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IsAEKolmogorovProcess.aemeasurable", "kind": "theorem", "module": "Mathlib.Probability.Process.Kolmogorov", "is_tactic_proof": true, "tactics": ["refine", "filter_upwards"], "tactic_count": 2}
{"name": "ProbabilityTheory.IsKolmogorovProcess.mk_of_secondCountableTopology", "kind": "theorem", "module": "Mathlib.Probability.Process.Kolmogorov", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IsAEKolmogorovProcess.edist_eq_zero", "kind": "theorem", "module": "Mathlib.Probability.Process.Kolmogorov", "is_tactic_proof": false, "tactics": ["suffices", "filter_upwards", "simpa", "rw", "calc"], "tactic_count": 5}
{"name": "ProbabilityTheory.IsKolmogorovProcess.edist_eq_zero", "kind": "theorem", "module": "Mathlib.Probability.Process.Kolmogorov", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.IsAEKolmogorovProcess.edist_eq_zero_of_const_eq_zero", "kind": "theorem", "module": "Mathlib.Probability.Process.Kolmogorov", "is_tactic_proof": false, "tactics": ["suffices", "filter_upwards", "simpa", "rw", "calc"], "tactic_count": 5}
{"name": "ProbabilityTheory.IsKolmogorovProcess.edist_eq_zero_of_const_eq_zero", "kind": "theorem", "module": "Mathlib.Probability.Process.Kolmogorov", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.partitionFiltration", "kind": "definition", "module": "Mathlib.Probability.Process.PartitionFiltration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.measurableSet_partitionFiltration_of_mem", "kind": "theorem", "module": "Mathlib.Probability.Process.PartitionFiltration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.measurableSet_partitionFiltration_memPartitionSet", "kind": "theorem", "module": "Mathlib.Probability.Process.PartitionFiltration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.measurable_memPartitionSet_subtype", "kind": "theorem", "module": "Mathlib.Probability.Process.PartitionFiltration", "is_tactic_proof": true, "tactics": ["refine", "rcases", "suffices", "convert", "ext", "simp", "simp_rw", "exact"], "tactic_count": 8}
{"name": "ProbabilityTheory.measurable_partitionFiltration_memPartitionSet", "kind": "theorem", "module": "Mathlib.Probability.Process.PartitionFiltration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.measurable_memPartitionSet", "kind": "theorem", "module": "Mathlib.Probability.Process.PartitionFiltration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iSup_partitionFiltration_eq_generateFrom_range", "kind": "theorem", "module": "Mathlib.Probability.Process.PartitionFiltration", "is_tactic_proof": true, "tactics": ["conv_rhs", "rfl"], "tactic_count": 2}
{"name": "ProbabilityTheory.iSup_partitionFiltration", "kind": "theorem", "module": "Mathlib.Probability.Process.PartitionFiltration", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ProbabilityTheory.countableFiltration", "kind": "definition", "module": "Mathlib.Probability.Process.PartitionFiltration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.measurableSet_countableFiltration_of_mem", "kind": "theorem", "module": "Mathlib.Probability.Process.PartitionFiltration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.measurableSet_countableFiltration_countablePartitionSet", "kind": "theorem", "module": "Mathlib.Probability.Process.PartitionFiltration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.measurable_countablePartitionSet_subtype", "kind": "theorem", "module": "Mathlib.Probability.Process.PartitionFiltration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.measurable_countableFiltration_countablePartitionSet", "kind": "theorem", "module": "Mathlib.Probability.Process.PartitionFiltration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.measurable_countablePartitionSet", "kind": "theorem", "module": "Mathlib.Probability.Process.PartitionFiltration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.iSup_countableFiltration", "kind": "theorem", "module": "Mathlib.Probability.Process.PartitionFiltration", "is_tactic_proof": true, "tactics": ["conv_rhs", "rfl"], "tactic_count": 2}
{"name": "MeasureTheory.Filtration.predictable", "kind": "definition", "module": "Mathlib.Probability.Process.Predictable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.IsPredictable", "kind": "definition", "module": "Mathlib.Probability.Process.Predictable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measurableSet_predictable_singleton_bot_prod", "kind": "theorem", "module": "Mathlib.Probability.Process.Predictable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measurableSet_predictable_Ioi_prod", "kind": "theorem", "module": "Mathlib.Probability.Process.Predictable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MeasureTheory.measurableSet_predictable_Ioc_prod", "kind": "theorem", "module": "Mathlib.Probability.Process.Predictable", "is_tactic_proof": true, "tactics": ["obtain", "simp", "rw", "exact"], "tactic_count": 4}
{"name": "MeasureTheory.measurableSpace_le_predictable_of_measurableSet", "kind": "theorem", "module": "Mathlib.Probability.Process.Predictable", "is_tactic_proof": true, "tactics": ["refine", "rintro", "exact", "exact"], "tactic_count": 4}
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{"name": "ProbabilityTheory.uniformOn", "kind": "definition", "module": "Mathlib.Probability.UniformOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ProbabilityTheory.uniformOn_empty_meas", "kind": "theorem", "module": "Mathlib.Probability.UniformOn", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "ProbabilityTheory.uniformOn_univ", "kind": "theorem", "module": "Mathlib.Probability.UniformOn", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "ProbabilityTheory.uniformOn_of_univ", "kind": "theorem", "module": "Mathlib.Probability.UniformOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProbabilityTheory.uniformOn_inter", "kind": "theorem", "module": "Mathlib.Probability.UniformOn", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "rw", "cond_apply", "mul_comm", "rwa", "exact"], "tactic_count": 7}
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{"name": "ProbabilityTheory.uniformOn_compl", "kind": "theorem", "module": "Mathlib.Probability.UniformOn", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "ProbabilityTheory.uniformOn_add_compl_eq", "kind": "theorem", "module": "Mathlib.Probability.UniformOn", "is_tactic_proof": false, "tactics": ["conv_rhs", "rw", "uniformOn_disjoint_union", "simp"], "tactic_count": 4}
{"name": "IsSimpleModule.algebraMap_end_bijective_of_isAlgClosed", "kind": "theorem", "module": "Mathlib.RepresentationTheory.AlgebraRepresentation.Basic", "is_tactic_proof": false, "tactics": ["have", "classical"], "tactic_count": 2}
{"name": "IsSimpleModule.finrank_eq_one_of_isMulCommutative", "kind": "theorem", "module": "Mathlib.RepresentationTheory.AlgebraRepresentation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.trivial", "kind": "definition", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.trivial_apply", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.instIsTrivialTrivial", "kind": "instance", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.isTrivial_def", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.isTrivial_apply", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.inv_self_apply", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Representation.self_inv_apply", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Representation.apply_bijective", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.asAlgebraHom", "kind": "definition", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.asAlgebraHom_def", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.asAlgebraHom_single", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Representation.asAlgebraHom_single_one", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Representation.asAlgebraHom_of", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Representation.asModule", "kind": "definition", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.instInhabitedAsModule", "kind": "instance", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.instModuleMonoidAlgebraAsModule", "kind": "instance", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.asModuleEquiv", "kind": "definition", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.asModuleEquiv_map_smul", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.asModuleEquiv_symm_map_smul", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Representation.asModuleEquiv_symm_map_rho", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Representation.instFiniteAsModule", "kind": "instance", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.ofModule'", "kind": "definition", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.ofModule", "kind": "definition", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.ofModule_asAlgebraHom_apply_apply", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": true, "tactics": ["apply", "intro", "simp", "intro", "simp", "intro", "simp"], "tactic_count": 7}
{"name": "Representation.ofModule_asModule_act", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "Representation.smul_ofModule_asModule", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "Representation.single_smul", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Representation.instIsScalarTowerMonoidAlgebraAsModule", "kind": "instance", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.norm", "kind": "definition", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.norm_comp_self", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": true, "tactics": ["ext", "simpa"], "tactic_count": 2}
{"name": "Representation.norm_self_apply", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.self_comp_norm", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": true, "tactics": ["ext", "simpa"], "tactic_count": 2}
{"name": "Representation.self_norm_apply", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.subrepresentation", "kind": "definition", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.quotient", "kind": "definition", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.apply_eq_of_coe_eq", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.ofQuotient", "kind": "definition", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.ofQuotient_coe_apply", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.instAddCommGroupAsModule", "kind": "instance", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.apply_sub_id_partialSum_eq", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "h", "have", "simp", "rw", "simp"], "tactic_count": 8}
{"name": "Representation.ofMulAction", "kind": "definition", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.leftRegular", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.diagonal", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.ofMulAction_def", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.ofMulAction_single", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.ofDistribMulAction", "kind": "definition", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.ofDistribMulAction_apply_apply", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.norm_ofDistribMulAction_eq", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Representation.ofMulDistribMulAction", "kind": "definition", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.ofMulDistribMulAction_apply_apply", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.norm_ofMulDistribMulAction_eq", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Representation.ofMulAction_apply", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": true, "tactics": ["conv_lhs", "let", "change", "have", "intro", "simp", "simp"], "tactic_count": 7}
{"name": "Representation.instHMulMonoidAlgebraAsModuleFinsuppOfMulAction", "kind": "instance", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.ofMulAction_self_smul_eq_mul", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": true, "tactics": ["induction", "hM", "change", "ext", "simp", "hadd", "hsmul"], "tactic_count": 7}
{"name": "Representation.ofMulActionSelfAsModuleEquiv", "kind": "definition", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.asGroupHom", "kind": "definition", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.asGroupHom_apply", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Representation.leftRegular_norm_apply", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": true, "tactics": ["ext", "simpa"], "tactic_count": 2}
{"name": "Representation.leftRegular_norm_eq_zero_iff", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": true, "tactics": ["rw", "constructor", "intro", "simpa", "intro", "ext", "simp_all"], "tactic_count": 7}
{"name": "Representation.ker_leftRegular_norm_eq", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "Representation.apply_eq_of_leftRegular_eq_of_generator", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": true, "tactics": ["rcases", "induction", "zero", "succ", "simpa", "pred"], "tactic_count": 6}
{"name": "Representation.directSum", "kind": "definition", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.prod", "kind": "definition", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.tprod", "kind": "definition", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RepresentationTheory.Basic.0.Representation.term_⊗_", "kind": "definition", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RepresentationTheory.Basic.0.Representation._aux_Mathlib_RepresentationTheory_Basic___macroRules__private_Mathlib_RepresentationTheory_Basic_0_Representation_term_⊗__1", "kind": "definition", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RepresentationTheory.Basic.0.Representation._aux_Mathlib_RepresentationTheory_Basic___unexpand_Representation_tprod_1", "kind": "definition", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.tprod_apply", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.smul_tprod_one_asModule", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": true, "tactics": ["change", "simp", "simp", "rfl"], "tactic_count": 4}
{"name": "Representation.smul_one_tprod_asModule", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": true, "tactics": ["change", "simp", "simp"], "tactic_count": 3}
{"name": "Representation.linHom", "kind": "definition", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.linHom_apply", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.dual", "kind": "definition", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.dual_apply", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.dualTensorHom_comm", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Representation.finsupp", "kind": "definition", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.finsupp_single", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Representation.free", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.instAddCommGroupAsModuleFinsuppFree", "kind": "instance", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.free_single_single", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Representation.finsuppLEquivFreeAsModule", "kind": "definition", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.freeAsModuleBasis", "kind": "definition", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.free_asModule_free", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FDRep.character", "kind": "definition", "module": "Mathlib.RepresentationTheory.Character", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FDRep.char_mul_comm", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Character", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FDRep.char_one", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Character", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FDRep.char_tensor", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Character", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "FDRep.char_iso", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Character", "is_tactic_proof": true, "tactics": ["ext", "simp", "exact"], "tactic_count": 3}
{"name": "FDRep.char_conj", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Character", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "FDRep.char_dual", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Character", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FDRep.char_linHom", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Character", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "FDRep.average_char_eq_finrank_invariants", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Character", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "FDRep.scalar_product_char_eq_finrank_equivariant", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Character", "is_tactic_proof": false, "tactics": ["conv_lhs", "rw", "rw", "simp"], "tactic_count": 4}
{"name": "FDRep.char_orthonormal", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Character", "is_tactic_proof": false, "tactics": ["rw", "rw_mod_cast"], "tactic_count": 2}
{"name": "Representation.coindV", "kind": "definition", "module": "Mathlib.RepresentationTheory.Coinduced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.coind", "kind": "definition", "module": "Mathlib.RepresentationTheory.Coinduced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.coind", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Coinduced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.coindMap", "kind": "definition", "module": "Mathlib.RepresentationTheory.Coinduced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.coindFunctor", "kind": "definition", "module": "Mathlib.RepresentationTheory.Coinduced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.instPreservesEpimorphismsSubtypeMemSubgroupCoindFunctorSubtype", "kind": "instance", "module": "Mathlib.RepresentationTheory.Coinduced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.coind'", "kind": "definition", "module": "Mathlib.RepresentationTheory.Coinduced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.coind'", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Coinduced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.coind'_ext", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Coinduced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.coindMap'", "kind": "definition", "module": "Mathlib.RepresentationTheory.Coinduced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.coindFunctor'", "kind": "definition", "module": "Mathlib.RepresentationTheory.Coinduced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.coindVEquiv", "kind": "definition", "module": "Mathlib.RepresentationTheory.Coinduced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.coindIso", "kind": "definition", "module": "Mathlib.RepresentationTheory.Coinduced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.coindFunctorIso", "kind": "definition", "module": "Mathlib.RepresentationTheory.Coinduced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.resCoindHomEquiv", "kind": "definition", "module": "Mathlib.RepresentationTheory.Coinduced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.resCoindAdjunction", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Coinduced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.instIsRightAdjointCoindFunctor", "kind": "instance", "module": "Mathlib.RepresentationTheory.Coinduced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.instIsLeftAdjointActionModuleCatRes", "kind": "instance", "module": "Mathlib.RepresentationTheory.Coinduced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.instPreservesProjectiveObjectsActionModuleCatSubtypeMemSubgroupResSubtype", "kind": "instance", "module": "Mathlib.RepresentationTheory.Coinduced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.Coinvariants.ker", "kind": "definition", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.Coinvariants", "kind": "definition", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.Coinvariants.instAddCommGroup", "kind": "instance", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.Coinvariants.instModule", "kind": "instance", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.Coinvariants.sub_mem_ker", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.Coinvariants.mem_ker_of_eq", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.Coinvariants.mk", "kind": "definition", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.Coinvariants.mk_eq_iff", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.Coinvariants.mk_eq_zero", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.Coinvariants.mk_surjective", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.Coinvariants.mk_self_apply", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.Coinvariants.induction_on", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.Coinvariants.lift", "kind": "definition", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.Coinvariants.lift_comp_mk", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.Coinvariants.lift_mk", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.Coinvariants.hom_ext", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.Coinvariants.map", "kind": "definition", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.Coinvariants.map_comp_mk", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.Coinvariants.map_mk", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.Coinvariants.map_id", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Representation.Coinvariants.map_comp", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.Coinvariants.le_comap_ker", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.toCoinvariantsKer", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.toCoinvariants", "kind": "definition", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.toCoinvariants_mk", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.instIsTrivialSubtypeMemSubgroupCoinvariantsCompLinearMapIdSubtypeToCoinvariants", "kind": "instance", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.quotientToCoinvariants", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.coinvariantsToFinsupp", "kind": "definition", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.coinvariantsToFinsupp_mk_single", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Representation.finsuppToCoinvariants", "kind": "definition", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.finsuppToCoinvariants_single_mk", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Representation.coinvariantsFinsuppLEquiv", "kind": "definition", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.coinvariantsFinsuppLEquiv_apply", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "Representation.Coinvariants.mk_inv_tmul", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.Coinvariants.mk_tmul_inv", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.ofCoinvariantsTprodLeftRegular", "kind": "definition", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.ofCoinvariantsTprodLeftRegular_mk_tmul_single", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.coinvariantsTprodLeftRegularLEquiv", "kind": "definition", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.coinvariantsTprodLeftRegularLEquiv_apply", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "Rep.toCoinvariantsKer", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.toCoinvariants", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.toCoinvariantsMkQ", "kind": "definition", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.toCoinvariantsMkQ_hom", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.quotientToCoinvariants", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.coinvariantsShortComplex", "kind": "definition", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.coinvariantsShortComplex_shortExact", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.coinvariantsFunctor", "kind": "definition", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.coinvariantsMk", "kind": "definition", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.instEpiModuleCatAppActionCoinvariantsMk", "kind": "instance", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.coinvariantsFunctor_hom_ext", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.desc", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.instAdditiveModuleCatCoinvariantsFunctor", "kind": "instance", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.instLinearModuleCatCoinvariantsFunctor", "kind": "instance", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.coinvariantsAdjunction", "kind": "definition", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.coinvariantsAdjunction_homEquiv_apply_hom", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "Rep.coinvariantsAdjunction_homEquiv_symm_apply_hom", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Rep.instPreservesZeroMorphismsModuleCatCoinvariantsFunctor", "kind": "instance", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.instIsLeftAdjointModuleCatCoinvariantsFunctor", "kind": "instance", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.coinvariantsTensor", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.coinvariantsTensorMk", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.coinvariantsTensorMk_apply", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.coinvariantsTensor_hom_ext", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.instAdditiveModuleCatObjFunctorCoinvariantsTensor", "kind": "instance", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.instLinearModuleCatObjFunctorCoinvariantsTensor", "kind": "instance", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.quotientToCoinvariantsFunctor", "kind": "definition", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.coinvariantsTensorFreeToFinsupp", "kind": "definition", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.coinvariantsTensorFreeToFinsupp_mk_tmul_single", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Rep.finsuppToCoinvariantsTensorFree", "kind": "definition", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.finsuppToCoinvariantsTensorFree_single", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Rep.coinvariantsTensorFreeLEquiv", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.coinvariantsTensorFreeLEquiv_apply", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Coinvariants", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "FDRep.endRingEquiv_symm_comp_ρ", "kind": "theorem", "module": "Mathlib.RepresentationTheory.FDRep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FDRep.endRingEquiv_comp_ρ", "kind": "theorem", "module": "Mathlib.RepresentationTheory.FDRep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FDRep.hom_hom_action_ρ", "kind": "theorem", "module": "Mathlib.RepresentationTheory.FDRep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FDRep.Iso.conj_ρ", "kind": "theorem", "module": "Mathlib.RepresentationTheory.FDRep", "is_tactic_proof": false, "tactics": ["rw", "dsimp", "rw", "cat_disch"], "tactic_count": 4}
{"name": "FDRep.of_ρ'", "kind": "theorem", "module": "Mathlib.RepresentationTheory.FDRep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FDRep.forget₂_ρ", "kind": "theorem", "module": "Mathlib.RepresentationTheory.FDRep", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "FDRep.finrank_hom_simple_simple", "kind": "theorem", "module": "Mathlib.RepresentationTheory.FDRep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FDRep.dualTensorIsoLinHom_hom_hom", "kind": "theorem", "module": "Mathlib.RepresentationTheory.FDRep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.instInjective", "kind": "instance", "module": "Mathlib.RepresentationTheory.FinGroupCharZero", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Rep.instProjective", "kind": "instance", "module": "Mathlib.RepresentationTheory.FinGroupCharZero", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "FDRep.instInjectiveOfNeZeroCastCard", "kind": "instance", "module": "Mathlib.RepresentationTheory.FinGroupCharZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FDRep.instProjectiveOfNeZeroCastCard", "kind": "instance", "module": "Mathlib.RepresentationTheory.FinGroupCharZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FDRep.simple_iff_end_is_rank_one", "kind": "theorem", "module": "Mathlib.RepresentationTheory.FinGroupCharZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FDRep.simple_iff_char_is_norm_one", "kind": "theorem", "module": "Mathlib.RepresentationTheory.FinGroupCharZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.indToCoindAux", "kind": "definition", "module": "Mathlib.RepresentationTheory.FiniteIndex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.indToCoindAux_self", "kind": "theorem", "module": "Mathlib.RepresentationTheory.FiniteIndex", "is_tactic_proof": true, "tactics": ["rw", "simp", "rfl"], "tactic_count": 3}
{"name": "Rep.indToCoindAux_of_not_rel", "kind": "theorem", "module": "Mathlib.RepresentationTheory.FiniteIndex", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Rep.indToCoindAux_mul_snd", "kind": "theorem", "module": "Mathlib.RepresentationTheory.FiniteIndex", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rw", "simp", "rw", "exact"], "tactic_count": 6}
{"name": "Rep.indToCoindAux_mul_fst", "kind": "theorem", "module": "Mathlib.RepresentationTheory.FiniteIndex", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rw", "map_mul]", "congr", "simp", "rw", "exact"], "tactic_count": 8}
{"name": "Rep.indToCoindAux_snd_mul_inv", "kind": "theorem", "module": "Mathlib.RepresentationTheory.FiniteIndex", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rw", "exact"], "tactic_count": 4}
{"name": "Rep.indToCoindAux_fst_mul_inv", "kind": "theorem", "module": "Mathlib.RepresentationTheory.FiniteIndex", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Rep.indToCoindAux_comm", "kind": "theorem", "module": "Mathlib.RepresentationTheory.FiniteIndex", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simp"], "tactic_count": 3}
{"name": "Rep.indToCoind", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.FiniteIndex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.coindToInd", "kind": "definition", "module": "Mathlib.RepresentationTheory.FiniteIndex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.coindToInd_of_support_subset_orbit", "kind": "theorem", "module": "Mathlib.RepresentationTheory.FiniteIndex", "is_tactic_proof": true, "tactics": ["rw", "simp", "intro", "induction", "h", "b", "have", "simp_all", "contrapose", "use", "simp_all", "simp"], "tactic_count": 12}
{"name": "Rep.indCoindIso", "kind": "definition", "module": "Mathlib.RepresentationTheory.FiniteIndex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.indCoindNatIso", "kind": "definition", "module": "Mathlib.RepresentationTheory.FiniteIndex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.resIndAdjunction", "kind": "definition", "module": "Mathlib.RepresentationTheory.FiniteIndex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.instIsRightAdjointSubtypeMemSubgroupIndFunctorSubtype", "kind": "theorem", "module": "Mathlib.RepresentationTheory.FiniteIndex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.resIndAdjunction_counit_app", "kind": "theorem", "module": "Mathlib.RepresentationTheory.FiniteIndex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.resIndAdjunction_unit_app", "kind": "theorem", "module": "Mathlib.RepresentationTheory.FiniteIndex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.resIndAdjunction_homEquiv_apply", "kind": "theorem", "module": "Mathlib.RepresentationTheory.FiniteIndex", "is_tactic_proof": true, "tactics": ["simp", "rfl"], "tactic_count": 2}
{"name": "Rep.resIndAdjunction_homEquiv_symm_apply", "kind": "theorem", "module": "Mathlib.RepresentationTheory.FiniteIndex", "is_tactic_proof": true, "tactics": ["simp", "rfl"], "tactic_count": 2}
{"name": "Rep.coindResAdjunction", "kind": "definition", "module": "Mathlib.RepresentationTheory.FiniteIndex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.instIsLeftAdjointSubtypeMemSubgroupCoindFunctorSubtype", "kind": "theorem", "module": "Mathlib.RepresentationTheory.FiniteIndex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.coindResAdjunction_counit_app", "kind": "theorem", "module": "Mathlib.RepresentationTheory.FiniteIndex", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Rep.coindResAdjunction_unit_app", "kind": "theorem", "module": "Mathlib.RepresentationTheory.FiniteIndex", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Rep.coindResAdjunction_homEquiv_apply", "kind": "theorem", "module": "Mathlib.RepresentationTheory.FiniteIndex", "is_tactic_proof": true, "tactics": ["simp", "rfl"], "tactic_count": 2}
{"name": "Rep.coindResAdjunction_homEquiv_symm_apply", "kind": "theorem", "module": "Mathlib.RepresentationTheory.FiniteIndex", "is_tactic_proof": true, "tactics": ["simp", "rfl"], "tactic_count": 2}
{"name": "Representation.FiniteCyclicGroup.coinvariantsKer_eq_range", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.FiniteCyclic", "is_tactic_proof": true, "tactics": ["refine", "rintro", "rcases", "induction", "zero", "succ", "use", "simpa", "rintro", "simpa"], "tactic_count": 10}
{"name": "Representation.FiniteCyclicGroup.coinvariantsEquiv", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.FiniteCyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.FiniteCyclicGroup.coinvariantsKer_leftRegular_eq_ker", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.FiniteCyclic", "is_tactic_proof": true, "tactics": ["have", "refine", "rintro", "simpa", "have", "ext", "by_cases", "simp_all", "simp_all", "rw", "exact"], "tactic_count": 11}
{"name": "Rep.FiniteCyclicGroup.leftRegular.range_norm_eq_ker_applyAsHom_sub", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.FiniteCyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.FiniteCyclicGroup.leftRegular.range_applyAsHom_sub_eq_ker_linearCombination", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.FiniteCyclic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Rep.FiniteCyclicGroup.leftRegular.range_applyAsHom_sub_eq_ker_norm", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.FiniteCyclic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Rep.FiniteCyclicGroup.chainComplexFunctor", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.FiniteCyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.FiniteCyclicGroup.normHomCompSub", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Homological.FiniteCyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.FiniteCyclicGroup.subCompNormHom", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Homological.FiniteCyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.FiniteCyclicGroup.moduleCatChainComplex", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Homological.FiniteCyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.FiniteCyclicGroup.moduleCatCochainComplex", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Homological.FiniteCyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.FiniteCyclicGroup.resolution.π", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.FiniteCyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.FiniteCyclicGroup.resolution_quasiIso", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.FiniteCyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.FiniteCyclicGroup.resolution", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.FiniteCyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inhomogeneousCochains.d", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inhomogeneousCochains.d_eq", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "groupCohomology.inhomogeneousCochains", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.inhomogeneousCochains.ext", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.inhomogeneousCochains.d_def", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "groupCohomology.inhomogeneousCochains.d_comp_d", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "groupCohomology.inhomogeneousCochainsIso", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Basic", "is_tactic_proof": true, "tactics": ["refine", "rintro", "subst", "simp"], "tactic_count": 4}
{"name": "groupCohomology.cocycles", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.cocyclesMk", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.iCocycles", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.toCocycles", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.iCocycles_mk", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Basic", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "groupCohomology", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.π", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology_induction_on", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Basic", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "groupCohomologyIsoExt", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomologyIso", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isZero_groupCohomology_succ_of_subsingleton", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.FiniteCyclicGroup.homResolutionIso", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.FiniteCyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.FiniteCyclicGroup.groupCohomologyIso₀", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.FiniteCyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.FiniteCyclicGroup.groupCohomologyIsoEven", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.FiniteCyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.FiniteCyclicGroup.groupCohomologyπEven", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.FiniteCyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.FiniteCyclicGroup.groupCohomologyπEven_eq_zero_iff", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.FiniteCyclic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Rep.FiniteCyclicGroup.groupCohomologyπEven_eq_iff", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.FiniteCyclic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Rep.FiniteCyclicGroup.groupCohomologyIsoOdd", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.FiniteCyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.FiniteCyclicGroup.groupCohomologyπOdd", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.FiniteCyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.FiniteCyclicGroup.groupCohomologyπOdd_eq_zero_iff", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.FiniteCyclic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Rep.FiniteCyclicGroup.groupCohomologyπOdd_eq_iff", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.FiniteCyclic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "groupCohomology.congr", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality", "is_tactic_proof": true, "tactics": ["subst", "rfl"], "tactic_count": 2}
{"name": "groupCohomology.cochainsMap", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.cochainsMap_id", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "groupCohomology.cochainsMap_id_f_hom_eq_compLeft", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "groupCohomology.cochainsMap_comp", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "groupCohomology.cochainsMap_id_comp", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "groupCohomology.cochainsMap_zero", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "groupCohomology.cochainsMap_f_map_mono", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "groupCohomology.cochainsMap_id_f_map_mono", "kind": "instance", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.cochainsMap_f_map_epi", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "groupCohomology.cochainsMap_id_f_map_epi", "kind": "instance", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.cocyclesMap", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.cocyclesMap_id", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.cocyclesMap_comp", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "groupCohomology.cocyclesMap_id_comp", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "groupCohomology.map", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.π_map", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "groupCohomology.map_id", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.map_comp", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "groupCohomology.map_id_comp", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "groupCohomology.cochainsMap₁", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.cochainsMap₂", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.cochainsMap₃", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.cochainsMap_f_0_comp_cochainsIso₀", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality", "is_tactic_proof": true, "tactics": ["ext", "simp", "rfl"], "tactic_count": 3}
{"name": "groupCohomology.cochainsMap_f_1_comp_cochainsIso₁", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.cochainsMap_f_2_comp_cochainsIso₂", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality", "is_tactic_proof": true, "tactics": ["ext", "change", "rcongr", "fin_cases"], "tactic_count": 4}
{"name": "groupCohomology.cochainsMap_f_3_comp_cochainsIso₃", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality", "is_tactic_proof": true, "tactics": ["ext", "change", "rcongr", "fin_cases"], "tactic_count": 4}
{"name": "groupCohomology.map_H0Iso_hom_f", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "groupCohomology.map_id_comp_H0Iso_hom", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality", "is_tactic_proof": true, "tactics": ["simp", "rfl"], "tactic_count": 2}
{"name": "groupCohomology.mono_map_0_of_mono", "kind": "instance", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.cocyclesMap_cocyclesIso₀_hom_f", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "groupCohomology.mapShortComplexH1", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.mapShortComplexH1_zero", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "groupCohomology.mapShortComplexH1_id", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "groupCohomology.mapShortComplexH1_comp", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.mapShortComplexH1_id_comp", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.mapCocycles₁", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.mapCocycles₁_comp_i", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "groupCohomology.coe_mapCocycles₁", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.cocyclesMap_comp_isoCocycles₁_hom", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality", "is_tactic_proof": true, "tactics": ["simp", "cochainsMap_f_1_comp_cochainsIso₁"], "tactic_count": 2}
{"name": "groupCohomology.mapCocycles₁_one", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp"], "tactic_count": 3}
{"name": "groupCohomology.H1π_comp_map", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "groupCohomology.map₁_one", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "groupCohomology.H1InfRes", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.instMonoModuleCatFH1InfRes", "kind": "instance", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality", "is_tactic_proof": true, "tactics": ["rw", "intro", "induction", "simp_all", "rcases", "refine", "funext", "simpa"], "tactic_count": 8}
{"name": "groupCohomology.H1InfRes_exact", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality", "is_tactic_proof": true, "tactics": ["rw", "intro", "induction", "x", "simp_all", "rcases", "have", "have", "refine", "intro", "calc", "simp", "simp", "abel", "simp", "intro", "have", "simp_all", "rw", "intro", "induction", "induction", "apply", "simp", "symm", "simp", "use", "ext", "simp"], "tactic_count": 29}
{"name": "groupCohomology.mapShortComplexH2", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.mapShortComplexH2_zero", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.mapShortComplexH2_id", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "groupCohomology.mapShortComplexH2_comp", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.mapShortComplexH2_id_comp", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.mapCocycles₂", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.mapCocycles₂_comp_i", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "groupCohomology.coe_mapCocycles₂", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.cocyclesMap_comp_isoCocycles₂_hom", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality", "is_tactic_proof": true, "tactics": ["simp", "cochainsMap_f_2_comp_cochainsIso₂"], "tactic_count": 2}
{"name": "groupCohomology.H2π_comp_map", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "groupCohomology.cochainsFunctor", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.instPreservesZeroMorphismsRepCochainComplexModuleCatNatCochainsFunctor", "kind": "instance", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.instAdditiveRepCochainComplexModuleCatNatCochainsFunctor", "kind": "instance", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.functor", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.instPreservesZeroMorphismsRepModuleCatFunctor", "kind": "instance", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.resNatTrans", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.infNatTrans", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.Hilbert90.aux", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Hilbert90", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.Hilbert90.aux_ne_zero", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Hilbert90", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.isMulCoboundary₁_of_isMulCocycle₁_of_aut_to_units", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Hilbert90", "is_tactic_proof": true, "tactics": ["obtain", "have", "simp", "use", "intro", "simp", "this,", "simp_rw", "exact"], "tactic_count": 9}
{"name": "groupCohomology.H1ofAutOnUnitsUnique", "kind": "instance", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Hilbert90", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.norm_ofAlgebraAutOnUnits_eq", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Hilbert90", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "groupCohomology.exists_div_of_norm_eq_one", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Hilbert90", "is_tactic_proof": true, "tactics": ["classical", "suffices", "have", "obtain", "use", "rw", "rw", "field_simp", "intro", "let", "have", "rw", "have", "rcases", "use", "simpa"], "tactic_count": 16}
{"name": "groupCohomology.exists_mul_galRestrict_of_norm_eq_one", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Hilbert90", "is_tactic_proof": false, "tactics": ["have", "rw", "exact", "have", "let", "obtain", "obtain", "obtain", "have", "rw", "refine", "rintro", "simp", "rw", "exact", "replace", "rw", "replace", "simp", "rw", "this]", "apply", "rw", "congr", "exact", "intro", "rw", "rw", "exact"], "tactic_count": 29}
{"name": "groupCohomology.map_cochainsFunctor_shortExact", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LongExactSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.mapShortComplex₁", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LongExactSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.mapShortComplex₂", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LongExactSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.mapShortComplex₃", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LongExactSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.mapShortComplex₁_exact", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LongExactSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.mapShortComplex₂_exact", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LongExactSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.mapShortComplex₃_exact", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LongExactSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.δ", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LongExactSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.epi_δ_of_isZero", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LongExactSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.mono_δ_of_isZero", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LongExactSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.isIso_δ_of_isZero", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LongExactSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.cocyclesMkOfCompEqD", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LongExactSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.δ_apply", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LongExactSequence", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "groupCohomology.mem_cocycles₁_of_comp_eq_d₀₁", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LongExactSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.δ₀_apply", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LongExactSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.mem_cocycles₂_of_comp_eq_d₁₂", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LongExactSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.δ₁_apply", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LongExactSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.cochainsIso₀", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.cochainsIso₁", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.cochainsIso₂", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.cochainsIso₃", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.d₀₁", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.d₀₁_ker_eq_invariants", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": true, "tactics": ["ext", "simp", "rfl"], "tactic_count": 3}
{"name": "groupCohomology.d₀₁_eq_zero", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": true, "tactics": ["ext", "rw", "rfl"], "tactic_count": 3}
{"name": "groupCohomology.subtype_comp_d₀₁", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": true, "tactics": ["ext", "replace", "rw", "exact"], "tactic_count": 4}
{"name": "groupCohomology.d₁₂", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.d₂₃", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.comp_d₀₁_eq", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": true, "tactics": ["ext", "change", "simp_rw", "rcongr"], "tactic_count": 4}
{"name": "groupCohomology.eq_d₀₁_comp_inv", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.comp_d₁₂_eq", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": true, "tactics": ["ext", "change", "rw", "simp", "add_assoc]", "rcongr"], "tactic_count": 6}
{"name": "groupCohomology.eq_d₁₂_comp_inv", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.comp_d₂₃_eq", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": true, "tactics": ["ext", "change", "dsimp", "rw", "simp", "pow_succ", "rcongr"], "tactic_count": 7}
{"name": "groupCohomology.eq_d₂₃_comp_inv", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.d₀₁_comp_d₁₂", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "groupCohomology.d₁₂_comp_d₂₃", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": true, "tactics": ["ext", "simp", "abel"], "tactic_count": 3}
{"name": "groupCohomology.shortComplexH0", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.shortComplexH1", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.shortComplexH2", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.cocycles₁", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.cocycles₂", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.instFunLikeSubtypeForallCarrierVModuleCatMemSubmoduleCocycles₁", "kind": "instance", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.cocycles₁.coe_mk", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.cocycles₁.val_eq_coe", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.cocycles₁_ext", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.mem_cocycles₁_def", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.mem_cocycles₁_iff", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "groupCohomology.cocycles₁_map_one", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "groupCohomology.cocycles₁_map_inv", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "groupCohomology.d₀₁_apply_mem_cocycles₁", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.cocycles₁.d₁₂_apply", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.cocycles₁_map_mul_of_isTrivial", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "groupCohomology.mem_cocycles₁_of_addMonoidHom", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.cocycles₁IsoOfIsTrivial", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.instFunLikeSubtypeForallProdCarrierVModuleCatMemSubmoduleCocycles₂", "kind": "instance", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.cocycles₂.coe_mk", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.cocycles₂.val_eq_coe", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.cocycles₂_ext", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.mem_cocycles₂_def", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.mem_cocycles₂_iff", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "groupCohomology.cocycles₂_map_one_fst", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "groupCohomology.cocycles₂_map_one_snd", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "groupCohomology.cocycles₂_ρ_map_inv_sub_map_inv", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": true, "tactics": ["have", "simp", "exact"], "tactic_count": 3}
{"name": "groupCohomology.d₁₂_apply_mem_cocycles₂", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.cocycles₂.d₂₃_apply", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.coboundaries₁", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.coboundaries₂", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.instFunLikeSubtypeForallCarrierVModuleCatMemSubmoduleCoboundaries₁", "kind": "instance", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.coboundaries₁.coe_mk", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.coboundaries₁.val_eq_coe", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.coboundaries₁_ext", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.coboundaries₁_le_cocycles₁", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "groupCohomology.coboundariesToCocycles₁", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.coboundariesToCocycles₁_apply", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.coboundaries₁_eq_bot_of_isTrivial", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "groupCohomology.instFunLikeSubtypeForallProdCarrierVModuleCatMemSubmoduleCoboundaries₂", "kind": "instance", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.coboundaries₂.coe_mk", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.coboundaries₂.val_eq_coe", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.coboundaries₂_ext", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.coboundaries₂_le_cocycles₂", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "groupCohomology.coboundariesToCocycles₂", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.coboundariesToCocycles₂_apply", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.IsCocycle₁", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.IsCocycle₂", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.map_one_of_isCocycle₁", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "groupCohomology.map_one_fst_of_isCocycle₂", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "groupCohomology.map_one_snd_of_isCocycle₂", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "groupCohomology.map_inv_of_isCocycle₁", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "groupCohomology.smul_map_inv_sub_map_inv_of_isCocycle₂", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": true, "tactics": ["have", "simp", "exact"], "tactic_count": 3}
{"name": "groupCohomology.IsCoboundary₁", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.IsCoboundary₂", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.cocyclesOfIsCocycle₁", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.isCocycle₁_of_mem_cocycles₁", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.coboundariesOfIsCoboundary₁", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.isCoboundary₁_of_mem_coboundaries₁", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "groupCohomology.cocyclesOfIsCocycle₂", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.isCocycle₂_of_mem_cocycles₂", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.coboundariesOfIsCoboundary₂", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.isCoboundary₂_of_mem_coboundaries₂", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "groupCohomology.IsMulCocycle₁", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.IsMulCocycle₂", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.map_one_of_isMulCocycle₁", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "groupCohomology.map_one_fst_of_isMulCocycle₂", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "groupCohomology.map_one_snd_of_isMulCocycle₂", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "groupCohomology.map_inv_of_isMulCocycle₁", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "groupCohomology.smul_map_inv_div_map_inv_of_isMulCocycle₂", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": true, "tactics": ["have", "simp", "exact"], "tactic_count": 3}
{"name": "groupCohomology.IsMulCoboundary₁", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.IsMulCoboundary₂", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.cocyclesOfIsMulCocycle₁", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.isMulCocycle₁_of_mem_cocycles₁", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.coboundariesOfIsMulCoboundary₁", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.isMulCoboundary₁_of_mem_coboundaries₁", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "groupCohomology.cocyclesOfIsMulCocycle₂", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.isMulCocycle₂_of_mem_cocycles₂", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.coboundariesOfIsMulCoboundary₂", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.isMulCoboundary₂_of_mem_coboundaries₂", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "groupCohomology.instMonoModuleCatFShortComplexH0", "kind": "instance", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "groupCohomology.shortComplexH0_exact", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": true, "tactics": ["rw", "intro", "refine", "rw", "exact"], "tactic_count": 5}
{"name": "groupCohomology.dArrowIso₀₁", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.cocyclesIso₀", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.cocyclesIso₀_hom_comp_f", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": true, "tactics": ["dsimp", "apply"], "tactic_count": 2}
{"name": "groupCohomology.cocyclesIso₀_inv_comp_iCocycles", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "groupCohomology.cocyclesMk₀_eq", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.isoShortComplexH1", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.isoCocycles₁", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.isoCocycles₁_hom_comp_i", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "groupCohomology.isoCocycles₁_inv_comp_iCocycles", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.toCocycles_comp_isoCocycles₁_hom", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "groupCohomology.cocyclesMk₁_eq", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": ["apply_fun", "simpa"], "tactic_count": 2}
{"name": "groupCohomology.isoShortComplexH2", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.isoCocycles₂", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.isoCocycles₂_hom_comp_i", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "groupCohomology.isoCocycles₂_inv_comp_iCocycles", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.toCocycles_comp_isoCocycles₂_hom", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "groupCohomology.cocyclesMk₂_eq", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": ["apply_fun", "simpa"], "tactic_count": 2}
{"name": "groupCohomology.H0", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.H0Iso", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.π_comp_H0Iso_hom", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "groupCohomology.H0_induction_on", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "groupCohomology.H0IsoOfIsTrivial", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.H0IsoOfIsTrivial_hom", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.π_comp_H0IsoOfIsTrivial_hom", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "groupCohomology.H0IsoOfIsTrivial_inv_apply", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.H1", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.H1π", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.instEpiModuleCatH1π", "kind": "instance", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "groupCohomology.H1π_eq_zero_iff", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": ["have", "leftHomologyπ_naturality'_assoc", "simp", "map_eq_zero_iff", "simp"], "tactic_count": 5}
{"name": "groupCohomology.H1π_eq_iff", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "groupCohomology.H1_induction_on", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.H1Iso", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.π_comp_H1Iso_hom", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "groupCohomology.H1IsoOfIsTrivial", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.H1π_comp_H1IsoOfIsTrivial_hom", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "groupCohomology.H1IsoOfIsTrivial_H1π_apply_apply", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "groupCohomology.H1IsoOfIsTrivial_inv_apply", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.H2", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.H2π", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.instEpiModuleCatH2π", "kind": "instance", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "groupCohomology.H2π_eq_zero_iff", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": ["have", "leftHomologyπ_naturality'_assoc", "simp", "map_eq_zero_iff", "simp"], "tactic_count": 5}
{"name": "groupCohomology.H2π_eq_iff", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "groupCohomology.H2_induction_on", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.H2Iso", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.π_comp_H2Iso_hom", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "groupCohomology.linearYonedaObjResProjectiveResolutionIso", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Shapiro", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupCohomology.coindIso", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupCohomology.Shapiro", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomologicalComplex.coinvariantsTensorObj", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.Tor", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.torIso", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.isZero_Tor_succ_of_projective", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.inhomogeneousChains.d", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.inhomogeneousChains.d_single", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "groupHomology.inhomogeneousChains.d_eq", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp", "barComplex.d_single"], "tactic_count": 3}
{"name": "groupHomology.inhomogeneousChains", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.inhomogeneousChains.ext", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.inhomogeneousChains.d_def", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "groupHomology.inhomogeneousChains.d_comp_d", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "groupHomology.inhomogeneousChainsIso", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Basic", "is_tactic_proof": true, "tactics": ["refine", "intro", "apply", "rintro", "simp"], "tactic_count": 5}
{"name": "groupHomology.cycles", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.cyclesMk", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.iCycles", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.iCycles_mk", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Basic", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "groupHomology.toCycles", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.π", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology_induction_on", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Basic", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "groupHomologyIsoTor", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomologyIso", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isZero_groupHomology_succ_of_subsingleton", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.FiniteCyclicGroup.coinvariantsTensorResolutionIso", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.FiniteCyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.FiniteCyclicGroup.groupHomologyIso₀", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.FiniteCyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.FiniteCyclicGroup.groupHomologyIsoEven", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.FiniteCyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.FiniteCyclicGroup.groupHomologyπEven", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.FiniteCyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.FiniteCyclicGroup.groupHomologyπEven_eq_zero_iff", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.FiniteCyclic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Rep.FiniteCyclicGroup.groupHomologyπEven_eq_iff", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.FiniteCyclic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Rep.FiniteCyclicGroup.groupHomologyIsoOdd", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.FiniteCyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.FiniteCyclicGroup.groupHomologyπOdd", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.FiniteCyclic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.FiniteCyclicGroup.groupHomologyπOdd_eq_zero_iff", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.FiniteCyclic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Rep.FiniteCyclicGroup.groupHomologyπOdd_eq_iff", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.FiniteCyclic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "groupHomology.congr", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": true, "tactics": ["subst", "rfl"], "tactic_count": 2}
{"name": "groupHomology.chainsMap", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.lsingle_comp_chainsMap_f", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "groupHomology.chainsMap_f_single", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "groupHomology.chainsMap_id", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.chainsMap_id_f_hom_eq_mapRange", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": true, "tactics": ["refine", "simp"], "tactic_count": 2}
{"name": "groupHomology.chainsMap_comp", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "groupHomology.chainsMap_id_comp", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.chainsMap_zero", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "groupHomology.chainsMap_f_map_mono", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "groupHomology.chainsMap_id_f_map_mono", "kind": "instance", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.chainsMap_f_map_epi", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "groupHomology.chainsMap_id_f_map_epi", "kind": "instance", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.cyclesMap", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.cyclesMap_id", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "groupHomology.cyclesMap_comp", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "groupHomology.cyclesMap_id_comp", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "groupHomology.map", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.π_map", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "groupHomology.map_id", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "groupHomology.map_comp", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "groupHomology.map_id_comp", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "groupHomology.chainsMap₁", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.chainsMap₂", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.chainsMap₃", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.chainsMap_f_0_comp_chainsIso₀", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "groupHomology.chainsMap_f_1_comp_chainsIso₁", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "groupHomology.chainsMap_f_2_comp_chainsIso₂", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "groupHomology.chainsMap_f_3_comp_chainsIso₃", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "groupHomology.cyclesMap_comp_cyclesIso₀_hom", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "groupHomology.cyclesIso₀_inv_comp_cyclesMap", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.H0π_comp_map", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "groupHomology.map_id_comp_H0Iso_hom", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": true, "tactics": ["rw", "ext", "simp"], "tactic_count": 3}
{"name": "groupHomology.epi_map_0_of_epi", "kind": "instance", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.mapShortComplexH1", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.mapShortComplexH1_zero", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": true, "tactics": ["refine", "all_goals", "simp", "ext", "simp"], "tactic_count": 5}
{"name": "groupHomology.mapShortComplexH1_id", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": true, "tactics": ["simp", "ext"], "tactic_count": 2}
{"name": "groupHomology.mapShortComplexH1_comp", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": true, "tactics": ["refine", "all_goals", "simp", "ext", "simp"], "tactic_count": 5}
{"name": "groupHomology.mapShortComplexH1_id_comp", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.mapCycles₁", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.mapCycles₁_hom", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.mapCycles₁_comp", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "groupHomology.mapCycles₁_id_comp", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.mapCycles₁_comp_i", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "groupHomology.coe_mapCycles₁", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.cyclesMap_comp_isoCycles₁_hom", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": true, "tactics": ["simp", "chainsMap_f_1_comp_chainsIso₁"], "tactic_count": 2}
{"name": "groupHomology.H1π_comp_map", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "groupHomology.map₁_one", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": true, "tactics": ["simp", "ext", "rw", "refine", "simpa"], "tactic_count": 5}
{"name": "groupHomology.mapCycles₁_quotientGroupMk'_epi", "kind": "instance", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": true, "tactics": ["rw", "rintro", "choose", "have", "refine", "simpa", "sum_mapDomain_index_inj", "simp"], "tactic_count": 8}
{"name": "groupHomology.H1CoresCoinfOfTrivial", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.map₁_quotientGroupMk'_epi", "kind": "instance", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": true, "tactics": ["convert", "rw", "exact"], "tactic_count": 3}
{"name": "groupHomology.H1CoresCoinfOfTrivial_g_epi", "kind": "instance", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.H1CoresCoinfOfTrivial_exact", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.H1CoresCoinf", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.comap_coinvariantsKer_pOpcycles_range_subtype_pOpcycles_eq_top", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": true, "tactics": ["rw", "intro", "rcases", "mapRange_surjective", "let", "let", "use", "apply", "change", "d₂₁", "simpa", "add_smul,"], "tactic_count": 12}
{"name": "groupHomology.instEpiModuleCatGH1CoresCoinf", "kind": "instance", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.H1CoresCoinf_exact", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.mapShortComplexH2", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.mapShortComplexH2_zero", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": true, "tactics": ["refine", "all_goals", "simp", "ext", "simp"], "tactic_count": 5}
{"name": "groupHomology.mapShortComplexH2_id", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": true, "tactics": ["refine", "all_goals", "simp", "ext", "simp"], "tactic_count": 5}
{"name": "groupHomology.mapShortComplexH2_comp", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": true, "tactics": ["refine", "all_goals", "simp", "ext", "simp"], "tactic_count": 5}
{"name": "groupHomology.mapShortComplexH2_id_comp", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.mapCycles₂", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.mapCycles₂_hom", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.mapCycles₂_comp", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "groupHomology.mapCycles₂_id_comp", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.mapCycles₂_comp_i", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "groupHomology.coe_mapCycles₂", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.cyclesMap_comp_isoCycles₂_hom", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": true, "tactics": ["simp", "chainsMap_f_2_comp_chainsIso₂"], "tactic_count": 2}
{"name": "groupHomology.H2π_comp_map", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "groupHomology.chainsFunctor", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.instPreservesZeroMorphismsRepChainComplexModuleCatNatChainsFunctor", "kind": "instance", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.functor", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.instPreservesZeroMorphismsRepModuleCatFunctor", "kind": "instance", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.coresNatTrans", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.coinfNatTrans", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.map_chainsFunctor_shortExact", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LongExactSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.mapShortComplex₁", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LongExactSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.mapShortComplex₂", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LongExactSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.mapShortComplex₃", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LongExactSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.mapShortComplex₁_exact", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LongExactSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.mapShortComplex₂_exact", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LongExactSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.mapShortComplex₃_exact", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LongExactSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.δ", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LongExactSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.epi_δ_of_isZero", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LongExactSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.mono_δ_of_isZero", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LongExactSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.isIso_δ_of_isZero", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LongExactSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.cyclesMkOfCompEqD", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LongExactSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.δ_apply", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LongExactSequence", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "groupHomology.δ₀_apply", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LongExactSequence", "is_tactic_proof": true, "tactics": ["simpa", "δ_apply"], "tactic_count": 2}
{"name": "groupHomology.mem_cycles₁_of_comp_eq_d₂₁", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LongExactSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.δ₁_apply", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LongExactSequence", "is_tactic_proof": true, "tactics": ["simpa", "δ_apply"], "tactic_count": 2}
{"name": "groupHomology.chainsIso₀", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.chainsIso₁", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.chainsIso₂", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.chainsIso₃", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.d₁₀", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.d₁₀_single", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "groupHomology.d₁₀_single_one", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "groupHomology.d₁₀_single_inv", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "groupHomology.range_d₁₀_eq_coinvariantsKer", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": true, "tactics": ["symm", "apply", "rintro", "use", "simp", "rintro", "induction", "zero", "single_add", "simpa"], "tactic_count": 10}
{"name": "groupHomology.d₁₀_comp_coinvariantsMk", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "groupHomology.chains₁ToCoinvariantsKer", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.chains₁ToCoinvariantsKer_surjective", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": true, "tactics": ["rintro", "rcases", "use"], "tactic_count": 3}
{"name": "groupHomology.d₁₀_eq_zero_of_isTrivial", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "groupHomology.d₂₁", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.d₂₁_single", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "groupHomology.d₂₁_single_one_fst", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "groupHomology.d₂₁_single_one_snd", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "groupHomology.d₂₁_single_inv_self_ρ_sub_self_inv", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": true, "tactics": ["simp", "abel"], "tactic_count": 2}
{"name": "groupHomology.d₂₁_single_self_inv_ρ_sub_inv_self", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": true, "tactics": ["simp", "abel"], "tactic_count": 2}
{"name": "groupHomology.d₂₁_single_ρ_add_single_inv_mul", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": true, "tactics": ["simp", "abel"], "tactic_count": 2}
{"name": "groupHomology.d₂₁_single_inv_mul_ρ_add_single", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": true, "tactics": ["simp", "abel"], "tactic_count": 2}
{"name": "groupHomology.d₃₂", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.d₃₂_single", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "groupHomology.d₃₂_single_one_fst", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "groupHomology.d₃₂_single_one_snd", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "groupHomology.d₃₂_single_one_thd", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "groupHomology.comp_d₁₀_eq", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.eq_d₁₀_comp_inv", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.comp_d₂₁_eq", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.eq_d₂₁_comp_inv", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.comp_d₃₂_eq", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.eq_d₃₂_comp_inv", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.d₂₁_comp_d₁₀", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "groupHomology.d₃₂_comp_d₂₁", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "groupHomology.shortComplexH0", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.shortComplexH1", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.shortComplexH2", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.cycles₁", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.cycles₂", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.mem_cycles₁_iff", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": true, "tactics": ["change", "rw"], "tactic_count": 2}
{"name": "groupHomology.single_mem_cycles₁_iff", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "groupHomology.single_mem_cycles₁_of_mem_invariants", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.d₂₁_apply_mem_cycles₁", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.cycles₁_eq_top_of_isTrivial", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "groupHomology.cycles₁IsoOfIsTrivial", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.cycles₁IsoOfIsTrivial_hom_apply", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.cycles₁IsoOfIsTrivial_inv_apply", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.mem_cycles₂_iff", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": true, "tactics": ["change", "simp"], "tactic_count": 2}
{"name": "groupHomology.single_mem_cycles₂_iff_inv", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "groupHomology.single_mem_cycles₂_iff", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "groupHomology.d₃₂_apply_mem_cycles₂", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.boundaries₁", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.boundaries₂", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.mem_cycles₁_of_mem_boundaries₁", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "groupHomology.boundaries₁_le_cycles₁", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.boundariesToCycles₁", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.boundariesToCycles₁_apply", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.single_one_mem_boundaries₁", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": true, "tactics": ["use", "simp"], "tactic_count": 2}
{"name": "groupHomology.single_ρ_self_add_single_inv_mem_boundaries₁", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "groupHomology.single_inv_ρ_self_add_single_mem_boundaries₁", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "groupHomology.mem_cycles₂_of_mem_boundaries₂", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "groupHomology.boundaries₂_le_cycles₂", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.boundariesToCycles₂", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.boundariesToCycles₂_apply", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.single_one_fst_sub_single_one_fst_mem_boundaries₂", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": true, "tactics": ["use", "simp"], "tactic_count": 2}
{"name": "groupHomology.single_one_fst_sub_single_one_snd_mem_boundaries₂", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": true, "tactics": ["use", "simp"], "tactic_count": 2}
{"name": "groupHomology.single_one_snd_sub_single_one_fst_mem_boundaries₂", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": true, "tactics": ["use", "simp"], "tactic_count": 2}
{"name": "groupHomology.single_one_snd_sub_single_one_snd_mem_boundaries₂", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": true, "tactics": ["use", "simp"], "tactic_count": 2}
{"name": "groupHomology.IsCycle₁", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.IsCycle₂", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.single_isCycle₁_iff", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "groupHomology.single_isCycle₁_of_mem_fixedPoints", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": true, "tactics": ["simp_all"], "tactic_count": 1}
{"name": "groupHomology.single_isCycle₂_iff_inv", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "groupHomology.single_isCycle₂_iff", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "groupHomology.IsBoundary₀", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.IsBoundary₁", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.IsBoundary₂", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.isBoundary₀_iff", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "use", "simp_all", "rintro", "use", "simp_all"], "tactic_count": 7}
{"name": "groupHomology.isBoundary₁_iff", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "use", "simp_all", "rintro", "use", "simp_all"], "tactic_count": 7}
{"name": "groupHomology.isBoundary₂_iff", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "use", "simp_all", "rintro", "use", "simp_all"], "tactic_count": 7}
{"name": "groupHomology.coinvariantsKerOfIsBoundary₀", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.isBoundary₀_of_mem_coinvariantsKer", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.cyclesOfIsCycle₁", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.isCycle₁_of_mem_cycles₁", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "groupHomology.boundariesOfIsBoundary₁", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.isBoundary₁_of_mem_boundaries₁", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.cyclesOfIsCycle₂", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.isCycle₂_of_mem_cycles₂", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.boundariesOfIsBoundary₂", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.isBoundary₂_of_mem_boundaries₂", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.instEpiModuleCatGShortComplexH0", "kind": "instance", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.shortComplexH0_exact", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "rcases", "use", "rfl"], "tactic_count": 6}
{"name": "groupHomology.cyclesIso₀", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.cyclesIso₀_inv_comp_iCycles", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "groupHomology.d₁₀ArrowIso", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.opcyclesIso₀", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.pOpcycles_comp_opcyclesIso_hom", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.coinvariantsMk_comp_opcyclesIso₀_inv", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.cyclesMk₀_eq", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.isoShortComplexH1", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.isoCycles₁", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.isoCycles₁_hom_comp_i", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "groupHomology.isoCycles₁_inv_comp_iCycles", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.toCycles_comp_isoCycles₁_hom", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "groupHomology.cyclesMk₁_eq", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.isoShortComplexH2", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.isoCycles₂", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.isoCycles₂_hom_comp_i", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "groupHomology.isoCycles₂_inv_comp_iCycles", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.toCycles_comp_isoCycles₂_hom", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "groupHomology.cyclesMk₂_eq", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.H0", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.H0Iso", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.H0π", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.instEpiModuleCatH0π", "kind": "instance", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "groupHomology.π_comp_H0Iso_hom", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "groupHomology.coinvariantsMk_comp_H0Iso_inv", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.H0π_comp_H0Iso_hom", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "groupHomology.cyclesIso₀_comp_H0π", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "groupHomology.H0_induction_on", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.H0IsoOfIsTrivial", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.H0IsoOfIsTrivial_inv_eq_π", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.π_comp_H0IsoOfIsTrivial_hom", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "groupHomology.H1", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.H1π", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.instEpiModuleCatH1π", "kind": "instance", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "groupHomology.H1π_eq_zero_iff", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": ["have", "leftHomologyπ_naturality'_assoc", "simp", "map_eq_zero_iff", "simp"], "tactic_count": 5}
{"name": "groupHomology.H1π_eq_iff", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "groupHomology.H1_induction_on", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.H1Iso", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.π_comp_H1Iso_hom", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "groupHomology.π_comp_H1Iso_inv", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.mkH1OfIsTrivial", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.mkH1OfIsTrivial_apply", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.H1ToTensorOfIsTrivial", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.H1ToTensorOfIsTrivial_H1π_single", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": ["simp", "change", "simp", "cycles₁IsoOfIsTrivial]"], "tactic_count": 4}
{"name": "groupHomology.H1AddEquivOfIsTrivial", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.H1AddEquivOfIsTrivial_single", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "groupHomology.H1AddEquivOfIsTrivial_symm_tmul", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "groupHomology.H2", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.H2π", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.instEpiModuleCatH2π", "kind": "instance", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "groupHomology.H2π_eq_zero_iff", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": ["have", "leftHomologyπ_naturality'_assoc", "simp", "map_eq_zero_iff", "simp"], "tactic_count": 5}
{"name": "groupHomology.H2π_eq_iff", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "groupHomology.H2_induction_on", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.H2Iso", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.π_comp_H2Iso_hom", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "groupHomology.π_comp_H2Iso_inv", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.coinvariantsTensorResProjectiveResolutionIso", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Shapiro", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupHomology.indIso", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.GroupHomology.Shapiro", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RepresentationTheory.Homological.Resolution.0.termGⁿ", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RepresentationTheory.Homological.Resolution.0._aux_Mathlib_RepresentationTheory_Homological_Resolution___macroRules__private_Mathlib_RepresentationTheory_Homological_Resolution_0_termGⁿ_1", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RepresentationTheory.Homological.Resolution.0.termGⁿ⁺¹", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RepresentationTheory.Homological.Resolution.0._aux_Mathlib_RepresentationTheory_Homological_Resolution___macroRules__private_Mathlib_RepresentationTheory_Homological_Resolution_0_termGⁿ⁺¹_1", "kind": "definition", "module": "Mathlib.RepresentationTheory.Homological.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.standardComplex.d_of", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.Resolution", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Rep.standardComplex.d_eq", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.Resolution", "is_tactic_proof": true, "tactics": ["refine", "simp"], "tactic_count": 2}
{"name": "Rep.standardComplex.forget₂ToModuleCatHomotopyEquiv_f_0_eq", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.Resolution", "is_tactic_proof": true, "tactics": ["refine", "change", "simp", "change", "simp"], "tactic_count": 5}
{"name": "Rep.standardComplex.d_comp_ε", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.Resolution", "is_tactic_proof": true, "tactics": ["ext", "have", "rw", "exact", "exact"], "tactic_count": 5}
{"name": "Rep.standardComplex.εToSingle₀_comp_eq", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.Resolution", "is_tactic_proof": true, "tactics": ["dsimp", "ext1", "simpa"], "tactic_count": 3}
{"name": "Rep.standardComplex.quasiIso_forget₂_εToSingle₀", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.Resolution", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "Rep.barComplex.d_single", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.Resolution", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Rep.barComplex.d_comp_diagonalSuccIsoFree_inv_eq", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.barComplex.d_def", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Homological.Resolution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.IndV", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Induced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.IndV.mk", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Induced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.IndV.hom_ext", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Induced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.ind", "kind": "definition", "module": "Mathlib.RepresentationTheory.Induced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.ind_mk", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Induced", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Rep.ind", "kind": "abbrev", "module": "Mathlib.RepresentationTheory.Induced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.indMap", "kind": "definition", "module": "Mathlib.RepresentationTheory.Induced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.indFunctor", "kind": "definition", "module": "Mathlib.RepresentationTheory.Induced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.indResHomEquiv", "kind": "definition", "module": "Mathlib.RepresentationTheory.Induced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.indResAdjunction", "kind": "definition", "module": "Mathlib.RepresentationTheory.Induced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.instIsLeftAdjointIndFunctor", "kind": "instance", "module": "Mathlib.RepresentationTheory.Induced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.instIsRightAdjointActionModuleCatRes", "kind": "instance", "module": "Mathlib.RepresentationTheory.Induced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.coinvariantsTensorIndHom", "kind": "definition", "module": "Mathlib.RepresentationTheory.Induced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.coinvariantsTensorIndHom_mk_tmul_indVMk", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Induced", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Rep.coinvariantsTensorIndInv", "kind": "definition", "module": "Mathlib.RepresentationTheory.Induced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.coinvariantsTensorIndInv_mk_tmul_indMk", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Induced", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Rep.coinvariantsTensorIndIso", "kind": "definition", "module": "Mathlib.RepresentationTheory.Induced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.coinvariantsTensorIndNatIso", "kind": "definition", "module": "Mathlib.RepresentationTheory.Induced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.IntertwiningMap.toLinearMap_injective", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Intertwining", "is_tactic_proof": true, "tactics": ["intro", "ext", "exact"], "tactic_count": 3}
{"name": "Representation.IntertwiningMap.toFun_injective", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Intertwining", "is_tactic_proof": true, "tactics": ["intro", "ext", "exact"], "tactic_count": 3}
{"name": "Representation.IntertwiningMap.instFunLike", "kind": "instance", "module": "Mathlib.RepresentationTheory.Intertwining", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.IntertwiningMap.coe_mk", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Intertwining", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.IntertwiningMap.isIntertwining", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Intertwining", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.IntertwiningMap.toLinearMap_apply", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Intertwining", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.IntertwiningMap.instZero", "kind": "instance", "module": "Mathlib.RepresentationTheory.Intertwining", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.IntertwiningMap.coe_zero", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Intertwining", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.IntertwiningMap.instAdd", "kind": "instance", "module": "Mathlib.RepresentationTheory.Intertwining", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.IntertwiningMap.coe_add", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Intertwining", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.IntertwiningMap.instSMul", "kind": "instance", "module": "Mathlib.RepresentationTheory.Intertwining", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.IntertwiningMap.coe_smul", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Intertwining", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.IntertwiningMap.instSMulNat", "kind": "instance", "module": "Mathlib.RepresentationTheory.Intertwining", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.IntertwiningMap.coe_nsmul", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Intertwining", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.IntertwiningMap.instAddCommMonoid", "kind": "instance", "module": "Mathlib.RepresentationTheory.Intertwining", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.IntertwiningMap.coeFnAddMonoidHom", "kind": "definition", "module": "Mathlib.RepresentationTheory.Intertwining", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.IntertwiningMap.instModule", "kind": "instance", "module": "Mathlib.RepresentationTheory.Intertwining", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.IntertwiningMap.equivLinearMapAsModule", "kind": "definition", "module": "Mathlib.RepresentationTheory.Intertwining", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.IntertwiningMap.id", "kind": "definition", "module": "Mathlib.RepresentationTheory.Intertwining", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.IntertwiningMap.llcomp", "kind": "definition", "module": "Mathlib.RepresentationTheory.Intertwining", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.IntertwiningMap.comp", "kind": "definition", "module": "Mathlib.RepresentationTheory.Intertwining", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.IntertwiningMap.instMul", "kind": "instance", "module": "Mathlib.RepresentationTheory.Intertwining", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.IntertwiningMap.coe_mul", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Intertwining", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.IntertwiningMap.mul_apply", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Intertwining", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.IntertwiningMap.instOne", "kind": "instance", "module": "Mathlib.RepresentationTheory.Intertwining", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.IntertwiningMap.coe_one", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Intertwining", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.IntertwiningMap.instSemigroup", "kind": "instance", "module": "Mathlib.RepresentationTheory.Intertwining", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.IntertwiningMap.instPowNat", "kind": "instance", "module": "Mathlib.RepresentationTheory.Intertwining", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.IntertwiningMap.instMonoid", "kind": "instance", "module": "Mathlib.RepresentationTheory.Intertwining", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.IntertwiningMap.instNatCast", "kind": "instance", "module": "Mathlib.RepresentationTheory.Intertwining", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.IntertwiningMap.instSemiring", "kind": "instance", "module": "Mathlib.RepresentationTheory.Intertwining", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.IntertwiningMap.instAlgebra", "kind": "instance", "module": "Mathlib.RepresentationTheory.Intertwining", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.IntertwiningMap.algebraMap_apply", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Intertwining", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.IntertwiningMap.equivAlgEnd", "kind": "definition", "module": "Mathlib.RepresentationTheory.Intertwining", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.IntertwiningMap.isIntertwiningMap_of_mem_center", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Intertwining", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "rw"], "tactic_count": 4}
{"name": "Representation.IntertwiningMap.centralMul", "kind": "definition", "module": "Mathlib.RepresentationTheory.Intertwining", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupAlgebra.mul_average_left", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Invariants", "is_tactic_proof": false, "tactics": ["simp", "set", "change", "rw"], "tactic_count": 4}
{"name": "GroupAlgebra.mul_average_right", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Invariants", "is_tactic_proof": false, "tactics": ["simp", "set", "change", "rw"], "tactic_count": 4}
{"name": "Representation.mem_invariants", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Invariants", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "Representation.invariants_eq_inter", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Invariants", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Representation.invariants_eq_top", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.mem_invariants_iff_of_forall_mem_zpowers", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.averageMap_invariant", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.averageMap_id", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Invariants", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Representation.isProj_averageMap", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.le_comap_invariants", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.linHom.mem_invariants_iff_comm", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Invariants", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "ρAut_apply_hom", "exact"], "tactic_count": 4}
{"name": "Rep.invariantsAdjunction_homEquiv_apply_hom", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.invariantsAdjunction_homEquiv_symm_apply_hom", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Invariants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.irreducible_iff_isSimpleModule_asModule", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Irreducible", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Representation.is_simple_module_iff_irreducible_ofModule", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Irreducible", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Representation.IsIrreducible.instIsSimpleModuleMonoidAlgebraAsModule", "kind": "instance", "module": "Mathlib.RepresentationTheory.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.IsIrreducible.injective_or_eq_zero", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Irreducible", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Representation.IsIrreducible.bijective_or_eq_zero", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Irreducible", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Representation.IsIrreducible.algebraMap_intertwiningMap_bijective_of_isAlgClosed", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Irreducible", "is_tactic_proof": false, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "Representation.IsIrreducible.finrank_eq_one_of_isMulCommutative", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Irreducible", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "LinearMap.conjugate", "kind": "definition", "module": "Mathlib.RepresentationTheory.Maschke", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.conjugate_apply", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Maschke", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.conjugate_i", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Maschke", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LinearMap.sumOfConjugates", "kind": "definition", "module": "Mathlib.RepresentationTheory.Maschke", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.sumOfConjugates_apply", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Maschke", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.sumOfConjugatesEquivariant", "kind": "definition", "module": "Mathlib.RepresentationTheory.Maschke", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.sumOfConjugatesEquivariant_apply", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Maschke", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.equivariantProjection", "kind": "definition", "module": "Mathlib.RepresentationTheory.Maschke", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.equivariantProjection_apply", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Maschke", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LinearMap.equivariantProjection_condition", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Maschke", "is_tactic_proof": true, "tactics": ["rw", "simp", "rw", "one_smul]"], "tactic_count": 4}
{"name": "MonoidAlgebra.exists_leftInverse_of_injective", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Maschke", "is_tactic_proof": true, "tactics": ["let", "letI", "letI", "have", "have", "set", "have", "apply", "simp", "refine", "exact"], "tactic_count": 11}
{"name": "MonoidAlgebra.Submodule.exists_isCompl", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Maschke", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "MonoidAlgebra.Submodule.instIsSemisimpleModule", "kind": "instance", "module": "Mathlib.RepresentationTheory.Maschke", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidAlgebra.Submodule.instIsSemisimpleRingAddMonoidAlgebra", "kind": "instance", "module": "Mathlib.RepresentationTheory.Maschke", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.coe_of", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Rep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.of_ρ", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Rep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.Action_ρ_eq_ρ", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Rep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.ρ_hom", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Rep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.ofHom_ρ", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Rep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.hom_comm_apply", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Rep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.trivial_def", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Rep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.applyAsHom_comm", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Rep", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Rep.epi_iff_surjective", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Rep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.mono_iff_injective", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Rep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.tensor_ρ", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Rep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.res_obj_ρ", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Rep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.coe_res_obj_ρ", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Rep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.coe_linearization_obj", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Rep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.linearization_obj_ρ", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Rep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.coe_linearization_obj_ρ", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Rep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.linearization_single", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Rep", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Rep.linearization_map_hom", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Rep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.linearization_map_hom_single", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Rep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.linearization_μ_hom", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Rep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.linearization_δ_hom", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Rep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.linearization_ε_hom", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Rep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.linearization_η_hom_apply", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Rep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.ofDistribMulAction_ρ_apply_apply", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Rep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.ofMulDistribMulAction_ρ_apply_apply", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Rep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.leftRegularHom_hom_single", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Rep", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Rep.leftRegularHomEquiv_symm_single", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Rep", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Rep.freeLift_hom_single_single", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Rep", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Rep.free_ext", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Rep", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Rep.leftRegularTensorTrivialIsoFree_hom_hom_single_tmul_single", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Rep", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Rep.leftRegularTensorTrivialIsoFree_inv_hom_single_single", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Rep", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Rep.diagonalSuccIsoTensorTrivial_hom_hom_single", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Rep", "is_tactic_proof": true, "tactics": ["simp", "finsuppTensorFinsupp'_symm_single_eq_single_one_tmul,"], "tactic_count": 2}
{"name": "Rep.diagonalSuccIsoTensorTrivial_inv_hom_single_single", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Rep", "is_tactic_proof": true, "tactics": ["have", "simp_all", "types_tensorObj_def,"], "tactic_count": 3}
{"name": "Rep.diagonalSuccIsoTensorTrivial_inv_hom_single_left", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Rep", "is_tactic_proof": true, "tactics": ["refine", "simp", "intro", "simpa", "diagonalSuccIsoTensorTrivial_inv_hom_single_single"], "tactic_count": 5}
{"name": "Rep.diagonalSuccIsoTensorTrivial_inv_hom_single_right", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Rep", "is_tactic_proof": true, "tactics": ["refine", "simp", "intro", "simpa", "diagonalSuccIsoTensorTrivial_inv_hom_single_single"], "tactic_count": 5}
{"name": "Rep.diagonalSuccIsoFree_hom_hom_single", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Rep", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Rep.diagonalSuccIsoFree_inv_hom_single_single", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Rep", "is_tactic_proof": true, "tactics": ["have", "simp_all"], "tactic_count": 2}
{"name": "Rep.diagonalSuccIsoFree_inv_hom_single", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Rep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.diagonalHomEquiv_apply", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Rep", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Rep.diagonalHomEquiv_symm_apply", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Rep", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Rep.norm_comm", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Rep", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Rep.ihom", "kind": "definition", "module": "Mathlib.RepresentationTheory.Rep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.ihom_obj_ρ_apply", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Rep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.ihom_obj_ρ_def", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Rep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.homEquiv_def", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Rep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.ihom_ev_app_hom", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Rep", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Rep.ihom_coev_app_hom", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Rep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.MonoidalClosed.linearHomEquiv_hom", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Rep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.MonoidalClosed.linearHomEquivComm_hom", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Rep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.MonoidalClosed.linearHomEquiv_symm_hom", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Rep", "is_tactic_proof": true, "tactics": ["simp", "rfl"], "tactic_count": 2}
{"name": "Rep.MonoidalClosed.linearHomEquivComm_symm_hom", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Rep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.repOfTprodIso_apply", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Rep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.repOfTprodIso_inv_apply", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Rep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.to_Module_monoidAlgebra_map_aux", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Rep", "is_tactic_proof": true, "tactics": ["apply", "intro", "simp", "exact", "intro", "intro", "simp"], "tactic_count": 7}
{"name": "Rep.ofModuleMonoidAlgebra_obj_coe", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Rep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.ofModuleMonoidAlgebra_obj_ρ", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Rep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rep.unit_iso_comm", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Rep", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Representation.invtSubmodule", "kind": "definition", "module": "Mathlib.RepresentationTheory.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.mem_invtSubmodule", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Submodule", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Representation.invtSubmodule.top_mem", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Submodule", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Representation.invtSubmodule.bot_mem", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Submodule", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Representation.invtSubmodule.instBoundedOrderSubtypeSubmoduleMemSublattice", "kind": "instance", "module": "Mathlib.RepresentationTheory.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.invtSubmodule.coe_top", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.invtSubmodule.coe_bot", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.invtSubmodule.nontrivial_iff", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Submodule", "is_tactic_proof": true, "tactics": ["refine", "contrapose", "infer_instance", "refine", "rw", "exact"], "tactic_count": 6}
{"name": "Representation.invtSubmodule.instNontrivialSubtypeSubmoduleMemSublattice", "kind": "instance", "module": "Mathlib.RepresentationTheory.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Representation.asAlgebraHom_mem_of_forall_mem", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Submodule", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "Representation.mapSubmodule", "kind": "definition", "module": "Mathlib.RepresentationTheory.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subrepresentation.toSubmodule_injective", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Subrepresentation", "is_tactic_proof": true, "tactics": ["rintro", "congr"], "tactic_count": 2}
{"name": "Subrepresentation.instSetLike", "kind": "instance", "module": "Mathlib.RepresentationTheory.Subrepresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subrepresentation.instPartialOrder", "kind": "instance", "module": "Mathlib.RepresentationTheory.Subrepresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subrepresentation.toRepresentation", "kind": "definition", "module": "Mathlib.RepresentationTheory.Subrepresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subrepresentation.instMax", "kind": "instance", "module": "Mathlib.RepresentationTheory.Subrepresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subrepresentation.instMin", "kind": "instance", "module": "Mathlib.RepresentationTheory.Subrepresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subrepresentation.coe_sup", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Subrepresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subrepresentation.coe_inf", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Subrepresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subrepresentation.toSubmodule_sup", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Subrepresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subrepresentation.toSubmodule_inf", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Subrepresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subrepresentation.instLattice", "kind": "instance", "module": "Mathlib.RepresentationTheory.Subrepresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subrepresentation.instBoundedOrder", "kind": "instance", "module": "Mathlib.RepresentationTheory.Subrepresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subrepresentation.asSubmodule", "kind": "definition", "module": "Mathlib.RepresentationTheory.Subrepresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subrepresentation.mem_asSubmodule_iff", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Subrepresentation", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "Subrepresentation.asSubmodule'", "kind": "definition", "module": "Mathlib.RepresentationTheory.Subrepresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subrepresentation.mem_asSubmodule'_iff", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Subrepresentation", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "Subrepresentation.ofSubmodule", "kind": "definition", "module": "Mathlib.RepresentationTheory.Subrepresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subrepresentation.mem_ofSubmodule_iff", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Subrepresentation", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "Subrepresentation.ofSubmodule'", "kind": "definition", "module": "Mathlib.RepresentationTheory.Subrepresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subrepresentation.mem_ofSubmodule'_iff", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Subrepresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subrepresentation.subrepresentationSubmoduleOrderIso", "kind": "definition", "module": "Mathlib.RepresentationTheory.Subrepresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subrepresentation.submoduleSubrepresentationOrderIso", "kind": "definition", "module": "Mathlib.RepresentationTheory.Subrepresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TannakaDuality.FiniteGroup.instMonoidalFDRepFGModuleCatForget₂", "kind": "instance", "module": "Mathlib.RepresentationTheory.Tannaka", "is_tactic_proof": true, "tactics": ["change"], "tactic_count": 1}
{"name": "TannakaDuality.FiniteGroup.forget", "kind": "definition", "module": "Mathlib.RepresentationTheory.Tannaka", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TannakaDuality.FiniteGroup.forget_obj", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Tannaka", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TannakaDuality.FiniteGroup.forget_map", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Tannaka", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TannakaDuality.FiniteGroup.equivApp", "kind": "definition", "module": "Mathlib.RepresentationTheory.Tannaka", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TannakaDuality.FiniteGroup.equivHom", "kind": "definition", "module": "Mathlib.RepresentationTheory.Tannaka", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TannakaDuality.FiniteGroup.rightRegular", "kind": "definition", "module": "Mathlib.RepresentationTheory.Tannaka", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TannakaDuality.FiniteGroup.rightRegular_apply", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Tannaka", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TannakaDuality.FiniteGroup.leftRegular", "kind": "definition", "module": "Mathlib.RepresentationTheory.Tannaka", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TannakaDuality.FiniteGroup.leftRegular_apply", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Tannaka", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TannakaDuality.FiniteGroup.rightFDRep", "kind": "definition", "module": "Mathlib.RepresentationTheory.Tannaka", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TannakaDuality.FiniteGroup.equivHom_injective", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Tannaka", "is_tactic_proof": true, "tactics": ["intro", "classical", "apply_fun", "simp_all"], "tactic_count": 4}
{"name": "TannakaDuality.FiniteGroup.mulRepHom", "kind": "definition", "module": "Mathlib.RepresentationTheory.Tannaka", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TannakaDuality.FiniteGroup.map_mul_toRightFDRepComp", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Tannaka", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "exact"], "tactic_count": 4}
{"name": "TannakaDuality.FiniteGroup.algHomOfRightFDRepComp", "kind": "definition", "module": "Mathlib.RepresentationTheory.Tannaka", "is_tactic_proof": true, "tactics": ["let", "let", "refine", "suffices", "have", "rwa", "have", "apply_fun", "exact"], "tactic_count": 9}
{"name": "TannakaDuality.FiniteGroup.sumSMulInv", "kind": "definition", "module": "Mathlib.RepresentationTheory.Tannaka", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TannakaDuality.FiniteGroup.sumSMulInv_single_id", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Tannaka", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "TannakaDuality.FiniteGroup.ofRightFDRep", "kind": "definition", "module": "Mathlib.RepresentationTheory.Tannaka", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TannakaDuality.FiniteGroup.toRightFDRepComp_injective", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Tannaka", "is_tactic_proof": true, "tactics": ["have", "classical", "ext", "have", "have", "rw", "simpa"], "tactic_count": 7}
{"name": "TannakaDuality.FiniteGroup.leftRegularFDRepHom", "kind": "definition", "module": "Mathlib.RepresentationTheory.Tannaka", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TannakaDuality.FiniteGroup.toRightFDRepComp_in_rightRegular", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Tannaka", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TannakaDuality.FiniteGroup.equivHom_surjective", "kind": "theorem", "module": "Mathlib.RepresentationTheory.Tannaka", "is_tactic_proof": true, "tactics": ["intro", "obtain", "exact"], "tactic_count": 3}
{"name": "TannakaDuality.FiniteGroup.equiv", "kind": "definition", "module": "Mathlib.RepresentationTheory.Tannaka", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.transitionMap_ideal_mk", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.transitionMap_map_one", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.transitionMap_map_mul", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.transitionMap_map_pow", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.val_one", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.val_mul", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.factor_evalₐ_eq_eval", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Algebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AdicCompletion.factor_eval_eq_evalₐ", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Algebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AdicCompletion.evalₐ_of", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Algebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AdicCompletion.surjective_evalₐ", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Algebra", "is_tactic_proof": true, "tactics": ["simp", "apply", "exact", "exact"], "tactic_count": 4}
{"name": "AdicCompletion.evalₐ_mk", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Algebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AdicCompletion.ext_evalₐ", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Algebra", "is_tactic_proof": true, "tactics": ["ext", "have", "exact"], "tactic_count": 3}
{"name": "AdicCompletion.evalOneₐ_of", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.factorₐ_evalₐ_one", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.evalOneₐ_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Algebra", "is_tactic_proof": true, "tactics": ["dsimp", "exact"], "tactic_count": 2}
{"name": "AdicCompletion.one_apply", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.mul_apply", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.evalₐ_mkₐ", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Algebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AdicCompletion.Ideal.mk_eq_mk", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Algebra", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "AdicCompletion.smul_mk", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Algebra", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AdicCompletion.mk_smul_mk", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.val_smul_eq_evalₐ_smul", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Algebra", "is_tactic_proof": true, "tactics": ["apply", "exact"], "tactic_count": 2}
{"name": "AdicCompletion.smul_eval", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.factor_eval_liftRingHom", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Algebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AdicCompletion.evalₐ_liftRingHom", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Algebra", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "AdicCompletion.evalₐ_comp_liftRingHom", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Algebra", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "AdicCompletion.evalₐ_liftAlgHom", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.evalOneₐ_liftAlgHom", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Algebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AdicCompletion.ofAlgEquiv_apply", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Algebra", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "AdicCompletion.of_ofAlgEquiv_symm", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Algebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AdicCompletion.ofAlgEquiv_symm_of", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Algebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AdicCompletion.mk_smul_top_ofAlgEquiv_symm", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Algebra", "is_tactic_proof": true, "tactics": ["nth_rw", "simp"], "tactic_count": 2}
{"name": "AdicCompletion.mk_ofAlgEquiv_symm", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Algebra", "is_tactic_proof": true, "tactics": ["simp", "rw", "simp"], "tactic_count": 3}
{"name": "AdicCompletion.mk_ofAlgEquiv_symm_eq_evalOneₐ", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Algebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AdicCompletion.kerProj_of", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.kerProj_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Algebra", "is_tactic_proof": true, "tactics": ["dsimp", "exact"], "tactic_count": 2}
{"name": "_private.Mathlib.RingTheory.AdicCompletion.AsTensorProduct.0.AdicCompletion.ofTensorProductBil_apply_apply", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.AsTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.ofTensorProduct_tmul", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.AsTensorProduct", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AdicCompletion.ofTensorProduct_naturality", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.AsTensorProduct", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "_private.Mathlib.RingTheory.AdicCompletion.AsTensorProduct.0.AdicCompletion.piEquivOfFintype_comp_ofTensorProduct_eq", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.AsTensorProduct", "is_tactic_proof": true, "tactics": ["ext", "suffices", "simpa", "split"], "tactic_count": 4}
{"name": "_private.Mathlib.RingTheory.AdicCompletion.AsTensorProduct.0.AdicCompletion.ofTensorProduct_eq", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.AsTensorProduct", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "_private.Mathlib.RingTheory.AdicCompletion.AsTensorProduct.0.AdicCompletion.ofTensorProductInvOfPiFintype_comp_ofTensorProduct", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.AsTensorProduct", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "simp"], "tactic_count": 3}
{"name": "_private.Mathlib.RingTheory.AdicCompletion.AsTensorProduct.0.AdicCompletion.ofTensorProduct_comp_ofTensorProductInvOfPiFintype", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.AsTensorProduct", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "nth_rw", "simp"], "tactic_count": 4}
{"name": "AdicCompletion.ofTensorProduct_bijective_of_pi_of_fintype", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.AsTensorProduct", "is_tactic_proof": true, "tactics": ["classical", "cases", "exact"], "tactic_count": 3}
{"name": "AdicCompletion.ofTensorProduct_surjective_of_finite", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.AsTensorProduct", "is_tactic_proof": true, "tactics": ["obtain", "let", "let", "have", "ext", "simp", "have", "simp", "apply", "exact", "exact", "exact"], "tactic_count": 12}
{"name": "_private.Mathlib.RingTheory.AdicCompletion.AsTensorProduct.0.AdicCompletion.tens_exact", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.AsTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.AdicCompletion.AsTensorProduct.0.AdicCompletion.tens_surj", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.AsTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.AdicCompletion.AsTensorProduct.0.AdicCompletion.adic_exact", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.AsTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.AdicCompletion.AsTensorProduct.0.AdicCompletion.adic_surj", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.AsTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.AdicCompletion.AsTensorProduct.0.AdicCompletion.ofTensorProduct_bijective_of_map_from_fin", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.AsTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.ofTensorProduct_bijective_of_finite_of_isNoetherian", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.AsTensorProduct", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "AdicCompletion.coe_ofTensorProductEquivOfFiniteNoetherian", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.AsTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.ofTensorProductEquivOfFiniteNoetherian_apply", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.AsTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.ofTensorProductEquivOfFiniteNoetherian_symm_of", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.AsTensorProduct", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "AdicCompletion.tensor_map_id_left_eq_map", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.AsTensorProduct", "is_tactic_proof": true, "tactics": ["rw", "ext", "simp"], "tactic_count": 3}
{"name": "AdicCompletion.tensor_map_id_left_injective_of_injective", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.AsTensorProduct", "is_tactic_proof": true, "tactics": ["rw", "simp", "exact"], "tactic_count": 3}
{"name": "IsHausdorff.haus", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isHausdorff_iff", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsHausdorff.eq_iff_smodEq", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "apply", "simpa"], "tactic_count": 4}
{"name": "IsHausdorff.map_algebraMap_iff", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": true, "tactics": ["simp", "congr", "simp", "rfl"], "tactic_count": 4}
{"name": "IsHausdorff.of_map", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": true, "tactics": ["refine", "apply", "rw", "simp", "rw", "intro", "rw", "apply", "have", "simp", "exact", "exact"], "tactic_count": 12}
{"name": "IsHausdorff.funext", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": true, "tactics": ["ext", "rw", "intro", "exact"], "tactic_count": 4}
{"name": "IsHausdorff.StrictMono.funext", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": true, "tactics": ["ext", "rw", "intro", "apply", "exact"], "tactic_count": 5}
{"name": "IsHausdorff.funext'", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": true, "tactics": ["ext", "rw", "intro", "simpa"], "tactic_count": 4}
{"name": "IsHausdorff.StrictMono.funext'", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": true, "tactics": ["ext", "rw", "intro", "apply", "simpa"], "tactic_count": 5}
{"name": "IsPrecomplete.prec", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isPrecomplete_iff", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsHausdorff.subsingleton", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsHausdorff.iInf_pow_smul", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hausdorffification.induction_on", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hausdorffification.lift_of", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hausdorffification.lift_comp_of", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Hausdorffification.lift_eq", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.val_zero", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.val_zero_apply", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.val_add", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.val_sub", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.val_neg", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.val_add_apply", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.val_sub_apply", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.val_neg_apply", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.val_smul", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.val_smul_apply", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.ext", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.val_sum", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "AdicCompletion.val_sum_apply", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AdicCompletion.of_apply", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.coe_eval", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.eval_apply", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.eval_of", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.eval_comp_of", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.eval_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.range_eval", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.transitionMap_comp_eval_apply", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.transitionMap_comp_eval", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "AdicCompletion.AdicCauchySequence.zero_apply", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.AdicCauchySequence.add_apply", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.AdicCauchySequence.sub_apply", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.AdicCauchySequence.smul_apply", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.AdicCauchySequence.ext", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.AdicCauchySequence.mk_eq_mk", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.isAdicCauchy_iff", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "intro", "induction", "base", "succ", "trans", "exact", "refine"], "tactic_count": 10}
{"name": "AdicCompletion.mk_zero_of", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": true, "tactics": ["obtain", "ext", "obtain", "rw", "simpa"], "tactic_count": 5}
{"name": "AdicCompletion.mk_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": true, "tactics": ["intro", "choose", "refine", "intro", "rw", "mkQ_apply,", "ext", "simp"], "tactic_count": 8}
{"name": "AdicCompletion.induction_on", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "AdicCompletion.eval_lift", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.eval_lift_apply", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.of_injective_iff", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": true, "tactics": ["constructor", "refine", "ext", "simpa", "intro", "rw", "ext", "simp", "refine", "rw", "simpa"], "tactic_count": 11}
{"name": "AdicCompletion.of_injective", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.of_inj", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.of_surjective_iff", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": true, "tactics": ["constructor", "refine", "let", "obtain", "refine", "simp", "rw", "simp", "intro", "choose", "obtain", "use", "ext", "simpa"], "tactic_count": 14}
{"name": "AdicCompletion.of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.of_bijective_iff", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.of_bijective", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.ofLinearEquiv_symm_of", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AdicCompletion.of_ofLinearEquiv_symm", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsAdicComplete.of_lift", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsAdicComplete.of_comp_lift", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": true, "tactics": ["ext1"], "tactic_count": 1}
{"name": "IsAdicComplete.mk_lift", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": true, "tactics": ["simp", "rw", "simp"], "tactic_count": 3}
{"name": "IsAdicComplete.mkQ_comp_lift", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "IsAdicComplete.eq_lift", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": true, "tactics": ["apply", "apply", "intro", "simp"], "tactic_count": 4}
{"name": "IsAdicComplete.StrictMono.factorPow_comp_eq_of_factorPow_comp_succ_eq", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": true, "tactics": ["ext", "symm", "refine", "exact", "intro", "simp", "simpa"], "tactic_count": 7}
{"name": "IsAdicComplete.StrictMono.extend_eq", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAdicComplete.StrictMono.factorPow_comp_extend", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "IsAdicComplete.StrictMono.of_lift", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAdicComplete.StrictMono.of_comp_lift", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAdicComplete.StrictMono.mk_lift", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": false, "tactics": ["simp", "rw", "simp"], "tactic_count": 3}
{"name": "IsAdicComplete.StrictMono.mkQ_comp_lift", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "IsAdicComplete.StrictMono.eq_lift", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": true, "tactics": ["apply", "apply", "intro", "simp"], "tactic_count": 4}
{"name": "IsAdicComplete.subsingleton", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAdicComplete.le_jacobson_bot", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Basic", "is_tactic_proof": true, "tactics": ["intro", "rw", "intro", "rw", "let", "have", "intro", "simp", "rw", "apply", "intro", "rw", "exact", "obtain", "rw", "use", "rw", "apply", "intro", "specialize", "rw", "rw", "suffices", "convert", "ring", "cases", "simp", "rw", "exact"], "tactic_count": 29}
{"name": "_private.Mathlib.RingTheory.AdicCompletion.Exactness.0.AdicCompletion.mapPreimageDelta", "kind": "definition", "module": "Mathlib.RingTheory.AdicCompletion.Exactness", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.AdicCompletion.Exactness.0.AdicCompletion.mapPreimage", "kind": "definition", "module": "Mathlib.RingTheory.AdicCompletion.Exactness", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.map_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Exactness", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.map_injective", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Exactness", "is_tactic_proof": true, "tactics": ["obtain", "rw", "intro", "apply", "intro", "refine", "rw", "apply", "nth_rw", "rw", "exact"], "tactic_count": 11}
{"name": "_private.Mathlib.RingTheory.AdicCompletion.Exactness.0.AdicCompletion.mapExactAuxDelta", "kind": "definition", "module": "Mathlib.RingTheory.AdicCompletion.Exactness", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.AdicCompletion.Exactness.0.AdicCompletion.mapExactAux", "kind": "definition", "module": "Mathlib.RingTheory.AdicCompletion.Exactness", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.map_exact", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Exactness", "is_tactic_proof": true, "tactics": ["refine", "rw", "apply", "intro", "obtain", "have", "let", "refine", "refine", "simp", "ext", "suffices", "rw", "have", "exact"], "tactic_count": 15}
{"name": "_private.Mathlib.RingTheory.AdicCompletion.Functoriality.0.LinearMap.reduceModIdealAux_apply", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.reduceModIdeal_apply", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.transitionMap_comp_reduceModIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Functoriality", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "AdicCompletion.AdicCauchySequence.map_id", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.AdicCauchySequence.map_comp", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.AdicCauchySequence.map_comp_apply", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.AdicCauchySequence.map_zero", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.AdicCompletion.Functoriality.0.AdicCompletion.adicCompletionAux_val_apply", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.map_val_apply", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.map_ext", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Functoriality", "is_tactic_proof": true, "tactics": ["ext", "apply"], "tactic_count": 2}
{"name": "AdicCompletion.map_ext'", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Functoriality", "is_tactic_proof": true, "tactics": ["ext", "apply"], "tactic_count": 2}
{"name": "AdicCompletion.map_ext''", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Functoriality", "is_tactic_proof": true, "tactics": ["ext", "apply"], "tactic_count": 2}
{"name": "AdicCompletion.map_id", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Functoriality", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "AdicCompletion.map_comp", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Functoriality", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "AdicCompletion.map_comp_apply", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Functoriality", "is_tactic_proof": true, "tactics": ["change", "rw"], "tactic_count": 2}
{"name": "AdicCompletion.map_mk", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.map_zero", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Functoriality", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "AdicCompletion.map_of", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.congr_apply", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.congr_symm_apply", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.sum_lof", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Functoriality", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AdicCompletion.sum_of", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Functoriality", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "AdicCompletion.component_sumInv", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Functoriality", "is_tactic_proof": true, "tactics": ["apply", "rfl"], "tactic_count": 2}
{"name": "AdicCompletion.sumInv_apply", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Functoriality", "is_tactic_proof": true, "tactics": ["apply", "rfl"], "tactic_count": 2}
{"name": "AdicCompletion.sumInv_comp_sum", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Functoriality", "is_tactic_proof": true, "tactics": ["ext", "apply", "ext", "simp", "rw", "split", "subst", "simp"], "tactic_count": 8}
{"name": "AdicCompletion.sum_comp_sumInv", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Functoriality", "is_tactic_proof": true, "tactics": ["ext", "simp", "rw", "simp", "simp"], "tactic_count": 5}
{"name": "AdicCompletion.sumEquivOfFintype_apply", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.sumEquivOfFintype_symm_apply", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Functoriality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdicCompletion.piEquivOfFintype_apply", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Functoriality", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AdicCompletion.piEquivFin_apply", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Functoriality", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AdicCompletion.exists_smodEq_pow_add_one_smul", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Functoriality", "is_tactic_proof": true, "tactics": ["induction", "smul", "obtain", "use", "simp", "rw", "exact", "add", "obtain", "obtain", "use", "simp", "exact"], "tactic_count": 13}
{"name": "AdicCompletion.exists_smodEq_pow_smul_top_and_smodEq_pow_add_one_smul_top", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Functoriality", "is_tactic_proof": true, "tactics": ["obtain", "use", "constructor", "simpa", "simpa"], "tactic_count": 5}
{"name": "AdicCompletion.exists_smodEq_pow_smul_top_and_mkQ_eq", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Functoriality", "is_tactic_proof": true, "tactics": ["obtain", "have", "rw", "obtain", "use", "rwa"], "tactic_count": 6}
{"name": "AdicCompletion.map_surjective_of_mkQ_comp_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Functoriality", "is_tactic_proof": true, "tactics": ["intro", "suffices", "obtain", "use", "ext", "simp", "let", "induction", "zero", "use", "apply_fun", "exact", "succ", "xn", "choose", "exact", "exact"], "tactic_count": 17}
{"name": "surjective_of_mkQ_comp_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Functoriality", "is_tactic_proof": true, "tactics": ["intro", "obtain", "obtain", "use", "rwa"], "tactic_count": 5}
{"name": "surjective_of_mk_map_comp_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Functoriality", "is_tactic_proof": true, "tactics": ["let", "let", "change", "have", "simp", "rfl", "have", "apply", "rwa"], "tactic_count": 9}
{"name": "isUnit_iff_notMem_of_isAdicComplete_maximal", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.LocalRing", "is_tactic_proof": true, "tactics": ["refine", "by_contra", "rcases", "absurd", "simp", "have", "induction", "zero", "absurd", "exact", "succ", "by_cases", "let", "let", "simpa", "apply", "simpa", "choose", "let", "have", "simpa", "have", "by_cases", "simp", "rw", "nth_rw", "simp", "rw", "simp", "rcases", "have", "by_cases", "apply", "simp", "rw", "have", "simp", "simp", "simp", "apply", "use", "exact"], "tactic_count": 42}
{"name": "isLocalRing_of_isAdicComplete_maximal", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.LocalRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsHausdorff.of_le_jacobson", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Noetherian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsHausdorff.of_isLocalRing", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Noetherian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsHausdorffMaximalIdeal", "kind": "instance", "module": "Mathlib.RingTheory.AdicCompletion.Noetherian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsHausdorff.of_isTorsionFree", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Noetherian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsHausdorff.of_isDomain", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Noetherian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAdicComplete.liftRingHom", "kind": "definition", "module": "Mathlib.RingTheory.AdicCompletion.RingHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAdicComplete.of_liftRingHom", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.RingHom", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsAdicComplete.ofAlgEquiv_comp_liftRingHom", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.RingHom", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "IsAdicComplete.mk_liftRingHom", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.RingHom", "is_tactic_proof": true, "tactics": ["simp", "rw", "simp"], "tactic_count": 3}
{"name": "IsAdicComplete.mk_comp_liftRingHom", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.RingHom", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "IsAdicComplete.eq_liftRingHom", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.RingHom", "is_tactic_proof": true, "tactics": ["apply", "apply", "intro", "simp"], "tactic_count": 4}
{"name": "IsAdicComplete.liftAlgHom", "kind": "definition", "module": "Mathlib.RingTheory.AdicCompletion.RingHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAdicComplete.mk_liftAlgHom", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.RingHom", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsAdicComplete.mkₐ_comp_liftAlgHom", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.RingHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAdicComplete.algHom_ext", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.RingHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAdicComplete.StrictMono.factorPow_comp_eq_of_factorPow_comp_succ_eq'", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.RingHom", "is_tactic_proof": true, "tactics": ["ext", "symm", "refine", "exact", "intro", "simp", "simpa"], "tactic_count": 7}
{"name": "IsAdicComplete.StrictMono.liftRingHom", "kind": "definition", "module": "Mathlib.RingTheory.AdicCompletion.RingHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAdicComplete.StrictMono.mk_liftRingHom", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.RingHom", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsAdicComplete.StrictMono.mk_comp_liftRingHom", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.RingHom", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "IsAdicComplete.StrictMono.eq_liftRingHom", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.RingHom", "is_tactic_proof": true, "tactics": ["apply", "apply", "intro", "simp"], "tactic_count": 4}
{"name": "IsAdic.isHausdorff_iff", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Topology", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "IsAdic.isPrecomplete_iff", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Topology", "is_tactic_proof": true, "tactics": ["have", "have", "simp", "constructor", "intro", "refine", "have", "simpa", "choose", "obtain", "use", "suffices", "refine", "have", "rwa", "intro", "obtain", "refine", "obtain", "simpa", "simpa"], "tactic_count": 21}
{"name": "IsAdic.isAdicComplete_iff", "kind": "theorem", "module": "Mathlib.RingTheory.AdicCompletion.Topology", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AdjoinRoot", "kind": "definition", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.instCommRing", "kind": "instance", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.instInhabited", "kind": "instance", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.instDecidableEq", "kind": "instance", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.nontrivial", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": ["simp", "rintro", "exact"], "tactic_count": 3}
{"name": "AdjoinRoot.mk", "kind": "definition", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.induction_on", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.of", "kind": "definition", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.instSMulAdjoinRoot", "kind": "instance", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.instDistribSMulOfIsScalarTower", "kind": "instance", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.smul_mk", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.smul_of", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AdjoinRoot.instIsScalarTower", "kind": "instance", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.instSMulCommClass", "kind": "instance", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.isScalarTower_right", "kind": "instance", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.instDistribMulActionOfIsScalarTower", "kind": "instance", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.instAlgebra", "kind": "instance", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.mkₐ", "kind": "definition", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.mkₐ_toRingHom", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.coe_mkₐ", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.algebraMap_eq", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.algebraMap_eq'", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.finiteType", "kind": "instance", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "AdjoinRoot.finitePresentation", "kind": "instance", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.root", "kind": "definition", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.ofAlgHom", "kind": "abbrev", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.toRingHom_ofAlgHom", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.coe_ofAlgHom", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.ringHom_ext", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.algHom_ext'", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "AdjoinRoot.hasCoeT", "kind": "instance", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.algHom_ext", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.mk_eq_mk", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.mk_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.mk_self", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.mk_C", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.mk_X", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.mk_ne_zero_of_degree_lt", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.mk_ne_zero_of_natDegree_lt", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.aeval_eq_of_algebra", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": true, "tactics": ["induction", "simp", "rw", "simp", "add", "monomial"], "tactic_count": 6}
{"name": "AdjoinRoot.aeval_eq", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AdjoinRoot.adjoinRoot_eq_top", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": true, "tactics": ["refine", "induction", "ih"], "tactic_count": 3}
{"name": "AdjoinRoot.eval₂_root", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AdjoinRoot.isRoot_root", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AdjoinRoot.isAlgebraic_root", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.of.injective_of_degree_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "by_cases", "exact", "contrapose", "rw", "apply", "rwa"], "tactic_count": 9}
{"name": "AdjoinRoot.lift", "kind": "definition", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": true, "tactics": ["apply", "intro", "rcases", "rw"], "tactic_count": 4}
{"name": "AdjoinRoot.lift_mk", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.lift_root", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AdjoinRoot.lift_of", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AdjoinRoot.lift_comp_of", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.liftAlgHom", "kind": "definition", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.toRingHom_liftAlgHom", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.coe_liftAlgHom", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.liftAlgHom_of", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AdjoinRoot.liftAlgHom_mk", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.liftAlgHom_root", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AdjoinRoot.liftHom", "kind": "definition", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.coe_liftHom", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.aeval_algHom_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": true, "tactics": ["have", "rw", "rfl"], "tactic_count": 3}
{"name": "AdjoinRoot.liftAlgHom_eq_algHom", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "AdjoinRoot.liftHom_eq_algHom", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.liftHom_mk", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AdjoinRoot.liftHom_root", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.liftHom_of", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.root_isInv", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "AdjoinRoot.algHom_subsingleton", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.isDomain_of_prime", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.noZeroSMulDivisors_of_prime_of_degree_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.map", "kind": "definition", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.map_of", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AdjoinRoot.map_root", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AdjoinRoot.map_comp_map", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "AdjoinRoot.mapRingEquiv", "kind": "definition", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.coe_mapRingEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.symm_mapRingEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.mapAlgHom", "kind": "definition", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.coe_mapAlgHom", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.mapAlgHom_comp_mapAlghom", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "AdjoinRoot.mapAlgEquiv", "kind": "definition", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.coe_mapAlgEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.symm_mapAlgEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.algHomOfDvd", "kind": "definition", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.coe_algHomOfDvd", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.algHomOfDvd_root", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AdjoinRoot.algEquivOfAssociated", "kind": "definition", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.coe_algEquivOfAssociated", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.algEquivOfAssociated_symm", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.algEquivOfAssociated_toAlgHom", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.algEquivOfAssociated_root", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AdjoinRoot.algEquivOfEq", "kind": "definition", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.coe_algEquivOfEq", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.algEquivOfEq_symm", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.algEquivOfEq_toAlgHom", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.algEquivOfEq_root", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AdjoinRoot.span_maximal_of_irreducible", "kind": "instance", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.instGroupWithZero", "kind": "instance", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.instField", "kind": "instance", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.coe_injective", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.coe_injective'", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.mul_div_root_cancel", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.instIsNoetherianRing", "kind": "instance", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.isIntegral_root'", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.modByMonicHom", "kind": "definition", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.modByMonicHom_mk", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.mk_leftInverse", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": true, "tactics": ["intro", "induction", "rw", "apply"], "tactic_count": 4}
{"name": "AdjoinRoot.mk_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.powerBasisAux'", "kind": "definition", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.powerBasisAux'_repr_symm_apply", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.powerBasisAux'_repr_apply_to_fun", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.powerBasis'", "kind": "definition", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Monic.free_adjoinRoot", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Monic.finite_adjoinRoot", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Monic.free_quotient", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Monic.finite_quotient", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.isIntegral_root", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.minpoly_root", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": true, "tactics": ["have", "refine", "rw", "intro", "have", "ext", "simp", "rfl", "simp", "rw", "natDegree_C,", "apply", "have", "exact", "exact", "rwa"], "tactic_count": 16}
{"name": "AdjoinRoot.powerBasisAux", "kind": "definition", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": true, "tactics": ["let", "have", "rw", "rwa", "have", "apply", "rw", "exact", "rintro", "rw", "apply", "obtain", "use", "rw", "rfl"], "tactic_count": 15}
{"name": "AdjoinRoot.powerBasis", "kind": "definition", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.minpoly_powerBasis_gen", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "finrank_quotient_span_eq_natDegree", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "exact", "rw", "exact"], "tactic_count": 5}
{"name": "AdjoinRoot.Minpoly.toAdjoin", "kind": "definition", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.Minpoly.coe_toAdjoin", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.Minpoly.coe_toAdjoin_mk_X", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AdjoinRoot.Minpoly.toAdjoin.surjective", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "AdjoinRoot.equiv'", "kind": "definition", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.equiv'_toAlgHom", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.equiv'_symm_toAlgHom", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.equiv", "kind": "definition", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.quotMapOfEquivQuotMapCMapSpanMk", "kind": "definition", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.quotMapOfEquivQuotMapCMapSpanMk_mk", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.quotMapOfEquivQuotMapCMapSpanMk_symm_mk", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "AdjoinRoot.quotMapCMapSpanMkEquivQuotMapCQuotMapSpanMk", "kind": "definition", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.quotMapCMapSpanMkEquivQuotMapCQuotMapSpanMk_mk", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.quotMapCMapSpanMkEquivQuotMapCQuotMapSpanMk_symm_quotQuotMk", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.Polynomial.quotQuotEquivComm", "kind": "definition", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.Polynomial.quotQuotEquivComm_mk", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AdjoinRoot.Polynomial.quotQuotEquivComm_symm_mk_mk", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AdjoinRoot.quotAdjoinRootEquivQuotPolynomialQuot", "kind": "definition", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.quotAdjoinRootEquivQuotPolynomialQuot_mk_of", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.quotAdjoinRootEquivQuotPolynomialQuot_symm_mk_mk", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": true, "tactics": ["rw", "quotMapCMapSpanMkEquivQuotMapCQuotMapSpanMk_symm_quotQuotMk,"], "tactic_count": 2}
{"name": "AdjoinRoot.quotEquivQuotMap", "kind": "definition", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.quotEquivQuotMap_apply_mk", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AdjoinRoot.quotEquivQuotMap_symm_apply_mk", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PowerBasis.quotientEquivQuotientMinpolyMap", "kind": "definition", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerBasis.quotientEquivQuotientMinpolyMap_apply_mk", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PowerBasis.quotientEquivQuotientMinpolyMap_symm_apply_mk", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Irreducible.exists_dvd_monic_irreducible_of_isIntegral", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": true, "tactics": ["haveI", "have", "have", "have", "exact"], "tactic_count": 5}
{"name": "Polynomial.Monic.exists_splits_map", "kind": "theorem", "module": "Mathlib.RingTheory.AdjoinRoot", "is_tactic_proof": true, "tactics": ["induction", "h", "by_cases", "obtain", "exact", "obtain", "simp", "have", "have", "have", "have", "obtain", "simp)", "hqm", "algebraize", "refine", "rw", "exact"], "tactic_count": 18}
{"name": "Algebra.adjoin_prod_le", "kind": "theorem", "module": "Mathlib.RingTheory.Adjoin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.adjoin_inl_union_inr_eq_prod", "kind": "theorem", "module": "Mathlib.RingTheory.Adjoin.Basic", "is_tactic_proof": true, "tactics": ["apply", "simp", "rintro", "let", "have", "mem_adjoin_of_map_mul", "have", "mem_adjoin_of_map_mul", "replace", "replace", "simpa"], "tactic_count": 11}
{"name": "Algebra.adjoin_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.Adjoin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.adjoin_algebraMap_image_union_eq_adjoin_adjoin", "kind": "theorem", "module": "Mathlib.RingTheory.Adjoin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.adjoin_adjoin_of_tower", "kind": "theorem", "module": "Mathlib.RingTheory.Adjoin.Basic", "is_tactic_proof": true, "tactics": ["apply", "exact", "rw", "exact"], "tactic_count": 4}
{"name": "Algebra.Subalgebra.restrictScalars_adjoin", "kind": "theorem", "module": "Mathlib.RingTheory.Adjoin.Basic", "is_tactic_proof": false, "tactics": ["refine", "le_antisymm", "adjoin_induction", "rintro"], "tactic_count": 4}
{"name": "Algebra.adjoin_top", "kind": "theorem", "module": "Mathlib.RingTheory.Adjoin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.adjoin_union_eq_adjoin_adjoin", "kind": "theorem", "module": "Mathlib.RingTheory.Adjoin.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Algebra.adjoin_eq_adjoin_union", "kind": "theorem", "module": "Mathlib.RingTheory.Adjoin.Basic", "is_tactic_proof": true, "tactics": ["have", "rw", "rw"], "tactic_count": 3}
{"name": "Algebra.pow_smul_mem_of_smul_subset_of_mem_adjoin", "kind": "theorem", "module": "Mathlib.RingTheory.Adjoin.Basic", "is_tactic_proof": true, "tactics": ["change", "rw", "rcases", "choose", "use", "intro", "rw", "refine", "intro", "have", "dsimp", "rw", "smul_smul", "apply", "refine", "change", "rw", "apply"], "tactic_count": 18}
{"name": "Algebra.pow_smul_mem_adjoin_smul", "kind": "theorem", "module": "Mathlib.RingTheory.Adjoin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.adjoin_nonUnitalSubalgebra_eq_span", "kind": "theorem", "module": "Mathlib.RingTheory.Adjoin.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subalgebra.adjoin_eq_span_basis", "kind": "theorem", "module": "Mathlib.RingTheory.Adjoin.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.restrictScalars_adjoin", "kind": "theorem", "module": "Mathlib.RingTheory.Adjoin.Basic", "is_tactic_proof": true, "tactics": ["conv_lhs"], "tactic_count": 1}
{"name": "Algebra.restrictScalars_adjoin_of_algEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.Adjoin.Basic", "is_tactic_proof": true, "tactics": ["apply_fun", "change", "rw"], "tactic_count": 3}
{"name": "Subalgebra.rank_sup_le_of_free", "kind": "theorem", "module": "Mathlib.RingTheory.Adjoin.Dimension", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "have", "rw", "change", "rw", "refine", "gcongr"], "tactic_count": 8}
{"name": "Subalgebra.finrank_sup_le_of_free", "kind": "theorem", "module": "Mathlib.RingTheory.Adjoin.Dimension", "is_tactic_proof": true, "tactics": ["by_cases", "obtain", "simpa", "wlog", "have", "rwa", "rw", "have", "rw", "show"], "tactic_count": 10}
{"name": "Algebra.fg_trans", "kind": "theorem", "module": "Mathlib.RingTheory.Adjoin.FG", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "refine", "rw", "intro", "change", "refine", "have", "rw", "exact", "exact", "have", "rw", "exact", "change", "rwa", "intro", "change", "rw", "change", "rw", "rcases", "have", "rw", "refine", "intro", "change", "have", "rw", "rcases", "have", "rw", "rw", "refine", "intro", "change", "rw", "refine", "exact"], "tactic_count": 39}
{"name": "Subalgebra.FG", "kind": "definition", "module": "Mathlib.RingTheory.Adjoin.FG", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.fg_adjoin_finset", "kind": "theorem", "module": "Mathlib.RingTheory.Adjoin.FG", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.fg_def", "kind": "theorem", "module": "Mathlib.RingTheory.Adjoin.FG", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.fg_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Adjoin.FG", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.fg_of_fg_toSubmodule", "kind": "theorem", "module": "Mathlib.RingTheory.Adjoin.FG", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.fg_of_noetherian", "kind": "theorem", "module": "Mathlib.RingTheory.Adjoin.FG", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.fg_of_submodule_fg", "kind": "theorem", "module": "Mathlib.RingTheory.Adjoin.FG", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.FG.prod", "kind": "theorem", "module": "Mathlib.RingTheory.Adjoin.FG", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "rw", "exact", "fg_def.2"], "tactic_count": 5}
{"name": "Subalgebra.FG.map", "kind": "theorem", "module": "Mathlib.RingTheory.Adjoin.FG", "is_tactic_proof": true, "tactics": ["let", "classical"], "tactic_count": 2}
{"name": "Subalgebra.fg_of_fg_map", "kind": "theorem", "module": "Mathlib.RingTheory.Adjoin.FG", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.fg_top", "kind": "theorem", "module": "Mathlib.RingTheory.Adjoin.FG", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.induction_on_adjoin", "kind": "theorem", "module": "Mathlib.RingTheory.Adjoin.FG", "is_tactic_proof": true, "tactics": ["classical", "obtain", "refine", "simpa", "intro", "rw", "simpa"], "tactic_count": 7}
{"name": "Subalgebra.FG.sup", "kind": "theorem", "module": "Mathlib.RingTheory.Adjoin.FG", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.isNoetherianRing_range", "kind": "instance", "module": "Mathlib.RingTheory.Adjoin.FG", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isNoetherianRing_of_fg", "kind": "theorem", "module": "Mathlib.RingTheory.Adjoin.FG", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "is_noetherian_subring_closure", "kind": "theorem", "module": "Mathlib.RingTheory.Adjoin.FG", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_fg_and_mem_baseChange", "kind": "theorem", "module": "Mathlib.RingTheory.Adjoin.FGBaseChange", "is_tactic_proof": true, "tactics": ["obtain", "classical", "refine", "exact", "exact", "hS"], "tactic_count": 6}
{"name": "AlgEquiv.adjoinSingletonEquivAdjoinRootMinpoly", "kind": "definition", "module": "Mathlib.RingTheory.Adjoin.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.adjoinSingletonEquivAdjoinRootMinpoly_symm_toAlgHom", "kind": "theorem", "module": "Mathlib.RingTheory.Adjoin.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.coe_adjoinSingletonEquivAdjoinRootMinpoly_symm", "kind": "theorem", "module": "Mathlib.RingTheory.Adjoin.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.adjoin.liftSingleton", "kind": "definition", "module": "Mathlib.RingTheory.Adjoin.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.lift_of_splits", "kind": "theorem", "module": "Mathlib.RingTheory.Adjoin.Field", "is_tactic_proof": true, "tactics": ["classical", "refine", "rw", "exact", "rw", "rcases", "obtain", "choose", "rw", "set", "haveI", "letI", "letI", "have", "have", "refine", "rw", "exact", "obtain", "rw", "exact"], "tactic_count": 21}
{"name": "IsIntegral.mem_range_algHom_of_minpoly_splits", "kind": "theorem", "module": "Mathlib.RingTheory.Adjoin.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegral.mem_range_algebraMap_of_minpoly_splits", "kind": "theorem", "module": "Mathlib.RingTheory.Adjoin.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "minpoly_neg_splits", "kind": "theorem", "module": "Mathlib.RingTheory.Adjoin.Field", "is_tactic_proof": true, "tactics": ["rw", "apply", "simpa"], "tactic_count": 3}
{"name": "minpoly_add_algebraMap_splits", "kind": "theorem", "module": "Mathlib.RingTheory.Adjoin.Field", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "minpoly_sub_algebraMap_splits", "kind": "theorem", "module": "Mathlib.RingTheory.Adjoin.Field", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "minpoly_algebraMap_add_splits", "kind": "theorem", "module": "Mathlib.RingTheory.Adjoin.Field", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "minpoly_algebraMap_sub_splits", "kind": "theorem", "module": "Mathlib.RingTheory.Adjoin.Field", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsIntegral.minpoly_splits_tower_top'", "kind": "theorem", "module": "Mathlib.RingTheory.Adjoin.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegral.minpoly_splits_tower_top", "kind": "theorem", "module": "Mathlib.RingTheory.Adjoin.Field", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Subalgebra.adjoin_rank_le", "kind": "theorem", "module": "Mathlib.RingTheory.Adjoin.Field", "is_tactic_proof": false, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Polynomial.adjoin_X", "kind": "theorem", "module": "Mathlib.RingTheory.Adjoin.Polynomial", "is_tactic_proof": true, "tactics": ["refine", "set", "rw", "exact"], "tactic_count": 4}
{"name": "Algebra.adjoin_singleton_eq_range_aeval", "kind": "theorem", "module": "Mathlib.RingTheory.Adjoin.Polynomial", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.aeval_mem_adjoin_singleton", "kind": "theorem", "module": "Mathlib.RingTheory.Adjoin.Polynomial", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Algebra.adjoin_mem_exists_aeval", "kind": "theorem", "module": "Mathlib.RingTheory.Adjoin.Polynomial", "is_tactic_proof": true, "tactics": ["rw", "simp_all"], "tactic_count": 2}
{"name": "Algebra.adjoin_eq_exists_aeval", "kind": "theorem", "module": "Mathlib.RingTheory.Adjoin.Polynomial", "is_tactic_proof": true, "tactics": ["have", "set", "rw", "simp_all"], "tactic_count": 4}
{"name": "Algebra.adjoin_singleton_induction", "kind": "theorem", "module": "Mathlib.RingTheory.Adjoin.Polynomial", "is_tactic_proof": true, "tactics": ["obtain", "grind"], "tactic_count": 2}
{"name": "Polynomial.instCommSemiringAdjoinSingleton", "kind": "instance", "module": "Mathlib.RingTheory.Adjoin.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.instCommRingAdjoinSingleton", "kind": "instance", "module": "Mathlib.RingTheory.Adjoin.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.adjoin.powerBasisAux", "kind": "definition", "module": "Mathlib.RingTheory.Adjoin.PowerBasis", "is_tactic_proof": true, "tactics": ["have", "have", "apply", "convert", "apply", "have", "rwa", "rintro", "have", "rw", "apply", "rw", "obtain", "use", "ext", "exact"], "tactic_count": 16}
{"name": "Algebra.adjoin.powerBasis", "kind": "definition", "module": "Mathlib.RingTheory.Adjoin.PowerBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerBasis.ofAdjoinEqTop", "kind": "definition", "module": "Mathlib.RingTheory.Adjoin.PowerBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerBasis.ofAdjoinEqTop_gen", "kind": "theorem", "module": "Mathlib.RingTheory.Adjoin.PowerBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerBasis.ofAdjoinEqTop_dim", "kind": "theorem", "module": "Mathlib.RingTheory.Adjoin.PowerBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerBasis.repr_gen_pow_isIntegral", "kind": "theorem", "module": "Mathlib.RingTheory.Adjoin.PowerBasis", "is_tactic_proof": true, "tactics": ["intro", "nontriviality", "let", "have", "rw", "simp", "by_cases", "simp", "have", "rw", "letI", "exact", "rw", "simp", "refine", "replace", "rw", "map_smul]", "simp", "by_cases", "simp", "rw", "exact", "simp"], "tactic_count": 24}
{"name": "PowerBasis.repr_mul_isIntegral", "kind": "theorem", "module": "Mathlib.RingTheory.Adjoin.PowerBasis", "is_tactic_proof": true, "tactics": ["intro", "rw", "refine", "simp", "refine", "simp", "exact"], "tactic_count": 7}
{"name": "PowerBasis.repr_pow_isIntegral", "kind": "theorem", "module": "Mathlib.RingTheory.Adjoin.PowerBasis", "is_tactic_proof": true, "tactics": ["nontriviality", "revert", "refine", "intro", "rw", "split_ifs", "exact", "exact", "intro", "rw", "exact"], "tactic_count": 11}
{"name": "PowerBasis.toMatrix_isIntegral", "kind": "theorem", "module": "Mathlib.RingTheory.Adjoin.PowerBasis", "is_tactic_proof": true, "tactics": ["intro", "rw", "refine", "rw", "refine", "rw", "exact"], "tactic_count": 7}
{"name": "Algebra.RingHom.adjoinAlgebraMap", "kind": "definition", "module": "Mathlib.RingTheory.Adjoin.Singleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.RingHom.adjoin_algebraMap_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Adjoin.Singleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.RingHom.adjoin_algebraMap_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Adjoin.Singleton", "is_tactic_proof": true, "tactics": ["intro", "obtain", "aesop"], "tactic_count": 3}
{"name": "Algebra.instSubtypeMemSubalgebraAdjoinSingletonSetCoeRingHomAlgebraMap", "kind": "instance", "module": "Mathlib.RingTheory.Adjoin.Singleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.instIsScalarTowerSubtypeMemSubalgebraAdjoinSingletonSetCoeRingHomAlgebraMap", "kind": "instance", "module": "Mathlib.RingTheory.Adjoin.Singleton", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.RingHom.adjoinAlgebraMapEquiv", "kind": "definition", "module": "Mathlib.RingTheory.Adjoin.Singleton", "is_tactic_proof": false, "tactics": ["apply", "induction", "f", "use", "aesop"], "tactic_count": 5}
{"name": "Algebra.adjoin_restrictScalars", "kind": "theorem", "module": "Mathlib.RingTheory.Adjoin.Tower", "is_tactic_proof": false, "tactics": ["suffices", "ext", "change", "rw", "ext", "constructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 10}
{"name": "Algebra.adjoin_res_eq_adjoin_res", "kind": "theorem", "module": "Mathlib.RingTheory.Adjoin.Tower", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Algebra.fg_trans'", "kind": "theorem", "module": "Mathlib.RingTheory.Adjoin.Tower", "is_tactic_proof": true, "tactics": ["classical", "rcases", "rcases", "exact", "rw"], "tactic_count": 5}
{"name": "exists_subalgebra_of_fg", "kind": "theorem", "module": "Mathlib.RingTheory.Adjoin.Tower", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "have", "simp_rw", "choose", "classical", "let", "have", "hf", "sum_mem", "smul_mem", "have", "span", "span", "span", "rw", "rintro", "rw", "exact", "rw", "exact", "rw", "exact", "rw", "exact", "smul_mem", "refine", "convert", "rw", "refine"], "tactic_count": 30}
{"name": "fg_of_fg_of_fg", "kind": "theorem", "module": "Mathlib.RingTheory.Adjoin.Tower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsScalarTower.Invertible.algebraTower", "kind": "definition", "module": "Mathlib.RingTheory.AlgebraTower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsScalarTower.invertibleAlgebraCoeNat", "kind": "definition", "module": "Mathlib.RingTheory.AlgebraTower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.algebraMapCoeffs", "kind": "definition", "module": "Mathlib.RingTheory.AlgebraTower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.algebraMapCoeffs_repr", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraTower", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "Module.Basis.algebraMapCoeffs_apply", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraTower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.coe_algebraMapCoeffs", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraTower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "linearIndependent_smul", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraTower", "is_tactic_proof": true, "tactics": ["classical", "rw", "linearCombination_smul]", "simpa"], "tactic_count": 4}
{"name": "Module.Basis.isScalarTower_of_nonempty", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraTower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.isScalarTower_finsupp", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraTower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.smulTower", "kind": "definition", "module": "Mathlib.RingTheory.AlgebraTower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.smulTower_repr", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraTower", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Module.Basis.smulTower_repr_mk", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraTower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.smulTower_apply", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraTower", "is_tactic_proof": true, "tactics": ["classical", "obtain", "rw", "ext", "rw", "dsimp", "split_ifs", "simp", "simp"], "tactic_count": 9}
{"name": "Module.Basis.smulTower'", "kind": "definition", "module": "Mathlib.RingTheory.AlgebraTower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.smulTower'_repr", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraTower", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Module.Basis.smulTower'_repr_mk", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraTower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.smulTower'_apply", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraTower", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Module.Basis.algebraMap_injective", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraTower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.restrictDomain", "kind": "definition", "module": "Mathlib.RingTheory.AlgebraTower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.extendScalars", "kind": "definition", "module": "Mathlib.RingTheory.AlgebraTower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "algHomEquivSigma", "kind": "definition", "module": "Mathlib.RingTheory.AlgebraTower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicIndependent.aevalEquivField", "kind": "definition", "module": "Mathlib.RingTheory.AlgebraicIndependent.Adjoin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicIndependent.aevalEquivField_apply_coe", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Adjoin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicIndependent.aevalEquivField_algebraMap_apply_coe", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Adjoin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicIndependent.reprField", "kind": "definition", "module": "Mathlib.RingTheory.AlgebraicIndependent.Adjoin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicIndependent.lift_reprField", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Adjoin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicIndependent.liftAlgHom_comp_reprField", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Adjoin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicIndependent.extendScalars", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.AlgebraicClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicIndependent.extendScalars_of_isIntegral", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.AlgebraicClosure", "is_tactic_proof": true, "tactics": ["nontriviality", "have", "exact"], "tactic_count": 3}
{"name": "AlgebraicIndependent.subalgebraAlgebraicClosure", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.AlgebraicClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicIndependent.integralClosure", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.AlgebraicClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicIndependent.algebraicClosure", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.AlgebraicClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsIntegral.algebraicIndependent_iff", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.AlgebraicClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsIntegral.isTranscendenceBasis_iff", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.AlgebraicClosure", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Algebra.IsAlgebraic.algebraicIndependent_iff", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.AlgebraicClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsAlgebraic.isTranscendenceBasis_iff", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.AlgebraicClosure", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "IntermediateField.isAlgebraic_adjoin_iff", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.AlgebraicClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.isAlgebraic_adjoin_iff_top", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.AlgebraicClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.isAlgebraic_adjoin_iff_bot", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.AlgebraicClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.transcendental_adjoin_iff", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.AlgebraicClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.algebraicIndependent_adjoin_iff", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.AlgebraicClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.isTranscendenceBasis_adjoin_iff", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.AlgebraicClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.trdeg", "kind": "definition", "module": "Mathlib.RingTheory.AlgebraicIndependent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "algebraicIndependent_iff_ker_eq_bot", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "algebraicIndependent_empty_type_iff", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "instNonemptySubtypeSetAlgebraicIndepOnIdOfFaithfulSMul", "kind": "instance", "module": "Mathlib.RingTheory.AlgebraicIndependent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicIndependent.algebraMap_injective", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "AlgebraicIndependent.linearIndependent", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Basic", "is_tactic_proof": true, "tactics": ["rw", "have", "ext", "simp", "rw", "refine", "rw", "exact"], "tactic_count": 8}
{"name": "AlgebraicIndependent.injective", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicIndependent.ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicIndependent.map", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Basic", "is_tactic_proof": true, "tactics": ["have", "have", "intro", "rw", "refine", "simp", "intro", "rw", "rw", "exact"], "tactic_count": 10}
{"name": "AlgebraicIndependent.map'", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicIndependent.aeval_of_algebraicIndependent", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Basic", "is_tactic_proof": true, "tactics": ["rw", "intro", "exact"], "tactic_count": 3}
{"name": "AlgebraicIndependent.of_aeval", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Basic", "is_tactic_proof": true, "tactics": ["rw", "intro", "exact"], "tactic_count": 3}
{"name": "isEmpty_algebraicIndependent", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "trdeg_eq_zero_of_not_injective", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Basic", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "MvPolynomial.algebraicIndependent_X", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "AlgHom.algebraicIndependent_iff", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicIndependent.of_subsingleton", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isTranscendenceBasis_iff_of_subsingleton", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Basic", "is_tactic_proof": true, "tactics": ["have", "refine", "by_contra", "have", "simp"], "tactic_count": 5}
{"name": "IsTranscendenceBasis.of_subsingleton", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "trdeg_subsingleton", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "algebraicIndependent_adjoin", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicIndependent.restrictScalars", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Basic", "is_tactic_proof": false, "tactics": ["have", "change", "rw", "exact"], "tactic_count": 4}
{"name": "AlgebraicIndependent.of_ringHom_of_comp_eq", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Basic", "is_tactic_proof": true, "tactics": ["rw", "intro", "have", "have", "rwa", "exact"], "tactic_count": 6}
{"name": "AlgebraicIndependent.ringHom_of_comp_eq", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Basic", "is_tactic_proof": true, "tactics": ["rw", "intro", "obtain", "rw", "map_zero]"], "tactic_count": 5}
{"name": "algebraicIndependent_ringHom_iff_of_comp_eq", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "algebraicIndependent_finset_map_embedding_subtype", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Basic", "is_tactic_proof": false, "tactics": ["let", "obtain", "rw", "obtain", "simp", "convert", "rintro", "rw", "obtain", "obtain", "simp"], "tactic_count": 11}
{"name": "algebraicIndependent_bounded_of_finset_algebraicIndependent_bounded", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Basic", "is_tactic_proof": true, "tactics": ["intro", "apply", "intro", "rw", "apply", "apply"], "tactic_count": 6}
{"name": "AlgebraicIndependent.restrict_of_comp_subtype", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "algebraicIndependent_empty_iff", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicIndependent.to_subtype_range", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Basic", "is_tactic_proof": true, "tactics": ["nontriviality", "rwa"], "tactic_count": 2}
{"name": "AlgebraicIndependent.to_subtype_range'", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsTranscendenceBasis.to_subtype_range", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Basic", "is_tactic_proof": true, "tactics": ["cases", "rw", "rwa"], "tactic_count": 3}
{"name": "IsTranscendenceBasis.to_subtype_range'", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsTranscendenceBasis.of_comp", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Basic", "is_tactic_proof": true, "tactics": ["refine", "intro", "have", "rwa"], "tactic_count": 4}
{"name": "IsTranscendenceBasis.of_comp_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.isTranscendenceBasis", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.isTranscendenceBasis_iff", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicIndependent.lift_cardinalMk_le_trdeg", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "AlgebraicIndependent.cardinalMk_le_trdeg", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "lift_trdeg_le_of_injective", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Basic", "is_tactic_proof": true, "tactics": ["nontriviality", "rw", "exact"], "tactic_count": 3}
{"name": "trdeg_le_of_injective", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "lift_trdeg_le_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Basic", "is_tactic_proof": true, "tactics": ["nontriviality", "rw", "refine", "convert"], "tactic_count": 4}
{"name": "trdeg_le_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgEquiv.lift_trdeg_eq", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.trdeg_eq", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "algebraicIndependent_comp_subtype", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Basic", "is_tactic_proof": true, "tactics": ["have", "have", "simp"], "tactic_count": 3}
{"name": "algebraicIndependent_subtype", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Basic", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "algebraicIndependent_of_finite", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "algebraicIndependent_of_finite_type", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicIndependent.image_of_comp", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Basic", "is_tactic_proof": true, "tactics": ["nontriviality", "have", "exact"], "tactic_count": 3}
{"name": "AlgebraicIndependent.image", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Basic", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "algebraicIndependent_iUnion_of_directed", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Basic", "is_tactic_proof": true, "tactics": ["refine", "rcases", "rcases", "exact"], "tactic_count": 4}
{"name": "algebraicIndependent_sUnion_of_directed", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Basic", "is_tactic_proof": true, "tactics": ["letI", "rw", "exact"], "tactic_count": 3}
{"name": "exists_maximal_algebraicIndependent", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Basic", "is_tactic_proof": false, "tactics": ["refine", "zorn_subset_nonempty", "exact", "exact"], "tactic_count": 4}
{"name": "AlgebraicIndependent.repr_ker", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin", "kind": "definition", "module": "Mathlib.RingTheory.AlgebraicIndependent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_apply", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_C'", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Basic", "is_tactic_proof": true, "tactics": ["congr", "apply_fun", "simp"], "tactic_count": 3}
{"name": "AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_C", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_X_none", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_X_some", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgebraicIndependent.aeval_comp_mvPolynomialOptionEquivPolynomialAdjoin", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Basic", "is_tactic_proof": false, "tactics": ["refine", "simp", "intro", "rw", "rintro", "rw", "rw", "aeval_X,"], "tactic_count": 8}
{"name": "algebraicIndependent_empty_type", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "algebraicIndependent_empty", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicIndependent", "kind": "definition", "module": "Mathlib.RingTheory.AlgebraicIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicIndepOn", "kind": "abbrev", "module": "Mathlib.RingTheory.AlgebraicIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "algebraicIndependent_iff", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicIndependent.eq_zero_of_aeval_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "algebraicIndependent_iff_injective_aeval", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicIndependent.of_comp", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Defs", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "AlgebraicIndependent.comp", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Defs", "is_tactic_proof": true, "tactics": ["intro", "simpa"], "tactic_count": 2}
{"name": "AlgebraicIndependent.coe_range", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "algebraicIndependent_equiv", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "algebraicIndependent_equiv'", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "algebraicIndependent_subtype_range", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "algebraicIndependent_image", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicIndepOn.mono", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "AlgebraicIndepOn.univ", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicIndependent.mono", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicIndependent.aevalEquiv", "kind": "definition", "module": "Mathlib.RingTheory.AlgebraicIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicIndependent.algebraMap_aevalEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicIndependent.repr", "kind": "definition", "module": "Mathlib.RingTheory.AlgebraicIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicIndependent.aeval_repr", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicIndependent.aeval_comp_repr", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicIndepOn.aevalEquiv", "kind": "definition", "module": "Mathlib.RingTheory.AlgebraicIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsTranscendenceBasis", "kind": "definition", "module": "Mathlib.RingTheory.AlgebraicIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isTranscendenceBasis_iff_maximal", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "isTranscendenceBasis_equiv", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Defs", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "isTranscendenceBasis_equiv'", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isTranscendenceBasis_subtype_range", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isTranscendenceBasis_image", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsTranscendenceBasis.lift_cardinalMk_eq_max_lift", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.RankAndCardinality", "is_tactic_proof": true, "tactics": ["let", "suffices", "haveI", "refine", "haveI", "simpa"], "tactic_count": 6}
{"name": "IsTranscendenceBasis.lift_rank_eq_max_lift", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.RankAndCardinality", "is_tactic_proof": true, "tactics": ["let", "haveI", "rw", "lift_max,", "refine", "mul_eq_left", "simp"], "tactic_count": 7}
{"name": "Algebra.Transcendental.rank_eq_cardinalMk", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.RankAndCardinality", "is_tactic_proof": true, "tactics": ["obtain", "haveI", "simpa"], "tactic_count": 3}
{"name": "IntermediateField.rank_sup_le", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.RankAndCardinality", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "by_cases", "exact", "rw", "haveI", "haveI", "haveI", "simp_rw", "rw", "refine", "calc", "gcongr", "rw", "exact"], "tactic_count": 15}
{"name": "exists_isTranscendenceBasis_superset", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "exists_isTranscendenceBasis", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis", "is_tactic_proof": true, "tactics": ["simpa", "exists_isTranscendenceBasis_superset"], "tactic_count": 2}
{"name": "exists_isTranscendenceBasis'", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "trdeg_eq_iSup_cardinalMk_isTranscendenceBasis", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis", "is_tactic_proof": true, "tactics": ["refine", "choose", "exact"], "tactic_count": 3}
{"name": "AlgebraicIndependent.isTranscendenceBasis_iff", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis", "is_tactic_proof": true, "tactics": ["fconstructor", "rintro", "have", "rw", "exact", "intro", "use", "intro", "specialize", "have", "dsimp", "rw", "simpa"], "tactic_count": 13}
{"name": "IsTranscendenceBasis.isAlgebraic", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "intro", "have", "rintro", "exact", "have", "intro", "have", "rw", "exact", "rcases", "have", "simpa", "exact"], "tactic_count": 16}
{"name": "AlgebraicIndependent.isTranscendenceBasis_iff_isAlgebraic", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis", "is_tactic_proof": true, "tactics": ["refine", "have", "have", "rw", "rw", "refine", "simpa"], "tactic_count": 7}
{"name": "isTranscendenceBasis_iff_algebraicIndependent_isAlgebraic", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsTranscendenceBasis.algebraMap_comp", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis", "is_tactic_proof": true, "tactics": ["let", "refine", "rw", "set", "let", "letI", "haveI", "have", "have", "exact"], "tactic_count": 10}
{"name": "IsTranscendenceBasis.isAlgebraic_iff", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis", "is_tactic_proof": true, "tactics": ["refine", "let", "let", "have", "have", "letI", "have", "have", "have", "have", "exact"], "tactic_count": 11}
{"name": "IsTranscendenceBasis.mvPolynomial", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis", "is_tactic_proof": true, "tactics": ["refine", "rw", "set", "have", "infer_instance"], "tactic_count": 5}
{"name": "IsTranscendenceBasis.mvPolynomial'", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis", "is_tactic_proof": true, "tactics": ["nontriviality"], "tactic_count": 1}
{"name": "IsTranscendenceBasis.polynomial", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis", "is_tactic_proof": true, "tactics": ["nontriviality", "have", "refine", "convert", "ext"], "tactic_count": 5}
{"name": "IsTranscendenceBasis.sumElim_comp", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis", "is_tactic_proof": true, "tactics": ["cases", "rw", "rw", "set", "let", "rw", "rw", "change", "have", "have", "have", "set", "let", "refine", "rintro", "have", "have", "have", "refine", "adjoin_induction", "rintro", "exact", "exact", "exact"], "tactic_count": 24}
{"name": "IsTranscendenceBasis.isEmpty_iff_isAlgebraic", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis", "is_tactic_proof": true, "tactics": ["refine", "have", "rw", "exact"], "tactic_count": 4}
{"name": "IsTranscendenceBasis.nonempty_iff_transcendental", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsTranscendenceBasis.isAlgebraic_field", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis", "is_tactic_proof": true, "tactics": ["haveI", "set", "letI", "haveI", "exact"], "tactic_count": 5}
{"name": "_private.Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis.0.AlgebraicIndependent.indepMatroid", "kind": "definition", "module": "Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicIndependent.matroid", "kind": "definition", "module": "Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicIndependent.instFinitaryMatroid", "kind": "instance", "module": "Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicIndependent.matroid_e", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicIndependent.matroid_cRank_eq", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicIndependent.matroid_indep_iff", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicIndependent.matroid_isBase_iff", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicIndependent.matroid_isBasis_iff", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "exact", "and_congr_right", "of_not_not", "max"], "tactic_count": 6}
{"name": "AlgebraicIndependent.matroid_isBasis_iff_of_subsingleton", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis", "is_tactic_proof": true, "tactics": ["have", "simp_rw", "le_iff_subset,"], "tactic_count": 3}
{"name": "AlgebraicIndependent.isAlgebraic_adjoin_iff_of_matroid_isBasis", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis", "is_tactic_proof": true, "tactics": ["cases", "apply", "have", "exact"], "tactic_count": 4}
{"name": "AlgebraicIndependent.matroid_closure_eq", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis", "is_tactic_proof": true, "tactics": ["have", "simp_rw", "matroid_isBasis_iff,", "exact"], "tactic_count": 4}
{"name": "AlgebraicIndependent.matroid_isFlat_iff", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis", "is_tactic_proof": true, "tactics": ["rw", "set", "refine", "rw", "rintro", "refine", "exact"], "tactic_count": 7}
{"name": "AlgebraicIndependent.matroid_spanning_iff", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "AlgebraicIndependent.matroid_isFlat_of_subsingleton", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "AlgebraicIndependent.matroid_closure_of_subsingleton", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "AlgebraicIndependent.matroid_spanning_iff_of_subsingleton", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "exists_isTranscendenceBasis_between", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis", "is_tactic_proof": true, "tactics": ["have", "have", "have", "have", "rw", "rw", "have", "exact"], "tactic_count": 8}
{"name": "exists_isTranscendenceBasis_subset", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis", "is_tactic_proof": false, "tactics": ["have", "exists_isTranscendenceBasis_between", "exact"], "tactic_count": 3}
{"name": "isAlgebraic_iff_exists_isTranscendenceBasis_subset", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "IsTranscendenceBasis.lift_cardinalMk_eq_trdeg", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis", "is_tactic_proof": true, "tactics": ["have", "rw", "lift_mk_eq'.mpr"], "tactic_count": 3}
{"name": "IsTranscendenceBasis.cardinalMk_eq_trdeg", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsTranscendenceBasis.lift_cardinalMk_eq", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis", "is_tactic_proof": true, "tactics": ["rw", "hy.lift_cardinalMk_eq_trdeg,"], "tactic_count": 2}
{"name": "IsTranscendenceBasis.cardinalMk_eq", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MvPolynomial.trdeg_of_isDomain", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "Polynomial.trdeg_of_isDomain", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "trdeg_lt_aleph0", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsAlgebraic.isDomain_of_adjoin_range", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsAlgebraic.trdeg_le_cardinalMk", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis", "is_tactic_proof": true, "tactics": ["by_cases", "on_goal", "have", "have", "rw", "exact"], "tactic_count": 6}
{"name": "Algebra.IsAlgebraic.isTranscendenceBasis_of_lift_le_trdeg_of_finite", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis", "is_tactic_proof": true, "tactics": ["have", "have", "refine", "have", "rw", "exact"], "tactic_count": 6}
{"name": "Algebra.IsAlgebraic.isTranscendenceBasis_of_le_trdeg_of_finite", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsAlgebraic.isTranscendenceBasis_of_lift_le_trdeg", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsAlgebraic.isTranscendenceBasis_of_le_trdeg", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicIndependent.isTranscendenceBasis_of_lift_trdeg_le", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis", "is_tactic_proof": true, "tactics": ["have", "rw", "exact", "matroid_indep_iff.mpr", "lift_le.mp"], "tactic_count": 5}
{"name": "AlgebraicIndependent.isTranscendenceBasis_of_trdeg_le", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicIndependent.isTranscendenceBasis_of_lift_trdeg_le_of_finite", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicIndependent.isTranscendenceBasis_of_trdeg_le_of_finite", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lift_trdeg_add_eq", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis", "is_tactic_proof": true, "tactics": ["have", "have", "have", "have", "rw"], "tactic_count": 5}
{"name": "trdeg_add_eq", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsTranscendenceBasis.of_isAlgebraic_adjoin_insert_diff", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis", "is_tactic_proof": true, "tactics": ["have", "have", "have", "have", "rw", "have", "have", "obtain", "cases", "have", "have", "rw", "rwa", "obtain", "classical", "convert", "simp", "simp", "have", "refine", "rintro", "exact", "exact", "have", "rw", "matroid_isBase_iff,", "rw", "exact"], "tactic_count": 28}
{"name": "IsTranscendenceBasis.of_isAlgebraic_adjoin_image_compl", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis", "is_tactic_proof": true, "tactics": ["obtain", "exact", "have", "rw", "exact"], "tactic_count": 5}
{"name": "algebraicIndependent_unique_type_iff", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Transcendental", "is_tactic_proof": true, "tactics": ["rw", "let", "have", "ext", "simp", "simp"], "tactic_count": 6}
{"name": "algebraicIndependent_singleton_iff", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Transcendental", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "algebraicIndependent_iff_transcendental", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Transcendental", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgebraicIndependent.transcendental", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Transcendental", "is_tactic_proof": true, "tactics": ["have", "have", "rwa"], "tactic_count": 3}
{"name": "AlgebraicIndependent.isEmpty_of_isAlgebraic", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Transcendental", "is_tactic_proof": true, "tactics": ["rcases", "exact", "exact"], "tactic_count": 3}
{"name": "trdeg_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Transcendental", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "trdeg_pos", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Transcendental", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "trdeg_eq_zero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Transcendental", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "rw", "rw", "exact"], "tactic_count": 5}
{"name": "trdeg_ne_zero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Transcendental", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgebraicIndependent.option_iff_transcendental", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Transcendental", "is_tactic_proof": false, "tactics": ["rw", "hx.aeval_comp_mvPolynomialOptionEquivPolynomialAdjoin,", "exact"], "tactic_count": 3}
{"name": "AlgebraicIndependent.option_iff", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Transcendental", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicIndepOn.insert_iff", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Transcendental", "is_tactic_proof": true, "tactics": ["classical", "convert", "ext", "rw"], "tactic_count": 4}
{"name": "AlgebraicIndepOn.insert", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Transcendental", "is_tactic_proof": true, "tactics": ["nontriviality", "have", "exact"], "tactic_count": 3}
{"name": "algebraicIndependent_of_set_of_finite", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Transcendental", "is_tactic_proof": true, "tactics": ["classical", "refine", "suffices", "this.comp", "refine", "hfin.diff.induction_on_subset", "have", "convert", "x", "by_cases"], "tactic_count": 10}
{"name": "algebraicIndependent_of_finite_type'", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Transcendental", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "algebraicIndependent_of_finite'", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Transcendental", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicIndependent.sumElim_iff", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Transcendental", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "let", "have", "simp_rw"], "tactic_count": 5}
{"name": "AlgebraicIndependent.iff_adjoin_image", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Transcendental", "is_tactic_proof": true, "tactics": ["rw", "convert", "classical", "ext"], "tactic_count": 4}
{"name": "AlgebraicIndependent.iff_adjoin_image_compl", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Transcendental", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "AlgebraicIndependent.iff_transcendental_adjoin_image", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Transcendental", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicIndependent.sumElim", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Transcendental", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicIndependent.sumElim_of_tower", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Transcendental", "is_tactic_proof": true, "tactics": ["let", "set", "let", "have", "refine", "simpa"], "tactic_count": 6}
{"name": "AlgebraicIndependent.sumElim_comp", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Transcendental", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicIndependent.adjoin_of_disjoint", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Transcendental", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicIndependent.adjoin_iff_disjoint", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Transcendental", "is_tactic_proof": true, "tactics": ["refine", "have", "refine", "exact"], "tactic_count": 4}
{"name": "AlgebraicIndependent.transcendental_adjoin", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Transcendental", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "AlgebraicIndependent.transcendental_adjoin_iff", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Transcendental", "is_tactic_proof": true, "tactics": ["rw", "convert", "rw"], "tactic_count": 3}
{"name": "lift_trdeg_add_le", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Transcendental", "is_tactic_proof": true, "tactics": ["simp_rw", "simp_rw", "refine", "have", "refine", "rw"], "tactic_count": 6}
{"name": "trdeg_add_le", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Transcendental", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MvPolynomial.algebraicIndependent_polynomial_aeval_X", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Transcendental", "is_tactic_proof": true, "tactics": ["set", "refine", "have", "rw", "intro", "rw", "refine", "simp_rw", "exact"], "tactic_count": 9}
{"name": "AlgebraicIndependent.polynomial_aeval_of_transcendental", "kind": "theorem", "module": "Mathlib.RingTheory.AlgebraicIndependent.Transcendental", "is_tactic_proof": true, "tactics": ["convert", "rw", "congr"], "tactic_count": 3}
{"name": "is_transcendental_of_subsingleton", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAlgebraic.nontrivial", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": true, "tactics": ["contrapose", "apply"], "tactic_count": 2}
{"name": "Algebra.IsAlgebraic.nontrivial", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.transcendental_of_subsingleton", "kind": "instance", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.transcendental_X", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsAlgebraic.of_aeval", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": true, "tactics": ["obtain", "have", "h1", "rwa", "leadingCoeff_eq_zero]", "exact"], "tactic_count": 6}
{"name": "Transcendental.aeval", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Transcendental.aeval_of_transcendental", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": true, "tactics": ["rw", "intro", "exact"], "tactic_count": 3}
{"name": "Transcendental.of_aeval", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": true, "tactics": ["rw", "intro", "exact"], "tactic_count": 3}
{"name": "IsAlgebraic.of_aeval_of_transcendental", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": true, "tactics": ["contrapose", "exact"], "tactic_count": 2}
{"name": "Polynomial.transcendental", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "isAlgebraic_iff_not_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "transcendental_iff_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "transcendental_iff_ker_eq_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Algebra.isAlgebraic_of_not_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.injective_of_transcendental", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": true, "tactics": ["rw", "contrapose", "exact"], "tactic_count": 3}
{"name": "isAlgebraic_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isAlgebraic_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isAlgebraic_one", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "isAlgebraic_nat", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "isAlgebraic_int", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "isAlgebraic_rat", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "isAlgebraic_of_mem_rootSet", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.isAlgebraic", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAlgebraic.algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAlgebraic.algHom", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isAlgebraic_algHom_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAlgebraic.ringHom_of_comp_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": true, "tactics": ["obtain", "refine", "change", "rw"], "tactic_count": 4}
{"name": "Transcendental.of_ringHom_of_comp_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsAlgebraic.ringHom_of_comp_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact"], "tactic_count": 3}
{"name": "Algebra.Transcendental.of_ringHom_of_comp_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsAlgebraic.of_ringHom_of_comp_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "refine", "change", "change", "rw"], "tactic_count": 6}
{"name": "Transcendental.ringHom_of_comp_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsAlgebraic.of_ringHom_of_comp_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Transcendental.ringHom_of_comp_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "isAlgebraic_ringHom_iff_of_comp_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "transcendental_ringHom_iff_of_comp_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.isAlgebraic_ringHom_iff_of_comp_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.transcendental_ringHom_iff_of_comp_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Algebra.IsAlgebraic.of_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.isAlgebraic", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.isAlgebraic_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isAlgebraic_algebraMap_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "transcendental_algebraMap_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Subalgebra.isAlgebraic_iff_isAlgebraic_val", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.isAlgebraic_of_isAlgebraic_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.isAlgebraic_bot_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.algebra_isAlgebraic_of_algebra_isAlgebraic_bot_left", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.algebra_isAlgebraic_bot_left_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Subalgebra.algebra_isAlgebraic_bot_right", "kind": "instance", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAlgebraic.of_pow", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Transcendental.pow", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAlgebraic.invOf", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": true, "tactics": ["obtain", "refine", "rwa"], "tactic_count": 3}
{"name": "IsAlgebraic.invOf_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAlgebraic.inv_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "letI", "exact"], "tactic_count": 4}
{"name": "IsAlgebraic.extendScalars", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAlgebraic.tower_top_of_subalgebra_le", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": true, "tactics": ["letI", "haveI", "exact"], "tactic_count": 3}
{"name": "Transcendental.restrictScalars", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Transcendental.of_tower_top_of_subalgebra_le", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsAlgebraic.extendScalars", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsAlgebraic.tower_bot_of_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAlgebraic.tower_top", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Transcendental.of_tower_top", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsAlgebraic.tower_top", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsAlgebraic.tower_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsAlgebraic.algHom_bijective", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": true, "tactics": ["refine", "obtain", "let", "have", "obtain", "exact"], "tactic_count": 6}
{"name": "Algebra.IsAlgebraic.algHom_bijective₂", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsAlgebraic.bijective_of_isScalarTower", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsAlgebraic.bijective_of_isScalarTower'", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsAlgebraic.algEquivEquivAlgHom", "kind": "definition", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAlgebraic.exists_nonzero_coeff_and_aeval_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "simp", "rw", "exact"], "tactic_count": 5}
{"name": "IsAlgebraic.exists_nonzero_eq_adjoin_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": true, "tactics": ["have", "have", "refine", "apply_fun", "rwa"], "tactic_count": 5}
{"name": "IsAlgebraic.exists_nonzero_dvd", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": true, "tactics": ["obtain", "have", "rw", "exact"], "tactic_count": 4}
{"name": "IsAlgebraic.exists_smul_eq_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsAlgebraic.exists_smul_eq_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsAlgebraic.injective_tower_top", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": true, "tactics": ["refine", "have", "refine", "simp_rw"], "tactic_count": 4}
{"name": "Algebra.IsAlgebraic.faithfulSMul_tower_top", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "inv_eq_of_aeval_divX_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": true, "tactics": ["rw", "conv_lhs", "rw", "exact"], "tactic_count": 4}
{"name": "inv_eq_of_root_of_coeff_zero_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": false, "tactics": ["convert", "inv_eq_of_aeval_divX_ne_zero", "rw", "rw", "convert", "conv_rhs", "rw"], "tactic_count": 7}
{"name": "Subalgebra.inv_mem_of_root_of_coeff_zero_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": false, "tactics": ["suffices", "rw", "exact", "have", "rw", "map_neg,"], "tactic_count": 6}
{"name": "Subalgebra.inv_mem_of_algebraic", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": true, "tactics": ["obtain", "rw", "revert", "refine", "intro", "contradiction", "intro", "refine", "rwa", "intro", "rw", "rcases", "exact", "rw", "exact"], "tactic_count": 15}
{"name": "Subalgebra.isField_of_algebraic", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Transcendental.infinite", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Transcendental.infinite", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsAlgebraic.lift_cardinalMk_le_sigma_polynomial", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Cardinality", "is_tactic_proof": false, "tactics": ["have", "let", "dsimp", "have", "rw", "intro", "simp", "refine", "simp", "rwa"], "tactic_count": 10}
{"name": "Algebra.IsAlgebraic.lift_cardinalMk_le_max", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Cardinality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsAlgebraic.cardinalMk_le_sigma_polynomial", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Cardinality", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Algebra.IsAlgebraic.cardinalMk_le_max", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Cardinality", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsAlgebraic", "kind": "definition", "module": "Mathlib.RingTheory.Algebraic.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Transcendental", "kind": "definition", "module": "Mathlib.RingTheory.Algebraic.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "transcendental_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Defs", "is_tactic_proof": true, "tactics": ["rw", "congr"], "tactic_count": 2}
{"name": "Subalgebra.IsAlgebraic", "kind": "definition", "module": "Mathlib.RingTheory.Algebraic.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.nontrivial_of_isAlgebraic", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Defs", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Algebra.isAlgebraic_def", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.transcendental_def", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.transcendental_iff_not_isAlgebraic", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Subalgebra.isAlgebraic_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Defs", "is_tactic_proof": true, "tactics": ["delta", "rw", "refine", "have", "conv_rhs", "rw"], "tactic_count": 6}
{"name": "Algebra.isAlgebraic_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Defs", "is_tactic_proof": true, "tactics": ["delta", "simp"], "tactic_count": 2}
{"name": "IsIntegral.isAlgebraic", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsIntegral.isAlgebraic", "kind": "instance", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isAlgebraic_iff_isIntegral", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": true, "tactics": ["refine", "rintro", "refine", "rw"], "tactic_count": 4}
{"name": "Algebra.isAlgebraic_iff_isIntegral", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Algebra.IsAlgebraic.isIntegral", "kind": "instance", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsAlgebraic.of_isIntegralClosure", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAlgebraic.of_finite", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsAlgebraic.of_finite", "kind": "instance", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "transcendental_aeval_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": true, "tactics": ["refine", "rw", "contrapose", "rw", "exact"], "tactic_count": 5}
{"name": "AlgHom.bijective", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "algEquivEquivAlgHom", "kind": "abbrev", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAlgebraic.exists_integral_multiple", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "have", "exact", "have", "set", "have", "have", "integralNormalization_aeval_eq_zero", "exact"], "tactic_count": 10}
{"name": "Algebra.IsAlgebraic.exists_integral_multiples", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": true, "tactics": ["have", "choose", "refine", "classical", "exact"], "tactic_count": 5}
{"name": "IsAlgebraic.of_smul_isIntegral", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": true, "tactics": ["have", "refine", "apply_fun", "have", "rw", "leadingCoeff_C_mul_X]", "exact", "rw"], "tactic_count": 8}
{"name": "IsAlgebraic.of_smul", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAlgebraic.iff_exists_smul_integral", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAlgebraic.restrictScalars_of_isIntegral", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": true, "tactics": ["by_cases", "on_goal", "exact", "have", "have", "cases", "have", "exact", "have", "refine", "rw", "exact"], "tactic_count": 12}
{"name": "IsAlgebraic.restrictScalars", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": true, "tactics": ["have", "by_cases", "on_goal", "exact", "rw", "have", "have", "have", "classical", "have", "let", "obtain", "exact", "have", "refine", "simpa", "smul_ne_zero_iff]", "rw", "eval_map_algebraMap,", "exact"], "tactic_count": 20}
{"name": "IsIntegral.trans_isAlgebraic", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": true, "tactics": ["cases", "have", "exact", "have", "exact"], "tactic_count": 5}
{"name": "IsAlgebraic.neg", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAlgebraic.smul", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAlgebraic.nsmul", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAlgebraic.zsmul", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAlgebraic.tmul", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": true, "tactics": ["rw", "have", "refine", "rw", "map_aeval_eq_aeval_map"], "tactic_count": 5}
{"name": "IsAlgebraic.mul", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": true, "tactics": ["have", "have", "refine", "simp_rw", "exact"], "tactic_count": 5}
{"name": "IsAlgebraic.add", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": true, "tactics": ["have", "have", "refine", "rw", "exact"], "tactic_count": 5}
{"name": "IsAlgebraic.sub", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAlgebraic.pow", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsAlgebraic.trans", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsIntegral.trans_isAlgebraic", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsAlgebraic.trans_isIntegral", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsIntegral.isAlgebraic_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsIntegral.isAlgebraic_iff_top", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Algebra.IsAlgebraic.isAlgebraic_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsAlgebraic.isAlgebraic_iff_top", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Algebra.IsAlgebraic.isAlgebraic_iff_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.algebraicClosure", "kind": "definition", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.mem_algebraicClosure", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "integralClosure_le_algebraicClosure", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.algebraicClosure_eq_integralClosure", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsAlgebraicSubtypeMemSubalgebraAlgebraicClosure", "kind": "instance", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.isAlgebraic_adjoin_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.isAlgebraic_adjoin_of_nonempty", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.isAlgebraic_adjoin_singleton_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAlgebraic.of_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "exact"], "tactic_count": 4}
{"name": "IsAlgebraic.adjoin_of_forall_isAlgebraic", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": true, "tactics": ["set", "set", "let", "let", "have", "have", "have", "have", "have", "rw", "intro", "by_cases", "exact", "exact", "have", "exact"], "tactic_count": 16}
{"name": "Transcendental.extendScalars_of_isIntegral", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": true, "tactics": ["contrapose", "rw", "exact"], "tactic_count": 3}
{"name": "Transcendental.extendScalars", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": true, "tactics": ["contrapose", "rw", "exact"], "tactic_count": 3}
{"name": "Transcendental.integralClosure", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Transcendental.subalgebraAlgebraicClosure", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsIntegral.transcendental_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsAlgebraic.transcendental_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsAlgebraic.instIsLocalizationAlgebraMapSubmonoidNonZeroDivisors", "kind": "instance", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsAlgebraic.instIsLocalizedModuleNonZeroDivisorsToLinearMapToAlgHom", "kind": "instance", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsAlgebraic.isBaseChange_of_isFractionRing", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsAlgebraic.instIsPushout", "kind": "instance", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsAlgebraic.instIsPushout_1", "kind": "instance", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsAlgebraic.lift_rank_of_isFractionRing", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Algebra.IsAlgebraic.finrank_of_isFractionRing", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Algebra.IsAlgebraic.rank_of_isFractionRing", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Algebra.IsAlgebraic.rank_fractionRing", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "rank_polynomial_polynomial", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "rank_mvPolynomial_mvPolynomial", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "Algebra.IsAlgebraic.tensorProduct", "kind": "instance", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsPushout.isAlgebraic'", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsPushout.isAlgebraic", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsAlgebraicPolynomialOfNoZeroDivisors", "kind": "instance", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsAlgebraicPolynomialOfNoZeroDivisors_1", "kind": "instance", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": true, "tactics": ["by_cases", "have", "rw", "exact"], "tactic_count": 4}
{"name": "Polynomial.exists_dvd_map_of_isAlgebraic", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsAlgebraicMvPolynomialOfNoZeroDivisors", "kind": "instance", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsAlgebraicMvPolynomialOfNoZeroDivisors_1", "kind": "instance", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": true, "tactics": ["by_cases", "have", "rw", "exact"], "tactic_count": 4}
{"name": "MvPolynomial.exists_dvd_map_of_isAlgebraic", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsPushoutFractionRingPolynomial", "kind": "instance", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsPushoutFractionRingPolynomial_1", "kind": "instance", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsPushoutFractionRingMvPolynomial", "kind": "instance", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsPushoutFractionRingMvPolynomial_1", "kind": "instance", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsAlgebraic.rank_fractionRing_polynomial", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "Algebra.IsAlgebraic.rank_fractionRing_mvPolynomial", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "instFiniteDimensionalFractionRingOfFinite", "kind": "instance", "module": "Mathlib.RingTheory.Algebraic.Integral", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Transcendental.linearIndependent_sub_inv", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.LinearIndependent", "is_tactic_proof": true, "tactics": ["classical", "rw", "refine", "have", "let", "have", "replace", "simp_rw", "let", "replace", "congr", "have", "have", "simp_rw", "simp_rw", "s.sum_erase_add", "exact", "eq_zero_of_ne_zero_of_mul_right_eq_zero"], "tactic_count": 18}
{"name": "MvPolynomial.transcendental_supported_polynomial_aeval_X", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.MvPolynomial", "is_tactic_proof": true, "tactics": ["classical", "rw", "let", "replace", "let", "g", "let", "replace", "simp", "apply", "simp", "apply", "simp", "have", "have", "simp", "ext1", "ext1", "simp", "simp", "simpa"], "tactic_count": 21}
{"name": "MvPolynomial.transcendental_polynomial_aeval_X", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.MvPolynomial", "is_tactic_proof": true, "tactics": ["have", "let", "rwa", "isAlgebraic_ringHom_iff_of_comp_eq"], "tactic_count": 4}
{"name": "MvPolynomial.transcendental_polynomial_aeval_X_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.MvPolynomial", "is_tactic_proof": true, "tactics": ["refine", "simp_rw", "exact"], "tactic_count": 3}
{"name": "MvPolynomial.transcendental_supported_polynomial_aeval_X_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.MvPolynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.transcendental_supported_X", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.MvPolynomial", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MvPolynomial.transcendental_X", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.MvPolynomial", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MvPolynomial.transcendental_supported_X_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.MvPolynomial", "is_tactic_proof": true, "tactics": ["simpa", "transcendental_supported_polynomial_aeval_X_iff"], "tactic_count": 2}
{"name": "Polynomial.hasSMulPi", "kind": "definition", "module": "Mathlib.RingTheory.Algebraic.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.hasSMulPi'", "kind": "definition", "module": "Mathlib.RingTheory.Algebraic.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "polynomial_smul_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "polynomial_smul_apply'", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.algebraPi", "kind": "definition", "module": "Mathlib.RingTheory.Algebraic.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.algebraMap_pi_eq_aeval", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.algebraMap_pi_self_eq_eval", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsStronglyTranscendental", "kind": "definition", "module": "Mathlib.RingTheory.Algebraic.StronglyTranscendental", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsStronglyTranscendental.transcendental", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.StronglyTranscendental", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isStronglyTranscendental_iff_of_field", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.StronglyTranscendental", "is_tactic_proof": true, "tactics": ["refine", "simpa", "ext_iff,"], "tactic_count": 3}
{"name": "IsStronglyTranscendental.of_map", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.StronglyTranscendental", "is_tactic_proof": true, "tactics": ["refine", "have", "rwa", "map_eq_zero_iff]", "exact"], "tactic_count": 5}
{"name": "IsStronglyTranscendental.of_isLocalization", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.StronglyTranscendental", "is_tactic_proof": true, "tactics": ["refine", "obtain", "obtain", "simpa", "have", "simpa", "congr", "refine", "simpa"], "tactic_count": 9}
{"name": "IsStronglyTranscendental.of_isLocalization_left", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.StronglyTranscendental", "is_tactic_proof": true, "tactics": ["intro", "obtain", "have", "simpa", "have", "rw", "rw", "simpa"], "tactic_count": 8}
{"name": "IsStronglyTranscendental.restrictScalars", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.StronglyTranscendental", "is_tactic_proof": true, "tactics": ["intro", "simpa"], "tactic_count": 2}
{"name": "IsStronglyTranscendental.of_surjective_left", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.StronglyTranscendental", "is_tactic_proof": true, "tactics": ["intro", "obtain", "simpa"], "tactic_count": 3}
{"name": "IsStronglyTranscendental.iff_of_isLocalization", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.StronglyTranscendental", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsStronglyTranscendental.iff_of_isFractionRing", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.StronglyTranscendental", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "IsStronglyTranscendental.of_transcendental", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.StronglyTranscendental", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "isStronglyTranscendental_mk_of_mem_minimalPrimes", "kind": "theorem", "module": "Mathlib.RingTheory.Algebraic.StronglyTranscendental", "is_tactic_proof": true, "tactics": ["refine", "rw", "have", "have", "let", "obtain", "exact", "ext", "simp", "have", "simpa", "exact"], "tactic_count": 12}
{"name": "IsArtinianRing.isUnit_of_isIntegral_of_nonZeroDivisor", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsArtinianRing.isUnit_iff_nonZeroDivisor_of_isIntegral", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsArtinianRing.isUnit_of_nonZeroDivisor_of_isIntegral'", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsArtinianRing.isUnit_iff_nonZeroDivisor_of_isIntegral'", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsArtinianRing.isUnit_submonoid_eq_of_isIntegral", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Algebra", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "StrongRankCondition.of_isArtinian", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsArtinianRing.instDecompositionMonoid", "kind": "instance", "module": "Mathlib.RingTheory.Artinian.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsArtinianRing.instDecompositionMonoidPolynomial", "kind": "instance", "module": "Mathlib.RingTheory.Artinian.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsArtinian", "kind": "abbrev", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isArtinian_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.isArtinian_iff_of_bijective", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isArtinian_of_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isArtinian_submodule'", "kind": "instance", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isArtinian_of_le", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isArtinian_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isArtinian_of_surjective_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": true, "tactics": ["apply", "refine", "intro", "refine", "intro", "obtain", "suffices", "apply", "intro", "rwa", "intro", "rfl"], "tactic_count": 12}
{"name": "isArtinian_range", "kind": "instance", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isArtinian_of_linearEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.isArtinian_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isArtinian_of_finite", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsArtinian.finite_of_linearIndependent", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "set_has_minimal_iff_artinian", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsArtinian.set_has_minimal", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monotone_stabilizes_iff_artinian", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsArtinian.monotone_stabilizes", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsArtinian.eventuallyConst_of_isArtinian", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "IsArtinian.induction", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsArtinian.surjective_of_injective_endomorphism", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": true, "tactics": ["have", "rw", "refine", "intro", "simp_rw", "refine", "rwa"], "tactic_count": 7}
{"name": "IsArtinian.bijective_of_injective_endomorphism", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsArtinian.disjoint_partial_infs_eventually_top", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": true, "tactics": ["rsuffices", "use", "rintro", "cases", "apply", "exact", "obtain", "refine", "simpa"], "tactic_count": 9}
{"name": "IsArtinian.subsingleton_of_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.eventually_iInf_range_pow_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": false, "tactics": ["obtain", "refine", "rcases", "rw", "exact"], "tactic_count": 5}
{"name": "isArtinian_of_quotient_of_artinian", "kind": "instance", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isArtinian_of_range_eq_ker", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isArtinian_iff_submodule_quotient", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": true, "tactics": ["refine", "apply", "rw"], "tactic_count": 3}
{"name": "isArtinian_prod", "kind": "instance", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isArtinian_sup", "kind": "instance", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "isArtinian_pi", "kind": "instance", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": true, "tactics": ["apply", "exact", "infer_instance", "exact"], "tactic_count": 4}
{"name": "isArtinian_pi'", "kind": "instance", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isArtinian_finsupp", "kind": "instance", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isArtinian_iSup", "kind": "instance", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": true, "tactics": ["apply", "intro", "intros", "intro"], "tactic_count": 4}
{"name": "IsArtinian.isSemisimpleModule_iff_jacobson", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.eventually_codisjoint_ker_pow_range_pow", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": false, "tactics": ["obtain", "refine", "simp_rw", "intro", "rsuffices", "exact", "simp_rw", "mem_range", "exact"], "tactic_count": 9}
{"name": "LinearMap.eventually_isCompl_ker_pow_range_pow", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": false, "tactics": ["filter_upwards", "simpa"], "tactic_count": 2}
{"name": "LinearMap.isCompl_iSup_ker_pow_iInf_range_pow", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": false, "tactics": ["obtain", "eventually_atTop.mp", "f.eventually_isCompl_ker_pow_range_pow.and", "obtain", "rwa"], "tactic_count": 5}
{"name": "IsArtinian.range_smul_pow_stabilizes", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsArtinian.exists_pow_succ_smul_dvd", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": true, "tactics": ["obtain", "simp_rw", "exact"], "tactic_count": 3}
{"name": "isArtinian_of_submodule_of_artinian", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isArtinian_of_tower", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsArtinianRing", "kind": "abbrev", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isArtinianRing_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DivisionSemiring.instIsArtinianRing", "kind": "instance", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DivisionRing.instIsArtinianRing", "kind": "instance", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ring.isArtinian_of_zero_eq_one", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsArtinianRingQuotientIdeal", "kind": "instance", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsDedekindFiniteMonoidOfIsArtinianRing", "kind": "instance", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isArtinian_of_fg_of_artinian'", "kind": "instance", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isArtinian_of_fg_of_artinian", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsArtinianRing.of_finite", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsNoetherianRingMatrix", "kind": "instance", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsArtinianRingMatrix", "kind": "instance", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isArtinian_span_of_finite", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.isArtinianRing", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "isArtinianRing_rangeS", "kind": "instance", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isArtinianRing_range", "kind": "instance", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.isArtinianRing", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsArtinianRingProd", "kind": "instance", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsArtinianRingForallOfFinite", "kind": "instance", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": true, "tactics": ["apply", "exact", "infer_instance", "exact"], "tactic_count": 4}
{"name": "IsArtinianRing.isUnit_iff_isRightRegular", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsArtinianRing.isUnit_iff_isRegular", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsArtinianRing.isUnit_iff_isLeftRegular", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsArtinianRing.isUnit_iff_isRegular_of_mulOpposite", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsArtinianRing.isUnit_of_mem_nonZeroDivisors", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "IsArtinianRing.isUnit_of_mem_nonZeroDivisors_of_mulOpposite", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "IsArtinianRing.isUnit_iff_mem_nonZeroDivisors", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsArtinianRing.isUnit_iff_mem_nonZeroDivisors_of_mulOpposite", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsArtinianRing.isUnitSubmonoid_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "IsArtinianRing.isUnitSubmonoid_eq_of_mulOpposite", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "IsArtinianRing.isUnitSubmonoid_eq_nonZeroDivisorsRight", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "IsArtinianRing.nonZeroDivisorsLeft_eq_isUnitSubmonoid", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "IsArtinianRing.setOf_isMaximal_finite", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": true, "tactics": ["have", "refine", "have", "rwa"], "tactic_count": 4}
{"name": "IsArtinianRing.instFiniteMaximalSpectrum", "kind": "instance", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsArtinianRing.isField_of_isDomain", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": true, "tactics": ["refine", "obtain", "replace", "rw", "convert", "simp", "rw", "exact", "consider"], "tactic_count": 9}
{"name": "IsArtinianRing.isMaximal_of_isPrime", "kind": "instance", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsArtinianRing.isPrime_iff_isMaximal", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsArtinianRing.primeSpectrumEquivMaximalSpectrum", "kind": "definition", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsArtinianRing.primeSpectrumEquivMaximalSpectrum_comp_asIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsArtinianRing.primeSpectrumEquivMaximalSpectrum_symm_comp_asIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsArtinianRing.primeSpectrum_asIdeal_range_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsArtinianRing.setOf_isPrime_finite", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsArtinianRing.instFinitePrimeSpectrum", "kind": "instance", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsArtinianRing.fieldOfSubtypeIsMaximal", "kind": "definition", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsArtinianRing.quotNilradicalEquivPi", "kind": "definition", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsArtinianRing.equivPi", "kind": "definition", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsArtinianRing.isSemisimpleRing_of_isReduced", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsArtinianRing.isSemisimpleRing_iff_jacobson", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsArtinianRing.instIsSemiprimaryRing", "kind": "instance", "module": "Mathlib.RingTheory.Artinian.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsArtinianRing.isNilpotent_jacobson_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsArtinianRing.jacobson_eq_radical", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Ring", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "IsArtinianRing.isNilpotent_nilradical", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Ring", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsArtinianRing.isField_of_isReduced_of_isLocalRing", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsArtinianRing.localization_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Ring", "is_tactic_proof": true, "tactics": ["intro", "obtain", "rsuffices", "exact", "obtain", "use", "rw", "apply_fun", "simp", "rw"], "tactic_count": 10}
{"name": "IsArtinianRing.localization_artinian", "kind": "theorem", "module": "Mathlib.RingTheory.Artinian.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsArtinianRing.instLocalization", "kind": "instance", "module": "Mathlib.RingTheory.Artinian.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBezout.iff_span_pair_isPrincipal", "kind": "theorem", "module": "Mathlib.RingTheory.Bezout", "is_tactic_proof": true, "tactics": ["classical", "constructor", "intro", "intro", "constructor", "apply", "exact", "rintro"], "tactic_count": 8}
{"name": "Function.Surjective.isBezout", "kind": "theorem", "module": "Mathlib.RingTheory.Bezout", "is_tactic_proof": true, "tactics": ["rw", "intro", "obtain", "use", "trans", "rw", "rw"], "tactic_count": 7}
{"name": "IsBezout.TFAE", "kind": "theorem", "module": "Mathlib.RingTheory.Bezout", "is_tactic_proof": true, "tactics": ["classical", "tfae_have", "tfae_have", "tfae_have", "tfae_have", "rw", "refine", "have", "choose", "exact", "inj", "map_rel_iff", "dsimp", "intro", "rw", "rfl", "tfae_finish"], "tactic_count": 17}
{"name": "Bialgebra.counit_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Bialgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bialgebra.comul_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Bialgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bialgebra.mk'", "kind": "definition", "module": "Mathlib.RingTheory.Bialgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bialgebra.counitAlgHom", "kind": "definition", "module": "Mathlib.RingTheory.Bialgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bialgebra.comulAlgHom", "kind": "definition", "module": "Mathlib.RingTheory.Bialgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bialgebra.toLinearMap_counitAlgHom", "kind": "theorem", "module": "Mathlib.RingTheory.Bialgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bialgebra.toLinearMap_comulAlgHom", "kind": "theorem", "module": "Mathlib.RingTheory.Bialgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bialgebra.counit_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.Bialgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bialgebra.comul_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.Bialgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bialgebra.counit_natCast", "kind": "theorem", "module": "Mathlib.RingTheory.Bialgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bialgebra.comul_natCast", "kind": "theorem", "module": "Mathlib.RingTheory.Bialgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bialgebra.counit_pow", "kind": "theorem", "module": "Mathlib.RingTheory.Bialgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bialgebra.comul_pow", "kind": "theorem", "module": "Mathlib.RingTheory.Bialgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommSemiring.toBialgebra", "kind": "instance", "module": "Mathlib.RingTheory.Bialgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bialgebra.counitAlgHom_self", "kind": "theorem", "module": "Mathlib.RingTheory.Bialgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bialgebra.ofAlgHom", "kind": "abbrev", "module": "Mathlib.RingTheory.Bialgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bialgebra.algebraMap_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Bialgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bialgebra.counit_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Bialgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bialgebra.nontrivial", "kind": "theorem", "module": "Mathlib.RingTheory.Bialgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "term_≃ₐc[_]_", "kind": "definition", "module": "Mathlib.RingTheory.Bialgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_RingTheory_Bialgebra_Equiv___macroRules_term_≃ₐc[_]__1", "kind": "definition", "module": "Mathlib.RingTheory.Bialgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_RingTheory_Bialgebra_Equiv___unexpand_BialgEquiv_1", "kind": "definition", "module": "Mathlib.RingTheory.Bialgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgEquivClass.toBialgHomClass", "kind": "instance", "module": "Mathlib.RingTheory.Bialgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgEquivClass.toBialgEquiv", "kind": "definition", "module": "Mathlib.RingTheory.Bialgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgEquivClass.instCoeToBialgEquiv", "kind": "instance", "module": "Mathlib.RingTheory.Bialgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgEquivClass.toAlgEquivClass", "kind": "instance", "module": "Mathlib.RingTheory.Bialgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgEquiv.toBialgHom", "kind": "definition", "module": "Mathlib.RingTheory.Bialgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgEquiv.toAlgEquiv", "kind": "definition", "module": "Mathlib.RingTheory.Bialgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgEquiv.toEquiv", "kind": "definition", "module": "Mathlib.RingTheory.Bialgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgEquiv.toEquiv_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Bialgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgEquiv.toEquiv_inj", "kind": "theorem", "module": "Mathlib.RingTheory.Bialgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgEquiv.toBialgHom_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Bialgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgEquiv.instEquivLike", "kind": "instance", "module": "Mathlib.RingTheory.Bialgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgEquiv.instFunLike", "kind": "instance", "module": "Mathlib.RingTheory.Bialgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgEquiv.instBialgEquivClass", "kind": "instance", "module": "Mathlib.RingTheory.Bialgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgEquiv.toBialgHom_inj", "kind": "theorem", "module": "Mathlib.RingTheory.Bialgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgEquiv.coe_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Bialgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgEquiv.coe_coe", "kind": "theorem", "module": "Mathlib.RingTheory.Bialgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgEquiv.toCoalgEquiv_eq_coe", "kind": "theorem", "module": "Mathlib.RingTheory.Bialgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgEquiv.toBialgHom_eq_coe", "kind": "theorem", "module": "Mathlib.RingTheory.Bialgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgEquiv.toAlgEquiv_eq_coe", "kind": "theorem", "module": "Mathlib.RingTheory.Bialgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgEquiv.coe_toCoalgEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.Bialgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgEquiv.coe_toBialgHom", "kind": "theorem", "module": "Mathlib.RingTheory.Bialgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgEquiv.coe_toAlgEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.Bialgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgEquiv.toCoalgEquiv_toCoalgHom", "kind": "theorem", "module": "Mathlib.RingTheory.Bialgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgEquiv.toBialgHom_toAlgHom", "kind": "theorem", "module": "Mathlib.RingTheory.Bialgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgEquiv.ext", "kind": "theorem", "module": "Mathlib.RingTheory.Bialgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgEquiv.congr_arg", "kind": "theorem", "module": "Mathlib.RingTheory.Bialgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgEquiv.congr_fun", "kind": "theorem", "module": "Mathlib.RingTheory.Bialgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgEquiv.Simps.apply", "kind": "definition", "module": "Mathlib.RingTheory.Bialgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgEquiv.Simps.symm_apply", "kind": "definition", "module": "Mathlib.RingTheory.Bialgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgEquiv.refl", "kind": "definition", "module": "Mathlib.RingTheory.Bialgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgEquiv.refl_toCoalgEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.Bialgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgEquiv.refl_toBialgHom", "kind": "theorem", "module": "Mathlib.RingTheory.Bialgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgEquiv.symm", "kind": "definition", "module": "Mathlib.RingTheory.Bialgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgEquiv.symm_toCoalgEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.Bialgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgEquiv.invFun_eq_symm", "kind": "theorem", "module": "Mathlib.RingTheory.Bialgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgEquiv.coe_toEquiv_symm", "kind": "theorem", "module": "Mathlib.RingTheory.Bialgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgEquiv.toEquiv_symm", "kind": "theorem", "module": "Mathlib.RingTheory.Bialgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgEquiv.coe_toEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.Bialgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgEquiv.coe_symm_toEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.Bialgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgEquiv.trans", "kind": "definition", "module": "Mathlib.RingTheory.Bialgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgEquiv.trans_toCoalgEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.Bialgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgEquiv.trans_toBialgHom", "kind": "theorem", "module": "Mathlib.RingTheory.Bialgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgEquiv.coe_toEquiv_trans", "kind": "theorem", "module": "Mathlib.RingTheory.Bialgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgEquiv.apply_symm_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Bialgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgEquiv.symm_apply_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Bialgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgEquiv.comp_symm", "kind": "theorem", "module": "Mathlib.RingTheory.Bialgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgEquiv.symm_comp", "kind": "theorem", "module": "Mathlib.RingTheory.Bialgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgEquiv.toRingEquiv_toRingHom", "kind": "theorem", "module": "Mathlib.RingTheory.Bialgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgEquiv.toAlgEquiv_toRingHom", "kind": "theorem", "module": "Mathlib.RingTheory.Bialgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgEquiv.ofBialgHom", "kind": "definition", "module": "Mathlib.RingTheory.Bialgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgEquiv.coe_ofBialgHom", "kind": "theorem", "module": "Mathlib.RingTheory.Bialgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgEquiv.ofBialgHom_symm", "kind": "theorem", "module": "Mathlib.RingTheory.Bialgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgEquiv.ofAlgEquiv", "kind": "definition", "module": "Mathlib.RingTheory.Bialgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgEquiv.toLinearMap_ofAlgEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.Bialgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgEquiv.ofBijective", "kind": "definition", "module": "Mathlib.RingTheory.Bialgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BialgEquiv.coe_ofBijective", "kind": "theorem", "module": "Mathlib.RingTheory.Bialgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGroupLikeElem.one", "kind": "theorem", "module": "Mathlib.RingTheory.Bialgebra.GroupLike", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGroupLikeElem.mul", "kind": "theorem", "module": "Mathlib.RingTheory.Bialgebra.GroupLike", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "IsGroupLikeElem.pow", "kind": "theorem", "module": "Mathlib.RingTheory.Bialgebra.GroupLike", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Polynomial.descPochhammer_smeval_eq_ascPochhammer", "kind": "theorem", "module": "Mathlib.RingTheory.Binomial", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "ih", "rw", "ascPochhammer_succ_left,", "smeval_C]", "simp"], "tactic_count": 8}
{"name": "Polynomial.descPochhammer_smeval_eq_descFactorial", "kind": "theorem", "module": "Mathlib.RingTheory.Binomial", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "ih", "rw", "smeval_natCast,", "by_cases", "simp", "rw"], "tactic_count": 9}
{"name": "Polynomial.ascPochhammer_smeval_neg_eq_descPochhammer", "kind": "theorem", "module": "Mathlib.RingTheory.Binomial", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "ih", "simp", "have", "rw"], "tactic_count": 7}
{"name": "Nat.instBinomialRing", "kind": "instance", "module": "Mathlib.RingTheory.Binomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.multichoose", "kind": "definition", "module": "Mathlib.RingTheory.Binomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.instBinomialRing", "kind": "instance", "module": "Mathlib.RingTheory.Binomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instBinomialRingOfModuleNNRat", "kind": "instance", "module": "Mathlib.RingTheory.Binomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ring.smeval_ascPochhammer_self_neg", "kind": "theorem", "module": "Mathlib.RingTheory.Binomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ring.smeval_ascPochhammer_succ_neg", "kind": "theorem", "module": "Mathlib.RingTheory.Binomial", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ring.smeval_ascPochhammer_neg_add", "kind": "theorem", "module": "Mathlib.RingTheory.Binomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ring.smeval_ascPochhammer_neg_of_lt", "kind": "theorem", "module": "Mathlib.RingTheory.Binomial", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ring.smeval_ascPochhammer_nat_cast", "kind": "theorem", "module": "Mathlib.RingTheory.Binomial", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ring.multichoose_neg_self", "kind": "theorem", "module": "Mathlib.RingTheory.Binomial", "is_tactic_proof": true, "tactics": ["rw", "smeval_ascPochhammer_self_neg,"], "tactic_count": 2}
{"name": "Ring.multichoose_neg_succ", "kind": "theorem", "module": "Mathlib.RingTheory.Binomial", "is_tactic_proof": true, "tactics": ["rw", "smeval_ascPochhammer_succ_neg,"], "tactic_count": 2}
{"name": "Ring.multichoose_neg_add", "kind": "theorem", "module": "Mathlib.RingTheory.Binomial", "is_tactic_proof": true, "tactics": ["rw", "smeval_ascPochhammer_neg_add,"], "tactic_count": 2}
{"name": "Ring.multichoose_neg_of_lt", "kind": "theorem", "module": "Mathlib.RingTheory.Binomial", "is_tactic_proof": true, "tactics": ["rw", "smeval_ascPochhammer_neg_of_lt"], "tactic_count": 2}
{"name": "Ring.multichoose_succ_neg_natCast", "kind": "theorem", "module": "Mathlib.RingTheory.Binomial", "is_tactic_proof": true, "tactics": ["rw", "smeval_neg_nat,"], "tactic_count": 2}
{"name": "Ring.smeval_ascPochhammer_int_ofNat", "kind": "theorem", "module": "Mathlib.RingTheory.Binomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ring.choose", "kind": "definition", "module": "Mathlib.RingTheory.Binomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ring.multichoose_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Binomial", "is_tactic_proof": true, "tactics": ["rw", "congr", "abel"], "tactic_count": 3}
{"name": "Ring.descPochhammer_eq_factorial_smul_choose", "kind": "theorem", "module": "Mathlib.RingTheory.Binomial", "is_tactic_proof": false, "tactics": ["rw", "smeval_add,", "have", "rw", "simp", "rw"], "tactic_count": 6}
{"name": "Ring.choose_natCast", "kind": "theorem", "module": "Mathlib.RingTheory.Binomial", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ring.choose_zero_right'", "kind": "theorem", "module": "Mathlib.RingTheory.Binomial", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "simp"], "tactic_count": 3}
{"name": "Ring.choose_zero_right", "kind": "theorem", "module": "Mathlib.RingTheory.Binomial", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ring.choose_zero_succ", "kind": "theorem", "module": "Mathlib.RingTheory.Binomial", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ring.choose_zero_pos", "kind": "theorem", "module": "Mathlib.RingTheory.Binomial", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ring.choose_zero_ite", "kind": "theorem", "module": "Mathlib.RingTheory.Binomial", "is_tactic_proof": true, "tactics": ["split_ifs", "rw", "rw"], "tactic_count": 3}
{"name": "Ring.choose_one_right'", "kind": "theorem", "module": "Mathlib.RingTheory.Binomial", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ring.choose_one_right", "kind": "theorem", "module": "Mathlib.RingTheory.Binomial", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ring.choose_neg", "kind": "theorem", "module": "Mathlib.RingTheory.Binomial", "is_tactic_proof": true, "tactics": ["apply", "rw", "descPochhammer_smeval_eq_ascPochhammer,", "ascPochhammer_smeval_neg_eq_descPochhammer]"], "tactic_count": 4}
{"name": "Ring.choose_neg'", "kind": "theorem", "module": "Mathlib.RingTheory.Binomial", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ring.descPochhammer_succ_succ_smeval", "kind": "theorem", "module": "Mathlib.RingTheory.Binomial", "is_tactic_proof": true, "tactics": ["nth_rw", "rw", "simp", "add_sub_cancel_right,", "rw", "add_comm"], "tactic_count": 6}
{"name": "Ring.choose_succ_succ", "kind": "theorem", "module": "Mathlib.RingTheory.Binomial", "is_tactic_proof": true, "tactics": ["rw", "simp", "rw"], "tactic_count": 3}
{"name": "Ring.choose_smul_choose", "kind": "theorem", "module": "Mathlib.RingTheory.Binomial", "is_tactic_proof": false, "tactics": ["rw", "mul_nsmul',", "nth_rw", "rw", "npow_zero,"], "tactic_count": 5}
{"name": "Ring.choose_add_smul_choose", "kind": "theorem", "module": "Mathlib.RingTheory.Binomial", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ring.choose_eq_smul", "kind": "theorem", "module": "Mathlib.RingTheory.Binomial", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "Ring.descPochhammer_smeval_add", "kind": "theorem", "module": "Mathlib.RingTheory.Binomial", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "ih", "rw", "sum_antidiagonal_choose_succ_mul", "sum_add_distrib,", "refine", "intro", "have", "refine", "exact", "rw", "mul_assoc", "simp", "have", "simp", "rw", "abel_nf", "rw"], "tactic_count": 20}
{"name": "Ring.add_choose_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Binomial", "is_tactic_proof": false, "tactics": ["rw", "descPochhammer_smeval_add", "refine", "intro", "rw", "tsub_eq_of_eq_add_rev", "mul_assoc", "simp"], "tactic_count": 8}
{"name": "Ring.map_choose", "kind": "theorem", "module": "Mathlib.RingTheory.Binomial", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Associates.isAtom_iff", "kind": "theorem", "module": "Mathlib.RingTheory.ChainOfDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DivisorChain.exists_chain_of_prime_pow", "kind": "theorem", "module": "Mathlib.RingTheory.ChainOfDivisors", "is_tactic_proof": true, "tactics": ["refine", "dsimp", "rw", "exact", "exact", "not_isUnit_of_not_isUnit_dvd", "obtain", "rw", "exact", "rintro", "exact"], "tactic_count": 11}
{"name": "DivisorChain.element_of_chain_not_isUnit_of_index_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.ChainOfDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DivisorChain.first_of_chain_isUnit", "kind": "theorem", "module": "Mathlib.RingTheory.ChainOfDivisors", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact"], "tactic_count": 3}
{"name": "DivisorChain.second_of_chain_is_irreducible", "kind": "theorem", "module": "Mathlib.RingTheory.ChainOfDivisors", "is_tactic_proof": true, "tactics": ["rcases", "refine", "exact", "obtain", "cases", "exact", "simpa"], "tactic_count": 7}
{"name": "DivisorChain.eq_second_of_chain_of_prime_dvd", "kind": "theorem", "module": "Mathlib.RingTheory.ChainOfDivisors", "is_tactic_proof": true, "tactics": ["rcases", "contradiction", "obtain", "refine", "rw", "rintro", "exact", "obtain", "cases", "refine", "not_irreducible_of_not_unit_dvdNotUnit", "hp.irreducible", "simpa", "refine", "simpa"], "tactic_count": 15}
{"name": "DivisorChain.card_subset_divisors_le_length_of_chain", "kind": "theorem", "module": "Mathlib.RingTheory.ChainOfDivisors", "is_tactic_proof": true, "tactics": ["classical", "have", "intro", "obtain", "exact", "rw", "exact"], "tactic_count": 7}
{"name": "DivisorChain.element_of_chain_eq_pow_second_of_chain", "kind": "theorem", "module": "Mathlib.RingTheory.ChainOfDivisors", "is_tactic_proof": true, "tactics": ["classical", "let", "have", "apply", "intro", "refine", "eq_second_of_chain_of_prime_dvd", "have", "have", "rw", "rw", "refine", "have", "conv_rhs", "cases", "contradiction", "rw", "refine", "refine", "exact", "suffices", "simp", "apply", "simp", "rintro", "refine", "use", "rw", "exact", "exact"], "tactic_count": 30}
{"name": "DivisorChain.eq_pow_second_of_chain_of_has_chain", "kind": "theorem", "module": "Mathlib.RingTheory.ChainOfDivisors", "is_tactic_proof": true, "tactics": ["classical", "obtain", "convert", "refine", "calc", "n", "intro", "obtain", "have", "rw", "have", "rcases", "refine", "rwa", "rw", "exact"], "tactic_count": 16}
{"name": "DivisorChain.isPrimePow_of_has_chain", "kind": "theorem", "module": "Mathlib.RingTheory.ChainOfDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "factor_orderIso_map_one_eq_bot", "kind": "theorem", "module": "Mathlib.RingTheory.ChainOfDivisors", "is_tactic_proof": true, "tactics": ["letI", "letI", "simp", "letI", "exact"], "tactic_count": 5}
{"name": "coe_factor_orderIso_map_eq_one_iff", "kind": "theorem", "module": "Mathlib.RingTheory.ChainOfDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pow_image_of_prime_by_factor_orderIso_dvd", "kind": "theorem", "module": "Mathlib.RingTheory.ChainOfDivisors", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "suffices", "rw", "apply", "obtain", "let", "have", "rw", "refine", "rw", "exact", "have", "suffices", "obtain", "use", "simp", "conv_rhs", "rw", "simpa", "rintro", "rw", "simpa", "exact"], "tactic_count": 24}
{"name": "map_prime_of_factor_orderIso", "kind": "theorem", "module": "Mathlib.RingTheory.ChainOfDivisors", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "rintro", "exact", "have", "obtain", "rw", "letI", "letI", "suffices", "rw", "refine", "simp", "obtain", "rw", "exact", "irreducible_of_normalized_factor", "a", "simp"], "tactic_count": 20}
{"name": "mem_normalizedFactors_factor_orderIso_of_mem_normalizedFactors", "kind": "theorem", "module": "Mathlib.RingTheory.ChainOfDivisors", "is_tactic_proof": false, "tactics": ["obtain", "exists_mem_normalizedFactors_of_dvd", "rw", "rwa"], "tactic_count": 4}
{"name": "emultiplicity_prime_le_emultiplicity_image_by_factor_orderIso", "kind": "theorem", "module": "Mathlib.RingTheory.ChainOfDivisors", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "by_cases", "simp", "rw", "pow_dvd_iff_le_emultiplicity]", "apply"], "tactic_count": 7}
{"name": "emultiplicity_prime_eq_emultiplicity_image_by_factor_orderIso", "kind": "theorem", "module": "Mathlib.RingTheory.ChainOfDivisors", "is_tactic_proof": true, "tactics": ["refine", "suffices", "emultiplicity", "emultiplicity", "rw", "exact", "letI", "simpa", "emultiplicity_prime_le_emultiplicity_image_by_factor_orderIso"], "tactic_count": 9}
{"name": "mkFactorOrderIsoOfFactorDvdEquiv", "kind": "definition", "module": "Mathlib.RingTheory.ChainOfDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_normalizedFactors_factor_dvd_iso_of_mem_normalizedFactors", "kind": "theorem", "module": "Mathlib.RingTheory.ChainOfDivisors", "is_tactic_proof": false, "tactics": ["suffices", "simp", "simp", "associatesEquivOfUniqueUnits_symm_apply]", "obtain", "exists_mem_normalizedFactors_of_dvd", "rwa", "have", "simp", "associatesEquivOfUniqueUnits_symm_apply]⟩", "simp", "exact", "rw", "letI", "refine", "obtain", "exists_mem_normalizedFactors_of_dvd", "simpa"], "tactic_count": 18}
{"name": "emultiplicity_factor_dvd_iso_eq_emultiplicity_of_mem_normalizedFactors", "kind": "theorem", "module": "Mathlib.RingTheory.ChainOfDivisors", "is_tactic_proof": true, "tactics": ["apply", "suffices", "emultiplicity", "emultiplicity", "simp", "simpa", "associatesEquivOfUniqueUnits_apply,", "have", "simp", "associatesEquivOfUniqueUnits_apply,", "rw", "exact", "rw", "refine", "emultiplicity_prime_eq_emultiplicity_image_by_factor_orderIso", "obtain", "exists_mem_normalizedFactors_of_dvd", "rwa"], "tactic_count": 18}
{"name": "definition._@.Mathlib.RingTheory.ClassGroup.3062443935._hygCtx._hyg.2", "kind": "definition", "module": "Mathlib.RingTheory.ClassGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "wrapped._@.Mathlib.RingTheory.ClassGroup.3062443935._hygCtx._hyg.2", "kind": "opaque", "module": "Mathlib.RingTheory.ClassGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toPrincipalIdeal", "kind": "definition", "module": "Mathlib.RingTheory.ClassGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toPrincipalIdeal_def", "kind": "theorem", "module": "Mathlib.RingTheory.ClassGroup", "is_tactic_proof": true, "tactics": ["intros", "delta", "rw", "rfl"], "tactic_count": 4}
{"name": "coe_toPrincipalIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.ClassGroup", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "toPrincipalIdeal_eq_iff", "kind": "theorem", "module": "Mathlib.RingTheory.ClassGroup", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "mem_principal_ideals_iff", "kind": "theorem", "module": "Mathlib.RingTheory.ClassGroup", "is_tactic_proof": true, "tactics": ["simp", "constructor", "exact", "refine", "rintro", "simp"], "tactic_count": 6}
{"name": "PrincipalIdeals.normal", "kind": "instance", "module": "Mathlib.RingTheory.ClassGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClassGroup", "kind": "definition", "module": "Mathlib.RingTheory.ClassGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCommGroupClassGroup", "kind": "instance", "module": "Mathlib.RingTheory.ClassGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInhabitedClassGroup", "kind": "instance", "module": "Mathlib.RingTheory.ClassGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClassGroup.mulEquivUnitsSubmoduleQuotRange", "kind": "definition", "module": "Mathlib.RingTheory.ClassGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClassGroup.mk", "kind": "definition", "module": "Mathlib.RingTheory.ClassGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClassGroup.mk_def", "kind": "theorem", "module": "Mathlib.RingTheory.ClassGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClassGroup.Quot_mk_eq_mk", "kind": "theorem", "module": "Mathlib.RingTheory.ClassGroup", "is_tactic_proof": false, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "ClassGroup.mk_eq_mk", "kind": "theorem", "module": "Mathlib.RingTheory.ClassGroup", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "ClassGroup.mk_eq_mk_of_coe_ideal", "kind": "theorem", "module": "Mathlib.RingTheory.ClassGroup", "is_tactic_proof": true, "tactics": ["rw", "constructor", "rintro", "rw", "exact", "rintro", "have", "simpa", "refine", "rw", "convert"], "tactic_count": 11}
{"name": "ClassGroup.mk_eq_one_of_coe_ideal", "kind": "theorem", "module": "Mathlib.RingTheory.ClassGroup", "is_tactic_proof": true, "tactics": ["rw", "any_goals", "constructor", "rintro", "rw", "rcases", "rw", "exact", "rintro", "exact"], "tactic_count": 10}
{"name": "ClassGroup.induction", "kind": "theorem", "module": "Mathlib.RingTheory.ClassGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClassGroup.equiv", "kind": "definition", "module": "Mathlib.RingTheory.ClassGroup", "is_tactic_proof": false, "tactics": ["haveI", "ext", "simp", "constructor", "rintro", "refine", "simp", "canonicalEquiv_spanSingleton]", "rfl", "rintro", "refine", "simp", "canonicalEquiv_spanSingleton]", "rfl", "simp", "canonicalEquiv_canonicalEquiv,", "exact"], "tactic_count": 17}
{"name": "ClassGroup.equiv_mk", "kind": "theorem", "module": "Mathlib.RingTheory.ClassGroup", "is_tactic_proof": true, "tactics": ["rw", "simp", "congr", "rw", "exact"], "tactic_count": 5}
{"name": "ClassGroup.mk_canonicalEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.ClassGroup", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "FractionalIdeal.mk0", "kind": "definition", "module": "Mathlib.RingTheory.ClassGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.coe_mk0", "kind": "theorem", "module": "Mathlib.RingTheory.ClassGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.canonicalEquiv_mk0", "kind": "theorem", "module": "Mathlib.RingTheory.ClassGroup", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FractionalIdeal.map_canonicalEquiv_mk0", "kind": "theorem", "module": "Mathlib.RingTheory.ClassGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClassGroup.mk0", "kind": "definition", "module": "Mathlib.RingTheory.ClassGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClassGroup.mk_mk0", "kind": "theorem", "module": "Mathlib.RingTheory.ClassGroup", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ClassGroup.equiv_mk0", "kind": "theorem", "module": "Mathlib.RingTheory.ClassGroup", "is_tactic_proof": true, "tactics": ["rw", "congr", "simp"], "tactic_count": 3}
{"name": "ClassGroup.mk0_eq_mk0_iff_exists_fraction_ring", "kind": "theorem", "module": "Mathlib.RingTheory.ClassGroup", "is_tactic_proof": true, "tactics": ["refine", "simp", "constructor", "rintro", "refine", "rintro", "simpa", "rintro", "refine", "simpa"], "tactic_count": 10}
{"name": "ClassGroup.mk0_eq_mk0_iff", "kind": "theorem", "module": "Mathlib.RingTheory.ClassGroup", "is_tactic_proof": true, "tactics": ["refine", "rintro", "obtain", "refine", "rintro", "rw", "exact", "rintro", "have", "refine", "contrapose", "rwa", "exact"], "tactic_count": 13}
{"name": "ClassGroup.integralRep", "kind": "definition", "module": "Mathlib.RingTheory.ClassGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClassGroup.integralRep_mem_nonZeroDivisors", "kind": "theorem", "module": "Mathlib.RingTheory.ClassGroup", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "ClassGroup.mk0_integralRep", "kind": "theorem", "module": "Mathlib.RingTheory.ClassGroup", "is_tactic_proof": true, "tactics": ["rw", "have", "exact", "refine", "apply", "rw", "exact"], "tactic_count": 7}
{"name": "ClassGroup.mk0_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.ClassGroup", "is_tactic_proof": true, "tactics": ["rintro", "refine", "rw"], "tactic_count": 3}
{"name": "ClassGroup.mk_eq_one_iff", "kind": "theorem", "module": "Mathlib.RingTheory.ClassGroup", "is_tactic_proof": true, "tactics": ["rw", "simp", "refine", "intro", "obtain", "have", "apply", "simp", "refine", "intro", "simp"], "tactic_count": 11}
{"name": "ClassGroup.mk0_eq_one_iff", "kind": "theorem", "module": "Mathlib.RingTheory.ClassGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClassGroup.mk0_eq_mk0_inv_iff", "kind": "theorem", "module": "Mathlib.RingTheory.ClassGroup", "is_tactic_proof": true, "tactics": ["rw", "refine", "by_contra", "rw", "exact"], "tactic_count": 5}
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{"name": "CoalgEquiv.invFun_eq_symm", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgEquiv.coe_toEquiv_symm", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgEquiv.toEquiv_symm", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgEquiv.coe_toEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgEquiv.coe_symm_toEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgEquiv.trans", "kind": "definition", "module": "Mathlib.RingTheory.Coalgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgEquiv.trans_toLinearEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgEquiv.trans_toCoalgHom", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgEquiv.coe_toEquiv_trans", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgEquiv.ofCoalgHom", "kind": "definition", "module": "Mathlib.RingTheory.Coalgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgEquiv.coe_ofCoalgHom", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgEquiv.ofCoalgHom_symm", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgEquiv.ofBijective", "kind": "definition", "module": "Mathlib.RingTheory.Coalgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgEquiv.coe_ofBijective", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgEquiv.toCoalgebra", "kind": "definition", "module": "Mathlib.RingTheory.Coalgebra.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isGroupLikeElem_self", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.GroupLike", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsGroupLikeElem.ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.GroupLike", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "IsGroupLikeElem.map", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.GroupLike", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isGroupLikeElem_map_equiv", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.GroupLike", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupLike.instCoeOut", "kind": "instance", "module": "Mathlib.RingTheory.Coalgebra.GroupLike", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupLike.val_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.GroupLike", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "GroupLike.val_inj", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.GroupLike", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupLike.valEquiv", "kind": "definition", "module": "Mathlib.RingTheory.Coalgebra.GroupLike", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "linearIndepOn_isGroupLikeElem", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.GroupLike", "is_tactic_proof": true, "tactics": ["classical", "rw", "rintro", "induction", "empty", "simp", "cons", "ih", "simp", "obtain", "specialize", "rw", "refine", "simp", "rintro", "replace", "simp_rw", "have", "calc", "simp_rw", "simp_rw", "apply", "replace", "by_contra", "have", "rw", "have", "mul_left_injective₀", "obtain", "contradiction", "simp_all"], "tactic_count": 31}
{"name": "linearIndep_groupLikeVal", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.GroupLike", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "term_→ₗc_", "kind": "definition", "module": "Mathlib.RingTheory.Coalgebra.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_RingTheory_Coalgebra_Hom___macroRules_term_→ₗc__1", "kind": "definition", "module": "Mathlib.RingTheory.Coalgebra.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "term_→ₗc[_]_", "kind": "definition", "module": "Mathlib.RingTheory.Coalgebra.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_RingTheory_Coalgebra_Hom___macroRules_term_→ₗc[_]__1", "kind": "definition", "module": "Mathlib.RingTheory.Coalgebra.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_RingTheory_Coalgebra_Hom___unexpand_CoalgHom_1", "kind": "definition", "module": "Mathlib.RingTheory.Coalgebra.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgHomClass.toCoalgHom", "kind": "definition", "module": "Mathlib.RingTheory.Coalgebra.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgHomClass.instCoeToCoalgHom", "kind": "instance", "module": "Mathlib.RingTheory.Coalgebra.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgHomClass.counit_comp_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgHomClass.map_comp_comul_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgHom.funLike", "kind": "instance", "module": "Mathlib.RingTheory.Coalgebra.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgHom.coalgHomClass", "kind": "instance", "module": "Mathlib.RingTheory.Coalgebra.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgHom.Simps.apply", "kind": "definition", "module": "Mathlib.RingTheory.Coalgebra.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgHom.coe_coe", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgHom.coe_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgHom.coe_mks", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgHom.coe_linearMap_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgHom.toLinearMap_eq_coe", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgHom.coe_toLinearMap", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgHom.coe_toAddMonoidHom", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgHom.coe_fn_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgHom.coe_fn_inj", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgHom.coe_linearMap_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgHom.coe_addMonoidHom_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgHom.congr_fun", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgHom.congr_arg", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgHom.ext", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgHom.ext_of_ring", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgHom.mk_coe", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgHom.copy", "kind": "definition", "module": "Mathlib.RingTheory.Coalgebra.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgHom.coe_copy", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgHom.copy_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgHom.id", "kind": "definition", "module": "Mathlib.RingTheory.Coalgebra.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgHom.coe_id", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgHom.id_toLinearMap", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgHom.comp", "kind": "definition", "module": "Mathlib.RingTheory.Coalgebra.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgHom.coe_comp", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgHom.comp_toLinearMap", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgHom.comp_id", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgHom.id_comp", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgHom.comp_assoc", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgHom.map_smul_of_tower", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgHom.End", "kind": "instance", "module": "Mathlib.RingTheory.Coalgebra.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgHom.one_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgHom.mul_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Coalgebra.counitCoalgHom", "kind": "definition", "module": "Mathlib.RingTheory.Coalgebra.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Coalgebra.counitCoalgHom_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Coalgebra.counitCoalgHom_toLinearMap", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Coalgebra.subsingleton_to_ring", "kind": "instance", "module": "Mathlib.RingTheory.Coalgebra.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Coalgebra.ext_to_ring", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Coalgebra.Repr.induced", "kind": "definition", "module": "Mathlib.RingTheory.Coalgebra.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidAlgebra.instCoalgebra", "kind": "instance", "module": "Mathlib.RingTheory.Coalgebra.MonoidAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidAlgebra.instIsCocomm", "kind": "instance", "module": "Mathlib.RingTheory.Coalgebra.MonoidAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidAlgebra.counit_single", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.MonoidAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidAlgebra.comul_single", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.MonoidAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LaurentPolynomial.instCoalgebra", "kind": "instance", "module": "Mathlib.RingTheory.Coalgebra.MonoidAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LaurentPolynomial.instIsCocomm", "kind": "instance", "module": "Mathlib.RingTheory.Coalgebra.MonoidAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LaurentPolynomial.comul_C", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.MonoidAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LaurentPolynomial.comul_C_mul_T", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.MonoidAlgebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LaurentPolynomial.comul_C_mul_T_self", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.MonoidAlgebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LaurentPolynomial.counit_C", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.MonoidAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LaurentPolynomial.counit_C_mul_T", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.MonoidAlgebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MulOpposite.instCoalgebraStruct", "kind": "instance", "module": "Mathlib.RingTheory.Coalgebra.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.comul_def", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.counit_def", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instCoalgebra", "kind": "instance", "module": "Mathlib.RingTheory.Coalgebra.MulOpposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.instCoalgebraStruct", "kind": "instance", "module": "Mathlib.RingTheory.Coalgebra.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.comul_def", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.counit_def", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.comul_tmul", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.counit_tmul", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.tacticHopf_tensor_induction_With__", "kind": "definition", "module": "Mathlib.RingTheory.Coalgebra.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct._aux_Mathlib_RingTheory_Coalgebra_TensorProduct___macroRules_TensorProduct_tacticHopf_tensor_induction_With___1", "kind": "definition", "module": "Mathlib.RingTheory.Coalgebra.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Coalgebra.TensorProduct.0.TensorProduct.coassoc", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.instCoalgebra", "kind": "instance", "module": "Mathlib.RingTheory.Coalgebra.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.instIsCocomm", "kind": "instance", "module": "Mathlib.RingTheory.Coalgebra.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Coalgebra.TensorProduct.map", "kind": "definition", "module": "Mathlib.RingTheory.Coalgebra.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Coalgebra.TensorProduct.map_tmul", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Coalgebra.TensorProduct.map_toLinearMap", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Coalgebra.TensorProduct.assoc", "kind": "definition", "module": "Mathlib.RingTheory.Coalgebra.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Coalgebra.TensorProduct.assoc_tmul", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Coalgebra.TensorProduct.assoc_symm_tmul", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Coalgebra.TensorProduct.assoc_toLinearEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Coalgebra.TensorProduct.lid", "kind": "definition", "module": "Mathlib.RingTheory.Coalgebra.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Coalgebra.TensorProduct.lid_toLinearEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Coalgebra.TensorProduct.lid_tmul", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Coalgebra.TensorProduct.lid_symm_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Coalgebra.TensorProduct.rid", "kind": "definition", "module": "Mathlib.RingTheory.Coalgebra.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Coalgebra.TensorProduct.rid_toLinearEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Coalgebra.TensorProduct.rid_tmul", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Coalgebra.TensorProduct.rid_symm_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Coalgebra.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgHom.lTensor", "kind": "abbrev", "module": "Mathlib.RingTheory.Coalgebra.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CoalgHom.rTensor", "kind": "abbrev", "module": "Mathlib.RingTheory.Coalgebra.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.leftMulMatrix_complex", "kind": "theorem", "module": "Mathlib.RingTheory.Complex", "is_tactic_proof": true, "tactics": ["ext", "rw", "fin_cases", "simp", "fin_cases", "simp", "fin_cases"], "tactic_count": 7}
{"name": "Algebra.trace_complex_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Complex", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Algebra.norm_complex_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Complex", "is_tactic_proof": false, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Algebra.norm_complex_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Conductor.0.term_<_>", "kind": "definition", "module": "Mathlib.RingTheory.Conductor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Conductor.0._aux_Mathlib_RingTheory_Conductor___macroRules__private_Mathlib_RingTheory_Conductor_0_term_<_>_1", "kind": "definition", "module": "Mathlib.RingTheory.Conductor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Conductor.0._aux_Mathlib_RingTheory_Conductor___unexpand_Algebra_adjoin_1", "kind": "definition", "module": "Mathlib.RingTheory.Conductor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "conductor", "kind": "definition", "module": "Mathlib.RingTheory.Conductor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "conductor_eq_of_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Conductor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "conductor_subset_adjoin", "kind": "theorem", "module": "Mathlib.RingTheory.Conductor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_conductor_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Conductor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "conductor_eq_top_of_adjoin_eq_top", "kind": "theorem", "module": "Mathlib.RingTheory.Conductor", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "conductor_eq_top_of_powerBasis", "kind": "theorem", "module": "Mathlib.RingTheory.Conductor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "adjoin_eq_top_of_conductor_eq_top", "kind": "theorem", "module": "Mathlib.RingTheory.Conductor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "conductor_eq_top_iff_adjoin_eq_top", "kind": "theorem", "module": "Mathlib.RingTheory.Conductor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_coeSubmodule_conductor", "kind": "theorem", "module": "Mathlib.RingTheory.Conductor", "is_tactic_proof": true, "tactics": ["cases", "rw", "trans", "simp", "constructor", "rintro", "exact", "intro", "obtain", "rw", "subst", "simp", "exact", "rw"], "tactic_count": 14}
{"name": "prod_mem_ideal_map_of_mem_conductor", "kind": "theorem", "module": "Mathlib.RingTheory.Conductor", "is_tactic_proof": true, "tactics": ["rw", "obtain", "rw", "rw", "have", "intro", "rw", "refine", "rw", "exact", "refine", "rw", "apply", "simp", "rfl", "refine", "rintro", "rw", "exact", "exact", "intro", "exact"], "tactic_count": 22}
{"name": "comap_map_eq_map_adjoin_of_coprime_conductor", "kind": "theorem", "module": "Mathlib.RingTheory.Conductor", "is_tactic_proof": true, "tactics": ["apply", "intro", "obtain", "obtain", "have", "simp", "suffices", "rw", "obtain", "use", "refine", "rfl⟩", "rw", "exact", "refine", "obtain", "have", "apply", "simp", "rw", "rwa", "rw", "apply"], "tactic_count": 23}
{"name": "quotAdjoinEquivQuotMap", "kind": "definition", "module": "Mathlib.RingTheory.Conductor", "is_tactic_proof": false, "tactics": ["let", "have", "rw", "exact", "refine", "refine", "rwa", "comap_map_eq_map_adjoin_of_coprime_conductor", "refine", "obtain", "have", "suffices", "rw", "replace", "rw", "exact", "hx", "rw", "obtain", "use", "simp", "rfl", "exact"], "tactic_count": 23}
{"name": "quotAdjoinEquivQuotMap_apply_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Conductor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.instSMulQuotient", "kind": "instance", "module": "Mathlib.RingTheory.Congruence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.coe_smul", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.instSMulCommClassQuotient", "kind": "instance", "module": "Mathlib.RingTheory.Congruence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.instIsScalarTowerQuotient", "kind": "instance", "module": "Mathlib.RingTheory.Congruence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.instIsCentralScalarQuotient", "kind": "instance", "module": "Mathlib.RingTheory.Congruence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.isScalarTower_right", "kind": "instance", "module": "Mathlib.RingTheory.Congruence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.smulCommClass", "kind": "instance", "module": "Mathlib.RingTheory.Congruence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.smulCommClass'", "kind": "instance", "module": "Mathlib.RingTheory.Congruence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.instDistribMulActionQuotientOfIsScalarTower", "kind": "instance", "module": "Mathlib.RingTheory.Congruence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.instMulSemiringActionQuotientOfIsScalarTower", "kind": "instance", "module": "Mathlib.RingTheory.Congruence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.instLE", "kind": "instance", "module": "Mathlib.RingTheory.Congruence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.le_def", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.comap_mono", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.instInfSet", "kind": "instance", "module": "Mathlib.RingTheory.Congruence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.sInf_toSetoid", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.coe_sInf", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "RingCon.coe_iInf", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RingCon.instPartialOrder", "kind": "instance", "module": "Mathlib.RingTheory.Congruence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.instCompleteLattice", "kind": "instance", "module": "Mathlib.RingTheory.Congruence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.coe_top", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.coe_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.toCon_top", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.toCon_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.toCon_eq_top", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RingCon.toCon_eq_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RingCon.subsingleton_quotient", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RingCon.nontrivial_quotient", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RingCon.coe_inf", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.inf_iff_and", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.instNontrivial", "kind": "instance", "module": "Mathlib.RingTheory.Congruence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.instSubsingleton", "kind": "instance", "module": "Mathlib.RingTheory.Congruence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.nontrivial_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Basic", "is_tactic_proof": true, "tactics": ["cases", "on_goal", "all_goals"], "tactic_count": 3}
{"name": "RingCon.subsingleton_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "RingCon.ringConGen_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.ringConGen_le", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RingCon.ringConGen_mono", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.ringConGen_of_ringCon", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.ringConGen_idem", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.sup_eq_ringConGen", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply", "simp"], "tactic_count": 3}
{"name": "RingCon.sup_def", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RingCon.sSup_eq_ringConGen", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply", "ext", "exact"], "tactic_count": 4}
{"name": "RingCon.sSup_def", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Basic", "is_tactic_proof": true, "tactics": ["rw", "congr", "simp"], "tactic_count": 3}
{"name": "RingCon.gi", "kind": "definition", "module": "Mathlib.RingTheory.Congruence.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.listSum", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.multisetSum", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.finsetSum", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingConGen.Rel", "kind": "inductive", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ringConGen", "kind": "definition", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.toCon_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.toCon_inj", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.instFunLikeForallProp", "kind": "instance", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.coe_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.rel_eq_coe", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.toCon_coe_eq_coe", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.refl", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.symm", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.trans", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.add", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.mul", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.sub", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.neg", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.nsmul", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.zsmul", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.instInhabited", "kind": "instance", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.rel_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.ext'", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.ext", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.ext''", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.coe_inj", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RingCon.comap", "kind": "definition", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.comap_rel", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.Quotient", "kind": "definition", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.toQuotient", "kind": "definition", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.instCoeTCQuotient", "kind": "instance", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.instDecidableEqQuotientOfDecidableCoeForallProp", "kind": "instance", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.quot_mk_eq_coe", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.eq", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.instAddQuotient", "kind": "instance", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.coe_add", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.instMulQuotient", "kind": "instance", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.coe_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.instZeroQuotient", "kind": "instance", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.coe_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.instOneQuotient", "kind": "instance", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.coe_one", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.instNegQuotient", "kind": "instance", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.coe_neg", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.instSubQuotient", "kind": "instance", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.coe_sub", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.hasZSMul", "kind": "instance", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.coe_zsmul", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.hasNSMul", "kind": "instance", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.coe_nsmul", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.instPowQuotientNat", "kind": "instance", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.coe_pow", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.instNatCastQuotient", "kind": "instance", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.coe_natCast", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.instIntCastQuotient", "kind": "instance", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.coe_intCast", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.instInhabitedQuotient", "kind": "instance", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.instNonUnitalNonAssocSemiringQuotient", "kind": "instance", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.instNonAssocSemiringQuotient", "kind": "instance", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.instNonUnitalSemiringQuotient", "kind": "instance", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.instSemiringQuotient", "kind": "instance", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.instCommSemiringQuotient", "kind": "instance", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.instNonUnitalNonAssocRingQuotient", "kind": "instance", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.instNonAssocRingQuotient", "kind": "instance", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.instNonUnitalRingQuotient", "kind": "instance", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.instRingQuotient", "kind": "instance", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.instCommRingQuotient", "kind": "instance", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.mk'", "kind": "definition", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.mk'_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.coe_mk'", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.ker", "kind": "definition", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.comap_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.ker_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.ker_mk'_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.ker_comp", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.comap_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RingCon.congr", "kind": "definition", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.congr_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.mapGen", "kind": "definition", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.mapGen_eq_map_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": true, "tactics": ["refine", "have", "intro", "induction", "of", "refl", "symm", "trans", "add", "rcases", "rcases", "exact", "mul", "rcases", "rcases", "exact"], "tactic_count": 16}
{"name": "RingCon.mapGen_apply_apply_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": true, "tactics": ["rw", "refine", "exact"], "tactic_count": 3}
{"name": "RingCon.correspondence", "kind": "definition", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.lift", "kind": "definition", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.lift_mk'", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.lift_coe", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.lift_comp_mk'", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.lift_apply_mk'", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "RingCon.Quotient.hom_ext", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.lift_unique", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.lift_surjective_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": true, "tactics": ["refine"], "tactic_count": 1}
{"name": "RingCon.lift_surjective_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.lift_injective_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": true, "tactics": ["refine", "rintro", "simp"], "tactic_count": 3}
{"name": "RingCon.lift_bijective_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": true, "tactics": ["unfold", "simp"], "tactic_count": 2}
{"name": "RingCon.ker_eq_lift_of_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.kerLift", "kind": "definition", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.kerLift_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.kerLift_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.map", "kind": "definition", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.map_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.rangeS_mk'", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.rangeS_lift", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.rangeS_kerLift", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.quotientKerEquivRangeS", "kind": "definition", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.coe_quotientKerEquivRangeS_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.quotientKerEquivOfRightInverse", "kind": "definition", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.quotientKerEquivOfRightInverse_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.quotientKerEquivOfSurjective", "kind": "definition", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.quotientKerEquivOfSurjective_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.comapQuotientEquivOfSurj", "kind": "definition", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.comapQuotientEquivOfSurj_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.comapQuotientEquivOfSurj_symm_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RingCon.comapQuotientEquivOfSurj_symm_mk'", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": true, "tactics": ["convert", "rw", "rfl"], "tactic_count": 3}
{"name": "RingCon.comapQuotientEquivRangeS", "kind": "definition", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.comapQuotientEquivRangeS_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.comapQuotientEquivRangeS_symm_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RingCon.quotientQuotientEquivQuotient", "kind": "definition", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.quotientQuotientEquivQuotient_mk_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.quotientQuotientEquivQuotient_coe_coe", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.quotientQuotientEquivQuotient_symm_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.range_mk'", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.range_lift", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.kerLift_range_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.quotientKerEquivRange", "kind": "definition", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.comapQuotientEquivRange", "kind": "definition", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.comapQuotientEquivRange_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.coe_comapQuotientEquivRange_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.comapQuotientEquivRange_symm_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RingCon.congrₐ", "kind": "definition", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.congrₐ_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.range_mkₐ", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.liftₐ", "kind": "definition", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.liftₐ_coe_toRingHom", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.coe_liftₐ", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.liftₐ_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.liftₐ_range", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.kerLiftₐ", "kind": "definition", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.kerLiftₐ_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "RingCon.kerLiftₐ_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.factorₐ", "kind": "definition", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.factorₐ_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.factorₐ_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.mkₐ_comp_factorₐ_comp_mkₐ", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.kerLiftₐ_range_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.quotientKerEquivRangeₐ", "kind": "definition", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.quotientKerEquivRangeₐ_mkₐ", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.coe_quotientKerEquivRangeₐ_mkₐ", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "RingCon.quotientKerEquivRangeₐ_comp_mkₐ", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.comapQuotientEquivRangeₐ", "kind": "definition", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.comapQuotientEquivRangeₐ_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.coe_comapQuotientEquivRangeₐ_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.coe_comapQuotientEquivRangeₐ_symm_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RingCon.quotientQuotientEquivQuotientₐ", "kind": "definition", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.quotientQuotientEquivQuotientₐ_mk_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.quotientQuotientEquivQuotientₐ_coe_coe", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.quotientQuotientEquivQuotientₐ_symm_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.op", "kind": "definition", "module": "Mathlib.RingTheory.Congruence.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.op_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.unop", "kind": "definition", "module": "Mathlib.RingTheory.Congruence.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.unop_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Congruence.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingCon.opOrderIso", "kind": "definition", "module": "Mathlib.RingTheory.Congruence.Opposite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCoprime", "kind": "definition", "module": "Mathlib.RingTheory.Coprime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCoprime.symm", "kind": "theorem", "module": "Mathlib.RingTheory.Coprime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCoprime_comm", "kind": "theorem", "module": "Mathlib.RingTheory.Coprime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCoprime_self", "kind": "theorem", "module": "Mathlib.RingTheory.Coprime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCoprime_zero_left", "kind": "theorem", "module": "Mathlib.RingTheory.Coprime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCoprime_zero_right", "kind": "theorem", "module": "Mathlib.RingTheory.Coprime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_isCoprime_zero_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Coprime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCoprime.intCast", "kind": "theorem", "module": "Mathlib.RingTheory.Coprime.Basic", "is_tactic_proof": true, "tactics": ["rcases", "use", "rw_mod_cast", "exact"], "tactic_count": 4}
{"name": "IsCoprime.ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Coprime.Basic", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "IsCoprime.ne_zero_or_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Coprime.Basic", "is_tactic_proof": true, "tactics": ["apply", "rintro", "exact"], "tactic_count": 3}
{"name": "isCoprime_one_left", "kind": "theorem", "module": "Mathlib.RingTheory.Coprime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCoprime_one_right", "kind": "theorem", "module": "Mathlib.RingTheory.Coprime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCoprime.dvd_of_dvd_mul_right", "kind": "theorem", "module": "Mathlib.RingTheory.Coprime.Basic", "is_tactic_proof": true, "tactics": ["let", "rw", "exact"], "tactic_count": 3}
{"name": "IsCoprime.dvd_of_dvd_mul_left", "kind": "theorem", "module": "Mathlib.RingTheory.Coprime.Basic", "is_tactic_proof": true, "tactics": ["let", "rw", "exact"], "tactic_count": 3}
{"name": "IsCoprime.mul_left", "kind": "theorem", "module": "Mathlib.RingTheory.Coprime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCoprime.mul_right", "kind": "theorem", "module": "Mathlib.RingTheory.Coprime.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsCoprime.mul_dvd", "kind": "theorem", "module": "Mathlib.RingTheory.Coprime.Basic", "is_tactic_proof": true, "tactics": ["obtain", "rw", "apply", "rw", "exact", "rw", "exact"], "tactic_count": 7}
{"name": "IsCoprime.of_mul_left_left", "kind": "theorem", "module": "Mathlib.RingTheory.Coprime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCoprime.of_mul_left_right", "kind": "theorem", "module": "Mathlib.RingTheory.Coprime.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsCoprime.of_mul_right_left", "kind": "theorem", "module": "Mathlib.RingTheory.Coprime.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsCoprime.of_mul_right_right", "kind": "theorem", "module": "Mathlib.RingTheory.Coprime.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsCoprime.mul_left_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Coprime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCoprime.mul_right_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Coprime.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsCoprime.of_isCoprime_of_dvd_left", "kind": "theorem", "module": "Mathlib.RingTheory.Coprime.Basic", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "IsCoprime.of_isCoprime_of_dvd_right", "kind": "theorem", "module": "Mathlib.RingTheory.Coprime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCoprime.mono", "kind": "theorem", "module": "Mathlib.RingTheory.Coprime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "IsCoprime.pow_right_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Coprime.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCoprime.pow_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Coprime.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRelPrime.prod_left", "kind": "theorem", "module": "Mathlib.RingTheory.Coprime.Lemmas", "is_tactic_proof": true, "tactics": ["classical", "refine", "rw", "rw", "exact"], "tactic_count": 5}
{"name": "IsRelPrime.prod_right", "kind": "theorem", "module": "Mathlib.RingTheory.Coprime.Lemmas", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsRelPrime.prod_left_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Coprime.Lemmas", "is_tactic_proof": true, "tactics": ["classical", "refine", "rw"], "tactic_count": 3}
{"name": "IsRelPrime.prod_right_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Coprime.Lemmas", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsRelPrime.of_prod_left", "kind": "theorem", "module": "Mathlib.RingTheory.Coprime.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRelPrime.of_prod_right", "kind": "theorem", "module": "Mathlib.RingTheory.Coprime.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.prod_dvd_of_isRelPrime", "kind": "theorem", "module": "Mathlib.RingTheory.Coprime.Lemmas", "is_tactic_proof": true, "tactics": ["classical", "exact", "intro", "rw", "have", "refine", "rintro", "exact", "simp"], "tactic_count": 9}
{"name": "Fintype.prod_dvd_of_isRelPrime", "kind": "theorem", "module": "Mathlib.RingTheory.Coprime.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pairwise_isRelPrime_iff_isRelPrime_prod", "kind": "theorem", "module": "Mathlib.RingTheory.Coprime.Lemmas", "is_tactic_proof": true, "tactics": ["refine", "rw", "obtain", "exact", "rintro", "apply", "grind"], "tactic_count": 7}
{"name": "IsRelPrime.pow_left", "kind": "theorem", "module": "Mathlib.RingTheory.Coprime.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsRelPrime.pow_right", "kind": "theorem", "module": "Mathlib.RingTheory.Coprime.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsRelPrime.pow", "kind": "theorem", "module": "Mathlib.RingTheory.Coprime.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRelPrime.pow_left_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Coprime.Lemmas", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "IsRelPrime.pow_right_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Coprime.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRelPrime.pow_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Coprime.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.HeightOneSpectrum.intValuationDef", "kind": "definition", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.HeightOneSpectrum.intValuationDef_if_pos", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.HeightOneSpectrum.intValuationDef_zero", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.HeightOneSpectrum.intValuationDef_if_neg", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.HeightOneSpectrum.intValuation.map_zero'", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.HeightOneSpectrum.intValuation.map_one'", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": true, "tactics": ["classical", "rw"], "tactic_count": 2}
{"name": "IsDedekindDomain.HeightOneSpectrum.intValuation.map_mul'", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": true, "tactics": ["classical", "simp", "by_cases", "rw", "by_cases", "rw", "rw"], "tactic_count": 7}
{"name": "IsDedekindDomain.HeightOneSpectrum.intValuation.le_max_iff_min_le", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsDedekindDomain.HeightOneSpectrum.intValuation.map_add_le_max'", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": true, "tactics": ["classical", "by_cases", "rw", "order", "by_cases", "rw", "order", "by_cases", "rw", "rw", "simp", "set", "min", "have", "rw", "exact", "exact", "have", "rw", "exact", "exact", "have", "rw", "exact", "rw", "exact", "exact"], "tactic_count": 27}
{"name": "IsDedekindDomain.HeightOneSpectrum.intValuation", "kind": "definition", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.HeightOneSpectrum.intValuation_apply", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.HeightOneSpectrum.intValuation_def", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.HeightOneSpectrum.intValuation_if_neg", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.HeightOneSpectrum.intValuation_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsDedekindDomain.HeightOneSpectrum.intValuation_ne_zero'", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.HeightOneSpectrum.intValuation_zero_lt", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsDedekindDomain.HeightOneSpectrum.intValuation_le_one", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "rw", "exact"], "tactic_count": 4}
{"name": "IsDedekindDomain.HeightOneSpectrum.intValuation_lt_one_iff_dvd", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": true, "tactics": ["classical", "by_cases", "simp", "rw", "have", "rw", "exact", "exact"], "tactic_count": 8}
{"name": "IsDedekindDomain.HeightOneSpectrum.intValuation_lt_one_iff_mem", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsDedekindDomain.HeightOneSpectrum.intValuation_le_pow_iff_dvd", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": true, "tactics": ["classical", "by_cases", "simp_rw", "rw"], "tactic_count": 4}
{"name": "IsDedekindDomain.HeightOneSpectrum.intValuation_le_pow_iff_mem", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsDedekindDomain.HeightOneSpectrum.intValuation_exists_uniformizer", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": true, "tactics": ["classical", "have", "have", "rw", "exact", "obtain", "have", "rw", "intro", "rw", "exact", "use", "rw", "apply", "rw", "rw", "rw", "rw", "exact"], "tactic_count": 19}
{"name": "IsDedekindDomain.HeightOneSpectrum.intValuation_singleton", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": true, "tactics": ["classical", "rw", "exact"], "tactic_count": 3}
{"name": "IsDedekindDomain.HeightOneSpectrum.intValuation_eq_one_iff", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "IsDedekindDomain.HeightOneSpectrum.valuation", "kind": "definition", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.HeightOneSpectrum.valuation_def", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.HeightOneSpectrum.valuation_of_mk'", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsDedekindDomain.HeightOneSpectrum.valuation_of_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsDedekindDomain.HeightOneSpectrum.valuation_le_one", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsDedekindDomain.HeightOneSpectrum.valuation_lt_one_iff_dvd", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsDedekindDomain.HeightOneSpectrum.valuation_lt_one_iff_mem", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsDedekindDomain.HeightOneSpectrum.valuation_div_le_one_iff", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": false, "tactics": ["refine", "contrapose", "have", "have", "have", "rw", "simpa"], "tactic_count": 7}
{"name": "IsDedekindDomain.HeightOneSpectrum.valuation_exists_uniformizer", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": true, "tactics": ["obtain", "use", "rw", "exact"], "tactic_count": 4}
{"name": "IsDedekindDomain.HeightOneSpectrum.instIsNontrivialWithZeroMultiplicativeIntValuation", "kind": "instance", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.HeightOneSpectrum.valuation_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": true, "tactics": ["intro", "rcases", "simp", "obtain", "refine", "simp"], "tactic_count": 6}
{"name": "IsDedekindDomain.HeightOneSpectrum.valuation_uniformizer_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.HeightOneSpectrum.mem_integers_of_valuation_le_one", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "obtain", "simp", "have", "suffices", "obtain", "use", "rw", "exact", "classical", "have", "rw", "rintro", "obtain", "have", "rw", "specialize", "simp_rw", "simpa"], "tactic_count": 20}
{"name": "IsDedekindDomain.HeightOneSpectrum.eq_of_valuation_isEquiv_valuation", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": true, "tactics": ["simp_all"], "tactic_count": 1}
{"name": "IsDedekindDomain.HeightOneSpectrum.adicValued", "kind": "definition", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.HeightOneSpectrum.adicValued_apply", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.HeightOneSpectrum.adicValued_apply'", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.HeightOneSpectrum.adicCompletion", "kind": "abbrev", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.HeightOneSpectrum.valuedAdicCompletion_def", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.HeightOneSpectrum.valuedAdicCompletion_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.HeightOneSpectrum.adicCompletionIntegers", "kind": "definition", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.HeightOneSpectrum.instInhabitedSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegers", "kind": "instance", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.HeightOneSpectrum.mem_adicCompletionIntegers", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.HeightOneSpectrum.notMem_adicCompletionIntegers", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsDedekindDomain.HeightOneSpectrum.adicValued.has_uniform_continuous_const_smul'", "kind": "instance", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.HeightOneSpectrum.adicValued.uniformContinuousConstSMul", "kind": "instance", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": true, "tactics": ["refine", "simp_rw", "exact"], "tactic_count": 3}
{"name": "IsDedekindDomain.HeightOneSpectrum.instAlgebraAdicCompletion", "kind": "instance", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.HeightOneSpectrum.coe_smul_adicCompletion", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.HeightOneSpectrum.algebraMap_adicCompletion", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.HeightOneSpectrum.coe_algebraMap_mem", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsDedekindDomain.HeightOneSpectrum.instAlgebraSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegers", "kind": "instance", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.HeightOneSpectrum.algebraMap_adicCompletionIntegers_apply", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.HeightOneSpectrum.instFaithfulSMulSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegers", "kind": "instance", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": true, "tactics": ["rw", "intro", "simp"], "tactic_count": 3}
{"name": "IsDedekindDomain.HeightOneSpectrum.valuedAdicCompletion_eq_valuation", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "IsDedekindDomain.HeightOneSpectrum.valuedAdicCompletion_eq_valuation'", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "IsDedekindDomain.HeightOneSpectrum.coe_mem_adicCompletionIntegers", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsDedekindDomain.HeightOneSpectrum.coe_smul_adicCompletionIntegers", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.HeightOneSpectrum.instIsTorsionFreeSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegers", "kind": "instance", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.HeightOneSpectrum.adicCompletion.instIsScalarTower'", "kind": "instance", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.HeightOneSpectrum.adicCompletion.mul_nonZeroDivisor_mem_adicCompletionIntegers", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": true, "tactics": ["by_cases", "use", "simp", "rw", "obtain", "have", "simp", "have", "refine", "simp", "exact"], "tactic_count": 11}
{"name": "IsDedekindDomain.HeightOneSpectrum.intAdicAbvDef", "kind": "definition", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.HeightOneSpectrum.isNonarchimedean_intAdicAbvDef", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": true, "tactics": ["intro", "simp", "have", "rw", "exact"], "tactic_count": 5}
{"name": "IsDedekindDomain.HeightOneSpectrum.intAdicAbv", "kind": "definition", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.HeightOneSpectrum.isNonarchimedean_intAdicAbv", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.HeightOneSpectrum.intAdicAbv_le_one", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsDedekindDomain.HeightOneSpectrum.intAdicAbv_lt_one_iff", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsDedekindDomain.HeightOneSpectrum.intAdicAbv_eq_one_iff", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": true, "tactics": ["contrapose", "rw", "exact"], "tactic_count": 3}
{"name": "IsDedekindDomain.HeightOneSpectrum.adicAbvDef", "kind": "definition", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.HeightOneSpectrum.isNonarchimedean_adicAbvDef", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": true, "tactics": ["intro", "simp", "have", "rw", "exact"], "tactic_count": 5}
{"name": "IsDedekindDomain.HeightOneSpectrum.adicAbv", "kind": "definition", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.HeightOneSpectrum.isNonarchimedean_adicAbv", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.HeightOneSpectrum.adicAbv_of_mk'", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsDedekindDomain.HeightOneSpectrum.adicAbv_of_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsDedekindDomain.HeightOneSpectrum.adicAbv_coe_le_one", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsDedekindDomain.HeightOneSpectrum.adicAbv_coe_lt_one_iff", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsDedekindDomain.HeightOneSpectrum.adicAbv_coe_eq_one_iff", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.AdicValuation", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
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{"name": "Ring.DimensionLEOne.isIntegralClosure", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ring.DimensionLEOne.integralClosure", "kind": "instance", "module": "Mathlib.RingTheory.DedekindDomain.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ring.DimensionLEOne.not_lt_lt", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ring.DimensionLEOne.eq_bot_of_lt", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isDedekindRing_iff", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsDedekindDomainOfIsDomainOfIsDedekindRing", "kind": "instance", "module": "Mathlib.RingTheory.DedekindDomain.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isDedekindDomain_iff", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrincipalIdealRing.isDedekindDomain", "kind": "instance", "module": "Mathlib.RingTheory.DedekindDomain.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.primesOver_eq", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Basic", "is_tactic_proof": true, "tactics": ["have", "refine", "obtain", "exact", "exact"], "tactic_count": 5}
{"name": "Submodule.traceDual", "kind": "definition", "module": "Mathlib.RingTheory.DedekindDomain.Different", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.DedekindDomain.Different.0.term_ᵛ", "kind": "definition", "module": "Mathlib.RingTheory.DedekindDomain.Different", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.DedekindDomain.Different.0._aux_Mathlib_RingTheory_DedekindDomain_Different___macroRules__private_Mathlib_RingTheory_DedekindDomain_Different_0_term_ᵛ_1", "kind": "definition", "module": "Mathlib.RingTheory.DedekindDomain.Different", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Submodule.mem_traceDual", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Different", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.le_traceDual_iff_map_le_one", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Different", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Submodule.le_traceDual_mul_iff", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Different", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Submodule.le_traceDual", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Different", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submodule.le_traceDual_comm", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Different", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submodule.le_traceDual_traceDual", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Different", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.restrictScalars_traceDual", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Different", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.traceDual_span_of_basis", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Different", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Submodule.traceDual_bot", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Different", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Submodule.traceDual_top'", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Different", "is_tactic_proof": true, "tactics": ["classical", "split_ifs", "rw", "exact", "simp", "forall_apply_eq_imp_iff,", "obtain", "simp_rw", "contrapose", "obtain", "simpa"], "tactic_count": 11}
{"name": "Submodule.traceDual_top", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Different", "is_tactic_proof": true, "tactics": ["convert", "rw", "simp"], "tactic_count": 3}
{"name": "map_equiv_traceDual", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Different", "is_tactic_proof": false, "tactics": ["change", "traceDual", "rw", "ext", "simp", "apply", "simp", "refine", "rw", "swap", "ext", "exact", "simp"], "tactic_count": 13}
{"name": "Submodule.mem_traceDual_iff_isIntegral", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Different", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.one_le_traceDual_one", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Different", "is_tactic_proof": true, "tactics": ["rw", "rintro", "rw", "apply", "apply", "rw", "exact"], "tactic_count": 7}
{"name": "isIntegral_discr_mul_of_mem_traceDual", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Different", "is_tactic_proof": true, "tactics": ["have", "have", "have", "rw", "rw", "apply", "intro", "rw", "refine", "apply", "rw", "apply", "intro", "rw", "split", "rw", "rw", "apply", "have", "rw", "exact", "exact"], "tactic_count": 22}
{"name": "FractionalIdeal.dual", "kind": "definition", "module": "Mathlib.RingTheory.DedekindDomain.Different", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.DedekindDomain.Different.0.FractionalIdeal.term_ᵛ", "kind": "definition", "module": "Mathlib.RingTheory.DedekindDomain.Different", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "FractionalIdeal.coe_dual", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Different", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "FractionalIdeal.coe_dual_one", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Different", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "FractionalIdeal.dual_zero", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Different", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "FractionalIdeal.mem_dual", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Different", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "FractionalIdeal.dual_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Different", "is_tactic_proof": true, "tactics": ["obtain", "suffices", "intro", "rw", "exact", "rw", "intro", "apply", "apply", "dsimp", "convert", "ext", "exact", "exact"], "tactic_count": 14}
{"name": "FractionalIdeal.dual_eq_zero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Different", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.dual_ne_zero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Different", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.le_dual_inv_aux", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Different", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "apply", "apply", "rw", "have", "rw", "exact"], "tactic_count": 9}
{"name": "FractionalIdeal.one_le_dual_one", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Different", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.le_dual_iff", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Different", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "rw"], "tactic_count": 3}
{"name": "FractionalIdeal.inv_le_dual", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Different", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "FractionalIdeal.dual_inv_le", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Different", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "exact"], "tactic_count": 3}
{"name": "FractionalIdeal.dual_eq_mul_inv", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Different", "is_tactic_proof": true, "tactics": ["by_cases", "apply", "rw", "rw"], "tactic_count": 4}
{"name": "FractionalIdeal.dual_div_dual", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Different", "is_tactic_proof": true, "tactics": ["rw", "exact", "simp"], "tactic_count": 3}
{"name": "FractionalIdeal.dual_mul_self", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Different", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "FractionalIdeal.self_mul_dual", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Different", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "FractionalIdeal.dual_inv", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Different", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "FractionalIdeal.dual_dual", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Different", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "FractionalIdeal.dual_le_dual", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Different", "is_tactic_proof": true, "tactics": ["nth_rewrite", "rw"], "tactic_count": 2}
{"name": "FractionalIdeal.dual_involutive", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Different", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.dual_injective", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Different", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.trace_mem_dual_one", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Different", "is_tactic_proof": false, "tactics": ["simp", "forall_exists_index,", "simpa"], "tactic_count": 3}
{"name": "FractionalIdeal.smul_mem_dual_one", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Different", "is_tactic_proof": false, "tactics": ["simp", "forall_exists_index,", "intro", "obtain", "obtain", "use", "simpa", "smul_comm"], "tactic_count": 8}
{"name": "FractionalIdeal.dual_eq_dual_mul_dual", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Different", "is_tactic_proof": true, "tactics": ["have", "have", "nonZeroDivisors_le_comap_nonZeroDivisors_of_injective", "have", "refine", "intro", "rw", "map_inv₀,", "coe_dual_one,", "rintro", "simp", "rw", "refine", "exact", "rw", "span_mul_span,", "rintro", "simp", "exact"], "tactic_count": 19}
{"name": "differentIdeal", "kind": "definition", "module": "Mathlib.RingTheory.DedekindDomain.Different", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "coeSubmodule_differentIdeal_fractionRing", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Different", "is_tactic_proof": true, "tactics": ["rw", "have", "have", "simp", "rw", "simpa", "exact", "exact"], "tactic_count": 8}
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{"name": "coeIdeal_differentIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Different", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "differentIdeal_ne_bot", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Different", "is_tactic_proof": true, "tactics": ["let", "let", "rw", "simp"], "tactic_count": 4}
{"name": "differentialIdeal_le_fractionalIdeal_iff", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Different", "is_tactic_proof": false, "tactics": ["rw", "refine", "simp"], "tactic_count": 3}
{"name": "differentialIdeal_le_iff", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Different", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "differentIdeal_eq_differentIdeal_mul_differentIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Different", "is_tactic_proof": false, "tactics": ["have", "isSeparable_tower_top_of_isSeparable", "have", "isSeparable_tower_bot_of_isSeparable", "haveI", "haveI", "haveI", "rw", "coeIdeal_differentIdeal", "rw", "mul_inv,", "exact"], "tactic_count": 12}
{"name": "traceForm_dualSubmodule_adjoin", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Different", "is_tactic_proof": true, "tactics": ["classical", "have", "let", "have", "have", "have", "have", "rw", "congr", "have", "rw", "simp", "simp", "exact", "clear_value", "conv_lhs", "rw", "change", "simp", "apply", "rintro", "rintro", "by_cases", "exact", "rw", "exact", "rw", "exact"], "tactic_count": 28}
{"name": "conductor_mul_differentIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Different", "is_tactic_proof": true, "tactics": ["classical", "have", "haveI", "apply", "simp", "rw", "swap", "exact", "apply", "simp", "ext", "have", "have", "rwa", "aeval_algebraMap_apply]", "rw", "mem_coeSubmodule_conductor]", "swap", "exact", "have", "rwa", "have", "simp_rw", "rw", "simp", "minpoly.isIntegrallyClosed_eq_field_fractions", "mul_assoc,", "simp_rw", "simp", "forall_apply_eq_imp_iff₂,", "exact"], "tactic_count": 31}
{"name": "aeval_derivative_mem_differentIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Different", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "pow_sub_one_dvd_differentIdeal_aux", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Different", "is_tactic_proof": true, "tactics": ["obtain", "have", "have", "have", "rintro", "rwa", "have", "obtain", "apply_fun", "apply_fun", "simp", "conv_lhs", "rw", "exact", "suffices", "have", "apply", "simp", "rw", "rw", "intro", "rw", "rw", "div_self", "simp", "intro", "obtain", "obtain", "have", "rw", "exact", "rwa", "intro", "rw", "refine", "rw", "exact"], "tactic_count": 37}
{"name": "pow_sub_one_dvd_differentIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Different", "is_tactic_proof": false, "tactics": ["have", "have", "by_cases", "rw", "exact"], "tactic_count": 5}
{"name": "not_dvd_differentIdeal_of_intTrace_not_mem", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Different", "is_tactic_proof": true, "tactics": ["by_cases", "subst", "simp", "obtain", "rw", "exact", "obtain", "simp", "letI", "rw", "exact", "let", "let", "have", "have", "rw", "intro", "replace", "replace", "rw", "replace", "simp", "apply", "suffices", "obtain", "rw", "exact", "refine", "rintro", "induction", "mem", "obtain", "obtain", "simp", "refine", "rw", "zero", "add", "simp", "exact", "smul", "simpa", "simp", "exact"], "tactic_count": 44}
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{"name": "Ring.DimensionLEOne.localization", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Dvr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.isDedekindDomain", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Dvr", "is_tactic_proof": false, "tactics": ["have", "rintro", "exact", "letI", "haveI", "haveI", "refine", "infer_instance", "exact", "exact", "intro", "obtain", "obtain", "refine", "rw", "rfl"], "tactic_count": 16}
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{"name": "Localization.AtPrime.isDedekindDomain", "kind": "instance", "module": "Mathlib.RingTheory.DedekindDomain.Dvr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.AtPrime.not_isField", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Dvr", "is_tactic_proof": true, "tactics": ["intro", "letI", "obtain", "exact"], "tactic_count": 4}
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{"name": "IsDedekindDomain.isDedekindDomainDvr", "kind": "instance", "module": "Mathlib.RingTheory.DedekindDomain.Dvr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomainDvr.ring_dimensionLEOne", "kind": "instance", "module": "Mathlib.RingTheory.DedekindDomain.Dvr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomainDvr.isIntegrallyClosed", "kind": "instance", "module": "Mathlib.RingTheory.DedekindDomain.Dvr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomainDvr.isDedekindDomain", "kind": "instance", "module": "Mathlib.RingTheory.DedekindDomain.Dvr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.HeightOneSpectrum.maxPowDividing", "kind": "definition", "module": "Mathlib.RingTheory.DedekindDomain.Factorization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.HeightOneSpectrum.maxPowDividing_eq_pow_multiset_count", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Factorization", "is_tactic_proof": true, "tactics": ["classical", "rw"], "tactic_count": 2}
{"name": "Ideal.finite_factors", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Factorization", "is_tactic_proof": true, "tactics": ["rw", "haveI", "refine", "intro", "exact"], "tactic_count": 5}
{"name": "Associates.finite_factors", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Factorization", "is_tactic_proof": false, "tactics": ["have", "ext", "simp_rw", "exact", "rw", "exact"], "tactic_count": 6}
{"name": "Ideal.finite_mulSupport", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Factorization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.finite_mulSupport_coe", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Factorization", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "exact"], "tactic_count": 3}
{"name": "Ideal.finite_mulSupport_inv", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Factorization", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "exact"], "tactic_count": 3}
{"name": "Ideal.finprod_not_dvd", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Factorization", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "intro", "have", "obtain", "have", "have", "rw", "exact"], "tactic_count": 10}
{"name": "Associates.finprod_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Factorization", "is_tactic_proof": true, "tactics": ["classical", "rw", "split_ifs", "rw", "intro", "apply", "exact"], "tactic_count": 7}
{"name": "Ideal.finprod_count", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Factorization", "is_tactic_proof": true, "tactics": ["have", "have", "have", "have", "simp", "rw", "simp", "rw", "rw", "apply"], "tactic_count": 10}
{"name": "Ideal.finprod_heightOneSpectrum_factorization", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Factorization", "is_tactic_proof": true, "tactics": ["rw", "classical", "apply", "apply", "apply", "intro", "obtain", "rw", "rw", "apply"], "tactic_count": 10}
{"name": "Ideal.finprod_heightOneSpectrum_factorization_coe", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Factorization", "is_tactic_proof": true, "tactics": ["conv_rhs", "rw", "simp_rw"], "tactic_count": 3}
{"name": "FractionalIdeal.finprod_heightOneSpectrum_factorization", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Factorization", "is_tactic_proof": true, "tactics": ["have", "have", "have", "have", "rw", "simp_rw", "rw", "apply", "intro", "rw"], "tactic_count": 10}
{"name": "FractionalIdeal.finprod_heightOneSpectrum_factorization_principal_fraction", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Factorization", "is_tactic_proof": false, "tactics": ["have", "map_ne_zero_of_mem_nonZeroDivisors", "have", "rw", "exact", "have", "rw", "apply", "rw", "exact"], "tactic_count": 10}
{"name": "FractionalIdeal.finprod_heightOneSpectrum_factorization_principal", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Factorization", "is_tactic_proof": true, "tactics": ["set", "set", "have", "have", "by_contra", "rw", "exact", "rw"], "tactic_count": 8}
{"name": "FractionalIdeal.count", "kind": "definition", "module": "Mathlib.RingTheory.DedekindDomain.Factorization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.count_zero", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Factorization", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FractionalIdeal.count_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Factorization", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FractionalIdeal.count_well_defined", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Factorization", "is_tactic_proof": true, "tactics": ["set", "set", "have", "have", "have", "have", "have", "have", "rw", "exact", "have", "rw", "rw", "exact", "have", "rw", "coeIdeal_span_singleton,", "rw", "coeIdeal_injective", "rw", "rw", "exact", "rw", "rw"], "tactic_count": 24}
{"name": "FractionalIdeal.count_mul", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Factorization", "is_tactic_proof": true, "tactics": ["classical", "have", "obtain", "have", "rw", "have", "obtain", "have", "rw", "have", "have", "rw", "spanSingleton_mul_spanSingleton,", "rw", "count_well_defined", "push_cast", "ring"], "tactic_count": 17}
{"name": "FractionalIdeal.count_mul'", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Factorization", "is_tactic_proof": true, "tactics": ["split_ifs", "exact", "rw", "rw"], "tactic_count": 4}
{"name": "FractionalIdeal.count_one", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Factorization", "is_tactic_proof": false, "tactics": ["have", "rw", "rw"], "tactic_count": 3}
{"name": "FractionalIdeal.count_prod", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Factorization", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "insert", "hrec", "have", "have", "have", "rw"], "tactic_count": 9}
{"name": "FractionalIdeal.count_pow", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Factorization", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "classical", "by_cases", "have", "rw", "rw", "ring"], "tactic_count": 9}
{"name": "FractionalIdeal.count_self", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Factorization", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "have", "classical", "rw"], "tactic_count": 6}
{"name": "FractionalIdeal.count_pow_self", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Factorization", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "FractionalIdeal.count_neg_zpow", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Factorization", "is_tactic_proof": true, "tactics": ["by_cases", "by_cases", "rw", "rw", "rw", "zpow_zero]", "exact"], "tactic_count": 7}
{"name": "FractionalIdeal.count_inv", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Factorization", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "FractionalIdeal.count_zpow", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Factorization", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact", "rw", "ring"], "tactic_count": 5}
{"name": "FractionalIdeal.count_zpow_self", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Factorization", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "FractionalIdeal.count_maximal_coprime", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Factorization", "is_tactic_proof": false, "tactics": ["have", "rw", "have", "have", "have", "classical", "rw", "pow_one", "simp", "rw", "exact"], "tactic_count": 11}
{"name": "FractionalIdeal.count_maximal", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Factorization", "is_tactic_proof": true, "tactics": ["split_ifs", "rw", "exact"], "tactic_count": 3}
{"name": "FractionalIdeal.count_finprod_coprime", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Factorization", "is_tactic_proof": true, "tactics": ["apply", "exact", "intro", "classical", "by_cases", "rw", "rw", "intro", "rw"], "tactic_count": 9}
{"name": "FractionalIdeal.count_finsuppProd", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Factorization", "is_tactic_proof": true, "tactics": ["rw", "classical", "simp", "ite_not,", "exact"], "tactic_count": 5}
{"name": "FractionalIdeal.count_finprod", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Factorization", "is_tactic_proof": true, "tactics": ["convert", "rw", "rfl", "rw", "intro", "rw", "exact"], "tactic_count": 7}
{"name": "FractionalIdeal.count_coe", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Factorization", "is_tactic_proof": false, "tactics": ["rw", "simpa", "simp"], "tactic_count": 3}
{"name": "FractionalIdeal.count_coe_nonneg", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Factorization", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "classical"], "tactic_count": 3}
{"name": "FractionalIdeal.count_mono", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Factorization", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "have", "rw", "obtain", "rw", "exact", "exact"], "tactic_count": 8}
{"name": "FractionalIdeal.finprod_heightOneSpectrum_factorization'", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Factorization", "is_tactic_proof": true, "tactics": ["have", "conv_rhs", "apply", "intro", "apply", "rw"], "tactic_count": 6}
{"name": "FractionalIdeal.finite_factors'", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Factorization", "is_tactic_proof": true, "tactics": ["have", "have", "have", "intro", "have", "by_contra", "rw", "push_neg", "rw", "rw", "exact", "exact", "h_subset"], "tactic_count": 13}
{"name": "FractionalIdeal.finite_factors", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Factorization", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "convert", "rw"], "tactic_count": 4}
{"name": "IsDedekindDomain.exists_sup_span_eq", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Factorization", "is_tactic_proof": true, "tactics": ["classical", "obtain", "simp", "obtain", "suffices", "obtain", "exact", "let", "have", "intro", "conv_rhs", "rw", "refine", "rw", "exact", "rw", "exact", "choose", "obtain", "rw", "exact", "refine", "by_contra", "obtain", "let", "have", "have", "replace", "have", "refine", "rw", "refine", "exact", "apply", "have", "simp", "have", "rw", "rintro", "by_cases", "subst", "convert", "rw", "refine", "exact"], "tactic_count": 45}
{"name": "IsDedekindDomain.exists_eq_span_pair", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Factorization", "is_tactic_proof": true, "tactics": ["obtain", "simp_rw", "use"], "tactic_count": 3}
{"name": "IsDedekindDomain.exists_add_spanSingleton_mul_eq", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Factorization", "is_tactic_proof": true, "tactics": ["wlog", "obtain", "use", "simpa", "subst", "have", "rw", "simp", "ring_nf", "gcongr", "obtain", "refine", "refine", "simp", "simp", "mul_eq_zero,", "rw", "simp_rw"], "tactic_count": 18}
{"name": "FractionalIdeal.divMod", "kind": "definition", "module": "Mathlib.RingTheory.DedekindDomain.Factorization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.divMod_spec", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Factorization", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "FractionalIdeal.divMod_zero_left", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Factorization", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FractionalIdeal.divMod_zero_right", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Factorization", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FractionalIdeal.zero_divMod", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Factorization", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FractionalIdeal.divMod_zero_of_not_le", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Factorization", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FractionalIdeal.quotientEquiv", "kind": "definition", "module": "Mathlib.RingTheory.DedekindDomain.Factorization", "is_tactic_proof": false, "tactics": ["haveI", "have", "rwa", "rintro", "exact", "refine", "intro", "refine", "exact", "rw", "refine", "intro", "refine", "simp", "exact", "rw", "by_cases", "obtain", "obtain", "exact", "rw", "inv_mul_cancel_left₀", "rw", "refine", "intro", "rw", "convert", "simp", "have", "ext", "simp", "rw", "inf_eq_right.mpr]", "exact", "exact", "exact"], "tactic_count": 36}
{"name": "Ideal.map_algebraMap_eq_finset_prod_pow", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Factorization", "is_tactic_proof": true, "tactics": ["classical", "have", "rw", "let", "rw", "let", "refine", "simp", "intro", "simpa"], "tactic_count": 10}
{"name": "IsDedekindDomain.HeightOneSpectrum.Support", "kind": "definition", "module": "Mathlib.RingTheory.DedekindDomain.FiniteAdeleRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.HeightOneSpectrum.Support.finite", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.FiniteAdeleRing", "is_tactic_proof": true, "tactics": ["obtain", "have", "suffices", "apply", "intro", "apply_fun", "simp", "rw", "have", "contrapose", "rw", "exact", "simp_rw", "apply", "simpa"], "tactic_count": 15}
{"name": "IsDedekindDomain.FiniteAdeleRing", "kind": "definition", "module": "Mathlib.RingTheory.DedekindDomain.FiniteAdeleRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.instCommRingFiniteAdeleRing", "kind": "instance", "module": "Mathlib.RingTheory.DedekindDomain.FiniteAdeleRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.instTopologicalSpaceFiniteAdeleRing", "kind": "instance", "module": "Mathlib.RingTheory.DedekindDomain.FiniteAdeleRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.instDFunLikeFiniteAdeleRingHeightOneSpectrumAdicCompletion", "kind": "instance", "module": "Mathlib.RingTheory.DedekindDomain.FiniteAdeleRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.FiniteAdeleRing.algebraMap", "kind": "definition", "module": "Mathlib.RingTheory.DedekindDomain.FiniteAdeleRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.FiniteAdeleRing.instAlgebra", "kind": "instance", "module": "Mathlib.RingTheory.DedekindDomain.FiniteAdeleRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.FiniteAdeleRing.instAlgebra_1", "kind": "instance", "module": "Mathlib.RingTheory.DedekindDomain.FiniteAdeleRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.FiniteAdeleRing.instIsScalarTower", "kind": "instance", "module": "Mathlib.RingTheory.DedekindDomain.FiniteAdeleRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.FiniteAdeleRing.ext", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.FiniteAdeleRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.FiniteAdeleRing.instDFunLikeHeightOneSpectrumAdicCompletion", "kind": "instance", "module": "Mathlib.RingTheory.DedekindDomain.FiniteAdeleRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.FiniteAdeleRing.instIsTopologicalRing", "kind": "instance", "module": "Mathlib.RingTheory.DedekindDomain.FiniteAdeleRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.gaussNorm_intAdicAbv_le_one", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.GaussLemma", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "simp"], "tactic_count": 3}
{"name": "Polynomial.gaussNorm_lt_one_iff_contentIdeal_le", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.GaussLemma", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "have", "simp", "constructor", "contrapose", "simp", "intro", "exact", "intro", "rw", "intro", "rw", "exact"], "tactic_count": 14}
{"name": "Polynomial.contentIdeal_eq_top_iff_forall_gaussNorm_eq_one", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.GaussLemma", "is_tactic_proof": true, "tactics": ["convert_to", "grind", "simp"], "tactic_count": 3}
{"name": "Polynomial.isPrimitive_iff_forall_gaussNorm_eq_one", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.GaussLemma", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsDedekindDomainInv", "kind": "definition", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isDedekindDomainInv_iff", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Basic", "is_tactic_proof": false, "tactics": ["let", "refine", "rw", "simp"], "tactic_count": 4}
{"name": "FractionalIdeal.adjoinIntegral_eq_one_of_isUnit", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Basic", "is_tactic_proof": true, "tactics": ["set", "have", "apply", "simp", "rw", "convert"], "tactic_count": 6}
{"name": "IsDedekindDomainInv.commGroupWithZero", "kind": "abbrev", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomainInv.mul_inv_eq_one", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Basic", "is_tactic_proof": true, "tactics": ["let"], "tactic_count": 1}
{"name": "IsDedekindDomainInv.inv_mul_eq_one", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Basic", "is_tactic_proof": true, "tactics": ["let"], "tactic_count": 1}
{"name": "IsDedekindDomainInv.isNoetherianRing", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Basic", "is_tactic_proof": true, "tactics": ["let", "refine", "by_cases", "rw", "have", "exact"], "tactic_count": 6}
{"name": "IsDedekindDomainInv.integrallyClosed", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Basic", "is_tactic_proof": false, "tactics": ["let", "h.commGroupWithZero", "refine", "rw", "exact", "exact"], "tactic_count": 6}
{"name": "IsDedekindDomainInv.dimensionLEOne", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Basic", "is_tactic_proof": true, "tactics": ["let", "constructor", "rintro", "refine", "have", "have", "suffices", "rw", "calc", "simp", "intro", "have", "obtain", "obtain", "have", "rw", "obtain", "rw", "exact"], "tactic_count": 19}
{"name": "IsDedekindDomainInv.isDedekindDomain", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_mem_inv_coe_ideal", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Basic", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "exact"], "tactic_count": 4}
{"name": "exists_multiset_prod_cons_le_and_prod_not_le", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Basic", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "wellFounded_lt.has_min", "obtain", "hM.isPrime.multiset_prod_le.mp", "obtain", "classical", "have", "obtain", "rwa", "have", "subst", "refine", "convert", "rw", "refine", "exact"], "tactic_count": 17}
{"name": "FractionalIdeal.not_inv_le_one_of_ne_bot", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Basic", "is_tactic_proof": false, "tactics": ["have", "letI", "wlog", "rcases", "have", "refine", "simpa", "have", "obtain", "replace", "let", "have", "have", "obtain", "obtain", "have", "refine", "exact", "rintro", "obtain", "rw", "have", "apply", "rw", "exact", "rw", "rcases", "rw", "apply", "refine", "rintro", "rw", "have", "contradiction"], "tactic_count": 34}
{"name": "FractionalIdeal.mul_inv_cancel_of_le_one", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Basic", "is_tactic_proof": true, "tactics": ["obtain", "le_one_iff_exists_coeIdeal.mp", "by_cases", "subst", "refine", "rw", "exact", "by_cases", "rw", "exact"], "tactic_count": 10}
{"name": "FractionalIdeal.coe_ideal_mul_inv", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Basic", "is_tactic_proof": true, "tactics": ["apply", "by_cases", "rw", "intro", "suffices", "rwa", "rw", "have", "intro", "rw", "rw", "simp", "intro", "exact", "hx", "refine", "isNoetherian_submodule.mp", "obtain", "rw", "refine", "clear", "induction", "zero", "succ"], "tactic_count": 24}
{"name": "FractionalIdeal.semifield", "kind": "instance", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.instPosMulStrictMonoNonZeroDivisors", "kind": "instance", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.instMulPosStrictMonoNonZeroDivisors", "kind": "instance", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.instPosMulReflectLENonZeroDivisors", "kind": "instance", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.instMulPosReflectLENonZeroDivisors", "kind": "instance", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.mul_inv_cancel", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.mul_right_le_iff", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.mul_left_le_iff", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.mul_left_strictMono", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.mul_right_strictMono", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.instPosMulReflectLEIdealOfIsDedekindDomain", "kind": "instance", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.div_eq_mul_inv", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isDedekindDomain_iff_isDedekindDomainInv", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.isCancelMulZero", "kind": "instance", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.isDomain", "kind": "instance", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instPosMulStrictMonoIdeal", "kind": "instance", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instMulPosStrictMonoIdeal", "kind": "instance", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.dvd_iff_le", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.liesOver_iff_dvd_map", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.dvdNotUnit_iff_lt", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instWfDvdMonoidIdeal", "kind": "instance", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.uniqueFactorizationMonoid", "kind": "instance", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.normalizationMonoid", "kind": "instance", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.exists_notMem_one_of_ne_bot", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.dvd_span_singleton", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.isPrime_of_prime", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": true, "tactics": ["refine", "rintro", "rw", "exact", "simp", "exact"], "tactic_count": 6}
{"name": "Ideal.prime_of_isPrime", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": true, "tactics": ["refine", "simpa"], "tactic_count": 2}
{"name": "Ideal.prime_of_mem_primesOver", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.prime_iff_isPrime", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.isPrime_iff_bot_or_prime", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.prime_span_singleton_iff", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": true, "tactics": ["rcases", "rw", "simp", "have", "rw"], "tactic_count": 5}
{"name": "Ideal.prime_generator_of_prime", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.mem_normalizedFactors_iff", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "by_cases", "rw", "simp", "rwa"], "tactic_count": 5}
{"name": "Ideal.mem_primesOver_iff_mem_normalizedFactors", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": false, "tactics": ["rw", "and_congr_right_iff,", "intro", "refine", "exact"], "tactic_count": 5}
{"name": "Ideal.pow_right_strictAnti", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.pow_lt_self", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": true, "tactics": ["convert", "dsimp", "rw"], "tactic_count": 3}
{"name": "Ideal.exists_mem_pow_notMem_pow_succ", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.eq_prime_pow_of_succ_lt_of_le", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": true, "tactics": ["refine", "have", "have", "have", "have", "rw", "normalizedFactors_irreducible", "rw", "normalizedFactors_irreducible", "all_goals"], "tactic_count": 10}
{"name": "Ideal.pow_succ_lt_pow", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associates.le_singleton_iff", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "FractionalIdeal.le_inv_comm", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "FractionalIdeal.inv_le_comm", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "FractionalIdeal.inv_le_inv_iff", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.exist_integer_multiples_notMem", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": true, "tactics": ["let", "have", "spanFinset_ne_zero.mpr", "suffices", "obtain", "rw", "refine", "exact", "contrapose", "refine", "rintro", "rw", "intro", "intro", "rw", "refine", "rw", "exact"], "tactic_count": 18}
{"name": "Ideal.mul_iInf", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "refine", "have", "obtain", "grw", "rw", "exact", "exact"], "tactic_count": 9}
{"name": "Ideal.iInf_mul", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Ideal.mul_inf", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "congr"], "tactic_count": 2}
{"name": "Ideal.inf_mul", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FractionalIdeal.mul_inf", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.inf_mul", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.sup_mul_inf", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": true, "tactics": ["letI", "have", "rw", "rw", "exact", "rw", "simp", "have", "rw", "rw", "simp", "rw", "exact", "rw"], "tactic_count": 14}
{"name": "Ideal.instNormalizedGCDMonoid", "kind": "instance", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.gcd_eq_sup", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.lcm_eq_inf", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.isCoprime_iff_gcd", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.factors_span_eq", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": true, "tactics": ["rcases", "have", "obtain", "exact", "rw", "factors_eq_normalizedFactors,"], "tactic_count": 6}
{"name": "FractionalIdeal.sup_mul_inf", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": false, "tactics": ["apply", "mul_left_injective₀", "have", "simp", "coeIdeal_span_singleton]", "rw", "mul_inf₀", "simp", "convert"], "tactic_count": 9}
{"name": "prod_normalizedFactors_eq_self", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "count_le_of_ideal_ge", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sup_eq_prod_inf_factors", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": false, "tactics": ["have", "normalizedFactors", "apply", "intro", "rw", "exact", "have", "prime_of_normalized_factor", "apply", "rw", "constructor", "rw", "exact", "rw", "exact", "rw", "intro", "rw", "exact", "intro", "rw", "exact", "exact", "exact"], "tactic_count": 24}
{"name": "irreducible_pow_sup", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "normalize_eq"], "tactic_count": 2}
{"name": "irreducible_pow_sup_of_le", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": true, "tactics": ["classical", "by_cases", "simp_all", "rw", "rw", "exact_mod_cast"], "tactic_count": 6}
{"name": "irreducible_pow_sup_of_ge", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": true, "tactics": ["classical", "rw", "congr", "rw", "emultiplicity_eq_count_normalizedFactors", "rw", "apply", "simp", "rw", "exact_mod_cast"], "tactic_count": 10}
{"name": "Ideal.eq_prime_pow_mul_coprime", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": true, "tactics": ["use", "constructor", "refine", "have", "exact", "nth_rw", "rw"], "tactic_count": 7}
{"name": "map_prime_of_equiv", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsDedekindDomain.HeightOneSpectrum.isMaximal", "kind": "instance", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.HeightOneSpectrum.prime", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.HeightOneSpectrum.ofPrime", "kind": "definition", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.HeightOneSpectrum.irreducible", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.HeightOneSpectrum.associates_irreducible", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.HeightOneSpectrum.equivMaximalSpectrum", "kind": "definition", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.HeightOneSpectrum.ideal_ne_top_iff_exists", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "constructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 6}
{"name": "IsDedekindDomain.HeightOneSpectrum.iInf_localization_eq_bot", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": true, "tactics": ["ext", "rw", "constructor", "on_goal", "rcases", "exact", "all_goals", "exact", "exact"], "tactic_count": 9}
{"name": "idealFactorsFunOfQuotHom", "kind": "definition", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "idealFactorsFunOfQuotHom_id", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "idealFactorsFunOfQuotHom_comp", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": true, "tactics": ["refine", "rw", "map_comap_of_surjective"], "tactic_count": 3}
{"name": "idealFactorsEquivOfQuotEquiv", "kind": "definition", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": true, "tactics": ["have", "have", "refine", "have", "simp", "rw", "have", "simp", "rw"], "tactic_count": 9}
{"name": "idealFactorsEquivOfQuotEquiv_symm", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "idealFactorsEquivOfQuotEquiv_is_dvd_iso", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": false, "tactics": ["suffices", "idealFactorsEquivOfQuotEquiv", "exact"], "tactic_count": 3}
{"name": "idealFactorsEquivOfQuotEquiv_mem_normalizedFactors_of_mem_normalizedFactors", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": false, "tactics": ["have", "intro", "rw", "exact", "refine", "mem_normalizedFactors_factor_dvd_iso_of_mem_normalizedFactors", "rintro", "rw", "apply"], "tactic_count": 9}
{"name": "normalizedFactorsEquivOfQuotEquiv", "kind": "definition", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "normalizedFactorsEquivOfQuotEquiv_symm", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "normalizedFactorsEquivOfQuotEquiv_emultiplicity_eq_emultiplicity", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "refine", "emultiplicity_factor_dvd_iso_eq_emultiplicity_of_mem_normalizedFactors", "exact"], "tactic_count": 4}
{"name": "Ring.DimensionLeOne.prime_le_prime_iff_eq", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.IsPrime.mul_mem_pow", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": true, "tactics": ["cases", "by_cases", "simp", "by_cases", "exact", "rw", "exact"], "tactic_count": 7}
{"name": "Ideal.IsPrime.mem_pow_mul", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "Ideal.count_normalizedFactors_eq", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "count_associates_factors_eq", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": true, "tactics": ["replace", "have", "simpa", "apply", "all_goals", "rw", "simp", "rw", "lia"], "tactic_count": 9}
{"name": "Ideal.count_associates_eq", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": true, "tactics": ["have", "classical", "rw", "exact", "exact", "simp", "exact", "simp", "rw", "exact", "simp", "aesop", "exact", "simp"], "tactic_count": 14}
{"name": "Ideal.count_associates_eq'", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": true, "tactics": ["obtain", "apply", "contrapose", "obtain", "use", "rw", "ring"], "tactic_count": 7}
{"name": "Ideal.le_mul_of_no_prime_factors", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": true, "tactics": ["simp", "by_cases", "simpa", "obtain", "rw", "refine", "exact"], "tactic_count": 7}
{"name": "IsDedekindDomain.inf_prime_pow_eq_prod", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": true, "tactics": ["letI", "revert", "refine", "simp", "intro", "specialize", "ih", "coprime", "rw", "refine", "intro", "obtain", "haveI", "haveI", "refine", "exact", "refine", "exact", "exact"], "tactic_count": 19}
{"name": "IsDedekindDomain.quotientEquivPiOfProdEq", "kind": "definition", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.quotientEquivPiFactors", "kind": "definition", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.quotientEquivPiFactors_mk", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.quotientEquivPiOfFinsetProdEq", "kind": "definition", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.exists_representative_mod_finset", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas", "is_tactic_proof": true, "tactics": ["let", "obtain", "obtain", "exact"], "tactic_count": 4}
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{"name": "Submodule.traceDual_eq_span_map_traceDual_of_linearDisjoint", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.LinearDisjoint", "is_tactic_proof": false, "tactics": ["have", "refine", "ext", "exact", "suffices", "apply", "refine", "rw", "exact", "exact", "have", "rwa", "extendedHomₐ_coeIdeal_eq_map", "coe_extendedHomₐ_eq_span,", "simp", "rw", "rw", "exact"], "tactic_count": 18}
{"name": "_private.Mathlib.RingTheory.DedekindDomain.LinearDisjoint.0.Module.Basis.ofIsCoprimeDifferentIdeal_aux", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.LinearDisjoint", "is_tactic_proof": true, "tactics": ["classical", "have", "have", "have", "congr_arg", "rw", "traceDual_eq_span_map_traceDual_of_linearDisjoint", "traceDual_span_of_basis", "map_coe,", "have", "refine", "rw", "b.trace_traceDual_mul", "rw", "rw", "ext"], "tactic_count": 16}
{"name": "Module.Basis.ofIsCoprimeDifferentIdeal", "kind": "definition", "module": "Mathlib.RingTheory.DedekindDomain.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.ofIsCoprimeDifferentIdeal_apply", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.LinearDisjoint", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsDedekindDomain.range_sup_range_eq_top_of_isCoprime_differentIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.LinearDisjoint", "is_tactic_proof": true, "tactics": ["let", "refine", "rw", "refine", "rw", "exact"], "tactic_count": 6}
{"name": "IsDedekindDomain.adjoin_union_eq_top_of_isCoprime_differentialIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.LinearDisjoint", "is_tactic_proof": false, "tactics": ["rw", "hs,", "exact"], "tactic_count": 3}
{"name": "Ideal.eq_span_singleton_of_mem_of_notMem_sq_of_notMem_prime_ne", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.PID", "is_tactic_proof": true, "tactics": ["letI", "have", "rintro", "exact", "by_cases", "subst", "rwa", "have", "have", "refine", "associated_iff_eq.mp", "rwa", "simp", "intro", "split_ifs", "subst", "refine", "assumption", "by_cases", "refine", "exact", "exact", "hQp"], "tactic_count": 23}
{"name": "FractionalIdeal.isPrincipal_of_unit_of_comap_mul_span_singleton_eq_top", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.PID", "is_tactic_proof": true, "tactics": ["have", "set", "have", "rw", "apply", "grw", "have", "rw", "exact", "obtain", "refine", "rw", "refine", "conv_rhs", "grw", "rw", "exact"], "tactic_count": 17}
{"name": "FractionalIdeal.isPrincipal.of_finite_maximals_of_inv", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.PID", "is_tactic_proof": true, "tactics": ["have", "rw", "let", "haveI", "have", "simp_rw", "rintro", "exact", "have", "left_lt_sup.1", "have", "intro", "obtain", "exact", "choose", "choose", "let", "have", "refine", "obtain", "replace", "have", "intro", "obtain", "exact", "have", "obtain", "refine", "have", "rwa", "simp_rw", "rw", "refine", "obtain", "rw", "rw", "obtain", "rw", "exact", "refine", "rw", "obtain", "rw", "specialize", "simp_rw", "exact"], "tactic_count": 46}
{"name": "Ideal.IsPrincipal.of_finite_maximals_of_isUnit", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.PID", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrincipalIdealRing.of_finite_maximals", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.PID", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrincipalIdealRing.of_finite_primes", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.PID", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.OverPrime.mem_normalizedFactors_of_isPrime", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.PID", "is_tactic_proof": false, "tactics": ["have", "map_le_nonZeroDivisors_of_injective", "letI", "haveI", "rw", "exact", "obtain", "have", "rw", "obtain", "exact", "rw", "normalizedFactors_irreducible", "dvd_iff_normalizedFactors_le_normalizedFactors", "hpu", "have", "exact", "exact", "exact", "rw", "assumption", "rw", "exact"], "tactic_count": 23}
{"name": "IsDedekindDomain.isPrincipalIdealRing_localization_over_prime", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.PID", "is_tactic_proof": true, "tactics": ["letI", "letI", "refine", "rw", "exact", "and_iff_right_of_imp", "or_iff_not_imp_left.mpr"], "tactic_count": 7}
{"name": "IsPrincipalIdealRing.of_isDedekindDomain_of_uniqueFactorizationMonoid", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.PID", "is_tactic_proof": true, "tactics": ["refine", "obtain", "suffices", "have", "exact"], "tactic_count": 5}
{"name": "Set.integer", "kind": "definition", "module": "Mathlib.RingTheory.DedekindDomain.SInteger", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.integer_eq", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.SInteger", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.integer_valuation_le_one", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.SInteger", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.integer_univ", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.SInteger", "is_tactic_proof": true, "tactics": ["ext", "tauto"], "tactic_count": 2}
{"name": "IsDedekindDomain.integer_empty", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.SInteger", "is_tactic_proof": true, "tactics": ["ext", "simp", "refine", "rintro", "exact"], "tactic_count": 5}
{"name": "Set.unit", "kind": "definition", "module": "Mathlib.RingTheory.DedekindDomain.SInteger", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.unit_eq", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.SInteger", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.unit_valuation_eq_one", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.SInteger", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.unitEquivUnitsInteger", "kind": "definition", "module": "Mathlib.RingTheory.DedekindDomain.SInteger", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.DedekindDomain.SelmerGroup.0.term_/__1", "kind": "definition", "module": "Mathlib.RingTheory.DedekindDomain.SelmerGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.DedekindDomain.SelmerGroup.0._aux_Mathlib_RingTheory_DedekindDomain_SelmerGroup___macroRules__private_Mathlib_RingTheory_DedekindDomain_SelmerGroup_0_term_/__1_1", "kind": "definition", "module": "Mathlib.RingTheory.DedekindDomain.SelmerGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.HeightOneSpectrum.valuationOfNeZeroToFun", "kind": "definition", "module": "Mathlib.RingTheory.DedekindDomain.SelmerGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.HeightOneSpectrum.valuationOfNeZeroToFun_eq", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.SelmerGroup", "is_tactic_proof": true, "tactics": ["classical", "rw", "rw", "change", "simp_rw", "if_neg", "valuationOfNeZeroToFun,"], "tactic_count": 7}
{"name": "IsDedekindDomain.HeightOneSpectrum.valuationOfNeZero", "kind": "definition", "module": "Mathlib.RingTheory.DedekindDomain.SelmerGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.HeightOneSpectrum.valuationOfNeZero_eq", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.SelmerGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.HeightOneSpectrum.valuation_of_unit_eq", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.SelmerGroup", "is_tactic_proof": true, "tactics": ["rw", "constructor", "exact", "obtain", "change", "apply_fun", "rw", "rw", "gcongr", "exact"], "tactic_count": 10}
{"name": "IsDedekindDomain.HeightOneSpectrum.valuationOfNeZeroMod", "kind": "definition", "module": "Mathlib.RingTheory.DedekindDomain.SelmerGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.HeightOneSpectrum.valuation_of_unit_mod_eq", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.SelmerGroup", "is_tactic_proof": true, "tactics": ["erw", "map_one]"], "tactic_count": 2}
{"name": "IsDedekindDomain.selmerGroup", "kind": "definition", "module": "Mathlib.RingTheory.DedekindDomain.SelmerGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.DedekindDomain.SelmerGroup.0.IsDedekindDomain.term_⟮_,_⟯", "kind": "definition", "module": "Mathlib.RingTheory.DedekindDomain.SelmerGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.DedekindDomain.SelmerGroup.0.IsDedekindDomain._aux_Mathlib_RingTheory_DedekindDomain_SelmerGroup___macroRules__private_Mathlib_RingTheory_DedekindDomain_SelmerGroup_0_IsDedekindDomain_term_⟮_,_⟯_1", "kind": "definition", "module": "Mathlib.RingTheory.DedekindDomain.SelmerGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.selmerGroup.monotone", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.SelmerGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.selmerGroup.valuation", "kind": "definition", "module": "Mathlib.RingTheory.DedekindDomain.SelmerGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.selmerGroup.valuation_ker_eq", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.SelmerGroup", "is_tactic_proof": true, "tactics": ["ext", "constructor", "intro", "by_cases", "exact", "exact", "exact"], "tactic_count": 7}
{"name": "IsDedekindDomain.selmerGroup.fromUnit", "kind": "definition", "module": "Mathlib.RingTheory.DedekindDomain.SelmerGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.selmerGroup.fromUnit_ker", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.SelmerGroup", "is_tactic_proof": true, "tactics": ["ext", "constructor", "intro", "rcases", "have", "have", "rw", "rw", "rcases", "rcases", "rw", "rw", "rw", "exact", "simpa", "rintro", "rw", "exact"], "tactic_count": 18}
{"name": "IsDedekindDomain.selmerGroup.fromUnitLift", "kind": "definition", "module": "Mathlib.RingTheory.DedekindDomain.SelmerGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.selmerGroup.fromUnitLift_injective", "kind": "theorem", "module": "Mathlib.RingTheory.DedekindDomain.SelmerGroup", "is_tactic_proof": true, "tactics": ["dsimp", "exact"], "tactic_count": 2}
{"name": "Derivation.instFunLike", "kind": "instance", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.instAddMonoidHomClass", "kind": "instance", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.toFun_eq_coe", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.Simps.apply", "kind": "definition", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.hasCoeToLinearMap", "kind": "instance", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.mk_coe", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.coeFn_coe", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.coe_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.ext", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.congr_fun", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.map_add", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.map_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.map_smul", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.leibniz", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.map_smul_of_tower", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.map_one_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.map_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Derivation.map_natCast", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Derivation.leibniz_pow", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rcases", "simp", "have", "simp", "add_zero,"], "tactic_count": 8}
{"name": "Derivation.map_aeval", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": true, "tactics": ["induction", "simp", "simp", "simp"], "tactic_count": 4}
{"name": "Derivation.eqOn_adjoin", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.ext_of_adjoin_eq_top", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.instZero", "kind": "instance", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.coe_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.coe_zero_linearMap", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.zero_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.instAdd", "kind": "instance", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.coe_add", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.coe_add_linearMap", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.add_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.instInhabited", "kind": "instance", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.instSMul", "kind": "instance", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.coe_smul", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.coe_smul_linearMap", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.smul_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.instAddCommMonoid", "kind": "instance", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.coeFnAddMonoidHom", "kind": "definition", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.coeFnAddMonoidHom_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.instDistribMulAction", "kind": "instance", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.instIsCentralScalar", "kind": "instance", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.instIsScalarTower", "kind": "instance", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.instSMulCommClass", "kind": "instance", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.instModule", "kind": "instance", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.compDer", "kind": "definition", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.coe_to_linearMap_comp", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.coe_comp", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.llcomp", "kind": "definition", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.compDer", "kind": "definition", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.linearEquiv_coe_to_linearMap_comp", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.linearEquiv_coe_comp", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.compAlgebraMap", "kind": "definition", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.compAlgebraMapL", "kind": "definition", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.restrictScalars", "kind": "definition", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.coe_restrictScalars", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.restrictScalars_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.liftOfRightInverse", "kind": "definition", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.liftOfRightInverse_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": true, "tactics": ["suffices", "apply", "simp"], "tactic_count": 3}
{"name": "Derivation.liftOfRightInverse_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": true, "tactics": ["ext", "obtain", "simp"], "tactic_count": 3}
{"name": "Derivation.liftOfSurjective", "kind": "abbrev", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.liftOfSurjective_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Derivation.mk'", "kind": "definition", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.coe_mk'", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.coe_mk'_linearMap", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.map_neg", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.map_sub", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.map_intCast", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Derivation.leibniz_of_mul_eq_one", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "calc"], "tactic_count": 3}
{"name": "Derivation.leibniz_invOf", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.leibniz_inv", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simp", "exact"], "tactic_count": 3}
{"name": "Derivation.leibniz_div", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": ["simp", "smul_add]", "rw", "ring_nf"], "tactic_count": 4}
{"name": "Derivation.leibniz_div_const", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": true, "tactics": ["simp", "rw", "ring_nf"], "tactic_count": 3}
{"name": "Derivation.leibniz_zpow", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "by_cases", "simp", "rcases", "rw", "simp", "rw", "congr", "lia", "rw", "trans", "ring_nf", "rw", "congr", "norm_cast", "lia"], "tactic_count": 17}
{"name": "Derivation.instNeg", "kind": "instance", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.coe_neg", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.coe_neg_linearMap", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.neg_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.instSub", "kind": "instance", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.coe_sub", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.coe_sub_linearMap", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.sub_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.instAddCommGroup", "kind": "instance", "module": "Mathlib.RingTheory.Derivation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Differential.term_′", "kind": "definition", "module": "Mathlib.RingTheory.Derivation.DifferentialRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Differential._aux_Mathlib_RingTheory_Derivation_DifferentialRing___macroRules_Differential_term_′_1", "kind": "definition", "module": "Mathlib.RingTheory.Derivation.DifferentialRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Differential._aux_Mathlib_RingTheory_Derivation_DifferentialRing___unexpand_Differential_deriv_1", "kind": "definition", "module": "Mathlib.RingTheory.Derivation.DifferentialRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "delabDeriv", "kind": "definition", "module": "Mathlib.RingTheory.Derivation.DifferentialRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "algebraMap.coe_deriv", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.DifferentialRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_range_of_deriv_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.DifferentialRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDifferentialAlgebra", "kind": "instance", "module": "Mathlib.RingTheory.Derivation.DifferentialRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instContainConstants", "kind": "instance", "module": "Mathlib.RingTheory.Derivation.DifferentialRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Differential.equiv", "kind": "definition", "module": "Mathlib.RingTheory.Derivation.DifferentialRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DifferentialAlgebra.equiv", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.DifferentialRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.instBracket", "kind": "instance", "module": "Mathlib.RingTheory.Derivation.Lie", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.commutator_coe_linear_map", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.Lie", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.commutator_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.Lie", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.instLieRing", "kind": "instance", "module": "Mathlib.RingTheory.Derivation.Lie", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.instLieAlgebra", "kind": "instance", "module": "Mathlib.RingTheory.Derivation.Lie", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.instLieRingModule", "kind": "instance", "module": "Mathlib.RingTheory.Derivation.Lie", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.instLieModule", "kind": "instance", "module": "Mathlib.RingTheory.Derivation.Lie", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.bracket_eq_fun", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.Lie", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.mapCoeffs", "kind": "definition", "module": "Mathlib.RingTheory.Derivation.MapCoeffs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.mapCoeffs_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.MapCoeffs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.mapCoeffs_monomial", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.MapCoeffs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.mapCoeffs_X", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.MapCoeffs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Derivation.mapCoeffs_C", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.MapCoeffs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Derivation.apply_aeval_eq'", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.MapCoeffs", "is_tactic_proof": true, "tactics": ["induction", "add", "monomial", "simp", "rw"], "tactic_count": 5}
{"name": "Derivation.apply_aeval_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.MapCoeffs", "is_tactic_proof": true, "tactics": ["convert", "apply", "intro", "rfl", "intro", "rfl"], "tactic_count": 6}
{"name": "Derivation.apply_eval_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.MapCoeffs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Differential.mapCoeffs", "kind": "definition", "module": "Mathlib.RingTheory.Derivation.MapCoeffs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Differential.coeff_mapCoeffs", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.MapCoeffs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Differential.mapCoeffs_monomial", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.MapCoeffs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Differential.mapCoeffs_X", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.MapCoeffs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Differential.mapCoeffs_C", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.MapCoeffs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Differential.deriv_aeval_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.MapCoeffs", "is_tactic_proof": true, "tactics": ["convert", "simp", "simp"], "tactic_count": 3}
{"name": "Differential.implicitDeriv", "kind": "definition", "module": "Mathlib.RingTheory.Derivation.MapCoeffs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Differential.implicitDeriv_C", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.MapCoeffs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Differential.implicitDeriv_X", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.MapCoeffs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Differential.deriv_aeval_eq_implicitDeriv", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.MapCoeffs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Differential.algHom_deriv", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.MapCoeffs", "is_tactic_proof": true, "tactics": ["let", "apply", "rw", "simp", "apply", "conv", "simp", "apply", "rw", "simp", "p]"], "tactic_count": 11}
{"name": "Differential.algEquiv_deriv", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.MapCoeffs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Differential.algHom_deriv'", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.MapCoeffs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Differential.algEquiv_deriv'", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.MapCoeffs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "diffToIdealOfQuotientCompEq", "kind": "definition", "module": "Mathlib.RingTheory.Derivation.ToSquareZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "diffToIdealOfQuotientCompEq_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.ToSquareZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "derivationToSquareZeroOfLift", "kind": "definition", "module": "Mathlib.RingTheory.Derivation.ToSquareZero", "is_tactic_proof": false, "tactics": ["refine", "diffToIdealOfQuotientCompEq", "map_one_eq_zero", "leibniz", "rw", "ext", "intro", "let", "have", "rw", "convert", "ext", "dsimp", "simp", "rw", "simp", "ring"], "tactic_count": 17}
{"name": "derivationToSquareZeroOfLift_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.ToSquareZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "liftOfDerivationToSquareZero", "kind": "definition", "module": "Mathlib.RingTheory.Derivation.ToSquareZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "liftOfDerivationToSquareZero_mk_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.ToSquareZero", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "liftOfDerivationToSquareZero_mk_apply'", "kind": "theorem", "module": "Mathlib.RingTheory.Derivation.ToSquareZero", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "derivationToSquareZeroEquivLift", "kind": "definition", "module": "Mathlib.RingTheory.Derivation.ToSquareZero", "is_tactic_proof": false, "tactics": ["refine", "ext", "intro", "rintro"], "tactic_count": 4}
{"name": "IsDiscreteValuationRing.not_a_field", "kind": "theorem", "module": "Mathlib.RingTheory.DiscreteValuationRing.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDiscreteValuationRing.not_isField", "kind": "theorem", "module": "Mathlib.RingTheory.DiscreteValuationRing.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDiscreteValuationRing.irreducible_of_span_eq_maximalIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.DiscreteValuationRing.Basic", "is_tactic_proof": true, "tactics": ["have", "refine", "intro", "by_contra", "rw", "rcases", "rcases", "rw", "apply", "apply", "exact"], "tactic_count": 11}
{"name": "IsDiscreteValuationRing.irreducible_iff_uniformizer", "kind": "theorem", "module": "Mathlib.RingTheory.DiscreteValuationRing.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Irreducible.maximalIdeal_eq", "kind": "theorem", "module": "Mathlib.RingTheory.DiscreteValuationRing.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDiscreteValuationRing.exists_irreducible", "kind": "theorem", "module": "Mathlib.RingTheory.DiscreteValuationRing.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "IsDiscreteValuationRing.exists_prime", "kind": "theorem", "module": "Mathlib.RingTheory.DiscreteValuationRing.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDiscreteValuationRing.iff_pid_with_one_nonzero_prime", "kind": "theorem", "module": "Mathlib.RingTheory.DiscreteValuationRing.Basic", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rcases", "constructor", "assumption", "use", "constructor", "exact", "rintro", "obtain", "have", "rintro", "apply", "simp", "rw", "replace", "rw", "exact", "rintro", "haveI", "refine", "rcases", "have", "order"], "tactic_count": 24}
{"name": "IsDiscreteValuationRing.associated_of_irreducible", "kind": "theorem", "module": "Mathlib.RingTheory.DiscreteValuationRing.Basic", "is_tactic_proof": true, "tactics": ["rw", "rw"], "tactic_count": 2}
{"name": "IsDiscreteValuationRing.HasUnitMulPowIrreducibleFactorization", "kind": "definition", "module": "Mathlib.RingTheory.DiscreteValuationRing.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDiscreteValuationRing.HasUnitMulPowIrreducibleFactorization.unique_irreducible", "kind": "theorem", "module": "Mathlib.RingTheory.DiscreteValuationRing.Basic", "is_tactic_proof": true, "tactics": ["rcases", "suffices", "clear", "intro", "obtain", "have", "rcases", "obtain", "clear", "revert", "decide", "simp", "simpa", "obtain", "rw", "rcases", "exact", "rw", "exact"], "tactic_count": 19}
{"name": "IsDiscreteValuationRing.HasUnitMulPowIrreducibleFactorization.toUniqueFactorizationMonoid", "kind": "theorem", "module": "Mathlib.RingTheory.DiscreteValuationRing.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDiscreteValuationRing.HasUnitMulPowIrreducibleFactorization.of_ufd_of_unique_irreducible", "kind": "theorem", "module": "Mathlib.RingTheory.DiscreteValuationRing.Basic", "is_tactic_proof": true, "tactics": ["obtain", "refine", "intro", "obtain", "refine", "have", "rw", "rw", "congr", "symm", "rw", "simp", "rintro", "rw", "apply"], "tactic_count": 15}
{"name": "IsDiscreteValuationRing.aux_pid_of_ufd_of_unique_irreducible", "kind": "theorem", "module": "Mathlib.RingTheory.DiscreteValuationRing.Basic", "is_tactic_proof": true, "tactics": ["classical", "constructor", "intro", "by_cases", "rw", "use", "simp", "obtain", "obtain", "have", "obtain", "refine", "simpa", "constructor", "use", "change", "apply", "intro", "by_cases", "simp", "obtain", "simp", "apply", "apply", "simpa", "rw", "exact"], "tactic_count": 27}
{"name": "IsDiscreteValuationRing.of_ufd_of_unique_irreducible", "kind": "theorem", "module": "Mathlib.RingTheory.DiscreteValuationRing.Basic", "is_tactic_proof": true, "tactics": ["rw", "haveI", "obtain", "refine", "rw", "exact", "rwa", "intro", "rw", "rintro", "apply", "apply", "rw", "rwa"], "tactic_count": 14}
{"name": "IsDiscreteValuationRing.ofHasUnitMulPowIrreducibleFactorization", "kind": "theorem", "module": "Mathlib.RingTheory.DiscreteValuationRing.Basic", "is_tactic_proof": true, "tactics": ["letI", "apply", "obtain", "exact"], "tactic_count": 4}
{"name": "IsDiscreteValuationRing.RingEquivClass.isDiscreteValuationRing", "kind": "theorem", "module": "Mathlib.RingTheory.DiscreteValuationRing.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDiscreteValuationRing.associated_pow_irreducible", "kind": "theorem", "module": "Mathlib.RingTheory.DiscreteValuationRing.Basic", "is_tactic_proof": true, "tactics": ["have", "obtain", "use", "have", "rw", "rw", "congr", "rw", "simp", "rintro", "rw", "refine", "apply", "assumption"], "tactic_count": 14}
{"name": "IsDiscreteValuationRing.eq_unit_mul_pow_irreducible", "kind": "theorem", "module": "Mathlib.RingTheory.DiscreteValuationRing.Basic", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "use", "apply"], "tactic_count": 4}
{"name": "IsDiscreteValuationRing.ideal_eq_span_pow_irreducible", "kind": "theorem", "module": "Mathlib.RingTheory.DiscreteValuationRing.Basic", "is_tactic_proof": false, "tactics": ["have", "rw", "assumption", "rcases", "use", "have", "rw", "use"], "tactic_count": 8}
{"name": "IsDiscreteValuationRing.unit_mul_pow_congr_pow", "kind": "theorem", "module": "Mathlib.RingTheory.DiscreteValuationRing.Basic", "is_tactic_proof": false, "tactics": ["have", "rw", "refine", "simp", "rw", "have", "refine", "all_goals", "intro", "obtain", "assumption", "simpa"], "tactic_count": 12}
{"name": "IsDiscreteValuationRing.unit_mul_pow_congr_unit", "kind": "theorem", "module": "Mathlib.RingTheory.DiscreteValuationRing.Basic", "is_tactic_proof": true, "tactics": ["obtain", "rw", "rw", "rcases", "rw", "exact", "apply"], "tactic_count": 7}
{"name": "IsDiscreteValuationRing.addVal", "kind": "definition", "module": "Mathlib.RingTheory.DiscreteValuationRing.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDiscreteValuationRing.addVal_def", "kind": "theorem", "module": "Mathlib.RingTheory.DiscreteValuationRing.Basic", "is_tactic_proof": true, "tactics": ["classical", "rw", "emultiplicity_eq_of_associated_left", "emultiplicity_eq_of_associated_right", "emultiplicity_pow_self_of_prime"], "tactic_count": 5}
{"name": "IsDiscreteValuationRing.addVal_def'", "kind": "theorem", "module": "Mathlib.RingTheory.DiscreteValuationRing.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDiscreteValuationRing.addVal_zero", "kind": "theorem", "module": "Mathlib.RingTheory.DiscreteValuationRing.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDiscreteValuationRing.addVal_one", "kind": "theorem", "module": "Mathlib.RingTheory.DiscreteValuationRing.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDiscreteValuationRing.addVal_uniformizer", "kind": "theorem", "module": "Mathlib.RingTheory.DiscreteValuationRing.Basic", "is_tactic_proof": true, "tactics": ["simpa", "addVal_def"], "tactic_count": 2}
{"name": "IsDiscreteValuationRing.addVal_mul", "kind": "theorem", "module": "Mathlib.RingTheory.DiscreteValuationRing.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDiscreteValuationRing.addVal_pow", "kind": "theorem", "module": "Mathlib.RingTheory.DiscreteValuationRing.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Irreducible.addVal_pow", "kind": "theorem", "module": "Mathlib.RingTheory.DiscreteValuationRing.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsDiscreteValuationRing.addVal_eq_top_iff", "kind": "theorem", "module": "Mathlib.RingTheory.DiscreteValuationRing.Basic", "is_tactic_proof": true, "tactics": ["have", "constructor", "contrapose", "intro", "obtain", "obtain", "rw", "nofun", "rintro", "exact"], "tactic_count": 10}
{"name": "IsDiscreteValuationRing.addVal_le_iff_dvd", "kind": "theorem", "module": "Mathlib.RingTheory.DiscreteValuationRing.Basic", "is_tactic_proof": true, "tactics": ["classical", "have", "constructor", "by_cases", "rw", "rw", "apply", "obtain", "rw", "emultiplicity_le_emultiplicity_iff]", "exact", "rw", "exact"], "tactic_count": 13}
{"name": "IsDiscreteValuationRing.addVal_add", "kind": "theorem", "module": "Mathlib.RingTheory.DiscreteValuationRing.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDiscreteValuationRing.addVal_eq_zero_of_unit", "kind": "theorem", "module": "Mathlib.RingTheory.DiscreteValuationRing.Basic", "is_tactic_proof": true, "tactics": ["obtain", "rw"], "tactic_count": 2}
{"name": "IsDiscreteValuationRing.addVal_eq_zero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.DiscreteValuationRing.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simp", "obtain", "obtain", "simp"], "tactic_count": 5}
{"name": "IsDiscreteValuationRing.instIsHausdorffMaximalIdeal", "kind": "instance", "module": "Mathlib.RingTheory.DiscreteValuationRing.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDiscreteValuationRing.quotient", "kind": "definition", "module": "Mathlib.RingTheory.DiscreteValuationRing.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDiscreteValuationRing.remainder", "kind": "definition", "module": "Mathlib.RingTheory.DiscreteValuationRing.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDiscreteValuationRing.toWithBotNat", "kind": "definition", "module": "Mathlib.RingTheory.DiscreteValuationRing.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDiscreteValuationRing.toWithBotNat_zero", "kind": "theorem", "module": "Mathlib.RingTheory.DiscreteValuationRing.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDiscreteValuationRing.toWithBotNat_eq_bot_iff", "kind": "theorem", "module": "Mathlib.RingTheory.DiscreteValuationRing.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDiscreteValuationRing.bot_lt_toWithBotNat_iff", "kind": "theorem", "module": "Mathlib.RingTheory.DiscreteValuationRing.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsDiscreteValuationRing.toWithBotNat_le_toWithBotNat_iff", "kind": "theorem", "module": "Mathlib.RingTheory.DiscreteValuationRing.Basic", "is_tactic_proof": true, "tactics": ["unfold", "generalize", "generalize", "cases", "top", "coe", "cases", "top", "coe", "rw", "exact"], "tactic_count": 11}
{"name": "IsDiscreteValuationRing.dvd_of_toWithBotNat_le_toWithBotNat", "kind": "theorem", "module": "Mathlib.RingTheory.DiscreteValuationRing.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "exact"], "tactic_count": 3}
{"name": "IsDiscreteValuationRing.toEuclideanDomain", "kind": "definition", "module": "Mathlib.RingTheory.DiscreteValuationRing.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "of_isDiscreteValuationRing", "kind": "instance", "module": "Mathlib.RingTheory.DiscreteValuationRing.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.Integers.maximalIdeal_eq_setOf_le_v_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.DiscreteValuationRing.Basic", "is_tactic_proof": true, "tactics": ["letI", "intro", "rw"], "tactic_count": 3}
{"name": "Valuation.Integers.maximalIdeal_pow_eq_setOf_le_v_algebraMap_pow", "kind": "theorem", "module": "Mathlib.RingTheory.DiscreteValuationRing.Basic", "is_tactic_proof": true, "tactics": ["letI", "intro", "have", "rw"], "tactic_count": 4}
{"name": "Irreducible.maximalIdeal_eq_setOf_le_v_coe", "kind": "theorem", "module": "Mathlib.RingTheory.DiscreteValuationRing.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Irreducible.maximalIdeal_pow_eq_setOf_le_v_coe_pow", "kind": "theorem", "module": "Mathlib.RingTheory.DiscreteValuationRing.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_maximalIdeal_pow_eq_of_principal", "kind": "theorem", "module": "Mathlib.RingTheory.DiscreteValuationRing.TFAE", "is_tactic_proof": true, "tactics": ["by_cases", "let", "exact", "classical", "obtain", "by_cases", "use", "have", "have", "rintro", "apply", "simp", "have", "have", "intro", "obtain", "have", "intro", "exact", "clear", "induction", "empty", "cons", "rcases", "use", "rw", "exact", "obtain", "use", "rw", "exact", "have", "obtain", "obtain", "use", "rwa", "use", "apply", "change", "by_contra", "apply", "by_cases", "obtain", "rw", "apply", "apply", "exact", "rw", "exact"], "tactic_count": 49}
{"name": "maximalIdeal_isPrincipal_of_isDedekindDomain", "kind": "theorem", "module": "Mathlib.RingTheory.DiscreteValuationRing.TFAE", "is_tactic_proof": true, "tactics": ["classical", "by_cases", "rw", "obtain", "have", "have", "rw", "apply", "exact", "refine", "rw", "have", "exact", "rcases", "have", "rw", "exact", "obtain", "exact", "have", "intro", "rw", "have", "let", "let", "let", "have", "by_cases", "have", "obtain", "refine", "apply", "rw", "rw", "exact", "apply", "have", "contrapose", "rintro", "obtain", "have", "rw", "exact", "obtain", "rw", "obtain", "rw", "exact", "refine", "apply", "intro", "rw", "rwa"], "tactic_count": 53}
{"name": "tfae_of_isNoetherianRing_of_isLocalRing_of_isDomain", "kind": "theorem", "module": "Mathlib.RingTheory.DiscreteValuationRing.TFAE", "is_tactic_proof": true, "tactics": ["tfae_have", "tfae_have", "tfae_have", "tfae_have", "tfae_have", "tfae_have", "tfae_have", "tfae_have", "rw", "intro", "constructor", "intro", "by_cases", "by_cases", "obtain", "obtain", "exact", "tfae_finish"], "tactic_count": 18}
{"name": "IsDiscreteValuationRing.TFAE", "kind": "theorem", "module": "Mathlib.RingTheory.DiscreteValuationRing.TFAE", "is_tactic_proof": false, "tactics": ["have", "simp", "rw", "have", "convert", "exact", "exact"], "tactic_count": 7}
{"name": "IsLocalRing.finrank_CotangentSpace_eq_one_iff", "kind": "theorem", "module": "Mathlib.RingTheory.DiscreteValuationRing.TFAE", "is_tactic_proof": true, "tactics": ["by_cases", "letI", "simp", "exact", "exact"], "tactic_count": 5}
{"name": "IsLocalRing.finrank_CotangentSpace_eq_one", "kind": "theorem", "module": "Mathlib.RingTheory.DiscreteValuationRing.TFAE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.isPrincipalIdealRing", "kind": "instance", "module": "Mathlib.RingTheory.DiscreteValuationRing.TFAE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.discr", "kind": "definition", "module": "Mathlib.RingTheory.Discriminant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.discr_def", "kind": "theorem", "module": "Mathlib.RingTheory.Discriminant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.discr_eq_discr_of_algEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.Discriminant", "is_tactic_proof": true, "tactics": ["rw", "simp_rw"], "tactic_count": 2}
{"name": "Algebra.discr_reindex", "kind": "theorem", "module": "Mathlib.RingTheory.Discriminant", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Algebra.discr_zero_of_not_linearIndependent", "kind": "theorem", "module": "Mathlib.RingTheory.Discriminant", "is_tactic_proof": true, "tactics": ["classical", "obtain", "have", "ext", "have", "intro", "simp", "simp", "by_contra", "rw", "simp"], "tactic_count": 11}
{"name": "Algebra.discr_of_matrix_vecMul", "kind": "theorem", "module": "Mathlib.RingTheory.Discriminant", "is_tactic_proof": true, "tactics": ["rw", "pow_two]"], "tactic_count": 2}
{"name": "Algebra.discr_of_matrix_mulVec", "kind": "theorem", "module": "Mathlib.RingTheory.Discriminant", "is_tactic_proof": true, "tactics": ["rw", "pow_two]"], "tactic_count": 2}
{"name": "Algebra.discr_not_zero_of_basis", "kind": "theorem", "module": "Mathlib.RingTheory.Discriminant", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Algebra.discr_isUnit_of_basis", "kind": "theorem", "module": "Mathlib.RingTheory.Discriminant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.discr_eq_det_embeddingsMatrixReindex_pow_two", "kind": "theorem", "module": "Mathlib.RingTheory.Discriminant", "is_tactic_proof": true, "tactics": ["rw", "det_transpose,"], "tactic_count": 2}
{"name": "Algebra.discr_powerBasis_eq_prod", "kind": "theorem", "module": "Mathlib.RingTheory.Discriminant", "is_tactic_proof": false, "tactics": ["rw", "det_transpose,", "congr", "rw"], "tactic_count": 4}
{"name": "Algebra.discr_powerBasis_eq_prod'", "kind": "theorem", "module": "Mathlib.RingTheory.Discriminant", "is_tactic_proof": true, "tactics": ["rw", "congr", "ring"], "tactic_count": 3}
{"name": "_private.Mathlib.RingTheory.Discriminant.0.Algebra.termN", "kind": "definition", "module": "Mathlib.RingTheory.Discriminant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Discriminant.0.Algebra._aux_Mathlib_RingTheory_Discriminant___macroRules__private_Mathlib_RingTheory_Discriminant_0_Algebra_termN_1", "kind": "definition", "module": "Mathlib.RingTheory.Discriminant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Discriminant.0.Algebra._aux_Mathlib_RingTheory_Discriminant___unexpand_Module_finrank_1", "kind": "definition", "module": "Mathlib.RingTheory.Discriminant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.discr_powerBasis_eq_prod''", "kind": "theorem", "module": "Mathlib.RingTheory.Discriminant", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "congr", "simp", "congr", "rw", "have", "simp_rw", "simp", "sum_add_distrib,", "rw", "have", "rw", "exact", "have", "have", "have", "rw", "infer_instance", "rw", "ring"], "tactic_count": 21}
{"name": "Algebra.discr_powerBasis_eq_norm", "kind": "theorem", "module": "Mathlib.RingTheory.Discriminant", "is_tactic_proof": true, "tactics": ["let", "letI", "have", "refine", "rw", "exact", "have", "nodup_roots", "have", "intro", "rw", "repeat", "apply", "rw", "congr", "rw", "conv_rhs", "congr", "rfl", "ext", "rw", "rw", "refine", "prod_bij", "simp", "true_and,", "simpa", "exact", "rintro", "rw", "exact", "exact"], "tactic_count": 32}
{"name": "Algebra.discr_isIntegral", "kind": "theorem", "module": "Mathlib.RingTheory.Discriminant", "is_tactic_proof": true, "tactics": ["classical", "rw", "exact"], "tactic_count": 3}
{"name": "Algebra.discr_mul_isIntegral_mem_adjoin", "kind": "theorem", "module": "Mathlib.RingTheory.Discriminant", "is_tactic_proof": true, "tactics": ["have", "have", "have", "suffices", "rw", "refine", "replace", "rw", "obtain", "rw", "rw", "refine", "rw", "exact", "intro", "rw", "replace", "rw", "rw", "refine", "by_cases", "simp", "exact", "simp", "exact"], "tactic_count": 25}
{"name": "Algebra.discr_eq_discr", "kind": "theorem", "module": "Mathlib.RingTheory.Discriminant", "is_tactic_proof": true, "tactics": ["convert", "rw", "suffices", "rw", "rw", "rw", "exact"], "tactic_count": 7}
{"name": "dividedPowersBot", "kind": "definition", "module": "Mathlib.RingTheory.DividedPowers.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dividedPowersBot_dpow_eq", "kind": "theorem", "module": "Mathlib.RingTheory.DividedPowers.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "instInhabitedDividedPowersBotIdeal", "kind": "instance", "module": "Mathlib.RingTheory.DividedPowers.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCoeFunDividedPowersForallNatForall", "kind": "instance", "module": "Mathlib.RingTheory.DividedPowers.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DividedPowers.ext", "kind": "theorem", "module": "Mathlib.RingTheory.DividedPowers.Basic", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "simp", "grind"], "tactic_count": 4}
{"name": "DividedPowers.coe_injective", "kind": "theorem", "module": "Mathlib.RingTheory.DividedPowers.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DividedPowers.dpow_add'", "kind": "theorem", "module": "Mathlib.RingTheory.DividedPowers.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "DividedPowers.exp", "kind": "definition", "module": "Mathlib.RingTheory.DividedPowers.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DividedPowers.exp_add'", "kind": "theorem", "module": "Mathlib.RingTheory.DividedPowers.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "DividedPowers.exp_add", "kind": "theorem", "module": "Mathlib.RingTheory.DividedPowers.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DividedPowers.dpow_smul", "kind": "theorem", "module": "Mathlib.RingTheory.DividedPowers.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DividedPowers.dpow_mul_right", "kind": "theorem", "module": "Mathlib.RingTheory.DividedPowers.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "DividedPowers.dpow_smul_right", "kind": "theorem", "module": "Mathlib.RingTheory.DividedPowers.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "DividedPowers.factorial_mul_dpow_eq_pow", "kind": "theorem", "module": "Mathlib.RingTheory.DividedPowers.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "nth_rewrite", "rw"], "tactic_count": 6}
{"name": "DividedPowers.dpow_eval_zero", "kind": "theorem", "module": "Mathlib.RingTheory.DividedPowers.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "DividedPowers.nilpotent_of_mem_dpIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.DividedPowers.Basic", "is_tactic_proof": false, "tactics": ["have", "rw", "rw", "exact"], "tactic_count": 4}
{"name": "DividedPowers.coincide_on_smul", "kind": "theorem", "module": "Mathlib.RingTheory.DividedPowers.Basic", "is_tactic_proof": true, "tactics": ["induction", "smul", "hb", "rw", "hI.factorial_mul_dpow_eq_pow", "ring", "add", "hy", "rw", "apply", "intro", "rw"], "tactic_count": 12}
{"name": "DividedPowers.prod_dpow", "kind": "theorem", "module": "Mathlib.RingTheory.DividedPowers.Basic", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "simp", "rw", "insert", "hrec", "rw", "mul_assoc]", "apply", "rw"], "tactic_count": 11}
{"name": "DividedPowers.dpow_sum'", "kind": "theorem", "module": "Mathlib.RingTheory.DividedPowers.Basic", "is_tactic_proof": true, "tactics": ["simp", "induction", "empty", "simp", "by_cases", "rw", "rw", "simp", "rw", "apply", "rw", "exact", "insert", "have", "simp_rw", "sum_sigma',", "apply", "sum_bij", "simp", "simp", "intro", "apply", "intro", "simp", "exact", "intro", "simp", "rw", "apply", "apply", "intro", "apply", "conv_lhs", "exact", "intro", "convert", "rw"], "tactic_count": 37}
{"name": "DividedPowers.dpow_sum", "kind": "theorem", "module": "Mathlib.RingTheory.DividedPowers.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DividedPowers.ofRingEquiv", "kind": "definition", "module": "Mathlib.RingTheory.DividedPowers.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DividedPowers.ofRingEquiv_dpow", "kind": "theorem", "module": "Mathlib.RingTheory.DividedPowers.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DividedPowers.ofRingEquiv_dpow_apply", "kind": "theorem", "module": "Mathlib.RingTheory.DividedPowers.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DividedPowers.equiv", "kind": "definition", "module": "Mathlib.RingTheory.DividedPowers.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DividedPowers.equiv_apply", "kind": "theorem", "module": "Mathlib.RingTheory.DividedPowers.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DividedPowers.equiv_apply'", "kind": "theorem", "module": "Mathlib.RingTheory.DividedPowers.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DividedPowers.isDPMorphism_def", "kind": "theorem", "module": "Mathlib.RingTheory.DividedPowers.DPMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DividedPowers.isDPMorphism_iff", "kind": "theorem", "module": "Mathlib.RingTheory.DividedPowers.DPMorphism", "is_tactic_proof": true, "tactics": ["rw", "refine", "by_cases", "intro", "rw", "exact"], "tactic_count": 6}
{"name": "DividedPowers.IsDPMorphism.map_dpow", "kind": "theorem", "module": "Mathlib.RingTheory.DividedPowers.DPMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DividedPowers.IsDPMorphism.comp", "kind": "theorem", "module": "Mathlib.RingTheory.DividedPowers.DPMorphism", "is_tactic_proof": true, "tactics": ["refine", "simp", "rw", "exact"], "tactic_count": 4}
{"name": "DividedPowers.DPMorphism.instFunLike", "kind": "instance", "module": "Mathlib.RingTheory.DividedPowers.DPMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DividedPowers.DPMorphism.coe_ringHom", "kind": "instance", "module": "Mathlib.RingTheory.DividedPowers.DPMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DividedPowers.DPMorphism.coe_toRingHom", "kind": "theorem", "module": "Mathlib.RingTheory.DividedPowers.DPMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DividedPowers.DPMorphism.toRingHom_apply", "kind": "theorem", "module": "Mathlib.RingTheory.DividedPowers.DPMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DividedPowers.DPMorphism.isDPMorphism", "kind": "theorem", "module": "Mathlib.RingTheory.DividedPowers.DPMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DividedPowers.DPMorphism.mk'", "kind": "definition", "module": "Mathlib.RingTheory.DividedPowers.DPMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DividedPowers.ideal_from_ringHom", "kind": "definition", "module": "Mathlib.RingTheory.DividedPowers.DPMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DividedPowers.DPMorphism.fromGens", "kind": "definition", "module": "Mathlib.RingTheory.DividedPowers.DPMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DividedPowers.DPMorphism.id", "kind": "definition", "module": "Mathlib.RingTheory.DividedPowers.DPMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DividedPowers.DPMorphism.instInhabited", "kind": "instance", "module": "Mathlib.RingTheory.DividedPowers.DPMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DividedPowers.DPMorphism.fromGens_coe", "kind": "theorem", "module": "Mathlib.RingTheory.DividedPowers.DPMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DividedPowers.IsDPMorphism.on_span", "kind": "theorem", "module": "Mathlib.RingTheory.DividedPowers.DPMorphism", "is_tactic_proof": false, "tactics": ["suffices", "exact", "rw", "rintro", "exact"], "tactic_count": 5}
{"name": "DividedPowers.IsDPMorphism.of_comp", "kind": "theorem", "module": "Mathlib.RingTheory.DividedPowers.DPMorphism", "is_tactic_proof": true, "tactics": ["apply", "rintro", "rw", "exact", "rintro", "rw"], "tactic_count": 6}
{"name": "DividedPowers.DPMorphism.comp", "kind": "definition", "module": "Mathlib.RingTheory.DividedPowers.DPMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DividedPowers.DPMorphism.comp_toRingHom", "kind": "theorem", "module": "Mathlib.RingTheory.DividedPowers.DPMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DividedPowers.dpow_comp_from_gens", "kind": "theorem", "module": "Mathlib.RingTheory.DividedPowers.DPMorphism", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DividedPowers.dpow_eq_from_gens", "kind": "theorem", "module": "Mathlib.RingTheory.DividedPowers.DPMorphism", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "refine", "intro", "simp", "exact", "intro", "simpa", "rw"], "tactic_count": 9}
{"name": "DividedPowers.ofInjective", "kind": "definition", "module": "Mathlib.RingTheory.DividedPowers.Padic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.DividedPowers.Padic.0.PadicInt.dpow'", "kind": "definition", "module": "Mathlib.RingTheory.DividedPowers.Padic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.DividedPowers.Padic.0.PadicInt.dpow'_norm_le_of_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.DividedPowers.Padic", "is_tactic_proof": true, "tactics": ["unfold", "by_cases", "rw", "simp", "cast_nonneg]", "have", "have", "simp", "exact", "rw", "simp", "rw", "gcongr", "exact_mod_cast", "simp", "apply", "conv_lhs", "gcongr", "norm_cast", "rwa"], "tactic_count": 20}
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{"name": "DividedPowers.OfInvertibleFactorial.dpow", "kind": "definition", "module": "Mathlib.RingTheory.DividedPowers.RatAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DividedPowers.OfInvertibleFactorial.dpow_eq_of_mem", "kind": "theorem", "module": "Mathlib.RingTheory.DividedPowers.RatAlgebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DividedPowers.OfInvertibleFactorial.dpow_eq_of_not_mem", "kind": "theorem", "module": "Mathlib.RingTheory.DividedPowers.RatAlgebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DividedPowers.OfInvertibleFactorial.dpow_null", "kind": "theorem", "module": "Mathlib.RingTheory.DividedPowers.RatAlgebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DividedPowers.OfInvertibleFactorial.dpow_zero", "kind": "theorem", "module": "Mathlib.RingTheory.DividedPowers.RatAlgebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DividedPowers.OfInvertibleFactorial.dpow_one", "kind": "theorem", "module": "Mathlib.RingTheory.DividedPowers.RatAlgebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "DividedPowers.OfInvertibleFactorial.dpow_add_of_lt", "kind": "theorem", "module": "Mathlib.RingTheory.DividedPowers.RatAlgebra", "is_tactic_proof": true, "tactics": ["rw", "simp", "rw", "apply", "intro", "rw", "ring_nf", "simp", "exact"], "tactic_count": 9}
{"name": "DividedPowers.OfInvertibleFactorial.dpow_add", "kind": "theorem", "module": "Mathlib.RingTheory.DividedPowers.RatAlgebra", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "have", "rw", "simp", "have", "rw", "exact", "rw", "apply", "intro", "rw", "apply", "rw", "apply", "rw", "exact"], "tactic_count": 17}
{"name": "DividedPowers.OfInvertibleFactorial.dpow_mul", "kind": "theorem", "module": "Mathlib.RingTheory.DividedPowers.RatAlgebra", "is_tactic_proof": true, "tactics": ["rw", "mul_assoc]"], "tactic_count": 2}
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{"name": "DividedPowers.OfInvertibleFactorial.dividedPowers", "kind": "definition", "module": "Mathlib.RingTheory.DividedPowers.RatAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DividedPowers.OfInvertibleFactorial.dpow_apply", "kind": "theorem", "module": "Mathlib.RingTheory.DividedPowers.RatAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DividedPowers.OfSquareZero.dividedPowers", "kind": "definition", "module": "Mathlib.RingTheory.DividedPowers.RatAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DividedPowers.OfSquareZero.dpow_of_two_le", "kind": "theorem", "module": "Mathlib.RingTheory.DividedPowers.RatAlgebra", "is_tactic_proof": true, "tactics": ["simp", "intro", "rw"], "tactic_count": 3}
{"name": "DividedPowers.IsNilpotent.dividedPowers", "kind": "definition", "module": "Mathlib.RingTheory.DividedPowers.RatAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DividedPowers.IsNilpotent.dpow_of_prime_le", "kind": "theorem", "module": "Mathlib.RingTheory.DividedPowers.RatAlgebra", "is_tactic_proof": true, "tactics": ["simp", "intro", "rw"], "tactic_count": 3}
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{"name": "DividedPowers.SubDPIdeal.toIdeal", "kind": "definition", "module": "Mathlib.RingTheory.DividedPowers.SubDPIdeal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DividedPowers.SubDPIdeal.instCoeOutIdeal", "kind": "instance", "module": "Mathlib.RingTheory.DividedPowers.SubDPIdeal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "DividedPowers.SubDPIdeal.toIsSubDPIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.DividedPowers.SubDPIdeal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "DividedPowers.SubDPIdeal.instCoeOutElemIdealIic", "kind": "instance", "module": "Mathlib.RingTheory.DividedPowers.SubDPIdeal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DividedPowers.SubDPIdeal.instLE", "kind": "instance", "module": "Mathlib.RingTheory.DividedPowers.SubDPIdeal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DividedPowers.SubDPIdeal.le_iff", "kind": "theorem", "module": "Mathlib.RingTheory.DividedPowers.SubDPIdeal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DividedPowers.SubDPIdeal.instLT", "kind": "instance", "module": "Mathlib.RingTheory.DividedPowers.SubDPIdeal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DividedPowers.SubDPIdeal.lt_iff", "kind": "theorem", "module": "Mathlib.RingTheory.DividedPowers.SubDPIdeal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DividedPowers.SubDPIdeal.instTop", "kind": "instance", "module": "Mathlib.RingTheory.DividedPowers.SubDPIdeal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DividedPowers.SubDPIdeal.inhabited", "kind": "instance", "module": "Mathlib.RingTheory.DividedPowers.SubDPIdeal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "DividedPowers.SubDPIdeal.inf_carrier_def", "kind": "theorem", "module": "Mathlib.RingTheory.DividedPowers.SubDPIdeal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "DividedPowers.SubDPIdeal.sInf_carrier_def", "kind": "theorem", "module": "Mathlib.RingTheory.DividedPowers.SubDPIdeal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "DividedPowers.SubDPIdeal.sup_carrier_def", "kind": "theorem", "module": "Mathlib.RingTheory.DividedPowers.SubDPIdeal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "DividedPowers.SubDPIdeal.sSup_carrier_def", "kind": "theorem", "module": "Mathlib.RingTheory.DividedPowers.SubDPIdeal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "DividedPowers.SubDPIdeal.span", "kind": "definition", "module": "Mathlib.RingTheory.DividedPowers.SubDPIdeal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DividedPowers.dpow_span_isSubideal", "kind": "theorem", "module": "Mathlib.RingTheory.DividedPowers.SubDPIdeal", "is_tactic_proof": true, "tactics": ["rw", "rintro", "exact"], "tactic_count": 3}
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{"name": "DividedPowers.DPMorphism.ker", "kind": "definition", "module": "Mathlib.RingTheory.DividedPowers.SubDPIdeal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DividedPowers.dpEqualizer", "kind": "definition", "module": "Mathlib.RingTheory.DividedPowers.SubDPIdeal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DividedPowers.mem_dpEqualizer_iff", "kind": "theorem", "module": "Mathlib.RingTheory.DividedPowers.SubDPIdeal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DividedPowers.dpEqualizer_is_dp_ideal_left", "kind": "theorem", "module": "Mathlib.RingTheory.DividedPowers.SubDPIdeal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DividedPowers.dpEqualizer_is_dp_ideal_right", "kind": "theorem", "module": "Mathlib.RingTheory.DividedPowers.SubDPIdeal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DividedPowers.le_equalizer_of_isDPMorphism", "kind": "theorem", "module": "Mathlib.RingTheory.DividedPowers.SubDPIdeal", "is_tactic_proof": true, "tactics": ["rw", "rintro", "exact"], "tactic_count": 3}
{"name": "DividedPowers.subDPIdeal_inf_of_quot", "kind": "definition", "module": "Mathlib.RingTheory.DividedPowers.SubDPIdeal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DividedPowers.Quotient.OfSurjective.dpow", "kind": "definition", "module": "Mathlib.RingTheory.DividedPowers.SubDPIdeal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DividedPowers.Quotient.OfSurjective.dpow_apply'", "kind": "theorem", "module": "Mathlib.RingTheory.DividedPowers.SubDPIdeal", "is_tactic_proof": true, "tactics": ["classical", "simp", "have", "rw", "apply", "rw"], "tactic_count": 6}
{"name": "DividedPowers.Quotient.OfSurjective.dividedPowers", "kind": "definition", "module": "Mathlib.RingTheory.DividedPowers.SubDPIdeal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DividedPowers.Quotient.OfSurjective.dpow_def", "kind": "theorem", "module": "Mathlib.RingTheory.DividedPowers.SubDPIdeal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DividedPowers.Quotient.OfSurjective.dpow_apply", "kind": "theorem", "module": "Mathlib.RingTheory.DividedPowers.SubDPIdeal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "DividedPowers.Quotient.OfSurjective.isDPMorphism", "kind": "theorem", "module": "Mathlib.RingTheory.DividedPowers.SubDPIdeal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DividedPowers.Quotient.OfSurjective.dividedPowers_unique", "kind": "theorem", "module": "Mathlib.RingTheory.DividedPowers.SubDPIdeal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DividedPowers.Quotient.dpow", "kind": "definition", "module": "Mathlib.RingTheory.DividedPowers.SubDPIdeal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "DividedPowers.Quotient.dpow_apply", "kind": "theorem", "module": "Mathlib.RingTheory.DividedPowers.SubDPIdeal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DividedPowers.Quotient.isDPMorphism", "kind": "theorem", "module": "Mathlib.RingTheory.DividedPowers.SubDPIdeal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DividedPowers.Quotient.dividedPowers_unique", "kind": "theorem", "module": "Mathlib.RingTheory.DividedPowers.SubDPIdeal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TrivSqZeroExt.isNilpotent_iff_isNilpotent_fst", "kind": "theorem", "module": "Mathlib.RingTheory.DualNumber", "is_tactic_proof": true, "tactics": ["constructor", "refine", "rw", "refine", "rw", "ext", "rw", "rw"], "tactic_count": 8}
{"name": "TrivSqZeroExt.isNilpotent_inl_iff", "kind": "theorem", "module": "Mathlib.RingTheory.DualNumber", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "TrivSqZeroExt.isNilpotent_inr", "kind": "theorem", "module": "Mathlib.RingTheory.DualNumber", "is_tactic_proof": true, "tactics": ["refine"], "tactic_count": 1}
{"name": "TrivSqZeroExt.isUnit_or_isNilpotent_of_isMaximal_isNilpotent", "kind": "theorem", "module": "Mathlib.RingTheory.DualNumber", "is_tactic_proof": true, "tactics": ["rw", "refine", "obtain", "refine", "exact"], "tactic_count": 5}
{"name": "TrivSqZeroExt.isUnit_or_isNilpotent", "kind": "theorem", "module": "Mathlib.RingTheory.DualNumber", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DualNumber.fst_eq_zero_iff_eps_dvd", "kind": "theorem", "module": "Mathlib.RingTheory.DualNumber", "is_tactic_proof": false, "tactics": ["simp_rw", "zero_smul,", "intro", "exact"], "tactic_count": 4}
{"name": "DualNumber.isNilpotent_eps", "kind": "theorem", "module": "Mathlib.RingTheory.DualNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DualNumber.isNilpotent_iff_eps_dvd", "kind": "theorem", "module": "Mathlib.RingTheory.DualNumber", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DualNumber.instIsLocalRing", "kind": "instance", "module": "Mathlib.RingTheory.DualNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DualNumber.ideal_trichotomy", "kind": "theorem", "module": "Mathlib.RingTheory.DualNumber", "is_tactic_proof": true, "tactics": ["refine", "refine", "have", "intro", "rcases", "exact", "rwa", "have", "intro", "obtain", "have", "rw", "have", "contrapose", "simp", "refine", "simp", "refine", "simp_rw", "intro", "simp_rw", "intro", "obtain", "obtain", "obtain", "rw", "exact"], "tactic_count": 27}
{"name": "DualNumber.isMaximal_span_singleton_eps", "kind": "theorem", "module": "Mathlib.RingTheory.DualNumber", "is_tactic_proof": true, "tactics": ["refine", "simp", "rcases", "first", "simp", "simp"], "tactic_count": 6}
{"name": "DualNumber.maximalIdeal_eq_span_singleton_eps", "kind": "theorem", "module": "Mathlib.RingTheory.DualNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DualNumber.instIsPrincipalIdealRing", "kind": "instance", "module": "Mathlib.RingTheory.DualNumber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DualNumber.exists_mul_left_or_mul_right", "kind": "theorem", "module": "Mathlib.RingTheory.DualNumber", "is_tactic_proof": true, "tactics": ["rcases", "lift", "exact", "rcases", "lift", "exact", "rw", "obtain", "obtain", "suffices", "rcases", "refine", "simp", "refine", "simp"], "tactic_count": 15}
{"name": "Algebra.EssFiniteType.finset", "kind": "definition", "module": "Mathlib.RingTheory.EssentialFiniteness", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.EssFiniteType.subalgebra", "kind": "abbrev", "module": "Mathlib.RingTheory.EssentialFiniteness", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.EssFiniteType.adjoin_mem_finset", "kind": "theorem", "module": "Mathlib.RingTheory.EssentialFiniteness", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.instFiniteTypeSubtypeMemSubalgebraSubalgebra", "kind": "instance", "module": "Mathlib.RingTheory.EssentialFiniteness", "is_tactic_proof": true, "tactics": ["constructor", "rw", "exact"], "tactic_count": 3}
{"name": "Algebra.EssFiniteType.submonoid", "kind": "definition", "module": "Mathlib.RingTheory.EssentialFiniteness", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.EssFiniteType.isLocalization", "kind": "instance", "module": "Mathlib.RingTheory.EssentialFiniteness", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.essFiniteType_cond_iff", "kind": "theorem", "module": "Mathlib.RingTheory.EssentialFiniteness", "is_tactic_proof": true, "tactics": ["constructor", "intro", "obtain", "exact", "constructor", "exact", "intro", "obtain", "exact", "intro", "exact"], "tactic_count": 11}
{"name": "Algebra.essFiniteType_iff", "kind": "theorem", "module": "Mathlib.RingTheory.EssentialFiniteness", "is_tactic_proof": true, "tactics": ["simp_rw", "constructor"], "tactic_count": 2}
{"name": "Algebra.EssFiniteType.of_finiteType", "kind": "instance", "module": "Mathlib.RingTheory.EssentialFiniteness", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact"], "tactic_count": 3}
{"name": "Algebra.EssFiniteType.of_isLocalization", "kind": "theorem", "module": "Mathlib.RingTheory.EssentialFiniteness", "is_tactic_proof": true, "tactics": ["rw", "use", "simp", "intro", "obtain", "exact"], "tactic_count": 6}
{"name": "Algebra.EssFiniteType.of_id", "kind": "theorem", "module": "Mathlib.RingTheory.EssentialFiniteness", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.EssFiniteType.aux", "kind": "theorem", "module": "Mathlib.RingTheory.EssentialFiniteness", "is_tactic_proof": true, "tactics": ["refine", "intro", "exact", "intro", "obtain", "refine", "rw", "exact", "rintro", "refine", "rw", "apply", "rintro", "refine", "rw", "exact"], "tactic_count": 16}
{"name": "Algebra.EssFiniteType.comp", "kind": "theorem", "module": "Mathlib.RingTheory.EssentialFiniteness", "is_tactic_proof": true, "tactics": ["rw", "classical", "obtain", "obtain", "use", "simp", "intro", "obtain", "obtain", "obtain", "refine", "rw", "exact", "rw", "exact", "rw", "exact"], "tactic_count": 17}
{"name": "Algebra.essFiniteType_iff_exists_subalgebra", "kind": "theorem", "module": "Mathlib.RingTheory.EssentialFiniteness", "is_tactic_proof": true, "tactics": ["refine", "rintro", "letI", "exact"], "tactic_count": 4}
{"name": "Algebra.EssFiniteType.baseChange", "kind": "instance", "module": "Mathlib.RingTheory.EssentialFiniteness", "is_tactic_proof": true, "tactics": ["classical", "rw", "obtain", "use", "intro", "induction", "zero", "tmul", "obtain", "have", "have", "rw", "apply", "simpa", "refine", "simp", "rw", "apply", "exact", "add", "obtain", "obtain", "refine", "rw", "exact"], "tactic_count": 25}
{"name": "Algebra.EssFiniteType.of_comp", "kind": "theorem", "module": "Mathlib.RingTheory.EssentialFiniteness", "is_tactic_proof": true, "tactics": ["rw", "classical", "obtain", "use", "intro", "obtain", "simp_rw", "exact"], "tactic_count": 8}
{"name": "Algebra.EssFiniteType.comp_iff", "kind": "theorem", "module": "Mathlib.RingTheory.EssentialFiniteness", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.instEssFiniteTypeQuotientIdeal", "kind": "instance", "module": "Mathlib.RingTheory.EssentialFiniteness", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.instEssFiniteTypeLocalization", "kind": "instance", "module": "Mathlib.RingTheory.EssentialFiniteness", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.EssFiniteType.of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.EssentialFiniteness", "is_tactic_proof": true, "tactics": ["let", "have", "have", "exact"], "tactic_count": 4}
{"name": "Algebra.EssFiniteType.iff_of_algEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.EssentialFiniteness", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.EssFiniteType.algHom_ext", "kind": "theorem", "module": "Mathlib.RingTheory.EssentialFiniteness", "is_tactic_proof": true, "tactics": ["suffices", "apply", "suffices", "exact", "apply", "exact", "rintro"], "tactic_count": 7}
{"name": "RingHom.EssFiniteType", "kind": "definition", "module": "Mathlib.RingTheory.EssentialFiniteness", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.essFiniteType_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.EssentialFiniteness", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RingHom.EssFiniteType.finset", "kind": "definition", "module": "Mathlib.RingTheory.EssentialFiniteness", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.FiniteType.essFiniteType", "kind": "theorem", "module": "Mathlib.RingTheory.EssentialFiniteness", "is_tactic_proof": true, "tactics": ["algebraize", "change", "infer_instance"], "tactic_count": 3}
{"name": "RingHom.EssFiniteType.ext", "kind": "theorem", "module": "Mathlib.RingTheory.EssentialFiniteness", "is_tactic_proof": true, "tactics": ["algebraize", "ext", "exact"], "tactic_count": 3}
{"name": "Algebra.FormallyEtale.instFormallyUnramified", "kind": "instance", "module": "Mathlib.RingTheory.Etale.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.FormallyEtale.instFormallySmooth", "kind": "instance", "module": "Mathlib.RingTheory.Etale.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.FormallyEtale.iff_formallyUnramified_and_formallySmooth", "kind": "theorem", "module": "Mathlib.RingTheory.Etale.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.FormallyEtale.of_formallyUnramified_and_formallySmooth", "kind": "theorem", "module": "Mathlib.RingTheory.Etale.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.FormallyEtale.comp_bijective", "kind": "theorem", "module": "Mathlib.RingTheory.Etale.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.FormallyEtale.iff_comp_bijective", "kind": "theorem", "module": "Mathlib.RingTheory.Etale.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.FormallyEtale.of_equiv", "kind": "theorem", "module": "Mathlib.RingTheory.Etale.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.FormallyEtale.iff_of_equiv", "kind": "theorem", "module": "Mathlib.RingTheory.Etale.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.FormallyEtale.comp", "kind": "theorem", "module": "Mathlib.RingTheory.Etale.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.FormallyEtale.of_restrictScalars", "kind": "theorem", "module": "Mathlib.RingTheory.Etale.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.FormallyEtale.iff_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Etale.Basic", "is_tactic_proof": true, "tactics": ["rw", "and_iff_right"], "tactic_count": 2}
{"name": "Algebra.FormallyEtale.instTensorProduct", "kind": "instance", "module": "Mathlib.RingTheory.Etale.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.FormallyEtale.of_isLocalization", "kind": "theorem", "module": "Mathlib.RingTheory.Etale.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.FormallyEtale.instLocalization", "kind": "instance", "module": "Mathlib.RingTheory.Etale.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.FormallyEtale.localization_base", "kind": "theorem", "module": "Mathlib.RingTheory.Etale.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.FormallyEtale.localization_map", "kind": "theorem", "module": "Mathlib.RingTheory.Etale.Basic", "is_tactic_proof": true, "tactics": ["haveI", "haveI", "exact"], "tactic_count": 3}
{"name": "Algebra.Etale.of_equiv", "kind": "theorem", "module": "Mathlib.RingTheory.Etale.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Etale.comp", "kind": "theorem", "module": "Mathlib.RingTheory.Etale.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Etale.baseChange", "kind": "instance", "module": "Mathlib.RingTheory.Etale.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Etale.of_isLocalizationAway", "kind": "theorem", "module": "Mathlib.RingTheory.Etale.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.FormallyEtale", "kind": "definition", "module": "Mathlib.RingTheory.Etale.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.formallyEtale_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.Etale.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Algebra.FormallyEtale.of_isSeparable_aux", "kind": "theorem", "module": "Mathlib.RingTheory.Etale.Field", "is_tactic_proof": true, "tactics": ["have", "have", "refine", "refine", "intro", "let", "obtain", "have", "have", "rw", "obtain", "have", "f", "rw", "obtain", "use", "rw", "use", "apply", "simp", "rw", "eval_map_algebraMap,", "exact", "rw", "apply", "rw"], "tactic_count": 26}
{"name": "Algebra.FormallyEtale.of_isSeparable", "kind": "theorem", "module": "Mathlib.RingTheory.Etale.Field", "is_tactic_proof": true, "tactics": ["refine", "refine", "intro", "have", "intro", "have", "have", "have", "have", "exact", "choose", "have", "intro", "have", "rw", "rintro", "exact", "rw", "rfl", "apply", "rw", "simp", "have", "intro", "have", "apply", "intro", "have", "obtain", "apply_fun", "rw", "simp", "have", "have", "exact", "refine", "change", "intro", "obtain", "simp", "rfl", "change", "intro", "obtain", "simp", "rfl", "intro", "change", "rw", "ext", "simpa"], "tactic_count": 51}
{"name": "Algebra.FormallyEtale.iff_isSeparable", "kind": "theorem", "module": "Mathlib.RingTheory.Etale.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.FormallyEtale.iff_exists_algEquiv_prod", "kind": "theorem", "module": "Mathlib.RingTheory.Etale.Field", "is_tactic_proof": true, "tactics": ["classical", "constructor", "intro", "have", "have", "have", "letI", "let", "let", "have", "rw", "exact", "intro", "rw", "exact"], "tactic_count": 15}
{"name": "Algebra.Etale.iff_exists_algEquiv_prod", "kind": "theorem", "module": "Mathlib.RingTheory.Etale.Field", "is_tactic_proof": true, "tactics": ["constructor", "intro", "obtain", "have", "exact", "inferInstance⟩⟩", "intro", "choose", "have", "refine", "exact"], "tactic_count": 11}
{"name": "KaehlerDifferential.tensorKaehlerEquivOfFormallyEtale", "kind": "definition", "module": "Mathlib.RingTheory.Etale.Kaehler", "is_tactic_proof": false, "tactics": ["refine", "rw", "intro", "obtain", "rw"], "tactic_count": 5}
{"name": "KaehlerDifferential.tensorKaehlerEquivOfFormallyEtale_symm_D_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.Etale.Kaehler", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "KaehlerDifferential.isBaseChange_of_formallyEtale", "kind": "theorem", "module": "Mathlib.RingTheory.Etale.Kaehler", "is_tactic_proof": true, "tactics": ["change", "convert", "change", "congr", "ext", "simp"], "tactic_count": 6}
{"name": "KaehlerDifferential.isLocalizedModule_map", "kind": "instance", "module": "Mathlib.RingTheory.Etale.Kaehler", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "KaehlerDifferential.span_range_map_derivation_of_isLocalization", "kind": "theorem", "module": "Mathlib.RingTheory.Etale.Kaehler", "is_tactic_proof": false, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "Algebra.Extension.tensorCotangentSpace", "kind": "definition", "module": "Mathlib.RingTheory.Etale.Kaehler", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Extension.tensorCotangentInvFun", "kind": "definition", "module": "Mathlib.RingTheory.Etale.Kaehler", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Extension.tensorCotangentInvFun_smul_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Etale.Kaehler", "is_tactic_proof": true, "tactics": ["letI", "haveI", "haveI", "letI", "trans", "simp", "change", "rw", "simp"], "tactic_count": 9}
{"name": "Algebra.Extension.tensorCotangent", "kind": "definition", "module": "Mathlib.RingTheory.Etale.Kaehler", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Extension.tensorH1Cotangent", "kind": "definition", "module": "Mathlib.RingTheory.Etale.Kaehler", "is_tactic_proof": true, "tactics": ["refine", "constructor", "rw", "intro", "apply", "apply", "simp", "rw", "change", "congr", "ext", "simp", "intro", "have", "obtain", "apply", "rw", "have", "ext", "simp", "exact", "refine", "change", "congr", "ext"], "tactic_count": 25}
{"name": "Algebra.tensorH1CotangentOfIsLocalization", "kind": "definition", "module": "Mathlib.RingTheory.Etale.Kaehler", "is_tactic_proof": true, "tactics": ["letI", "letI", "letI", "letI", "intro", "obtain", "obtain", "obtain", "refine", "simp", "rw", "simp)", "letI", "toRingHom_algebraMap", "algebraMap_toRingHom", "haveI", "haveI", "haveI", "haveI", "letI", "letI", "letI", "haveI", "haveI", "haveI", "rw", "convert", "exact", "refine", "exact", "let", "refine", "have", "rw", "ext", "obtain", "simp", "have", "rw", "rfl", "simp", "have", "rw", "exact"], "tactic_count": 44}
{"name": "Algebra.tensorH1CotangentOfIsLocalization_toLinearMap", "kind": "theorem", "module": "Mathlib.RingTheory.Etale.Kaehler", "is_tactic_proof": true, "tactics": ["ext", "simp", "simp", "letI", "letI", "letI", "letI", "intro", "obtain", "obtain", "obtain", "refine", "simp", "rw", "simp)", "letI", "toRingHom_algebraMap", "algebraMap_toRingHom", "have", "ext", "change", "simp", "exact", "rw"], "tactic_count": 24}
{"name": "Algebra.H1Cotangent.isLocalizedModule", "kind": "instance", "module": "Mathlib.RingTheory.Etale.Kaehler", "is_tactic_proof": true, "tactics": ["rw", "change", "rw", "exact"], "tactic_count": 4}
{"name": "Algebra.IsEtaleAt", "kind": "abbrev", "module": "Mathlib.RingTheory.Etale.Locus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.etaleLocus", "kind": "definition", "module": "Mathlib.RingTheory.Etale.Locus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.mem_etaleLocus_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Etale.Locus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsEtaleAt.comp", "kind": "theorem", "module": "Mathlib.RingTheory.Etale.Locus", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "Algebra.etaleLocus_eq_unramfiedLocus_inter_smoothLocus", "kind": "theorem", "module": "Mathlib.RingTheory.Etale.Locus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.etaleLocus_eq_compl_support", "kind": "theorem", "module": "Mathlib.RingTheory.Etale.Locus", "is_tactic_proof": true, "tactics": ["ext", "simp", "have", "have", "exact"], "tactic_count": 5}
{"name": "Algebra.basicOpen_subset_etaleLocus_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Etale.Locus", "is_tactic_proof": false, "tactics": ["rw", "formallyEtale_iff]", "exact", "and_congr"], "tactic_count": 4}
{"name": "Algebra.etaleLocus_eq_univ_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Etale.Locus", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Algebra.isOpen_etaleLocus", "kind": "theorem", "module": "Mathlib.RingTheory.Etale.Locus", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Algebra.basicOpen_subset_etaleLocus_iff_etale", "kind": "theorem", "module": "Mathlib.RingTheory.Etale.Locus", "is_tactic_proof": true, "tactics": ["rw", "refine"], "tactic_count": 2}
{"name": "Algebra.etaleLocus_eq_univ_iff_etale", "kind": "theorem", "module": "Mathlib.RingTheory.Etale.Locus", "is_tactic_proof": true, "tactics": ["rw", "refine"], "tactic_count": 2}
{"name": "Algebra.exists_etale_of_isEtaleAt", "kind": "theorem", "module": "Mathlib.RingTheory.Etale.Locus", "is_tactic_proof": false, "tactics": ["obtain", "isOpen_etaleLocus", "exact"], "tactic_count": 3}
{"name": "Algebra.FormallyEtale.pi_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Etale.Pi", "is_tactic_proof": true, "tactics": ["simp_rw", "rw"], "tactic_count": 2}
{"name": "Algebra.FormallyEtale.instForallOfFinite", "kind": "instance", "module": "Mathlib.RingTheory.Etale.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.fiberIsoOfBijectiveResidueField", "kind": "definition", "module": "Mathlib.RingTheory.Etale.QuasiFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.comap_fiberIsoOfBijectiveResidueField_symm", "kind": "theorem", "module": "Mathlib.RingTheory.Etale.QuasiFinite", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Ideal.comap_fiberIsoOfBijectiveResidueField_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Etale.QuasiFinite", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Ideal.eq_of_comap_eq_comap_of_bijective_residueFieldMap", "kind": "theorem", "module": "Mathlib.RingTheory.Etale.QuasiFinite", "is_tactic_proof": true, "tactics": ["refine", "congr_arg"], "tactic_count": 2}
{"name": "Algebra.exists_etale_isIdempotentElem_forall_liesOver_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Etale.QuasiFinite", "is_tactic_proof": true, "tactics": ["classical", "obtain", "obtain", "f.Monic", "have", "let", "obtain", "exists_eq_pow_rootMultiplicity_mul_and_not_dvd", "have", "set", "refine", "simpa", "obtain", "exists_etale_bijective_residueFieldMap_and_map_eq_mul_and_isCoprime", "hab", "let", "have", "show", "let", "have", "dsimp", "nth_rw", "rw", "simp", "let", "have", "have", "have", "simpa", "show", "rw", "have", "rw", "simp", "have", "intro", "have", "rw", "exact", "refine", "apply", "rw", "contrapose", "have", "hs", "simp", "rw", "simp"], "tactic_count": 48}
{"name": "Localization.exists_finite_awayMapₐ_of_surjective_awayMapₐ", "kind": "theorem", "module": "Mathlib.RingTheory.Etale.QuasiFinite", "is_tactic_proof": false, "tactics": ["have", "obtain", "rintro", "have", "have", "rw", "simp_all", "refine", "have", "simp", "have", "have", "f.toRingHom", "intro", "obtain", "suffices", "simpa", "have", "simpa", "simp", "obtain", "obtain", "have", "simp_rw", "refine", "simp", "convert", "refine", "simp", "algebraize", "have", "refine", "exact"], "tactic_count": 33}
{"name": "StandardEtalePair.Ring", "kind": "definition", "module": "Mathlib.RingTheory.Etale.StandardEtale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StandardEtalePair.X", "kind": "definition", "module": "Mathlib.RingTheory.Etale.StandardEtale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StandardEtalePair.HasMap", "kind": "definition", "module": "Mathlib.RingTheory.Etale.StandardEtale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StandardEtalePair.lift", "kind": "definition", "module": "Mathlib.RingTheory.Etale.StandardEtale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StandardEtalePair.lift_X", "kind": "theorem", "module": "Mathlib.RingTheory.Etale.StandardEtale", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "StandardEtalePair.HasMap.map", "kind": "theorem", "module": "Mathlib.RingTheory.Etale.StandardEtale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StandardEtalePair.HasMap.isUnit_derivative_f", "kind": "theorem", "module": "Mathlib.RingTheory.Etale.StandardEtale", "is_tactic_proof": true, "tactics": ["obtain", "have", "exact"], "tactic_count": 3}
{"name": "StandardEtalePair.aeval_X_g_mul_mk_X", "kind": "theorem", "module": "Mathlib.RingTheory.Etale.StandardEtale", "is_tactic_proof": false, "tactics": ["have", "simp", "rw", "dsimp", "rw", "exact"], "tactic_count": 6}
{"name": "StandardEtalePair.hasMap_X", "kind": "theorem", "module": "Mathlib.RingTheory.Etale.StandardEtale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StandardEtalePair.hom_ext", "kind": "theorem", "module": "Mathlib.RingTheory.Etale.StandardEtale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StandardEtalePair.lift_X_left", "kind": "theorem", "module": "Mathlib.RingTheory.Etale.StandardEtale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StandardEtalePair.inv_aeval_X_g", "kind": "theorem", "module": "Mathlib.RingTheory.Etale.StandardEtale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StandardEtalePair.homEquiv", "kind": "definition", "module": "Mathlib.RingTheory.Etale.StandardEtale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StandardEtalePair.existsUnique_hasMap_of_hasMap_quotient_of_sq_eq_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Etale.StandardEtale", "is_tactic_proof": false, "tactics": ["have", "obtain", "obtain", "simp_rw", "obtain", "apply_fun", "simp", "obtain", "refine", "convert_to", "linear_combination", "exact", "have", "have", "refine", "rw", "rw", "exact", "rintro", "rw", "have", "grind"], "tactic_count": 22}
{"name": "StandardEtalePair.instFormallyEtaleRing", "kind": "instance", "module": "Mathlib.RingTheory.Etale.StandardEtale", "is_tactic_proof": true, "tactics": ["refine", "rw", "suffices", "simpa", "intro", "obtain", "exact"], "tactic_count": 7}
{"name": "StandardEtalePair.instEtaleRing", "kind": "instance", "module": "Mathlib.RingTheory.Etale.StandardEtale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StandardEtalePair.equivPolynomialQuotient", "kind": "definition", "module": "Mathlib.RingTheory.Etale.StandardEtale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StandardEtalePair.equivAwayAdjoinRoot", "kind": "definition", "module": "Mathlib.RingTheory.Etale.StandardEtale", "is_tactic_proof": false, "tactics": ["refine", "rw", "rw", "exact", "change", "simpa", "ext", "ext"], "tactic_count": 8}
{"name": "StandardEtalePair.equivAwayQuotient", "kind": "definition", "module": "Mathlib.RingTheory.Etale.StandardEtale", "is_tactic_proof": false, "tactics": ["refine", "rw", "rw", "exact", "change", "simpa", "change", "simpa", "apply", "ext", "simp", "ext"], "tactic_count": 12}
{"name": "StandardEtalePair.equivMvPolynomialQuotient", "kind": "definition", "module": "Mathlib.RingTheory.Etale.StandardEtale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StandardEtalePair.equivMvPolynomialQuotient_symm_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Etale.StandardEtale", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "StandardEtalePresentation.equivRing", "kind": "definition", "module": "Mathlib.RingTheory.Etale.StandardEtale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StandardEtalePresentation.equivRing_symm_X", "kind": "theorem", "module": "Mathlib.RingTheory.Etale.StandardEtale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StandardEtalePresentation.equivRing_x", "kind": "theorem", "module": "Mathlib.RingTheory.Etale.StandardEtale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StandardEtalePresentation.toPresentation", "kind": "definition", "module": "Mathlib.RingTheory.Etale.StandardEtale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StandardEtalePresentation.aeval_val_equivMvPolynomial", "kind": "theorem", "module": "Mathlib.RingTheory.Etale.StandardEtale", "is_tactic_proof": true, "tactics": ["change", "congr", "ext", "simp"], "tactic_count": 4}
{"name": "StandardEtalePresentation.toSubmersivePresentation", "kind": "definition", "module": "Mathlib.RingTheory.Etale.StandardEtale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StandardEtalePresentation.toSubmersivePresentation_jacobian", "kind": "theorem", "module": "Mathlib.RingTheory.Etale.StandardEtale", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "StandardEtalePresentation.exists_mul_aeval_x_g_pow_eq_aeval_x", "kind": "theorem", "module": "Mathlib.RingTheory.Etale.StandardEtale", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "obtain", "refine", "simpa", "congr"], "tactic_count": 6}
{"name": "StandardEtalePresentation.mapEquiv", "kind": "definition", "module": "Mathlib.RingTheory.Etale.StandardEtale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.instIsStandardEtaleRing", "kind": "instance", "module": "Mathlib.RingTheory.Etale.StandardEtale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.instEtaleOfIsStandardEtale", "kind": "instance", "module": "Mathlib.RingTheory.Etale.StandardEtale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsStandardEtale.of_equiv", "kind": "theorem", "module": "Mathlib.RingTheory.Etale.StandardEtale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.instIsStandardEtale", "kind": "instance", "module": "Mathlib.RingTheory.Etale.StandardEtale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsStandardEtale.of_isLocalizationAway", "kind": "theorem", "module": "Mathlib.RingTheory.Etale.StandardEtale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsStandardEtale.of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Etale.StandardEtale", "is_tactic_proof": true, "tactics": ["letI", "have", "obtain", "have", "exact"], "tactic_count": 5}
{"name": "left_div_gcd_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.EuclideanDomain", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "nth_rw", "rw", "exact"], "tactic_count": 5}
{"name": "right_div_gcd_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.EuclideanDomain", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "nth_rw", "rw", "exact"], "tactic_count": 5}
{"name": "isCoprime_div_gcd_div_gcd", "kind": "theorem", "module": "Mathlib.RingTheory.EuclideanDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCoprime_div_gcd_div_gcd_of_gcd_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.EuclideanDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanDomain.gcdMonoid", "kind": "definition", "module": "Mathlib.RingTheory.EuclideanDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanDomain.span_gcd", "kind": "theorem", "module": "Mathlib.RingTheory.EuclideanDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanDomain.gcd_isUnit_iff", "kind": "theorem", "module": "Mathlib.RingTheory.EuclideanDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanDomain.isCoprime_of_dvd", "kind": "theorem", "module": "Mathlib.RingTheory.EuclideanDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanDomain.dvd_or_coprime", "kind": "theorem", "module": "Mathlib.RingTheory.EuclideanDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Extension.instRingOfIsScalarTower", "kind": "instance", "module": "Mathlib.RingTheory.Extension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Extension.instIsScalarTowerRing", "kind": "instance", "module": "Mathlib.RingTheory.Extension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Extension.instIsScalarTowerRing_1", "kind": "instance", "module": "Mathlib.RingTheory.Extension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Extension.instIsScalarTowerRing_2", "kind": "instance", "module": "Mathlib.RingTheory.Extension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Extension.σ_smul", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Algebra.Extension.σ_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Basic", "is_tactic_proof": true, "tactics": ["intro", "rw"], "tactic_count": 2}
{"name": "Algebra.Extension.algebraMap_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Extension.ofSurjective", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Extension.self", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Extension.ker", "kind": "abbrev", "module": "Mathlib.RingTheory.Extension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Extension.localization", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Extension.baseChange", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Extension.Hom.toAlgHom", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Extension.Hom.toAlgHom_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Extension.Hom.id", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Extension.Hom.toAlgHom_id", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Basic", "is_tactic_proof": true, "tactics": ["ext1"], "tactic_count": 1}
{"name": "Algebra.Extension.Hom.comp", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Extension.Hom.comp_id", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Algebra.Extension.Hom.id_comp", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Algebra.Extension.Hom.mapKer", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Extension.infinitesimal", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Extension.toInfinitesimal", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Extension.ker_infinitesimal", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Extension.Cotangent", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Extension.instAddCommGroupCotangent", "kind": "instance", "module": "Mathlib.RingTheory.Extension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Extension.Cotangent.of", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Extension.Cotangent.val", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Extension.Cotangent.ext", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Extension.Cotangent.val_add", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Extension.Cotangent.val_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Extension.Cotangent.of_add", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Extension.Cotangent.of_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Extension.Cotangent.of_val", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Extension.Cotangent.val_of", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Extension.Cotangent.val_sub", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Extension.Cotangent.smul_eq_zero_of_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Extension.Cotangent.module", "kind": "instance", "module": "Mathlib.RingTheory.Extension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Extension.instModuleCotangent", "kind": "instance", "module": "Mathlib.RingTheory.Extension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Extension.instIsScalarTowerCotangent", "kind": "instance", "module": "Mathlib.RingTheory.Extension.Basic", "is_tactic_proof": true, "tactics": ["constructor", "intro", "change", "rw"], "tactic_count": 4}
{"name": "Algebra.Extension.Cotangent.val_smul'''", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Extension.Cotangent.val_smul", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Extension.Cotangent.val_smul'", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Algebra.Extension.Cotangent.val_smul''", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Algebra.Extension.Cotangent.mk", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Extension.Cotangent.val_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Extension.Cotangent.mk_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Extension.Cotangent.mk_eq_zero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Algebra.Extension.Cotangent.mk_eq_mk_iff_sub_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Algebra.Extension.Cotangent.ker_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Algebra.Extension.Cotangent.span_eq_top_of_span_eq_ker", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply", "rw", "simp"], "tactic_count": 4}
{"name": "Algebra.Extension.Cotangent.map", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Extension.Cotangent.map_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Extension.Cotangent.map_id", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Basic", "is_tactic_proof": true, "tactics": ["ext", "obtain", "simp"], "tactic_count": 3}
{"name": "Algebra.Extension.Cotangent.map_comp", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Basic", "is_tactic_proof": true, "tactics": ["ext", "obtain", "simp"], "tactic_count": 3}
{"name": "Algebra.Extension.Cotangent.finite", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "Algebra.Extension.cotangentEquiv", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Extension.contangentEquiv_tmul", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Extension.CotangentSpace", "kind": "abbrev", "module": "Mathlib.RingTheory.Extension.Cotangent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Extension.cotangentComplex", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Cotangent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Extension.cotangentComplex_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Cotangent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "KaehlerDifferential.cotangentComplexBaseChange", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Cotangent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "KaehlerDifferential.cotangentComplexBaseChange_tmul", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Cotangent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Extension.cotangentComplexBaseChange_eq_lTensor_cotangentComplex", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Cotangent.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Algebra.Extension.lTensor_cotangentComplex_eq_cotangentComplexBaseChange", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Cotangent.Basic", "is_tactic_proof": true, "tactics": ["apply", "dsimp", "rw", "exact"], "tactic_count": 4}
{"name": "Algebra.Extension.CotangentSpace.map", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Cotangent.Basic", "is_tactic_proof": true, "tactics": ["letI", "haveI", "letI", "haveI", "apply", "refine"], "tactic_count": 6}
{"name": "Algebra.Extension.CotangentSpace.map_tmul", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Cotangent.Basic", "is_tactic_proof": false, "tactics": ["simp", "rw", "rfl"], "tactic_count": 3}
{"name": "Algebra.Extension.CotangentSpace.map_id", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Cotangent.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Algebra.Extension.CotangentSpace.map_comp", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Cotangent.Basic", "is_tactic_proof": true, "tactics": ["ext", "induction", "zero", "add", "tmul", "obtain", "induction", "zero", "add", "tmul", "simp"], "tactic_count": 11}
{"name": "Algebra.Extension.CotangentSpace.map_comp_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Cotangent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Extension.CotangentSpace.map_cotangentComplex", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Cotangent.Basic", "is_tactic_proof": true, "tactics": ["obtain", "rw"], "tactic_count": 2}
{"name": "Algebra.Extension.CotangentSpace.map_comp_cotangentComplex", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Cotangent.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Algebra.Extension.Hom.sub_aux", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Cotangent.Basic", "is_tactic_proof": true, "tactics": ["letI", "have", "rw", "refine", "simp", "algebraMap_toRingHom,", "convert", "simp", "ring"], "tactic_count": 9}
{"name": "Algebra.Extension.Hom.subToKer", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Cotangent.Basic", "is_tactic_proof": true, "tactics": ["refine", "intro", "simp", "map_sub,"], "tactic_count": 4}
{"name": "Algebra.Extension.Hom.sub", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Cotangent.Basic", "is_tactic_proof": true, "tactics": ["letI", "haveI", "letI", "haveI", "haveI", "show", "rw", "refine", "refine", "map_one_eq_zero", "leibniz", "ext", "simp", "intro", "ext", "simp", "exact"], "tactic_count": 17}
{"name": "Algebra.Extension.Hom.sub_one_tmul", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Cotangent.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Algebra.Extension.Hom.sub_tmul", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Cotangent.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Algebra.Extension.CotangentSpace.map_sub_map", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Cotangent.Basic", "is_tactic_proof": true, "tactics": ["ext", "induction", "zero", "add", "tmul", "obtain", "induction", "zero", "add", "tmul", "simp", "tmul_sub,"], "tactic_count": 12}
{"name": "Algebra.Extension.Cotangent.map_sub_map", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Cotangent.Basic", "is_tactic_proof": true, "tactics": ["ext", "obtain", "simp", "one_smul,", "apply", "ext", "simp"], "tactic_count": 7}
{"name": "Algebra.Extension.toKaehler", "kind": "abbrev", "module": "Mathlib.RingTheory.Extension.Cotangent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Extension.toKaehler_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Cotangent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Extension.exact_cotangentComplex_toKaehler", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Cotangent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Extension.H1Cotangent", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Cotangent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Extension.instAddCommGroupH1Cotangent", "kind": "instance", "module": "Mathlib.RingTheory.Extension.Cotangent.Basic", "is_tactic_proof": true, "tactics": ["delta"], "tactic_count": 1}
{"name": "Algebra.Extension.instModuleH1CotangentOfIsScalarTowerCotangent", "kind": "instance", "module": "Mathlib.RingTheory.Extension.Cotangent.Basic", "is_tactic_proof": true, "tactics": ["delta"], "tactic_count": 1}
{"name": "Algebra.Extension.H1Cotangent.val_add", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Cotangent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Extension.H1Cotangent.val_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Cotangent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Extension.H1Cotangent.val_smul", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Cotangent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Extension.instIsScalarTowerH1CotangentOfCotangent", "kind": "instance", "module": "Mathlib.RingTheory.Extension.Cotangent.Basic", "is_tactic_proof": true, "tactics": ["delta"], "tactic_count": 1}
{"name": "Algebra.Extension.subsingleton_h1Cotangent", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Cotangent.Basic", "is_tactic_proof": true, "tactics": ["delta", "rw", "simp"], "tactic_count": 3}
{"name": "Algebra.Extension.h1Cotangentι", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Cotangent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Extension.h1Cotangentι_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Cotangent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Extension.h1Cotangentι_ext", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Cotangent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Extension.H1Cotangent.map", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Cotangent.Basic", "is_tactic_proof": false, "tactics": ["refine", "simp", "apply_fun", "rw", "rw", "exact"], "tactic_count": 6}
{"name": "Algebra.Extension.H1Cotangent.map_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Cotangent.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp", "rw", "simp"], "tactic_count": 4}
{"name": "Algebra.Extension.H1Cotangent.map_id", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Cotangent.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Algebra.Extension.H1Cotangent.map_comp", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Cotangent.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Algebra.Extension.H1Cotangent.equiv", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Cotangent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.cotangentSpaceBasis", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Cotangent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.cotangentSpaceBasis_repr_tmul", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Cotangent.Basic", "is_tactic_proof": true, "tactics": ["classical", "simp", "mul_comm"], "tactic_count": 3}
{"name": "Algebra.Generators.cotangentSpaceBasis_repr_one_tmul", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Cotangent.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Algebra.Generators.cotangentSpaceBasis_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Cotangent.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Algebra.Generators.instFreeCotangentSpaceToExtension", "kind": "instance", "module": "Mathlib.RingTheory.Extension.Cotangent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.cotangentRestrict", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Cotangent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.cotangentRestrict_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Cotangent.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp", "simp"], "tactic_count": 3}
{"name": "Algebra.Generators.repr_CotangentSpaceMap", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Cotangent.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp", "rw", "erw"], "tactic_count": 4}
{"name": "Algebra.Generators.toKaehler_tmul_D", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Cotangent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.toKaehler_cotangentSpaceBasis", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Cotangent.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Algebra.instFinitePresentationKaehlerDifferentialOfFinitePresentation", "kind": "instance", "module": "Mathlib.RingTheory.Extension.Cotangent.Basic", "is_tactic_proof": true, "tactics": ["let", "have", "refine", "rw", "exact"], "tactic_count": 5}
{"name": "Algebra.Generators.H1Cotangent.equiv", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Cotangent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.H1Cotangent", "kind": "abbrev", "module": "Mathlib.RingTheory.Extension.Cotangent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.H1Cotangent.map", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Cotangent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.H1Cotangent.mapEquiv", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Cotangent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.equivH1Cotangent", "kind": "abbrev", "module": "Mathlib.RingTheory.Extension.Cotangent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.instFiniteH1CotangentOfFinitePresentationOfProjectiveKaehlerDifferential", "kind": "instance", "module": "Mathlib.RingTheory.Extension.Cotangent.Basic", "is_tactic_proof": true, "tactics": ["let", "have", "suffices", "rw", "have", "have", "rw", "exact", "exact"], "tactic_count": 9}
{"name": "Algebra.Generators.PresentationOfFreeCotangent.Aux.T", "kind": "abbrev", "module": "Mathlib.RingTheory.Extension.Cotangent.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.PresentationOfFreeCotangent.Aux.hom", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Cotangent.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.PresentationOfFreeCotangent.Aux.instT", "kind": "instance", "module": "Mathlib.RingTheory.Extension.Cotangent.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.PresentationOfFreeCotangent.Aux.instNontrivialT", "kind": "instance", "module": "Mathlib.RingTheory.Extension.Cotangent.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.PresentationOfFreeCotangent.Aux.instIsScalarTowerRingT", "kind": "instance", "module": "Mathlib.RingTheory.Extension.Cotangent.Basis", "is_tactic_proof": true, "tactics": ["refine", "obtain", "obtain", "simp", "rfl"], "tactic_count": 5}
{"name": "Algebra.Generators.PresentationOfFreeCotangent.Aux.gbar", "kind": "abbrev", "module": "Mathlib.RingTheory.Extension.Cotangent.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.PresentationOfFreeCotangent.Aux.instAwayTGbar", "kind": "instance", "module": "Mathlib.RingTheory.Extension.Cotangent.Basis", "is_tactic_proof": true, "tactics": ["refine", "refine", "convert", "ext", "exact", "simp", "suffices", "rw", "exact"], "tactic_count": 9}
{"name": "Algebra.Generators.PresentationOfFreeCotangent.Aux.presLeft", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Cotangent.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.PresentationOfFreeCotangent.Aux.kerGen", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Cotangent.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.PresentationOfFreeCotangent.Aux.fhom", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Cotangent.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.PresentationOfFreeCotangent.Aux.toAlgHom_fhom", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Cotangent.Basis", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Algebra.Generators.PresentationOfFreeCotangent.Aux.ker_presLeft_le", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Cotangent.Basis", "is_tactic_proof": true, "tactics": ["intro", "simpa"], "tactic_count": 2}
{"name": "Algebra.Generators.PresentationOfFreeCotangent.Aux.tensorCotangentHom", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Cotangent.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.PresentationOfFreeCotangent.Aux.tensorCotangentHom_tmul", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Cotangent.Basis", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Algebra.Generators.PresentationOfFreeCotangent.Aux.tensorCotangentInv", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Cotangent.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.PresentationOfFreeCotangent.Aux.tensorCotangentInv_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Cotangent.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.PresentationOfFreeCotangent.Aux.span_range_mk_kerGen", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Cotangent.Basis", "is_tactic_proof": true, "tactics": ["refine", "dsimp", "exact"], "tactic_count": 3}
{"name": "Algebra.Generators.PresentationOfFreeCotangent.Aux.tensorCotangentEquiv", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Cotangent.Basis", "is_tactic_proof": true, "tactics": ["refine", "refine", "simpa", "ext", "refine", "simp"], "tactic_count": 6}
{"name": "Algebra.Generators.PresentationOfFreeCotangent.Aux.tensorCotangentEquiv_symm_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Cotangent.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.PresentationOfFreeCotangent.Aux.presRight", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Cotangent.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.PresentationOfFreeCotangent.Aux.pres", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Cotangent.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.PresentationOfFreeCotangent.Aux.map_ofComp_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Cotangent.Basis", "is_tactic_proof": true, "tactics": ["simp_rw", "congr", "have", "dsimp", "rw", "exact", "rw", "rw", "simp"], "tactic_count": 9}
{"name": "Algebra.Generators.PresentationOfFreeCotangent.Aux.cotangentEquivProd", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Cotangent.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.PresentationOfFreeCotangent.Aux.cotangentEquivProd_symm_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Cotangent.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.PresentationOfFreeCotangent.Aux.basisLeft", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Cotangent.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.PresentationOfFreeCotangent.Aux.basisRight", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Cotangent.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.PresentationOfFreeCotangent.Aux.basis", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Cotangent.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.PresentationOfFreeCotangent.Aux.basis_inl", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Cotangent.Basis", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Algebra.Generators.PresentationOfFreeCotangent.Aux.basis_inr", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Cotangent.Basis", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Algebra.Generators.PresentationOfFreeCotangent.Aux.pres_val_comp_inr", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Cotangent.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.PresentationOfFreeCotangent.Aux.basis_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Cotangent.Basis", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact", "rw", "rfl"], "tactic_count": 5}
{"name": "Algebra.Generators.exists_presentation_of_basis_cotangent", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Cotangent.Basis", "is_tactic_proof": true, "tactics": ["cases", "let", "relation", "span_range_relation_eq_ker", "have", "exact", "classical", "choose", "let", "let", "have", "rw", "apply", "convert", "simp", "have", "suffices", "obtain", "let", "exact", "rw", "simp", "rw", "dsimp", "simp", "refine", "rw", "convert", "exact"], "tactic_count": 29}
{"name": "Algebra.Generators.exists_presentation_of_free_cotangent", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Cotangent.Basis", "is_tactic_proof": true, "tactics": ["cases", "let", "relation", "span_range_relation_eq_ker", "have", "exact", "have", "exact"], "tactic_count": 8}
{"name": "Algebra.Generators.cotangentRestrict_bijective_of_isCompl", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Cotangent.Free", "is_tactic_proof": true, "tactics": ["rw", "set", "let", "have", "simp", "exact", "apply", "exact", "simp", "apply", "rw", "simpa", "exact", "simpa"], "tactic_count": 14}
{"name": "Algebra.Generators.disjoint_ker_toKaehler_of_linearIndependent", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Cotangent.Free", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "obtain", "simp", "obtain", "simp"], "tactic_count": 7}
{"name": "Algebra.Generators.cotangentRestrict_bijective_of_basis_kaehlerDifferential", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Cotangent.Free", "is_tactic_proof": true, "tactics": ["refine", "simp_rw", "exact", "apply", "simp_rw", "exact"], "tactic_count": 6}
{"name": "Algebra.PreSubmersivePresentation.isUnit_jacobian_of_cotangentRestrict_bijective", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Cotangent.Free", "is_tactic_proof": false, "tactics": ["have", "ext", "simp", "apply", "rw", "exact", "rw"], "tactic_count": 7}
{"name": "Algebra.Generators.comp_localizationAway_ker", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Cotangent.LocalizationAway", "is_tactic_proof": false, "tactics": ["have", "rw", "toAlgHom_ofComp_rename,", "rw", "simp"], "tactic_count": 5}
{"name": "Algebra.Generators.compLocalizationAwayAlgHom", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Cotangent.LocalizationAway", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.compLocalizationAwayAlgHom_toAlgHom_toComp", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Cotangent.LocalizationAway", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Algebra.Generators.compLocalizationAwayAlgHom_X_inl", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Cotangent.LocalizationAway", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Algebra.Generators.compLocalizationAwayAlgHom_relation_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Cotangent.LocalizationAway", "is_tactic_proof": true, "tactics": ["rw", "change", "rw", "simp"], "tactic_count": 4}
{"name": "Algebra.Generators.sq_ker_comp_le_ker_compLocalizationAwayAlgHom", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Cotangent.LocalizationAway", "is_tactic_proof": false, "tactics": ["have", "obtain", "rw", "rw", "apply", "apply", "rw", "intro", "simp", "rw", "rw", "intro", "simp", "apply", "rw", "intro", "simp"], "tactic_count": 17}
{"name": "Algebra.Generators.liftBaseChange_injective_of_isLocalizationAway", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Cotangent.LocalizationAway", "is_tactic_proof": true, "tactics": ["set", "algebraize", "let", "let", "refine", "obtain", "suffices", "rw", "obtain", "rw", "use", "dsimp", "rw", "simp", "rw", "simpa", "rw", "apply", "simpa"], "tactic_count": 19}
{"name": "Algebra.Generators.cotangentCompAwaySec", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Cotangent.LocalizationAway", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.cotangentCompAwaySec_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Cotangent.LocalizationAway", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Algebra.Generators.map_comp_cotangentCompAwaySec", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Cotangent.LocalizationAway", "is_tactic_proof": true, "tactics": ["refine", "simpa"], "tactic_count": 2}
{"name": "Algebra.Generators.cotangentCompLocalizationAwayEquiv", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Cotangent.LocalizationAway", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.cotangentCompLocalizationAwayEquiv_symm_inr", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Cotangent.LocalizationAway", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Algebra.Generators.cotangentCompLocalizationAwayEquiv_symm_comp_inl", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Cotangent.LocalizationAway", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.cotangentCompLocalizationAwayEquiv_symm_inl", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Cotangent.LocalizationAway", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Algebra.Generators.snd_comp_cotangentCompLocalizationAwayEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Cotangent.LocalizationAway", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.snd_cotangentCompLocalizationAwayEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Cotangent.LocalizationAway", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Algebra.Generators.Ring", "kind": "abbrev", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.instRing", "kind": "instance", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.σ", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.Simps.σ", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.aeval_val_σ", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.instIsScalarTowerRing", "kind": "instance", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.algebraMap_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Algebra.Generators.σ_smul", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Algebra.Generators.σ_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": true, "tactics": ["intro", "rw"], "tactic_count": 2}
{"name": "Algebra.Generators.aeval_val_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.algebraMap_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.ofSurjective", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.ofSurjectiveAlgebraMap", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.id", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.ofAlgHom", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.ofSet", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": true, "tactics": ["refine", "rwa"], "tactic_count": 2}
{"name": "Algebra.Generators.self", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.toExtension", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.ofAlgEquiv", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.ofAlgEquiv_val", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.localizationAway", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.comp", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.extendScalars", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.baseChange", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": true, "tactics": ["apply", "intro", "induction", "zero", "tmul", "let", "use", "simp", "have", "intro", "induction", "rw", "add", "mul_X", "rw", "add", "obtain", "obtain", "use", "rw"], "tactic_count": 20}
{"name": "Algebra.Generators.extend", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.extend_val_inl", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.extend_val_inr", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.reindex", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.reindex_val", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.naive_σ", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.finiteType", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.FiniteType.iff_exists_generators", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact"], "tactic_count": 3}
{"name": "Algebra.Generators.Hom.toAlgHom", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.Hom.algebraMap_toAlgHom", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": false, "tactics": ["suffices", "from", "apply", "intro", "simp"], "tactic_count": 5}
{"name": "Algebra.Generators.Hom.algebraMap_toAlgHom'", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.Hom.toAlgHom_X", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.Hom.toAlgHom_C", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.Hom.toAlgHom_monomial", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Algebra.Generators.Hom.equivAlgHom", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.defaultHom", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.instInhabitedHom", "kind": "instance", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.Hom.id", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.Hom.toAlgHom_id", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": true, "tactics": ["ext1"], "tactic_count": 1}
{"name": "Algebra.Generators.Hom.comp", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.Hom.comp_id", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Algebra.Generators.Hom.id_comp", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Algebra.Generators.Hom.toAlgHom_comp_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": true, "tactics": ["induction", "add", "mul_X"], "tactic_count": 3}
{"name": "Algebra.Generators.toComp", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.toComp_toAlgHom", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.ofComp", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.ofComp_toAlgHom_monomial_sumElim", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": true, "tactics": ["rw", "simp", "rw", "simp", "nth_rw"], "tactic_count": 5}
{"name": "Algebra.Generators.toComp_toAlgHom_monomial", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": true, "tactics": ["convert", "ext"], "tactic_count": 2}
{"name": "Algebra.Generators.toAlgHom_ofComp_rename", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.toAlgHom_ofComp_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": true, "tactics": ["intro", "induction", "use", "simp", "simp_rw", "simp", "add", "obtain", "obtain", "use", "simp", "mul_X", "obtain", "use", "simp"], "tactic_count": 15}
{"name": "Algebra.Generators.toExtendScalars", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.Hom.toExtensionHom", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.Hom.toExtensionHom_id", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Algebra.Generators.Hom.toExtensionHom_comp", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Algebra.Generators.Hom.toExtensionHom_toAlgHom_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.ker", "kind": "abbrev", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.ker_eq_ker_aeval_val", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": true, "tactics": ["simp", "rfl"], "tactic_count": 2}
{"name": "Algebra.Generators.aeval_val_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Algebra.Generators.ker_naive", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.ker_ofAlgHom", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": true, "tactics": ["change", "congr", "exact"], "tactic_count": 3}
{"name": "Algebra.Generators.ker_ofAlgEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Algebra.Generators.map_toComp_ker", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": true, "tactics": ["letI", "apply", "rw", "rintro", "have", "simp", "rw", "rintro", "let", "suffices", "simpa", "rw", "refine", "convert_to", "monomial", "rw", "refine", "obtain", "obtain", "clear", "have", "monomial", "toComp_toAlgHom_monomial", "simp", "rw", "apply", "refine", "simp", "rw", "clear", "have", "rw", "intro", "obtain", "simp_all", "rw", "induction", "monomial", "rw", "obtain", "conv_rhs", "simp", "classical", "simp", "rw", "simp", "split", "simp", "congr", "add", "simp", "rw", "refine", "convert", "refine", "convert"], "tactic_count": 56}
{"name": "Algebra.Generators.kerCompPreimage", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": true, "tactics": ["refine", "refine", "exacts", "simp", "conv_rhs", "simp", "map_one,", "congr", "simp_rw"], "tactic_count": 9}
{"name": "Algebra.Generators.ofComp_kerCompPreimage", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": true, "tactics": ["conv_rhs", "rw", "refine", "simp", "rw", "rw", "simp", "congr", "rw", "simp"], "tactic_count": 10}
{"name": "Algebra.Generators.map_ofComp_ker", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": true, "tactics": ["ext", "rw", "constructor", "rintro", "simp", "rw", "intro", "exact"], "tactic_count": 8}
{"name": "Algebra.Generators.ker_comp_eq_sup", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": true, "tactics": ["rw", "rw", "apply", "simp", "intro", "simp", "rw", "rw"], "tactic_count": 8}
{"name": "Algebra.Generators.toAlgHom_ofComp_localizationAway", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Generators", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Algebra.Presentation.aeval_val_relation", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Presentation.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Algebra.Presentation.relation_mem_ker", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Presentation.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply", "use"], "tactic_count": 3}
{"name": "Algebra.Presentation.Quotient", "kind": "abbrev", "module": "Mathlib.RingTheory.Extension.Presentation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Presentation.quotientEquiv", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Presentation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Presentation.quotientEquiv_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Presentation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Presentation.quotientEquiv_symm", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Presentation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Presentation.dimension", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Presentation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Presentation.fg_ker", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Presentation.Basic", "is_tactic_proof": true, "tactics": ["use", "simp"], "tactic_count": 2}
{"name": "Algebra.Presentation.instFinitePresentationQuotientOfFinite", "kind": "instance", "module": "Mathlib.RingTheory.Extension.Presentation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Presentation.finitePresentation_of_isFinite", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Presentation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Presentation.exists_presentation_fin", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Presentation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Presentation.ofFinitePresentationVars", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Presentation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Presentation.ofFinitePresentationRels", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Presentation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Presentation.ofFinitePresentation", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Presentation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Presentation.ofAlgEquiv", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Presentation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Presentation.dimension_ofAlgEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Presentation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Presentation.ofBijectiveAlgebraMap", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Presentation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Presentation.ofBijectiveAlgebraMap_dimension", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Presentation.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Algebra.Presentation.id", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Presentation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Presentation.id_dimension", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Presentation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.ker_localizationAway", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Presentation.Basic", "is_tactic_proof": false, "tactics": ["have", "aeval", "ext", "simp", "rw", "rw", "simp", "change", "simp"], "tactic_count": 9}
{"name": "Algebra.Presentation.localizationAway", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Presentation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Presentation.localizationAway_dimension_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Presentation.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Algebra.Generators.C_mul_X_sub_one_mem_ker", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Presentation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Extension.Presentation.Basic.0.Algebra.Presentation.span_range_relation_eq_ker_baseChange", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Presentation.Basic", "is_tactic_proof": true, "tactics": ["apply", "rw", "intro", "have", "apply_fun", "rw", "simp", "erw", "change", "rw", "rfl", "intro", "rw", "have", "let", "have", "rw", "clear", "induction", "simp", "rw", "simp", "add", "mul_X", "rw", "replace", "rw", "convert", "simp"], "tactic_count": 29}
{"name": "Algebra.Presentation.baseChange", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Presentation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Presentation.baseChange_toGenerators", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Presentation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Algebra.Presentation.comp_relation_inr", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Presentation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Presentation.comp_aeval_relation_inl", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Presentation.Basic", "is_tactic_proof": true, "tactics": ["change", "simp"], "tactic_count": 2}
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{"name": "Algebra.Presentation.naive_relation", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Presentation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Algebra.Generators.fg_ker_of_finitePresentation", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Presentation.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
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{"name": "Algebra.Presentation.coeffs_relation_subset_coeffs", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Presentation.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Algebra.Presentation.instCommRingCore", "kind": "instance", "module": "Mathlib.RingTheory.Extension.Presentation.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Presentation.instCore", "kind": "instance", "module": "Mathlib.RingTheory.Extension.Presentation.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Presentation.instFaithfulSMulCore", "kind": "instance", "module": "Mathlib.RingTheory.Extension.Presentation.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Presentation.instCore_1", "kind": "instance", "module": "Mathlib.RingTheory.Extension.Presentation.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Presentation.instIsScalarTowerCore", "kind": "instance", "module": "Mathlib.RingTheory.Extension.Presentation.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Presentation.instFiniteTypeIntCoreOfFinite", "kind": "instance", "module": "Mathlib.RingTheory.Extension.Presentation.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Presentation.instHasCoeffsCore", "kind": "instance", "module": "Mathlib.RingTheory.Extension.Presentation.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Algebra.Presentation.HasCoeffs.of_isScalarTower", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Presentation.Core", "is_tactic_proof": true, "tactics": ["refine", "simp"], "tactic_count": 2}
{"name": "Algebra.Presentation.instHasCoeffsSubtypeMemSubalgebraAdjoin", "kind": "instance", "module": "Mathlib.RingTheory.Extension.Presentation.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Presentation.HasCoeffs.coeffs_relation_mem_range", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Presentation.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Presentation.HasCoeffs.relation_mem_range_map", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Presentation.Core", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Algebra.Presentation.relationOfHasCoeffs", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Presentation.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Presentation.map_relationOfHasCoeffs", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Presentation.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Algebra.Presentation.algebraTensorAlgEquiv_symm_relation", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Presentation.Core", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Algebra.Presentation.ModelOfHasCoeffs", "kind": "abbrev", "module": "Mathlib.RingTheory.Extension.Presentation.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Presentation.instFinitePresentationModelOfHasCoeffsOfFinite", "kind": "instance", "module": "Mathlib.RingTheory.Extension.Presentation.Core", "is_tactic_proof": true, "tactics": ["classical", "cases", "exact"], "tactic_count": 3}
{"name": "Algebra.Presentation.tensorModelOfHasCoeffsHom", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Presentation.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Presentation.tensorModelOfHasCoeffsHom_tmul", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Presentation.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Algebra.Presentation.tensorModelOfHasCoeffsInv_aeval_val", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Presentation.Core", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
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{"name": "Algebra.SubmersivePresentation.jacobianRelations_spec", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Presentation.Core", "is_tactic_proof": true, "tactics": ["delta", "convert"], "tactic_count": 2}
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{"name": "Algebra.SubmersivePresentation.finite_coeffs", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Presentation.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Algebra.SubmersivePresentation.jacobianOfHasCoeffs", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Presentation.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Algebra.SubmersivePresentation.invJacobianOfHasCoeffs", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Presentation.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.SubmersivePresentation.map_invJacobianOfHasCoeffs", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Presentation.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Algebra.PreSubmersivePresentation.differential", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Presentation.Submersive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.PreSubmersivePresentation.aevalDifferential", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Presentation.Submersive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.PreSubmersivePresentation.aevalDifferential_single", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Presentation.Submersive", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "Algebra.PreSubmersivePresentation.jacobian", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Presentation.Submersive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.PreSubmersivePresentation.jacobiMatrix", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Presentation.Submersive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.PreSubmersivePresentation.jacobian_eq_jacobiMatrix_det", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Presentation.Submersive", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Algebra.PreSubmersivePresentation.jacobiMatrix_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Presentation.Submersive", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Algebra.PreSubmersivePresentation.aevalDifferential_toMatrix'_eq_mapMatrix_jacobiMatrix", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Presentation.Submersive", "is_tactic_proof": true, "tactics": ["ext", "rw", "rw", "simp"], "tactic_count": 4}
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{"name": "Algebra.PreSubmersivePresentation.isUnit_jacobian_iff_aevalDifferential_bijective", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Presentation.Submersive", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Algebra.PreSubmersivePresentation.isUnit_jacobian_of_linearIndependent_of_span_eq_top", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Presentation.Submersive", "is_tactic_proof": true, "tactics": ["classical", "rw", "exact"], "tactic_count": 3}
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{"name": "Algebra.PreSubmersivePresentation.jacobiMatrix_ofAlgEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Presentation.Submersive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Algebra.PreSubmersivePresentation.ofBijectiveAlgebraMap_jacobian", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Presentation.Submersive", "is_tactic_proof": true, "tactics": ["classical", "have", "ext", "contradiction", "rw"], "tactic_count": 5}
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{"name": "Algebra.PreSubmersivePresentation.localizationAway_jacobiMatrix", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Presentation.Submersive", "is_tactic_proof": true, "tactics": ["have", "ext", "rwa"], "tactic_count": 3}
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{"name": "Algebra.PreSubmersivePresentation.toPresentation_comp", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Presentation.Submersive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.PreSubmersivePresentation.toGenerators_comp", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Presentation.Submersive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.PreSubmersivePresentation.dimension_comp_eq_dimension_add_dimension", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Presentation.Submersive", "is_tactic_proof": true, "tactics": ["simp", "have", "have", "simp", "lia"], "tactic_count": 5}
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{"name": "Algebra.SubmersivePresentation.aevalDifferentialEquiv", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Presentation.Submersive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.SubmersivePresentation.aevalDifferentialEquiv_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Extension.Presentation.Submersive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.SubmersivePresentation.basisDeriv", "kind": "definition", "module": "Mathlib.RingTheory.Extension.Presentation.Submersive", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "IsFiltration.F_lt_le_F", "kind": "theorem", "module": "Mathlib.RingTheory.FilteredAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Ideal.Filtration.instTop", "kind": "instance", "module": "Mathlib.RingTheory.Filtration", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "IsFiniteLength", "kind": "inductive", "module": "Mathlib.RingTheory.FiniteLength", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Matrix.isNilpotent_transpose_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Finiteness.Nilpotent", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
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{"name": "Matrix.isNilpotent_iff_forall_row", "kind": "theorem", "module": "Mathlib.RingTheory.Finiteness.Nilpotent", "is_tactic_proof": true, "tactics": ["rw", "refine", "obtain", "exact", "choose", "suffices", "exact"], "tactic_count": 7}
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{"name": "module_finite_of_liesOver", "kind": "instance", "module": "Mathlib.RingTheory.Finiteness.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "isNoetherian_of_liesOver", "kind": "instance", "module": "Mathlib.RingTheory.Finiteness.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientMapQuotient.isNoetherian", "kind": "instance", "module": "Mathlib.RingTheory.Finiteness.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Submodule.instSemilatticeSupSubtypeSmallMem", "kind": "instance", "module": "Mathlib.RingTheory.Finiteness.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.instInhabitedSubtypeSmallMem", "kind": "instance", "module": "Mathlib.RingTheory.Finiteness.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.small_iSup", "kind": "instance", "module": "Mathlib.RingTheory.Finiteness.Small", "is_tactic_proof": true, "tactics": ["classical", "rw", "apply"], "tactic_count": 3}
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{"name": "Submodule.small_span_singleton", "kind": "instance", "module": "Mathlib.RingTheory.Finiteness.Small", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.small_span", "kind": "theorem", "module": "Mathlib.RingTheory.Finiteness.Small", "is_tactic_proof": false, "tactics": ["suffices", "rw", "apply", "simp"], "tactic_count": 4}
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{"name": "Algebra.FiniteType.small", "kind": "theorem", "module": "Mathlib.RingTheory.Finiteness.Small", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "Subalgebra.fg_bot_toSubmodule", "kind": "theorem", "module": "Mathlib.RingTheory.Finiteness.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.finite_bot", "kind": "instance", "module": "Mathlib.RingTheory.Finiteness.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.fg_unit", "kind": "theorem", "module": "Mathlib.RingTheory.Finiteness.Subalgebra", "is_tactic_proof": true, "tactics": ["obtain", "refine", "rw", "conv_rhs", "grw"], "tactic_count": 5}
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{"name": "Submodule.FG.mul", "kind": "theorem", "module": "Mathlib.RingTheory.Finiteness.Subalgebra", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submodule.FG.pow", "kind": "theorem", "module": "Mathlib.RingTheory.Finiteness.Subalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.univ_of_card_le_two", "kind": "theorem", "module": "Mathlib.RingTheory.Fintype", "is_tactic_proof": true, "tactics": ["rcases", "exact", "refine", "convert", "simp"], "tactic_count": 5}
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{"name": "natCard_units_lt", "kind": "theorem", "module": "Mathlib.RingTheory.Fintype", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "orderOf_lt_card", "kind": "theorem", "module": "Mathlib.RingTheory.Fintype", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "exact", "rw", "exact"], "tactic_count": 5}
{"name": "ZMod.orderOf_lt", "kind": "theorem", "module": "Mathlib.RingTheory.Fintype", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.rTensor_injective_of_fg", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.rTensor_injective_iff_subtype", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.Basic", "is_tactic_proof": false, "tactics": ["simp_rw", "rTensor_comp]", "rfl"], "tactic_count": 3}
{"name": "Module.Flat.rTensor_preserves_injective_linearMap", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "have", "let", "have", "rw", "exact"], "tactic_count": 7}
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{"name": "Module.Flat.iff_rTensor_preserves_injective_linearMapₛ", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Flat.iff_lTensor_preserves_injective_linearMapₛ", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Module.Flat.iff_rTensor_injectiveₛ", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Flat.iff_lTensor_injectiveₛ", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
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{"name": "Module.Flat.self", "kind": "instance", "module": "Mathlib.RingTheory.Flat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Flat.of_retract", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "refine", "simp"], "tactic_count": 5}
{"name": "Module.Flat.of_linearEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Flat.equiv_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Flat.ulift", "kind": "instance", "module": "Mathlib.RingTheory.Flat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Flat.of_ulift", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Flat.shrink", "kind": "instance", "module": "Mathlib.RingTheory.Flat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Flat.of_shrink", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Module.Flat.dfinsupp_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Flat.directSum", "kind": "instance", "module": "Mathlib.RingTheory.Flat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Module.Flat.instTensorProduct", "kind": "instance", "module": "Mathlib.RingTheory.Flat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Flat._example", "kind": "example", "module": "Mathlib.RingTheory.Flat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Flat.linearIndependent_one_tmul", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.Basic", "is_tactic_proof": true, "tactics": ["classical", "simpa"], "tactic_count": 2}
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{"name": "Algebra.TensorProduct.includeLeft_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.Basic", "is_tactic_proof": false, "tactics": ["convert", "ext"], "tactic_count": 2}
{"name": "Algebra.TensorProduct.includeRight_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.Basic", "is_tactic_proof": false, "tactics": ["convert", "ext"], "tactic_count": 2}
{"name": "TensorProduct.nontrivial_of_linearMap_injective_of_flat_left", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.nontrivial_of_linearMap_injective_of_flat_right", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.map_injective_of_flat_flat", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "TensorProduct.map_injective_of_flat_flat'", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
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{"name": "Module.Flat.tensorProduct_mapIncl_injective_of_right", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Flat.tensorProduct_mapIncl_injective_of_left", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "IsSMulRegular.of_flat", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsReduced.tensorProduct_of_flat_of_forall_fg", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.Basic", "is_tactic_proof": true, "tactics": ["by_contra", "obtain", "obtain", "have", "obtain", "have", "simp_rw", "exact", "tauto"], "tactic_count": 9}
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{"name": "Module.Flat.iff_preservesFiniteLimits_tensorLeft", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.CategoryTheory", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
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{"name": "Module.Flat.eqLocus_lTensor_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.Equalizer", "is_tactic_proof": true, "tactics": ["rw", "rw"], "tactic_count": 2}
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{"name": "LinearMap.tensorKerBil", "kind": "definition", "module": "Mathlib.RingTheory.Flat.Equalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.tensorEqLocus", "kind": "definition", "module": "Mathlib.RingTheory.Flat.Equalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.tensorKer", "kind": "definition", "module": "Mathlib.RingTheory.Flat.Equalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.tensorKer_tmul", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.Equalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.tensorKer_coe", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.Equalizer", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "LinearMap.tensorEqLocus_tmul", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.Equalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.tensorEqLocus_coe", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.Equalizer", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "_private.Mathlib.RingTheory.Flat.Equalizer.0.LinearMap.tensorKerInv", "kind": "definition", "module": "Mathlib.RingTheory.Flat.Equalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Flat.Equalizer.0.LinearMap.lTensor_ker_subtype_tensorKerInv", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.Equalizer", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "_private.Mathlib.RingTheory.Flat.Equalizer.0.LinearMap.tensorEqLocusInv", "kind": "definition", "module": "Mathlib.RingTheory.Flat.Equalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Flat.Equalizer.0.LinearMap.lTensor_eqLocus_subtype_tensorEqLocusInv", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.Equalizer", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "LinearMap.tensorKerEquiv", "kind": "definition", "module": "Mathlib.RingTheory.Flat.Equalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.tensorKerEquiv_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.Equalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.lTensor_ker_subtype_tensorKerEquiv_symm", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.Equalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.tensorEqLocusEquiv", "kind": "definition", "module": "Mathlib.RingTheory.Flat.Equalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.tensorEqLocusEquiv_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.Equalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.lTensor_eqLocus_subtype_tensoreqLocusEquiv_symm", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.Equalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.lTensor_injective_of_exact_of_flat", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.Equalizer", "is_tactic_proof": true, "tactics": ["and", "to", "let", "let", "have", "let", "have", "rw", "simpa"], "tactic_count": 9}
{"name": "LinearMap.kerLTensorEquivOfSurjective", "kind": "definition", "module": "Mathlib.RingTheory.Flat.Equalizer", "is_tactic_proof": false, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "LinearMap.tensorKerEquivOfSurjective_symm_tmul", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.Equalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Flat.Equalizer.0.AlgHom.tensorEqualizerAux", "kind": "definition", "module": "Mathlib.RingTheory.Flat.Equalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Flat.Equalizer.0.instAddHomClassAlgHom", "kind": "instance", "module": "Mathlib.RingTheory.Flat.Equalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Flat.Equalizer.0.AlgHom.coe_tensorEqualizerAux", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.Equalizer", "is_tactic_proof": true, "tactics": ["induction", "zero", "tmul", "add"], "tactic_count": 4}
{"name": "_private.Mathlib.RingTheory.Flat.Equalizer.0.AlgHom.tensorEqualizerAux_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.Equalizer", "is_tactic_proof": true, "tactics": ["apply", "rw", "simp"], "tactic_count": 3}
{"name": "AlgHom.tensorEqualizer", "kind": "definition", "module": "Mathlib.RingTheory.Flat.Equalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.coe_tensorEqualizer", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.Equalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.tensorEqualizerEquiv", "kind": "definition", "module": "Mathlib.RingTheory.Flat.Equalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.tensorEqualizerEquiv_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.Equalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.kerTensorProductMapIdToAlgHomEquiv", "kind": "definition", "module": "Mathlib.RingTheory.Flat.Equalizer", "is_tactic_proof": true, "tactics": ["let", "let", "let", "let", "e₃", "let", "map_smul", "x", "dsimp", "induction", "zero", "add", "tmul", "induction", "zero", "add", "tmul", "induction", "zero", "add", "tmul", "rw", "ext1", "dsimp", "change", "rw", "exact"], "tactic_count": 27}
{"name": "Algebra.kerTensorProductMapIdToAlgHomEquiv_symm_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.Equalizer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.IsTrivialRelation", "kind": "abbrev", "module": "Mathlib.RingTheory.Flat.EquationalCriterion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.isTrivialRelation_iff_vanishesTrivially", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.EquationalCriterion", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Equiv.isTrivialRelation_comp", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.EquationalCriterion", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Module.sum_smul_eq_zero_of_isTrivialRelation", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.EquationalCriterion", "is_tactic_proof": true, "tactics": ["simpa", "congr_arg", "sum_tmul_eq_zero_of_vanishesTrivially"], "tactic_count": 3}
{"name": "Module.Flat.tfae_equational_criterion", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.EquationalCriterion", "is_tactic_proof": true, "tactics": ["classical", "tfae_have", "tfae_have", "tfae_have", "tfae_have", "h₄,", "let", "let", "have", "calc", "obtain", "use", "use", "use", "constructor", "apply", "intro", "simpa", "ext", "simp", "exact", "tfae_have", "h₅,", "let", "let", "have", "obtain", "refine", "simpa", "simp_rw", "smul_eq_mul,", "simpa", "tfae_finish"], "tactic_count": 33}
{"name": "Module.Flat.iff_forall_isTrivialRelation", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.EquationalCriterion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Flat.isTrivialRelation_of_sum_smul_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.EquationalCriterion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Flat.of_forall_isTrivialRelation", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.EquationalCriterion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Flat.iff_forall_exists_factorization", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.EquationalCriterion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Flat.of_forall_exists_factorization", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.EquationalCriterion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Flat.exists_factorization_of_apply_eq_zero_of_free", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.EquationalCriterion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Flat.EquationalCriterion.0.Module.Flat.exists_factorization_of_comp_eq_zero_of_free_aux", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.EquationalCriterion", "is_tactic_proof": false, "tactics": ["have", "x", "revert", "apply", "intro", "have", "simpa", "intro", "obtain", "have", "obtain", "use", "simp_rw", "exact", "convert", "simp"], "tactic_count": 16}
{"name": "Module.Flat.exists_factorization_of_comp_eq_zero_of_free", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.EquationalCriterion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Flat.exists_factorization_of_isFinitelyPresented", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.EquationalCriterion", "is_tactic_proof": true, "tactics": ["have", "haveI", "have", "simp_rw", "obtain", "use", "apply", "apply", "simpa"], "tactic_count": 9}
{"name": "Module.Flat.projective_of_finitePresentation", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.EquationalCriterion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.FaithfullyFlat.of_comap_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.FaithfullyFlat.Algebra", "is_tactic_proof": true, "tactics": ["refine", "obtain", "have", "rw", "exact", "m'.isPrime.ne_top"], "tactic_count": 6}
{"name": "Module.FaithfullyFlat.of_flat_of_isLocalHom", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.FaithfullyFlat.Algebra", "is_tactic_proof": true, "tactics": ["refine", "rw", "by_contra", "have", "rw", "exact"], "tactic_count": 6}
{"name": "Module.FaithfullyFlat.tensorProduct_mk_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.FaithfullyFlat.Algebra", "is_tactic_proof": true, "tactics": ["rw", "have", "apply", "intro", "simp", "rw", "exact"], "tactic_count": 7}
{"name": "Module.FaithfullyFlat.faithfulSMul", "kind": "instance", "module": "Mathlib.RingTheory.Flat.FaithfullyFlat.Algebra", "is_tactic_proof": true, "tactics": ["constructor", "intro", "apply", "simp", "rw", "simp"], "tactic_count": 6}
{"name": "Ideal.comap_map_eq_self_of_faithfullyFlat", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.FaithfullyFlat.Algebra", "is_tactic_proof": true, "tactics": ["refine", "have", "rw", "exact", "intro", "rw", "rw", "apply", "have", "simp", "simp"], "tactic_count": 11}
{"name": "Ideal.comap_surjective_of_faithfullyFlat", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.FaithfullyFlat.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.exists_isPrime_liesOver_of_faithfullyFlat", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.FaithfullyFlat.Algebra", "is_tactic_proof": false, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "PrimeSpectrum.comap_surjective_of_faithfullyFlat", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.FaithfullyFlat.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.FaithfullyFlat.self", "kind": "instance", "module": "Mathlib.RingTheory.Flat.FaithfullyFlat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.FaithfullyFlat.iff_flat_and_proper_ideal", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.FaithfullyFlat.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "obtain", "exact"], "tactic_count": 4}
{"name": "Module.FaithfullyFlat.iff_flat_and_ideal_smul_eq_top", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.FaithfullyFlat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.FaithfullyFlat.rTensor_nontrivial", "kind": "instance", "module": "Mathlib.RingTheory.Flat.FaithfullyFlat.Basic", "is_tactic_proof": true, "tactics": ["obtain", "let", "by_cases", "rw", "contradiction", "let", "simpa", "have", "eq_bot_iff.2", "intro", "induction", "h", "simpa", "have", "refine", "rw", "exact"], "tactic_count": 17}
{"name": "Module.FaithfullyFlat.lTensor_nontrivial", "kind": "instance", "module": "Mathlib.RingTheory.Flat.FaithfullyFlat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.FaithfullyFlat.rTensor_reflects_triviality", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.FaithfullyFlat.Basic", "is_tactic_proof": true, "tactics": ["revert", "intro", "infer_instance"], "tactic_count": 3}
{"name": "Module.FaithfullyFlat.lTensor_reflects_triviality", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.FaithfullyFlat.Basic", "is_tactic_proof": true, "tactics": ["haveI", "apply"], "tactic_count": 2}
{"name": "Module.FaithfullyFlat.iff_flat_and_rTensor_faithful", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.FaithfullyFlat.Basic", "is_tactic_proof": true, "tactics": ["refine", "intro", "specialize", "haveI", "have", "refine", "rwa"], "tactic_count": 7}
{"name": "Module.FaithfullyFlat.iff_flat_and_rTensor_reflects_triviality", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.FaithfullyFlat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.FaithfullyFlat.iff_flat_and_lTensor_faithful", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.FaithfullyFlat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.FaithfullyFlat.iff_flat_and_lTensor_reflects_triviality", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.FaithfullyFlat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.FaithfullyFlat.of_linearEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.FaithfullyFlat.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Module.FaithfullyFlat.directSum", "kind": "instance", "module": "Mathlib.RingTheory.Flat.FaithfullyFlat.Basic", "is_tactic_proof": true, "tactics": ["classical", "rw", "refine", "obtain", "obtain", "haveI", "apply"], "tactic_count": 7}
{"name": "Module.FaithfullyFlat.finsupp", "kind": "instance", "module": "Mathlib.RingTheory.Flat.FaithfullyFlat.Basic", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Module.FaithfullyFlat.instOfNontrivialOfFree", "kind": "instance", "module": "Mathlib.RingTheory.Flat.FaithfullyFlat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.FaithfullyFlat.subsingleton_tensorProduct_iff_right", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.FaithfullyFlat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.FaithfullyFlat.subsingleton_tensorProduct_iff_left", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.FaithfullyFlat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.FaithfullyFlat.nontrivial_tensorProduct_iff_right", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.FaithfullyFlat.Basic", "is_tactic_proof": true, "tactics": ["contrapose"], "tactic_count": 1}
{"name": "Module.FaithfullyFlat.nontrivial_tensorProduct_iff_left", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.FaithfullyFlat.Basic", "is_tactic_proof": true, "tactics": ["contrapose"], "tactic_count": 1}
{"name": "Module.FaithfullyFlat.range_le_ker_of_exact_rTensor", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.FaithfullyFlat.Basic", "is_tactic_proof": true, "tactics": ["rintro", "rw", "by_contra", "let", "have", "have", "ex.apply_apply_eq_zero", "have", "ext", "simp", "have", "rw", "obtain", "choose", "let", "have", "refine", "show", "rw", "have", "subsingleton_iff_forall_eq", "show", "eq0", "exact"], "tactic_count": 24}
{"name": "Module.FaithfullyFlat.rTensor_reflects_exact", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.FaithfullyFlat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.FaithfullyFlat.lTensor_reflects_exact", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.FaithfullyFlat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.FaithfullyFlat.rTensor_exact_iff_exact", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.FaithfullyFlat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.FaithfullyFlat.lTensor_exact_iff_exact", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.FaithfullyFlat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.FaithfullyFlat.lTensor_injective_iff_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.FaithfullyFlat.Basic", "is_tactic_proof": true, "tactics": ["rw", "conv_rhs", "simp"], "tactic_count": 3}
{"name": "Module.FaithfullyFlat.lTensor_surjective_iff_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.FaithfullyFlat.Basic", "is_tactic_proof": true, "tactics": ["rw", "conv_rhs", "simp"], "tactic_count": 3}
{"name": "Module.FaithfullyFlat.lTensor_bijective_iff_bijective", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.FaithfullyFlat.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Module.FaithfullyFlat.iff_exact_iff_rTensor_exact", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.FaithfullyFlat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.FaithfullyFlat.iff_exact_iff_lTensor_exact", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.FaithfullyFlat.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Module.FaithfullyFlat.zero_iff_lTensor_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.FaithfullyFlat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.FaithfullyFlat.zero_iff_rTensor_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.FaithfullyFlat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.FaithfullyFlat.one_tmul_eq_zero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.FaithfullyFlat.Basic", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "intro", "let", "suffices", "rw", "ext", "apply_fun", "rw", "simpa"], "tactic_count": 10}
{"name": "Module.FaithfullyFlat.iff_zero_iff_lTensor_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.FaithfullyFlat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.FaithfullyFlat.iff_zero_iff_rTensor_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.FaithfullyFlat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.FaithfullyFlat.trans", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.FaithfullyFlat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.FaithfullyFlat.instTensorProduct", "kind": "instance", "module": "Mathlib.RingTheory.Flat.FaithfullyFlat.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "let", "have", "have", "exact"], "tactic_count": 6}
{"name": "IsBaseChange.map_smul_top_ne_top_iff_of_faithfullyFlat", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.FaithfullyFlat.Basic", "is_tactic_proof": true, "tactics": ["simpa", "not_congr", "subsingleton_tensorProduct_iff_right"], "tactic_count": 3}
{"name": "Module.Flat.of_flat_tensorProduct", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.FaithfullyFlat.Basic", "is_tactic_proof": true, "tactics": ["rw", "intro", "have", "rw", "have", "ext", "simp", "simpa"], "tactic_count": 8}
{"name": "Module.Flat.iff_flat_tensorProduct", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.FaithfullyFlat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.FaithfullyFlat.injective_of_tensorProduct", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.FaithfullyFlat.Descent", "is_tactic_proof": false, "tactics": ["have", "apply", "simpa"], "tactic_count": 3}
{"name": "Module.FaithfullyFlat.surjective_of_tensorProduct", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.FaithfullyFlat.Descent", "is_tactic_proof": false, "tactics": ["have", "apply", "simpa"], "tactic_count": 3}
{"name": "Module.FaithfullyFlat.bijective_of_tensorProduct", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.FaithfullyFlat.Descent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.FaithfullyFlat.codescendsAlong_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.FaithfullyFlat.Descent", "is_tactic_proof": true, "tactics": ["apply", "introv", "rw", "exact"], "tactic_count": 4}
{"name": "RingHom.FaithfullyFlat.codescendsAlong_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.FaithfullyFlat.Descent", "is_tactic_proof": true, "tactics": ["apply", "introv", "rw", "exact"], "tactic_count": 4}
{"name": "RingHom.FaithfullyFlat.codescendsAlong_bijective", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.FaithfullyFlat.Descent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.flat", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.Localization", "is_tactic_proof": true, "tactics": ["refine", "have", "let", "have", "simp", "simpa"], "tactic_count": 6}
{"name": "Localization.flat", "kind": "instance", "module": "Mathlib.RingTheory.Flat.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.flat_iff_of_isLocalization", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.flat_of_isLocalized_maximal", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.Localization", "is_tactic_proof": true, "tactics": ["simp_rw", "simp_rw", "refine", "injective_of_isLocalized_maximal", "simpa"], "tactic_count": 5}
{"name": "Module.flat_of_localized_maximal", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.flat_of_isLocalized_span", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.Localization", "is_tactic_proof": true, "tactics": ["simp_rw", "simp_rw", "refine", "injective_of_isLocalized_span", "simpa"], "tactic_count": 5}
{"name": "Module.flat_of_localized_span", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFlatAtPrime", "kind": "instance", "module": "Mathlib.RingTheory.Flat.Localization", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsSMulRegular.of_isLocalizedModule", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSMulRegular.of_isLocalization", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Flat.trans", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.Stability", "is_tactic_proof": true, "tactics": ["rw", "introv", "rw", "iterate", "exact"], "tactic_count": 5}
{"name": "Module.Flat.baseChange", "kind": "instance", "module": "Mathlib.RingTheory.Flat.Stability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Flat.isBaseChange", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.Stability", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Flat.localizedModule", "kind": "instance", "module": "Mathlib.RingTheory.Flat.Stability", "is_tactic_proof": true, "tactics": ["apply", "rw", "exact"], "tactic_count": 3}
{"name": "Module.Flat.of_isLocalizedModule", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.Stability", "is_tactic_proof": true, "tactics": ["fapply", "exact"], "tactic_count": 2}
{"name": "Module.Flat.injective_characterModule_iff_rTensor_preserves_injective_linearMap", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.Tensor", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Module.Flat.iff_characterModule_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.Tensor", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Module.Flat.iff_characterModule_baer", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.Tensor", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Module.Flat.iff_rTensor_injective'", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.Tensor", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Module.Flat.iff_lTensor_injective'", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.Tensor", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Module.Flat.iff_rTensor_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.Tensor", "is_tactic_proof": false, "tactics": ["refine", "obtain", "rw", "rw"], "tactic_count": 4}
{"name": "Module.Flat.iff_lTensor_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.Tensor", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Module.Flat.iff_lift_lsmul_comp_subtype_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.Tensor", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Module.Flat.isSMulRegular_of_isRegular", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.TorsionFree", "is_tactic_proof": true, "tactics": ["have", "have", "simp", "rw", "simp"], "tactic_count": 5}
{"name": "Module.Flat.isSMulRegular_of_nonZeroDivisors", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.TorsionFree", "is_tactic_proof": true, "tactics": ["apply", "exact"], "tactic_count": 2}
{"name": "Module.Flat.torsion_eq_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.TorsionFree", "is_tactic_proof": false, "tactics": ["rw", "rintro", "exact"], "tactic_count": 3}
{"name": "Module.Flat.flat_iff_torsion_eq_bot_of_isBezout", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.TorsionFree", "is_tactic_proof": true, "tactics": ["refine", "intro", "rw", "rintro", "obtain", "rintro", "apply", "have", "have", "apply", "rw", "rw", "refine", "rw", "convert", "ext", "simp"], "tactic_count": 17}
{"name": "Module.Flat.flat_iff_torsion_eq_bot_of_valuationRing_localization_isMaximal", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.TorsionFree", "is_tactic_proof": true, "tactics": ["refine", "apply", "intro", "rw", "rw", "infer_instance"], "tactic_count": 6}
{"name": "IsDedekindDomain.flat_iff_torsion_eq_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Flat.TorsionFree", "is_tactic_proof": true, "tactics": ["apply", "exact"], "tactic_count": 2}
{"name": "Module.Flat.instOfIsDedekindDomainOfIsTorsionFree", "kind": "instance", "module": "Mathlib.RingTheory.Flat.TorsionFree", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "IsFractional", "kind": "definition", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal", "kind": "definition", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.coeToSubmodule", "kind": "definition", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.instCoeOutSubmodule", "kind": "instance", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.isFractional", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.den", "kind": "definition", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.num", "kind": "definition", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.den_mul_self_eq_num", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "rintro", "exact"], "tactic_count": 4}
{"name": "FractionalIdeal.equivNumOfIsSMulRegular", "kind": "abbrev", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": ["refine", "rw", "exact", "simpa", "rw", "obtain", "exact"], "tactic_count": 7}
{"name": "FractionalIdeal.equivNum", "kind": "definition", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.equivNumOfIsLocalization", "kind": "definition", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.instSetLike", "kind": "instance", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.instPartialOrder", "kind": "instance", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.mem_coe", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.coe_ext", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.coe_ext_iff", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.ext", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.equivNum_apply", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": true, "tactics": ["change", "rw"], "tactic_count": 2}
{"name": "FractionalIdeal.copy", "kind": "definition", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.coe_copy", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.coe_eq", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.zero_mem", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.val_eq_coe", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.coe_mk", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.coeToSet_coeToSubmodule", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.instModuleSubtypeMemSubmoduleCoeToSubmodule", "kind": "instance", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.coeToSubmodule_injective", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.coeToSubmodule_inj", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.isFractional_of_le_one", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": true, "tactics": ["use", "intro", "rw", "obtain", "exact"], "tactic_count": 5}
{"name": "FractionalIdeal.isFractional_of_le", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": true, "tactics": ["obtain", "use", "intro", "exact"], "tactic_count": 4}
{"name": "FractionalIdeal.coeIdeal", "kind": "definition", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.instCoeTCIdeal", "kind": "instance", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.coe_coeIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.mem_coeIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.mem_coeSubmodule", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.mem_coeIdeal_of_mem", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.coeIdeal_le_coeIdeal'", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.coeIdeal_le_coeIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.instZero", "kind": "instance", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.mem_zero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.coe_zero", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.coeIdeal_bot", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.exists_mem_algebraMap_eq", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.coeIdeal_injective'", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.coeIdeal_inj'", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.coeIdeal_eq_zero'", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.coeIdeal_ne_zero'", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.coeToSubmodule_eq_bot", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.coeToSubmodule_ne_bot", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.instInhabited", "kind": "instance", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.instOne", "kind": "instance", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.zero_of_num_eq_bot", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": true, "tactics": ["rw", "intro", "suffices", "have", "exact"], "tactic_count": 5}
{"name": "FractionalIdeal.num_zero_eq", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "FractionalIdeal.coeIdeal_top", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.mem_one_iff", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.coe_mem_one", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FractionalIdeal.one_mem_one", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.coe_one_eq_coeSubmodule_top", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.coe_one", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "FractionalIdeal.coe_le_coe", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.zero_le", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": true, "tactics": ["intro", "convert", "rw"], "tactic_count": 3}
{"name": "FractionalIdeal.orderBot", "kind": "instance", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.bot_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.le_zero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.eq_zero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractional.sup", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractional.inf_right", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.instMin", "kind": "instance", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.coe_inf", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.instMax", "kind": "instance", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.coe_sup", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.lattice", "kind": "instance", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.instSemilatticeSup", "kind": "instance", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.instAdd", "kind": "instance", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.sup_eq_add", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.coe_add", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.mem_add", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "FractionalIdeal.coeIdeal_inf", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": true, "tactics": ["apply", "exact"], "tactic_count": 2}
{"name": "FractionalIdeal.coeIdeal_sup", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractional.nsmul", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.instSMulNat", "kind": "instance", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.coe_nsmul", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractional.mul", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractional.pow", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.definition._@.Mathlib.RingTheory.FractionalIdeal.Basic.1107666208._hygCtx._hyg.2", "kind": "definition", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.wrapped._@.Mathlib.RingTheory.FractionalIdeal.Basic.1107666208._hygCtx._hyg.2", "kind": "opaque", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.mul", "kind": "definition", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.mul_def'", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": true, "tactics": ["intros", "delta", "rw", "rfl"], "tactic_count": 4}
{"name": "FractionalIdeal.instMul", "kind": "instance", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.mul_eq_mul", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.mul_def", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FractionalIdeal.coe_mul", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FractionalIdeal.coeIdeal_mul", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "FractionalIdeal.instMulLeftMono", "kind": "instance", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.instMulRightMono", "kind": "instance", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.mul_left_mono", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.mul_right_mono", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.mul_mem_mul", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "FractionalIdeal.mul_le", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "FractionalIdeal.instPowNat", "kind": "instance", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.coe_pow", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.mul_induction_on", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "FractionalIdeal.instNatCast", "kind": "instance", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.coe_natCast", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.commSemiring", "kind": "instance", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.instCanonicallyOrderedAdd", "kind": "instance", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.instIsOrderedRing", "kind": "instance", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.coeSubmoduleHom", "kind": "definition", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.add_le_add_left", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.mul_le_mul_left", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.le_self_mul_self", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.mul_self_le_self", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.coeIdeal_le_one", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.le_one_iff_exists_coeIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": true, "tactics": ["constructor", "intro", "refine", "intro", "rw", "exact", "rw", "exact", "intro", "rw", "exact", "ext", "constructor", "rintro", "rwa", "intro", "obtain", "exact", "rintro", "rw", "apply"], "tactic_count": 21}
{"name": "FractionalIdeal.one_le", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "FractionalIdeal.coeIdealHom", "kind": "definition", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.coeIdeal_pow", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.coeIdeal_finprod", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.fg_of_isNoetherianRing", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Basic", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "FractionalIdeal.extended", "kind": "definition", "module": "Mathlib.RingTheory.FractionalIdeal.Extended", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.FractionalIdeal.Extended.0.FractionalIdeal.termMap_f", "kind": "definition", "module": "Mathlib.RingTheory.FractionalIdeal.Extended", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.FractionalIdeal.Extended.0.FractionalIdeal._aux_Mathlib_RingTheory_FractionalIdeal_Extended___macroRules__private_Mathlib_RingTheory_FractionalIdeal_Extended_0_FractionalIdeal_termMap_f_1", "kind": "definition", "module": "Mathlib.RingTheory.FractionalIdeal.Extended", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.mem_extended_iff", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Extended", "is_tactic_proof": true, "tactics": ["constructor"], "tactic_count": 1}
{"name": "FractionalIdeal.coe_extended_eq_span", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Extended", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "FractionalIdeal.extended_zero", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Extended", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.extended_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Extended", "is_tactic_proof": false, "tactics": ["simp", "obtain", "refine", "exact"], "tactic_count": 4}
{"name": "FractionalIdeal.extended_eq_zero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Extended", "is_tactic_proof": true, "tactics": ["refine", "contrapose", "exact"], "tactic_count": 3}
{"name": "FractionalIdeal.extended_one", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Extended", "is_tactic_proof": false, "tactics": ["refine", "coeToSubmodule_injective", "span_induction", "rintro", "rw", "exact", "rintro", "exact"], "tactic_count": 8}
{"name": "FractionalIdeal.extended_le_one_of_le_one", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Extended", "is_tactic_proof": true, "tactics": ["obtain", "intro", "simp", "rw", "obtain", "refine", "obtain", "have", "rw", "exact", "exact"], "tactic_count": 11}
{"name": "FractionalIdeal.one_le_extended_of_one_le", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Extended", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "FractionalIdeal.extended_add", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Extended", "is_tactic_proof": true, "tactics": ["apply", "simp", "apply", "rintro", "obtain", "rw", "exact", "add_mem", "rintro", "suffices", "exact", "hy.elim"], "tactic_count": 12}
{"name": "FractionalIdeal.extended_mul", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Extended", "is_tactic_proof": true, "tactics": ["apply", "simp", "refine", "rcases", "replace", "rw", "refine", "rcases", "exact", "exact", "rw", "exact", "rcases", "exact"], "tactic_count": 14}
{"name": "FractionalIdeal.extended_coeIdeal_eq_map", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Extended", "is_tactic_proof": false, "tactics": ["rw", "refine", "rintro", "exact", "rintro", "exact"], "tactic_count": 6}
{"name": "FractionalIdeal.extendedHom", "kind": "definition", "module": "Mathlib.RingTheory.FractionalIdeal.Extended", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.extendedHomₐ", "kind": "abbrev", "module": "Mathlib.RingTheory.FractionalIdeal.Extended", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.extendedHomₐ_eq_zero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Extended", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.extendedHomₐ_coeIdeal_eq_map", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Extended", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.coe_extendedHomₐ_eq_span", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Extended", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "FractionalIdeal.le_one_of_extendedHomₐ_le_one", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Extended", "is_tactic_proof": true, "tactics": ["contrapose", "rw", "obtain", "refine", "simpa", "subset_span", "contrapose", "rw", "exact"], "tactic_count": 9}
{"name": "FractionalIdeal.extendedHomₐ_le_one_iff", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Extended", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.one_le_extendedHomₐ_iff", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Extended", "is_tactic_proof": true, "tactics": ["rw", "extendedHomₐ_le_one_iff,"], "tactic_count": 2}
{"name": "FractionalIdeal.extendedHomₐ_eq_one_iff", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Extended", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "FractionalIdeal.extendedHomₐ_injective", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Extended", "is_tactic_proof": true, "tactics": ["intro", "dsimp", "by_cases", "rwa", "by_cases", "rwa", "rwa", "extendedHomₐ_eq_one_iff"], "tactic_count": 8}
{"name": "FractionalIdeal.instInvNonZeroDivisors", "kind": "instance", "module": "Mathlib.RingTheory.FractionalIdeal.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.inv_eq", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.inv_zero'", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.inv_of_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.coe_inv_of_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Inverse", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "FractionalIdeal.mem_inv_iff", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.inv_anti_mono", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Inverse", "is_tactic_proof": true, "tactics": ["intro", "simp", "exact"], "tactic_count": 3}
{"name": "FractionalIdeal.le_self_mul_inv", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.coe_ideal_le_self_mul_inv", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.right_inverse_eq", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.mul_inv_cancel_iff", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.mul_inv_cancel_iff_isUnit", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.map_inv", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Inverse", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "FractionalIdeal.spanSingleton_inv", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.spanSingleton_div_spanSingleton", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Inverse", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "FractionalIdeal.spanSingleton_div_self", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Inverse", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "FractionalIdeal.coe_ideal_span_singleton_div_self", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Inverse", "is_tactic_proof": true, "tactics": ["rw", "spanSingleton_div_self"], "tactic_count": 2}
{"name": "FractionalIdeal.spanSingleton_mul_inv", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Inverse", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "FractionalIdeal.coe_ideal_span_singleton_mul_inv", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Inverse", "is_tactic_proof": true, "tactics": ["rw", "spanSingleton_mul_inv"], "tactic_count": 2}
{"name": "FractionalIdeal.spanSingleton_inv_mul", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Inverse", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "FractionalIdeal.coe_ideal_span_singleton_inv_mul", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Inverse", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "FractionalIdeal.mul_generator_self_inv", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Inverse", "is_tactic_proof": true, "tactics": ["conv_lhs", "rw", "intro", "apply", "rw"], "tactic_count": 5}
{"name": "FractionalIdeal.invertible_of_principal", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.invertible_iff_generator_nonzero", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Inverse", "is_tactic_proof": true, "tactics": ["constructor", "intro", "apply", "rw", "intro", "apply", "rw", "intro", "have", "rw", "contradiction"], "tactic_count": 11}
{"name": "FractionalIdeal.isPrincipal_inv", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Inverse", "is_tactic_proof": true, "tactics": ["rw", "use", "have", "exact"], "tactic_count": 4}
{"name": "FractionalIdeal.den_mem_inv", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Inverse", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "suffices", "this", "apply", "rw"], "tactic_count": 7}
{"name": "FractionalIdeal.num_le_mul_inv", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Inverse", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "rw", "gcongr", "exact"], "tactic_count": 5}
{"name": "FractionalIdeal.bot_lt_mul_inv", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.instInvOneClassNonZeroDivisors", "kind": "instance", "module": "Mathlib.RingTheory.FractionalIdeal.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.absNorm_div_norm_eq_absNorm_div_norm", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Norm", "is_tactic_proof": true, "tactics": ["rw", "replace", "have", "dsimp", "rw", "rw", "simp_rw", "rw", "exact", "all_goals"], "tactic_count": 10}
{"name": "FractionalIdeal.absNorm", "kind": "definition", "module": "Mathlib.RingTheory.FractionalIdeal.Norm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.absNorm_eq", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Norm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.absNorm_eq'", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Norm", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "FractionalIdeal.absNorm_nonneg", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Norm", "is_tactic_proof": true, "tactics": ["dsimp"], "tactic_count": 1}
{"name": "FractionalIdeal.absNorm_bot", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Norm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.absNorm_one", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Norm", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "FractionalIdeal.absNorm_eq_zero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Norm", "is_tactic_proof": true, "tactics": ["refine", "rw", "refine", "simp"], "tactic_count": 4}
{"name": "FractionalIdeal.coeIdeal_absNorm", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Norm", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "FractionalIdeal.abs_det_basis_change", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Norm", "is_tactic_proof": true, "tactics": ["have", "let", "let", "rw", "change", "rw", "show", "b₀.toMatrix", "ext", "simp_rw", "rfl]", "rw", "show", "mul_div_cancel₀", "rw", "exact"], "tactic_count": 16}
{"name": "FractionalIdeal.absNorm_span_singleton", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Norm", "is_tactic_proof": true, "tactics": ["have", "obtain", "rw", "rw", "simp_rw", "rw", "mul_div_cancel₀", "rw", "exact", "ext", "simp_rw"], "tactic_count": 11}
{"name": "IsFractional.map", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.map", "kind": "definition", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.coe_map", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.mem_map", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.map_id", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.map_comp", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.map_coeIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "FractionalIdeal.map_one", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.map_zero", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.map_add", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.map_mul", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "FractionalIdeal.map_map_symm", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "FractionalIdeal.map_symm_map", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "FractionalIdeal.map_mem_map", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.map_injective", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.mapEquiv", "kind": "definition", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.coeFun_mapEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.mapEquiv_apply", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.mapEquiv_symm", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.mapEquiv_refl", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.isFractional_span_iff", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.isFractional_of_fg", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "rw", "exact"], "tactic_count": 4}
{"name": "FractionalIdeal.mem_span_mul_finite_of_mem_mul", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.submodule_isFractional", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.unitsMulEquivSubmodule", "kind": "definition", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.coeIdeal_fg", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.fg_unit", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.fg_of_isUnit", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.fg_of_isUnit", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "FractionalIdeal.definition._@.Mathlib.RingTheory.FractionalIdeal.Operations.2078496209._hygCtx._hyg.2", "kind": "definition", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.wrapped._@.Mathlib.RingTheory.FractionalIdeal.Operations.2078496209._hygCtx._hyg.2", "kind": "opaque", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.canonicalEquiv", "kind": "definition", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.canonicalEquiv_def", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": true, "tactics": ["intros", "delta", "rw", "rfl"], "tactic_count": 4}
{"name": "FractionalIdeal.mem_canonicalEquiv_apply", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "FractionalIdeal.canonicalEquiv_symm", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.canonicalEquiv_flip", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "FractionalIdeal.canonicalEquiv_canonicalEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "FractionalIdeal.canonicalEquiv_trans_canonicalEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.canonicalEquiv_coeIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "FractionalIdeal.canonicalEquiv_self", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": true, "tactics": ["rw", "convert", "exact"], "tactic_count": 3}
{"name": "FractionalIdeal.exists_ne_zero_mem_isInteger", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": true, "tactics": ["obtain", "have", "obtain", "refine", "rw", "exact", "rw", "exact"], "tactic_count": 8}
{"name": "FractionalIdeal.map_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": true, "tactics": ["obtain", "contrapose", "refine", "exact"], "tactic_count": 4}
{"name": "FractionalIdeal.map_eq_zero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.coeIdeal_injective", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.coeIdeal_inj", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.coeIdeal_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.coeIdeal_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.coeIdeal_eq_one", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "FractionalIdeal.coeIdeal_ne_one", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.num_eq_zero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.instNontrivialNonZeroDivisors", "kind": "instance", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.ne_zero_of_mul_eq_one", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractional.div_of_nonzero", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.isFractional_div_of_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.instDivNonZeroDivisors", "kind": "instance", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.div_zero", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.div_of_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.coe_div", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.mem_div_iff_of_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "FractionalIdeal.mul_one_div_le_one", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "exact", "rw", "apply"], "tactic_count": 5}
{"name": "FractionalIdeal.le_self_mul_one_div", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "rw", "rw", "exact"], "tactic_count": 5}
{"name": "FractionalIdeal.le_div_iff_of_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.le_div_iff_mul_le", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "FractionalIdeal.div_one", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": true, "tactics": ["rw", "ext", "constructor", "simpa", "apply", "rintro", "convert", "rw"], "tactic_count": 8}
{"name": "FractionalIdeal.eq_one_div_of_mul_eq_one_right", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": true, "tactics": ["have", "suffices", "congr_arg", "apply", "apply", "intro", "rw", "exact", "rw", "gcongr", "apply", "intro", "rw", "exact"], "tactic_count": 14}
{"name": "FractionalIdeal.mul_div_self_cancel_iff", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.map_div", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "simp"], "tactic_count": 3}
{"name": "FractionalIdeal.map_one_div", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "FractionalIdeal.eq_zero_or_one", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": true, "tactics": ["rw", "intro", "simp_rw", "intro", "constructor", "intro", "obtain", "refine", "rw", "rintro", "obtain", "rw", "exact"], "tactic_count": 13}
{"name": "FractionalIdeal.eq_zero_or_one_of_isField", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.spanFinset", "kind": "definition", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.spanFinset_coe", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.spanFinset_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": true, "tactics": ["simp", "forall_exists_index,"], "tactic_count": 2}
{"name": "FractionalIdeal.spanFinset_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FractionalIdeal.isFractional_span_singleton", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.definition._@.Mathlib.RingTheory.FractionalIdeal.Operations.2527798090._hygCtx._hyg.2", "kind": "definition", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.wrapped._@.Mathlib.RingTheory.FractionalIdeal.Operations.2527798090._hygCtx._hyg.2", "kind": "opaque", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.spanSingleton", "kind": "definition", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.spanSingleton_def", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": true, "tactics": ["intros", "delta", "rw", "rfl"], "tactic_count": 4}
{"name": "FractionalIdeal.coe_spanSingleton", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "FractionalIdeal.mem_spanSingleton", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "FractionalIdeal.mem_spanSingleton_self", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.den_mul_self_eq_num'", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": true, "tactics": ["apply", "dsimp", "rw", "convert", "ext", "rw", "simp"], "tactic_count": 7}
{"name": "FractionalIdeal.spanSingleton_le_iff_mem", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "FractionalIdeal.spanSingleton_eq_spanSingleton", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "FractionalIdeal.eq_spanSingleton_of_principal", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "FractionalIdeal.isPrincipal_iff", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.spanSingleton_zero", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "FractionalIdeal.spanSingleton_eq_zero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.spanSingleton_ne_zero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.spanSingleton_one", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": true, "tactics": ["ext", "refine", "intro", "rw"], "tactic_count": 4}
{"name": "FractionalIdeal.spanSingleton_mul_spanSingleton", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "FractionalIdeal.spanSingleton_pow", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "FractionalIdeal.coeIdeal_span_singleton", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": true, "tactics": ["ext", "refine", "constructor", "rintro", "obtain", "use", "rw", "rintro", "refine", "rw"], "tactic_count": 10}
{"name": "FractionalIdeal.canonicalEquiv_spanSingleton", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": true, "tactics": ["apply", "intro", "constructor", "rw", "obtain", "obtain", "use", "rw", "rw", "obtain", "use", "use", "simp"], "tactic_count": 13}
{"name": "FractionalIdeal.mem_singleton_mul", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": true, "tactics": ["constructor", "intro", "refine", "intro", "obtain", "use", "rw", "rintro", "exact", "rintro", "exact"], "tactic_count": 11}
{"name": "FractionalIdeal.mk'_mul_coeIdeal_eq_coeIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": false, "tactics": ["have", "rw", "spanSingleton_one]", "let", "have", "refine", "rw", "spanSingleton_mul_spanSingleton,"], "tactic_count": 8}
{"name": "FractionalIdeal.spanSingleton_mul_coeIdeal_eq_coeIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "FractionalIdeal.one_div_spanSingleton", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "FractionalIdeal.div_spanSingleton", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": true, "tactics": ["rw", "by_cases", "simp", "have", "apply", "intro", "rw", "specialize", "have", "rw", "exact", "rw", "inv_mul_cancel₀"], "tactic_count": 13}
{"name": "FractionalIdeal.exists_eq_spanSingleton_mul", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": true, "tactics": ["obtain", "have", "have", "refine", "ext", "intro", "obtain", "rw", "refine", "exact", "rw", "rintro", "obtain", "obtain", "rw", "rwa"], "tactic_count": 16}
{"name": "FractionalIdeal.ideal_factor_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.constant_factor_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.isPrincipal", "kind": "instance", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": true, "tactics": ["obtain", "use", "suffices", "rw", "exact", "conv_lhs", "rw"], "tactic_count": 7}
{"name": "FractionalIdeal.le_spanSingleton_mul_iff", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.spanSingleton_mul_le_iff", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": true, "tactics": ["simp", "constructor", "intro", "exact", "rintro", "rw", "exact"], "tactic_count": 7}
{"name": "FractionalIdeal.eq_spanSingleton_mul", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FractionalIdeal.num_le", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "exact"], "tactic_count": 4}
{"name": "FractionalIdeal.isNoetherian_zero", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.isNoetherian_iff", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.isNoetherian_coeIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": true, "tactics": ["rw", "intro", "obtain", "exact"], "tactic_count": 4}
{"name": "FractionalIdeal.isNoetherian_spanSingleton_inv_to_map_mul", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": true, "tactics": ["classical", "by_cases", "rw", "exact", "have", "mt", "have", "rw", "intro", "rw", "obtain", "use", "rw", "spanSingleton_mul_spanSingleton,"], "tactic_count": 14}
{"name": "FractionalIdeal.isNoetherian", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": true, "tactics": ["obtain", "apply", "apply"], "tactic_count": 3}
{"name": "FractionalIdeal.isFractional_adjoin_integral", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.adjoinIntegral", "kind": "definition", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.adjoinIntegral_coe", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionalIdeal.mem_adjoinIntegral_self", "kind": "theorem", "module": "Mathlib.RingTheory.FractionalIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeCommRing", "kind": "definition", "module": "Mathlib.RingTheory.FreeCommRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeCommRing.of", "kind": "definition", "module": "Mathlib.RingTheory.FreeCommRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeCommRing.of_injective", "kind": "theorem", "module": "Mathlib.RingTheory.FreeCommRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeCommRing.of_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.FreeCommRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeCommRing.zero_ne_of", "kind": "theorem", "module": "Mathlib.RingTheory.FreeCommRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeCommRing.of_ne_one", "kind": "theorem", "module": "Mathlib.RingTheory.FreeCommRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeCommRing.one_ne_of", "kind": "theorem", "module": "Mathlib.RingTheory.FreeCommRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeCommRing.of_cons", "kind": "theorem", "module": "Mathlib.RingTheory.FreeCommRing", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "FreeCommRing.induction_on", "kind": "theorem", "module": "Mathlib.RingTheory.FreeCommRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.FreeCommRing.0.FreeCommRing.liftToMultiset", "kind": "definition", "module": "Mathlib.RingTheory.FreeCommRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeCommRing.lift", "kind": "definition", "module": "Mathlib.RingTheory.FreeCommRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeCommRing.lift_of", "kind": "theorem", "module": "Mathlib.RingTheory.FreeCommRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeCommRing.lift_comp_of", "kind": "theorem", "module": "Mathlib.RingTheory.FreeCommRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeCommRing.hom_ext", "kind": "theorem", "module": "Mathlib.RingTheory.FreeCommRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeCommRing.map", "kind": "definition", "module": "Mathlib.RingTheory.FreeCommRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeCommRing.map_of", "kind": "theorem", "module": "Mathlib.RingTheory.FreeCommRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeCommRing.IsSupported", "kind": "definition", "module": "Mathlib.RingTheory.FreeCommRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeCommRing.isSupported_upwards", "kind": "theorem", "module": "Mathlib.RingTheory.FreeCommRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeCommRing.isSupported_add", "kind": "theorem", "module": "Mathlib.RingTheory.FreeCommRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeCommRing.isSupported_neg", "kind": "theorem", "module": "Mathlib.RingTheory.FreeCommRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeCommRing.isSupported_sub", "kind": "theorem", "module": "Mathlib.RingTheory.FreeCommRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeCommRing.isSupported_mul", "kind": "theorem", "module": "Mathlib.RingTheory.FreeCommRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeCommRing.isSupported_zero", "kind": "theorem", "module": "Mathlib.RingTheory.FreeCommRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeCommRing.isSupported_one", "kind": "theorem", "module": "Mathlib.RingTheory.FreeCommRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeCommRing.isSupported_int", "kind": "theorem", "module": "Mathlib.RingTheory.FreeCommRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeCommRing.restriction", "kind": "definition", "module": "Mathlib.RingTheory.FreeCommRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeCommRing.restriction_of", "kind": "theorem", "module": "Mathlib.RingTheory.FreeCommRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeCommRing.isSupported_of", "kind": "theorem", "module": "Mathlib.RingTheory.FreeCommRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeCommRing.map_subtype_val_restriction", "kind": "theorem", "module": "Mathlib.RingTheory.FreeCommRing", "is_tactic_proof": true, "tactics": ["refine", "rw", "rfl", "rw", "rfl", "rintro", "rw", "intro", "rw"], "tactic_count": 9}
{"name": "FreeCommRing.exists_finite_support", "kind": "theorem", "module": "Mathlib.RingTheory.FreeCommRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeCommRing.exists_finset_support", "kind": "theorem", "module": "Mathlib.RingTheory.FreeCommRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeRing.toFreeCommRing", "kind": "definition", "module": "Mathlib.RingTheory.FreeCommRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeRing.castFreeCommRing", "kind": "definition", "module": "Mathlib.RingTheory.FreeCommRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeRing.FreeCommRing.instCoe", "kind": "instance", "module": "Mathlib.RingTheory.FreeCommRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeRing.coeRingHom", "kind": "definition", "module": "Mathlib.RingTheory.FreeCommRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeRing.coe_zero", "kind": "theorem", "module": "Mathlib.RingTheory.FreeCommRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeRing.coe_one", "kind": "theorem", "module": "Mathlib.RingTheory.FreeCommRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeRing.coe_of", "kind": "theorem", "module": "Mathlib.RingTheory.FreeCommRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeRing.coe_neg", "kind": "theorem", "module": "Mathlib.RingTheory.FreeCommRing", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "FreeRing.coe_add", "kind": "theorem", "module": "Mathlib.RingTheory.FreeCommRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeRing.coe_sub", "kind": "theorem", "module": "Mathlib.RingTheory.FreeCommRing", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "FreeRing.coe_mul", "kind": "theorem", "module": "Mathlib.RingTheory.FreeCommRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeRing.coe_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.FreeCommRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeRing.coe_eq", "kind": "theorem", "module": "Mathlib.RingTheory.FreeCommRing", "is_tactic_proof": true, "tactics": ["funext", "dsimp", "rw", "apply", "simp", "exact", "rw", "conv_lhs", "rfl"], "tactic_count": 9}
{"name": "FreeRing.subsingletonEquivFreeCommRing", "kind": "definition", "module": "Mathlib.RingTheory.FreeCommRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeRing.instCommRing", "kind": "instance", "module": "Mathlib.RingTheory.FreeCommRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "freeCommRingEquivMvPolynomialInt", "kind": "definition", "module": "Mathlib.RingTheory.FreeCommRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "freeCommRingPemptyEquivInt", "kind": "definition", "module": "Mathlib.RingTheory.FreeCommRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "freeCommRingPunitEquivPolynomialInt", "kind": "definition", "module": "Mathlib.RingTheory.FreeCommRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "freeRingPemptyEquivInt", "kind": "definition", "module": "Mathlib.RingTheory.FreeCommRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "freeRingPunitEquivPolynomialInt", "kind": "definition", "module": "Mathlib.RingTheory.FreeCommRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeRing", "kind": "definition", "module": "Mathlib.RingTheory.FreeRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instRingFreeRing", "kind": "instance", "module": "Mathlib.RingTheory.FreeRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInhabitedFreeRing", "kind": "instance", "module": "Mathlib.RingTheory.FreeRing", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "instNontrivialFreeRing", "kind": "instance", "module": "Mathlib.RingTheory.FreeRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeRing.of", "kind": "definition", "module": "Mathlib.RingTheory.FreeRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeRing.of_injective", "kind": "theorem", "module": "Mathlib.RingTheory.FreeRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeRing.of_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.FreeRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeRing.zero_ne_of", "kind": "theorem", "module": "Mathlib.RingTheory.FreeRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeRing.of_ne_one", "kind": "theorem", "module": "Mathlib.RingTheory.FreeRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeRing.one_ne_of", "kind": "theorem", "module": "Mathlib.RingTheory.FreeRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeRing.induction_on", "kind": "theorem", "module": "Mathlib.RingTheory.FreeRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeRing.lift", "kind": "definition", "module": "Mathlib.RingTheory.FreeRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeRing.lift_of", "kind": "theorem", "module": "Mathlib.RingTheory.FreeRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeRing.lift_comp_of", "kind": "theorem", "module": "Mathlib.RingTheory.FreeRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeRing.hom_ext", "kind": "theorem", "module": "Mathlib.RingTheory.FreeRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeRing.map", "kind": "definition", "module": "Mathlib.RingTheory.FreeRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FreeRing.map_of", "kind": "theorem", "module": "Mathlib.RingTheory.FreeRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.IsArithFrobAt", "kind": "definition", "module": "Mathlib.RingTheory.Frobenius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.IsArithFrobAt.mk_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Frobenius", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "AlgHom.IsArithFrobAt.finite_quotient", "kind": "theorem", "module": "Mathlib.RingTheory.Frobenius", "is_tactic_proof": true, "tactics": ["by_contra", "obtain", "simp", "exact"], "tactic_count": 4}
{"name": "AlgHom.IsArithFrobAt.card_pos", "kind": "theorem", "module": "Mathlib.RingTheory.Frobenius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.IsArithFrobAt.le_comap", "kind": "theorem", "module": "Mathlib.RingTheory.Frobenius", "is_tactic_proof": true, "tactics": ["intro", "simp_all"], "tactic_count": 2}
{"name": "AlgHom.IsArithFrobAt.restrict", "kind": "definition", "module": "Mathlib.RingTheory.Frobenius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.IsArithFrobAt.restrict_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Frobenius", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "AlgHom.IsArithFrobAt.restrict_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Frobenius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.IsArithFrobAt.restrict_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Frobenius", "is_tactic_proof": true, "tactics": ["rw", "intro", "simpa"], "tactic_count": 3}
{"name": "AlgHom.IsArithFrobAt.comap_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Frobenius", "is_tactic_proof": true, "tactics": ["refine", "rwa"], "tactic_count": 2}
{"name": "AlgHom.IsArithFrobAt.apply_of_pow_eq_one", "kind": "theorem", "module": "Mathlib.RingTheory.Frobenius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.IsArithFrobAt.localize", "kind": "definition", "module": "Mathlib.RingTheory.Frobenius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.IsArithFrobAt.localize_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.Frobenius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.IsArithFrobAt.isArithFrobAt_localize", "kind": "theorem", "module": "Mathlib.RingTheory.Frobenius", "is_tactic_proof": false, "tactics": ["have", "congr", "rw", "intro", "obtain", "simp", "rw", "simp", "simp"], "tactic_count": 9}
{"name": "AlgHom.IsArithFrobAt.eq_of_isUnramifiedAt", "kind": "theorem", "module": "Mathlib.RingTheory.Frobenius", "is_tactic_proof": false, "tactics": ["have", "apply", "intro", "rw", "ext", "apply", "rw"], "tactic_count": 7}
{"name": "IsArithFrobAt", "kind": "abbrev", "module": "Mathlib.RingTheory.Frobenius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsArithFrobAt.mul_inv_mem_inertia", "kind": "theorem", "module": "Mathlib.RingTheory.Frobenius", "is_tactic_proof": true, "tactics": ["intro", "simpa"], "tactic_count": 2}
{"name": "IsArithFrobAt.conj", "kind": "theorem", "module": "Mathlib.RingTheory.Frobenius", "is_tactic_proof": true, "tactics": ["intro", "have", "rw", "congr", "exact", "rw", "simpa"], "tactic_count": 7}
{"name": "IsArithFrobAt.exists_of_isInvariant", "kind": "theorem", "module": "Mathlib.RingTheory.Frobenius", "is_tactic_proof": true, "tactics": ["let", "have", "have", "obtain", "have", "cases", "obtain", "have", "have", "let", "commutes", "r", "dsimp", "rw", "obtain", "refine", "rw", "exact"], "tactic_count": 18}
{"name": "IsArithFrobAt.exists_primesOver_isConj", "kind": "theorem", "module": "Mathlib.RingTheory.Frobenius", "is_tactic_proof": true, "tactics": ["obtain", "have", "choose", "obtain", "refine"], "tactic_count": 5}
{"name": "arithFrobAt", "kind": "definition", "module": "Mathlib.RingTheory.Frobenius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsArithFrobAt.arithFrobAt", "kind": "theorem", "module": "Mathlib.RingTheory.Frobenius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isConj_arithFrobAt", "kind": "theorem", "module": "Mathlib.RingTheory.Frobenius", "is_tactic_proof": false, "tactics": ["obtain", "convert", "subst", "subst"], "tactic_count": 4}
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{"name": "DirectSum.decompose_one", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.decompose_symm_one", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.decompose_mul", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.decompose_symm_mul", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GradedRing.proj", "kind": "definition", "module": "Mathlib.RingTheory.GradedAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GradedRing.proj_apply", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "GradedRing.mem_support_iff", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.coe_decompose_mul_add_of_left_mem", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Basic", "is_tactic_proof": true, "tactics": ["lift", "rw"], "tactic_count": 2}
{"name": "DirectSum.coe_decompose_mul_add_of_right_mem", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Basic", "is_tactic_proof": true, "tactics": ["lift", "rw"], "tactic_count": 2}
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{"name": "HomogeneousLocalization.Away.eventually_smul_mem", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.HomogeneousLocalization", "is_tactic_proof": true, "tactics": ["obtain", "apply", "rintro", "simp", "by_cases", "refine", "rw", "rw", "rw", "exact"], "tactic_count": 10}
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{"name": "HomogeneousLocalization.mapId", "kind": "abbrev", "module": "Mathlib.RingTheory.GradedAlgebra.HomogeneousLocalization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomogeneousLocalization.map_mk", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.HomogeneousLocalization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "HomogeneousLocalization.range_awayMapAux_subset", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.HomogeneousLocalization", "is_tactic_proof": true, "tactics": ["rintro", "obtain", "use", "simp", "apply", "exact", "rw", "apply", "exact"], "tactic_count": 9}
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{"name": "HomogeneousLocalization.val_awayMap_eq_aux", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.HomogeneousLocalization", "is_tactic_proof": false, "tactics": ["let", "dsimp", "convert_to", "rw"], "tactic_count": 4}
{"name": "HomogeneousLocalization.val_awayMap", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.HomogeneousLocalization", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "HomogeneousLocalization.awayMap_fromZeroRingHom", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.HomogeneousLocalization", "is_tactic_proof": true, "tactics": ["ext", "simp", "convert"], "tactic_count": 3}
{"name": "HomogeneousLocalization.val_awayMap_mk", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.HomogeneousLocalization", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HomogeneousLocalization.awayMapₐ", "kind": "definition", "module": "Mathlib.RingTheory.GradedAlgebra.HomogeneousLocalization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomogeneousLocalization.awayMapₐ_apply", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.HomogeneousLocalization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomogeneousLocalization.Away.mk", "kind": "definition", "module": "Mathlib.RingTheory.GradedAlgebra.HomogeneousLocalization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomogeneousLocalization.Away.val_mk", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.HomogeneousLocalization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomogeneousLocalization.Away.mk_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.HomogeneousLocalization", "is_tactic_proof": true, "tactics": ["obtain", "by_cases", "have", "exact", "obtain", "exact"], "tactic_count": 6}
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{"name": "HomogeneousLocalization.Away.isLocalizationElem", "kind": "abbrev", "module": "Mathlib.RingTheory.GradedAlgebra.HomogeneousLocalization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomogeneousLocalization.Away.isLocalization_mul", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.HomogeneousLocalization", "is_tactic_proof": true, "tactics": ["letI", "constructor", "rintro", "rw", "let", "convert", "ring", "refine", "ext", "simp", "rw", "use", "simp", "ring", "intro", "obtain", "rcases", "contradiction", "let", "convert", "refine", "ext", "simp", "rw", "exact", "intro", "obtain", "obtain", "replace", "simp", "obtain", "refine", "ext", "simp", "refine", "rcases", "contradiction", "subst", "convert"], "tactic_count": 39}
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{"name": "_private.Mathlib.RingTheory.GradedAlgebra.HomogeneousLocalization.0.HomogeneousLocalization.Away.adjoin_mk_prod_pow_eq_top_of_pos", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.HomogeneousLocalization", "is_tactic_proof": true, "tactics": ["rw", "change", "rw", "rintro", "have", "rw", "conv", "simp_rw", "simp", "have", "apply", "simp", "simp", "congr", "ext", "congr", "exact", "simp", "rw", "rcases", "simp", "rw", "simp_rw", "gcongr", "exact", "rw", "apply", "apply", "refine", "rcases", "have", "simp", "exact", "apply", "classical", "rintro", "apply", "apply", "refine", "simp", "aesop", "ext", "simp"], "tactic_count": 43}
{"name": "HomogeneousLocalization.Away.adjoin_mk_prod_pow_eq_top", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.HomogeneousLocalization", "is_tactic_proof": true, "tactics": ["classical", "let", "have", "swap", "rw", "intro", "rcases", "exact", "exact", "rw", "apply", "rintro", "refine", "simpa", "simp", "congr", "change", "simp"], "tactic_count": 18}
{"name": "HomogeneousLocalization.Away.finiteType", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.HomogeneousLocalization", "is_tactic_proof": true, "tactics": ["constructor", "obtain", "choose", "simp_rw", "rcases", "let", "refine", "rw", "rintro", "obtain", "simp", "convert", "ext", "simp", "refine", "let", "let", "let", "apply", "rintro", "refine", "rw", "simp_rw", "gcongr", "exact"], "tactic_count": 25}
{"name": "Ideal.IsHomogeneous", "kind": "abbrev", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.IsHomogeneous.mem_iff", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomogeneousIdeal", "kind": "abbrev", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomogeneousIdeal.toIdeal", "kind": "abbrev", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomogeneousIdeal.isHomogeneous", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomogeneousIdeal.toIdeal_injective", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomogeneousIdeal.setLike", "kind": "instance", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instPartialOrderHomogeneousIdeal", "kind": "instance", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomogeneousIdeal.ext", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomogeneousIdeal.ext'", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomogeneousIdeal.mem_iff", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.homogeneousCore'", "kind": "definition", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.homogeneousCore'_mono", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.homogeneousCore'_le", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.isHomogeneous_iff_forall_subset", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.isHomogeneous_iff_subset_iInter", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.mul_homogeneous_element_mem_of_mem", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": true, "tactics": ["classical", "rw", "apply", "intro", "obtain", "have", "rw", "split_ifs", "exact", "exact"], "tactic_count": 10}
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{"name": "Ideal.homogeneousCore_mono", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.toIdeal_homogeneousCore_le", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.mem_homogeneousCore_of_homogeneous_of_mem", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.IsHomogeneous.toIdeal_homogeneousCore_eq_self", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": true, "tactics": ["apply", "intro", "classical", "rw", "exact"], "tactic_count": 5}
{"name": "HomogeneousIdeal.toIdeal_homogeneousCore_eq_self", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": true, "tactics": ["ext1", "convert"], "tactic_count": 2}
{"name": "Ideal.IsHomogeneous.iff_eq", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.IsHomogeneous.iff_exists", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Ideal.IsHomogeneous.bot", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.IsHomogeneous.top", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.IsHomogeneous.inf", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.IsHomogeneous.sup", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": true, "tactics": ["rw", "obtain", "refine", "rw", "exact"], "tactic_count": 5}
{"name": "Ideal.IsHomogeneous.iSup", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": true, "tactics": ["simp_rw", "choose", "refine", "simp_rw", "congr", "exact"], "tactic_count": 6}
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{"name": "Ideal.IsHomogeneous.iSup₂", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.IsHomogeneous.iInf₂", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.IsHomogeneous.sSup", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Ideal.IsHomogeneous.sInf", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "HomogeneousIdeal.instTop", "kind": "instance", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomogeneousIdeal.instBot", "kind": "instance", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomogeneousIdeal.instMax", "kind": "instance", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomogeneousIdeal.instMin", "kind": "instance", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomogeneousIdeal.instSupSet", "kind": "instance", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomogeneousIdeal.instInfSet", "kind": "instance", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomogeneousIdeal.coe_top", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomogeneousIdeal.coe_bot", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomogeneousIdeal.coe_sup", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomogeneousIdeal.coe_inf", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomogeneousIdeal.toIdeal_top", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomogeneousIdeal.toIdeal_bot", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomogeneousIdeal.toIdeal_sup", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomogeneousIdeal.toIdeal_inf", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomogeneousIdeal.toIdeal_sSup", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomogeneousIdeal.toIdeal_sInf", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomogeneousIdeal.toIdeal_iSup", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HomogeneousIdeal.toIdeal_iInf", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HomogeneousIdeal.toIdeal_iSup₂", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "HomogeneousIdeal.toIdeal_iInf₂", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "HomogeneousIdeal.eq_top_iff", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomogeneousIdeal.eq_bot_iff", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomogeneousIdeal.completeLattice", "kind": "instance", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomogeneousIdeal.instAdd", "kind": "instance", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomogeneousIdeal.toIdeal_add", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomogeneousIdeal.instInhabited", "kind": "instance", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.IsHomogeneous.mul", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": true, "tactics": ["rw", "obtain", "rw", "exact"], "tactic_count": 4}
{"name": "instMulHomogeneousIdeal", "kind": "instance", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomogeneousIdeal.toIdeal_mul", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.homogeneousCore.gc", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.homogeneousCore.gi", "kind": "definition", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.homogeneousCore_eq_sSup", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.homogeneousCore'_eq_sSup", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": true, "tactics": ["refine", "apply", "have", "convert", "ext", "rw", "refine", "rintro", "exact"], "tactic_count": 9}
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{"name": "Ideal.le_toIdeal_homogeneousHull", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": true, "tactics": ["intro", "classical", "rw", "refine", "intro", "apply", "use", "use"], "tactic_count": 8}
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{"name": "Ideal.IsHomogeneous.toIdeal_homogeneousHull_eq_self", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": true, "tactics": ["apply", "apply", "rintro", "exact"], "tactic_count": 4}
{"name": "HomogeneousIdeal.homogeneousHull_toIdeal_eq_self", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.toIdeal_homogeneousHull_eq_iSup", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": true, "tactics": ["rw", "apply", "ext1", "simp"], "tactic_count": 4}
{"name": "Ideal.homogeneousHull_eq_iSup", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": true, "tactics": ["ext1", "rw"], "tactic_count": 2}
{"name": "Ideal.homogeneousHull.gc", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.homogeneousHull.gi", "kind": "definition", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.homogeneousHull_eq_sInf", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomogeneousIdeal.irrelevant", "kind": "definition", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal.0.HomogeneousIdeal.term_₊", "kind": "definition", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal.0.HomogeneousIdeal._aux_Mathlib_RingTheory_GradedAlgebra_Homogeneous_Ideal___macroRules__private_Mathlib_RingTheory_GradedAlgebra_Homogeneous_Ideal_0_HomogeneousIdeal_term_₊_1", "kind": "definition", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal.0.HomogeneousIdeal._aux_Mathlib_RingTheory_GradedAlgebra_Homogeneous_Ideal___unexpand_HomogeneousIdeal_irrelevant_1", "kind": "definition", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomogeneousIdeal.mem_irrelevant_iff", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomogeneousIdeal.toIdeal_irrelevant", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomogeneousIdeal.mem_irrelevant_of_mem", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HomogeneousIdeal.irrelevant_eq_iSup", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": true, "tactics": ["refine", "classical", "refine", "by_cases", "classical", "exact"], "tactic_count": 6}
{"name": "HomogeneousIdeal.irrelevant_eq_closure", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": true, "tactics": ["rw", "exact", "le_antisymm", "closure_le.mpr"], "tactic_count": 4}
{"name": "HomogeneousIdeal.irrelevant_eq_span", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomogeneousIdeal.toAddSubmonoid_irrelevant_le", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HomogeneousIdeal.toIdeal_irrelevant_le", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomogeneousIdeal.irrelevant_le", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.IsHomogeneous", "kind": "definition", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.IsHomogeneous.mem_iff", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instSetLikeHomogeneousSubmodule", "kind": "instance", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instPartialOrderHomogeneousSubmodule", "kind": "instance", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instAddSubmonoidClassHomogeneousSubmodule", "kind": "instance", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instSMulMemClassHomogeneousSubmodule", "kind": "instance", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomogeneousSubmodule.isHomogeneous", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomogeneousSubmodule.toSubmodule_injective", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomogeneousSubmodule.setLike", "kind": "instance", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instPartialOrderHomogeneousSubmodule_1", "kind": "instance", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomogeneousSubmodule.ext", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomogeneousSubmodule.ext'", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Submodule", "is_tactic_proof": true, "tactics": ["ext", "rw", "apply", "exact"], "tactic_count": 4}
{"name": "HomogeneousSubmodule.mem_toSubmodule_iff", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirectSum.SetLike.IsHomogeneous.mem_iff", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Subsemiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomogeneousSubsemiring.toSubsemiring_injective", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Subsemiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomogeneousSubsemiring.setLike", "kind": "instance", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Subsemiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomogeneousSubsemiring.instPartialOrder", "kind": "instance", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Subsemiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomogeneousSubsemiring.isHomogeneous", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Subsemiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomogeneousSubsemiring.subsemiringClass", "kind": "instance", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Subsemiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomogeneousSubsemiring.ext", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Subsemiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomogeneousSubsemiring.ext'", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Subsemiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomogeneousSubsemiring.mem_iff", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Subsemiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsHomogeneous.subsemiringClosure", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Subsemiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsHomogeneous.subsemiringClosure_of_isHomogeneousElem", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Subsemiring", "is_tactic_proof": true, "tactics": ["rw", "refine", "obtain", "simp", "obtain", "obtain"], "tactic_count": 6}
{"name": "Subsemiring.homogeneousCore", "kind": "definition", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Subsemiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.homogeneousCore_mono", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Subsemiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.toSubsemiring_homogeneousCore_le", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Subsemiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.isHomogeneous_iff_forall_subset", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Subsemiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.isHomogeneous_iff_subset_iInter", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Homogeneous.Subsemiring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GradedRing.GradeZero.isNoetherianRing", "kind": "instance", "module": "Mathlib.RingTheory.GradedAlgebra.Noetherian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.IsHomogeneous.isPrime_of_homogeneous_mem_or_mem", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Radical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.IsHomogeneous.isPrime_iff", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Radical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.IsPrime.homogeneousCore", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Radical", "is_tactic_proof": true, "tactics": ["apply", "exact", "rintro", "have", "refine", "exact", "exact"], "tactic_count": 7}
{"name": "Ideal.IsHomogeneous.radical_eq", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Radical", "is_tactic_proof": true, "tactics": ["rw", "apply", "exact", "refine", "rintro", "refine", "refine", "exact"], "tactic_count": 8}
{"name": "Ideal.IsHomogeneous.radical", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Radical", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "HomogeneousIdeal.radical", "kind": "definition", "module": "Mathlib.RingTheory.GradedAlgebra.Radical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomogeneousIdeal.coe_radical", "kind": "theorem", "module": "Mathlib.RingTheory.GradedAlgebra.Radical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Grassmannian.termG(_,_;_)", "kind": "definition", "module": "Mathlib.RingTheory.Grassmannian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Grassmannian._aux_Mathlib_RingTheory_Grassmannian___macroRules_Module_Grassmannian_termG(_,_;_)_1", "kind": "definition", "module": "Mathlib.RingTheory.Grassmannian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Grassmannian._aux_Mathlib_RingTheory_Grassmannian___unexpand_Module_Grassmannian_1", "kind": "definition", "module": "Mathlib.RingTheory.Grassmannian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Grassmannian.instCoeOutSubmodule", "kind": "instance", "module": "Mathlib.RingTheory.Grassmannian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Grassmannian.ext", "kind": "theorem", "module": "Mathlib.RingTheory.Grassmannian", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "HahnSeries.instSMul", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.support_smul_subset", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.coeff_smul'", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.coeff_smul", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.instSMulZeroClass", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.orderTop_smul_not_lt", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "exact", "simp", "exact"], "tactic_count": 5}
{"name": "HahnSeries.orderTop_le_orderTop_smul", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.order_smul_not_lt", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": true, "tactics": ["have", "simp_all", "exact"], "tactic_count": 3}
{"name": "HahnSeries.le_order_smul", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.truncLT_smul", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "HahnSeries.instAdd", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.support_add_subset", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.coeff_add'", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.coeff_add", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.single_add", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "HahnSeries.instAddMonoid", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.coeff_nsmul", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.map_add", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "HahnSeries.addOppositeEquiv", "kind": "definition", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.addOppositeEquiv_support", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "HahnSeries.addOppositeEquiv_symm_support", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HahnSeries.addOppositeEquiv_orderTop", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": true, "tactics": ["classical", "simp", "simp", "simp_rw", "simp"], "tactic_count": 5}
{"name": "HahnSeries.addOppositeEquiv_symm_orderTop", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HahnSeries.addOppositeEquiv_leadingCoeff", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": true, "tactics": ["classical", "obtain", "simp", "simp", "leadingCoeff_of_ne_zero,", "simp"], "tactic_count": 6}
{"name": "HahnSeries.addOppositeEquiv_symm_leadingCoeff", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": true, "tactics": ["apply", "rw"], "tactic_count": 2}
{"name": "HahnSeries.min_le_min_add", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "HahnSeries.min_orderTop_le_orderTop_add", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": true, "tactics": ["by_cases", "by_cases", "by_cases", "rw", "exact"], "tactic_count": 5}
{"name": "HahnSeries.min_order_le_order_add", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": true, "tactics": ["by_cases", "by_cases", "rw", "exact"], "tactic_count": 4}
{"name": "HahnSeries.orderTop_add_eq_left", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": true, "tactics": ["have", "let", "have", "rw", "exact", "have", "rw", "exact", "exact"], "tactic_count": 9}
{"name": "HahnSeries.orderTop_add_eq_right", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": true, "tactics": ["simpa", "orderTop_add_eq_left"], "tactic_count": 2}
{"name": "HahnSeries.leadingCoeff_add_eq_left", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": true, "tactics": ["have", "have", "by_cases", "rw", "rw", "simp_rw", "rw"], "tactic_count": 7}
{"name": "HahnSeries.leadingCoeff_add_eq_right", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": true, "tactics": ["simpa", "leadingCoeff_add_eq_left"], "tactic_count": 2}
{"name": "HahnSeries.ne_zero_of_eq_add_single", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": true, "tactics": ["by_contra", "simp", "exact"], "tactic_count": 3}
{"name": "HahnSeries.coeff_order_of_eq_add_single", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HahnSeries.order_lt_order_of_eq_add_single", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": false, "tactics": ["have", "intro", "have", "rw", "exact", "refine", "simp", "refine", "obtain", "simpa", "have", "rw", "simpa"], "tactic_count": 13}
{"name": "HahnSeries.single.addMonoidHom", "kind": "definition", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.coeff.addMonoidHom", "kind": "definition", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.embDomain_add", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "obtain", "simp", "simp"], "tactic_count": 5}
{"name": "HahnSeries.truncLT_add", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": true, "tactics": ["ext", "by_cases"], "tactic_count": 2}
{"name": "HahnSeries.instAddCommMonoid", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.coeff_sum", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.instNeg", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.support_neg_subset", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.coeff_neg'", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.coeff_neg", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.instSub", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.support_sub_subset", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.coeff_sub'", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.coeff_sub", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.instAddGroup", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.single_sub", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.single_neg", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.support_neg", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "HahnSeries.map_neg", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "HahnSeries.orderTop_neg", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "HahnSeries.order_neg", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": true, "tactics": ["classical", "by_cases", "simp", "simp"], "tactic_count": 4}
{"name": "HahnSeries.leadingCoeff_neg", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "HahnSeries.map_sub", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "HahnSeries.min_orderTop_le_orderTop_sub", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "HahnSeries.orderTop_sub", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "HahnSeries.leadingCoeff_sub", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "HahnSeries.orderTop_sub_ne", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": true, "tactics": ["refine", "have", "rw", "have", "rw", "simp", "untop_orderTop_of_ne_zero", "rwa"], "tactic_count": 8}
{"name": "HahnSeries.le_orderTop_of_leadingCoeff_eq", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.instAddCommGroup", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.instDistribMulAction", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.instIsScalarTower", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.instSMulCommClass", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.instModule", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.single.linearMap", "kind": "definition", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.coeff.linearMap", "kind": "definition", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.map_smul", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "HahnSeries.ofFinsuppLinearMap", "kind": "definition", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.coeff_ofFinsuppLinearMap", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.embDomain_smul", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "obtain", "simp", "simp"], "tactic_count": 5}
{"name": "HahnSeries.embDomainLinearMap", "kind": "definition", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.truncLTLinearMap", "kind": "definition", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.coe_truncLTLinearMap", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Addition", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "HahnSeries.term__⟦_⟧", "kind": "definition", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries._aux_Mathlib_RingTheory_HahnSeries_Basic___macroRules_HahnSeries_term__⟦_⟧_1", "kind": "definition", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.unexpander", "kind": "definition", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.coeff_injective", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.coeff_inj", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.support", "kind": "definition", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.support_mk", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.isPWO_support", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.isWF_support", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.mem_support", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.instZero", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.instInhabited", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.instSubsingleton", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.coeff_zero'", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.coeff_zero", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.coeff_fun_eq_zero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.ne_zero_of_coeff_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.support_zero", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.support_nonempty_iff", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HahnSeries.support_eq_empty_iff", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.map", "kind": "definition", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.map_zero", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "HahnSeries.support_map_subset", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.ofIterate", "kind": "definition", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.mk_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "HahnSeries.toIterate", "kind": "definition", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.iterateEquiv", "kind": "definition", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.single", "kind": "definition", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.coeff_single_same", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "HahnSeries.coeff_single_of_ne", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "HahnSeries.coeff_single", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": true, "tactics": ["split_ifs"], "tactic_count": 1}
{"name": "HahnSeries.support_single_of_ne", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "HahnSeries.support_single_subset", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "HahnSeries.eq_of_mem_support_single", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.single_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.single_injective", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.single_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.single_eq_zero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.map_single", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": true, "tactics": ["ext", "by_cases"], "tactic_count": 2}
{"name": "HahnSeries.instNontrivialOfNonempty", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.orderTop", "kind": "definition", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.orderTop_zero", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.orderTop_of_subsingleton", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.orderTop_of_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.orderTop_eq_top", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HahnSeries.orderTop_lt_top", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HahnSeries.orderTop_ne_top", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.ne_zero_iff_orderTop", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.orderTop_eq_of_le", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HahnSeries.untop_orderTop_of_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.coeff_orderTop_ne", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "rw", "exact"], "tactic_count": 5}
{"name": "HahnSeries.orderTop_ne_of_coeff_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.orderTop_le_of_coeff_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "HahnSeries.orderTop_single", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.orderTop_single_le", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "rw"], "tactic_count": 3}
{"name": "HahnSeries.lt_orderTop_single", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.coeff_eq_zero_of_lt_orderTop", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": true, "tactics": ["rcases", "exact", "contrapose", "rw", "rw", "exact"], "tactic_count": 6}
{"name": "HahnSeries.leadingCoeff", "kind": "definition", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.leadingCoeff_zero", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HahnSeries.leadingCoeff_of_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HahnSeries.leadingCoeff_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "HahnSeries.leadingCoeff_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.leadingCoeff_of_single", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "HahnSeries.coeff_untop_eq_leadingCoeff", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": true, "tactics": ["rw", "rw"], "tactic_count": 2}
{"name": "HahnSeries.order", "kind": "definition", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.order_zero", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.order_of_ne", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.order_eq_orderTop_of_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HahnSeries.coeff_order_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "HahnSeries.coeff_order_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.order_le_of_coeff_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.order_single", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.coeff_eq_zero_of_lt_order", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simp", "contrapose", "rw", "rw", "exact"], "tactic_count": 6}
{"name": "HahnSeries.zero_lt_orderTop_iff", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": true, "tactics": ["simp_all"], "tactic_count": 1}
{"name": "HahnSeries.zero_lt_orderTop_of_order", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simp_all", "exact"], "tactic_count": 3}
{"name": "HahnSeries.zero_le_orderTop_iff", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simp_all", "simp_all"], "tactic_count": 3}
{"name": "HahnSeries.leadingCoeff_eq", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "simp"], "tactic_count": 3}
{"name": "HahnSeries.ofFinsupp", "kind": "definition", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.coeff_ofFinsupp", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.embDomain", "kind": "definition", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.embDomain_coeff", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": true, "tactics": ["rw", "dsimp", "by_cases", "rw", "exact", "rw", "contrapose", "obtain", "rwa"], "tactic_count": 9}
{"name": "HahnSeries.embDomain_mk_coeff", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.embDomain_notin_image_support", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.support_embDomain_subset", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": true, "tactics": ["intro", "contrapose", "rw"], "tactic_count": 3}
{"name": "HahnSeries.embDomain_notin_range", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.embDomain_zero", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "HahnSeries.embDomain_single", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "simp", "rw", "by_cases", "simp", "rwa"], "tactic_count": 7}
{"name": "HahnSeries.embDomain_injective", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.orderTop_embDomain", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": true, "tactics": ["obtain", "simp", "rw", "apply", "simpa", "intro", "obtain", "rw", "apply", "simpa"], "tactic_count": 10}
{"name": "HahnSeries.forallLTEqZero_supp_BddBelow", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": true, "tactics": ["refine", "contrapose", "simp_all"], "tactic_count": 3}
{"name": "HahnSeries.BddBelow_zero", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HahnSeries.le_orderTop_iff_forall", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.orderTop_lt_iff_exists", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "HahnSeries.le_order_iff_forall", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.order_lt_iff_exists", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "HahnSeries.suppBddBelow_supp_PWO", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.ofSuppBddBelow", "kind": "definition", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.ofSuppBddBelow_zero", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.ofSuppBddBelow_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.coeff_ofSuppBddBelow", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.order_ofForallLtEqZero", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact", "simpa"], "tactic_count": 3}
{"name": "HahnSeries.truncLT", "kind": "definition", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.support_truncLT", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HahnSeries.support_truncLT_subset", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "HahnSeries.coeff_truncLT", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.coeff_truncLT_of_lt", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HahnSeries.coeff_truncLT_of_le", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HahnSeries.SummableFamily.binomialFamily", "kind": "definition", "module": "Mathlib.RingTheory.HahnSeries.Binomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.SummableFamily.binomialFamily_apply", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Binomial", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HahnSeries.SummableFamily.binomialFamily_apply_of_orderTop_nonpos", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Binomial", "is_tactic_proof": true, "tactics": ["rw", "by_cases"], "tactic_count": 2}
{"name": "HahnSeries.SummableFamily.binomialFamily_orderTop_pos", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Binomial", "is_tactic_proof": false, "tactics": ["simp", "smul_assoc,", "have", "calc"], "tactic_count": 4}
{"name": "HahnSeries.SummableFamily.binomialFamily_mem_support", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Binomial", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "le_of_lt"], "tactic_count": 3}
{"name": "HahnSeries.SummableFamily.orderTop_hsum_binomialFamily_pos", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Binomial", "is_tactic_proof": true, "tactics": ["obtain", "simp", "refine", "constructor", "exact", "hsum_orderTop_of_le", "coeff_eq_zero_of_lt_orderTop", "have", "rw", "refine", "intro", "exact", "intro", "exact"], "tactic_count": 14}
{"name": "HahnSeries.instPowSubtypeUnitsMemSubgroupOrderTopSubOnePos", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Binomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.binomial_power", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Binomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.pow_add", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Binomial", "is_tactic_proof": true, "tactics": ["suffices", "suffices", "simp"], "tactic_count": 3}
{"name": "HahnSeries.coeff_toOrderTopSubOnePos_pow", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Binomial", "is_tactic_proof": true, "tactics": ["simp", "rw", "coeff_single_same", "intro", "rw", "contrapose", "apply", "by_cases"], "tactic_count": 8}
{"name": "HahnSeries.cardSupp", "kind": "definition", "module": "Mathlib.RingTheory.HahnSeries.Cardinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.cardSupp_congr", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Cardinal", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "HahnSeries.cardSupp_mono", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Cardinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.cardSupp_zero", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Cardinal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HahnSeries.cardSupp_single_of_ne", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Cardinal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HahnSeries.cardSupp_single_le", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Cardinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.cardSupp_one_le", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Cardinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.cardSupp_one", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Cardinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.cardSupp_map_le", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Cardinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.cardSupp_truncLT_le", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Cardinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.cardSupp_smul_le", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Cardinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.cardSupp_neg_le", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Cardinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.cardSupp_add_le", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Cardinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.cardSupp_neg", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Cardinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.cardSupp_sub_le", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Cardinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.cardSupp_mul_le", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Cardinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.cardSupp_single_mul_le", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Cardinal", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HahnSeries.cardSupp_mul_single_le", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Cardinal", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HahnSeries.cardSupp_pow_le", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Cardinal", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "HahnSeries.cardSupp_hsum_le", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Cardinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.cardSupp_hsum_powers_le", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Cardinal", "is_tactic_proof": true, "tactics": ["grw", "intro", "rw", "split_ifs", "exact", "cases"], "tactic_count": 6}
{"name": "HahnSeries.cardSupp_inv_le", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Cardinal", "is_tactic_proof": true, "tactics": ["obtain", "apply", "gcongr", "refine", "aesop"], "tactic_count": 5}
{"name": "HahnSeries.cardSupp_div_le", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Cardinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.cardSuppLTAddSubmonoid", "kind": "definition", "module": "Mathlib.RingTheory.HahnSeries.Cardinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.mem_cardSuppLTAddSubmonoid", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Cardinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.cardSuppLTAddSubgroup", "kind": "definition", "module": "Mathlib.RingTheory.HahnSeries.Cardinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.mem_cardSuppLTAddSubgroup", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Cardinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.cardSuppLTSubring", "kind": "definition", "module": "Mathlib.RingTheory.HahnSeries.Cardinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.mem_cardSuppLTSubring", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Cardinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.cardSuppLTSubfield", "kind": "definition", "module": "Mathlib.RingTheory.HahnSeries.Cardinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.mem_cardSuppLTSubfield", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Cardinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.SummableFamily.powerSeriesFamily", "kind": "abbrev", "module": "Mathlib.RingTheory.HahnSeries.HEval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.SummableFamily.powerSeriesFamily_of_not_orderTop_pos", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.HEval", "is_tactic_proof": true, "tactics": ["ext", "obtain"], "tactic_count": 2}
{"name": "HahnSeries.SummableFamily.powerSeriesFamily_of_orderTop_pos", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.HEval", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HahnSeries.SummableFamily.powerSeriesFamily_hsum_zero", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.HEval", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "simp", "rw", "simp", "rw", "simp"], "tactic_count": 7}
{"name": "HahnSeries.SummableFamily.powerSeriesFamily_add", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.HEval", "is_tactic_proof": true, "tactics": ["ext1", "by_cases"], "tactic_count": 2}
{"name": "HahnSeries.SummableFamily.powerSeriesFamily_smul", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.HEval", "is_tactic_proof": true, "tactics": ["ext1", "simp"], "tactic_count": 2}
{"name": "HahnSeries.SummableFamily.support_powerSeriesFamily_subset", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.HEval", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "intro", "have", "refine", "simpa", "simp", "obtain", "simp", "use", "simp", "rw", "pow_add,", "simp", "simp", "intro", "by_cases", "have", "simp", "use", "simp", "simp"], "tactic_count": 22}
{"name": "HahnSeries.SummableFamily.hsum_powerSeriesFamily_mul", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.HEval", "is_tactic_proof": true, "tactics": ["by_cases", "ext", "simp", "rw", "simp", "rw", "refine", "intro", "simp", "and_true]", "use", "simp_all", "intro", "have", "intro", "contrapose", "simp", "exact", "simp", "rw", "exact", "simp", "hsum_mul]", "rw"], "tactic_count": 24}
{"name": "PowerSeries.heval", "kind": "definition", "module": "Mathlib.RingTheory.HahnSeries.HEval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.heval_mul", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.HEval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.heval_C", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.HEval", "is_tactic_proof": true, "tactics": ["ext", "simp", "smul_eq_mul,", "rw", "by_cases"], "tactic_count": 5}
{"name": "PowerSeries.heval_X", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.HEval", "is_tactic_proof": true, "tactics": ["rw", "simp", "ext", "rw", "simp"], "tactic_count": 5}
{"name": "PowerSeries.heval_unit", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.HEval", "is_tactic_proof": true, "tactics": ["refine", "use", "rw"], "tactic_count": 3}
{"name": "PowerSeries.coeff_heval", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.HEval", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "PowerSeries.coeff_heval_zero", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.HEval", "is_tactic_proof": false, "tactics": ["rw", "simp", "intro", "simp", "refine", "by_cases", "refine", "simp", "simp"], "tactic_count": 9}
{"name": "instNonemptySeedRatReal", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.HahnEmbedding", "is_tactic_proof": true, "tactics": ["obtain", "choose", "refine", "apply", "simpa", "simpa"], "tactic_count": 6}
{"name": "hahnEmbedding_isOrderedModule_rat", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.HahnEmbedding", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "hahnEmbedding_isOrderedAddMonoid", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.HahnEmbedding", "is_tactic_proof": true, "tactics": ["let", "have", "have", "obtain", "let", "have", "have", "mk", "let", "have", "have", "rw", "simp", "refine", "intro", "simp_rw", "cases", "top", "coe"], "tactic_count": 19}
{"name": "HahnSeries.instPartialOrderLex", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.lt_iff", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Lex", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "HahnSeries.instLinearOrderLex", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.leadingCoeff_pos_iff", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Lex", "is_tactic_proof": true, "tactics": ["rw", "constructor", "intro", "have", "have", "refine", "intro", "simpa", "intro", "have", "apply", "simpa", "intro", "contrapose", "simpa", "have", "have", "have", "rw", "simpa"], "tactic_count": 20}
{"name": "HahnSeries.leadingCoeff_nonneg_iff", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Lex", "is_tactic_proof": true, "tactics": ["constructor", "obtain", "exact", "exact", "obtain", "simp", "exact"], "tactic_count": 7}
{"name": "HahnSeries.leadingCoeff_neg_iff", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Lex", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HahnSeries.leadingCoeff_nonpos_iff", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Lex", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HahnSeries.instIsOrderedAddMonoidLex", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.support_abs", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Lex", "is_tactic_proof": true, "tactics": ["obtain", "rw", "simp", "rw"], "tactic_count": 4}
{"name": "HahnSeries.orderTop_abs", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Lex", "is_tactic_proof": true, "tactics": ["obtain", "rw", "rw"], "tactic_count": 3}
{"name": "HahnSeries.order_abs", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Lex", "is_tactic_proof": true, "tactics": ["obtain", "simp", "have", "have", "apply", "rw", "apply"], "tactic_count": 7}
{"name": "HahnSeries.leadingCoeff_abs", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Lex", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "rw", "simp", "obtain", "rw"], "tactic_count": 6}
{"name": "HahnSeries.abs_lt_abs_of_orderTop_ofLex", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Lex", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp", "simpa"], "tactic_count": 4}
{"name": "HahnSeries.archimedeanClassMk_le_archimedeanClassMk_iff_of_orderTop_ofLex", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Lex", "is_tactic_proof": true, "tactics": ["simp_rw", "obtain", "simp_all", "have", "have", "constructor", "intro", "refine", "have", "obtain", "simp_rw", "simp_rw", "rw", "simp_rw", "obtain", "have", "simp", "convert", "exact", "intro", "refine", "refine", "intro", "trans", "apply", "simpa", "suffices", "apply", "simpa", "rw", "suffices", "simp_rw", "rw", "convert", "refine", "rwa"], "tactic_count": 36}
{"name": "HahnSeries.archimedeanClassMk_le_archimedeanClassMk_iff", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Lex", "is_tactic_proof": true, "tactics": ["obtain", "simpa", "simpa", "simp_rw", "refine", "intro", "contrapose", "rw", "have", "apply", "simpa", "exact"], "tactic_count": 12}
{"name": "HahnSeries.archimedeanClassMk_eq_archimedeanClassMk_iff", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Lex", "is_tactic_proof": false, "tactics": ["rw", "constructor", "simpa", "intro", "exact"], "tactic_count": 5}
{"name": "HahnSeries.finiteArchimedeanClassOrderHomLex", "kind": "definition", "module": "Mathlib.RingTheory.HahnSeries.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.finiteArchimedeanClassOrderHomInvLex", "kind": "definition", "module": "Mathlib.RingTheory.HahnSeries.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.finiteArchimedeanClassOrderIsoLex", "kind": "definition", "module": "Mathlib.RingTheory.HahnSeries.Lex", "is_tactic_proof": true, "tactics": ["apply", "ext", "cases", "h", "obtain", "induction", "mk", "simp", "ext", "induction", "mk", "simp", "archimedeanClassMk_eq_archimedeanClassMk_iff,"], "tactic_count": 13}
{"name": "HahnSeries.finiteArchimedeanClassOrderIsoLex_apply_fst", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Lex", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HahnSeries.finiteArchimedeanClassOrderIsoLex_apply_snd", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Lex", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HahnSeries.finiteArchimedeanClassOrderIso", "kind": "definition", "module": "Mathlib.RingTheory.HahnSeries.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.finiteArchimedeanClassOrderIso_apply", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Lex", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HahnSeries.archimedeanClassOrderIsoWithTop", "kind": "definition", "module": "Mathlib.RingTheory.HahnSeries.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.archimedeanClassOrderIsoWithTop_apply", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Lex", "is_tactic_proof": true, "tactics": ["unfold", "obtain"], "tactic_count": 2}
{"name": "HahnSeries.instIsOrderedRingLexOfNoZeroDivisors", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.instIsStrictOrderedRingLexOfIsDomain", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.embDomainOrderEmbedding", "kind": "definition", "module": "Mathlib.RingTheory.HahnSeries.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.embDomainOrderAddMonoidHom", "kind": "definition", "module": "Mathlib.RingTheory.HahnSeries.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.embDomainOrderAddMonoidHom_injective", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Lex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.instOne", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.instNatCast", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.instIntCast", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.instNNRatCast", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.instRatCast", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.coeff_one", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.single_zero_one", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.single_zero_natCast", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.single_zero_intCast", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.single_zero_nnratCast", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.single_zero_ratCast", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.single_zero_ofNat", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.support_one", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.orderTop_one", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HahnSeries.order_one", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": true, "tactics": ["cases", "rw", "exact"], "tactic_count": 3}
{"name": "HahnSeries.leadingCoeff_one", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HahnSeries.map_one", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.instAddCommMonoidWithOne", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.instAddCommGroupWithOne", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnModule", "kind": "definition", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnModule.of", "kind": "definition", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnModule.rec", "kind": "definition", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnModule.ext", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnModule.instZero", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnModule.instAddCommMonoid", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnModule.instAddCommGroup", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnModule.instBaseSMul", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnModule.of_zero", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnModule.of_add", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnModule.of_sub", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnModule.of_symm_zero", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnModule.of_symm_add", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnModule.of_symm_sub", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnModule.instSMul", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnModule.coeff_smul", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnModule.instBaseSMulZeroClass", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnModule.of_smul", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnModule.of_symm_smul", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnModule.instSMulZeroClass", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnModule.coeff_smul_right", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": true, "tactics": ["classical", "rw", "apply", "intro", "simp", "rw"], "tactic_count": 6}
{"name": "HahnModule.coeff_smul_left", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": true, "tactics": ["classical", "rw", "apply", "intro", "simp", "rw"], "tactic_count": 6}
{"name": "HahnModule.smul_add", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": true, "tactics": ["ext", "have", "rw", "simp_all", "rw", "simp_all", "intro", "simp_all", "contrapose", "intro", "rw"], "tactic_count": 11}
{"name": "HahnModule.instDistribSMul", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnModule.add_smul", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": true, "tactics": ["ext", "have", "rw", "simp_all", "rw", "simp", "intro", "simp_all", "ne_eq,", "contrapose", "intro", "rw"], "tactic_count": 12}
{"name": "HahnModule.coeff_single_smul_vadd", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": true, "tactics": ["by_cases", "simp_all", "simp", "by_cases", "simp", "rw", "ext", "simp", "rintro", "rw", "exact", "trans", "apply", "ext", "simp", "constructor", "rintro", "exact", "rintro", "exact", "simp"], "tactic_count": 21}
{"name": "HahnModule.coeff_single_zero_smul", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": true, "tactics": ["nth_rw", "exact"], "tactic_count": 2}
{"name": "HahnModule.single_zero_smul_eq_smul", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "HahnModule.zero_smul'", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "HahnModule.one_smul'", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "HahnModule.support_smul_subset_vadd_support'", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": true, "tactics": ["apply", "exact", "exact", "intro", "simp", "contrapose", "simp"], "tactic_count": 7}
{"name": "HahnModule.support_smul_subset_vadd_support", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "HahnModule.orderTop_vAdd_le_orderTop_smul", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": true, "tactics": ["by_cases", "by_cases", "have", "rw", "by_cases", "rw", "exact", "rw", "exact"], "tactic_count": 9}
{"name": "HahnModule.coeff_smul_order_add_order", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": true, "tactics": ["by_cases", "by_cases", "rw", "simp"], "tactic_count": 4}
{"name": "HahnSeries.instMul", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.of_symm_smul_of_eq_mul", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.coeff_mul", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.map_mul", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": true, "tactics": ["ext", "simp", "refine", "simp_all", "exact", "simp_all", "by_cases", "exact", "exact"], "tactic_count": 9}
{"name": "HahnSeries.coeff_mul_left'", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.coeff_mul_right'", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.instDistrib", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.coeff_single_mul_add", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "HahnSeries.coeff_mul_single_add", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "simp", "by_cases", "simp", "rw", "ext", "simp", "rintro", "rw", "exact", "trans", "apply", "ext", "simp", "constructor", "rintro", "exact", "rintro", "simp", "simp"], "tactic_count": 21}
{"name": "HahnSeries.coeff_single_mul", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HahnSeries.coeff_mul_single", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HahnSeries.coeff_mul_single_zero", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HahnSeries.coeff_single_zero_mul", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HahnSeries.single_zero_mul_eq_smul", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "HahnSeries.support_mul_subset", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "HahnSeries.instNonUnitalNonAssocSemiring", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.coeff_mul_order_add_order", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "HahnSeries.orderTop_mul_of_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": true, "tactics": ["by_cases", "by_cases", "have", "have", "rw", "refine", "rw", "exact"], "tactic_count": 8}
{"name": "HahnSeries.orderTop_mul", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": true, "tactics": ["by_cases", "by_cases", "apply", "simp_all"], "tactic_count": 4}
{"name": "HahnSeries.orderTop_add_le_mul", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "HahnSeries.order_mul_of_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": true, "tactics": ["have", "have", "have", "refine", "le_antisymm", "rw", "order_of_ne", "exact"], "tactic_count": 8}
{"name": "HahnSeries.leadingCoeff_mul_of_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HahnSeries.leadingCoeff_mul", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": true, "tactics": ["by_cases", "by_cases", "apply", "simp_all"], "tactic_count": 4}
{"name": "HahnSeries.order_single_mul_of_isRegular", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": true, "tactics": ["obtain", "exact", "have", "rwa", "rw"], "tactic_count": 5}
{"name": "_private.Mathlib.RingTheory.HahnSeries.Multiplication.0.HahnSeries.mul_assoc'", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": true, "tactics": ["ext", "rw", "coeff_mul_right", "simp", "apply", "aesop"], "tactic_count": 6}
{"name": "HahnSeries.instNonUnitalSemiring", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.instNonAssocSemiring", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.instSemiring", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.instNonUnitalCommSemiring", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.instCommSemiring", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.instNonUnitalNonAssocRing", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.instNonUnitalRing", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.instNonAssocRing", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.instRing", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.instNonUnitalCommRing", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.instCommRing", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.orderTop_nsmul_le_orderTop_pow", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": true, "tactics": ["induction", "zero", "simp", "by_cases", "simp", "have", "simp", "succ", "rw", "calc", "n"], "tactic_count": 11}
{"name": "HahnSeries.orderTop_self_sub_one_pos_iff", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": true, "tactics": ["constructor", "intro", "constructor", "rw", "exact", "rw", "exact", "intro", "refine", "lt_of_le_of_ne", "rw"], "tactic_count": 11}
{"name": "HahnSeries.orderTop_sub_pos", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "HahnSeries.orderTopSubOnePos", "kind": "definition", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.mem_orderTopSubOnePos_iff", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.HahnSeries.Multiplication.0.HahnModule.mul_smul'", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": true, "tactics": ["ext", "rw", "coeff_smul_right", "simp", "apply", "aesop"], "tactic_count": 6}
{"name": "HahnModule.instBaseModule", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnModule.instModule", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnModule.instIsScalarTowerHahnSeries", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnModule.instIsScalarTowerHahnSeries_1", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnModule.SMulCommClass", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnModule.instIsTorsionFree", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.single_mul_single", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "rw", "simp", "rw", "simp_rw", "rintro", "rw", "exact"], "tactic_count": 9}
{"name": "HahnSeries.single_pow", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "HahnSeries.C", "kind": "definition", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.C_zero", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.C_one", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.map_C", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": true, "tactics": ["ext", "by_cases"], "tactic_count": 2}
{"name": "HahnSeries.C_injective", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": true, "tactics": ["intro", "rw", "have", "rwa"], "tactic_count": 4}
{"name": "HahnSeries.C_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.order_C", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "exact"], "tactic_count": 3}
{"name": "HahnSeries.C_mul_eq_smul", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.embDomain_mul", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "obtain", "simp", "trans", "simp", "apply", "rintro", "simp", "obtain", "simp", "rintro", "contrapose", "obtain", "obtain", "simp", "simp", "exact", "rw", "contrapose", "obtain", "obtain", "obtain", "exact"], "tactic_count": 24}
{"name": "HahnSeries.embDomain_one", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.embDomainRingHom", "kind": "definition", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.embDomainRingHom_C", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.instAlgebra", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.C_eq_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.algebraMap_apply", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.instNontrivialSubalgebra", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.embDomainAlgHom", "kind": "definition", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.instIsCancelMulZeroOfIsCancelAdd", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.instNoZeroDivisors", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.order_mul", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": true, "tactics": ["apply", "apply", "simp", "rw", "exact"], "tactic_count": 5}
{"name": "HahnSeries.order_pow", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.instIsDomainOfIsCancelAdd", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.toPowerSeries", "kind": "definition", "module": "Mathlib.RingTheory.HahnSeries.PowerSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.coeff_toPowerSeries", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.PowerSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.coeff_toPowerSeries_symm", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.PowerSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.ofPowerSeries", "kind": "definition", "module": "Mathlib.RingTheory.HahnSeries.PowerSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.ofPowerSeries_injective", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.PowerSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.ofPowerSeries_apply", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.PowerSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.ofPowerSeries_apply_coeff", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.PowerSeries", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HahnSeries.ofPowerSeries_C", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.PowerSeries", "is_tactic_proof": true, "tactics": ["ext", "simp", "split_ifs", "subst", "convert", "rw", "simp", "intro", "simp"], "tactic_count": 9}
{"name": "HahnSeries.ofPowerSeries_X", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.PowerSeries", "is_tactic_proof": true, "tactics": ["ext", "simp", "split_ifs", "rw", "convert", "rw", "simp", "intro", "simp"], "tactic_count": 9}
{"name": "HahnSeries.ofPowerSeries_X_pow", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.PowerSeries", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HahnSeries.toMvPowerSeries", "kind": "definition", "module": "Mathlib.RingTheory.HahnSeries.PowerSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.instNoZeroDivisorsFinsuppNat", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.PowerSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.coeff_toMvPowerSeries", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.PowerSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.coeff_toMvPowerSeries_symm", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.PowerSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.toPowerSeriesAlg", "kind": "definition", "module": "Mathlib.RingTheory.HahnSeries.PowerSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.ofPowerSeriesAlg", "kind": "definition", "module": "Mathlib.RingTheory.HahnSeries.PowerSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.powerSeriesAlgebra", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.PowerSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.algebraMap_apply'", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.PowerSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.algebraMap_hahnSeries_apply", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.PowerSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.algebraMap_hahnSeries_injective", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.PowerSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.SummableFamily.instFunLike", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.SummableFamily.coe_mk", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.SummableFamily.isPWO_iUnion_support", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.SummableFamily.finite_co_support", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.SummableFamily.coe_injective", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.SummableFamily.ext", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.SummableFamily.instAdd", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.SummableFamily.instZero", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.SummableFamily.instInhabited", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.SummableFamily.coe_add", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.SummableFamily.add_apply", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.SummableFamily.coe_zero", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.SummableFamily.zero_apply", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.SummableFamily.instSMul", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.SummableFamily.coe_smul'", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.SummableFamily.smul_apply'", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.SummableFamily.instAddCommMonoid", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.SummableFamily.coeff", "kind": "definition", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.SummableFamily.coeff_def", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.SummableFamily.hsum", "kind": "definition", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.SummableFamily.coeff_hsum", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.SummableFamily.hsum_zero", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "HahnSeries.SummableFamily.support_hsum_subset", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.SummableFamily.hsum_add", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": true, "tactics": ["ext", "simp", "exact"], "tactic_count": 3}
{"name": "HahnSeries.SummableFamily.coeff_hsum_eq_sum_of_subset", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "HahnSeries.SummableFamily.coeff_hsum_eq_sum", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HahnSeries.SummableFamily.single", "kind": "definition", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.SummableFamily.hsum_single", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": true, "tactics": ["ext", "rw", "simp"], "tactic_count": 3}
{"name": "HahnSeries.SummableFamily.const", "kind": "definition", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.SummableFamily.hsum_unique", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "HahnSeries.SummableFamily.Equiv", "kind": "definition", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.SummableFamily.hsum_equiv", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": true, "tactics": ["ext", "simp", "exact"], "tactic_count": 3}
{"name": "HahnSeries.SummableFamily.smulFamily", "kind": "definition", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.SummableFamily.hsum_smulFamily", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.SummableFamily.le_hsum_support_mem", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": true, "tactics": ["rw", "obtain", "exact"], "tactic_count": 3}
{"name": "HahnSeries.SummableFamily.hsum_orderTop_of_le", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.SummableFamily.hsum_leadingCoeff_of_le", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": true, "tactics": ["have", "rw", "have", "by_contra", "simp", "simp", "simp", "rw"], "tactic_count": 8}
{"name": "HahnSeries.SummableFamily.instNeg", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.SummableFamily.coe_neg", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.SummableFamily.neg_apply", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.SummableFamily.instSub", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.SummableFamily.coe_sub", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.SummableFamily.sub_apply", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.SummableFamily.instAddCommGroup", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.SummableFamily.smul_support_subset_prod", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": true, "tactics": ["intro", "simp_all", "exact"], "tactic_count": 3}
{"name": "HahnSeries.SummableFamily.smul_support_finite", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.SummableFamily.isPWO_iUnion_support_prod_smul", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": true, "tactics": ["apply", "have", "support", "intro", "refine", "simp", "contrapose", "rw", "refine", "simp_all", "exact"], "tactic_count": 11}
{"name": "HahnSeries.SummableFamily.finite_co_support_prod_smul", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": false, "tactics": ["apply", "exact", "simp", "obtain", "simp", "exact", "hij.2⟩"], "tactic_count": 7}
{"name": "HahnSeries.SummableFamily.smul", "kind": "definition", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.SummableFamily.sum_vAddAntidiagonal_eq", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": true, "tactics": ["refine", "simp_all", "exact", "by_cases", "exact", "simp_all"], "tactic_count": 6}
{"name": "HahnSeries.SummableFamily.coeff_smul", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": true, "tactics": ["rw", "simp", "simp_rw", "rw", "refine", "rw", "refine", "have", "simp_all", "coeff_support,", "exact"], "tactic_count": 11}
{"name": "HahnSeries.SummableFamily.smul_hsum", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": true, "tactics": ["ext", "rw", "refine", "simp_all", "constructor", "rw", "have", "simpa", "by_contra", "simp_all", "simp", "by_cases", "exact", "simp_all"], "tactic_count": 14}
{"name": "HahnSeries.SummableFamily.instSMulOfSMulWithZero", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.SummableFamily.smul_eq", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.SummableFamily.smul_apply", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.SummableFamily.hsum_smul_module", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HahnSeries.SummableFamily.instModule", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.SummableFamily.hsum_smul", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HahnSeries.SummableFamily.lsum", "kind": "definition", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.SummableFamily.hsum_sub", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HahnSeries.SummableFamily.isPWO_iUnion_support_prod_mul", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.SummableFamily.finite_co_support_prod_mul", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.SummableFamily.mul", "kind": "definition", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.SummableFamily.mul_eq_smul", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.SummableFamily.coeff_hsum_mul", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "HahnSeries.SummableFamily.hsum_mul", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "HahnSeries.SummableFamily.ofFinsupp", "kind": "definition", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.SummableFamily.coe_ofFinsupp", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.SummableFamily.hsum_ofFinsupp", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": true, "tactics": ["ext", "simp", "simp_rw", "rw", "intro", "simp", "contrapose", "simp"], "tactic_count": 8}
{"name": "HahnSeries.SummableFamily.embDomain", "kind": "definition", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.SummableFamily.embDomain_apply", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.SummableFamily.embDomain_image", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "HahnSeries.SummableFamily.embDomain_notin_range", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HahnSeries.SummableFamily.hsum_embDomain", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": true, "tactics": ["classical", "ext", "simp", "exact"], "tactic_count": 4}
{"name": "HahnSeries.SummableFamily.support_pow_subset_closure", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": true, "tactics": ["intro", "induction", "zero", "simp", "simp", "exact", "succ", "obtain", "exact"], "tactic_count": 9}
{"name": "HahnSeries.SummableFamily.isPWO_iUnion_support_powers", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.SummableFamily.co_support_zero", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": true, "tactics": ["simp", "intro", "by_contra", "simp_all"], "tactic_count": 4}
{"name": "HahnSeries.SummableFamily.pow_finite_co_support", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": false, "tactics": ["have", "by_cases", "by_cases", "swap", "apply", "intro", "refine", "hy", "obtain", "exact", "lt_add_of_pos_left", "lt_of_lt_of_le", "rintro", "exact", "obtain", "refine", "simp", "exact"], "tactic_count": 18}
{"name": "HahnSeries.SummableFamily.powers", "kind": "definition", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.SummableFamily.powers_of_orderTop_pos", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HahnSeries.SummableFamily.powers_of_not_orderTop_pos", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": true, "tactics": ["ext", "obtain"], "tactic_count": 2}
{"name": "HahnSeries.SummableFamily.powers_zero", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": true, "tactics": ["ext", "rw", "obtain"], "tactic_count": 3}
{"name": "HahnSeries.SummableFamily.coe_powers", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": true, "tactics": ["ext1", "simp"], "tactic_count": 2}
{"name": "HahnSeries.SummableFamily.embDomain_succ_smul_powers", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": true, "tactics": ["apply", "rintro", "simp", "simp"], "tactic_count": 4}
{"name": "HahnSeries.SummableFamily.one_sub_self_mul_hsum_powers", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": false, "tactics": ["rw", "hsum_embDomain", "simp"], "tactic_count": 3}
{"name": "HahnSeries.one_minus_single_neg_mul", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": true, "tactics": ["nth_rw", "rw", "sub_eq_zero_of_eq"], "tactic_count": 3}
{"name": "HahnSeries.unit_aux", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": true, "tactics": ["let", "by_cases", "have", "simp", "have", "have", "rw", "refine", "rw", "exact", "rw", "exact"], "tactic_count": 12}
{"name": "HahnSeries.isUnit_of_isUnit_leadingCoeff_AddUnitOrder", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": true, "tactics": ["let", "rw", "rw", "have", "rw", "exact"], "tactic_count": 6}
{"name": "HahnSeries.isUnit_of_orderTop_pos", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": true, "tactics": ["obtain", "exact", "refine", "rw", "exact", "have", "rw", "rw", "exact"], "tactic_count": 9}
{"name": "HahnSeries.toOrderTopSubOnePos", "kind": "definition", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.isUnit_iff", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "refine", "rw", "rw", "rintro", "rw", "rw", "have", "rw", "exact"], "tactic_count": 11}
{"name": "HahnSeries.instDivInvMonoid", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.inv_single", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": true, "tactics": ["obtain", "simp", "simp"], "tactic_count": 3}
{"name": "HahnSeries.single_div_single", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HahnSeries.instField", "kind": "instance", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries._example", "kind": "example", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries._example", "kind": "example", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.single_zero_ofScientific", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Summable", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HahnSeries.addVal", "kind": "definition", "module": "Mathlib.RingTheory.HahnSeries.Valuation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.addVal_apply", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Valuation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.addVal_apply_of_ne", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Valuation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HahnSeries.addVal_le_of_coeff_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.HahnSeries.Valuation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLocalHom_of_le_jacobson_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Henselian", "is_tactic_proof": true, "tactics": ["constructor", "intro", "have", "rw", "obtain", "obtain", "use", "rw", "exact", "obtain", "obtain", "rw", "specialize", "have", "exact"], "tactic_count": 15}
{"name": "Field.henselian", "kind": "instance", "module": "Mathlib.RingTheory.Henselian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HenselianLocalRing.TFAE", "kind": "theorem", "module": "Mathlib.RingTheory.Henselian", "is_tactic_proof": false, "tactics": ["tfae_have", "tfae_have", "constructor", "intro", "specialize", "have", "simp", "obtain", "refine", "rw", "rwa", "tfae_have", "hR,", "obtain", "have", "simp", "obtain", "contrapose", "rwa", "refine", "rwa", "tfae_finish"], "tactic_count": 22}
{"name": "instHenselianRingMaximalIdeal", "kind": "instance", "module": "Mathlib.RingTheory.Henselian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAdicComplete.henselianRing", "kind": "instance", "module": "Mathlib.RingTheory.Henselian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HopfAlgebra.mul_antipode_rTensor_comul_apply", "kind": "theorem", "module": "Mathlib.RingTheory.HopfAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HopfAlgebra.mul_antipode_lTensor_comul_apply", "kind": "theorem", "module": "Mathlib.RingTheory.HopfAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HopfAlgebra.antipode_one", "kind": "theorem", "module": "Mathlib.RingTheory.HopfAlgebra.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HopfAlgebra.sum_antipode_mul_eq_algebraMap_counit", "kind": "theorem", "module": "Mathlib.RingTheory.HopfAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HopfAlgebra.sum_mul_antipode_eq_algebraMap_counit", "kind": "theorem", "module": "Mathlib.RingTheory.HopfAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HopfAlgebra.sum_antipode_mul_eq_smul", "kind": "theorem", "module": "Mathlib.RingTheory.HopfAlgebra.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HopfAlgebra.sum_mul_antipode_eq_smul", "kind": "theorem", "module": "Mathlib.RingTheory.HopfAlgebra.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HopfAlgebra.counit_antipode", "kind": "theorem", "module": "Mathlib.RingTheory.HopfAlgebra.Basic", "is_tactic_proof": true, "tactics": ["calc", "counit", "simp_rw"], "tactic_count": 3}
{"name": "HopfAlgebra.counit_comp_antipode", "kind": "theorem", "module": "Mathlib.RingTheory.HopfAlgebra.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CommSemiring.toHopfAlgebra", "kind": "instance", "module": "Mathlib.RingTheory.HopfAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommSemiring.antipode_eq_id", "kind": "theorem", "module": "Mathlib.RingTheory.HopfAlgebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGroupLikeElem.antipode_mul_cancel", "kind": "theorem", "module": "Mathlib.RingTheory.HopfAlgebra.GroupLike", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsGroupLikeElem.mul_antipode_cancel", "kind": "theorem", "module": "Mathlib.RingTheory.HopfAlgebra.GroupLike", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "GroupLike.toUnits", "kind": "definition", "module": "Mathlib.RingTheory.HopfAlgebra.GroupLike", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGroupLikeElem.isUnit", "kind": "theorem", "module": "Mathlib.RingTheory.HopfAlgebra.GroupLike", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGroupLikeElem.antipode", "kind": "theorem", "module": "Mathlib.RingTheory.HopfAlgebra.GroupLike", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGroupLikeElem.antipode_antipode", "kind": "theorem", "module": "Mathlib.RingTheory.HopfAlgebra.GroupLike", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupLike.instInv", "kind": "instance", "module": "Mathlib.RingTheory.HopfAlgebra.GroupLike", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupLike.val_inv", "kind": "theorem", "module": "Mathlib.RingTheory.HopfAlgebra.GroupLike", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupLike.instGroup", "kind": "instance", "module": "Mathlib.RingTheory.HopfAlgebra.GroupLike", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupLike.instCommGroup", "kind": "instance", "module": "Mathlib.RingTheory.HopfAlgebra.GroupLike", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidAlgebra.instHopfAlgebraStruct", "kind": "instance", "module": "Mathlib.RingTheory.HopfAlgebra.MonoidAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidAlgebra.antipode_single", "kind": "theorem", "module": "Mathlib.RingTheory.HopfAlgebra.MonoidAlgebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MonoidAlgebra.instHopfAlgebra", "kind": "instance", "module": "Mathlib.RingTheory.HopfAlgebra.MonoidAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LaurentPolynomial.instHopfAlgebra", "kind": "instance", "module": "Mathlib.RingTheory.HopfAlgebra.MonoidAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LaurentPolynomial.antipode_C", "kind": "theorem", "module": "Mathlib.RingTheory.HopfAlgebra.MonoidAlgebra", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "LaurentPolynomial.antipode_T", "kind": "theorem", "module": "Mathlib.RingTheory.HopfAlgebra.MonoidAlgebra", "is_tactic_proof": true, "tactics": ["unfold", "rw", "simp"], "tactic_count": 3}
{"name": "LaurentPolynomial.antipode_C_mul_T", "kind": "theorem", "module": "Mathlib.RingTheory.HopfAlgebra.MonoidAlgebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HopfAlgebra.ofAlgHom", "kind": "abbrev", "module": "Mathlib.RingTheory.HopfAlgebra.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.instHopfAlgebra", "kind": "instance", "module": "Mathlib.RingTheory.HopfAlgebra.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.antipode_def", "kind": "theorem", "module": "Mathlib.RingTheory.HopfAlgebra.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSemiprimaryRing.induction", "kind": "theorem", "module": "Mathlib.RingTheory.HopkinsLevitzki", "is_tactic_proof": true, "tactics": ["have", "set", "replace", "have", "rw", "intro", "let", "have", "exact", "induction", "zero", "succ", "obtain", "rw", "refine", "rwa", "rw", "exact"], "tactic_count": 18}
{"name": "_private.Mathlib.RingTheory.HopkinsLevitzki.0.IsSemiprimaryRing.finite_of_isNoetherian_or_isArtinian", "kind": "theorem", "module": "Mathlib.RingTheory.HopkinsLevitzki", "is_tactic_proof": false, "tactics": ["refine", "let", "have", "simp_rw", "exact", "let", "have", "have", "exact"], "tactic_count": 9}
{"name": "IsSemiprimaryRing.finite_of_isNoetherian", "kind": "theorem", "module": "Mathlib.RingTheory.HopkinsLevitzki", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSemiprimaryRing.finite_of_isArtinian", "kind": "theorem", "module": "Mathlib.RingTheory.HopkinsLevitzki", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSemiprimaryRing.isNoetherian_iff_isArtinian", "kind": "theorem", "module": "Mathlib.RingTheory.HopkinsLevitzki", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSemiprimaryRing.isNoetherian_iff_finite_of_jacobson_fg", "kind": "theorem", "module": "Mathlib.RingTheory.HopkinsLevitzki", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSemiprimaryRing.isNoetherianRing_iff_jacobson_fg", "kind": "theorem", "module": "Mathlib.RingTheory.HopkinsLevitzki", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsArtinianRing.tfae", "kind": "theorem", "module": "Mathlib.RingTheory.HopkinsLevitzki", "is_tactic_proof": true, "tactics": ["tfae_have", "tfae_have", "tfae_have", "rw", "tfae_have", "tfae_have", "tfae_finish"], "tactic_count": 7}
{"name": "isArtinianRing_iff_isFiniteLength", "kind": "theorem", "module": "Mathlib.RingTheory.HopkinsLevitzki", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsNoetherianRingOfIsArtinianRing", "kind": "instance", "module": "Mathlib.RingTheory.HopkinsLevitzki", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isNoetherian_of_finite_isArtinian", "kind": "theorem", "module": "Mathlib.RingTheory.HopkinsLevitzki", "is_tactic_proof": true, "tactics": ["obtain", "rw", "rw", "rw", "have", "rw", "let", "rw", "refine", "rw", "infer_instance", "infer_instance"], "tactic_count": 12}
{"name": "IsNoetherianRing.isArtinianRing_of_krullDimLE_zero", "kind": "theorem", "module": "Mathlib.RingTheory.HopkinsLevitzki", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isArtinianRing_iff_isNoetherianRing_krullDimLE_zero", "kind": "theorem", "module": "Mathlib.RingTheory.HopkinsLevitzki", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isArtinianRing_iff_krullDimLE_zero", "kind": "theorem", "module": "Mathlib.RingTheory.HopkinsLevitzki", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "isArtinianRing_iff_isNilpotent_maximalIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.HopkinsLevitzki", "is_tactic_proof": false, "tactics": ["rw", "and_iff_left", "and_iff_right]", "exact"], "tactic_count": 4}
{"name": "IdealFilter", "kind": "abbrev", "module": "Mathlib.RingTheory.IdealFilter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IdealFilter.IsTorsionElem", "kind": "definition", "module": "Mathlib.RingTheory.IdealFilter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IdealFilter.IsTorsion", "kind": "definition", "module": "Mathlib.RingTheory.IdealFilter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IdealFilter.IsTorsionQuot", "kind": "definition", "module": "Mathlib.RingTheory.IdealFilter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IdealFilter.isTorsionQuot_inter_left_iff", "kind": "theorem", "module": "Mathlib.RingTheory.IdealFilter.Basic", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rcases", "have", "exact"], "tactic_count": 5}
{"name": "IdealFilter.isTorsion_def", "kind": "theorem", "module": "Mathlib.RingTheory.IdealFilter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IdealFilter.isTorsionQuot_def", "kind": "theorem", "module": "Mathlib.RingTheory.IdealFilter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IdealFilter.isTorsionQuot_self", "kind": "theorem", "module": "Mathlib.RingTheory.IdealFilter.Basic", "is_tactic_proof": true, "tactics": ["intro", "obtain", "exact"], "tactic_count": 3}
{"name": "IdealFilter.IsTorsionQuot.mono_left", "kind": "theorem", "module": "Mathlib.RingTheory.IdealFilter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IdealFilter.IsTorsionQuot.anti_right", "kind": "theorem", "module": "Mathlib.RingTheory.IdealFilter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IdealFilter.IsTorsionQuot.mono", "kind": "theorem", "module": "Mathlib.RingTheory.IdealFilter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IdealFilter.IsTorsionQuot.inf", "kind": "theorem", "module": "Mathlib.RingTheory.IdealFilter.Basic", "is_tactic_proof": true, "tactics": ["intro", "obtain", "obtain", "exact"], "tactic_count": 4}
{"name": "IdealFilter.isPFilter_gabrielComposition", "kind": "theorem", "module": "Mathlib.RingTheory.IdealFilter.Basic", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact", "rintro", "refine", "exact", "intro", "exact"], "tactic_count": 8}
{"name": "IdealFilter.gabrielComposition", "kind": "definition", "module": "Mathlib.RingTheory.IdealFilter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IdealFilter.term_•_", "kind": "definition", "module": "Mathlib.RingTheory.IdealFilter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IdealFilter._aux_Mathlib_RingTheory_IdealFilter_Basic___macroRules_IdealFilter_term_•__1", "kind": "definition", "module": "Mathlib.RingTheory.IdealFilter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IdealFilter._aux_Mathlib_RingTheory_IdealFilter_Basic___unexpand_IdealFilter_gabrielComposition_1", "kind": "definition", "module": "Mathlib.RingTheory.IdealFilter.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IdealFilter.isGabriel_iff", "kind": "theorem", "module": "Mathlib.RingTheory.IdealFilter.Basic", "is_tactic_proof": true, "tactics": ["constructor", "intro", "refine", "ext", "constructor", "rcases", "refine", "rcases", "exact", "exact", "rintro", "refine", "rintro", "exact"], "tactic_count": 14}
{"name": "IdealFilter.addGroupFilterBasis", "kind": "definition", "module": "Mathlib.RingTheory.IdealFilter.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IdealFilter.ringFilterBasis", "kind": "definition", "module": "Mathlib.RingTheory.IdealFilter.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IdealFilter.isUniform_iff_exists_ringFilterBasis", "kind": "theorem", "module": "Mathlib.RingTheory.IdealFilter.Topology", "is_tactic_proof": true, "tactics": ["refine", "obtain", "obtain", "exact"], "tactic_count": 4}
{"name": "WithIdealFilter", "kind": "definition", "module": "Mathlib.RingTheory.IdealFilter.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithIdealFilter.instRing", "kind": "instance", "module": "Mathlib.RingTheory.IdealFilter.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithIdealFilter.idealSet", "kind": "abbrev", "module": "Mathlib.RingTheory.IdealFilter.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithIdealFilter.instTopologicalSpace", "kind": "instance", "module": "Mathlib.RingTheory.IdealFilter.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithIdealFilter.instIsTopologicalAddGroup", "kind": "instance", "module": "Mathlib.RingTheory.IdealFilter.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithIdealFilter.mem_nhds_iff", "kind": "theorem", "module": "Mathlib.RingTheory.IdealFilter.Topology", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rcases", "rcases", "exact", "rintro", "refine", "exact"], "tactic_count": 8}
{"name": "WithIdealFilter.mem_nhds_zero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.IdealFilter.Topology", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "WithIdealFilter.instIsLinearTopology", "kind": "instance", "module": "Mathlib.RingTheory.IdealFilter.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithIdealFilter.instIsTopologicalRing", "kind": "instance", "module": "Mathlib.RingTheory.IdealFilter.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAssociatedPrime", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.AssociatedPrime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "associatedPrimes", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.AssociatedPrime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AssociatePrimes.mem_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.AssociatedPrime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAssociatedPrime.isPrime", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.AssociatedPrime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAssociatedPrime.map_of_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.AssociatedPrime.Basic", "is_tactic_proof": true, "tactics": ["obtain", "refine", "ext", "simp_rw"], "tactic_count": 4}
{"name": "LinearEquiv.isAssociatedPrime_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.AssociatedPrime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_isAssociatedPrime_of_subsingleton", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.AssociatedPrime.Basic", "is_tactic_proof": true, "tactics": ["rintro", "apply", "simp"], "tactic_count": 3}
{"name": "exists_le_isAssociatedPrime_of_isNoetherianRing", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.AssociatedPrime.Basic", "is_tactic_proof": false, "tactics": ["obtain", "set_has_maximal_iff_noetherian.mpr", "refine", "intro", "rw", "intro", "rw", "have", "intro", "rw", "rw", "rwa"], "tactic_count": 12}
{"name": "associatedPrimes.subset_of_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.AssociatedPrime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "associatedPrimes.subset_union_of_exact", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.AssociatedPrime.Basic", "is_tactic_proof": true, "tactics": ["rintro", "by_cases", "obtain", "left", "refine", "rw", "rw", "apply_fun", "rw", "rw", "apply_fun", "rw", "contrapose", "exact", "right", "refine", "rw", "rw", "rw", "rw", "obtain", "by_contra", "exact"], "tactic_count": 23}
{"name": "associatedPrimes.prod", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.AssociatedPrime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.AssociatedPrimes.eq", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.AssociatedPrime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "associatedPrimes.eq_empty_of_subsingleton", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.AssociatedPrime.Basic", "is_tactic_proof": true, "tactics": ["ext", "apply"], "tactic_count": 2}
{"name": "associatedPrimes.nonempty", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.AssociatedPrime.Basic", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "exact"], "tactic_count": 3}
{"name": "biUnion_associatedPrimes_eq_zero_divisors", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.AssociatedPrime.Basic", "is_tactic_proof": true, "tactics": ["refine", "rintro", "exact", "intro", "obtain", "exact"], "tactic_count": 6}
{"name": "biUnion_associatedPrimes_eq_compl_nonZeroDivisors", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.AssociatedPrime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAssociatedPrime.annihilator_le", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.AssociatedPrime.Basic", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact"], "tactic_count": 3}
{"name": "isAssociatedPrime_iff_exists_injective_linearMap", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.AssociatedPrime.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "replace", "exact", "conv_lhs", "simp"], "tactic_count": 6}
{"name": "IsAssociatedPrime.eq_radical", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.AssociatedPrime.Basic", "is_tactic_proof": true, "tactics": ["obtain", "have", "rintro", "apply", "rwa", "obtain", "replace", "intro", "rw", "apply", "intro", "exact", "rw", "intro", "exact"], "tactic_count": 15}
{"name": "associatedPrimes.eq_singleton_of_isPrimary", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.AssociatedPrime.Basic", "is_tactic_proof": true, "tactics": ["ext", "rw", "refine", "rintro", "haveI", "refine", "rw", "exact", "obtain", "exact"], "tactic_count": 10}
{"name": "Submodule.IsQuotientEquivQuotientPrime", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.AssociatedPrime.Finiteness", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.isQuotientEquivQuotientPrime_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.AssociatedPrime.Finiteness", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsNoetherianRing.exists_relSeries_isQuotientEquivQuotientPrime", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.AssociatedPrime.Finiteness", "is_tactic_proof": true, "tactics": ["refine", "rintro", "have", "obtain", "obtain", "have", "have", "refine"], "tactic_count": 8}
{"name": "IsNoetherianRing.induction_on_isQuotientEquivQuotientPrime", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.AssociatedPrime.Finiteness", "is_tactic_proof": false, "tactics": ["have", "exact", "obtain", "suffices", "replace", "rw", "exact", "intro", "induction", "zero", "change", "rw", "exact", "succ", "specialize", "obtain", "replace", "exact", "exact"], "tactic_count": 19}
{"name": "associatedPrimes.finite", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.AssociatedPrime.Finiteness", "is_tactic_proof": true, "tactics": ["induction", "subsingleton", "quotient", "have", "simp", "exact"], "tactic_count": 6}
{"name": "Ideal.IsMaximal.mem_associatedPrimes_of_isFractionRing", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.AssociatedPrime.Finiteness", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFiniteMaximalSpectrumOfIsFractionRing", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.AssociatedPrime.Finiteness", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.bot_lt_annihilator_of_disjoint_nonZeroDivisors", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.AssociatedPrime.Finiteness", "is_tactic_proof": false, "tactics": ["obtain", "biUnion_associatedPrimes_eq_compl_nonZeroDivisors", "exact", "simpa"], "tactic_count": 4}
{"name": "Ideal.nonempty_inter_nonZeroDivisors_of_faithfulSMul", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.AssociatedPrime.Finiteness", "is_tactic_proof": true, "tactics": ["by_contra", "exact", "rwa"], "tactic_count": 3}
{"name": "Module.associatedPrimes.mem_associatedPrimes_of_comap_mem_associatedPrimes_of_isLocalizedModule", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.AssociatedPrime.Localization", "is_tactic_proof": true, "tactics": ["rcases", "constructor", "refine", "by_contra", "simp", "use", "ext", "rcases", "rw", "refine", "use", "simp", "have", "rw", "simp", "rw", "exact", "have", "rw", "have", "rw", "simp", "simpa"], "tactic_count": 23}
{"name": "Module.associatedPrimes.mem_associatedPrimes_atPrime_of_mem_associatedPrimes", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.AssociatedPrime.Localization", "is_tactic_proof": false, "tactics": ["apply", "mem_associatedPrimes_of_comap_mem_associatedPrimes_of_isLocalizedModule", "simpa"], "tactic_count": 3}
{"name": "Module.associatedPrimes.comap_mem_associatedPrimes_of_mem_associatedPrimes_of_isLocalizedModule_of_fg", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.AssociatedPrime.Localization", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "rcases", "simp", "have", "simp", "choose", "refine", "rw", "intro", "simp", "obtain", "rw", "exact", "simp", "have", "simpa", "hr]", "have", "have", "tauto"], "tactic_count": 21}
{"name": "Module.associatedPrimes.preimage_comap_associatedPrimes_eq_associatedPrimes_of_isLocalizedModule", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.AssociatedPrime.Localization", "is_tactic_proof": true, "tactics": ["ext", "exact", "comap_mem_associatedPrimes_of_mem_associatedPrimes_of_isLocalizedModule_of_fg"], "tactic_count": 3}
{"name": "Module.associatedPrimes.minimalPrimes_annihilator_subset_associatedPrimes", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.AssociatedPrime.Localization", "is_tactic_proof": true, "tactics": ["intro", "have", "let", "have", "simpa", "rcases", "have", "simp", "preimage_comap_associatedPrimes_eq_associatedPrimes_of_isLocalizedModule", "have", "le_of_eq_of_le", "have", "have", "simpa", "simpa"], "tactic_count": 15}
{"name": "Ideal.pi", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.mem_pi", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.pi_span", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Ideal.instIsTwoSidedForallPi", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.single_mem_pi", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Basic", "is_tactic_proof": true, "tactics": ["intro", "obtain", "simpa", "simp"], "tactic_count": 4}
{"name": "Ideal.pi_le_pi_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.add_pow_mem_of_pow_mem_of_le_of_commute", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "apply", "intro", "apply", "by_cases", "rw", "exact", "refine", "lia"], "tactic_count": 9}
{"name": "Ideal.add_pow_add_pred_mem_of_pow_mem_of_commute", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.add_pow_mem_of_pow_mem_of_le", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.add_pow_add_pred_mem_of_pow_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.pow_multiset_sum_mem_span_pow", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Basic", "is_tactic_proof": false, "tactics": ["induction", "empty", "cons", "simp", "add_pow]", "refine", "intro", "rw", "by_cases", "refine", "rw", "simp_rw", "rw", "use", "simp_rw", "refine", "replace", "have", "rw", "rw", "simp_rw", "exact"], "tactic_count": 22}
{"name": "Ideal.sum_pow_mem_span_pow", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Basic", "is_tactic_proof": true, "tactics": ["classical", "simpa"], "tactic_count": 2}
{"name": "Ideal.span_pow_eq_top", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Basic", "is_tactic_proof": true, "tactics": ["rw", "rcases", "obtain", "rw", "trivial", "exact", "rw", "rcases", "simp", "smul_eq_mul]", "have", "rw", "refine", "rintro", "simp_rw", "rcases", "have", "rw", "exact", "refine", "rw", "exact"], "tactic_count": 22}
{"name": "Ideal.span_range_pow_eq_top", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Basic", "is_tactic_proof": true, "tactics": ["have", "refine", "top_unique", "span_le.mpr", "rintro", "rw", "simp_rw", "exact"], "tactic_count": 8}
{"name": "Ideal.prod_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Basic", "is_tactic_proof": true, "tactics": ["classical", "rw", "exact"], "tactic_count": 3}
{"name": "Ideal.span_single_eq_top", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Basic", "is_tactic_proof": true, "tactics": ["rw", "rintro", "induction", "zero", "add", "single", "rw", "exact"], "tactic_count": 8}
{"name": "Ideal.equivFinTwo", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.instFinite", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.isSimpleOrder", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ring.exists_not_isUnit_of_not_isField", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Basic", "is_tactic_proof": true, "tactics": ["have", "simp_rw", "push_neg", "obtain", "exact"], "tactic_count": 5}
{"name": "Ring.isField_iff_maximal_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Basic", "is_tactic_proof": false, "tactics": ["refine", "let", "bot_isMaximal,", "by_contra", "obtain", "exact"], "tactic_count": 6}
{"name": "Ring.exists_maximal_of_not_isField", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Basic", "is_tactic_proof": true, "tactics": ["contrapose", "simp", "refine"], "tactic_count": 3}
{"name": "Ring.not_isField_of_ne_of_ne", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Basic", "is_tactic_proof": true, "tactics": ["contrapose", "exact"], "tactic_count": 2}
{"name": "Ring.not_isField_iff_exists_ideal_bot_lt_and_lt_top", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Basic", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact"], "tactic_count": 3}
{"name": "Ring.not_isField_iff_exists_prime", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Basic", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact"], "tactic_count": 3}
{"name": "Ring.isField_iff_isSimpleOrder_ideal", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Basic", "is_tactic_proof": true, "tactics": ["cases", "exact", "rw", "contrapose", "simp_rw", "exact"], "tactic_count": 6}
{"name": "Ring.ne_bot_of_isMaximal_of_not_isField", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Basic", "is_tactic_proof": true, "tactics": ["rintro", "obtain", "exact"], "tactic_count": 3}
{"name": "Ideal.bot_lt_of_maximal", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.basisSpanSingleton", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.basisSpanSingleton_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Basis", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Ideal.constr_basisSpanSingleton", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Basis.mem_ideal_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Basis.mem_ideal_iff'", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Basis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.sum_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.colon", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Colon", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mem_colon", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Colon", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mem_colon_singleton", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Colon", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Submodule.instIsTwoSidedColonCoe", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Colon", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.colon_univ", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Colon", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Submodule.bot_colon", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Colon", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Submodule.colon_mono", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Colon", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.le_colon", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Colon", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.iInf_colon_iUnion", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Colon", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Submodule.colon_inf_eq_left_of_subset", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Colon", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Submodule.colon_eq_top_iff_subset", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Colon", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Submodule.inf_colon", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Colon", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Submodule.iInf_colon", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Colon", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Submodule.colon_finsetInf", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Colon", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Submodule.top_colon", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Colon", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Submodule.colon_union", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Colon", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Submodule.colon_iUnion", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Colon", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Submodule.colon_empty", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Colon", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Submodule.colon_singleton_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Colon", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Submodule.colon_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Colon", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Submodule.mem_colon'", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Colon", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mem_colon_iff_le", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Colon", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Submodule.bot_colon'", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Colon", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Submodule.colon_span", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Colon", "is_tactic_proof": true, "tactics": ["refine", "induction", "mem", "zero", "add", "smul"], "tactic_count": 6}
{"name": "Ideal.colon_span", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Colon", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mem_colon_span_singleton", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Colon", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Ideal.mem_colon_span_singleton", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Colon", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Submodule.annihilator_map_mkQ_eq_colon", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Colon", "is_tactic_proof": true, "tactics": ["ext", "rw", "exact", "hpm"], "tactic_count": 4}
{"name": "Submodule.annihilator_quotient", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Colon", "is_tactic_proof": true, "tactics": ["ext", "have", "simpa", "rw"], "tactic_count": 4}
{"name": "Ideal.annihilator_quotient", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Colon", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.Cotangent", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Cotangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.toCotangent", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Cotangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.map_toCotangent_ker", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Cotangent", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.mem_toCotangent_ker", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Cotangent", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Ideal.toCotangent_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Cotangent", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Ideal.toCotangent_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Cotangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.toCotangent_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Cotangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.toCotangent_range", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Cotangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.cotangent_subsingleton_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Cotangent", "is_tactic_proof": true, "tactics": ["constructor", "intro", "refine", "exact", "exact"], "tactic_count": 5}
{"name": "Ideal.cotangentToQuotientSquare", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Cotangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.to_quotient_square_comp_toCotangent", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Cotangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.toCotangent_to_quotient_square", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Cotangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Cotangent.smul_eq_zero_of_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Cotangent", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact"], "tactic_count": 3}
{"name": "Ideal.isTorsionBySet_cotangent", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Cotangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.cotangentIdeal", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Cotangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.cotangentIdeal_square", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Cotangent", "is_tactic_proof": true, "tactics": ["rw", "intro", "refine", "rintro", "rw", "intro"], "tactic_count": 6}
{"name": "Ideal.mk_mem_cotangentIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Cotangent", "is_tactic_proof": true, "tactics": ["refine", "simpa"], "tactic_count": 2}
{"name": "Ideal.comap_cotangentIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Cotangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.range_cotangentToQuotientSquare", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Cotangent", "is_tactic_proof": true, "tactics": ["trans", "rw", "rw"], "tactic_count": 3}
{"name": "Ideal.cotangentEquivIdeal", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Cotangent", "is_tactic_proof": false, "tactics": ["refine", "rw", "rintro", "replace", "obtain", "obtain", "rw", "dsimp", "rwa", "rintro", "exact"], "tactic_count": 11}
{"name": "Ideal.cotangentEquivIdeal_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Cotangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.cotangentEquivIdeal_symm_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Cotangent", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AlgHom.kerSquareLift", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Cotangent", "is_tactic_proof": true, "tactics": ["refine", "intro", "intro", "rw", "exact"], "tactic_count": 5}
{"name": "AlgHom.kerSquareLift_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Cotangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.ker_kerSquareLift", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Cotangent", "is_tactic_proof": true, "tactics": ["apply", "intro", "rintro"], "tactic_count": 3}
{"name": "Ideal.Algebra.kerSquareLift", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Cotangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.instIsScalarTowerQuotientHPowKerRingHomAlgebraMapOfNat", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Cotangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.quotCotangent", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Cotangent", "is_tactic_proof": true, "tactics": ["refine", "refine", "exact"], "tactic_count": 3}
{"name": "Ideal.mapCotangent", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Cotangent", "is_tactic_proof": false, "tactics": ["refine", "exact", "intro", "rw", "refine", "rintro", "simp", "convert", "ext", "exact"], "tactic_count": 10}
{"name": "Ideal.mapCotangent_toCotangent", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Cotangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.CotangentSpace", "kind": "abbrev", "module": "Mathlib.RingTheory.Ideal.Cotangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.instModuleResidueFieldCotangentSpace", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Cotangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.instIsScalarTowerResidueFieldCotangentSpace", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Cotangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.instFiniteDimensionalResidueFieldCotangentSpaceOfIsNoetherianRing", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Cotangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.subsingleton_cotangentSpace_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Cotangent", "is_tactic_proof": true, "tactics": ["refine", "rw", "simp"], "tactic_count": 3}
{"name": "IsLocalRing.CotangentSpace.map_eq_top_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Cotangent", "is_tactic_proof": true, "tactics": ["refine", "refine", "rw", "apply", "rw"], "tactic_count": 5}
{"name": "IsLocalRing.CotangentSpace.span_image_eq_top_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Cotangent", "is_tactic_proof": true, "tactics": ["rw", "simp", "exact"], "tactic_count": 3}
{"name": "IsLocalRing.finrank_cotangentSpace_eq_zero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Cotangent", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsLocalRing.finrank_cotangentSpace_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Cotangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.finrank_cotangentSpace_le_one_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Cotangent", "is_tactic_proof": false, "tactics": ["rw", "isPrincipal_iff]", "simp_rw", "range_subtype,", "exact"], "tactic_count": 5}
{"name": "Ideal", "kind": "abbrev", "module": "Mathlib.RingTheory.Ideal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.zero_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.add_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.mul_mem_left", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.mul_mem_right", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.ext", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.unit_mul_mem_iff_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Defs", "is_tactic_proof": true, "tactics": ["refine", "obtain", "have", "rwa"], "tactic_count": 4}
{"name": "Ideal.pow_mem_of_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.pow_mem_of_pow_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Module.eqIdeal", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.instIsTwoSided", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.instIsTwoSided_1", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.mul_unit_mem_iff_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.mem_of_dvd", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Defs", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "Ideal.neg_mem_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.add_mem_iff_left", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.add_mem_iff_right", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.sub_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.mul_sub_mul_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Ideal.exists_ideal_le_liesOver_of_le", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.GoingDown", "is_tactic_proof": true, "tactics": ["by_cases", "subst", "use", "have", "subst", "exact"], "tactic_count": 6}
{"name": "Ideal.exists_ideal_lt_liesOver_of_lt", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.GoingDown", "is_tactic_proof": true, "tactics": ["obtain", "refine", "by_contra", "have", "subst", "simp"], "tactic_count": 6}
{"name": "Ideal.exists_ltSeries_of_hasGoingDown", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.GoingDown", "is_tactic_proof": true, "tactics": ["induction", "singleton", "use", "simp", "ext", "simpa", "cons", "simp", "obtain", "have", "constructor", "rw", "have", "rw", "rwa", "obtain", "use", "simp", "exact"], "tactic_count": 19}
{"name": "Algebra.HasGoingDown.iff_generalizingMap_primeSpectrumComap", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.GoingDown", "is_tactic_proof": true, "tactics": ["refine", "intro", "rw", "obtain", "refine", "ext", "exact", "have", "obtain", "refine", "simpa"], "tactic_count": 11}
{"name": "Algebra.HasGoingDown.trans", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.GoingDown", "is_tactic_proof": true, "tactics": ["rw", "simp", "apply", "rwa", "rwa"], "tactic_count": 5}
{"name": "Algebra.HasGoingDown.of_comap_localRingHom_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.GoingDown", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.HasGoingDown.of_flat", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.GoingDown", "is_tactic_proof": true, "tactics": ["apply", "intro", "have", "rw", "exact", "have", "apply"], "tactic_count": 7}
{"name": "Ideal.coeff_zero_mem_comap_of_root_mem_of_eval_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.GoingUp", "is_tactic_proof": true, "tactics": ["rw", "refine", "exact"], "tactic_count": 3}
{"name": "Ideal.coeff_zero_mem_comap_of_root_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.GoingUp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.exists_coeff_ne_zero_mem_comap_of_non_zero_divisor_root_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.GoingUp", "is_tactic_proof": true, "tactics": ["refine", "intro", "contradiction", "intro", "refine", "simp", "intro", "rw", "obtain", "refine", "simp", "simpa"], "tactic_count": 12}
{"name": "Ideal.injective_quotient_le_comap_map", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.GoingUp", "is_tactic_proof": true, "tactics": ["refine", "rw", "refine", "refine", "simpa"], "tactic_count": 5}
{"name": "Ideal.quotient_mk_maps_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.GoingUp", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Ideal.exists_nonzero_mem_of_ne_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.GoingUp", "is_tactic_proof": true, "tactics": ["obtain", "refine", "refine", "refine", "rw", "exact"], "tactic_count": 6}
{"name": "Ideal.exists_coeff_ne_zero_mem_comap_of_root_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.GoingUp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.exists_coeff_mem_comap_sdiff_comap_of_root_mem_sdiff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.GoingUp", "is_tactic_proof": true, "tactics": ["obtain", "have", "have", "have", "have", "convert", "exact", "obtain", "rw", "refine", "simpa", "simp"], "tactic_count": 12}
{"name": "Ideal.comap_lt_comap_of_root_mem_sdiff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.GoingUp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.mem_of_one_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.GoingUp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.comap_lt_comap_of_integral_mem_sdiff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.GoingUp", "is_tactic_proof": true, "tactics": ["obtain", "refine", "convert"], "tactic_count": 3}
{"name": "Ideal.comap_ne_bot_of_root_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.GoingUp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.isMaximal_of_isIntegral_of_isMaximal_comap", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.GoingUp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.isMaximal_of_isIntegral_of_isMaximal_comap'", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.GoingUp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.comap_ne_bot_of_algebraic_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.GoingUp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.comap_ne_bot_of_integral_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.GoingUp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.eq_bot_of_comap_eq_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.GoingUp", "is_tactic_proof": true, "tactics": ["refine", "by_cases", "exact", "exact"], "tactic_count": 4}
{"name": "Ideal.isMaximal_comap_of_isIntegral_of_isMaximal", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.GoingUp", "is_tactic_proof": true, "tactics": ["refine", "haveI", "exact", "isField_of_isIntegral_of_isField"], "tactic_count": 4}
{"name": "Ideal.isMaximal_comap_of_isIntegral_of_isMaximal'", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.GoingUp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.IsIntegralClosure.comap_lt_comap", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.GoingUp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.IsIntegralClosure.isMaximal_of_isMaximal_comap", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.GoingUp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.IsIntegralClosure.comap_ne_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.GoingUp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.IsIntegralClosure.eq_bot_of_comap_eq_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.GoingUp", "is_tactic_proof": true, "tactics": ["contrapose", "exact"], "tactic_count": 2}
{"name": "Ideal.IntegralClosure.comap_lt_comap", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.GoingUp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.IntegralClosure.isMaximal_of_isMaximal_comap", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.GoingUp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.IntegralClosure.comap_ne_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.GoingUp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.IntegralClosure.eq_bot_of_comap_eq_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.GoingUp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.exists_ideal_over_prime_of_isIntegral_of_isDomain", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.GoingUp", "is_tactic_proof": false, "tactics": ["have", "rintro", "exact", "let", "let", "letI", "obtain", "let", "have", "have", "refine", "convert", "rw", "rfl"], "tactic_count": 14}
{"name": "Ideal.exists_ideal_over_prime_of_isIntegral_of_isPrime", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.GoingUp", "is_tactic_proof": false, "tactics": ["obtain", "refine", "rw", "refine", "rw", "exact", "refine", "simpa"], "tactic_count": 8}
{"name": "Ideal.exists_ideal_over_prime_of_isIntegral", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.GoingUp", "is_tactic_proof": true, "tactics": ["have", "obtain", "exact"], "tactic_count": 3}
{"name": "Ideal.nonempty_primesOver", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.GoingUp", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Ideal.exists_ideal_over_maximal_of_isIntegral", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.GoingUp", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Ideal.exists_maximal_ideal_liesOver_of_isIntegral", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.GoingUp", "is_tactic_proof": true, "tactics": ["simp_rw", "exact", "exists_ideal_over_maximal_of_isIntegral"], "tactic_count": 3}
{"name": "Ideal.map_eq_top_iff_of_ker_le", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.GoingUp", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "contrapose", "intro", "obtain", "let", "have", "obtain", "rw", "exact"], "tactic_count": 10}
{"name": "Ideal.map_eq_top_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.GoingUp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.IsMaximal.under", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.GoingUp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.IsMaximal.of_liesOver_isMaximal", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.GoingUp", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Ideal.IsMaximal.of_isMaximal_liesOver", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.GoingUp", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Ideal.eq_bot_of_liesOver_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.GoingUp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.under_ne_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.GoingUp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.algebra_isIntegral_of_liesOver", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.GoingUp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.primesOver.isMaximal", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.GoingUp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.isMaximal_of_mem_primesOver", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.GoingUp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.primesOver_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.GoingUp", "is_tactic_proof": true, "tactics": ["ext", "refine", "rintro", "exact"], "tactic_count": 4}
{"name": "Ideal.primeHeight", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Height", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.height", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Height", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.height_eq_primeHeight", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Height", "is_tactic_proof": true, "tactics": ["unfold", "simp_rw", "simp"], "tactic_count": 3}
{"name": "Ideal.finiteHeight_iff_lt", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Height", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.height_ne_top", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Height", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.height_lt_top", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Height", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.primeHeight_ne_top", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Height", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Ideal.primeHeight_lt_top", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Height", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Ideal.exists_ltSeries_length_eq_height", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Height", "is_tactic_proof": true, "tactics": ["obtain", "rw", "obtain", "rw", "exact"], "tactic_count": 5}
{"name": "Ideal.primeHeight_mono", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Height", "is_tactic_proof": true, "tactics": ["unfold", "gcongr", "exact"], "tactic_count": 3}
{"name": "Ideal.primeHeight_add_one_le_of_lt", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Height", "is_tactic_proof": true, "tactics": ["unfold", "exact"], "tactic_count": 2}
{"name": "Ideal.height_top", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Height", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Ideal.primeHeight_strict_mono", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Height", "is_tactic_proof": true, "tactics": ["rw", "have", "rw", "right", "exact", "exact"], "tactic_count": 6}
{"name": "Ideal.height_mono", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Height", "is_tactic_proof": true, "tactics": ["simp", "refine", "have", "obtain", "haveI", "exact"], "tactic_count": 6}
{"name": "Ideal.height_strict_mono_of_is_prime", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Height", "is_tactic_proof": true, "tactics": ["rw", "by_cases", "rw", "exact", "rw", "refine", "haveI", "have", "exact"], "tactic_count": 9}
{"name": "Ideal.primeHeight_le_ringKrullDim", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Height", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.height_le_ringKrullDim_of_ne_top", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Height", "is_tactic_proof": true, "tactics": ["rw", "obtain", "have", "refine", "simpa"], "tactic_count": 5}
{"name": "Ideal.exists_isMaximal_height", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Height", "is_tactic_proof": true, "tactics": ["let", "obtain", "refine", "trans", "rw", "exact", "norm_cast", "exact"], "tactic_count": 8}
{"name": "Ideal.finiteHeight_of_finiteRingKrullDim", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Height", "is_tactic_proof": true, "tactics": ["rw", "intro", "have", "have", "exact"], "tactic_count": 5}
{"name": "Ideal.finiteHeight_of_le", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Height", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.mem_minimalPrimes_of_height_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Height", "is_tactic_proof": true, "tactics": ["obtain", "convert", "refine", "have", "have", "exact"], "tactic_count": 6}
{"name": "Ideal.primeHeight_eq_zero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Height", "is_tactic_proof": true, "tactics": ["rw", "simp", "constructor", "intro", "refine", "by_contra", "exact", "rintro", "exact"], "tactic_count": 9}
{"name": "Ideal.height_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Height", "is_tactic_proof": true, "tactics": ["obtain", "simp", "exact", "haveI", "primeHeight_eq_zero_iff.mpr"], "tactic_count": 5}
{"name": "Ideal.height_of_subsingleton", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Height", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.isMaximal_of_primeHeight_eq_ringKrullDim", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Height", "is_tactic_proof": false, "tactics": ["have", "intro", "simp", "exact", "obtain", "rcases", "have", "have", "simp", "exact"], "tactic_count": 10}
{"name": "IsLocalRing.maximalIdeal_primeHeight_eq_ringKrullDim", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Height", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "IsLocalRing.maximalIdeal_height_eq_ringKrullDim", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Height", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.primeHeight_eq_ringKrullDim_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Height", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "rintro", "exact"], "tactic_count": 5}
{"name": "Ideal.height_le_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Height", "is_tactic_proof": false, "tactics": ["rw", "congr", "rw", "rfl"], "tactic_count": 4}
{"name": "Ideal.height_le_iff_covBy", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Height", "is_tactic_proof": true, "tactics": ["rw", "constructor", "intro", "exact", "intro", "obtain", "exact"], "tactic_count": 7}
{"name": "_private.Mathlib.RingTheory.Ideal.Height.0.RingEquiv.height_comap_of_isPrime", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Height", "is_tactic_proof": false, "tactics": ["rw", "have", "congr"], "tactic_count": 3}
{"name": "RingEquiv.height_comap", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Height", "is_tactic_proof": true, "tactics": ["refine", "refine", "rw", "exact", "have", "simp"], "tactic_count": 6}
{"name": "RingEquiv.height_map", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Height", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ringKrullDim_le_iff_height_le", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Height", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "exact", "specialize", "rwa"], "tactic_count": 6}
{"name": "ringKrullDim_le_iff_isMaximal_height_le", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Height", "is_tactic_proof": true, "tactics": ["rw", "refine", "obtain", "refine", "norm_cast", "exact"], "tactic_count": 6}
{"name": "IsLocalization.primeHeight_comap", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Height", "is_tactic_proof": false, "tactics": ["rw", "let", "have", "exact", "invFun", "left_inv", "right_inv", "map_rel_iff"], "tactic_count": 8}
{"name": "IsLocalization.height_comap", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Height", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "iInf_image]"], "tactic_count": 3}
{"name": "IsLocalization.AtPrime.ringKrullDim_eq_height", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Height", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "IsLocalization.height_map_of_disjoint", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Height", "is_tactic_proof": true, "tactics": ["let", "have", "have", "simp_rw", "have", "ringKrullDim_eq_of_ringEquiv", "rw", "exact"], "tactic_count": 8}
{"name": "mem_minimalPrimes_of_primeHeight_eq_height", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Height", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "exists_spanRank_le_and_le_height_of_le_height", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Height", "is_tactic_proof": true, "tactics": ["induction", "zero", "refine", "rw", "exact", "succ", "obtain", "let", "have", "have", "refine", "rintro", "rw", "exact", "push_neg", "intro", "have", "rw", "rw", "norm_cast", "exact", "simp_rw", "obtain", "refine", "rwa", "apply", "push_cast", "exact", "refine", "have", "by_cases", "rw", "exact", "have", "have", "suffices", "push_cast", "have", "rw", "exact", "intro", "apply", "have", "apply", "rwa", "rwa", "refine", "rwa", "exact"], "tactic_count": 49}
{"name": "Ideal.sup_height_eq_ringKrullDim", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Height", "is_tactic_proof": true, "tactics": ["apply", "rw", "refine", "by_cases", "simp", "simp", "refine", "rw", "apply", "exact", "exact", "apply", "exact", "exact"], "tactic_count": 14}
{"name": "Ideal.sup_primeHeight_eq_ringKrullDim", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Height", "is_tactic_proof": true, "tactics": ["rw", "apply", "exact", "refine", "by_cases", "exact", "obtain", "refine", "exact"], "tactic_count": 9}
{"name": "Ideal.sup_primeHeight_of_maximal_eq_ringKrullDim", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Height", "is_tactic_proof": true, "tactics": ["rw", "apply", "exact", "refine", "obtain", "exact", "obtain", "exact"], "tactic_count": 8}
{"name": "Ring.krullDimLE_of_isLocalization_maximal", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Height", "is_tactic_proof": true, "tactics": ["simp_rw", "nontriviality", "rw", "refine", "rw", "rw", "exact"], "tactic_count": 7}
{"name": "Ideal.isIdempotentElem_iff_of_fg", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.IdempotentFG", "is_tactic_proof": true, "tactics": ["constructor", "intro", "obtain", "rw", "exact", "simp_rw", "refine", "intro", "rw", "exact", "rintro", "simp"], "tactic_count": 12}
{"name": "Ideal.isIdempotentElem_iff_eq_bot_or_top", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.IdempotentFG", "is_tactic_proof": true, "tactics": ["constructor", "intro", "obtain", "simp", "apply", "rintro", "simp", "rintro"], "tactic_count": 8}
{"name": "Int.ideal_span_isMaximal_of_prime", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Int", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.liesOver_span_absNorm", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Int", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.cast_mem_ideal_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Int", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.absNorm_under_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Int", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.absNorm_under_eq_sInf", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Int", "is_tactic_proof": true, "tactics": ["by_cases", "have", "refine", "intro", "rw", "rw", "exact", "rw", "have", "refine", "by_contra", "have", "rw", "exact"], "tactic_count": 14}
{"name": "Int.absNorm_under_dvd_absNorm", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Int", "is_tactic_proof": true, "tactics": ["cases", "have", "have", "simp_rw", "exact", "rw", "simp_rw", "exact", "rw", "exact"], "tactic_count": 10}
{"name": "Ideal.ringChar_quot", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Int", "is_tactic_proof": true, "tactics": ["refine", "change", "rw"], "tactic_count": 3}
{"name": "Nat.absNorm_under_prime", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Int", "is_tactic_proof": true, "tactics": ["rw", "infer_instance", "refine", "have", "contrapose", "exact"], "tactic_count": 6}
{"name": "Ideal.IsPrimary", "kind": "abbrev", "module": "Mathlib.RingTheory.Ideal.IsPrimary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.isPrimary_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.IsPrimary", "is_tactic_proof": true, "tactics": ["rw", "simp", "span_singleton_le_iff_mem]"], "tactic_count": 3}
{"name": "Ideal.IsPrime.isPrimary", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.IsPrimary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.isPrime_radical", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.IsPrimary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.isPrimary_of_isMaximal_radical", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.IsPrimary", "is_tactic_proof": true, "tactics": ["rw", "constructor", "rintro", "exact", "intro", "by_cases", "rw", "add_le_iff,", "exact", "obtain", "rw", "exact"], "tactic_count": 12}
{"name": "Ideal.IsPrimary.inf", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.IsPrimary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.isPrimary_finsetInf", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.IsPrimary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.IsPrimary.comap", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.IsPrimary", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp", "exact"], "tactic_count": 4}
{"name": "Ideal.isPrincipalSubmonoid", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.IsPrincipal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.mem_isPrincipalSubmonoid_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.IsPrincipal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.span_singleton_mem_isPrincipalSubmonoid", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.IsPrincipal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.isPrincipalNonZeroDivisorsSubmonoid", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.IsPrincipal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.associatesEquivIsPrincipal", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.IsPrincipal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.associatesEquivIsPrincipal_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.IsPrincipal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.associatesEquivIsPrincipal_symm_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.IsPrincipal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.associatesEquivIsPrincipal_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.IsPrincipal", "is_tactic_proof": true, "tactics": ["rw", "simp_rw"], "tactic_count": 2}
{"name": "Ideal.associatesEquivIsPrincipal_map_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.IsPrincipal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.associatesEquivIsPrincipal_map_one", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.IsPrincipal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.associatesMulEquivIsPrincipal", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.IsPrincipal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.associatesNonZeroDivisorsEquivIsPrincipal", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.IsPrincipal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.associatesNonZeroDivisorsEquivIsPrincipal_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.IsPrincipal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.associatesNonZeroDivisorsEquivIsPrincipal_coe", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.IsPrincipal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.associatesNonZeroDivisorsEquivIsPrincipal_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.IsPrincipal", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Ideal.associatesNonZeroDivisorsEquivIsPrincipal_map_one", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.IsPrincipal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.associatesNonZeroDivisorsMulEquivIsPrincipal", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.IsPrincipal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.isoBaseOfIsPrincipal", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.IsPrincipal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.isoBaseOfIsPrincipal_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.IsPrincipal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.subtype_isoBaseOfIsPrincipal_eq_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.IsPrincipal", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Ideal.quotEquivPowQuotPowSucc", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.IsPrincipalPowQuotient", "is_tactic_proof": true, "tactics": ["let", "let", "have", "have", "let", "simp", "exact", "have", "ext", "simp", "constructor", "exact", "rw", "obtain", "rw", "rw", "exact", "contrapose", "rw", "let", "refine", "refine", "rintro", "rw", "refine", "simp"], "tactic_count": 26}
{"name": "Ideal.quotEquivPowQuotPowSuccEquiv", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.IsPrincipalPowQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.quotient_artinian_of_mem_minimalPrimes_of_isLocalRing", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.KrullsHeightTheorem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.height_le_one_of_isPrincipal_of_mem_minimalPrimes_of_isLocalRing", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.KrullsHeightTheorem", "is_tactic_proof": true, "tactics": ["refine", "suffices", "rw", "ringKrullDimZero_iff_ringKrullDim_eq_zero,", "isArtinianRing_iff_isNilpotent_maximalIdeal,", "have", "let", "let", "monotone", "obtain", "refine", "apply", "rotate_left", "rw", "exact", "rw", "refine", "rw", "exacts", "replace", "simp", "intro", "obtain", "refine", "obtain", "rw", "refine", "dsimp", "rwa", "mul_comm,", "refine", "change", "rw", "exact"], "tactic_count": 34}
{"name": "Ideal.height_le_one_of_isPrincipal_of_mem_minimalPrimes", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.KrullsHeightTheorem", "is_tactic_proof": true, "tactics": ["have", "let", "have", "rwa", "rwa"], "tactic_count": 5}
{"name": "Ideal.map_height_le_one_of_mem_minimalPrimes", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.KrullsHeightTheorem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.mem_minimalPrimes_span_of_mem_minimalPrimes_span_insert", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.KrullsHeightTheorem", "is_tactic_proof": true, "tactics": ["let", "have", "have", "have", "have", "have", "suffices", "have", "hqp.not_ge", "simpa", "sup_eq_left.mpr", "have", "have", "rw", "have", "rw", "have", "rwa", "refine", "height_le_one_of_isPrincipal_of_mem_minimalPrimes", "rw", "have", "refine", "rw", "exact", "conv_rhs", "rw", "exact"], "tactic_count": 28}
{"name": "Ideal.height_le_spanRank_toENat_of_mem_minimal_primes", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.KrullsHeightTheorem", "is_tactic_proof": true, "tactics": ["classical", "rw", "rintro", "induction", "h", "replace", "have", "cases", "zero", "rw", "simp_all", "succ", "wlog", "rw", "rw", "rw", "exact", "this", "obtain", "simp_rw", "intro", "obtain", "have", "rw", "exact", "obtain", "exact", "have", "rw", "exact", "by_contra", "hq", "hJ)", "have", "have", "rw", "exact", "obtain", "let", "suffices", "have", "hn)", "rw", "convert", "simp", "refine", "rw"], "tactic_count": 47}
{"name": "Ideal.height_le_card_of_mem_minimalPrimes_span_finset", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.KrullsHeightTheorem", "is_tactic_proof": true, "tactics": ["trans", "exact", "simpa"], "tactic_count": 3}
{"name": "Ideal.height_le_card_of_mem_minimalPrimes_span", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.KrullsHeightTheorem", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Ideal.height_le_spanRank_toENat", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.KrullsHeightTheorem", "is_tactic_proof": true, "tactics": ["obtain", "refine", "convert", "exact"], "tactic_count": 4}
{"name": "Ideal.height_le_spanFinrank", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.KrullsHeightTheorem", "is_tactic_proof": false, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "Ideal.height_le_spanRank", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.KrullsHeightTheorem", "is_tactic_proof": true, "tactics": ["trans", "exact_mod_cast", "exact"], "tactic_count": 3}
{"name": "Ideal.finiteHeight_of_isNoetherianRing", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.KrullsHeightTheorem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFiniteRingKrullDimOfIsNoetherianRingOfIsLocalRing", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.KrullsHeightTheorem", "is_tactic_proof": true, "tactics": ["apply", "rw", "constructor", "exact", "rw", "exact"], "tactic_count": 6}
{"name": "Ideal.exists_spanRank_eq_and_height_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.KrullsHeightTheorem", "is_tactic_proof": false, "tactics": ["obtain", "rw", "refine", "convert", "exact", "exact", "rintro", "exact"], "tactic_count": 8}
{"name": "Ideal.height_le_iff_exists_minimalPrimes", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.KrullsHeightTheorem", "is_tactic_proof": true, "tactics": ["constructor", "intro", "obtain", "refine", "norm_cast", "rintro", "exact", "le_trans"], "tactic_count": 8}
{"name": "Ideal.exists_finset_card_eq_height_of_isNoetherianRing", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.KrullsHeightTheorem", "is_tactic_proof": true, "tactics": ["obtain", "have", "refine", "rw", "refine", "rw", "exact", "convert_to", "symm", "simpa", "exact"], "tactic_count": 11}
{"name": "Ideal.height_le_height_add_spanFinrank_of_le", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.KrullsHeightTheorem", "is_tactic_proof": true, "tactics": ["classical", "let", "have", "obtain", "have", "have", "refine", "obtain", "exact", "obtain", "have", "let", "suffices", "refine", "norm_cast", "have", "rw", "exact", "grind", "refine", "rw", "refine", "convert", "simp"], "tactic_count": 24}
{"name": "height_le_ringKrullDim_quotient_add_spanFinrank", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.KrullsHeightTheorem", "is_tactic_proof": true, "tactics": ["trans", "norm_cast", "gcongr", "have", "exact"], "tactic_count": 5}
{"name": "ringKrullDim_le_ringKrullDim_quotient_add_spanFinrank", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.KrullsHeightTheorem", "is_tactic_proof": true, "tactics": ["nontriviality", "rw", "intro", "exact"], "tactic_count": 4}
{"name": "Ideal.height_le_height_add_encard_of_subset", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.KrullsHeightTheorem", "is_tactic_proof": true, "tactics": ["apply", "rwa", "gcongr", "exact"], "tactic_count": 4}
{"name": "Ideal.height_le_ringKrullDim_quotient_add_encard", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.KrullsHeightTheorem", "is_tactic_proof": true, "tactics": ["refine", "simpa", "gcongr"], "tactic_count": 3}
{"name": "Ideal.height_le_height_add_one_of_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.KrullsHeightTheorem", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "Ideal.height_le_ringKrullDim_quotient_add_one", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.KrullsHeightTheorem", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "ringKrullDim_le_ringKrullDim_quotient_add_encard", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.KrullsHeightTheorem", "is_tactic_proof": true, "tactics": ["refine", "simpa", "gcongr"], "tactic_count": 3}
{"name": "ringKrullDim_le_ringKrullDim_quotient_add_card", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.KrullsHeightTheorem", "is_tactic_proof": true, "tactics": ["convert", "norm_cast"], "tactic_count": 2}
{"name": "Ideal.height_le_height_add_of_liesOver", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.KrullsHeightTheorem", "is_tactic_proof": true, "tactics": ["classical", "obtain", "let", "obtain", "have", "hP'.1.2", "have", "refine", "obtain", "rw", "use", "rw", "obtain", "let", "suffices", "rw", "apply", "norm_cast", "refine", "rw", "refine", "have", "refine", "convert", "simp"], "tactic_count": 25}
{"name": "Ideal.height_eq_height_add_of_liesOver_of_hasGoingDown", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.KrullsHeightTheorem", "is_tactic_proof": true, "tactics": ["refine", "obtain", "obtain", "let", "lq.map", "have", "simp", "refine", "refine", "rw", "simp", "conv_rhs", "refine", "simp", "obtain", "have", "rw", "apply", "simp"], "tactic_count": 19}
{"name": "Ideal.instIsTwoSidedBot", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.instIsTwoSidedTop", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.instIsTwoSidedIInf", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.eq_top_of_unit_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.eq_top_of_isUnit_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.eq_top_iff_one", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.ne_top_iff_one", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.mem_sup_left", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.mem_sup_right", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.mem_iSup_of_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.mem_sSup_of_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.mem_sInf", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.mem_inf", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.mem_iInf", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.mem_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.eq_bot_or_top", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Lattice", "is_tactic_proof": true, "tactics": ["rw", "change", "rw", "intro", "rw", "intro", "by_cases", "simpa"], "tactic_count": 8}
{"name": "Ideal.map", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.comap", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.coe_comap", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.comap_coe", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.map_coe", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.map_mono", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.mem_map_of_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.apply_coe_mem_map", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.map_le_iff_le_comap", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.mem_comap", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.comap_mono", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.comap_ne_top", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.exists_ideal_comap_le_prime", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.map_le_comap_of_inv_on", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": true, "tactics": ["refine", "rintro", "rw", "exact"], "tactic_count": 4}
{"name": "Ideal.comap_le_map_of_inv_on", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.map_le_comap_of_inverse", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.instIsTwoSidedComap", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.comap_le_map_of_inverse", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.IsPrime.comap", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.map_top", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.gc_map_comap", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.comap_id", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.comap_idₐ", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.map_id", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.map_idₐ", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.comap_comap", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.comap_comapₐ", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.map_map", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.map_mapₐ", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.map_span", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": true, "tactics": ["refine", "rintro", "rw", "exact"], "tactic_count": 4}
{"name": "Ideal.map_le_of_le_comap", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.le_comap_of_map_le", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.le_comap_map", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.map_comap_le", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.comap_top", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.comap_eq_top_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.map_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.ne_bot_of_map_ne_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.map_comap_map", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.comap_map_comap", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.map_sup", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.comap_inf", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.map_iSup", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.comap_iInf", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.comap_finsetInf", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Ideal.map_sSup", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.comap_sInf", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.comap_sInf'", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.comap_isPrime", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.map_inf_le", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.le_comap_sup", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "element_smul_restrictScalars", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.smul_restrictScalars", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": ["simp_rw", "element_smul_restrictScalars,", "exact"], "tactic_count": 3}
{"name": "Ideal.smul_top_eq_map", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.coe_restrictScalars", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.restrictScalars_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.map_comap_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.giMapComap", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.map_surjective_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.comap_injective_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.map_sup_comap_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.map_iSup_comap_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.map_inf_comap_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.map_iInf_comap_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.mem_image_of_mem_map_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.mem_map_iff_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.le_map_of_comap_le_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.map_comap_eq_self_of_equiv", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.map_eq_submodule_map", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.instIsTwoSidedMapRingHomOfRingHomSurjective", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.IsMaximal.comap_piEvalRingHom", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": true, "tactics": ["refine", "have", "classical", "convert", "ext", "obtain", "simpa", "simp"], "tactic_count": 8}
{"name": "Ideal.comap_le_comap_iff_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.orderEmbeddingOfSurjective", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.map_eq_top_or_isMaximal_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.map_evalRingHom_pi", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": true, "tactics": ["ext", "rw", "classical", "rintro", "exact"], "tactic_count": 5}
{"name": "Ideal.piOrderIso", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.instIsPrincipalIdealRingForallOfFinite", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.comap_bot_le_of_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "Ideal.comap_bot_of_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.map_of_equiv", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.comap_of_equiv", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.map_comap_of_equiv", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.comap_symm", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.map_symm", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.symm_apply_mem_of_equiv_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.apply_mem_of_equiv_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.mem_map_of_equiv", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": true, "tactics": ["constructor", "intro", "simp_rw", "exact", "rintro", "exact"], "tactic_count": 6}
{"name": "Ideal.relIsoOfBijective", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.comap_le_iff_le_map", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.comap_map_of_bijective", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.isMaximal_map_iff_of_bijective", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Ideal.isMaximal_comap_iff_of_bijective", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Ideal.map_isMaximal_of_equiv", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.comap_isMaximal_of_equiv", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.isMaximal_iff_of_bijective", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.comap_map_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.relIsoOfSurjective", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.comap_isMaximal_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": true, "tactics": ["refine", "suffices", "have", "rw", "rw", "exact", "refine", "ne_of_lt", "rw", "exact"], "tactic_count": 10}
{"name": "Ideal.map_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.mapHom", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.map_pow", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.comap_radical", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Ideal.IsRadical.comap", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "Ideal.map_radical_le", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.le_comap_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.le_comap_pow", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": true, "tactics": ["induction", "zero", "rw", "exact", "succ", "rw", "exact"], "tactic_count": 7}
{"name": "Ideal.disjoint_map_primeCompl_iff_comap_le", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.comap_map_eq_self_iff_of_isPrime", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact", "rintro", "simp"], "tactic_count": 5}
{"name": "Ideal.comap_map_eq_self_of_isMaximal", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.ker", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.instIsTwoSidedKer", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.mem_ker", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RingHom.ker_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.ker_eq_comap_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.comap_ker", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RingHom.one_notMem_ker", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "RingHom.ker_ne_top", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.ker_eq_top_of_subsingleton", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.ker_ringHom", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "RingHom.ker_rangeSRestrict", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.ker_coe_equiv", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "RingHom.ker_coe_toRingHom", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.ker_equiv", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "RingHom.ker_equiv_comp", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RingHom.injective_iff_ker_eq_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "RingHom.ker_eq_bot_iff_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RingHom.ker_comp_of_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AlgHom.ker_coe_equiv", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.sub_mem_ker_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RingHom.ker_rangeRestrict", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.ker_isPrime", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.ker_isMaximal_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.annihilator", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.mem_annihilator", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsTwoSidedAnnihilator", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.annihilator_le_of_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.annihilator_le_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.annihilator_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.comap_annihilator", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Module.annihilator_eq_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "exact", "exact"], "tactic_count": 5}
{"name": "Module.annihilator_eq_top_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.annihilator_prod", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": true, "tactics": ["ext", "simp_rw", "forall_and_right]"], "tactic_count": 3}
{"name": "Module.annihilator_finsupp", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.annihilator_dfinsupp", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": true, "tactics": ["ext", "constructor", "intro", "classical", "intro"], "tactic_count": 5}
{"name": "Module.annihilator_pi", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": true, "tactics": ["ext", "constructor", "intro", "classical", "intro"], "tactic_count": 5}
{"name": "Submodule.annihilator", "kind": "abbrev", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.annihilator_top", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mem_annihilator", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Submodule.annihilator_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.annihilator_eq_top_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submodule.annihilator_mono", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.annihilator_iSup", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.le_annihilator_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Submodule.annihilator_smul", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.annihilator_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mem_annihilator'", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mem_annihilator_span", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": true, "tactics": ["rw", "constructor", "intro", "exact", "intro", "refine", "intro", "exact", "exact", "intro", "rw", "intro", "rw"], "tactic_count": 13}
{"name": "Submodule.mem_annihilator_span_singleton", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Submodule.annihilator_span", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Submodule.annihilator_span_singleton", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Submodule.mul_annihilator", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.map_eq_bot_iff_le_ker", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.ker_le_comap", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.map_isPrime_of_equiv", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "Ideal.map_eq_bot_iff_of_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Ideal.map_pointwise_smul", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": true, "tactics": ["rw", "smul_eq_mul,"], "tactic_count": 2}
{"name": "Ideal.comap_map_of_surjective'", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.map_sInf", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": true, "tactics": ["refine", "intro", "obtain", "obtain", "rw", "exact", "intro", "obtain", "refine", "have", "rw", "intro", "rcases", "have", "apply", "rw", "simpa"], "tactic_count": 17}
{"name": "Ideal.map_isPrime_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": true, "tactics": ["refine", "replace", "rw", "exact", "refine", "rw", "rcases", "rw", "have", "convert", "abel", "exact"], "tactic_count": 12}
{"name": "Ideal.IsMaximal.map_of_surjective_of_ker_le", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": true, "tactics": ["refine", "apply", "rw", "exact"], "tactic_count": 4}
{"name": "Ideal.map_ne_bot_of_ne_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.map_eq_iff_sup_ker_eq_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.map_radical_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": true, "tactics": ["rw", "have", "convert", "refine", "rintro", "haveI", "exact", "rintro", "haveI", "exact"], "tactic_count": 10}
{"name": "RingHom.liftOfRightInverseAux", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.liftOfRightInverseAux_comp_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.liftOfRightInverse", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.liftOfSurjective", "kind": "abbrev", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.liftOfRightInverse_comp_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.liftOfRightInverse_comp", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.eq_liftOfRightInverse", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "RingHom.liftOfSurjective_comp_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.liftOfSurjective_comp", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.eq_liftOfSurjective", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.idealComapOrderIso", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.idealComapOrderIso_symm_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.ker_coe", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.coe_ideal_map", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.comap_ker", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.idealMap", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FaithfulSMul.ker_algebraMap_eq_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "instIsPrincipalMapRingHom", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "RingHom.ker_evalRingHom", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maps", "is_tactic_proof": true, "tactics": ["refine", "simp", "rw", "use", "simp"], "tactic_count": 5}
{"name": "Ideal.isMaximal_def", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maximal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.IsMaximal.ne_top", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maximal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.isMaximal_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maximal", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Ideal.IsMaximal.eq_of_le", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maximal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.instIsCoatomic", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Maximal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.IsMaximal.coprime_of_ne", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maximal", "is_tactic_proof": true, "tactics": ["contrapose", "exact"], "tactic_count": 2}
{"name": "Ideal.exists_le_maximal", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maximal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.exists_maximal", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maximal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.ne_top_iff_exists_maximal", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maximal", "is_tactic_proof": true, "tactics": ["refine", "contrapose", "rintro", "rw", "exact"], "tactic_count": 5}
{"name": "Ideal.instNontrivial", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Maximal", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "Ideal.maximal_of_no_maximal", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maximal", "is_tactic_proof": true, "tactics": ["by_contra", "rcases", "exact"], "tactic_count": 3}
{"name": "Ideal.IsMaximal.exists_inv", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maximal", "is_tactic_proof": true, "tactics": ["obtain", "rcases", "mem_span_insert.1", "refine", "rwa"], "tactic_count": 5}
{"name": "Ideal.sInf_isPrime_of_isChain", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maximal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.span_singleton_prime", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maximal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Ideal.IsMaximal.isPrime", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maximal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.IsMaximal.isPrime'", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Maximal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.exists_disjoint_powers_of_span_eq_top", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maximal", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "have", "exact"], "tactic_count": 5}
{"name": "Ideal.span_singleton_lt_span_singleton", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maximal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.isPrime_of_maximally_disjoint", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maximal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.exists_le_prime_disjoint", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maximal", "is_tactic_proof": false, "tactics": ["have", "exact", "cases", "exact", "refine", "have", "exact"], "tactic_count": 7}
{"name": "Ideal.exists_le_prime_notMem_of_isIdempotentElem", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maximal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.isPrime_iff_of_isPrincipalIdealRing", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maximal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.isPrime_iff_of_isPrincipalIdealRing_of_noZeroDivisors", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maximal", "is_tactic_proof": false, "tactics": ["rw", "or_iff_right_of_imp]", "rintro"], "tactic_count": 3}
{"name": "Ideal.bot_isMaximal", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Maximal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.minimalPrimes", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.MinimalPrime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "minimalPrimes", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.MinimalPrime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "minimalPrimes_eq_minimals", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.MinimalPrime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.minimalPrimes_isPrime", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.MinimalPrime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.exists_minimalPrimes_le", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.MinimalPrime.Basic", "is_tactic_proof": true, "tactics": ["set", "suffices", "obtain", "exact", "apply", "swap", "refine", "rintro", "refine", "rw", "exact", "rintro", "rw", "exact"], "tactic_count": 14}
{"name": "Ideal.nonempty_minimalPrimes", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.MinimalPrime.Basic", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "exact"], "tactic_count": 3}
{"name": "Ideal.eq_bot_of_minimalPrimes_eq_empty", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.MinimalPrime.Basic", "is_tactic_proof": true, "tactics": ["by_contra", "obtain", "exact"], "tactic_count": 3}
{"name": "Ideal.radical_minimalPrimes", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.MinimalPrime.Basic", "is_tactic_proof": true, "tactics": ["rw", "ext", "refine", "refine", "simp", "exact", "refine", "simp", "exact"], "tactic_count": 9}
{"name": "Ideal.sInf_minimalPrimes", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.MinimalPrime.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply", "intro", "rw", "rintro", "obtain", "exact", "apply", "intro", "exact"], "tactic_count": 10}
{"name": "Ideal.minimalPrimes_eq_subsingleton", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.MinimalPrime.Basic", "is_tactic_proof": true, "tactics": ["ext", "constructor", "exact", "let", "rintro", "exact"], "tactic_count": 6}
{"name": "Ideal.minimalPrimes_eq_subsingleton_self", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.MinimalPrime.Basic", "is_tactic_proof": true, "tactics": ["ext", "constructor", "exact", "rintro", "exact"], "tactic_count": 5}
{"name": "IsDomain.minimalPrimes_eq_singleton_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.MinimalPrime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.minimalPrimes_top", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.MinimalPrime.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp", "intro", "exact"], "tactic_count": 4}
{"name": "Ideal.minimalPrimes_eq_empty_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.MinimalPrime.Basic", "is_tactic_proof": true, "tactics": ["constructor", "intro", "by_contra", "have", "have", "rw", "apply", "rintro", "exact"], "tactic_count": 9}
{"name": "Ideal.mem_minimalPrimes_sup", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.MinimalPrime.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact", "rw", "have", "h.2", "simpa"], "tactic_count": 7}
{"name": "Ideal.map_sup_mem_minimalPrimes_of_map_quotientMk_mem_minimalPrimes", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.MinimalPrime.Basic", "is_tactic_proof": true, "tactics": ["refine", "refine", "rw", "exact", "simp", "have", "rw", "refine", "convert", "exact", "have", "hJ.2", "simpa"], "tactic_count": 13}
{"name": "Ideal.iUnion_minimalPrimes", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.MinimalPrime.Localization", "is_tactic_proof": true, "tactics": ["classical", "ext", "simp", "constructor", "rintro", "have", "rw", "rintro", "obtain", "rw", "exact", "obtain", "rw", "obtain", "rw", "obtain", "refine", "simp", "have", "rw", "exact", "rintro", "obtain", "refine", "exact"], "tactic_count": 25}
{"name": "Ideal.exists_mul_mem_of_mem_minimalPrimes", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.MinimalPrime.Localization", "is_tactic_proof": true, "tactics": ["classical", "obtain", "have", "have", "refine", "rw", "exact"], "tactic_count": 7}
{"name": "IsSMulRegular.notMem_of_mem_minimalPrimes", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.MinimalPrime.Localization", "is_tactic_proof": true, "tactics": ["intro", "rcases", "rcases", "exact"], "tactic_count": 4}
{"name": "Ideal.disjoint_nonZeroDivisors_of_mem_minimalPrimes", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.MinimalPrime.Localization", "is_tactic_proof": false, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Ideal.exists_comap_eq_of_mem_minimalPrimes", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.MinimalPrime.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.exists_comap_eq_of_mem_minimalPrimes_of_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.MinimalPrime.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.exists_minimalPrimes_comap_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.MinimalPrime.Localization", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "refine", "have", "have", "exact"], "tactic_count": 6}
{"name": "Ideal.minimalPrimes_comap_subset", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.MinimalPrime.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.minimal_primes_comap_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.MinimalPrime.Localization", "is_tactic_proof": true, "tactics": ["have", "refine", "rintro", "have", "rw", "apply", "apply", "exact", "exact"], "tactic_count": 9}
{"name": "Ideal.comap_minimalPrimes_eq_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.MinimalPrime.Localization", "is_tactic_proof": true, "tactics": ["ext", "constructor", "intro", "obtain", "exact", "rintro", "exact"], "tactic_count": 7}
{"name": "Ideal.minimalPrimes_map_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.MinimalPrime.Localization", "is_tactic_proof": true, "tactics": ["apply", "rw", "intro", "exact"], "tactic_count": 4}
{"name": "Ideal.minimalPrimes_eq_comap", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.MinimalPrime.Localization", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsLocalization.minimalPrimes_map", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.MinimalPrime.Localization", "is_tactic_proof": true, "tactics": ["ext", "constructor", "intro", "haveI", "refine", "rintro", "have", "refine", "exact", "exact", "intro", "refine", "rw", "refine", "rintro", "exact", "intro", "rw", "haveI", "exact"], "tactic_count": 20}
{"name": "IsLocalization.minimalPrimes_comap", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.MinimalPrime.Localization", "is_tactic_proof": true, "tactics": ["conv_rhs", "refine", "exact"], "tactic_count": 3}
{"name": "Ideal.finite_minimalPrimes_of_isNoetherianRing", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.MinimalPrime.Noetherian", "is_tactic_proof": true, "tactics": ["by_contra", "obtain", "set_has_maximal_iff_noetherian.mpr", "simp", "have", "have", "obtain", "rw", "refine", "rcases", "exact", "exact"], "tactic_count": 12}
{"name": "minimalPrimes.finite_of_isNoetherianRing", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.MinimalPrime.Noetherian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsLocalRingNat", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.NatInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.mem_maximalIdeal_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.NatInt", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.coe_maximalIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.NatInt", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Nat.maximalIdeal_eq_span_two_three", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.NatInt", "is_tactic_proof": true, "tactics": ["refine", "obtain", "obtain", "exact"], "tactic_count": 4}
{"name": "Nat.one_mem_span_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.NatInt", "is_tactic_proof": true, "tactics": ["rw", "simp_rw"], "tactic_count": 2}
{"name": "Nat.one_mem_closure_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.NatInt", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Ideal.isPrime_nat_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.NatInt", "is_tactic_proof": false, "tactics": ["refine", "or_iff_not_imp_left.mpr", "or_iff_not_imp_right.mpr", "rintro", "exact", "exact", "rwa", "rw", "classical", "let", "have", "have", "have", "have", "push_neg", "have", "obtain", "exact", "have", "have", "exact"], "tactic_count": 21}
{"name": "Ideal.map_comap_natCastRingHom_int", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.NatInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.isPrime_int_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.NatInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ringKrullDim_nat", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.NatInt", "is_tactic_proof": true, "tactics": ["refine", "replace", "let", "have", "have", "obtain", "exact", "obtain", "exact", "exact", "hq.not_isUnit", "hp", "refine", "le_iSup_of_le", "le_rfl", "fin_cases", "exact", "simp_rw", "exact"], "tactic_count": 19}
{"name": "nonunits", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Nonunits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_nonunits_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Nonunits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_mem_nonunits_right", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Nonunits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_mem_nonunits_left", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Nonunits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zero_mem_nonunits", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Nonunits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_notMem_nonunits", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Nonunits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "map_mem_nonunits_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Nonunits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "coe_subset_nonunits", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Nonunits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_max_ideal_of_mem_nonunits", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Nonunits", "is_tactic_proof": false, "tactics": ["have", "intro", "rw", "contradiction", "rcases", "use", "apply", "apply", "exact"], "tactic_count": 9}
{"name": "Submonoid.inv_mem_of_isUnit", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Nonunits", "is_tactic_proof": true, "tactics": ["obtain", "convert", "exact"], "tactic_count": 3}
{"name": "Submonoid.isUnit_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Nonunits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.mem_nonunits_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Nonunits", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submonoid.isUnit_iff_and", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Nonunits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.isUnit_iff_of_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Nonunits", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submonoid.mem_nonunits_iff_or", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Nonunits", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submonoid.mem_nonunits_iff_of_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Nonunits", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submodule.cardQuot", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Norm.AbsNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.cardQuot_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.AbsNorm", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "Submodule.cardQuot_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.AbsNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.cardQuot_top", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.AbsNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.cardQuot_eq_one_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.AbsNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cardQuot_mul_of_coprime", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.AbsNorm", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.mul_add_mem_pow_succ_inj", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.AbsNorm", "is_tactic_proof": false, "tactics": ["have", "simp", "exact", "convert", "ring"], "tactic_count": 5}
{"name": "Ideal.exists_mul_add_mem_pow_succ", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.AbsNorm", "is_tactic_proof": false, "tactics": ["suffices", "rw", "simp", "exact", "refine", "contrapose", "rw", "exact"], "tactic_count": 8}
{"name": "Ideal.mem_prime_of_mul_mem_pow", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.AbsNorm", "is_tactic_proof": false, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Ideal.mul_add_mem_pow_succ_unique", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.AbsNorm", "is_tactic_proof": false, "tactics": ["have", "convert", "ring", "exact"], "tactic_count": 4}
{"name": "cardQuot_pow_of_prime", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.AbsNorm", "is_tactic_proof": false, "tactics": ["induction", "zero", "succ", "have", "suffices", "rw", "card_quotient_mul_card_quotient", "choose", "choose", "choose", "refine", "rintro", "rw", "hf", "refine", "simpa", "intro", "refine", "have", "refine", "simp", "refine", "rw", "exact"], "tactic_count": 24}
{"name": "cardQuot_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.AbsNorm", "is_tactic_proof": true, "tactics": ["let", "haveI", "exact", "have", "cardQuot_pow_of_prime", "cardQuot_mul_of_coprime"], "tactic_count": 6}
{"name": "Ideal.absNorm", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Norm.AbsNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.absNorm_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.AbsNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.absNorm_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.AbsNorm", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.absNorm_top", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.AbsNorm", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.absNorm_eq_one_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.AbsNorm", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.absNorm_ne_zero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.AbsNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.absNorm_dvd_absNorm_of_le", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.AbsNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.irreducible_of_irreducible_absNorm", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.AbsNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.isPrime_of_irreducible_absNorm", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.AbsNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.prime_of_irreducible_absNorm_span", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.AbsNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.absNorm_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.AbsNorm", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.span_singleton_absNorm_le", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.AbsNorm", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Ideal.span_singleton_absNorm", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.AbsNorm", "is_tactic_proof": false, "tactics": ["have", "rwa", "apply", "exact", "rw", "exact", "rw", "exact"], "tactic_count": 8}
{"name": "Ideal.natAbs_det_equiv", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.AbsNorm", "is_tactic_proof": true, "tactics": ["by_cases", "subst", "have", "have", "contradiction", "exact"], "tactic_count": 6}
{"name": "Ideal.natAbs_det_basis_change", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.AbsNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.absNorm_span_singleton", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.AbsNorm", "is_tactic_proof": true, "tactics": ["rw", "by_cases", "simp", "let", "rw", "congr", "refine", "simp"], "tactic_count": 8}
{"name": "Ideal.absNorm_dvd_norm_of_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.AbsNorm", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Ideal.absNorm_span_insert", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.AbsNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.absNorm_eq_zero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.AbsNorm", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "intro", "rw", "zero_dvd_iff,", "apply", "rwa", "rintro", "exact"], "tactic_count": 10}
{"name": "Ideal.absNorm_ne_zero_iff_mem_nonZeroDivisors", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.AbsNorm", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Ideal.absNorm_pos_iff_mem_nonZeroDivisors", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.AbsNorm", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.absNorm_ne_zero_of_nonZeroDivisors", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.AbsNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.absNorm_pos_of_nonZeroDivisors", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.AbsNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.finite_setOf_absNorm_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.AbsNorm", "is_tactic_proof": true, "tactics": ["obtain", "simp", "let", "refine", "suffices", "let", "refine", "exact", "rw", "simpa", "intro", "rw", "hJ.symm]", "congr"], "tactic_count": 14}
{"name": "Ideal.finite_setOf_absNorm_le", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.AbsNorm", "is_tactic_proof": false, "tactics": ["rw", "refine"], "tactic_count": 2}
{"name": "Ideal.finite_setOf_absNorm_le₀", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.AbsNorm", "is_tactic_proof": false, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "Ideal.card_norm_le_eq_card_norm_le_add_one", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.AbsNorm", "is_tactic_proof": true, "tactics": ["classical", "have", "have", "rw", "let", "refine", "intro", "simp_rw", "exact", "simp_rw", "conv_lhs", "enter", "rw", "and_iff_left_iff_imp.mpr", "rw"], "tactic_count": 15}
{"name": "Ideal.norm_dvd_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.AbsNorm", "is_tactic_proof": false, "tactics": ["rw", "rwa"], "tactic_count": 2}
{"name": "Int.ideal_span_absNorm_eq_self", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.AbsNorm", "is_tactic_proof": true, "tactics": ["obtain", "simp"], "tactic_count": 2}
{"name": "Ideal.spanNorm", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Norm.RelNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.spanNorm_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.RelNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.spanNorm_eq_bot_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.RelNorm", "is_tactic_proof": true, "tactics": ["simp", "forall_apply_eq_imp_iff₂,"], "tactic_count": 2}
{"name": "Ideal.intNorm_mem_spanNorm", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.RelNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.norm_mem_spanNorm", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.RelNorm", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "Ideal.spanNorm_singleton", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.RelNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.spanNorm_top", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.RelNorm", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Ideal.map_spanIntNorm", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.RelNorm", "is_tactic_proof": true, "tactics": ["rw", "nth_rw", "simp"], "tactic_count": 3}
{"name": "Ideal.spanNorm_mono", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.RelNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.spanIntNorm_localization", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.RelNorm", "is_tactic_proof": true, "tactics": ["let", "let", "let", "let", "hM.trans", "algebraize", "have", "let", "have", "have", "apply", "apply", "rw", "let", "rw", "refine", "intro", "simp", "obtain", "refine", "simp", "apply_fun", "apply_fun", "simp", "rw", "apply", "simp", "rwa", "intro", "rw", "exact"], "tactic_count": 31}
{"name": "Ideal.spanNorm_mul_spanNorm_le", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.RelNorm", "is_tactic_proof": true, "tactics": ["rw", "nth_rw", "rw", "refine", "rintro", "exact"], "tactic_count": 6}
{"name": "Ideal.spanNorm_mul_of_bot_or_top", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.RelNorm", "is_tactic_proof": true, "tactics": ["refine", "rcases", "rw", "exact", "rw", "rcases", "rw", "rw", "exact"], "tactic_count": 9}
{"name": "Ideal.spanNorm_le_comap", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.RelNorm", "is_tactic_proof": true, "tactics": ["rw", "intro", "induction", "mem", "obtain", "exact", "zero", "add", "smul"], "tactic_count": 9}
{"name": "Ideal.spanNorm_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.RelNorm", "is_tactic_proof": true, "tactics": ["nontriviality", "cases", "have", "simp", "refine", "by_cases", "subst", "rw", "intro", "exact", "have", "let", "simp", "rw", "spanNorm_singleton,"], "tactic_count": 15}
{"name": "Ideal.le_spanNorm_spanNorm", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.RelNorm", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "rintro", "exact"], "tactic_count": 4}
{"name": "Ideal.spanNorm_spanNorm_of_bot_or_top", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.RelNorm", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact"], "tactic_count": 3}
{"name": "Ideal.spanNorm_spanNorm", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.RelNorm", "is_tactic_proof": true, "tactics": ["refine", "by_cases", "subst", "rw", "exact", "let", "let", "let", "have", "have", "algebraMapSubmonoid_le_nonZeroDivisors_of_faithfulSMul", "rw", "spanIntNorm_localization", "spanIntNorm_localization"], "tactic_count": 14}
{"name": "Ideal.relNorm", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Norm.RelNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.relNorm_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.RelNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.spanNorm_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.RelNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.relNorm_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.RelNorm", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Ideal.relNorm_top", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.RelNorm", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Ideal.relNorm_eq_bot_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.RelNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.norm_mem_relNorm", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.RelNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.relNorm_singleton", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.RelNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.map_relNorm", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.RelNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.relNorm_mono", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.RelNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Ideal.Norm.RelNorm.0.Ideal.relNorm_map_algEquiv_aux", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.RelNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.relNorm_map_algEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.RelNorm", "is_tactic_proof": true, "tactics": ["refine", "convert", "change", "simp"], "tactic_count": 4}
{"name": "Ideal.relNorm_comap_algEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.RelNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.relNorm_smul", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.RelNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.relNorm_le_comap", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.RelNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.relNorm_relNorm", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.RelNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.relNorm_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.RelNorm", "is_tactic_proof": true, "tactics": ["rw", "refine", "let", "let", "let", "rw", "congr", "apply", "rw"], "tactic_count": 9}
{"name": "Ideal.relNorm_algebraMap'", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.RelNorm", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.exists_relNorm_eq_pow_of_isPrime", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.RelNorm", "is_tactic_proof": true, "tactics": ["by_cases", "refine", "have", "rw", "have", "relNorm_mono", "rw", "obtain", "exact"], "tactic_count": 9}
{"name": "Ideal.relNorm_eq_pow_of_isPrime_isGalois", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.RelNorm", "is_tactic_proof": true, "tactics": ["let", "let", "have", "by_cases", "have", "have", "rw", "exact", "rw", "rwa", "obtain", "suffices", "have", "relNorm", "intro", "rw", "have", "have", "rw", "obtain", "rw", "have", "simp", "rwa", "mul_right_inj", "inertiaDegIn_eq_inertiaDeg", "rw", "exact"], "tactic_count": 28}
{"name": "Ideal.relNorm_eq_pow_of_isMaximal", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.RelNorm", "is_tactic_proof": true, "tactics": ["let", "obtain", "have", "have", "have", "rwa", "pow_left_inj]", "exact"], "tactic_count": 8}
{"name": "Ideal.absNorm_relNorm", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.RelNorm", "is_tactic_proof": true, "tactics": ["have", "by_cases", "simp", "rw", "refine", "intro", "rw", "simp", "intro", "have", "rw", "have", "let", "let", "have", "have", "have", "have", "have", "rw", "inertiaDeg_algebra_tower"], "tactic_count": 21}
{"name": "Ideal.relNorm_int", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.RelNorm", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.absNorm_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Norm.RelNorm", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.IsOka.isPrime_of_maximal_not", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Oka", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.IsOka.forall_of_forall_prime", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Oka", "is_tactic_proof": true, "tactics": ["by_contra", "obtain", "exact"], "tactic_count": 3}
{"name": "Ideal.IsOka.forall_of_forall_prime'", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Oka", "is_tactic_proof": true, "tactics": ["refine", "obtain", "refine", "intro", "obtain", "exact", "exact"], "tactic_count": 7}
{"name": "Submodule.coe_span_smul", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.span_singleton_toAddSubgroup_eq_zmultiples", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Ideal.span_singleton_toAddSubgroup_eq_zmultiples", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.smul_eq_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.smul_le_right", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.map_le_smul_top", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["rintro", "rw", "exact"], "tactic_count": 3}
{"name": "Submodule.top_smul", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mul_smul", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mem_of_span_top_of_smul_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": ["suffices", "rw", "exact", "rw", "exact"], "tactic_count": 5}
{"name": "Submodule.map_smul''", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mem_smul_top_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": ["have", "rw", "simp"], "tactic_count": 3}
{"name": "Submodule.smul_comap_le_comap_smul", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["refine", "rw", "rw", "exact"], "tactic_count": 4}
{"name": "Submodule.comap_smul''", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["refine", "conv_lhs", "rw"], "tactic_count": 3}
{"name": "Submodule.mem_smul_span_singleton", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.span_smul_span", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mem_smul_span", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["rw", "rw"], "tactic_count": 2}
{"name": "Submodule.mem_ideal_smul_span_iff_exists_sum", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "exact", "refine", "rintro", "refine", "letI", "rw", "split_ifs", "assumption", "exact", "refine", "simp", "exact", "rintro", "refine", "simp", "rintro", "refine", "rw"], "tactic_count": 20}
{"name": "Submodule.mem_ideal_smul_span_iff_exists_sum'", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submodule.smul_eq_map₂", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.ideal_span_singleton_smul", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["conv_lhs", "simpa"], "tactic_count": 2}
{"name": "Submodule.mem_of_span_eq_top_of_smul_pow_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["choose", "apply", "rintro", "exact"], "tactic_count": 4}
{"name": "Submodule.map_pointwise_smul", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Ideal.add_eq_sup", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.zero_eq_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.sum_eq_sup", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.one_eq_top", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.add_eq_one_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.mul_mem_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.bot_pow", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.pow_mem_pow", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.mul_le", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.mul_le_left", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.sup_mul_left_self", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.mul_left_self_sup", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.mul_le_right", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.sup_mul_right_self", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.mul_right_self_sup", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.mul_assoc", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.mul_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Ideal.bot_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Ideal.top_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.mul_mono", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.mul_mono_left", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.mul_mono_right", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.mul_sup", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.sup_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.mul_iSup", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.iSup_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.pow_le_pow_right", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["obtain", "rw", "obtain", "rw", "exact"], "tactic_count": 5}
{"name": "Ideal.pow_le_self", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.pow_right_mono", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "exact"], "tactic_count": 5}
{"name": "Ideal.IsTwoSided.instHMul", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.IsTwoSided.instHPowNat", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.IsTwoSided.mul_one", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.IsTwoSided.pow_add", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact"], "tactic_count": 3}
{"name": "Ideal.IsTwoSided.pow_succ", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.mul_eq_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.instNoZeroDivisors", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.instIsTorsionFreeSubtypeMemSubmodule", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.span_mul_span", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.span_mul_span'", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.span_singleton_mul_span_singleton", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.span_singleton_pow", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "obtain", "simp"], "tactic_count": 5}
{"name": "Ideal.mem_mul_span_singleton", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.span_singleton_mul_left_mono", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Ideal.span_singleton_mul_left_inj", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Ideal.mul_le_inf", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.sup_mul_eq_of_coprime_left", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.sup_mul_eq_of_coprime_right", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.mul_sup_eq_of_coprime_left", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["rw", "rw"], "tactic_count": 2}
{"name": "Ideal.mul_sup_eq_of_coprime_right", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["rw", "rw"], "tactic_count": 2}
{"name": "Ideal.sup_iInf_eq_top", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["classical", "exact", "s.induction_on", "top_unique", "rw", "refine", "simpa"], "tactic_count": 7}
{"name": "Ideal.iInf_sup_eq_top", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.sup_pow_eq_top", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Ideal.sup_pow_eq_top'", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "obtain", "rwa"], "tactic_count": 5}
{"name": "Ideal.pow_sup_eq_top", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.pow_sup_eq_top'", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.pow_sup_pow_eq_top", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.pow_sup_pow_eq_top'", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.mul_top", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.span_pair_mul_span_pair", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.top_pow", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.pow_eq_top_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": ["refine", "rintro", "rw", "rw"], "tactic_count": 4}
{"name": "Ideal.natCast_eq_top", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "obtain", "rw"], "tactic_count": 5}
{"name": "Ideal.ofNat_eq_top", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.pow_eq_zero_of_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Ideal.mul_mem_mul_rev", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.prod_mem_prod", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["classical", "refine", "grind", "grind"], "tactic_count": 4}
{"name": "Ideal.sup_pow_add_le_pow_sup_pow", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["rw", "apply", "intro", "by_cases", "exact", "refine", "lia"], "tactic_count": 7}
{"name": "Ideal.mul_comm", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.mem_span_singleton_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Ideal.range_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Ideal.range_mul'", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.le_span_singleton_mul_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.span_singleton_mul_le_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Ideal.span_singleton_mul_le_span_singleton_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Ideal.span_singleton_mul_right_mono", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Ideal.span_singleton_mul_right_inj", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Ideal.span_singleton_mul_right_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.span_singleton_mul_left_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.eq_span_singleton_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Ideal.span_singleton_mul_eq_span_singleton_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Ideal.prod_span", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.prod_span_singleton", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.multiset_prod_span_singleton", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.finset_inf_span_singleton", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["ext", "simp", "exact"], "tactic_count": 3}
{"name": "Ideal.iInf_span_singleton", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["rw", "rwa"], "tactic_count": 2}
{"name": "Ideal.iInf_span_singleton_natCast", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Ideal.sup_eq_top_iff_isCoprime", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["rw", "constructor", "rintro", "rw", "rw", "exact", "exact"], "tactic_count": 7}
{"name": "Ideal.multiset_prod_le_inf", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["classical", "refine", "rw", "exact", "intro", "rw", "exact"], "tactic_count": 7}
{"name": "Ideal.prod_le_inf", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.mul_eq_inf_of_coprime", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.sup_prod_eq_top", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.sup_multiset_prod_eq_top", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.prod_sup_eq_top", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.multiset_prod_eq_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.isCoprime_iff_codisjoint", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["rw", "constructor", "rintro", "rw", "apply", "rw", "simp", "intro", "refine", "simpa"], "tactic_count": 10}
{"name": "Ideal.isCoprime_of_isMaximal", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Ideal.isCoprime_iff_add", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.isCoprime_iff_exists", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.isCoprime_iff_sup_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.coprime_of_no_prime_ge", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["rw", "by_contra", "obtain", "exact"], "tactic_count": 4}
{"name": "Ideal.isCoprime_tfae", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "IsCoprime.codisjoint", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCoprime.add_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCoprime.exists", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCoprime.sup_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.inf_eq_mul_of_isCoprime", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.isCoprime_span_singleton_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["simp_rw", "constructor", "rintro", "rintro"], "tactic_count": 4}
{"name": "Ideal.isCoprime_biInf", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Ideal.radical", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.mem_radical_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.IsRadical", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.le_radical", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.radical_eq_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.isRadical_iff_pow_one_lt", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.radical_top", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.radical_mono", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.radical_isRadical", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.radical_idem", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.IsRadical.radical_le_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.radical_le_radical_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.radical_eq_top", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.IsPrime.isRadical", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.IsPrime.radical", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.mem_radical_of_pow_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.disjoint_powers_iff_notMem", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["refine", "rintro", "exact"], "tactic_count": 3}
{"name": "Ideal.radical_sup", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.radical_inf", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.IsRadical.inf", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.isRadical_bot_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Ideal.isRadical_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Ideal.radicalInfTopHom", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.radicalInfTopHom_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.radical_finset_inf", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Ideal.radical_iInf_le", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.isRadical_iInf", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.radical_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["refine", "have", "simp_rw", "assumption"], "tactic_count": 4}
{"name": "Ideal.IsPrime.radical_le_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.radical_eq_sInf", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.isRadical_bot_of_noZeroDivisors", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.radical_bot_of_noZeroDivisors", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.instIdemCommSemiring", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.radical_pow", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.IsPrime.mul_le", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["rw", "simp_rw"], "tactic_count": 2}
{"name": "Ideal.IsPrime.inf_le", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.IsPrime.multiset_prod_le", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.IsPrime.multiset_prod_map_le", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Ideal.IsPrime.multiset_prod_mem_iff_exists_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Ideal.IsPrime.pow_le_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["have", "simp_rw", "exact"], "tactic_count": 3}
{"name": "Ideal.IsPrime.le_of_pow_le", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "exact", "exact"], "tactic_count": 4}
{"name": "Ideal.IsPrime.prod_le", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.IsPrime.prod_mem_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Ideal.IsPrime.prod_mem_iff_exists_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Ideal.IsPrime.inf_le'", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.eq_inf_of_isPrime_inf", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.IsPrime.notMem_of_isCoprime_of_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.subset_union", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.subset_union_prime'", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": ["suffices", "refine", "exact", "generalize", "induction", "zero", "clear", "rw", "subst", "rw", "simpa", "succ", "classical", "replace", "rcases", "replace", "by_cases", "obtain", "obtain", "have", "rw", "exact", "have", "have", "rwa", "exacts", "have", "rw", "rw", "simp", "rw", "exact", "specialize", "refine", "exact", "by_cases", "have", "rw", "exact", "specialize", "right", "rcases", "exact", "exact", "exact", "by_cases", "have", "rw", "exact", "specialize", "rcases", "exact", "exact", "exact", "by_cases", "exact", "have", "simp", "exact", "rcases", "by_cases", "specialize", "rcases", "order", "order", "right", "right", "exact", "exfalso", "rcases", "rw", "have", "rcases", "exact", "exact", "exact", "rw", "rcases", "simp", "exact"], "tactic_count": 80}
{"name": "Ideal.subset_union_prime", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.subset_union_prime_finite", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["rcases", "have", "ext", "simpa", "have", "rw", "exact"], "tactic_count": 7}
{"name": "Ideal.le_of_dvd", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.dvd_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.isUnit_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.uniqueUnits", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.finsuppTotal", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.finsuppTotal_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "exact"], "tactic_count": 3}
{"name": "Ideal.finsuppTotal_apply_eq_of_fintype", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Ideal.range_finsuppTotal", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["ext", "rw", "refine", "rintro", "classical", "refine", "rw", "apply", "intro", "rw", "exact"], "tactic_count": 11}
{"name": "Finsupp.mem_ideal_span_range_iff_exists_finsupp", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.mem_span_range_iff_exists_fun", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associates.mk_ne_zero'", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.span_singleton_nonZeroDivisors", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["cases", "simp_rw", "exact", "rw"], "tactic_count": 4}
{"name": "Ideal.primeCompl_le_nonZeroDivisors", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.moduleSubmodule", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.span_smul_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submodule.set_smul_top_eq_span", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.smul_le_span", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Submodule.algebraIdeal", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mapAlgHom", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mapAlgEquiv", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instNonUnitalSubsemiringClassIdeal", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instNonUnitalSubringClassIdeal", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.exists_subset_radical_span_sup_of_subset_radical_sup", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Operations", "is_tactic_proof": false, "tactics": ["replace", "rintro", "simp", "obtain", "exact", "choose", "refine", "exact"], "tactic_count": 8}
{"name": "Ideal.comap_eq_of_scalar_tower_quotient", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Over", "is_tactic_proof": true, "tactics": ["ext", "rw", "constructor", "intro", "exact", "intro", "rw"], "tactic_count": 7}
{"name": "Ideal.Quotient.algebraQuotientMapQuotient", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.algebraMap_quotient_map_quotient", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.mk_smul_mk_quotient_map_quotient", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.tower_quotient_map_quotient", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.under", "kind": "abbrev", "module": "Mathlib.RingTheory.Ideal.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.under_def", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.IsPrime.under", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.under_smul", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Over", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "Ideal.under_top", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.over_under", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.over_def", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.mem_of_liesOver", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Over", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Ideal.top_liesOver_top", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.eq_top_iff_of_liesOver", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Over", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Ideal.ne_top_iff_of_liesOver", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.LiesOver.of_eq_comap", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.LiesOver.of_eq_map_equiv", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Over", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Ideal.LiesOver.smul", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.comap_liesOver", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.map_equiv_liesOver", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.under_under", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Over", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Ideal.LiesOver.trans", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.LiesOver.tower_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.map_under_le_under_map", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Over", "is_tactic_proof": true, "tactics": ["apply", "rw", "exact"], "tactic_count": 3}
{"name": "Ideal.under_map_eq_map_under", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.disjoint_primeCompl_of_liesOver", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Over", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "Ideal.under_liesOver_of_liesOver", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.under_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.bot_liesOver_bot", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.ne_bot_of_liesOver_of_ne_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Over", "is_tactic_proof": true, "tactics": ["contrapose", "rw"], "tactic_count": 2}
{"name": "Ideal.Quotient.algebraOfLiesOver", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.algebraMap_mk_of_liesOver", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.isScalarTower_of_liesOver", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.instFaithfulSMul", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Over", "is_tactic_proof": true, "tactics": ["rw", "rintro", "apply", "rw", "exact"], "tactic_count": 5}
{"name": "Ideal.Quotient.nontrivial_of_liesOver_of_ne_top", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Over", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Ideal.Quotient.nontrivial_of_liesOver_of_isPrime", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.algEquivOfEqMap", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.algEquivOfEqMap_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.algEquivOfEqComap", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.algEquivOfEqComap_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.stabilizerHom", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.stabilizerHom_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.ker_stabilizerHom", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Over", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Ideal.Quotient.map_ker_stabilizer_subtype", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Over", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Ideal.Quotient.instIsPrimeQuotientMapRingHomAlgebraMapMkOfLiesOver", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Over", "is_tactic_proof": true, "tactics": ["apply", "rw"], "tactic_count": 2}
{"name": "Ideal.primesOver", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.primesOver.isPrime", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.primesOver.liesOver", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.primesOver.mk", "kind": "abbrev", "module": "Mathlib.RingTheory.Ideal.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.ne_bot_of_mem_primesOver", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Over", "is_tactic_proof": true, "tactics": ["have"], "tactic_count": 1}
{"name": "Ideal.pointwiseDistribMulAction", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.pointwiseMulSemiringAction", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.pointwise_smul_def", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.smul_mem_pointwise_smul", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.instCovariantClassHSMulLe", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.smul_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.smul_sup", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.smul_closure", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.pointwise_central_scalar", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.pointwise_smul_toAddSubmonoid", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Pointwise", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "Ideal.pointwise_smul_toAddSubgroup", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Pointwise", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "Ideal.pointwise_smul_eq_comap", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Pointwise", "is_tactic_proof": true, "tactics": ["ext", "simp", "rfl"], "tactic_count": 3}
{"name": "Ideal.smul_mem_pointwise_smul_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.mem_pointwise_smul_iff_inv_smul_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.mem_inv_pointwise_smul_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Pointwise", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.pointwise_smul_le_pointwise_smul_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.pointwise_smul_subset_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Pointwise", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.subset_pointwise_smul_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Pointwise", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.IsPrime.smul", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Pointwise", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "Ideal.IsPrime.smul_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.inertia_le_stabilizer", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Pointwise", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "Ideal.isPrime_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.IsPrime.ne_top", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.IsPrime.one_notMem", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.one_notMem", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.IsPrime.mem_or_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.IsPrime.mul_notMem", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.IsPrime.mem_or_mem_of_mul_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.IsPrime.mem_of_pow_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Prime", "is_tactic_proof": true, "tactics": ["induction", "zero", "rw", "exact", "succ", "rw", "exact"], "tactic_count": 7}
{"name": "Ideal.not_isPrime_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Prime", "is_tactic_proof": true, "tactics": ["simp_rw", "exact", "or_congr"], "tactic_count": 3}
{"name": "Ideal.isPrime_bot", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.bot_prime", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.IsPrime.mul_mem_iff_mem_or_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.IsPrime.pow_mem_iff_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.IsPrime.mul_mem_left_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Prime", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Ideal.IsPrime.mul_mem_right_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Prime", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.primeCompl", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.mem_primeCompl_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDomain.of_bot_isPrime", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.eq_bot_of_prime", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.prod", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.coe_prod", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.mem_prod", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.prod_top_top", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.prod_bot_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.prod_mono", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.prod_mono_left", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.prod_mono_right", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.ideal_prod_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Prod", "is_tactic_proof": true, "tactics": ["apply", "rintro", "rw", "mem_map_iff_of_surjective", "refine", "rintro", "simpa"], "tactic_count": 7}
{"name": "Ideal.map_fst_prod", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Prod", "is_tactic_proof": true, "tactics": ["ext", "rw", "exact", "rintro", "exact"], "tactic_count": 5}
{"name": "Ideal.map_snd_prod", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Prod", "is_tactic_proof": true, "tactics": ["ext", "rw", "exact", "rintro", "exact"], "tactic_count": 5}
{"name": "Ideal.map_prodComm_prod", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Prod", "is_tactic_proof": true, "tactics": ["refine", "simp"], "tactic_count": 2}
{"name": "Ideal.idealProdEquiv", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.idealProdEquiv_symm_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.span_prod_le", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Prod", "is_tactic_proof": true, "tactics": ["rw", "gcongr", "exact", "exact"], "tactic_count": 4}
{"name": "Ideal.span_prod", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Prod", "is_tactic_proof": true, "tactics": ["simp_rw", "obtain", "conv_lhs", "congr", "rw", "simp", "rw", "simp", "simp"], "tactic_count": 9}
{"name": "Ideal.prod_inj", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Prod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Ideal.prod_eq_bot_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Prod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.prod_eq_top_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Prod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.isPrime_of_isPrime_prod_top", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Prod", "is_tactic_proof": true, "tactics": ["constructor", "contrapose", "rw", "simp", "intro", "have", "rw", "exact", "simpa"], "tactic_count": 9}
{"name": "Ideal.isPrime_of_isPrime_prod_top'", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Prod", "is_tactic_proof": true, "tactics": ["apply", "rw", "exact"], "tactic_count": 3}
{"name": "Ideal.isPrime_ideal_prod_top", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.isPrime_ideal_prod_top'", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Prod", "is_tactic_proof": true, "tactics": ["letI", "rw", "exact"], "tactic_count": 3}
{"name": "Ideal.ideal_prod_prime_aux", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Prod", "is_tactic_proof": true, "tactics": ["contrapose", "simp", "exact"], "tactic_count": 3}
{"name": "Ideal.ideal_prod_prime", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Prod", "is_tactic_proof": true, "tactics": ["constructor", "rw", "intro", "rcases", "right", "rw", "exact", "left", "rw", "exact", "rintro", "exact", "exact"], "tactic_count": 13}
{"name": "instIsPrincipalIdealRingProd", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Prod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.mk_span_range", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Ideal.Quotient.zero_eq_one_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.zero_ne_one_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.subsingleton_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.nontrivial_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.nontrivial", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.instUniqueQuotientTop", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Quotient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.isScalarTower_right", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Quotient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.smulCommClass", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Quotient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.smulCommClass'", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Quotient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.eq_zero_iff_dvd", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.Quotient.mk_singleton_self", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.noZeroDivisors", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Quotient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.isDomain", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Quotient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.isDomain_iff_prime", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Basic", "is_tactic_proof": true, "tactics": ["refine", "haveI", "exact", "simp", "haveI", "exact"], "tactic_count": 6}
{"name": "Ideal.Quotient.exists_inv", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Basic", "is_tactic_proof": true, "tactics": ["apply", "rintro", "rcases", "refine", "simp", "rw", "rwa"], "tactic_count": 7}
{"name": "Ideal.Quotient.groupWithZero", "kind": "abbrev", "module": "Mathlib.RingTheory.Ideal.Quotient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.divisionRing", "kind": "abbrev", "module": "Mathlib.RingTheory.Ideal.Quotient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.field", "kind": "abbrev", "module": "Mathlib.RingTheory.Ideal.Quotient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.maximal_of_isField", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Basic", "is_tactic_proof": true, "tactics": ["apply", "constructor", "intro", "rcases", "exact", "intro", "rcases", "rw", "exact"], "tactic_count": 9}
{"name": "Ideal.Quotient.maximal_ideal_iff_isField_quotient", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.modulePi", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Quotient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.piQuotEquiv", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Quotient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.map_pi", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Basic", "is_tactic_proof": true, "tactics": ["classical", "cases", "rw", "simp", "exact"], "tactic_count": 5}
{"name": "Ideal.univ_eq_iUnion_image_add", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finite_iff_ideal_quotient", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finite.of_ideal_quotient", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.pi_mkQ_rTensor", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.ChineseRemainder", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Ideal.pi_tensorProductMk_quotient_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.ChineseRemainder", "is_tactic_proof": true, "tactics": ["have", "classical", "simpa"], "tactic_count": 3}
{"name": "Ideal.ker_tensorProductMk_quotient", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.ChineseRemainder", "is_tactic_proof": true, "tactics": ["have", "rw", "convert", "classical", "refine", "simpa", "rintro", "refine", "simpa", "simpa"], "tactic_count": 10}
{"name": "Ideal.instHasQuotient", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.instHasQuotient_1", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.one", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.ringCon", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.ring", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.commRing", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.instRingQuotient", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.commSemiring", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.semiring", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient._example", "kind": "example", "module": "Mathlib.RingTheory.Ideal.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.mk", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.instCoeQuotient", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.ringHom_ext", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.instNonemptyQuotient", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.eq", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.mk_eq_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.eq_zero_iff_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.mk_eq_mk_iff_sub_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.Quotient.mk_eq_one_iff_sub_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.Quotient.mk_out", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.mk_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.instRingHomSurjectiveQuotientMk", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.quotient_ring_saturate", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Defs", "is_tactic_proof": true, "tactics": ["ext", "simp", "exact"], "tactic_count": 3}
{"name": "Ideal.Quotient.lift", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.lift_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.lift_comp_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.lift_surjective_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Defs", "is_tactic_proof": true, "tactics": ["intro", "obtain", "use", "simp"], "tactic_count": 4}
{"name": "Ideal.Quotient.factor", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.factor_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.factor_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Defs", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Ideal.Quotient.factor_comp_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Defs", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "Ideal.Quotient.factor_comp", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Defs", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Ideal.Quotient.factor_comp_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Defs", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Ideal.Quotient.factor_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.quotEquivOfEq", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.quotEquivOfEq_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.quotEquivOfEq_symm", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Defs", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Ideal.quotEquivOfEq_eq_factor", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.finite_quotient_smul", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Index", "is_tactic_proof": true, "tactics": ["suffices", "suffices", "constructor", "rw", "have", "exact", "let", "rw", "have", "have", "exact"], "tactic_count": 11}
{"name": "Submodule.index_smul_le", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Index", "is_tactic_proof": true, "tactics": ["classical", "cases", "rw", "gcongr", "change", "let", "rw", "have", "rw", "let", "have", "have", "refine", "simp"], "tactic_count": 14}
{"name": "Ideal.finite_quotient_prod", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Index", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "insert", "rw", "have", "have", "exact"], "tactic_count": 8}
{"name": "Ideal.finite_quotient_pow", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Index", "is_tactic_proof": true, "tactics": ["induction", "zero", "simp", "infer_instance", "succ"], "tactic_count": 5}
{"name": "Ideal.index_pow_le", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Index", "is_tactic_proof": true, "tactics": ["have", "induction", "zero", "succ", "refine", "refine", "rw"], "tactic_count": 7}
{"name": "Ideal.isRadical_iff_quotient_reduced", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Nilpotent", "is_tactic_proof": true, "tactics": ["conv_lhs", "exact"], "tactic_count": 2}
{"name": "Ideal.IsNilpotent.induction_on", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Nilpotent", "is_tactic_proof": true, "tactics": ["obtain", "induction", "by_cases", "subst", "apply", "rw", "rcases", "rw", "haveI", "exact", "rcases", "rw", "exact", "apply", "apply", "rw", "apply", "exact", "apply", "rw"], "tactic_count": 20}
{"name": "IsNilpotent.isUnit_quotient_mk_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Nilpotent", "is_tactic_proof": true, "tactics": ["refine", "revert", "apply", "swap", "introv", "apply", "apply", "exact", "introv", "obtain", "have", "rw", "have", "rw", "exact", "have", "rw", "ring", "exact"], "tactic_count": 19}
{"name": "Ideal.Quotient.isNoetherianRing", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Quotient.Noetherian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.kerLift", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.kerLift_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.lift_injective_of_ker_le_ideal", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": true, "tactics": ["rw", "intro", "obtain", "rw", "rw", "exact"], "tactic_count": 6}
{"name": "RingHom.kerLift_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.quotientKerEquivOfRightInverse", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.quotientKerEquivOfRightInverse.apply", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.quotientKerEquivOfRightInverse.Symm.apply", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.quotientKerEquivOfSurjective", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.quotientKerEquivOfSurjective_apply_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.quotientKerEquivRangeS", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.quotientKerEquivRange", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.map_quotient_self", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.mk_ker", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "Ideal.map_mk_eq_bot_of_le", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Ideal.ker_quotient_lift", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": true, "tactics": ["apply", "intro", "constructor", "intro", "obtain", "rw", "rw", "exact", "intro", "rw", "obtain", "rw", "exact"], "tactic_count": 13}
{"name": "Ideal.injective_lift_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": true, "tactics": ["rw", "constructor", "exact", "rintro"], "tactic_count": 4}
{"name": "Ideal.ker_Pi_Quotient_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Ideal.bot_quotient_isMaximal_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.mem_quotient_iff_mem_sup", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.mem_quotient_iff_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.quotientInfToPiQuotient", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.quotientInfToPiQuotient_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.quotientInfToPiQuotient_mk'", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.quotientInfToPiQuotient_inj", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.quotientInfToPiQuotient_surj", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": true, "tactics": ["classical", "cases", "intro", "choose", "have", "intro", "have", "intro", "exact", "rcases", "replace", "refine", "simp", "exact", "choose", "use", "ext", "rw", "simp", "intro", "simp"], "tactic_count": 21}
{"name": "Ideal.quotientInfRingEquivPiQuotient", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.pi_quotient_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "exact"], "tactic_count": 3}
{"name": "Ideal.pi_mkQ_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.exists_forall_sub_mem_ideal", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Ideal.quotientInfEquivQuotientProd", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.quotientInfEquivQuotientProd_fst", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.quotientInfEquivQuotientProd_snd", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.fst_comp_quotientInfEquivQuotientProd", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "Ideal.snd_comp_quotientInfEquivQuotientProd", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "Ideal.quotientMulEquivQuotientProd", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.quotientMulEquivQuotientProd_fst", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.quotientMulEquivQuotientProd_snd", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.fst_comp_quotientMulEquivQuotientProd", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "Ideal.snd_comp_quotientMulEquivQuotientProd", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "Ideal.Quotient.algebra", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.instAlgebraQuotient", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.isScalarTower", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.mkₐ", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.algHom_ext", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.alg_map_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.mkₐ_toRingHom", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.mkₐ_eq_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.algebraMap_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.mk_comp_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.mk_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.mkₐ_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.mkₐ_ker", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.mk_bijective_iff_eq_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "exact", "exact"], "tactic_count": 5}
{"name": "Ideal.Quotient.factorₐ", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.coe_factorₐ", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.factorₐ_apply_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.factorₐ_comp_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.factorₐ_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.factorₐ_refl", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Ideal.Quotient.factorₐ_comp", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.liftₐ", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.liftₐ_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.liftₐ_comp", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.span_singleton_one", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.Quotient.smul_top", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Ideal.KerLift.map_smul", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Ideal.kerLiftAlg", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.kerLiftAlg_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "Ideal.kerLiftAlg_toRingHom", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.kerLiftAlg_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.quotientKerAlgEquivOfRightInverse", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.quotientKerAlgEquivOfSurjective", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.quotientKerAlgEquivOfSurjective_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.quotientKerAlgEquivOfSurjective_symm_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "AlgHom.liftOfSurjective", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.liftOfSurjective_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": true, "tactics": ["dsimp", "erw", "rw", "rfl"], "tactic_count": 4}
{"name": "AlgHom.liftOfSurjective_comp", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "AlgHom.liftOfSurjective_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.quotientMap", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.quotientMap_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.quotientMap_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.quotientMap_comp_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.ker_quotientMap_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.quotientEquiv", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.quotientEquiv_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.quotientEquiv_symm_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.quotientMap_injective'", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": true, "tactics": ["refine", "obtain", "rw", "exact"], "tactic_count": 4}
{"name": "Ideal.quotientMap_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.quotientMap_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.comp_quotientMap_eq_of_comp_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": true, "tactics": ["refine", "obtain", "simp", "exact"], "tactic_count": 4}
{"name": "Ideal.quotientMapₐ", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.quotient_map_mkₐ", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.quotient_map_comp_mkₐ", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.quotientEquivAlg", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.quotientEquivAlg_symm", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.quotientEquivAlg_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.algebraQuotientOfLEComap", "kind": "abbrev", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.quotientAlgebra", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.instAlgebraQuotientComapRingHomAlgebraMap", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.algebraMap_quotient_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": true, "tactics": ["rintro", "replace", "rw", "exact"], "tactic_count": 4}
{"name": "Ideal.quotientEquivAlgOfEq", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.quotientEquivAlgOfEq_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.quotientEquivAlgOfEq_coe_eq_factorₐ", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.quotientEquivAlgOfEq_coe_eq_factor", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.quotientEquivAlgOfEq_symm", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "Ideal.comap_map_quotientMk", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Ideal.comap_map_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Ideal.isPrime_map_quotientMk_of_isPrime", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": true, "tactics": ["apply", "exact", "simpa"], "tactic_count": 3}
{"name": "Ideal.quotientKerEquivRange", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.quotientBot", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.quotientBot_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.quotientBot_symm_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.quotientBot", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.quotientBot_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.quotientBot_symm_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DoubleQuot.quotLeftToQuotSup", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DoubleQuot.ker_quotLeftToQuotSup", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": true, "tactics": ["simp", "map_eq_iff_sup_ker_eq_of_surjective"], "tactic_count": 2}
{"name": "DoubleQuot.quotQuotToQuotSup", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DoubleQuot.quotQuotMk", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DoubleQuot.ker_quotQuotMk", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": true, "tactics": ["rw", "comap_map_of_surjective"], "tactic_count": 2}
{"name": "DoubleQuot.liftSupQuotQuotMk", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DoubleQuot.quotQuotEquivQuotSup", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DoubleQuot.quotQuotEquivQuotSup_quotQuotMk", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DoubleQuot.quotQuotEquivQuotSup_symm_quotQuotMk", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DoubleQuot.quotQuotEquivComm", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DoubleQuot.quotQuotEquivComm_quotQuotMk", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DoubleQuot.quotQuotEquivComm_comp_quotQuotMk", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DoubleQuot.quotQuotEquivComm_symm", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "DoubleQuot.quotQuotEquivQuotOfLE", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DoubleQuot.quotQuotEquivQuotOfLE_quotQuotMk", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DoubleQuot.quotQuotEquivQuotOfLE_symm_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DoubleQuot.quotQuotEquivQuotOfLE_comp_quotQuotMk", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "DoubleQuot.quotQuotEquivQuotOfLE_symm_comp_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "DoubleQuot.quotQuotEquivComm_mk_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DoubleQuot.quotQuotEquivQuotSup_quot_quot_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DoubleQuot.quotQuotEquivComm_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DoubleQuot.quotLeftToQuotSupₐ", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DoubleQuot.quotLeftToQuotSupₐ_toRingHom", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DoubleQuot.coe_quotLeftToQuotSupₐ", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DoubleQuot.quotQuotToQuotSupₐ", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DoubleQuot.quotQuotToQuotSupₐ_toRingHom", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DoubleQuot.coe_quotQuotToQuotSupₐ", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DoubleQuot.quotQuotMkₐ", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DoubleQuot.quotQuotMkₐ_toRingHom", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DoubleQuot.coe_quotQuotMkₐ", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DoubleQuot.liftSupQuotQuotMkₐ", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DoubleQuot.liftSupQuotQuotMkₐ_toRingHom", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DoubleQuot.coe_liftSupQuotQuotMkₐ", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DoubleQuot.quotQuotEquivQuotSupₐ", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DoubleQuot.quotQuotEquivQuotSupₐ_toRingEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DoubleQuot.coe_quotQuotEquivQuotSupₐ", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DoubleQuot.quotQuotEquivQuotSupₐ_symm_toRingEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DoubleQuot.coe_quotQuotEquivQuotSupₐ_symm", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DoubleQuot.quotQuotEquivCommₐ", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DoubleQuot.quotQuotEquivCommₐ_toRingEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DoubleQuot.coe_quotQuotEquivCommₐ", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DoubleQuot.quotQuotEquivComm_symmₐ", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "DoubleQuot.quotQuotEquivComm_comp_quotQuotMkₐ", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DoubleQuot.quotQuotEquivQuotOfLEₐ", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DoubleQuot.quotQuotEquivQuotOfLEₐ_toRingEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DoubleQuot.coe_quotQuotEquivQuotOfLEₐ", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DoubleQuot.quotQuotEquivQuotOfLEₐ_symm_toRingEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DoubleQuot.coe_quotQuotEquivQuotOfLEₐ_symm", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DoubleQuot.quotQuotEquivQuotOfLE_comp_quotQuotMkₐ", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DoubleQuot.quotQuotEquivQuotOfLE_symm_comp_mkₐ", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DoubleQuot.quotQuotEquivQuotOfLEₐ_comp_mkₐ", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": true, "tactics": ["ext", "obtain", "rfl"], "tactic_count": 3}
{"name": "Ideal.powQuotPowSuccLinearEquivMapMkPowSuccPow", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": ["refine", "intro", "simp", "intro", "obtain", "simp", "intro", "obtain", "obtain", "simp", "intro", "rw", "obtain", "refine", "simp"], "tactic_count": 15}
{"name": "Ideal.powQuotPowSuccEquivMapMkPowSuccPow", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Quotient.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.factor_ker", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.PowTransition", "is_tactic_proof": true, "tactics": ["ext", "refine", "rcases", "rw", "simp", "exact", "rcases", "simpa"], "tactic_count": 8}
{"name": "Submodule.eq_factor_of_eq_factor_succ", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.PowTransition", "is_tactic_proof": true, "tactics": ["have", "induction", "zero", "rw", "subst", "simp", "succ", "rw", "subst", "rw", "simp", "lia"], "tactic_count": 12}
{"name": "Ideal.Quotient.eq_factor_of_eq_factor_succ", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.PowTransition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.map_mk_comap_factor", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.PowTransition", "is_tactic_proof": true, "tactics": ["ext", "refine", "rcases", "have", "rcases", "rw", "exact", "rcases", "simpa"], "tactic_count": 9}
{"name": "Submodule.mapQ_eq_factor", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.PowTransition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.factor_eq_factor", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.PowTransition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.pow_smul_top_le", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.PowTransition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.factorPow", "kind": "abbrev", "module": "Mathlib.RingTheory.Ideal.Quotient.PowTransition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.factorPowSucc", "kind": "abbrev", "module": "Mathlib.RingTheory.Ideal.Quotient.PowTransition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.factorPow", "kind": "abbrev", "module": "Mathlib.RingTheory.Ideal.Quotient.PowTransition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Quotient.factorPowSucc", "kind": "abbrev", "module": "Mathlib.RingTheory.Ideal.Quotient.PowTransition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.map_mk_comap_factorPow", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.PowTransition", "is_tactic_proof": true, "tactics": ["apply", "exact"], "tactic_count": 2}
{"name": "factorPowSucc.isUnit_of_isUnit_image", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Quotient.PowTransition", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "rw", "apply", "rw", "rcases", "refine", "calc", "rw", "apply", "simpa"], "tactic_count": 11}
{"name": "Ideal.span", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Span", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.submodule_span_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Span", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.span_empty", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Span", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.span_univ", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Span", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.span_union", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Span", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.span_iUnion", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Span", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.iSup_eq_span", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Span", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.mem_span", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Span", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.subset_span", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Span", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.span_le", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Span", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.span_mono", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Span", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.span_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Span", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.span_singleton_one", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Span", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.isCompactElement_top", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Span", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Ideal.mem_span_insert", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Span", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.mem_span_range_self", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Span", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.mem_span_singleton'", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Span", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.mem_span_singleton_self", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Span", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.span_singleton_le_iff_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Span", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.span_singleton_mul_left_unit", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Span", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.span_insert", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Span", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.span_eq_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Span", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.span_singleton_eq_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Span", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.span_singleton_ne_top", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Span", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.span_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Span", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.span_singleton_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Span", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.span_insert_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Span", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.span_sdiff_singleton_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Span", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.span_one", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Span", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.span_eq_top_iff_finite", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Span", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Ideal.mem_span_singleton_sup", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Span", "is_tactic_proof": true, "tactics": ["rw", "constructor", "rintro", "obtain", "exact", "rintro", "exact"], "tactic_count": 7}
{"name": "Ideal.ofRel", "kind": "definition", "module": "Mathlib.RingTheory.Ideal.Span", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.zero_ne_one_of_proper", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Span", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.span_pair_comm", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Span", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Ideal.mem_span_pair", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Span", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.span_pair_add_mul_left", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Span", "is_tactic_proof": true, "tactics": ["ext", "rw", "exact", "rw", "ring1⟩,", "rw", "ring1⟩⟩"], "tactic_count": 7}
{"name": "Ideal.span_pair_add_mul_right", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Span", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.mem_span_singleton", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Span", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.span_singleton_le_span_singleton", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Span", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.span_singleton_eq_span_singleton", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Span", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "Ideal.span_pair_eq_span_left_iff_dvd", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Span", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.span_pair_eq_span_right_iff_dvd", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Span", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.span_singleton_mul_right_unit", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Span", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.span_singleton_eq_top", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Span", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.factors_decreasing", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Span", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.mem_iff_of_associated", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Span", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Ideal.mem_span_insert'", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Span", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.span_singleton_neg", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Span", "is_tactic_proof": true, "tactics": ["ext", "simp", "exact"], "tactic_count": 3}
{"name": "Ideal.span_singleton_abs", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Span", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "IsIdempotentElem.ker_toSpanSingleton_eq_span", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Span", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIdempotentElem.ker_toSpanSingleton_one_sub_eq_span", "kind": "theorem", "module": "Mathlib.RingTheory.Ideal.Span", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "instIsPrincipalSpanSingletonSet", "kind": "instance", "module": "Mathlib.RingTheory.Ideal.Span", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrthogonalIdempotents.mul_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Idempotents", "is_tactic_proof": true, "tactics": ["split", "simp", "exact"], "tactic_count": 3}
{"name": "OrthogonalIdempotents.iff_mul_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Idempotents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrthogonalIdempotents.isIdempotentElem_sum", "kind": "theorem", "module": "Mathlib.RingTheory.Idempotents", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "OrthogonalIdempotents.mul_sum_of_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Idempotents", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "OrthogonalIdempotents.mul_sum_of_notMem", "kind": "theorem", "module": "Mathlib.RingTheory.Idempotents", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "OrthogonalIdempotents.map", "kind": "theorem", "module": "Mathlib.RingTheory.Idempotents", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "OrthogonalIdempotents.map_injective_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Idempotents", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "OrthogonalIdempotents.embedding", "kind": "theorem", "module": "Mathlib.RingTheory.Idempotents", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "OrthogonalIdempotents.equiv", "kind": "theorem", "module": "Mathlib.RingTheory.Idempotents", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "OrthogonalIdempotents.unique", "kind": "theorem", "module": "Mathlib.RingTheory.Idempotents", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "OrthogonalIdempotents.option", "kind": "theorem", "module": "Mathlib.RingTheory.Idempotents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteOrthogonalIdempotents.iff_ortho_complete", "kind": "theorem", "module": "Mathlib.RingTheory.Idempotents", "is_tactic_proof": true, "tactics": ["rw", "intro", "apply_fun", "rwa"], "tactic_count": 4}
{"name": "CompleteOrthogonalIdempotents.pair_iff'ₛ", "kind": "theorem", "module": "Mathlib.RingTheory.Idempotents", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CompleteOrthogonalIdempotents.pair_iffₛ", "kind": "theorem", "module": "Mathlib.RingTheory.Idempotents", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CompleteOrthogonalIdempotents.unique_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Idempotents", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CompleteOrthogonalIdempotents.single", "kind": "theorem", "module": "Mathlib.RingTheory.Idempotents", "is_tactic_proof": true, "tactics": ["refine", "intro", "ext", "by_cases", "subst", "simp"], "tactic_count": 6}
{"name": "CompleteOrthogonalIdempotents.map", "kind": "theorem", "module": "Mathlib.RingTheory.Idempotents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteOrthogonalIdempotents.map_injective_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Idempotents", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CompleteOrthogonalIdempotents.equiv", "kind": "theorem", "module": "Mathlib.RingTheory.Idempotents", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CompleteOrthogonalIdempotents.of_subsingleton", "kind": "theorem", "module": "Mathlib.RingTheory.Idempotents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isIdempotentElem_one_sub_one_sub_pow_pow", "kind": "theorem", "module": "Mathlib.RingTheory.Idempotents", "is_tactic_proof": false, "tactics": ["have", "conv_rhs", "nth_rw", "rw", "simp", "rw", "exact", "simp", "refine", "simp", "exact", "rwa"], "tactic_count": 12}
{"name": "exists_isIdempotentElem_mul_eq_zero_of_ker_isNilpotent_aux", "kind": "theorem", "module": "Mathlib.RingTheory.Idempotents", "is_tactic_proof": true, "tactics": ["obtain", "cases", "exact", "let", "have", "have", "have", "obtain", "refine", "rcases", "simp", "simp", "obtain", "apply_fun", "have", "rw", "rcases", "simp", "rw"], "tactic_count": 19}
{"name": "exists_isIdempotentElem_mul_eq_zero_of_ker_isNilpotent", "kind": "theorem", "module": "Mathlib.RingTheory.Idempotents", "is_tactic_proof": false, "tactics": ["obtain", "refine", "rw", "rw", "rw", "rw"], "tactic_count": 6}
{"name": "exists_isIdempotentElem_eq_of_ker_isNilpotent", "kind": "theorem", "module": "Mathlib.RingTheory.Idempotents", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "OrthogonalIdempotents.lift_of_isNilpotent_ker_aux", "kind": "theorem", "module": "Mathlib.RingTheory.Idempotents", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "obtain", "have", "obtain", "exists_isIdempotentElem_mul_eq_zero_of_ker_isNilpotent", "refine", "obtain"], "tactic_count": 9}
{"name": "OrthogonalIdempotents.lift_of_isNilpotent_ker", "kind": "theorem", "module": "Mathlib.RingTheory.Idempotents", "is_tactic_proof": true, "tactics": ["cases", "obtain", "lift_of_isNilpotent_ker_aux", "refine"], "tactic_count": 4}
{"name": "CompleteOrthogonalIdempotents.pair_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Idempotents", "is_tactic_proof": true, "tactics": ["rw", "rintro", "simp"], "tactic_count": 3}
{"name": "CompleteOrthogonalIdempotents.of_isIdempotentElem", "kind": "theorem", "module": "Mathlib.RingTheory.Idempotents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteOrthogonalIdempotents.option", "kind": "theorem", "module": "Mathlib.RingTheory.Idempotents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteOrthogonalIdempotents.lift_of_isNilpotent_ker_aux", "kind": "theorem", "module": "Mathlib.RingTheory.Idempotents", "is_tactic_proof": true, "tactics": ["cases", "choose", "exact", "cases", "obtain", "simp", "rcases", "simpa", "obtain", "refine", "funext", "have", "cases", "zero", "succ"], "tactic_count": 15}
{"name": "CompleteOrthogonalIdempotents.lift_of_isNilpotent_ker", "kind": "theorem", "module": "Mathlib.RingTheory.Idempotents", "is_tactic_proof": false, "tactics": ["obtain", "refine"], "tactic_count": 2}
{"name": "eq_of_isNilpotent_sub_of_isIdempotentElem_of_commute", "kind": "theorem", "module": "Mathlib.RingTheory.Idempotents", "is_tactic_proof": false, "tactics": ["have", "simp", "simp", "abel", "obtain", "have", "induction", "rwa"], "tactic_count": 8}
{"name": "CompleteOrthogonalIdempotents.of_ker_isNilpotent_of_isMulCentral", "kind": "theorem", "module": "Mathlib.RingTheory.Idempotents", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "ext", "refine", "simpa", "exact"], "tactic_count": 6}
{"name": "eq_of_isNilpotent_sub_of_isIdempotentElem", "kind": "theorem", "module": "Mathlib.RingTheory.Idempotents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "existsUnique_isIdempotentElem_eq_of_ker_isNilpotent", "kind": "theorem", "module": "Mathlib.RingTheory.Idempotents", "is_tactic_proof": true, "tactics": ["obtain", "exact", "eq_of_isNilpotent_sub_of_isIdempotentElem"], "tactic_count": 3}
{"name": "OrthogonalIdempotents.surjective_pi", "kind": "theorem", "module": "Mathlib.RingTheory.Idempotents", "is_tactic_proof": false, "tactics": ["suffices", "intro", "obtain", "obtain", "exact", "intro", "rw", "exact"], "tactic_count": 8}
{"name": "OrthogonalIdempotents.prod_one_sub", "kind": "theorem", "module": "Mathlib.RingTheory.Idempotents", "is_tactic_proof": true, "tactics": ["induction", "empty", "cons"], "tactic_count": 3}
{"name": "CompleteOrthogonalIdempotents.of_ker_isNilpotent", "kind": "theorem", "module": "Mathlib.RingTheory.Idempotents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteOrthogonalIdempotents.prod_one_sub", "kind": "theorem", "module": "Mathlib.RingTheory.Idempotents", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CompleteOrthogonalIdempotents.of_prod_one_sub", "kind": "theorem", "module": "Mathlib.RingTheory.Idempotents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteOrthogonalIdempotents.bijective_pi", "kind": "theorem", "module": "Mathlib.RingTheory.Idempotents", "is_tactic_proof": true, "tactics": ["classical", "refine", "rw", "intro", "simp", "suffices", "refine", "intro", "suffices", "obtain", "rw"], "tactic_count": 11}
{"name": "CompleteOrthogonalIdempotents.bijective_pi'", "kind": "theorem", "module": "Mathlib.RingTheory.Idempotents", "is_tactic_proof": false, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "RingHom.pi_bijective_of_isIdempotentElem", "kind": "theorem", "module": "Mathlib.RingTheory.Idempotents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.prod_bijective_of_isIdempotentElem", "kind": "theorem", "module": "Mathlib.RingTheory.Idempotents", "is_tactic_proof": false, "tactics": ["let", "change", "rw", "apply", "intro", "fin_cases", "intro", "fin_cases", "simpa"], "tactic_count": 9}
{"name": "AlgEquiv.prodQuotientOfIsIdempotentElem", "kind": "definition", "module": "Mathlib.RingTheory.Idempotents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.corner", "kind": "definition", "module": "Mathlib.RingTheory.Idempotents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.mem_corner_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Idempotents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.mem_corner_iff_mul_left", "kind": "theorem", "module": "Mathlib.RingTheory.Idempotents", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subsemigroup.mem_corner_iff_mul_right", "kind": "theorem", "module": "Mathlib.RingTheory.Idempotents", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subsemigroup.mem_corner_iff_mem_range_mul_left", "kind": "theorem", "module": "Mathlib.RingTheory.Idempotents", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Subsemigroup.mem_corner_iff_mem_range_mul_right", "kind": "theorem", "module": "Mathlib.RingTheory.Idempotents", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "IsIdempotentElem.Corner", "kind": "definition", "module": "Mathlib.RingTheory.Idempotents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.corner", "kind": "definition", "module": "Mathlib.RingTheory.Idempotents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRing.corner", "kind": "definition", "module": "Mathlib.RingTheory.Idempotents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instSemiringCorner", "kind": "instance", "module": "Mathlib.RingTheory.Idempotents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCommSemiringCorner", "kind": "instance", "module": "Mathlib.RingTheory.Idempotents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instRingCorner", "kind": "instance", "module": "Mathlib.RingTheory.Idempotents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCommRingCorner", "kind": "instance", "module": "Mathlib.RingTheory.Idempotents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteOrthogonalIdempotents.ringEquivOfIsMulCentral", "kind": "definition", "module": "Mathlib.RingTheory.Idempotents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteOrthogonalIdempotents.ringEquivOfComm", "kind": "definition", "module": "Mathlib.RingTheory.Idempotents", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.isCoprime_iff_nat_coprime", "kind": "theorem", "module": "Mathlib.RingTheory.Int.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.gcd_ne_one_iff_gcd_mul_right_ne_one", "kind": "theorem", "module": "Mathlib.RingTheory.Int.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Int.sq_of_gcd_eq_one", "kind": "theorem", "module": "Mathlib.RingTheory.Int.Basic", "is_tactic_proof": false, "tactics": ["have", "rw", "exact", "obtain", "use", "rw", "rcases", "rw", "simp"], "tactic_count": 9}
{"name": "Int.sq_of_isCoprime", "kind": "theorem", "module": "Mathlib.RingTheory.Int.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.natAbs_euclideanDomain_gcd", "kind": "theorem", "module": "Mathlib.RingTheory.Int.Basic", "is_tactic_proof": true, "tactics": ["apply", "rw", "exact", "rw", "exact"], "tactic_count": 5}
{"name": "Int.Prime.dvd_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Int.Basic", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Int.Prime.dvd_mul'", "kind": "theorem", "module": "Mathlib.RingTheory.Int.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Int.Prime.dvd_pow", "kind": "theorem", "module": "Mathlib.RingTheory.Int.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Int.Prime.dvd_pow'", "kind": "theorem", "module": "Mathlib.RingTheory.Int.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "prime_two_or_dvd_of_dvd_two_mul_pow_self_two", "kind": "theorem", "module": "Mathlib.RingTheory.Int.Basic", "is_tactic_proof": true, "tactics": ["rcases", "apply", "exact", "apply", "rw", "exact"], "tactic_count": 6}
{"name": "Int.exists_prime_and_dvd", "kind": "theorem", "module": "Mathlib.RingTheory.Int.Basic", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Int.prime_iff_natAbs_prime", "kind": "theorem", "module": "Mathlib.RingTheory.Int.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.instDecidablePredPrime", "kind": "instance", "module": "Mathlib.RingTheory.Int.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.instDecidablePredIrreducible", "kind": "instance", "module": "Mathlib.RingTheory.Int.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.span_natAbs", "kind": "theorem", "module": "Mathlib.RingTheory.Int.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Int.eq_pow_of_mul_eq_pow_odd_left", "kind": "theorem", "module": "Mathlib.RingTheory.Int.Basic", "is_tactic_proof": true, "tactics": ["obtain", "replace", "rw", "obtain"], "tactic_count": 4}
{"name": "Int.eq_pow_of_mul_eq_pow_odd_right", "kind": "theorem", "module": "Mathlib.RingTheory.Int.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.eq_pow_of_mul_eq_pow_odd", "kind": "theorem", "module": "Mathlib.RingTheory.Int.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.isIntegral_iff", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsIntegral.of_injective", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsIntegral.of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.isIntegral_iff", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.isIntegral", "kind": "instance", "module": "Mathlib.RingTheory.IntegralClosure.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegral.of_finite", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isIntegral_of_noetherian", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsIntegral.of_finite", "kind": "instance", "module": "Mathlib.RingTheory.IntegralClosure.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.isIntegral_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegral.of_mem_of_fg", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isIntegral_of_submodule_noetherian", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isIntegral_of_smul_mem_submodule", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.Algebra.Basic", "is_tactic_proof": false, "tactics": ["let", "mul_mem", "one_mem", "add_mem", "zero_mem", "algebraMap_mem", "let", "map_add", "map_smul", "obtain", "by_contra", "apply", "rwa", "have", "change", "rw", "intro", "have", "exact", "change", "rw", "haveI", "apply"], "tactic_count": 23}
{"name": "RingHom.Finite.to_isIntegral", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.IsIntegralElem.of_mem_closure", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.Algebra.Basic", "is_tactic_proof": true, "tactics": ["letI", "have", "rw", "exact"], "tactic_count": 4}
{"name": "IsIntegral.of_mem_closure", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.IsIntegralElem.add", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegral.add", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.IsIntegralElem.neg", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.IsIntegralElem.of_neg", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.IsIntegralElem.neg_iff", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegral.neg", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegral.of_neg", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegral.neg_iff", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.IsIntegralElem.sub", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.Algebra.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsIntegral.sub", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.IsIntegralElem.mul", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegral.mul", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegral.smul", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "integralClosure", "kind": "definition", "module": "Mathlib.RingTheory.IntegralClosure.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_integralClosure_iff", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsIntegral.prod", "kind": "instance", "module": "Mathlib.RingTheory.IntegralClosure.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegral.tmul", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.Algebra.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact", "smul"], "tactic_count": 3}
{"name": "Algebra.IsIntegral.tensorProduct", "kind": "instance", "module": "Mathlib.RingTheory.IntegralClosure.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instMulSemiringActionSubtypeMemSubalgebraIntegralClosure", "kind": "instance", "module": "Mathlib.RingTheory.IntegralClosure.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "integralClosure.coe_smul", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instSMulCommClassSubtypeMemSubalgebraIntegralClosure", "kind": "instance", "module": "Mathlib.RingTheory.IntegralClosure.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instSMulDistribClassSubtypeMemSubalgebraIntegralClosure", "kind": "instance", "module": "Mathlib.RingTheory.IntegralClosure.Algebra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.isIntegral_def", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.Algebra.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "algebraMap_isIntegral_iff", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.Algebra.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coeff_mem_pow_of_mem_adjoin_C_mul_X", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.Algebra.Ideal", "is_tactic_proof": true, "tactics": ["induction", "mem", "obtain", "simp", "algebraMap", "add", "mul", "rw", "refine", "obtain", "exact"], "tactic_count": 11}
{"name": "Polynomial.exists_monic_aeval_eq_zero_forall_mem_pow_of_isIntegral", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.Algebra.Ideal", "is_tactic_proof": true, "tactics": ["cases", "use", "obtain", "let", "have", "refine", "exact", "simp", "refine", "simpa", "replace", "simp", "simp", "refine", "simp", "rw", "simp", "rw", "simp"], "tactic_count": 19}
{"name": "Polynomial.exists_monic_aeval_eq_zero_forall_mem_pow_of_mem_map", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.Algebra.Ideal", "is_tactic_proof": true, "tactics": ["classical", "let", "letI", "refine", "induction", "zero", "add", "mem", "obtain", "simpa", "smul", "simp", "refine", "exact"], "tactic_count": 14}
{"name": "Polynomial.exists_monic_aeval_eq_zero_forall_mem_of_mem_map", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.Algebra.Ideal", "is_tactic_proof": true, "tactics": ["obtain", "refine", "obtain", "exact", "simp"], "tactic_count": 5}
{"name": "Polynomial.coeff_mem_radical_span_coeff_of_dvd", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.GoingDown", "is_tactic_proof": true, "tactics": ["rw", "rintro", "have", "ext", "obtain", "simpa", "simp", "simp", "obtain", "obtain", "rw", "obtain", "simpa"], "tactic_count": 13}
{"name": "instHasGoingDownOfIsDomainOfFaithfulSMulOfIsIntegralOfIsIntegrallyClosed", "kind": "instance", "module": "Mathlib.RingTheory.IntegralClosure.GoingDown", "is_tactic_proof": true, "tactics": ["have", "constructor", "intro", "let", "suffices", "obtain", "refine", "exact", "intro", "obtain", "simpa", "obtain", "obtain", "set", "by_contra", "have", "ext", "obtain", "simpa", "simp", "simp", "have", "simpa", "congr", "exact", "haQ", "by_cases", "have", "simp", "coeff_scaleRoots,", "refine", "simp"], "tactic_count": 32}
{"name": "galRestrict'", "kind": "definition", "module": "Mathlib.RingTheory.IntegralClosure.IntegralRestrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "algebraMap_galRestrict'_apply", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IntegralRestrict", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "galRestrict'_id", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IntegralRestrict", "is_tactic_proof": true, "tactics": ["ext", "apply", "simp"], "tactic_count": 3}
{"name": "galRestrict'_comp", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IntegralRestrict", "is_tactic_proof": true, "tactics": ["ext", "apply", "ext", "simp"], "tactic_count": 4}
{"name": "galLift", "kind": "definition", "module": "Mathlib.RingTheory.IntegralClosure.IntegralRestrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "galLift_algebraMap_apply", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IntegralRestrict", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "galLift_id", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IntegralRestrict", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "galLift_comp", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IntegralRestrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "galLift_galRestrict'", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IntegralRestrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "galRestrict'_galLift", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IntegralRestrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "galLiftEquiv", "kind": "definition", "module": "Mathlib.RingTheory.IntegralClosure.IntegralRestrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "galLiftEquiv_algebraMap_apply", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IntegralRestrict", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "galRestrictHom", "kind": "definition", "module": "Mathlib.RingTheory.IntegralClosure.IntegralRestrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "algebraMap_galRestrictHom_apply", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IntegralRestrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "galRestrictHom_symm_algebraMap_apply", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IntegralRestrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "galRestrict", "kind": "definition", "module": "Mathlib.RingTheory.IntegralClosure.IntegralRestrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "coe_galRestrict_apply", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IntegralRestrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "galRestrict_apply", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IntegralRestrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "algebraMap_galRestrict_apply", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IntegralRestrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "galRestrict_symm_algebraMap_apply", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IntegralRestrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "prod_galRestrict_eq_norm", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IntegralRestrict", "is_tactic_proof": true, "tactics": ["apply", "rw", "simp"], "tactic_count": 3}
{"name": "instFintypeAlgEquivOfIsDomainOfIsIntegrallyClosedOfFiniteOfIsTorsionFree", "kind": "instance", "module": "Mathlib.RingTheory.IntegralClosure.IntegralRestrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.intTraceAux", "kind": "definition", "module": "Mathlib.RingTheory.IntegralClosure.IntegralRestrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.map_intTraceAux", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IntegralRestrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.intTrace", "kind": "definition", "module": "Mathlib.RingTheory.IntegralClosure.IntegralRestrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.algebraMap_intTrace", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IntegralRestrict", "is_tactic_proof": false, "tactics": ["haveI", "haveI", "haveI", "haveI", "haveI", "apply", "rw", "apply", "ext", "exact"], "tactic_count": 10}
{"name": "Algebra.algebraMap_intTrace_fractionRing", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IntegralRestrict", "is_tactic_proof": false, "tactics": ["haveI", "haveI", "haveI", "haveI", "exact"], "tactic_count": 5}
{"name": "Algebra.intTrace_eq_trace", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IntegralRestrict", "is_tactic_proof": true, "tactics": ["ext", "haveI", "haveI", "haveI", "apply", "rw"], "tactic_count": 6}
{"name": "Algebra.intTrace_eq_of_isLocalization", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IntegralRestrict", "is_tactic_proof": true, "tactics": ["by_cases", "subsingleton", "replace", "let", "let", "have", "haveI", "have", "let", "letI", "have", "letI", "let", "letI", "have", "letI", "have", "have", "apply", "apply", "rw", "letI", "have", "have", "apply", "rw"], "tactic_count": 26}
{"name": "Algebra.intNormAux", "kind": "definition", "module": "Mathlib.RingTheory.IntegralClosure.IntegralRestrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.map_intNormAux", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IntegralRestrict", "is_tactic_proof": true, "tactics": ["dsimp", "exact"], "tactic_count": 2}
{"name": "Algebra.intNorm", "kind": "definition", "module": "Mathlib.RingTheory.IntegralClosure.IntegralRestrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.algebraMap_intNorm", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IntegralRestrict", "is_tactic_proof": true, "tactics": ["haveI", "apply", "rw", "apply", "ext", "exact"], "tactic_count": 6}
{"name": "Algebra.algebraMap_intNorm_fractionRing", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IntegralRestrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.intNorm_intNorm", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IntegralRestrict", "is_tactic_proof": true, "tactics": ["apply", "rw"], "tactic_count": 2}
{"name": "Algebra.intNorm_eq_norm", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IntegralRestrict", "is_tactic_proof": true, "tactics": ["ext", "haveI", "apply", "rw"], "tactic_count": 4}
{"name": "Algebra.intNorm_zero", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IntegralRestrict", "is_tactic_proof": true, "tactics": ["haveI", "apply", "simp"], "tactic_count": 3}
{"name": "Algebra.intNorm_map_algEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IntegralRestrict", "is_tactic_proof": true, "tactics": ["apply", "rw", "galLiftEquiv_algebraMap_apply"], "tactic_count": 3}
{"name": "Algebra.intNorm_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IntegralRestrict", "is_tactic_proof": false, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Algebra.intNorm_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IntegralRestrict", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Algebra.intNorm_eq_of_isLocalization", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IntegralRestrict", "is_tactic_proof": true, "tactics": ["by_cases", "subsingleton", "replace", "let", "let", "let", "letI", "have", "letI", "let", "letI", "have", "letI", "have", "have", "apply", "apply", "rw", "letI", "have", "apply", "rw"], "tactic_count": 22}
{"name": "Algebra.algebraMap_intNorm_of_isGalois", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IntegralRestrict", "is_tactic_proof": true, "tactics": ["haveI", "rw", "simp", "convert"], "tactic_count": 4}
{"name": "Algebra.dvd_algebraMap_intNorm_self", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IntegralRestrict", "is_tactic_proof": true, "tactics": ["classical", "haveI", "by_cases", "exact", "let", "let", "let", "suffices", "obtain", "refine", "apply", "rw", "exact", "rw", "map_inv₀,", "norm_eq_prod_roots", "have", "rw", "inv_mul_cancel_left₀]", "refine", "exact", "replace", "suffices", "rw", "simp", "exact", "exact", "simp", "refine", "simp"], "tactic_count": 30}
{"name": "IsIntegrallyClosedIn", "kind": "abbrev", "module": "Mathlib.RingTheory.IntegralClosure.IntegrallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegrallyClosed", "kind": "abbrev", "module": "Mathlib.RingTheory.IntegralClosure.IntegrallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.isIntegrallyClosedIn", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IntegrallyClosed", "is_tactic_proof": true, "tactics": ["rintro", "refine", "convert", "aesop", "obtain", "aesop", "rintro", "apply", "simp_all"], "tactic_count": 9}
{"name": "AlgEquiv.isIntegrallyClosedIn", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IntegrallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isIntegrallyClosed_iff_isIntegrallyClosedIn", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IntegrallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isIntegrallyClosed_iff_isIntegralClosure", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IntegrallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isIntegrallyClosedIn_iff", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IntegrallyClosed", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "simp_all", "rintro", "refine", "rintro", "apply"], "tactic_count": 7}
{"name": "isIntegrallyClosed_iff", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IntegrallyClosed", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "instIsIntegrallyClosedInSubtypeMemSubalgebraIntegralClosure", "kind": "instance", "module": "Mathlib.RingTheory.IntegralClosure.IntegrallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsIntegrallyClosedInSubtypeMemSubringToSubringIntegralClosure", "kind": "instance", "module": "Mathlib.RingTheory.IntegralClosure.IntegrallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.isIntegrallyClosedIn_iff", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IntegrallyClosed", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Subring.isIntegrallyClosed_iff", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IntegrallyClosed", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subring.integralClosure_le_iff", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IntegrallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.integralClosure_subring_le_iff", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IntegrallyClosed", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsIntegrallyClosedIn.inst", "kind": "instance", "module": "Mathlib.RingTheory.IntegralClosure.IntegrallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegrallyClosedIn.algebraMap_eq_of_integral", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IntegrallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegrallyClosedIn.isIntegral_iff", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IntegrallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegrallyClosedIn.exists_algebraMap_eq_of_isIntegral_pow", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IntegrallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegrallyClosedIn.exists_algebraMap_eq_of_pow_mem_subalgebra", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IntegrallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegrallyClosedIn.integralClosure_eq_bot_iff", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IntegrallyClosed", "is_tactic_proof": true, "tactics": ["refine", "constructor", "intro", "refine", "rintro", "apply", "intro", "rw", "exact"], "tactic_count": 9}
{"name": "IsIntegrallyClosedIn.integralClosure_eq_bot", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IntegrallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegrallyClosedIn.of_isIntegralClosure", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IntegrallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegralClosure.of_isIntegrallyClosedIn", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IntegrallyClosed", "is_tactic_proof": false, "tactics": ["refine", "rintro", "exact"], "tactic_count": 3}
{"name": "IsIntegrallyClosed.instIsIntegralClosure", "kind": "instance", "module": "Mathlib.RingTheory.IntegralClosure.IntegrallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegrallyClosed.algebraMap_eq_of_integral", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IntegrallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegrallyClosed.isIntegral_iff", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IntegrallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegrallyClosed.exists_algebraMap_eq_of_isIntegral_pow", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IntegrallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegrallyClosed.exists_algebraMap_eq_of_pow_mem_subalgebra", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IntegrallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegrallyClosed.of_equiv", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IntegrallyClosed", "is_tactic_proof": true, "tactics": ["let", "let", "let", "refine", "rcases", "exact"], "tactic_count": 6}
{"name": "IsIntegralClosure.of_isIntegrallyClosed", "kind": "instance", "module": "Mathlib.RingTheory.IntegralClosure.IntegrallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegrallyClosed.of_isIntegrallyClosedIn", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IntegrallyClosed", "is_tactic_proof": true, "tactics": ["have", "let", "rw", "intro", "convert", "simp"], "tactic_count": 6}
{"name": "IsIntegralClosure.of_isIntegralClosure_of_isIntegrallyClosedIn", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IntegrallyClosed", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact", "intro", "refine", "obtain", "rw", "obtain", "exact", "rintro", "rw", "exact"], "tactic_count": 12}
{"name": "IsIntegrallyClosed.of_isIntegrallyClosed_of_isIntegrallyClosedIn", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IntegrallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegrallyClosed.integralClosure_eq_bot_iff", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IntegrallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegrallyClosed.pow_dvd_pow_iff", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IntegrallyClosed", "is_tactic_proof": true, "tactics": ["refine", "by_cases", "simpa", "let", "replace", "let", "have", "refine", "simp", "replace", "rw", "simp", "obtain", "refine", "rw"], "tactic_count": 15}
{"name": "Associated.pow_iff", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IntegrallyClosed", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "IsIntegrallyClosed.integralClosure_eq_bot", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IntegrallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "integralClosure.isIntegrallyClosedOfFiniteExtension", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IntegrallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isIntegrallyClosed_of_isLocalization", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IntegrallyClosed", "is_tactic_proof": true, "tactics": ["let", "let", "letI", "have", "have", "refine", "intro", "obtain", "obtain", "refine", "rw"], "tactic_count": 11}
{"name": "Field.instIsIntegrallyClosed", "kind": "instance", "module": "Mathlib.RingTheory.IntegralClosure.IntegrallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegral.isUnit", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isField_of_isIntegral_of_isField'", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegral.inv_mem_adjoin", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": true, "tactics": ["obtain", "rw", "have", "obtain", "rwa"], "tactic_count": 5}
{"name": "IsIntegral.inv_mem", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsIntegral.inv_mem", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegral.inv", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegral.mem_of_inv_mem", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Algebra.IsIntegral.finite", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.finite_iff_isIntegral_and_finiteType", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.IsIntegral.to_finite", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.finite_iff_isIntegral_and_finiteType", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_integralClosure_iff_mem_fg", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "adjoin_le_integralClosure", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp", "exact"], "tactic_count": 3}
{"name": "le_integralClosure_iff_isIntegral", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsIntegral.adjoin", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "integralClosure_eq_top_iff", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Algebra.isIntegral_sup", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Algebra.isIntegral_iSup", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "integralClosure_map_algEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": true, "tactics": ["ext", "rw", "constructor", "rintro", "exact", "intro", "use", "simp"], "tactic_count": 8}
{"name": "AlgHom.mapIntegralClosure", "kind": "definition", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.coe_mapIntegralClosure", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.mapIntegralClosure", "kind": "definition", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgEquiv.coe_mapIntegralClosure", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "integralClosure.isIntegral", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "integralClosure.AlgebraIsIntegral", "kind": "instance", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegral.of_mul_unit", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": true, "tactics": ["obtain", "refine", "convert", "rw", "rw"], "tactic_count": 5}
{"name": "RingHom.IsIntegralElem.of_mul_unit", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegral.of_mem_closure'", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegral.of_mem_closure''", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegral.pow", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegral.nsmul", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegral.zsmul", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegral.multiset_prod", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegral.multiset_sum", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegral.prod", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegral.sum", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegral.det", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsIntegral.pow_iff", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsPushout.isIntegral'", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsPushout.isIntegral", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsIntegralPolynomial", "kind": "instance", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsIntegralMvPolynomial", "kind": "instance", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.isIntegralElem_leadingCoeff_mul", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "use", "have", "rw", "exact", "use", "rw", "by_cases", "apply_fun", "rw", "rw", "exact", "rw", "rw", "suffices", "rw"], "tactic_count": 16}
{"name": "isIntegral_leadingCoeff_smul", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "Polynomial.Monic.quotient_isIntegralElem", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": true, "tactics": ["exact", "rw", "nth_rw", "simp"], "tactic_count": 4}
{"name": "Polynomial.Monic.quotient_isIntegral", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": ["have", "ext", "constructor", "simp", "intro", "obtain", "have", "nth_rw", "simp", "exact", "exact"], "tactic_count": 11}
{"name": "integralClosure.isIntegralClosure", "kind": "instance", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegralClosure.isIntegral", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegralClosure.isIntegral_algebra", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegralClosure.isTorsionFree", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": true, "tactics": ["refine", "simp"], "tactic_count": 2}
{"name": "IsIntegralClosure.mk'", "kind": "definition", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegralClosure.algebraMap_mk'", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegralClosure.mk'_add", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegralClosure.mk'_mul", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegralClosure.isField", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegralClosure.lift", "kind": "definition", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegralClosure.algebraMap_lift", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegralClosure.equiv", "kind": "definition", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegralClosure.algebraMap_equiv", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isIntegral_trans", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": true, "tactics": ["rcases", "let", "have", "fg_adjoin_of_finite", "let", "have", "rw", "convert", "let", "let", "have", "refine", "rw", "letI", "have", "exact"], "tactic_count": 16}
{"name": "Algebra.IsIntegral.trans", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.IsIntegral.trans", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegralClosure.tower_top", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.isIntegral_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegral.tower_bot", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.IsIntegral.tower_bot", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsIntegral.tower_bot", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegral.tower_bot_of_field", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.isIntegralElem.of_comp", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.IsIntegral.tower_top", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsIntegral.tower_top", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.IsIntegral.quotient", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": true, "tactics": ["rintro", "obtain", "refine", "simpa"], "tactic_count": 4}
{"name": "instIsIntegralQuotientIdeal", "kind": "instance", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsIntegral.quotient", "kind": "instance", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isIntegral_quotientMap_iff", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": ["let", "have", "refine", "refine", "exact"], "tactic_count": 5}
{"name": "RingHom.IsIntegral.isLocalHom", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsIntegral.isLocalHom", "kind": "instance", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isField_of_isIntegral_of_isField", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsIntegral.isField_iff_isField", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "integralClosure_idem", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsDomainSubtypeMemSubalgebraIntegralClosure", "kind": "instance", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "roots_mem_integralClosure", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAlmostIntegral", "kind": "definition", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegral.AlmostIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "completeIntegralClosure", "kind": "definition", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegral.AlmostIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_completeIntegralClosure", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegral.AlmostIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegral.isAlmostIntegral_of_exists_smul_mem_range", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegral.AlmostIntegral", "is_tactic_proof": false, "tactics": ["obtain", "obtain", "refine", "rw", "exact", "refine", "induction", "h", "obtain", "exact", "have", "rw", "minpoly.monic", "rw", "simp_rw", "refine", "simp", "lia"], "tactic_count": 18}
{"name": "IsIntegral.isAlmostIntegral_of_isLocalization", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegral.AlmostIntegral", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "IsIntegral.isAlmostIntegral", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegral.AlmostIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "integralClosure_le_completeIntegralClosure", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegral.AlmostIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAlmostIntegral.isIntegral_of_nonZeroDivisors_le_comap", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegral.AlmostIntegral", "is_tactic_proof": true, "tactics": ["obtain", "let", "change", "rw", "rintro", "obtain", "refine", "suffices", "algebraMap", "algebraMap", "simpa", "mul_left_comm]", "simp", "have", "have", "apply", "exact", "exact", "have", "rw", "exact", "exact"], "tactic_count": 22}
{"name": "IsAlmostIntegral.isIntegral", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegral.AlmostIntegral", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "isAlmostIntegral_iff_isIntegral", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegral.AlmostIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "completeIntegralClosure_eq_integralClosure", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegral.AlmostIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.isIntegralElem_map", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isIntegral_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.IsIntegralElem.map", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegral.Basic", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "RingHom.IsIntegralElem.of_map", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegral.Basic", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "RingHom.IsIntegralElem.map_iff", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.IsIntegralElem.of_comp", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegral.Basic", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "IsIntegral.map", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegral.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "isIntegral_algHom_iff", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegral.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Submodule.span_range_natDegree_eq_adjoin", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegral.Basic", "is_tactic_proof": true, "tactics": ["nontriviality", "have", "refine", "rcases", "exact", "rw", "rcases", "rw", "eval₂_sum,", "refine", "rw", "exact", "smul_mem"], "tactic_count": 13}
{"name": "IsIntegral.fg_adjoin_singleton", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegral.Basic", "is_tactic_proof": true, "tactics": ["classical", "rcases", "use", "exact"], "tactic_count": 4}
{"name": "RingHom.isIntegralElem_zero", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isIntegral_zero", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.isIntegralElem_one", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isIntegral_one", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegral.of_pow", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegral.of_aeval_monic", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegral.map_of_comp_eq", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isIntegral_algEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegral.tower_top", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.isIntegral_iff", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegral.Basic", "is_tactic_proof": true, "tactics": ["constructor", "letI", "letI", "exact", "have", "simp", "letI", "letI", "exact"], "tactic_count": 9}
{"name": "map_isIntegral_int", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegral.of_subring", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegral.algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegral.Basic", "is_tactic_proof": true, "tactics": ["rcases", "use", "rw"], "tactic_count": 3}
{"name": "isIntegral_algebraMap_iff", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isIntegral_iff_isIntegral_closure_finite", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegral.Basic", "is_tactic_proof": true, "tactics": ["constructor", "rcases", "refine", "rw", "rcases", "exact"], "tactic_count": 6}
{"name": "fg_adjoin_of_finite", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegral.Basic", "is_tactic_proof": true, "tactics": ["induction", "empty", "refine", "rw", "rw", "exact"], "tactic_count": 6}
{"name": "Algebra.finite_adjoin_of_finite_of_isIntegral", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.finite_adjoin_simple_of_isIntegral", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isNoetherian_adjoin_finset", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegral.pair", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegral.Basic", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "refine", "rw", "rw"], "tactic_count": 5}
{"name": "IsIntegral.pair_iff", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.IsIntegralElem", "kind": "definition", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegral.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.IsIntegral", "kind": "definition", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegral.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegral", "kind": "definition", "module": "Mathlib.RingTheory.IntegralClosure.IsIntegral.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_right_bijective_of_finite₀", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_left_bijective_of_finite₀", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.groupWithZeroOfCancel", "kind": "definition", "module": "Mathlib.RingTheory.IntegralDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_eq_pow_of_mul_eq_pow_of_coprime", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralDomain", "is_tactic_proof": true, "tactics": ["refine", "obtain", "rw", "exact"], "tactic_count": 4}
{"name": "Finset.exists_eq_pow_of_mul_eq_pow_of_coprime", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralDomain", "is_tactic_proof": true, "tactics": ["classical", "intro", "rw", "refine", "exists_eq_pow_of_mul_eq_pow_of_coprime", "rw", "exact"], "tactic_count": 7}
{"name": "Fintype.divisionRingOfIsDomain", "kind": "definition", "module": "Mathlib.RingTheory.IntegralDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.fieldOfDomain", "kind": "definition", "module": "Mathlib.RingTheory.IntegralDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finite.isField_of_domain", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralDomain", "is_tactic_proof": true, "tactics": ["cases", "exact"], "tactic_count": 2}
{"name": "card_nthRoots_subgroup_units", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralDomain", "is_tactic_proof": true, "tactics": ["haveI", "calc"], "tactic_count": 2}
{"name": "isCyclic_of_subgroup_isDomain", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralDomain", "is_tactic_proof": true, "tactics": ["classical", "cases", "apply", "intro", "exact"], "tactic_count": 5}
{"name": "instIsCyclicUnitsOfFinite", "kind": "instance", "module": "Mathlib.RingTheory.IntegralDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "subgroup_units_cyclic", "kind": "instance", "module": "Mathlib.RingTheory.IntegralDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.div_eq_quo_add_rem_div", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralDomain", "is_tactic_proof": true, "tactics": ["refine", "exact", "have", "field_simp", "rw"], "tactic_count": 5}
{"name": "sum_hom_units_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralDomain", "is_tactic_proof": true, "tactics": ["classical", "obtain", "have", "rintro", "apply", "ext", "rw", "obtain", "rwa", "replace", "let", "calc", "show", "apply", "simpa", "exact", "show", "calc", "sum_nbij", "let", "rw", "norm_cast", "simp"], "tactic_count": 23}
{"name": "sum_hom_units", "kind": "theorem", "module": "Mathlib.RingTheory.IntegralDomain", "is_tactic_proof": true, "tactics": ["split_ifs", "simp", "rw", "exact"], "tactic_count": 4}
{"name": "IsIntegralClosure.MulSemiringAction", "kind": "definition", "module": "Mathlib.RingTheory.Invariant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instSMulDistribClassAlgEquiv", "kind": "instance", "module": "Mathlib.RingTheory.Invariant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.isInvariant_of_isGalois", "kind": "theorem", "module": "Mathlib.RingTheory.Invariant.Basic", "is_tactic_proof": true, "tactics": ["replace", "letI", "refine", "replace", "rintro", "exact", "rw", "obtain", "have", "rw", "isIntegral_algebraMap_iff", "obtain", "rw", "exact"], "tactic_count": 14}
{"name": "Algebra.isInvariant_of_isGalois'", "kind": "theorem", "module": "Mathlib.RingTheory.Invariant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instMulSemiringActionQuotientSubgroupSubtypeMemSubringSubring", "kind": "instance", "module": "Mathlib.RingTheory.Invariant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instMulSemiringActionQuotientSubgroupSubtypeMemSubalgebraSubalgebra", "kind": "instance", "module": "Mathlib.RingTheory.Invariant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instSMulCommClassQuotientSubgroupSubtypeMemSubalgebraSubalgebra", "kind": "instance", "module": "Mathlib.RingTheory.Invariant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsInvariantSubtypeMemSubalgebraSubalgebraSubgroupQuotient", "kind": "instance", "module": "Mathlib.RingTheory.Invariant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulSemiringAction.charpoly", "kind": "definition", "module": "Mathlib.RingTheory.Invariant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulSemiringAction.charpoly_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Invariant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulSemiringAction.charpoly_eq_prod_smul", "kind": "theorem", "module": "Mathlib.RingTheory.Invariant.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MulSemiringAction.monic_charpoly", "kind": "theorem", "module": "Mathlib.RingTheory.Invariant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulSemiringAction.eval_charpoly", "kind": "theorem", "module": "Mathlib.RingTheory.Invariant.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply", "rw"], "tactic_count": 3}
{"name": "MulSemiringAction.smul_charpoly", "kind": "theorem", "module": "Mathlib.RingTheory.Invariant.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MulSemiringAction.smul_coeff_charpoly", "kind": "theorem", "module": "Mathlib.RingTheory.Invariant.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Algebra.IsInvariant.charpoly_mem_lifts", "kind": "theorem", "module": "Mathlib.RingTheory.Invariant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsInvariant.isIntegral", "kind": "theorem", "module": "Mathlib.RingTheory.Invariant.Basic", "is_tactic_proof": true, "tactics": ["cases", "refine", "obtain", "exact"], "tactic_count": 4}
{"name": "Algebra.IsInvariant.exists_smul_of_under_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Invariant.Basic", "is_tactic_proof": true, "tactics": ["cases", "have", "intro", "rw", "intro", "suffices", "obtain", "apply", "obtain", "rw", "exact", "obtain", "obtain", "exact"], "tactic_count": 14}
{"name": "Algebra.IsInvariant.orbit_eq_primesOver", "kind": "theorem", "module": "Mathlib.RingTheory.Invariant.Basic", "is_tactic_proof": true, "tactics": ["refine", "have", "obtain", "exact"], "tactic_count": 4}
{"name": "_private.Mathlib.RingTheory.Invariant.Basic.0.fixed_of_fixed1_aux1", "kind": "theorem", "module": "Mathlib.RingTheory.Invariant.Basic", "is_tactic_proof": true, "tactics": ["obtain", "let", "have", "rw", "rintro", "exact", "obtain", "replace", "let", "obtain", "rw", "let", "let", "let", "have", "ext", "rw", "simp", "split_ifs", "rw", "rw", "have", "have", "rw", "replace", "rw", "rwa", "or_iff_right", "let", "have", "have", "intro", "have", "rw", "zero_add,", "simp", "rw", "exact", "refine", "rwa", "rw", "simp", "split_ifs", "rwa", "rw", "exact"], "tactic_count": 46}
{"name": "_private.Mathlib.RingTheory.Invariant.Basic.0.fixed_of_fixed1_aux2", "kind": "theorem", "module": "Mathlib.RingTheory.Invariant.Basic", "is_tactic_proof": true, "tactics": ["obtain", "refine", "rw", "specialize", "split_ifs", "rw", "rw"], "tactic_count": 7}
{"name": "_private.Mathlib.RingTheory.Invariant.Basic.0.fixed_of_fixed1_aux3", "kind": "theorem", "module": "Mathlib.RingTheory.Invariant.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "have", "rw", "simp_rw", "eval_X,", "sub_eq_zero]", "exact"], "tactic_count": 8}
{"name": "_private.Mathlib.RingTheory.Invariant.Basic.0.fixed_of_fixed1", "kind": "theorem", "module": "Mathlib.RingTheory.Invariant.Basic", "is_tactic_proof": true, "tactics": ["classical", "cases", "obtain", "rw", "obtain", "obtain", "replace", "rw", "have", "intro", "rw", "split_ifs", "rfl", "rw", "simp", "replace", "rw", "replace", "fixed_of_fixed1_aux3", "simp", "obtain", "rwa", "algebraMap_apply", "rwa", "algebraMap_apply"], "tactic_count": 25}
{"name": "IsFractionRing.stabilizerHom", "kind": "definition", "module": "Mathlib.RingTheory.Invariant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Invariant.Basic.0.fixed_of_fixed2", "kind": "theorem", "module": "Mathlib.RingTheory.Invariant.Basic", "is_tactic_proof": true, "tactics": ["obtain", "have", "have", "obtain", "obtain", "replace", "rwa", "replace", "replace", "rw", "rw", "simp", "simp", "exact", "fixed_of_fixed1"], "tactic_count": 15}
{"name": "IsFractionRing.stabilizerHom_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Invariant.Basic", "is_tactic_proof": true, "tactics": ["let", "intro", "obtain", "exact"], "tactic_count": 4}
{"name": "Ideal.Quotient.stabilizerHom_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Invariant.Basic", "is_tactic_proof": true, "tactics": ["have", "let", "have", "rw", "exact", "key.of_comp_left"], "tactic_count": 6}
{"name": "Ideal.Quotient.exists_algHom_fixedPoint_quotient_under", "kind": "theorem", "module": "Mathlib.RingTheory.Invariant.Basic", "is_tactic_proof": true, "tactics": ["let", "have", "suffices", "let", "exact", "congr_arg", "rintro", "obtain", "cases", "algebraize", "haveI", "haveI", "obtain", "have", "rw", "have", "refine", "rw", "rw", "obtain", "simpa", "exact"], "tactic_count": 22}
{"name": "Ideal.Quotient.exists_algEquiv_fixedPoint_quotient_under", "kind": "theorem", "module": "Mathlib.RingTheory.Invariant.Basic", "is_tactic_proof": true, "tactics": ["let", "have", "obtain", "obtain", "refine", "intro", "obtain", "obtain", "apply", "dsimp", "refine", "rw", "intro", "obtain", "obtain", "apply", "dsimp", "refine", "rw"], "tactic_count": 19}
{"name": "Ideal.Quotient.normal", "kind": "theorem", "module": "Mathlib.RingTheory.Invariant.Basic", "is_tactic_proof": true, "tactics": ["cases", "cases", "have", "constructor", "intro", "obtain", "cases", "obtain", "have", "rw", "have", "minpoly.dvd", "refine", "rw", "exact", "exact"], "tactic_count": 16}
{"name": "Ideal.Quotient.finite_of_isInvariant", "kind": "theorem", "module": "Mathlib.RingTheory.Invariant.Basic", "is_tactic_proof": true, "tactics": ["have", "have", "exact"], "tactic_count": 3}
{"name": "Algebra.IsInvariant.isIntegral_of_profinite", "kind": "theorem", "module": "Mathlib.RingTheory.Invariant.Profinite", "is_tactic_proof": true, "tactics": ["constructor", "intro", "obtain", "have", "exact"], "tactic_count": 5}
{"name": "Algebra.IsInvariant.exists_smul_of_under_eq_of_profinite", "kind": "theorem", "module": "Mathlib.RingTheory.Invariant.Profinite", "is_tactic_proof": true, "tactics": ["let", "let", "map", "x", "have", "obtain", "obtain", "simpa", "congr", "map_id", "map_comp", "have", "obtain", "exact", "obtain", "let", "have", "change", "simp", "rw", "simp", "refine", "ext", "obtain", "lift", "change", "rw", "simp", "congr", "ext", "simp", "rfl"], "tactic_count": 32}
{"name": "Ideal.Quotient.stabilizerHomSurjectiveAuxFunctor_aux", "kind": "theorem", "module": "Mathlib.RingTheory.Invariant.Profinite", "is_tactic_proof": true, "tactics": ["change", "have", "obtain", "replace", "simpa"], "tactic_count": 5}
{"name": "Ideal.Quotient.stabilizerHomSurjectiveAuxFunctor", "kind": "definition", "module": "Mathlib.RingTheory.Invariant.Profinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFiniteObjOpenNormalSubgroupStabilizerHomSurjectiveAuxFunctor", "kind": "instance", "module": "Mathlib.RingTheory.Invariant.Profinite", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "instNonemptyObjOpenNormalSubgroupStabilizerHomSurjectiveAuxFunctor", "kind": "instance", "module": "Mathlib.RingTheory.Invariant.Profinite", "is_tactic_proof": false, "tactics": ["have", "obtain", "σ", "obtain", "refine", "ext", "obtain", "exact"], "tactic_count": 8}
{"name": "Ideal.Quotient.stabilizerHom_surjective_of_profinite", "kind": "theorem", "module": "Mathlib.RingTheory.Invariant.Profinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAdjoinRoot.root", "kind": "definition", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAdjoinRoot.subsingleton", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": true, "tactics": ["have"], "tactic_count": 1}
{"name": "IsAdjoinRoot.algebraMap_apply", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAdjoinRoot.mem_ker_map", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsAdjoinRoot.map_eq_zero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsAdjoinRoot.map_X", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAdjoinRoot.map_self", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsAdjoinRoot.aeval_root_eq_map", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "IsAdjoinRoot.aeval_root_self", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsAdjoinRoot.adjoin_root_eq_top", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsAdjoinRoot.ext_map", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": true, "tactics": ["cases", "exact"], "tactic_count": 2}
{"name": "IsAdjoinRoot.ext", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAdjoinRoot.repr", "kind": "definition", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAdjoinRoot.map_repr", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAdjoinRoot.repr_zero_mem_span", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsAdjoinRoot.repr_add_sub_repr_add_repr_mem_span", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsAdjoinRoot.adjoinRootAlgEquiv", "kind": "definition", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAdjoinRoot.adjoinRootAlgEquiv_apply_mk", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAdjoinRoot.adjoinRootAlgEquiv_apply_eq_map", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsAdjoinRoot.adjoinRootAlgEquiv_symm_apply_eq_mk", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsAdjoinRoot.adjoinRootAlgEquiv_apply_root", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAdjoinRoot.adjoinRootAlgEquiv_symm_apply_root", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAdjoinRoot.algEquiv", "kind": "definition", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAdjoinRoot.algEquiv_def", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAdjoinRoot.algEquiv_root", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsAdjoinRoot.algEquiv_map", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "IsAdjoinRoot.algEquiv_apply_map", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsAdjoinRoot.algEquiv_self", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "IsAdjoinRoot.algEquiv_symm", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAdjoinRoot.algEquiv_algEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsAdjoinRoot.algEquiv_trans", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "IsAdjoinRoot.ofAlgEquiv", "kind": "definition", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAdjoinRoot.ofAlgEquiv_root", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAdjoinRoot.algEquiv_ofAlgEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "IsAdjoinRoot.ofAlgEquiv_algEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": true, "tactics": ["ext", "simp_rw", "adjoinRootAlgEquiv_apply_eq_map,"], "tactic_count": 3}
{"name": "IsAdjoinRoot.eval₂_repr_eq_eval₂_of_map_eq", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": true, "tactics": ["rw", "obtain", "rw"], "tactic_count": 3}
{"name": "IsAdjoinRoot.lift", "kind": "definition", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAdjoinRoot.lift_map", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsAdjoinRoot.lift_root", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsAdjoinRoot.lift_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsAdjoinRoot.apply_eq_lift", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "IsAdjoinRoot.eq_lift", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAdjoinRoot.liftHom", "kind": "definition", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAdjoinRoot.coe_liftHom", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAdjoinRoot.lift_algebraMap_apply", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAdjoinRoot.liftHom_map", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsAdjoinRoot.liftHom_root", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsAdjoinRoot.eq_liftHom", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAdjoinRoot.isAlgebraic_root", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.isAdjoinRoot", "kind": "definition", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.isAdjoinRootMonic", "kind": "definition", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.isAdjoinRootMonic_toAdjoinRoot", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.isAdjoinRoot_map_eq_mkₐ", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AdjoinRoot.isAdjoinRootMonic_map_eq_mk", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AdjoinRoot.isAdjoinRoot_root_eq_root", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AdjoinRoot.isAdjoinRootMonic_root_eq_root", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsAdjoinRoot.ofAdjoinRootEquiv", "kind": "abbrev", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAdjoinRootMonic.map_modByMonic", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": false, "tactics": ["rw", "dvd_neg]", "exact"], "tactic_count": 3}
{"name": "IsAdjoinRootMonic.modByMonic_repr_map", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAdjoinRootMonic.modByMonicHom", "kind": "definition", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAdjoinRootMonic.modByMonicHom_map", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAdjoinRootMonic.map_modByMonicHom", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsAdjoinRootMonic.modByMonicHom_root_pow", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": true, "tactics": ["nontriviality", "rw", "contrapose", "simpa"], "tactic_count": 4}
{"name": "IsAdjoinRootMonic.modByMonicHom_root", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsAdjoinRootMonic.basis", "kind": "definition", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAdjoinRootMonic.basis_apply", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAdjoinRootMonic.deg_pos", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "IsAdjoinRootMonic.deg_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAdjoinRootMonic.powerBasis", "kind": "definition", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAdjoinRootMonic.basis_repr", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsAdjoinRootMonic.basis_one", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsAdjoinRootMonic.finite", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAdjoinRootMonic.finrank", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finrank_quotient_span_eq_natDegree'", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAdjoinRootMonic.liftPolyₗ", "kind": "definition", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAdjoinRootMonic.coeff", "kind": "definition", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAdjoinRootMonic.coeff_apply_lt", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsAdjoinRootMonic.coeff_apply_coe", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAdjoinRootMonic.coeff_apply_le", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": true, "tactics": ["simp", "nontriviality", "exact"], "tactic_count": 3}
{"name": "IsAdjoinRootMonic.coeff_apply", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": true, "tactics": ["split_ifs", "exact", "exact"], "tactic_count": 3}
{"name": "IsAdjoinRootMonic.coeff_root_pow", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": true, "tactics": ["ext", "rw", "split_ifs", "calc", "h.basis.repr", "rw", "rw", "rintro", "simp"], "tactic_count": 9}
{"name": "IsAdjoinRootMonic.coeff_one", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsAdjoinRootMonic.coeff_root", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsAdjoinRootMonic.coeff_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": true, "tactics": ["ext", "rw", "refine", "simp"], "tactic_count": 4}
{"name": "IsAdjoinRootMonic.ext_elem", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAdjoinRootMonic.ext_elem_iff", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAdjoinRootMonic.coeff_injective", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAdjoinRootMonic.isIntegral_root", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAdjoinRoot.lift_self_apply", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsAdjoinRoot.lift_self", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAdjoinRoot.mkOfAdjoinEqTop", "kind": "definition", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAdjoinRootMonic.mkOfAdjoinEqTop", "kind": "abbrev", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAdjoinRoot.mkOfAdjoinEqTop_root", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsAdjoinRoot.lift_algEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsAdjoinRoot.liftHom_algEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAdjoinRootMonic.minpoly_eq", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.adjoin.powerBasis'_minpoly_gen", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "isAdjoinRoot_root_eq_root", "minpoly_eq"], "tactic_count": 5}
{"name": "IsAdjoinRoot.primitive_element_root", "kind": "theorem", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAdjoinRoot.mkOfPrimitiveElement", "kind": "abbrev", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAdjoinRootMonic.mkOfPrimitiveElement", "kind": "abbrev", "module": "Mathlib.RingTheory.IsAdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.IsPrimary", "kind": "definition", "module": "Mathlib.RingTheory.IsPrimary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.IsPrimary.ne_top", "kind": "theorem", "module": "Mathlib.RingTheory.IsPrimary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.IsPrimary.mem_or_mem", "kind": "theorem", "module": "Mathlib.RingTheory.IsPrimary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.IsPrimary.inf", "kind": "theorem", "module": "Mathlib.RingTheory.IsPrimary", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "refine", "simp_rw", "and_or_right]", "exact"], "tactic_count": 6}
{"name": "Submodule.isPrimary_finsetInf", "kind": "theorem", "module": "Mathlib.RingTheory.IsPrimary", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "insert", "rcases", "simp", "simpa", "simp", "have", "rw", "refine", "rw"], "tactic_count": 12}
{"name": "Submodule.IsPrimary.isPrime_radical_colon", "kind": "theorem", "module": "Mathlib.RingTheory.IsPrimary", "is_tactic_proof": true, "tactics": ["refine", "simp_rw", "refine", "simp", "exact"], "tactic_count": 5}
{"name": "Submodule.IsPrimary.radical_colon_singleton_of_notMem", "kind": "theorem", "module": "Mathlib.RingTheory.IsPrimary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.isPrimary_iff_zero_divisor_quotient_imp_nilpotent_smul", "kind": "theorem", "module": "Mathlib.RingTheory.IsPrimary", "is_tactic_proof": true, "tactics": ["refine", "simp_rw", "congr", "rw", "simp_rw"], "tactic_count": 5}
{"name": "IsTensorProduct", "kind": "definition", "module": "Mathlib.RingTheory.IsTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.isTensorProduct", "kind": "theorem", "module": "Mathlib.RingTheory.IsTensorProduct", "is_tactic_proof": true, "tactics": ["delta", "convert_to", "apply", "simp", "exact"], "tactic_count": 5}
{"name": "IsTensorProduct.equiv", "kind": "definition", "module": "Mathlib.RingTheory.IsTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsTensorProduct.equiv_toLinearMap", "kind": "theorem", "module": "Mathlib.RingTheory.IsTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsTensorProduct.equiv_symm_apply", "kind": "theorem", "module": "Mathlib.RingTheory.IsTensorProduct", "is_tactic_proof": true, "tactics": ["apply", "refine", "simp"], "tactic_count": 3}
{"name": "IsTensorProduct.lift", "kind": "definition", "module": "Mathlib.RingTheory.IsTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsTensorProduct.lift_eq", "kind": "theorem", "module": "Mathlib.RingTheory.IsTensorProduct", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsTensorProduct.map", "kind": "definition", "module": "Mathlib.RingTheory.IsTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsTensorProduct.map_eq", "kind": "theorem", "module": "Mathlib.RingTheory.IsTensorProduct", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsTensorProduct.inductionOn", "kind": "theorem", "module": "Mathlib.RingTheory.IsTensorProduct", "is_tactic_proof": true, "tactics": ["rw", "generalize", "change", "induction", "zero", "tmul", "rw", "apply", "add", "rw", "apply"], "tactic_count": 11}
{"name": "IsTensorProduct.of_equiv", "kind": "theorem", "module": "Mathlib.RingTheory.IsTensorProduct", "is_tactic_proof": false, "tactics": ["have", "ext", "simp", "simpa"], "tactic_count": 4}
{"name": "IsTensorProduct.map_comp", "kind": "theorem", "module": "Mathlib.RingTheory.IsTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsTensorProduct.map_map", "kind": "theorem", "module": "Mathlib.RingTheory.IsTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsTensorProduct.map_id", "kind": "theorem", "module": "Mathlib.RingTheory.IsTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsTensorProduct.map_one", "kind": "theorem", "module": "Mathlib.RingTheory.IsTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsTensorProduct.map_mul", "kind": "theorem", "module": "Mathlib.RingTheory.IsTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsTensorProduct.map_pow", "kind": "theorem", "module": "Mathlib.RingTheory.IsTensorProduct", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "IsBaseChange", "kind": "definition", "module": "Mathlib.RingTheory.IsTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBaseChange.lift", "kind": "definition", "module": "Mathlib.RingTheory.IsTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBaseChange.lift_eq", "kind": "theorem", "module": "Mathlib.RingTheory.IsTensorProduct", "is_tactic_proof": true, "tactics": ["have", "convert"], "tactic_count": 2}
{"name": "IsBaseChange.lift_comp", "kind": "theorem", "module": "Mathlib.RingTheory.IsTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBaseChange.inductionOn", "kind": "theorem", "module": "Mathlib.RingTheory.IsTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBaseChange.algHom_ext", "kind": "theorem", "module": "Mathlib.RingTheory.IsTensorProduct", "is_tactic_proof": true, "tactics": ["ext", "refine", "rw", "assumption", "intro", "rw", "intro", "rw"], "tactic_count": 8}
{"name": "IsBaseChange.algHom_ext'", "kind": "theorem", "module": "Mathlib.RingTheory.IsTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.isBaseChange", "kind": "theorem", "module": "Mathlib.RingTheory.IsTensorProduct", "is_tactic_proof": true, "tactics": ["delta", "convert", "ext", "change", "rw", "congr", "exact"], "tactic_count": 7}
{"name": "IsBaseChange.equiv", "kind": "definition", "module": "Mathlib.RingTheory.IsTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBaseChange.equiv_tmul", "kind": "theorem", "module": "Mathlib.RingTheory.IsTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBaseChange.equiv_symm_apply", "kind": "theorem", "module": "Mathlib.RingTheory.IsTensorProduct", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsBaseChange.of_equiv", "kind": "theorem", "module": "Mathlib.RingTheory.IsTensorProduct", "is_tactic_proof": true, "tactics": ["apply", "intro", "simp"], "tactic_count": 3}
{"name": "IsBaseChange.linearMap", "kind": "theorem", "module": "Mathlib.RingTheory.IsTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isBaseChange_tensorProduct_map", "kind": "theorem", "module": "Mathlib.RingTheory.IsTensorProduct", "is_tactic_proof": false, "tactics": ["let", "refine", "induction", "zero", "tmul", "add"], "tactic_count": 6}
{"name": "IsBaseChange.of_lift_unique", "kind": "theorem", "module": "Mathlib.RingTheory.IsTensorProduct", "is_tactic_proof": false, "tactics": ["obtain", "let", "change", "let", "refine", "map_smul", "dsimp", "dsimp", "simp_rw", "let", "exact", "rw", "refine", "ext", "simp", "apply", "ext", "change", "rw", "rfl"], "tactic_count": 20}
{"name": "IsBaseChange.iff_lift_unique", "kind": "theorem", "module": "Mathlib.RingTheory.IsTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBaseChange.ofEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.IsTensorProduct", "is_tactic_proof": true, "tactics": ["apply", "intro", "have", "ext", "change", "dsimp", "rw", "cases", "refine", "ext", "simp,", "rintro", "ext", "simp"], "tactic_count": 14}
{"name": "IsBaseChange.comp", "kind": "theorem", "module": "Mathlib.RingTheory.IsTensorProduct", "is_tactic_proof": true, "tactics": ["apply", "intro", "letI", "haveI", "rw", "rfl⟩", "have", "refine", "change", "rw", "rfl", "refine", "ext", "simp", "rintro", "refine", "rw", "ext", "rfl"], "tactic_count": 19}
{"name": "IsBaseChange.of_comp", "kind": "theorem", "module": "Mathlib.RingTheory.IsTensorProduct", "is_tactic_proof": true, "tactics": ["apply", "intro", "letI", "haveI", "haveI", "let", "let", "refine", "apply", "simp", "intro", "apply", "apply_fun", "rw", "rw"], "tactic_count": 15}
{"name": "IsBaseChange.comp_iff", "kind": "theorem", "module": "Mathlib.RingTheory.IsTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBaseChange.tensorEquiv", "kind": "definition", "module": "Mathlib.RingTheory.IsTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBaseChange.map_id_lsmul_eq_lsmul_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.IsTensorProduct", "is_tactic_proof": true, "tactics": ["ext", "refine", "intro", "rw", "simpa"], "tactic_count": 5}
{"name": "Algebra.IsPushout.equiv", "kind": "definition", "module": "Mathlib.RingTheory.IsTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsPushout.equiv_tmul", "kind": "theorem", "module": "Mathlib.RingTheory.IsTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsPushout.equiv_symm_algebraMap_left", "kind": "theorem", "module": "Mathlib.RingTheory.IsTensorProduct", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Algebra.IsPushout.equiv_symm_algebraMap_right", "kind": "theorem", "module": "Mathlib.RingTheory.IsTensorProduct", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Algebra.IsPushout.symm", "kind": "theorem", "module": "Mathlib.RingTheory.IsTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsPushout.comm", "kind": "theorem", "module": "Mathlib.RingTheory.IsTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsPushout", "kind": "instance", "module": "Mathlib.RingTheory.IsTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsPushout_1", "kind": "instance", "module": "Mathlib.RingTheory.IsTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.isPushout", "kind": "instance", "module": "Mathlib.RingTheory.IsTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.isPushout'", "kind": "instance", "module": "Mathlib.RingTheory.IsTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsPushout.tensorProduct_tensorProduct", "kind": "theorem", "module": "Mathlib.RingTheory.IsTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.pushoutDesc", "kind": "definition", "module": "Mathlib.RingTheory.IsTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.pushoutDesc_left", "kind": "theorem", "module": "Mathlib.RingTheory.IsTensorProduct", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Algebra.lift_algHom_comp_left", "kind": "theorem", "module": "Mathlib.RingTheory.IsTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.pushoutDesc_right", "kind": "theorem", "module": "Mathlib.RingTheory.IsTensorProduct", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Algebra.lift_algHom_comp_right", "kind": "theorem", "module": "Mathlib.RingTheory.IsTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsPushout.algHom_ext", "kind": "theorem", "module": "Mathlib.RingTheory.IsTensorProduct", "is_tactic_proof": true, "tactics": ["ext", "refine", "simp", "exact", "intro", "rw", "congr", "exact", "intro", "rw"], "tactic_count": 10}
{"name": "Algebra.IsPushout.comp_iff", "kind": "theorem", "module": "Mathlib.RingTheory.IsTensorProduct", "is_tactic_proof": true, "tactics": ["let", "haveI", "have", "ext", "simp", "rw", "exact"], "tactic_count": 7}
{"name": "Algebra.IsPushout.of_equiv", "kind": "theorem", "module": "Mathlib.RingTheory.IsTensorProduct", "is_tactic_proof": true, "tactics": ["rw", "refine", "simpa"], "tactic_count": 3}
{"name": "Algebra.IsPushout.cancelBaseChangeAux", "kind": "definition", "module": "Mathlib.RingTheory.IsTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsPushout.cancelBaseChangeAux_symm_tmul", "kind": "theorem", "module": "Mathlib.RingTheory.IsTensorProduct", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Algebra.IsPushout.cancelBaseChange", "kind": "definition", "module": "Mathlib.RingTheory.IsTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsPushout.cancelBaseChange_tmul", "kind": "theorem", "module": "Mathlib.RingTheory.IsTensorProduct", "is_tactic_proof": true, "tactics": ["change", "simp"], "tactic_count": 2}
{"name": "Algebra.IsPushout.cancelBaseChange_symm_tmul", "kind": "theorem", "module": "Mathlib.RingTheory.IsTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.finite_of_isSemisimpleRing", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Artinian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.finite_of_isArtinianRing", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Artinian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.finite_iff_isArtinianRing", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Artinian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.finite_iff_krullDimLE_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Artinian", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "Ideal.jacobson", "kind": "definition", "module": "Mathlib.RingTheory.Jacobson.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.le_jacobson", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.jacobson_idem", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.jacobson_top", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.jacobson_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ideal", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Ideal.jacobson_eq_top_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.jacobson_eq_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.jacobson_eq_self_of_isMaximal", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.jacobson.isMaximal", "kind": "instance", "module": "Mathlib.RingTheory.Jacobson.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.mem_jacobson_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.exists_mul_add_sub_mem_of_mem_jacobson", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ideal", "is_tactic_proof": true, "tactics": ["obtain", "use", "rw", "simpa"], "tactic_count": 4}
{"name": "Ideal.exists_mul_sub_mem_of_sub_one_mem_jacobson", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ideal", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "Ideal.eq_jacobson_iff_sInf_maximal", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ideal", "is_tactic_proof": true, "tactics": ["use", "rintro", "refine", "rw", "intro", "rcases", "exact", "exact"], "tactic_count": 8}
{"name": "Ideal.eq_jacobson_iff_sInf_maximal'", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.eq_jacobson_iff_notMem", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ideal", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "push_neg", "exact", "refine", "contrapose", "rw", "push_neg", "exact"], "tactic_count": 10}
{"name": "Ideal.map_jacobson_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ideal", "is_tactic_proof": true, "tactics": ["intro", "unfold", "have", "refine", "refine", "haveI", "exact", "refine", "rw", "rcases", "exact", "exact"], "tactic_count": 12}
{"name": "Ideal.map_jacobson_of_bijective", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.comap_jacobson", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.comap_jacobson_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ideal", "is_tactic_proof": true, "tactics": ["unfold", "refine", "rw", "refine", "have", "rcases", "exact", "exact", "simp_rw", "intro", "haveI", "exact"], "tactic_count": 12}
{"name": "Ideal.jacobson_mono", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ideal", "is_tactic_proof": true, "tactics": ["intro", "rw", "exact"], "tactic_count": 3}
{"name": "Ideal.ringJacobson_le_jacobson", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.instIsTwoSidedJacobson", "kind": "instance", "module": "Mathlib.RingTheory.Jacobson.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.radical_le_jacobson", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.isRadical_of_eq_jacobson", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.isRadical_jacobson", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.isUnit_of_sub_one_mem_jacobson_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ideal", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact"], "tactic_count": 3}
{"name": "Ideal.mem_jacobson_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.jacobson_eq_iff_jacobson_quotient_eq_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ideal", "is_tactic_proof": true, "tactics": ["have", "constructor", "intro", "replace", "rw", "simpa", "intro", "replace", "rw", "simpa"], "tactic_count": 10}
{"name": "Ideal.radical_eq_jacobson_iff_radical_quotient_eq_jacobson_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ideal", "is_tactic_proof": true, "tactics": ["have", "constructor", "intro", "have", "rw", "simpa", "intro", "have", "rw", "simpa"], "tactic_count": 10}
{"name": "Ideal.jacobson_radical_eq_jacobson", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.isLocal_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.isLocal_of_isMaximal_radical", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.IsLocal.le_jacobson", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.IsLocal.mem_jacobson_or_exists_inv", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ideal", "is_tactic_proof": false, "tactics": ["let", "let"], "tactic_count": 2}
{"name": "TwoSidedIdeal.jacobson", "kind": "definition", "module": "Mathlib.RingTheory.Jacobson.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.asIdeal_jacobson", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ideal", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "TwoSidedIdeal.mem_jacobson_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ideal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Ideal.jacobson_bot_polynomial_le_sInf_map_maximal", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Polynomial", "is_tactic_proof": true, "tactics": ["refine", "haveI", "refine", "suffices", "rw", "replace", "rwa", "exact", "refine", "have", "simpa"], "tactic_count": 11}
{"name": "Ideal.jacobson_bot_polynomial_of_jacobson_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Polynomial", "is_tactic_proof": true, "tactics": ["refine", "refine", "suffices", "exact"], "tactic_count": 4}
{"name": "Module.jacobson", "kind": "definition", "module": "Mathlib.RingTheory.Jacobson.Radical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.le_comap_jacobson", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Radical", "is_tactic_proof": true, "tactics": ["conv_rhs", "refine", "obtain", "exact", "simpa"], "tactic_count": 5}
{"name": "Module.map_jacobson_le", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Radical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.jacobson_eq_bot_of_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Radical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.map_jacobson_of_ker_le", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Radical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.comap_jacobson_of_ker_le", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Radical", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Module.map_jacobson_of_bijective", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Radical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.comap_jacobson_of_bijective", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Radical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.jacobson_quotient_of_le", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Radical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.jacobson_le_of_eq_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Radical", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Module.jacobson_quotient_jacobson", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Radical", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Module.jacobson_lt_top", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Radical", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Module._example", "kind": "example", "module": "Mathlib.RingTheory.Jacobson.Radical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.jacobson_pi_le", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Radical", "is_tactic_proof": true, "tactics": ["simp_rw", "intro", "exact"], "tactic_count": 3}
{"name": "Module.jacobson_pi_eq_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Radical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ring.jacobson", "kind": "abbrev", "module": "Mathlib.RingTheory.Jacobson.Radical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ring.jacobson_eq_sInf_isMaximal", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Radical", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Ring.instIsTwoSidedJacobson", "kind": "instance", "module": "Mathlib.RingTheory.Jacobson.Radical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ring.jacobson_le_of_isMaximal", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Radical", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Ring.le_comap_jacobson", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Radical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ring.map_jacobson_le", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Radical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ring.map_jacobson_of_ker_le", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Radical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ring.coe_jacobson_quotient", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Radical", "is_tactic_proof": true, "tactics": ["let", "rw", "apply", "rintro"], "tactic_count": 4}
{"name": "Ring.jacobson_quotient_of_le", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Radical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ring.jacobson_le_of_eq_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Radical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ring.jacobson_quotient_jacobson", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Radical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ring.jacobson_lt_top", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Radical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ring.jacobson_smul_top_le", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Radical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.jacobson_smul_lt_top", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Radical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.FG.jacobson_smul_lt", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Radical", "is_tactic_proof": true, "tactics": ["rw", "rw", "convert", "on_goal", "all_goals"], "tactic_count": 5}
{"name": "Submodule.FG.eq_bot_of_le_jacobson_smul", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Radical", "is_tactic_proof": true, "tactics": ["contrapose"], "tactic_count": 1}
{"name": "isJacobsonRing_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsJacobsonRing.out", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isJacobsonRing_iff_prime_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ring", "is_tactic_proof": true, "tactics": ["refine", "refine", "rw", "intro", "rw", "rw", "rw", "exact"], "tactic_count": 8}
{"name": "isJacobsonRing_iff_sInf_maximal", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isJacobsonRing_iff_sInf_maximal'", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.radical_eq_jacobson", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsJacobsonRingOfIsArtinianRing", "kind": "instance", "module": "Mathlib.RingTheory.Jacobson.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isJacobsonRing_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ring", "is_tactic_proof": true, "tactics": ["rintro", "rw", "intro", "use", "use", "have", "exact"], "tactic_count": 7}
{"name": "isJacobsonRing_quotient", "kind": "instance", "module": "Mathlib.RingTheory.Jacobson.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isJacobsonRing_iso", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isJacobsonRing_of_isIntegral", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ring", "is_tactic_proof": true, "tactics": ["rw", "intro", "by_cases", "simp", "have", "rw", "refine", "rw", "jacobson_eq_iff_jacobson_quotient_eq_bot.1", "comap_jacobson]", "refine", "simp", "have", "exact"], "tactic_count": 14}
{"name": "isJacobsonRing_of_isIntegral'", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.isMaximal_iff_isMaximal_disjoint", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ring", "is_tactic_proof": true, "tactics": ["constructor", "refine", "have", "rw", "have", "rw", "push_neg", "rcases", "convert", "by_cases", "rw", "rwa", "have", "refine", "rwa", "have", "exact", "refine", "rwa", "have", "rwa", "refine", "rw", "exact"], "tactic_count": 24}
{"name": "IsLocalization.isMaximal_of_isMaximal_disjoint", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ring", "is_tactic_proof": false, "tactics": ["rw", "comap_map_of_isPrime_disjoint", "exact"], "tactic_count": 3}
{"name": "IsLocalization.orderIsoOfMaximal", "kind": "definition", "module": "Mathlib.RingTheory.Jacobson.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isJacobsonRing_localization", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ring", "is_tactic_proof": true, "tactics": ["rw", "refine", "obtain", "have", "refine", "have", "intro", "have", "rw", "intro", "by_cases", "exact", "exact", "rw", "rcases", "exact", "exact", "refine", "rw", "refine", "exact", "isMaximal_of_isMaximal_disjoint", "exact"], "tactic_count": 23}
{"name": "Polynomial.mem_closure_X_union_C", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ring", "is_tactic_proof": true, "tactics": ["refine", "intro", "apply", "apply", "exact", "intro", "exact", "intro", "rw", "apply", "apply", "apply"], "tactic_count": 12}
{"name": "Polynomial.isIntegral_isLocalization_polynomial_quotient", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ring", "is_tactic_proof": true, "tactics": ["let", "let", "let", "let", "let", "have", "intro", "obtain", "suffices", "obtain", "obtain", "refine", "rw", "simp", "dsimp", "refine", "rintro", "push", "rcases", "rw", "refine", "φ.isIntegralElem_localization_at_leadingCoeff", "rwa", "use", "simp", "rw", "rw", "refine", "simp", "rw", "simp", "obtain", "rw", "apply", "apply"], "tactic_count": 35}
{"name": "Polynomial.jacobson_bot_of_integral_localization", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ring", "is_tactic_proof": false, "tactics": ["have", "map_le_nonZeroDivisors_of_injective", "letI", "let", "suffices", "have", "rw", "exact", "have", "have", "refine", "rw", "exact", "sInf_le_sInf", "let", "hJ.2", "intro", "have", "have", "have", "have", "let", "let", "have", "have", "have", "rw", "refine", "isMaximal_of_isIntegral_of_isMaximal_comap", "exact"], "tactic_count": 30}
{"name": "_private.Mathlib.RingTheory.Jacobson.Ring.0.Polynomial.isJacobsonRing_polynomial_of_domain", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ring", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "rw", "let", "have", "have", "obtain", "let", "have", "let", "let", "let", "let", "refine", "exact"], "tactic_count": 15}
{"name": "Polynomial.isJacobsonRing_polynomial_of_isJacobsonRing", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ring", "is_tactic_proof": true, "tactics": ["rw", "intro", "let", "let", "have", "have", "intro", "apply", "intro", "replace", "change", "rw", "rwa", "have", "let", "have", "have", "suffices", "replace", "rw", "comap_map_of_surjective", "refine", "exact", "apply", "exact"], "tactic_count": 25}
{"name": "Polynomial.isJacobsonRing_polynomial_iff_isJacobsonRing", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ring", "is_tactic_proof": true, "tactics": ["refine", "intro", "exact", "isJacobsonRing_of_surjective"], "tactic_count": 4}
{"name": "Polynomial.instIsJacobsonRing", "kind": "instance", "module": "Mathlib.RingTheory.Jacobson.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.isMaximal_comap_C_of_isMaximal", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ring", "is_tactic_proof": true, "tactics": ["let", "have", "obtain", "have", "let", "let", "let", "rw", "have", "hm", "map_injective", "rwa", "have", "suffices", "rw", "exact", "let", "have", "suffices", "rw", "refine", "have", "exact", "rw", "let", "refine", "apply", "rwa"], "tactic_count": 28}
{"name": "_private.Mathlib.RingTheory.Jacobson.Ring.0.Polynomial.quotient_mk_comp_C_isIntegral_of_jacobson'", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ring", "is_tactic_proof": true, "tactics": ["refine", "let", "obtain", "let", "let", "let", "have", "have", "let", "refine", "refine", "exact", "let", "quotientMap_injective", "suffices", "rw", "refine", "exact", "have", "exact", "rw"], "tactic_count": 21}
{"name": "Polynomial.quotient_mk_comp_C_isIntegral_of_isJacobsonRing", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ring", "is_tactic_proof": true, "tactics": ["let", "have", "let", "have", "have", "rw", "refine", "refine", "simpa", "refine", "rw", "refine", "have", "apply", "any_goals", "obtain", "rwa"], "tactic_count": 17}
{"name": "Polynomial.isMaximal_comap_C_of_isJacobsonRing", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ring", "is_tactic_proof": true, "tactics": ["rw", "have", "exact"], "tactic_count": 3}
{"name": "Polynomial.comp_C_integral_of_surjective_of_isJacobsonRing", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ring", "is_tactic_proof": true, "tactics": ["have", "let", "have", "rw", "refine", "rw", "norm_num", "exact"], "tactic_count": 8}
{"name": "MvPolynomial.isJacobsonRing_MvPolynomial_fin", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.isJacobsonRing", "kind": "instance", "module": "Mathlib.RingTheory.Jacobson.Ring", "is_tactic_proof": true, "tactics": ["cases", "let", "rw", "exact"], "tactic_count": 4}
{"name": "_private.Mathlib.RingTheory.Jacobson.Ring.0.MvPolynomial.Cₐ", "kind": "definition", "module": "Mathlib.RingTheory.Jacobson.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Jacobson.Ring.0.MvPolynomial.aux_IH", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ring", "is_tactic_proof": true, "tactics": ["let", "have", "have", "let", "let", "let", "have", "ext", "simp", "rw", "apply", "apply", "apply", "apply", "suffices", "rw", "rw", "apply", "rfl", "apply", "exact"], "tactic_count": 21}
{"name": "_private.Mathlib.RingTheory.Jacobson.Ring.0.MvPolynomial.quotient_mk_comp_C_isIntegral_of_isJacobsonRing'", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ring", "is_tactic_proof": true, "tactics": ["induction", "zero", "apply", "apply", "exact", "succ"], "tactic_count": 6}
{"name": "MvPolynomial.quotient_mk_comp_C_isIntegral_of_isJacobsonRing", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ring", "is_tactic_proof": true, "tactics": ["change", "apply", "infer_instance"], "tactic_count": 3}
{"name": "MvPolynomial.comp_C_integral_of_surjective_of_isJacobsonRing", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ring", "is_tactic_proof": true, "tactics": ["cases", "have", "let", "have", "change", "have", "have", "let", "have", "rw", "refine", "rw", "norm_num", "exact", "rw", "convert", "refine", "exact"], "tactic_count": 18}
{"name": "isJacobsonRing_of_finiteType", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ring", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "RingHom.FiniteType.isJacobsonRing", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finite_of_finite_type_of_isJacobsonRing", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ring", "is_tactic_proof": true, "tactics": ["obtain", "have", "rw", "exact", "have", "exact"], "tactic_count": 6}
{"name": "RingHom.finite_iff_finiteType_of_isJacobsonRing", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finite_of_algHom_finiteType_of_isJacobsonRing", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ring", "is_tactic_proof": true, "tactics": ["obtain", "letI", "have", "exact"], "tactic_count": 4}
{"name": "RingHom.finite_of_algHom_finiteType_of_isJacobsonRing", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Ring", "is_tactic_proof": true, "tactics": ["algebraize", "exact"], "tactic_count": 2}
{"name": "IsSimpleModule.jacobson_eq_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Semiprimary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSemisimpleModule.jacobson_eq_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Semiprimary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSemisimpleRing.jacobson_eq_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Semiprimary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSemisimpleModule.jacobson_le_ker", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Semiprimary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSemisimpleModule.jacobson_le_annihilator", "kind": "theorem", "module": "Mathlib.RingTheory.Jacobson.Semiprimary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsReducedOfIsSemisimpleRing", "kind": "instance", "module": "Mathlib.RingTheory.Jacobson.Semiprimary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "KaehlerDifferential.one_smul_sub_smul_one_mem_ideal", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Derivation.tensorProductTo_tmul", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.tensorProductTo_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "swap", "intro", "rw", "intro", "refine", "rw", "swap", "intro", "rw", "intro", "simp", "dsimp", "rw", "simp"], "tactic_count": 16}
{"name": "KaehlerDifferential.submodule_span_range_eq_ideal", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.Basic", "is_tactic_proof": true, "tactics": ["apply", "rw", "rintro", "exact", "rintro", "have", "rw", "clear", "refine", "rw", "intro", "have", "simp_rw", "rw", "refine", "apply", "exact", "intro", "rw", "exact"], "tactic_count": 20}
{"name": "KaehlerDifferential.span_range_eq_ideal", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.Basic", "is_tactic_proof": true, "tactics": ["apply", "rw", "rintro", "exact", "change", "rw", "conv_rhs", "exact"], "tactic_count": 8}
{"name": "termΩ[_⁄_]", "kind": "definition", "module": "Mathlib.RingTheory.Kaehler.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_RingTheory_Kaehler_Basic___macroRules_termΩ[_⁄_]_1", "kind": "definition", "module": "Mathlib.RingTheory.Kaehler.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_RingTheory_Kaehler_Basic___unexpand_KaehlerDifferential_1", "kind": "definition", "module": "Mathlib.RingTheory.Kaehler.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "KaehlerDifferential.DLinearMap_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "KaehlerDifferential.D_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "KaehlerDifferential.span_range_derivation", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.Basic", "is_tactic_proof": true, "tactics": ["rw", "rintro", "obtain", "have", "rw", "suffices", "refine", "rintro", "refine", "apply", "exact", "exact", "rintro", "rintro", "exact"], "tactic_count": 15}
{"name": "KaehlerDifferential.subsingleton_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.Basic", "is_tactic_proof": true, "tactics": ["suffices", "rw", "rintro"], "tactic_count": 3}
{"name": "Derivation.liftKaehlerDifferential_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.liftKaehlerDifferential_comp", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.Basic", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "refine", "rw"], "tactic_count": 4}
{"name": "Derivation.liftKaehlerDifferential_comp_D", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Derivation.liftKaehlerDifferential_unique", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.Basic", "is_tactic_proof": true, "tactics": ["apply", "intro", "have", "rw", "refine", "rintro", "rw", "intro", "intro"], "tactic_count": 9}
{"name": "Derivation.liftKaehlerDifferential_D", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "KaehlerDifferential.D_tensorProductTo", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.Basic", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "KaehlerDifferential.tensorProductTo_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.Basic", "is_tactic_proof": true, "tactics": ["intro", "exact"], "tactic_count": 2}
{"name": "KaehlerDifferential.End_equiv_aux", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply", "intro", "have", "have", "constructor", "intro", "exact", "e₂.symm", "intro", "exact"], "tactic_count": 11}
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{"name": "_private.Mathlib.RingTheory.Kaehler.Basic.0._aux_Mathlib_RingTheory_Kaehler_Basic___macroRules__private_Mathlib_RingTheory_Kaehler_Basic_0_term_𝖣__1", "kind": "definition", "module": "Mathlib.RingTheory.Kaehler.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Kaehler.Basic.0._aux_Mathlib_RingTheory_Kaehler_Basic___delab_app__private_Mathlib_RingTheory_Kaehler_Basic_0_term_𝖣__1", "kind": "definition", "module": "Mathlib.RingTheory.Kaehler.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "KaehlerDifferential.kerTotal_mkQ_single_add", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.Basic", "is_tactic_proof": false, "tactics": ["rw", "simp_rw", "exact"], "tactic_count": 3}
{"name": "KaehlerDifferential.kerTotal_mkQ_single_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.Basic", "is_tactic_proof": false, "tactics": ["rw", "simp_rw", "exact"], "tactic_count": 3}
{"name": "KaehlerDifferential.kerTotal_mkQ_single_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "KaehlerDifferential.kerTotal_mkQ_single_algebraMap_one", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "KaehlerDifferential.kerTotal_mkQ_single_smul", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.Basic", "is_tactic_proof": true, "tactics": ["letI", "rw", "add_zero,"], "tactic_count": 3}
{"name": "KaehlerDifferential.derivationQuotKerTotal_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "KaehlerDifferential.derivationQuotKerTotal_lift_comp_linearCombination", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.Basic", "is_tactic_proof": true, "tactics": ["apply", "intro", "conv_rhs", "simp"], "tactic_count": 4}
{"name": "KaehlerDifferential.kerTotal_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.Basic", "is_tactic_proof": true, "tactics": ["apply", "conv_rhs", "rw", "exact", "rw", "rintro"], "tactic_count": 6}
{"name": "KaehlerDifferential.linearCombination_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "KaehlerDifferential.quotKerTotalEquiv_symm_comp_D", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.Basic", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "_private.Mathlib.RingTheory.Kaehler.Basic.0.termFinsupp_map", "kind": "definition", "module": "Mathlib.RingTheory.Kaehler.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Kaehler.Basic.0._aux_Mathlib_RingTheory_Kaehler_Basic___macroRules__private_Mathlib_RingTheory_Kaehler_Basic_0_termFinsupp_map_1", "kind": "definition", "module": "Mathlib.RingTheory.Kaehler.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "KaehlerDifferential.kerTotal_map", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.Basic", "is_tactic_proof": false, "tactics": ["rw", "simp_rw", "simp", "simp_rw", "congr", "rw", "apply", "simp_rw", "exact"], "tactic_count": 9}
{"name": "KaehlerDifferential.kerTotal_map'", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.Basic", "is_tactic_proof": true, "tactics": ["rw", "congr", "ext"], "tactic_count": 3}
{"name": "KaehlerDifferential.map_compDer", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "KaehlerDifferential.map_D", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "KaehlerDifferential.ker_map", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.Basic", "is_tactic_proof": true, "tactics": ["rw", "congr", "ext", "simp", "simp", "rw", "simp", "simp", "simp", "simp"], "tactic_count": 10}
{"name": "KaehlerDifferential.ker_map_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.Basic", "is_tactic_proof": false, "tactics": ["rw", "convert", "rw"], "tactic_count": 3}
{"name": "KaehlerDifferential.map_surjective_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.Basic", "is_tactic_proof": false, "tactics": ["rw", "rintro", "obtain", "rw", "exact"], "tactic_count": 5}
{"name": "KaehlerDifferential.map_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "KaehlerDifferential.mapBaseChange_tmul", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.Basic", "is_tactic_proof": true, "tactics": ["conv_lhs", "congr", "exact"], "tactic_count": 3}
{"name": "KaehlerDifferential.range_mapBaseChange", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.Basic", "is_tactic_proof": true, "tactics": ["apply", "rintro", "induction", "zero", "tmul", "obtain", "simp", "induction", "simp", "simp", "simp", "add", "convert_to", "rw", "congr", "convert", "ext", "rw", "rintro", "use", "use", "use"], "tactic_count": 22}
{"name": "KaehlerDifferential.exact_mapBaseChange_map", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "KaehlerDifferential.kerCotangentToTensor_toCotangent", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "KaehlerDifferential.range_kerCotangentToTensor", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.Basic", "is_tactic_proof": true, "tactics": ["classical", "ext", "constructor", "rintro", "obtain", "simp", "map_D,", "intro", "obtain", "obtain", "replace", "rw", "obtain", "simp", "rw", "simp", "apply", "intro", "simp", "simp", "have", "simpa", "obtain", "use", "simp", "simp_rw", "simp", "rw", "have", "convert", "simp_rw", "simp"], "tactic_count": 32}
{"name": "KaehlerDifferential.exact_kerCotangentToTensor_mapBaseChange", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "KaehlerDifferential.mapBaseChange_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.Basic", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "Algebra.Generators.Cotangent.surjective_map_ofComp", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.JacobiZariski", "is_tactic_proof": true, "tactics": ["intro", "obtain", "have", "rw", "obtain", "exact"], "tactic_count": 6}
{"name": "Algebra.Generators.Cotangent.exact", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.JacobiZariski", "is_tactic_proof": true, "tactics": ["apply", "rw", "ext", "obtain", "simp", "convert", "trans", "congr", "refine", "change", "simp", "simp", "intro", "obtain", "replace", "simpa", "rw", "obtain", "rw", "rw", "let", "have", "have", "simpa", "rw", "refine", "rw", "rintro", "simp", "toExtension_Ring,", "refine", "simp", "rw", "rw", "rfl"], "tactic_count": 35}
{"name": "Algebra.Generators.CotangentSpace.compEquiv", "kind": "definition", "module": "Mathlib.RingTheory.Kaehler.JacobiZariski", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.CotangentSpace.compEquiv_symm_inr", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.JacobiZariski", "is_tactic_proof": true, "tactics": ["classical", "apply", "intro", "apply", "ext", "simp", "pderiv_X,", "obtain", "simp", "reduceCtorEq]"], "tactic_count": 10}
{"name": "Algebra.Generators.CotangentSpace.compEquiv_symm_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.JacobiZariski", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.CotangentSpace.fst_compEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.JacobiZariski", "is_tactic_proof": true, "tactics": ["classical", "apply", "intro", "apply", "ext", "simp", "obtain", "simp"], "tactic_count": 8}
{"name": "Algebra.Generators.CotangentSpace.fst_compEquiv_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.JacobiZariski", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.CotangentSpace.map_toComp_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.JacobiZariski", "is_tactic_proof": true, "tactics": ["rw", "apply", "exact"], "tactic_count": 3}
{"name": "Algebra.Generators.CotangentSpace.map_ofComp_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.JacobiZariski", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Algebra.Generators.CotangentSpace.exact", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.JacobiZariski", "is_tactic_proof": true, "tactics": ["rw", "conv_rhs", "rw", "exact"], "tactic_count": 4}
{"name": "Algebra.Generators.H1Cotangent.δAux", "kind": "definition", "module": "Mathlib.RingTheory.Kaehler.JacobiZariski", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.H1Cotangent.δAux_monomial", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.JacobiZariski", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.H1Cotangent.δAux_X", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.JacobiZariski", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Algebra.Generators.H1Cotangent.δAux_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.JacobiZariski", "is_tactic_proof": true, "tactics": ["induction", "monomial", "induction", "monomial", "s", "simp", "algebraMap_apply,", "rw", "simp", "add", "add"], "tactic_count": 11}
{"name": "Algebra.Generators.H1Cotangent.δAux_C", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.JacobiZariski", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Algebra.Generators.H1Cotangent.δAux_toAlgHom", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.JacobiZariski", "is_tactic_proof": true, "tactics": ["letI", "have", "induction", "add", "simp", "rw", "mul_X", "simp", "aeval_X,", "rw", "rfl"], "tactic_count": 11}
{"name": "Algebra.Generators.H1Cotangent.δAux_ofComp", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.JacobiZariski", "is_tactic_proof": true, "tactics": ["letI", "have", "induction", "simp", "add", "mul_X", "simp", "algebraMap_apply,", "obtain", "simp", "simp", "add_left_inj,", "rfl"], "tactic_count": 13}
{"name": "Algebra.Generators.H1Cotangent.map_comp_cotangentComplex_baseChange", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.JacobiZariski", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Algebra.Generators.H1Cotangent.δ", "kind": "definition", "module": "Mathlib.RingTheory.Kaehler.JacobiZariski", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.H1Cotangent.exact_δ_map", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.JacobiZariski", "is_tactic_proof": true, "tactics": ["simp", "apply", "apply", "intro", "simp", "toKaehler_cotangentSpaceBasis,", "rw", "conv_rhs", "simp", "simp", "exact"], "tactic_count": 11}
{"name": "Algebra.Generators.H1Cotangent.δ_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.JacobiZariski", "is_tactic_proof": true, "tactics": ["simp", "apply", "exacts"], "tactic_count": 3}
{"name": "Algebra.Generators.H1Cotangent.δ_eq_δAux", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.JacobiZariski", "is_tactic_proof": true, "tactics": ["let", "have", "simp", "congr", "exact", "let", "rw", "rw", "rfl", "exact", "rw", "apply", "simp", "ext", "swap", "change", "rw"], "tactic_count": 17}
{"name": "Algebra.Generators.H1Cotangent.δ_eq_δ", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.JacobiZariski", "is_tactic_proof": true, "tactics": ["ext", "obtain", "rw"], "tactic_count": 3}
{"name": "Algebra.Generators.H1Cotangent.exact_map_δ", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.JacobiZariski", "is_tactic_proof": true, "tactics": ["simp", "apply", "ext", "exact"], "tactic_count": 4}
{"name": "Algebra.Generators.H1Cotangent.δ_map", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.JacobiZariski", "is_tactic_proof": true, "tactics": ["letI", "obtain", "obtain", "change", "replace", "simpa", "simp", "refine", "rw"], "tactic_count": 9}
{"name": "Algebra.Generators.H1Cotangent.δ_comp_equiv", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.JacobiZariski", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "Algebra.Generators.H1Cotangent.exact_map_δ'", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.JacobiZariski", "is_tactic_proof": true, "tactics": ["refine", "change", "rw", "exact"], "tactic_count": 4}
{"name": "Algebra.H1Cotangent.δ", "kind": "definition", "module": "Mathlib.RingTheory.Kaehler.JacobiZariski", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.H1Cotangent.exact_map_δ", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.JacobiZariski", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.H1Cotangent.exact_δ_mapBaseChange", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.JacobiZariski", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "KaehlerDifferential.mvPolynomialBasis_repr_comp_D", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "KaehlerDifferential.mvPolynomialBasis_repr_D", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "KaehlerDifferential.mvPolynomialBasis_repr_D_X", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.Polynomial", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "KaehlerDifferential.mvPolynomialBasis_repr_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.Polynomial", "is_tactic_proof": true, "tactics": ["classical", "suffices", "rw", "apply", "simp"], "tactic_count": 5}
{"name": "KaehlerDifferential.mvPolynomialBasis_repr_symm_single", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.Polynomial", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "KaehlerDifferential.mvPolynomialBasis_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "KaehlerDifferential.polynomial_D_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.Polynomial", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "KaehlerDifferential.polynomialEquiv_comp_D", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "KaehlerDifferential.polynomialEquiv_D", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "KaehlerDifferential.polynomialEquiv_symm", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "KaehlerDifferential.mulActionBaseChange", "kind": "abbrev", "module": "Mathlib.RingTheory.Kaehler.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "KaehlerDifferential.mulActionBaseChange_smul_tmul", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "KaehlerDifferential.mulActionBaseChange_smul_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.TensorProduct", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "KaehlerDifferential.mulActionBaseChange_smul_add", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.TensorProduct", "is_tactic_proof": true, "tactics": ["change", "rw", "rfl"], "tactic_count": 3}
{"name": "KaehlerDifferential.moduleBaseChange", "kind": "abbrev", "module": "Mathlib.RingTheory.Kaehler.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "KaehlerDifferential.instIsScalarTowerTensorProduct", "kind": "instance", "module": "Mathlib.RingTheory.Kaehler.TensorProduct", "is_tactic_proof": true, "tactics": ["apply", "intro", "induction", "simp", "rw", "simp"], "tactic_count": 6}
{"name": "KaehlerDifferential.instSMulCommClassTensorProduct", "kind": "instance", "module": "Mathlib.RingTheory.Kaehler.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "KaehlerDifferential.instSMulCommClassTensorProduct_1", "kind": "instance", "module": "Mathlib.RingTheory.Kaehler.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "KaehlerDifferential.moduleBaseChange'", "kind": "definition", "module": "Mathlib.RingTheory.Kaehler.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "KaehlerDifferential.instIsScalarTowerTensorProduct_1", "kind": "instance", "module": "Mathlib.RingTheory.Kaehler.TensorProduct", "is_tactic_proof": true, "tactics": ["apply", "intro", "change", "x", "r", "simp"], "tactic_count": 6}
{"name": "KaehlerDifferential.instIsScalarTowerTensorProduct_2", "kind": "instance", "module": "Mathlib.RingTheory.Kaehler.TensorProduct", "is_tactic_proof": true, "tactics": ["apply", "intro", "change", "x", "r", "simp"], "tactic_count": 6}
{"name": "KaehlerDifferential.map_liftBaseChange_smul", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.TensorProduct", "is_tactic_proof": true, "tactics": ["induction", "zero", "smul", "add", "tmul", "induction", "simp", "simp", "simp"], "tactic_count": 9}
{"name": "KaehlerDifferential.derivationTensorProduct", "kind": "definition", "module": "Mathlib.RingTheory.Kaehler.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "KaehlerDifferential.derivationTensorProduct_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "KaehlerDifferential.tensorKaehlerEquiv_left_inv", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.TensorProduct", "is_tactic_proof": true, "tactics": ["refine", "apply", "intro", "obtain", "induction", "simp", "simp", "derivationTensorProduct_algebraMap]", "rw", "rfl", "simp"], "tactic_count": 11}
{"name": "KaehlerDifferential.tensorKaehlerEquivBase", "kind": "definition", "module": "Mathlib.RingTheory.Kaehler.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "KaehlerDifferential.tensorKaehlerEquivBase_tmul", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "KaehlerDifferential.isBaseChange", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.TensorProduct", "is_tactic_proof": true, "tactics": ["convert", "refine", "simp", "tensorKaehlerEquivBase_tmul,"], "tactic_count": 4}
{"name": "KaehlerDifferential.isLocalizedModule", "kind": "instance", "module": "Mathlib.RingTheory.Kaehler.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "KaehlerDifferential.isLocalizedModule_of_isLocalizedModule", "kind": "instance", "module": "Mathlib.RingTheory.Kaehler.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "KaehlerDifferential.tensorKaehlerEquiv", "kind": "definition", "module": "Mathlib.RingTheory.Kaehler.TensorProduct", "is_tactic_proof": true, "tactics": ["have", "let", "let", "e₁.restrictScalars", "refine", "intro", "obtain", "dsimp", "induction", "zero", "add", "tmul", "induction", "zero", "add", "tmul", "obtain", "induction", "zero", "add", "tmul", "z", "suffices", "b", "simpa", "simp", "ring_nf"], "tactic_count": 27}
{"name": "KaehlerDifferential.tensorKaehlerEquiv_tmul_D", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.TensorProduct", "is_tactic_proof": true, "tactics": ["have", "obtain", "induction", "zero", "add", "tmul", "trans", "simp", "simp"], "tactic_count": 9}
{"name": "KaehlerDifferential.tensorKaehlerEquiv_symm_D_tmul", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.TensorProduct", "is_tactic_proof": true, "tactics": ["apply", "simp", "tensorKaehlerEquiv_tmul_D]", "rw"], "tactic_count": 4}
{"name": "KaehlerDifferential.tensorKaehlerEquiv_symm_D_tmul'", "kind": "theorem", "module": "Mathlib.RingTheory.Kaehler.TensorProduct", "is_tactic_proof": true, "tactics": ["apply", "simp", "tensorKaehlerEquiv_tmul_D]", "rw", "simp"], "tactic_count": 5}
{"name": "ringKrullDim", "kind": "definition", "module": "Mathlib.RingTheory.KrullDimension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ring.KrullDimLE", "kind": "abbrev", "module": "Mathlib.RingTheory.KrullDimension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ring.krullDimLE_iff", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ringKrullDim_eq_bot_of_subsingleton", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ringKrullDim_nonneg_of_nontrivial", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ringKrullDim_le_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ringKrullDim_quotient_le", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ringKrullDim_eq_of_ringEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteRingKrullDim", "kind": "abbrev", "module": "Mathlib.RingTheory.KrullDimension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ringKrullDim_ne_top", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ringKrullDim_lt_top", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ringKrullDim_ne_bot", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finiteRingKrullDim_iff_ne_bot_and_top", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nontrivial.of_finiteRingKrullDim", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MvPolynomial.fin_ringKrullDim_eq_add_of_isNoetherianRing", "kind": "proofWanted", "module": "Mathlib.RingTheory.KrullDimension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ring.krullDimLE_zero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Basic", "is_tactic_proof": false, "tactics": ["simp_rw", "rfl"], "tactic_count": 2}
{"name": "Ring.KrullDimLE.mk₀", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Basic", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Ideal.isMaximal_of_isPrime", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.IsPrime.isMaximal'", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsMaximalOfIsPrimeOfKrullDimLEOfNatNat", "kind": "instance", "module": "Mathlib.RingTheory.KrullDimension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.isMaximal_iff_isPrime", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.mem_minimalPrimes_of_krullDimLE_zero", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.mem_minimalPrimes_iff_isPrime", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nilradical_le_jacobson", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ring.jacobson_eq_nilradical_of_krullDimLE_zero", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instKrullDimLEOfNatNat", "kind": "instance", "module": "Mathlib.RingTheory.KrullDimension.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ring.krullDimLE_one_iff", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Basic", "is_tactic_proof": false, "tactics": ["simp_rw", "rfl"], "tactic_count": 2}
{"name": "Ring.KrullDimLE.mk₁", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Basic", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Ring.krullDimLE_one_iff_of_isPrime_bot", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Basic", "is_tactic_proof": true, "tactics": ["letI", "simp_rw", "ne_eq,", "rfl"], "tactic_count": 4}
{"name": "Ring.krullDimLE_one_iff_of_noZeroDivisors", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Basic", "is_tactic_proof": true, "tactics": ["cases", "exact", "exact"], "tactic_count": 3}
{"name": "Ring.KrullDimLE.mk₁'", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "rwa", "suffices", "exact"], "tactic_count": 4}
{"name": "ringKrullDim_eq_zero_of_field", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ringKrullDim_eq_zero_of_isField", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ringKrullDim_eq_one_iff_of_isLocalRing_isDomain", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.LocalRing", "is_tactic_proof": true, "tactics": ["refine", "exact", "intro", "rw", "refine", "have", "exact", "have", "have", "exact", "suffices", "rw", "exact", "refine", "obtain", "apply", "simp", "exact", "have", "le_trans", "have", "exact"], "tactic_count": 22}
{"name": "Module.supportDim", "kind": "definition", "module": "Mathlib.RingTheory.KrullDimension.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.supportDim_eq_bot_of_subsingleton", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Module", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Module.supportDim_ne_bot_of_nontrivial", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Module", "is_tactic_proof": true, "tactics": ["have", "simp"], "tactic_count": 2}
{"name": "Module.supportDim_eq_bot_iff_subsingleton", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Module", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Module.supportDim_ne_bot_iff_nontrivial", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Module", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Module.supportDim_eq_ringKrullDim_quotient_annihilator", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Module", "is_tactic_proof": true, "tactics": ["simp", "rw"], "tactic_count": 2}
{"name": "Module.supportDim_self_eq_ringKrullDim", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Module", "is_tactic_proof": false, "tactics": ["have", "annihilator_eq_bot.mpr", "rw", "exact"], "tactic_count": 4}
{"name": "Module.supportDim_le_ringKrullDim", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.supportDim_quotient_eq_ringKrullDim", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Module", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Module.supportDim_le_of_injective", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.supportDim_le_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.supportDim_eq_of_equiv", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "support_of_supportDim_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Module", "is_tactic_proof": true, "tactics": ["let", "rw", "apply", "intro", "by_contra", "push", "have", "lt_of_le_of_ne", "have", "simp", "use", "simpa", "exact", "simpa"], "tactic_count": 14}
{"name": "ringKrullDim_quotient", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.NonZeroDivisors", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ringKrullDim_quotient_succ_le_of_nonZeroDivisor", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.NonZeroDivisors", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "simp", "have", "rwa", "have", "have", "rw", "intro", "obtain", "let", "have", "lt_of_le_of_ne", "refine", "simp"], "tactic_count": 15}
{"name": "ringKrullDim_succ_le_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.NonZeroDivisors", "is_tactic_proof": true, "tactics": ["refine", "gcongr", "exact", "ringKrullDim_le_of_surjective"], "tactic_count": 4}
{"name": "ringKrullDim_succ_le_ringKrullDim_polynomial", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ringKrullDim_mvPolynomial_of_isEmpty", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ringKrullDim_add_natCard_le_ringKrullDim_mvPolynomial", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.NonZeroDivisors", "is_tactic_proof": true, "tactics": ["induction", "of_equiv", "convert", "rw", "exact", "h_empty", "h_option", "simp", "grw", "exact"], "tactic_count": 10}
{"name": "ringKrullDim_add_enatCard_le_ringKrullDim_mvPolynomial", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.NonZeroDivisors", "is_tactic_proof": true, "tactics": ["nontriviality", "cases", "rw", "push_cast", "exact", "simp", "suffices", "rw", "intro", "let", "have", "refine", "refine", "simp", "trans", "norm_cast", "simp", "exact"], "tactic_count": 18}
{"name": "ringKrullDim_succ_le_ringKrullDim_powerseries", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrincipalIdealRing.krullDimLE_one", "kind": "instance", "module": "Mathlib.RingTheory.KrullDimension.PID", "is_tactic_proof": true, "tactics": ["refine", "rw", "obtain", "have", "have", "have", "refine", "rw", "exact", "have", "simpa"], "tactic_count": 11}
{"name": "IsPrincipalIdealRing.ringKrullDim_eq_one", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.PID", "is_tactic_proof": true, "tactics": ["apply", "rw", "infer_instance", "have", "rw", "exact"], "tactic_count": 6}
{"name": "IsPrincipalIdealRing.height_eq_one_of_isMaximal", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.PID", "is_tactic_proof": true, "tactics": ["refine", "suffices", "rw", "exact", "rw", "exact"], "tactic_count": 6}
{"name": "Polynomial.ringKrullDim_le", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Polynomial", "is_tactic_proof": true, "tactics": ["rw", "apply", "exact", "rw", "ringKrullDim_eq_of_ringEquiv", "infer_instance"], "tactic_count": 6}
{"name": "_private.Mathlib.RingTheory.KrullDimension.Polynomial.0.Polynomial.height_eq_height_add_one_of_isMaximal", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Polynomial", "is_tactic_proof": true, "tactics": ["let", "suffices", "rw", "let", "let", "have", "refine", "rw", "exact", "have", "have", "rwa"], "tactic_count": 12}
{"name": "Polynomial.height_map_C", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Polynomial", "is_tactic_proof": true, "tactics": ["have", "simp"], "tactic_count": 2}
{"name": "Polynomial.height_eq_height_add_one", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Polynomial", "is_tactic_proof": true, "tactics": ["have", "let", "set", "have", "rw", "exact", "let", "have", "refine", "rwa", "have", "have", "have", "have", "have", "rw", "exact", "have", "rw", "apply"], "tactic_count": 20}
{"name": "Polynomial.ringKrullDim_of_isNoetherianRing", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Polynomial", "is_tactic_proof": true, "tactics": ["refine", "nontriviality", "refine", "rw", "gcongr", "exact", "exact"], "tactic_count": 7}
{"name": "MvPolynomial.ringKrullDim_of_isNoetherianRing", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Polynomial", "is_tactic_proof": true, "tactics": ["induction", "of_equiv", "convert", "exact", "rw", "h_empty", "h_option", "simp", "rw"], "tactic_count": 9}
{"name": "Module.exists_ltSeries_support_isMaximal_last_of_ltSeries_support", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Regular", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "use", "simpa", "use"], "tactic_count": 5}
{"name": "Module.supportDim_le_supportDim_quotSMulTop_succ_of_mem_jacobson", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Regular", "is_tactic_proof": true, "tactics": ["nontriviality", "refine", "wlog", "obtain", "have", "exact", "this", "obtain", "exist_ltSeries_mem_one_of_mem_last", "by_cases", "have", "rw", "exact", "let", "toFun", "intro", "have", "exact", "simpa", "q.monotone", "step", "grw"], "tactic_count": 22}
{"name": "Module.supportDim_quotSMulTop_succ_le_of_notMem_minimalPrimes", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Regular", "is_tactic_proof": true, "tactics": ["nontriviality", "nontriviality", "have", "have", "simp", "apply", "simp", "intro", "have", "simp", "have", "simp", "let", "p.map", "obtain", "let", "have", "exact"], "tactic_count": 18}
{"name": "Module.supportDim_quotSMulTop_succ_eq_of_notMem_minimalPrimes_of_mem_jacobson", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.supportDim_quotSMulTop_succ_eq_supportDim_mem_jacobson", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ringKrullDim_quotSMulTop_succ_eq_ringKrullDim_of_mem_jacobson", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Regular", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ringKrullDim_quotient_span_singleton_succ_eq_ringKrullDim_of_mem_jacobson", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Regular", "is_tactic_proof": true, "tactics": ["have", "rw", "ringKrullDim_quotSMulTop_succ_eq_ringKrullDim_of_mem_jacobson"], "tactic_count": 3}
{"name": "Module.ringKrullDim_quotient_add_one_of_mem_nonZeroDivisors", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Regular", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "Module.supportDim_le_supportDim_quotSMulTop_succ", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ringKrullDim_le_ringKrullDim_quotSMulTop_succ", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Regular", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ringKrullDim_le_ringKrullDim_add_card", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Regular", "is_tactic_proof": true, "tactics": ["apply", "rwa"], "tactic_count": 2}
{"name": "ringKrullDim_le_ringKrullDim_add_spanFinrank", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Regular", "is_tactic_proof": true, "tactics": ["apply", "rw", "exact"], "tactic_count": 3}
{"name": "Module.supportDim_quotSMulTop_succ_eq_of_notMem_minimalPrimes_of_mem_maximalIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.supportDim_quotSMulTop_succ_eq_supportDim", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ringKrullDim_quotSMulTop_succ_eq_ringKrullDim", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ringKrullDim_quotient_span_singleton_succ_eq_ringKrullDim", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ringKrullDim_quotient_span_singleton_succ_eq_ringKrullDim_of_mem_nonZeroDivisors", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.supportDim_add_length_eq_supportDim_of_isRegular", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Regular", "is_tactic_proof": true, "tactics": ["induction", "nil", "rw", "simpa", "cons", "ih", "have", "simp"], "tactic_count": 8}
{"name": "ringKrullDim_add_length_eq_ringKrullDim_of_isRegular", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Regular", "is_tactic_proof": true, "tactics": ["have", "rw", "supportDim_self_eq_ringKrullDim]", "exact"], "tactic_count": 4}
{"name": "Ring.KrullDimLE.mem_minimalPrimes_iff", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ring.KrullDimLE.mem_minimalPrimes_iff_le_of_isPrime", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Zero", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Ring.KrullDimLE.minimalPrimes_eq_setOf_isPrime", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Zero", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Ring.KrullDimLE.minimalPrimes_eq_setOf_isMaximal", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Zero", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "_example", "kind": "example", "module": "Mathlib.RingTheory.KrullDimension.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ring.KrullDimLE.isField_of_isDomain", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Zero", "is_tactic_proof": true, "tactics": ["by_contra", "obtain", "exact"], "tactic_count": 3}
{"name": "ringKrullDimZero_iff_ringKrullDim_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Zero", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Ring.krullDimLE_zero_and_isLocalRing_tfae", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Zero", "is_tactic_proof": false, "tactics": ["tfae_have", "intro", "change", "rw", "simp", "tfae_have", "refine", "obtain", "exact", "obtain", "exact", "tfae_have", "tfae_have", "rintro", "obtain", "obtain", "exact", "tfae_finish"], "tactic_count": 18}
{"name": "le_isUnit_iff_zero_notMem", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Zero", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "Ring.KrullDimLE.existsUnique_isPrime", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ring.KrullDimLE.eq_maximalIdeal_of_isPrime", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ring.KrullDimLE.radical_eq_maximalIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Zero", "is_tactic_proof": true, "tactics": ["rw", "refine", "exact", "rintro", "exact"], "tactic_count": 5}
{"name": "Ring.KrullDimLE.subsingleton_primeSpectrum", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ring.KrullDimLE.isNilpotent_iff_mem_maximalIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ring.KrullDimLE.isNilpotent_iff_mem_nonunits", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ring.KrullDimLE.nilradical_eq_maximalIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.of_isMaximal_nilradical", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ring.KrullDimLE.of_isMaximal_nilradical", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ring.KrullDimLE.of_isLocalization", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ring.KrullDimLE.isField_of_isReduced", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Zero", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PrimeSpectrum.unique_of_ringKrullDimLE_zero", "kind": "instance", "module": "Mathlib.RingTheory.KrullDimension.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.jacobson_eq_radical", "kind": "theorem", "module": "Mathlib.RingTheory.KrullDimension.Zero", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "instIsJacobsonRingOfKrullDimLEOfNatNat", "kind": "instance", "module": "Mathlib.RingTheory.KrullDimension.Zero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLasker", "kind": "definition", "module": "Mathlib.RingTheory.Lasker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.decomposition_erase_inf", "kind": "theorem", "module": "Mathlib.RingTheory.Lasker", "is_tactic_proof": true, "tactics": ["induction", "by_cases", "exact", "obtain", "refine", "rw", "simp"], "tactic_count": 7}
{"name": "Submodule.isPrimary_decomposition_pairwise_ne_radical", "kind": "theorem", "module": "Mathlib.RingTheory.Lasker", "is_tactic_proof": true, "tactics": ["classical", "refine", "ext", "grind", "simp", "intro", "refine", "simp", "simp", "intro", "simp", "intro", "simp", "obtain", "obtain", "simp", "contrapose", "suffices", "rw", "rw"], "tactic_count": 20}
{"name": "Submodule.exists_minimal_isPrimary_decomposition_of_isPrimary_decomposition", "kind": "theorem", "module": "Mathlib.RingTheory.Lasker", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "exact"], "tactic_count": 3}
{"name": "Submodule.IsLasker.exists_isMinimalPrimaryDecomposition", "kind": "theorem", "module": "Mathlib.RingTheory.Lasker", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "exact"], "tactic_count": 3}
{"name": "InfIrred.isPrimary", "kind": "theorem", "module": "Mathlib.RingTheory.Lasker", "is_tactic_proof": true, "tactics": ["rw", "refine", "let", "add_mem", "zero_mem", "smul_mem", "have", "intro", "simpa", "obtain", "rcases", "specialize", "refine", "simp", "obtain", "have", "rw", "rwa", "rw", "refine", "replace", "rw", "rw", "simpa"], "tactic_count": 24}
{"name": "Submodule.isLasker", "kind": "theorem", "module": "Mathlib.RingTheory.Lasker", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LaurentSeries", "kind": "abbrev", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LaurentSeries.term_⸨X⸩", "kind": "definition", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LaurentSeries._aux_Mathlib_RingTheory_LaurentSeries___macroRules_LaurentSeries_term_⸨X⸩_1", "kind": "definition", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LaurentSeries._aux_Mathlib_RingTheory_LaurentSeries___unexpand_LaurentSeries_1", "kind": "definition", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LaurentSeries.hasseDeriv", "kind": "definition", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LaurentSeries.hasseDeriv_coeff", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LaurentSeries.hasseDeriv_zero", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "LaurentSeries.hasseDeriv_single_add", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "by_cases", "simp", "simp"], "tactic_count": 5}
{"name": "LaurentSeries.hasseDeriv_single", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LaurentSeries.hasseDeriv_comp_coeff", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": true, "tactics": ["rw", "simp", "rw"], "tactic_count": 3}
{"name": "LaurentSeries.hasseDeriv_comp", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "LaurentSeries.derivative", "kind": "definition", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LaurentSeries.derivative_apply", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "LaurentSeries.derivative_iterate", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": true, "tactics": ["ext", "induction", "zero", "succ", "rw"], "tactic_count": 5}
{"name": "LaurentSeries.derivative_iterate_coeff", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": true, "tactics": ["rw", "smul_assoc]"], "tactic_count": 2}
{"name": "LaurentSeries.instCoePowerSeries", "kind": "instance", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LaurentSeries.coeff_coe_powerSeries", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "LaurentSeries.powerSeriesPart", "kind": "definition", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LaurentSeries.powerSeriesPart_coeff", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LaurentSeries.powerSeriesPart_zero", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "LaurentSeries.powerSeriesPart_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": true, "tactics": ["constructor", "contrapose", "simp", "intro", "rw", "use", "simpa", "rintro", "simp"], "tactic_count": 9}
{"name": "LaurentSeries.single_order_mul_powerSeriesPart", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": true, "tactics": ["ext", "rw", "by_cases", "rw", "rw", "contrapose", "exact", "contrapose", "simp", "lia"], "tactic_count": 10}
{"name": "LaurentSeries.ofPowerSeries_powerSeriesPart", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "LaurentSeries.X_order_mul_powerSeriesPart", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": true, "tactics": ["simp", "single_order_mul_powerSeriesPart]"], "tactic_count": 2}
{"name": "LaurentSeries.instAlgebraPowerSeries", "kind": "instance", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LaurentSeries.coe_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LaurentSeries.of_powerSeries_localization", "kind": "instance", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LaurentSeries.instIsFractionRingPowerSeries", "kind": "instance", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.coe_zero", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.coe_one", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.coe_add", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.coe_sub", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.coe_neg", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.coe_mul", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.coeff_coe", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": true, "tactics": ["cases", "rw", "rw", "simp", "toPowerSeries_symm_apply_coeff,"], "tactic_count": 5}
{"name": "PowerSeries.coe_C", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.coe_X", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.coe_smul", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "PowerSeries.coe_pow", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RatFunc.instFaithfulSMulPolynomialLaurentSeries", "kind": "instance", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "RatFunc.coeToLaurentSeries", "kind": "instance", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RatFunc.coe_coe", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RatFunc.coe_X", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RatFunc.single_one_eq_pow", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RatFunc.single_inv", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "RatFunc.single_zpow", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": true, "tactics": ["rw", "zpow_natCast,"], "tactic_count": 2}
{"name": "RatFunc.algebraMap_apply_div", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PowerSeries.idealX", "kind": "definition", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.intValuation_eq_of_coe", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "rw", "simp", "have", "simp", "and_self_iff]", "have", "simp", "classical", "rw", "count_associates_factors_eq]", "on_goal", "exacts", "count_span_normalizedFactors_eq_of_normUnit", "span_ne_zero'.2]"], "tactic_count": 16}
{"name": "PowerSeries.intValuation_X", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "RatFunc.valuation_eq_LaurentSeries_valuation", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": true, "tactics": ["refine", "intro", "rw", "convert", "simp", "exacts"], "tactic_count": 6}
{"name": "LaurentSeries.instValuedWithZeroMultiplicativeInt", "kind": "instance", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LaurentSeries.valuation_def", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LaurentSeries.valuation_coe_ratFunc", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LaurentSeries.valuation_X_pow", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": true, "tactics": ["rw", "smul_neg,"], "tactic_count": 2}
{"name": "LaurentSeries.valuation_single_zpow", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": true, "tactics": ["obtain", "rw", "rw"], "tactic_count": 3}
{"name": "LaurentSeries.coeff_zero_of_lt_intValuation", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": true, "tactics": ["intro", "apply", "rwa", "intValuation_le_pow_iff_dvd", "span_singleton_dvd_span_singleton_iff_dvd]"], "tactic_count": 5}
{"name": "LaurentSeries.intValuation_le_iff_coeff_lt_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": false, "tactics": ["have", "rw", "span_singleton_dvd_span_singleton_iff_dvd,", "apply"], "tactic_count": 4}
{"name": "LaurentSeries.coeff_zero_of_lt_valuation", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": true, "tactics": ["intro", "by_cases", "exact", "set", "by_cases", "obtain", "obtain", "obtain", "rw", "apply", "rw", "gcongr", "obtain", "obtain", "obtain", "rw", "apply", "rw", "neg_neg]", "gcongr"], "tactic_count": 20}
{"name": "LaurentSeries.valuation_le_iff_coeff_lt_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": true, "tactics": ["refine", "let", "by_cases", "obtain", "rw", "exp_neg,", "by_cases", "apply", "rwa", "obtain", "rw", "apply", "intro", "rw", "apply", "lia", "simp", "obtain", "rw", "rw", "exp_neg,", "by_cases", "apply", "rw", "lia", "obtain", "rw", "apply", "intro", "rw", "apply", "lia", "simp"], "tactic_count": 33}
{"name": "LaurentSeries.valuation_le_iff_coeff_lt_log_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": true, "tactics": ["cases", "simp_all", "rename_i", "cases", "rename_i", "rw", "small"], "tactic_count": 7}
{"name": "LaurentSeries.eq_coeff_of_valuation_sub_lt", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "intro", "apply", "rw", "apply"], "tactic_count": 6}
{"name": "LaurentSeries.val_le_one_iff_eq_coe", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": true, "tactics": ["rw", "refine", "on_goal", "simp", "on_goal", "on_goal", "all_goals", "apply", "simp", "reduceCtorEq]", "intro", "simp", "lia"], "tactic_count": 13}
{"name": "LaurentSeries.uniformContinuous_coeff", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": true, "tactics": ["refine", "let", "use", "refine", "rw", "exact"], "tactic_count": 6}
{"name": "LaurentSeries.Cauchy.coeff", "kind": "definition", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LaurentSeries.Cauchy.coeff_tendsto", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LaurentSeries.Cauchy.exists_lb_eventual_support", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": true, "tactics": ["let", "let", "obtain", "mem_prod_iff.mp", "obtain", "obtain", "by_cases", "refine", "rw", "exact", "refine", "rw", "exact", "f.2.isWF.not_lt_min", "lt_trans", "exact", "use", "apply", "intro", "have", "refine", "simpa"], "tactic_count": 22}
{"name": "LaurentSeries.Cauchy.exists_lb_support", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": true, "tactics": ["let", "obtain", "refine", "simp", "apply"], "tactic_count": 5}
{"name": "LaurentSeries.Cauchy.coeff_support_bddBelow", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": true, "tactics": ["refine", "by_contra", "exact"], "tactic_count": 3}
{"name": "LaurentSeries.Cauchy.limit", "kind": "definition", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LaurentSeries.Cauchy.exists_lb_coeff_ne", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": true, "tactics": ["obtain", "refine", "rw", "filter"], "tactic_count": 4}
{"name": "LaurentSeries.Cauchy.coeff_eventually_equal", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": true, "tactics": ["let", "have", "intro", "simpa", "let", "let", "have", "simp", "intro", "simp", "by_cases", "exacts", "suffices", "exact", "simp", "constructor", "have", "rw", "convert", "ext", "simp", "rw", "intro", "apply", "simp"], "tactic_count": 25}
{"name": "LaurentSeries.Cauchy.eventually_mem_nhds", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": true, "tactics": ["obtain", "suffices", "set", "have", "rw", "simp", "apply", "intro", "apply", "intro", "rw", "exact"], "tactic_count": 12}
{"name": "LaurentSeries.instLaurentSeriesComplete", "kind": "instance", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LaurentSeries.exists_Polynomial_intValuation_lt", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": true, "tactics": ["by_cases", "use", "simpa", "rw", "obtain", "use", "have", "apply", "simpa", "rw", "rw", "apply", "rw", "gcongr", "exact", "rw", "exact"], "tactic_count": 17}
{"name": "LaurentSeries.exists_ratFunc_val_lt", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": true, "tactics": ["set", "by_cases", "set", "obtain", "use", "have", "obtain", "rw", "have", "rw", "inv_eq_one_div", "simp", "rw", "apply", "rwa", "simp", "not_false_iff]", "obtain", "obtain", "use", "rw", "adicValued_apply,", "exact"], "tactic_count": 23}
{"name": "LaurentSeries.coe_range_dense", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": true, "tactics": ["rw", "ext", "simp", "intro", "rw", "obtain", "obtain", "obtain", "use", "apply", "apply", "simpa"], "tactic_count": 12}
{"name": "LaurentSeries.exists_ratFunc_eq_v", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": true, "tactics": ["by_cases", "use", "simp", "use", "rw", "simp"], "tactic_count": 6}
{"name": "LaurentSeries.inducing_coe", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": true, "tactics": ["rw", "ext", "simp", "constructor", "rintro", "obtain", "use", "simp", "refine", "apply", "simp", "rw", "assumption", "rintro", "obtain", "let", "refine", "refine", "simp", "use", "refine", "apply", "rw", "assumption"], "tactic_count": 24}
{"name": "LaurentSeries.continuous_coe", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LaurentSeries.ratfuncAdicComplPkg", "kind": "abbrev", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LaurentSeries.LaurentSeriesPkg", "kind": "definition", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LaurentSeries.instTopologicalSpaceSpaceRatFuncLaurentSeriesPkg", "kind": "instance", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LaurentSeries.LaurentSeries_coe", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LaurentSeries.extensionAsRingHom", "kind": "abbrev", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LaurentSeries.RatFuncAdicCompl", "kind": "abbrev", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LaurentSeries.instUniformSpaceRatFuncAdicCompl", "kind": "instance", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LaurentSeries.instUniformSpace", "kind": "instance", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LaurentSeries.comparePkg", "kind": "abbrev", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LaurentSeries.comparePkg_eq_extension", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LaurentSeries.ratfuncAdicComplRingEquiv", "kind": "abbrev", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LaurentSeries.LaurentSeriesRingEquiv", "kind": "abbrev", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LaurentSeries.LaurentSeriesRingEquiv_def", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LaurentSeries.ratfuncAdicComplRingEquiv_apply", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LaurentSeries.coe_X_compare", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "LaurentSeries.algebraMap_apply", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LaurentSeries.instAlgebraRatFuncAdicCompl", "kind": "instance", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LaurentSeries.LaurentSeriesAlgEquiv", "kind": "definition", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LaurentSeries.valuation_LaurentSeries_equal_extension", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": true, "tactics": ["apply", "intro", "rw", "rfl", "exact"], "tactic_count": 5}
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{"name": "LaurentSeries.powerSeries_as_subring", "kind": "abbrev", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LaurentSeries.powerSeriesEquivSubring", "kind": "abbrev", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LaurentSeries.powerSeriesEquivSubring_apply", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LaurentSeries.powerSeriesEquivSubring_coe_apply", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LaurentSeries.mem_integers_of_powerSeries", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": true, "tactics": ["simp", "exact", "series"], "tactic_count": 3}
{"name": "LaurentSeries.exists_powerSeries_of_memIntegers", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": true, "tactics": ["set", "have", "congr_fun", "rw", "obtain", "exact"], "tactic_count": 6}
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{"name": "LaurentSeries.powerSeriesRingEquiv", "kind": "abbrev", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LaurentSeries.powerSeriesRingEquiv_coe_apply", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LaurentSeries.LaurentSeriesRingEquiv_mem_valuationSubring", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": true, "tactics": ["simp", "rw", "use"], "tactic_count": 3}
{"name": "LaurentSeries.algebraMap_C_mem_adicCompletionIntegers", "kind": "theorem", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": true, "tactics": ["have", "simp", "apply"], "tactic_count": 3}
{"name": "LaurentSeries.instAlgebraSubtypeAdicCompletionPolynomialRatFuncIdealXMemValuationSubringAdicCompletionIntegers", "kind": "instance", "module": "Mathlib.RingTheory.LaurentSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Module.length", "kind": "definition", "module": "Mathlib.RingTheory.Length", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.coe_length", "kind": "theorem", "module": "Mathlib.RingTheory.Length", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.length_eq_height", "kind": "theorem", "module": "Mathlib.RingTheory.Length", "is_tactic_proof": true, "tactics": ["apply", "rw"], "tactic_count": 2}
{"name": "Module.length_eq_coheight", "kind": "theorem", "module": "Mathlib.RingTheory.Length", "is_tactic_proof": true, "tactics": ["apply", "rw"], "tactic_count": 2}
{"name": "Module.length_eq_zero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Length", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Module.length_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Length", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.length_eq_zero_of_subsingleton_ring", "kind": "theorem", "module": "Mathlib.RingTheory.Length", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.length_pos_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Length", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Module.length_pos", "kind": "theorem", "module": "Mathlib.RingTheory.Length", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.length_compositionSeries", "kind": "theorem", "module": "Mathlib.RingTheory.Length", "is_tactic_proof": true, "tactics": ["have", "have", "have", "rw", "apply", "exact", "rw", "intro", "refine", "obtain", "have", "have", "have", "simpa"], "tactic_count": 14}
{"name": "Module.length_eq_top_iff_infiniteDimensionalOrder", "kind": "theorem", "module": "Mathlib.RingTheory.Length", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Module.length_ne_top_iff_finiteDimensionalOrder", "kind": "theorem", "module": "Mathlib.RingTheory.Length", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Module.length_ne_top_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Length", "is_tactic_proof": true, "tactics": ["refine", "rw", "rw", "let", "change", "exact", "obtain", "rw", "simp"], "tactic_count": 9}
{"name": "Module.length_ne_top", "kind": "theorem", "module": "Mathlib.RingTheory.Length", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Module.length_submodule", "kind": "theorem", "module": "Mathlib.RingTheory.Length", "is_tactic_proof": true, "tactics": ["apply", "rw"], "tactic_count": 2}
{"name": "Module.length_quotient", "kind": "theorem", "module": "Mathlib.RingTheory.Length", "is_tactic_proof": true, "tactics": ["apply", "rw"], "tactic_count": 2}
{"name": "LinearEquiv.length_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Length", "is_tactic_proof": true, "tactics": ["apply", "rw"], "tactic_count": 2}
{"name": "Module.length_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Length", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.length_top", "kind": "theorem", "module": "Mathlib.RingTheory.Length", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submodule.height_lt_top", "kind": "theorem", "module": "Mathlib.RingTheory.Length", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Submodule.height_strictMono", "kind": "theorem", "module": "Mathlib.RingTheory.Length", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.length_lt", "kind": "theorem", "module": "Mathlib.RingTheory.Length", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Module.length_eq_add_of_exact", "kind": "theorem", "module": "Mathlib.RingTheory.Length", "is_tactic_proof": true, "tactics": ["by_cases", "by_cases", "obtain", "obtain", "let", "let", "have", "rw", "let", "rw", "simp_rw", "have", "rw", "rw", "have", "rw", "rw"], "tactic_count": 17}
{"name": "Module.length_le_of_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Length", "is_tactic_proof": false, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Module.length_le_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Length", "is_tactic_proof": false, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Module.length_prod", "kind": "theorem", "module": "Mathlib.RingTheory.Length", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.length_pi_of_fintype", "kind": "theorem", "module": "Mathlib.RingTheory.Length", "is_tactic_proof": true, "tactics": ["apply", "intro", "let", "rw", "intro", "simp", "intro", "rw"], "tactic_count": 8}
{"name": "Module.length_finsupp", "kind": "theorem", "module": "Mathlib.RingTheory.Length", "is_tactic_proof": true, "tactics": ["cases", "cases", "simp", "nontriviality", "rw", "intro", "obtain", "have", "refine", "le_trans", "rw", "exact"], "tactic_count": 12}
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{"name": "Module.length_of_free", "kind": "theorem", "module": "Mathlib.RingTheory.Length", "is_tactic_proof": true, "tactics": ["let", "nontriviality", "nontriviality", "by_cases", "rw", "congr", "simp", "rw", "cases", "let", "rw"], "tactic_count": 11}
{"name": "Module.length_of_free_of_finite", "kind": "theorem", "module": "Mathlib.RingTheory.Length", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Module.length_eq_one_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Length", "is_tactic_proof": true, "tactics": ["rw", "isSimpleModule_iff]"], "tactic_count": 2}
{"name": "Module.length_eq_one", "kind": "theorem", "module": "Mathlib.RingTheory.Length", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.length_eq_rank", "kind": "theorem", "module": "Mathlib.RingTheory.Length", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Module.length_eq_finrank", "kind": "theorem", "module": "Mathlib.RingTheory.Length", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Subalgebra.LinearDisjoint", "kind": "abbrev", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.linearDisjoint_iff", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.LinearDisjoint.of_subsingleton", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.LinearDisjoint.of_subsingleton_top", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.LinearDisjoint.symm_of_commute", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.linearDisjoint_comm_of_commute", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.LinearDisjoint.map", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.LinearDisjoint.bot_left", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Subalgebra.LinearDisjoint.bot_right", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Subalgebra.LinearDisjoint.include_range", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": true, "tactics": ["rw", "change", "rw", "exact"], "tactic_count": 4}
{"name": "Subalgebra.LinearDisjoint.symm", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.linearDisjoint_comm", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.linearDisjoint_iff_injective", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Subalgebra.LinearDisjoint.mulMap", "kind": "definition", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.LinearDisjoint.val_mulMap_tmul", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.LinearDisjoint.mulMapLeftOfSupEqTop", "kind": "definition", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.LinearDisjoint.mulMapLeftOfSupEqTop_tmul", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.LinearDisjoint.basisOfBasisRight", "kind": "definition", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.LinearDisjoint.algebraMap_basisOfBasisRight_apply", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Subalgebra.LinearDisjoint.mulMapLeftOfSupEqTop_symm_apply", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.LinearDisjoint.algebraMap_basisOfBasisRight_repr_apply", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Subalgebra.LinearDisjoint.leftMulMatrix_basisOfBasisRight_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Subalgebra.LinearDisjoint.basisOfBasisLeft", "kind": "definition", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.LinearDisjoint.basisOfBasisLeft_apply", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.LinearDisjoint.basisOfBasisLeft_repr_apply", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.LinearDisjoint.sup_free_of_free", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.LinearDisjoint.isDomain", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.LinearDisjoint.isDomain_of_injective", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.LinearDisjoint.mulLeftMap_ker_eq_bot_iff_linearIndependent_op", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": true, "tactics": ["simp_rw", "let", "let", "suffices", "change", "simp_rw", "ext", "simp", "exact"], "tactic_count": 9}
{"name": "Subalgebra.LinearDisjoint.linearIndependent_left_op_of_flat", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "Subalgebra.LinearDisjoint.of_basis_left_op", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Subalgebra.LinearDisjoint.mulRightMap_ker_eq_bot_iff_linearIndependent", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": true, "tactics": ["simp_rw", "let", "let", "suffices", "ext", "simp", "exact"], "tactic_count": 7}
{"name": "Subalgebra.LinearDisjoint.linearIndependent_right_of_flat", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "Subalgebra.LinearDisjoint.of_basis_right", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Subalgebra.LinearDisjoint.linearIndependent_left_of_flat_of_commute", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.LinearDisjoint.of_basis_left_of_commute", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.LinearDisjoint.linearIndependent_mul_of_flat_left", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.LinearDisjoint.linearIndependent_mul_of_flat_right", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.LinearDisjoint.linearIndependent_mul_of_flat", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.LinearDisjoint.of_basis_mul", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.LinearDisjoint.of_le_left_of_flat", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.LinearDisjoint.of_le_right_of_flat", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.LinearDisjoint.of_le_of_flat_right", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.LinearDisjoint.of_le_of_flat_left", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.LinearDisjoint.rank_inf_eq_one_of_commute_of_flat_of_inj", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": true, "tactics": ["nontriviality", "refine", "have", "lift_rank_range_of_injective", "rw", "rw", "change", "exact"], "tactic_count": 8}
{"name": "Subalgebra.LinearDisjoint.rank_inf_eq_one_of_commute_of_flat_left_of_inj", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.LinearDisjoint.rank_inf_eq_one_of_commute_of_flat_right_of_inj", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.LinearDisjoint.rank_eq_one_of_commute_of_flat_of_self_of_inj", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Subalgebra.LinearDisjoint.trace_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": true, "tactics": ["simp_rw", "leftMulMatrix_basisOfBasisRight_algebraMap,"], "tactic_count": 2}
{"name": "Subalgebra.LinearDisjoint.norm_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": true, "tactics": ["simp_rw", "leftMulMatrix_basisOfBasisRight_algebraMap,"], "tactic_count": 2}
{"name": "Subalgebra.LinearDisjoint.linearIndependent_left_of_flat", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.LinearDisjoint.of_basis_left", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.LinearDisjoint.exists_field_of_isDomain_of_injective", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.LinearDisjoint.of_isField", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": true, "tactics": ["nontriviality", "rw", "letI", "letI", "exact"], "tactic_count": 5}
{"name": "Subalgebra.LinearDisjoint.of_isField'", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": true, "tactics": ["apply", "exact"], "tactic_count": 2}
{"name": "Algebra.TensorProduct.not_isField_of_transcendental", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.TensorProduct.isAlgebraic_of_isField", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": true, "tactics": ["by_contra", "simp_rw", "obtain", "exact"], "tactic_count": 4}
{"name": "Subalgebra.LinearDisjoint.rank_inf_eq_one_of_flat_of_inj", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.LinearDisjoint.rank_inf_eq_one_of_flat_left_of_inj", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.LinearDisjoint.rank_inf_eq_one_of_flat_right_of_inj", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.LinearDisjoint.rank_eq_one_of_flat_of_self_of_inj", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.LinearDisjoint.rank_sup_of_free", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": true, "tactics": ["nontriviality", "rw"], "tactic_count": 2}
{"name": "Subalgebra.LinearDisjoint.finrank_sup_of_free", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Subalgebra.LinearDisjoint.of_finrank_sup_of_free", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": true, "tactics": ["nontriviality", "rw", "obtain", "rw", "let", "replace", "have", "haveI", "rw", "exact"], "tactic_count": 10}
{"name": "Subalgebra.LinearDisjoint.adjoin_rank_eq_rank_left", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": false, "tactics": ["rw", "change", "have", "rw"], "tactic_count": 4}
{"name": "Subalgebra.LinearDisjoint.adjoin_rank_eq_rank_right", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.LinearDisjoint.of_finrank_coprime_of_free", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": true, "tactics": ["nontriviality", "by_cases", "rw", "rw", "exact", "by_cases", "rw", "rw", "exact", "haveI", "haveI", "haveI", "have", "exact", "of_finrank_sup_of_free"], "tactic_count": 15}
{"name": "Subalgebra.LinearDisjoint.of_linearDisjoint_finite_left", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": true, "tactics": ["rw", "intro", "obtain", "obtain", "have", "let", "have", "fg_adjoin_of_finite", "replace", "have", "replace", "have", "rfl", "rw", "exact", "obtain", "obtain", "rw", "exact"], "tactic_count": 19}
{"name": "Subalgebra.LinearDisjoint.of_linearDisjoint_finite_right", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.LinearDisjoint.of_linearDisjoint_finite", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.LinearDisjoint.inf_eq_bot_of_commute", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.LinearDisjoint.eq_bot_of_commute_of_self", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Subalgebra.LinearDisjoint.inf_eq_bot", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.LinearDisjoint.eq_bot_of_self", "kind": "theorem", "module": "Mathlib.RingTheory.LinearDisjoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.LittleWedderburn.0.LittleWedderburn.InductionHyp", "kind": "definition", "module": "Mathlib.RingTheory.LittleWedderburn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.LittleWedderburn.0.LittleWedderburn.InductionHyp.field", "kind": "definition", "module": "Mathlib.RingTheory.LittleWedderburn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.LittleWedderburn.0.LittleWedderburn.InductionHyp.center_eq_top", "kind": "theorem", "module": "Mathlib.RingTheory.LittleWedderburn", "is_tactic_proof": true, "tactics": ["classical", "cases", "set", "by_contra", "letI", "set", "have", "let", "have", "have", "have", "rw", "card_D]", "let", "apply_fun", "rw", "suffices", "have", "rw", "refine", "exact", "convert", "clear_value", "simp", "by_contra", "obtain", "refine", "obtain", "obtain", "rw", "rw", "apply", "rintro", "simp", "set", "rw", "card_units,", "have", "by_contra", "refine", "exact", "letI", "letI", "let", "have", "have", "haveI", "rw", "apply", "have", "simp", "rw", "refine", "refine", "rw", "obtain", "refine", "rintro", "exact"], "tactic_count": 59}
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{"name": "littleWedderburn", "kind": "instance", "module": "Mathlib.RingTheory.LittleWedderburn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finite.isDomain_to_isField", "kind": "theorem", "module": "Mathlib.RingTheory.LittleWedderburn", "is_tactic_proof": true, "tactics": ["classical", "cases", "let", "let", "exact"], "tactic_count": 5}
{"name": "LocalizationPreserves", "kind": "definition", "module": "Mathlib.RingTheory.LocalProperties.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OfLocalizationMaximal", "kind": "definition", "module": "Mathlib.RingTheory.LocalProperties.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.ContainsIdentities", "kind": "definition", "module": "Mathlib.RingTheory.LocalProperties.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.LocalizationPreserves", "kind": "definition", "module": "Mathlib.RingTheory.LocalProperties.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.LocalizationAwayPreserves", "kind": "definition", "module": "Mathlib.RingTheory.LocalProperties.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.OfLocalizationFiniteSpan", "kind": "definition", "module": "Mathlib.RingTheory.LocalProperties.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.OfLocalizationSpan", "kind": "definition", "module": "Mathlib.RingTheory.LocalProperties.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.HoldsForLocalization", "kind": "definition", "module": "Mathlib.RingTheory.LocalProperties.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.HoldsForLocalizationAway", "kind": "definition", "module": "Mathlib.RingTheory.LocalProperties.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.StableUnderCompositionWithLocalizationAwaySource", "kind": "definition", "module": "Mathlib.RingTheory.LocalProperties.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.StableUnderCompositionWithLocalizationAwayTarget", "kind": "definition", "module": "Mathlib.RingTheory.LocalProperties.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.StableUnderCompositionWithLocalizationAway", "kind": "definition", "module": "Mathlib.RingTheory.LocalProperties.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.OfLocalizationFiniteSpanTarget", "kind": "definition", "module": "Mathlib.RingTheory.LocalProperties.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.OfLocalizationSpanTarget", "kind": "definition", "module": "Mathlib.RingTheory.LocalProperties.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.OfLocalizationPrime", "kind": "definition", "module": "Mathlib.RingTheory.LocalProperties.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.ofLocalizationSpan_iff_finite", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Basic", "is_tactic_proof": true, "tactics": ["delta", "apply", "intros", "constructor", "intro", "intro", "obtain", "exact"], "tactic_count": 8}
{"name": "RingHom.ofLocalizationSpanTarget_iff_finite", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Basic", "is_tactic_proof": true, "tactics": ["delta", "apply", "intros", "constructor", "intro", "intro", "obtain", "exact"], "tactic_count": 8}
{"name": "RingHom.OfLocalizationSpan.mk", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Basic", "is_tactic_proof": true, "tactics": ["introv", "algebraize", "let", "refine", "have", "algebraMap", "apply", "ext", "simp", "rw", "exact"], "tactic_count": 11}
{"name": "RingHom.HoldsForLocalization.mk", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Basic", "is_tactic_proof": true, "tactics": ["introv", "rw", "exact"], "tactic_count": 3}
{"name": "RingHom.HoldsForLocalization.holdsForLocalizationAway", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.HoldsForLocalization.isLocalizationMap", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Basic", "is_tactic_proof": true, "tactics": ["have", "letI", "have", "have", "have", "apply", "ext", "simp", "rw", "exact"], "tactic_count": 10}
{"name": "RingHom.HoldsForLocalization.localRingHom", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.HoldsForLocalizationAway.of_bijective", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Basic", "is_tactic_proof": true, "tactics": ["letI", "have", "have", "exact"], "tactic_count": 4}
{"name": "RingHom.StableUnderComposition.stableUnderCompositionWithLocalizationAway", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Basic", "is_tactic_proof": true, "tactics": ["constructor", "introv", "exact", "introv", "exact"], "tactic_count": 5}
{"name": "RingHom.HoldsForLocalizationAway.containsIdentities", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Basic", "is_tactic_proof": true, "tactics": ["introv", "exact"], "tactic_count": 2}
{"name": "RingHom.LocalizationAwayPreserves.respectsIso", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.StableUnderCompositionWithLocalizationAway.respectsIso", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.PropertyIsLocal.respectsIso", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.LocalizationPreserves.away", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Basic", "is_tactic_proof": true, "tactics": ["intro", "have", "exact"], "tactic_count": 3}
{"name": "RingHom.PropertyIsLocal.HoldsForLocalizationAway", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Basic", "is_tactic_proof": true, "tactics": ["introv", "have", "rw", "apply", "apply"], "tactic_count": 5}
{"name": "RingHom.OfLocalizationSpanTarget.ofLocalizationSpan", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Basic", "is_tactic_proof": true, "tactics": ["introv", "apply_fun", "rw", "apply", "rintro", "rw", "apply", "exact"], "tactic_count": 8}
{"name": "RingHom.OfLocalizationSpan.ofIsLocalization", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Basic", "is_tactic_proof": true, "tactics": ["apply", "intro", "obtain", "let", "let", "have", "apply", "ext", "have", "simp", "rw", "apply", "apply", "exact"], "tactic_count": 14}
{"name": "RingHom.OfLocalizationSpan.ofIsLocalization'", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Basic", "is_tactic_proof": true, "tactics": ["apply", "intro", "obtain", "exact"], "tactic_count": 4}
{"name": "RingHom.OfLocalizationSpanTarget.ofIsLocalization", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Basic", "is_tactic_proof": true, "tactics": ["apply", "intro", "obtain", "convert", "rw"], "tactic_count": 5}
{"name": "RingHom.OfLocalizationSpanTarget.and", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Basic", "is_tactic_proof": true, "tactics": ["introv", "exact"], "tactic_count": 2}
{"name": "RingHom.OfLocalizationSpan.and", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Basic", "is_tactic_proof": true, "tactics": ["introv", "exact"], "tactic_count": 2}
{"name": "RingHom.LocalizationAwayPreserves.and", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Basic", "is_tactic_proof": true, "tactics": ["introv", "exact"], "tactic_count": 2}
{"name": "RingHom.StableUnderCompositionWithLocalizationAwayTarget.and", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Basic", "is_tactic_proof": true, "tactics": ["introv", "exact"], "tactic_count": 2}
{"name": "RingHom.PropertyIsLocal.and", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.IsStableUnderBaseChange.of_isLocalization", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.IsStableUnderBaseChange.isLocalization_map", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Basic", "is_tactic_proof": false, "tactics": ["algebraize", "haveI", "haveI", "apply"], "tactic_count": 4}
{"name": "RingHom.IsStableUnderBaseChange.localizationPreserves", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Basic", "is_tactic_proof": true, "tactics": ["introv", "exact"], "tactic_count": 2}
{"name": "Ideal.localized'_eq_map", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.localized₀_eq_restrictScalars_map", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.idealMap_eq_ofEq_comp_toLocalized₀", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.mem_of_localization_maximal", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.le_of_localization_maximal", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.eq_of_localization_maximal", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ideal_eq_bot_of_localization'", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_zero_of_localization", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ideal_eq_bot_of_localization", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "injective_of_isLocalized_maximal", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Exactness", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "surjective_of_isLocalized_maximal", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Exactness", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bijective_of_isLocalized_maximal", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Exactness", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exact_of_isLocalized_maximal", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Exactness", "is_tactic_proof": true, "tactics": ["simp", "apply", "intro", "rw", "have", "ext", "simp", "exact"], "tactic_count": 8}
{"name": "LinearIndependent.of_isLocalized_maximal", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Exactness", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "injective_of_localized_maximal", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Exactness", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "surjective_of_localized_maximal", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Exactness", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bijective_of_localized_maximal", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Exactness", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exact_of_localized_maximal", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Exactness", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "injective_of_isLocalized_span", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Exactness", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "surjective_of_isLocalized_span", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Exactness", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bijective_of_isLocalized_span", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Exactness", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exact_of_isLocalized_span", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Exactness", "is_tactic_proof": true, "tactics": ["simp", "apply", "intro", "rw", "rw", "have", "ext", "simp", "exact"], "tactic_count": 9}
{"name": "injective_of_localized_span", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Exactness", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "surjective_of_localized_span", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Exactness", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bijective_of_localized_span", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Exactness", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exact_of_localized_span", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Exactness", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalizedModule.map_linearMap_of_isLocalization", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Exactness", "is_tactic_proof": false, "tactics": ["apply", "ext", "simp", "rw", "simp"], "tactic_count": 5}
{"name": "injective_of_isLocalization_isMaximal", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Exactness", "is_tactic_proof": false, "tactics": ["apply", "injective_of_isLocalized_maximal", "intro", "convert_to", "rw", "apply", "exact"], "tactic_count": 7}
{"name": "surjective_of_isLocalization_isMaximal", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Exactness", "is_tactic_proof": false, "tactics": ["apply", "surjective_of_isLocalized_maximal", "intro", "convert_to", "rw", "apply", "exact"], "tactic_count": 7}
{"name": "bijective_of_isLocalization_isMaximal", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Exactness", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "injective_of_isLocalization_of_span_eq_top", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Exactness", "is_tactic_proof": true, "tactics": ["algebraize", "letI", "have", "have", "letI", "have", "apply", "injective_of_isLocalized_span", "simpa"], "tactic_count": 9}
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{"name": "bijective_of_isLocalization_of_span_eq_top", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Exactness", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegrallyClosed.iInf", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.IntegrallyClosed", "is_tactic_proof": true, "tactics": ["refine", "intro", "have", "algebraize", "have", "rcases", "rwa"], "tactic_count": 7}
{"name": "IsIntegrallyClosed.of_iInf_eq_bot", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.IntegrallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegrallyClosed.of_localization_submonoid", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.IntegrallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegrallyClosed.of_localization", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.IntegrallyClosed", "is_tactic_proof": false, "tactics": ["apply", "ext", "simp"], "tactic_count": 3}
{"name": "IsIntegrallyClosed.of_localization_maximal", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.IntegrallyClosed", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "refine", "rintro", "exact", "rw", "convert", "rw"], "tactic_count": 8}
{"name": "isIntegrallyClosed_ofLocalizationMaximal", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.IntegrallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegrallyClosed.of_isLocalization_maximal", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.IntegrallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.free_of_isLocalizedModule", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Projective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.lift_rank_of_isLocalizedModule_of_free", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Projective", "is_tactic_proof": true, "tactics": ["apply", "have", "have", "simp", "convert", "exact"], "tactic_count": 6}
{"name": "Module.finrank_of_isLocalizedModule_of_free", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Projective", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Module.projective_of_isLocalizedModule", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Projective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.split_surjective_of_localization_maximal", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Projective", "is_tactic_proof": true, "tactics": ["change", "refine", "rw", "have", "convert", "ext", "constructor", "intro", "obtain", "obtain", "use", "apply", "dsimp", "conv_rhs", "conv_lhs", "rw", "apply", "apply", "exact", "ext", "simp", "rintro", "obtain", "simp", "refine", "apply", "simp", "apply", "apply", "exact", "ext", "simp"], "tactic_count": 32}
{"name": "Module.projective_of_localization_maximal", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Projective", "is_tactic_proof": true, "tactics": ["have", "obtain", "let", "let", "have", "rw", "convert", "have", "letI", "obtain", "exact"], "tactic_count": 11}
{"name": "Module.projective_of_localization_maximal'", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Projective", "is_tactic_proof": true, "tactics": ["apply", "intro", "refine", "map_smul", "intro", "obtain", "apply", "dsimp", "simp"], "tactic_count": 9}
{"name": "isReduced_localizationPreserves", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Reduced", "is_tactic_proof": true, "tactics": ["introv", "constructor", "rintro", "simpa", "obtain", "dsimp", "let", "simp", "rw", "obtain", "apply_fun", "simp", "rw", "replace", "rw", "exact"], "tactic_count": 16}
{"name": "instIsReducedLocalization", "kind": "instance", "module": "Mathlib.RingTheory.LocalProperties.Reduced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isReduced_ofLocalizationMaximal", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Reduced", "is_tactic_proof": true, "tactics": ["introv", "constructor", "intro", "apply", "intro", "specialize", "exact"], "tactic_count": 7}
{"name": "Module.Finite.of_isLocalized_maximal", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Semilocal", "is_tactic_proof": true, "tactics": ["classical", "have", "choose", "choose", "use", "refine", "rw", "intro", "lift", "rw", "exact"], "tactic_count": 11}
{"name": "Submodule.fg_of_isLocalized_maximal", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Semilocal", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Module.Finite.of_localized_maximal", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Semilocal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.fg_of_localized_maximal", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Semilocal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsNoetherianRing.of_isLocalization_maximal", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Semilocal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isPrincipalIdealRing_of_isPrincipalIdealRing_isLocalization_maximal", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Semilocal", "is_tactic_proof": true, "tactics": ["have", "have", "refine", "have", "infer_instance", "have", "rw", "have", "have", "rw", "exact", "exact"], "tactic_count": 12}
{"name": "Submodule.mem_of_localization_maximal", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Submodule", "is_tactic_proof": true, "tactics": ["let", "suffices", "refine", "obtain", "rw", "obtain", "simp_rw", "exact"], "tactic_count": 8}
{"name": "Submodule.le_of_localization_maximal", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.eq_of_localization₀_maximal", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.eq_bot_of_localization₀_maximal", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.eq_top_of_localization₀_maximal", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.eq_of_localization_maximal", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Submodule", "is_tactic_proof": true, "tactics": ["rw", "by_contra", "have", "have", "exact"], "tactic_count": 5}
{"name": "Module.eq_zero_of_localization_maximal", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.eq_of_localization_maximal", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.subsingleton_of_localization_maximal", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Submodule", "is_tactic_proof": true, "tactics": ["rw", "intro", "exact"], "tactic_count": 3}
{"name": "Submodule.eq_of_localization_maximal", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.eq_bot_of_localization_maximal", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.eq_top_of_localization_maximal", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.eq_of_isLocalized_span", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Submodule", "is_tactic_proof": true, "tactics": ["suffices", "by_contra", "have", "let", "have", "exact"], "tactic_count": 6}
{"name": "Module.eq_zero_of_isLocalized_span", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mem_of_isLocalized_span", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Submodule", "is_tactic_proof": true, "tactics": ["let", "suffices", "by_contra", "have", "let", "obtain", "rw", "have", "simp_rw", "exact"], "tactic_count": 10}
{"name": "Submodule.le_of_isLocalized_span", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.eq_of_isLocalized₀_span", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.eq_bot_of_isLocalized₀_span", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.eq_top_of_isLocalized₀_span", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.eq_of_isLocalized'_span", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.eq_bot_of_isLocalized'_span", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.eq_top_of_isLocalized'_span", "kind": "theorem", "module": "Mathlib.RingTheory.LocalProperties.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.of_isUnit_or_isUnit_of_isUnit_add", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.of_nonunits_add", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.of_unique_max_ideal", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.of_unique_nonzero_prime", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.isUnit_or_isUnit_of_isUnit_add", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.Basic", "is_tactic_proof": true, "tactics": ["rcases", "rw", "apply"], "tactic_count": 3}
{"name": "IsLocalRing.nonunits_add", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.of_isUnit_or_isUnit_one_sub_self", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.isUnit_or_isUnit_one_sub_self", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.isUnit_of_mem_nonunits_one_sub_self", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.isUnit_one_sub_self_of_mem_nonunits", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.of_surjective'", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Field.instIsLocalRing", "kind": "instance", "module": "Mathlib.RingTheory.LocalRing.Basic", "is_tactic_proof": true, "tactics": ["classical", "exact"], "tactic_count": 2}
{"name": "instIsLocalRingSubtypeMemSubringMapOfNontrivial", "kind": "instance", "module": "Mathlib.RingTheory.LocalRing.LocalSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLocalRing_top", "kind": "instance", "module": "Mathlib.RingTheory.LocalRing.LocalSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocalSubring.toSubring_injective", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.LocalSubring", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "LocalSubring.copy", "kind": "definition", "module": "Mathlib.RingTheory.LocalRing.LocalSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocalSubring.map", "kind": "definition", "module": "Mathlib.RingTheory.LocalRing.LocalSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocalSubring.range", "kind": "definition", "module": "Mathlib.RingTheory.LocalRing.LocalSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocalSubring.instPartialOrder", "kind": "instance", "module": "Mathlib.RingTheory.LocalRing.LocalSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocalSubring.le_def", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.LocalSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocalSubring.toSubring_mono", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.LocalSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocalSubring.ofPrime", "kind": "definition", "module": "Mathlib.RingTheory.LocalRing.LocalSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocalSubring.le_ofPrime", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.LocalSubring", "is_tactic_proof": true, "tactics": ["intro", "exact"], "tactic_count": 2}
{"name": "LocalSubring.instAlgebraSubtypeMemSubringToSubringOfPrime", "kind": "instance", "module": "Mathlib.RingTheory.LocalRing.LocalSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocalSubring.instIsScalarTowerSubtypeMemSubringToSubringOfPrime", "kind": "instance", "module": "Mathlib.RingTheory.LocalRing.LocalSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocalSubring.ofPrimeEquiv", "kind": "definition", "module": "Mathlib.RingTheory.LocalRing.LocalSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocalSubring.instAtPrimeSubtypeMemSubringToSubringOfPrime", "kind": "instance", "module": "Mathlib.RingTheory.LocalRing.LocalSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.mem_maximalIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.MaximalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.maximalIdeal.isMaximal", "kind": "instance", "module": "Mathlib.RingTheory.LocalRing.MaximalIdeal.Basic", "is_tactic_proof": true, "tactics": ["rw", "constructor", "intro", "apply", "exact", "intro", "rw", "rcases", "simpa"], "tactic_count": 9}
{"name": "IsLocalRing.isMaximal_iff", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.MaximalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.maximal_ideal_unique", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.MaximalIdeal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsLocalRing.eq_maximalIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.MaximalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.instUniqueMaximalSpectrum", "kind": "instance", "module": "Mathlib.RingTheory.LocalRing.MaximalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.of_singleton_maximalSpectrum", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.MaximalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.le_maximalIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.MaximalIdeal.Basic", "is_tactic_proof": true, "tactics": ["rcases", "rwa"], "tactic_count": 2}
{"name": "IsLocalRing.le_maximalIdeal_of_isPrime", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.MaximalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.notMem_maximalIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.MaximalIdeal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsLocalRing.isField_iff_maximalIdeal_eq", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.MaximalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.maximalIdeal_le_jacobson", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.MaximalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.jacobson_eq_maximalIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.MaximalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.ringJacobson_eq_maximalIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.MaximalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.ker_eq_maximalIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.MaximalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.maximalIdeal_eq_bot", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.MaximalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.isLocalRing_of_unit", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.MaximalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.isLocalRing_of_unit", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.MaximalIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.maximalIdeal", "kind": "definition", "module": "Mathlib.RingTheory.LocalRing.MaximalIdeal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.LocalRing.Module.0.termK", "kind": "definition", "module": "Mathlib.RingTheory.LocalRing.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.LocalRing.Module.0._aux_Mathlib_RingTheory_LocalRing_Module___macroRules__private_Mathlib_RingTheory_LocalRing_Module_0_termK_1", "kind": "definition", "module": "Mathlib.RingTheory.LocalRing.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.LocalRing.Module.0._aux_Mathlib_RingTheory_LocalRing_Module___unexpand_IsLocalRing_ResidueField_1", "kind": "definition", "module": "Mathlib.RingTheory.LocalRing.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.LocalRing.Module.0.term𝔪", "kind": "definition", "module": "Mathlib.RingTheory.LocalRing.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.LocalRing.Module.0._aux_Mathlib_RingTheory_LocalRing_Module___macroRules__private_Mathlib_RingTheory_LocalRing_Module_0_term𝔪_1", "kind": "definition", "module": "Mathlib.RingTheory.LocalRing.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.LocalRing.Module.0._aux_Mathlib_RingTheory_LocalRing_Module___unexpand_IsLocalRing_maximalIdeal_1", "kind": "definition", "module": "Mathlib.RingTheory.LocalRing.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.map_mkQ_eq", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.Module", "is_tactic_proof": true, "tactics": ["constructor", "intro", "have", "rw", "exact", "h.antisymm", "rintro"], "tactic_count": 7}
{"name": "IsLocalRing.map_mkQ_eq_top", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.Module", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsLocalRing.map_tensorProduct_mk_eq_top", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.Module", "is_tactic_proof": true, "tactics": ["constructor", "intro", "letI", "letI", "inferInstanceAs", "let", "have", "have", "intro", "rw", "apply_fun", "rwa", "rintro", "exact"], "tactic_count": 14}
{"name": "IsLocalRing.subsingleton_tensorProduct", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.Module", "is_tactic_proof": true, "tactics": ["rw", "subsingleton_iff_bot_eq_top,"], "tactic_count": 2}
{"name": "IsLocalRing.span_eq_top_of_tmul_eq_basis", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.Module", "is_tactic_proof": false, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Module.mem_support_iff_nontrivial_residueField_tensorProduct", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.Module", "is_tactic_proof": true, "tactics": ["let", "let", "rw", "not_nontrivial_iff_subsingleton,"], "tactic_count": 4}
{"name": "lTensor_injective_of_exact_of_exact_of_rTensor_injective", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.Module", "is_tactic_proof": true, "tactics": ["rw", "intro", "obtain", "have", "rw", "obtain", "have", "apply", "trans", "rw", "rw", "simp", "obtain", "obtain", "apply", "simp", "rw", "simp"], "tactic_count": 18}
{"name": "Module.exists_basis_of_basis_baseChange", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.Module", "is_tactic_proof": true, "tactics": ["let", "haveI", "letI", "let", "have", "rw", "refine", "have", "let", "refine", "rw", "subsingleton_iff_forall_eq", "have", "have", "refine", "rw", "simp", "rw", "intro", "refine", "lTensor_injective_of_exact_of_exact_of_rTensor_injective", "apply", "exact", "apply", "rw", "erw", "rw", "simp", "use", "intro", "simp"], "tactic_count": 31}
{"name": "Module.exists_basis_of_span_of_maximalIdeal_rTensor_injective", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.Module", "is_tactic_proof": true, "tactics": ["have", "rw", "have", "rw", "exact", "obtain", "rw", "obtain", "use"], "tactic_count": 9}
{"name": "Module.exists_basis_of_span_of_flat", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.free_of_maximalIdeal_rTensor_injective", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.Module", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Module.IsLocalRing.linearIndependent_of_flat", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.Module", "is_tactic_proof": true, "tactics": ["rw", "classical", "induction", "empty", "insert", "rw", "have", "have", "set", "obtain", "contrapose", "rw", "exact", "let", "have", "have", "rw", "convert", "simp_rw", "let", "specialize", "convert", "ext", "simp_rw", "rw", "simp_rw", "s.sum_neg_distrib,", "congr", "exact", "obtain", "rw", "intro", "exact"], "tactic_count": 33}
{"name": "Module.IsLocalRing.linearCombination_bijective_of_flat", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.Module", "is_tactic_proof": true, "tactics": ["use", "rw", "refine", "simpa", "simp"], "tactic_count": 5}
{"name": "Module.free_of_flat_of_isLocalRing", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.free_of_lTensor_residueField_injective", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.Module", "is_tactic_proof": false, "tactics": ["have", "apply", "rw", "apply", "lTensor_injective_of_exact_of_exact_of_rTensor_injective"], "tactic_count": 5}
{"name": "IsLocalRing.split_injective_iff_lTensor_residueField_injective", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.Module", "is_tactic_proof": true, "tactics": ["constructor", "intro", "have", "rw", "exact", "intro", "have", "l.exact_map_mkQ_range", "have", "have", "obtain", "exact", "obtain", "have", "rw", "have", "exact", "have", "refine", "exact", "have", "apply_fun", "rw", "exact", "have", "refine", "rw", "l.exact_subtype_ker_map.linearMap_comp_eq_zero,", "have", "rwa", "have", "rw", "exact"], "tactic_count": 33}
{"name": "Module.nonempty_basis_of_flat_of_finrank_eq", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.Module", "is_tactic_proof": true, "tactics": ["let", "have", "to", "choose", "pi_tensorProductMk_quotient_surjective", "it", "refine", "bijective_of_isLocalized_maximal", "rw", "which", "apply", "rw", "convert", "refine", "simp"], "tactic_count": 15}
{"name": "Module.free_of_flat_of_finrank_eq", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.not_isLocalRing_def", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.NonLocalRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.not_isLocalRing_of_nontrivial_pi", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.NonLocalRing", "is_tactic_proof": true, "tactics": ["classical", "let", "have", "not_isUnit_zero", "have", "not_isUnit_zero", "exact"], "tactic_count": 7}
{"name": "IsLocalRing.not_isLocalRing_of_prod_of_nontrivial", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.NonLocalRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.not_isLocalRing_tfae", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.NonLocalRing", "is_tactic_proof": false, "tactics": ["tfae_have", "h", "tfae_have", "tfae_have", "tfae_finish"], "tactic_count": 5}
{"name": "IsLocalRing.exists_surjective_of_not_isLocalRing", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.NonLocalRing", "is_tactic_proof": true, "tactics": ["obtain", "let", "let", "use", "apply"], "tactic_count": 5}
{"name": "_private.Mathlib.RingTheory.LocalRing.Quotient.0.IsLocalRing.termP", "kind": "definition", "module": "Mathlib.RingTheory.LocalRing.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.LocalRing.Quotient.0.IsLocalRing._aux_Mathlib_RingTheory_LocalRing_Quotient___macroRules__private_Mathlib_RingTheory_LocalRing_Quotient_0_IsLocalRing_termP_1", "kind": "definition", "module": "Mathlib.RingTheory.LocalRing.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.LocalRing.Quotient.0.IsLocalRing._aux_Mathlib_RingTheory_LocalRing_Quotient___unexpand_IsLocalRing_maximalIdeal_1", "kind": "definition", "module": "Mathlib.RingTheory.LocalRing.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.LocalRing.Quotient.0.IsLocalRing.termPS", "kind": "definition", "module": "Mathlib.RingTheory.LocalRing.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.LocalRing.Quotient.0.IsLocalRing._aux_Mathlib_RingTheory_LocalRing_Quotient___macroRules__private_Mathlib_RingTheory_LocalRing_Quotient_0_IsLocalRing_termPS_1", "kind": "definition", "module": "Mathlib.RingTheory.LocalRing.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.LocalRing.Quotient.0.IsLocalRing._aux_Mathlib_RingTheory_LocalRing_Quotient___unexpand_Ideal_map_1", "kind": "definition", "module": "Mathlib.RingTheory.LocalRing.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.quotient_span_eq_top_iff_span_eq_top", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.Quotient", "is_tactic_proof": false, "tactics": ["have", "rw", "constructor", "intro", "rw", "apply", "exact", "exact", "rw", "rintro", "have", "simp", "rw", "exact", "intro", "rwa", "rw", "exact"], "tactic_count": 18}
{"name": "IsLocalRing.finrank_quotient_map", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.Quotient", "is_tactic_proof": true, "tactics": ["classical", "have", "apply", "let", "conv_rhs", "apply", "rw", "apply", "let", "choose", "conv_rhs", "refine", "apply", "rw", "exact"], "tactic_count": 15}
{"name": "IsLocalRing.basisQuotient", "kind": "definition", "module": "Mathlib.RingTheory.LocalRing.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.basisQuotient_apply", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.Quotient", "is_tactic_proof": true, "tactics": ["delta", "rw"], "tactic_count": 2}
{"name": "IsLocalRing.basisQuotient_repr", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.Quotient", "is_tactic_proof": true, "tactics": ["refine", "apply", "apply", "simp", "rw", "simp", "rw"], "tactic_count": 7}
{"name": "IsLocalRing.exists_maximalIdeal_pow_le_of_isArtinianRing_quotient", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.Quotient", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "have", "have", "have", "obtain", "have", "ext", "obtain", "simp", "rw", "exact"], "tactic_count": 12}
{"name": "IsLocalRing.finite_quotient_iff", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.Quotient", "is_tactic_proof": true, "tactics": ["refine", "rintro", "have", "have", "exact"], "tactic_count": 5}
{"name": "IsLocalRing.residue_def", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.ker_residue", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.residue_eq_zero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsLocalRing.residue_ne_zero_iff_isUnit", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsLocalRing.residue_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.ResidueField.algebra", "kind": "instance", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.instIsScalarTowerResidueField", "kind": "instance", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Basic", "is_tactic_proof": true, "tactics": ["delta"], "tactic_count": 1}
{"name": "IsLocalRing.ResidueField.algebraMap_eq", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.instIsLocalHomResidueFieldRingHomResidue", "kind": "instance", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.instFiniteResidueField", "kind": "instance", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.ResidueField.lift", "kind": "definition", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.ResidueField.lift_comp_residue", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.ResidueField.lift_residue_apply", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.ResidueField.map", "kind": "definition", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.ResidueField.map_id", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.ResidueField.map_comp", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.ResidueField.map_comp_residue", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.ResidueField.map_residue", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.ResidueField.map_id_apply", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.ResidueField.map_map", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.ResidueField.mapEquiv", "kind": "definition", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.ResidueField.mapEquiv.symm", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.ResidueField.mapEquiv_trans", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.ResidueField.mapEquiv_refl", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.ResidueField.mapAut", "kind": "definition", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.ResidueField.instMulSemiringAction", "kind": "instance", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.ResidueField.residue_smul", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.ResidueField.instLiesOverMaximalIdeal", "kind": "instance", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.ResidueField.instAlgebra", "kind": "instance", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.ResidueField.algebraMap_residue", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.ResidueField.instIsScalarTower", "kind": "instance", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.ResidueField.instIsScalarTower_1", "kind": "instance", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Basic", "is_tactic_proof": true, "tactics": ["refine", "obtain", "simp"], "tactic_count": 3}
{"name": "IsLocalRing.ResidueField.finite_of_module_finite", "kind": "instance", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.ResidueField.finite_of_finite", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.ResidueField", "kind": "definition", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.ResidueField.field", "kind": "instance", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.residue", "kind": "definition", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.ResidueField.exists_smul_eq_tmul_one", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Fiber", "is_tactic_proof": false, "tactics": ["obtain", "obtain", "obtain", "simp", "not_or,", "refine", "rw", "simpa"], "tactic_count": 8}
{"name": "Ideal.Fiber", "kind": "abbrev", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Fiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.Fiber.exists_smul_eq_one_tmul", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Fiber", "is_tactic_proof": true, "tactics": ["obtain", "refine"], "tactic_count": 2}
{"name": "PrimeSpectrum.preimageEquivFiber", "kind": "definition", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Fiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.preimageOrderIsoFiber", "kind": "definition", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Fiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.primesOverOrderIsoFiber", "kind": "definition", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Fiber", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.preimageHomeomorphFiber", "kind": "definition", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Fiber", "is_tactic_proof": false, "tactics": ["letI", "refine", "have", "exact", "exact", "continuous_toFun", "convert", "ext1", "obtain", "simp", "simp", "continuous_invFun"], "tactic_count": 12}
{"name": "Ideal.ResidueField", "kind": "abbrev", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.ResidueField.map", "kind": "abbrev", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.ResidueField.map_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Ideal", "is_tactic_proof": true, "tactics": ["rw", "simp", "rfl"], "tactic_count": 3}
{"name": "RingHom.SurjectiveOnStalks.residueFieldMap_bijective", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Ideal", "is_tactic_proof": true, "tactics": ["subst", "exact"], "tactic_count": 2}
{"name": "Ideal.ResidueField.mapₐ", "kind": "definition", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.ResidueField.mapₐ_apply", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.algebraMap_residueField_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Ideal", "is_tactic_proof": false, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Ideal.ker_algebraMap_residueField", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instAlgebraQuotientIdealResidueField", "kind": "instance", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsScalarTowerQuotientIdealResidueField", "kind": "instance", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.algebraMap_quotient_residueField_mk", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.injective_algebraMap_quotient_residueField", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Ideal", "is_tactic_proof": true, "tactics": ["rw", "refine", "change", "rw"], "tactic_count": 4}
{"name": "instIsFractionRingQuotientIdealResidueField", "kind": "instance", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.bijective_algebraMap_quotient_residueField", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.algebraMap_residueField_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Ideal", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "instFiniteResidueField", "kind": "instance", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.surjectiveOnStalks_residueField", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsLocalHomAtPrimeRingHomAlgebraMap", "kind": "instance", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.ResidueField.lift", "kind": "definition", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.ResidueField.lift_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Ideal", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Ideal.ResidueField.liftₐ", "kind": "definition", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.ResidueField.liftₐ_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.ResidueField.liftₐ_comp_toAlgHom", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.ResidueField.ringHom_ext", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.ResidueField.algHom_ext", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsSeparableResidueFieldOfQuotientIdeal", "kind": "instance", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Instances", "is_tactic_proof": false, "tactics": ["refine", "ext", "simp"], "tactic_count": 3}
{"name": "instIsSeparableQuotientIdealOfResidueField", "kind": "instance", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Instances", "is_tactic_proof": false, "tactics": ["refine", "apply", "obtain", "obtain", "apply", "simp", "simp"], "tactic_count": 7}
{"name": "Algebra.isSeparable_residueField_iff", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsAlgebraicQuotientIdealResidueField", "kind": "instance", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsAlgebraicResidueFieldOfIsIntegral", "kind": "instance", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Instances", "is_tactic_proof": true, "tactics": ["have", "letI", "haveI", "haveI", "haveI", "refine", "obtain", "simp", "refine"], "tactic_count": 9}
{"name": "Polynomial.residueFieldMapCAlgEquiv", "kind": "definition", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.residueFieldMapCAlgEquiv_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Polynomial", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.residueFieldMapCAlgEquiv_symm_C", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.residueFieldMapCAlgEquiv_symm_X", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.fiberEquivQuotient", "kind": "definition", "module": "Mathlib.RingTheory.LocalRing.ResidueField.Polynomial", "is_tactic_proof": false, "tactics": ["refine", "simp", "change", "rw", "have", "exact", "apply", "ext", "simp", "ext", "obtain", "simpa"], "tactic_count": 12}
{"name": "isLocalHom_id", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.RingHom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLocalHom_toRingHom", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.RingHom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.isLocalHom_comp", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.RingHom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLocalHom_of_comp", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.RingHom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.domain_isLocalRing", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.RingHom.Basic", "is_tactic_proof": true, "tactics": ["haveI", "apply", "intro", "simp_rw", "exact"], "tactic_count": 5}
{"name": "map_nonunit", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.RingHom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.local_hom_TFAE", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.RingHom.Basic", "is_tactic_proof": false, "tactics": ["tfae_have", "tfae_have", "tfae_have", "tfae_have", "tfae_have", "tfae_have", "tfae_finish"], "tactic_count": 7}
{"name": "IsLocalRing.of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.RingHom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalHom.of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.RingHom.Basic", "is_tactic_proof": true, "tactics": ["have", "refine", "have", "exact"], "tactic_count": 4}
{"name": "IsLocalRing.surjective_units_map_of_local_ringHom", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.RingHom.Basic", "is_tactic_proof": true, "tactics": ["intro", "obtain", "use", "ext", "exact"], "tactic_count": 5}
{"name": "IsLocalRing.instIsLocalHomRingHomOfNontrivial", "kind": "instance", "module": "Mathlib.RingTheory.LocalRing.RingHom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.isLocalRing", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.RingHom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsLocalHomZModRingHomOfIsLocalRingOfNontrivial", "kind": "instance", "module": "Mathlib.RingTheory.LocalRing.RingHom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.of_injective", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.Subring", "is_tactic_proof": true, "tactics": ["haveI", "refine", "exact"], "tactic_count": 3}
{"name": "IsLocalRing.of_subring", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.Subring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.of_subring'", "kind": "theorem", "module": "Mathlib.RingTheory.LocalRing.Subring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.idealMap_isLocalizedModule", "kind": "instance", "module": "Mathlib.RingTheory.Localization.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.ker_map", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Algebra", "is_tactic_proof": true, "tactics": ["ext", "obtain", "simp"], "tactic_count": 3}
{"name": "RingHom.toKerIsLocalization", "kind": "definition", "module": "Mathlib.RingTheory.Localization.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.toKerIsLocalization_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.toKerIsLocalization_isLocalizedModule", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Algebra", "is_tactic_proof": true, "tactics": ["let", "convert_to", "apply"], "tactic_count": 3}
{"name": "IsLocalization.isLocalization_algebraMapSubmonoid_map_algHom", "kind": "instance", "module": "Mathlib.RingTheory.Localization.Algebra", "is_tactic_proof": false, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "IsLocalization.mapₐ", "kind": "definition", "module": "Mathlib.RingTheory.Localization.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.mapₐ_coe", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.mapₐ_injective_of_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.mapₐ_surjective_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.mapExtendScalars_eq_toLinearMap_mapₐ", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Algebra", "is_tactic_proof": true, "tactics": ["refine", "apply", "ext", "rw", "simp"], "tactic_count": 5}
{"name": "IsLocalization.map_eq_toLinearMap_mapₐ", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Algebra", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "IsLocalization.map_linearMap_eq_toLinearMap_mapₐ", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.toKerIsLocalization", "kind": "definition", "module": "Mathlib.RingTheory.Localization.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.toKerIsLocalization_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.toKerIsLocalization_isLocalizedModule", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.isLocalization", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.map_isUnit_of_le", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.AsSubring", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "Localization.mapToFractionRing", "kind": "definition", "module": "Mathlib.RingTheory.Localization.AsSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.mapToFractionRing_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.AsSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.mem_range_mapToFractionRing_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.AsSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.isLocalization_range_mapToFractionRing", "kind": "instance", "module": "Mathlib.RingTheory.Localization.AsSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.isFractionRing_range_mapToFractionRing", "kind": "instance", "module": "Mathlib.RingTheory.Localization.AsSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.subalgebra", "kind": "definition", "module": "Mathlib.RingTheory.Localization.AsSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.subalgebra.isLocalization_subalgebra", "kind": "instance", "module": "Mathlib.RingTheory.Localization.AsSubring", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "infer_instance"], "tactic_count": 3}
{"name": "Localization.subalgebra.isFractionRing", "kind": "instance", "module": "Mathlib.RingTheory.Localization.AsSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.subalgebra.mem_range_mapToFractionRing_iff_ofField", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.AsSubring", "is_tactic_proof": true, "tactics": ["rw", "convert", "congr", "rw", "rfl"], "tactic_count": 5}
{"name": "Localization.subalgebra.ofField", "kind": "definition", "module": "Mathlib.RingTheory.Localization.AsSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.subalgebra.ofField_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.AsSubring", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Localization.subalgebra.isLocalization_ofField", "kind": "instance", "module": "Mathlib.RingTheory.Localization.AsSubring", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Localization.subalgebra.instIsFractionRingSubtypeMemSubalgebra", "kind": "instance", "module": "Mathlib.RingTheory.Localization.AsSubring", "is_tactic_proof": true, "tactics": ["refine", "rcases", "exact"], "tactic_count": 3}
{"name": "Localization.subalgebra.isFractionRing_ofField", "kind": "instance", "module": "Mathlib.RingTheory.Localization.AsSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.AtPrime", "kind": "abbrev", "module": "Mathlib.RingTheory.Localization.AtPrime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.AtPrime", "kind": "abbrev", "module": "Mathlib.RingTheory.Localization.AtPrime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.AtPrime.nontrivial", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.AtPrime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.AtPrime.isLocalRing", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.AtPrime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.isDomain_of_local_atPrime", "kind": "instance", "module": "Mathlib.RingTheory.Localization.AtPrime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.AtPrime.isLocalRing", "kind": "instance", "module": "Mathlib.RingTheory.Localization.AtPrime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.instIsTorsionFreeAtPrimeAlgebraMapSubmonoidPrimeComplOfIsDomain", "kind": "instance", "module": "Mathlib.RingTheory.Localization.AtPrime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.AtPrime.faithfulSMul", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.AtPrime.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Localization.instFaithfulSMulAtPrimeOfNoZeroDivisors", "kind": "instance", "module": "Mathlib.RingTheory.Localization.AtPrime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.isDomain_of_atPrime", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.AtPrime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.AtPrime.orderIsoOfPrime", "kind": "definition", "module": "Mathlib.RingTheory.Localization.AtPrime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.AtPrime.primeSpectrumOrderIso", "kind": "definition", "module": "Mathlib.RingTheory.Localization.AtPrime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.AtPrime.isUnit_to_map_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.AtPrime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.AtPrime.isUnit_mk'_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.AtPrime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.AtPrime.comap_maximalIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.AtPrime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.AtPrime.map_eq_maximalIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.AtPrime.Basic", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "Localization.AtPrime.eq_maximalIdeal_iff_comap_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.AtPrime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.le_comap_primeCompl_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.AtPrime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.localRingHom", "kind": "definition", "module": "Mathlib.RingTheory.Localization.AtPrime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.localRingHom_to_map", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.AtPrime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.localRingHom_mk'", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.AtPrime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.isLocalHom_localRingHom", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.AtPrime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.localRingHom_unique", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.AtPrime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.localRingHom_id", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.AtPrime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.localRingHom_comp", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.AtPrime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.AtPrime.instAlgebraOfLiesOver", "kind": "instance", "module": "Mathlib.RingTheory.Localization.AtPrime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.AtPrime.instIsScalarTower", "kind": "instance", "module": "Mathlib.RingTheory.Localization.AtPrime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.AtPrime.instIsScalarTower_1", "kind": "instance", "module": "Mathlib.RingTheory.Localization.AtPrime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.AtPrime.mapPiEvalRingHom", "kind": "abbrev", "module": "Mathlib.RingTheory.Localization.AtPrime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.AtPrime.mapPiEvalRingHom_bijective", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.AtPrime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.AtPrime.mapPiEvalRingHom_comp_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.AtPrime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.AtPrime.mapPiEvalRingHom_algebraMap_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.AtPrime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.isPrime_map_of_isLocalizationAtPrime", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.AtPrime.Basic", "is_tactic_proof": true, "tactics": ["have", "apply"], "tactic_count": 2}
{"name": "Ideal.under_map_of_isLocalizationAtPrime", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.AtPrime.Basic", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "IsLocalization.subsingleton_primeSpectrum_of_mem_minimalPrimes", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.AtPrime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.liesOver_of_isPrime_of_disjoint", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.AtPrime.Basic", "is_tactic_proof": false, "tactics": ["suffices", "rw"], "tactic_count": 2}
{"name": "Ideal.IsMaximal.of_isLocalization_of_disjoint", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.AtPrime.Basic", "is_tactic_proof": false, "tactics": ["obtain", "exists_le_maximal", "rintro", "exact", "apply", "rwa"], "tactic_count": 6}
{"name": "IsLocalization.AtPrime.isPrime_map_of_liesOver", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.AtPrime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.AtPrime.map_eq_maximalIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.AtPrime.Basic", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "IsLocalization.AtPrime.isMaximal_map", "kind": "instance", "module": "Mathlib.RingTheory.Localization.AtPrime.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsLocalization.AtPrime.comap_map_of_isMaximal", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.AtPrime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.AtPrime.equivQuotMaximalIdeal", "kind": "definition", "module": "Mathlib.RingTheory.Localization.AtPrime.Basic", "is_tactic_proof": false, "tactics": ["refine", "rw", "intro", "obtain", "obtain", "obtain", "simp", "use", "rw", "have", "rw", "exact", "refine", "rw", "map_sub,", "rw", "exact"], "tactic_count": 17}
{"name": "IsLocalization.AtPrime.equivQuotMaximalIdeal_apply_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.AtPrime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.AtPrime.equivQuotMaximalIdeal_symm_apply_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.AtPrime.Basic", "is_tactic_proof": false, "tactics": ["have", "simpa", "have", "rw", "equivQuotMaximalIdeal_apply_mk,"], "tactic_count": 5}
{"name": "_private.Mathlib.RingTheory.Localization.AtPrime.Basic.0.IsLocalization.AtPrime.termPS", "kind": "definition", "module": "Mathlib.RingTheory.Localization.AtPrime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Localization.AtPrime.Basic.0.IsLocalization.AtPrime._aux_Mathlib_RingTheory_Localization_AtPrime_Basic___macroRules__private_Mathlib_RingTheory_Localization_AtPrime_Basic_0_IsLocalization_AtPrime_termPS_1", "kind": "definition", "module": "Mathlib.RingTheory.Localization.AtPrime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Localization.AtPrime.Basic.0.IsLocalization.AtPrime._aux_Mathlib_RingTheory_Localization_AtPrime_Basic___unexpand_Ideal_map_1", "kind": "definition", "module": "Mathlib.RingTheory.Localization.AtPrime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Localization.AtPrime.Basic.0.IsLocalization.AtPrime.termPSₚ", "kind": "definition", "module": "Mathlib.RingTheory.Localization.AtPrime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Localization.AtPrime.Basic.0.IsLocalization.AtPrime._aux_Mathlib_RingTheory_Localization_AtPrime_Basic___macroRules__private_Mathlib_RingTheory_Localization_AtPrime_Basic_0_IsLocalization_AtPrime_termPSₚ_1", "kind": "definition", "module": "Mathlib.RingTheory.Localization.AtPrime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Localization.AtPrime.Basic.0.IsLocalization.AtPrime._aux_Mathlib_RingTheory_Localization_AtPrime_Basic___unexpand_Ideal_map_2", "kind": "definition", "module": "Mathlib.RingTheory.Localization.AtPrime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.AtPrime.comap_map_eq_map", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.AtPrime.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply", "intro", "obtain", "have", "rw", "obtain", "obtain", "refine", "rw", "exact", "obtain", "obtain", "refine", "rw", "rwa", "rw", "have", "rw", "refine", "rw", "apply", "exact"], "tactic_count": 23}
{"name": "IsLocalization.AtPrime.equivQuotientMapMaximalIdeal", "kind": "definition", "module": "Mathlib.RingTheory.Localization.AtPrime.Basic", "is_tactic_proof": false, "tactics": ["haveI", "rw", "refine", "rw", "intro", "obtain", "obtain", "obtain", "obtain", "obtain", "refine", "rw", "rwa", "rw", "use", "rw", "map_sub,", "rw", "refine", "rw", "apply", "exact", "simp", "rw"], "tactic_count": 24}
{"name": "IsLocalization.AtPrime.mem_primesOver_of_isPrime", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.AtPrime.Extension", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "IsLocalization.AtPrime.liesOver_comap_of_liesOver", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.AtPrime.Extension", "is_tactic_proof": false, "tactics": ["have", "have", "exact", "exact"], "tactic_count": 4}
{"name": "IsLocalization.AtPrime.liesOver_map_of_liesOver", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.AtPrime.Extension", "is_tactic_proof": true, "tactics": ["rw", "exact", "under_map_eq_map_under"], "tactic_count": 3}
{"name": "IsLocalization.AtPrime.exists_algebraMap_quot_eq_of_mem_quot", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.AtPrime.Extension", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "obtain", "simp", "use", "rw", "have", "have", "have", "rwa", "refine", "rw", "comap_map_eq_self_of_isMaximal", "inv_mul_cancel_right₀"], "tactic_count": 14}
{"name": "IsLocalization.AtPrime.equivQuotientMapOfIsMaximal", "kind": "definition", "module": "Mathlib.RingTheory.Localization.AtPrime.Extension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.AtPrime.equivQuotientMapOfIsMaximal_apply_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.AtPrime.Extension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.AtPrime.equivQuotientMapOfIsMaximal_symm_apply_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.AtPrime.Extension", "is_tactic_proof": true, "tactics": ["have", "have", "have", "rw", "equivQuotientMapOfIsMaximal_apply_mk,", "equivQuotientMapOfIsMaximal_apply_mk,"], "tactic_count": 6}
{"name": "IsLocalization.AtPrime.algebraMap_equivQuotMaximalIdeal_symm_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.AtPrime.Extension", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "simp"], "tactic_count": 3}
{"name": "IsLocalization.AtPrime.equivQuotientMapMaximalIdeal_apply_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.AtPrime.Extension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.AtPrime.inertiaDeg_map_eq_inertiaDeg", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.AtPrime.Extension", "is_tactic_proof": true, "tactics": ["rw", "refine", "ext", "exact"], "tactic_count": 4}
{"name": "IsLocalization.AtPrime.ramificationIdx_map_eq_ramificationIdx", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.AtPrime.Extension", "is_tactic_proof": false, "tactics": ["have", "rw", "exact", "have", "by_cases", "simp_rw", "ramificationIdx_bot", "have", "rw", "exact", "have", "rwa", "ramificationIdx_map_self_eq_one", "rw", "exact"], "tactic_count": 15}
{"name": "IsDedekindDomain.primesOverEquivPrimesOver", "kind": "definition", "module": "Mathlib.RingTheory.Localization.AtPrime.Extension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.primesOverEquivPrimesOver_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.AtPrime.Extension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.primesOverEquivPrimesOver_symm_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.AtPrime.Extension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDedekindDomain.primesOverEquivPrimesOver_inertiagDeg_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.AtPrime.Extension", "is_tactic_proof": true, "tactics": ["have", "have", "have", "exact"], "tactic_count": 4}
{"name": "IsDedekindDomain.primesOverEquivPrimesOver_ramificationIdx_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.AtPrime.Extension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.awayEquivAdjoin", "kind": "definition", "module": "Mathlib.RingTheory.Localization.Away.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.adjoin_inv", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Away.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.Away.finitePresentation", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Away.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.FinitePresentation.of_isLocalizationAway", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Away.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFinitePresentationAway", "kind": "instance", "module": "Mathlib.RingTheory.Localization.Away.AdjoinRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.Away", "kind": "abbrev", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.Away.invSelf", "kind": "definition", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.Away.mul_invSelf", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": true, "tactics": ["convert", "symm", "apply"], "tactic_count": 3}
{"name": "IsLocalization.Away.sec", "kind": "definition", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.Away.sec_spec", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": true, "tactics": ["simp", "congr", "exact"], "tactic_count": 3}
{"name": "IsLocalization.Away.algebraMap_pow_isUnit", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.Away.algebraMap_isUnit", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.Away.associated_sec_fst", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsLocalization.Away.algebraMap_isUnit_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.Away.surj", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": true, "tactics": ["obtain", "use", "simpa"], "tactic_count": 3}
{"name": "IsLocalization.Away.exists_of_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": true, "tactics": ["obtain", "use"], "tactic_count": 2}
{"name": "IsLocalization.Away.mk", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.Away.of_associated", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": true, "tactics": ["obtain", "refine", "simp", "obtain", "use", "simp", "obtain", "use", "rw"], "tactic_count": 9}
{"name": "IsLocalization.Away.iff_of_associated", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.Away.isUnit_of_dvd", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.Away.lift", "kind": "definition", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.Away.lift_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.Away.lift_comp", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.Away.awayToAwayLeft", "kind": "definition", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.Away.awayToAwayRight", "kind": "definition", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.Away.awayToAwayLeft_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.Away.awayToAwayRight_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.Away.map", "kind": "definition", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.Away.map_injective_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": true, "tactics": ["rw", "trans", "simp", "refine", "obtain", "exact"], "tactic_count": 6}
{"name": "IsLocalization.Away.map_surjective_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": true, "tactics": ["trans", "simp", "refine", "obtain", "exact"], "tactic_count": 5}
{"name": "IsLocalization.Away.instMapRingHomPowersOfCoe", "kind": "instance", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsLocalization.Away.instAlgebraMapSubmonoidPowersOfCoeRingHomAlgebraMap", "kind": "instance", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsLocalization.Away.mapₐ", "kind": "definition", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.Away.mapₐ_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.Away.mapₐ_injective_of_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.Away.mapₐ_surjective_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.Away.mul", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": true, "tactics": ["refine", "simp", "exact", "obtain", "obtain", "use", "simp", "ring", "repeat", "obtain", "simp", "obtain", "use", "convert_to", "ring", "ring", "rw"], "tactic_count": 17}
{"name": "IsLocalization.Away.mul'", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.Away.instHMulAwayCoeRingHomAlgebraMap", "kind": "instance", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.Away.instHMulAwayCoeRingHomAlgebraMap_1", "kind": "instance", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.Away.commutes", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": true, "tactics": ["convert", "ext", "simp"], "tactic_count": 3}
{"name": "IsLocalization.atUnit", "kind": "definition", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.atOne", "kind": "definition", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.away_of_isUnit_of_bijective", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.Away.mul_of_isUnit", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.Away.mul_of_isUnit'", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.Away.mul_of_associated", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "IsLocalization.away_of_isIdempotentElem_of_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.away_of_isIdempotentElem", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.away_fst", "kind": "instance", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.away_snd", "kind": "instance", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.Away.of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact", "rw", "exact"], "tactic_count": 5}
{"name": "IsLocalization.Away.of_surjective_of_isScalarTower", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": true, "tactics": ["refine", "rwa", "rw", "rwa"], "tactic_count": 4}
{"name": "Localization.awayLift", "kind": "abbrev", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.awayLift_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Localization.awayMap", "kind": "abbrev", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.awayMap_injective_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.awayMap_surjective_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.awayMapₐ", "kind": "abbrev", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.algebraMap_injective_of_span_eq_top", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.existsUnique_algebraMap_eq_of_span_eq_top", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": true, "tactics": ["have", "wlog", "have", "have", "refine", "replace", "classical", "have", "this", "exact", "have", "refine", "existsUnique_of_exists_of_unique", "algebraMap_injective_of_span_eq_top", "obtain", "choose", "let", "let", "have", "rw", "have", "simp_rw", "choose", "let", "have", "rw", "mul_assoc,", "let", "let", "have", "rw", "have", "rw", "have", "refine", "simp_rw", "smul_eq_mul"], "tactic_count": 37}
{"name": "selfZPow", "kind": "definition", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "selfZPow_of_nonneg", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "selfZPow_natCast", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "selfZPow_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "selfZPow_of_neg", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "selfZPow_of_nonpos", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "simp"], "tactic_count": 3}
{"name": "selfZPow_neg_natCast", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "selfZPow_sub_natCast", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "map_pow,", "rw", "simp"], "tactic_count": 5}
{"name": "selfZPow_add", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": true, "tactics": ["rcases", "rw", "have", "rw", "rw", "have", "rw", "rw", "rw", "congr", "ext", "simp"], "tactic_count": 12}
{"name": "selfZPow_mul_neg", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "apply", "rwa", "rw", "refine", "rwa"], "tactic_count": 7}
{"name": "selfZPow_neg_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "selfZPow_pow_sub", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": true, "tactics": ["rw", "constructor", "intro", "have", "simp", "rwa", "intro", "have", "simp", "rwa"], "tactic_count": 10}
{"name": "exists_reduced_fraction'", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Away.Basic", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "have", "haveI", "simp", "apply", "rw", "apply", "exact", "exact", "simp", "obtain", "refine", "rw", "mul_comm", "exact"], "tactic_count": 16}
{"name": "IsLocalization.Away.mulNumerator", "kind": "definition", "module": "Mathlib.RingTheory.Localization.Away.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.Away.span_range_mulNumerator_eq_top", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Away.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "intro", "haveI", "inferInstanceAs", "have", "rw", "intro", "rw", "refine", "use", "rw", "have", "rw", "apply", "simp", "rw", "obtain", "rw", "obtain", "simp", "use", "simpa"], "tactic_count": 22}
{"name": "IsLocalization.Away.quotient_of_isIdempotentElem", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Away.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalizedModule.isBaseChange", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.BaseChange", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLocalizedModule_iff_isBaseChange", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.BaseChange", "is_tactic_proof": true, "tactics": ["refine", "letI", "have", "let", "convert", "ext", "rw"], "tactic_count": 7}
{"name": "LocalizedModule.equivTensorProduct", "kind": "definition", "module": "Mathlib.RingTheory.Localization.BaseChange", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocalizedModule.equivTensorProduct_symm_apply_tmul", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.BaseChange", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LocalizedModule.equivTensorProduct_symm_apply_tmul_one", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.BaseChange", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LocalizedModule.equivTensorProduct_apply_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.BaseChange", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "IsLocalization.tensorProduct_isLocalizedModule", "kind": "instance", "module": "Mathlib.RingTheory.Localization.BaseChange", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.tensorProduct_compatibleSMul", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.BaseChange", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.instCompatibleSMulLocalizationOfIsScalarTower_1", "kind": "instance", "module": "Mathlib.RingTheory.Localization.BaseChange", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.instIsLocalizedModuleTensorProductMap", "kind": "instance", "module": "Mathlib.RingTheory.Localization.BaseChange", "is_tactic_proof": true, "tactics": ["let", "let", "convert", "ext"], "tactic_count": 4}
{"name": "IsLocalization.moduleTensorEquiv", "kind": "definition", "module": "Mathlib.RingTheory.Localization.BaseChange", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.moduleLid", "kind": "definition", "module": "Mathlib.RingTheory.Localization.BaseChange", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.algebraTensorEquiv", "kind": "definition", "module": "Mathlib.RingTheory.Localization.BaseChange", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.algebraLid", "kind": "definition", "module": "Mathlib.RingTheory.Localization.BaseChange", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.bijective_linearMap_mul'", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.BaseChange", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.isLocalization_iff_isPushout", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.BaseChange", "is_tactic_proof": true, "tactics": ["rw", "rw"], "tactic_count": 2}
{"name": "Algebra.isPushout_of_isLocalization", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.BaseChange", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsLocalizedModuleFinsuppLinearMap", "kind": "instance", "module": "Mathlib.RingTheory.Localization.BaseChange", "is_tactic_proof": true, "tactics": ["classical", "let", "let", "finsuppRight", "suffices", "convert", "ext", "simp", "rw", "convert", "ext", "apply", "ext", "apply", "suffices", "simpa", "split_ifs", "simp", "simp"], "tactic_count": 19}
{"name": "IsLocalizedModule.map_linearCombination", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.BaseChange", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalizedModule.rTensor", "kind": "instance", "module": "Mathlib.RingTheory.Localization.BaseChange", "is_tactic_proof": true, "tactics": ["let", "letI", "haveI", "haveI", "rw", "exact"], "tactic_count": 6}
{"name": "IsLocalizedModule.map_lTensor", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.BaseChange", "is_tactic_proof": true, "tactics": ["apply", "rw", "ext", "simp"], "tactic_count": 4}
{"name": "IsLocalization.tensor", "kind": "instance", "module": "Mathlib.RingTheory.Localization.BaseChange", "is_tactic_proof": true, "tactics": ["let", "rw", "infer_instance"], "tactic_count": 3}
{"name": "IsLocalization.tensorRight", "kind": "instance", "module": "Mathlib.RingTheory.Localization.BaseChange", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "IsLocalization.tmul_mk'", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.BaseChange", "is_tactic_proof": true, "tactics": ["rw", "tmul_one_eq_one_tmul,"], "tactic_count": 2}
{"name": "IsLocalization.mk'_tmul", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.BaseChange", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsLocalization.tensorProduct_tensorProduct", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.BaseChange", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.Away.tensor", "kind": "instance", "module": "Mathlib.RingTheory.Localization.BaseChange", "is_tactic_proof": true, "tactics": ["simp", "infer_instance"], "tactic_count": 2}
{"name": "IsLocalization.Away.tensorEquiv", "kind": "abbrev", "module": "Mathlib.RingTheory.Localization.BaseChange", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.Away.tensorRight", "kind": "instance", "module": "Mathlib.RingTheory.Localization.BaseChange", "is_tactic_proof": true, "tactics": ["simp", "infer_instance"], "tactic_count": 2}
{"name": "IsLocalization.Away.tensorRightEquiv", "kind": "abbrev", "module": "Mathlib.RingTheory.Localization.BaseChange", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.mapPiEvalRingHom", "kind": "abbrev", "module": "Mathlib.RingTheory.Localization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.mapPiEvalRingHom_bijective", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Basic", "is_tactic_proof": true, "tactics": ["let", "classical", "refine", "obtain", "obtain", "simp_rw", "rw", "obtain", "refine", "obtain", "simpa", "simp", "obtain", "exact"], "tactic_count": 14}
{"name": "IsLocalization.finite", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Basic", "is_tactic_proof": false, "tactics": ["have", "simpa", "exact"], "tactic_count": 3}
{"name": "IsLocalization.linearMap_compatibleSMul", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.instCompatibleSMulLocalizationOfIsScalarTower", "kind": "instance", "module": "Mathlib.RingTheory.Localization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.algHom_subsingleton", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.algEquiv", "kind": "definition", "module": "Mathlib.RingTheory.Localization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.algEquiv_mk'", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsLocalization.algEquiv_symm_mk'", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsLocalization.bijective", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.liftAlgHom", "kind": "definition", "module": "Mathlib.RingTheory.Localization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.liftAlgHom_toRingHom", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.coe_liftAlgHom", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.liftAlgHom_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.algEquivOfAlgEquiv", "kind": "definition", "module": "Mathlib.RingTheory.Localization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.algEquivOfAlgEquiv_eq_map", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.algEquivOfAlgEquiv_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsLocalization.algEquivOfAlgEquiv_mk'", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsLocalization.algEquivOfAlgEquiv_symm", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.smul_mem_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Basic", "is_tactic_proof": true, "tactics": ["refine", "rwa"], "tactic_count": 2}
{"name": "IsLocalization.atUnits", "kind": "definition", "module": "Mathlib.RingTheory.Localization.Basic", "is_tactic_proof": true, "tactics": ["refine", "intro", "obtain", "obtain", "rwa", "intro", "obtain", "obtain", "use", "dsimp", "rw", "simp"], "tactic_count": 12}
{"name": "IsLocalization.isLocalization_of_algEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Basic", "is_tactic_proof": true, "tactics": ["constructor", "intro", "convert", "exact", "intro", "obtain", "apply_fun", "simp", "exact", "intro", "rw", "exact"], "tactic_count": 12}
{"name": "IsLocalization.self", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.isLocalization_iff_of_algEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.isLocalization_iff_of_ringEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.isLocalization_iff_of_isLocalization", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.iff_of_le_of_exists_dvd", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.commutes", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.algEquiv_comp_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Basic", "is_tactic_proof": true, "tactics": ["refine", "simp", "rw"], "tactic_count": 3}
{"name": "IsLocalization.algEquiv_comp_algebraMap_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Localization.mk_natCast", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Localization.algEquiv", "kind": "definition", "module": "Mathlib.RingTheory.Localization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.unique", "kind": "definition", "module": "Mathlib.RingTheory.Localization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.algEquiv_mk'", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.algEquiv_symm_mk'", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.algEquiv_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Localization.algEquiv_symm_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Localization.coe_algEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.coe_algEquiv_symm", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsField.localization_map_bijective", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Basic", "is_tactic_proof": true, "tactics": ["letI", "replace", "refine", "obtain", "obtain", "exact"], "tactic_count": 6}
{"name": "Field.localization_map_bijective", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "localizationAlgebra", "kind": "definition", "module": "Mathlib.RingTheory.Localization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instAlgebraLocalizationAlgebraMapSubmonoid", "kind": "instance", "module": "Mathlib.RingTheory.Localization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsScalarTowerLocalizationAlgebraMapSubmonoid", "kind": "instance", "module": "Mathlib.RingTheory.Localization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.map_units_map_submonoid", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsLocalization.algebraMap_mk'", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Basic", "is_tactic_proof": false, "tactics": ["rw", "map_mul,", "exact"], "tactic_count": 3}
{"name": "IsLocalization.algebraMap_eq_map_map_submonoid", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.algebraMap_apply_eq_map_map_submonoid", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.lift_algebraMap_eq_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "localizationAlgebraMap_def", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "localizationAlgebra_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsLocalizationAlgebraMapSubmonoid", "kind": "instance", "module": "Mathlib.RingTheory.Localization.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsLocalization.map_injective_of_injective'", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Basic", "is_tactic_proof": true, "tactics": ["refine", "obtain", "aesop"], "tactic_count": 3}
{"name": "Localization.mk_intCast", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsLocalization.algHom_ext", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.algHom_ext", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.lift_cardinalMk_le", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Cardinality", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "IsLocalization.cardinalMk_le", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Cardinality", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Localization.cardinalMk", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Cardinality", "is_tactic_proof": true, "tactics": ["apply", "rwa"], "tactic_count": 2}
{"name": "IsLocalization.lift_cardinalMk", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Cardinality", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "IsLocalization.cardinalMk", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Cardinality", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Cardinal.mk_fractionRing", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Cardinality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractionRing.lift_cardinalMk", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Cardinality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractionRing.cardinalMk", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Cardinality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization", "kind": "abbrev", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLocalization_iff_isLocalizationMap", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLocalization_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsLocalization.map_units", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.surj", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.exists_of_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.smul_bijective", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsLocalization.toLocalizationMap", "kind": "abbrev", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.toLocalizationMap_toMonoidHom", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.coe_toLocalizationMap", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.toLocalizationMap_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.surj₂", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.eq_iff_exists", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.injective_iff_isRegular", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.of_le", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.of_le_of_exists_dvd", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.algebraMap_isUnit_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": true, "tactics": ["refine", "have", "have", "apply_fun", "rw", "have", "exact"], "tactic_count": 7}
{"name": "IsLocalization.sec", "kind": "definition", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.toLocalizationMap_sec", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.sec_spec", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.sec_spec'", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsLocalization.subsingleton", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.subsingleton_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.map_right_cancel", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.map_left_cancel", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.eq_zero_of_fst_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsLocalization.map_eq_zero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.mk'", "kind": "definition", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.mk'_sec", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.mk'_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.mk'_one", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.mk'_spec", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.mk'_spec'", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.mk'_spec_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.mk'_spec'_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.eq_mk'_iff_mul_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.eq_mk'_of_mul_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.mk'_eq_iff_eq_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.mk'_add_eq_iff_add_mul_eq_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsLocalization.mk'_pow", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": true, "tactics": ["simp_rw", "simp"], "tactic_count": 2}
{"name": "IsLocalization.mk'_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.exists_mk'_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.fintype'", "kind": "definition", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.uniqueOfZeroMem", "kind": "definition", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.mk'_eq_iff_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.mk'_eq_iff_eq'", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.eq", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.mk'_eq_zero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.mk'_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.ne_zero_of_mk'_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "IsLocalization.isRegular_mk'", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": true, "tactics": ["have", "simp", "simp_rw", "exact"], "tactic_count": 4}
{"name": "IsLocalization.noZeroDivisors", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.sec_fst_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.eq_iff_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.mk'_eq_iff_mk'_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.mk'_eq_of_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.mk'_eq_of_eq'", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.mk'_cancel", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.mk'_self", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.mk'_self'", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.mk'_self''", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.mul_mk'_eq_mk'_of_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.mk'_eq_mul_mk'_one", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.mk'_mul_cancel_left", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.mk'_mul_cancel_right", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.mk'_mul_mk'_eq_one", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsLocalization.mk'_mul_mk'_eq_one'", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.smul_mk'", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": true, "tactics": ["nth_rw", "rw"], "tactic_count": 2}
{"name": "IsLocalization.smul_mk'_one", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsLocalization.smul_mk'_self", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsLocalization.invertible_mk'_one", "kind": "instance", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.isUnit_comp", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.eq_of_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.mk'_add", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.mul_add_inv_left", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "IsLocalization.lift_spec_mul_add", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "IsLocalization.lift", "kind": "definition", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.lift_mk'", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.lift_mk'_spec", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.lift_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.lift_eq_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.lift_comp", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.lift_of_comp", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.monoidHom_ext", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.ringHom_ext", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.ext", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.lift_unique", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.lift_id", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.lift_surjective_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.lift_injective_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.injective_iff_map_algebraMap_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "IsLocalization.map", "kind": "definition", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.map_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.map_comp", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.map_mk'", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.map_unique", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.map_comp_map", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.map_map", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsLocalization.map_smul", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsLocalization.map_id_mk'", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.ringEquivOfRingEquiv", "kind": "definition", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.ringEquivOfRingEquiv_eq_map", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.ringEquivOfRingEquiv_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsLocalization.ringEquivOfRingEquiv_mk'", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsLocalization.ringEquivOfRingEquiv_symm", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.at_units", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.map_injective_of_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.map_surjective_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.isLocalization_of_base_ringEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": true, "tactics": ["letI", "constructor", "rintro", "convert", "dsimp", "exact", "intro", "obtain", "refine", "dsimp", "convert", "intro", "rw", "simp"], "tactic_count": 14}
{"name": "IsLocalization.isLocalization_iff_of_base_ringEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": true, "tactics": ["letI", "refine", "intro", "convert", "rw", "exact", "rw", "simp", "apply", "intro", "rw"], "tactic_count": 11}
{"name": "IsLocalization.nonZeroDivisors_le_comap", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.map_nonZeroDivisors_le", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.instUniqueLocalization", "kind": "instance", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.add_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Localization.add_mk_self", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp", "ring"], "tactic_count": 4}
{"name": "Localization.mkAddMonoidHom", "kind": "definition", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.mk_sum", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.mk_list_sum", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.mk_multiset_sum", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.isLocalization", "kind": "instance", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.instNoZeroDivisors", "kind": "instance", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.toLocalizationMap_eq_monoidOf", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.monoidOf_eq_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.mk_one_eq_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.mk_eq_mk'_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Localization.mk_eq_mk'", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.mk_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsLocalization.to_map_eq_zero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": true, "tactics": ["constructor", "obtain", "exact", "rw"], "tactic_count": 4}
{"name": "IsLocalization.injectiveₛ", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.to_map_ne_zero_of_mem_nonZeroDivisors", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsLocalization.sec_snd_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.isDomain_of_le_nonZeroDivisors", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.isDomain_localization", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.neg_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Localization.sub_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsLocalization.mk'_neg", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsLocalization.mk'_sub", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsLocalization.injective_of_map_algebraMap_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "apply", "rwa"], "tactic_count": 5}
{"name": "IsLocalization.injective", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Finite.of_isLocalizedModule", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Finiteness", "is_tactic_proof": true, "tactics": ["classical", "obtain", "use", "simpa"], "tactic_count": 4}
{"name": "Module.Finite.instLocalizationLocalizedModule", "kind": "instance", "module": "Mathlib.RingTheory.Localization.Finiteness", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Finite.of_localizationSpan_finite'", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Finiteness", "is_tactic_proof": true, "tactics": ["classical", "constructor", "choose", "let", "use", "rw", "rintro", "refine", "set", "obtain", "multiple_mem_span_of_mem_localization_span", "rw", "obtain", "rw", "use", "apply", "rw", "exact"], "tactic_count": 18}
{"name": "Module.Finite.of_localizationSpan'", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Finiteness", "is_tactic_proof": true, "tactics": ["rw", "obtain", "have", "have", "h₂", "apply"], "tactic_count": 6}
{"name": "Module.Finite.of_localizationSpan_finite", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Finiteness", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Finite.of_localizationSpan", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Finiteness", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.fg_of_localizationSpan", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Finiteness", "is_tactic_proof": true, "tactics": ["apply", "let", "exact"], "tactic_count": 3}
{"name": "RingHom.ker_fg_of_localizationSpan", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Finiteness", "is_tactic_proof": true, "tactics": ["apply", "intro", "rw", "exact"], "tactic_count": 4}
{"name": "IsFractionRing", "kind": "abbrev", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsFractionRing", "kind": "instance", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.isFractionRing", "kind": "instance", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsLocalizationIntPosRat", "kind": "instance", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.isFractionRing", "kind": "instance", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractionRing.of_field", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractionRing.to_map_eq_zero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractionRing.injective", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractionRing.nonZeroDivisors_eq_isUnit", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": true, "tactics": ["refine", "have", "let", "mem_nonZeroDivisors_of_injective", "exact"], "tactic_count": 5}
{"name": "IsFractionRing.algEquiv", "kind": "definition", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractionRing.idem", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractionRing.trans", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractionRing.instFaithfulSMul", "kind": "instance", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractionRing.self_iff_nonZeroDivisors_eq_isUnit", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractionRing.self_iff_nonZeroDivisors_le_isUnit", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsFractionRing.self_iff_bijective", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractionRing.self_iff_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsFractionRing.coe_inj", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractionRing.to_map_ne_zero_of_mem_nonZeroDivisors", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractionRing.isDomain", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractionRing.definition._@.Mathlib.RingTheory.Localization.FractionRing.1935392398._hygCtx._hyg.2", "kind": "definition", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractionRing.wrapped._@.Mathlib.RingTheory.Localization.FractionRing.1935392398._hygCtx._hyg.2", "kind": "opaque", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractionRing.inv", "kind": "definition", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractionRing.inv_def", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": true, "tactics": ["intros", "delta", "rw", "rfl"], "tactic_count": 4}
{"name": "IsFractionRing.mul_inv_cancel", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": false, "tactics": ["rw", "mem_nonZeroDivisors_iff_ne_zero.2", "hx", "one_mul,", "rw", "exact"], "tactic_count": 6}
{"name": "IsFractionRing.toField", "kind": "abbrev", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractionRing.surjective_iff_isField", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractionRing.mk'_mk_eq_div", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractionRing.mk'_eq_div", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractionRing.div_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractionRing.isUnit_map_of_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractionRing.mk'_eq_zero_iff_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": true, "tactics": ["haveI", "simp"], "tactic_count": 2}
{"name": "IsFractionRing.mk'_eq_one_iff_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": true, "tactics": ["haveI", "refine", "intro", "have", "rw", "exact"], "tactic_count": 6}
{"name": "IsFractionRing.algHom_commutes", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": true, "tactics": ["obtain", "simp_rw"], "tactic_count": 2}
{"name": "IsFractionRing.algEquiv_commutes", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "IsFractionRing.closure_range_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractionRing.ringHom_fieldRange_eq_of_comp_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": true, "tactics": ["rw", "g.coe_range]"], "tactic_count": 2}
{"name": "IsFractionRing.ringHom_fieldRange_eq_of_comp_eq_of_range_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": true, "tactics": ["rw", "ext", "simp_rw"], "tactic_count": 3}
{"name": "IsFractionRing.lift", "kind": "definition", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractionRing.lift_unique", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractionRing.ringHom_ext", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": true, "tactics": ["ext", "obtain", "rw"], "tactic_count": 3}
{"name": "IsFractionRing.injective_comp_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractionRing.liftAlgHom", "kind": "definition", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractionRing.liftAlgHom_toRingHom", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractionRing.coe_liftAlgHom", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractionRing.liftAlgHom_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractionRing.lift_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractionRing.lift_fieldRange", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractionRing.lift_fieldRange_eq_of_range_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractionRing.lift_mk'", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsFractionRing.map", "kind": "definition", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractionRing.ringEquivOfRingEquiv", "kind": "definition", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractionRing.ringEquivOfRingEquiv_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsFractionRing.ringEquivOfRingEquiv_symm", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractionRing.algEquivOfAlgEquiv", "kind": "definition", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractionRing.algEquivOfAlgEquiv_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsFractionRing.algEquivOfAlgEquiv_symm", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractionRing.fieldEquivOfAlgEquiv", "kind": "definition", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractionRing.restrictScalars_fieldEquivOfAlgEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "IsFractionRing.fieldEquivOfAlgEquiv_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractionRing.fieldEquivOfAlgEquiv_refl", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": true, "tactics": ["ext", "obtain", "simp"], "tactic_count": 3}
{"name": "IsFractionRing.fieldEquivOfAlgEquiv_trans", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": true, "tactics": ["ext", "obtain", "simp"], "tactic_count": 3}
{"name": "IsFractionRing.fieldEquivOfAlgEquivHom", "kind": "definition", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractionRing.fieldEquivOfAlgEquivHom_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractionRing.fieldEquivOfAlgEquivHom_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": true, "tactics": ["intro", "ext", "simpa"], "tactic_count": 3}
{"name": "IsFractionRing.isFractionRing_iff_of_base_ringEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": true, "tactics": ["delta", "convert", "exact"], "tactic_count": 3}
{"name": "IsFractionRing.nontrivial_iff_nontrivial", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": true, "tactics": ["by_contra", "obtain", "simp", "apply", "rw"], "tactic_count": 5}
{"name": "IsFractionRing.nontrivial", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "algebraMap_injective_of_field_isFractionRing", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "FaithfulSMul.of_field_isFractionRing", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionRing", "kind": "abbrev", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionRing.instIsFractionRing", "kind": "instance", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionRing.unique", "kind": "instance", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionRing.instNontrivial", "kind": "instance", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionRing.field", "kind": "instance", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionRing.mk_eq_div", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "FractionRing.liftAlgebra", "kind": "abbrev", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionRing.isScalarTower_liftAlgebra", "kind": "instance", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionRing.algebraMap_liftAlgebra", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionRing.instIsScalarTower", "kind": "instance", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionRing.algEquiv", "kind": "definition", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FractionRing.instFaithfulSMul", "kind": "instance", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "FractionRing.instIsScalarTower_1", "kind": "instance", "module": "Mathlib.RingTheory.Localization.FractionRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.FinitePresentation.exists_basis_localizedModule_powers", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Free", "is_tactic_proof": true, "tactics": ["have", "obtain", "let", "refine", "exact", "intro", "have", "simp", "change", "replace", "simp", "apply", "rw", "simp"], "tactic_count": 14}
{"name": "Module.FinitePresentation.exists_free_localizedModule_powers", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Free", "is_tactic_proof": true, "tactics": ["let", "let", "have", "obtain", "have", "refine", "rw"], "tactic_count": 7}
{"name": "IsLocalization.mk'_mem_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Ideal", "is_tactic_proof": true, "tactics": ["constructor", "rw", "exact", "rw", "obtain", "have", "rwa"], "tactic_count": 7}
{"name": "_private.Mathlib.RingTheory.Localization.Ideal.0.IsLocalization.map_ideal", "kind": "definition", "module": "Mathlib.RingTheory.Localization.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.mem_map_algebraMap_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Ideal", "is_tactic_proof": true, "tactics": ["constructor", "change", "refine", "obtain", "let", "use", "simp", "rintro", "rw", "exact"], "tactic_count": 10}
{"name": "IsLocalization.mk'_mem_map_algebraMap_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Ideal", "is_tactic_proof": false, "tactics": ["rw", "simp_rw", "exact"], "tactic_count": 3}
{"name": "IsLocalization.algebraMap_mem_map_algebraMap_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Ideal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsLocalization.map_algebraMap_ne_top_iff_disjoint", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Ideal", "is_tactic_proof": false, "tactics": ["simp", "simp"], "tactic_count": 2}
{"name": "IsLocalization.map_inf", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Ideal", "is_tactic_proof": true, "tactics": ["refine", "simp", "obtain", "simp", "obtain", "rw", "refine", "rwa"], "tactic_count": 8}
{"name": "IsLocalization.mapFrameHom", "kind": "definition", "module": "Mathlib.RingTheory.Localization.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.mapFrameHom_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.map_comap", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.comap_map_of_isPrimary_disjoint", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Ideal", "is_tactic_proof": false, "tactics": ["have", "contrapose", "rw", "obtain", "exact", "refine", "rw", "obtain", "replace", "obtain", "have", "rw", "exact", "exact"], "tactic_count": 14}
{"name": "IsLocalization.comap_map_of_isPrime_disjoint", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.orderEmbedding", "kind": "definition", "module": "Mathlib.RingTheory.Localization.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.isPrime_iff_isPrime_disjoint", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Ideal", "is_tactic_proof": true, "tactics": ["constructor", "refine", "refine", "rw", "exact", "intro", "rw", "exact", "refine", "rwa", "intro", "obtain", "obtain", "have", "rw", "have", "rw", "rwa"], "tactic_count": 18}
{"name": "IsLocalization.isPrime_of_isPrime_disjoint", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Ideal", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsLocalization.disjoint_comap_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Ideal", "is_tactic_proof": true, "tactics": ["rw", "constructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 6}
{"name": "IsLocalization.orderIsoOfPrime", "kind": "definition", "module": "Mathlib.RingTheory.Localization.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.primeSpectrumOrderIso", "kind": "definition", "module": "Mathlib.RingTheory.Localization.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.map_radical", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Ideal", "is_tactic_proof": true, "tactics": ["refine", "rintro", "obtain", "simp", "obtain", "refine"], "tactic_count": 6}
{"name": "IsLocalization.ideal_eq_iInf_comap_map_away", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Ideal", "is_tactic_proof": true, "tactics": ["apply", "simp", "intro", "apply", "rintro", "simp", "obtain", "dsimp", "rw", "obtain", "use", "dsimp", "rw", "exact"], "tactic_count": 14}
{"name": "IsLocalization.surjective_quotientMap_of_maximal_of_localization", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Ideal", "is_tactic_proof": true, "tactics": ["intro", "obtain", "obtain", "by_cases", "have", "rw", "rw", "convert", "rw", "exact", "rw", "obtain", "obtain", "refine", "replace", "rw", "rw", "simp", "refine", "rw"], "tactic_count": 20}
{"name": "IsLocalization.bot_lt_comap_prime", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Ideal", "is_tactic_proof": true, "tactics": ["haveI", "rw", "convert"], "tactic_count": 3}
{"name": "Module.IsTorsionFree.of_isLocalization", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Ideal", "is_tactic_proof": false, "tactics": ["have", "hM.trans", "have", "have", "algebraMap", "apply", "simp", "rw", "intro", "obtain", "simp", "obtain", "simp", "exact"], "tactic_count": 14}
{"name": "IsLocalization.of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.instIsDomainLocalizationAlgebraMapSubmonoidPrimeComplOfFaithfulSMul", "kind": "instance", "module": "Mathlib.RingTheory.Localization.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.IsInteger", "kind": "definition", "module": "Mathlib.RingTheory.Localization.Integer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.isInteger_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Integer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.isInteger_one", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Integer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.isInteger_add", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Integer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.isInteger_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Integer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.isInteger_smul", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Integer", "is_tactic_proof": true, "tactics": ["rcases", "use", "rw"], "tactic_count": 3}
{"name": "IsLocalization.exists_integer_multiple'", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Integer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.exists_integer_multiple", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Integer", "is_tactic_proof": true, "tactics": ["simp_rw", "apply"], "tactic_count": 2}
{"name": "IsLocalization.exist_integer_multiples", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Integer", "is_tactic_proof": true, "tactics": ["haveI", "refine", "exact", "rw", "congr", "refine", "rw", "rfl"], "tactic_count": 8}
{"name": "IsLocalization.exist_integer_multiples_of_finite", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Integer", "is_tactic_proof": true, "tactics": ["cases", "obtain", "exact"], "tactic_count": 3}
{"name": "IsLocalization.exist_integer_multiples_of_finset", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Integer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.commonDenom", "kind": "definition", "module": "Mathlib.RingTheory.Localization.Integer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.integerMultiple", "kind": "definition", "module": "Mathlib.RingTheory.Localization.Integer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.map_integerMultiple", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Integer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.commonDenomOfFinset", "kind": "definition", "module": "Mathlib.RingTheory.Localization.Integer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.finsetIntegerMultiple", "kind": "definition", "module": "Mathlib.RingTheory.Localization.Integer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.finsetIntegerMultiple_image", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Integer", "is_tactic_proof": true, "tactics": ["delta", "rw", "ext", "constructor", "rintro", "rw", "exact", "rintro", "exact"], "tactic_count": 9}
{"name": "IsLocalization.coeffIntegerNormalization", "kind": "definition", "module": "Mathlib.RingTheory.Localization.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.coeffIntegerNormalization_of_coeff_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Integral", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsLocalization.coeffIntegerNormalization_mem_support", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Integral", "is_tactic_proof": true, "tactics": ["contrapose", "rw"], "tactic_count": 2}
{"name": "IsLocalization.integerNormalization", "kind": "definition", "module": "Mathlib.RingTheory.Localization.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.integerNormalization_coeff", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Integral", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsLocalization.integerNormalization_spec", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Integral", "is_tactic_proof": true, "tactics": ["classical", "use", "intro", "rw", "split_ifs", "exact", "rw"], "tactic_count": 7}
{"name": "IsLocalization.integerNormalization_map_to_map", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.integerNormalization_eval₂_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.integerNormalization_aeval_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Integral", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "IsFractionRing.integerNormalization_eq_zero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Integral", "is_tactic_proof": true, "tactics": ["refine", "obtain", "constructor", "rw", "have", "rw", "apply", "intro", "apply", "exact"], "tactic_count": 10}
{"name": "IsFractionRing.isAlgebraic_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Integral", "is_tactic_proof": true, "tactics": ["constructor", "refine", "have", "exact", "exact", "exact"], "tactic_count": 6}
{"name": "IsFractionRing.comap_isAlgebraic_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.isIntegralElem_localization_at_leadingCoeff", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Integral", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "haveI", "obtain", "refine", "refine", "rwa", "refine", "refine", "rw", "exact"], "tactic_count": 11}
{"name": "is_integral_localization_at_leadingCoeff", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isIntegral_localization", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Integral", "is_tactic_proof": true, "tactics": ["intro", "obtain", "obtain", "obtain", "refine", "replace", "rw", "exact", "obtain", "exact"], "tactic_count": 10}
{"name": "isIntegral_localization'", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.scaleRoots_commonDenom_mem_lifts", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Integral", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "by_cases", "on_goal", "rwa", "have", "rw", "change", "apply", "exact", "rw", "exact", "rw", "rw", "exact"], "tactic_count": 16}
{"name": "IsIntegral.exists_multiple_integral_of_isLocalization", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Integral", "is_tactic_proof": true, "tactics": ["rcases", "haveI", "exact", "obtain", "have", "obtain", "refine", "rw", "exact", "rw", "exact", "rwa"], "tactic_count": 12}
{"name": "IsLocalization.exists_isIntegral_smul_of_isIntegral_map", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Integral", "is_tactic_proof": true, "tactics": ["obtain", "simp", "obtain", "exact", "simpa"], "tactic_count": 5}
{"name": "isIntegral_of_isIntegral_adjoin_of_mul_eq_one", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Integral", "is_tactic_proof": true, "tactics": ["nontriviality", "let", "obtain", "obtain", "have", "obtain", "exact", "let", "have", "by_cases", "exact", "simp_all", "let", "have", "letI", "rw", "simp", "refine", "refine", "refine", "grw", "simp", "simp", "rw", "simp", "intro", "have", "add_comm", "simpa", "coeff_eq_zero_of_natDegree_lt", "simp", "trans", "simp", "simp_rw"], "tactic_count": 34}
{"name": "IsLocalization.Away.isIntegral_of_isIntegral_map", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Integral", "is_tactic_proof": true, "tactics": ["obtain", "simp", "obtain", "exact"], "tactic_count": 4}
{"name": "IsIntegralClosure.isFractionRing_of_algebraic", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIntegralClosure.isFractionRing_of_finite_extension", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "integralClosure.isFractionRing_of_algebraic", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "integralClosure.isFractionRing_of_finite_extension", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.integralClosure", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Integral", "is_tactic_proof": true, "tactics": ["refine", "rintro", "convert", "simp", "rintro", "obtain", "simp", "obtain", "simp", "obtain", "simp", "exact", "refine", "apply", "simp", "ring", "rintro", "have", "have", "obtain", "refine", "simpa"], "tactic_count": 22}
{"name": "IsLocalization.Away.integralClosure", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Integral", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "IsFractionRing.isAlgebraic_iff'", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Integral", "is_tactic_proof": true, "tactics": ["simp", "constructor", "intro", "letI", "letI", "have", "rw", "obtain", "obtain", "rw", "refine", "exact", "intro", "obtain", "use", "rw", "exact"], "tactic_count": 17}
{"name": "IsFractionRing.ideal_span_singleton_map_subset", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Integral", "is_tactic_proof": true, "tactics": ["intro", "obtain", "obtain", "obtain", "have", "refine", "rwa", "have", "map_mem_nonZeroDivisors", "have", "rw", "exact", "suffices", "rw", "div_eq_mul_inv,", "exact", "refine", "rw", "exact"], "tactic_count": 19}
{"name": "isAlgebraic_of_isFractionRing", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Integral", "is_tactic_proof": true, "tactics": ["constructor", "intro", "obtain", "apply", "rw", "apply", "apply", "apply", "exact", "change", "rw", "apply", "apply", "exact"], "tactic_count": 14}
{"name": "IsLocalization.invSubmonoid", "kind": "definition", "module": "Mathlib.RingTheory.Localization.InvSubmonoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.submonoid_map_le_is_unit", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.InvSubmonoid", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "IsLocalization.equivInvSubmonoid", "kind": "abbrev", "module": "Mathlib.RingTheory.Localization.InvSubmonoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.toInvSubmonoid", "kind": "definition", "module": "Mathlib.RingTheory.Localization.InvSubmonoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.toInvSubmonoid_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.InvSubmonoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.toInvSubmonoid_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.InvSubmonoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.mul_toInvSubmonoid", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.InvSubmonoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.smul_toInvSubmonoid", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.InvSubmonoid", "is_tactic_proof": true, "tactics": ["convert", "ext", "rw", "rfl"], "tactic_count": 4}
{"name": "IsLocalization.surj''", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.InvSubmonoid", "is_tactic_proof": true, "tactics": ["rcases", "refine", "rw", "simp"], "tactic_count": 4}
{"name": "IsLocalization.toInvSubmonoid_eq_mk'", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.InvSubmonoid", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "IsLocalization.mem_invSubmonoid_iff_exists_mk'", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.InvSubmonoid", "is_tactic_proof": true, "tactics": ["simp_rw", "exact", "h.choose_spec"], "tactic_count": 3}
{"name": "IsLocalization.span_invSubmonoid", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.InvSubmonoid", "is_tactic_proof": true, "tactics": ["rw", "rintro", "rcases", "exact"], "tactic_count": 4}
{"name": "IsLocalization.finiteType_of_monoid_fg", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.InvSubmonoid", "is_tactic_proof": true, "tactics": ["have", "rw", "rcases", "refine", "rw", "rintro", "change", "rw", "trivial"], "tactic_count": 9}
{"name": "IsLocalization.instFiniteTypeLocalizationOfFGSubtypeMemSubmonoid", "kind": "instance", "module": "Mathlib.RingTheory.Localization.InvSubmonoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.localizationLocalizationSubmodule", "kind": "definition", "module": "Mathlib.RingTheory.Localization.LocalizationLocalization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.mem_localizationLocalizationSubmodule", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.LocalizationLocalization", "is_tactic_proof": true, "tactics": ["rw", "constructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 6}
{"name": "IsLocalization.localization_localization_map_units", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.LocalizationLocalization", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact"], "tactic_count": 3}
{"name": "IsLocalization.localization_localization_surj", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.LocalizationLocalization", "is_tactic_proof": false, "tactics": ["rcases", "rcases", "rcases", "dsimp", "refine", "rw", "refine", "rw", "simp", "ring"], "tactic_count": 10}
{"name": "IsLocalization.localization_localization_exists_of_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.LocalizationLocalization", "is_tactic_proof": false, "tactics": ["rw", "rintro", "rcases", "dsimp", "suffices", "obtain", "refine", "rw", "refine", "rw", "rwa", "rw"], "tactic_count": 12}
{"name": "IsLocalization.localization_localization_isLocalization", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.LocalizationLocalization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.localization_localization_isLocalization_of_has_all_units", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.LocalizationLocalization", "is_tactic_proof": true, "tactics": ["convert", "dsimp", "congr", "symm", "rw", "rintro", "exact"], "tactic_count": 7}
{"name": "IsLocalization.isLocalization_isLocalization_atPrime_isLocalization", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.LocalizationLocalization", "is_tactic_proof": true, "tactics": ["apply", "intro", "exact"], "tactic_count": 3}
{"name": "IsLocalization.instAlgebraAtPrimeLocalization", "kind": "instance", "module": "Mathlib.RingTheory.Localization.LocalizationLocalization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.instIsScalarTowerLocalizationAtPrime", "kind": "instance", "module": "Mathlib.RingTheory.Localization.LocalizationLocalization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.isLocalization_atPrime_localization_atPrime", "kind": "instance", "module": "Mathlib.RingTheory.Localization.LocalizationLocalization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.localizationLocalizationAtPrimeIsoLocalization", "kind": "definition", "module": "Mathlib.RingTheory.Localization.LocalizationLocalization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.localizationAlgebraOfSubmonoidLe", "kind": "abbrev", "module": "Mathlib.RingTheory.Localization.LocalizationLocalization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.localization_isScalarTower_of_submonoid_le", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.LocalizationLocalization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.instAlgebraLocalizationAtPrime", "kind": "instance", "module": "Mathlib.RingTheory.Localization.LocalizationLocalization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.instIsScalarTowerAtPrimeFractionRing", "kind": "instance", "module": "Mathlib.RingTheory.Localization.LocalizationLocalization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.isLocalization_of_submonoid_le", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.LocalizationLocalization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.isLocalization_of_is_exists_mul_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.LocalizationLocalization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.mk'_eq_algebraMap_mk'_of_submonoid_le", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.LocalizationLocalization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractionRing.isFractionRing_of_isLocalization", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.LocalizationLocalization", "is_tactic_proof": true, "tactics": ["have", "refine", "exact", "rintro", "obtain", "use", "rw", "refine", "intro", "apply", "rw", "apply", "rw"], "tactic_count": 13}
{"name": "IsFractionRing.isFractionRing_of_isDomain_of_isLocalization", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.LocalizationLocalization", "is_tactic_proof": true, "tactics": ["haveI", "haveI", "apply", "intro", "rw", "intro", "apply", "rw", "exact"], "tactic_count": 9}
{"name": "IsFractionRing.instAtPrimeFractionRing", "kind": "instance", "module": "Mathlib.RingTheory.Localization.LocalizationLocalization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "span_eq_top_of_isLocalizedModule", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIndependent.of_isLocalizedModule", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Module", "is_tactic_proof": true, "tactics": ["rw", "intro", "choose", "simp_rw", "apply_fun", "simp_rw", "map_sum,", "t.sum_coe_sort", "have", "simp_rw", "have", "simpa"], "tactic_count": 12}
{"name": "LinearIndependent.of_isLocalizedModule_of_isRegular", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIndependent.localization", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Module", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "IsLocalizedModule.linearIndependent_lift", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Module", "is_tactic_proof": true, "tactics": ["cases", "exact", "have", "choose", "use", "rw", "intro", "refine", "hf", "simp_rw"], "tactic_count": 10}
{"name": "Module.Basis.ofIsLocalizedModule", "kind": "definition", "module": "Mathlib.RingTheory.Localization.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.ofIsLocalizedModule_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Module", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Module.Basis.ofIsLocalizedModule_repr_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Module", "is_tactic_proof": false, "tactics": ["suffices", "refine", "rw", "b.ofIsLocalizedModule_apply", "repr_self,"], "tactic_count": 5}
{"name": "Module.Basis.ofIsLocalizedModule_span", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Module", "is_tactic_proof": true, "tactics": ["calc", "span"], "tactic_count": 2}
{"name": "LinearIndependent.localization_localization", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "span_eq_top_localization_localization", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.localizationLocalization", "kind": "definition", "module": "Mathlib.RingTheory.Localization.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.localizationLocalization_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.localizationLocalization_repr_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.localizationLocalization_span", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIndependent.iff_fractionRing", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.extendScalarsOfIsLocalization", "kind": "definition", "module": "Mathlib.RingTheory.Localization.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.restrictScalars_extendScalarsOfIsLocalization", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.extendScalarsOfIsLocalization_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.extendScalarsOfIsLocalization_apply'", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.extendScalarsOfIsLocalizationEquiv", "kind": "definition", "module": "Mathlib.RingTheory.Localization.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.extendScalarsOfIsLocalization", "kind": "definition", "module": "Mathlib.RingTheory.Localization.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.extendScalarsOfIsLocalizationEquiv", "kind": "definition", "module": "Mathlib.RingTheory.Localization.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalizedModule.mapExtendScalars", "kind": "definition", "module": "Mathlib.RingTheory.Localization.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalizedModule.mapEquiv", "kind": "definition", "module": "Mathlib.RingTheory.Localization.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocalizedModule.map", "kind": "definition", "module": "Mathlib.RingTheory.Localization.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocalizedModule.map_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Module", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "LocalizedModule.map_id", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocalizedModule.map_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocalizedModule.map_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocalizedModule.restrictScalars_map_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Module", "is_tactic_proof": true, "tactics": ["rw", "apply", "rw", "ext", "simp"], "tactic_count": 5}
{"name": "LocalizedModule.coe_map_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Module", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "IsLocalizedModule.map_injective_iff_localizedModuleMap_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Module", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsLocalizedModule.map_surjective_iff_localizedModuleMap_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Module", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsLocalizedModule.map_bijective_iff_localizedModuleMap_bijective", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Module", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Algebra.map_leftMulMatrix_localization", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.NormTrace", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Algebra.norm_localization", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.NormTrace", "is_tactic_proof": true, "tactics": ["cases", "haveI", "simp", "let", "letI", "rw"], "tactic_count": 6}
{"name": "Algebra.norm_eq_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.NormTrace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.trace_localization", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.NormTrace", "is_tactic_proof": true, "tactics": ["cases", "haveI", "simp", "let", "letI", "rw", "exact"], "tactic_count": 7}
{"name": "Algebra.traceMatrix_localizationLocalization", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.NormTrace", "is_tactic_proof": true, "tactics": ["have", "have", "ext", "simp_rw", "exact"], "tactic_count": 5}
{"name": "Algebra.discr_localizationLocalization", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.NormTrace", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsFractionRing.exists_reduced_fraction", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.NumDen", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "obtain", "refine", "refine", "simp", "rw"], "tactic_count": 7}
{"name": "IsFractionRing.num", "kind": "definition", "module": "Mathlib.RingTheory.Localization.NumDen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractionRing.den", "kind": "definition", "module": "Mathlib.RingTheory.Localization.NumDen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractionRing.num_den_reduced", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.NumDen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractionRing.mk'_num_den", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.NumDen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractionRing.mk'_num_den'", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.NumDen", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "IsFractionRing.num_mul_den_eq_num_iff_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.NumDen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractionRing.num_mul_den_eq_num_iff_eq'", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.NumDen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractionRing.num_mul_den_eq_num_mul_den_iff_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.NumDen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractionRing.eq_zero_of_num_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.NumDen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractionRing.num_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.NumDen", "is_tactic_proof": true, "tactics": ["have", "simp", "simp_all"], "tactic_count": 3}
{"name": "IsFractionRing.num_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.NumDen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractionRing.isInteger_of_isUnit_den", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.NumDen", "is_tactic_proof": true, "tactics": ["obtain", "have", "use", "refine", "rw", "apply", "rw"], "tactic_count": 7}
{"name": "IsFractionRing.isUnit_den_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.NumDen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractionRing.isUnit_den_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.NumDen", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsFractionRing.associated_den_num_inv", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.NumDen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractionRing.associated_num_den_inv", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.NumDen", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "IsFractionRing.num_den_unique", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.NumDen", "is_tactic_proof": false, "tactics": ["rw", "refine", "associated_of_dvd_dvd"], "tactic_count": 3}
{"name": "IsLocalization.instForallPiUniv", "kind": "instance", "module": "Mathlib.RingTheory.Localization.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.iff_map_piEvalRingHom", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.isUnit_piRingHom_algebraMap_comp_piEvalRingHom", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.bijective_lift_piRingHom_algebraMap_comp_piEvalRingHom", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.surjective_piRingHom_algebraMap_comp_piEvalRingHom", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Pi", "is_tactic_proof": true, "tactics": ["apply", "by_cases", "have", "exact", "exact"], "tactic_count": 5}
{"name": "IsLocalization.algebraMap_pi_surjective_of_isLocalization", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Pi", "is_tactic_proof": true, "tactics": ["intro", "set", "obtain", "surjective_piRingHom_algebraMap_comp_piEvalRingHom", "refine", "rwa"], "tactic_count": 6}
{"name": "Rat.isLocalizationIsInteger_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Rat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Rat.associated_num_den", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.isFractionRingDen", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Rat", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Rat.isFractionRingNum", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.coeSubmodule", "kind": "definition", "module": "Mathlib.RingTheory.Localization.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.mem_coeSubmodule", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.coeSubmodule_mono", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.coeSubmodule_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Submodule", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsLocalization.coeSubmodule_top", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Submodule", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsLocalization.coeSubmodule_sup", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.coeSubmodule_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.coeSubmodule_fg", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.coeSubmodule_span", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Submodule", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "IsLocalization.coeSubmodule_span_singleton", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Submodule", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsLocalization.isNoetherianRing", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Submodule", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsLocalization.instIsNoetherianRingLocalization", "kind": "instance", "module": "Mathlib.RingTheory.Localization.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.EssFiniteType.isNoetherianRing", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Submodule", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "IsLocalization.coeSubmodule_le_coeSubmodule", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.coeSubmodule_strictMono", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.coeSubmodule_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.coeSubmodule_isPrincipal", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Submodule", "is_tactic_proof": true, "tactics": ["constructor", "have", "obtain", "refine", "rw", "refine", "rw"], "tactic_count": 7}
{"name": "IsLocalization.mem_span_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Submodule", "is_tactic_proof": true, "tactics": ["constructor", "intro", "refine", "rintro", "exact", "exact", "rintro", "refine", "z", "rw", "smul_smul]", "congr", "rw", "rw", "rintro", "obtain", "refine", "rw", "mul_mk'_eq_mk'_of_mul]", "rintro", "exact"], "tactic_count": 21}
{"name": "IsLocalization.mem_span_map", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Submodule", "is_tactic_proof": true, "tactics": ["refine", "constructor", "rw", "rintro", "refine", "rw", "rintro", "refine", "rw"], "tactic_count": 9}
{"name": "IsFractionRing.coeSubmodule_le_coeSubmodule", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractionRing.coeSubmodule_strictMono", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractionRing.coeSubmodule_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFractionRing.coeSubmodule_isPrincipal", "kind": "theorem", "module": "Mathlib.RingTheory.Localization.Submodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "kroneckerTMulLinearEquiv", "kind": "definition", "module": "Mathlib.RingTheory.MatrixAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "kroneckerTMulLinearEquiv_tmul", "kind": "theorem", "module": "Mathlib.RingTheory.MatrixAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "kroneckerTMulLinearEquiv_symm_kroneckerTMul", "kind": "theorem", "module": "Mathlib.RingTheory.MatrixAlgebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "kroneckerTMulAlgEquiv_symm_single_tmul", "kind": "theorem", "module": "Mathlib.RingTheory.MatrixAlgebra", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "kroneckerTMulLinearEquiv_one", "kind": "theorem", "module": "Mathlib.RingTheory.MatrixAlgebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "kroneckerTMulLinearEquiv_mul", "kind": "theorem", "module": "Mathlib.RingTheory.MatrixAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "kroneckerLinearEquiv", "kind": "definition", "module": "Mathlib.RingTheory.MatrixAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "kroneckerLinearEquiv_tmul", "kind": "theorem", "module": "Mathlib.RingTheory.MatrixAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "kroneckerLinearEquiv_symm_kronecker", "kind": "theorem", "module": "Mathlib.RingTheory.MatrixAlgebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MatrixEquivTensor.toFunBilinear", "kind": "definition", "module": "Mathlib.RingTheory.MatrixAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MatrixEquivTensor.toFunBilinear_apply", "kind": "theorem", "module": "Mathlib.RingTheory.MatrixAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MatrixEquivTensor.toFunLinear", "kind": "definition", "module": "Mathlib.RingTheory.MatrixAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MatrixEquivTensor.toFunAlgHom", "kind": "definition", "module": "Mathlib.RingTheory.MatrixAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MatrixEquivTensor.toFunAlgHom_apply", "kind": "theorem", "module": "Mathlib.RingTheory.MatrixAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MatrixEquivTensor.invFun", "kind": "definition", "module": "Mathlib.RingTheory.MatrixAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MatrixEquivTensor.invFun_zero", "kind": "theorem", "module": "Mathlib.RingTheory.MatrixAlgebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MatrixEquivTensor.invFun_add", "kind": "theorem", "module": "Mathlib.RingTheory.MatrixAlgebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MatrixEquivTensor.invFun_smul", "kind": "theorem", "module": "Mathlib.RingTheory.MatrixAlgebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MatrixEquivTensor.invFun_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.MatrixAlgebra", "is_tactic_proof": true, "tactics": ["dsimp", "simp", "congr", "conv_rhs", "convert"], "tactic_count": 5}
{"name": "MatrixEquivTensor.right_inv", "kind": "theorem", "module": "Mathlib.RingTheory.MatrixAlgebra", "is_tactic_proof": true, "tactics": ["simp", "convert", "conv_lhs", "refine", "dsimp", "split_ifs"], "tactic_count": 6}
{"name": "MatrixEquivTensor.left_inv", "kind": "theorem", "module": "Mathlib.RingTheory.MatrixAlgebra", "is_tactic_proof": true, "tactics": ["induction", "zero", "tmul", "add", "rw", "conv_rhs"], "tactic_count": 6}
{"name": "MatrixEquivTensor.equiv", "kind": "definition", "module": "Mathlib.RingTheory.MatrixAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "matrixEquivTensor", "kind": "definition", "module": "Mathlib.RingTheory.MatrixAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "matrixEquivTensor_apply", "kind": "theorem", "module": "Mathlib.RingTheory.MatrixAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "matrixEquivTensor_apply_single", "kind": "theorem", "module": "Mathlib.RingTheory.MatrixAlgebra", "is_tactic_proof": true, "tactics": ["have", "simp"], "tactic_count": 2}
{"name": "matrixEquivTensor_apply_symm", "kind": "theorem", "module": "Mathlib.RingTheory.MatrixAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.kroneckerTMulAlgEquiv", "kind": "definition", "module": "Mathlib.RingTheory.MatrixAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.kroneckerTMulAlgEquiv_apply", "kind": "theorem", "module": "Mathlib.RingTheory.MatrixAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.kroneckerTMulAlgEquiv_symm_apply", "kind": "theorem", "module": "Mathlib.RingTheory.MatrixAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.kroneckerTMulStarAlgEquiv", "kind": "definition", "module": "Mathlib.RingTheory.MatrixAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.toAlgEquiv_kroneckerTMulStarAlgEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.MatrixAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.kroneckerTMulStarAlgEquiv_apply", "kind": "theorem", "module": "Mathlib.RingTheory.MatrixAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.kroneckerTMulStarAlgEquiv_symm_apply", "kind": "theorem", "module": "Mathlib.RingTheory.MatrixAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.kroneckerAlgEquiv", "kind": "definition", "module": "Mathlib.RingTheory.MatrixAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.toLinearEquiv_kroneckerAlgEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.MatrixAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.kroneckerAlgEquiv_apply", "kind": "theorem", "module": "Mathlib.RingTheory.MatrixAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.kroneckerAlgEquiv_symm_apply", "kind": "theorem", "module": "Mathlib.RingTheory.MatrixAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.kroneckerStarAlgEquiv", "kind": "definition", "module": "Mathlib.RingTheory.MatrixAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.toAlgEquiv_kroneckerStarAlgEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.MatrixAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.kroneckerStarAlgEquiv_apply", "kind": "theorem", "module": "Mathlib.RingTheory.MatrixAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.kroneckerStarAlgEquiv_symm_apply", "kind": "theorem", "module": "Mathlib.RingTheory.MatrixAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "matPolyEquiv", "kind": "definition", "module": "Mathlib.RingTheory.MatrixPolynomialAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "matPolyEquiv_symm_C", "kind": "theorem", "module": "Mathlib.RingTheory.MatrixPolynomialAlgebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "matPolyEquiv_map_C", "kind": "theorem", "module": "Mathlib.RingTheory.MatrixPolynomialAlgebra", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "matPolyEquiv_symm_X", "kind": "theorem", "module": "Mathlib.RingTheory.MatrixPolynomialAlgebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "matPolyEquiv_diagonal_X", "kind": "theorem", "module": "Mathlib.RingTheory.MatrixPolynomialAlgebra", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "matPolyEquiv_coeff_apply_aux_1", "kind": "theorem", "module": "Mathlib.RingTheory.MatrixPolynomialAlgebra", "is_tactic_proof": true, "tactics": ["simp", "apply", "simp", "simp", "rw", "congr"], "tactic_count": 6}
{"name": "matPolyEquiv_coeff_apply_aux_2", "kind": "theorem", "module": "Mathlib.RingTheory.MatrixPolynomialAlgebra", "is_tactic_proof": true, "tactics": ["refine", "intro", "ext", "simp", "intro", "simp", "split_ifs", "funext", "simp"], "tactic_count": 9}
{"name": "matPolyEquiv_coeff_apply", "kind": "theorem", "module": "Mathlib.RingTheory.MatrixPolynomialAlgebra", "is_tactic_proof": true, "tactics": ["refine", "simp", "intro", "simp", "intro", "rw", "dsimp", "split_ifs", "constructor", "simp"], "tactic_count": 10}
{"name": "matPolyEquiv_symm_apply_coeff", "kind": "theorem", "module": "Mathlib.RingTheory.MatrixPolynomialAlgebra", "is_tactic_proof": true, "tactics": ["have", "conv_rhs", "simp"], "tactic_count": 3}
{"name": "matPolyEquiv_smul_one", "kind": "theorem", "module": "Mathlib.RingTheory.MatrixPolynomialAlgebra", "is_tactic_proof": true, "tactics": ["ext", "simp", "algebraMap_matrix_apply,", "split_ifs"], "tactic_count": 4}
{"name": "matPolyEquiv_map_smul", "kind": "theorem", "module": "Mathlib.RingTheory.MatrixPolynomialAlgebra", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "matPolyEquiv_symm_map_eval", "kind": "theorem", "module": "Mathlib.RingTheory.MatrixPolynomialAlgebra", "is_tactic_proof": false, "tactics": ["suffices", "from", "ext", "ext", "simp", "simp"], "tactic_count": 6}
{"name": "matPolyEquiv_eval_eq_map", "kind": "theorem", "module": "Mathlib.RingTheory.MatrixPolynomialAlgebra", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "matPolyEquiv_eval", "kind": "theorem", "module": "Mathlib.RingTheory.MatrixPolynomialAlgebra", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "support_subset_support_matPolyEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.MatrixPolynomialAlgebra", "is_tactic_proof": true, "tactics": ["intro", "contrapose", "simp", "intro", "rw"], "tactic_count": 5}
{"name": "eval_det", "kind": "theorem", "module": "Mathlib.RingTheory.MatrixPolynomialAlgebra", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "eval_det_add_X_smul", "kind": "theorem", "module": "Mathlib.RingTheory.MatrixPolynomialAlgebra", "is_tactic_proof": true, "tactics": ["simp", "simp"], "tactic_count": 2}
{"name": "RingHom.polyToMatrix", "kind": "definition", "module": "Mathlib.RingTheory.MatrixPolynomialAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "evalRingHom_mapMatrix_comp_polyToMatrix", "kind": "theorem", "module": "Mathlib.RingTheory.MatrixPolynomialAlgebra", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "evalRingHom_mapMatrix_comp_compRingEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.MatrixPolynomialAlgebra", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "MoritaEquivalence.instAdditiveModuleCatFunctorEqv", "kind": "instance", "module": "Mathlib.RingTheory.Morita.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MoritaEquivalence.refl", "kind": "definition", "module": "Mathlib.RingTheory.Morita.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MoritaEquivalence.symm", "kind": "definition", "module": "Mathlib.RingTheory.Morita.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MoritaEquivalence.trans", "kind": "definition", "module": "Mathlib.RingTheory.Morita.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MoritaEquivalence.ofAlgEquiv", "kind": "definition", "module": "Mathlib.RingTheory.Morita.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMoritaEquivalent.refl", "kind": "theorem", "module": "Mathlib.RingTheory.Morita.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMoritaEquivalent.symm", "kind": "theorem", "module": "Mathlib.RingTheory.Morita.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMoritaEquivalent.trans", "kind": "theorem", "module": "Mathlib.RingTheory.Morita.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMoritaEquivalent.of_algEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.Morita.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.toMatrixModCat", "kind": "definition", "module": "Mathlib.RingTheory.Morita.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MatrixModCat.toModuleCatObj", "kind": "definition", "module": "Mathlib.RingTheory.Morita.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MatrixModCat.mem_toModuleCatObj", "kind": "theorem", "module": "Mathlib.RingTheory.Morita.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MatrixModCat.fromMatrixLinear", "kind": "definition", "module": "Mathlib.RingTheory.Morita.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MatrixModCat.isScalarTower_toModuleCat", "kind": "theorem", "module": "Mathlib.RingTheory.Morita.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MatrixModCat.toModuleCat", "kind": "definition", "module": "Mathlib.RingTheory.Morita.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fromModuleCatToModuleCatLinearEquivtoModuleCatObj", "kind": "definition", "module": "Mathlib.RingTheory.Morita.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fromModuleCatToModuleCatLinearEquiv", "kind": "definition", "module": "Mathlib.RingTheory.Morita.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MatrixModCat.unitIso", "kind": "definition", "module": "Mathlib.RingTheory.Morita.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toModuleCatFromModuleCatLinearEquiv", "kind": "definition", "module": "Mathlib.RingTheory.Morita.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MatrixModCat.counitIso", "kind": "definition", "module": "Mathlib.RingTheory.Morita.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.matrixEquivalence", "kind": "definition", "module": "Mathlib.RingTheory.Morita.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "moritaEquivalenceMatrix", "kind": "definition", "module": "Mathlib.RingTheory.Morita.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMoritaEquivalent.matrix", "kind": "theorem", "module": "Mathlib.RingTheory.Morita.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteMultiplicity", "kind": "abbrev", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "emultiplicity", "kind": "definition", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "multiplicity", "kind": "definition", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "emultiplicity_eq_top", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "emultiplicity_lt_top", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "finiteMultiplicity_iff_emultiplicity_ne_top", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "finiteMultiplicity_of_emultiplicity_eq_natCast", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": true, "tactics": ["by_contra", "rw", "trivial"], "tactic_count": 3}
{"name": "multiplicity_eq_of_emultiplicity_eq_some", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": true, "tactics": ["simp", "rfl"], "tactic_count": 2}
{"name": "emultiplicity_ne_of_multiplicity_ne", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteMultiplicity.emultiplicity_eq_multiplicity", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": true, "tactics": ["cases", "simp", "rw"], "tactic_count": 3}
{"name": "FiniteMultiplicity.emultiplicity_eq_iff_multiplicity_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "emultiplicity_eq_iff_multiplicity_eq_of_ne_one", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": true, "tactics": ["constructor", "exact", "intro", "simpa"], "tactic_count": 4}
{"name": "emultiplicity_eq_zero_iff_multiplicity_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "multiplicity_eq_one_of_not_finiteMultiplicity", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "multiplicity_le_emultiplicity", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "simp"], "tactic_count": 3}
{"name": "multiplicity_eq_of_emultiplicity_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": true, "tactics": ["unfold", "rw"], "tactic_count": 2}
{"name": "multiplicity_le_of_emultiplicity_le", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": true, "tactics": ["exact_mod_cast"], "tactic_count": 1}
{"name": "FiniteMultiplicity.emultiplicity_le_of_multiplicity_le", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": true, "tactics": ["rw", "assumption_mod_cast"], "tactic_count": 2}
{"name": "le_emultiplicity_of_le_multiplicity", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": true, "tactics": ["exact_mod_cast"], "tactic_count": 1}
{"name": "FiniteMultiplicity.le_multiplicity_of_le_emultiplicity", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": true, "tactics": ["rw", "assumption_mod_cast"], "tactic_count": 2}
{"name": "multiplicity_lt_of_emultiplicity_lt", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": true, "tactics": ["exact_mod_cast"], "tactic_count": 1}
{"name": "FiniteMultiplicity.emultiplicity_lt_of_multiplicity_lt", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": true, "tactics": ["rw", "assumption_mod_cast"], "tactic_count": 2}
{"name": "lt_emultiplicity_of_lt_multiplicity", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": true, "tactics": ["exact_mod_cast"], "tactic_count": 1}
{"name": "FiniteMultiplicity.lt_multiplicity_of_lt_emultiplicity", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": true, "tactics": ["rw", "assumption_mod_cast"], "tactic_count": 2}
{"name": "emultiplicity_pos_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FiniteMultiplicity.def", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteMultiplicity.not_dvd_of_one_right", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.natCast_emultiplicity", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": true, "tactics": ["unfold", "congr"], "tactic_count": 2}
{"name": "Int.natCast_multiplicity", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteMultiplicity.not_iff_forall", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteMultiplicity.not_unit", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteMultiplicity.mul_left", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pow_dvd_of_le_emultiplicity", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": true, "tactics": ["classical", "cases", "simp", "unfold", "split", "norm_cast", "simpa", "apply"], "tactic_count": 8}
{"name": "pow_dvd_of_le_multiplicity", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pow_multiplicity_dvd", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_pow_dvd_of_emultiplicity_lt", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteMultiplicity.not_pow_dvd_of_multiplicity_lt", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": true, "tactics": ["apply", "rw", "norm_cast"], "tactic_count": 3}
{"name": "multiplicity_pos_of_dvd", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": true, "tactics": ["refine", "simpa"], "tactic_count": 2}
{"name": "emultiplicity_pos_of_dvd", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "emultiplicity_eq_of_dvd_of_not_dvd", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": true, "tactics": ["classical", "have", "simp", "true_and]", "exact"], "tactic_count": 5}
{"name": "multiplicity_eq_of_dvd_of_not_dvd", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_emultiplicity_of_pow_dvd", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteMultiplicity.le_multiplicity_of_pow_dvd", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pow_dvd_iff_le_emultiplicity", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteMultiplicity.pow_dvd_iff_le_multiplicity", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": true, "tactics": ["exact_mod_cast"], "tactic_count": 1}
{"name": "emultiplicity_lt_iff_not_dvd", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "FiniteMultiplicity.multiplicity_lt_iff_not_dvd", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "emultiplicity_eq_coe", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": true, "tactics": ["constructor", "intro", "constructor", "apply", "simp", "apply", "rw", "norm_cast", "simp", "rw", "apply"], "tactic_count": 11}
{"name": "FiniteMultiplicity.multiplicity_eq_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "emultiplicity_eq_ofNat", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteMultiplicity.not_of_isUnit_left", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteMultiplicity.not_of_one_left", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "emultiplicity_one_left", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteMultiplicity.one_right", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FiniteMultiplicity.not_of_unit_left", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "emultiplicity_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "simp", "simpa"], "tactic_count": 4}
{"name": "multiplicity_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "emultiplicity_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "multiplicity_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FiniteMultiplicity.exists_eq_pow_mul_and_not_dvd", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": true, "tactics": ["obtain", "refine", "rintro", "rw", "have", "exact"], "tactic_count": 6}
{"name": "emultiplicity_le_emultiplicity_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": true, "tactics": ["classical", "constructor", "exact", "intro", "unfold", "split", "obtain", "split", "simp_all", "not_false_eq_true,", "simp_all", "simp_all", "imp_false,"], "tactic_count": 13}
{"name": "FiniteMultiplicity.multiplicity_le_multiplicity_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": false, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "emultiplicity_eq_emultiplicity_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_emultiplicity_map", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "emultiplicity_map_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "multiplicity_map_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "emultiplicity_le_emultiplicity_of_dvd_right", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "emultiplicity_eq_of_associated_right", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "multiplicity_eq_of_associated_right", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dvd_of_emultiplicity_pos", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dvd_of_multiplicity_pos", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dvd_iff_multiplicity_pos", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dvd_iff_emultiplicity_pos", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.finiteMultiplicity_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": true, "tactics": ["rw", "exact", "or_iff_not_imp_right.2", "have", "have", "lt_of_not_ge", "b", "not_lt_of_ge"], "tactic_count": 8}
{"name": "FiniteMultiplicity.mul_right", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "emultiplicity_of_isUnit_right", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "multiplicity_of_isUnit_right", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "emultiplicity_of_one_right", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "multiplicity_of_one_right", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "emultiplicity_of_unit_right", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "multiplicity_of_unit_right", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "emultiplicity_le_emultiplicity_of_dvd_left", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "emultiplicity_eq_of_associated_left", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "multiplicity_eq_of_associated_left", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "emultiplicity_mk_eq_emultiplicity", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FiniteMultiplicity.ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "emultiplicity_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "emultiplicity_zero_eq_zero_of_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "multiplicity_zero_eq_zero_of_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteMultiplicity.or_of_add", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": true, "tactics": ["by_contra", "obtain", "simp_all"], "tactic_count": 3}
{"name": "min_le_emultiplicity_add", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": true, "tactics": ["cases", "simp", "contrapose", "simp", "exact", "apply", "simp"], "tactic_count": 7}
{"name": "FiniteMultiplicity.neg_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": true, "tactics": ["unfold", "congr", "simp"], "tactic_count": 3}
{"name": "emultiplicity_neg", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "multiplicity_neg", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "finiteMultiplicity_mul_aux", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prime.finiteMultiplicity_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "FiniteMultiplicity.pow", "kind": "theorem", "module": "Mathlib.RingTheory.Multiplicity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MvPolynomial.instSmall", "kind": "instance", "module": "Mathlib.RingTheory.MvPolynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MvPolynomial.instExpChar", "kind": "instance", "module": "Mathlib.RingTheory.MvPolynomial.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "MvPolynomial.mapRange_eq_map", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw"], "tactic_count": 3}
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{"name": "MvPolynomial.totalDegree_zero_iff_isHomogeneous", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Homogeneous", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MvPolynomial.homogeneousSubmodule_zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Homogeneous", "is_tactic_proof": true, "tactics": ["ext", "rw", "grind"], "tactic_count": 3}
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{"name": "MvPolynomial.isHomogeneous_zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Homogeneous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MvPolynomial.isHomogeneous_X", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Homogeneous", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
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{"name": "MvPolynomial.IsHomogeneous.sub", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Homogeneous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.IsHomogeneous.totalDegree_le", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Homogeneous", "is_tactic_proof": true, "tactics": ["apply", "intro", "rw", "simp_rw"], "tactic_count": 4}
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{"name": "MvPolynomial.IsHomogeneous.finSuccEquiv_coeff_isHomogeneous", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Homogeneous", "is_tactic_proof": true, "tactics": ["intro", "rw", "have", "simpa", "simp", "exact"], "tactic_count": 6}
{"name": "MvPolynomial.IsHomogeneous.coeff_isHomogeneous_of_optionEquivLeft_symm", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Homogeneous", "is_tactic_proof": true, "tactics": ["obtain", "let", "let", "let", "let", "have", "suffices", "convert", "dsimp", "rw", "simp"], "tactic_count": 11}
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{"name": "MvPolynomial.irreducible_of_totalDegree_eq_one", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.IrreducibleQuadratic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MonomialOrder.degree", "kind": "definition", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonomialOrder.leadingCoeff", "kind": "definition", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonomialOrder.Monic", "kind": "definition", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonomialOrder.leadingTerm", "kind": "definition", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonomialOrder.C_mul_leadingCoeff_monomial_degree", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MonomialOrder.Monic.of_subsingleton", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonomialOrder.Monic.decidable", "kind": "instance", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
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{"name": "MonomialOrder.Monic.ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["rintro", "simp"], "tactic_count": 2}
{"name": "MonomialOrder.degree_monomial_le", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["simp", "apply", "simp"], "tactic_count": 3}
{"name": "MonomialOrder.degree_monomial", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["simp", "split_ifs"], "tactic_count": 2}
{"name": "MonomialOrder.degree_X_le_single", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonomialOrder.degree_X", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["classical", "change", "rw"], "tactic_count": 3}
{"name": "MonomialOrder.degree_one", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["nontriviality", "classical", "simp"], "tactic_count": 3}
{"name": "MonomialOrder.leadingCoeff_monomial", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["classical", "simp", "split_ifs"], "tactic_count": 3}
{"name": "MonomialOrder.monic_monomial_one", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonomialOrder.monic_monomial", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MonomialOrder.leadingCoeff_X", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonomialOrder.monic_X", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonomialOrder.leadingCoeff_one", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonomialOrder.monic_one", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonomialOrder.degree_le_iff", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["unfold", "simp"], "tactic_count": 2}
{"name": "MonomialOrder.degree_lt_iff", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["simp", "unfold", "simp", "exact"], "tactic_count": 4}
{"name": "MonomialOrder.le_degree", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["unfold", "simp"], "tactic_count": 2}
{"name": "MonomialOrder.coeff_eq_zero_of_lt", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["rw", "by_contra", "apply"], "tactic_count": 3}
{"name": "MonomialOrder.leadingCoeff_ne_zero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["constructor", "rw", "intro", "rw", "intro", "rw", "rw", "suffices", "obtain", "rw", "exact", "exact"], "tactic_count": 12}
{"name": "MonomialOrder.leadingCoeff_eq_zero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MonomialOrder.coeff_degree_ne_zero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonomialOrder.degree_mem_support_iff", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonomialOrder.coeff_degree_eq_zero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonomialOrder.degree_mem_support", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "MonomialOrder.degree_eq_zero_iff_totalDegree_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["rw", "rw", "rw", "rw", "apply", "intro", "apply", "rw", "simp", "exact"], "tactic_count": 10}
{"name": "MonomialOrder.degree_C", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MonomialOrder.leadingCoeff_C", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MonomialOrder.eq_C_of_degree_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["ext", "simp", "classical", "by_cases", "simp", "rw", "apply", "rw", "exact"], "tactic_count": 9}
{"name": "MonomialOrder.degree_eq_zero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonomialOrder.degree_add_le", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["conv_rhs", "rw", "simp", "intro", "by_cases", "left", "exact", "right", "apply", "simp", "simpa"], "tactic_count": 11}
{"name": "MonomialOrder.degree_sum_le", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["induction", "empty", "cons", "rw", "exact"], "tactic_count": 5}
{"name": "MonomialOrder.degree_add_of_lt", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["apply", "apply", "apply", "simp", "apply", "rw", "intro", "rw", "apply", "simp", "apply"], "tactic_count": 11}
{"name": "MonomialOrder.degree_add_eq_right_of_lt", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MonomialOrder.leadingCoeff_add_of_lt", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MonomialOrder.Monic.add_of_lt", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MonomialOrder.degree_add_of_ne", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "rw", "rw", "simp"], "tactic_count": 5}
{"name": "MonomialOrder.degree_mul_le", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["classical", "rw", "intro", "rw", "intro", "rw", "apply", "rintro", "simp", "dsimp", "by_cases", "rw", "suffices", "simp", "apply", "grw", "exact"], "tactic_count": 17}
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{"name": "MonomialOrder.coeff_mul_of_degree_add", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonomialOrder.degree_mul_of_mul_leadingCoeff_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["apply", "apply", "apply", "rw", "exact"], "tactic_count": 5}
{"name": "MonomialOrder.leadingCoeff_mul_of_mul_leadingCoeff_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MonomialOrder.degree_mul_of_left_mem_nonZeroDivisors", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["apply", "apply", "simp"], "tactic_count": 3}
{"name": "MonomialOrder.degree_mul_of_right_mem_nonZeroDivisors", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonomialOrder.leadingCoeff_mul_of_left_mem_nonZeroDivisors", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MonomialOrder.leadingCoeff_mul_of_right_mem_nonZeroDivisors", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MonomialOrder.degree_mul_of_isRegular_left", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["apply", "simp", "exact"], "tactic_count": 3}
{"name": "MonomialOrder.leadingCoeff_mul_of_isRegular_left", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MonomialOrder.degree_mul_of_isRegular_right", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MonomialOrder.leadingCoeff_mul_of_isRegular_right", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MonomialOrder.Monic.mul", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["nontriviality", "suffices", "rw", "rw", "exact", "rw"], "tactic_count": 6}
{"name": "MonomialOrder.degree_mul", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["apply", "simp", "tauto"], "tactic_count": 3}
{"name": "MonomialOrder.leadingCoeff_mul", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MonomialOrder.degree_pow_le", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "simp", "apply", "simp", "exact"], "tactic_count": 7}
{"name": "MonomialOrder.coeff_pow_nsmul_degree", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "simp", "rw"], "tactic_count": 5}
{"name": "MonomialOrder.degree_pow_of_pow_leadingCoeff_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["apply", "apply", "apply", "rw", "exact"], "tactic_count": 5}
{"name": "MonomialOrder.leadingCoeff_pow_of_pow_leadingCoeff_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MonomialOrder.Monic.pow", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["nontriviality", "rw", "rw", "exact"], "tactic_count": 4}
{"name": "MonomialOrder.degree_pow", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "by_cases", "rw", "rw", "apply", "apply", "rw", "exact"], "tactic_count": 9}
{"name": "MonomialOrder.leadingCoeff_pow", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MonomialOrder.degree_smul_le", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["rw", "apply", "simp"], "tactic_count": 3}
{"name": "MonomialOrder.degree_smul_of_mem_nonZeroDivisors", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "apply", "apply", "apply", "simp", "rw", "simp"], "tactic_count": 8}
{"name": "MonomialOrder.degree_smul_of_isRegular", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonomialOrder.degree_prod_le", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "simp", "rw", "insert", "rw", "apply", "simp"], "tactic_count": 9}
{"name": "MonomialOrder.coeff_prod_sum_degree", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "insert", "simp", "rw", "exact"], "tactic_count": 7}
{"name": "MonomialOrder.degree_prod_of_mem_nonZeroDivisors", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["cases", "inl", "inr", "apply", "refine", "rw", "exact", "nonZeroDivisors.ne_zero"], "tactic_count": 8}
{"name": "MonomialOrder.degree_prod_of_regular", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["cases", "inl", "inr", "apply", "refine", "rw", "exact"], "tactic_count": 7}
{"name": "MonomialOrder.degree_prod", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["cases", "inl", "inr", "apply", "refine", "simpa"], "tactic_count": 6}
{"name": "MonomialOrder.degree_mul'", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["apply", "exact"], "tactic_count": 2}
{"name": "MonomialOrder.notMem_support_of_degree_lt", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MonomialOrder.leadingCoeff_prod_of_mem_nonZeroDivisors", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MonomialOrder.leadingCoeff_prod_of_regular", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MonomialOrder.Monic.prod", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["rw", "exact", "intro", "rw", "exact"], "tactic_count": 5}
{"name": "MonomialOrder.leadingTerm_eq_zero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MonomialOrder.leadingTerm_zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MonomialOrder.image_leadingTerm_sdiff_singleton_zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "MonomialOrder.image_leadingTerm_insert_zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "MonomialOrder.degree_leadingTerm", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["classical", "simp", "simp_intro"], "tactic_count": 3}
{"name": "MonomialOrder.leadingCoeff_leadingTerm", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MonomialOrder.leadingTerm_leadingTerm", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "MonomialOrder.leadingTerm_C", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MonomialOrder.leadingTerm_monomial", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "MonomialOrder.degree_leadingTerm_mul", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["wlog", "obtain", "classical"], "tactic_count": 3}
{"name": "MonomialOrder.degree_mul_leadingTerm", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonomialOrder.degree_lt_of_left_ne_zero_of_degree_mul_lt", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["wlog", "simp", "apply", "simpa"], "tactic_count": 4}
{"name": "MonomialOrder.degree_mul_lt_iff_left_lt_of_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["refine", "intro", "simpa"], "tactic_count": 3}
{"name": "MonomialOrder.sPolynomial", "kind": "definition", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonomialOrder.sPolynomial_def", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": false, "tactics": ["suffices", "rw", "intro", "ext", "obtain"], "tactic_count": 5}
{"name": "MonomialOrder.degree_ne_zero_of_sub_leadingTerm_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["contrapose", "rw"], "tactic_count": 2}
{"name": "MonomialOrder.degree_neg", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["unfold", "rw"], "tactic_count": 2}
{"name": "MonomialOrder.leadingCoeff_neg", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MonomialOrder.degree_sub_le", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["rw", "apply", "rw"], "tactic_count": 3}
{"name": "MonomialOrder.degree_sub_of_lt", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["rw", "apply", "simp"], "tactic_count": 3}
{"name": "MonomialOrder.leadingCoeff_sub_of_lt", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["rw", "apply", "simp"], "tactic_count": 3}
{"name": "MonomialOrder.degree_sub_leadingTerm_le", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "MonomialOrder.degree_sub_leadingTerm_lt_degree", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["classical", "by_cases", "simpa", "apply", "by_contra", "simp", "apply", "rw", "simp"], "tactic_count": 9}
{"name": "MonomialOrder.degree_sub_leadingTerm_lt_iff", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["refine", "intro", "simp", "exact"], "tactic_count": 4}
{"name": "MonomialOrder.sPolynomial_antisymm", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonomialOrder.sPolynomial_left_zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MonomialOrder.sPolynomial_right_zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MonomialOrder.sPolynomial_self", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonomialOrder.degree_sPolynomial_le", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["classical", "wlog", "simp", "apply", "apply", "simp"], "tactic_count": 6}
{"name": "MonomialOrder.coeff_sPolynomial_sup_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["rw", "nth_rewrite", "nth_rewrite", "unfold", "ring"], "tactic_count": 5}
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{"name": "MonomialOrder.degree_sPolynomial_lt_sup_degree", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonomialOrder.sPolynomial_lt_of_degree_ne_zero_of_degree_eq", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MonomialOrder.sPolynomial_monomial_mul", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["classical", "simp", "wlog", "rcases", "have", "have", "simp_rw", "m.leadingCoeff_mul", "reduceIte,", "rw", "tsub_add_tsub_cancel", "tsub_add_eq_add_tsub", "add_tsub_add_eq_tsub_right,"], "tactic_count": 13}
{"name": "MonomialOrder.sPolynomial_monomial_mul'", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["classical", "wlog", "simp"], "tactic_count": 3}
{"name": "MonomialOrder.sPolynomial_leadingTerm_mul", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MonomialOrder.sPolynomial_leadingTerm_mul'", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["classical", "wlog", "simp"], "tactic_count": 3}
{"name": "MonomialOrder.sPolynomial_decomposition", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "insert", "by_cases", "simp_all", "simp", "simp", "obtain", "use", "simp", "simp", "sPolynomial_self,", "simp", "trans", "suffices", "rw", "neg_mul,", "rw", "trans", "unfold", "congr", "apply", "intro", "rcases", "rw", "exact", "apply", "intro", "rw", "obtain", "simp"], "tactic_count": 32}
{"name": "MonomialOrder.isUnit_leadingCoeff", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MonomialOrder.sPolynomial_decomposition'", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["refine", "simpa"], "tactic_count": 2}
{"name": "MonomialOrder.degree_X_add_C", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["rw", "simp", "rw", "simp"], "tactic_count": 4}
{"name": "MonomialOrder.degree_X_sub_C", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MonomialOrder.monic_X_add_C", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["nontriviality", "apply", "simp"], "tactic_count": 3}
{"name": "MonomialOrder.monic_X_sub_C", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "MvPolynomial.degree_degLexDegree", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder.DegLex", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "apply", "exact", "unfold", "apply", "intro", "exact"], "tactic_count": 8}
{"name": "MvPolynomial.degLex_totalDegree_monotone", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.MonomialOrder.DegLex", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Multiset.esymm", "kind": "definition", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.esymm_map_val", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.Defs", "is_tactic_proof": true, "tactics": ["simp", "simp"], "tactic_count": 2}
{"name": "Multiset.pow_smul_esymm", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.Defs", "is_tactic_proof": true, "tactics": ["rw", "trans", "refine", "rw", "simp_rw"], "tactic_count": 5}
{"name": "Multiset.esymm_pair_one", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multiset.esymm_pair_two", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MvPolynomial.IsSymmetric", "kind": "definition", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.symmetricSubalgebra", "kind": "definition", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.mem_symmetricSubalgebra", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.IsSymmetric.C", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.IsSymmetric.zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.IsSymmetric.one", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.IsSymmetric.add", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.IsSymmetric.mul", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.IsSymmetric.smul", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.IsSymmetric.map", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.IsSymmetric.rename", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.isSymmetric_rename", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.IsSymmetric.neg", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.IsSymmetric.sub", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.renameSymmetricSubalgebra", "kind": "definition", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MvPolynomial.esymmPart", "kind": "definition", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.esymm_eq_multiset_esymm", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.Defs", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "MvPolynomial.aeval_esymm_eq_multiset_esymm", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.Defs", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MvPolynomial.esymm_eq_sum_subtype", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.esymm_eq_sum_monomial", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.Defs", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MvPolynomial.esymm_zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MvPolynomial.esymm_one", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MvPolynomial.esymmPart_zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MvPolynomial.esymmPart_indiscrete", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.Defs", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "MvPolynomial.map_esymm", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.Defs", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MvPolynomial.rename_esymm", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.esymm_isSymmetric", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.Defs", "is_tactic_proof": true, "tactics": ["intro", "rw"], "tactic_count": 2}
{"name": "MvPolynomial.support_esymm''", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.Defs", "is_tactic_proof": true, "tactics": ["rw", "simp", "refine", "intro", "rw", "rw", "simp", "rintro", "have", "rw", "have", "intro", "rw", "have", "have", "rw", "simp", "exact", "all_goals"], "tactic_count": 19}
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{"name": "MvPolynomial.support_esymm", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MvPolynomial.degrees_esymm", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.Defs", "is_tactic_proof": true, "tactics": ["classical", "have", "funext", "simp", "rw", "have", "refine", "rw", "obtain", "simpa"], "tactic_count": 10}
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{"name": "MvPolynomial.hsymmPart", "kind": "definition", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.hsymm_zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MvPolynomial.hsymm_one", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.Defs", "is_tactic_proof": true, "tactics": ["symm", "apply", "simp"], "tactic_count": 3}
{"name": "MvPolynomial.hsymmPart_zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MvPolynomial.hsymmPart_indiscrete", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.Defs", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "MvPolynomial.map_hsymm", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MvPolynomial.rename_hsymm", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.Defs", "is_tactic_proof": true, "tactics": ["simp_rw", "apply", "simp"], "tactic_count": 3}
{"name": "MvPolynomial.hsymm_isSymmetric", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.psum", "kind": "definition", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.psumPart", "kind": "definition", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.psum_zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MvPolynomial.psum_one", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MvPolynomial.psumPart_zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MvPolynomial.psumPart_indiscrete", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MvPolynomial.rename_psum", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.Defs", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MvPolynomial.psum_isSymmetric", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.msymm", "kind": "definition", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.msymm_zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.Defs", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "MvPolynomial.msymm_one", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.Defs", "is_tactic_proof": false, "tactics": ["have", "simp_rw", "symm", "rw", "apply", "intro", "congr", "intro", "rw", "congr"], "tactic_count": 10}
{"name": "MvPolynomial.rename_msymm", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.Defs", "is_tactic_proof": true, "tactics": ["rw", "apply", "intro", "rw", "simp"], "tactic_count": 5}
{"name": "MvPolynomial.msymm_isSymmetric", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.accumulate", "kind": "definition", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.FundamentalTheorem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.invAccumulate", "kind": "definition", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.FundamentalTheorem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.accumulate_rec", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.FundamentalTheorem", "is_tactic_proof": true, "tactics": ["simp_rw", "convert", "ext", "rw", "simp_rw", "rw", "exact"], "tactic_count": 7}
{"name": "Fin.accumulate_last", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.FundamentalTheorem", "is_tactic_proof": true, "tactics": ["rw", "apply", "rw", "refine", "rw", "exact"], "tactic_count": 6}
{"name": "Fin.accumulate_injective", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.FundamentalTheorem", "is_tactic_proof": true, "tactics": ["refine", "obtain", "have", "rwa", "have", "rw", "iterate"], "tactic_count": 7}
{"name": "Fin.accumulate_invAccumulate", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.FundamentalTheorem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.esymmAlgHom", "kind": "definition", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.FundamentalTheorem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.esymmAlgHom_apply", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.FundamentalTheorem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.rename_esymmAlgHom", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.FundamentalTheorem", "is_tactic_proof": true, "tactics": ["ext", "simp_rw", "renameSymmetricSubalgebra_apply_coe,"], "tactic_count": 3}
{"name": "MvPolynomial.esymmAlgHomMonomial", "kind": "definition", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.FundamentalTheorem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.isSymmetric_esymmAlgHomMonomial", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.FundamentalTheorem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.esymmAlgHomMonomial_single", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.FundamentalTheorem", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MvPolynomial.esymmAlgHomMonomial_single_one", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.FundamentalTheorem", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MvPolynomial.esymmAlgHomMonomial_add", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.FundamentalTheorem", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MvPolynomial.esymmAlgHom_zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.FundamentalTheorem", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "_private.Mathlib.RingTheory.MvPolynomial.Symmetric.FundamentalTheorem.0.MvPolynomial.supDegree_monic_esymm", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.FundamentalTheorem", "is_tactic_proof": false, "tactics": ["have", "supDegree_leadingCoeff_sum_eq", "rwa", "supDegree_single_ne_zero", "exact", "intro", "have", "simp_rw", "rw", "simp_rw", "have", "refine", "all_goals", "have", "rw", "by_contra", "exact", "rw"], "tactic_count": 18}
{"name": "MvPolynomial.supDegree_esymm", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.FundamentalTheorem", "is_tactic_proof": true, "tactics": ["rw", "ext", "simp_rw", "mem_filter_univ,"], "tactic_count": 4}
{"name": "MvPolynomial.monic_esymm", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.FundamentalTheorem", "is_tactic_proof": true, "tactics": ["cases", "zero", "rw", "exact", "succ", "nontriviality", "exact"], "tactic_count": 7}
{"name": "MvPolynomial.leadingCoeff_esymmAlgHomMonomial", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Symmetric.FundamentalTheorem", "is_tactic_proof": true, "tactics": ["induction", "zero", "add_single", "ih", "rw", "exacts"], "tactic_count": 6}
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{"name": "MvPolynomial.aeval_map_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Tower", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MvPolynomial.aeval_algebraMap_apply", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Tower", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MvPolynomial.aeval_C_comp_left", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Tower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.aeval_algebraMap_eq_zero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.Tower", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "MvPolynomial.weightedTotalDegree'_eq_bot_iff", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.WeightedHomogeneous", "is_tactic_proof": false, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "MvPolynomial.weightedTotalDegree'_zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.WeightedHomogeneous", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MvPolynomial.weightedTotalDegree", "kind": "definition", "module": "Mathlib.RingTheory.MvPolynomial.WeightedHomogeneous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.weightedTotalDegree_coe", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.WeightedHomogeneous", "is_tactic_proof": true, "tactics": ["rw", "obtain", "apply", "simp", "intro", "exact", "simp", "have", "rw", "simpa"], "tactic_count": 10}
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{"name": "MvPolynomial.IsWeightedHomogeneous", "kind": "definition", "module": "Mathlib.RingTheory.MvPolynomial.WeightedHomogeneous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MvPolynomial.mem_weightedHomogeneousSubmodule", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.WeightedHomogeneous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.weightedHomogeneousSubmodule_eq_finsupp_supported", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.WeightedHomogeneous", "is_tactic_proof": true, "tactics": ["ext", "rw", "simp", "rfl"], "tactic_count": 4}
{"name": "MvPolynomial.weightedHomogeneousSubmodule_mul", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.WeightedHomogeneous", "is_tactic_proof": true, "tactics": ["classical", "rw", "intro", "rw", "obtain", "have", "contrapose", "by_cases", "rw"], "tactic_count": 9}
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{"name": "MvPolynomial.isWeightedHomogeneous_C", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.WeightedHomogeneous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.isWeightedHomogeneous_zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.WeightedHomogeneous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.isWeightedHomogeneous_one", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.WeightedHomogeneous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.isWeightedHomogeneous_X", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.WeightedHomogeneous", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "MvPolynomial.IsWeightedHomogeneous.coeff_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.WeightedHomogeneous", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "MvPolynomial.IsWeightedHomogeneous.inj_right", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.WeightedHomogeneous", "is_tactic_proof": true, "tactics": ["obtain", "rw"], "tactic_count": 2}
{"name": "MvPolynomial.IsWeightedHomogeneous.add", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.WeightedHomogeneous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.IsWeightedHomogeneous.sum", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.WeightedHomogeneous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.IsWeightedHomogeneous.mul", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.WeightedHomogeneous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.IsWeightedHomogeneous.C_mul", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.WeightedHomogeneous", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MvPolynomial.IsWeightedHomogeneous.pow", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.WeightedHomogeneous", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "MvPolynomial.IsWeightedHomogeneous.prod", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.WeightedHomogeneous", "is_tactic_proof": true, "tactics": ["classical", "refine", "intro", "simp", "intro", "simp", "apply", "intro", "exact"], "tactic_count": 9}
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{"name": "MvPolynomial.weightedHomogeneousComponent", "kind": "definition", "module": "Mathlib.RingTheory.MvPolynomial.WeightedHomogeneous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.coeff_weightedHomogeneousComponent", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.WeightedHomogeneous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.weightedHomogeneousComponent_apply", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.WeightedHomogeneous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.weightedHomogeneousComponent_isWeightedHomogeneous", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.WeightedHomogeneous", "is_tactic_proof": true, "tactics": ["classical", "intro", "contrapose", "rw"], "tactic_count": 4}
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{"name": "MvPolynomial.weightedHomogeneousComponent_C_mul", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.WeightedHomogeneous", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MvPolynomial.weightedHomogeneousComponent_eq_zero'", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.WeightedHomogeneous", "is_tactic_proof": true, "tactics": ["classical", "rw", "intro", "exfalso"], "tactic_count": 4}
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{"name": "MvPolynomial.DirectSum.coeLinearMap_eq_dfinsuppSum", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.WeightedHomogeneous", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MvPolynomial.DirectSum.coeAddMonoidHom_eq_support_sum", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.WeightedHomogeneous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.DirectSum.coeLinearMap_eq_finsum", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.WeightedHomogeneous", "is_tactic_proof": true, "tactics": ["classical", "rw", "apply"], "tactic_count": 3}
{"name": "MvPolynomial.weightedHomogeneousComponent_directSum", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.WeightedHomogeneous", "is_tactic_proof": true, "tactics": ["classical", "rw", "convert", "rw", "intro", "exact", "rw", "intro"], "tactic_count": 8}
{"name": "MvPolynomial.weightedHomogeneousComponent_zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.WeightedHomogeneous", "is_tactic_proof": true, "tactics": ["classical", "ext1", "rcases", "simp", "rw", "simp", "simp", "obtain", "exact"], "tactic_count": 9}
{"name": "MvPolynomial.NonTorsionWeight", "kind": "definition", "module": "Mathlib.RingTheory.MvPolynomial.WeightedHomogeneous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.nonTorsionWeight_of", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.WeightedHomogeneous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.weightedDegree_eq_zero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.WeightedHomogeneous", "is_tactic_proof": false, "tactics": ["simp", "rw", "apply", "intro", "rw", "constructor", "intro", "by_contra", "exact", "order"], "tactic_count": 10}
{"name": "MvPolynomial.isWeightedHomogeneous_zero_iff_weightedTotalDegree_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.WeightedHomogeneous", "is_tactic_proof": true, "tactics": ["rw", "apply", "intro", "rw"], "tactic_count": 4}
{"name": "MvPolynomial.weightedTotalDegree_eq_zero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.WeightedHomogeneous", "is_tactic_proof": true, "tactics": ["rw", "apply", "intro", "rw", "apply", "intro", "exact"], "tactic_count": 7}
{"name": "MvPolynomial.weightedHomogeneousComponent_eq_zero_of_notMem", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.WeightedHomogeneous", "is_tactic_proof": true, "tactics": ["apply", "simp", "exact"], "tactic_count": 3}
{"name": "MvPolynomial.decompose'", "kind": "definition", "module": "Mathlib.RingTheory.MvPolynomial.WeightedHomogeneous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.decompose'_apply", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.WeightedHomogeneous", "is_tactic_proof": true, "tactics": ["rw", "by_cases", "simp", "rw"], "tactic_count": 4}
{"name": "MvPolynomial.weightedDecomposition", "kind": "definition", "module": "Mathlib.RingTheory.MvPolynomial.WeightedHomogeneous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.weightedGradedAlgebra", "kind": "definition", "module": "Mathlib.RingTheory.MvPolynomial.WeightedHomogeneous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.weightedDecomposition.decompose'_eq", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.WeightedHomogeneous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.weightedDecomposition.decompose'_apply", "kind": "theorem", "module": "Mathlib.RingTheory.MvPolynomial.WeightedHomogeneous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries", "kind": "definition", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.instInhabited", "kind": "instance", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.instZero", "kind": "instance", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.instAddMonoid", "kind": "instance", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.instAddGroup", "kind": "instance", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.instAddCommMonoid", "kind": "instance", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.instAddCommGroup", "kind": "instance", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.instNontrivial", "kind": "instance", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.instModule", "kind": "instance", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.instIsScalarTower", "kind": "instance", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.monomial", "kind": "definition", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.coeff", "kind": "definition", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.coeff_apply", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.ext", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.monomial_def", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": ["rw", "convert"], "tactic_count": 2}
{"name": "MvPowerSeries.coeff_monomial", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "MvPowerSeries.coeff_monomial_same", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": true, "tactics": ["classical", "rw", "exact"], "tactic_count": 3}
{"name": "MvPowerSeries.coeff_monomial_ne", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": true, "tactics": ["classical", "rw", "exact"], "tactic_count": 3}
{"name": "MvPowerSeries.eq_of_coeff_monomial_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.coeff_comp_monomial", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.coeff_zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.eq_zero_iff_forall_coeff_zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.ne_zero_iff_exists_coeff_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MvPowerSeries.instOne", "kind": "instance", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.coeff_one", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.coeff_zero_one", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.monomial_zero_one", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.instAddMonoidWithOne", "kind": "instance", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.instMul", "kind": "instance", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.coeff_mul", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "MvPowerSeries.zero_mul", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.mul_zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.coeff_monomial_mul", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": true, "tactics": ["classical", "have", "rw", "simp"], "tactic_count": 4}
{"name": "MvPowerSeries.coeff_mul_monomial", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": true, "tactics": ["classical", "have", "rw", "simp"], "tactic_count": 4}
{"name": "MvPowerSeries.coeff_add_monomial_mul", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MvPowerSeries.coeff_add_mul_monomial", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MvPowerSeries.commute_monomial", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "have", "rwa", "rw", "split_ifs"], "tactic_count": 6}
{"name": "MvPowerSeries.one_mul", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.mul_one", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.mul_add", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.add_mul", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.mul_assoc", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": true, "tactics": ["ext1", "classical", "simp", "apply", "aesop"], "tactic_count": 5}
{"name": "MvPowerSeries.instSemiring", "kind": "instance", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.instCommSemiring", "kind": "instance", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.instRing", "kind": "instance", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.instCommRing", "kind": "instance", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.monomial_mul_monomial", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": true, "tactics": ["classical", "ext", "simp", "split_ifs", "rw", "exact", "rw", "exact", "exact", "rw", "exact"], "tactic_count": 11}
{"name": "MvPowerSeries.C", "kind": "definition", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.monomial_zero_eq_C", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.monomial_zero_eq_C_apply", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.coeff_C", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.coeff_zero_C", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.X", "kind": "definition", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.coeff_X", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.coeff_index_single_X", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MvPowerSeries.coeff_index_single_self_X", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.coeff_zero_X", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": true, "tactics": ["classical", "rw", "intro", "exact"], "tactic_count": 4}
{"name": "MvPowerSeries.commute_X", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.X_mul", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.commute_X_pow", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.X_pow_mul", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.X_def", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.X_pow_eq", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "MvPowerSeries.coeff_X_pow", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MvPowerSeries.coeff_mul_C", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MvPowerSeries.coeff_C_mul", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MvPowerSeries.coeff_zero_mul_X", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": true, "tactics": ["have", "simp"], "tactic_count": 2}
{"name": "MvPowerSeries.coeff_zero_X_mul", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MvPowerSeries.constantCoeff", "kind": "definition", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.coeff_zero_eq_constantCoeff", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.coeff_zero_eq_constantCoeff_apply", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.constantCoeff_C", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.constantCoeff_comp_C", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.constantCoeff_zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.constantCoeff_one", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.constantCoeff_X", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.constantCoeff_smul", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.isUnit_constantCoeff", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.coeff_smul", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.smul_eq_C_mul", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "MvPowerSeries.X_inj", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.map", "kind": "definition", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.map_id", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.map_comp", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.coeff_map", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.constantCoeff_map", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.map_monomial", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": true, "tactics": ["classical", "ext", "simp"], "tactic_count": 3}
{"name": "MvPowerSeries.map_C", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.map_X", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MvPowerSeries.map_map", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "MvPowerSeries.toSubring", "kind": "definition", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.coeff_toSubring", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.constantCoeff_toSubring", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.map_toSubring", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.map_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": true, "tactics": ["simp", "congr", "simp"], "tactic_count": 3}
{"name": "MvPowerSeries.X_pow_dvd_iff", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": true, "tactics": ["classical", "constructor", "rintro", "rw", "rintro", "rw", "contrapose", "dsimp", "subst", "rw", "rw", "exact", "intro", "refine", "ext", "by_cases", "rw", "rw", "simpa", "rintro", "rw", "rw", "split_ifs", "exfalso", "apply", "rw", "refine", "ext", "simp", "exact", "intro", "exfalso", "apply", "rwa", "rw", "rintro", "rw", "rw", "split_ifs", "exfalso", "apply", "rw", "ext", "rw", "exact", "contrapose", "ext", "by_cases", "subst", "simpa", "simp"], "tactic_count": 51}
{"name": "MvPowerSeries.X_dvd_iff", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": true, "tactics": ["rw", "constructor", "exact", "exact"], "tactic_count": 4}
{"name": "MvPowerSeries.coeff_prod", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": true, "tactics": ["induction", "empty", "simp", "split_ifs", "simp", "simp", "insert", "rw", "apply", "simp", "rintro", "rw", "apply", "simp", "rintro", "rw", "intro", "rw", "exact", "simp", "mem_attach,", "forall_exists_index,", "rintro", "obtain", "simp", "exact"], "tactic_count": 26}
{"name": "MvPowerSeries.prod_monomial", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": true, "tactics": ["induction", "empty", "cons"], "tactic_count": 3}
{"name": "MvPowerSeries.coeff_pow", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": true, "tactics": ["suffices", "rw"], "tactic_count": 2}
{"name": "MvPowerSeries.monomial_pow", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MvPowerSeries.coeff_eq_zero_of_constantCoeff_nilpotent", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": true, "tactics": ["classical", "rw", "apply", "intro", "rw", "set", "have", "have", "simp", "rw", "have", "simp", "rw", "rw", "apply", "rw", "suffices", "obtain", "rw", "rw", "apply", "simp", "rw", "convert", "simp", "simp", "simp", "intro", "rw", "exact"], "tactic_count": 30}
{"name": "MvPowerSeries.instAlgebra", "kind": "instance", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.c_eq_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.algebraMap_apply", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": true, "tactics": ["change", "simp"], "tactic_count": 2}
{"name": "MvPowerSeries.mapAlgHom", "kind": "definition", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.mapAlgHom_apply", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.instNontrivialSubalgebraOfNonempty", "kind": "instance", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.toMvPowerSeries", "kind": "definition", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.coeToMvPowerSeries", "kind": "instance", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.coe_def", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.coeff_coe", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.coe_monomial", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.coe_zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.coe_one", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.coe_add", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.coe_mul", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.coe_smul", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.coe_C", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.coe_X", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.coe_injective", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": true, "tactics": ["intro", "ext", "simp_rw"], "tactic_count": 3}
{"name": "MvPolynomial.coe_inj", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.coe_eq_zero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MvPolynomial.coe_eq_one_iff", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MvPolynomial.coeToMvPowerSeries.ringHom", "kind": "definition", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.coe_pow", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.coeToMvPowerSeries.ringHom_apply", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.monomial_one_eq", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": true, "tactics": ["simp", "simp"], "tactic_count": 2}
{"name": "MvPowerSeries.monomial_eq'", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": true, "tactics": ["conv_lhs", "rw"], "tactic_count": 2}
{"name": "MvPowerSeries.monomial_smul_eq", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "MvPolynomial.coeToMvPowerSeries.algHom", "kind": "definition", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.coeToMvPowerSeries.algHom_apply", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.prod_smul_X_eq_smul_monomial_one", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": true, "tactics": ["rw", "have", "rw", "simp", "simp", "intro", "rw"], "tactic_count": 7}
{"name": "MvPowerSeries.monomial_eq", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MvPowerSeries.monomial_smul_const", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "MvPowerSeries.algebraMvPolynomial", "kind": "instance", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.algebraMvPowerSeries", "kind": "instance", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.algebraMap_apply'", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.algebraMap_apply''", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.HasEval.mono", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Evaluation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.HasEval.zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Evaluation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.HasEval.add", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Evaluation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.HasEval.mul_left", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Evaluation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.HasEval.mul_right", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Evaluation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.HasEval.map", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Evaluation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.HasEval.X", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Evaluation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.hasEvalIdeal", "kind": "definition", "module": "Mathlib.RingTheory.MvPowerSeries.Evaluation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.mem_hasEvalIdeal_iff", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Evaluation", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MvPowerSeries.HasEval.pow", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Evaluation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.MvPowerSeries.Evaluation.0.MvPowerSeries.instUniformSpaceMvPolynomial", "kind": "instance", "module": "Mathlib.RingTheory.MvPowerSeries.Evaluation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.MvPowerSeries.Evaluation.0.MvPowerSeries.instIsUniformAddGroupMvPolynomial", "kind": "instance", "module": "Mathlib.RingTheory.MvPowerSeries.Evaluation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.toMvPowerSeries_isUniformInducing", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Evaluation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.toMvPowerSeries_isDenseInducing", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Evaluation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.toMvPowerSeries_uniformContinuous", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Evaluation", "is_tactic_proof": true, "tactics": ["classical", "apply", "rw", "intro", "let", "have", "rcases", "use", "simpa", "have", "change", "filter_upwards", "simpa", "let", "let", "have", "have", "have", "hφ.comp", "filter_upwards", "simpa", "rw", "filter_upwards", "rw", "apply", "intro", "by_cases", "exact", "apply", "simp", "push_neg", "rcases", "exact"], "tactic_count": 33}
{"name": "MvPowerSeries.eval₂", "kind": "definition", "module": "Mathlib.RingTheory.MvPowerSeries.Evaluation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.eval₂_coe", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Evaluation", "is_tactic_proof": true, "tactics": ["have", "rw", "congr", "rw"], "tactic_count": 4}
{"name": "MvPowerSeries.eval₂_C", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Evaluation", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MvPowerSeries.eval₂_X", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Evaluation", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MvPowerSeries.eval₂Hom", "kind": "definition", "module": "Mathlib.RingTheory.MvPowerSeries.Evaluation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.eval₂Hom_eq_extend", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Evaluation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.coe_eval₂Hom", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Evaluation", "is_tactic_proof": true, "tactics": ["ext", "simp", "split_ifs", "obtain", "simpa", "toMvPowerSeries_isDenseInducing.extend_eq", "rw"], "tactic_count": 7}
{"name": "MvPowerSeries.uniformContinuous_eval₂", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Evaluation", "is_tactic_proof": true, "tactics": ["rw", "exact", "uniformContinuous_uniformly_extend"], "tactic_count": 3}
{"name": "MvPowerSeries.continuous_eval₂", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Evaluation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.hasSum_eval₂", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Evaluation", "is_tactic_proof": true, "tactics": ["rw", "convert", "simp", "rw"], "tactic_count": 4}
{"name": "MvPowerSeries.eval₂_eq_tsum", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Evaluation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.eval₂_unique", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Evaluation", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MvPowerSeries.comp_eval₂", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Evaluation", "is_tactic_proof": true, "tactics": ["apply", "exact", "intro", "simp", "rw", "simp"], "tactic_count": 6}
{"name": "MvPowerSeries.aeval", "kind": "definition", "module": "Mathlib.RingTheory.MvPowerSeries.Evaluation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.coe_aeval", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Evaluation", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MvPowerSeries.continuous_aeval", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Evaluation", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MvPowerSeries.aeval_coe", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Evaluation", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MvPowerSeries.aeval_unique", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Evaluation", "is_tactic_proof": true, "tactics": ["apply", "rw", "refine", "intro", "trans", "simp", "conv_lhs", "simp"], "tactic_count": 8}
{"name": "MvPowerSeries.hasSum_aeval", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Evaluation", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "MvPowerSeries.aeval_eq_sum", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Evaluation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.comp_aeval", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Evaluation", "is_tactic_proof": true, "tactics": ["apply", "simp", "rw", "congr", "simp"], "tactic_count": 5}
{"name": "MvPowerSeries.expand", "kind": "definition", "module": "Mathlib.RingTheory.MvPowerSeries.Expand", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.expand_C", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Expand", "is_tactic_proof": true, "tactics": ["conv_lhs"], "tactic_count": 1}
{"name": "MvPowerSeries.expand_X", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Expand", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.expand_monomial", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Expand", "is_tactic_proof": false, "tactics": ["rw", "simp", "simp"], "tactic_count": 3}
{"name": "MvPowerSeries.expand_one", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Expand", "is_tactic_proof": true, "tactics": ["ext1", "simp"], "tactic_count": 2}
{"name": "MvPowerSeries.expand_one_apply", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Expand", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MvPowerSeries.map_expand", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Expand", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MvPowerSeries.HasSubst.expand", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Expand", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.expand_comp_substAlgHom", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Expand", "is_tactic_proof": true, "tactics": ["ext1", "simp"], "tactic_count": 2}
{"name": "MvPowerSeries.expand_substAlgHom", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Expand", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MvPowerSeries.expand_subst", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Expand", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MvPowerSeries.expand_mul_eq_comp", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Expand", "is_tactic_proof": true, "tactics": ["ext1", "simp", "subst_X"], "tactic_count": 3}
{"name": "MvPowerSeries.expand_mul", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Expand", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.coeff_expand_smul", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Expand", "is_tactic_proof": true, "tactics": ["classical", "simp", "have", "rw", "rw", "intro", "rw", "simp"], "tactic_count": 8}
{"name": "MvPowerSeries.constantCoeff_expand", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Expand", "is_tactic_proof": true, "tactics": ["conv_lhs", "simp"], "tactic_count": 2}
{"name": "MvPowerSeries.coeff_expand_of_not_dvd", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Expand", "is_tactic_proof": true, "tactics": ["classical", "contrapose", "simp", "obtain", "by_contra", "rw", "contradiction", "have", "rw", "have", "by_contra", "rw", "contradiction", "simp"], "tactic_count": 14}
{"name": "MvPowerSeries.support_expand_subset", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Expand", "is_tactic_proof": true, "tactics": ["intro", "have", "letI", "have", "rw", "exact"], "tactic_count": 6}
{"name": "MvPowerSeries.support_expand", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Expand", "is_tactic_proof": true, "tactics": ["classical", "refine", "intro", "obtain", "simp", "by_contra", "rw", "contradiction"], "tactic_count": 8}
{"name": "MvPowerSeries.order_expand", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Expand", "is_tactic_proof": true, "tactics": ["by_cases", "simpa", "apply", "obtain", "have", "rw", "exact", "refine", "by_cases", "obtain", "rw", "simp", "exact", "obtain", "exact"], "tactic_count": 15}
{"name": "MvPowerSeries.expand_eq_expand", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Expand", "is_tactic_proof": true, "tactics": ["ext", "simp", "by_cases", "obtain", "rw", "obtain", "rw"], "tactic_count": 7}
{"name": "MvPowerSeries.trunc'_expand", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Expand", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "obtain", "by_cases", "rw", "have", "obtain", "by_contra", "exact", "have", "exact", "rw", "obtain", "rw", "by_cases", "rw", "rw"], "tactic_count": 17}
{"name": "MvPowerSeries.trunc'_expand_trunc'", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Expand", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MvPowerSeries.map_frobenius_expand", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Expand", "is_tactic_proof": true, "tactics": ["classical", "rw", "intro", "use", "refine", "have", "simp", "congr", "ext", "simp", "rw", "trunc'_expand_trunc"], "tactic_count": 12}
{"name": "MvPowerSeries.map_iterateFrobenius_expand", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Expand", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "symm", "conv_lhs", "simp_rw", "expand_mul,"], "tactic_count": 7}
{"name": "MvPowerSeries.inv.aux", "kind": "definition", "module": "Mathlib.RingTheory.MvPowerSeries.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.coeff_inv_aux", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.invOfUnit", "kind": "definition", "module": "Mathlib.RingTheory.MvPowerSeries.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.coeff_invOfUnit", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Inverse", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "MvPowerSeries.constantCoeff_invOfUnit", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Inverse", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "MvPowerSeries.mul_invOfUnit", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.invOfUnit_mul", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Inverse", "is_tactic_proof": false, "tactics": ["rw", "apply", "simp"], "tactic_count": 3}
{"name": "MvPowerSeries.isUnit_iff_constantCoeff", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Inverse", "is_tactic_proof": true, "tactics": ["constructor", "exact", "intro", "exact"], "tactic_count": 4}
{"name": "MvPowerSeries.instIsLocalRing", "kind": "instance", "module": "Mathlib.RingTheory.MvPowerSeries.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.map.isLocalHom", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.inv", "kind": "definition", "module": "Mathlib.RingTheory.MvPowerSeries.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.instInv", "kind": "instance", "module": "Mathlib.RingTheory.MvPowerSeries.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.coeff_inv", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.constantCoeff_inv", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Inverse", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "MvPowerSeries.inv_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.zero_inv", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Inverse", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MvPowerSeries.invOfUnit_eq", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.invOfUnit_eq'", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Inverse", "is_tactic_proof": true, "tactics": ["rw", "apply", "rw", "exact"], "tactic_count": 4}
{"name": "MvPowerSeries.mul_inv_cancel", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Inverse", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MvPowerSeries.inv_mul_cancel", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Inverse", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MvPowerSeries.eq_mul_inv_iff_mul_eq", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.eq_inv_iff_mul_eq_one", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Inverse", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MvPowerSeries.inv_eq_iff_mul_eq_one", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Inverse", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MvPowerSeries.mul_inv_rev", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Inverse", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "simp", "rcases", "rw", "simp", "rw"], "tactic_count": 7}
{"name": "MvPowerSeries.instInvOneClass", "kind": "instance", "module": "Mathlib.RingTheory.MvPowerSeries.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.C_inv", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Inverse", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rw", "simpa"], "tactic_count": 4}
{"name": "MvPowerSeries.X_inv", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Inverse", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MvPowerSeries.smul_inv", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Inverse", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MvPowerSeries.lexOrder", "kind": "definition", "module": "Mathlib.RingTheory.MvPowerSeries.LexOrder", "is_tactic_proof": true, "tactics": ["classical", "exact", "have", "simp", "apply", "apply", "exact", "exact"], "tactic_count": 8}
{"name": "MvPowerSeries.lexOrder_def_of_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.LexOrder", "is_tactic_proof": false, "tactics": ["suffices", "use", "unfold", "simp", "simp"], "tactic_count": 5}
{"name": "MvPowerSeries.lexOrder_eq_top_iff_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.LexOrder", "is_tactic_proof": true, "tactics": ["unfold", "split_ifs", "simp", "simp"], "tactic_count": 4}
{"name": "MvPowerSeries.lexOrder_zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.LexOrder", "is_tactic_proof": true, "tactics": ["unfold", "rw"], "tactic_count": 2}
{"name": "MvPowerSeries.exists_finsupp_eq_lexOrder_of_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.LexOrder", "is_tactic_proof": true, "tactics": ["simp", "obtain", "exact"], "tactic_count": 3}
{"name": "MvPowerSeries.coeff_ne_zero_of_lexOrder", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.LexOrder", "is_tactic_proof": false, "tactics": ["have", "have", "rcases", "simp", "suffices", "simp", "apply", "rw", "apply"], "tactic_count": 9}
{"name": "MvPowerSeries.coeff_eq_zero_of_lt_lexOrder", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.LexOrder", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "rcases", "rw", "by_contra", "exact"], "tactic_count": 6}
{"name": "MvPowerSeries.lexOrder_le_of_coeff_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.LexOrder", "is_tactic_proof": true, "tactics": ["rw", "intro", "exact"], "tactic_count": 3}
{"name": "MvPowerSeries.le_lexOrder_iff", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.LexOrder", "is_tactic_proof": true, "tactics": ["constructor", "intro", "apply", "exact", "intro", "rw", "intro", "have", "rw", "exact", "obtain", "refine", "rwa"], "tactic_count": 13}
{"name": "MvPowerSeries.min_lexOrder_le", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.LexOrder", "is_tactic_proof": true, "tactics": ["rw", "intro", "simp", "rw"], "tactic_count": 4}
{"name": "MvPowerSeries.coeff_mul_of_add_lexOrder", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.LexOrder", "is_tactic_proof": true, "tactics": ["rw", "rintro", "simp", "rcases", "exact", "rw", "rw", "norm_cast", "rw", "rw", "norm_cast"], "tactic_count": 11}
{"name": "MvPowerSeries.le_lexOrder_mul", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.LexOrder", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "apply", "rintro", "simp", "simp", "suffices", "rcases", "rw", "rw", "rw", "intro", "rw", "apply", "simp"], "tactic_count": 16}
{"name": "MvPowerSeries.lexOrder_mul", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.LexOrder", "is_tactic_proof": true, "tactics": ["obtain", "simp", "obtain", "simp", "rcases", "rcases", "apply", "rw", "apply", "rw", "exact"], "tactic_count": 11}
{"name": "MvPowerSeries.LinearTopology.basis", "kind": "definition", "module": "Mathlib.RingTheory.MvPowerSeries.LinearTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.LinearTopology.mem_basis_iff", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.LinearTopology", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MvPowerSeries.LinearTopology.basis_le", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.LinearTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.LinearTopology.basis_le_iff", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.LinearTopology", "is_tactic_proof": true, "tactics": ["classical", "constructor", "simp", "intro", "constructor", "intro", "have", "simpa", "by_contra", "apply", "rw", "intro", "have", "rw", "split_ifs", "simpa", "rintro", "exact"], "tactic_count": 18}
{"name": "MvPowerSeries.LinearTopology.hasBasis_nhds_zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.LinearTopology", "is_tactic_proof": true, "tactics": ["classical", "rw", "refine", "intro", "refine", "rw", "convert", "intro", "refine", "simpa"], "tactic_count": 10}
{"name": "MvPowerSeries.LinearTopology.instIsLinearTopologyOfMulOpposite", "kind": "instance", "module": "Mathlib.RingTheory.MvPowerSeries.LinearTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.LinearTopology.instIsLinearTopologyMulOpposite", "kind": "instance", "module": "Mathlib.RingTheory.MvPowerSeries.LinearTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.LinearTopology.isTopologicallyNilpotent_of_constantCoeff", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.LinearTopology", "is_tactic_proof": false, "tactics": ["simp_rw", "intro", "replace", "simp_rw", "constantCoeff_map]", "obtain", "use", "intro", "simpa"], "tactic_count": 9}
{"name": "MvPowerSeries.LinearTopology.isTopologicallyNilpotent_iff_constantCoeff", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.LinearTopology", "is_tactic_proof": true, "tactics": ["refine", "replace", "continuous_constantCoeff", "simpa"], "tactic_count": 4}
{"name": "MvPowerSeries.mem_nonZeroDivisorsRight_of_constantCoeff", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.NoZeroDivisors", "is_tactic_proof": true, "tactics": ["classical", "intro", "ext", "apply", "intro", "rw", "convert", "rw", "rintro", "suffices", "apply", "simp", "rintro", "simp_all", "simp"], "tactic_count": 15}
{"name": "MvPowerSeries.mem_nonZeroDivisorsLeft_of_constantCoeff", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.NoZeroDivisors", "is_tactic_proof": true, "tactics": ["classical", "intro", "ext", "apply", "intro", "rw", "convert", "rw", "rintro", "suffices", "apply", "simp", "rintro", "simp_all", "simp"], "tactic_count": 15}
{"name": "MvPowerSeries.mem_nonZeroDivisors_of_constantCoeff", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.NoZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.monomial_mem_nonzeroDivisorsLeft", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.NoZeroDivisors", "is_tactic_proof": true, "tactics": ["constructor", "intro", "have", "simpa", "intro", "ext", "have", "rw", "simpa"], "tactic_count": 9}
{"name": "MvPowerSeries.monomial_mem_nonzeroDivisorsRight", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.NoZeroDivisors", "is_tactic_proof": true, "tactics": ["constructor", "intro", "have", "simpa", "intro", "ext", "have", "rw", "simpa"], "tactic_count": 9}
{"name": "MvPowerSeries.monomial_mem_nonzeroDivisors", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.NoZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.X_mem_nonzeroDivisors", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.NoZeroDivisors", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MvPowerSeries.instNoZeroDivisors", "kind": "instance", "module": "Mathlib.RingTheory.MvPowerSeries.NoZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.weightedOrder_mul", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.NoZeroDivisors", "is_tactic_proof": true, "tactics": ["apply", "by_cases", "by_cases", "let", "have", "let", "have", "have", "simp", "intro", "rcases", "refine", "simp", "rw", "exact", "rw", "rw", "intro", "apply", "apply", "rw", "simp", "rw", "simp"], "tactic_count": 24}
{"name": "MvPowerSeries.weightedOrder_prod", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.NoZeroDivisors", "is_tactic_proof": true, "tactics": ["induction", "empty", "cons"], "tactic_count": 3}
{"name": "MvPowerSeries.order_mul", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.NoZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.order_prod", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.NoZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.ne_zero_iff_exists_coeff_ne_zero_and_weight", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MvPowerSeries.weightedOrder", "kind": "definition", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "MvPowerSeries.weightedOrder_zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MvPowerSeries.ne_zero_iff_weightedOrder_finite", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MvPowerSeries.weightedOrder_eq_top_iff", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MvPowerSeries.exists_coeff_ne_zero_and_weightedOrder", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": true, "tactics": ["classical", "simp_rw", "generalize_proofs", "exact"], "tactic_count": 4}
{"name": "MvPowerSeries.weightedOrder_le", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": true, "tactics": ["rw", "simp", "exact", "exact"], "tactic_count": 4}
{"name": "MvPowerSeries.coeff_eq_zero_of_lt_weightedOrder", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": true, "tactics": ["contrapose"], "tactic_count": 1}
{"name": "MvPowerSeries.nat_le_weightedOrder", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": true, "tactics": ["by_contra", "have", "obtain", "rw", "exact"], "tactic_count": 5}
{"name": "MvPowerSeries.le_weightedOrder", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": true, "tactics": ["cases", "rw", "ext", "apply"], "tactic_count": 4}
{"name": "MvPowerSeries.weightedOrder_eq_nat", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": true, "tactics": ["constructor", "intro", "obtain", "exact", "f.coeff_eq_zero_of_lt_weightedOrder", "rintro", "exact"], "tactic_count": 7}
{"name": "MvPowerSeries.weightedOrder_monomial", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": true, "tactics": ["classical", "split_ifs", "rw", "rw", "constructor", "use", "simp", "intro", "rw", "rintro", "exact"], "tactic_count": 11}
{"name": "MvPowerSeries.weightedOrder_monomial_of_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "MvPowerSeries.weightedOrder_one", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.min_weightedOrder_le_add", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "_private.Mathlib.RingTheory.MvPowerSeries.Order.0.MvPowerSeries.weightedOrder_add_of_weightedOrder_lt.aux", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": true, "tactics": ["obtain", "rw", "obtain", "constructor", "refine", "rw", "rw", "exact", "intro", "suffices", "rw", "coeff_eq_zero_of_lt_weightedOrder", "rw", "exact"], "tactic_count": 14}
{"name": "MvPowerSeries.weightedOrder_add_of_weightedOrder_ne", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": true, "tactics": ["refine", "wlog", "rw", "exact", "simp", "exact"], "tactic_count": 6}
{"name": "MvPowerSeries.le_weightedOrder_mul", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": true, "tactics": ["classical", "apply", "intro", "rw", "rintro", "by_cases", "rw", "by_cases", "rw", "simp", "exfalso", "apply", "rw"], "tactic_count": 13}
{"name": "MvPowerSeries.le_weightedOrder_pow", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "MvPowerSeries.le_weightedOrder_prod", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": true, "tactics": ["induction", "empty", "cons"], "tactic_count": 3}
{"name": "MvPowerSeries.le_weightedOrder_smul", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.le_weightedOrder_map", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.coeff_mul_left_one_sub_of_lt_weightedOrder", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": true, "tactics": ["simp", "apply", "exact"], "tactic_count": 3}
{"name": "MvPowerSeries.coeff_mul_right_one_sub_of_lt_weightedOrder", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": true, "tactics": ["simp", "apply", "apply"], "tactic_count": 3}
{"name": "MvPowerSeries.coeff_mul_prod_one_sub_of_lt_weightedOrder", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "insert", "simp", "rw"], "tactic_count": 6}
{"name": "MvPowerSeries.weightedOrder_neg", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": true, "tactics": ["by_contra", "have", "simp"], "tactic_count": 3}
{"name": "MvPowerSeries.weightedOrder_toSubring", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": true, "tactics": ["refine", "refine", "refine", "le_weightedOrder", "exact_mod_cast"], "tactic_count": 5}
{"name": "MvPowerSeries.ne_zero_iff_exists_coeff_ne_zero_and_degree", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "MvPowerSeries.order", "kind": "definition", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.order_zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.ne_zero_iff_order_finite", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.order_eq_top_iff", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.exists_coeff_ne_zero_and_order", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "MvPowerSeries.order_le", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MvPowerSeries.coeff_of_lt_order", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MvPowerSeries.nat_le_order", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "MvPowerSeries.le_order", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "MvPowerSeries.order_eq_nat", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "MvPowerSeries.order_monomial", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MvPowerSeries.order_monomial_of_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MvPowerSeries.min_order_le_add", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.order_add_of_order_ne", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.le_order_mul", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.le_order_pow", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.le_order_prod", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.one_le_order_iff_constCoeff_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": true, "tactics": ["constructor", "intro", "apply", "simpa", "intro", "refine", "rw", "simp"], "tactic_count": 8}
{"name": "MvPowerSeries.order_ne_zero_iff_constCoeff_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MvPowerSeries.le_order_pow_of_constantCoeff_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": true, "tactics": ["refine", "simpa"], "tactic_count": 2}
{"name": "MvPowerSeries.le_order_smul", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.le_order_map", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.coeff_mul_left_one_sub_of_lt_order", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MvPowerSeries.coeff_mul_right_one_sub_of_lt_order", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MvPowerSeries.coeff_mul_prod_one_sub_of_lt_order", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MvPowerSeries.order_neg", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.order_toSubring", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": true, "tactics": ["refine", "exact", "exact"], "tactic_count": 3}
{"name": "MvPowerSeries.IsWeightedHomogeneous", "kind": "definition", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.IsWeightedHomogeneous.coeff_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MvPowerSeries.IsWeightedHomogeneous.add", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.IsWeightedHomogeneous.mul", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.weightedHomogeneousComponent", "kind": "definition", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.coeff_weightedHomogeneousComponent", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.weightedHomogeneousComponent_of_lt_weightedOrder_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": true, "tactics": ["ext", "rw", "split_ifs", "rw", "apply", "rw", "exact", "rw"], "tactic_count": 8}
{"name": "MvPowerSeries.weightedHomogeneousComponent_of_weightedOrder", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": true, "tactics": ["intro", "obtain", "simp", "apply", "rw", "specialize", "simp", "exact"], "tactic_count": 8}
{"name": "MvPowerSeries.isWeightedHomogeneous_weightedHomogeneousComponent", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.isWeightedHomogeneous_iff_eq_weightedHomogeneousComponent", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": true, "tactics": ["constructor", "intro", "ext", "rw", "split_ifs", "rfl", "exact", "intro", "rw", "exact"], "tactic_count": 10}
{"name": "MvPowerSeries.weightedHomogeneousComponent_mul_of_le_weightedOrder", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": true, "tactics": ["classical", "ext", "rw", "split_ifs", "apply", "intro", "rw", "rw", "simp", "rcases", "rw", "rw", "rw", "rw", "rw", "rw", "rw", "symm", "apply", "exact"], "tactic_count": 20}
{"name": "MvPowerSeries.IsHomogeneous", "kind": "definition", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.IsHomogeneous.coeff_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": true, "tactics": ["apply", "rwa"], "tactic_count": 2}
{"name": "MvPowerSeries.IsHomogeneous.add", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.IsHomogeneous.mul", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.homogeneousComponent", "kind": "definition", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.coeff_homogeneousComponent", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MvPowerSeries.homogeneousComponent_of_lt_order_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.homogeneousComponent_of_order", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.isHomogeneous_homogeneousComponent", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.isHomogeneous_iff_eq_homogeneousComponent", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.homogeneousComponent_mul_of_le_order", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.WithPiTopology.instTopologicalSpace", "kind": "instance", "module": "Mathlib.RingTheory.MvPowerSeries.PiTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.WithPiTopology.instTopologicalSpace_mono", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.PiTopology", "is_tactic_proof": true, "tactics": ["simp", "grw", "exact"], "tactic_count": 3}
{"name": "MvPowerSeries.WithPiTopology.instT0Space", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.PiTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.WithPiTopology.instT2Space", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.PiTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.WithPiTopology.continuous_coeff", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.PiTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.WithPiTopology.continuous_constantCoeff", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.PiTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.WithPiTopology.tendsto_iff_coeff_tendsto", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.PiTopology", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MvPowerSeries.WithPiTopology.tendsto_trunc'_atTop", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.PiTopology", "is_tactic_proof": true, "tactics": ["rw", "intro", "exact"], "tactic_count": 3}
{"name": "MvPowerSeries.WithPiTopology.tendsto_trunc_atTop", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.PiTopology", "is_tactic_proof": true, "tactics": ["rw", "intro", "obtain", "apply", "intro", "rw", "apply", "simp", "refine"], "tactic_count": 9}
{"name": "MvPowerSeries.WithPiTopology.denseRange_toMvPowerSeries", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.PiTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.WithPiTopology.instIsTopologicalSemiring", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.PiTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.WithPiTopology.instIsTopologicalRing", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.PiTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.WithPiTopology.continuous_C", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.PiTopology", "is_tactic_proof": true, "tactics": ["classical", "simp", "refine", "simp", "split_ifs", "exact", "exact"], "tactic_count": 7}
{"name": "MvPowerSeries.WithPiTopology.instContinuousSMul", "kind": "instance", "module": "Mathlib.RingTheory.MvPowerSeries.PiTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.WithPiTopology.variables_tendsto_zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.PiTopology", "is_tactic_proof": true, "tactics": ["classical", "simp", "refine", "by_cases", "obtain", "filter_upwards", "simp", "simpa"], "tactic_count": 8}
{"name": "MvPowerSeries.WithPiTopology.isTopologicallyNilpotent_of_constantCoeff_isNilpotent", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.PiTopology", "is_tactic_proof": true, "tactics": ["classical", "obtain", "simp_rw", "exact"], "tactic_count": 4}
{"name": "MvPowerSeries.WithPiTopology.isTopologicallyNilpotent_of_constantCoeff_zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.PiTopology", "is_tactic_proof": true, "tactics": ["apply", "rw", "exact"], "tactic_count": 3}
{"name": "MvPowerSeries.WithPiTopology.isTopologicallyNilpotent_iff_constantCoeff_isNilpotent", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.PiTopology", "is_tactic_proof": true, "tactics": ["refine", "replace", "simp_rw", "exact"], "tactic_count": 4}
{"name": "MvPowerSeries.WithPiTopology.hasSum_of_monomials_self", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.PiTopology", "is_tactic_proof": true, "tactics": ["rw", "intro", "simpa"], "tactic_count": 3}
{"name": "MvPowerSeries.WithPiTopology.as_tsum", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.PiTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.WithPiTopology.hasSum_iff_hasSum_coeff", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.PiTopology", "is_tactic_proof": true, "tactics": ["simp_rw", "apply"], "tactic_count": 2}
{"name": "MvPowerSeries.WithPiTopology.summable_iff_summable_coeff", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.PiTopology", "is_tactic_proof": true, "tactics": ["simp_rw", "constructor", "rintro", "exact", "intro", "choose", "exact"], "tactic_count": 7}
{"name": "MvPowerSeries.WithPiTopology.summable_of_tendsto_weightedOrder_atTop_nhds_top", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.PiTopology", "is_tactic_proof": true, "tactics": ["rcases", "apply", "rw", "simp_rw", "intro", "obtain", "refine", "simp_rw", "intro", "contrapose", "exact"], "tactic_count": 11}
{"name": "MvPowerSeries.WithPiTopology.summable_of_tendsto_order_atTop_nhds_top", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.PiTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.WithPiTopology.summable_pow_of_constantCoeff_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.PiTopology", "is_tactic_proof": true, "tactics": ["apply", "simp_rw", "refine", "refine", "simpa"], "tactic_count": 5}
{"name": "MvPowerSeries.WithPiTopology.tsum_pow_mul_one_sub_of_constantCoeff_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.PiTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.WithPiTopology.one_sub_mul_tsum_pow_of_constantCoeff_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.PiTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.WithPiTopology.summable_prod_of_tendsto_weightedOrder_atTop_nhds_top", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.PiTopology", "is_tactic_proof": true, "tactics": ["rcases", "apply", "refine", "simp_rw", "obtain", "apply", "suffices", "intro", "contrapose", "obtain", "rw", "refine", "apply"], "tactic_count": 13}
{"name": "MvPowerSeries.WithPiTopology.summable_prod_of_tendsto_order_atTop_nhds_top", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.PiTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.WithPiTopology.multipliable_one_add_of_tendsto_weightedOrder_atTop_nhds_top", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.PiTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.WithPiTopology.multipliable_one_add_of_tendsto_order_atTop_nhds_top", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.PiTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.WithPiTopology.instUniformSpace", "kind": "instance", "module": "Mathlib.RingTheory.MvPowerSeries.PiTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.WithPiTopology.uniformContinuous_coeff", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.PiTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.WithPiTopology.instCompleteSpace", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.PiTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.WithPiTopology.instIsUniformAddGroup", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.PiTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.coeff_zero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MvPowerSeries.hasSubst_iff_hasEval_of_discreteTopology", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "MvPowerSeries.HasSubst.hasEval", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Substitution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.HasSubst.zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["letI", "simpa"], "tactic_count": 2}
{"name": "MvPowerSeries.HasSubst.add", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["letI", "rw", "exact"], "tactic_count": 3}
{"name": "MvPowerSeries.HasSubst.mul_left", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["letI", "rw", "exact"], "tactic_count": 3}
{"name": "MvPowerSeries.HasSubst.mul_right", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Substitution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.HasSubst.smul", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Substitution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.HasSubst.X", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["letI", "simpa"], "tactic_count": 2}
{"name": "MvPowerSeries.HasSubst.smul_X", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "MvPowerSeries.hasSubstIdeal", "kind": "definition", "module": "Mathlib.RingTheory.MvPowerSeries.Substitution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.hasSubst_of_constantCoeff_nilpotent", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Substitution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.hasSubst_of_constantCoeff_zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Substitution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.HasSubst.X_pow", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Substitution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.subst", "kind": "definition", "module": "Mathlib.RingTheory.MvPowerSeries.Substitution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.subst_eq_eval₂", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "MvPowerSeries.subst_coe", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["letI", "letI", "rw"], "tactic_count": 3}
{"name": "MvPowerSeries.substAlgHom", "kind": "definition", "module": "Mathlib.RingTheory.MvPowerSeries.Substitution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.substAlgHom_eq_aeval", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["simp", "convert"], "tactic_count": 2}
{"name": "MvPowerSeries.coe_substAlgHom", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["letI", "letI", "rw"], "tactic_count": 3}
{"name": "MvPowerSeries.subst_self", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["rw", "letI", "ext1", "simp", "have", "rw", "exact"], "tactic_count": 7}
{"name": "MvPowerSeries.substAlgHom_apply", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MvPowerSeries.subst_add", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MvPowerSeries.subst_mul", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MvPowerSeries.subst_pow", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MvPowerSeries.subst_smul", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MvPowerSeries.substAlgHom_coe", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MvPowerSeries.substAlgHom_X", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MvPowerSeries.substAlgHom_monomial", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MvPowerSeries.subst_X", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MvPowerSeries.subst_monomial", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MvPowerSeries.continuous_subst", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MvPowerSeries.coeff_subst_finite", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Substitution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.coeff_subst", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["letI", "letI", "have", "simp"], "tactic_count": 4}
{"name": "MvPowerSeries.constantCoeff_subst", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MvPowerSeries.constantCoeff_subst_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["rw", "intro", "by_cases", "simp", "have", "obtain", "by_contra", "exact", "simpa", "rw"], "tactic_count": 10}
{"name": "MvPowerSeries.map_algebraMap_eq_subst_X", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["ext", "rw", "rw", "intro", "rw"], "tactic_count": 5}
{"name": "MvPowerSeries.map_subst", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["ext", "have", "rw", "this,", "intro", "simp"], "tactic_count": 6}
{"name": "MvPowerSeries.comp_substAlgHom", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["ext", "simp", "exact"], "tactic_count": 3}
{"name": "MvPowerSeries.comp_subst", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MvPowerSeries.comp_subst_apply", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Substitution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.eval₂_subst", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["let", "have", "simpa", "coe_aeval]"], "tactic_count": 4}
{"name": "MvPowerSeries.IsNilpotent_subst", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["classical", "rw", "apply", "intro", "by_cases", "rw", "apply", "simpa", "apply", "rw", "obtain", "rw", "apply", "rw", "simpa", "intro", "simp", "exact"], "tactic_count": 18}
{"name": "MvPowerSeries.HasSubst.comp", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Substitution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.substAlgHom_comp_substAlgHom", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["letI", "letI", "letI", "apply", "simpa"], "tactic_count": 5}
{"name": "MvPowerSeries.substAlgHom_comp_substAlgHom_apply", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Substitution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.subst_comp_subst", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MvPowerSeries.subst_comp_subst_apply", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Substitution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.le_weightedOrder_subst", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["classical", "apply", "intro", "rw", "intro", "by_cases", "simp", "rw", "refine", "simp", "exact"], "tactic_count": 11}
{"name": "MvPowerSeries.le_weightedOrder_subst_of_forall_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["refine", "simp", "refine", "simp"], "tactic_count": 4}
{"name": "MvPowerSeries.le_order_subst", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["refine", "simp", "intro", "trans", "refine", "simp", "exact"], "tactic_count": 7}
{"name": "MvPowerSeries.rescale", "kind": "definition", "module": "Mathlib.RingTheory.MvPowerSeries.Substitution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.coeff_rescale", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MvPowerSeries.rescale_zero", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["classical", "ext", "simp", "split_ifs", "simp", "simp", "convert", "simp", "obtain", "simp", "apply", "simpa"], "tactic_count": 12}
{"name": "MvPowerSeries.rescale_zero_apply", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MvPowerSeries.rescale_one", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "MvPowerSeries.rescale_rescale", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "MvPowerSeries.rescale_mul", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "MvPowerSeries.rescale_homogeneous_eq_smul", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["ext", "simp", "smul_eq_mul]", "by_cases", "rw", "simp", "simp"], "tactic_count": 7}
{"name": "MvPowerSeries.rescaleMonoidHom", "kind": "definition", "module": "Mathlib.RingTheory.MvPowerSeries.Substitution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.rescale_eq_subst", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["classical", "ext", "rw", "rw", "simp", "rw", "simp", "intro", "rw", "intro", "simpa"], "tactic_count": 11}
{"name": "MvPowerSeries.rescaleAlgHom", "kind": "definition", "module": "Mathlib.RingTheory.MvPowerSeries.Substitution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.rescaleAlgHom_apply", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MvPowerSeries.rescaleAlgHom_mul", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["ext1", "simp"], "tactic_count": 2}
{"name": "MvPowerSeries.rescaleAlgHom_one", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["ext1", "simp"], "tactic_count": 2}
{"name": "MvPowerSeries.truncFun", "kind": "definition", "module": "Mathlib.RingTheory.MvPowerSeries.Trunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.coeff_truncFun", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Trunc", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "MvPowerSeries.trunc", "kind": "definition", "module": "Mathlib.RingTheory.MvPowerSeries.Trunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.coeff_trunc", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Trunc", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "MvPowerSeries.trunc_one", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Trunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.trunc_C", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Trunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.trunc_C_mul", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Trunc", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "MvPowerSeries.trunc_map", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Trunc", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "MvPowerSeries.truncFun'", "kind": "definition", "module": "Mathlib.RingTheory.MvPowerSeries.Trunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.coeff_truncFun'", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Trunc", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "MvPowerSeries.trunc'", "kind": "definition", "module": "Mathlib.RingTheory.MvPowerSeries.Trunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.coeff_trunc'", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Trunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.trunc'_trunc'", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Trunc", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "symm", "simp", "intro", "have", "contradiction", "simp"], "tactic_count": 8}
{"name": "MvPowerSeries.trunc'_one", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Trunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.trunc'_C", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Trunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.coeff_mul_eq_coeff_trunc'_mul_trunc'", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Trunc", "is_tactic_proof": true, "tactics": ["classical", "simp", "apply", "rintro", "simp", "rw", "simp", "apply", "rw", "rw"], "tactic_count": 10}
{"name": "MvPowerSeries.trunc'_trunc'_pow", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Trunc", "is_tactic_proof": true, "tactics": ["induction", "base", "succ", "ext", "by_cases", "rw", "if_pos", "intro", "have", "have", "simp", "simp"], "tactic_count": 12}
{"name": "MvPowerSeries.trunc'_C_mul", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Trunc", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "MvPowerSeries.trunc'_map", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Trunc", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "MvPowerSeries.totalDegree_trunc'", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Trunc", "is_tactic_proof": false, "tactics": ["have", "simp", "by_contra", "simp", "have", "refine", "simp", "intro", "simp", "exact", "rw", "exact"], "tactic_count": 12}
{"name": "MvPowerSeries.ext_trunc'", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Trunc", "is_tactic_proof": true, "tactics": ["refine", "ext", "specialize", "have", "simp_rw"], "tactic_count": 5}
{"name": "MvPowerSeries.eq_iff_frequently_trunc'_eq", "kind": "theorem", "module": "Mathlib.RingTheory.MvPowerSeries.Trunc", "is_tactic_proof": true, "tactics": ["refine", "ext", "obtain", "have", "simp"], "tactic_count": 5}
{"name": "Submodule.eq_smul_of_le_smul_of_le_jacobson", "kind": "theorem", "module": "Mathlib.RingTheory.Nakayama", "is_tactic_proof": true, "tactics": ["refine", "intro", "obtain", "obtain", "have", "rw", "exact"], "tactic_count": 7}
{"name": "Submodule.eq_bot_of_eq_ideal_smul_of_le_jacobson_annihilator", "kind": "theorem", "module": "Mathlib.RingTheory.Nakayama", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.eq_bot_of_eq_pointwise_smul_of_mem_jacobson_annihilator", "kind": "theorem", "module": "Mathlib.RingTheory.Nakayama", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.eq_bot_of_set_smul_eq_of_subset_jacobson_annihilator", "kind": "theorem", "module": "Mathlib.RingTheory.Nakayama", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.top_ne_ideal_smul_of_le_jacobson_annihilator", "kind": "theorem", "module": "Mathlib.RingTheory.Nakayama", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.top_ne_set_smul_of_subset_jacobson_annihilator", "kind": "theorem", "module": "Mathlib.RingTheory.Nakayama", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.top_ne_pointwise_smul_of_mem_jacobson_annihilator", "kind": "theorem", "module": "Mathlib.RingTheory.Nakayama", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.eq_bot_of_le_smul_of_le_jacobson_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Nakayama", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submodule.sup_eq_sup_smul_of_le_smul_of_le_jacobson", "kind": "theorem", "module": "Mathlib.RingTheory.Nakayama", "is_tactic_proof": false, "tactics": ["have", "le_antisymm", "have", "have", "simpa", "have", "hIJ", "rwa", "sup_comm"], "tactic_count": 9}
{"name": "Submodule.sup_smul_eq_sup_smul_of_le_smul_of_le_jacobson", "kind": "theorem", "module": "Mathlib.RingTheory.Nakayama", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.le_of_le_smul_of_le_jacobson_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Nakayama", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submodule.smul_le_of_le_smul_of_le_jacobson_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Nakayama", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.exists_sub_one_mem_and_smul_le_of_fg_of_le_sup", "kind": "theorem", "module": "Mathlib.RingTheory.Nakayama", "is_tactic_proof": true, "tactics": ["have", "have", "refine", "simpa", "have", "apply", "simpa", "rw", "simp", "have", "conv_lhs", "simp", "obtain", "refine", "induction", "smul₀", "rw", "exact", "smul₁", "add", "zero"], "tactic_count": 21}
{"name": "Submodule.le_of_map_mkQ_le_map_mkQ_of_le_jacobson_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Nakayama", "is_tactic_proof": true, "tactics": ["apply", "apply_fun", "on_goal", "simp", "grw"], "tactic_count": 5}
{"name": "Submodule.eq_of_map_mkQ_eq_map_mkQ_of_le_jacobson_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Nakayama", "is_tactic_proof": true, "tactics": ["apply", "exact", "apply_fun", "simp", "rw"], "tactic_count": 5}
{"name": "Submodule.exists_injOn_mkQ_image_span_eq_of_span_eq_map_mkQ_of_le_jacobson_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Nakayama", "is_tactic_proof": true, "tactics": ["use", "split_ands", "simp", "simp", "symm", "simp"], "tactic_count": 6}
{"name": "IsNilpotent.neg", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Basic", "is_tactic_proof": true, "tactics": ["obtain", "use", "rw"], "tactic_count": 3}
{"name": "isNilpotent_neg_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsNilpotent.smul", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Basic", "is_tactic_proof": true, "tactics": ["obtain", "use", "rw"], "tactic_count": 3}
{"name": "IsNilpotent.isUnit_sub_one", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Basic", "is_tactic_proof": true, "tactics": ["obtain", "refine", "simp", "simp"], "tactic_count": 4}
{"name": "IsNilpotent.isUnit_one_sub", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsNilpotent.isUnit_add_one", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsNilpotent.isUnit_one_add", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsNilpotent.isUnit_add_left_of_commute", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Basic", "is_tactic_proof": true, "tactics": ["rw", "replace", "refine", "exact"], "tactic_count": 4}
{"name": "IsNilpotent.isUnit_add_right_of_commute", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUnit.not_isNilpotent", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Basic", "is_tactic_proof": true, "tactics": ["intro", "simpa"], "tactic_count": 2}
{"name": "IsNilpotent.not_isUnit", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIdempotentElem.eq_zero_of_isNilpotent", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Basic", "is_tactic_proof": true, "tactics": ["obtain", "rw", "rw"], "tactic_count": 3}
{"name": "instIsReducedProd", "kind": "instance", "module": "Mathlib.RingTheory.Nilpotent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prime.isRadical", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zero_isRadical_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "isReduced_iff_pow_one_lt", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "IsRadical.of_dvd", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.add_pow_eq_zero_of_add_le_succ_of_pow_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply", "rintro", "suffices", "by_cases", "rw", "rw", "linarith"], "tactic_count": 8}
{"name": "Commute.add_pow_add_eq_zero_of_pow_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.isNilpotent_add", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Basic", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "exact"], "tactic_count": 3}
{"name": "Commute.isNilpotent_sum", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Basic", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "insert", "rw", "apply", "exact", "apply", "exact"], "tactic_count": 9}
{"name": "Commute.isNilpotent_finsum", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Basic", "is_tactic_proof": true, "tactics": ["classical", "by_cases", "rw", "exact", "simp"], "tactic_count": 5}
{"name": "Commute.isNilpotent_mul_right_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Basic", "is_tactic_proof": true, "tactics": ["refine", "rintro", "rw", "exact"], "tactic_count": 4}
{"name": "Commute.isNilpotent_mul_left_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Basic", "is_tactic_proof": true, "tactics": ["refine", "rintro", "rw", "exact"], "tactic_count": 4}
{"name": "Commute.isNilpotent_sub", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Basic", "is_tactic_proof": true, "tactics": ["rw", "rw", "rw", "exact"], "tactic_count": 4}
{"name": "isNilpotent_sum", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isNilpotent_finsum", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NoZeroSMulDivisors.isReduced", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Basic", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "IsNilpotent.map", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Defs", "is_tactic_proof": true, "tactics": ["use", "rw"], "tactic_count": 2}
{"name": "IsNilpotent.map_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUnit.isNilpotent_mul_unit_of_commute_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUnit.isNilpotent_unit_mul_of_commute_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nilpotencyClass", "kind": "definition", "module": "Mathlib.RingTheory.Nilpotent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nilpotencyClass_eq_zero_of_subsingleton", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Defs", "is_tactic_proof": true, "tactics": ["let", "suffices", "exact"], "tactic_count": 3}
{"name": "isNilpotent_of_pos_nilpotencyClass", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Defs", "is_tactic_proof": true, "tactics": ["let", "change", "change", "by_contra", "simp"], "tactic_count": 5}
{"name": "pow_nilpotencyClass", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nilpotencyClass_eq_succ_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Defs", "is_tactic_proof": true, "tactics": ["let", "have", "simp"], "tactic_count": 3}
{"name": "nilpotencyClass_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pos_nilpotencyClass_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Defs", "is_tactic_proof": true, "tactics": ["refine", "replace", "rw", "exact"], "tactic_count": 4}
{"name": "pow_pred_nilpotencyClass", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_zero_of_nilpotencyClass_eq_one", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Defs", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "nilpotencyClass_eq_one", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isReduced_of_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Defs", "is_tactic_proof": true, "tactics": ["constructor", "intro", "apply", "rw", "exact"], "tactic_count": 5}
{"name": "instIsReducedForall", "kind": "instance", "module": "Mathlib.RingTheory.Nilpotent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRadical", "kind": "definition", "module": "Mathlib.RingTheory.Nilpotent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isRadical_iff_pow_one_lt", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.isNilpotent_mul_right", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Defs", "is_tactic_proof": true, "tactics": ["obtain", "use", "rw"], "tactic_count": 3}
{"name": "Commute.isNilpotent_mul_left", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsNilpotent.exp", "kind": "definition", "module": "Mathlib.RingTheory.Nilpotent.Exp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsNilpotent.exp_eq_sum", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Exp", "is_tactic_proof": false, "tactics": ["have", "suffices", "dsimp", "rw", "exact"], "tactic_count": 5}
{"name": "IsNilpotent.exp_smul_eq_sum", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Exp", "is_tactic_proof": true, "tactics": ["rcases", "simp_rw", "rw", "suffices", "simp_rw", "refine", "rw"], "tactic_count": 7}
{"name": "IsNilpotent.exp_add_of_commute", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Exp", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "let", "have", "have", "rw", "exp_eq_sum", "set", "set", "have", "calc", "refine", "rw", "simp_rw", "refine", "simp", "replace", "suffices", "rw", "smul_assoc]", "norm_cast", "rw", "simp", "rw", "apply", "simp", "lia", "simp", "rintro", "simp_all", "lia", "simp", "exact", "simp", "have", "sum_eq_zero", "rw", "cases", "inl", "inr", "have", "sum_filter_add_sum_filter_not", "rw", "rw", "have", "sum_eq_zero", "simp", "cases", "inl", "inr", "have", "sum_filter_add_sum_filter_not", "rw", "rw", "have", "apply", "ext", "simp", "lia", "tauto", "rw", "have", "calc", "rw", "refine", "rw", "rw", "apply", "exact", "simp", "simp", "rwa"], "tactic_count": 72}
{"name": "IsNilpotent.exp_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Exp", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsNilpotent.exp_mul_exp_neg_self", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Exp", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsNilpotent.exp_neg_mul_exp_self", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Exp", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsNilpotent.isUnit_exp", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Exp", "is_tactic_proof": true, "tactics": ["apply", "use", "exact"], "tactic_count": 3}
{"name": "IsNilpotent.map_exp", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Exp", "is_tactic_proof": true, "tactics": ["obtain", "have", "simp"], "tactic_count": 3}
{"name": "IsNilpotent.exp_smul", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Exp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsNilpotent.isNilpotent_exp_sub_one", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Exp", "is_tactic_proof": true, "tactics": ["nontriviality", "rw", "norm_num", "apply", "simp"], "tactic_count": 5}
{"name": "Module.End.commute_exp_left_of_commute", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Exp", "is_tactic_proof": true, "tactics": ["ext", "obtain", "obtain", "let", "replace", "replace", "have", "simpa", "simp"], "tactic_count": 9}
{"name": "Module.End.exp_mul_of_derivation", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Exp", "is_tactic_proof": true, "tactics": ["let", "let", "have", "have", "have", "set", "have", "suffices", "apply", "ext", "simp", "have", "have", "simp"], "tactic_count": 14}
{"name": "Algebra.instIsReducedTensorProductOfIsAlgebraicOfIsGeometricallyReduced", "kind": "instance", "module": "Mathlib.RingTheory.Nilpotent.GeometricallyReduced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsGeometricallyReduced.of_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.GeometricallyReduced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.isReduced_of_isGeometricallyReduced", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.GeometricallyReduced", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsGeometricallyReduced.of_forall_fg", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.GeometricallyReduced", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "RingHom.ker_isRadical_iff_reduced_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Lemmas", "is_tactic_proof": true, "tactics": ["simp_rw", "rfl"], "tactic_count": 2}
{"name": "isRadical_iff_span_singleton", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Lemmas", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "isNilpotent_iff_zero_mem_powers", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nilradical", "kind": "definition", "module": "Mathlib.RingTheory.Nilpotent.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_nilradical", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nilradical_eq_sInf", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nilpotent_iff_mem_prime", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "nilradical_le_prime", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nilradical_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nilradical_eq_bot_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Lemmas", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "LinearMap.isNilpotent_mulLeft_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Lemmas", "is_tactic_proof": true, "tactics": ["constructor"], "tactic_count": 1}
{"name": "LinearMap.isNilpotent_mulRight_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Lemmas", "is_tactic_proof": true, "tactics": ["constructor"], "tactic_count": 1}
{"name": "LinearMap.isNilpotent_toMatrix_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Lemmas", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "Matrix.isNilpotent_toLin'_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Lemmas", "is_tactic_proof": true, "tactics": ["have", "conv_rhs", "rw"], "tactic_count": 3}
{"name": "Module.End.isNilpotent_restrict_of_le", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Lemmas", "is_tactic_proof": true, "tactics": ["obtain", "use", "ext", "replace", "simp_rw", "rw", "ext", "exact"], "tactic_count": 8}
{"name": "Module.End.isNilpotent.restrict", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Lemmas", "is_tactic_proof": true, "tactics": ["obtain", "exact", "simp"], "tactic_count": 3}
{"name": "Module.End.IsNilpotent.mapQ", "kind": "theorem", "module": "Mathlib.RingTheory.Nilpotent.Lemmas", "is_tactic_proof": true, "tactics": ["obtain", "use", "simp"], "tactic_count": 3}
{"name": "_private.Mathlib.RingTheory.NoetherNormalization.0.NoetherNormalization.termUp", "kind": "definition", "module": "Mathlib.RingTheory.NoetherNormalization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.NoetherNormalization.0.NoetherNormalization._aux_Mathlib_RingTheory_NoetherNormalization___macroRules__private_Mathlib_RingTheory_NoetherNormalization_0_NoetherNormalization_termUp_1", "kind": "definition", "module": "Mathlib.RingTheory.NoetherNormalization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.NoetherNormalization.0.NoetherNormalization._aux_Mathlib_RingTheory_NoetherNormalization___delab_app__private_Mathlib_RingTheory_NoetherNormalization_0_NoetherNormalization_termUp_1", "kind": "definition", "module": "Mathlib.RingTheory.NoetherNormalization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.NoetherNormalization.0.NoetherNormalization.lt_up", "kind": "theorem", "module": "Mathlib.RingTheory.NoetherNormalization", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "_private.Mathlib.RingTheory.NoetherNormalization.0.NoetherNormalization.termR", "kind": "definition", "module": "Mathlib.RingTheory.NoetherNormalization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.NoetherNormalization.0.NoetherNormalization._aux_Mathlib_RingTheory_NoetherNormalization___macroRules__private_Mathlib_RingTheory_NoetherNormalization_0_NoetherNormalization_termR_1", "kind": "definition", "module": "Mathlib.RingTheory.NoetherNormalization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.NoetherNormalization.0.NoetherNormalization._aux_Mathlib_RingTheory_NoetherNormalization___delab_app__private_Mathlib_RingTheory_NoetherNormalization_0_NoetherNormalization_termR_1", "kind": "definition", "module": "Mathlib.RingTheory.NoetherNormalization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NoetherNormalization.T1", "kind": "abbrev", "module": "Mathlib.RingTheory.NoetherNormalization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.NoetherNormalization.0.NoetherNormalization.t1_comp_t1_neg", "kind": "theorem", "module": "Mathlib.RingTheory.NoetherNormalization", "is_tactic_proof": true, "tactics": ["rw", "ext", "cases", "simp"], "tactic_count": 4}
{"name": "_private.Mathlib.RingTheory.NoetherNormalization.0.NoetherNormalization.T", "kind": "abbrev", "module": "Mathlib.RingTheory.NoetherNormalization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.NoetherNormalization.0.NoetherNormalization.sum_r_mul_neq", "kind": "theorem", "module": "Mathlib.RingTheory.NoetherNormalization", "is_tactic_proof": true, "tactics": ["intro", "refine", "apply", "simpa"], "tactic_count": 4}
{"name": "_private.Mathlib.RingTheory.NoetherNormalization.0.NoetherNormalization.degreeOf_zero_t", "kind": "theorem", "module": "Mathlib.RingTheory.NoetherNormalization", "is_tactic_proof": true, "tactics": ["rw", "simp", "finSuccEquiv_X_zero,", "have", "pow_ne_zero", "rw", "natDegree_mul", "natDegree_finSuccEquiv,", "simpa"], "tactic_count": 9}
{"name": "_private.Mathlib.RingTheory.NoetherNormalization.0.NoetherNormalization.degreeOf_t_neq_of_neq", "kind": "theorem", "module": "Mathlib.RingTheory.NoetherNormalization", "is_tactic_proof": true, "tactics": ["rw", "refine", "exact"], "tactic_count": 3}
{"name": "_private.Mathlib.RingTheory.NoetherNormalization.0.NoetherNormalization.leadingCoeff_finSuccEquiv_t", "kind": "theorem", "module": "Mathlib.RingTheory.NoetherNormalization", "is_tactic_proof": true, "tactics": ["rw", "simp", "rw", "simp", "have", "by_cases", "simp", "simp", "obtain", "simp", "simp", "exact", "pow_zero"], "tactic_count": 13}
{"name": "_private.Mathlib.RingTheory.NoetherNormalization.0.NoetherNormalization.T_leadingcoeff_isUnit", "kind": "theorem", "module": "Mathlib.RingTheory.NoetherNormalization", "is_tactic_proof": false, "tactics": ["obtain", "set", "simp", "replace", "intro", "obtain", "apply", "simpa", "have", "simp", "rw", "apply", "have", "replace", "h2", "exact", "nth_rw", "rw", "rw", "simpa"], "tactic_count": 20}
{"name": "_private.Mathlib.RingTheory.NoetherNormalization.0.NoetherNormalization.hom1", "kind": "abbrev", "module": "Mathlib.RingTheory.NoetherNormalization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.NoetherNormalization.0.NoetherNormalization.hom1_isIntegral", "kind": "theorem", "module": "Mathlib.RingTheory.NoetherNormalization", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "_private.Mathlib.RingTheory.NoetherNormalization.0.NoetherNormalization.eqv1", "kind": "abbrev", "module": "Mathlib.RingTheory.NoetherNormalization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.NoetherNormalization.0.NoetherNormalization.eqv2", "kind": "abbrev", "module": "Mathlib.RingTheory.NoetherNormalization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.NoetherNormalization.0.NoetherNormalization.hom2", "kind": "definition", "module": "Mathlib.RingTheory.NoetherNormalization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.NoetherNormalization.0.NoetherNormalization.hom2_isIntegral", "kind": "theorem", "module": "Mathlib.RingTheory.NoetherNormalization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_integral_inj_algHom_of_quotient", "kind": "theorem", "module": "Mathlib.RingTheory.NoetherNormalization", "is_tactic_proof": true, "tactics": ["induction", "zero", "refine", "rw", "by_contra", "have", "have", "obtain", "have", "exact", "succ", "by_cases", "have", "exact", "obtain", "set", "have", "obtain", "have", "exact", "intg.trans"], "tactic_count": 21}
{"name": "exists_integral_inj_algHom_of_fg", "kind": "theorem", "module": "Mathlib.RingTheory.NoetherNormalization", "is_tactic_proof": true, "tactics": ["obtain", "set", "obtain", "use", "simp", "exact"], "tactic_count": 6}
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{"name": "isNoetherian_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Noetherian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isNoetherian_range", "kind": "instance", "module": "Mathlib.RingTheory.Noetherian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isNoetherian_quotient", "kind": "instance", "module": "Mathlib.RingTheory.Noetherian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isNoetherian_of_linearEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.Noetherian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.isNoetherian_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Noetherian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isNoetherian_top_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Noetherian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isNoetherian_of_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Noetherian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fg_of_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Noetherian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isNoetherian_of_finite", "kind": "instance", "module": "Mathlib.RingTheory.Noetherian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.IsNoetherian.finite", "kind": "instance", "module": "Mathlib.RingTheory.Noetherian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.instFiniteSubtypeMemIdealOfIsNoetherian", "kind": "instance", "module": "Mathlib.RingTheory.Noetherian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Finite.of_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Noetherian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isNoetherian_of_ker_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Noetherian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fg_of_ker_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Noetherian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isNoetherian_prod", "kind": "instance", "module": "Mathlib.RingTheory.Noetherian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isNoetherian_sup", "kind": "instance", "module": "Mathlib.RingTheory.Noetherian.Basic", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "isNoetherian_pi", "kind": "instance", "module": "Mathlib.RingTheory.Noetherian.Basic", "is_tactic_proof": true, "tactics": ["apply", "exact", "infer_instance", "exact"], "tactic_count": 4}
{"name": "isNoetherian_pi'", "kind": "instance", "module": "Mathlib.RingTheory.Noetherian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isNoetherian_iSup", "kind": "instance", "module": "Mathlib.RingTheory.Noetherian.Basic", "is_tactic_proof": true, "tactics": ["apply", "intro", "intros", "intro"], "tactic_count": 4}
{"name": "isNoetherian_of_range_eq_ker", "kind": "theorem", "module": "Mathlib.RingTheory.Noetherian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isNoetherian_iff_submodule_quotient", "kind": "theorem", "module": "Mathlib.RingTheory.Noetherian.Basic", "is_tactic_proof": true, "tactics": ["refine", "apply", "rw"], "tactic_count": 3}
{"name": "isNoetherian_linearMap_pi", "kind": "instance", "module": "Mathlib.RingTheory.Noetherian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isNoetherian_linearMap", "kind": "instance", "module": "Mathlib.RingTheory.Noetherian.Basic", "is_tactic_proof": true, "tactics": ["obtain", "let", "exact"], "tactic_count": 3}
{"name": "IsNoetherian.induction", "kind": "theorem", "module": "Mathlib.RingTheory.Noetherian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.isNoetherian_iff_of_bijective", "kind": "theorem", "module": "Mathlib.RingTheory.Noetherian.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "let", "exact"], "tactic_count": 3}
{"name": "Submodule.finite_ne_bot_of_iSupIndep", "kind": "theorem", "module": "Mathlib.RingTheory.Noetherian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIndependent.finite_of_isNoetherian", "kind": "theorem", "module": "Mathlib.RingTheory.Noetherian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsNoetherian.subsingleton_of_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Noetherian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearIndependent.set_finite_of_isNoetherian", "kind": "theorem", "module": "Mathlib.RingTheory.Noetherian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsNoetherian.disjoint_partialSups_eventually_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Noetherian.Basic", "is_tactic_proof": true, "tactics": ["suffices", "obtain", "use", "rintro", "cases", "apply", "exact", "obtain", "refine", "simpa"], "tactic_count": 10}
{"name": "isNoetherian_of_subsingleton", "kind": "instance", "module": "Mathlib.RingTheory.Noetherian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isNoetherian_of_submodule_of_noetherian", "kind": "theorem", "module": "Mathlib.RingTheory.Noetherian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isNoetherian_of_tower", "kind": "theorem", "module": "Mathlib.RingTheory.Noetherian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isNoetherian_of_isNoetherianRing_of_finite", "kind": "instance", "module": "Mathlib.RingTheory.Noetherian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isNoetherian_of_fg_of_noetherian", "kind": "theorem", "module": "Mathlib.RingTheory.Noetherian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isNoetherian_span_of_finite", "kind": "theorem", "module": "Mathlib.RingTheory.Noetherian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsNoetherianRing.of_finite", "kind": "theorem", "module": "Mathlib.RingTheory.Noetherian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isNoetherianRing_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Noetherian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isNoetherianRing_rangeS", "kind": "instance", "module": "Mathlib.RingTheory.Noetherian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isNoetherianRing_range", "kind": "instance", "module": "Mathlib.RingTheory.Noetherian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isNoetherianRing_of_ringEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.Noetherian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsNoetherianRingProd", "kind": "instance", "module": "Mathlib.RingTheory.Noetherian.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "instIsNoetherianRingForallOfFinite", "kind": "instance", "module": "Mathlib.RingTheory.Noetherian.Basic", "is_tactic_proof": true, "tactics": ["apply", "exact", "infer_instance", "exact"], "tactic_count": 4}
{"name": "Submodule.FG.of_le_of_isNoetherian", "kind": "theorem", "module": "Mathlib.RingTheory.Noetherian.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.FG.of_le", "kind": "theorem", "module": "Mathlib.RingTheory.Noetherian.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Module.exists_finite_presentation", "kind": "theorem", "module": "Mathlib.RingTheory.Noetherian.Basic", "is_tactic_proof": true, "tactics": ["rcases", "let", "f'.comp", "use", "simpa"], "tactic_count": 5}
{"name": "isNoetherian_def", "kind": "theorem", "module": "Mathlib.RingTheory.Noetherian.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isNoetherian_submodule", "kind": "theorem", "module": "Mathlib.RingTheory.Noetherian.Defs", "is_tactic_proof": false, "tactics": ["refine", "have", "specialize", "exact"], "tactic_count": 4}
{"name": "isNoetherian_submodule_left", "kind": "theorem", "module": "Mathlib.RingTheory.Noetherian.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isNoetherian_submodule_right", "kind": "theorem", "module": "Mathlib.RingTheory.Noetherian.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isNoetherian_submodule'", "kind": "instance", "module": "Mathlib.RingTheory.Noetherian.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isNoetherian_of_le", "kind": "theorem", "module": "Mathlib.RingTheory.Noetherian.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isNoetherian_iff'", "kind": "theorem", "module": "Mathlib.RingTheory.Noetherian.Defs", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "isNoetherian_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Noetherian.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "wellFoundedGT", "kind": "instance", "module": "Mathlib.RingTheory.Noetherian.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isNoetherian_iff_fg_wellFounded", "kind": "theorem", "module": "Mathlib.RingTheory.Noetherian.Defs", "is_tactic_proof": true, "tactics": ["let", "constructor", "intro", "let", "exact", "intro", "constructor", "intro", "obtain", "convert", "refine", "by_contra", "obtain", "apply", "rw", "sup_le", "exact"], "tactic_count": 17}
{"name": "set_has_maximal_iff_noetherian", "kind": "theorem", "module": "Mathlib.RingTheory.Noetherian.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "monotone_stabilizes_iff_noetherian", "kind": "theorem", "module": "Mathlib.RingTheory.Noetherian.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Module.End.eventually_disjoint_ker_pow_range_pow", "kind": "theorem", "module": "Mathlib.RingTheory.Noetherian.Defs", "is_tactic_proof": false, "tactics": ["obtain", "monotone_stabilizes_iff_noetherian.mpr", "refine", "rw", "rintro", "apply", "replace", "simpa", "rwa"], "tactic_count": 9}
{"name": "LinearMap.eventually_iSup_ker_pow_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Noetherian.Defs", "is_tactic_proof": false, "tactics": ["obtain", "monotone_stabilizes_iff_noetherian.mpr", "refine", "refine", "rcases", "rw", "exact"], "tactic_count": 7}
{"name": "IsNoetherianRing", "kind": "abbrev", "module": "Mathlib.RingTheory.Noetherian.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isNoetherianRing_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Noetherian.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isNoetherianRing_iff_ideal_fg", "kind": "theorem", "module": "Mathlib.RingTheory.Noetherian.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.fg_of_isNoetherianRing", "kind": "theorem", "module": "Mathlib.RingTheory.Noetherian.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eventuallyConst_of_isNoetherian", "kind": "theorem", "module": "Mathlib.RingTheory.Noetherian.Filter", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "IsNoetherianRing.isNilpotent_nilradical", "kind": "theorem", "module": "Mathlib.RingTheory.Noetherian.Nilpotent", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Ideal.FG.isNilpotent_iff_le_nilradical", "kind": "theorem", "module": "Mathlib.RingTheory.Noetherian.Nilpotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.isOka_fg", "kind": "theorem", "module": "Mathlib.RingTheory.Noetherian.OfPrime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsNoetherianRing.of_prime", "kind": "theorem", "module": "Mathlib.RingTheory.Noetherian.OfPrime", "is_tactic_proof": true, "tactics": ["refine", "obtain", "obtain", "refine", "simp", "exact", "suffices", "exact"], "tactic_count": 8}
{"name": "IsNoetherianRing.of_prime_ne_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Noetherian.OfPrime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsNoetherian.injective_of_surjective_of_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Noetherian.Orzech", "is_tactic_proof": true, "tactics": ["haveI", "obtain", "monotone_stabilizes_iff_noetherian.2", "exact"], "tactic_count": 4}
{"name": "IsNoetherian.injective_of_surjective_of_submodule", "kind": "theorem", "module": "Mathlib.RingTheory.Noetherian.Orzech", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsNoetherian.injective_of_surjective_endomorphism", "kind": "theorem", "module": "Mathlib.RingTheory.Noetherian.Orzech", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsNoetherian.bijective_of_surjective_endomorphism", "kind": "theorem", "module": "Mathlib.RingTheory.Noetherian.Orzech", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsNoetherian.subsingleton_of_prod_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Noetherian.Orzech", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsNoetherian.equivPUnitOfProdInjective", "kind": "definition", "module": "Mathlib.RingTheory.Noetherian.Orzech", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsNoetherianRing.orzechProperty", "kind": "instance", "module": "Mathlib.RingTheory.Noetherian.Orzech", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsNoetherianRing.wfDvdMonoid", "kind": "instance", "module": "Mathlib.RingTheory.Noetherian.UniqueFactorizationDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.list_sum_mem", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.multiset_sum_mem", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.sum_mem", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.instTop", "kind": "instance", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.mem_top", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.coe_top", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.toNonUnitalSubsemiring_top", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.toAddSubgroup_top", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.toNonUnitalSubsemiring_eq_top", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NonUnitalSubring.toAddSubgroup_eq_top", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NonUnitalSubring.topEquiv", "kind": "definition", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.comap", "kind": "definition", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.coe_comap", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.mem_comap", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.comap_comap", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.map", "kind": "definition", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.coe_map", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.mem_map", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.map_id", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.map_map", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.map_le_iff_le_comap", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.gc_map_comap", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.equivMapOfInjective", "kind": "definition", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.coe_equivMapOfInjective_apply", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.range", "kind": "definition", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.coe_range", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.mem_range", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.range_eq_map", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "NonUnitalRingHom.mem_range_self", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.map_range", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "NonUnitalRingHom.fintypeRange", "kind": "instance", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.instBot", "kind": "instance", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.instInhabited", "kind": "instance", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.coe_bot", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.mem_bot", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.instMin", "kind": "instance", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.coe_inf", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.mem_inf", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.instInfSet", "kind": "instance", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.coe_sInf", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.mem_sInf", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.coe_iInf", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NonUnitalSubring.mem_iInf", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NonUnitalSubring.sInf_toSubsemigroup", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.sInf_toAddSubgroup", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.instCompleteLattice", "kind": "instance", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.eq_top_iff'", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.center", "kind": "definition", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.coe_center", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.center_toNonUnitalSubsemiring", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.center.instNonUnitalCommRing", "kind": "instance", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.centerCongr", "kind": "definition", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.centerToMulOpposite", "kind": "definition", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring._example", "kind": "example", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": true, "tactics": ["with_reducible_and_instances"], "tactic_count": 1}
{"name": "NonUnitalSubring.mem_center_iff", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.decidableMemCenter", "kind": "instance", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.center_eq_top", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.closure", "kind": "definition", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.mem_closure", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.subset_closure", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.mem_closure_of_mem", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.notMem_of_notMem_closure", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.closure_le", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.closure_mono", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.closure_eq_of_le", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.closure_induction", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.closure_induction₂", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": true, "tactics": ["induction", "mem", "induction", "mem", "zero", "mul", "add", "neg", "zero", "mul", "add", "neg"], "tactic_count": 12}
{"name": "NonUnitalSubring.mem_closure_iff", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.closureNonUnitalCommRingOfComm", "kind": "definition", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.gi", "kind": "definition", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.closure_eq", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.closure_empty", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.closure_univ", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.closure_union", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.closure_iUnion", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.closure_sUnion", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.map_sup", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.map_iSup", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.map_inf", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.map_iInf", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": true, "tactics": ["apply", "simpa"], "tactic_count": 2}
{"name": "NonUnitalSubring.comap_inf", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.comap_iInf", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.map_bot", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.comap_top", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.prod", "kind": "definition", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.coe_prod", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.mem_prod", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.prod_mono", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.prod_mono_right", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.prod_mono_left", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.prod_top", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.top_prod", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.top_prod_top", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.prodEquiv", "kind": "definition", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.mem_iSup_of_directed", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": true, "tactics": ["refine", "let", "suffices", "exact"], "tactic_count": 4}
{"name": "NonUnitalSubring.coe_iSup_of_directed", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.mem_sSup_of_directedOn", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": true, "tactics": ["haveI", "simp"], "tactic_count": 2}
{"name": "NonUnitalSubring.coe_sSup_of_directedOn", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.mem_map_equiv", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.map_equiv_eq_comap_symm", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.comap_equiv_eq_map_symm", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.rangeRestrict", "kind": "definition", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.coe_rangeRestrict", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.rangeRestrict_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.range_eq_top", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.range_eq_top_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.eqLocus", "kind": "definition", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.mem_eqLocus", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.eqLocus_same", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.eqOn_set_closure", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.eq_of_eqOn_set_top", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.eq_of_eqOn_set_dense", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.closure_preimage_le", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.map_closure", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.range_subtype", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.range_fst", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.range_snd", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.nonUnitalSubringCongr", "kind": "definition", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.ofLeftInverse'", "kind": "definition", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.ofLeftInverse'_apply", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.ofLeftInverse'_symm_apply", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.closure_preimage_le", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubringClass.addSubgroupClass", "kind": "instance", "module": "Mathlib.RingTheory.NonUnitalSubring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubringClass.toNonUnitalNonAssocRing", "kind": "instance", "module": "Mathlib.RingTheory.NonUnitalSubring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubringClass.toNonUnitalRing", "kind": "instance", "module": "Mathlib.RingTheory.NonUnitalSubring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubringClass.toNonUnitalCommRing", "kind": "instance", "module": "Mathlib.RingTheory.NonUnitalSubring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubringClass.subtype", "kind": "definition", "module": "Mathlib.RingTheory.NonUnitalSubring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubringClass.subtype_apply", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubringClass.subtype_injective", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubringClass.coe_subtype", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.toSubsemigroup", "kind": "definition", "module": "Mathlib.RingTheory.NonUnitalSubring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.instSetLike", "kind": "instance", "module": "Mathlib.RingTheory.NonUnitalSubring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.instPartialOrder", "kind": "instance", "module": "Mathlib.RingTheory.NonUnitalSubring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.ofClass", "kind": "definition", "module": "Mathlib.RingTheory.NonUnitalSubring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.instCanLiftSetCoeAndMemOfNatForallForallForallForallHAddForallForallForallForallHMulForallForallNeg", "kind": "instance", "module": "Mathlib.RingTheory.NonUnitalSubring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.instNonUnitalSubringClass", "kind": "instance", "module": "Mathlib.RingTheory.NonUnitalSubring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.mem_carrier", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.mem_mk", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.coe_set_mk", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.mk_le_mk", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.ext", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.copy", "kind": "definition", "module": "Mathlib.RingTheory.NonUnitalSubring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.coe_copy", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.copy_eq", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.toNonUnitalSubsemiring_injective", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.toNonUnitalSubsemiring_strictMono", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.toNonUnitalSubsemiring_mono", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.toAddSubgroup_injective", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.toAddSubgroup_strictMono", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.toAddSubgroup_mono", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.toSubsemigroup_injective", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.toSubsemigroup_strictMono", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.toSubsemigroup_mono", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.mk'", "kind": "definition", "module": "Mathlib.RingTheory.NonUnitalSubring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.coe_mk'", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.mem_mk'", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.mk'_toSubsemigroup", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.mk'_toAddSubgroup", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.zero_mem", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.mul_mem", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.add_mem", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.neg_mem", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.sub_mem", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.toNonUnitalRing", "kind": "instance", "module": "Mathlib.RingTheory.NonUnitalSubring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.zsmul_mem", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.val_add", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.val_neg", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.val_mul", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.val_zero", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.coe_eq_zero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NonUnitalSubring.toNonUnitalCommRing", "kind": "instance", "module": "Mathlib.RingTheory.NonUnitalSubring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.mem_toSubsemigroup", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.coe_toSubsemigroup", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.mem_toAddSubgroup", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.coe_toAddSubgroup", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.mem_toNonUnitalSubsemiring", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.coe_toNonUnitalSubsemiring", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.inclusion", "kind": "definition", "module": "Mathlib.RingTheory.NonUnitalSubring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.toSubsemigroup_strictMono", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.toSubsemigroup_mono", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.toAddSubmonoid_strictMono", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.toAddSubmonoid_mono", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.topEquiv", "kind": "definition", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.comap", "kind": "definition", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.coe_comap", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.mem_comap", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.comap_comap", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.map", "kind": "definition", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.coe_map", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.mem_map", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.map_id", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.map_map", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.map_le_iff_le_comap", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.gc_map_comap", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.equivMapOfInjective", "kind": "definition", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.coe_equivMapOfInjective_apply", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.srange", "kind": "definition", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.coe_srange", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.mem_srange", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.srange_eq_map", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "NonUnitalRingHom.mem_srange_self", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.map_srange", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "NonUnitalRingHom.finite_srange", "kind": "instance", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.instInfSet", "kind": "instance", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.coe_sInf", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.mem_sInf", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.coe_iInf", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NonUnitalSubsemiring.mem_iInf", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NonUnitalSubsemiring.sInf_toSubsemigroup", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.sInf_toAddSubmonoid", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.instCompleteLattice", "kind": "instance", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.eq_top_iff'", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.center", "kind": "definition", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.coe_center", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.center_toSubsemigroup", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.center.instNonUnitalCommSemiring", "kind": "instance", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.mem_center_iff_addMonoidHom", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "NonUnitalSubsemiring.centerCongr", "kind": "definition", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.centerToMulOpposite", "kind": "definition", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring._example", "kind": "example", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": true, "tactics": ["with_reducible_and_instances"], "tactic_count": 1}
{"name": "NonUnitalSubsemiring.mem_center_iff", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "NonUnitalSubsemiring.decidableMemCenter", "kind": "instance", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.center_eq_top", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.centralizer", "kind": "definition", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.coe_centralizer", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.centralizer_toSubsemigroup", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.mem_centralizer_iff", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.center_le_centralizer", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.centralizer_le", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.centralizer_eq_top_iff_subset", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.centralizer_univ", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.closure", "kind": "definition", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.mem_closure", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.subset_closure", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.mem_closure_of_mem", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.notMem_of_notMem_closure", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.closure_le", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.closure_mono", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.closure_eq_of_le", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.closure_le_centralizer_centralizer", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.closureNonUnitalCommSemiringOfComm", "kind": "abbrev", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.mem_map_equiv", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "NonUnitalSubsemiring.map_equiv_eq_comap_symm", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.comap_equiv_eq_map_symm", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.nonUnitalSubsemiringClosure", "kind": "definition", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.nonUnitalSubsemiringClosure_coe", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.nonUnitalSubsemiringClosure_toAddSubmonoid", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.nonUnitalSubsemiringClosure_eq_closure", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": true, "tactics": ["ext", "refine", "rintro", "rintro", "exact", "exact"], "tactic_count": 6}
{"name": "NonUnitalSubsemiring.closure_subsemigroup_closure", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.coe_closure_eq", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NonUnitalSubsemiring.mem_closure_iff", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.closure_addSubmonoid_closure", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": true, "tactics": ["ext", "refine", "rintro", "rintro", "refine", "refine", "exact"], "tactic_count": 7}
{"name": "NonUnitalSubsemiring.closure_induction", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.closure_induction₂", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": true, "tactics": ["induction", "mem", "induction", "mem", "zero", "mul", "add", "zero", "mul", "add"], "tactic_count": 10}
{"name": "NonUnitalSubsemiring.gi", "kind": "definition", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.closure_eq", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.closure_empty", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.closure_univ", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.closure_union", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.closure_iUnion", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.closure_sUnion", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.map_sup", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.map_iSup", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.map_inf", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.map_iInf", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": true, "tactics": ["apply", "simpa"], "tactic_count": 2}
{"name": "NonUnitalSubsemiring.comap_inf", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.comap_iInf", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.map_bot", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.comap_top", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.prod", "kind": "definition", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.coe_prod", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.mem_prod", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.prod_mono", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.prod_mono_right", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.prod_mono_left", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.prod_top", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.top_prod", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.top_prod_top", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.prodEquiv", "kind": "definition", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.mem_iSup_of_directed", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": true, "tactics": ["refine", "let", "suffices", "exact"], "tactic_count": 4}
{"name": "NonUnitalSubsemiring.coe_iSup_of_directed", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.mem_sSup_of_directedOn", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": true, "tactics": ["haveI", "simp"], "tactic_count": 2}
{"name": "NonUnitalSubsemiring.coe_sSup_of_directedOn", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.eq_of_eqOn_stop", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.srangeRestrict", "kind": "definition", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.coe_srangeRestrict", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.srangeRestrict_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.srange_eq_top_iff_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.srange_eq_top_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.eqOn_sclosure", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.eq_of_eqOn_sdense", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.sclosure_preimage_le", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.map_sclosure", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.srange_subtype", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.range_fst", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.range_snd", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.nonUnitalSubsemiringCongr", "kind": "definition", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.sofLeftInverse'", "kind": "definition", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.sofLeftInverse'_apply", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.sofLeftInverse'_symm_apply", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.nonUnitalSubsemiringMap", "kind": "definition", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "neg_mul_mem", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "mul_neg_mem", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "_example", "kind": "example", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Defs", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "NonUnitalSubsemiringClass.mulMemClass", "kind": "instance", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiringClass.toNonUnitalNonAssocSemiring", "kind": "instance", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiringClass.noZeroDivisors", "kind": "instance", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiringClass.subtype", "kind": "definition", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiringClass.subtype_apply", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiringClass.subtype_injective", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiringClass.coe_subtype", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiringClass.toNonUnitalSemiring", "kind": "instance", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiringClass.toNonUnitalCommSemiring", "kind": "instance", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.toAddSubmonoid_injective", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.toAddSubmonoid_inj", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.instSetLike", "kind": "instance", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.toSubsemigroup_injective", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.instPartialOrder", "kind": "instance", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.ofClass", "kind": "definition", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.instCanLiftSetCoeAndMemOfNatForallForallForallForallHAddForallForallForallForallHMul", "kind": "instance", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.instNonUnitalSubsemiringClass", "kind": "instance", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.mem_carrier", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.ext", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.copy", "kind": "definition", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.coe_copy", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.copy_eq", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.mk'", "kind": "definition", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.coe_mk'", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.mem_mk'", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.mk'_toSubsemigroup", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.mk'_toAddSubmonoid", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.coe_zero", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.coe_add", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.coe_mul", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.mem_toSubsemigroup", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.coe_toSubsemigroup", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.mem_toAddSubmonoid", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.coe_toAddSubmonoid", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.instTop", "kind": "instance", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.mem_top", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.coe_top", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.toAddSubmonoid_top", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.toAddSubmonoid_eq_top", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NonUnitalSubsemiring.instBot", "kind": "instance", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.instInhabited", "kind": "instance", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.coe_bot", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.mem_bot", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.instMin", "kind": "instance", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.coe_inf", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.mem_inf", "kind": "theorem", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.codRestrict", "kind": "definition", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalRingHom.eqSlocus", "kind": "definition", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.inclusion", "kind": "definition", "module": "Mathlib.RingTheory.NonUnitalSubsemiring.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.norm_one_add_smul", "kind": "theorem", "module": "Mathlib.RingTheory.NormTrace", "is_tactic_proof": true, "tactics": ["classical", "let", "let", "haveI", "clear_value", "simp_rw", "simp", "exact"], "tactic_count": 8}
{"name": "Algebra.PowerBasis.norm_gen_eq_coeff_zero_minpoly", "kind": "theorem", "module": "Mathlib.RingTheory.Norm.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Algebra.PowerBasis.norm_gen_eq_prod_roots", "kind": "theorem", "module": "Mathlib.RingTheory.Norm.Basic", "is_tactic_proof": true, "tactics": ["haveI", "have", "rw", "hf.coeff_zero_eq_prod_roots_of_monic", "simp"], "tactic_count": 5}
{"name": "Algebra.norm_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Norm.Basic", "is_tactic_proof": true, "tactics": ["nontriviality", "rw"], "tactic_count": 2}
{"name": "Algebra.norm_eq_zero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Norm.Basic", "is_tactic_proof": true, "tactics": ["constructor", "swap", "rintro", "let", "let", "rw", "rintro", "rw", "refine", "simpa", "contrapose", "apply", "rw"], "tactic_count": 13}
{"name": "Algebra.norm_ne_zero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Norm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.norm_eq_zero_iff'", "kind": "theorem", "module": "Mathlib.RingTheory.Norm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.norm_eq_zero_iff_of_basis", "kind": "theorem", "module": "Mathlib.RingTheory.Norm.Basic", "is_tactic_proof": true, "tactics": ["haveI", "haveI", "exact"], "tactic_count": 3}
{"name": "Algebra.norm_ne_zero_iff_of_basis", "kind": "theorem", "module": "Mathlib.RingTheory.Norm.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.norm_inv", "kind": "theorem", "module": "Mathlib.RingTheory.Norm.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "exact"], "tactic_count": 3}
{"name": "IntermediateField.AdjoinSimple.norm_gen_eq_one", "kind": "theorem", "module": "Mathlib.RingTheory.Norm.Basic", "is_tactic_proof": true, "tactics": ["rw", "contrapose", "obtain", "refine", "exact", "exact"], "tactic_count": 6}
{"name": "IntermediateField.AdjoinSimple.norm_gen_eq_prod_roots", "kind": "theorem", "module": "Mathlib.RingTheory.Norm.Basic", "is_tactic_proof": true, "tactics": ["have", "by_cases", "simp", "rw", "rw", "simp"], "tactic_count": 6}
{"name": "Algebra.norm_eq_prod_embeddings_gen", "kind": "theorem", "module": "Mathlib.RingTheory.Norm.Basic", "is_tactic_proof": true, "tactics": ["letI", "rw", "rw", "rw", "exact", "intro", "intro"], "tactic_count": 7}
{"name": "Algebra.prod_embeddings_eq_finrank_pow", "kind": "theorem", "module": "Mathlib.RingTheory.Norm.Basic", "is_tactic_proof": true, "tactics": ["haveI", "haveI", "letI", "rw", "refine", "letI", "simp_rw", "congr", "exact", "intro", "simp"], "tactic_count": 11}
{"name": "Algebra.norm_eq_of_algEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.Norm.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Algebra.norm_eq_of_ringEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.Norm.Basic", "is_tactic_proof": true, "tactics": ["classical", "by_cases", "obtain", "letI", "letI", "rw", "congr", "ext", "simp", "rw", "intro", "exact"], "tactic_count": 12}
{"name": "Algebra.norm_eq_of_equiv_equiv", "kind": "theorem", "module": "Mathlib.RingTheory.Norm.Basic", "is_tactic_proof": true, "tactics": ["letI", "let", "rw", "simp", "intro", "apply", "simp"], "tactic_count": 7}
{"name": "Algebra.norm", "kind": "definition", "module": "Mathlib.RingTheory.Norm.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.norm_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Norm.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.norm_self", "kind": "theorem", "module": "Mathlib.RingTheory.Norm.Defs", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Algebra.norm_eq_one_of_not_exists_basis", "kind": "theorem", "module": "Mathlib.RingTheory.Norm.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Algebra.norm_eq_one_of_not_module_finite", "kind": "theorem", "module": "Mathlib.RingTheory.Norm.Defs", "is_tactic_proof": true, "tactics": ["refine", "rintro", "exact"], "tactic_count": 3}
{"name": "Algebra.norm_eq_matrix_det", "kind": "theorem", "module": "Mathlib.RingTheory.Norm.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Algebra.norm_algebraMap_of_basis", "kind": "theorem", "module": "Mathlib.RingTheory.Norm.Defs", "is_tactic_proof": true, "tactics": ["haveI", "rw", "convert", "ext", "rw"], "tactic_count": 5}
{"name": "Algebra.norm_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.Norm.Defs", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "rw", "assumption_mod_cast"], "tactic_count": 4}
{"name": "Algebra.Norm.Transitivity.auxMat", "kind": "definition", "module": "Mathlib.RingTheory.Norm.Transitivity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Norm.Transitivity.auxMat_blockTriangular", "kind": "theorem", "module": "Mathlib.RingTheory.Norm.Transitivity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Norm.Transitivity.auxMat_toSquareBlock_ne", "kind": "theorem", "module": "Mathlib.RingTheory.Norm.Transitivity", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Algebra.Norm.Transitivity.auxMat_toSquareBlock_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Norm.Transitivity", "is_tactic_proof": true, "tactics": ["ext", "rw", "simp"], "tactic_count": 3}
{"name": "Algebra.Norm.Transitivity.mul_auxMat_blockTriangular", "kind": "theorem", "module": "Mathlib.RingTheory.Norm.Transitivity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Norm.Transitivity.mul_auxMat_corner", "kind": "theorem", "module": "Mathlib.RingTheory.Norm.Transitivity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Algebra.Norm.Transitivity.mul_auxMat_toSquareBlock_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Norm.Transitivity", "is_tactic_proof": true, "tactics": ["ext", "rw", "simp"], "tactic_count": 3}
{"name": "Algebra.Norm.Transitivity.termMulAuxMatBlock", "kind": "definition", "module": "Mathlib.RingTheory.Norm.Transitivity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Norm.Transitivity._aux_Mathlib_RingTheory_Norm_Transitivity___macroRules_Algebra_Norm_Transitivity_termMulAuxMatBlock_1", "kind": "definition", "module": "Mathlib.RingTheory.Norm.Transitivity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Norm.Transitivity.det_mul_corner_pow", "kind": "theorem", "module": "Mathlib.RingTheory.Norm.Transitivity", "is_tactic_proof": true, "tactics": ["trans", "simp", "rw", "simp_rw", "convert"], "tactic_count": 5}
{"name": "Algebra.Norm.Transitivity.cornerAddX", "kind": "definition", "module": "Mathlib.RingTheory.Norm.Transitivity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Norm.Transitivity.polyToMatrix_cornerAddX", "kind": "theorem", "module": "Mathlib.RingTheory.Norm.Transitivity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Algebra.Norm.Transitivity.eval_zero_det_det", "kind": "theorem", "module": "Mathlib.RingTheory.Norm.Transitivity", "is_tactic_proof": false, "tactics": ["rw", "congr"], "tactic_count": 2}
{"name": "Algebra.Norm.Transitivity.eval_zero_comp_det", "kind": "theorem", "module": "Mathlib.RingTheory.Norm.Transitivity", "is_tactic_proof": false, "tactics": ["simp_rw", "congr", "simp"], "tactic_count": 3}
{"name": "Algebra.Norm.Transitivity.comp_det_mul_pow", "kind": "theorem", "module": "Mathlib.RingTheory.Norm.Transitivity", "is_tactic_proof": true, "tactics": ["trans", "simp_rw", "det_reindex_self,", "diagonal_one,", "simp", "simp_rw", "comp_toSquareBlock", "smul_one_eq_diagonal,", "simp"], "tactic_count": 9}
{"name": "Algebra.Norm.Transitivity.det_det_aux", "kind": "theorem", "module": "Mathlib.RingTheory.Norm.Transitivity", "is_tactic_proof": true, "tactics": ["rw", "sub_self]"], "tactic_count": 2}
{"name": "Matrix.det_det", "kind": "theorem", "module": "Mathlib.RingTheory.Norm.Transitivity", "is_tactic_proof": true, "tactics": ["induction", "zero", "rw", "simp_rw", "succ", "have", "let", "let", "have", "refine", "sub_eq_zero.mp", "mem_nonZeroDivisors_iff_right.mp", "rw", "exact", "rw"], "tactic_count": 15}
{"name": "LinearMap.det_restrictScalars", "kind": "theorem", "module": "Mathlib.RingTheory.Norm.Transitivity", "is_tactic_proof": true, "tactics": ["classical", "nontriviality", "nontriviality", "have", "let", "let", "have", "have", "cases", "rw", "det_eq_one_of_not_module_finite", "cases", "rw", "det_eq_one_of_not_module_finite", "rw", "det_toMatrix"], "tactic_count": 16}
{"name": "Algebra.norm_norm", "kind": "theorem", "module": "Mathlib.RingTheory.Norm.Transitivity", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Algebra.isIntegral_norm", "kind": "theorem", "module": "Mathlib.RingTheory.Norm.Transitivity", "is_tactic_proof": true, "tactics": ["by_cases", "swap", "simpa", "let", "rw", "norm_algebraMap_of_basis", "apply", "rw", "norm_gen_eq_prod_roots", "refine", "suffices", "obtain", "simp"], "tactic_count": 13}
{"name": "Algebra.norm_eq_norm_adjoin", "kind": "theorem", "module": "Mathlib.RingTheory.Norm.Transitivity", "is_tactic_proof": true, "tactics": ["by_cases", "swap", "rw", "by_cases", "have", "h", "have", "exact", "simp", "rw", "simp", "refine", "rw", "exact", "let", "nth_rw", "rw", "norm_algebraMap_of_basis"], "tactic_count": 18}
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{"name": "OreLocalization.instNegOreLocalization", "kind": "instance", "module": "Mathlib.RingTheory.OreLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OreLocalization.neg_def", "kind": "theorem", "module": "Mathlib.RingTheory.OreLocalization.Basic", "is_tactic_proof": true, "tactics": ["with_unfolding_all"], "tactic_count": 1}
{"name": "OreLocalization.neg_add_cancel", "kind": "theorem", "module": "Mathlib.RingTheory.OreLocalization.Basic", "is_tactic_proof": true, "tactics": ["induction", "simp"], "tactic_count": 2}
{"name": "OreLocalization.zsmul", "kind": "definition", "module": "Mathlib.RingTheory.OreLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OreLocalization.instAddGroupOreLocalization", "kind": "instance", "module": "Mathlib.RingTheory.OreLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OreLocalization.instAddCommGroup", "kind": "instance", "module": "Mathlib.RingTheory.OreLocalization.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OreLocalization.cardinalMk", "kind": "theorem", "module": "Mathlib.RingTheory.OreLocalization.Cardinality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OreLocalization.nontrivial_of_nonZeroDivisorsLeft", "kind": "theorem", "module": "Mathlib.RingTheory.OreLocalization.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OreLocalization.nontrivial_of_nonZeroDivisorsRight", "kind": "theorem", "module": "Mathlib.RingTheory.OreLocalization.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OreLocalization.nontrivial_of_nonZeroDivisors", "kind": "theorem", "module": "Mathlib.RingTheory.OreLocalization.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OreLocalization.nontrivial", "kind": "instance", "module": "Mathlib.RingTheory.OreLocalization.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OreLocalization.inv", "kind": "definition", "module": "Mathlib.RingTheory.OreLocalization.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OreLocalization.inv'", "kind": "instance", "module": "Mathlib.RingTheory.OreLocalization.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OreLocalization.inv_def", "kind": "theorem", "module": "Mathlib.RingTheory.OreLocalization.NonZeroDivisors", "is_tactic_proof": true, "tactics": ["with_unfolding_all"], "tactic_count": 1}
{"name": "OreLocalization.mul_inv_cancel", "kind": "theorem", "module": "Mathlib.RingTheory.OreLocalization.NonZeroDivisors", "is_tactic_proof": false, "tactics": ["induction", "rw", "have", "rintro", "simp", "simp", "with_unfolding_all"], "tactic_count": 7}
{"name": "OreLocalization.inv_zero", "kind": "theorem", "module": "Mathlib.RingTheory.OreLocalization.NonZeroDivisors", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "OreLocalization.instGroupWithZeroNonZeroDivisors", "kind": "instance", "module": "Mathlib.RingTheory.OreLocalization.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OreLocalization.instCommGroupWithZeroNonZeroDivisors", "kind": "instance", "module": "Mathlib.RingTheory.OreLocalization.NonZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OreLocalization.oreSetOfIsCancelMulZero", "kind": "definition", "module": "Mathlib.RingTheory.OreLocalization.OreSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OreLocalization.oreSetOfNoZeroDivisors", "kind": "definition", "module": "Mathlib.RingTheory.OreLocalization.OreSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OreLocalization.nonempty_oreSet_iff", "kind": "theorem", "module": "Mathlib.RingTheory.OreLocalization.OreSet", "is_tactic_proof": true, "tactics": ["constructor", "exact", "intro", "choose", "exact"], "tactic_count": 5}
{"name": "OreLocalization.nonempty_oreSet_iff_of_noZeroDivisors", "kind": "theorem", "module": "Mathlib.RingTheory.OreLocalization.OreSet", "is_tactic_proof": true, "tactics": ["constructor", "exact", "intro", "choose", "exact"], "tactic_count": 5}
{"name": "OreLocalization.zero_smul", "kind": "theorem", "module": "Mathlib.RingTheory.OreLocalization.Ring", "is_tactic_proof": false, "tactics": ["induction", "rw"], "tactic_count": 2}
{"name": "OreLocalization.add_smul", "kind": "theorem", "module": "Mathlib.RingTheory.OreLocalization.Ring", "is_tactic_proof": false, "tactics": ["induction", "induction", "induction", "rcases", "rw", "clear", "rw", "rcases", "rw", "clear", "have", "rw", "norm_cast", "apply", "rw", "have", "rw", "rcases", "rw", "rw", "rw", "simp", "rw", "rw", "simp"], "tactic_count": 25}
{"name": "OreLocalization.zero_mul", "kind": "theorem", "module": "Mathlib.RingTheory.OreLocalization.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OreLocalization.mul_zero", "kind": "theorem", "module": "Mathlib.RingTheory.OreLocalization.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OreLocalization.left_distrib", "kind": "theorem", "module": "Mathlib.RingTheory.OreLocalization.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OreLocalization.right_distrib", "kind": "theorem", "module": "Mathlib.RingTheory.OreLocalization.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OreLocalization.instSemiring", "kind": "instance", "module": "Mathlib.RingTheory.OreLocalization.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OreLocalization.instModule", "kind": "instance", "module": "Mathlib.RingTheory.OreLocalization.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OreLocalization.instModuleOfIsScalarTower", "kind": "instance", "module": "Mathlib.RingTheory.OreLocalization.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OreLocalization.nsmul_eq_nsmul", "kind": "theorem", "module": "Mathlib.RingTheory.OreLocalization.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OreLocalization.numeratorRingHom", "kind": "abbrev", "module": "Mathlib.RingTheory.OreLocalization.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OreLocalization.instAlgebra", "kind": "instance", "module": "Mathlib.RingTheory.OreLocalization.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OreLocalization.universalHom", "kind": "definition", "module": "Mathlib.RingTheory.OreLocalization.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OreLocalization.universalHom_apply", "kind": "theorem", "module": "Mathlib.RingTheory.OreLocalization.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OreLocalization.universalHom_commutes", "kind": "theorem", "module": "Mathlib.RingTheory.OreLocalization.Ring", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "OreLocalization.universalHom_unique", "kind": "theorem", "module": "Mathlib.RingTheory.OreLocalization.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OreLocalization.instRing", "kind": "instance", "module": "Mathlib.RingTheory.OreLocalization.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OreLocalization.zsmul_eq_zsmul", "kind": "theorem", "module": "Mathlib.RingTheory.OreLocalization.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OreLocalization.numeratorHom_inj", "kind": "theorem", "module": "Mathlib.RingTheory.OreLocalization.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OreLocalization.instDivisionRingNonZeroDivisors", "kind": "instance", "module": "Mathlib.RingTheory.OreLocalization.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OreLocalization.instCommSemiring", "kind": "instance", "module": "Mathlib.RingTheory.OreLocalization.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OreLocalization.instCommRing", "kind": "instance", "module": "Mathlib.RingTheory.OreLocalization.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OreLocalization.instFieldNonZeroDivisors", "kind": "instance", "module": "Mathlib.RingTheory.OreLocalization.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrzechProperty.instOfFinite", "kind": "instance", "module": "Mathlib.RingTheory.OrzechProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrzechProperty.injective_of_surjective_of_injective", "kind": "theorem", "module": "Mathlib.RingTheory.OrzechProperty", "is_tactic_proof": true, "tactics": ["obtain", "haveI", "letI", "letI", "let", "haveI", "let", "replace", "let", "replace", "simpa"], "tactic_count": 11}
{"name": "OrzechProperty.injective_of_surjective_of_submodule", "kind": "theorem", "module": "Mathlib.RingTheory.OrzechProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrzechProperty.injective_of_surjective_endomorphism", "kind": "theorem", "module": "Mathlib.RingTheory.OrzechProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrzechProperty.bijective_of_surjective_endomorphism", "kind": "theorem", "module": "Mathlib.RingTheory.OrzechProperty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monoid.perfection", "kind": "definition", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ring.perfectionSubsemiring", "kind": "definition", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ring.perfectionSubring", "kind": "definition", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ring.Perfection", "kind": "definition", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Perfection.commSemiring", "kind": "instance", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Perfection.charP", "kind": "instance", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Perfection.ring", "kind": "instance", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Perfection.commRing", "kind": "instance", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Perfection.instInhabitedPerfection", "kind": "instance", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Perfection.coeff", "kind": "definition", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Perfection.ext", "kind": "theorem", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Perfection.pthRoot", "kind": "definition", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Perfection.coeff_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Perfection.coeff_pthRoot", "kind": "theorem", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Perfection.coeff_pow_p", "kind": "theorem", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Perfection.coeff_pow_p'", "kind": "theorem", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Perfection.coeff_frobenius", "kind": "theorem", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "Perfection.coeff_iterate_frobenius", "kind": "theorem", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Perfection.coeff_iterate_frobenius'", "kind": "theorem", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Perfection.pthRoot_frobenius", "kind": "theorem", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Perfection.frobenius_pthRoot", "kind": "theorem", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Perfection.coeff_add_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Perfection.coeff_ne_zero_of_le", "kind": "theorem", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Perfection.perfectRing", "kind": "instance", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Perfection.coeff_frobeniusEquiv_symm", "kind": "theorem", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": true, "tactics": ["nth_rw", "rw"], "tactic_count": 2}
{"name": "Perfection.coeff_iterate_frobeniusEquiv_symm", "kind": "theorem", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Perfection.coeff_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": true, "tactics": ["intro", "refine", "induction", "refl", "le_succ_of_le", "choose", "use", "intro", "obtain", "have", "simp", "exact", "subst", "simp", "have", "have", "simp", "simp"], "tactic_count": 18}
{"name": "Perfection.lift", "kind": "definition", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Perfection.hom_ext", "kind": "theorem", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Perfection.map", "kind": "definition", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Perfection.coeff_map", "kind": "theorem", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PerfectionMap.mk'", "kind": "theorem", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PerfectionMap.of", "kind": "theorem", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PerfectionMap.id", "kind": "theorem", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PerfectionMap.equiv", "kind": "definition", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PerfectionMap.equiv_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PerfectionMap.comp_equiv", "kind": "theorem", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PerfectionMap.comp_equiv'", "kind": "theorem", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PerfectionMap.comp_symm_equiv", "kind": "theorem", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PerfectionMap.comp_symm_equiv'", "kind": "theorem", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PerfectionMap.lift", "kind": "definition", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PerfectionMap.hom_ext", "kind": "theorem", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PerfectionMap.map", "kind": "definition", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PerfectionMap.comp_map", "kind": "theorem", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PerfectionMap.map_map", "kind": "theorem", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PerfectionMap.map_eq_map", "kind": "theorem", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModP", "kind": "abbrev", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModP.commRing", "kind": "instance", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModP.charP", "kind": "instance", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModP.nontrivial", "kind": "instance", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModP.preVal", "kind": "definition", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModP.preVal_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModP.preVal_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": false, "tactics": ["obtain", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "ModP.preVal_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": true, "tactics": ["have", "have", "obtain", "obtain", "rw", "rw"], "tactic_count": 6}
{"name": "ModP.preVal_add", "kind": "theorem", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "by_cases", "rw", "by_cases", "rw", "obtain", "obtain", "rw", "rw"], "tactic_count": 10}
{"name": "ModP.v_p_lt_preVal", "kind": "theorem", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": true, "tactics": ["refine", "obtain", "rw", "rw"], "tactic_count": 4}
{"name": "ModP.preVal_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModP.v_p_lt_val", "kind": "theorem", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ModP.mul_ne_zero_of_pow_p_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "have", "rw", "rw", "rw", "rw", "mul_one_div_cancel", "rw", "by_cases", "rw", "replace", "conv_lhs", "rw", "refine", "rw"], "tactic_count": 16}
{"name": "PreTilt", "kind": "definition", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PreTilt.instCommRing", "kind": "instance", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PreTilt.instCharP", "kind": "instance", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PreTilt.instPerfectRing", "kind": "instance", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PreTilt.coeff", "kind": "definition", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PreTilt.coeff_def", "kind": "theorem", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PreTilt.coeff_frobenius", "kind": "theorem", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PreTilt.coeff_iterate_frobenius", "kind": "theorem", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PreTilt.coeff_iterate_frobenius'", "kind": "theorem", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PreTilt.coeff_pow_p", "kind": "theorem", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PreTilt.coeff_frobeniusEquiv_symm", "kind": "theorem", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PreTilt.coeff_iterate_frobeniusEquiv_symm", "kind": "theorem", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PreTilt.valAux", "kind": "definition", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PreTilt.coeff_nat_find_add_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PreTilt.valAux_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "PreTilt.valAux_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "by_cases", "rw", "obtain", "obtain", "replace", "replace", "have", "rw", "refine", "rw", "rw", "rw", "rw"], "tactic_count": 15}
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{"name": "PreTilt.map_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "obtain", "change", "rw", "replace", "rwa"], "tactic_count": 7}
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{"name": "Tilt", "kind": "definition", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tilt.instField", "kind": "instance", "module": "Mathlib.RingTheory.Perfection", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Perfectoid.BDeRham.0.term𝕎_", "kind": "definition", "module": "Mathlib.RingTheory.Perfectoid.BDeRham", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "fontaineThetaInvertP", "kind": "definition", "module": "Mathlib.RingTheory.Perfectoid.BDeRham", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BDeRhamPlus", "kind": "definition", "module": "Mathlib.RingTheory.Perfectoid.BDeRham", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCommRingBDeRhamPlus", "kind": "instance", "module": "Mathlib.RingTheory.Perfectoid.BDeRham", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BDeRham", "kind": "definition", "module": "Mathlib.RingTheory.Perfectoid.BDeRham", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Perfectoid.BDeRham.0.term𝔹_dR^+(_)", "kind": "definition", "module": "Mathlib.RingTheory.Perfectoid.BDeRham", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Perfectoid.BDeRham.0._aux_Mathlib_RingTheory_Perfectoid_BDeRham___macroRules__private_Mathlib_RingTheory_Perfectoid_BDeRham_0_term𝔹_dR^+(_)_1", "kind": "definition", "module": "Mathlib.RingTheory.Perfectoid.BDeRham", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Perfectoid.BDeRham.0._aux_Mathlib_RingTheory_Perfectoid_BDeRham___unexpand_BDeRhamPlus_1", "kind": "definition", "module": "Mathlib.RingTheory.Perfectoid.BDeRham", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Perfectoid.BDeRham.0.term𝔹_dR(_)", "kind": "definition", "module": "Mathlib.RingTheory.Perfectoid.BDeRham", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Perfectoid.BDeRham.0._aux_Mathlib_RingTheory_Perfectoid_BDeRham___macroRules__private_Mathlib_RingTheory_Perfectoid_BDeRham_0_term𝔹_dR(_)_1", "kind": "definition", "module": "Mathlib.RingTheory.Perfectoid.BDeRham", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "_private.Mathlib.RingTheory.Perfectoid.FontaineTheta.0.term𝕎_", "kind": "definition", "module": "Mathlib.RingTheory.Perfectoid.FontaineTheta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Perfectoid.FontaineTheta.0._aux_Mathlib_RingTheory_Perfectoid_FontaineTheta___macroRules__private_Mathlib_RingTheory_Perfectoid_FontaineTheta_0_term𝕎__1", "kind": "definition", "module": "Mathlib.RingTheory.Perfectoid.FontaineTheta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Perfectoid.FontaineTheta.0._aux_Mathlib_RingTheory_Perfectoid_FontaineTheta___unexpand_WittVector_1", "kind": "definition", "module": "Mathlib.RingTheory.Perfectoid.FontaineTheta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "_private.Mathlib.RingTheory.Perfectoid.FontaineTheta.0._aux_Mathlib_RingTheory_Perfectoid_FontaineTheta___macroRules__private_Mathlib_RingTheory_Perfectoid_FontaineTheta_0_term_♭_1", "kind": "definition", "module": "Mathlib.RingTheory.Perfectoid.FontaineTheta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Perfectoid.FontaineTheta.0._aux_Mathlib_RingTheory_Perfectoid_FontaineTheta___unexpand_PreTilt_1", "kind": "definition", "module": "Mathlib.RingTheory.Perfectoid.FontaineTheta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Perfectoid.FontaineTheta.0.term𝔭", "kind": "definition", "module": "Mathlib.RingTheory.Perfectoid.FontaineTheta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Perfectoid.FontaineTheta.0._aux_Mathlib_RingTheory_Perfectoid_FontaineTheta___macroRules__private_Mathlib_RingTheory_Perfectoid_FontaineTheta_0_term𝔭_1", "kind": "definition", "module": "Mathlib.RingTheory.Perfectoid.FontaineTheta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Perfectoid.FontaineTheta.0._aux_Mathlib_RingTheory_Perfectoid_FontaineTheta___delab_app__private_Mathlib_RingTheory_Perfectoid_FontaineTheta_0_term𝔭_1", "kind": "definition", "module": "Mathlib.RingTheory.Perfectoid.FontaineTheta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.ker_map_le_ker_mk_comp_ghostComponent", "kind": "theorem", "module": "Mathlib.RingTheory.Perfectoid.FontaineTheta", "is_tactic_proof": true, "tactics": ["intro", "simp", "intro", "simp", "apply_fun", "simp", "simp", "exact"], "tactic_count": 8}
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{"name": "WittVector.ghostComponentModPPow_map_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Perfectoid.FontaineTheta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.quotEquivOfEq_ghostComponentModPPow", "kind": "theorem", "module": "Mathlib.RingTheory.Perfectoid.FontaineTheta", "is_tactic_proof": true, "tactics": ["obtain", "simp"], "tactic_count": 2}
{"name": "WittVector.ghostComponentModPPow_teichmuller_coeff", "kind": "theorem", "module": "Mathlib.RingTheory.Perfectoid.FontaineTheta", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
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{"name": "WittVector.fontaineThetaModPPow_teichmuller", "kind": "theorem", "module": "Mathlib.RingTheory.Perfectoid.FontaineTheta", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WittVector.factorPowSucc_comp_fontaineThetaModPPow", "kind": "theorem", "module": "Mathlib.RingTheory.Perfectoid.FontaineTheta", "is_tactic_proof": false, "tactics": ["apply", "eq_of_apply_teichmuller_eq", "use", "have", "rw", "exact", "simp"], "tactic_count": 7}
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{"name": "WittVector.fontaineTheta", "kind": "definition", "module": "Mathlib.RingTheory.Perfectoid.FontaineTheta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.mk_pow_fontaineTheta", "kind": "theorem", "module": "Mathlib.RingTheory.Perfectoid.FontaineTheta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "PreTilt.untiltAux", "kind": "definition", "module": "Mathlib.RingTheory.Perfectoid.Untilt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PreTilt.pow_dvd_untiltAux_sub_untiltAux", "kind": "theorem", "module": "Mathlib.RingTheory.Perfectoid.Untilt", "is_tactic_proof": true, "tactics": ["cases", "zero", "succ", "let", "have", "simp", "rw", "refine", "rw", "simp", "calc"], "tactic_count": 11}
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{"name": "PreTilt.exists_smodEq_untiltAux", "kind": "theorem", "module": "Mathlib.RingTheory.Perfectoid.Untilt", "is_tactic_proof": true, "tactics": ["refine", "simpa", "x.pow_dvd_untiltAux_sub_untiltAux"], "tactic_count": 3}
{"name": "PreTilt.untiltFun", "kind": "definition", "module": "Mathlib.RingTheory.Perfectoid.Untilt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PreTilt.untiltAux_smodEq_untiltFun", "kind": "theorem", "module": "Mathlib.RingTheory.Perfectoid.Untilt", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "PreTilt.untilt", "kind": "definition", "module": "Mathlib.RingTheory.Perfectoid.Untilt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PreTilt.mk_untilt_eq_coeff_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Perfectoid.Untilt", "is_tactic_proof": true, "tactics": ["simp", "rw", "simpa"], "tactic_count": 3}
{"name": "PreTilt.mk_comp_untilt_eq_coeff_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Perfectoid.Untilt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PreTilt.untilt_iterate_frobeniusEquiv_symm_pow", "kind": "theorem", "module": "Mathlib.RingTheory.Perfectoid.Untilt", "is_tactic_proof": true, "tactics": ["simp", "congr", "simp"], "tactic_count": 3}
{"name": "PiTensorProduct.instOne", "kind": "instance", "module": "Mathlib.RingTheory.PiTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiTensorProduct.one_def", "kind": "theorem", "module": "Mathlib.RingTheory.PiTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiTensorProduct.instAddCommMonoidWithOne", "kind": "instance", "module": "Mathlib.RingTheory.PiTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiTensorProduct.mul", "kind": "definition", "module": "Mathlib.RingTheory.PiTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiTensorProduct.mul_tprod_tprod", "kind": "theorem", "module": "Mathlib.RingTheory.PiTensorProduct", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PiTensorProduct.instMul", "kind": "instance", "module": "Mathlib.RingTheory.PiTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiTensorProduct.mul_def", "kind": "theorem", "module": "Mathlib.RingTheory.PiTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiTensorProduct.tprod_mul_tprod", "kind": "theorem", "module": "Mathlib.RingTheory.PiTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiconjBy.tprod", "kind": "theorem", "module": "Mathlib.RingTheory.PiTensorProduct", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Commute.tprod", "kind": "theorem", "module": "Mathlib.RingTheory.PiTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiTensorProduct.smul_tprod_mul_smul_tprod", "kind": "theorem", "module": "Mathlib.RingTheory.PiTensorProduct", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PiTensorProduct.instNonUnitalNonAssocSemiring", "kind": "instance", "module": "Mathlib.RingTheory.PiTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiTensorProduct.one_mul", "kind": "theorem", "module": "Mathlib.RingTheory.PiTensorProduct", "is_tactic_proof": true, "tactics": ["induction", "smul_tprod", "add"], "tactic_count": 3}
{"name": "PiTensorProduct.mul_one", "kind": "theorem", "module": "Mathlib.RingTheory.PiTensorProduct", "is_tactic_proof": true, "tactics": ["induction", "smul_tprod", "add"], "tactic_count": 3}
{"name": "PiTensorProduct.instNonAssocSemiring", "kind": "instance", "module": "Mathlib.RingTheory.PiTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiTensorProduct.tprodMonoidHom", "kind": "definition", "module": "Mathlib.RingTheory.PiTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiTensorProduct.mul_assoc", "kind": "theorem", "module": "Mathlib.RingTheory.PiTensorProduct", "is_tactic_proof": true, "tactics": ["suffices", "ext", "dsimp", "simpa"], "tactic_count": 4}
{"name": "PiTensorProduct.instNonUnitalSemiring", "kind": "instance", "module": "Mathlib.RingTheory.PiTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiTensorProduct.instSemiring", "kind": "instance", "module": "Mathlib.RingTheory.PiTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiTensorProduct.instAlgebra", "kind": "instance", "module": "Mathlib.RingTheory.PiTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "PiTensorProduct.singleAlgHom", "kind": "definition", "module": "Mathlib.RingTheory.PiTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiTensorProduct.liftAlgHom", "kind": "definition", "module": "Mathlib.RingTheory.PiTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiTensorProduct.tprod_noncommProd", "kind": "theorem", "module": "Mathlib.RingTheory.PiTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiTensorProduct.algHom_ext", "kind": "theorem", "module": "Mathlib.RingTheory.PiTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiTensorProduct.instRing", "kind": "instance", "module": "Mathlib.RingTheory.PiTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "PiTensorProduct.tprod_prod", "kind": "theorem", "module": "Mathlib.RingTheory.PiTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiTensorProduct.constantBaseRingEquiv", "kind": "definition", "module": "Mathlib.RingTheory.PiTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiTensorProduct.constantBaseRingEquiv_tprod", "kind": "theorem", "module": "Mathlib.RingTheory.PiTensorProduct", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PiTensorProduct.constantBaseRingEquiv_symm", "kind": "theorem", "module": "Mathlib.RingTheory.PiTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiTensorProduct.instCommRing", "kind": "instance", "module": "Mathlib.RingTheory.PiTensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Invertible.linearEquiv", "kind": "definition", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Invertible.leftCancelEquiv", "kind": "abbrev", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Invertible.rightCancelEquiv", "kind": "abbrev", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Invertible.leftCancelEquiv_comp_lTensor_comp_symm", "kind": "theorem", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Module.Invertible.rightCancelEquiv_comp_rTensor_comp_symm", "kind": "theorem", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Module.Invertible.rTensorInv", "kind": "definition", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Invertible.rTensorInv_leftInverse", "kind": "theorem", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Module.Invertible.rTensorEquiv", "kind": "definition", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Invertible.bijective_curry", "kind": "theorem", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": ["have", "curry", "rTensorHom", "rw", "simp", "simpa"], "tactic_count": 6}
{"name": "Module.Invertible.linearEquivDual", "kind": "definition", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Invertible.right", "kind": "theorem", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Invertible.left", "kind": "theorem", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Invertible.inst", "kind": "instance", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Invertible.congr", "kind": "theorem", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Invertible.instDual", "kind": "instance", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Invertible.instTensorProduct", "kind": "instance", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.PicardGroup.0.Module.Invertible.finite_projective", "kind": "theorem", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": true, "tactics": ["let", "let", "have", "let", "have", "rw", "use", "simp_rw", "rw", "rwa", "have", "classical", "let", "let", "let", "have", "refine", "simp"], "tactic_count": 18}
{"name": "Module.Invertible.instFinite", "kind": "instance", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Invertible.instProjective", "kind": "instance", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Invertible._example", "kind": "example", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Invertible.lTensor_injective_iff", "kind": "theorem", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": true, "tactics": ["refine", "rw", "simpa"], "tactic_count": 3}
{"name": "Module.Invertible.rTensor_injective_iff", "kind": "theorem", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Module.Invertible.lTensor_surjective_iff", "kind": "theorem", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": true, "tactics": ["refine", "rw", "simpa"], "tactic_count": 3}
{"name": "Module.Invertible.rTensor_surjective_iff", "kind": "theorem", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Module.Invertible.lTensor_bijective_iff", "kind": "theorem", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Module.Invertible.rTensor_bijective_iff", "kind": "theorem", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Module.Invertible.free_iff_linearEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": true, "tactics": ["refine", "nontriviality", "have", "have", "card_eq_of_linearEquiv", "linearEquiv", "have", "exact", "considering", "see"], "tactic_count": 10}
{"name": "Module.Invertible.finrank_eq_one", "kind": "theorem", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": true, "tactics": ["cases", "rw", "rw"], "tactic_count": 3}
{"name": "Module.Invertible.rank_eq_one", "kind": "theorem", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Invertible.toModuleEnd_bijective", "kind": "theorem", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": ["have", "toModuleEnd", "rTensorEquiv", "simpa"], "tactic_count": 4}
{"name": "Module.Invertible.instFaithfulSMul", "kind": "instance", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.PicardGroup.0.Module.Invertible.bijective_self_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Invertible.bijective_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": true, "tactics": ["simpa", "bijective_self_of_surjective"], "tactic_count": 2}
{"name": "Module.Invertible.rightInverse_of_leftInverse", "kind": "theorem", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Invertible.leftInverse_of_rightInverse", "kind": "theorem", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Invertible.leftInverse_iff_rightInverse", "kind": "theorem", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Invertible.linearEquivOfLeftInverse", "kind": "definition", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Invertible.linearEquivOfLeftInverse_apply", "kind": "theorem", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Invertible.linearEquivOfLeftInverse_symm_apply", "kind": "theorem", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Invertible.linearEquivOfRightInverse", "kind": "definition", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Invertible.linearEquivOfRightInverse_apply", "kind": "theorem", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Invertible.linearEquivOfRightInverse_symm_apply", "kind": "theorem", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Invertible.algEquivOfRing", "kind": "definition", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Invertible.algEquivOfRing_apply", "kind": "theorem", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Invertible.instTensorProduct_1", "kind": "instance", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Invertible.of_isLocalization", "kind": "theorem", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Invertible.instLocalizationLocalizedModule", "kind": "instance", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Invertible.instTensorProduct_2", "kind": "instance", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInvertibleCarrierOutSemimoduleCatValSkeleton", "kind": "instance", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInvertibleCarrierOutModuleCatValSkeleton", "kind": "instance", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instSmallUnitsSkeletonSemimoduleCat", "kind": "instance", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instSmallUnitsSkeletonModuleCat", "kind": "instance", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRing.Pic", "kind": "definition", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCommGroupPic", "kind": "instance", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInvertibleReprₛ", "kind": "instance", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRing.Pic.AsModule", "kind": "abbrev", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRing.Pic.instCoeSortType", "kind": "instance", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRing.Pic.instAddCommGroupAsModule", "kind": "instance", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.PicardGroup.0.CommRing.Pic.equivShrinkLinearEquiv", "kind": "definition", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRing.Pic.mk", "kind": "definition", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRing.Pic.mk.linearEquiv", "kind": "definition", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRing.Pic.mk_eq_iff", "kind": "theorem", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRing.Pic.mk_eq_self", "kind": "theorem", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRing.Pic.ext_iff", "kind": "theorem", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CommRing.Pic.mk_eq_mk_iff", "kind": "theorem", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRing.Pic.mk_self", "kind": "theorem", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRing.Pic.mk_eq_one_iff", "kind": "theorem", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CommRing.Pic.mk_eq_one_iff_free", "kind": "theorem", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRing.Pic.mk_eq_one", "kind": "theorem", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRing.Pic.instFreeAsModuleOfNat", "kind": "instance", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRing.Pic.mk_tensor", "kind": "theorem", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRing.Pic.mk_dual", "kind": "theorem", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRing.Pic.inv_eq_dual", "kind": "theorem", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CommRing.Pic.mul_eq_tensor", "kind": "theorem", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CommRing.Pic.subsingleton_iffₛ", "kind": "theorem", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRing.Pic.subsingleton_iff", "kind": "theorem", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRing.Pic.instFreeOfSubsingleton", "kind": "instance", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRing.Pic.instSubsingletonOfIsLocalRing", "kind": "instance", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRing.Pic.instSubsingletonOfFiniteMaximalSpectrum", "kind": "instance", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRing.Pic.mapAlgebra", "kind": "definition", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRing.Pic.mapAlgebra_mapAlgebra", "kind": "theorem", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRing.Pic.mapAlgebra_comp_mapAlgebra", "kind": "theorem", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CommRing.Pic.mapAlgebra_self_apply", "kind": "theorem", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRing.Pic.mapAlgebra_self", "kind": "theorem", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CommRing.Pic.mapRingHom", "kind": "definition", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRing.Pic.mapRingHom_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CommRing.Pic.mapRingHom_comp_mapRingHom", "kind": "theorem", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": true, "tactics": ["algebraize", "simp_rw"], "tactic_count": 2}
{"name": "CommRing.Pic.mapRingHom_mapRingHom", "kind": "theorem", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRing.Pic.mapRingHom_id", "kind": "theorem", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CommRing.Pic.mapRingHom_id_apply", "kind": "theorem", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRing.Pic.functor", "kind": "definition", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRing.relPic", "kind": "definition", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CommRing.relPic_eq_top", "kind": "theorem", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Invertible.tensorProductComm_eq_refl", "kind": "theorem", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": true, "tactics": ["let", "let", "refine", "apply", "ext", "apply", "let", "have", "have", "ext", "refine", "suffices", "conv_lhs", "rw", "mul_one]"], "tactic_count": 15}
{"name": "Module.Invertible.tmul_comm", "kind": "theorem", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.PicardGroup.0.Submodule.projective_units_and_mul'_comp_lTensor_bijective", "kind": "theorem", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": true, "tactics": ["obtain", "classical", "rw", "set", "obtain", "choose", "let", "restrict", "exact", "have", "dsimp", "exact", "let", "have", "simp", "simp_rw", "set", "have", "ext", "have", "injective_of_comp_eq_id", "rw", "refine", "rw", "map_top,"], "tactic_count": 25}
{"name": "Submodule.projective_units", "kind": "instance", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.projective_of_isUnit", "kind": "theorem", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.tensorEquivMul", "kind": "definition", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": true, "tactics": ["refine", "convert", "simp_rw", "congr"], "tactic_count": 4}
{"name": "Submodule.tensorInvEquiv", "kind": "definition", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.instInvertibleSubtypeMemVal", "kind": "instance", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.unitsToPic", "kind": "definition", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.unitsToPicEquiv", "kind": "definition", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.ker_unitsToPic", "kind": "theorem", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mulExact_unitsMap_spanSingleton_unitsToPic", "kind": "theorem", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Flat.toAlgebra", "kind": "definition", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Flat.toAlgebra_injective", "kind": "theorem", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Module.Flat.submoduleAlgebra", "kind": "abbrev", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Flat.submoduleAlgebraEquiv", "kind": "definition", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Flat.instSubtypeMemSubmoduleSubmoduleAlgebra", "kind": "instance", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Flat.instInvertibleSubtypeMemSubmoduleSubmoduleAlgebra", "kind": "instance", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Flat.tensorSubmoduleAlgebraEquiv", "kind": "definition", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Flat.top_mul_submoduleAlgebra", "kind": "theorem", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": true, "tactics": ["rw", "convert", "ext"], "tactic_count": 3}
{"name": "Module.Flat.tensorSubmoduleAlgebraEquivMul", "kind": "definition", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": true, "tactics": ["refine", "convert", "simp_rw", "congr"], "tactic_count": 4}
{"name": "Submodule.range_unitsToPic", "kind": "theorem", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": true, "tactics": ["ext", "obtain", "exact", "mk_eq_one_iff.mpr", "have", "have", "refine", "mk_eq_iff.mpr", "have", "eq_span_singleton_of_surjective", "tensorSubmoduleAlgebraEquivMul", "rw", "apply_fun", "simp_rw", "obtain", "exact"], "tactic_count": 16}
{"name": "Submodule.mulExact_unitsToPic_mapAlgebra", "kind": "theorem", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.unitsQuotEquivRelPic", "kind": "definition", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClassGroup.equivPic", "kind": "definition", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Invertible.exists_linearEquiv_ideal", "kind": "theorem", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_example", "kind": "example", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_example", "kind": "example", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.eq_top_of_mk_tensor_eq_one", "kind": "theorem", "module": "Mathlib.RingTheory.PicardGroup", "is_tactic_proof": true, "tactics": ["have", "have", "have", "isRightRegular_iff_isRegular.mp", "rw", "convert", "rw", "constructor", "exacts"], "tactic_count": 9}
{"name": "PolyEquivTensor.toFunBilinear", "kind": "definition", "module": "Mathlib.RingTheory.PolynomialAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PolyEquivTensor.toFunBilinear_apply_apply", "kind": "theorem", "module": "Mathlib.RingTheory.PolynomialAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PolyEquivTensor.toFunBilinear_apply_eq_smul", "kind": "theorem", "module": "Mathlib.RingTheory.PolynomialAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PolyEquivTensor.toFunBilinear_apply_eq_sum", "kind": "theorem", "module": "Mathlib.RingTheory.PolynomialAlgebra", "is_tactic_proof": true, "tactics": ["conv_lhs", "simp"], "tactic_count": 2}
{"name": "PolyEquivTensor.toFunLinear", "kind": "definition", "module": "Mathlib.RingTheory.PolynomialAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PolyEquivTensor.toFunLinear_tmul_apply", "kind": "theorem", "module": "Mathlib.RingTheory.PolynomialAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PolyEquivTensor.toFunLinear_mul_tmul_mul_aux_1", "kind": "theorem", "module": "Mathlib.RingTheory.PolynomialAlgebra", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "PolyEquivTensor.toFunLinear_mul_tmul_mul_aux_2", "kind": "theorem", "module": "Mathlib.RingTheory.PolynomialAlgebra", "is_tactic_proof": true, "tactics": ["simp_rw", "congr", "simp_rw"], "tactic_count": 3}
{"name": "PolyEquivTensor.toFunLinear_mul_tmul_mul", "kind": "theorem", "module": "Mathlib.RingTheory.PolynomialAlgebra", "is_tactic_proof": true, "tactics": ["classical", "simp", "ext", "simp_rw", "conv_rhs", "simp_rw", "zero_mul]", "simp_rw", "simp_rw", "simp_rw"], "tactic_count": 10}
{"name": "PolyEquivTensor.toFunLinear_one_tmul_one", "kind": "theorem", "module": "Mathlib.RingTheory.PolynomialAlgebra", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PolyEquivTensor.toFunAlgHom", "kind": "definition", "module": "Mathlib.RingTheory.PolynomialAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PolyEquivTensor.toFunAlgHom_apply_tmul_eq_smul", "kind": "theorem", "module": "Mathlib.RingTheory.PolynomialAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PolyEquivTensor.toFunAlgHom_apply_tmul", "kind": "theorem", "module": "Mathlib.RingTheory.PolynomialAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PolyEquivTensor.invFun", "kind": "definition", "module": "Mathlib.RingTheory.PolynomialAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PolyEquivTensor.invFun_add", "kind": "theorem", "module": "Mathlib.RingTheory.PolynomialAlgebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PolyEquivTensor.invFun_monomial", "kind": "theorem", "module": "Mathlib.RingTheory.PolynomialAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PolyEquivTensor.left_inv", "kind": "theorem", "module": "Mathlib.RingTheory.PolynomialAlgebra", "is_tactic_proof": true, "tactics": ["refine", "simp", "intro", "dsimp", "rw", "simp_rw", "conv_rhs", "simp", "rfl", "intro", "simp"], "tactic_count": 11}
{"name": "PolyEquivTensor.right_inv", "kind": "theorem", "module": "Mathlib.RingTheory.PolynomialAlgebra", "is_tactic_proof": true, "tactics": ["refine", "intro", "simp", "intro", "rw", "toFunAlgHom_apply_tmul,", "simp"], "tactic_count": 7}
{"name": "PolyEquivTensor.equiv", "kind": "definition", "module": "Mathlib.RingTheory.PolynomialAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "polyEquivTensor", "kind": "definition", "module": "Mathlib.RingTheory.PolynomialAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "polyEquivTensor_apply", "kind": "theorem", "module": "Mathlib.RingTheory.PolynomialAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "polyEquivTensor_symm_apply_tmul_eq_smul", "kind": "theorem", "module": "Mathlib.RingTheory.PolynomialAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "polyEquivTensor_symm_apply_tmul", "kind": "theorem", "module": "Mathlib.RingTheory.PolynomialAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "polyEquivTensor'", "kind": "definition", "module": "Mathlib.RingTheory.PolynomialAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "coe_polyEquivTensor'", "kind": "theorem", "module": "Mathlib.RingTheory.PolynomialAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "coe_polyEquivTensor'_symm", "kind": "theorem", "module": "Mathlib.RingTheory.PolynomialAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.algebra", "kind": "definition", "module": "Mathlib.RingTheory.PolynomialAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.algebraMap_def", "kind": "theorem", "module": "Mathlib.RingTheory.PolynomialAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsScalarTowerPolynomial", "kind": "instance", "module": "Mathlib.RingTheory.PolynomialAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFaithfulSMulPolynomial", "kind": "instance", "module": "Mathlib.RingTheory.PolynomialAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsPushoutPolynomial", "kind": "instance", "module": "Mathlib.RingTheory.PolynomialAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsPushoutPolynomial_1", "kind": "instance", "module": "Mathlib.RingTheory.PolynomialAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "term_→ₚₗ[_]_", "kind": "definition", "module": "Mathlib.RingTheory.PolynomialLaw.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_RingTheory_PolynomialLaw_Basic___macroRules_term_→ₚₗ[_]__1", "kind": "definition", "module": "Mathlib.RingTheory.PolynomialLaw.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_RingTheory_PolynomialLaw_Basic___unexpand_PolynomialLaw_1", "kind": "definition", "module": "Mathlib.RingTheory.PolynomialLaw.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PolynomialLaw.isCompat_apply'", "kind": "theorem", "module": "Mathlib.RingTheory.PolynomialLaw.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "PolynomialLaw.instZero", "kind": "instance", "module": "Mathlib.RingTheory.PolynomialLaw.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PolynomialLaw.zero_def", "kind": "theorem", "module": "Mathlib.RingTheory.PolynomialLaw.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PolynomialLaw.instInhabited", "kind": "instance", "module": "Mathlib.RingTheory.PolynomialLaw.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PolynomialLaw.id", "kind": "definition", "module": "Mathlib.RingTheory.PolynomialLaw.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PolynomialLaw.id_apply'", "kind": "theorem", "module": "Mathlib.RingTheory.PolynomialLaw.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PolynomialLaw.add", "kind": "definition", "module": "Mathlib.RingTheory.PolynomialLaw.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PolynomialLaw.instAdd", "kind": "instance", "module": "Mathlib.RingTheory.PolynomialLaw.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PolynomialLaw.add_def", "kind": "theorem", "module": "Mathlib.RingTheory.PolynomialLaw.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PolynomialLaw.add_def_apply", "kind": "theorem", "module": "Mathlib.RingTheory.PolynomialLaw.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PolynomialLaw.smul", "kind": "definition", "module": "Mathlib.RingTheory.PolynomialLaw.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PolynomialLaw.instSMul", "kind": "instance", "module": "Mathlib.RingTheory.PolynomialLaw.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PolynomialLaw.smul_def", "kind": "theorem", "module": "Mathlib.RingTheory.PolynomialLaw.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PolynomialLaw.smul_def_apply", "kind": "theorem", "module": "Mathlib.RingTheory.PolynomialLaw.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PolynomialLaw.add_smul", "kind": "theorem", "module": "Mathlib.RingTheory.PolynomialLaw.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "PolynomialLaw.zero_smul", "kind": "theorem", "module": "Mathlib.RingTheory.PolynomialLaw.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "PolynomialLaw.one_smul", "kind": "theorem", "module": "Mathlib.RingTheory.PolynomialLaw.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "PolynomialLaw.instMulAction", "kind": "instance", "module": "Mathlib.RingTheory.PolynomialLaw.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PolynomialLaw.instAddCommMonoid", "kind": "instance", "module": "Mathlib.RingTheory.PolynomialLaw.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PolynomialLaw.instModule", "kind": "instance", "module": "Mathlib.RingTheory.PolynomialLaw.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PolynomialLaw.neg", "kind": "definition", "module": "Mathlib.RingTheory.PolynomialLaw.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PolynomialLaw.instNeg", "kind": "instance", "module": "Mathlib.RingTheory.PolynomialLaw.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PolynomialLaw.neg_def", "kind": "theorem", "module": "Mathlib.RingTheory.PolynomialLaw.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PolynomialLaw.instAddCommGroup", "kind": "instance", "module": "Mathlib.RingTheory.PolynomialLaw.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PolynomialLaw.ground", "kind": "definition", "module": "Mathlib.RingTheory.PolynomialLaw.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PolynomialLaw.ground_apply", "kind": "theorem", "module": "Mathlib.RingTheory.PolynomialLaw.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PolynomialLaw.instCoeFunForall", "kind": "instance", "module": "Mathlib.RingTheory.PolynomialLaw.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PolynomialLaw.one_tmul_ground_apply'", "kind": "theorem", "module": "Mathlib.RingTheory.PolynomialLaw.Basic", "is_tactic_proof": true, "tactics": ["rw", "convert", "simp", "rw"], "tactic_count": 4}
{"name": "PolynomialLaw.lground", "kind": "definition", "module": "Mathlib.RingTheory.PolynomialLaw.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PolynomialLaw.ground_id", "kind": "theorem", "module": "Mathlib.RingTheory.PolynomialLaw.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "PolynomialLaw.ground_id_apply", "kind": "theorem", "module": "Mathlib.RingTheory.PolynomialLaw.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PolynomialLaw.comp", "kind": "definition", "module": "Mathlib.RingTheory.PolynomialLaw.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PolynomialLaw.comp_toFun'", "kind": "theorem", "module": "Mathlib.RingTheory.PolynomialLaw.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PolynomialLaw.comp_assoc", "kind": "theorem", "module": "Mathlib.RingTheory.PolynomialLaw.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PolynomialLaw.comp_id", "kind": "theorem", "module": "Mathlib.RingTheory.PolynomialLaw.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "PolynomialLaw.id_comp", "kind": "theorem", "module": "Mathlib.RingTheory.PolynomialLaw.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "PolynomialLaw.lifts", "kind": "definition", "module": "Mathlib.RingTheory.PolynomialLaw.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PolynomialLaw.φ", "kind": "definition", "module": "Mathlib.RingTheory.PolynomialLaw.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PolynomialLaw.range_φ", "kind": "theorem", "module": "Mathlib.RingTheory.PolynomialLaw.Basic", "is_tactic_proof": true, "tactics": ["simp", "rw", "congr", "rw", "simp"], "tactic_count": 5}
{"name": "PolynomialLaw.π", "kind": "definition", "module": "Mathlib.RingTheory.PolynomialLaw.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PolynomialLaw.toFunLifted", "kind": "definition", "module": "Mathlib.RingTheory.PolynomialLaw.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PolynomialLaw.toFun", "kind": "definition", "module": "Mathlib.RingTheory.PolynomialLaw.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PolynomialLaw.exists_range_φ_eq_of_fg", "kind": "theorem", "module": "Mathlib.RingTheory.PolynomialLaw.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PolynomialLaw.toFun'_eq_of_diagram", "kind": "theorem", "module": "Mathlib.RingTheory.PolynomialLaw.Basic", "is_tactic_proof": true, "tactics": ["let", "have", "ψ.range.val.comp", "simp", "simp", "rw", "quotientKerEquivRangeₐ_comp_mkₐ", "simp", "apply", "rw", "rTensor_comp_apply,", "apply", "simp", "rw", "comp_toLinearMap,", "simp"], "tactic_count": 16}
{"name": "PolynomialLaw.toFun'_eq_of_inclusion", "kind": "theorem", "module": "Mathlib.RingTheory.PolynomialLaw.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PolynomialLaw.factorsThrough_toFunLifted_π", "kind": "theorem", "module": "Mathlib.RingTheory.PolynomialLaw.Basic", "is_tactic_proof": true, "tactics": ["rintro", "simp", "set", "have", "rw", "exact", "set", "have", "rw", "exact", "have", "simp", "simp", "obtain", "rw", "have", "have", "have", "rTensor", "rTensor", "rTensor_surjective", "obtain", "rw", "simp", "rw", "simp", "rfl", "simp", "congr"], "tactic_count": 29}
{"name": "PolynomialLaw.toFun_eq_rTensor_φ_toFun'", "kind": "theorem", "module": "Mathlib.RingTheory.PolynomialLaw.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PolynomialLaw.exists_lift_of_mem_range_rTensor", "kind": "theorem", "module": "Mathlib.RingTheory.PolynomialLaw.Basic", "is_tactic_proof": true, "tactics": ["obtain", "suffices", "obtain", "use", "rw", "simp", "exact"], "tactic_count": 7}
{"name": "PolynomialLaw.π_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.PolynomialLaw.Basic", "is_tactic_proof": true, "tactics": ["classical", "intro", "obtain", "obtain", "obtain", "exact"], "tactic_count": 6}
{"name": "PolynomialLaw.exists_lift", "kind": "theorem", "module": "Mathlib.RingTheory.PolynomialLaw.Basic", "is_tactic_proof": true, "tactics": ["obtain", "use"], "tactic_count": 2}
{"name": "PolynomialLaw.exists_lift'", "kind": "theorem", "module": "Mathlib.RingTheory.PolynomialLaw.Basic", "is_tactic_proof": true, "tactics": ["classical", "obtain", "have", "obtain", "have", "rw", "obtain", "have", "rw", "apply", "simp", "exact", "use"], "tactic_count": 13}
{"name": "PolynomialLaw.toFun'_eq_toFun", "kind": "theorem", "module": "Mathlib.RingTheory.PolynomialLaw.Basic", "is_tactic_proof": true, "tactics": ["ext", "obtain", "simp", "exact"], "tactic_count": 4}
{"name": "PolynomialLaw.isCompat_apply", "kind": "theorem", "module": "Mathlib.RingTheory.PolynomialLaw.Basic", "is_tactic_proof": true, "tactics": ["classical", "obtain", "let", "let", "rintro", "simp", "simp", "exact", "let", "have", "ext", "simp", "congr", "ext", "simp", "let", "have", "simp", "rw", "comp_toLinearMap]", "apply", "simp", "simp", "congr", "ext", "simp", "simp"], "tactic_count": 27}
{"name": "PolynomialLaw.isCompat", "kind": "theorem", "module": "Mathlib.RingTheory.PolynomialLaw.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "PolynomialLaw.toFun_zero", "kind": "theorem", "module": "Mathlib.RingTheory.PolynomialLaw.Basic", "is_tactic_proof": true, "tactics": ["ext", "obtain", "simp"], "tactic_count": 3}
{"name": "PolynomialLaw.toFun_add_apply", "kind": "theorem", "module": "Mathlib.RingTheory.PolynomialLaw.Basic", "is_tactic_proof": true, "tactics": ["obtain", "simp"], "tactic_count": 2}
{"name": "PolynomialLaw.toFun_add", "kind": "theorem", "module": "Mathlib.RingTheory.PolynomialLaw.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "PolynomialLaw.toFun_neg", "kind": "theorem", "module": "Mathlib.RingTheory.PolynomialLaw.Basic", "is_tactic_proof": true, "tactics": ["ext", "obtain", "simp"], "tactic_count": 3}
{"name": "PolynomialLaw.toFun_smul", "kind": "theorem", "module": "Mathlib.RingTheory.PolynomialLaw.Basic", "is_tactic_proof": true, "tactics": ["ext", "obtain", "simp"], "tactic_count": 3}
{"name": "PolynomialLaw.one_tmul_ground", "kind": "theorem", "module": "Mathlib.RingTheory.PolynomialLaw.Basic", "is_tactic_proof": true, "tactics": ["simp", "convert", "simp", "congr", "rw"], "tactic_count": 5}
{"name": "PolynomialLaw.toFun_comp", "kind": "theorem", "module": "Mathlib.RingTheory.PolynomialLaw.Basic", "is_tactic_proof": true, "tactics": ["ext", "obtain", "have", "rw"], "tactic_count": 4}
{"name": "PolynomialLaw.toFun_comp_apply", "kind": "theorem", "module": "Mathlib.RingTheory.PolynomialLaw.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.instCharP", "kind": "instance", "module": "Mathlib.RingTheory.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.instExpChar", "kind": "instance", "module": "Mathlib.RingTheory.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Polynomial.degreeLE", "kind": "definition", "module": "Mathlib.RingTheory.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degreeLT", "kind": "definition", "module": "Mathlib.RingTheory.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.mem_degreeLE", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.degreeLE_mono", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degreeLE_eq_span_X_pow", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["apply", "intro", "replace", "rw", "refine", "have", "rw", "refine", "rw", "intro", "apply", "exact"], "tactic_count": 12}
{"name": "Polynomial.mem_degreeLT", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Polynomial.degreeLT_mono", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degreeLT_eq_span_X_pow", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["apply", "intro", "replace", "rw", "refine", "have", "rw", "refine", "rw", "intro", "apply", "exact"], "tactic_count": 12}
{"name": "Polynomial.degreeLTEquiv", "kind": "definition", "module": "Mathlib.RingTheory.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degreeLTEquiv_eq_zero_iff_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.eval_eq_sum_degreeLTEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Polynomial.degreeLT_succ_eq_degreeLE", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "simp_rw", "rw"], "tactic_count": 4}
{"name": "Polynomial.monicEquivDegreeLT", "kind": "definition", "module": "Mathlib.RingTheory.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.exists_degree_le_of_mem_span", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["by_contra", "by_cases", "rw", "rcases", "exact", "have", "refine", "rw", "exact", "rwa"], "tactic_count": 10}
{"name": "Polynomial.exists_degree_le_of_mem_span_of_finite", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["obtain", "refine", "obtain", "exact"], "tactic_count": 4}
{"name": "Polynomial.span_le_degreeLE_of_finite", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "rcases", "exact", "rw", "rw", "exact"], "tactic_count": 6}
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{"name": "Polynomial.toSubring", "kind": "definition", "module": "Mathlib.RingTheory.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Ideal.ofPolynomial", "kind": "definition", "module": "Mathlib.RingTheory.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Ideal.degreeLE", "kind": "definition", "module": "Mathlib.RingTheory.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.leadingCoeffNth", "kind": "definition", "module": "Mathlib.RingTheory.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.leadingCoeff", "kind": "definition", "module": "Mathlib.RingTheory.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Ideal.is_fg_degreeLE", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "span_le_of_C_coeff_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Basic", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
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{"name": "MvPolynomial.instFiniteOfIsEmpty", "kind": "instance", "module": "Mathlib.RingTheory.Polynomial.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "bernsteinPolynomial", "kind": "definition", "module": "Mathlib.RingTheory.Polynomial.Bernstein", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "bernsteinPolynomial.eq_zero_of_lt", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Bernstein", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "bernsteinPolynomial.eval_at_0", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Bernstein", "is_tactic_proof": true, "tactics": ["rw", "split_ifs", "subst", "simp"], "tactic_count": 4}
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{"name": "Polynomial.Chebyshev.aeval_U", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Chebyshev", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "Polynomial.Chebyshev.algebraMap_eval_U", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Chebyshev", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.Chebyshev.algebraMap_eval_C", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Chebyshev", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "Polynomial.IsPrimitive.ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Content", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
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{"name": "Polynomial.IsPrimitive.mul", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Content", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.primPart_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Content", "is_tactic_proof": true, "tactics": ["rw", "apply", "conv_lhs", "rw", "ring"], "tactic_count": 5}
{"name": "Polynomial.IsPrimitive.dvd_primPart_iff_dvd", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Content", "is_tactic_proof": true, "tactics": ["refine", "rcases", "apply", "rw"], "tactic_count": 4}
{"name": "Polynomial.exists_primitive_lcm_of_isPrimitive", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Content", "is_tactic_proof": true, "tactics": ["classical", "have", "rcases", "refine", "suffices", "clear", "by_contra", "rcases", "have", "contrapose", "simp", "have", "rw", "by_cases", "rw", "normalize_eq_one]", "rw", "apply", "have", "rw", "apply", "refine", "rw", "rw", "have", "nontriviality", "have", "rw", "rw", "rcases", "apply", "rw"], "tactic_count": 32}
{"name": "Polynomial.dvd_iff_content_dvd_content_and_primPart_dvd_primPart", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Content", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "rw", "exact", "rintro", "rw", "gcongr"], "tactic_count": 7}
{"name": "Polynomial.normalizedGcdMonoid", "kind": "instance", "module": "Mathlib.RingTheory.Polynomial.Content", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_gcd_le_left", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Content", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "Polynomial.degree_gcd_le_right", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Content", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Polynomial.contentIdeal", "kind": "definition", "module": "Mathlib.RingTheory.Polynomial.ContentIdeal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.contentIdeal_def", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.ContentIdeal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.contentIdeal_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.ContentIdeal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.contentIdeal_eq_bot_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.ContentIdeal", "is_tactic_proof": true, "tactics": ["simp", "refine", "contrapose", "exact"], "tactic_count": 4}
{"name": "Polynomial.coeff_mem_contentIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.ContentIdeal", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "apply", "simpa"], "tactic_count": 4}
{"name": "Polynomial.contentIdeal_monomial", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.ContentIdeal", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "Polynomial.contentIdeal_C", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.ContentIdeal", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Polynomial.contentIdeal_one", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.ContentIdeal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.contentIdeal_FG", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.ContentIdeal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.contentIdeal_map_eq_map_contentIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.ContentIdeal", "is_tactic_proof": true, "tactics": ["suffices", "congr", "ext", "by_cases", "simp", "aesop"], "tactic_count": 6}
{"name": "Polynomial.contentIdeal_mul_le_mul_contentIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.ContentIdeal", "is_tactic_proof": true, "tactics": ["rw", "simp", "rintro", "simp"], "tactic_count": 4}
{"name": "Polynomial.contentIdeal_le_contentIdeal_of_dvd", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.ContentIdeal", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Submodule.IsPrincipal.contentIdeal_generator_dvd_coeff", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.ContentIdeal", "is_tactic_proof": true, "tactics": ["have", "rw", "obtain", "simp"], "tactic_count": 4}
{"name": "Submodule.IsPrincipal.contentIdeal_generator_dvd", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.ContentIdeal", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Submodule.IsPrincipal.contentIdeal_le_span_iff_dvd", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.ContentIdeal", "is_tactic_proof": true, "tactics": ["constructor", "rw", "intro", "calc", "apply", "rwa", "rw", "exact"], "tactic_count": 8}
{"name": "Polynomial.isPrimitive_of_contentIdeal_eq_top", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.ContentIdeal", "is_tactic_proof": false, "tactics": ["have", "rw", "exact", "intro", "simp"], "tactic_count": 5}
{"name": "Submodule.IsPrincipal.isPrimitive_iff_contentIdeal_eq_top", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.ContentIdeal", "is_tactic_proof": true, "tactics": ["refine", "contrapose", "simp", "intro", "use", "simp_all"], "tactic_count": 6}
{"name": "Polynomial.contentIdeal_eq_top_of_contentIdeal_mul_eq_top", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.ContentIdeal", "is_tactic_proof": true, "tactics": ["apply", "calc"], "tactic_count": 2}
{"name": "Polynomial.mul_contentIdeal_le_radical_contentIdeal_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.ContentIdeal", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "rw", "simpa", "contentIdeal_eq_bot_iff,"], "tactic_count": 6}
{"name": "Polynomial.contentIdeal_mul_eq_top_of_contentIdeal_eq_top", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.ContentIdeal", "is_tactic_proof": true, "tactics": ["rw", "apply", "calc"], "tactic_count": 3}
{"name": "Polynomial.contentIdeal_le_span_content", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.ContentIdeal", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "obtain", "rw", "exact"], "tactic_count": 6}
{"name": "Submodule.IsPrincipal.contentIdeal_eq_span_content_of_isPrincipal", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.ContentIdeal", "is_tactic_proof": true, "tactics": ["apply", "rw", "exact"], "tactic_count": 3}
{"name": "Polynomial.isPrimitive_iff_contentIdeal_eq_top", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.ContentIdeal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.cyclotomic'", "kind": "definition", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.cyclotomic'_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.cyclotomic'_one", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.cyclotomic'_two", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["rw", "have", "simp", "exact", "simp"], "tactic_count": 5}
{"name": "Polynomial.cyclotomic'.monic", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.cyclotomic'_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natDegree_cyclotomic'", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["rw", "rw", "simp", "nsmul_eq_mul]", "intro", "exact"], "tactic_count": 6}
{"name": "Polynomial.degree_cyclotomic'", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.roots_of_cyclotomic", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.X_pow_sub_one_eq_prod", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["classical", "rw", "simp", "rw", "have", "symm", "apply", "rw", "exact"], "tactic_count": 9}
{"name": "Polynomial.cyclotomic'_splits", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["apply", "intro", "simp"], "tactic_count": 3}
{"name": "Polynomial.X_pow_sub_one_splits", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.prod_cyclotomic'_eq_X_pow_sub_one", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["classical", "have", "simp"], "tactic_count": 3}
{"name": "Polynomial.cyclotomic'_eq_X_pow_sub_one_div", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["rw", "have", "apply", "intro", "exact", "rw", "simp", "refine", "rw", "intro", "exact"], "tactic_count": 11}
{"name": "Polynomial.int_coeff_of_cyclotomic'", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["refine", "induction", "rcases", "use", "simp", "let", "have", "apply", "intro", "exact", "have", "refine", "intro", "have", "obtain", "rw", "exact", "replace", "obtain", "let", "have", "constructor", "rw", "simpa", "replace", "simp", "use", "rw", "simp"], "tactic_count": 29}
{"name": "Polynomial.unique_int_coeff_of_cycl", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["obtain", "refine", "apply", "rw"], "tactic_count": 4}
{"name": "Polynomial.cyclotomic", "kind": "definition", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.int_cyclotomic_rw", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["simp", "ext", "simp"], "tactic_count": 3}
{"name": "Polynomial.map_cyclotomic_int", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "simp"], "tactic_count": 3}
{"name": "Polynomial.int_cyclotomic_spec", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "rw", "exact"], "tactic_count": 4}
{"name": "Polynomial.int_cyclotomic_unique", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["apply", "rw"], "tactic_count": 2}
{"name": "Polynomial.map_cyclotomic", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["rw", "have", "congr"], "tactic_count": 3}
{"name": "Polynomial.cyclotomic.eval_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.cyclotomic.eval_apply_ofReal", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.cyclotomic_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.cyclotomic_one", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": ["have", "simp", "symm", "rw", "simp"], "tactic_count": 5}
{"name": "Polynomial.cyclotomic.monic", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Polynomial.cyclotomic.isPrimitive", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.cyclotomic_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_cyclotomic", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["rw", "rw", "rcases", "simp", "rw", "exact", "simp", "one_ne_zero]"], "tactic_count": 8}
{"name": "Polynomial.natDegree_cyclotomic", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.natDegree_cyclotomic_le", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["nontriviality", "rw"], "tactic_count": 2}
{"name": "Polynomial.degree_cyclotomic_pos", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Polynomial.prod_cyclotomic_eq_X_pow_sub_one", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": ["have", "apply", "simp", "exact", "simpa"], "tactic_count": 5}
{"name": "Polynomial.cyclotomic.dvd_X_pow_sub_one", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": ["suffices", "simpa", "rcases", "simp", "rw", "exact"], "tactic_count": 6}
{"name": "Polynomial.prod_cyclotomic_eq_geom_sum", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": ["suffices", "simpa", "congr_arg", "rw", "geom_sum_mul,"], "tactic_count": 5}
{"name": "Polynomial.cyclotomic_prime", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": ["suffices", "simpa", "congr_arg", "rw", "prod_singleton]"], "tactic_count": 5}
{"name": "Polynomial.cyclotomic_prime_mul_X_sub_one", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.cyclotomic_two", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.cyclotomic_three", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.cyclotomic_dvd_geom_sum_of_dvd", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": ["suffices", "simpa", "map_dvd", "rcases", "simp", "rw", "apply", "simp"], "tactic_count": 8}
{"name": "Polynomial.X_pow_sub_one_mul_prod_cyclotomic_eq_X_pow_sub_one_of_dvd", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "Polynomial.X_pow_sub_one_mul_cyclotomic_dvd_X_pow_sub_one_of_dvd", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["rw", "use", "rw", "exact", "exact", "exact"], "tactic_count": 6}
{"name": "Polynomial.cyclotomic_eq_prod_X_pow_sub_one_pow_moebius", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simp", "have", "intro", "rw", "rw", "simp_rw", "simp", "intro", "apply", "apply"], "tactic_count": 11}
{"name": "Polynomial.cyclotomic_eq_X_pow_sub_one_div", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["nontriviality", "rw", "have", "apply", "intro", "exact", "rw", "simp", "constructor", "rw", "rw", "intro", "exact"], "tactic_count": 13}
{"name": "Polynomial.X_pow_sub_one_dvd_prod_cyclotomic", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": ["replace", "rw", "exact"], "tactic_count": 3}
{"name": "Polynomial.cyclotomic_eq_prod_X_sub_primitiveRoots", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["rw", "induction", "obtain", "simp", "have", "intro", "obtain", "rw", "exact", "rw"], "tactic_count": 10}
{"name": "Polynomial.eq_cyclotomic_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["nontriviality", "refine", "rw", "have", "apply", "intro", "exact", "rw", "refine", "rw", "intro", "exact"], "tactic_count": 12}
{"name": "Polynomial.cyclotomic_prime_pow_eq_geom_sum", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": ["have", "intro", "have", "rw", "rw", "induction", "zero", "succ", "rw", "rw", "rw", "rw", "simp"], "tactic_count": 13}
{"name": "Polynomial.cyclotomic_prime_pow_mul_X_pow_sub_one", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.cyclotomic_coeff_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": ["induction", "have", "rw", "have", "intro", "apply", "exact", "have", "intro", "exact", "have", "rw", "simp", "simp", "have", "rw", "have", "rw", "simp", "rw", "exact"], "tactic_count": 21}
{"name": "Polynomial.coprime_of_root_cyclotomic", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["apply", "rw", "intro", "replace", "rw", "by_cases", "simp", "coeff_sub]", "rw", "exact"], "tactic_count": 10}
{"name": "Polynomial.orderOf_root_cyclotomic_dvd", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["apply", "suffices", "simp", "apply", "simp", "rw", "rw", "eval_mul,"], "tactic_count": 8}
{"name": "Polynomial.dvd_C_mul_X_sub_one_pow_add_one", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["have", "rwa", "simp", "simp"], "tactic_count": 4}
{"name": "_private.Mathlib.RingTheory.Polynomial.Cyclotomic.Basic.0.IsPrimitiveRoot.pow_sub_pow_eq_prod_sub_mul_field", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "congr", "rw", "convert", "simp", "simp"], "tactic_count": 7}
{"name": "IsPrimitiveRoot.pow_sub_pow_eq_prod_sub_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["let", "apply", "rw", "simp_rw", "have", "rw", "refine", "have", "obtain", "exact"], "tactic_count": 10}
{"name": "IsPrimitiveRoot.pow_add_pow_eq_prod_add_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Polynomial.separable_cyclotomic", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.squarefree_cyclotomic", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eval_one_cyclotomic_prime", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Eval", "is_tactic_proof": true, "tactics": ["simp", "smul_one_eq_cast]"], "tactic_count": 2}
{"name": "Polynomial.eval₂_one_cyclotomic_prime", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Eval", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.eval_one_cyclotomic_prime_pow", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Eval", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.eval₂_one_cyclotomic_prime_pow", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Eval", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "_private.Mathlib.RingTheory.Polynomial.Cyclotomic.Eval.0.Polynomial.cyclotomic_neg_one_pos", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Eval", "is_tactic_proof": true, "tactics": ["haveI", "rw", "suffices", "rw", "simpa", "simp", "have", "rw", "by_contra", "have", "obtain", "rw", "rw", "exact"], "tactic_count": 14}
{"name": "Polynomial.cyclotomic_pos", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Eval", "is_tactic_proof": false, "tactics": ["induction", "have", "have", "have", "apply_fun", "rw", "eval_geom_sum]", "rcases", "apply", "rwa", "rw", "refine", "simp", "rw", "rcases", "refine", "exact", "exact", "rcases", "simpa", "refine", "rintro", "exact", "rw", "exact", "apply", "rwa", "rw", "have", "rw", "exact", "rw", "apply", "refine", "simp", "refine", "rintro", "rw", "exact", "simpa"], "tactic_count": 40}
{"name": "Polynomial.cyclotomic_pos_and_nonneg", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Eval", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simp", "simp", "constructor", "constructor"], "tactic_count": 6}
{"name": "Polynomial.cyclotomic_pos'", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Eval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.cyclotomic_nonneg", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Eval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eval_one_cyclotomic_not_prime_pow", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Eval", "is_tactic_proof": true, "tactics": ["rcases", "simp", "have", "rsuffices", "have", "simpa", "exfalso", "linarith", "rw", "intro", "haveI", "have", "apply_fun", "rw", "simp_rw", "rw", "swap", "simp", "not_exists,", "exact", "rw", "obtain", "rw", "have", "simp", "exact", "rintro", "apply", "exact"], "tactic_count": 29}
{"name": "Polynomial.sub_one_pow_totient_lt_cyclotomic_eval", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Eval", "is_tactic_proof": true, "tactics": ["have", "have", "have", "intro", "rw", "convert", "rw", "rw", "let", "have", "have", "refine", "suffices", "convert", "simp", "rw", "push_neg", "refine", "rw", "clear_value", "rintro", "linarith", "have", "suffices", "simp", "convert", "rw", "simp", "simp", "convert", "swap", "simp", "simp", "norm_nonneg,", "intro", "simpa", "simp", "simpa"], "tactic_count": 38}
{"name": "Polynomial.sub_one_pow_totient_le_cyclotomic_eval", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Eval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.cyclotomic_eval_lt_add_one_pow_totient", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Eval", "is_tactic_proof": true, "tactics": ["have", "have", "have", "intro", "rw", "convert", "rw", "rw", "let", "have", "have", "refine", "suffices", "convert", "rw", "symm", "exact", "simp", "rw", "push_neg", "refine", "rw", "intro", "rw", "have", "clear_value", "rintro", "exact", "have", "rw", "rw", "linarith", "contrapose", "apply", "have", "suffices", "simp", "convert", "rw", "simp", "rw", "linarith", "simp", "convert", "swap", "simp", "simp", "intro", "have", "simp", "simp", "obtain", "exact"], "tactic_count": 53}
{"name": "Polynomial.cyclotomic_eval_le_add_one_pow_totient", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Eval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.sub_one_pow_totient_lt_natAbs_cyclotomic_eval", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Eval", "is_tactic_proof": true, "tactics": ["rcases", "rw", "exact", "rw", "refine", "convert", "simp"], "tactic_count": 7}
{"name": "Polynomial.sub_one_lt_natAbs_cyclotomic_eval", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Eval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.cyclotomic_expand_eq_cyclotomic_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Expand", "is_tactic_proof": true, "tactics": ["rcases", "simp", "haveI", "suffices", "rw", "refine", "eq_of_monic_of_dvd_of_natDegree_le", "refine", "rw", "refine", "replace", "exact", "have", "have", "rw", "refine", "rw", "convert", "rw", "have", "rw", "refine", "rw", "map_cyclotomic,", "exact", "rw", "natDegree_cyclotomic,"], "tactic_count": 27}
{"name": "Polynomial.cyclotomic_six", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Expand", "is_tactic_proof": false, "tactics": ["suffices", "rw", "simp", "apply", "rw", "simp"], "tactic_count": 6}
{"name": "Polynomial.cyclotomic_expand_eq_cyclotomic", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Expand", "is_tactic_proof": true, "tactics": ["rcases", "simp", "haveI", "suffices", "rw", "refine", "have", "have", "rw", "refine", "rw", "convert", "rw", "rw"], "tactic_count": 14}
{"name": "Polynomial.cyclotomic_irreducible_pow_of_irreducible_pow", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Expand", "is_tactic_proof": true, "tactics": ["rcases", "simpa", "obtain", "induction", "zero", "succ", "have", "rw", "exact"], "tactic_count": 9}
{"name": "Polynomial.cyclotomic_irreducible_of_irreducible_pow", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Expand", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.cyclotomic_mul_prime_eq_pow_of_not_dvd", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Expand", "is_tactic_proof": true, "tactics": ["letI", "suffices", "rw", "apply", "rw", "conv_rhs", "rw"], "tactic_count": 7}
{"name": "Polynomial.cyclotomic_mul_prime_dvd_eq_pow", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Expand", "is_tactic_proof": true, "tactics": ["letI", "suffices", "rw", "rw", "map_cyclotomic]"], "tactic_count": 5}
{"name": "Polynomial.cyclotomic_mul_prime_pow_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Expand", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.isRoot_cyclotomic_prime_pow_mul_iff_of_charP", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Expand", "is_tactic_proof": true, "tactics": ["rcases", "rw", "refine", "rw", "replace", "rwa", "rw", "rw", "exact"], "tactic_count": 9}
{"name": "_private.Mathlib.RingTheory.Polynomial.Cyclotomic.Factorization.0.Polynomial.f_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Factorization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Polynomial.Cyclotomic.Factorization.0.Polynomial.natDegree_of_dvd_cyclotomic_of_irreducible_of_monic", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Factorization", "is_tactic_proof": true, "tactics": ["have", "have", "have", "have", "have", "suffices", "have", "exact", "simpa", "let", "rw", "have", "isOfFinOrder_iff_pow_eq_one.mpr", "refine", "dvd_antisymm", "simp", "nth_rewrite", "rw", "simpa", "let", "have", "simp", "rw", "natCast_eq_natCast_iff,"], "tactic_count": 24}
{"name": "Polynomial.natDegree_of_dvd_cyclotomic_of_irreducible", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Factorization", "is_tactic_proof": true, "tactics": ["obtain", "have", "refine", "calc", "simpa", "natDegree_of_dvd_cyclotomic_of_irreducible_of_monic"], "tactic_count": 6}
{"name": "Polynomial.irreducible_of_dvd_cyclotomic_of_natDegree", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Factorization", "is_tactic_proof": true, "tactics": ["classical", "have", "obtain", "exists_mem_normalizedFactors", "not_isUnit_of_natDegree_pos", "pos_of_ne_zero", "refine", "rw", "exact", "dvd_of_mem_normalizedFactors", "mem_of_le"], "tactic_count": 11}
{"name": "ZMod.irreducible_of_dvd_cyclotomic_of_natDegree", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Factorization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natDegree_of_mem_normalizedFactors_cyclotomic", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Factorization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.normalizedFactors_cyclotomic_card", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Factorization", "is_tactic_proof": true, "tactics": ["have", "have", "natDegree_of_mem_normalizedFactors_cyclotomic", "have", "rw", "simp", "rw", "refine", "by_contra", "have", "refine", "have", "exact", "hp.out.coprime_iff_not_dvd.mp", "have", "refine", "have", "refine", "by_cases", "simp", "lia", "simp", "have", "simp", "exact"], "tactic_count": 25}
{"name": "Polynomial.isRoot_of_unity_of_root_cyclotomic", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Roots", "is_tactic_proof": true, "tactics": ["rcases", "exact", "have", "rw", "convert", "convert", "apply", "exact"], "tactic_count": 8}
{"name": "isRoot_of_unity_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Roots", "is_tactic_proof": true, "tactics": ["rw", "isRoot_prod]"], "tactic_count": 2}
{"name": "IsPrimitiveRoot.isRoot_cyclotomic", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Roots", "is_tactic_proof": false, "tactics": ["rw", "rwa"], "tactic_count": 2}
{"name": "_private.Mathlib.RingTheory.Polynomial.Cyclotomic.Roots.0.Polynomial.isRoot_cyclotomic_iff'", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Roots", "is_tactic_proof": true, "tactics": ["have", "refine", "have", "rw", "exact", "by_contra", "have", "have", "rw", "obtain", "replace", "rw", "rw", "have", "have", "rw", "have", "obtain", "obtain", "have", "rw", "have", "rw", "specialize", "simp"], "tactic_count": 25}
{"name": "Polynomial.isRoot_cyclotomic_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Roots", "is_tactic_proof": true, "tactics": ["have", "haveI", "rw"], "tactic_count": 3}
{"name": "Polynomial.roots_cyclotomic_nodup", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Roots", "is_tactic_proof": true, "tactics": ["obtain", "exact", "rw", "refine", "hζ.nthRoots_one_nodup"], "tactic_count": 5}
{"name": "Polynomial.cyclotomic.roots_to_finset_eq_primitiveRoots", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Roots", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Polynomial.cyclotomic.roots_eq_primitiveRoots_val", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Roots", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.isRoot_cyclotomic_iff_charZero", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Roots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.cyclotomic_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Roots", "is_tactic_proof": true, "tactics": ["intro", "simp", "rcases", "rw", "replace", "rwa", "haveI", "rw", "replace", "replace", "rw", "have", "have", "rw", "haveI", "rw", "replace", "rwa"], "tactic_count": 18}
{"name": "IsPrimitiveRoot.minpoly_dvd_cyclotomic", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Roots", "is_tactic_proof": true, "tactics": ["apply", "simpa"], "tactic_count": 2}
{"name": "IsPrimitiveRoot.minpoly_eq_cyclotomic_of_irreducible", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Roots", "is_tactic_proof": true, "tactics": ["haveI", "refine", "rwa"], "tactic_count": 3}
{"name": "Polynomial.cyclotomic_eq_minpoly", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Roots", "is_tactic_proof": false, "tactics": ["refine", "eq_of_monic_of_dvd_of_natDegree_le", "simpa"], "tactic_count": 3}
{"name": "Polynomial.cyclotomic_eq_minpoly_rat", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Roots", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Polynomial.cyclotomic.irreducible", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Roots", "is_tactic_proof": true, "tactics": ["rw", "apply", "exact"], "tactic_count": 3}
{"name": "Polynomial.cyclotomic.irreducible_rat", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Roots", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Polynomial.cyclotomic.isCoprime_rat", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Roots", "is_tactic_proof": true, "tactics": ["rcases", "exact", "rcases", "exact", "rw", "exact", "h", "cyclotomic_injective", "eq_of_monic_of_associated"], "tactic_count": 9}
{"name": "IsPrimitiveRoot.sum_eq_zero_iff_forall_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Roots", "is_tactic_proof": true, "tactics": ["haveI", "let", "have", "have", "trans", "rw", "refine", "rw", "have", "obtain", "simp", "lift", "simp"], "tactic_count": 13}
{"name": "IsPrimitiveRoot.sum_eq_zero_iff_forall_eq_int", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Cyclotomic.Roots", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Polynomial.term_[X]__", "kind": "definition", "module": "Mathlib.RingTheory.Polynomial.DegreeLT", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial._aux_Mathlib_RingTheory_Polynomial_DegreeLT___macroRules_Polynomial_term_[X]___1", "kind": "definition", "module": "Mathlib.RingTheory.Polynomial.DegreeLT", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial._aux_Mathlib_RingTheory_Polynomial_DegreeLT___unexpand_Polynomial_degreeLT_1", "kind": "definition", "module": "Mathlib.RingTheory.Polynomial.DegreeLT", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degreeLT.basis", "kind": "definition", "module": "Mathlib.RingTheory.Polynomial.DegreeLT", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degreeLT.instFiniteSubtypeMemSubmodule", "kind": "instance", "module": "Mathlib.RingTheory.Polynomial.DegreeLT", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degreeLT.instFreeSubtypeMemSubmodule", "kind": "instance", "module": "Mathlib.RingTheory.Polynomial.DegreeLT", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degreeLT.basis_repr", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.DegreeLT", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degreeLT.basis_val", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.DegreeLT", "is_tactic_proof": false, "tactics": ["change", "refine", "simp"], "tactic_count": 3}
{"name": "Polynomial.degreeLT.basisProd", "kind": "definition", "module": "Mathlib.RingTheory.Polynomial.DegreeLT", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degreeLT.basisProd_castAdd", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.DegreeLT", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.degreeLT.basisProd_natAdd", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.DegreeLT", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.degreeLT.addLinearEquiv", "kind": "definition", "module": "Mathlib.RingTheory.Polynomial.DegreeLT", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degreeLT.addLinearEquiv_castAdd", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.DegreeLT", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.degreeLT.addLinearEquiv_natAdd", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.DegreeLT", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.degreeLT.addLinearEquiv_symm_apply_inl_basis", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.DegreeLT", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degreeLT.addLinearEquiv_symm_apply_inr_basis", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.DegreeLT", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degreeLT.addLinearEquiv_symm_apply_inl", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.DegreeLT", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Polynomial.degreeLT.addLinearEquiv_symm_apply_inr", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.DegreeLT", "is_tactic_proof": true, "tactics": ["rw", "simp", "add_comm]"], "tactic_count": 3}
{"name": "Polynomial.degreeLT.addLinearEquiv_symm_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.DegreeLT", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degreeLT.addLinearEquiv_symm_apply'", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.DegreeLT", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.degreeLT.addLinearEquiv_apply'", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.DegreeLT", "is_tactic_proof": true, "tactics": ["rw", "nontriviality", "rw", "rw"], "tactic_count": 4}
{"name": "Polynomial.degreeLT.addLinearEquiv_apply_fst", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.DegreeLT", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degreeLT.addLinearEquiv_apply_snd", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.DegreeLT", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degreeLT.addLinearEquiv_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.DegreeLT", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.taylor_mem_degreeLT", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.DegreeLT", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.comap_taylorEquiv_degreeLT", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.DegreeLT", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Polynomial.map_taylorEquiv_degreeLT", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.DegreeLT", "is_tactic_proof": true, "tactics": ["nth_rw", "exact"], "tactic_count": 2}
{"name": "Polynomial.taylorLinearEquiv", "kind": "definition", "module": "Mathlib.RingTheory.Polynomial.DegreeLT", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.taylorLinearEquiv_symm", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.DegreeLT", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.det_taylorLinearEquiv_toLinearMap", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.DegreeLT", "is_tactic_proof": true, "tactics": ["nontriviality", "rw", "intro", "rw", "change", "rw", "intro", "rw", "change", "rw"], "tactic_count": 10}
{"name": "Polynomial.det_taylorLinearEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.DegreeLT", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.dickson", "kind": "definition", "module": "Mathlib.RingTheory.Polynomial.Dickson", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.dickson_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Dickson", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.dickson_one", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Dickson", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.dickson_two", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Dickson", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.dickson_add_two", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Dickson", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.dickson_of_two_le", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Dickson", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact"], "tactic_count": 3}
{"name": "Polynomial.map_dickson", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Dickson", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.dickson_two_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Dickson", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.dickson_one_one_eval_add_inv", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Dickson", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Polynomial.Dickson.0.Polynomial.two_mul_C_half_eq_one", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Dickson", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "_private.Mathlib.RingTheory.Polynomial.Dickson.0.Polynomial.C_half_mul_two_eq_one", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Dickson", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.dickson_one_one_eq_chebyshev_C", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Dickson", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.dickson_one_one_eq_chebyshev_T", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Dickson", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.chebyshev_T_eq_dickson_one_one", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Dickson", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.dickson_two_one_eq_chebyshev_S", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Dickson", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.dickson_two_one_eq_chebyshev_U", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Dickson", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.chebyshev_U_eq_dickson_two_one", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Dickson", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.dickson_one_one_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Dickson", "is_tactic_proof": true, "tactics": ["have", "rw", "simp", "congr", "apply", "simp", "simp", "apply", "rw", "apply", "rw"], "tactic_count": 11}
{"name": "Polynomial.dickson_one_one_comp_comm", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Dickson", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.dickson_one_one_zmod_p", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Dickson", "is_tactic_proof": true, "tactics": ["obtain", "let", "let", "have", "rw", "infer_instance", "haveI", "refine", "apply", "rw", "apply", "apply", "rintro", "simp", "dickson_one_one_eval_add_inv", "intro", "rw", "apply", "suffices", "rw", "clear", "refine", "h.biUnion", "let", "have", "intro", "have", "simpa", "one_ne_zero]", "classical", "convert", "ext1", "simp", "eval_add,", "by_cases", "simp", "apply", "rw", "apply", "ring", "apply", "intro", "simp", "by_cases", "simp", "exact", "simp", "exact"], "tactic_count": 48}
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{"name": "Polynomial.IsWeaklyEisensteinAt.map", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Eisenstein.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
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{"name": "Polynomial.IsWeaklyEisensteinAt.exists_mem_adjoin_mul_eq_pow_natDegree", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Eisenstein.Basic", "is_tactic_proof": false, "tactics": ["rw", "sum_range,", "replace", "have", "intro", "exact", "choose", "conv_rhs", "congr", "congr", "skip", "ext", "rw", "rw", "refine", "exact"], "tactic_count": 16}
{"name": "Polynomial.IsWeaklyEisensteinAt.exists_mem_adjoin_mul_eq_pow_natDegree_le", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Eisenstein.Basic", "is_tactic_proof": true, "tactics": ["intro", "obtain", "rw", "obtain", "refine", "exact", "rw"], "tactic_count": 7}
{"name": "Polynomial.IsWeaklyEisensteinAt.pow_natDegree_le_of_root_of_monic_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Eisenstein.Basic", "is_tactic_proof": true, "tactics": ["intro", "obtain", "rw", "suffices", "rw", "hmo.coeff_natDegree,", "rw", "exact"], "tactic_count": 8}
{"name": "Polynomial.IsWeaklyEisensteinAt.pow_natDegree_le_of_aeval_zero_of_monic_mem_map", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Eisenstein.Basic", "is_tactic_proof": false, "tactics": ["suffices", "intro", "obtain", "rw", "exact", "rw", "exact"], "tactic_count": 7}
{"name": "Polynomial.scaleRoots.isWeaklyEisensteinAt", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Eisenstein.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "rw", "exact"], "tactic_count": 4}
{"name": "Polynomial.dvd_pow_natDegree_of_eval₂_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Eisenstein.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "have", "rwa"], "tactic_count": 5}
{"name": "Polynomial.dvd_pow_natDegree_of_aeval_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Eisenstein.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Monic.leadingCoeff_notMem", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Eisenstein.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.Monic.isEisensteinAt_of_mem_of_notMem", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Eisenstein.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.IsEisensteinAt.isWeaklyEisensteinAt", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Eisenstein.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.IsEisensteinAt.coeff_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Eisenstein.Basic", "is_tactic_proof": true, "tactics": ["rcases", "exact", "rw", "exact"], "tactic_count": 4}
{"name": "Polynomial.IsEisensteinAt.irreducible", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Eisenstein.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Polynomial.Eisenstein.Criterion.0.Polynomial.generalizedEisenstein_aux", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Eisenstein.Criterion", "is_tactic_proof": true, "tactics": ["set", "have", "have", "simp", "obtain", "simp", "exact", "have", "rw", "exact", "simp_all", "obtain", "set", "have", "have", "obtain", "obtain", "suffices", "simp", "rw", "use", "intro", "rw", "rw", "suffices", "obtain", "apply", "apply", "rwa", "by_contra", "apply", "rw"], "tactic_count": 32}
{"name": "Polynomial.generalizedEisenstein", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Eisenstein.Criterion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.irreducible_of_eisenstein_criterion", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Eisenstein.Criterion", "is_tactic_proof": false, "tactics": ["apply", "generalizedEisenstein", "monic_X", "simp", "rw", "exact", "rw", "simp", "congr", "ext", "simp", "simp", "split_ifs", "rw", "exact", "by_cases", "exact", "rw", "exact", "simp", "rw", "convert", "rw", "rw", "ext", "exact"], "tactic_count": 26}
{"name": "Polynomial.IsDistinguishedAt.mul", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Eisenstein.Distinguished", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.IsDistinguishedAt.map_eq_X_pow", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Eisenstein.Distinguished", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "simp", "rcases", "simpa", "simp"], "tactic_count": 6}
{"name": "Polynomial.IsDistinguishedAt.map_ne_zero_of_eq_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Eisenstein.Distinguished", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.IsDistinguishedAt.degree_eq_coe_lift_order_map", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Eisenstein.Distinguished", "is_tactic_proof": false, "tactics": ["have", "rw", "have", "constructor", "simp", "intro", "simp"], "tactic_count": 7}
{"name": "Polynomial.IsDistinguishedAt.coe_natDegree_eq_order_map", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Eisenstein.Distinguished", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "_private.Mathlib.RingTheory.Polynomial.Eisenstein.IsIntegral.0.term𝓟", "kind": "definition", "module": "Mathlib.RingTheory.Polynomial.Eisenstein.IsIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "_private.Mathlib.RingTheory.Polynomial.Eisenstein.IsIntegral.0._aux_Mathlib_RingTheory_Polynomial_Eisenstein_IsIntegral___unexpand_Submodule_span_1", "kind": "definition", "module": "Mathlib.RingTheory.Polynomial.Eisenstein.IsIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cyclotomic_comp_X_add_one_isEisensteinAt", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Eisenstein.IsIntegral", "is_tactic_proof": false, "tactics": ["refine", "rw", "refine", "rw", "exact", "rw", "conv", "congr", "congr", "skip", "congr", "skip", "ext", "rw", "rw", "simp", "exact", "rw", "one_geom_sum,", "intro", "obtain", "have", "have", "cases"], "tactic_count": 24}
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{"name": "_private.Mathlib.RingTheory.Polynomial.Eisenstein.IsIntegral.0._aux_Mathlib_RingTheory_Polynomial_Eisenstein_IsIntegral___unexpand_Submodule_span_2", "kind": "definition", "module": "Mathlib.RingTheory.Polynomial.Eisenstein.IsIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Polynomial.Monic.irreducible_iff_irreducible_map_fraction_map", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.GaussLemma", "is_tactic_proof": true, "tactics": ["refine", "irreducible_iff.mpr", "obtain", "obtain", "have", "rw", "rw", "rw", "refine", "exact", "by_contra", "refine", "rw", "exact"], "tactic_count": 14}
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{"name": "Polynomial.Monic.dvd_of_fraction_map_dvd_fraction_map", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.GaussLemma", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "rw", "rw", "exact", "exact"], "tactic_count": 6}
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{"name": "Polynomial.IsPrimitive.dvd_of_fraction_map_dvd_fraction_map", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.GaussLemma", "is_tactic_proof": true, "tactics": ["rcases", "obtain", "rw", "have", "use", "apply", "rw", "simp", "have", "rw", "exact", "symm", "rcases", "use", "rw", "iterate", "apply", "rw", "contrapose", "simp"], "tactic_count": 20}
{"name": "Polynomial.IsPrimitive.dvd_iff_fraction_map_dvd_fraction_map", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.GaussLemma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.IsPrimitive.Int.irreducible_iff_irreducible_map_cast", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.GaussLemma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.IsPrimitive.Int.dvd_iff_map_cast_dvd_map_cast", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.GaussLemma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.gaussNorm", "kind": "definition", "module": "Mathlib.RingTheory.Polynomial.GaussNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.gaussNorm_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.GaussNorm", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.exists_eq_gaussNorm", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.GaussNorm", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "obtain", "exact", "simp_all"], "tactic_count": 5}
{"name": "Polynomial.gaussNorm_C", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.GaussNorm", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "Polynomial.gaussNorm_monomial", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.GaussNorm", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "_private.Mathlib.RingTheory.Polynomial.GaussNorm.0.Polynomial.sup'_nonneg_of_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.GaussNorm", "is_tactic_proof": true, "tactics": ["simp", "use", "simp_all", "positivity"], "tactic_count": 4}
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{"name": "Polynomial.gaussNorm_coe_powerSeries", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.GaussNorm", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "simp", "apply", "apply", "intro", "by_cases", "exact", "simp_all", "obtain", "simp", "rw", "exact"], "tactic_count": 13}
{"name": "Polynomial.gaussNorm_eq_zero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.GaussNorm", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.gaussNorm_nonneg", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.GaussNorm", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "Polynomial.le_gaussNorm", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.GaussNorm", "is_tactic_proof": true, "tactics": ["rw", "apply", "simpa"], "tactic_count": 3}
{"name": "PowerSeries.gaussNorm_C", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.GaussNorm", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PowerSeries.gaussNorm_monomial", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.GaussNorm", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.hermite", "kind": "definition", "module": "Mathlib.RingTheory.Polynomial.Hermite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.hermite_succ", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Hermite.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.hermite_eq_iterate", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Hermite.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Polynomial.hermite_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Hermite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.hermite_one", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Hermite.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Polynomial.coeff_hermite_succ_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Hermite.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.coeff_hermite_succ_succ", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Hermite.Basic", "is_tactic_proof": true, "tactics": ["rw", "norm_cast"], "tactic_count": 2}
{"name": "Polynomial.coeff_hermite_of_lt", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Hermite.Basic", "is_tactic_proof": true, "tactics": ["obtain", "clear", "induction", "zero", "succ", "have", "rw"], "tactic_count": 7}
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{"name": "Polynomial.natDegree_hermite", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Hermite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.leadingCoeff_hermite", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Hermite.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.hermite_monic", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Hermite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coeff_hermite_of_odd_add", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Hermite.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "rw", "exact", "succ", "cases", "zero", "rw", "rw", "succ", "rw", "rwa", "rw", "exact"], "tactic_count": 14}
{"name": "Polynomial.coeff_hermite_explicit", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Hermite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coeff_hermite_of_even_add", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Hermite.Basic", "is_tactic_proof": true, "tactics": ["rcases", "rw", "obtain", "rw", "coeff_hermite_explicit]", "simp"], "tactic_count": 6}
{"name": "Polynomial.coeff_hermite", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Hermite.Basic", "is_tactic_proof": true, "tactics": ["split_ifs", "exact", "exact"], "tactic_count": 3}
{"name": "Polynomial.deriv_gaussian_eq_hermite_mul_gaussian", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Hermite.Gaussian", "is_tactic_proof": true, "tactics": ["rw", "induction", "zero", "succ", "replace", "have", "rw", "simp", "rw", "hermite_succ,", "ring", "apply", "apply", "simp"], "tactic_count": 14}
{"name": "Polynomial.hermite_eq_deriv_gaussian", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Hermite.Gaussian", "is_tactic_proof": true, "tactics": ["rw", "field_simp", "rw", "simp"], "tactic_count": 4}
{"name": "Polynomial.hermite_eq_deriv_gaussian'", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Hermite.Gaussian", "is_tactic_proof": true, "tactics": ["rw", "field"], "tactic_count": 2}
{"name": "Polynomial.preHilbertPoly", "kind": "definition", "module": "Mathlib.RingTheory.Polynomial.HilbertPoly", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.natDegree_preHilbertPoly", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.HilbertPoly", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "Polynomial.coeff_preHilbertPoly_self", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.HilbertPoly", "is_tactic_proof": true, "tactics": ["delta", "have", "have", "nth_rw", "calc", "simp", "simp"], "tactic_count": 7}
{"name": "Polynomial.leadingCoeff_preHilbertPoly", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.HilbertPoly", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.preHilbertPoly_eq_choose_sub_add", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.HilbertPoly", "is_tactic_proof": true, "tactics": ["have", "calc", "simp"], "tactic_count": 3}
{"name": "Polynomial.hilbertPoly", "kind": "definition", "module": "Mathlib.RingTheory.Polynomial.HilbertPoly", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.hilbertPoly_zero_left", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.HilbertPoly", "is_tactic_proof": true, "tactics": ["delta", "induction", "zero", "succ"], "tactic_count": 4}
{"name": "Polynomial.hilbertPoly_zero_right", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.HilbertPoly", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.hilbertPoly_succ", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.HilbertPoly", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.hilbertPoly_X_pow_succ", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.HilbertPoly", "is_tactic_proof": true, "tactics": ["delta"], "tactic_count": 1}
{"name": "Polynomial.hilbertPoly_add_left", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.HilbertPoly", "is_tactic_proof": true, "tactics": ["delta", "induction", "zero", "succ", "simp", "rw", "exact"], "tactic_count": 7}
{"name": "Polynomial.hilbertPoly_smul", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.HilbertPoly", "is_tactic_proof": true, "tactics": ["delta", "induction", "zero", "succ", "simp", "rw", "sum_smul_index", "simp"], "tactic_count": 8}
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{"name": "Polynomial.coeff_mul_invOneSubPow_eq_hilbertPoly_eval", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.HilbertPoly", "is_tactic_proof": true, "tactics": ["delta", "induction", "zero", "simp", "exact", "succ", "simp", "rw", "have", "have", "rw", "simp_rw", "rw", "invOneSubPow_val_eq_mk_sub_one_add_choose_of_pos", "simp", "symm", "refine", "rw", "exact", "simp", "rw", "rw"], "tactic_count": 22}
{"name": "Polynomial.existsUnique_hilbertPoly", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.HilbertPoly", "is_tactic_proof": true, "tactics": ["use", "use", "exact", "rintro", "apply", "apply", "rintro", "simp", "rw"], "tactic_count": 9}
{"name": "Polynomial.eq_hilbertPoly_of_forall_coeff_eq_eval", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.HilbertPoly", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.hilbertPoly_mul_one_sub_succ", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.HilbertPoly", "is_tactic_proof": true, "tactics": ["apply", "intro", "have", "rw", "coeff_mul_invOneSubPow_eq_hilbertPoly_eval"], "tactic_count": 5}
{"name": "Polynomial.hilbertPoly_mul_one_sub_pow_add", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.HilbertPoly", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Polynomial.hilbertPoly_eq_zero_of_le_rootMultiplicity_one", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.HilbertPoly", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "rcases", "have", "simp", "exact", "rw", "hilbertPoly]"], "tactic_count": 8}
{"name": "Polynomial.natDegree_hilbertPoly_of_ne_zero_of_rootMultiplicity_lt", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.HilbertPoly", "is_tactic_proof": true, "tactics": ["rcases", "have", "simp", "exact", "nth_rw", "delta", "apply", "apply", "apply", "rw", "have", "simp", "pow_eq_zero_iff',", "exact"], "tactic_count": 14}
{"name": "Polynomial.natDegree_hilbertPoly_of_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.HilbertPoly", "is_tactic_proof": false, "tactics": ["have", "intro", "rw", "exact", "have", "by_contra", "exact", "exact"], "tactic_count": 8}
{"name": "Polynomial.mem_span_C_X_sub_C_X_sub_C_iff_eval_eval_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Ideal", "is_tactic_proof": true, "tactics": ["rw", "constructor", "rcases", "simp", "rcases", "rcases", "exact"], "tactic_count": 7}
{"name": "Polynomial.ker_evalRingHom", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Ideal", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Polynomial.ker_modByMonicHom", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.ker_constantCoeff", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Ideal", "is_tactic_proof": true, "tactics": ["refine", "simp", "rwa"], "tactic_count": 3}
{"name": "Algebra.mem_ideal_map_adjoin", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Ideal", "is_tactic_proof": true, "tactics": ["constructor", "intro", "induction", "mem", "obtain", "exact", "zero", "add", "obtain", "obtain", "exact", "smul", "obtain", "have", "refine", "rw", "exact", "rintro", "have", "trans", "ext1", "simp", "congr", "simp", "simp_rw", "exact"], "tactic_count": 26}
{"name": "Algebra.exists_aeval_invOf_eq_zero_of_idealMap_adjoin_sup_span_eq_top", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Ideal", "is_tactic_proof": true, "tactics": ["rw", "have", "have", "have", "have", "use", "have", "apply_fun", "dsimp", "rw", "exact", "exact"], "tactic_count": 12}
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{"name": "Polynomial.integralNormalization_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.IntegralNormalization", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.integralNormalization_C", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.IntegralNormalization", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.integralNormalization_coeff", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.IntegralNormalization", "is_tactic_proof": true, "tactics": ["have", "simp"], "tactic_count": 2}
{"name": "Polynomial.support_integralNormalization_subset", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.IntegralNormalization", "is_tactic_proof": true, "tactics": ["intro", "simp"], "tactic_count": 2}
{"name": "Polynomial.integralNormalization_coeff_degree", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.IntegralNormalization", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.integralNormalization_coeff_natDegree", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.IntegralNormalization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.integralNormalization_coeff_degree_ne", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.IntegralNormalization", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.integralNormalization_coeff_ne_natDegree", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.IntegralNormalization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_integralNormalization", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.IntegralNormalization", "is_tactic_proof": true, "tactics": ["nontriviality", "by_cases", "rw", "refine", "exact"], "tactic_count": 5}
{"name": "Polynomial.natDegree_integralNormalization", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.IntegralNormalization", "is_tactic_proof": true, "tactics": ["nontriviality", "by_cases", "exact"], "tactic_count": 3}
{"name": "Polynomial.monic_integralNormalization", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.IntegralNormalization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.integralNormalization_coeff_mul_leadingCoeff_pow", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.IntegralNormalization", "is_tactic_proof": true, "tactics": ["rw", "split_ifs", "simp", "tsub_add_cancel_of_le", "simp", "by_cases", "rw", "rw", "exact", "simp"], "tactic_count": 10}
{"name": "Polynomial.integralNormalization_mul_C_leadingCoeff", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.IntegralNormalization", "is_tactic_proof": true, "tactics": ["ext", "rw", "split_ifs", "simp", "simp", "by_cases", "rw", "rw", "exact", "simp"], "tactic_count": 10}
{"name": "Polynomial.leadingCoeff_smul_integralNormalization", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.IntegralNormalization", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.integralNormalization_eval₂_leadingCoeff_mul_of_commute", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.IntegralNormalization", "is_tactic_proof": true, "tactics": ["rw", "apply", "rw", "intro", "rw", "f.map_mul,"], "tactic_count": 6}
{"name": "Polynomial.integralNormalization_eval₂_leadingCoeff_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.IntegralNormalization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.integralNormalization_eval₂_eq_zero_of_commute", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.IntegralNormalization", "is_tactic_proof": true, "tactics": ["obtain", "by_cases", "rw", "simp", "rw", "exact", "rw"], "tactic_count": 7}
{"name": "Polynomial.integralNormalization_eval₂_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.IntegralNormalization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.integralNormalization_aeval_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.IntegralNormalization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.integralNormalization_map", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.IntegralNormalization", "is_tactic_proof": true, "tactics": ["ext", "simp", "leadingCoeff_map_of_leadingCoeff_ne_zero"], "tactic_count": 3}
{"name": "Polynomial.support_integralNormalization", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.IntegralNormalization", "is_tactic_proof": true, "tactics": ["nontriviality", "have", "by_cases", "ext", "refine", "simp", "intro", "split_ifs"], "tactic_count": 8}
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{"name": "Polynomial.isIntegral_coeff_prod", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.IsIntegral", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "insert", "rw", "exact"], "tactic_count": 6}
{"name": "Polynomial.isIntegral_coeff_of_factors", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.IsIntegral", "is_tactic_proof": true, "tactics": ["classical", "obtain", "rw", "refine", "have", "rw", "simpa", "rintro", "obtain", "simp"], "tactic_count": 10}
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{"name": "Polynomial.isIntegral_iff_isIntegral_coeff", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.IsIntegral", "is_tactic_proof": true, "tactics": ["refine", "rw", "simp", "exact"], "tactic_count": 4}
{"name": "IsIntegral.of_aeval_monic_of_isIntegral_coeff", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.IsIntegral", "is_tactic_proof": false, "tactics": ["obtain", "lifts_and_natDegree_eq_and_monic", "exact"], "tactic_count": 3}
{"name": "instIsIntegrallyClosedPolynomialOfIsDomain", "kind": "instance", "module": "Mathlib.RingTheory.Polynomial.IsIntegral", "is_tactic_proof": true, "tactics": ["let", "have", "suffices", "refine", "refine", "exact"], "tactic_count": 6}
{"name": "MvPolynomial.isIntegral_iff_isIntegral_coeff", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.IsIntegral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Polynomial.isNilpotent_C_mul_pow_X_of_isNilpotent", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Nilpotent", "is_tactic_proof": true, "tactics": ["refine", "obtain", "refine", "rw"], "tactic_count": 4}
{"name": "Polynomial.isNilpotent_pow_X_mul_C_of_isNilpotent", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Nilpotent", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Polynomial.isNilpotent_monomial_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Nilpotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.isNilpotent_C_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Nilpotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Polynomial.isNilpotent_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Nilpotent", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact", "have", "obtain", "replace", "refine", "simpa", "rcases", "simpa", "simp", "apply", "simpa", "rcases", "simp", "simpa"], "tactic_count": 16}
{"name": "Polynomial.isNilpotent_reflect_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Nilpotent", "is_tactic_proof": true, "tactics": ["simp", "refine", "simpa", "simp", "simpa", "simpa"], "tactic_count": 6}
{"name": "Polynomial.isNilpotent_reverse_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Nilpotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.isUnit_of_coeff_isUnit_isNilpotent", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Nilpotent", "is_tactic_proof": false, "tactics": ["induction", "by_cases", "rw", "exact", "set", "suffices", "rw", "refine", "exact", "have", "refine", "simp_rw", "simp_rw", "by_cases", "simp_rw", "simp_rw"], "tactic_count": 16}
{"name": "Polynomial.coeff_isUnit_isNilpotent_of_isUnit", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Nilpotent", "is_tactic_proof": true, "tactics": ["obtain", "constructor", "refine", "have", "rwa", "intro", "rw", "intro", "let", "have", "rw", "have", "refine", "rw", "exact", "rw", "exact"], "tactic_count": 17}
{"name": "Polynomial.isUnit_iff_coeff_isUnit_isNilpotent", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Nilpotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.isUnit_C_add_X_mul_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Nilpotent", "is_tactic_proof": true, "tactics": ["have", "simp_rw", "simp"], "tactic_count": 3}
{"name": "Polynomial.isUnit_iff'", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Nilpotent", "is_tactic_proof": true, "tactics": ["suffices", "conv_lhs", "simp"], "tactic_count": 3}
{"name": "Polynomial.not_isUnit_of_natDegree_pos_of_isReduced", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Nilpotent", "is_tactic_proof": false, "tactics": ["simp", "intro", "refine", "contrapose", "simp", "simp"], "tactic_count": 6}
{"name": "Polynomial.not_isUnit_of_degree_pos_of_isReduced", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Nilpotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.instIsLocalHomRingHomC", "kind": "instance", "module": "Mathlib.RingTheory.Polynomial.Nilpotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.instIsLocalHomRingHomAlgebraMap", "kind": "instance", "module": "Mathlib.RingTheory.Polynomial.Nilpotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.isNilpotent_aeval_sub_of_isNilpotent_sub", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Nilpotent", "is_tactic_proof": true, "tactics": ["simp", "have", "exact"], "tactic_count": 3}
{"name": "Polynomial.isUnit_aeval_of_isUnit_aeval_of_isNilpotent_sub", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Nilpotent", "is_tactic_proof": true, "tactics": ["rw", "refine", "exact"], "tactic_count": 3}
{"name": "Polynomial.opRingEquiv", "kind": "definition", "module": "Mathlib.RingTheory.Polynomial.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.opRingEquiv_op_monomial", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Opposites", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.opRingEquiv_op_C", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.opRingEquiv_op_X", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.opRingEquiv_op_C_mul_X_pow", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Opposites", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.opRingEquiv_symm_monomial", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.opRingEquiv_symm_C", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.opRingEquiv_symm_X", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.opRingEquiv_symm_C_mul_X_pow", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Opposites", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.coeff_opRingEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Opposites", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.support_opRingEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Opposites", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Polynomial.natDegree_opRingEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Opposites", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "simp", "unop_eq_zero_iff]"], "tactic_count": 4}
{"name": "Polynomial.leadingCoeff_opRingEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Opposites", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.isLeftCancelMulZero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Opposites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.isRightCancelMulZero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Opposites", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.isCancelMulZero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Opposites", "is_tactic_proof": true, "tactics": ["simp_rw", "rw"], "tactic_count": 2}
{"name": "Polynomial.isDomain_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Opposites", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "ascPochhammer", "kind": "definition", "module": "Mathlib.RingTheory.Polynomial.Pochhammer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ascPochhammer_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Pochhammer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ascPochhammer_one", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Pochhammer", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ascPochhammer_succ_left", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Pochhammer", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "monic_ascPochhammer", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Pochhammer", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "have", "rw", "leadingCoeff_comp", "one_mul,"], "tactic_count": 7}
{"name": "ascPochhammer_map", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Pochhammer", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "ascPochhammer_eval₂", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Pochhammer", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ascPochhammer_eval_comp", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Pochhammer", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ascPochhammer_eval_cast", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Pochhammer", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ascPochhammer_eval_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Pochhammer", "is_tactic_proof": true, "tactics": ["cases", "simp", "simp"], "tactic_count": 3}
{"name": "ascPochhammer_zero_eval_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Pochhammer", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ascPochhammer_ne_zero_eval_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Pochhammer", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ascPochhammer_succ_right", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Pochhammer", "is_tactic_proof": false, "tactics": ["suffices", "apply_fun", "simpa", "induction", "zero", "succ", "conv_lhs", "rw", "add_assoc,"], "tactic_count": 9}
{"name": "ascPochhammer_succ_eval", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Pochhammer", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ascPochhammer_succ_comp_X_add_one", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Pochhammer", "is_tactic_proof": false, "tactics": ["suffices", "nth_rw", "rw", "add_assoc]", "ring"], "tactic_count": 5}
{"name": "ascPochhammer_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Pochhammer", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "ascPochhammer_succ_right,"], "tactic_count": 5}
{"name": "ascPochhammer_nat_eq_ascFactorial", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Pochhammer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ascPochhammer_nat_eq_natCast_ascFactorial", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Pochhammer", "is_tactic_proof": true, "tactics": ["norm_cast", "rw"], "tactic_count": 2}
{"name": "ascPochhammer_nat_eq_descFactorial", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Pochhammer", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ascPochhammer_nat_eq_natCast_descFactorial", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Pochhammer", "is_tactic_proof": true, "tactics": ["norm_cast", "rw"], "tactic_count": 2}
{"name": "ascPochhammer_natDegree", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Pochhammer", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "have", "rw", "cases", "simp", "refine"], "tactic_count": 8}
{"name": "ascPochhammer_pos", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Pochhammer", "is_tactic_proof": true, "tactics": ["induction", "zero", "simp", "exact", "succ", "ih", "rw", "mul_add]", "exact"], "tactic_count": 9}
{"name": "ascPochhammer_eval_one", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Pochhammer", "is_tactic_proof": true, "tactics": ["rw_mod_cast"], "tactic_count": 1}
{"name": "factorial_mul_ascPochhammer", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Pochhammer", "is_tactic_proof": true, "tactics": ["rw_mod_cast"], "tactic_count": 1}
{"name": "ascPochhammer_nat_eval_succ", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Pochhammer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ascPochhammer_eval_succ", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Pochhammer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.cast_ascFactorial", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Pochhammer", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.cast_descFactorial", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Pochhammer", "is_tactic_proof": true, "tactics": ["rw", "induction", "zero", "succ", "simp_rw", "obtain", "rw", "rw", "rw"], "tactic_count": 9}
{"name": "Nat.cast_factorial", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Pochhammer", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "descPochhammer", "kind": "definition", "module": "Mathlib.RingTheory.Polynomial.Pochhammer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "descPochhammer_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Pochhammer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "descPochhammer_one", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Pochhammer", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "descPochhammer_succ_left", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Pochhammer", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "monic_descPochhammer", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Pochhammer", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "have", "have", "rw", "one_pow]"], "tactic_count": 7}
{"name": "descPochhammer_map", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Pochhammer", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "descPochhammer_eval_cast", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Pochhammer", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "descPochhammer_eval_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Pochhammer", "is_tactic_proof": true, "tactics": ["cases", "simp", "simp"], "tactic_count": 3}
{"name": "descPochhammer_zero_eval_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Pochhammer", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "descPochhammer_ne_zero_eval_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Pochhammer", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "descPochhammer_succ_right", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Pochhammer", "is_tactic_proof": false, "tactics": ["suffices", "apply_fun", "simpa", "induction", "zero", "succ", "ih", "conv_lhs", "rw", "natCast_comp]", "rw"], "tactic_count": 11}
{"name": "descPochhammer_natDegree", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Pochhammer", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "have", "rw", "cases", "simp", "refine"], "tactic_count": 8}
{"name": "descPochhammer_succ_eval", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Pochhammer", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "descPochhammer_succ_comp_X_sub_one", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Pochhammer", "is_tactic_proof": false, "tactics": ["suffices", "simpa", "nth_rw", "rw", "ring"], "tactic_count": 5}
{"name": "descPochhammer_eq_ascPochhammer", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Pochhammer", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "mul_X_comp,"], "tactic_count": 5}
{"name": "descPochhammer_eval_eq_ascPochhammer", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Pochhammer", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "eval_mul_X,", "show", "simp", "ascPochhammer_eval_comp,"], "tactic_count": 8}
{"name": "descPochhammer_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Pochhammer", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "descPochhammer_succ_right,"], "tactic_count": 5}
{"name": "ascPochhammer_eval_neg_eq_descPochhammer", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Pochhammer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "descPochhammer_eval_eq_descFactorial", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Pochhammer", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "ih", "rw", "eval_natCast_mul,", "by_cases", "rw", "rw"], "tactic_count": 9}
{"name": "descPochhammer_int_eq_ascFactorial", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Pochhammer", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ascPochhammer_eval_neg_coe_nat_of_lt", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Pochhammer", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "rcases", "simp", "simp", "lia"], "tactic_count": 8}
{"name": "ascPochhammer_eval_eq_zero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Pochhammer", "is_tactic_proof": true, "tactics": ["refine", "induction", "zero", "succ", "rw", "cases", "inl", "obtain", "exact", "inr", "obtain", "convert", "simp"], "tactic_count": 13}
{"name": "descPochhammer_eval_coe_nat_of_lt", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Pochhammer", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "descPochhammer_eval_eq_prod_range", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Pochhammer", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "descPochhammer_pos", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Pochhammer", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "descPochhammer_nonneg", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Pochhammer", "is_tactic_proof": true, "tactics": ["rcases", "rw", "positivity", "exact"], "tactic_count": 4}
{"name": "pow_le_descPochhammer_eval", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Pochhammer", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "have", "rw", "apply", "exact"], "tactic_count": 8}
{"name": "monotoneOn_descPochhammer_eval", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Pochhammer", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "intro", "rw", "have", "have", "simp_rw", "exact", "mul_le_mul"], "tactic_count": 10}
{"name": "Nat.cast_choose_eq_ascPochhammer_div", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Pochhammer", "is_tactic_proof": true, "tactics": ["rw", "descFactorial_eq_factorial_mul_choose,"], "tactic_count": 2}
{"name": "Nat.cast_choose_eq_descPochhammer_div", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Pochhammer", "is_tactic_proof": true, "tactics": ["rw", "descFactorial_eq_factorial_mul_choose,"], "tactic_count": 2}
{"name": "Polynomial.quotientSpanXSubCAlgEquiv", "kind": "definition", "module": "Mathlib.RingTheory.Polynomial.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.quotientSpanXSubCAlgEquiv_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.quotientSpanXSubCAlgEquiv_symm_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.quotientSpanCXSubCAlgEquiv", "kind": "definition", "module": "Mathlib.RingTheory.Polynomial.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.quotientSpanCXSubCXSubCAlgEquiv", "kind": "definition", "module": "Mathlib.RingTheory.Polynomial.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.modByMonic_eq_zero_iff_quotient_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Quotient", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ideal.quotient_map_C_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Quotient", "is_tactic_proof": true, "tactics": ["intro", "rw", "exact"], "tactic_count": 3}
{"name": "Ideal.eval₂_C_mk_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Quotient", "is_tactic_proof": true, "tactics": ["intro", "rw", "dsimp", "rw", "refine", "dsimp", "rw", "refine", "rw", "by_cases", "simpa", "simp"], "tactic_count": 12}
{"name": "Ideal.polynomialQuotientEquivQuotientPolynomial", "kind": "definition", "module": "Mathlib.RingTheory.Polynomial.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.polynomialQuotientEquivQuotientPolynomial_symm_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Quotient", "is_tactic_proof": true, "tactics": ["rw", "coe_eval₂RingHom,"], "tactic_count": 2}
{"name": "Ideal.polynomialQuotientEquivQuotientPolynomial_map_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Quotient", "is_tactic_proof": true, "tactics": ["apply", "rw"], "tactic_count": 2}
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{"name": "Ideal.eq_zero_of_polynomial_mem_map_range", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Quotient", "is_tactic_proof": true, "tactics": ["let", "have", "refine", "rw", "rw", "replace", "simp", "rwa", "obtain", "obtain", "refine", "simp", "suffices", "obtain", "mem_image_of_mem_map_of_surjective", "refine", "rw", "exact"], "tactic_count": 18}
{"name": "Ideal.IsField.of_isPrincipalIdealRing_polynomial", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Quotient", "is_tactic_proof": true, "tactics": ["apply", "rw", "exact"], "tactic_count": 3}
{"name": "MvPolynomial.quotient_map_C_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Quotient", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "MvPolynomial.eval₂_C_mk_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Quotient", "is_tactic_proof": true, "tactics": ["rw", "rw", "refine", "simp", "refine", "suffices", "rw", "simp", "exact"], "tactic_count": 9}
{"name": "MvPolynomial.quotientEquivQuotientMvPolynomial_rightInverse", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Quotient", "is_tactic_proof": true, "tactics": ["intro", "apply", "intro", "obtain", "rw", "intro", "simp", "rw", "intro", "simp", "simp"], "tactic_count": 11}
{"name": "MvPolynomial.quotientEquivQuotientMvPolynomial_leftInverse", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Quotient", "is_tactic_proof": true, "tactics": ["intro", "obtain", "apply", "intro", "rw", "intro", "rw", "simp", "rw", "intro", "simp", "simp"], "tactic_count": 12}
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{"name": "degree_radical_le", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Radical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "natDegree_radical_le", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Radical", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "exact"], "tactic_count": 3}
{"name": "divRadical_dvd_derivative", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Radical", "is_tactic_proof": true, "tactics": ["induction", "rw", "apply", "exact", "cases", "rw", "apply", "i", "rw", "derivative_pow_succ,", "apply", "rw", "apply", "rw", "hy", "have", "hp", "rw", "exact"], "tactic_count": 19}
{"name": "divRadical_dvd_wronskian_left", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Radical", "is_tactic_proof": true, "tactics": ["rw", "apply", "apply", "exact", "apply", "exact"], "tactic_count": 6}
{"name": "divRadical_dvd_wronskian_right", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Radical", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "scaleRoots_aeval_eq_zero_of_aeval_mk'_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.RationalRoot", "is_tactic_proof": true, "tactics": ["convert", "funext", "rw"], "tactic_count": 3}
{"name": "num_isRoot_scaleRoots_of_aeval_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.RationalRoot", "is_tactic_proof": true, "tactics": ["apply", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "num_dvd_of_is_root", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.RationalRoot", "is_tactic_proof": false, "tactics": ["suffices", "simp", "haveI", "by_cases", "simp_all", "refine", "intro", "apply", "exact", "convert", "rw", "intro", "apply", "convert", "exact"], "tactic_count": 15}
{"name": "den_dvd_of_is_root", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.RationalRoot", "is_tactic_proof": false, "tactics": ["suffices", "refine", "intro", "apply", "exact", "rw", "apply", "intro", "by_cases", "rw", "refine", "convert", "exact", "simpa", "rw", "rw", "exact"], "tactic_count": 17}
{"name": "isInteger_of_is_root_of_monic", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.RationalRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_integer_of_is_root_of_monic", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.RationalRoot", "is_tactic_proof": true, "tactics": ["but", "obtain", "use", "have", "simpa", "have", "nth_rw", "rw"], "tactic_count": 8}
{"name": "UniqueFactorizationMonoid.integer_of_integral", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.RationalRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniqueFactorizationMonoid.instIsIntegrallyClosed", "kind": "instance", "module": "Mathlib.RingTheory.Polynomial.RationalRoot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.sylvester", "kind": "definition", "module": "Mathlib.RingTheory.Polynomial.Resultant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.sylvester_zero_left_deg", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Resultant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.sylvester_comm", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Resultant.Basic", "is_tactic_proof": true, "tactics": ["ext", "induction"], "tactic_count": 2}
{"name": "Polynomial.sylvester_map_map", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Resultant.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Polynomial.sylvesterDeriv", "kind": "definition", "module": "Mathlib.RingTheory.Polynomial.Resultant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.sylvesterDeriv_updateRow", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Resultant.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "ext", "ext", "rw", "rcases", "rw", "simp", "split_ifs", "on_goal", "on_goal", "rw", "norm_num", "on_goal", "rw", "these", "have", "simp", "all_goals"], "tactic_count": 18}
{"name": "Polynomial.resultant_map_map", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Resultant.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.resultant_zero_left_deg", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Resultant.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.resultant_C_zero_left", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Resultant.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.resultant_comm", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Resultant.Basic", "is_tactic_proof": true, "tactics": ["classical", "rw", "congr", "dsimp", "simp", "simp_rw", "simp", "finSumFinEquiv_apply_left,", "add_lt_add_iff_left,", "simp"], "tactic_count": 10}
{"name": "Polynomial.resultant_zero_right_deg", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Resultant.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.resultant_C_zero_right", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Resultant.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.resultant_zero_right", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Resultant.Basic", "is_tactic_proof": true, "tactics": ["obtain", "have", "simp", "simpa"], "tactic_count": 4}
{"name": "Polynomial.resultant_zero_left", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Resultant.Basic", "is_tactic_proof": true, "tactics": ["rw", "cases"], "tactic_count": 2}
{"name": "Polynomial.resultant_zero_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Resultant.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "_private.Mathlib.RingTheory.Polynomial.Resultant.Basic.0.Polynomial.resultant_add_mul_monomial_right", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Resultant.Basic", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "let", "let", "let", "have", "induction", "zero", "succ", "rw", "congr", "ext", "simp", "neg_mul,", "obtain", "simp", "induction", "left", "dsimp", "have", "simp", "split_ifs", "rw", "exact", "lia", "right", "simp", "have", "simp", "rw", "lia", "lia", "rw", "congr", "ext", "induction"], "tactic_count": 36}
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{"name": "Polynomial.resultant_add_mul_left", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Resultant.Basic", "is_tactic_proof": false, "tactics": ["rw", "two_mul,", "ring"], "tactic_count": 3}
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{"name": "Polynomial.resultant_add_right_deg", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Resultant.Basic", "is_tactic_proof": false, "tactics": ["rw", "simp", "ring_nf", "simp"], "tactic_count": 4}
{"name": "Polynomial.resultant_eq_zero_of_lt_lt", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Resultant.Basic", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "rw", "simp"], "tactic_count": 4}
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{"name": "Polynomial.resultant_C_right", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Resultant.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
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{"name": "Polynomial.resultant_X_sub_C_left", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Resultant.Basic", "is_tactic_proof": true, "tactics": ["nontriviality", "obtain", "obtain", "simp", "conv_lhs", "rw", "simp", "rw", "lia"], "tactic_count": 9}
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{"name": "Polynomial.resultant_X_sub_C_right", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Resultant.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
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{"name": "Polynomial.induction_of_Splits_of_injective_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Resultant.Basic", "is_tactic_proof": true, "tactics": ["wlog", "exact", "surjective", "wlog", "exact", "injective", "wlog", "letI", "exact", "injective", "letI", "exact"], "tactic_count": 12}
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{"name": "Polynomial.resultant_self", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Resultant.Basic", "is_tactic_proof": true, "tactics": ["induction", "by_cases", "obtain", "rw", "simp", "injective", "apply", "simpa", "surjective", "obtain", "rw"], "tactic_count": 11}
{"name": "Polynomial.resultant_self_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Resultant.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.resultant_dvd_leadingCoeff_pow", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Resultant.Basic", "is_tactic_proof": true, "tactics": ["obtain", "simp", "aesop", "obtain", "simp", "aesop", "have", "obtain", "obtain", "simp", "obtain", "obtain", "simp", "have", "rw", "exact", "by_contra", "rw", "have", "simp", "lia"], "tactic_count": 21}
{"name": "Polynomial.resultant_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Resultant.Basic", "is_tactic_proof": true, "tactics": ["obtain", "simp", "aesop", "intro", "simpa"], "tactic_count": 5}
{"name": "Polynomial.resultant_prod_left", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Resultant.Basic", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "insert", "have", "rw", "resultant_mul_left"], "tactic_count": 7}
{"name": "Polynomial.resultant_prod_right", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Resultant.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "rw", "natDegree_prod"], "tactic_count": 3}
{"name": "Polynomial.resultant_pow_left", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Resultant.Basic", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "Polynomial.resultant_pow_right", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Resultant.Basic", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "Polynomial.resultant_X_sub_C_pow_left", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Resultant.Basic", "is_tactic_proof": true, "tactics": ["nontriviality", "convert"], "tactic_count": 2}
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{"name": "Polynomial.resultant_X_pow_right", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Resultant.Basic", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "Polynomial.resultant_scaleRoots", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Resultant.Basic", "is_tactic_proof": true, "tactics": ["rw", "obtain", "obtain", "induction", "by_cases", "obtain", "by_cases", "obtain", "obtain", "rw", "simp", "conv_lhs", "rw", "roots_scaleRoots", "simp", "simp", "ring", "injective", "have", "apply", "rw", "simpa", "all_goals", "surjective", "obtain", "obtain", "obtain", "have", "simp_rw", "have", "simp_rw", "rw", "natDegree_eq_natDegree", "rw", "simp"], "tactic_count": 35}
{"name": "Polynomial.resultant_integralNormalization", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Resultant.Basic", "is_tactic_proof": true, "tactics": ["rw", "wlog", "by_cases", "by_cases", "let", "let", "have", "obtain", "obtain", "have", "simp_rw", "have", "simp_rw", "rw", "this", "simp", "by_cases", "apply", "dsimp", "have", "rw", "resultant_C_mul_right]", "rw"], "tactic_count": 23}
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{"name": "Polynomial.toMatrix_sylvesterMap", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Resultant.Basic", "is_tactic_proof": true, "tactics": ["ext", "suffices", "simpa", "rw", "split_ifs", "exact", "suffices", "simpa", "rw", "split_ifs", "exact"], "tactic_count": 11}
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{"name": "Polynomial.adjSylvester_comp_sylveserMap", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Resultant.Basic", "is_tactic_proof": true, "tactics": ["let", "let", "have", "rwa", "resultant]"], "tactic_count": 5}
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{"name": "Polynomial.isUnit_resultant_iff_isCoprime", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Resultant.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "obtain", "refine", "obtain", "exact", "simp", "intro", "suffices", "have", "obtain", "rw", "simpa", "rw", "simpa", "by_contra", "replace", "rw", "have", "simp", "lia"], "tactic_count": 20}
{"name": "Polynomial.resultant_eq_zero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Resultant.Basic", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "simpa", "have", "simp", "have", "rw", "isCoprime_mul_unit_left_left", "simp"], "tactic_count": 9}
{"name": "Polynomial.discr", "kind": "definition", "module": "Mathlib.RingTheory.Polynomial.Resultant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.discr_C", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Resultant.Basic", "is_tactic_proof": true, "tactics": ["let", "simp"], "tactic_count": 2}
{"name": "Polynomial.discr_of_degree_eq_one", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Resultant.Basic", "is_tactic_proof": true, "tactics": ["rw", "let", "have", "have", "ext", "obtain", "obtain", "simp", "simp"], "tactic_count": 9}
{"name": "Polynomial.discr_of_degree_eq_two", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Resultant.Basic", "is_tactic_proof": true, "tactics": ["rw", "let", "rw", "have", "ext", "fin_cases", "simp", "simp", "ring_nf"], "tactic_count": 9}
{"name": "Polynomial.resultant_deriv", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Resultant.Basic", "is_tactic_proof": true, "tactics": ["rw", "rw", "discr,", "ring_nf", "rw"], "tactic_count": 5}
{"name": "_private.Mathlib.RingTheory.Polynomial.Resultant.Basic.0.Polynomial.sylvesterDeriv_of_natDegree_eq_three", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Resultant.Basic", "is_tactic_proof": false, "tactics": ["ext", "simp", "eq_rec_constant,", "have", "have", "fin_cases", "simp", "zero_add,", "fin_cases"], "tactic_count": 9}
{"name": "Polynomial.discr_of_degree_eq_three", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Resultant.Basic", "is_tactic_proof": true, "tactics": ["apply", "let", "rw", "simp", "ring_nf"], "tactic_count": 5}
{"name": "Polynomial.scaleRoots", "kind": "definition", "module": "Mathlib.RingTheory.Polynomial.ScaleRoots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coeff_scaleRoots", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.ScaleRoots", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.coeff_scaleRoots_natDegree", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.ScaleRoots", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.zero_scaleRoots", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.ScaleRoots", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Polynomial.scaleRoots_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.ScaleRoots", "is_tactic_proof": true, "tactics": ["intro", "have", "have", "rw", "contradiction"], "tactic_count": 5}
{"name": "Polynomial.support_scaleRoots_le", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.ScaleRoots", "is_tactic_proof": true, "tactics": ["intro", "simpa"], "tactic_count": 2}
{"name": "Polynomial.support_scaleRoots_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.ScaleRoots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.degree_scaleRoots", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.ScaleRoots", "is_tactic_proof": true, "tactics": ["haveI", "by_cases", "rw", "refine", "rw", "intro", "have", "contradiction"], "tactic_count": 8}
{"name": "Polynomial.natDegree_scaleRoots", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.ScaleRoots", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.leadingCoeff_scaleRoots", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.ScaleRoots", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.monic_scaleRoots_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.ScaleRoots", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Polynomial.map_scaleRoots", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.ScaleRoots", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Polynomial.scaleRoots_C", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.ScaleRoots", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Polynomial.scaleRoots_one", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.ScaleRoots", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Polynomial.scaleRoots_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.ScaleRoots", "is_tactic_proof": true, "tactics": ["ext", "simp", "smul_eq_mul]", "split_ifs", "subst", "exact", "exact", "rfl"], "tactic_count": 8}
{"name": "Polynomial.one_scaleRoots", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.ScaleRoots", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Polynomial.X_add_C_scaleRoots", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.ScaleRoots", "is_tactic_proof": true, "tactics": ["nontriviality", "ext"], "tactic_count": 2}
{"name": "Polynomial.scaleRoots_eval₂_mul_of_commute", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.ScaleRoots", "is_tactic_proof": true, "tactics": ["calc", "simp", "let", "simp", "rw", "exact"], "tactic_count": 6}
{"name": "Polynomial.scaleRoots_eval₂_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.ScaleRoots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.scaleRoots_eval₂_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.ScaleRoots", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.scaleRoots_eval_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.ScaleRoots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.scaleRoots_aeval_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.ScaleRoots", "is_tactic_proof": true, "tactics": ["rw", "apply", "intros"], "tactic_count": 3}
{"name": "Polynomial.scaleRoots_eval₂_eq_zero_of_eval₂_div_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.ScaleRoots", "is_tactic_proof": true, "tactics": ["nontriviality", "convert", "rw", "exact"], "tactic_count": 4}
{"name": "Polynomial.scaleRoots_aeval_eq_zero_of_aeval_div_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.ScaleRoots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.scaleRoots_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.ScaleRoots", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Polynomial.mul_scaleRoots", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.ScaleRoots", "is_tactic_proof": true, "tactics": ["ext", "trans", "rw", "cases", "inl", "inr", "rw", "apply", "simp", "intro", "cases", "inl", "inr", "cases", "inl", "inr", "simp", "rw"], "tactic_count": 18}
{"name": "Polynomial.mul_scaleRoots'", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.ScaleRoots", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.mul_scaleRoots_of_noZeroDivisors", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.ScaleRoots", "is_tactic_proof": true, "tactics": ["by_cases", "by_cases", "apply", "simp"], "tactic_count": 4}
{"name": "Polynomial.pow_scaleRoots'", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.ScaleRoots", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "refine", "rwa"], "tactic_count": 6}
{"name": "Polynomial.pow_scaleRoots_of_isReduced", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.ScaleRoots", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "by_cases", "simp", "exact"], "tactic_count": 5}
{"name": "Polynomial.add_scaleRoots_of_natDegree_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.ScaleRoots", "is_tactic_proof": true, "tactics": ["ext", "but", "rw", "cases", "inl", "inr"], "tactic_count": 6}
{"name": "Polynomial.scaleRoots_dvd'", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.ScaleRoots", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact"], "tactic_count": 3}
{"name": "Polynomial.scaleRoots_dvd", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.ScaleRoots", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact"], "tactic_count": 3}
{"name": "Polynomial.scaleRoots_dvd_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.ScaleRoots", "is_tactic_proof": true, "tactics": ["refine", "simp"], "tactic_count": 2}
{"name": "Polynomial.isCoprime_scaleRoots", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.ScaleRoots", "is_tactic_proof": true, "tactics": ["obtain", "let", "have", "apply", "rw", "use", "use", "simp"], "tactic_count": 8}
{"name": "Polynomial.Splits.scaleRoots", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.ScaleRoots", "is_tactic_proof": true, "tactics": ["cases", "rwa", "obtain", "simp", "obtain", "rw", "clear", "refine", "induction", "empty", "cons", "rw", "exact", "simp", "exact", "rw", "simpa"], "tactic_count": 17}
{"name": "Polynomial.X_sub_C_scaleRoots", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.ScaleRoots", "is_tactic_proof": true, "tactics": ["nontriviality", "ext"], "tactic_count": 2}
{"name": "Polynomial.rootMultiplicity_scaleRoots", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.ScaleRoots", "is_tactic_proof": true, "tactics": ["cases", "simp", "obtain", "simp", "obtain", "have", "conv_lhs", "rw", "rootMultiplicity_mul_X_sub_C_pow", "rw", "simp", "rw", "tauto", "simp", "rwa"], "tactic_count": 15}
{"name": "Polynomial.roots_scaleRoots", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.ScaleRoots", "is_tactic_proof": true, "tactics": ["classical", "ext", "have", "obtain", "simp"], "tactic_count": 5}
{"name": "Polynomial.X_pow_sub_X_sub_one_irreducible_aux", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Selmer", "is_tactic_proof": true, "tactics": ["rintro", "replace", "have", "rw", "have", "interval_cases", "have", "zero_ne_one", "rcases", "exact", "exact", "exact"], "tactic_count": 12}
{"name": "Polynomial.X_pow_sub_X_sub_one_irreducible", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Selmer", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "exact", "have", "have", "rw", "apply", "rintro", "apply", "rw", "simp_rw", "map_one]", "replace", "replace", "rw", "rw", "exact"], "tactic_count": 17}
{"name": "Polynomial.X_pow_sub_X_sub_one_irreducible_rat", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Selmer", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "exact", "have", "have", "have", "rwa", "exact"], "tactic_count": 8}
{"name": "Polynomial.IsSeparableContraction", "kind": "definition", "module": "Mathlib.RingTheory.Polynomial.SeparableDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.HasSeparableContraction", "kind": "definition", "module": "Mathlib.RingTheory.Polynomial.SeparableDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.HasSeparableContraction.contraction", "kind": "definition", "module": "Mathlib.RingTheory.Polynomial.SeparableDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.HasSeparableContraction.degree", "kind": "definition", "module": "Mathlib.RingTheory.Polynomial.SeparableDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.HasSeparableContraction.isSeparableContraction", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.SeparableDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.IsSeparableContraction.dvd_degree'", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.SeparableDegree", "is_tactic_proof": true, "tactics": ["obtain", "use", "rw"], "tactic_count": 3}
{"name": "Polynomial.HasSeparableContraction.dvd_degree'", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.SeparableDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.HasSeparableContraction.dvd_degree", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.SeparableDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.HasSeparableContraction.eq_degree", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.SeparableDegree", "is_tactic_proof": true, "tactics": ["let", "rw"], "tactic_count": 2}
{"name": "Irreducible.hasSeparableContraction", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.SeparableDegree", "is_tactic_proof": true, "tactics": ["cases", "exact", "rcases", "exact"], "tactic_count": 4}
{"name": "Polynomial.contraction_degree_eq_or_insep", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.SeparableDegree", "is_tactic_proof": true, "tactics": ["wlog", "exact", "obtain", "rw", "subst", "rcases", "rw", "rw"], "tactic_count": 8}
{"name": "Polynomial.IsSeparableContraction.degree_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.SeparableDegree", "is_tactic_proof": true, "tactics": ["cases", "rcases", "rw", "rw", "rcases", "let", "obtain", "haveI", "refine", "rw"], "tactic_count": 10}
{"name": "Polynomial.shiftedLegendre", "kind": "definition", "module": "Mathlib.RingTheory.Polynomial.ShiftedLegendre", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.factorial_mul_shiftedLegendre_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.ShiftedLegendre", "is_tactic_proof": true, "tactics": ["symm", "calc", "congr", "rw", "congr", "rw", "mul_assoc,", "rw", "linarith", "rw", "congr", "rw", "iterate_derivative_X_pow_eq_smul,", "simp", "ring", "congr", "rw", "congr", "rw", "simp", "norm_cast", "rw", "rw", "simp"], "tactic_count": 24}
{"name": "Polynomial.coeff_shiftedLegendre", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.ShiftedLegendre", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "simp"], "tactic_count": 3}
{"name": "Polynomial.degree_shiftedLegendre", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.ShiftedLegendre", "is_tactic_proof": true, "tactics": ["refine", "rw", "intro", "norm_cast", "simp", "simp"], "tactic_count": 6}
{"name": "Polynomial.natDegree_shiftedLegendre", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.ShiftedLegendre", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.neg_one_pow_mul_shiftedLegendre_comp_one_sub_X_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.ShiftedLegendre", "is_tactic_proof": true, "tactics": ["refine", "rw", "iterate_derivative_comp_one_sub_X]", "simp"], "tactic_count": 4}
{"name": "Polynomial.shiftedLegendre_eval_symm", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.ShiftedLegendre", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "Polynomial.eq_quadratic_of_degree_le_two", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.SmallDegreeVieta", "is_tactic_proof": true, "tactics": ["rw", "simp", "abel"], "tactic_count": 3}
{"name": "Polynomial.eq_neg_mul_add_of_roots_quadratic_eq_pair", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.SmallDegreeVieta", "is_tactic_proof": true, "tactics": ["let", "have", "le_antisymm", "have", "simpa", "coeff_eq_esymm_roots_of_card"], "tactic_count": 6}
{"name": "Polynomial.eq_mul_mul_of_roots_quadratic_eq_pair", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.SmallDegreeVieta", "is_tactic_proof": true, "tactics": ["let", "have", "le_antisymm", "have", "simpa", "coeff_eq_esymm_roots_of_card"], "tactic_count": 6}
{"name": "Polynomial.eq_neg_mul_add_of_aroots_quadratic_eq_pair", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.SmallDegreeVieta", "is_tactic_proof": false, "tactics": ["rw", "show", "map", "exact"], "tactic_count": 4}
{"name": "Polynomial.eq_mul_mul_of_aroots_quadratic_eq_pair", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.SmallDegreeVieta", "is_tactic_proof": false, "tactics": ["rw", "show", "map", "exact"], "tactic_count": 4}
{"name": "Polynomial.roots_quadratic_eq_pair_iff_of_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.SmallDegreeVieta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.aroots_quadratic_eq_pair_iff_of_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.SmallDegreeVieta", "is_tactic_proof": false, "tactics": ["rw", "show", "map", "exact"], "tactic_count": 4}
{"name": "Polynomial.roots_quadratic_eq_pair_iff_of_ne_zero'", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.SmallDegreeVieta", "is_tactic_proof": true, "tactics": ["rw", "field_simp", "exact", "and_congr"], "tactic_count": 4}
{"name": "Polynomial.aroots_quadratic_eq_pair_iff_of_ne_zero'", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.SmallDegreeVieta", "is_tactic_proof": false, "tactics": ["rw", "show", "map", "exact"], "tactic_count": 4}
{"name": "Polynomial.aeval_map_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Tower", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.aeval_algebraMap_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Tower", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.aeval_algebraMap_eq_zero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Tower", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.aeval_algebraMap_eq_zero_iff_of_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Tower", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subalgebra.aeval_coe", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Tower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.aeval_root_of_mapAlg_eq_multiset_prod_X_sub_C", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.Tower", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "Polynomial.wfDvdMonoid", "kind": "instance", "module": "Mathlib.RingTheory.Polynomial.UniqueFactorization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.exists_irreducible_of_degree_pos", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.UniqueFactorization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.exists_irreducible_of_natDegree_pos", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.UniqueFactorization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.exists_irreducible_of_natDegree_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.UniqueFactorization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.uniqueFactorizationMonoid", "kind": "instance", "module": "Mathlib.RingTheory.Polynomial.UniqueFactorization", "is_tactic_proof": true, "tactics": ["letI", "exact"], "tactic_count": 2}
{"name": "Polynomial.fintypeSubtypeMonicDvd", "kind": "definition", "module": "Mathlib.RingTheory.Polynomial.UniqueFactorization", "is_tactic_proof": true, "tactics": ["set", "let", "have", "let", "let", "let", "refine", "rw", "exact"], "tactic_count": 9}
{"name": "_private.Mathlib.RingTheory.Polynomial.UniqueFactorization.0.MvPolynomial.uniqueFactorizationMonoid_of_fintype", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.UniqueFactorization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.uniqueFactorizationMonoid", "kind": "instance", "module": "Mathlib.RingTheory.Polynomial.UniqueFactorization", "is_tactic_proof": true, "tactics": ["rw", "intro", "obtain", "iff_exists_prime_factors.1", "exact", "let", "he", "rw"], "tactic_count": 8}
{"name": "Polynomial.exists_monic_irreducible_factor", "kind": "theorem", "module": "Mathlib.RingTheory.Polynomial.UniqueFactorization", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "obtain", "have", "associated_mul_unit_right", "exact"], "tactic_count": 6}
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{"name": "Polynomial.instFiniteUniversalFactorizationRing", "kind": "instance", "module": "Mathlib.RingTheory.Polynomial.UniversalFactorizationRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "PowerBasis.dim_le_natDegree_of_root", "kind": "theorem", "module": "Mathlib.RingTheory.PowerBasis", "is_tactic_proof": true, "tactics": ["refine", "rw", "refine", "simp_rw", "have", "rw"], "tactic_count": 6}
{"name": "PowerBasis.dim_le_degree_of_root", "kind": "theorem", "module": "Mathlib.RingTheory.PowerBasis", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "PowerBasis.degree_minpolyGen", "kind": "theorem", "module": "Mathlib.RingTheory.PowerBasis", "is_tactic_proof": true, "tactics": ["unfold", "rw", "apply"], "tactic_count": 3}
{"name": "PowerBasis.natDegree_minpolyGen", "kind": "theorem", "module": "Mathlib.RingTheory.PowerBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerBasis.minpolyGen_eq", "kind": "theorem", "module": "Mathlib.RingTheory.PowerBasis", "is_tactic_proof": true, "tactics": ["nontriviality", "refine", "exact"], "tactic_count": 3}
{"name": "PowerBasis.isIntegral_gen", "kind": "theorem", "module": "Mathlib.RingTheory.PowerBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerBasis.degree_minpoly", "kind": "theorem", "module": "Mathlib.RingTheory.PowerBasis", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PowerBasis.natDegree_minpoly", "kind": "theorem", "module": "Mathlib.RingTheory.PowerBasis", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PowerBasis.leftMulMatrix", "kind": "theorem", "module": "Mathlib.RingTheory.PowerBasis", "is_tactic_proof": true, "tactics": ["cases", "rw", "refine", "simp_rw", "apply", "split_ifs", "simp_rw", "convert", "rw", "natDegree_minpolyGen,", "rw", "rfl", "intro", "rw", "apply"], "tactic_count": 15}
{"name": "PowerBasis.constr_pow_aeval", "kind": "theorem", "module": "Mathlib.RingTheory.PowerBasis", "is_tactic_proof": true, "tactics": ["cases", "rw", "rw", "by_cases", "simp", "have", "rw", "apply", "exact", "rw", "refine", "rw", "rw", "congr", "rw"], "tactic_count": 15}
{"name": "PowerBasis.constr_pow_gen", "kind": "theorem", "module": "Mathlib.RingTheory.PowerBasis", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "PowerBasis.constr_pow_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.PowerBasis", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "PowerBasis.constr_pow_mul", "kind": "theorem", "module": "Mathlib.RingTheory.PowerBasis", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "simp"], "tactic_count": 3}
{"name": "PowerBasis.lift", "kind": "definition", "module": "Mathlib.RingTheory.PowerBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerBasis.lift_gen", "kind": "theorem", "module": "Mathlib.RingTheory.PowerBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerBasis.lift_aeval", "kind": "theorem", "module": "Mathlib.RingTheory.PowerBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerBasis.liftEquiv", "kind": "definition", "module": "Mathlib.RingTheory.PowerBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerBasis.liftEquiv'", "kind": "definition", "module": "Mathlib.RingTheory.PowerBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerBasis.AlgHom.fintype", "kind": "definition", "module": "Mathlib.RingTheory.PowerBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerBasis.equivOfRoot", "kind": "definition", "module": "Mathlib.RingTheory.PowerBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerBasis.equivOfRoot_aeval", "kind": "theorem", "module": "Mathlib.RingTheory.PowerBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerBasis.equivOfRoot_gen", "kind": "theorem", "module": "Mathlib.RingTheory.PowerBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerBasis.equivOfRoot_symm", "kind": "theorem", "module": "Mathlib.RingTheory.PowerBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerBasis.equivOfMinpoly", "kind": "definition", "module": "Mathlib.RingTheory.PowerBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerBasis.equivOfMinpoly_aeval", "kind": "theorem", "module": "Mathlib.RingTheory.PowerBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerBasis.equivOfMinpoly_gen", "kind": "theorem", "module": "Mathlib.RingTheory.PowerBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerBasis.equivOfMinpoly_symm", "kind": "theorem", "module": "Mathlib.RingTheory.PowerBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "linearIndependent_pow", "kind": "theorem", "module": "Mathlib.RingTheory.PowerBasis", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "exact", "refine", "simp", "simp_rw", "apply", "simp_rw", "exact", "apply_fun", "simp_rw", "exact"], "tactic_count": 12}
{"name": "IsIntegral.mem_span_pow", "kind": "theorem", "module": "Mathlib.RingTheory.PowerBasis", "is_tactic_proof": true, "tactics": ["obtain", "apply", "have", "refine", "conv_lhs", "simp"], "tactic_count": 6}
{"name": "PowerBasis.map", "kind": "definition", "module": "Mathlib.RingTheory.PowerBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerBasis.minpolyGen_map", "kind": "theorem", "module": "Mathlib.RingTheory.PowerBasis", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PowerBasis.equivOfRoot_map", "kind": "theorem", "module": "Mathlib.RingTheory.PowerBasis", "is_tactic_proof": true, "tactics": ["ext", "obtain", "simp"], "tactic_count": 3}
{"name": "PowerBasis.equivOfMinpoly_map", "kind": "theorem", "module": "Mathlib.RingTheory.PowerBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerBasis.adjoin_gen_eq_top", "kind": "theorem", "module": "Mathlib.RingTheory.PowerBasis", "is_tactic_proof": true, "tactics": ["rw", "rintro", "rw", "exact"], "tactic_count": 4}
{"name": "PowerBasis.adjoin_eq_top_of_gen_mem_adjoin", "kind": "theorem", "module": "Mathlib.RingTheory.PowerBasis", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp"], "tactic_count": 3}
{"name": "PowerSeries", "kind": "abbrev", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.term_⟦X⟧", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries._aux_Mathlib_RingTheory_PowerSeries_Basic___macroRules_PowerSeries_term_⟦X⟧_1", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries._aux_Mathlib_RingTheory_PowerSeries_Basic___unexpand_PowerSeries_1", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.instInhabited", "kind": "instance", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "PowerSeries.instZero", "kind": "instance", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "PowerSeries.instAddMonoid", "kind": "instance", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "PowerSeries.instAddGroup", "kind": "instance", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "PowerSeries.instAddCommMonoid", "kind": "instance", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "PowerSeries.instAddCommGroup", "kind": "instance", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "PowerSeries.instSemiring", "kind": "instance", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "PowerSeries.instCommSemiring", "kind": "instance", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "PowerSeries.instRing", "kind": "instance", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "PowerSeries.instCommRing", "kind": "instance", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "PowerSeries.instNontrivial", "kind": "instance", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "PowerSeries.instModule", "kind": "instance", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "PowerSeries.instIsScalarTower", "kind": "instance", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.instAlgebra", "kind": "instance", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "PowerSeries.coeff", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.monomial", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.coeff_def", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PowerSeries.ext", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.forall_coeff_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.instSubsingleton", "kind": "instance", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["simp", "subsingleton"], "tactic_count": 2}
{"name": "PowerSeries.mk", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.coeff_mk", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.coeff_monomial", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.monomial_eq_mk", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.coeff_monomial_same", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.coeff_comp_monomial", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.monomial_mul_monomial", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "PowerSeries.constantCoeff", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.C", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.algebraMap_eq", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.X", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.commute_X", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.X_mul", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.commute_X_pow", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.X_pow_mul", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.coeff_zero_eq_constantCoeff", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "PowerSeries.coeff_zero_eq_constantCoeff_apply", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PowerSeries.monomial_zero_eq_C", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "PowerSeries.monomial_zero_eq_C_apply", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PowerSeries.coeff_C", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PowerSeries.coeff_zero_C", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PowerSeries.coeff_ne_zero_C", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PowerSeries.coeff_succ_C", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.C_injective", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["intro", "simp_rw", "simpa"], "tactic_count": 3}
{"name": "PowerSeries.subsingleton_iff", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "PowerSeries.X_eq", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.coeff_X", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PowerSeries.coeff_zero_X", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PowerSeries.coeff_one_X", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PowerSeries.X_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.X_pow_eq", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.coeff_X_pow", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PowerSeries.coeff_X_pow_self", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PowerSeries.coeff_one", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.coeff_zero_one", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.coeff_mul", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "rfl"], "tactic_count": 3}
{"name": "PowerSeries.coeff_mul_C", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.coeff_C_mul", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.coeff_smul", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.constantCoeff_smul", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.smul_eq_C_mul", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "PowerSeries.coeff_succ_mul_X", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["simp", "convert", "rw"], "tactic_count": 3}
{"name": "PowerSeries.coeff_succ_X_mul", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["simp", "convert", "rw"], "tactic_count": 3}
{"name": "PowerSeries.mul_X_cancel", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["rw", "intro", "simpa"], "tactic_count": 3}
{"name": "PowerSeries.mul_X_injective", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.mul_X_inj", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.X_mul_cancel", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["rw", "intro", "simpa"], "tactic_count": 3}
{"name": "PowerSeries.X_mul_injective", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.X_mul_inj", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.constantCoeff_C", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.constantCoeff_comp_C", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.constantCoeff_zero", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.constantCoeff_one", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.constantCoeff_X", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.constantCoeff_mk", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.coeff_zero_mul_X", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PowerSeries.coeff_zero_X_mul", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PowerSeries.constantCoeff_surj", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.coeff_C_mul_X_pow", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PowerSeries.coeff_mul_X_pow", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["rw", "rintro", "rw", "rintro", "apply", "rw", "subst", "rfl", "exact"], "tactic_count": 9}
{"name": "PowerSeries.coeff_X_pow_mul", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["rw", "rintro", "rw", "rintro", "apply", "rw", "subst", "rfl", "rw", "exact"], "tactic_count": 10}
{"name": "PowerSeries.mul_X_pow_cancel", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["rw", "intro", "simpa"], "tactic_count": 3}
{"name": "PowerSeries.mul_X_pow_injective", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.mul_X_pow_inj", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.X_pow_mul_cancel", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["rw", "intro", "simpa"], "tactic_count": 3}
{"name": "PowerSeries.X_pow_mul_injective", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.X_pow_mul_inj", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.coeff_mul_X_pow'", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["split_ifs", "rw", "refine", "rw", "exact"], "tactic_count": 5}
{"name": "PowerSeries.coeff_X_pow_mul'", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["split_ifs", "rw", "simp", "refine", "rw", "have", "rw", "exact"], "tactic_count": 8}
{"name": "PowerSeries.isUnit_constantCoeff", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.eq_shift_mul_X_add_const", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp", "simp"], "tactic_count": 3}
{"name": "PowerSeries.eq_X_mul_shift_add_const", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp", "simp"], "tactic_count": 3}
{"name": "PowerSeries.map", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.map_id", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.map_comp", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.coeff_map", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.map_C", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "PowerSeries.map_X", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "PowerSeries.map_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["intro", "use", "ext", "simp", "exact"], "tactic_count": 5}
{"name": "PowerSeries.map_injective", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["intro", "ext", "apply", "rw"], "tactic_count": 4}
{"name": "PowerSeries.map_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.X_pow_dvd_iff", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["convert", "constructor", "rw", "convert", "apply", "simpa"], "tactic_count": 6}
{"name": "PowerSeries.X_dvd_iff", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["rw", "constructor", "exact", "intro", "rwa"], "tactic_count": 5}
{"name": "PowerSeries.toSubring", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.coeff_toSubring", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PowerSeries.constantCoeff_toSubring", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.map_toSubring", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.rescale", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.coeff_rescale", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.rescale_zero", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp", "split_ifs"], "tactic_count": 3}
{"name": "PowerSeries.rescale_zero_apply", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PowerSeries.rescale_one", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "PowerSeries.rescale_mk", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "PowerSeries.rescale_rescale", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp_rw", "rw"], "tactic_count": 3}
{"name": "PowerSeries.rescale_mul", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "PowerSeries.coeff_prod", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["simp", "rw", "intro", "apply", "intro", "congr", "simp"], "tactic_count": 7}
{"name": "PowerSeries.prod_monomial", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "PowerSeries.monomial_pow", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "PowerSeries.coeff_pow", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["have", "have", "apply", "rw", "apply"], "tactic_count": 5}
{"name": "PowerSeries.coeff_one_mul", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["have", "rw", "simp"], "tactic_count": 3}
{"name": "PowerSeries.coeff_one_pow", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simp", "induction", "zero", "succ", "have", "have", "rw", "simp", "have", "rcases", "by_contra", "rw", "simp", "norm_num", "rw", "conv", "move_mul", "conv", "rw", "conv", "ring", "exact", "decide"], "tactic_count": 24}
{"name": "PowerSeries.not_isField", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "nontriviality", "rw", "use", "constructor", "rw", "exact", "rw", "exact"], "tactic_count": 10}
{"name": "PowerSeries.rescale_X", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp", "split_ifs"], "tactic_count": 3}
{"name": "PowerSeries.rescale_neg_one_X", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PowerSeries.evalNegHom", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.evalNegHom_X", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.C_eq_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.algebraMap_apply", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.instNontrivialSubalgebra", "kind": "instance", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.mapAlgHom", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.mapAlgHom_apply", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.toPowerSeries", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coeToPowerSeries", "kind": "instance", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coe_def", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coeff_coe", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coe_monomial", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Polynomial.coe_zero", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coe_one", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "Polynomial.coe_add", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Polynomial.coe_mul", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coe_smul", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coe_C", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "Polynomial.coe_X", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.polynomial_map_coe", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Polynomial.constantCoeff_coe", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coe_injective", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coe_inj", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coe_eq_zero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.coe_eq_one_iff", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Polynomial.coeToPowerSeries.ringHom", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coeToPowerSeries.ringHom_apply", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coe_pow", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.eval₂_C_X_eq_coe", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["nth_rw", "rw", "apply", "intros", "rw"], "tactic_count": 5}
{"name": "MvPolynomial.toMvPowerSeries_pUnitAlgEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["induction", "monomial", "have", "simp", "add"], "tactic_count": 5}
{"name": "Polynomial.pUnitAlgEquiv_symm_toPowerSeries", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": true, "tactics": ["set", "have", "rw"], "tactic_count": 3}
{"name": "Polynomial.coeToPowerSeries.algHom", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coeToPowerSeries.algHom_apply", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coe_neg", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coe_sub", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.algebraPolynomial", "kind": "instance", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.algebraPowerSeries", "kind": "instance", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.algebraPolynomial'", "kind": "instance", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.algebraMap_apply'", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.algebraMap_apply''", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.binomialSeries_coeff", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Binomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.binomialSeries_constantCoeff", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Binomial", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PowerSeries.binomialSeries_add", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Binomial", "is_tactic_proof": true, "tactics": ["ext", "simp", "sum_smul]", "refine", "rw"], "tactic_count": 5}
{"name": "PowerSeries.binomialSeries_nat", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Binomial", "is_tactic_proof": true, "tactics": ["ext", "have", "rw", "simp"], "tactic_count": 4}
{"name": "PowerSeries.binomialSeries_zero", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Binomial", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "PowerSeries.rescale_neg_one_invOneSubPow", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Binomial", "is_tactic_proof": true, "tactics": ["ext", "rw", "cases", "zero", "succ", "d", "simp", "rw", "show", "norm_cast"], "tactic_count": 10}
{"name": "PowerSeries.catalanSeries", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.Catalan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.catalanSeries_coeff", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Catalan", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PowerSeries.catalanSeries_constantCoeff", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Catalan", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "PowerSeries.catalanSeries_sq_mul_X_add_one", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Catalan", "is_tactic_proof": true, "tactics": ["ext", "cases", "zero", "succ", "simp_rw", "catalanSeries_coeff,"], "tactic_count": 6}
{"name": "PowerSeries.coeff_mul_mem_ideal_mul_ideal_of_coeff_mem_ideal", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.CoeffMulMem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.coeff_mul_mem_ideal_mul_ideal_of_coeff_mem_ideal'", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.CoeffMulMem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.coeff_mul_mem_ideal_of_coeff_right_mem_ideal", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.CoeffMulMem", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "PowerSeries.coeff_mul_mem_ideal_of_coeff_right_mem_ideal'", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.CoeffMulMem", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "PowerSeries.coeff_mul_mem_ideal_of_coeff_left_mem_ideal", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.CoeffMulMem", "is_tactic_proof": true, "tactics": ["simpa", "coeff_mul_mem_ideal_mul_ideal_of_coeff_mem_ideal"], "tactic_count": 2}
{"name": "PowerSeries.coeff_mul_mem_ideal_of_coeff_left_mem_ideal'", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.CoeffMulMem", "is_tactic_proof": true, "tactics": ["simpa", "coeff_mul_mem_ideal_mul_ideal_of_coeff_mem_ideal"], "tactic_count": 2}
{"name": "PowerSeries.derivativeFun", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.Derivative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.coeff_derivativeFun", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Derivative", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PowerSeries.derivativeFun_coe", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Derivative", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "PowerSeries.derivativeFun_add", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Derivative", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "PowerSeries.derivativeFun_C", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Derivative", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "PowerSeries.trunc_derivativeFun", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Derivative", "is_tactic_proof": true, "tactics": ["ext", "rw", "split_ifs", "have", "rw", "have", "rw"], "tactic_count": 7}
{"name": "_private.Mathlib.RingTheory.PowerSeries.Derivative.0.PowerSeries.derivativeFun_coe_mul_coe", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Derivative", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PowerSeries.derivativeFun_mul", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Derivative", "is_tactic_proof": true, "tactics": ["ext", "have", "have", "rw", "coeff_mul_eq_coeff_trunc_mul_trunc₂", "coeff_mul_eq_coeff_trunc_mul_trunc₂", "derivativeFun_coe_mul_coe,"], "tactic_count": 7}
{"name": "PowerSeries.derivativeFun_one", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Derivative", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PowerSeries.derivativeFun_smul", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Derivative", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PowerSeries.derivative", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.Derivative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.termD⁄dX", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.Derivative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries._aux_Mathlib_RingTheory_PowerSeries_Derivative___macroRules_PowerSeries_termD⁄dX_1", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.Derivative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries._aux_Mathlib_RingTheory_PowerSeries_Derivative___unexpand_PowerSeries_derivative_1", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.Derivative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.derivative_C", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Derivative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.coeff_derivative", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Derivative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.derivative_coe", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Derivative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.derivative_X", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Derivative", "is_tactic_proof": true, "tactics": ["ext", "rw", "simp_rw", "split_ifs", "rw", "rfl"], "tactic_count": 6}
{"name": "PowerSeries.trunc_derivative", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Derivative", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.trunc_derivative'", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Derivative", "is_tactic_proof": true, "tactics": ["cases", "zero", "succ"], "tactic_count": 3}
{"name": "PowerSeries.derivative.ext", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Derivative", "is_tactic_proof": true, "tactics": ["ext", "cases", "zero", "succ", "have", "rwa", "smul_right_inj"], "tactic_count": 7}
{"name": "PowerSeries.derivative_inv", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Derivative", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "PowerSeries.derivative_invOf", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Derivative", "is_tactic_proof": true, "tactics": ["rw", "there"], "tactic_count": 2}
{"name": "PowerSeries.derivative_inv'", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Derivative", "is_tactic_proof": true, "tactics": ["by_cases", "suffices", "rwa", "apply", "exact"], "tactic_count": 5}
{"name": "PowerSeries.HasEval", "kind": "abbrev", "module": "Mathlib.RingTheory.PowerSeries.Evaluation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.hasEval_def", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Evaluation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.hasEval_iff", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Evaluation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.hasEval", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Evaluation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.HasEval.mono", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Evaluation", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "PowerSeries.HasEval.zero", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Evaluation", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PowerSeries.HasEval.add", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Evaluation", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "PowerSeries.HasEval.mul_left", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Evaluation", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "PowerSeries.HasEval.mul_right", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Evaluation", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "PowerSeries.HasEval.map", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Evaluation", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "PowerSeries.HasEval.X", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Evaluation", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "PowerSeries.hasEvalIdeal", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.Evaluation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.mem_hasEvalIdeal_iff", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Evaluation", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PowerSeries.eval₂", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.Evaluation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.eval₂_coe", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Evaluation", "is_tactic_proof": true, "tactics": ["let", "have", "simp", "rw"], "tactic_count": 4}
{"name": "PowerSeries.eval₂_C", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Evaluation", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PowerSeries.eval₂_X", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Evaluation", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PowerSeries.eval₂Hom", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.Evaluation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.coe_eval₂Hom", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Evaluation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.uniformContinuous_eval₂", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Evaluation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.continuous_eval₂", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Evaluation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.hasSum_eval₂", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Evaluation", "is_tactic_proof": true, "tactics": ["have", "simp", "rw", "convert", "intro", "exact"], "tactic_count": 6}
{"name": "PowerSeries.eval₂_eq_tsum", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Evaluation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.eval₂_unique", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Evaluation", "is_tactic_proof": true, "tactics": ["apply", "intro", "rw"], "tactic_count": 3}
{"name": "PowerSeries.comp_eval₂", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Evaluation", "is_tactic_proof": true, "tactics": ["apply", "exact", "intro", "simp", "exact", "simp"], "tactic_count": 6}
{"name": "PowerSeries.aeval", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.Evaluation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.coe_aeval", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Evaluation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.continuous_aeval", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Evaluation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.aeval_coe", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Evaluation", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PowerSeries.aeval_unique", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Evaluation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.hasSum_aeval", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Evaluation", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "PowerSeries.aeval_eq_sum", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Evaluation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.comp_aeval", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Evaluation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.exp", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.Exp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.coeff_exp", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Exp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.constantCoeff_exp", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Exp", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "PowerSeries.map_exp", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Exp", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "PowerSeries.derivative_exp", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Exp", "is_tactic_proof": true, "tactics": ["ext", "rw", "have", "rw", "congr", "field_simp"], "tactic_count": 6}
{"name": "PowerSeries.exp_unique_of_derivative_eq_self", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Exp", "is_tactic_proof": true, "tactics": ["ext", "induction", "zero", "succ", "have", "rw", "have", "rw", "rw", "have", "rw", "exact"], "tactic_count": 12}
{"name": "PowerSeries.isUnit_exp", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Exp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.order_exp", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Exp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.exp_mul_exp_eq_exp_add", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Exp", "is_tactic_proof": true, "tactics": ["ext", "simp", "apply", "rintro", "suffices", "a", "a", "congr", "rw", "refine", "rw", "symm", "rw", "norm_cast", "rw", "apply", "apply", "rintro", "apply", "rw"], "tactic_count": 20}
{"name": "PowerSeries.exp_mul_exp_neg_eq_one", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Exp", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "PowerSeries.exp_pow_eq_rescale_exp", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Exp", "is_tactic_proof": true, "tactics": ["induction", "zero", "simp", "succ", "simpa", "pow_succ"], "tactic_count": 6}
{"name": "PowerSeries.exp_pow_sum", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Exp", "is_tactic_proof": true, "tactics": ["simp", "ext", "simp"], "tactic_count": 3}
{"name": "PowerSeries.expand", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.Expand", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.expand_apply", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Expand", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PowerSeries.expand_C", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Expand", "is_tactic_proof": true, "tactics": ["conv_lhs"], "tactic_count": 1}
{"name": "PowerSeries.expand_mul_eq_comp", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Expand", "is_tactic_proof": true, "tactics": ["ext1", "simp"], "tactic_count": 2}
{"name": "PowerSeries.expand_mul", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Expand", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.expand_smul", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Expand", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.expand_X", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Expand", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.expand_monomial", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Expand", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PowerSeries.expand_one", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Expand", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PowerSeries.expand_one_apply", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Expand", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PowerSeries.map_expand", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Expand", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PowerSeries.expand_subst", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Expand", "is_tactic_proof": true, "tactics": ["rw", "here,", "and"], "tactic_count": 3}
{"name": "PowerSeries.coeff_expand_mul", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Expand", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PowerSeries.constantCoeff_expand", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Expand", "is_tactic_proof": true, "tactics": ["conv_lhs", "simp"], "tactic_count": 2}
{"name": "PowerSeries.coeff_expand_of_not_dvd", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Expand", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "PowerSeries.support_expand_subset", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Expand", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PowerSeries.support_expand", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Expand", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PowerSeries.coeff_expand", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Expand", "is_tactic_proof": true, "tactics": ["split_ifs", "obtain", "rw", "exact"], "tactic_count": 4}
{"name": "PowerSeries.order_expand", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Expand", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "PowerSeries.gaussNorm", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.GaussNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.le_gaussNorm", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.GaussNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.gaussNorm_zero", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.GaussNorm", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PowerSeries.gaussNorm_nonneg", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.GaussNorm", "is_tactic_proof": true, "tactics": ["by_cases", "calc", "simp"], "tactic_count": 3}
{"name": "PowerSeries.gaussNorm_eq_zero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.GaussNorm", "is_tactic_proof": true, "tactics": ["refine", "contrapose", "intro", "apply", "obtain", "calc", "have", "positivity"], "tactic_count": 8}
{"name": "PowerSeries.map_constantCoeff_le_self_of_X_mem", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Ideal", "is_tactic_proof": true, "tactics": ["suffices", "intro", "rw", "exact"], "tactic_count": 4}
{"name": "PowerSeries.eq_span_insert_X_of_X_mem_of_span_eq", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Ideal", "is_tactic_proof": true, "tactics": ["rw", "refine", "exact"], "tactic_count": 3}
{"name": "PowerSeries.spanFinrank_le_spanFinrank_map_constantCoeff_add_one_of_X_mem", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Ideal", "is_tactic_proof": true, "tactics": ["by_cases", "swap", "replace", "have", "exact", "nth_rw", "refine", "simpa", "simp", "refine", "rw"], "tactic_count": 11}
{"name": "PowerSeries.eq_of_le_of_X_notMem_of_fg_of_isPrime", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.exist_eq_span_eq_ncard_of_X_notMem", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Ideal", "is_tactic_proof": false, "tactics": ["have", "intro", "simpa", "obtain", "refine", "eq_of_le_of_X_notMem_of_fg_of_isPrime", "rw", "intro", "rw", "replace", "refine", "obtain", "exact", "intro", "exact", "intro", "exact"], "tactic_count": 17}
{"name": "PowerSeries.spanFinrank_eq_spanFinrank_map_constantCoeff_of_X_notMem_of_fg_of_isPrime", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Ideal", "is_tactic_proof": true, "tactics": ["refine", "swap", "have", "obtain", "exist_eq_span_eq_ncard_of_X_notMem", "refine", "rw", "exact"], "tactic_count": 8}
{"name": "PowerSeries.spanFinrank_le_spanFinrank_map_constantCoeff_add_one_of_isPrime", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Ideal", "is_tactic_proof": true, "tactics": ["by_cases", "swap", "by_cases", "exact", "exact"], "tactic_count": 5}
{"name": "PowerSeries.fg_iff_of_isPrime", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Ideal", "is_tactic_proof": true, "tactics": ["constructor", "exact", "intro", "by_cases", "have", "have", "lift", "exact", "obtain", "lift", "exact"], "tactic_count": 11}
{"name": "PowerSeries.instIsNoetherianRing", "kind": "instance", "module": "Mathlib.RingTheory.PowerSeries.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.instUniqueFactorizationMonoidOfIsPrincipalIdealRingOfIsDomain", "kind": "instance", "module": "Mathlib.RingTheory.PowerSeries.Ideal", "is_tactic_proof": true, "tactics": ["refine", "by_cases", "exact", "obtain", "obtain", "simp", "obtain", "exact"], "tactic_count": 8}
{"name": "PowerSeries.inv.aux", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.coeff_inv_aux", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Inverse", "is_tactic_proof": true, "tactics": ["rw", "simp", "split_ifs", "congr", "symm", "apply", "aesop", "aesop", "aesop", "aesop", "rintro", "obtain", "aesop", "rw", "rfl", "refine", "rintro", "simpa", "simpa"], "tactic_count": 19}
{"name": "PowerSeries.invOfUnit", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.coeff_invOfUnit", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.constantCoeff_invOfUnit", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Inverse", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PowerSeries.mul_invOfUnit", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.invOfUnit_mul", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.isUnit_iff_constantCoeff", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.sub_const_eq_shift_mul_X", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.sub_const_eq_X_mul_shift", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.inv", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.instInv", "kind": "instance", "module": "Mathlib.RingTheory.PowerSeries.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.inv_eq_inv_aux", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.coeff_inv", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Inverse", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PowerSeries.constantCoeff_inv", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.inv_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.zero_inv", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.invOfUnit_eq", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.invOfUnit_eq'", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.mul_inv_cancel", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.inv_mul_cancel", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.eq_mul_inv_iff_mul_eq", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.eq_inv_iff_mul_eq_one", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.inv_eq_iff_mul_eq_one", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.mul_inv_rev", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.instInvOneClass", "kind": "instance", "module": "Mathlib.RingTheory.PowerSeries.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.C_inv", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.X_inv", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.smul_inv", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.firstUnitCoeff", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.Inv_divided_by_X_pow_order", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.Inv_divided_by_X_pow_order_rightInv", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.Inv_divided_by_X_pow_order_leftInv", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Inverse", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "PowerSeries.Unit_of_divided_by_X_pow_order", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.isUnit_divided_by_X_pow_order", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.Unit_of_divided_by_X_pow_order_nonzero", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Inverse", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PowerSeries.Unit_of_divided_by_X_pow_order_zero", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Inverse", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PowerSeries.eq_divided_by_X_pow_order_Iff_Unit", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.map.isLocalHom", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.instIsLocalRing", "kind": "instance", "module": "Mathlib.RingTheory.PowerSeries.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.hasUnitMulPowIrreducibleFactorization", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.instUniqueFactorizationMonoid", "kind": "instance", "module": "Mathlib.RingTheory.PowerSeries.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.instIsDiscreteValuationRing", "kind": "instance", "module": "Mathlib.RingTheory.PowerSeries.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.isNoetherianRing", "kind": "instance", "module": "Mathlib.RingTheory.PowerSeries.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.maximalIdeal_eq_span_X", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Inverse", "is_tactic_proof": false, "tactics": ["have", "rw", "constructor", "rw", "exact", "intro", "rw", "have", "have", "rw", "apply", "apply", "rw", "sub_eq_zero,", "rfl", "rw", "apply", "rw"], "tactic_count": 18}
{"name": "PowerSeries.instNormalizationMonoid", "kind": "instance", "module": "Mathlib.RingTheory.PowerSeries.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.normUnit_X", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Inverse", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PowerSeries.X_eq_normalizeX", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Inverse", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PowerSeries.normalized_count_X_eq_of_coe", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Inverse", "is_tactic_proof": true, "tactics": ["apply", "simp", "rw", "emultiplicity_eq_count_normalizedFactors", "simp"], "tactic_count": 5}
{"name": "PowerSeries.ker_coeff_eq_max_ideal", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.residueFieldOfPowerSeries", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.Inverse", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.instNoZeroDivisors", "kind": "instance", "module": "Mathlib.RingTheory.PowerSeries.NoZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.instIsDomain", "kind": "instance", "module": "Mathlib.RingTheory.PowerSeries.NoZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.span_X_isPrime", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.NoZeroDivisors", "is_tactic_proof": false, "tactics": ["suffices", "rw", "exact", "apply", "intro", "rw"], "tactic_count": 6}
{"name": "PowerSeries.X_prime", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.NoZeroDivisors", "is_tactic_proof": true, "tactics": ["rw", "exact", "intro", "simpa"], "tactic_count": 4}
{"name": "PowerSeries.X_irreducible", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.NoZeroDivisors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.rescale_injective", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.NoZeroDivisors", "is_tactic_proof": true, "tactics": ["intro", "rw", "intro", "specialize", "rwa"], "tactic_count": 5}
{"name": "PowerSeries.exists_coeff_ne_zero_iff_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Order", "is_tactic_proof": true, "tactics": ["contrapose", "simp"], "tactic_count": 2}
{"name": "PowerSeries.order", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.order_zero", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.order_finite_iff_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Order", "is_tactic_proof": true, "tactics": ["simp", "split_ifs"], "tactic_count": 2}
{"name": "PowerSeries.order_eq_top", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Order", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "PowerSeries.coe_toNat_order", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Order", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PowerSeries.coeff_order", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Order", "is_tactic_proof": true, "tactics": ["classical", "simp", "generalize_proofs", "exact"], "tactic_count": 4}
{"name": "PowerSeries.order_le", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Order", "is_tactic_proof": true, "tactics": ["classical", "rw", "simpa", "exact"], "tactic_count": 4}
{"name": "PowerSeries.coeff_of_lt_order", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Order", "is_tactic_proof": true, "tactics": ["contrapose", "exact"], "tactic_count": 2}
{"name": "PowerSeries.coeff_of_lt_order_toNat", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Order", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "refine", "rwa"], "tactic_count": 4}
{"name": "PowerSeries.nat_le_order", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Order", "is_tactic_proof": true, "tactics": ["classical", "simp", "split_ifs", "simp", "simpa"], "tactic_count": 5}
{"name": "PowerSeries.le_order", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Order", "is_tactic_proof": true, "tactics": ["cases", "top", "coe", "convert", "simpa"], "tactic_count": 5}
{"name": "PowerSeries.order_eq_nat", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Order", "is_tactic_proof": true, "tactics": ["classical", "rcases", "simp", "simp"], "tactic_count": 4}
{"name": "PowerSeries.order_eq", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Order", "is_tactic_proof": true, "tactics": ["cases", "top", "coe"], "tactic_count": 3}
{"name": "PowerSeries.order_eq_order", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Order", "is_tactic_proof": true, "tactics": ["refine", "refine", "have", "have", "exact", "refine", "le_order", "rw", "exact"], "tactic_count": 9}
{"name": "PowerSeries.min_order_le_order_add", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Order", "is_tactic_proof": true, "tactics": ["refine", "simp"], "tactic_count": 2}
{"name": "_private.Mathlib.RingTheory.PowerSeries.Order.0.PowerSeries.order_add_of_order_ne.aux", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Order", "is_tactic_proof": false, "tactics": ["suffices", "rw", "exact", "rw", "constructor", "intro", "rw", "rw", "exact", "intro", "rw"], "tactic_count": 11}
{"name": "PowerSeries.order_add_of_order_ne", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Order", "is_tactic_proof": true, "tactics": ["refine", "rcases", "apply", "simpa"], "tactic_count": 4}
{"name": "PowerSeries.le_order_map", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.le_order_smul", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.le_order_mul", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Order", "is_tactic_proof": true, "tactics": ["apply", "intro", "rintro", "by_cases", "rw", "by_cases", "rw", "rw", "exfalso", "apply", "rw"], "tactic_count": 11}
{"name": "PowerSeries.le_order_pow", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Order", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "PowerSeries.le_order_prod", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Order", "is_tactic_proof": true, "tactics": ["induction", "empty", "cons"], "tactic_count": 3}
{"name": "PowerSeries.one_le_order_iff_constCoeff_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Order", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "apply", "simpa", "intro", "refine", "rw", "simp"], "tactic_count": 9}
{"name": "PowerSeries.order_ne_zero_iff_constCoeff_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Order", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PowerSeries.le_order_pow_of_constantCoeff_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Order", "is_tactic_proof": true, "tactics": ["refine", "simpa"], "tactic_count": 2}
{"name": "PowerSeries.order_monomial", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Order", "is_tactic_proof": true, "tactics": ["split_ifs", "rw", "rw", "constructor", "simp", "rwa", "simp", "rw", "exact"], "tactic_count": 9}
{"name": "PowerSeries.order_monomial_of_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Order", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "PowerSeries.coeff_mul_of_lt_order", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Order", "is_tactic_proof": true, "tactics": ["suffices", "rw", "apply", "intro", "refine", "rw", "norm_cast", "lia"], "tactic_count": 8}
{"name": "PowerSeries.coeff_mul_one_sub_of_lt_order", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Order", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PowerSeries.coeff_mul_prod_one_sub_of_lt_order", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Order", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "insert", "intro", "simp", "rw", "exact"], "tactic_count": 8}
{"name": "PowerSeries.order_neg", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Order", "is_tactic_proof": true, "tactics": ["by_contra", "have", "simp"], "tactic_count": 3}
{"name": "PowerSeries.divXPowOrder", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.coeff_divXPowOrder", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.divXPowOrder_zero", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Order", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "PowerSeries.constantCoeff_divXPowOrder", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Order", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PowerSeries.constantCoeff_divXPowOrder_eq_zero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Order", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "simp"], "tactic_count": 3}
{"name": "PowerSeries.X_pow_order_mul_divXPowOrder", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Order", "is_tactic_proof": true, "tactics": ["ext", "rw", "split_ifs", "simp", "push_neg", "rw"], "tactic_count": 6}
{"name": "PowerSeries.X_pow_order_dvd", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Order", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "PowerSeries.order_eq_emultiplicity_X", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Order", "is_tactic_proof": true, "tactics": ["classical", "rcases", "simp", "cases", "top", "coe", "have", "rw", "apply", "apply", "apply", "apply", "rw", "rintro", "have", "rw", "exact", "rw", "split_ifs", "simp", "rw", "simp"], "tactic_count": 22}
{"name": "PowerSeries.order_one", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Order", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "PowerSeries.order_zero_of_unit", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Order", "is_tactic_proof": true, "tactics": ["rintro", "apply", "rw", "exact"], "tactic_count": 4}
{"name": "PowerSeries.order_X", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Order", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "PowerSeries.order_X_pow", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Order", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "PowerSeries.divXPowOrder_X", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Order", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "PowerSeries.divXPowOrder_one", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Order", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "PowerSeries.order_mul", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Order", "is_tactic_proof": true, "tactics": ["apply", "by_cases", "rcases", "rw", "apply", "rw", "exact", "intro", "rcases", "exact", "rw", "rw"], "tactic_count": 12}
{"name": "PowerSeries.divXPowOrder_mul", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Order", "is_tactic_proof": true, "tactics": ["by_cases", "rcases", "apply", "calc", "rw", "simp", "rw"], "tactic_count": 7}
{"name": "PowerSeries.divXPowOrder_mul_divXPowOrder", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.orderHom", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.coe_orderHom", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.order_pow", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.order_prod", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.divXPowOrderHom", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.coe_divXPowOrderHom", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.divXPowOrder_pow", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.divXPowOrder_prod", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.order_toSubring", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Order", "is_tactic_proof": true, "tactics": ["refine", "refine", "exact"], "tactic_count": 3}
{"name": "PowerSeries.WithPiTopology.instTopologicalSpace", "kind": "instance", "module": "Mathlib.RingTheory.PowerSeries.PiTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.WithPiTopology.instT0Space", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.PiTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.WithPiTopology.instT2Space", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.PiTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.WithPiTopology.continuous_coeff", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.PiTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.WithPiTopology.continuous_constantCoeff", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.PiTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.WithPiTopology.tendsto_iff_coeff_tendsto", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.PiTopology", "is_tactic_proof": true, "tactics": ["rw", "apply", "intro", "simp", "apply", "congr", "ext", "ext"], "tactic_count": 8}
{"name": "PowerSeries.WithPiTopology.tendsto_trunc_atTop", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.PiTopology", "is_tactic_proof": true, "tactics": ["rw", "intro", "exact"], "tactic_count": 3}
{"name": "PowerSeries.WithPiTopology.denseRange_toPowerSeries", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.PiTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.WithPiTopology.instIsTopologicalSemiring", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.PiTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.WithPiTopology.instIsTopologicalRing", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.PiTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.WithPiTopology.hasSum_iff_hasSum_coeff", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.PiTopology", "is_tactic_proof": true, "tactics": ["simp_rw", "apply"], "tactic_count": 2}
{"name": "PowerSeries.WithPiTopology.summable_iff_summable_coeff", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.PiTopology", "is_tactic_proof": true, "tactics": ["simp_rw", "constructor", "rintro", "exact", "intro", "choose", "exact"], "tactic_count": 7}
{"name": "PowerSeries.WithPiTopology.summable_of_tendsto_order_atTop_nhds_top", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.PiTopology", "is_tactic_proof": true, "tactics": ["rcases", "apply", "rw", "intro", "simp_rw", "obtain", "refine", "simp_rw", "intro", "contrapose", "exact"], "tactic_count": 11}
{"name": "PowerSeries.WithPiTopology.summable_pow_of_constantCoeff_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.PiTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.WithPiTopology.tsum_pow_mul_one_sub_of_constantCoeff_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.PiTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.WithPiTopology.one_sub_mul_tsum_pow_of_constantCoeff_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.PiTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.WithPiTopology.summable_prod_of_tendsto_order_atTop_nhds_top", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.PiTopology", "is_tactic_proof": true, "tactics": ["rcases", "apply", "refine", "simp_rw", "obtain", "apply", "suffices", "intro", "contrapose", "obtain", "rw", "refine", "apply"], "tactic_count": 13}
{"name": "PowerSeries.WithPiTopology.multipliable_one_add_of_tendsto_order_atTop_nhds_top", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.PiTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.WithPiTopology.multipliable_one_sub_X_pow", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.PiTopology", "is_tactic_proof": true, "tactics": ["nontriviality", "simp_rw", "apply", "refine", "intro", "rw", "norm_cast", "exact"], "tactic_count": 8}
{"name": "PowerSeries.WithPiTopology.tprod_one_sub_X_pow_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.PiTopology", "is_tactic_proof": true, "tactics": ["by_contra", "obtain", "simp"], "tactic_count": 3}
{"name": "PowerSeries.WithPiTopology.instUniformSpace", "kind": "instance", "module": "Mathlib.RingTheory.PowerSeries.PiTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.WithPiTopology.uniformContinuous_coeff", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.PiTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.WithPiTopology.instCompleteSpace", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.PiTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.WithPiTopology.instIsUniformAddGroup", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.PiTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.WithPiTopology.continuous_C", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.PiTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.WithPiTopology.isTopologicallyNilpotent_of_constantCoeff_isNilpotent", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.PiTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.WithPiTopology.isTopologicallyNilpotent_of_constantCoeff_zero", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.PiTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.WithPiTopology.isTopologicallyNilpotent_iff_constantCoeff_isNilpotent", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.PiTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.hasSum_of_monomials_self", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.PiTopology", "is_tactic_proof": true, "tactics": ["rw", "convert", "simp", "congr", "all_goals"], "tactic_count": 5}
{"name": "PowerSeries.as_tsum", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.PiTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.IsRestricted", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.Restricted", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.IsRestricted.isRestricted_iff", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Restricted", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PowerSeries.IsRestricted.isRestricted_iff_abs", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Restricted", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PowerSeries.IsRestricted.zero", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Restricted", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PowerSeries.IsRestricted.one", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Restricted", "is_tactic_proof": true, "tactics": ["simp", "refine", "split", "lia", "simpa"], "tactic_count": 5}
{"name": "PowerSeries.IsRestricted.monomial", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Restricted", "is_tactic_proof": true, "tactics": ["simp", "refine", "split", "lia", "simpa"], "tactic_count": 5}
{"name": "PowerSeries.IsRestricted.C", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Restricted", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "PowerSeries.IsRestricted.add", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Restricted", "is_tactic_proof": true, "tactics": ["simp", "intro", "obtain", "obtain", "simp", "refine", "calc"], "tactic_count": 7}
{"name": "PowerSeries.IsRestricted.neg", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Restricted", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "PowerSeries.IsRestricted.smul", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Restricted", "is_tactic_proof": true, "tactics": ["simp_rw", "intro", "obtain", "refine", "calc"], "tactic_count": 5}
{"name": "PowerSeries.IsRestricted.convergenceSet", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.Restricted", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.IsRestricted.convergenceSet_BddAbove", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Restricted", "is_tactic_proof": true, "tactics": ["simp_rw", "obtain", "rw", "use", "simp", "intro", "rcases", "right", "apply", "simp", "exact", "left", "calc"], "tactic_count": 13}
{"name": "PowerSeries.IsRestricted.mul", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Restricted", "is_tactic_proof": false, "tactics": ["obtain", "obtain", "simp", "simp", "intro", "obtain", "obtain", "refine", "obtain", "exists_norm_finset_sum_le", "obtain", "calc", "grw", "rw", "grind", "have", "rcases", "calc", "grw", "gcongr", "exact", "rw", "bound", "calc", "grw", "gcongr", "exact", "rw", "bound"], "tactic_count": 29}
{"name": "PowerSeries.largeSchroderSeries", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.Schroder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.coeff_largeSchroderSeries", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Schroder", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PowerSeries.constantCoeff_largeSchroderSeries", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Schroder", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PowerSeries.coeff_X_mul_largeSchroderSeries", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Schroder", "is_tactic_proof": false, "tactics": ["simp", "succ_eq_add_one]", "simp", "nonpos_iff_eq_zero]", "rintro", "simp_all"], "tactic_count": 6}
{"name": "PowerSeries.coeff_X_mul_largeSchroderSeriesSeries_sq", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Schroder", "is_tactic_proof": true, "tactics": ["rw", "rw", "simp", "have", "apply", "intro", "simp_all", "split", "simp_all", "simp", "simp_all", "constantCoeff_largeSchroderSeries,", "rw", "simp", "have", "apply", "intros", "have", "rw", "rw", "grind"], "tactic_count": 21}
{"name": "PowerSeries.largeSchroderSeries_eq_one_add_X_mul_largeSchroderSeries_add_X_mul_largeSchroderSeries_sq", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Schroder", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "aesop", "have", "simp", "rw", "show", "simp", "rw"], "tactic_count": 9}
{"name": "PowerSeries.HasSubst", "kind": "abbrev", "module": "Mathlib.RingTheory.PowerSeries.Substitution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.hasSubst_iff", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Substitution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.HasSubst.const", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Substitution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.hasSubst_iff_hasEval_of_discreteTopology", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PowerSeries.HasSubst.hasEval", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Substitution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.HasSubst.of_constantCoeff_zero", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PowerSeries.HasSubst.of_constantCoeff_zero'", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Substitution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.HasSubst.X", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PowerSeries.HasSubst.X'", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Substitution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.HasSubst.X_pow", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Substitution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.HasSubst.monomial", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["classical", "apply", "rw"], "tactic_count": 3}
{"name": "PowerSeries.HasSubst.monomial'", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Substitution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.HasSubst.zero", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "PowerSeries.HasSubst.zero'", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Substitution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.HasSubst.add", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Substitution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.HasSubst.mul_left", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "PowerSeries.HasSubst.mul_right", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "PowerSeries.HasSubst.smul", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Substitution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.HasSubst.ideal", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.Substitution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.HasSubst.smul'", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "PowerSeries.HasSubst.smul_X", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Substitution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.HasSubst.smul_X'", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Substitution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.subst", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.Substitution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.substAlgHom", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.Substitution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.coe_substAlgHom", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Substitution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.substAlgHom_eq_aeval", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["ext1", "simpa"], "tactic_count": 2}
{"name": "PowerSeries.subst_add", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PowerSeries.subst_pow", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PowerSeries.subst_mul", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PowerSeries.subst_smul", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PowerSeries.coeff_subst_finite", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Substitution", "is_tactic_proof": false, "tactics": ["convert", "rw", "apply", "rw", "ext", "simp"], "tactic_count": 6}
{"name": "PowerSeries.coeff_subst_finite'", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Substitution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.coeff_subst", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Substitution", "is_tactic_proof": false, "tactics": ["rw", "finsum_comp_equiv", "apply", "intro", "congr"], "tactic_count": 5}
{"name": "PowerSeries.coeff_subst'", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PowerSeries.constantCoeff_subst", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PowerSeries.constantCoeff_subst_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["rw", "intro", "by_cases", "simp", "simp"], "tactic_count": 5}
{"name": "PowerSeries.map_algebraMap_eq_subst_X", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Substitution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.toPowerSeries_toMvPowerSeries", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Substitution", "is_tactic_proof": false, "tactics": ["suffices", "rw", "apply", "apply", "simp"], "tactic_count": 5}
{"name": "PowerSeries.substAlgHom_coe", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Substitution", "is_tactic_proof": false, "tactics": ["rw", "apply", "apply", "simp"], "tactic_count": 4}
{"name": "PowerSeries.substAlgHom_X", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PowerSeries.subst_coe", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PowerSeries.subst_X", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PowerSeries.map_subst", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["ext", "have", "rw", "intro", "simp"], "tactic_count": 5}
{"name": "PowerSeries.le_weightedOrder_subst", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["refine", "simp", "intro", "trans", "exact", "simp"], "tactic_count": 6}
{"name": "PowerSeries.le_order_subst", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["refine", "simp"], "tactic_count": 2}
{"name": "PowerSeries.le_order_subst_left", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Substitution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.le_order_subst_right", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Substitution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.le_order_subst_left'", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["conv_rhs", "exact"], "tactic_count": 2}
{"name": "PowerSeries.le_order_subst_right'", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "PowerSeries.HasSubst.comp", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Substitution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.substAlgHom_comp_substAlgHom", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Substitution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.substAlgHom_comp_substAlgHom_apply", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Substitution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.subst_comp_subst", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "PowerSeries.subst_comp_subst_apply", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Substitution", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPowerSeries.rescaleUnit", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Substitution", "is_tactic_proof": true, "tactics": ["ext", "rw", "simp"], "tactic_count": 3}
{"name": "_private.Mathlib.RingTheory.PowerSeries.Trunc.0.PowerSeries.trunc_aux", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.Trunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.PowerSeries.Trunc.0.PowerSeries.coeff_trunc_aux", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Trunc", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PowerSeries.trunc", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.Trunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.trunc_apply", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Trunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.coeff_trunc", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Trunc", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PowerSeries.trunc_one", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Trunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.trunc_C", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Trunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.trunc_succ", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Trunc", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PowerSeries.natDegree_trunc_lt", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Trunc", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PowerSeries.trunc_zero'", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Trunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.degree_trunc_lt", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Trunc", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PowerSeries.eval₂_trunc_eq_sum_range", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Trunc", "is_tactic_proof": true, "tactics": ["cases", "zero", "succ", "have", "rw", "apply", "intro", "rw", "congr", "rw"], "tactic_count": 10}
{"name": "PowerSeries.trunc_X", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Trunc", "is_tactic_proof": true, "tactics": ["ext", "rw", "split_ifs", "rw", "rw", "rw", "intro", "apply", "rw", "exact"], "tactic_count": 10}
{"name": "PowerSeries.trunc_X_of", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Trunc", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "PowerSeries.trunc_one_left", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Trunc", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "PowerSeries.trunc_one_X", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Trunc", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PowerSeries.trunc_C_mul", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Trunc", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "PowerSeries.trunc_mul_C", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Trunc", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "PowerSeries.eq_shift_mul_X_pow_add_trunc", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Trunc", "is_tactic_proof": true, "tactics": ["ext", "rw", "simp_rw", "simp"], "tactic_count": 4}
{"name": "PowerSeries.eq_X_pow_mul_shift_add_trunc", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Trunc", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PowerSeries.monomial_eq_C_mul_X_pow", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Trunc", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "PowerSeries.trunc_X_pow_self_mul", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Trunc", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "PowerSeries.trunc_trunc", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Trunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.trunc_trunc_mul", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Trunc", "is_tactic_proof": true, "tactics": ["ext", "rw", "split_ifs", "rw", "intro", "have", "rw", "rfl"], "tactic_count": 8}
{"name": "PowerSeries.trunc_mul_trunc", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Trunc", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PowerSeries.trunc_trunc_mul_trunc", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Trunc", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PowerSeries.trunc_trunc_pow", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Trunc", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw"], "tactic_count": 4}
{"name": "PowerSeries.trunc_coe_eq_self", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Trunc", "is_tactic_proof": true, "tactics": ["rw", "ext", "rw", "split", "rfl", "rw", "rw", "exact"], "tactic_count": 8}
{"name": "PowerSeries.coeff_coe_trunc_of_lt", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Trunc", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "PowerSeries.coeff_mul_eq_coeff_trunc_mul_trunc₂", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Trunc", "is_tactic_proof": true, "tactics": ["symm", "rw", "trunc_trunc_mul_trunc,"], "tactic_count": 3}
{"name": "PowerSeries.coeff_mul_eq_coeff_trunc_mul_trunc", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Trunc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.trunc_sub", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Trunc", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "PowerSeries.trunc_map", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.Trunc", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "PowerSeries.IsWeierstrassDivision", "kind": "abbrev", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.isWeierstrassDivisionAt_zero", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": true, "tactics": ["constructor", "rw", "exact", "simp"], "tactic_count": 4}
{"name": "PowerSeries.IsWeierstrassDivisionAt.coeff_f_sub_r_mem", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": true, "tactics": ["replace", "rw", "rw", "refine", "have", "rwa"], "tactic_count": 6}
{"name": "PowerSeries.IsWeierstrassDivisionAt.add", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.IsWeierstrassDivisionAt.smul", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.IsWeierstrassDivisorAt", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.IsWeierstrassDivisor", "kind": "abbrev", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.IsWeierstrassDivisor.of_map_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": true, "tactics": ["rw", "have", "contrapose", "rwa"], "tactic_count": 4}
{"name": "Polynomial.IsDistinguishedAt.isWeierstrassDivisorAt", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": false, "tactics": ["have", "congr", "simp"], "tactic_count": 3}
{"name": "Polynomial.IsDistinguishedAt.isWeierstrassDivisorAt'", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": true, "tactics": ["rcases", "have", "exact", "exact"], "tactic_count": 4}
{"name": "_private.Mathlib.RingTheory.PowerSeries.WeierstrassPreparation.0.PowerSeries.coeff_trunc_order_mem", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": true, "tactics": ["rw", "split_ifs", "simpa", "exact"], "tactic_count": 4}
{"name": "PowerSeries.IsWeierstrassDivisorAt.isUnit_shift", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "PowerSeries.IsWeierstrassDivisorAt.seq", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.IsWeierstrassDivisorAt.coeff_seq_mem", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "set", "set", "set", "have", "set", "set", "set", "have", "trans", "simp_rw", "simp_rw", "rw", "nth_rw", "rw", "ring", "rw", "refine", "refine", "rw", "exact"], "tactic_count": 24}
{"name": "PowerSeries.IsWeierstrassDivisorAt.coeff_seq_succ_sub_seq_mem", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "PowerSeries.IsWeierstrassDivisorAt.seq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.IsWeierstrassDivisorAt.seq_one", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "PowerSeries.IsWeierstrassDivisorAt.divCoeff", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.IsWeierstrassDivisorAt.div", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.IsWeierstrassDivisorAt.coeff_div", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PowerSeries.IsWeierstrassDivisorAt.coeff_div_sub_seq_mem", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "PowerSeries.IsWeierstrassDivisorAt.mod", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.IsWeierstrassDivisorAt.isWeierstrassDivisionAt_div_mod", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": true, "tactics": ["rcases", "have", "rw", "exact", "constructor", "exact", "rw", "ext", "rw", "split_ifs", "rfl", "refine", "rw", "show", "exact", "coeff_mul_mem_ideal_of_coeff_right_mem_ideal"], "tactic_count": 16}
{"name": "PowerSeries.IsWeierstrassDivisorAt.eq_zero_of_mul_eq", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": false, "tactics": ["suffices", "have", "ext", "refine", "rw", "exact", "rw", "exact", "intro", "induction", "zero", "succ", "rw", "have", "rcases", "rw", "refine", "rw", "refine", "simp_rw", "simp_rw", "rw", "replace", "rw", "intro", "rw", "refine", "rw", "refine", "rw", "refine", "simp_rw"], "tactic_count": 32}
{"name": "PowerSeries.IsWeierstrassDivisorAt.eq_of_mul_add_eq_mul_add", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": false, "tactics": ["replace", "rw", "rw", "ring", "have", "simp_rw", "exact"], "tactic_count": 7}
{"name": "PowerSeries.IsWeierstrassDivisorAt.div_add", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": true, "tactics": ["have", "have", "exact"], "tactic_count": 3}
{"name": "PowerSeries.IsWeierstrassDivisorAt.div_smul", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": true, "tactics": ["have", "have", "exact"], "tactic_count": 3}
{"name": "PowerSeries.IsWeierstrassDivisorAt.div_zero", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "PowerSeries.IsWeierstrassDivisorAt.mod_add", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": true, "tactics": ["have", "have", "exact"], "tactic_count": 3}
{"name": "PowerSeries.IsWeierstrassDivisorAt.mod_smul", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": true, "tactics": ["have", "have", "exact"], "tactic_count": 3}
{"name": "PowerSeries.IsWeierstrassDivisorAt.mod_zero", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "PowerSeries.IsWeierstrassDivisorAt.mod'", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.IsWeierstrassDivisorAt.mod'_mk_eq_mod", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.IsWeierstrassDivisorAt.div_coe_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "PowerSeries.IsWeierstrassDivisorAt.mod_coe_eq_self", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "PowerSeries.IsWeierstrassDivisorAt.mk_mod'_eq_self", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": true, "tactics": ["obtain", "rw", "use", "rw"], "tactic_count": 4}
{"name": "Polynomial.IsDistinguishedAt.algEquivQuotient", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.exists_isWeierstrassDivision", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.weierstrassDiv", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.weierstrassMod", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.term_/ʷ_", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries._aux_Mathlib_RingTheory_PowerSeries_WeierstrassPreparation___macroRules_PowerSeries_term_/ʷ__1", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries._aux_Mathlib_RingTheory_PowerSeries_WeierstrassPreparation___unexpand_PowerSeries_weierstrassDiv_1", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.term_%ʷ_", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries._aux_Mathlib_RingTheory_PowerSeries_WeierstrassPreparation___macroRules_PowerSeries_term_%ʷ__1", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries._aux_Mathlib_RingTheory_PowerSeries_WeierstrassPreparation___unexpand_PowerSeries_weierstrassMod_1", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.weierstrassDiv_zero_right", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PowerSeries.weierstrassMod_zero_right", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PowerSeries.degree_weierstrassMod_lt", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": true, "tactics": ["rw", "split_ifs", "exact", "nontriviality", "rw", "exact"], "tactic_count": 6}
{"name": "PowerSeries.isWeierstrassDivision_weierstrassDiv_weierstrassMod", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "PowerSeries.eq_mul_weierstrassDiv_add_weierstrassMod", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "PowerSeries.IsWeierstrassDivision.elim", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.IsWeierstrassDivision.eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.IsWeierstrassDivision.unique", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.add_weierstrassDiv", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": true, "tactics": ["simp_rw", "split_ifs"], "tactic_count": 2}
{"name": "PowerSeries.smul_weierstrassDiv", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": true, "tactics": ["simp_rw", "split_ifs"], "tactic_count": 2}
{"name": "PowerSeries.weierstrassDiv_zero_left", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": true, "tactics": ["simp_rw", "split_ifs"], "tactic_count": 2}
{"name": "PowerSeries.add_weierstrassMod", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": true, "tactics": ["simp_rw", "split_ifs"], "tactic_count": 2}
{"name": "PowerSeries.smul_weierstrassMod", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": true, "tactics": ["simp_rw", "split_ifs"], "tactic_count": 2}
{"name": "PowerSeries.weierstrassMod_zero_left", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": true, "tactics": ["simp_rw", "split_ifs"], "tactic_count": 2}
{"name": "PowerSeries.IsWeierstrassFactorization", "kind": "abbrev", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.IsWeierstrassFactorizationAt.map_ne_zero_of_ne_top", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": true, "tactics": ["have", "rw", "exact_mod_cast"], "tactic_count": 3}
{"name": "PowerSeries.IsWeierstrassFactorizationAt.degree_eq_coe_lift_order_map_of_ne_top", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": true, "tactics": ["refine", "contrapose", "exact"], "tactic_count": 3}
{"name": "PowerSeries.IsWeierstrassFactorizationAt.natDegree_eq_toNat_order_map_of_ne_top", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "PowerSeries.IsWeierstrassFactorizationAt.algEquivQuotient", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.IsWeierstrassFactorizationAt.algEquivQuotient_symm_apply", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PowerSeries.IsWeierstrassFactorizationAt.mul", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.IsWeierstrassFactorizationAt.smul", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact", "simp"], "tactic_count": 4}
{"name": "PowerSeries.IsWeierstrassFactorization.map_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.IsWeierstrassFactorization.degree_eq_coe_lift_order_map", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.IsWeierstrassFactorization.natDegree_eq_toNat_order_map", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.IsWeierstrassDivision.isUnit_of_map_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": true, "tactics": ["obtain", "set", "replace", "simp_rw", "rw", "rw", "coeff_map,", "exact", "rw", "rw", "rw", "refine", "contrapose", "rwa"], "tactic_count": 14}
{"name": "PowerSeries.IsWeierstrassDivision.isWeierstrassFactorization", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.IsWeierstrassFactorization.isWeierstrassDivision", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": true, "tactics": ["set", "constructor", "refine", "simp_rw", "rw", "simp_rw", "add_sub_cancel]"], "tactic_count": 7}
{"name": "PowerSeries.IsWeierstrassFactorization.elim", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact"], "tactic_count": 3}
{"name": "PowerSeries.exists_isWeierstrassFactorization", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "PowerSeries.weierstrassDistinguished", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.weierstrassUnit", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.isWeierstrassFactorization_weierstrassDistinguished_weierstrassUnit", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.algEquivQuotientWeierstrassDistinguished", "kind": "abbrev", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.isDistinguishedAt_weierstrassDistinguished", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.isUnit_weierstrassUnit", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.eq_weierstrassDistinguished_mul_weierstrassUnit", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.IsWeierstrassFactorization.unique", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.weierstrassDistinguished_mul", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": true, "tactics": ["have", "have", "have", "exact"], "tactic_count": 4}
{"name": "PowerSeries.weierstrassUnit_mul", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": true, "tactics": ["have", "have", "have", "exact"], "tactic_count": 4}
{"name": "PowerSeries.weierstrassDistinguished_smul", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": false, "tactics": ["have", "g.isWeierstrassFactorization_weierstrassDistinguished_weierstrassUnit", "have", "have", "exact"], "tactic_count": 5}
{"name": "PowerSeries.weierstrassUnit_smul", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WeierstrassPreparation", "is_tactic_proof": false, "tactics": ["have", "g.isWeierstrassFactorization_weierstrassDistinguished_weierstrassUnit", "have", "have", "exact"], "tactic_count": 5}
{"name": "PowerSeries.invUnitsSub", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.WellKnown", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.coeff_invUnitsSub", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WellKnown", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.constantCoeff_invUnitsSub", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WellKnown", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PowerSeries.invUnitsSub_mul_X", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WellKnown", "is_tactic_proof": true, "tactics": ["ext", "simp", "simp"], "tactic_count": 3}
{"name": "PowerSeries.invUnitsSub_mul_sub", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WellKnown", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PowerSeries.map_invUnitsSub", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WellKnown", "is_tactic_proof": true, "tactics": ["ext", "simp", "rfl"], "tactic_count": 3}
{"name": "PowerSeries.mk_one_mul_one_sub_eq_one", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WellKnown", "is_tactic_proof": true, "tactics": ["rw", "intro", "cases", "zero", "succ"], "tactic_count": 5}
{"name": "PowerSeries.mk_one_pow_eq_mk_choose_add", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WellKnown", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "ext", "rw", "simp_rw", "norm_cast", "rw"], "tactic_count": 8}
{"name": "PowerSeries.invOneSubPow", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.WellKnown", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.invOneSubPow_zero", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WellKnown", "is_tactic_proof": true, "tactics": ["delta", "simp"], "tactic_count": 2}
{"name": "PowerSeries.invOneSubPow_val_eq_mk_sub_one_add_choose_of_pos", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WellKnown", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PowerSeries.invOneSubPow_val_succ_eq_mk_add_choose", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WellKnown", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.invOneSubPow_val_one_eq_invUnitSub_one", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WellKnown", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PowerSeries.invOneSubPow_eq_inv_one_sub_pow", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WellKnown", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "exact", "rw", "exact"], "tactic_count": 7}
{"name": "PowerSeries.invOneSubPow_inv_eq_one_sub_pow", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WellKnown", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "PowerSeries.invOneSubPow_inv_zero_eq_one", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WellKnown", "is_tactic_proof": true, "tactics": ["delta", "simp"], "tactic_count": 2}
{"name": "PowerSeries.mk_add_choose_mul_one_sub_pow_eq_one", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WellKnown", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.invOneSubPow_add", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WellKnown", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "PowerSeries.one_sub_pow_mul_invOneSubPow_val_add_eq_invOneSubPow_val", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WellKnown", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PowerSeries.one_sub_pow_add_mul_invOneSubPow_val_eq_one_sub_pow", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WellKnown", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PowerSeries.sin", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.WellKnown", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.cos", "kind": "definition", "module": "Mathlib.RingTheory.PowerSeries.WellKnown", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PowerSeries.map_sin", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WellKnown", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "PowerSeries.map_cos", "kind": "theorem", "module": "Mathlib.RingTheory.PowerSeries.WellKnown", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "mul_eq_mul_prime_prod", "kind": "theorem", "module": "Mathlib.RingTheory.Prime", "is_tactic_proof": true, "tactics": ["induction", "empty", "insert", "rw", "have", "rcases", "have", "have", "obtain", "rw", "exact", "simp", "rw", "exact", "simp"], "tactic_count": 15}
{"name": "mul_eq_mul_prime_pow", "kind": "theorem", "module": "Mathlib.RingTheory.Prime", "is_tactic_proof": false, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "Prime.neg", "kind": "theorem", "module": "Mathlib.RingTheory.Prime", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Prime.abs", "kind": "theorem", "module": "Mathlib.RingTheory.Prime", "is_tactic_proof": true, "tactics": ["obtain", "exact", "exact"], "tactic_count": 3}
{"name": "bot_isPrincipal", "kind": "instance", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "top_isPrincipal", "kind": "instance", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBezout.of_isPrincipalIdealRing", "kind": "instance", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DivisionSemiring.isPrincipalIdealRing", "kind": "instance", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.span_singleton_generator", "kind": "theorem", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.IsPrincipal.generator_mem", "kind": "theorem", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": true, "tactics": ["have", "convert", "exact"], "tactic_count": 3}
{"name": "Submodule.IsPrincipal.mem_iff_eq_smul_generator", "kind": "theorem", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Submodule.IsPrincipal.eq_bot_iff_generator_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submodule.IsPrincipal.fg", "kind": "theorem", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrincipalIdealRing.isNoetherianRing", "kind": "instance", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrincipalIdealRing.of_isNoetherianRing_of_isBezout", "kind": "instance", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.IsPrincipal.associated_generator_span_self", "kind": "theorem", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Submodule.IsPrincipal.mem_iff_generator_dvd", "kind": "theorem", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.IsPrincipal.prime_generator_of_isPrime", "kind": "theorem", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.IsPrincipal.generator_map_dvd_of_mem", "kind": "theorem", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Submodule.IsPrincipal.generator_submoduleImage_dvd_of_mem", "kind": "theorem", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Submodule.IsPrincipal.dvd_generator_span_iff", "kind": "theorem", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBezout.span_pair_isPrincipal", "kind": "instance", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "IsBezout.gcd", "kind": "definition", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBezout.span_gcd", "kind": "theorem", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBezout.gcd_dvd_left", "kind": "theorem", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBezout.gcd_dvd_right", "kind": "theorem", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBezout.dvd_gcd", "kind": "theorem", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "IsBezout.gcd_eq_sum", "kind": "theorem", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRelPrime.isCoprime", "kind": "theorem", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": false, "tactics": ["rw", "span_gcd,", "exact"], "tactic_count": 3}
{"name": "isRelPrime_iff_isCoprime", "kind": "theorem", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBezout.toGCDDomain", "kind": "definition", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBezout.nonemptyGCDMonoid", "kind": "instance", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "IsBezout.associated_gcd_gcd", "kind": "theorem", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrime.to_maximal_ideal", "kind": "theorem", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mod_mem_iff", "kind": "theorem", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanDomain.to_principal_ideal_domain", "kind": "instance", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsField.isPrincipalIdealRing", "kind": "theorem", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrincipalIdealRing.isMaximal_of_irreducible", "kind": "theorem", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrincipalIdealRing.factors", "kind": "definition", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrincipalIdealRing.factors_spec", "kind": "theorem", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": true, "tactics": ["unfold", "exact"], "tactic_count": 2}
{"name": "PrincipalIdealRing.ne_zero_of_mem_factors", "kind": "theorem", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrincipalIdealRing.mem_submonoid_of_factors_subset_of_units_subset", "kind": "theorem", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": true, "tactics": ["rcases", "rw", "exact"], "tactic_count": 3}
{"name": "PrincipalIdealRing.ringHom_mem_submonoid_of_factors_subset_of_units_subset", "kind": "theorem", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrincipalIdealRing.to_uniqueFactorizationMonoid", "kind": "instance", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.IsPrincipal.map", "kind": "theorem", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.IsPrincipal.of_comap", "kind": "theorem", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Submodule.IsPrincipal.map_ringHom", "kind": "theorem", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.IsPrincipal.of_comap", "kind": "theorem", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsPrincipalIdealRing.of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isPrincipalIdealRing_prod_iff", "kind": "theorem", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isPrincipalIdealRing_pi_iff", "kind": "theorem", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCoprime_of_dvd", "kind": "theorem", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dvd_or_isCoprime", "kind": "theorem", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Irreducible.coprime_iff_not_dvd", "kind": "theorem", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Irreducible.dvd_iff_not_isCoprime", "kind": "theorem", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Irreducible.coprime_pow_of_not_dvd", "kind": "theorem", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Irreducible.isCoprime_or_dvd", "kind": "theorem", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBezout.span_gcd_eq_span_gcd", "kind": "theorem", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": true, "tactics": ["rw", "exact", "associated_of_dvd_dvd"], "tactic_count": 3}
{"name": "span_gcd", "kind": "theorem", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "gcd_dvd_iff_exists", "kind": "theorem", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "exists_gcd_eq_mul_add_mul", "kind": "theorem", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "gcd_isUnit_iff", "kind": "theorem", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Prime.coprime_iff_not_dvd", "kind": "theorem", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_associated_pow_of_mul_eq_pow'", "kind": "theorem", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": true, "tactics": ["classical", "letI", "exact"], "tactic_count": 3}
{"name": "exists_associated_pow_of_associated_pow_mul", "kind": "theorem", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": true, "tactics": ["obtain", "exact", "exists_associated_pow_of_mul_eq_pow"], "tactic_count": 3}
{"name": "isCoprime_of_irreducible_dvd", "kind": "theorem", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCoprime_of_prime_dvd", "kind": "theorem", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.nonPrincipals", "kind": "abbrev", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.nonPrincipals_eq_empty_iff", "kind": "theorem", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Ideal.nonPrincipals_zorn", "kind": "theorem", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": true, "tactics": ["by_cases", "obtain", "refine", "have", "obtain", "have", "exact", "simpa"], "tactic_count": 8}
{"name": "Ideal.exists_maximal_not_isPrincipal", "kind": "theorem", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nonPrincipals", "kind": "definition", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nonPrincipals_def", "kind": "theorem", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nonPrincipals_eq_empty_iff", "kind": "theorem", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "nonPrincipals_zorn", "kind": "theorem", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": true, "tactics": ["refine", "rintro", "have", "obtain", "have", "specialize", "rw", "exact"], "tactic_count": 8}
{"name": "span_singleton_inf_span_singleton", "kind": "theorem", "module": "Mathlib.RingTheory.PrincipalIdealDomain", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "simp", "exact"], "tactic_count": 5}
{"name": "Ideal.isOka_isPrincipal", "kind": "theorem", "module": "Mathlib.RingTheory.PrincipalIdealDomainOfPrime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrincipalIdealRing.of_prime", "kind": "theorem", "module": "Mathlib.RingTheory.PrincipalIdealDomainOfPrime", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "IsPrincipalIdealRing.of_prime_ne_bot", "kind": "theorem", "module": "Mathlib.RingTheory.PrincipalIdealDomainOfPrime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.QuasiFinite.instIsArtinianRingFiber", "kind": "instance", "module": "Mathlib.RingTheory.QuasiFinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.QuasiFinite.finite_comap_preimage_singleton", "kind": "theorem", "module": "Mathlib.RingTheory.QuasiFinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.QuasiFinite.finite_primesOver", "kind": "theorem", "module": "Mathlib.RingTheory.QuasiFinite.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "refine", "exact", "convert", "by_contra", "obtain", "exact"], "tactic_count": 7}
{"name": "Algebra.QuasiFinite.finite_comap_preimage", "kind": "theorem", "module": "Mathlib.RingTheory.QuasiFinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.QuasiFinite.isDiscrete_comap_preimage_singleton", "kind": "theorem", "module": "Mathlib.RingTheory.QuasiFinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.QuasiFinite.isDiscrete_comap_preimage", "kind": "theorem", "module": "Mathlib.RingTheory.QuasiFinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.QuasiFinite.instOfFinite", "kind": "instance", "module": "Mathlib.RingTheory.QuasiFinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.QuasiFinite.baseChange", "kind": "instance", "module": "Mathlib.RingTheory.QuasiFinite.Basic", "is_tactic_proof": true, "tactics": ["refine", "let", "let", "exact"], "tactic_count": 4}
{"name": "_private.Mathlib.RingTheory.QuasiFinite.Basic.0.Algebra.QuasiFinite.finite_of_isArtinianRing_of_isLocalRing", "kind": "theorem", "module": "Mathlib.RingTheory.QuasiFinite.Basic", "is_tactic_proof": false, "tactics": ["let", "have", "have", "refine", "refine", "rw", "exact", "rw", "exact"], "tactic_count": 9}
{"name": "Module.Finite.of_quasiFinite", "kind": "theorem", "module": "Mathlib.RingTheory.QuasiFinite.Basic", "is_tactic_proof": true, "tactics": ["classical", "let", "have", "let", "have", "have", "have", "finite_of_isArtinianRing_of_isLocalRing", "exact"], "tactic_count": 9}
{"name": "Algebra.QuasiFinite.iff_of_isArtinianRing", "kind": "theorem", "module": "Mathlib.RingTheory.QuasiFinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.QuasiFinite.trans", "kind": "theorem", "module": "Mathlib.RingTheory.QuasiFinite.Basic", "is_tactic_proof": true, "tactics": ["refine", "have", "have", "let", "let", "let", "exact"], "tactic_count": 7}
{"name": "Algebra.QuasiFinite.of_surjective_algHom", "kind": "theorem", "module": "Mathlib.RingTheory.QuasiFinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.QuasiFinite.instQuotientIdeal", "kind": "instance", "module": "Mathlib.RingTheory.QuasiFinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.QuasiFinite.of_isLocalization", "kind": "theorem", "module": "Mathlib.RingTheory.QuasiFinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.QuasiFinite.instLocalization", "kind": "instance", "module": "Mathlib.RingTheory.QuasiFinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.QuasiFinite.instOfIsFractionRing", "kind": "instance", "module": "Mathlib.RingTheory.QuasiFinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.QuasiFinite.instResidueField", "kind": "instance", "module": "Mathlib.RingTheory.QuasiFinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.QuasiFinite.of_restrictScalars", "kind": "theorem", "module": "Mathlib.RingTheory.QuasiFinite.Basic", "is_tactic_proof": true, "tactics": ["refine", "let", "have", "rw", "rintro", "exact", "have", "exact"], "tactic_count": 8}
{"name": "Algebra.QuasiFinite.discreteTopology_primeSpectrum", "kind": "theorem", "module": "Mathlib.RingTheory.QuasiFinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.QuasiFinite.finite_primeSpectrum", "kind": "theorem", "module": "Mathlib.RingTheory.QuasiFinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.QuasiFinite.of_forall_exists_mul_mem_range", "kind": "theorem", "module": "Mathlib.RingTheory.QuasiFinite.Basic", "is_tactic_proof": false, "tactics": ["let", "suffices", "intro", "obtain", "refine", "simpa"], "tactic_count": 6}
{"name": "Algebra.QuasiFinite.eq_of_le_of_under_eq", "kind": "theorem", "module": "Mathlib.RingTheory.QuasiFinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.QuasiFinite.instFiniteResidueField", "kind": "instance", "module": "Mathlib.RingTheory.QuasiFinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.QuasiFinite.iff_finite_comap_preimage_singleton", "kind": "theorem", "module": "Mathlib.RingTheory.QuasiFinite.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "have", "have", "exact"], "tactic_count": 5}
{"name": "Algebra.QuasiFinite.iff_finite_primesOver", "kind": "theorem", "module": "Mathlib.RingTheory.QuasiFinite.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "congr", "ext", "simp"], "tactic_count": 6}
{"name": "Algebra.QuasiFinite.of_isIntegral_of_finiteType", "kind": "theorem", "module": "Mathlib.RingTheory.QuasiFinite.Basic", "is_tactic_proof": true, "tactics": ["let", "let", "let", "let", "let", "let", "let", "have", "have", "have", "have", "refine", "obtain", "have", "convert", "rw", "simp", "trans", "simp", "simp", "ring", "have", "have", "have", "have", "exact"], "tactic_count": 26}
{"name": "Algebra.QuasiFiniteAt", "kind": "abbrev", "module": "Mathlib.RingTheory.QuasiFinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.QuasiFiniteAt.baseChange", "kind": "theorem", "module": "Mathlib.RingTheory.QuasiFinite.Basic", "is_tactic_proof": false, "tactics": ["let", "simp", "let", "have", "replace", "refine", "obtain", "refine", "rw", "exact"], "tactic_count": 10}
{"name": "Algebra.QuasiFiniteAt.of_surjectiveOnStalks", "kind": "theorem", "module": "Mathlib.RingTheory.QuasiFinite.Basic", "is_tactic_proof": true, "tactics": ["subst", "refine", "simp"], "tactic_count": 3}
{"name": "Algebra.QuasiFiniteAt.of_surjectiveOnStalks_of_liesOver", "kind": "theorem", "module": "Mathlib.RingTheory.QuasiFinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.QuasiFiniteAt.comap_algEquiv", "kind": "instance", "module": "Mathlib.RingTheory.QuasiFinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.QuasiFiniteAt.of_le", "kind": "theorem", "module": "Mathlib.RingTheory.QuasiFinite.Basic", "is_tactic_proof": false, "tactics": ["let", "simp", "exact", "refine", "obtain", "exact"], "tactic_count": 6}
{"name": "Algebra.QuasiFiniteAt.eq_of_le_of_under_eq", "kind": "theorem", "module": "Mathlib.RingTheory.QuasiFinite.Basic", "is_tactic_proof": true, "tactics": ["have", "have", "have", "convert", "rw", "rw", "rw"], "tactic_count": 7}
{"name": "Algebra.instFiniteResidueFieldOfQuasiFiniteAt", "kind": "instance", "module": "Mathlib.RingTheory.QuasiFinite.Basic", "is_tactic_proof": true, "tactics": ["let", "let", "let", "exact"], "tactic_count": 4}
{"name": "Algebra.QuasiFiniteAt.exists_basicOpen_eq_singleton", "kind": "theorem", "module": "Mathlib.RingTheory.QuasiFinite.Basic", "is_tactic_proof": false, "tactics": ["have", "simpa", "have", "have", "have", "have", "have", "obtain", "have", "let", "refine", "obtain", "obtain", "obtain", "ext1", "dsimp", "rw", "exact"], "tactic_count": 18}
{"name": "Algebra.QuasiFiniteAt.isClopen_singleton", "kind": "theorem", "module": "Mathlib.RingTheory.QuasiFinite.Basic", "is_tactic_proof": true, "tactics": ["have", "have", "refine", "obtain", "exact"], "tactic_count": 5}
{"name": "Ideal.exists_not_mem_forall_mem_of_ne_of_liesOver", "kind": "theorem", "module": "Mathlib.RingTheory.QuasiFinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.not_quasiFiniteAt", "kind": "theorem", "module": "Mathlib.RingTheory.QuasiFinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.map_under_lt_comap_of_quasiFiniteAt", "kind": "theorem", "module": "Mathlib.RingTheory.QuasiFinite.Basic", "is_tactic_proof": true, "tactics": ["algebraize", "refine", "rw", "have", "have", "exact"], "tactic_count": 6}
{"name": "Polynomial.not_ker_le_map_C_of_surjective_of_quasiFiniteAt", "kind": "theorem", "module": "Mathlib.RingTheory.QuasiFinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotSMulTop", "kind": "abbrev", "module": "Mathlib.RingTheory.QuotSMulTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotSMulTop.congr", "kind": "definition", "module": "Mathlib.RingTheory.QuotSMulTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotSMulTop.equivQuotTensor", "kind": "definition", "module": "Mathlib.RingTheory.QuotSMulTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotSMulTop.equivTensorQuot", "kind": "definition", "module": "Mathlib.RingTheory.QuotSMulTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotSMulTop.map", "kind": "definition", "module": "Mathlib.RingTheory.QuotSMulTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotSMulTop.map_apply_mk", "kind": "theorem", "module": "Mathlib.RingTheory.QuotSMulTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotSMulTop.map_comp_mkQ", "kind": "theorem", "module": "Mathlib.RingTheory.QuotSMulTop", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "QuotSMulTop.map_id", "kind": "theorem", "module": "Mathlib.RingTheory.QuotSMulTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotSMulTop.map_comp", "kind": "theorem", "module": "Mathlib.RingTheory.QuotSMulTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotSMulTop.equivQuotTensor_naturality_mk", "kind": "theorem", "module": "Mathlib.RingTheory.QuotSMulTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotSMulTop.equivQuotTensor_naturality", "kind": "theorem", "module": "Mathlib.RingTheory.QuotSMulTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotSMulTop.equivTensorQuot_naturality_mk", "kind": "theorem", "module": "Mathlib.RingTheory.QuotSMulTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotSMulTop.equivTensorQuot_naturality", "kind": "theorem", "module": "Mathlib.RingTheory.QuotSMulTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotSMulTop.map_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.QuotSMulTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotSMulTop.map_exact", "kind": "theorem", "module": "Mathlib.RingTheory.QuotSMulTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotSMulTop.tensorQuotSMulTopEquivQuotSMulTop", "kind": "definition", "module": "Mathlib.RingTheory.QuotSMulTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotSMulTop.quotSMulTopTensorEquivQuotSMulTop", "kind": "definition", "module": "Mathlib.RingTheory.QuotSMulTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotSMulTop.algebraMapTensorEquivTensorQuotSMulTop", "kind": "definition", "module": "Mathlib.RingTheory.QuotSMulTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniqueFactorizationMonoid.primeFactors", "kind": "definition", "module": "Mathlib.RingTheory.Radical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniqueFactorizationMonoid.mem_primeFactors", "kind": "theorem", "module": "Mathlib.RingTheory.Radical", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Associated.primeFactors_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Radical", "is_tactic_proof": true, "tactics": ["unfold", "rw"], "tactic_count": 2}
{"name": "UniqueFactorizationMonoid.primeFactors_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Radical", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "UniqueFactorizationMonoid.primeFactors_one", "kind": "theorem", "module": "Mathlib.RingTheory.Radical", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "UniqueFactorizationMonoid.pairwise_primeFactors_isRelPrime", "kind": "theorem", "module": "Mathlib.RingTheory.Radical", "is_tactic_proof": true, "tactics": ["obtain", "simp", "intro", "simp", "rw", "contrapose", "have", "exact"], "tactic_count": 8}
{"name": "UniqueFactorizationMonoid.primeFactors_pow", "kind": "theorem", "module": "Mathlib.RingTheory.Radical", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "UniqueFactorizationMonoid.primeFactors_pow'", "kind": "theorem", "module": "Mathlib.RingTheory.Radical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniqueFactorizationMonoid.normalizedFactors_nodup", "kind": "theorem", "module": "Mathlib.RingTheory.Radical", "is_tactic_proof": true, "tactics": ["obtain", "simp", "rwa"], "tactic_count": 3}
{"name": "UniqueFactorizationMonoid.primeFactors_of_isUnit", "kind": "theorem", "module": "Mathlib.RingTheory.Radical", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "UniqueFactorizationMonoid.primeFactors_eq_empty_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Radical", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "UniqueFactorizationMonoid.primeFactors_val_eq_normalizedFactors", "kind": "theorem", "module": "Mathlib.RingTheory.Radical", "is_tactic_proof": true, "tactics": ["classical", "rw", "exact"], "tactic_count": 3}
{"name": "UniqueFactorizationMonoid.primeFactors_mul_eq_union", "kind": "theorem", "module": "Mathlib.RingTheory.Radical", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "UniqueFactorizationMonoid.disjoint_primeFactors", "kind": "theorem", "module": "Mathlib.RingTheory.Radical", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "UniqueFactorizationMonoid.primeFactors_mul_eq_disjUnion", "kind": "theorem", "module": "Mathlib.RingTheory.Radical", "is_tactic_proof": true, "tactics": ["obtain", "rw", "simp", "obtain", "rw", "simp", "classical"], "tactic_count": 7}
{"name": "UniqueFactorizationMonoid.radical", "kind": "definition", "module": "Mathlib.RingTheory.Radical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniqueFactorizationMonoid.radical_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Radical", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "UniqueFactorizationMonoid.radical_one", "kind": "theorem", "module": "Mathlib.RingTheory.Radical", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "UniqueFactorizationMonoid.radical_eq_of_associated", "kind": "theorem", "module": "Mathlib.RingTheory.Radical", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "UniqueFactorizationMonoid.radical_associated", "kind": "theorem", "module": "Mathlib.RingTheory.Radical", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsRadical.dvd_radical", "kind": "theorem", "module": "Mathlib.RingTheory.Radical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniqueFactorizationMonoid.radical_of_isUnit", "kind": "theorem", "module": "Mathlib.RingTheory.Radical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniqueFactorizationMonoid.radical_mul_of_isUnit_left", "kind": "theorem", "module": "Mathlib.RingTheory.Radical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniqueFactorizationMonoid.radical_mul_of_isUnit_right", "kind": "theorem", "module": "Mathlib.RingTheory.Radical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniqueFactorizationMonoid.radical_pow", "kind": "theorem", "module": "Mathlib.RingTheory.Radical", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "UniqueFactorizationMonoid.radical_dvd_self", "kind": "theorem", "module": "Mathlib.RingTheory.Radical", "is_tactic_proof": true, "tactics": ["classical", "by_cases", "rw", "apply", "rw", "apply", "rw", "apply"], "tactic_count": 8}
{"name": "UniqueFactorizationMonoid.radical_of_prime", "kind": "theorem", "module": "Mathlib.RingTheory.Radical", "is_tactic_proof": true, "tactics": ["rw", "rw", "simp"], "tactic_count": 3}
{"name": "UniqueFactorizationMonoid.radical_pow_of_prime", "kind": "theorem", "module": "Mathlib.RingTheory.Radical", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "UniqueFactorizationMonoid.radical_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Radical", "is_tactic_proof": true, "tactics": ["rw", "apply", "rw", "simp", "exact"], "tactic_count": 5}
{"name": "UniqueFactorizationMonoid.dvd_radical_iff_of_irreducible", "kind": "theorem", "module": "Mathlib.RingTheory.Radical", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "intro", "obtain", "exact"], "tactic_count": 6}
{"name": "UniqueFactorizationMonoid.isRadical_radical", "kind": "theorem", "module": "Mathlib.RingTheory.Radical", "is_tactic_proof": true, "tactics": ["intro", "rw", "apply", "exact", "intro", "simp", "have", "rw", "exact", "exact", "rintro", "simp", "exact"], "tactic_count": 13}
{"name": "UniqueFactorizationMonoid.squarefree_radical", "kind": "theorem", "module": "Mathlib.RingTheory.Radical", "is_tactic_proof": true, "tactics": ["nontriviality", "exact"], "tactic_count": 2}
{"name": "UniqueFactorizationMonoid.primeFactors_radical", "kind": "theorem", "module": "Mathlib.RingTheory.Radical", "is_tactic_proof": true, "tactics": ["obtain", "simp", "have", "ext", "simp"], "tactic_count": 5}
{"name": "UniqueFactorizationMonoid.radical_eq_iff_primeFactors_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Radical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniqueFactorizationMonoid.radical_eq_of_primeFactors_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Radical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniqueFactorizationMonoid.radical_eq_one_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Radical", "is_tactic_proof": true, "tactics": ["refine", "intro", "rw", "intro", "have", "rwa"], "tactic_count": 6}
{"name": "UniqueFactorizationMonoid.radical_radical", "kind": "theorem", "module": "Mathlib.RingTheory.Radical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniqueFactorizationMonoid.radical_dvd_radical_iff_normalizedFactors_subset_normalizedFactors", "kind": "theorem", "module": "Mathlib.RingTheory.Radical", "is_tactic_proof": true, "tactics": ["obtain", "simp", "have", "rw", "simp"], "tactic_count": 5}
{"name": "UniqueFactorizationMonoid.radical_dvd_radical_iff_primeFactors_subset_primeFactors", "kind": "theorem", "module": "Mathlib.RingTheory.Radical", "is_tactic_proof": true, "tactics": ["classical", "rw"], "tactic_count": 2}
{"name": "UniqueFactorizationMonoid.radical_dvd_radical", "kind": "theorem", "module": "Mathlib.RingTheory.Radical", "is_tactic_proof": true, "tactics": ["obtain", "simp", "rw", "rw", "exact"], "tactic_count": 5}
{"name": "UniqueFactorizationMonoid.dvd_radical_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Radical", "is_tactic_proof": true, "tactics": ["refine", "obtain", "simp_all", "exact"], "tactic_count": 4}
{"name": "UniqueFactorizationMonoid.radical_dvd_iff_primeFactors_subset", "kind": "theorem", "module": "Mathlib.RingTheory.Radical", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "UniqueFactorizationMonoid.radical_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Radical", "is_tactic_proof": true, "tactics": ["simp_rw", "rw"], "tactic_count": 2}
{"name": "UniqueFactorizationMonoid.radical_prod", "kind": "theorem", "module": "Mathlib.RingTheory.Radical", "is_tactic_proof": true, "tactics": ["induction", "empty", "cons", "simp", "rw", "rw", "exact"], "tactic_count": 7}
{"name": "UniqueFactorizationMonoid.radical_mul_dvd", "kind": "theorem", "module": "Mathlib.RingTheory.Radical", "is_tactic_proof": true, "tactics": ["classical", "obtain", "simp", "obtain", "simp", "nontriviality", "simp", "primeFactors_radical]"], "tactic_count": 8}
{"name": "UniqueFactorizationMonoid.radical_prod_dvd", "kind": "theorem", "module": "Mathlib.RingTheory.Radical", "is_tactic_proof": true, "tactics": ["induction", "empty", "cons", "simp", "exact"], "tactic_count": 5}
{"name": "UniqueFactorizationDomain.radical_neg", "kind": "theorem", "module": "Mathlib.RingTheory.Radical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniqueFactorizationDomain.radical_neg_one", "kind": "theorem", "module": "Mathlib.RingTheory.Radical", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "EuclideanDomain.divRadical", "kind": "definition", "module": "Mathlib.RingTheory.Radical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EuclideanDomain.radical_mul_divRadical", "kind": "theorem", "module": "Mathlib.RingTheory.Radical", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EuclideanDomain.divRadical_mul_radical", "kind": "theorem", "module": "Mathlib.RingTheory.Radical", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "EuclideanDomain.divRadical_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Radical", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "EuclideanDomain.divRadical_isUnit", "kind": "theorem", "module": "Mathlib.RingTheory.Radical", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "EuclideanDomain.eq_divRadical", "kind": "theorem", "module": "Mathlib.RingTheory.Radical", "is_tactic_proof": true, "tactics": ["apply", "rwa"], "tactic_count": 2}
{"name": "EuclideanDomain.divRadical_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Radical", "is_tactic_proof": true, "tactics": ["symm", "rw", "rw"], "tactic_count": 3}
{"name": "EuclideanDomain.divRadical_dvd_self", "kind": "theorem", "module": "Mathlib.RingTheory.Radical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCoprime.divRadical", "kind": "theorem", "module": "Mathlib.RingTheory.Radical", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "UniqueFactorizationMonoid.primeFactors_eq_natPrimeFactors", "kind": "theorem", "module": "Mathlib.RingTheory.Radical", "is_tactic_proof": true, "tactics": ["ext", "rw", "convert"], "tactic_count": 3}
{"name": "Nat.radical_le_self_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Radical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.two_le_radical_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Radical", "is_tactic_proof": true, "tactics": ["refine", "intro", "obtain", "trans", "apply", "apply", "rwa"], "tactic_count": 7}
{"name": "Nat.one_lt_radical_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Radical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.radical_le_one_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Radical", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Nat.radical_pos", "kind": "theorem", "module": "Mathlib.RingTheory.Radical", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "reesAlgebra", "kind": "definition", "module": "Mathlib.RingTheory.ReesAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_reesAlgebra_iff", "kind": "theorem", "module": "Mathlib.RingTheory.ReesAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_reesAlgebra_iff_support", "kind": "theorem", "module": "Mathlib.RingTheory.ReesAlgebra", "is_tactic_proof": true, "tactics": ["apply", "intro", "rw", "exact"], "tactic_count": 4}
{"name": "reesAlgebra.monomial_mem", "kind": "theorem", "module": "Mathlib.RingTheory.ReesAlgebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "monomial_mem_adjoin_monomial", "kind": "theorem", "module": "Mathlib.RingTheory.ReesAlgebra", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "refine", "intro", "rw", "exact", "intro", "rw", "exact"], "tactic_count": 11}
{"name": "adjoin_monomial_eq_reesAlgebra", "kind": "theorem", "module": "Mathlib.RingTheory.ReesAlgebra", "is_tactic_proof": true, "tactics": ["apply", "apply", "rintro", "exact", "intro", "rw", "apply", "rintro", "exact"], "tactic_count": 9}
{"name": "reesAlgebra.fg", "kind": "theorem", "module": "Mathlib.RingTheory.ReesAlgebra", "is_tactic_proof": true, "tactics": ["classical", "obtain", "rw", "use", "rw", "change", "rw"], "tactic_count": 7}
{"name": "instFiniteTypeSubtypePolynomialMemSubalgebraReesAlgebraOfIsNoetherianRing", "kind": "instance", "module": "Mathlib.RingTheory.ReesAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsNoetherianRingSubtypePolynomialMemSubalgebraReesAlgebra", "kind": "instance", "module": "Mathlib.RingTheory.ReesAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.exact_smul_id_smul_top_mkQ", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.Category", "is_tactic_proof": true, "tactics": ["intro", "simp"], "tactic_count": 2}
{"name": "ModuleCat.smulShortComplex", "kind": "definition", "module": "Mathlib.RingTheory.Regular.Category", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleCat.smulShortComplex_exact", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.Category", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ModuleCat.smulShortComplex_g_epi", "kind": "instance", "module": "Mathlib.RingTheory.Regular.Category", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsSMulRegular.smulShortComplex_shortExact", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.Category", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSMulRegular.linearMap_subsingleton_of_mem_annihilator", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.Depth", "is_tactic_proof": true, "tactics": ["apply", "have", "simpa"], "tactic_count": 3}
{"name": "IsSMulRegular.subsingleton_linearMap_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.Depth", "is_tactic_proof": true, "tactics": ["refine", "cases", "exact", "by_contra", "have", "rcases", "apply", "rw", "exact", "exact", "rcases", "let", "let", "have", "rw", "let", "let", "let", "let", "have", "let", "let", "have", "rcases", "have", "rcases", "let", "map_smul", "x", "simp", "convert", "let", "to_res'.comp", "replace", "hx.trans", "let", "have", "let", "have", "intro", "absurd", "apply", "intro", "induction", "change", "apply", "change", "simp", "absurd", "let", "contrapose", "exact"], "tactic_count": 52}
{"name": "RingTheory.Sequence.IsWeaklyRegular.of_flat_of_isBaseChange", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.Flat", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "simp", "have", "have", "exact"], "tactic_count": 7}
{"name": "RingTheory.Sequence.IsWeaklyRegular.of_flat", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.Flat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingTheory.Sequence.IsWeaklyRegular.of_isLocalizedModule", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.Flat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingTheory.Sequence.IsWeaklyRegular.of_isLocalization", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.Flat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingTheory.Sequence.IsWeaklyRegular.isRegular_of_isLocalizedModule_of_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.Flat", "is_tactic_proof": true, "tactics": ["have", "refine", "reg.of_isLocalizedModule", "rcases", "simpa"], "tactic_count": 5}
{"name": "RingTheory.Sequence.IsWeaklyRegular.isRegular_of_isLocalization_of_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.Flat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingTheory.Sequence.IsRegular.of_faithfullyFlat_of_isBaseChange", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.Flat", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "RingTheory.Sequence.IsRegular.of_faithfullyFlat", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.Flat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.isSMulRegular_congr'", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.IsSMulRegular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.isSMulRegular_congr", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.IsSMulRegular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSMulRegular.submodule", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.IsSMulRegular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSMulRegular.lTensor", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.IsSMulRegular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSMulRegular.rTensor", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.IsSMulRegular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isSMulRegular_submodule_iff_right_eq_zero_of_smul", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.IsSMulRegular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isSMulRegular_quotient_iff_mem_of_smul_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.IsSMulRegular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_of_isSMulRegular_quotient_of_smul_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.IsSMulRegular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isSMulRegular_of_range_eq_ker", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.IsSMulRegular", "is_tactic_proof": true, "tactics": ["refine", "intro", "obtain", "h2.right_eq_zero_of_smul", "refine", "exact"], "tactic_count": 6}
{"name": "isSMulRegular_of_isSMulRegular_on_submodule_on_quotient", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.IsSMulRegular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "biUnion_associatedPrimes_eq_compl_regular", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.IsSMulRegular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isSMulRegular_iff_ker_lsmul_eq_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.IsSMulRegular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isSMulRegular_on_submodule_iff_disjoint_ker_lsmul_submodule", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.IsSMulRegular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isSMulRegular_on_quot_iff_lsmul_comap_le", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.IsSMulRegular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isSMulRegular_on_quot_iff_lsmul_comap_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.IsSMulRegular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSMulRegular.isSMulRegular_on_quot_iff_smul_top_inf_eq_smul", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.IsSMulRegular", "is_tactic_proof": true, "tactics": ["intro", "rw", "rfl"], "tactic_count": 3}
{"name": "isSMulRegular_of_ker_lsmul_eq_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.IsSMulRegular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smul_top_inf_eq_smul_of_isSMulRegular_on_quot", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.IsSMulRegular", "is_tactic_proof": true, "tactics": ["convert", "exact"], "tactic_count": 2}
{"name": "QuotSMulTop.map_first_exact_on_four_term_exact_of_isSMulRegular_last", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.IsSMulRegular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.ofList", "kind": "abbrev", "module": "Mathlib.RingTheory.Regular.RegularSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.ofList_nil", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.RegularSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.ofList_append", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.RegularSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.ofList_singleton", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.RegularSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.ofList_cons", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.RegularSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.map_ofList", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.RegularSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.ofList_cons_smul", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.RegularSequence", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Submodule.smul_top_le_comap_smul_top", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.RegularSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.quotOfListConsSMulTopEquivQuotSMulTopInner", "kind": "definition", "module": "Mathlib.RingTheory.Regular.RegularSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.quotOfListConsSMulTopEquivQuotSMulTopOuter", "kind": "definition", "module": "Mathlib.RingTheory.Regular.RegularSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.quotOfListConsSMulTopEquivQuotSMulTopInner_naturality", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.RegularSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.top_eq_ofList_cons_smul_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.RegularSequence", "is_tactic_proof": true, "tactics": ["conv", "exact"], "tactic_count": 2}
{"name": "RingTheory.Sequence.isWeaklyRegular_iff_Fin", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.RegularSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Regular.RegularSequence.0.AddHom.map_smul_top_toAddSubgroup_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.RegularSequence", "is_tactic_proof": true, "tactics": ["induction", "nil", "ih", "conv", "congr", "rw", "top_toAddSubgroup,", "apply", "rw"], "tactic_count": 9}
{"name": "AddEquiv.isWeaklyRegular_congr", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.RegularSequence", "is_tactic_proof": true, "tactics": ["conv", "let", "refine", "exact"], "tactic_count": 4}
{"name": "LinearEquiv.isWeaklyRegular_congr'", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.RegularSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.isWeaklyRegular_congr", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.RegularSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddEquiv.isRegular_congr", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.RegularSequence", "is_tactic_proof": true, "tactics": ["conv", "let", "exact"], "tactic_count": 3}
{"name": "LinearEquiv.isRegular_congr'", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.RegularSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.isRegular_congr", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.RegularSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingTheory.Sequence.isWeaklyRegular_map_algebraMap_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.RegularSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingTheory.Sequence.isWeaklyRegular_cons_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.RegularSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingTheory.Sequence.isWeaklyRegular_cons_iff'", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.RegularSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingTheory.Sequence.isRegular_cons_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.RegularSequence", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RingTheory.Sequence.isRegular_cons_iff'", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.RegularSequence", "is_tactic_proof": true, "tactics": ["conv", "rw"], "tactic_count": 2}
{"name": "RingTheory.Sequence.IsWeaklyRegular.nil", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.RegularSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingTheory.Sequence.IsWeaklyRegular.cons", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.RegularSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingTheory.Sequence.IsWeaklyRegular.cons'", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.RegularSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingTheory.Sequence.IsWeaklyRegular.recIterModByRegular", "kind": "definition", "module": "Mathlib.RingTheory.Regular.RegularSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingTheory.Sequence.IsWeaklyRegular.ndrecIterModByRegular", "kind": "definition", "module": "Mathlib.RingTheory.Regular.RegularSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingTheory.Sequence.IsWeaklyRegular.recIterModByRegularWithRing", "kind": "definition", "module": "Mathlib.RingTheory.Regular.RegularSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingTheory.Sequence.IsWeaklyRegular.ndrecWithRing", "kind": "definition", "module": "Mathlib.RingTheory.Regular.RegularSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingTheory.Sequence.isWeaklyRegular_singleton_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.RegularSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingTheory.Sequence.isWeaklyRegular_append_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.RegularSequence", "is_tactic_proof": true, "tactics": ["induction", "nil", "refine", "refine", "rw", "cons", "let", "rw", "e.isWeaklyRegular_congr"], "tactic_count": 9}
{"name": "RingTheory.Sequence.isWeaklyRegular_append_iff'", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.RegularSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingTheory.Sequence.IsRegular.nil", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.RegularSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingTheory.Sequence.IsRegular.cons", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.RegularSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingTheory.Sequence.IsRegular.cons'", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.RegularSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingTheory.Sequence.IsRegular.recIterModByRegular", "kind": "definition", "module": "Mathlib.RingTheory.Regular.RegularSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingTheory.Sequence.IsRegular.ndrecIterModByRegular", "kind": "definition", "module": "Mathlib.RingTheory.Regular.RegularSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingTheory.Sequence.IsRegular.recIterModByRegularWithRing", "kind": "definition", "module": "Mathlib.RingTheory.Regular.RegularSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingTheory.Sequence.IsRegular.ndrecIterModByRegularWithRing", "kind": "definition", "module": "Mathlib.RingTheory.Regular.RegularSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingTheory.Sequence.IsRegular.quot_ofList_smul_nontrivial", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.RegularSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingTheory.Sequence.IsRegular.nontrivial", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.RegularSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingTheory.Sequence.isRegular_iff_isWeaklyRegular_of_subset_jacobson_annihilator", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.RegularSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.isRegular_iff_isWeaklyRegular_of_subset_maximalIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.RegularSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingTheory.Sequence.eq_nil_of_isRegular_on_artinian", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.RegularSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingTheory.Sequence.IsWeaklyRegular.isWeaklyRegular_lTensor", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.RegularSequence", "is_tactic_proof": true, "tactics": ["induction", "nil", "let", "exact"], "tactic_count": 4}
{"name": "RingTheory.Sequence.IsWeaklyRegular.isWeaklyRegular_rTensor", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.RegularSequence", "is_tactic_proof": true, "tactics": ["induction", "nil", "let", "exact"], "tactic_count": 4}
{"name": "RingTheory.Sequence.map_first_exact_on_four_term_right_exact_of_isSMulRegular_last", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.RegularSequence", "is_tactic_proof": true, "tactics": ["induction", "nil", "apply", "any_goals", "all_goals", "cons", "ih", "specialize", "ih", "have", "have", "exact"], "tactic_count": 12}
{"name": "_private.Mathlib.RingTheory.Regular.RegularSequence.0.RingTheory.Sequence.IsWeaklyRegular.swap", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.RegularSequence", "is_tactic_proof": true, "tactics": ["rw", "obtain", "rw", "specialize", "refine", "le_of_eq_of_le", "smul_top_inf_eq_smul_of_isSMulRegular_on_quot", "ha.of_injective", "rw", "exact", "rwa", "h2.isSMulRegular_on_quot_iff_smul_top_inf_eq_smul,"], "tactic_count": 12}
{"name": "RingTheory.Sequence.IsWeaklyRegular.prototype_perm", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.RegularSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingTheory.Sequence.IsWeaklyRegular.of_perm_of_subset_jacobson_annihilator", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.RegularSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingTheory.Sequence.IsRegular.of_perm_of_subset_jacobson_annihilator", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.RegularSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.isWeaklyRegular_of_perm_of_subset_maximalIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.RegularSequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.isRegular_of_perm", "kind": "theorem", "module": "Mathlib.RingTheory.Regular.RegularSequence", "is_tactic_proof": true, "tactics": ["obtain", "refine", "intro", "refine", "exact", "refine", "exact"], "tactic_count": 7}
{"name": "RingHom.RespectsIso", "kind": "definition", "module": "Mathlib.RingTheory.RingHomProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.RespectsIso.cancel_left_isIso", "kind": "theorem", "module": "Mathlib.RingTheory.RingHomProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.RespectsIso.cancel_right_isIso", "kind": "theorem", "module": "Mathlib.RingTheory.RingHomProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.RespectsIso.isLocalization_away_iff", "kind": "theorem", "module": "Mathlib.RingTheory.RingHomProperties", "is_tactic_proof": true, "tactics": ["let", "let", "refine", "refine", "rw", "congr", "let", "suffices", "apply", "ext1", "dsimp", "simp"], "tactic_count": 12}
{"name": "RingHom.RespectsIso.and", "kind": "theorem", "module": "Mathlib.RingTheory.RingHomProperties", "is_tactic_proof": true, "tactics": ["refine", "introv", "exact", "introv", "exact"], "tactic_count": 5}
{"name": "RingHom.StableUnderComposition", "kind": "definition", "module": "Mathlib.RingTheory.RingHomProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.StableUnderComposition.respectsIso", "kind": "theorem", "module": "Mathlib.RingTheory.RingHomProperties", "is_tactic_proof": true, "tactics": ["constructor", "introv", "apply", "exacts", "introv", "apply", "exacts"], "tactic_count": 7}
{"name": "RingHom.StableUnderComposition.and", "kind": "theorem", "module": "Mathlib.RingTheory.RingHomProperties", "is_tactic_proof": true, "tactics": ["introv", "exact"], "tactic_count": 2}
{"name": "RingHom.IsStableUnderBaseChange", "kind": "definition", "module": "Mathlib.RingTheory.RingHomProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.IsStableUnderBaseChange.mk", "kind": "theorem", "module": "Mathlib.RingTheory.RingHomProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.IsStableUnderBaseChange.pushout_inl", "kind": "theorem", "module": "Mathlib.RingTheory.RingHomProperties", "is_tactic_proof": true, "tactics": ["letI", "letI", "rw", "show", "colimit.isoColimitCocone_ι_inv", "dsimp", "apply", "exact"], "tactic_count": 8}
{"name": "RingHom.IsStableUnderBaseChange.and", "kind": "theorem", "module": "Mathlib.RingTheory.RingHomProperties", "is_tactic_proof": true, "tactics": ["introv", "exact"], "tactic_count": 2}
{"name": "RingHom.toMorphismProperty", "kind": "definition", "module": "Mathlib.RingTheory.RingHomProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.toMorphismProperty_respectsIso_iff", "kind": "theorem", "module": "Mathlib.RingTheory.RingHomProperties", "is_tactic_proof": true, "tactics": ["refine", "intro", "exact", "intro", "exact", "intro", "exact", "intro", "exact"], "tactic_count": 9}
{"name": "RingHom.isStableUnderCobaseChange_toMorphismProperty_iff", "kind": "theorem", "module": "Mathlib.RingTheory.RingHomProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.RespectsIso.arrow_mk_iso_iff", "kind": "theorem", "module": "Mathlib.RingTheory.RingHomProperties", "is_tactic_proof": true, "tactics": ["have", "change", "rw"], "tactic_count": 3}
{"name": "RingHom.CodescendsAlong", "kind": "definition", "module": "Mathlib.RingTheory.RingHomProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.CodescendsAlong.mk", "kind": "theorem", "module": "Mathlib.RingTheory.RingHomProperties", "is_tactic_proof": true, "tactics": ["introv", "let", "have", "ext", "simp", "apply", "rw", "exact"], "tactic_count": 8}
{"name": "RingHom.CodescendsAlong.algebraMap_tensorProduct", "kind": "theorem", "module": "Mathlib.RingTheory.RingHomProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.CodescendsAlong.includeRight", "kind": "theorem", "module": "Mathlib.RingTheory.RingHomProperties", "is_tactic_proof": true, "tactics": ["let", "apply"], "tactic_count": 2}
{"name": "RingHom.CodescendsAlong.and", "kind": "theorem", "module": "Mathlib.RingTheory.RingHomProperties", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.Bijective.containsIdentities", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Bijective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.Bijective.stableUnderComposition", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Bijective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.Bijective.respectsIso", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Bijective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.Bijective.isStableUnderBaseChange", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Bijective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.Bijective.ofLocalizationSpan", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Bijective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.EssFiniteType.comp", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.EssFiniteType", "is_tactic_proof": true, "tactics": ["algebraize", "exact"], "tactic_count": 2}
{"name": "RingHom.EssFiniteType.comp_iff", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.EssFiniteType", "is_tactic_proof": true, "tactics": ["algebraize", "exact"], "tactic_count": 2}
{"name": "RingHom.EssFiniteType.of_comp", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.EssFiniteType", "is_tactic_proof": true, "tactics": ["algebraize", "exact"], "tactic_count": 2}
{"name": "RingHom.EssFiniteType.stableUnderComposition", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.EssFiniteType", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.EssFiniteType.respectsIso", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.EssFiniteType", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.EssFiniteType.isStableUnderBaseChange", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.EssFiniteType", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.EssFiniteType.holdsForLocalization", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.EssFiniteType", "is_tactic_proof": true, "tactics": ["introv", "rw", "exact"], "tactic_count": 3}
{"name": "RingHom.EssFiniteType.residueFieldMap", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.EssFiniteType", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "RingHom.Etale", "kind": "definition", "module": "Mathlib.RingTheory.RingHom.Etale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.Etale.toAlgebra", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Etale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.etale_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Etale", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RingHom.etale_iff_formallyUnramified_and_smooth", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Etale", "is_tactic_proof": true, "tactics": ["algebraize", "simp", "exact"], "tactic_count": 3}
{"name": "RingHom.Etale.eq_formallyUnramified_and_smooth", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Etale", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "RingHom.Etale.of_bijective", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Etale", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "RingHom.Etale.isStableUnderBaseChange", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Etale", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "RingHom.Etale.propertyIsLocal", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Etale", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "RingHom.Etale.respectsIso", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Etale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.Etale.ofLocalizationSpanTarget", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Etale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.Etale.ofLocalizationSpan", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Etale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.Etale.stableUnderComposition", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Etale", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "RingHom.FaithfullyFlat", "kind": "definition", "module": "Mathlib.RingTheory.RingHom.FaithfullyFlat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.faithfullyFlat_algebraMap_iff", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.FaithfullyFlat", "is_tactic_proof": true, "tactics": ["simp", "congr", "exact"], "tactic_count": 3}
{"name": "RingHom.FaithfullyFlat.flat", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.FaithfullyFlat", "is_tactic_proof": true, "tactics": ["algebraize", "exact"], "tactic_count": 2}
{"name": "RingHom.FaithfullyFlat.iff_flat_and_comap_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.FaithfullyFlat", "is_tactic_proof": true, "tactics": ["algebraize", "rw", "exact"], "tactic_count": 3}
{"name": "RingHom.FaithfullyFlat.eq_and", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.FaithfullyFlat", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "RingHom.FaithfullyFlat.stableUnderComposition", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.FaithfullyFlat", "is_tactic_proof": true, "tactics": ["introv", "algebraize", "rw", "exact"], "tactic_count": 4}
{"name": "RingHom.FaithfullyFlat.of_bijective", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.FaithfullyFlat", "is_tactic_proof": true, "tactics": ["rw", "refine", "use", "have", "ext", "exact", "rw"], "tactic_count": 7}
{"name": "RingHom.FaithfullyFlat.injective", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.FaithfullyFlat", "is_tactic_proof": true, "tactics": ["algebraize", "exact"], "tactic_count": 2}
{"name": "RingHom.FaithfullyFlat.respectsIso", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.FaithfullyFlat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.FaithfullyFlat.isStableUnderBaseChange", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.FaithfullyFlat", "is_tactic_proof": true, "tactics": ["refine", "rw", "infer_instance"], "tactic_count": 3}
{"name": "RingHom.finite_stableUnderComposition", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Finite", "is_tactic_proof": true, "tactics": ["introv", "exact"], "tactic_count": 2}
{"name": "RingHom.finite_respectsIso", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Finite", "is_tactic_proof": true, "tactics": ["apply", "intros", "exact"], "tactic_count": 3}
{"name": "RingHom.finite_containsIdentities", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.finite_isStableUnderBaseChange", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Finite", "is_tactic_proof": true, "tactics": ["refine", "simp", "intros", "infer_instance"], "tactic_count": 4}
{"name": "Module.Finite.of_isLocalization", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Finite", "is_tactic_proof": true, "tactics": ["classical", "have", "algebraMap", "apply", "simp", "obtain", "use", "simpa"], "tactic_count": 8}
{"name": "instFiniteFractionRingLocalizationAlgebraMapSubmonoidNonZeroDivisors", "kind": "instance", "module": "Mathlib.RingTheory.RingHom.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.finite_localizationPreserves", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Finite", "is_tactic_proof": true, "tactics": ["introv", "letI", "letI", "let", "letI", "have", "have", "have", "rwa", "have", "exact"], "tactic_count": 11}
{"name": "RingHom.localization_away_map_finite", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.smul_mem_finsetIntegerMultiple_span", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Finite", "is_tactic_proof": true, "tactics": ["let", "have", "let", "have", "obtain", "have", "simp_rw", "rw", "replace", "rw", "replace", "rw", "obtain", "obtain", "use", "convert", "hx", "convert", "rw", "exact", "exact"], "tactic_count": 21}
{"name": "multiple_mem_span_of_mem_localization_span", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Finite", "is_tactic_proof": true, "tactics": ["classical", "obtain", "rsuffices", "exact", "clear", "induction", "empty", "insert", "simp", "rcases", "rcases", "apply", "simp", "rcases", "refine", "rw", "simp"], "tactic_count": 17}
{"name": "multiple_mem_adjoin_of_mem_localization_adjoin", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Finite", "is_tactic_proof": true, "tactics": ["change", "change", "simp_rw", "exact"], "tactic_count": 4}
{"name": "RingHom.finite_ofLocalizationSpan", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Finite", "is_tactic_proof": true, "tactics": ["classical", "rw", "introv", "letI", "letI", "have", "intro", "haveI", "constructor", "replace", "choose", "let", "use", "rw", "rintro", "apply", "intro", "obtain", "multiple_mem_span_of_mem_localization_span", "dsimp", "rw", "obtain", "rw", "simp_rw", "use", "exact"], "tactic_count": 26}
{"name": "instFiniteAtPrimeLocalizationAlgebraMapSubmonoidPrimeCompl", "kind": "instance", "module": "Mathlib.RingTheory.RingHom.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.FinitePresentation.of_span_eq_top_target_aux", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.FinitePresentation", "is_tactic_proof": true, "tactics": ["apply", "apply", "intro", "let", "have", "haveI", "apply", "exact"], "tactic_count": 8}
{"name": "Algebra.FinitePresentation.of_span_eq_top_target", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.FinitePresentation", "is_tactic_proof": true, "tactics": ["obtain", "replace", "classical", "of", "we", "have", "apply", "intro", "have", "infer_instance", "obtain", "obtain", "choose", "choose", "let", "let", "have", "intro", "simp", "obtain", "simp", "rw", "rw", "simp", "rintro", "simp", "let", "have", "let", "have", "rw", "have", "apply", "rw", "apply", "simp", "simp_rw", "refine", "simp", "have", "apply", "simp", "exact", "have", "have", "obtain", "convert", "simp", "obtain", "simp", "rw", "simp_rw", "rw", "apply", "exact"], "tactic_count": 55}
{"name": "Algebra.FinitePresentation.of_span_eq_top_target_of_isLocalizationAway", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.FinitePresentation", "is_tactic_proof": true, "tactics": ["apply", "rintro", "exact"], "tactic_count": 3}
{"name": "Algebra.FinitePresentation.pi", "kind": "instance", "module": "Mathlib.RingTheory.RingHom.FinitePresentation", "is_tactic_proof": true, "tactics": ["classical", "let", "have", "refine", "simp", "exact"], "tactic_count": 6}
{"name": "RingHom.finitePresentation_stableUnderComposition", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.FinitePresentation", "is_tactic_proof": true, "tactics": ["introv", "exact"], "tactic_count": 2}
{"name": "RingHom.finitePresentation_respectsIso", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.FinitePresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.finitePresentation_isStableUnderBaseChange", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.FinitePresentation", "is_tactic_proof": true, "tactics": ["apply", "exact", "simp", "intros", "infer_instance"], "tactic_count": 5}
{"name": "RingHom.finitePresentation_localizationPreserves", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.FinitePresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.finitePresentation_holdsForLocalizationAway", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.FinitePresentation", "is_tactic_proof": true, "tactics": ["introv", "rw", "exact"], "tactic_count": 3}
{"name": "RingHom.finitePresentation_ofLocalizationSpanTarget", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.FinitePresentation", "is_tactic_proof": true, "tactics": ["introv", "algebraize", "replace", "intro", "simp_rw", "exact"], "tactic_count": 6}
{"name": "RingHom.finitePresentation_isLocal", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.FinitePresentation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalization.exists_smul_mem_of_mem_adjoin", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.FiniteType", "is_tactic_proof": true, "tactics": ["let", "let", "have", "obtain", "obtain", "rw", "obtain", "use", "convert", "rw"], "tactic_count": 10}
{"name": "IsLocalization.lift_mem_adjoin_finsetIntegerMultiple", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.FiniteType", "is_tactic_proof": false, "tactics": ["obtain", "refine", "simpa"], "tactic_count": 3}
{"name": "Algebra.FiniteType.of_span_eq_top_target", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.FiniteType", "is_tactic_proof": true, "tactics": ["obtain", "replace", "classical", "replace", "choose", "obtain", "let", "use", "rw", "rintro", "apply", "intro", "apply", "rw", "exact", "intro", "by_cases", "apply", "rw", "exact", "intro", "rw", "rw", "refine", "intro", "apply", "exact", "rw", "apply", "exact", "rw"], "tactic_count": 31}
{"name": "Algebra.FiniteType.of_span_eq_top_source", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.FiniteType", "is_tactic_proof": true, "tactics": ["obtain", "replace", "classical", "letI", "set", "constructor", "replace", "choose", "let", "use", "convert", "rw", "rintro", "apply", "intro", "obtain", "multiple_mem_adjoin_of_mem_localization_adjoin", "rw", "obtain", "rw", "simp_rw", "use", "exact"], "tactic_count": 23}
{"name": "RingHom.finiteType_stableUnderComposition", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.FiniteType", "is_tactic_proof": true, "tactics": ["introv", "exact"], "tactic_count": 2}
{"name": "RingHom.finiteType_respectsIso", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.FiniteType", "is_tactic_proof": true, "tactics": ["refine", "algebraize", "apply"], "tactic_count": 3}
{"name": "RingHom.finiteType_isStableUnderBaseChange", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.FiniteType", "is_tactic_proof": true, "tactics": ["apply", "exact", "introv", "rw", "suffices", "rfl", "infer_instance"], "tactic_count": 7}
{"name": "RingHom.finiteType_localizationPreserves", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.FiniteType", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.localization_away_map_finiteType", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.FiniteType", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.finiteType_ofLocalizationSpan", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.FiniteType", "is_tactic_proof": true, "tactics": ["refine", "simp_rw", "exact"], "tactic_count": 3}
{"name": "RingHom.finiteType_holdsForLocalizationAway", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.FiniteType", "is_tactic_proof": true, "tactics": ["introv", "rw", "exact"], "tactic_count": 3}
{"name": "RingHom.finiteType_ofLocalizationSpanTarget", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.FiniteType", "is_tactic_proof": true, "tactics": ["introv", "algebraize", "replace", "intro", "simp_rw", "exact"], "tactic_count": 6}
{"name": "RingHom.finiteType_isLocal", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.FiniteType", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.Flat", "kind": "definition", "module": "Mathlib.RingTheory.RingHom.Flat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.flat_algebraMap_iff", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Flat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RingHom.Flat.id", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Flat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.Flat.comp", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Flat", "is_tactic_proof": true, "tactics": ["algebraize", "exact"], "tactic_count": 2}
{"name": "RingHom.Flat.of_bijective", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Flat", "is_tactic_proof": true, "tactics": ["algebraize", "exact"], "tactic_count": 2}
{"name": "RingHom.Flat.containsIdentities", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Flat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.Flat.stableUnderComposition", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Flat", "is_tactic_proof": true, "tactics": ["introv", "exact"], "tactic_count": 2}
{"name": "RingHom.Flat.respectsIso", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Flat", "is_tactic_proof": true, "tactics": ["apply", "introv", "exact"], "tactic_count": 3}
{"name": "RingHom.Flat.isStableUnderBaseChange", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Flat", "is_tactic_proof": true, "tactics": ["apply", "introv", "rw", "infer_instance"], "tactic_count": 4}
{"name": "RingHom.Flat.holdsForLocalizationAway", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Flat", "is_tactic_proof": true, "tactics": ["introv", "suffices", "exact"], "tactic_count": 3}
{"name": "RingHom.Flat.ofLocalizationSpanTarget", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Flat", "is_tactic_proof": true, "tactics": ["introv", "algebraize_only", "refine", "dsimp", "convert", "apply"], "tactic_count": 6}
{"name": "RingHom.Flat.propertyIsLocal", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Flat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.Flat.ofLocalizationPrime", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Flat", "is_tactic_proof": true, "tactics": ["introv", "algebraize_only", "rw", "apply", "intro", "algebraize_only", "have", "replace", "exact"], "tactic_count": 9}
{"name": "RingHom.Flat.localRingHom", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Flat", "is_tactic_proof": true, "tactics": ["subst", "algebraize", "have", "rw", "exact"], "tactic_count": 5}
{"name": "RingHom.Flat.generalizingMap_comap", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Flat", "is_tactic_proof": true, "tactics": ["algebraize", "change", "rw", "infer_instance"], "tactic_count": 4}
{"name": "RingHom.injective_stableUnderComposition", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Injective", "is_tactic_proof": true, "tactics": ["intro", "simp", "exact"], "tactic_count": 3}
{"name": "RingHom.injective_respectsIso", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Injective", "is_tactic_proof": true, "tactics": ["apply", "intro", "exact"], "tactic_count": 3}
{"name": "RingHom.isIntegral_stableUnderComposition", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Integral", "is_tactic_proof": true, "tactics": ["introv"], "tactic_count": 1}
{"name": "RingHom.isIntegral_respectsIso", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Integral", "is_tactic_proof": true, "tactics": ["apply", "introv", "rw", "apply"], "tactic_count": 4}
{"name": "RingHom.isIntegral_isStableUnderBaseChange", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Integral", "is_tactic_proof": true, "tactics": ["refine", "introv", "rw", "infer_instance"], "tactic_count": 4}
{"name": "RingHom.isIntegral_ofLocalizationSpan", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Integral", "is_tactic_proof": true, "tactics": ["introv", "letI", "change", "apply", "rintro", "letI", "haveI", "have", "obtain", "rw", "map_mul,", "obtain", "by_cases", "obtain", "exact", "refine", "have", "simp", "rw"], "tactic_count": 19}
{"name": "RingHom.Locally", "kind": "definition", "module": "Mathlib.RingTheory.RingHom.Locally", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.locally_iff_finite", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Locally", "is_tactic_proof": true, "tactics": ["constructor", "intro", "obtain", "exact", "intro", "use"], "tactic_count": 6}
{"name": "RingHom.locally_of_exists", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Locally", "is_tactic_proof": true, "tactics": ["use", "rintro", "let", "have", "rw", "exact"], "tactic_count": 6}
{"name": "RingHom.locally_iff_exists", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Locally", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.locally_iff_isLocalization", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Locally", "is_tactic_proof": true, "tactics": ["rw", "refine", "let", "have", "rw", "exact", "exact"], "tactic_count": 7}
{"name": "RingHom.locally_of", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Locally", "is_tactic_proof": true, "tactics": ["use", "let", "simp", "exact"], "tactic_count": 4}
{"name": "RingHom.locally_of_locally", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Locally", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "RingHom.locally_iff_of_localizationSpanTarget", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Locally", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.locally_ofLocalizationSpanTarget", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Locally", "is_tactic_proof": true, "tactics": ["intro", "choose", "rw", "refine", "inferInstance,", "haveI", "apply", "rw", "apply", "rw", "exact", "apply", "intro", "rw", "apply"], "tactic_count": 15}
{"name": "RingHom.locally_respectsIso", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Locally", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.locally_holdsForLocalizationAway", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Locally", "is_tactic_proof": true, "tactics": ["introv", "use", "simp", "let", "haveI", "rw", "apply"], "tactic_count": 7}
{"name": "RingHom.locally_stableUnderComposition", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Locally", "is_tactic_proof": true, "tactics": ["classical", "intro", "rw", "obtain", "obtain", "rw", "refine", "inferInstance,", "rw", "intro", "have", "simp", "obtain", "let", "use", "simp", "intro", "let", "let", "have", "ext", "simp", "change", "simp", "rfl", "simp", "apply", "apply", "exact"], "tactic_count": 29}
{"name": "RingHom.locally_StableUnderCompositionWithLocalizationAwayTarget", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Locally", "is_tactic_proof": true, "tactics": ["intro", "simp", "obtain", "refine", "rw", "rintro", "letI", "have", "rw", "haveI", "apply", "intro", "simp", "haveI", "apply", "apply"], "tactic_count": 16}
{"name": "RingHom.locally_StableUnderCompositionWithLocalizationAwaySource", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Locally", "is_tactic_proof": true, "tactics": ["intro", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "RingHom.locally_isStableUnderBaseChange", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Locally", "is_tactic_proof": true, "tactics": ["apply", "introv", "obtain", "rw", "letI", "letI", "haveI", "haveI", "haveI", "intro", "simp", "haveI", "rw", "infer_instance", "refine", "inferInstance,", "rw", "intro", "convert_to", "simp", "rfl", "rw", "isLocalizedModule_iff_isBaseChange", "exact", "intro", "rw", "apply", "rw", "exact"], "tactic_count": 29}
{"name": "RingHom.locally_localizationAwayPreserves", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Locally", "is_tactic_proof": true, "tactics": ["introv", "obtain", "rw", "let", "let", "haveI", "inferInstanceAs", "haveI", "convert", "simp", "have", "letI", "haveI", "refine", "rw", "convert", "simp", "rw", "exact"], "tactic_count": 19}
{"name": "RingHom.locally_localizationPreserves", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Locally", "is_tactic_proof": true, "tactics": ["introv", "obtain", "rw", "let", "let", "have", "haveI", "rw", "infer_instance", "haveI", "inferInstanceAs", "letI", "haveI", "refine", "rw", "convert", "simp", "rw", "apply", "exact"], "tactic_count": 20}
{"name": "RingHom.locally_propertyIsLocal", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Locally", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.IsStandardSmooth.smooth", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.LocallyStandardSmooth", "is_tactic_proof": true, "tactics": ["algebraize", "rw", "infer_instance"], "tactic_count": 3}
{"name": "RingHom.Smooth.locally_isStandardSmooth", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.LocallyStandardSmooth", "is_tactic_proof": true, "tactics": ["algebraize", "obtain", "refine", "dsimp", "rw", "exact"], "tactic_count": 6}
{"name": "RingHom.smooth_iff_locally_isStandardSmooth", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.LocallyStandardSmooth", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "Algebra.instIsStandardOpenImmersionAway", "kind": "instance", "module": "Mathlib.RingTheory.RingHom.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsStandardOpenImmersion.trans", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.instIsStandardOpenImmersionTensorProduct", "kind": "instance", "module": "Mathlib.RingTheory.RingHom.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.IsStandardOpenImmersion", "kind": "definition", "module": "Mathlib.RingTheory.RingHom.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.isStandardOpenImmersion_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.OpenImmersion", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RingHom.IsStandardOpenImmersion.algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.IsStandardOpenImmersion.toAlgebra", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.IsStandardOpenImmersion.of_bijective", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.IsStandardOpenImmersion.id", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.IsStandardOpenImmersion.comp", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.OpenImmersion", "is_tactic_proof": true, "tactics": ["algebraize", "obtain", "obtain", "exact"], "tactic_count": 4}
{"name": "RingHom.IsStandardOpenImmersion.containsIdentities", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.IsStandardOpenImmersion.stableUnderComposition", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.IsStandardOpenImmersion.respectsIso", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.OpenImmersion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.IsStandardOpenImmersion.isStableUnderBaseChange", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.OpenImmersion", "is_tactic_proof": true, "tactics": ["refine", "introv", "rw", "infer_instance"], "tactic_count": 4}
{"name": "RingHom.IsStandardOpenImmersion.holdsForLocalizationAway", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.OpenImmersion", "is_tactic_proof": true, "tactics": ["introv", "exact"], "tactic_count": 2}
{"name": "RingHom.QuasiFinite", "kind": "definition", "module": "Mathlib.RingTheory.RingHom.QuasiFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.QuasiFinite.toAlgebra", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.QuasiFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.quasiFinite_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.QuasiFinite", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RingHom.QuasiFinite.comp", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.QuasiFinite", "is_tactic_proof": true, "tactics": ["algebraize", "exact"], "tactic_count": 2}
{"name": "RingHom.QuasiFinite.of_comp", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.QuasiFinite", "is_tactic_proof": true, "tactics": ["algebraize", "exact"], "tactic_count": 2}
{"name": "RingHom.QuasiFinite.of_finite", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.QuasiFinite", "is_tactic_proof": true, "tactics": ["algebraize", "exact"], "tactic_count": 2}
{"name": "RingHom.QuasiFinite.stableUnderComposition", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.QuasiFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.QuasiFinite.respectsIso", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.QuasiFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.QuasiFinite.isStableUnderBaseChange", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.QuasiFinite", "is_tactic_proof": true, "tactics": ["refine", "introv", "rw", "infer_instance"], "tactic_count": 4}
{"name": "RingHom.QuasiFinite.holdsForLocalizationAway", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.QuasiFinite", "is_tactic_proof": true, "tactics": ["introv", "exact"], "tactic_count": 2}
{"name": "RingHom.QuasiFinite.ofLocalizationSpanTarget", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.QuasiFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.QuasiFinite.propertyIsLocal", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.QuasiFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.QuasiFinite.of_isIntegral_of_finiteType", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.QuasiFinite", "is_tactic_proof": true, "tactics": ["algebraize", "obtain", "exact"], "tactic_count": 3}
{"name": "RingHom.FormallySmooth", "kind": "definition", "module": "Mathlib.RingTheory.RingHom.Smooth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.FormallySmooth.toAlgebra", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Smooth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.formallySmooth_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Smooth", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RingHom.FormallySmooth.of_bijective", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Smooth", "is_tactic_proof": true, "tactics": ["algebraize", "exact"], "tactic_count": 2}
{"name": "RingHom.FormallySmooth.holdsForLocalizationAway", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Smooth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.FormallySmooth.stableUnderComposition", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Smooth", "is_tactic_proof": true, "tactics": ["intro", "algebraize", "exact"], "tactic_count": 3}
{"name": "RingHom.FormallySmooth.respectsIso", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Smooth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.FormallySmooth.isStableUnderBaseChange", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Smooth", "is_tactic_proof": true, "tactics": ["refine", "introv", "rw", "infer_instance"], "tactic_count": 4}
{"name": "RingHom.FormallySmooth.localizationPreserves", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Smooth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.Smooth", "kind": "definition", "module": "Mathlib.RingTheory.RingHom.Smooth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.Smooth.toAlgebra", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Smooth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.smooth_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Smooth", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RingHom.smooth_def", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Smooth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.Smooth.comp", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Smooth", "is_tactic_proof": true, "tactics": ["algebraize", "exact"], "tactic_count": 2}
{"name": "RingHom.Smooth.stableUnderComposition", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Smooth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.Smooth.isStableUnderBaseChange", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Smooth", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "RingHom.Smooth.holdsForLocalizationAway", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Smooth", "is_tactic_proof": true, "tactics": ["introv", "rw", "exact"], "tactic_count": 3}
{"name": "RingHom.Smooth.of_bijective", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Smooth", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "RingHom.Smooth.id", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Smooth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.Smooth.ofLocalizationSpanTarget", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Smooth", "is_tactic_proof": true, "tactics": ["introv", "have", "algebraize", "refine", "rw", "simp", "exact"], "tactic_count": 7}
{"name": "RingHom.Smooth.propertyIsLocal", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Smooth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.IsStandardSmooth", "kind": "definition", "module": "Mathlib.RingTheory.RingHom.StandardSmooth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.isStandardSmooth_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.StandardSmooth", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RingHom.IsStandardSmooth.toAlgebra", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.StandardSmooth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.IsStandardSmoothOfRelativeDimension", "kind": "definition", "module": "Mathlib.RingTheory.RingHom.StandardSmooth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.isStandardSmoothOfRelativeDimension_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.StandardSmooth", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RingHom.IsStandardSmoothOfRelativeDimension.toAlgebra", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.StandardSmooth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.IsStandardSmoothOfRelativeDimension.isStandardSmooth", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.StandardSmooth", "is_tactic_proof": true, "tactics": ["algebraize", "exact"], "tactic_count": 2}
{"name": "RingHom.IsStandardSmoothOfRelativeDimension.id", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.StandardSmooth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.IsStandardSmoothOfRelativeDimension.equiv", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.StandardSmooth", "is_tactic_proof": true, "tactics": ["algebraize", "exact"], "tactic_count": 2}
{"name": "RingHom.IsStandardSmooth.comp", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.StandardSmooth", "is_tactic_proof": true, "tactics": ["rw", "algebraize", "exact"], "tactic_count": 3}
{"name": "RingHom.IsStandardSmoothOfRelativeDimension.comp", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.StandardSmooth", "is_tactic_proof": true, "tactics": ["rw", "algebraize", "exact"], "tactic_count": 3}
{"name": "RingHom.isStandardSmooth_stableUnderComposition", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.StandardSmooth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.isStandardSmooth_respectsIso", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.StandardSmooth", "is_tactic_proof": true, "tactics": ["apply", "introv", "exact"], "tactic_count": 3}
{"name": "RingHom.isStandardSmoothOfRelativeDimension_respectsIso", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.StandardSmooth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.isStandardSmooth_isStableUnderBaseChange", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.StandardSmooth", "is_tactic_proof": true, "tactics": ["apply", "exact", "introv", "replace", "simp_rw", "suffices", "simp_rw", "infer_instance"], "tactic_count": 8}
{"name": "RingHom.isStandardSmoothOfRelativeDimension_isStableUnderBaseChange", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.StandardSmooth", "is_tactic_proof": true, "tactics": ["apply", "exact", "introv", "replace", "rw", "convert", "suffices", "rw", "convert", "infer_instance"], "tactic_count": 10}
{"name": "RingHom.IsStandardSmoothOfRelativeDimension.algebraMap_isLocalizationAway", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.StandardSmooth", "is_tactic_proof": false, "tactics": ["have", "ext", "rw", "rfl", "rw", "exact"], "tactic_count": 6}
{"name": "RingHom.isStandardSmooth_localizationPreserves", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.StandardSmooth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.isStandardSmoothOfRelativeDimension_localizationPreserves", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.StandardSmooth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.isStandardSmooth_holdsForLocalizationAway", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.StandardSmooth", "is_tactic_proof": true, "tactics": ["introv", "exact"], "tactic_count": 2}
{"name": "RingHom.isStandardSmoothOfRelativeDimension_holdsForLocalizationAway", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.StandardSmooth", "is_tactic_proof": true, "tactics": ["introv", "exact"], "tactic_count": 2}
{"name": "RingHom.isStandardSmooth_stableUnderCompositionWithLocalizationAway", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.StandardSmooth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.isStandardSmoothOfRelativeDimension_stableUnderCompositionWithLocalizationAway", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.StandardSmooth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsStandardSmoothOfRelativeDimension.exists_etale_mvPolynomial", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.StandardSmooth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.IsStandardSmoothOfRelativeDimension.exists_etale_mvPolynomial", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.StandardSmooth", "is_tactic_proof": true, "tactics": ["classical", "algebraize", "obtain", "exact"], "tactic_count": 4}
{"name": "RingHom.IsStandardSmooth.exists_etale_mvPolynomial", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.StandardSmooth", "is_tactic_proof": true, "tactics": ["obtain", "let", "exact"], "tactic_count": 3}
{"name": "_private.Mathlib.RingTheory.RingHom.Surjective.0.RingHom.termSurjective", "kind": "definition", "module": "Mathlib.RingTheory.RingHom.Surjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.RingHom.Surjective.0.RingHom._aux_Mathlib_RingTheory_RingHom_Surjective___macroRules__private_Mathlib_RingTheory_RingHom_Surjective_0_RingHom_termSurjective_1", "kind": "definition", "module": "Mathlib.RingTheory.RingHom.Surjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.surjective_stableUnderComposition", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Surjective", "is_tactic_proof": true, "tactics": ["introv"], "tactic_count": 1}
{"name": "RingHom.surjective_respectsIso", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Surjective", "is_tactic_proof": true, "tactics": ["apply", "intro", "exact"], "tactic_count": 3}
{"name": "RingHom.surjective_isStableUnderBaseChange", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Surjective", "is_tactic_proof": true, "tactics": ["refine", "classical", "introv", "induction", "zero", "tmul", "obtain", "rw", "add"], "tactic_count": 9}
{"name": "RingHom.surjective_localizationPreserves", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Surjective", "is_tactic_proof": true, "tactics": ["introv", "obtain", "obtain", "use", "rw"], "tactic_count": 5}
{"name": "RingHom.surjective_ofLocalizationSpan", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Surjective", "is_tactic_proof": true, "tactics": ["introv", "rw", "letI", "intro", "apply", "intro", "obtain", "obtain", "rw", "obtain", "dsimp", "rw", "exact"], "tactic_count": 13}
{"name": "RingHom.surjective_localRingHom_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Surjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.FormallyUnramified", "kind": "definition", "module": "Mathlib.RingTheory.RingHom.Unramified", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.formallyUnramified_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Unramified", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RingHom.FormallyUnramified.of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Unramified", "is_tactic_proof": true, "tactics": ["algebraize", "exact"], "tactic_count": 2}
{"name": "RingHom.FormallyUnramified.stableUnderComposition", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Unramified", "is_tactic_proof": true, "tactics": ["intro", "algebraize", "exact"], "tactic_count": 3}
{"name": "RingHom.FormallyUnramified.respectsIso", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Unramified", "is_tactic_proof": true, "tactics": ["refine", "intro", "exact"], "tactic_count": 3}
{"name": "RingHom.FormallyUnramified.isStableUnderBaseChange", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Unramified", "is_tactic_proof": true, "tactics": ["refine", "introv", "rw", "infer_instance"], "tactic_count": 4}
{"name": "RingHom.FormallyUnramified.holdsForLocalizationAway", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Unramified", "is_tactic_proof": true, "tactics": ["intro", "rw", "exact"], "tactic_count": 3}
{"name": "RingHom.FormallyUnramified.ofLocalizationPrime", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Unramified", "is_tactic_proof": true, "tactics": ["intro", "algebraize", "rw", "intro", "let", "let", "letI", "have", "have", "exact"], "tactic_count": 10}
{"name": "RingHom.FormallyUnramified.ofLocalizationSpanTarget", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Unramified", "is_tactic_proof": true, "tactics": ["intro", "algebraize", "rw", "intro", "obtain", "simpa", "refine", "convert", "dsimp", "rw"], "tactic_count": 10}
{"name": "RingHom.FormallyUnramified.propertyIsLocal", "kind": "theorem", "module": "Mathlib.RingTheory.RingHom.Unramified", "is_tactic_proof": true, "tactics": ["constructor", "exact", "exact", "exact", "ofLocalizationSpanTarget.ofLocalizationSpan", "exact"], "tactic_count": 6}
{"name": "RingInvoClass.toRingInvo", "kind": "definition", "module": "Mathlib.RingTheory.RingInvo", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingInvo.instCoeTCOfRingInvoClass", "kind": "instance", "module": "Mathlib.RingTheory.RingInvo", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingInvo.instEquivLikeMulOpposite", "kind": "instance", "module": "Mathlib.RingTheory.RingInvo", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingInvo.instRingInvoClass", "kind": "instance", "module": "Mathlib.RingTheory.RingInvo", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingInvo.mk'", "kind": "definition", "module": "Mathlib.RingTheory.RingInvo", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingInvo.involution", "kind": "theorem", "module": "Mathlib.RingTheory.RingInvo", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingInvo.coe_ringEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.RingInvo", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingInvo.map_eq_zero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.RingInvo", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingInvo.id", "kind": "definition", "module": "Mathlib.RingTheory.RingInvo", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInhabitedRingInvo", "kind": "instance", "module": "Mathlib.RingTheory.RingInvo", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSepClosed.hasEnoughRootsOfUnity", "kind": "instance", "module": "Mathlib.RingTheory.RootsOfUnity.AlgebraicallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSepClosed.hasEnoughRootsOfUnity_pow", "kind": "instance", "module": "Mathlib.RingTheory.RootsOfUnity.AlgebraicallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicClosure.hasEnoughRootsOfUnity", "kind": "instance", "module": "Mathlib.RingTheory.RootsOfUnity.AlgebraicallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicClosure.hasEnoughRootsOfUnity_pow", "kind": "instance", "module": "Mathlib.RingTheory.RootsOfUnity.AlgebraicallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparableClosure.hasEnoughRootsOfUnity", "kind": "instance", "module": "Mathlib.RingTheory.RootsOfUnity.AlgebraicallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparableClosure.hasEnoughRootsOfUnity_pow", "kind": "instance", "module": "Mathlib.RingTheory.RootsOfUnity.AlgebraicallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "rootsOfUnity", "kind": "definition", "module": "Mathlib.RingTheory.RootsOfUnity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_rootsOfUnity", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "rootsOfUnity_eq_ker", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.Basic", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "ker_zpowGroupHom_eq_rootsOfUnity", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "mem_rootsOfUnity'", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "rootsOfUnity_one", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.Basic", "is_tactic_proof": true, "tactics": ["ext1", "simp"], "tactic_count": 2}
{"name": "rootsOfUnity_zero", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.Basic", "is_tactic_proof": true, "tactics": ["ext1", "simp"], "tactic_count": 2}
{"name": "rootsOfUnity.coe_injective", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "rootsOfUnity.mkOfPowEq", "kind": "definition", "module": "Mathlib.RingTheory.RootsOfUnity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "rootsOfUnity.coe_mkOfPowEq", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "rootsOfUnity_le_of_dvd", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.Basic", "is_tactic_proof": true, "tactics": ["obtain", "intro", "simp_all"], "tactic_count": 3}
{"name": "map_rootsOfUnity", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.Basic", "is_tactic_proof": true, "tactics": ["rintro", "simp_all"], "tactic_count": 2}
{"name": "instSubsingletonSubtypeUnitsMemSubgroupRootsOfUnityOfNatNat", "kind": "instance", "module": "Mathlib.RingTheory.RootsOfUnity.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "rootsOfUnity_inf_rootsOfUnity", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "disjoint_rootsOfUnity_of_coprime", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "rootsOfUnity.coe_pow", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "rootsOfUnityUnitsMulEquiv", "kind": "definition", "module": "Mathlib.RingTheory.RootsOfUnity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "restrictRootsOfUnity", "kind": "definition", "module": "Mathlib.RingTheory.RootsOfUnity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "restrictRootsOfUnity_coe_apply", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.restrictRootsOfUnity", "kind": "definition", "module": "Mathlib.RingTheory.RootsOfUnity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.restrictRootsOfUnity_coe_apply", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.restrictRootsOfUnity_symm", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.val_set_image_rootsOfUnity", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.Basic", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "Units.val_set_image_rootsOfUnity_one", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Units.val_set_image_rootsOfUnity_two", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "mem_rootsOfUnity_iff_mem_nthRoots", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "rootsOfUnityEquivNthRoots", "kind": "definition", "module": "Mathlib.RingTheory.RootsOfUnity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "rootsOfUnityEquivNthRoots_apply", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "rootsOfUnityEquivNthRoots_symm_apply", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "rootsOfUnity.fintype", "kind": "instance", "module": "Mathlib.RingTheory.RootsOfUnity.Basic", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "rootsOfUnity.isCyclic", "kind": "instance", "module": "Mathlib.RingTheory.RootsOfUnity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "card_rootsOfUnity", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.Basic", "is_tactic_proof": true, "tactics": ["classical", "calc"], "tactic_count": 2}
{"name": "map_rootsOfUnity_eq_pow_self", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.Basic", "is_tactic_proof": true, "tactics": ["obtain", "rw", "rootsOfUnity.coe_pow]", "exact"], "tactic_count": 4}
{"name": "mem_rootsOfUnity_prime_pow_mul_iff", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "mem_rootsOfUnity_prime_pow_mul_iff'", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsCyclic.monoidHomMulEquivRootsOfUnityOfGenerator", "kind": "definition", "module": "Mathlib.RingTheory.RootsOfUnity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCyclic.monoidHom_mulEquiv_rootsOfUnity", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.Basic", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Complex.isPrimitiveRoot_exp_of_isCoprime", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.Complex", "is_tactic_proof": true, "tactics": ["rw", "simp", "constructor", "use", "simp", "simp", "have", "rintro", "field_simp", "norm_cast", "exact"], "tactic_count": 11}
{"name": "Complex.isPrimitiveRoot_exp_of_coprime", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.isPrimitiveRoot_exp_rat", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.Complex", "is_tactic_proof": true, "tactics": ["convert", "nth_rw", "simp"], "tactic_count": 3}
{"name": "Complex.isPrimitiveRoot_exp_rat_of_even_num", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.Complex", "is_tactic_proof": true, "tactics": ["have", "convert", "nth_rw", "push_cast", "ring_nf", "rw", "apply", "convert", "grind"], "tactic_count": 9}
{"name": "Complex.isPrimitiveRoot_exp_rat_of_odd_num", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.Complex", "is_tactic_proof": true, "tactics": ["convert", "push_cast", "ring_nf", "nth_rw", "rw"], "tactic_count": 5}
{"name": "Complex.isPrimitiveRoot_exp", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.Complex", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Complex.isPrimitiveRoot_iff", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.Complex", "is_tactic_proof": true, "tactics": ["have", "constructor", "rintro", "intro", "have", "obtain", "refine", "rw", "congr", "ring"], "tactic_count": 10}
{"name": "Complex.mem_rootsOfUnity", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.Complex", "is_tactic_proof": true, "tactics": ["rw", "have", "constructor", "intro", "obtain", "simpa", "refine", "rw", "congr", "ring", "rintro", "rw", "use", "simp"], "tactic_count": 14}
{"name": "Complex.card_rootsOfUnity", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.card_primitiveRoots", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.Complex", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "exact"], "tactic_count": 3}
{"name": "IsPrimitiveRoot.norm'_eq_one", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimitiveRoot.nnnorm_eq_one", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimitiveRoot.arg_ext", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimitiveRoot.arg_eq_zero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimitiveRoot.arg_eq_pi_iff", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.Complex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimitiveRoot.arg", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.Complex", "is_tactic_proof": true, "tactics": ["rw", "obtain", "rw", "refine", "replace", "split_ifs", "exact", "convert", "rw", "split_ifs", "convert", "push_cast", "push_cast", "simp", "refine", "rw", "positivity", "refine", "rw", "exact", "rw", "convert", "push_cast", "rw", "exact", "push_cast", "rw", "exact", "simp", "field_simp", "constructor", "push_neg", "rify", "linear_combination", "rify", "linear_combination"], "tactic_count": 36}
{"name": "Complex.norm_eq_one_of_mem_rootsOfUnity", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.Complex", "is_tactic_proof": true, "tactics": ["refine", "norm_cast", "rw", "rw"], "tactic_count": 4}
{"name": "Complex.conj_rootsOfUnity", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.Complex", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsPrimitiveRoot.associated_sub_one_pow_sub_one_of_coprime", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.CyclotomicUnits", "is_tactic_proof": true, "tactics": ["refine", "n", "obtain", "use", "rw"], "tactic_count": 5}
{"name": "IsPrimitiveRoot.associated_pow_sub_one_pow_of_coprime", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.CyclotomicUnits", "is_tactic_proof": true, "tactics": ["suffices", "exact"], "tactic_count": 2}
{"name": "IsPrimitiveRoot.associated_sub_one_map_sub_one", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.CyclotomicUnits", "is_tactic_proof": true, "tactics": ["rw", "apply", "exact"], "tactic_count": 3}
{"name": "IsPrimitiveRoot.associated_map_sub_one_map_sub_one", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.CyclotomicUnits", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "IsPrimitiveRoot.geom_sum_isUnit", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.CyclotomicUnits", "is_tactic_proof": true, "tactics": ["obtain", "convert", "apply", "grind"], "tactic_count": 4}
{"name": "IsPrimitiveRoot.geom_sum_isUnit'", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.CyclotomicUnits", "is_tactic_proof": true, "tactics": ["n"], "tactic_count": 1}
{"name": "IsPrimitiveRoot.pow_sub_one_eq_geom_sum_mul_geom_sum_inv_mul_pow_sub_one", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.CyclotomicUnits", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "IsPrimitiveRoot.associated_pow_add_sub_sub_one", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.CyclotomicUnits", "is_tactic_proof": true, "tactics": ["use", "suffices", "grind"], "tactic_count": 3}
{"name": "IsPrimitiveRoot.ntRootsFinset_pairwise_associated_sub_one_sub_of_prime", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.CyclotomicUnits", "is_tactic_proof": true, "tactics": ["intro", "have", "obtain", "obtain", "wlog", "simpa", "have", "obtain", "simp", "rw"], "tactic_count": 10}
{"name": "HasEnoughRootsOfUnity.exists_primitiveRoot", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.EnoughRootsOfUnity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasEnoughRootsOfUnity.rootsOfUnity_isCyclic", "kind": "instance", "module": "Mathlib.RingTheory.RootsOfUnity.EnoughRootsOfUnity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasEnoughRootsOfUnity.of_dvd", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.EnoughRootsOfUnity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasEnoughRootsOfUnity.finite_rootsOfUnity", "kind": "instance", "module": "Mathlib.RingTheory.RootsOfUnity.EnoughRootsOfUnity", "is_tactic_proof": true, "tactics": ["have", "obtain", "have", "let", "refine", "obtain", "refine", "simpa"], "tactic_count": 8}
{"name": "HasEnoughRootsOfUnity.natCard_rootsOfUnity", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.EnoughRootsOfUnity", "is_tactic_proof": true, "tactics": ["obtain", "rw", "refine", "exact", "nth_rewrite", "rw", "let", "rw", "exact", "simp", "rw"], "tactic_count": 11}
{"name": "HasEnoughRootsOfUnity.of_card_le", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.EnoughRootsOfUnity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.hasEnoughRootsOfUnity", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.EnoughRootsOfUnity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCyclic.monoidHom_equiv_self", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.EnoughRootsOfUnity", "is_tactic_proof": true, "tactics": ["have", "have", "let", "exact"], "tactic_count": 4}
{"name": "instHasEnoughRootsOfUnityOfNatNat", "kind": "instance", "module": "Mathlib.RingTheory.RootsOfUnity.EnoughRootsOfUnity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimitiveRoot.prod_one_sub_pow_eq_order", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.Lemmas", "is_tactic_proof": true, "tactics": ["have", "rw", "replace", "apply_fun", "simpa", "card_range,"], "tactic_count": 6}
{"name": "IsPrimitiveRoot.prod_pow_sub_one_eq_order", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.Lemmas", "is_tactic_proof": true, "tactics": ["have", "simp"], "tactic_count": 2}
{"name": "IsPrimitiveRoot.self_sub_one_pow_dvd_order", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.Lemmas", "is_tactic_proof": true, "tactics": ["let", "obtain", "have", "refine", "exact", "let", "have", "refine", "apply", "apply", "exact", "exact", "refine", "apply", "exact", "exact", "push_cast", "have", "rw", "congr", "conv", "rw", "conv"], "tactic_count": 23}
{"name": "IsPrimitiveRoot.isIntegral", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.Minpoly", "is_tactic_proof": true, "tactics": ["use", "constructor", "exact", "simp"], "tactic_count": 4}
{"name": "IsPrimitiveRoot.minpoly_dvd_x_pow_sub_one", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.Minpoly", "is_tactic_proof": true, "tactics": ["rcases", "simp", "apply", "simp"], "tactic_count": 4}
{"name": "IsPrimitiveRoot.separable_minpoly_mod", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.Minpoly", "is_tactic_proof": false, "tactics": ["have", "convert", "simp", "refine", "by_contra", "exact"], "tactic_count": 6}
{"name": "IsPrimitiveRoot.squarefree_minpoly_mod", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.Minpoly", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimitiveRoot.minpoly_dvd_expand", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.Minpoly", "is_tactic_proof": true, "tactics": ["rcases", "simp_all", "letI", "refine", "rw", "eval₂_eq_eval_map,", "exact"], "tactic_count": 7}
{"name": "IsPrimitiveRoot.minpoly_dvd_pow_mod", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.Minpoly", "is_tactic_proof": true, "tactics": ["set", "have", "rw", "rw", "apply", "exact"], "tactic_count": 6}
{"name": "IsPrimitiveRoot.minpoly_dvd_mod_p", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.Minpoly", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimitiveRoot.minpoly_eq_pow", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.Minpoly", "is_tactic_proof": true, "tactics": ["classical", "by_cases", "simp_all", "have", "by_contra", "set", "set", "have", "have", "have", "have", "have", "have", "rw", "refine", "have", "refine", "rw", "intro", "refine", "exact", "apply", "exact", "apply", "exact", "replace", "rw", "obtain", "rw", "have", "replace", "have", "rcases", "rw", "replace", "rw", "exact", "simp"], "tactic_count": 38}
{"name": "IsPrimitiveRoot.minpoly_eq_pow_coprime", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.Minpoly", "is_tactic_proof": true, "tactics": ["revert", "refine", "intro", "congr", "simpa", "intro", "congr", "simp", "intro", "rw", "replace", "have", "haveI", "rw", "congr", "ring"], "tactic_count": 16}
{"name": "IsPrimitiveRoot.pow_isRoot_minpoly", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.Minpoly", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "IsPrimitiveRoot.is_roots_of_minpoly", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.Minpoly", "is_tactic_proof": true, "tactics": ["by_cases", "have", "have", "intro", "obtain", "simp", "convert", "rw", "exact"], "tactic_count": 9}
{"name": "IsPrimitiveRoot.totient_le_degree_minpoly", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.Minpoly", "is_tactic_proof": true, "tactics": ["classical", "let", "let", "calc", "n.totient"], "tactic_count": 5}
{"name": "IsPrimitiveRoot.toRootsOfUnity", "kind": "definition", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "primitiveRoots", "kind": "definition", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_primitiveRoots", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": true, "tactics": ["classical", "rw", "exact"], "tactic_count": 3}
{"name": "primitiveRoots_zero", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "isPrimitiveRoot_of_mem_primitiveRoots", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimitiveRoot.mk_of_lt", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": true, "tactics": ["refine", "suffices", "refine", "exact"], "tactic_count": 4}
{"name": "IsPrimitiveRoot.of_subsingleton", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimitiveRoot.pow_eq_one_iff_dvd", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimitiveRoot.isUnit", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimitiveRoot.pow_ne_one_of_pos_of_lt", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimitiveRoot.ne_one", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimitiveRoot.pow_inj", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": true, "tactics": ["wlog", "exact", "apply", "rw", "apply", "apply", "rw"], "tactic_count": 7}
{"name": "IsPrimitiveRoot.one", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimitiveRoot.one_right_iff", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rintro"], "tactic_count": 3}
{"name": "IsPrimitiveRoot.coe_submonoidClass_iff", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": true, "tactics": ["simp_rw", "norm_cast"], "tactic_count": 2}
{"name": "IsPrimitiveRoot.coe_units_iff", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsPrimitiveRoot.isUnit_unit", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimitiveRoot.isUnit_unit'", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimitiveRoot.pow_of_coprime", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": true, "tactics": ["by_cases", "subst", "rcases", "rw", "rw", "refine", "dvd_of_pow_eq_one", "rw", "mul_right_comm]", "simp"], "tactic_count": 10}
{"name": "IsPrimitiveRoot.pow_of_prime", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimitiveRoot.pow_iff_coprime", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": true, "tactics": ["refine", "obtain", "obtain", "suffices", "rw", "rw", "apply", "rw"], "tactic_count": 8}
{"name": "IsPrimitiveRoot.orderOf", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimitiveRoot.unique", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimitiveRoot.eq_orderOf", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimitiveRoot.iff", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "IsPrimitiveRoot.not_iff", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimitiveRoot.iff_orderOf", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimitiveRoot.pow_mul_pow_lcm", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": true, "tactics": ["convert", "convert", "all_goals"], "tactic_count": 3}
{"name": "IsPrimitiveRoot.pow_of_dvd", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "IsPrimitiveRoot.mem_rootsOfUnity", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimitiveRoot.pow", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": true, "tactics": ["subst", "simp", "intro", "exact"], "tactic_count": 4}
{"name": "IsPrimitiveRoot.injOn_pow", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": true, "tactics": ["intro", "rw", "exact"], "tactic_count": 3}
{"name": "IsPrimitiveRoot.exists_pos", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimitiveRoot.existsUnique", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isPrimitiveRoot_of_mem_rootsOfUnity", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimitiveRoot.map_of_injective", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimitiveRoot.of_map_of_injective", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimitiveRoot.map_iff_of_injective", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimitiveRoot.zero", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimitiveRoot.ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimitiveRoot.injOn_pow_mul", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimitiveRoot.zpow_eq_one", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": true, "tactics": ["exact_mod_cast"], "tactic_count": 1}
{"name": "IsPrimitiveRoot.zpow_eq_one_iff_dvd", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": true, "tactics": ["by_cases", "lift", "have", "lift", "rw", "norm_cast", "rw"], "tactic_count": 7}
{"name": "IsPrimitiveRoot.inv", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimitiveRoot.inv_iff", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimitiveRoot.zpow_of_gcd_eq_one", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": true, "tactics": ["by_cases", "lift", "exact_mod_cast", "have", "lift", "rw", "apply", "rwa"], "tactic_count": 8}
{"name": "IsPrimitiveRoot.sub_one_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimitiveRoot.primitiveRoots_one", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": true, "tactics": ["refine", "simp", "rwa"], "tactic_count": 3}
{"name": "IsPrimitiveRoot.neZero'", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": true, "tactics": ["let", "refine", "obtain", "have", "have", "have", "refine", "rw"], "tactic_count": 8}
{"name": "IsPrimitiveRoot.mem_nthRootsFinset", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimitiveRoot.eq_neg_one_of_two_right", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimitiveRoot.neg_one", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "IsPrimitiveRoot.geom_sum_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "IsPrimitiveRoot.pow_sub_one_eq", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": true, "tactics": ["rw", "hζ.geom_sum_eq_zero"], "tactic_count": 2}
{"name": "IsPrimitiveRoot.zmodEquivZPowers", "kind": "definition", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimitiveRoot.zmodEquivZPowers_apply_coe_int", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": false, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsPrimitiveRoot.zmodEquivZPowers_apply_coe_nat", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": true, "tactics": ["have", "simp"], "tactic_count": 2}
{"name": "IsPrimitiveRoot.zmodEquivZPowers_symm_apply_zpow", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsPrimitiveRoot.zmodEquivZPowers_symm_apply_zpow'", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimitiveRoot.zmodEquivZPowers_symm_apply_pow", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsPrimitiveRoot.zmodEquivZPowers_symm_apply_pow'", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimitiveRoot.zpowers_eq", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": true, "tactics": ["apply", "have", "refine", "calc"], "tactic_count": 4}
{"name": "IsPrimitiveRoot.map_rootsOfUnity", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": true, "tactics": ["letI", "replace", "rw"], "tactic_count": 3}
{"name": "rootsOfUnityEquivOfPrimitiveRoots", "kind": "definition", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "rootsOfUnityEquivOfPrimitiveRoots_symm_apply", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": true, "tactics": ["obtain", "rw"], "tactic_count": 2}
{"name": "IsPrimitiveRoot.eq_pow_of_mem_rootsOfUnity", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": true, "tactics": ["obtain", "have", "let", "have", "lift", "refine", "zify", "rw"], "tactic_count": 8}
{"name": "IsPrimitiveRoot.eq_pow_of_pow_eq_one", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": true, "tactics": ["lift", "lift", "simp", "rw", "exact"], "tactic_count": 5}
{"name": "IsPrimitiveRoot.isPrimitiveRoot_iff'", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": true, "tactics": ["constructor", "intro", "obtain", "rw", "exact", "rintro"], "tactic_count": 6}
{"name": "IsPrimitiveRoot.isPrimitiveRoot_iff", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": true, "tactics": ["constructor", "intro", "obtain", "rw", "exact", "rintro"], "tactic_count": 6}
{"name": "IsPrimitiveRoot.nthRoots_eq", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": true, "tactics": ["obtain", "by_cases", "rw", "simp", "classical", "symm", "rw", "intro", "simp", "obtain", "rw", "simpa"], "tactic_count": 12}
{"name": "IsPrimitiveRoot.adjoin_pair_eq", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": true, "tactics": ["have", "refine", "refine", "obtain", "exact", "obtain", "exact", "have", "obtain", "aesop"], "tactic_count": 10}
{"name": "IsPrimitiveRoot.card_nthRoots", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": true, "tactics": ["split_ifs", "obtain", "rw", "obtain", "push_neg", "simpa"], "tactic_count": 6}
{"name": "IsPrimitiveRoot.card_rootsOfUnity'", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": true, "tactics": ["let", "have", "calc"], "tactic_count": 3}
{"name": "IsPrimitiveRoot.card_rootsOfUnity", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact"], "tactic_count": 3}
{"name": "card_rootsOfUnity_eq_iff_exists_isPrimitiveRoot", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": true, "tactics": ["refine", "obtain", "rw", "use"], "tactic_count": 4}
{"name": "IsPrimitiveRoot.card_nthRoots_one", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsPrimitiveRoot.nthRoots_nodup", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": true, "tactics": ["obtain", "by_cases", "obtain", "by_cases", "exact", "rw", "exact", "suffices", "simpa"], "tactic_count": 9}
{"name": "IsPrimitiveRoot.nthRoots_one_nodup", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimitiveRoot.card_nthRootsFinset", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "IsPrimitiveRoot.card_primitiveRoots", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "have", "symm", "refine", "simp", "rintro", "rw", "exact", "simp", "rintro", "exact", "simp", "intro", "rw", "rcases", "exact"], "tactic_count": 17}
{"name": "IsPrimitiveRoot.primitiveRootsPowEquiv", "kind": "definition", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimitiveRoot.primitiveRootsPowEquivOfCoprime", "kind": "definition", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimitiveRoot.disjoint", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots.0.IsPrimitiveRoot.nthRoots_one_eq_biUnion_primitiveRoots'", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": true, "tactics": ["ext", "suffices", "simpa", "constructor", "intro", "obtain", "exact", "rintro", "have", "rw", "rw"], "tactic_count": 11}
{"name": "IsPrimitiveRoot.nthRoots_one_eq_biUnion_primitiveRoots", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "have", "exact"], "tactic_count": 4}
{"name": "IsPrimitiveRoot.autToPow", "kind": "definition", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimitiveRoot.coe_autToPow_apply", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrimitiveRoot.autToPow_spec", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": true, "tactics": ["rw", "generalize_proofs", "refine", "rw", "congr", "rw", "conv", "rw", "exact"], "tactic_count": 9}
{"name": "IsCyclic.exists_apply_ne_one", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": true, "tactics": ["let", "obtain", "obtain", "have", "rw", "let", "have", "use", "contrapose", "specialize", "rw", "obtain", "rw", "obtain", "rw"], "tactic_count": 15}
{"name": "ZMod.exists_monoidHom_apply_ne_one", "kind": "theorem", "module": "Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots", "is_tactic_proof": true, "tactics": ["obtain", "have", "simp", "exact", "simp"], "tactic_count": 5}
{"name": "instIsSemisimpleModuleOfIsSimpleModule", "kind": "instance", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsSimpleModule", "kind": "instance", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSemisimpleRing", "kind": "abbrev", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsSemisimpleRingOfSubsingleton", "kind": "instance", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.isSemisimpleRing", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.isSemisimpleRing_iff", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSimpleModule.nontrivial", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.isSimpleModule_iff_of_bijective", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "IsSimpleModule.congr", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.isSimpleModule_iff", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isSimpleModule_iff_isAtom", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "isSimpleModule_iff_isCoatom", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "covBy_iff_quot_is_simple", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": true, "tactics": ["set", "rw", "simp"], "tactic_count": 3}
{"name": "IsSimpleModule.isAtom", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSimpleModule.span_singleton_eq_top", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSimpleModule.instIsPrincipal", "kind": "instance", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSimpleModule.toSpanSingleton_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsSimpleModule.ker_toSpanSingleton_isMaximal", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsSimpleModule.instIsNoetherian", "kind": "instance", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isSimpleModule_iff_quot_maximal", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": true, "tactics": ["refine", "have", "have", "exact", "convert"], "tactic_count": 5}
{"name": "IsSimpleModule.annihilator_isMaximal", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "isSimpleModule_iff_toSpanSingleton_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isSimpleModule_self_iff_isUnit", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSemisimpleModule.of_sSup_simples_eq_top", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Finite.of_isComplemented_domain", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Finite.instLinearMapIdSubtypeMemSubmoduleOfIsSemisimpleModule", "kind": "instance", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Finite.of_isComplemented_codomain", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Finite.instLinearMapIdSubtypeMemSubmoduleOfIsSemisimpleModule_1", "kind": "instance", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSemisimpleModule.eq_bot_or_exists_simple_le", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "IsSemisimpleModule.exists_submodule_linearEquiv_quotient", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSemisimpleModule.exists_quotient_linearEquiv_submodule", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSemisimpleModule.extension_property", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSemisimpleModule.lifting_property", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": true, "tactics": ["have", "let", "refine", "obtain", "simp", "simp"], "tactic_count": 6}
{"name": "IsSemisimpleModule.sSup_simples_le", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsSemisimpleModule.exists_simple_submodule", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsSemisimpleModule.sSup_simples_eq_top", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsSemisimpleModule.exists_sSupIndep_sSup_simples_eq_top", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": true, "tactics": ["have", "simp_rw", "exact"], "tactic_count": 3}
{"name": "IsSemisimpleModule.annihilator_isRadical", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsSemisimpleModule.submodule", "kind": "instance", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSemisimpleModule.congr", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSemisimpleModule.of_injective", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSemisimpleModule.quotient", "kind": "instance", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSemisimpleModule.instIsNoetherianOfFinite", "kind": "instance", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSemisimpleModule.range", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSemisimpleModule.of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.isSemisimpleModule_iff_of_bijective", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "LinearMap.isSemisimpleModule_of_injective", "kind": "proofWanted", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.isSemisimpleModule_of_surjective", "kind": "proofWanted", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.isSemisimpleModule_iff", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sSup_simples_eq_top_iff_isSemisimpleModule", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isSemisimpleModule_of_isSemisimpleModule_submodule", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "simpa"], "tactic_count": 3}
{"name": "isSemisimpleModule_biSup_of_isSemisimpleModule_submodule", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": false, "tactics": ["refine", "isSemisimpleModule_of_isSemisimpleModule_submodule", "simp_rw"], "tactic_count": 3}
{"name": "isSemisimpleModule_of_isSemisimpleModule_submodule'", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsSemisimpleModuleDFinsupp", "kind": "instance", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "IsSemisimpleModule.exists_linearEquiv_dfinsupp", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": true, "tactics": ["have", "refine", "rw", "classical", "exact"], "tactic_count": 5}
{"name": "isSemisimpleModule_iff_exists_linearEquiv_dfinsupp", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": true, "tactics": ["refine", "have", "exact"], "tactic_count": 3}
{"name": "IsSemisimpleModule.exists_linearEquiv_fin_dfinsupp", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsSemisimpleModuleForallOfFinite", "kind": "instance", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": true, "tactics": ["classical", "exact", "isSemisimpleModule_of_isSemisimpleModule_submodule"], "tactic_count": 3}
{"name": "IsSemisimpleModule.sup", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": true, "tactics": ["let", "rw", "exact"], "tactic_count": 3}
{"name": "IsSemisimpleRing.exists_linearEquiv_ideal_of_isSimpleModule", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsSemisimpleModuleFinsupp", "kind": "instance", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSemisimpleRing.isSemisimpleModule", "kind": "instance", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSemisimpleModule.isCoatomic_submodule", "kind": "instance", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsSemisimpleRingForallOfFinite", "kind": "instance", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": true, "tactics": ["letI", "let", "have", "infer_instance"], "tactic_count": 4}
{"name": "instIsSemisimpleRingProd", "kind": "instance", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": true, "tactics": ["letI", "letI", "let", "let", "rw", "rw", "rw", "exact"], "tactic_count": 8}
{"name": "RingHom.isSemisimpleRing_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": true, "tactics": ["letI", "haveI", "let", "rw", "infer_instance"], "tactic_count": 5}
{"name": "IsSemisimpleRing.ideal_eq_span_idempotent", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "exact", "rw"], "tactic_count": 4}
{"name": "instIsPrincipalIdealRingOfIsSemisimpleRing", "kind": "instance", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.injective_or_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "LinearMap.injective_of_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.surjective_or_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "LinearMap.surjective_of_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.bijective_or_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.bijective_of_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.isCoatom_ker_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "LinearMap.linearEquiv_of_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.instDivisionRing", "kind": "instance", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.instIsSimpleModuleEndOfNontrivial", "kind": "instance", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "JordanHolderModule.instJordanHolderLattice", "kind": "instance", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "jacobson_density", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Finite.toModuleEnd_moduleEnd_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.injective_of_isSemisimpleRing", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.InjectiveProjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.projective_of_isSemisimpleRing", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.InjectiveProjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSimpleRing.exists_algEquiv_matrix_of_isAlgClosed", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.IsAlgClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSemisimpleRing.exists_algEquiv_pi_matrix_of_isAlgClosed", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.IsAlgClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIsotypicOfType", "kind": "definition", "module": "Mathlib.RingTheory.SimpleModule.Isotypic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIsotypic", "kind": "definition", "module": "Mathlib.RingTheory.SimpleModule.Isotypic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIsotypicOfType.isIsotypic", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Isotypic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIsotypicOfType.of_subsingleton", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Isotypic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIsotypic.of_subsingleton", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Isotypic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIsotypicOfType.of_isSimpleModule", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Isotypic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIsotypic.of_self", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Isotypic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIsotypicOfType.of_linearEquiv_type", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Isotypic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIsotypicOfType.of_injective", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Isotypic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIsotypic.of_injective", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Isotypic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.isIsotypicOfType_iff", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Isotypic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.isIsotypicOfType_iff_type", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Isotypic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.isIsotypic_iff", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Isotypic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isIsotypicOfType_submodule_iff", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Isotypic", "is_tactic_proof": true, "tactics": ["rw", "have", "simp_rw", "exact"], "tactic_count": 4}
{"name": "isIsotypic_submodule_iff", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Isotypic", "is_tactic_proof": true, "tactics": ["rw", "have", "simp_rw"], "tactic_count": 3}
{"name": "IsIsotypicOfType.linearEquiv_finsupp", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Isotypic", "is_tactic_proof": true, "tactics": ["have", "classical", "exact"], "tactic_count": 3}
{"name": "IsIsotypic.linearEquiv_finsupp", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Isotypic", "is_tactic_proof": true, "tactics": ["have", "rw", "have", "exact"], "tactic_count": 4}
{"name": "IsIsotypicOfType.linearEquiv_fun", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Isotypic", "is_tactic_proof": true, "tactics": ["have", "classical", "exact"], "tactic_count": 3}
{"name": "IsIsotypic.linearEquiv_fun", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Isotypic", "is_tactic_proof": true, "tactics": ["have", "rw", "have", "exact"], "tactic_count": 4}
{"name": "IsIsotypic.submodule_linearEquiv_fun", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Isotypic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isotypicComponent", "kind": "definition", "module": "Mathlib.RingTheory.SimpleModule.Isotypic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isotypicComponents", "kind": "definition", "module": "Mathlib.RingTheory.SimpleModule.Isotypic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.le_isotypicComponent", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Isotypic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bot_lt_isotypicComponent", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Isotypic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bot_lt_isotypicComponents", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Isotypic", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "instNontrivialSubtypeMemSubmoduleValSetIsotypicComponents", "kind": "instance", "module": "Mathlib.RingTheory.SimpleModule.Isotypic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsSemisimpleModuleSubtypeMemSubmoduleIsotypicComponent", "kind": "instance", "module": "Mathlib.RingTheory.SimpleModule.Isotypic", "is_tactic_proof": true, "tactics": ["rw", "refine", "have", "infer_instance"], "tactic_count": 4}
{"name": "instIsSemisimpleModuleSubtypeMemSubmoduleValSetIsotypicComponents", "kind": "instance", "module": "Mathlib.RingTheory.SimpleModule.Isotypic", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "LinearEquiv.isotypicComponent_eq", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Isotypic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.le_linearEquiv_of_sSup_eq_top", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Isotypic", "is_tactic_proof": true, "tactics": ["have", "have", "have", "exists_ne_zero_of_sSup_eq_top", "have", "exact"], "tactic_count": 6}
{"name": "Submodule.linearEquiv_of_sSup_eq_top", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Isotypic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.le_linearEquiv_of_le_sSup", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Isotypic", "is_tactic_proof": true, "tactics": ["rw", "have", "have", "have", "obtain", "rw", "exact"], "tactic_count": 7}
{"name": "Submodule.linearEquiv_of_le_sSup", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Isotypic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsSimpleModuleSubtypeMemSubmoduleValSetSetOfNonemptyLinearEquivId", "kind": "instance", "module": "Mathlib.RingTheory.SimpleModule.Isotypic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIsotypicOfType.isotypicComponent", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Isotypic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIsotypic.isotypicComponent", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Isotypic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIsotypic.isotypicComponents", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Isotypic", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "eq_isotypicComponent_of_le", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Isotypic", "is_tactic_proof": true, "tactics": ["obtain", "have", "exact"], "tactic_count": 3}
{"name": "sSupIndep_isotypicComponents", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Isotypic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFiniteElemSubmoduleIsotypicComponentsOfIsNoetherian", "kind": "instance", "module": "Mathlib.RingTheory.SimpleModule.Isotypic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIsotypicOfType.of_isotypicComponent_eq_top", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Isotypic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.map_le_isotypicComponent", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Isotypic", "is_tactic_proof": true, "tactics": ["conv_lhs", "obtain", "exact", "simp_rw"], "tactic_count": 4}
{"name": "LinearMap.le_comap_isotypicComponent", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Isotypic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.IsFullyInvariant", "kind": "definition", "module": "Mathlib.RingTheory.SimpleModule.Isotypic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isFullyInvariant_iff_isTwoSided", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Isotypic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "fullyInvariantSubmodule", "kind": "definition", "module": "Mathlib.RingTheory.SimpleModule.Isotypic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_fullyInvariantSubmodule_iff", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Isotypic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSupIndep.ringEquiv", "kind": "definition", "module": "Mathlib.RingTheory.SimpleModule.Isotypic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSupIndep.algEquiv", "kind": "definition", "module": "Mathlib.RingTheory.SimpleModule.Isotypic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.IsFullyInvariant.isotypicComponent", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Isotypic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.IsFullyInvariant.of_mem_isotypicComponents", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Isotypic", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "GaloisCoinsertion.setIsotypicComponents", "kind": "definition", "module": "Mathlib.RingTheory.SimpleModule.Isotypic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_isotypicComponent_iff", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Isotypic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isotypicComponent_eq_top_iff", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Isotypic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "isFullyInvariant_iff_le_imp_isotypicComponent_le", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Isotypic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_isotypicComponent_iff", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Isotypic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isIsotypic_iff_isFullyInvariant_imp_bot_or_top", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Isotypic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_isotypicComponents_iff", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Isotypic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.setIsotypicComponents", "kind": "definition", "module": "Mathlib.RingTheory.SimpleModule.Isotypic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isFullyInvariant_iff_sSup_isotypicComponents", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Isotypic", "is_tactic_proof": true, "tactics": ["refine", "rintro", "convert", "simp", "rintro", "exact"], "tactic_count": 6}
{"name": "sSup_isotypicComponents", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Isotypic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSemisimpleModule.endAlgEquiv", "kind": "definition", "module": "Mathlib.RingTheory.SimpleModule.Isotypic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSemisimpleModule.endRingEquiv", "kind": "definition", "module": "Mathlib.RingTheory.SimpleModule.Isotypic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isSimpleModule_iff_finrank_eq_one", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.Rank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSimpleRing.tfae", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.WedderburnArtin", "is_tactic_proof": true, "tactics": ["tfae_have", "tfae_have", "tfae_have", "have", "simp_rw", "have", "obtain", "exact", "exact", "tfae_finish"], "tactic_count": 10}
{"name": "IsSimpleRing.isSemisimpleRing_iff_isArtinianRing", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.WedderburnArtin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isSimpleRing_isArtinianRing_iff", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.WedderburnArtin", "is_tactic_proof": true, "tactics": ["refine", "on_goal", "all_goals", "simp_rw", "isSimpleRing_iff_isTwoSided_imp]", "exact", "exact"], "tactic_count": 7}
{"name": "IsSimpleRing.instIsSemisimpleRing", "kind": "instance", "module": "Mathlib.RingTheory.SimpleModule.WedderburnArtin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSimpleRing.isIsotypic", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.WedderburnArtin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSimpleRing.exists_ringEquiv_matrix_end_mulOpposite", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.WedderburnArtin", "is_tactic_proof": true, "tactics": ["have", "refine", "exact"], "tactic_count": 3}
{"name": "IsSimpleRing.exists_ringEquiv_matrix_divisionRing", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.WedderburnArtin", "is_tactic_proof": true, "tactics": ["have", "classical"], "tactic_count": 2}
{"name": "IsSimpleRing.exists_algEquiv_matrix_end_mulOpposite", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.WedderburnArtin", "is_tactic_proof": true, "tactics": ["have", "refine", "exact"], "tactic_count": 3}
{"name": "IsSimpleRing.exists_algEquiv_matrix_divisionRing", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.WedderburnArtin", "is_tactic_proof": true, "tactics": ["have", "classical"], "tactic_count": 2}
{"name": "IsSimpleRing.exists_algEquiv_matrix_divisionRing_finite", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.WedderburnArtin", "is_tactic_proof": true, "tactics": ["have", "have", "classical", "exact"], "tactic_count": 4}
{"name": "IsSemisimpleModule.exists_end_algEquiv_pi_matrix_end", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.WedderburnArtin", "is_tactic_proof": false, "tactics": ["choose", "classical", "exact"], "tactic_count": 3}
{"name": "IsSemisimpleModule.exists_end_ringEquiv_pi_matrix_end", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.WedderburnArtin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSemisimpleModule.exists_end_algEquiv_pi_matrix_divisionRing", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.WedderburnArtin", "is_tactic_proof": true, "tactics": ["have", "classical"], "tactic_count": 2}
{"name": "IsSemisimpleModule.exists_end_ringEquiv_pi_matrix_divisionRing", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.WedderburnArtin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSemisimpleRing.moduleEnd", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.WedderburnArtin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSemisimpleRing.exists_algEquiv_pi_matrix_end_mulOpposite", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.WedderburnArtin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSemisimpleRing.exists_algEquiv_pi_matrix_divisionRing", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.WedderburnArtin", "is_tactic_proof": true, "tactics": ["have", "classical"], "tactic_count": 2}
{"name": "IsSemisimpleRing.exists_algEquiv_pi_matrix_divisionRing_finite", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.WedderburnArtin", "is_tactic_proof": true, "tactics": ["have", "have", "refine", "let", "exact"], "tactic_count": 5}
{"name": "IsSemisimpleRing.exists_ringEquiv_pi_matrix_end_mulOpposite", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.WedderburnArtin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSemisimpleRing.exists_ringEquiv_pi_matrix_divisionRing", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.WedderburnArtin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSemisimpleRing.instMatrix", "kind": "instance", "module": "Mathlib.RingTheory.SimpleModule.WedderburnArtin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSemisimpleRing.instMulOpposite", "kind": "instance", "module": "Mathlib.RingTheory.SimpleModule.WedderburnArtin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isSemisimpleRing_mulOpposite_iff", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.WedderburnArtin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isSemisimpleRing_iff_pi_matrix_divisionRing", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleModule.WedderburnArtin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSemiprimaryRing.mulOpposite", "kind": "proofWanted", "module": "Mathlib.RingTheory.SimpleModule.WedderburnArtin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isSemiprimaryRing_mulOpposite_iff", "kind": "proofWanted", "module": "Mathlib.RingTheory.SimpleModule.WedderburnArtin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsArtinianRing.isNoetherianRing_iff_isArtinianRing_mulOpposite", "kind": "proofWanted", "module": "Mathlib.RingTheory.SimpleModule.WedderburnArtin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSimpleRing.instNontrivial", "kind": "instance", "module": "Mathlib.RingTheory.SimpleRing.Basic", "is_tactic_proof": true, "tactics": ["obtain", "use"], "tactic_count": 2}
{"name": "IsSimpleRing.one_mem_of_ne_bot", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleRing.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSimpleRing.one_mem_of_ne_zero_mem", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleRing.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSimpleRing.of_eq_bot_or_eq_top", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleRing.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DivisionRing.isSimpleRing", "kind": "instance", "module": "Mathlib.RingTheory.SimpleRing.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSimpleRing.injective_ringHom_or_subsingleton_codomain", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleRing.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.injective", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleRing.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSimpleRing.iff_injective_ringHom_or_subsingleton_codomain", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleRing.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSimpleRing.iff_injective_ringHom", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleRing.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSimpleRing.instMulOpposite", "kind": "instance", "module": "Mathlib.RingTheory.SimpleRing.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSimpleRing.of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleRing.Congr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSimpleRing.of_ringEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleRing.Congr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isSimpleRing_iff_isTwoSided_imp", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleRing.Congr", "is_tactic_proof": true, "tactics": ["let", "simp_rw", "e.forall_congr_left,", "simp"], "tactic_count": 4}
{"name": "IsSimpleRing.isField_center", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleRing.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isSimpleRing_iff_isField", "kind": "theorem", "module": "Mathlib.RingTheory.SimpleRing.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSimpleRing.matrix", "kind": "instance", "module": "Mathlib.RingTheory.SimpleRing.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsSimpleOrderIdeal", "kind": "instance", "module": "Mathlib.RingTheory.SimpleRing.Principal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPrincipalIdealRing.of_isSimpleRing", "kind": "instance", "module": "Mathlib.RingTheory.SimpleRing.Principal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDomain.of_isSimpleRing", "kind": "instance", "module": "Mathlib.RingTheory.SimpleRing.Principal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.FormallySmooth.liftAdicCompletionAux", "kind": "definition", "module": "Mathlib.RingTheory.Smooth.AdicCompletion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.FormallySmooth.factorₐ_comp_liftAdicCompletionAux", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.AdicCompletion", "is_tactic_proof": true, "tactics": ["cases", "zero", "ext", "apply", "simp", "succ", "rw", "ext", "simp"], "tactic_count": 9}
{"name": "Algebra.FormallySmooth.factorₐ_comp_liftAdicCompletionAux_of_le", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.AdicCompletion", "is_tactic_proof": true, "tactics": ["induction", "base", "succ", "ih", "rw", "simpa"], "tactic_count": 6}
{"name": "Algebra.FormallySmooth.exists_adicCompletionEvalOneₐ_comp_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.AdicCompletion", "is_tactic_proof": false, "tactics": ["refine", "ext", "simp"], "tactic_count": 3}
{"name": "Algebra.FormallySmooth.exists_mkₐ_comp_eq_of_isAdicComplete", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.AdicCompletion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.FormallySmooth.exists_kerProj_comp_eq_id", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.AdicCompletion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.FormallySmooth.comp_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.mvPolynomial", "kind": "instance", "module": "Mathlib.RingTheory.Smooth.Basic", "is_tactic_proof": true, "tactics": ["let", "have", "have", "have", "exact"], "tactic_count": 5}
{"name": "Algebra.FormallySmooth.exists_lift", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.Basic", "is_tactic_proof": true, "tactics": ["revert", "change", "revert", "apply", "intro", "intro", "let", "commutes", "obtain", "obtain", "replace", "conv_rhs", "rw", "exact"], "tactic_count": 14}
{"name": "Algebra.FormallySmooth.lift", "kind": "definition", "module": "Mathlib.RingTheory.Smooth.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.FormallySmooth.comp_lift", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.FormallySmooth.mk_lift", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.FormallySmooth.liftOfSurjective", "kind": "definition", "module": "Mathlib.RingTheory.Smooth.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.FormallySmooth.liftOfSurjective_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.Basic", "is_tactic_proof": true, "tactics": ["apply", "conv_rhs", "apply", "rw", "simp"], "tactic_count": 5}
{"name": "Algebra.FormallySmooth.comp_liftOfSurjective", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.FormallySmooth.instFinitePresentationKaehlerDifferentialOfEssFiniteType", "kind": "instance", "module": "Mathlib.RingTheory.Smooth.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Extension.homInfinitesimal", "kind": "definition", "module": "Mathlib.RingTheory.Smooth.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Extension.H1Cotangent.equivOfFormallySmooth", "kind": "definition", "module": "Mathlib.RingTheory.Smooth.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Extension.H1Cotangent.equivOfFormallySmooth_toLinearMap", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.Basic", "is_tactic_proof": true, "tactics": ["ext1", "refine", "change", "rw"], "tactic_count": 4}
{"name": "Algebra.Extension.H1Cotangent.equivOfFormallySmooth_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Algebra.Extension.H1Cotangent.equivOfFormallySmooth_symm", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Extension.equivH1CotangentOfFormallySmooth", "kind": "definition", "module": "Mathlib.RingTheory.Smooth.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Extension.cotangentComplex_injective_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Algebra.FormallySmooth.kerCotangentToTensor_injective_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.FormallySmooth.iff_split_injection", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.Basic", "is_tactic_proof": false, "tactics": ["rw", "convert", "rw", "simp", "rw"], "tactic_count": 5}
{"name": "Algebra.Extension.formallySmooth_iff_split_injection", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.Basic", "is_tactic_proof": true, "tactics": ["refine", "let", "constructor", "intro", "exact", "intro", "exact"], "tactic_count": 7}
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{"name": "Algebra.FormallySmooth.of_split", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.FormallySmooth.of_comp_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Algebra.FormallySmooth.of_equiv", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.FormallySmooth.iff_of_equiv", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.FormallySmooth.polynomial", "kind": "instance", "module": "Mathlib.RingTheory.Smooth.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.FormallySmooth.inst", "kind": "instance", "module": "Mathlib.RingTheory.Smooth.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.FormallySmooth.comp", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.Basic", "is_tactic_proof": true, "tactics": ["refine", "obtain", "letI", "obtain", "apply_fun", "exact"], "tactic_count": 6}
{"name": "Algebra.FormallySmooth.of_restrictScalars", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.FormallySmooth.iff_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.Basic", "is_tactic_proof": true, "tactics": ["rw", "constructor", "intro", "let", "rw", "e.toAlgHom.comp_algebraMap,", "intro", "let", "exact"], "tactic_count": 9}
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{"name": "Algebra.FormallySmooth.of_isLocalization", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.Basic", "is_tactic_proof": true, "tactics": ["refine", "have", "intro", "apply", "convert", "simp", "let", "use", "apply", "refine", "ext", "simp"], "tactic_count": 12}
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{"name": "Algebra.FormallySmooth.localization_base", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.Basic", "is_tactic_proof": true, "tactics": ["refine", "letI", "letI", "let", "refine", "intro", "change", "algebraMap", "congr", "refine", "rw", "use", "ext", "simp"], "tactic_count": 14}
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{"name": "Algebra.Smooth.of_equiv", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Smooth.of_isLocalization_Away", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Smooth.comp", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Smooth.baseChange", "kind": "instance", "module": "Mathlib.RingTheory.Smooth.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.FormallySmooth.adjoin_of_algebraicIndependent", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.Field", "is_tactic_proof": true, "tactics": ["have", "have", "exact"], "tactic_count": 3}
{"name": "Algebra.FormallySmooth.of_algebraicIndependent", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.Field", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
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{"name": "Algebra.Smooth.flat_of_isNoetherianRing", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.Flat", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
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{"name": "TensorProduct.toIntegralClosure", "kind": "definition", "module": "Mathlib.RingTheory.Smooth.IntegralClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.toIntegralClosure_injective_of_flat", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.IntegralClosure", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "TensorProduct.toIntegralClosure_bijective_of_tower", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.IntegralClosure", "is_tactic_proof": false, "tactics": ["let", "convert", "rw", "congr", "ext"], "tactic_count": 5}
{"name": "TensorProduct.toIntegralClosure_bijective_of_isLocalizationAway", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.IntegralClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TensorProduct.toIntegralClosure_mvPolynomial_bijective", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.IntegralClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "derivationOfSectionOfKerSqZero", "kind": "definition", "module": "Mathlib.RingTheory.Smooth.Kaehler", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isScalarTower_of_section_of_ker_sqZero", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.Kaehler", "is_tactic_proof": true, "tactics": ["letI", "constructor", "intro", "ext", "change", "simp", "congr", "rw", "refine", "simpa"], "tactic_count": 10}
{"name": "retractionOfSectionOfKerSqZero", "kind": "definition", "module": "Mathlib.RingTheory.Smooth.Kaehler", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "retractionOfSectionOfKerSqZero_tmul_D", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.Kaehler", "is_tactic_proof": true, "tactics": ["letI", "haveI", "simp", "erw", "exact"], "tactic_count": 5}
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{"name": "sectionOfRetractionKerToTensorAux_prop", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.Kaehler", "is_tactic_proof": false, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "sectionOfRetractionKerToTensorAux", "kind": "definition", "module": "Mathlib.RingTheory.Smooth.Kaehler", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sectionOfRetractionKerToTensorAux_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.Kaehler", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toAlgHom_comp_sectionOfRetractionKerToTensorAux", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.Kaehler", "is_tactic_proof": true, "tactics": ["ext", "obtain", "simp"], "tactic_count": 3}
{"name": "sectionOfRetractionKerToTensor", "kind": "definition", "module": "Mathlib.RingTheory.Smooth.Kaehler", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "toAlgHom_comp_sectionOfRetractionKerToTensor", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.Kaehler", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "retractionKerToTensorEquivSection", "kind": "definition", "module": "Mathlib.RingTheory.Smooth.Kaehler", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "derivationQuotKerSq", "kind": "definition", "module": "Mathlib.RingTheory.Smooth.Kaehler", "is_tactic_proof": false, "tactics": ["letI", "refine", "rintro", "simp", "simp", "refine", "intro", "simp", "intro", "change", "intro", "obtain", "obtain", "change", "simp"], "tactic_count": 15}
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{"name": "tensorKaehlerQuotKerSqEquiv", "kind": "definition", "module": "Mathlib.RingTheory.Smooth.Kaehler", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tensorKaehlerQuotKerSqEquiv_tmul_D", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.Kaehler", "is_tactic_proof": true, "tactics": ["change", "simp"], "tactic_count": 2}
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{"name": "retractionKerCotangentToTensorEquivSection", "kind": "definition", "module": "Mathlib.RingTheory.Smooth.Kaehler", "is_tactic_proof": true, "tactics": ["let", "have", "have", "rw", "let", "let", "have", "ext", "obtain", "exact", "refine", "refine", "rintro", "obtain", "simp", "exact", "ext1", "rw", "obtain", "exact", "ext", "rw", "apply", "simp", "exact", "intro", "ext", "simp", "intro", "ext", "simp"], "tactic_count": 31}
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{"name": "Algebra.smoothLocus", "kind": "definition", "module": "Mathlib.RingTheory.Smooth.Locus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Algebra.IsSmoothAt.exists_notMem_smooth", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.Locus", "is_tactic_proof": false, "tactics": ["obtain", "isBasis_basic_opens.exists_subset_of_mem_open", "refine", "rwa"], "tactic_count": 4}
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{"name": "Algebra.Smooth.DescentAux.instCommRingSubtypeMemSubalgebraSubalgebra", "kind": "instance", "module": "Mathlib.RingTheory.Smooth.NoetherianDescent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Smooth.DescentAux.algebra₀", "kind": "instance", "module": "Mathlib.RingTheory.Smooth.NoetherianDescent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Smooth.DescentAux.algebra₁", "kind": "instance", "module": "Mathlib.RingTheory.Smooth.NoetherianDescent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Smooth.DescentAux.algebra₂", "kind": "instance", "module": "Mathlib.RingTheory.Smooth.NoetherianDescent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Smooth.DescentAux.instIsScalarTowerSubtypeMemSubalgebraSubalgebra", "kind": "instance", "module": "Mathlib.RingTheory.Smooth.NoetherianDescent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Smooth.DescentAux.instFaithfulSMulSubtypeMemSubalgebraSubalgebra", "kind": "instance", "module": "Mathlib.RingTheory.Smooth.NoetherianDescent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Smooth.DescentAux.fg_subalgebra", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.NoetherianDescent", "is_tactic_proof": true, "tactics": ["refine", "refine", "exact", "refine", "refine", "exact", "refine", "exact"], "tactic_count": 8}
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{"name": "Algebra.FormallySmooth.of_pi", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.Pi", "is_tactic_proof": true, "tactics": ["classical", "fapply", "apply", "change", "rw", "have", "convert", "simp", "intro", "change", "simp", "ext", "change", "simp"], "tactic_count": 14}
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{"name": "Algebra.SubmersivePresentation.isStandardSmooth", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.StandardSmooth", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "Algebra.IsStandardSmooth.relativeDimension", "kind": "definition", "module": "Mathlib.RingTheory.Smooth.StandardSmooth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.SubmersivePresentation.isStandardSmoothOfRelativeDimension", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.StandardSmooth", "is_tactic_proof": true, "tactics": ["refine", "simp"], "tactic_count": 2}
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{"name": "Algebra.IsStandardSmoothOfRelativeDimension.of_algebraMap_bijective", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.StandardSmooth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsStandardSmoothOfRelativeDimension.id", "kind": "instance", "module": "Mathlib.RingTheory.Smooth.StandardSmooth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsStandardSmooth.finitePresentation", "kind": "instance", "module": "Mathlib.RingTheory.Smooth.StandardSmooth", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Algebra.IsStandardSmooth.of_algEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.StandardSmooth", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Algebra.IsStandardSmoothOfRelativeDimension.of_algEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.StandardSmooth", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Algebra.IsStandardSmooth.trans", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.StandardSmooth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsStandardSmoothOfRelativeDimension.trans", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.StandardSmooth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsStandardSmooth.localization_away", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.StandardSmooth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsStandardSmoothOfRelativeDimension.localization_away", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.StandardSmooth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsStandardSmooth.baseChange", "kind": "instance", "module": "Mathlib.RingTheory.Smooth.StandardSmooth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsStandardSmoothOfRelativeDimension.baseChange", "kind": "instance", "module": "Mathlib.RingTheory.Smooth.StandardSmooth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.instIsStandardSmoothOfSubsingleton", "kind": "instance", "module": "Mathlib.RingTheory.Smooth.StandardSmooth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.instIsStandardSmoothOfRelativeDimensionOfNatNatOfSubsingleton", "kind": "instance", "module": "Mathlib.RingTheory.Smooth.StandardSmooth", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.PreSubmersivePresentation.cotangentComplexAux", "kind": "definition", "module": "Mathlib.RingTheory.Smooth.StandardSmoothCotangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.PreSubmersivePresentation.cotangentComplexAux_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.StandardSmoothCotangent", "is_tactic_proof": false, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "Algebra.PreSubmersivePresentation.cotangentComplexAux_zero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.StandardSmoothCotangent", "is_tactic_proof": true, "tactics": ["rw", "simp_rw"], "tactic_count": 2}
{"name": "Algebra.SubmersivePresentation.cotangentComplexAux_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.StandardSmoothCotangent", "is_tactic_proof": true, "tactics": ["rw", "intro", "obtain", "rw", "rw", "have", "rw", "exact", "obtain", "have", "rw", "apply", "simp", "zero_mul,", "have", "ext", "simp", "apply", "have", "have", "rw", "have", "this", "exact", "change", "rw", "apply", "intro", "rw", "apply", "rw", "simpa", "exact"], "tactic_count": 33}
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{"name": "Algebra.SubmersivePresentation.cotangentComplex_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.StandardSmoothCotangent", "is_tactic_proof": true, "tactics": ["have", "simp", "exact"], "tactic_count": 3}
{"name": "Algebra.SubmersivePresentation.subsingleton_h1Cotangent", "kind": "instance", "module": "Mathlib.RingTheory.Smooth.StandardSmoothCotangent", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Algebra.SubmersivePresentation.basisCotangent", "kind": "definition", "module": "Mathlib.RingTheory.Smooth.StandardSmoothCotangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.SubmersivePresentation.basisCotangent_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.StandardSmoothCotangent", "is_tactic_proof": true, "tactics": ["symm", "apply", "ext", "simp_rw", "apply"], "tactic_count": 5}
{"name": "Algebra.SubmersivePresentation.free_cotangent", "kind": "instance", "module": "Mathlib.RingTheory.Smooth.StandardSmoothCotangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.SubmersivePresentation.sectionCotangent", "kind": "definition", "module": "Mathlib.RingTheory.Smooth.StandardSmoothCotangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.SubmersivePresentation.sectionCotangent_eq_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.StandardSmoothCotangent", "is_tactic_proof": true, "tactics": ["simp", "rw", "simp"], "tactic_count": 3}
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{"name": "Algebra.SubmersivePresentation.sectionCotangent_zero_of_notMem_range", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.StandardSmoothCotangent", "is_tactic_proof": true, "tactics": ["classical", "contrapose", "rw", "simp", "grind"], "tactic_count": 5}
{"name": "Algebra.SubmersivePresentation.basisKaehlerOfIsCompl", "kind": "definition", "module": "Mathlib.RingTheory.Smooth.StandardSmoothCotangent", "is_tactic_proof": false, "tactics": ["apply", "intro", "apply", "simp", "simp", "apply", "convert", "classical", "ext", "simp", "simp", "exact"], "tactic_count": 12}
{"name": "Algebra.SubmersivePresentation.basisKaehlerOfIsCompl_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.StandardSmoothCotangent", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Algebra.SubmersivePresentation.basisKaehler", "kind": "definition", "module": "Mathlib.RingTheory.Smooth.StandardSmoothCotangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.SubmersivePresentation.basisKaehler_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.StandardSmoothCotangent", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Algebra.SubmersivePresentation.free_kaehlerDifferential", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.StandardSmoothCotangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.SubmersivePresentation.rank_kaehlerDifferential", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.StandardSmoothCotangent", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Algebra.instFreeCotangentToExtensionUnitLocalizationAway", "kind": "instance", "module": "Mathlib.RingTheory.Smooth.StandardSmoothCotangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.cMulXSubOneCotangent", "kind": "abbrev", "module": "Mathlib.RingTheory.Smooth.StandardSmoothCotangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.cMulXSubOneCotangent_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.StandardSmoothCotangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.SubmersivePresentation.basisCotangent_localizationAway_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.StandardSmoothCotangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.basisCotangentAway", "kind": "definition", "module": "Mathlib.RingTheory.Smooth.StandardSmoothCotangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Generators.basisCotangentAway_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.StandardSmoothCotangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsStandardSmooth.free_kaehlerDifferential", "kind": "instance", "module": "Mathlib.RingTheory.Smooth.StandardSmoothCotangent", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Algebra.IsStandardSmooth.subsingleton_h1Cotangent", "kind": "instance", "module": "Mathlib.RingTheory.Smooth.StandardSmoothCotangent", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Algebra.IsStandardSmoothOfRelativeDimension.rank_kaehlerDifferential", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.StandardSmoothCotangent", "is_tactic_proof": true, "tactics": ["obtain", "rw"], "tactic_count": 2}
{"name": "Algebra.IsStandardSmoothOfRelativeDimension.iff_of_isStandardSmooth", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.StandardSmoothCotangent", "is_tactic_proof": true, "tactics": ["refine", "obtain", "refine", "apply", "rwa"], "tactic_count": 5}
{"name": "Algebra.IsStandardSmoothOfRelationDimension.subsingleton_kaehlerDifferential", "kind": "instance", "module": "Mathlib.RingTheory.Smooth.StandardSmoothCotangent", "is_tactic_proof": true, "tactics": ["cases", "exact", "haveI", "exact"], "tactic_count": 4}
{"name": "Algebra.instSmoothOfIsStandardSmooth", "kind": "instance", "module": "Mathlib.RingTheory.Smooth.StandardSmoothCotangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.instEtaleOfIsStandardSmoothOfRelativeDimensionOfNatNat", "kind": "instance", "module": "Mathlib.RingTheory.Smooth.StandardSmoothCotangent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsStandardSmooth.of_basis_kaehlerDifferential", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.StandardSmoothOfFree", "is_tactic_proof": true, "tactics": ["nontriviality", "obtain", "choose", "let", "have", "have", "hb", "let", "have", "obtain", "let", "map", "map_inj", "have", "simp", "have", "apply", "intro", "simp", "let", "exact"], "tactic_count": 21}
{"name": "Algebra.IsStandardSmooth.iff_exists_basis_kaehlerDifferential", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.StandardSmoothOfFree", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact"], "tactic_count": 3}
{"name": "Algebra.Etale.iff_isStandardSmoothOfRelativeDimension_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.StandardSmoothOfFree", "is_tactic_proof": true, "tactics": ["refine", "nontriviality", "suffices", "rw", "refine", "simp"], "tactic_count": 6}
{"name": "Algebra.IsSmoothAt.exists_notMem_isStandardSmooth", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.StandardSmoothOfFree", "is_tactic_proof": true, "tactics": ["wlog", "obtain", "have", "apply", "rwa", "obtain", "have", "let", "refine", "refine", "rw", "exact", "obtain", "let", "let", "let", "let", "have", "ext", "trans", "simp", "simp", "have", "have", "obtain", "let", "let", "rw", "let", "refine", "rintro", "exact"], "tactic_count": 32}
{"name": "Algebra.Smooth.exists_span_eq_top_isStandardSmooth", "kind": "theorem", "module": "Mathlib.RingTheory.Smooth.StandardSmoothOfFree", "is_tactic_proof": true, "tactics": ["choose", "refine", "simp", "grind"], "tactic_count": 4}
{"name": "MaximalSpectrum.equivSubtype", "kind": "definition", "module": "Mathlib.RingTheory.Spectrum.Maximal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MaximalSpectrum.range_asIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Maximal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MaximalSpectrum.instNonemptyOfNontrivial", "kind": "instance", "module": "Mathlib.RingTheory.Spectrum.Maximal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MaximalSpectrum.toPrimeSpectrum", "kind": "definition", "module": "Mathlib.RingTheory.Spectrum.Maximal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MaximalSpectrum.toPrimeSpectrum_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Maximal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MaximalSpectrum.iInf_localization_eq_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Maximal.Localization", "is_tactic_proof": true, "tactics": ["ext", "rw", "constructor", "contrapose", "intro", "let", "have", "rcases", "rcases", "exact", "hd", "simp", "mul_inv_cancel₀", "rintro", "exact"], "tactic_count": 15}
{"name": "PrimeSpectrum.iInf_localization_eq_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Maximal.Localization", "is_tactic_proof": true, "tactics": ["refine", "simpa"], "tactic_count": 2}
{"name": "MaximalSpectrum.PiLocalization", "kind": "abbrev", "module": "Mathlib.RingTheory.Spectrum.Maximal.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MaximalSpectrum.toPiLocalization", "kind": "definition", "module": "Mathlib.RingTheory.Spectrum.Maximal.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MaximalSpectrum.toPiLocalization_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Maximal.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MaximalSpectrum.toPiLocalization_apply_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Maximal.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MaximalSpectrum.mapPiLocalization", "kind": "definition", "module": "Mathlib.RingTheory.Spectrum.Maximal.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MaximalSpectrum.mapPiLocalization_naturality", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Maximal.Localization", "is_tactic_proof": true, "tactics": ["ext", "change", "simp_rw", "rfl"], "tactic_count": 4}
{"name": "MaximalSpectrum.mapPiLocalization_id", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Maximal.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MaximalSpectrum.mapPiLocalization_comp", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Maximal.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MaximalSpectrum.mapPiLocalization_bijective", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Maximal.Localization", "is_tactic_proof": true, "tactics": ["let", "let", "exact", "rw", "simp_rw", "rw", "simp_rw"], "tactic_count": 7}
{"name": "MaximalSpectrum.toPiLocalization_not_surjective_of_infinite", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Maximal.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MaximalSpectrum.finite_of_toPiLocalization_pi_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Maximal.Localization", "is_tactic_proof": true, "tactics": ["contrapose", "exact"], "tactic_count": 2}
{"name": "MaximalSpectrum.finite_of_toPiLocalization_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Maximal.Localization", "is_tactic_proof": true, "tactics": ["replace", "rw", "exact"], "tactic_count": 3}
{"name": "PrimeSpectrum.PiLocalization", "kind": "abbrev", "module": "Mathlib.RingTheory.Spectrum.Maximal.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.toPiLocalization", "kind": "definition", "module": "Mathlib.RingTheory.Spectrum.Maximal.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.toPiLocalization_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Maximal.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.piLocalizationToMaximal", "kind": "definition", "module": "Mathlib.RingTheory.Spectrum.Maximal.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.piLocalizationToMaximal_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Maximal.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.piLocalizationToMaximalEquiv", "kind": "definition", "module": "Mathlib.RingTheory.Spectrum.Maximal.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.piLocalizationToMaximal_bijective", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Maximal.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.piLocalizationToMaximal_comp_toPiLocalization", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Maximal.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.isMaximal_of_toPiLocalization_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Maximal.Localization", "is_tactic_proof": true, "tactics": ["classical", "have", "obtain", "by_contra", "have", "have", "rw", "exact", "intro", "exact"], "tactic_count": 10}
{"name": "PrimeSpectrum.mapPiLocalization", "kind": "definition", "module": "Mathlib.RingTheory.Spectrum.Maximal.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.mapPiLocalization_naturality", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Maximal.Localization", "is_tactic_proof": true, "tactics": ["ext", "change", "simp_rw", "rfl"], "tactic_count": 4}
{"name": "PrimeSpectrum.mapPiLocalization_id", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Maximal.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.mapPiLocalization_comp", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Maximal.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.mapPiLocalization_bijective", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Maximal.Localization", "is_tactic_proof": true, "tactics": ["let", "let", "exact", "rw", "rw"], "tactic_count": 5}
{"name": "PrimeSpectrum.toPiLocalization_not_surjective_of_infinite", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Maximal.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.finite_of_toPiLocalization_pi_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Maximal.Localization", "is_tactic_proof": true, "tactics": ["contrapose", "exact"], "tactic_count": 2}
{"name": "PrimeSpectrum.finite_of_toPiLocalization_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Maximal.Localization", "is_tactic_proof": true, "tactics": ["replace", "rw", "exact"], "tactic_count": 3}
{"name": "MaximalSpectrum.toPrimeSpectrum_range", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Maximal.Topology", "is_tactic_proof": true, "tactics": ["simp", "ext", "exact"], "tactic_count": 3}
{"name": "MaximalSpectrum.zariskiTopology", "kind": "instance", "module": "Mathlib.RingTheory.Spectrum.Maximal.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MaximalSpectrum.instT1Space", "kind": "instance", "module": "Mathlib.RingTheory.Spectrum.Maximal.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MaximalSpectrum.toPrimeSpectrum_continuous", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Maximal.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.nonempty_iff_nontrivial", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": true, "tactics": ["refine", "simp", "obtain", "exact"], "tactic_count": 4}
{"name": "PrimeSpectrum.isEmpty_iff_subsingleton", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": true, "tactics": ["contrapose"], "tactic_count": 1}
{"name": "PrimeSpectrum.instNonemptyOfNontrivial", "kind": "instance", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.instIsEmptyOfSubsingleton", "kind": "instance", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.nontrivial", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.range_asIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.primeSpectrumProdOfSum", "kind": "definition", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.primeSpectrumProd", "kind": "definition", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.primeSpectrumProd_symm_inl_asIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": true, "tactics": ["cases", "rfl"], "tactic_count": 2}
{"name": "PrimeSpectrum.primeSpectrumProd_symm_inr_asIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": true, "tactics": ["cases", "rfl"], "tactic_count": 2}
{"name": "PrimeSpectrum.zeroLocus", "kind": "definition", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.mem_zeroLocus", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.zeroLocus_span", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "PrimeSpectrum.vanishingIdeal", "kind": "definition", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.coe_vanishingIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": true, "tactics": ["ext", "rw", "apply", "rw"], "tactic_count": 4}
{"name": "PrimeSpectrum.mem_vanishingIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PrimeSpectrum.vanishingIdeal_singleton", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PrimeSpectrum.subset_zeroLocus_iff_le_vanishingIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.gc", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.gc_set", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "PrimeSpectrum.subset_zeroLocus_iff_subset_vanishingIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.subset_vanishingIdeal_zeroLocus", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.le_vanishingIdeal_zeroLocus", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.vanishingIdeal_zeroLocus_eq_radical", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.nilradical_eq_iInf", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "PrimeSpectrum.vanishingIdeal_univ", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PrimeSpectrum.zeroLocus_radical", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.subset_zeroLocus_vanishingIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.zeroLocus_anti_mono", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.zeroLocus_anti_mono_ideal", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.vanishingIdeal_anti_mono", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.zeroLocus_subset_zeroLocus_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PrimeSpectrum.zeroLocus_subset_zeroLocus_singleton_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PrimeSpectrum.zeroLocus_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.zeroLocus_nilradical", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PrimeSpectrum.zeroLocus_singleton_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.zeroLocus_empty", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.vanishingIdeal_empty", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "PrimeSpectrum.zeroLocus_empty_of_one_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "have", "have", "rw", "exact", "apply"], "tactic_count": 8}
{"name": "PrimeSpectrum.zeroLocus_singleton_one", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.zeroLocus_empty_iff_eq_top", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": true, "tactics": ["constructor", "contrapose", "intro", "rcases", "exact", "rintro", "apply", "trivial"], "tactic_count": 8}
{"name": "PrimeSpectrum.zeroLocus_univ", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.vanishingIdeal_eq_top_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PrimeSpectrum.zeroLocus_eq_univ_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PrimeSpectrum.zeroLocus_sup", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.zeroLocus_union", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.vanishingIdeal_union", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.zeroLocus_iSup", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.zeroLocus_iUnion", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.zeroLocus_iUnion₂", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.zeroLocus_bUnion", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PrimeSpectrum.vanishingIdeal_iUnion", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.zeroLocus_inf", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.union_zeroLocus", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "PrimeSpectrum.zeroLocus_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.zeroLocus_singleton_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.zeroLocus_pow", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.zeroLocus_singleton_pow", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.sup_vanishingIdeal_le", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": true, "tactics": ["intro", "rw", "rintro", "rw", "apply"], "tactic_count": 5}
{"name": "PrimeSpectrum.mem_compl_zeroLocus_iff_notMem", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PrimeSpectrum.zeroLocus_insert_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PrimeSpectrum.zeroLocus_diff_singleton_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PrimeSpectrum.zeroLocus_smul_of_isUnit", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "PrimeSpectrum.instOrderBotOfIsDomain", "kind": "instance", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.asIdeal_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.instUnique", "kind": "instance", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.isMax_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": true, "tactics": ["refine", "by_contra", "obtain", "exact"], "tactic_count": 4}
{"name": "PrimeSpectrum.zeroLocus_eq_singleton", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": true, "tactics": ["ext", "refine", "simp", "simpa", "simp"], "tactic_count": 5}
{"name": "PrimeSpectrum.isMin_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": true, "tactics": ["change", "simp", "exact"], "tactic_count": 3}
{"name": "PrimeSpectrum.exists_primeSpectrum_prod_le", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": true, "tactics": ["induction", "hgt", "change", "by_cases", "use", "rw", "by_cases", "rw", "exact", "have", "intro", "refine", "rw", "exact", "obtain", "obtain", "obtain", "use", "rw", "apply", "rw", "apply", "rw", "apply", "rwa"], "tactic_count": 25}
{"name": "PrimeSpectrum.exists_primeSpectrum_prod_le_and_ne_bot_of_domain", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Basic", "is_tactic_proof": true, "tactics": ["induction", "hgt", "change", "have", "by_cases", "rcases", "obtain", "apply", "use", "rwa", "by_cases", "use", "rw", "exact", "obtain", "have", "intro", "refine", "rw", "exact", "obtain", "obtain", "use", "rw", "refine", "rw", "apply", "rw", "apply", "rwa", "rintro"], "tactic_count": 31}
{"name": "PrimeSpectrum.isConstructible_comap_C", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Chevalley", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "rw", "exact"], "tactic_count": 4}
{"name": "PrimeSpectrum.isConstructible_comap_image", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Chevalley", "is_tactic_proof": false, "tactics": ["refine", "hf.polynomial_induction", "intro", "refine", "rw", "exact", "intro", "simp", "exact"], "tactic_count": 9}
{"name": "PrimeSpectrum.isConstructible_range_comap", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Chevalley", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.isOpenMap_comap_of_hasGoingDown_of_finitePresentation", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Chevalley", "is_tactic_proof": true, "tactics": ["rw", "rintro", "exact", "isOpen_of_stableUnderGeneralization_of_isConstructible"], "tactic_count": 4}
{"name": "_private.Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity.0.ChevalleyThm.PolynomialC.termCoeff(_)", "kind": "definition", "module": "Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity.0.ChevalleyThm.PolynomialC._aux_Mathlib_RingTheory_Spectrum_Prime_ChevalleyComplexity___macroRules__private_Mathlib_RingTheory_Spectrum_Prime_ChevalleyComplexity_0_ChevalleyThm_PolynomialC_termCoeff(_)_1", "kind": "definition", "module": "Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity.0.ChevalleyThm.PolynomialC._aux_Mathlib_RingTheory_Spectrum_Prime_ChevalleyComplexity___delab_app__private_Mathlib_RingTheory_Spectrum_Prime_ChevalleyComplexity_0_ChevalleyThm_PolynomialC_termCoeff(_)_1", "kind": "definition", "module": "Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity.0.ChevalleyThm.PolynomialC.DegreeType", "kind": "abbrev", "module": "Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity.0.ChevalleyThm.PolynomialC.InductionObj.instCoeFunInductionObjForallFinPolynomial", "kind": "instance", "module": "Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity.0.ChevalleyThm.PolynomialC.InductionObj.coeffSubmodule", "kind": "definition", "module": "Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity.0.ChevalleyThm.PolynomialC.InductionObj.coeffSubmodule_mapRingHom_comp", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "_private.Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity.0.ChevalleyThm.PolynomialC.InductionObj.coeff_mem_coeffSubmodule", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity.0.ChevalleyThm.PolynomialC.InductionObj.one_mem_coeffSubmodule", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity.0.ChevalleyThm.PolynomialC.InductionObj.one_le_coeffSubmodule", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "_private.Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity.0.ChevalleyThm.PolynomialC.InductionObj.degree", "kind": "definition", "module": "Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity.0.ChevalleyThm.PolynomialC.InductionObj.ofLex_degree_fst", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity.0.ChevalleyThm.PolynomialC.InductionObj.ofLex_degree_snd", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity.0.ChevalleyThm.PolynomialC.InductionObj.degBound", "kind": "definition", "module": "Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity.0.ChevalleyThm.PolynomialC.InductionObj.powBound", "kind": "definition", "module": "Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity.0.ChevalleyThm.PolynomialC.InductionObj.powBound_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity.0.ChevalleyThm.PolynomialC.InductionObj.Statement", "kind": "definition", "module": "Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity.0.ChevalleyThm.PolynomialC.induction_structure", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity", "is_tactic_proof": true, "tactics": ["classical", "set", "clear_value", "induction", "ind", "by_cases", "exact", "cases", "convert", "simp", "by_cases", "obtain", "by_cases", "e.1", "exact", "obtain", "replace", "apply", "refine", "intro", "simp", "split_ifs", "rw", "exact", "exact", "simp", "use", "simp", "refine", "obtain", "have", "exact", "let", "obtain", "refine", "refine", "rw", "exact", "apply", "rw", "constructor", "intro", "simp", "refine", "simp", "rw", "simp", "show", "simp", "not_forall,", "intro", "refine", "rw", "intro", "rw", "refine", "intro", "simp", "intro", "replace", "simp", "not_true_eq_false,", "exact"], "tactic_count": 63}
{"name": "_private.Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity.0.ChevalleyThm.PolynomialC.induction_aux", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity", "is_tactic_proof": true, "tactics": ["set", "set", "have", "set", "set", "have", "unfold", "gcongr", "exact", "have", "unfold", "refine", "dsimp", "gcongr", "exact", "gcongr", "exact", "intro", "obtain", "obtain", "simp", "obtain", "obtain", "let", "simp", "have", "e₁.coeffSubmodule", "unfold", "rw", "simp", "congr", "change", "simp", "ext", "simp", "replace", "simp", "choose", "choose", "change", "rw", "choose", "choose", "change", "classical", "let", "let", "refine", "calc", "comap", "comap", "comap", "rw", "exact", "congr", "convert", "dsimp", "rw", "congr", "refine", "exact", "rw", "simp_rw", "congr", "apply", "dsimp", "rw", "exact", "exact", "rw", "preimage_comap_zeroLocus,", "swap", "simp", "simp", "simp", "zeroLocus_smul_of_isUnit", "convert", "rw", "rw", "simp_rw", "congr", "apply", "rw", "simp", "exact", "exact", "simp", "have", "simp", "preimage_comap_zeroLocus,", "simp", "simp", "rw", "simp", "refine", "norm_cast", "calc", "span", "unfold", "gcongr", "exact", "exact", "lia", "exact", "unfold", "gcongr", "exact", "lia"], "tactic_count": 108}
{"name": "_private.Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity.0.ChevalleyThm.PolynomialC.statement", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity", "is_tactic_proof": true, "tactics": ["intro", "classical", "apply", "intro", "refine", "convert", "simp", "congr", "rw", "rintro", "exact", "suffices", "simp", "eq_compl_comm", "trans", "refine", "rintro", "by_cases", "exact", "exact", "ext", "simp", "intro", "let", "have", "have", "refine", "ext", "have", "rw", "refine", "by_cases", "subst", "rw", "rw", "isNilpotent_tensor_residueField_iff]", "simp", "simp", "intro", "cases", "use", "simp", "obtain", "refine", "rw", "intro", "let", "have", "dsimp", "gcongr", "rw", "split_ifs", "subst", "rfl", "refine", "change", "delta", "suffices", "by_cases", "gcongr", "exact", "refine", "exact", "refine", "simp", "split_ifs", "rintro", "exact", "exact", "rw", "refine", "refine", "rw", "apply", "have", "dsimp", "apply", "intro", "rw", "split_ifs", "subst", "rfl", "gcongr", "calc", "gcongr", "delta", "exact", "rw", "simp", "constructor", "apply", "rw", "exact", "intro", "rw", "split_ifs", "convert", "coeff_modByMonic_mem_pow_natDegree_mul", "rw", "intro", "simp", "have", "rw", "apply", "refine", "rw", "intro", "simp", "refine", "exact", "intro", "exact"], "tactic_count": 112}
{"name": "ChevalleyThm.chevalley_polynomialC", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity", "is_tactic_proof": true, "tactics": ["classical", "choose", "refine", "simp", "simp", "intro", "have", "refine", "gcongr", "simpa", "refine", "simp", "delta", "by_cases", "have", "rw", "gcongr", "rwa"], "tactic_count": 18}
{"name": "ChevalleyThm.MvPolynomialC.degBound_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ChevalleyThm.MvPolynomialC.numBound_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ChevalleyThm.MvPolynomialC.degBound_succ", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ChevalleyThm.MvPolynomialC.numBound_succ", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ChevalleyThm.MvPolynomialC.degBound_pos", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ChevalleyThm.chevalley_mvPolynomialC", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity", "is_tactic_proof": true, "tactics": ["classical", "induction", "zero", "refine", "rw", "change", "rw", "rfl", "simp", "degBound_zero,", "exact", "succ", "let", "let", "have", "apply", "simp", "obtain", "trans", "gcongr", "simp", "by_cases", "rw", "simp", "rw", "simp", "exact", "simp", "gcongr", "exact", "let", "obtain", "chevalley_polynomialC", "simp", "e]", "obtain", "simp", "constructor", "intro", "simp", "exact", "simp", "replace", "simp", "intro", "exact", "let", "have", "refine", "refine", "refine", "simpa", "rw", "refine", "simp", "have", "obtain", "simp", "have", "intro", "change", "rw", "obtain", "exact", "simp", "change", "rw", "simp", "refine", "unfold", "rw", "change", "rw", "simp", "congr", "exact", "refine", "simp", "refine", "simp"], "tactic_count": 80}
{"name": "ChevalleyThm.numBound", "kind": "definition", "module": "Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ChevalleyThm.degBound", "kind": "definition", "module": "Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "chevalley_mvPolynomial_mvPolynomial", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity", "is_tactic_proof": true, "tactics": ["classical", "let", "have", "let", "have", "have", "have", "let", "let", "have", "rw", "congr", "have", "simp", "simp", "refine", "obtain", "clear", "obtain", "simp_rw", "induction", "add", "obtain", "obtain", "refine", "mul_X", "obtain", "simp", "commAlgEquiv_X]", "refine", "exact", "add_mem", "simp", "obtain", "simpa", "have", "refine", "simp", "simp", "rw", "simp", "have", "simp", "simp", "obtain", "chevalley_mvPolynomialC", "intro", "obtain", "simp", "mem_degreesLE]", "constructor", "intro", "obtain", "simp", "simp", "refine", "simp", "split_ifs", "refine", "simp", "simp", "obtain", "simp", "exact", "refine", "simp", "exact", "refine", "rwa", "have", "rw", "simpa"], "tactic_count": 72}
{"name": "PrimeSpectrum.BasicConstructibleSetData.instDecidableEq", "kind": "instance", "module": "Mathlib.RingTheory.Spectrum.Prime.ConstructibleSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.BasicConstructibleSetData.map", "kind": "definition", "module": "Mathlib.RingTheory.Spectrum.Prime.ConstructibleSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.BasicConstructibleSetData.map_id", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.ConstructibleSet", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PrimeSpectrum.BasicConstructibleSetData.map_id'", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.ConstructibleSet", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "PrimeSpectrum.BasicConstructibleSetData.map_comp", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.ConstructibleSet", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PrimeSpectrum.BasicConstructibleSetData.map_comp'", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.ConstructibleSet", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "PrimeSpectrum.BasicConstructibleSetData.toSet", "kind": "definition", "module": "Mathlib.RingTheory.Spectrum.Prime.ConstructibleSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.BasicConstructibleSetData.toSet_map", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.ConstructibleSet", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PrimeSpectrum.ConstructibleSetData", "kind": "abbrev", "module": "Mathlib.RingTheory.Spectrum.Prime.ConstructibleSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.ConstructibleSetData.map", "kind": "definition", "module": "Mathlib.RingTheory.Spectrum.Prime.ConstructibleSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.ConstructibleSetData.map_id", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.ConstructibleSet", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PrimeSpectrum.ConstructibleSetData.map_comp", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.ConstructibleSet", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PrimeSpectrum.ConstructibleSetData.toSet", "kind": "definition", "module": "Mathlib.RingTheory.Spectrum.Prime.ConstructibleSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.ConstructibleSetData.toSet_map", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.ConstructibleSet", "is_tactic_proof": true, "tactics": ["unfold", "rw", "simp"], "tactic_count": 3}
{"name": "PrimeSpectrum.ConstructibleSetData.degBound", "kind": "definition", "module": "Mathlib.RingTheory.Spectrum.Prime.ConstructibleSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.ConstructibleSetData.isConstructible_toSet", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.ConstructibleSet", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact", "rw", "exact"], "tactic_count": 5}
{"name": "PrimeSpectrum.exists_constructibleSetData_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.ConstructibleSet", "is_tactic_proof": true, "tactics": ["refine", "induction", "isCompact_basis", "sdiff", "have", "refine", "simp", "congr", "ext", "simp", "union", "obtain", "obtain", "refine", "simp"], "tactic_count": 15}
{"name": "PrimeSpectrum.exists_range_eq_of_isConstructible", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.ConstructibleSet", "is_tactic_proof": true, "tactics": ["obtain", "refine", "rw", "simp_rw", "congr", "let", "let", "trans", "rw", "rw", "zeroLocus_span]"], "tactic_count": 11}
{"name": "PrimeSpectrum.isClosed_of_stableUnderSpecialization_of_isConstructible", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.ConstructibleSet", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "PrimeSpectrum.isOpen_of_stableUnderGeneralization_of_isConstructible", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.ConstructibleSet", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "PrimeSpectrum.instPartialOrder", "kind": "instance", "module": "Mathlib.RingTheory.Spectrum.Prime.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.asIdeal_le_asIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.asIdeal_lt_asIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.equivSubtype", "kind": "definition", "module": "Mathlib.RingTheory.Spectrum.Prime.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.freeLocus", "kind": "definition", "module": "Mathlib.RingTheory.Spectrum.Prime.FreeLocus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.mem_freeLocus", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.FreeLocus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.mem_freeLocus_of_isLocalization", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.FreeLocus", "is_tactic_proof": false, "tactics": ["apply", "refine", "intro", "obtain", "apply", "simp", "simp"], "tactic_count": 7}
{"name": "Module.mem_freeLocus_iff_tensor", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.FreeLocus", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "Module.freeLocus_congr", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.FreeLocus", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "Module.comap_freeLocus_le", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.FreeLocus", "is_tactic_proof": true, "tactics": ["intro", "let", "let", "rw", "rw", "letI", "have", "simp", "let", "exact"], "tactic_count": 10}
{"name": "Module.freeLocus_localization", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.FreeLocus", "is_tactic_proof": true, "tactics": ["ext", "simp", "let", "have", "p.isPrime.ne_top", "let", "let", "letI", "have", "have", "have", "apply", "rintro", "rintro", "obtain", "refine", "rw", "exact", "letI", "have", "show", "simp", "have", "let", "have", "have", "inferInstanceAs", "have", "apply", "rintro", "rintro", "obtain", "refine", "rw", "exact", "rw", "rfl"], "tactic_count": 37}
{"name": "Module.freeLocus_eq_univ_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.FreeLocus", "is_tactic_proof": true, "tactics": ["simp_rw", "exact", "have"], "tactic_count": 3}
{"name": "Module.freeLocus_eq_univ", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.FreeLocus", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Module.basicOpen_subset_freeLocus_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.FreeLocus", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Module.isOpen_freeLocus", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.FreeLocus", "is_tactic_proof": true, "tactics": ["refine", "have", "obtain", "exact"], "tactic_count": 4}
{"name": "Module.rankAtStalk", "kind": "definition", "module": "Mathlib.RingTheory.Spectrum.Prime.FreeLocus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.isLocallyConstant_rankAtStalk_freeLocus", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.FreeLocus", "is_tactic_proof": true, "tactics": ["refine", "have", "obtain", "refine", "rintro", "let", "have", "let", "let", "letI", "have", "letI", "have", "show", "simp", "have", "let", "have", "have", "inferInstanceAs", "have", "have", "simp"], "tactic_count": 23}
{"name": "Module.isLocallyConstant_rankAtStalk", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.FreeLocus", "is_tactic_proof": false, "tactics": ["let", "convert"], "tactic_count": 2}
{"name": "Module.rankAtStalk_eq_zero_of_subsingleton", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.FreeLocus", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "Module.nontrivial_of_rankAtStalk_pos", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.FreeLocus", "is_tactic_proof": true, "tactics": ["by_contra", "simp"], "tactic_count": 2}
{"name": "Module.rankAtStalk_eq_of_equiv", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.FreeLocus", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "Module.rankAtStalk_eq_finrank_of_free", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.FreeLocus", "is_tactic_proof": true, "tactics": ["ext", "simp", "finrank_of_isLocalizedModule_of_free"], "tactic_count": 3}
{"name": "Module.rankAtStalk_self", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.FreeLocus", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Module.rankAtStalk_pi", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.FreeLocus", "is_tactic_proof": true, "tactics": ["cases", "let", "let", "p.asIdeal.primeCompl", "have", "free_of_flat_of_isLocalRing", "simp_rw"], "tactic_count": 7}
{"name": "Module.rankAtStalk_eq_finrank_tensorProduct", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.FreeLocus", "is_tactic_proof": false, "tactics": ["let", "rw"], "tactic_count": 2}
{"name": "Module.rankAtStalk_eq_zero_iff_notMem_support", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.FreeLocus", "is_tactic_proof": true, "tactics": ["rw", "refine", "apply", "dsimp", "simp"], "tactic_count": 5}
{"name": "Module.rankAtStalk_pos_iff_mem_support", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.FreeLocus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.rankAtStalk_eq_zero_iff_subsingleton", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.FreeLocus", "is_tactic_proof": true, "tactics": ["refine", "simp_rw", "intro", "rw"], "tactic_count": 4}
{"name": "Module.rankAtStalk_prod", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.FreeLocus", "is_tactic_proof": true, "tactics": ["ext", "let", "p.asIdeal.primeCompl", "simp"], "tactic_count": 4}
{"name": "Module.rankAtStalk_baseChange", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.FreeLocus", "is_tactic_proof": true, "tactics": ["let", "let", "rw", "apply"], "tactic_count": 4}
{"name": "Module.rankAtStalk_tensorProduct", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.FreeLocus", "is_tactic_proof": true, "tactics": ["ext", "let", "rw"], "tactic_count": 3}
{"name": "Module.rankAtStalk_tensorProduct_of_isScalarTower", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.FreeLocus", "is_tactic_proof": true, "tactics": ["simp", "rankAtStalk_baseChange]"], "tactic_count": 2}
{"name": "Module.rankAtStalk_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.FreeLocus", "is_tactic_proof": true, "tactics": ["let", "let", "rw"], "tactic_count": 3}
{"name": "PrimeSpectrum.isHomeomorph_comap", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Homeomorph", "is_tactic_proof": false, "tactics": ["have", "intro", "ext", "obtain", "rw", "rw", "apply", "have", "have", "let", "have", "refine", "rw", "rintro", "obtain", "have", "exact"], "tactic_count": 17}
{"name": "PrimeSpectrum.isHomeomorph_comap_of_isPurelyInseparable", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Homeomorph", "is_tactic_proof": true, "tactics": ["let", "refine", "convert", "rw", "exact"], "tactic_count": 5}
{"name": "PrimeSpectrum.isHomeomorph_comap_tensorProductMap_of_isPurelyInseparable", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Homeomorph", "is_tactic_proof": true, "tactics": ["let", "let", "have", "rw", "simp", "exact"], "tactic_count": 6}
{"name": "AlgebraicGeometry.Polynomial.imageOfDf", "kind": "definition", "module": "Mathlib.RingTheory.Spectrum.Prime.IsOpenComapC", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Polynomial.isOpen_imageOfDf", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.IsOpenComapC", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "AlgebraicGeometry.Polynomial.comap_C_mem_imageOfDf", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.IsOpenComapC", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgebraicGeometry.Polynomial.imageOfDf_eq_comap_C_compl_zeroLocus", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.IsOpenComapC", "is_tactic_proof": true, "tactics": ["ext", "refine", "rw", "obtain", "exact", "ext", "refine", "rw", "exact", "rintro", "exact"], "tactic_count": 11}
{"name": "AlgebraicGeometry.Polynomial.isOpenMap_comap_C", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.IsOpenComapC", "is_tactic_proof": true, "tactics": ["rintro", "rw", "simp_rw", "exact"], "tactic_count": 4}
{"name": "PrimeSpectrum.exists_isClosed_singleton_of_isJacobsonRing", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Jacobson", "is_tactic_proof": true, "tactics": ["simp_rw", "obtain", "simp_rw", "have", "contrapose", "simp_rw", "rw", "refine", "rintro", "exact"], "tactic_count": 10}
{"name": "PrimeSpectrum.instJacobsonSpaceOfIsJacobsonRing", "kind": "instance", "module": "Mathlib.RingTheory.Spectrum.Prime.Jacobson", "is_tactic_proof": true, "tactics": ["rw", "rintro", "simp", "obtain", "simp", "le_sInf_iff]", "contrapose", "rintro", "exact"], "tactic_count": 9}
{"name": "PrimeSpectrum.isJacobsonRing_iff_jacobsonSpace", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Jacobson", "is_tactic_proof": true, "tactics": ["refine", "rw", "conv_rhs", "simp_rw", "apply", "rw", "rintro", "change", "exact"], "tactic_count": 9}
{"name": "PrimeSpectrum.isOpen_singleton_tfae_of_isNoetherian_of_isJacobsonRing", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Jacobson", "is_tactic_proof": false, "tactics": ["tfae_have", "h", "obtain", "exact", "tfae_have", "h", "tfae_have", "rw", "suffices", "rw", "refine", "exact", "ext", "simp", "and_imp,", "constructor", "rintro", "rw", "exact", "intro", "apply", "obtain", "exact", "tfae_finish"], "tactic_count": 24}
{"name": "_private.Mathlib.RingTheory.Spectrum.Prime.LTSeries.0.term𝔪", "kind": "definition", "module": "Mathlib.RingTheory.Spectrum.Prime.LTSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Spectrum.Prime.LTSeries.0._aux_Mathlib_RingTheory_Spectrum_Prime_LTSeries___macroRules__private_Mathlib_RingTheory_Spectrum_Prime_LTSeries_0_term𝔪_1", "kind": "definition", "module": "Mathlib.RingTheory.Spectrum.Prime.LTSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Spectrum.Prime.LTSeries.0._aux_Mathlib_RingTheory_Spectrum_Prime_LTSeries___unexpand_IsLocalRing_maximalIdeal_1", "kind": "definition", "module": "Mathlib.RingTheory.Spectrum.Prime.LTSeries", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.exist_mem_one_of_mem_maximal_ideal", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.LTSeries", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "let", "obtain", "sup_le", "let", "have", "have", "refine", "refine", "have", "simp_rw", "have", "refine", "simpa"], "tactic_count": 15}
{"name": "PrimeSpectrum.exist_mem_one_of_mem_two", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.LTSeries", "is_tactic_proof": true, "tactics": ["let", "have", "obtain", "rw", "exact", "rw", "have", "have", "rwa", "exact"], "tactic_count": 10}
{"name": "PrimeSpectrum.exist_ltSeries_mem_one_of_mem_last", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.LTSeries", "is_tactic_proof": true, "tactics": ["generalize", "induction", "zero", "use", "simp", "and_true,", "rw", "succ", "by_cases", "use", "have", "rw", "exact", "simpa", "obtain", "obtain", "hn", "have", "have", "exact"], "tactic_count": 20}
{"name": "IsLocalRing.closedPoint_mem_support", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Module", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "LocalizedModule.subsingleton_iff_disjoint", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Module", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Module.stableUnderSpecialization_support", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.isClosed_support", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Module", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "Module.support_subset_preimage_comap", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Module", "is_tactic_proof": true, "tactics": ["intro", "simp", "not_imp_not]", "obtain", "exact"], "tactic_count": 5}
{"name": "PrimeSpectrum.instNoetherianSpace", "kind": "instance", "module": "Mathlib.RingTheory.Spectrum.Prime.Noetherian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.finite_setOf_isMin", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Noetherian", "is_tactic_proof": true, "tactics": ["have", "refine", "simp_rw", "exact"], "tactic_count": 4}
{"name": "PrimeSpectrum.instKrullDimLEOfNatNat", "kind": "instance", "module": "Mathlib.RingTheory.Spectrum.Prime.Noetherian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.instDiscreteTopology", "kind": "instance", "module": "Mathlib.RingTheory.Spectrum.Prime.Noetherian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsArtinianRing.exists_not_mem_forall_mem_of_ne", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Noetherian", "is_tactic_proof": true, "tactics": ["classical", "obtain", "have", "simpa", "funext_iff.mp", "refine", "rw", "simp", "apply", "simp", "intro", "have", "have", "simpa", "funext_iff.mp", "rw", "simp"], "tactic_count": 17}
{"name": "isNilpotent_tensor_residueField_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Polynomial", "is_tactic_proof": true, "tactics": ["cases", "have", "simp", "have", "rw", "rw", "simp", "rw", "simp_rw", "constructor", "intro", "replace", "simpa", "intro", "ext", "obtain", "simp", "rw", "obtain", "simpa", "simp"], "tactic_count": 21}
{"name": "PrimeSpectrum.mem_image_comap_zeroLocus_sdiff", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Polynomial", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "simp", "have", "rwa", "let", "have", "rw", "exact", "intro", "rw", "simp", "obtain", "have", "simp", "refine", "rw", "comap_comp_apply,", "ext", "exact"], "tactic_count": 20}
{"name": "PrimeSpectrum.mem_image_comap_basicOpen", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Polynomial", "is_tactic_proof": false, "tactics": ["have", "refine", "rw", "exact", "rw"], "tactic_count": 5}
{"name": "PrimeSpectrum.exists_image_comap_of_finite_of_free", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Polynomial", "is_tactic_proof": true, "tactics": ["classical", "use", "ext", "rw", "isNilpotent_tensor_residueField_iff]", "simp"], "tactic_count": 6}
{"name": "Polynomial.mem_image_comap_C_basicOpen", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Polynomial", "is_tactic_proof": true, "tactics": ["trans", "refine", "let", "rw", "change", "congr", "ext1", "ext", "simp", "simp"], "tactic_count": 10}
{"name": "Polynomial.image_comap_C_basicOpen", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Polynomial", "is_tactic_proof": true, "tactics": ["ext", "rw", "simp"], "tactic_count": 3}
{"name": "Polynomial.isOpenMap_comap_C", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Polynomial", "is_tactic_proof": true, "tactics": ["intro", "obtain", "rw", "apply", "rintro", "obtain", "simp", "exact"], "tactic_count": 8}
{"name": "Polynomial.comap_C_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Polynomial", "is_tactic_proof": true, "tactics": ["intro", "refine", "rw"], "tactic_count": 3}
{"name": "Polynomial.exists_image_comap_of_monic", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Polynomial", "is_tactic_proof": true, "tactics": ["apply", "exact", "exact"], "tactic_count": 3}
{"name": "Polynomial.isCompact_image_comap_of_monic", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Polynomial", "is_tactic_proof": true, "tactics": ["obtain", "rw", "apply", "exact"], "tactic_count": 4}
{"name": "Polynomial.isOpen_image_comap_of_monic", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Polynomial", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact"], "tactic_count": 3}
{"name": "MvPolynomial.mem_image_comap_C_basicOpen", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Polynomial", "is_tactic_proof": true, "tactics": ["classical", "trans", "refine", "let", "scalarRTensorAlgEquiv", "rw", "change", "congr", "ext", "simp", "simp", "simp"], "tactic_count": 12}
{"name": "MvPolynomial.image_comap_C_basicOpen", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Polynomial", "is_tactic_proof": true, "tactics": ["ext", "rw", "simp"], "tactic_count": 3}
{"name": "MvPolynomial.isOpenMap_comap_C", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Polynomial", "is_tactic_proof": true, "tactics": ["intro", "obtain", "rw", "apply", "rintro", "obtain", "simp", "exact"], "tactic_count": 8}
{"name": "MvPolynomial.comap_C_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Polynomial", "is_tactic_proof": true, "tactics": ["intro", "refine", "rw"], "tactic_count": 3}
{"name": "PrimeSpectrum.comap", "kind": "definition", "module": "Mathlib.RingTheory.Spectrum.Prime.RingHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.comap_asIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.RingHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.comap_id", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.RingHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.comap_comp", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.RingHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.comap_comp_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.RingHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.preimage_comap_zeroLocus_aux", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.RingHom", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "PrimeSpectrum.preimage_comap_zeroLocus", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.RingHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.comap_injective_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.RingHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.instLiesOverAsIdealComapAlgebraMap", "kind": "instance", "module": "Mathlib.RingTheory.Spectrum.Prime.RingHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.comapEquiv", "kind": "definition", "module": "Mathlib.RingTheory.Spectrum.Prime.RingHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.comapEquiv_symm", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.RingHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.sigmaToPi", "kind": "definition", "module": "Mathlib.RingTheory.Spectrum.Prime.RingHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.sigmaToPi_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.RingHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.exists_maximal_notMem_range_sigmaToPi_of_infinite", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.RingHom", "is_tactic_proof": true, "tactics": ["classical", "let", "smul_mem", "rintro", "refine", "simp_rw", "refine", "rw", "have", "rintro", "have", "simpa", "refine", "have", "rw", "exact"], "tactic_count": 16}
{"name": "PrimeSpectrum.sigmaToPi_not_surjective_of_infinite", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.RingHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.exists_comap_evalRingHom_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.RingHom", "is_tactic_proof": true, "tactics": ["classical", "cases", "let", "have", "ext", "rw", "simp", "obtain", "let", "have", "intro", "convert", "ext", "by_cases", "subst", "simp", "have", "rwa", "exact"], "tactic_count": 19}
{"name": "PrimeSpectrum.sigmaToPi_bijective", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.RingHom", "is_tactic_proof": true, "tactics": ["refine", "intro", "obtain", "exact"], "tactic_count": 4}
{"name": "PrimeSpectrum.iUnion_range_comap_comp_evalRingHom", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.RingHom", "is_tactic_proof": true, "tactics": ["simp_rw", "apply", "exact", "rintro", "obtain", "exact"], "tactic_count": 6}
{"name": "image_comap_zeroLocus_eq_zeroLocus_comap", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.RingHom", "is_tactic_proof": true, "tactics": ["simp", "refine", "rintro", "exact", "have", "refine", "obtain", "exact", "ext", "rw", "refine", "rintro", "rw", "refine", "rwa"], "tactic_count": 15}
{"name": "range_comap_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.RingHom", "is_tactic_proof": true, "tactics": ["rw", "convert", "rw"], "tactic_count": 3}
{"name": "Ideal.primeSpectrumOrderIsoZeroLocusOfSurj", "kind": "definition", "module": "Mathlib.RingTheory.Spectrum.Prime.RingHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.primeSpectrumQuotientOrderIsoZeroLocus", "kind": "definition", "module": "Mathlib.RingTheory.Spectrum.Prime.RingHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.mem_range_comap_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.RingHom", "is_tactic_proof": true, "tactics": ["refine", "rw", "rintro", "exact"], "tactic_count": 4}
{"name": "PrimeSpectrum.nontrivial_iff_mem_rangeComap", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.RingHom", "is_tactic_proof": true, "tactics": ["let", "refine", "obtain", "use", "ext", "rw", "simp", "obtain", "let", "exact"], "tactic_count": 10}
{"name": "RingHom.strictMono_comap_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.RingHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.residueField_comap", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.RingHom", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsLocalHom.of_comap_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.RingHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.tensorProductTo", "kind": "definition", "module": "Mathlib.RingTheory.Spectrum.Prime.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.continuous_tensorProductTo", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.isEmbedding_tensorProductTo_of_surjectiveOnStalks_aux", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.TensorProduct", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.isEmbedding_tensorProductTo_of_surjectiveOnStalks", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.TensorProduct", "is_tactic_proof": false, "tactics": ["refine", "let", "refine", "rintro", "rw", "rintro", "obtain", "refine", "rintro", "apply", "rw", "exact", "have", "rw", "exact", "rwa"], "tactic_count": 16}
{"name": "PrimeSpectrum.zariskiTopology", "kind": "instance", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.isOpen_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PrimeSpectrum.isClosed_iff_zeroLocus", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PrimeSpectrum.isClosed_iff_zeroLocus_ideal", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.isClosed_iff_zeroLocus_radical_ideal", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.isClosed_zeroLocus", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "PrimeSpectrum.zeroLocus_vanishingIdeal_eq_closure", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["rcases", "rw", "exact"], "tactic_count": 3}
{"name": "PrimeSpectrum.vanishingIdeal_closure", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.closure_singleton", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PrimeSpectrum.isClosed_singleton_iff_isMaximal", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["rw", "constructor", "rcases", "exact", "exact"], "tactic_count": 5}
{"name": "PrimeSpectrum.isRadical_vanishingIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "PrimeSpectrum.zeroLocus_eq_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["constructor", "intro", "intro"], "tactic_count": 3}
{"name": "PrimeSpectrum.vanishingIdeal_anti_mono_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.vanishingIdeal_strict_anti_mono_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PrimeSpectrum.closedsEmbedding", "kind": "definition", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.t1Space_iff_isField", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["refine", "intro", "exact", "refine", "by_cases", "letI", "exact", "exact"], "tactic_count": 8}
{"name": "_private.Mathlib.RingTheory.Spectrum.Prime.Topology.0.PrimeSpectrum.termZ(_)", "kind": "definition", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Spectrum.Prime.Topology.0.PrimeSpectrum._aux_Mathlib_RingTheory_Spectrum_Prime_Topology___macroRules__private_Mathlib_RingTheory_Spectrum_Prime_Topology_0_PrimeSpectrum_termZ(_)_1", "kind": "definition", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Spectrum.Prime.Topology.0.PrimeSpectrum._aux_Mathlib_RingTheory_Spectrum_Prime_Topology___unexpand_PrimeSpectrum_zeroLocus_1", "kind": "definition", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.isIrreducible_zeroLocus_iff_of_radical", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["rw", "apply", "rw", "trans", "simp_rw", "constructor", "rintro", "exact", "rintro", "exact", "simp_rw", "constructor", "simp_rw", "refine", "rw", "simpa", "simp_rw", "rintro", "exact"], "tactic_count": 19}
{"name": "PrimeSpectrum.isIrreducible_zeroLocus_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.isIrreducible_iff_vanishingIdeal_isPrime", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["rw", "isIrreducible_zeroLocus_iff_of_radical"], "tactic_count": 2}
{"name": "PrimeSpectrum.vanishingIdeal_isIrreducible", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.vanishingIdeal_isClosed_isIrreducible", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["refine", "exact", "rintro", "exact"], "tactic_count": 4}
{"name": "PrimeSpectrum.irreducibleSpace", "kind": "instance", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "PrimeSpectrum.quasiSober", "kind": "instance", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.instQuasiSoberElemZeroLocus", "kind": "instance", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.compactSpace", "kind": "instance", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["refine", "choose", "simp_rw", "exact"], "tactic_count": 4}
{"name": "PrimeSpectrum.discreteTopology_iff_finite_and_krullDimLE_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.discreteTopology_iff_finite_isMaximal_and_sInf_le_nilradical", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": ["rw", "refine", "have", "replace", "rw", "have", "rw", "rwa", "exact"], "tactic_count": 9}
{"name": "PrimeSpectrum.discreteTopology_of_toLocalization_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.continuous_comap", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["simp", "rintro", "exact"], "tactic_count": 3}
{"name": "PrimeSpectrum.comap_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.localization_comap_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["intro", "replace", "dsimp", "rw", "ext1", "exact"], "tactic_count": 6}
{"name": "PrimeSpectrum.localization_comap_range", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["refine", "rintro", "exact", "use", "ext1", "exact"], "tactic_count": 6}
{"name": "PrimeSpectrum.localization_comap_isInducing", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["refine", "simp_rw", "preimage_comap_zeroLocus]", "constructor", "rintro", "refine", "rw", "rintro", "exact"], "tactic_count": 9}
{"name": "PrimeSpectrum.localization_comap_isEmbedding", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.comap_isInducing_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.isEmbedding_comap_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.homeomorphOfRingEquiv", "kind": "definition", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.isHomeomorph_comap_of_bijective", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.comap_singleton_isClosed_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.comap_quotientMk_bijective_of_le_nilradical", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["refine", "simpa"], "tactic_count": 2}
{"name": "PrimeSpectrum.isClosed_range_comap_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "PrimeSpectrum.isClosedEmbedding_comap_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.primeSpectrumProd_symm_inl", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "PrimeSpectrum.primeSpectrumProd_symm_inr", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "PrimeSpectrum.range_comap_fst", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["refine", "rintro", "obtain", "exact", "refine", "simpa"], "tactic_count": 6}
{"name": "PrimeSpectrum.range_comap_snd", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["refine", "rintro", "obtain", "refine", "simpa", "exact"], "tactic_count": 6}
{"name": "PrimeSpectrum.isClosedEmbedding_comap_fst", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.isClosedEmbedding_comap_snd", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.primeSpectrumProdHomeo", "kind": "definition", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["refine", "refine", "rw", "simp", "exact", "simp_rw", "exact"], "tactic_count": 7}
{"name": "PrimeSpectrum.basicOpen", "kind": "definition", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.mem_basicOpen", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.isOpen_basicOpen", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.basicOpen_eq_zeroLocus_compl", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.basicOpen_one", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.basicOpen_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.basicOpen_le_basicOpen_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["rw", "zeroLocus_subset_zeroLocus_singleton_iff]"], "tactic_count": 2}
{"name": "PrimeSpectrum.basicOpen_le_basicOpen_iff_algebraMap_isUnit", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "PrimeSpectrum.basicOpen_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.basicOpen_mul_le_left", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "PrimeSpectrum.basicOpen_mul_le_right", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "PrimeSpectrum.basicOpen_pow", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.isTopologicalBasis_basic_opens", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["apply", "rintro", "exact", "rintro", "rw", "obtain", "refine", "rw", "exact"], "tactic_count": 9}
{"name": "PrimeSpectrum.eq_biUnion_of_isOpen", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.isBasis_basic_opens", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["unfold", "convert", "rw", "rfl"], "tactic_count": 4}
{"name": "PrimeSpectrum.basicOpen_eq_bot_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["rw", "simp", "exact"], "tactic_count": 3}
{"name": "PrimeSpectrum.localization_away_comap_range", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["rw", "ext", "simp", "constructor", "intro", "exact", "rintro", "exact"], "tactic_count": 8}
{"name": "PrimeSpectrum.localization_away_isOpenEmbedding", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.isCompact_basicOpen", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "PrimeSpectrum.comap_basicOpen", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.iSup_basicOpen_eq_top_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["rw", "simp", "rw", "simp"], "tactic_count": 4}
{"name": "PrimeSpectrum.iSup_basicOpen_eq_top_iff'", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["conv_rhs", "simp"], "tactic_count": 2}
{"name": "PrimeSpectrum.isLocalization_away_iff_atPrime_of_basicOpen_eq_singleton", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.range_comap_algebraMap_localization_compl_eq_range_comap_quotientMk", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["letI", "have", "rw", "have", "rw", "simp"], "tactic_count": 6}
{"name": "PrimeSpectrum.instQuasiSeparatedSpace", "kind": "instance", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.toPiLocalization_surjective_of_discreteTopology", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.maximalSpectrumToPiLocalization_surjective_of_discreteTopology", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MaximalSpectrum.toPiLocalizationEquiv", "kind": "definition", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.discreteTopology_iff_toPiLocalization_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.discreteTopology_iff_toPiLocalization_bijective", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.toPiLocalization_bijective", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.le_iff_mem_closure", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PrimeSpectrum.le_iff_specializes", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.nhdsOrderEmbedding", "kind": "definition", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.instT0Space", "kind": "instance", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.instPrespectralSpace", "kind": "instance", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.instSpectralSpace", "kind": "instance", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.localizationMapOfSpecializes", "kind": "definition", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.isClosed_image_of_stableUnderSpecialization", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["obtain", "refine", "rintro", "exact", "obtain", "exact"], "tactic_count": 6}
{"name": "PrimeSpectrum.isClosed_range_of_stableUnderSpecialization", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "PrimeSpectrum.stableUnderSpecialization_range_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.stableUnderSpecialization_image_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.isQuotientMap_of_specializingMap", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["rw", "exact", "isClosed_image_of_stableUnderSpecialization"], "tactic_count": 3}
{"name": "PrimeSpectrum.isQuotientMap_of_generalizingMap", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["rw", "refine", "apply", "rw", "convert", "rw"], "tactic_count": 6}
{"name": "PrimeSpectrum.vanishingIdeal_range_comap", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["ext", "rw", "simp", "exact"], "tactic_count": 4}
{"name": "PrimeSpectrum.closure_range_comap", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PrimeSpectrum.denseRange_comap_iff_ker_le_nilRadical", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PrimeSpectrum.denseRange_comap_iff_minimalPrimes", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["constructor", "intro", "have", "rw", "simp", "convert", "exact", "obtain", "exact", "intro", "obtain", "exact"], "tactic_count": 12}
{"name": "PrimeSpectrum.pointsEquivIrreducibleCloseds", "kind": "definition", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.zeroLocusEquivIrreducibleCloseds", "kind": "definition", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.stableUnderSpecialization_singleton", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": ["simp_rw", "forall_eq]", "exact"], "tactic_count": 3}
{"name": "PrimeSpectrum.stableUnderGeneralization_singleton", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": ["simp_rw", "forall_eq]", "exact"], "tactic_count": 3}
{"name": "PrimeSpectrum.isCompact_isOpen_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": ["rw", "simp", "exact"], "tactic_count": 3}
{"name": "PrimeSpectrum.isCompact_isOpen_iff_ideal", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "PrimeSpectrum.basicOpen_eq_zeroLocus_of_mul_add", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["ext", "suffices", "refine", "rw", "exact"], "tactic_count": 5}
{"name": "PrimeSpectrum.zeroLocus_eq_basicOpen_of_mul_add", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PrimeSpectrum.isClopen_basicOpen_of_mul_add", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.basicOpen_injOn_isIdempotentElem", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.exists_mul_eq_zero_add_eq_one_basicOpen_eq_of_isClopen", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["cases", "refine", "obtain", "obtain", "simp", "have", "refine", "rw", "obtain", "have", "rw", "have", "rw", "constructor", "rintro", "rintro", "rw", "rw", "obtain", "have", "have", "refine", "rw", "exact", "rw", "exact", "refine", "rw"], "tactic_count": 28}
{"name": "PrimeSpectrum.exists_idempotent_basicOpen_eq_of_isClopen", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.existsUnique_idempotent_basicOpen_eq_of_isClopen", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["refine", "rintro", "exact"], "tactic_count": 3}
{"name": "PrimeSpectrum.isClopen_iff_mul_add", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["refine", "have", "exact", "rintro", "exact"], "tactic_count": 5}
{"name": "PrimeSpectrum.isClopen_iff_mul_add_zeroLocus", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "intro", "rw"], "tactic_count": 5}
{"name": "PrimeSpectrum.mulZeroAddOneEquivClopens", "kind": "definition", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.isRetrocompact_zeroLocus_compl", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.isRetrocompact_zeroLocus_compl_of_fg", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact"], "tactic_count": 3}
{"name": "PrimeSpectrum.isRetrocompact_basicOpen", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "PrimeSpectrum.isConstructible_basicOpen", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.isClosedMap_comap_of_isIntegral", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["refine", "rintro", "algebraize", "obtain", "refine"], "tactic_count": 5}
{"name": "PrimeSpectrum.isClosed_comap_singleton_of_isIntegral", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "PrimeSpectrum.closure_image_comap_zeroLocus", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["apply", "rw", "exact", "rintro", "obtain", "obtain", "let", "apply", "isClosed_closure.stableUnderSpecialization"], "tactic_count": 9}
{"name": "PrimeSpectrum.isIntegral_of_isClosedMap_comap_mapRingHom", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["algebraize", "suffices", "nontriviality", "nontriviality", "constructor", "intro", "let", "have", "have", "rw", "rw", "suffices", "intro", "have", "exact", "obtain", "obtain", "refine", "refine", "have", "have", "rw", "have", "rw", "reflect_mul", "simp"], "tactic_count": 26}
{"name": "RingHom.IsIntegral.comap_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["algebraize", "intro", "obtain", "exact"], "tactic_count": 4}
{"name": "Ideal.minimalPrimes.equivIrreducibleComponents", "kind": "definition", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": ["let", "rw", "exact"], "tactic_count": 3}
{"name": "minimalPrimes.equivIrreducibleComponents", "kind": "definition", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": ["let", "rw", "exact"], "tactic_count": 3}
{"name": "PrimeSpectrum.vanishingIdeal_irreducibleComponents", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": ["rw", "image_antitone_setOf_maximal", "funext", "rfl"], "tactic_count": 4}
{"name": "PrimeSpectrum.zeroLocus_minimalPrimes", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["rw", "intro", "simpa"], "tactic_count": 3}
{"name": "PrimeSpectrum.vanishingIdeal_mem_minimalPrimes", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["constructor", "rw", "exact", "rw", "exact"], "tactic_count": 5}
{"name": "PrimeSpectrum.zeroLocus_ideal_mem_irreducibleComponents", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["rw", "conv_lhs", "exact"], "tactic_count": 3}
{"name": "IsLocalRing.closedPoint", "kind": "definition", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.instOrderTopPrimeSpectrum", "kind": "instance", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.instBoundedOrderPrimeSpectrumOfIsDomain", "kind": "instance", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.PrimeSpectrum.asIdeal_top", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.isLocalHom_iff_comap_closedPoint", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["have", "rw", "rfl"], "tactic_count": 3}
{"name": "IsLocalRing.comap_closedPoint", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.specializes_closedPoint", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.closedPoint_mem_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["constructor", "rw", "exact", "rintro", "exact"], "tactic_count": 5}
{"name": "IsLocalRing.closed_point_mem_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.PrimeSpectrum.comap_residue", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["rw", "ext1", "exact"], "tactic_count": 3}
{"name": "IsLocalRing.isClosed_singleton_closedPoint", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "IsLocalRing.Ring.KrullDimLE.eq_bot_or_eq_top", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.topologicalKrullDim_eq_ringKrullDim", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.basicOpen_eq_zeroLocus_of_isIdempotentElem", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.zeroLocus_eq_basicOpen_of_isIdempotentElem", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PrimeSpectrum.isClopen_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": true, "tactics": ["refine", "rintro", "refine", "rw", "exact"], "tactic_count": 5}
{"name": "PrimeSpectrum.isClopen_iff_zeroLocus", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.isIdempotentElemEquivClopens", "kind": "definition", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.basicOpen_isIdempotentElemEquivClopens_symm", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.coe_isIdempotentElemEquivClopens_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.isIdempotentElemEquivClopens_apply_toOpens", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.isIdempotentElemEquivClopens_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.isIdempotentElemEquivClopens_one_sub", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.isIdempotentElemEquivClopens_symm_inf", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.isIdempotentElemEquivClopens_symm_compl", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.isIdempotentElemEquivClopens_symm_top", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.isIdempotentElemEquivClopens_symm_bot", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimeSpectrum.isIdempotentElemEquivClopens_symm_sup", "kind": "theorem", "module": "Mathlib.RingTheory.Spectrum.Prime.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.support", "kind": "definition", "module": "Mathlib.RingTheory.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.mem_support_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.notMem_support_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.notMem_support_iff'", "kind": "theorem", "module": "Mathlib.RingTheory.Support", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Module.mem_support_iff'", "kind": "theorem", "module": "Mathlib.RingTheory.Support", "is_tactic_proof": true, "tactics": ["rw", "push_neg", "rfl"], "tactic_count": 3}
{"name": "Module.mem_support_iff_exists_annihilator", "kind": "theorem", "module": "Mathlib.RingTheory.Support", "is_tactic_proof": true, "tactics": ["rw", "simp_rw"], "tactic_count": 2}
{"name": "Module.mem_support_mono", "kind": "theorem", "module": "Mathlib.RingTheory.Support", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Module.mem_support_iff_of_span_eq_top", "kind": "theorem", "module": "Mathlib.RingTheory.Support", "is_tactic_proof": true, "tactics": ["constructor", "contrapose", "rw", "simp_rw", "push_neg", "simp_rw", "exact", "intro", "exact"], "tactic_count": 9}
{"name": "Module.annihilator_le_of_mem_support", "kind": "theorem", "module": "Mathlib.RingTheory.Support", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "LocalizedModule.subsingleton_iff_support_subset", "kind": "theorem", "module": "Mathlib.RingTheory.Support", "is_tactic_proof": true, "tactics": ["rw", "constructor", "rintro", "obtain", "obtain", "exact", "intro", "by_cases", "rw", "exact", "obtain", "rw", "rintro", "simpa", "exact"], "tactic_count": 15}
{"name": "Module.support_eq_empty_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Support", "is_tactic_proof": false, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Module.nonempty_support_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Support", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Module.nonempty_support_of_nontrivial", "kind": "theorem", "module": "Mathlib.RingTheory.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.support_eq_empty", "kind": "theorem", "module": "Mathlib.RingTheory.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.support_of_algebra", "kind": "theorem", "module": "Mathlib.RingTheory.Support", "is_tactic_proof": true, "tactics": ["ext", "simp", "refine", "simpa", "exact"], "tactic_count": 5}
{"name": "Module.support_of_noZeroSMulDivisors", "kind": "theorem", "module": "Mathlib.RingTheory.Support", "is_tactic_proof": true, "tactics": ["simp", "obtain", "exact"], "tactic_count": 3}
{"name": "Module.support_subset_of_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Support", "is_tactic_proof": true, "tactics": ["simp_rw", "rintro", "exact"], "tactic_count": 3}
{"name": "Module.support_subset_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Support", "is_tactic_proof": true, "tactics": ["simp_rw", "rintro", "obtain", "exact"], "tactic_count": 4}
{"name": "Module.support_of_exact", "kind": "theorem", "module": "Mathlib.RingTheory.Support", "is_tactic_proof": false, "tactics": ["refine", "subset_antisymm", "intro", "contrapose", "simp", "intro", "obtain", "rw", "obtain", "obtain", "exact"], "tactic_count": 11}
{"name": "LinearEquiv.support_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.mem_support_iff_of_finite", "kind": "theorem", "module": "Mathlib.RingTheory.Support", "is_tactic_proof": true, "tactics": ["classical", "obtain", "refine", "simp", "contrapose", "choose", "refine", "rw", "intro", "obtain", "rw", "exact"], "tactic_count": 12}
{"name": "Module.support_eq_zeroLocus", "kind": "theorem", "module": "Mathlib.RingTheory.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocalizedModule.exists_subsingleton_away", "kind": "theorem", "module": "Mathlib.RingTheory.Support", "is_tactic_proof": true, "tactics": ["have", "rw", "obtain", "exact"], "tactic_count": 4}
{"name": "IsLocalizedModule.exists_subsingleton_away", "kind": "theorem", "module": "Mathlib.RingTheory.Support", "is_tactic_proof": true, "tactics": ["let", "have", "exact"], "tactic_count": 3}
{"name": "Module.support_quotient", "kind": "theorem", "module": "Mathlib.RingTheory.Support", "is_tactic_proof": true, "tactics": ["apply", "refine", "exact", "rw", "apply", "rw", "exact", "rintro", "rw", "let", "let", "set", "let", "let", "have", "rw", "apply", "refine", "rw", "exact", "exact"], "tactic_count": 21}
{"name": "Module.support_quotSMulTop", "kind": "theorem", "module": "Mathlib.RingTheory.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.SurjectiveOnStalks", "kind": "definition", "module": "Mathlib.RingTheory.SurjectiveOnStalks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.surjective_localRingHom_iff", "kind": "theorem", "module": "Mathlib.RingTheory.SurjectiveOnStalks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.surjectiveOnStalks_iff_forall_ideal", "kind": "theorem", "module": "Mathlib.RingTheory.SurjectiveOnStalks", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "obtain", "obtain", "exact"], "tactic_count": 5}
{"name": "RingHom.surjectiveOnStalks_iff_forall_maximal", "kind": "theorem", "module": "Mathlib.RingTheory.SurjectiveOnStalks", "is_tactic_proof": true, "tactics": ["refine", "simp_rw", "intro", "obtain", "obtain", "exact"], "tactic_count": 6}
{"name": "RingHom.surjectiveOnStalks_iff_forall_maximal'", "kind": "theorem", "module": "Mathlib.RingTheory.SurjectiveOnStalks", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RingHom.surjectiveOnStalks_of_exists_div", "kind": "theorem", "module": "Mathlib.RingTheory.SurjectiveOnStalks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.surjectiveOnStalks_of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.SurjectiveOnStalks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.surjectiveOnStalks", "kind": "theorem", "module": "Mathlib.RingTheory.SurjectiveOnStalks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.SurjectiveOnStalks.comp", "kind": "theorem", "module": "Mathlib.RingTheory.SurjectiveOnStalks", "is_tactic_proof": true, "tactics": ["intro", "have", "rwa"], "tactic_count": 3}
{"name": "RingHom.SurjectiveOnStalks.of_comp", "kind": "theorem", "module": "Mathlib.RingTheory.SurjectiveOnStalks", "is_tactic_proof": true, "tactics": ["intro", "have", "rw", "exact"], "tactic_count": 4}
{"name": "RingHom.SurjectiveOnStalks.exists_mul_eq_tmul", "kind": "theorem", "module": "Mathlib.RingTheory.SurjectiveOnStalks", "is_tactic_proof": true, "tactics": ["induction", "zero", "tmul", "obtain", "simp_rw", "refine", "rw", "mul_comm]", "add", "obtain", "obtain", "have", "refine", "rw", "mul_assoc,"], "tactic_count": 15}
{"name": "RingHom.surjectiveOnStalks_of_isLocalization", "kind": "theorem", "module": "Mathlib.RingTheory.SurjectiveOnStalks", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact"], "tactic_count": 3}
{"name": "RingHom.SurjectiveOnStalks.baseChange", "kind": "theorem", "module": "Mathlib.RingTheory.SurjectiveOnStalks", "is_tactic_proof": true, "tactics": ["let", "intro", "rw", "intro", "obtain", "refine", "intro", "simp", "id_apply,", "rw", "exact", "simp", "rw"], "tactic_count": 13}
{"name": "RingHom.SurjectiveOnStalks.baseChange'", "kind": "theorem", "module": "Mathlib.RingTheory.SurjectiveOnStalks", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "_private.Mathlib.RingTheory.SurjectiveOnStalks.0.RingHom.SurjectiveOnStalks.tensorProductMap_id", "kind": "theorem", "module": "Mathlib.RingTheory.SurjectiveOnStalks", "is_tactic_proof": true, "tactics": ["letI", "have", "change", "convert_to", "congr", "exact"], "tactic_count": 6}
{"name": "RingHom.SurjectiveOnStalks.tensorProductMap", "kind": "theorem", "module": "Mathlib.RingTheory.SurjectiveOnStalks", "is_tactic_proof": false, "tactics": ["convert", "simp", "congr", "ext"], "tactic_count": 4}
{"name": "RingHom.surjectiveOnStalks_iff_of_isLocalHom", "kind": "theorem", "module": "Mathlib.RingTheory.SurjectiveOnStalks", "is_tactic_proof": true, "tactics": ["refine", "obtain", "simp", "refine", "apply", "apply", "simp"], "tactic_count": 7}
{"name": "LinearMap.liftBaseChangeEquiv", "kind": "definition", "module": "Mathlib.RingTheory.TensorProduct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.liftBaseChange", "kind": "abbrev", "module": "Mathlib.RingTheory.TensorProduct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.liftBaseChange_tmul", "kind": "theorem", "module": "Mathlib.RingTheory.TensorProduct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.liftBaseChange_one_tmul", "kind": "theorem", "module": "Mathlib.RingTheory.TensorProduct.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LinearMap.liftBaseChangeEquiv_symm_apply", "kind": "theorem", "module": "Mathlib.RingTheory.TensorProduct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.liftBaseChange_comp", "kind": "theorem", "module": "Mathlib.RingTheory.TensorProduct.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "LinearMap.range_liftBaseChange", "kind": "theorem", "module": "Mathlib.RingTheory.TensorProduct.Basic", "is_tactic_proof": true, "tactics": ["apply", "rintro", "induction", "simp", "rw", "exact", "rw", "exact", "rw", "rintro", "exact"], "tactic_count": 11}
{"name": "Algebra.TensorProduct.instOneTensorProduct", "kind": "instance", "module": "Mathlib.RingTheory.TensorProduct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.TensorProduct.one_def", "kind": "theorem", "module": "Mathlib.RingTheory.TensorProduct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.TensorProduct.instAddCommMonoidWithOne", "kind": "instance", "module": "Mathlib.RingTheory.TensorProduct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.TensorProduct.natCast_def", "kind": "theorem", "module": "Mathlib.RingTheory.TensorProduct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.TensorProduct.natCast_def'", "kind": "theorem", "module": "Mathlib.RingTheory.TensorProduct.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Algebra.TensorProduct.mul", "kind": "definition", "module": "Mathlib.RingTheory.TensorProduct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.TensorProduct.mul_apply", "kind": "theorem", "module": "Mathlib.RingTheory.TensorProduct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.TensorProduct.instMul", "kind": "instance", "module": "Mathlib.RingTheory.TensorProduct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.TensorProduct.tmul_mul_tmul", "kind": "theorem", "module": "Mathlib.RingTheory.TensorProduct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SemiconjBy.tmul", "kind": "theorem", "module": "Mathlib.RingTheory.TensorProduct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.tmul", "kind": "theorem", "module": "Mathlib.RingTheory.TensorProduct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.TensorProduct.instNonUnitalNonAssocSemiring", "kind": "instance", "module": "Mathlib.RingTheory.TensorProduct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.TensorProduct.isScalarTower_right", "kind": "instance", "module": "Mathlib.RingTheory.TensorProduct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.TensorProduct.sMulCommClass_right", "kind": "instance", "module": "Mathlib.RingTheory.TensorProduct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.TensorProduct.one_mul", "kind": "theorem", "module": "Mathlib.RingTheory.TensorProduct.Basic", "is_tactic_proof": true, "tactics": ["refine"], "tactic_count": 1}
{"name": "Algebra.TensorProduct.mul_one", "kind": "theorem", "module": "Mathlib.RingTheory.TensorProduct.Basic", "is_tactic_proof": true, "tactics": ["refine"], "tactic_count": 1}
{"name": "Algebra.TensorProduct.instNonAssocSemiring", "kind": "instance", "module": "Mathlib.RingTheory.TensorProduct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.TensorProduct.mul_assoc", "kind": "theorem", "module": "Mathlib.RingTheory.TensorProduct.Basic", "is_tactic_proof": true, "tactics": ["suffices", "ext", "exact"], "tactic_count": 3}
{"name": "Algebra.TensorProduct.instNonUnitalSemiring", "kind": "instance", "module": "Mathlib.RingTheory.TensorProduct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.TensorProduct.instSemiring", "kind": "instance", "module": "Mathlib.RingTheory.TensorProduct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.TensorProduct.tmul_pow", "kind": "theorem", "module": "Mathlib.RingTheory.TensorProduct.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Algebra.TensorProduct.includeLeftRingHom", "kind": "definition", "module": "Mathlib.RingTheory.TensorProduct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.TensorProduct.leftAlgebra", "kind": "instance", "module": "Mathlib.RingTheory.TensorProduct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.TensorProduct.algebraMap_def", "kind": "theorem", "module": "Mathlib.RingTheory.TensorProduct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.TensorProduct._example", "kind": "example", "module": "Mathlib.RingTheory.TensorProduct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.TensorProduct.instAlgebra", "kind": "instance", "module": "Mathlib.RingTheory.TensorProduct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.TensorProduct.algebraMap_apply", "kind": "theorem", "module": "Mathlib.RingTheory.TensorProduct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.TensorProduct.algebraMap_apply'", "kind": "theorem", "module": "Mathlib.RingTheory.TensorProduct.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Algebra.TensorProduct.includeLeft", "kind": "definition", "module": "Mathlib.RingTheory.TensorProduct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.TensorProduct.includeLeft_apply", "kind": "theorem", "module": "Mathlib.RingTheory.TensorProduct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.TensorProduct.includeRight", "kind": "definition", "module": "Mathlib.RingTheory.TensorProduct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.TensorProduct.includeRight_apply", "kind": "theorem", "module": "Mathlib.RingTheory.TensorProduct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Algebra.TensorProduct.tmul_one_eq_one_tmul", "kind": "theorem", "module": "Mathlib.RingTheory.TensorProduct.Maps", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "traceForm_nondegenerate_tfae", "kind": "theorem", "module": "Mathlib.RingTheory.Trace.Basic", "is_tactic_proof": true, "tactics": ["tfae_have", "tfae_have", "tfae_have", "tfae_finish"], "tactic_count": 4}
{"name": "Algebra.trace_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Trace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.trace_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Trace.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply", "rw", "exact"], "tactic_count": 4}
{"name": "Algebra.isNilpotent_trace_of_isNilpotent", "kind": "theorem", "module": "Mathlib.RingTheory.Trace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.traceDual", "kind": "definition", "module": "Mathlib.RingTheory.Trace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.traceDual_def", "kind": "theorem", "module": "Mathlib.RingTheory.Trace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.traceDual_repr_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Trace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.trace_traceDual_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Trace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.trace_mul_traceDual", "kind": "theorem", "module": "Mathlib.RingTheory.Trace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.traceDual_traceDual", "kind": "theorem", "module": "Mathlib.RingTheory.Trace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.traceDual_involutive", "kind": "theorem", "module": "Mathlib.RingTheory.Trace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.traceDual_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Trace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.traceDual_inj", "kind": "theorem", "module": "Mathlib.RingTheory.Trace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.traceDual_eq_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Trace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.traceDual_powerBasis_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Trace.Basic", "is_tactic_proof": true, "tactics": ["revert", "rw", "intro", "apply", "have", "congr_arg", "simp", "smul_eq_mul,", "rw", "simp", "rw", "apply", "intro", "simp", "ring"], "tactic_count": 15}
{"name": "Algebra.trace", "kind": "definition", "module": "Mathlib.RingTheory.Trace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.trace_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Trace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.trace_eq_zero_of_not_exists_basis", "kind": "theorem", "module": "Mathlib.RingTheory.Trace.Defs", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Algebra.trace_eq_matrix_trace", "kind": "theorem", "module": "Mathlib.RingTheory.Trace.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Algebra.trace_algebraMap_of_basis", "kind": "theorem", "module": "Mathlib.RingTheory.Trace.Defs", "is_tactic_proof": true, "tactics": ["haveI", "rw", "convert", "simp"], "tactic_count": 4}
{"name": "Algebra.trace_self", "kind": "theorem", "module": "Mathlib.RingTheory.Trace.Defs", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Algebra.trace_self_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Trace.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Algebra.trace_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.Trace.Defs", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "simp"], "tactic_count": 3}
{"name": "Algebra.trace_trace_of_basis", "kind": "theorem", "module": "Mathlib.RingTheory.Trace.Defs", "is_tactic_proof": true, "tactics": ["haveI", "haveI", "cases", "cases", "rw", "refine", "simp"], "tactic_count": 7}
{"name": "Algebra.trace_comp_trace_of_basis", "kind": "theorem", "module": "Mathlib.RingTheory.Trace.Defs", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "Algebra.trace_trace", "kind": "theorem", "module": "Mathlib.RingTheory.Trace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.trace_comp_trace", "kind": "theorem", "module": "Mathlib.RingTheory.Trace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.trace_prod_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Trace.Defs", "is_tactic_proof": true, "tactics": ["let", "have", "simp_rw", "exact"], "tactic_count": 4}
{"name": "Algebra.trace_prod", "kind": "theorem", "module": "Mathlib.RingTheory.Trace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.traceForm", "kind": "definition", "module": "Mathlib.RingTheory.Trace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.traceForm_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Trace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.traceForm_isSymm", "kind": "theorem", "module": "Mathlib.RingTheory.Trace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.traceForm_toMatrix", "kind": "theorem", "module": "Mathlib.RingTheory.Trace.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "_private.Mathlib.RingTheory.Trace.Quotient.0.termP", "kind": "definition", "module": "Mathlib.RingTheory.Trace.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Trace.Quotient.0._aux_Mathlib_RingTheory_Trace_Quotient___macroRules__private_Mathlib_RingTheory_Trace_Quotient_0_termP_1", "kind": "definition", "module": "Mathlib.RingTheory.Trace.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Trace.Quotient.0._aux_Mathlib_RingTheory_Trace_Quotient___unexpand_IsLocalRing_maximalIdeal_1", "kind": "definition", "module": "Mathlib.RingTheory.Trace.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Trace.Quotient.0.termPS", "kind": "definition", "module": "Mathlib.RingTheory.Trace.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Trace.Quotient.0._aux_Mathlib_RingTheory_Trace_Quotient___macroRules__private_Mathlib_RingTheory_Trace_Quotient_0_termPS_1", "kind": "definition", "module": "Mathlib.RingTheory.Trace.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Trace.Quotient.0._aux_Mathlib_RingTheory_Trace_Quotient___unexpand_Ideal_map_1", "kind": "definition", "module": "Mathlib.RingTheory.Trace.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.trace_quotient_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Trace.Quotient", "is_tactic_proof": true, "tactics": ["classical", "let", "let", "rw", "congr", "ext", "simp"], "tactic_count": 7}
{"name": "_private.Mathlib.RingTheory.Trace.Quotient.0.termPS_1", "kind": "definition", "module": "Mathlib.RingTheory.Trace.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Trace.Quotient.0._aux_Mathlib_RingTheory_Trace_Quotient___macroRules__private_Mathlib_RingTheory_Trace_Quotient_0_termPS_1_1", "kind": "definition", "module": "Mathlib.RingTheory.Trace.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Trace.Quotient.0._aux_Mathlib_RingTheory_Trace_Quotient___unexpand_Ideal_map_2", "kind": "definition", "module": "Mathlib.RingTheory.Trace.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Trace.Quotient.0.termPSₚ", "kind": "definition", "module": "Mathlib.RingTheory.Trace.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Trace.Quotient.0._aux_Mathlib_RingTheory_Trace_Quotient___macroRules__private_Mathlib_RingTheory_Trace_Quotient_0_termPSₚ_1", "kind": "definition", "module": "Mathlib.RingTheory.Trace.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Trace.Quotient.0._aux_Mathlib_RingTheory_Trace_Quotient___unexpand_Ideal_map_3", "kind": "definition", "module": "Mathlib.RingTheory.Trace.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "trace_quotient_eq_trace_localization_quotient", "kind": "theorem", "module": "Mathlib.RingTheory.Trace.Quotient", "is_tactic_proof": false, "tactics": ["have", "apply", "rw", "rw", "congr", "ext", "simp", "rw"], "tactic_count": 8}
{"name": "Algebra.trace_quotient_eq_of_isDedekindDomain", "kind": "theorem", "module": "Mathlib.RingTheory.Trace.Quotient", "is_tactic_proof": true, "tactics": ["let", "let", "letI", "haveI", "haveI", "inferInstanceAs", "have", "p.primeCompl_le_nonZeroDivisors.trans", "haveI", "haveI", "rw", "simp", "haveI", "haveI", "have", "by_cases", "infer_instance", "have", "infer_instance", "haveI", "apply", "rw", "simp"], "tactic_count": 23}
{"name": "TwoSidedIdeal.instNontrivial", "kind": "instance", "module": "Mathlib.RingTheory.TwoSidedIdeal.Basic", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "TwoSidedIdeal.setLike", "kind": "instance", "module": "Mathlib.RingTheory.TwoSidedIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.instPartialOrder", "kind": "instance", "module": "Mathlib.RingTheory.TwoSidedIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.mem_iff", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.mem_mk", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.coe_mk", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.rel_iff", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Basic", "is_tactic_proof": true, "tactics": ["rw", "constructor", "intro", "intro"], "tactic_count": 4}
{"name": "TwoSidedIdeal.coeOrderEmbedding", "kind": "definition", "module": "Mathlib.RingTheory.TwoSidedIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.le_iff", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.orderIsoRingCon", "kind": "definition", "module": "Mathlib.RingTheory.TwoSidedIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.ringCon_injective", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Basic", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "TwoSidedIdeal.ringCon_le_iff", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.ext", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.lt_iff", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "TwoSidedIdeal.zero_mem", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.add_mem", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "TwoSidedIdeal.neg_mem", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "TwoSidedIdeal.instAddSubgroupClass", "kind": "instance", "module": "Mathlib.RingTheory.TwoSidedIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.sub_mem", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.mul_mem_left", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "TwoSidedIdeal.mul_mem_right", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "TwoSidedIdeal.nsmul_mem", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.zsmul_mem", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.mk'", "kind": "definition", "module": "Mathlib.RingTheory.TwoSidedIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.mem_mk'", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "TwoSidedIdeal.coe_mk'", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.instSMulMemClass", "kind": "instance", "module": "Mathlib.RingTheory.TwoSidedIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.instSMulMemClassMulOpposite", "kind": "instance", "module": "Mathlib.RingTheory.TwoSidedIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.instAddSubtypeMem", "kind": "instance", "module": "Mathlib.RingTheory.TwoSidedIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.instZeroSubtypeMem", "kind": "instance", "module": "Mathlib.RingTheory.TwoSidedIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.instSMulNatSubtypeMem", "kind": "instance", "module": "Mathlib.RingTheory.TwoSidedIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.instNegSubtypeMem", "kind": "instance", "module": "Mathlib.RingTheory.TwoSidedIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.instSubSubtypeMem", "kind": "instance", "module": "Mathlib.RingTheory.TwoSidedIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.instSMulIntSubtypeMem", "kind": "instance", "module": "Mathlib.RingTheory.TwoSidedIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.addCommGroup", "kind": "instance", "module": "Mathlib.RingTheory.TwoSidedIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.coeAddMonoidHom", "kind": "definition", "module": "Mathlib.RingTheory.TwoSidedIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.op", "kind": "definition", "module": "Mathlib.RingTheory.TwoSidedIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.mem_op_iff", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.coe_op", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.unop", "kind": "definition", "module": "Mathlib.RingTheory.TwoSidedIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.mem_unop_iff", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.coe_unop", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.opOrderIso", "kind": "definition", "module": "Mathlib.RingTheory.TwoSidedIdeal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.listSum_mem", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.BigOperators", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "TwoSidedIdeal.multisetSum_mem", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.BigOperators", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "TwoSidedIdeal.finsetSum_mem", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.BigOperators", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "TwoSidedIdeal.listProd_mem", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.BigOperators", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "simp", "rcases", "simpa", "simpa"], "tactic_count": 7}
{"name": "TwoSidedIdeal.multiSetProd_mem", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.BigOperators", "is_tactic_proof": true, "tactics": ["rcases", "simpa"], "tactic_count": 2}
{"name": "TwoSidedIdeal.finsetProd_mem", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.BigOperators", "is_tactic_proof": true, "tactics": ["rcases", "simpa"], "tactic_count": 2}
{"name": "instNonUnitalSubringClassTwoSidedIdeal", "kind": "instance", "module": "Mathlib.RingTheory.TwoSidedIdeal.Instances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.ker", "kind": "definition", "module": "Mathlib.RingTheory.TwoSidedIdeal.Kernel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.ker_ringCon", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Kernel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.mem_ker", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Kernel", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "TwoSidedIdeal.ker_eq_bot", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Kernel", "is_tactic_proof": true, "tactics": ["fconstructor", "intro", "simpa", "exact"], "tactic_count": 4}
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{"name": "TwoSidedIdeal.instSemilatticeSup", "kind": "instance", "module": "Mathlib.RingTheory.TwoSidedIdeal.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.sup_ringCon", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.mem_sup_left", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.mem_sup_right", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "TwoSidedIdeal.instSemilatticeInf", "kind": "instance", "module": "Mathlib.RingTheory.TwoSidedIdeal.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.inf_ringCon", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.mem_inf", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.instSupSet", "kind": "instance", "module": "Mathlib.RingTheory.TwoSidedIdeal.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.sSup_ringCon", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.iSup_ringCon", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Lattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "TwoSidedIdeal.instCompleteSemilatticeSup", "kind": "instance", "module": "Mathlib.RingTheory.TwoSidedIdeal.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.instInfSet", "kind": "instance", "module": "Mathlib.RingTheory.TwoSidedIdeal.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.sInf_ringCon", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.iInf_ringCon", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Lattice", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "TwoSidedIdeal.instCompleteSemilatticeInf", "kind": "instance", "module": "Mathlib.RingTheory.TwoSidedIdeal.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.mem_iInf", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.mem_sInf", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.instTop", "kind": "instance", "module": "Mathlib.RingTheory.TwoSidedIdeal.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.top_ringCon", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.mem_top", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.instBot", "kind": "instance", "module": "Mathlib.RingTheory.TwoSidedIdeal.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.bot_ringCon", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.mem_bot", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.instCompleteLattice", "kind": "instance", "module": "Mathlib.RingTheory.TwoSidedIdeal.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.coe_bot", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.coe_top", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.one_mem_iff", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.span", "kind": "abbrev", "module": "Mathlib.RingTheory.TwoSidedIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.subset_span", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Operations", "is_tactic_proof": true, "tactics": ["intro", "rw", "exact"], "tactic_count": 3}
{"name": "TwoSidedIdeal.mem_span_iff", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Operations", "is_tactic_proof": true, "tactics": ["refine", "delta", "rw", "intro", "refine", "intro", "specialize", "rwa"], "tactic_count": 8}
{"name": "TwoSidedIdeal.span_mono", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Operations", "is_tactic_proof": true, "tactics": ["intro", "rw", "exact"], "tactic_count": 3}
{"name": "TwoSidedIdeal.span_le", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Operations", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "TwoSidedIdeal.span_induction", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.map", "kind": "definition", "module": "Mathlib.RingTheory.TwoSidedIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.map_mono", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.comap", "kind": "definition", "module": "Mathlib.RingTheory.TwoSidedIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.comap_le_comap", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.mem_comap", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "RingEquiv.mapTwoSidedIdeal", "kind": "definition", "module": "Mathlib.RingTheory.TwoSidedIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.mapTwoSidedIdeal_apply", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingEquiv.mapTwoSidedIdeal_symm", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.comap_comap", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Operations", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "TwoSidedIdeal.mem_span_iff_mem_addSubgroup_closure_absorbing", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Operations", "is_tactic_proof": false, "tactics": ["have", "have", "refine", "rintro", "exact", "have", "have", "refine", "rintro", "exact", "let", "suffices", "rw", "refine", "simpa", "simp", "induction", "mem", "zero", "add", "neg"], "tactic_count": 21}
{"name": "TwoSidedIdeal.set_mul_subset", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Operations", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "TwoSidedIdeal.subset_mul_set", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Operations", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "TwoSidedIdeal.mem_span_iff_mem_addSubgroup_closure_nonunital", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Operations", "is_tactic_proof": true, "tactics": ["trans", "refine", "refine", "simp", "exact", "subset_mul_set", "refine", "rintro", "exact", "exact", "exact", "refine", "all_goals", "rintro", "exact", "exact", "exact", "refine", "simp"], "tactic_count": 19}
{"name": "TwoSidedIdeal.mem_span_iff_mem_addSubgroup_closure", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Operations", "is_tactic_proof": true, "tactics": ["trans", "refine", "exact", "exact", "refine", "intro", "rw", "obtain", "exact", "rintro", "exact"], "tactic_count": 11}
{"name": "TwoSidedIdeal.instSMulSubtypeMem", "kind": "instance", "module": "Mathlib.RingTheory.TwoSidedIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.instSMulMulOppositeSubtypeMem", "kind": "instance", "module": "Mathlib.RingTheory.TwoSidedIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.leftModule", "kind": "instance", "module": "Mathlib.RingTheory.TwoSidedIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.coe_smul", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.rightModule", "kind": "instance", "module": "Mathlib.RingTheory.TwoSidedIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.coe_mop_smul", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.instSMulCommClassMulOppositeSubtypeMem", "kind": "instance", "module": "Mathlib.RingTheory.TwoSidedIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.subtype", "kind": "definition", "module": "Mathlib.RingTheory.TwoSidedIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.subtype_injective", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.coe_subtype", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.subtypeMop", "kind": "definition", "module": "Mathlib.RingTheory.TwoSidedIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.subtypeMop_injective", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.fromIdeal", "kind": "definition", "module": "Mathlib.RingTheory.TwoSidedIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.mem_fromIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "TwoSidedIdeal.asIdeal", "kind": "definition", "module": "Mathlib.RingTheory.TwoSidedIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.mem_asIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "TwoSidedIdeal.gc", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.coe_asIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.bot_asIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.top_asIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.instIsTwoSidedCoeOrderHomIdealAsIdeal", "kind": "instance", "module": "Mathlib.RingTheory.TwoSidedIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.asIdealOpposite", "kind": "definition", "module": "Mathlib.RingTheory.TwoSidedIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.mem_asIdealOpposite", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Operations", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "TwoSidedIdeal.orderIsoIdeal", "kind": "definition", "module": "Mathlib.RingTheory.TwoSidedIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.toTwoSided", "kind": "definition", "module": "Mathlib.RingTheory.TwoSidedIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.mem_toTwoSided", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Ideal.coe_toTwoSided", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Operations", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Ideal.toTwoSided_asIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Operations", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Ideal.asIdeal_toTwoSided", "kind": "theorem", "module": "Mathlib.RingTheory.TwoSidedIdeal.Operations", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Ideal.instCanLiftTwoSidedIdealCoeOrderHomAsIdealIsTwoSided", "kind": "instance", "module": "Mathlib.RingTheory.TwoSidedIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TwoSidedIdeal.orderIsoIsTwoSided", "kind": "definition", "module": "Mathlib.RingTheory.TwoSidedIdeal.Operations", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.UniqueFactorizationDomain.Basic.0.term_~ᵤ_", "kind": "definition", "module": "Mathlib.RingTheory.UniqueFactorizationDomain.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.UniqueFactorizationDomain.Basic.0._aux_Mathlib_RingTheory_UniqueFactorizationDomain_Basic___macroRules__private_Mathlib_RingTheory_UniqueFactorizationDomain_Basic_0_term_~ᵤ__1", "kind": "definition", "module": "Mathlib.RingTheory.UniqueFactorizationDomain.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.UniqueFactorizationDomain.Basic.0._aux_Mathlib_RingTheory_UniqueFactorizationDomain_Basic___unexpand_Associated_1", "kind": "definition", "module": "Mathlib.RingTheory.UniqueFactorizationDomain.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WfDvdMonoid.of_wfDvdMonoid_associates", "kind": "theorem", "module": "Mathlib.RingTheory.UniqueFactorizationDomain.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WfDvdMonoid.wfDvdMonoid_associates", "kind": "instance", "module": "Mathlib.RingTheory.UniqueFactorizationDomain.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WfDvdMonoid.wellFoundedLT_associates", "kind": "theorem", "module": "Mathlib.RingTheory.UniqueFactorizationDomain.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WfDvdMonoid.of_wellFoundedLT_associates", "kind": "theorem", "module": "Mathlib.RingTheory.UniqueFactorizationDomain.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WfDvdMonoid.iff_wellFounded_associates", "kind": "theorem", "module": "Mathlib.RingTheory.UniqueFactorizationDomain.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associates.ufm", "kind": "instance", "module": "Mathlib.RingTheory.UniqueFactorizationDomain.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "prime_factors_unique", "kind": "theorem", "module": "Mathlib.RingTheory.UniqueFactorizationDomain.Basic", "is_tactic_proof": true, "tactics": ["classical", "intro", "induction", "empty", "intro", "exact", "have", "cons", "intro", "let", "hfg.dvd_iff_dvd_right.1", "haveI", "rw", "exact"], "tactic_count": 14}
{"name": "UniqueFactorizationMonoid.factors_unique", "kind": "theorem", "module": "Mathlib.RingTheory.UniqueFactorizationDomain.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associated.card_factors_eq", "kind": "theorem", "module": "Mathlib.RingTheory.UniqueFactorizationDomain.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simp_all", "have", "apply", "apply", "exact"], "tactic_count": 6}
{"name": "prime_factors_irreducible", "kind": "theorem", "module": "Mathlib.RingTheory.UniqueFactorizationDomain.Basic", "is_tactic_proof": true, "tactics": ["haveI", "refine", "intro", "rintro", "use", "have", "by_contra", "obtain", "apply", "refine", "rw", "mul_assoc]", "simp", "apply", "apply", "simp", "exact"], "tactic_count": 17}
{"name": "irreducible_iff_prime_of_existsUnique_irreducible_factors", "kind": "theorem", "module": "Mathlib.RingTheory.UniqueFactorizationDomain.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniqueFactorizationMonoid.factors_one", "kind": "theorem", "module": "Mathlib.RingTheory.UniqueFactorizationDomain.Basic", "is_tactic_proof": true, "tactics": ["nontriviality", "rw", "refine", "rw", "exact"], "tactic_count": 5}
{"name": "UniqueFactorizationMonoid.exists_mem_factors_of_dvd", "kind": "theorem", "module": "Mathlib.RingTheory.UniqueFactorizationDomain.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniqueFactorizationMonoid.exists_mem_factors", "kind": "theorem", "module": "Mathlib.RingTheory.UniqueFactorizationDomain.Basic", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "exact"], "tactic_count": 3}
{"name": "UniqueFactorizationMonoid.factors_eq_singleton_of_irreducible", "kind": "theorem", "module": "Mathlib.RingTheory.UniqueFactorizationDomain.Basic", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "UniqueFactorizationMonoid.factors_mul", "kind": "theorem", "module": "Mathlib.RingTheory.UniqueFactorizationDomain.Basic", "is_tactic_proof": false, "tactics": ["refine", "factors_unique", "rw", "exact"], "tactic_count": 4}
{"name": "UniqueFactorizationMonoid.factors_pow", "kind": "theorem", "module": "Mathlib.RingTheory.UniqueFactorizationDomain.Basic", "is_tactic_proof": true, "tactics": ["n", "by_cases", "simp", "rw", "refine", "refine", "exact"], "tactic_count": 7}
{"name": "UniqueFactorizationMonoid.factors_pow_count_prod", "kind": "theorem", "module": "Mathlib.RingTheory.UniqueFactorizationDomain.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniqueFactorizationMonoid.factors_rel_of_associated", "kind": "theorem", "module": "Mathlib.RingTheory.UniqueFactorizationDomain.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simp", "refine", "exact"], "tactic_count": 4}
{"name": "UniqueFactorizationMonoid.factors_of_isUnit", "kind": "theorem", "module": "Mathlib.RingTheory.UniqueFactorizationDomain.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "UniqueFactorizationMonoid.factors_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.UniqueFactorizationDomain.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniqueFactorizationMonoid.factors_pos", "kind": "theorem", "module": "Mathlib.RingTheory.UniqueFactorizationDomain.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Associates.unique'", "kind": "theorem", "module": "Mathlib.RingTheory.UniqueFactorizationDomain.Basic", "is_tactic_proof": true, "tactics": ["apply", "apply", "intro", "refine", "exact", "exact", "have", "rwa"], "tactic_count": 8}
{"name": "Associates.prod_le_prod_iff_le", "kind": "theorem", "module": "Mathlib.RingTheory.UniqueFactorizationDomain.Basic", "is_tactic_proof": true, "tactics": ["refine", "rintro", "refine", "obtain", "exact", "exact", "rw", "congr", "refine", "refine", "rw"], "tactic_count": 11}
{"name": "WfDvdMonoid.of_exists_prime_factors", "kind": "theorem", "module": "Mathlib.RingTheory.UniqueFactorizationDomain.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "irreducible_iff_prime_of_exists_prime_factors", "kind": "theorem", "module": "Mathlib.RingTheory.UniqueFactorizationDomain.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "refine", "obtain", "obtain", "rw", "exact"], "tactic_count": 7}
{"name": "UniqueFactorizationMonoid.of_exists_prime_factors", "kind": "theorem", "module": "Mathlib.RingTheory.UniqueFactorizationDomain.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniqueFactorizationMonoid.iff_exists_prime_factors", "kind": "theorem", "module": "Mathlib.RingTheory.UniqueFactorizationDomain.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.uniqueFactorizationMonoid", "kind": "theorem", "module": "Mathlib.RingTheory.UniqueFactorizationDomain.Basic", "is_tactic_proof": true, "tactics": ["have", "rw", "intro", "obtain", "hα", "ha", "convert", "simp", "exact", "let", "he", "rw"], "tactic_count": 12}
{"name": "MulEquiv.uniqueFactorizationMonoid_iff", "kind": "theorem", "module": "Mathlib.RingTheory.UniqueFactorizationDomain.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniqueFactorizationMonoid.of_existsUnique_irreducible_factors", "kind": "theorem", "module": "Mathlib.RingTheory.UniqueFactorizationDomain.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "UniqueFactorizationMonoid.normalizedFactors_pos", "kind": "theorem", "module": "Mathlib.RingTheory.UniqueFactorizationDomain.NormalizedFactors", "is_tactic_proof": true, "tactics": ["constructor", "intro", "obtain", "exact", "intro", "obtain", "exact"], "tactic_count": 7}
{"name": "UniqueFactorizationMonoid.normalizedFactors_eq_zero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.UniqueFactorizationDomain.NormalizedFactors", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "UniqueFactorizationMonoid.normalizedFactors_of_isUnit", "kind": "theorem", "module": "Mathlib.RingTheory.UniqueFactorizationDomain.NormalizedFactors", "is_tactic_proof": true, "tactics": ["obtain", "simp", "rwa"], "tactic_count": 3}
{"name": "UniqueFactorizationMonoid.dvdNotUnit_iff_normalizedFactors_lt_normalizedFactors", "kind": "theorem", "module": "Mathlib.RingTheory.UniqueFactorizationDomain.NormalizedFactors", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "simp", "normalizedFactors_pos,", "intro", "exact", "dvdNotUnit_of_dvd_of_not_dvd"], "tactic_count": 7}
{"name": "UniqueFactorizationMonoid.normalizedFactors_multiset_prod", "kind": "theorem", "module": "Mathlib.RingTheory.UniqueFactorizationDomain.NormalizedFactors", "is_tactic_proof": true, "tactics": ["cases", "obtain", "apply", "intro", "convert", "simp", "induction", "empty", "cons", "rw", "exact", "exact", "apply", "exact"], "tactic_count": 14}
{"name": "UniqueFactorizationMonoid.normalizedFactorsEquiv", "kind": "definition", "module": "Mathlib.RingTheory.UniqueFactorizationDomain.NormalizedFactors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniqueFactorizationMonoid.normalizedFactorsEquiv_apply", "kind": "theorem", "module": "Mathlib.RingTheory.UniqueFactorizationDomain.NormalizedFactors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniqueFactorizationMonoid.normalizedFactorsEquiv_symm_apply", "kind": "theorem", "module": "Mathlib.RingTheory.UniqueFactorizationDomain.NormalizedFactors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniqueFactorizationMonoid.normalizationMonoid", "kind": "definition", "module": "Mathlib.RingTheory.UniqueFactorizationDomain.NormalizedFactors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.FormallyUnramified.comp_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Unramified.Basic", "is_tactic_proof": true, "tactics": ["intro", "letI", "haveI", "have", "exact"], "tactic_count": 5}
{"name": "Algebra.FormallyUnramified.iff_comp_injective_of_small", "kind": "theorem", "module": "Mathlib.RingTheory.Unramified.Basic", "is_tactic_proof": true, "tactics": ["constructor", "intros", "intro", "replace", "intro", "simpa", "constructor", "by_contra", "obtain", "apply", "ext1", "let", "refine", "rw", "exact", "ext", "apply", "simpa"], "tactic_count": 18}
{"name": "Algebra.FormallyUnramified.iff_comp_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Unramified.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.FormallyUnramified.lift_unique", "kind": "theorem", "module": "Mathlib.RingTheory.Unramified.Basic", "is_tactic_proof": true, "tactics": ["revert", "change", "revert", "apply", "intro", "intro", "apply", "apply", "ext", "replace", "dsimp", "rwa"], "tactic_count": 12}
{"name": "Algebra.FormallyUnramified.ext", "kind": "theorem", "module": "Mathlib.RingTheory.Unramified.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.FormallyUnramified.lift_unique_of_ringHom", "kind": "theorem", "module": "Mathlib.RingTheory.Unramified.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.FormallyUnramified.ext'", "kind": "theorem", "module": "Mathlib.RingTheory.Unramified.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.FormallyUnramified.lift_unique'", "kind": "theorem", "module": "Mathlib.RingTheory.Unramified.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.FormallyUnramified.ext_of_iInf", "kind": "theorem", "module": "Mathlib.RingTheory.Unramified.Basic", "is_tactic_proof": false, "tactics": ["have", "by_cases", "ext", "have", "rw", "infer_instance", "exact", "apply", "intro", "dsimp", "rw", "exact", "simpa", "exact", "ext", "rw", "intro", "rw", "exact"], "tactic_count": 19}
{"name": "Algebra.FormallyUnramified.inst", "kind": "instance", "module": "Mathlib.RingTheory.Unramified.Basic", "is_tactic_proof": true, "tactics": ["rw", "intro", "exact"], "tactic_count": 3}
{"name": "Algebra.FormallyUnramified.of_equiv", "kind": "theorem", "module": "Mathlib.RingTheory.Unramified.Basic", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "congr", "refine", "rw"], "tactic_count": 6}
{"name": "Algebra.FormallyUnramified.comp", "kind": "theorem", "module": "Mathlib.RingTheory.Unramified.Basic", "is_tactic_proof": true, "tactics": ["rw", "intro", "have", "letI", "let", "let", "ext1", "change", "congr", "exact"], "tactic_count": 10}
{"name": "Algebra.FormallyUnramified.of_restrictScalars", "kind": "theorem", "module": "Mathlib.RingTheory.Unramified.Basic", "is_tactic_proof": true, "tactics": ["rw", "intro", "letI", "letI", "refine", "refine", "intro", "exact"], "tactic_count": 8}
{"name": "Algebra.FormallyUnramified.of_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Unramified.Basic", "is_tactic_proof": true, "tactics": ["rw", "intro", "ext", "obtain", "rw", "congr", "apply", "ext"], "tactic_count": 8}
{"name": "Algebra.FormallyUnramified.quotient", "kind": "instance", "module": "Mathlib.RingTheory.Unramified.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.FormallyUnramified.iff_of_equiv", "kind": "theorem", "module": "Mathlib.RingTheory.Unramified.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.FormallyUnramified.base_change", "kind": "instance", "module": "Mathlib.RingTheory.Unramified.Basic", "is_tactic_proof": true, "tactics": ["rw", "intro", "letI", "haveI", "ext", "subsingleton", "exact"], "tactic_count": 7}
{"name": "Algebra.FormallyUnramified.of_isLocalization", "kind": "theorem", "module": "Mathlib.RingTheory.Unramified.Basic", "is_tactic_proof": true, "tactics": ["rw", "intro", "apply", "refine", "ext", "simp"], "tactic_count": 6}
{"name": "Algebra.FormallyUnramified.instLocalization", "kind": "instance", "module": "Mathlib.RingTheory.Unramified.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.FormallyUnramified.localization_base", "kind": "theorem", "module": "Mathlib.RingTheory.Unramified.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.FormallyUnramified.localization_map", "kind": "theorem", "module": "Mathlib.RingTheory.Unramified.Basic", "is_tactic_proof": true, "tactics": ["haveI", "haveI", "exact"], "tactic_count": 3}
{"name": "Algebra.Unramified.of_equiv", "kind": "theorem", "module": "Mathlib.RingTheory.Unramified.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Unramified.of_isLocalization_Away", "kind": "theorem", "module": "Mathlib.RingTheory.Unramified.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Unramified.comp", "kind": "theorem", "module": "Mathlib.RingTheory.Unramified.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.Unramified.baseChange", "kind": "instance", "module": "Mathlib.RingTheory.Unramified.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.FormallyUnramified.of_isSeparable", "kind": "theorem", "module": "Mathlib.RingTheory.Unramified.Field", "is_tactic_proof": true, "tactics": ["rw", "intro", "ext", "have", "have", "simp", "zero_add]", "rwa", "f₂).mul_right_eq_zero,", "sub_eq_zero]"], "tactic_count": 10}
{"name": "Algebra.FormallyUnramified.bijective_of_isAlgClosed_of_isLocalRing", "kind": "theorem", "module": "Mathlib.RingTheory.Unramified.Field", "is_tactic_proof": true, "tactics": ["have", "have", "have", "rw", "exact", "exact", "let", "let", "let", "have", "dsimp", "rw", "congr", "apply", "apply", "intro", "obtain", "suffices", "simp", "have", "rw", "exact", "have", "rw", "sub_self]", "have", "apply", "rw", "have", "obtain", "have", "rw", "exact", "rw", "refine", "have", "ext", "conv_rhs", "rw", "algebraMap_eq_smul_one]", "rw", "simp", "mul_one]"], "tactic_count": 43}
{"name": "Algebra.FormallyUnramified.isField_of_isAlgClosed_of_isLocalRing", "kind": "theorem", "module": "Mathlib.RingTheory.Unramified.Field", "is_tactic_proof": true, "tactics": ["rw", "intro", "obtain", "change", "rw", "by_contra", "exact"], "tactic_count": 7}
{"name": "Algebra.FormallyUnramified.isReduced_of_field", "kind": "theorem", "module": "Mathlib.RingTheory.Unramified.Field", "is_tactic_proof": true, "tactics": ["constructor", "intro", "let", "have", "have", "rw", "suffices", "exact", "apply", "exact", "apply", "rw", "apply", "intro", "have", "generalize", "have", "have", "have", "have", "letI", "exact"], "tactic_count": 22}
{"name": "Algebra.FormallyUnramified.range_eq_top_of_isPurelyInseparable", "kind": "theorem", "module": "Mathlib.RingTheory.Unramified.Field", "is_tactic_proof": true, "tactics": ["classical", "have", "rw", "rank_zero_iff,", "infer_instance", "rw", "intro", "obtain", "have", "refine", "have", "rw", "obtain", "rw", "have", "have", "exact", "by_cases", "have", "let", "let", "have", "let", "have", "by_cases", "obtain", "exact", "have", "simp", "rw", "simp", "obtain", "have", "rw", "rintro", "rw", "cases", "use", "rw", "smul_smul,"], "tactic_count": 40}
{"name": "Algebra.FormallyUnramified.isSeparable", "kind": "theorem", "module": "Mathlib.RingTheory.Unramified.Field", "is_tactic_proof": true, "tactics": ["have", "rw", "have", "have", "ext", "change", "rw", "simp"], "tactic_count": 8}
{"name": "Algebra.FormallyUnramified.iff_isSeparable", "kind": "theorem", "module": "Mathlib.RingTheory.Unramified.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.FormallyUnramified.iff_exists_tensorProduct", "kind": "theorem", "module": "Mathlib.RingTheory.Unramified.Finite", "is_tactic_proof": false, "tactics": ["rw", "have", "intro", "simp", "simp_rw", "constructor", "rintro", "refine", "intro", "obtain", "rw", "exact", "rw", "rw", "rintro", "use", "rw", "constructor", "suffices", "simpa", "exact", "simpa", "ht₂", "apply", "simp", "intro", "use", "linear_combination"], "tactic_count": 28}
{"name": "Algebra.FormallyUnramified.finite_of_free_aux", "kind": "theorem", "module": "Mathlib.RingTheory.Unramified.Finite", "is_tactic_proof": true, "tactics": ["rw", "subst", "let", "conv_lhs", "simp", "conv_lhs", "simp", "have", "intro", "rw", "congr", "ext", "rw", "simp", "intro", "intro", "intros", "have", "simpa", "simp", "simp_rw", "apply", "intro", "apply", "exact", "simp", "forall_exists_index]", "simp", "exact"], "tactic_count": 29}
{"name": "Algebra.FormallyUnramified.elem", "kind": "definition", "module": "Mathlib.RingTheory.Unramified.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.FormallyUnramified.one_tmul_sub_tmul_one_mul_elem", "kind": "theorem", "module": "Mathlib.RingTheory.Unramified.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.FormallyUnramified.one_tmul_mul_elem", "kind": "theorem", "module": "Mathlib.RingTheory.Unramified.Finite", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Algebra.FormallyUnramified.lmul_elem", "kind": "theorem", "module": "Mathlib.RingTheory.Unramified.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.FormallyUnramified.finite_of_free", "kind": "theorem", "module": "Mathlib.RingTheory.Unramified.Finite", "is_tactic_proof": true, "tactics": ["classical", "let", "let", "have", "let", "use", "conv_lhs", "congr", "simp", "constructor", "use", "rw", "rintro", "let", "b.repr", "let", "have", "intro", "simp", "simp", "trans", "refine", "simp", "intro", "rw", "simp", "let", "have", "apply", "apply", "apply", "suffices", "have", "intro", "simp_rw", "congr", "exact", "rw", "trans", "simp_rw", "rw", "rfl", "intro", "intro", "simp", "have", "intro", "apply", "exact", "rw", "simp", "smul_mul_assoc]", "apply", "apply", "apply", "apply", "use"], "tactic_count": 57}
{"name": "Algebra.FormallyUnramified.sec", "kind": "definition", "module": "Mathlib.RingTheory.Unramified.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.FormallyUnramified.comp_sec", "kind": "theorem", "module": "Mathlib.RingTheory.Unramified.Finite", "is_tactic_proof": true, "tactics": ["ext", "simp", "trans", "induction", "zero", "tmul", "add", "rw"], "tactic_count": 8}
{"name": "Algebra.FormallyUnramified.flat_of_restrictScalars", "kind": "theorem", "module": "Mathlib.RingTheory.Unramified.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.FormallyUnramified.projective_of_restrictScalars", "kind": "theorem", "module": "Mathlib.RingTheory.Unramified.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.instFormallyUnramifiedResidueField", "kind": "instance", "module": "Mathlib.RingTheory.Unramified.LocalRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.instFormallyUnramifiedResidueField_1", "kind": "instance", "module": "Mathlib.RingTheory.Unramified.LocalRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.instFiniteResidueFieldOfFormallyUnramified", "kind": "instance", "module": "Mathlib.RingTheory.Unramified.LocalRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.instIsSeparableResidueFieldOfFormallyUnramified", "kind": "instance", "module": "Mathlib.RingTheory.Unramified.LocalRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.FormallyUnramified.isField_quotient_map_maximalIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.Unramified.LocalRing", "is_tactic_proof": true, "tactics": ["let", "have", "letI", "have", "have", "have", "have", "have", "have", "have", "have", "have", "rw", "nilradical_eq_zero]", "rwa"], "tactic_count": 15}
{"name": "Algebra.FormallyUnramified.map_maximalIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.Unramified.LocalRing", "is_tactic_proof": true, "tactics": ["apply", "rw", "exact"], "tactic_count": 3}
{"name": "Algebra.FormallyUnramified.of_map_maximalIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.Unramified.LocalRing", "is_tactic_proof": true, "tactics": ["constructor", "have", "have", "rw", "refine", "obtain", "x).mp", "obtain", "simp", "replace", "induction", "zero", "mem", "add", "smul", "have", "simp"], "tactic_count": 17}
{"name": "Algebra.FormallyUnramified.iff_map_maximalIdeal_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Unramified.LocalRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.isUnramifiedAt_iff_map_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Unramified.LocalRing", "is_tactic_proof": false, "tactics": ["letI", "have", "letI", "have", "trans", "exact", "rw", "congr", "rw"], "tactic_count": 9}
{"name": "Algebra.IsUnramifiedAt", "kind": "abbrev", "module": "Mathlib.RingTheory.Unramified.Locus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.unramifiedLocus", "kind": "definition", "module": "Mathlib.RingTheory.Unramified.Locus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.IsUnramifiedAt.comp", "kind": "theorem", "module": "Mathlib.RingTheory.Unramified.Locus", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "Algebra.IsUnramifiedAt.of_restrictScalars", "kind": "theorem", "module": "Mathlib.RingTheory.Unramified.Locus", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.unramifiedLocus_eq_compl_support", "kind": "theorem", "module": "Mathlib.RingTheory.Unramified.Locus", "is_tactic_proof": true, "tactics": ["ext", "simp", "have", "exact"], "tactic_count": 4}
{"name": "Algebra.basicOpen_subset_unramifiedLocus_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Unramified.Locus", "is_tactic_proof": false, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Algebra.unramifiedLocus_eq_univ_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Unramified.Locus", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Algebra.isOpen_unramifiedLocus", "kind": "theorem", "module": "Mathlib.RingTheory.Unramified.Locus", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Algebra.FormallyUnramified.pi_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Unramified.Pi", "is_tactic_proof": true, "tactics": ["classical", "cases", "constructor", "intro", "exact", "intro", "rw", "intro", "ext", "rw", "refine", "rintro", "have", "intro", "rw", "exact", "let", "have", "have", "rw", "apply", "convert", "rw", "have", "rw", "apply", "convert", "rw", "have", "trans", "rw", "rw", "let", "let", "apply", "simp", "rw", "intro", "let", "apply", "simp", "rw", "intro", "suffices", "have", "simp", "obtain", "apply_fun", "rwa", "apply", "rw", "ext", "rw", "simp", "exact"], "tactic_count": 55}
{"name": "Algebra.FormallyUnramified.instForall", "kind": "instance", "module": "Mathlib.RingTheory.Unramified.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.instAlgebraSubtypeMemValuationSubringWithZeroMultiplicativeInt", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.AlgebraInstances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.algebraMap_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.AlgebraInstances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.isIntegral_of_mem_ringOfIntegers", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.AlgebraInstances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.isIntegral_of_mem_ringOfIntegers'", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.AlgebraInstances", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "ValuationSubring.instIsScalarTowerSubtypeMemValuationSubringWithZeroMultiplicativeInt", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.AlgebraInstances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.algebra", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.AlgebraInstances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.equiv", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.AlgebraInstances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.integralClosure_algebraMap_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.AlgebraInstances", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidWithZeroHom.instLinearOrderedCommGroupWithZeroMrange", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.instLinearOrderedCommGroupWithZeroMrange", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.Integers.wfDvdMonoid_iff_wellFounded_gt_on_v", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Archimedean", "is_tactic_proof": true, "tactics": ["refine"], "tactic_count": 1}
{"name": "Valuation.Integers.wellFounded_gt_on_v_iff_discrete_mrange", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Archimedean", "is_tactic_proof": false, "tactics": ["rw", "classical", "refine", "rintro", "simp", "intro", "obtain", "exact", "exact", "intro", "simp", "rintro", "simp", "simp"], "tactic_count": 14}
{"name": "Valuation.Integers.isPrincipalIdealRing_iff_not_denselyOrdered", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Archimedean", "is_tactic_proof": true, "tactics": ["refine", "rcases", "have", "exact", "have", "have", "have", "rw", "exact"], "tactic_count": 9}
{"name": "Valuation.Integers.isPrincipalIdealRing_iff_not_denselyOrdered_mrange", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCoeTCValuationOfValuationClass", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.instFunLike", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.instValuationClass", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.coe_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.toFun_eq_coe", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.toMonoidWithZeroHom_coe_eq_coe", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.ext", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.coe_coe", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.map_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.map_one", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.map_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.map_add", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.map_add'", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": true, "tactics": ["intro", "rw", "apply"], "tactic_count": 3}
{"name": "Valuation.map_add_le", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.map_add_lt", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.map_sum_le", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": true, "tactics": ["classical", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "Valuation.map_sum_lt", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": true, "tactics": ["classical", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "Valuation.map_sum_lt'", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.map_pow", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.toPreorder", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.zero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.ne_zero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.pos_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Valuation.unit_map_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.ne_zero_of_unit", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Valuation.ne_zero_of_isUnit", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Valuation.comap", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.comap_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.comap_id", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.comap_comp", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.map", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.map_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.IsEquiv", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.map_neg", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.map_sub_swap", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.map_sub", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.map_sub_le", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Valuation.map_sub_lt", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Valuation.le_one_of_subsingleton", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Valuation.map_add_of_distinct_val", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": true, "tactics": ["suffices", "intro", "wlog", "refine", "rwa", "rw", "apply", "calc", "v"], "tactic_count": 9}
{"name": "Valuation.map_add_eq_of_lt_right", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.map_add_eq_of_lt_left", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Valuation.map_sub_eq_of_lt_right", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": true, "tactics": ["rw", "rwa"], "tactic_count": 2}
{"name": "Valuation.map_sum_eq_of_lt", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": true, "tactics": ["rcases", "aesop", "rw", "exact"], "tactic_count": 4}
{"name": "Valuation.map_sub_eq_of_lt_left", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": true, "tactics": ["rw", "rwa"], "tactic_count": 2}
{"name": "Valuation.map_eq_of_sub_lt", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": true, "tactics": ["have", "rw", "simpa"], "tactic_count": 3}
{"name": "Valuation.map_sub_of_left_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simpa", "simp"], "tactic_count": 3}
{"name": "Valuation.map_sub_of_right_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Valuation.map_add_of_left_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Valuation.map_add_of_right_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Valuation.map_one_add_of_lt", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "Valuation.map_one_sub_of_lt", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": true, "tactics": ["rw", "rw", "simpa"], "tactic_count": 3}
{"name": "Valuation.congr", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.one", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.one_apply_def", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.toMonoidWithZeroHom_one", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.one_apply_of_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.one_apply_eq_zero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.one_apply_le_one", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": true, "tactics": ["rw", "split_ifs"], "tactic_count": 2}
{"name": "Valuation.one_apply_lt_one_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": true, "tactics": ["rw", "split_ifs"], "tactic_count": 2}
{"name": "Valuation.one_apply_eq_one_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.map_inv", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.map_div", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.one_lt_val_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Valuation.one_le_val_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Valuation.val_lt_one_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Valuation.val_le_one_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Valuation.val_eq_one_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Valuation.val_le_one_or_val_inv_lt_one", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "simp"], "tactic_count": 3}
{"name": "Valuation.val_le_one_or_val_inv_le_one", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "simp"], "tactic_count": 3}
{"name": "Valuation.leAddSubgroup", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.mem_leAddSubgroup_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.leAddSubgroup_monotone", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.ltAddSubgroup", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.mem_ltAddSubgroup_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.ltAddSubgroup_monotone", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.ltAddSubgroup_le_leAddSubgroup", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.leAddSubgroup_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Valuation.IsNontrivial.nontrivial_codomain", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Valuation.not_isNontrivial_one", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": true, "tactics": ["rintro", "rcases"], "tactic_count": 2}
{"name": "Valuation.instNontrivialSubtypeUnitsMemSubmonoidValueMonoidOfIsNontrivial", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": true, "tactics": ["obtain", "rw", "use", "simpa"], "tactic_count": 4}
{"name": "Valuation.instNontrivialSubtypeUnitsMemSubgroupValueGroupOfIsNontrivial", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": true, "tactics": ["obtain", "rw", "use", "simpa"], "tactic_count": 4}
{"name": "Valuation.isNontrivial_iff_exists_unit", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.IsNontrivial.exists_lt_one", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": true, "tactics": ["obtain", "rw", "rcases", "use", "simp", "use", "simp"], "tactic_count": 7}
{"name": "Valuation.isNontrivial_iff_exists_lt_one", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.IsNontrivial.exists_one_lt", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": true, "tactics": ["obtain", "use", "simp"], "tactic_count": 3}
{"name": "Valuation.IsNontrivial_iff_exists_one_lt", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.IsTrivialOn.valuation_algebraMap_le_one", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "Valuation.IsEquiv.refl", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.IsEquiv.symm", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.IsEquiv.trans", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.IsEquiv.of_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "Valuation.IsEquiv.map", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.IsEquiv.comap", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.IsEquiv.val_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Valuation.IsEquiv.eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "Valuation.IsEquiv.ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.IsEquiv.pos_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Valuation.IsEquiv.lt_iff_lt", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Valuation.IsEquiv.le_one_iff_le_one", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Valuation.IsEquiv.one_le_iff_one_le", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Valuation.IsEquiv.eq_one_iff_eq_one", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Valuation.IsEquiv.lt_one_iff_lt_one", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Valuation.IsEquiv.one_lt_iff_one_lt", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Valuation.isEquiv_map_self_of_strictMono", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.isEquiv_iff_val_lt_val", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Valuation.isNontrivial_of_isEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": true, "tactics": ["obtain", "use", "simpa"], "tactic_count": 3}
{"name": "Valuation.IsEquiv.isNontrivial_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.isEquiv_of_val_le_one", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": true, "tactics": ["intro", "obtain", "simp", "rw"], "tactic_count": 4}
{"name": "Valuation.isEquiv_iff_val_le_one", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.isEquiv_iff_val_eq_one", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "intro", "apply", "intro", "constructor", "intro", "rcases", "have", "rw", "apply", "simpa", "rw", "rw", "refine", "simp", "rw", "exact", "intro", "rcases", "have", "rw", "apply", "simpa", "rw", "rw", "refine", "simp", "rw", "exact"], "tactic_count": 31}
{"name": "Valuation.isEquiv_iff_val_lt_one", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "rw", "intro", "by_cases", "simp", "constructor", "intro", "by_contra", "cases", "inl", "inr", "rw", "exact", "intro", "by_contra", "cases", "inl", "inr", "rw", "exact"], "tactic_count": 22}
{"name": "Valuation.isEquiv_iff_val_sub_one_lt_one", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Valuation.isEquiv_tfae", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": true, "tactics": ["tfae_have", "tfae_have", "tfae_have", "tfae_have", "tfae_have", "tfae_finish"], "tactic_count": 6}
{"name": "Valuation.supp", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.mem_supp_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.instIsPrimeSuppOfNontrivialOfNoZeroDivisors", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.map_add_supp", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": ["have", "intro", "refine", "simp", "apply", "calc", "v"], "tactic_count": 7}
{"name": "Valuation.comap_supp", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddValuation", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddValuation.instFunLike", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddValuation.of", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddValuation.of_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddValuation.toValuation", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddValuation.ofValuation", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddValuation.ofValuation_symm_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddValuation.toValuation_symm_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddValuation.ofValuation_toValuation", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddValuation.toValuation_ofValuation", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddValuation.toValuation_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddValuation.ofValuation_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddValuation.map_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddValuation.map_one", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddValuation.asFun", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddValuation.map_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddValuation.map_add", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddValuation.map_add'", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": true, "tactics": ["intro", "rw", "apply"], "tactic_count": 3}
{"name": "AddValuation.map_le_add", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddValuation.map_lt_add", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddValuation.map_le_sum", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddValuation.map_lt_sum", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddValuation.map_lt_sum'", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddValuation.map_pow", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddValuation.ext", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddValuation.toPreorder", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddValuation.top_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddValuation.ne_top_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddValuation.comap", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddValuation.comap_id", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddValuation.comap_comp", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddValuation.map", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddValuation.map_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddValuation.IsEquiv", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddValuation.map_neg", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddValuation.map_sub_swap", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddValuation.map_sub", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddValuation.map_le_sub", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddValuation.map_add_of_distinct_val", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddValuation.map_add_eq_of_lt_left", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AddValuation.map_add_eq_of_lt_right", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddValuation.map_sub_eq_of_lt_left", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply", "rwa"], "tactic_count": 3}
{"name": "AddValuation.map_sub_eq_of_lt_right", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddValuation.map_eq_of_lt_sub", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddValuation.map_inv", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddValuation.map_div", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddValuation.IsEquiv.refl", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddValuation.IsEquiv.symm", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddValuation.IsEquiv.trans", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddValuation.IsEquiv.of_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddValuation.IsEquiv.map", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddValuation.IsEquiv.comap", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddValuation.IsEquiv.val_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddValuation.IsEquiv.ne_top", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddValuation.supp", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddValuation.mem_supp_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddValuation.map_add_supp", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.toAddValuation", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.ofAddValuation", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.ofAddValuation_symm_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.toAddValuation_symm_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.ofAddValuation_toAddValuation", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.toValuation_ofValuation", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.toAddValuation_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.ofAddValuation_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.instCommMonoidWithZeroSubtypeMemSubmonoidMrange", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.val_mrange_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "Valuation.instCommGroupWithZeroSubtypeMemSubmonoidMrange", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.nonempty_orderIso_withZeroMul_int_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.DiscreteValuativeRel", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "let", "have", "have", "refine", "rcases", "simp", "rw", "rw", "simp", "linarith", "rintro", "rw", "rw", "intro", "obtain", "obtain", "exact"], "tactic_count": 19}
{"name": "ValuativeRel.IsDiscrete.of_compatible_withZeroMulInt", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.DiscreteValuativeRel", "is_tactic_proof": true, "tactics": ["have", "by_cases", "by_cases", "exfalso", "refine", "rw", "exact", "rw", "rw", "rw", "exact", "rw", "refine", "contrapose", "have", "exact"], "tactic_count": 16}
{"name": "Valuation.IsRankOneDiscrete.exists_generator_lt_one", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Discrete.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.IsRankOneDiscrete.generator", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.Discrete.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.IsRankOneDiscrete.generator_zpowers_eq_valueGroup", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Discrete.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.IsRankOneDiscrete.generator_mem_valueGroup", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Discrete.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Valuation.IsRankOneDiscrete.generator_lt_one", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Discrete.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.IsRankOneDiscrete.generator_ne_one", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Discrete.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.IsRankOneDiscrete.generator_zpowers_eq_range", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Discrete.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Valuation.IsRankOneDiscrete.generator_mem_range", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Discrete.Basic", "is_tactic_proof": true, "tactics": ["apply", "rw", "exact"], "tactic_count": 3}
{"name": "Valuation.IsRankOneDiscrete.generator_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Discrete.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Valuation.IsRankOneDiscrete.instIsCyclicSubtypeUnitsMemSubgroupValueGroup", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.Discrete.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Valuation.IsRankOneDiscrete.instIsNontrivial", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.Discrete.Basic", "is_tactic_proof": true, "tactics": ["apply", "by_contra", "have", "simp", "subset_singleton_iff,", "intro", "specialize", "aesop", "aesop", "simp_all", "have", "have", "simp_all"], "tactic_count": 13}
{"name": "Valuation.IsRankOneDiscrete.valueGroup_genLTOne_eq_generator", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Discrete.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.IsUniformizer", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.Discrete.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.IsUniformizer.iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Discrete.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.IsUniformizer.ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Discrete.Basic", "is_tactic_proof": true, "tactics": ["intro", "rw", "exact"], "tactic_count": 3}
{"name": "Valuation.IsUniformizer.val", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Discrete.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.IsUniformizer.val_lt_one", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Discrete.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.IsUniformizer.val_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Discrete.Basic", "is_tactic_proof": true, "tactics": ["by_contra", "simp", "exact"], "tactic_count": 3}
{"name": "Valuation.IsUniformizer.val_pos", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Discrete.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Valuation.IsUniformizer.zpowers_eq_valueGroup", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Discrete.Basic", "is_tactic_proof": true, "tactics": ["rw", "congr", "simp", "exact"], "tactic_count": 4}
{"name": "Valuation.Uniformizer.mk'", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.Discrete.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.Uniformizer.instCoeSubtypeMemSubringInteger", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.Discrete.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.Uniformizer.ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Discrete.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.IsUniformizer.not_isUnit", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Discrete.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.IsRankOneDiscrete.mk'", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.Discrete.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Valuation.Discrete.Basic.0.Valuation.termK₀", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.Discrete.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Valuation.Discrete.Basic.0.Valuation._aux_Mathlib_RingTheory_Valuation_Discrete_Basic___macroRules__private_Mathlib_RingTheory_Valuation_Discrete_Basic_0_Valuation_termK₀_1", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.Discrete.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.exists_isUniformizer_of_isCyclic_of_nontrivial", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Discrete.Basic", "is_tactic_proof": true, "tactics": ["simp", "set", "obtain", "rw", "exact", "use", "rw", "exact"], "tactic_count": 8}
{"name": "Valuation.instNonemptyUniformizer", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.Discrete.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.IsUniformizer.of_associated", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Discrete.Basic", "is_tactic_proof": true, "tactics": ["obtain", "have", "rwa"], "tactic_count": 3}
{"name": "Valuation.associated_of_isUniformizer", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Discrete.Basic", "is_tactic_proof": true, "tactics": ["have", "set", "use", "apply_fun", "simp"], "tactic_count": 5}
{"name": "Valuation.exists_pow_Uniformizer", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Discrete.Basic", "is_tactic_proof": true, "tactics": ["have", "set", "have", "apply", "rw", "exact", "rw", "obtain", "have", "rw", "rw", "simp", "have", "rw", "exact", "obtain", "use", "have", "set", "have", "simp", "refine", "rw", "exact", "have", "use", "rw", "mul_inv_cancel₀"], "tactic_count": 28}
{"name": "Valuation.Uniformizer.is_generator", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Discrete.Basic", "is_tactic_proof": true, "tactics": ["apply", "intro", "rw", "apply", "intro", "by_cases", "simp", "obtain", "rw", "have", "replace", "simp"], "tactic_count": 12}
{"name": "Valuation.IsUniformizer.is_generator", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Discrete.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.pow_Uniformizer_is_pow_generator", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Discrete.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Valuation.valuationSubring_not_isField", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Discrete.Basic", "is_tactic_proof": true, "tactics": ["obtain", "rintro", "have", "simp", "specialize", "rw", "exact"], "tactic_count": 7}
{"name": "Valuation.isUniformizer_of_maximalIdeal_eq_span", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Discrete.Basic", "is_tactic_proof": false, "tactics": ["have", "intro", "rw", "exact", "obtain", "obtain", "rw", "exact"], "tactic_count": 8}
{"name": "Valuation.ideal_isPrincipal", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Discrete.Basic", "is_tactic_proof": false, "tactics": ["suffices", "intro", "by_cases", "rw", "let", "obtain", "obtain", "by_cases", "rw", "refine", "simp", "rw", "rw", "rw", "exact"], "tactic_count": 15}
{"name": "Valuation.valuationSubring_isPrincipalIdealRing", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Discrete.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.valuationSubring_isDiscreteValuationRing", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.Discrete.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDiscreteValuationRing.maximalIdeal", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.Discrete.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDiscreteValuationRing.isRankOneDiscrete", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.Discrete.Basic", "is_tactic_proof": false, "tactics": ["have", "let", "let", "have", "rw", "use", "constructor", "apply", "simp", "use", "simpa", "infer_instance"], "tactic_count": 12}
{"name": "IsDiscreteValuationRing.exists_lift_of_le_one", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Discrete.Basic", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "by_cases", "rw", "use", "rw", "rw", "obtain", "obtain", "replace", "rw", "map_inv₀,", "map_div₀,", "have", "have", "have", "zify", "rw", "zpow_add₀", "rwa", "use", "simp", "mul_div_assoc", "congr", "rw", "congr", "rw", "apply", "rw", "exact"], "tactic_count": 30}
{"name": "IsDiscreteValuationRing.map_algebraMap_eq_valuationSubring", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Discrete.Basic", "is_tactic_proof": true, "tactics": ["ext", "refine", "obtain", "apply", "obtain", "rw", "exact"], "tactic_count": 7}
{"name": "IsDiscreteValuationRing.equivValuationSubring", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.Discrete.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.extendToLocalization", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.ExtendToLocalization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.extendToLocalization_mk'", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ExtendToLocalization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.extendToLocalization_apply_map_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ExtendToLocalization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.HasExtension.val_map_le_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Extension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.HasExtension.val_map_lt_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Extension", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Valuation.HasExtension.val_map_eq_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Extension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.HasExtension.val_map_le_one_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Extension", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Valuation.HasExtension.val_map_lt_one_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Extension", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Valuation.HasExtension.val_map_eq_one_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Extension", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Valuation.HasExtension.id", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.Extension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.HasExtension.ofComapInteger", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Extension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.HasExtension.instAlgebraInteger", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.Extension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.HasExtension.val_smul", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Extension", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "Valuation.HasExtension.mk_smul_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Extension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.HasExtension.val_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Extension", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "Valuation.HasExtension.instIsScalarTowerInteger", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.Extension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.HasExtension.instIsTorsionFreeInteger", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.Extension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.HasExtension.algebraMap_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Extension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.HasExtension.instIsLocalHomValuationInteger", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Extension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Valuation.Extension.0.Valuation.HasExtension.termK₀", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.Extension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Valuation.Extension.0.Valuation.HasExtension._aux_Mathlib_RingTheory_Valuation_Extension___macroRules__private_Mathlib_RingTheory_Valuation_Extension_0_Valuation_HasExtension_termK₀_1", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.Extension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Valuation.Extension.0.Valuation.HasExtension._aux_Mathlib_RingTheory_Valuation_Extension___unexpand_Valuation_valuationSubring_1", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.Extension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Valuation.Extension.0.Valuation.HasExtension.termL₀", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.Extension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Valuation.Extension.0.Valuation.HasExtension._aux_Mathlib_RingTheory_Valuation_Extension___macroRules__private_Mathlib_RingTheory_Valuation_Extension_0_Valuation_HasExtension_termL₀_1", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.Extension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Valuation.Extension.0.Valuation.HasExtension._aux_Mathlib_RingTheory_Valuation_Extension___unexpand_Valuation_valuationSubring_2", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.Extension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.HasExtension.algebraMap_mem_valuationSubring", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Extension", "is_tactic_proof": false, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Valuation.HasExtension.instAlgebra_valuationSubring", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.Extension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.HasExtension.coe_algebraMap_valuationSubring_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Extension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.HasExtension.instIsScalarTower_valuationSubring", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.Extension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.HasExtension.instIsScalarTower_valuationSubring'", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.Extension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.HasExtension.instIsLocalHomSubtypeMemValuationSubringValuationSubringRingHomAlgebraMap", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.Extension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.HasExtension.algebraMap_mem_maximalIdeal_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Extension", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Valuation.HasExtension.maximalIdeal_comap_algebraMap_eq_maximalIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Extension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.HasExtension.instLiesOverSubtypeMemValuationSubringValuationSubringMaximalIdeal", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.Extension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.HasExtension.algebraMap_residue_eq_residue_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Extension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.FiniteField.algebraMap_eq_one", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.FiniteField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.FiniteField.algebraMap_le_one", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.FiniteField", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "Valuation.FiniteField.instIsTrivialOn", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.FiniteField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.integer", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.Integers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.mem_integer_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Integers", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "Valuation.instAlgebraSubtypeMemSubringInteger", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.Integers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.integer.integers", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Integers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.Integers.one_of_isUnit'", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Integers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.Integers.one_of_isUnit", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Integers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.Integers.isUnit_of_one", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Integers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.Integers.le_of_dvd", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Integers", "is_tactic_proof": true, "tactics": ["obtain", "grw"], "tactic_count": 2}
{"name": "Valuation.Integers.nontrivial_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Integers", "is_tactic_proof": true, "tactics": ["constructor", "exact", "obtain", "obtain", "refine", "rintro", "simp"], "tactic_count": 7}
{"name": "Valuation.integers_nontrivial", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Integers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.Integers.dvd_of_le", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Integers", "is_tactic_proof": false, "tactics": ["have", "hx.symm", "have", "grw", "let"], "tactic_count": 5}
{"name": "Valuation.Integers.dvd_iff_le", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Integers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.Integers.le_iff_dvd", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Integers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.Integers.isUnit_of_one'", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Integers", "is_tactic_proof": true, "tactics": ["refine", "simp"], "tactic_count": 2}
{"name": "Valuation.Integers.isUnit_iff_valuation_eq_one", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Integers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.Integers.valuation_irreducible_lt_one", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Integers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.Integers.valuation_unit", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Integers", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Valuation.Integers.valuation_pos_iff_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Integers", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp"], "tactic_count": 3}
{"name": "Valuation.Integers.valuation_irreducible_pos", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Integers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.Integers.dvdNotUnit_iff_lt", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Integers", "is_tactic_proof": true, "tactics": ["rw", "refine", "rintro", "refine", "rw", "rw", "simp", "contrapose", "refine", "simp"], "tactic_count": 10}
{"name": "Valuation.Integers.eq_algebraMap_or_inv_eq_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Integers", "is_tactic_proof": true, "tactics": ["rcases", "exacts"], "tactic_count": 2}
{"name": "Valuation.Integers.coe_span_singleton_eq_setOf_le_v_algebraMap", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Integers", "is_tactic_proof": true, "tactics": ["rcases", "simp", "ext", "simp"], "tactic_count": 4}
{"name": "Valuation.Integers.bijective_algebraMap_of_subsingleton_units_mrange", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Integers", "is_tactic_proof": true, "tactics": ["refine", "rcases", "simp", "exact"], "tactic_count": 4}
{"name": "Valuation.Integers.isPrincipal_iff_exists_isGreatest", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Integers", "is_tactic_proof": true, "tactics": ["constructor", "refine", "refine", "simp", "intro", "simp", "obtain", "exact", "obtain", "refine", "ext", "simp", "exact"], "tactic_count": 13}
{"name": "Valuation.Integers.isPrincipal_iff_exists_eq_setOf_valuation_le", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Integers", "is_tactic_proof": true, "tactics": ["rw", "constructor", "obtain", "refine", "ext", "simp", "constructor", "exact", "rw", "exact", "refine", "simp", "simp"], "tactic_count": 13}
{"name": "Valuation.Integers.not_denselyOrdered_of_isPrincipalIdealRing", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Integers", "is_tactic_proof": true, "tactics": ["intro", "set", "add_mem", "zero_mem", "smul_mem", "intro", "simp", "intro", "exact", "obtain", "simpa", "obtain", "simpa", "obtain", "exact"], "tactic_count": 15}
{"name": "Valuation.Integer.not_isUnit_iff_valuation_lt_one", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Integers", "is_tactic_proof": true, "tactics": ["rw", "exacts"], "tactic_count": 2}
{"name": "Valuation.integer.v_irreducible_lt_one", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Integers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.integer.v_irreducible_pos", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Integers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.integer.coe_span_singleton_eq_setOf_le_v_coe", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Integers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Valuation.Integers.0.Valuation.term𝓞", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.Integers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.Valuation.Integers.0.Valuation._aux_Mathlib_RingTheory_Valuation_Integers___macroRules__private_Mathlib_RingTheory_Valuation_Integers_0_Valuation_term𝓞_1", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.Integers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.leSubmodule", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.Integers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.ltSubmodule", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.Integers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.leSubmodule_monotone", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Integers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.ltSubmodule_monotone", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Integers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.ltSubmodule_le_leSubmodule", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Integers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.mem_leSubmodule_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Integers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.mem_ltSubmodule_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Integers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.leSubmodule_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Integers", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Valuation.leSubmodule_v_le_of_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Integers", "is_tactic_proof": true, "tactics": ["rcases", "simp", "intro", "have", "simpa"], "tactic_count": 5}
{"name": "Valuation.ltSubmodule_v_le_of_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Integers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.leIdeal", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.Integers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.ltIdeal", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.Integers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.leIdeal_mono", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Integers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.ltIdeal_mono", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Integers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.ltIdeal_le_leIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Integers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.mem_leIdeal_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Integers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.mem_ltIdeal_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Integers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.leIdeal_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Integers", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Valuation.leSubmodule_comap_algebraMap_eq_leIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Integers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.leIdeal_map_algebraMap_eq_leSubmodule_min", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Integers", "is_tactic_proof": true, "tactics": ["ext", "simp", "constructor", "rintro", "rcases", "rw", "exact", "rw", "exact", "intro", "rcases", "exact", "exact"], "tactic_count": 13}
{"name": "Valuation.leIdeal_v_le_of_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Integers", "is_tactic_proof": true, "tactics": ["rcases", "simp", "intro", "have", "convert", "simp"], "tactic_count": 6}
{"name": "Valuation.ltIdeal_v_le_of_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Integers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.Integers.isIntegral_iff_v_le_one", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Integral", "is_tactic_proof": true, "tactics": ["nontriviality", "have", "constructor", "rintro", "by_cases", "rw", "obtain", "simp", "simp", "add_eq_zero_iff_eq_neg]", "apply_fun", "simp", "contrapose", "refine", "simp", "simp", "intro", "exact", "intro", "obtain", "exact"], "tactic_count": 21}
{"name": "Valuation.Integers.mem_of_integral", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.Integers.integralClosure", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.Integers.isIntegrallyClosed", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Integral", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "Valuation.Integers.isIntegrallyClosed_integers", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.Integral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsIntegrallyClosedSubtypeMemSubring", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.LocalSubring", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "instIsIntegrallyClosedSubtypeMemValuationSubring", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.LocalSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.toLocalSubring", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.LocalSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.toLocalSubring_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.LocalSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocalSubring.map_maximalIdeal_eq_top_of_isMax", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.LocalSubring", "is_tactic_proof": true, "tactics": ["set", "by_contra", "obtain", "let", "have", "refine", "conv_rhs", "refine", "rw", "exact"], "tactic_count": 10}
{"name": "LocalSubring.mem_of_isMax_of_isIntegral", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.LocalSubring", "is_tactic_proof": true, "tactics": ["let", "have", "obtain", "have", "have", "refine", "conv_rhs", "refine", "rw", "rw", "exact"], "tactic_count": 11}
{"name": "ValuationSubring.isMax_toLocalSubring", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.LocalSubring", "is_tactic_proof": true, "tactics": ["intro", "refine", "by_contra", "have", "have", "isUnit_iff_exists_inv.mpr", "obtain", "have", "exact"], "tactic_count": 9}
{"name": "LocalSubring.exists_valuationRing_of_isMax", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.LocalSubring", "is_tactic_proof": false, "tactics": ["suffices", "refine", "have", "let", "let", "have", "have", "have", "exact"], "tactic_count": 9}
{"name": "LocalSubring.isMax_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.LocalSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocalSubring.exists_le_valuationSubring", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.LocalSubring", "is_tactic_proof": false, "tactics": ["suffices", "obtain", "obtain", "exact", "refine", "intro", "have", "have", "refine", "intro", "obtain", "obtain", "obtain", "refine", "exact", "exact", "intro", "refine", "rintro", "obtain", "obtain", "obtain", "apply", "exact"], "tactic_count": 24}
{"name": "Ideal.image_subset_nonunits_valuationSubring", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.LocalSubring", "is_tactic_proof": true, "tactics": ["have", "have", "refine", "rw", "refine", "rw", "refine", "rintro", "exact"], "tactic_count": 9}
{"name": "Subring.exists_le_valuationSubring_of_isIntegrallyClosedIn", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.LocalSubring", "is_tactic_proof": true, "tactics": ["obtain", "exact", "let", "let", "let", "have", "hxR", "have", "have", "exact"], "tactic_count": 10}
{"name": "LocalSubring.exists_le_valuationSubring_of_isIntegrallyClosedIn", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.LocalSubring", "is_tactic_proof": true, "tactics": ["obtain", "exact", "let", "let", "let", "have", "hxR", "have", "have", "have", "refine", "rw", "obtain", "exact"], "tactic_count": 14}
{"name": "Subring.eq_iInf_of_isIntegrallyClosedIn", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.LocalSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocalSubring.eq_iInf_of_isIntegrallyClosedIn", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.LocalSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iInf_valuationSubring_superset", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.LocalSubring", "is_tactic_proof": true, "tactics": ["refine", "simp_rw", "congr", "have", "rw", "exact"], "tactic_count": 6}
{"name": "bijective_rangeRestrict_comp_of_valuationRing", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.LocalSubring", "is_tactic_proof": true, "tactics": ["refine", "exact", "let", "suffices", "rintro", "obtain", "exact", "apply", "have", "refine", "rintro", "suffices", "apply", "apply", "convert", "simp"], "tactic_count": 16}
{"name": "IsLocalRing.exists_factor_valuationRing", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.LocalSubring", "is_tactic_proof": true, "tactics": ["obtain", "refine", "exact"], "tactic_count": 3}
{"name": "Valuation.coeff_zero_minpoly", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Minpoly", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Valuation.pow_coeff_zero_ne_zero_of_unit", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Minpoly", "is_tactic_proof": true, "tactics": ["have", "have", "have", "rw", "exact"], "tactic_count": 5}
{"name": "multiplicity_addValuation", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.PrimeMultiplicity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "multiplicity_addValuation_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.PrimeMultiplicity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.onQuotVal", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.onQuot", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.onQuot_comap_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.self_le_supp_comap", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Quotient", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Valuation.comap_onQuot_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.supp_quot", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Quotient", "is_tactic_proof": true, "tactics": ["apply", "rintro", "apply", "exact", "rw", "intro", "exact"], "tactic_count": 7}
{"name": "Valuation.supp_quot_supp", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Quotient", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "AddValuation.onQuotVal", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddValuation.onQuot", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddValuation.onQuot_comap_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddValuation.comap_supp", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddValuation.self_le_supp_comap", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddValuation.comap_onQuot_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddValuation.supp_quot", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddValuation.supp_quot_supp", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.decompositionSubgroup", "kind": "abbrev", "module": "Mathlib.RingTheory.Valuation.RamificationGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.subMulAction", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.RamificationGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.decompositionSubgroupMulSemiringAction", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.RamificationGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.inertiaSubgroup", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.RamificationGroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.nonempty_rankOne_iff_mulArchimedean", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.RankOne", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "exact", "intro", "obtain", "let", "have", "simp", "exact", "let", "x", "rw", "positivity", "map_one", "map_mul", "rw", "simp", "have", "refine", "intro", "simpa", "exact", "withZeroUnitsEquiv.toMonoidWithZeroHom.comp", "strictMono"], "tactic_count": 24}
{"name": "Valuation.RankOne.strictMono", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.RankOne", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.RankOne.nontrivial", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.RankOne", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.RankOne.zero_of_hom_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.RankOne", "is_tactic_proof": true, "tactics": ["refine", "have", "rw", "exact"], "tactic_count": 4}
{"name": "Valuation.RankOne.hom_eq_zero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.RankOne", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.RankOne.unit", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.RankOne", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.RankOne.unit_ne_one", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.RankOne", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Valuation.RankOne.instIsNontrivial", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.RankOne", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.instRankOneCompletion", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.RankOne", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.RankOne.ofRankLeOneStruct", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.RankOne", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instRankOneValueGroupWithZeroValuationOfIsNontrivialOfIsRankLeOne", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.RankOne", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.RankOne.rankLeOneStruct", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.RankOne", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.isRankLeOne_of_rankOne", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.RankOne", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.isNontrivial_of_rankOne", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.RankOne", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.isRankLeOne_iff_mulArchimedean", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.RankOne", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "exact", "intro", "by_cases", "rw", "rw", "obtain", "exact", "refine", "intro", "contrapose", "obtain", "rcases", "simp_all", "rcases", "exact", "exact"], "tactic_count": 18}
{"name": "ValuativeRel.IsRankLeOne.of_compatible_mulArchimedean", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.RankOne", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "PreValuationRing.cond", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationRing.ValueGroup", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.ValuationRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationRing.instInhabitedValueGroup", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.ValuationRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationRing.instLEValueGroup", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.ValuationRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationRing.instZeroValueGroup", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.ValuationRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationRing.instOneValueGroup", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.ValuationRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationRing.instMulValueGroup", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.ValuationRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationRing.instInvValueGroup", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.ValuationRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationRing.instNontrivialValueGroup", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.ValuationRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationRing.le_total", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationRing", "is_tactic_proof": true, "tactics": ["rcases", "obtain", "obtain", "have", "have", "obtain", "right", "use", "rw", "field_simp", "simp", "left", "use", "rw", "field_simp", "simp"], "tactic_count": 16}
{"name": "ValuationRing.linearOrder", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.ValuationRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationRing.commGroupWithZero", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.ValuationRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationRing.linearOrderedCommGroupWithZero", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.ValuationRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationRing.valuation", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.ValuationRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationRing.mem_integer_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationRing", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "use", "rw", "rintro", "use", "rw"], "tactic_count": 7}
{"name": "ValuationRing.equivInteger", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.ValuationRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationRing.coe_equivInteger_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationRing.range_algebraMap_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationRing", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "ValuationRing.isLocalRing", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.ValuationRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationRing.le_total_ideal", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.ValuationRing", "is_tactic_proof": true, "tactics": ["constructor", "by_cases", "exact", "obtain", "right", "intro", "obtain", "rw", "exact", "exfalso", "apply"], "tactic_count": 11}
{"name": "ValuationRing.instLinearOrderIdealOfDecidableLE", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.ValuationRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PreValuationRing.iff_dvd_total", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationRing", "is_tactic_proof": true, "tactics": ["classical", "refine", "obtain", "obtain"], "tactic_count": 4}
{"name": "PreValuationRing.iff_ideal_total", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationRing", "is_tactic_proof": true, "tactics": ["classical", "refine", "have", "simp_rw", "exact"], "tactic_count": 5}
{"name": "ValuationRing.dvd_total", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationRing.iff_dvd_total", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationRing.iff_ideal_total", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationRing.unique_irreducible", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationRing", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "ValuationRing.iff_isInteger_or_isInteger", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationRing", "is_tactic_proof": true, "tactics": ["constructor", "intro", "obtain", "have", "obtain", "exact", "exact", "intro", "suffices", "constructor", "intro", "by_cases", "by_cases", "replace", "replace", "obtain", "rw", "exact", "rw", "exact"], "tactic_count": 20}
{"name": "ValuationRing.isInteger_or_isInteger", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationRing.instIsBezout", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.ValuationRing", "is_tactic_proof": true, "tactics": ["classical", "rw", "intro", "rw", "rcases", "rw", "rw"], "tactic_count": 7}
{"name": "ValuationRing.instOfIsLocalRingOfIsBezout", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.ValuationRing", "is_tactic_proof": true, "tactics": ["classical", "refine", "obtain", "obtain", "obtain", "obtain", "rcases", "simp", "have", "rcases", "all_goals"], "tactic_count": 11}
{"name": "ValuationRing.iff_local_bezout_domain", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationRing.TFAE", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationRing", "is_tactic_proof": true, "tactics": ["tfae_have", "tfae_have", "tfae_have", "tfae_have", "tfae_finish"], "tactic_count": 5}
{"name": "Function.Surjective.preValuationRing", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.valuationRing", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isFractionRing_of_exists_eq_algebraMap_or_inv_eq_algebraMap_of_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationRing", "is_tactic_proof": true, "tactics": ["have", "have", "have", "refine", "intro", "obtain", "by_cases", "refine", "have", "rw", "cases", "inl", "inr"], "tactic_count": 13}
{"name": "Valuation.Integers.isFractionRing", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationRing.instIsFractionRingInteger", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.ValuationRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationRing.of_integers", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationRing", "is_tactic_proof": true, "tactics": ["haveI", "suffices", "constructor", "intro", "rcases", "obtain", "use", "obtain", "use"], "tactic_count": 9}
{"name": "ValuationRing.instValuationRingInteger", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.ValuationRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationRing.isFractionRing_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationRing", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exacts", "exact"], "tactic_count": 4}
{"name": "ValuationRing.of_field", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.ValuationRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.instSetLike", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.instPartialOrder", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.mem_carrier", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.mem_toSubring", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.ext", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.zero_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.one_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.add_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.mul_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.neg_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.mem_or_inv_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.instSubringClass", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.toSubring_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.instCommRingSubtypeMem", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.instIsDomainSubtypeMem", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.instTop", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.toSubring_top", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.mem_top", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.le_top", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.instFieldSubtypeMemTop", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.top_coe_div", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.top_coe_inv", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.instOrderTop", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.instInhabited", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.instValuationRingSubtypeMem", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.instAlgebraSubtypeMem", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.isLocalRing", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.algebraMap_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.instIsFractionRingSubtypeMem", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.ValueGroup", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.valuation", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.inhabitedValueGroup", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.valuation_le_one", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.mem_of_valuation_le_one", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.valuation_le_one_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.valuation_eq_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.valuation_le_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.valuation_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.valuation_unit", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ValuationSubring.valuation_eq_one_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.eq_top_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ValuationSubring.valuation_lt_one_or_eq_one", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.valuation_lt_one_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": true, "tactics": ["rw", "dsimp", "exact"], "tactic_count": 3}
{"name": "ValuationSubring.ofSubring", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.mem_ofSubring", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.ofLE", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.instSemilatticeSup", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.inclusion", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.subtype", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.subtype_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.subtype_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.coe_subtype", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.mapOfLE", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.monotone_mapOfLE", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "ValuationSubring.mapOfLE_comp_valuation", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "ValuationSubring.mapOfLE_valuation_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.idealOfLE", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.prime_idealOfLE", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.ofPrime", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.ofPrimeAlgebra", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.ofPrime_scalar_tower", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.ofPrime_localization", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "ValuationSubring.le_ofPrime", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.ofPrime_valuation_eq_one_iff_mem_primeCompl", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ValuationSubring.idealOfLE_ofPrime", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": true, "tactics": ["refine", "apply", "exact"], "tactic_count": 3}
{"name": "ValuationSubring.ofPrime_idealOfLE", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": true, "tactics": ["ext", "rintro", "rw", "exact", "simpa", "exact", "intro", "have", "replace", "refine", "simp", "change", "refine", "ext", "simp", "simp"], "tactic_count": 16}
{"name": "ValuationSubring.ofPrime_le_of_le", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.idealOfLE_le_of_le", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.primeSpectrumEquiv", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.primeSpectrumOrderEquiv", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.le_total_ideal", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": true, "tactics": ["classical", "let", "exact"], "tactic_count": 3}
{"name": "ValuationSubring.linearOrderOverring", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.valuationSubring", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.mem_valuationSubring_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.isEquiv_iff_valuationSubring", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": true, "tactics": ["constructor", "intro", "intro", "intro", "have", "simpa"], "tactic_count": 6}
{"name": "Valuation.isEquiv_valuation_valuationSubring", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw"], "tactic_count": 3}
{"name": "Valuation.isNontrivial_valuation_valuationSubring_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.valuationSubring.integers", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.valuationSubring_eq_top_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ValuationSubring.valuationSubring_valuation", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "ValuationSubring.integer_valuation", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.unitGroup", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.mem_unitGroup_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.unitGroupMulEquiv", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.coe_unitGroupMulEquiv_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.coe_unitGroupMulEquiv_symm_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.unitGroup_le_unitGroup", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "by_cases", "by_cases", "simp", "rcases", "have", "simpa", "have", "exact", "rintro", "apply_fun", "simpa"], "tactic_count": 14}
{"name": "ValuationSubring.unitGroup_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.eq_iff_unitGroup", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.unitGroupOrderEmbedding", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.unitGroup_strictMono", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.nonunits", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.mem_nonunits_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.mem_nonunits_iff_or", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": ["rw", "mem_nonunits_iff,", "rintro", "exact"], "tactic_count": 4}
{"name": "ValuationSubring.inv_mem_nonunits_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ValuationSubring.nonunits_le_nonunits", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": true, "tactics": ["constructor", "intro", "by_cases", "rw", "by_contra", "intro", "by_contra"], "tactic_count": 7}
{"name": "ValuationSubring.nonunits_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.nonunits_inj", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.nonunitsOrderEmbedding", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.coe_mem_nonunits_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.nonunits_le", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.nonunits_subset", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.mem_nonunits_iff_exists_mem_maximalIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.image_maximalIdeal", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": true, "tactics": ["ext", "simp", "rw", "simp_rw"], "tactic_count": 4}
{"name": "ValuationSubring.principalUnitGroup", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.principal_units_le_units", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.mem_principalUnitGroup_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.principalUnitGroup_le_principalUnitGroup", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": true, "tactics": ["constructor", "intro", "by_cases", "by_cases", "rw", "simpa", "rw", "simpa", "intro", "by_contra"], "tactic_count": 10}
{"name": "ValuationSubring.principalUnitGroup_injective", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.eq_iff_principalUnitGroup", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.principalUnitGroupOrderEmbedding", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.coe_mem_principalUnitGroup_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": true, "tactics": ["rw", "let", "rw", "simp"], "tactic_count": 4}
{"name": "ValuationSubring.principalUnitGroupEquiv", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.principalUnitGroupEquiv_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.principalUnitGroup_symm_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.unitGroupToResidueFieldUnits", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.coe_unitGroupToResidueFieldUnits_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.ker_unitGroupToResidueFieldUnits", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": true, "tactics": ["ext", "simp_rw"], "tactic_count": 2}
{"name": "ValuationSubring.surjective_unitGroupToResidueFieldUnits", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.unitsModPrincipalUnitsEquivResidueFieldUnits", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.unitsModPrincipalUnitsEquivResidueFieldUnits_comp_quotientGroup_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.unitsModPrincipalUnitsEquivResidueFieldUnits_comp_quotientGroup_mk_apply", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.pointwiseHasSMul", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.coe_pointwise_smul", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.pointwise_smul_toSubring", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.pointwiseMulAction", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.smul_mem_pointwise_smul", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.instCovariantClassHSMulLe", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.mem_smul_pointwise_iff_exists", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.pointwise_central_scalar", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.smul_mem_pointwise_smul_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.mem_pointwise_smul_iff_inv_smul_mem", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.mem_inv_pointwise_smul_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.pointwise_smul_le_pointwise_smul_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.pointwise_smul_subset_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.subset_pointwise_smul_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.comap", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.coe_comap", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.mem_comap", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuationSubring.comap_comap", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.mem_unitGroup_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.mem_maximalIdeal_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuationSubring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "term_≤ᵥ_", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_RingTheory_Valuation_ValuativeRel_Basic___macroRules_term_≤ᵥ__1", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_RingTheory_Valuation_ValuativeRel_Basic___unexpand_ValuativeRel_vle_1", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_RingTheory_Valuation_ValuativeRel_Basic___macroRules_term_≤ᵥ__2", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.vlt", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.term_<ᵥ_", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel._aux_Mathlib_RingTheory_Valuation_ValuativeRel_Basic___macroRules_ValuativeRel_term_<ᵥ__1", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel._aux_Mathlib_RingTheory_Valuation_ValuativeRel_Basic___unexpand_ValuativeRel_vlt_1", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel._aux_Mathlib_RingTheory_Valuation_ValuativeRel_Basic___macroRules_ValuativeRel_term_<ᵥ__2", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.veq", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.term_=ᵥ_", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel._aux_Mathlib_RingTheory_Valuation_ValuativeRel_Basic___macroRules_ValuativeRel_term_=ᵥ__1", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel._aux_Mathlib_RingTheory_Valuation_ValuativeRel_Basic___unexpand_ValuativeRel_veq_1", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel._aux_Mathlib_RingTheory_Valuation_ValuativeRel_Basic___macroRules_ValuativeRel_term_=ᵥ__2", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.not_vle", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.not_vlt", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.veq_def", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.srel_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.veq_comm", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.instSymmVeq", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.vle_of_veq", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.vge_of_veq", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.not_vlt_of_veq", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.not_vgt_of_veq", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.vle_refl", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.vle_rfl", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.instReflVle", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.veq_refl", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.veq_rfl", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.instReflVeq", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.zero_vle", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ValuativeRel.zero_vlt_one", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.vle_mul_right", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.mul_vle_mul_right", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ValuativeRel.vle_mul_left", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.instTransVle", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.vle_trans'", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.veq_trans", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.instTransVeq", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.mul_vle_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.mul_vle_mul_iff_left", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.mul_vle_mul_iff_right", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ValuativeRel.mul_vlt_mul_iff_left", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.mul_vlt_mul_iff_right", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.mul_veq_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.vle_add_cases", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.zero_vlt_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": true, "tactics": ["contrapose", "rw", "rw", "exact"], "tactic_count": 4}
{"name": "ValuativeRel.posSubmonoid", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.zero_vlt_coe_posSubmonoid", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.posSubmonoid_def", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.right_cancel_posSubmonoid", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ValuativeRel.left_cancel_posSubmonoid", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ValuativeRel.val_posSubmonoid_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": true, "tactics": ["have", "rw", "contrapose", "simp"], "tactic_count": 4}
{"name": "ValuativeRel.valueSetoid", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.ValueGroupWithZero", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.ValueGroupWithZero.mk", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.ValueGroupWithZero.sound", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.ValueGroupWithZero.exact", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.ValueGroupWithZero.ind", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.ValueGroupWithZero.lift", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.ValueGroupWithZero.lift_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.ValueGroupWithZero.lift₂", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.ValueGroupWithZero.lift₂_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.ValueGroupWithZero.mk_eq_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.instZeroValueGroupWithZero", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.ValueGroupWithZero.mk_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.ValueGroupWithZero.mk_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.instOneValueGroupWithZero", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.ValueGroupWithZero.mk_self", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.ValueGroupWithZero.mk_one_one", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.ValueGroupWithZero.mk_eq_one", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ValuativeRel.ValueGroupWithZero.lift_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.ValueGroupWithZero.lift_one", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.instMulValueGroupWithZero", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.ValueGroupWithZero.mk_mul_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.ValueGroupWithZero.lift_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": true, "tactics": ["induction", "induction", "simpa"], "tactic_count": 3}
{"name": "ValuativeRel.instCommMonoidWithZeroValueGroupWithZero", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.instLEValueGroupWithZero", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.ValueGroupWithZero.mk_le_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.instLinearOrderValueGroupWithZero", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.ValueGroupWithZero.mk_lt_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ValuativeRel.ValueGroupWithZero.mk_pos", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ValuativeRel.instBotValueGroupWithZero", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.ValueGroupWithZero.bot_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.instOrderBotValueGroupWithZero", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.instIsOrderedMonoidValueGroupWithZero", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.instInvValueGroupWithZero", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.ValueGroupWithZero.inv_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.instLinearOrderedCommGroupWithZeroValueGroupWithZero", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.valuation", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.instCompatibleValueGroupWithZeroValuation", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.ValueGroupWithZero.lift_valuation", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.valuation_eq_zero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.valuation_posSubmonoid_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ValuativeRel.ValueGroupWithZero.mk_eq_div", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "ValuativeRel.ofValuation", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.Compatible.ofValuation", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.isEquiv", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": true, "tactics": ["intro", "simp_rw"], "tactic_count": 2}
{"name": "Valuation.vle_iff_le", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.vlt_iff_lt", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Valuation.veq_iff_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Valuation.vle_one_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Valuation.vlt_one_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Valuation.one_vle_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Valuation.one_vlt_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Valuation.apply_posSubmonoid_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Valuation.apply_posSubmonoid_pos", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.WithPreorder", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.instCommRingWithPreorder", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.instPreorderWithPreorder", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.instWithPreorder", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.instValuativePreorderWithPreorder", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.supp", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.supp_def", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.supp_eq_valuation_supp", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": true, "tactics": ["ext", "simpa"], "tactic_count": 2}
{"name": "ValuativeRel.instIsPrimeSupp", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "ValuativeRel.vlt_of_vlt_of_vle", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.vlt_of_vle_of_vlt", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.vlt.vle", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.vlt.trans", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.mul_vlt_mul_of_vlt_of_vle", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.mul_vlt_mul_of_vle_of_vlt", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.mul_vlt_mul", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.pow_vle_pow", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "ValuativeRel.pow_vlt_pow", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": true, "tactics": ["induction", "zero", "one", "more"], "tactic_count": 4}
{"name": "ValuativeRel.pow_vle_pow_of_vle_one", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": true, "tactics": ["obtain", "simpa"], "tactic_count": 2}
{"name": "ValuativeRel.pow_vle_pow_of_one_vle", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": true, "tactics": ["obtain", "simpa"], "tactic_count": 2}
{"name": "ValuativeRel.vle_zero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ValuativeRel.zero_vlt_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ValuativeRel.zero_veq_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.veq_zero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ValuativeRel.vle_div_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ValuativeRel.div_vle_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ValuativeRel.one_vle_div_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ValuativeRel.div_vle_one_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ValuativeRel.one_vle_inv", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ValuativeRel.inv_vle_one", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ValuativeRel.inv_vlt_one", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.one_vlt_inv", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.IsNontrivial.exists_lt_one", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "exact", "exact"], "tactic_count": 4}
{"name": "ValuativeRel.isNontrivial_iff_nontrivial_units", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "refine", "simp", "rintro", "rcases", "exact", "exact"], "tactic_count": 8}
{"name": "ValuativeRel.isNontrivial_iff_isNontrivial", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "induction", "mk", "have", "have", "by_cases", "exact", "exact", "rintro", "exact", "simpa"], "tactic_count": 12}
{"name": "ValuativeRel.instIsNontrivialOfIsNontrivialOfCompatible", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "ValuativeRel.ValueGroupWithZero.mk_eq_valuation", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ValuativeRel.exists_valuation_div_valuation_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": ["induction", "mk", "use", "simp"], "tactic_count": 4}
{"name": "ValuativeRel.exists_valuation_posSubmonoid_div_valuation_posSubmonoid_eq", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": true, "tactics": ["obtain", "lift", "contrapose", "rw", "simp", "use"], "tactic_count": 6}
{"name": "ValuativeRel.valuation_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.uniformizer", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.uniformizer_lt_one", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.le_uniformizer_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.uniformizer_pos", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "ValuativeRel.uniformizer_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.uniformizer_inv_le_iff", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "replace", "rw"], "tactic_count": 4}
{"name": "ValuativeRel.ValueGroupWithZero.embed", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.ValueGroupWithZero.embed_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.ValueGroupWithZero.embed_valuation", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": true, "tactics": ["induction", "simp"], "tactic_count": 2}
{"name": "ValuativeRel.ValueGroupWithZero.embed_strictMono", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": true, "tactics": ["intro", "obtain", "obtain", "simp", "rw", "any_goals", "rw", "simpa"], "tactic_count": 8}
{"name": "ValuativeRel.one_apply_posSubmonoid", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeExtension.vlt_iff_vlt", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ValuativeExtension.mapPosSubmonoid", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeExtension.compatible_comap", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": true, "tactics": ["constructor", "simp"], "tactic_count": 2}
{"name": "ValuativeExtension.mapValueGroupWithZero", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeExtension.mapValueGroupWithZero_mk", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ValuativeExtension.mapValueGroupWithZero_valuation", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ValuativeExtension.mapValueGroupWithZero_strictMono", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.IsRankLeOne.of_valuativeExtension", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "ValuativeRel.instMulArchimedeanValueGroupWithZeroOfIsRankLeOne", "kind": "instance", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Basic", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "ValuativeRel.trivialRel", "kind": "definition", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Trivial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ValuativeRel.eq_trivialRel_of_compatible_one", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Trivial", "is_tactic_proof": true, "tactics": ["ext", "change", "rw", "split_ifs"], "tactic_count": 4}
{"name": "ValuativeRel.trivialRel_eq_ofValuation_one", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Trivial", "is_tactic_proof": true, "tactics": ["convert", "exact"], "tactic_count": 2}
{"name": "ValuativeRel.subsingleton_units_valueGroupWithZero_of_trivialRel", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Trivial", "is_tactic_proof": true, "tactics": ["constructor", "intro", "have", "obtain", "obtain", "rw"], "tactic_count": 6}
{"name": "ValuativeRel.not_isNontrivial_of_trivialRel", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Trivial", "is_tactic_proof": true, "tactics": ["rintro", "have", "rcases", "simp_all", "simp_all"], "tactic_count": 5}
{"name": "ValuativeRel.isDiscrete_trivialRel", "kind": "theorem", "module": "Mathlib.RingTheory.Valuation.ValuativeRel.Trivial", "is_tactic_proof": true, "tactics": ["refine", "have", "rcases", "simp_all", "rw", "simp"], "tactic_count": 6}
{"name": "_private.Mathlib.RingTheory.WittVector.Basic.0.term𝕎", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.WittVector.Basic.0._aux_Mathlib_RingTheory_WittVector_Basic___macroRules__private_Mathlib_RingTheory_WittVector_Basic_0_term𝕎_1", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.WittVector.Basic.0._aux_Mathlib_RingTheory_WittVector_Basic___unexpand_WittVector_1", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.WittVector.Basic.0.termW_", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.WittVector.Basic.0._aux_Mathlib_RingTheory_WittVector_Basic___macroRules__private_Mathlib_RingTheory_WittVector_Basic_0_termW__1", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.WittVector.Basic.0._aux_Mathlib_RingTheory_WittVector_Basic___unexpand_wittPolynomial_1", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.mapFun", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.mapFun.injective", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.mapFun.surjective", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.mapFun.tacticMap_fun_tac", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.mapFun._aux_Mathlib_RingTheory_WittVector_Basic___macroRules_WittVector_mapFun_tacticMap_fun_tac_1", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.mapFun.zero", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Basic", "is_tactic_proof": true, "tactics": ["map_fun_tac"], "tactic_count": 1}
{"name": "WittVector.mapFun.one", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Basic", "is_tactic_proof": true, "tactics": ["map_fun_tac"], "tactic_count": 1}
{"name": "WittVector.mapFun.add", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Basic", "is_tactic_proof": true, "tactics": ["map_fun_tac"], "tactic_count": 1}
{"name": "WittVector.mapFun.sub", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Basic", "is_tactic_proof": true, "tactics": ["map_fun_tac"], "tactic_count": 1}
{"name": "WittVector.mapFun.mul", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Basic", "is_tactic_proof": true, "tactics": ["map_fun_tac"], "tactic_count": 1}
{"name": "WittVector.mapFun.neg", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Basic", "is_tactic_proof": true, "tactics": ["map_fun_tac"], "tactic_count": 1}
{"name": "WittVector.mapFun.nsmul", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Basic", "is_tactic_proof": true, "tactics": ["map_fun_tac"], "tactic_count": 1}
{"name": "WittVector.mapFun.zsmul", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Basic", "is_tactic_proof": true, "tactics": ["map_fun_tac"], "tactic_count": 1}
{"name": "WittVector.mapFun.pow", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Basic", "is_tactic_proof": true, "tactics": ["map_fun_tac"], "tactic_count": 1}
{"name": "WittVector.mapFun.natCast", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.mapFun.intCast", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.WittVector.Basic.0.WittVector.ghostFun", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.tacticGhost_fun_tac_,_", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector._aux_Mathlib_RingTheory_WittVector_Basic___elabRules_WittVector_tacticGhost_fun_tac_,__1", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.matrix_vecEmpty_coeff", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Basic", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "_private.Mathlib.RingTheory.WittVector.Basic.0.WittVector.ghostFun_zero", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Basic", "is_tactic_proof": true, "tactics": ["ghost_fun_tac"], "tactic_count": 1}
{"name": "_private.Mathlib.RingTheory.WittVector.Basic.0.WittVector.ghostFun_one", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Basic", "is_tactic_proof": true, "tactics": ["ghost_fun_tac"], "tactic_count": 1}
{"name": "_private.Mathlib.RingTheory.WittVector.Basic.0.WittVector.ghostFun_add", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Basic", "is_tactic_proof": true, "tactics": ["ghost_fun_tac"], "tactic_count": 1}
{"name": "_private.Mathlib.RingTheory.WittVector.Basic.0.WittVector.ghostFun_natCast", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.WittVector.Basic.0.WittVector.ghostFun_sub", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Basic", "is_tactic_proof": true, "tactics": ["ghost_fun_tac"], "tactic_count": 1}
{"name": "_private.Mathlib.RingTheory.WittVector.Basic.0.WittVector.ghostFun_mul", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Basic", "is_tactic_proof": true, "tactics": ["ghost_fun_tac"], "tactic_count": 1}
{"name": "_private.Mathlib.RingTheory.WittVector.Basic.0.WittVector.ghostFun_neg", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Basic", "is_tactic_proof": true, "tactics": ["ghost_fun_tac"], "tactic_count": 1}
{"name": "_private.Mathlib.RingTheory.WittVector.Basic.0.WittVector.ghostFun_intCast", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.WittVector.Basic.0.WittVector.ghostFun_nsmul", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Basic", "is_tactic_proof": true, "tactics": ["ghost_fun_tac"], "tactic_count": 1}
{"name": "_private.Mathlib.RingTheory.WittVector.Basic.0.WittVector.ghostFun_zsmul", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Basic", "is_tactic_proof": true, "tactics": ["ghost_fun_tac"], "tactic_count": 1}
{"name": "_private.Mathlib.RingTheory.WittVector.Basic.0.WittVector.ghostFun_pow", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Basic", "is_tactic_proof": true, "tactics": ["ghost_fun_tac"], "tactic_count": 1}
{"name": "_private.Mathlib.RingTheory.WittVector.Basic.0.WittVector.ghostEquiv'", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.WittVector.Basic.0.WittVector.comm_ring_aux₁", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.WittVector.Basic.0.WittVector.comm_ring_aux₂", "kind": "abbrev", "module": "Mathlib.RingTheory.WittVector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.instCommRing", "kind": "instance", "module": "Mathlib.RingTheory.WittVector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.map", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.map_injective", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.map_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.map_coeff", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.map_id", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "WittVector.map_eq_zero_iff", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Basic", "is_tactic_proof": true, "tactics": ["refine", "apply_fun", "simpa", "ext", "simpa"], "tactic_count": 5}
{"name": "WittVector.ghostMap", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.ghostComponent", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.ghostComponent_apply", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.pow_dvd_ghostComponent_of_dvd_coeff", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply", "intro", "simp", "have", "rw", "gcongr", "exact", "exact"], "tactic_count": 9}
{"name": "WittVector.ghostMap_apply", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.ghostEquiv", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.ghostEquiv_coe", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.ghostMap.bijective_of_invertible", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.constantCoeff", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.instNontrivial", "kind": "instance", "module": "Mathlib.RingTheory.WittVector.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.WittVector.Compare.0.term𝕎", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Compare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.WittVector.Compare.0._aux_Mathlib_RingTheory_WittVector_Compare___macroRules__private_Mathlib_RingTheory_WittVector_Compare_0_term𝕎_1", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Compare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.WittVector.Compare.0._aux_Mathlib_RingTheory_WittVector_Compare___unexpand_WittVector_1", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Compare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TruncatedWittVector.eq_of_le_of_cast_pow_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Compare", "is_tactic_proof": true, "tactics": ["contrapose", "replace", "have", "rw", "use", "rw", "haveI", "exact"], "tactic_count": 8}
{"name": "TruncatedWittVector.card_zmod", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Compare", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "TruncatedWittVector.charP_zmod", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Compare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TruncatedWittVector.zmodEquivTrunc", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Compare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TruncatedWittVector.zmodEquivTrunc_apply", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Compare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TruncatedWittVector.commutes", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Compare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TruncatedWittVector.commutes'", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Compare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TruncatedWittVector.commutes_symm'", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Compare", "is_tactic_proof": true, "tactics": ["apply", "rw", "simp"], "tactic_count": 3}
{"name": "TruncatedWittVector.commutes_symm", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Compare", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "WittVector.toZModPow", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Compare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.toZModPow_compat", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Compare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.toPadicInt", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Compare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.zmodEquivTrunc_compat", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Compare", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "WittVector.fromPadicInt", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Compare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.toPadicInt_comp_fromPadicInt", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Compare", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "simp", "rw", "simp"], "tactic_count": 6}
{"name": "WittVector.toPadicInt_comp_fromPadicInt_ext", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Compare", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "WittVector.fromPadicInt_comp_toPadicInt", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Compare", "is_tactic_proof": true, "tactics": ["apply", "intro", "rw", "simp"], "tactic_count": 4}
{"name": "WittVector.fromPadicInt_comp_toPadicInt_ext", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Compare", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "WittVector.equiv", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Compare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.WittVector.Complete.0.WittVector.term𝕎", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Complete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.WittVector.Complete.0.WittVector._aux_Mathlib_RingTheory_WittVector_Complete___macroRules__private_Mathlib_RingTheory_WittVector_Complete_0_WittVector_term𝕎_1", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Complete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.WittVector.Complete.0.WittVector._aux_Mathlib_RingTheory_WittVector_Complete___unexpand_WittVector_1", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Complete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.le_coeff_eq_iff_le_sub_coeff_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Complete", "is_tactic_proof": true, "tactics": ["calc", "refine", "ext", "simp", "rw"], "tactic_count": 5}
{"name": "WittVector.eq_zero_of_p_mul_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Complete", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "WittVector.mem_span_p_iff_coeff_zero_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Complete", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "rw", "use", "calc", "rw"], "tactic_count": 6}
{"name": "WittVector.mem_span_p_pow_iff_le_coeff_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Complete", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "rw", "use", "rw", "calc", "congr", "rw", "rw", "simp", "rw", "simp"], "tactic_count": 12}
{"name": "WittVector.ker_constantCoeff", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Complete", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "WittVector.quotientPEquiv", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Complete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.quotientPEquiv_mk", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Complete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.isAdicCompleteIdealSpanP", "kind": "instance", "module": "Mathlib.RingTheory.WittVector.Complete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.mk", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.WittVector.Defs.0.term𝕎", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.WittVector.Defs.0._aux_Mathlib_RingTheory_WittVector_Defs___macroRules__private_Mathlib_RingTheory_WittVector_Defs_0_term𝕎_1", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.WittVector.Defs.0._aux_Mathlib_RingTheory_WittVector_Defs___unexpand_WittVector_1", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.ext", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Defs", "is_tactic_proof": true, "tactics": ["cases", "cases", "simp", "simp"], "tactic_count": 4}
{"name": "WittVector.coeff_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.coeff_mk", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.instFunctor", "kind": "instance", "module": "Mathlib.RingTheory.WittVector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.instLawfulFunctor", "kind": "instance", "module": "Mathlib.RingTheory.WittVector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.wittZero", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.wittOne", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.wittAdd", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.wittNSMul", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.wittZSMul", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.wittSub", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.wittMul", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.wittNeg", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.wittPow", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.peval", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.eval", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.instZero", "kind": "instance", "module": "Mathlib.RingTheory.WittVector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.instInhabited", "kind": "instance", "module": "Mathlib.RingTheory.WittVector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.instOne", "kind": "instance", "module": "Mathlib.RingTheory.WittVector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.instAdd", "kind": "instance", "module": "Mathlib.RingTheory.WittVector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.instSub", "kind": "instance", "module": "Mathlib.RingTheory.WittVector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.hasNatScalar", "kind": "instance", "module": "Mathlib.RingTheory.WittVector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.hasIntScalar", "kind": "instance", "module": "Mathlib.RingTheory.WittVector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.instMul", "kind": "instance", "module": "Mathlib.RingTheory.WittVector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.instNeg", "kind": "instance", "module": "Mathlib.RingTheory.WittVector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.hasNatPow", "kind": "instance", "module": "Mathlib.RingTheory.WittVector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.instNatCast", "kind": "instance", "module": "Mathlib.RingTheory.WittVector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.instIntCast", "kind": "instance", "module": "Mathlib.RingTheory.WittVector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.wittZero_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Defs", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "WittVector.wittOne_zero_eq_one", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Defs", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "WittVector.wittOne_pos_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Defs", "is_tactic_proof": true, "tactics": ["apply", "simp", "induction", "h", "rw", "simp", "rw", "rw", "simp", "simp", "intro", "rw", "rw", "grind"], "tactic_count": 14}
{"name": "WittVector.wittAdd_zero", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Defs", "is_tactic_proof": true, "tactics": ["apply", "simp", "map_wittStructureInt]"], "tactic_count": 3}
{"name": "WittVector.wittSub_zero", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Defs", "is_tactic_proof": true, "tactics": ["apply", "simp", "map_wittStructureInt]"], "tactic_count": 3}
{"name": "WittVector.wittMul_zero", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Defs", "is_tactic_proof": true, "tactics": ["apply", "simp", "map_wittStructureInt]"], "tactic_count": 3}
{"name": "WittVector.wittNeg_zero", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Defs", "is_tactic_proof": true, "tactics": ["apply", "simp", "map_wittStructureInt]"], "tactic_count": 3}
{"name": "WittVector.constantCoeff_wittAdd", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Defs", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "WittVector.constantCoeff_wittSub", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Defs", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "WittVector.constantCoeff_wittMul", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Defs", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "WittVector.constantCoeff_wittNeg", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Defs", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "WittVector.constantCoeff_wittNSMul", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Defs", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "WittVector.constantCoeff_wittZSMul", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Defs", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "WittVector.zero_coeff", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.one_coeff_zero", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.one_coeff_eq_of_pos", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.v2_coeff", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Defs", "is_tactic_proof": true, "tactics": ["fin_cases"], "tactic_count": 1}
{"name": "WittVector.add_coeff", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WittVector.sub_coeff", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WittVector.mul_coeff", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WittVector.neg_coeff", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WittVector.nsmul_coeff", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WittVector.zsmul_coeff", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WittVector.pow_coeff", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WittVector.add_coeff_zero", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WittVector.mul_coeff_zero", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WittVector.wittAdd_vars", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.wittSub_vars", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.wittMul_vars", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.wittNeg_vars", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.wittNSMul_vars", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.wittZSMul_vars", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.wittPow_vars", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.WittVector.DiscreteValuationRing.0.WittVector.term𝕎", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.DiscreteValuationRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.WittVector.DiscreteValuationRing.0.WittVector._aux_Mathlib_RingTheory_WittVector_DiscreteValuationRing___macroRules__private_Mathlib_RingTheory_WittVector_DiscreteValuationRing_0_WittVector_term𝕎_1", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.DiscreteValuationRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.WittVector.DiscreteValuationRing.0.WittVector._aux_Mathlib_RingTheory_WittVector_DiscreteValuationRing___unexpand_WittVector_1", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.DiscreteValuationRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.succNthValUnits", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.DiscreteValuationRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.inverseCoeff", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.DiscreteValuationRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.mkUnit", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.DiscreteValuationRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.coe_mkUnit", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.DiscreteValuationRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.isUnit_of_coeff_zero_ne_zero", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.DiscreteValuationRing", "is_tactic_proof": true, "tactics": ["let", "have", "exact"], "tactic_count": 3}
{"name": "WittVector.irreducible", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.DiscreteValuationRing", "is_tactic_proof": false, "tactics": ["have", "intro", "simpa", "refine", "obtain", "obtain", "obtain", "cases", "rcases", "rw", "apply_fun", "simp", "verschiebung_coeff_add_one,", "exact"], "tactic_count": 14}
{"name": "WittVector.exists_eq_pow_p_mul", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.DiscreteValuationRing", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "rw", "have", "simp", "rw", "refine", "contrapose", "simp", "simp_rw", "convert", "ext1", "rw"], "tactic_count": 13}
{"name": "WittVector.exists_eq_pow_p_mul'", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.DiscreteValuationRing", "is_tactic_proof": true, "tactics": ["obtain", "let", "have", "exact"], "tactic_count": 4}
{"name": "WittVector.isDiscreteValuationRing", "kind": "instance", "module": "Mathlib.RingTheory.WittVector.DiscreteValuationRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.WittVector.Domain.0.WittVector.term𝕎", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Domain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.WittVector.Domain.0.WittVector._aux_Mathlib_RingTheory_WittVector_Domain___macroRules__private_Mathlib_RingTheory_WittVector_Domain_0_WittVector_term𝕎_1", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Domain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.WittVector.Domain.0.WittVector._aux_Mathlib_RingTheory_WittVector_Domain___unexpand_WittVector_1", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Domain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.shift", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Domain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.shift_coeff", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Domain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.verschiebung_shift", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Domain", "is_tactic_proof": true, "tactics": ["ext", "rw", "apply", "simp", "congr", "rw"], "tactic_count": 6}
{"name": "WittVector.eq_iterate_verschiebung", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Domain", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "dsimp", "exact", "exact"], "tactic_count": 6}
{"name": "WittVector.verschiebung_nonzero", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Domain", "is_tactic_proof": true, "tactics": ["classical", "have", "by_contra", "apply", "ext", "simp", "let", "use", "refine", "exact"], "tactic_count": 10}
{"name": "WittVector.instNoZeroDivisorsOfCharP", "kind": "instance", "module": "Mathlib.RingTheory.WittVector.Domain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.instIsDomain", "kind": "instance", "module": "Mathlib.RingTheory.WittVector.Domain", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.WittVector.Frobenius.0.WittVector.term𝕎", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Frobenius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.WittVector.Frobenius.0.WittVector._aux_Mathlib_RingTheory_WittVector_Frobenius___macroRules__private_Mathlib_RingTheory_WittVector_Frobenius_0_WittVector_term𝕎_1", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Frobenius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.WittVector.Frobenius.0.WittVector._aux_Mathlib_RingTheory_WittVector_Frobenius___unexpand_WittVector_1", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Frobenius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.frobeniusPolyRat", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Frobenius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.bind₁_frobeniusPolyRat_wittPolynomial", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Frobenius", "is_tactic_proof": true, "tactics": ["delta", "rw"], "tactic_count": 2}
{"name": "_private.Mathlib.RingTheory.WittVector.Frobenius.0.WittVector.termV", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Frobenius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.WittVector.Frobenius.0.WittVector._aux_Mathlib_RingTheory_WittVector_Frobenius___macroRules__private_Mathlib_RingTheory_WittVector_Frobenius_0_WittVector_termV_1", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Frobenius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.WittVector.Frobenius.0.WittVector._aux_Mathlib_RingTheory_WittVector_Frobenius___unexpand_multiplicity_1", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Frobenius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.frobeniusPolyAux", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Frobenius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.frobeniusPolyAux_eq", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Frobenius", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "WittVector.frobeniusPoly", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Frobenius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.map_frobeniusPoly.key₁", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Frobenius", "is_tactic_proof": true, "tactics": ["apply", "rw"], "tactic_count": 2}
{"name": "WittVector.map_frobeniusPoly.key₂", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Frobenius", "is_tactic_proof": true, "tactics": ["generalize", "rsuffices", "rw", "tsub_right_comm,", "have", "exact"], "tactic_count": 6}
{"name": "WittVector.map_frobeniusPoly", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Frobenius", "is_tactic_proof": true, "tactics": ["rw", "refine", "intro", "rw", "simp", "have", "rw", "add_tsub_cancel_left,", "mul_right_comm", "mul_sub,", "eq_comm]", "simp", "apply", "intro", "rw", "rw", "clear", "rw", "mul_one,", "add_sub_cancel_right,", "apply", "intro", "rw", "rw", "rw", "simp", "apply", "apply", "rw", "simp", "rw", "simp", "rw", "push_cast", "linear_combination", "congr", "field"], "tactic_count": 37}
{"name": "WittVector.frobeniusPoly_zmod", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Frobenius", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "WittVector.bind₁_frobeniusPoly_wittPolynomial", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Frobenius", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "WittVector.frobeniusFun", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Frobenius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.coeff_frobeniusFun", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Frobenius", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "WittVector.frobeniusFun_isPoly", "kind": "instance", "module": "Mathlib.RingTheory.WittVector.Frobenius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.ghostComponent_frobeniusFun", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Frobenius", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WittVector.frobenius", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Frobenius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.coeff_frobenius", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Frobenius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.ghostComponent_frobenius", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Frobenius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.frobenius_isPoly", "kind": "instance", "module": "Mathlib.RingTheory.WittVector.Frobenius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.coeff_frobenius_charP", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Frobenius", "is_tactic_proof": true, "tactics": ["rw", "letI", "calc", "aeval", "aeval", "conv_rhs", "apply", "rw", "rw"], "tactic_count": 9}
{"name": "WittVector.frobenius_eq_map_frobenius", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Frobenius", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "WittVector.frobenius_zmodp", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Frobenius", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WittVector.frobeniusEquiv", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Frobenius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.frobenius_bijective", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Frobenius", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.WittVector.FrobeniusFractionField.0.WittVector.term𝕎", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.FrobeniusFractionField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "_private.Mathlib.RingTheory.WittVector.FrobeniusFractionField.0.WittVector._aux_Mathlib_RingTheory_WittVector_FrobeniusFractionField___unexpand_WittVector_1", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.FrobeniusFractionField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.RecursionMain.succNthDefiningPoly", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.FrobeniusFractionField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.RecursionMain.succNthDefiningPoly_degree", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.FrobeniusFractionField", "is_tactic_proof": false, "tactics": ["have", "rw", "simp", "exact", "have", "rw", "rw", "exact", "exact", "rw", "apply", "rw", "exact"], "tactic_count": 13}
{"name": "WittVector.RecursionMain.root_exists", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.FrobeniusFractionField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.RecursionMain.succNthVal", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.FrobeniusFractionField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.RecursionMain.succNthVal_spec", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.FrobeniusFractionField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.RecursionMain.succNthVal_spec'", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.FrobeniusFractionField", "is_tactic_proof": true, "tactics": ["rw", "have", "simp", "convert", "ring"], "tactic_count": 5}
{"name": "WittVector.RecursionBase.solution_pow", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.FrobeniusFractionField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.RecursionBase.solution", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.FrobeniusFractionField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.RecursionBase.solution_spec", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.FrobeniusFractionField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.RecursionBase.solution_nonzero", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.FrobeniusFractionField", "is_tactic_proof": true, "tactics": ["intro", "have", "rw", "simpa", "exact"], "tactic_count": 5}
{"name": "WittVector.RecursionBase.solution_spec'", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.FrobeniusFractionField", "is_tactic_proof": true, "tactics": ["have", "have", "grind"], "tactic_count": 3}
{"name": "WittVector.frobeniusRotationCoeff", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.FrobeniusFractionField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.frobeniusRotation", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.FrobeniusFractionField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.frobeniusRotation_nonzero", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.FrobeniusFractionField", "is_tactic_proof": true, "tactics": ["intro", "apply", "simpa"], "tactic_count": 3}
{"name": "WittVector.frobenius_frobeniusRotation", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.FrobeniusFractionField", "is_tactic_proof": true, "tactics": ["ext", "rcases", "simp", "frobeniusRotationCoeff]", "exact", "simp", "have", "simp", "convert", "apply", "intro", "simp", "rfl"], "tactic_count": 13}
{"name": "_private.Mathlib.RingTheory.WittVector.FrobeniusFractionField.0.WittVector.termφ", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.FrobeniusFractionField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.WittVector.FrobeniusFractionField.0.WittVector._aux_Mathlib_RingTheory_WittVector_FrobeniusFractionField___macroRules__private_Mathlib_RingTheory_WittVector_FrobeniusFractionField_0_WittVector_termφ_1", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.FrobeniusFractionField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.WittVector.FrobeniusFractionField.0.WittVector._aux_Mathlib_RingTheory_WittVector_FrobeniusFractionField___unexpand_IsFractionRing_ringEquivOfRingEquiv_1", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.FrobeniusFractionField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.exists_frobenius_solution_fractionRing_aux", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.FrobeniusFractionField", "is_tactic_proof": true, "tactics": ["intro", "have", "have", "have", "simpa", "rw", "simp", "convert", "simp", "simp"], "tactic_count": 10}
{"name": "WittVector.exists_frobenius_solution_fractionRing", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.FrobeniusFractionField", "is_tactic_proof": true, "tactics": ["revert", "refine", "rintro", "have", "have", "obtain", "obtain", "let", "refine", "simpa", "exact"], "tactic_count": 11}
{"name": "_private.Mathlib.RingTheory.WittVector.Identities.0.WittVector.term𝕎", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Identities", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.WittVector.Identities.0.WittVector._aux_Mathlib_RingTheory_WittVector_Identities___macroRules__private_Mathlib_RingTheory_WittVector_Identities_0_WittVector_term𝕎_1", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Identities", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "WittVector.frobenius_verschiebung", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Identities", "is_tactic_proof": false, "tactics": ["have", "have", "ghost_calc", "ghost_simp"], "tactic_count": 4}
{"name": "WittVector.verschiebung_zmod", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Identities", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "WittVector.coeff_p_pow", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Identities", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "WittVector.coeff_p_pow_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Identities", "is_tactic_proof": true, "tactics": ["induction", "zero", "rw", "exact", "succ", "rw", "cases", "rw", "rw"], "tactic_count": 9}
{"name": "WittVector.coeff_p", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Identities", "is_tactic_proof": true, "tactics": ["split_ifs", "simpa", "simpa"], "tactic_count": 3}
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{"name": "WittVector.coeff_p_one", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Identities", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "WittVector.p_nonzero", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Identities", "is_tactic_proof": true, "tactics": ["intro", "simpa"], "tactic_count": 2}
{"name": "WittVector.FractionRing.p_nonzero", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Identities", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "WittVector.verschiebung_mul_frobenius", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Identities", "is_tactic_proof": false, "tactics": ["have", "have", "ghost_calc", "rintro"], "tactic_count": 4}
{"name": "WittVector.mul_charP_coeff_zero", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Identities", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "WittVector.mul_charP_coeff_succ", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Identities", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "WittVector.mul_pow_charP_coeff_zero", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Identities", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "cases", "zero", "succ", "rw", "simpa"], "tactic_count": 9}
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{"name": "WittVector.iterate_verschiebung_coeff_eq_zero", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Identities", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "cases", "zero", "succ", "rw", "simpa"], "tactic_count": 9}
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{"name": "TruncatedWittVector", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Truncated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInhabitedTruncatedWittVector", "kind": "instance", "module": "Mathlib.RingTheory.WittVector.Truncated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TruncatedWittVector.mk", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Truncated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TruncatedWittVector.coeff", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Truncated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TruncatedWittVector.ext", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Truncated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TruncatedWittVector.coeff_mk", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Truncated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TruncatedWittVector.mk_coeff", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Truncated", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "TruncatedWittVector.out", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Truncated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TruncatedWittVector.coeff_out", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Truncated", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "TruncatedWittVector.out_injective", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Truncated", "is_tactic_proof": true, "tactics": ["intro", "ext", "rw", "simpa"], "tactic_count": 4}
{"name": "WittVector.truncateFun", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Truncated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.coeff_truncateFun", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Truncated", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "WittVector.out_truncateFun", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Truncated", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "split_ifs", "rw"], "tactic_count": 4}
{"name": "TruncatedWittVector.truncateFun_out", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Truncated", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "TruncatedWittVector.instZero", "kind": "instance", "module": "Mathlib.RingTheory.WittVector.Truncated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TruncatedWittVector.instOne", "kind": "instance", "module": "Mathlib.RingTheory.WittVector.Truncated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TruncatedWittVector.instNatCast", "kind": "instance", "module": "Mathlib.RingTheory.WittVector.Truncated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TruncatedWittVector.instIntCast", "kind": "instance", "module": "Mathlib.RingTheory.WittVector.Truncated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TruncatedWittVector.instAdd", "kind": "instance", "module": "Mathlib.RingTheory.WittVector.Truncated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TruncatedWittVector.instMul", "kind": "instance", "module": "Mathlib.RingTheory.WittVector.Truncated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TruncatedWittVector.instNeg", "kind": "instance", "module": "Mathlib.RingTheory.WittVector.Truncated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TruncatedWittVector.instSub", "kind": "instance", "module": "Mathlib.RingTheory.WittVector.Truncated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TruncatedWittVector.hasNatScalar", "kind": "instance", "module": "Mathlib.RingTheory.WittVector.Truncated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TruncatedWittVector.hasIntScalar", "kind": "instance", "module": "Mathlib.RingTheory.WittVector.Truncated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TruncatedWittVector.hasNatPow", "kind": "instance", "module": "Mathlib.RingTheory.WittVector.Truncated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TruncatedWittVector.coeff_zero", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Truncated", "is_tactic_proof": true, "tactics": ["change", "rw"], "tactic_count": 2}
{"name": "witt_truncateFun_tac", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Truncated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_RingTheory_WittVector_Truncated___macroRules_witt_truncateFun_tac_1", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Truncated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.truncateFun_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Truncated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.truncateFun_zero", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Truncated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.truncateFun_one", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Truncated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.truncateFun_add", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Truncated", "is_tactic_proof": true, "tactics": ["witt_truncateFun_tac"], "tactic_count": 1}
{"name": "WittVector.truncateFun_mul", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Truncated", "is_tactic_proof": true, "tactics": ["witt_truncateFun_tac"], "tactic_count": 1}
{"name": "WittVector.truncateFun_neg", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Truncated", "is_tactic_proof": true, "tactics": ["witt_truncateFun_tac"], "tactic_count": 1}
{"name": "WittVector.truncateFun_sub", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Truncated", "is_tactic_proof": true, "tactics": ["witt_truncateFun_tac"], "tactic_count": 1}
{"name": "WittVector.truncateFun_nsmul", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Truncated", "is_tactic_proof": true, "tactics": ["witt_truncateFun_tac"], "tactic_count": 1}
{"name": "WittVector.truncateFun_zsmul", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Truncated", "is_tactic_proof": true, "tactics": ["witt_truncateFun_tac"], "tactic_count": 1}
{"name": "WittVector.truncateFun_pow", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Truncated", "is_tactic_proof": true, "tactics": ["witt_truncateFun_tac"], "tactic_count": 1}
{"name": "WittVector.truncateFun_natCast", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Truncated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.truncateFun_intCast", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Truncated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TruncatedWittVector.instCommRing", "kind": "instance", "module": "Mathlib.RingTheory.WittVector.Truncated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.truncate", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Truncated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.truncate_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Truncated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.coeff_truncate", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Truncated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.mem_ker_truncate", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Truncated", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "WittVector.truncate_mk'", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Truncated", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "TruncatedWittVector.truncate", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Truncated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TruncatedWittVector.truncate_comp_wittVector_truncate", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Truncated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TruncatedWittVector.truncate_wittVector_truncate", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Truncated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TruncatedWittVector.truncate_truncate", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Truncated", "is_tactic_proof": true, "tactics": ["obtain", "simp"], "tactic_count": 2}
{"name": "TruncatedWittVector.truncate_comp", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Truncated", "is_tactic_proof": true, "tactics": ["ext1"], "tactic_count": 1}
{"name": "TruncatedWittVector.truncate_surjective", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Truncated", "is_tactic_proof": true, "tactics": ["intro", "obtain", "exact"], "tactic_count": 3}
{"name": "TruncatedWittVector.coeff_truncate", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Truncated", "is_tactic_proof": true, "tactics": ["obtain", "simp"], "tactic_count": 2}
{"name": "TruncatedWittVector.instFintype", "kind": "instance", "module": "Mathlib.RingTheory.WittVector.Truncated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TruncatedWittVector.card", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Truncated", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "TruncatedWittVector.iInf_ker_truncate", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Truncated", "is_tactic_proof": true, "tactics": ["rw", "intro", "ext", "simp", "exact"], "tactic_count": 5}
{"name": "WittVector.liftFun", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Truncated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.truncate_liftFun", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Truncated", "is_tactic_proof": true, "tactics": ["ext", "simp", "rw", "congr"], "tactic_count": 4}
{"name": "WittVector.lift", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Truncated", "is_tactic_proof": true, "tactics": ["refine", "map_zero", "map_one", "map_add", "map_mul", "rw", "simp"], "tactic_count": 7}
{"name": "WittVector.truncate_lift", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Truncated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.truncate_comp_lift", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Truncated", "is_tactic_proof": true, "tactics": ["ext1"], "tactic_count": 1}
{"name": "WittVector.lift_unique", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Truncated", "is_tactic_proof": true, "tactics": ["ext1", "rw", "intro", "simp"], "tactic_count": 4}
{"name": "WittVector.liftEquiv", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Truncated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.hom_ext", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Truncated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.WittVector.Verschiebung.0.WittVector.term𝕎", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Verschiebung", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.WittVector.Verschiebung.0.WittVector._aux_Mathlib_RingTheory_WittVector_Verschiebung___macroRules__private_Mathlib_RingTheory_WittVector_Verschiebung_0_WittVector_term𝕎_1", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Verschiebung", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.RingTheory.WittVector.Verschiebung.0.WittVector._aux_Mathlib_RingTheory_WittVector_Verschiebung___unexpand_WittVector_1", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Verschiebung", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.verschiebungFun", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Verschiebung", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.verschiebungFun_coeff", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Verschiebung", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "WittVector.verschiebungFun_coeff_zero", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Verschiebung", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "WittVector.verschiebungFun_coeff_succ", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Verschiebung", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.ghostComponent_zero_verschiebungFun", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Verschiebung", "is_tactic_proof": true, "tactics": ["rw", "pow_zero,"], "tactic_count": 2}
{"name": "WittVector.ghostComponent_verschiebungFun", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Verschiebung", "is_tactic_proof": true, "tactics": ["simp", "rw", "add_zero,", "rintro", "simp"], "tactic_count": 5}
{"name": "WittVector.verschiebungPoly", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Verschiebung", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.verschiebungPoly_zero", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Verschiebung", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.aeval_verschiebung_poly'", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Verschiebung", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rw"], "tactic_count": 3}
{"name": "WittVector.verschiebungFun_isPoly", "kind": "instance", "module": "Mathlib.RingTheory.WittVector.Verschiebung", "is_tactic_proof": true, "tactics": ["use", "simp"], "tactic_count": 2}
{"name": "WittVector._example", "kind": "example", "module": "Mathlib.RingTheory.WittVector.Verschiebung", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.verschiebung", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.Verschiebung", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.verschiebung_isPoly", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Verschiebung", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.map_verschiebung", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Verschiebung", "is_tactic_proof": true, "tactics": ["ext", "exact", "rfl"], "tactic_count": 3}
{"name": "WittVector.ghostComponent_zero_verschiebung", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Verschiebung", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.ghostComponent_verschiebung", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Verschiebung", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.verschiebung_coeff_zero", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Verschiebung", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.verschiebung_coeff_add_one", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Verschiebung", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.verschiebung_coeff_succ", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Verschiebung", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.verschiebung_injective", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Verschiebung", "is_tactic_proof": true, "tactics": ["rw", "intro", "ext", "rw", "simp"], "tactic_count": 5}
{"name": "WittVector.aeval_verschiebungPoly", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Verschiebung", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WittVector.bind₁_verschiebungPoly_wittPolynomial", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.Verschiebung", "is_tactic_proof": true, "tactics": ["apply", "intro", "split_ifs", "simp", "obtain", "rw", "simp", "rw", "calc", "apply", "funext", "simp", "exact"], "tactic_count": 13}
{"name": "wittPolynomial", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.WittPolynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "wittPolynomial_eq_sum_C_mul_X_pow", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.WittPolynomial", "is_tactic_proof": true, "tactics": ["apply", "rintro", "rw", "rw"], "tactic_count": 4}
{"name": "Witt.termW_", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.WittPolynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Witt._aux_Mathlib_RingTheory_WittVector_WittPolynomial___macroRules_Witt_termW__1", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.WittPolynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Witt._aux_Mathlib_RingTheory_WittVector_WittPolynomial___unexpand_wittPolynomial_1", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.WittPolynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Witt.termW", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.WittPolynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Witt._aux_Mathlib_RingTheory_WittVector_WittPolynomial___macroRules_Witt_termW_1", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.WittPolynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Witt._aux_Mathlib_RingTheory_WittVector_WittPolynomial___unexpand_wittPolynomial_2", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.WittPolynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "map_wittPolynomial", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.WittPolynomial", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw"], "tactic_count": 3}
{"name": "constantCoeff_wittPolynomial", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.WittPolynomial", "is_tactic_proof": true, "tactics": ["simp", "rw", "rintro", "rw", "rw", "exact"], "tactic_count": 6}
{"name": "wittPolynomial_zero", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.WittPolynomial", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "wittPolynomial_one", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.WittPolynomial", "is_tactic_proof": true, "tactics": ["simp", "pow_zero,"], "tactic_count": 2}
{"name": "aeval_wittPolynomial", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.WittPolynomial", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "wittPolynomial_zmod_self", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.WittPolynomial", "is_tactic_proof": true, "tactics": ["simp", "rw", "map_sum,", "intro", "rw", "congr", "rw", "rw"], "tactic_count": 8}
{"name": "wittPolynomial_vars", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.WittPolynomial", "is_tactic_proof": false, "tactics": ["have", "intro", "refine", "rw", "exact", "rw", "simp", "simp", "intro", "apply", "rwa"], "tactic_count": 11}
{"name": "wittPolynomial_vars_subset", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.WittPolynomial", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "xInTermsOfW", "kind": "definition", "module": "Mathlib.RingTheory.WittVector.WittPolynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "xInTermsOfW_eq", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.WittPolynomial", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "constantCoeff_xInTermsOfW", "kind": "theorem", "module": "Mathlib.RingTheory.WittVector.WittPolynomial", "is_tactic_proof": false, "tactics": ["induction", "ind", "rw", "neg_eq_zero,", "intro", "rw", "simp", "rw", "exact"], "tactic_count": 9}
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{"name": "ZMod.ringHom_eq_of_ker_eq", "kind": "theorem", "module": "Mathlib.RingTheory.ZMod", "is_tactic_proof": true, "tactics": ["have", "rw", "rw"], "tactic_count": 3}
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{"name": "instIsReducedZModOfFactSquarefreeNat", "kind": "instance", "module": "Mathlib.RingTheory.ZMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.rootsOfUnity_eq_top", "kind": "theorem", "module": "Mathlib.RingTheory.ZMod.Torsion", "is_tactic_proof": true, "tactics": ["ext", "simpa"], "tactic_count": 2}
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{"name": "Algebra.ZariskisMainProperty", "kind": "definition", "module": "Mathlib.RingTheory.ZariskisMainTheorem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Algebra.zariskisMainProperty_iff", "kind": "theorem", "module": "Mathlib.RingTheory.ZariskisMainTheorem", "is_tactic_proof": true, "tactics": ["simp", "refine", "rw", "and_iff_right", "simp"], "tactic_count": 5}
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{"name": "Algebra.ZariskisMainProperty.of_isIntegral", "kind": "theorem", "module": "Mathlib.RingTheory.ZariskisMainTheorem", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Cardinal.lift_preAleph", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.lift_preOmega", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.isNormal_preAleph", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.preAleph_le_of_isSuccPrelimit", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": true, "tactics": ["obtain", "simp", "exact"], "tactic_count": 3}
{"name": "Cardinal.preAleph_limit", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": true, "tactics": ["obtain", "simp", "exact"], "tactic_count": 3}
{"name": "Cardinal.preAleph_le_of_strictMono", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Cardinal.aleph", "kind": "definition", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.termℵ_", "kind": "definition", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal._aux_Mathlib_SetTheory_Cardinal_Aleph___macroRules_Cardinal_termℵ__1", "kind": "definition", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal._aux_Mathlib_SetTheory_Cardinal_Aleph___unexpand_Cardinal_aleph_1", "kind": "definition", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.termℵ₁", "kind": "definition", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal._aux_Mathlib_SetTheory_Cardinal_Aleph___macroRules_Cardinal_termℵ₁_1", "kind": "definition", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.aleph_eq_preAleph", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.card_omega", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.ord_aleph", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.aleph_lt_aleph", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.aleph_le_aleph", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.aleph_max", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.preAleph_le_aleph", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.aleph_succ", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.aleph_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.lift_aleph", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Ordinal.lift_omega", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Cardinal.isNormal_aleph", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.aleph_limit", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.aleph0_le_aleph", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Cardinal.aleph_pos", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.card_le_aleph", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.le_aleph_ord", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Cardinal.aleph_toNat", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.aleph_toENat", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.isSuccLimit_omega", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Cardinal.range_aleph", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": true, "tactics": ["ext", "refine", "rw", "rwa"], "tactic_count": 4}
{"name": "Cardinal.mem_range_aleph_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.succ_aleph0", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.aleph0_lt_aleph_one", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "Cardinal.countable_iff_lt_aleph_one", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.aleph_one_le_lift", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Cardinal.lift_le_aleph_one", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Cardinal.aleph_one_lt_lift", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Cardinal.lift_lt_aleph_one", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Cardinal.aleph_one_eq_lift", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Cardinal.lift_eq_aleph_one", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Cardinal.lt_omega_iff_card_lt", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.preBeth", "kind": "definition", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.preBeth_strictMono", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": true, "tactics": ["intro", "conv_rhs", "rw", "exact"], "tactic_count": 4}
{"name": "Cardinal.preBeth_mono", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.preAleph_le_preBeth", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.preBeth_lt_preBeth", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.preBeth_le_preBeth", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.preBeth_inj", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.preBeth_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Cardinal.preBeth_succ", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Cardinal.preBeth_limit", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": true, "tactics": ["rw", "apply", "rw", "intro", "rw", "exact"], "tactic_count": 6}
{"name": "Cardinal.isNormal_preBeth", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp"], "tactic_count": 3}
{"name": "Cardinal.preBeth_nat", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.preBeth_one", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Cardinal.preBeth_omega", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": true, "tactics": ["apply", "rw", "rintro", "obtain", "rw", "exact", "simpa"], "tactic_count": 7}
{"name": "Cardinal.preBeth_pos", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Ordinal.card_le_preBeth", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.le_preBeth_ord", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Cardinal.preBeth_eq_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Cardinal.isStrongLimit_preBeth", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": true, "tactics": ["by_cases", "refine", "rw", "rcases", "have", "rw", "exact", "apply", "rw", "obtain", "simp", "intro", "simpa"], "tactic_count": 13}
{"name": "Cardinal.lift_preBeth", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": true, "tactics": ["induction", "succ", "isSuccPrelimit", "rw", "apply", "ext", "constructor", "refine", "simpa", "obtain", "rw", "exact"], "tactic_count": 12}
{"name": "Cardinal.beth", "kind": "definition", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.termℶ_", "kind": "definition", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal._aux_Mathlib_SetTheory_Cardinal_Aleph___macroRules_Cardinal_termℶ__1", "kind": "definition", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal._aux_Mathlib_SetTheory_Cardinal_Aleph___unexpand_Cardinal_beth_1", "kind": "definition", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.beth_eq_preBeth", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.preBeth_le_beth", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.beth_strictMono", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.beth_mono", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.beth_lt_beth", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.beth_le_beth", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.beth_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Cardinal.beth_succ", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Cardinal.isNormal_beth", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.beth_limit", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.aleph_le_beth", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.aleph0_le_beth", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.beth_pos", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.beth_ne_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.card_le_beth", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.le_beth_ord", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Cardinal.isStrongLimit_beth", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.lift_beth", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Aleph", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.mul_eq_self", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": false, "tactics": ["refine", "le_antisymm", "refine", "rcases", "classical", "letI", "haveI", "let", "let", "let", "f", "haveI", "suffices", "refine", "rcases", "rw", "refine", "have", "intro", "simp", "exact", "suffices", "refine", "apply", "rcases", "exact", "suffices", "rw", "apply", "rw", "apply"], "tactic_count": 31}
{"name": "Cardinal.mul_eq_max", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mul_mk_eq_max", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.aleph_mul_aleph", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.aleph0_mul_eq", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mul_aleph0_eq", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.aleph0_mul_mk_eq", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_mul_aleph0_eq", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.aleph0_mul_aleph", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.aleph_mul_aleph0", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mul_lt_of_lt", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mul_le_max_of_aleph0_le_left", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["convert", "rw", "exact"], "tactic_count": 3}
{"name": "Cardinal.mul_eq_max_of_aleph0_le_left", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["rcases", "exact", "refine", "have", "rw", "convert", "rw"], "tactic_count": 7}
{"name": "Cardinal.mul_le_max_of_aleph0_le_right", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Cardinal.mul_eq_max_of_aleph0_le_right", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Cardinal.mul_eq_max'", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["rcases", "exact", "exact"], "tactic_count": 3}
{"name": "Cardinal.mul_le_max", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "rcases", "rw", "exact", "rcases", "rw", "exact", "exact"], "tactic_count": 9}
{"name": "Cardinal.mul_eq_left", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.mul_eq_right", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.le_mul_left", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "Cardinal.le_mul_right", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Cardinal.mul_eq_left_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["rw", "refine", "rcases", "have", "rintro", "exact", "left", "rw", "use", "constructor", "rw", "exact", "rintro", "apply", "rw", "exact", "right", "by_cases", "exact", "have", "rintro", "apply", "rw", "exact", "left", "rw", "rcases", "contradiction", "contradiction", "rw", "rw", "norm_cast", "apply", "rw", "apply", "conv_rhs", "rw", "exact", "apply", "rintro", "rw", "all_goals"], "tactic_count": 42}
{"name": "Cardinal.add_eq_self", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.add_eq_max", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.add_eq_max'", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.add_mk_eq_max", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.add_mk_eq_max'", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.add_mk_eq_self", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Cardinal.add_le_max", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["rcases", "rw", "exact", "rcases", "rw", "exact", "exact"], "tactic_count": 7}
{"name": "Cardinal.add_le_of_le", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.add_lt_of_lt", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.eq_of_add_eq_of_aleph0_le", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["apply", "rw", "apply", "rw", "have", "simp"], "tactic_count": 6}
{"name": "Cardinal.add_eq_left", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.add_eq_right", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.add_eq_left_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["rw", "refine", "rcases", "left", "use", "rw", "apply", "intro", "exact", "right", "rw", "rcases", "norm_cast", "rw", "rintro", "rw", "rw"], "tactic_count": 17}
{"name": "Cardinal.add_eq_right_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.add_nat_eq", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.nat_add_eq", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.add_one_eq", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_add_one_eq", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.eq_of_add_eq_add_left", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["rcases", "have", "rw", "rw", "have", "rw", "intro", "apply", "apply", "rw", "apply", "rw", "rcases", "rcases", "rcases", "norm_cast", "apply"], "tactic_count": 17}
{"name": "Cardinal.eq_of_add_eq_add_right", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Cardinal.ciSup_add", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["have", "refine", "have", "obtain", "obtain", "exact", "rw", "exact"], "tactic_count": 8}
{"name": "Cardinal.add_ciSup", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.ciSup_add_ciSup", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Cardinal.ciSup_mul", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["cases", "obtain", "by_cases", "have", "hf", "simp", "have", "refine", "have", "obtain", "obtain", "exact", "rw", "obtain", "exact"], "tactic_count": 15}
{"name": "Cardinal.mul_ciSup", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.ciSup_mul_ciSup", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Cardinal.sum_eq_lift_iSup_of_lift_mk_le_lift_iSup", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["rw", "apply", "convert", "rw", "lift_iSup"], "tactic_count": 5}
{"name": "Cardinal.sum_eq_iSup_of_lift_mk_le_iSup", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["rw", "apply", "rwa"], "tactic_count": 3}
{"name": "Cardinal.sum_eq_iSup_of_mk_le_iSup", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.aleph_add_aleph", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.add_right_inj_of_lt_aleph0", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.add_nat_inj", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.add_one_inj", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.add_le_add_iff_of_lt_aleph0", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["refine", "contrapose", "rw", "exact"], "tactic_count": 4}
{"name": "Cardinal.add_nat_le_add_nat_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.add_one_le_add_one_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.pow_le", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.pow_eq", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.power_self_eq", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["apply", "exact", "rw"], "tactic_count": 3}
{"name": "Cardinal.prod_eq_two_power", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["rw", "apply", "refine", "rw", "rw", "refine", "rw", "exact"], "tactic_count": 8}
{"name": "Cardinal.power_eq_two_power", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.nat_power_eq", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.power_nat_le", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.power_nat_eq", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.power_nat_le_max", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["rcases", "exact", "exact"], "tactic_count": 3}
{"name": "Cardinal.power_le_aleph0", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["lift"], "tactic_count": 1}
{"name": "Cardinal.powerlt_aleph0", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["apply", "rw", "intro", "rw", "rintro", "apply", "convert"], "tactic_count": 7}
{"name": "Cardinal.powerlt_aleph0_le", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["rcases", "rw", "apply", "rw", "exact"], "tactic_count": 5}
{"name": "Cardinal.mk_equiv_eq_zero_iff_lift_ne", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.mk_equiv_eq_zero_iff_ne", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.mk_equiv_comm", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_embedding_eq_zero_iff_lift_lt", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.mk_embedding_eq_zero_iff_lt", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.mk_arrow_eq_zero_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Cardinal.mk_surjective_eq_zero_iff_lift", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["contrapose", "rw", "simp_rw", "nonempty_fun]"], "tactic_count": 4}
{"name": "Cardinal.mk_surjective_eq_zero_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.mk_equiv_le_embedding", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_embedding_le_arrow", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_perm_eq_self_power", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_perm_eq_two_power", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.mk_equiv_eq_arrow_of_lift_eq", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["obtain", "have", "have", "rw", "rw"], "tactic_count": 5}
{"name": "Cardinal.mk_equiv_eq_arrow_of_eq", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_equiv_of_lift_eq", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["erw", "mk_perm_eq_two_power,", "rfl"], "tactic_count": 3}
{"name": "Cardinal.mk_equiv_of_eq", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.mk_embedding_eq_arrow_of_lift_le", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_embedding_eq_arrow_of_le", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_surjective_eq_arrow_of_lift_le", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_surjective_eq_arrow_of_le", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_list_eq_mk", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_list_eq_aleph0", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_list_eq_max", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["cases", "rw", "exact", "rw", "exact"], "tactic_count": 5}
{"name": "Cardinal.mk_list_eq_max_mk_aleph0", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.sum_pow_eq_max_aleph0", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["have", "conv_lhs"], "tactic_count": 2}
{"name": "Cardinal.mk_list_le_max", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["cases", "exact", "rw", "apply"], "tactic_count": 4}
{"name": "Cardinal.sum_pow_le_max_aleph0", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Cardinal.mk_finset_of_infinite", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["classical", "exact", "le_antisymm", "calc"], "tactic_count": 4}
{"name": "Cardinal.mk_bounded_set_le_of_infinite", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["rw", "induction", "fapply", "intro", "use", "refine", "apply", "rintro", "classical", "use", "apply", "constructor", "rintro", "dsimp", "by_cases", "rw", "cases", "exact", "rw", "cases", "intro", "have", "use", "dsimp", "rw", "congr", "suffices", "apply", "exact"], "tactic_count": 29}
{"name": "Cardinal.mk_bounded_set_le", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["trans", "refine", "apply", "use", "apply", "intro", "exact", "apply", "rw"], "tactic_count": 9}
{"name": "Cardinal.mk_bounded_subset_le", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["refine", "refine", "use", "rintro", "apply", "dsimp", "refine", "rintro"], "tactic_count": 8}
{"name": "Cardinal.mk_compl_of_infinite", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "Cardinal.mk_compl_finset_of_infinite", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["apply", "exact"], "tactic_count": 2}
{"name": "Cardinal.mk_compl_eq_mk_compl_infinite", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.mk_compl_eq_mk_compl_finite_lift", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["cases", "rcases", "replace", "classical", "lift", "lift", "simp", "simp"], "tactic_count": 8}
{"name": "Cardinal.mk_compl_eq_mk_compl_finite", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "Cardinal.mk_compl_eq_mk_compl_finite_same", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.extend_function", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["classical", "have", "let", "refine"], "tactic_count": 4}
{"name": "Cardinal.extend_function_finite", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["apply", "rw", "rw", "rw"], "tactic_count": 4}
{"name": "Cardinal.extend_function_of_lt", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Arithmetic", "is_tactic_proof": true, "tactics": ["cases", "exact", "apply", "obtain", "haveI", "rw", "rwa", "rwa"], "tactic_count": 8}
{"name": "Cardinal.mk_preimage_down", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["rw", "constructor", "let", "have", "exact"], "tactic_count": 5}
{"name": "Cardinal.lift_mk_shrink", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.lift_mk_shrink'", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.lift_mk_shrink''", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.prod_eq_of_fintype", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["revert", "refine", "intro", "letI", "rw", "exact", "intro", "rw", "intro", "rw", "simp"], "tactic_count": 11}
{"name": "Cardinal.le_one_iff_subsingleton", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_le_one_iff_set_subsingleton", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.one_lt_iff_nontrivial", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.sInf_eq_zero_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["refine", "rcases", "exact", "exact", "rcases", "exact", "exact"], "tactic_count": 7}
{"name": "Cardinal.iInf_eq_zero_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Cardinal.iSup_of_empty", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.lift_sInf", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["rcases", "simp", "exact"], "tactic_count": 3}
{"name": "Cardinal.lift_iInf", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["unfold", "convert", "simp_rw"], "tactic_count": 3}
{"name": "Cardinal.small_Iic", "kind": "instance", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply", "rintro", "simpa"], "tactic_count": 4}
{"name": "Cardinal.small_Iio", "kind": "instance", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.small_Icc", "kind": "instance", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.small_Ico", "kind": "instance", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.small_Ioc", "kind": "instance", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.small_Ioo", "kind": "instance", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.bddAbove_iff_small", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.bddAbove_of_small", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.bddAbove_range", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.bddAbove_image", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Cardinal.bddAbove_range_comp", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "not_small_cardinal", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["intro", "have", "rw", "exact"], "tactic_count": 4}
{"name": "Cardinal.uncountable", "kind": "instance", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.sum_le_lift_mk_mul_iSup_lift", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": ["rw", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "Cardinal.sum_le_lift_mk_mul_iSup", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Cardinal.sum_le_mk_mul_iSup", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Cardinal.lift_sSup", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["apply", "intro", "by_contra", "obtain", "simp_rw", "rw", "exact", "rintro", "exact"], "tactic_count": 9}
{"name": "Cardinal.lift_iSup", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Cardinal.lift_iSup_le", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Cardinal.lift_iSup_le_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Cardinal.lift_iSup_le_lift_iSup", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Cardinal.lift_iSup_le_lift_iSup'", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.lift_iSup_le_sum", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Cardinal.mk_finset_of_fintype", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Cardinal.nat_succ", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "Cardinal.succ_natCast", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["rw", "norm_cast"], "tactic_count": 2}
{"name": "Cardinal.natCast_add_one_le_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.two_le_iff_one_lt", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["convert", "norm_cast"], "tactic_count": 2}
{"name": "Cardinal.succ_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["norm_cast"], "tactic_count": 1}
{"name": "Cardinal.one_lt_two", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["norm_cast"], "tactic_count": 1}
{"name": "Cardinal.exists_finset_eq_card", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["obtain", "let", "obtain", "exact", "obtain", "exact"], "tactic_count": 6}
{"name": "Cardinal.exists_finset_le_card", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.card_le_of", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["contrapose", "apply", "simpa"], "tactic_count": 3}
{"name": "Cardinal.cantor'", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Cardinal.one_le_iff_pos", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.one_le_iff_ne_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.lt_one_iff_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Cardinal.natCast_lt_aleph0", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Cardinal.nat_lt_aleph0", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.natCast_le_aleph0", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.ofNat_lt_aleph0", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.ofNat_le_aleph0", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.one_lt_aleph0", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Cardinal.one_le_aleph0", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.lt_aleph0", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.succ_eq_of_lt_aleph0", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["obtain", "rw"], "tactic_count": 2}
{"name": "Cardinal.aleph0_le", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.isSuccPrelimit_aleph0", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.isSuccLimit_aleph0", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Cardinal.not_isSuccLimit_natCast", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.not_isSuccLimit_of_lt_aleph0", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Cardinal.aleph0_le_of_isSuccLimit", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["contrapose", "exact"], "tactic_count": 2}
{"name": "Cardinal.isStrongLimit_aleph0", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact"], "tactic_count": 3}
{"name": "Cardinal.IsStrongLimit.aleph0_le", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.exists_eq_natCast_of_iSup_eq", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.range_natCast", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_eq_nat_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.lt_aleph0_iff_finite", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Cardinal.lt_aleph0_iff_fintype", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.lt_aleph0_of_finite", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.lt_aleph0_iff_set_finite", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.lt_aleph0_iff_subtype_finite", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_le_aleph0_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.mk_le_aleph0", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.le_aleph0_iff_set_countable", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.le_aleph0_iff_subtype_countable", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.aleph0_lt_mk_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.aleph0_lt_mk", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.canLiftCardinalNat", "kind": "instance", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.add_lt_aleph0", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.add_lt_aleph0_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.aleph0_le_add_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Cardinal.nsmul_lt_aleph0_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.nsmul_lt_aleph0_iff_of_ne_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mul_lt_aleph0", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mul_lt_aleph0_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["refine", "by_cases", "exact", "right", "by_cases", "exact", "right", "rw", "constructor", "rw", "exact", "rw", "exact", "rintro"], "tactic_count": 14}
{"name": "Cardinal.aleph0_le_mul_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["let", "rwa"], "tactic_count": 2}
{"name": "Cardinal.aleph0_le_mul_iff'", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["have", "simp", "simp"], "tactic_count": 3}
{"name": "Cardinal.mul_lt_aleph0_iff_of_ne_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Cardinal.power_lt_aleph0", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.eq_one_iff_unique", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.infinite_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.aleph0_le_mk_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_lt_aleph0_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Cardinal.mk_lt_aleph0", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.aleph0_le_mk", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_eq_aleph0", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.denumerable_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_denumerable", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.countable_infinite_iff_nonempty_denumerable", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.aleph0_add_aleph0", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.aleph0_mul_aleph0", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.nat_mul_aleph0", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.aleph0_mul_nat", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.ofNat_mul_aleph0", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.aleph0_mul_ofNat", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.add_le_aleph0", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.aleph0_add_nat", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.nat_add_aleph0", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.ofNat_add_aleph0", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.aleph0_add_ofNat", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.exists_nat_eq_of_le_nat", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["lift", "exact"], "tactic_count": 2}
{"name": "Cardinal.mk_int", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_pnat", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_additive", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_multiplicative", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_mulOpposite", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_singleton", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_vector", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_list_eq_sum_pow", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.sum_zero_pow", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.mk_quot_le", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_quotient_le", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_subtype_le_of_subset", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_le_mk_of_subset", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_emptyCollection", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_emptyCollection_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.mk_set_ne_zero_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.mk_univ", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_setProd", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.mk_image_le", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_image2_le", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Cardinal.mk_image_le_lift", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_range_le", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_range_le_lift", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_range_eq", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_range_eq_of_injective", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_range_eq_lift", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.lift_mk_le_lift_mk_of_injective", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Cardinal.lift_mk_le_lift_mk_of_surjective", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_image_eq_of_injOn", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_image_eq_of_injOn_lift", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_image_eq", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_image_eq_lift", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_image_embedding_lift", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_image_embedding", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Cardinal.iSup_mk_le_mk_iUnion", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_iUnion_le_sum_mk", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_iUnion_le_sum_mk_lift", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_iUnion_eq_sum_mk", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_iUnion_eq_sum_mk_lift", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_iUnion_le", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_iUnion_le_lift", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "Cardinal.mk_sUnion_le", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "Cardinal.mk_biUnion_le", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "Cardinal.mk_biUnion_le_lift", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "Cardinal.finset_card_lt_aleph0", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_set_eq_nat_iff_finset", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["constructor", "intro", "lift", "simpa", "rintro", "exact"], "tactic_count": 6}
{"name": "Cardinal.mk_eq_nat_iff_finset", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.mk_eq_nat_iff_fintype", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["rw", "constructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 6}
{"name": "Cardinal.mk_union_add_mk_inter", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Cardinal.mk_union_le", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_union_of_disjoint", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Cardinal.mk_insert", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "Cardinal.mk_insert_le", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "rw"], "tactic_count": 3}
{"name": "Cardinal.mk_sum_compl", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Cardinal.mk_le_iff_forall_finset_subset_card_le", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["refine", "apply", "classical", "let", "have", "grind"], "tactic_count": 6}
{"name": "Cardinal.mk_subtype_mono", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.le_mk_diff_add_mk", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_diff_add_mk", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "Cardinal.diff_nonempty_of_mk_lt_mk", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["rw", "intro", "exact"], "tactic_count": 3}
{"name": "Cardinal.compl_nonempty_of_mk_lt_mk", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "Cardinal.mk_union_le_aleph0", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Cardinal.mk_sep", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_preimage_of_injective_lift", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["rw", "use", "apply"], "tactic_count": 3}
{"name": "Cardinal.mk_preimage_of_subset_range_lift", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["rw", "nth_rewrite", "apply"], "tactic_count": 3}
{"name": "Cardinal.mk_preimage_of_injective_of_subset_range_lift", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_preimage_of_injective_of_subset_range", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "Cardinal.mk_preimage_equiv_lift", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["apply", "rw", "exact"], "tactic_count": 3}
{"name": "Cardinal.mk_preimage_equiv", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Cardinal.mk_preimage_of_injective", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Cardinal.mk_preimage_of_subset_range", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Cardinal.mk_subset_ge_of_subset_image_lift", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["rw", "convert", "rw", "rfl"], "tactic_count": 4}
{"name": "Cardinal.mk_subset_ge_of_subset_image", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["rw", "convert", "rw", "rfl"], "tactic_count": 4}
{"name": "Cardinal.le_mk_iff_exists_subset", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "Cardinal.mk_range_inl", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.mk_range_inr", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.two_le_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.two_le_iff'", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.mk_eq_two_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["classical", "simp", "constructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 7}
{"name": "Cardinal.mk_eq_two_iff'", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["rw", "rintro", "simp", "rcases", "exacts", "rintro", "exact"], "tactic_count": 7}
{"name": "Cardinal.exists_notMem_of_length_lt", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["classical", "contrapose", "calc"], "tactic_count": 3}
{"name": "Cardinal.three_le", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["have", "have", "have", "simpa"], "tactic_count": 4}
{"name": "Cardinal.powerlt", "kind": "definition", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.term_^<_", "kind": "definition", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal._aux_Mathlib_SetTheory_Cardinal_Basic___macroRules_Cardinal_term_^<__1", "kind": "definition", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal._aux_Mathlib_SetTheory_Cardinal_Basic___unexpand_Cardinal_powerlt_1", "kind": "definition", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.le_powerlt", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "Cardinal.powerlt_le", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp", "rw", "exact"], "tactic_count": 4}
{"name": "Cardinal.powerlt_le_powerlt_left", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.powerlt_mono_left", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.powerlt_succ", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.powerlt_min", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.powerlt_max", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.zero_powerlt", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["apply", "rw", "exact"], "tactic_count": 3}
{"name": "Cardinal.powerlt_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Basic", "is_tactic_proof": true, "tactics": ["convert", "exact"], "tactic_count": 2}
{"name": "Order.cof", "kind": "definition", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.SetTheory.Cardinal.Cofinality.0.Order.cof_nonempty", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.cof_le", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.le_cof", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": true, "tactics": ["rw", "use", "rintro", "exact"], "tactic_count": 4}
{"name": "_private.Mathlib.SetTheory.Cardinal.Cofinality.0.RelIso.cof_le_lift", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": true, "tactics": ["rw", "rintro", "apply", "refine", "rcases", "refine", "rwa"], "tactic_count": 7}
{"name": "RelIso.cof_eq_lift", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelIso.cof_eq", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.cof", "kind": "definition", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.cof_type", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.cof_type_lt", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordinal.cof_eq_cof_toType", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": true, "tactics": ["conv_lhs"], "tactic_count": 1}
{"name": "Ordinal.le_cof_type", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.cof_type_le", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.lt_cof_type", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Ordinal.cof_eq", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.ord_cof_eq", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": true, "tactics": ["let", "let", "let", "suffices", "refine", "rw", "refine", "let", "aS⟩", "rcases", "rcases", "change", "refine", "exact", "intro", "injection", "subst", "exact", "intro", "have", "let", "let", "have", "refine", "rw", "exact"], "tactic_count": 26}
{"name": "_private.Mathlib.SetTheory.Cardinal.Cofinality.0.Ordinal.card_mem_cof", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.cof_lsub_def_nonempty", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.cof_eq_sInf_lsub", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": true, "tactics": ["refine", "rintro", "rw", "refine", "let", "rwa", "have", "simp_rw", "obtain", "refine", "rw", "apply", "rw", "exact", "rwa", "rcases", "let", "refine", "rwa", "rw", "rcases", "rw", "exact"], "tactic_count": 23}
{"name": "Ordinal.lift_cof", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": true, "tactics": ["refine", "rw", "apply", "simp"], "tactic_count": 4}
{"name": "Ordinal.cof_le_card", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Ordinal.cof_ord_le", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Ordinal.ord_cof_le", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.exists_lsub_cof", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Ordinal.cof_lsub_le", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Ordinal.cof_lsub_le_lift", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": true, "tactics": ["rw", "convert", "exact", "lsub_eq_of_range_eq."], "tactic_count": 4}
{"name": "Ordinal.le_cof_iff_lsub", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": true, "tactics": ["rw", "exact", "rw", "exact"], "tactic_count": 4}
{"name": "Ordinal.lsub_lt_ord_lift", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.lsub_lt_ord", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.cof_iSup_le_lift", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "Ordinal.cof_iSup_le", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Ordinal.iSup_lt_ord_lift", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.iSup_lt_ord", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.iSup_lt_lift", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "apply"], "tactic_count": 4}
{"name": "Ordinal.iSup_lt", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.nfpFamily_lt_ord_lift", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": true, "tactics": ["refine", "rw", "apply", "rwa", "induction", "nil", "cons"], "tactic_count": 7}
{"name": "Ordinal.nfpFamily_lt_ord", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.nfp_lt_ord", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.exists_blsub_cof", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "rw", "rw", "exact"], "tactic_count": 5}
{"name": "Ordinal.le_cof_iff_blsub", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.cof_blsub_le_lift", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Ordinal.cof_blsub_le", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Ordinal.blsub_lt_ord_lift", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.blsub_lt_ord", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.cof_bsup_le_lift", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "Ordinal.cof_bsup_le", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Ordinal.bsup_lt_ord_lift", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.bsup_lt_ord", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.cof_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "Ordinal.cof_eq_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.cof_ne_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.cof_succ", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": true, "tactics": ["apply", "refine", "change", "rw", "apply", "refine", "rcases", "simp", "rw", "simpa", "succ_ne_zero"], "tactic_count": 11}
{"name": "Ordinal.cof_eq_one_iff_is_succ", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.IsFundamentalSequence", "kind": "definition", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.IsFundamentalSequence.cof_eq", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.IsFundamentalSequence.strict_mono", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.IsFundamentalSequence.blsub_eq", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.IsFundamentalSequence.ord_cof", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": true, "tactics": ["have", "subst", "exact"], "tactic_count": 3}
{"name": "Ordinal.IsFundamentalSequence.id_of_le_cof", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.IsFundamentalSequence.zero", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.IsFundamentalSequence.succ", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": true, "tactics": ["refine", "rw", "rw", "rw", "exact"], "tactic_count": 5}
{"name": "Ordinal.IsFundamentalSequence.monotone", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": true, "tactics": ["rcases", "exact", "rfl"], "tactic_count": 3}
{"name": "Ordinal.IsFundamentalSequence.trans", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact", "rw", "exact", "exact"], "tactic_count": 6}
{"name": "Ordinal.IsFundamentalSequence.lt", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.exists_fundamental_sequence", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": false, "tactics": ["suffices", "rcases", "exact", "rcases", "rcases", "let", "let", "haveI", "refine", "le_antisymm", "rw", "change", "rwa", "rw", "intro", "suffices", "rcases", "exact", "by_cases", "refine", "rw", "obtain", "refine", "by_contra", "exact", "rwa"], "tactic_count": 26}
{"name": "Ordinal.cof_cof", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "exact"], "tactic_count": 3}
{"name": "Ordinal.IsFundamentalSequence.of_isNormal", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": true, "tactics": ["refine", "rcases", "rw", "suffices", "rw", "apply", "have", "have", "rw", "simpa", "refine", "rcases", "exact", "have", "rw", "obtain", "rcases", "exact", "rw", "exact"], "tactic_count": 20}
{"name": "Ordinal.cof_eq_of_isNormal", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.cof_le_of_isNormal", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": true, "tactics": ["rcases", "rw", "exact", "rw", "exact", "rw"], "tactic_count": 6}
{"name": "Ordinal.cof_add", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.aleph0_le_cof", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simp", "simp", "refine", "obtain", "have", "rw", "cases", "apply", "simpa", "rw", "rw", "rcases", "exact"], "tactic_count": 15}
{"name": "Ordinal.cof_preOmega", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "exact"], "tactic_count": 3}
{"name": "Ordinal.cof_omega", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.cof_omega0", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.cof_eq'", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.cof_univ", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_bounded_subset", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": true, "tactics": ["rcases", "rw", "haveI", "rw", "constructor", "rintro", "exact", "have", "have", "apply", "have", "rw", "refine", "mk_iUnion_le_sum_mk.trans", "rw", "apply", "intro", "rw", "apply", "rw", "apply", "refine", "apply", "rw", "apply", "intro", "simpa"], "tactic_count": 27}
{"name": "Cardinal.mk_subset_mk_lt_cof", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": true, "tactics": ["rcases", "simp", "have", "rcases", "apply", "conv_rhs", "apply", "intro", "rw", "exact", "refine", "rw", "exact", "intro", "simpa"], "tactic_count": 15}
{"name": "Cardinal.unbounded_of_unbounded_sUnion", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": true, "tactics": ["by_contra", "simp_rw", "let", "refine", "rcases", "exact"], "tactic_count": 6}
{"name": "Cardinal.unbounded_of_unbounded_iUnion", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": true, "tactics": ["rw", "rcases", "exact"], "tactic_count": 3}
{"name": "Cardinal.lt_power_cof", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.lt_cof_power", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Cofinality", "is_tactic_proof": true, "tactics": ["have", "apply", "rw", "exact"], "tactic_count": 4}
{"name": "Cardinal.continuum", "kind": "definition", "module": "Mathlib.SetTheory.Cardinal.Continuum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.term𝔠", "kind": "definition", "module": "Mathlib.SetTheory.Cardinal.Continuum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal._aux_Mathlib_SetTheory_Cardinal_Continuum___macroRules_Cardinal_term𝔠_1", "kind": "definition", "module": "Mathlib.SetTheory.Cardinal.Continuum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal._aux_Mathlib_SetTheory_Cardinal_Continuum___unexpand_Cardinal_continuum_1", "kind": "definition", "module": "Mathlib.SetTheory.Cardinal.Continuum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.two_power_aleph0", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Continuum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.lift_continuum", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Continuum", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.continuum_le_lift", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Continuum", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.lift_le_continuum", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Continuum", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.continuum_lt_lift", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Continuum", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.lift_lt_continuum", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Continuum", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.aleph0_lt_continuum", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Continuum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.aleph0_le_continuum", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Continuum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.beth_one", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Continuum", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Cardinal.nat_lt_continuum", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Continuum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_set_nat", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Continuum", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Cardinal.continuum_pos", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Continuum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.continuum_ne_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Continuum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.aleph_one_le_continuum", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Continuum", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Cardinal.continuum_toNat", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Continuum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.continuum_toENat", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Continuum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.aleph0_add_continuum", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Continuum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.continuum_add_aleph0", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Continuum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.continuum_add_self", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Continuum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.nat_add_continuum", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Continuum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.continuum_add_nat", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Continuum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.ofNat_add_continuum", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Continuum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.continuum_add_ofNat", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Continuum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.continuum_mul_self", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Continuum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.continuum_mul_aleph0", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Continuum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.aleph0_mul_continuum", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Continuum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.nat_mul_continuum", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Continuum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.continuum_mul_nat", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Continuum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.ofNat_mul_continuum", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Continuum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.continuum_mul_ofNat", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Continuum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.aleph0_power_aleph0", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Continuum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.nat_power_aleph0", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Continuum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.continuum_power_aleph0", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Continuum", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.power_aleph0_of_le_continuum", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Continuum", "is_tactic_proof": true, "tactics": ["apply", "rw", "exact", "rw", "exact"], "tactic_count": 5}
{"name": "Cardinal.mk_subtype_le_of_countable_eventually_mem_aux", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.CountableCover", "is_tactic_proof": true, "tactics": ["rcases", "obtain", "apply", "have", "have", "rcases", "have", "let", "have", "have", "exact", "have", "exact", "have", "intro", "obtain", "exact", "calc"], "tactic_count": 18}
{"name": "Cardinal.mk_subtype_le_of_countable_eventually_mem", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.CountableCover", "is_tactic_proof": true, "tactics": ["let", "suffices", "let", "have", "apply", "intro", "simpa", "intro", "simpa"], "tactic_count": 9}
{"name": "Cardinal.mk_le_of_countable_eventually_mem", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.CountableCover", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Cardinal.mk_of_countable_eventually_mem", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.CountableCover", "is_tactic_proof": true, "tactics": ["apply", "apply", "obtain", "rw", "exact"], "tactic_count": 5}
{"name": "Cardinal.isEquivalent", "kind": "instance", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal", "kind": "definition", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Cardinal.term#_", "kind": "definition", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal._aux_Mathlib_SetTheory_Cardinal_Defs___macroRules_Cardinal_term#__1", "kind": "definition", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal._aux_Mathlib_SetTheory_Cardinal_Defs___unexpand_Cardinal_mk_1", "kind": "definition", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.canLiftCardinalType", "kind": "instance", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.inductionOn", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.inductionOn₂", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.inductionOn₃", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.induction_on_pi", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.eq", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_out", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.outMkEquiv", "kind": "definition", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_congr", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.map", "kind": "definition", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.map_mk", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.map₂", "kind": "definition", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.lift", "kind": "definition", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_uLift", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.lift_umax", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Cardinal.lift_uzero", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Cardinal.out_lift_equiv", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Cardinal.lift_mk_eq", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Cardinal.mk_congr_lift", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.instZero", "kind": "instance", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.instInhabited", "kind": "instance", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_eq_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Cardinal.mk_eq_zero_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_ne_zero_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Cardinal.nonempty_out", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Cardinal.instOne", "kind": "instance", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.instNontrivial", "kind": "instance", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_eq_one", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.instAdd", "kind": "instance", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.add_def", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.instNatCast", "kind": "instance", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_sum", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_option", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.mk_psum", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.instMul", "kind": "instance", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mul_def", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_prod", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.instPowCardinal", "kind": "instance", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.power_def", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_arrow", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.lift_power", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.power_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.power_one", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.power_add", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.one_power", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.zero_power", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.power_ne_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mul_power", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.lift_one", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.lift_add", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.sum", "kind": "definition", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_sigma", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_sigma_congr_lift", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_sigma_congr", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_sigma_congr'", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_sigma_congrRight", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_psigma_congrRight", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_psigma_congrRight_prop", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_sigma_arrow", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.sum_const", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.sum_const'", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Cardinal.lift_sum", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.sum_nat_eq_add_sum_succ", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": true, "tactics": ["refine", "simp"], "tactic_count": 2}
{"name": "Cardinal.prod", "kind": "definition", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_pi", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_pi_congr_lift", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_pi_congr", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_pi_congr_prop", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_pi_congr'", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_pi_congrRight", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_pi_congrRight_prop", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.prod_const", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.prod_const'", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.prod_eq_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": true, "tactics": ["lift", "simp"], "tactic_count": 2}
{"name": "Cardinal.prod_ne_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Cardinal.lift_power_sum", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": true, "tactics": ["induction", "induction", "simp_rw", "apply", "refine", "refine", "refine", "exact"], "tactic_count": 8}
{"name": "Cardinal.power_sum", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Cardinal.lift_prod", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": true, "tactics": ["lift", "simp", "exact"], "tactic_count": 3}
{"name": "Cardinal.aleph0", "kind": "definition", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.termℵ₀", "kind": "definition", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal._aux_Mathlib_SetTheory_Cardinal_Defs___macroRules_Cardinal_termℵ₀_1", "kind": "definition", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal._aux_Mathlib_SetTheory_Cardinal_Defs___unexpand_Cardinal_aleph0_1", "kind": "definition", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_nat", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.aleph0_ne_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.lift_aleph0", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.lift_mk_fin", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_empty", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_pempty", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_punit", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_unit", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_plift_true", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_plift_false", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_subtype_of_equiv", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.isUnit_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Divisibility", "is_tactic_proof": false, "tactics": ["refine", "rintro", "exact", "rcases", "exact", "rw", "obtain", "rw", "exact", "exact", "apply", "intro", "rw", "exact"], "tactic_count": 14}
{"name": "Cardinal.instUniqueUnits", "kind": "instance", "module": "Mathlib.SetTheory.Cardinal.Divisibility", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.le_of_dvd", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Divisibility", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.dvd_of_le_of_aleph0_le", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Divisibility", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.prime_of_aleph0_le", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Divisibility", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact", "rcases", "rcases", "wlog", "cases", "apply_assumption", "assumption", "all_goals", "left", "have", "rwa"], "tactic_count": 13}
{"name": "Cardinal.not_irreducible_of_aleph0_le", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Divisibility", "is_tactic_proof": true, "tactics": ["rw", "refine", "simpa"], "tactic_count": 3}
{"name": "Cardinal.nat_coe_dvd_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Divisibility", "is_tactic_proof": true, "tactics": ["refine", "rintro", "have", "rw", "rcases", "iterate", "lift", "exact"], "tactic_count": 8}
{"name": "Cardinal.nat_is_prime_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Divisibility", "is_tactic_proof": true, "tactics": ["simp", "refine", "simp", "exact", "exact", "rcases", "rcases", "simp", "simp", "lift", "lift", "exact", "rcases", "have", "intro", "rw", "cases", "wlog", "apply", "rwa", "rwa", "exact"], "tactic_count": 22}
{"name": "Cardinal.is_prime_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Divisibility", "is_tactic_proof": true, "tactics": ["rcases", "simp", "lift", "simp"], "tactic_count": 4}
{"name": "Cardinal.isPrimePow_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Divisibility", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "simp", "lift", "rw", "refine", "rintro", "have", "rw", "lift", "exact"], "tactic_count": 11}
{"name": "Cardinal.ofENat", "kind": "definition", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.instCoeENat", "kind": "instance", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.ofENat_top", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.ofENat_nat", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.ofENat_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.ofENat_one", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.ofENat_ofNat", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.ofENat_strictMono", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.ofENat_lt_ofENat", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.ofENat_lt_aleph0", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.ofENat_lt_nat", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": true, "tactics": ["norm_cast"], "tactic_count": 1}
{"name": "Cardinal.ofENat_lt_ofNat", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.nat_lt_ofENat", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": true, "tactics": ["norm_cast"], "tactic_count": 1}
{"name": "Cardinal.ofENat_pos", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": true, "tactics": ["norm_cast"], "tactic_count": 1}
{"name": "Cardinal.one_lt_ofENat", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": true, "tactics": ["norm_cast"], "tactic_count": 1}
{"name": "Cardinal.ofNat_lt_ofENat", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.ofENat_mono", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.ofENat_le_ofENat", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.ofENat_le_aleph0", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.ofENat_le_nat", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": true, "tactics": ["norm_cast"], "tactic_count": 1}
{"name": "Cardinal.ofENat_le_one", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": true, "tactics": ["norm_cast"], "tactic_count": 1}
{"name": "Cardinal.ofENat_le_ofNat", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.nat_le_ofENat", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": true, "tactics": ["norm_cast"], "tactic_count": 1}
{"name": "Cardinal.one_le_ofENat", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": true, "tactics": ["norm_cast"], "tactic_count": 1}
{"name": "Cardinal.ofNat_le_ofENat", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.ofENat_injective", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.ofENat_inj", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.ofENat_eq_nat", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": true, "tactics": ["norm_cast"], "tactic_count": 1}
{"name": "Cardinal.nat_eq_ofENat", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": true, "tactics": ["norm_cast"], "tactic_count": 1}
{"name": "Cardinal.ofENat_eq_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": true, "tactics": ["norm_cast"], "tactic_count": 1}
{"name": "Cardinal.zero_eq_ofENat", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": true, "tactics": ["norm_cast"], "tactic_count": 1}
{"name": "Cardinal.ofENat_eq_one", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": true, "tactics": ["norm_cast"], "tactic_count": 1}
{"name": "Cardinal.one_eq_ofENat", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": true, "tactics": ["norm_cast"], "tactic_count": 1}
{"name": "Cardinal.ofENat_eq_ofNat", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.ofNat_eq_ofENat", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.lift_ofENat", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.lift_lt_ofENat", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.lift_le_ofENat", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.lift_eq_ofENat", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.ofENat_lt_lift", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.ofENat_le_lift", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.ofENat_eq_lift", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.range_ofENat", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": true, "tactics": ["refine", "rcases", "lift", "exact", "exact"], "tactic_count": 5}
{"name": "Cardinal.instCanLiftENatOfENatLeAleph0", "kind": "instance", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.toENatAux", "kind": "definition", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.toENatAux_nat", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.toENatAux_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.toENatAux_eq_top", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.toENatAux_ofENat", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.toENatAux_gc", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.toENatAux_le_nat", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": true, "tactics": ["cases", "inl", "inr"], "tactic_count": 3}
{"name": "Cardinal.toENatAux_eq_nat", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Cardinal.toENatAux_eq_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.toENat", "kind": "definition", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.enat_gc", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.toENat_ofENat", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.toENat_comp_ofENat", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.gciENat", "kind": "definition", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.toENat_strictMonoOn", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Cardinal.toENat_injOn", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.ofENat_toENat_le", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.ofENat_toENat_eq_self", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "Cardinal.toENat_nat", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.toENat_le_nat", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.toENat_eq_nat", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.toENat_eq_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.toENat_le_one", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.toENat_eq_one", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.toENat_le_ofNat", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.toENat_eq_ofNat", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.toENat_eq_top", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.toENat_ne_top", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Cardinal.toENat_lt_top", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Cardinal.toENat_lift", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": true, "tactics": ["cases", "inl", "inr"], "tactic_count": 3}
{"name": "Cardinal.toENat_congr", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.toENat_le_iff_of_le_aleph0", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": true, "tactics": ["lift", "simp_rw"], "tactic_count": 2}
{"name": "Cardinal.toENat_le_iff_of_lt_aleph0", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": true, "tactics": ["lift", "simp_rw"], "tactic_count": 2}
{"name": "Cardinal.toENat_eq_iff_of_le_aleph0", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.ofENat_add", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "Cardinal.aleph0_add_ofENat", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.ofENat_add_aleph0", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.ofENat_mul_aleph0", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": true, "tactics": ["induction", "top", "coe"], "tactic_count": 3}
{"name": "Cardinal.aleph0_mul_ofENat", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.ofENat_mul", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.ofENatHom", "kind": "definition", "module": "Mathlib.SetTheory.Cardinal.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.Embedding.exists_embedding_disjoint_range_of_add_le_ENat_card", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Embedding", "is_tactic_proof": true, "tactics": ["rsuffices", "use", "rw", "rintro", "simpa", "rcases", "let", "classical", "apply", "rwa", "ncard_add_ncard_compl,", "exact"], "tactic_count": 12}
{"name": "Fin.Embedding.exists_embedding_disjoint_range_of_add_le_Nat_card", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Embedding", "is_tactic_proof": true, "tactics": ["apply", "rwa"], "tactic_count": 2}
{"name": "Fin.Embedding.restrictSurjective_of_add_le_ENatCard", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Embedding", "is_tactic_proof": true, "tactics": ["intro", "obtain", "exists_embedding_disjoint_range_of_add_le_ENat_card", "use", "ext", "simp"], "tactic_count": 6}
{"name": "Fin.Embedding.restrictSurjective_of_le_ENatCard", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Embedding", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Fin.Embedding.restrictSurjective_of_add_le_natCard", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Embedding", "is_tactic_proof": true, "tactics": ["apply", "rwa"], "tactic_count": 2}
{"name": "Fin.Embedding.restrictSurjective_of_le_natCard", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Embedding", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Nat.card", "kind": "definition", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.card_eq_fintype_card", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fintype.card_eq_nat_card", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.card_eq_finsetCard", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.card_eq_card_toFinset", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.card_eq_card_finite_toFinset", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.subtype_card", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.card_of_isEmpty", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.card_eq_zero_of_infinite", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.cast_card", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.Infinite.card_eq_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.card_eq_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.card_ne_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.card_pos_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.card_pos", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.finite_of_card_ne_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.card_congr", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.card_le_card_of_injective", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Nat.card_le_card_of_surjective", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "Nat.card_eq_of_bijective", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.bijective_iff_injective_and_card", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": true, "tactics": ["rw", "intro", "have", "have", "revert", "rw"], "tactic_count": 6}
{"name": "Nat.bijective_iff_surjective_and_card", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": true, "tactics": ["classical", "rw", "intro", "have", "have", "revert", "rw"], "tactic_count": 7}
{"name": "Function.Injective.bijective_of_nat_card_le", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.bijective_of_nat_card_le", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.card_eq_of_equiv_fin", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Nat.card_fin", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.card_mono", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.card_image_le", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.card_image_of_injOn", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": true, "tactics": ["classical", "obtain", "have", "have", "simp_rw", "have", "have", "simp"], "tactic_count": 8}
{"name": "Nat.card_image_of_injective", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.card_image_equiv", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.card_preimage_of_injOn", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.card_preimage_of_injective", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.card_univ", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.card_range_of_injective", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Nat.equivFinOfCardPos", "kind": "definition", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": true, "tactics": ["cases", "simpa", "simp"], "tactic_count": 3}
{"name": "Nat.card_of_subsingleton", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": true, "tactics": ["letI", "rw"], "tactic_count": 2}
{"name": "Nat.card_eq_one_iff_unique", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.card_unique", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.card_eq_one_iff_exists", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Nat.card_eq_two_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.card_eq_two_iff'", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.card_subtype_true", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.card_sum", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": true, "tactics": ["have", "have", "simp_rw"], "tactic_count": 3}
{"name": "Nat.card_prod", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Nat.card_ulift", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.card_plift", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.card_sigma", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": true, "tactics": ["letI", "simp_rw"], "tactic_count": 2}
{"name": "Nat.card_pi", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Nat.card_fun", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": true, "tactics": ["haveI", "rw"], "tactic_count": 2}
{"name": "Nat.card_zmod", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": true, "tactics": ["cases", "exact", "rw"], "tactic_count": 3}
{"name": "Set.card_singleton_prod", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.card_prod_singleton", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.natCard_pos", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.natCard_graphOn", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENat.card", "kind": "definition", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.card_eq_coe_fintype_card", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENat.card_eq_top_of_infinite", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENat.card_eq_top", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENat.card_lt_top_of_finite", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENat.card_lt_top", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENat.card_sum", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENat.card_congr", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.card_ulift", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.card_plift", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.card_image_of_injOn", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.card_image_of_injective", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.card_le_card_of_injective", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Cardinal.natCast_le_toENat_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.toENat_le_natCast_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Cardinal.natCast_eq_toENat_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.toENat_eq_natCast_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Cardinal.natCast_lt_toENat_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Cardinal.toENat_lt_natCast_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENat.card_eq_zero_iff_empty", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "ENat.card_ne_zero_iff_nonempty", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENat.one_le_card_iff_nonempty", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENat.card_pos", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ENat.card_le_one_iff_subsingleton", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "ENat.card_le_one", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ENat.card_eq_one_iff_unique", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ENat.one_lt_card_iff_nontrivial", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": true, "tactics": ["rw", "conv_rhs", "rw", "simp"], "tactic_count": 4}
{"name": "ENat.one_lt_card", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ENat.card_prod", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENat.card_fun", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finite", "is_tactic_proof": true, "tactics": ["classical", "rcases", "simp", "rcases", "rcases", "letI", "letI", "simp", "simp", "exact", "rw", "rcases", "rw", "rw", "simp", "rw", "apply", "letI", "exact", "letI", "exact", "rw", "rw", "exact"], "tactic_count": 24}
{"name": "Cardinal.mk_finsupp_lift_of_fintype", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finsupp", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Cardinal.mk_finsupp_of_fintype", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finsupp", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Cardinal.mk_finsupp_lift_of_infinite", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finsupp", "is_tactic_proof": true, "tactics": ["apply", "calc", "apply", "obtain", "exact", "inhabit", "exact"], "tactic_count": 7}
{"name": "Cardinal.mk_finsupp_of_infinite", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finsupp", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Cardinal.mk_finsupp_lift_of_infinite'", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finsupp", "is_tactic_proof": true, "tactics": ["cases", "rw", "have", "rw", "exacts", "apply"], "tactic_count": 6}
{"name": "Cardinal.mk_finsupp_of_infinite'", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finsupp", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Cardinal.mk_finsupp_nat", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finsupp", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Cardinal.mk_multiset_of_isEmpty", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_multiset_of_nonempty", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finsupp", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Cardinal.mk_multiset_of_infinite", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Finsupp", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "instInfiniteFreeMonoidOfNonempty", "kind": "instance", "module": "Mathlib.SetTheory.Cardinal.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInfiniteFreeGroupOfNonempty", "kind": "instance", "module": "Mathlib.SetTheory.Cardinal.Free", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "instInfiniteFreeAbelianGroupOfNonempty", "kind": "instance", "module": "Mathlib.SetTheory.Cardinal.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInfiniteFreeRing", "kind": "instance", "module": "Mathlib.SetTheory.Cardinal.Free", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "instInfiniteFreeCommRing", "kind": "instance", "module": "Mathlib.SetTheory.Cardinal.Free", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "instCountableFreeMonoid", "kind": "instance", "module": "Mathlib.SetTheory.Cardinal.Free", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "instCountableFreeGroup", "kind": "instance", "module": "Mathlib.SetTheory.Cardinal.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCountableFreeAbelianGroup", "kind": "instance", "module": "Mathlib.SetTheory.Cardinal.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCountableFreeRing", "kind": "instance", "module": "Mathlib.SetTheory.Cardinal.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCountableFreeCommRing", "kind": "instance", "module": "Mathlib.SetTheory.Cardinal.Free", "is_tactic_proof": true, "tactics": ["unfold", "infer_instance"], "tactic_count": 2}
{"name": "Cardinal.mk_abelianization_le", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_freeMonoid", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_freeGroup", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Free", "is_tactic_proof": true, "tactics": ["classical", "apply", "apply", "simp", "obtain", "simp", "exact", "rw", "exact", "apply", "exact", "simp"], "tactic_count": 12}
{"name": "Cardinal.mk_freeAbelianGroup", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Free", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Cardinal.mk_freeRing", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Free", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Cardinal.mk_freeCommRing", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Free", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "nonempty_commRing", "kind": "instance", "module": "Mathlib.SetTheory.Cardinal.Free", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "have", "classical", "obtain", "exact", "have", "exact"], "tactic_count": 8}
{"name": "nonempty_commRing_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nonempty_ring_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nonempty_commSemiring_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nonempty_semiring_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Free", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasCardinalLT", "kind": "definition", "module": "Mathlib.SetTheory.Cardinal.HasCardinalLT", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasCardinalLT_iff_cardinal_mk_lt", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.HasCardinalLT", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HasCardinalLT.small", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.HasCardinalLT", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "simpa"], "tactic_count": 3}
{"name": "HasCardinalLT.of_le", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.HasCardinalLT", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasCardinalLT.of_injective", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.HasCardinalLT", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "rw", "exact", "lt_of_le_of_lt", "h"], "tactic_count": 6}
{"name": "HasCardinalLT.of_surjective", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.HasCardinalLT", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "rw", "exact", "lt_of_le_of_lt", "h"], "tactic_count": 6}
{"name": "hasCardinalLT_iff_of_equiv", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.HasCardinalLT", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasCardinalLT_aleph0_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.HasCardinalLT", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "hasCardinalLT_of_finite", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.HasCardinalLT", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasCardinalLT_lift_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.HasCardinalLT", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "hasCardinalLT_ulift_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.HasCardinalLT", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasCardinalLT_sum_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.HasCardinalLT", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "rintro", "dsimp", "rw", "rw", "simp", "exact"], "tactic_count": 9}
{"name": "hasCardinalLT_option_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.HasCardinalLT", "is_tactic_proof": false, "tactics": ["rw", "and_iff_left_iff_imp]", "refine", "rw", "infer_instance"], "tactic_count": 5}
{"name": "hasCardinalLT_subtype_max", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.HasCardinalLT", "is_tactic_proof": false, "tactics": ["have", "rw", "exact", "refine", "rintro", "exact", "exact"], "tactic_count": 7}
{"name": "hasCardinalLT_union", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.HasCardinalLT", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasCardinalLT_sigma'", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.HasCardinalLT", "is_tactic_proof": true, "tactics": ["simp", "rw", "exact"], "tactic_count": 3}
{"name": "hasCardinalLT_sigma", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.HasCardinalLT", "is_tactic_proof": true, "tactics": ["have", "have", "hasCardinalLT_sigma", "rw", "exact"], "tactic_count": 5}
{"name": "hasCardinalLT_subtype_iSup", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.HasCardinalLT", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasCardinalLT_iUnion", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.HasCardinalLT", "is_tactic_proof": true, "tactics": ["convert", "aesop"], "tactic_count": 2}
{"name": "hasCardinalLT_prod'", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.HasCardinalLT", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "hasCardinalLT_prod", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.HasCardinalLT", "is_tactic_proof": false, "tactics": ["have", "hasCardinalLT_prod", "simp", "exact", "this.of_surjective"], "tactic_count": 5}
{"name": "HasCardinalLT.exists_regular_cardinal", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.HasCardinalLT", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasCardinalLT.exists_regular_cardinal_forall", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.HasCardinalLT", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Nat.count_le_cardinal", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.NatCount", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Nat.count_le_setENCard", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.NatCount", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Nat.count_le_setNCard", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.NatCount", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Cardinal.instLE", "kind": "instance", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.partialOrder", "kind": "instance", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.linearOrder", "kind": "instance", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.le_def", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_le_of_injective", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.cardinal_le", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_le_of_surjective", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.le_mk_iff_exists_set", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_subtype_le", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_set_le", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.out_embedding", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": true, "tactics": ["conv_lhs"], "tactic_count": 1}
{"name": "Cardinal.lift_mk_le", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.lift_mk_le'", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.liftInitialSeg", "kind": "definition", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": true, "tactics": ["refine", "refine", "rw", "refine", "obtain", "replace", "refine", "apply", "rintro", "exact"], "tactic_count": 10}
{"name": "Cardinal.mem_range_lift_of_le", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.lift_injective", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.lift_inj", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.lift_le", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.lift_lt", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.lift_strictMono", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.lift_monotone", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.lift_min", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.lift_max", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.lift_umax_eq", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.le_lift_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.lt_lift_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.lift_eq_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_fintype", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.SetTheory.Cardinal.Order.0.Cardinal.cast_succ", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": true, "tactics": ["change", "rw", "simp"], "tactic_count": 3}
{"name": "Cardinal.commSemiring", "kind": "instance", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_bool", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Cardinal.mk_Prop", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Cardinal.power_mul", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Cardinal.power_natCast", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.lift_eq_one", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.lift_mul", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.lift_two", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Cardinal.mk_set", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Cardinal.mk_powerset", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.lift_two_power", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Cardinal.zero_le", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "_private.Mathlib.SetTheory.Cardinal.Order.0.Cardinal.add_le_add'", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "Cardinal.addLeftMono", "kind": "instance", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.addRightMono", "kind": "instance", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.canonicallyOrderedAdd", "kind": "instance", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.isOrderedRing", "kind": "instance", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.orderBot", "kind": "instance", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.noZeroDivisors", "kind": "instance", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.instCommMonoidWithZero", "kind": "instance", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.instCommMonoid", "kind": "instance", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.zero_power_le", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "rw", "apply"], "tactic_count": 4}
{"name": "Cardinal.power_le_power_left", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": true, "tactics": ["rintro", "let", "exact"], "tactic_count": 3}
{"name": "Cardinal.self_le_power", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": true, "tactics": ["rcases", "exact", "convert", "exact"], "tactic_count": 4}
{"name": "Cardinal.cantor", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": ["induction", "rw", "refine", "rintro", "exact"], "tactic_count": 5}
{"name": "Cardinal.instNoMaxOrder", "kind": "instance", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.instDistribLattice", "kind": "instance", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.power_le_max_power_one", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "exact"], "tactic_count": 3}
{"name": "Cardinal.power_le_power_right", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.power_pos", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.lt_wf", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.instWellFoundedRelation", "kind": "instance", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.instWellFoundedLT", "kind": "instance", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.instConditionallyCompleteLinearOrderBot", "kind": "instance", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.sInf_empty", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.instSuccOrder", "kind": "instance", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.succ_def", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.succ_pos", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.succ_ne_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.add_one_le_succ", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": true, "tactics": ["have", "simp_rw", "intro", "rcases", "obtain", "have", "simp", "rcases", "calc"], "tactic_count": 9}
{"name": "Cardinal.lift_succ", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.ne_zero_of_isSuccLimit", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.isSuccPrelimit_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.isSuccLimit_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.not_isSuccLimit_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.IsStrongLimit.isSuccLimit", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Cardinal.IsStrongLimit.isSuccPrelimit", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.not_isStrongLimit_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.lift_le_sum", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Cardinal.le_sum", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Cardinal.iSup_le_sum", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.sum_add_distrib", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": true, "tactics": ["have", "simp", "exact"], "tactic_count": 3}
{"name": "Cardinal.sum_add_distrib'", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.sum_le_sum", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_le_mk_mul_of_mk_preimage_le", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Cardinal.lift_mk_le_lift_mk_mul_of_lift_mk_preimage_le", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nonempty_embedding_to_cardinal", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "embeddingToCardinal", "kind": "definition", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WellOrderingRel", "kind": "definition", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WellOrderingRel.isWellOrder", "kind": "instance", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsWellOrder.subtype_nonempty", "kind": "instance", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_wellOrder", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Cardinal.exists_eq_of_iSup_eq_of_not_isSuccPrelimit", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": true, "tactics": ["subst", "suffices", "contrapose", "rw", "exact"], "tactic_count": 5}
{"name": "Cardinal.exists_eq_of_iSup_eq_of_not_isSuccLimit", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": true, "tactics": ["rw", "refine", "cases", "rw", "exact"], "tactic_count": 5}
{"name": "Cardinal.sum_lt_prod", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.prod_le_prod", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.aleph0_pos", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.aleph0_le_lift", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Cardinal.lift_le_aleph0", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Cardinal.aleph0_lt_lift", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Cardinal.lift_lt_aleph0", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Cardinal.aleph0_eq_lift", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Cardinal.lift_eq_aleph0", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Cardinal.mk_fin", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Cardinal.lift_natCast", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "Cardinal.lift_ofNat", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.lift_eq_nat_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.lift_eq_ofNat_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.nat_eq_lift_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.zero_eq_lift_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Cardinal.one_eq_lift_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Cardinal.ofNat_eq_lift_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.lift_le_nat_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.lift_le_one_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Cardinal.lift_le_ofNat_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.nat_le_lift_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.one_le_lift_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Cardinal.ofNat_le_lift_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.lift_lt_nat_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.lift_lt_ofNat_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.nat_lt_lift_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.zero_lt_lift_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Cardinal.one_lt_lift_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Cardinal.ofNat_lt_lift_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_coe_finset", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Cardinal.card_le_of_finset", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.instCharZero", "kind": "instance", "module": "Mathlib.SetTheory.Cardinal.Order", "is_tactic_proof": true, "tactics": ["refine", "rwa"], "tactic_count": 2}
{"name": "Cardinal.mk_biUnion_le_of_le_lift", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Ordinal", "is_tactic_proof": true, "tactics": ["simp_rw", "rw", "apply", "rw", "refine", "intro", "simpa"], "tactic_count": 7}
{"name": "Cardinal.mk_biUnion_le_of_le", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Ordinal", "is_tactic_proof": true, "tactics": ["apply", "rwa"], "tactic_count": 2}
{"name": "Ordinal.lift_card_iSup_le_sum_card", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Ordinal", "is_tactic_proof": true, "tactics": ["simp_rw", "rw", "apply", "lift_mk_le_lift_mk_of_surjective", "rw", "rintro", "obtain", "exact"], "tactic_count": 8}
{"name": "Ordinal.card_iSup_le_sum_card", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Ordinal", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "Ordinal.card_iSup_Iio_le_sum_card", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Ordinal", "is_tactic_proof": true, "tactics": ["apply", "simpa"], "tactic_count": 2}
{"name": "Ordinal.card_iSup_Iio_le_card_mul_iSup", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Ordinal", "is_tactic_proof": true, "tactics": ["apply", "convert", "exact", "exact"], "tactic_count": 4}
{"name": "Ordinal.card_opow_le_of_omega0_le_left", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Ordinal", "is_tactic_proof": true, "tactics": ["refine", "simpa", "intro", "rw", "grw", "rw", "grw", "rw", "rintro", "cases", "rwa", "intro", "rw", "apply", "rw", "apply", "apply", "rintro", "grw", "simpa", "refine", "exact", "simpa"], "tactic_count": 23}
{"name": "Ordinal.card_opow_le_of_omega0_le_right", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Ordinal", "is_tactic_proof": true, "tactics": ["obtain", "apply", "apply", "simp", "exact"], "tactic_count": 5}
{"name": "Ordinal.card_opow_le", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Ordinal", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "rw", "exact", "exact", "exact"], "tactic_count": 6}
{"name": "Ordinal.card_opow_eq_of_omega0_le_left", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Ordinal", "is_tactic_proof": true, "tactics": ["apply", "exact", "exact"], "tactic_count": 3}
{"name": "Ordinal.card_opow_eq_of_omega0_le_right", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Ordinal", "is_tactic_proof": true, "tactics": ["apply", "exact", "exact"], "tactic_count": 3}
{"name": "Ordinal.card_omega0_opow", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Ordinal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordinal.card_opow_omega0", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Ordinal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordinal.principal_opow_omega", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Ordinal", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact", "intro", "rw", "apply", "rwa"], "tactic_count": 7}
{"name": "Ordinal.IsInitial.principal_opow", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Ordinal", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Ordinal.principal_opow_ord", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Ordinal", "is_tactic_proof": true, "tactics": ["apply", "rwa"], "tactic_count": 2}
{"name": "Ordinal.principal_add_ord", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Ordinal", "is_tactic_proof": true, "tactics": ["intro", "rw", "exact"], "tactic_count": 3}
{"name": "Ordinal.IsInitial.principal_add", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Ordinal", "is_tactic_proof": true, "tactics": ["rw", "apply", "rwa"], "tactic_count": 3}
{"name": "Ordinal.principal_add_omega", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.principal_mul_ord", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Ordinal", "is_tactic_proof": true, "tactics": ["intro", "rw", "exact"], "tactic_count": 3}
{"name": "Ordinal.IsInitial.principal_mul", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Ordinal", "is_tactic_proof": true, "tactics": ["rw", "apply", "rwa"], "tactic_count": 3}
{"name": "Ordinal.principal_mul_omega", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.infinite_pigeonhole", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Pigeonhole", "is_tactic_proof": false, "tactics": ["have", "by_contra", "apply", "rw", "exact", "mk_iUnion_le_sum_mk.trans_lt", "obtain", "refine", "rw", "exact"], "tactic_count": 10}
{"name": "Cardinal.infinite_pigeonhole_card", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Pigeonhole", "is_tactic_proof": true, "tactics": ["rcases", "obtain", "use", "exact"], "tactic_count": 4}
{"name": "Cardinal.infinite_pigeonhole_set", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Pigeonhole", "is_tactic_proof": true, "tactics": ["obtain", "refine", "rintro", "exact", "refine", "simp", "rfl", "rintro"], "tactic_count": 8}
{"name": "Cardinal.infinite_pigeonhole_card_lt", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Pigeonhole", "is_tactic_proof": true, "tactics": ["simp_rw", "exact", "infinite_pigeonhole_card"], "tactic_count": 3}
{"name": "Cardinal.exists_infinite_fiber", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Pigeonhole", "is_tactic_proof": true, "tactics": ["simp_rw", "obtain", "exact"], "tactic_count": 3}
{"name": "Cardinal.le_range_of_union_finset_eq_top", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Pigeonhole", "is_tactic_proof": false, "tactics": ["have", "rw", "apply", "rw", "exact", "by_contra", "simp", "let", "let", "have", "rintro", "have", "rw", "apply", "obtain", "exact"], "tactic_count": 16}
{"name": "Cardinal.IsRegular", "kind": "definition", "module": "Mathlib.SetTheory.Cardinal.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.IsRegular.aleph0_le", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.IsRegular.cof_eq", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.IsRegular.cof_omega_eq", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Regular", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.IsRegular.pos", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.IsRegular.nat_lt", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.IsRegular.ord_pos", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Regular", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Cardinal.isRegular_cof", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.IsRegular.ne_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.isRegular_aleph0", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.fact_isRegular_aleph0", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.isRegular_succ", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.isRegular_aleph_one", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Regular", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Cardinal.isRegular_preAleph_succ", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Regular", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Cardinal.isRegular_aleph_succ", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Regular", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Cardinal.IsRegular.lift", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Regular", "is_tactic_proof": true, "tactics": ["obtain", "constructor", "simpa", "rwa"], "tactic_count": 4}
{"name": "Cardinal.isRegular_lift_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.lsub_lt_ord_lift_of_isRegular", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.lsub_lt_ord_of_isRegular", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.iSup_lt_ord_lift_of_isRegular", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.iSup_lt_ord_of_isRegular", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.blsub_lt_ord_lift_of_isRegular", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.blsub_lt_ord_of_isRegular", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.bsup_lt_ord_lift_of_isRegular", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.bsup_lt_ord_of_isRegular", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.iSup_lt_lift_of_isRegular", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.iSup_lt_of_isRegular", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.sum_lt_lift_of_isRegular", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.sum_lt_of_isRegular", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.card_lt_of_card_iUnion_lt", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.card_iUnion_lt_iff_forall_of_isRegular", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Regular", "is_tactic_proof": true, "tactics": ["refine", "apply", "apply", "apply", "simpa"], "tactic_count": 5}
{"name": "Cardinal.card_lt_of_card_biUnion_lt", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Regular", "is_tactic_proof": true, "tactics": ["rw", "have", "simp_all"], "tactic_count": 3}
{"name": "Cardinal.card_biUnion_lt_iff_forall_of_isRegular", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Regular", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.nfpFamily_lt_ord_lift_of_isRegular", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Regular", "is_tactic_proof": true, "tactics": ["apply", "exact", "exact"], "tactic_count": 3}
{"name": "Cardinal.nfpFamily_lt_ord_of_isRegular", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.nfp_lt_ord_of_isRegular", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.derivFamily_lt_ord_lift", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Regular", "is_tactic_proof": false, "tactics": ["have", "rw", "exact", "induction", "zero", "rw", "exact", "succ", "intro", "rw", "exact", "limit", "intro", "have", "rw", "exact", "bsup_lt_ord_of_isRegular."], "tactic_count": 17}
{"name": "Cardinal.derivFamily_lt_ord", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.deriv_lt_ord", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.IsInaccessible", "kind": "definition", "module": "Mathlib.SetTheory.Cardinal.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.IsInaccessible.aleph0_lt", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.IsInaccessible.nat_lt", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.IsInaccessible.pos", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.IsInaccessible.ne_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.IsInaccessible.isRegular", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.IsInaccessible.isStrongLimit", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.isInaccessible_def", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.IsInaccessible.univ", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.iSup_sequence_lt_omega_one", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Regular", "is_tactic_proof": true, "tactics": ["apply", "rw", "exact"], "tactic_count": 3}
{"name": "Function.Embedding.schroeder_bernstein_of_rel", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.SchroederBernstein", "is_tactic_proof": true, "tactics": ["classical", "rcases", "have", "exact", "set", "monotone", "set", "have", "have", "set", "have", "have", "set", "have", "have", "refine", "intro", "obtain", "obtain", "rw", "rw", "intro", "obtain", "rw", "exact", "refine", "simp", "split", "exact", "have", "have", "obtain", "exact", "grind"], "tactic_count": 34}
{"name": "Function.Embedding.schroeder_bernstein", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.SchroederBernstein", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Function.Embedding.antisymm", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.SchroederBernstein", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.SetTheory.Cardinal.SchroederBernstein.0.Function.Embedding.sets", "kind": "abbrev", "module": "Mathlib.SetTheory.Cardinal.SchroederBernstein", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.min_injective", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.SchroederBernstein", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Embedding.total", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.SchroederBernstein", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.SetTheory.Cardinal.Subfield.0.Subfield.Operands", "kind": "abbrev", "module": "Mathlib.SetTheory.Cardinal.Subfield", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.SetTheory.Cardinal.Subfield.0.Subfield.operate", "kind": "definition", "module": "Mathlib.SetTheory.Cardinal.Subfield", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.SetTheory.Cardinal.Subfield.0.Subfield.rangeOfWType", "kind": "definition", "module": "Mathlib.SetTheory.Cardinal.Subfield", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.SetTheory.Cardinal.Subfield.0.Subfield.rangeOfWType_eq_top", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Subfield", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.SetTheory.Cardinal.Subfield.0.Subfield.surjective_ofWType", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Subfield", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Subfield.cardinalMk_closure_le_max", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Subfield", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.cardinalMk_closure", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.Subfield", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.toNat", "kind": "definition", "module": "Mathlib.SetTheory.Cardinal.ToNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.toNat_toENat", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ToNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.toNat_ofENat", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ToNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.toNat_natCast", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ToNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.toNat_eq_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ToNat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.toNat_ne_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ToNat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Cardinal.toNat_pos", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ToNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.cast_toNat_of_lt_aleph0", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ToNat", "is_tactic_proof": true, "tactics": ["lift", "rw"], "tactic_count": 2}
{"name": "Cardinal.toNat_apply_of_lt_aleph0", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ToNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.toNat_apply_of_aleph0_le", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ToNat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Cardinal.cast_toNat_of_aleph0_le", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ToNat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.cast_toNat_eq_iff_lt_aleph0", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ToNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.toNat_strictMonoOn", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ToNat", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Cardinal.toNat_monotoneOn", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ToNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.toNat_injOn", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ToNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.toNat_inj_of_lt_aleph0", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ToNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.toNat_le_iff_le_of_lt_aleph0", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ToNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.toNat_lt_iff_lt_of_lt_aleph0", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ToNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.toNat_le_toNat", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ToNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.toNat_lt_toNat", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ToNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.toNat_ofNat", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ToNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.toNat_rightInverse", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ToNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.toNat_surjective", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ToNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_toNat_of_infinite", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ToNat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Cardinal.aleph0_toNat", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ToNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.mk_toNat_eq_card", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ToNat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Cardinal.zero_toNat", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ToNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.one_toNat", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ToNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.toNat_eq_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ToNat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.toNat_eq_ofNat", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ToNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.toNat_eq_one", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ToNat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.toNat_eq_one_iff_unique", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ToNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.toNat_lift", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ToNat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Cardinal.toNat_congr", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ToNat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.toNat_mul", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ToNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.toNat_add", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ToNat", "is_tactic_proof": true, "tactics": ["lift", "lift", "norm_cast"], "tactic_count": 3}
{"name": "Cardinal.toNat_lift_add_lift", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ToNat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Cardinal.natCast_toNat_le", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.ToNat", "is_tactic_proof": true, "tactics": ["obtain", "simp", "simp"], "tactic_count": 3}
{"name": "univLE_iff_cardinal_le", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.UnivLE", "is_tactic_proof": true, "tactics": ["simp_rw", "contrapose", "refine", "rw", "exact", "obtain", "rw", "exact"], "tactic_count": 8}
{"name": "univLE_iff_exists_embedding", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.UnivLE", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Ordinal.univLE_of_injective", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.UnivLE", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "univLE_total", "kind": "theorem", "module": "Mathlib.SetTheory.Cardinal.UnivLE", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Descriptive.tree", "kind": "definition", "module": "Mathlib.SetTheory.Descriptive.Tree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Descriptive.instSetLikeSubtypeSetListMemCompleteSublatticeTree", "kind": "instance", "module": "Mathlib.SetTheory.Descriptive.Tree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Descriptive.instPartialOrderSubtypeSetListMemCompleteSublatticeTree", "kind": "instance", "module": "Mathlib.SetTheory.Descriptive.Tree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Descriptive.Tree.mem_of_append", "kind": "theorem", "module": "Mathlib.SetTheory.Descriptive.Tree", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "Descriptive.Tree.mem_of_prefix", "kind": "theorem", "module": "Mathlib.SetTheory.Descriptive.Tree", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "Descriptive.Tree.instTransListSubtypeSetMemCompleteSublatticeTreeIsPrefix", "kind": "instance", "module": "Mathlib.SetTheory.Descriptive.Tree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Descriptive.Tree.singleton_mem", "kind": "theorem", "module": "Mathlib.SetTheory.Descriptive.Tree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Descriptive.Tree.tree_eq_bot", "kind": "theorem", "module": "Mathlib.SetTheory.Descriptive.Tree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Descriptive.Tree.take_mem", "kind": "theorem", "module": "Mathlib.SetTheory.Descriptive.Tree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Descriptive.Tree.take", "kind": "definition", "module": "Mathlib.SetTheory.Descriptive.Tree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Descriptive.Tree.take_take", "kind": "theorem", "module": "Mathlib.SetTheory.Descriptive.Tree", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Descriptive.Tree.take_eq_take", "kind": "theorem", "module": "Mathlib.SetTheory.Descriptive.Tree", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Descriptive.Tree.subAt", "kind": "definition", "module": "Mathlib.SetTheory.Descriptive.Tree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Descriptive.Tree.mem_subAt", "kind": "theorem", "module": "Mathlib.SetTheory.Descriptive.Tree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Descriptive.Tree.subAt_nil", "kind": "theorem", "module": "Mathlib.SetTheory.Descriptive.Tree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Descriptive.Tree.subAt_append", "kind": "theorem", "module": "Mathlib.SetTheory.Descriptive.Tree", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Descriptive.Tree.subAt_mono", "kind": "theorem", "module": "Mathlib.SetTheory.Descriptive.Tree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Descriptive.Tree.drop", "kind": "definition", "module": "Mathlib.SetTheory.Descriptive.Tree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Descriptive.Tree.pullSub", "kind": "definition", "module": "Mathlib.SetTheory.Descriptive.Tree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Descriptive.Tree.mem_pullSub_short", "kind": "theorem", "module": "Mathlib.SetTheory.Descriptive.Tree", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Descriptive.Tree.mem_pullSub_long", "kind": "theorem", "module": "Mathlib.SetTheory.Descriptive.Tree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Descriptive.Tree.mem_pullSub_append", "kind": "theorem", "module": "Mathlib.SetTheory.Descriptive.Tree", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Descriptive.Tree.mem_pullSub_self", "kind": "theorem", "module": "Mathlib.SetTheory.Descriptive.Tree", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Descriptive.Tree.pullSub_subAt", "kind": "theorem", "module": "Mathlib.SetTheory.Descriptive.Tree", "is_tactic_proof": true, "tactics": ["intro", "rw", "rw"], "tactic_count": 3}
{"name": "Descriptive.Tree.subAt_pullSub", "kind": "theorem", "module": "Mathlib.SetTheory.Descriptive.Tree", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Descriptive.Tree.pullSub_mono", "kind": "theorem", "module": "Mathlib.SetTheory.Descriptive.Tree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Descriptive.Tree.pullSub_adjunction", "kind": "theorem", "module": "Mathlib.SetTheory.Descriptive.Tree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Descriptive.Tree.pullSub_nil", "kind": "theorem", "module": "Mathlib.SetTheory.Descriptive.Tree", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Descriptive.Tree.pullSub_append", "kind": "theorem", "module": "Mathlib.SetTheory.Descriptive.Tree", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "obtain", "simp", "constructor", "cases", "rw", "simpa"], "tactic_count": 8}
{"name": "SetTheory.Game", "kind": "abbrev", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.Game.instNeg", "kind": "instance", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.Game.instZero", "kind": "instance", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.Game.instAdd", "kind": "instance", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.Game.instAddCommGroupWithOneGame", "kind": "instance", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.Game.instInhabited", "kind": "instance", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.Game.zero_def", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.Game.instPartialOrderGame", "kind": "instance", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.Game.LF", "kind": "definition", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.Game.not_le", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "SetTheory.Game.not_lf", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "SetTheory.Game.Fuzzy", "kind": "definition", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.Game.instIsTrichotomousLF", "kind": "instance", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.le_iff_game_le", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.lf_iff_game_lf", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.lt_iff_game_lt", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.equiv_iff_game_eq", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.fuzzy_iff_game_fuzzy", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.SetTheory.Game.Basic.0.SetTheory.Game.term_⧏_", "kind": "definition", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.SetTheory.Game.Basic.0.SetTheory.Game._aux_Mathlib_SetTheory_Game_Basic___macroRules__private_Mathlib_SetTheory_Game_Basic_0_SetTheory_Game_term_⧏__1", "kind": "definition", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.SetTheory.Game.Basic.0.SetTheory.Game._aux_Mathlib_SetTheory_Game_Basic___unexpand_SetTheory_Game_LF_1", "kind": "definition", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.SetTheory.Game.Basic.0.SetTheory.Game.term_‖_", "kind": "definition", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.SetTheory.Game.Basic.0.SetTheory.Game._aux_Mathlib_SetTheory_Game_Basic___macroRules__private_Mathlib_SetTheory_Game_Basic_0_SetTheory_Game_term_‖__1", "kind": "definition", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.SetTheory.Game.Basic.0.SetTheory.Game._aux_Mathlib_SetTheory_Game_Basic___unexpand_SetTheory_Game_Fuzzy_1", "kind": "definition", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.Game.addLeftMono", "kind": "instance", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.Game.addRightMono", "kind": "instance", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.Game.addLeftStrictMono", "kind": "instance", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.Game.addRightStrictMono", "kind": "instance", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.Game.add_lf_add_right", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": true, "tactics": ["rintro", "apply"], "tactic_count": 2}
{"name": "SetTheory.Game.add_lf_add_left", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": true, "tactics": ["rintro", "apply"], "tactic_count": 2}
{"name": "SetTheory.Game.isOrderedAddMonoid", "kind": "instance", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.Game.bddAbove_range_of_small", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": true, "tactics": ["obtain", "refine", "simpa"], "tactic_count": 3}
{"name": "SetTheory.Game.bddAbove_of_small", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "SetTheory.Game.bddBelow_range_of_small", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": true, "tactics": ["obtain", "refine", "simpa"], "tactic_count": 3}
{"name": "SetTheory.Game.bddBelow_of_small", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "SetTheory.PGame.quot_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.quot_one", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.quot_neg", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.quot_add", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.quot_sub", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.quot_natCast", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.quot_eq_of_mk'_quot_eq", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.instMul", "kind": "instance", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.leftMoves_mul", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.rightMoves_mul", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.toLeftMovesMul", "kind": "definition", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.toRightMovesMul", "kind": "definition", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.mk_mul_moveLeft_inl", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.mul_moveLeft_inl", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": true, "tactics": ["cases", "cases", "rfl"], "tactic_count": 3}
{"name": "SetTheory.PGame.mk_mul_moveLeft_inr", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.mul_moveLeft_inr", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": true, "tactics": ["cases", "cases", "rfl"], "tactic_count": 3}
{"name": "SetTheory.PGame.mk_mul_moveRight_inl", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.mul_moveRight_inl", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": true, "tactics": ["cases", "cases", "rfl"], "tactic_count": 3}
{"name": "SetTheory.PGame.mk_mul_moveRight_inr", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.mul_moveRight_inr", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": true, "tactics": ["cases", "cases", "rfl"], "tactic_count": 3}
{"name": "SetTheory.PGame.neg_mk_mul_moveLeft_inl", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.neg_mk_mul_moveLeft_inr", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.neg_mk_mul_moveRight_inl", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.neg_mk_mul_moveRight_inr", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.leftMoves_mul_cases", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": true, "tactics": ["rw", "rcases", "apply", "apply"], "tactic_count": 4}
{"name": "SetTheory.PGame.rightMoves_mul_cases", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": true, "tactics": ["rw", "rcases", "apply", "apply"], "tactic_count": 4}
{"name": "SetTheory.PGame.mul_comm", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.mulCommRelabelling", "kind": "definition", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.quot_mul_comm", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.mul_comm_equiv", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.isEmpty_leftMoves_mul", "kind": "instance", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": true, "tactics": ["cases", "cases", "assumption"], "tactic_count": 3}
{"name": "SetTheory.PGame.isEmpty_rightMoves_mul", "kind": "instance", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": true, "tactics": ["cases", "cases", "assumption"], "tactic_count": 3}
{"name": "SetTheory.PGame.mul_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.mulZeroRelabelling", "kind": "definition", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.mul_zero_equiv", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.quot_mul_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.zero_mul", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.zeroMulRelabelling", "kind": "definition", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.zero_mul_equiv", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.quot_zero_mul", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.negMulRelabelling", "kind": "definition", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.mul_neg", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.neg_mul", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.quot_neg_mul", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.mulNegRelabelling", "kind": "definition", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.quot_mul_neg", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.quot_neg_mul_neg", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SetTheory.PGame.quot_left_distrib", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.left_distrib_equiv", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.quot_left_distrib_sub", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": true, "tactics": ["change", "rw"], "tactic_count": 2}
{"name": "SetTheory.PGame.quot_right_distrib", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SetTheory.PGame.right_distrib_equiv", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.quot_right_distrib_sub", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": true, "tactics": ["change", "rw"], "tactic_count": 2}
{"name": "SetTheory.PGame.mulOneRelabelling", "kind": "definition", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.one_mul", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.mul_one", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.quot_mul_one", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.mul_one_equiv", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.oneMulRelabelling", "kind": "definition", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.quot_one_mul", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.one_mul_equiv", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.quot_mul_assoc", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.mul_assoc_equiv", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.mulOption", "kind": "definition", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.mulOption_neg_neg", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SetTheory.PGame.mulOption_symm", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "congr", "on_goal", "all_goals"], "tactic_count": 5}
{"name": "SetTheory.PGame.leftMoves_mul_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": true, "tactics": ["cases", "constructor", "on_goal", "constructor", "exact", "convert", "on_goal", "rintro", "exact", "convert", "all_goals", "dsimp", "rw", "congr", "on_goal", "all_goals"], "tactic_count": 16}
{"name": "SetTheory.PGame.rightMoves_mul_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": true, "tactics": ["cases", "constructor", "on_goal", "constructor", "on_goal", "on_goal", "on_goal", "rintro", "on_goal", "on_goal", "all_goals", "dsimp", "rw", "congr", "on_goal", "any_goals", "iterate"], "tactic_count": 17}
{"name": "SetTheory.PGame.InvTy", "kind": "inductive", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.instIsEmptyInvTyTrue", "kind": "instance", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.InvTy.instInhabited", "kind": "instance", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.uniqueInvTy", "kind": "instance", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.invVal", "kind": "definition", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.invVal_isEmpty", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": true, "tactics": ["obtain", "rfl", "all_goals"], "tactic_count": 3}
{"name": "SetTheory.PGame.inv'", "kind": "definition", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.zero_lf_inv'", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.inv'Zero", "kind": "definition", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": true, "tactics": ["change", "refine", "apply", "apply", "simp", "dsimp", "infer_instance"], "tactic_count": 7}
{"name": "SetTheory.PGame.inv'_zero_equiv", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.inv'_one", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": true, "tactics": ["rw", "constructor", "simp", "simp"], "tactic_count": 4}
{"name": "SetTheory.PGame.inv'One", "kind": "definition", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": true, "tactics": ["change", "have", "rw", "infer_instance", "refine", "apply", "apply", "simp", "infer_instance"], "tactic_count": 9}
{"name": "SetTheory.PGame.inv'_one_equiv", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.instInv", "kind": "instance", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.instDiv", "kind": "instance", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.inv_eq_of_equiv_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "SetTheory.PGame.inv_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.inv_eq_of_pos", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "SetTheory.PGame.inv_eq_of_lf_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "SetTheory.PGame.inv_one", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SetTheory.PGame.invOne", "kind": "definition", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SetTheory.PGame.inv_one_equiv", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.birthday", "kind": "definition", "module": "Mathlib.SetTheory.Game.Birthday", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.birthday_def", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Birthday", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "SetTheory.PGame.birthday_moveLeft_lt", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Birthday", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "SetTheory.PGame.birthday_moveRight_lt", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Birthday", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "SetTheory.PGame.lt_birthday_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Birthday", "is_tactic_proof": true, "tactics": ["constructor", "rw", "intro", "rcases", "left", "rwa", "right", "rwa", "rintro", "exact", "exact"], "tactic_count": 11}
{"name": "SetTheory.PGame.Relabelling.birthday_congr", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Birthday", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.birthday_eq_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Birthday", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SetTheory.PGame.birthday_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Birthday", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SetTheory.PGame.birthday_one", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Birthday", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SetTheory.PGame.birthday_star", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Birthday", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SetTheory.PGame.birthday_neg", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Birthday", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.birthday_ordinalToPGame", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Birthday", "is_tactic_proof": false, "tactics": ["induction", "rw", "simp", "conv_rhs", "congr", "exact"], "tactic_count": 6}
{"name": "SetTheory.PGame.le_birthday", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Birthday", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.neg_birthday_le", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Birthday", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "SetTheory.PGame.birthday_add", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Birthday", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.birthday_sub", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Birthday", "is_tactic_proof": true, "tactics": ["apply", "rw"], "tactic_count": 2}
{"name": "SetTheory.PGame.birthday_natCast", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Birthday", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.Game.birthday", "kind": "definition", "module": "Mathlib.SetTheory.Game.Birthday", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.Game.birthday_eq_pGameBirthday", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Birthday", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "SetTheory.Game.birthday_quot_le_pGameBirthday", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Birthday", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.Game.birthday_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Birthday", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SetTheory.Game.birthday_eq_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Birthday", "is_tactic_proof": true, "tactics": ["constructor", "intro", "let", "rw", "rw", "exact", "rintro", "exact"], "tactic_count": 8}
{"name": "SetTheory.Game.birthday_ordinalToGame", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Birthday", "is_tactic_proof": true, "tactics": ["apply", "conv_rhs", "apply", "let", "rw", "rw", "exact"], "tactic_count": 7}
{"name": "SetTheory.Game.birthday_natCast", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Birthday", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SetTheory.Game.birthday_ofNat", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Birthday", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.Game.birthday_one", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Birthday", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SetTheory.Game.birthday_star", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Birthday", "is_tactic_proof": true, "tactics": ["apply", "rw", "exact", "rw", "exact"], "tactic_count": 5}
{"name": "_private.Mathlib.SetTheory.Game.Birthday.0.SetTheory.Game.birthday_neg'", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Birthday", "is_tactic_proof": true, "tactics": ["let", "rw", "conv_lhs", "apply"], "tactic_count": 4}
{"name": "SetTheory.Game.birthday_neg", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Birthday", "is_tactic_proof": true, "tactics": ["apply", "conv_lhs", "exact"], "tactic_count": 3}
{"name": "SetTheory.Game.le_birthday", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Birthday", "is_tactic_proof": true, "tactics": ["let", "rw", "apply", "rw"], "tactic_count": 4}
{"name": "SetTheory.Game.neg_birthday_le", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Birthday", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SetTheory.Game.birthday_add_le", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Birthday", "is_tactic_proof": true, "tactics": ["let", "let", "rw", "exact"], "tactic_count": 4}
{"name": "SetTheory.Game.birthday_sub_le", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Birthday", "is_tactic_proof": true, "tactics": ["apply", "rw", "https://mathoverflow.net/a/476829/147705."], "tactic_count": 3}
{"name": "SetTheory.Game.small_setOf_birthday_lt", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Birthday", "is_tactic_proof": true, "tactics": ["induction", "h", "let", "let", "obtain", "simp_rw", "exact", "simp_rw", "convert", "exact", "let", "suffices", "rintro", "obtain", "refine", "apply", "obtain", "exact", "obtain", "exact", "refine", "suffices", "refine", "exact", "refine", "suffices", "refine", "exact", "convert", "change", "simpa"], "tactic_count": 31}
{"name": "SetTheory.PGame.Domineering.shiftUp", "kind": "definition", "module": "Mathlib.SetTheory.Game.Domineering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.Domineering.shiftRight", "kind": "definition", "module": "Mathlib.SetTheory.Game.Domineering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.Domineering.Board", "kind": "abbrev", "module": "Mathlib.SetTheory.Game.Domineering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.Domineering.left", "kind": "definition", "module": "Mathlib.SetTheory.Game.Domineering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.Domineering.right", "kind": "definition", "module": "Mathlib.SetTheory.Game.Domineering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.Domineering.mem_left", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Domineering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.Domineering.mem_right", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Domineering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.Domineering.moveLeft", "kind": "definition", "module": "Mathlib.SetTheory.Game.Domineering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.Domineering.moveRight", "kind": "definition", "module": "Mathlib.SetTheory.Game.Domineering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.Domineering.fst_pred_mem_erase_of_mem_right", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Domineering", "is_tactic_proof": true, "tactics": ["rw", "apply", "exact"], "tactic_count": 3}
{"name": "SetTheory.PGame.Domineering.snd_pred_mem_erase_of_mem_left", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Domineering", "is_tactic_proof": true, "tactics": ["rw", "apply", "exact"], "tactic_count": 3}
{"name": "SetTheory.PGame.Domineering.card_of_mem_left", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Domineering", "is_tactic_proof": true, "tactics": ["have", "have", "have", "have", "exact"], "tactic_count": 5}
{"name": "SetTheory.PGame.Domineering.card_of_mem_right", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Domineering", "is_tactic_proof": true, "tactics": ["have", "have", "have", "have", "exact"], "tactic_count": 5}
{"name": "SetTheory.PGame.Domineering.moveLeft_card", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Domineering", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "rw", "exact"], "tactic_count": 4}
{"name": "SetTheory.PGame.Domineering.moveRight_card", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Domineering", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "rw", "exact"], "tactic_count": 4}
{"name": "SetTheory.PGame.Domineering.moveLeft_smaller", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Domineering", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SetTheory.PGame.Domineering.moveRight_smaller", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Domineering", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SetTheory.PGame.Domineering.state", "kind": "instance", "module": "Mathlib.SetTheory.Game.Domineering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.domineering", "kind": "definition", "module": "Mathlib.SetTheory.Game.Domineering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.shortDomineering", "kind": "instance", "module": "Mathlib.SetTheory.Game.Domineering", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "SetTheory.PGame.domineering.one", "kind": "definition", "module": "Mathlib.SetTheory.Game.Domineering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.domineering.L", "kind": "definition", "module": "Mathlib.SetTheory.Game.Domineering", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.shortOne", "kind": "instance", "module": "Mathlib.SetTheory.Game.Domineering", "is_tactic_proof": true, "tactics": ["dsimp"], "tactic_count": 1}
{"name": "SetTheory.PGame.shortL", "kind": "instance", "module": "Mathlib.SetTheory.Game.Domineering", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "_private.Mathlib.SetTheory.Game.Impartial.0.SetTheory.PGame.ImpartialAux", "kind": "definition", "module": "Mathlib.SetTheory.Game.Impartial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.SetTheory.Game.Impartial.0.SetTheory.PGame.impartial_iff_aux", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Impartial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.impartial_def", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Impartial", "is_tactic_proof": true, "tactics": ["simp_rw", "rw"], "tactic_count": 2}
{"name": "SetTheory.PGame.Impartial.impartial_zero", "kind": "instance", "module": "Mathlib.SetTheory.Game.Impartial", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "SetTheory.PGame.Impartial.impartial_star", "kind": "instance", "module": "Mathlib.SetTheory.Game.Impartial", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "SetTheory.PGame.Impartial.neg_equiv_self", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Impartial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.Impartial.mk'_neg_equiv_self", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Impartial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.Impartial.moveLeft_impartial", "kind": "instance", "module": "Mathlib.SetTheory.Game.Impartial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.Impartial.moveRight_impartial", "kind": "instance", "module": "Mathlib.SetTheory.Game.Impartial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.Impartial.impartial_congr", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Impartial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.Impartial.impartial_add", "kind": "instance", "module": "Mathlib.SetTheory.Game.Impartial", "is_tactic_proof": true, "tactics": ["rw", "refine", "apply", "all_goals", "intro", "apply", "apply", "all_goals", "intro", "apply", "termination_by"], "tactic_count": 11}
{"name": "SetTheory.PGame.Impartial.impartial_neg", "kind": "instance", "module": "Mathlib.SetTheory.Game.Impartial", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "exact", "rw", "exact", "rw", "exact", "termination_by"], "tactic_count": 9}
{"name": "SetTheory.PGame.Impartial.nonpos", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Impartial", "is_tactic_proof": true, "tactics": ["apply", "rwa"], "tactic_count": 2}
{"name": "SetTheory.PGame.Impartial.nonneg", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Impartial", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "SetTheory.PGame.Impartial.equiv_or_fuzzy_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Impartial", "is_tactic_proof": true, "tactics": ["rcases", "exact", "exact", "exact", "exact"], "tactic_count": 5}
{"name": "SetTheory.PGame.Impartial.not_equiv_zero_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Impartial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.Impartial.not_fuzzy_zero_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Impartial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.Impartial.add_self", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Impartial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.Impartial.mk'_add_self", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Impartial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.Impartial.equiv_iff_add_equiv_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Impartial", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SetTheory.PGame.Impartial.equiv_iff_add_equiv_zero'", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Impartial", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SetTheory.PGame.Impartial.le_zero_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Impartial", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SetTheory.PGame.Impartial.lf_zero_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Impartial", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SetTheory.PGame.Impartial.equiv_zero_iff_le", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Impartial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.Impartial.fuzzy_zero_iff_lf", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Impartial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.Impartial.equiv_zero_iff_ge", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Impartial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.Impartial.fuzzy_zero_iff_gf", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Impartial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.Impartial.forall_leftMoves_fuzzy_iff_equiv_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Impartial", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact", "rw", "exact"], "tactic_count": 5}
{"name": "SetTheory.PGame.Impartial.forall_rightMoves_fuzzy_iff_equiv_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Impartial", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact", "rw", "exact"], "tactic_count": 5}
{"name": "SetTheory.PGame.Impartial.exists_left_move_equiv_iff_fuzzy_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Impartial", "is_tactic_proof": true, "tactics": ["refine", "rw", "obtain", "exact"], "tactic_count": 4}
{"name": "SetTheory.PGame.Impartial.exists_right_move_equiv_iff_fuzzy_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Impartial", "is_tactic_proof": true, "tactics": ["refine", "rw", "obtain", "exact"], "tactic_count": 4}
{"name": "SetTheory.PGame.nim", "kind": "definition", "module": "Mathlib.SetTheory.Game.Nim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.leftMoves_nim", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Nim", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SetTheory.PGame.rightMoves_nim", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Nim", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SetTheory.PGame.moveLeft_nim_heq", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Nim", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SetTheory.PGame.moveRight_nim_heq", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Nim", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SetTheory.PGame.toLeftMovesNim", "kind": "definition", "module": "Mathlib.SetTheory.Game.Nim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.toRightMovesNim", "kind": "definition", "module": "Mathlib.SetTheory.Game.Nim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.toLeftMovesNim_symm_lt", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Nim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.toRightMovesNim_symm_lt", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Nim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.moveLeft_nim", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Nim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.moveLeft_toLeftMovesNim", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Nim", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SetTheory.PGame.moveRight_nim", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Nim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.moveRight_toRightMovesNim", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Nim", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SetTheory.PGame.leftMovesNimRecOn", "kind": "definition", "module": "Mathlib.SetTheory.Game.Nim", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SetTheory.PGame.rightMovesNimRecOn", "kind": "definition", "module": "Mathlib.SetTheory.Game.Nim", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SetTheory.PGame.isEmpty_nim_zero_leftMoves", "kind": "instance", "module": "Mathlib.SetTheory.Game.Nim", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SetTheory.PGame.isEmpty_nim_zero_rightMoves", "kind": "instance", "module": "Mathlib.SetTheory.Game.Nim", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SetTheory.PGame.nimZeroRelabelling", "kind": "definition", "module": "Mathlib.SetTheory.Game.Nim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.nim_zero_equiv", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Nim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.uniqueNimOneLeftMoves", "kind": "instance", "module": "Mathlib.SetTheory.Game.Nim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.uniqueNimOneRightMoves", "kind": "instance", "module": "Mathlib.SetTheory.Game.Nim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.default_nim_one_leftMoves_eq", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Nim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.default_nim_one_rightMoves_eq", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Nim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.toLeftMovesNim_one_symm", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Nim", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SetTheory.PGame.toRightMovesNim_one_symm", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Nim", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SetTheory.PGame.nim_one_moveLeft", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Nim", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SetTheory.PGame.nim_one_moveRight", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Nim", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SetTheory.PGame.nimOneRelabelling", "kind": "definition", "module": "Mathlib.SetTheory.Game.Nim", "is_tactic_proof": true, "tactics": ["rw", "refine", "any_goals", "all_goals"], "tactic_count": 4}
{"name": "SetTheory.PGame.nim_one_equiv", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Nim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.nim_birthday", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Nim", "is_tactic_proof": false, "tactics": ["induction", "rw", "dsimp", "rw", "convert", "exact"], "tactic_count": 6}
{"name": "SetTheory.PGame.neg_nim", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Nim", "is_tactic_proof": false, "tactics": ["induction", "rw"], "tactic_count": 2}
{"name": "SetTheory.PGame.impartial_nim", "kind": "instance", "module": "Mathlib.SetTheory.Game.Nim", "is_tactic_proof": false, "tactics": ["induction", "rw", "refine"], "tactic_count": 3}
{"name": "SetTheory.PGame.nim_fuzzy_zero_of_ne_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Nim", "is_tactic_proof": true, "tactics": ["rw", "use", "simp"], "tactic_count": 3}
{"name": "SetTheory.PGame.nim_add_equiv_zero_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Nim", "is_tactic_proof": true, "tactics": ["constructor", "refine", "wlog", "exact", "rw", "use", "simpa", "rintro", "exact"], "tactic_count": 9}
{"name": "SetTheory.PGame.nim_add_fuzzy_zero_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Nim", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SetTheory.PGame.nim_equiv_iff_eq", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Nim", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SetTheory.PGame.grundyValue", "kind": "definition", "module": "Mathlib.SetTheory.Game.Nim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.grundyValue_eq_sInf_moveLeft", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Nim", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SetTheory.PGame.grundyValue_ne_moveLeft", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Nim", "is_tactic_proof": true, "tactics": ["conv_rhs", "have", "csInf_mem", "rw", "exact"], "tactic_count": 5}
{"name": "SetTheory.PGame.le_grundyValue_of_Iio_subset_moveLeft", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Nim", "is_tactic_proof": true, "tactics": ["by_contra", "obtain", "exact"], "tactic_count": 3}
{"name": "SetTheory.PGame.exists_grundyValue_moveLeft_of_lt", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Nim", "is_tactic_proof": true, "tactics": ["rw", "by_contra", "exact"], "tactic_count": 3}
{"name": "SetTheory.PGame.grundyValue_le_of_forall_moveLeft", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Nim", "is_tactic_proof": true, "tactics": ["contrapose", "exact"], "tactic_count": 2}
{"name": "SetTheory.PGame.equiv_nim_grundyValue", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Nim", "is_tactic_proof": true, "tactics": ["rw", "intro", "apply", "rw", "nim_add_fuzzy_zero_iff]", "exact", "rw", "obtain", "use", "rw", "exact", "termination_by"], "tactic_count": 12}
{"name": "SetTheory.PGame.grundyValue_eq_iff_equiv_nim", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Nim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.nim_grundyValue", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Nim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.grundyValue_eq_iff_equiv", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Nim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.grundyValue_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Nim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.grundyValue_iff_equiv_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Nim", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SetTheory.PGame.grundyValue_star", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Nim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.grundyValue_neg", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Nim", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SetTheory.PGame.grundyValue_eq_sInf_moveRight", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Nim", "is_tactic_proof": true, "tactics": ["obtain", "rw", "iterate", "ext", "exact"], "tactic_count": 5}
{"name": "SetTheory.PGame.grundyValue_ne_moveRight", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Nim", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "SetTheory.PGame.le_grundyValue_of_Iio_subset_moveRight", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Nim", "is_tactic_proof": true, "tactics": ["by_contra", "obtain", "exact"], "tactic_count": 3}
{"name": "SetTheory.PGame.exists_grundyValue_moveRight_of_lt", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Nim", "is_tactic_proof": true, "tactics": ["rw", "obtain", "use", "rwa"], "tactic_count": 4}
{"name": "SetTheory.PGame.grundyValue_le_of_forall_moveRight", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Nim", "is_tactic_proof": true, "tactics": ["contrapose", "exact"], "tactic_count": 2}
{"name": "SetTheory.PGame.grundyValue_nim_add_nim", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Nim", "is_tactic_proof": true, "tactics": ["apply", "intro", "apply", "simpa", "simpa", "intro", "obtain", "let", "use", "simp", "let", "use", "simp", "termination_by"], "tactic_count": 14}
{"name": "SetTheory.PGame.nim_add_nim_equiv", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Nim", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SetTheory.PGame.grundyValue_add", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Nim", "is_tactic_proof": false, "tactics": ["rw", "grundyValue_eq_iff_equiv]", "exact"], "tactic_count": 3}
{"name": "Ordinal.toPGame", "kind": "definition", "module": "Mathlib.SetTheory.Game.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.toPGame_leftMoves", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Ordinal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordinal.toPGame_rightMoves", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Ordinal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordinal.isEmpty_zero_toPGame_leftMoves", "kind": "instance", "module": "Mathlib.SetTheory.Game.Ordinal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordinal.isEmpty_toPGame_rightMoves", "kind": "instance", "module": "Mathlib.SetTheory.Game.Ordinal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordinal.toLeftMovesToPGame", "kind": "definition", "module": "Mathlib.SetTheory.Game.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.toLeftMovesToPGame_symm_lt", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.toPGame_moveLeft_hEq", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Ordinal", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Ordinal.toPGame_moveLeft'", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.toPGame_moveLeft", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Ordinal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Ordinal.zeroToPGameRelabelling", "kind": "definition", "module": "Mathlib.SetTheory.Game.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.toPGame_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.uniqueOneToPGameLeftMoves", "kind": "instance", "module": "Mathlib.SetTheory.Game.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.one_toPGame_leftMoves_default_eq", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.to_leftMoves_one_toPGame_symm", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Ordinal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Ordinal.one_toPGame_moveLeft", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Ordinal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Ordinal.oneToPGameRelabelling", "kind": "definition", "module": "Mathlib.SetTheory.Game.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.toPGame_one", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.toPGame_lf", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Ordinal", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "Ordinal.toPGame_le", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Ordinal", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "Ordinal.toPGame_lt", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.toPGame_nonneg", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.toPGame_lf_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.toPGame_le_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.toPGame_lt_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.toPGame_equiv_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Ordinal", "is_tactic_proof": true, "tactics": ["change", "rw"], "tactic_count": 2}
{"name": "Ordinal.toPGame_injective", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.toPGame_inj", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.toPGameEmbedding", "kind": "definition", "module": "Mathlib.SetTheory.Game.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.toGame", "kind": "definition", "module": "Mathlib.SetTheory.Game.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.mk_toPGame", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.toGame_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.toGame_one", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.toGame_injective", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.toGame_lf_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.toGame_le_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.toGame_lt_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.toGame_inj", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.toPGame_nadd", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Ordinal", "is_tactic_proof": true, "tactics": ["refine", "rw", "rcases", "rw", "apply", "apply", "rwa", "apply", "rwa", "apply", "rw", "exact", "exact", "termination_by"], "tactic_count": 14}
{"name": "Ordinal.toGame_nadd", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.toPGame_nmul", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Ordinal", "is_tactic_proof": true, "tactics": ["refine", "rw", "rcases", "rw", "le_sub_iff_add_le]", "refine", "lf_of_le_of_lf", "moveLeft_lf", "simp", "repeat", "rfl", "apply", "intro", "rw", "le_sub_iff_add_le]", "repeat", "simp_rw", "apply", "termination_by"], "tactic_count": 19}
{"name": "Ordinal.toGame_nmul", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.toGame_natCast", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.toPGame_natCast", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Ordinal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SetTheory.PGame.Short", "kind": "inductive", "module": "Mathlib.SetTheory.Game.Short", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.subsingleton_short", "kind": "instance", "module": "Mathlib.SetTheory.Game.Short", "is_tactic_proof": true, "tactics": ["induction", "mk", "constructor", "intro", "cases", "congr"], "tactic_count": 6}
{"name": "SetTheory.PGame.subsingleton_short_example", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Short", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.Short.mk'", "kind": "definition", "module": "Mathlib.SetTheory.Game.Short", "is_tactic_proof": true, "tactics": ["convert", "cases", "dsimp"], "tactic_count": 3}
{"name": "SetTheory.PGame.fintypeLeft", "kind": "definition", "module": "Mathlib.SetTheory.Game.Short", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "SetTheory.PGame.fintypeLeftMoves", "kind": "instance", "module": "Mathlib.SetTheory.Game.Short", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "SetTheory.PGame.fintypeRight", "kind": "definition", "module": "Mathlib.SetTheory.Game.Short", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "SetTheory.PGame.fintypeRightMoves", "kind": "instance", "module": "Mathlib.SetTheory.Game.Short", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "SetTheory.PGame.moveLeftShort", "kind": "instance", "module": "Mathlib.SetTheory.Game.Short", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "SetTheory.PGame.moveLeftShort'", "kind": "definition", "module": "Mathlib.SetTheory.Game.Short", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "SetTheory.PGame.moveRightShort", "kind": "instance", "module": "Mathlib.SetTheory.Game.Short", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "SetTheory.PGame.moveRightShort'", "kind": "definition", "module": "Mathlib.SetTheory.Game.Short", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "SetTheory.PGame.short_birthday", "kind": "theorem", "module": "Mathlib.SetTheory.Game.Short", "is_tactic_proof": true, "tactics": ["induction", "mk", "intro", "rcases", "rw", "constructor", "all_goals", "rw", "refine", "rw", "apply", "apply"], "tactic_count": 12}
{"name": "SetTheory.PGame.Short.ofIsEmpty", "kind": "definition", "module": "Mathlib.SetTheory.Game.Short", "is_tactic_proof": true, "tactics": ["have", "have", "exact"], "tactic_count": 3}
{"name": "SetTheory.PGame.short0", "kind": "instance", "module": "Mathlib.SetTheory.Game.Short", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.short1", "kind": "instance", "module": "Mathlib.SetTheory.Game.Short", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.ListShort", "kind": "classInductive", "module": "Mathlib.SetTheory.Game.Short", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.ListShort.cons", "kind": "instance", "module": "Mathlib.SetTheory.Game.Short", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.listShortGet", "kind": "instance", "module": "Mathlib.SetTheory.Game.Short", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.shortOfLists", "kind": "instance", "module": "Mathlib.SetTheory.Game.Short", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.shortOfRelabelling", "kind": "definition", "module": "Mathlib.SetTheory.Game.Short", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.shortNeg", "kind": "instance", "module": "Mathlib.SetTheory.Game.Short", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.shortAdd", "kind": "instance", "module": "Mathlib.SetTheory.Game.Short", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.shortNat", "kind": "instance", "module": "Mathlib.SetTheory.Game.Short", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.shortOfNat", "kind": "instance", "module": "Mathlib.SetTheory.Game.Short", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.shortBit0", "kind": "instance", "module": "Mathlib.SetTheory.Game.Short", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "SetTheory.PGame.shortBit1", "kind": "instance", "module": "Mathlib.SetTheory.Game.Short", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.leLFDecidable", "kind": "definition", "module": "Mathlib.SetTheory.Game.Short", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.leDecidable", "kind": "instance", "module": "Mathlib.SetTheory.Game.Short", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.lfDecidable", "kind": "instance", "module": "Mathlib.SetTheory.Game.Short", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.ltDecidable", "kind": "instance", "module": "Mathlib.SetTheory.Game.Short", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.equivDecidable", "kind": "instance", "module": "Mathlib.SetTheory.Game.Short", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame._example", "kind": "example", "module": "Mathlib.SetTheory.Game.Short", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "SetTheory.PGame._example", "kind": "example", "module": "Mathlib.SetTheory.Game.Short", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "SetTheory.PGame._example", "kind": "example", "module": "Mathlib.SetTheory.Game.Short", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "SetTheory.PGame._example", "kind": "example", "module": "Mathlib.SetTheory.Game.Short", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "SetTheory.PGame._example", "kind": "example", "module": "Mathlib.SetTheory.Game.Short", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "SetTheory.PGame._example", "kind": "example", "module": "Mathlib.SetTheory.Game.Short", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "SetTheory.PGame._example", "kind": "example", "module": "Mathlib.SetTheory.Game.Short", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "SetTheory.PGame._example", "kind": "example", "module": "Mathlib.SetTheory.Game.Short", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "SetTheory.PGame.turnBound_ne_zero_of_left_move", "kind": "theorem", "module": "Mathlib.SetTheory.Game.State", "is_tactic_proof": true, "tactics": ["intro", "have", "rw", "exact"], "tactic_count": 4}
{"name": "SetTheory.PGame.turnBound_ne_zero_of_right_move", "kind": "theorem", "module": "Mathlib.SetTheory.Game.State", "is_tactic_proof": true, "tactics": ["intro", "have", "lia"], "tactic_count": 3}
{"name": "SetTheory.PGame.turnBound_of_left", "kind": "theorem", "module": "Mathlib.SetTheory.Game.State", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.turnBound_of_right", "kind": "theorem", "module": "Mathlib.SetTheory.Game.State", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.ofStateAux", "kind": "definition", "module": "Mathlib.SetTheory.Game.State", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.ofStateAuxRelabelling", "kind": "definition", "module": "Mathlib.SetTheory.Game.State", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.ofState", "kind": "definition", "module": "Mathlib.SetTheory.Game.State", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.leftMovesOfStateAux", "kind": "definition", "module": "Mathlib.SetTheory.Game.State", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "SetTheory.PGame.leftMovesOfState", "kind": "definition", "module": "Mathlib.SetTheory.Game.State", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.rightMovesOfStateAux", "kind": "definition", "module": "Mathlib.SetTheory.Game.State", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "SetTheory.PGame.rightMovesOfState", "kind": "definition", "module": "Mathlib.SetTheory.Game.State", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.relabellingMoveLeftAux", "kind": "definition", "module": "Mathlib.SetTheory.Game.State", "is_tactic_proof": true, "tactics": ["induction", "have", "exfalso", "rfl"], "tactic_count": 4}
{"name": "SetTheory.PGame.relabellingMoveLeft", "kind": "definition", "module": "Mathlib.SetTheory.Game.State", "is_tactic_proof": true, "tactics": ["trans", "apply", "apply"], "tactic_count": 3}
{"name": "SetTheory.PGame.relabellingMoveRightAux", "kind": "definition", "module": "Mathlib.SetTheory.Game.State", "is_tactic_proof": true, "tactics": ["induction", "have", "exfalso", "rfl"], "tactic_count": 4}
{"name": "SetTheory.PGame.relabellingMoveRight", "kind": "definition", "module": "Mathlib.SetTheory.Game.State", "is_tactic_proof": true, "tactics": ["trans", "apply", "apply"], "tactic_count": 3}
{"name": "SetTheory.PGame.fintypeLeftMovesOfStateAux", "kind": "instance", "module": "Mathlib.SetTheory.Game.State", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "SetTheory.PGame.fintypeRightMovesOfStateAux", "kind": "instance", "module": "Mathlib.SetTheory.Game.State", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "SetTheory.PGame.shortOfStateAux", "kind": "instance", "module": "Mathlib.SetTheory.Game.State", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.shortOfState", "kind": "instance", "module": "Mathlib.SetTheory.Game.State", "is_tactic_proof": true, "tactics": ["dsimp", "infer_instance"], "tactic_count": 2}
{"name": "SetTheory.Game.ofState", "kind": "definition", "module": "Mathlib.SetTheory.Game.State", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lists'", "kind": "inductive", "module": "Mathlib.SetTheory.Lists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDecidableEqLists'", "kind": "instance", "module": "Mathlib.SetTheory.Lists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lists", "kind": "definition", "module": "Mathlib.SetTheory.Lists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lists'.instInhabited", "kind": "instance", "module": "Mathlib.SetTheory.Lists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lists'.cons", "kind": "definition", "module": "Mathlib.SetTheory.Lists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lists'.toList", "kind": "definition", "module": "Mathlib.SetTheory.Lists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lists'.toList_cons", "kind": "theorem", "module": "Mathlib.SetTheory.Lists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lists'.ofList", "kind": "definition", "module": "Mathlib.SetTheory.Lists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lists'.to_ofList", "kind": "theorem", "module": "Mathlib.SetTheory.Lists", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "Lists'.of_toList", "kind": "theorem", "module": "Mathlib.SetTheory.Lists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lists'.recOfList", "kind": "definition", "module": "Mathlib.SetTheory.Lists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.SetTheory.Lists.0.term_~_", "kind": "definition", "module": "Mathlib.SetTheory.Lists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.SetTheory.Lists.0._aux_Mathlib_SetTheory_Lists___macroRules__private_Mathlib_SetTheory_Lists_0_term_~__1", "kind": "definition", "module": "Mathlib.SetTheory.Lists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.SetTheory.Lists.0._aux_Mathlib_SetTheory_Lists___unexpand_Lists_Equiv_1", "kind": "definition", "module": "Mathlib.SetTheory.Lists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lists'.instHasSubsetTrue", "kind": "instance", "module": "Mathlib.SetTheory.Lists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lists'.instMembershipLists", "kind": "instance", "module": "Mathlib.SetTheory.Lists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lists'.mem_def", "kind": "theorem", "module": "Mathlib.SetTheory.Lists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lists'.mem_cons", "kind": "theorem", "module": "Mathlib.SetTheory.Lists", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Lists'.cons_subset", "kind": "theorem", "module": "Mathlib.SetTheory.Lists", "is_tactic_proof": true, "tactics": ["refine", "generalize", "obtain", "cases", "cases", "cases"], "tactic_count": 6}
{"name": "Lists'.ofList_subset", "kind": "theorem", "module": "Mathlib.SetTheory.Lists", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "refine", "simp"], "tactic_count": 5}
{"name": "Lists'.Subset.refl", "kind": "theorem", "module": "Mathlib.SetTheory.Lists", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Lists'.subset_nil", "kind": "theorem", "module": "Mathlib.SetTheory.Lists", "is_tactic_proof": true, "tactics": ["rw", "induction", "rfl", "rcases"], "tactic_count": 4}
{"name": "Lists'.mem_of_subset'", "kind": "theorem", "module": "Mathlib.SetTheory.Lists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lists'.subset_def", "kind": "theorem", "module": "Mathlib.SetTheory.Lists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lists.atom", "kind": "definition", "module": "Mathlib.SetTheory.Lists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lists.of'", "kind": "definition", "module": "Mathlib.SetTheory.Lists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lists.toList", "kind": "definition", "module": "Mathlib.SetTheory.Lists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lists.IsList", "kind": "definition", "module": "Mathlib.SetTheory.Lists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lists.ofList", "kind": "definition", "module": "Mathlib.SetTheory.Lists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lists.isList_toList", "kind": "theorem", "module": "Mathlib.SetTheory.Lists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lists.to_ofList", "kind": "theorem", "module": "Mathlib.SetTheory.Lists", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Lists.of_toList", "kind": "theorem", "module": "Mathlib.SetTheory.Lists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lists.instInhabited", "kind": "instance", "module": "Mathlib.SetTheory.Lists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lists.instDecidableEq", "kind": "instance", "module": "Mathlib.SetTheory.Lists", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "Lists.instSizeOf", "kind": "instance", "module": "Mathlib.SetTheory.Lists", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "Lists.inductionMut", "kind": "definition", "module": "Mathlib.SetTheory.Lists", "is_tactic_proof": false, "tactics": ["suffices", "true,", "false,", "intro", "induction", "atom", "nil", "cons", "have", "exact"], "tactic_count": 10}
{"name": "Lists.mem", "kind": "definition", "module": "Mathlib.SetTheory.Lists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lists.instMembership", "kind": "instance", "module": "Mathlib.SetTheory.Lists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lists.isList_of_mem", "kind": "theorem", "module": "Mathlib.SetTheory.Lists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lists.Equiv.antisymm_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Lists", "is_tactic_proof": true, "tactics": ["refine", "obtain", "simp", "exact"], "tactic_count": 4}
{"name": "Lists.equiv_atom", "kind": "theorem", "module": "Mathlib.SetTheory.Lists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lists.Equiv.symm", "kind": "theorem", "module": "Mathlib.SetTheory.Lists", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "Lists.Equiv.trans", "kind": "theorem", "module": "Mathlib.SetTheory.Lists", "is_tactic_proof": true, "tactics": ["let", "suffices", "apply", "intro", "rwa", "intro", "obtain", "exact", "obtain", "exact", "obtain", "obtain", "apply", "intro", "rcases", "rcases", "exact", "intro", "rcases", "rcases", "exact", "rintro", "intro", "simpa"], "tactic_count": 24}
{"name": "Lists.instSetoidLists", "kind": "instance", "module": "Mathlib.SetTheory.Lists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lists.sizeof_pos", "kind": "theorem", "module": "Mathlib.SetTheory.Lists", "is_tactic_proof": true, "tactics": ["cases", "simp", "zero_lt_one]"], "tactic_count": 3}
{"name": "Lists.lt_sizeof_cons'", "kind": "theorem", "module": "Mathlib.SetTheory.Lists", "is_tactic_proof": true, "tactics": ["simp", "apply"], "tactic_count": 2}
{"name": "Lists.instDecidableRelEquiv", "kind": "instance", "module": "Mathlib.SetTheory.Lists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lists'.mem_equiv_left", "kind": "theorem", "module": "Mathlib.SetTheory.Lists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lists'.mem_of_subset", "kind": "theorem", "module": "Mathlib.SetTheory.Lists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lists'.Subset.trans", "kind": "theorem", "module": "Mathlib.SetTheory.Lists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsets", "kind": "definition", "module": "Mathlib.SetTheory.Lists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsets.instEmptyCollection", "kind": "instance", "module": "Mathlib.SetTheory.Lists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsets.instInhabited", "kind": "instance", "module": "Mathlib.SetTheory.Lists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finsets.instDecidableEq", "kind": "instance", "module": "Mathlib.SetTheory.Lists", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nimber", "kind": "definition", "module": "Mathlib.SetTheory.Nimber.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nimber.instLinearOrder", "kind": "instance", "module": "Mathlib.SetTheory.Nimber.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nimber.instSuccOrder", "kind": "instance", "module": "Mathlib.SetTheory.Nimber.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nimber.instOrderBot", "kind": "instance", "module": "Mathlib.SetTheory.Nimber.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nimber.instNoMaxOrder", "kind": "instance", "module": "Mathlib.SetTheory.Nimber.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nimber.instZeroLEOneClass", "kind": "instance", "module": "Mathlib.SetTheory.Nimber.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nimber.instNeZeroOne", "kind": "instance", "module": "Mathlib.SetTheory.Nimber.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.toNimber", "kind": "definition", "module": "Mathlib.SetTheory.Nimber.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nimber.toOrdinal", "kind": "definition", "module": "Mathlib.SetTheory.Nimber.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nimber.term∗_", "kind": "definition", "module": "Mathlib.SetTheory.Nimber.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nimber._aux_Mathlib_SetTheory_Nimber_Basic___macroRules_Nimber_term∗__1", "kind": "definition", "module": "Mathlib.SetTheory.Nimber.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nimber._aux_Mathlib_SetTheory_Nimber_Basic___unexpand_Ordinal_toNimber_1", "kind": "definition", "module": "Mathlib.SetTheory.Nimber.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nimber.toOrdinal_symm_eq", "kind": "theorem", "module": "Mathlib.SetTheory.Nimber.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nimber.toOrdinal_toNimber", "kind": "theorem", "module": "Mathlib.SetTheory.Nimber.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nimber.lt_wf", "kind": "theorem", "module": "Mathlib.SetTheory.Nimber.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nimber.instWellFoundedLT", "kind": "instance", "module": "Mathlib.SetTheory.Nimber.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nimber.instConditionallyCompleteLinearOrderBot", "kind": "instance", "module": "Mathlib.SetTheory.Nimber.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nimber.bot_eq_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Nimber.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nimber.toOrdinal_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Nimber.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nimber.toOrdinal_one", "kind": "theorem", "module": "Mathlib.SetTheory.Nimber.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nimber.toOrdinal_eq_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Nimber.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nimber.toOrdinal_eq_one", "kind": "theorem", "module": "Mathlib.SetTheory.Nimber.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nimber.toOrdinal_max", "kind": "theorem", "module": "Mathlib.SetTheory.Nimber.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nimber.toOrdinal_min", "kind": "theorem", "module": "Mathlib.SetTheory.Nimber.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nimber.succ_def", "kind": "theorem", "module": "Mathlib.SetTheory.Nimber.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nimber.rec", "kind": "definition", "module": "Mathlib.SetTheory.Nimber.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nimber.induction", "kind": "theorem", "module": "Mathlib.SetTheory.Nimber.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nimber.le_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Nimber.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nimber.not_lt_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Nimber.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nimber.pos_iff_ne_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Nimber.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Nimber.one_le_iff_ne_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Nimber.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Nimber.small_Ioc", "kind": "instance", "module": "Mathlib.SetTheory.Nimber.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nimber.not_bddAbove_compl_of_small", "kind": "theorem", "module": "Mathlib.SetTheory.Nimber.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Nimber.uncountable", "kind": "instance", "module": "Mathlib.SetTheory.Nimber.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.toNimber_symm_eq", "kind": "theorem", "module": "Mathlib.SetTheory.Nimber.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.toNimber_toOrdinal", "kind": "theorem", "module": "Mathlib.SetTheory.Nimber.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.toNimber_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Nimber.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.toNimber_one", "kind": "theorem", "module": "Mathlib.SetTheory.Nimber.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.toNimber_eq_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Nimber.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Ordinal.toNimber_max", "kind": "theorem", "module": "Mathlib.SetTheory.Nimber.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.toNimber_min", "kind": "theorem", "module": "Mathlib.SetTheory.Nimber.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nimber.add", "kind": "definition", "module": "Mathlib.SetTheory.Nimber.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nimber.instAdd", "kind": "instance", "module": "Mathlib.SetTheory.Nimber.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Nimber.add_le_of_forall_ne", "kind": "theorem", "module": "Mathlib.SetTheory.Nimber.Basic", "is_tactic_proof": true, "tactics": ["by_contra", "have", "tauto"], "tactic_count": 3}
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{"name": "Nimber.instIsLeftCancelAdd", "kind": "instance", "module": "Mathlib.SetTheory.Nimber.Basic", "is_tactic_proof": true, "tactics": ["constructor", "intro", "apply", "exact", "exact"], "tactic_count": 5}
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{"name": "Nimber.add_self", "kind": "theorem", "module": "Mathlib.SetTheory.Nimber.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Nimber.instNeg", "kind": "instance", "module": "Mathlib.SetTheory.Nimber.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nimber.neg_eq", "kind": "theorem", "module": "Mathlib.SetTheory.Nimber.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nimber.instAddCommGroupWithOne", "kind": "instance", "module": "Mathlib.SetTheory.Nimber.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nimber.add_cancel_right", "kind": "theorem", "module": "Mathlib.SetTheory.Nimber.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nimber.add_cancel_left", "kind": "theorem", "module": "Mathlib.SetTheory.Nimber.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nimber.add_trichotomy", "kind": "theorem", "module": "Mathlib.SetTheory.Nimber.Basic", "is_tactic_proof": true, "tactics": ["rw", "obtain", "obtain", "rw", "exact", "rw", "exact", "rw", "exact"], "tactic_count": 9}
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{"name": "Nimber.instCharPOfNatNat", "kind": "instance", "module": "Mathlib.SetTheory.Nimber.Field", "is_tactic_proof": true, "tactics": ["apply", "rw"], "tactic_count": 2}
{"name": "_private.Mathlib.SetTheory.Nimber.Field.0.Nimber.two_zsmul", "kind": "theorem", "module": "Mathlib.SetTheory.Nimber.Field", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "_private.Mathlib.SetTheory.Nimber.Field.0.Nimber.add_eq_iff_eq_add", "kind": "theorem", "module": "Mathlib.SetTheory.Nimber.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nimber.mul", "kind": "definition", "module": "Mathlib.SetTheory.Nimber.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nimber.instMul", "kind": "instance", "module": "Mathlib.SetTheory.Nimber.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nimber.mul_def", "kind": "theorem", "module": "Mathlib.SetTheory.Nimber.Field", "is_tactic_proof": true, "tactics": ["change", "rw", "simp_rw", "rfl"], "tactic_count": 4}
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{"name": "Nimber.instNoZeroDivisors", "kind": "instance", "module": "Mathlib.SetTheory.Nimber.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Nimber.instCommRing", "kind": "instance", "module": "Mathlib.SetTheory.Nimber.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Nimber.zero_mem_invSet", "kind": "theorem", "module": "Mathlib.SetTheory.Nimber.Field", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
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{"name": "_private.Mathlib.SetTheory.Nimber.Field.0.Nimber.invSet_nonempty", "kind": "theorem", "module": "Mathlib.SetTheory.Nimber.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nimber.invAux_ne_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Nimber.Field", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
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{"name": "Nimber.invAux_notMem_invSet", "kind": "theorem", "module": "Mathlib.SetTheory.Nimber.Field", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
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{"name": "Nimber.inv_eq_invAux", "kind": "theorem", "module": "Mathlib.SetTheory.Nimber.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nimber.instField", "kind": "instance", "module": "Mathlib.SetTheory.Nimber.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.lift_add", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.lift_succ", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Ordinal.instAddLeftReflectLE", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.instIsLeftCancelAdd", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Ordinal.instAddLeftStrictMono", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.instAddLeftReflectLT", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.instAddRightReflectLT", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.add_le_add_iff_right", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Ordinal.add_eq_zero_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.left_eq_zero_of_add_eq_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.right_eq_zero_of_add_eq_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.isSuccLimit_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Ordinal.isSuccPrelimit_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.not_isSuccLimit_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Ordinal.isSuccLimit_lift", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.natCast_lt_of_isSuccLimit", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Ordinal.one_lt_of_isSuccLimit", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.zero_or_succ_or_isSuccLimit", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Ordinal.limitRecOn", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Ordinal.limitRecOn_succ", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.limitRecOn_limit", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.boundedLimitRecOn", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["obtain", "induction", "zero", "succ", "have", "exact", "limit"], "tactic_count": 7}
{"name": "Ordinal.boundedLimitRec_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["rw", "dsimp", "rw"], "tactic_count": 3}
{"name": "Ordinal.boundedLimitRec_succ", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["rw", "dsimp", "rw", "rfl"], "tactic_count": 4}
{"name": "Ordinal.boundedLimitRec_limit", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["rw", "dsimp", "rw", "rfl"], "tactic_count": 4}
{"name": "Ordinal.orderTopToTypeSucc", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.enum_succ_eq_top", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.has_succ_of_type_succ_lt", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["use", "convert", "rw", "rw"], "tactic_count": 4}
{"name": "Ordinal.toType_noMax_of_succ_lt", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.bounded_singleton", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["refine", "intro", "rw", "nth_rw", "rw", "apply"], "tactic_count": 6}
{"name": "Ordinal.typein_ordinal", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["refine", "rintro", "constructor"], "tactic_count": 3}
{"name": "Ordinal.mk_Iio_ordinal", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Ordinal.pred", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.pred_succ", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.pred_eq_of_isSuccPrelimit", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Order.IsSuccLimit.ordinalPred_eq", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.pred_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.pred_le_iff_le_succ", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["obtain", "simp", "rw"], "tactic_count": 3}
{"name": "Ordinal.lt_pred_iff_succ_lt", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.pred_le_self", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Ordinal.pred_succ_gi", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.pred_surjective", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.self_le_succ_pred", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.pred_eq_iff_isSuccPrelimit", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["obtain", "simpa", "simp_rw"], "tactic_count": 3}
{"name": "Ordinal.pred_lt_iff_not_isSuccPrelimit", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Ordinal.succ_pred_eq_iff_not_isSuccPrelimit", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordinal.lift_pred", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["obtain", "simp", "rwa"], "tactic_count": 3}
{"name": "Ordinal.IsNormal", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.IsNormal.limit_le", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.IsNormal.limit_lt", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.IsNormal.strictMono", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.IsNormal.monotone", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.isNormal_iff_strictMono_limit", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.IsNormal.lt_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.IsNormal.le_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.IsNormal.inj", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.IsNormal.id_le", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.IsNormal.le_apply", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.IsNormal.le_iff_eq", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.IsNormal.le_set", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["have", "refine", "simpa"], "tactic_count": 3}
{"name": "Ordinal.IsNormal.le_set'", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Ordinal.IsNormal.refl", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.IsNormal.trans", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.IsNormal.isSuccLimit", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.sub", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.SetTheory.Ordinal.Arithmetic.0.Ordinal.sub_eq_zero_of_lt", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.add_sub_cancel_of_le", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["change", "rw", "exact"], "tactic_count": 3}
{"name": "Ordinal.add_sub_cancel", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Ordinal.le_add_sub", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["obtain", "exact", "simpa"], "tactic_count": 3}
{"name": "Ordinal.sub_le", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["refine", "obtain", "rwa", "simp"], "tactic_count": 4}
{"name": "Ordinal.lt_sub", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.sub_eq_of_add_eq", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.sub_le_self", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.le_sub_of_le", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordinal.sub_lt_of_le", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.sub_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Ordinal.zero_sub", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Ordinal.sub_self", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Ordinal.sub_eq_zero_iff_le", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Ordinal.sub_ne_zero_iff_lt", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Ordinal.sub_sub", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.add_sub_add_cancel", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordinal.le_sub_of_add_le", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Ordinal.sub_lt_of_lt_add", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["obtain", "rwa", "rwa"], "tactic_count": 3}
{"name": "Ordinal.lt_add_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["use", "rintro", "exact"], "tactic_count": 3}
{"name": "Ordinal.add_le_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Ordinal.lt_add_iff_of_isSuccLimit", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["rw", "constructor", "refine", "rwa", "exact"], "tactic_count": 5}
{"name": "Ordinal.add_le_iff_of_isSuccLimit", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Ordinal.isNormal_add_right", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Ordinal.isSuccLimit_add", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.isSuccLimit_sub", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "rw", "exact"], "tactic_count": 5}
{"name": "Ordinal.monoid", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.type_prod_lex", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.SetTheory.Ordinal.Arithmetic.0.Ordinal.mul_eq_zero'", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.monoidWithZero", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.noZeroDivisors", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.lift_mul", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.card_mul", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.leftDistribClass", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.mul_succ", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.mulLeftMono", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.mulRightMono", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.le_mul_left", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "Ordinal.le_mul_right", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "_private.Mathlib.SetTheory.Ordinal.Arithmetic.0.Ordinal.mul_le_of_limit_aux", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": ["suffices", "obtain", "exact", "intro", "rw", "have", "rw", "have", "refine", "rcases", "by_cases", "refine", "subst", "obtain", "exact", "exact", "refine", "obtain", "exact", "exact", "rcases", "rcases", "intro", "by_cases", "substs", "simpa", "subst", "simp", "obtain", "simp", "simpa"], "tactic_count": 31}
{"name": "Ordinal.mul_le_iff_of_isSuccLimit", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.isNormal_mul_right", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["refine", "simpa", "simpa", "mul_le_mul_right"], "tactic_count": 4}
{"name": "Ordinal.lt_mul_iff_of_isSuccLimit", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Ordinal.instPosMulStrictMono", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.mul_lt_mul_iff_left", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.mul_le_mul_iff_left", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.mul_lt_mul_of_pos_left", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.mul_pos", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.mul_ne_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.le_of_mul_le_mul_left", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.mul_right_inj", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.isSuccLimit_mul", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.isSuccLimit_mul_left", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["rcases", "exact", "rw", "exact", "exact"], "tactic_count": 5}
{"name": "Ordinal.smul_eq_mul", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.SetTheory.Ordinal.Arithmetic.0.Ordinal.add_mul_limit_aux", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.add_mul_succ", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "limit"], "tactic_count": 4}
{"name": "Ordinal.add_mul_of_isSuccLimit", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.SetTheory.Ordinal.Arithmetic.0.Ordinal.div_nonempty", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.div", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.div_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.SetTheory.Ordinal.Arithmetic.0.Ordinal.div_def", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.lt_mul_succ_div", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordinal.lt_mul_div_add", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Ordinal.div_le", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.lt_div", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordinal.div_pos", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Ordinal.le_div", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "limit", "revert", "simp"], "tactic_count": 6}
{"name": "Ordinal.div_lt", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.div_le_of_le_mul", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["obtain", "simp", "exact"], "tactic_count": 3}
{"name": "Ordinal.mul_lt_of_lt_div", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.zero_div", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.mul_div_le", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.div_le_left", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["obtain", "rw", "rw", "exact"], "tactic_count": 4}
{"name": "Ordinal.mul_add_div", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["apply", "apply", "rw", "apply", "rw", "apply"], "tactic_count": 6}
{"name": "Ordinal.div_eq_zero_of_lt", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "Ordinal.mul_div_cancel", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Ordinal.mul_add_div_mul", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["have", "obtain", "rw", "have", "apply", "rw", "apply", "rw", "gcongr", "rw", "exact", "grw"], "tactic_count": 12}
{"name": "Ordinal.mul_div_mul_cancel", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "Ordinal.div_one", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Ordinal.div_self", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Ordinal.mul_sub", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.isSuccLimit_add_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["constructor", "by_cases", "rw", "right", "exact", "left", "rw", "apply", "suffices", "rwa", "rcases", "exact", "simpa"], "tactic_count": 13}
{"name": "Ordinal.isSuccLimit_add_iff_of_isSuccLimit", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["rw", "obtain", "simpa", "simp"], "tactic_count": 4}
{"name": "Ordinal.dvd_add_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.div_mul_cancel", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.le_of_dvd", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.dvd_antisymm", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.antisymm", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.mod", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.mod_def", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.mod_le", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.mod_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Ordinal.mod_eq_of_lt", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Ordinal.zero_mod", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Ordinal.div_add_mod", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.mod_lt", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.mod_self", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.mod_one", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Ordinal.dvd_of_mod_eq_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.mod_eq_zero_of_dvd", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "simp", "simp"], "tactic_count": 4}
{"name": "Ordinal.dvd_iff_mod_eq_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.mul_add_mod_self", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rwa"], "tactic_count": 3}
{"name": "Ordinal.mul_mod", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Ordinal.mul_add_mod_mul", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["rw", "apply", "rw"], "tactic_count": 3}
{"name": "Ordinal.mul_mod_mul", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["obtain", "simp", "convert"], "tactic_count": 3}
{"name": "Ordinal.mod_mod_of_dvd", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["nth_rw", "rcases", "rw"], "tactic_count": 3}
{"name": "Ordinal.mod_mod", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.instCharZero", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["refine", "rwa"], "tactic_count": 2}
{"name": "Ordinal.one_add_natCast", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Ordinal.one_add_ofNat", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.natCast_mul", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.natCast_sub", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["rcases", "rw", "rw"], "tactic_count": 3}
{"name": "Ordinal.natCast_div", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["rcases", "simp", "have", "apply", "rw", "apply", "rw", "apply"], "tactic_count": 8}
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{"name": "Ordinal.lift_natCast", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.lift_ofNat", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.lt_omega0", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Ordinal.nat_lt_omega0", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.eq_nat_or_omega0_le", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["obtain", "exact", "exact"], "tactic_count": 3}
{"name": "Ordinal.omega0_pos", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.omega0_ne_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.one_lt_omega0", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Ordinal.isSuccLimit_omega0", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["rw", "refine", "obtain", "exact"], "tactic_count": 4}
{"name": "Ordinal.omega0_le", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.omega0_le_of_isSuccLimit", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.natCast_add_omega0", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["refine", "obtain", "obtain", "apply", "exact_mod_cast"], "tactic_count": 5}
{"name": "Ordinal.one_add_omega0", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.add_omega0", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Ordinal.natCast_add_of_omega0_le", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "Ordinal.isSuccLimit_iff_omega0_dvd", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["refine", "refine", "rw", "add_le_iff_of_isSuccLimit", "intro", "rcases", "grw", "exact", "rcases", "refine", "intro", "simp"], "tactic_count": 12}
{"name": "Ordinal.natCast_mod_omega0", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.add_one_of_aleph0_le", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["rw", "rwa"], "tactic_count": 2}
{"name": "Cardinal.isSuccLimit_ord", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "simpa", "rw", "rwa", "rw", "exact", "rw", "exact"], "tactic_count": 10}
{"name": "Cardinal.noMaxOrder", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Arithmetic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WellOrder.inhabited", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.isEquivalent", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "hasWellFounded_toType", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "linearOrder_toType", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "wellFoundedLT_toType", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.instSuccOrderToType", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.type", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.termTypeLT_", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal._aux_Mathlib_SetTheory_Ordinal_Basic___macroRules_Ordinal_termTypeLT__1", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.zero", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.inhabited", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.one", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "RelIso.ordinal_type_eq", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.type_eq_zero_of_empty", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.type_eq_zero_iff_isEmpty", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.type_ne_zero_iff_nonempty", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Ordinal.type_ne_zero_of_nonempty", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.type_pEmpty", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.type_empty", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.type_eq_one_of_unique", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": true, "tactics": ["cases", "exact"], "tactic_count": 2}
{"name": "Ordinal.type_eq_one_iff_unique", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.type_pUnit", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.type_unit", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.toType_empty_iff_eq_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordinal.isEmpty_toType_zero", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.toType_nonempty_iff_ne_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordinal.one_ne_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.nontrivial", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.inductionOn", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.inductionOn₂", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.inductionOn₃", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.inductionOnWellOrder", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.liftOnWellOrder", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.liftOnWellOrder_type", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": true, "tactics": ["change", "rw", "congr", "exact"], "tactic_count": 4}
{"name": "Ordinal.partialOrder", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.instLinearOrder", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "InitialSeg.ordinal_type_le", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelEmbedding.ordinal_type_le", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrincipalSeg.ordinal_type_lt", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.SetTheory.Ordinal.Basic.0.Ordinal.zero_le", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.instOrderBot", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.bot_eq_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.instIsEmptyIioZero", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Ordinal.le_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.SetTheory.Ordinal.Basic.0.Ordinal.pos_iff_ne_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.not_lt_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.eq_zero_or_pos", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.instZeroLEOneClass", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.instNeZeroOne", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.type_le_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.type_le_iff'", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.type_lt_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.initialSegToType", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": true, "tactics": ["apply", "rwa"], "tactic_count": 2}
{"name": "Ordinal.principalSegToType", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": true, "tactics": ["apply", "rwa"], "tactic_count": 2}
{"name": "Ordinal.typein", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": ["refine", "rintro", "exact", "exact", "rintro", "exact", "refine", "rintro", "exact"], "tactic_count": 9}
{"name": "Ordinal.type_subrel", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.top_typein", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.typein_lt_type", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.typein_lt_self", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "apply"], "tactic_count": 2}
{"name": "Ordinal.typein_top", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.typein_lt_typein", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.typein_le_typein", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordinal.typein_injective", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.typein_inj", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.mem_range_typein_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.typein_surj", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.typein_surjOn", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.enum", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.typein_enum", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.enum_type", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.enum_typein", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.enum_lt_enum", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.enum_le_enum", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordinal.enum_le_enum'", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordinal.enum_inj", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.enum_zero_le", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "Ordinal.enum_zero_le'", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "Ordinal.relIso_enum'", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "Ordinal.relIso_enum", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.ToType.mk", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.ToType.toOrd", "kind": "abbrev", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.instCoeToTypeElemIio", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.instCoeOutToType", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.small_Iio", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.small_Iic", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "Ordinal.small_Ico", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.small_Icc", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.small_Ioo", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.small_Ioc", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.toTypeOrderBot", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.enum_zero_eq_bot", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.lt_wf", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.wellFoundedRelation", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.wellFoundedLT", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.instConditionallyCompleteLinearOrderBot", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.induction", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.typein_apply", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordinal.card", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.card_type", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.card_typein", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.card_le_card", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.card_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.card_one", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.lift", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.type_uLift", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RelIso.ordinal_lift_type_eq", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.type_preimage", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.type_lift_preimage", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.lift_umax", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.lift_id'", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.lift_id", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.lift_uzero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.lift_type_le", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": true, "tactics": ["constructor", "exact", "exact"], "tactic_count": 3}
{"name": "Ordinal.lift_type_eq", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": true, "tactics": ["refine", "exact", "exact"], "tactic_count": 3}
{"name": "Ordinal.lift_type_lt", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": true, "tactics": ["constructor", "exact", "exact"], "tactic_count": 3}
{"name": "Ordinal.lift_le", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.lift_inj", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Ordinal.lift_lt", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Ordinal.lift_typein_top", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.liftInitialSeg", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "obtain", "use", "rw"], "tactic_count": 5}
{"name": "Ordinal.liftInitialSeg_coe", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.lift_lift", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.lift_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.lift_one", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.lift_card", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.mem_range_lift_of_le", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.le_lift_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.lt_lift_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.omega0", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.termω", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal._aux_Mathlib_SetTheory_Ordinal_Basic___macroRules_Ordinal_termω_1", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal._aux_Mathlib_SetTheory_Ordinal_Basic___unexpand_Ordinal_omega0_1", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.type_nat_lt", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.card_omega0", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.lift_omega0", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.add", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.addMonoidWithOne", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.card_add", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.type_sum_lex", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.card_nat", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "Ordinal.card_ofNat", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.instAddLeftMono", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.instAddRightMono", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.existsAddOfLE", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.canonicallyOrderedAdd", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.le_add_right", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.le_add_left", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.max_zero_left", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.max_zero_right", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.max_eq_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.sInf_empty", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.SetTheory.Ordinal.Basic.0.Ordinal.succ_le_iff'", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": true, "tactics": ["refine", "refine", "simpa", "apply", "simpa"], "tactic_count": 5}
{"name": "Ordinal.instNoMaxOrder", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.instSuccOrder", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.instSuccAddOrder", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.add_one_eq_succ", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.succ_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.succ_one", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": true, "tactics": ["congr"], "tactic_count": 1}
{"name": "Ordinal.add_succ", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.one_le_iff_ne_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordinal.succ_pos", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.succ_ne_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.lt_one_iff_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Ordinal.le_one_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Ordinal.card_succ", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Ordinal.natCast_succ", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.uniqueIioOne", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.Iio_one_default_eq", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.uniqueToTypeOne", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.one_toType_eq", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.typein_one_toType", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordinal.typein_le_typein'", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Ordinal.le_enum_succ", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "Ordinal.univ", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.univ_id", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.lift_univ", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.univ_umax", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.liftPrincipalSeg", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.liftPrincipalSeg_coe", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.liftPrincipalSeg_top", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.liftPrincipalSeg_top'", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Cardinal.mk_toType", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.ord", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.ord_eq_Inf", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.ord_eq", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.ord_le_type", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.ord_le", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": true, "tactics": ["refine", "let", "constructor", "rw", "exact", "obtain", "have", "have", "exact"], "tactic_count": 9}
{"name": "Cardinal.gc_ord_card", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.lt_ord", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.card_ord", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.card_surjective", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.bddAbove_ord_image_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.gciOrdCard", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.ord_card_le", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.lt_ord_succ_card", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.card_le_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.card_le_of_le_ord", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.ord_strictMono", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.ord_mono", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.ord_le_ord", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.ord_lt_ord", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.ord_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.ord_nat", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": true, "tactics": ["apply", "induction", "zero", "succ"], "tactic_count": 4}
{"name": "Cardinal.ord_ofNat", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.ord_one", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Cardinal.isNormal_ord", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.ord_aleph0", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": true, "tactics": ["refine", "rcases", "rw", "exact"], "tactic_count": 4}
{"name": "Cardinal.lift_ord", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": true, "tactics": ["refine", "rcases", "rwa", "rw"], "tactic_count": 4}
{"name": "Cardinal.mk_ord_toType", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Cardinal.card_typein_lt", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "Cardinal.card_typein_toType_lt", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "Cardinal.mk_Iio_ord_toType", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.ord_injective", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": true, "tactics": ["intro", "rw"], "tactic_count": 2}
{"name": "Cardinal.ord_inj", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.ord_eq_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.ord_eq_one", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.omega0_le_ord", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.ord_le_omega0", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Cardinal.ord_lt_omega0", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.omega0_lt_ord", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.ord_eq_omega0", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.ord.orderEmbedding", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.ord.orderEmbedding_coe", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.univ", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.univ_id", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.lift_univ", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.univ_umax", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.lift_lt_univ", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": true, "tactics": ["simpa", "le_of_lt"], "tactic_count": 2}
{"name": "Cardinal.lift_lt_univ'", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "Cardinal.aleph0_lt_univ", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Cardinal.nat_lt_univ", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.univ_pos", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.univ_ne_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.ord_univ", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": true, "tactics": ["refine", "have", "rcases", "rw", "apply"], "tactic_count": 5}
{"name": "Cardinal.lt_univ", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.lt_univ'", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.IsStrongLimit.univ", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cardinal.small_iff_lift_mk_lt_univ", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": true, "tactics": ["rw", "constructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 6}
{"name": "Cardinal.toTypeOrderBot", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.card_univ", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.nat_le_card", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordinal.one_le_card", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Ordinal.ofNat_le_card", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.aleph0_le_card", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordinal.card_lt_aleph0", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.nat_lt_card", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Ordinal.zero_lt_card", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Ordinal.one_lt_card", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Ordinal.ofNat_lt_card", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.card_lt_nat", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.card_lt_ofNat", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.card_le_nat", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.card_le_one", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Ordinal.card_le_ofNat", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.card_eq_nat", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Ordinal.card_eq_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Ordinal.card_eq_one", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Ordinal.mem_range_lift_of_card_le", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Ordinal.card_eq_ofNat", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.type_fintype", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordinal.type_fin", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "List.SortedGT.lt_ord_of_lt", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Basic", "is_tactic_proof": true, "tactics": ["replace", "cases", "nil", "cons", "cases", "nil", "cons", "intro", "suffices", "cases", "head", "tail", "exact"], "tactic_count": 13}
{"name": "Ordinal.CNF.rec", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.CantorNormalForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.CNF.rec_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.CantorNormalForm", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordinal.CNF.rec_pos", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.CantorNormalForm", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordinal.CNF", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.CantorNormalForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.CNF.zero_right", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.CantorNormalForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.CNF.ne_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.CantorNormalForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.CNF.zero_left", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.CantorNormalForm", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Ordinal.CNF.one_left", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.CantorNormalForm", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Ordinal.CNF.of_le_one", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.CantorNormalForm", "is_tactic_proof": true, "tactics": ["rcases", "exacts"], "tactic_count": 2}
{"name": "Ordinal.CNF.of_lt", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.CantorNormalForm", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordinal.CNF.foldr", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.CantorNormalForm", "is_tactic_proof": true, "tactics": ["refine", "rw", "intro", "rw"], "tactic_count": 4}
{"name": "Ordinal.CNF.fst_le_log", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.CantorNormalForm", "is_tactic_proof": true, "tactics": ["refine", "simp", "rw", "rintro", "rfl", "exact"], "tactic_count": 6}
{"name": "Ordinal.CNF.lt_snd", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.CantorNormalForm", "is_tactic_proof": true, "tactics": ["refine", "rw", "rintro", "exact", "exact"], "tactic_count": 5}
{"name": "Ordinal.CNF.snd_lt", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.CantorNormalForm", "is_tactic_proof": true, "tactics": ["refine", "simp", "rw", "intro", "obtain", "exact", "exact"], "tactic_count": 7}
{"name": "Ordinal.CNF.sorted", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.CantorNormalForm", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "rw", "exact", "rcases", "rw", "exact", "obtain", "rw", "exact", "rw", "refine", "rw", "rcases", "exact"], "tactic_count": 15}
{"name": "_private.Mathlib.SetTheory.Ordinal.CantorNormalForm.0.Ordinal.CNF.nodupKeys", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.CantorNormalForm", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Ordinal.CNF.coeff", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.CantorNormalForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.CNF.coeff_of_mem_CNF", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.CantorNormalForm", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "Ordinal.CNF.coeff_of_not_mem_CNF", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.CantorNormalForm", "is_tactic_proof": true, "tactics": ["rw", "simp_all"], "tactic_count": 2}
{"name": "Ordinal.CNF.coeff_zero_apply", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.CantorNormalForm", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "Ordinal.CNF.coeff_zero_right", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.CantorNormalForm", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "Ordinal.CNF.coeff_of_le_one", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.CantorNormalForm", "is_tactic_proof": true, "tactics": ["ext", "obtain", "simp", "obtain", "apply", "rw", "simp", "rw", "apply", "rw", "simpa"], "tactic_count": 11}
{"name": "Ordinal.CNF.coeff_zero_left", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.CantorNormalForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.CNF.coeff_one_left", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.CantorNormalForm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.enumOrd", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.Enum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.enumOrd_le_of_forall_lt", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Enum", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "_private.Mathlib.SetTheory.Ordinal.Enum.0.Ordinal.enumOrd_nonempty", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Enum", "is_tactic_proof": true, "tactics": ["rw", "obtain", "obtain", "exact"], "tactic_count": 4}
{"name": "_private.Mathlib.SetTheory.Ordinal.Enum.0.Ordinal.enumOrd_mem_aux", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Enum", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Ordinal.enumOrd_mem", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Enum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.enumOrd_strictMono", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Enum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.enumOrd_injective", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Enum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.enumOrd_inj", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Enum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.enumOrd_le_enumOrd", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Enum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.enumOrd_lt_enumOrd", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Enum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.id_le_enumOrd", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Enum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.le_enumOrd_self", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Enum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.enumOrd_succ_le", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Enum", "is_tactic_proof": true, "tactics": ["apply", "intro", "rw", "exact"], "tactic_count": 4}
{"name": "Ordinal.range_enumOrd", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Enum", "is_tactic_proof": true, "tactics": ["ext", "let", "constructor", "rintro", "exact", "intro", "refine", "intro", "by_contra", "exact", "exact"], "tactic_count": 11}
{"name": "Ordinal.enumOrd_surjective", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Enum", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Ordinal.enumOrd_le_of_subset", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Enum", "is_tactic_proof": true, "tactics": ["intro", "rw", "gcongr", "exacts", "termination_by"], "tactic_count": 5}
{"name": "Ordinal.eq_enumOrd", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Enum", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "exact", "rintro", "rwa"], "tactic_count": 5}
{"name": "Ordinal.enumOrd_range", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Enum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.isNormal_enumOrd", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Enum", "is_tactic_proof": true, "tactics": ["refine", "trans", "refine", "have", "apply", "rintro", "exact", "exact", "exact"], "tactic_count": 9}
{"name": "Ordinal.enumOrd_univ", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Enum", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Ordinal.enumOrd_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Enum", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordinal.enumOrdOrderIso", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.Enum", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.instPow", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.SetTheory.Ordinal.Exponential.0.Ordinal.opow_of_ne_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.zero_opow'", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.zero_opow_le", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Ordinal.zero_opow", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Ordinal.opow_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": true, "tactics": ["obtain", "rw", "rw"], "tactic_count": 3}
{"name": "Ordinal.opow_succ", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": true, "tactics": ["obtain", "rw", "rw"], "tactic_count": 3}
{"name": "Ordinal.opow_limit", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Ordinal.opow_le_of_isSuccLimit", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Ordinal.lt_opow_of_isSuccLimit", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Ordinal.opow_one", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Ordinal.one_opow", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "limit", "refine", "rw", "exact"], "tactic_count": 7}
{"name": "Ordinal.opow_pos", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": true, "tactics": ["have", "induction", "zero", "succ", "rw", "exact", "limit"], "tactic_count": 7}
{"name": "Ordinal.opow_ne_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.opow_eq_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "Ordinal.opow_natCast", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Ordinal.isNormal_opow", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": true, "tactics": ["have", "refine", "simpa", "simp"], "tactic_count": 4}
{"name": "Ordinal.opow_lt_opow_iff_right", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.opow_le_opow_iff_right", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.opow_right_inj", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.isSuccLimit_opow", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.isSuccLimit_opow_left", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": true, "tactics": ["rcases", "exact", "rw", "exact", "exact"], "tactic_count": 5}
{"name": "Ordinal.opow_le_opow_right", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": true, "tactics": ["rcases", "simp_all", "exact"], "tactic_count": 3}
{"name": "Ordinal.opow_le_opow_left", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": true, "tactics": ["by_cases", "by_cases", "induction", "zero", "succ", "limit", "exact"], "tactic_count": 7}
{"name": "Ordinal.opow_le_opow", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.left_le_opow", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": true, "tactics": ["nth_rw", "rcases", "rcases", "rw", "rw", "exact", "rw", "rwa"], "tactic_count": 8}
{"name": "Ordinal.left_lt_opow", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": true, "tactics": ["conv_lhs", "rwa"], "tactic_count": 2}
{"name": "Ordinal.right_le_opow", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.opow_lt_opow_left_of_succ", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Ordinal.opow_add", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "have", "rw", "exact", "obtain", "induction", "zero", "succ", "limit", "refine", "simpa"], "tactic_count": 12}
{"name": "Ordinal.opow_one_add", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordinal.opow_dvd_opow", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.opow_dvd_opow_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.opow_mul", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "have", "by_cases", "obtain", "induction", "zero", "succ", "limit", "refine", "simpa"], "tactic_count": 11}
{"name": "Ordinal.opow_mul_add_pos", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.opow_mul_add_lt_opow_mul", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": true, "tactics": ["apply", "rwa", "grw"], "tactic_count": 3}
{"name": "Ordinal.opow_mul_add_lt_opow_mul_succ", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.opow_mul_add_lt_opow", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": true, "tactics": ["apply", "rw", "exact"], "tactic_count": 3}
{"name": "Ordinal.opow_mul_add_lt_opow_succ", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.log", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.SetTheory.Ordinal.Exponential.0.Ordinal.log_nonempty", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.log_def", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.log_of_left_le_one", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.log_zero_left", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.log_zero_right", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": true, "tactics": ["obtain", "rw", "apply", "rw", "exact", "rw"], "tactic_count": 6}
{"name": "Ordinal.log_one_left", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.succ_log_def", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": true, "tactics": ["let", "have", "rcases", "refine", "simpa", "rw", "simpa", "rcases", "exact"], "tactic_count": 9}
{"name": "Ordinal.lt_opow_succ_log_self", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": true, "tactics": ["rcases", "apply", "rw", "exact"], "tactic_count": 4}
{"name": "Ordinal.opow_log_le_self", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": true, "tactics": ["rcases", "exact", "rcases", "refine", "have", "rwa", "rwa"], "tactic_count": 7}
{"name": "Ordinal.opow_le_iff_le_log", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": true, "tactics": ["constructor", "apply", "intro", "apply", "exact"], "tactic_count": 5}
{"name": "Ordinal.opow_le_iff_le_log'", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": true, "tactics": ["obtain", "simp", "exact"], "tactic_count": 3}
{"name": "Ordinal.le_log_of_opow_le", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact", "exact"], "tactic_count": 4}
{"name": "Ordinal.opow_le_of_le_log", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact", "rwa"], "tactic_count": 4}
{"name": "Ordinal.lt_opow_iff_log_lt", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.lt_opow_iff_log_lt'", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.lt_opow_of_log_lt", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.lt_log_of_lt_opow", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.log_pos", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Ordinal.log_eq_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": true, "tactics": ["rcases", "exact", "rcases", "rcases", "exact", "exact", "rwa"], "tactic_count": 7}
{"name": "Ordinal.log_mono_right", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": true, "tactics": ["obtain", "simp_rw", "obtain", "exact", "rw"], "tactic_count": 5}
{"name": "Ordinal.log_le_self", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": true, "tactics": ["obtain", "rw", "obtain", "exact", "simp_rw"], "tactic_count": 5}
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{"name": "Ordinal.mod_opow_log_lt_self", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": true, "tactics": ["rcases", "simpa", "exact"], "tactic_count": 3}
{"name": "Ordinal.log_mod_opow_log_lt_log_self", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": true, "tactics": ["rcases", "rw", "exact", "rw", "apply", "apply", "rw", "exact"], "tactic_count": 8}
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{"name": "Ordinal.log_opow_mul_add", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": true, "tactics": ["rw", "constructor", "grw", "apply", "rw", "gcongr", "rw", "exact", "exact"], "tactic_count": 9}
{"name": "Ordinal.log_opow_mul", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Ordinal.log_opow", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": true, "tactics": ["convert", "rw", "rw"], "tactic_count": 3}
{"name": "Ordinal.div_opow_log_pos", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": true, "tactics": ["rcases", "simpa", "rw", "exact"], "tactic_count": 4}
{"name": "Ordinal.div_opow_log_lt", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Ordinal.add_log_le_log_mul", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact", "simpa"], "tactic_count": 4}
{"name": "Ordinal.omega0_opow_mul_nat_lt", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": true, "tactics": ["apply", "rw", "gcongr", "exacts"], "tactic_count": 4}
{"name": "Ordinal.lt_omega0_opow", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": true, "tactics": ["refine", "obtain", "use", "rw", "exact"], "tactic_count": 5}
{"name": "Ordinal.lt_omega0_opow_succ", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": true, "tactics": ["refine", "obtain", "refine", "grw", "exact"], "tactic_count": 5}
{"name": "Ordinal.natCast_opow", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.iSup_pow_natCast", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Exponential", "is_tactic_proof": true, "tactics": ["simp_rw", "rcases", "exact", "rw", "refine", "exact_mod_cast"], "tactic_count": 6}
{"name": "Ordinal.bfamilyOfFamily'", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.bfamilyOfFamily", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.familyOfBFamily'", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.familyOfBFamily", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.bfamilyOfFamily'_typein", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Ordinal.bfamilyOfFamily_typein", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.familyOfBFamily'_enum", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Ordinal.familyOfBFamily_enum", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.brange", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.mem_brange", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.mem_brange_self", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.range_familyOfBFamily'", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": true, "tactics": ["refine", "rintro", "apply", "rintro", "exact"], "tactic_count": 5}
{"name": "Ordinal.range_familyOfBFamily", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.brange_bfamilyOfFamily'", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": true, "tactics": ["refine", "rintro", "apply", "rintro", "exact"], "tactic_count": 5}
{"name": "Ordinal.brange_bfamilyOfFamily", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.brange_const", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Ordinal.comp_bfamilyOfFamily'", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.comp_bfamilyOfFamily", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.comp_familyOfBFamily'", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.comp_familyOfBFamily", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.bddAbove_range", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.bddAbove_of_small", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": true, "tactics": ["obtain", "use", "intro", "simpa"], "tactic_count": 4}
{"name": "Ordinal.bddAbove_iff_small", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.bddAbove_image", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Ordinal.bddAbove_range_comp", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Ordinal.le_iSup", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.iSup_le_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.iSup_le", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.lt_iSup_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.succ_lt_iSup_of_ne_iSup", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": true, "tactics": ["by_contra", "exact", "hao.not_ge"], "tactic_count": 3}
{"name": "Ordinal.iSup_eq_zero_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "Ordinal.iSup_eq_of_range_eq", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.iSup_sum", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": true, "tactics": ["apply", "rintro", "exact", "exact", "all_goals", "apply", "rintro", "apply"], "tactic_count": 8}
{"name": "Ordinal.unbounded_range_of_le_iSup", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.IsNormal.map_iSup_of_bddAbove", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.IsNormal.map_iSup", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.IsNormal.map_sSup_of_bddAbove", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.IsNormal.map_sSup", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.IsNormal.apply_of_isSuccLimit", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.sSup_ord", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": true, "tactics": ["obtain", "simp", "by_cases", "exact", "rw", "simp"], "tactic_count": 6}
{"name": "Ordinal.iSup_ord", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordinal.lift_card_sInf_compl_le", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "Ordinal.card_sInf_range_compl_le_lift", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": true, "tactics": ["rw", "apply", "rw", "exact"], "tactic_count": 4}
{"name": "Ordinal.card_sInf_range_compl_le", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.sInf_compl_lt_lift_ord_succ", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Ordinal.sInf_compl_lt_ord_succ", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.iSup_eq_iSup", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.bsup", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.iSup_eq_bsup", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.iSup'_eq_bsup", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.sSup_eq_bsup", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": true, "tactics": ["congr", "rw"], "tactic_count": 2}
{"name": "Ordinal.bsup'_eq_iSup", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Ordinal.bsup_eq_iSup", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.bsup_eq_bsup", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordinal.bsup_congr", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": true, "tactics": ["subst", "rfl"], "tactic_count": 2}
{"name": "Ordinal.bsup_le_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.bsup_le", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.le_bsup", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.lt_bsup", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Ordinal.IsNormal.bsup", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.lt_bsup_of_ne_bsup", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.bsup_not_succ_of_ne_bsup", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Ordinal.bsup_eq_zero_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "Ordinal.lt_bsup_of_limit", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.bsup_succ_of_mono", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.bsup_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.bsup_const", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.bsup_one", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Ordinal.bsup_le_of_brange_subset", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.bsup_eq_of_brange_eq", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.iSup_Iio_eq_bsup", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Ordinal.lsub", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.iSup_eq_lsub", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.lsub_le_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Ordinal.lsub_le", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.lt_lsub", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.lt_lsub_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Ordinal.iSup_le_lsub", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.lsub_le_succ_iSup", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.iSup_eq_lsub_or_succ_iSup_eq_lsub", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": true, "tactics": ["rcases", "exact", "exact"], "tactic_count": 3}
{"name": "Ordinal.succ_iSup_le_lsub_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": true, "tactics": ["refine", "by_contra", "have", "exact", "rintro", "rw", "exact"], "tactic_count": 7}
{"name": "Ordinal.succ_iSup_eq_lsub_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.iSup_eq_lsub_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact", "by_contra", "have", "have", "hf", "rw", "exact", "rw", "exact"], "tactic_count": 11}
{"name": "Ordinal.iSup_eq_lsub_iff_lt_iSup", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.lsub_empty", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Ordinal.lsub_pos", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.lsub_eq_zero_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": true, "tactics": ["refine", "have", "rw", "exact"], "tactic_count": 4}
{"name": "Ordinal.lsub_const", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.lsub_unique", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.lsub_le_of_range_subset", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.lsub_eq_of_range_eq", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.lsub_sum", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.lsub_notMem_range", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.nonempty_compl_range", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.lsub_typein", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.iSup_typein_limit", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": true, "tactics": ["rw", "assumption"], "tactic_count": 2}
{"name": "Ordinal.iSup_typein_succ", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": ["rcases", "rw", "simp", "exact", "rw", "apply"], "tactic_count": 6}
{"name": "Ordinal.blsub", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.bsup_eq_blsub", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.lsub_eq_blsub'", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.lsub_eq_lsub", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordinal.lsub_eq_blsub", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.blsub_eq_lsub'", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.blsub_eq_blsub", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordinal.blsub_eq_lsub", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.blsub_congr", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": true, "tactics": ["subst", "rfl"], "tactic_count": 2}
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{"name": "Ordinal.blsub_le", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.lt_blsub", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.lt_blsub_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Ordinal.bsup_le_blsub", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.blsub_le_bsup_succ", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.bsup_eq_blsub_or_succ_bsup_eq_blsub", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Ordinal.bsup_succ_le_blsub", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": true, "tactics": ["refine", "by_contra", "exact", "rintro", "rw", "exact"], "tactic_count": 6}
{"name": "Ordinal.bsup_succ_eq_blsub", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.bsup_eq_blsub_iff_succ", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "Ordinal.bsup_eq_blsub_iff_lt_bsup", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.bsup_eq_blsub_of_lt_succ_limit", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Ordinal.blsub_succ_of_mono", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.blsub_eq_zero_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Ordinal.blsub_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordinal.blsub_pos", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.blsub_type", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.blsub_const", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.blsub_one", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.blsub_id", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.bsup_id_limit", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.bsup_id_succ", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.blsub_le_of_brange_subset", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.blsub_eq_of_brange_eq", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.bsup_comp", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": true, "tactics": ["apply", "apply", "rw", "rcases", "exact"], "tactic_count": 5}
{"name": "Ordinal.blsub_comp", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.IsNormal.bsup_eq", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordinal.IsNormal.blsub_eq", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Ordinal.isNormal_iff_lt_succ_and_bsup_eq", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.isNormal_iff_lt_succ_and_blsub_eq", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": true, "tactics": ["rw", "intro", "constructor"], "tactic_count": 3}
{"name": "Ordinal.IsNormal.eq_iff_zero_and_succ", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_surjective_of_ordinal", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": true, "tactics": ["intro", "obtain", "apply", "rw", "exact"], "tactic_count": 5}
{"name": "not_injective_of_ordinal", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_small_ordinal", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.uncountable", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.not_bddAbove_compl_of_small", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": true, "tactics": ["rw", "intro", "have", "rw", "exact"], "tactic_count": 5}
{"name": "Ordinal.iSup_natCast", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.apply_omega0_of_isNormal", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordinal.iSup_add_natCast", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.iSup_mul_natCast", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Family", "is_tactic_proof": true, "tactics": ["rcases", "rw", "exact", "exact"], "tactic_count": 4}
{"name": "Ordinal.nfpFamily", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.foldr_le_nfpFamily", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.le_nfpFamily", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.lt_nfpFamily_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.nfpFamily_le_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.nfpFamily_le", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.nfpFamily_monotone", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.apply_lt_nfpFamily", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.apply_lt_nfpFamily_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": true, "tactics": ["refine", "let", "exact"], "tactic_count": 3}
{"name": "Ordinal.nfpFamily_le_apply", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": true, "tactics": ["contrapose"], "tactic_count": 1}
{"name": "Ordinal.nfpFamily_le_fp", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": true, "tactics": ["apply", "induction", "nil", "cons"], "tactic_count": 4}
{"name": "Ordinal.nfpFamily_fp", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": true, "tactics": ["rw", "apply", "exact", "exact"], "tactic_count": 4}
{"name": "Ordinal.apply_le_nfpFamily", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact", "rw", "exact"], "tactic_count": 5}
{"name": "Ordinal.nfpFamily_eq_self", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": true, "tactics": ["apply", "intro", "rw"], "tactic_count": 3}
{"name": "Ordinal.not_bddAbove_fp_family", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": true, "tactics": ["rw", "refine", "rintro", "exact"], "tactic_count": 4}
{"name": "Ordinal.derivFamily", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.derivFamily_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.derivFamily_succ", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.derivFamily_limit", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.isNormal_derivFamily", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact", "rw", "have", "exact"], "tactic_count": 6}
{"name": "Ordinal.derivFamily_strictMono", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.derivFamily_fp", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": true, "tactics": ["induction", "zero", "rw", "exact", "succ", "rw", "exact", "limit", "have", "rw", "refine", "rw", "refine", "rw"], "tactic_count": 14}
{"name": "Ordinal.le_iff_derivFamily", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.fp_iff_derivFamily", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.mem_range_derivFamily", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.derivFamily_eq_enumOrd", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": true, "tactics": ["rw", "use", "rw", "refine", "rintro", "rw", "exact", "rw", "rwa"], "tactic_count": 9}
{"name": "Ordinal.nfp", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.nfp_eq_nfpFamily", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.iSup_iterate_eq_nfp", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": true, "tactics": ["apply", "rw", "intro", "rw", "exact", "apply", "intro", "rw", "exact"], "tactic_count": 9}
{"name": "Ordinal.iterate_le_nfp", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Ordinal.le_nfp", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.lt_nfp_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Ordinal.nfp_le_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Ordinal.nfp_le", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.nfp_id", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": true, "tactics": ["ext", "simp_rw", "exact"], "tactic_count": 3}
{"name": "Ordinal.nfp_monotone", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.iterate_lt_nfp", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": true, "tactics": ["apply", "rw", "exact"], "tactic_count": 3}
{"name": "Ordinal.apply_lt_nfp", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": true, "tactics": ["unfold", "rw", "exact"], "tactic_count": 3}
{"name": "Ordinal.nfp_le_apply", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.nfp_le_fp", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.nfp_fp", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.apply_le_nfp", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.nfp_eq_self", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.not_bddAbove_fp", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": true, "tactics": ["convert", "exact"], "tactic_count": 2}
{"name": "Ordinal.deriv", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.deriv_eq_derivFamily", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.deriv_zero_right", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.deriv_succ", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.deriv_limit", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.isNormal_deriv", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.deriv_strictMono", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.deriv_eq_id_of_nfp_eq_id", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.deriv_fp", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.le_iff_deriv", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": true, "tactics": ["unfold", "rw", "exact"], "tactic_count": 3}
{"name": "Ordinal.mem_range_deriv", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordinal.fp_iff_deriv", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.deriv_eq_enumOrd", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": true, "tactics": ["convert", "exact"], "tactic_count": 2}
{"name": "Ordinal.nfp_zero_left", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": true, "tactics": ["rw", "apply", "intro", "cases", "rfl", "rw", "simp"], "tactic_count": 7}
{"name": "Ordinal.nfp_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "Ordinal.deriv_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.deriv_zero_left", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordinal.nfp_add_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": true, "tactics": ["simp_rw", "congr", "induction", "zero", "succ"], "tactic_count": 5}
{"name": "Ordinal.nfp_add_eq_mul_omega0", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": true, "tactics": ["apply", "rw", "exact", "dsimp"], "tactic_count": 4}
{"name": "Ordinal.add_eq_right_iff_mul_omega0_le", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": true, "tactics": ["refine", "rw", "obtain", "rw", "exact", "have", "nth_rw", "rwa"], "tactic_count": 8}
{"name": "Ordinal.add_le_right_iff_mul_omega0_le", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Ordinal.deriv_add_eq_mul_omega0_add", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": true, "tactics": ["revert", "rw", "refine", "rw", "exact", "rw", "exact"], "tactic_count": 7}
{"name": "Ordinal.nfp_mul_one", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": true, "tactics": ["rw", "congr", "funext", "induction", "zero", "succ"], "tactic_count": 6}
{"name": "Ordinal.nfp_mul_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": true, "tactics": ["rw", "intro", "induction", "zero", "succ"], "tactic_count": 5}
{"name": "Ordinal.nfp_mul_eq_opow_omega0", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": true, "tactics": ["rcases", "rw", "simp_rw", "exact", "apply", "apply", "rw", "rw", "exact"], "tactic_count": 9}
{"name": "Ordinal.eq_zero_or_opow_omega0_le_of_mul_eq_right", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": true, "tactics": ["rcases", "rw", "exact", "rw", "intro", "rw", "rw", "exact"], "tactic_count": 8}
{"name": "Ordinal.mul_eq_right_iff_opow_omega0_dvd", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": true, "tactics": ["rcases", "rw", "exact", "refine", "rw", "rw", "rcases", "exact", "refine", "rwa", "obtain", "rw"], "tactic_count": 12}
{"name": "Ordinal.mul_le_right_iff_opow_omega0_dvd", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Ordinal.nfp_mul_opow_omega0_add", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": true, "tactics": ["apply", "apply", "rw", "gcongr", "dsimp", "obtain", "rw", "apply", "have", "rw", "have", "rw", "rwa"], "tactic_count": 13}
{"name": "Ordinal.deriv_mul_eq_opow_omega0_mul", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPoint", "is_tactic_proof": true, "tactics": ["revert", "rw", "refine", "rw", "rw", "exact"], "tactic_count": 6}
{"name": "Cardinal.not_injective_limitation_set", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPointApproximants", "is_tactic_proof": true, "tactics": ["intro", "have", "have", "simpa", "rw", "exact"], "tactic_count": 6}
{"name": "OrdinalApprox.lfpApprox", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.FixedPointApproximants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrdinalApprox.lfpApprox_monotone", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPointApproximants", "is_tactic_proof": true, "tactics": ["intro", "rw", "gcongr", "simp", "intro", "use", "exact"], "tactic_count": 7}
{"name": "OrdinalApprox.le_lfpApprox", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPointApproximants", "is_tactic_proof": true, "tactics": ["rw", "apply", "simp"], "tactic_count": 3}
{"name": "OrdinalApprox.lfpApprox_add_one", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPointApproximants", "is_tactic_proof": true, "tactics": ["apply", "conv", "apply", "simp", "apply", "apply", "apply", "exact", "intro", "apply", "conv", "apply", "simp", "rw", "apply", "simp", "use"], "tactic_count": 17}
{"name": "OrdinalApprox.lfpApprox_mono_left", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPointApproximants", "is_tactic_proof": true, "tactics": ["intro", "induction", "h", "rw", "apply", "simp", "le_sup_left,", "intro", "apply", "apply", "use", "apply", "simp", "exact"], "tactic_count": 14}
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{"name": "OrdinalApprox.lfpApprox_eq_of_mem_fixedPoints", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPointApproximants", "is_tactic_proof": true, "tactics": ["rw", "induction", "h", "apply", "conv", "apply", "simp", "forall_exists_index,", "apply", "intro", "by_cases", "rw", "apply", "simp", "exact", "rw", "exact"], "tactic_count": 17}
{"name": "OrdinalApprox.exists_lfpApprox_eq_lfpApprox", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPointApproximants", "is_tactic_proof": true, "tactics": ["have", "rw", "let", "use", "use", "apply", "intro", "exact"], "tactic_count": 8}
{"name": "OrdinalApprox.lfpApprox_mem_fixedPoints_of_eq", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPointApproximants", "is_tactic_proof": false, "tactics": ["have", "rw", "exact", "rw", "exact", "exact", "exact"], "tactic_count": 7}
{"name": "OrdinalApprox.lfpApprox_ord_mem_fixedPoint", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPointApproximants", "is_tactic_proof": true, "tactics": ["let", "cases", "inl", "inr"], "tactic_count": 4}
{"name": "OrdinalApprox.lfpApprox_le_of_mem_fixedPoints", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPointApproximants", "is_tactic_proof": true, "tactics": ["induction", "h", "rw", "apply", "simp", "intro", "simp", "cases", "inl", "let", "rw", "exact", "inr", "rw", "exact"], "tactic_count": 15}
{"name": "OrdinalApprox.lfpApprox_ord_eq_lfp", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPointApproximants", "is_tactic_proof": true, "tactics": ["apply", "have", "let", "exact", "have", "simpa", "lfpApprox_ord_mem_fixedPoint", "let", "exact"], "tactic_count": 9}
{"name": "OrdinalApprox.lfp_mem_range_lfpApprox", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPointApproximants", "is_tactic_proof": true, "tactics": ["use", "exact"], "tactic_count": 2}
{"name": "OrdinalApprox.gfpApprox", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.FixedPointApproximants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrdinalApprox.gfpApprox_antitone", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPointApproximants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrdinalApprox.gfpApprox_le", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPointApproximants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrdinalApprox.gfpApprox_add_one", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPointApproximants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrdinalApprox.gfpApprox_mono_left", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPointApproximants", "is_tactic_proof": true, "tactics": ["intro", "have", "exact"], "tactic_count": 3}
{"name": "OrdinalApprox.gfpApprox_mono_mid", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPointApproximants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrdinalApprox.gfpApprox_eq_of_mem_fixedPoints", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPointApproximants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrdinalApprox.exists_gfpApprox_eq_gfpApprox", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPointApproximants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrdinalApprox.gfpApprox_ord_mem_fixedPoint", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPointApproximants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrdinalApprox.le_gfpApprox_of_mem_fixedPoints", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPointApproximants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrdinalApprox.gfpApprox_ord_eq_gfp", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPointApproximants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrdinalApprox.gfp_mem_range_gfpApprox", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.FixedPointApproximants", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NatOrdinal", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NatOrdinal.instNeZeroOne", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.toNatOrdinal", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NatOrdinal.toOrdinal", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NatOrdinal.toOrdinal_symm_eq", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NatOrdinal.toOrdinal_toNatOrdinal", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NatOrdinal.lt_wf", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NatOrdinal.instWellFoundedLT", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NatOrdinal.instConditionallyCompleteLinearOrderBot", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NatOrdinal.bot_eq_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NatOrdinal.toOrdinal_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NatOrdinal.toOrdinal_one", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NatOrdinal.toOrdinal_eq_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NatOrdinal.toOrdinal_eq_one", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NatOrdinal.toOrdinal_max", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NatOrdinal.toOrdinal_min", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NatOrdinal.succ_def", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NatOrdinal.zero_le", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NatOrdinal.not_lt_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NatOrdinal.lt_one_iff_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NatOrdinal.rec", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NatOrdinal.induction", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "NatOrdinal.small_Iic", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NatOrdinal.small_Ico", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NatOrdinal.small_Icc", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NatOrdinal.small_Ioo", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NatOrdinal.small_Ioc", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.toNatOrdinal_symm_eq", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.toNatOrdinal_toOrdinal", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.toNatOrdinal_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.toNatOrdinal_one", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.toNatOrdinal_eq_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.toNatOrdinal_eq_one", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.toNatOrdinal_max", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.toNatOrdinal_min", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.nadd", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NaturalOps.term_♯_", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NaturalOps._aux_Mathlib_SetTheory_Ordinal_NaturalOps___macroRules_NaturalOps_term_♯__1", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NaturalOps._aux_Mathlib_SetTheory_Ordinal_NaturalOps___unexpand_Ordinal_nadd_1", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.nmul", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NaturalOps.term_⨳_", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Ordinal.lt_nadd_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Ordinal.nadd_le_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Ordinal.nadd_lt_nadd_left", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.nadd_lt_nadd_right", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.nadd_le_nadd_left", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": true, "tactics": ["rcases", "exact", "exact"], "tactic_count": 3}
{"name": "Ordinal.nadd_le_nadd_right", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": true, "tactics": ["rcases", "exact", "exact"], "tactic_count": 3}
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{"name": "_private.Mathlib.SetTheory.Ordinal.NaturalOps.0.Ordinal.iSup_nadd_of_monotone", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": true, "tactics": ["apply", "rw", "rintro", "obtain", "exact", "exact", "all_goals", "apply", "rintro", "refine", "apply_rules"], "tactic_count": 11}
{"name": "Ordinal.nadd_assoc", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": true, "tactics": ["unfold", "rw", "congr", "exact", "exact", "termination_by"], "tactic_count": 6}
{"name": "Ordinal.nadd_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": true, "tactics": ["rw", "convert", "rename_i", "cases", "exact", "termination_by"], "tactic_count": 6}
{"name": "Ordinal.zero_nadd", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordinal.nadd_one", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": ["rw", "rintro", "rwa", "termination_by"], "tactic_count": 4}
{"name": "Ordinal.one_nadd", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordinal.nadd_succ", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordinal.succ_nadd", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordinal.nadd_nat", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Ordinal.nat_nadd", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordinal.add_le_nadd", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "limit", "rw", "rintro", "exact"], "tactic_count": 7}
{"name": "NatOrdinal.instAdd", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NatOrdinal.instSuccAddOrder", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NatOrdinal.lt_add_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NatOrdinal.add_le_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NatOrdinal.instAddLeftStrictMono", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NatOrdinal.instAddLeftMono", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NatOrdinal.instAddLeftReflectLE", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NatOrdinal.instAddCommMonoid", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NatOrdinal.instIsOrderedCancelAddMonoid", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NatOrdinal.instAddMonoidWithOne", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NatOrdinal.toOrdinal_natCast", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "change", "rw"], "tactic_count": 5}
{"name": "NatOrdinal.instCharZero", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.nadd_eq_add", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.toNatOrdinal_natCast", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Ordinal.lt_of_nadd_lt_nadd_left", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.lt_of_nadd_lt_nadd_right", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.le_of_nadd_le_nadd_left", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.le_of_nadd_le_nadd_right", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.nadd_lt_nadd_iff_left", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.nadd_lt_nadd_iff_right", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.nadd_le_nadd_iff_left", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.nadd_le_nadd_iff_right", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.nadd_le_nadd", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.nadd_lt_nadd", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.nadd_lt_nadd_of_lt_of_le", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.nadd_lt_nadd_of_le_of_lt", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.nadd_left_cancel", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.nadd_right_cancel", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.nadd_left_cancel_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.nadd_right_cancel_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.le_nadd_self", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Ordinal.le_nadd_left", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.le_self_nadd", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Ordinal.le_nadd_right", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.nadd_left_comm", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.nadd_right_comm", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.SetTheory.Ordinal.NaturalOps.0.Ordinal.nmul_nonempty", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Ordinal.nmul_nadd_lt", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": true, "tactics": ["conv_rhs", "exact"], "tactic_count": 2}
{"name": "Ordinal.nmul_nadd_le", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "exact", "rw", "exact"], "tactic_count": 5}
{"name": "Ordinal.lt_nmul_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": true, "tactics": ["refine", "rw", "simpa", "rintro", "have", "rwa"], "tactic_count": 6}
{"name": "Ordinal.nmul_le_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordinal.nmul_comm", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": true, "tactics": ["rw", "congr", "rw", "exact", "rw", "exact", "termination_by"], "tactic_count": 7}
{"name": "Ordinal.nmul_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Ordinal.zero_nmul", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordinal.nmul_one", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": true, "tactics": ["rw", "convert", "ext", "refine", "simpa", "simpa", "termination_by"], "tactic_count": 7}
{"name": "Ordinal.one_nmul", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordinal.nmul_lt_nmul_of_pos_left", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.nmul_lt_nmul_of_pos_right", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.nmul_le_nmul_right", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": true, "tactics": ["rcases", "exact", "all_goals"], "tactic_count": 3}
{"name": "Ordinal.nmul_le_nmul_left", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Ordinal.nmul_le_nmul", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.nmul_nadd", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": true, "tactics": ["refine", "rw", "rcases", "have", "rw", "simp", "rwa", "nadd_left_comm", "have", "rw", "simp", "rwa", "nadd_lt_nadd_iff_left,", "nadd_left_comm", "nadd_assoc]", "rcases", "have", "rw", "simp", "rwa", "nadd_left_comm", "nadd_left_comm,", "rcases", "have", "rw", "simp", "rwa", "nadd_lt_nadd_iff_left,", "nadd_comm", "termination_by"], "tactic_count": 30}
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{"name": "Ordinal.nmul_nadd_lt₃", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
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{"name": "_private.Mathlib.SetTheory.Ordinal.NaturalOps.0.Ordinal.nmul_nadd_lt₃'", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": true, "tactics": ["simp", "convert"], "tactic_count": 2}
{"name": "Ordinal.lt_nmul_iff₃", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": true, "tactics": ["refine", "rcases", "rcases", "refine", "have", "simp", "rw", "nadd_left_comm", "nadd_left_comm", "simpa", "have", "repeat", "assumption"], "tactic_count": 13}
{"name": "Ordinal.nmul_le_iff₃", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "_private.Mathlib.SetTheory.Ordinal.NaturalOps.0.Ordinal.nmul_le_iff₃'", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": true, "tactics": ["simp", "constructor", "convert", "convert"], "tactic_count": 4}
{"name": "Ordinal.nmul_assoc", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": true, "tactics": ["apply", "rw", "intro", "repeat", "exact", "rw", "intro", "repeat", "exact", "termination_by"], "tactic_count": 10}
{"name": "NatOrdinal.instMul", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NatOrdinal.lt_mul_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NatOrdinal.mul_le_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NatOrdinal.mul_add_lt", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NatOrdinal.nmul_nadd_le", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NatOrdinal.instCommSemiring", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NatOrdinal.instIsOrderedMonoid", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NatOrdinal.instIsOrderedRing", "kind": "instance", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.nmul_eq_mul", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.NaturalOps", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Ordinal.mem_closed_iff_bsup", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Topology", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordinal.isClosed_iff_iSup", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Topology", "is_tactic_proof": true, "tactics": ["use", "rw", "intro", "rcases", "exact"], "tactic_count": 5}
{"name": "Ordinal.isClosed_iff_bsup", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Topology", "is_tactic_proof": true, "tactics": ["rw", "refine", "exact", "rw", "apply", "exact", "hf"], "tactic_count": 7}
{"name": "Ordinal.isSuccLimit_of_mem_frontier", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Topology", "is_tactic_proof": true, "tactics": ["simp", "by_contra", "rw", "rcases", "rcases", "rw", "subst", "exact"], "tactic_count": 8}
{"name": "Ordinal.isNormal_iff_strictMono_and_continuous", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.enumOrd_isNormal_iff_isClosed", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Topology", "is_tactic_proof": true, "tactics": ["have", "refine", "let", "suffices", "rw", "exact", "rw", "congr", "ext", "change", "rw", "rw", "suffices", "obtain", "rw", "apply", "by_contra", "apply", "rw", "exact"], "tactic_count": 20}
{"name": "Ordinal.IsAcc", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.IsClosedBelow", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.isAcc_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Topology", "is_tactic_proof": true, "tactics": ["dsimp", "constructor", "rw", "intro", "constructor", "rintro", "obtain", "exact", "intro", "obtain", "use", "refine", "have", "rwa", "rw", "intro", "obtain", "obtain", "use", "exact"], "tactic_count": 20}
{"name": "Ordinal.IsAcc.forall_lt", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.IsAcc.pos", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.IsAcc.isSuccLimit", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Topology", "is_tactic_proof": true, "tactics": ["rw", "rw", "refine", "rcases", "exact"], "tactic_count": 5}
{"name": "Ordinal.IsAcc.mono", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Topology", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Ordinal.IsAcc.inter_Ioo_nonempty", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.accPt_subtype", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Topology", "is_tactic_proof": true, "tactics": ["constructor", "intro", "have", "rw", "intro", "obtain", "obtain", "use", "refine", "exact", "intro", "rw", "intro", "by_cases", "have", "rintro", "rw", "specialize", "obtain", "exact", "have", "contrapose", "obtain", "use", "constructor", "exact", "intro", "have", "have", "rw", "subst", "exact", "obtain", "obtain", "use", "exact", "have", "have", "rintro", "obtain", "have", "simp_rw", "exact", "obtain", "obtain", "use", "refine", "rw", "exact"], "tactic_count": 49}
{"name": "Ordinal.isClosedBelow_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Topology", "is_tactic_proof": true, "tactics": ["dsimp", "constructor", "intro", "have", "rw", "exact", "intro", "rw", "intro"], "tactic_count": 9}
{"name": "Ordinal.IsClosedBelow.sInter", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Topology", "is_tactic_proof": true, "tactics": ["rw", "intro", "exact"], "tactic_count": 3}
{"name": "Ordinal.IsClosedBelow.iInter", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.veblenWith", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.veblenWith_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordinal.veblenWith_of_ne_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordinal.isNormal_veblenWith'", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Ordinal.isNormal_veblenWith", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": true, "tactics": ["obtain", "rwa", "exact"], "tactic_count": 3}
{"name": "Ordinal.mem_range_veblenWith", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Ordinal.veblenWith_veblenWith_of_lt", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "Ordinal.veblenWith_eq_self_of_le", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": true, "tactics": ["obtain", "assumption", "rw"], "tactic_count": 3}
{"name": "Ordinal.veblenWith_mem_range", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": true, "tactics": ["obtain", "simp", "rw", "simp"], "tactic_count": 4}
{"name": "Ordinal.veblenWith_succ", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": false, "tactics": ["rw", "apply", "ext", "rw", "use", "rintro", "obtain", "rw", "rw", "exact", "exact"], "tactic_count": 11}
{"name": "Ordinal.veblenWith_right_strictMono", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.veblenWith_lt_veblenWith_iff_right", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.veblenWith_le_veblenWith_iff_right", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.veblenWith_injective", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.veblenWith_inj", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.right_le_veblenWith", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.veblenWith_left_monotone", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "exact"], "tactic_count": 4}
{"name": "Ordinal.veblenWith_pos", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": false, "tactics": ["have", "rw", "exact", "obtain", "exact", "rw", "exact"], "tactic_count": 7}
{"name": "Ordinal.veblenWith_zero_strictMono", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": true, "tactics": ["intro", "dsimp", "rw", "exact"], "tactic_count": 4}
{"name": "Ordinal.veblenWith_zero_lt_veblenWith_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.veblenWith_zero_le_veblenWith_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.veblenWith_zero_inj", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.left_le_veblenWith", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.isNormal_veblenWith_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "apply", "suffices", "obtain", "exact", "induction", "nil", "cons", "obtain", "refine", "hb'.trans", "rw", "rw", "exact"], "tactic_count": 16}
{"name": "Ordinal.veblenWith_veblenWith_eq_veblenWith_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Ordinal.veblenWith_lt_veblenWith_veblenWith_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Ordinal.veblenWith_apply_eq_apply_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Ordinal.apply_lt_veblenWith_apply_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Ordinal.cmp_veblenWith", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": true, "tactics": ["obtain", "on_goal", "all_goals", "conv_lhs", "simp"], "tactic_count": 5}
{"name": "Ordinal.veblenWith_lt_veblenWith_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": true, "tactics": ["rw", "aesop"], "tactic_count": 2}
{"name": "Ordinal.veblenWith_le_veblenWith_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": true, "tactics": ["rw", "aesop"], "tactic_count": 2}
{"name": "Ordinal.veblenWith_eq_veblenWith_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": true, "tactics": ["rw", "aesop"], "tactic_count": 2}
{"name": "Ordinal.veblen", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.veblen_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordinal.veblen_zero_apply", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordinal.veblen_of_ne_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.isNormal_veblen", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.mem_range_veblen", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.veblen_veblen_of_lt", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.veblen_eq_self_of_le", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.veblen_mem_range_opow", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.veblen_succ", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.veblen_right_strictMono", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.veblen_lt_veblen_iff_right", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.veblen_le_veblen_iff_right", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.veblen_injective", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.veblen_inj", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.right_le_veblen", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.veblen_left_monotone", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.veblen_pos", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.veblen_zero_strictMono", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.veblen_zero_lt_veblen_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.veblen_zero_le_veblen_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.veblen_zero_inj", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.left_le_veblen", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.isNormal_veblen_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.veblen_veblen_eq_veblen_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.veblen_lt_veblen_veblen_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.veblen_opow_eq_opow_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.opow_lt_veblen_opow_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.lt_veblen", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": true, "tactics": ["obtain", "simp", "apply", "simpa"], "tactic_count": 4}
{"name": "Ordinal.cmp_veblen", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.veblen_lt_veblen_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.veblen_le_veblen_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.veblen_eq_veblen_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.invVeblen₁", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.veblen_eq_of_lt_invVeblen₁", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Ordinal.invVeblen₁_le", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.lt_veblen_invVeblen₁", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.lt_veblen_iff_invVeblen₁_le", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": true, "tactics": ["obtain", "rw", "simpa", "simpa"], "tactic_count": 4}
{"name": "Ordinal.mem_range_veblen_iff_le_invVeblen₁", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": true, "tactics": ["obtain", "exact", "apply", "by_cases", "simp", "simp_rw", "exact", "apply", "rintro", "have", "rw", "exact"], "tactic_count": 12}
{"name": "Ordinal.invVeblen₁_veblen", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": true, "tactics": ["apply", "rwa", "rw", "obtain", "simp", "rw", "simp"], "tactic_count": 7}
{"name": "Ordinal.invVeblen₁_of_lt_opow", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Ordinal.invVeblen₁_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.invVeblen₂", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.veblen_invVeblen₁_invVeblen₂", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.invVeblen₂_eq_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordinal.invVeblen₂_lt_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordinal.invVeblen₂_le_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordinal.lt_invVeblen₂_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordinal.le_invVeblen₂_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordinal.invVeblen₂_lt", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Ordinal.invVeblen₂_le", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": true, "tactics": ["obtain", "rw", "convert", "rw"], "tactic_count": 4}
{"name": "Ordinal.invVeblen₂_of_lt_opow", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ordinal.invVeblen₂_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "Ordinal.invVeblen₂_veblen", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Ordinal.veblen_eq_opow_iff", "kind": "theorem", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": true, "tactics": ["refine", "obtain", "rw", "have", "have", "aesop", "rw", "rintro", "simp", "convert"], "tactic_count": 10}
{"name": "Ordinal.epsilon", "kind": "abbrev", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.termε_", "kind": "definition", "module": "Mathlib.SetTheory.Ordinal.Veblen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SetTheory.PGame.mk_add_moveLeft_inr", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.add_moveLeft_inr", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Algebra", "is_tactic_proof": true, "tactics": ["cases", "cases", "rfl"], "tactic_count": 3}
{"name": "SetTheory.PGame.mk_add_moveRight_inr", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.add_moveRight_inr", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Algebra", "is_tactic_proof": true, "tactics": ["cases", "cases", "rfl"], "tactic_count": 3}
{"name": "SetTheory.PGame.leftMoves_add_cases", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Algebra", "is_tactic_proof": true, "tactics": ["rw", "rcases", "exact", "exact"], "tactic_count": 4}
{"name": "SetTheory.PGame.rightMoves_add_cases", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Algebra", "is_tactic_proof": true, "tactics": ["rw", "rcases", "exact", "exact"], "tactic_count": 4}
{"name": "SetTheory.PGame.isEmpty_nat_rightMoves", "kind": "instance", "module": "Mathlib.SetTheory.PGame.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.add_comm", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.add_assoc", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.add_zero", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.zero_add", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.neg_add", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.neg_add_rev", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.identical_zero_iff", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.identical_zero", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SetTheory.PGame.Identical.add_right", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SetTheory.PGame.Identical.add", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SetTheory.PGame.Relabelling.addCongr", "kind": "definition", "module": "Mathlib.SetTheory.PGame.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.instSub", "kind": "instance", "module": "Mathlib.SetTheory.PGame.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.sub_zero_eq_add_zero", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.sub_zero", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.neg_sub'", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.Identical.sub", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.Relabelling.subCongr", "kind": "definition", "module": "Mathlib.SetTheory.PGame.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.negAddRelabelling", "kind": "definition", "module": "Mathlib.SetTheory.PGame.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.neg_add_le", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.addCommRelabelling", "kind": "definition", "module": "Mathlib.SetTheory.PGame.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.add_comm_le", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.add_comm_equiv", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.addAssocRelabelling", "kind": "definition", "module": "Mathlib.SetTheory.PGame.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.add_assoc_equiv", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.neg_add_cancel_le_zero", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.zero_le_neg_add_cancel", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Algebra", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SetTheory.PGame.neg_add_cancel_equiv", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SetTheory.PGame.add_lf_add_right", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SetTheory.PGame.add_lf_add_of_lf_of_le", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SetTheory.PGame.add_congr", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SetTheory.PGame.neg_insertRight_neg", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Algebra", "is_tactic_proof": true, "tactics": ["cases", "cases", "dsimp", "congr"], "tactic_count": 4}
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{"name": "SetTheory.PGame.zero_lf_star", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Algebra", "is_tactic_proof": true, "tactics": ["rw", "use", "rintro"], "tactic_count": 3}
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{"name": "SetTheory.PGame.up", "kind": "definition", "module": "Mathlib.SetTheory.PGame.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.up_leftMoves", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SetTheory.PGame.instZeroLEOneClass", "kind": "instance", "module": "Mathlib.SetTheory.PGame.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.zero_lf_one", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame", "kind": "inductive", "module": "Mathlib.SetTheory.PGame.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.LeftMoves", "kind": "definition", "module": "Mathlib.SetTheory.PGame.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.RightMoves", "kind": "definition", "module": "Mathlib.SetTheory.PGame.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.moveLeft", "kind": "definition", "module": "Mathlib.SetTheory.PGame.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SetTheory.PGame.leftMoves_ofLists", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SetTheory.PGame.toOfListsRightMoves", "kind": "abbrev", "module": "Mathlib.SetTheory.PGame.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.ofLists_moveLeft'", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SetTheory.PGame.moveRecOn", "kind": "definition", "module": "Mathlib.SetTheory.PGame.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.IsOption", "kind": "inductive", "module": "Mathlib.SetTheory.PGame.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.IsOption.mk_left", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SetTheory.PGame.wf_isOption", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SetTheory.PGame.instIsTransSubsequent", "kind": "instance", "module": "Mathlib.SetTheory.PGame.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.Subsequent.trans", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.wf_subsequent", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.instWellFoundedRelation", "kind": "instance", "module": "Mathlib.SetTheory.PGame.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.Subsequent.moveLeft", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.Subsequent.moveRight", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SetTheory.PGame.instZero", "kind": "instance", "module": "Mathlib.SetTheory.PGame.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.zero_leftMoves", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.zero_rightMoves", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.isEmpty_zero_leftMoves", "kind": "instance", "module": "Mathlib.SetTheory.PGame.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SetTheory.PGame.instOnePGame", "kind": "instance", "module": "Mathlib.SetTheory.PGame.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.one_leftMoves", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.one_moveLeft", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.one_rightMoves", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.uniqueOneLeftMoves", "kind": "instance", "module": "Mathlib.SetTheory.PGame.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SetTheory.PGame.Identical", "kind": "definition", "module": "Mathlib.SetTheory.PGame.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.term_≡_", "kind": "definition", "module": "Mathlib.SetTheory.PGame.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SetTheory.PGame.Identical.refl", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.Identical.rfl", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.Identical.symm", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SetTheory.PGame.Identical.trans", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.memₗ", "kind": "definition", "module": "Mathlib.SetTheory.PGame.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SetTheory.PGame.instReflIdentical", "kind": "instance", "module": "Mathlib.SetTheory.PGame.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SetTheory.PGame.instIsTransIdentical", "kind": "instance", "module": "Mathlib.SetTheory.PGame.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SetTheory.PGame.Relabelling", "kind": "inductive", "module": "Mathlib.SetTheory.PGame.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SetTheory.PGame.insertRight", "kind": "definition", "module": "Mathlib.SetTheory.PGame.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SetTheory.PGame.moveLeft_lf_of_le", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.lf_moveRight_of_le", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.lf_of_moveRight_le", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SetTheory.PGame.Identical.le", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.Identical.ge", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.lt_iff_le_and_lf", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SetTheory.PGame.lf_of_lt", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SetTheory.PGame.instIrreflLF", "kind": "instance", "module": "Mathlib.SetTheory.PGame.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.not_lt", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.lf_of_le_of_lf", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Order", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SetTheory.PGame.instTransLeLF", "kind": "instance", "module": "Mathlib.SetTheory.PGame.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.lf_of_lf_of_le", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Order", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
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{"name": "SetTheory.PGame.lf_of_lt_of_lf", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SetTheory.PGame.moveLeft_lf", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.lf_moveRight", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SetTheory.PGame.mk_lf", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SetTheory.PGame.rightResponse_spec", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.leftResponse", "kind": "definition", "module": "Mathlib.SetTheory.PGame.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.leftResponse_spec", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.bddAbove_range_of_small", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Order", "is_tactic_proof": false, "tactics": ["let", "refine", "rw", "simpa"], "tactic_count": 4}
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{"name": "SetTheory.PGame.fuzzy_of_fuzzy_of_equiv", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.fuzzy_of_equiv_of_fuzzy", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.lt_or_equiv_or_gt_or_fuzzy", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Order", "is_tactic_proof": true, "tactics": ["rcases", "right", "left", "exact", "left", "exact", "right", "right", "left", "exact", "right", "right", "right", "exact"], "tactic_count": 14}
{"name": "SetTheory.PGame.lt_or_equiv_or_gf", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Order", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "SetTheory.PGame.Relabelling.le", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.Relabelling.ge", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.Relabelling.equiv", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.Equiv.isEmpty", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.instCoeRelabellingEquiv", "kind": "instance", "module": "Mathlib.SetTheory.PGame.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.le_insertLeft", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Order", "is_tactic_proof": true, "tactics": ["rw", "constructor", "intro", "left", "rcases", "simp", "left", "use", "intro", "right", "rcases", "simp", "use"], "tactic_count": 13}
{"name": "SetTheory.PGame.insertRight_le", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Order", "is_tactic_proof": true, "tactics": ["rw", "constructor", "intro", "left", "rcases", "simp", "use", "intro", "right", "rcases", "simp", "left", "use"], "tactic_count": 13}
{"name": "SetTheory.PGame.insertLeft_equiv_of_lf", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Order", "is_tactic_proof": true, "tactics": ["rw", "constructor", "rw", "constructor", "intro", "rcases", "simp", "rcases", "rw", "left", "use", "rw", "simpa", "intro", "right", "rcases", "simp", "use", "apply"], "tactic_count": 19}
{"name": "SetTheory.PGame.insertRight_equiv_of_lf", "kind": "theorem", "module": "Mathlib.SetTheory.PGame.Order", "is_tactic_proof": true, "tactics": ["rw", "constructor", "apply", "rw", "constructor", "intro", "left", "rcases", "simp", "use", "intro", "rcases", "simp", "rcases", "rw", "right", "use", "rw", "simpa"], "tactic_count": 19}
{"name": "SetTheory.PGame.Numeric", "kind": "definition", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.numeric_def", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "SetTheory.PGame.Numeric.mk", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.Numeric.left_lt_right", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "SetTheory.PGame.Numeric.moveLeft", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "SetTheory.PGame.Numeric.moveRight", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "SetTheory.PGame.Numeric.isOption", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": true, "tactics": ["cases", "apply", "apply"], "tactic_count": 3}
{"name": "SetTheory.PGame.numeric_rec", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.Relabelling.numeric_imp", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": false, "tactics": ["induction", "apply", "rw", "apply", "exact", "exact"], "tactic_count": 6}
{"name": "SetTheory.PGame.Relabelling.numeric_congr", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.lf_asymm", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": false, "tactics": ["refine", "numeric_rec", "ox", "refine", "rw", "exact", "exact", "exact", "exact"], "tactic_count": 9}
{"name": "SetTheory.PGame.le_of_lf", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.lt_of_lf", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.lf_iff_lt", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.le_iff_forall_lt", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": true, "tactics": ["refine", "apply_rules"], "tactic_count": 2}
{"name": "SetTheory.PGame.lt_iff_exists_le", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SetTheory.PGame.lt_of_exists_le", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.lt_def", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "refine", "apply_rules"], "tactic_count": 4}
{"name": "SetTheory.PGame.not_fuzzy", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.lt_or_equiv_or_gt", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.numeric_of_isEmpty", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.numeric_of_isEmpty_leftMoves", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.numeric_of_isEmpty_rightMoves", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.numeric_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.numeric_one", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.Numeric.neg", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.insertLeft_numeric", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": true, "tactics": ["rw", "unfold", "rcases", "simp", "constructor", "simp", "simp", "exact", "simp"], "tactic_count": 9}
{"name": "SetTheory.PGame.insertRight_numeric", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply", "exact"], "tactic_count": 3}
{"name": "SetTheory.PGame.Numeric.moveLeft_lt", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.Numeric.moveLeft_le", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.Numeric.lt_moveRight", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.Numeric.le_moveRight", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.Numeric.add", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.Numeric.sub", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.numeric_nat", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.numeric_toPGame", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": false, "tactics": ["induction", "apply", "simpa"], "tactic_count": 3}
{"name": "Surreal", "kind": "definition", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Surreal.mk", "kind": "definition", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Surreal.instZero", "kind": "instance", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Surreal.instOne", "kind": "instance", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Surreal.instInhabited", "kind": "instance", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Surreal.mk_eq_mk", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Surreal.mk_eq_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Surreal.lift", "kind": "definition", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Surreal.lift₂", "kind": "definition", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Surreal.instLE", "kind": "instance", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Surreal.mk_le_mk", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Surreal.zero_le_mk", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Surreal.instLT", "kind": "instance", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Surreal.mk_lt_mk", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Surreal.zero_lt_mk", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Surreal.mk_moveLeft_lt_mk", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Surreal.mk_lt_mk_moveRight", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Surreal.instAdd", "kind": "instance", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Surreal.instNeg", "kind": "instance", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Surreal.addCommGroup", "kind": "instance", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Surreal.partialOrder", "kind": "instance", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Surreal.isOrderedAddMonoid", "kind": "instance", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Surreal.mk_add", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "Surreal.mk_sub", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "Surreal.zero_def", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "Surreal.instLinearOrder", "kind": "instance", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Surreal.instAddMonoidWithOne", "kind": "instance", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Surreal.toGame", "kind": "definition", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Surreal.zero_toGame", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Surreal.one_toGame", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Surreal.nat_toGame", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Surreal.bddAbove_range_of_small", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": false, "tactics": ["induction", "let", "have", "conv", "clear_value", "clear", "let", "refine", "rw", "simpa"], "tactic_count": 10}
{"name": "Surreal.bddAbove_of_small", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Surreal.bddBelow_range_of_small", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": false, "tactics": ["induction", "let", "have", "conv", "clear_value", "clear", "let", "refine", "rw", "simpa"], "tactic_count": 10}
{"name": "Surreal.bddBelow_of_small", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Ordinal.toSurreal", "kind": "definition", "module": "Mathlib.SetTheory.Surreal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.powHalf", "kind": "definition", "module": "Mathlib.SetTheory.Surreal.Dyadic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.powHalf_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Dyadic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.powHalf_leftMoves", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Dyadic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "SetTheory.PGame.powHalf_zero_rightMoves", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Dyadic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.powHalf_succ_rightMoves", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Dyadic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.powHalf_moveLeft", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Dyadic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "SetTheory.PGame.powHalf_succ_moveRight", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Dyadic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.uniquePowHalfLeftMoves", "kind": "instance", "module": "Mathlib.SetTheory.Surreal.Dyadic", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "SetTheory.PGame.isEmpty_powHalf_zero_rightMoves", "kind": "instance", "module": "Mathlib.SetTheory.Surreal.Dyadic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.uniquePowHalfSuccRightMoves", "kind": "instance", "module": "Mathlib.SetTheory.Surreal.Dyadic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.birthday_half", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Dyadic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SetTheory.PGame.numeric_powHalf", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Dyadic", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "constructor", "simpa", "exact"], "tactic_count": 6}
{"name": "SetTheory.PGame.powHalf_succ_lt_powHalf", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Dyadic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.powHalf_succ_le_powHalf", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Dyadic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.powHalf_le_one", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Dyadic", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "SetTheory.PGame.powHalf_succ_lt_one", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Dyadic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.powHalf_pos", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Dyadic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SetTheory.PGame.zero_le_powHalf", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Dyadic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetTheory.PGame.add_powHalf_succ_self_eq_powHalf", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Dyadic", "is_tactic_proof": false, "tactics": ["induction", "constructor", "rintro", "calc", "calc", "powHalf", "rcases", "rintro", "rintro", "apply", "swap", "exact", "calc", "powHalf", "grw", "simp", "apply", "calc", "rintro", "calc", "powHalf", "calc", "powHalf"], "tactic_count": 23}
{"name": "SetTheory.PGame.half_add_half_equiv_one", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Dyadic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Surreal.powHalf", "kind": "definition", "module": "Mathlib.SetTheory.Surreal.Dyadic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Surreal.powHalf_zero", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Dyadic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Surreal.double_powHalf_succ_eq_powHalf", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Dyadic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Surreal.nsmul_pow_two_powHalf", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Dyadic", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "rw", "mul_comm"], "tactic_count": 5}
{"name": "Surreal.nsmul_pow_two_powHalf'", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Dyadic", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "hk", "rw", "mul_assoc]", "rw", "simpa"], "tactic_count": 8}
{"name": "Surreal.zsmul_pow_two_powHalf", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Dyadic", "is_tactic_proof": true, "tactics": ["rw", "congr", "exact"], "tactic_count": 3}
{"name": "Surreal.dyadic_aux", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Dyadic", "is_tactic_proof": true, "tactics": ["revert", "wlog", "intro", "intro", "obtain", "rw", "rcases", "rw", "simp_rw", "have", "norm_cast"], "tactic_count": 11}
{"name": "Surreal.dyadicMap", "kind": "definition", "module": "Mathlib.SetTheory.Surreal.Dyadic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Surreal.dyadicMap_apply", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Dyadic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Surreal.dyadicMap_apply_pow", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Dyadic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
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{"name": "Surreal.Multiplication.P1", "kind": "definition", "module": "Mathlib.SetTheory.Surreal.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Surreal.Multiplication.P2", "kind": "definition", "module": "Mathlib.SetTheory.Surreal.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Surreal.Multiplication.P3", "kind": "definition", "module": "Mathlib.SetTheory.Surreal.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Surreal.Multiplication.P4", "kind": "definition", "module": "Mathlib.SetTheory.Surreal.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Surreal.Multiplication.P24", "kind": "definition", "module": "Mathlib.SetTheory.Surreal.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Surreal.Multiplication.P3.trans", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Multiplication", "is_tactic_proof": true, "tactics": ["rw", "rw", "convert"], "tactic_count": 3}
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{"name": "Surreal.Multiplication.P24_neg_left", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Multiplication", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "Surreal.Multiplication.argsRel_wf", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Surreal.Multiplication.P124", "kind": "definition", "module": "Mathlib.SetTheory.Surreal.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Surreal.Multiplication.IH1", "kind": "definition", "module": "Mathlib.SetTheory.Surreal.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Surreal.Multiplication.P3_of_ih", "kind": "theorem", "module": "Mathlib.SetTheory.Surreal.Multiplication", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ZFSet.toSet_inj", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.instAntisymmSubset", "kind": "instance", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.instIsNonstrictStrictOrderSubsetSSubset", "kind": "instance", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.empty", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.instEmptyCollection", "kind": "instance", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.instInhabited", "kind": "instance", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.notMem_empty", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.coe_empty", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "ZFSet.empty_subset", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.not_nonempty_empty", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ZFSet.nonempty_mk_iff", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": true, "tactics": ["refine", "rintro", "induction", "exact"], "tactic_count": 4}
{"name": "ZFSet.eq_empty", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ZFSet.eq_empty_or_nonempty", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "ZFSet.Insert", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.instInsert", "kind": "instance", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.instSingleton", "kind": "instance", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.instLawfulSingleton", "kind": "instance", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.mem_insert_iff", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.mem_insert", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.mem_insert_of_mem", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.coe_insert", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "ZFSet.mem_singleton", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.notMem_singleton", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.coe_singleton", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "ZFSet.insert_nonempty", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.singleton_nonempty", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.mem_pair", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ZFSet.pair_eq_singleton", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "ZFSet.pair_eq_singleton_iff", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "simp", "rintro", "exact"], "tactic_count": 5}
{"name": "ZFSet.singleton_eq_pair_iff", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp_rw"], "tactic_count": 2}
{"name": "ZFSet.omega", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.omega_zero", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.omega_succ", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.sep", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.instSep", "kind": "instance", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.mem_sep", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.sep_empty", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.sep_subset", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.coe_sep", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "ZFSet.powerset", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.mem_powerset", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.sUnion_lem", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.sUnion", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.term⋃₀_", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet._aux_Mathlib_SetTheory_ZFC_Basic___macroRules_ZFSet_term⋃₀__1", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet._aux_Mathlib_SetTheory_ZFC_Basic___unexpand_ZFSet_sUnion_1", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.sInter", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.term⋂₀_", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet._aux_Mathlib_SetTheory_ZFC_Basic___macroRules_ZFSet_term⋂₀__1", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet._aux_Mathlib_SetTheory_ZFC_Basic___unexpand_ZFSet_sInter_1", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.mem_sUnion", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.mem_sInter", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": true, "tactics": ["unfold", "simp", "intro", "apply", "replace", "exact"], "tactic_count": 6}
{"name": "ZFSet.sUnion_empty", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "ZFSet.sInter_empty", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ZFSet.mem_of_mem_sInter", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": true, "tactics": ["rcases", "exact", "exact"], "tactic_count": 3}
{"name": "ZFSet.mem_sUnion_of_mem", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.notMem_sInter_of_notMem", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.sUnion_singleton", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.sInter_singleton", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.coe_sUnion", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "ZFSet.coe_sInter", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "ZFSet.singleton_injective", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.singleton_inj", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.union", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.inter", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.diff", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.instUnion", "kind": "instance", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.instInter", "kind": "instance", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.instSDiff", "kind": "instance", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.sUnion_pair", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.sep_mem", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.sep_notMem", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.mem_union", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ZFSet.mem_inter", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ZFSet.mem_sdiff", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ZFSet.coe_union", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "ZFSet.coe_inter", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "ZFSet.coe_sdiff", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "ZFSet.inter_eq_left_of_subset", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "ZFSet.inter_eq_right_of_subset", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "ZFSet.powersetEquiv", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.insert_eq", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "ZFSet.mem_wf", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.inductionOn", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.instIsWellFoundedMem", "kind": "instance", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.instWellFoundedRelation", "kind": "instance", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.mem_asymm", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.mem_irrefl", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.not_subset_of_mem", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.notMem_of_subset", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.regularity", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": ["h", "ne", "let"], "tactic_count": 3}
{"name": "ZFSet.image", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.image.mk", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.mem_image", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.coe_image", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "ZFSet.range", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.mem_range", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.coe_range", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "ZFSet.mem_range_self", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ZFSet.iUnion", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.term⋃_,_", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet._aux_Mathlib_SetTheory_ZFC_Basic___macroRules_ZFSet_term⋃_,__1", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet._aux_Mathlib_SetTheory_ZFC_Basic___delab_app_ZFSet_term⋃_,__1", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.mem_iUnion", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ZFSet.coe_iUnion", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "ZFSet.subset_iUnion", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": true, "tactics": ["intro", "simpa"], "tactic_count": 2}
{"name": "ZFSet.pair", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.coe_pair", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ZFSet.pairSep", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.mem_pairSep", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": true, "tactics": ["refine", "grind"], "tactic_count": 2}
{"name": "ZFSet.pair_injective", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": true, "tactics": ["intro", "simp_rw", "obtain", "have", "rintro", "simpa", "have", "simp_rw", "refine", "simpa"], "tactic_count": 10}
{"name": "ZFSet.pair_inj", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.prod", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.mem_prod", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ZFSet.pair_mem_prod", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ZFSet.IsFunc", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.funs", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.mem_funs", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ZFSet.instDefinable₁Singleton", "kind": "instance", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.instDefinable₂Insert", "kind": "instance", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.instDefinable₂Pair", "kind": "instance", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "ZFSet.map", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.mem_map", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.map_unique", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.map_isFunc", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.Hereditarily", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.hereditarily_iff", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ZFSet.Hereditarily.self", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ZFSet.cardinalMk_coe_sort", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Cardinal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "ZFSet.card_pair_of_ne", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Cardinal", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "ZFSet.card_union_le", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Cardinal", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
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{"name": "ZFSet.card_image_le", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Cardinal", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ZFSet.lift_card_range_le", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Cardinal", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "ZFSet.iSup_card_le_card_iUnion", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Cardinal", "is_tactic_proof": true, "tactics": ["simpa", "iSup_mk_le_mk_iUnion"], "tactic_count": 2}
{"name": "ZFSet.lift_card_iUnion_le_sum_card", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Cardinal", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "Class", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Class.univ", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Class.ToSet", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Class.instMembership", "kind": "instance", "module": "Mathlib.SetTheory.ZFC.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Class.mem_def", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Class.notMem_empty", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Class.mem_wf", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Class.instIsWellFoundedMem", "kind": "instance", "module": "Mathlib.SetTheory.ZFC.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Class.instWellFoundedRelation", "kind": "instance", "module": "Mathlib.SetTheory.ZFC.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Class.mem_irrefl", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Class.univ_notMem_univ", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Class.congToClass", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Class.congToClass_empty", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Class", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "Class.classToCong", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Class.classToCong_empty", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Class", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Class.powerset", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Class.sUnion", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Class.term⋃₀_", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Class._aux_Mathlib_SetTheory_ZFC_Class___macroRules_Class_term⋃₀__1", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Class._aux_Mathlib_SetTheory_ZFC_Class___unexpand_Class_sUnion_1", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Class._aux_Mathlib_SetTheory_ZFC_Class___unexpand_Class_sInter_1", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Class.toSet_of_ZFSet", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Class.coe_mem", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Class.coe_subset", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Class.powerset_apply", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Class.sUnion_apply", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Class", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "exact", "exact"], "tactic_count": 4}
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{"name": "Class.coe_sInter", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Class.mem_of_mem_sInter", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Class", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
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{"name": "Class.sInter_empty", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Class", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Class.eq_univ_of_powerset_subset", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Class.iota", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Class.iota_val", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Class.iota_ex", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Class.fval", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Class.term_′_", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Class._aux_Mathlib_SetTheory_ZFC_Class___macroRules_Class_term_′__1", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Class._aux_Mathlib_SetTheory_ZFC_Class___unexpand_Class_fval_1", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Class.fval_ex", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.map_fval", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.choice", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.choice_mem_aux", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.choice_isFunc", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.choice_mem", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Class", "is_tactic_proof": true, "tactics": ["delta", "rw", "exact"], "tactic_count": 3}
{"name": "_private.Mathlib.SetTheory.ZFC.Class.0.ZFSet.coe_equiv_aux", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Class", "is_tactic_proof": true, "tactics": ["ext", "rw", "refine", "rintro", "rw", "simp", "simp"], "tactic_count": 7}
{"name": "ZFSet.coeEquiv", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.Class", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.isOrdinal_notMem_univ", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Class", "is_tactic_proof": true, "tactics": ["rintro", "suffices", "apply", "rwa", "refine", "exacts"], "tactic_count": 6}
{"name": "ZFSet.IsTransitive", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.isTransitive_empty", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.IsTransitive.subset_of_mem", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.isTransitive_iff_mem_trans", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ZFSet.IsTransitive.sUnion", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.IsTransitive.sUnion'", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.IsTransitive.iUnion", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.IsTransitive.union", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Ordinal", "is_tactic_proof": true, "tactics": ["rw", "apply", "intro", "rw", "rintro", "assumption"], "tactic_count": 6}
{"name": "ZFSet.IsTransitive.powerset", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.isTransitive_iff_sUnion_subset", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Ordinal", "is_tactic_proof": true, "tactics": ["constructor", "obtain", "exact", "exact"], "tactic_count": 4}
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{"name": "ZFSet.IsOrdinal.subset_of_mem", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ZFSet.IsOrdinal.isTrans", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.isOrdinal_iff_isTrans", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.IsOrdinal.mem", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.isOrdinal_iff_forall_mem_isTransitive", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.isOrdinal_iff_forall_mem_isOrdinal", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ZFSet.IsOrdinal.notMem_iff_subset", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Ordinal", "is_tactic_proof": true, "tactics": ["refine", "revert", "apply", "intro", "by_contra", "exact"], "tactic_count": 6}
{"name": "ZFSet.IsOrdinal.not_subset_iff_mem", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Ordinal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ZFSet.IsOrdinal.mem_or_subset", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Ordinal", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ZFSet.IsOrdinal.subset_total", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Ordinal", "is_tactic_proof": true, "tactics": ["obtain", "exact", "exact"], "tactic_count": 3}
{"name": "ZFSet.IsOrdinal.mem_trichotomous", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Ordinal", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ZFSet.IsOrdinal.isTrichotomous", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.isOrdinal_iff_isTrichotomous", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.IsOrdinal.isWellOrder", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.isOrdinal_iff_isWellOrder", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Ordinal", "is_tactic_proof": true, "tactics": ["use", "rintro", "refine", "infer_instance"], "tactic_count": 4}
{"name": "ZFSet.IsOrdinal.rank_lt_iff_mem", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Ordinal", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "ZFSet.IsOrdinal.rank_le_iff_subset", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Ordinal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ZFSet.IsOrdinal.rank_inj", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Ordinal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ZFSet.isOrdinal_empty", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.isOrdinal_succ", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Ordinal", "is_tactic_proof": true, "tactics": ["refine", "obtain", "on_goal", "all_goals", "obtain", "exacts"], "tactic_count": 6}
{"name": "Ordinal.toPSet", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.type_toPSet", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Ordinal", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Ordinal.mem_toPSet_iff", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Ordinal", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "Ordinal.rank_toPSet", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Ordinal", "is_tactic_proof": true, "tactics": ["rw", "conv_rhs", "convert", "rw", "termination_by", "decreasing_by"], "tactic_count": 6}
{"name": "Ordinal.toZFSet", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.mk_toPSet", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.mem_toZFSet_iff", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Ordinal", "is_tactic_proof": true, "tactics": ["induction", "rw", "congr", "rw"], "tactic_count": 4}
{"name": "Ordinal.rank_toZFSet", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.coe_toZFSet", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Ordinal", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "_private.Mathlib.SetTheory.ZFC.Ordinal.0.Ordinal.toZFSet_mem_toZFSet_of_lt", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Ordinal", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Ordinal.toZFSet_monotone", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Ordinal", "is_tactic_proof": true, "tactics": ["intro", "obtain", "exact"], "tactic_count": 3}
{"name": "Ordinal.toZFSet_mem_toZFSet_iff", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Ordinal", "is_tactic_proof": true, "tactics": ["refine", "contrapose", "exact"], "tactic_count": 3}
{"name": "Ordinal.toZFSet_subset_toZFSet_iff", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Ordinal", "is_tactic_proof": true, "tactics": ["refine", "contrapose", "exact"], "tactic_count": 3}
{"name": "Ordinal.toZFSet_strictMono", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.toZFSet_injective", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.toZFSet_zero", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Ordinal", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Ordinal.toZFSet_succ", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Ordinal", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "Ordinal.card_toZFSet", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Ordinal", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ZFSet.isOrdinal_toZFSet", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Ordinal", "is_tactic_proof": true, "tactics": ["refine", "all_goals", "obtain", "obtain", "exact", "obtain", "exact"], "tactic_count": 7}
{"name": "ZFSet.IsOrdinal.toZFSet_rank_eq", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.isOrdinal_iff_mem_range_toZFSet", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Ordinal", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact", "rintro", "exact"], "tactic_count": 5}
{"name": "Ordinal.toZFSetIso", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet", "kind": "inductive", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.Type", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.Func", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.mk_type", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.mk_func", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.eta", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.Equiv", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.equiv_iff", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.Equiv.exists_left", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.Equiv.exists_right", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.Equiv.refl", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.Equiv.rfl", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.Equiv.euc", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.Equiv.symm", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.Equiv.comm", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.Equiv.trans", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.equiv_of_isEmpty", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.setoid", "kind": "instance", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.Subset", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.instHasSubset", "kind": "instance", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.instReflSubset", "kind": "instance", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.instIsTransSubset", "kind": "instance", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.Equiv.ext", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.Subset.congr_left", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.Subset.congr_right", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.instPreorder", "kind": "instance", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.instHasSSubset", "kind": "instance", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.le_def", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.lt_def", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.instIsNonstrictStrictOrderSubsetSSubset", "kind": "instance", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.Mem", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.instMembership", "kind": "instance", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.mem_def", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.Mem.mk", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.func_mem", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": true, "tactics": ["cases", "apply"], "tactic_count": 2}
{"name": "PSet.Mem.ext", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.Mem.congr_right", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.equiv_iff_mem", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.Mem.congr_left", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.mem_of_subset", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.subset_iff", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.SetTheory.ZFC.PSet.0.PSet.mem_wf_aux", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.mem_wf", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.instIsWellFoundedMem", "kind": "instance", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.instWellFoundedRelation", "kind": "instance", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.mem_asymm", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.mem_irrefl", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.not_subset_of_mem", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.notMem_of_subset", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.toSet", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.mem_toSet", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.Nonempty", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.nonempty_def", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.nonempty_of_mem", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.nonempty_toSet_iff", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.nonempty_type_iff_nonempty", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.nonempty_of_nonempty_type", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.Equiv.eq", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.instCoeSet", "kind": "instance", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.empty", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.instEmptyCollection", "kind": "instance", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.instInhabited", "kind": "instance", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.instIsEmptyTypeEmptyCollection", "kind": "instance", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.empty_def", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PSet.notMem_empty", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.toSet_empty", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PSet.empty_subset", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.not_nonempty_empty", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PSet.equiv_empty", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.insert", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.instInsert", "kind": "instance", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.instSingleton", "kind": "instance", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.instLawfulSingleton", "kind": "instance", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.instInhabitedTypeInsert", "kind": "instance", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.mem_insert_iff", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.mem_insert", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.mem_insert_of_mem", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.mem_singleton", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.mem_pair", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PSet.ofNat", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.omega", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "PSet.instSep", "kind": "instance", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.mem_sep", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.powerset", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.mem_powerset", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.sUnion", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.term⋃₀_", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet._aux_Mathlib_SetTheory_ZFC_PSet___macroRules_PSet_term⋃₀__1", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet._aux_Mathlib_SetTheory_ZFC_PSet___unexpand_PSet_sUnion_1", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.mem_sUnion", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "PSet.image", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "PSet.embed", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.PSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "PSet.rank", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.Rank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.rank_congr", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Rank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.rank_lt_of_mem", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Rank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.rank_le_iff", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Rank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.lt_rank_iff", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Rank", "is_tactic_proof": true, "tactics": ["contrapose"], "tactic_count": 1}
{"name": "PSet.rank_mono", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Rank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.rank_empty", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Rank", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PSet.rank_insert", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Rank", "is_tactic_proof": true, "tactics": ["apply", "simp_rw", "rintro", "simp", "simp", "apply", "exact", "exact"], "tactic_count": 8}
{"name": "PSet.rank_singleton", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Rank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PSet.rank_pair", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Rank", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PSet.rank_powerset", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Rank", "is_tactic_proof": true, "tactics": ["apply", "simp_rw", "intro", "exact", "rw", "apply", "simp"], "tactic_count": 7}
{"name": "PSet.rank_sUnion_le", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Rank", "is_tactic_proof": true, "tactics": ["simp_rw", "intro", "trans"], "tactic_count": 3}
{"name": "PSet.le_succ_rank_sUnion", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Rank", "is_tactic_proof": true, "tactics": ["rw", "apply", "rw", "intro", "rw", "intro", "rw", "exists"], "tactic_count": 8}
{"name": "PSet.rank_eq_wfRank", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Rank", "is_tactic_proof": false, "tactics": ["induction", "rw", "simp_rw", "apply", "rw", "rintro", "simpa", "simpa"], "tactic_count": 8}
{"name": "ZFSet.rank", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.Rank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.rank_mk", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Rank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.rank_lt_of_mem", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Rank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.rank_le_iff", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Rank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.lt_rank_iff", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Rank", "is_tactic_proof": true, "tactics": ["contrapose"], "tactic_count": 1}
{"name": "ZFSet.rank_mono", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Rank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.rank_empty", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Rank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.rank_insert", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Rank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.rank_singleton", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Rank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.rank_pair", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Rank", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ZFSet.rank_union", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Rank", "is_tactic_proof": true, "tactics": ["apply", "simp_rw", "intro", "apply", "apply"], "tactic_count": 5}
{"name": "ZFSet.rank_powerset", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Rank", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.rank_sUnion_le", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Rank", "is_tactic_proof": true, "tactics": ["simp_rw", "intro", "trans"], "tactic_count": 3}
{"name": "ZFSet.le_succ_rank_sUnion", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Rank", "is_tactic_proof": true, "tactics": ["rw", "apply", "intro", "rw", "intro", "rw", "exists"], "tactic_count": 7}
{"name": "ZFSet.rank_range", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Rank", "is_tactic_proof": true, "tactics": ["apply", "simpa", "simp"], "tactic_count": 3}
{"name": "ZFSet.rank_iUnion", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Rank", "is_tactic_proof": true, "tactics": ["apply", "simp_rw", "intro", "exact", "exact"], "tactic_count": 5}
{"name": "ZFSet.rank_eq_wfRank", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.Rank", "is_tactic_proof": false, "tactics": ["induction", "rw", "simp_rw", "apply", "rw", "rintro", "simpa", "simpa"], "tactic_count": 8}
{"name": "ZFSet.vonNeumann", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.VonNeumann", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.termV_", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.VonNeumann", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet._aux_Mathlib_SetTheory_ZFC_VonNeumann___macroRules_ZFSet_termV__1", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.VonNeumann", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet._aux_Mathlib_SetTheory_ZFC_VonNeumann___unexpand_ZFSet_vonNeumann_1", "kind": "definition", "module": "Mathlib.SetTheory.ZFC.VonNeumann", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.mem_vonNeumann'", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.VonNeumann", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ZFSet.isTransitive_vonNeumann", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.VonNeumann", "is_tactic_proof": true, "tactics": ["rw", "exact", "termination_by"], "tactic_count": 3}
{"name": "ZFSet.vonNeumann_mem_of_lt", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.VonNeumann", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ZFSet.vonNeumann_subset_of_le", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.VonNeumann", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.subset_vonNeumann", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.VonNeumann", "is_tactic_proof": true, "tactics": ["rw", "constructor", "apply", "simp_rw", "rintro", "exact", "rw", "have", "exact", "termination_by"], "tactic_count": 10}
{"name": "ZFSet.subset_vonNeumann_self", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.VonNeumann", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ZFSet.mem_vonNeumann", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.VonNeumann", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "ZFSet.mem_vonNeumann_succ", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.VonNeumann", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ZFSet.exists_mem_vonNeumann", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.VonNeumann", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.rank_vonNeumann", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.VonNeumann", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.vonNeumann_mem_vonNeumann_iff", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.VonNeumann", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ZFSet.vonNeumann_subset_vonNeumann_iff", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.VonNeumann", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ZFSet.mem_vonNeumann_of_subset", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.VonNeumann", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ZFSet.vonNeumann_strictMono", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.VonNeumann", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.vonNeumann_injective", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.VonNeumann", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.vonNeumann_inj", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.VonNeumann", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.vonNeumann_zero", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.VonNeumann", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.vonNeumann_succ", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.VonNeumann", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.vonNeumann_of_isSuccPrelimit", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.VonNeumann", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZFSet.iUnion_vonNeumann", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.VonNeumann", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ordinal.toZFSet_subset_vonNeumann", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.VonNeumann", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Ordinal.card_le_card_vonNeumann", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.VonNeumann", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ZFSet.card_vonNeumann", "kind": "theorem", "module": "Mathlib.SetTheory.ZFC.VonNeumann", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "limit", "ih", "simp_rw", "vonNeumann_of_isSuccPrelimit", "apply", "rw", "apply", "refine", "rw", "exact", "rw", "by_contra", "refine", "rw", "refine", "exact"], "tactic_count": 19}
{"name": "Std.HashMap.mapVal", "kind": "definition", "module": "Mathlib.Std.Data.HashMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Abel.initFn._@.Mathlib.Tactic.Abel.1000861767._hygCtx._hyg.2", "kind": "definition", "module": "Mathlib.Tactic.Abel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Abel.initFn._@.Mathlib.Tactic.Abel.1862938006._hygCtx._hyg.2", "kind": "definition", "module": "Mathlib.Tactic.Abel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Tactic.Abel.mkContext", "kind": "definition", "module": "Mathlib.Tactic.Abel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Abel.M", "kind": "abbrev", "module": "Mathlib.Tactic.Abel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Tactic.Abel.addG", "kind": "definition", "module": "Mathlib.Tactic.Abel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Abel.iapp", "kind": "definition", "module": "Mathlib.Tactic.Abel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Abel.term", "kind": "definition", "module": "Mathlib.Tactic.Abel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Tactic.Abel.intToExpr", "kind": "definition", "module": "Mathlib.Tactic.Abel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Tactic.Abel.instCoeNormalExprExpr", "kind": "instance", "module": "Mathlib.Tactic.Abel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Tactic.Abel.NormalExpr.zero'", "kind": "definition", "module": "Mathlib.Tactic.Abel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Abel.const_add_term", "kind": "theorem", "module": "Mathlib.Tactic.Abel", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Abel.const_add_termg", "kind": "theorem", "module": "Mathlib.Tactic.Abel", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Abel.term_add_const", "kind": "theorem", "module": "Mathlib.Tactic.Abel", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Abel.term_add_constg", "kind": "theorem", "module": "Mathlib.Tactic.Abel", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "Mathlib.Tactic.Abel.term_add_termg", "kind": "theorem", "module": "Mathlib.Tactic.Abel", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
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{"name": "Mathlib.Tactic.Abel.evalAdd", "kind": "definition", "module": "Mathlib.Tactic.Abel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Tactic.Abel.term_smulg", "kind": "theorem", "module": "Mathlib.Tactic.Abel", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "Mathlib.Tactic.Abel.term_atom_pf", "kind": "theorem", "module": "Mathlib.Tactic.Abel", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Abel.term_atom_pfg", "kind": "theorem", "module": "Mathlib.Tactic.Abel", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "Mathlib.Tactic.Abel.unfold_sub", "kind": "theorem", "module": "Mathlib.Tactic.Abel", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "Mathlib.Tactic.Abel.unfold_zsmul", "kind": "theorem", "module": "Mathlib.Tactic.Abel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Abel.subst_into_smul", "kind": "theorem", "module": "Mathlib.Tactic.Abel", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Abel.subst_into_smulg", "kind": "theorem", "module": "Mathlib.Tactic.Abel", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "Mathlib.Tactic.Abel.subst_into_add", "kind": "theorem", "module": "Mathlib.Tactic.Abel", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Abel.subst_into_addg", "kind": "theorem", "module": "Mathlib.Tactic.Abel", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Abel.subst_into_negg", "kind": "theorem", "module": "Mathlib.Tactic.Abel", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Abel.evalSMul'", "kind": "definition", "module": "Mathlib.Tactic.Abel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Tactic.Abel.abel1", "kind": "definition", "module": "Mathlib.Tactic.Abel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "_aux_Mathlib_Tactic_Bound___elabRules_tacticBound[_]_1", "kind": "definition", "module": "Mathlib.Tactic.Bound", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Tactic.Bound.ineqPriority", "kind": "definition", "module": "Mathlib.Tactic.Bound.Attribute", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Bound.hypPriority", "kind": "definition", "module": "Mathlib.Tactic.Bound.Attribute", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Bound.typePriority", "kind": "definition", "module": "Mathlib.Tactic.Bound.Attribute", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Tactic.Bound.scoreToConfig", "kind": "definition", "module": "Mathlib.Tactic.Bound.Attribute", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Tactic.Bound._aux_Mathlib_Tactic_Bound_Attribute___macroRules_Mathlib_Tactic_Bound_attrBound_forward_1", "kind": "definition", "module": "Mathlib.Tactic.Bound.Attribute", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Tactic.BicategoryLike.Eval.instInhabitedResult", "kind": "instance", "module": "Mathlib.Tactic.CategoryTheory.Coherence.Normalize", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.BicategoryLike.evalCompNil", "kind": "definition", "module": "Mathlib.Tactic.CategoryTheory.Coherence.Normalize", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.BicategoryLike.evalComp", "kind": "definition", "module": "Mathlib.Tactic.CategoryTheory.Coherence.Normalize", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.BicategoryLike.evalWhiskerLeft", "kind": "definition", "module": "Mathlib.Tactic.CategoryTheory.Coherence.Normalize", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.BicategoryLike.traceProof", "kind": "definition", "module": "Mathlib.Tactic.CategoryTheory.Coherence.Normalize", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.BicategoryLike.eval", "kind": "definition", "module": "Mathlib.Tactic.CategoryTheory.Coherence.Normalize", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.BicategoryLike.Normalize.instInhabitedResult.default", "kind": "definition", "module": "Mathlib.Tactic.CategoryTheory.Coherence.PureCoherence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.BicategoryLike.Normalize.instInhabitedResult", "kind": "instance", "module": "Mathlib.Tactic.CategoryTheory.Coherence.PureCoherence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.BicategoryLike.normalize", "kind": "definition", "module": "Mathlib.Tactic.CategoryTheory.Coherence.PureCoherence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.BicategoryLike.naturality", "kind": "definition", "module": "Mathlib.Tactic.CategoryTheory.Coherence.PureCoherence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.BicategoryLike.pureCoherence", "kind": "definition", "module": "Mathlib.Tactic.CategoryTheory.Coherence.PureCoherence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.Elementwise.forall_congr_forget_Type", "kind": "theorem", "module": "Mathlib.Tactic.CategoryTheory.Elementwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.Elementwise.forget_hom_Type", "kind": "theorem", "module": "Mathlib.Tactic.CategoryTheory.Elementwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.Elementwise.hom_elementwise", "kind": "theorem", "module": "Mathlib.Tactic.CategoryTheory.Elementwise", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Tactic.Elementwise.elementwiseThms", "kind": "definition", "module": "Mathlib.Tactic.CategoryTheory.Elementwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Tactic.CategoryTheory.Elementwise.0.Tactic.Elementwise.mkUnusedName", "kind": "definition", "module": "Mathlib.Tactic.CategoryTheory.Elementwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.Elementwise.elementwise", "kind": "definition", "module": "Mathlib.Tactic.CategoryTheory.Elementwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.Elementwise.initFn._@.Mathlib.Tactic.CategoryTheory.Elementwise.3754623819._hygCtx._hyg.2", "kind": "definition", "module": "Mathlib.Tactic.CategoryTheory.Elementwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.Elementwise.termElementwise_of%_", "kind": "definition", "module": "Mathlib.Tactic.CategoryTheory.Elementwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.Elementwise._aux_Mathlib_Tactic_CategoryTheory_Elementwise___elabRules_Tactic_Elementwise_termElementwise_of%__1", "kind": "definition", "module": "Mathlib.Tactic.CategoryTheory.Elementwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Reassoc.Iso.eq_whisker", "kind": "theorem", "module": "Mathlib.Tactic.CategoryTheory.IsoReassoc", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Reassoc.categoryIsoSimp", "kind": "definition", "module": "Mathlib.Tactic.CategoryTheory.IsoReassoc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Reassoc.reassocExprIso", "kind": "definition", "module": "Mathlib.Tactic.CategoryTheory.IsoReassoc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Reassoc.initFn._@.Mathlib.Tactic.CategoryTheory.IsoReassoc.2449083756._hygCtx._hyg.2", "kind": "definition", "module": "Mathlib.Tactic.CategoryTheory.IsoReassoc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.term⊗𝟙", "kind": "definition", "module": "Mathlib.Tactic.CategoryTheory.MonoidalComp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory._aux_Mathlib_Tactic_CategoryTheory_MonoidalComp___macroRules_CategoryTheory_MonoidalCategory_term⊗𝟙_1", "kind": "definition", "module": "Mathlib.Tactic.CategoryTheory.MonoidalComp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory._aux_Mathlib_Tactic_CategoryTheory_MonoidalComp___unexpand_CategoryTheory_MonoidalCoherence_iso_1", "kind": "definition", "module": "Mathlib.Tactic.CategoryTheory.MonoidalComp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.monoidalIso", "kind": "abbrev", "module": "Mathlib.Tactic.CategoryTheory.MonoidalComp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.monoidalComp", "kind": "definition", "module": "Mathlib.Tactic.CategoryTheory.MonoidalComp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.term_⊗≫_", "kind": "definition", "module": "Mathlib.Tactic.CategoryTheory.MonoidalComp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory._aux_Mathlib_Tactic_CategoryTheory_MonoidalComp___macroRules_CategoryTheory_MonoidalCategory_term_⊗≫__1", "kind": "definition", "module": "Mathlib.Tactic.CategoryTheory.MonoidalComp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory._aux_Mathlib_Tactic_CategoryTheory_MonoidalComp___unexpand_CategoryTheory_monoidalComp_1", "kind": "definition", "module": "Mathlib.Tactic.CategoryTheory.MonoidalComp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.monoidalIsoComp", "kind": "definition", "module": "Mathlib.Tactic.CategoryTheory.MonoidalComp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory.term_≪⊗≫_", "kind": "definition", "module": "Mathlib.Tactic.CategoryTheory.MonoidalComp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory._aux_Mathlib_Tactic_CategoryTheory_MonoidalComp___macroRules_CategoryTheory_MonoidalCategory_term_≪⊗≫__1", "kind": "definition", "module": "Mathlib.Tactic.CategoryTheory.MonoidalComp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCategory._aux_Mathlib_Tactic_CategoryTheory_MonoidalComp___unexpand_CategoryTheory_monoidalIsoComp_1", "kind": "definition", "module": "Mathlib.Tactic.CategoryTheory.MonoidalComp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCoherence.refl", "kind": "instance", "module": "Mathlib.Tactic.CategoryTheory.MonoidalComp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCoherence.whiskerLeft", "kind": "instance", "module": "Mathlib.Tactic.CategoryTheory.MonoidalComp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCoherence.whiskerRight", "kind": "instance", "module": "Mathlib.Tactic.CategoryTheory.MonoidalComp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCoherence.tensor_right", "kind": "instance", "module": "Mathlib.Tactic.CategoryTheory.MonoidalComp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCoherence.tensor_right'", "kind": "instance", "module": "Mathlib.Tactic.CategoryTheory.MonoidalComp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCoherence.left", "kind": "instance", "module": "Mathlib.Tactic.CategoryTheory.MonoidalComp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCoherence.left'", "kind": "instance", "module": "Mathlib.Tactic.CategoryTheory.MonoidalComp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCoherence.right", "kind": "instance", "module": "Mathlib.Tactic.CategoryTheory.MonoidalComp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCoherence.right'", "kind": "instance", "module": "Mathlib.Tactic.CategoryTheory.MonoidalComp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCoherence.assoc", "kind": "instance", "module": "Mathlib.Tactic.CategoryTheory.MonoidalComp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.MonoidalCoherence.assoc'", "kind": "instance", "module": "Mathlib.Tactic.CategoryTheory.MonoidalComp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CategoryTheory.monoidalComp_refl", "kind": "theorem", "module": "Mathlib.Tactic.CategoryTheory.MonoidalComp", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Monoidal.monoidalNf", "kind": "definition", "module": "Mathlib.Tactic.CategoryTheory.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Monoidal.tacticMonoidal_nf", "kind": "definition", "module": "Mathlib.Tactic.CategoryTheory.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Monoidal._aux_Mathlib_Tactic_CategoryTheory_Monoidal_Basic___elabRules_Mathlib_Tactic_Monoidal_tacticMonoidal_nf_1", "kind": "definition", "module": "Mathlib.Tactic.CategoryTheory.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Monoidal.monoidal", "kind": "definition", "module": "Mathlib.Tactic.CategoryTheory.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Monoidal.tacticMonoidal", "kind": "definition", "module": "Mathlib.Tactic.CategoryTheory.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Monoidal._aux_Mathlib_Tactic_CategoryTheory_Monoidal_Basic___elabRules_Mathlib_Tactic_Monoidal_tacticMonoidal_1", "kind": "definition", "module": "Mathlib.Tactic.CategoryTheory.Monoidal.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Monoidal.srcExpr", "kind": "definition", "module": "Mathlib.Tactic.CategoryTheory.Monoidal.Datatypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Monoidal.tgtExpr", "kind": "definition", "module": "Mathlib.Tactic.CategoryTheory.Monoidal.Datatypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Monoidal.srcExprOfIso", "kind": "definition", "module": "Mathlib.Tactic.CategoryTheory.Monoidal.Datatypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Monoidal.tgtExprOfIso", "kind": "definition", "module": "Mathlib.Tactic.CategoryTheory.Monoidal.Datatypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Monoidal.initFn._@.Mathlib.Tactic.CategoryTheory.Monoidal.Datatypes.76606406._hygCtx._hyg.2", "kind": "definition", "module": "Mathlib.Tactic.CategoryTheory.Monoidal.Datatypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Monoidal.mkContext?", "kind": "definition", "module": "Mathlib.Tactic.CategoryTheory.Monoidal.Datatypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Monoidal.instContextContext", "kind": "instance", "module": "Mathlib.Tactic.CategoryTheory.Monoidal.Datatypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Monoidal.MonoidalM", "kind": "abbrev", "module": "Mathlib.Tactic.CategoryTheory.Monoidal.Datatypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Monoidal.synthMonoidalError", "kind": "definition", "module": "Mathlib.Tactic.CategoryTheory.Monoidal.Datatypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Monoidal.instMonadMor₁MonoidalM", "kind": "instance", "module": "Mathlib.Tactic.CategoryTheory.Monoidal.Datatypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Monoidal.structuralIsoOfExpr_comp", "kind": "theorem", "module": "Mathlib.Tactic.CategoryTheory.Monoidal.Datatypes", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Monoidal.StructuralOfExpr_monoidalComp", "kind": "theorem", "module": "Mathlib.Tactic.CategoryTheory.Monoidal.Datatypes", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Monoidal.structuralIsoOfExpr_whiskerLeft", "kind": "theorem", "module": "Mathlib.Tactic.CategoryTheory.Monoidal.Datatypes", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Monoidal.structuralIsoOfExpr_whiskerRight", "kind": "theorem", "module": "Mathlib.Tactic.CategoryTheory.Monoidal.Datatypes", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Monoidal.structuralIsoOfExpr_horizontalComp", "kind": "theorem", "module": "Mathlib.Tactic.CategoryTheory.Monoidal.Datatypes", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Monoidal.instMonadMor₂IsoMonoidalM", "kind": "instance", "module": "Mathlib.Tactic.CategoryTheory.Monoidal.Datatypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Monoidal.instMonadMor₂MonoidalM", "kind": "instance", "module": "Mathlib.Tactic.CategoryTheory.Monoidal.Datatypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Monoidal.id₁?", "kind": "definition", "module": "Mathlib.Tactic.CategoryTheory.Monoidal.Datatypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Monoidal.comp?", "kind": "definition", "module": "Mathlib.Tactic.CategoryTheory.Monoidal.Datatypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Monoidal.mor₁OfExpr", "kind": "definition", "module": "Mathlib.Tactic.CategoryTheory.Monoidal.Datatypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Monoidal.instMkMor₁MonoidalM", "kind": "instance", "module": "Mathlib.Tactic.CategoryTheory.Monoidal.Datatypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Monoidal.Mor₂IsoOfExpr", "kind": "definition", "module": "Mathlib.Tactic.CategoryTheory.Monoidal.Datatypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Monoidal.Mor₂OfExpr", "kind": "definition", "module": "Mathlib.Tactic.CategoryTheory.Monoidal.Datatypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Monoidal.instMkMor₂MonoidalM", "kind": "instance", "module": "Mathlib.Tactic.CategoryTheory.Monoidal.Datatypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Monoidal.instMonadCoherehnceHomMonoidalM", "kind": "instance", "module": "Mathlib.Tactic.CategoryTheory.Monoidal.Datatypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Monoidal.evalComp_nil_nil", "kind": "theorem", "module": "Mathlib.Tactic.CategoryTheory.Monoidal.Normalize", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Monoidal.evalComp_nil_cons", "kind": "theorem", "module": "Mathlib.Tactic.CategoryTheory.Monoidal.Normalize", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Monoidal.evalComp_cons", "kind": "theorem", "module": "Mathlib.Tactic.CategoryTheory.Monoidal.Normalize", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Monoidal.eval_comp", "kind": "theorem", "module": "Mathlib.Tactic.CategoryTheory.Monoidal.Normalize", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Monoidal.eval_of", "kind": "theorem", "module": "Mathlib.Tactic.CategoryTheory.Monoidal.Normalize", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Monoidal.eval_monoidalComp", "kind": "theorem", "module": "Mathlib.Tactic.CategoryTheory.Monoidal.Normalize", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Monoidal.evalWhiskerLeft_nil", "kind": "theorem", "module": "Mathlib.Tactic.CategoryTheory.Monoidal.Normalize", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Monoidal.evalWhiskerLeft_of_cons", "kind": "theorem", "module": "Mathlib.Tactic.CategoryTheory.Monoidal.Normalize", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Monoidal.evalWhiskerLeft_comp", "kind": "theorem", "module": "Mathlib.Tactic.CategoryTheory.Monoidal.Normalize", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Monoidal.evalWhiskerLeft_id", "kind": "theorem", "module": "Mathlib.Tactic.CategoryTheory.Monoidal.Normalize", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Monoidal.eval_whiskerLeft", "kind": "theorem", "module": "Mathlib.Tactic.CategoryTheory.Monoidal.Normalize", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Monoidal.eval_whiskerRight", "kind": "theorem", "module": "Mathlib.Tactic.CategoryTheory.Monoidal.Normalize", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Monoidal.eval_tensorHom", "kind": "theorem", "module": "Mathlib.Tactic.CategoryTheory.Monoidal.Normalize", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Monoidal.evalWhiskerRight_nil", "kind": "theorem", "module": "Mathlib.Tactic.CategoryTheory.Monoidal.Normalize", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Monoidal.evalWhiskerRight_cons_of_of", "kind": "theorem", "module": "Mathlib.Tactic.CategoryTheory.Monoidal.Normalize", "is_tactic_proof": true, "tactics": ["simp_all"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Monoidal.evalWhiskerRight_cons_whisker", "kind": "theorem", "module": "Mathlib.Tactic.CategoryTheory.Monoidal.Normalize", "is_tactic_proof": true, "tactics": ["simp", "simp"], "tactic_count": 2}
{"name": "Mathlib.Tactic.Monoidal.evalWhiskerRight_comp", "kind": "theorem", "module": "Mathlib.Tactic.CategoryTheory.Monoidal.Normalize", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Monoidal.evalWhiskerRight_id", "kind": "theorem", "module": "Mathlib.Tactic.CategoryTheory.Monoidal.Normalize", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Monoidal.evalWhiskerRightAux_of", "kind": "theorem", "module": "Mathlib.Tactic.CategoryTheory.Monoidal.Normalize", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Monoidal.evalWhiskerRightAux_cons", "kind": "theorem", "module": "Mathlib.Tactic.CategoryTheory.Monoidal.Normalize", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Monoidal.evalWhiskerRight_cons_of", "kind": "theorem", "module": "Mathlib.Tactic.CategoryTheory.Monoidal.Normalize", "is_tactic_proof": true, "tactics": ["simp_all"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Monoidal.evalHorizontalCompAux_of", "kind": "theorem", "module": "Mathlib.Tactic.CategoryTheory.Monoidal.Normalize", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Monoidal.evalHorizontalCompAux_cons", "kind": "theorem", "module": "Mathlib.Tactic.CategoryTheory.Monoidal.Normalize", "is_tactic_proof": true, "tactics": ["simp_all"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Monoidal.evalHorizontalCompAux'_whisker", "kind": "theorem", "module": "Mathlib.Tactic.CategoryTheory.Monoidal.Normalize", "is_tactic_proof": true, "tactics": ["simp", "simp"], "tactic_count": 2}
{"name": "Mathlib.Tactic.Monoidal.evalHorizontalCompAux'_of_whisker", "kind": "theorem", "module": "Mathlib.Tactic.CategoryTheory.Monoidal.Normalize", "is_tactic_proof": true, "tactics": ["simp", "simp"], "tactic_count": 2}
{"name": "Mathlib.Tactic.Monoidal.evalHorizontalComp_nil_nil", "kind": "theorem", "module": "Mathlib.Tactic.CategoryTheory.Monoidal.Normalize", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Monoidal.evalHorizontalComp_nil_cons", "kind": "theorem", "module": "Mathlib.Tactic.CategoryTheory.Monoidal.Normalize", "is_tactic_proof": true, "tactics": ["simp_all"], "tactic_count": 1}
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{"name": "Mathlib.Tactic.Reassoc.eq_whisker'", "kind": "theorem", "module": "Mathlib.Tactic.CategoryTheory.Reassoc", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "Mathlib.Tactic.ComputeDegree.natDegree_zero_le", "kind": "theorem", "module": "Mathlib.Tactic.ComputeDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Tactic.ComputeDegree.coeff_add_of_eq", "kind": "theorem", "module": "Mathlib.Tactic.ComputeDegree", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
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{"name": "Mathlib.Tactic.ComputeDegree.natDegree_smul_le_of_le", "kind": "theorem", "module": "Mathlib.Tactic.ComputeDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Tactic.ComputeDegree.natDegree_eq_of_le_of_coeff_ne_zero'", "kind": "theorem", "module": "Mathlib.Tactic.ComputeDegree", "is_tactic_proof": true, "tactics": ["subst", "exact"], "tactic_count": 2}
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{"name": "Mathlib.Tactic.ComputeDegree.coeff_sub_of_eq", "kind": "theorem", "module": "Mathlib.Tactic.ComputeDegree", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
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{"name": "Mathlib.Tactic.ComputeDegree.miscomputedDegree?", "kind": "definition", "module": "Mathlib.Tactic.ComputeDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.ComputeDegree.computeDegree", "kind": "definition", "module": "Mathlib.Tactic.ComputeDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Tactic.ComputeDegree._aux_Mathlib_Tactic_ComputeDegree___elabRules_Mathlib_Tactic_ComputeDegree_computeDegree_1", "kind": "definition", "module": "Mathlib.Tactic.ComputeDegree", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Tactic.failIfNoProgress", "kind": "definition", "module": "Mathlib.Tactic.FailIfNoProgress", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Tactic.FieldSimp.field", "kind": "definition", "module": "Mathlib.Tactic.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.FieldSimp._aux_Mathlib_Tactic_Field___elabRules_Mathlib_Tactic_FieldSimp_field_1", "kind": "definition", "module": "Mathlib.Tactic.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Tactic.FieldSimp.qNF", "kind": "abbrev", "module": "Mathlib.Tactic.FieldSimp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.FieldSimp.qNF.toNF", "kind": "definition", "module": "Mathlib.Tactic.FieldSimp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.FieldSimp.qNF.onExponent", "kind": "definition", "module": "Mathlib.Tactic.FieldSimp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.FieldSimp.qNF.evalPrettyMonomial", "kind": "definition", "module": "Mathlib.Tactic.FieldSimp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Tactic.FieldSimp.qNF.removeZeros", "kind": "definition", "module": "Mathlib.Tactic.FieldSimp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Tactic.FieldSimp.qNF.evalPretty", "kind": "definition", "module": "Mathlib.Tactic.FieldSimp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.FieldSimp.qNF.mul", "kind": "definition", "module": "Mathlib.Tactic.FieldSimp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.FieldSimp.qNF.mkMulProof", "kind": "definition", "module": "Mathlib.Tactic.FieldSimp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.FieldSimp.qNF.div", "kind": "definition", "module": "Mathlib.Tactic.FieldSimp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.FieldSimp.qNF.mkDivProof", "kind": "definition", "module": "Mathlib.Tactic.FieldSimp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.FieldSimp.DenomCondition", "kind": "inductive", "module": "Mathlib.Tactic.FieldSimp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.FieldSimp.DenomCondition.proof", "kind": "definition", "module": "Mathlib.Tactic.FieldSimp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.FieldSimp.DenomCondition.proofZero", "kind": "definition", "module": "Mathlib.Tactic.FieldSimp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.FieldSimp.mkDenomConditionProofSucc", "kind": "definition", "module": "Mathlib.Tactic.FieldSimp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.FieldSimp.mkDenomConditionProofSucc'", "kind": "definition", "module": "Mathlib.Tactic.FieldSimp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.FieldSimp.qNF.gcd", "kind": "definition", "module": "Mathlib.Tactic.FieldSimp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.FieldSimp.normalize", "kind": "definition", "module": "Mathlib.Tactic.FieldSimp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.FieldSimp.reduceExprQ", "kind": "definition", "module": "Mathlib.Tactic.FieldSimp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.FieldSimp.reduceEqQ", "kind": "definition", "module": "Mathlib.Tactic.FieldSimp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.FieldSimp.reduceLeQ", "kind": "definition", "module": "Mathlib.Tactic.FieldSimp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.FieldSimp.reduceLtQ", "kind": "definition", "module": "Mathlib.Tactic.FieldSimp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.FieldSimp.reduceExpr", "kind": "definition", "module": "Mathlib.Tactic.FieldSimp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.FieldSimp.reduceProp", "kind": "definition", "module": "Mathlib.Tactic.FieldSimp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.FieldSimp.parseDischarger", "kind": "definition", "module": "Mathlib.Tactic.FieldSimp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.FieldSimp.fieldSimp", "kind": "definition", "module": "Mathlib.Tactic.FieldSimp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.FieldSimp._aux_Mathlib_Tactic_FieldSimp___elabRules_Mathlib_Tactic_FieldSimp_fieldSimp_1", "kind": "definition", "module": "Mathlib.Tactic.FieldSimp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.FieldSimp.convField_simp__", "kind": "definition", "module": "Mathlib.Tactic.FieldSimp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.FieldSimp._aux_Mathlib_Tactic_FieldSimp___elabRules_Mathlib_Tactic_FieldSimp_convField_simp___1", "kind": "definition", "module": "Mathlib.Tactic.FieldSimp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.FieldSimp.proc", "kind": "definition", "module": "Mathlib.Tactic.FieldSimp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fieldEq", "kind": "definition", "module": "Mathlib.Tactic.FieldSimp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "fieldLe", "kind": "definition", "module": "Mathlib.Tactic.FieldSimp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "fieldSimpExt", "kind": "opaque", "module": "Mathlib.Tactic.FieldSimp.Attr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Tactic.FieldSimp.Discharger.0.Mathlib.Tactic.FieldSimp.dischargerTraceMessage", "kind": "definition", "module": "Mathlib.Tactic.FieldSimp.Discharger", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.FieldSimp.discharge", "kind": "definition", "module": "Mathlib.Tactic.FieldSimp.Discharger", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.FieldSimp.tacticField_simp_discharge", "kind": "definition", "module": "Mathlib.Tactic.FieldSimp.Discharger", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.FieldSimp._aux_Mathlib_Tactic_FieldSimp_Discharger___elabRules_Mathlib_Tactic_FieldSimp_tacticField_simp_discharge_1", "kind": "definition", "module": "Mathlib.Tactic.FieldSimp.Discharger", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.FieldSimp.zpow'", "kind": "definition", "module": "Mathlib.Tactic.FieldSimp.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.FieldSimp.zpow'_add", "kind": "theorem", "module": "Mathlib.Tactic.FieldSimp.Lemmas", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "by_cases", "simp", "simp", "simp"], "tactic_count": 6}
{"name": "Mathlib.Tactic.FieldSimp.zpow'_of_ne_zero_right", "kind": "theorem", "module": "Mathlib.Tactic.FieldSimp.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.FieldSimp.zpow'_of_ne_zero_left", "kind": "theorem", "module": "Mathlib.Tactic.FieldSimp.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.FieldSimp.zero_zpow'", "kind": "theorem", "module": "Mathlib.Tactic.FieldSimp.Lemmas", "is_tactic_proof": true, "tactics": ["simp", "intro", "exact"], "tactic_count": 3}
{"name": "Mathlib.Tactic.FieldSimp.zpow'_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Tactic.FieldSimp.Lemmas", "is_tactic_proof": true, "tactics": ["obtain", "simp", "simp", "tauto"], "tactic_count": 4}
{"name": "Mathlib.Tactic.FieldSimp.one_zpow'", "kind": "theorem", "module": "Mathlib.Tactic.FieldSimp.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.FieldSimp.zpow'_one", "kind": "theorem", "module": "Mathlib.Tactic.FieldSimp.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.FieldSimp.zpow'_zero_eq_div", "kind": "theorem", "module": "Mathlib.Tactic.FieldSimp.Lemmas", "is_tactic_proof": true, "tactics": ["simp", "by_cases", "simp", "simp"], "tactic_count": 4}
{"name": "Mathlib.Tactic.FieldSimp.zpow'_zero_of_ne_zero", "kind": "theorem", "module": "Mathlib.Tactic.FieldSimp.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.FieldSimp.zpow'_neg", "kind": "theorem", "module": "Mathlib.Tactic.FieldSimp.Lemmas", "is_tactic_proof": true, "tactics": ["simp", "split_ifs", "tauto", "tauto"], "tactic_count": 4}
{"name": "Mathlib.Tactic.FieldSimp.zpow'_mul", "kind": "theorem", "module": "Mathlib.Tactic.FieldSimp.Lemmas", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "by_cases", "rw", "simp", "by_cases", "rw", "simp", "simpa"], "tactic_count": 9}
{"name": "Mathlib.Tactic.FieldSimp.zpow'_ofNat", "kind": "theorem", "module": "Mathlib.Tactic.FieldSimp.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "simp", "exact_mod_cast"], "tactic_count": 3}
{"name": "Mathlib.Tactic.FieldSimp.mul_zpow'", "kind": "theorem", "module": "Mathlib.Tactic.FieldSimp.Lemmas", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "by_cases", "simp", "simpa"], "tactic_count": 5}
{"name": "Mathlib.Tactic.FieldSimp.list_prod_zpow'", "kind": "theorem", "module": "Mathlib.Tactic.FieldSimp.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.FieldSimp.subst_add", "kind": "theorem", "module": "Mathlib.Tactic.FieldSimp.Lemmas", "is_tactic_proof": true, "tactics": ["subst", "simp"], "tactic_count": 2}
{"name": "Mathlib.Tactic.FieldSimp.subst_sub", "kind": "theorem", "module": "Mathlib.Tactic.FieldSimp.Lemmas", "is_tactic_proof": true, "tactics": ["subst", "simp"], "tactic_count": 2}
{"name": "Mathlib.Tactic.FieldSimp.eq_div_of_eq_one_of_subst", "kind": "theorem", "module": "Mathlib.Tactic.FieldSimp.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Mathlib.Tactic.FieldSimp.eq_div_of_eq_one_of_subst'", "kind": "theorem", "module": "Mathlib.Tactic.FieldSimp.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Mathlib.Tactic.FieldSimp.eq_div_of_subst", "kind": "theorem", "module": "Mathlib.Tactic.FieldSimp.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Mathlib.Tactic.FieldSimp.eq_mul_of_eq_eq_eq_mul", "kind": "theorem", "module": "Mathlib.Tactic.FieldSimp.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Mathlib.Tactic.FieldSimp.eq_eq_cancel_eq", "kind": "theorem", "module": "Mathlib.Tactic.FieldSimp.Lemmas", "is_tactic_proof": true, "tactics": ["subst", "rw"], "tactic_count": 2}
{"name": "Mathlib.Tactic.FieldSimp.le_eq_cancel_le", "kind": "theorem", "module": "Mathlib.Tactic.FieldSimp.Lemmas", "is_tactic_proof": true, "tactics": ["subst", "apply", "exact"], "tactic_count": 3}
{"name": "Mathlib.Tactic.FieldSimp.lt_eq_cancel_lt", "kind": "theorem", "module": "Mathlib.Tactic.FieldSimp.Lemmas", "is_tactic_proof": true, "tactics": ["subst", "apply", "exact"], "tactic_count": 3}
{"name": "Mathlib.Tactic.FieldSimp.NF", "kind": "definition", "module": "Mathlib.Tactic.FieldSimp.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.FieldSimp.NF.cons", "kind": "definition", "module": "Mathlib.Tactic.FieldSimp.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.FieldSimp.NF.term_::ᵣ_", "kind": "definition", "module": "Mathlib.Tactic.FieldSimp.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.FieldSimp.NF._aux_Mathlib_Tactic_FieldSimp_Lemmas___macroRules_Mathlib_Tactic_FieldSimp_NF_term_::ᵣ__1", "kind": "definition", "module": "Mathlib.Tactic.FieldSimp.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.FieldSimp.NF._aux_Mathlib_Tactic_FieldSimp_Lemmas___unexpand_Mathlib_Tactic_FieldSimp_NF_cons_1", "kind": "definition", "module": "Mathlib.Tactic.FieldSimp.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.FieldSimp.NF.eval", "kind": "definition", "module": "Mathlib.Tactic.FieldSimp.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.FieldSimp.NF.eval_cons", "kind": "theorem", "module": "Mathlib.Tactic.FieldSimp.Lemmas", "is_tactic_proof": true, "tactics": ["unfold", "simp"], "tactic_count": 2}
{"name": "Mathlib.Tactic.FieldSimp.NF.cons_ne_zero", "kind": "theorem", "module": "Mathlib.Tactic.FieldSimp.Lemmas", "is_tactic_proof": true, "tactics": ["unfold", "apply", "simp"], "tactic_count": 3}
{"name": "Mathlib.Tactic.FieldSimp.NF.cons_pos", "kind": "theorem", "module": "Mathlib.Tactic.FieldSimp.Lemmas", "is_tactic_proof": true, "tactics": ["unfold", "apply", "simp", "rw", "apply"], "tactic_count": 5}
{"name": "Mathlib.Tactic.FieldSimp.NF.atom_eq_eval", "kind": "theorem", "module": "Mathlib.Tactic.FieldSimp.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.FieldSimp.NF.one_eq_eval", "kind": "theorem", "module": "Mathlib.Tactic.FieldSimp.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.FieldSimp.NF.mul_eq_eval₁", "kind": "theorem", "module": "Mathlib.Tactic.FieldSimp.Lemmas", "is_tactic_proof": true, "tactics": ["simp", "ac_rfl"], "tactic_count": 2}
{"name": "Mathlib.Tactic.FieldSimp.NF.mul_eq_eval₂", "kind": "theorem", "module": "Mathlib.Tactic.FieldSimp.Lemmas", "is_tactic_proof": true, "tactics": ["simp", "ac_rfl"], "tactic_count": 2}
{"name": "Mathlib.Tactic.FieldSimp.NF.mul_eq_eval₃", "kind": "theorem", "module": "Mathlib.Tactic.FieldSimp.Lemmas", "is_tactic_proof": true, "tactics": ["simp", "ac_rfl"], "tactic_count": 2}
{"name": "Mathlib.Tactic.FieldSimp.NF.mul_eq_eval", "kind": "theorem", "module": "Mathlib.Tactic.FieldSimp.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "Mathlib.Tactic.FieldSimp.NF.div_eq_eval₂", "kind": "theorem", "module": "Mathlib.Tactic.FieldSimp.Lemmas", "is_tactic_proof": true, "tactics": ["simp", "ac_rfl"], "tactic_count": 2}
{"name": "Mathlib.Tactic.FieldSimp.NF.div_eq_eval₃", "kind": "theorem", "module": "Mathlib.Tactic.FieldSimp.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "Mathlib.Tactic.FieldSimp.NF.cons_zero_eq_div_of_eq_div", "kind": "theorem", "module": "Mathlib.Tactic.FieldSimp.Lemmas", "is_tactic_proof": true, "tactics": ["simp", "ac_rfl"], "tactic_count": 2}
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{"name": "Mathlib.Tactic.FieldSimp.NF.eval_inv", "kind": "theorem", "module": "Mathlib.Tactic.FieldSimp.Lemmas", "is_tactic_proof": true, "tactics": ["simp", "congr", "ext", "simp"], "tactic_count": 4}
{"name": "Mathlib.Tactic.FieldSimp.NF.one_div_eq_eval", "kind": "theorem", "module": "Mathlib.Tactic.FieldSimp.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.FieldSimp.NF.inv_eq_eval", "kind": "theorem", "module": "Mathlib.Tactic.FieldSimp.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "Mathlib.Tactic.FieldSimp.NF.zpow_apply", "kind": "theorem", "module": "Mathlib.Tactic.FieldSimp.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.FieldSimp.NF.eval_zpow'", "kind": "theorem", "module": "Mathlib.Tactic.FieldSimp.Lemmas", "is_tactic_proof": true, "tactics": ["unfold", "simp", "congr", "ext", "simp"], "tactic_count": 5}
{"name": "Mathlib.Tactic.FieldSimp.NF.zpow_eq_eval", "kind": "theorem", "module": "Mathlib.Tactic.FieldSimp.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "Mathlib.Tactic.FieldSimp.NF.pow_apply", "kind": "theorem", "module": "Mathlib.Tactic.FieldSimp.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.FieldSimp.NF.eval_pow", "kind": "theorem", "module": "Mathlib.Tactic.FieldSimp.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.FieldSimp.NF.pow_eq_eval", "kind": "theorem", "module": "Mathlib.Tactic.FieldSimp.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "rw"], "tactic_count": 2}
{"name": "Mathlib.Tactic.FieldSimp.NF.eval_cons_of_pow_eq_zero", "kind": "theorem", "module": "Mathlib.Tactic.FieldSimp.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "Mathlib.Tactic.FieldSimp.Sign.mul", "kind": "definition", "module": "Mathlib.Tactic.FieldSimp.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Tactic.GCongr.instInhabitedGCongrLemma.default", "kind": "definition", "module": "Mathlib.Tactic.GCongr.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.GCongr.instInhabitedGCongrLemma", "kind": "instance", "module": "Mathlib.Tactic.GCongr.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.GCongr.GCongrLemmas", "kind": "abbrev", "module": "Mathlib.Tactic.GCongr.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.GCongr.GCongrLemma.prioLE", "kind": "definition", "module": "Mathlib.Tactic.GCongr.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.GCongr.addGCongrLemmaEntry", "kind": "definition", "module": "Mathlib.Tactic.GCongr.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.GCongr.initFn._@.Mathlib.Tactic.GCongr.Core.2585311888._hygCtx._hyg.2", "kind": "definition", "module": "Mathlib.Tactic.GCongr.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.GCongr.gcongrExt", "kind": "opaque", "module": "Mathlib.Tactic.GCongr.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.GCongr.getCongrAppFnArgs", "kind": "definition", "module": "Mathlib.Tactic.GCongr.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.GCongr.getRel", "kind": "definition", "module": "Mathlib.Tactic.GCongr.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.GCongr.updateRel", "kind": "definition", "module": "Mathlib.Tactic.GCongr.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.GCongr.makeGCongrLemma", "kind": "definition", "module": "Mathlib.Tactic.GCongr.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.GCongr.initFn._@.Mathlib.Tactic.GCongr.Core.4164341304._hygCtx._hyg.2", "kind": "definition", "module": "Mathlib.Tactic.GCongr.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.GCongr.initFn._@.Mathlib.Tactic.GCongr.Core.1465912347._hygCtx._hyg.2", "kind": "definition", "module": "Mathlib.Tactic.GCongr.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.GCongr.tacticGcongr_discharger", "kind": "definition", "module": "Mathlib.Tactic.GCongr.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.GCongr.gcongrDischarger", "kind": "definition", "module": "Mathlib.Tactic.GCongr.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.GCongr.exactRefl", "kind": "definition", "module": "Mathlib.Tactic.GCongr.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.GCongr.symmExact", "kind": "definition", "module": "Mathlib.Tactic.GCongr.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.GCongr.exact", "kind": "definition", "module": "Mathlib.Tactic.GCongr.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lean.MVarId.gcongrForward", "kind": "definition", "module": "Mathlib.Tactic.GCongr.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.GCongr.gcongrForwardDischarger", "kind": "definition", "module": "Mathlib.Tactic.GCongr.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.GCongr.mkHoleAnnotation", "kind": "definition", "module": "Mathlib.Tactic.GCongr.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.GCongr.hasHoleAnnotation", "kind": "definition", "module": "Mathlib.Tactic.GCongr.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.GCongr.containsHoleAnnotation", "kind": "definition", "module": "Mathlib.Tactic.GCongr.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.GCongr.gcongrHoleExpand", "kind": "definition", "module": "Mathlib.Tactic.GCongr.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.GCongr.elabCHoleExpand", "kind": "definition", "module": "Mathlib.Tactic.GCongr.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.GCongr.rel_imp_rel", "kind": "theorem", "module": "Mathlib.Tactic.GCongr.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.GCongr.relImpRelLemma", "kind": "definition", "module": "Mathlib.Tactic.GCongr.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.GCongr.tacticGcongr___With___", "kind": "definition", "module": "Mathlib.Tactic.GCongr.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.GCongr._aux_Mathlib_Tactic_GCongr_Core___elabRules_Mathlib_Tactic_GCongr_tacticGcongr___With____1", "kind": "definition", "module": "Mathlib.Tactic.GCongr.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.GCongr.tacticRel[_]", "kind": "definition", "module": "Mathlib.Tactic.GCongr.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.GCongr._aux_Mathlib_Tactic_GCongr_Core___elabRules_Mathlib_Tactic_GCongr_tacticRel[_]_1", "kind": "definition", "module": "Mathlib.Tactic.GCongr.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.GCongr.imp_trans", "kind": "theorem", "module": "Mathlib.Tactic.GCongr.CoreAttrs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.GCongr.imp_right_mono", "kind": "theorem", "module": "Mathlib.Tactic.GCongr.CoreAttrs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.GCongr.and_right_mono", "kind": "theorem", "module": "Mathlib.Tactic.GCongr.CoreAttrs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.GCongr.mkForwardExt", "kind": "definition", "module": "Mathlib.Tactic.GCongr.ForwardAttr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.GCongr.initFn._@.Mathlib.Tactic.GCongr.ForwardAttr.242967595._hygCtx._hyg.2", "kind": "definition", "module": "Mathlib.Tactic.GCongr.ForwardAttr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.GCongr.forwardExt", "kind": "opaque", "module": "Mathlib.Tactic.GCongr.ForwardAttr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.GCongr.initFn._@.Mathlib.Tactic.GCongr.ForwardAttr.3318740503._hygCtx._hyg.2", "kind": "definition", "module": "Mathlib.Tactic.GCongr.ForwardAttr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.GRewrite.dischargeMain", "kind": "definition", "module": "Mathlib.Tactic.GRewrite.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lean.MVarId.grewrite", "kind": "definition", "module": "Mathlib.Tactic.GRewrite.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.grewriteTarget", "kind": "definition", "module": "Mathlib.Tactic.GRewrite.Elab", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.grewriteLocalDecl", "kind": "definition", "module": "Mathlib.Tactic.GRewrite.Elab", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.evalUnsafe._@.Mathlib.Tactic.GRewrite.Elab.1373484378._hygCtx._hyg.3", "kind": "definition", "module": "Mathlib.Tactic.GRewrite.Elab", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.eval._@.Mathlib.Tactic.GRewrite.Elab.1373484378._hygCtx._hyg.3", "kind": "opaque", "module": "Mathlib.Tactic.GRewrite.Elab", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.elabGRewriteConfig", "kind": "definition", "module": "Mathlib.Tactic.GRewrite.Elab", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.grewriteSeq", "kind": "definition", "module": "Mathlib.Tactic.GRewrite.Elab", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.evalGRewriteSeq", "kind": "definition", "module": "Mathlib.Tactic.GRewrite.Elab", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.grwSeq", "kind": "definition", "module": "Mathlib.Tactic.GRewrite.Elab", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic._aux_Mathlib_Tactic_GRewrite_Elab___macroRules_Mathlib_Tactic_grwSeq_1", "kind": "definition", "module": "Mathlib.Tactic.GRewrite.Elab", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.tacticApply_rewrite___", "kind": "definition", "module": "Mathlib.Tactic.GRewrite.Elab", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic._aux_Mathlib_Tactic_GRewrite_Elab___macroRules_Mathlib_Tactic_tacticApply_rewrite____1", "kind": "definition", "module": "Mathlib.Tactic.GRewrite.Elab", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.applyRwSeq", "kind": "definition", "module": "Mathlib.Tactic.GRewrite.Elab", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic._aux_Mathlib_Tactic_GRewrite_Elab___macroRules_Mathlib_Tactic_applyRwSeq_1", "kind": "definition", "module": "Mathlib.Tactic.GRewrite.Elab", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.tacticNth_grewrite_____", "kind": "definition", "module": "Mathlib.Tactic.GRewrite.Elab", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic._aux_Mathlib_Tactic_GRewrite_Elab___macroRules_Mathlib_Tactic_tacticNth_grewrite______1", "kind": "definition", "module": "Mathlib.Tactic.GRewrite.Elab", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.tacticNth_grw_____", "kind": "definition", "module": "Mathlib.Tactic.GRewrite.Elab", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic._aux_Mathlib_Tactic_GRewrite_Elab___macroRules_Mathlib_Tactic_tacticNth_grw______1", "kind": "definition", "module": "Mathlib.Tactic.GRewrite.Elab", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tacticGeneralize'_:_=_", "kind": "definition", "module": "Mathlib.Tactic.Generalize", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Tactic_Generalize___elabRules_tacticGeneralize'_:_=__1", "kind": "definition", "module": "Mathlib.Tactic.Generalize", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Group.zpow_trick", "kind": "theorem", "module": "Mathlib.Tactic.Group", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Group.zpow_trick_one", "kind": "theorem", "module": "Mathlib.Tactic.Group", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Group.zpow_trick_one'", "kind": "theorem", "module": "Mathlib.Tactic.Group", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Group.aux_group₁", "kind": "definition", "module": "Mathlib.Tactic.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Group._aux_Mathlib_Tactic_Group___macroRules_Mathlib_Tactic_Group_aux_group₁_1", "kind": "definition", "module": "Mathlib.Tactic.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Group.aux_group₂", "kind": "definition", "module": "Mathlib.Tactic.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Group._aux_Mathlib_Tactic_Group___macroRules_Mathlib_Tactic_Group_aux_group₂_1", "kind": "definition", "module": "Mathlib.Tactic.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Group.group", "kind": "definition", "module": "Mathlib.Tactic.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Group._aux_Mathlib_Tactic_Group___macroRules_Mathlib_Tactic_Group_group_1", "kind": "definition", "module": "Mathlib.Tactic.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "guardGoalNums", "kind": "definition", "module": "Mathlib.Tactic.GuardGoalNums", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Tactic_GuardGoalNums___elabRules_guardGoalNums_1", "kind": "definition", "module": "Mathlib.Tactic.GuardGoalNums", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "guardHypNums", "kind": "definition", "module": "Mathlib.Tactic.GuardHypNums", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Tactic_GuardHypNums___elabRules_guardHypNums_1", "kind": "definition", "module": "Mathlib.Tactic.GuardHypNums", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.optBinderIdent", "kind": "definition", "module": "Mathlib.Tactic.Have", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.optBinderIdent.name", "kind": "definition", "module": "Mathlib.Tactic.Have", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.haveIdLhs'", "kind": "definition", "module": "Mathlib.Tactic.Have", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.tacticHave_", "kind": "definition", "module": "Mathlib.Tactic.Have", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.tacticLet_", "kind": "definition", "module": "Mathlib.Tactic.Have", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.tacticSuffices_", "kind": "definition", "module": "Mathlib.Tactic.Have", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.haveLetCore", "kind": "definition", "module": "Mathlib.Tactic.Have", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic._aux_Mathlib_Tactic_Have___elabRules_Mathlib_Tactic_tacticHave__1", "kind": "definition", "module": "Mathlib.Tactic.Have", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic._aux_Mathlib_Tactic_Have___elabRules_Mathlib_Tactic_tacticSuffices__1", "kind": "definition", "module": "Mathlib.Tactic.Have", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic._aux_Mathlib_Tactic_Have___elabRules_Mathlib_Tactic_tacticLet__1", "kind": "definition", "module": "Mathlib.Tactic.Have", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Tactic.HaveI.0.Mathlib.Tactic.HaveI.termHaveIDummy_", "kind": "definition", "module": "Mathlib.Tactic.HaveI", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.HaveI._aux_Mathlib_Tactic_HaveI___macroRules_Lean_Parser_Term_assert_1", "kind": "definition", "module": "Mathlib.Tactic.HaveI", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.HaveI.doElemHaveI'_", "kind": "definition", "module": "Mathlib.Tactic.HaveI", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.HaveI._aux_Mathlib_Tactic_HaveI___macroRules_Mathlib_Tactic_HaveI_doElemHaveI'__1", "kind": "definition", "module": "Mathlib.Tactic.HaveI", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Tactic.HaveI.0.Mathlib.Tactic.HaveI.termLetIDummy_", "kind": "definition", "module": "Mathlib.Tactic.HaveI", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.HaveI._aux_Mathlib_Tactic_HaveI___macroRules_Lean_Parser_Term_assert_2", "kind": "definition", "module": "Mathlib.Tactic.HaveI", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.HaveI.doElemLetI'_", "kind": "definition", "module": "Mathlib.Tactic.HaveI", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.HaveI._aux_Mathlib_Tactic_HaveI___macroRules_Mathlib_Tactic_HaveI_doElemLetI'__1", "kind": "definition", "module": "Mathlib.Tactic.HaveI", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lean.Parser.Attr.higherOrder", "kind": "definition", "module": "Mathlib.Tactic.HigherOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.mkComp", "kind": "definition", "module": "Mathlib.Tactic.HigherOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.mkHigherOrderType", "kind": "definition", "module": "Mathlib.Tactic.HigherOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.higherOrderGetParam", "kind": "definition", "module": "Mathlib.Tactic.HigherOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.initFn._@.Mathlib.Tactic.HigherOrder.2684385311._hygCtx._hyg.2", "kind": "definition", "module": "Mathlib.Tactic.HigherOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.higherOrderAttr", "kind": "opaque", "module": "Mathlib.Tactic.HigherOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Hint.initFn._@.Mathlib.Tactic.Hint.2826036628._hygCtx._hyg.2", "kind": "definition", "module": "Mathlib.Tactic.Hint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Hint.hintExtension", "kind": "opaque", "module": "Mathlib.Tactic.Hint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Hint.addHint", "kind": "definition", "module": "Mathlib.Tactic.Hint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Hint.getHints", "kind": "definition", "module": "Mathlib.Tactic.Hint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Hint.registerHintStx", "kind": "definition", "module": "Mathlib.Tactic.Hint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Hint._aux_Mathlib_Tactic_Hint___elabRules_Mathlib_Tactic_Hint_registerHintStx_1", "kind": "definition", "module": "Mathlib.Tactic.Hint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Hint.initFn._@.Mathlib.Tactic.Hint.3357253919._hygCtx._hyg.2", "kind": "definition", "module": "Mathlib.Tactic.Hint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Hint.suggestion", "kind": "definition", "module": "Mathlib.Tactic.Hint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Hint.hint", "kind": "definition", "module": "Mathlib.Tactic.Hint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Hint.hintStx", "kind": "definition", "module": "Mathlib.Tactic.Hint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Hint._aux_Mathlib_Tactic_Hint___elabRules_Mathlib_Tactic_Hint_hintStx_1", "kind": "definition", "module": "Mathlib.Tactic.Hint", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.ITauto.AndKind", "kind": "inductive", "module": "Mathlib.Tactic.ITauto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.ITauto.instToExprAndKind", "kind": "instance", "module": "Mathlib.Tactic.ITauto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.ITauto.instDecidableEqAndKind", "kind": "instance", "module": "Mathlib.Tactic.ITauto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.ITauto.instInhabitedAndKind", "kind": "instance", "module": "Mathlib.Tactic.ITauto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.ITauto.IProp", "kind": "inductive", "module": "Mathlib.Tactic.ITauto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.ITauto.instToExprIProp", "kind": "instance", "module": "Mathlib.Tactic.ITauto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.ITauto.IProp.and", "kind": "definition", "module": "Mathlib.Tactic.ITauto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.ITauto.IProp.iff", "kind": "definition", "module": "Mathlib.Tactic.ITauto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.ITauto.IProp.eq", "kind": "definition", "module": "Mathlib.Tactic.ITauto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.ITauto.IProp.not", "kind": "definition", "module": "Mathlib.Tactic.ITauto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.ITauto.IProp.xor", "kind": "definition", "module": "Mathlib.Tactic.ITauto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.ITauto.instInhabitedIProp", "kind": "instance", "module": "Mathlib.Tactic.ITauto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.ITauto.AndKind.sides", "kind": "definition", "module": "Mathlib.Tactic.ITauto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.ITauto.IProp.format", "kind": "definition", "module": "Mathlib.Tactic.ITauto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.ITauto.instToFormatIProp", "kind": "instance", "module": "Mathlib.Tactic.ITauto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.ITauto.AndKind.cmp", "kind": "definition", "module": "Mathlib.Tactic.ITauto", "is_tactic_proof": true, "tactics": ["cases", "exacts"], "tactic_count": 2}
{"name": "Mathlib.Tactic.ITauto.IProp.cmp", "kind": "definition", "module": "Mathlib.Tactic.ITauto", "is_tactic_proof": true, "tactics": ["cases", "exact", "exact", "exact", "exact", "exact", "exact", "exacts"], "tactic_count": 8}
{"name": "Mathlib.Tactic.ITauto.instLTIProp", "kind": "instance", "module": "Mathlib.Tactic.ITauto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.ITauto.instDecidableLTIProp", "kind": "instance", "module": "Mathlib.Tactic.ITauto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.ITauto.Proof", "kind": "inductive", "module": "Mathlib.Tactic.ITauto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.ITauto.instToExprProof", "kind": "instance", "module": "Mathlib.Tactic.ITauto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.ITauto.instInhabitedProof", "kind": "instance", "module": "Mathlib.Tactic.ITauto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.ITauto.Proof.format", "kind": "definition", "module": "Mathlib.Tactic.ITauto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.ITauto.instToFormatProof", "kind": "instance", "module": "Mathlib.Tactic.ITauto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.ITauto.Proof.exfalso", "kind": "definition", "module": "Mathlib.Tactic.ITauto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.ITauto.Proof.orElim", "kind": "definition", "module": "Mathlib.Tactic.ITauto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.ITauto.Proof.app", "kind": "definition", "module": "Mathlib.Tactic.ITauto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.ITauto.freshName", "kind": "definition", "module": "Mathlib.Tactic.ITauto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.ITauto.Context", "kind": "abbrev", "module": "Mathlib.Tactic.ITauto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.ITauto.Context.format", "kind": "definition", "module": "Mathlib.Tactic.ITauto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.ITauto.instToFormatContext", "kind": "instance", "module": "Mathlib.Tactic.ITauto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.ITauto.Context.add", "kind": "definition", "module": "Mathlib.Tactic.ITauto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.ITauto.Context.withAdd", "kind": "definition", "module": "Mathlib.Tactic.ITauto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.ITauto.mapProof", "kind": "definition", "module": "Mathlib.Tactic.ITauto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.ITauto.isOk", "kind": "definition", "module": "Mathlib.Tactic.ITauto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.ITauto.whenOk", "kind": "definition", "module": "Mathlib.Tactic.ITauto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.ITauto.reify", "kind": "definition", "module": "Mathlib.Tactic.ITauto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.ITauto.applyProof", "kind": "definition", "module": "Mathlib.Tactic.ITauto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.ITauto.itautoCore", "kind": "definition", "module": "Mathlib.Tactic.ITauto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.ITauto.itauto", "kind": "definition", "module": "Mathlib.Tactic.ITauto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.ITauto._aux_Mathlib_Tactic_ITauto___elabRules_Mathlib_Tactic_ITauto_itauto_1", "kind": "definition", "module": "Mathlib.Tactic.ITauto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.ITauto.itauto!", "kind": "definition", "module": "Mathlib.Tactic.ITauto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.ITauto._aux_Mathlib_Tactic_ITauto___macroRules_Mathlib_Tactic_ITauto_itauto!_1", "kind": "definition", "module": "Mathlib.Tactic.ITauto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.inferOptParam", "kind": "definition", "module": "Mathlib.Tactic.InferParam", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic._aux_Mathlib_Tactic_InferParam___elabRules_Mathlib_Tactic_inferOptParam_1", "kind": "definition", "module": "Mathlib.Tactic.InferParam", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lean.Elab.Tactic.nonempty_to_inhabited", "kind": "definition", "module": "Mathlib.Tactic.Inhabit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lean.Elab.Tactic.nonempty_prop_to_inhabited", "kind": "definition", "module": "Mathlib.Tactic.Inhabit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lean.Elab.Tactic.inhabit", "kind": "definition", "module": "Mathlib.Tactic.Inhabit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lean.Elab.Tactic.evalInhabit", "kind": "definition", "module": "Mathlib.Tactic.Inhabit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lean.Elab.Tactic._aux_Mathlib_Tactic_Inhabit___elabRules_Lean_Elab_Tactic_inhabit_1", "kind": "definition", "module": "Mathlib.Tactic.Inhabit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.IntervalCases.Bound", "kind": "inductive", "module": "Mathlib.Tactic.IntervalCases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.IntervalCases.Bound.asLower", "kind": "definition", "module": "Mathlib.Tactic.IntervalCases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.IntervalCases.Bound.asUpper", "kind": "definition", "module": "Mathlib.Tactic.IntervalCases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.IntervalCases.parseBound", "kind": "definition", "module": "Mathlib.Tactic.IntervalCases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.IntervalCases.of_not_lt_left", "kind": "theorem", "module": "Mathlib.Tactic.IntervalCases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.IntervalCases.of_not_lt_right", "kind": "theorem", "module": "Mathlib.Tactic.IntervalCases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.IntervalCases.of_not_le_left", "kind": "theorem", "module": "Mathlib.Tactic.IntervalCases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.IntervalCases.of_not_le_right", "kind": "theorem", "module": "Mathlib.Tactic.IntervalCases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.IntervalCases.of_lt_left", "kind": "theorem", "module": "Mathlib.Tactic.IntervalCases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.IntervalCases.of_lt_right", "kind": "theorem", "module": "Mathlib.Tactic.IntervalCases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.IntervalCases.of_le_left", "kind": "theorem", "module": "Mathlib.Tactic.IntervalCases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.IntervalCases.of_le_right", "kind": "theorem", "module": "Mathlib.Tactic.IntervalCases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.IntervalCases.Methods.getBound", "kind": "definition", "module": "Mathlib.Tactic.IntervalCases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.IntervalCases.le_of_not_le_of_le", "kind": "theorem", "module": "Mathlib.Tactic.IntervalCases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.IntervalCases.Methods.inconsistentBounds", "kind": "definition", "module": "Mathlib.Tactic.IntervalCases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.IntervalCases.Methods.bisect", "kind": "definition", "module": "Mathlib.Tactic.IntervalCases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.IntervalCases.natMethods", "kind": "definition", "module": "Mathlib.Tactic.IntervalCases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.add_one_le_of_not_le", "kind": "theorem", "module": "Mathlib.Tactic.IntervalCases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.le_sub_one_of_not_le", "kind": "theorem", "module": "Mathlib.Tactic.IntervalCases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.IntervalCases.intMethods", "kind": "definition", "module": "Mathlib.Tactic.IntervalCases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.intervalCases", "kind": "definition", "module": "Mathlib.Tactic.IntervalCases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic._aux_Mathlib_Tactic_IntervalCases___elabRules_Mathlib_Tactic_intervalCases_1", "kind": "definition", "module": "Mathlib.Tactic.IntervalCases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Tactic.IrreducibleDef.0.Lean.Elab.Command.termEta_helper_", "kind": "definition", "module": "Mathlib.Tactic.IrreducibleDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lean.Elab.Command._aux_Mathlib_Tactic_IrreducibleDef___elabRules__private_Mathlib_Tactic_IrreducibleDef_0_Lean_Elab_Command_termEta_helper__1", "kind": "definition", "module": "Mathlib.Tactic.IrreducibleDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Tactic.IrreducibleDef.0.Lean.Elab.Command.termVal_proj_", "kind": "definition", "module": "Mathlib.Tactic.IrreducibleDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "_private.Mathlib.Tactic.IrreducibleDef.0.Lean.Elab.Command.commandStop_at_first_error__", "kind": "definition", "module": "Mathlib.Tactic.IrreducibleDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lean.Elab.Command._aux_Mathlib_Tactic_IrreducibleDef___elabRules__private_Mathlib_Tactic_IrreducibleDef_0_Lean_Elab_Command_commandStop_at_first_error___1", "kind": "definition", "module": "Mathlib.Tactic.IrreducibleDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lean.Elab.Command.irredDefLemma", "kind": "definition", "module": "Mathlib.Tactic.IrreducibleDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lean.Elab.Command.command_Irreducible_def____", "kind": "definition", "module": "Mathlib.Tactic.IrreducibleDef", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "lemma", "kind": "definition", "module": "Mathlib.Tactic.Lemma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "expandLemma", "kind": "definition", "module": "Mathlib.Tactic.Lemma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCanLiftIntNatCastLeOfNat", "kind": "instance", "module": "Mathlib.Tactic.Lift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.canLift", "kind": "instance", "module": "Mathlib.Tactic.Lift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "PiSubtype.canLift", "kind": "instance", "module": "Mathlib.Tactic.Lift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiSubtype.canLift'", "kind": "instance", "module": "Mathlib.Tactic.Lift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Tactic.lift", "kind": "definition", "module": "Mathlib.Tactic.Lift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Lift.getInst", "kind": "definition", "module": "Mathlib.Tactic.Lift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "initFn._@.Mathlib.Tactic.Linarith.Datatypes.189509315._hygCtx._hyg.2", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Datatypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Tactic.Linarith.linarithTraceProofs", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Datatypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.Linexp", "kind": "abbrev", "module": "Mathlib.Tactic.Linarith.Datatypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.Linexp.add", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Datatypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Tactic.Linarith.Linexp.cmp", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Datatypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Tactic.Linarith.Comp.coeffOf", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Datatypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.Comp.scale", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Datatypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Tactic.Linarith.Comp.isContr", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Datatypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.Comp.ToFormat", "kind": "instance", "module": "Mathlib.Tactic.Linarith.Datatypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.Branch", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Datatypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.Preprocessor.globalize", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Datatypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.GlobalPreprocessor.branching", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Datatypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.GlobalBranchingPreprocessor.process", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Datatypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.PreprocessorToGlobalBranchingPreprocessor", "kind": "instance", "module": "Mathlib.Tactic.Linarith.Datatypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.GlobalPreprocessorToGlobalBranchingPreprocessor", "kind": "instance", "module": "Mathlib.Tactic.Linarith.Datatypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.parseCompAndExpr", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Datatypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.mkSingleCompZeroOf", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Datatypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.LinarithConfig.updateReducibility", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Frontend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.getContrLemma", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Frontend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.applyContrLemma", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Frontend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.ExprMultiMap", "kind": "abbrev", "module": "Mathlib.Tactic.Linarith.Frontend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.ExprMultiMap.find", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Frontend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.ExprMultiMap.insert", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Frontend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.partitionByTypeIdx", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Frontend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.findLinarithContradiction", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Frontend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.runLinarith", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Frontend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.linarithArgsRest", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Frontend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.linarith", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Frontend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.linarith?", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Frontend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.tacticLinarith!_", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Frontend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic._aux_Mathlib_Tactic_Linarith_Frontend___macroRules_Mathlib_Tactic_tacticLinarith!__1", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Frontend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.tacticLinarith?!_", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Frontend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Tactic.nlinarith", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Frontend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.tacticNlinarith!_", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Frontend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic._aux_Mathlib_Tactic_Linarith_Frontend___macroRules_Mathlib_Tactic_tacticNlinarith!__1", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Frontend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.evalUnsafe._@.Mathlib.Tactic.Linarith.Frontend.3485179979._hygCtx._hyg.3", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Frontend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.eval._@.Mathlib.Tactic.Linarith.Frontend.3485179979._hygCtx._hyg.3", "kind": "opaque", "module": "Mathlib.Tactic.Linarith.Frontend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.elabLinarithConfig", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Frontend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic._aux_Mathlib_Tactic_Linarith_Frontend___elabRules_Mathlib_Tactic_linarith_1", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Frontend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Tactic.Linarith.Frontend.0.Mathlib.Tactic.minimize", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Frontend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic._aux_Mathlib_Tactic_Linarith_Frontend___elabRules_Mathlib_Tactic_linarith?_1", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Frontend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic._aux_Mathlib_Tactic_Linarith_Frontend___elabRules_Mathlib_Tactic_nlinarith_1", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Frontend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.lt_irrefl", "kind": "theorem", "module": "Mathlib.Tactic.Linarith.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.eq_of_eq_of_eq", "kind": "theorem", "module": "Mathlib.Tactic.Linarith.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Linarith.zero_lt_one", "kind": "theorem", "module": "Mathlib.Tactic.Linarith.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.le_of_eq_of_le", "kind": "theorem", "module": "Mathlib.Tactic.Linarith.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Linarith.lt_of_eq_of_lt", "kind": "theorem", "module": "Mathlib.Tactic.Linarith.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Linarith.le_of_le_of_eq", "kind": "theorem", "module": "Mathlib.Tactic.Linarith.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Linarith.lt_of_lt_of_eq", "kind": "theorem", "module": "Mathlib.Tactic.Linarith.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Linarith.add_nonpos", "kind": "theorem", "module": "Mathlib.Tactic.Linarith.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.add_lt_of_le_of_neg", "kind": "theorem", "module": "Mathlib.Tactic.Linarith.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.add_lt_of_neg_of_le", "kind": "theorem", "module": "Mathlib.Tactic.Linarith.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.add_neg", "kind": "theorem", "module": "Mathlib.Tactic.Linarith.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.natCast_nonneg", "kind": "theorem", "module": "Mathlib.Tactic.Linarith.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.mul_eq", "kind": "theorem", "module": "Mathlib.Tactic.Linarith.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Linarith.mul_neg", "kind": "theorem", "module": "Mathlib.Tactic.Linarith.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.mul_nonpos", "kind": "theorem", "module": "Mathlib.Tactic.Linarith.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.sub_nonpos_of_le", "kind": "theorem", "module": "Mathlib.Tactic.Linarith.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.sub_neg_of_lt", "kind": "theorem", "module": "Mathlib.Tactic.Linarith.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Ineq.toConstMulName", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.eq_of_not_lt_of_not_gt", "kind": "theorem", "module": "Mathlib.Tactic.Linarith.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.mul_zero_eq", "kind": "theorem", "module": "Mathlib.Tactic.Linarith.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Linarith.zero_mul_eq", "kind": "theorem", "module": "Mathlib.Tactic.Linarith.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Linarith.CompSource", "kind": "inductive", "module": "Mathlib.Tactic.Linarith.Oracle.FourierMotzkin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.instInhabitedCompSource.default", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Oracle.FourierMotzkin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.instInhabitedCompSource", "kind": "instance", "module": "Mathlib.Tactic.Linarith.Oracle.FourierMotzkin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.CompSource.flatten", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Oracle.FourierMotzkin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.CompSource.toString", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Oracle.FourierMotzkin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.instToFormatCompSource", "kind": "instance", "module": "Mathlib.Tactic.Linarith.Oracle.FourierMotzkin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.PComp.maybeMinimal", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Oracle.FourierMotzkin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.PComp.cmp", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Oracle.FourierMotzkin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.PComp.scale", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Oracle.FourierMotzkin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.PComp.add", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Oracle.FourierMotzkin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.PComp.assump", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Oracle.FourierMotzkin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.instToFormatPComp", "kind": "instance", "module": "Mathlib.Tactic.Linarith.Oracle.FourierMotzkin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.instToStringPComp", "kind": "instance", "module": "Mathlib.Tactic.Linarith.Oracle.FourierMotzkin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.PCompSet", "kind": "abbrev", "module": "Mathlib.Tactic.Linarith.Oracle.FourierMotzkin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.elimVar", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Oracle.FourierMotzkin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.pelimVar", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Oracle.FourierMotzkin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.PComp.isContr", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Oracle.FourierMotzkin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.elimWithSet", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Oracle.FourierMotzkin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.LinarithM", "kind": "abbrev", "module": "Mathlib.Tactic.Linarith.Oracle.FourierMotzkin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.getMaxVar", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Oracle.FourierMotzkin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.getPCompSet", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Oracle.FourierMotzkin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.validate", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Oracle.FourierMotzkin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.update", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Oracle.FourierMotzkin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.splitSetByVarSign", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Oracle.FourierMotzkin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.elimVarM", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Oracle.FourierMotzkin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.elimAllVarsM", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Oracle.FourierMotzkin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Tactic.Linarith.CertificateOracle.fourierMotzkin", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Oracle.FourierMotzkin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.SimplexAlgorithm.preprocess", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Oracle.SimplexAlgorithm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Tactic.Linarith.CertificateOracle.simplexAlgorithmSparse", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Oracle.SimplexAlgorithm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.CertificateOracle.simplexAlgorithmDense", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Oracle.SimplexAlgorithm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.SimplexAlgorithm.instGetElemProdNatRatAndLtFstSndOfUsableInSimplexAlgorithm", "kind": "instance", "module": "Mathlib.Tactic.Linarith.Oracle.SimplexAlgorithm.Datatypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.SimplexAlgorithm.instUsableInSimplexAlgorithmDenseMatrix", "kind": "instance", "module": "Mathlib.Tactic.Linarith.Oracle.SimplexAlgorithm.Datatypes", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Tactic.Linarith.SimplexAlgorithm.Gauss.GaussM", "kind": "abbrev", "module": "Mathlib.Tactic.Linarith.Oracle.SimplexAlgorithm.Gauss", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.SimplexAlgorithm.Gauss.findNonzeroRow", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Oracle.SimplexAlgorithm.Gauss", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.SimplexAlgorithm.Gauss.getTableauImp", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Oracle.SimplexAlgorithm.Gauss", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Tactic.Linarith.SimplexAlgorithm.stateLP", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Oracle.SimplexAlgorithm.PositiveVector", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Tactic.Linarith.SimplexAlgorithm.findPositiveVector", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Oracle.SimplexAlgorithm.PositiveVector", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.SimplexAlgorithm.SimplexAlgorithmException", "kind": "inductive", "module": "Mathlib.Tactic.Linarith.Oracle.SimplexAlgorithm.SimplexAlgorithm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.SimplexAlgorithm.SimplexAlgorithmM", "kind": "abbrev", "module": "Mathlib.Tactic.Linarith.Oracle.SimplexAlgorithm.SimplexAlgorithm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.SimplexAlgorithm.doPivotOperation", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Oracle.SimplexAlgorithm.SimplexAlgorithm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.SimplexAlgorithm.checkSuccess", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Oracle.SimplexAlgorithm.SimplexAlgorithm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.SimplexAlgorithm.chooseEnteringVar", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Oracle.SimplexAlgorithm.SimplexAlgorithm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "List.findDefeq", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Parsing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instAddTreeMapOfZeroOfDecidableEq_mathlib", "kind": "instance", "module": "Mathlib.Tactic.Linarith.Parsing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Tactic.Linarith.Monom", "kind": "abbrev", "module": "Mathlib.Tactic.Linarith.Parsing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.Monom.one", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Parsing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Tactic.Linarith.Sum", "kind": "abbrev", "module": "Mathlib.Tactic.Linarith.Parsing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.Sum.one", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Parsing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.Sum.scaleByMonom", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Parsing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.Sum.mul", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Parsing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.Sum.pow", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Parsing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.SumOfMonom", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Parsing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.one", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Parsing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.scalar", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Parsing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.var", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Parsing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.ExprMap", "kind": "abbrev", "module": "Mathlib.Tactic.Linarith.Parsing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.linearFormOfAtom", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Parsing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.linearFormOfExpr", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Parsing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.elimMonom", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Parsing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.toComp", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Parsing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.toCompFold", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Parsing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.linearFormsAndMaxVar", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Parsing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.splitConjunctions", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Preprocessing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.filterComparisons", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Preprocessing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.flipNegatedComparison", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Preprocessing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.removeNegations", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Preprocessing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.isNatProp", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Preprocessing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.isNatCoe", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Preprocessing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.getNatComparisons", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Preprocessing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.mk_natCast_nonneg_prf", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Preprocessing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.Expr.Ord", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Preprocessing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.natToInt", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Preprocessing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.mkNonstrictIntProof", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Preprocessing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.strengthenStrictInt", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Preprocessing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.rearrangeComparison", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Preprocessing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.compWithZero", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Preprocessing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.without_one_mul", "kind": "theorem", "module": "Mathlib.Tactic.Linarith.Preprocessing", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Linarith.normalizeDenominatorsLHS", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Preprocessing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.cancelDenoms", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Preprocessing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.findSquares", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Preprocessing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Tactic.Linarith.Preprocessing.0.Mathlib.Tactic.Linarith.nlinarithGetSquareProofs", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Preprocessing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Tactic.Linarith.Preprocessing.0.Mathlib.Tactic.Linarith.nlinarithGetProductsProofs", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Preprocessing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.nlinarithExtras", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Preprocessing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.removeNe_aux", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Preprocessing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.removeNe", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Preprocessing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.defaultPreprocessors", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Preprocessing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.preprocess", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Preprocessing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Qq.ofNatQ", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Verification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.mulExpr'", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Verification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.mulExpr", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Verification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.addExprs'", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Verification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.addExprs", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Verification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.addIneq", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Verification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.mkLTZeroProof", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Verification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.leftOfIneqProof", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Verification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.typeOfIneqProof", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Verification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.mkNegOneLtZeroProof", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Verification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.addNegEqProofsIdx", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Verification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.proveEqZeroUsing", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Verification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Linarith.proveFalseByLinarith", "kind": "definition", "module": "Mathlib.Tactic.Linarith.Verification", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.LinearCombination'.pf_add_c", "kind": "theorem", "module": "Mathlib.Tactic.LinearCombination'", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.LinearCombination'.c_add_pf", "kind": "theorem", "module": "Mathlib.Tactic.LinearCombination'", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.LinearCombination'.add_pf", "kind": "theorem", "module": "Mathlib.Tactic.LinearCombination'", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.LinearCombination'.pf_sub_c", "kind": "theorem", "module": "Mathlib.Tactic.LinearCombination'", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.LinearCombination'.c_sub_pf", "kind": "theorem", "module": "Mathlib.Tactic.LinearCombination'", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.LinearCombination'.sub_pf", "kind": "theorem", "module": "Mathlib.Tactic.LinearCombination'", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.LinearCombination'.neg_pf", "kind": "theorem", "module": "Mathlib.Tactic.LinearCombination'", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.LinearCombination'.pf_mul_c", "kind": "theorem", "module": "Mathlib.Tactic.LinearCombination'", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.LinearCombination'.c_mul_pf", "kind": "theorem", "module": "Mathlib.Tactic.LinearCombination'", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.LinearCombination'.mul_pf", "kind": "theorem", "module": "Mathlib.Tactic.LinearCombination'", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.LinearCombination'.inv_pf", "kind": "theorem", "module": "Mathlib.Tactic.LinearCombination'", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.LinearCombination'.pf_div_c", "kind": "theorem", "module": "Mathlib.Tactic.LinearCombination'", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.LinearCombination'.c_div_pf", "kind": "theorem", "module": "Mathlib.Tactic.LinearCombination'", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.LinearCombination'.div_pf", "kind": "theorem", "module": "Mathlib.Tactic.LinearCombination'", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.LinearCombination'.Expanded", "kind": "inductive", "module": "Mathlib.Tactic.LinearCombination'", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.LinearCombination'.expandLinearCombo", "kind": "definition", "module": "Mathlib.Tactic.LinearCombination'", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.LinearCombination'.eq_trans₃", "kind": "theorem", "module": "Mathlib.Tactic.LinearCombination'", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.LinearCombination'.eq_of_add", "kind": "theorem", "module": "Mathlib.Tactic.LinearCombination'", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Mathlib.Tactic.LinearCombination'.eq_of_add_pow", "kind": "theorem", "module": "Mathlib.Tactic.LinearCombination'", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Mathlib.Tactic.LinearCombination'.normStx", "kind": "definition", "module": "Mathlib.Tactic.LinearCombination'", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.LinearCombination'.expStx", "kind": "definition", "module": "Mathlib.Tactic.LinearCombination'", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.LinearCombination'.linearCombination'", "kind": "definition", "module": "Mathlib.Tactic.LinearCombination'", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.LinearCombination'._aux_Mathlib_Tactic_LinearCombination'___elabRules_Mathlib_Tactic_LinearCombination'_linearCombination'_1", "kind": "definition", "module": "Mathlib.Tactic.LinearCombination'", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.LinearCombination'.tacticLinear_combination2____", "kind": "definition", "module": "Mathlib.Tactic.LinearCombination'", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.LinearCombination'._aux_Mathlib_Tactic_LinearCombination'___elabRules_Mathlib_Tactic_LinearCombination'_tacticLinear_combination2_____1", "kind": "definition", "module": "Mathlib.Tactic.LinearCombination'", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.LinearCombination.Expanded", "kind": "inductive", "module": "Mathlib.Tactic.LinearCombination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.LinearCombination.rescale", "kind": "definition", "module": "Mathlib.Tactic.LinearCombination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.LinearCombination.expandLinearCombo", "kind": "definition", "module": "Mathlib.Tactic.LinearCombination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.LinearCombination.elabLinearCombination", "kind": "definition", "module": "Mathlib.Tactic.LinearCombination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.LinearCombination.normStx", "kind": "definition", "module": "Mathlib.Tactic.LinearCombination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.LinearCombination.expStx", "kind": "definition", "module": "Mathlib.Tactic.LinearCombination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.LinearCombination.linearCombination", "kind": "definition", "module": "Mathlib.Tactic.LinearCombination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.LinearCombination._aux_Mathlib_Tactic_LinearCombination___elabRules_Mathlib_Tactic_LinearCombination_linearCombination_1", "kind": "definition", "module": "Mathlib.Tactic.LinearCombination", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.LinearCombination.add_eq_eq", "kind": "theorem", "module": "Mathlib.Tactic.LinearCombination.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.LinearCombination.add_le_eq", "kind": "theorem", "module": "Mathlib.Tactic.LinearCombination.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.LinearCombination.add_eq_le", "kind": "theorem", "module": "Mathlib.Tactic.LinearCombination.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.LinearCombination.add_lt_eq", "kind": "theorem", "module": "Mathlib.Tactic.LinearCombination.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.LinearCombination.add_eq_lt", "kind": "theorem", "module": "Mathlib.Tactic.LinearCombination.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.LinearCombination.mul_eq_const", "kind": "theorem", "module": "Mathlib.Tactic.LinearCombination.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.LinearCombination.mul_le_const", "kind": "theorem", "module": "Mathlib.Tactic.LinearCombination.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.LinearCombination.mul_lt_const", "kind": "theorem", "module": "Mathlib.Tactic.LinearCombination.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.LinearCombination.mul_lt_const_weak", "kind": "theorem", "module": "Mathlib.Tactic.LinearCombination.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.LinearCombination.mul_const_eq", "kind": "theorem", "module": "Mathlib.Tactic.LinearCombination.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.LinearCombination.mul_const_le", "kind": "theorem", "module": "Mathlib.Tactic.LinearCombination.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.LinearCombination.mul_const_lt", "kind": "theorem", "module": "Mathlib.Tactic.LinearCombination.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.LinearCombination.mul_const_lt_weak", "kind": "theorem", "module": "Mathlib.Tactic.LinearCombination.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.LinearCombination.smul_eq_const", "kind": "theorem", "module": "Mathlib.Tactic.LinearCombination.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.LinearCombination.smul_le_const", "kind": "theorem", "module": "Mathlib.Tactic.LinearCombination.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.LinearCombination.smul_lt_const", "kind": "theorem", "module": "Mathlib.Tactic.LinearCombination.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.LinearCombination.smul_lt_const_weak", "kind": "theorem", "module": "Mathlib.Tactic.LinearCombination.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.LinearCombination.smul_const_eq", "kind": "theorem", "module": "Mathlib.Tactic.LinearCombination.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.LinearCombination.smul_const_le", "kind": "theorem", "module": "Mathlib.Tactic.LinearCombination.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.LinearCombination.smul_const_lt", "kind": "theorem", "module": "Mathlib.Tactic.LinearCombination.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.LinearCombination.smul_const_lt_weak", "kind": "theorem", "module": "Mathlib.Tactic.LinearCombination.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.LinearCombination.div_eq_const", "kind": "theorem", "module": "Mathlib.Tactic.LinearCombination.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.LinearCombination.div_le_const", "kind": "theorem", "module": "Mathlib.Tactic.LinearCombination.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.LinearCombination.div_lt_const", "kind": "theorem", "module": "Mathlib.Tactic.LinearCombination.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.LinearCombination.div_lt_const_weak", "kind": "theorem", "module": "Mathlib.Tactic.LinearCombination.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.LinearCombination.eq_of_eq", "kind": "theorem", "module": "Mathlib.Tactic.LinearCombination.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Mathlib.Tactic.LinearCombination.le_of_le", "kind": "theorem", "module": "Mathlib.Tactic.LinearCombination.Lemmas", "is_tactic_proof": true, "tactics": ["grw"], "tactic_count": 1}
{"name": "Mathlib.Tactic.LinearCombination.le_of_eq", "kind": "theorem", "module": "Mathlib.Tactic.LinearCombination.Lemmas", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Mathlib.Tactic.LinearCombination.le_of_lt", "kind": "theorem", "module": "Mathlib.Tactic.LinearCombination.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.LinearCombination.lt_of_le", "kind": "theorem", "module": "Mathlib.Tactic.LinearCombination.Lemmas", "is_tactic_proof": true, "tactics": ["grw"], "tactic_count": 1}
{"name": "Mathlib.Tactic.LinearCombination.lt_of_eq", "kind": "theorem", "module": "Mathlib.Tactic.LinearCombination.Lemmas", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Mathlib.Tactic.LinearCombination.lt_of_lt", "kind": "theorem", "module": "Mathlib.Tactic.LinearCombination.Lemmas", "is_tactic_proof": true, "tactics": ["grw", "gcongr"], "tactic_count": 2}
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{"name": "Mathlib.Tactic.Module.NF", "kind": "definition", "module": "Mathlib.Tactic.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Module.NF.cons", "kind": "definition", "module": "Mathlib.Tactic.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Module.NF.term_::ᵣ_", "kind": "definition", "module": "Mathlib.Tactic.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Module.NF._aux_Mathlib_Tactic_Module___macroRules_Mathlib_Tactic_Module_NF_term_::ᵣ__1", "kind": "definition", "module": "Mathlib.Tactic.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Module.NF._aux_Mathlib_Tactic_Module___unexpand_Mathlib_Tactic_Module_NF_cons_1", "kind": "definition", "module": "Mathlib.Tactic.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Module.NF.eval", "kind": "definition", "module": "Mathlib.Tactic.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Module.NF.eval_cons", "kind": "theorem", "module": "Mathlib.Tactic.Module", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Module.NF.atom_eq_eval", "kind": "theorem", "module": "Mathlib.Tactic.Module", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Module.NF.zero_eq_eval", "kind": "theorem", "module": "Mathlib.Tactic.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Module.NF.add_eq_eval₁", "kind": "theorem", "module": "Mathlib.Tactic.Module", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Module.NF.add_eq_eval₂", "kind": "theorem", "module": "Mathlib.Tactic.Module", "is_tactic_proof": true, "tactics": ["simp", "congr", "simp", "congr", "rw"], "tactic_count": 5}
{"name": "Mathlib.Tactic.Module.NF.add_eq_eval₃", "kind": "theorem", "module": "Mathlib.Tactic.Module", "is_tactic_proof": true, "tactics": ["simp", "nth_rw", "simp", "congr", "rw"], "tactic_count": 5}
{"name": "Mathlib.Tactic.Module.NF.add_eq_eval", "kind": "theorem", "module": "Mathlib.Tactic.Module", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Module.NF.sub_eq_eval₁", "kind": "theorem", "module": "Mathlib.Tactic.Module", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Module.NF.sub_eq_eval₂", "kind": "theorem", "module": "Mathlib.Tactic.Module", "is_tactic_proof": true, "tactics": ["simp", "congr", "simp", "congr", "rw"], "tactic_count": 5}
{"name": "Mathlib.Tactic.Module.NF.sub_eq_eval₃", "kind": "theorem", "module": "Mathlib.Tactic.Module", "is_tactic_proof": true, "tactics": ["simp", "congr", "rw"], "tactic_count": 3}
{"name": "Mathlib.Tactic.Module.NF.sub_eq_eval", "kind": "theorem", "module": "Mathlib.Tactic.Module", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Module.NF.instNeg", "kind": "instance", "module": "Mathlib.Tactic.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Module.NF.eval_neg", "kind": "theorem", "module": "Mathlib.Tactic.Module", "is_tactic_proof": true, "tactics": ["simp", "congr", "ext", "simp"], "tactic_count": 4}
{"name": "Mathlib.Tactic.Module.NF.zero_sub_eq_eval", "kind": "theorem", "module": "Mathlib.Tactic.Module", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Module.NF.neg_eq_eval", "kind": "theorem", "module": "Mathlib.Tactic.Module", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Module.NF.instSMulOfMul", "kind": "instance", "module": "Mathlib.Tactic.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Module.NF.smul_apply", "kind": "theorem", "module": "Mathlib.Tactic.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Module.NF.eval_smul", "kind": "theorem", "module": "Mathlib.Tactic.Module", "is_tactic_proof": true, "tactics": ["unfold", "simp", "congr", "ext", "simp"], "tactic_count": 5}
{"name": "Mathlib.Tactic.Module.NF.smul_eq_eval", "kind": "theorem", "module": "Mathlib.Tactic.Module", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Mathlib.Tactic.Module.NF.eq_cons_cons", "kind": "theorem", "module": "Mathlib.Tactic.Module", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Module.NF.eq_cons_const", "kind": "theorem", "module": "Mathlib.Tactic.Module", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Module.NF.eq_const_cons", "kind": "theorem", "module": "Mathlib.Tactic.Module", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Module.NF.eq_of_eval_eq_eval", "kind": "theorem", "module": "Mathlib.Tactic.Module", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Module.NF.algebraMap", "kind": "definition", "module": "Mathlib.Tactic.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Module.NF.eval_algebraMap", "kind": "theorem", "module": "Mathlib.Tactic.Module", "is_tactic_proof": true, "tactics": ["simp", "congr", "ext", "simp"], "tactic_count": 4}
{"name": "Mathlib.Tactic.Module.qNF", "kind": "abbrev", "module": "Mathlib.Tactic.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Module.qNF.toNF", "kind": "definition", "module": "Mathlib.Tactic.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Module.qNF.onScalar", "kind": "definition", "module": "Mathlib.Tactic.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Module.qNF.add", "kind": "definition", "module": "Mathlib.Tactic.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Module.qNF.mkAddProof", "kind": "definition", "module": "Mathlib.Tactic.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Module.qNF.sub", "kind": "definition", "module": "Mathlib.Tactic.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Module.qNF.mkSubProof", "kind": "definition", "module": "Mathlib.Tactic.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Module.qNF.matchRings", "kind": "definition", "module": "Mathlib.Tactic.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Module.parse", "kind": "definition", "module": "Mathlib.Tactic.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Module.reduceCoefficientwise", "kind": "definition", "module": "Mathlib.Tactic.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Module.matchScalarsAux", "kind": "definition", "module": "Mathlib.Tactic.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Module.algebraMapThms", "kind": "definition", "module": "Mathlib.Tactic.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Module.postprocess", "kind": "definition", "module": "Mathlib.Tactic.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Module.matchScalars", "kind": "definition", "module": "Mathlib.Tactic.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Module.tacticMatch_scalars", "kind": "definition", "module": "Mathlib.Tactic.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Module._aux_Mathlib_Tactic_Module___elabRules_Mathlib_Tactic_Module_tacticMatch_scalars_1", "kind": "definition", "module": "Mathlib.Tactic.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Module.tacticModule", "kind": "definition", "module": "Mathlib.Tactic.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Module._aux_Mathlib_Tactic_Module___elabRules_Mathlib_Tactic_Module_tacticModule_1", "kind": "definition", "module": "Mathlib.Tactic.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Monotonicity.mono.side", "kind": "definition", "module": "Mathlib.Tactic.Monotonicity.Attr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Monotonicity.Attr.mono", "kind": "definition", "module": "Mathlib.Tactic.Monotonicity.Attr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Monotonicity.Attr.initFn._@.Mathlib.Tactic.Monotonicity.Attr.3666813829._hygCtx._hyg.8", "kind": "definition", "module": "Mathlib.Tactic.Monotonicity.Attr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Monotonicity.Attr.ext", "kind": "opaque", "module": "Mathlib.Tactic.Monotonicity.Attr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Monotonicity.mono", "kind": "definition", "module": "Mathlib.Tactic.Monotonicity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Monotonicity._aux_Mathlib_Tactic_Monotonicity_Basic___elabRules_Mathlib_Tactic_Monotonicity_mono_1", "kind": "definition", "module": "Mathlib.Tactic.Monotonicity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lean.Expr.getExprInputs", "kind": "definition", "module": "Mathlib.Tactic.MoveAdd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lean.Expr.size", "kind": "definition", "module": "Mathlib.Tactic.MoveAdd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.MoveAdd.uniquify", "kind": "definition", "module": "Mathlib.Tactic.MoveAdd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.MoveAdd.weight", "kind": "definition", "module": "Mathlib.Tactic.MoveAdd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.MoveAdd.reorderUsing", "kind": "definition", "module": "Mathlib.Tactic.MoveAdd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.MoveAdd.prepareOp", "kind": "definition", "module": "Mathlib.Tactic.MoveAdd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.MoveAdd.sumList", "kind": "definition", "module": "Mathlib.Tactic.MoveAdd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.MoveAdd.getAddends", "kind": "definition", "module": "Mathlib.Tactic.MoveAdd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.MoveAdd.getOps", "kind": "definition", "module": "Mathlib.Tactic.MoveAdd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.MoveAdd.rankSums", "kind": "definition", "module": "Mathlib.Tactic.MoveAdd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.MoveAdd.permuteExpr", "kind": "definition", "module": "Mathlib.Tactic.MoveAdd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.MoveAdd.pairUp", "kind": "definition", "module": "Mathlib.Tactic.MoveAdd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.MoveAdd.moveOperSimpCtx", "kind": "definition", "module": "Mathlib.Tactic.MoveAdd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.MoveAdd.reorderAndSimp", "kind": "definition", "module": "Mathlib.Tactic.MoveAdd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.MoveAdd.unifyMovements", "kind": "definition", "module": "Mathlib.Tactic.MoveAdd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.MoveAdd.parseArrows", "kind": "definition", "module": "Mathlib.Tactic.MoveAdd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.MoveAdd.initFn._@.Mathlib.Tactic.MoveAdd.331066901._hygCtx._hyg.2", "kind": "definition", "module": "Mathlib.Tactic.MoveAdd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.MoveAdd.moveOperTac", "kind": "definition", "module": "Mathlib.Tactic.MoveAdd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.MoveAdd._aux_Mathlib_Tactic_MoveAdd___elabRules_Mathlib_MoveAdd_moveOperTac_1", "kind": "definition", "module": "Mathlib.Tactic.MoveAdd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.MoveAdd.tacticMove_add_", "kind": "definition", "module": "Mathlib.Tactic.MoveAdd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.MoveAdd._aux_Mathlib_Tactic_MoveAdd___elabRules_Mathlib_MoveAdd_tacticMove_add__1", "kind": "definition", "module": "Mathlib.Tactic.MoveAdd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.MoveAdd.tacticMove_mul_", "kind": "definition", "module": "Mathlib.Tactic.MoveAdd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.MoveAdd._aux_Mathlib_Tactic_MoveAdd___elabRules_Mathlib_MoveAdd_tacticMove_mul__1", "kind": "definition", "module": "Mathlib.Tactic.MoveAdd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.NoncommRing.nat_lit_mul_eq_nsmul", "kind": "theorem", "module": "Mathlib.Tactic.NoncommRing", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.NoncommRing.mul_nat_lit_eq_nsmul", "kind": "theorem", "module": "Mathlib.Tactic.NoncommRing", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.NoncommRing.noncomm_ring", "kind": "definition", "module": "Mathlib.Tactic.NoncommRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.NoncommRing._aux_Mathlib_Tactic_NoncommRing___macroRules_Mathlib_Tactic_NoncommRing_noncomm_ring_1", "kind": "definition", "module": "Mathlib.Tactic.NoncommRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_auxTryTactic17094331852794326707", "kind": "definition", "module": "Mathlib.Tactic.NoncommRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Nontriviality.subsingleton_or_nontrivial_elim", "kind": "theorem", "module": "Mathlib.Tactic.Nontriviality.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Nontriviality.nontrivialityByElim", "kind": "definition", "module": "Mathlib.Tactic.Nontriviality.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Nontriviality.nontrivialityByAssumption", "kind": "definition", "module": "Mathlib.Tactic.Nontriviality.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Nontriviality.nontriviality", "kind": "definition", "module": "Mathlib.Tactic.Nontriviality.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Nontriviality.elabNontriviality", "kind": "definition", "module": "Mathlib.Tactic.Nontriviality.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isNat_abs_nonneg", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Abs", "is_tactic_proof": true, "tactics": ["rw", "constructor", "rfl"], "tactic_count": 3}
{"name": "Mathlib.Meta.NormNum.isNat_abs_neg", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Abs", "is_tactic_proof": true, "tactics": ["rw", "constructor", "simp"], "tactic_count": 3}
{"name": "Mathlib.Meta.NormNum.isNNRat_abs_nonneg", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Abs", "is_tactic_proof": true, "tactics": ["obtain", "refine", "apply", "exact", "simp"], "tactic_count": 5}
{"name": "Mathlib.Meta.NormNum.isNNRat_abs_neg", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Abs", "is_tactic_proof": true, "tactics": ["obtain", "simp", "refine", "apply", "exact", "simp"], "tactic_count": 6}
{"name": "Mathlib.Meta.NormNum.evalAbs", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Abs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.IsInt.raw_refl", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isNat_zero", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.evalZero", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isNat_one", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.evalOne", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isNat_ofNat", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.evalOfNat", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isNat_intOfNat", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.evalIntOfNat", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isInt_negOfNat", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.evalNegOfNat", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isNat_natAbs_pos", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isNat_natAbs_neg", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.evalIntNatAbs", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isNat_natCast", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "Mathlib.Meta.NormNum.evalNatCast", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isNat_intCast", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "Mathlib.Meta.NormNum.isintCast", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": true, "tactics": ["rintro"], "tactic_count": 1}
{"name": "Mathlib.Meta.NormNum.evalIntCast", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LibraryNote.norm_num_lemma_function_equality", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isNat_add", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isInt_add", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.invertibleOfMul", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.invertibleOfMul'", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isNNRat_add", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": true, "tactics": ["rintro", "have", "have", "use", "have", "have", "simp", "have", "simp", "rw", "simp"], "tactic_count": 11}
{"name": "Mathlib.Meta.NormNum.isRat_add", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": true, "tactics": ["rintro", "have", "have", "use", "have", "have", "simp", "have", "simp", "rw", "simp"], "tactic_count": 11}
{"name": "Mathlib.Meta.monadLiftOptionMetaM", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.evalAdd", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isInt_neg", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isRat_neg", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.evalNeg", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isInt_sub", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isRat_sub", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw"], "tactic_count": 3}
{"name": "Mathlib.Meta.NormNum.evalSub", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isNat_mul", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isInt_mul", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isNNRat_mul", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": true, "tactics": ["rintro", "have", "have", "refine", "have", "have", "simp", "simp", "have", "simp", "simp", "simp"], "tactic_count": 12}
{"name": "Mathlib.Meta.NormNum.isRat_mul", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": true, "tactics": ["rintro", "have", "have", "refine", "have", "have", "simp", "simp", "have", "simp", "simp", "simp"], "tactic_count": 12}
{"name": "Mathlib.Meta.NormNum.evalMul", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isNNRat_div", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isRat_div", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.inferDivisionSemiring", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.inferDivisionRing", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.evalDiv", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.evalTrue", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.evalFalse", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.evalNot", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isNat_eq_true", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.ble_eq_false", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Mathlib.Meta.NormNum.isInt_eq_true", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isNNRat_eq_true", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isRat_eq_true", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.eq_of_true", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.ne_of_false_of_true", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.ne_of_true_of_false", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.eq_of_false", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isNat_natSucc", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.evalNatSucc", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isNat_natSub", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.evalNatSub", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isNat_natMod", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.evalNatMod", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isNat_natDiv", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.evalNatDiv", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isNat_dvd_true", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isNat_dvd_false", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.evalNatDvd", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Nat.UnifyZeroOrSuccResult", "kind": "inductive", "module": "Mathlib.Tactic.NormNum.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Nat.unifyZeroOrSucc", "kind": "definition", "module": "Mathlib.Tactic.NormNum.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.List.ProveNilOrConsResult", "kind": "inductive", "module": "Mathlib.Tactic.NormNum.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.List.ProveNilOrConsResult.uncheckedCast", "kind": "definition", "module": "Mathlib.Tactic.NormNum.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.List.ProveNilOrConsResult.eq_trans", "kind": "definition", "module": "Mathlib.Tactic.NormNum.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.List.range_zero'", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.BigOperators", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Mathlib.Meta.List.range_succ_eq_map'", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.BigOperators", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Mathlib.Meta.List.proveNilOrCons", "kind": "definition", "module": "Mathlib.Tactic.NormNum.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Multiset.ProveZeroOrConsResult", "kind": "inductive", "module": "Mathlib.Tactic.NormNum.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Multiset.ProveZeroOrConsResult.uncheckedCast", "kind": "definition", "module": "Mathlib.Tactic.NormNum.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Multiset.ProveZeroOrConsResult.eq_trans", "kind": "definition", "module": "Mathlib.Tactic.NormNum.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Multiset.insert_eq_cons", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Multiset.range_zero'", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.BigOperators", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Mathlib.Meta.Multiset.range_succ'", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.BigOperators", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Mathlib.Meta.Multiset.proveZeroOrCons", "kind": "definition", "module": "Mathlib.Tactic.NormNum.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Finset.ProveEmptyOrConsResult", "kind": "inductive", "module": "Mathlib.Tactic.NormNum.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Finset.ProveEmptyOrConsResult.uncheckedCast", "kind": "definition", "module": "Mathlib.Tactic.NormNum.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Finset.ProveEmptyOrConsResult.eq_trans", "kind": "definition", "module": "Mathlib.Tactic.NormNum.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Finset.insert_eq_cons", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.BigOperators", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Meta.Finset.range_zero'", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.BigOperators", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Mathlib.Meta.Finset.range_succ'", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.BigOperators", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Mathlib.Meta.Finset.univ_eq_elems", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.BigOperators", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Mathlib.Meta.Finset.proveEmptyOrCons", "kind": "definition", "module": "Mathlib.Tactic.NormNum.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.Result.eq_trans", "kind": "definition", "module": "Mathlib.Tactic.NormNum.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.Finset.sum_empty", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.Finset.prod_empty", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.evalFinsetBigop", "kind": "definition", "module": "Mathlib.Tactic.NormNum.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.evalFinsetProd", "kind": "definition", "module": "Mathlib.Tactic.NormNum.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.evalFinsetSum", "kind": "definition", "module": "Mathlib.Tactic.NormNum.BigOperators", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "norm_num", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.initFn._@.Mathlib.Tactic.NormNum.Core.3041507515._hygCtx._hyg.2", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.mkNormNumExt", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.Entry", "kind": "abbrev", "module": "Mathlib.Tactic.NormNum.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.instInhabitedNormNums.default", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.instInhabitedNormNums", "kind": "instance", "module": "Mathlib.Tactic.NormNum.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.initFn._@.Mathlib.Tactic.NormNum.Core.525676807._hygCtx._hyg.2", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.normNumExt", "kind": "opaque", "module": "Mathlib.Tactic.NormNum.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.deriveBool", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.deriveBoolOfIff", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.NormNums.eraseCore", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.NormNums.erase", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.initFn._@.Mathlib.Tactic.NormNum.Core.1919626320._hygCtx._hyg.2", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.normNum", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic._aux_Mathlib_Tactic_NormNum_Core___elabRules_Mathlib_Tactic_normNum_1", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.normNum1", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic._aux_Mathlib_Tactic_NormNum_Core___elabRules_Mathlib_Tactic_normNum1_1", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.normNum1Conv", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.elabNormNum1Conv", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.normNumConv", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.elabNormNumConv", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.normNumCmd", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic._aux_Mathlib_Tactic_NormNum_Core___macroRules_Mathlib_Tactic_normNumCmd_1", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_auxTryTactic14848873054137305619", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isInt_ediv_zero", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.DivMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isInt_ediv", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.DivMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isInt_ediv_neg", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.DivMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isNat_neg_of_isNegNat", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.DivMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.evalIntDiv", "kind": "definition", "module": "Mathlib.Tactic.NormNum.DivMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isInt_emod_zero", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.DivMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isInt_emod", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.DivMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isInt_emod_neg", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.DivMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.evalIntMod", "kind": "definition", "module": "Mathlib.Tactic.NormNum.DivMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isInt_dvd_true", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.DivMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isInt_dvd_false", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.DivMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.evalIntDvd", "kind": "definition", "module": "Mathlib.Tactic.NormNum.DivMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isNat_eq_false", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Eq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isInt_eq_false", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Eq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.NNRat.invOf_denom_swap", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Eq", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Mathlib.Meta.NormNum.isNNRat_eq_false", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Eq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.Rat.invOf_denom_swap", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Eq", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Mathlib.Meta.NormNum.isRat_eq_false", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Eq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.evalEq", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Eq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.NormNum.int_gcd_helper'", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.GCD", "is_tactic_proof": true, "tactics": ["refine", "rw", "apply", "exact", "exact"], "tactic_count": 5}
{"name": "Tactic.NormNum.nat_gcd_helper_dvd_left", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.GCD", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.NormNum.nat_gcd_helper_dvd_right", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.GCD", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.NormNum.nat_gcd_helper_2", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.GCD", "is_tactic_proof": true, "tactics": ["rw", "apply", "int_gcd_helper", "rw", "exact"], "tactic_count": 5}
{"name": "Tactic.NormNum.nat_gcd_helper_1", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.GCD", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.NormNum.nat_gcd_helper_1'", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.GCD", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.NormNum.nat_gcd_helper_2'", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.GCD", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.NormNum.nat_lcm_helper", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.GCD", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.NormNum.int_gcd_helper", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.GCD", "is_tactic_proof": true, "tactics": ["subst_vars"], "tactic_count": 1}
{"name": "Tactic.NormNum.int_lcm_helper", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.GCD", "is_tactic_proof": true, "tactics": ["subst_vars"], "tactic_count": 1}
{"name": "Tactic.NormNum.isNat_gcd", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.GCD", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.NormNum.isNat_lcm", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.GCD", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.NormNum.isInt_gcd", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.GCD", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.NormNum.isInt_lcm", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.GCD", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.NormNum.proveNatGCD", "kind": "definition", "module": "Mathlib.Tactic.NormNum.GCD", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.NormNum.evalNatGCD", "kind": "definition", "module": "Mathlib.Tactic.NormNum.GCD", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.NormNum.proveNatLCM", "kind": "definition", "module": "Mathlib.Tactic.NormNum.GCD", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.NormNum.evalNatLCM", "kind": "definition", "module": "Mathlib.Tactic.NormNum.GCD", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.NormNum.proveIntGCD", "kind": "definition", "module": "Mathlib.Tactic.NormNum.GCD", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.NormNum.evalIntGCD", "kind": "definition", "module": "Mathlib.Tactic.NormNum.GCD", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.NormNum.proveIntLCM", "kind": "definition", "module": "Mathlib.Tactic.NormNum.GCD", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.NormNum.evalIntLCM", "kind": "definition", "module": "Mathlib.Tactic.NormNum.GCD", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.NormNum.isInt_ratNum", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.GCD", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.NormNum.isNat_ratDen", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.GCD", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.NormNum.evalRatNum", "kind": "definition", "module": "Mathlib.Tactic.NormNum.GCD", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.NormNum.evalRatDen", "kind": "definition", "module": "Mathlib.Tactic.NormNum.GCD", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.inferOrderedSemiring", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Ineq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.inferOrderedRing", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Ineq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.inferLinearOrderedSemifield", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Ineq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.inferLinearOrderedField", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Ineq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isNat_le_true", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Ineq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isNat_lt_false", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Ineq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isNNRat_le_true", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Ineq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isNNRat_lt_true", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Ineq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isNNRat_le_false", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Ineq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isNNRat_lt_false", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Ineq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isRat_le_true", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Ineq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isRat_lt_true", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Ineq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isRat_le_false", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Ineq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isRat_lt_false", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Ineq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isNat_lt_true", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Ineq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isNat_le_false", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Ineq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isInt_le_true", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Ineq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isInt_lt_true", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Ineq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isInt_le_false", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Ineq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isInt_lt_false", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Ineq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.evalLE", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Ineq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.evalLT", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Ineq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isRat_mkRat", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.evalMkRat", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isNat_ratCast", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isInt_ratCast", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isNNRat_ratCast", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isRat_ratCast", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.evalRatCast", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isNNRat_inv_pos", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Inv", "is_tactic_proof": true, "tactics": ["rintro", "have", "exact"], "tactic_count": 3}
{"name": "Mathlib.Meta.NormNum.isRat_inv_pos", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Inv", "is_tactic_proof": true, "tactics": ["rintro", "have", "exact"], "tactic_count": 3}
{"name": "Mathlib.Meta.NormNum.isNat_inv_one", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isNat_inv_zero", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isInt_inv_neg_one", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isRat_inv_neg", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Inv", "is_tactic_proof": true, "tactics": ["rintro", "simp", "have", "generalize", "use", "simp"], "tactic_count": 6}
{"name": "Mathlib.Meta.NormNum.Result.inv", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.evalInv", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Inv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Tactic.NormNum.Irrational.0.Tactic.NormNum.irrational_rpow_rat_of_not_power", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Irrational", "is_tactic_proof": true, "tactics": ["simp", "intro", "absurd", "rify", "rw", "lia", "assumption"], "tactic_count": 7}
{"name": "_private.Mathlib.Tactic.NormNum.Irrational.0.Tactic.NormNum.not_power_nat_pow", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Irrational", "is_tactic_proof": true, "tactics": ["by_cases", "specialize", "simp", "contrapose", "apply_fun", "simp", "suffices", "obtain", "have", "rw", "intro", "apply_fun", "rw", "rw", "exact", "have", "apply_fun", "simp", "cases", "lia", "assumption", "rw", "apply", "use", "exact", "simp", "existsAndEq,", "tauto", "use", "ext", "apply_fun", "simp", "rw", "apply", "rwa"], "tactic_count": 35}
{"name": "_private.Mathlib.Tactic.NormNum.Irrational.0.Tactic.NormNum.not_power_nat_of_bounds", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Irrational", "is_tactic_proof": true, "tactics": ["intro", "rw", "have", "have", "lia"], "tactic_count": 5}
{"name": "_private.Mathlib.Tactic.NormNum.Irrational.0.Tactic.NormNum.not_power_nat_pow_of_bounds", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Irrational", "is_tactic_proof": true, "tactics": ["apply", "intro", "apply"], "tactic_count": 3}
{"name": "_private.Mathlib.Tactic.NormNum.Irrational.0.Tactic.NormNum.eq_of_mul_eq_mul_of_coprime_aux", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Irrational", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Tactic.NormNum.Irrational.0.Tactic.NormNum.eq_of_mul_eq_mul_of_coprime", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Irrational", "is_tactic_proof": true, "tactics": ["apply", "exact", "exact"], "tactic_count": 3}
{"name": "_private.Mathlib.Tactic.NormNum.Irrational.0.Tactic.NormNum.not_power_rat_of_num_aux", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Irrational", "is_tactic_proof": true, "tactics": ["by_cases", "subst", "contrapose", "simp", "subst", "use", "simp", "by_contra", "rw", "set", "set", "obtain", "rw", "specialize", "simp", "rw", "rotate_left", "simpa", "simp", "replace", "qify", "assumption", "apply", "conv", "apply", "apply", "apply", "apply", "simpa"], "tactic_count": 29}
{"name": "_private.Mathlib.Tactic.NormNum.Irrational.0.Tactic.NormNum.not_power_rat_of_num", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Irrational", "is_tactic_proof": true, "tactics": ["by_cases", "apply", "rcases", "have", "rwa", "contrapose", "rw", "positivity"], "tactic_count": 8}
{"name": "_private.Mathlib.Tactic.NormNum.Irrational.0.Tactic.NormNum.irrational_rpow_rat_rat_of_num", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Irrational", "is_tactic_proof": false, "tactics": ["have", "by_contra", "simp", "simp", "lia", "rcases", "rcases", "rw", "have", "simp", "rfl", "have", "simp", "rfl", "rw", "refine", "simp", "apply", "apply", "apply", "positivity"], "tactic_count": 21}
{"name": "_private.Mathlib.Tactic.NormNum.Irrational.0.Tactic.NormNum.irrational_rpow_rat_rat_of_den", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Irrational", "is_tactic_proof": true, "tactics": ["rcases", "apply", "rw", "apply", "irrational_rpow_rat_rat_of_num", "hy_coprime", "refine", "simp_all"], "tactic_count": 8}
{"name": "_private.Mathlib.Tactic.NormNum.Irrational.0.Tactic.NormNum.irrational_rpow_nat_rat", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Irrational", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Tactic.NormNum.Irrational.0.Tactic.NormNum.irrational_sqrt_rat_of_num", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Irrational", "is_tactic_proof": true, "tactics": ["rw", "apply", "exact"], "tactic_count": 3}
{"name": "_private.Mathlib.Tactic.NormNum.Irrational.0.Tactic.NormNum.irrational_sqrt_rat_of_den", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Irrational", "is_tactic_proof": true, "tactics": ["rw", "apply", "exact"], "tactic_count": 3}
{"name": "_private.Mathlib.Tactic.NormNum.Irrational.0.Tactic.NormNum.irrational_sqrt_nat", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Irrational", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.NormNum.findNotPowerCertificateCore", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Irrational", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.NormNum.findNotPowerCertificate", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Irrational", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.NormNum.evalIrrationalRpow", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Irrational", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.NormNum.evalIrrationalSqrt", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Irrational", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.NormNum.int_not_isCoprime_helper", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.IsCoprime", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Tactic.NormNum.isInt_isCoprime", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.IsCoprime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.NormNum.isInt_not_isCoprime", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.IsCoprime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.NormNum.proveIntIsCoprime", "kind": "definition", "module": "Mathlib.Tactic.NormNum.IsCoprime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.NormNum.evalIntIsCoprime", "kind": "definition", "module": "Mathlib.Tactic.NormNum.IsCoprime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isSquare_nat_of_isNat", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.IsSquare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.not_isSquare_nat_of_isNat", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.IsSquare", "is_tactic_proof": true, "tactics": ["rcases", "subst", "rintro", "simp", "rw", "grind"], "tactic_count": 6}
{"name": "Mathlib.Meta.NormNum.iff_isSquare_int_of_isNat", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.IsSquare", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Meta.NormNum.iff_isSquare_of_isInt_int", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.IsSquare", "is_tactic_proof": true, "tactics": ["refine", "rw", "rcases", "simp_all", "refine", "exact"], "tactic_count": 6}
{"name": "Mathlib.Meta.NormNum.iff_isSquare_of_isNat_rat", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.IsSquare", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Meta.NormNum.iff_isSquare_of_isInt_rat", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.IsSquare", "is_tactic_proof": true, "tactics": ["refine", "rw", "rcases", "simp_all", "refine", "exact"], "tactic_count": 6}
{"name": "Mathlib.Meta.NormNum.isSquare_of_isNNRat_rat", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.IsSquare", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "use", "simp"], "tactic_count": 4}
{"name": "Mathlib.Meta.NormNum.not_isSquare_of_isNNRat_rat_of_num", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.IsSquare", "is_tactic_proof": true, "tactics": ["rw", "simp", "contrapose", "have", "simp_all", "simpa"], "tactic_count": 6}
{"name": "Mathlib.Meta.NormNum.not_isSquare_of_isNNRat_rat_of_den", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.IsSquare", "is_tactic_proof": false, "tactics": ["rw", "simp", "contrapose", "simp_all", "simpa"], "tactic_count": 5}
{"name": "Mathlib.Meta.NormNum.not_isSquare_of_isRat_neg", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.IsSquare", "is_tactic_proof": true, "tactics": ["rw", "rintro", "refine", "calc"], "tactic_count": 4}
{"name": "Mathlib.Meta.NormNum.evalIsSquareNat", "kind": "definition", "module": "Mathlib.Tactic.NormNum.IsSquare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.evalIsSquareInt", "kind": "definition", "module": "Mathlib.Tactic.NormNum.IsSquare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.evalIsSquareRat", "kind": "definition", "module": "Mathlib.Tactic.NormNum.IsSquare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.jacobiSymNat", "kind": "definition", "module": "Mathlib.Tactic.NormNum.LegendreSymbol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.jacobiSymNat.zero_right", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.LegendreSymbol", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Mathlib.Meta.NormNum.jacobiSymNat.one_right", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.LegendreSymbol", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Mathlib.Meta.NormNum.jacobiSymNat.zero_left", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.LegendreSymbol", "is_tactic_proof": true, "tactics": ["rw", "calc"], "tactic_count": 2}
{"name": "Mathlib.Meta.NormNum.jacobiSymNat.one_left", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.LegendreSymbol", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Mathlib.Meta.NormNum.LegendreSym.to_jacobiSym", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.LegendreSymbol", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Mathlib.Meta.NormNum.JacobiSym.mod_left", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.LegendreSymbol", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Mathlib.Meta.NormNum.jacobiSymNat.mod_left", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.LegendreSymbol", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Mathlib.Meta.NormNum.jacobiSymNat.even_even", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.LegendreSymbol", "is_tactic_proof": false, "tactics": ["refine", "jacobiSym.eq_zero_iff.mpr", "have", "change", "rw", "exact"], "tactic_count": 6}
{"name": "Mathlib.Meta.NormNum.jacobiSymNat.odd_even", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.LegendreSymbol", "is_tactic_proof": false, "tactics": ["have", "simp", "decide", "rcases", "rw", "haveI", "rwa", "jacobiSym.legendreSym.to_jacobiSym,"], "tactic_count": 8}
{"name": "Mathlib.Meta.NormNum.jacobiSymNat.double_even", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.LegendreSymbol", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Mathlib.Meta.NormNum.jacobiSymNat.even_odd₁", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.LegendreSymbol", "is_tactic_proof": true, "tactics": ["simp", "rw", "rw"], "tactic_count": 3}
{"name": "Mathlib.Meta.NormNum.jacobiSymNat.even_odd₇", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.LegendreSymbol", "is_tactic_proof": true, "tactics": ["simp", "rw", "rw"], "tactic_count": 3}
{"name": "Mathlib.Meta.NormNum.jacobiSymNat.even_odd₃", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.LegendreSymbol", "is_tactic_proof": true, "tactics": ["simp", "rw", "rw"], "tactic_count": 3}
{"name": "Mathlib.Meta.NormNum.jacobiSymNat.even_odd₅", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.LegendreSymbol", "is_tactic_proof": true, "tactics": ["simp", "rw", "rw"], "tactic_count": 3}
{"name": "Mathlib.Meta.NormNum.jacobiSymNat.qr₁", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.LegendreSymbol", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Mathlib.Meta.NormNum.jacobiSymNat.qr₁_mod", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.LegendreSymbol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.jacobiSymNat.qr₁'", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.LegendreSymbol", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Mathlib.Meta.NormNum.jacobiSymNat.qr₁'_mod", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.LegendreSymbol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.jacobiSymNat.qr₃", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.LegendreSymbol", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Mathlib.Meta.NormNum.jacobiSymNat.qr₃_mod", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.LegendreSymbol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isInt_jacobiSym", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.LegendreSymbol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isInt_jacobiSymNat", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.LegendreSymbol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Tactic.NormNum.LegendreSymbol.0.Mathlib.Meta.NormNum.mkRawIntLit'", "kind": "definition", "module": "Mathlib.Tactic.NormNum.LegendreSymbol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.proveJacobiSymOdd", "kind": "definition", "module": "Mathlib.Tactic.NormNum.LegendreSymbol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.proveJacobiSymNat", "kind": "definition", "module": "Mathlib.Tactic.NormNum.LegendreSymbol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.proveJacobiSym", "kind": "definition", "module": "Mathlib.Tactic.NormNum.LegendreSymbol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.NormNum.evalJacobiSym", "kind": "definition", "module": "Mathlib.Tactic.NormNum.LegendreSymbol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.NormNum.evalJacobiSymNat", "kind": "definition", "module": "Mathlib.Tactic.NormNum.LegendreSymbol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.NormNum.evalLegendreSym", "kind": "definition", "module": "Mathlib.Tactic.NormNum.LegendreSymbol", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.evalNatModEq", "kind": "definition", "module": "Mathlib.Tactic.NormNum.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.evalIntModEq", "kind": "definition", "module": "Mathlib.Tactic.NormNum.ModEq", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.asc_factorial_aux", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.NatFactorial", "is_tactic_proof": true, "tactics": ["rw", "symm", "apply"], "tactic_count": 3}
{"name": "Mathlib.Meta.NormNum.proveAscFactorial", "kind": "definition", "module": "Mathlib.Tactic.NormNum.NatFactorial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isNat_factorial", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.NatFactorial", "is_tactic_proof": true, "tactics": ["constructor", "simp"], "tactic_count": 2}
{"name": "Mathlib.Meta.NormNum.evalNatFactorial", "kind": "definition", "module": "Mathlib.Tactic.NormNum.NatFactorial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isNat_ascFactorial", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.NatFactorial", "is_tactic_proof": true, "tactics": ["constructor", "simp"], "tactic_count": 2}
{"name": "Mathlib.Meta.NormNum.evalNatAscFactorial", "kind": "definition", "module": "Mathlib.Tactic.NormNum.NatFactorial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isNat_descFactorial", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.NatFactorial", "is_tactic_proof": true, "tactics": ["constructor", "simpa"], "tactic_count": 2}
{"name": "Mathlib.Meta.NormNum.isNat_descFactorial_zero", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.NatFactorial", "is_tactic_proof": true, "tactics": ["constructor", "simp"], "tactic_count": 2}
{"name": "_private.Mathlib.Tactic.NormNum.NatFactorial.0.Mathlib.Meta.NormNum.evalNatDescFactorialNotZero", "kind": "definition", "module": "Mathlib.Tactic.NormNum.NatFactorial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Tactic.NormNum.NatFactorial.0.Mathlib.Meta.NormNum.evalNatDescFactorialZero", "kind": "definition", "module": "Mathlib.Tactic.NormNum.NatFactorial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.evalNatDescFactorial", "kind": "definition", "module": "Mathlib.Tactic.NormNum.NatFactorial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.IsFibAux", "kind": "definition", "module": "Mathlib.Tactic.NormNum.NatFib", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isFibAux_zero", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.NatFib", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isFibAux_one", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.NatFib", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isFibAux_two_mul", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.NatFib", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isFibAux_two_mul_add_one", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.NatFib", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.proveNatFibAux", "kind": "definition", "module": "Mathlib.Tactic.NormNum.NatFib", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isFibAux_two_mul_done", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.NatFib", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isFibAux_two_mul_add_one_done", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.NatFib", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.proveNatFib", "kind": "definition", "module": "Mathlib.Tactic.NormNum.NatFib", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isNat_fib", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.NatFib", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.evalNatFib", "kind": "definition", "module": "Mathlib.Tactic.NormNum.NatFib", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Tactic.NormNum.NatLog.0.Mathlib.Meta.NormNum.nat_log_zero", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.NatLog", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Tactic.NormNum.NatLog.0.Mathlib.Meta.NormNum.nat_log_one", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.NatLog", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Tactic.NormNum.NatLog.0.Mathlib.Meta.NormNum.nat_log_helper0", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.NatLog", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "_private.Mathlib.Tactic.NormNum.NatLog.0.Mathlib.Meta.NormNum.nat_log_helper", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.NatLog", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Tactic.NormNum.NatLog.0.Mathlib.Meta.NormNum.isNat_log", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.NatLog", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.proveNatLog", "kind": "definition", "module": "Mathlib.Tactic.NormNum.NatLog", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.evalNatLog", "kind": "definition", "module": "Mathlib.Tactic.NormNum.NatLog", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Tactic.NormNum.NatLog.0.Mathlib.Meta.NormNum.nat_clog_zero_left", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.NatLog", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Tactic.NormNum.NatLog.0.Mathlib.Meta.NormNum.nat_clog_zero_right", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.NatLog", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.nat_clog_helper", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.NatLog", "is_tactic_proof": true, "tactics": ["rw", "rw", "rw", "lia"], "tactic_count": 4}
{"name": "_private.Mathlib.Tactic.NormNum.NatLog.0.Mathlib.Meta.NormNum.isNat_clog", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.NatLog", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.proveNatClog", "kind": "definition", "module": "Mathlib.Tactic.NormNum.NatLog", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.evalNatClog", "kind": "definition", "module": "Mathlib.Tactic.NormNum.NatLog", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.NormNum.nat_sqrt_helper", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.NatSqrt", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "Tactic.NormNum.isNat_sqrt", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.NatSqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.NormNum.proveNatSqrt", "kind": "definition", "module": "Mathlib.Tactic.NormNum.NatSqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.NormNum.evalNatSqrt", "kind": "definition", "module": "Mathlib.Tactic.NormNum.NatSqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isNNRat_ofScientific_of_true", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.OfScientific", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isNat_ofScientific_of_false", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.OfScientific", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.evalOfScientific", "kind": "definition", "module": "Mathlib.Tactic.NormNum.OfScientific", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isNat_ordinalMul", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.evalOrdinalMul", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isNat_ordinalLE_true", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isNat_ordinalLE_false", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isNat_ordinalLT_true", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isNat_ordinalLT_false", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.evalOrdinalLE", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.evalOrdinalLT", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isNat_ordinalSub", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.evalOrdinalSub", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isNat_ordinalDiv", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.evalOrdinalDiv", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isNat_ordinalMod", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.evalOrdinalMod", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isNat_ordinalOPow", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.evalOrdinalOPow", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isNat_ordinalNPow", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.evalOrdinalNPow", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Ordinal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.evalEven", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Parity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.evalOdd", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Parity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.natPow_zero", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.natPow_one", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.zero_natPow", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.one_natPow", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.IsNatPowT.run", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.IsNatPowT.trans", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.IsNatPowT.bit0", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.IsNatPowT.bit1", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.evalNatPow", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.intPow_ofNat", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Pow", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Meta.NormNum.intPow_negOfNat_bit0", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Pow", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Mathlib.Meta.NormNum.intPow_negOfNat_bit1", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Pow", "is_tactic_proof": false, "tactics": ["rw", "hc,", "simp"], "tactic_count": 3}
{"name": "Mathlib.Meta.NormNum.evalIntPow", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isNat_pow", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isInt_pow", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isRat_pow", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Pow", "is_tactic_proof": true, "tactics": ["rintro", "have", "rw", "use"], "tactic_count": 4}
{"name": "Mathlib.Meta.NormNum.isNNRat_pow", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Pow", "is_tactic_proof": true, "tactics": ["rintro", "have", "rw", "use"], "tactic_count": 4}
{"name": "Mathlib.Meta.NormNum.evalPow.core", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.evalPow", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isNat_zpow_pos", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Pow", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Mathlib.Meta.NormNum.isNat_zpow_neg", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Pow", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Mathlib.Meta.NormNum.isInt_zpow_pos", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Pow", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Mathlib.Meta.NormNum.isInt_zpow_neg", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Pow", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Mathlib.Meta.NormNum.isNNRat_zpow_pos", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Pow", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Mathlib.Meta.NormNum.isNNRat_zpow_neg", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Pow", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Mathlib.Meta.NormNum.isRat_zpow_pos", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Pow", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Mathlib.Meta.NormNum.isRat_zpow_neg", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Pow", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Mathlib.Meta.NormNum.evalZPow", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Pow", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.IsNatPowModT.run", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.PowMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.IsNatPowModT.trans", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.PowMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.IsNatPowModT.bit0", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.PowMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.natPow_zero_natMod_zero", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.PowMod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Meta.NormNum.natPow_zero_natMod_one", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.PowMod", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Meta.NormNum.natPow_zero_natMod_succ_succ", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.PowMod", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "Mathlib.Meta.NormNum.natPow_one_natMod", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.PowMod", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Mathlib.Meta.NormNum.IsNatPowModT.bit1", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.PowMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.evalNatPowMod", "kind": "definition", "module": "Mathlib.Tactic.NormNum.PowMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.not_prime_mul_of_ble", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.deriveNotPrime", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.MinFacHelper", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.MinFacHelper.one_lt", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Prime", "is_tactic_proof": true, "tactics": ["have", "obtain", "contradiction", "rcases", "simp_all", "exact"], "tactic_count": 6}
{"name": "Mathlib.Meta.NormNum.minFacHelper_0", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Prime", "is_tactic_proof": true, "tactics": ["refine", "refine", "rcases", "simp", "exact"], "tactic_count": 5}
{"name": "Mathlib.Meta.NormNum.minFacHelper_1", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Prime", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "exact", "rcases", "exact", "rcases", "refine", "have", "rw", "norm_num", "exact", "exact"], "tactic_count": 13}
{"name": "Mathlib.Meta.NormNum.minFacHelper_2", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Prime", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "Mathlib.Meta.NormNum.minFacHelper_3", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Prime", "is_tactic_proof": true, "tactics": ["refine", "have", "rw", "exact"], "tactic_count": 4}
{"name": "Mathlib.Meta.NormNum.isNat_minFac_1", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isNat_minFac_2", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isNat_minFac_3", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isNat_minFac_4", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.evalMinFac", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isNat_prime_0", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isNat_prime_1", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isNat_prime_2", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.isNat_not_prime", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.evalNatPrime", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Prime", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.NormNum.isNat_realSqrt", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.RealSqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.NormNum.isNat_nnrealSqrt", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.RealSqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.NormNum.isNNRat_nnrealSqrt_of_isNNRat", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.RealSqrt", "is_tactic_proof": true, "tactics": ["obtain", "refine", "apply", "rw", "exact", "simp"], "tactic_count": 6}
{"name": "Tactic.NormNum.isNat_realSqrt_neg", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.RealSqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.NormNum.isNat_realSqrt_of_isRat_negOfNat", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.RealSqrt", "is_tactic_proof": true, "tactics": ["refine", "obtain", "have", "simpa"], "tactic_count": 4}
{"name": "Tactic.NormNum.isNNRat_realSqrt_of_isNNRat", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.RealSqrt", "is_tactic_proof": true, "tactics": ["obtain", "refine", "apply", "rw", "exact", "simp"], "tactic_count": 6}
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{"name": "Tactic.NormNum.evalNNRealSqrt", "kind": "definition", "module": "Mathlib.Tactic.NormNum.RealSqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Meta.NormNum.inferAddMonoidWithOne", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Result", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Meta.NormNum.inferRing", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Result", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.mkRawIntLit", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Result", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.mkRawRatLit", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Result", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.rawIntLitNatAbs", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Result", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.mkOfNat", "kind": "definition", "module": "Mathlib.Tactic.NormNum.Result", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.NormNum.IsNat.raw_refl", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Result", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Meta.NormNum.IsNat.of_raw", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Result", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Meta.NormNum.IsRat.to_isNNRat", "kind": "theorem", "module": "Mathlib.Tactic.NormNum.Result", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Tactic.Order.orderArgs", "kind": "definition", "module": "Mathlib.Tactic.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Order.order_core", "kind": "definition", "module": "Mathlib.Tactic.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Order._aux_Mathlib_Tactic_Order___elabRules_Mathlib_Tactic_Order_order_core_1", "kind": "definition", "module": "Mathlib.Tactic.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Order.tacticOrder_", "kind": "definition", "module": "Mathlib.Tactic.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Order._aux_Mathlib_Tactic_Order___macroRules_Mathlib_Tactic_Order_tacticOrder__1", "kind": "definition", "module": "Mathlib.Tactic.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Order.AtomicFact", "kind": "inductive", "module": "Mathlib.Tactic.Order.CollectFacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Order.instInhabitedAtomicFact.default", "kind": "definition", "module": "Mathlib.Tactic.Order.CollectFacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Order.instInhabitedAtomicFact", "kind": "instance", "module": "Mathlib.Tactic.Order.CollectFacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Order.instBEqAtomicFact", "kind": "instance", "module": "Mathlib.Tactic.Order.CollectFacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Order.instToStringAtomicFact", "kind": "instance", "module": "Mathlib.Tactic.Order.CollectFacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Order.CollectFactsState", "kind": "abbrev", "module": "Mathlib.Tactic.Order.CollectFacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Order.CollectFactsM", "kind": "abbrev", "module": "Mathlib.Tactic.Order.CollectFacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Order.addType", "kind": "definition", "module": "Mathlib.Tactic.Order.CollectFacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Order.addFact", "kind": "definition", "module": "Mathlib.Tactic.Order.CollectFacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Order.addAtom", "kind": "definition", "module": "Mathlib.Tactic.Order.CollectFacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Order.collectFactsImp", "kind": "definition", "module": "Mathlib.Tactic.Order.CollectFacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Order.collectFacts", "kind": "definition", "module": "Mathlib.Tactic.Order.CollectFacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Order.instToStringEdge", "kind": "instance", "module": "Mathlib.Tactic.Order.Graph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Order.Graph", "kind": "abbrev", "module": "Mathlib.Tactic.Order.Graph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Order.Graph.addEdge", "kind": "definition", "module": "Mathlib.Tactic.Order.Graph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Order.Graph.constructLeGraph", "kind": "definition", "module": "Mathlib.Tactic.Order.Graph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Order.Graph.buildTransitiveLeProofDFS", "kind": "definition", "module": "Mathlib.Tactic.Order.Graph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Order.Graph.buildTransitiveLeProof", "kind": "definition", "module": "Mathlib.Tactic.Order.Graph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Order.Graph.tarjanDFS", "kind": "definition", "module": "Mathlib.Tactic.Order.Graph.Tarjan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Order.Graph.findSCCsImp", "kind": "definition", "module": "Mathlib.Tactic.Order.Graph.Tarjan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Order.Graph.findSCCs", "kind": "definition", "module": "Mathlib.Tactic.Order.Graph.Tarjan", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Order.not_lt_of_not_le", "kind": "theorem", "module": "Mathlib.Tactic.Order.Preprocessing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Order.le_of_not_lt_le", "kind": "theorem", "module": "Mathlib.Tactic.Order.Preprocessing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Order.OrderType", "kind": "inductive", "module": "Mathlib.Tactic.Order.Preprocessing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Order.instBEqOrderType.beq", "kind": "definition", "module": "Mathlib.Tactic.Order.Preprocessing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Order.instBEqOrderType", "kind": "instance", "module": "Mathlib.Tactic.Order.Preprocessing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Order.instToStringOrderType", "kind": "instance", "module": "Mathlib.Tactic.Order.Preprocessing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Order.findBestOrderInstance", "kind": "definition", "module": "Mathlib.Tactic.Order.Preprocessing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Order.replaceBotTop", "kind": "definition", "module": "Mathlib.Tactic.Order.Preprocessing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Order.preprocessFactsPreorder", "kind": "definition", "module": "Mathlib.Tactic.Order.Preprocessing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Order.preprocessFactsPartial", "kind": "definition", "module": "Mathlib.Tactic.Order.Preprocessing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Order.preprocessFactsLinear", "kind": "definition", "module": "Mathlib.Tactic.Order.Preprocessing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Order.preprocessFacts", "kind": "definition", "module": "Mathlib.Tactic.Order.Preprocessing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Order.ToInt.exists_translation", "kind": "theorem", "module": "Mathlib.Tactic.Order.ToInt", "is_tactic_proof": true, "tactics": ["let", "let", "have", "apply", "rw", "simp", "use", "intro", "simp", "by_cases", "simp", "generalize_proofs", "rw", "conv_lhs", "have", "li.pairwise_mergeSort", "rw", "refine", "contrapose", "exact", "simpa"], "tactic_count": 21}
{"name": "Mathlib.Tactic.Order.ToInt.toInt", "kind": "definition", "module": "Mathlib.Tactic.Order.ToInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Order.ToInt.toInt_le_toInt", "kind": "theorem", "module": "Mathlib.Tactic.Order.ToInt", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Order.ToInt.toInt_lt_toInt", "kind": "theorem", "module": "Mathlib.Tactic.Order.ToInt", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Order.ToInt.toInt_eq_toInt", "kind": "theorem", "module": "Mathlib.Tactic.Order.ToInt", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Order.ToInt.toInt_ne_toInt", "kind": "theorem", "module": "Mathlib.Tactic.Order.ToInt", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Order.ToInt.toInt_nle_toInt", "kind": "theorem", "module": "Mathlib.Tactic.Order.ToInt", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Order.ToInt.toInt_nlt_toInt", "kind": "theorem", "module": "Mathlib.Tactic.Order.ToInt", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Order.ToInt.toInt_sup_toInt_eq_toInt", "kind": "theorem", "module": "Mathlib.Tactic.Order.ToInt", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Order.ToInt.toInt_inf_toInt_eq_toInt", "kind": "theorem", "module": "Mathlib.Tactic.Order.ToInt", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Order.ToInt.mkFinFun", "kind": "definition", "module": "Mathlib.Tactic.Order.ToInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Order.ToInt.translateToInt", "kind": "definition", "module": "Mathlib.Tactic.Order.ToInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.PNatToNat.tacticPnat_positivity", "kind": "definition", "module": "Mathlib.Tactic.PNatToNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.PNatToNat._aux_Mathlib_Tactic_PNatToNat___elabRules_Mathlib_Tactic_PNatToNat_tacticPnat_positivity_1", "kind": "definition", "module": "Mathlib.Tactic.PNatToNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.PNatToNat.coe_inj", "kind": "theorem", "module": "Mathlib.Tactic.PNatToNat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.PNatToNat.coe_le_coe", "kind": "theorem", "module": "Mathlib.Tactic.PNatToNat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.PNatToNat.coe_lt_coe", "kind": "theorem", "module": "Mathlib.Tactic.PNatToNat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.PNatToNat.sub_coe", "kind": "theorem", "module": "Mathlib.Tactic.PNatToNat", "is_tactic_proof": true, "tactics": ["cases", "cases", "simp", "split_ifs"], "tactic_count": 4}
{"name": "Mathlib.Tactic.PNatToNat.tacticPnat_to_nat", "kind": "definition", "module": "Mathlib.Tactic.PNatToNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.PNatToNat._aux_Mathlib_Tactic_PNatToNat___macroRules_Mathlib_Tactic_PNatToNat_tacticPnat_to_nat_1", "kind": "definition", "module": "Mathlib.Tactic.PNatToNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.PPWithUniv.delabWithUniv", "kind": "definition", "module": "Mathlib.Tactic.PPWithUniv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.PPWithUniv.ppWithUnivAttr", "kind": "definition", "module": "Mathlib.Tactic.PPWithUniv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.PPWithUniv.initFn._@.Mathlib.Tactic.PPWithUniv.1553184991._hygCtx._hyg.2", "kind": "definition", "module": "Mathlib.Tactic.PPWithUniv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Peel.peel", "kind": "definition", "module": "Mathlib.Tactic.Peel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Tactic.Peel.0.Mathlib.Tactic.Peel.and_imp_left_of_imp_imp", "kind": "theorem", "module": "Mathlib.Tactic.Peel", "is_tactic_proof": true, "tactics": ["tauto"], "tactic_count": 1}
{"name": "_private.Mathlib.Tactic.Peel.0.Mathlib.Tactic.Peel.eventually_imp", "kind": "theorem", "module": "Mathlib.Tactic.Peel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Tactic.Peel.0.Mathlib.Tactic.Peel.frequently_imp", "kind": "theorem", "module": "Mathlib.Tactic.Peel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Tactic.Peel.0.Mathlib.Tactic.Peel.eventually_congr", "kind": "theorem", "module": "Mathlib.Tactic.Peel", "is_tactic_proof": true, "tactics": ["congr"], "tactic_count": 1}
{"name": "_private.Mathlib.Tactic.Peel.0.Mathlib.Tactic.Peel.frequently_congr", "kind": "theorem", "module": "Mathlib.Tactic.Peel", "is_tactic_proof": true, "tactics": ["congr"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Peel.quantifiers", "kind": "definition", "module": "Mathlib.Tactic.Peel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Peel.whnfQuantifier", "kind": "definition", "module": "Mathlib.Tactic.Peel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Peel.throwPeelError", "kind": "definition", "module": "Mathlib.Tactic.Peel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Peel.mkFreshBinderName", "kind": "definition", "module": "Mathlib.Tactic.Peel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Peel.applyPeelThm", "kind": "definition", "module": "Mathlib.Tactic.Peel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Peel.peelCore", "kind": "definition", "module": "Mathlib.Tactic.Peel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Peel.peelIffAux", "kind": "definition", "module": "Mathlib.Tactic.Peel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Peel.peelArgsIff", "kind": "definition", "module": "Mathlib.Tactic.Peel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Peel._aux_Mathlib_Tactic_Peel___elabRules_Mathlib_Tactic_Peel_peel_1", "kind": "definition", "module": "Mathlib.Tactic.Peel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Peel._aux_Mathlib_Tactic_Peel___macroRules_Mathlib_Tactic_Peel_peel_1", "kind": "definition", "module": "Mathlib.Tactic.Peel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Polyrith.tacticPolyrithOnly[_]", "kind": "definition", "module": "Mathlib.Tactic.Polyrith", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Polyrith._aux_Mathlib_Tactic_Polyrith___elabRules_Mathlib_Tactic_Polyrith_tacticPolyrithOnly[_]_1", "kind": "definition", "module": "Mathlib.Tactic.Polyrith", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.ite_pos", "kind": "theorem", "module": "Mathlib.Tactic.Positivity.Basic", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "Mathlib.Meta.Positivity.ite_nonneg", "kind": "theorem", "module": "Mathlib.Tactic.Positivity.Basic", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "Mathlib.Meta.Positivity.ite_nonneg_of_pos_of_nonneg", "kind": "theorem", "module": "Mathlib.Tactic.Positivity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.ite_nonneg_of_nonneg_of_pos", "kind": "theorem", "module": "Mathlib.Tactic.Positivity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.ite_ne_zero", "kind": "theorem", "module": "Mathlib.Tactic.Positivity.Basic", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "Mathlib.Meta.Positivity.ite_ne_zero_of_pos_of_ne_zero", "kind": "theorem", "module": "Mathlib.Tactic.Positivity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.ite_ne_zero_of_ne_zero_of_pos", "kind": "theorem", "module": "Mathlib.Tactic.Positivity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalIte", "kind": "definition", "module": "Mathlib.Tactic.Positivity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.le_min_of_lt_of_le", "kind": "theorem", "module": "Mathlib.Tactic.Positivity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.le_min_of_le_of_lt", "kind": "theorem", "module": "Mathlib.Tactic.Positivity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.min_ne", "kind": "theorem", "module": "Mathlib.Tactic.Positivity.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Mathlib.Meta.Positivity.min_ne_of_ne_of_lt", "kind": "theorem", "module": "Mathlib.Tactic.Positivity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.min_ne_of_lt_of_ne", "kind": "theorem", "module": "Mathlib.Tactic.Positivity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.max_ne", "kind": "theorem", "module": "Mathlib.Tactic.Positivity.Basic", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Mathlib.Meta.Positivity.evalMin", "kind": "definition", "module": "Mathlib.Tactic.Positivity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalMax", "kind": "definition", "module": "Mathlib.Tactic.Positivity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalAdd", "kind": "definition", "module": "Mathlib.Tactic.Positivity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalMul", "kind": "definition", "module": "Mathlib.Tactic.Positivity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.int_div_self_pos", "kind": "theorem", "module": "Mathlib.Tactic.Positivity.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Mathlib.Meta.Positivity.int_div_nonneg_of_pos_of_nonneg", "kind": "theorem", "module": "Mathlib.Tactic.Positivity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.int_div_nonneg_of_nonneg_of_pos", "kind": "theorem", "module": "Mathlib.Tactic.Positivity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.int_div_nonneg_of_pos_of_pos", "kind": "theorem", "module": "Mathlib.Tactic.Positivity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalIntDiv", "kind": "definition", "module": "Mathlib.Tactic.Positivity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.pow_zero_pos", "kind": "theorem", "module": "Mathlib.Tactic.Positivity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalPowZeroNat", "kind": "definition", "module": "Mathlib.Tactic.Positivity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalPow", "kind": "definition", "module": "Mathlib.Tactic.Positivity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.abs_pos_of_ne_zero", "kind": "theorem", "module": "Mathlib.Tactic.Positivity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalAbs", "kind": "definition", "module": "Mathlib.Tactic.Positivity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.int_natAbs_pos", "kind": "theorem", "module": "Mathlib.Tactic.Positivity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalNatAbs", "kind": "definition", "module": "Mathlib.Tactic.Positivity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalNatCast", "kind": "definition", "module": "Mathlib.Tactic.Positivity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalIntCast", "kind": "definition", "module": "Mathlib.Tactic.Positivity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalNatSucc", "kind": "definition", "module": "Mathlib.Tactic.Positivity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalPNatVal", "kind": "definition", "module": "Mathlib.Tactic.Positivity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalFactorial", "kind": "definition", "module": "Mathlib.Tactic.Positivity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalAscFactorial", "kind": "definition", "module": "Mathlib.Tactic.Positivity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalNatGCD", "kind": "definition", "module": "Mathlib.Tactic.Positivity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalNatLCM", "kind": "definition", "module": "Mathlib.Tactic.Positivity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalNatSqrt", "kind": "definition", "module": "Mathlib.Tactic.Positivity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalIntGCD", "kind": "definition", "module": "Mathlib.Tactic.Positivity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalIntLCM", "kind": "definition", "module": "Mathlib.Tactic.Positivity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalNNRatNum", "kind": "definition", "module": "Mathlib.Tactic.Positivity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalNNRatDen", "kind": "definition", "module": "Mathlib.Tactic.Positivity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity._example", "kind": "example", "module": "Mathlib.Tactic.Positivity.Basic", "is_tactic_proof": true, "tactics": ["positivity"], "tactic_count": 1}
{"name": "Mathlib.Meta.Positivity._example", "kind": "example", "module": "Mathlib.Tactic.Positivity.Basic", "is_tactic_proof": true, "tactics": ["positivity"], "tactic_count": 1}
{"name": "Mathlib.Meta.Positivity._example", "kind": "example", "module": "Mathlib.Tactic.Positivity.Basic", "is_tactic_proof": true, "tactics": ["positivity"], "tactic_count": 1}
{"name": "Mathlib.Meta.Positivity.evalRatNum", "kind": "definition", "module": "Mathlib.Tactic.Positivity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalRatDen", "kind": "definition", "module": "Mathlib.Tactic.Positivity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalPosPart", "kind": "definition", "module": "Mathlib.Tactic.Positivity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalNegPart", "kind": "definition", "module": "Mathlib.Tactic.Positivity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalMap", "kind": "definition", "module": "Mathlib.Tactic.Positivity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "positivity", "kind": "definition", "module": "Mathlib.Tactic.Positivity.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ne_of_ne_of_eq'", "kind": "theorem", "module": "Mathlib.Tactic.Positivity.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.Strictness", "kind": "inductive", "module": "Mathlib.Tactic.Positivity.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Meta.Positivity.Strictness.toPositive", "kind": "definition", "module": "Mathlib.Tactic.Positivity.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.Strictness.toNonneg", "kind": "definition", "module": "Mathlib.Tactic.Positivity.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Meta.Positivity.mkPositivityExt", "kind": "definition", "module": "Mathlib.Tactic.Positivity.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.Entry", "kind": "abbrev", "module": "Mathlib.Tactic.Positivity.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Meta.Positivity.pos_of_isNat", "kind": "theorem", "module": "Mathlib.Tactic.Positivity.Core", "is_tactic_proof": true, "tactics": ["rw", "apply", "simpa"], "tactic_count": 3}
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{"name": "Mathlib.Meta.Positivity.nz_of_isNegNat", "kind": "theorem", "module": "Mathlib.Tactic.Positivity.Core", "is_tactic_proof": true, "tactics": ["rw", "simp", "apply", "simpa"], "tactic_count": 4}
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{"name": "Mathlib.Meta.Positivity.nz_of_isRat", "kind": "theorem", "module": "Mathlib.Tactic.Positivity.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Meta.Positivity.throwNone", "kind": "definition", "module": "Mathlib.Tactic.Positivity.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.normNumPositivity", "kind": "definition", "module": "Mathlib.Tactic.Positivity.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.positivityCanon", "kind": "definition", "module": "Mathlib.Tactic.Positivity.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.compareHypLE", "kind": "definition", "module": "Mathlib.Tactic.Positivity.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.compareHypLT", "kind": "definition", "module": "Mathlib.Tactic.Positivity.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.compareHypEq", "kind": "definition", "module": "Mathlib.Tactic.Positivity.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Meta.Positivity.orElse", "kind": "definition", "module": "Mathlib.Tactic.Positivity.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Meta.Positivity.positivity", "kind": "definition", "module": "Mathlib.Tactic.Positivity.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Tactic.Push.not_iff", "kind": "theorem", "module": "Mathlib.Tactic.Push", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Tactic.Push.resolvePushId?", "kind": "definition", "module": "Mathlib.Tactic.Push", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "pushFun", "kind": "definition", "module": "Mathlib.Tactic.Push", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pullFun", "kind": "definition", "module": "Mathlib.Tactic.Push", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Push.convPush_____", "kind": "definition", "module": "Mathlib.Tactic.Push", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Push._aux_Mathlib_Tactic_Push___elabRules_Mathlib_Tactic_Push_convPush______1", "kind": "definition", "module": "Mathlib.Tactic.Push", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Push.convPush_neg_", "kind": "definition", "module": "Mathlib.Tactic.Push", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Tactic.Push.pushCommand", "kind": "definition", "module": "Mathlib.Tactic.Push", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Push._aux_Mathlib_Tactic_Push___macroRules_Mathlib_Tactic_Push_pushCommand_1", "kind": "definition", "module": "Mathlib.Tactic.Push", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Push.pushNegCommand", "kind": "definition", "module": "Mathlib.Tactic.Push", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Push._aux_Mathlib_Tactic_Push___macroRules_Mathlib_Tactic_Push_pushNegCommand_1", "kind": "definition", "module": "Mathlib.Tactic.Push", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Push.convPull____", "kind": "definition", "module": "Mathlib.Tactic.Push", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Push._aux_Mathlib_Tactic_Push___elabRules_Mathlib_Tactic_Push_convPull_____1", "kind": "definition", "module": "Mathlib.Tactic.Push", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Push.pullCommand", "kind": "definition", "module": "Mathlib.Tactic.Push", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Push._aux_Mathlib_Tactic_Push___macroRules_Mathlib_Tactic_Push_pullCommand_1", "kind": "definition", "module": "Mathlib.Tactic.Push", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Push.pushTree", "kind": "definition", "module": "Mathlib.Tactic.Push", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Push.elabPushTree", "kind": "definition", "module": "Mathlib.Tactic.Push", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Push.Head", "kind": "inductive", "module": "Mathlib.Tactic.Push.Attr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Push.instInhabitedHead.default", "kind": "definition", "module": "Mathlib.Tactic.Push.Attr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Push.instInhabitedHead", "kind": "instance", "module": "Mathlib.Tactic.Push.Attr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Push.instBEqHead", "kind": "instance", "module": "Mathlib.Tactic.Push.Attr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Push.Head.toString", "kind": "definition", "module": "Mathlib.Tactic.Push.Attr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Push.instToStringHead", "kind": "instance", "module": "Mathlib.Tactic.Push.Attr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Push.Head.ofExpr?", "kind": "definition", "module": "Mathlib.Tactic.Push.Attr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Push.initFn._@.Mathlib.Tactic.Push.Attr.1668288364._hygCtx._hyg.2", "kind": "definition", "module": "Mathlib.Tactic.Push.Attr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Push.pushExt", "kind": "opaque", "module": "Mathlib.Tactic.Push.Attr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Push.isPullThm", "kind": "definition", "module": "Mathlib.Tactic.Push.Attr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Push.PullTheorem", "kind": "abbrev", "module": "Mathlib.Tactic.Push.Attr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Push.initFn._@.Mathlib.Tactic.Push.Attr.3484215244._hygCtx._hyg.2", "kind": "definition", "module": "Mathlib.Tactic.Push.Attr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Push.pullExt", "kind": "opaque", "module": "Mathlib.Tactic.Push.Attr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Push.pushAttr", "kind": "definition", "module": "Mathlib.Tactic.Push.Attr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Push.initFn._@.Mathlib.Tactic.Push.Attr.2591766601._hygCtx._hyg.2", "kind": "definition", "module": "Mathlib.Tactic.Push.Attr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Qify.qify", "kind": "definition", "module": "Mathlib.Tactic.Qify", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Qify._aux_Mathlib_Tactic_Qify___macroRules_Mathlib_Tactic_Qify_qify_1", "kind": "definition", "module": "Mathlib.Tactic.Qify", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Qify.intCast_eq", "kind": "theorem", "module": "Mathlib.Tactic.Qify", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Qify.intCast_le", "kind": "theorem", "module": "Mathlib.Tactic.Qify", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Qify.intCast_lt", "kind": "theorem", "module": "Mathlib.Tactic.Qify", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Qify.intCast_ne", "kind": "theorem", "module": "Mathlib.Tactic.Qify", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.rsuffices", "kind": "definition", "module": "Mathlib.Tactic.RSuffices", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic._aux_Mathlib_Tactic_RSuffices___macroRules_Mathlib_Tactic_rsuffices_1", "kind": "definition", "module": "Mathlib.Tactic.RSuffices", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Recall.recall", "kind": "definition", "module": "Mathlib.Tactic.Recall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Recall._aux_Mathlib_Tactic_Recall___elabRules_Mathlib_Tactic_Recall_recall_1", "kind": "definition", "module": "Mathlib.Tactic.Recall", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.getUnassignedGoalMVarDependencies", "kind": "definition", "module": "Mathlib.Tactic.Recover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.tacticRecover_", "kind": "definition", "module": "Mathlib.Tactic.Recover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic._aux_Mathlib_Tactic_Recover___elabRules_Mathlib_Tactic_tacticRecover__1", "kind": "definition", "module": "Mathlib.Tactic.Recover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.ReduceModChar.CharP.isInt_of_mod", "kind": "theorem", "module": "Mathlib.Tactic.ReduceModChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.ReduceModChar.CharP.isNat_pow", "kind": "theorem", "module": "Mathlib.Tactic.ReduceModChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.ReduceModChar.normBareNumeral", "kind": "definition", "module": "Mathlib.Tactic.ReduceModChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.ReduceModChar.CharP.intCast_eq_mod", "kind": "theorem", "module": "Mathlib.Tactic.ReduceModChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.ReduceModChar.normIntNumeral", "kind": "definition", "module": "Mathlib.Tactic.ReduceModChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.ReduceModChar.CharP.neg_eq_sub_one_mul", "kind": "theorem", "module": "Mathlib.Tactic.ReduceModChar", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Tactic.ReduceModChar.normNeg", "kind": "definition", "module": "Mathlib.Tactic.ReduceModChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.ReduceModChar.CharP.neg_mul_eq_sub_one_mul", "kind": "theorem", "module": "Mathlib.Tactic.ReduceModChar", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Tactic.ReduceModChar.normNegCoeffMul", "kind": "definition", "module": "Mathlib.Tactic.ReduceModChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.ReduceModChar.TypeToCharPResult", "kind": "inductive", "module": "Mathlib.Tactic.ReduceModChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.ReduceModChar.instInhabitedTypeToCharPResult", "kind": "instance", "module": "Mathlib.Tactic.ReduceModChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.ReduceModChar.reduce_mod_char", "kind": "definition", "module": "Mathlib.Tactic.ReduceModChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.ReduceModChar.reduce_mod_char!", "kind": "definition", "module": "Mathlib.Tactic.ReduceModChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.ReduceModChar._aux_Mathlib_Tactic_ReduceModChar___elabRules_Tactic_ReduceModChar_reduce_mod_char_1", "kind": "definition", "module": "Mathlib.Tactic.ReduceModChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.ReduceModChar._aux_Mathlib_Tactic_ReduceModChar___elabRules_Tactic_ReduceModChar_reduce_mod_char!_1", "kind": "definition", "module": "Mathlib.Tactic.ReduceModChar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "initFn._@.Mathlib.Tactic.ReduceModChar.Ext.445482845._hygCtx._hyg.2", "kind": "definition", "module": "Mathlib.Tactic.ReduceModChar.Ext", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "reduceModCharExt", "kind": "opaque", "module": "Mathlib.Tactic.ReduceModChar.Ext", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.rflTac", "kind": "definition", "module": "Mathlib.Tactic.Relation.Rfl", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lean.Expr.relSidesIfRefl?", "kind": "definition", "module": "Mathlib.Tactic.Relation.Rfl", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Lean.Expr.relSidesIfSymm?", "kind": "definition", "module": "Mathlib.Tactic.Relation.Symm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.renameArg", "kind": "definition", "module": "Mathlib.Tactic.Rename", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.rename'", "kind": "definition", "module": "Mathlib.Tactic.Rename", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic._aux_Mathlib_Tactic_Rename___elabRules_Mathlib_Tactic_rename'_1", "kind": "definition", "module": "Mathlib.Tactic.Rename", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.renameBVarHyp", "kind": "definition", "module": "Mathlib.Tactic.RenameBVar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.renameBVarTarget", "kind": "definition", "module": "Mathlib.Tactic.RenameBVar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.tacticRename_bvar_→__", "kind": "definition", "module": "Mathlib.Tactic.RenameBVar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic._aux_Mathlib_Tactic_RenameBVar___elabRules_Mathlib_Tactic_tacticRename_bvar_→___1", "kind": "definition", "module": "Mathlib.Tactic.RenameBVar", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.replace'", "kind": "definition", "module": "Mathlib.Tactic.Replace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic._aux_Mathlib_Tactic_Replace___elabRules_Mathlib_Tactic_replace'_1", "kind": "definition", "module": "Mathlib.Tactic.Replace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.RewriteSearch.tacticRw_search_", "kind": "definition", "module": "Mathlib.Tactic.RewriteSearch", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.RewriteSearch._aux_Mathlib_Tactic_RewriteSearch___elabRules_Mathlib_Tactic_RewriteSearch_tacticRw_search__1", "kind": "definition", "module": "Mathlib.Tactic.RewriteSearch", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Rify.rify", "kind": "definition", "module": "Mathlib.Tactic.Rify", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Rify._aux_Mathlib_Tactic_Rify___macroRules_Mathlib_Tactic_Rify_rify_1", "kind": "definition", "module": "Mathlib.Tactic.Rify", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Rify.ratCast_eq", "kind": "theorem", "module": "Mathlib.Tactic.Rify", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Rify.ratCast_le", "kind": "theorem", "module": "Mathlib.Tactic.Rify", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Rify.ratCast_lt", "kind": "theorem", "module": "Mathlib.Tactic.Rify", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Rify.ratCast_ne", "kind": "theorem", "module": "Mathlib.Tactic.Rify", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Rify.ofNat_rat_real", "kind": "theorem", "module": "Mathlib.Tactic.Rify", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.instCommSemiringNat", "kind": "definition", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.instCommSemiringInt", "kind": "definition", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.sℕ", "kind": "definition", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.sℤ", "kind": "definition", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.instInhabitedSigmaQuotedExBase", "kind": "instance", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.instInhabitedSigmaQuotedExSum", "kind": "instance", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.instInhabitedSigmaQuotedExProd", "kind": "instance", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.instInhabitedResultOfSigmaQuoted", "kind": "instance", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.ExProd.mkNat", "kind": "definition", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.ExProd.mkNegNat", "kind": "definition", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.ExProd.mkNNRat", "kind": "definition", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.ExProd.mkNegNNRat", "kind": "definition", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.ExBase.toProd", "kind": "definition", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.ExProd.toSum", "kind": "definition", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.ExProd.coeff", "kind": "definition", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.Overlap", "kind": "inductive", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.add_overlap_pf", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": true, "tactics": ["subst_vars"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Ring.add_overlap_pf_zero", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Tactic.Ring.Basic.0.Mathlib.Tactic.Ring.instMonadLiftOptionOptionTOfPure_mathlib", "kind": "instance", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.evalAddOverlap", "kind": "definition", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.add_pf_zero_add", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Ring.add_pf_add_zero", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Ring.add_pf_add_overlap", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": true, "tactics": ["subst_vars"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Ring.add_pf_add_overlap_zero", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": true, "tactics": ["subst_vars"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Ring.add_pf_add_lt", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Ring.add_pf_add_gt", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": true, "tactics": ["subst_vars"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Ring.evalAdd", "kind": "definition", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.one_mul", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Ring.mul_one", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Ring.mul_pf_left", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": true, "tactics": ["subst_vars"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Ring.mul_pf_right", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": true, "tactics": ["subst_vars"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Ring.mul_pp_pf_overlap", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": true, "tactics": ["subst_vars"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Ring.evalMulProd", "kind": "definition", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.mul_zero", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Ring.mul_add", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": true, "tactics": ["subst_vars"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Ring.evalMul₁", "kind": "definition", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.zero_mul", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Ring.add_mul", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": true, "tactics": ["subst_vars"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Ring.evalMul", "kind": "definition", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.natCast_nat", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Ring.natCast_mul", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": true, "tactics": ["subst_vars"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Ring.natCast_zero", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.natCast_add", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": true, "tactics": ["subst_vars"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Ring.smul_nat", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.smul_eq_cast", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": true, "tactics": ["subst_vars"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Ring.evalNSMul", "kind": "definition", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.natCast_int", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Ring.intCast_negOfNat_Int", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Ring.intCast_mul", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": true, "tactics": ["subst_vars"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Ring.intCast_zero", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.intCast_add", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": true, "tactics": ["subst_vars"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Ring.smul_int", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.smul_eq_intCast", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": true, "tactics": ["subst_vars"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Ring.evalZSMul", "kind": "definition", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.neg_one_mul", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": true, "tactics": ["subst_vars"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Ring.neg_mul", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": true, "tactics": ["subst_vars"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Ring.evalNegProd", "kind": "definition", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.neg_zero", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Ring.neg_add", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": true, "tactics": ["subst_vars"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Ring.evalNeg", "kind": "definition", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.sub_pf", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": true, "tactics": ["subst_vars"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Ring.evalSub", "kind": "definition", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.pow_prod_atom", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Ring.evalPowProdAtom", "kind": "definition", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.pow_atom", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Ring.evalPowAtom", "kind": "definition", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.const_pos", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.mul_exp_pos", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.add_pos_left", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.add_pos_right", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.pow_one", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Ring.pow_bit0", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": true, "tactics": ["subst_vars"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Ring.pow_bit1", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": true, "tactics": ["subst_vars"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Ring.evalPowNat", "kind": "definition", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.one_pow", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Ring.mul_pow", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": true, "tactics": ["subst_vars"], "tactic_count": 1}
{"name": "_private.Mathlib.Tactic.Ring.Basic.0.Mathlib.Tactic.Ring.instMonadLiftTOptionTOfMonad_mathlib", "kind": "instance", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.evalPowProd", "kind": "definition", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.coeff_one", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Ring.coeff_mul", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": true, "tactics": ["subst_vars"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Ring.extractCoeff", "kind": "definition", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.pow_one_cast", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Ring.zero_pow", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.single_pow", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Ring.pow_nat", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": true, "tactics": ["subst_vars"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Ring.evalPow₁", "kind": "definition", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.pow_zero", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Ring.pow_add", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": true, "tactics": ["subst_vars"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Ring.evalPow", "kind": "definition", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.mkCache", "kind": "definition", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.cast_pos", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.cast_zero", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.cast_neg", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.cast_nnrat", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.cast_rat", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.evalCast", "kind": "definition", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.toProd_pf", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Ring.atom_pf", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Ring.atom_pf'", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Ring.evalAtom", "kind": "definition", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.inv_mul", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": true, "tactics": ["subst_vars"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Ring.inv_zero", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.inv_single", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Ring.inv_add", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": true, "tactics": ["subst_vars"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Ring.evalInvAtom", "kind": "definition", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.ExProd.evalInv", "kind": "definition", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.ExSum.evalInv", "kind": "definition", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.div_pf", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": true, "tactics": ["subst_vars"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Ring.evalDiv", "kind": "definition", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.add_congr", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": true, "tactics": ["subst_vars"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Ring.mul_congr", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": true, "tactics": ["subst_vars"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Ring.nsmul_congr", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": true, "tactics": ["subst_vars"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Ring.zsmul_congr", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": true, "tactics": ["subst_vars"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Ring.pow_congr", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": true, "tactics": ["subst_vars"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Ring.neg_congr", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": true, "tactics": ["subst_vars"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Ring.sub_congr", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": true, "tactics": ["subst_vars"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Ring.inv_congr", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": true, "tactics": ["subst_vars"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Ring.div_congr", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": true, "tactics": ["subst_vars"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Ring.Cache.nat", "kind": "definition", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.Cache.int", "kind": "definition", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.isAtomOrDerivable", "kind": "definition", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.eval", "kind": "definition", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.instCSLiftValLift", "kind": "instance", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.of_lift", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.of_eq", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": true, "tactics": ["subst_vars"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Ring.initFn._@.Mathlib.Tactic.Ring.Basic.3588287011._hygCtx._hyg.2", "kind": "definition", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.ringCleanupRef", "kind": "opaque", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.proveEq", "kind": "definition", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.ring1", "kind": "definition", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring._aux_Mathlib_Tactic_Ring_Basic___elabRules_Mathlib_Tactic_Ring_ring1_1", "kind": "definition", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.tacticRing1!", "kind": "definition", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring._aux_Mathlib_Tactic_Ring_Basic___macroRules_Mathlib_Tactic_Ring_tacticRing1!_1", "kind": "definition", "module": "Mathlib.Tactic.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.amwo_of_cs", "kind": "abbrev", "module": "Mathlib.Tactic.Ring.Compare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.le_of_po", "kind": "abbrev", "module": "Mathlib.Tactic.Ring.Compare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.lt_of_po", "kind": "abbrev", "module": "Mathlib.Tactic.Ring.Compare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.add_le_add_left", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Compare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.add_le_of_nonpos_left", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Compare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.le_add_of_nonneg_left", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Compare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.add_lt_add_left", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Compare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.add_lt_of_neg_left", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Compare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.lt_add_of_pos_left", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Compare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.ExceptType", "kind": "inductive", "module": "Mathlib.Tactic.Ring.Compare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.evalLE", "kind": "definition", "module": "Mathlib.Tactic.Ring.Compare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.evalLT", "kind": "definition", "module": "Mathlib.Tactic.Ring.Compare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.le_congr", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Compare", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Ring.lt_congr", "kind": "theorem", "module": "Mathlib.Tactic.Ring.Compare", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Mathlib.Tactic.Ring.proveLE", "kind": "definition", "module": "Mathlib.Tactic.Ring.Compare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.proveLT", "kind": "definition", "module": "Mathlib.Tactic.Ring.Compare", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.namePolyVarsOver", "kind": "definition", "module": "Mathlib.Tactic.Ring.NamePolyVars", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.elabNameVariablesOver", "kind": "definition", "module": "Mathlib.Tactic.Ring.NamePolyVars", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.instCSLiftPNatNat", "kind": "instance", "module": "Mathlib.Tactic.Ring.PNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.instCSLiftValPNatNatOfNatHAdd", "kind": "instance", "module": "Mathlib.Tactic.Ring.PNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.instCSLiftValPNatNatToPNat", "kind": "instance", "module": "Mathlib.Tactic.Ring.PNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.instCSLiftValPNatNatSuccPNatHAddOfNat", "kind": "instance", "module": "Mathlib.Tactic.Ring.PNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Ring.instCSLiftValPNatNatToPNat'HAddPredOfNat", "kind": "instance", "module": "Mathlib.Tactic.Ring.PNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Tactic.Tauto.distribNotAux", "kind": "definition", "module": "Mathlib.Tactic.Tauto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Tauto.distribNot", "kind": "definition", "module": "Mathlib.Tactic.Tauto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Tauto.evalUnsafe._@.Mathlib.Tactic.Tauto.1055794184._hygCtx._hyg.3", "kind": "definition", "module": "Mathlib.Tactic.Tauto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Tactic.Tauto.elabConfig", "kind": "definition", "module": "Mathlib.Tactic.Tauto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Tauto.coreConstructorMatcher", "kind": "definition", "module": "Mathlib.Tactic.Tauto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Tauto.casesMatcher", "kind": "definition", "module": "Mathlib.Tactic.Tauto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Tactic.Tauto.0.Mathlib.Tactic.Tauto.term_<;>_", "kind": "definition", "module": "Mathlib.Tactic.Tauto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Tactic.Tauto.tautoCore", "kind": "definition", "module": "Mathlib.Tactic.Tauto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Tauto.finishingConstructorMatcher", "kind": "definition", "module": "Mathlib.Tactic.Tauto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Tauto.tautology", "kind": "definition", "module": "Mathlib.Tactic.Tauto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Tauto.tauto", "kind": "definition", "module": "Mathlib.Tactic.Tauto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Tauto._aux_Mathlib_Tactic_Tauto___elabRules_Mathlib_Tactic_Tauto_tauto_1", "kind": "definition", "module": "Mathlib.Tactic.Tauto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "tautoToGrindRegressions", "kind": "definition", "module": "Mathlib.Tactic.Tauto", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.TautoSet.specialize_all", "kind": "definition", "module": "Mathlib.Tactic.TautoSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.TautoSet._aux_Mathlib_Tactic_TautoSet___elabRules_Mathlib_Tactic_TautoSet_specialize_all_1", "kind": "definition", "module": "Mathlib.Tactic.TautoSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.TautoSet.tacticTauto_set", "kind": "definition", "module": "Mathlib.Tactic.TautoSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.TautoSet._aux_Mathlib_Tactic_TautoSet___macroRules_Mathlib_Tactic_TautoSet_tacticTauto_set_1", "kind": "definition", "module": "Mathlib.Tactic.TautoSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.TermCongr.initFn._@.Mathlib.Tactic.TermCongr.920020848._hygCtx._hyg.2", "kind": "definition", "module": "Mathlib.Tactic.TermCongr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.TermCongr.termCongr", "kind": "definition", "module": "Mathlib.Tactic.TermCongr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Tactic.TermCongr.0.Mathlib.Tactic.TermCongr.congrHoleForLhsKey", "kind": "definition", "module": "Mathlib.Tactic.TermCongr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Tactic.TermCongr.0.Mathlib.Tactic.TermCongr.congrHoleIndex", "kind": "definition", "module": "Mathlib.Tactic.TermCongr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.TermCongr.cHole", "kind": "definition", "module": "Mathlib.Tactic.TermCongr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.TermCongr.unexpandCHole", "kind": "definition", "module": "Mathlib.Tactic.TermCongr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.TermCongr.mkCHole", "kind": "definition", "module": "Mathlib.Tactic.TermCongr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.TermCongr.hasCHole", "kind": "definition", "module": "Mathlib.Tactic.TermCongr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.TermCongr.removeCHoles", "kind": "definition", "module": "Mathlib.Tactic.TermCongr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.TermCongr.elabCHole", "kind": "definition", "module": "Mathlib.Tactic.TermCongr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.TermCongr.cHoleExpand", "kind": "definition", "module": "Mathlib.Tactic.TermCongr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.TermCongr.elabCHoleExpand", "kind": "definition", "module": "Mathlib.Tactic.TermCongr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.TermCongr.processAntiquot", "kind": "definition", "module": "Mathlib.Tactic.TermCongr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.TermCongr.elaboratePattern", "kind": "definition", "module": "Mathlib.Tactic.TermCongr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.TermCongr.mkEqForExpectedType", "kind": "definition", "module": "Mathlib.Tactic.TermCongr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.TermCongr.mkHEqForExpectedType", "kind": "definition", "module": "Mathlib.Tactic.TermCongr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.TermCongr.mkIffForExpectedType", "kind": "definition", "module": "Mathlib.Tactic.TermCongr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.TermCongr.ensureIff", "kind": "definition", "module": "Mathlib.Tactic.TermCongr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.TermCongr.CongrType", "kind": "inductive", "module": "Mathlib.Tactic.TermCongr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.TermCongr.CongrResult.isRfl", "kind": "definition", "module": "Mathlib.Tactic.TermCongr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.TermCongr.CongrResult.eq", "kind": "definition", "module": "Mathlib.Tactic.TermCongr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.TermCongr.CongrResult.heq", "kind": "definition", "module": "Mathlib.Tactic.TermCongr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.TermCongr.CongrResult.iff", "kind": "definition", "module": "Mathlib.Tactic.TermCongr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.TermCongr.CongrResult.trans", "kind": "definition", "module": "Mathlib.Tactic.TermCongr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.TermCongr.CongrResult.mk'", "kind": "definition", "module": "Mathlib.Tactic.TermCongr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.TermCongr.CongrResult.defeq", "kind": "definition", "module": "Mathlib.Tactic.TermCongr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.TermCongr.CongrResult.mkDefault", "kind": "definition", "module": "Mathlib.Tactic.TermCongr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.TermCongr.CongrResult.mkDefault'", "kind": "definition", "module": "Mathlib.Tactic.TermCongr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.TermCongr.throwCongrEx", "kind": "definition", "module": "Mathlib.Tactic.TermCongr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.TermCongr.mkCongrOfCHole?", "kind": "definition", "module": "Mathlib.Tactic.TermCongr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Tactic.TermCongr.0.Mathlib.Tactic.TermCongr.getJointAppFns", "kind": "definition", "module": "Mathlib.Tactic.TermCongr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.TermCongr.M", "kind": "abbrev", "module": "Mathlib.Tactic.TermCongr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.TermCongr.mkCongrOf", "kind": "definition", "module": "Mathlib.Tactic.TermCongr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.TermCongr.elabTermCongr", "kind": "definition", "module": "Mathlib.Tactic.TermCongr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.instToExprULift_mathlib", "kind": "instance", "module": "Mathlib.Tactic.ToExpr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.instToExprSourceInfo_mathlib", "kind": "instance", "module": "Mathlib.Tactic.ToExpr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.instToExprSyntax_mathlib", "kind": "instance", "module": "Mathlib.Tactic.ToExpr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.instToExprMVarId_mathlib", "kind": "instance", "module": "Mathlib.Tactic.ToExpr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.instToExprLevelMVarId_mathlib", "kind": "instance", "module": "Mathlib.Tactic.ToExpr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.instToExprLevel_mathlib", "kind": "instance", "module": "Mathlib.Tactic.ToExpr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.instToExprExpr_mathlib", "kind": "instance", "module": "Mathlib.Tactic.ToExpr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.to_fun", "kind": "definition", "module": "Mathlib.Tactic.ToFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Lean.Parser.Tactic.trace", "kind": "definition", "module": "Mathlib.Tactic.Trace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Tactic.Translate.attrOption", "kind": "definition", "module": "Mathlib.Tactic.Translate.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Translate.reorderOption", "kind": "definition", "module": "Mathlib.Tactic.Translate.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Translate.relevantArgOption", "kind": "definition", "module": "Mathlib.Tactic.Translate.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Translate.dontTranslateOption", "kind": "definition", "module": "Mathlib.Tactic.Translate.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Translate.bracketedOption", "kind": "definition", "module": "Mathlib.Tactic.Translate.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Translate.translationHint", "kind": "definition", "module": "Mathlib.Tactic.Translate.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Translate.attrArgs", "kind": "definition", "module": "Mathlib.Tactic.Translate.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Tactic.Translate.linter.existingAttributeWarning", "kind": "opaque", "module": "Mathlib.Tactic.Translate.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Tactic.Translate.linter.translateExisting", "kind": "opaque", "module": "Mathlib.Tactic.Translate.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Tactic.Translate.linter.translateReorder", "kind": "opaque", "module": "Mathlib.Tactic.Translate.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Tactic.Translate.linter.translateRedundant", "kind": "opaque", "module": "Mathlib.Tactic.Translate.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Translate.instBEqArgInfo", "kind": "instance", "module": "Mathlib.Tactic.Translate.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Translate.findTranslation?", "kind": "definition", "module": "Mathlib.Tactic.Translate.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Translate.findPrefixTranslation", "kind": "definition", "module": "Mathlib.Tactic.Translate.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Translate.ArgInfo.reverse", "kind": "definition", "module": "Mathlib.Tactic.Translate.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Translate.insertTranslation", "kind": "definition", "module": "Mathlib.Tactic.Translate.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Translate.instReprConfig", "kind": "instance", "module": "Mathlib.Tactic.Translate.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Translate.etaExpandN", "kind": "definition", "module": "Mathlib.Tactic.Translate.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Tactic.Translate.Core.0.Mathlib.Tactic.Translate.shouldTranslateUnsafe", "kind": "definition", "module": "Mathlib.Tactic.Translate.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Translate.List.swapFirstTwo", "kind": "definition", "module": "Mathlib.Tactic.Translate.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Translate.changeNumeral", "kind": "definition", "module": "Mathlib.Tactic.Translate.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Translate.renameBinderNames", "kind": "definition", "module": "Mathlib.Tactic.Translate.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Translate.reorderForall", "kind": "definition", "module": "Mathlib.Tactic.Translate.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Translate.reorderLambda", "kind": "definition", "module": "Mathlib.Tactic.Translate.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Translate.applyReplacementForall", "kind": "definition", "module": "Mathlib.Tactic.Translate.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Translate.applyReplacementLambda", "kind": "definition", "module": "Mathlib.Tactic.Translate.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Translate.updateDecl", "kind": "definition", "module": "Mathlib.Tactic.Translate.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Translate.findRelevantArg", "kind": "definition", "module": "Mathlib.Tactic.Translate.Core", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Tactic.Widget.commSquareM?", "kind": "definition", "module": "Mathlib.Tactic.Widget.CommDiag", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "tacticCongrm?", "kind": "definition", "module": "Mathlib.Tactic.Widget.CongrM", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Tactic.Conv.Path.ofSubExprPosArray", "kind": "definition", "module": "Mathlib.Tactic.Widget.Conv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Conv.insertEnterSyntax", "kind": "definition", "module": "Mathlib.Tactic.Widget.Conv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Conv.insertEnter", "kind": "definition", "module": "Mathlib.Tactic.Widget.Conv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Tactic.Conv.tacticConv?", "kind": "definition", "module": "Mathlib.Tactic.Widget.Conv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "GCongrSelectionPanel", "kind": "definition", "module": "Mathlib.Tactic.Widget.GCongr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tacticGcongr?", "kind": "definition", "module": "Mathlib.Tactic.Widget.GCongr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Tactic.InteractiveUnfold.unfoldProjDefaultInst?", "kind": "definition", "module": "Mathlib.Tactic.Widget.InteractiveUnfold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Tactic.InteractiveUnfold.isUserFriendly", "kind": "definition", "module": "Mathlib.Tactic.Widget.InteractiveUnfold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Tactic.InteractiveUnfold.tacticUnfold?", "kind": "definition", "module": "Mathlib.Tactic.Widget.InteractiveUnfold", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Tactic.LibraryRewrite.eqOrIff?", "kind": "definition", "module": "Mathlib.Tactic.Widget.LibraryRewrite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "String.renameMetaVar", "kind": "definition", "module": "Mathlib.Tactic.Widget.SelectPanelUtils", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Tactic.Widget.StringDiagram.Node.vPos", "kind": "definition", "module": "Mathlib.Tactic.Widget.StringDiagram", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Widget.StringDiagram.Node.hPosSrc", "kind": "definition", "module": "Mathlib.Tactic.Widget.StringDiagram", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Tactic.Widget.StringDiagram.Strand.vPos", "kind": "definition", "module": "Mathlib.Tactic.Widget.StringDiagram", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.BicategoryLike.WhiskerRight.nodes", "kind": "definition", "module": "Mathlib.Tactic.Widget.StringDiagram", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.BicategoryLike.HorizontalComp.nodes", "kind": "definition", "module": "Mathlib.Tactic.Widget.StringDiagram", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.BicategoryLike.WhiskerLeft.nodes", "kind": "definition", "module": "Mathlib.Tactic.Widget.StringDiagram", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Tactic.Widget.StringDiagram.mkStringDiagram", "kind": "definition", "module": "Mathlib.Tactic.Widget.StringDiagram", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Tactic.Widget.StringDiagram.Kind", "kind": "inductive", "module": "Mathlib.Tactic.Widget.StringDiagram", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Tactic.Widget.StringDiagram.stringM?", "kind": "definition", "module": "Mathlib.Tactic.Widget.StringDiagram", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Widget.StringDiagram.mkEqHtml", "kind": "definition", "module": "Mathlib.Tactic.Widget.StringDiagram", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Widget.StringDiagram.stringEqM?", "kind": "definition", "module": "Mathlib.Tactic.Widget.StringDiagram", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Tactic.Widget.StringDiagram.stringMorOrEqM?", "kind": "definition", "module": "Mathlib.Tactic.Widget.StringDiagram", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "_private.Mathlib.Tactic.WithoutCDot.0.Lean.Elab.Term.withoutCDotContents", "kind": "definition", "module": "Mathlib.Tactic.WithoutCDot", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Tactic.Zify.natCast_eq", "kind": "theorem", "module": "Mathlib.Tactic.Zify", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Mathlib.Tactic.Zify.Nat.cast_sub_of_add_le", "kind": "theorem", "module": "Mathlib.Tactic.Zify", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Plausible.TotalFunction.zeroDefaultSupp", "kind": "definition", "module": "Mathlib.Testing.Plausible.Functions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Plausible.TotalFunction.applyFinsupp", "kind": "definition", "module": "Mathlib.Testing.Plausible.Functions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Plausible.InjectiveFunction", "kind": "inductive", "module": "Mathlib.Testing.Plausible.Functions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Plausible.instInhabitedInjectiveFunction", "kind": "instance", "module": "Mathlib.Testing.Plausible.Functions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Plausible.InjectiveFunction.apply", "kind": "definition", "module": "Mathlib.Testing.Plausible.Functions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Plausible.InjectiveFunction.instRepr", "kind": "instance", "module": "Mathlib.Testing.Plausible.Functions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Plausible.InjectiveFunction.List.applyId_cons", "kind": "theorem", "module": "Mathlib.Testing.Plausible.Functions", "is_tactic_proof": true, "tactics": ["simp", "split_ifs"], "tactic_count": 2}
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{"name": "alexandrovDiscrete_iff_isClosed", "kind": "theorem", "module": "Mathlib.Topology.AlexandrovDiscrete", "is_tactic_proof": true, "tactics": ["conv_lhs", "tactic", "simp_rw", "compl_sUnion,"], "tactic_count": 4}
{"name": "DiscreteTopology.toAlexandrovDiscrete", "kind": "instance", "module": "Mathlib.Topology.AlexandrovDiscrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finite.toAlexandrovDiscrete", "kind": "instance", "module": "Mathlib.Topology.AlexandrovDiscrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpen_sInter", "kind": "theorem", "module": "Mathlib.Topology.AlexandrovDiscrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpen_iInter", "kind": "theorem", "module": "Mathlib.Topology.AlexandrovDiscrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "isClosed_sUnion", "kind": "theorem", "module": "Mathlib.Topology.AlexandrovDiscrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "isClopen_iInter", "kind": "theorem", "module": "Mathlib.Topology.AlexandrovDiscrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "interior_sInter", "kind": "theorem", "module": "Mathlib.Topology.AlexandrovDiscrete", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "closure_iUnion", "kind": "theorem", "module": "Mathlib.Topology.AlexandrovDiscrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "closure_sUnion", "kind": "theorem", "module": "Mathlib.Topology.AlexandrovDiscrete", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Topology.IsInducing.alexandrovDiscrete", "kind": "theorem", "module": "Mathlib.Topology.AlexandrovDiscrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlexandrovDiscrete.sup", "kind": "theorem", "module": "Mathlib.Topology.AlexandrovDiscrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "alexandrovDiscrete_iSup", "kind": "theorem", "module": "Mathlib.Topology.AlexandrovDiscrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpen_nhdsKer", "kind": "theorem", "module": "Mathlib.Topology.AlexandrovDiscrete", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "nhdsKer_mem_nhdsSet", "kind": "theorem", "module": "Mathlib.Topology.AlexandrovDiscrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsKer_eq_iff_isOpen", "kind": "theorem", "module": "Mathlib.Topology.AlexandrovDiscrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsKer_subset_iff_isOpen", "kind": "theorem", "module": "Mathlib.Topology.AlexandrovDiscrete", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "nhdsKer_subset_iff", "kind": "theorem", "module": "Mathlib.Topology.AlexandrovDiscrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsKer_subset_iff_mem_nhdsSet", "kind": "theorem", "module": "Mathlib.Topology.AlexandrovDiscrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsKer_singleton_subset_iff_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.AlexandrovDiscrete", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "gc_nhdsKer_interior", "kind": "theorem", "module": "Mathlib.Topology.AlexandrovDiscrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "principal_nhdsKer", "kind": "theorem", "module": "Mathlib.Topology.AlexandrovDiscrete", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "principal_nhdsKer_singleton", "kind": "theorem", "module": "Mathlib.Topology.AlexandrovDiscrete", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "nhdsSet_basis_nhdsKer", "kind": "theorem", "module": "Mathlib.Topology.AlexandrovDiscrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhds_basis_nhdsKer_singleton", "kind": "theorem", "module": "Mathlib.Topology.AlexandrovDiscrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpen_iff_forall_specializes", "kind": "theorem", "module": "Mathlib.Topology.AlexandrovDiscrete", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "alexandrovDiscrete_iff_nhds", "kind": "theorem", "module": "Mathlib.Topology.AlexandrovDiscrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Sum.instAlexandrovDiscrete", "kind": "instance", "module": "Mathlib.Topology.AlexandrovDiscrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.instAlexandrovDiscrete", "kind": "instance", "module": "Mathlib.Topology.AlexandrovDiscrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instAlexandrovDiscrete", "kind": "instance", "module": "Mathlib.Topology.AlexandrovDiscrete", "is_tactic_proof": true, "tactics": ["simp_rw", "prod_principal_principal,"], "tactic_count": 2}
{"name": "Pi.instAlexandrovDiscreteOfFinite", "kind": "instance", "module": "Mathlib.Topology.AlexandrovDiscrete", "is_tactic_proof": true, "tactics": ["simp_rw", "forall_true_iff]"], "tactic_count": 2}
{"name": "AffineMap.continuous_linear_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Affine", "is_tactic_proof": true, "tactics": ["inhabit", "have", "ext", "simp", "rw", "simp"], "tactic_count": 6}
{"name": "AffineMap.continuous_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineMap.isOpenMap_linear_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Affine", "is_tactic_proof": true, "tactics": ["inhabit", "have", "ext", "simp", "rw", "simp"], "tactic_count": 6}
{"name": "AffineMap.lineMap_continuous_uncurry", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Affine", "is_tactic_proof": true, "tactics": ["simp", "fun_prop"], "tactic_count": 2}
{"name": "AffineMap.lineMap_continuous", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Affine", "is_tactic_proof": true, "tactics": ["fun_prop"], "tactic_count": 1}
{"name": "Filter.Tendsto.lineMap", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.midpoint", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.lineMap", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.lineMap", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Affine", "is_tactic_proof": true, "tactics": ["fun_prop"], "tactic_count": 1}
{"name": "ContinuousOn.lineMap", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Affine", "is_tactic_proof": true, "tactics": ["fun_prop"], "tactic_count": 1}
{"name": "Continuous.lineMap", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Affine", "is_tactic_proof": true, "tactics": ["fun_prop"], "tactic_count": 1}
{"name": "AffineMap.homothety_continuous", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Affine", "is_tactic_proof": true, "tactics": ["rw", "fun_prop"], "tactic_count": 2}
{"name": "eventually_homothety_mem_of_mem_interior", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Affine", "is_tactic_proof": true, "tactics": ["have", "filter_upwards", "interior_subset"], "tactic_count": 3}
{"name": "eventually_homothety_image_subset_of_finite_subset_interior", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Affine", "is_tactic_proof": false, "tactics": ["suffices", "simp_rw", "exact", "intro", "exact"], "tactic_count": 5}
{"name": "AffineMap.homothety_isOpenMap", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Affine", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "AffineSubspace.subtypeA", "kind": "definition", "module": "Mathlib.Topology.Algebra.AffineSubspace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.coe_subtypeA", "kind": "theorem", "module": "Mathlib.Topology.Algebra.AffineSubspace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.subtypeA_toAffineMap", "kind": "theorem", "module": "Mathlib.Topology.Algebra.AffineSubspace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.instIsTopologicalAddTorsorSubtypeMemSubmoduleDirection", "kind": "instance", "module": "Mathlib.Topology.Algebra.AffineSubspace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AffineSubspace.isClosed_direction_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.AffineSubspace", "is_tactic_proof": true, "tactics": ["rcases", "rw", "simp"], "tactic_count": 3}
{"name": "continuous_algebraMap", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": true, "tactics": ["rw", "fun_prop"], "tactic_count": 2}
{"name": "continuous_algebraMap_iff_smul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": ["refine", "have", "continuous_algebraMap", "simp", "exact"], "tactic_count": 5}
{"name": "continuousSMul_of_algebraMap", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.continuousSMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "algebraMapCLM", "kind": "definition", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "coe_algebraMapCLM", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toLinearMap_algebraMapCLM", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.toSpanSingleton_one_eq_algebraMapCLM", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "DiscreteTopology.instContinuousSMul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "term_→A[_]_", "kind": "definition", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Topology_Algebra_Algebra___macroRules_term_→A[_]__1", "kind": "definition", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Topology_Algebra_Algebra___unexpand_ContinuousAlgHom_1", "kind": "definition", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.instFunLike", "kind": "instance", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.instAlgHomClass", "kind": "instance", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.toAlgHom_eq_coe", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.coe_inj", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "ContinuousAlgHom.coe_mk", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.coe_mk'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.coe_coe", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.instContinuousMapClass", "kind": "instance", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.continuous", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.uniformContinuous", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.Simps.apply", "kind": "definition", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.Simps.coe", "kind": "definition", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.ext", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.copy", "kind": "definition", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.coe_copy", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.copy_eq", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.map_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.map_add", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.map_smul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.map_smul_of_tower", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.map_sum", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.ext_ring", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.ext_ring_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.eqOn_closure_adjoin", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.ext_on", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.toContinuousLinearMap", "kind": "definition", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.coe_toContinuousLinearMap", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.topologicalClosure", "kind": "definition", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.map_topologicalClosure_le", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.topologicalClosure_map_le", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.topologicalClosure_map", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.topologicalClosure_coe", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DenseRange.topologicalClosure_map_subalgebra", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": true, "tactics": ["rw", "simp", "exact"], "tactic_count": 3}
{"name": "ContinuousAlgHom.id", "kind": "definition", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.instOne", "kind": "instance", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.one_def", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.id_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.coe_id", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.coe_id'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.coe_eq_id", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ContinuousAlgHom.one_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.comp", "kind": "definition", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.coe_comp", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.coe_comp'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.comp_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.comp_id", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.id_comp", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.comp_assoc", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.instMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.mul_def", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.coe_mul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.mul_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.instMonoid", "kind": "instance", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.coe_pow", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.toAlgHomMonoidHom", "kind": "definition", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.prod", "kind": "definition", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.coe_prod", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.prod_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.instCompleteSpaceSubtypeMemSubalgebraEqualizerOfT2SpaceOfContinuousMapClass", "kind": "instance", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.fst", "kind": "definition", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.snd", "kind": "definition", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.coe_fst", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.coe_fst'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.coe_snd", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.coe_snd'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.fst_prod_snd", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.fst_comp_prod", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.snd_comp_prod", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.prodMap", "kind": "definition", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.coe_prodMap", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.coe_prodMap'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.prodEquiv", "kind": "definition", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.codRestrict", "kind": "definition", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.coe_codRestrict", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.coe_codRestrict_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.rangeRestrict", "kind": "definition", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.coe_rangeRestrict", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.valA", "kind": "definition", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.coe_valA", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.coe_valA'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.valA_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.range_valA", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.map_neg", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.map_sub", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.restrictScalars", "kind": "definition", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.coe_restrictScalars", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlgHom.coe_restrictScalars'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsTopologicalSemiringSubtypeMemSubalgebra", "kind": "instance", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.le_topologicalClosure", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "asymptoticCone_affineSubspace", "kind": "theorem", "module": "Mathlib.Topology.Algebra.AsymptoticCone", "is_tactic_proof": true, "tactics": ["have", "ext", "simp_rw", "frequently_map,"], "tactic_count": 4}
{"name": "asymptoticCone_univ", "kind": "theorem", "module": "Mathlib.Topology.Algebra.AsymptoticCone", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "asymptoticCone_closure", "kind": "theorem", "module": "Mathlib.Topology.Algebra.AsymptoticCone", "is_tactic_proof": true, "tactics": ["ext", "simp_rw"], "tactic_count": 2}
{"name": "isClosed_asymptoticCone", "kind": "theorem", "module": "Mathlib.Topology.Algebra.AsymptoticCone", "is_tactic_proof": true, "tactics": ["have", "rw", "intro", "simp_rw", "exact"], "tactic_count": 5}
{"name": "asymptoticCone_asymptoticCone", "kind": "theorem", "module": "Mathlib.Topology.Algebra.AsymptoticCone", "is_tactic_proof": true, "tactics": ["ext", "simp_rw"], "tactic_count": 2}
{"name": "StarConvex.smul_vadd_mem_of_isClosed_of_mem_asymptoticCone", "kind": "theorem", "module": "Mathlib.Topology.Algebra.AsymptoticCone", "is_tactic_proof": false, "tactics": ["refine", "isClosed_iff_frequently.mp", "tendsto_snd", "rw", "map_prod_eq_map₂,", "apply", "filter_upwards", "change", "apply", "simp_rw", "exact"], "tactic_count": 11}
{"name": "Convex.smul_vadd_mem_of_isClosed_of_mem_asymptoticCone", "kind": "theorem", "module": "Mathlib.Topology.Algebra.AsymptoticCone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Convex.asymptoticCone", "kind": "theorem", "module": "Mathlib.Topology.Algebra.AsymptoticCone", "is_tactic_proof": true, "tactics": ["wlog", "rw", "rcases", "rw", "intro", "rw", "refine", "tendsto_id.atTop_smul_const_tendsto_asymptoticNhds", "filter_upwards", "simp_rw", "have", "have", "apply", "rw", "exists", "module"], "tactic_count": 16}
{"name": "Convex.smul_vadd_mem_of_mem_nhds_of_mem_asymptoticCone", "kind": "theorem", "module": "Mathlib.Topology.Algebra.AsymptoticCone", "is_tactic_proof": false, "tactics": ["rw", "map_prod_eq_map₂,", "refine", "have", "filter_upwards", "apply", "simp_rw", "rw", "exact"], "tactic_count": 9}
{"name": "instCoeSortProfiniteGrpType", "kind": "instance", "module": "Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProfiniteGrp.of", "kind": "abbrev", "module": "Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProfiniteGrp.coe_of", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCategoryProfiniteGrp", "kind": "instance", "module": "Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instConcreteCategoryProfiniteGrpContinuousMonoidHomCarrierToTopTotallyDisconnectedSpaceToProfinite", "kind": "instance", "module": "Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProfiniteGrp.Hom.hom", "kind": "abbrev", "module": "Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProfiniteGrp.ofHom", "kind": "abbrev", "module": "Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProfiniteGrp.instCoeFunHomForallCarrierToTopTotallyDisconnectedSpaceToProfinite", "kind": "instance", "module": "Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProfiniteGrp.hom_id", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProfiniteGrp.id_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ProfiniteGrp.hom_comp", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProfiniteGrp.comp_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ProfiniteGrp.hom_ext", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProfiniteGrp.hom_ofHom", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProfiniteGrp.ofHom_hom", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProfiniteGrp.ofHom_id", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProfiniteGrp.ofHom_comp", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProfiniteGrp.ofHom_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProfiniteGrp.inv_hom_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ProfiniteGrp.hom_inv_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ProfiniteGrp.coe_id", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProfiniteGrp.coe_comp", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProfiniteGrp.ofProfinite", "kind": "abbrev", "module": "Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProfiniteGrp.pi", "kind": "definition", "module": "Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProfiniteGrp.ofFiniteGrp", "kind": "definition", "module": "Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProfiniteGrp.instHasForget₂FiniteGrp", "kind": "instance", "module": "Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProfiniteGrp.instHasForget₂GrpCat", "kind": "instance", "module": "Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProfiniteGrp.ofClosedSubgroup", "kind": "definition", "module": "Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProfiniteGrp.ofContinuousMulEquiv", "kind": "definition", "module": "Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProfiniteGrp.ContinuousMulEquiv.toProfiniteGrpIso", "kind": "definition", "module": "Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProfiniteGrp.instHasForget₂Profinite", "kind": "instance", "module": "Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProfiniteGrp.instFaithfulProfiniteForget₂", "kind": "instance", "module": "Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProfiniteGrp.instReflectsIsomorphismsProfiniteForget₂", "kind": "instance", "module": "Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProfiniteGrp.instReflectsIsomorphismsForget", "kind": "instance", "module": "Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProfiniteGrp.limitConePtAux", "kind": "definition", "module": "Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProfiniteGrp.instGroupCarrierToTopTotallyDisconnectedSpacePtProfiniteLimitConeCompForget₂", "kind": "instance", "module": "Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProfiniteGrp.instIsTopologicalGroupCarrierToTopTotallyDisconnectedSpacePtProfiniteLimitConeCompForget₂", "kind": "instance", "module": "Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProfiniteGrp.limitCone", "kind": "abbrev", "module": "Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProfiniteGrp.limitConeIsLimit", "kind": "definition", "module": "Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProfiniteGrp.instHasLimit", "kind": "instance", "module": "Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProfiniteGrp.instPreservesLimitsProfiniteForget₂", "kind": "instance", "module": "Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProfiniteGrp.instCompactSpaceSubtypeForallCarrierToTopTotallyDisconnectedSpaceToProfiniteObjMemSubgroupLimitConePtAux", "kind": "instance", "module": "Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProfiniteGrp.limit", "kind": "abbrev", "module": "Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProfiniteGrp.limit_ext", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProfiniteGrp.limit_one_val", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProfiniteGrp.limit_mul_val", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProfiniteGrp.instSmallCategoryOpenNormalSubgroupCarrierToTopTotallyDisconnectedSpaceToProfinite", "kind": "instance", "module": "Mathlib.Topology.Algebra.Category.ProfiniteGrp.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProfiniteGrp.toFiniteQuotientFunctor", "kind": "definition", "module": "Mathlib.Topology.Algebra.Category.ProfiniteGrp.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProfiniteGrp.toLimit_fun", "kind": "definition", "module": "Mathlib.Topology.Algebra.Category.ProfiniteGrp.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProfiniteGrp.toLimit_fun_continuous", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Category.ProfiniteGrp.Limits", "is_tactic_proof": true, "tactics": ["apply", "intro", "dsimp", "apply", "intro", "rw", "refine", "convert", "ext", "simp", "nth_rw", "exact"], "tactic_count": 12}
{"name": "ProfiniteGrp.toLimit", "kind": "definition", "module": "Mathlib.Topology.Algebra.Category.ProfiniteGrp.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProfiniteGrp.denseRange_toLimit", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Category.ProfiniteGrp.Limits", "is_tactic_proof": true, "tactics": ["apply", "rintro", "simp_rw", "rcases", "let", "have", "have", "rw", "exact", "let", "rcases", "use", "refine", "rw", "apply", "intro", "let", "rw", "change", "rw", "exact"], "tactic_count": 21}
{"name": "ProfiniteGrp.toLimit_surjective", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Category.ProfiniteGrp.Limits", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "ProfiniteGrp.toLimit_injective", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Category.ProfiniteGrp.Limits", "is_tactic_proof": true, "tactics": ["change", "rw", "intro", "by_contra", "rcases", "exist_openNormalSubgroup_sub_open_nhds_of_one", "exact"], "tactic_count": 7}
{"name": "ProfiniteGrp.continuousMulEquivLimittoFiniteQuotientFunctor", "kind": "definition", "module": "Mathlib.Topology.Algebra.Category.ProfiniteGrp.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProfiniteGrp.isIso_toLimit", "kind": "instance", "module": "Mathlib.Topology.Algebra.Category.ProfiniteGrp.Limits", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ProfiniteGrp.isoLimittoFiniteQuotientFunctor", "kind": "definition", "module": "Mathlib.Topology.Algebra.Category.ProfiniteGrp.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsTopologicalGroup.exist_openNormalSubgroup_sub_clopen_nhds_of_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ClopenNhdofOne", "is_tactic_proof": true, "tactics": ["rcases", "have", "use", "toSubgroup", "isOpen", "exact"], "tactic_count": 6}
{"name": "ProfiniteGrp.exist_openNormalSubgroup_sub_open_nhds_of_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ClopenNhdofOne", "is_tactic_proof": false, "tactics": ["rcases", "rcases", "exact"], "tactic_count": 3}
{"name": "instContinuousConstSMulULift", "kind": "instance", "module": "Mathlib.Topology.Algebra.ConstMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.const_smul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ConstMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.const_smul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ConstMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.const_smul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ConstMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.const_smul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ConstMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.const_smul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ConstMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousConstSMul.op", "kind": "instance", "module": "Mathlib.Topology.Algebra.ConstMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.continuousConstSMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.ConstMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instContinuousConstSMulOrderDual", "kind": "instance", "module": "Mathlib.Topology.Algebra.ConstMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.continuousConstSMul'", "kind": "instance", "module": "Mathlib.Topology.Algebra.ConstMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.continuousConstSMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.ConstMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instContinuousConstSMulForall", "kind": "instance", "module": "Mathlib.Topology.Algebra.ConstMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.smul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ConstMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Specializes.const_smul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ConstMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Inseparable.const_smul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ConstMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsInducing.continuousConstSMul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ConstMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smul_closure_subset", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ConstMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "set_smul_closure_subset", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ConstMulAction", "is_tactic_proof": true, "tactics": ["simp", "exact", "iUnion₂_subset"], "tactic_count": 3}
{"name": "isClosed_setOf_map_smul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ConstMulAction", "is_tactic_proof": true, "tactics": ["simp", "exact", "isClosed_iInter", "isClosed_iInter"], "tactic_count": 4}
{"name": "Units.continuousConstSMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.ConstMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smul_closure_orbit_subset", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ConstMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_const_smul_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ConstMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousWithinAt_const_smul_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ConstMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousOn_const_smul_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ConstMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousAt_const_smul_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ConstMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_const_smul_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ConstMulAction", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Homeomorph.smul", "kind": "definition", "module": "Mathlib.Topology.Algebra.ConstMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isHomeomorph_smul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ConstMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpenMap_smul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ConstMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.smul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ConstMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosedMap_smul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ConstMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.smul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ConstMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "closure_smul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ConstMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dense.smul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ConstMulAction", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "interior_smul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ConstMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.smul_left", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ConstMulAction", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "subset_interior_smul_right", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ConstMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smul_mem_nhds_smul_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ConstMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smul_mem_nhds_self", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ConstMulAction", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MulAction.IsPretransitive.t1Space_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ConstMulAction", "is_tactic_proof": true, "tactics": ["refine", "rcases", "rw", "exact"], "tactic_count": 4}
{"name": "MulAction.IsPretransitive.discreteTopology_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ConstMulAction", "is_tactic_proof": true, "tactics": ["rw", "refine", "rcases", "rw", "exact"], "tactic_count": 5}
{"name": "tendsto_const_smul_iff₀", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ConstMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousWithinAt_const_smul_iff₀", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ConstMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ContinuousAffineEquiv.coe_toEquiv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineEquiv.Simps.apply", "kind": "definition", "module": "Mathlib.Topology.Algebra.ContinuousAffineEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineEquiv.Simps.symm_apply", "kind": "definition", "module": "Mathlib.Topology.Algebra.ContinuousAffineEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineEquiv.ext", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineEquiv.continuous", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineEquiv.toContinuousAffineMap", "kind": "definition", "module": "Mathlib.Topology.Algebra.ContinuousAffineEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineEquiv.ContinuousAffineMap.coe", "kind": "instance", "module": "Mathlib.Topology.Algebra.ContinuousAffineEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineEquiv.coe_toContinuousAffineMap", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineEquiv.toContinuousAffineMap_injective", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineEquiv", "is_tactic_proof": true, "tactics": ["intro", "ext", "simp_rw"], "tactic_count": 3}
{"name": "ContinuousAffineEquiv.toContinuousAffineMap_toAffineMap", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineEquiv.toContinuousAffineMap_toContinuousMap", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineEquiv.refl", "kind": "definition", "module": "Mathlib.Topology.Algebra.ContinuousAffineEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineEquiv.coe_refl", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineEquiv.refl_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineEquiv.toAffineEquiv_refl", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineEquiv.toEquiv_refl", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineEquiv.symm", "kind": "definition", "module": "Mathlib.Topology.Algebra.ContinuousAffineEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineEquiv.toAffineEquiv_symm", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineEquiv.coe_symm_toAffineEquiv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineEquiv.toEquiv_symm", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineEquiv.coe_symm_toEquiv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineEquiv.apply_symm_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineEquiv.symm_apply_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineEquiv.apply_eq_iff_eq_symm_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineEquiv.apply_eq_iff_eq", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineEquiv.symm_symm", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineEquiv.symm_bijective", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineEquiv.symm_symm_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineEquiv.symm_apply_eq", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineEquiv.eq_symm_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineEquiv.image_symm", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineEquiv.preimage_symm", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineEquiv.bijective", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineEquiv.surjective", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineEquiv.injective", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineEquiv.image_eq_preimage_symm", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineEquiv.image_symm_eq_preimage", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineEquiv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ContinuousAffineEquiv.image_preimage", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineEquiv.preimage_image", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineEquiv.symm_image_image", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineEquiv.image_symm_image", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineEquiv.refl_symm", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineEquiv.symm_refl", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineEquiv.trans", "kind": "definition", "module": "Mathlib.Topology.Algebra.ContinuousAffineEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineEquiv.coe_trans", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineEquiv.trans_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineEquiv.trans_assoc", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineEquiv.trans_refl", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineEquiv.refl_trans", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineEquiv.self_trans_symm", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineEquiv.symm_trans_self", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineEquiv.trans_toContinuousAffineMap", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.toContinuousAffineEquiv", "kind": "definition", "module": "Mathlib.Topology.Algebra.ContinuousAffineEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.coe_toContinuousAffineEquiv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.toContinuousAffineEquiv_toContinuousAffineMap", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineEquiv.constVAdd", "kind": "definition", "module": "Mathlib.Topology.Algebra.ContinuousAffineEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineEquiv.constVAdd_coe", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineEquiv.prodCongr", "kind": "definition", "module": "Mathlib.Topology.Algebra.ContinuousAffineEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineEquiv.prodCongr_symm", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineEquiv.prodCongr_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineEquiv.prodCongr_toContinuousAffineMap", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineEquiv.prodComm", "kind": "definition", "module": "Mathlib.Topology.Algebra.ContinuousAffineEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineEquiv.prodComm_symm", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "term_→ᴬ[_]_", "kind": "definition", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Topology_Algebra_ContinuousAffineMap___macroRules_term_→ᴬ[_]__1", "kind": "definition", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Topology_Algebra_ContinuousAffineMap___unexpand_ContinuousAffineMap_1", "kind": "definition", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineMap.instCoeAffineMap", "kind": "instance", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineMap.toAffineMap_injective", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": true, "tactics": ["cases", "cases", "congr"], "tactic_count": 3}
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{"name": "ContinuousAffineMap.instContinuousMapClass", "kind": "instance", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineMap.toFun_eq_coe", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ContinuousAffineMap.ext", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineMap.congr_fun", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineMap.toContinuousMap", "kind": "definition", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineMap.instCoeHeadContinuousMap", "kind": "instance", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineMap.toContinuousMap_coe", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineMap.coe_toAffineMap", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ContinuousAffineMap.const", "kind": "definition", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineMap.coe_const", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineMap.instInhabited", "kind": "instance", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineMap.id", "kind": "definition", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineMap.coe_id", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ContinuousAffineMap.coe_comp", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineMap.comp_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineMap.comp_id", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ContinuousAffineMap.apply_lineMap", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "ContinuousAffineMap.lineMap_toAffineMap", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineMap.coe_lineMap_eq", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineMap.apply_lineMap'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
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{"name": "ContinuousAffineMap.coe_contLinear", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineMap.coe_contLinear_eq_linear", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineMap.coe_mk_contLinear_eq_linear", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineMap.coe_linear_eq_coe_contLinear", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineMap.comp_contLinear", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ContinuousAffineMap.const_contLinear", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineMap.contLinear_eq_zero_iff_exists_const", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": ["have", "refine", "rw", "rw", "have", "intro", "refine", "rw", "rw", "simp_rw", "exact"], "tactic_count": 11}
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{"name": "ContinuousAffineMap.coe_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ContinuousAffineMap.coe_smul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ContinuousAffineMap.instIsCentralScalar", "kind": "instance", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineMap.instMulAction", "kind": "instance", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineMap.smul_contLinear", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineMap.instAdd", "kind": "instance", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineMap.coe_add", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineMap.add_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineMap.instSub", "kind": "instance", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineMap.coe_sub", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineMap.sub_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineMap.instNeg", "kind": "instance", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineMap.coe_neg", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineMap.neg_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineMap.instAddCommGroup", "kind": "instance", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineMap.instDistribMulActionOfSMulCommClassOfContinuousConstSMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineMap.instModuleOfSMulCommClassOfContinuousConstSMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineMap.zero_contLinear", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineMap.add_contLinear", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineMap.sub_contLinear", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineMap.neg_contLinear", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineMap.instAddTorsor", "kind": "instance", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineMap.vadd_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineMap.vsub_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineMap.vadd_toAffineMap", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineMap.vsub_toAffineMap", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineMap.lineMap_apply'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousAffineMap.vadd_contLinear", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineMap.vsub_contLinear", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineMap.prod", "kind": "definition", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineMap.coe_prod", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineMap.prod_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineMap.prodMap", "kind": "definition", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineMap.coe_prodMap", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineMap.prodMap_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineMap.prod_contLinear", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineMap.prodMap_contLinear", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.toContinuousAffineMap", "kind": "definition", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.coe_toContinuousAffineMap", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.toContinuousAffineMap_map_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousLinearMap.toContinuousAffineMap_contLinear", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAffineMap.decomp", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousAffineMap", "is_tactic_proof": true, "tactics": ["rcases", "rw"], "tactic_count": 2}
{"name": "ContinuousMonoidHom.term_→ₜ+_", "kind": "definition", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMonoidHom._aux_Mathlib_Topology_Algebra_ContinuousMonoidHom___macroRules_ContinuousMonoidHom_term_→ₜ+__1", "kind": "definition", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ContinuousMonoidHom.term_→ₜ*_", "kind": "definition", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMonoidHom._aux_Mathlib_Topology_Algebra_ContinuousMonoidHom___macroRules_ContinuousMonoidHom_term_→ₜ*__1", "kind": "definition", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ContinuousMonoidHom.instFunLike", "kind": "instance", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMonoidHom.instMonoidHomClass", "kind": "instance", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMonoidHom.instContinuousMapClass", "kind": "instance", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMonoidHom.coe_toMonoidHom", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMonoidHom.coe_toContinuousMap", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMonoidHom.toContinuousMonoidHom", "kind": "definition", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMonoidHom.instCoeOutOfMonoidHomClassOfContinuousMapClass", "kind": "instance", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMonoidHom.coe_coe", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMonoidHom.toMonoidHom_toContinuousMonoidHom", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMonoidHom.toContinuousMap_toContinuousMonoidHom", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMonoidHom.ext", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMonoidHom.toContinuousMap_injective", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMonoidHom.toMonoidHom_injective", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMonoidHom.comp", "kind": "definition", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ContinuousMonoidHom.prod", "kind": "definition", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMonoidHom.prodMap", "kind": "definition", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ContinuousMonoidHom.coe_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMonoidHom.instInhabited", "kind": "instance", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMonoidHom.id", "kind": "definition", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMonoidHom.coe_id", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMonoidHom.fst", "kind": "definition", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMonoidHom.snd", "kind": "definition", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMonoidHom.inl", "kind": "definition", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMonoidHom.inr", "kind": "definition", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMonoidHom.diag", "kind": "definition", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMonoidHom.swap", "kind": "definition", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMonoidHom.mul", "kind": "definition", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMonoidHom.instCommMonoid", "kind": "instance", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMonoidHom.coprod", "kind": "definition", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMonoidHom.inv", "kind": "definition", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMonoidHom.instCommGroup", "kind": "instance", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMonoidHom.ofClass", "kind": "definition", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "term_≃ₜ*_", "kind": "definition", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Topology_Algebra_ContinuousMonoidHom___macroRules_term_≃ₜ*__1", "kind": "definition", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Topology_Algebra_ContinuousMonoidHom___unexpand_ContinuousMulEquiv_1", "kind": "definition", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "term_≃ₜ+_", "kind": "definition", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Topology_Algebra_ContinuousMonoidHom___macroRules_term_≃ₜ+__1", "kind": "definition", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Topology_Algebra_ContinuousMonoidHom___unexpand_ContinuousAddEquiv_1", "kind": "definition", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMulEquiv.instEquivLike", "kind": "instance", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMulEquiv.instMulEquivClass", "kind": "instance", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMulEquiv.instHomeomorphClass", "kind": "instance", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMulEquiv.ext", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMulEquiv.coe_mk", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMulEquiv.toEquiv_eq_coe", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMulEquiv.toMulEquiv_eq_coe", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMulEquiv.toHomeomorph_eq_coe", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMulEquiv.mk'", "kind": "definition", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMulEquiv.coe_mk'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMulEquiv.bijective", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMulEquiv.injective", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMulEquiv.surjective", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMulEquiv.apply_eq_iff_eq", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMulEquiv.refl", "kind": "definition", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMulEquiv.instInhabited", "kind": "instance", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMulEquiv.coe_refl", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMulEquiv.refl_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMulEquiv.symm", "kind": "definition", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMulEquiv.Simps.symm_apply", "kind": "definition", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMulEquiv.invFun_eq_symm", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMulEquiv.coe_toHomeomorph_symm", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMulEquiv.equivLike_inv_eq_symm", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMulEquiv.symm_symm", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMulEquiv.symm_bijective", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMulEquiv.apply_symm_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMulEquiv.symm_apply_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMulEquiv.symm_comp_self", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMulEquiv.self_comp_symm", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMulEquiv.apply_eq_iff_symm_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMulEquiv.symm_apply_eq", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMulEquiv.eq_symm_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMulEquiv.eq_comp_symm", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMulEquiv.comp_symm_eq", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMulEquiv.eq_symm_comp", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMulEquiv.symm_comp_eq", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMulEquiv.trans", "kind": "definition", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMulEquiv.coe_trans", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMulEquiv.trans_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMulEquiv.symm_trans_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMulEquiv.symm_trans_self", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMulEquiv.self_trans_symm", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMulEquiv.ofUnique", "kind": "definition", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMulEquiv.instUnique", "kind": "instance", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.toContinuousMulEquiv", "kind": "definition", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.toMulEquiv_toContinuousMulEquiv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.toHomeomorph_toContinuousMulEquiv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulEquiv.symm_toContinuousMulEquiv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.ContinuousMonoidHom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "equicontinuous_of_equicontinuousAt_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Equicontinuity", "is_tactic_proof": true, "tactics": ["rw", "rw", "let", "map_one", "map_mul", "exact"], "tactic_count": 6}
{"name": "uniformEquicontinuous_of_equicontinuousAt_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Equicontinuity", "is_tactic_proof": true, "tactics": ["rw", "rw", "let", "map_one", "map_mul", "exact"], "tactic_count": 6}
{"name": "Filter.tendsto_cocompact_mul_left₀", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_cocompact_mul_right₀", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DivisionRing.finite_of_compactSpace_of_t2Space", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Field", "is_tactic_proof": true, "tactics": ["suffices", "rw", "exact"], "tactic_count": 3}
{"name": "Subfield.topologicalClosure", "kind": "definition", "module": "Mathlib.Topology.Algebra.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.le_topologicalClosure", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.isClosed_topologicalClosure", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.topologicalClosure_minimal", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nonneg.unitsHomeomorphPos", "kind": "definition", "module": "Mathlib.Topology.Algebra.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "affineHomeomorph", "kind": "definition", "module": "Mathlib.Topology.Algebra.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "affineHomeomorph_image_Icc", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Field", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "affineHomeomorph_image_Ico", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Field", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "affineHomeomorph_image_Ioc", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Field", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "affineHomeomorph_image_Ioo", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Field", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsLocalMin.inv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Field", "is_tactic_proof": true, "tactics": ["filter_upwards"], "tactic_count": 1}
{"name": "IsPreconnected.eq_one_or_eq_neg_one_of_sq_eq", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Field", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "IsPreconnected.eq_or_eq_neg_of_sq_eq", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Field", "is_tactic_proof": false, "tactics": ["have", "simpa", "simpa"], "tactic_count": 3}
{"name": "IsPreconnected.eq_of_sq_eq", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.continuousSMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "groupFilterBasisOfComm", "kind": "definition", "module": "Mathlib.Topology.Algebra.FilterBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupFilterBasis.instMembershipSet", "kind": "instance", "module": "Mathlib.Topology.Algebra.FilterBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupFilterBasis.one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.FilterBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupFilterBasis.mul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.FilterBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupFilterBasis.inv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.FilterBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupFilterBasis.conj", "kind": "theorem", "module": "Mathlib.Topology.Algebra.FilterBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupFilterBasis.instInhabited", "kind": "instance", "module": "Mathlib.Topology.Algebra.FilterBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupFilterBasis.subset_mul_self", "kind": "theorem", "module": "Mathlib.Topology.Algebra.FilterBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupFilterBasis.N", "kind": "definition", "module": "Mathlib.Topology.Algebra.FilterBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupFilterBasis.N_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.FilterBasis", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "GroupFilterBasis.hasBasis", "kind": "theorem", "module": "Mathlib.Topology.Algebra.FilterBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupFilterBasis.topology", "kind": "definition", "module": "Mathlib.Topology.Algebra.FilterBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupFilterBasis.nhds_eq", "kind": "theorem", "module": "Mathlib.Topology.Algebra.FilterBasis", "is_tactic_proof": true, "tactics": ["apply", "intro", "exact", "intro", "rcases", "filter_upwards", "rintro", "calc"], "tactic_count": 8}
{"name": "GroupFilterBasis.nhds_one_eq", "kind": "theorem", "module": "Mathlib.Topology.Algebra.FilterBasis", "is_tactic_proof": true, "tactics": ["rw", "simp", "exact"], "tactic_count": 3}
{"name": "GroupFilterBasis.nhds_hasBasis", "kind": "theorem", "module": "Mathlib.Topology.Algebra.FilterBasis", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "GroupFilterBasis.nhds_one_hasBasis", "kind": "theorem", "module": "Mathlib.Topology.Algebra.FilterBasis", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "GroupFilterBasis.mem_nhds_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.FilterBasis", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "GroupFilterBasis.isTopologicalGroup", "kind": "instance", "module": "Mathlib.Topology.Algebra.FilterBasis", "is_tactic_proof": true, "tactics": ["letI", "have", "have", "refine", "rw", "suffices", "intro", "rcases", "refine", "intro", "exact", "rw", "intro", "simpa", "intro", "rw", "rfl", "intro", "rw", "intro", "exact"], "tactic_count": 21}
{"name": "GroupFilterBasis.t2Space_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.FilterBasis", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "GroupFilterBasis.t2Space_iff_sInter_subset", "kind": "theorem", "module": "Mathlib.Topology.Algebra.FilterBasis", "is_tactic_proof": true, "tactics": ["rw", "rintro", "simpa"], "tactic_count": 3}
{"name": "RingFilterBasis.instMembershipSet", "kind": "instance", "module": "Mathlib.Topology.Algebra.FilterBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingFilterBasis.mul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.FilterBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingFilterBasis.mul_left", "kind": "theorem", "module": "Mathlib.Topology.Algebra.FilterBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingFilterBasis.mul_right", "kind": "theorem", "module": "Mathlib.Topology.Algebra.FilterBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingFilterBasis.topology", "kind": "definition", "module": "Mathlib.Topology.Algebra.FilterBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingFilterBasis.isTopologicalRing", "kind": "instance", "module": "Mathlib.Topology.Algebra.FilterBasis", "is_tactic_proof": true, "tactics": ["let", "letI", "have", "have", "haveI", "apply", "rw", "suffices", "intro", "rcases", "refine", "intro", "exact", "intro", "rw", "intro", "simpa", "intro", "rw", "intro", "simpa"], "tactic_count": 21}
{"name": "ModuleFilterBasis.GroupFilterBasis.hasMem", "kind": "instance", "module": "Mathlib.Topology.Algebra.FilterBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleFilterBasis.smul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.FilterBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleFilterBasis.smul_left", "kind": "theorem", "module": "Mathlib.Topology.Algebra.FilterBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleFilterBasis.smul_right", "kind": "theorem", "module": "Mathlib.Topology.Algebra.FilterBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleFilterBasis.instInhabitedOfDiscreteTopology", "kind": "instance", "module": "Mathlib.Topology.Algebra.FilterBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleFilterBasis.topology", "kind": "definition", "module": "Mathlib.Topology.Algebra.FilterBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleFilterBasis.topology'", "kind": "definition", "module": "Mathlib.Topology.Algebra.FilterBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousSMul.of_basis_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.FilterBasis", "is_tactic_proof": true, "tactics": ["apply", "rw", "intro", "rcases", "apply", "rintro", "exact", "intro", "rw", "intro", "exact", "intro", "rw", "intro", "rcases", "exact"], "tactic_count": 16}
{"name": "ModuleFilterBasis.continuousSMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.FilterBasis", "is_tactic_proof": true, "tactics": ["let", "let", "have", "exact"], "tactic_count": 4}
{"name": "ModuleFilterBasis.ofBases", "kind": "definition", "module": "Mathlib.Topology.Algebra.FilterBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instZeroCompletion", "kind": "instance", "module": "Mathlib.Topology.Algebra.GroupCompletion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instNegCompletion", "kind": "instance", "module": "Mathlib.Topology.Algebra.GroupCompletion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instAddCompletion", "kind": "instance", "module": "Mathlib.Topology.Algebra.GroupCompletion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instSubCompletion", "kind": "instance", "module": "Mathlib.Topology.Algebra.GroupCompletion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.coe_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.GroupCompletion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.coe_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.GroupCompletion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.instMulActionWithZeroOfUniformContinuousConstSMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.GroupCompletion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.coe_neg", "kind": "theorem", "module": "Mathlib.Topology.Algebra.GroupCompletion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.coe_sub", "kind": "theorem", "module": "Mathlib.Topology.Algebra.GroupCompletion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.coe_add", "kind": "theorem", "module": "Mathlib.Topology.Algebra.GroupCompletion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.instAddMonoid", "kind": "instance", "module": "Mathlib.Topology.Algebra.GroupCompletion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.instSubNegMonoid", "kind": "instance", "module": "Mathlib.Topology.Algebra.GroupCompletion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.addGroup", "kind": "instance", "module": "Mathlib.Topology.Algebra.GroupCompletion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.isUniformAddGroup", "kind": "instance", "module": "Mathlib.Topology.Algebra.GroupCompletion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.instDistribMulActionOfUniformContinuousConstSMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.GroupCompletion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.toCompl", "kind": "definition", "module": "Mathlib.Topology.Algebra.GroupCompletion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.continuous_toCompl", "kind": "theorem", "module": "Mathlib.Topology.Algebra.GroupCompletion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.isDenseInducing_toCompl", "kind": "theorem", "module": "Mathlib.Topology.Algebra.GroupCompletion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.instAddCommGroup", "kind": "instance", "module": "Mathlib.Topology.Algebra.GroupCompletion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.instModule", "kind": "instance", "module": "Mathlib.Topology.Algebra.GroupCompletion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.extension", "kind": "definition", "module": "Mathlib.Topology.Algebra.GroupCompletion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.extension_coe", "kind": "theorem", "module": "Mathlib.Topology.Algebra.GroupCompletion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.continuous_extension", "kind": "theorem", "module": "Mathlib.Topology.Algebra.GroupCompletion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.completion", "kind": "definition", "module": "Mathlib.Topology.Algebra.GroupCompletion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.continuous_completion", "kind": "theorem", "module": "Mathlib.Topology.Algebra.GroupCompletion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.completion_coe", "kind": "theorem", "module": "Mathlib.Topology.Algebra.GroupCompletion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.completion_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.GroupCompletion", "is_tactic_proof": true, "tactics": ["ext", "refine", "apply", "exact", "simp"], "tactic_count": 5}
{"name": "AddMonoidHom.completion_add", "kind": "theorem", "module": "Mathlib.Topology.Algebra.GroupCompletion", "is_tactic_proof": true, "tactics": ["have", "ext", "refine", "exact", "isClosed_eq", "simp"], "tactic_count": 6}
{"name": "Filter.Tendsto.div_const", "kind": "theorem", "module": "Mathlib.Topology.Algebra.GroupWithZero", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ContinuousAt.div_const", "kind": "theorem", "module": "Mathlib.Topology.Algebra.GroupWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.div_const", "kind": "theorem", "module": "Mathlib.Topology.Algebra.GroupWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.div_const", "kind": "theorem", "module": "Mathlib.Topology.Algebra.GroupWithZero", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Continuous.div_const", "kind": "theorem", "module": "Mathlib.Topology.Algebra.GroupWithZero", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "tendsto_inv₀", "kind": "theorem", "module": "Mathlib.Topology.Algebra.GroupWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousOn_inv₀", "kind": "theorem", "module": "Mathlib.Topology.Algebra.GroupWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.inv₀", "kind": "theorem", "module": "Mathlib.Topology.Algebra.GroupWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.inv₀", "kind": "theorem", "module": "Mathlib.Topology.Algebra.GroupWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.inv₀", "kind": "theorem", "module": "Mathlib.Topology.Algebra.GroupWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.inv₀", "kind": "theorem", "module": "Mathlib.Topology.Algebra.GroupWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.inv₀", "kind": "theorem", "module": "Mathlib.Topology.Algebra.GroupWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.isEmbedding_val₀", "kind": "theorem", "module": "Mathlib.Topology.Algebra.GroupWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitsHomeomorphNeZero", "kind": "definition", "module": "Mathlib.Topology.Algebra.GroupWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.inv₀", "kind": "definition", "module": "Mathlib.Topology.Algebra.GroupWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhds_inv₀", "kind": "theorem", "module": "Mathlib.Topology.Algebra.GroupWithZero", "is_tactic_proof": true, "tactics": ["refine", "simpa"], "tactic_count": 2}
{"name": "tendsto_inv_iff₀", "kind": "theorem", "module": "Mathlib.Topology.Algebra.GroupWithZero", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.Tendsto.div", "kind": "theorem", "module": "Mathlib.Topology.Algebra.GroupWithZero", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Filter.tendsto_mul_iff_of_ne_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.GroupWithZero", "is_tactic_proof": true, "tactics": ["refine", "rw", "refine", "exact"], "tactic_count": 4}
{"name": "ContinuousWithinAt.div", "kind": "theorem", "module": "Mathlib.Topology.Algebra.GroupWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.div", "kind": "theorem", "module": "Mathlib.Topology.Algebra.GroupWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.div", "kind": "theorem", "module": "Mathlib.Topology.Algebra.GroupWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.div", "kind": "theorem", "module": "Mathlib.Topology.Algebra.GroupWithZero", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "continuousOn_div", "kind": "theorem", "module": "Mathlib.Topology.Algebra.GroupWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.div₀", "kind": "theorem", "module": "Mathlib.Topology.Algebra.GroupWithZero", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ContinuousAt.div₀", "kind": "theorem", "module": "Mathlib.Topology.Algebra.GroupWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.div₀", "kind": "theorem", "module": "Mathlib.Topology.Algebra.GroupWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.comp_div_cases", "kind": "theorem", "module": "Mathlib.Topology.Algebra.GroupWithZero", "is_tactic_proof": true, "tactics": ["change", "by_cases", "rw", "simp_rw", "exact", "fun_prop"], "tactic_count": 6}
{"name": "Continuous.comp_div_cases", "kind": "theorem", "module": "Mathlib.Topology.Algebra.GroupWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.mulLeft₀", "kind": "definition", "module": "Mathlib.Topology.Algebra.GroupWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.mulRight₀", "kind": "definition", "module": "Mathlib.Topology.Algebra.GroupWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.coe_mulLeft₀", "kind": "theorem", "module": "Mathlib.Topology.Algebra.GroupWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.mulLeft₀_symm_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.GroupWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.coe_mulRight₀", "kind": "theorem", "module": "Mathlib.Topology.Algebra.GroupWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.mulRight₀_symm_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.GroupWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "map_mul_left_nhds₀", "kind": "theorem", "module": "Mathlib.Topology.Algebra.GroupWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "map_mul_left_nhds_one₀", "kind": "theorem", "module": "Mathlib.Topology.Algebra.GroupWithZero", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "map_mul_right_nhds₀", "kind": "theorem", "module": "Mathlib.Topology.Algebra.GroupWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "map_mul_right_nhds_one₀", "kind": "theorem", "module": "Mathlib.Topology.Algebra.GroupWithZero", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "nhds_translation_mul_inv₀", "kind": "theorem", "module": "Mathlib.Topology.Algebra.GroupWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousInv₀.of_nhds_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.GroupWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousAt_zpow₀", "kind": "theorem", "module": "Mathlib.Topology.Algebra.GroupWithZero", "is_tactic_proof": true, "tactics": ["rcases", "simpa", "simp", "have", "exact"], "tactic_count": 5}
{"name": "continuousOn_zpow₀", "kind": "theorem", "module": "Mathlib.Topology.Algebra.GroupWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.zpow₀", "kind": "theorem", "module": "Mathlib.Topology.Algebra.GroupWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.zpow₀", "kind": "theorem", "module": "Mathlib.Topology.Algebra.GroupWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.zpow₀", "kind": "theorem", "module": "Mathlib.Topology.Algebra.GroupWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.zpow₀", "kind": "theorem", "module": "Mathlib.Topology.Algebra.GroupWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.zpow₀", "kind": "theorem", "module": "Mathlib.Topology.Algebra.GroupWithZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.vsub", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.AddTorsor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.vsub", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.AddTorsor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.vsub", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.AddTorsor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.vsub", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.AddTorsor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.vsub", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.AddTorsor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsTopologicalAddTorsor.to_isTopologicalAddGroup", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.AddTorsor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.vaddConst", "kind": "definition", "module": "Mathlib.Topology.Algebra.Group.AddTorsor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsTopologicalAddTorsor", "kind": "instance", "module": "Mathlib.Topology.Algebra.Group.AddTorsor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsTopologicalAddTorsorProd", "kind": "instance", "module": "Mathlib.Topology.Algebra.Group.AddTorsor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsTopologicalAddTorsorForall", "kind": "instance", "module": "Mathlib.Topology.Algebra.Group.AddTorsor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.isClosed_centralizer", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "rintro", "refine", "all_goals"], "tactic_count": 5}
{"name": "Homeomorph.mulLeft", "kind": "definition", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.coe_mulLeft", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.mulLeft_symm", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "isOpenMap_mul_left", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.leftCoset", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosedMap_mul_left", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.leftCoset", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.mulRight", "kind": "definition", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.coe_mulRight", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.mulRight_symm", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "isOpenMap_mul_right", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.rightCoset", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosedMap_mul_right", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.rightCoset", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "discreteTopology_iff_isOpen_singleton_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "discreteTopology_of_isOpen_singleton_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousInv.induced", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["let", "refine", "simp", "fun_prop"], "tactic_count": 4}
{"name": "Specializes.inv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Inseparable.inv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Specializes.zpow", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Inseparable.zpow", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instContinuousInvULift", "kind": "instance", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousOn_inv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousWithinAt_inv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousAt_inv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_inv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instContinuousInv", "kind": "instance", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.continuousInv", "kind": "instance", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.continuousInv", "kind": "instance", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.has_continuous_inv'", "kind": "instance", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousInv_of_discreteTopology", "kind": "instance", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "topologicalGroup_of_discreteTopology", "kind": "instance", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosed_setOf_map_inv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "instContinuousNegAdditiveOfContinuousInv", "kind": "instance", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instContinuousInvMultiplicativeOfContinuousNeg", "kind": "instance", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_inv_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.inv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Homeomorph.inv", "kind": "definition", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.coe_inv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhds_inv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpenMap_inv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosedMap_inv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.inv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.inv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_closure", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_inv_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousAt_inv_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousOn_inv_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousInv_sInf", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousInv_iInf", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "continuousInv_inf", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "cases"], "tactic_count": 3}
{"name": "Topology.IsInducing.continuousInv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConjAct.units_continuousConstSMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsTopologicalGroup.continuous_conj_prod", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsTopologicalGroup.continuous_conj", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsTopologicalGroup.continuous_conj'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsTopologicalGroupULift", "kind": "instance", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_zpow", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddGroup.continuousConstSMul_int", "kind": "instance", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddGroup.continuousSMul_int", "kind": "instance", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.zpow", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousOn_zpow", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousAt_zpow", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.zpow", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.zpow", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.zpow", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.zpow", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_inv_nhdsGT", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_inv_nhdsLT", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_inv_nhdsGT_inv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "tendsto_inv_nhdsLT_inv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "tendsto_inv_nhdsGE", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_inv_nhdsLE", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_inv_nhdsGE_inv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "tendsto_inv_nhdsLE_inv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Prod.instIsTopologicalGroup", "kind": "instance", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instIsTopologicalGroup", "kind": "instance", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.topologicalGroup", "kind": "instance", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instContinuousInvMulOpposite", "kind": "instance", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsTopologicalGroupMulOpposite", "kind": "instance", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhds_one_symm", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhds_one_symm'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_mem_nhds_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Homeomorph.shearMulRight", "kind": "definition", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.shearMulRight_coe", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.shearMulRight_symm_coe", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsInducing.topologicalGroup", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "topologicalGroup_induced", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.instIsTopologicalGroupSubtypeMem", "kind": "instance", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.topologicalClosure", "kind": "definition", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.topologicalClosure_coe", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.le_topologicalClosure", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.isClosed_topologicalClosure", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.topologicalClosure_minimal", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DenseRange.topologicalClosure_map_subgroup", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp", "exact"], "tactic_count": 3}
{"name": "Subgroup.is_normal_topologicalClosure", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_mem_connectedComponent_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw", "have", "apply", "rw", "exact", "simpa"], "tactic_count": 6}
{"name": "inv_mem_connectedComponent_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Subgroup.connectedComponentOfOne", "kind": "definition", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.commGroupTopologicalClosure", "kind": "abbrev", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.coe_topologicalClosure_bot", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "exists_nhds_split_inv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": ["have", "continuousAt_fst.mul", "simpa"], "tactic_count": 3}
{"name": "nhds_translation_mul_inv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "map_mul_left_nhds", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "map_mul_left_nhds_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "map_mul_right_nhds", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "map_mul_right_nhds_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.HasBasis.nhds_of_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "exact"], "tactic_count": 3}
{"name": "mem_closure_iff_nhds_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp_rw"], "tactic_count": 2}
{"name": "continuous_of_continuousAt_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_of_continuousAt_one₂", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsTopologicalGroup.isInducing_iff_nhds_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "congr", "ext"], "tactic_count": 5}
{"name": "IsTopologicalGroup.isOpenMap_iff_nhds_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["refine", "have", "simpa", "rw", "refine", "simp"], "tactic_count": 6}
{"name": "MonoidHom.isOpenQuotientMap_of_isQuotientMap", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsTopologicalGroup.ext", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsTopologicalGroup.ext_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousInv.of_nhds_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["refine", "have", "simpa", "inv_mul_cancel_left]"], "tactic_count": 4}
{"name": "IsTopologicalGroup.of_nhds_one'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsTopologicalGroup.of_nhds_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["refine", "replace", "map_eq_of_inverse", "rw", "simpa"], "tactic_count": 5}
{"name": "IsTopologicalGroup.of_comm_of_nhds_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsTopologicalGroup.exists_antitone_basis_nhds_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rcases", "have", "simp", "have", "intro", "rcases", "refine", "rintro", "exact", "obtain", "exact"], "tactic_count": 11}
{"name": "Filter.Tendsto.const_div'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_const_div_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["refine", "convert"], "tactic_count": 2}
{"name": "Filter.Tendsto.div_const'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_div_const_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["refine", "convert"], "tactic_count": 2}
{"name": "Filter.tendsto_sub_const_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["refine", "convert"], "tactic_count": 2}
{"name": "continuous_div_left'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["fun_prop"], "tactic_count": 1}
{"name": "continuous_div_right'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["fun_prop"], "tactic_count": 1}
{"name": "Homeomorph.divLeft", "kind": "definition", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpenMap_div_left", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosedMap_div_left", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.divRight", "kind": "definition", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpenMap_div_right", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosedMap_div_right", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_div_nhds_one_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhds_translation_div", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsTopologicalGroup.t1Space", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.properlyDiscontinuousSMul_of_tendsto_cofinite", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.properlyDiscontinuousSMul_opposite_of_tendsto_cofinite", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "compact_open_separated_mul_right", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["refine", "exact", "rintro", "exact", "rintro", "use", "rw", "exact", "union_subset", "intro", "have", "rw", "rcases", "rw", "exact"], "tactic_count": 15}
{"name": "compact_open_separated_mul_left", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": ["rcases", "refine", "rwa"], "tactic_count": 3}
{"name": "compact_covered_by_mul_left_translates", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": ["obtain", "refine", "obtain", "refine", "refine", "rwa", "exact"], "tactic_count": 7}
{"name": "SeparableWeaklyLocallyCompactGroup.sigmaCompactSpace", "kind": "instance", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["obtain", "refine", "intro", "exact", "refine", "obtain", "rw", "exact", "exact"], "tactic_count": 9}
{"name": "exists_disjoint_smul_of_isCompact", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["have", "obtain", "contrapose", "exact", "refine", "refine", "rcases", "refine", "simp"], "tactic_count": 9}
{"name": "nhds_mul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsMulHom", "kind": "definition", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsTopologicalAddGroupAdditiveOfIsTopologicalGroup", "kind": "instance", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsTopologicalGroupMultiplicativeOfIsTopologicalAddGroup", "kind": "instance", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toUnits_homeomorph", "kind": "definition", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.isEmbedding_val", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.of_coeHom_comp", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["apply", "refine", "simp_rw", "exact"], "tactic_count": 4}
{"name": "Units.range_embedProduct", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.instIsTopologicalGroupOfContinuousMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.isClosedEmbedding_embedProduct", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.instCompactSpaceOfT1SpaceOfContinuousMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.instWeaklyLocallyCompactSpaceOfT1SpaceOfContinuousMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.instLocallyCompactSpaceOfT1SpaceOfContinuousMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.units_isCompact", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "Homeomorph.prodUnits", "kind": "definition", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "topologicalGroup_sInf", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "topologicalGroup_iInf", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "topologicalGroup_inf", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "cases"], "tactic_count": 3}
{"name": "ClosedSubgroup.toSubgroup_injective", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.ClosedSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClosedSubgroup.instSetLike", "kind": "instance", "module": "Mathlib.Topology.Algebra.Group.ClosedSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClosedSubgroup.instPartialOrder", "kind": "instance", "module": "Mathlib.Topology.Algebra.Group.ClosedSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClosedSubgroup.instSubgroupClass", "kind": "instance", "module": "Mathlib.Topology.Algebra.Group.ClosedSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClosedSubgroup.instCoeSubgroup", "kind": "instance", "module": "Mathlib.Topology.Algebra.Group.ClosedSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClosedSubgroup.instInfClosedSubgroup", "kind": "instance", "module": "Mathlib.Topology.Algebra.Group.ClosedSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClosedSubgroup.instSemilatticeInfClosedSubgroup", "kind": "instance", "module": "Mathlib.Topology.Algebra.Group.ClosedSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClosedSubgroup.instCompactSpaceSubtypeMem", "kind": "instance", "module": "Mathlib.Topology.Algebra.Group.ClosedSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.normalCore_isClosed", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.ClosedSubgroup", "is_tactic_proof": true, "tactics": ["rw", "push_cast", "apply", "intro", "convert", "exact"], "tactic_count": 6}
{"name": "Subgroup.isOpen_of_isClosed_of_finiteIndex", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.ClosedSubgroup", "is_tactic_proof": true, "tactics": ["rw", "rw", "infer_instance"], "tactic_count": 3}
{"name": "TopologicalSpace.PositiveCompacts.locallyCompactSpace_of_group", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMonoidHom.instTopologicalSpace", "kind": "instance", "module": "Mathlib.Topology.Algebra.Group.CompactOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMonoidHom.isInducing_toContinuousMap", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.CompactOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMonoidHom.isEmbedding_toContinuousMap", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.CompactOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMonoidHom.instContinuousEvalConst", "kind": "instance", "module": "Mathlib.Topology.Algebra.Group.CompactOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMonoidHom.instContinuousEval", "kind": "instance", "module": "Mathlib.Topology.Algebra.Group.CompactOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMonoidHom.range_toContinuousMap", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.CompactOpen", "is_tactic_proof": true, "tactics": ["refine", "rintro", "exact"], "tactic_count": 3}
{"name": "ContinuousMonoidHom.isClosedEmbedding_toContinuousMap", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.CompactOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMonoidHom.instT2Space", "kind": "instance", "module": "Mathlib.Topology.Algebra.Group.CompactOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMonoidHom.instIsTopologicalGroup", "kind": "instance", "module": "Mathlib.Topology.Algebra.Group.CompactOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMonoidHom.continuous_of_continuous_uncurry", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.CompactOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMonoidHom.continuous_comp", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.CompactOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMonoidHom.continuous_comp_left", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.CompactOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMonoidHom.continuous_comp_right", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.CompactOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMonoidHom.compLeft", "kind": "definition", "module": "Mathlib.Topology.Algebra.Group.CompactOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMonoidHom.compRight", "kind": "definition", "module": "Mathlib.Topology.Algebra.Group.CompactOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMonoidHom.isClosedEmbedding_coe", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.CompactOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMonoidHom.instCompactSpace", "kind": "instance", "module": "Mathlib.Topology.Algebra.Group.CompactOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMonoidHom.locallyCompactSpace_of_equicontinuousAt", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.CompactOpen", "is_tactic_proof": true, "tactics": ["replace", "obtain", "let", "let", "let", "let", "replace", "have", "ext", "constructor", "rintro", "exact", "rintro", "exact", "replace", "rw", "rwa", "replace", "simp_rw", "exact", "replace", "hS4.symm", "have", "let", "have", "have", "have", "exact", "exact", "hS2⟩"], "tactic_count": 30}
{"name": "ContinuousMonoidHom.locallyCompactSpace_of_hasBasis", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.CompactOpen", "is_tactic_proof": true, "tactics": ["obtain", "let", "let", "let", "have", "have", "have", "have", "intro", "induction", "zero", "succ", "apply", "rw", "refine", "rw", "exact"], "tactic_count": 17}
{"name": "Filter.Tendsto.inv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.inv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.inv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.inv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.inv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsTopologicalGroup.to_continuousDiv", "kind": "instance", "module": "Mathlib.Topology.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.div'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.div'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.div'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.div'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.div'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupTopology.continuous_mul'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.GroupTopology", "is_tactic_proof": true, "tactics": ["letI", "haveI", "exact"], "tactic_count": 3}
{"name": "GroupTopology.continuous_inv'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.GroupTopology", "is_tactic_proof": true, "tactics": ["letI", "haveI", "exact"], "tactic_count": 3}
{"name": "GroupTopology.toTopologicalSpace_injective", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.GroupTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupTopology.ext'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.GroupTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupTopology.instPartialOrder", "kind": "instance", "module": "Mathlib.Topology.Algebra.Group.GroupTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupTopology.toTopologicalSpace_le", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.GroupTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupTopology.instTop", "kind": "instance", "module": "Mathlib.Topology.Algebra.Group.GroupTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupTopology.toTopologicalSpace_top", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.GroupTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupTopology.instBot", "kind": "instance", "module": "Mathlib.Topology.Algebra.Group.GroupTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupTopology.toTopologicalSpace_bot", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.GroupTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupTopology.instBoundedOrder", "kind": "instance", "module": "Mathlib.Topology.Algebra.Group.GroupTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupTopology.instMin", "kind": "instance", "module": "Mathlib.Topology.Algebra.Group.GroupTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupTopology.toTopologicalSpace_inf", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.GroupTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupTopology.instSemilatticeInf", "kind": "instance", "module": "Mathlib.Topology.Algebra.Group.GroupTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupTopology.instInhabited", "kind": "instance", "module": "Mathlib.Topology.Algebra.Group.GroupTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupTopology.instInfSet", "kind": "instance", "module": "Mathlib.Topology.Algebra.Group.GroupTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupTopology.toTopologicalSpace_sInf", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.GroupTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupTopology.toTopologicalSpace_iInf", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.GroupTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupTopology.instCompleteSemilatticeInf", "kind": "instance", "module": "Mathlib.Topology.Algebra.Group.GroupTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupTopology.instCompleteLattice", "kind": "instance", "module": "Mathlib.Topology.Algebra.Group.GroupTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupTopology.coinduced", "kind": "definition", "module": "Mathlib.Topology.Algebra.Group.GroupTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GroupTopology.coinduced_continuous", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.GroupTopology", "is_tactic_proof": true, "tactics": ["rw", "rintro", "exact"], "tactic_count": 3}
{"name": "smul_singleton_mem_nhds_of_sigmaCompact", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.OpenMapping", "is_tactic_proof": true, "tactics": ["countably", "the", "space.", "so", "a", "obtain", "exists_closed_nhds_one_inv_eq_mul_subset", "obtain", "countable_cover_nhds_of_sigmaCompact", "let", "let", "obtain", "have", "have", "apply", "rintro", "apply", "suffices", "apply", "exact", "apply", "obtain", "obtain", "obtain", "simp", "exact", "have", "apply", "apply", "exact", "obtain", "rw", "exact", "obtain", "have", "apply", "rwa", "have", "apply", "apply", "rw", "exact", "exact"], "tactic_count": 43}
{"name": "isOpenMap_smul_of_sigmaCompact", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.OpenMapping", "is_tactic_proof": true, "tactics": ["point", "simp_rw", "intro", "have", "ext", "simp", "rw", "apply", "simpa"], "tactic_count": 9}
{"name": "MonoidHom.isOpenMap_of_sigmaCompact", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.OpenMapping", "is_tactic_proof": true, "tactics": ["let", "have", "have", "have", "rw", "exact"], "tactic_count": 6}
{"name": "subset_interior_smul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.smul_left_of_isCompact", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Pointwise", "is_tactic_proof": false, "tactics": ["let", "invFun", "left_inv", "right_inv", "have", "subset_antisymm", "rw", "have", "exact"], "tactic_count": 9}
{"name": "MulAction.isClosedMap_quotient", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Pointwise", "is_tactic_proof": true, "tactics": ["intro", "rw", "convert", "rw", "simp"], "tactic_count": 5}
{"name": "IsOpen.mul_left", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "subset_interior_mul_right", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "subset_interior_mul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "singleton_mul_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Pointwise", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "singleton_mul_mem_nhds_of_nhds_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Pointwise", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsOpen.mul_right", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Pointwise", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "subset_interior_mul_left", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "subset_interior_mul'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mul_singleton_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Pointwise", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "mul_singleton_mem_nhds_of_nhds_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Pointwise", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsOpen.div_left", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Pointwise", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsOpen.div_right", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Pointwise", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "subset_interior_div_left", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "subset_interior_div_right", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "subset_interior_div", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.mul_closure", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Pointwise", "is_tactic_proof": true, "tactics": ["refine", "rw", "have", "obtain", "exact"], "tactic_count": 5}
{"name": "IsOpen.closure_mul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Pointwise", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsOpen.div_closure", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Pointwise", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "IsOpen.closure_div", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Pointwise", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "IsClosed.mul_left_of_isCompact", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.mul_right_of_isCompact", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Pointwise", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "subset_mul_closure_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Pointwise", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "IsCompact.mul_closure_one_eq_closure", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Pointwise", "is_tactic_proof": true, "tactics": ["apply", "calc", "have", "rw", "exact"], "tactic_count": 5}
{"name": "IsClosed.mul_closure_one_eq", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Pointwise", "is_tactic_proof": true, "tactics": ["refine", "calc"], "tactic_count": 2}
{"name": "compl_mul_closure_one_eq", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Pointwise", "is_tactic_proof": true, "tactics": ["refine", "rintro", "by_contra", "have", "rw", "simp", "exact", "rw", "exact"], "tactic_count": 9}
{"name": "compl_mul_closure_one_eq_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.mul_closure_one_eq", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsTopologicalGroup.regularSpace", "kind": "instance", "module": "Mathlib.Topology.Algebra.Group.Pointwise", "is_tactic_proof": true, "tactics": ["refine", "have", "rcases", "rw", "refine", "calc", "closure"], "tactic_count": 7}
{"name": "group_inseparable_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Pointwise", "is_tactic_proof": false, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "IsTopologicalGroup.t2Space_iff_one_closed", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsTopologicalGroup.t2Space_of_one_sep", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Pointwise", "is_tactic_proof": true, "tactics": ["suffices", "refine", "rcases", "exact"], "tactic_count": 4}
{"name": "exists_closed_nhds_one_inv_eq_mul_subset", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Pointwise", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "refine", "calc"], "tactic_count": 4}
{"name": "IsDiscrete.exists_nhds_eq_one_of_image_mulLeft_inter_nonempty", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Pointwise", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "refine", "rintro", "refine", "rw", "exact"], "tactic_count": 7}
{"name": "IsDiscrete.exists_nhds_eq_one_of_image_mulRight_inter_nonempty", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Pointwise", "is_tactic_proof": true, "tactics": ["have", "refine", "rwa"], "tactic_count": 3}
{"name": "IsCompact.locallyCompactSpace_of_mem_nhds_of_group", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Pointwise", "is_tactic_proof": true, "tactics": ["suffices", "refine", "exact", "rw", "exact"], "tactic_count": 5}
{"name": "eq_zero_or_locallyCompactSpace_of_support_subset_isCompact_of_group", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Pointwise", "is_tactic_proof": true, "tactics": ["refine", "simp_rw", "push_neg", "obtain", "have", "exact"], "tactic_count": 6}
{"name": "HasCompactSupport.eq_zero_or_locallyCompactSpace_of_group", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Pointwise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.instTopologicalSpace", "kind": "instance", "module": "Mathlib.Topology.Algebra.Group.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.instCompactSpaceQuotientSubgroup", "kind": "instance", "module": "Mathlib.Topology.Algebra.Group.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.isQuotientMap_mk", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.continuous_mk", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.isOpenMap_coe", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.isOpenQuotientMap_mk", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.dense_preimage_mk", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.dense_image_mk", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Quotient", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "QuotientGroup.instContinuousSMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.Group.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.instContinuousConstSMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.Group.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.t1Space_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Quotient", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "QuotientGroup.discreteTopology_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Quotient", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "QuotientGroup.instT1Space", "kind": "instance", "module": "Mathlib.Topology.Algebra.Group.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.discreteTopology", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.instLocallyCompactSpace", "kind": "instance", "module": "Mathlib.Topology.Algebra.Group.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.nhds_eq", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.instFirstCountableTopology", "kind": "instance", "module": "Mathlib.Topology.Algebra.Group.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.instSecondCountableTopology", "kind": "instance", "module": "Mathlib.Topology.Algebra.Group.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.instIsTopologicalGroup", "kind": "instance", "module": "Mathlib.Topology.Algebra.Group.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.isClosedMap_coe", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Quotient", "is_tactic_proof": true, "tactics": ["intro", "rw", "exact"], "tactic_count": 3}
{"name": "QuotientGroup.instT3Space", "kind": "instance", "module": "Mathlib.Topology.Algebra.Group.Quotient", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "mapClusterPt_atTop_zpow_iff_pow", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.SubmonoidClosure", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "mapClusterPt_self_zpow_atTop_pow", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.SubmonoidClosure", "is_tactic_proof": true, "tactics": ["obtain", "rw", "have", "have", "simpa", "suffices", "refine", "simp", "exact"], "tactic_count": 9}
{"name": "mapClusterPt_one_atTop_pow", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.SubmonoidClosure", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "mapClusterPt_self_atTop_pow", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.SubmonoidClosure", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "mapClusterPt_atTop_pow_tfae", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.SubmonoidClosure", "is_tactic_proof": true, "tactics": ["tfae_have", "tfae_have", "refine", "exact", "tfae_have", "refine", "exact", "tfae_have", "rw", "exact", "tfae_finish"], "tactic_count": 11}
{"name": "mapClusterPt_atTop_pow_iff_mem_topologicalClosure_zpowers", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.SubmonoidClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mapClusterPt_inv_atTop_pow", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.SubmonoidClosure", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "closure_range_zpow_eq_pow", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.SubmonoidClosure", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "denseRange_zpow_iff_pow", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.SubmonoidClosure", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "topologicalClosure_subgroupClosure_toSubmonoid", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.SubmonoidClosure", "is_tactic_proof": true, "tactics": ["refine", "refine", "rw", "refine", "refine", "rw", "exact"], "tactic_count": 7}
{"name": "closure_submonoidClosure_eq_closure_subgroupClosure", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.SubmonoidClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dense_submonoidClosure_iff_subgroupClosure", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.SubmonoidClosure", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "instNormalCommutatorClosure", "kind": "instance", "module": "Mathlib.Topology.Algebra.Group.TopologicalAbelianization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalAbelianization", "kind": "abbrev", "module": "Mathlib.Topology.Algebra.Group.TopologicalAbelianization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.Algebra.Group.TopologicalAbelianization.0.termG_ab", "kind": "definition", "module": "Mathlib.Topology.Algebra.Group.TopologicalAbelianization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.Algebra.Group.TopologicalAbelianization.0._aux_Mathlib_Topology_Algebra_Group_TopologicalAbelianization___macroRules__private_Mathlib_Topology_Algebra_Group_TopologicalAbelianization_0_termG_ab_1", "kind": "definition", "module": "Mathlib.Topology.Algebra.Group.TopologicalAbelianization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.Algebra.Group.TopologicalAbelianization.0._aux_Mathlib_Topology_Algebra_Group_TopologicalAbelianization___unexpand_TopologicalAbelianization_1", "kind": "definition", "module": "Mathlib.Topology.Algebra.Group.TopologicalAbelianization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalAbelianization.commGroup", "kind": "instance", "module": "Mathlib.Topology.Algebra.Group.TopologicalAbelianization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.isOpen_units", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMulEquiv.piUnits", "kind": "definition", "module": "Mathlib.Topology.Algebra.Group.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.mapContinuousMulEquiv", "kind": "definition", "module": "Mathlib.Topology.Algebra.Group.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.symm_mapContinuousMulEquiv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.toMulEquiv_mapContinuousMulEquiv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Group.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_mulIndicator", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Indicator", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Continuous.mulIndicator", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Indicator", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "ContinuousOn.continuousAt_mulIndicator", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Indicator", "is_tactic_proof": true, "tactics": ["rw", "obtain", "have", "exact", "exact"], "tactic_count": 5}
{"name": "IsClopen.continuous_mulIndicator", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Indicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasProd_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "hasProd_empty", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "HasProd.of_subsingleton_cod", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "multipliable_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "multipliable_empty", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multipliable.of_subsingleton_cod", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "multipliable_congr", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multipliable.congr", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasProd.congr_fun", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasProd.hasProd_of_prod_eq", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasProd_iff_hasProd", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.multipliable_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasProd_extend_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "multipliable_extend_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasProd_subtype_iff_mulIndicator", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": true, "tactics": ["rw", "hasProd_subtype_iff_of_mulSupport_subset"], "tactic_count": 2}
{"name": "multipliable_subtype_iff_mulIndicator", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasProd_subtype_mulSupport", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.multipliable", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.multipliable", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "multipliable_of_finite_mulSupport", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "Multipliable.of_finite", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasProd_singleton", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.hasProd_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.hasProd_range_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.multipliable_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.hasProd_iff_of_mulSupport", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "hasProd_iff_hasProd_of_ne_one_bij", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.multipliable_iff_of_mulSupport", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasProd.map", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": true, "tactics": ["have", "unfold", "rw", "exact"], "tactic_count": 4}
{"name": "Topology.IsInducing.hasProd_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Multipliable.map", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multipliable.map_iff_of_leftInverse", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multipliable.map_tprod", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsClosedEmbedding.map_tprod", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "by_cases", "exact", "rw", "contrapose", "simp", "obtain", "obtain", "use", "simp", "simpa"], "tactic_count": 11}
{"name": "Function.LeftInverse.map_tprod", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsInducing.multipliable_iff_tprod_comp_mem_range", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": true, "tactics": ["constructor", "intro", "constructor", "exact", "by_cases", "exact", "by_cases", "simp", "exact", "rintro", "use", "have", "simp_rw", "exact"], "tactic_count": 14}
{"name": "Multipliable.map_iff_of_equiv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.multipliable_iff_of_hasProd_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasProd.mul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": true, "tactics": ["dsimp", "simp_rw", "exact"], "tactic_count": 3}
{"name": "Multipliable.mul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasProd_prod", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": true, "tactics": ["classical", "exact", "simp", "exact"], "tactic_count": 4}
{"name": "multipliable_prod", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasProd.mul_disjoint", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "hasProd_prod_disjoint", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "rw", "exact"], "tactic_count": 3}
{"name": "HasProd.mul_isCompl", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasProd.mul_compl", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multipliable.mul_compl", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasProd.compl_mul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multipliable.compl_add", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasProd.update'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": false, "tactics": ["have", "intro", "split_ifs", "simpa", "simp", "have", "simp_rw", "exact"], "tactic_count": 8}
{"name": "eq_mul_of_hasProd_ite", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": true, "tactics": ["refine", "convert", "apply"], "tactic_count": 3}
{"name": "tprod_congr_set_coe", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "tprod_congr_subtype", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tprod_eq_finprod", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "tprod_eq_prod'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "tprod_eq_prod", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tprod_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": true, "tactics": ["rw", "eq_true_intro"], "tactic_count": 2}
{"name": "tprod_empty", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "tprod_congr", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tprod_congr₂", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tprod_fintype", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "tprod_bool", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "tprod_eq_mulSingle", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "tprod_tprod_eq_mulSingle", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.tprod_subtype", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.tprod_subtype'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "tprod_singleton", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Function.Injective.tprod_eq", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": true, "tactics": ["classical", "have", "rw", "by_cases", "have", "lift", "simp_rw", "refine", "simp", "have", "simp_rw", "show", "true_and,", "simp"], "tactic_count": 14}
{"name": "Equiv.tprod_eq", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tprod_comp_neg", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tprod_subtype_eq_of_mulSupport_subset", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tprod_subtype_mulSupport", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tprod_subtype", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "tprod_univ", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tprod_image", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tprod_range", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp_rw"], "tactic_count": 2}
{"name": "tprod_setElem_eq_tprod_setElem_diff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tprod_eq_tprod_diff_singleton", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tprod_eq_tprod_of_ne_one_bij", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Equiv.tprod_eq_tprod_of_mulSupport", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tprod_dite_right", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "tprod_dite_left", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "tprod_extend_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": true, "tactics": ["have", "simp_rw"], "tactic_count": 2}
{"name": "Function.Surjective.tprod_eq_tprod_of_hasProd_iff_hasProd", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": false, "tactics": ["have", "simp"], "tactic_count": 2}
{"name": "tprod_eq_tprod_of_hasProd_iff_hasProd", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multipliable.tprod_mul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multipliable.tprod_finsetProd", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multipliable.tprod_eq_mul_tprod_ite'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multipliable.tprod_mul_tprod_compl", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multipliable.tprod_union_disjoint", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multipliable.tprod_finset_bUnion_disjoint", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasProd_zero_of_exists_eq_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": true, "tactics": ["obtain", "apply", "filter_upwards", "exact"], "tactic_count": 4}
{"name": "multipliable_of_exists_eq_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tprod_of_exists_eq_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SummationFilter.symmetricIcc", "kind": "definition", "module": "Mathlib.Topology.Algebra.InfiniteSum.ConditionalInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SummationFilter.symmetricIoo", "kind": "definition", "module": "Mathlib.Topology.Algebra.InfiniteSum.ConditionalInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SummationFilter.symmetricIco", "kind": "definition", "module": "Mathlib.Topology.Algebra.InfiniteSum.ConditionalInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SummationFilter.symmetricIoc", "kind": "definition", "module": "Mathlib.Topology.Algebra.InfiniteSum.ConditionalInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SummationFilter.instNeBotSymmetricIcc", "kind": "instance", "module": "Mathlib.Topology.Algebra.InfiniteSum.ConditionalInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SummationFilter.instNeBotSymmetricIco", "kind": "instance", "module": "Mathlib.Topology.Algebra.InfiniteSum.ConditionalInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SummationFilter.instNeBotSymmetricIoc", "kind": "instance", "module": "Mathlib.Topology.Algebra.InfiniteSum.ConditionalInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SummationFilter.instNeBotSymmetricIoo", "kind": "instance", "module": "Mathlib.Topology.Algebra.InfiniteSum.ConditionalInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SummationFilter.symmetricIcc_le_Conditional", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ConditionalInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SummationFilter.instLeAtTopSymmetricIcc", "kind": "instance", "module": "Mathlib.Topology.Algebra.InfiniteSum.ConditionalInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SummationFilter.instLeAtTopSymmetricIco", "kind": "instance", "module": "Mathlib.Topology.Algebra.InfiniteSum.ConditionalInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SummationFilter.instLeAtTopSymmetricIoc", "kind": "instance", "module": "Mathlib.Topology.Algebra.InfiniteSum.ConditionalInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SummationFilter.instLeAtTopSymmetricIoo", "kind": "instance", "module": "Mathlib.Topology.Algebra.InfiniteSum.ConditionalInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SummationFilter.symmetricIcc_eq_map_Icc_nat", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ConditionalInt", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "ENNReal.tsum_eq_iSup_nat", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.tsum_eq_liminf_sum_nat", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.tsum_eq_limsup_sum_nat", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.le_tsum", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.tsum_eq_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.tsum_eq_top_of_eq_top", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.lt_top_of_tsum_ne_top", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": true, "tactics": ["contrapose", "exact"], "tactic_count": 2}
{"name": "ENNReal.tsum_top", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.tsum_const_eq_top_of_ne_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": false, "tactics": ["have", "apply", "simp", "have", "rcases", "simpa", "simpa"], "tactic_count": 7}
{"name": "ENNReal.ne_top_of_tsum_ne_top", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.tsum_mul_left", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "rw", "have", "simp", "exact", "exact"], "tactic_count": 7}
{"name": "ENNReal.tsum_mul_right", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.tsum_const_smul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ENNReal.tsum_iSup_eq", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.hasSum_iff_tendsto_nat", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact", "exact"], "tactic_count": 4}
{"name": "ENNReal.tendsto_nat_tsum", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ENNReal.toNNReal_apply_of_tsum_ne_top", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.summable_toNNReal_of_tsum_ne_top", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ENNReal.tendsto_cofinite_zero_of_tsum_ne_top", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": true, "tactics": ["have", "have", "rw", "exact"], "tactic_count": 4}
{"name": "ENNReal.tendsto_atTop_zero_of_tsum_ne_top", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ENNReal.tendsto_tsum_compl_atTop_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": true, "tactics": ["lift", "convert", "rw", "exact"], "tactic_count": 4}
{"name": "ENNReal.tsum_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.tsum_sub", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.tsum_comp_le_tsum_of_injective", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.tsum_le_tsum_comp_of_surjective", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.tsum_mono_subtype", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.tsum_iUnion_le_tsum", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.tsum_biUnion_le_tsum", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.tsum_biUnion_le", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.tsum_iUnion_le", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ENNReal.tsum_union_le", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.tsum_eq_add_tsum_ite", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.tsum_add_one_eq_top", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ENNReal.finite_const_le_of_tsum_ne_top", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": true, "tactics": ["by_contra", "have", "refine", "calc"], "tactic_count": 4}
{"name": "ENNReal.finset_card_const_le_le_of_tsum_le", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": false, "tactics": ["have", "finite_const_le_of_tsum_ne_top", "refine", "calc"], "tactic_count": 4}
{"name": "ENNReal.tsum_fiberwise", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": true, "tactics": ["apply", "let", "apply", "exact"], "tactic_count": 4}
{"name": "ENNReal.tsum_coe_ne_top_iff_summable_coe", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ENNReal.tsum_coe_eq_top_iff_not_summable_coe", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.hasSum_toReal", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": true, "tactics": ["lift", "simp", "exact"], "tactic_count": 3}
{"name": "ENNReal.summable_toReal", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.tsum_eq_toNNReal_tsum", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "have", "simp", "simp"], "tactic_count": 5}
{"name": "NNReal.exists_le_hasSum_of_le", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.summable_of_le", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Summable.countable_support_nnreal", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "NNReal.hasSum_iff_tendsto_nat", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": true, "tactics": ["rw", "simp", "exact"], "tactic_count": 3}
{"name": "NNReal.not_summable_iff_tendsto_nat_atTop", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": true, "tactics": ["constructor", "intro", "refine", "exacts", "rintro", "exact"], "tactic_count": 6}
{"name": "NNReal.summable_iff_not_tendsto_nat_atTop", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NNReal.summable_of_sum_range_le", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": true, "tactics": ["refine", "rcases", "exact"], "tactic_count": 3}
{"name": "NNReal.tsum_le_of_sum_range_le", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.tsum_comp_le_tsum_of_inj", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.summable_sigma", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": true, "tactics": ["constructor", "simp", "exact", "rintro", "simpa"], "tactic_count": 5}
{"name": "NNReal.indicator_summable", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": true, "tactics": ["classical", "refine", "split_ifs", "exact", "exact"], "tactic_count": 5}
{"name": "NNReal.tsum_indicator_ne_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.tendsto_sum_nat_add", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": true, "tactics": ["rw", "convert", "norm_cast"], "tactic_count": 3}
{"name": "NNReal.hasSum_lt", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": true, "tactics": ["have", "have", "exact"], "tactic_count": 3}
{"name": "NNReal.hasSum_strict_mono", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.tsum_lt_tsum", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.tsum_strict_mono", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.tsum_pos", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "NNReal.tsum_eq_add_tsum_ite", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": true, "tactics": ["refine", "rw", "split_ifs"], "tactic_count": 3}
{"name": "ENNReal.tsum_toNNReal_eq", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.tsum_toReal_eq", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.tendsto_sum_nat_add", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": true, "tactics": ["lift", "replace", "simp", "exact"], "tactic_count": 4}
{"name": "ENNReal.tsum_le_of_sum_range_le", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.hasSum_lt", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "have", "lift", "lift", "lift", "lift", "simp", "exact"], "tactic_count": 9}
{"name": "ENNReal.tsum_lt_tsum", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tsum_comp_le_tsum_of_inj", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": true, "tactics": ["lift", "rw", "simpa"], "tactic_count": 3}
{"name": "Summable.of_nonneg_of_le", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": true, "tactics": ["lift", "lift", "rw", "exact"], "tactic_count": 4}
{"name": "Summable.toNNReal", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": true, "tactics": ["apply", "refine", "simp"], "tactic_count": 3}
{"name": "Summable.tsum_ofReal_lt_top", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": true, "tactics": ["unfold", "rw", "exact"], "tactic_count": 3}
{"name": "Summable.tsum_ofReal_ne_top", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Summable.countable_support_ennreal", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": true, "tactics": ["lift", "simpa"], "tactic_count": 2}
{"name": "hasSum_iff_tendsto_nat_of_nonneg", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": true, "tactics": ["lift", "simp", "exact"], "tactic_count": 3}
{"name": "ENNReal.ofReal_tsum_of_nonneg", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "ENNReal.multipliable_of_le_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.hasProd_iInf_prod", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.tprod_eq_iInf_prod", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cauchySeq_of_edist_le_of_summable", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": false, "tactics": ["refine", "replace", "let", "refine", "specialize", "rw", "max_lt_iff]", "rw", "refine", "exact"], "tactic_count": 10}
{"name": "cauchySeq_of_edist_le_of_tsum_ne_top", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": true, "tactics": ["lift", "rw", "exact"], "tactic_count": 3}
{"name": "edist_le_tsum_of_edist_le_of_tendsto", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": true, "tactics": ["refine", "change", "refine", "rw", "exact"], "tactic_count": 5}
{"name": "edist_le_tsum_of_edist_le_of_tendsto₀", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ENNReal.tsum_set_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": true, "tactics": ["obtain", "lift", "simp", "have", "rw"], "tactic_count": 5}
{"name": "ENNReal.tsum_set_const", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.tsum_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.tsum_const", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.ENNReal", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HasProd.norm", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Field", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Multipliable.norm", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multipliable.norm_tprod", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasProd.inv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Group", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Multipliable.inv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multipliable.of_inv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Group", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "multipliable_inv_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasProd.div", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Group", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Multipliable.div", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multipliable.trans_div", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Group", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "multipliable_iff_of_multipliable_div", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasProd.update", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Group", "is_tactic_proof": true, "tactics": ["convert", "by_cases", "rw", "simp", "simp"], "tactic_count": 5}
{"name": "Multipliable.update", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasProd.hasProd_compl_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Group", "is_tactic_proof": true, "tactics": ["refine", "rw", "rw", "simpa"], "tactic_count": 4}
{"name": "HasProd.hasProd_iff_compl", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multipliable.multipliable_compl_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.hasProd_compl_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.hasProd_iff_compl", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.multipliable_compl_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.multipliable_compl_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasProd_ite_div_hasProd", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Group", "is_tactic_proof": true, "tactics": ["convert", "ext", "rw", "rw"], "tactic_count": 4}
{"name": "Multipliable.congr_cofinite", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "multipliable_congr_cofinite", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multipliable.congr_atTop", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "multipliable_congr_atTop", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tprod_inv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multipliable.tprod_div", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multipliable.prod_mul_tprod_compl", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multipliable.tprod_eq_mul_tprod_ite", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Group", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "multipliable_iff_cauchySeq_finset", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Group", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "cauchySeq_finset_iff_prod_vanishing", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Group", "is_tactic_proof": true, "tactics": ["classical", "simp", "rw", "constructor", "intro", "obtain", "use", "intro", "specialize", "simpa", "rintro", "rcases", "rcases", "use", "rintro", "have", "rw", "simp", "exact"], "tactic_count": 19}
{"name": "cauchySeq_finset_iff_tprod_vanishing", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Group", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "obtain", "obtain", "refine", "by_cases", "classical", "refine", "rw", "apply", "simp_rw", "rintro", "exact", "exact", "obtain", "exact"], "tactic_count": 16}
{"name": "multipliable_iff_vanishing", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Group", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "multipliable_iff_tprod_vanishing", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Group", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multipliable.multipliable_of_eq_one_or_self", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Group", "is_tactic_proof": true, "tactics": ["classical", "exact", "multipliable_iff_vanishing.2", "let", "have", "calc", "refine", "intro", "simp", "exact", "eq"], "tactic_count": 11}
{"name": "Multipliable.mulIndicator", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multipliable.comp_injective", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Group", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Multipliable.subtype", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "multipliable_subtype_and_compl", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multipliable.tprod_subtype_mul_tprod_subtype_compl", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multipliable.prod_mul_tprod_subtype_compl", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Group", "is_tactic_proof": true, "tactics": ["rw", "simp", "rfl"], "tactic_count": 3}
{"name": "Multipliable.vanishing", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Group", "is_tactic_proof": true, "tactics": ["classical", "letI", "have", "exact"], "tactic_count": 4}
{"name": "Multipliable.tprod_vanishing", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Group", "is_tactic_proof": true, "tactics": ["classical", "letI", "have", "exact"], "tactic_count": 4}
{"name": "tendsto_tprod_compl_atTop_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Group", "is_tactic_proof": true, "tactics": ["classical", "by_cases", "intro", "obtain", "rw", "exact", "refine", "rwa"], "tactic_count": 8}
{"name": "Multipliable.tendsto_cofinite_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Group", "is_tactic_proof": true, "tactics": ["intro", "rw", "rcases", "refine", "simpa"], "tactic_count": 5}
{"name": "Multipliable.finite_mulSupport_of_discreteTopology", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multipliable.countable_mulSupport", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Group", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "multipliable_const_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Group", "is_tactic_proof": true, "tactics": ["refine", "by_contra", "have", "have", "exact", "rintro", "exact"], "tactic_count": 7}
{"name": "tprod_const", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Group", "is_tactic_proof": true, "tactics": ["rcases", "letI", "rw", "simp", "simp", "rcases", "simp", "apply", "simpa"], "tactic_count": 9}
{"name": "HasProd.congr_cofinite₀", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Group", "is_tactic_proof": true, "tactics": ["classical", "refine", "filter_upwards", "calc", "conv_lhs", "rw", "rw", "exact"], "tactic_count": 8}
{"name": "Multipliable.tsum_congr_cofinite₀", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multipliable.congr_cofinite₀", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Group", "is_tactic_proof": true, "tactics": ["classical", "obtain", "obtain", "exact"], "tactic_count": 4}
{"name": "hasSum_iff_hasSum_compl", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.GroupCompletion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "summable_iff_summable_compl_and_tsum_mem", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.GroupCompletion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "summable_iff_cauchySeq_finset_and_tsum_mem", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.GroupCompletion", "is_tactic_proof": true, "tactics": ["classical", "constructor", "rintro", "exact", "rintro", "apply", "constructor", "apply", "simp_rw", "exact", "exact"], "tactic_count": 11}
{"name": "Summable.toCompl_tsum", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.GroupCompletion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasSum.const_smul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Summable.const_smul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Summable.tsum_const_smul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tsum_const_smul'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tsum_const_smul''", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Module", "is_tactic_proof": true, "tactics": ["rcases", "simp", "exact"], "tactic_count": 3}
{"name": "HasSum.smul_const", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Summable.smul_const", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Summable.tsum_smul_const", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasSum.smul_eq", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasSum.smul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tsum_smul_tsum", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.hasSum", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Module", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ContinuousLinearMap.summable", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.map_tsum", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.hasSum", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.hasSum'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Module", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ContinuousLinearEquiv.summable", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.tsum_eq_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Module", "is_tactic_proof": true, "tactics": ["by_cases", "by_cases", "exact", "simp", "constructor", "exacts", "have", "rw", "refine", "rintro", "simp", "simpa"], "tactic_count": 12}
{"name": "ContinuousLinearEquiv.map_tsum", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Module", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "MulAction.automorphize", "kind": "definition", "module": "Mathlib.Topology.Algebra.InfiniteSum.Module", "is_tactic_proof": true, "tactics": ["refine", "intro", "simp", "rw", "convert", "simp", "congr", "ext", "congr", "simp"], "tactic_count": 10}
{"name": "MulAction.automorphize_smul_left", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Module", "is_tactic_proof": true, "tactics": ["ext", "apply", "intro", "simp", "set", "have", "intro", "apply", "use", "change", "simp_rw", "exact"], "tactic_count": 12}
{"name": "AddAction.automorphize_smul_left", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Module", "is_tactic_proof": true, "tactics": ["ext", "apply", "intro", "simp", "set", "have", "intro", "apply", "use", "change", "simp_rw", "exact"], "tactic_count": 12}
{"name": "QuotientGroup.automorphize", "kind": "definition", "module": "Mathlib.Topology.Algebra.InfiniteSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientGroup.automorphize_smul_left", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientAddGroup.automorphize_smul_left", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasProd.tendsto_prod_nat", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.NatInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multipliable.tendsto_prod_tprod_nat", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.NatInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasProd.prod_range_mul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.NatInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasProd.zero_mul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.NatInt", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasProd.even_mul_odd", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.NatInt", "is_tactic_proof": true, "tactics": ["have", "replace", "refine", "simpa"], "tactic_count": 4}
{"name": "Multipliable.hasProd_iff_tendsto_nat", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.NatInt", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "Multipliable.comp_nat_add", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.NatInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multipliable.even_mul_odd", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.NatInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tprod_iSup_decode₂", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.NatInt", "is_tactic_proof": true, "tactics": ["rw", "refine", "rcases", "simp", "rw", "rw", "simp"], "tactic_count": 7}
{"name": "tprod_iUnion_decode₂", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.NatInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "rel_iSup_tprod", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.NatInt", "is_tactic_proof": true, "tactics": ["cases", "rw", "exact"], "tactic_count": 3}
{"name": "rel_iSup_prod", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.NatInt", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "rel_sup_mul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.NatInt", "is_tactic_proof": true, "tactics": ["convert", "simp", "rw"], "tactic_count": 3}
{"name": "Multipliable.prod_mul_tprod_nat_mul'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.NatInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tprod_eq_zero_mul'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.NatInt", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "tprod_even_mul_odd", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.NatInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasProd_nat_add_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.NatInt", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "multipliable_nat_add_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.NatInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasProd_nat_add_iff'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.NatInt", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Multipliable.prod_mul_tprod_nat_add", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.NatInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multipliable.tprod_eq_zero_mul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.NatInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_prod_nat_add", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.NatInt", "is_tactic_proof": true, "tactics": ["by_cases", "have", "ext1", "rw", "have", "simpa", "refine", "rwa"], "tactic_count": 8}
{"name": "cauchySeq_finset_iff_nat_tprod_vanishing", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.NatInt", "is_tactic_proof": true, "tactics": ["refine", "obtain", "refine", "split_ifs", "exact", "exact", "obtain", "exact"], "tactic_count": 8}
{"name": "multipliable_iff_nat_tprod_vanishing", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.NatInt", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multipliable.nat_tprod_vanishing", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.NatInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multipliable.tendsto_atTop_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.NatInt", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "HasProd.nat_mul_neg_add_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.NatInt", "is_tactic_proof": true, "tactics": ["change", "have", "refine", "refine", "simp", "cases", "exact", "exact", "rw", "simp", "not_false_eq_true,"], "tactic_count": 11}
{"name": "Multipliable.nat_mul_neg_add_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.NatInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tprod_nat_mul_neg_add_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.NatInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasProd.of_nat_of_neg_add_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.NatInt", "is_tactic_proof": true, "tactics": ["have", "have", "constructor", "rw", "rintro", "rw", "rintro", "exact"], "tactic_count": 8}
{"name": "Multipliable.of_nat_of_neg_add_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.NatInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tprod_of_nat_of_neg_add_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.NatInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasProd.int_rec", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.NatInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multipliable.int_rec", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.NatInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tprod_int_rec", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.NatInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasProd.nat_mul_neg", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.NatInt", "is_tactic_proof": true, "tactics": ["apply", "refine", "let", "let", "have", "intro", "simp", "rcases", "refine", "simp", "refine", "simp", "exact", "calc", "rw", "congr", "refine", "intro", "suffices", "rintro", "simp", "intro", "simp", "suffices", "lia"], "tactic_count": 25}
{"name": "Multipliable.nat_mul_neg", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.NatInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tprod_nat_mul_neg", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.NatInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasProd.of_add_one_of_neg_add_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.NatInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multipliable.of_add_one_of_neg_add_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.NatInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tprod_of_add_one_of_neg_add_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.NatInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasProd.of_nat_of_neg", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.NatInt", "is_tactic_proof": true, "tactics": ["refine", "rwa"], "tactic_count": 2}
{"name": "Multipliable.of_nat_of_neg", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.NatInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multipliable.tprod_of_nat_of_neg", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.NatInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "multipliable_int_iff_multipliable_nat_and_neg_add_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.NatInt", "is_tactic_proof": false, "tactics": ["refine", "exacts"], "tactic_count": 2}
{"name": "multipliable_int_iff_multipliable_nat_and_neg", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.NatInt", "is_tactic_proof": true, "tactics": ["refine", "exacts"], "tactic_count": 2}
{"name": "Summable.alternating", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.NatInt", "is_tactic_proof": true, "tactics": ["apply", "simp", "exact", "simp", "apply", "apply", "exact"], "tactic_count": 7}
{"name": "multipliable_pnat_iff_multipliable_succ", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.NatInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "multipliable_pnat_iff_multipliable_nat", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.NatInt", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "tprod_pnat_eq_tprod_succ", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.NatInt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tprod_zero_pnat_eq_tprod_nat", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.NatInt", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "tprod_int_eq_zero_mul_tprod_pnat", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.NatInt", "is_tactic_proof": true, "tactics": ["have", "have", "have", "rwa", "have", "rwa", "multipliable_nat_add_iff", "have", "simp", "mul_assoc,", "simp"], "tactic_count": 11}
{"name": "tprod_int_eq_zero_mul_tprod_pnat_sq", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.NatInt", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "NonarchimedeanGroup.cauchySeq_prod_of_tendsto_cofinite_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Nonarchimedean", "is_tactic_proof": true, "tactics": ["that", "apply", "intro", "rcases", "finite.", "use", "intro", "apply", "apply", "intro", "simpa"], "tactic_count": 11}
{"name": "NonarchimedeanGroup.cauchySeq_of_tendsto_div_nhds_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Nonarchimedean", "is_tactic_proof": false, "tactics": ["suffices", "simpa", "rw", "intro", "obtain", "obtain", "refine", "rintro", "apply", "wlog", "simpa", "obtain", "clear", "induction", "zero", "succ"], "tactic_count": 16}
{"name": "NonarchimedeanGroup.multipliable_of_tendsto_cofinite_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Nonarchimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonarchimedeanGroup.multipliable_iff_tendsto_cofinite_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Nonarchimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.Algebra.InfiniteSum.Nonarchimedean.0.Summable.mul_of_complete_nonarchimedean", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Nonarchimedean", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "HasSum.mul_of_nonarchimedean", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Nonarchimedean", "is_tactic_proof": true, "tactics": ["rw", "simp", "exact"], "tactic_count": 3}
{"name": "Summable.mul_of_nonarchimedean", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Nonarchimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tsum_mul_tsum_of_nonarchimedean", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Nonarchimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasProd_le_of_prod_le", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_hasProd_of_le_prod", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multipliable.tprod_le_of_prod_range_le", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasProd_le", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasProd_mono", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasProd_le_inj", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Order", "is_tactic_proof": true, "tactics": ["rw", "refine", "obtain", "rw", "exact", "rw", "exact"], "tactic_count": 7}
{"name": "Multipliable.tprod_le_tprod_of_inj", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multipliable.tprod_subtype_le", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Order", "is_tactic_proof": false, "tactics": ["apply", "apply"], "tactic_count": 2}
{"name": "prod_le_hasProd", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Order", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "isLUB_hasProd", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Order", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "le_hasProd", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lt_hasProd", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Order", "is_tactic_proof": true, "tactics": ["classical", "calc", "f"], "tactic_count": 3}
{"name": "Multipliable.prod_le_tprod", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multipliable.le_tprod", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multipliable.tprod_le_tprod", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multipliable.tprod_mono", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multipliable.tprod_le_of_prod_le", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tprod_le_of_prod_le'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Order", "is_tactic_proof": true, "tactics": ["by_cases", "by_cases", "exact", "rwa", "by_cases", "simpa", "rwa"], "tactic_count": 7}
{"name": "HasProd.one_le", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasProd.le_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_le_tprod", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Order", "is_tactic_proof": true, "tactics": ["by_cases", "by_cases", "exact", "simpa", "rw"], "tactic_count": 5}
{"name": "tprod_le_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Order", "is_tactic_proof": true, "tactics": ["by_cases", "by_cases", "exact", "simp", "exact", "rw"], "tactic_count": 6}
{"name": "hasProd_one_iff_of_one_le", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Order", "is_tactic_proof": true, "tactics": ["refine", "ext", "exact", "rintro", "exact"], "tactic_count": 5}
{"name": "hasProd_lt", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Order", "is_tactic_proof": true, "tactics": ["classical", "have", "have", "simpa"], "tactic_count": 4}
{"name": "hasProd_strict_mono", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multipliable.tprod_lt_tprod", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multipliable.tprod_strict_mono", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multipliable.one_lt_tprod", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Order", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "le_hasProd'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multipliable.le_tprod'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasProd_one_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multipliable.tprod_eq_one_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Order", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Multipliable.tprod_ne_one_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Order", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "isLUB_hasProd'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Order", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "hasProd_of_isLUB_of_one_le", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasProd_of_isGLB_of_le_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasProd_of_isLUB", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "multipliable_mabs_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finite.of_summable_const", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Order", "is_tactic_proof": false, "tactics": ["have", "obtain", "have", "have", "infer_instance"], "tactic_count": 5}
{"name": "Set.Finite.of_summable_const", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasProd.abs", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Order", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Multipliable.abs", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multipliable.abs_tprod", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Summable.tendsto_atTop_of_pos", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalTsum", "kind": "definition", "module": "Mathlib.Topology.Algebra.InfiniteSum.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cauchySeq_of_dist_le_of_summable", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Real", "is_tactic_proof": true, "tactics": ["lift", "apply", "exact_mod_cast", "exact_mod_cast"], "tactic_count": 4}
{"name": "cauchySeq_of_summable_dist", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dist_le_tsum_of_dist_le_of_tendsto", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Real", "is_tactic_proof": true, "tactics": ["refine", "refine", "rw", "refine", "exact"], "tactic_count": 5}
{"name": "dist_le_tsum_of_dist_le_of_tendsto₀", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Real", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "dist_le_tsum_dist_of_tendsto", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dist_le_tsum_dist_of_tendsto₀", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Real", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "not_summable_iff_tendsto_nat_atTop_of_nonneg", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Real", "is_tactic_proof": true, "tactics": ["lift", "simpa"], "tactic_count": 2}
{"name": "summable_iff_not_tendsto_nat_atTop_of_nonneg", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "summable_sigma_of_nonneg", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Real", "is_tactic_proof": true, "tactics": ["lift", "simpa"], "tactic_count": 2}
{"name": "summable_partition", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Real", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "summable_prod_of_nonneg", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "summable_of_sum_le", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "summable_of_sum_range_le", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Real", "is_tactic_proof": true, "tactics": ["refine", "rcases", "exact"], "tactic_count": 3}
{"name": "Real.tsum_le_of_sum_le", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.tsum_le_of_sum_range_le", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Summable.tsum_lt_tsum_of_nonneg", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasSum.mul_left", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Ring", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasSum.mul_right", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Ring", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Summable.mul_left", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Summable.mul_right", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Summable.tsum_mul_left", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Summable.tsum_mul_right", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Commute.tsum_right", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Ring", "is_tactic_proof": true, "tactics": ["classical", "by_cases", "exact", "exact"], "tactic_count": 4}
{"name": "Commute.tsum_left", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasSum.div_const", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Ring", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Summable.div_const", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasSum_mul_left_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasSum_mul_right_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasSum_div_const_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Ring", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "summable_mul_left_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "summable_mul_right_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "summable_div_const_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Ring", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "tsum_mul_left", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Ring", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "exact"], "tactic_count": 3}
{"name": "tsum_mul_right", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Ring", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "exact"], "tactic_count": 3}
{"name": "tsum_div_const", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Ring", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasSum.const_div", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Ring", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "Summable.const_div", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasSum_const_div_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Ring", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "summable_const_div_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Ring", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasSum.mul_eq", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasSum.mul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Summable.tsum_mul_tsum", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "summable_mul_prod_iff_summable_mul_sigma_antidiagonal", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "summable_sum_mul_antidiagonal_of_summable_mul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Ring", "is_tactic_proof": true, "tactics": ["rw", "conv", "exact"], "tactic_count": 3}
{"name": "Summable.tsum_mul_tsum_eq_tsum_sum_antidiagonal", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Ring", "is_tactic_proof": true, "tactics": ["conv_rhs", "rw", "exact"], "tactic_count": 3}
{"name": "summable_sum_mul_range_of_summable_mul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Ring", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Summable.tsum_mul_tsum_eq_tsum_sum_range", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Ring", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Summable.tsum_pow_mul_one_sub", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Ring", "is_tactic_proof": true, "tactics": ["refine", "simpa"], "tactic_count": 2}
{"name": "Summable.one_sub_mul_tsum_pow", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Ring", "is_tactic_proof": true, "tactics": ["refine", "simpa"], "tactic_count": 2}
{"name": "hasProd_one_add_of_hasSum_prod", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Ring", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "multipliable_one_add_of_summable_prod", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Ring", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "tprod_one_add", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Ring", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tprod_one_add_ordered", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Ring", "is_tactic_proof": true, "tactics": ["rcases", "simp", "obtain", "obtain", "convert", "unfold", "conv", "rw", "rw", "refine", "apply", "convert", "refine", "congr", "grind"], "tactic_count": 15}
{"name": "tprod_one_sub_ordered", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.Ring", "is_tactic_proof": true, "tactics": ["simp_rw", "obtain", "simp_rw", "simp_rw", "exact"], "tactic_count": 5}
{"name": "SummationFilter.instNeBotFinsetFilterOfNeBot", "kind": "instance", "module": "Mathlib.Topology.Algebra.InfiniteSum.SummationFilter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SummationFilter.neBot_or_eq_bot", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.SummationFilter", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "exact"], "tactic_count": 3}
{"name": "SummationFilter.support", "kind": "definition", "module": "Mathlib.Topology.Algebra.InfiniteSum.SummationFilter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SummationFilter.support_eq_limsInf", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.SummationFilter", "is_tactic_proof": true, "tactics": ["refine", "simpa", "singleton_subset_iff.mp"], "tactic_count": 3}
{"name": "SummationFilter.support_eq_univ_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.SummationFilter", "is_tactic_proof": true, "tactics": ["simp", "refine", "obtain", "have", "exact", "filter_upwards"], "tactic_count": 6}
{"name": "SummationFilter.support_eq_univ", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.SummationFilter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SummationFilter.instLeAtTopOfIsEmpty", "kind": "instance", "module": "Mathlib.Topology.Algebra.InfiniteSum.SummationFilter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SummationFilter.leAtTop_of_not_NeBot", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.SummationFilter", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "SummationFilter.instDecidablePredMemSetSupportOfLeAtTop", "kind": "instance", "module": "Mathlib.Topology.Algebra.InfiniteSum.SummationFilter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SummationFilter.instHasSupportOfLeAtTop", "kind": "instance", "module": "Mathlib.Topology.Algebra.InfiniteSum.SummationFilter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SummationFilter.eventually_mem_or_not_mem", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.SummationFilter", "is_tactic_proof": true, "tactics": ["rw", "intro", "filter_upwards"], "tactic_count": 3}
{"name": "SummationFilter.map", "kind": "definition", "module": "Mathlib.Topology.Algebra.InfiniteSum.SummationFilter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SummationFilter.support_map", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.SummationFilter", "is_tactic_proof": true, "tactics": ["ext", "rcases", "simp", "exact", "have"], "tactic_count": 5}
{"name": "SummationFilter.instHasSupportMap", "kind": "instance", "module": "Mathlib.Topology.Algebra.InfiniteSum.SummationFilter", "is_tactic_proof": true, "tactics": ["constructor", "by_cases", "simp", "filter_upwards", "have", "simp"], "tactic_count": 6}
{"name": "SummationFilter.comap", "kind": "definition", "module": "Mathlib.Topology.Algebra.InfiniteSum.SummationFilter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SummationFilter.support_comap", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.SummationFilter", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SummationFilter.instHasSupportComap", "kind": "instance", "module": "Mathlib.Topology.Algebra.InfiniteSum.SummationFilter", "is_tactic_proof": true, "tactics": ["constructor", "simp", "filter_upwards"], "tactic_count": 3}
{"name": "SummationFilter.instLeAtTopComap", "kind": "instance", "module": "Mathlib.Topology.Algebra.InfiniteSum.SummationFilter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SummationFilter.unconditional", "kind": "definition", "module": "Mathlib.Topology.Algebra.InfiniteSum.SummationFilter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SummationFilter.instLeAtTopUnconditional", "kind": "instance", "module": "Mathlib.Topology.Algebra.InfiniteSum.SummationFilter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SummationFilter.instNeBotUnconditional", "kind": "instance", "module": "Mathlib.Topology.Algebra.InfiniteSum.SummationFilter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SummationFilter.instIsCountablyGeneratedFinsetFilterUnconditionalOfCountable", "kind": "instance", "module": "Mathlib.Topology.Algebra.InfiniteSum.SummationFilter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SummationFilter.comap_unconditional", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.SummationFilter", "is_tactic_proof": true, "tactics": ["classical", "simp", "congr", "simp", "constructor", "refine", "simpa", "exact"], "tactic_count": 8}
{"name": "SummationFilter.eq_unconditional_of_finite", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.SummationFilter", "is_tactic_proof": true, "tactics": ["classical", "haveI", "have", "rw", "have", "have", "cases", "mk", "simp", "congr", "refine", "contrapose", "obtain", "simpa"], "tactic_count": 14}
{"name": "SummationFilter.conditional", "kind": "definition", "module": "Mathlib.Topology.Algebra.InfiniteSum.SummationFilter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SummationFilter.instLeAtTopConditional", "kind": "instance", "module": "Mathlib.Topology.Algebra.InfiniteSum.SummationFilter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SummationFilter.instNeBotConditionalOfNonemptyOfIsDirectedOrderOfIsCodirectedOrder", "kind": "instance", "module": "Mathlib.Topology.Algebra.InfiniteSum.SummationFilter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SummationFilter.instIsCountablyGeneratedFinsetFilterConditionalOfAtTopOfAtBot", "kind": "instance", "module": "Mathlib.Topology.Algebra.InfiniteSum.SummationFilter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SummationFilter.conditional_filter_eq_map_Iic", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.SummationFilter", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SummationFilter.conditional_filter_eq_map_Ici", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.SummationFilter", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SummationFilter.conditional_filter_eq_map_range", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.SummationFilter", "is_tactic_proof": true, "tactics": ["have", "simp", "apply", "rintro", "exact", "exact"], "tactic_count": 6}
{"name": "HasSumUniformlyOn.of_norm_le_summable", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.TsumUniformlyOn", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HasSumUniformlyOn.of_norm_le_summable_eventually", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.TsumUniformlyOn", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SummableLocallyUniformlyOn.of_locally_bounded_eventually", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.TsumUniformlyOn", "is_tactic_proof": true, "tactics": ["apply", "rw", "intro", "obtain", "exact"], "tactic_count": 5}
{"name": "SummableLocallyUniformlyOn_of_locally_bounded", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.TsumUniformlyOn", "is_tactic_proof": true, "tactics": ["apply", "intro", "obtain", "exact"], "tactic_count": 4}
{"name": "derivWithin_tsum", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.TsumUniformlyOn", "is_tactic_proof": true, "tactics": ["apply", "apply", "apply", "hasDerivAt_of_tendstoLocallyUniformlyOn", "obtain", "apply", "exact", "filter_upwards"], "tactic_count": 8}
{"name": "iteratedDerivWithin_tsum", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.TsumUniformlyOn", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "simp_rw", "rw", "exact", "derivWithin_congr", "intro", "by_cases", "simp", "exact", "exact"], "tactic_count": 12}
{"name": "HasProdUniformlyOn", "kind": "definition", "module": "Mathlib.Topology.Algebra.InfiniteSum.UniformOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultipliableUniformlyOn", "kind": "definition", "module": "Mathlib.Topology.Algebra.InfiniteSum.UniformOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultipliableUniformlyOn.exists", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.UniformOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasProdUniformlyOn.multipliableUniformlyOn", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.UniformOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasProdUniformlyOn_iff_tendstoUniformlyOn", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.UniformOn", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasProdUniformlyOn.congr", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.UniformOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasProdUniformlyOn.congr_right", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.UniformOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasProdUniformlyOn.tendstoUniformlyOn_finsetRange", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.UniformOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasProdUniformlyOn.hasProd", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.UniformOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasProdUniformlyOn.tprod_eqOn", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.UniformOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultipliableUniformlyOn.multipliable", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.UniformOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultipliableUniformlyOn.hasProdUniformlyOn", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.UniformOn", "is_tactic_proof": true, "tactics": ["obtain", "have", "rw", "exact", "hg.congr_inseparable_right", "tendsto_nhds_unique_inseparable"], "tactic_count": 6}
{"name": "multipliableUniformlyOn_iff_hasProdUniformlyOn", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.UniformOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasProdUniformlyOn.mono", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.UniformOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultipliableUniformlyOn.mono", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.UniformOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasProdLocallyUniformlyOn", "kind": "definition", "module": "Mathlib.Topology.Algebra.InfiniteSum.UniformOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultipliableLocallyUniformlyOn", "kind": "definition", "module": "Mathlib.Topology.Algebra.InfiniteSum.UniformOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasProdLocallyUniformlyOn_iff_tendstoLocallyUniformlyOn", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.UniformOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasProdLocallyUniformlyOn_of_of_forall_exists_nhds", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.UniformOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasProdLocallyUniformlyOn.hasProdUniformlyOn_of_isCompact", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.UniformOn", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "HasProdLocallyUniformlyOn.exists_hasProdUniformlyOn", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.UniformOn", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "HasProdUniformlyOn.hasProdLocallyUniformlyOn", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.UniformOn", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "hasProdLocallyUniformlyOn_of_forall_compact", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.UniformOn", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "HasProdLocallyUniformlyOn.multipliableLocallyUniformlyOn", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.UniformOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasProdLocallyUniformlyOn.mono", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.UniformOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultipliableLocallyUniformlyOn.mono", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.UniformOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "multipliableLocallyUniformlyOn_of_of_forall_exists_nhds", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.UniformOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultipliableLocallyUniformlyOn.multipliableUniformlyOn_of_isCompact", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.UniformOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultipliableLocallyUniformlyOn.exists_multipliableUniformlyOn", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.UniformOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasProdLocallyUniformlyOn.hasProd", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.UniformOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultipliableLocallyUniformlyOn.multipliable", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.UniformOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultipliableLocallyUniformlyOn.hasProdLocallyUniformlyOn", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.UniformOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasProdLocallyUniformlyOn.tprod_eqOn", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.UniformOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultipliableLocallyUniformlyOn_congr", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.UniformOn", "is_tactic_proof": true, "tactics": ["apply", "exact"], "tactic_count": 2}
{"name": "HasProdLocallyUniformlyOn.tendstoLocallyUniformlyOn_finsetRange", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.UniformOn", "is_tactic_proof": true, "tactics": ["rw", "intro", "obtain", "exact"], "tactic_count": 4}
{"name": "multipliableLocallyUniformlyOn_iff_hasProdLocallyUniformlyOn", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.UniformOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasProdUniformly", "kind": "definition", "module": "Mathlib.Topology.Algebra.InfiniteSum.UniformOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultipliableUniformly", "kind": "definition", "module": "Mathlib.Topology.Algebra.InfiniteSum.UniformOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultipliableUniformly.exists", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.UniformOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasProdUniformly.multipliableUniformly", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.UniformOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasProdUniformly_iff_tendstoUniformly", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.UniformOn", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasProdUniformly.hasProdUniformlyOn", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.UniformOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasProdUniformlyOn_univ_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.UniformOn", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MultipliableUniformly.multipliableUniformlyOn", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.UniformOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "multipliableUniformlyOn_univ_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.UniformOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasProdUniformly.congr", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.UniformOn", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "HasProdUniformly.tendstoUniformlyOn_finsetRange", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.UniformOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasProdUniformly.hasProd", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.UniformOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultipliableUniformly.multipliable", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.UniformOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultipliableUniformly.hasProdUniformly", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.UniformOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "multipliableUniformly_iff_hasProdUniformly", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.UniformOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasProdLocallyUniformly", "kind": "definition", "module": "Mathlib.Topology.Algebra.InfiniteSum.UniformOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultipliableLocallyUniformly", "kind": "definition", "module": "Mathlib.Topology.Algebra.InfiniteSum.UniformOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MultipliableLocallyUniformly.exists", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.UniformOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasProdLocallyUniformly.multipliableLocallyUniformly", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.UniformOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasProdLocallyUniformly_iff_tendstoLocallyUniformly", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.UniformOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "MultipliableLocallyUniformly.multipliableLocallyUniformlyOn", "kind": "theorem", "module": "Mathlib.Topology.Algebra.InfiniteSum.UniformOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "IntermediateField.continuousSMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.IntermediateField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IntermediateField.botContinuousSMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.IntermediateField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsOpenUnitsOfDiscreteTopology", "kind": "instance", "module": "Mathlib.Topology.Algebra.IsOpenUnits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsOpenUnitsOfContinuousInv", "kind": "instance", "module": "Mathlib.Topology.Algebra.IsOpenUnits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsOpenUnitsOfContinuousInv₀OfT1Space", "kind": "instance", "module": "Mathlib.Topology.Algebra.IsOpenUnits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpenUnits.of_isAdic", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsOpenUnits", "is_tactic_proof": true, "tactics": ["refine", "refine", "rw", "simp", "intro", "have", "have", "simp", "and_self,", "have", "simpa", "obtain", "obtain", "exact", "rw", "refine", "rintro", "have", "rw", "refine", "have", "trans", "rw", "simp", "rw", "exact"], "tactic_count": 26}
{"name": "isUniformEmbedding_translate_mul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUniformGroup.cauchy_iff_tendsto", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsUniformGroup.cauchy_iff_tendsto_swapped", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsUniformGroup.cauchy_map_iff_tendsto", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsUniformGroup.cauchy_map_iff_tendsto_swapped", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsRightUniformGroup.completeSpace_of_weaklyLocallyCompactSpace", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.isUniformGroup", "kind": "instance", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauchySeq.mul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauchySeq.mul_const", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauchySeq.const_mul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauchySeq.inv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "totallyBounded_iff_subset_finite_iUnion_nhds_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "totallyBounded_inv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Basic", "is_tactic_proof": true, "tactics": ["convert", "aesop"], "tactic_count": 2}
{"name": "TendstoUniformlyOnFilter.mul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TendstoUniformlyOnFilter.div", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TendstoUniformlyOn.mul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TendstoUniformlyOn.div", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TendstoUniformly.mul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TendstoUniformly.div", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformCauchySeqOn.mul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformCauchySeqOn.div", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TendstoLocallyUniformlyOn.mul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TendstoLocallyUniformlyOn.div", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TendstoLocallyUniformlyOn.inv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TendstoLocallyUniformly.mul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TendstoLocallyUniformly.div", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TendstoLocallyUniformly.inv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUniformGroup.of_compactSpace", "kind": "instance", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "topologicalGroup_is_uniform_of_compactSpace", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.isClosed_of_discrete", "kind": "instance", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Basic", "is_tactic_proof": true, "tactics": ["have", "obtain", "nhds_inter_eq_singleton_of_mem_discrete", "have", "apply", "intro", "contrapose", "simp", "rintro", "have", "exact"], "tactic_count": 11}
{"name": "Subgroup.tendsto_coe_cofinite_of_discrete", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.tendsto_coe_cofinite_of_discrete", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Basic", "is_tactic_proof": true, "tactics": ["replace", "exact"], "tactic_count": 2}
{"name": "IsTopologicalGroup.tendstoUniformly_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsTopologicalGroup.tendstoUniformlyOn_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsTopologicalGroup.tendstoLocallyUniformly_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsTopologicalGroup.tendstoLocallyUniformlyOn_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_div_comap_self", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Basic", "is_tactic_proof": false, "tactics": ["have", "ext", "simp", "have", "simpa", "simpa"], "tactic_count": 6}
{"name": "_private.Mathlib.Topology.Algebra.IsUniformGroup.Basic.0.IsDenseInducing.extend_Z_bilin_aux", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Basic", "is_tactic_proof": true, "tactics": ["let", "let", "have", "have", "rw", "exact", "have", "have", "rw", "simp_rw", "exact"], "tactic_count": 11}
{"name": "_private.Mathlib.Topology.Algebra.IsUniformGroup.Basic.0.IsDenseInducing.extend_Z_bilin_key", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Basic", "is_tactic_proof": true, "tactics": ["let", "let", "have", "have", "have", "have", "rwa", "rw", "exact", "rcases", "have", "rcases", "rw", "rcases", "rcases", "exists", "intro", "exact", "rcases", "obtain", "obtain", "have", "change", "exact", "rcases", "rcases", "exists", "rintro", "have", "simp", "rw", "have", "have", "have", "have", "exact"], "tactic_count": 36}
{"name": "IsDenseInducing.extend_Z_bilin", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Basic", "is_tactic_proof": true, "tactics": ["refine", "rintro", "constructor", "apply", "apply", "intro", "rcases", "exists", "simp_all", "suffices", "map", "rwa", "intro", "have", "rcases", "rw", "rcases", "rw", "rcases", "rw", "exists", "rw", "have", "grind"], "tactic_count": 24}
{"name": "QuotientGroup.completeSpace'", "kind": "instance", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Basic", "is_tactic_proof": true, "tactics": ["the", "sequential", "this", "countably", "letI", "letI", "haveI", "obtain", "obtain", "rw", "refine", "of", "have", "have", "simpa", "rw", "simp", "intro", "rcases", "refine", "obtain", "hM", "refine", "rw", "set", "have", "φ", "choose_spec", "successive", "term", "set", "have", "is", "have", "have", "simpa", "rw", "simp", "exact", "the", "since", "rcases", "refine", "convert", "exact"], "tactic_count": 45}
{"name": "QuotientGroup.completeSpace", "kind": "instance", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Basic", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "isUniformGroup_sInf", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isUniformGroup_iInf", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Constructions", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "isUniformGroup_inf", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Constructions", "is_tactic_proof": true, "tactics": ["rw", "refine", "cases"], "tactic_count": 3}
{"name": "IsUniformInducing.isUniformGroup", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUniformGroup.comap", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instIsUniformGroup", "kind": "instance", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Constructions", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Pi.instIsUniformGroup", "kind": "instance", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Constructions", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "instIsUniformGroupOfDiscreteUniformity", "kind": "instance", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformity_eq_comap_mul_inv_nhds_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformity_eq_comap_inv_mul_nhds_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformity_eq_comap_mul_inv_nhds_one_swapped", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Defs", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "uniformity_eq_comap_inv_mul_nhds_one_swapped", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Defs", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "uniformity_eq_comap_nhds_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Defs", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "uniformity_eq_comap_nhds_one_swapped", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Defs", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "IsUniformGroup.mk'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformContinuous_div", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformContinuous.div", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformContinuous.inv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Defs", "is_tactic_proof": true, "tactics": ["have", "simp_all"], "tactic_count": 2}
{"name": "uniformContinuous_inv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformContinuous.mul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Defs", "is_tactic_proof": true, "tactics": ["have", "simp_all"], "tactic_count": 2}
{"name": "Finset.uniformContinuous_prod", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Defs", "is_tactic_proof": true, "tactics": ["induction", "empty", "cons", "simp_rw", "simpa"], "tactic_count": 5}
{"name": "uniformContinuous_mul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformContinuous.mul_const", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformContinuous.const_mul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformContinuous_mul_left", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformContinuous_mul_right", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformContinuous.div_const", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformContinuous_div_const", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.uniformity_mul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.uniformity_inv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.uniformity_inv_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.uniformity_div", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Filter.Tendsto.uniformity_mul_iff_right", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.uniformity_mul_iff_left", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformContinuous.pow_const", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformContinuous_pow_const", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformContinuous.zpow_const", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformContinuous_zpow_const", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUniformGroup.to_topologicalGroup", "kind": "instance", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformity_translate_mul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instIsUniformGroup", "kind": "instance", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUniformGroup.isRightUniformGroup", "kind": "instance", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUniformGroup.isLeftUniformGroup", "kind": "instance", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUniformGroup.ext", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUniformGroup.ext_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUniformGroup.uniformity_countably_generated", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "comap_conj_nhds_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Defs", "is_tactic_proof": true, "tactics": ["let", "let", "let", "let", "have", "have", "rw", "uniformity_eq_comap_inv_mul_nhds_one,"], "tactic_count": 8}
{"name": "tendsto_conj_nhds_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.Tendsto.conj_nhds_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Defs", "is_tactic_proof": false, "tactics": ["have", "rwa", "convert"], "tactic_count": 3}
{"name": "IsUniformGroup.of_left_right", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isUniformGroup_iff_left_right", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eventually_forall_conj_nhds_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Filter.HasBasis.uniformity_of_nhds_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Filter.HasBasis.uniformity_of_nhds_one_inv_mul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Filter.HasBasis.uniformity_of_nhds_one_swapped", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Filter.HasBasis.uniformity_of_nhds_one_inv_mul_swapped", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "uniformContinuous_of_tendsto_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Defs", "is_tactic_proof": false, "tactics": ["have", "simp", "rw", "exact"], "tactic_count": 4}
{"name": "uniformContinuous_of_continuousAt_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.uniformContinuous_of_continuousAt_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUniformGroup.uniformContinuous_iff_isOpen_ker", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Defs", "is_tactic_proof": true, "tactics": ["refine", "apply", "apply", "rw", "exact"], "tactic_count": 5}
{"name": "uniformContinuous_monoidHom_of_continuous", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.isUniformInducing_of_isInducing", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsTopologicalGroup.rightUniformSpace", "kind": "definition", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformity_eq_comap_nhds_one'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isUniformGroup_of_commGroup", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Defs", "is_tactic_proof": true, "tactics": ["constructor", "simp", "tendsto_map'_iff,", "exact"], "tactic_count": 4}
{"name": "IsUniformGroup.rightUniformSpace_eq", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Defs", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "Subgroup.subgroupOfContinuousMulEquivOfLe", "kind": "definition", "module": "Mathlib.Topology.Algebra.IsUniformGroup.DiscreteSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.subgroupOfContinuousMulEquivOfLe_symm_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.DiscreteSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.subgroupOfContinuousMulEquivOfLe_toMulEquiv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.DiscreteSubgroup", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "Subgroup.discreteTopology_iff_of_finiteIndex", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.DiscreteSubgroup", "is_tactic_proof": true, "tactics": ["refine", "suffices", "rw", "this.isOpenEmbedding_subtypeVal.map_nhds_eq,", "exact"], "tactic_count": 5}
{"name": "Subgroup.discreteTopology_iff_of_isFiniteRelIndex", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.DiscreteSubgroup", "is_tactic_proof": true, "tactics": ["haveI", "rw"], "tactic_count": 2}
{"name": "Subgroup.Commensurable.discreteTopology_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.DiscreteSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TendstoUniformlyOn.eventually_forall_lt", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Order", "is_tactic_proof": false, "tactics": ["simp", "eventually_comap,", "conv", "have", "hf", "filter_upwards", "simpa"], "tactic_count": 7}
{"name": "TendstoUniformlyOn.eventually_forall_le", "kind": "theorem", "module": "Mathlib.Topology.Algebra.IsUniformGroup.Order", "is_tactic_proof": true, "tactics": ["filter_upwards"], "tactic_count": 1}
{"name": "ContinuousLinearMap.completion", "kind": "definition", "module": "Mathlib.Topology.Algebra.LinearMapCompletion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.toAddMonoidHom_completion", "kind": "theorem", "module": "Mathlib.Topology.Algebra.LinearMapCompletion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.coe_completion", "kind": "theorem", "module": "Mathlib.Topology.Algebra.LinearMapCompletion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.completion_apply_coe", "kind": "theorem", "module": "Mathlib.Topology.Algebra.LinearMapCompletion", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsLinearTopology.hasBasis_submodule", "kind": "theorem", "module": "Mathlib.Topology.Algebra.LinearTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLinearTopology.hasBasis_open_submodule", "kind": "theorem", "module": "Mathlib.Topology.Algebra.LinearTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLinearTopology.mk_of_hasBasis'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.LinearTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLinearTopology.mk_of_hasBasis", "kind": "theorem", "module": "Mathlib.Topology.Algebra.LinearTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLinearTopology_iff_hasBasis_submodule", "kind": "theorem", "module": "Mathlib.Topology.Algebra.LinearTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLinearTopology_iff_hasBasis_open_submodule", "kind": "theorem", "module": "Mathlib.Topology.Algebra.LinearTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLinearTopology.instOfDiscreteTopology", "kind": "instance", "module": "Mathlib.Topology.Algebra.LinearTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLinearTopology.hasBasis_subbimodule", "kind": "theorem", "module": "Mathlib.Topology.Algebra.LinearTopology", "is_tactic_proof": true, "tactics": ["refine", "rcases", "set", "set", "have", "have", "have", "have", "set", "have", "have", "calc", "uR", "have", "calc", "uR", "set", "have", "refine", "exact", "simp_rw", "simp_rw", "simp_rw", "have", "refine", "exact", "simp_rw", "simp_rw", "simp_rw", "have", "have", "exact"], "tactic_count": 32}
{"name": "IsLinearTopology.hasBasis_open_subbimodule", "kind": "theorem", "module": "Mathlib.Topology.Algebra.LinearTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLinearTopology.tendsto_smul_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.LinearTopology", "is_tactic_proof": true, "tactics": ["rw", "intro", "filter_upwards", "exact"], "tactic_count": 4}
{"name": "IsCentralScalar.isLinearTopology_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.LinearTopology", "is_tactic_proof": true, "tactics": ["constructor", "exact", "mk_of_hasBasis", "exact", "mk_of_hasBasis", "unop_smul_eq_smul"], "tactic_count": 6}
{"name": "IsLinearTopology.hasBasis_ideal", "kind": "theorem", "module": "Mathlib.Topology.Algebra.LinearTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLinearTopology.hasBasis_open_ideal", "kind": "theorem", "module": "Mathlib.Topology.Algebra.LinearTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLinearTopology_iff_hasBasis_ideal", "kind": "theorem", "module": "Mathlib.Topology.Algebra.LinearTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLinearTopology_iff_hasBasis_open_ideal", "kind": "theorem", "module": "Mathlib.Topology.Algebra.LinearTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLinearTopology.hasBasis_right_ideal", "kind": "theorem", "module": "Mathlib.Topology.Algebra.LinearTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLinearTopology.hasBasis_twoSidedIdeal", "kind": "theorem", "module": "Mathlib.Topology.Algebra.LinearTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLinearTopology.hasBasis_open_twoSidedIdeal", "kind": "theorem", "module": "Mathlib.Topology.Algebra.LinearTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLinearTopology_iff_hasBasis_twoSidedIdeal", "kind": "theorem", "module": "Mathlib.Topology.Algebra.LinearTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLinearTopology_iff_hasBasis_open_twoSidedIdeal", "kind": "theorem", "module": "Mathlib.Topology.Algebra.LinearTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLinearTopology.tendsto_mul_zero_of_left", "kind": "theorem", "module": "Mathlib.Topology.Algebra.LinearTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLinearTopology.tendsto_mul_zero_of_right", "kind": "theorem", "module": "Mathlib.Topology.Algebra.LinearTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLinearTopology.instMulOpposite", "kind": "instance", "module": "Mathlib.Topology.Algebra.LinearTopology", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Localization.ringTopology", "kind": "definition", "module": "Mathlib.Topology.Algebra.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instTopologicalSpaceLocalization", "kind": "instance", "module": "Mathlib.Topology.Algebra.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsTopologicalRingLocalization", "kind": "instance", "module": "Mathlib.Topology.Algebra.Localization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzWith.cauchySeq_comp", "kind": "theorem", "module": "Mathlib.Topology.Algebra.MetricSpace.Lipschitz", "is_tactic_proof": true, "tactics": ["rcases", "refine", "exact", "exact", "rw", "exact"], "tactic_count": 6}
{"name": "LipschitzOnWith.cauchySeq_comp", "kind": "theorem", "module": "Mathlib.Topology.Algebra.MetricSpace.Lipschitz", "is_tactic_proof": true, "tactics": ["rcases", "refine", "exact", "intro", "have", "apply", "exact", "rw", "exact"], "tactic_count": 9}
{"name": "continuousAt_of_locally_lipschitz", "kind": "theorem", "module": "Mathlib.Topology.Algebra.MetricSpace.Lipschitz", "is_tactic_proof": true, "tactics": ["refine", "tendsto_iff_dist_tendsto_zero.2", "exact"], "tactic_count": 3}
{"name": "LocallyLipschitzOn.exists_lipschitzOnWith_of_compact", "kind": "theorem", "module": "Mathlib.Topology.Algebra.MetricSpace.Lipschitz", "is_tactic_proof": true, "tactics": ["ball", "have", "replace", "let", "let", "exact", "choose", "have", "let", "refine", "simp_rw", "refine", "exact", "simp", "choose", "obtain", "hs.elim_nhdsWithin_subcover", "use", "intro", "let", "by_cases", "on", "refine", "mul_le_mul_of_nonneg_right", "exact", "the", "using", "calc", "edist", "exact", "simp_rw", "gcongr"], "tactic_count": 32}
{"name": "term_[⋀^_]→L[_]_", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Topology_Algebra_Module_Alternating_Basic___macroRules_term_[⋀^_]→L[_]__1", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Topology_Algebra_Module_Alternating_Basic___unexpand_ContinuousAlternatingMap_1", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.toContinuousMultilinearMap_injective", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.range_toContinuousMultilinearMap", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.funLike", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.continuousMapClass", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.coe_continuous", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.coe_toContinuousMultilinearMap", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.coe_mk", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.coe_toAlternatingMap", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.ext", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.toAlternatingMap_injective", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.range_toAlternatingMap", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.map_update_add", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.map_update_smul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.map_coord_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.map_update_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.map_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.map_eq_zero_of_eq", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.map_eq_zero_of_not_injective", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.codRestrict", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.instZero", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.instInhabited", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.coe_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.toContinuousMultilinearMap_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.toAlternatingMap_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.instSMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.coe_smul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.smul_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.toContinuousMultilinearMap_smul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.toAlternatingMap_smul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.instSMulCommClass", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.instIsScalarTower", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.instIsCentralScalar", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.instMulAction", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.instAdd", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.coe_add", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.add_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.toContinuousMultilinearMap_add", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.toAlternatingMap_add", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.addCommMonoid", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.applyAddHom", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.sum_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.toMultilinearAddHom", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.toContinuousLinearMap", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.prod", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.pi", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.coe_pi", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.pi_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.ofSubsingleton", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.ofSubsingleton_toAlternatingMap", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.constOfIsEmpty", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.constOfIsEmpty_toAlternatingMap", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.compContinuousLinearMap", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.compContinuousLinearMap_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.compContinuousAlternatingMap", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.compContinuousAlternatingMap_coe", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.continuousAlternatingMapCongrLeftEquiv", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.continuousAlternatingMapCongrRightEquiv", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.compContinuousAlternatingMap_coe", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.continuousAlternatingMapCongrEquiv", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.piEquiv", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.cons_add", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.vecCons_add", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.cons_smul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.vecCons_smul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.map_piecewise_add", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.map_add_univ", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.map_sum_finset", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.map_sum", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.restrictScalars", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.coe_restrictScalars", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.map_update_sub", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.map_vecCons_sub", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "ContinuousAlternatingMap.instNeg", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.coe_neg", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.neg_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.instSub", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.coe_sub", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.sub_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.instAddCommGroup", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.map_piecewise_smul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.map_smul_univ", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.ext_ring", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.uniqueOfCommRing", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.instDistribMulAction", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.instModule", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.toContinuousMultilinearMapLinear", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.toAlternatingMapLinear", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.piLinearEquiv", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.smulRight", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.compContinuousLinearMapₗ", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.compContinuousAlternatingMapₗ", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.alternatization", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.alternatization_apply_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousMultilinearMap.alternatization_apply_toAlternatingMap", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "ContinuousAlternatingMap.instTopologicalSpace", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.Alternating.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.isClosed_range_toContinuousMultilinearMap", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Topology", "is_tactic_proof": true, "tactics": ["simp", "repeat", "exact"], "tactic_count": 3}
{"name": "ContinuousAlternatingMap.instUniformSpace", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.Alternating.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.isUniformEmbedding_toContinuousMultilinearMap", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.uniformContinuous_toContinuousMultilinearMap", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.uniformContinuous_coe_fun", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.uniformContinuous_eval_const", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.instIsUniformAddGroup", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.Alternating.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.instUniformContinuousConstSMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.Alternating.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.isUniformInducing_postcomp", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Topology", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ContinuousAlternatingMap.completeSpace", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Topology", "is_tactic_proof": true, "tactics": ["wlog", "rw", "exact", "intro", "use", "ext", "simp", "have", "rw", "apply"], "tactic_count": 10}
{"name": "ContinuousAlternatingMap.instCompleteSpace", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.Alternating.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.isUniformEmbedding_restrictScalars", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Topology", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ContinuousAlternatingMap.uniformContinuous_restrictScalars", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.isEmbedding_toContinuousMultilinearMap", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.instIsTopologicalAddGroup", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.Alternating.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.continuous_toContinuousMultilinearMap", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.instContinuousConstSMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.Alternating.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.instContinuousSMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.Alternating.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.hasBasis_nhds_zero_of_basis", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Topology", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ContinuousAlternatingMap.hasBasis_nhds_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.isClosedEmbedding_toContinuousMultilinearMap", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.instContinuousEvalConst", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.Alternating.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.instT2Space", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.Alternating.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.instT3Space", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.Alternating.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.toContinuousMultilinearMapCLM", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Alternating.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.isEmbedding_restrictScalars", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.continuous_restrictScalars", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.restrictScalarsCLM", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Alternating.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.liftCLM", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Alternating.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.liftCLM_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.apply", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Alternating.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.apply_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.hasSum_eval", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAlternatingMap.tsum_eval", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Alternating.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousSMul.of_nhds_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousNeg.of_continuousConstSMul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.eq_top_of_nonempty_interior'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Basic", "is_tactic_proof": true, "tactics": ["rcases", "refine", "rw", "have", "tendsto_const_nhds.add", "rw", "obtain", "have", "rwa"], "tactic_count": 9}
{"name": "Module.punctured_nhds_neBot", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Basic", "is_tactic_proof": true, "tactics": ["rcases", "suffices", "refine", "convert", "rw", "intro", "simpa"], "tactic_count": 7}
{"name": "continuousSMul_inducedₛₗ", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousSMul_induced", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.IsSeparable.span", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "have", "apply", "rwa", "apply", "exact"], "tactic_count": 7}
{"name": "Submodule.topologicalAddGroup", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.mapsTo_smul_closure", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.smul_closure_subset", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.topologicalClosure", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.topologicalClosure_coe", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.le_topologicalClosure", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.closure_subset_topologicalClosure_span", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Submodule.isClosed_topologicalClosure", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.topologicalClosure_minimal", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.topologicalClosure_mono", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.submodule_topologicalClosure_eq", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.dense_iff_topologicalClosure_eq_top", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Submodule.topologicalClosure.completeSpace", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.isClosed_or_dense_of_isCoatom", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Basic", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "instCompleteSpaceSubtypeMemSubmoduleOfIsClosedCoe", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.closure_coe_iSup_map_single", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "exact", "simp", "intro", "rcases", "refine", "simp_all", "exact"], "tactic_count": 9}
{"name": "Submodule.topologicalClosure_iSup_map_single", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.continuous_on_pi", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Basic", "is_tactic_proof": true, "tactics": ["cases", "classical", "have", "ext", "exact", "rw", "fun_prop"], "tactic_count": 7}
{"name": "linearMapOfMemClosureRangeCoe", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "linearMapOfTendsto", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.isClosed_range_coe", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientModule.Quotient.topologicalSpace", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.isOpenMap_mkQ", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.isOpenQuotientMap_mkQ", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.topologicalAddGroup_quotient", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.continuousSMul_quotient", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.t3_quotient_of_isClosed", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuum_le_cardinal_of_nontriviallyNormedField", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Cardinality", "is_tactic_proof": false, "tactics": ["suffices", "rcases", "simpa", "apply", "refine", "rcases", "have", "tendsto_const_nhds.add", "rw", "have", "rcases", "refine", "simp", "apply", "simpa"], "tactic_count": 15}
{"name": "continuum_le_cardinal_of_module", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Cardinality", "is_tactic_proof": false, "tactics": ["have", "simpa", "simpa"], "tactic_count": 3}
{"name": "cardinal_eq_of_mem_nhds_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Cardinality", "is_tactic_proof": true, "tactics": ["therefore", "obtain", "have", "intro", "apply", "rintro", "simp", "exact", "have", "intro", "have", "have", "simp_rw", "apply", "rw", "exact", "exact", "rw", "filter_upwards", "exact", "have", "intro", "have", "invFun", "left_inv", "right_inv", "exact", "apply"], "tactic_count": 28}
{"name": "cardinal_eq_of_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Cardinality", "is_tactic_proof": true, "tactics": ["let", "let", "have", "have", "have", "rwa"], "tactic_count": 6}
{"name": "cardinal_eq_of_isOpen", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Cardinality", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "continuum_le_cardinal_of_isOpen", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Cardinality", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.Countable.dense_compl", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Cardinality", "is_tactic_proof": true, "tactics": ["rw", "by_contra", "apply", "calc"], "tactic_count": 4}
{"name": "WeakDual.characterSpace", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.CharacterSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakDual.CharacterSpace.instFunLike", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.CharacterSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakDual.CharacterSpace.instContinuousLinearMapClass", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.CharacterSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakDual.CharacterSpace.coe_coe", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.CharacterSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakDual.CharacterSpace.ext", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.CharacterSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakDual.CharacterSpace.toCLM", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.CharacterSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakDual.CharacterSpace.coe_toCLM", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.CharacterSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "WeakDual.CharacterSpace.instIsEmpty", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.CharacterSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "WeakDual.CharacterSpace.union_zero_isClosed", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.CharacterSpace", "is_tactic_proof": true, "tactics": ["simp", "exact", "isClosed_iInter", "isClosed_iInter"], "tactic_count": 4}
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{"name": "WeakDual.CharacterSpace.eq_set_map_one_map_mul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.CharacterSpace", "is_tactic_proof": true, "tactics": ["ext", "refine", "rintro", "lift", "exact", "rintro", "refine", "rintro", "exact"], "tactic_count": 9}
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{"name": "ClosedSubmodule.instSetLike", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.ClosedSubmodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClosedSubmodule.instPartialOrder", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.ClosedSubmodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClosedSubmodule.toCloseds_injective", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.ClosedSubmodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ClosedSubmodule.instSMulMemClass", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.ClosedSubmodule", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ContinuousLinearEquiv.map_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.map_add", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.map_smulₛₗ", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.map_smul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.map_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.continuous", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.continuousOn", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.continuousAt", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.continuousWithinAt", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.comp_continuousOn_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.comp_continuous_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.ext₁", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.refl", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.refl_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.coe_refl", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.coe_refl'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.symm", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.toLinearEquiv_symm", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.coe_symm_toLinearEquiv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.toHomeomorph_symm", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.coe_symm_toHomeomorph", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.Simps.apply", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.Simps.symm_apply", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.symm_map_nhds_eq", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.trans", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.trans_toLinearEquiv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "ContinuousLinearEquiv.prodCongr", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.prodCongr_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.coe_prodCongr", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.prodCongr_symm", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.prodComm", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.prodComm_symm", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.prodAssoc", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.prodAssoc_toLinearEquiv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.coe_prodAssoc", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.prodAssoc_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.prodAssoc_symm_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.prodProdProdComm", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.prodProdProdComm_symm", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.prodProdProdComm_toLinearEquiv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.coe_prodProdProdComm", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.prodProdProdComm_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.prodUnique", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.coe_prodUnique", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.prodUnique_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.prodUnique_symm_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.uniqueProd", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.coe_uniqueProd", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.uniqueProd_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.uniqueProd_symm_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.bijective", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.injective", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.surjective", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.trans_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.apply_symm_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.symm_apply_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.symm_trans_self", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.self_trans_symm", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.symm_trans_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.symm_image_image", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.image_symm_image", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.comp_coe", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.coe_comp_coe_symm", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.coe_symm_comp_coe", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.symm_comp_self", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "ContinuousLinearEquiv.self_comp_symm", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "ContinuousLinearEquiv.symm_symm", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.symm_bijective", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.refl_symm", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.symm_symm_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.symm_apply_eq", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.eq_symm_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.image_eq_preimage_symm", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.image_symm_eq_preimage", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ContinuousLinearEquiv.symm_preimage_preimage", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.preimage_symm_preimage", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.isUniformEmbedding", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.isUniformEmbedding", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.equivOfInverse", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.equivOfInverse_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.symm_equivOfInverse", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.equivOfInverse'", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.equivOfInverse'_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.symm_equivOfInverse'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.eq_comp_toContinuousLinearMap_symm", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "ContinuousLinearEquiv.automorphismGroup", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.ulift", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.arrowCongrEquiv", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.piCongrLeft", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.sumPiEquivProdPi", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.piUnique", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.piCongrRight", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.piCongrRight_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.piCongrRight_symm_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.smulLeft", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.ofUnit", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.toUnit", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.unitsEquiv", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.unitsEquiv_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.unitsEquivAut", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.unitsEquivAut_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.unitsEquivAut_apply_symm", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.unitsEquivAut_symm_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.funUnique", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.coe_funUnique", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.coe_funUnique_symm", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.piFinTwo", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.finTwoArrow", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.consEquivL", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.finCons", "kind": "abbrev", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.skewProd", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.skewProd_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.skewProd_symm_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.neg", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.coe_neg", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.neg_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousLinearEquiv.symm_neg", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.map_sub", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.map_neg", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.equivOfRightInverse", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.fst_equivOfRightInverse", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.snd_equivOfRightInverse", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.equivOfRightInverse_symm_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.IsInvertible", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.inverse", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.isInvertible_equiv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.inverse_equiv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousLinearMap.inverse_of_not_isInvertible", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.isInvertible_zero_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": true, "tactics": ["refine", "have", "refine", "simp", "exact", "rintro", "let", "invFun", "left_inv", "right_inv", "map_add", "map_smul", "refine", "ext", "exact"], "tactic_count": 15}
{"name": "ContinuousLinearMap.inverse_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": true, "tactics": ["by_cases", "rcases", "ext", "exact", "exact"], "tactic_count": 5}
{"name": "ContinuousLinearMap.IsInvertible.comp", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "exact"], "tactic_count": 3}
{"name": "ContinuousLinearMap.IsInvertible.of_inverse", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.inverse_eq", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": true, "tactics": ["have", "rw", "rfl"], "tactic_count": 3}
{"name": "ContinuousLinearMap.IsInvertible.inverse_apply_eq", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": true, "tactics": ["rcases", "simp", "exact"], "tactic_count": 3}
{"name": "ContinuousLinearMap.isInvertible_equiv_comp", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "have", "rw", "simp", "rintro", "simp"], "tactic_count": 7}
{"name": "ContinuousLinearMap.isInvertible_comp_equiv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "have", "rw", "simp", "rintro", "simp"], "tactic_count": 7}
{"name": "ContinuousLinearMap.inverse_equiv_comp", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": true, "tactics": ["by_cases", "rcases", "simp", "rfl", "rw"], "tactic_count": 5}
{"name": "ContinuousLinearMap.inverse_comp_equiv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": true, "tactics": ["by_cases", "rcases", "simp", "rfl", "rw"], "tactic_count": 5}
{"name": "ContinuousLinearMap.IsInvertible.inverse_comp_of_left", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": true, "tactics": ["rcases", "simp"], "tactic_count": 2}
{"name": "ContinuousLinearMap.IsInvertible.inverse_comp_apply_of_left", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousLinearMap.IsInvertible.inverse_comp_of_right", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": true, "tactics": ["rcases", "simp"], "tactic_count": 2}
{"name": "ContinuousLinearMap.IsInvertible.inverse_comp_apply_of_right", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousLinearMap.ringInverse_equiv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": true, "tactics": ["suffices", "simp", "rfl"], "tactic_count": 3}
{"name": "ContinuousLinearMap.inverse_eq_ringInverse", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": true, "tactics": ["by_cases", "obtain", "rw", "change", "ext", "simp", "suffices", "contrapose", "rcases", "use", "ext", "dsimp", "rw", "simp"], "tactic_count": 14}
{"name": "ContinuousLinearMap.ringInverse_eq_inverse", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "ContinuousLinearMap.inverse_id", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ContinuousLinearMap.IsInvertible.self_comp_inverse", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": true, "tactics": ["rcases", "simp"], "tactic_count": 2}
{"name": "ContinuousLinearMap.IsInvertible.self_apply_inverse", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": true, "tactics": ["rcases", "simp"], "tactic_count": 2}
{"name": "ContinuousLinearMap.IsInvertible.inverse_comp_self", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": true, "tactics": ["rcases", "simp"], "tactic_count": 2}
{"name": "ContinuousLinearMap.IsInvertible.inverse_apply_self", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": true, "tactics": ["rcases", "simp"], "tactic_count": 2}
{"name": "ContinuousLinearMap.IsInvertible.bijective", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": true, "tactics": ["rcases", "simp"], "tactic_count": 2}
{"name": "ContinuousLinearMap.IsInvertible.injective", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.IsInvertible.surjective", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.IsInvertible.inverse", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": true, "tactics": ["rcases", "simp"], "tactic_count": 2}
{"name": "ContinuousLinearMap.IsInvertible.inverse_inverse", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": true, "tactics": ["rcases", "simp"], "tactic_count": 2}
{"name": "ContinuousLinearMap.IsInvertible.of_isInvertible_inverse", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": true, "tactics": ["by_contra", "obtain", "simp_all"], "tactic_count": 3}
{"name": "ContinuousLinearMap.isInvertible_inverse_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.coprod_comp_prodComm", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "ContinuousLinearEquiv.ofEq", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.submoduleMap", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.submoduleMap_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "ContinuousLinearEquiv.submoduleMap_symm_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "ContinuousLinearEquiv.ofSubmodules", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.ofSubmodules_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.ofSubmodules_symm_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.ofSubmodule'", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.ofSubmodule'_toContinuousLinearMap", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "ContinuousLinearEquiv.ofSubmodule'_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.ofSubmodule'_symm_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.ClosedComplemented.exists_submodule_equiv_prod", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.opContinuousLinearEquiv", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.instModuleFinite", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.finiteDimensional", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unique_topology_of_t2", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.FiniteDimension", "is_tactic_proof": true, "tactics": ["refine", "rw", "intro", "rcases", "have", "mem_compl_singleton_iff.mpr", "have", "refine", "mem_of_superset", "by_cases", "rw", "exact", "rw", "by_contra", "suffices", "rw", "exact", "notMem_compl_iff.mpr", "refine", "rw", "exact", "calc", "map_id.symm", "conv_rhs", "congr", "ext", "rw"], "tactic_count": 27}
{"name": "LinearMap.continuous_of_isClosed_ker", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.FiniteDimension", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "rw", "exact", "have", "le_antisymm", "have", "rw", "exact", "have", "rw", "exact", "let", "have", "rfl", "suffices", "rw", "exact", "have", "refine", "unique_topology_of_t2", "rw", "exact", "simp_rw", "exact"], "tactic_count": 25}
{"name": "LinearMap.continuous_iff_isClosed_ker", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.continuous_of_nonzero_on_open", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.FiniteDimension", "is_tactic_proof": true, "tactics": ["refine", "rcases", "have", "rw", "exact", "rwa"], "tactic_count": 6}
{"name": "_private.Mathlib.Topology.Algebra.Module.FiniteDimension.0.continuous_equivFun_basis_aux", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.FiniteDimension", "is_tactic_proof": true, "tactics": ["letI", "letI", "suffices", "intro", "induction", "zero", "rw", "exact", "succ", "haveI", "have", "intro", "letI", "let", "have", "have", "rw", "exact", "have", "exact", "have", "exact", "have", "intro", "by_cases", "rw", "rw", "exact", "have", "have", "rw", "have", "le_antisymm", "rw", "exact", "have", "exact", "rw", "intro", "change", "exact"], "tactic_count": 41}
{"name": "isModuleTopologyOfFiniteDimensional", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.continuous_of_finiteDimensional", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.continuousLinearMapClassOfFiniteDimensional", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_equivFun_basis", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.toContinuousLinearMap", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.End.toContinuousLinearMap", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.coe_toContinuousLinearMap'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.coe_toContinuousLinearMap", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.coe_toContinuousLinearMap_symm", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.det_toContinuousLinearMap", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.ker_toContinuousLinearMap", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.FiniteDimension", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LinearMap.range_toContinuousLinearMap", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.isOpenMap_of_finiteDimensional", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.canLiftContinuousLinearMap", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.toContinuousLinearMap_eq_iff_eq_toLinearMap", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.FiniteDimension", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousLinearMap.toLinearMap_eq_iff_eq_toContinuousLinearMap", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.FiniteDimension", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LinearEquiv.toContinuousLinearEquiv", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.coe_toContinuousLinearEquiv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.coe_toContinuousLinearEquiv'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.coe_toContinuousLinearEquiv_symm", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.coe_toContinuousLinearEquiv_symm'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearEquiv.toLinearEquiv_toContinuousLinearEquiv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.FiniteDimension", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "LinearEquiv.toLinearEquiv_toContinuousLinearEquiv_symm", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.FiniteDimension", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "LinearEquiv.canLiftContinuousLinearEquiv", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteDimensional.nonempty_continuousLinearEquiv_of_finrank_eq", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteDimensional.nonempty_continuousLinearEquiv_iff_finrank_eq", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.ofFinrankEq", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.constrL", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.coe_constrL", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.equivFunL", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.equivFunL_symm_apply_repr", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.constrL_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Module.Basis.constrL_basis", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.toContinuousLinearEquivOfDetNeZero", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.coe_toContinuousLinearEquivOfDetNeZero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.FiniteDimension", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "ContinuousLinearMap.toContinuousLinearEquivOfDetNeZero_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.toLin_finTwoProd_toContinuousLinearMap", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiniteDimensional.complete", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.FiniteDimension", "is_tactic_proof": true, "tactics": ["set", "have", "exact"], "tactic_count": 3}
{"name": "Submodule.complete_of_finiteDimensional", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.closed_of_finiteDimensional", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearMap.isClosedEmbedding_of_injective", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosedEmbedding_smul_left", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosedMap_smul_left", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.FiniteDimension", "is_tactic_proof": true, "tactics": ["by_cases", "simp_rw", "exact", "exact"], "tactic_count": 4}
{"name": "ContinuousLinearMap.exists_right_inverse_of_surjective", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyCompactSpace.of_finiteDimensional_of_complete", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.FiniteDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "term_→SL[_]_", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Topology_Algebra_Module_LinearMap___macroRules_term_→SL[_]__1", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Topology_Algebra_Module_LinearMap___unexpand_ContinuousLinearMap_1", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "term_→L[_]_", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Submodule.topologicalClosure_map", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DenseRange.topologicalClosure_map_submodule", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": true, "tactics": ["rw", "simp", "exact"], "tactic_count": 3}
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{"name": "ContinuousLinearMap.inhabited", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ContinuousLinearMap.toContinuousAddMonoidHom_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.uniqueOfLeft", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.uniqueOfRight", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.exists_ne_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": true, "tactics": ["by_contra", "exact"], "tactic_count": 2}
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{"name": "ContinuousLinearMap.one", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ContinuousLinearMap.applySMulCommClass", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ContinuousLinearMap.isComplete_ker", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ContinuousLinearMap.completeSpace_eqLocus", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.codRestrict", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.coe_codRestrict", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Submodule.range_subtypeL", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.ker_subtypeL", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.smulRight", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.smulRight_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.smulRight_comp_smulRight", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "ContinuousLinearMap.range_smulRight_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.toSpanSingleton", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.toSpanSingleton_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.toSpanSingleton_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "ContinuousLinearMap.toSpanSingleton_apply_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.toSpanSingleton_apply_map_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "ContinuousLinearMap.toSpanSingleton_add", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.toSpanSingleton_smul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.smulRight_id", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.smulRight_one_eq_toSpanSingleton", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.toLinearMap_toSpanSingleton", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.comp_toSpanSingleton", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.toSpanSingleton_comp", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.toSpanSingleton_inj", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousLinearMap.toSpanSingleton_comp_toSpanSingleton", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.map_neg", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "ContinuousLinearMap.map_sub", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "ContinuousLinearMap.sub_apply'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.neg", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.neg_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.coe_neg", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.coe_neg'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.toContinuousAddMonoidHom_neg", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.sub", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.addCommGroup", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.sub_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.coe_sub", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.coe_sub'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.toContinuousAddMonoidHom_sub", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.comp_neg", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "ContinuousLinearMap.neg_comp", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "ContinuousLinearMap.comp_sub", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "ContinuousLinearMap.sub_comp", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "ContinuousLinearMap.ring", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.intCast_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.toSpanSingleton_pow", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "ContinuousLinearMap.projKerOfRightInverse", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.coe_projKerOfRightInverse_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.projKerOfRightInverse_apply_idem", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": true, "tactics": ["ext1", "simp"], "tactic_count": 2}
{"name": "ContinuousLinearMap.projKerOfRightInverse_comp_inv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.isOpenMap_of_ne_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.smul_comp", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.comp_smul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "ContinuousLinearMap.comp_smulₛₗ", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "ContinuousLinearMap.distribMulAction", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.module", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.isCentralScalar", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.coeLM", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.coeLMₛₗ", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.toSpanSingletonLE", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.smulRightₗ", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.coe_smulRightₗ", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.algebra", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.algebraMap_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.restrictScalars", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.coe_restrictScalars", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.coe_restrictScalars'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.toContinuousAddMonoidHom_restrictScalars", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.restrictScalars_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.restrictScalars_add", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.restrictScalars_smul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.restrictScalarsₗ", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.coe_restrictScalarsₗ", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.restrictScalars_sub", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.restrictScalars_neg", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.ClosedComplemented", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.ClosedComplemented.exists_isClosed_isCompl", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.ClosedComplemented.isClosed", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": true, "tactics": ["rcases", "have", "exact"], "tactic_count": 3}
{"name": "Submodule.closedComplemented_bot", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.closedComplemented_top", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.closedComplemented_ker_of_rightInverse", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.isIdempotentElem_toLinearMap_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousLinearMap.IsIdempotentElem.ext_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ContinuousLinearMap.IsIdempotentElem.range_mem_invtSubmodule_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ContinuousLinearMap.IsIdempotentElem.ker_mem_invtSubmodule_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ContinuousLinearMap.IsIdempotentElem.commute_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ContinuousLinearMap.IsIdempotentElem.commute_iff_of_isUnit", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": true, "tactics": ["have", "lift", "simpa"], "tactic_count": 3}
{"name": "ContinuousLinearMap.IsIdempotentElem.isClosed_range", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "topDualPairing", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "topDualPairing_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.prod", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.LinearMapPiProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.coe_prod", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMapPiProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.prod_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMapPiProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.inl", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.LinearMapPiProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.inr", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.LinearMapPiProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.inl_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMapPiProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.inr_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMapPiProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.coe_inl", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMapPiProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.coe_inr", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMapPiProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.comp_inl_add_comp_inr", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMapPiProd", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousLinearMap.ker_prod", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMapPiProd", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousLinearMap.fst", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.LinearMapPiProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.snd", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.LinearMapPiProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.coe_fst", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMapPiProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.coe_fst'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMapPiProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.coe_snd", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMapPiProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.coe_snd'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMapPiProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.fst_prod_snd", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMapPiProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.fst_comp_prod", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMapPiProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.snd_comp_prod", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMapPiProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.fst_comp_inl", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMapPiProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.fst_comp_inr", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMapPiProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.snd_comp_inl", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMapPiProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.snd_comp_inr", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMapPiProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.prodMap", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.LinearMapPiProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.coe_prodMap", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMapPiProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.coe_prodMap'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMapPiProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.pi", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.LinearMapPiProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.coe_pi'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMapPiProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.coe_pi", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMapPiProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.pi_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMapPiProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.pi_eq_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMapPiProd", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "ContinuousLinearMap.pi_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMapPiProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.pi_comp", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMapPiProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.proj", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.LinearMapPiProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.proj_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMapPiProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.proj_pi", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMapPiProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.coe_proj", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMapPiProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.pi_proj", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMapPiProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.pi_proj_comp", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMapPiProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.iInf_ker_proj", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMapPiProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.compRightL", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.LinearMapPiProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.compRightL_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMapPiProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.single", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.LinearMapPiProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.sum_comp_single", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMapPiProd", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousLinearMap.range_prod_eq", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMapPiProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.ker_prod_ker_le_ker_coprod", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMapPiProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.prodEquiv", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.LinearMapPiProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.prod_ext_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMapPiProd", "is_tactic_proof": true, "tactics": ["simp", "rfl"], "tactic_count": 2}
{"name": "ContinuousLinearMap.prod_ext", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMapPiProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.prodₗ", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.LinearMapPiProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.coprod", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.LinearMapPiProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.coprod_add", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMapPiProd", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "ContinuousLinearMap.range_coprod", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMapPiProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.comp_fst_add_comp_snd", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMapPiProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.comp_coprod", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMapPiProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.coprod_comp_inl", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMapPiProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.coprod_comp_inr", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMapPiProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.coprod_inl_inr", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMapPiProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.coprodEquiv", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.LinearMapPiProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.ker_coprod_of_disjoint_range", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearMapPiProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearPMap.IsClosed", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.LinearPMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearPMap.IsClosable", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.LinearPMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearPMap.IsClosed.isClosable", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearPMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearPMap.IsClosable.leIsClosable", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearPMap", "is_tactic_proof": true, "tactics": ["obtain", "have", "rw", "exact", "use", "rw", "exact"], "tactic_count": 7}
{"name": "LinearPMap.IsClosable.existsUnique", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearPMap", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "LinearPMap.closure", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.LinearPMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearPMap.closure_def", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearPMap", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LinearPMap.closure_def'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearPMap", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LinearPMap.IsClosable.graph_closure_eq_closure_graph", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearPMap", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "LinearPMap.le_closure", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearPMap", "is_tactic_proof": true, "tactics": ["by_cases", "refine", "rw", "exact", "rw"], "tactic_count": 5}
{"name": "LinearPMap.IsClosable.closure_mono", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearPMap", "is_tactic_proof": true, "tactics": ["refine", "rw", "rw", "exact"], "tactic_count": 4}
{"name": "LinearPMap.IsClosable.closure_isClosed", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearPMap", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "LinearPMap.IsClosable.closureIsClosable", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearPMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearPMap.isClosable_iff_exists_closed_extension", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearPMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearPMap.hasCore_def", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearPMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearPMap.closureHasCore", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearPMap", "is_tactic_proof": true, "tactics": ["refine", "congr", "ext", "simp", "intro", "exact", "let", "have", "rw", "exact"], "tactic_count": 10}
{"name": "LinearPMap.inverse_closed_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearPMap", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "LinearPMap.closure_inverse_graph", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearPMap", "is_tactic_proof": true, "tactics": ["rw", "apply", "simp", "apply", "have", "have", "simp", "rw", "apply"], "tactic_count": 9}
{"name": "LinearPMap.inverse_isClosable_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearPMap", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "intro", "simp", "rw", "have", "rw", "rw", "apply", "simp", "exact", "exact", "intro", "use", "exact"], "tactic_count": 16}
{"name": "LinearPMap.inverse_closure", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LinearPMap", "is_tactic_proof": true, "tactics": ["apply", "rw"], "tactic_count": 2}
{"name": "locallyConvexSpace_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LocallyConvex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConvexSpace.ofBases", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LocallyConvex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConvexSpace.convex_basis_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LocallyConvex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "locallyConvexSpace_iff_exists_convex_subset", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LocallyConvex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConvexSpace.ofBasisZero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LocallyConvex", "is_tactic_proof": false, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "locallyConvexSpace_iff_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LocallyConvex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "locallyConvexSpace_iff_exists_convex_subset_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LocallyConvex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConvexSpace.toLocPathConnectedSpace", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.LocallyConvex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Convex.locPathConnectedSpace", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LocallyConvex", "is_tactic_proof": true, "tactics": ["refine", "let", "let", "refine", "exact", "refine", "exact"], "tactic_count": 7}
{"name": "LocallyConvexSpace.convex_open_basis_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LocallyConvex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Disjoint.exists_open_convexes", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LocallyConvex", "is_tactic_proof": true, "tactics": ["letI", "haveI", "have", "rw", "rcases", "refine", "subset_add_left", "simp_rw", "simp_rw", "exact"], "tactic_count": 10}
{"name": "exists_open_convex_of_notMem", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LocallyConvex", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "LocallyConvexSpace.sInf", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LocallyConvex", "is_tactic_proof": true, "tactics": ["letI", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "LocallyConvexSpace.iInf", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LocallyConvex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConvexSpace.inf", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LocallyConvex", "is_tactic_proof": true, "tactics": ["rw", "refine", "cases"], "tactic_count": 3}
{"name": "LocallyConvexSpace.induced", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LocallyConvex", "is_tactic_proof": true, "tactics": ["letI", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "Topology.IsInducing.locallyConvexSpace", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LocallyConvex", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "instLocallyConvexSpaceSubtypeMemSubmodule", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.LocallyConvex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.locallyConvexSpace", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.LocallyConvex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.locallyConvexSpace", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.LocallyConvex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearOrderedSemiring.toLocallyConvexSpace", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.LocallyConvex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Convex.eventually_nhdsWithin_segment", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.LocallyConvex", "is_tactic_proof": true, "tactics": ["rw", "obtain", "refine", "suffices", "exact"], "tactic_count": 5}
{"name": "moduleTopology", "kind": "abbrev", "module": "Mathlib.Topology.Algebra.Module.ModuleTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_moduleTopology", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.ModuleTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsModuleTopology", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.ModuleTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleTopology.continuousSMul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.ModuleTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleTopology.continuousAdd", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.ModuleTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsModuleTopology.toContinuousSMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.ModuleTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsModuleTopology.toContinuousAdd", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.ModuleTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "moduleTopology_le", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.ModuleTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsModuleTopology.of_continuous_id", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.ModuleTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsModuleTopology.instSubsingleton", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.ModuleTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsModuleTopology.isoₛₗ", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.ModuleTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsModuleTopology.iso", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.ModuleTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsTopologicalSemiring.toIsModuleTopology", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.ModuleTopology", "is_tactic_proof": true, "tactics": ["apply", "rw", "sense,", "topology", "a", "apply", "this", "exact", "that", "on", "exact"], "tactic_count": 11}
{"name": "IsTopologicalSemiring.toOppositeIsModuleTopology", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.ModuleTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsModuleTopology.continuous_of_distribMulActionHomₑ", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.ModuleTopology", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsModuleTopology.continuous_of_distribMulActionHom", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.ModuleTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsModuleTopology.continuous_of_linearMapₛₗ", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.ModuleTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsModuleTopology.continuous_of_linearMap", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.ModuleTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsModuleTopology.continuous_neg", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.ModuleTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsModuleTopology.continuousNeg", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.ModuleTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsModuleTopology.topologicalAddGroup", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.ModuleTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsModuleTopology.continuous_of_ringHom", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.ModuleTopology", "is_tactic_proof": true, "tactics": ["let", "let", "have", "exact"], "tactic_count": 4}
{"name": "IsModuleTopology.isQuotientMap_of_surjectiveₛₗ", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.ModuleTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsModuleTopology.isQuotientMap_of_surjective", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.ModuleTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsModuleTopology.isOpenQuotientMap_of_surjectiveₛₗ", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.ModuleTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsModuleTopology.isOpenQuotientMap_of_surjective", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.ModuleTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsModuleTopology.isOpenMap_of_surjectiveₛₗ", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.ModuleTopology", "is_tactic_proof": false, "tactics": ["have", "letI", "have", "isOpenQuotientMap_of_surjectiveₛₗ", "intro", "exact"], "tactic_count": 6}
{"name": "IsModuleTopology.isOpenMap_of_surjective", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.ModuleTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ModuleTopology.eq_coinduced_of_surjectiveₛₗ", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.ModuleTopology", "is_tactic_proof": true, "tactics": ["letI", "haveI", "exact"], "tactic_count": 3}
{"name": "ModuleTopology.eq_coinduced_of_surjective", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.ModuleTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsModuleTopology.instQuot", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.ModuleTopology", "is_tactic_proof": true, "tactics": ["constructor", "have", "have", "have", "rw"], "tactic_count": 5}
{"name": "IsModuleTopology.instProd", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.ModuleTopology", "is_tactic_proof": true, "tactics": ["constructor", "have", "have", "refine", "le_antisymm", "sInf_le", "let", "let", "have", "have", "let", "rw", "change", "let", "let", "rw", "ext", "fun_prop"], "tactic_count": 18}
{"name": "IsModuleTopology.instPi", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.ModuleTopology", "is_tactic_proof": true, "tactics": ["induction", "exact", "infer_instance", "let", "suffices", "suffices", "have", "infer_instance"], "tactic_count": 8}
{"name": "IsModuleTopology.continuous_bilinear_of_pi_fintype", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.ModuleTopology", "is_tactic_proof": true, "tactics": ["classical", "cases", "have", "ext", "nth_rw", "simp_rw", "refine", "rw", "push_cast", "simp", "rw", "haveI", "fun_prop"], "tactic_count": 13}
{"name": "IsModuleTopology.continuous_bilinear_of_finite_left", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.ModuleTopology", "is_tactic_proof": true, "tactics": ["obtain", "let", "let", "have", "rw", "exact"], "tactic_count": 6}
{"name": "IsModuleTopology.continuous_bilinear_of_finite_right", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.ModuleTopology", "is_tactic_proof": true, "tactics": ["rw", "fun_prop"], "tactic_count": 2}
{"name": "IsModuleTopology.continuous_mul_of_finite", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.ModuleTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsModuleTopology.isTopologicalRing", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.ModuleTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "term_[×_]→L[_]_", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Topology_Algebra_Module_Multilinear_Basic___macroRules_term_[×_]→L[_]__1", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Topology_Algebra_Module_Multilinear_Basic___unexpand_ContinuousMultilinearMap_1", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.toMultilinearMap_injective", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.funLike", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.continuousMapClass", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.Simps.apply", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.coe_continuous", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.coe_coe", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.ext", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.map_update_add", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.map_update_smul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.map_coord_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.map_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.instZero", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.instInhabited", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.zero_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.toMultilinearMap_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.instSMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.smul_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.toMultilinearMap_smul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.instSMulCommClass", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.instIsScalarTower", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.instIsCentralScalar", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.instMulAction", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.instAdd", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.add_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.toMultilinearMap_add", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.addCommMonoid", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.applyAddHom", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.sum_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.toContinuousLinearMap", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.prod", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.prod_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.pi", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.coe_pi", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.pi_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.codRestrict", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.ofSubsingleton", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.constOfIsEmpty", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.compContinuousLinearMap", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.compContinuousLinearMap_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.compContinuousMultilinearMap", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.compContinuousMultilinearMap_coe", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "ContinuousMultilinearMap.prodEquiv", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.prod_ext_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ContinuousMultilinearMap.prod_ext", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.eq_prod_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.add_prod_add", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.smul_prod_smul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.zero_prod_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.piEquiv", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.domDomCongr", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.domDomCongrEquiv", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.linearDeriv", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.linearDeriv_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": true, "tactics": ["unfold", "simp", "rfl"], "tactic_count": 3}
{"name": "ContinuousMultilinearMap.cons_add", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.cons_smul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.map_piecewise_add", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.map_add_univ", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.map_sum_finset", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.map_sum", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.restrictScalars", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.coe_restrictScalars", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.map_update_sub", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.instNeg", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.neg_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.instSub", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.sub_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.instAddCommGroup", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.neg_prod_neg", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.sub_prod_sub", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.map_piecewise_smul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.map_smul_univ", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.ext_ring", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.instDistribMulAction", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.instModule", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.toMultilinearMapLinear", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.piLinearEquiv", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.mkPiAlgebraFin", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.mkPiAlgebraFin_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.mkPiAlgebra", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.mkPiAlgebra_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.mkPiAlgebra_eq_mkPiAlgebraFin", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "ContinuousMultilinearMap.smulRight", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.mkPiRing", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.mkPiRing_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.mkPiRing_apply_one_eq_self", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.mkPiRing_eq_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ContinuousMultilinearMap.mkPiRing_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "ContinuousMultilinearMap.mkPiRing_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Bornology.IsVonNBounded.image_multilinear'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.IsVonNBounded.image_multilinear", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Bounded", "is_tactic_proof": true, "tactics": ["cases", "inl", "exact", "inr"], "tactic_count": 4}
{"name": "ContinuousMultilinearMap.toUniformOnFun", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.range_toUniformOnFun", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Topology", "is_tactic_proof": true, "tactics": ["ext", "constructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 6}
{"name": "ContinuousMultilinearMap.toUniformOnFun_toFun", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.instTopologicalSpace", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.instUniformSpace", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.isUniformInducing_toUniformOnFun", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.isUniformEmbedding_toUniformOnFun", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.isEmbedding_toUniformOnFun", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.uniformContinuous_coe_fun", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.uniformContinuous_eval_const", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.instIsUniformAddGroup", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.instUniformContinuousConstSMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.isUniformInducing_postcomp", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Topology", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ContinuousMultilinearMap.completeSpace", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Topology", "is_tactic_proof": true, "tactics": ["classical", "wlog", "rw", "exact", "intro", "use", "simp", "have", "rw", "simp", "apply_rules", "exact", "exact", "isClosed_iInter", "isClosed_iInter", "exact", "isClosed_iInter", "isClosed_iInter"], "tactic_count": 18}
{"name": "ContinuousMultilinearMap.instCompleteSpace", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.isUniformEmbedding_restrictScalars", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Topology", "is_tactic_proof": false, "tactics": ["letI", "rw", "convert", "exact"], "tactic_count": 4}
{"name": "ContinuousMultilinearMap.uniformContinuous_restrictScalars", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.instIsTopologicalAddGroup", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.instContinuousConstSMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Topology", "is_tactic_proof": true, "tactics": ["letI", "haveI", "infer_instance"], "tactic_count": 3}
{"name": "ContinuousMultilinearMap.instContinuousSMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.hasBasis_nhds_zero_of_basis", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Topology", "is_tactic_proof": true, "tactics": ["letI", "haveI", "rw", "refine", "exact", "exact"], "tactic_count": 6}
{"name": "ContinuousMultilinearMap.hasBasis_nhds_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.instContinuousEvalConstForall", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.instT2Space", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMultilinearMap.instT3Space", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.Multilinear.Topology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ContinuousLinearMap.isUniformEmbedding_postcomp", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.StrongTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.isInducing_postcomp", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.StrongTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.isEmbedding_postcomp", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.StrongTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.precompUniformConvergenceCLM", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.StrongTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.precomp", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.StrongTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.postcompUniformConvergenceCLM", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.StrongTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.postcomp", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.StrongTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.toUniformConvergenceCLM_continuous", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.StrongTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.map_add₂", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.StrongTopology", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ContinuousLinearMap.map_zero₂", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.StrongTopology", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ContinuousLinearMap.map_smulₛₗ₂", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.StrongTopology", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ContinuousLinearMap.toLinearMap₁₂", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.StrongTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.toLinearMap₁₂_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.StrongTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.toLinearMap₁₂_injective", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.StrongTopology", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousLinearMap.toLinearMap₁₂_inj", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.StrongTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.map_smul₂", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.StrongTopology", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ContinuousLinearMap.map_sub₂", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.StrongTopology", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ContinuousLinearMap.map_neg₂", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.StrongTopology", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ContinuousLinearMap.toBilinForm", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.StrongTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.toBilinForm_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.StrongTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.toBilinForm_injective", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.StrongTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.toBilinForm_inj", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.StrongTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.isUniformEmbedding_restrictScalars", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.StrongTopology", "is_tactic_proof": true, "tactics": ["rw", "convert", "exact"], "tactic_count": 3}
{"name": "ContinuousLinearMap.uniformContinuous_restrictScalars", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.StrongTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.isEmbedding_restrictScalars", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.StrongTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.continuous_restrictScalars", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.StrongTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.restrictScalarsL", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.StrongTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.coe_restrictScalarsL", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.StrongTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.coe_restrict_scalarsL'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.StrongTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.coprodEquivL", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.StrongTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.prodL", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.StrongTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.toSpanSingletonCLE", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.StrongTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.arrowCongrSL", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.StrongTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.arrowCongr", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.StrongTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.arrowCongr_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.StrongTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.arrowCongr_symm", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.StrongTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.conjContinuousAlgEquiv", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.StrongTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.conjContinuousAlgEquiv_apply_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.StrongTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.symm_conjContinuousAlgEquiv_apply_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.StrongTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.conjContinuousAlgEquiv_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.StrongTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.symm_conjContinuousAlgEquiv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.StrongTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.conjContinuousAlgEquiv_refl", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.StrongTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.conjContinuousAlgEquiv_trans", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.StrongTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompactConvergenceCLM", "kind": "abbrev", "module": "Mathlib.Topology.Algebra.Module.StrongTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompactConvergenceCLM.term_→SL_c[_]_", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.StrongTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompactConvergenceCLM._aux_Mathlib_Topology_Algebra_Module_StrongTopology___macroRules_CompactConvergenceCLM_term_→SL_c[_]__1", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.StrongTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompactConvergenceCLM._aux_Mathlib_Topology_Algebra_Module_StrongTopology___unexpand_CompactConvergenceCLM_1", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.StrongTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompactConvergenceCLM.term_→L_c[_]_", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.StrongTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompactConvergenceCLM._aux_Mathlib_Topology_Algebra_Module_StrongTopology___macroRules_CompactConvergenceCLM_term_→L_c[_]__1", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.StrongTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompactConvergenceCLM._aux_Mathlib_Topology_Algebra_Module_StrongTopology___unexpand_CompactConvergenceCLM_2", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.StrongTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompactConvergenceCLM.continuousSMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.StrongTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompactConvergenceCLM.instContinuousEvalConst", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.StrongTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompactConvergenceCLM.instT2Space", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.StrongTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompactConvergenceCLM.hasBasis_nhds_zero_of_basis", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.StrongTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompactConvergenceCLM.hasBasis_nhds_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.StrongTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.precompCompactConvergenceCLM", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.StrongTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.postcompCompactConvergenceCLM", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.StrongTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.continuousLinearEquiv", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.TransferInstance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.toLinearEquiv_continuousLinearEquiv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.TransferInstance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Shrink.continuousLinearEquiv", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.TransferInstance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformFun.continuousSMul_induced_of_range_bounded", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.UniformConvergence", "is_tactic_proof": false, "tactics": ["have", "let", "have", "simp", "exact", "apply", "intro", "have", "rcases", "refine", "rw", "exact", "intro", "have", "refine", "simpa", "intro", "simp", "simpa"], "tactic_count": 19}
{"name": "UniformOnFun.continuousSMul_induced_of_image_bounded", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.UniformConvergence", "is_tactic_proof": true, "tactics": ["obtain", "simp", "refine", "letI", "set", "map_add", "refine", "simpa"], "tactic_count": 8}
{"name": "UniformOnFun.continuousSMul_submodule_of_image_bounded", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakBilin", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.WeakBilin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakBilin.instAddCommGroup", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.WeakBilin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakBilin.instModule'", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.WeakBilin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakBilin.instIsScalarTower", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.WeakBilin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakBilin.instTopologicalSpace", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.WeakBilin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakBilin.coeFn_continuous", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.WeakBilin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakBilin.eval_continuous", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.WeakBilin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakBilin.continuous_of_continuous_eval", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.WeakBilin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakBilin.isEmbedding", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.WeakBilin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakBilin.tendsto_iff_forall_eval_tendsto", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.WeakBilin", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "WeakBilin.instContinuousAdd", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.WeakBilin", "is_tactic_proof": true, "tactics": ["refine", "refine", "cast", "ext", "simp"], "tactic_count": 5}
{"name": "WeakBilin.instContinuousSMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.WeakBilin", "is_tactic_proof": true, "tactics": ["refine", "refine", "ext", "simp"], "tactic_count": 4}
{"name": "WeakBilin.eval", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.WeakBilin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakBilin.instIsTopologicalAddGroup", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.WeakBilin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakDual", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.WeakDual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakDual.instMulAction", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.WeakDual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakDual.instDistribMulAction", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.WeakDual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakDual.instModule'", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.WeakDual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakDual.instContinuousConstSMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.WeakDual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakDual.instContinuousSMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.WeakDual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakDual.coeFn_continuous", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.WeakDual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakDual.eval_continuous", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.WeakDual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakDual.continuous_of_continuous_eval", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.WeakDual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakDual.instT2Space", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.WeakDual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakDual.instAddCommGroup", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.WeakDual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakDual.instIsTopologicalAddGroup", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.WeakDual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakSpace", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.WeakDual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakSpace.instModule'", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.WeakDual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakSpace.instIsScalarTower", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.WeakDual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakSpace.instContinuousSMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.WeakDual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakSpace.map", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.WeakDual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakSpace.map_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.WeakDual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakSpace.coe_map", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.WeakDual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toWeakSpace", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.WeakDual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toWeakSpaceCLM", "kind": "definition", "module": "Mathlib.Topology.Algebra.Module.WeakDual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toWeakSpaceCLM_eq_toWeakSpace", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.WeakDual", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "toWeakSpaceCLM_bijective", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.WeakDual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpenMap_toWeakSpace_symm", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.WeakDual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakSpace.isOpen_of_isOpen", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.WeakDual", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "tendsto_iff_forall_eval_tendsto_topDualPairing", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Module.WeakDual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakSpace.instAddCommGroup", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.WeakDual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakSpace.instIsTopologicalAddGroup", "kind": "instance", "module": "Mathlib.Topology.Algebra.Module.WeakDual", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instContinuousMulOrderDual", "kind": "instance", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instContinuousMulULift", "kind": "instance", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMul.to_continuousSMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMul.to_continuousSMul_op", "kind": "instance", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMul.induced", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": true, "tactics": ["let", "refine", "simp", "fun_prop"], "tactic_count": 4}
{"name": "continuous_mul_left", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": true, "tactics": ["fun_prop"], "tactic_count": 1}
{"name": "continuous_mul_right", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": true, "tactics": ["fun_prop"], "tactic_count": 1}
{"name": "tendsto_mul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.const_mul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.mul_const", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_nhds_mul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "nhds_one_mul_nhds", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhds_mul_nhds_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "one_le_nhds_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.TendstoNhdsWithinIoi.const_mul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.TendstoNhdsWithinIio.const_mul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.TendstoNhdsWithinIoi.mul_const", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.TendstoNhdsWithinIio.mul_const", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Specializes.mul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Inseparable.mul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Specializes.pow", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Inseparable.pow", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.units", "kind": "definition", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.continuousMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.continuousMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.continuousMul'", "kind": "instance", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousMul_of_discreteTopology", "kind": "instance", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMul.of_nhds_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousMul_of_comm_of_nhds_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": true, "tactics": ["apply", "intro", "simp_rw"], "tactic_count": 3}
{"name": "isClosed_setOf_map_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosed_setOf_map_mul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "mulHomOfMemClosureRangeCoe", "kind": "definition", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mulHomOfTendsto", "kind": "definition", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulHom.isClosed_range_coe", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monoidHomOfMemClosureRangeCoe", "kind": "definition", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monoidHomOfTendsto", "kind": "definition", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.isClosed_range_coe", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsInducing.continuousMul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousMul_induced", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.continuousMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.continuousMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_mem_nhds_zero_mul_subset", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": true, "tactics": ["refine", "exact", "rintro", "exact", "rintro", "use", "rw", "exact", "union_subset", "intro", "have", "rw", "rcases", "rw", "exact"], "tactic_count": 15}
{"name": "tendsto_mul_nhds_zero_prod_of_disjoint_cocompact", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_mul_prod_nhds_zero_of_disjoint_cocompact", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_mul_coprod_nhds_zero_inf_of_disjoint_cocompact", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": ["have", "calc", "apply", "apply", "exact", "apply", "exact"], "tactic_count": 7}
{"name": "tendsto_mul_nhds_zero_of_disjoint_cocompact", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Tendsto.tendsto_mul_zero_of_disjoint_cocompact_right", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tendsto.tendsto_mul_zero_of_disjoint_cocompact_left", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_mul_cocompact_nhds_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": true, "tactics": ["set", "set", "have", "have", "eventually_map.mpr", "have", "rw", "exact", "have", "rw", "exact", "exact"], "tactic_count": 12}
{"name": "tendsto_mul_cofinite_nhds_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": true, "tactics": ["letI", "haveI", "letI", "haveI", "rw", "exact"], "tactic_count": 6}
{"name": "GroupWithZero.isOpen_singleton_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "by_cases", "obtain", "cases", "obtain", "simpa"], "tactic_count": 7}
{"name": "exists_open_nhds_one_split", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "exists_nhds_one_split", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_open_nhds_one_mul_subset", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Filter.HasBasis.mul_self", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "Subsemigroup.top_closure_mul_self_subset", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.topologicalClosure", "kind": "definition", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.coe_topologicalClosure", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.le_topologicalClosure", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.isClosed_topologicalClosure", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.topologicalClosure_minimal", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemigroup.commSemigroupTopologicalClosure", "kind": "abbrev", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.mul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Submonoid.top_closure_mul_self_subset", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.top_closure_mul_self_eq", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.topologicalClosure", "kind": "definition", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.coe_topologicalClosure", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.le_topologicalClosure", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.isClosed_topologicalClosure", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.topologicalClosure_minimal", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.commMonoidTopologicalClosure", "kind": "abbrev", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_nhds_one_split4", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "use", "intro", "simpa"], "tactic_count": 5}
{"name": "tendsto_list_prod", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_list_prod", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousOn_list_prod", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": true, "tactics": ["intro", "rw", "refine", "specialize", "rw", "exact"], "tactic_count": 6}
{"name": "continuous_pow", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoid.continuousConstSMul_nat", "kind": "instance", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoid.continuousSMul_nat", "kind": "instance", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.pow", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousOn_pow", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousAt_pow", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.pow", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.pow", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.pow", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.pow", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_cocompact_mul_left", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": true, "tactics": ["refine", "convert", "ext", "simp"], "tactic_count": 4}
{"name": "Filter.tendsto_cocompact_mul_right", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": true, "tactics": ["refine", "simp", "exact"], "tactic_count": 3}
{"name": "IsScalarTower.continuousConstSMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SMulCommClass.continuousConstSMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instContinuousMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.instContinuousMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.units_map", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.mem_nhds_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_multiset_prod", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": true, "tactics": ["rcases", "simpa"], "tactic_count": 2}
{"name": "tendsto_finset_prod", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_multiset_prod", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": true, "tactics": ["rcases", "simpa"], "tactic_count": 2}
{"name": "continuousOn_multiset_prod", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": true, "tactics": ["rcases", "simpa"], "tactic_count": 2}
{"name": "continuous_finset_prod", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousOn_finset_prod", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eventuallyEq_prod", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": true, "tactics": ["replace", "filter_upwards", "simp"], "tactic_count": 3}
{"name": "LocallyFinite.exists_finset_mulSupport", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": true, "tactics": ["rcases", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "finprod_eventually_eq_prod", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_finprod", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": true, "tactics": ["refine", "rcases", "refine", "exact"], "tactic_count": 4}
{"name": "continuous_finprod_cond", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "instContinuousAddAdditiveOfContinuousMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instContinuousMulMultiplicativeOfContinuousAdd", "kind": "instance", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousMul_sInf", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousMul_iInf", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "continuousMul_inf", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": true, "tactics": ["rw", "refine", "cases"], "tactic_count": 3}
{"name": "ContinuousMap.mulRight", "kind": "definition", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.coe_mulRight", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.mulLeft", "kind": "definition", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.coe_mulLeft", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DenseRange.addChar_eq_of_eval_one_eq", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid.AddChar", "is_tactic_proof": true, "tactics": ["refine", "simp"], "tactic_count": 2}
{"name": "continuous_mul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.mul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_of_div_tendsto_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Continuous.mul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.mul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.mul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.mul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FunOnFinite.continuous_map", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid.FunOnFinite", "is_tactic_proof": true, "tactics": ["classical", "have", "refine", "simp", "exact"], "tactic_count": 5}
{"name": "FunOnFinite.continuous_linearMap", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Monoid.FunOnFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsScalarTower.continuousSMul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.MulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instContinuousSMulULift", "kind": "instance", "module": "Mathlib.Topology.Algebra.MulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousSMul.continuousConstSMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.MulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousSMul.induced", "kind": "theorem", "module": "Mathlib.Topology.Algebra.MulAction", "is_tactic_proof": true, "tactics": ["let", "refine", "simp", "fun_prop"], "tactic_count": 4}
{"name": "Filter.Tendsto.smul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.MulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.smul_const", "kind": "theorem", "module": "Mathlib.Topology.Algebra.MulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.smul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.MulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.smul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.MulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.smul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.MulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.smul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.MulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousSMul.op", "kind": "instance", "module": "Mathlib.Topology.Algebra.MulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.continuousSMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.MulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Specializes.smul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.MulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Inseparable.smul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.MulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.smul_set", "kind": "theorem", "module": "Mathlib.Topology.Algebra.MulAction", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "smul_set_closure_subset", "kind": "theorem", "module": "Mathlib.Topology.Algebra.MulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsInducing.continuousSMul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.MulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SMulMemClass.continuousSMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.MulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.continuousSMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.MulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulAction.continuousSMul_compHom", "kind": "theorem", "module": "Mathlib.Topology.Algebra.MulAction", "is_tactic_proof": true, "tactics": ["let", "exact"], "tactic_count": 2}
{"name": "Submonoid.continuousSMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.MulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.continuousSMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.MulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "stabilizer_isOpen", "kind": "theorem", "module": "Mathlib.Topology.Algebra.MulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.univ_smul_nhds_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.MulAction", "is_tactic_proof": true, "tactics": ["refine", "have", "rcases", "simp", "simp", "exact"], "tactic_count": 6}
{"name": "Filter.top_smul_nhds_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.MulAction", "is_tactic_proof": true, "tactics": ["rw", "rintro", "exact"], "tactic_count": 3}
{"name": "Prod.continuousSMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.MulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instContinuousSMulForall", "kind": "instance", "module": "Mathlib.Topology.Algebra.MulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousSMul_sInf", "kind": "theorem", "module": "Mathlib.Topology.Algebra.MulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousSMul_iInf", "kind": "theorem", "module": "Mathlib.Topology.Algebra.MulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousSMul_inf", "kind": "theorem", "module": "Mathlib.Topology.Algebra.MulAction", "is_tactic_proof": true, "tactics": ["rw", "refine", "cases"], "tactic_count": 3}
{"name": "AddTorsor.connectedSpace", "kind": "theorem", "module": "Mathlib.Topology.Algebra.MulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MvPolynomial.continuous_eval", "kind": "theorem", "module": "Mathlib.Topology.Algebra.MvPolynomial", "is_tactic_proof": true, "tactics": ["continuity"], "tactic_count": 1}
{"name": "NonUnitalSubalgebra.instIsTopologicalSemiring", "kind": "instance", "module": "Mathlib.Topology.Algebra.NonUnitalAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.topologicalClosure", "kind": "definition", "module": "Mathlib.Topology.Algebra.NonUnitalAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.le_topologicalClosure", "kind": "theorem", "module": "Mathlib.Topology.Algebra.NonUnitalAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.isClosed_topologicalClosure", "kind": "theorem", "module": "Mathlib.Topology.Algebra.NonUnitalAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.topologicalClosure_minimal", "kind": "theorem", "module": "Mathlib.Topology.Algebra.NonUnitalAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.nonUnitalCommSemiringTopologicalClosure", "kind": "abbrev", "module": "Mathlib.Topology.Algebra.NonUnitalAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.map_topologicalClosure_le", "kind": "theorem", "module": "Mathlib.Topology.Algebra.NonUnitalAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.topologicalClosure_map_le", "kind": "theorem", "module": "Mathlib.Topology.Algebra.NonUnitalAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.topologicalClosure_map", "kind": "theorem", "module": "Mathlib.Topology.Algebra.NonUnitalAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.topologicalClosure_adjoin_le_centralizer_centralizer", "kind": "theorem", "module": "Mathlib.Topology.Algebra.NonUnitalAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.instIsTopologicalRing", "kind": "instance", "module": "Mathlib.Topology.Algebra.NonUnitalAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubalgebra.nonUnitalCommRingTopologicalClosure", "kind": "abbrev", "module": "Mathlib.Topology.Algebra.NonUnitalAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgebra.elemental", "kind": "definition", "module": "Mathlib.Topology.Algebra.NonUnitalAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgebra.elemental.self_mem", "kind": "theorem", "module": "Mathlib.Topology.Algebra.NonUnitalAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgebra.elemental.le_of_mem", "kind": "theorem", "module": "Mathlib.Topology.Algebra.NonUnitalAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgebra.elemental.le_iff_mem", "kind": "theorem", "module": "Mathlib.Topology.Algebra.NonUnitalAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgebra.elemental.isClosed", "kind": "instance", "module": "Mathlib.Topology.Algebra.NonUnitalAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgebra.elemental.instNonUnitalCommSemiringSubtypeMemNonUnitalSubalgebraOfT2Space", "kind": "instance", "module": "Mathlib.Topology.Algebra.NonUnitalAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgebra.elemental.instNonUnitalCommRingSubtypeMemNonUnitalSubalgebraOfT2Space", "kind": "instance", "module": "Mathlib.Topology.Algebra.NonUnitalAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgebra.elemental.instCompleteSpaceSubtypeMemNonUnitalSubalgebra", "kind": "instance", "module": "Mathlib.Topology.Algebra.NonUnitalAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgebra.elemental.isClosedEmbedding_coe", "kind": "theorem", "module": "Mathlib.Topology.Algebra.NonUnitalAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalAlgebra.elemental.le_centralizer_centralizer", "kind": "theorem", "module": "Mathlib.Topology.Algebra.NonUnitalAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.instIsTopologicalSemiring", "kind": "instance", "module": "Mathlib.Topology.Algebra.NonUnitalStarAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.topologicalClosure", "kind": "definition", "module": "Mathlib.Topology.Algebra.NonUnitalStarAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.le_topologicalClosure", "kind": "theorem", "module": "Mathlib.Topology.Algebra.NonUnitalStarAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.isClosed_topologicalClosure", "kind": "theorem", "module": "Mathlib.Topology.Algebra.NonUnitalStarAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.topologicalClosure_minimal", "kind": "theorem", "module": "Mathlib.Topology.Algebra.NonUnitalStarAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.nonUnitalCommSemiringTopologicalClosure", "kind": "abbrev", "module": "Mathlib.Topology.Algebra.NonUnitalStarAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.map_topologicalClosure_le", "kind": "theorem", "module": "Mathlib.Topology.Algebra.NonUnitalStarAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.topologicalClosure_map_le", "kind": "theorem", "module": "Mathlib.Topology.Algebra.NonUnitalStarAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.topologicalClosure_map", "kind": "theorem", "module": "Mathlib.Topology.Algebra.NonUnitalStarAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.topologicalClosure_adjoin_le_centralizer_centralizer", "kind": "theorem", "module": "Mathlib.Topology.Algebra.NonUnitalStarAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.instIsTopologicalRing", "kind": "instance", "module": "Mathlib.Topology.Algebra.NonUnitalStarAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarSubalgebra.nonUnitalCommRingTopologicalClosure", "kind": "abbrev", "module": "Mathlib.Topology.Algebra.NonUnitalStarAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarAlgebra.elemental", "kind": "definition", "module": "Mathlib.Topology.Algebra.NonUnitalStarAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarAlgebra.elemental.self_mem", "kind": "theorem", "module": "Mathlib.Topology.Algebra.NonUnitalStarAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarAlgebra.elemental.star_self_mem", "kind": "theorem", "module": "Mathlib.Topology.Algebra.NonUnitalStarAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarAlgebra.elemental.le_of_mem", "kind": "theorem", "module": "Mathlib.Topology.Algebra.NonUnitalStarAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarAlgebra.elemental.le_iff_mem", "kind": "theorem", "module": "Mathlib.Topology.Algebra.NonUnitalStarAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarAlgebra.elemental.isClosed", "kind": "theorem", "module": "Mathlib.Topology.Algebra.NonUnitalStarAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarAlgebra.elemental.instNonUnitalCommSemiringSubtypeMemNonUnitalStarSubalgebraOfT2SpaceOfIsStarNormal", "kind": "instance", "module": "Mathlib.Topology.Algebra.NonUnitalStarAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarAlgebra.elemental.instNonUnitalCommRingSubtypeMemNonUnitalStarSubalgebraOfT2SpaceOfIsStarNormal", "kind": "instance", "module": "Mathlib.Topology.Algebra.NonUnitalStarAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarAlgebra.elemental.instCompleteSpaceSubtypeMemNonUnitalStarSubalgebra", "kind": "instance", "module": "Mathlib.Topology.Algebra.NonUnitalStarAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarAlgebra.elemental.isClosedEmbedding_coe", "kind": "theorem", "module": "Mathlib.Topology.Algebra.NonUnitalStarAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalStarAlgebra.elemental.le_centralizer_centralizer", "kind": "theorem", "module": "Mathlib.Topology.Algebra.NonUnitalStarAlgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.adic_basis", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Nonarchimedean.AdicTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.ringFilterBasis", "kind": "definition", "module": "Mathlib.Topology.Algebra.Nonarchimedean.AdicTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.adicTopology", "kind": "definition", "module": "Mathlib.Topology.Algebra.Nonarchimedean.AdicTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.nonarchimedean", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Nonarchimedean.AdicTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.hasBasis_nhds_zero_adic", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Nonarchimedean.AdicTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.hasBasis_nhds_adic", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Nonarchimedean.AdicTopology", "is_tactic_proof": true, "tactics": ["letI", "have", "rwa"], "tactic_count": 3}
{"name": "Ideal.adic_module_basis", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Nonarchimedean.AdicTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.adicModuleTopology", "kind": "definition", "module": "Mathlib.Topology.Algebra.Nonarchimedean.AdicTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.openAddSubgroup", "kind": "definition", "module": "Mathlib.Topology.Algebra.Nonarchimedean.AdicTopology", "is_tactic_proof": true, "tactics": ["letI", "refine", "convert", "change", "simp"], "tactic_count": 5}
{"name": "IsAdic", "kind": "definition", "module": "Mathlib.Topology.Algebra.Nonarchimedean.AdicTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isAdic_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Nonarchimedean.AdicTopology", "is_tactic_proof": true, "tactics": ["constructor", "intro", "change", "rw", "letI", "constructor", "intro", "exact", "intro", "simpa", "rintro", "apply", "apply", "apply", "ext", "letI", "rw", "constructor", "rcases", "exact", "rcases", "rw", "exact"], "tactic_count": 23}
{"name": "is_ideal_adic_pow", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Nonarchimedean.AdicTopology", "is_tactic_proof": true, "tactics": ["rw", "constructor", "intro", "rw", "apply", "intro", "obtain", "use", "refine", "cases", "exfalso", "exact", "rw", "apply", "apply"], "tactic_count": 15}
{"name": "is_bot_adic_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Nonarchimedean.AdicTopology", "is_tactic_proof": true, "tactics": ["rw", "constructor", "rintro", "rw", "simpa", "intros", "constructor", "simp", "intro", "use", "simp"], "tactic_count": 11}
{"name": "IsAdic.hasBasis_nhds_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Nonarchimedean.AdicTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAdic.hasBasis_nhds", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Nonarchimedean.AdicTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithIdeal.instTopologicalSpace", "kind": "instance", "module": "Mathlib.Topology.Algebra.Nonarchimedean.AdicTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithIdeal.instNonarchimedeanRing", "kind": "instance", "module": "Mathlib.Topology.Algebra.Nonarchimedean.AdicTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithIdeal.instUniformSpace", "kind": "instance", "module": "Mathlib.Topology.Algebra.Nonarchimedean.AdicTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithIdeal.instIsUniformAddGroup", "kind": "instance", "module": "Mathlib.Topology.Algebra.Nonarchimedean.AdicTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithIdeal.topologicalSpaceModule", "kind": "definition", "module": "Mathlib.Topology.Algebra.Nonarchimedean.AdicTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithIdeal._example", "kind": "example", "module": "Mathlib.Topology.Algebra.Nonarchimedean.AdicTopology", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "WithIdeal._example", "kind": "example", "module": "Mathlib.Topology.Algebra.Nonarchimedean.AdicTopology", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "WithIdeal._example", "kind": "example", "module": "Mathlib.Topology.Algebra.Nonarchimedean.AdicTopology", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "WithIdeal._example", "kind": "example", "module": "Mathlib.Topology.Algebra.Nonarchimedean.AdicTopology", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "WithIdeal._example", "kind": "example", "module": "Mathlib.Topology.Algebra.Nonarchimedean.AdicTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingSubgroupsBasis.of_comm", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Nonarchimedean.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingSubgroupsBasis.toRingFilterBasis", "kind": "definition", "module": "Mathlib.Topology.Algebra.Nonarchimedean.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingSubgroupsBasis.mem_addGroupFilterBasis_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Nonarchimedean.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingSubgroupsBasis.mem_addGroupFilterBasis", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Nonarchimedean.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingSubgroupsBasis.topology", "kind": "definition", "module": "Mathlib.Topology.Algebra.Nonarchimedean.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingSubgroupsBasis.hasBasis_nhds_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Nonarchimedean.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingSubgroupsBasis.hasBasis_nhds", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Nonarchimedean.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingSubgroupsBasis.openAddSubgroup", "kind": "definition", "module": "Mathlib.Topology.Algebra.Nonarchimedean.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingSubgroupsBasis.nonarchimedean", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Nonarchimedean.Bases", "is_tactic_proof": true, "tactics": ["letI", "constructor", "intro", "obtain", "exact"], "tactic_count": 5}
{"name": "SubmodulesRingBasis.toRing_subgroups_basis", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Nonarchimedean.Bases", "is_tactic_proof": true, "tactics": ["apply", "intro", "rcases", "use", "rintro", "exact"], "tactic_count": 6}
{"name": "SubmodulesRingBasis.topology", "kind": "definition", "module": "Mathlib.Topology.Algebra.Nonarchimedean.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubmodulesBasis.toModuleFilterBasis", "kind": "definition", "module": "Mathlib.Topology.Algebra.Nonarchimedean.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubmodulesBasis.topology", "kind": "definition", "module": "Mathlib.Topology.Algebra.Nonarchimedean.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubmodulesBasis.openAddSubgroup", "kind": "definition", "module": "Mathlib.Topology.Algebra.Nonarchimedean.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubmodulesBasis.nonarchimedean", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Nonarchimedean.Bases", "is_tactic_proof": true, "tactics": ["letI", "constructor", "intro", "obtain", "hB.toModuleFilterBasis.toAddGroupFilterBasis.nhds_zero_hasBasis.mem_iff.mp", "exact"], "tactic_count": 6}
{"name": "LibraryNote.non-Archimedean_non-instances", "kind": "definition", "module": "Mathlib.Topology.Algebra.Nonarchimedean.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SubmodulesRingBasis.toSubmodulesBasis", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Nonarchimedean.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_example", "kind": "example", "module": "Mathlib.Topology.Algebra.Nonarchimedean.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingFilterBasis.submodulesBasisIsBasis", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Nonarchimedean.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingFilterBasis.moduleFilterBasis", "kind": "definition", "module": "Mathlib.Topology.Algebra.Nonarchimedean.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonarchimedeanRing.to_nonarchimedeanAddGroup", "kind": "instance", "module": "Mathlib.Topology.Algebra.Nonarchimedean.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonarchimedeanGroup.nonarchimedean_of_emb", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Nonarchimedean.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonarchimedeanGroup.prod_subset", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Nonarchimedean.Basic", "is_tactic_proof": true, "tactics": ["rw", "rcases", "obtain", "obtain", "use", "grind"], "tactic_count": 6}
{"name": "NonarchimedeanGroup.prod_self_subset", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Nonarchimedean.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonarchimedeanGroup.Prod.instNonarchimedeanGroup", "kind": "instance", "module": "Mathlib.Topology.Algebra.Nonarchimedean.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonarchimedeanRing.instProd", "kind": "instance", "module": "Mathlib.Topology.Algebra.Nonarchimedean.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonarchimedeanRing.left_mul_subset", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Nonarchimedean.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonarchimedeanRing.mul_subset", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Nonarchimedean.Basic", "is_tactic_proof": false, "tactics": ["let", "prod_self_subset", "simpa", "use", "rintro", "have", "simp", "rw", "exact"], "tactic_count": 9}
{"name": "instNonarchimedeanAddGroupCompletion", "kind": "instance", "module": "Mathlib.Topology.Algebra.Nonarchimedean.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instNonarchimedeanRingCompletion", "kind": "instance", "module": "Mathlib.Topology.Algebra.Nonarchimedean.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonarchimedeanGroup.exists_openSubgroup_separating", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Nonarchimedean.TotallyDisconnected", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "use", "simp", "intro", "by_contra", "have", "have", "rw", "refine", "simpa"], "tactic_count": 11}
{"name": "NonarchimedeanGroup.instTotallySeparated", "kind": "instance", "module": "Mathlib.Topology.Algebra.Nonarchimedean.TotallyDisconnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenSubgroup.hasCoeSubgroup", "kind": "instance", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenSubgroup.toSubgroup_injective", "kind": "theorem", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenSubgroup.instSetLike", "kind": "instance", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenSubgroup.instPartialOrder", "kind": "instance", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenSubgroup.instSubgroupClass", "kind": "instance", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenSubgroup.toOpens", "kind": "definition", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenSubgroup.hasCoeOpens", "kind": "instance", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenSubgroup.coe_toOpens", "kind": "theorem", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenSubgroup.coe_toSubgroup", "kind": "theorem", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenSubgroup.mem_toOpens", "kind": "theorem", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenSubgroup.mem_toSubgroup", "kind": "theorem", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenSubgroup.ext", "kind": "theorem", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenSubgroup.isOpen", "kind": "theorem", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenSubgroup.mem_nhds_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenSubgroup.instTop", "kind": "instance", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenSubgroup.mem_top", "kind": "theorem", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenSubgroup.coe_top", "kind": "theorem", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenSubgroup.toSubgroup_top", "kind": "theorem", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenSubgroup.toOpens_top", "kind": "theorem", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenSubgroup.instInhabited", "kind": "instance", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenSubgroup.isClosed", "kind": "theorem", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "OpenSubgroup.isClopen", "kind": "theorem", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenSubgroup.prod", "kind": "definition", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenSubgroup.coe_prod", "kind": "theorem", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenSubgroup.toSubgroup_prod", "kind": "theorem", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenSubgroup.instInfOpenSubgroup", "kind": "instance", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenSubgroup.coe_inf", "kind": "theorem", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenSubgroup.toSubgroup_inf", "kind": "theorem", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenSubgroup.toOpens_inf", "kind": "theorem", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenSubgroup.mem_inf", "kind": "theorem", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenSubgroup.instPartialOrderOpenSubgroup", "kind": "instance", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenSubgroup.instSemilatticeInfOpenSubgroup", "kind": "instance", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenSubgroup.instOrderTop", "kind": "instance", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenSubgroup.toSubgroup_le", "kind": "theorem", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenSubgroup.comap", "kind": "definition", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenSubgroup.coe_comap", "kind": "theorem", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenSubgroup.toSubgroup_comap", "kind": "theorem", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenSubgroup.mem_comap", "kind": "theorem", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenSubgroup.comap_comap", "kind": "theorem", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.isOpen_of_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": true, "tactics": ["refine", "have", "have", "simpa"], "tactic_count": 4}
{"name": "Subgroup.isOpen_mono", "kind": "theorem", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.isOpen_of_openSubgroup", "kind": "theorem", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.isOpen_of_one_mem_interior", "kind": "theorem", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.isClosed_of_isOpen", "kind": "theorem", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.subgroupOf_isOpen", "kind": "theorem", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.discreteTopology", "kind": "theorem", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.instDiscreteTopologyQuotientOfContinuousMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.quotient_finite_of_isOpen", "kind": "theorem", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.instFiniteQuotientOfContinuousMulOfCompactSpace", "kind": "instance", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.quotient_finite_of_isOpen'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.instFiniteQuotientSubtypeMemOpenSubgroupOfIsTopologicalGroupOfCompactSpace", "kind": "instance", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenSubgroup.instMax", "kind": "instance", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenSubgroup.toSubgroup_sup", "kind": "theorem", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenSubgroup.instLattice", "kind": "instance", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submodule.isOpen_mono", "kind": "theorem", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.isOpen_of_isOpen_subideal", "kind": "theorem", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenNormalSubgroup.instNormal", "kind": "instance", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenNormalSubgroup.toSubgroup_injective", "kind": "theorem", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenNormalSubgroup.instSetLike", "kind": "instance", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenNormalSubgroup.instPartialOrder", "kind": "instance", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenNormalSubgroup.instSubgroupClass", "kind": "instance", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenNormalSubgroup.instCoeSubgroup", "kind": "instance", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenNormalSubgroup.instPartialOrderOpenNormalSubgroup", "kind": "instance", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenNormalSubgroup.instInfOpenNormalSubgroup", "kind": "instance", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenNormalSubgroup.instSemilatticeInfOpenNormalSubgroup", "kind": "instance", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenNormalSubgroup.instMaxOfContinuousMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenNormalSubgroup.instSemilatticeSupOpenNormalSubgroup", "kind": "instance", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenNormalSubgroup.instLatticeOfContinuousMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsTopologicalGroup.exist_mul_closure_nhds", "kind": "theorem", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": false, "tactics": ["apply", "rw", "exact", "union_subset", "intro", "have", "rcases", "have", "exact", "h6"], "tactic_count": 10}
{"name": "IsTopologicalGroup.exists_mulInvClosureNhd", "kind": "theorem", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "use", "constructor", "simp", "simp", "exact", "exact"], "tactic_count": 8}
{"name": "IsTopologicalGroup.exist_openSubgroup_sub_clopen_nhds_of_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.OpenSubgroup", "is_tactic_proof": true, "tactics": ["rcases", "let", "mul_mem", "rcases", "rcases", "apply", "use", "rw", "exact", "one_mem", "apply", "use", "simp", "inv_mem", "rcases", "apply", "use", "rw", "simpa", "have", "refine", "rw", "exact", "use", "have", "induction", "zero", "succ", "rw", "exact", "have", "intro", "rw", "use", "rw", "apply"], "tactic_count": 36}
{"name": "Rat.denseRange_cast", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Archimedean", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.dense_of_not_isolated_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Archimedean", "is_tactic_proof": true, "tactics": ["cases", "refine", "rw", "exact", "refine", "rcases", "rcases", "rw", "refine", "rwa"], "tactic_count": 10}
{"name": "Subgroup.dense_of_no_min", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Archimedean", "is_tactic_proof": true, "tactics": ["refine", "contrapose", "exact"], "tactic_count": 3}
{"name": "Subgroup.dense_or_cyclic", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Archimedean", "is_tactic_proof": true, "tactics": ["refine", "push_neg", "rcases", "exact"], "tactic_count": 4}
{"name": "Subgroup.dense_xor'_cyclic", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Archimedean", "is_tactic_proof": true, "tactics": ["simp", "rintro", "exact", "simp", "exact"], "tactic_count": 5}
{"name": "Subgroup.dense_iff_ne_zpowers", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Archimedean", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Subgroup.instDiscreteTopologyZMultiples", "kind": "instance", "module": "Mathlib.Topology.Algebra.Order.ArchimedeanDiscrete", "is_tactic_proof": true, "tactics": ["wlog", "specialize", "rwa", "rcases", "rw", "exact", "rw", "refine", "ext", "constructor", "simp", "intro", "rw", "simp", "simp_all"], "tactic_count": 15}
{"name": "Subgroup.instIsCyclicOfDiscreteTopology", "kind": "instance", "module": "Mathlib.Topology.Algebra.Order.ArchimedeanDiscrete", "is_tactic_proof": true, "tactics": ["nontriviality", "exact", "have", "false_of_nontrivial_of_subsingleton"], "tactic_count": 4}
{"name": "Subgroup.discrete_iff_cyclic", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.ArchimedeanDiscrete", "is_tactic_proof": true, "tactics": ["nontriviality", "rw", "constructor", "rintro", "infer_instance", "have", "simp", "refine", "obtain", "have", "exact"], "tactic_count": 11}
{"name": "Filter.Tendsto.atTop_mul_pos", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Field", "is_tactic_proof": true, "tactics": ["refine", "filter_upwards", "mul_le_mul_of_nonneg_left"], "tactic_count": 3}
{"name": "Filter.Tendsto.pos_mul_atTop", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Field", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "inv_atTop₀", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_nhdsGT_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Field", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "tendsto_inv_nhdsGT_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_inv_atTop_nhdsGT_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_inv_atTop_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.inv_tendsto_atTop", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.inv_tendsto_nhdsGT_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_pow_neg_atTop", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Field", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "tendsto_zpow_atTop_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Field", "is_tactic_proof": true, "tactics": ["lift", "rw", "simpa"], "tactic_count": 3}
{"name": "IsStrictOrderedRing.toContinuousInv₀", "kind": "instance", "module": "Mathlib.Topology.Algebra.Order.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsTopologicalRing.of_norm", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Field", "is_tactic_proof": false, "tactics": ["have", "refine", "rcases", "refine", "exact", "apply", "refine", "refine", "simp", "calc", "norm", "exact", "exact"], "tactic_count": 13}
{"name": "IsStrictOrderedRing.topologicalRing", "kind": "instance", "module": "Mathlib.Topology.Algebra.Order.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.atTop_mul_neg", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Field", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "Filter.Tendsto.neg_mul_atTop", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Field", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Filter.Tendsto.atBot_mul_pos", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Field", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "Filter.Tendsto.atBot_mul_neg", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Field", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "Filter.Tendsto.pos_mul_atBot", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Field", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Filter.Tendsto.neg_mul_atBot", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Field", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "inv_atBot₀", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_nhdsLT_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Field", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "tendsto_inv_nhdsLT_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_inv_atBot_nhdsLT_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_inv_atBot_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.div_atTop", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Field", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Filter.Tendsto.div_atBot", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Field", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Filter.Tendsto.const_div_atTop", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.const_div_atBot", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.inv_tendsto_atBot", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.inv_tendsto_nhdsLT_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bdd_le_mul_tendsto_zero'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Field", "is_tactic_proof": true, "tactics": ["rw", "have", "convert", "simp_rw", "apply", "filter_upwards", "filter_upwards", "simp", "exact"], "tactic_count": 9}
{"name": "bdd_le_mul_tendsto_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Field", "is_tactic_proof": true, "tactics": ["set", "have", "have", "apply", "filter_upwards", "exact"], "tactic_count": 6}
{"name": "tendsto_bdd_div_atTop_nhds_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Field", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "tendsto_const_mul_zpow_atTop_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_const_mul_pow_nhds_iff'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Field", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rcases", "have", "simp", "simp", "have", "simp"], "tactic_count": 8}
{"name": "tendsto_const_mul_pow_nhds_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Field", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "tendsto_const_mul_zpow_atTop_nhds_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Field", "is_tactic_proof": true, "tactics": ["refine", "cases", "ofNat", "left", "simpa", "negSucc", "have", "exact", "rcases", "simp", "exact", "exact"], "tactic_count": 12}
{"name": "IsStrictOrderedRing.toIsTopologicalDivisionRing", "kind": "instance", "module": "Mathlib.Topology.Algebra.Order.Field", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "comap_mulLeft_nhdsGT_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Field", "is_tactic_proof": true, "tactics": ["rw", "congr", "refine", "simp"], "tactic_count": 4}
{"name": "eventually_nhdsGT_zero_mul_left", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Field", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "FloorSemiring.tendsto_mul_pow_div_factorial_sub_atTop", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Floor", "is_tactic_proof": true, "tactics": ["rw", "constructor", "all_goals", "intro", "filter_upwards", "rw", "rw", "rwa", "rw", "rwa"], "tactic_count": 10}
{"name": "FloorSemiring.tendsto_pow_div_factorial_atTop", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Floor", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "tendsto_floor_atTop", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Floor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_floor_atBot", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Floor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_ceil_atTop", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Floor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_ceil_atBot", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Floor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousOn_floor", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Floor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousOn_ceil", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Floor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_floor_right_pure_floor", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Floor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_floor_right_pure", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Floor", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "tendsto_ceil_left_pure_ceil", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Floor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_ceil_left_pure", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Floor", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "tendsto_floor_left_pure_ceil_sub_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Floor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_floor_left_pure_sub_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Floor", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "tendsto_ceil_right_pure_floor_add_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Floor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_ceil_right_pure_add_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Floor", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "tendsto_floor_right", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Floor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_floor_right'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Floor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_ceil_left", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Floor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_ceil_left'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Floor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_floor_left", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Floor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_ceil_right", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Floor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_floor_left'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Floor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_ceil_right'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Floor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousOn_fract", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Floor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousAt_fract", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Floor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_fract_left'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Floor", "is_tactic_proof": true, "tactics": ["rw", "refine", "exact"], "tactic_count": 3}
{"name": "tendsto_fract_left", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Floor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_fract_right'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Floor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_fract_right", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Floor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.Algebra.Order.Floor.0.termI", "kind": "definition", "module": "Mathlib.Topology.Algebra.Order.Floor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.Algebra.Order.Floor.0._aux_Mathlib_Topology_Algebra_Order_Floor___macroRules__private_Mathlib_Topology_Algebra_Order_Floor_0_termI_1", "kind": "definition", "module": "Mathlib.Topology.Algebra.Order.Floor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.comp_fract'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Floor", "is_tactic_proof": true, "tactics": ["change", "rw", "rintro", "rcases", "rw", "constructor", "refine", "rw", "exact", "simp", "refine", "simp", "replace", "refine", "exact"], "tactic_count": 15}
{"name": "ContinuousOn.comp_fract", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Floor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.comp_fract''", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Floor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearOrderedCommGroup.toIsTopologicalGroup", "kind": "instance", "module": "Mathlib.Topology.Algebra.Order.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_mabs", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.mabs", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "comap_mabs_nhds_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Group", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "tendsto_one_iff_mabs_tendsto_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Group", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Continuous.mabs", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.mabs", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.mabs", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.mabs", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_mabs_nhdsNE_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "denseRange_zpow_iff_surjective", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Group", "is_tactic_proof": true, "tactics": ["refine", "wlog", "simp", "rcases", "simpa", "have", "simpa", "rw", "apply", "intro", "obtain", "have", "simpa", "rcases", "suffices", "rcases", "have", "lia", "rcases", "refine", "simpa", "use", "simp", "exact"], "tactic_count": 24}
{"name": "not_denseRange_zpow", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Group", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_limsup_mul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": ["have", "have", "have", "have", "le_limsup_of_frequently_le", "refine", "refine", "replace", "have", "have", "apply", "exact"], "tactic_count": 12}
{"name": "limsup_mul_le", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": ["have", "have", "refine", "filter_upwards", "apply", "rcases", "apply", "exact", "exact"], "tactic_count": 9}
{"name": "le_liminf_mul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.LiminfLimsup", "is_tactic_proof": true, "tactics": ["have", "have", "apply", "mul_le_of_forall_lt_of_nonneg", "intro", "refine", "filter_upwards", "eventually_lt_of_lt_liminf", "exact"], "tactic_count": 9}
{"name": "liminf_mul_le", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.LiminfLimsup", "is_tactic_proof": true, "tactics": ["have", "have", "refine", "refine", "exact"], "tactic_count": 5}
{"name": "limsup_const_add", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "limsup_add_const", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "liminf_const_add", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "liminf_add_const", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "limsup_const_sub", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.LiminfLimsup", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simp", "rcases", "refine", "refine", "simp", "exact", "refine", "simp", "exact"], "tactic_count": 11}
{"name": "limsup_sub_const", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.LiminfLimsup", "is_tactic_proof": true, "tactics": ["rcases", "have", "apply", "simp", "rcases", "refine", "simp", "simp", "exact", "apply", "exact", "exact"], "tactic_count": 12}
{"name": "liminf_const_sub", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "liminf_sub_const", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instContinuousConstSMulSubtypeLeOfNat", "kind": "instance", "module": "Mathlib.Topology.Algebra.Order.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instContinuousSMulSubtypeLeOfNat", "kind": "instance", "module": "Mathlib.Topology.Algebra.Order.Module", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasCompactMulSupport.sup", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Support", "is_tactic_proof": true, "tactics": ["apply", "rw", "apply", "exact"], "tactic_count": 4}
{"name": "HasCompactMulSupport.inf", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.Support", "is_tactic_proof": true, "tactics": ["apply", "rw", "apply", "exact"], "tactic_count": 4}
{"name": "IsOrderedMonoid.to_hasUpperLowerClosure", "kind": "instance", "module": "Mathlib.Topology.Algebra.Order.UpperLower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUpperSet.closure", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.UpperLower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLowerSet.closure", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.UpperLower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.upperClosure", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.UpperLower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.lowerClosure", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.UpperLower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instHasUpperLowerClosureOrderDual", "kind": "instance", "module": "Mathlib.Topology.Algebra.Order.UpperLower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUpperSet.interior", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.UpperLower", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsLowerSet.interior", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.UpperLower", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.OrdConnected.interior", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Order.UpperLower", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Polynomial.continuous_eval₂", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Polynomial", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Polynomial.continuous", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.continuousAt", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.continuousWithinAt", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.continuousOn", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.continuous_aeval", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.continuousAt_aeval", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.continuousWithinAt_aeval", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.continuousOn_aeval", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.tendsto_abv_eval₂_atTop", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Polynomial", "is_tactic_proof": true, "tactics": ["revert", "rintro", "rw", "simpa", "intro", "rw", "simpa", "intro", "rw", "refine", "refine", "simpa"], "tactic_count": 12}
{"name": "Polynomial.tendsto_abv_atTop", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Polynomial", "is_tactic_proof": true, "tactics": ["apply", "exact"], "tactic_count": 2}
{"name": "Polynomial.tendsto_abv_aeval_atTop", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.tendsto_norm_atTop", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.exists_forall_norm_le", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.isProperMap_eval", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.isClosedMap_eval", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Polynomial", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact"], "tactic_count": 3}
{"name": "isClosedMap_pow", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Polynomial", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Polynomial.eq_one_of_roots_le", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.coeff_le_of_roots_le", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Polynomial", "is_tactic_proof": true, "tactics": ["obtain", "rw", "split_ifs", "rw", "obtain", "rw", "positivity", "rw", "one_pow,", "apply", "rw", "mul_comm,", "intro", "simp_rw", "obtain", "rw", "lift", "rw", "refine", "obtain", "exact"], "tactic_count": 21}
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{"name": "RestrictedProduct.mapAlong_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.RestrictedProduct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "RestrictedProduct.mapAlongMonoidHom_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.RestrictedProduct.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "RestrictedProduct.topologicalSpace_eq_of_principal", "kind": "theorem", "module": "Mathlib.Topology.Algebra.RestrictedProduct.TopologicalSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "RestrictedProduct.topologicalSpace_eq_of_bot", "kind": "theorem", "module": "Mathlib.Topology.Algebra.RestrictedProduct.TopologicalSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "RestrictedProduct.topologicalSpace_eq_iSup", "kind": "theorem", "module": "Mathlib.Topology.Algebra.RestrictedProduct.TopologicalSpace", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "RestrictedProduct.continuous_dom", "kind": "theorem", "module": "Mathlib.Topology.Algebra.RestrictedProduct.TopologicalSpace", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "RestrictedProduct.isEmbedding_inclusion_principal", "kind": "theorem", "module": "Mathlib.Topology.Algebra.RestrictedProduct.TopologicalSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RestrictedProduct.isEmbedding_inclusion_top", "kind": "theorem", "module": "Mathlib.Topology.Algebra.RestrictedProduct.TopologicalSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RestrictedProduct.isEmbedding_structureMap", "kind": "theorem", "module": "Mathlib.Topology.Algebra.RestrictedProduct.TopologicalSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RestrictedProduct.isOpen_forall_imp_mem_of_principal", "kind": "theorem", "module": "Mathlib.Topology.Algebra.RestrictedProduct.TopologicalSpace", "is_tactic_proof": true, "tactics": ["rw", "convert", "ext", "refine", "by_cases", "exact", "exact"], "tactic_count": 7}
{"name": "RestrictedProduct.isOpen_forall_mem_of_principal", "kind": "theorem", "module": "Mathlib.Topology.Algebra.RestrictedProduct.TopologicalSpace", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "RestrictedProduct.isOpen_forall_imp_mem", "kind": "theorem", "module": "Mathlib.Topology.Algebra.RestrictedProduct.TopologicalSpace", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "RestrictedProduct.isOpen_forall_mem", "kind": "theorem", "module": "Mathlib.Topology.Algebra.RestrictedProduct.TopologicalSpace", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "RestrictedProduct.isOpenEmbedding_inclusion_principal", "kind": "theorem", "module": "Mathlib.Topology.Algebra.RestrictedProduct.TopologicalSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RestrictedProduct.isOpenEmbedding_structureMap", "kind": "theorem", "module": "Mathlib.Topology.Algebra.RestrictedProduct.TopologicalSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RestrictedProduct.nhds_eq_map_inclusion", "kind": "theorem", "module": "Mathlib.Topology.Algebra.RestrictedProduct.TopologicalSpace", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RestrictedProduct.nhds_eq_map_structureMap", "kind": "theorem", "module": "Mathlib.Topology.Algebra.RestrictedProduct.TopologicalSpace", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "RestrictedProduct.weaklyLocallyCompactSpace_of_cofinite", "kind": "theorem", "module": "Mathlib.Topology.Algebra.RestrictedProduct.TopologicalSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RestrictedProduct.instWeaklyLocallyCompactSpaceCofiniteOfFactForallIsOpenOfCompactSpaceElem", "kind": "instance", "module": "Mathlib.Topology.Algebra.RestrictedProduct.TopologicalSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RestrictedProduct.continuous_dom_prod_right", "kind": "theorem", "module": "Mathlib.Topology.Algebra.RestrictedProduct.TopologicalSpace", "is_tactic_proof": true, "tactics": ["refine", "simp_rw", "rintro", "set", "have", "have", "rcases", "rw", "nhds_prod_eq,", "exact"], "tactic_count": 10}
{"name": "RestrictedProduct.continuous_dom_prod_left", "kind": "theorem", "module": "Mathlib.Topology.Algebra.RestrictedProduct.TopologicalSpace", "is_tactic_proof": true, "tactics": ["refine", "simp_rw", "rintro", "set", "have", "have", "rcases", "rw", "nhds_prod_eq,", "exact"], "tactic_count": 10}
{"name": "RestrictedProduct.continuous_dom_prod", "kind": "theorem", "module": "Mathlib.Topology.Algebra.RestrictedProduct.TopologicalSpace", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "set", "have", "have", "have", "exact"], "tactic_count": 7}
{"name": "RestrictedProduct.continuous_dom_pi", "kind": "theorem", "module": "Mathlib.Topology.Algebra.RestrictedProduct.TopologicalSpace", "is_tactic_proof": true, "tactics": ["refine", "simp_rw", "intro", "set", "have", "rw", "change", "simp", "let", "have", "simp_rw", "nhds_pi]", "exact"], "tactic_count": 13}
{"name": "RestrictedProduct.instContinuousInvCoe", "kind": "instance", "module": "Mathlib.Topology.Algebra.RestrictedProduct.TopologicalSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RestrictedProduct.instContinuousConstSMulCoe", "kind": "instance", "module": "Mathlib.Topology.Algebra.RestrictedProduct.TopologicalSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RestrictedProduct.instContinuousMulCoePrincipal", "kind": "instance", "module": "Mathlib.Topology.Algebra.RestrictedProduct.TopologicalSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RestrictedProduct.instContinuousSMulCoePrincipal", "kind": "instance", "module": "Mathlib.Topology.Algebra.RestrictedProduct.TopologicalSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RestrictedProduct.instIsTopologicalGroupCoePrincipal", "kind": "instance", "module": "Mathlib.Topology.Algebra.RestrictedProduct.TopologicalSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RestrictedProduct.instIsTopologicalRingCoePrincipal", "kind": "instance", "module": "Mathlib.Topology.Algebra.RestrictedProduct.TopologicalSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RestrictedProduct.nhds_zero_eq_map_ofPre", "kind": "theorem", "module": "Mathlib.Topology.Algebra.RestrictedProduct.TopologicalSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RestrictedProduct.nhds_zero_eq_map_structureMap", "kind": "theorem", "module": "Mathlib.Topology.Algebra.RestrictedProduct.TopologicalSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RestrictedProduct.instContinuousMulCoeCofinite", "kind": "instance", "module": "Mathlib.Topology.Algebra.RestrictedProduct.TopologicalSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RestrictedProduct.continuousSMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.RestrictedProduct.TopologicalSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RestrictedProduct.isTopologicalGroup", "kind": "instance", "module": "Mathlib.Topology.Algebra.RestrictedProduct.TopologicalSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RestrictedProduct.isTopologicalRing", "kind": "instance", "module": "Mathlib.Topology.Algebra.RestrictedProduct.TopologicalSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RestrictedProduct.locallyCompactSpace_of_group", "kind": "theorem", "module": "Mathlib.Topology.Algebra.RestrictedProduct.TopologicalSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RestrictedProduct.instLocallyCompactSpaceCoeCofiniteOfSubgroupClassOfIsTopologicalGroupOfCompactSpaceSubtypeMem", "kind": "instance", "module": "Mathlib.Topology.Algebra.RestrictedProduct.TopologicalSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RestrictedProduct.mapAlong_continuous", "kind": "theorem", "module": "Mathlib.Topology.Algebra.RestrictedProduct.TopologicalSpace", "is_tactic_proof": true, "tactics": ["rw", "intro", "set", "have", "rw", "exact", "have", "have", "have", "rw", "exact", "continuous_inclusion", "continuous_rng_of_principal.mpr"], "tactic_count": 13}
{"name": "IsTopologicalSemiring.continuousNeg_of_mul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsTopologicalSemiring.toIsTopologicalRing", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsTopologicalRing.to_topologicalAddGroup", "kind": "instance", "module": "Mathlib.Topology.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteTopology.topologicalSemiring", "kind": "instance", "module": "Mathlib.Topology.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteTopology.topologicalRing", "kind": "instance", "module": "Mathlib.Topology.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.instIsTopologicalSemiring", "kind": "instance", "module": "Mathlib.Topology.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.topologicalClosure", "kind": "definition", "module": "Mathlib.Topology.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.topologicalClosure_coe", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.le_topologicalClosure", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.isClosed_topologicalClosure", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.topologicalClosure_minimal", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubsemiring.nonUnitalCommSemiringTopologicalClosure", "kind": "abbrev", "module": "Mathlib.Topology.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsTopologicalSemiringULift", "kind": "instance", "module": "Mathlib.Topology.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.topologicalSemiring", "kind": "instance", "module": "Mathlib.Topology.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.continuousSMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.topologicalClosure", "kind": "definition", "module": "Mathlib.Topology.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.topologicalClosure_coe", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.le_topologicalClosure", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.isClosed_topologicalClosure", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.topologicalClosure_minimal", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsemiring.commSemiringTopologicalClosure", "kind": "abbrev", "module": "Mathlib.Topology.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsTopologicalSemiringProd", "kind": "instance", "module": "Mathlib.Topology.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsTopologicalRingProd", "kind": "instance", "module": "Mathlib.Topology.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instContinuousAddForallOfIsTopologicalSemiring", "kind": "instance", "module": "Mathlib.Topology.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instIsTopologicalSemiring", "kind": "instance", "module": "Mathlib.Topology.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instIsTopologicalRing", "kind": "instance", "module": "Mathlib.Topology.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instContinuousAddMulOpposite", "kind": "instance", "module": "Mathlib.Topology.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsTopologicalSemiringMulOpposite", "kind": "instance", "module": "Mathlib.Topology.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instContinuousNegMulOpposite", "kind": "instance", "module": "Mathlib.Topology.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsTopologicalRingMulOpposite", "kind": "instance", "module": "Mathlib.Topology.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instContinuousMulAddOpposite", "kind": "instance", "module": "Mathlib.Topology.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsTopologicalSemiringAddOpposite", "kind": "instance", "module": "Mathlib.Topology.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsTopologicalRingAddOpposite", "kind": "instance", "module": "Mathlib.Topology.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsTopologicalRing.of_addGroup_of_nhds_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsTopologicalRing.of_nhds_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsTopologicalRingULift", "kind": "instance", "module": "Mathlib.Topology.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mulLeft_continuous", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mulRight_continuous", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.instIsTopologicalRing", "kind": "instance", "module": "Mathlib.Topology.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.topologicalClosure", "kind": "definition", "module": "Mathlib.Topology.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.le_topologicalClosure", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.isClosed_topologicalClosure", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.topologicalClosure_minimal", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonUnitalSubring.nonUnitalCommRingTopologicalClosure", "kind": "abbrev", "module": "Mathlib.Topology.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.instIsTopologicalRing", "kind": "instance", "module": "Mathlib.Topology.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.continuousSMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.topologicalClosure", "kind": "definition", "module": "Mathlib.Topology.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.le_topologicalClosure", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.isClosed_topologicalClosure", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.topologicalClosure_minimal", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subring.commRingTopologicalClosure", "kind": "abbrev", "module": "Mathlib.Topology.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingTopology.inhabited", "kind": "instance", "module": "Mathlib.Topology.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingTopology.toTopologicalSpace_injective", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Ring.Basic", "is_tactic_proof": true, "tactics": ["intro"], "tactic_count": 1}
{"name": "RingTopology.ext", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingTopology.instPartialOrder", "kind": "instance", "module": "Mathlib.Topology.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.Algebra.Ring.Basic.0.RingTopology.def_sInf", "kind": "definition", "module": "Mathlib.Topology.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingTopology.instCompleteSemilatticeInf", "kind": "instance", "module": "Mathlib.Topology.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingTopology.instCompleteLattice", "kind": "instance", "module": "Mathlib.Topology.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingTopology.coinduced", "kind": "definition", "module": "Mathlib.Topology.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingTopology.coinduced_continuous", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingTopology.toAddGroupTopology", "kind": "definition", "module": "Mathlib.Topology.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingTopology.toAddGroupTopology.orderEmbedding", "kind": "definition", "module": "Mathlib.Topology.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AbsoluteValue.comp", "kind": "definition", "module": "Mathlib.Topology.Algebra.Ring.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsArtinianRing.finite_of_compactSpace_of_t2Space", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Ring.Compact", "is_tactic_proof": true, "tactics": ["obtain", "have", "rw", "gcongr", "rw", "exact", "have", "have", "rw", "exact"], "tactic_count": 10}
{"name": "Ideal.isOpen_of_isMaximal", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Ring.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.isOpen_pow_of_isMaximal", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Ring.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFiniteQuotientIdealOfIsMaximal", "kind": "instance", "module": "Mathlib.Topology.Algebra.Ring.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.isOpen_maximalIdeal_pow", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Ring.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.isOpen_maximalIdeal", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Ring.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.finite_residueField_of_compactSpace", "kind": "instance", "module": "Mathlib.Topology.Algebra.Ring.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalRing.isOpen_iff_finite_quotient", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Ring.Compact", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact"], "tactic_count": 3}
{"name": "IsDedekindDomain.isOpen_of_ne_bot", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Ring.Compact", "is_tactic_proof": false, "tactics": ["rw", "finprod_eq_finset_prod_of_mulSupport_subset", "refine", "refine", "refine", "exact"], "tactic_count": 6}
{"name": "IsDedekindDomain.isOpen_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Ring.Compact", "is_tactic_proof": true, "tactics": ["refine", "rintro", "have", "exact"], "tactic_count": 4}
{"name": "IsDiscreteValuationRing.isOpen_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Ring.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.closure", "kind": "definition", "module": "Mathlib.Topology.Algebra.Ring.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.coe_closure", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Ring.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ideal.closure_eq_of_isClosed", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Ring.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "topologicalRingQuotientTopology", "kind": "instance", "module": "Mathlib.Topology.Algebra.Ring.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientRing.isOpenMap_coe", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Ring.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientRing.isOpenQuotientMap_mk", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Ring.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuotientRing.isQuotientMap_coe_coe", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Ring.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "topologicalRing_quotient", "kind": "instance", "module": "Mathlib.Topology.Algebra.Ring.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCompactSpaceQuotientIdeal", "kind": "instance", "module": "Mathlib.Topology.Algebra.Ring.Ideal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instNoncompactSpaceReal", "kind": "instance", "module": "Mathlib.Topology.Algebra.Ring.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Continuous.star", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.star", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.star", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.star", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "starContinuousMap", "kind": "definition", "module": "Mathlib.Topology.Algebra.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instContinuousStarProd", "kind": "instance", "module": "Mathlib.Topology.Algebra.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instContinuousStarForall", "kind": "instance", "module": "Mathlib.Topology.Algebra.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instContinuousStarMulOpposite", "kind": "instance", "module": "Mathlib.Topology.Algebra.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instContinuousStarUnits", "kind": "instance", "module": "Mathlib.Topology.Algebra.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.instIsTopologicalSemiringSubtypeMem", "kind": "instance", "module": "Mathlib.Topology.Algebra.StarSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.isEmbedding_inclusion", "kind": "theorem", "module": "Mathlib.Topology.Algebra.StarSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.isClosedEmbedding_inclusion", "kind": "theorem", "module": "Mathlib.Topology.Algebra.StarSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.topologicalClosure", "kind": "definition", "module": "Mathlib.Topology.Algebra.StarSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.topologicalClosure_toSubalgebra_comm", "kind": "theorem", "module": "Mathlib.Topology.Algebra.StarSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.topologicalClosure_coe", "kind": "theorem", "module": "Mathlib.Topology.Algebra.StarSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.le_topologicalClosure", "kind": "theorem", "module": "Mathlib.Topology.Algebra.StarSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.isClosed_topologicalClosure", "kind": "theorem", "module": "Mathlib.Topology.Algebra.StarSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.instCompleteSpaceSubtypeMemTopologicalClosure", "kind": "instance", "module": "Mathlib.Topology.Algebra.StarSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.topologicalClosure_minimal", "kind": "theorem", "module": "Mathlib.Topology.Algebra.StarSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.topologicalClosure_mono", "kind": "theorem", "module": "Mathlib.Topology.Algebra.StarSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.topologicalClosure_map_le", "kind": "theorem", "module": "Mathlib.Topology.Algebra.StarSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.map_topologicalClosure_le", "kind": "theorem", "module": "Mathlib.Topology.Algebra.StarSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.topologicalClosure_map", "kind": "theorem", "module": "Mathlib.Topology.Algebra.StarSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.topologicalClosure_adjoin_le_centralizer_centralizer", "kind": "theorem", "module": "Mathlib.Topology.Algebra.StarSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.topologicalClosure_star_comm", "kind": "theorem", "module": "Mathlib.Topology.Algebra.StarSubalgebra", "is_tactic_proof": false, "tactics": ["suffices", "le_antisymm", "exact"], "tactic_count": 3}
{"name": "StarSubalgebra.commSemiringTopologicalClosure", "kind": "abbrev", "module": "Mathlib.Topology.Algebra.StarSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarSubalgebra.commRingTopologicalClosure", "kind": "abbrev", "module": "Mathlib.Topology.Algebra.StarSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarAlgHom.ext_topologicalClosure", "kind": "theorem", "module": "Mathlib.Topology.Algebra.StarSubalgebra", "is_tactic_proof": true, "tactics": ["rw", "have", "refine", "rintro", "simpa"], "tactic_count": 5}
{"name": "StarAlgHomClass.ext_topologicalClosure", "kind": "theorem", "module": "Mathlib.Topology.Algebra.StarSubalgebra", "is_tactic_proof": false, "tactics": ["have", "refine", "simpa", "rw", "apply"], "tactic_count": 5}
{"name": "StarAlgebra.elemental", "kind": "definition", "module": "Mathlib.Topology.Algebra.StarSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarAlgebra.elemental.self_mem", "kind": "theorem", "module": "Mathlib.Topology.Algebra.StarSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarAlgebra.elemental.star_self_mem", "kind": "theorem", "module": "Mathlib.Topology.Algebra.StarSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarAlgebra.elemental.instCommSemiringSubtypeMemStarSubalgebraOfT2SpaceOfIsStarNormal", "kind": "instance", "module": "Mathlib.Topology.Algebra.StarSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarAlgebra.elemental.instCommRingSubtypeMemStarSubalgebraOfT2SpaceOfIsStarNormal", "kind": "instance", "module": "Mathlib.Topology.Algebra.StarSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarAlgebra.elemental.isClosed", "kind": "theorem", "module": "Mathlib.Topology.Algebra.StarSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarAlgebra.elemental.instCompleteSpaceSubtypeMemStarSubalgebra", "kind": "instance", "module": "Mathlib.Topology.Algebra.StarSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarAlgebra.elemental.le_of_mem", "kind": "theorem", "module": "Mathlib.Topology.Algebra.StarSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarAlgebra.elemental.le_iff_mem", "kind": "theorem", "module": "Mathlib.Topology.Algebra.StarSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarAlgebra.elemental.isClosedEmbedding_coe", "kind": "theorem", "module": "Mathlib.Topology.Algebra.StarSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarAlgebra.elemental.le_centralizer_centralizer", "kind": "theorem", "module": "Mathlib.Topology.Algebra.StarSubalgebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StarAlgebra.elemental.induction_on", "kind": "theorem", "module": "Mathlib.Topology.Algebra.StarSubalgebra", "is_tactic_proof": true, "tactics": ["apply", "rw", "induction", "mem", "obtain", "exact", "simp_rw", "exact", "algebraMap", "add", "mul"], "tactic_count": 11}
{"name": "StarAlgebra.elemental.starAlgHomClass_ext", "kind": "theorem", "module": "Mathlib.Topology.Algebra.StarSubalgebra", "is_tactic_proof": true, "tactics": ["refine", "refine", "exacts", "simp"], "tactic_count": 4}
{"name": "instContinuousStarReal", "kind": "instance", "module": "Mathlib.Topology.Algebra.Star.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.instContinuousStar", "kind": "instance", "module": "Mathlib.Topology.Algebra.Star.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instContinuousStarSubtypeMemSubmonoidUnitary", "kind": "instance", "module": "Mathlib.Topology.Algebra.Star.Unitary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instContinuousInvSubtypeMemSubmonoidUnitaryOfContinuousStar", "kind": "instance", "module": "Mathlib.Topology.Algebra.Star.Unitary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsTopologicalGroupSubtypeMemSubmonoidUnitaryOfContinuousMulOfContinuousStar", "kind": "instance", "module": "Mathlib.Topology.Algebra.Star.Unitary", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosed_unitary", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Star.Unitary", "is_tactic_proof": true, "tactics": ["let", "have", "rw", "exact"], "tactic_count": 4}
{"name": "mulTSupport", "kind": "definition", "module": "Mathlib.Topology.Algebra.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "subset_mulTSupport", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosed_mulTSupport", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mulTSupport_eq_empty_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Support", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mulTSupport_fun_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Support", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mulTSupport_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Support", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mulTSupport_binop_subset", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mulTSupport_comp_subset", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mulTSupport_subset_comp", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mulTSupport_comp_eq", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Support", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mulTSupport_comp_eq_of_range_subset", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Support", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mulTSupport_comp_subset_preimage", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Support", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "mulTSupport_comp_eq_preimage", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Support", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "image_eq_one_of_notMem_mulTSupport", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "range_subset_insert_image_mulTSupport", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Support", "is_tactic_proof": true, "tactics": ["grw"], "tactic_count": 1}
{"name": "range_eq_image_mulTSupport_or", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tsupport_mul_subset_left", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tsupport_mul_subset_right", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mulTSupport_mul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mulTSupport_pow", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mulTSupport_fun_inv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mulTSupport_inv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mulTSupport_mul_inv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mulTSupport_div", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tsupport_smul_subset_left", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tsupport_smul_subset_right", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "notMem_mulTSupport_iff_eventuallyEq", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Support", "is_tactic_proof": true, "tactics": ["simp_rw", "disjoint_iff_inter_eq_empty,"], "tactic_count": 2}
{"name": "continuous_of_mulTSupport", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.continuous_of_mulTSupport_subset", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasCompactMulSupport", "kind": "definition", "module": "Mathlib.Topology.Algebra.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasCompactMulSupport_def", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Support", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "exists_compact_iff_hasCompactMulSupport", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Support", "is_tactic_proof": true, "tactics": ["simp_rw", "exists_isCompact_superset_iff]"], "tactic_count": 2}
{"name": "HasCompactMulSupport.intro", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasCompactMulSupport.intro'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Support", "is_tactic_proof": false, "tactics": ["have", "rw", "apply", "exact"], "tactic_count": 4}
{"name": "HasCompactMulSupport.of_mulSupport_subset_isCompact", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasCompactMulSupport.isCompact", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasCompactMulSupport_iff_eventuallyEq", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCompact_range_of_mulSupport_subset_isCompact", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Support", "is_tactic_proof": true, "tactics": ["rcases", "exacts"], "tactic_count": 2}
{"name": "HasCompactMulSupport.isCompact_range", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasCompactMulSupport.mono'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasCompactMulSupport.mono", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasCompactMulSupport.comp_left", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasCompactMulSupport_comp_left", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Support", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "HasCompactMulSupport.comp_isClosedEmbedding", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Support", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "HasCompactMulSupport.comp₂_left", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Support", "is_tactic_proof": true, "tactics": ["rw", "filter_upwards", "simp_rw"], "tactic_count": 3}
{"name": "HasCompactMulSupport.isCompact_preimage", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Support", "is_tactic_proof": true, "tactics": ["apply", "apply", "aesop"], "tactic_count": 3}
{"name": "HasCompactMulSupport.mulTSupport_extend_one_subset", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasCompactMulSupport.extend_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasCompactMulSupport.mulTSupport_extend_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasCompactMulSupport.continuous_extend_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasCompactMulSupport.is_one_at_infty", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Support", "is_tactic_proof": true, "tactics": ["intro", "rw", "refine", "rw", "intro", "rw", "exact"], "tactic_count": 7}
{"name": "HasCompactMulSupport.of_compactSpace", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasCompactMulSupport.mul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasCompactMulSupport.one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Support", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HasCompactMulSupport.inv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Support", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "HasCompactSupport.div", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasCompactSupport.smul_left", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Support", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "HasCompactSupport.smul_right", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Support", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "HasCompactSupport.mul_right", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Support", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "HasCompactSupport.mul_left", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Support", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "HasCompactSupport.abs", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyFinite.exists_finset_nhds_mulSupport_subset", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Support", "is_tactic_proof": true, "tactics": ["obtain", "classical", "let", "let", "refine", "exact", "exact", "have", "rw", "exact", "replace", "simp", "suffices", "refine", "specialize", "contrapose", "simp", "intro", "simp", "exact"], "tactic_count": 20}
{"name": "locallyFinite_mulSupport_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyFinite.smul_left", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyFinite.smul_right", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasCompactMulSupport.comp_homeomorph", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Support", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsTopologicallyNilpotent", "kind": "definition", "module": "Mathlib.Topology.Algebra.TopologicallyNilpotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsTopologicallyNilpotent.map", "kind": "theorem", "module": "Mathlib.Topology.Algebra.TopologicallyNilpotent", "is_tactic_proof": true, "tactics": ["unfold", "simp_rw", "exact"], "tactic_count": 3}
{"name": "IsTopologicallyNilpotent.zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.TopologicallyNilpotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsNilpotent.isTopologicallyNilpotent", "kind": "theorem", "module": "Mathlib.Topology.Algebra.TopologicallyNilpotent", "is_tactic_proof": true, "tactics": ["obtain", "apply", "intro", "rw"], "tactic_count": 4}
{"name": "IsTopologicallyNilpotent.exists_pow_mem_of_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Algebra.TopologicallyNilpotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsTopologicallyNilpotent.mul_right_of_commute", "kind": "theorem", "module": "Mathlib.Topology.Algebra.TopologicallyNilpotent", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "IsTopologicallyNilpotent.mul_left_of_commute", "kind": "theorem", "module": "Mathlib.Topology.Algebra.TopologicallyNilpotent", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "IsTopologicallyNilpotent.add_of_commute", "kind": "theorem", "module": "Mathlib.Topology.Algebra.TopologicallyNilpotent", "is_tactic_proof": true, "tactics": ["simp", "intro", "obtain", "obtain", "exact"], "tactic_count": 5}
{"name": "IsTopologicallyNilpotent.mul_right", "kind": "theorem", "module": "Mathlib.Topology.Algebra.TopologicallyNilpotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsTopologicallyNilpotent.mul_left", "kind": "theorem", "module": "Mathlib.Topology.Algebra.TopologicallyNilpotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsTopologicallyNilpotent.add", "kind": "theorem", "module": "Mathlib.Topology.Algebra.TopologicallyNilpotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "topologicalNilradical", "kind": "definition", "module": "Mathlib.Topology.Algebra.TopologicallyNilpotent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsTopologicallyNilpotent.mem_topologicalNilradical_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.TopologicallyNilpotent", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "instOneUniformFun", "kind": "instance", "module": "Mathlib.Topology.Algebra.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformFun.toFun_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformFun.ofFun_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instOneUniformOnFun", "kind": "instance", "module": "Mathlib.Topology.Algebra.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformOnFun.toFun_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformOnFun.one_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instMulUniformFun", "kind": "instance", "module": "Mathlib.Topology.Algebra.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformFun.toFun_mul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformFun.ofFun_mul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instMulUniformOnFun", "kind": "instance", "module": "Mathlib.Topology.Algebra.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformOnFun.toFun_mul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformOnFun.ofFun_mul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInvUniformFun", "kind": "instance", "module": "Mathlib.Topology.Algebra.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformFun.toFun_inv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformFun.ofFun_inv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInvUniformOnFun", "kind": "instance", "module": "Mathlib.Topology.Algebra.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformOnFun.toFun_inv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformOnFun.ofFun_inv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDivUniformFun", "kind": "instance", "module": "Mathlib.Topology.Algebra.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformFun.toFun_div", "kind": "theorem", "module": "Mathlib.Topology.Algebra.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformFun.ofFun_div", "kind": "theorem", "module": "Mathlib.Topology.Algebra.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDivUniformOnFun", "kind": "instance", "module": "Mathlib.Topology.Algebra.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformOnFun.toFun_div", "kind": "theorem", "module": "Mathlib.Topology.Algebra.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformOnFun.ofFun_div", "kind": "theorem", "module": "Mathlib.Topology.Algebra.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instMonoidUniformFun", "kind": "instance", "module": "Mathlib.Topology.Algebra.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instMonoidUniformOnFun", "kind": "instance", "module": "Mathlib.Topology.Algebra.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCommMonoidUniformFun", "kind": "instance", "module": "Mathlib.Topology.Algebra.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCommMonoidUniformOnFun", "kind": "instance", "module": "Mathlib.Topology.Algebra.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instGroupUniformFun", "kind": "instance", "module": "Mathlib.Topology.Algebra.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instGroupUniformOnFun", "kind": "instance", "module": "Mathlib.Topology.Algebra.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCommGroupUniformFun", "kind": "instance", "module": "Mathlib.Topology.Algebra.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCommGroupUniformOnFun", "kind": "instance", "module": "Mathlib.Topology.Algebra.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instSMulUniformFun", "kind": "instance", "module": "Mathlib.Topology.Algebra.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformFun.toFun_smul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformFun.ofFun_smul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instSMulUniformOnFun", "kind": "instance", "module": "Mathlib.Topology.Algebra.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformOnFun.toFun_smul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformOnFun.ofFun_smul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsScalarTowerUniformFun", "kind": "instance", "module": "Mathlib.Topology.Algebra.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsScalarTowerUniformOnFun", "kind": "instance", "module": "Mathlib.Topology.Algebra.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instSMulCommClassUniformFun", "kind": "instance", "module": "Mathlib.Topology.Algebra.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instSMulCommClassUniformOnFun", "kind": "instance", "module": "Mathlib.Topology.Algebra.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instMulActionUniformFun", "kind": "instance", "module": "Mathlib.Topology.Algebra.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instMulActionUniformOnFun", "kind": "instance", "module": "Mathlib.Topology.Algebra.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDistribMulActionUniformFun", "kind": "instance", "module": "Mathlib.Topology.Algebra.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDistribMulActionUniformOnFun", "kind": "instance", "module": "Mathlib.Topology.Algebra.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instModuleUniformFun", "kind": "instance", "module": "Mathlib.Topology.Algebra.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instModuleUniformOnFun", "kind": "instance", "module": "Mathlib.Topology.Algebra.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsUniformGroupUniformFun", "kind": "instance", "module": "Mathlib.Topology.Algebra.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformFun.hasBasis_nhds_one_of_basis", "kind": "theorem", "module": "Mathlib.Topology.Algebra.UniformConvergence", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "UniformFun.hasBasis_nhds_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsUniformGroupUniformOnFun", "kind": "instance", "module": "Mathlib.Topology.Algebra.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformOnFun.hasBasis_nhds_one_of_basis", "kind": "theorem", "module": "Mathlib.Topology.Algebra.UniformConvergence", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "UniformOnFun.hasBasis_nhds_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformOnFun.ofFun_prod", "kind": "theorem", "module": "Mathlib.Topology.Algebra.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformOnFun.toFun_prod", "kind": "theorem", "module": "Mathlib.Topology.Algebra.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformFun.ofFun_prod", "kind": "theorem", "module": "Mathlib.Topology.Algebra.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformFun.toFun_prod", "kind": "theorem", "module": "Mathlib.Topology.Algebra.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformFun.uniformContinuousConstSMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformFunOn.uniformContinuousConstSMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.Algebra.UniformField.0.termHat", "kind": "definition", "module": "Mathlib.Topology.Algebra.UniformField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.Algebra.UniformField.0._aux_Mathlib_Topology_Algebra_UniformField___macroRules__private_Mathlib_Topology_Algebra_UniformField_0_termHat_1", "kind": "definition", "module": "Mathlib.Topology.Algebra.UniformField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.Algebra.UniformField.0._aux_Mathlib_Topology_Algebra_UniformField___unexpand_UniformSpace_Completion_1", "kind": "definition", "module": "Mathlib.Topology.Algebra.UniformField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.instNontrivialOfT0Space", "kind": "instance", "module": "Mathlib.Topology.Algebra.UniformField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.hatInv", "kind": "definition", "module": "Mathlib.Topology.Algebra.UniformField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.continuous_hatInv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.UniformField", "is_tactic_proof": true, "tactics": ["refine", "apply", "intro", "rw", "apply", "have", "simp", "rw", "apply", "apply", "haveI", "apply", "rw", "have", "by_contra", "exact", "rw", "norm_cast", "rw", "exact"], "tactic_count": 20}
{"name": "UniformSpace.Completion.instInvCompletion", "kind": "instance", "module": "Mathlib.Topology.Algebra.UniformField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.hatInv_extends", "kind": "theorem", "module": "Mathlib.Topology.Algebra.UniformField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.coe_inv", "kind": "theorem", "module": "Mathlib.Topology.Algebra.UniformField", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "dsimp", "norm_cast", "simp", "conv_lhs", "rw", "exact", "exact"], "tactic_count": 9}
{"name": "UniformSpace.Completion.mul_hatInv_cancel", "kind": "theorem", "module": "Mathlib.Topology.Algebra.UniformField", "is_tactic_proof": true, "tactics": ["haveI", "let", "let", "change", "have", "have", "have", "rw", "apply", "rw", "exact", "have", "have", "rw", "rintro", "rw", "rw", "dsimp", "rw", "rw", "replace", "rwa"], "tactic_count": 22}
{"name": "UniformSpace.Completion.instField", "kind": "instance", "module": "Mathlib.Topology.Algebra.UniformField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.instIsTopologicalDivisionRing", "kind": "instance", "module": "Mathlib.Topology.Algebra.UniformField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subfield.completableTopField", "kind": "instance", "module": "Mathlib.Topology.Algebra.UniformField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "completableTopField_of_complete", "kind": "instance", "module": "Mathlib.Topology.Algebra.UniformField", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUniformInducing.completableTopField", "kind": "theorem", "module": "Mathlib.Topology.Algebra.UniformField", "is_tactic_proof": true, "tactics": ["refine", "rw", "have", "rw", "apply", "rw"], "tactic_count": 6}
{"name": "AddGroupFilterBasis.uniformSpace", "kind": "definition", "module": "Mathlib.Topology.Algebra.UniformFilterBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddGroupFilterBasis.isUniformAddGroup", "kind": "theorem", "module": "Mathlib.Topology.Algebra.UniformFilterBasis", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddGroupFilterBasis.cauchy_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.UniformFilterBasis", "is_tactic_proof": true, "tactics": ["letI", "haveI", "suffices", "constructor", "rw", "change", "simp"], "tactic_count": 7}
{"name": "AddMonoid.uniformContinuousConstSMul_nat", "kind": "instance", "module": "Mathlib.Topology.Algebra.UniformMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddGroup.uniformContinuousConstSMul_int", "kind": "instance", "module": "Mathlib.Topology.Algebra.UniformMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformContinuousConstSMul_of_continuousConstSMul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.UniformMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ring.uniformContinuousConstSMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.UniformMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ring.uniformContinuousConstSMul_op", "kind": "instance", "module": "Mathlib.Topology.Algebra.UniformMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformContinuousConstSMul.to_continuousConstSMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.UniformMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformContinuous.const_smul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.UniformMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUniformInducing.uniformContinuousConstSMul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.UniformMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformContinuousConstSMul.op", "kind": "instance", "module": "Mathlib.Topology.Algebra.UniformMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.uniformContinuousConstSMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.UniformMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUniformGroup.to_uniformContinuousConstSMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.UniformMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformContinuous.const_mul'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.UniformMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformContinuous.mul_const'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.UniformMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformContinuous_mul_left'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.UniformMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformContinuous_mul_right'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.UniformMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformContinuous.div_const'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.UniformMulAction", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "uniformContinuous_div_const'", "kind": "theorem", "module": "Mathlib.Topology.Algebra.UniformMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUnit.smul_uniformity", "kind": "theorem", "module": "Mathlib.Topology.Algebra.UniformMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smul_uniformity", "kind": "theorem", "module": "Mathlib.Topology.Algebra.UniformMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "smul_uniformity₀", "kind": "theorem", "module": "Mathlib.Topology.Algebra.UniformMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.instSMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.UniformMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.smul_def", "kind": "theorem", "module": "Mathlib.Topology.Algebra.UniformMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.instUniformContinuousConstSMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.UniformMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.instIsScalarTower", "kind": "instance", "module": "Mathlib.Topology.Algebra.UniformMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.instSMulCommClassOfUniformContinuousConstSMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.UniformMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.instIsCentralScalar", "kind": "instance", "module": "Mathlib.Topology.Algebra.UniformMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.coe_smul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.UniformMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.instMulActionOfUniformContinuousConstSMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.UniformMulAction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.one", "kind": "instance", "module": "Mathlib.Topology.Algebra.UniformRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.mul", "kind": "instance", "module": "Mathlib.Topology.Algebra.UniformRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.coe_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.UniformRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.coe_eq_one_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.UniformRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.coe_mul", "kind": "theorem", "module": "Mathlib.Topology.Algebra.UniformRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.instContinuousMul", "kind": "instance", "module": "Mathlib.Topology.Algebra.UniformRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.ring", "kind": "instance", "module": "Mathlib.Topology.Algebra.UniformRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.coeRingHom", "kind": "definition", "module": "Mathlib.Topology.Algebra.UniformRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.continuous_coeRingHom", "kind": "theorem", "module": "Mathlib.Topology.Algebra.UniformRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.extensionHom", "kind": "definition", "module": "Mathlib.Topology.Algebra.UniformRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.extensionHom_coe", "kind": "theorem", "module": "Mathlib.Topology.Algebra.UniformRing", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "UniformSpace.Completion.topologicalRing", "kind": "instance", "module": "Mathlib.Topology.Algebra.UniformRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.mapRingHom", "kind": "definition", "module": "Mathlib.Topology.Algebra.UniformRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.mapRingHom_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.UniformRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.coe_mapRingHom", "kind": "theorem", "module": "Mathlib.Topology.Algebra.UniformRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.mapRingHom_coe", "kind": "theorem", "module": "Mathlib.Topology.Algebra.UniformRing", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "UniformSpace.Completion.mapRingHom_comp", "kind": "theorem", "module": "Mathlib.Topology.Algebra.UniformRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.mapRingHom_id", "kind": "theorem", "module": "Mathlib.Topology.Algebra.UniformRing", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "UniformSpace.Completion.mapRingEquiv", "kind": "definition", "module": "Mathlib.Topology.Algebra.UniformRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.map_smul_eq_mul_coe", "kind": "theorem", "module": "Mathlib.Topology.Algebra.UniformRing", "is_tactic_proof": true, "tactics": ["ext", "refine", "exact", "simp_rw"], "tactic_count": 4}
{"name": "UniformSpace.Completion.algebra", "kind": "instance", "module": "Mathlib.Topology.Algebra.UniformRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.algebraMap_def", "kind": "theorem", "module": "Mathlib.Topology.Algebra.UniformRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.commRing", "kind": "instance", "module": "Mathlib.Topology.Algebra.UniformRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.algebra'", "kind": "instance", "module": "Mathlib.Topology.Algebra.UniformRing", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "UniformSpace.inseparableSetoid_ring", "kind": "theorem", "module": "Mathlib.Topology.Algebra.UniformRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.sepQuotHomeomorphRingQuot", "kind": "definition", "module": "Mathlib.Topology.Algebra.UniformRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.commRing", "kind": "instance", "module": "Mathlib.Topology.Algebra.UniformRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.sepQuotRingEquivRingQuot", "kind": "definition", "module": "Mathlib.Topology.Algebra.UniformRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.topologicalRing", "kind": "instance", "module": "Mathlib.Topology.Algebra.UniformRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDenseInducing.extendRingHom", "kind": "definition", "module": "Mathlib.Topology.Algebra.UniformRing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedField.v_eq_valuation", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Valued.LocallyCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valued.integer.mem_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Valued.LocallyCompact", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Valued.integer.norm_le_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Valued.LocallyCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valued.integer.norm_coe_unit", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Valued.LocallyCompact", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Valued.integer.norm_unit", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Valued.LocallyCompact", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Valued.integer.isUnit_iff_norm_eq_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Valued.LocallyCompact", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Valued.integer.norm_irreducible_lt_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Valued.LocallyCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valued.integer.norm_irreducible_pos", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Valued.LocallyCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valued.integer.coe_span_singleton_eq_closedBall", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Valued.LocallyCompact", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Irreducible.maximalIdeal_eq_closedBall", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Valued.LocallyCompact", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Irreducible.maximalIdeal_pow_eq_closedBall_pow", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Valued.LocallyCompact", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Valued.integer.exists_norm_coe_lt_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Valued.LocallyCompact", "is_tactic_proof": true, "tactics": ["obtain", "refine", "simpa"], "tactic_count": 3}
{"name": "Valued.integer.exists_norm_lt_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Valued.LocallyCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valued.integer.exists_nnnorm_lt_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Valued.LocallyCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valued.integer.finite_quotient_maximalIdeal_pow_of_finite_residueField", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Valued.LocallyCompact", "is_tactic_proof": true, "tactics": ["induction", "zero", "simp", "exact", "succ", "have", "replace", "suffices", "exact"], "tactic_count": 9}
{"name": "Valued.integer.totallyBounded_iff_finite_residueField", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Valued.LocallyCompact", "is_tactic_proof": true, "tactics": ["constructor", "intro", "obtain", "have", "simp", "obtain", "rw", "refine", "rintro", "replace", "simp", "obtain", "simp", "refine", "convert", "rw", "rw", "simpa", "intro", "rw", "intro", "obtain", "have", "obtain", "have", "refine", "have", "ext", "simp", "simp", "intro", "exact"], "tactic_count": 32}
{"name": "Valued.integer.locallyFiniteOrder_units_mrange_of_isCompact_integer", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Valued.LocallyCompact", "is_tactic_proof": true, "tactics": ["constructor", "refine", "suffices", "rintro", "rcases", "rw", "exact", "simp", "simp", "wlog", "specialize", "refine", "rw", "intro", "simp", "generalize_proofs", "rcases", "exact", "have", "refine", "rw", "simp", "intro", "obtain", "rcases", "rw", "exact", "simp", "have", "have", "have", "simp", "let", "have", "specialize", "intro", "simp", "split_ifs", "exact", "refine", "push_neg", "refine", "simp", "intro", "simp", "intro", "use", "split_ifs", "simp_all", "obtain", "classical", "refine", "refine", "push_neg", "exact", "intro", "simp", "obtain", "intro", "have", "simp", "obtain", "use", "split_ifs", "simp", "simp", "simp", "rw", "simp"], "tactic_count": 69}
{"name": "Valued.integer.mulArchimedean_mrange_of_isCompact_integer", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Valued.LocallyCompact", "is_tactic_proof": true, "tactics": ["rw", "obtain", "exact"], "tactic_count": 3}
{"name": "Valued.integer.isPrincipalIdealRing_of_compactSpace", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Valued.LocallyCompact", "is_tactic_proof": true, "tactics": ["have", "have", "obtain", "have", "refine", "hi.isPrincipalIdealRing_iff_not_denselyOrdered_mrange.mpr", "exact", "not_subsingleton"], "tactic_count": 8}
{"name": "Valuation.isNontrivial_iff_not_a_field", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Valued.LocallyCompact", "is_tactic_proof": false, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Valued.integer.isDiscreteValuationRing_of_compactSpace", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Valued.LocallyCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valued.integer.compactSpace_iff_completeSpace_and_isDiscreteValuationRing_and_finite_residueField", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Valued.LocallyCompact", "is_tactic_proof": true, "tactics": ["refine", "have", "refine", "rw", "exact", "rw", "rw", "exact"], "tactic_count": 8}
{"name": "Valued.integer.properSpace_iff_compactSpace_integer", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Valued.LocallyCompact", "is_tactic_proof": false, "tactics": ["simp", "toNormedField.setOf_mem_integer_eq_closedBall]", "constructor", "exact", "suffices", "exact"], "tactic_count": 6}
{"name": "Valued.integer.properSpace_iff_completeSpace_and_isDiscreteValuationRing_integer_and_finite_residueField", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Valued.LocallyCompact", "is_tactic_proof": true, "tactics": ["simp", "compactSpace_iff_completeSpace_and_isDiscreteValuationRing_and_finite_residueField,", "toNormedField.setOf_mem_integer_eq_closedBall,"], "tactic_count": 3}
{"name": "NormedField.valuation", "kind": "definition", "module": "Mathlib.Topology.Algebra.Valued.NormedValued", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedField.valuation_apply", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Valued.NormedValued", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedField.toValued", "kind": "definition", "module": "Mathlib.Topology.Algebra.Valued.NormedValued", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormedField.instRankOneNNRealValuation", "kind": "instance", "module": "Mathlib.Topology.Algebra.Valued.NormedValued", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valued.norm", "kind": "definition", "module": "Mathlib.Topology.Algebra.Valued.NormedValued", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valued.norm_def", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Valued.NormedValued", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valued.norm_nonneg", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Valued.NormedValued", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Valued.norm_add_le", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Valued.NormedValued", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Valued.norm_eq_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Valued.NormedValued", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Valued.norm_pos_iff_valuation_pos", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Valued.NormedValued", "is_tactic_proof": false, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Valued.toNormedField", "kind": "definition", "module": "Mathlib.Topology.Algebra.Valued.NormedValued", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valued.isNonarchimedean_norm", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Valued.NormedValued", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valued.instIsUltrametricDist", "kind": "instance", "module": "Mathlib.Topology.Algebra.Valued.NormedValued", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valued.coe_valuation_eq_rankOne_hom_comp_valuation", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Valued.NormedValued", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valued.toNormedField.norm_le_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Valued.NormedValued", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valued.toNormedField.norm_lt_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Valued.NormedValued", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valued.toNormedField.norm_le_one_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Valued.NormedValued", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Valued.toNormedField.norm_lt_one_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Valued.NormedValued", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Valued.toNormedField.one_le_norm_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Valued.NormedValued", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Valued.toNormedField.one_lt_norm_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Valued.NormedValued", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Valued.toNormedField.setOf_mem_integer_eq_closedBall", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Valued.NormedValued", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Valued.toNontriviallyNormedField", "kind": "definition", "module": "Mathlib.Topology.Algebra.Valued.NormedValued", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valuation.map_eq_one_of_forall_lt", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Valued.ValuationTopology", "is_tactic_proof": true, "tactics": ["lift", "rcases", "obtain", "specialize", "simp", "simpa", "rw", "obtain", "specialize", "simp", "simp"], "tactic_count": 11}
{"name": "Valuation.subgroups_basis", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Valued.ValuationTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valued.mk'", "kind": "definition", "module": "Mathlib.Topology.Algebra.Valued.ValuationTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valued.hasBasis_nhds_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Valued.ValuationTopology", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Valued.hasBasis_uniformity", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Valued.ValuationTopology", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Valued.toUniformSpace_eq", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Valued.ValuationTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valued.mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Valued.ValuationTopology", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Valued.mem_nhds_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Valued.ValuationTopology", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Valued.loc_const", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Valued.ValuationTopology", "is_tactic_proof": true, "tactics": ["rw", "use", "rw", "intro", "exact"], "tactic_count": 5}
{"name": "Valued.instIsTopologicalRing", "kind": "instance", "module": "Mathlib.Topology.Algebra.Valued.ValuationTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valued.discreteTopology_of_forall_map_eq_one", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Valued.ValuationTopology", "is_tactic_proof": false, "tactics": ["simp", "mem_nhds_zero,", "use", "contrapose", "obtain", "exact"], "tactic_count": 6}
{"name": "Valued.discreteTopology_of_forall_lt", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Valued.ValuationTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valued.cauchy_iff", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Valued.ValuationTopology", "is_tactic_proof": true, "tactics": ["rw", "apply", "simp_rw", "constructor", "intro", "exact", "rintro", "exact"], "tactic_count": 8}
{"name": "Valued.isOpen_ball", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Valued.ValuationTopology", "is_tactic_proof": true, "tactics": ["rw", "rcases", "simp", "intro", "rw", "simp", "exact"], "tactic_count": 7}
{"name": "Valued.isClosed_ball", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Valued.ValuationTopology", "is_tactic_proof": true, "tactics": ["rcases", "simp", "exact"], "tactic_count": 3}
{"name": "Valued.isClopen_ball", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Valued.ValuationTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valued.isOpen_closedBall", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Valued.ValuationTopology", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "simp", "exact"], "tactic_count": 5}
{"name": "Valued.isClosed_closedBall", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Valued.ValuationTopology", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "have", "exact", "ne_of_lt"], "tactic_count": 6}
{"name": "Valued.isClopen_closedBall", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Valued.ValuationTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valued.isClopen_sphere", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Valued.ValuationTopology", "is_tactic_proof": false, "tactics": ["have", "ext", "simp", "rw", "exact"], "tactic_count": 5}
{"name": "Valued.isOpen_sphere", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Valued.ValuationTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valued.isClosed_sphere", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Valued.ValuationTopology", "is_tactic_proof": true, "tactics": ["rcases", "simpa", "exact"], "tactic_count": 3}
{"name": "Valued.isOpen_integer", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Valued.ValuationTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valued.isClosed_integer", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Valued.ValuationTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valued.isClopen_integer", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Valued.ValuationTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valued.isOpen_valuationSubring", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Valued.ValuationTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valued.isClosed_valuationSubring", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Valued.ValuationTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Valued.isClopen_valuationSubring", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Valued.ValuationTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.Algebra.Valued.ValuativeRel.0.IsValuativeTopology.termV", "kind": "definition", "module": "Mathlib.Topology.Algebra.Valued.ValuativeRel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.Algebra.Valued.ValuativeRel.0.IsValuativeTopology._aux_Mathlib_Topology_Algebra_Valued_ValuativeRel___macroRules__private_Mathlib_Topology_Algebra_Valued_ValuativeRel_0_IsValuativeTopology_termV_1", "kind": "definition", "module": "Mathlib.Topology.Algebra.Valued.ValuativeRel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.Algebra.Valued.ValuativeRel.0.IsValuativeTopology._aux_Mathlib_Topology_Algebra_Valued_ValuativeRel___unexpand_ValuativeRel_valuation_1", "kind": "definition", "module": "Mathlib.Topology.Algebra.Valued.ValuativeRel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsValuativeTopology.of_zero", "kind": "theorem", "module": "Mathlib.Topology.Algebra.Valued.ValuativeRel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.Algebra.Valued.ValuativeRel.0.IsValuativeTopology.termV_1", "kind": "definition", "module": "Mathlib.Topology.Algebra.Valued.ValuativeRel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.Algebra.Valued.ValuativeRel.0.IsValuativeTopology._aux_Mathlib_Topology_Algebra_Valued_ValuativeRel___macroRules__private_Mathlib_Topology_Algebra_Valued_ValuativeRel_0_IsValuativeTopology_termV_1_1", "kind": "definition", "module": "Mathlib.Topology.Algebra.Valued.ValuativeRel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.Algebra.Valued.ValuativeRel.0.IsValuativeTopology._aux_Mathlib_Topology_Algebra_Valued_ValuativeRel___unexpand_ValuativeRel_valuation_2", "kind": "definition", "module": "Mathlib.Topology.Algebra.Valued.ValuativeRel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "TopologicalSpace.IsTopologicalBasis.isOpen", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "TopologicalSpace.IsTopologicalBasis.insert_empty", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.IsTopologicalBasis.diff_empty", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.IsTopologicalBasis.mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.IsTopologicalBasis.exists_subset_of_mem_open", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.IsTopologicalBasis.open_eq_sUnion'", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.IsTopologicalBasis.open_eq_sUnion", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.IsTopologicalBasis.open_iff_eq_sUnion", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.IsTopologicalBasis.open_eq_iUnion", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.IsTopologicalBasis.isOpen_induction", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "TopologicalSpace.IsTopologicalBasis.subset_of_forall_subset", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "TopologicalSpace.IsTopologicalBasis.eq_of_forall_subset_iff", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "TopologicalSpace.IsTopologicalBasis.mem_closure_iff", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.IsTopologicalBasis.dense_iff", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "TopologicalSpace.IsTopologicalBasis.isOpenMap_iff", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "TopologicalSpace.IsTopologicalBasis.exists_nonempty_subset", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.isTopologicalBasis_opens", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.IsTopologicalBasis.isInducing", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.IsTopologicalBasis.induced", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.IsTopologicalBasis.inf", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": true, "tactics": ["refine", "rw", "convert", "aesop"], "tactic_count": 4}
{"name": "TopologicalSpace.IsTopologicalBasis.inf_induced", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "TopologicalSpace.IsTopologicalBasis.prod", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.isTopologicalBasis_of_cover", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": true, "tactics": ["refine", "simp", "rcases", "exact", "intro", "rcases", "lift", "rcases", "exact"], "tactic_count": 9}
{"name": "TopologicalSpace.IsTopologicalBasis.continuous_iff", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "TopologicalSpace.isTopologicalBasis_empty", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.exists_countable_dense", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.exists_dense_seq", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "exact"], "tactic_count": 3}
{"name": "TopologicalSpace.denseSeq", "kind": "definition", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.denseRange_denseSeq", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Countable.to_separableSpace", "kind": "instance", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.SeparableSpace.of_denseRange", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DenseRange.separableSpace", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsQuotientMap.separableSpace", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpenMap.separableSpace_of_isInducing", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": true, "tactics": ["cases", "infer_instance", "obtain", "refine", "simp_rw", "intro", "obtain", "s_dense.inter_open_nonempty", "refine", "rwa"], "tactic_count": 10}
{"name": "IsOpenMap.separableSpace_of_injective", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsOpenEmbedding.separableSpace", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.instSeparableSpaceProd", "kind": "instance", "module": "Mathlib.Topology.Bases", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "exact"], "tactic_count": 3}
{"name": "TopologicalSpace.instSeparableSpaceForallOfCountable", "kind": "instance", "module": "Mathlib.Topology.Bases", "is_tactic_proof": true, "tactics": ["choose", "haveI", "nontriviality", "classical", "set", "refine", "rcases", "have", "choose", "lift", "refine", "simp", "exact"], "tactic_count": 13}
{"name": "TopologicalSpace.instSeparableSpaceQuot", "kind": "instance", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.instSeparableSpaceQuotient", "kind": "instance", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.instSeparableSpaceSum", "kind": "instance", "module": "Mathlib.Topology.Bases", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "refine", "simp_rw"], "tactic_count": 4}
{"name": "TopologicalSpace.separableSpace_sum_iff", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.separableSpace_iff_countable", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Pairwise.countable_of_isOpen_disjoint", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": true, "tactics": ["rcases", "choose", "have", "have", "exact"], "tactic_count": 5}
{"name": "Set.PairwiseDisjoint.countable_of_isOpen", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.PairwiseDisjoint.countable_of_nonempty_interior", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.IsSeparable", "kind": "definition", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.IsSeparable.mono", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "TopologicalSpace.IsSeparable.iUnion", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": true, "tactics": ["choose", "refine", "exact"], "tactic_count": 3}
{"name": "TopologicalSpace.isSeparable_iUnion", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.isSeparable_union", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "TopologicalSpace.IsSeparable.union", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.isSeparable_closure", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.Countable.isSeparable", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.isSeparable", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.IsSeparable.univ_pi", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": true, "tactics": ["classical", "rcases", "rw", "exact", "choose", "haveI", "set", "refine", "rcases", "rsuffices", "exact", "suffices", "choose", "refine", "simpa", "intro", "exact"], "tactic_count": 17}
{"name": "TopologicalSpace.isSeparable_pi", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "TopologicalSpace.IsSeparable.prod", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "refine", "rw", "gcongr"], "tactic_count": 5}
{"name": "TopologicalSpace.IsSeparable.image", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": true, "tactics": ["rcases", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "Dense.isSeparable_iff", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": true, "tactics": ["simp_rw", "isClosed_closure.closure_subset_iff]"], "tactic_count": 2}
{"name": "TopologicalSpace.isSeparable_univ_iff", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.isSeparable_range", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.IsSeparable.of_subtype", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "TopologicalSpace.IsSeparable.of_separableSpace", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsTopologicalBasis.iInf", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": true, "tactics": ["let", "refine", "rintro", "refine", "intro", "rcases", "refine", "exact", "exact", "exact"], "tactic_count": 10}
{"name": "IsTopologicalBasis.iInf_induced", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": true, "tactics": ["convert", "constructor", "exact", "choose", "exact"], "tactic_count": 5}
{"name": "isTopologicalBasis_pi", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "isTopologicalBasis_singletons", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isTopologicalBasis_subtype", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpenMap_eval", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": true, "tactics": ["classical", "refine", "rintro", "obtain", "simp", "by_cases", "rw", "exact", "rw", "exact"], "tactic_count": 10}
{"name": "Dense.exists_countable_dense_subset", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dense.exists_countable_dense_subset_bot_top", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": true, "tactics": ["rcases", "refine", "exacts", "htd.mono"], "tactic_count": 4}
{"name": "separableSpace_univ", "kind": "instance", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_countable_dense_bot_top", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "TopologicalSpace.firstCountableTopology_induced", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Subtype.firstCountableTopology", "kind": "instance", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsInducing.firstCountableTopology", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Topology.IsEmbedding.firstCountableTopology", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.FirstCountableTopology.tendsto_subseq", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.instFirstCountableTopologyProd", "kind": "instance", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.instFirstCountableTopologyForallOfCountable", "kind": "instance", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.isCountablyGenerated_nhdsWithin", "kind": "instance", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.IsTopologicalBasis.secondCountableTopology", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.SecondCountableTopology.mk'", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finite.toSecondCountableTopology", "kind": "instance", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.exists_countable_basis", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": true, "tactics": ["obtain", "refine", "exacts"], "tactic_count": 3}
{"name": "TopologicalSpace.countableBasis", "kind": "definition", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.countable_countableBasis", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.encodableCountableBasis", "kind": "instance", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.empty_notMem_countableBasis", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.isBasis_countableBasis", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.eq_generateFrom_countableBasis", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.isOpen_of_mem_countableBasis", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.nonempty_of_mem_countableBasis", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.SecondCountableTopology.to_firstCountableTopology", "kind": "instance", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.instSecondCountableTopologyOfCountableOfFirstCountableTopology", "kind": "instance", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.secondCountableTopology_induced", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": true, "tactics": ["rcases", "letI", "refine", "rw"], "tactic_count": 4}
{"name": "TopologicalSpace.Subtype.secondCountableTopology", "kind": "instance", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.secondCountableTopology_iInf", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": true, "tactics": ["rw", "exact", "countable_iUnion"], "tactic_count": 3}
{"name": "TopologicalSpace.instSecondCountableTopologyProd", "kind": "instance", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.instSecondCountableTopologyForallOfCountable", "kind": "instance", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.SecondCountableTopology.to_separableSpace", "kind": "instance", "module": "Mathlib.Topology.Bases", "is_tactic_proof": true, "tactics": ["choose", "exact"], "tactic_count": 2}
{"name": "TopologicalSpace.secondCountableTopology_of_countable_cover", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.isOpen_iUnion_countable", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": true, "tactics": ["let", "choose", "haveI", "refine", "rintro", "rcases", "exact"], "tactic_count": 7}
{"name": "TopologicalSpace.isOpen_biUnion_countable", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": true, "tactics": ["simp_rw", "rcases", "exact"], "tactic_count": 3}
{"name": "TopologicalSpace.isOpen_sUnion_countable", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "TopologicalSpace.countable_cover_nhds", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": true, "tactics": ["rcases", "suffices", "simp", "exact"], "tactic_count": 4}
{"name": "TopologicalSpace.countable_cover_nhdsWithin", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": true, "tactics": ["have", "rcases", "refine", "simp", "exact"], "tactic_count": 5}
{"name": "TopologicalSpace.IsTopologicalBasis.exists_countable_biUnion_of_isOpen", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": true, "tactics": ["have", "choose", "obtain", "apply", "rintro", "exact", "refine", "simp", "rintro", "exact", "rw", "apply", "intro", "simp", "grind", "simp", "grind"], "tactic_count": 17}
{"name": "TopologicalSpace.IsTopologicalBasis.exists_countable", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": ["have", "ht.exists_countable_biUnion_of_isOpen", "choose", "refine", "apply", "simp", "have", "grind", "intro", "simp", "obtain", "have", "convert", "exact", "obtain", "refine", "apply", "exact"], "tactic_count": 18}
{"name": "TopologicalSpace.exists_countable_of_generateFrom", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": true, "tactics": ["let", "have", "obtain", "have", "simpa", "choose", "refine", "apply", "intro", "exact", "apply", "apply", "simp", "intro", "rw", "apply", "exact", "rw", "apply", "intro", "rw", "change", "apply", "apply", "intro", "apply", "simp", "grind"], "tactic_count": 28}
{"name": "TopologicalSpace.IsTopologicalBasis.sigma", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": true, "tactics": ["refine", "rw", "convert", "aesop"], "tactic_count": 4}
{"name": "TopologicalSpace.instSecondCountableTopologySigmaOfCountable", "kind": "instance", "module": "Mathlib.Topology.Bases", "is_tactic_proof": true, "tactics": ["let", "have", "have", "exact"], "tactic_count": 4}
{"name": "TopologicalSpace.IsTopologicalBasis.sum", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": true, "tactics": ["apply", "rintro", "exact", "exact", "rintro", "obtain", "hs.exists_subset_of_mem_open", "exact", "obtain", "ht.exists_subset_of_mem_open", "exact"], "tactic_count": 11}
{"name": "TopologicalSpace.instSecondCountableTopologySum", "kind": "instance", "module": "Mathlib.Topology.Bases", "is_tactic_proof": true, "tactics": ["let", "have", "have", "exact"], "tactic_count": 4}
{"name": "TopologicalSpace.IsTopologicalBasis.isQuotientMap", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": true, "tactics": ["apply", "rintro", "apply", "intro", "obtain", "let", "have", "have", "obtain", "have", "exact"], "tactic_count": 11}
{"name": "Topology.IsQuotientMap.secondCountableTopology", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.IsTopologicalBasis.quotient", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Quotient.secondCountableTopology", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsInducing.secondCountableTopology", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Topology.IsEmbedding.secondCountableTopology", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsEmbedding.separableSpace", "kind": "theorem", "module": "Mathlib.Topology.Bases", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "TopologicalSpace.ofClosed", "kind": "definition", "module": "Mathlib.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpen_mk", "kind": "theorem", "module": "Mathlib.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.ext", "kind": "theorem", "module": "Mathlib.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.ext_iff", "kind": "theorem", "module": "Mathlib.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpen_fold", "kind": "theorem", "module": "Mathlib.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpen_iUnion", "kind": "theorem", "module": "Mathlib.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpen_biUnion", "kind": "theorem", "module": "Mathlib.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.union", "kind": "theorem", "module": "Mathlib.Topology.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "isOpen_iff_of_cover", "kind": "theorem", "module": "Mathlib.Topology.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "isOpen_empty", "kind": "theorem", "module": "Mathlib.Topology.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.Finite.isOpen_sInter", "kind": "theorem", "module": "Mathlib.Topology.Basic", "is_tactic_proof": true, "tactics": ["induction", "empty", "insert", "simp", "exact"], "tactic_count": 5}
{"name": "Set.Finite.isOpen_biInter", "kind": "theorem", "module": "Mathlib.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpen_iInter_of_finite", "kind": "theorem", "module": "Mathlib.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpen_biInter_finset", "kind": "theorem", "module": "Mathlib.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpen_const", "kind": "theorem", "module": "Mathlib.Topology.Basic", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "IsOpen.and", "kind": "theorem", "module": "Mathlib.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpen_compl_iff", "kind": "theorem", "module": "Mathlib.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.ext_iff_isClosed", "kind": "theorem", "module": "Mathlib.Topology.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "isClosed_const", "kind": "theorem", "module": "Mathlib.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosed_empty", "kind": "theorem", "module": "Mathlib.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosed_univ", "kind": "theorem", "module": "Mathlib.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.isLocallyClosed", "kind": "theorem", "module": "Mathlib.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.isLocallyClosed", "kind": "theorem", "module": "Mathlib.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.union", "kind": "theorem", "module": "Mathlib.Topology.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "isClosed_sInter", "kind": "theorem", "module": "Mathlib.Topology.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "isClosed_iInter", "kind": "theorem", "module": "Mathlib.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosed_biInter", "kind": "theorem", "module": "Mathlib.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosed_compl_iff", "kind": "theorem", "module": "Mathlib.Topology.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsOpen.sdiff", "kind": "theorem", "module": "Mathlib.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.inter", "kind": "theorem", "module": "Mathlib.Topology.Basic", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "IsClosed.sdiff", "kind": "theorem", "module": "Mathlib.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.isClosed_biUnion", "kind": "theorem", "module": "Mathlib.Topology.Basic", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "isClosed_biUnion_finset", "kind": "theorem", "module": "Mathlib.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosed_iUnion_of_finite", "kind": "theorem", "module": "Mathlib.Topology.Basic", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "isClosed_imp", "kind": "theorem", "module": "Mathlib.Topology.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsClosed.not", "kind": "theorem", "module": "Mathlib.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.and", "kind": "theorem", "module": "Mathlib.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_nhds_lim", "kind": "theorem", "module": "Mathlib.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_nhds_limUnder", "kind": "theorem", "module": "Mathlib.Topology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "limUnder_of_not_tendsto", "kind": "theorem", "module": "Mathlib.Topology.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "simp_rw"], "tactic_count": 2}
{"name": "Absorbs", "kind": "definition", "module": "Mathlib.Topology.Bornology.Absorbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Absorbent", "kind": "definition", "module": "Mathlib.Topology.Bornology.Absorbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Absorbs.empty", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Absorbs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Absorbs.eventually", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Absorbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Absorbs.of_boundedSpace", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Absorbs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Absorbs.mono_left", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Absorbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Absorbs.mono_right", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Absorbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Absorbs.mono", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Absorbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "absorbs_union", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Absorbs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Absorbs.union", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Absorbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.absorbs_sUnion", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Absorbs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Absorbs.sUnion", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Absorbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "absorbs_iUnion", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Absorbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.absorbs_biUnion", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Absorbs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "absorbs_biUnion_finset", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Absorbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Absorbs.add", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Absorbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Absorbs.zero", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Absorbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Absorbs.univ", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Absorbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "absorbs_iff_eventually_cobounded_mapsTo", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Absorbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "absorbs_inter", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Absorbs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Absorbs.inter", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Absorbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.absorbing", "kind": "definition", "module": "Mathlib.Topology.Bornology.Absorbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_absorbing", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Absorbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.absorbs_sInter", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Absorbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "absorbs_iInter", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Absorbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.absorbs_biInter", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Absorbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "absorbs_zero_iff", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Absorbs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "absorbs_neg_neg", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Absorbs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Absorbs.sub", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Absorbs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Absorbent.mono", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Absorbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "absorbent_iff_forall_absorbs_singleton", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Absorbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Absorbent.absorbs", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Absorbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Absorbent.absorbs_finite", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Absorbs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Absorbent.vadd_absorbs", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Absorbs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "absorbent_univ", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Absorbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "absorbent_iff_inv_smul", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Absorbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Absorbent.zero_mem", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Absorbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Absorbs.restrict_scalars", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Absorbs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.ext", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Basic", "is_tactic_proof": true, "tactics": ["cases", "cases", "congr"], "tactic_count": 3}
{"name": "Bornology.ofBounded", "kind": "definition", "module": "Mathlib.Topology.Bornology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.ofBounded'", "kind": "definition", "module": "Mathlib.Topology.Bornology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.IsCobounded", "kind": "definition", "module": "Mathlib.Topology.Bornology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.IsBounded", "kind": "definition", "module": "Mathlib.Topology.Bornology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.isCobounded_def", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.isBounded_def", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.isBounded_compl_iff", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Bornology.isCobounded_compl_iff", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.isBounded_empty", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Bornology.nonempty_of_not_isBounded", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Basic", "is_tactic_proof": true, "tactics": ["rw", "rintro", "exact"], "tactic_count": 3}
{"name": "Bornology.isBounded_singleton", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Bornology.isBounded_iff_forall_mem", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.isCobounded_univ", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.isCobounded_inter", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.IsCobounded.inter", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.isBounded_union", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Bornology.IsBounded.union", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.IsCobounded.superset", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.IsBounded.subset", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.sUnion_bounded_univ", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.IsBounded.insert", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.isBounded_insert", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.comap_cobounded_le_iff", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Basic", "is_tactic_proof": false, "tactics": ["refine", "obtain", "rw", "exact"], "tactic_count": 4}
{"name": "Bornology.ext_iff'", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.ext_iff_isBounded", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.isCobounded_ofBounded_iff", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.isBounded_ofBounded_iff", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Bornology.isCobounded_biInter", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.isCobounded_biInter_finset", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.isCobounded_iInter", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.isCobounded_sInter", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.isBounded_biUnion", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Bornology.isBounded_biUnion_finset", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.isBounded_sUnion", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Bornology.isBounded_iUnion", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Bornology.eventually_ne_cobounded", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.disjoint_cobounded_iff", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.isBounded", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.eventually_ne_cobounded", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instBornologyPUnit", "kind": "instance", "module": "Mathlib.Topology.Bornology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.cofinite", "kind": "abbrev", "module": "Mathlib.Topology.Bornology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedSpace.of_finite", "kind": "instance", "module": "Mathlib.Topology.Bornology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.isBounded_univ", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.cobounded_eq_bot_iff", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Bornology.IsBounded.all", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.IsCobounded.all", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.cobounded_eq_bot", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instBornology", "kind": "instance", "module": "Mathlib.Topology.Bornology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.isCobounded_preimage_ofDual", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.isCobounded_preimage_toDual", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.isBounded_preimage_ofDual", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.isBounded_preimage_toDual", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isBounded_sub", "kind": "theorem", "module": "Mathlib.Topology.Bornology.BoundedOperation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sub_bounded_of_bounded_of_bounded", "kind": "theorem", "module": "Mathlib.Topology.Bornology.BoundedOperation", "is_tactic_proof": false, "tactics": ["obtain", "isBounded_sub", "use", "intro", "exact", "hC"], "tactic_count": 6}
{"name": "boundedSub_of_lipschitzWith_sub", "kind": "theorem", "module": "Mathlib.Topology.Bornology.BoundedOperation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isBounded_mul", "kind": "theorem", "module": "Mathlib.Topology.Bornology.BoundedOperation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isBounded_pow", "kind": "theorem", "module": "Mathlib.Topology.Bornology.BoundedOperation", "is_tactic_proof": true, "tactics": ["induction", "zero", "by_cases", "simp", "simp_rw", "simp", "succ", "hn", "have", "intro", "simp", "obtain", "rw", "apply", "use", "exact"], "tactic_count": 16}
{"name": "mul_bounded_of_bounded_of_bounded", "kind": "theorem", "module": "Mathlib.Topology.Bornology.BoundedOperation", "is_tactic_proof": false, "tactics": ["obtain", "isBounded_mul", "use", "intro", "exact", "hC"], "tactic_count": 6}
{"name": "instBoundedMulOfLipschitzMul", "kind": "instance", "module": "Mathlib.Topology.Bornology.BoundedOperation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeminormedAddCommGroup.lipschitzWith_sub", "kind": "theorem", "module": "Mathlib.Topology.Bornology.BoundedOperation", "is_tactic_proof": true, "tactics": ["convert", "norm_num"], "tactic_count": 2}
{"name": "instBoundedSub", "kind": "instance", "module": "Mathlib.Topology.Bornology.BoundedOperation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_add_const_cobounded", "kind": "theorem", "module": "Mathlib.Topology.Bornology.BoundedOperation", "is_tactic_proof": true, "tactics": ["intro", "rw", "rw", "rw", "convert", "ext", "simp"], "tactic_count": 7}
{"name": "tendsto_const_add_cobounded", "kind": "theorem", "module": "Mathlib.Topology.Bornology.BoundedOperation", "is_tactic_proof": true, "tactics": ["intro", "rw", "rw", "rw", "convert", "ext", "simp"], "tactic_count": 7}
{"name": "tendsto_sub_const_cobounded", "kind": "theorem", "module": "Mathlib.Topology.Bornology.BoundedOperation", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "tendsto_const_sub_cobounded", "kind": "theorem", "module": "Mathlib.Topology.Bornology.BoundedOperation", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "instBoundedMul", "kind": "instance", "module": "Mathlib.Topology.Bornology.BoundedOperation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instBoundedSubNNReal", "kind": "instance", "module": "Mathlib.Topology.Bornology.BoundedOperation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instBoundedMulNNReal", "kind": "instance", "module": "Mathlib.Topology.Bornology.BoundedOperation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instBornology", "kind": "instance", "module": "Mathlib.Topology.Bornology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instBornology", "kind": "instance", "module": "Mathlib.Topology.Bornology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.induced", "kind": "abbrev", "module": "Mathlib.Topology.Bornology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instBornologySubtype", "kind": "instance", "module": "Mathlib.Topology.Bornology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.cobounded_prod", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.isBounded_image_fst_and_snd", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.IsBounded.image_fst", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.IsBounded.image_snd", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.IsBounded.fst_of_prod", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.IsBounded.snd_of_prod", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.IsBounded.prod", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.isBounded_prod_of_nonempty", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.isBounded_prod", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Constructions", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "simp"], "tactic_count": 3}
{"name": "Bornology.isBounded_prod_self", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Constructions", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "Bornology.cobounded_pi", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.forall_isBounded_image_eval_iff", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.IsBounded.image_eval", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.IsBounded.pi", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.isBounded_pi_of_nonempty", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.isBounded_pi", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Constructions", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "simp", "simp", "exact"], "tactic_count": 5}
{"name": "Bornology.isBounded_induced", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.isBounded_image_subtype_val", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instBoundedSpaceProd", "kind": "instance", "module": "Mathlib.Topology.Bornology.Constructions", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "instBoundedSpaceForall", "kind": "instance", "module": "Mathlib.Topology.Bornology.Constructions", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "boundedSpace_induced_iff", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Constructions", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "boundedSpace_subtype_iff", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Constructions", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "boundedSpace_val_set_iff", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instBoundedSpaceSubtype", "kind": "instance", "module": "Mathlib.Topology.Bornology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instBornologyAdditive", "kind": "instance", "module": "Mathlib.Topology.Bornology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instBornologyMultiplicative", "kind": "instance", "module": "Mathlib.Topology.Bornology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instBoundedSpaceAdditive", "kind": "instance", "module": "Mathlib.Topology.Bornology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instBoundedSpaceMultiplicative", "kind": "instance", "module": "Mathlib.Topology.Bornology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instBornologyOrderDual", "kind": "instance", "module": "Mathlib.Topology.Bornology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instBoundedSpaceOrderDual", "kind": "instance", "module": "Mathlib.Topology.Bornology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.IsBounded.image", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyBoundedMapClass.toLocallyBoundedMap", "kind": "definition", "module": "Mathlib.Topology.Bornology.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCoeTCLocallyBoundedMapOfLocallyBoundedMapClass", "kind": "instance", "module": "Mathlib.Topology.Bornology.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyBoundedMap.instFunLike", "kind": "instance", "module": "Mathlib.Topology.Bornology.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyBoundedMap.instLocallyBoundedMapClass", "kind": "instance", "module": "Mathlib.Topology.Bornology.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyBoundedMap.ext", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyBoundedMap.copy", "kind": "definition", "module": "Mathlib.Topology.Bornology.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyBoundedMap.coe_copy", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyBoundedMap.copy_eq", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyBoundedMap.ofMapBounded", "kind": "definition", "module": "Mathlib.Topology.Bornology.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyBoundedMap.coe_ofMapBounded", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyBoundedMap.ofMapBounded_apply", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyBoundedMap.id", "kind": "definition", "module": "Mathlib.Topology.Bornology.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyBoundedMap.instInhabited", "kind": "instance", "module": "Mathlib.Topology.Bornology.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyBoundedMap.coe_id", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyBoundedMap.id_apply", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyBoundedMap.comp", "kind": "definition", "module": "Mathlib.Topology.Bornology.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyBoundedMap.coe_comp", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyBoundedMap.comp_apply", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyBoundedMap.comp_assoc", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyBoundedMap.comp_id", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyBoundedMap.id_comp", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyBoundedMap.cancel_right", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyBoundedMap.cancel_left", "kind": "theorem", "module": "Mathlib.Topology.Bornology.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.instIsOrderBornology", "kind": "instance", "module": "Mathlib.Topology.Bornology.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.instOrderTopology", "kind": "instance", "module": "Mathlib.Topology.Bornology.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.instIsOrderBornology", "kind": "instance", "module": "Mathlib.Topology.Bornology.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.RelativeCWComplex.basicCell", "kind": "abbrev", "module": "Mathlib.Topology.CWComplex.Abstract.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.RelativeCWComplex", "kind": "abbrev", "module": "Mathlib.Topology.CWComplex.Abstract.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.CWComplex", "kind": "abbrev", "module": "Mathlib.Topology.CWComplex.Abstract.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.CWComplex.instRelCWComplex", "kind": "instance", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.RelCWComplex.toCWComplex", "kind": "definition", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.RelCWComplex.toCWComplex_eq", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.RelCWComplex.openCell", "kind": "definition", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.RelCWComplex.closedCell", "kind": "definition", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.RelCWComplex.cellFrontier", "kind": "definition", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.CWComplex.mapsTo", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": true, "tactics": ["have", "simp_rw", "exact"], "tactic_count": 3}
{"name": "Topology.RelCWComplex.pairwiseDisjoint", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.RelCWComplex.disjointBase", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.RelCWComplex.disjoint_openCell_of_ne", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.RelCWComplex.cellFrontier_subset_base_union_finite_closedCell", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": true, "tactics": ["rcases", "use", "rw", "exact"], "tactic_count": 4}
{"name": "Topology.CWComplex.cellFrontier_subset_finite_closedCell", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": true, "tactics": ["rcases", "use", "rw", "exact"], "tactic_count": 4}
{"name": "Topology.RelCWComplex.union", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.CWComplex.union", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "Topology.RelCWComplex.openCell_subset_closedCell", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.RelCWComplex.cellFrontier_subset_closedCell", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.RelCWComplex.cellFrontier_union_openCell_eq_closedCell", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": true, "tactics": ["rw", "congrm", "exact"], "tactic_count": 3}
{"name": "Topology.RelCWComplex.map_zero_mem_openCell", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "Topology.RelCWComplex.map_zero_mem_closedCell", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.CWComplex.Classical.Basic.0.Topology.RelCWComplex.subset_of_eq_union_iUnion", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": true, "tactics": ["intro", "by_contra", "have", "hIJ.symm", "subset_union_of_subset_right", "have", "simp_rw", "exact", "rw", "exact"], "tactic_count": 10}
{"name": "Topology.RelCWComplex.eq_of_eq_union_iUnion", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "Topology.CWComplex.eq_of_eq_union_iUnion", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": true, "tactics": ["apply", "simp_rw"], "tactic_count": 2}
{"name": "Topology.RelCWComplex.isCompact_closedCell", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.RelCWComplex.isClosed_closedCell", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.RelCWComplex.isCompact_cellFrontier", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.RelCWComplex.isClosed_cellFrontier", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.RelCWComplex.closure_openCell_eq_closedCell", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": true, "tactics": ["apply", "rw", "apply", "rw", "exact"], "tactic_count": 5}
{"name": "Topology.RelCWComplex.closed", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "Topology.CWComplex.closed", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": true, "tactics": ["have", "simp_all"], "tactic_count": 2}
{"name": "Topology.RelCWComplex.closedCell_subset_complex", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Topology.RelCWComplex.openCell_subset_complex", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.RelCWComplex.cellFrontier_subset_complex", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.RelCWComplex.closedCell_zero_eq_singleton", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Topology.RelCWComplex.openCell_zero_eq_singleton", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Topology.RelCWComplex.cellFrontier_zero_eq_empty", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Topology.RelCWComplex.base_subset_complex", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Topology.RelCWComplex.isClosed", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": true, "tactics": ["rw", "constructor", "intros", "rw", "exact", "rw", "exact"], "tactic_count": 7}
{"name": "_private.Mathlib.Topology.CWComplex.Classical.Basic.0.Topology.RelCWComplex.iUnion_openCell_eq_iUnion_closedCell", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": true, "tactics": ["apply", "apply", "exact", "apply", "apply", "apply", "apply", "exact", "apply", "refine", "rw", "apply", "induction", "hz", "hi", "obtain", "apply", "apply", "apply", "rw", "apply", "exact", "apply", "exact", "exact"], "tactic_count": 25}
{"name": "Topology.RelCWComplex.union_iUnion_openCell_eq_complex", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": false, "tactics": ["suffices", "simpa", "simp_rw"], "tactic_count": 3}
{"name": "Topology.CWComplex.iUnion_openCell_eq_complex", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Topology.RelCWComplex.eq_of_not_disjoint_openCell", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": true, "tactics": ["contrapose", "exact"], "tactic_count": 2}
{"name": "Topology.RelCWComplex.disjoint_base_iUnion_openCell", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "intro", "rw"], "tactic_count": 3}
{"name": "Topology.RelCWComplex.isClosed_inter_cellFrontier_succ_of_le_isClosed_inter_closedCell", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": true, "tactics": ["obtain", "rw", "refine", "simp_rw", "iUnion_subtype", "apply", "apply", "intro", "rw", "exact"], "tactic_count": 10}
{"name": "Topology.CWComplex.isClosed_inter_cellFrontier_succ_of_le_isClosed_inter_closedCell", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.RelCWComplex.isClosed_of_isClosed_inter_openCell_or_isClosed_inter_closedCell", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "intro", "induction", "hz", "rw", "exact", "hi", "specialize", "rcases", "rw", "exact", "exact"], "tactic_count": 13}
{"name": "Topology.RelCWComplex.isClosed_of_disjoint_openCell_or_isClosed_inter_closedCell", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": true, "tactics": ["apply", "intro", "rcases", "left", "rw", "exact", "exact"], "tactic_count": 7}
{"name": "Topology.CWComplex.isClosed_of_isClosed_inter_openCell_or_isClosed_inter_closedCell", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.CWComplex.isClosed_of_disjoint_openCell_or_isClosed_inter_closedCell", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.RelCWComplex.cellFrontier_subset_finite_openCell", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": true, "tactics": ["induction", "hz", "hi", "classical", "obtain", "choose", "let", "use", "intro", "specialize", "simp", "rcases", "exact", "obtain", "rw", "rcases", "specialize", "simp_rw", "refine", "simp", "exact", "right", "use", "simp", "exact"], "tactic_count": 25}
{"name": "Topology.CWComplex.cellFrontier_subset_finite_openCell", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Topology.RelCWComplex.Subcomplex.instSetLike", "kind": "instance", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.RelCWComplex.Subcomplex.instPartialOrder", "kind": "instance", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.RelCWComplex.Subcomplex.mem_carrier", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.RelCWComplex.Subcomplex.coe_eq_carrier", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.RelCWComplex.Subcomplex.ext", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.RelCWComplex.Subcomplex.eq_iff", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Topology.RelCWComplex.Subcomplex.copy_eq", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.RelCWComplex.Subcomplex.union", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Topology.RelCWComplex.Subcomplex.closed", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.CWComplex.Subcomplex.union", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
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{"name": "Topology.RelCWComplex.Subcomplex.mk''", "kind": "definition", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.CWComplex.Subcomplex.mk''", "kind": "definition", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.RelCWComplex.Subcomplex.subset_complex", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Topology.RelCWComplex.Subcomplex.base_subset", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Topology.RelCWComplex.skeletonLT", "kind": "definition", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.RelCWComplex.skeleton", "kind": "abbrev", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.RelCWComplex.skeletonLT_zero_eq_base", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Topology.CWComplex.skeletonLT_zero_eq_empty", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.RelCWComplex.skeletonLT_top", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Topology.RelCWComplex.skeleton_top", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.RelCWComplex.skeletonLT_mono", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "apply", "intro", "simp_rw", "obtain", "exact"], "tactic_count": 6}
{"name": "Topology.RelCWComplex.skeletonLT_monotone", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.RelCWComplex.skeleton_mono", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.RelCWComplex.skeleton_monotone", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.RelCWComplex.closedCell_subset_skeletonLT", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": true, "tactics": ["intro", "rw", "right", "simp_rw", "refine"], "tactic_count": 5}
{"name": "Topology.RelCWComplex.closedCell_subset_skeleton", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.RelCWComplex.openCell_subset_skeletonLT", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.RelCWComplex.openCell_subset_skeleton", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.RelCWComplex.cellFrontier_subset_skeletonLT", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": true, "tactics": ["obtain", "apply", "rw", "apply", "intro", "simp", "obtain", "exact"], "tactic_count": 8}
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{"name": "Topology.RelCWComplex.iUnion_cellFrontier_subset_skeleton", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.RelCWComplex.skeletonLT_union_iUnion_closedCell_eq_skeletonLT_succ", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": true, "tactics": ["rw", "congr", "norm_cast", "exact"], "tactic_count": 4}
{"name": "Topology.RelCWComplex.skeleton_union_iUnion_closedCell_eq_skeleton_succ", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.RelCWComplex.iUnion_openCell_eq_skeletonLT", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.CWComplex.iUnion_openCell_eq_skeletonLT", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Topology.RelCWComplex.iUnion_openCell_eq_skeleton", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.CWComplex.iUnion_openCell_eq_skeleton", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.RelCWComplex.iUnion_skeletonLT_eq_complex", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": true, "tactics": ["apply", "simp_rw", "exact", "subset_iUnion_of_subset"], "tactic_count": 4}
{"name": "Topology.RelCWComplex.iUnion_skeleton_eq_complex", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": true, "tactics": ["apply", "simp_rw", "exact", "subset_iUnion_of_subset"], "tactic_count": 4}
{"name": "Topology.RelCWComplex.mem_skeletonLT_iff", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Topology.CWComplex.mem_skeletonLT_iff", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Topology.RelCWComplex.mem_skeleton_iff", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": true, "tactics": ["rw", "suffices", "intro", "cases", "simp", "rw"], "tactic_count": 6}
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{"name": "Topology.RelCWComplex.disjoint_skeletonLT_openCell", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "intro", "apply", "intro", "simp_all", "exact"], "tactic_count": 7}
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{"name": "Topology.RelCWComplex.skeletonLT_inter_closedCell_eq_skeletonLT_inter_cellFrontier", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "apply", "rw", "exact"], "tactic_count": 5}
{"name": "Topology.RelCWComplex.skeleton_inter_closedCell_eq_skeleton_inter_cellFrontier", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.RelCWComplex.disjoint_interior_base_closedCell", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Basic", "is_tactic_proof": true, "tactics": ["rw", "by_contra", "rw", "rcases", "suffices", "rwa", "exact"], "tactic_count": 7}
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{"name": "Topology.RelCWComplex.finite_of_finiteDimensional_finiteType", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.RelCWComplex.mkFiniteType", "kind": "definition", "module": "Mathlib.Topology.CWComplex.Classical.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.RelCWComplex.finiteType_mkFiniteType", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Topology.CWComplex.finiteType_mkFiniteType", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Finite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Topology.RelCWComplex.Subcomplex.closedCell_subset_of_mem", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Subcomplex", "is_tactic_proof": true, "tactics": ["rw", "apply", "exact"], "tactic_count": 3}
{"name": "Topology.RelCWComplex.Subcomplex.openCell_subset_of_mem", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Subcomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.RelCWComplex.Subcomplex.cellFrontier_subset_of_mem", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Subcomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.RelCWComplex.Subcomplex.union_closedCell", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Subcomplex", "is_tactic_proof": true, "tactics": ["apply", "apply", "exact", "rw", "apply", "apply", "exact"], "tactic_count": 7}
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{"name": "Topology.CWComplex.Subcomplex.instCWComplex", "kind": "instance", "module": "Mathlib.Topology.CWComplex.Classical.Subcomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.CWComplex.Subcomplex.cell_def", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Subcomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.CWComplex.Subcomplex.map_def", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Subcomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.RelCWComplex.Subcomplex.openCell_eq", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Subcomplex", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "Topology.RelCWComplex.Subcomplex.closedCell_eq", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Subcomplex", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "Topology.RelCWComplex.Subcomplex.cellFrontier_eq", "kind": "theorem", "module": "Mathlib.Topology.CWComplex.Classical.Subcomplex", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "Topology.RelCWComplex.Subcomplex.finiteType_subcomplex_of_finiteType", "kind": "instance", "module": "Mathlib.Topology.CWComplex.Classical.Subcomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.RelCWComplex.Subcomplex.finiteDimensional_subcomplex_of_finiteDimensional", "kind": "instance", "module": "Mathlib.Topology.CWComplex.Classical.Subcomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.RelCWComplex.Subcomplex.finite_subcomplex_of_finite", "kind": "instance", "module": "Mathlib.Topology.CWComplex.Classical.Subcomplex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Born.instLargeCategory", "kind": "instance", "module": "Mathlib.Topology.Category.Born", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Born.instConcreteCategoryLocallyBoundedMapCarrier", "kind": "instance", "module": "Mathlib.Topology.Category.Born", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.instCoeSortType", "kind": "instance", "module": "Mathlib.Topology.Category.CompHausLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.category", "kind": "instance", "module": "Mathlib.Topology.Category.CompHausLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.concreteCategory", "kind": "instance", "module": "Mathlib.Topology.Category.CompHausLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.hasForget₂", "kind": "instance", "module": "Mathlib.Topology.Category.CompHausLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.instHasPropCarrierToTop", "kind": "instance", "module": "Mathlib.Topology.Category.CompHausLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.of", "kind": "abbrev", "module": "Mathlib.Topology.Category.CompHausLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.coe_of", "kind": "theorem", "module": "Mathlib.Topology.Category.CompHausLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.coe_id", "kind": "theorem", "module": "Mathlib.Topology.Category.CompHausLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.coe_comp", "kind": "theorem", "module": "Mathlib.Topology.Category.CompHausLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.ofHom", "kind": "abbrev", "module": "Mathlib.Topology.Category.CompHausLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.hom_ofHom", "kind": "theorem", "module": "Mathlib.Topology.Category.CompHausLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.ofHom_id", "kind": "theorem", "module": "Mathlib.Topology.Category.CompHausLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.ofHom_comp", "kind": "theorem", "module": "Mathlib.Topology.Category.CompHausLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.toCompHausLike", "kind": "definition", "module": "Mathlib.Topology.Category.CompHausLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.fullyFaithfulToCompHausLike", "kind": "definition", "module": "Mathlib.Topology.Category.CompHausLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.instFullToCompHausLike", "kind": "instance", "module": "Mathlib.Topology.Category.CompHausLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.instFaithfulToCompHausLike", "kind": "instance", "module": "Mathlib.Topology.Category.CompHausLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.compHausLikeToTop", "kind": "definition", "module": "Mathlib.Topology.Category.CompHausLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike._example", "kind": "example", "module": "Mathlib.Topology.Category.CompHausLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.fullyFaithfulCompHausLikeToTop", "kind": "definition", "module": "Mathlib.Topology.Category.CompHausLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.instFullTopCatCompHausLikeToTop", "kind": "instance", "module": "Mathlib.Topology.Category.CompHausLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.instFaithfulTopCatCompHausLikeToTop", "kind": "instance", "module": "Mathlib.Topology.Category.CompHausLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.instCompactSpaceCarrierObjTopCatCompHausLikeToTop", "kind": "instance", "module": "Mathlib.Topology.Category.CompHausLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.instT2SpaceCarrierObjTopCatCompHausLikeToTop", "kind": "instance", "module": "Mathlib.Topology.Category.CompHausLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.epi_of_surjective", "kind": "theorem", "module": "Mathlib.Topology.Category.CompHausLike.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CompHausLike.mono_iff_injective", "kind": "theorem", "module": "Mathlib.Topology.Category.CompHausLike.Basic", "is_tactic_proof": true, "tactics": ["constructor", "intro", "let", "let", "have", "exact", "rw", "apply"], "tactic_count": 8}
{"name": "CompHausLike.isClosedMap", "kind": "theorem", "module": "Mathlib.Topology.Category.CompHausLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.isIso_of_bijective", "kind": "theorem", "module": "Mathlib.Topology.Category.CompHausLike.Basic", "is_tactic_proof": true, "tactics": ["let", "have", "rw", "intro", "rw", "exact", "refine", "ext", "apply", "ext", "apply"], "tactic_count": 11}
{"name": "CompHausLike.forget_reflectsIsomorphisms", "kind": "instance", "module": "Mathlib.Topology.Category.CompHausLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.isoOfBijective", "kind": "definition", "module": "Mathlib.Topology.Category.CompHausLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.isoOfHomeo", "kind": "definition", "module": "Mathlib.Topology.Category.CompHausLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.homeoOfIso", "kind": "definition", "module": "Mathlib.Topology.Category.CompHausLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.isoEquivHomeo", "kind": "definition", "module": "Mathlib.Topology.Category.CompHausLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.const", "kind": "definition", "module": "Mathlib.Topology.Category.CompHausLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.const_comp", "kind": "theorem", "module": "Mathlib.Topology.Category.CompHausLike.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.productCone", "kind": "definition", "module": "Mathlib.Topology.Category.CompHausLike.Cartesian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.productIsLimit", "kind": "definition", "module": "Mathlib.Topology.Category.CompHausLike.Cartesian", "is_tactic_proof": false, "tactics": ["refine", "ext", "exacts"], "tactic_count": 3}
{"name": "CompHausLike.cartesianMonoidalCategory", "kind": "definition", "module": "Mathlib.Topology.Category.CompHausLike.Cartesian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.coproductCocone", "kind": "definition", "module": "Mathlib.Topology.Category.CompHausLike.Cartesian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.coproductIsColimit", "kind": "definition", "module": "Mathlib.Topology.Category.CompHausLike.Cartesian", "is_tactic_proof": false, "tactics": ["refine", "ext", "exacts"], "tactic_count": 3}
{"name": "CompHausLike.effectiveEpiStruct", "kind": "definition", "module": "Mathlib.Topology.Category.CompHausLike.EffectiveEpi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.preregular", "kind": "theorem", "module": "Mathlib.Topology.Category.CompHausLike.EffectiveEpi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.precoherent", "kind": "theorem", "module": "Mathlib.Topology.Category.CompHausLike.EffectiveEpi", "is_tactic_proof": true, "tactics": ["have", "infer_instance"], "tactic_count": 2}
{"name": "CompHausLike.HasExplicitFiniteCoproduct", "kind": "abbrev", "module": "Mathlib.Topology.Category.CompHausLike.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.finiteCoproduct", "kind": "definition", "module": "Mathlib.Topology.Category.CompHausLike.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.finiteCoproduct.ι", "kind": "definition", "module": "Mathlib.Topology.Category.CompHausLike.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.finiteCoproduct.desc", "kind": "definition", "module": "Mathlib.Topology.Category.CompHausLike.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.finiteCoproduct.ι_desc", "kind": "theorem", "module": "Mathlib.Topology.Category.CompHausLike.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.finiteCoproduct.hom_ext", "kind": "theorem", "module": "Mathlib.Topology.Category.CompHausLike.Limits", "is_tactic_proof": true, "tactics": ["ext", "specialize", "apply_fun", "exact"], "tactic_count": 4}
{"name": "CompHausLike.finiteCoproduct.cofan", "kind": "abbrev", "module": "Mathlib.Topology.Category.CompHausLike.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.finiteCoproduct.isColimit", "kind": "definition", "module": "Mathlib.Topology.Category.CompHausLike.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.finiteCoproduct.ι_injective", "kind": "theorem", "module": "Mathlib.Topology.Category.CompHausLike.Limits", "is_tactic_proof": true, "tactics": ["intro", "exact"], "tactic_count": 2}
{"name": "CompHausLike.finiteCoproduct.ι_jointly_surjective", "kind": "theorem", "module": "Mathlib.Topology.Category.CompHausLike.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.finiteCoproduct.ι_desc_apply", "kind": "theorem", "module": "Mathlib.Topology.Category.CompHausLike.Limits", "is_tactic_proof": true, "tactics": ["tauto"], "tactic_count": 1}
{"name": "CompHausLike.instHasCoproduct", "kind": "instance", "module": "Mathlib.Topology.Category.CompHausLike.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.instHasColimitsOfShapeDiscreteOfHasExplicitFiniteCoproductsOfFinite", "kind": "instance", "module": "Mathlib.Topology.Category.CompHausLike.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.instHasFiniteCoproductsOfHasExplicitFiniteCoproducts", "kind": "instance", "module": "Mathlib.Topology.Category.CompHausLike.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike._example", "kind": "example", "module": "Mathlib.Topology.Category.CompHausLike.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.finiteCoproduct.isOpenEmbedding_ι", "kind": "theorem", "module": "Mathlib.Topology.Category.CompHausLike.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.Sigma.isOpenEmbedding_ι", "kind": "theorem", "module": "Mathlib.Topology.Category.CompHausLike.Limits", "is_tactic_proof": false, "tactics": ["refine", "convert", "ext", "change", "simp"], "tactic_count": 5}
{"name": "CompHausLike.instPreservesFiniteCoproductsTopCatCompHausLikeToTopOfHasExplicitFiniteCoproducts", "kind": "instance", "module": "Mathlib.Topology.Category.CompHausLike.Limits", "is_tactic_proof": true, "tactics": ["refine", "suffices", "preservesColimit_of_iso_diagram", "exact", "preservesColimit_of_preserves_colimit_cocone"], "tactic_count": 5}
{"name": "CompHausLike.instPreservesFiniteCoproductsToCompHausLike", "kind": "instance", "module": "Mathlib.Topology.Category.CompHausLike.Limits", "is_tactic_proof": false, "tactics": ["have", "inferInstanceAs", "exact"], "tactic_count": 3}
{"name": "CompHausLike.HasExplicitPullback", "kind": "abbrev", "module": "Mathlib.Topology.Category.CompHausLike.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.pullback", "kind": "definition", "module": "Mathlib.Topology.Category.CompHausLike.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.pullback.fst", "kind": "definition", "module": "Mathlib.Topology.Category.CompHausLike.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.pullback.snd", "kind": "definition", "module": "Mathlib.Topology.Category.CompHausLike.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.pullback.condition", "kind": "theorem", "module": "Mathlib.Topology.Category.CompHausLike.Limits", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "CompHausLike.pullback.lift", "kind": "definition", "module": "Mathlib.Topology.Category.CompHausLike.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.pullback.lift_fst", "kind": "theorem", "module": "Mathlib.Topology.Category.CompHausLike.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.pullback.lift_snd", "kind": "theorem", "module": "Mathlib.Topology.Category.CompHausLike.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.pullback.hom_ext", "kind": "theorem", "module": "Mathlib.Topology.Category.CompHausLike.Limits", "is_tactic_proof": true, "tactics": ["ext", "apply_fun", "apply", "apply", "exact", "exact"], "tactic_count": 6}
{"name": "CompHausLike.pullback.cone", "kind": "definition", "module": "Mathlib.Topology.Category.CompHausLike.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.pullback.isLimit", "kind": "definition", "module": "Mathlib.Topology.Category.CompHausLike.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.instHasLimitWalkingCospanCospan", "kind": "instance", "module": "Mathlib.Topology.Category.CompHausLike.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.instCreatesLimitTopCatWalkingCospanCospanCompHausLikeToTop", "kind": "instance", "module": "Mathlib.Topology.Category.CompHausLike.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.instPreservesLimitTopCatWalkingCospanCospanCompHausLikeToTop", "kind": "instance", "module": "Mathlib.Topology.Category.CompHausLike.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.instPreservesLimitWalkingCospanCospanToCompHausLike", "kind": "instance", "module": "Mathlib.Topology.Category.CompHausLike.Limits", "is_tactic_proof": false, "tactics": ["have", "inferInstanceAs", "exact"], "tactic_count": 3}
{"name": "CompHausLike.instHasPullbacksOfHasExplicitPullbacks", "kind": "instance", "module": "Mathlib.Topology.Category.CompHausLike.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.instHasExplicitPullbacksOfInclusionsOfHasExplicitPullbacks", "kind": "instance", "module": "Mathlib.Topology.Category.CompHausLike.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.instHasPullbacksOfInclusionsOfHasExplicitPullbacksOfInclusions", "kind": "instance", "module": "Mathlib.Topology.Category.CompHausLike.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.hasPullbacksOfInclusions", "kind": "theorem", "module": "Mathlib.Topology.Category.CompHausLike.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.instPreservesPullbacksOfInclusionsTopCatCompHausLikeToTopOfHasExplicitPullbacksOfInclusions", "kind": "instance", "module": "Mathlib.Topology.Category.CompHausLike.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.instFinitaryExtensiveOfHasExplicitPullbacksOfInclusions", "kind": "instance", "module": "Mathlib.Topology.Category.CompHausLike.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.finitaryExtensive", "kind": "theorem", "module": "Mathlib.Topology.Category.CompHausLike.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.isTerminalPUnit", "kind": "definition", "module": "Mathlib.Topology.Category.CompHausLike.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.instHasPropSigma", "kind": "instance", "module": "Mathlib.Topology.Category.CompHausLike.SigmaComparison", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.sigmaComparison", "kind": "definition", "module": "Mathlib.Topology.Category.CompHausLike.SigmaComparison", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausLike.sigmaComparison_eq_comp_isos", "kind": "theorem", "module": "Mathlib.Topology.Category.CompHausLike.SigmaComparison", "is_tactic_proof": true, "tactics": ["ext", "simp", "have", "simp", "rw", "simp", "apply", "congr", "rw", "simp", "simp", "erw", "rfl"], "tactic_count": 13}
{"name": "CompHausLike.isIsoSigmaComparison", "kind": "instance", "module": "Mathlib.Topology.Category.CompHausLike.SigmaComparison", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "CompHaus", "kind": "abbrev", "module": "Mathlib.Topology.Category.CompHaus.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHaus.instInhabited", "kind": "instance", "module": "Mathlib.Topology.Category.CompHaus.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHaus.instCoeSortType", "kind": "instance", "module": "Mathlib.Topology.Category.CompHaus.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHaus.instCompactSpaceCarrierToTopTrue", "kind": "instance", "module": "Mathlib.Topology.Category.CompHaus.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHaus.instT2SpaceCarrierToTopTrue", "kind": "instance", "module": "Mathlib.Topology.Category.CompHaus.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHaus.instHasPropTrue", "kind": "instance", "module": "Mathlib.Topology.Category.CompHaus.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHaus.of", "kind": "abbrev", "module": "Mathlib.Topology.Category.CompHaus.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "compHausToTop", "kind": "abbrev", "module": "Mathlib.Topology.Category.CompHaus.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "stoneCechObj", "kind": "definition", "module": "Mathlib.Topology.Category.CompHaus.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "stoneCechEquivalence", "kind": "definition", "module": "Mathlib.Topology.Category.CompHaus.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "topToCompHaus", "kind": "definition", "module": "Mathlib.Topology.Category.CompHaus.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "topToCompHaus_obj", "kind": "theorem", "module": "Mathlib.Topology.Category.CompHaus.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "compHausToTop.reflective", "kind": "instance", "module": "Mathlib.Topology.Category.CompHaus.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "compHausToTop.createsLimits", "kind": "instance", "module": "Mathlib.Topology.Category.CompHaus.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHaus.hasLimits", "kind": "instance", "module": "Mathlib.Topology.Category.CompHaus.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHaus.hasColimits", "kind": "instance", "module": "Mathlib.Topology.Category.CompHaus.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHaus.limitCone", "kind": "definition", "module": "Mathlib.Topology.Category.CompHaus.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHaus.limitConeIsLimit", "kind": "definition", "module": "Mathlib.Topology.Category.CompHaus.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHaus.epi_iff_surjective", "kind": "theorem", "module": "Mathlib.Topology.Category.CompHaus.Basic", "is_tactic_proof": true, "tactics": ["constructor", "dsimp", "contrapose", "rintro", "let", "have", "let", "have", "have", "rw", "rintro", "exact", "obtain", "haveI", "haveI", "let", "let", "ofHom", "let", "have", "rw", "ext", "simp", "apply_fun", "dsimp", "simp", "exact", "rw", "apply"], "tactic_count": 29}
{"name": "compHausLikeToCompHaus", "kind": "abbrev", "module": "Mathlib.Topology.Category.CompHaus.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHaus.effectiveEpi_tfae", "kind": "theorem", "module": "Mathlib.Topology.Category.CompHaus.EffectiveEpi", "is_tactic_proof": true, "tactics": ["tfae_have", "tfae_have", "tfae_have", "tfae_finish"], "tactic_count": 4}
{"name": "CompHaus.instPreregular", "kind": "instance", "module": "Mathlib.Topology.Category.CompHaus.EffectiveEpi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHaus._example", "kind": "example", "module": "Mathlib.Topology.Category.CompHaus.EffectiveEpi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHaus.effectiveEpiFamily_tfae", "kind": "theorem", "module": "Mathlib.Topology.Category.CompHaus.EffectiveEpi", "is_tactic_proof": false, "tactics": ["tfae_have", "tfae_have", "tfae_have", "e", "rw", "intro", "obtain", "refine", "change", "simpa", "tfae_have", "e", "rw", "let", "intro", "obtain", "let", "refine", "have", "rw", "change", "suffices", "rw", "apply", "rintro", "simp", "colimit.comp_coconePointUniqueUpToIso_hom_assoc]", "ext", "tfae_finish"], "tactic_count": 29}
{"name": "CompHaus.effectiveEpiFamily_of_jointly_surjective", "kind": "theorem", "module": "Mathlib.Topology.Category.CompHaus.EffectiveEpi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CompactlyGenerated.isoOfHomeo", "kind": "definition", "module": "Mathlib.Topology.Category.CompactlyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CompactlyGenerated.isoEquivHomeo", "kind": "definition", "module": "Mathlib.Topology.Category.CompactlyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LightProfinite.proj_comp_transitionMapLE'", "kind": "theorem", "module": "Mathlib.Topology.Category.LightProfinite.AsLimit", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "LightProfinite.surjective_transitionMap", "kind": "theorem", "module": "Mathlib.Topology.Category.LightProfinite.AsLimit", "is_tactic_proof": true, "tactics": ["apply", "simpa"], "tactic_count": 2}
{"name": "LightProfinite.surjective_transitionMapLE", "kind": "theorem", "module": "Mathlib.Topology.Category.LightProfinite.AsLimit", "is_tactic_proof": true, "tactics": ["apply", "simpa"], "tactic_count": 2}
{"name": "LightProfinite", "kind": "abbrev", "module": "Mathlib.Topology.Category.LightProfinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightProfinite.instHasPropAndTotallyDisconnectedSpaceCarrierSecondCountableTopology", "kind": "instance", "module": "Mathlib.Topology.Category.LightProfinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightProfinite.of", "kind": "abbrev", "module": "Mathlib.Topology.Category.LightProfinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightProfinite.instInhabited", "kind": "instance", "module": "Mathlib.Topology.Category.LightProfinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightProfinite.instTotallyDisconnectedSpaceCarrierToTopAndSecondCountableTopology", "kind": "instance", "module": "Mathlib.Topology.Category.LightProfinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightProfinite.instSecondCountableTopologyCarrierToTopAndTotallyDisconnectedSpace", "kind": "instance", "module": "Mathlib.Topology.Category.LightProfinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lightToProfinite", "kind": "abbrev", "module": "Mathlib.Topology.Category.LightProfinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lightToProfiniteFullyFaithful", "kind": "abbrev", "module": "Mathlib.Topology.Category.LightProfinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lightProfiniteToCompHaus", "kind": "abbrev", "module": "Mathlib.Topology.Category.LightProfinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightProfinite.toTopCat", "kind": "abbrev", "module": "Mathlib.Topology.Category.LightProfinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FintypeCat.toLightProfinite", "kind": "definition", "module": "Mathlib.Topology.Category.LightProfinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FintypeCat.toLightProfiniteFullyFaithful", "kind": "definition", "module": "Mathlib.Topology.Category.LightProfinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFaithfulFintypeCatLightProfiniteToLightProfinite", "kind": "instance", "module": "Mathlib.Topology.Category.LightProfinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFullFintypeCatLightProfiniteToLightProfinite", "kind": "instance", "module": "Mathlib.Topology.Category.LightProfinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFintypeCarrierToTopAndTotallyDisconnectedSpaceSecondCountableTopologyObjFintypeCatLightProfiniteToLightProfinite", "kind": "instance", "module": "Mathlib.Topology.Category.LightProfinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFintypeCarrierToTopAndTotallyDisconnectedSpaceSecondCountableTopologyOfCarrier", "kind": "instance", "module": "Mathlib.Topology.Category.LightProfinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightProfinite.instTotallyDisconnectedSpaceCarrierToTopTruePtCompHausLimitConeCompLightProfiniteToCompHaus", "kind": "instance", "module": "Mathlib.Topology.Category.LightProfinite.Basic", "is_tactic_proof": true, "tactics": ["change", "exact"], "tactic_count": 2}
{"name": "LightProfinite.limitCone", "kind": "definition", "module": "Mathlib.Topology.Category.LightProfinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightProfinite.limitConeIsLimit", "kind": "definition", "module": "Mathlib.Topology.Category.LightProfinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightProfinite.createsCountableLimits", "kind": "instance", "module": "Mathlib.Topology.Category.LightProfinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightProfinite.instHasCountableLimits", "kind": "instance", "module": "Mathlib.Topology.Category.LightProfinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightProfinite.instPreservesLimitsOfShapeOppositeNatForget", "kind": "instance", "module": "Mathlib.Topology.Category.LightProfinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightProfinite.isClosedMap", "kind": "theorem", "module": "Mathlib.Topology.Category.LightProfinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightProfinite.isIso_of_bijective", "kind": "theorem", "module": "Mathlib.Topology.Category.LightProfinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightProfinite.isoOfBijective", "kind": "definition", "module": "Mathlib.Topology.Category.LightProfinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightProfinite.forget_reflectsIsomorphisms", "kind": "instance", "module": "Mathlib.Topology.Category.LightProfinite.Basic", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "exact"], "tactic_count": 4}
{"name": "LightProfinite.epi_iff_surjective", "kind": "theorem", "module": "Mathlib.Topology.Category.LightProfinite.Basic", "is_tactic_proof": true, "tactics": ["constructor", "dsimp", "contrapose", "rintro", "let", "have", "let", "have", "refine", "rintro", "exact", "have", "obtain", "classical", "let", "let", "let", "have", "rw", "ext", "dsimp", "rw", "refine", "simp", "apply_fun", "dsimp", "rw", "exact", "rw", "apply"], "tactic_count": 30}
{"name": "LightProfinite.instPreservesEpimorphismsProfiniteLightToProfinite", "kind": "instance", "module": "Mathlib.Topology.Category.LightProfinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightDiagram.toProfinite", "kind": "definition", "module": "Mathlib.Topology.Category.LightProfinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightDiagram.instCategory", "kind": "instance", "module": "Mathlib.Topology.Category.LightProfinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightDiagram.hasForget", "kind": "instance", "module": "Mathlib.Topology.Category.LightProfinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lightDiagramToProfinite", "kind": "definition", "module": "Mathlib.Topology.Category.LightProfinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFaithfulLightDiagramProfiniteLightDiagramToProfinite", "kind": "instance", "module": "Mathlib.Topology.Category.LightProfinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFullLightDiagramProfiniteLightDiagramToProfinite", "kind": "instance", "module": "Mathlib.Topology.Category.LightProfinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightProfinite.instCountableClopensCarrierToTopAndTotallyDisconnectedSpaceSecondCountableTopology", "kind": "instance", "module": "Mathlib.Topology.Category.LightProfinite.Basic", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "LightProfinite.instCountableDiscreteQuotient", "kind": "instance", "module": "Mathlib.Topology.Category.LightProfinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightProfinite.toLightDiagram", "kind": "definition", "module": "Mathlib.Topology.Category.LightProfinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lightProfiniteToLightDiagram", "kind": "definition", "module": "Mathlib.Topology.Category.LightProfinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instSecondCountableTopologyCarrierToTopTotallyDisconnectedSpacePtOppositeNatProfiniteCone", "kind": "instance", "module": "Mathlib.Topology.Category.LightProfinite.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "refine", "apply", "intro", "refine", "refine", "refine", "simp", "exact", "exact", "intro", "obtain", "exact"], "tactic_count": 14}
{"name": "lightDiagramToLightProfinite", "kind": "definition", "module": "Mathlib.Topology.Category.LightProfinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightProfinite.equivDiagram", "kind": "definition", "module": "Mathlib.Topology.Category.LightProfinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsEquivalenceLightProfiniteLightDiagramLightProfiniteToLightDiagram", "kind": "instance", "module": "Mathlib.Topology.Category.LightProfinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsEquivalenceLightDiagramLightProfiniteLightDiagramToLightProfinite", "kind": "instance", "module": "Mathlib.Topology.Category.LightProfinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightDiagram'.toProfinite", "kind": "definition", "module": "Mathlib.Topology.Category.LightProfinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCategoryLightDiagram'", "kind": "instance", "module": "Mathlib.Topology.Category.LightProfinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightDiagram'.toLightFunctor", "kind": "definition", "module": "Mathlib.Topology.Category.LightProfinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFaithfulLightDiagram'LightDiagramToLightFunctor", "kind": "instance", "module": "Mathlib.Topology.Category.LightProfinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFullLightDiagram'LightDiagramToLightFunctor", "kind": "instance", "module": "Mathlib.Topology.Category.LightProfinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instEssSurjLightDiagram'LightDiagramToLightFunctor", "kind": "instance", "module": "Mathlib.Topology.Category.LightProfinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsEquivalenceLightDiagram'LightDiagramToLightFunctor", "kind": "instance", "module": "Mathlib.Topology.Category.LightProfinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightDiagram.equivSmall", "kind": "definition", "module": "Mathlib.Topology.Category.LightProfinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instEssentiallySmallLightDiagram", "kind": "instance", "module": "Mathlib.Topology.Category.LightProfinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instEssentiallySmallLightProfinite", "kind": "instance", "module": "Mathlib.Topology.Category.LightProfinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightProfinite.instCartesianMonoidalCategory", "kind": "instance", "module": "Mathlib.Topology.Category.LightProfinite.Cartesian", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightProfinite.effectiveEpi_iff_surjective", "kind": "theorem", "module": "Mathlib.Topology.Category.LightProfinite.EffectiveEpi", "is_tactic_proof": true, "tactics": ["refine", "rw", "infer_instance"], "tactic_count": 3}
{"name": "LightProfinite.instPreregular", "kind": "instance", "module": "Mathlib.Topology.Category.LightProfinite.EffectiveEpi", "is_tactic_proof": true, "tactics": ["apply", "intro", "exact"], "tactic_count": 3}
{"name": "LightProfinite._example", "kind": "example", "module": "Mathlib.Topology.Category.LightProfinite.EffectiveEpi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightProfinite.Extend.functor", "kind": "definition", "module": "Mathlib.Topology.Category.LightProfinite.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightProfinite.Extend._example", "kind": "example", "module": "Mathlib.Topology.Category.LightProfinite.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightProfinite.Extend.functorOp", "kind": "definition", "module": "Mathlib.Topology.Category.LightProfinite.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightProfinite.Extend._example", "kind": "example", "module": "Mathlib.Topology.Category.LightProfinite.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightProfinite.Extend._example", "kind": "example", "module": "Mathlib.Topology.Category.LightProfinite.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightProfinite.Extend.functor_initial", "kind": "theorem", "module": "Mathlib.Topology.Category.LightProfinite.Extend", "is_tactic_proof": true, "tactics": ["rw", "have", "inferInstanceAs", "exact"], "tactic_count": 4}
{"name": "LightProfinite.Extend.functorOp_final", "kind": "theorem", "module": "Mathlib.Topology.Category.LightProfinite.Extend", "is_tactic_proof": true, "tactics": ["have", "have", "have", "exact"], "tactic_count": 4}
{"name": "LightProfinite.Extend.cone", "kind": "definition", "module": "Mathlib.Topology.Category.LightProfinite.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightProfinite.Extend._example", "kind": "example", "module": "Mathlib.Topology.Category.LightProfinite.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightProfinite.Extend.isLimitCone", "kind": "definition", "module": "Mathlib.Topology.Category.LightProfinite.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightProfinite.Extend.cocone", "kind": "definition", "module": "Mathlib.Topology.Category.LightProfinite.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightProfinite.Extend._example", "kind": "example", "module": "Mathlib.Topology.Category.LightProfinite.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightProfinite.Extend.isColimitCocone", "kind": "definition", "module": "Mathlib.Topology.Category.LightProfinite.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightProfinite.fintypeDiagram'", "kind": "abbrev", "module": "Mathlib.Topology.Category.LightProfinite.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightProfinite.diagram'", "kind": "abbrev", "module": "Mathlib.Topology.Category.LightProfinite.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightProfinite.asLimitCone'", "kind": "definition", "module": "Mathlib.Topology.Category.LightProfinite.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightProfinite.instEpiAppOppositeNatπAsLimitCone", "kind": "instance", "module": "Mathlib.Topology.Category.LightProfinite.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightProfinite.asLimit'", "kind": "definition", "module": "Mathlib.Topology.Category.LightProfinite.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightProfinite.lim'", "kind": "definition", "module": "Mathlib.Topology.Category.LightProfinite.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.exists_lift_of_finite_of_injective_of_surjective", "kind": "theorem", "module": "Mathlib.Topology.Category.LightProfinite.Injective", "is_tactic_proof": true, "tactics": ["have", "let", "have", "have", "rw", "simp", "rintro", "rw", "let", "g", "have", "have", "intro", "rw", "obtain", "have", "simp_all", "obtain", "exists_clopen_partition_of_clopen_cover", "have", "intro", "simp", "obtain", "grind", "have", "univ_subset_iff.mp", "have", "rw", "exact", "refine", "rw", "intro", "convert", "ext", "simp", "ext", "have", "obtain", "simpa", "ext", "simp"], "tactic_count": 41}
{"name": "Profinite.exists_lift_of_finite_of_mono_of_epi", "kind": "theorem", "module": "Mathlib.Topology.Category.LightProfinite.Injective", "is_tactic_proof": false, "tactics": ["obtain", "exists_lift_of_finite_of_injective_of_surjective", "exact"], "tactic_count": 3}
{"name": "Profinite.injective_of_finite", "kind": "instance", "module": "Mathlib.Topology.Category.LightProfinite.Injective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.injective_of_light", "kind": "instance", "module": "Mathlib.Topology.Category.LightProfinite.Injective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightProfinite.injective", "kind": "instance", "module": "Mathlib.Topology.Category.LightProfinite.Injective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightProfinite.instHasExplicitPullbacksAndTotallyDisconnectedSpaceCarrierSecondCountableTopology", "kind": "instance", "module": "Mathlib.Topology.Category.LightProfinite.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightProfinite.instHasExplicitFiniteCoproductsAndTotallyDisconnectedSpaceCarrierSecondCountableTopology", "kind": "instance", "module": "Mathlib.Topology.Category.LightProfinite.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightProfinite.isTerminalPUnit", "kind": "abbrev", "module": "Mathlib.Topology.Category.LightProfinite.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightProfinite._example", "kind": "example", "module": "Mathlib.Topology.Category.LightProfinite.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightProfinite._example", "kind": "example", "module": "Mathlib.Topology.Category.LightProfinite.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightProfinite.natUnionInftyEmbedding", "kind": "definition", "module": "Mathlib.Topology.Category.LightProfinite.Sequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightProfinite.isClosedEmbedding_natUnionInftyEmbedding", "kind": "theorem", "module": "Mathlib.Topology.Category.LightProfinite.Sequence", "is_tactic_proof": true, "tactics": ["refine", "rintro", "rfl", "simp", "assumption_mod_cast", "simp", "assumption_mod_cast", "simp", "rw", "exact"], "tactic_count": 10}
{"name": "LightProfinite.instMetrizableSpaceOnePointNat", "kind": "instance", "module": "Mathlib.Topology.Category.LightProfinite.Sequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightProfinite.NatUnionInfty", "kind": "abbrev", "module": "Mathlib.Topology.Category.LightProfinite.Sequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightProfinite.termℕ∪{∞}", "kind": "definition", "module": "Mathlib.Topology.Category.LightProfinite.Sequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightProfinite._aux_Mathlib_Topology_Category_LightProfinite_Sequence___macroRules_LightProfinite_termℕ∪{∞}_1", "kind": "definition", "module": "Mathlib.Topology.Category.LightProfinite.Sequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightProfinite._aux_Mathlib_Topology_Category_LightProfinite_Sequence___unexpand_LightProfinite_NatUnionInfty_1", "kind": "definition", "module": "Mathlib.Topology.Category.LightProfinite.Sequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightProfinite.instCoeNatCarrierToTopAndTotallyDisconnectedSpaceSecondCountableTopologyNatUnionInfty", "kind": "instance", "module": "Mathlib.Topology.Category.LightProfinite.Sequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LightProfinite.continuous_iff_convergent", "kind": "theorem", "module": "Mathlib.Topology.Category.LightProfinite.Sequence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Locale", "kind": "definition", "module": "Mathlib.Topology.Category.Locale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Locale.instCoeSortType", "kind": "instance", "module": "Mathlib.Topology.Category.Locale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Locale.instFrameCarrierUnopFrm", "kind": "instance", "module": "Mathlib.Topology.Category.Locale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Locale.of", "kind": "definition", "module": "Mathlib.Topology.Category.Locale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Locale.coe_of", "kind": "theorem", "module": "Mathlib.Topology.Category.Locale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Locale.instInhabited", "kind": "instance", "module": "Mathlib.Topology.Category.Locale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "topToLocale", "kind": "definition", "module": "Mathlib.Topology.Category.Locale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHausToLocale.faithful", "kind": "instance", "module": "Mathlib.Topology.Category.Locale", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.fintypeDiagram", "kind": "definition", "module": "Mathlib.Topology.Category.Profinite.AsLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.diagram", "kind": "abbrev", "module": "Mathlib.Topology.Category.Profinite.AsLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.asLimitCone", "kind": "definition", "module": "Mathlib.Topology.Category.Profinite.AsLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.isIso_asLimitCone_lift", "kind": "instance", "module": "Mathlib.Topology.Category.Profinite.AsLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.isoAsLimitConeLift", "kind": "definition", "module": "Mathlib.Topology.Category.Profinite.AsLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.asLimitConeIso", "kind": "definition", "module": "Mathlib.Topology.Category.Profinite.AsLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.asLimit", "kind": "definition", "module": "Mathlib.Topology.Category.Profinite.AsLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.lim", "kind": "definition", "module": "Mathlib.Topology.Category.Profinite.AsLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Profinite.instInhabited", "kind": "instance", "module": "Mathlib.Topology.Category.Profinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.instTotallyDisconnectedSpaceCarrierToTop", "kind": "instance", "module": "Mathlib.Topology.Category.Profinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "instTotallyDisconnectedSpaceCarrierToTopTrueObjProfiniteCompHausProfiniteToCompHaus", "kind": "instance", "module": "Mathlib.Topology.Category.Profinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CompHaus.toProfiniteObj", "kind": "definition", "module": "Mathlib.Topology.Category.Profinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.toCompHausEquivalence", "kind": "definition", "module": "Mathlib.Topology.Category.Profinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHaus.toProfinite", "kind": "definition", "module": "Mathlib.Topology.Category.Profinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHaus.toProfinite_obj'", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FintypeCat.botTopology", "kind": "definition", "module": "Mathlib.Topology.Category.Profinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FintypeCat.discreteTopology", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FintypeCat.toProfinite", "kind": "definition", "module": "Mathlib.Topology.Category.Profinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FintypeCat.toProfiniteFullyFaithful", "kind": "definition", "module": "Mathlib.Topology.Category.Profinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFaithfulFintypeCatProfiniteToProfinite", "kind": "instance", "module": "Mathlib.Topology.Category.Profinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFullFintypeCatProfiniteToProfinite", "kind": "instance", "module": "Mathlib.Topology.Category.Profinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFintypeCarrierToTopTotallyDisconnectedSpaceObjFintypeCatProfiniteToProfinite", "kind": "instance", "module": "Mathlib.Topology.Category.Profinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFintypeCarrierToTopTotallyDisconnectedSpaceOfCarrier", "kind": "instance", "module": "Mathlib.Topology.Category.Profinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Profinite.limitConeIsLimit", "kind": "definition", "module": "Mathlib.Topology.Category.Profinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.toProfiniteAdjToCompHaus", "kind": "definition", "module": "Mathlib.Topology.Category.Profinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.toCompHaus.reflective", "kind": "instance", "module": "Mathlib.Topology.Category.Profinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.toCompHaus.createsLimits", "kind": "instance", "module": "Mathlib.Topology.Category.Profinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.toTopCat.reflective", "kind": "instance", "module": "Mathlib.Topology.Category.Profinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.toTopCat.createsLimits", "kind": "instance", "module": "Mathlib.Topology.Category.Profinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.hasLimits", "kind": "instance", "module": "Mathlib.Topology.Category.Profinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.hasColimits", "kind": "instance", "module": "Mathlib.Topology.Category.Profinite.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Profinite.exists_isClopen_of_cofiltered", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.CofilteredLimit", "is_tactic_proof": true, "tactics": ["have", "rotate_left", "intro", "change", "apply", "rintro", "refine", "continuity", "obtain", "clear", "let", "let", "have", "have", "intro", "exact", "have", "dsimp", "rw", "rintro", "refine", "dsimp", "rwa", "have", "obtain", "classical", "obtain", "let", "let", "refine", "apply", "intro", "dsimp", "rw", "exact", "ext", "constructor", "intro", "simp_rw", "obtain", "refine", "rwa", "intro", "simp_rw", "obtain", "rw", "refine", "rw", "rwa"], "tactic_count": 49}
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{"name": "Profinite.instEffectivelyEnoughCompHausProfiniteToCompHaus", "kind": "instance", "module": "Mathlib.Topology.Category.Profinite.EffectiveEpi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.instPreregular", "kind": "instance", "module": "Mathlib.Topology.Category.Profinite.EffectiveEpi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Profinite.effectiveEpiFamily_tfae", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.EffectiveEpi", "is_tactic_proof": false, "tactics": ["tfae_have", "tfae_have", "tfae_have", "erw", "exact", "tfae_finish"], "tactic_count": 6}
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{"name": "Profinite.asLimitCone'", "kind": "abbrev", "module": "Mathlib.Topology.Category.Profinite.Extend", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Profinite.instHasExplicitPullbacksTotallyDisconnectedSpaceCarrier", "kind": "instance", "module": "Mathlib.Topology.Category.Profinite.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.instHasExplicitFiniteCoproductsTotallyDisconnectedSpaceCarrier", "kind": "instance", "module": "Mathlib.Topology.Category.Profinite.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.isTerminalPUnit", "kind": "abbrev", "module": "Mathlib.Topology.Category.Profinite.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Profinite.NobelingProof.projRestricts_eq_id", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
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{"name": "Profinite.NobelingProof.spanFunctorIsoIndexFunctor", "kind": "definition", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.NobelingProof.spanCone_isLimit", "kind": "definition", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Profinite.NobelingProof.Products.lt_iff_lex_lt", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "Profinite.NobelingProof.Products.rel_head!_of_mem", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.NobelingProof.Products.head!_le_of_lt", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.NobelingProof.GoodProducts", "kind": "definition", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.NobelingProof.GoodProducts.eval", "kind": "definition", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.NobelingProof.GoodProducts.injective", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Basic", "is_tactic_proof": true, "tactics": ["intro", "dsimp", "by_contra", "cases", "inl", "inr"], "tactic_count": 6}
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{"name": "Profinite.NobelingProof.GoodProducts.equiv_range", "kind": "definition", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.NobelingProof.GoodProducts.equiv_toFun_eq_eval", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.NobelingProof.GoodProducts.linearIndependent_iff_range", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
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{"name": "Profinite.NobelingProof.Products.evalFacProp", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Basic", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "rw", "simp"], "tactic_count": 4}
{"name": "Profinite.NobelingProof.Products.evalFacProps", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Basic", "is_tactic_proof": false, "tactics": ["have", "simp", "rw"], "tactic_count": 3}
{"name": "Profinite.NobelingProof.Products.prop_of_isGood", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Basic", "is_tactic_proof": true, "tactics": ["intro", "by_contra", "apply", "suffices", "rw", "exact", "ext", "rw", "simpa"], "tactic_count": 9}
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{"name": "Profinite.NobelingProof.ord", "kind": "definition", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.NobelingProof.term", "kind": "definition", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.NobelingProof.term_ord_aux", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "Profinite.NobelingProof.P", "kind": "definition", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.NobelingProof.Products.prop_of_isGood_of_contained", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Basic", "is_tactic_proof": true, "tactics": ["by_contra", "apply", "suffices", "ext", "simp", "contrapose", "exact"], "tactic_count": 7}
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{"name": "Profinite.NobelingProof.isClosed_proj", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.NobelingProof.contained_proj", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Basic", "is_tactic_proof": true, "tactics": ["intro", "aesop"], "tactic_count": 2}
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{"name": "Profinite.NobelingProof.coe_πs", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Basic", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "Profinite.NobelingProof.injective_πs", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.NobelingProof.πs'", "kind": "definition", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.NobelingProof.coe_πs'", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Basic", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "Profinite.NobelingProof.injective_πs'", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.NobelingProof.Products.lt_ord_of_lt", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.NobelingProof.Products.eval_πs", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Profinite.NobelingProof.Products.eval_πs'", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Profinite.NobelingProof.Products.eval_πs_image", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp", "apply", "apply", "rw"], "tactic_count": 5}
{"name": "Profinite.NobelingProof.Products.eval_πs_image'", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp", "apply", "apply", "rw"], "tactic_count": 5}
{"name": "Profinite.NobelingProof.Products.head_lt_ord_of_isGood", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.NobelingProof.Products.isGood_mono", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Basic", "is_tactic_proof": true, "tactics": ["intro", "apply", "rwa"], "tactic_count": 3}
{"name": "Profinite.NobelingProof.GoodProducts.P0", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Induction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.NobelingProof.GoodProducts.Plimit", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Induction", "is_tactic_proof": true, "tactics": ["intro", "rw", "exact", "linearIndepOn_iUnion_of_directed"], "tactic_count": 4}
{"name": "Profinite.NobelingProof.GoodProducts.linearIndependentAux", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Induction", "is_tactic_proof": false, "tactics": ["refine", "have", "rw", "refine", "exact", "exact", "linearIndependent_comp_of_eval"], "tactic_count": 7}
{"name": "Profinite.NobelingProof.GoodProducts.linearIndependent", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Induction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.NobelingProof.GoodProducts.Basis", "kind": "definition", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Induction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.NobelingProof.Nobeling_aux", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Induction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.Nobeling.ι", "kind": "definition", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Induction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.Nobeling.isClosedEmbedding", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Induction", "is_tactic_proof": true, "tactics": ["apply", "dsimp", "refine", "intro", "rw", "refine", "rintro", "refine", "convert", "ext", "simp", "refine", "convert", "ext", "simp", "intro", "by_contra", "obtain", "apply", "dsimp", "rw", "exact"], "tactic_count": 22}
{"name": "LocallyConstant.freeOfProfinite", "kind": "instance", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Induction", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Profinite.NobelingProof.πJ", "kind": "definition", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Span", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.NobelingProof.eval_eq_πJ", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Span", "is_tactic_proof": true, "tactics": ["ext", "simp", "exact"], "tactic_count": 3}
{"name": "Profinite.NobelingProof.instFintypeElemForallBoolπMemFinset", "kind": "instance", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Span", "is_tactic_proof": true, "tactics": ["let", "refine", "intro", "ext", "by_cases", "exact", "simp"], "tactic_count": 7}
{"name": "Profinite.NobelingProof.spanFinBasis", "kind": "definition", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Span", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.NobelingProof.spanFinBasis.span", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Span", "is_tactic_proof": true, "tactics": ["intro", "rw", "use", "ext", "change", "simp", "spanFinBasis,", "ne_eq,", "split_ifs"], "tactic_count": 9}
{"name": "Profinite.NobelingProof.factors", "kind": "definition", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Span", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.NobelingProof.list_prod_apply", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Span", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Profinite.NobelingProof.factors_prod_eq_basis_of_eq", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Span", "is_tactic_proof": true, "tactics": ["rw", "apply", "simp", "rintro", "dsimp", "split_ifs", "rw", "rw", "simp"], "tactic_count": 9}
{"name": "Profinite.NobelingProof.e_mem_of_eq_true", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Span", "is_tactic_proof": true, "tactics": ["rcases", "simp", "refine", "aesop"], "tactic_count": 4}
{"name": "Profinite.NobelingProof.one_sub_e_mem_of_false", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Span", "is_tactic_proof": true, "tactics": ["simp", "use", "simp", "rcases", "aesop"], "tactic_count": 5}
{"name": "Profinite.NobelingProof.factors_prod_eq_basis_of_ne", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Span", "is_tactic_proof": true, "tactics": ["rw", "apply", "simp", "obtain", "cases", "rw", "refine", "rw", "refine", "rw", "rw"], "tactic_count": 11}
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{"name": "Profinite.NobelingProof.GoodProducts.finsuppSum_mem_span_eval", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Span", "is_tactic_proof": true, "tactics": ["apply", "intro", "have", "dsimp", "rw", "apply", "apply", "have", "apply", "simpa", "refine", "simp"], "tactic_count": 12}
{"name": "Profinite.NobelingProof.GoodProducts.spanFin", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Span", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "rintro", "rw", "let", "dsimp", "suffices", "l.SortedGT", "from", "rw", "induction", "nil", "intro", "apply", "exact", "cons", "rw", "intro", "specialize", "rw", "simp", "obtain", "rw", "have", "dsimp", "split_ifs", "rw", "exact", "noncomm_ring", "rw", "apply", "apply", "intro", "apply", "apply", "refine", "simp", "have", "refine", "cases", "nil", "cons", "apply", "rw", "exact", "apply", "exact"], "tactic_count": 48}
{"name": "Profinite.NobelingProof.fin_comap_jointlySurjective", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Span", "is_tactic_proof": false, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Profinite.NobelingProof.GoodProducts.span", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Span", "is_tactic_proof": true, "tactics": ["rw", "intro", "obtain", "refine", "rintro", "exact"], "tactic_count": 6}
{"name": "Profinite.NobelingProof.C0", "kind": "definition", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Successor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.NobelingProof.C1", "kind": "definition", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Successor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.NobelingProof.isClosed_C0", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Successor", "is_tactic_proof": true, "tactics": ["refine", "have", "exact"], "tactic_count": 3}
{"name": "Profinite.NobelingProof.isClosed_C1", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Successor", "is_tactic_proof": true, "tactics": ["refine", "have", "exact"], "tactic_count": 3}
{"name": "Profinite.NobelingProof.contained_C1", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Successor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.NobelingProof.union_C0C1_eq", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Successor", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Profinite.NobelingProof.C'", "kind": "definition", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Successor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.NobelingProof.isClosed_C'", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Successor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.NobelingProof.contained_C'", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Successor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.NobelingProof.SwapTrue", "kind": "definition", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Successor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.NobelingProof.continuous_swapTrue", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Successor", "is_tactic_proof": true, "tactics": ["dsimp", "apply", "intro", "apply", "apply", "apply"], "tactic_count": 6}
{"name": "Profinite.NobelingProof.swapTrue_mem_C1", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Successor", "is_tactic_proof": true, "tactics": ["obtain", "convert", "dsimp", "ext", "split_ifs", "rw", "simpa", "simp", "specialize", "intro", "contrapose", "exact"], "tactic_count": 12}
{"name": "Profinite.NobelingProof.CC'₀", "kind": "definition", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Successor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.NobelingProof.CC'₁", "kind": "definition", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Successor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.NobelingProof.continuous_CC'₀", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Successor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.NobelingProof.continuous_CC'₁", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Successor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.NobelingProof.Linear_CC'₀", "kind": "definition", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Successor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.NobelingProof.Linear_CC'₁", "kind": "definition", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Successor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.NobelingProof.Linear_CC'", "kind": "definition", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Successor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.NobelingProof.CC_comp_zero", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Successor", "is_tactic_proof": true, "tactics": ["intro", "ext", "dsimp", "simp", "congr", "ext", "dsimp", "apply", "simp", "intro", "exact"], "tactic_count": 11}
{"name": "Profinite.NobelingProof.C0_projOrd", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Successor", "is_tactic_proof": true, "tactics": ["ext", "simp", "intro", "rcases", "specialize", "rw", "simp", "exact", "simp", "rw", "rw"], "tactic_count": 11}
{"name": "Profinite.NobelingProof.C1_projOrd", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Successor", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "split_ifs", "rw", "rw", "rfl", "simp", "have", "specialize", "rw", "simp", "exact"], "tactic_count": 12}
{"name": "Profinite.NobelingProof.CC_exact", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Successor", "is_tactic_proof": true, "tactics": ["dsimp", "simp", "let", "have", "let", "have", "refine", "rintro", "simp", "rw", "refine", "rwa", "intro", "simpa", "ext", "rw", "rcases", "have", "simpa", "simp", "have", "simpa", "simp", "congr", "simp", "exact"], "tactic_count": 26}
{"name": "Profinite.NobelingProof.succ_mono", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Successor", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Profinite.NobelingProof.succ_exact", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Successor", "is_tactic_proof": true, "tactics": ["rw", "intro", "exact"], "tactic_count": 3}
{"name": "Profinite.NobelingProof.GoodProducts.MaxProducts", "kind": "definition", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Successor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.NobelingProof.GoodProducts.union_succ", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Successor", "is_tactic_proof": true, "tactics": ["ext", "simp", "refine", "by_cases", "exact", "left", "intro", "apply", "have", "simp", "simp", "have", "intro", "refine", "rw", "rintro", "contradiction", "rwa", "refine", "have", "rwa"], "tactic_count": 21}
{"name": "Profinite.NobelingProof.GoodProducts.sum_to", "kind": "definition", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Successor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.NobelingProof.GoodProducts.injective_sum_to", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Successor", "is_tactic_proof": false, "tactics": ["refine", "rw", "have", "simp"], "tactic_count": 4}
{"name": "Profinite.NobelingProof.GoodProducts.sum_to_range", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Successor", "is_tactic_proof": true, "tactics": ["have", "simp_all"], "tactic_count": 2}
{"name": "Profinite.NobelingProof.GoodProducts.sum_equiv", "kind": "definition", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Successor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.NobelingProof.GoodProducts.sum_equiv_comp_eval_eq_elim", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Successor", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Profinite.NobelingProof.GoodProducts.SumEval", "kind": "definition", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Successor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.NobelingProof.GoodProducts.linearIndependent_iff_sum", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Successor", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Profinite.NobelingProof.GoodProducts.span_sum", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Successor", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Profinite.NobelingProof.GoodProducts.square_commutes", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Successor", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "rw", "simp"], "tactic_count": 4}
{"name": "Profinite.NobelingProof.swapTrue_eq_true", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Successor", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Profinite.NobelingProof.mem_C'_eq_false", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Successor", "is_tactic_proof": true, "tactics": ["rintro", "simp"], "tactic_count": 2}
{"name": "Profinite.NobelingProof.Products.Tail", "kind": "definition", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Successor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.NobelingProof.Products.max_eq_o_cons_tail", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Successor", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Profinite.NobelingProof.Products.max_eq_o_cons_tail'", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Successor", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Profinite.NobelingProof.GoodProducts.head!_eq_o_of_maxProducts", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Successor", "is_tactic_proof": true, "tactics": ["rw", "have", "have", "simp", "refine", "have", "simp", "exact", "rwa"], "tactic_count": 9}
{"name": "Profinite.NobelingProof.GoodProducts.max_eq_o_cons_tail", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Successor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.NobelingProof.Products.evalCons", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Successor", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Profinite.NobelingProof.Products.max_eq_eval", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Successor", "is_tactic_proof": false, "tactics": ["have", "rw", "ext", "simp", "rw", "simp", "have", "intro", "simp", "rintro", "exact", "have", "apply", "simp", "split_ifs", "rw", "rfl", "simp", "push_neg", "push_neg"], "tactic_count": 20}
{"name": "Profinite.NobelingProof.GoodProducts.max_eq_eval", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Successor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.NobelingProof.GoodProducts.max_eq_eval_unapply", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Successor", "is_tactic_proof": true, "tactics": ["ext1", "exact"], "tactic_count": 2}
{"name": "Profinite.NobelingProof.GoodProducts.isChain_cons_of_lt", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Successor", "is_tactic_proof": true, "tactics": ["have", "rw", "simp", "refine", "refine", "by_cases", "rw", "simp", "have", "rw", "exact"], "tactic_count": 11}
{"name": "Profinite.NobelingProof.GoodProducts.good_lt_maxProducts", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Successor", "is_tactic_proof": true, "tactics": ["have", "by_cases", "rw", "exact", "rw", "apply", "rw", "simp", "exact"], "tactic_count": 9}
{"name": "Profinite.NobelingProof.GoodProducts.maxTail_isGood", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Successor", "is_tactic_proof": false, "tactics": ["have", "intro", "rw", "obtain", "rw", "have", "rw", "simp", "apply", "intro", "rw", "rw", "have", "have", "simp", "obtain", "rw", "dsimp", "rw", "have", "rw", "dsimp", "rw", "obtain", "rw", "have", "rw", "obtain", "rw", "apply", "rw", "apply", "apply", "intro", "rw", "apply", "apply", "dsimp", "rw", "refine", "simp", "exact", "apply", "intro", "apply", "apply", "rw", "rw", "refine", "simp", "rw", "exact"], "tactic_count": 52}
{"name": "Profinite.NobelingProof.GoodProducts.MaxToGood", "kind": "definition", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Successor", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.NobelingProof.GoodProducts.maxToGood_injective", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Successor", "is_tactic_proof": true, "tactics": ["intro", "apply", "rw", "dsimp", "rw"], "tactic_count": 5}
{"name": "Profinite.NobelingProof.GoodProducts.linearIndependent_comp_of_eval", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.Successor", "is_tactic_proof": true, "tactics": ["dsimp", "rw", "intro", "let", "have", "have", "rw", "exact"], "tactic_count": 8}
{"name": "Profinite.NobelingProof.instSubsingletonLocallyConstantElemForallBoolEmptyCollectionSetInt", "kind": "instance", "module": "Mathlib.Topology.Category.Profinite.Nobeling.ZeroLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.NobelingProof.instIsEmptySubtypeProductsIsGoodEmptyCollectionSetForallBool", "kind": "instance", "module": "Mathlib.Topology.Category.Profinite.Nobeling.ZeroLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.NobelingProof.GoodProducts.linearIndependentEmpty", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.ZeroLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.NobelingProof.Products.nil", "kind": "definition", "module": "Mathlib.Topology.Category.Profinite.Nobeling.ZeroLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.NobelingProof.Products.lt_nil_empty", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.ZeroLimit", "is_tactic_proof": true, "tactics": ["ext", "refine", "simp"], "tactic_count": 3}
{"name": "Profinite.NobelingProof.instNontrivialLocallyConstantIntOfNonempty", "kind": "instance", "module": "Mathlib.Topology.Category.Profinite.Nobeling.ZeroLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.NobelingProof.Products.isGood_nil", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.ZeroLimit", "is_tactic_proof": true, "tactics": ["intro", "simp"], "tactic_count": 2}
{"name": "Profinite.NobelingProof.Products.span_nil_eq_top", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.ZeroLimit", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "refine", "simp", "ext", "obtain", "rfl"], "tactic_count": 8}
{"name": "Profinite.NobelingProof.instUniqueSubtypeProductsIsGoodSingletonForallBoolSetFalse", "kind": "instance", "module": "Mathlib.Topology.Category.Profinite.Nobeling.ZeroLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.NobelingProof.instIsAddTorsionFreeLocallyConstantInt", "kind": "instance", "module": "Mathlib.Topology.Category.Profinite.Nobeling.ZeroLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.NobelingProof.GoodProducts.linearIndependentSingleton", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.ZeroLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.NobelingProof.GoodProducts.smaller", "kind": "definition", "module": "Mathlib.Topology.Category.Profinite.Nobeling.ZeroLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.NobelingProof.GoodProducts.range_equiv_smaller_toFun", "kind": "definition", "module": "Mathlib.Topology.Category.Profinite.Nobeling.ZeroLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.NobelingProof.GoodProducts.range_equiv_smaller_toFun_bijective", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.ZeroLimit", "is_tactic_proof": true, "tactics": ["dsimp", "refine", "ext1", "simp", "exact", "use", "simpa"], "tactic_count": 7}
{"name": "Profinite.NobelingProof.GoodProducts.range_equiv_smaller", "kind": "definition", "module": "Mathlib.Topology.Category.Profinite.Nobeling.ZeroLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.NobelingProof.GoodProducts.smaller_factorization", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.ZeroLimit", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "Profinite.NobelingProof.GoodProducts.linearIndependent_iff_smaller", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.ZeroLimit", "is_tactic_proof": false, "tactics": ["rw", "smaller_factorization", "exact"], "tactic_count": 3}
{"name": "Profinite.NobelingProof.GoodProducts.smaller_mono", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.ZeroLimit", "is_tactic_proof": true, "tactics": ["rintro", "simp", "use", "obtain", "refine", "use", "ext", "rw", "rw", "projRestricts_comp_projRestrict", "rfl"], "tactic_count": 11}
{"name": "Profinite.NobelingProof.Products.limitOrdinal", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.ZeroLimit", "is_tactic_proof": true, "tactics": ["refine", "use", "have", "simp", "exact", "refine", "have", "intro", "simp", "exact", "rwa"], "tactic_count": 11}
{"name": "Profinite.NobelingProof.GoodProducts.union", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.ZeroLimit", "is_tactic_proof": true, "tactics": ["ext", "simp", "refine", "obtain", "rw", "obtain", "refine", "exact", "obtain", "refine", "rw", "exact"], "tactic_count": 12}
{"name": "Profinite.NobelingProof.GoodProducts.range_equiv", "kind": "definition", "module": "Mathlib.Topology.Category.Profinite.Nobeling.ZeroLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.NobelingProof.GoodProducts.range_equiv_factorization", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.ZeroLimit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.NobelingProof.GoodProducts.linearIndependent_iff_union_smaller", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Nobeling.ZeroLimit", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Profinite.IndexFunctor.obj", "kind": "definition", "module": "Mathlib.Topology.Category.Profinite.Product", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.IndexFunctor.π_app", "kind": "definition", "module": "Mathlib.Topology.Category.Profinite.Product", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.IndexFunctor.map", "kind": "definition", "module": "Mathlib.Topology.Category.Profinite.Product", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.IndexFunctor.surjective_π_app", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Product", "is_tactic_proof": true, "tactics": ["intro", "obtain", "exact"], "tactic_count": 3}
{"name": "Profinite.IndexFunctor.map_comp_π_app", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Product", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.IndexFunctor.eq_of_forall_π_app_eq", "kind": "theorem", "module": "Mathlib.Topology.Category.Profinite.Product", "is_tactic_proof": true, "tactics": ["ext", "specialize", "rw", "simp", "exact"], "tactic_count": 5}
{"name": "Profinite.indexFunctor", "kind": "definition", "module": "Mathlib.Topology.Category.Profinite.Product", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.indexCone", "kind": "definition", "module": "Mathlib.Topology.Category.Profinite.Product", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.isIso_indexCone_lift", "kind": "instance", "module": "Mathlib.Topology.Category.Profinite.Product", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.isoindexConeLift", "kind": "definition", "module": "Mathlib.Topology.Category.Profinite.Product", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.asLimitindexConeIso", "kind": "definition", "module": "Mathlib.Topology.Category.Profinite.Product", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.indexCone_isLimit", "kind": "definition", "module": "Mathlib.Topology.Category.Profinite.Product", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.projective_ultrafilter", "kind": "instance", "module": "Mathlib.Topology.Category.Profinite.Projective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.projectivePresentation", "kind": "definition", "module": "Mathlib.Topology.Category.Profinite.Projective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.instEnoughProjectives", "kind": "instance", "module": "Mathlib.Topology.Category.Profinite.Projective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sequential.instInhabited", "kind": "instance", "module": "Mathlib.Topology.Category.Sequential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sequential.instCoeSortType", "kind": "instance", "module": "Mathlib.Topology.Category.Sequential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sequential.instCategory", "kind": "instance", "module": "Mathlib.Topology.Category.Sequential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sequential.instConcreteCategoryContinuousMapCarrierToTop", "kind": "instance", "module": "Mathlib.Topology.Category.Sequential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sequential.of", "kind": "abbrev", "module": "Mathlib.Topology.Category.Sequential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sequential.sequentialToTop", "kind": "definition", "module": "Mathlib.Topology.Category.Sequential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sequential.fullyFaithfulSequentialToTop", "kind": "definition", "module": "Mathlib.Topology.Category.Sequential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sequential.instFullTopCatSequentialToTop", "kind": "instance", "module": "Mathlib.Topology.Category.Sequential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sequential.instFaithfulTopCatSequentialToTop", "kind": "instance", "module": "Mathlib.Topology.Category.Sequential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sequential.isoOfHomeo", "kind": "definition", "module": "Mathlib.Topology.Category.Sequential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sequential.homeoOfIso", "kind": "definition", "module": "Mathlib.Topology.Category.Sequential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sequential.isoEquivHomeo", "kind": "definition", "module": "Mathlib.Topology.Category.Sequential", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stonean.stoneCechObj", "kind": "definition", "module": "Mathlib.Topology.Category.Stonean.Adjunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stonean.stoneCechEquivalence", "kind": "definition", "module": "Mathlib.Topology.Category.Stonean.Adjunctions", "is_tactic_proof": true, "tactics": ["letI", "haveI", "refine", "exact"], "tactic_count": 4}
{"name": "typeToStonean", "kind": "definition", "module": "Mathlib.Topology.Category.Stonean.Adjunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stonean.stoneCechAdjunction", "kind": "definition", "module": "Mathlib.Topology.Category.Stonean.Adjunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stonean.forget.preservesLimits", "kind": "instance", "module": "Mathlib.Topology.Category.Stonean.Adjunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stonean", "kind": "abbrev", "module": "Mathlib.Topology.Category.Stonean.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHaus.instExtremallyDisconnectedCarrierToTopTrueOfProjective", "kind": "instance", "module": "Mathlib.Topology.Category.Stonean.Basic", "is_tactic_proof": true, "tactics": ["apply", "intro", "let", "let", "let", "let", "have", "rw", "assumption", "obtain", "refine", "ext", "apply_fun", "exact"], "tactic_count": 14}
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{"name": "Stonean.toCompHaus", "kind": "abbrev", "module": "Mathlib.Topology.Category.Stonean.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stonean.fullyFaithfulToCompHaus", "kind": "abbrev", "module": "Mathlib.Topology.Category.Stonean.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stonean.instHasPropExtremallyDisconnectedCarrier", "kind": "instance", "module": "Mathlib.Topology.Category.Stonean.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stonean.of", "kind": "abbrev", "module": "Mathlib.Topology.Category.Stonean.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stonean.instExtremallyDisconnectedCarrierToTop", "kind": "instance", "module": "Mathlib.Topology.Category.Stonean.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stonean.toProfinite", "kind": "abbrev", "module": "Mathlib.Topology.Category.Stonean.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stonean.mkFinite", "kind": "definition", "module": "Mathlib.Topology.Category.Stonean.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stonean.epi_iff_surjective", "kind": "theorem", "module": "Mathlib.Topology.Category.Stonean.Basic", "is_tactic_proof": true, "tactics": ["refine", "dsimp", "intro", "by_contra", "let", "have", "let", "have", "obtain", "classical", "let", "let", "have", "rw", "ext", "apply", "change", "ite", "rw", "refine", "mt", "simpa", "apply_fun", "change", "rw", "exact"], "tactic_count": 26}
{"name": "Stonean.instProjectiveCompHausCompHaus", "kind": "instance", "module": "Mathlib.Topology.Category.Stonean.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stonean.instProjectiveProfiniteObjToProfinite", "kind": "instance", "module": "Mathlib.Topology.Category.Stonean.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stonean.instProjective", "kind": "instance", "module": "Mathlib.Topology.Category.Stonean.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHaus.presentation", "kind": "definition", "module": "Mathlib.Topology.Category.Stonean.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHaus.presentation.π", "kind": "definition", "module": "Mathlib.Topology.Category.Stonean.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHaus.presentation.epi_π", "kind": "instance", "module": "Mathlib.Topology.Category.Stonean.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stonean.compHaus", "kind": "abbrev", "module": "Mathlib.Topology.Category.Stonean.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHaus.lift", "kind": "definition", "module": "Mathlib.Topology.Category.Stonean.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompHaus.lift_lifts", "kind": "theorem", "module": "Mathlib.Topology.Category.Stonean.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CompHaus.Gleason", "kind": "theorem", "module": "Mathlib.Topology.Category.Stonean.Basic", "is_tactic_proof": true, "tactics": ["constructor", "intro", "change", "infer_instance", "intro", "let", "change", "apply"], "tactic_count": 8}
{"name": "Profinite.presentation", "kind": "definition", "module": "Mathlib.Topology.Category.Stonean.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.presentation.π", "kind": "definition", "module": "Mathlib.Topology.Category.Stonean.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.presentation.epi_π", "kind": "instance", "module": "Mathlib.Topology.Category.Stonean.Basic", "is_tactic_proof": true, "tactics": ["have", "rw", "rw", "exact"], "tactic_count": 4}
{"name": "Profinite.lift", "kind": "definition", "module": "Mathlib.Topology.Category.Stonean.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Profinite.lift_lifts", "kind": "theorem", "module": "Mathlib.Topology.Category.Stonean.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Profinite.projective_of_extrDisc", "kind": "theorem", "module": "Mathlib.Topology.Category.Stonean.Basic", "is_tactic_proof": true, "tactics": ["change", "exact"], "tactic_count": 2}
{"name": "Stonean.effectiveEpi_tfae", "kind": "theorem", "module": "Mathlib.Topology.Category.Stonean.EffectiveEpi", "is_tactic_proof": true, "tactics": ["tfae_have", "tfae_have", "tfae_have", "tfae_finish"], "tactic_count": 4}
{"name": "Stonean.instPreservesEffectiveEpisCompHausToCompHaus", "kind": "instance", "module": "Mathlib.Topology.Category.Stonean.EffectiveEpi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stonean.instReflectsEffectiveEpisCompHausToCompHaus", "kind": "instance", "module": "Mathlib.Topology.Category.Stonean.EffectiveEpi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stonean.stoneanToCompHausEffectivePresentation", "kind": "definition", "module": "Mathlib.Topology.Category.Stonean.EffectiveEpi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stonean.instEffectivelyEnoughCompHausToCompHaus", "kind": "instance", "module": "Mathlib.Topology.Category.Stonean.EffectiveEpi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stonean.instPreregular", "kind": "instance", "module": "Mathlib.Topology.Category.Stonean.EffectiveEpi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stonean._example", "kind": "example", "module": "Mathlib.Topology.Category.Stonean.EffectiveEpi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stonean.effectiveEpiFamily_tfae", "kind": "theorem", "module": "Mathlib.Topology.Category.Stonean.EffectiveEpi", "is_tactic_proof": false, "tactics": ["tfae_have", "tfae_have", "tfae_have", "erw", "exact", "tfae_finish"], "tactic_count": 6}
{"name": "Stonean.effectiveEpiFamily_of_jointly_surjective", "kind": "theorem", "module": "Mathlib.Topology.Category.Stonean.EffectiveEpi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stonean.instHasExplicitFiniteCoproductsExtremallyDisconnectedCarrier", "kind": "instance", "module": "Mathlib.Topology.Category.Stonean.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stonean.extremallyDisconnected_preimage", "kind": "theorem", "module": "Mathlib.Topology.Category.Stonean.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stonean.extremallyDisconnected_pullback", "kind": "theorem", "module": "Mathlib.Topology.Category.Stonean.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stonean.instHasExplicitPullbacksOfInclusionsExtremallyDisconnectedCarrier", "kind": "instance", "module": "Mathlib.Topology.Category.Stonean.Limits", "is_tactic_proof": true, "tactics": ["apply", "intro", "exact"], "tactic_count": 3}
{"name": "Stonean._example", "kind": "example", "module": "Mathlib.Topology.Category.Stonean.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stonean._example", "kind": "example", "module": "Mathlib.Topology.Category.Stonean.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Stonean._example", "kind": "example", "module": "Mathlib.Topology.Category.Stonean.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.adj₁", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Adjunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.adj₂", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Adjunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.instIsRightAdjointForget", "kind": "instance", "module": "Mathlib.Topology.Category.TopCat.Adjunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.instIsLeftAdjointForget", "kind": "instance", "module": "Mathlib.Topology.Category.TopCat.Adjunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.instCoeSortType", "kind": "instance", "module": "Mathlib.Topology.Category.TopCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.coe_of", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.of_carrier", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.instCategory", "kind": "instance", "module": "Mathlib.Topology.Category.TopCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.instConcreteCategoryContinuousMapCarrier", "kind": "instance", "module": "Mathlib.Topology.Category.TopCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Hom.hom", "kind": "abbrev", "module": "Mathlib.Topology.Category.TopCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.ofHom", "kind": "abbrev", "module": "Mathlib.Topology.Category.TopCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Hom.Simps.hom", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.hom_id", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.id_app", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.coe_id", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.hom_comp", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.comp_app", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.coe_comp", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.hom_ext", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.ext", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.hom_ofHom", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.ofHom_hom", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.ofHom_id", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.ofHom_comp", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.ofHom_apply", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.hom_inv_id_apply", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "TopCat.inv_hom_id_apply", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "TopCat.coe_of_of", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.inhabited", "kind": "instance", "module": "Mathlib.Topology.Category.TopCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.discrete", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.instDiscreteTopologyCarrierObjDiscrete", "kind": "instance", "module": "Mathlib.Topology.Category.TopCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.trivial", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.isoOfHomeo", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.homeoOfIso", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.of_isoOfHomeo", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Basic", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "TopCat.of_homeoOfIso", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Basic", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "TopCat.isIso_of_bijective_of_isOpenMap", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.isIso_of_bijective_of_isClosedMap", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.isIso_iff_isHomeomorph", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.isOpenEmbedding_iff_comp_isIso", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.isOpenEmbedding_iff_comp_isIso'", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Basic", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "TopCat.isOpenEmbedding_iff_isIso_comp", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Basic", "is_tactic_proof": true, "tactics": ["constructor", "intro", "convert", "exact", "exact"], "tactic_count": 5}
{"name": "TopCat.isOpenEmbedding_iff_isIso_comp'", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Basic", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "TopCat.effectiveEpiStructOfQuotientMap", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.EffectiveEpi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.effectiveEpi_iff_isQuotientMap", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.EffectiveEpi", "is_tactic_proof": true, "tactics": ["refine", "a", "an", "exact"], "tactic_count": 4}
{"name": "TopCat.epi_iff_surjective", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.EpiMono", "is_tactic_proof": false, "tactics": ["suffices", "rw", "rfl", "constructor", "intro", "infer_instance", "apply"], "tactic_count": 7}
{"name": "TopCat.mono_iff_injective", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.EpiMono", "is_tactic_proof": false, "tactics": ["suffices", "rw", "rfl", "constructor", "intro", "infer_instance", "apply"], "tactic_count": 7}
{"name": "_private.Mathlib.Topology.Category.TopCat.Limits.Basic.0.termForget", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Limits.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.Category.TopCat.Limits.Basic.0._aux_Mathlib_Topology_Category_TopCat_Limits_Basic___macroRules__private_Mathlib_Topology_Category_TopCat_Limits_Basic_0_termForget_1", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Limits.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.Category.TopCat.Limits.Basic.0._aux_Mathlib_Topology_Category_TopCat_Limits_Basic___unexpand_CategoryTheory_forget_1", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Limits.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.limitCone", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Limits.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.limitConeIsLimit", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Limits.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.conePtOfConeForget", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Limits.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.topologicalSpaceConePtOfConeForget", "kind": "instance", "module": "Mathlib.Topology.Category.TopCat.Limits.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.coneOfConeForget", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Limits.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.isLimitConeOfForget", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Limits.Basic", "is_tactic_proof": false, "tactics": ["refine", "rw", "dsimp", "rw", "intro", "rw", "convert", "exact"], "tactic_count": 8}
{"name": "TopCat.induced_of_isLimit", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Limits.Basic", "is_tactic_proof": true, "tactics": ["let", "let", "let", "have", "apply", "dsimp", "conv_rhs", "simp"], "tactic_count": 8}
{"name": "TopCat.limit_topology", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Limits.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.hasLimit_iff_small_sections", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Limits.Basic", "is_tactic_proof": true, "tactics": ["rw", "constructor", "infer_instance", "exact"], "tactic_count": 4}
{"name": "TopCat.topCat_hasLimitsOfShape", "kind": "instance", "module": "Mathlib.Topology.Category.TopCat.Limits.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.topCat_hasLimitsOfSize", "kind": "instance", "module": "Mathlib.Topology.Category.TopCat.Limits.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.topCat_hasLimits", "kind": "instance", "module": "Mathlib.Topology.Category.TopCat.Limits.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.forget_preservesLimitsOfSize", "kind": "instance", "module": "Mathlib.Topology.Category.TopCat.Limits.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.forget_preservesLimits", "kind": "instance", "module": "Mathlib.Topology.Category.TopCat.Limits.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.coconePtOfCoconeForget", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Limits.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.topologicalSpaceCoconePtOfCoconeForget", "kind": "instance", "module": "Mathlib.Topology.Category.TopCat.Limits.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.coconeOfCoconeForget", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Limits.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.isColimitCoconeOfForget", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Limits.Basic", "is_tactic_proof": false, "tactics": ["refine", "rw", "dsimp", "rw", "intro", "rw", "convert", "exact"], "tactic_count": 8}
{"name": "TopCat.coinduced_of_isColimit", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Limits.Basic", "is_tactic_proof": true, "tactics": ["let", "let", "let", "have", "apply", "dsimp", "simp", "conv_rhs", "rfl"], "tactic_count": 9}
{"name": "TopCat.isOpen_iff_of_isColimit", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Limits.Basic", "is_tactic_proof": true, "tactics": ["trans", "rw", "simp", "apply"], "tactic_count": 4}
{"name": "TopCat.isClosed_iff_of_isColimit", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Limits.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "TopCat.continuous_iff_of_isColimit", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Limits.Basic", "is_tactic_proof": true, "tactics": ["simp", "tauto"], "tactic_count": 2}
{"name": "TopCat.colimit_topology", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Limits.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.colimit_isOpen_iff", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Limits.Basic", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "TopCat.hasColimit_iff_small_colimitType", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Limits.Basic", "is_tactic_proof": true, "tactics": ["rw", "constructor", "infer_instance", "exact"], "tactic_count": 4}
{"name": "TopCat.topCat_hasColimitsOfShape", "kind": "instance", "module": "Mathlib.Topology.Category.TopCat.Limits.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.topCat_hasColimitsOfSize", "kind": "instance", "module": "Mathlib.Topology.Category.TopCat.Limits.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.topCat_hasColimits", "kind": "instance", "module": "Mathlib.Topology.Category.TopCat.Limits.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.forget_preservesColimitsOfSize", "kind": "instance", "module": "Mathlib.Topology.Category.TopCat.Limits.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.forget_preservesColimits", "kind": "instance", "module": "Mathlib.Topology.Category.TopCat.Limits.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.isTerminalPUnit", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Limits.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.terminalIsoPUnit", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Limits.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.isInitialPEmpty", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Limits.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.initialIsoPEmpty", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Limits.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.isTopologicalBasis_cofiltered_limit", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Limits.Cofiltered", "is_tactic_proof": true, "tactics": ["classical", "convert", "exact", "ext", "constructor", "rintro", "let", "refine", "simp", "rintro", "simpa", "simp", "rintro", "obtain", "let", "let", "let", "refine", "have", "intro", "induction", "empty", "intro", "simpa", "insert", "intro", "rw", "refine", "intro", "exact", "hh5", "refine", "intro", "dsimp", "rw", "exact", "rw", "change", "rw", "apply", "ext1", "rw", "apply", "ext1", "simp"], "tactic_count": 45}
{"name": "_private.Mathlib.Topology.Category.TopCat.Limits.Konig.0.TopCat.FiniteDiagramArrow", "kind": "abbrev", "module": "Mathlib.Topology.Category.TopCat.Limits.Konig", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.Category.TopCat.Limits.Konig.0.TopCat.FiniteDiagram", "kind": "abbrev", "module": "Mathlib.Topology.Category.TopCat.Limits.Konig", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.partialSections", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Limits.Konig", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.partialSections.nonempty", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Limits.Konig", "is_tactic_proof": true, "tactics": ["classical", "cases", "exact", "haveI", "use", "rintro", "dsimp", "rwa"], "tactic_count": 8}
{"name": "TopCat.partialSections.directed", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Limits.Konig", "is_tactic_proof": true, "tactics": ["classical", "intro", "let", "let", "refine", "rintro", "have", "apply", "rw", "exact", "exact", "rintro", "have", "apply", "rw", "exact", "exact"], "tactic_count": 17}
{"name": "TopCat.partialSections.closed", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Limits.Konig", "is_tactic_proof": false, "tactics": ["have", "ext1", "simp", "rfl", "rw", "apply", "intro", "apply"], "tactic_count": 8}
{"name": "TopCat.nonempty_limitCone_of_compact_t2_cofiltered_system", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Limits.Konig", "is_tactic_proof": true, "tactics": ["classical", "obtain", "use", "intro", "let", "exact"], "tactic_count": 6}
{"name": "TopCat.piπ", "kind": "abbrev", "module": "Mathlib.Topology.Category.TopCat.Limits.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.piFan", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Limits.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.piFanIsLimit", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Limits.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.piIsoPi", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Limits.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.piIsoPi_inv_π", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Limits.Products", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "TopCat.piIsoPi_inv_π_apply", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Limits.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.piIsoPi_hom_apply", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Limits.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.sigmaι", "kind": "abbrev", "module": "Mathlib.Topology.Category.TopCat.Limits.Products", "is_tactic_proof": true, "tactics": ["refine", "dsimp", "apply", "dsimp"], "tactic_count": 4}
{"name": "TopCat.sigmaCofan", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Limits.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.sigmaCofanIsColimit", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Limits.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.sigmaIsoSigma", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Limits.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.sigmaIsoSigma_hom_ι", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Limits.Products", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "TopCat.sigmaIsoSigma_hom_ι_apply", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Limits.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.sigmaIsoSigma_inv_apply", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Limits.Products", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "TopCat.prodFst", "kind": "abbrev", "module": "Mathlib.Topology.Category.TopCat.Limits.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.prodSnd", "kind": "abbrev", "module": "Mathlib.Topology.Category.TopCat.Limits.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.prodBinaryFan", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Limits.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.prodBinaryFanIsLimit", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Limits.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.prodIsoProd", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Limits.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.prodIsoProd_hom_fst", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Limits.Products", "is_tactic_proof": true, "tactics": ["simp", "rfl"], "tactic_count": 2}
{"name": "TopCat.prodIsoProd_hom_snd", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Limits.Products", "is_tactic_proof": true, "tactics": ["simp", "rfl"], "tactic_count": 2}
{"name": "TopCat.prodIsoProd_hom_apply", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Limits.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.prodIsoProd_inv_fst", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Limits.Products", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "TopCat.prodIsoProd_inv_snd", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Limits.Products", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "TopCat.prod_topology", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Limits.Products", "is_tactic_proof": true, "tactics": ["let", "refine", "change", "simp", "rfl"], "tactic_count": 5}
{"name": "TopCat.range_prod_map", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Limits.Products", "is_tactic_proof": true, "tactics": ["ext", "constructor", "rintro", "simp_rw", "rintro", "use", "apply", "rintro", "rw", "erw", "rw", "exact", "rw", "erw", "rw", "exact"], "tactic_count": 16}
{"name": "TopCat.isInducing_prodMap", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Limits.Products", "is_tactic_proof": true, "tactics": ["constructor", "simp_rw", "induced_compose", "rw"], "tactic_count": 4}
{"name": "TopCat.isEmbedding_prodMap", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Limits.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.binaryCofan", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Limits.Products", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.binaryCofanIsColimit", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Limits.Products", "is_tactic_proof": false, "tactics": ["refine", "continuity", "intro", "ext", "rfl", "intro", "ext", "rfl", "intro", "ext", "exacts"], "tactic_count": 11}
{"name": "TopCat.binaryCofan_isColimit_iff", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Limits.Products", "is_tactic_proof": true, "tactics": ["classical", "constructor", "rintro", "rw", "show", "dsimp", "refine", "rw", "conv_rhs", "erw", "rintro", "have", "rw", "exact", "refine", "intro", "refine", "exact", "rw", "intro", "by_cases", "revert", "apply", "rw", "convert_to", "ext", "exact", "continuity", "exact", "revert", "apply", "rw", "have", "rintro", "rwa", "convert_to", "ext", "exact", "apply", "exact", "apply", "continuity", "rw", "exact", "change", "rw", "exact", "intro", "ext", "dsimp", "rw", "conv_lhs", "intro", "ext", "dsimp", "rw", "exact", "rintro", "have", "rwa", "rintro", "ext", "change", "split_ifs"], "tactic_count": 64}
{"name": "TopCat.pullbackFst", "kind": "abbrev", "module": "Mathlib.Topology.Category.TopCat.Limits.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.pullbackFst_apply", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Limits.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.pullbackSnd", "kind": "abbrev", "module": "Mathlib.Topology.Category.TopCat.Limits.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.pullbackSnd_apply", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Limits.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.pullbackCone", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Limits.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.pullbackConeIsLimit", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Limits.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.pullbackIsoProdSubtype", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Limits.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.pullbackIsoProdSubtype_inv_fst", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Limits.Pullbacks", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "TopCat.pullbackIsoProdSubtype_inv_fst_apply", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Limits.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.pullbackIsoProdSubtype_inv_snd", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Limits.Pullbacks", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "TopCat.pullbackIsoProdSubtype_inv_snd_apply", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Limits.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.pullbackIsoProdSubtype_hom_fst", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Limits.Pullbacks", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "TopCat.pullbackIsoProdSubtype_hom_snd", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Limits.Pullbacks", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "TopCat.pullbackIsoProdSubtype_hom_apply", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Limits.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.pullback_topology", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Limits.Pullbacks", "is_tactic_proof": true, "tactics": ["let", "refine", "change", "simp", "rfl"], "tactic_count": 5}
{"name": "TopCat.range_pullback_to_prod", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Limits.Pullbacks", "is_tactic_proof": true, "tactics": ["ext", "constructor", "rintro", "simp", "simp", "rintro", "use", "apply", "rintro", "cat_disch"], "tactic_count": 10}
{"name": "TopCat.pullbackHomeoPreimage", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Limits.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.isInducing_pullback_to_prod", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Limits.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.isEmbedding_pullback_to_prod", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Limits.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.range_pullback_map", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Limits.Pullbacks", "is_tactic_proof": true, "tactics": ["ext", "constructor", "rintro", "simp", "rw", "simp", "exact", "rintro", "have", "apply", "rw", "use", "apply", "rintro", "simp", "simp", "simp"], "tactic_count": 17}
{"name": "TopCat.pullback_fst_range", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Limits.Pullbacks", "is_tactic_proof": true, "tactics": ["ext", "constructor", "rintro", "use", "exact", "rintro", "use", "rw"], "tactic_count": 8}
{"name": "TopCat.pullback_snd_range", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Limits.Pullbacks", "is_tactic_proof": true, "tactics": ["ext", "constructor", "rintro", "use", "exact", "rintro", "use", "rw"], "tactic_count": 8}
{"name": "TopCat.pullback_map_isEmbedding", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Limits.Pullbacks", "is_tactic_proof": false, "tactics": ["refine", "suffices", "simpa", "rw", "exact"], "tactic_count": 5}
{"name": "TopCat.pullback_map_isOpenEmbedding", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Limits.Pullbacks", "is_tactic_proof": true, "tactics": ["constructor", "apply", "rw", "apply", "apply", "exact", "apply", "exact"], "tactic_count": 8}
{"name": "TopCat.snd_isEmbedding_of_left", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Limits.Pullbacks", "is_tactic_proof": false, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "TopCat.fst_isEmbedding_of_right", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Limits.Pullbacks", "is_tactic_proof": false, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "TopCat.isEmbedding_of_pullback", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Limits.Pullbacks", "is_tactic_proof": true, "tactics": ["convert", "rw", "rfl"], "tactic_count": 3}
{"name": "TopCat.snd_isOpenEmbedding_of_left", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Limits.Pullbacks", "is_tactic_proof": false, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "TopCat.fst_isOpenEmbedding_of_right", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Limits.Pullbacks", "is_tactic_proof": false, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "TopCat.isOpenEmbedding_of_pullback", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Limits.Pullbacks", "is_tactic_proof": true, "tactics": ["convert", "rw", "rfl"], "tactic_count": 3}
{"name": "TopCat.fst_iso_of_right_embedding_range_subset", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Limits.Pullbacks", "is_tactic_proof": false, "tactics": ["let", "invFun", "rw", "exact", "convert"], "tactic_count": 5}
{"name": "TopCat.snd_iso_of_left_embedding_range_subset", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Limits.Pullbacks", "is_tactic_proof": false, "tactics": ["let", "invFun", "rw", "exact", "convert"], "tactic_count": 5}
{"name": "TopCat.pullback_snd_image_fst_preimage", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Limits.Pullbacks", "is_tactic_proof": true, "tactics": ["ext", "constructor", "rintro", "exact", "rintro", "refine", "simp", "convert", "rw", "rw"], "tactic_count": 10}
{"name": "TopCat.pullback_fst_image_snd_preimage", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Limits.Pullbacks", "is_tactic_proof": true, "tactics": ["ext", "constructor", "rintro", "exact", "rintro", "refine", "simp", "convert", "rw", "rw"], "tactic_count": 10}
{"name": "TopCat.isOpen_iff_of_isColimit_cofork", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Limits.Pullbacks", "is_tactic_proof": true, "tactics": ["rw", "constructor", "intro", "exact", "rintro", "rw", "exact", "exact"], "tactic_count": 8}
{"name": "TopCat.isQuotientMap_of_isColimit_cofork", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Limits.Pullbacks", "is_tactic_proof": true, "tactics": ["rw", "constructor", "simpa", "exact"], "tactic_count": 4}
{"name": "TopCat.coequalizer_isOpen_iff", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Limits.Pullbacks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.OpenNhds", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.OpenNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.OpenNhds.partialOrder", "kind": "instance", "module": "Mathlib.Topology.Category.TopCat.OpenNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.OpenNhds.instLattice", "kind": "instance", "module": "Mathlib.Topology.Category.TopCat.OpenNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.OpenNhds.instOrderTop", "kind": "instance", "module": "Mathlib.Topology.Category.TopCat.OpenNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.OpenNhds.instInhabited", "kind": "instance", "module": "Mathlib.Topology.Category.TopCat.OpenNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.OpenNhds.opensNhds.instFunLike", "kind": "instance", "module": "Mathlib.Topology.Category.TopCat.OpenNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.OpenNhds.apply_mk", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.OpenNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.OpenNhds.val_apply", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.OpenNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.OpenNhds.coe_id", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.OpenNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.OpenNhds.id_apply", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.OpenNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.OpenNhds.comp_apply", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.OpenNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.OpenNhds.infLELeft", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.OpenNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.OpenNhds.infLERight", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.OpenNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.OpenNhds.inclusion", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.OpenNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.OpenNhds.inclusion_obj", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.OpenNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.OpenNhds.isOpenEmbedding", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.OpenNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.OpenNhds.map", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.OpenNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.OpenNhds.map_obj", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.OpenNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.OpenNhds.map_id_obj", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.OpenNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.OpenNhds.map_id_obj'", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.OpenNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.OpenNhds.map_id_obj_unop", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.OpenNhds", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "TopologicalSpace.OpenNhds.op_map_id_obj", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.OpenNhds", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "TopologicalSpace.OpenNhds.inclusionMapIso", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.OpenNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.OpenNhds.inclusionMapIso_hom", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.OpenNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.OpenNhds.inclusionMapIso_inv", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.OpenNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpenMap.functorNhds", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.OpenNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpenMap.adjunctionNhds", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.OpenNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsInducing.functorNhds", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.OpenNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsInducing.adjunctionNhds", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.OpenNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.opensHom.instFunLike", "kind": "instance", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.apply_def", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.apply_mk", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.val_apply", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.coe_id", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.id_apply", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.comp_apply", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.infLELeft", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.infLERight", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.leSupr", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.botLE", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.leTop", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.infLELeft_apply", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.infLELeft_apply_mk", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.leSupr_apply_mk", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.toTopCat", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.toTopCat_map", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.inclusion'", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.coe_inclusion'", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.isOpenEmbedding", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.inclusionTopIso", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.map", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.map_coe", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.mem_map", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.map_obj", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.map_homOfLE", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.map_id_obj", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.map_id_obj'", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.map_id_obj_unop", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "TopologicalSpace.Opens.op_map_id_obj", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "TopologicalSpace.Opens.map_top", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.leMapTop", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.map_comp_obj", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.map_comp_obj'", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.map_comp_map", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.map_comp_obj_unop", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.op_map_comp_obj", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.map_iSup", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "TopologicalSpace.Opens.mapId", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.map_id_eq", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "TopologicalSpace.Opens.mapComp", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.map_comp_eq", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.mapIso", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.map_eq", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": true, "tactics": ["subst", "rfl"], "tactic_count": 2}
{"name": "TopologicalSpace.Opens.mapIso_refl", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.mapIso_hom_app", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.mapIso_inv_app", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.mapMapIso", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpenMap.functor", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpenMap.adjunction", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpenMap.functorFullOfMono", "kind": "instance", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpenMap.functor_faithful", "kind": "instance", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsOpenEmbedding.functor_obj_injective", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsInducing.functorObj", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsInducing.map_functorObj", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": true, "tactics": ["apply", "rintro", "intro", "obtain", "obtain", "exact"], "tactic_count": 6}
{"name": "Topology.IsInducing.mem_functorObj_iff", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": true, "tactics": ["conv_rhs", "rfl"], "tactic_count": 2}
{"name": "Topology.IsInducing.le_functorObj_iff", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "constructor", "exact", "intro", "refine", "dsimp", "rwa"], "tactic_count": 8}
{"name": "Topology.IsInducing.opensGI", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsInducing.functor", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsInducing.adjunction", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.isOpenEmbedding_obj_top", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": true, "tactics": ["ext1", "exact"], "tactic_count": 2}
{"name": "TopologicalSpace.Opens.inclusion'_map_eq_top", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": true, "tactics": ["ext1", "exact"], "tactic_count": 2}
{"name": "TopologicalSpace.Opens.adjunction_counit_app_self", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.inclusion'_top_functor", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": true, "tactics": ["refine", "intro", "ext", "exact", "subsingleton"], "tactic_count": 5}
{"name": "TopologicalSpace.Opens.functor_obj_map_obj", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": true, "tactics": ["ext", "constructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 6}
{"name": "TopologicalSpace.Opens.set_range_inclusion'", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": true, "tactics": ["ext", "constructor", "rintro", "exact", "intro", "exact"], "tactic_count": 6}
{"name": "TopologicalSpace.Opens.functor_map_eq_inf", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": true, "tactics": ["ext1", "simp"], "tactic_count": 2}
{"name": "TopologicalSpace.Opens.map_functor_eq'", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.map_functor_eq", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.adjunction_counit_map_functor", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Opens", "is_tactic_proof": true, "tactics": ["subsingleton"], "tactic_count": 1}
{"name": "TopCat.disk", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Sphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.diskBoundary", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Sphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.sphere", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Sphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.ball", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Sphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.term𝔻_", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Sphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat._aux_Mathlib_Topology_Category_TopCat_Sphere___macroRules_TopCat_term𝔻__1", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Sphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat._aux_Mathlib_Topology_Category_TopCat_Sphere___unexpand_TopCat_disk_1", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Sphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.term∂𝔻_", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Sphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat._aux_Mathlib_Topology_Category_TopCat_Sphere___macroRules_TopCat_term∂𝔻__1", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Sphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat._aux_Mathlib_Topology_Category_TopCat_Sphere___unexpand_TopCat_diskBoundary_1", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Sphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.term𝕊_", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Sphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat._aux_Mathlib_Topology_Category_TopCat_Sphere___macroRules_TopCat_term𝕊__1", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Sphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat._aux_Mathlib_Topology_Category_TopCat_Sphere___unexpand_TopCat_sphere_1", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Sphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.term𝔹_", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Sphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat._aux_Mathlib_Topology_Category_TopCat_Sphere___macroRules_TopCat_term𝔹__1", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Sphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat._aux_Mathlib_Topology_Category_TopCat_Sphere___unexpand_TopCat_ball_1", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Sphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.diskBoundaryInclusion", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Sphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.ballInclusion", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Sphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.instMonoDiskBoundaryInclusion", "kind": "instance", "module": "Mathlib.Topology.Category.TopCat.Sphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.instMonoBallInclusion", "kind": "instance", "module": "Mathlib.Topology.Category.TopCat.Sphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.instCompactSpaceCarrierDisk", "kind": "instance", "module": "Mathlib.Topology.Category.TopCat.Sphere", "is_tactic_proof": true, "tactics": ["convert", "infer_instance"], "tactic_count": 2}
{"name": "TopCat.instCompactSpaceCarrierDiskBoundary", "kind": "instance", "module": "Mathlib.Topology.Category.TopCat.Sphere", "is_tactic_proof": true, "tactics": ["convert", "infer_instance"], "tactic_count": 2}
{"name": "TopCat.uliftFunctor", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.uliftFunctorObjHomeo", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.uliftFunctorObjHomeo_naturality_apply", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.uliftFunctorObjHomeo_symm_naturality_apply", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.uliftFunctorCompForgetIso", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.uliftFunctorFullyFaithful", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.instFullUliftFunctor", "kind": "instance", "module": "Mathlib.Topology.Category.TopCat.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.instFaithfulUliftFunctor", "kind": "instance", "module": "Mathlib.Topology.Category.TopCat.ULift", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.yonedaPresheaf", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Yoneda", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.yonedaPresheaf'", "kind": "definition", "module": "Mathlib.Topology.Category.TopCat.Yoneda", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.comp_yonedaPresheaf'", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Yoneda", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.piComparison_fac", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCat.Yoneda", "is_tactic_proof": true, "tactics": ["rw", "ext", "simp", "rfl"], "tactic_count": 4}
{"name": "ContinuousMap.instPreservesFiniteProductsOppositeTopCatYonedaPresheaf'", "kind": "instance", "module": "Mathlib.Topology.Category.TopCat.Yoneda", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCommRingCat.instInhabited", "kind": "instance", "module": "Mathlib.Topology.Category.TopCommRingCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCommRingCat.instCoeSortType", "kind": "instance", "module": "Mathlib.Topology.Category.TopCommRingCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCommRingCat.instCategory", "kind": "instance", "module": "Mathlib.Topology.Category.TopCommRingCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCommRingCat.instFunLikeSubtypeRingHomαContinuousCoe", "kind": "instance", "module": "Mathlib.Topology.Category.TopCommRingCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCommRingCat.instConcreteCategorySubtypeRingHomαContinuousCoe", "kind": "instance", "module": "Mathlib.Topology.Category.TopCommRingCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCommRingCat.coe_of", "kind": "theorem", "module": "Mathlib.Topology.Category.TopCommRingCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCommRingCat.hasForgetToCommRingCat", "kind": "instance", "module": "Mathlib.Topology.Category.TopCommRingCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCommRingCat.forgetToCommRingCatTopologicalSpace", "kind": "instance", "module": "Mathlib.Topology.Category.TopCommRingCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCommRingCat.hasForgetToTopCat", "kind": "instance", "module": "Mathlib.Topology.Category.TopCommRingCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCommRingCat.forgetToTopCatCommRing", "kind": "instance", "module": "Mathlib.Topology.Category.TopCommRingCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCommRingCat.forgetToTopCatTopologicalRing", "kind": "instance", "module": "Mathlib.Topology.Category.TopCommRingCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCommRingCat.instReflectsIsomorphismsTopCatForget₂", "kind": "instance", "module": "Mathlib.Topology.Category.TopCommRingCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpaceCat.instCoeSortType", "kind": "instance", "module": "Mathlib.Topology.Category.UniformSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpaceCat.instLargeCategory", "kind": "instance", "module": "Mathlib.Topology.Category.UniformSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpaceCat.instFunLike", "kind": "instance", "module": "Mathlib.Topology.Category.UniformSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpaceCat.instConcreteCategorySubtypeForallCarrierUniformContinuous", "kind": "instance", "module": "Mathlib.Topology.Category.UniformSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpaceCat.Hom.hom", "kind": "abbrev", "module": "Mathlib.Topology.Category.UniformSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpaceCat.ofHom", "kind": "abbrev", "module": "Mathlib.Topology.Category.UniformSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpaceCat.instInhabited", "kind": "instance", "module": "Mathlib.Topology.Category.UniformSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpaceCat.coe_of", "kind": "theorem", "module": "Mathlib.Topology.Category.UniformSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpaceCat.hom_comp", "kind": "theorem", "module": "Mathlib.Topology.Category.UniformSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpaceCat.hom_id", "kind": "theorem", "module": "Mathlib.Topology.Category.UniformSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpaceCat.hom_ofHom", "kind": "theorem", "module": "Mathlib.Topology.Category.UniformSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpaceCat.coe_comp", "kind": "theorem", "module": "Mathlib.Topology.Category.UniformSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpaceCat.coe_id", "kind": "theorem", "module": "Mathlib.Topology.Category.UniformSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpaceCat.coe_mk", "kind": "theorem", "module": "Mathlib.Topology.Category.UniformSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpaceCat.hom_ext", "kind": "theorem", "module": "Mathlib.Topology.Category.UniformSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpaceCat.hasForgetToTop", "kind": "instance", "module": "Mathlib.Topology.Category.UniformSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CpltSepUniformSpace.instCoeSortType", "kind": "instance", "module": "Mathlib.Topology.Category.UniformSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CpltSepUniformSpace.toUniformSpace", "kind": "definition", "module": "Mathlib.Topology.Category.UniformSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CpltSepUniformSpace.completeSpace", "kind": "instance", "module": "Mathlib.Topology.Category.UniformSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CpltSepUniformSpace.category", "kind": "instance", "module": "Mathlib.Topology.Category.UniformSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CpltSepUniformSpace.instFunLike", "kind": "instance", "module": "Mathlib.Topology.Category.UniformSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CpltSepUniformSpace.concreteCategory", "kind": "instance", "module": "Mathlib.Topology.Category.UniformSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CpltSepUniformSpace.hasForgetToUniformSpace", "kind": "instance", "module": "Mathlib.Topology.Category.UniformSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CpltSepUniformSpace.hom_comp", "kind": "theorem", "module": "Mathlib.Topology.Category.UniformSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CpltSepUniformSpace.hom_id", "kind": "theorem", "module": "Mathlib.Topology.Category.UniformSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CpltSepUniformSpace.hom_ofHom", "kind": "theorem", "module": "Mathlib.Topology.Category.UniformSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpaceCat.completionFunctor", "kind": "definition", "module": "Mathlib.Topology.Category.UniformSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpaceCat.completionHom", "kind": "definition", "module": "Mathlib.Topology.Category.UniformSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpaceCat.completionHom_val", "kind": "theorem", "module": "Mathlib.Topology.Category.UniformSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpaceCat.extensionHom", "kind": "definition", "module": "Mathlib.Topology.Category.UniformSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpaceCat.extensionHom_val", "kind": "theorem", "module": "Mathlib.Topology.Category.UniformSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpaceCat.extension_comp_hom", "kind": "theorem", "module": "Mathlib.Topology.Category.UniformSpace", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "UniformSpaceCat.adj", "kind": "definition", "module": "Mathlib.Topology.Category.UniformSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpaceCat.instReflectiveCpltSepUniformSpaceForget₂", "kind": "instance", "module": "Mathlib.Topology.Category.UniformSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpaceCat._example", "kind": "example", "module": "Mathlib.Topology.Category.UniformSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClopen.isOpen", "kind": "theorem", "module": "Mathlib.Topology.Clopen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClopen.isClosed", "kind": "theorem", "module": "Mathlib.Topology.Clopen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClopen_iff_frontier_eq_empty", "kind": "theorem", "module": "Mathlib.Topology.Clopen", "is_tactic_proof": true, "tactics": ["rw", "refine", "exact"], "tactic_count": 3}
{"name": "IsClopen.union", "kind": "theorem", "module": "Mathlib.Topology.Clopen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClopen.inter", "kind": "theorem", "module": "Mathlib.Topology.Clopen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClopen_empty", "kind": "theorem", "module": "Mathlib.Topology.Clopen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClopen_univ", "kind": "theorem", "module": "Mathlib.Topology.Clopen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClopen.compl", "kind": "theorem", "module": "Mathlib.Topology.Clopen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClopen_compl_iff", "kind": "theorem", "module": "Mathlib.Topology.Clopen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClopen.diff", "kind": "theorem", "module": "Mathlib.Topology.Clopen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClopen.himp", "kind": "theorem", "module": "Mathlib.Topology.Clopen", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsClopen.prod", "kind": "theorem", "module": "Mathlib.Topology.Clopen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClopen_iUnion_of_finite", "kind": "theorem", "module": "Mathlib.Topology.Clopen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.isClopen_biUnion", "kind": "theorem", "module": "Mathlib.Topology.Clopen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClopen_biUnion_finset", "kind": "theorem", "module": "Mathlib.Topology.Clopen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClopen_iInter_of_finite", "kind": "theorem", "module": "Mathlib.Topology.Clopen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.isClopen_biInter", "kind": "theorem", "module": "Mathlib.Topology.Clopen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClopen_biInter_finset", "kind": "theorem", "module": "Mathlib.Topology.Clopen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClopen.preimage", "kind": "theorem", "module": "Mathlib.Topology.Clopen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.preimage_isClopen_of_isClopen", "kind": "theorem", "module": "Mathlib.Topology.Clopen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClopen_inter_of_disjoint_cover_clopen", "kind": "theorem", "module": "Mathlib.Topology.Clopen", "is_tactic_proof": true, "tactics": ["refine", "have", "convert", "refine", "rintro", "exact"], "tactic_count": 6}
{"name": "isClopen_of_disjoint_cover_open", "kind": "theorem", "module": "Mathlib.Topology.Clopen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClopen_discrete", "kind": "theorem", "module": "Mathlib.Topology.Clopen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClopen_range_inl", "kind": "theorem", "module": "Mathlib.Topology.Clopen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClopen_range_inr", "kind": "theorem", "module": "Mathlib.Topology.Clopen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClopen_range_sigmaMk", "kind": "theorem", "module": "Mathlib.Topology.Clopen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsQuotientMap.isClopen_preimage", "kind": "theorem", "module": "Mathlib.Topology.Clopen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_boolIndicator_iff_isClopen", "kind": "theorem", "module": "Mathlib.Topology.Clopen", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "continuousOn_boolIndicator_iff_isClopen", "kind": "theorem", "module": "Mathlib.Topology.Clopen", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "TopologicalSpace.Clopens.exists_prod_subset", "kind": "theorem", "module": "Mathlib.Topology.ClopenBox", "is_tactic_proof": true, "tactics": ["have", "let", "have", "let", "have", "exact", "simp"], "tactic_count": 7}
{"name": "TopologicalSpace.Clopens.exists_finset_eq_sup_prod", "kind": "theorem", "module": "Mathlib.Topology.ClopenBox", "is_tactic_proof": true, "tactics": ["choose", "rcases", "classical", "use", "rw", "refine", "rcases", "exact", "exact"], "tactic_count": 9}
{"name": "TopologicalSpace.Clopens.surjective_finset_sup_prod", "kind": "theorem", "module": "Mathlib.Topology.ClopenBox", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Clopens.countable_prod", "kind": "instance", "module": "Mathlib.Topology.ClopenBox", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Clopens.finite_prod", "kind": "instance", "module": "Mathlib.Topology.ClopenBox", "is_tactic_proof": true, "tactics": ["cases", "cases", "exact"], "tactic_count": 3}
{"name": "TopologicalSpace.Clopens.countable_iff_secondCountable", "kind": "theorem", "module": "Mathlib.Topology.ClopenBox", "is_tactic_proof": true, "tactics": ["refine", "let", "exact", "apply", "exact", "have", "eq_sUnion_finset_of_isTopologicalBasis_of_isCompact_open", "let", "have", "intro", "ext1", "rw", "exact"], "tactic_count": 13}
{"name": "mem_interior", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "isOpen_interior", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "interior_subset", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "interior_maximal", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.interior_eq", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "forall_isOpen_iff", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_isOpen_iff", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "interior_eq_iff_isOpen", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "subset_interior_iff_isOpen", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsOpen.subset_interior_iff", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "subset_interior_iff", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "interior_subset_iff", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "interior_mono", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "subset_interior_union", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "interior_empty", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "interior_univ", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "interior_eq_univ", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "interior_interior", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "interior_inter", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.interior_biInter", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": true, "tactics": ["induction", "empty", "insert"], "tactic_count": 3}
{"name": "Set.Finite.interior_sInter", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.interior_iInter", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "interior_iInter_of_finite", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "interior_iInter₂_lt_nat", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "interior_iInter₂_le_nat", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "interior_union_inter_interior_compl_left_subset", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "interior_union_inter_interior_compl_right_subset", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "interior_union_isClosed_of_interior_empty", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpen_iff_forall_mem_open", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "interior_iInter_subset", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "interior_iInter₂_subset", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "interior_sInter_subset", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.lift'_interior", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.lift'_interior_le", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.lift'_interior_eq_self", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosed_closure", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "subset_closure", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "notMem_of_notMem_closure", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "closure_minimal", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Disjoint.closure_left", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Disjoint.closure_right", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.closure_eq", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "forall_isClosed_iff", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_isClosed_iff", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.closure_subset", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.closure_subset_iff", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.mem_iff_closure_subset", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "closure_mono", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monotone_closure", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "closure_inter_subset", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "diff_subset_closure_iff", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "closure_inter_subset_inter_closure", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosed_of_closure_subset", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "closure_eq_iff_isClosed", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "closure_subset_iff_isClosed", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "closure_empty", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "closure_empty_iff", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "closure_nonempty_iff", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "closure_univ", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "closure_closure", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "closure_eq_compl_interior_compl", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "closure_union", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.Finite.closure_biUnion", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.Finite.closure_sUnion", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.closure_biUnion", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "closure_iUnion_of_finite", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "closure_iUnion₂_lt_nat", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "closure_iUnion₂_le_nat", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "subset_closure_inter_union_closure_compl_left", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "subset_closure_inter_union_closure_compl_right", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "interior_subset_closure", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "interior_compl", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "closure_compl", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "interior_eq_compl_closure_compl", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "interior_union_of_disjoint_closure", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": true, "tactics": ["have", "refine", "rw", "exact", "union_subset"], "tactic_count": 5}
{"name": "closure_inter_of_codisjoint_interior", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": true, "tactics": ["rw", "simp", "apply", "simpa"], "tactic_count": 4}
{"name": "mem_closure_iff", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "closure_inter_open_nonempty_iff", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.le_lift'_closure", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.lift'_closure", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.lift'_closure_eq_self", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.lift'_closure_eq_bot", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dense_iff_closure_eq", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "interior_eq_empty_iff_dense_compl", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Dense.interior_compl", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dense_closure", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "dense_univ", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dense_iff_inter_open", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "exact", "intro", "rw", "intro", "exact"], "tactic_count": 7}
{"name": "Dense.exists_mem_open", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dense.nonempty_iff", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dense.nonempty", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dense.mono", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DenseRange.of_comp", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dense_compl_singleton_iff_not_open", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "refine", "obtain", "exact"], "tactic_count": 6}
{"name": "Dense.induction", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.subset_interior_closure", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.closure_interior_subset", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "closure_interior_idem", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "interior_closure_idem", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "closure_diff_interior", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "disjoint_interior_frontier", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": true, "tactics": ["rw", "compl_inter_self,"], "tactic_count": 2}
{"name": "closure_diff_frontier", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "self_diff_frontier", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": true, "tactics": ["rw", "empty_union]"], "tactic_count": 2}
{"name": "frontier_eq_closure_inter_closure", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "frontier_subset_closure", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "frontier_subset_iff_isClosed", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "frontier_closure_subset", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "frontier_interior_subset", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "frontier_compl", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "frontier_univ", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "frontier_empty", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "frontier_inter_subset", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": true, "tactics": ["simp", "refine", "simp"], "tactic_count": 3}
{"name": "frontier_union_subset", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsClosed.frontier_eq", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsOpen.frontier_eq", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsOpen.inter_frontier_eq", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "disjoint_frontier_iff_isOpen", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "isClosed_frontier", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "interior_frontier", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": true, "tactics": ["have", "have", "have", "have", "rwa"], "tactic_count": 5}
{"name": "closure_eq_interior_union_frontier", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "closure_eq_self_union_frontier", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Disjoint.frontier_left", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Disjoint.frontier_right", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "frontier_eq_inter_compl_interior", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "compl_frontier_eq_union_interior", "kind": "theorem", "module": "Mathlib.Topology.Closure", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "ClusterPt.top", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "clusterPt_sup", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ClusterPt.neBot", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.clusterPt_iff", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.clusterPt_iff_frequently", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "clusterPt_iff_frequently", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClusterPt.frequently", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.clusterPt_iff_frequently'", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "clusterPt_iff_frequently'", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClusterPt.frequently'", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "clusterPt_iff_nonempty", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "clusterPt_iff_not_disjoint", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.HasBasis.clusterPt_iff_forall_mem_closure", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": true, "tactics": ["simp", "tauto"], "tactic_count": 2}
{"name": "clusterPt_iff_forall_mem_closure", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "clusterPt_principal_iff", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "clusterPt_principal_iff_frequently", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ClusterPt.of_le_nhds", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "ClusterPt.of_le_nhds'", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClusterPt.of_nhds_le", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ClusterPt.mono", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClusterPt.of_inf_left", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClusterPt.of_inf_right", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mapClusterPt_def", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.mapClusterPt_iff", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MapClusterPt.mono", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MapClusterPt.tendsto_comp'", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MapClusterPt.tendsto_comp", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mapClusterPt_id_iff", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MapClusterPt.continuousAt_comp", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.mapClusterPt", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.mapClusterPt_iff_frequently", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "mapClusterPt_iff_frequently", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MapClusterPt.frequently", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mapClusterPt_comp", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.mapClusterPt", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MapClusterPt.of_comp", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.mem_of_mapClusterPt", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "accPt_sup", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "accPt_iff_clusterPt", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "accPt_principal_iff_clusterPt", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "accPt_iff_nhds", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "accPt_iff_frequently", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "accPt_iff_frequently_nhdsNE", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": false, "tactics": ["have", "frequently_inf_principal.trans", "rw", "congr", "tauto"], "tactic_count": 5}
{"name": "accPt_principal_iff_nhdsWithin", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AccPt.mono", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AccPt.clusterPt", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "clusterPt_principal", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": true, "tactics": ["constructor", "intro", "by_contra", "rw", "simp_all", "rintro", "exact", "exact"], "tactic_count": 8}
{"name": "isClosed_setOf_clusterPt", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "mem_closure_iff_clusterPt", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_closure_iff_nhds_ne_bot", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_closure_iff_nhdsWithin_neBot", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "notMem_closure_iff_nhdsWithin_eq_bot", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mem_interior_iff_not_clusterPt_compl", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "dense_compl_singleton", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": true, "tactics": ["intro", "rcases", "rwa", "exact"], "tactic_count": 4}
{"name": "closure_compl_singleton", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "interior_singleton", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_isOpen_singleton", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "closure_eq_cluster_pts", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_closure_iff_nhds", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_closure_iff_nhds'", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "mem_closure_iff_comap_neBot", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "mem_closure_iff_nhds_basis'", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_closure_iff_nhds_basis", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "clusterPt_iff_lift'_closure", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": true, "tactics": ["simp_rw", "singleton_subset_iff,"], "tactic_count": 2}
{"name": "clusterPt_iff_lift'_closure'", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": true, "tactics": ["rw", "constructor", "intro", "simp", "intro", "simp_rw", "simpa"], "tactic_count": 7}
{"name": "clusterPt_lift'_closure_iff", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "isClosed_iff_clusterPt", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosed_iff_nhds", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "isClosed_iff_forall_filter", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": true, "tactics": ["simp_rw", "exact", "hs"], "tactic_count": 3}
{"name": "mem_closure_of_mem_closure_union", "kind": "theorem", "module": "Mathlib.Topology.ClusterPt", "is_tactic_proof": true, "tactics": ["rw", "rwa"], "tactic_count": 2}
{"name": "Topology.IsCoherentWith.isOpen_iff", "kind": "theorem", "module": "Mathlib.Topology.Coherent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsCoherentWith.isClosed_iff", "kind": "theorem", "module": "Mathlib.Topology.Coherent", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Topology.IsCoherentWith.continuous_iff", "kind": "theorem", "module": "Mathlib.Topology.Coherent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsCoherentWith.of_continuous_prop", "kind": "theorem", "module": "Mathlib.Topology.Coherent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsCoherentWith.of_isClosed", "kind": "theorem", "module": "Mathlib.Topology.Coherent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsCoherentWith.enlarge", "kind": "theorem", "module": "Mathlib.Topology.Coherent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsCoherentWith.mono", "kind": "theorem", "module": "Mathlib.Topology.Coherent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsCoherentWith.of_seq", "kind": "theorem", "module": "Mathlib.Topology.Coherent", "is_tactic_proof": true, "tactics": ["refine", "rcases", "rw", "suffices", "refine", "specialize", "simp_all"], "tactic_count": 7}
{"name": "Topology.IsCoherentWith.of_nhds", "kind": "theorem", "module": "Mathlib.Topology.Coherent", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.compactOpen", "kind": "instance", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.compactOpen_eq", "kind": "theorem", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.isOpen_setOf_mapsTo", "kind": "theorem", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.eventually_mapsTo", "kind": "theorem", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.nhds_compactOpen", "kind": "theorem", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": true, "tactics": ["simp_rw", "biInf_prod,"], "tactic_count": 2}
{"name": "ContinuousMap.tendsto_nhds_compactOpen", "kind": "theorem", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousMap.continuous_compactOpen", "kind": "theorem", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.hasBasis_nhds", "kind": "theorem", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": true, "tactics": ["refine", "simp_rw", "simp"], "tactic_count": 3}
{"name": "ContinuousMap.mem_nhds_iff", "kind": "theorem", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.HasBasis.nhds_continuousMapConst", "kind": "theorem", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": true, "tactics": ["refine", "rcases", "choose", "have", "simp", "rintro", "exact", "rcases", "refine", "intro", "rcases", "exact", "refine", "exact", "rcases", "filter_upwards", "mem_interior_iff_mem_nhds.mpr", "f", "exact"], "tactic_count": 19}
{"name": "ContinuousMap.continuous_postcomp", "kind": "theorem", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.isInducing_postcomp", "kind": "theorem", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.isEmbedding_postcomp", "kind": "theorem", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.continuous_precomp", "kind": "theorem", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.compRightContinuousMap", "kind": "definition", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.arrowCongr", "kind": "definition", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.continuous_prodMk_const", "kind": "theorem", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": true, "tactics": ["simp_rw", "rintro", "obtain", "generalized_tube_lemma", "refine", "rintro", "exact"], "tactic_count": 7}
{"name": "ContinuousMap.continuous_comp'", "kind": "theorem", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": true, "tactics": ["simp_rw", "intro", "obtain", "exists_mem_nhdsSet_isCompact_mapsTo", "rw", "exact", "hg'.comp"], "tactic_count": 7}
{"name": "Filter.Tendsto.compCM", "kind": "theorem", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.compCM", "kind": "theorem", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.compCM", "kind": "theorem", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.compCM", "kind": "theorem", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.compCM", "kind": "theorem", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instContinuousEvalOfLocallyCompactPair", "kind": "instance", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instContinuousEvalConst", "kind": "instance", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.isClosed_setOf_mapsTo", "kind": "theorem", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.isClopen_setOf_mapsTo", "kind": "theorem", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.specializes_coe", "kind": "theorem", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": true, "tactics": ["refine", "suffices", "simpa", "exact"], "tactic_count": 4}
{"name": "ContinuousMap.inseparable_coe", "kind": "theorem", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousMap.instT0Space", "kind": "instance", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instR0Space", "kind": "instance", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instT1Space", "kind": "instance", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instR1Space", "kind": "instance", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instT2Space", "kind": "instance", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instRegularSpace", "kind": "instance", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instT3Space", "kind": "instance", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.homeoFnOfDiscrete", "kind": "definition", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.coe_homeoFnOfDiscrete", "kind": "theorem", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.homeoFnOfDiscrete_symm_apply", "kind": "theorem", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.isHomeomorph_coe", "kind": "theorem", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.continuous_restrict", "kind": "theorem", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.compactOpen_le_induced", "kind": "theorem", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.compactOpen_eq_iInf_induced", "kind": "theorem", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": true, "tactics": ["refine", "refine", "refine", "convert", "simp"], "tactic_count": 5}
{"name": "ContinuousMap.nhds_compactOpen_eq_iInf_nhds_induced", "kind": "theorem", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "ContinuousMap.tendsto_compactOpen_restrict", "kind": "theorem", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.tendsto_compactOpen_iff_forall", "kind": "theorem", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "ContinuousMap.exists_tendsto_compactOpen_iff_forall", "kind": "theorem", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "exact", "intro", "choose", "have", "f", "rintro", "haveI", "haveI", "have", "have", "exact", "refine", "rw", "intro", "rw", "exact"], "tactic_count": 18}
{"name": "ContinuousMap.coev", "kind": "definition", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.image_coev", "kind": "theorem", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousMap.continuous_coev", "kind": "theorem", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.curry", "kind": "definition", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.curry_apply", "kind": "theorem", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.continuous_of_continuous_uncurry", "kind": "theorem", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.continuousOn_of_continuousOn_uncurry", "kind": "theorem", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.continuous_curry", "kind": "theorem", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": true, "tactics": ["apply", "apply", "rw", "exact"], "tactic_count": 4}
{"name": "ContinuousMap.continuous_uncurry_of_continuous", "kind": "theorem", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.uncurry", "kind": "definition", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.continuous_uncurry", "kind": "theorem", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": true, "tactics": ["apply", "rw", "dsimp", "exact"], "tactic_count": 4}
{"name": "ContinuousMap.const'", "kind": "definition", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.coe_const'", "kind": "theorem", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.continuous_const'", "kind": "theorem", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.continuous_mkD_of_uncurry", "kind": "theorem", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": true, "tactics": ["have", "refine", "conv", "exact"], "tactic_count": 4}
{"name": "ContinuousMap.continuousOn_mkD_of_uncurry", "kind": "theorem", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": false, "tactics": ["have", "simp_rw", "refine", "conv", "exact"], "tactic_count": 5}
{"name": "ContinuousMap.continuous_mkD_restrict_of_uncurry", "kind": "theorem", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": false, "tactics": ["have", "refine", "conv", "exact"], "tactic_count": 4}
{"name": "ContinuousMap.continuousOn_mkD_restrict_of_uncurry", "kind": "theorem", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": false, "tactics": ["have", "f_cont.comp", "simp_rw", "refine", "conv", "exact"], "tactic_count": 6}
{"name": "Homeomorph.curry", "kind": "definition", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.continuousMapOfUnique", "kind": "definition", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.continuousMapOfUnique_apply", "kind": "theorem", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.continuousMapOfUnique_symm_apply", "kind": "theorem", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsQuotientMap.continuous_lift_prod_left", "kind": "theorem", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": true, "tactics": ["let", "have", "intro", "obtain", "exact", "let", "have", "rw", "exact", "exact"], "tactic_count": 10}
{"name": "Topology.IsQuotientMap.continuous_lift_prod_right", "kind": "theorem", "module": "Mathlib.Topology.CompactOpen", "is_tactic_proof": true, "tactics": ["have", "have", "exact"], "tactic_count": 3}
{"name": "OnePoint", "kind": "definition", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instReprOnePoint", "kind": "instance", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.infty", "kind": "definition", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.term∞", "kind": "definition", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint._aux_Mathlib_Topology_Compactification_OnePoint_Basic___macroRules_OnePoint_term∞_1", "kind": "definition", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint._aux_Mathlib_Topology_Compactification_OnePoint_Basic___unexpand_OnePoint_infty_1", "kind": "definition", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.some", "kind": "definition", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.some_eq_iff", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "OnePoint.instCoeTC", "kind": "instance", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.instInhabited", "kind": "instance", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.forall", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.exists", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.instFintype", "kind": "instance", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.infinite", "kind": "instance", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.coe_injective", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.coe_eq_coe", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.coe_ne_infty", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.infty_ne_coe", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.rec", "kind": "definition", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.elim", "kind": "definition", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.elim_infty", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.elim_some", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.isCompl_range_coe_infty", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.range_coe_union_infty", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.insert_infty_range_coe", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.range_coe_inter_infty", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "OnePoint.compl_range_coe", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.compl_infty", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.compl_image_coe", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "OnePoint.ne_infty_iff_exists", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "OnePoint.canLift", "kind": "instance", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.notMem_range_coe_iff", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "OnePoint.infty_notMem_range_coe", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.infty_notMem_image_coe", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.coe_preimage_infty", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "OnePoint.map", "kind": "definition", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.map_infty", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.map_some", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.map_id", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.map_comp", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.instTopologicalSpace", "kind": "instance", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.isOpen_def", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.isOpen_iff_of_mem'", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "OnePoint.isOpen_iff_of_mem", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "OnePoint.isOpen_iff_of_notMem", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "OnePoint.isClosed_iff_of_mem", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "OnePoint.isClosed_iff_of_notMem", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "OnePoint.isOpen_image_coe", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "OnePoint.isOpen_compl_image_coe", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "OnePoint.isClosed_image_coe", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "OnePoint.opensOfCompl", "kind": "definition", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.infty_mem_opensOfCompl", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.continuous_coe", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.isOpenMap_coe", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.isOpenEmbedding_coe", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.isOpen_range_coe", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.isClosed_infty", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "OnePoint.nhds_coe_eq", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.nhdsWithin_coe_image", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.nhdsWithin_coe", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.comap_coe_nhds", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.nhdsNE_coe_neBot", "kind": "instance", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "OnePoint.nhdsNE_infty_eq", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": true, "tactics": ["refine", "rintro", "refine", "simp", "rintro", "refine", "simp"], "tactic_count": 7}
{"name": "OnePoint.nhdsNE_infty_neBot", "kind": "instance", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "OnePoint.nhdsNE_neBot", "kind": "instance", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.nhds_infty_eq", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "OnePoint.tendsto_coe_infty", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "OnePoint.hasBasis_nhds_infty", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "OnePoint.comap_coe_nhds_infty", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "OnePoint.le_nhds_infty", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "OnePoint.ultrafilter_le_nhds_infty", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "OnePoint.tendsto_nhds_infty'", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "OnePoint.tendsto_nhds_infty", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.continuousAt_infty'", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.continuousAt_infty", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.continuousAt_coe", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "OnePoint.continuous_iff", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "OnePoint.continuousMapMk", "kind": "definition", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.continuous_iff_from_discrete", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "OnePoint.continuousMapMkDiscrete", "kind": "definition", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.continuousMapDiscreteEquiv", "kind": "definition", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.continuous_iff_from_nat", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "OnePoint.continuousMapMkNat", "kind": "definition", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.continuousMapNatEquiv", "kind": "definition", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": true, "tactics": ["refine", "invFun"], "tactic_count": 2}
{"name": "OnePoint.denseRange_coe", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "OnePoint.isDenseEmbedding_coe", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.specializes_coe", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.inseparable_coe", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.not_specializes_infty_coe", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.not_inseparable_infty_coe", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.not_inseparable_coe_infty", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.inseparable_iff", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": true, "tactics": ["induction", "simp"], "tactic_count": 2}
{"name": "OnePoint.continuous_map_iff", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": ["simp_rw", "isOpenEmbedding_coe.isInducing.continuous_iff", "exact"], "tactic_count": 3}
{"name": "OnePoint.continuous_map", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.instCompactSpace", "kind": "instance", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.instT0Space", "kind": "instance", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": true, "tactics": ["refine", "rcases", "exacts"], "tactic_count": 3}
{"name": "OnePoint.instT1Space", "kind": "instance", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.instNormalSpaceOfWeaklyLocallyCompactSpaceOfR1Space", "kind": "instance", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": true, "tactics": ["suffices", "have", "rw", "principal_singleton,", "exact", "refine", "induction", "exact", "exact", "exact", "rw", "apply"], "tactic_count": 12}
{"name": "OnePoint._example", "kind": "example", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.instConnectedSpaceOfPreconnectedSpaceOfNoncompactSpace", "kind": "instance", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.not_continuous_cofiniteTopology_of_symm", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": true, "tactics": ["inhabit", "simp", "use", "simpa"], "tactic_count": 4}
{"name": "OnePoint.instTotallySeparatedSpaceOfDiscreteTopology", "kind": "instance", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.equivOfIsEmbeddingOfRangeEq", "kind": "definition", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.equivOfIsEmbeddingOfRangeEq_apply_coe", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.equivOfIsEmbeddingOfRangeEq_apply_infty", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.onePointCongr", "kind": "definition", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.homeoOfEquivCompactToT2.t1_counterexample", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instModuleMatrixFinOfNatNatProd", "kind": "instance", "module": "Mathlib.Topology.Compactification.OnePoint.ProjectiveLine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instSMulCommClassMatrixFinOfNatNatProd", "kind": "instance", "module": "Mathlib.Topology.Compactification.OnePoint.ProjectiveLine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.fin_two_smul_prod", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.ProjectiveLine", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Matrix.GeneralLinearGroup.fin_two_smul_prod", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.ProjectiveLine", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "OnePoint.equivProjectivization", "kind": "definition", "module": "Mathlib.Topology.Compactification.OnePoint.ProjectiveLine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.equivProjectivization_apply_infinity", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.ProjectiveLine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.equivProjectivization_apply_coe", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.ProjectiveLine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.equivProjectivization_symm_apply_mk", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.ProjectiveLine", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "OnePoint.instGLAction", "kind": "instance", "module": "Mathlib.Topology.Compactification.OnePoint.ProjectiveLine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OnePoint.smul_infty_def", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.ProjectiveLine", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "OnePoint.smul_infty_eq_ite", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.ProjectiveLine", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "OnePoint.smul_infty_eq_self_iff", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.ProjectiveLine", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "OnePoint.smul_some_eq_ite", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.ProjectiveLine", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "OnePoint.map_smul", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.ProjectiveLine", "is_tactic_proof": true, "tactics": ["cases", "infty", "coe"], "tactic_count": 3}
{"name": "Matrix.GeneralLinearGroup.fixpointPolynomial_aeval_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.ProjectiveLine", "is_tactic_proof": false, "tactics": ["simp", "split_ifs", "refine", "rw", "grind", "rw", "grind"], "tactic_count": 7}
{"name": "Matrix.GeneralLinearGroup.parabolicFixedPoint", "kind": "definition", "module": "Mathlib.Topology.Compactification.OnePoint.ProjectiveLine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.GeneralLinearGroup.IsParabolic.smul_eq_self_iff", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.ProjectiveLine", "is_tactic_proof": true, "tactics": ["rcases", "rw", "cases", "infty", "coe", "c", "suffices", "simpa", "by_cases", "have", "suffices", "simpa", "refine", "simp", "have", "simpa", "quadratic_eq_zero_iff_of_discrim_eq_zero"], "tactic_count": 17}
{"name": "Matrix.GeneralLinearGroup.IsParabolic.parabolicFixedPoint_pow", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.ProjectiveLine", "is_tactic_proof": true, "tactics": ["rw", "clear", "induction", "zero", "succ"], "tactic_count": 5}
{"name": "Matrix.GeneralLinearGroup.IsElliptic.smul_ne_self", "kind": "theorem", "module": "Mathlib.Topology.Compactification.OnePoint.ProjectiveLine", "is_tactic_proof": true, "tactics": ["cases", "infty", "rw", "refine", "have", "simp", "grind", "rw", "apply", "coe", "refine", "have", "replace", "simpa", "simp", "grind", "rw", "apply"], "tactic_count": 18}
{"name": "onePointHyperplaneHomeoUnitSphere", "kind": "definition", "module": "Mathlib.Topology.Compactification.OnePoint.Sphere", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "onePointEquivSphereOfFinrankEq", "kind": "definition", "module": "Mathlib.Topology.Compactification.OnePoint.Sphere", "is_tactic_proof": true, "tactics": ["classical", "have", "let", "have", "have", "have", "have", "letI", "exact"], "tactic_count": 9}
{"name": "ultrafilterBasis", "kind": "definition", "module": "Mathlib.Topology.Compactification.StoneCech", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ultrafilter.topologicalSpace", "kind": "instance", "module": "Mathlib.Topology.Compactification.StoneCech", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ultrafilterBasis_is_basis", "kind": "theorem", "module": "Mathlib.Topology.Compactification.StoneCech", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ultrafilter_isOpen_basic", "kind": "theorem", "module": "Mathlib.Topology.Compactification.StoneCech", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ultrafilter_isClosed_basic", "kind": "theorem", "module": "Mathlib.Topology.Compactification.StoneCech", "is_tactic_proof": true, "tactics": ["rw", "convert", "ext", "exact"], "tactic_count": 4}
{"name": "ultrafilter_converges_iff", "kind": "theorem", "module": "Mathlib.Topology.Compactification.StoneCech", "is_tactic_proof": true, "tactics": ["rw", "change", "simp", "constructor", "intro", "exact", "rintro", "exact"], "tactic_count": 8}
{"name": "ultrafilter_compact", "kind": "instance", "module": "Mathlib.Topology.Compactification.StoneCech", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ultrafilter.t2Space", "kind": "instance", "module": "Mathlib.Topology.Compactification.StoneCech", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instTotallyDisconnectedSpaceUltrafilter", "kind": "instance", "module": "Mathlib.Topology.Compactification.StoneCech", "is_tactic_proof": true, "tactics": ["rw", "intro", "simp", "intro", "rw", "intro", "rw", "let", "have", "exact"], "tactic_count": 10}
{"name": "Ultrafilter.tendsto_pure_self", "kind": "theorem", "module": "Mathlib.Topology.Compactification.StoneCech", "is_tactic_proof": true, "tactics": ["rw", "ext", "change", "simp_rw"], "tactic_count": 4}
{"name": "ultrafilter_comap_pure_nhds", "kind": "theorem", "module": "Mathlib.Topology.Compactification.StoneCech", "is_tactic_proof": true, "tactics": ["rw", "simp", "intro", "rw", "refine", "refine", "exact"], "tactic_count": 7}
{"name": "denseRange_pure", "kind": "theorem", "module": "Mathlib.Topology.Compactification.StoneCech", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "induced_topology_pure", "kind": "theorem", "module": "Mathlib.Topology.Compactification.StoneCech", "is_tactic_proof": true, "tactics": ["apply", "intro", "use", "simp"], "tactic_count": 4}
{"name": "isDenseInducing_pure", "kind": "theorem", "module": "Mathlib.Topology.Compactification.StoneCech", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isDenseEmbedding_pure", "kind": "theorem", "module": "Mathlib.Topology.Compactification.StoneCech", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ultrafilter.extend", "kind": "definition", "module": "Mathlib.Topology.Compactification.StoneCech", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ultrafilter_extend_extends", "kind": "theorem", "module": "Mathlib.Topology.Compactification.StoneCech", "is_tactic_proof": true, "tactics": ["letI", "haveI", "exact"], "tactic_count": 3}
{"name": "ultrafilter_extend_pure", "kind": "theorem", "module": "Mathlib.Topology.Compactification.StoneCech", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_ultrafilter_extend", "kind": "theorem", "module": "Mathlib.Topology.Compactification.StoneCech", "is_tactic_proof": false, "tactics": ["have", "let", "let", "exact"], "tactic_count": 4}
{"name": "ultrafilter_extend_eq_iff", "kind": "theorem", "module": "Mathlib.Topology.Compactification.StoneCech", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PreStoneCech", "kind": "definition", "module": "Mathlib.Topology.Compactification.StoneCech", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instTopologicalSpacePreStoneCech", "kind": "instance", "module": "Mathlib.Topology.Compactification.StoneCech", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCompactSpacePreStoneCech", "kind": "instance", "module": "Mathlib.Topology.Compactification.StoneCech", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInhabitedPreStoneCech", "kind": "instance", "module": "Mathlib.Topology.Compactification.StoneCech", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "preStoneCechUnit", "kind": "definition", "module": "Mathlib.Topology.Compactification.StoneCech", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_preStoneCechUnit", "kind": "theorem", "module": "Mathlib.Topology.Compactification.StoneCech", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "denseRange_preStoneCechUnit", "kind": "theorem", "module": "Mathlib.Topology.Compactification.StoneCech", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "preStoneCech_hom_ext", "kind": "theorem", "module": "Mathlib.Topology.Compactification.StoneCech", "is_tactic_proof": true, "tactics": ["apply", "rintro", "apply"], "tactic_count": 3}
{"name": "preStoneCechCompat", "kind": "theorem", "module": "Mathlib.Topology.Compactification.StoneCech", "is_tactic_proof": true, "tactics": ["replace", "replace", "rwa"], "tactic_count": 3}
{"name": "preStoneCechExtend", "kind": "definition", "module": "Mathlib.Topology.Compactification.StoneCech", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "preStoneCechExtend_extends", "kind": "theorem", "module": "Mathlib.Topology.Compactification.StoneCech", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "preStoneCechExtend_preStoneCechUnit", "kind": "theorem", "module": "Mathlib.Topology.Compactification.StoneCech", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_if_preStoneCechUnit_eq", "kind": "theorem", "module": "Mathlib.Topology.Compactification.StoneCech", "is_tactic_proof": true, "tactics": ["have", "rw", "rw", "generalize", "generalize", "induction", "rel", "exact", "let", "preStoneCechCompat", "refl", "symm", "trans"], "tactic_count": 13}
{"name": "continuous_preStoneCechExtend", "kind": "theorem", "module": "Mathlib.Topology.Compactification.StoneCech", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StoneCech", "kind": "definition", "module": "Mathlib.Topology.Compactification.StoneCech", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instTopologicalSpaceStoneCech", "kind": "instance", "module": "Mathlib.Topology.Compactification.StoneCech", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instT2SpaceStoneCech", "kind": "instance", "module": "Mathlib.Topology.Compactification.StoneCech", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCompactSpaceStoneCech", "kind": "instance", "module": "Mathlib.Topology.Compactification.StoneCech", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInhabitedStoneCech", "kind": "instance", "module": "Mathlib.Topology.Compactification.StoneCech", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "stoneCechUnit", "kind": "definition", "module": "Mathlib.Topology.Compactification.StoneCech", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_stoneCechUnit", "kind": "theorem", "module": "Mathlib.Topology.Compactification.StoneCech", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "denseRange_stoneCechUnit", "kind": "theorem", "module": "Mathlib.Topology.Compactification.StoneCech", "is_tactic_proof": true, "tactics": ["unfold", "have", "exact"], "tactic_count": 3}
{"name": "stoneCech_hom_ext", "kind": "theorem", "module": "Mathlib.Topology.Compactification.StoneCech", "is_tactic_proof": true, "tactics": ["apply", "rintro", "exact"], "tactic_count": 3}
{"name": "stoneCechExtend", "kind": "definition", "module": "Mathlib.Topology.Compactification.StoneCech", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "stoneCechExtend_extends", "kind": "theorem", "module": "Mathlib.Topology.Compactification.StoneCech", "is_tactic_proof": true, "tactics": ["ext", "rw", "apply"], "tactic_count": 3}
{"name": "stoneCechExtend_stoneCechUnit", "kind": "theorem", "module": "Mathlib.Topology.Compactification.StoneCech", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_stoneCechExtend", "kind": "theorem", "module": "Mathlib.Topology.Compactification.StoneCech", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_if_stoneCechUnit_eq", "kind": "theorem", "module": "Mathlib.Topology.Compactification.StoneCech", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "eq_finite_iUnion_of_isTopologicalBasis_of_isCompact_open", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Bases", "is_tactic_proof": true, "tactics": ["obtain", "choose", "have", "subst", "obtain", "classical", "refine", "refine", "simp", "intro", "simpa", "apply", "rintro", "obtain", "rw", "exact"], "tactic_count": 16}
{"name": "eq_sUnion_finset_of_isTopologicalBasis_of_isCompact_open", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Bases", "is_tactic_proof": true, "tactics": ["have", "rw", "choose", "have", "let", "use", "simp"], "tactic_count": 7}
{"name": "isCompact_open_iff_eq_finite_iUnion_of_isTopologicalBasis", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Bases", "is_tactic_proof": true, "tactics": ["constructor", "exact", "rintro", "constructor", "exact", "exact"], "tactic_count": 6}
{"name": "IsCompact.exists_clusterPt", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.exists_mapClusterPt", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.exists_clusterPt_of_frequently", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.exists_mapClusterPt_of_frequently", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.compl_mem_sets", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["contrapose", "simp", "exact"], "tactic_count": 3}
{"name": "IsCompact.compl_mem_sets_of_nhdsWithin", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["refine", "rcases", "replace", "apply", "rintro", "exact"], "tactic_count": 6}
{"name": "IsCompact.induction_on", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["let", "have", "rwa"], "tactic_count": 3}
{"name": "IsCompact.inter_right", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["intro", "obtain", "have", "exact"], "tactic_count": 4}
{"name": "IsCompact.inter_left", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.diff", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.of_isClosed_subset", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.image_of_continuousOn", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["intro", "have", "obtain", "haveI", "use", "have", "convert", "rw", "ac_rfl", "exact"], "tactic_count": 10}
{"name": "IsCompact.image", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.adherence_nhdset", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCompact_iff_ultrafilter_le_nhds", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["refine", "rintro", "exact", "simp"], "tactic_count": 4}
{"name": "isCompact_iff_ultrafilter_le_nhds'", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsCompact.le_nhds_of_unique_clusterPt", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["refine", "rcases", "convert", "exact"], "tactic_count": 4}
{"name": "IsCompact.tendsto_nhds_of_unique_mapClusterPt", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.elim_directed_cover", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.elim_finite_subcover", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.elim_nhds_subcover_nhdsSet'", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": ["rcases", "hs.elim_finite_subcover", "mem_iUnion.2", "refine", "rcases", "refine", "exact"], "tactic_count": 7}
{"name": "IsCompact.elim_nhds_subcover_nhdsSet", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["let", "classical", "exact", "let", "hyx"], "tactic_count": 5}
{"name": "IsCompact.elim_nhds_subcover'", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.elim_nhds_subcover", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.elim_nhdsWithin_subcover'", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["choose", "refine", "simpa"], "tactic_count": 3}
{"name": "IsCompact.elim_nhdsWithin_subcover", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["choose", "refine", "simpa"], "tactic_count": 3}
{"name": "IsCompact.disjoint_nhdsSet_left", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["refine", "choose", "choose", "rcases", "refine", "rw", "exact"], "tactic_count": 7}
{"name": "IsCompact.disjoint_nhdsSet_right", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsCompact.elim_directed_family_closed", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.elim_finite_subfamily_closed", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.inter_iInter_nonempty", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["contrapose", "exact"], "tactic_count": 2}
{"name": "IsCompact.nonempty_iInter_of_directed_nonempty_isCompact_isClosed", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["let", "suffices", "simp", "apply", "push_neg", "simp", "refine", "rcases", "exact"], "tactic_count": 9}
{"name": "IsCompact.nonempty_sInter_of_directed_nonempty_isCompact_isClosed", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsCompact.nonempty_iInter_of_sequence_nonempty_isCompact_isClosed", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.elim_finite_subcover_image", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["simp", "rcases", "refine", "simp", "rwa"], "tactic_count": 5}
{"name": "isCompact_of_finite_subcover", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCompact_of_finite_subfamily_closed", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCompact_iff_finite_subcover", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCompact_iff_finite_subfamily_closed", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.mem_nhdsSet_prod_of_forall", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["refine", "exact", "simp", "rcases", "refine", "exact"], "tactic_count": 6}
{"name": "IsCompact.nhdsSet_prod_eq_biSup", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.prod_nhdsSet_eq_biSup", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsCompact.mem_prod_nhdsSet_of_forall", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.nhdsSet_inf_eq_biSup", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": ["have", "simpa", "simp_rw"], "tactic_count": 3}
{"name": "IsCompact.inf_nhdsSet_eq_biSup", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsCompact.mem_nhdsSet_inf_of_forall", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.mem_inf_nhdsSet_of_forall", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.eventually_forall_of_forall_eventually", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "isCompact_empty", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCompact_singleton", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Subsingleton.isCompact", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.isCompact_biUnion", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.isCompact_biUnion", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCompact_accumulate", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.isCompact_sUnion", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "isCompact_iUnion", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.isCompact", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.sUnion_isCompact_eq_univ", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.finite_of_discrete", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["have", "rcases", "simp", "exact"], "tactic_count": 4}
{"name": "isCompact_iff_finite", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.union", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsCompact.insert", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_subset_nhds_of_isCompact'", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["obtain", "suffices", "by_contra", "replace", "have", "refine", "rcases", "refine", "have", "contradiction"], "tactic_count": 10}
{"name": "isCompact_generateFrom", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["rw", "intro", "by_contra", "have", "choose", "obtain", "h", "have", "have", "have", "exact"], "tactic_count": 11}
{"name": "isCompact_generateFrom'", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.hasBasis_cocompact", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_cocompact", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_cocompact'", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.compl_mem_cocompact", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.cocompact_le_cofinite", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.cocompact_eq_cofinite", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.disjoint_cocompact_left", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["simp_rw", "tauto"], "tactic_count": 2}
{"name": "Filter.disjoint_cocompact_right", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["simp_rw", "tauto"], "tactic_count": 2}
{"name": "Filter.Tendsto.isCompact_insert_range_of_cocompact", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["intro", "by_cases", "exact", "simp", "rcases", "rcases", "have", "filter_upwards", "rcases", "exacts", "mem_image_of_mem", "rcases", "exact"], "tactic_count": 13}
{"name": "Filter.Tendsto.isCompact_insert_range_of_cofinite", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["letI", "rw", "exact"], "tactic_count": 3}
{"name": "Filter.Tendsto.isCompact_insert_range", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.hasBasis_coclosedCompact", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["simp", "refine", "rintro", "exact"], "tactic_count": 4}
{"name": "Filter.mem_coclosedCompact_iff", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["refine", "rintro", "exact", "exact"], "tactic_count": 4}
{"name": "Filter.compl_mem_coclosedCompact", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.cocompact_le_coclosedCompact", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.compl_mem_coclosedCompact_of_isClosed", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.inCompact", "kind": "definition", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.inCompact.isBounded_iff", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["change", "rw", "simp"], "tactic_count": 3}
{"name": "IsCompact.nhdsSet_prod_eq", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "nhdsSet_prod_le_of_disjoint_cocompact", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["obtain", "calc"], "tactic_count": 2}
{"name": "prod_nhdsSet_le_of_disjoint_cocompact", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["obtain", "calc", "f"], "tactic_count": 3}
{"name": "nhds_prod_le_of_disjoint_cocompact", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "prod_nhds_le_of_disjoint_cocompact", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "generalized_tube_lemma", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["rw", "rcases", "exact"], "tactic_count": 3}
{"name": "IsCompact.nhdsSetWithin_prod_eq", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "generalized_tube_lemma'", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "generalized_tube_lemma_left", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "generalized_tube_lemma_right", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["rw", "obtain", "exact"], "tactic_count": 3}
{"name": "Subsingleton.compactSpace", "kind": "instance", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCompact_univ_iff", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCompact_univ", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_clusterPt_of_compactSpace", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Ultrafilter.le_nhds_lim", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompactSpace.elim_nhds_subcover", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "compactSpace_of_finite_subfamily_closed", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompactSpace.iInter_nonempty", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "compactSpace_generateFrom", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "compactSpace_generateFrom'", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.isCompact", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_nhds_of_unique_clusterPt", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_nhds_of_unique_mapClusterPt", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "noncompact_univ", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.ne_univ", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instNeBotCocompactOfNoncompactSpace", "kind": "instance", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["refine", "contrapose", "rw"], "tactic_count": 3}
{"name": "Filter.cocompact_eq_bot", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instNeBotCoclosedCompactOfNoncompactSpace", "kind": "instance", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "noncompactSpace_of_neBot", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.cocompact_neBot_iff", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_compactSpace_iff", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instNoncompactSpaceInt", "kind": "instance", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finite_of_compact_of_discrete", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Infinite.exists_accPt_cofinite_inf_principal_of_subset_isCompact", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Infinite.exists_accPt_of_subset_isCompact", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Infinite.exists_accPt_cofinite_inf_principal", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["simpa", "hs.exists_accPt_cofinite_inf_principal_of_subset_isCompact"], "tactic_count": 2}
{"name": "Set.Infinite.exists_accPt_principal", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_nhds_ne_neBot", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "finite_cover_nhds_interior", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "finite_cover_nhds", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.comap_cocompact_le", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["rw", "intro", "refine", "simpa"], "tactic_count": 4}
{"name": "disjoint_map_cocompact", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["rw", "calc", "f"], "tactic_count": 3}
{"name": "isCompact_range", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "isCompact_diagonal", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_subset_nhds_of_compactSpace", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsInducing.isCompact_iff", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact"], "tactic_count": 3}
{"name": "Topology.IsEmbedding.isCompact_iff", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsInducing.isCompact_preimage", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["replace", "rwa"], "tactic_count": 2}
{"name": "Topology.IsInducing.isCompact_preimage_iff", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Topology.IsInducing.isCompact_preimage'", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsClosedEmbedding.isCompact_preimage", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsClosedEmbedding.tendsto_cocompact", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.isCompact_iff", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCompact_iff_isCompact_univ", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsCompact.elim_finite_subfamily_isClosed_subtype", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": ["suffices", "simpa", "simpa"], "tactic_count": 3}
{"name": "isCompact_iff_compactSpace", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.finite", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_nhds_ne_inf_principal_neBot", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsClosedEmbedding.noncompactSpace", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsClosedEmbedding.compactSpace", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.prod", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["rw", "intro", "obtain", "hs", "obtain", "ht", "rw", "refine", "rw"], "tactic_count": 9}
{"name": "Finite.compactSpace", "kind": "instance", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.compactSpace", "kind": "instance", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCompactSpaceProd", "kind": "instance", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCompactSpaceSum", "kind": "instance", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCompactSpaceSigmaOfFinite", "kind": "instance", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "Set.isCompact_sigma", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsCompact.sigma_exists_finite_sigma_eq", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": ["obtain", "hu.elim_finite_subcover", "use", "exact", "ext", "simp", "intro", "obtain", "simp_all"], "tactic_count": 9}
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{"name": "Prod.noncompactSpace_iff", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Prod.noncompactSpace_left", "kind": "instance", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.noncompactSpace_right", "kind": "instance", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCompact_pi_infinite", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["simp", "intro", "have", "refine", "exact", "choose", "exact"], "tactic_count": 7}
{"name": "isCompact_univ_pi", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "Pi.compactSpace", "kind": "instance", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.compactSpace", "kind": "instance", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.isCompact_iff_of_isClosed", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["constructor", "exact", "exact"], "tactic_count": 3}
{"name": "Pi.exists_compact_superset_iff", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "intro", "choose", "exact"], "tactic_count": 6}
{"name": "Filter.coprodᵢ_cocompact", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["refine", "refine", "simp", "choose", "exact"], "tactic_count": 5}
{"name": "Quot.compactSpace", "kind": "instance", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quotient.compactSpace", "kind": "instance", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.exists_minimal_nonempty_closed_subset", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Compact", "is_tactic_proof": true, "tactics": ["let", "obtain", "zorn_subset", "by_cases", "obtain", "haveI", "obtain", "use", "refine", "exact", "exact", "convert_to", "ext", "simp", "apply", "rintro", "obtain", "exact", "exact", "exact", "exact", "use", "refine", "rw", "exact", "obtain", "refine", "intro", "have", "refine", "exact", "simp", "rw"], "tactic_count": 33}
{"name": "CompactlyCoherentSpace.isOpen_iff", "kind": "theorem", "module": "Mathlib.Topology.Compactness.CompactlyCoherentSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompactlyCoherentSpace.isClosed_iff", "kind": "theorem", "module": "Mathlib.Topology.Compactness.CompactlyCoherentSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompactlyCoherentSpace.of_isOpen", "kind": "theorem", "module": "Mathlib.Topology.Compactness.CompactlyCoherentSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompactlyCoherentSpace.of_isClosed", "kind": "theorem", "module": "Mathlib.Topology.Compactness.CompactlyCoherentSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompactlyCoherentSpace.of_weaklyLocallyCompactSpace", "kind": "instance", "module": "Mathlib.Topology.Compactness.CompactlyCoherentSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompactlyCoherentSpace.of_sequentialSpace", "kind": "instance", "module": "Mathlib.Topology.Compactness.CompactlyCoherentSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompactlyCoherentSpace.isOpen_iff_forall_compactSpace", "kind": "theorem", "module": "Mathlib.Topology.Compactness.CompactlyCoherentSpace", "is_tactic_proof": true, "tactics": ["refine", "intro", "have", "exact"], "tactic_count": 4}
{"name": "CompactlyCoherentSpace.of_isOpen_forall_compactSpace", "kind": "theorem", "module": "Mathlib.Topology.Compactness.CompactlyCoherentSpace", "is_tactic_proof": true, "tactics": ["refine", "specialize", "have", "rwa"], "tactic_count": 4}
{"name": "TopologicalSpace.compactlyGenerated", "kind": "definition", "module": "Mathlib.Topology.Compactness.CompactlyGeneratedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_from_compactlyGenerated", "kind": "theorem", "module": "Mathlib.Topology.Compactness.CompactlyGeneratedSpace", "is_tactic_proof": true, "tactics": ["rw", "continuity"], "tactic_count": 2}
{"name": "eq_compactlyGenerated", "kind": "theorem", "module": "Mathlib.Topology.Compactness.CompactlyGeneratedSpace", "is_tactic_proof": true, "tactics": ["apply", "exact", "simp", "exact"], "tactic_count": 4}
{"name": "instUCompactlyGeneratedSpaceOfDiscreteTopology", "kind": "instance", "module": "Mathlib.Topology.Compactness.CompactlyGeneratedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uCompactlyGeneratedSpace_of_continuous_maps", "kind": "theorem", "module": "Mathlib.Topology.Compactness.CompactlyGeneratedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_from_uCompactlyGeneratedSpace", "kind": "theorem", "module": "Mathlib.Topology.Compactness.CompactlyGeneratedSpace", "is_tactic_proof": true, "tactics": ["apply", "exact"], "tactic_count": 2}
{"name": "uCompactlyGeneratedSpace_of_isClosed", "kind": "theorem", "module": "Mathlib.Topology.Compactness.CompactlyGeneratedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uCompactlyGeneratedSpace_of_isOpen", "kind": "theorem", "module": "Mathlib.Topology.Compactness.CompactlyGeneratedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UCompactlyGeneratedSpace.isClosed", "kind": "theorem", "module": "Mathlib.Topology.Compactness.CompactlyGeneratedSpace", "is_tactic_proof": false, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "UCompactlyGeneratedSpace.isOpen", "kind": "theorem", "module": "Mathlib.Topology.Compactness.CompactlyGeneratedSpace", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "uCompactlyGeneratedSpace_of_coinduced", "kind": "theorem", "module": "Mathlib.Topology.Compactness.CompactlyGeneratedSpace", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "instUCompactlyGeneratedSpaceQuotient", "kind": "instance", "module": "Mathlib.Topology.Compactness.CompactlyGeneratedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instUCompactlyGeneratedSpaceSum", "kind": "instance", "module": "Mathlib.Topology.Compactness.CompactlyGeneratedSpace", "is_tactic_proof": true, "tactics": ["refine", "all_goals", "let", "have", "exact", "let", "have", "exact"], "tactic_count": 8}
{"name": "instUCompactlyGeneratedSpaceSigma", "kind": "instance", "module": "Mathlib.Topology.Compactness.CompactlyGeneratedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instUCompactlyGeneratedSpaceOfSequentialSpace", "kind": "instance", "module": "Mathlib.Topology.Compactness.CompactlyGeneratedSpace", "is_tactic_proof": true, "tactics": ["refine", "let", "change", "have", "rw", "exact", "apply", "simp", "exact", "exact"], "tactic_count": 10}
{"name": "CompactlyGeneratedSpace", "kind": "abbrev", "module": "Mathlib.Topology.Compactness.CompactlyGeneratedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_from_compactlyGeneratedSpace", "kind": "theorem", "module": "Mathlib.Topology.Compactness.CompactlyGeneratedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "compactlyGeneratedSpace_of_continuous_maps", "kind": "theorem", "module": "Mathlib.Topology.Compactness.CompactlyGeneratedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "compactlyGeneratedSpace_of_isClosed", "kind": "theorem", "module": "Mathlib.Topology.Compactness.CompactlyGeneratedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompactlyGeneratedSpace.isClosed'", "kind": "theorem", "module": "Mathlib.Topology.Compactness.CompactlyGeneratedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompactlyGeneratedSpace.isClosed", "kind": "theorem", "module": "Mathlib.Topology.Compactness.CompactlyGeneratedSpace", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "compactlyGeneratedSpace_of_isOpen", "kind": "theorem", "module": "Mathlib.Topology.Compactness.CompactlyGeneratedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompactlyGeneratedSpace.isOpen'", "kind": "theorem", "module": "Mathlib.Topology.Compactness.CompactlyGeneratedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompactlyGeneratedSpace.isOpen", "kind": "theorem", "module": "Mathlib.Topology.Compactness.CompactlyGeneratedSpace", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "compactlyGeneratedSpace_of_coinduced", "kind": "theorem", "module": "Mathlib.Topology.Compactness.CompactlyGeneratedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCompactlyGeneratedSpaceSigma", "kind": "instance", "module": "Mathlib.Topology.Compactness.CompactlyGeneratedSpace", "is_tactic_proof": false, "tactics": ["refine", "compactlyGeneratedSpace_of_isClosed", "isClosed_sigma_iff.2", "let", "have", "exact"], "tactic_count": 6}
{"name": "CompactlyGeneratedSpace.isClosed_iff_of_t2", "kind": "theorem", "module": "Mathlib.Topology.Compactness.CompactlyGeneratedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "compactlyGeneratedSpace_of_isClosed_of_t2", "kind": "theorem", "module": "Mathlib.Topology.Compactness.CompactlyGeneratedSpace", "is_tactic_proof": true, "tactics": ["refine", "rw", "apply", "have", "exact"], "tactic_count": 5}
{"name": "compactlyGeneratedSpace_of_isOpen_of_t2", "kind": "theorem", "module": "Mathlib.Topology.Compactness.CompactlyGeneratedSpace", "is_tactic_proof": true, "tactics": ["refine", "have", "exact"], "tactic_count": 3}
{"name": "instCompactlyGeneratedSpaceOfWeaklyLocallyCompactSpace", "kind": "instance", "module": "Mathlib.Topology.Compactness.CompactlyGeneratedSpace", "is_tactic_proof": true, "tactics": ["refine", "rw", "intro", "rcases", "exact", "isClosed_iff_forall_filter.1"], "tactic_count": 6}
{"name": "to_compactlyCoherentSpace", "kind": "instance", "module": "Mathlib.Topology.Compactness.CompactlyGeneratedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "of_compactlyCoherentSpace_of_t2", "kind": "instance", "module": "Mathlib.Topology.Compactness.CompactlyGeneratedSpace", "is_tactic_proof": true, "tactics": ["apply", "intro", "rw", "intro", "rw", "exact"], "tactic_count": 6}
{"name": "TopologicalSpace.deltaGenerated", "kind": "definition", "module": "Mathlib.Topology.Compactness.DeltaGeneratedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "deltaGenerated_eq_coinduced", "kind": "theorem", "module": "Mathlib.Topology.Compactness.DeltaGeneratedSpace", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "deltaGenerated_le", "kind": "theorem", "module": "Mathlib.Topology.Compactness.DeltaGeneratedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpen_deltaGenerated_iff", "kind": "theorem", "module": "Mathlib.Topology.Compactness.DeltaGeneratedSpace", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "_private.Mathlib.Topology.Compactness.DeltaGeneratedSpace.0.continuous_euclidean_to_deltaGenerated", "kind": "theorem", "module": "Mathlib.Topology.Compactness.DeltaGeneratedSpace", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "simp_rw", "exact"], "tactic_count": 4}
{"name": "deltaGenerated_deltaGenerated_eq", "kind": "theorem", "module": "Mathlib.Topology.Compactness.DeltaGeneratedSpace", "is_tactic_proof": true, "tactics": ["ext", "refine", "forall_congr", "refine", "exact", "exact"], "tactic_count": 6}
{"name": "eq_deltaGenerated", "kind": "theorem", "module": "Mathlib.Topology.Compactness.DeltaGeneratedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DeltaGeneratedSpace.isOpen_iff", "kind": "theorem", "module": "Mathlib.Topology.Compactness.DeltaGeneratedSpace", "is_tactic_proof": true, "tactics": ["nth_rewrite"], "tactic_count": 1}
{"name": "DeltaGeneratedSpace.continuous_iff", "kind": "theorem", "module": "Mathlib.Topology.Compactness.DeltaGeneratedSpace", "is_tactic_proof": true, "tactics": ["simp_rw", "nth_rewrite", "simp"], "tactic_count": 3}
{"name": "continuous_to_deltaGenerated", "kind": "theorem", "module": "Mathlib.Topology.Compactness.DeltaGeneratedSpace", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "deltaGeneratedSpace_deltaGenerated", "kind": "theorem", "module": "Mathlib.Topology.Compactness.DeltaGeneratedSpace", "is_tactic_proof": true, "tactics": ["let"], "tactic_count": 1}
{"name": "deltaGenerated_mono", "kind": "theorem", "module": "Mathlib.Topology.Compactness.DeltaGeneratedSpace", "is_tactic_proof": false, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "DeltaGeneratedSpace.of", "kind": "definition", "module": "Mathlib.Topology.Compactness.DeltaGeneratedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DeltaGeneratedSpace.instTopologicalSpaceOf", "kind": "instance", "module": "Mathlib.Topology.Compactness.DeltaGeneratedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DeltaGeneratedSpace.instOf", "kind": "instance", "module": "Mathlib.Topology.Compactness.DeltaGeneratedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DeltaGeneratedSpace.counit", "kind": "definition", "module": "Mathlib.Topology.Compactness.DeltaGeneratedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DeltaGeneratedSpace.continuous_counit", "kind": "theorem", "module": "Mathlib.Topology.Compactness.DeltaGeneratedSpace", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "DeltaGeneratedSpace.instLocPathConnectedSpace", "kind": "instance", "module": "Mathlib.Topology.Compactness.DeltaGeneratedSpace", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "DeltaGeneratedSpace.instSequentialSpace", "kind": "instance", "module": "Mathlib.Topology.Compactness.DeltaGeneratedSpace", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "DeltaGeneratedSpace.coinduced", "kind": "theorem", "module": "Mathlib.Topology.Compactness.DeltaGeneratedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DeltaGeneratedSpace.iSup", "kind": "theorem", "module": "Mathlib.Topology.Compactness.DeltaGeneratedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DeltaGeneratedSpace.sup", "kind": "theorem", "module": "Mathlib.Topology.Compactness.DeltaGeneratedSpace", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Topology.IsQuotientMap.deltaGeneratedSpace", "kind": "theorem", "module": "Mathlib.Topology.Compactness.DeltaGeneratedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quot.deltaGeneratedSpace", "kind": "instance", "module": "Mathlib.Topology.Compactness.DeltaGeneratedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quotient.deltaGeneratedSpace", "kind": "instance", "module": "Mathlib.Topology.Compactness.DeltaGeneratedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.deltaGeneratedSpace", "kind": "instance", "module": "Mathlib.Topology.Compactness.DeltaGeneratedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.deltaGeneratedSpace", "kind": "instance", "module": "Mathlib.Topology.Compactness.DeltaGeneratedSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLindelof", "kind": "definition", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLindelof.compl_mem_sets", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": true, "tactics": ["contrapose", "simp", "exact"], "tactic_count": 3}
{"name": "IsLindelof.compl_mem_sets_of_nhdsWithin", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "IsLindelof.induction_on", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": true, "tactics": ["let", "have", "rwa"], "tactic_count": 3}
{"name": "IsLindelof.inter_right", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": true, "tactics": ["intro", "rw", "obtain", "have", "exact"], "tactic_count": 5}
{"name": "IsLindelof.inter_left", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLindelof.diff", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLindelof.of_isClosed_subset", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLindelof.image_of_continuousOn", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": true, "tactics": ["intro", "have", "obtain", "haveI", "use", "have", "convert", "rw", "ac_rfl", "exact"], "tactic_count": 10}
{"name": "IsLindelof.image", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLindelof.adherence_nhdset", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLindelof.elim_countable_subcover", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": false, "tactics": ["have", "s", "intro", "exact", "have", "intro", "choose", "refine", "refine", "simp", "exact", "have", "intro", "let", "refine", "simp", "exact", "exact"], "tactic_count": 18}
{"name": "IsLindelof.elim_nhds_subcover'", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": false, "tactics": ["have", "hs.elim_countable_subcover", "mem_iUnion.2", "rcases", "use", "apply", "apply", "intro", "apply", "exact"], "tactic_count": 10}
{"name": "IsLindelof.elim_nhds_subcover", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": true, "tactics": ["let", "refine", "constructor", "intro", "simp", "tauto", "have", "rwa"], "tactic_count": 8}
{"name": "IsLindelof.indexed_countable_subcover", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": true, "tactics": ["obtain", "rcases", "simp", "simp", "obtain", "refine", "intro", "obtain", "exact"], "tactic_count": 9}
{"name": "IsLindelof.disjoint_nhdsSet_left", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": true, "tactics": ["refine", "choose", "choose", "rcases", "refine", "rw", "exact"], "tactic_count": 7}
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{"name": "IsLindelof.elim_countable_subfamily_closed", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": true, "tactics": ["let", "have", "have", "simp", "rw", "apply", "simp", "apply", "exact", "rcases", "use", "rw", "simp", "exact"], "tactic_count": 14}
{"name": "IsLindelof.inter_iInter_nonempty", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": true, "tactics": ["contrapose", "rcases", "exact"], "tactic_count": 3}
{"name": "IsLindelof.elim_countable_subcover_image", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": true, "tactics": ["simp", "rcases", "refine", "rw", "exact"], "tactic_count": 5}
{"name": "isLindelof_of_countable_subcover", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLindelof_of_countable_subfamily_closed", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLindelof_iff_countable_subcover", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLindelof_iff_countable_subfamily_closed", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLindelof_empty", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLindelof_singleton", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Subsingleton.isLindelof", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Countable.isLindelof_biUnion", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": true, "tactics": ["apply", "intro", "have", "have", "choose", "use", "constructor", "refine", "exact", "refine", "intro", "simp", "intro", "exact"], "tactic_count": 14}
{"name": "Set.Finite.isLindelof_biUnion", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.isLindelof_biUnion", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLindelof_accumulate", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Countable.isLindelof_sUnion", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.Finite.isLindelof_sUnion", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "isLindelof_iUnion", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Countable.isLindelof", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.isLindelof", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLindelof.countable_of_discrete", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": true, "tactics": ["have", "rcases", "rw", "exact"], "tactic_count": 4}
{"name": "isLindelof_iff_countable", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLindelof.union", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsLindelof.insert", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLindelof_open_iff_eq_countable_iUnion_of_isTopologicalBasis", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "obtain", "choose", "have", "subst", "obtain", "refine", "refine", "simp", "intro", "rw", "exact", "apply", "rintro", "obtain", "exact", "rintro", "constructor", "exact", "exact"], "tactic_count": 21}
{"name": "Filter.coLindelof", "kind": "definition", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasBasis_coLindelof", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_coLindelof", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_coLindelof'", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "hasBasis_coclosedLindelof", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": true, "tactics": ["simp", "refine", "rintro", "exact"], "tactic_count": 4}
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{"name": "coLindelof_le_coclosedLindelof", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Subsingleton.lindelofSpace", "kind": "instance", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLindelof_univ_iff", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "cluster_point_of_Lindelof", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
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{"name": "lindelofSpace_of_countable_subfamily_closed", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.isLindelof", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.isLindelof", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": true, "tactics": ["tauto"], "tactic_count": 1}
{"name": "IsSigmaCompact.isLindelof", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": true, "tactics": ["rw", "rcases", "rw", "have", "exact"], "tactic_count": 5}
{"name": "instLindelofSpaceOfCompactSpace", "kind": "instance", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instLindelofSpaceOfSigmaCompactSpace", "kind": "instance", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nonLindelof_univ", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLindelof.ne_univ", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instNeBotCoLindelofOfNonLindelofSpace", "kind": "instance", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": true, "tactics": ["refine", "contrapose", "rw", "rw", "exact"], "tactic_count": 5}
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{"name": "instNeBotCoclosedLindelofOfNonLindelofSpace", "kind": "instance", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nonLindelofSpace_of_neBot", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "not_LindelofSpace_iff", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "countable_of_Lindelof_of_discrete", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "countable_cover_nhds_interior", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "countable_cover_nhds", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.comap_coLindelof_le", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": true, "tactics": ["rw", "intro", "refine", "simpa"], "tactic_count": 4}
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{"name": "isLindelof_diagonal", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsInducing.isLindelof_iff", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact"], "tactic_count": 3}
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{"name": "Topology.IsInducing.isLindelof_preimage", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": true, "tactics": ["replace", "rwa"], "tactic_count": 2}
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{"name": "isLindelof_iff_lindelofSpace", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "instLindelofSpaceSum", "kind": "instance", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instLindelofSpaceSigmaOfCountable", "kind": "instance", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quot.lindelofSpace", "kind": "instance", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "HereditarilyLindelofSpace.isLindelof", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": true, "tactics": ["apply", "exact"], "tactic_count": 2}
{"name": "HereditarilyLindelofSpace.of_forall_isOpen", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact"], "tactic_count": 3}
{"name": "SecondCountableTopology.toHereditarilyLindelof", "kind": "instance", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_open_union_countable", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": true, "tactics": ["have", "rcases", "use", "apply"], "tactic_count": 4}
{"name": "eq_open_union_nat", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": true, "tactics": ["obtain", "rcases", "simp_rw", "simp", "obtain", "use", "rwa"], "tactic_count": 7}
{"name": "eq_closed_inter_countable", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": true, "tactics": ["conv", "exact"], "tactic_count": 2}
{"name": "eq_closed_inter_nat", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": true, "tactics": ["conv", "exact"], "tactic_count": 2}
{"name": "HereditarilyLindelof.lindelofSpace_subtype", "kind": "instance", "module": "Mathlib.Topology.Compactness.Lindelof", "is_tactic_proof": true, "tactics": ["apply", "exact"], "tactic_count": 2}
{"name": "instWeaklyLocallyCompactSpaceProd", "kind": "instance", "module": "Mathlib.Topology.Compactness.LocallyCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instWeaklyLocallyCompactSpaceForallOfFinite", "kind": "instance", "module": "Mathlib.Topology.Compactness.LocallyCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instWeaklyLocallyCompactSpaceOfCompactSpace", "kind": "instance", "module": "Mathlib.Topology.Compactness.LocallyCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsClosedEmbedding.weaklyLocallyCompactSpace", "kind": "theorem", "module": "Mathlib.Topology.Compactness.LocallyCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.weaklyLocallyCompactSpace", "kind": "theorem", "module": "Mathlib.Topology.Compactness.LocallyCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpenQuotientMap.weaklyLocallyCompactSpace", "kind": "theorem", "module": "Mathlib.Topology.Compactness.LocallyCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_compact_superset", "kind": "theorem", "module": "Mathlib.Topology.Compactness.LocallyCompact", "is_tactic_proof": true, "tactics": ["choose", "rcases", "refine", "exact"], "tactic_count": 4}
{"name": "disjoint_nhds_cocompact", "kind": "theorem", "module": "Mathlib.Topology.Compactness.LocallyCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "compact_basis_nhds", "kind": "theorem", "module": "Mathlib.Topology.Compactness.LocallyCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "local_compact_nhds", "kind": "theorem", "module": "Mathlib.Topology.Compactness.LocallyCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyCompactSpace.of_hasBasis", "kind": "theorem", "module": "Mathlib.Topology.Compactness.LocallyCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.locallyCompactSpace", "kind": "instance", "module": "Mathlib.Topology.Compactness.LocallyCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.locallyCompactSpace_of_finite", "kind": "instance", "module": "Mathlib.Topology.Compactness.LocallyCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.locallyCompactSpace", "kind": "instance", "module": "Mathlib.Topology.Compactness.LocallyCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.locallyCompactSpace_of_finite", "kind": "instance", "module": "Mathlib.Topology.Compactness.LocallyCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.locallyCompactSpace", "kind": "instance", "module": "Mathlib.Topology.Compactness.LocallyCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instLocallyCompactPairOfLocallyCompactSpace", "kind": "instance", "module": "Mathlib.Topology.Compactness.LocallyCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instWeaklyLocallyCompactSpaceOfLocallyCompactSpace", "kind": "instance", "module": "Mathlib.Topology.Compactness.LocallyCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_compact_subset", "kind": "theorem", "module": "Mathlib.Topology.Compactness.LocallyCompact", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "exists_mem_nhdsSet_isCompact_mapsTo", "kind": "theorem", "module": "Mathlib.Topology.Compactness.LocallyCompact", "is_tactic_proof": true, "tactics": ["choose", "rcases", "exact"], "tactic_count": 3}
{"name": "exists_compact_between", "kind": "theorem", "module": "Mathlib.Topology.Compactness.LocallyCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.nhdsSet_basis_isCompact", "kind": "theorem", "module": "Mathlib.Topology.Compactness.LocallyCompact", "is_tactic_proof": true, "tactics": ["rw", "intro", "obtain", "exact"], "tactic_count": 4}
{"name": "IsOpenQuotientMap.locallyCompactSpace", "kind": "theorem", "module": "Mathlib.Topology.Compactness.LocallyCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsInducing.locallyCompactSpace", "kind": "theorem", "module": "Mathlib.Topology.Compactness.LocallyCompact", "is_tactic_proof": true, "tactics": ["rcases", "have", "have", "rw", "exact", "refine", "rw", "exacts"], "tactic_count": 8}
{"name": "Topology.IsClosedEmbedding.locallyCompactSpace", "kind": "theorem", "module": "Mathlib.Topology.Compactness.LocallyCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsOpenEmbedding.locallyCompactSpace", "kind": "theorem", "module": "Mathlib.Topology.Compactness.LocallyCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocallyClosed.locallyCompactSpace", "kind": "theorem", "module": "Mathlib.Topology.Compactness.LocallyCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.locallyCompactSpace", "kind": "theorem", "module": "Mathlib.Topology.Compactness.LocallyCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.locallyCompactSpace", "kind": "theorem", "module": "Mathlib.Topology.Compactness.LocallyCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyFinite.finite_nonempty_inter_compact", "kind": "theorem", "module": "Mathlib.Topology.Compactness.LocallyFinite", "is_tactic_proof": true, "tactics": ["choose", "rcases", "refine", "rintro", "rcases", "exact"], "tactic_count": 6}
{"name": "LocallyFinite.finite_nonempty_of_compact", "kind": "theorem", "module": "Mathlib.Topology.Compactness.LocallyFinite", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "LocallyFinite.finite_of_compact", "kind": "theorem", "module": "Mathlib.Topology.Compactness.LocallyFinite", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "LocallyFinite.fintypeOfCompact", "kind": "definition", "module": "Mathlib.Topology.Compactness.LocallyFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.nhdsKer_iff", "kind": "theorem", "module": "Mathlib.Topology.Compactness.NhdsKer", "is_tactic_proof": true, "tactics": ["simp", "peel", "simp"], "tactic_count": 3}
{"name": "precise_refinement", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Paracompact", "is_tactic_proof": true, "tactics": ["have", "simp", "choose", "choose", "choose", "refine", "exact", "simp", "exact", "refine", "simp", "rintro", "exact", "simp", "rintro", "exact"], "tactic_count": 16}
{"name": "precise_refinement_set", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Paracompact", "is_tactic_proof": false, "tactics": ["have", "apply", "simp_rw", "apply", "rcases", "refine", "simp", "exact"], "tactic_count": 8}
{"name": "ParacompactSpace.of_hasBasis", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Paracompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsClosedEmbedding.paracompactSpace", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Paracompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.paracompactSpace_iff", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Paracompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instParacompactSpaceProdOfCompactSpace", "kind": "instance", "module": "Mathlib.Topology.Compactness.Paracompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instParacompactSpaceProdOfCompactSpace_1", "kind": "instance", "module": "Mathlib.Topology.Compactness.Paracompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "paracompact_of_compact", "kind": "instance", "module": "Mathlib.Topology.Compactness.Paracompact", "is_tactic_proof": true, "tactics": ["refine", "rcases", "refine", "simpa"], "tactic_count": 4}
{"name": "refinement_of_locallyCompact_sigmaCompact_of_nhds_basis_set", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Paracompact", "is_tactic_proof": true, "tactics": ["classical", "set", "set", "set", "interior", "have", "simpa", "have", "have", "choose", "have", "choose", "set", "refine", "rintro", "exact", "refine", "rcases", "exact", "intro", "refine", "have", "apply", "rintro", "simp", "rintro", "refine", "have", "contrapose", "exact"], "tactic_count": 30}
{"name": "refinement_of_locallyCompact_sigmaCompact_of_nhds_basis", "kind": "theorem", "module": "Mathlib.Topology.Compactness.Paracompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "paracompact_of_locallyCompact_sigmaCompact", "kind": "instance", "module": "Mathlib.Topology.Compactness.Paracompact", "is_tactic_proof": true, "tactics": ["refine", "choose", "have", "rcases", "exact"], "tactic_count": 5}
{"name": "T4Space.of_paracompactSpace_t2Space", "kind": "instance", "module": "Mathlib.Topology.Compactness.Paracompact", "is_tactic_proof": true, "tactics": ["have", "open", "choose", "rcases", "refine", "disjoint_compl_right.mono", "rw", "refine", "exact", "refine", "rcases", "this", "simp_rw", "exact", "exact"], "tactic_count": 15}
{"name": "IsSigmaCompact", "kind": "definition", "module": "Mathlib.Topology.Compactness.SigmaCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.isSigmaCompact", "kind": "theorem", "module": "Mathlib.Topology.Compactness.SigmaCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isSigmaCompact_empty", "kind": "theorem", "module": "Mathlib.Topology.Compactness.SigmaCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isSigmaCompact_iUnion_of_isCompact", "kind": "theorem", "module": "Mathlib.Topology.Compactness.SigmaCompact", "is_tactic_proof": true, "tactics": ["rcases", "simp", "obtain", "exact"], "tactic_count": 4}
{"name": "isSigmaCompact_sUnion_of_isCompact", "kind": "theorem", "module": "Mathlib.Topology.Compactness.SigmaCompact", "is_tactic_proof": true, "tactics": ["have", "rw", "apply"], "tactic_count": 3}
{"name": "isSigmaCompact_iUnion", "kind": "theorem", "module": "Mathlib.Topology.Compactness.SigmaCompact", "is_tactic_proof": true, "tactics": ["choose", "have", "calc", "rw", "exact"], "tactic_count": 5}
{"name": "isSigmaCompact_sUnion", "kind": "theorem", "module": "Mathlib.Topology.Compactness.SigmaCompact", "is_tactic_proof": true, "tactics": ["have", "apply"], "tactic_count": 2}
{"name": "isSigmaCompact_biUnion", "kind": "theorem", "module": "Mathlib.Topology.Compactness.SigmaCompact", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "IsSigmaCompact.of_isClosed_subset", "kind": "theorem", "module": "Mathlib.Topology.Compactness.SigmaCompact", "is_tactic_proof": true, "tactics": ["rcases", "refine", "rw", "exact"], "tactic_count": 4}
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{"name": "IsSigmaCompact.image", "kind": "theorem", "module": "Mathlib.Topology.Compactness.SigmaCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsInducing.isSigmaCompact_iff", "kind": "theorem", "module": "Mathlib.Topology.Compactness.SigmaCompact", "is_tactic_proof": true, "tactics": ["constructor", "exact", "rintro", "refine", "intro", "have", "rw", "exact", "apply", "calc"], "tactic_count": 10}
{"name": "Topology.IsEmbedding.isSigmaCompact_iff", "kind": "theorem", "module": "Mathlib.Topology.Compactness.SigmaCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.isSigmaCompact_iff", "kind": "theorem", "module": "Mathlib.Topology.Compactness.SigmaCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isSigmaCompact_univ_iff", "kind": "theorem", "module": "Mathlib.Topology.Compactness.SigmaCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isSigmaCompact_univ", "kind": "theorem", "module": "Mathlib.Topology.Compactness.SigmaCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SigmaCompactSpace_iff_exists_compact_covering", "kind": "theorem", "module": "Mathlib.Topology.Compactness.SigmaCompact", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SigmaCompactSpace.exists_compact_covering", "kind": "theorem", "module": "Mathlib.Topology.Compactness.SigmaCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isSigmaCompact_range", "kind": "theorem", "module": "Mathlib.Topology.Compactness.SigmaCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isSigmaCompact_iff_isSigmaCompact_univ", "kind": "theorem", "module": "Mathlib.Topology.Compactness.SigmaCompact", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "isSigmaCompact_iff_sigmaCompactSpace", "kind": "theorem", "module": "Mathlib.Topology.Compactness.SigmaCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompactSpace.sigmaCompact", "kind": "instance", "module": "Mathlib.Topology.Compactness.SigmaCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SigmaCompactSpace.of_countable", "kind": "theorem", "module": "Mathlib.Topology.Compactness.SigmaCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sigmaCompactSpace_of_locallyCompact_secondCountable", "kind": "instance", "module": "Mathlib.Topology.Compactness.SigmaCompact", "is_tactic_proof": true, "tactics": ["choose", "rcases", "refine", "rwa"], "tactic_count": 4}
{"name": "compactCovering", "kind": "definition", "module": "Mathlib.Topology.Compactness.SigmaCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCompact_compactCovering", "kind": "theorem", "module": "Mathlib.Topology.Compactness.SigmaCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iUnion_compactCovering", "kind": "theorem", "module": "Mathlib.Topology.Compactness.SigmaCompact", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "iUnion_closure_compactCovering", "kind": "theorem", "module": "Mathlib.Topology.Compactness.SigmaCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "compactCovering_subset", "kind": "theorem", "module": "Mathlib.Topology.Compactness.SigmaCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_mem_compactCovering", "kind": "theorem", "module": "Mathlib.Topology.Compactness.SigmaCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instSigmaCompactSpaceProd", "kind": "instance", "module": "Mathlib.Topology.Compactness.SigmaCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instSigmaCompactSpaceForallOfFinite", "kind": "instance", "module": "Mathlib.Topology.Compactness.SigmaCompact", "is_tactic_proof": false, "tactics": ["refine", "isCompact_univ_pi", "rw", "simp", "exact"], "tactic_count": 5}
{"name": "instSigmaCompactSpaceSum", "kind": "instance", "module": "Mathlib.Topology.Compactness.SigmaCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instSigmaCompactSpaceSigmaOfCountable", "kind": "instance", "module": "Mathlib.Topology.Compactness.SigmaCompact", "is_tactic_proof": true, "tactics": ["cases", "infer_instance", "rcases", "refine", "refine", "exact", "simp", "intro", "rcases", "refine", "exact"], "tactic_count": 11}
{"name": "Topology.IsClosedEmbedding.sigmaCompactSpace", "kind": "theorem", "module": "Mathlib.Topology.Compactness.SigmaCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.sigmaCompactSpace", "kind": "theorem", "module": "Mathlib.Topology.Compactness.SigmaCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instSigmaCompactSpaceULift", "kind": "instance", "module": "Mathlib.Topology.Compactness.SigmaCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyFinite.countable_univ", "kind": "theorem", "module": "Mathlib.Topology.Compactness.SigmaCompact", "is_tactic_proof": true, "tactics": ["have", "refine", "rcases", "rcases", "exact"], "tactic_count": 5}
{"name": "LocallyFinite.encodable", "kind": "definition", "module": "Mathlib.Topology.Compactness.SigmaCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "countable_cover_nhdsWithin_of_sigmaCompact", "kind": "theorem", "module": "Mathlib.Topology.Compactness.SigmaCompact", "is_tactic_proof": true, "tactics": ["simp", "choose", "refine", "rcases", "rcases", "exact"], "tactic_count": 6}
{"name": "countable_cover_nhds_of_sigmaCompact", "kind": "theorem", "module": "Mathlib.Topology.Compactness.SigmaCompact", "is_tactic_proof": true, "tactics": ["simp", "rcases", "exact"], "tactic_count": 3}
{"name": "CompactExhaustion.instFunLikeNatSet", "kind": "instance", "module": "Mathlib.Topology.Compactness.SigmaCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompactExhaustion.instRelHomClassNatSetLeSubset", "kind": "instance", "module": "Mathlib.Topology.Compactness.SigmaCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompactExhaustion.toFun_eq_coe", "kind": "theorem", "module": "Mathlib.Topology.Compactness.SigmaCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompactExhaustion.isCompact", "kind": "theorem", "module": "Mathlib.Topology.Compactness.SigmaCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompactExhaustion.subset_interior_succ", "kind": "theorem", "module": "Mathlib.Topology.Compactness.SigmaCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompactExhaustion.subset", "kind": "theorem", "module": "Mathlib.Topology.Compactness.SigmaCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompactExhaustion.subset_succ", "kind": "theorem", "module": "Mathlib.Topology.Compactness.SigmaCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "CompactExhaustion.iUnion_eq", "kind": "theorem", "module": "Mathlib.Topology.Compactness.SigmaCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompactExhaustion.exists_mem", "kind": "theorem", "module": "Mathlib.Topology.Compactness.SigmaCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompactExhaustion.exists_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Compactness.SigmaCompact", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "CompactExhaustion.exists_superset_of_isCompact", "kind": "theorem", "module": "Mathlib.Topology.Compactness.SigmaCompact", "is_tactic_proof": true, "tactics": ["suffices", "refine", "intro", "rcases", "exact", "exact"], "tactic_count": 6}
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{"name": "CompactExhaustion.mem_iff_find_le", "kind": "theorem", "module": "Mathlib.Topology.Compactness.SigmaCompact", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "CompactExhaustion.shiftr", "kind": "definition", "module": "Mathlib.Topology.Compactness.SigmaCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompactExhaustion.find_shiftr", "kind": "theorem", "module": "Mathlib.Topology.Compactness.SigmaCompact", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "CompactExhaustion.mem_diff_shiftr_find", "kind": "theorem", "module": "Mathlib.Topology.Compactness.SigmaCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompactExhaustion.choice", "kind": "definition", "module": "Mathlib.Topology.Compactness.SigmaCompact", "is_tactic_proof": true, "tactics": ["apply", "let", "refine", "exact", "refine", "exact"], "tactic_count": 6}
{"name": "CompactExhaustion.instInhabitedOfSigmaCompactSpaceOfWeaklyLocallyCompactSpace", "kind": "instance", "module": "Mathlib.Topology.Compactness.SigmaCompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPreconnected", "kind": "definition", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsConnected", "kind": "definition", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsConnected.nonempty", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsConnected.isPreconnected", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPreirreducible.isPreconnected", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIrreducible.isConnected", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isPreconnected_empty", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isConnected_singleton", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isPreconnected_singleton", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Subsingleton.isPreconnected", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isPreconnected_of_forall", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": true, "tactics": ["rintro", "have", "rcases", "exact", "cases", "inl", "rcases", "have", "exact", "inr", "rcases", "have", "exact"], "tactic_count": 13}
{"name": "isPreconnected_of_forall_pair", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": true, "tactics": ["rcases", "exacts"], "tactic_count": 2}
{"name": "isPreconnected_sUnion", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": true, "tactics": ["apply", "rintro", "exact"], "tactic_count": 3}
{"name": "isPreconnected_iUnion", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPreconnected.union", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPreconnected.union'", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "IsConnected.union", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": true, "tactics": ["rcases", "refine", "exact"], "tactic_count": 3}
{"name": "IsPreconnected.sUnion_directed", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": true, "tactics": ["rintro", "obtain", "have", "have", "exact"], "tactic_count": 5}
{"name": "IsPreconnected.biUnion_of_reflTransGen", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": true, "tactics": ["let", "have", "induction", "refl", "refine", "rw", "exact", "obtain", "refine", "rw", "refine", "rw", "exact", "refine", "intro", "obtain", "obtain", "obtain", "exact"], "tactic_count": 19}
{"name": "IsConnected.biUnion_of_reflTransGen", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPreconnected.iUnion_of_reflTransGen", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsConnected.iUnion_of_reflTransGen", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPreconnected.iUnion_of_chain", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsConnected.iUnion_of_chain", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPreconnected.biUnion_of_chain", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": ["have", "have", "ht.out", "have", "refine", "exact", "reflTransGen_of_succ"], "tactic_count": 7}
{"name": "IsConnected.biUnion_of_chain", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPreconnected.subset_closure", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsConnected.subset_closure", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPreconnected.closure", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsConnected.closure", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPreconnected.image", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": true, "tactics": ["rintro", "rcases", "rcases", "replace", "rw", "replace", "rw", "exact", "obtain", "refine", "exacts", "rw", "v'_eq]", "exact"], "tactic_count": 14}
{"name": "IsConnected.image", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isPreconnected_closed_iff", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsInducing.isPreconnected_image", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": true, "tactics": ["refine", "rintro", "rcases", "rcases", "replace", "rcases", "exact"], "tactic_count": 7}
{"name": "IsPreconnected.preimage_of_isOpenMap", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPreconnected.preimage_of_isClosedMap", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsConnected.preimage_of_isOpenMap", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsConnected.preimage_of_isClosedMap", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPreconnected.subset_or_subset", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": true, "tactics": ["specialize", "obtain", "exact", "replace", "simp_rw", "exact"], "tactic_count": 6}
{"name": "IsPreconnected.subset_left_of_subset_union", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPreconnected.subset_right_of_subset_union", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPreconnected.subset_of_closure_inter_subset", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": ["have", "intro", "by_cases", "exact", "right", "intro", "exact", "apply", "exact"], "tactic_count": 9}
{"name": "IsPreconnected.prod", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": true, "tactics": ["apply", "rintro", "refine", "rintro", "exacts", "exact"], "tactic_count": 6}
{"name": "IsConnected.prod", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isPreconnected_univ_pi", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": true, "tactics": ["rintro", "classical", "rcases", "induction", "empty", "refine", "simpa", "insert", "rw", "have", "refine", "set", "have", "refine", "rwa", "exact", "have", "have", "have", "refine", "exact"], "tactic_count": 21}
{"name": "isConnected_univ_pi", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": true, "tactics": ["simp", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "connectedComponent", "kind": "definition", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "connectedComponentIn", "kind": "definition", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "connectedComponentIn_eq_image", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "connectedComponentIn_eq_empty", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_connectedComponent", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_connectedComponentIn", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "connectedComponent_nonempty", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "connectedComponentIn_nonempty_iff", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": true, "tactics": ["rw", "split_ifs"], "tactic_count": 2}
{"name": "connectedComponentIn_subset", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": true, "tactics": ["rw", "split_ifs"], "tactic_count": 2}
{"name": "isPreconnected_connectedComponent", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isPreconnected_connectedComponentIn", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact", "exact"], "tactic_count": 3}
{"name": "isConnected_connectedComponent", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isConnected_connectedComponentIn_iff", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "IsPreconnected.subset_connectedComponent", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPreconnected.subset_connectedComponentIn", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": ["have", "refine", "rwa", "have", "rw", "exact", "have", "rw", "refine", "rw"], "tactic_count": 10}
{"name": "IsConnected.subset_connectedComponent", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPreconnected.connectedComponentIn", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "connectedComponent_eq", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "connectedComponent_eq_iff_mem", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "connectedComponentIn_eq", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": true, "tactics": ["have", "simp_rw", "obtain", "simp_rw"], "tactic_count": 4}
{"name": "connectedComponentIn_univ", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "connectedComponent_disjoint", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosed_connectedComponent", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.image_connectedComponent_subset", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.image_connectedComponentIn_subset", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.mapsTo_connectedComponent", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.mapsTo_connectedComponentIn", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "irreducibleComponent_subset_connectedComponent", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "connectedComponentIn_mono", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "show", "exact", "rw", "exact"], "tactic_count": 6}
{"name": "isConnected_univ", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "preconnectedSpace_iff_univ", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "connectedSpace_iff_univ", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isPreconnected_range", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isConnected_range", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.connectedSpace", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Quotient.instConnectedSpace", "kind": "instance", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DenseRange.preconnectedSpace", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "connectedSpace_iff_connectedComponent", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "exact", "rintro", "haveI", "exact"], "tactic_count": 6}
{"name": "preconnectedSpace_iff_connectedComponent", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "intro", "rcases", "exact", "exact"], "tactic_count": 7}
{"name": "PreconnectedSpace.connectedComponent_eq_univ", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instPreconnectedSpaceProd", "kind": "instance", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instConnectedSpaceProd", "kind": "instance", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instPreconnectedSpaceForall", "kind": "instance", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instConnectedSpaceForall", "kind": "instance", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PreirreducibleSpace.preconnectedSpace", "kind": "instance", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IrreducibleSpace.connectedSpace", "kind": "instance", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.preconnectedSpace", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.connectedSpace", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isPreconnected_iff_preconnectedSpace", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isConnected_iff_connectedSpace", "kind": "theorem", "module": "Mathlib.Topology.Connected.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPreconnected.subset_isClopen", "kind": "theorem", "module": "Mathlib.Topology.Connected.Clopen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.isConnected_iff", "kind": "theorem", "module": "Mathlib.Topology.Connected.Clopen", "is_tactic_proof": true, "tactics": ["refine", "obtain", "have", "exact", "rintro", "exact"], "tactic_count": 6}
{"name": "Sigma.isPreconnected_iff", "kind": "theorem", "module": "Mathlib.Topology.Connected.Clopen", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact", "obtain", "exact", "rintro", "exact"], "tactic_count": 7}
{"name": "Sum.isConnected_iff", "kind": "theorem", "module": "Mathlib.Topology.Connected.Clopen", "is_tactic_proof": true, "tactics": ["refine", "obtain", "have", "refine", "exact", "exact", "have", "refine", "exact", "exact", "rintro", "exact", "exact"], "tactic_count": 13}
{"name": "Sum.isPreconnected_iff", "kind": "theorem", "module": "Mathlib.Topology.Connected.Clopen", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact", "obtain", "exact", "exact", "rintro", "exact", "exact"], "tactic_count": 9}
{"name": "Continuous.exists_lift_sigma", "kind": "theorem", "module": "Mathlib.Topology.Connected.Clopen", "is_tactic_proof": false, "tactics": ["obtain", "rcases", "exact", "rcases", "refine", "rwa"], "tactic_count": 6}
{"name": "nonempty_inter", "kind": "theorem", "module": "Mathlib.Topology.Connected.Clopen", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "isClopen_iff", "kind": "theorem", "module": "Mathlib.Topology.Connected.Clopen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClopen.eq_univ", "kind": "theorem", "module": "Mathlib.Topology.Connected.Clopen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClopen_preimage_val", "kind": "theorem", "module": "Mathlib.Topology.Connected.Clopen", "is_tactic_proof": true, "tactics": ["refine", "refine", "apply", "simp", "rw"], "tactic_count": 5}
{"name": "subsingleton_of_disjoint_isClopen", "kind": "theorem", "module": "Mathlib.Topology.Connected.Clopen", "is_tactic_proof": true, "tactics": ["rw", "by_contra", "replace", "simpa", "rcases", "exact", "rw", "exact"], "tactic_count": 8}
{"name": "subsingleton_of_disjoint_isOpen_iUnion_eq_univ", "kind": "theorem", "module": "Mathlib.Topology.Connected.Clopen", "is_tactic_proof": true, "tactics": ["refine", "rw", "refine", "rcases", "simp", "simpa"], "tactic_count": 6}
{"name": "subsingleton_of_disjoint_isClosed_iUnion_eq_univ", "kind": "theorem", "module": "Mathlib.Topology.Connected.Clopen", "is_tactic_proof": true, "tactics": ["refine", "rw", "refine", "rcases", "simp", "simpa"], "tactic_count": 6}
{"name": "frontier_eq_empty_iff", "kind": "theorem", "module": "Mathlib.Topology.Connected.Clopen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nonempty_frontier_iff", "kind": "theorem", "module": "Mathlib.Topology.Connected.Clopen", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PreconnectedSpace.induction₂'", "kind": "theorem", "module": "Mathlib.Topology.Connected.Clopen", "is_tactic_proof": true, "tactics": ["let", "have", "apply", "rcases", "exact", "have", "apply", "filter_upwards", "exact", "have", "have", "change", "simp"], "tactic_count": 13}
{"name": "PreconnectedSpace.induction₂", "kind": "theorem", "module": "Mathlib.Topology.Connected.Clopen", "is_tactic_proof": true, "tactics": ["refine", "filter_upwards", "exact"], "tactic_count": 3}
{"name": "IsPreconnected.induction₂'", "kind": "theorem", "module": "Mathlib.Topology.Connected.Clopen", "is_tactic_proof": true, "tactics": ["let", "change", "have", "apply", "rintro", "have", "rwa", "rintro", "exact"], "tactic_count": 9}
{"name": "IsPreconnected.induction₂", "kind": "theorem", "module": "Mathlib.Topology.Connected.Clopen", "is_tactic_proof": true, "tactics": ["apply", "filter_upwards", "exact"], "tactic_count": 3}
{"name": "isPreconnected_iff_subset_of_disjoint", "kind": "theorem", "module": "Mathlib.Topology.Connected.Clopen", "is_tactic_proof": true, "tactics": ["constructor", "intro", "specialize", "contrapose", "simp", "rcases", "have", "have", "exact", "intro", "by_contra", "specialize", "apply", "rcases", "rcases", "exact", "rcases", "exact"], "tactic_count": 18}
{"name": "isConnected_iff_sUnion_disjoint_open", "kind": "theorem", "module": "Mathlib.Topology.Connected.Clopen", "is_tactic_proof": true, "tactics": ["rw", "classical", "refine", "induction", "empty", "insert", "simp", "sUnion_insert,", "refine", "refine", "exact", "exact", "simpa", "rw", "have", "simpa"], "tactic_count": 16}
{"name": "disjoint_or_subset_of_isClopen", "kind": "theorem", "module": "Mathlib.Topology.Connected.Clopen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isPreconnected_iff_subset_of_disjoint_closed", "kind": "theorem", "module": "Mathlib.Topology.Connected.Clopen", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "specialize", "contrapose", "simp", "rcases", "have", "have", "exact", "rw", "intro", "by_contra", "specialize", "apply", "rcases", "rcases", "exact", "rcases", "exact"], "tactic_count": 20}
{"name": "isPreconnected_iff_subset_of_fully_disjoint_closed", "kind": "theorem", "module": "Mathlib.Topology.Connected.Clopen", "is_tactic_proof": true, "tactics": ["refine", "apply", "rw", "have", "rw", "simp", "apply", "rw", "exact", "rwa"], "tactic_count": 10}
{"name": "IsClopen.connectedComponent_subset", "kind": "theorem", "module": "Mathlib.Topology.Connected.Clopen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "connectedComponent_subset_iInter_isClopen", "kind": "theorem", "module": "Mathlib.Topology.Connected.Clopen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClopen.biUnion_connectedComponent_eq", "kind": "theorem", "module": "Mathlib.Topology.Connected.Clopen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClopen.biUnion_connectedComponentIn", "kind": "theorem", "module": "Mathlib.Topology.Connected.Clopen", "is_tactic_proof": true, "tactics": ["have", "simp", "inter_eq_right.mpr", "nth_rw", "congr", "simp", "exact", "le_antisymm"], "tactic_count": 8}
{"name": "preimage_connectedComponent_connected", "kind": "theorem", "module": "Mathlib.Topology.Connected.Clopen", "is_tactic_proof": true, "tactics": ["have", "refine", "have", "rw", "intro", "let", "let", "have", "intro", "apply", "exact", "rw", "have", "apply", "rw", "refine", "rw", "exact", "rintro", "constructor", "exact", "refine", "exact", "uv_disj.subset_compl_right", "have", "apply", "rw", "refine", "rw", "exact", "rintro", "constructor", "exact", "refine", "exact", "uv_disj.subset_compl_left", "have", "have", "have", "rw", "rcases", "left", "right", "have", "refine", "rw", "rcases", "h", "left", "rw", "suffices", "exact", "right", "rw", "suffices", "exact"], "tactic_count": 56}
{"name": "Topology.IsQuotientMap.preimage_connectedComponent", "kind": "theorem", "module": "Mathlib.Topology.Connected.Clopen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsQuotientMap.image_connectedComponent", "kind": "theorem", "module": "Mathlib.Topology.Connected.Clopen", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "connectedComponentSetoid", "kind": "definition", "module": "Mathlib.Topology.Connected.Clopen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConnectedComponents", "kind": "definition", "module": "Mathlib.Topology.Connected.Clopen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConnectedComponents.mk", "kind": "definition", "module": "Mathlib.Topology.Connected.Clopen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConnectedComponents.instCoeTC", "kind": "instance", "module": "Mathlib.Topology.Connected.Clopen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConnectedComponents.coe_eq_coe", "kind": "theorem", "module": "Mathlib.Topology.Connected.Clopen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConnectedComponents.coe_ne_coe", "kind": "theorem", "module": "Mathlib.Topology.Connected.Clopen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConnectedComponents.coe_eq_coe'", "kind": "theorem", "module": "Mathlib.Topology.Connected.Clopen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConnectedComponents.instInhabited", "kind": "instance", "module": "Mathlib.Topology.Connected.Clopen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConnectedComponents.instTopologicalSpace", "kind": "instance", "module": "Mathlib.Topology.Connected.Clopen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConnectedComponents.surjective_coe", "kind": "theorem", "module": "Mathlib.Topology.Connected.Clopen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConnectedComponents.isQuotientMap_coe", "kind": "theorem", "module": "Mathlib.Topology.Connected.Clopen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConnectedComponents.continuous_coe", "kind": "theorem", "module": "Mathlib.Topology.Connected.Clopen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConnectedComponents.range_coe", "kind": "theorem", "module": "Mathlib.Topology.Connected.Clopen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "connectedComponents_preimage_singleton", "kind": "theorem", "module": "Mathlib.Topology.Connected.Clopen", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "connectedComponents_preimage_image", "kind": "theorem", "module": "Mathlib.Topology.Connected.Clopen", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "isPreconnected_of_forall_constant", "kind": "theorem", "module": "Mathlib.Topology.Connected.Clopen", "is_tactic_proof": true, "tactics": ["unfold", "by_contra", "have", "have", "apply", "rw", "exact", "exact", "simpa"], "tactic_count": 9}
{"name": "preconnectedSpace_of_forall_constant", "kind": "theorem", "module": "Mathlib.Topology.Connected.Clopen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "preconnectedSpace_iff_clopen", "kind": "theorem", "module": "Mathlib.Topology.Connected.Clopen", "is_tactic_proof": true, "tactics": ["refine", "refine", "have", "obtain"], "tactic_count": 4}
{"name": "connectedSpace_iff_clopen", "kind": "theorem", "module": "Mathlib.Topology.Connected.Clopen", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "instCompactSpaceConnectedComponents", "kind": "instance", "module": "Mathlib.Topology.Connected.Clopen", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocPathConnectedSpace.of_bases", "kind": "theorem", "module": "Mathlib.Topology.Connected.LocPathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.pathComponentIn", "kind": "theorem", "module": "Mathlib.Topology.Connected.LocPathConnected", "is_tactic_proof": true, "tactics": ["rw", "intro", "let", "exact"], "tactic_count": 4}
{"name": "IsOpen.pathComponent", "kind": "theorem", "module": "Mathlib.Topology.Connected.LocPathConnected", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsClosed.pathComponent", "kind": "theorem", "module": "Mathlib.Topology.Connected.LocPathConnected", "is_tactic_proof": true, "tactics": ["rw", "intro", "rcases", "filter_upwards", "exact"], "tactic_count": 5}
{"name": "IsClopen.pathComponent", "kind": "theorem", "module": "Mathlib.Topology.Connected.LocPathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pathComponentIn_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Connected.LocPathConnected", "is_tactic_proof": true, "tactics": ["let", "exact", "mem_nhds_iff.mpr"], "tactic_count": 3}
{"name": "PathConnectedSpace.of_locPathConnectedSpace", "kind": "theorem", "module": "Mathlib.Topology.Connected.LocPathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pathConnectedSpace_iff_connectedSpace", "kind": "theorem", "module": "Mathlib.Topology.Connected.LocPathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pathComponent_eq_connectedComponent", "kind": "theorem", "module": "Mathlib.Topology.Connected.LocPathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pathConnected_subset_basis", "kind": "theorem", "module": "Mathlib.Topology.Connected.LocPathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpen_isPathConnected_basis", "kind": "theorem", "module": "Mathlib.Topology.Connected.LocPathConnected", "is_tactic_proof": true, "tactics": ["refine", "have", "exact", "pathComponentIn_subset.trans"], "tactic_count": 4}
{"name": "Topology.IsOpenEmbedding.locPathConnectedSpace", "kind": "theorem", "module": "Mathlib.Topology.Connected.LocPathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.locPathConnectedSpace", "kind": "theorem", "module": "Mathlib.Topology.Connected.LocPathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.isConnected_iff_isPathConnected", "kind": "theorem", "module": "Mathlib.Topology.Connected.LocPathConnected", "is_tactic_proof": true, "tactics": ["rw", "haveI", "exact"], "tactic_count": 3}
{"name": "instLocallyConnectedSpace", "kind": "instance", "module": "Mathlib.Topology.Connected.LocPathConnected", "is_tactic_proof": true, "tactics": ["refine", "refine", "let", "exact"], "tactic_count": 4}
{"name": "locPathConnectedSpace_iff_isOpen_pathComponentIn", "kind": "theorem", "module": "Mathlib.Topology.Connected.LocPathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "locPathConnectedSpace_iff_pathComponentIn_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Connected.LocPathConnected", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "refine", "exact", "isOpen_iff_mem_nhds.mpr"], "tactic_count": 5}
{"name": "LocPathConnectedSpace.coinduced", "kind": "theorem", "module": "Mathlib.Topology.Connected.LocPathConnected", "is_tactic_proof": true, "tactics": ["let", "refine", "locPathConnectedSpace_iff_isOpen_pathComponentIn.mpr", "isOpen_coinduced.mpr", "have", "refine", "mem_nhds_iff.mpr", "rw", "exact"], "tactic_count": 9}
{"name": "Topology.IsQuotientMap.locPathConnectedSpace", "kind": "theorem", "module": "Mathlib.Topology.Connected.LocPathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quot.locPathConnectedSpace", "kind": "instance", "module": "Mathlib.Topology.Connected.LocPathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quotient.locPathConnectedSpace", "kind": "instance", "module": "Mathlib.Topology.Connected.LocPathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.locPathConnectedSpace", "kind": "instance", "module": "Mathlib.Topology.Connected.LocPathConnected", "is_tactic_proof": true, "tactics": ["rw", "obtain", "refine", "apply", "exact", "exact", "exact", "exact", "exact", "refine", "apply", "exact", "exact", "exact", "exact", "exact"], "tactic_count": 16}
{"name": "Sigma.locPathConnectedSpace", "kind": "instance", "module": "Mathlib.Topology.Connected.LocPathConnected", "is_tactic_proof": true, "tactics": ["rw", "refine", "apply", "exact", "exact", "exact", "exact", "exact"], "tactic_count": 8}
{"name": "AlexandrovDiscrete.locPathConnectedSpace", "kind": "instance", "module": "Mathlib.Topology.Connected.LocPathConnected", "is_tactic_proof": true, "tactics": ["apply", "simp", "intro", "exists", "intro", "symm", "apply"], "tactic_count": 7}
{"name": "instDiscreteTopologyZerothHomotopy", "kind": "instance", "module": "Mathlib.Topology.Connected.LocPathConnected", "is_tactic_proof": true, "tactics": ["refine", "obtain", "rw", "grind"], "tactic_count": 4}
{"name": "instFiniteZerothHomotopyOfCompactSpace", "kind": "instance", "module": "Mathlib.Topology.Connected.LocPathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "locallyConnectedSpace_iff_hasBasis_isOpen_isConnected", "kind": "theorem", "module": "Mathlib.Topology.Connected.LocallyConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "locallyConnectedSpace_iff_subsets_isOpen_isConnected", "kind": "theorem", "module": "Mathlib.Topology.Connected.LocallyConnected", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "constructor", "intro", "rcases", "exact", "exact", "let"], "tactic_count": 8}
{"name": "DiscreteTopology.toLocallyConnectedSpace", "kind": "instance", "module": "Mathlib.Topology.Connected.LocallyConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "connectedComponentIn_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Connected.LocallyConnected", "is_tactic_proof": true, "tactics": ["rw", "rcases", "exact"], "tactic_count": 3}
{"name": "IsOpen.connectedComponentIn", "kind": "theorem", "module": "Mathlib.Topology.Connected.LocallyConnected", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "exact"], "tactic_count": 4}
{"name": "isOpen_connectedComponent", "kind": "theorem", "module": "Mathlib.Topology.Connected.LocallyConnected", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "isClopen_connectedComponent", "kind": "theorem", "module": "Mathlib.Topology.Connected.LocallyConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "locallyConnectedSpace_iff_connectedComponentIn_open", "kind": "theorem", "module": "Mathlib.Topology.Connected.LocallyConnected", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "intro", "rw", "refine", "h", "exact"], "tactic_count": 8}
{"name": "locallyConnectedSpace_iff_connected_subsets", "kind": "theorem", "module": "Mathlib.Topology.Connected.LocallyConnected", "is_tactic_proof": true, "tactics": ["constructor", "rw", "intro", "rcases", "exact", "rw", "refine", "rw", "rcases", "exact"], "tactic_count": 10}
{"name": "locallyConnectedSpace_iff_connected_basis", "kind": "theorem", "module": "Mathlib.Topology.Connected.LocallyConnected", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "locallyConnectedSpace_of_connected_bases", "kind": "theorem", "module": "Mathlib.Topology.Connected.LocallyConnected", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "TopologicalSpace.IsTopologicalBasis.isOpen_isPreconnected", "kind": "theorem", "module": "Mathlib.Topology.Connected.LocallyConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "locallyConnectedSpace_iff_isTopologicalBasis_isOpen_isPreconnected", "kind": "theorem", "module": "Mathlib.Topology.Connected.LocallyConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsOpenEmbedding.locallyConnectedSpace", "kind": "theorem", "module": "Mathlib.Topology.Connected.LocallyConnected", "is_tactic_proof": false, "tactics": ["refine", "locallyConnectedSpace_of_connected_bases", "rw", "exact"], "tactic_count": 4}
{"name": "IsOpen.locallyConnectedSpace", "kind": "theorem", "module": "Mathlib.Topology.Connected.LocallyConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDiscreteTopologyConnectedComponentsOfLocallyConnectedSpace", "kind": "instance", "module": "Mathlib.Topology.Connected.LocallyConnected", "is_tactic_proof": true, "tactics": ["refine", "obtain", "simp", "isOpen_connectedComponent]"], "tactic_count": 4}
{"name": "instFiniteConnectedComponentsOfLocallyConnectedSpaceOfCompactSpace", "kind": "instance", "module": "Mathlib.Topology.Connected.LocallyConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenNormalSubgroup.pathComponentOne", "kind": "definition", "module": "Mathlib.Topology.Connected.PathComponentOne", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenNormalSubgroup.instIsClosedCoePathComponentOne", "kind": "instance", "module": "Mathlib.Topology.Connected.PathComponentOne", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Joined", "kind": "definition", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Joined.refl", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Joined.somePath", "kind": "definition", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Joined.symm", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Joined.trans", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Joined.mul", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Joined.listProd", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons"], "tactic_count": 3}
{"name": "Joined.inv", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pathSetoid", "kind": "definition", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZerothHomotopy", "kind": "definition", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instTopologicalSpaceZerothHomotopy", "kind": "instance", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZerothHomotopy.inhabited", "kind": "instance", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "JoinedIn", "kind": "definition", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "JoinedIn.mem", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": true, "tactics": ["rcases", "have", "simpa"], "tactic_count": 3}
{"name": "JoinedIn.source_mem", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "JoinedIn.target_mem", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "JoinedIn.somePath", "kind": "definition", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "JoinedIn.somePath_mem", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "JoinedIn.joined_subtype", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "JoinedIn.ofLine", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "JoinedIn.joined", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "joinedIn_iff_joined", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "joinedIn_univ", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "JoinedIn.mono", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "JoinedIn.refl", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "JoinedIn.symm", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": true, "tactics": ["obtain", "simp_all", "exact"], "tactic_count": 3}
{"name": "JoinedIn.trans", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "simp_all", "exact"], "tactic_count": 4}
{"name": "Specializes.joinedIn", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": true, "tactics": ["refine", "exact", "simp", "split_ifs"], "tactic_count": 4}
{"name": "Inseparable.joinedIn", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "JoinedIn.map_continuousOn", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "JoinedIn.map", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsInducing.joinedIn_image", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": true, "tactics": ["refine", "rintro", "choose", "have", "have", "have", "refine", "simpa", "exact"], "tactic_count": 9}
{"name": "JoinedIn.mul", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "JoinedIn.inv", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pathComponent", "kind": "definition", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_pathComponent_iff", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_pathComponent_self", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pathComponent.nonempty", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_pathComponent_of_mem", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pathComponent_symm", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pathComponent_congr", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": true, "tactics": ["ext", "constructor", "intro", "rw", "exact", "intro", "rw", "exact"], "tactic_count": 8}
{"name": "pathComponent_subset_component", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pathComponentIn", "kind": "definition", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pathComponentIn_univ", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Joined.mem_pathComponent", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_pathComponentIn_self", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pathComponentIn_subset", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pathComponentIn_nonempty_iff", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pathComponentIn_congr", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "pathComponentIn_mono", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.pathComponentOne", "kind": "definition", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.pathComponentOne", "kind": "definition", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.Normal.pathComponentOne", "kind": "instance", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPathConnected", "kind": "definition", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isPathConnected_iff_eq", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": true, "tactics": ["constructor", "ext", "exact", "intro", "rwa"], "tactic_count": 5}
{"name": "IsPathConnected.joinedIn", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isPathConnected_iff", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPathConnected.nonempty", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPathConnected.image'", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": true, "tactics": ["rcases", "use", "rintro", "refine", "exact"], "tactic_count": 5}
{"name": "IsPathConnected.image", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPathConnected.mul", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPathConnected.inv", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsInducing.isPathConnected_iff", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": true, "tactics": ["simp", "refine", "rw"], "tactic_count": 3}
{"name": "Homeomorph.isPathConnected_image", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.isPathConnected_preimage", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsPathConnected.mem_pathComponent", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPathConnected.subset_pathComponent", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPathConnected.subset_pathComponentIn", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isPathConnected_singleton", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": true, "tactics": ["refine", "rintro", "exact"], "tactic_count": 3}
{"name": "isPathConnected_pathComponentIn", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isPathConnected_pathComponent", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsPathConnected.union", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": true, "tactics": ["rcases", "use", "rintro", "exact", "exact"], "tactic_count": 5}
{"name": "IsPathConnected.preimage_coe", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "IsPathConnected.exists_path_through_family", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": false, "tactics": ["cases", "simp", "obtain", "induction", "h0", "simp", "use", "simp", "hp₂", "simp", "obtain", "specialize", "obtain", "obtain", "rw", "use", "simp", "tauto"], "tactic_count": 18}
{"name": "IsPathConnected.exists_path_through_family'", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "simp", "rw", "choose", "exact"], "tactic_count": 6}
{"name": "pathConnectedSpace_iff_zerothHomotopy", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": true, "tactics": ["letI", "constructor", "intro", "refine", "rintro", "exact", "unfold", "rintro", "exact"], "tactic_count": 9}
{"name": "PathConnectedSpace.somePath", "kind": "definition", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pathConnectedSpace_iff_univ", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "isPathConnected_iff_pathConnectedSpace", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": true, "tactics": ["rw", "setOf_mem_eq]"], "tactic_count": 2}
{"name": "isPathConnected_univ", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isPathConnected_range", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Function.Surjective.pathConnectedSpace", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Quotient.instPathConnectedSpace", "kind": "instance", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.instPathConnectedSpace", "kind": "instance", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pathConnectedSpace_iff_eq", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PathConnectedSpace.connectedSpace", "kind": "instance", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": true, "tactics": ["rw", "rcases", "use", "rw", "exact"], "tactic_count": 5}
{"name": "IsPathConnected.isConnected", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "PathConnectedSpace.exists_path_through_family", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": true, "tactics": ["have", "rcases", "exact"], "tactic_count": 3}
{"name": "PathConnectedSpace.exists_path_through_family'", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": true, "tactics": ["have", "rcases", "exact"], "tactic_count": 3}
{"name": "ZerothHomotopy.preimage_singleton_eq_pathComponent", "kind": "theorem", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": true, "tactics": ["ext", "rw", "exact"], "tactic_count": 3}
{"name": "instCompactSpaceZerothHomotopy", "kind": "instance", "module": "Mathlib.Topology.Connected.PathConnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TotallySeparatedSpace.t2Space", "kind": "instance", "module": "Mathlib.Topology.Connected.Separation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsTotallyDisconnected", "kind": "definition", "module": "Mathlib.Topology.Connected.TotallyDisconnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isTotallyDisconnected_empty", "kind": "theorem", "module": "Mathlib.Topology.Connected.TotallyDisconnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isTotallyDisconnected_singleton", "kind": "theorem", "module": "Mathlib.Topology.Connected.TotallyDisconnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPreconnected.subsingleton", "kind": "theorem", "module": "Mathlib.Topology.Connected.TotallyDisconnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.totallyDisconnectedSpace", "kind": "instance", "module": "Mathlib.Topology.Connected.TotallyDisconnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.totallyDisconnectedSpace", "kind": "instance", "module": "Mathlib.Topology.Connected.TotallyDisconnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instTotallyDisconnectedSpaceSum", "kind": "instance", "module": "Mathlib.Topology.Connected.TotallyDisconnected", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact", "exact"], "tactic_count": 4}
{"name": "instTotallyDisconnectedSpaceSigma", "kind": "instance", "module": "Mathlib.Topology.Connected.TotallyDisconnected", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact", "obtain", "exact"], "tactic_count": 5}
{"name": "totallyDisconnectedSpace_iff_connectedComponent_subsingleton", "kind": "theorem", "module": "Mathlib.Topology.Connected.TotallyDisconnected", "is_tactic_proof": true, "tactics": ["constructor", "intro", "apply", "exact", "exact", "intro", "intro", "rcases", "exact", "exact"], "tactic_count": 10}
{"name": "totallyDisconnectedSpace_iff_connectedComponent_singleton", "kind": "theorem", "module": "Mathlib.Topology.Connected.TotallyDisconnected", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "connectedComponent_eq_singleton", "kind": "theorem", "module": "Mathlib.Topology.Connected.TotallyDisconnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.image_connectedComponent_eq_singleton", "kind": "theorem", "module": "Mathlib.Topology.Connected.TotallyDisconnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isTotallyDisconnected_of_totallyDisconnectedSpace", "kind": "theorem", "module": "Mathlib.Topology.Connected.TotallyDisconnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TotallyDisconnectedSpace.eq_of_continuous", "kind": "theorem", "module": "Mathlib.Topology.Connected.TotallyDisconnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TotallyDisconnectedSpace.continuousMapEquivOfConnectedSpace", "kind": "definition", "module": "Mathlib.Topology.Connected.TotallyDisconnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isTotallyDisconnected_of_image", "kind": "theorem", "module": "Mathlib.Topology.Connected.TotallyDisconnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsEmbedding.isTotallyDisconnected", "kind": "theorem", "module": "Mathlib.Topology.Connected.TotallyDisconnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsEmbedding.isTotallyDisconnected_image", "kind": "theorem", "module": "Mathlib.Topology.Connected.TotallyDisconnected", "is_tactic_proof": true, "tactics": ["refine", "obtain", "rw", "exact"], "tactic_count": 4}
{"name": "Topology.IsEmbedding.isTotallyDisconnected_range", "kind": "theorem", "module": "Mathlib.Topology.Connected.TotallyDisconnected", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "totallyDisconnectedSpace_subtype_iff", "kind": "theorem", "module": "Mathlib.Topology.Connected.TotallyDisconnected", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subtype.totallyDisconnectedSpace", "kind": "instance", "module": "Mathlib.Topology.Connected.TotallyDisconnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsTotallySeparated", "kind": "definition", "module": "Mathlib.Topology.Connected.TotallyDisconnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isTotallySeparated_empty", "kind": "theorem", "module": "Mathlib.Topology.Connected.TotallyDisconnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isTotallySeparated_singleton", "kind": "theorem", "module": "Mathlib.Topology.Connected.TotallyDisconnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isTotallyDisconnected_of_isTotallySeparated", "kind": "theorem", "module": "Mathlib.Topology.Connected.TotallyDisconnected", "is_tactic_proof": true, "tactics": ["intro", "by_contra", "obtain", "refine", "rw"], "tactic_count": 5}
{"name": "TotallySeparatedSpace.totallyDisconnectedSpace", "kind": "instance", "module": "Mathlib.Topology.Connected.TotallyDisconnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TotallySeparatedSpace.of_discrete", "kind": "instance", "module": "Mathlib.Topology.Connected.TotallyDisconnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "totallySeparatedSpace_iff_exists_isClopen", "kind": "theorem", "module": "Mathlib.Topology.Connected.TotallyDisconnected", "is_tactic_proof": true, "tactics": ["simp", "refine", "exact", "exact"], "tactic_count": 4}
{"name": "exists_isClopen_of_totally_separated", "kind": "theorem", "module": "Mathlib.Topology.Connected.TotallyDisconnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.image_eq_of_connectedComponent_eq", "kind": "theorem", "module": "Mathlib.Topology.Connected.TotallyDisconnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.connectedComponentsLift", "kind": "definition", "module": "Mathlib.Topology.Connected.TotallyDisconnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.connectedComponentsLift_continuous", "kind": "theorem", "module": "Mathlib.Topology.Connected.TotallyDisconnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.connectedComponentsLift_apply_coe", "kind": "theorem", "module": "Mathlib.Topology.Connected.TotallyDisconnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.connectedComponentsLift_comp_coe", "kind": "theorem", "module": "Mathlib.Topology.Connected.TotallyDisconnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "connectedComponents_lift_unique'", "kind": "theorem", "module": "Mathlib.Topology.Connected.TotallyDisconnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.connectedComponentsLift_unique", "kind": "theorem", "module": "Mathlib.Topology.Connected.TotallyDisconnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConnectedComponents.totallyDisconnectedSpace", "kind": "instance", "module": "Mathlib.Topology.Connected.TotallyDisconnected", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "image_preimage_eq", "refine", "rw", "exact"], "tactic_count": 7}
{"name": "Continuous.connectedComponentsMap", "kind": "definition", "module": "Mathlib.Topology.Connected.TotallyDisconnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.connectedComponentsMap_continuous", "kind": "theorem", "module": "Mathlib.Topology.Connected.TotallyDisconnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPreconnected.constant", "kind": "theorem", "module": "Mathlib.Topology.Connected.TotallyDisconnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PreconnectedSpace.constant", "kind": "theorem", "module": "Mathlib.Topology.Connected.TotallyDisconnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPreconnected.constant_of_mapsTo", "kind": "theorem", "module": "Mathlib.Topology.Connected.TotallyDisconnected", "is_tactic_proof": true, "tactics": ["let", "suffices", "rw", "exact"], "tactic_count": 4}
{"name": "IsPreconnected.eqOn_const_of_mapsTo", "kind": "theorem", "module": "Mathlib.Topology.Connected.TotallyDisconnected", "is_tactic_proof": true, "tactics": ["rcases", "exact", "exact"], "tactic_count": 3}
{"name": "IsRetrocompact", "kind": "definition", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRetrocompact.empty", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsRetrocompact.univ", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsRetrocompact.singleton", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRetrocompact.union", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.Constructible.0.supClosed_isRetrocompact", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRetrocompact.finsetSup", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": true, "tactics": ["induction", "empty", "cons", "rw", "exact"], "tactic_count": 5}
{"name": "IsRetrocompact.finsetSup'", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsRetrocompact.iUnion", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRetrocompact.sUnion", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRetrocompact.biUnion", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRetrocompact.inter", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.Constructible.0.infClosed_isRetrocompact", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRetrocompact.finsetInf", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": true, "tactics": ["induction", "empty", "cons", "rw", "exact"], "tactic_count": 5}
{"name": "IsRetrocompact.finsetInf'", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsRetrocompact.iInter", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRetrocompact.sInter", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRetrocompact.biInter", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRetrocompact.inter_isOpen", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRetrocompact.isOpen_inter", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRetrocompact_iff_isSpectralMap_subtypeVal", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": true, "tactics": ["refine", "rw", "inter_comm]", "exact", "simpa"], "tactic_count": 5}
{"name": "IsRetrocompact.image_of_isEmbedding", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": true, "tactics": ["rintro", "rw", "refine", "rw", "exact"], "tactic_count": 5}
{"name": "IsRetrocompact.preimage_of_isOpenEmbedding", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": true, "tactics": ["rintro", "rw", "exact"], "tactic_count": 3}
{"name": "IsRetrocompact.preimage_of_isClosedEmbedding", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": true, "tactics": ["rintro", "have", "simpa", "have", "simpa", "image_preimage_inter]"], "tactic_count": 6}
{"name": "Topology.IsConstructible", "kind": "definition", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsConstructible.empty", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsConstructible.univ", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsConstructible.union", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsConstructible.inter", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsConstructible.sdiff", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsConstructible.himp", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.isConstructible_compl", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsConstructible.iUnion", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsConstructible.iInter", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsConstructible.sUnion", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsConstructible.sInter", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsConstructible.biUnion", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsConstructible.biInter", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRetrocompact.isConstructible", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsConstructible.empty_union_induction", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": true, "tactics": ["induction", "mem", "bot", "sup", "compl"], "tactic_count": 5}
{"name": "Topology.IsConstructible.preimage", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": true, "tactics": ["induction", "open_retrocompact", "union", "compl"], "tactic_count": 4}
{"name": "Topology.IsConstructible.preimage_of_isOpenEmbedding", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsConstructible.preimage_of_isClosedEmbedding", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsConstructible.image_of_isOpenEmbedding", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": true, "tactics": ["induction", "open_retrocompact", "exact", "union", "compl", "rw", "exact"], "tactic_count": 7}
{"name": "Topology.IsConstructible.image_of_isClosedEmbedding", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": true, "tactics": ["induction", "open_retrocompact", "hUcomp", "have", "simpa", "suffices", "simpa", "rintro", "rw", "exact", "hfcomp", "union", "compl", "rw", "exact"], "tactic_count": 15}
{"name": "Topology.isConstructible_preimage_iff_of_isOpenEmbedding", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuasiSeparatedSpace.of_isOpenCover", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRetrocompact.isCompact", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsCompact.isRetrocompact", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.isConstructible", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuasiSeparatedSpace.isRetrocompact_iff_isCompact", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsConstructible.induction_of_isTopologicalBasis", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": true, "tactics": ["induction", "isSublattice", "exact", "bot_mem", "top_mem", "sdiff", "hV", "have", "obtain", "obtain", "simp_rw", "induction", "empty", "simp_rw", "exact", "union", "sup"], "tactic_count": 17}
{"name": "Topology.IsLocallyConstructible", "kind": "definition", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsConstructible.isLocallyConstructible", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsRetrocompact.isLocallyConstructible", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsLocallyConstructible.empty", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsLocallyConstructible.univ", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsLocallyConstructible.inter", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": true, "tactics": ["rintro", "obtain", "obtain", "refine", "change", "exact"], "tactic_count": 6}
{"name": "Topology.IsLocallyConstructible.finsetInf", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": true, "tactics": ["induction", "empty", "cons", "rw", "exact"], "tactic_count": 5}
{"name": "Topology.IsLocallyConstructible.finsetInf'", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "_private.Mathlib.Topology.Constructible.0.Topology.infClosed_isLocallyConstructible", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsLocallyConstructible.iInter", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsLocallyConstructible.sInter", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsLocallyConstructible.union", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": true, "tactics": ["rintro", "obtain", "obtain", "refine", "have", "ext", "rw", "exact"], "tactic_count": 8}
{"name": "Topology.IsLocallyConstructible.iUnion", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsLocallyConstructible.biUnion", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsLocallyConstructible.sUnion", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsLocallyConstructible.preimage_of_isOpenEmbedding", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": true, "tactics": ["intro", "obtain", "exact"], "tactic_count": 3}
{"name": "Topology.IsLocallyConstructible.isConstructible_of_subset_of_isCompact", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": false, "tactics": ["have", "have", "have", "have", "have", "have", "rwa", "choose", "obtain", "convert", "apply", "rw", "exact", "exact"], "tactic_count": 14}
{"name": "Topology.IsLocallyConstructible.isConstructible", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsLocallyConstructible.inter_of_isOpen_isCompact", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsLocallyConstructible.of_isOpenCover", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": true, "tactics": ["intro", "have", "have", "refine", "let", "convert", "ext", "simp"], "tactic_count": 8}
{"name": "Topology.IsLocallyConstructible.of_isOpenCover'", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsLocallyConstructible.iff_of_isOpenCover", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsLocallyConstructible.iff_isConstructible_of_isOpenCover", "kind": "theorem", "module": "Mathlib.Topology.Constructible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instTopologicalSpaceQuot", "kind": "instance", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instTopologicalSpaceQuotient", "kind": "instance", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instTopologicalSpaceSigma", "kind": "instance", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.topologicalSpace", "kind": "instance", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.topologicalSpace", "kind": "instance", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instTopologicalSpaceAdditive", "kind": "instance", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instTopologicalSpaceMultiplicative", "kind": "instance", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDiscreteTopologyAdditive", "kind": "instance", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDiscreteTopologyMultiplicative", "kind": "instance", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCompactSpaceAdditive", "kind": "instance", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCompactSpaceMultiplicative", "kind": "instance", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instNoncompactSpaceAdditive", "kind": "instance", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instNoncompactSpaceMultiplicative", "kind": "instance", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instWeaklyLocallyCompactSpaceAdditive", "kind": "instance", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instWeaklyLocallyCompactSpaceMultiplicative", "kind": "instance", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instLocallyCompactSpaceAdditive", "kind": "instance", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instLocallyCompactSpaceMultiplicative", "kind": "instance", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_ofMul", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_toMul", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_ofAdd", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_toAdd", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpenMap_ofMul", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpenMap_toMul", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpenMap_ofAdd", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpenMap_toAdd", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosedMap_ofMul", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosedMap_toMul", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosedMap_ofAdd", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosedMap_toAdd", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhds_ofMul", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhds_ofAdd", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhds_toMul", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhds_toAdd", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instTopologicalSpace", "kind": "instance", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instDiscreteTopology", "kind": "instance", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_toDual", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_ofDual", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpenMap_toDual", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpenMap_ofDual", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosedMap_toDual", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosedMap_ofDual", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhds_toDual", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhds_ofDual", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instNeBotNhdsWithinIoi", "kind": "instance", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instNeBotNhdsWithinIio", "kind": "instance", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quotient.preimage_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dense.quotient", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DenseRange.quotient", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_map_of_le", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_map_sInf", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDiscreteTopologySubtype", "kind": "instance", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.discreteTopology", "kind": "instance", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.discreteTopology", "kind": "instance", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "comap_nhdsWithin_range", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_nhds_subtype", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhds_subtype", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhds_subtype_eq_comap_nhdsWithin", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "nhdsWithin_subtype_eq_bot_iff", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "nhds_ne_subtype_eq_bot_iff", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "nhds_ne_subtype_neBot_iff", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "isDiscrete_iff_discreteTopology", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetLike.isDiscrete_iff_discreteTopology", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteTopology.isDiscrete", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CofiniteTopology", "kind": "definition", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CofiniteTopology.of", "kind": "definition", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CofiniteTopology.instInhabited", "kind": "instance", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CofiniteTopology.instTopologicalSpace", "kind": "instance", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CofiniteTopology.isOpen_iff", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CofiniteTopology.isOpen_iff'", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CofiniteTopology.isClosed_iff", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CofiniteTopology.nhds_eq", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": true, "tactics": ["ext", "rw", "constructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 7}
{"name": "CofiniteTopology.mem_nhds_iff", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MapClusterPt.curry_prodMap", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": true, "tactics": ["rw", "rw", "rintro", "rw", "exact"], "tactic_count": 5}
{"name": "MapClusterPt.prodMap", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_bool_rng", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Topology.IsInducing.subtypeVal", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsInducing.of_codRestrict", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsEmbedding.subtypeVal", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsClosedEmbedding.subtypeVal", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_subtype_val", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.subtype_val", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.isOpenEmbedding_subtypeVal", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.isOpenMap_subtype_val", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpenMap.restrict", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.isClosedEmbedding_subtypeVal", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.isClosedMap_subtype_val", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosedMap.restrict", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.subtype_mk", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpenMap.subtype_mk", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosedMap.subtype_mk", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.subtype_coind", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpenMap.subtype_coind", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosedMap.subtype_coind", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.subtype_map", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpenMap.subtype_map", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosedMap.subtype_map", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_inclusion", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.isOpenMap_inclusion", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.isClosedMap_inclusion", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_rangeFactorization_iff", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.rangeFactorization", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousAt_subtype_val", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.ofEqSubtypes", "kind": "definition", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.ofEqSubtypes_toEquiv", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.dense_iff", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "denseRange_inclusion_iff", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "map_nhds_subtype_val", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "map_nhds_subtype_coe_eq_nhds", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhds_subtype_eq_comap", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_subtype_rng", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "closure_subtype", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousAt_codRestrict_iff", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.restrict", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.restrictPreimage", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.codRestrict", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpenMap.codRestrict", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosedMap.codRestrict", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.restrict", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpenMap.mapsToRestrict", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosedMap.mapsToRestrict", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.restrictPreimage", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsEmbedding.restrict", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsOpenEmbedding.restrict", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsInducing.codRestrict", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsEmbedding.codRestrict", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsEmbedding.inclusion", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsOpenEmbedding.inclusion", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsClosedEmbedding.inclusion", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteTopology.of_subset", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDiscrete.mono", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteTopology.preimage_of_continuous_injective", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsQuotientMap.restrictPreimage_isOpen", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "isClosed_preimage_val", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": ["rw", "subset_antisymm_iff,", "exacts"], "tactic_count": 3}
{"name": "frontier_inter_open_inter", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": true, "tactics": ["simp", "ht.isOpenMap_subtype_val.preimage_frontier_eq_frontier_preimage"], "tactic_count": 2}
{"name": "IsOpen.preimage_val", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_open_dense_of_open_dense_subtype", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": true, "tactics": ["choose", "refine", "rw", "intro", "subst", "refine", "exact", "obtain", "simpa"], "tactic_count": 9}
{"name": "IsClosed.preimage_val", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.inter_preimage_val_iff", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.inter_preimage_val_iff", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isQuotientMap_quot_mk", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_quot_mk", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_quot_lift", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isQuotientMap_quotient_mk'", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_quotient_mk'", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.quotient_lift", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.quotient_liftOn'", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.quotient_map'", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_pi_iff", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "continuous_pi", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_apply", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_apply_apply", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousAt_apply", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.apply_nhds", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.piMap", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhds_pi", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsOpenMap.piMap", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "IsOpenQuotientMap.piMap", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_pi_nhds", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "continuousAt_pi", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousAt_pi'", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.piMap", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsInducing.piMap", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Topology.IsEmbedding.piMap", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.continuous_precomp'", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.continuous_precomp", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.continuous_postcomp'", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.continuous_postcomp", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.induced_precomp'", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Pi.induced_precomp", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.piCurry", "kind": "definition", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.continuous_restrict", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.continuous_restrict₂", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.continuous_restrict", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.continuous_restrict₂", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.continuous_restrict_apply", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.continuous_restrict₂_apply", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.continuous_restrict_apply", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.continuous_restrict₂_apply", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.induced_restrict", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Pi.induced_restrict_sUnion", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Filter.Tendsto.update", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.update", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.update", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_update", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_mulSingle", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.finCons", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.finCons", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.finCons", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.matrixVecCons", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.matrixVecCons", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.matrixVecCons", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.finSnoc", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.finSnoc", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.finSnoc", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.finInsertNth", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.finInsertNth", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.finInsertNth", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.finInit", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.finInit", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.finInit", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.finTail", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.finTail", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.finTail", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpen_set_pi", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "isOpen_pi_iff", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "refine", "rintro", "refine", "simp_rw", "exact", "exact", "rintro", "classical", "refine", "by_cases", "use", "simp_rw", "exact", "use", "simp_rw", "exact", "rw", "simp"], "tactic_count": 20}
{"name": "isOpen_pi_iff'", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": true, "tactics": ["cases", "rw", "simp_rw", "refine", "rintro", "refine", "rw", "exact", "exact"], "tactic_count": 9}
{"name": "isClosed_set_pi", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Topology.IsClosedEmbedding.piMap", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsOpenEmbedding.piMap", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_nhds_of_pi_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "set_pi_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "set_pi_mem_nhds_iff", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "interior_pi_set", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "exists_finset_piecewise_mem_of_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": true, "tactics": ["simp", "rcases", "refine", "simpa"], "tactic_count": 4}
{"name": "pi_generateFrom_eq", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": true, "tactics": ["refine", "apply", "rintro", "letI", "exact", "classical", "refine", "refine", "simp"], "tactic_count": 9}
{"name": "pi_eq_generateFrom", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pi_generateFrom_eq_finite", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": true, "tactics": ["cases", "rw", "refine", "exact", "rintro", "letI", "refine", "choose", "refine", "classical", "rw", "refine", "by_cases"], "tactic_count": 13}
{"name": "induced_to_pi", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "inducing_iInf_to_pi", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.discreteTopology", "kind": "instance", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.isEmbedding_comp", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": true, "tactics": ["refine", "simp"], "tactic_count": 2}
{"name": "continuous_sigmaMk", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpen_sigma_iff", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "isClosed_sigma_iff", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "isOpenMap_sigmaMk", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": true, "tactics": ["intro", "rw", "intro", "rcases", "rwa", "rw", "exact"], "tactic_count": 7}
{"name": "isOpen_range_sigmaMk", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosedMap_sigmaMk", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": true, "tactics": ["intro", "rw", "intro", "rcases", "rwa", "rw", "exact"], "tactic_count": 7}
{"name": "isClosed_range_sigmaMk", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsOpenEmbedding.sigmaMk", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsClosedEmbedding.sigmaMk", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsEmbedding.sigmaMk", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.nhds_mk", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.nhds_eq", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": true, "tactics": ["cases", "apply"], "tactic_count": 2}
{"name": "comap_sigmaMk_nhds", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpen_sigma_fst_preimage", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": true, "tactics": ["rw", "simp", "exact"], "tactic_count": 3}
{"name": "continuous_sigma_iff", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": true, "tactics": ["delta", "rw", "exact"], "tactic_count": 3}
{"name": "continuous_sigma", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inducing_sigma", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": true, "tactics": ["refine", "rcases", "refine", "simpa", "refine", "rw", "rcases", "filter_upwards", "simpa"], "tactic_count": 9}
{"name": "continuous_sigma_map", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.sigma_map", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpenMap_sigma", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "isOpenMap_sigma_map", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.isInducing_sigmaMap", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": true, "tactics": ["simp", "map_inj"], "tactic_count": 2}
{"name": "Topology.isEmbedding_sigmaMap", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Topology.isOpenEmbedding_sigmaMap", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ULift.isOpen_iff", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ULift.isClosed_iff", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "continuous_uliftDown", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_uliftUp", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_uliftMap", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": true, "tactics": ["change", "fun_prop"], "tactic_count": 2}
{"name": "Topology.IsEmbedding.uliftDown", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsClosedEmbedding.uliftDown", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDiscreteTopologyULift", "kind": "instance", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.trans", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": true, "tactics": ["rcases", "rw", "exact"], "tactic_count": 3}
{"name": "IsClosed.trans", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": true, "tactics": ["rcases", "rw", "exact"], "tactic_count": 3}
{"name": "nhdsSet_prod_le", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.eventually_nhdsSet_prod_iff", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Filter.Eventually.prod_nhdsSet", "kind": "theorem", "module": "Mathlib.Topology.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instTopologicalSpaceSum", "kind": "instance", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instTopologicalSpaceProd", "kind": "instance", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_prodMk", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_fst", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.fst", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.fst'", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousAt_fst", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.fst", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.fst'", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.fst''", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.fst_nhds", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_snd", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.snd", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.snd'", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousAt_snd", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.snd", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.snd'", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.snd''", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.snd_nhds", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.prodMk", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.prodMk_right", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": true, "tactics": ["fun_prop"], "tactic_count": 1}
{"name": "Continuous.prodMk_left", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": true, "tactics": ["fun_prop"], "tactic_count": 1}
{"name": "IsClosed.setOf_mapsTo", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Continuous.comp₂", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.comp₃", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.comp₄", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.prodMap", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_inf_dom_left₂", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": true, "tactics": ["have", "have", "have", "exact"], "tactic_count": 4}
{"name": "continuous_inf_dom_right₂", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": true, "tactics": ["have", "have", "have", "exact"], "tactic_count": 4}
{"name": "continuous_sInf_dom₂", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": true, "tactics": ["have", "have", "have", "exact"], "tactic_count": 4}
{"name": "Filter.Eventually.prod_inl_nhds", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Eventually.prod_inr_nhds", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Eventually.prodMk_nhds", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_swap", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosedMap_swap", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.uncurry_left", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.uncurry_right", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_curry", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.prod", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhds_prod_eq", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": true, "tactics": ["rw", "nhds_inf", "nhds_induced]"], "tactic_count": 3}
{"name": "nhdsWithin_prod_eq", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Prod.instNeBotNhdsWithinIio", "kind": "instance", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "Prod.instNeBotNhdsWithinIoi", "kind": "instance", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "mem_nhds_prod_iff", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mem_nhdsWithin_prod_iff", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.HasBasis.prod_nhds", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Filter.HasBasis.prod_nhds'", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_nhds_prod_iff'", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.tendsto_iff", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "instDiscreteTopologyProd", "kind": "instance", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "prod_mem_nhds_iff", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "prod_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpen_setOf_disjoint_nhds_nhds", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": true, "tactics": ["simp", "intro", "obtain", "exact", "mem_nhds_prod_iff'.mpr", "disjoint_of_disjoint_of_mem"], "tactic_count": 6}
{"name": "Filter.Eventually.prod_nhds", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.prodMap_nhds", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Filter.EventuallyLE.prodMap_nhds", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "nhds_swap", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.Tendsto.prodMk_nhds", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Filter.Tendsto.prodMap_nhds", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Filter.Eventually.curry_nhds", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ContinuousAt.prodMk", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.prodMap", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.prodMap'", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.comp₂", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.comp₂_of_eq", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Continuous.curry_left", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.curry_right", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "prod_generateFrom_generateFrom_eq", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "prod_eq_generateFrom", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpen_prod_iff", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "prod_induced_induced", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": true, "tactics": ["delta", "simp_rw", "rfl"], "tactic_count": 3}
{"name": "exists_nhds_square", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "map_fst_nhdsWithin", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": true, "tactics": ["refine", "rcases", "rw", "rcases", "simp", "exact"], "tactic_count": 6}
{"name": "map_fst_nhds", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpenMap_fst", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "map_snd_nhdsWithin", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": true, "tactics": ["refine", "rcases", "rw", "rcases", "simp", "exact"], "tactic_count": 6}
{"name": "map_snd_nhds", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpenMap_snd", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpen_prod_iff'", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": true, "tactics": ["rcases", "simp", "have", "constructor", "intro", "refine", "simpa", "simpa", "intro", "simp", "exact"], "tactic_count": 11}
{"name": "isQuotientMap_fst", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isQuotientMap_snd", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "closure_prod_eq", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "interior_prod_eq", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "frontier_prod_eq", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "frontier_prod_univ_eq", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "frontier_univ_prod_eq", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "map_mem_closure₂", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.prod", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dense.prod", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DenseRange.prodMap", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Topology.IsInducing.prodMap", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.isInducing_const_prod", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": true, "tactics": ["simp_rw", "top_inf_eq]"], "tactic_count": 2}
{"name": "Topology.isInducing_prod_const", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": true, "tactics": ["simp_rw", "inf_top_eq]"], "tactic_count": 2}
{"name": "isInducing_prodMkLeft", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isInducing_prodMkRight", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsEmbedding.prodMap", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpenMap.prodMap", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": true, "tactics": ["rw", "rintro", "rw", "exact"], "tactic_count": 4}
{"name": "Topology.IsOpenEmbedding.prodMap", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isEmbedding_graph", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isEmbedding_prodMkLeft", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isEmbedding_prodMkRight", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpenQuotientMap.prodMap", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.prod_mono", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.prodCongr", "kind": "definition", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.prodCongr_symm", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.coe_prodCongr", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.prodComm", "kind": "definition", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.prodComm_symm", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.coe_prodComm", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.prodAssoc", "kind": "definition", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.prodAssoc_toEquiv", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.prodProdProdComm", "kind": "definition", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.prodProdProdComm_symm", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.prodPUnit", "kind": "definition", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.punitProd", "kind": "definition", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.coe_punitProd", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_sum_dom", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_sumElim", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.sumElim", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_isLeft", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_isRight", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_inl", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_inr", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_sum_swap", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpen_sum_iff", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosed_sum_iff", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "isOpenMap_inl", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpenMap_inr", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosedMap_inl", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosedMap_inr", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsOpenEmbedding.inl", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsOpenEmbedding.inr", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsEmbedding.inl", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsEmbedding.inr", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpen_range_inl", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpen_range_inr", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosed_range_inl", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "isClosed_range_inr", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Topology.IsClosedEmbedding.inl", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsClosedEmbedding.inr", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhds_inl", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhds_inr", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_sumMap", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.sumMap", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpenMap_sum", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsOpenMap.sumMap", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpenMap_sumElim", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsOpenMap.sumElim", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpenEmbedding.sumElim", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "isClosedMap_sum", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "rintro", "rw", "convert", "ext", "simp"], "tactic_count": 8}
{"name": "IsClosedMap.sumMap", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosedMap_sumElim", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsClosedMap.sumElim", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosedEmbedding.sumElim", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Homeomorph.sumCongr", "kind": "definition", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.sumCongr_symm", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.sumCongr_refl", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": true, "tactics": ["ext", "cases"], "tactic_count": 2}
{"name": "Homeomorph.sumCongr_trans", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": true, "tactics": ["ext", "cases"], "tactic_count": 2}
{"name": "Homeomorph.sumComm", "kind": "definition", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.sumComm_symm", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.coe_sumComm", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.continuous_sumAssoc", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.continuous_sumAssoc_symm", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.sumAssoc", "kind": "definition", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.sumAssoc_toEquiv", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.sumSumSumComm", "kind": "definition", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.sumSumSumComm_toEquiv", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.sumSumSumComm_symm", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.sumEmpty", "kind": "definition", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.emptySum", "kind": "definition", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.coe_emptySum", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.sumProdDistrib", "kind": "definition", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.prodSumDistrib", "kind": "definition", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsInducing.sumElim_left", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsInducing.sumElim_right", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsInducing.sumElim", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": true, "tactics": ["rw", "rw", "rw", "intro", "apply", "obtain", "simp", "sup_le_iff,", "convert", "rw", "rw", "exact", "rw", "exact"], "tactic_count": 14}
{"name": "Topology.IsInducing.disjoint_of_sumElim_aux", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": true, "tactics": ["rcases", "have", "rw", "have", "rw", "image_univ]", "exact", "exact"], "tactic_count": 8}
{"name": "IsOpenEmbedding.sumSwap", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsInducing.sumSwap", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isInducing_sumElim", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsInducing.sumElim_of_separatedNhds", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsEmbedding.sumElim_left", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsEmbedding.sumElim_right", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isEmbedding_sumElim", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": true, "tactics": ["simp_rw", "constructor", "intro", "exact", "intro", "refine", "exact"], "tactic_count": 7}
{"name": "Topology.IsEmbedding.sumElim", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsEmbedding.sumElim_of_separatedNhds", "kind": "theorem", "module": "Mathlib.Topology.Constructions.SumProd", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_def", "kind": "theorem", "module": "Mathlib.Topology.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.preimage", "kind": "theorem", "module": "Mathlib.Topology.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.continuous_symm_iff", "kind": "theorem", "module": "Mathlib.Topology.Continuous", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Equiv.isOpenMap_symm_iff", "kind": "theorem", "module": "Mathlib.Topology.Continuous", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "continuous_congr", "kind": "theorem", "module": "Mathlib.Topology.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.congr", "kind": "theorem", "module": "Mathlib.Topology.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.tendsto", "kind": "theorem", "module": "Mathlib.Topology.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousAt_def", "kind": "theorem", "module": "Mathlib.Topology.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousAt_congr", "kind": "theorem", "module": "Mathlib.Topology.Continuous", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousAt.congr", "kind": "theorem", "module": "Mathlib.Topology.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.preimage_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.eventually_mem", "kind": "theorem", "module": "Mathlib.Topology.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_continuousAt_of_tendsto", "kind": "theorem", "module": "Mathlib.Topology.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClusterPt.map", "kind": "theorem", "module": "Mathlib.Topology.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "preimage_interior_subset_interior_preimage", "kind": "theorem", "module": "Mathlib.Topology.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_id", "kind": "theorem", "module": "Mathlib.Topology.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_id'", "kind": "theorem", "module": "Mathlib.Topology.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.comp", "kind": "theorem", "module": "Mathlib.Topology.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.comp'", "kind": "theorem", "module": "Mathlib.Topology.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.iterate", "kind": "theorem", "module": "Mathlib.Topology.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.comp", "kind": "theorem", "module": "Mathlib.Topology.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.comp'", "kind": "theorem", "module": "Mathlib.Topology.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.comp_of_eq", "kind": "theorem", "module": "Mathlib.Topology.Continuous", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "Continuous.tendsto", "kind": "theorem", "module": "Mathlib.Topology.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.tendsto'", "kind": "theorem", "module": "Mathlib.Topology.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.continuousAt", "kind": "theorem", "module": "Mathlib.Topology.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_iff_continuousAt", "kind": "theorem", "module": "Mathlib.Topology.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousAt_const", "kind": "theorem", "module": "Mathlib.Topology.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_const", "kind": "theorem", "module": "Mathlib.Topology.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.continuousAt", "kind": "theorem", "module": "Mathlib.Topology.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_of_const", "kind": "theorem", "module": "Mathlib.Topology.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousAt_id", "kind": "theorem", "module": "Mathlib.Topology.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousAt_id'", "kind": "theorem", "module": "Mathlib.Topology.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.iterate", "kind": "theorem", "module": "Mathlib.Topology.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_iff_isClosed", "kind": "theorem", "module": "Mathlib.Topology.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.preimage", "kind": "theorem", "module": "Mathlib.Topology.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_closure_image", "kind": "theorem", "module": "Mathlib.Topology.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.closure_preimage_subset", "kind": "theorem", "module": "Mathlib.Topology.Continuous", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Continuous.frontier_preimage_subset", "kind": "theorem", "module": "Mathlib.Topology.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.MapsTo.closure", "kind": "theorem", "module": "Mathlib.Topology.Continuous", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "image_closure_subset_closure_image", "kind": "theorem", "module": "Mathlib.Topology.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "closure_image_closure", "kind": "theorem", "module": "Mathlib.Topology.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "closure_subset_preimage_closure_image", "kind": "theorem", "module": "Mathlib.Topology.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "map_mem_closure", "kind": "theorem", "module": "Mathlib.Topology.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.MapsTo.closure_left", "kind": "theorem", "module": "Mathlib.Topology.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.lift'_closure", "kind": "theorem", "module": "Mathlib.Topology.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_lift'_closure_nhds", "kind": "theorem", "module": "Mathlib.Topology.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Surjective.denseRange", "kind": "theorem", "module": "Mathlib.Topology.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "denseRange_id", "kind": "theorem", "module": "Mathlib.Topology.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "denseRange_iff_closure_range", "kind": "theorem", "module": "Mathlib.Topology.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DenseRange.closure_range", "kind": "theorem", "module": "Mathlib.Topology.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "denseRange_subtype_val", "kind": "theorem", "module": "Mathlib.Topology.Continuous", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Dense.denseRange_val", "kind": "theorem", "module": "Mathlib.Topology.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.range_subset_closure_image_dense", "kind": "theorem", "module": "Mathlib.Topology.Continuous", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "DenseRange.dense_image", "kind": "theorem", "module": "Mathlib.Topology.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DenseRange.subset_closure_image_preimage_of_isOpen", "kind": "theorem", "module": "Mathlib.Topology.Continuous", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "DenseRange.dense_of_mapsTo", "kind": "theorem", "module": "Mathlib.Topology.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DenseRange.comp", "kind": "theorem", "module": "Mathlib.Topology.Continuous", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "DenseRange.nonempty_iff", "kind": "theorem", "module": "Mathlib.Topology.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DenseRange.nonempty", "kind": "theorem", "module": "Mathlib.Topology.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DenseRange.some", "kind": "definition", "module": "Mathlib.Topology.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DenseRange.exists_mem_open", "kind": "theorem", "module": "Mathlib.Topology.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DenseRange.mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LibraryNote.continuity_lemma_statement", "kind": "definition", "module": "Mathlib.Topology.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LibraryNote.comp_of_eq_lemmas", "kind": "definition", "module": "Mathlib.Topology.Continuous", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousFunctions.instCoeFunElemForallSetOfContinuous", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instMul", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.coe_mul", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.mul_apply", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.mul_comp", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instOne", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.coe_one", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.one_apply", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.one_comp", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.comp_one", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.const_one", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instNatCast", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.coe_natCast", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.natCast_apply", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instIntCast", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.coe_intCast", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.intCast_apply", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instNSMul", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instPow", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.coe_pow", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.pow_apply", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.pow_comp", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instInvOfContinuousInv", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.coe_inv", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.inv_apply", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.inv_comp", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instDivOfContinuousDiv", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.coe_div", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.div_apply", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.div_comp", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instZSMul", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instZPow", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.coe_zpow", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.zpow_apply", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.zpow_comp", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousSubmonoid", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousSubgroup", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instSemigroupOfContinuousMul", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instCommSemigroupOfContinuousMul", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instMulOneClassOfContinuousMul", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instMulZeroClassOfContinuousMul", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instSemigroupWithZeroOfContinuousMul", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instMonoidOfContinuousMul", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instMonoidWithZeroOfContinuousMul", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instCommMonoidOfContinuousMul", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instCommMonoidWithZeroOfContinuousMul", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instContinuousMulOfLocallyCompactSpace", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.coeFnMonoidHom", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonoidHom.compLeftContinuous", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.compMonoidHom'", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.coe_prod", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.prod_apply", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousMap.instGroupOfIsTopologicalGroup", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instCommGroupContinuousMap", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instIsTopologicalGroup", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.hasProd_apply", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": true, "tactics": ["let", "exact"], "tactic_count": 2}
{"name": "ContinuousMap.multipliable_apply", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.tprod_apply", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousSubsemiring", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousSubring", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instNonUnitalNonAssocSemiringOfIsTopologicalSemiring", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instNonUnitalSemiringOfIsTopologicalSemiring", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instAddMonoidWithOneOfContinuousAdd", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instNonAssocSemiringOfIsTopologicalSemiring", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instSemiringOfIsTopologicalSemiring", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instNonUnitalNonAssocRingOfIsTopologicalRing", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instNonUnitalRingOfIsTopologicalRing", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instNonAssocRingOfIsTopologicalRing", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instRing", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instNonUnitalCommSemiringOfIsTopologicalSemiring", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instCommSemiringOfIsTopologicalSemiring", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instNonUnitalCommRingOfIsTopologicalRing", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instCommRingOfIsTopologicalRing", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instIsTopologicalSemiringOfLocallyCompactSpace", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instIsTopologicalRingOfLocallyCompactSpace", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RingHom.compLeftContinuous", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.coeFnRingHom", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousSubmodule", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instSMul", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instContinuousConstSMul", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instContinuousSMul", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.coe_smul", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.smul_apply", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.smul_comp", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instSMulCommClass", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instIsScalarTower", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instIsCentralScalar", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instIsScalarTower_1", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instSMulCommClass_1", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instSMulCommClass_2", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instMulActionOfContinuousConstSMul", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instDistribMulActionOfContinuousConstSMul", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.module", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.compLeftContinuous", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.const", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.coeFnLinearMap", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.evalCLM", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousSubalgebra", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.C", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.C_apply", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.algebra", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlgHom.compLeftContinuous", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.compRightAlgHom", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.compRightAlgHom_continuous", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.coeFnAlgHom", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.SeparatesPoints", "kind": "abbrev", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.separatesPoints_monotone", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "algebraMap_apply", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Set.SeparatesPointsStrongly", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subalgebra.SeparatesPoints.strongly", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.subsingleton_subalgebra", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instSMul'", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.coe_smul'", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.smul_apply'", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.module'", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.evalAlgHom", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "map_continuousAt", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "map_continuousWithinAt", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.continuousAt", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.map_specializes", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.equivFnOfDiscrete", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.coe_equivFnOfDiscrete", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.equivFnOfDiscrete_symm_apply", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.id", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.coe_id", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.const", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.coe_const", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.constPi", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instInhabited", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.id_apply", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.const_apply", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.comp", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.coe_comp", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.comp_apply", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.comp_assoc", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.id_comp", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.comp_id", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.const_comp", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.comp_const", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.cancel_right", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.cancel_left", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instNontrivialOfNonempty", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.continuousMapCongr", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.fst", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.snd", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.prodMk", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.prodMap", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.prod_eval", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.prodSwap", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.sigmaMk", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.sigma", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.sigmaEquiv", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.pi", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.pi_eval", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.eval", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.piEquiv", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.piMap", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.precomp", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.restrict", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.coe_restrict", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.restrict_apply", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.restrict_apply_mk", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.injective_restrict", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.restrictPreimage", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.mkD", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.mkD_of_continuous", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousMap.mkD_of_not_continuous", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousMap.mkD_apply_of_continuous", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ContinuousMap.mkD_of_continuousOn", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.mkD_of_not_continuousOn", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ContinuousMap.mkD_apply_of_continuousOn", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ContinuousMap.mkD_eq_self", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.liftCover", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.liftCover_coe", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ContinuousMap.liftCover_restrict", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "ContinuousMap.liftCover'", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.liftCover_coe'", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.liftCover_restrict'", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.inclusion", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.RightInverse.homeomorph", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsQuotientMap.homeomorph", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsQuotientMap.lift", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsQuotientMap.lift_comp", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": true, "tactics": ["ext", "simpa"], "tactic_count": 2}
{"name": "Topology.IsQuotientMap.liftEquiv", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.instContinuousMapClass", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.coe_refl", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.coe_trans", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.symm_comp_toContinuousMap", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Homeomorph.toContinuousMap_comp_symm", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "compactlySupported", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.BoundedCompactlySupported", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.termC_cb(_,_)", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.BoundedCompactlySupported", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction._aux_Mathlib_Topology_ContinuousMap_BoundedCompactlySupported___macroRules_BoundedContinuousFunction_termC_cb(_,_)_1", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.BoundedCompactlySupported", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction._aux_Mathlib_Topology_ContinuousMap_BoundedCompactlySupported___unexpand_compactlySupported_1", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.BoundedCompactlySupported", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_compactlySupported", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.BoundedCompactlySupported", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exist_norm_eq", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.BoundedCompactlySupported", "is_tactic_proof": true, "tactics": ["by_cases", "obtain", "refine", "by_cases", "exact", "simp", "suffices", "rwa"], "tactic_count": 8}
{"name": "norm_lt_iff_of_compactlySupported", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.BoundedCompactlySupported", "is_tactic_proof": true, "tactics": ["refine", "obtain", "simpa", "obtain", "exact"], "tactic_count": 5}
{"name": "norm_lt_iff_of_nonempty_compactlySupported", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.BoundedCompactlySupported", "is_tactic_proof": true, "tactics": ["obtain", "exact", "exact"], "tactic_count": 3}
{"name": "compactlySupported_eq_top_of_isCompact", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.BoundedCompactlySupported", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "compactlySupported_eq_top", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.BoundedCompactlySupported", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "compactlySupported_eq_top_iff", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.BoundedCompactlySupported", "is_tactic_proof": true, "tactics": ["refine", "obtain", "simpa"], "tactic_count": 3}
{"name": "ofCompactSupport", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.BoundedCompactlySupported", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofCompactSupport_mem", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.BoundedCompactlySupported", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instSMulContinuousMapSubtypeBoundedContinuousFunctionMemTwoSidedIdealCompactlySupported", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.BoundedCompactlySupported", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.arzela_ascoli₁", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.ArzelaAscoli", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "refine", "rcases", "let", "ε₁", "that", "provided", "slightly", "sets", "data", "continuity", "have", "have", "let", "let", "choose", "obtain", "isCompact_univ.elim_finite_subcover_image", "rcases", "obtain", "rcases", "choose", "show", "simpa", "htβ", "to", "classical", "refine", "rintro", "refine", "obtain", "calc", "dist", "refine", "exact", "exact", "have", "calc", "dist"], "tactic_count": 40}
{"name": "BoundedContinuousFunction.arzela_ascoli₂", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.ArzelaAscoli", "is_tactic_proof": true, "tactics": ["using", "have", "let", "refine", "haveI", "refine", "rw", "exact", "let", "rw", "exact"], "tactic_count": 11}
{"name": "BoundedContinuousFunction.arzela_ascoli", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.ArzelaAscoli", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.term_→ᵇ_", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction._aux_Mathlib_Topology_ContinuousMap_Bounded_Basic___macroRules_BoundedContinuousFunction_term_→ᵇ__1", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction._aux_Mathlib_Topology_ContinuousMap_Bounded_Basic___unexpand_BoundedContinuousFunction_1", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.instFunLike", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.instBoundedContinuousMapClass", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.instCoeTC", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.coe_toContinuousMap", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.Simps.apply", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.bounded", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.continuous", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.ext", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.coe_mk", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.isBounded_range", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.isBounded_image", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.eq_of_empty", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.mkOfBound", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.mkOfBound_coe", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.mkOfCompact", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.mkOfCompact_apply", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.mkOfDiscrete", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.instDist", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.dist_eq", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.dist_set_exists", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": true, "tactics": ["rcases", "refine", "apply"], "tactic_count": 3}
{"name": "BoundedContinuousFunction.dist_coe_le_dist", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.ContinuousMap.Bounded.Basic.0.BoundedContinuousFunction.dist_nonneg'", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.dist_le", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.dist_le_iff_of_nonempty", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.dist_lt_of_nonempty_compact", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": true, "tactics": ["have", "obtain", "exact"], "tactic_count": 3}
{"name": "BoundedContinuousFunction.dist_lt_iff_of_compact", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": true, "tactics": ["fconstructor", "intro", "exact", "by_cases", "exact", "rintro", "convert", "apply", "rw", "exact"], "tactic_count": 10}
{"name": "BoundedContinuousFunction.dist_lt_iff_of_nonempty_compact", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.instPseudoMetricSpace", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.instMetricSpace", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.nndist_eq", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.nndist_set_exists", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.nndist_coe_le_nndist", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.dist_zero_of_empty", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "BoundedContinuousFunction.dist_eq_iSup", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": true, "tactics": ["cases", "rw", "refine", "exact"], "tactic_count": 4}
{"name": "BoundedContinuousFunction.nndist_eq_iSup", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.edist_eq_iSup", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "rintro", "exact"], "tactic_count": 4}
{"name": "BoundedContinuousFunction.tendsto_iff_tendstoUniformly", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.isInducing_coeFn", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "simp"], "tactic_count": 4}
{"name": "BoundedContinuousFunction.isEmbedding_coeFn", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.const", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.const_apply'", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "BoundedContinuousFunction.lipschitz_eval_const", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.uniformContinuous_coe", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.continuous_coe", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.instContinuousEval", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.instContinuousEvalConst", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.instCompleteSpace", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.compContinuous", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.coe_compContinuous", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.compContinuous_apply", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.lipschitz_compContinuous", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.continuous_compContinuous", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.restrict", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "BoundedContinuousFunction.uniformContinuous_comp", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "BoundedContinuousFunction.extend", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.extend_apply", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.extend_comp", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.extend_apply'", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.extend_of_empty", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "BoundedContinuousFunction.indicator", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "BoundedContinuousFunction.mul_apply", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.coe_nsmulRec", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "BoundedContinuousFunction.coe_pow", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "BoundedContinuousFunction.toContinuousMapMonoidHom", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "BoundedContinuousFunction.sub_apply", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "BoundedContinuousFunction.natCast_apply", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "BoundedContinuousFunction.intCast_apply", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "BoundedContinuousFunction.instIsCentralScalar", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.instIsBoundedSMul", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.instMulAction", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.instDistribMulAction", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.instModule", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.evalCLM", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.toContinuousMapLinearMap", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.NNReal.upper_bound", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Basic", "is_tactic_proof": true, "tactics": ["have", "simp", "rwa"], "tactic_count": 3}
{"name": "BoundedContinuousFunction.instNorm", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.norm_def", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.norm_eq", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "BoundedContinuousFunction.norm_eq_of_nonempty", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": true, "tactics": ["obtain", "rw", "congr", "ext", "simp", "exact"], "tactic_count": 6}
{"name": "BoundedContinuousFunction.norm_eq_zero_of_empty", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.norm_coe_le_norm", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.neg_norm_le_apply", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.apply_le_norm", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.dist_le_two_norm'", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.dist_le_two_norm", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.norm_le", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "BoundedContinuousFunction.norm_le_of_nonempty", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "BoundedContinuousFunction.norm_lt_iff_of_compact", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "BoundedContinuousFunction.norm_lt_iff_of_nonempty_compact", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "BoundedContinuousFunction.norm_const_le", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.norm_const_eq", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.ofNormedAddCommGroup", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.coe_ofNormedAddCommGroup", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.norm_ofNormedAddCommGroup_le", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.ofNormedAddCommGroupDiscrete", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.coe_ofNormedAddCommGroupDiscrete", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.normComp", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.coe_normComp", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.norm_normComp", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "BoundedContinuousFunction.bddAbove_range_norm_comp", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.norm_eq_iSup_norm", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "BoundedContinuousFunction.instNormOneClass", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.instNeg", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.coe_neg", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "BoundedContinuousFunction.mkOfCompact_neg", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.mkOfCompact_sub", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.coe_zsmulRec", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.instSMulInt", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.coe_zsmul", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.zsmul_apply", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.instAddCommGroup", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.instSeminormedAddCommGroup", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.instNormedAddCommGroup", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.nnnorm_def", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.nnnorm_coe_le_nnnorm", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.nndist_le_two_nnnorm", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.nnnorm_le", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.nnnorm_const_le", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.nnnorm_const_eq", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.nnnorm_eq_iSup_nnnorm", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.enorm_eq_iSup_enorm", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "BoundedContinuousFunction.abs_diff_coe_le_dist", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
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{"name": "ContinuousLinearMap.compLeftContinuousBounded", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.compLeftContinuousBounded_apply", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "BoundedContinuousFunction.instNonUnitalSeminormedCommRing", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.instNonUnitalNormedRing", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "BoundedContinuousFunction.coe_intCast", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "BoundedContinuousFunction.C", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.instAlgebra", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "BoundedContinuousFunction.coe_toContinuousMapₐ", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "BoundedContinuousFunction.coe_sup", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "BoundedContinuousFunction.instSemilatticeInf", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.instLattice", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.coe_abs", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.coe_posPart", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.coe_negPart", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.instHasSolidNorm", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.instIsOrderedAddMonoid", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.nnrealPart", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.nnrealPart_coeFn_eq", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "BoundedContinuousFunction.nnnorm_coeFn_eq", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.self_eq_nnrealPart_sub_nnrealPart_neg", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": true, "tactics": ["funext", "dsimp", "simp"], "tactic_count": 3}
{"name": "BoundedContinuousFunction.abs_self_eq_nnrealPart_add_nnrealPart_neg", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Normed", "is_tactic_proof": true, "tactics": ["funext", "dsimp", "simp"], "tactic_count": 3}
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{"name": "BoundedContinuousFunction.instStarAddMonoid", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Bounded.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.coe_star", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.star_apply", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.instNormedStarGroup", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Bounded.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.instStarModule", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Bounded.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.instStarRing", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Bounded.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.instCStarRing", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Bounded.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.toContinuousMapStarₐ", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Bounded.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.coe_toContinuousMapStarₐ", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Bounded.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CocompactMapClass.toCocompactMap", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.CocompactMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CocompactMapClass.instCoeTCCocompactMap", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.CocompactMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CocompactMap.instFunLike", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.CocompactMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CocompactMap.instCocompactMapClass", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.CocompactMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CocompactMap.coe_toContinuousMap", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.CocompactMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CocompactMap.ext", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.CocompactMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CocompactMap.copy", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.CocompactMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CocompactMap.coe_copy", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.CocompactMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CocompactMap.copy_eq", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.CocompactMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CocompactMap.coe_mk", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.CocompactMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CocompactMap.id", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.CocompactMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CocompactMap.coe_id", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.CocompactMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CocompactMap.instInhabited", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.CocompactMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CocompactMap.comp", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.CocompactMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CocompactMap.coe_comp", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.CocompactMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CocompactMap.comp_apply", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.CocompactMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CocompactMap.comp_assoc", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.CocompactMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CocompactMap.id_comp", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.CocompactMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CocompactMap.comp_id", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.CocompactMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CocompactMap.tendsto_of_forall_preimage", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.CocompactMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CocompactMap.isCompact_preimage_of_isClosed", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.CocompactMap", "is_tactic_proof": false, "tactics": ["obtain", "mem_cocompact'.mp", "simpa", "mem_map.mp", "exact"], "tactic_count": 5}
{"name": "CocompactMap.isCompact_preimage", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.CocompactMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.toCocompactMap", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.CocompactMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.equivBoundedOfCompact", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.isUniformInducing_equivBoundedOfCompact", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.isUniformEmbedding_equivBoundedOfCompact", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.addEquivBoundedOfCompact", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instPseudoMetricSpace", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instMetricSpace", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.isometryEquivBoundedOfCompact", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.dist_mkOfCompact", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.dist_toContinuousMap", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.dist_apply_le_dist", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Compact", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousMap.dist_le", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Compact", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousMap.dist_le_iff_of_nonempty", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Compact", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousMap.dist_lt_iff_of_nonempty", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Compact", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousMap.dist_lt_of_nonempty", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.dist_lt_iff", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Compact", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "ContinuousMap.dist_eq_iSup", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Compact", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousMap.nndist_eq_iSup", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Compact", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousMap.edist_eq_iSup", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Compact", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousMap.instIsBoundedSMul", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instNorm", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.norm_mkOfCompact", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedContinuousFunction.norm_toContinuousMap_eq", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instSeminormedAddCommGroup", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instNormedAddCommGroup", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instNormOneClassOfNonempty", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.norm_coe_le_norm", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.dist_le_two_norm", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.norm_le", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.norm_le_of_nonempty", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.norm_lt_iff", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.nnnorm_lt_iff", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.norm_lt_iff_of_nonempty", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.nnnorm_lt_iff_of_nonempty", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.apply_le_norm", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.neg_norm_le_apply", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.nnnorm_eq_iSup_nnnorm", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.norm_eq_iSup_norm", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.enorm_eq_iSup_enorm", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instCompactSpaceElemCoeCompacts", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.norm_restrict_mono_set", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instNonUnitalSeminormedRing", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instNonUnitalSeminormedCommRing", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instSeminormedRing", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instSeminormedCommRing", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instNonUnitalNormedRing", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instNonUnitalNormedCommRing", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instNormedRing", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instNormedCommRing", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.normedSpace", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.linearIsometryBoundedOfCompact", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.linearIsometryBoundedOfCompact_symm_apply", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.linearIsometryBoundedOfCompact_apply_apply", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.linearIsometryBoundedOfCompact_toIsometryEquiv", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.linearIsometryBoundedOfCompact_toAddEquiv", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.linearIsometryBoundedOfCompact_of_compact_toEquiv", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.nnnorm_smul_const", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Compact", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousMap.norm_smul_const", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Compact", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousMap.instNormedAlgebra", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.uniform_continuity", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.modulus", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.modulus_pos", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.dist_lt_of_dist_lt_modulus", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.summable_of_locally_summable_norm", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Compact", "is_tactic_proof": true, "tactics": ["classical", "refine", "lift", "have", "intro", "ext1", "simp", "simpa"], "tactic_count": 8}
{"name": "BoundedContinuousFunction.mkOfCompact_star", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instNormedStarGroup", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instCStarRing", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompactlySupported.termC_c(_,_)", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.CompactlySupported", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompactlySupported._aux_Mathlib_Topology_ContinuousMap_CompactlySupported___macroRules_CompactlySupported_termC_c(_,_)_1", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.CompactlySupported", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompactlySupported._aux_Mathlib_Topology_ContinuousMap_CompactlySupported___unexpand_CompactlySupportedContinuousMap_1", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.CompactlySupported", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompactlySupported.term_→C_c_", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.CompactlySupported", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompactlySupported._aux_Mathlib_Topology_ContinuousMap_CompactlySupported___macroRules_CompactlySupported_term_→C_c__1", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.CompactlySupported", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompactlySupported._aux_Mathlib_Topology_ContinuousMap_CompactlySupported___unexpand_CompactlySupportedContinuousMap_2", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.CompactlySupported", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompactlySupportedContinuousMap.instFunLike", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.CompactlySupported", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompactlySupportedContinuousMap.hasCompactSupport", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.CompactlySupported", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompactlySupportedContinuousMap.instCompactlySupportedContinuousMapClass", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.CompactlySupported", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompactlySupportedContinuousMap.coe_toContinuousMap", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.CompactlySupported", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompactlySupportedContinuousMap.ext", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.CompactlySupported", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompactlySupportedContinuousMap.coe_mk", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.CompactlySupported", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompactlySupportedContinuousMap.copy", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.CompactlySupported", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompactlySupportedContinuousMap.coe_copy", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.CompactlySupported", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompactlySupportedContinuousMap.copy_eq", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.CompactlySupported", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompactlySupportedContinuousMap.eq_of_empty", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.CompactlySupported", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompactlySupportedContinuousMap.continuousMapEquiv", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.CompactlySupported", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompactlySupportedContinuousMap.compLeft", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.CompactlySupported", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompactlySupportedContinuousMap.toContinuousMap_compLeft", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.CompactlySupported", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompactlySupportedContinuousMap.coe_compLeft", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.CompactlySupported", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CompactlySupportedContinuousMap.compLeft_apply", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.CompactlySupported", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
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{"name": "CompactlySupportedContinuousMap.toRealLinear_nonneg", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.CompactlySupported", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.termC(_,_)₀", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero._aux_Mathlib_Topology_ContinuousMap_ContinuousMapZero___macroRules_ContinuousMapZero_termC(_,_)₀_1", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero._aux_Mathlib_Topology_ContinuousMap_ContinuousMapZero___unexpand_ContinuousMapZero_1", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.instFunLike", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.instContinuousMapClass", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.instZeroHomClass", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.zeroOfFactMem", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.ext", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.coe_mk", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.toContinuousMap_injective", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.range_toContinuousMap", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.comp", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.comp_apply", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.instPartialOrder", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.le_def", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.instTopologicalSpace", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.isEmbedding_toContinuousMap", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.instT0Space", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.instR0Space", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.instT1Space", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.instR1Space", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.instT2Space", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.instRegularSpace", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.instT3Space", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.instContinuousEvalConst", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.instContinuousEval", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.isClosedEmbedding_toContinuousMap", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.continuous_comp_left", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": true, "tactics": ["rw", "change", "fun_prop"], "tactic_count": 3}
{"name": "ContinuousMapZero.id", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.toContinuousMap_id", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.mkD", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.mkD_of_continuous", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousMapZero.mkD_of_not_continuous", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousMapZero.mkD_of_not_zero", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousMapZero.mkD_apply_of_continuous", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ContinuousMapZero.mkD_of_continuousOn", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.mkD_of_not_continuousOn", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ContinuousMapZero.mkD_apply_of_continuousOn", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ContinuousMapZero.mkD_eq_mkD_of_map_zero", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": true, "tactics": ["ext", "by_cases", "simp"], "tactic_count": 3}
{"name": "ContinuousMapZero.mkD_eq_self", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.instZero", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.coe_zero", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.instAdd", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.coe_add", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.instNeg", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.coe_neg", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.instSub", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.coe_sub", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.instMul", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.coe_mul", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.instSMul", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.coe_smul", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.instAddCommMonoid", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.instModule", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.instSMulCommClass", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.instIsScalarTower", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.instAddCommGroup", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.instNonUnitalCommSemiring", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.instSMulCommClass'", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.instIsScalarTower'", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.instStarRing", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.instStarModule", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.coe_star", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.instTrivialStar", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.instCanLift", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.toContinuousMapHom", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.coe_toContinuousMapHom", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.toContinuousMapCLM", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.evalCLM", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.evalCLM_apply", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.coeFnAddMonoidHom", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.coeFnAddMonoidHom_apply", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.coe_sum", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.instNonUnitalCommRing", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.instContinuousNeg", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.instUniformSpace", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.isUniformEmbedding_toContinuousMap", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.instCompleteSpaceOfT1SpaceOfContinuousMap", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.isUniformEmbedding_comp", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformEquiv.arrowCongrLeft₀", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.nonUnitalStarAlgHom_precomp", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.nonUnitalStarAlgHom_postcomp", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.instMetricSpace", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.isometry_toContinuousMap", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.instNorm", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.norm_def", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.instNormedAddCommGroup", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.instNonUnitalNormedCommRing", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.instNormedSpaceOfNormedAlgebra", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.instCStarRing", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ContinuousMapZero", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instContinuousSqrtRCLike", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ContinuousSqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instContinuousSqrtReal", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ContinuousSqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instContinuousSqrtComplex", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ContinuousSqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instContinuousSqrtNNReal", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ContinuousSqrt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "termC(_,_)", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Topology_ContinuousMap_Defs___macroRules_termC(_,_)_1", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Topology_ContinuousMap_Defs___unexpand_ContinuousMap_1", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toContinuousMap", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCoeTCContinuousMap", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instFunLike", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instContinuousMapClass", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.toFun_eq_coe", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instCanLiftForallCoeContinuous", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.Simps.apply", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.coe_coe", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.coe_apply", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.coe_injective'", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.ext", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.copy", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.coe_copy", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.copy_eq", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.continuous", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.congr_fun", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.congr_arg", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.coe_injective", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.coe_mk", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instSubsingleton", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instSubsingletonOfIsEmpty", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.idealOfSet", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Ideals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.idealOfSet_closed", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Ideals", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "ContinuousMap.mem_idealOfSet", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Ideals", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "ContinuousMap.notMem_idealOfSet", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Ideals", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "ContinuousMap.setOfIdeal", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Ideals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.notMem_setOfIdeal", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Ideals", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ContinuousMap.mem_setOfIdeal", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Ideals", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "ContinuousMap.setOfIdeal_open", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Ideals", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "ContinuousMap.opensOfIdeal", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Ideals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.setOfTop_eq_univ", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Ideals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.idealOfEmpty_eq_bot", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Ideals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.mem_idealOfSet_compl_singleton", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Ideals", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousMap.ideal_gc", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Ideals", "is_tactic_proof": true, "tactics": ["refine", "by_contra", "rcases", "exact", "obtain", "by_contra", "exact"], "tactic_count": 7}
{"name": "ContinuousMap.exists_mul_le_one_eqOn_ge", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Ideals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.idealOfSet_ofIdeal_eq_closure", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Ideals", "is_tactic_proof": true, "tactics": ["suffices", "refine", "le_antisymm", "refine", "lift", "replace", "simp_rw", "norm_cast", "set", "have", "have", "refine", "simpa", "and", "suffices", "obtain", "refine", "rw", "refine", "simp", "by_cases", "simpa", "sub_self,", "refine", "have", "calc", "simp", "simp", "one_smul]", "calc", "simpa", "mul_le_mul_right", "neighborhood", "this", "have", "refine", "refine", "convert", "ext", "simp", "rintro", "rintro", "refine", "convert", "ext", "simp", "rcases", "simpa", "simpa", "intro", "replace", "rw", "obtain", "have", "refine", "convert", "ext", "simp", "star_def]", "simp", "rfl", "compactness", "obtain", "obtain", "t.eq_empty_or_nonempty.elim", "let", "obtain", "refine", "convert", "ext", "simp"], "tactic_count": 71}
{"name": "ContinuousMap.idealOfSet_ofIdeal_isClosed", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Ideals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.setOfIdeal_ofSet_eq_interior", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Ideals", "is_tactic_proof": false, "tactics": ["refine", "let", "rw", "simp_rw", "obtain", "exists_continuous_zero_one_of_isClosed", "exact", "simpa", "simpa"], "tactic_count": 9}
{"name": "ContinuousMap.setOfIdeal_ofSet_of_isOpen", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Ideals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.idealOpensGI", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Ideals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.idealOfSet_isMaximal_iff", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Ideals", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "ContinuousMap.idealOf_compl_singleton_isMaximal", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Ideals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.setOfIdeal_eq_compl_singleton", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Ideals", "is_tactic_proof": false, "tactics": ["have", "obtain", "exact"], "tactic_count": 3}
{"name": "ContinuousMap.ideal_isMaximal_iff", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Ideals", "is_tactic_proof": false, "tactics": ["refine", "let", "hx", "intro", "obtain", "exact", "simpa"], "tactic_count": 7}
{"name": "WeakDual.CharacterSpace.continuousMapEval", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Ideals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakDual.CharacterSpace.continuousMapEval_apply_apply", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Ideals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeakDual.CharacterSpace.continuousMapEval_bijective", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Ideals", "is_tactic_proof": true, "tactics": ["refine", "contrapose", "rcases", "exists_continuous_zero_one_of_isClosed", "rw", "use", "simpa", "obtain", "refine", "simpa"], "tactic_count": 10}
{"name": "WeakDual.CharacterSpace.homeoEval", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Ideals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.IccInclusionLeft", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.IccInclusionRight", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.projIccCM", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.IccExtendCM", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.IccExtendCM_of_mem", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Interval", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousMap.concat", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Interval", "is_tactic_proof": true, "tactics": ["by_cases", "let", "suffices", "apply", "rintro", "simpa", "exact"], "tactic_count": 7}
{"name": "ContinuousMap.concat_comp_IccInclusionLeft", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Interval", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "ContinuousMap.concat_comp_IccInclusionRight", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Interval", "is_tactic_proof": true, "tactics": ["ext", "obtain", "simpa", "have", "simp"], "tactic_count": 5}
{"name": "ContinuousMap.concat_left", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Interval", "is_tactic_proof": true, "tactics": ["nth_rewrite", "rfl"], "tactic_count": 2}
{"name": "ContinuousMap.concat_right", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Interval", "is_tactic_proof": true, "tactics": ["nth_rewrite", "rfl"], "tactic_count": 2}
{"name": "ContinuousMap.tendsto_concat", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Interval", "is_tactic_proof": true, "tactics": ["rw", "rintro", "have", "let", "let", "have", "have", "have", "rw", "apply", "rintro", "simpa", "have", "rw", "apply", "rintro", "simpa", "filter_upwards", "by_cases", "rw", "refine", "simp", "replace", "rw", "refine", "simp"], "tactic_count": 26}
{"name": "ContinuousMap.concatCM", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.concatCM_left", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Interval", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "ContinuousMap.concatCM_right", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Interval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instIsOrderedMonoid", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.coe_mabs", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.mabs_apply", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.toContinuousMapMonoidHom", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.LocallyConstant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.toContinuousMapLinearMap", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.LocallyConstant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.toContinuousMapAlgHom", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.LocallyConstant", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instLocallyConvexSpace", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.LocallyConvex", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.partialOrder", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Ordered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.le_def", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Ordered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.lt_def", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Ordered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.sup", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Ordered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.coe_sup", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Ordered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.sup_apply", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Ordered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.semilatticeSup", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Ordered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.sup'_apply", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Ordered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.coe_sup'", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Ordered", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "ContinuousMap.inf", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Ordered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.coe_inf", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Ordered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.inf_apply", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Ordered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.semilatticeInf", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Ordered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.inf'_apply", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Ordered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.coe_inf'", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Ordered", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "ContinuousMap.instLatticeOfTopologicalLattice", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Ordered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.IccExtend", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Ordered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.coe_IccExtend", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Ordered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.periodic_tsum_comp_add_zsmul", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Periodic", "is_tactic_proof": true, "tactics": ["intro", "by_cases", "convert", "have", "simp_rw", "simp", "rw", "simp"], "tactic_count": 8}
{"name": "Polynomial.toContinuousMap", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.toContinuousMap_X_eq_id", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Polynomial", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Polynomial.toContinuousMapOn", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.toContinuousMapOn_X_eq_restrict_id", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Polynomial", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Polynomial.aeval_continuousMap_apply", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Polynomial", "is_tactic_proof": true, "tactics": ["refine", "intro", "simp", "intro", "simp"], "tactic_count": 5}
{"name": "Polynomial.toContinuousMapAlgHom", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Polynomial.toContinuousMapOnAlgHom", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "polynomialFunctions", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "polynomialFunctions_coe", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Polynomial", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "polynomialFunctions_separatesPoints", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Polynomial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "polynomialFunctions.comap_compRightAlgHom_iccHomeoI", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Polynomial", "is_tactic_proof": true, "tactics": ["ext", "fconstructor", "rintro", "rw", "dsimp", "let", "refine", "simp", "ext", "simp", "convert", "ext", "simp", "replace", "field", "change", "rw", "have", "have", "have", "fconstructor", "exact", "rw", "exact", "rintro", "let", "refine", "simp", "ext", "simp"], "tactic_count": 30}
{"name": "polynomialFunctions.eq_adjoin_X", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Polynomial", "is_tactic_proof": true, "tactics": ["refine", "rintro", "rw", "refine", "rw", "exact", "rw", "exact", "rw", "exact"], "tactic_count": 10}
{"name": "polynomialFunctions.le_equalizer", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Polynomial", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "polynomialFunctions.starClosure_eq_adjoin_X", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Polynomial", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "polynomialFunctions.starClosure_le_equalizer", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Polynomial", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ContinuousMap.compactOpen_eq_generateFrom", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.SecondCountableSpace", "is_tactic_proof": true, "tactics": ["apply", "apply_rules", "intro", "exact", "refine", "simp", "intro", "simp", "obtain", "rw", "obtain", "refine", "rwa", "rw", "obtain", "have", "intro", "rcases", "rcases", "exact", "choose", "rcases", "refine", "rw", "exact", "have", "simp", "exact", "refine", "refine", "exact"], "tactic_count": 31}
{"name": "ContinuousMap.secondCountableTopology", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.SecondCountableSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instSecondCountableTopology", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.SecondCountableSpace", "is_tactic_proof": true, "tactics": ["apply", "have", "set", "use", "refine", "simp", "rintro", "exact", "intro", "obtain", "rw", "exact", "lift", "lift", "rcases", "refine", "rw", "exacts", "rw", "exact"], "tactic_count": 20}
{"name": "ContinuousMap.instSeparableSpace", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.SecondCountableSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.isEmbedding_sigmaMk_comp", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.exists_lift_sigma", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.sigmaCodHomeomorph", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Sigma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instStar", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.coe_star", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.star_apply", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instTrivialStar", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instInvolutiveStarOfContinuousStar", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.starAddMonoid", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.starMul", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instStarRingOfContinuousStar", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instStarModule", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.compStarAlgHom'", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.compStarAlgHom'_id", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.compStarAlgHom'_comp", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.compStarAlgHom", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.compStarAlgHom_id", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.compStarAlgHom_comp", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.compStarAlgEquiv'", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.evalStarAlgHom", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Star", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instStarOrderedRingOfContinuousSqrt", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.StarOrdered", "is_tactic_proof": true, "tactics": ["refine", "intro", "constructor", "rw", "intro", "use", "ext", "simpa", "rintro", "exact"], "tactic_count": 10}
{"name": "ContinuousMapZero.instStarOrderedRing", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.StarOrdered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.attachBound", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.StoneWeierstrass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.attachBound_apply_coe", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.StoneWeierstrass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.polynomial_comp_attachBound", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.StoneWeierstrass", "is_tactic_proof": true, "tactics": ["ext", "simp", "simp"], "tactic_count": 3}
{"name": "ContinuousMap.polynomial_comp_attachBound_mem", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.StoneWeierstrass", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "ContinuousMap.comp_attachBound_mem_closure", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.StoneWeierstrass", "is_tactic_proof": true, "tactics": ["have", "continuousMap_mem_polynomialFunctions_closure", "have", "apply", "refine", "frequently_mem_polynomials", "rintro", "simp", "apply"], "tactic_count": 9}
{"name": "ContinuousMap.abs_mem_subalgebra_closure", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.StoneWeierstrass", "is_tactic_proof": true, "tactics": ["let", "let", "change", "apply"], "tactic_count": 4}
{"name": "ContinuousMap.inf_mem_subalgebra_closure", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.StoneWeierstrass", "is_tactic_proof": true, "tactics": ["rw", "refine", "exact"], "tactic_count": 3}
{"name": "ContinuousMap.inf_mem_closed_subalgebra", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.StoneWeierstrass", "is_tactic_proof": true, "tactics": ["convert", "apply", "symm", "rw", "exact"], "tactic_count": 5}
{"name": "ContinuousMap.sup_mem_subalgebra_closure", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.StoneWeierstrass", "is_tactic_proof": true, "tactics": ["rw", "refine", "exact"], "tactic_count": 3}
{"name": "ContinuousMap.sup_mem_closed_subalgebra", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.StoneWeierstrass", "is_tactic_proof": true, "tactics": ["convert", "apply", "symm", "dsimp", "rw", "exact"], "tactic_count": 6}
{"name": "ContinuousMap.sublattice_closure_eq_top", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.StoneWeierstrass", "is_tactic_proof": true, "tactics": ["rw", "rintro", "refine", "simp", "by_cases", "swap", "exact", "and", "as", "dsimp", "choose", "let", "have", "intro", "refine", "apply", "rw", "exact", "let", "let", "have", "let", "have", "intro", "obtain", "dsimp", "simp", "exact", "have", "simp", "let", "have", "intro", "refine", "apply", "dsimp", "rw", "exact", "let", "let", "have", "let", "refine", "rw", "intro", "rw", "simp", "fconstructor", "dsimp", "simp", "exact", "dsimp", "simp", "rintro", "apply"], "tactic_count": 55}
{"name": "ContinuousMap.subalgebra_topologicalClosure_eq_top_of_separatesPoints", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.StoneWeierstrass", "is_tactic_proof": true, "tactics": ["apply", "let", "have", "convert", "sublattice_closure_eq_top", "simp"], "tactic_count": 6}
{"name": "ContinuousMap.continuousMap_mem_subalgebra_closure_of_separatesPoints", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.StoneWeierstrass", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "ContinuousMap.exists_mem_subalgebra_near_continuousMap_of_separatesPoints", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.StoneWeierstrass", "is_tactic_proof": true, "tactics": ["have", "rw", "obtain", "rw", "exact"], "tactic_count": 5}
{"name": "ContinuousMap.exists_mem_subalgebra_near_continuous_of_separatesPoints", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.StoneWeierstrass", "is_tactic_proof": true, "tactics": ["obtain", "use", "rwa"], "tactic_count": 3}
{"name": "ContinuousMap.exists_mem_subalgebra_near_continuous_of_isCompact_of_separatesPoints", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.StoneWeierstrass", "is_tactic_proof": false, "tactics": ["let", "let", "have", "intro", "obtain", "simp", "use", "refine", "use", "simp", "obtain", "hsep", "obtain", "use", "intro", "have", "rw", "exact"], "tactic_count": 18}
{"name": "Subalgebra.SeparatesPoints.rclike_to_real", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.StoneWeierstrass", "is_tactic_proof": true, "tactics": ["intro", "obtain", "let", "f", "const", "have", "refine", "ext1", "simp", "refine", "rw", "convert", "ext1", "simp", "simpa"], "tactic_count": 15}
{"name": "ContinuousMap.starSubalgebra_topologicalClosure_eq_top_of_separatesPoints", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.StoneWeierstrass", "is_tactic_proof": false, "tactics": ["rw", "let", "have", "let", "have", "haveI", "congr_arg", "rw", "have", "have", "exact", "h₁.trans", "intro", "let", "let", "have", "have", "key", "have", "rw", "convert", "ext", "apply", "simp"], "tactic_count": 24}
{"name": "polynomialFunctions.topologicalClosure", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.StoneWeierstrass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "polynomialFunctions.starClosure_topologicalClosure", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.StoneWeierstrass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.elemental_id_eq_top", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.StoneWeierstrass", "is_tactic_proof": false, "tactics": ["rw", "polynomialFunctions.starClosure_eq_adjoin_X]", "congr", "exact"], "tactic_count": 4}
{"name": "ContinuousMap.induction_on", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.StoneWeierstrass", "is_tactic_proof": true, "tactics": ["refine", "rw", "induction", "mem", "push", "rw", "obtain", "all_goals", "algebraMap", "add", "mul"], "tactic_count": 11}
{"name": "ContinuousMap.induction_on_of_compact", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.StoneWeierstrass", "is_tactic_proof": true, "tactics": ["refine", "have", "rw", "exact"], "tactic_count": 4}
{"name": "ContinuousMap.algHom_ext_map_X", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.StoneWeierstrass", "is_tactic_proof": true, "tactics": ["suffices", "rw", "exact"], "tactic_count": 3}
{"name": "ContinuousMap.starAlgHom_ext_map_X", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.StoneWeierstrass", "is_tactic_proof": true, "tactics": ["suffices", "rw", "exact"], "tactic_count": 3}
{"name": "ContinuousMap.adjoin_id_eq_span_one_union", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.StoneWeierstrass", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "ContinuousMap.adjoin_id_eq_span_one_add", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.StoneWeierstrass", "is_tactic_proof": true, "tactics": ["ext", "rw", "simp"], "tactic_count": 3}
{"name": "ContinuousMap.nonUnitalStarAlgebraAdjoin_id_subset_ker_evalStarAlgHom", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.StoneWeierstrass", "is_tactic_proof": true, "tactics": ["intro", "induction", "mem", "obtain", "rfl", "add", "zero", "mul", "smul", "rw", "rw", "star", "rw", "rw"], "tactic_count": 14}
{"name": "ContinuousMap.ker_evalStarAlgHom_inter_adjoin_id", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.StoneWeierstrass", "is_tactic_proof": true, "tactics": ["ext", "constructor", "rintro", "rw", "simp_rw", "obtain", "have", "simp", "rw", "rwa", "simp", "refine", "exact"], "tactic_count": 13}
{"name": "ContinuousMap.AlgHom.closure_ker_inter", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.StoneWeierstrass", "is_tactic_proof": true, "tactics": ["refine", "simpa", "closure_inter_subset_inter_closure", "intro", "rw", "have", "conv", "exact", "refine", "filter_upwards"], "tactic_count": 10}
{"name": "ContinuousMap.ker_evalStarAlgHom_eq_closure_adjoin_id", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.StoneWeierstrass", "is_tactic_proof": false, "tactics": ["rw", "convert", "rw", "polynomialFunctions.starClosure_eq_adjoin_X", "congrm"], "tactic_count": 5}
{"name": "ContinuousMapZero.adjoin_id_dense", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.StoneWeierstrass", "is_tactic_proof": true, "tactics": ["have", "rw", "isClosedEmbedding_toContinuousMap.closure_image_eq,", "apply", "simp", "exact"], "tactic_count": 6}
{"name": "ContinuousMapZero.elemental_eq_top", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.StoneWeierstrass", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMapZero.induction_on", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.StoneWeierstrass", "is_tactic_proof": true, "tactics": ["refine", "induction", "mem", "push", "rw", "obtain", "all_goals", "zero", "add", "mul", "smul"], "tactic_count": 11}
{"name": "ContinuousMapZero.induction_on_of_compact", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.StoneWeierstrass", "is_tactic_proof": true, "tactics": ["refine", "have", "exact"], "tactic_count": 3}
{"name": "ContinuousMapZero.nonUnitalStarAlgHom_apply_mul_eq_zero", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.StoneWeierstrass", "is_tactic_proof": true, "tactics": ["induction", "zero", "id", "star_id", "add", "mul", "smul", "frequently"], "tactic_count": 8}
{"name": "ContinuousMapZero.mul_nonUnitalStarAlgHom_apply_eq_zero", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.StoneWeierstrass", "is_tactic_proof": true, "tactics": ["induction", "zero", "id", "star_id", "add", "mul", "smul", "frequently"], "tactic_count": 8}
{"name": "TopologicalSpace.eq_induced_by_maps_to_sierpinski", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.T0Sierpinski", "is_tactic_proof": true, "tactics": ["apply", "rw", "exact", "intro", "rw", "apply", "simp", "exact"], "tactic_count": 8}
{"name": "TopologicalSpace.productOfMemOpens", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.T0Sierpinski", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.productOfMemOpens_isInducing", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.T0Sierpinski", "is_tactic_proof": true, "tactics": ["convert", "apply"], "tactic_count": 2}
{"name": "TopologicalSpace.productOfMemOpens_injective", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.T0Sierpinski", "is_tactic_proof": true, "tactics": ["intro", "apply", "rw"], "tactic_count": 3}
{"name": "TopologicalSpace.productOfMemOpens_isEmbedding", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.T0Sierpinski", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.unitsLift", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.unitsLift_apply_inv_apply", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.unitsLift_symm_apply_apply_inv'", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Units", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "ContinuousMap.continuous_isUnit_unit", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Units", "is_tactic_proof": false, "tactics": ["refine", "continuous_induced_rng.2", "have", "simp", "simp", "exact"], "tactic_count": 6}
{"name": "ContinuousMap.unitsOfForallIsUnit", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.canLift", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.isUnit_iff_forall_isUnit", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Units", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.isUnit_iff_forall_ne_zero", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Units", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "ContinuousMap.spectrum_eq_preimage_range", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Units", "is_tactic_proof": true, "tactics": ["ext", "simp", "sub_eq_zero,"], "tactic_count": 3}
{"name": "ContinuousMap.spectrum_eq_range", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Units", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "polynomialFunctions_closure_eq_top'", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Weierstrass", "is_tactic_proof": true, "tactics": ["apply", "rintro", "refine", "apply", "rintro", "rw", "use", "ext", "simp"], "tactic_count": 9}
{"name": "polynomialFunctions_closure_eq_top", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Weierstrass", "is_tactic_proof": true, "tactics": ["rcases", "let", "let", "have", "have", "apply_fun", "simp", "rw", "rw", "exact", "subsingleton"], "tactic_count": 11}
{"name": "continuousMap_mem_polynomialFunctions_closure", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Weierstrass", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "exists_polynomial_near_continuousMap", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Weierstrass", "is_tactic_proof": true, "tactics": ["have", "rw", "obtain", "rw", "exact"], "tactic_count": 5}
{"name": "exists_polynomial_near_of_continuousOn", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.Weierstrass", "is_tactic_proof": true, "tactics": ["let", "obtain", "use", "rw", "intro", "exact"], "tactic_count": 6}
{"name": "ZeroAtInfty.termC₀(_,_)", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInfty._aux_Mathlib_Topology_ContinuousMap_ZeroAtInfty___macroRules_ZeroAtInfty_termC₀(_,_)_1", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInfty._aux_Mathlib_Topology_ContinuousMap_ZeroAtInfty___unexpand_ZeroAtInftyContinuousMap_1", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInfty.term_→C₀_", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInfty._aux_Mathlib_Topology_ContinuousMap_ZeroAtInfty___macroRules_ZeroAtInfty_term_→C₀__1", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInfty._aux_Mathlib_Topology_ContinuousMap_ZeroAtInfty___unexpand_ZeroAtInftyContinuousMap_2", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.instFunLike", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.instZeroAtInftyContinuousMapClass", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.instCoeTC", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.coe_toContinuousMap", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.ext", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.coe_mk", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.copy", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.coe_copy", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.copy_eq", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.eq_of_empty", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.ContinuousMap.liftZeroAtInfty", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.zeroAtInftyContinuousMapClass.ofCompact", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.instZero", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.instInhabited", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.coe_zero", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.zero_apply", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.instMul", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.coe_mul", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.mul_apply", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.instMulZeroClass", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.instSemigroupWithZero", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.instAdd", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.coe_add", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.add_apply", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.instAddZeroClass", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.instSMul", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.coe_smul", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.smul_apply", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.instAddMonoid", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.instAddCommMonoid", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.instNeg", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.coe_neg", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.neg_apply", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.instSub", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.coe_sub", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.sub_apply", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.instAddGroup", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.instAddCommGroup", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.instIsCentralScalar", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.instSMulWithZero", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.instMulActionWithZero", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.instModule", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.instNonUnitalNonAssocSemiring", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.instNonUnitalSemiring", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.instNonUnitalCommSemiring", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.instNonUnitalNonAssocRing", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.instNonUnitalRing", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.instNonUnitalCommRing", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.instIsScalarTower", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.instSMulCommClass", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.uniformContinuous", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.bounded", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": ["obtain", "mem_cocompact.mp", "obtain", "refine", "have", "intro", "by_cases", "exact", "exact", "exact"], "tactic_count": 10}
{"name": "ZeroAtInftyContinuousMap.isBounded_range", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.isBounded_image", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.instBoundedContinuousMapClass", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.toBCF", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.toBCF_injective", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.instPseudoMetricSpace", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.instMetricSpace", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.dist_toBCF_eq_dist", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.tendsto_iff_tendstoUniformly", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ZeroAtInftyContinuousMap.isometry_toBCF", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": true, "tactics": ["tauto"], "tactic_count": 1}
{"name": "ZeroAtInftyContinuousMap.isClosed_range_toBCF", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": true, "tactics": ["refine", "rw", "have", "refine", "obtain", "refine", "calc", "dist", "exact"], "tactic_count": 9}
{"name": "ZeroAtInftyContinuousMap.instCompleteSpace", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.instSeminormedAddCommGroup", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.instNormedAddCommGroup", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.norm_toBCF_eq_norm", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.instNormedSpace", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.instNonUnitalSeminormedRing", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.instNonUnitalNormedRing", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.instNonUnitalSeminormedCommRing", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.instNonUnitalNormedCommRing", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.instStar", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.coe_star", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.star_apply", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.instStarAddMonoid", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.instNormedStarGroup", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.instStarModule", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.instStarRing", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.instCStarRing", "kind": "instance", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.ContinuousMap.ZeroAtInfty.0.ZeroAtInftyContinuousMap.term_→co_", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.ContinuousMap.ZeroAtInfty.0.ZeroAtInftyContinuousMap._aux_Mathlib_Topology_ContinuousMap_ZeroAtInfty___macroRules__private_Mathlib_Topology_ContinuousMap_ZeroAtInfty_0_ZeroAtInftyContinuousMap_term_→co__1", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.ContinuousMap.ZeroAtInfty.0.ZeroAtInftyContinuousMap._aux_Mathlib_Topology_ContinuousMap_ZeroAtInfty___unexpand_CocompactMap_1", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.comp", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.coe_comp_to_continuous_fun", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.comp_id", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.comp_assoc", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.zero_comp", "kind": "theorem", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.compAddMonoidHom", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.compMulHom", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.compLinearMap", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZeroAtInftyContinuousMap.compNonUnitalAlgHom", "kind": "definition", "module": "Mathlib.Topology.ContinuousMap.ZeroAtInfty", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.tendsto", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousWithinAt_univ", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "continuousOn_univ", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "continuousWithinAt_iff_continuousAt_restrict", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.tendsto_nhdsWithin", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.tendsto_nhdsWithin_image", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsWithin_le_comap", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.preimage_mem_nhdsWithin", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.preimage_mem_nhdsWithin'", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.preimage_mem_nhdsWithin''", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "continuousWithinAt_of_notMem_closure", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "continuousOn_iff", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousOn.continuousWithinAt", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousOn_iff_continuous_restrict", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": true, "tactics": ["rw", "rintro", "exact", "intro", "exact"], "tactic_count": 5}
{"name": "ContinuousOn.mapsToRestrict", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousOn_iff'", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": ["have", "intro", "rw", "simp", "constructor", "rintro", "exact", "rw"], "tactic_count": 8}
{"name": "ContinuousOn.mono_dom", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.mono_rng", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousOn_iff_isClosed", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": ["have", "intro", "rw", "simp", "rw"], "tactic_count": 5}
{"name": "continuous_of_cover_nhds", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousOn_empty", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousOn_singleton", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Subsingleton.continuousOn", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousOn_open_iff", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": true, "tactics": ["rw", "constructor", "intro", "rcases", "rw", "apply", "intro", "refine", "rw"], "tactic_count": 9}
{"name": "ContinuousOn.isOpen_inter_preimage", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.isOpen_preimage", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "ContinuousOn.preimage_isClosed_of_isClosed", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": true, "tactics": ["rcases", "rw", "apply"], "tactic_count": 3}
{"name": "ContinuousOn.preimage_interior_subset_interior_preimage", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousOn_of_locally_continuousOn", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": true, "tactics": ["intro", "rcases", "have", "rwa"], "tactic_count": 4}
{"name": "continuousOn_to_generateFrom_iff", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousOn_isOpen_of_generateFrom", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.mono", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.mono_of_mem_nhdsWithin", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousWithinAt_congr_set", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousWithinAt.congr_set", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousWithinAt_inter'", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "continuousWithinAt_inter", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "continuousWithinAt_union", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousWithinAt.union", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousWithinAt_singleton", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "continuousWithinAt_insert_self", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousWithinAt.diff_iff", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousWithinAt_diff_self", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousWithinAt_of_not_accPt", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": true, "tactics": ["rw", "simp_all"], "tactic_count": 2}
{"name": "continuousWithinAt_compl_self", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "continuousAt_of_not_accPt", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "continuousAt_of_not_accPt_top", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.mono", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "antitone_continuousOn", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.continuousWithinAt", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousWithinAt_iff_continuousAt", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ContinuousWithinAt.continuousAt", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.continuousOn_iff", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.continuousAt", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousOn_of_forall_continuousAt", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.continuousOn", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Continuous.continuousWithinAt", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.congr_mono", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": true, "tactics": ["intro", "unfold", "have", "unfold", "rw", "exact"], "tactic_count": 6}
{"name": "ContinuousOn.congr", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousOn_congr", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.congr_continuousWithinAt", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ContinuousWithinAt.congr_of_eventuallyEq", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.congr_of_eventuallyEq_of_mem", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.congr_continuousWithinAt_of_mem", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.congr_of_eventuallyEq_insert", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.congr_continuousWithinAt_of_insert", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.congr", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousWithinAt_congr", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.congr_of_mem", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousWithinAt_congr_of_mem", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.congr_of_insert", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousWithinAt_congr_of_insert", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.congr_mono", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.congr_of_eventuallyEq", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.comp", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.comp_of_eq", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "ContinuousWithinAt.comp_inter", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.comp_inter_of_eq", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "ContinuousWithinAt.comp_of_preimage_mem_nhdsWithin", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.comp_of_preimage_mem_nhdsWithin_of_eq", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "ContinuousWithinAt.comp_of_mem_nhdsWithin_image", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.comp_of_mem_nhdsWithin_image_of_eq", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "ContinuousAt.comp_continuousWithinAt", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.comp_continuousWithinAt_of_eq", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": true, "tactics": ["subst"], "tactic_count": 1}
{"name": "ContinuousOn.comp", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.comp'", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.comp_inter", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.comp_continuousOn", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.comp_continuousOn'", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.comp_continuous", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ContinuousOn.image_comp_continuous", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.comp₂_continuousWithinAt", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.comp₂_continuousWithinAt_of_eq", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ContinuousWithinAt.mem_closure_image", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.mem_closure", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.MapsTo.closure_of_continuousWithinAt", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.MapsTo.closure_of_continuousOn", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.image_closure", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.image_closure", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.prodMk", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.prodMk", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousOn_fst", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousWithinAt_fst", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.fst", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.fst", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousOn_snd", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousWithinAt_snd", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.snd", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.snd", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousWithinAt_prod_iff", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.prodMap", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.prodMap", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousWithinAt_prod_of_discrete_left", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": true, "tactics": ["rw", "simp_rw"], "tactic_count": 2}
{"name": "continuousWithinAt_prod_of_discrete_right", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": true, "tactics": ["rw", "simp_rw"], "tactic_count": 2}
{"name": "continuousAt_prod_of_discrete_left", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "continuousAt_prod_of_discrete_right", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "continuousOn_prod_of_discrete_left", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "continuousOn_prod_of_discrete_right", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "continuous_prod_of_discrete_left", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "continuous_prod_of_discrete_right", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "isOpenMap_prod_of_discrete_left", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": true, "tactics": ["simp_rw", "rfl"], "tactic_count": 2}
{"name": "isOpenMap_prod_of_discrete_right", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": true, "tactics": ["simp_rw", "map_map]", "rfl"], "tactic_count": 3}
{"name": "ContinuousOn.uncurry_left", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": true, "tactics": ["let", "refine", "exact"], "tactic_count": 3}
{"name": "ContinuousOn.uncurry_right", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": true, "tactics": ["let", "refine", "exact"], "tactic_count": 3}
{"name": "continuousWithinAt_pi", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousOn_pi", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousOn_pi'", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousOn_apply", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousOn_const", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousWithinAt_const", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousOn_id", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousOn_id'", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousWithinAt_id", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.iterate", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.finCons", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.finCons", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.matrixVecCons", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.matrixVecCons", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.finSnoc", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.finSnoc", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.finInsertNth", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.finInsertNth", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.LeftInvOn.map_nhdsWithin_eq", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": true, "tactics": ["apply", "exact", "have", "refine", "simpa"], "tactic_count": 5}
{"name": "Function.LeftInverse.map_nhds_eq", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Topology.IsInducing.continuousWithinAt_iff", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Topology.IsInducing.continuousOn_iff", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Topology.IsInducing.map_nhdsWithin_eq", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Topology.IsInducing.continuousOn_image_iff", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Topology.IsEmbedding.continuousOn_iff", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsEmbedding.map_nhdsWithin_eq", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsOpenEmbedding.map_nhdsWithin_preimage_eq", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": true, "tactics": ["rw", "apply", "rw"], "tactic_count": 3}
{"name": "Topology.IsQuotientMap.continuousOn_isOpen_iff", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": true, "tactics": ["simp", "rfl"], "tactic_count": 2}
{"name": "IsOpenMap.continuousOn_image_of_leftInvOn", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact", "rw"], "tactic_count": 4}
{"name": "IsOpenMap.continuousOn_range_of_leftInverse", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ContinuousOn.union_continuousAt", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.union_of_isClosed", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": true, "tactics": ["refine", "refine", "rwa", "refine", "rwa"], "tactic_count": 5}
{"name": "continouousOn_union_iff_of_isClosed", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.union_of_isOpen", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continouousOn_union_iff_of_isOpen", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.iUnion_of_isOpen", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": true, "tactics": ["rintro", "exact"], "tactic_count": 2}
{"name": "continuousOn_iUnion_iff_of_isOpen", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_of_continuousOn_iUnion_of_isOpen", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ContinuousOn.tendsto_nhdsSet", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": true, "tactics": ["obtain", "refine", "exact", "intro", "rw", "exact"], "tactic_count": 6}
{"name": "Continuous.tendsto_nhdsSet", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.tendsto_nhdsSet_nhds", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ContinuousOn.preimage_mem_nhdsSetWithin", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": true, "tactics": ["have", "have", "refine", "exact", "rw", "exact"], "tactic_count": 6}
{"name": "ContinuousOn.preimage_mem_nhdsSetWithin_of_mem_nhdsSet", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Continuous.preimage_mem_nhdsSetWithin", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Continuous.preimage_mem_nhdsSet", "kind": "theorem", "module": "Mathlib.Topology.ContinuousOn", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "TopologicalSpace.generatedBy", "kind": "definition", "module": "Mathlib.Topology.Convenient.GeneratedBy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithGeneratedByTopology", "kind": "definition", "module": "Mathlib.Topology.Convenient.GeneratedBy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithGeneratedByTopology.equiv", "kind": "definition", "module": "Mathlib.Topology.Convenient.GeneratedBy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithGeneratedByTopology.instTopologicalSpace", "kind": "instance", "module": "Mathlib.Topology.Convenient.GeneratedBy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithGeneratedByTopology.isOpen_iff", "kind": "theorem", "module": "Mathlib.Topology.Convenient.GeneratedBy", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Topology.WithGeneratedByTopology.isClosed_iff", "kind": "theorem", "module": "Mathlib.Topology.Convenient.GeneratedBy", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Topology.WithGeneratedByTopology.continuous_from_iff", "kind": "theorem", "module": "Mathlib.Topology.Convenient.GeneratedBy", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Topology.WithGeneratedByTopology.continuous_equiv", "kind": "theorem", "module": "Mathlib.Topology.Convenient.GeneratedBy", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "intro", "exact"], "tactic_count": 5}
{"name": "TopologicalSpace.generatedBy_le", "kind": "theorem", "module": "Mathlib.Topology.Convenient.GeneratedBy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.generatedBy_mono", "kind": "theorem", "module": "Mathlib.Topology.Convenient.GeneratedBy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsGeneratedBy.le_generatedBy", "kind": "theorem", "module": "Mathlib.Topology.Convenient.GeneratedBy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsGeneratedBy.generatedBy_eq", "kind": "theorem", "module": "Mathlib.Topology.Convenient.GeneratedBy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsGeneratedBy.iff_le_generatedBy", "kind": "theorem", "module": "Mathlib.Topology.Convenient.GeneratedBy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsGeneratedBy.homeomorph", "kind": "definition", "module": "Mathlib.Topology.Convenient.GeneratedBy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsGeneratedBy.homeomorph_coe", "kind": "theorem", "module": "Mathlib.Topology.Convenient.GeneratedBy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsGeneratedBy.homeomorph_symm_coe", "kind": "theorem", "module": "Mathlib.Topology.Convenient.GeneratedBy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsGeneratedBy.isOpen_iff", "kind": "theorem", "module": "Mathlib.Topology.Convenient.GeneratedBy", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Topology.IsGeneratedBy.isClosed_iff", "kind": "theorem", "module": "Mathlib.Topology.Convenient.GeneratedBy", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Topology.IsGeneratedBy.continuous_iff", "kind": "theorem", "module": "Mathlib.Topology.Convenient.GeneratedBy", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Topology.IsGeneratedBy.equiv_symm_comp_continuous_iff", "kind": "theorem", "module": "Mathlib.Topology.Convenient.GeneratedBy", "is_tactic_proof": true, "tactics": ["refine", "rw", "intro", "rw", "intro", "rw", "exact"], "tactic_count": 7}
{"name": "Topology.IsGeneratedBy.inst", "kind": "instance", "module": "Mathlib.Topology.Convenient.GeneratedBy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsGeneratedBy.instWithGeneratedByTopology", "kind": "instance", "module": "Mathlib.Topology.Convenient.GeneratedBy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsGeneratedBy.instPUnit", "kind": "instance", "module": "Mathlib.Topology.Convenient.GeneratedBy", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Topology.IsGeneratedBy.coinduced", "kind": "theorem", "module": "Mathlib.Topology.Convenient.GeneratedBy", "is_tactic_proof": true, "tactics": ["let", "refine", "exact"], "tactic_count": 3}
{"name": "Topology.IsGeneratedBy.iSup", "kind": "theorem", "module": "Mathlib.Topology.Convenient.GeneratedBy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsGeneratedBy.sup", "kind": "theorem", "module": "Mathlib.Topology.Convenient.GeneratedBy", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Topology.IsQuotientMap.isGeneratedBy", "kind": "theorem", "module": "Mathlib.Topology.Convenient.GeneratedBy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quot.isGeneratedBy", "kind": "instance", "module": "Mathlib.Topology.Convenient.GeneratedBy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quotient.isGeneratedBy", "kind": "instance", "module": "Mathlib.Topology.Convenient.GeneratedBy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.isGeneratedBy", "kind": "instance", "module": "Mathlib.Topology.Convenient.GeneratedBy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.isGeneratedBy", "kind": "instance", "module": "Mathlib.Topology.Convenient.GeneratedBy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCircle.isAddQuotientCoveringMap_coe", "kind": "theorem", "module": "Mathlib.Topology.Covering.AddCircle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCircle.isCoveringMap_coe", "kind": "theorem", "module": "Mathlib.Topology.Covering.AddCircle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCircle.isLocalHomeomorph_coe", "kind": "theorem", "module": "Mathlib.Topology.Covering.AddCircle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCircle.isAddQuotientCoveringMap_zsmul", "kind": "theorem", "module": "Mathlib.Topology.Covering.AddCircle", "is_tactic_proof": false, "tactics": ["refine", "hn.isQuotientMap_zsmul", "isQuotientMap_quotient_mk", "simp_rw", "apply"], "tactic_count": 5}
{"name": "AddCircle.isAddQuotientCoveringMap_nsmul", "kind": "theorem", "module": "Mathlib.Topology.Covering.AddCircle", "is_tactic_proof": true, "tactics": ["convert", "all_goals"], "tactic_count": 2}
{"name": "AddCircle.isAddQuotientCoveringMap_zsmul_of_ne_zero", "kind": "theorem", "module": "Mathlib.Topology.Covering.AddCircle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCircle.isAddQuotientCoveringMap_nsmul_of_ne_zero", "kind": "theorem", "module": "Mathlib.Topology.Covering.AddCircle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsEvenlyCovered", "kind": "definition", "module": "Mathlib.Topology.Covering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsEvenlyCovered.fiberHomeomorph", "kind": "definition", "module": "Mathlib.Topology.Covering.Basic", "is_tactic_proof": true, "tactics": ["choose", "exact", "invFun", "left_inv", "right_inv", "e", "continuous_toFun", "continuous_invFun"], "tactic_count": 8}
{"name": "IsEvenlyCovered.discreteTopology_fiber", "kind": "theorem", "module": "Mathlib.Topology.Covering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsEvenlyCovered.toTrivialization'", "kind": "definition", "module": "Mathlib.Topology.Covering.Basic", "is_tactic_proof": true, "tactics": ["choose", "classical", "exact", "invFun", "source", "target", "map_source", "map_target", "left_inv", "right_inv", "open_source", "open_target", "continuousOn_toFun", "continuousOn_iff_continuous_restrict.mpr", "simp", "continuousOn_invFun", "continuousOn_iff_continuous_restrict.mpr", "baseSet", "open_baseSet", "source_eq", "target_eq", "proj_toFun"], "tactic_count": 22}
{"name": "IsEvenlyCovered.toTrivialization", "kind": "definition", "module": "Mathlib.Topology.Covering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsEvenlyCovered.mem_toTrivialization_baseSet", "kind": "theorem", "module": "Mathlib.Topology.Covering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsEvenlyCovered.toTrivialization_apply", "kind": "theorem", "module": "Mathlib.Topology.Covering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsEvenlyCovered.continuousAt", "kind": "theorem", "module": "Mathlib.Topology.Covering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsEvenlyCovered.of_fiber_homeomorph", "kind": "theorem", "module": "Mathlib.Topology.Covering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsEvenlyCovered.to_isEvenlyCovered_preimage", "kind": "theorem", "module": "Mathlib.Topology.Covering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsEvenlyCovered.of_trivialization", "kind": "theorem", "module": "Mathlib.Topology.Covering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsEvenlyCovered.of_preimage_eq_empty", "kind": "theorem", "module": "Mathlib.Topology.Covering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsEvenlyCovered.restrictPreimage", "kind": "theorem", "module": "Mathlib.Topology.Covering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsEvenlyCovered.subtypeVal_comp", "kind": "theorem", "module": "Mathlib.Topology.Covering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsEvenlyCovered.comp_subtypeVal", "kind": "theorem", "module": "Mathlib.Topology.Covering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsEvenlyCovered.comp_homeomorph", "kind": "theorem", "module": "Mathlib.Topology.Covering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsEvenlyCovered.comp_homeomorph_iff", "kind": "theorem", "module": "Mathlib.Topology.Covering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsEvenlyCovered.homeomorph_comp", "kind": "theorem", "module": "Mathlib.Topology.Covering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsEvenlyCovered.homeomorph_comp_iff", "kind": "theorem", "module": "Mathlib.Topology.Covering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCoveringMapOn", "kind": "definition", "module": "Mathlib.Topology.Covering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCoveringMapOn.of_isEmpty", "kind": "theorem", "module": "Mathlib.Topology.Covering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCoveringMapOn.mk'", "kind": "theorem", "module": "Mathlib.Topology.Covering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCoveringMapOn.mk", "kind": "theorem", "module": "Mathlib.Topology.Covering.Basic", "is_tactic_proof": true, "tactics": ["cases", "exact", "refine", "exact"], "tactic_count": 4}
{"name": "IsCoveringMapOn.mono", "kind": "theorem", "module": "Mathlib.Topology.Covering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCoveringMapOn.continuousAt", "kind": "theorem", "module": "Mathlib.Topology.Covering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCoveringMapOn.continuousOn", "kind": "theorem", "module": "Mathlib.Topology.Covering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCoveringMapOn.isLocalHomeomorphOn", "kind": "theorem", "module": "Mathlib.Topology.Covering.Basic", "is_tactic_proof": true, "tactics": ["refine", "have", "let", "have", "let", "refine", "invFun", "source", "target", "open_source", "open_target", "map_source", "map_target", "left_inv", "right_inv", "continuousOn_toFun", "continuousOn_invFun"], "tactic_count": 17}
{"name": "IsCoveringMapOn.restrictPreimage", "kind": "theorem", "module": "Mathlib.Topology.Covering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCoveringMapOn.comp_homeomorph", "kind": "theorem", "module": "Mathlib.Topology.Covering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCoveringMapOn.comp_homeomorph_iff", "kind": "theorem", "module": "Mathlib.Topology.Covering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCoveringMapOn.homeomorph_comp", "kind": "theorem", "module": "Mathlib.Topology.Covering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCoveringMapOn.homeomorph_comp_iff", "kind": "theorem", "module": "Mathlib.Topology.Covering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCoveringMap", "kind": "definition", "module": "Mathlib.Topology.Covering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCoveringMap_iff_isCoveringMapOn_univ", "kind": "theorem", "module": "Mathlib.Topology.Covering.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsCoveringMap.isCoveringMapOn", "kind": "theorem", "module": "Mathlib.Topology.Covering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCoveringMapOn.isCoveringMap_restrictPreimage", "kind": "theorem", "module": "Mathlib.Topology.Covering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCoveringMapOn.of_isCoveringMap_restrictPreimage", "kind": "theorem", "module": "Mathlib.Topology.Covering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCoveringMap.of_isEmpty", "kind": "theorem", "module": "Mathlib.Topology.Covering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCoveringMap.of_discreteTopology", "kind": "theorem", "module": "Mathlib.Topology.Covering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCoveringMap.mk'", "kind": "theorem", "module": "Mathlib.Topology.Covering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCoveringMap.mk", "kind": "theorem", "module": "Mathlib.Topology.Covering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCoveringMap.continuous", "kind": "theorem", "module": "Mathlib.Topology.Covering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCoveringMap.isLocalHomeomorph", "kind": "theorem", "module": "Mathlib.Topology.Covering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCoveringMap.isOpenMap", "kind": "theorem", "module": "Mathlib.Topology.Covering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCoveringMap.isQuotientMap", "kind": "theorem", "module": "Mathlib.Topology.Covering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCoveringMap.isSeparatedMap", "kind": "theorem", "module": "Mathlib.Topology.Covering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCoveringMap.eq_of_comp_eq", "kind": "theorem", "module": "Mathlib.Topology.Covering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCoveringMap.const_of_comp", "kind": "theorem", "module": "Mathlib.Topology.Covering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCoveringMap.eqOn_of_comp_eqOn", "kind": "theorem", "module": "Mathlib.Topology.Covering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCoveringMap.constOn_of_comp", "kind": "theorem", "module": "Mathlib.Topology.Covering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCoveringMap.restrictPreimage", "kind": "theorem", "module": "Mathlib.Topology.Covering.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsCoveringMap.comp_homeomorph", "kind": "theorem", "module": "Mathlib.Topology.Covering.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsCoveringMap.homeomorph_comp", "kind": "theorem", "module": "Mathlib.Topology.Covering.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsCoveringMap.comp_homeomorph_iff", "kind": "theorem", "module": "Mathlib.Topology.Covering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCoveringMap.homeomorph_comp_iff", "kind": "theorem", "module": "Mathlib.Topology.Covering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCoveringMapOn.of_isCoveringMap_subtype", "kind": "theorem", "module": "Mathlib.Topology.Covering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsFiberBundle.isCoveringMap", "kind": "theorem", "module": "Mathlib.Topology.Covering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiberBundle.isCoveringMap", "kind": "theorem", "module": "Mathlib.Topology.Covering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.trivializationDiscrete", "kind": "definition", "module": "Mathlib.Topology.Covering.Basic", "is_tactic_proof": true, "tactics": ["have", "simp_rw", "choose", "choose", "classical", "let", "invFun", "target", "map_target", "left_inv", "he", "simp_rw", "exact", "right_inv", "hx", "rw", "refine", "rw", "by_contra", "have", "convert", "rw", "exact", "have", "have", "refine", "continuousOn_toFun", "cont_f.prodMk", "continuousOn_of_forall_continuousAt", "continuous_const", "mem_nhds_iff.mpr", "continuousOn_invFun", "source_eq", "by_contra", "dsimp", "rwa", "simp_rw", "refine", "rw", "convert", "refine", "rw"], "tactic_count": 42}
{"name": "IsDiscrete.of_openPartialHomeomorph", "kind": "theorem", "module": "Mathlib.Topology.Covering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosedMap.isEvenlyCovered_of_openPartialHomeomorph", "kind": "theorem", "module": "Mathlib.Topology.Covering.Basic", "is_tactic_proof": false, "tactics": ["have", "from", "choose", "h", "e.2", "have", "let", "have", "have", "mem_iUnion_of_mem", "have", "cases", "exact", "have", "let", "have", "have", "hU.inter", "isOpen_iInter_of_finite", "exact", "have", "have", "refine", "hU'.trivializationDiscrete", "convert", "simp_rw", "have", "hs.trans", "rw", "inter_comm]", "convert", "refine", "have", "rwa", "convert"], "tactic_count": 35}
{"name": "IsClosedMap.isCoveringMapOn_of_openPartialHomeomorph", "kind": "theorem", "module": "Mathlib.Topology.Covering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsEvenlyCovered.of_openPartialHomeomorph", "kind": "theorem", "module": "Mathlib.Topology.Covering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCoveringMapOn.of_openPartialHomeomorph", "kind": "theorem", "module": "Mathlib.Topology.Covering.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsQuotientCoveringMap.subgroup_congr", "kind": "theorem", "module": "Mathlib.Topology.Covering.Quotient", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsQuotientCoveringMap.isCancelSMul", "kind": "theorem", "module": "Mathlib.Topology.Covering.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsQuotientCoveringMap.homeomorph_comp", "kind": "theorem", "module": "Mathlib.Topology.Covering.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsQuotientCoveringMap.homeomorph_comp_iff", "kind": "theorem", "module": "Mathlib.Topology.Covering.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsQuotientMap.trivializationOfSMulDisjoint", "kind": "definition", "module": "Mathlib.Topology.Covering.Quotient", "is_tactic_proof": true, "tactics": ["have", "have", "ext", "obtain", "intro", "have", "refine", "hf.isOpen_preimage.mp", "disjoint_iff_inf_le.mpr", "preim_im.subset", "rw", "exact", "convert", "ext", "have", "obtain", "refine", "apply", "apply", "rintro", "rw", "have", "rw", "apply", "rintro", "simp_rw"], "tactic_count": 26}
{"name": "Topology.IsQuotientMap.isCoveringMapOn_of_smul_disjoint", "kind": "theorem", "module": "Mathlib.Topology.Covering.Quotient", "is_tactic_proof": true, "tactics": ["letI", "suffices", "choose", "rintro", "have", "refine", "mem_interior_iff_mem_nhds.mpr", "rw", "exact"], "tactic_count": 9}
{"name": "Topology.IsQuotientMap.isCoveringMapOn_of_properlyDiscontinuousSMul", "kind": "theorem", "module": "Mathlib.Topology.Covering.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsQuotientMap.isQuotientCoveringMap_of_properlyDiscontinuousSMul", "kind": "theorem", "module": "Mathlib.Topology.Covering.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCoveringMapOn_quotientMk_of_properlyDiscontinuousSMul", "kind": "theorem", "module": "Mathlib.Topology.Covering.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isQuotientCoveringMap_quotientMk_of_properlyDiscontinuousSMul", "kind": "theorem", "module": "Mathlib.Topology.Covering.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsQuotientMap.isQuotientCoveringMap_of_subgroup", "kind": "theorem", "module": "Mathlib.Topology.Covering.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsQuotientMap.isQuotientCoveringMap_of_subgroupOp", "kind": "theorem", "module": "Mathlib.Topology.Covering.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsQuotientMap.isQuotientCoveringMap_of_isDiscrete_ker_monoidHom", "kind": "theorem", "module": "Mathlib.Topology.Covering.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.isQuotientCoveringMap", "kind": "theorem", "module": "Mathlib.Topology.Covering.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subgroup.isQuotientCoveringMap_of_comm", "kind": "theorem", "module": "Mathlib.Topology.Covering.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsQuotientCoveringMap.isCoveringMap", "kind": "theorem", "module": "Mathlib.Topology.Covering.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsQuotientCoveringMap.isOpenQuotientMap", "kind": "theorem", "module": "Mathlib.Topology.Covering.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isQuotientCoveringMap_iff_isCoveringMap_and", "kind": "theorem", "module": "Mathlib.Topology.Covering.Quotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen", "kind": "definition", "module": "Mathlib.Topology.Defs.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpen_univ", "kind": "theorem", "module": "Mathlib.Topology.Defs.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.inter", "kind": "theorem", "module": "Mathlib.Topology.Defs.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpen_sUnion", "kind": "theorem", "module": "Mathlib.Topology.Defs.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClopen", "kind": "definition", "module": "Mathlib.Topology.Defs.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocallyClosed", "kind": "definition", "module": "Mathlib.Topology.Defs.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "interior", "kind": "definition", "module": "Mathlib.Topology.Defs.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "closure", "kind": "definition", "module": "Mathlib.Topology.Defs.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "frontier", "kind": "definition", "module": "Mathlib.Topology.Defs.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "coborder", "kind": "definition", "module": "Mathlib.Topology.Defs.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dense", "kind": "definition", "module": "Mathlib.Topology.Defs.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DenseRange", "kind": "definition", "module": "Mathlib.Topology.Defs.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpenMap", "kind": "definition", "module": "Mathlib.Topology.Defs.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Topology.IsOpen_of", "kind": "definition", "module": "Mathlib.Topology.Defs.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "DenseRange.equalizer", "kind": "theorem", "module": "Mathlib.Topology.DenseEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.hasBasis_of_isDenseInducing", "kind": "theorem", "module": "Mathlib.Topology.DenseEmbedding", "is_tactic_proof": true, "tactics": ["rw", "intro", "refine", "obtain", "have", "rw", "exact", "obtain", "exact", "obtain", "suffices", "replace", "exact"], "tactic_count": 13}
{"name": "AccPt.map", "kind": "theorem", "module": "Mathlib.Topology.DerivedSet", "is_tactic_proof": true, "tactics": ["apply", "rw", "gcongr", "apply", "simpa"], "tactic_count": 5}
{"name": "derivedSet", "kind": "definition", "module": "Mathlib.Topology.DerivedSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_derivedSet", "kind": "theorem", "module": "Mathlib.Topology.DerivedSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "derivedSet_union", "kind": "theorem", "module": "Mathlib.Topology.DerivedSet", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "derivedSet_mono", "kind": "theorem", "module": "Mathlib.Topology.DerivedSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.image_derivedSet", "kind": "theorem", "module": "Mathlib.Topology.DerivedSet", "is_tactic_proof": true, "tactics": ["intro", "simp", "obtain", "convert", "simp"], "tactic_count": 5}
{"name": "derivedSet_subset_closure", "kind": "theorem", "module": "Mathlib.Topology.DerivedSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosed_iff_derivedSet_subset", "kind": "theorem", "module": "Mathlib.Topology.DerivedSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "closure_eq_self_union_derivedSet", "kind": "theorem", "module": "Mathlib.Topology.DerivedSet", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "derivedSet_closure", "kind": "theorem", "module": "Mathlib.Topology.DerivedSet", "is_tactic_proof": true, "tactics": ["refine", "rw", "peel", "obtain", "exact"], "tactic_count": 5}
{"name": "isClosed_derivedSet", "kind": "theorem", "module": "Mathlib.Topology.DerivedSet", "is_tactic_proof": true, "tactics": ["rw", "apply", "simp"], "tactic_count": 3}
{"name": "preperfect_iff_subset_derivedSet", "kind": "theorem", "module": "Mathlib.Topology.DerivedSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "perfect_iff_eq_derivedSet", "kind": "theorem", "module": "Mathlib.Topology.DerivedSet", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsPreconnected.inter_derivedSet_nonempty", "kind": "theorem", "module": "Mathlib.Topology.DerivedSet", "is_tactic_proof": true, "tactics": ["by_cases", "apply", "simp", "simp", "trans", "apply", "rw", "exact", "exact", "exact", "obtain", "simp_all"], "tactic_count": 12}
{"name": "DiscreteQuotient.toSetoid_injective", "kind": "theorem", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteQuotient.ofIsClopen", "kind": "definition", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteQuotient.refl", "kind": "theorem", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteQuotient.symm", "kind": "theorem", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteQuotient.trans", "kind": "theorem", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteQuotient.instCoeSortType", "kind": "instance", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteQuotient.instTopologicalSpaceQuotient", "kind": "instance", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteQuotient.proj", "kind": "definition", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteQuotient.fiber_eq", "kind": "theorem", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteQuotient.proj_surjective", "kind": "theorem", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteQuotient.proj_isQuotientMap", "kind": "theorem", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteQuotient.proj_continuous", "kind": "theorem", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteQuotient.instDiscreteTopologyQuotient", "kind": "instance", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteQuotient.proj_isLocallyConstant", "kind": "theorem", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteQuotient.isClopen_preimage", "kind": "theorem", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteQuotient.isOpen_preimage", "kind": "theorem", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteQuotient.isClosed_preimage", "kind": "theorem", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteQuotient.isClopen_setOf_rel", "kind": "theorem", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "DiscreteQuotient.instMin", "kind": "instance", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteQuotient.instSemilatticeInf", "kind": "instance", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteQuotient.instOrderTop", "kind": "instance", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteQuotient.instInhabited", "kind": "instance", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteQuotient.inhabitedQuotient", "kind": "instance", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteQuotient.instNonemptyQuotient", "kind": "instance", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteQuotient.instSubsingletonQuotientTop", "kind": "instance", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteQuotient.comap", "kind": "definition", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteQuotient.comap_id", "kind": "theorem", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteQuotient.comap_comp", "kind": "theorem", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteQuotient.comap_mono", "kind": "theorem", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": true, "tactics": ["tauto"], "tactic_count": 1}
{"name": "DiscreteQuotient.ofLE", "kind": "definition", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteQuotient.ofLE_refl", "kind": "theorem", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "DiscreteQuotient.ofLE_refl_apply", "kind": "theorem", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DiscreteQuotient.ofLE_ofLE", "kind": "theorem", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": true, "tactics": ["rcases", "rfl"], "tactic_count": 2}
{"name": "DiscreteQuotient.ofLE_comp_ofLE", "kind": "theorem", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteQuotient.ofLE_continuous", "kind": "theorem", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteQuotient.ofLE_proj", "kind": "theorem", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteQuotient.ofLE_comp_proj", "kind": "theorem", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteQuotient.instOrderBotOfLocallyConnectedSpace", "kind": "instance", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteQuotient.proj_bot_eq", "kind": "theorem", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteQuotient.proj_bot_inj", "kind": "theorem", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DiscreteQuotient.proj_bot_injective", "kind": "theorem", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteQuotient.proj_bot_bijective", "kind": "theorem", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteQuotient.LEComap", "kind": "definition", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteQuotient.leComap_id", "kind": "theorem", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteQuotient.leComap_id_iff", "kind": "theorem", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteQuotient.LEComap.comp", "kind": "theorem", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": true, "tactics": ["tauto"], "tactic_count": 1}
{"name": "DiscreteQuotient.LEComap.mono", "kind": "theorem", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteQuotient.map", "kind": "definition", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteQuotient.map_continuous", "kind": "theorem", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteQuotient.map_comp_proj", "kind": "theorem", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteQuotient.map_proj", "kind": "theorem", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteQuotient.map_id", "kind": "theorem", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "DiscreteQuotient.map_comp", "kind": "theorem", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "DiscreteQuotient.ofLE_map", "kind": "theorem", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": true, "tactics": ["rcases", "rfl"], "tactic_count": 2}
{"name": "DiscreteQuotient.ofLE_comp_map", "kind": "theorem", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteQuotient.map_ofLE", "kind": "theorem", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": true, "tactics": ["rcases", "rfl"], "tactic_count": 2}
{"name": "DiscreteQuotient.map_comp_ofLE", "kind": "theorem", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteQuotient.eq_of_forall_proj_eq", "kind": "theorem", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": true, "tactics": ["rw", "rintro", "exact"], "tactic_count": 3}
{"name": "DiscreteQuotient.fiber_subset_ofLE", "kind": "theorem", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": true, "tactics": ["rcases", "rw", "exact"], "tactic_count": 3}
{"name": "DiscreteQuotient.exists_of_compat", "kind": "theorem", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": false, "tactics": ["have", "rw", "exact", "obtain", "exact"], "tactic_count": 5}
{"name": "DiscreteQuotient.instFiniteQuotientOfCompactSpace", "kind": "instance", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "DiscreteQuotient.finsetClopens", "kind": "definition", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteQuotient.comp_finsetClopens", "kind": "theorem", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": true, "tactics": ["ext", "simp", "constructor", "refine", "ext", "simpa", "exact"], "tactic_count": 7}
{"name": "DiscreteQuotient.finsetClopens_inj", "kind": "theorem", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": true, "tactics": ["apply", "rw", "intro", "congr", "rw", "exact"], "tactic_count": 6}
{"name": "DiscreteQuotient.equivFinsetClopens", "kind": "definition", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.discreteQuotient", "kind": "definition", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.lift", "kind": "definition", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.lift_comp_proj", "kind": "theorem", "module": "Mathlib.Topology.DiscreteQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "discreteTopology_subtype_iff", "kind": "theorem", "module": "Mathlib.Topology.DiscreteSubset", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "isDiscrete_iff_nhdsNE", "kind": "theorem", "module": "Mathlib.Topology.DiscreteSubset", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "discreteTopology_of_noAccPts", "kind": "theorem", "module": "Mathlib.Topology.DiscreteSubset", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "discreteTopology_subtype_iff'", "kind": "theorem", "module": "Mathlib.Topology.DiscreteSubset", "is_tactic_proof": true, "tactics": ["simp", "grind"], "tactic_count": 2}
{"name": "isDiscrete_iff_forall_exists_isOpen", "kind": "theorem", "module": "Mathlib.Topology.DiscreteSubset", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.Subsingleton.isDiscrete", "kind": "theorem", "module": "Mathlib.Topology.DiscreteSubset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isDiscrete_iff_nhdsWithin", "kind": "theorem", "module": "Mathlib.Topology.DiscreteSubset", "is_tactic_proof": true, "tactics": ["simp", "nhds_induced,"], "tactic_count": 2}
{"name": "IsDiscrete.of_nhdsWithin", "kind": "theorem", "module": "Mathlib.Topology.DiscreteSubset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isDiscrete_univ_iff", "kind": "theorem", "module": "Mathlib.Topology.DiscreteSubset", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsDiscrete.univ", "kind": "theorem", "module": "Mathlib.Topology.DiscreteSubset", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "IsDiscrete.image_of_isOpenMap", "kind": "theorem", "module": "Mathlib.Topology.DiscreteSubset", "is_tactic_proof": true, "tactics": ["refine", "rintro", "rw", "grw"], "tactic_count": 4}
{"name": "IsDiscrete.image_of_isOpenMap_of_isOpen", "kind": "theorem", "module": "Mathlib.Topology.DiscreteSubset", "is_tactic_proof": true, "tactics": ["refine", "rintro", "rw", "exact"], "tactic_count": 4}
{"name": "IsOpenMap.isDiscrete_range", "kind": "theorem", "module": "Mathlib.Topology.DiscreteSubset", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsDiscrete.image", "kind": "theorem", "module": "Mathlib.Topology.DiscreteSubset", "is_tactic_proof": true, "tactics": ["refine", "rintro", "rw"], "tactic_count": 3}
{"name": "IsEmbedding.isDiscrete_range", "kind": "theorem", "module": "Mathlib.Topology.DiscreteSubset", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsDiscrete.preimage", "kind": "theorem", "module": "Mathlib.Topology.DiscreteSubset", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "IsDiscrete.preimage'", "kind": "theorem", "module": "Mathlib.Topology.DiscreteSubset", "is_tactic_proof": true, "tactics": ["refine", "have", "grw", "inf_eq_right.mpr", "exact"], "tactic_count": 5}
{"name": "IsDiscrete.eq_of_specializes", "kind": "theorem", "module": "Mathlib.Topology.DiscreteSubset", "is_tactic_proof": true, "tactics": ["letI", "simpa", "specializes_iff_eq"], "tactic_count": 3}
{"name": "tendsto_cofinite_cocompact_iff", "kind": "theorem", "module": "Mathlib.Topology.DiscreteSubset", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp"], "tactic_count": 3}
{"name": "Continuous.discrete_of_tendsto_cofinite_cocompact", "kind": "theorem", "module": "Mathlib.Topology.DiscreteSubset", "is_tactic_proof": true, "tactics": ["refine", "obtain", "obtain", "have", "exact"], "tactic_count": 5}
{"name": "tendsto_cofinite_cocompact_of_discrete", "kind": "theorem", "module": "Mathlib.Topology.DiscreteSubset", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "IsClosed.tendsto_coe_cofinite_of_isDiscrete", "kind": "theorem", "module": "Mathlib.Topology.DiscreteSubset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.tendsto_coe_cofinite_iff", "kind": "theorem", "module": "Mathlib.Topology.DiscreteSubset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosed_and_discrete_iff", "kind": "theorem", "module": "Mathlib.Topology.DiscreteSubset", "is_tactic_proof": true, "tactics": ["rw", "congrm", "rw", "constructor", "by_cases", "exacts", "refine", "simpa"], "tactic_count": 8}
{"name": "Filter.codiscreteWithin", "kind": "definition", "module": "Mathlib.Topology.DiscreteSubset", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_codiscreteWithin", "kind": "theorem", "module": "Mathlib.Topology.DiscreteSubset", "is_tactic_proof": false, "tactics": ["simp", "mem_compl_iff]", "congr", "tauto"], "tactic_count": 4}
{"name": "mem_codiscreteWithin_iff_forall_mem_nhdsNE", "kind": "theorem", "module": "Mathlib.Topology.DiscreteSubset", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "mem_codiscreteWithin_accPt", "kind": "theorem", "module": "Mathlib.Topology.DiscreteSubset", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.self_mem_codiscreteWithin", "kind": "theorem", "module": "Mathlib.Topology.DiscreteSubset", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.codiscreteWithin.mono", "kind": "theorem", "module": "Mathlib.Topology.DiscreteSubset", "is_tactic_proof": true, "tactics": ["refine", "gcongr"], "tactic_count": 2}
{"name": "isDiscrete_of_codiscreteWithin", "kind": "theorem", "module": "Mathlib.Topology.DiscreteSubset", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "simp_all"], "tactic_count": 3}
{"name": "codiscreteWithin_iff_locallyEmptyComplementWithin", "kind": "theorem", "module": "Mathlib.Topology.DiscreteSubset", "is_tactic_proof": true, "tactics": ["simp", "refine", "rw", "obtain", "use"], "tactic_count": 5}
{"name": "isClosed_sdiff_of_codiscreteWithin", "kind": "theorem", "module": "Mathlib.Topology.DiscreteSubset", "is_tactic_proof": true, "tactics": ["rw", "intro", "by_cases", "rw", "filter_upwards", "intro", "by_cases", "tauto_set", "specialize", "tauto_set", "rw", "use", "intro", "tauto_set"], "tactic_count": 14}
{"name": "nhdsNE_of_nhdsNE_sdiff_finite", "kind": "theorem", "module": "Mathlib.Topology.DiscreteSubset", "is_tactic_proof": true, "tactics": ["rw", "obtain", "use", "constructor", "rw", "exact", "tauto_set"], "tactic_count": 7}
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{"name": "variationOnFromTo.eq_zero_iff", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.BoundedVariation", "is_tactic_proof": true, "tactics": ["rcases", "rw", "exact", "rw", "exact"], "tactic_count": 5}
{"name": "variationOnFromTo.monotoneOn", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.BoundedVariation", "is_tactic_proof": true, "tactics": ["rintro", "rw", "exact"], "tactic_count": 3}
{"name": "variationOnFromTo.antitoneOn", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.BoundedVariation", "is_tactic_proof": true, "tactics": ["rintro", "dsimp", "rw", "exact"], "tactic_count": 4}
{"name": "variationOnFromTo.sub_self_monotoneOn", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.BoundedVariation", "is_tactic_proof": true, "tactics": ["rintro", "rw", "calc", "f", "rw", "apply", "apply", "exacts", "rw"], "tactic_count": 9}
{"name": "variationOnFromTo.comp_eq_of_monotoneOn", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.BoundedVariation", "is_tactic_proof": true, "tactics": ["rcases", "rw", "eVariationOn.comp_inter_Icc_eq_of_monotoneOn", "rw", "eVariationOn.comp_inter_Icc_eq_of_monotoneOn"], "tactic_count": 5}
{"name": "LocallyBoundedVariationOn.exists_monotoneOn_sub_monotoneOn", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.BoundedVariation", "is_tactic_proof": true, "tactics": ["rcases", "exact", "exact"], "tactic_count": 3}
{"name": "LipschitzOnWith.comp_eVariationOn_le", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.BoundedVariation", "is_tactic_proof": true, "tactics": ["apply", "rintro", "calc"], "tactic_count": 3}
{"name": "LipschitzOnWith.comp_boundedVariationOn", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.BoundedVariation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzOnWith.comp_locallyBoundedVariationOn", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.BoundedVariation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzWith.comp_boundedVariationOn", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.BoundedVariation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzWith.comp_locallyBoundedVariationOn", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.BoundedVariation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzOnWith.locallyBoundedVariationOn", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.BoundedVariation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzWith.locallyBoundedVariationOn", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.BoundedVariation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformity_dist_of_mem_uniformity", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformSpaceOfEDist", "kind": "definition", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformSpaceOfEDistOfHasBasis", "kind": "definition", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoEMetricSpace.ext", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "congr", "exact"], "tactic_count": 4}
{"name": "edist_triangle_left", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "edist_triangle_right", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "edist_congr_right", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": true, "tactics": ["apply", "rw", "apply", "rw", "rw", "apply"], "tactic_count": 6}
{"name": "edist_congr_left", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "edist_congr", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "edist_triangle4", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": true, "tactics": ["grw"], "tactic_count": 1}
{"name": "uniformity_pseudoedist", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformSpace_edist", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformity_basis_edist", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_uniformity_edist", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EMetric.mk_uniformity_basis", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": true, "tactics": ["refine", "constructor", "rintro", "rcases", "exact", "exact"], "tactic_count": 6}
{"name": "EMetric.mk_uniformity_basis_le", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": true, "tactics": ["refine", "constructor", "rintro", "rcases", "rcases", "exact", "exact"], "tactic_count": 7}
{"name": "uniformity_basis_edist_le", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformity_basis_edist'", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformity_basis_edist_le'", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformity_basis_edist_nnreal", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformity_basis_edist_nnreal_le", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformity_basis_edist_inv_nat", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformity_basis_edist_inv_two_pow", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "edist_mem_uniformity", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EMetric.instIsCountablyGeneratedUniformity", "kind": "instance", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EMetric.uniformContinuousOn_iff", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EMetric.uniformContinuous_iff", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoEMetricSpace.replaceUniformity", "kind": "abbrev", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoEMetricSpace.induced", "kind": "abbrev", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instPseudoEMetricSpaceSubtype", "kind": "instance", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.edist_eq", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.edist_mk_mk", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoEMetricSpace.ofEDistOfTopology", "kind": "definition", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instPseudoEMetricSpace", "kind": "instance", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.edist_unop", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.edist_op", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instPseudoEMetricSpaceULift", "kind": "instance", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.edist_eq", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.edist_up_up", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.pseudoEMetricSpaceMax", "kind": "instance", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.edist_eq", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.eball", "kind": "definition", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.mem_eball", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.mem_eball'", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Metric.closedEBall", "kind": "definition", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.mem_closedEBall", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.mem_closedEBall'", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Metric.closedEBall_top", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.eball_subset_closedEBall", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.pos_of_mem_eball", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.mem_eball_self", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Metric.mem_closedEBall_self", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Metric.mem_eball_comm", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Metric.mem_closedEBall_comm", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Metric.eball_subset_eball", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.closedEBall_subset_closedEBall", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.eball_disjoint", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.eball_subset", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.exists_eball_subset_eball", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": true, "tactics": ["have", "refine", "exact"], "tactic_count": 3}
{"name": "Metric.eball_eq_empty_iff", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.ordConnected_setOf_closedEBall_subset", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.ordConnected_setOf_eball_subset", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.edistLtTopSetoid", "kind": "definition", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.eball_zero", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Metric.nhds_basis_eball", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.nhdsWithin_basis_eball", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.nhds_basis_closedEBall", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.nhdsWithin_basis_closedEBall", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EMetric.nhds_eq", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EMetric.mem_nhds_iff", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EMetric.mem_nhdsWithin_iff", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EMetric.isOpen_iff", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "EMetric.mem_closure_iff", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EMetric.dense_iff", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EMetric.tendsto_nhds", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EMetric.tendsto_atTop", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EMetric.tendsto_nhdsWithin_nhdsWithin", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EMetric.tendsto_nhdsWithin_nhds", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "EMetric.tendsto_nhds_nhds", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.isOpen_eball", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.isClosed_eball_top", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.eball_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.closedEBall_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.eball_prod_same", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.closedEBall_prod_same", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.preimage_eball", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.preimage_closedEBall", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.image_eball", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subtype.image_closedEBall", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EMetricSpace.ext", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": true, "tactics": ["cases", "cases", "congr", "ext1", "assumption"], "tactic_count": 5}
{"name": "edist_eq_zero", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zero_eq_edist", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "edist_le_zero", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "edist_pos", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Metric.closedEBall_zero", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "eq_of_forall_edist_le", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EMetricSpace.replaceUniformity", "kind": "abbrev", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EMetricSpace.replaceTopology", "kind": "abbrev", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EMetricSpace.induced", "kind": "abbrev", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instEMetricSpaceSubtype", "kind": "instance", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instEMetricSpaceMulOpposite", "kind": "instance", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instEMetricSpaceULift", "kind": "instance", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformity_edist", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instEDistAdditive", "kind": "instance", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instEDistMultiplicative", "kind": "instance", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "edist_ofMul", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "edist_ofAdd", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "edist_toMul", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "edist_toAdd", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instPseudoEMetricSpaceAdditive", "kind": "instance", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instPseudoEMetricSpaceMultiplicative", "kind": "instance", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instEMetricSpaceAdditive", "kind": "instance", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instEMetricSpaceMultiplicative", "kind": "instance", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instEDistOrderDual", "kind": "instance", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "edist_toDual", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "edist_ofDual", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instPseudoEMetricSpaceOrderDual", "kind": "instance", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instEMetricSpaceOrderDual", "kind": "instance", "module": "Mathlib.Topology.EMetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.ediam", "kind": "definition", "module": "Mathlib.Topology.EMetricSpace.Diam", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.ediam_eq_sSup", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Diam", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.ediam_le_iff", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Diam", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Metric.ediam_image_le_iff", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Diam", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Metric.edist_le_of_ediam_le", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Diam", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.edist_le_ediam_of_mem", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Diam", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.ediam_le", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Diam", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.ediam_subsingleton", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Diam", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.ediam_empty", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Diam", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.ediam_singleton", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Diam", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.ediam_one", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Diam", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.ediam_iUnion_mem_option", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Diam", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Metric.ediam_insert", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Diam", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.ediam_pair", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Diam", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Metric.ediam_triple", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Diam", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Metric.ediam_mono", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Diam", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.ediam_union_le_add_edist", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Diam", "is_tactic_proof": false, "tactics": ["have", "calc", "edist", "gcongr", "exacts", "refine", "rw", "rcases", "calc", "edist", "exact", "have", "rwa", "calc", "edist"], "tactic_count": 15}
{"name": "Metric.ediam_union_le", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Diam", "is_tactic_proof": true, "tactics": ["let", "simpa"], "tactic_count": 2}
{"name": "Metric.ediam_closedEBall_le", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Diam", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.ediam_eball_le", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Diam", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.ediam_pi_le_of_le", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Diam", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "Metric.ediam_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Diam", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.ediam_pos_iff", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Diam", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Metric.ediam_pos_iff'", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Diam", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LipschitzWith", "kind": "definition", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzOnWith", "kind": "definition", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyLipschitz", "kind": "definition", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyLipschitzOn", "kind": "definition", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lipschitzOnWith_empty", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "locallyLipschitzOn_empty", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzOnWith.mono", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyLipschitzOn.mono", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lipschitzOnWith_univ", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "locallyLipschitzOn_univ", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LocallyLipschitz.locallyLipschitzOn", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lipschitzOnWith_iff_restrict", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "lipschitzOnWith_restrict", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "locallyLipschitzOn_iff_restrict", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": ["simp", "nhds_subtype_eq_comap_nhdsWithin,", "congr", "constructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 8}
{"name": "Set.MapsTo.lipschitzOnWith_iff_restrict", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzWith.lipschitzOnWith", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzWith.edist_le_mul", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzWith.edist_le_mul_of_le", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzWith.edist_lt_mul_of_lt", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": true, "tactics": ["grw"], "tactic_count": 1}
{"name": "LipschitzWith.mapsTo_closedEBall", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzWith.mapsTo_eball", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzWith.edist_lt_top", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzWith.mul_edist_le", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "LipschitzWith.of_edist_le", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzWith.weaken", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzWith.ediam_image_le", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": true, "tactics": ["apply", "rintro", "exact"], "tactic_count": 3}
{"name": "LipschitzWith.edist_lt_of_edist_lt_div", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzWith.uniformContinuous", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzWith.continuous", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzWith.const", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzWith.const'", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzWith.zero_iff", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LipschitzWith.id", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzWith.subtype_val", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzWith.subtype_mk", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzWith.eval", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzWith.restrict", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzWith.comp", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzWith.comp_lipschitzOnWith", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzWith.prod_fst", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzWith.prod_snd", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzWith.prodMk", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": true, "tactics": ["intro", "rw", "exact"], "tactic_count": 3}
{"name": "LipschitzWith.prodMk_left", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "LipschitzWith.prodMk_right", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "LipschitzWith.uncurry", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": true, "tactics": ["rintro", "simp", "apply", "exact", "add_le_add"], "tactic_count": 5}
{"name": "LipschitzWith.iterate", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzWith.edist_iterate_succ_le_geometric", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "LipschitzWith.mul_end", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzWith.list_prod", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzWith.pow_end", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzOnWith.zero_iff", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LipschitzOnWith.uniformContinuousOn", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzOnWith.continuousOn", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzOnWith.edist_le_mul_of_le", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzOnWith.edist_lt_of_edist_lt_div", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzOnWith.comp", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzOnWith.prodMk", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": true, "tactics": ["intro", "rw", "exact"], "tactic_count": 3}
{"name": "LipschitzOnWith.ediam_image2_le", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": true, "tactics": ["simp", "intro", "refine", "exact", "add_le_add"], "tactic_count": 5}
{"name": "LipschitzWith.locallyLipschitz", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyLipschitz.id", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyLipschitz.const", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyLipschitz.continuous", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": true, "tactics": ["rw", "intro", "rcases", "exact"], "tactic_count": 4}
{"name": "LocallyLipschitz.comp", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": true, "tactics": ["intro", "rcases", "rcases", "refine", "exact"], "tactic_count": 5}
{"name": "LocallyLipschitz.prodMk", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": true, "tactics": ["intro", "rcases", "rcases", "refine", "exact"], "tactic_count": 5}
{"name": "LocallyLipschitz.prodMk_left", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyLipschitz.prodMk_right", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyLipschitz.iterate", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyLipschitz.mul_end", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyLipschitz.pow_end", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyLipschitzOn.continuousOn", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousOn_prod_of_subset_closure_continuousOn_lipschitzOnWith", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": true, "tactics": ["rintro", "refine", "replace", "obtain", "rw", "rcases", "have", "have", "inter_mem", "filter_upwards", "calc", "edist", "edist", "edist_triangle4", "gcongr", "refine", "exact", "exact", "exact"], "tactic_count": 19}
{"name": "continuousOn_prod_of_continuousOn_lipschitzOnWith", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_prod_of_dense_continuous_lipschitzWith", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": true, "tactics": ["simp", "exact", "continuousOn_prod_of_subset_closure_continuousOn_lipschitzOnWith", "hb"], "tactic_count": 4}
{"name": "continuous_prod_of_continuous_lipschitzWith", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousOn_prod_of_subset_closure_continuousOn_lipschitzOnWith'", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousOn_prod_of_continuousOn_lipschitzOnWith'", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_prod_of_dense_continuous_lipschitzWith'", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_prod_of_continuous_lipschitzWith'", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PairReduction.exists_radius_le", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.PairReduction", "is_tactic_proof": false, "tactics": ["have", "simp", "obtain", "exact"], "tactic_count": 4}
{"name": "PairReduction.logSizeRadius", "kind": "definition", "module": "Mathlib.Topology.EMetricSpace.PairReduction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PairReduction.one_le_logSizeRadius", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.PairReduction", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "PairReduction.card_le_logSizeRadius_le_pow_logSizeRadius", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.PairReduction", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "PairReduction.pow_logSizeRadius_le_card_le_logSizeRadius", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.PairReduction", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "exact", "rw", "have", "have", "simp", "exact"], "tactic_count": 8}
{"name": "PairReduction.logSizeBallStruct.smallBall", "kind": "definition", "module": "Mathlib.Topology.EMetricSpace.PairReduction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PairReduction.logSizeBallStruct.ball", "kind": "definition", "module": "Mathlib.Topology.EMetricSpace.PairReduction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PairReduction.logSizeBallSeq", "kind": "definition", "module": "Mathlib.Topology.EMetricSpace.PairReduction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PairReduction.finset_logSizeBallSeq_zero", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.PairReduction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PairReduction.point_logSizeBallSeq_zero", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.PairReduction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PairReduction.radius_logSizeBallSeq_zero", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.PairReduction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PairReduction.finset_logSizeBallSeq_add_one", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.PairReduction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PairReduction.point_logSizeBallSeq_add_one", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.PairReduction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PairReduction.radius_logSizeBallSeq_add_one", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.PairReduction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PairReduction.finset_logSizeBallSeq_add_one_subset", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.PairReduction", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PairReduction.antitone_logSizeBallSeq_add_one_subset", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.PairReduction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PairReduction.finset_logSizeBallSeq_subset_logSizeBallSeq_init", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.PairReduction", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "PairReduction.radius_logSizeBallSeq_le", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.PairReduction", "is_tactic_proof": true, "tactics": ["simp", "exact", "i", "simp", "refine", "gcongr", "exact"], "tactic_count": 7}
{"name": "PairReduction.one_le_radius_logSizeBallSeq", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.PairReduction", "is_tactic_proof": true, "tactics": ["i"], "tactic_count": 1}
{"name": "PairReduction.point_mem_finset_logSizeBallSeq", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.PairReduction", "is_tactic_proof": true, "tactics": ["i"], "tactic_count": 1}
{"name": "PairReduction.point_mem_logSizeBallSeq_init", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.PairReduction", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "by_cases", "refine", "apply", "simp"], "tactic_count": 7}
{"name": "PairReduction.point_notMem_finset_logSizeBallSeq_add_one", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.PairReduction", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PairReduction.finset_logSizeBallSeq_add_one_ssubset", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.PairReduction", "is_tactic_proof": true, "tactics": ["apply", "simp", "refine", "exact", "exact"], "tactic_count": 5}
{"name": "PairReduction.card_finset_logSizeBallSeq_add_one_lt", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.PairReduction", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PairReduction.card_finset_logSizeBallSeq_le", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.PairReduction", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "by_cases", "have", "lia", "apply", "suffices", "rwa"], "tactic_count": 9}
{"name": "PairReduction.card_finset_logSizeBallSeq_card_eq_zero", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.PairReduction", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "PairReduction.disjoint_smallBall_logSizeBallSeq", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.PairReduction", "is_tactic_proof": true, "tactics": ["wlog", "exact", "apply", "exact", "simp"], "tactic_count": 5}
{"name": "PairReduction.pairSetSeq", "kind": "definition", "module": "Mathlib.Topology.EMetricSpace.PairReduction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PairReduction.pairSet", "kind": "definition", "module": "Mathlib.Topology.EMetricSpace.PairReduction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PairReduction.pairSet_empty_eq_empty", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.PairReduction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PairReduction.pairSet_subset", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.PairReduction", "is_tactic_proof": true, "tactics": ["unfold", "rw", "intro", "by_cases", "simp", "apply", "exact", "exact", "simp"], "tactic_count": 9}
{"name": "PairReduction.card_pairSetSeq_le_logSizeRadius_mul", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.PairReduction", "is_tactic_proof": true, "tactics": ["induction", "zero", "simpa", "card_le_logSizeRadius_le_pow_logSizeRadius", "succ", "by_cases", "simpa", "simp"], "tactic_count": 8}
{"name": "PairReduction.logSizeRadius_le_card_smallBall", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.PairReduction", "is_tactic_proof": true, "tactics": ["simpa", "pow_logSizeRadius_le_card_le_logSizeRadius", "i", "by_cases", "simpa", "pow_logSizeRadius_le_card_le_logSizeRadius", "simp"], "tactic_count": 7}
{"name": "PairReduction.card_pairSet_le", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.PairReduction", "is_tactic_proof": true, "tactics": ["wlog", "simp", "unfold", "grw", "conv_lhs", "grw", "gcongr", "grw", "gcongr", "unfold", "rw", "intro", "exact"], "tactic_count": 13}
{"name": "PairReduction.edist_le_of_mem_pairSet", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.PairReduction", "is_tactic_proof": true, "tactics": ["obtain", "have", "wlog", "convert", "convert", "simp", "have", "exact", "simp", "obtain", "grw"], "tactic_count": 11}
{"name": "PairReduction.iSup_edist_pairSet", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.PairReduction", "is_tactic_proof": true, "tactics": ["rw", "rw", "have", "let", "let", "obtain", "apply", "simpa", "wlog", "have", "have", "by_contra", "simp", "have", "refine", "dsimp", "grw", "rfl", "apply", "suffices", "rw", "apply", "simp", "have", "simpa", "have", "rw", "have", "simp", "simp", "exact", "simp", "true_and,", "have", "simp", "grw", "have", "simp", "apply", "apply", "nth_rw", "rw", "congr", "rw", "rw", "gcongr", "exact", "have", "have", "have", "edist", "simp", "apply", "apply", "exact", "refine", "refine", "exact", "rw", "apply", "rw", "apply"], "tactic_count": 62}
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{"name": "Metric.instParacompactSpace", "kind": "instance", "module": "Mathlib.Topology.EMetricSpace.Paracompact", "is_tactic_proof": true, "tactics": ["the", "have", "have", "have", "simp", "refine", "simp", "obtain", "let", "have", "have", "set", "hD", "have", "eball", "simp", "rw", "have", "y", "rw", "simp", "have", "obtain", "rcases", "have", "rcases", "refine", "simpa", "by_contra", "apply", "exact", "memD.2", "have", "rw", "iterate", "exact", "have", "rw", "rintro", "refine", "norm_num1", "refine", "refine", "rcases", "exact", "intro", "rcases", "have", "rcases", "set", "refine", "have", "rw", "rintro", "rcases", "have", "apply", "calc", "edist", "rw", "have", "rintro", "by_contra", "wlog", "exact", "rcases", "rcases", "suffices", "calc", "edist", "rw", "have", "refine", "simp", "refine", "exact"], "tactic_count": 76}
{"name": "Metric.t4Space", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Paracompact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instEDistForall", "kind": "instance", "module": "Mathlib.Topology.EMetricSpace.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "edist_pi_def", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "edist_le_pi_edist", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "edist_pi_le_iff", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "edist_pi_const_le", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "edist_pi_const", "kind": "theorem", "module": "Mathlib.Topology.EMetricSpace.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pseudoEMetricSpacePi", "kind": "instance", "module": "Mathlib.Topology.EMetricSpace.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "emetricSpacePi", "kind": "instance", "module": "Mathlib.Topology.EMetricSpace.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "extendFrom", "kind": "definition", "module": "Mathlib.Topology.ExtendFrom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_extendFrom", "kind": "theorem", "module": "Mathlib.Topology.ExtendFrom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "extendFrom_eq", "kind": "theorem", "module": "Mathlib.Topology.ExtendFrom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "extendFrom_extends", "kind": "theorem", "module": "Mathlib.Topology.ExtendFrom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousOn_extendFrom", "kind": "theorem", "module": "Mathlib.Topology.ExtendFrom", "is_tactic_proof": true, "tactics": ["set", "intro", "suffices", "simpa", "intro", "obtain", "have", "rcases", "exact", "suffices", "rintro", "haveI", "have", "have", "have", "exact"], "tactic_count": 16}
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{"name": "extremallyDisconnected_of_homeo", "kind": "theorem", "module": "Mathlib.Topology.ExtremallyDisconnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instTotallySeparatedSpaceOfExtremallyDisconnectedOfT2Space", "kind": "instance", "module": "Mathlib.Topology.ExtremallyDisconnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompactT2.Projective", "kind": "definition", "module": "Mathlib.Topology.ExtremallyDisconnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StoneCech.projective", "kind": "theorem", "module": "Mathlib.Topology.ExtremallyDisconnected", "is_tactic_proof": true, "tactics": ["intro", "let", "have", "let", "have", "let", "have", "refine", "rw"], "tactic_count": 9}
{"name": "CompactT2.Projective.extremallyDisconnected", "kind": "theorem", "module": "Mathlib.Topology.ExtremallyDisconnected", "is_tactic_proof": true, "tactics": ["refine", "let", "let", "let", "have", "have", "have", "have", "let", "have", "have", "intro", "by_cases", "exact", "exact", "haveI", "obtain", "let", "have", "have", "suffices", "rw", "exact", "rw", "refine", "intro", "have", "rcases", "exact", "exact", "rw", "exact"], "tactic_count": 32}
{"name": "exists_compact_surjective_zorn_subset", "kind": "theorem", "module": "Mathlib.Topology.ExtremallyDisconnected", "is_tactic_proof": true, "tactics": ["let", "suffices", "rcases", "obtain", "refine", "intro", "contrapose", "exact", "eq_univ_of_image_val_eq", "intro", "refine", "mem_iInter.mp", "by_cases", "refine", "eq_univ_of_forall", "inter_nonempty_iff_exists_left.mp", "refine", "iInter_inter", "replace", "have", "exact", "rw", "exact", "all_goals", "rw"], "tactic_count": 25}
{"name": "image_subset_closure_compl_image_compl_of_isOpen", "kind": "theorem", "module": "Mathlib.Topology.ExtremallyDisconnected", "is_tactic_proof": true, "tactics": ["by_cases", "simpa", "intro", "rw", "intro", "rcases", "have", "have", "have", "rcases", "have", "rcases", "have", "exact"], "tactic_count": 14}
{"name": "ExtremallyDisconnected.disjoint_closure_of_disjoint_isOpen", "kind": "theorem", "module": "Mathlib.Topology.ExtremallyDisconnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.ExtremallyDisconnected.0.ExtremallyDisconnected.homeoCompactToT2_injective", "kind": "theorem", "module": "Mathlib.Topology.ExtremallyDisconnected", "is_tactic_proof": true, "tactics": ["intro", "by_contra", "rcases", "have", "have", "have", "have", "have", "rw", "compl_empty,", "have", "disjoint_closure_of_disjoint_isOpen", "have", "image_subset_closure_compl_image_compl_of_isOpen", "have", "image_subset_closure_compl_image_compl_of_isOpen", "exact"], "tactic_count": 17}
{"name": "ExtremallyDisconnected.homeoCompactToT2", "kind": "definition", "module": "Mathlib.Topology.ExtremallyDisconnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompactT2.ExtremallyDisconnected.projective", "kind": "theorem", "module": "Mathlib.Topology.ExtremallyDisconnected", "is_tactic_proof": true, "tactics": ["intro", "let", "have", "isCompact_iff_compactSpace.mp", "let", "have", "have", "rcases", "let", "have", "have", "exact", "let", "let", "have", "refine", "suffices", "ext", "exact"], "tactic_count": 19}
{"name": "CompactT2.projective_iff_extremallyDisconnected", "kind": "theorem", "module": "Mathlib.Topology.ExtremallyDisconnected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "FiberBundle.totalSpaceMk_isInducing", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiberBundle.trivializationAtlas", "kind": "abbrev", "module": "Mathlib.Topology.FiberBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "FiberBundle.mem_baseSet_trivializationAt", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "FiberBundle.map_proj_nhds", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "FiberBundle.surjective_proj", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiberBundle.isQuotientMap_proj", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiberBundle.continuous_totalSpaceMk", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiberBundle.totalSpaceMk_isEmbedding", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiberBundle.totalSpaceMk_isClosedEmbedding", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiberBundle.mem_trivializationAt_proj_source", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "FiberBundleCore.TotalSpace", "kind": "abbrev", "module": "Mathlib.Topology.FiberBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "FiberBundleCore.mem_trivChange_source", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
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{"name": "FiberBundleCore.mem_localTrivAsPartialEquiv_source", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "FiberBundleCore.localTrivAt_def", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiberBundleCore.localTrivAt_snd", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiberBundleCore.continuous_const_section", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Basic", "is_tactic_proof": true, "tactics": ["refine", "have", "refine", "exact", "apply", "simp", "have", "refine", "exact"], "tactic_count": 9}
{"name": "FiberBundleCore.localTrivAsPartialEquiv_coe", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiberBundleCore.localTrivAsPartialEquiv_source", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiberBundleCore.localTrivAsPartialEquiv_target", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiberBundleCore.localTrivAsPartialEquiv_symm", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiberBundleCore.baseSet_at", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiberBundleCore.localTriv_apply", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiberBundleCore.localTrivAt_apply", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "FiberBundleCore.localTrivAt_apply_mk", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiberBundleCore.mem_localTriv_source", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiberBundleCore.mem_localTrivAt_source", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiberBundleCore.mem_localTriv_target", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiberBundleCore.mem_localTrivAt_target", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiberBundleCore.localTriv_symm_apply", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiberBundleCore.mem_localTrivAt_baseSet", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "FiberBundleCore.mk_mem_localTrivAt_source", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "FiberBundleCore.fiberBundle", "kind": "instance", "module": "Mathlib.Topology.FiberBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiberBundleCore.continuous_totalSpaceMk", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiberBundleCore.continuous_proj", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiberBundleCore.isOpenMap_proj", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiberPrebundle.totalSpaceTopology", "kind": "definition", "module": "Mathlib.Topology.FiberBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiberPrebundle.continuous_symm_of_mem_pretrivializationAtlas", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Basic", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "FiberPrebundle.isOpen_source", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Basic", "is_tactic_proof": true, "tactics": ["refine", "refine", "ext", "simp"], "tactic_count": 4}
{"name": "FiberPrebundle.isOpen_target_of_mem_pretrivializationAtlas_inter", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Basic", "is_tactic_proof": true, "tactics": ["letI", "obtain", "continuousOn_iff'.mp", "rw", "exact"], "tactic_count": 5}
{"name": "FiberPrebundle.trivializationOfMemPretrivializationAtlas", "kind": "definition", "module": "Mathlib.Topology.FiberBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiberPrebundle.mem_pretrivializationAt_source", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Basic", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "FiberPrebundle.totalSpaceMk_preimage_source", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiberPrebundle.continuous_totalSpaceMk", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Basic", "is_tactic_proof": true, "tactics": ["letI", "let", "rw", "exact"], "tactic_count": 4}
{"name": "FiberPrebundle.inducing_totalSpaceMk_of_inducing_comp", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Basic", "is_tactic_proof": true, "tactics": ["letI", "rw", "apply", "refine", "h.of_comp", "exact"], "tactic_count": 6}
{"name": "FiberPrebundle.toFiberBundle", "kind": "definition", "module": "Mathlib.Topology.FiberBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiberPrebundle.continuous_proj", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Basic", "is_tactic_proof": true, "tactics": ["letI", "letI", "exact"], "tactic_count": 3}
{"name": "FiberPrebundle.instMemTrivializationAtlasTrivializationOfMemPretrivializationAtlas", "kind": "instance", "module": "Mathlib.Topology.FiberBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiberPrebundle.continuousOn_of_comp_right", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Basic", "is_tactic_proof": true, "tactics": ["letI", "intro", "let", "refine", "exact", "exact", "refine", "rw", "exact", "rw", "exact"], "tactic_count": 11}
{"name": "Bundle.Trivial.topologicalSpace", "kind": "instance", "module": "Mathlib.Topology.FiberBundle.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bundle.Trivial.isInducing_toProd", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bundle.Trivial.homeomorphProd", "kind": "definition", "module": "Mathlib.Topology.FiberBundle.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bundle.Trivial.trivialization", "kind": "definition", "module": "Mathlib.Topology.FiberBundle.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bundle.Trivial.trivialization_symm_apply", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Constructions", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Bundle.Trivial.toOpenPartialHomeomorph_trivialization_symm_apply", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bundle.Trivial.fiberBundle", "kind": "instance", "module": "Mathlib.Topology.FiberBundle.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bundle.Trivial.eq_trivialization", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiberBundle.Prod.topologicalSpace", "kind": "instance", "module": "Mathlib.Topology.FiberBundle.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiberBundle.Prod.isInducing_diag", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.Prod.toFun'", "kind": "definition", "module": "Mathlib.Topology.FiberBundle.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.Prod.continuous_to_fun", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Constructions", "is_tactic_proof": false, "tactics": ["let", "let", "let", "have", "have", "e₁.toOpenPartialHomeomorph.continuousOn.prodMap", "have", "refine", "rw", "exact", "rintro", "simp", "rw", "rw", "exact"], "tactic_count": 15}
{"name": "Trivialization.Prod.invFun'", "kind": "definition", "module": "Mathlib.Topology.FiberBundle.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.Prod.left_inv", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Constructions", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "simp"], "tactic_count": 3}
{"name": "Trivialization.Prod.right_inv", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Constructions", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "simp"], "tactic_count": 3}
{"name": "Trivialization.Prod.continuous_inv_fun", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Constructions", "is_tactic_proof": true, "tactics": ["rw", "have", "refine", "exact"], "tactic_count": 4}
{"name": "Trivialization.prod", "kind": "definition", "module": "Mathlib.Topology.FiberBundle.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.prod_symm_apply", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiberBundle.prod", "kind": "instance", "module": "Mathlib.Topology.FiberBundle.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instMemTrivializationAtlasProdProd", "kind": "instance", "module": "Mathlib.Topology.FiberBundle.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instTopologicalSpacePullback", "kind": "instance", "module": "Mathlib.Topology.FiberBundle.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "definition._@.Mathlib.Topology.FiberBundle.Constructions.2778828462._hygCtx._hyg.2", "kind": "definition", "module": "Mathlib.Topology.FiberBundle.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "wrapped._@.Mathlib.Topology.FiberBundle.Constructions.2778828462._hygCtx._hyg.2", "kind": "opaque", "module": "Mathlib.Topology.FiberBundle.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pullbackTopology", "kind": "definition", "module": "Mathlib.Topology.FiberBundle.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pullbackTopology_def", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Constructions", "is_tactic_proof": true, "tactics": ["intros", "delta", "rw", "rfl"], "tactic_count": 4}
{"name": "Pullback.TotalSpace.topologicalSpace", "kind": "instance", "module": "Mathlib.Topology.FiberBundle.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pullback.continuous_proj", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Constructions", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Pullback.continuous_lift", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Constructions", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "inducing_pullbackTotalSpaceEmbedding", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Constructions", "is_tactic_proof": true, "tactics": ["constructor", "simp_rw", "pullbackTopology_def]", "rfl"], "tactic_count": 4}
{"name": "Pullback.continuous_totalSpaceMk", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Constructions", "is_tactic_proof": false, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Trivialization.pullback", "kind": "definition", "module": "Mathlib.Topology.FiberBundle.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FiberBundle.pullback", "kind": "instance", "module": "Mathlib.Topology.FiberBundle.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsHomeomorphicTrivialFiberBundle", "kind": "definition", "module": "Mathlib.Topology.FiberBundle.IsHomeomorphicTrivialBundle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsHomeomorphicTrivialFiberBundle.proj_eq", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.IsHomeomorphicTrivialBundle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsHomeomorphicTrivialFiberBundle.surjective_proj", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.IsHomeomorphicTrivialBundle", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "IsHomeomorphicTrivialFiberBundle.continuous_proj", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.IsHomeomorphicTrivialBundle", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "IsHomeomorphicTrivialFiberBundle.isOpenMap_proj", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.IsHomeomorphicTrivialBundle", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "IsHomeomorphicTrivialFiberBundle.isQuotientMap_proj", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.IsHomeomorphicTrivialBundle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isHomeomorphicTrivialFiberBundle_fst", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.IsHomeomorphicTrivialBundle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isHomeomorphicTrivialFiberBundle_snd", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.IsHomeomorphicTrivialBundle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pretrivialization.toFun'", "kind": "definition", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pretrivialization.instCoeFunForallProd", "kind": "instance", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pretrivialization.ext'", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": true, "tactics": ["cases", "congr"], "tactic_count": 2}
{"name": "Pretrivialization.ext", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": true, "tactics": ["ext1", "apply", "apply", "rw"], "tactic_count": 4}
{"name": "Pretrivialization.toPartialEquiv_injective", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": true, "tactics": ["refine", "simpa"], "tactic_count": 2}
{"name": "Pretrivialization.coe_coe", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pretrivialization.coe_fst", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pretrivialization.mem_source", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Pretrivialization.coe_fst'", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pretrivialization.eqOn", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pretrivialization.mk_proj_snd", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pretrivialization.mk_proj_snd'", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pretrivialization.setSymm", "kind": "definition", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pretrivialization.mem_target", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Pretrivialization.proj_symm_apply", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": true, "tactics": ["have", "rwa"], "tactic_count": 2}
{"name": "Pretrivialization.proj_symm_apply'", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pretrivialization.proj_surjOn_baseSet", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pretrivialization.apply_symm_apply", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pretrivialization.apply_symm_apply'", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pretrivialization.symm_apply_apply", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pretrivialization.symm_apply_mk_proj", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Pretrivialization.preimage_symm_proj_baseSet", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": true, "tactics": ["refine", "simp", "exact"], "tactic_count": 3}
{"name": "Pretrivialization.preimage_symm_proj_inter", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": true, "tactics": ["ext", "suffices", "simpa", "intro", "rw"], "tactic_count": 5}
{"name": "Pretrivialization.target_inter_preimage_symm_source_eq", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Pretrivialization.trans_source", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Pretrivialization.symm_trans_symm", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Pretrivialization.symm_trans_source_eq", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": true, "tactics": ["rw", "e.preimage_symm_proj_inter,"], "tactic_count": 2}
{"name": "Pretrivialization.symm_trans_target_eq", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Pretrivialization.coe_mem_source", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pretrivialization.coe_coe_fst", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Pretrivialization.mk_mem_target", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pretrivialization.symm_coe_proj", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pretrivialization.symm", "kind": "definition", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pretrivialization.symm_apply", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pretrivialization.symm_apply_of_notMem", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pretrivialization.coe_symm_of_notMem", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pretrivialization.mk_symm", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Pretrivialization.symm_proj_apply", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Pretrivialization.symm_apply_apply_mk", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pretrivialization.apply_mk_symm", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Pretrivialization.restrictPreimage'", "kind": "definition", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pretrivialization.restrictPreimage", "kind": "definition", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pretrivialization.domExtend", "kind": "definition", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pretrivialization.codExtend'", "kind": "definition", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pretrivialization.codExtend", "kind": "definition", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.ext'", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Trivialization.toFun'", "kind": "definition", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.toPretrivialization", "kind": "definition", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.instCoeFunForallProd", "kind": "instance", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.instCoePretrivialization", "kind": "instance", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.Simps.apply", "kind": "definition", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.Simps.symm_apply", "kind": "definition", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.toPretrivialization_injective", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.coe_coe", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.coe_fst", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.eqOn", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.mem_source", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Trivialization.coe_fst'", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.mk_proj_snd", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.mk_proj_snd'", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.source_inter_preimage_target_inter", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.coe_mk", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.mem_target", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.map_target", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.proj_symm_apply", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.proj_symm_apply'", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.proj_surjOn_baseSet", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.apply_symm_apply", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.apply_symm_apply'", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.symm_apply_mk_proj", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.symm_trans_source_eq", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.symm_trans_target_eq", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.coe_fst_eventuallyEq_proj", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.coe_fst_eventuallyEq_proj'", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.map_proj_nhds", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": true, "tactics": ["rw", "map_fst_nhds]"], "tactic_count": 2}
{"name": "Trivialization.preimage_subset_source", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.image_preimage_eq_prod_univ", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.tendsto_nhds_iff", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": ["rw", "coe_fst", "by_cases", "simp", "refine", "exact", "simp", "rw", "exact"], "tactic_count": 9}
{"name": "Trivialization.nhds_eq_inf_comap", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "Trivialization.preimageHomeomorph", "kind": "definition", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.preimageHomeomorph_apply", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.preimageHomeomorph_symm_apply.aux", "kind": "definition", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.preimageHomeomorph_symm_apply", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.sourceHomeomorphBaseSetProd", "kind": "definition", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.sourceHomeomorphBaseSetProd_apply", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.sourceHomeomorphBaseSetProd_symm_apply.aux", "kind": "definition", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.sourceHomeomorphBaseSetProd_symm_apply", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.preimageSingletonHomeomorph", "kind": "definition", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.preimageSingletonHomeomorph_apply", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.preimageSingletonHomeomorph_symm_apply", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.continuousAt_proj", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.continuousOn_proj", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.compHomeomorph", "kind": "definition", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.homeomorphComp", "kind": "definition", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.continuousAt_of_comp_right", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": ["have", "rw", "exact", "rwa"], "tactic_count": 4}
{"name": "Trivialization.continuousAt_of_comp_left", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": true, "tactics": ["rw", "exact", "rw", "exact"], "tactic_count": 4}
{"name": "Trivialization.continuousOn", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.coe_mem_source", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.coe_coe_fst", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.mk_mem_target", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.symm_apply_apply", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.symm_coe_proj", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.symm", "kind": "definition", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.symm_apply", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.symm_apply_of_notMem", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.mk_symm", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.symm_proj_apply", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.symm_apply_apply_mk", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.apply_mk_symm", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.continuousOn_symm", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": ["have", "rintro", "rw", "refine", "rw", "exact"], "tactic_count": 6}
{"name": "Trivialization.transFiberHomeomorph", "kind": "definition", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.transFiberHomeomorph_apply", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.coordChange", "kind": "definition", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.mk_coordChange", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": true, "tactics": ["refine", "rw", "rwa", "rwa"], "tactic_count": 4}
{"name": "Trivialization.coordChange_apply_snd", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Trivialization.coordChange_same_apply", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Trivialization.coordChange_same", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.coordChange_coordChange", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": true, "tactics": ["rw", "rwa"], "tactic_count": 2}
{"name": "Trivialization.continuous_coordChange", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": ["refine", "continuous_snd.comp", "fun_prop", "exact", "intro", "rwa"], "tactic_count": 6}
{"name": "Trivialization.coordChangeHomeomorph", "kind": "definition", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.coordChangeHomeomorph_coe", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.isImage_preimage_prod", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.restrOpen", "kind": "definition", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.restrictPreimage'", "kind": "definition", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.restrictPreimage", "kind": "definition", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.domExtend", "kind": "definition", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.codExtend'", "kind": "definition", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.codExtend", "kind": "definition", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.frontier_preimage", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Trivialization.piecewise", "kind": "definition", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.piecewiseLeOfEq", "kind": "definition", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.piecewiseLe", "kind": "definition", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.disjointUnion", "kind": "definition", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.lift", "kind": "definition", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.lift_self", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.proj_lift", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.liftCM", "kind": "definition", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.clift", "kind": "definition", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": true, "tactics": ["let", "refine", "simpa"], "tactic_count": 3}
{"name": "Trivialization.clift_self", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": true, "tactics": ["have", "simp"], "tactic_count": 2}
{"name": "Trivialization.proj_clift", "kind": "theorem", "module": "Mathlib.Topology.FiberBundle.Trivialization", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "TopologicalSpace.Fiber.sigmaIsoHom", "kind": "definition", "module": "Mathlib.Topology.FiberPartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Fiber.sigmaIsoHom_inj", "kind": "theorem", "module": "Mathlib.Topology.FiberPartition", "is_tactic_proof": true, "tactics": ["rintro", "refine", "simp", "rw", "simp"], "tactic_count": 5}
{"name": "TopologicalSpace.Fiber.sigmaIsoHom_surj", "kind": "theorem", "module": "Mathlib.Topology.FiberPartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Fiber.sigmaIncl", "kind": "definition", "module": "Mathlib.Topology.FiberPartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Fiber.sigmaInclIncl", "kind": "definition", "module": "Mathlib.Topology.FiberPartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Fiber.instCompactSpaceElemValSetMemRangeCoeLocallyConstantPreimageSingleton", "kind": "instance", "module": "Mathlib.Topology.FiberPartition", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact"], "tactic_count": 3}
{"name": "TopologicalSpace.Fiber.instFiniteFiberCoeLocallyConstant", "kind": "instance", "module": "Mathlib.Topology.FiberPartition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.instTopologicalSpace", "kind": "instance", "module": "Mathlib.Topology.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.isOpen_Iic_principal", "kind": "theorem", "module": "Mathlib.Topology.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.isOpen_setOf_mem", "kind": "theorem", "module": "Mathlib.Topology.Filter", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Filter.isTopologicalBasis_Iic_principal", "kind": "theorem", "module": "Mathlib.Topology.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.isOpen_iff", "kind": "theorem", "module": "Mathlib.Topology.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.nhds_eq", "kind": "theorem", "module": "Mathlib.Topology.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.nhds_eq'", "kind": "theorem", "module": "Mathlib.Topology.Filter", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Filter.tendsto_nhds", "kind": "theorem", "module": "Mathlib.Topology.Filter", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.HasBasis.nhds", "kind": "theorem", "module": "Mathlib.Topology.Filter", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Filter.tendsto_pure_self", "kind": "theorem", "module": "Mathlib.Topology.Filter", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Filter.instIsCountablyGeneratedNhds", "kind": "instance", "module": "Mathlib.Topology.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.nhds'", "kind": "theorem", "module": "Mathlib.Topology.Filter", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Filter.mem_nhds_iff", "kind": "theorem", "module": "Mathlib.Topology.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.mem_nhds_iff'", "kind": "theorem", "module": "Mathlib.Topology.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.nhds_bot", "kind": "theorem", "module": "Mathlib.Topology.Filter", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.nhds_top", "kind": "theorem", "module": "Mathlib.Topology.Filter", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.nhds_principal", "kind": "theorem", "module": "Mathlib.Topology.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.nhds_pure", "kind": "theorem", "module": "Mathlib.Topology.Filter", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.nhds_iInf", "kind": "theorem", "module": "Mathlib.Topology.Filter", "is_tactic_proof": true, "tactics": ["simp", "apply"], "tactic_count": 2}
{"name": "Filter.nhds_inf", "kind": "theorem", "module": "Mathlib.Topology.Filter", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Filter.monotone_nhds", "kind": "theorem", "module": "Mathlib.Topology.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.sInter_nhds", "kind": "theorem", "module": "Mathlib.Topology.Filter", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Filter.nhds_mono", "kind": "theorem", "module": "Mathlib.Topology.Filter", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "Filter.mem_interior", "kind": "theorem", "module": "Mathlib.Topology.Filter", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.mem_closure", "kind": "theorem", "module": "Mathlib.Topology.Filter", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.closure_singleton", "kind": "theorem", "module": "Mathlib.Topology.Filter", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Filter.specializes_iff_le", "kind": "theorem", "module": "Mathlib.Topology.Filter", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.instT0Space", "kind": "instance", "module": "Mathlib.Topology.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.nhds_atTop", "kind": "theorem", "module": "Mathlib.Topology.Filter", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.tendsto_nhds_atTop_iff", "kind": "theorem", "module": "Mathlib.Topology.Filter", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.nhds_atBot", "kind": "theorem", "module": "Mathlib.Topology.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_nhds_atBot_iff", "kind": "theorem", "module": "Mathlib.Topology.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.nhds_nhds", "kind": "theorem", "module": "Mathlib.Topology.Filter", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.isInducing_nhds", "kind": "theorem", "module": "Mathlib.Topology.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.continuous_nhds", "kind": "theorem", "module": "Mathlib.Topology.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.nhds", "kind": "theorem", "module": "Mathlib.Topology.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.nhds", "kind": "theorem", "module": "Mathlib.Topology.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.nhds", "kind": "theorem", "module": "Mathlib.Topology.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.nhds", "kind": "theorem", "module": "Mathlib.Topology.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.nhds", "kind": "theorem", "module": "Mathlib.Topology.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGδ", "kind": "definition", "module": "Mathlib.Topology.GDelta.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.isGδ", "kind": "theorem", "module": "Mathlib.Topology.GDelta.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGδ.empty", "kind": "theorem", "module": "Mathlib.Topology.GDelta.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGδ.univ", "kind": "theorem", "module": "Mathlib.Topology.GDelta.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGδ.biInter_of_isOpen", "kind": "theorem", "module": "Mathlib.Topology.GDelta.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGδ.iInter_of_isOpen", "kind": "theorem", "module": "Mathlib.Topology.GDelta.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isGδ_iff_eq_iInter_nat", "kind": "theorem", "module": "Mathlib.Topology.GDelta.Basic", "is_tactic_proof": true, "tactics": ["refine", "rintro", "rcases", "exact", "obtain", "exact", "rintro", "exact"], "tactic_count": 8}
{"name": "IsGδ.iInter", "kind": "theorem", "module": "Mathlib.Topology.GDelta.Basic", "is_tactic_proof": true, "tactics": ["choose", "obtain", "refine", "simpa"], "tactic_count": 4}
{"name": "IsGδ.biInter", "kind": "theorem", "module": "Mathlib.Topology.GDelta.Basic", "is_tactic_proof": true, "tactics": ["rw", "haveI", "exact"], "tactic_count": 3}
{"name": "IsGδ.sInter", "kind": "theorem", "module": "Mathlib.Topology.GDelta.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsGδ.inter", "kind": "theorem", "module": "Mathlib.Topology.GDelta.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsGδ.union", "kind": "theorem", "module": "Mathlib.Topology.GDelta.Basic", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "rw", "refine", "rintro", "exact"], "tactic_count": 6}
{"name": "IsGδ.sUnion", "kind": "theorem", "module": "Mathlib.Topology.GDelta.Basic", "is_tactic_proof": true, "tactics": ["induction", "empty", "insert", "simp", "exact"], "tactic_count": 5}
{"name": "IsGδ.biUnion", "kind": "theorem", "module": "Mathlib.Topology.GDelta.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsGδ.iUnion", "kind": "theorem", "module": "Mathlib.Topology.GDelta.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isGδ_induced", "kind": "theorem", "module": "Mathlib.Topology.GDelta.Basic", "is_tactic_proof": true, "tactics": ["obtain", "simp_all", "exact"], "tactic_count": 3}
{"name": "residual", "kind": "definition", "module": "Mathlib.Topology.GDelta.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "countableInterFilter_residual", "kind": "instance", "module": "Mathlib.Topology.GDelta.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "residual_of_dense_open", "kind": "theorem", "module": "Mathlib.Topology.GDelta.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "residual_of_dense_Gδ", "kind": "theorem", "module": "Mathlib.Topology.GDelta.Basic", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "mem_residual_iff", "kind": "theorem", "module": "Mathlib.Topology.GDelta.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsNowhereDense", "kind": "definition", "module": "Mathlib.Topology.GDelta.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isNowhereDense_empty", "kind": "theorem", "module": "Mathlib.Topology.GDelta.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsNowhereDense.mono", "kind": "theorem", "module": "Mathlib.Topology.GDelta.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.isNowhereDense_iff", "kind": "theorem", "module": "Mathlib.Topology.GDelta.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsNowhereDense.closure", "kind": "theorem", "module": "Mathlib.Topology.GDelta.Basic", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "IsNowhereDense.subset_of_closed_isNowhereDense", "kind": "theorem", "module": "Mathlib.Topology.GDelta.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosed_isNowhereDense_iff_compl", "kind": "theorem", "module": "Mathlib.Topology.GDelta.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "isNowhereDense_iff_disjoint", "kind": "theorem", "module": "Mathlib.Topology.GDelta.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isNowhereDense_iff_forall_notMem_nhds", "kind": "theorem", "module": "Mathlib.Topology.GDelta.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Topology.IsInducing.isNowhereDense_image", "kind": "theorem", "module": "Mathlib.Topology.GDelta.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "exact"], "tactic_count": 3}
{"name": "IsNowhereDense.image_val", "kind": "theorem", "module": "Mathlib.Topology.GDelta.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMeagre", "kind": "definition", "module": "Mathlib.Topology.GDelta.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMeagre.empty", "kind": "theorem", "module": "Mathlib.Topology.GDelta.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsMeagre.mono", "kind": "theorem", "module": "Mathlib.Topology.GDelta.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMeagre.inter", "kind": "theorem", "module": "Mathlib.Topology.GDelta.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMeagre.union", "kind": "theorem", "module": "Mathlib.Topology.GDelta.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "isMeagre_iUnion", "kind": "theorem", "module": "Mathlib.Topology.GDelta.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "isMeagre_biUnion", "kind": "theorem", "module": "Mathlib.Topology.GDelta.Basic", "is_tactic_proof": true, "tactics": ["suffices", "have", "apply", "intro", "exact"], "tactic_count": 5}
{"name": "isMeagre_iff_countable_union_isNowhereDense", "kind": "theorem", "module": "Mathlib.Topology.GDelta.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "compl_iUnion₂,", "refine", "rw", "intro", "use", "rw", "exact", "hsub.trans"], "tactic_count": 10}
{"name": "nonempty_of_not_isMeagre", "kind": "theorem", "module": "Mathlib.Topology.GDelta.Basic", "is_tactic_proof": true, "tactics": ["contrapose", "simpa"], "tactic_count": 2}
{"name": "IsNowhereDense.isMeagre", "kind": "theorem", "module": "Mathlib.Topology.GDelta.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "exists_of_not_isMeagre_biUnion", "kind": "theorem", "module": "Mathlib.Topology.GDelta.Basic", "is_tactic_proof": true, "tactics": ["contrapose", "exact"], "tactic_count": 2}
{"name": "Topology.IsInducing.isMeagre_image", "kind": "theorem", "module": "Mathlib.Topology.GDelta.Basic", "is_tactic_proof": true, "tactics": ["rw", "obtain", "refine", "intro", "rw", "apply", "rw", "grw"], "tactic_count": 8}
{"name": "IsMeagre.image_val", "kind": "theorem", "module": "Mathlib.Topology.GDelta.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instNormalSpaceOfPseudoMetrizableSpace", "kind": "instance", "module": "Mathlib.Topology.GDelta.MetrizableSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instPerfectlyNormalSpaceOfPseudoMetrizableSpace", "kind": "instance", "module": "Mathlib.Topology.GDelta.MetrizableSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instT4SpaceOfMetrizableSpace", "kind": "instance", "module": "Mathlib.Topology.GDelta.MetrizableSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instT6SpaceOfMetrizableSpace", "kind": "instance", "module": "Mathlib.Topology.GDelta.MetrizableSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGδ.setOf_continuousAt", "kind": "theorem", "module": "Mathlib.Topology.GDelta.MetrizableSpace", "is_tactic_proof": true, "tactics": ["let", "have", "obtain", "simp", "simp", "refine", "rintro", "filter_upwards"], "tactic_count": 8}
{"name": "Filter.Germ.value", "kind": "definition", "module": "Mathlib.Topology.Germ", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.value_smul", "kind": "theorem", "module": "Mathlib.Topology.Germ", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.valueMulHom", "kind": "definition", "module": "Mathlib.Topology.Germ", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.valueₗ", "kind": "definition", "module": "Mathlib.Topology.Germ", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.valueRingHom", "kind": "definition", "module": "Mathlib.Topology.Germ", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.valueOrderRingHom", "kind": "definition", "module": "Mathlib.Topology.Germ", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RestrictGermPredicate", "kind": "definition", "module": "Mathlib.Topology.Germ", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Eventually.germ_congr_set", "kind": "theorem", "module": "Mathlib.Topology.Germ", "is_tactic_proof": true, "tactics": ["rw", "intro", "apply", "intro", "convert", "exact"], "tactic_count": 6}
{"name": "restrictGermPredicate_congr", "kind": "theorem", "module": "Mathlib.Topology.Germ", "is_tactic_proof": true, "tactics": ["intro", "apply", "rintro", "rwa"], "tactic_count": 4}
{"name": "forall_restrictGermPredicate_iff", "kind": "theorem", "module": "Mathlib.Topology.Germ", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "forall_restrictGermPredicate_of_forall", "kind": "theorem", "module": "Mathlib.Topology.Germ", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.sliceLeft", "kind": "definition", "module": "Mathlib.Topology.Germ", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.sliceLeft_coe", "kind": "theorem", "module": "Mathlib.Topology.Germ", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.sliceRight", "kind": "definition", "module": "Mathlib.Topology.Germ", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.sliceRight_coe", "kind": "theorem", "module": "Mathlib.Topology.Germ", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Germ.isConstant_comp_subtype", "kind": "theorem", "module": "Mathlib.Topology.Germ", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocallyConstant.of_germ_isConstant", "kind": "theorem", "module": "Mathlib.Topology.Germ", "is_tactic_proof": true, "tactics": ["intro", "rw", "intro", "obtain", "apply", "intro", "have", "rw", "exact"], "tactic_count": 9}
{"name": "eq_of_germ_isConstant", "kind": "theorem", "module": "Mathlib.Topology.Germ", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_of_germ_isConstant_on", "kind": "theorem", "module": "Mathlib.Topology.Germ", "is_tactic_proof": true, "tactics": ["let", "change", "have", "exact"], "tactic_count": 4}
{"name": "Germ.coe_prod", "kind": "theorem", "module": "Mathlib.Topology.Germ", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.Gluing.0.TopCat.GlueData.term𝖣", "kind": "definition", "module": "Mathlib.Topology.Gluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.Gluing.0.TopCat.GlueData._aux_Mathlib_Topology_Gluing___macroRules__private_Mathlib_Topology_Gluing_0_TopCat_GlueData_term𝖣_1", "kind": "definition", "module": "Mathlib.Topology.Gluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.GlueData.π_surjective", "kind": "theorem", "module": "Mathlib.Topology.Gluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.GlueData.isOpen_iff", "kind": "theorem", "module": "Mathlib.Topology.Gluing", "is_tactic_proof": true, "tactics": ["delta", "simp_rw", "rw", "rw", "tauto"], "tactic_count": 5}
{"name": "TopCat.GlueData.ι_jointly_surjective", "kind": "theorem", "module": "Mathlib.Topology.Gluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.GlueData.Rel", "kind": "definition", "module": "Mathlib.Topology.Gluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.GlueData.rel_equiv", "kind": "theorem", "module": "Mathlib.Topology.Gluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.GlueData.eqvGen_of_π_eq", "kind": "theorem", "module": "Mathlib.Topology.Gluing", "is_tactic_proof": true, "tactics": ["delta", "replace", "coequalizer.π", "coequalizer.π", "let", "have", "dsimp", "rw", "simp_all", "have", "this", "simp", "exact"], "tactic_count": 13}
{"name": "TopCat.GlueData.ι_eq_iff_rel", "kind": "theorem", "module": "Mathlib.Topology.Gluing", "is_tactic_proof": true, "tactics": ["constructor", "delta", "simp_rw", "intro", "rw", "rw", "change", "rw", "refine", "rintro", "obtain", "unfold", "rw", "erw", "erw", "exact", "rintro", "dsimp", "rw", "rw"], "tactic_count": 20}
{"name": "TopCat.GlueData.ι_injective", "kind": "theorem", "module": "Mathlib.Topology.Gluing", "is_tactic_proof": true, "tactics": ["intro", "rcases", "dsimp", "rw", "simp"], "tactic_count": 5}
{"name": "TopCat.GlueData.ι_mono", "kind": "instance", "module": "Mathlib.Topology.Gluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.GlueData.image_inter", "kind": "theorem", "module": "Mathlib.Topology.Gluing", "is_tactic_proof": true, "tactics": ["ext", "constructor", "rintro", "obtain", "substs", "exact", "rintro", "refine", "rw", "exact"], "tactic_count": 10}
{"name": "TopCat.GlueData.preimage_range", "kind": "theorem", "module": "Mathlib.Topology.Gluing", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "TopCat.GlueData.preimage_image_eq_image", "kind": "theorem", "module": "Mathlib.Topology.Gluing", "is_tactic_proof": false, "tactics": ["have", "ext", "conv_rhs", "simp", "rw", "symm", "apply", "rw", "exact"], "tactic_count": 9}
{"name": "TopCat.GlueData.preimage_image_eq_image'", "kind": "theorem", "module": "Mathlib.Topology.Gluing", "is_tactic_proof": true, "tactics": ["convert", "rw", "congr", "rw", "change", "rw", "rw", "apply"], "tactic_count": 8}
{"name": "TopCat.GlueData.open_image_open", "kind": "theorem", "module": "Mathlib.Topology.Gluing", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "apply", "apply", "exact"], "tactic_count": 6}
{"name": "TopCat.GlueData.ι_isOpenEmbedding", "kind": "theorem", "module": "Mathlib.Topology.Gluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.GlueData.MkCore.t_inv", "kind": "theorem", "module": "Mathlib.Topology.Gluing", "is_tactic_proof": true, "tactics": ["have", "rw", "convert", "rw", "trivial"], "tactic_count": 5}
{"name": "TopCat.GlueData.instIsIsoT", "kind": "instance", "module": "Mathlib.Topology.Gluing", "is_tactic_proof": true, "tactics": ["use"], "tactic_count": 1}
{"name": "TopCat.GlueData.MkCore.t'", "kind": "definition", "module": "Mathlib.Topology.Gluing", "is_tactic_proof": true, "tactics": ["refine", "intro", "refine", "rcases", "exact", "fun_prop"], "tactic_count": 6}
{"name": "TopCat.GlueData.mk'", "kind": "definition", "module": "Mathlib.Topology.Gluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.GlueData.ofOpenSubsets", "kind": "definition", "module": "Mathlib.Topology.Gluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.GlueData.fromOpenSubsetsGlue", "kind": "definition", "module": "Mathlib.Topology.Gluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.GlueData.ι_fromOpenSubsetsGlue", "kind": "theorem", "module": "Mathlib.Topology.Gluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.GlueData.fromOpenSubsetsGlue_injective", "kind": "theorem", "module": "Mathlib.Topology.Gluing", "is_tactic_proof": true, "tactics": ["intro", "obtain", "obtain", "rw", "subst", "rw", "exact"], "tactic_count": 7}
{"name": "TopCat.GlueData.fromOpenSubsetsGlue_isOpenMap", "kind": "theorem", "module": "Mathlib.Topology.Gluing", "is_tactic_proof": true, "tactics": ["intro", "rw", "rw", "rintro", "obtain", "use", "use", "constructor", "rw", "apply", "convert", "rw", "congr", "exact", "refine", "rw", "exact"], "tactic_count": 17}
{"name": "TopCat.GlueData.fromOpenSubsetsGlue_isOpenEmbedding", "kind": "theorem", "module": "Mathlib.Topology.Gluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.GlueData.range_fromOpenSubsetsGlue", "kind": "theorem", "module": "Mathlib.Topology.Gluing", "is_tactic_proof": true, "tactics": ["ext", "constructor", "rintro", "obtain", "rw", "exact", "rintro", "rename_i", "exact"], "tactic_count": 9}
{"name": "TopCat.GlueData.openCoverGlueHomeo", "kind": "definition", "module": "Mathlib.Topology.Gluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.eval", "kind": "theorem", "module": "Mathlib.Topology.Hom.ContinuousEval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousEval.toContinuousMapClass", "kind": "instance", "module": "Mathlib.Topology.Hom.ContinuousEval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousEval.toContinuousEvalConst", "kind": "instance", "module": "Mathlib.Topology.Hom.ContinuousEval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.eval", "kind": "theorem", "module": "Mathlib.Topology.Hom.ContinuousEval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.eval", "kind": "theorem", "module": "Mathlib.Topology.Hom.ContinuousEval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.eval", "kind": "theorem", "module": "Mathlib.Topology.Hom.ContinuousEval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.eval", "kind": "theorem", "module": "Mathlib.Topology.Hom.ContinuousEval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.eval_const", "kind": "theorem", "module": "Mathlib.Topology.Hom.ContinuousEvalConst", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_coeFun", "kind": "theorem", "module": "Mathlib.Topology.Hom.ContinuousEvalConst", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.coeFun", "kind": "theorem", "module": "Mathlib.Topology.Hom.ContinuousEvalConst", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.eval_const", "kind": "theorem", "module": "Mathlib.Topology.Hom.ContinuousEvalConst", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.coeFun", "kind": "theorem", "module": "Mathlib.Topology.Hom.ContinuousEvalConst", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.eval_const", "kind": "theorem", "module": "Mathlib.Topology.Hom.ContinuousEvalConst", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.coeFun", "kind": "theorem", "module": "Mathlib.Topology.Hom.ContinuousEvalConst", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.eval_const", "kind": "theorem", "module": "Mathlib.Topology.Hom.ContinuousEvalConst", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.coeFun", "kind": "theorem", "module": "Mathlib.Topology.Hom.ContinuousEvalConst", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.eval_const", "kind": "theorem", "module": "Mathlib.Topology.Hom.ContinuousEvalConst", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.coeFun", "kind": "theorem", "module": "Mathlib.Topology.Hom.ContinuousEvalConst", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "term_→CO_", "kind": "definition", "module": "Mathlib.Topology.Hom.Open", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Topology_Hom_Open___macroRules_term_→CO__1", "kind": "definition", "module": "Mathlib.Topology.Hom.Open", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Topology_Hom_Open___unexpand_ContinuousOpenMap_1", "kind": "definition", "module": "Mathlib.Topology.Hom.Open", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCoeTCContinuousOpenMapOfContinuousOpenMapClass", "kind": "instance", "module": "Mathlib.Topology.Hom.Open", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOpenMap.instFunLike", "kind": "instance", "module": "Mathlib.Topology.Hom.Open", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOpenMap.instContinuousOpenMapClass", "kind": "instance", "module": "Mathlib.Topology.Hom.Open", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOpenMap.toFun_eq_coe", "kind": "theorem", "module": "Mathlib.Topology.Hom.Open", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOpenMap.coe_toContinuousMap", "kind": "theorem", "module": "Mathlib.Topology.Hom.Open", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOpenMap.ext", "kind": "theorem", "module": "Mathlib.Topology.Hom.Open", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOpenMap.copy", "kind": "definition", "module": "Mathlib.Topology.Hom.Open", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOpenMap.coe_copy", "kind": "theorem", "module": "Mathlib.Topology.Hom.Open", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOpenMap.copy_eq", "kind": "theorem", "module": "Mathlib.Topology.Hom.Open", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOpenMap.id", "kind": "definition", "module": "Mathlib.Topology.Hom.Open", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOpenMap.instInhabited", "kind": "instance", "module": "Mathlib.Topology.Hom.Open", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOpenMap.coe_id", "kind": "theorem", "module": "Mathlib.Topology.Hom.Open", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOpenMap.id_apply", "kind": "theorem", "module": "Mathlib.Topology.Hom.Open", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOpenMap.comp", "kind": "definition", "module": "Mathlib.Topology.Hom.Open", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOpenMap.coe_comp", "kind": "theorem", "module": "Mathlib.Topology.Hom.Open", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOpenMap.comp_apply", "kind": "theorem", "module": "Mathlib.Topology.Hom.Open", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOpenMap.comp_assoc", "kind": "theorem", "module": "Mathlib.Topology.Hom.Open", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOpenMap.comp_id", "kind": "theorem", "module": "Mathlib.Topology.Hom.Open", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOpenMap.id_comp", "kind": "theorem", "module": "Mathlib.Topology.Hom.Open", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOpenMap.cancel_right", "kind": "theorem", "module": "Mathlib.Topology.Hom.Open", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOpenMap.cancel_left", "kind": "theorem", "module": "Mathlib.Topology.Hom.Open", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "term_≃ₜ_", "kind": "definition", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Topology_Homeomorph_Defs___macroRules_term_≃ₜ__1", "kind": "definition", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Topology_Homeomorph_Defs___unexpand_Homeomorph_1", "kind": "definition", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.toEquiv_injective", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.instEquivLike", "kind": "instance", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.homeomorph_mk_coe", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.empty", "kind": "definition", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.symm", "kind": "definition", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.symm_symm", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.symm_bijective", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.Simps.symm_apply", "kind": "definition", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.coe_toEquiv", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.coe_symm_toEquiv", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.ext", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.refl", "kind": "definition", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.trans", "kind": "definition", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.trans_apply", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.symm_trans_apply", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.homeomorph_mk_coe_symm", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.refl_symm", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.continuous", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.continuous_symm", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.apply_symm_apply", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.symm_apply_apply", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.self_trans_symm", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": true, "tactics": ["ext", "apply"], "tactic_count": 2}
{"name": "Homeomorph.symm_trans_self", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": true, "tactics": ["ext", "apply"], "tactic_count": 2}
{"name": "Homeomorph.bijective", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.injective", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.surjective", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.changeInv", "kind": "definition", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.symm_comp_self", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.self_comp_symm", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.range_coe", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Homeomorph.image_symm", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.preimage_symm", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.image_preimage", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.preimage_image", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.image_eq_preimage_symm", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.image_compl", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.isInducing", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.induced_eq", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.isQuotientMap", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.coinduced_eq", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.isEmbedding", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.discreteTopology", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.discreteTopology_iff", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.indiscreteTopology", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.indiscreteTopology_iff", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.nontrivialTopology", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.nontrivialTopology_iff", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.isOpen_preimage", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.isOpen_image", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Homeomorph.isOpenMap", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.isOpenQuotientMap", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.isClosed_preimage", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Homeomorph.isClosed_image", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Homeomorph.isClosedMap", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.isOpenEmbedding", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.isClosedEmbedding", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.preimage_closure", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.image_closure", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Homeomorph.preimage_interior", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.image_interior", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Homeomorph.preimage_frontier", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.image_frontier", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Homeomorph.comp_continuous_iff", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.comp_continuous_iff'", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.comp_continuousAt_iff", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.comp_continuousAt_iff'", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.comp_isOpenMap_iff", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": true, "tactics": ["refine", "intro", "rw", "exact"], "tactic_count": 4}
{"name": "Homeomorph.comp_isOpenMap_iff'", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": true, "tactics": ["refine", "intro", "rw", "exact"], "tactic_count": 4}
{"name": "Homeomorph.homeomorphOfUnique", "kind": "definition", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.map_nhds_eq", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.symm_map_nhds_eq", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Homeomorph.nhds_eq_comap", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.comap_nhds_eq", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Homeomorph.isClosed_setOf_iff", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Equiv.toHomeomorph", "kind": "definition", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.coe_toHomeomorph", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.toHomeomorph_apply", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.toHomeomorph_refl", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.symm_toHomeomorph", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.toHomeomorph_trans", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.toHomeomorphOfIsInducing", "kind": "definition", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.toHomeomorphOfIsInducing_apply", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.toHomeomorphOfIsInducing_symm_apply", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.toHomeomorphOfContinuousOpen", "kind": "definition", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.toHomeomorphOfContinuousOpen_apply", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.toHomeomorphOfContinuousOpen_symm_apply", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.toHomeomorphOfContinuousClosed", "kind": "definition", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.toHomeomorphOfContinuousClosed_apply", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.toHomeomorphOfContinuousClosed_symm_apply", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.toHomeomorphOfDiscrete", "kind": "definition", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomeomorphClass.toHomeomorph", "kind": "definition", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomeomorphClass.coe_coe", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomeomorphClass.instCoeOutHomeomorph", "kind": "instance", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomeomorphClass.toHomeomorph_injective", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomeomorphClass.instContinuousMapClass", "kind": "instance", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HomeomorphClass.instHomeomorph", "kind": "instance", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.isHomeomorph", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsHomeomorph.injective", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsHomeomorph.surjective", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsHomeomorph.id", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsHomeomorph.comp", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.secondCountableTopology", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.baireSpace", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.isCompact_image", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.isCompact_preimage", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Homeomorph.isSigmaCompact_image", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.isSigmaCompact_preimage", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Homeomorph.isPreconnected_image", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.isPreconnected_preimage", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Homeomorph.isConnected_image", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.isConnected_preimage", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Homeomorph.image_connectedComponentIn", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": true, "tactics": ["refine", "have", "rwa"], "tactic_count": 3}
{"name": "Homeomorph.comap_cocompact", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.map_cocompact", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Homeomorph.compactSpace", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.isDenseEmbedding", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.totallyDisconnectedSpace", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.map_punctured_nhds_eq", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "Homeomorph.comap_coclosedCompact", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.map_coclosedCompact", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Homeomorph.locallyConnectedSpace", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": false, "tactics": ["have", "rw", "exact", "refine", "exact"], "tactic_count": 5}
{"name": "Homeomorph.locallyCompactSpace_iff", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "Homeomorph.comp_continuousOn_iff", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.comp_continuousWithinAt_iff", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.subtype", "kind": "definition", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.subtype_toEquiv", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.sets", "kind": "abbrev", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.setCongr", "kind": "definition", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.prodUnique", "kind": "definition", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.coe_prodUnique", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.uniqueProd", "kind": "definition", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.coe_uniqueProd", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.sumPiEquivProdPi", "kind": "definition", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.piUnique", "kind": "definition", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.piCongrLeft", "kind": "definition", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.piCongrLeft_refl", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.piCongrLeft_symm_apply", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.piCongrLeft_apply_apply", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.piCongrRight", "kind": "definition", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.piCongrRight_symm", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.piCongr", "kind": "definition", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.ulift", "kind": "definition", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.sumArrowHomeomorphProdArrow", "kind": "definition", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.Homeomorph.Lemmas.0.Fin.appendEquiv_eq_homeomorph", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": true, "tactics": ["apply", "ext"], "tactic_count": 2}
{"name": "Fin.continuous_append", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": true, "tactics": ["suffices", "rw", "exact"], "tactic_count": 3}
{"name": "Fin.appendHomeomorph", "kind": "definition", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.appendHomeomorph_toEquiv", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.sigmaProdDistrib", "kind": "definition", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.funUnique", "kind": "definition", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.piFinTwo", "kind": "definition", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.finTwoArrow", "kind": "definition", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.image", "kind": "definition", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.Set.univ", "kind": "definition", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.Set.prod", "kind": "definition", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.piEquivPiSubtypeProd", "kind": "definition", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.piSplitAt", "kind": "definition", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.funSplitAt", "kind": "definition", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsEmbedding.toHomeomorph", "kind": "definition", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsEmbedding.toHomeomorphOfSurjective", "kind": "definition", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsEmbedding.homeomorphImage", "kind": "definition", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsEmbedding.homeomorphOfSubsetRange", "kind": "definition", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsEmbedding.homeomorphOfSubsetRange_apply_coe", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.continuous_symm_of_equiv_compact_to_t2", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "intro", "have", "rwa"], "tactic_count": 4}
{"name": "Continuous.homeoOfEquivCompactToT2", "kind": "definition", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsHomeomorph.homeomorph", "kind": "definition", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsHomeomorph.isClosedMap", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsHomeomorph.isInducing", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsHomeomorph.isQuotientMap", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsHomeomorph.isEmbedding", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsHomeomorph.isOpenEmbedding", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsHomeomorph.isClosedEmbedding", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsHomeomorph.isDenseEmbedding", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isHomeomorph_iff_exists_homeomorph", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isHomeomorph_iff_exists_inverse", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": true, "tactics": ["refine", "let", "exact", "exact"], "tactic_count": 4}
{"name": "isHomeomorph_iff_isEmbedding_surjective", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isHomeomorph_iff_continuous_isClosedMap_bijective", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isHomeomorph_iff_continuous_bijective", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw"], "tactic_count": 3}
{"name": "IsHomeomorph.sumMap", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsHomeomorph.prodMap", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsHomeomorph.sigmaMap", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "IsHomeomorph.pi_map", "kind": "theorem", "module": "Mathlib.Topology.Homeomorph.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.topologicalSpace", "kind": "abbrev", "module": "Mathlib.Topology.Homeomorph.TransferInstance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.homeomorph", "kind": "definition", "module": "Mathlib.Topology.Homeomorph.TransferInstance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.Homotopy.affine", "kind": "definition", "module": "Mathlib.Topology.Homotopy.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.Homotopy.evalAt_affine", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Affine", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.Homotopy.instFunLike", "kind": "instance", "module": "Mathlib.Topology.Homotopy.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.Homotopy.instHomotopyLike", "kind": "instance", "module": "Mathlib.Topology.Homotopy.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.Homotopy.ext", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.Homotopy.Simps.apply", "kind": "definition", "module": "Mathlib.Topology.Homotopy.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.Homotopy.continuous", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.Homotopy.apply_zero", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.Homotopy.apply_one", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.Homotopy.coe_toContinuousMap", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.Homotopy.curry", "kind": "definition", "module": "Mathlib.Topology.Homotopy.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.Homotopy.curry_apply", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.Homotopy.curry_zero", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "ContinuousMap.Homotopy.curry_one", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "ContinuousMap.Homotopy.extend", "kind": "definition", "module": "Mathlib.Topology.Homotopy.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.Homotopy.extend_apply_of_le_zero", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ContinuousMap.Homotopy.extend_apply_of_one_le", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ContinuousMap.Homotopy.extend_apply_coe", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.Homotopy.extend_of_mem_I", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.Homotopy.extend_zero", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousMap.Homotopy.extend_one", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousMap.Homotopy.extend_apply_of_mem_I", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousMap.Homotopy.congr_fun", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.Homotopy.congr_arg", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.Homotopy.refl", "kind": "definition", "module": "Mathlib.Topology.Homotopy.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.Homotopy.instInhabitedId", "kind": "instance", "module": "Mathlib.Topology.Homotopy.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.Homotopy.symm", "kind": "definition", "module": "Mathlib.Topology.Homotopy.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.Homotopy.symm_symm", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "ContinuousMap.Homotopy.symm_bijective", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.Homotopy.trans", "kind": "definition", "module": "Mathlib.Topology.Homotopy.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.Homotopy.trans_apply", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ContinuousMap.Homotopic", "kind": "definition", "module": "Mathlib.Topology.Homotopy.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ContinuousMap.HomotopyWith.prop", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Homeomorph.coe_toHomotopyEquiv", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Homeomorph.refl_toHomotopyEquiv", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Equiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LocallyContractibleSpace", "kind": "definition", "module": "Mathlib.Topology.Homotopy.LocallyContractible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StronglyLocallyContractibleSpace.of_bases", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.LocallyContractible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "contractible_subset_basis", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.LocallyContractible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instLocPathConnectedSpace", "kind": "instance", "module": "Mathlib.Topology.Homotopy.LocallyContractible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsOpenEmbedding.stronglyLocallyContractibleSpace", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.LocallyContractible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.stronglyLocallyContractibleSpace", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.LocallyContractible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instStronglyLocallyContractibleSpaceProd", "kind": "instance", "module": "Mathlib.Topology.Homotopy.LocallyContractible", "is_tactic_proof": false, "tactics": ["refine", "intro", "rw", "exact", "intro", "haveI", "haveI", "exact"], "tactic_count": 8}
{"name": "StronglyLocallyContractibleSpace.locallyContractible", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.LocallyContractible", "is_tactic_proof": true, "tactics": ["intro", "obtain", "refine", "obtain", "refine", "convert", "ext", "simp"], "tactic_count": 8}
{"name": "Path.Homotopy", "kind": "abbrev", "module": "Mathlib.Topology.Homotopy.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopy.coeFn_injective", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopy.source", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopy.target", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopy.eval", "kind": "definition", "module": "Mathlib.Topology.Homotopy.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopy.eval_zero", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Path", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Path.Homotopy.eval_one", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Path", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Path.Homotopy.refl", "kind": "definition", "module": "Mathlib.Topology.Homotopy.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopy.symm", "kind": "definition", "module": "Mathlib.Topology.Homotopy.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopy.symm_symm", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopy.symm_bijective", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopy.trans", "kind": "definition", "module": "Mathlib.Topology.Homotopy.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopy.trans_apply", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopy.symm_trans", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopy.cast", "kind": "definition", "module": "Mathlib.Topology.Homotopy.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopy.pathCast", "kind": "definition", "module": "Mathlib.Topology.Homotopy.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopy.hcomp", "kind": "definition", "module": "Mathlib.Topology.Homotopy.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopy.hcomp_apply", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopy.hcomp_half", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopy.reparam", "kind": "definition", "module": "Mathlib.Topology.Homotopy.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopy.symm₂", "kind": "definition", "module": "Mathlib.Topology.Homotopy.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopy.map", "kind": "definition", "module": "Mathlib.Topology.Homotopy.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopic", "kind": "definition", "module": "Mathlib.Topology.Homotopy.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopic.refl", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopic.symm", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopic.symm₂", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopic.trans", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopic.equivalence", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopic.instIsEquiv", "kind": "instance", "module": "Mathlib.Topology.Homotopy.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopic.map", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopic.hcomp", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopic.pathCast", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopic.setoid", "kind": "definition", "module": "Mathlib.Topology.Homotopy.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopic.Quotient", "kind": "definition", "module": "Mathlib.Topology.Homotopy.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopic.instInhabitedQuotientUnitUnit", "kind": "instance", "module": "Mathlib.Topology.Homotopy.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopic.Quotient.mk", "kind": "definition", "module": "Mathlib.Topology.Homotopy.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopic.Quotient.mk_surjective", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopic.Quotient.mk'_eq_mk", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopic.Quotient.mk''_eq_mk", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopic.Quotient.exact", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Path", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "Path.Homotopic.Quotient.eq", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopic.Quotient.ind", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopic.Quotient.ind₂", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Path", "is_tactic_proof": true, "tactics": ["induction", "mk", "induction", "mk"], "tactic_count": 4}
{"name": "Path.Homotopic.Quotient.refl", "kind": "definition", "module": "Mathlib.Topology.Homotopy.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopic.Quotient.mk_refl", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopic.Quotient.symm", "kind": "definition", "module": "Mathlib.Topology.Homotopy.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopic.Quotient.mk_symm", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopic.Quotient.cast", "kind": "definition", "module": "Mathlib.Topology.Homotopy.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopic.Quotient.mk_cast", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopic.Quotient.cast_rfl_rfl", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Path", "is_tactic_proof": true, "tactics": ["induction", "mk"], "tactic_count": 2}
{"name": "Path.Homotopic.Quotient.cast_cast", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Path", "is_tactic_proof": true, "tactics": ["induction", "mk"], "tactic_count": 2}
{"name": "Path.Homotopic.Quotient.trans", "kind": "definition", "module": "Mathlib.Topology.Homotopy.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopic.Quotient.mk_trans", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopic.Quotient.map", "kind": "definition", "module": "Mathlib.Topology.Homotopy.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopic.Quotient.mk_map", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopic.hpath_hext", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Path", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "rw"], "tactic_count": 3}
{"name": "Path.toHomotopyConst", "kind": "definition", "module": "Mathlib.Topology.Homotopy.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.homotopic_const_iff", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Path", "is_tactic_proof": true, "tactics": ["inhabit", "refine", "simp"], "tactic_count": 3}
{"name": "ContinuousMap.Homotopy.evalAt", "kind": "definition", "module": "Mathlib.Topology.Homotopy.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.Homotopy.pathExtend_evalAt", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.HomotopyRel.pi", "kind": "definition", "module": "Mathlib.Topology.Homotopy.Product", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.Homotopy.prod", "kind": "definition", "module": "Mathlib.Topology.Homotopy.Product", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.HomotopyRel.prod", "kind": "definition", "module": "Mathlib.Topology.Homotopy.Product", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.Homotopy.Product.0.Path.Homotopic.term_⬝_", "kind": "definition", "module": "Mathlib.Topology.Homotopy.Product", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.Homotopy.Product.0.Path.Homotopic._aux_Mathlib_Topology_Homotopy_Product___macroRules__private_Mathlib_Topology_Homotopy_Product_0_Path_Homotopic_term_⬝__1", "kind": "definition", "module": "Mathlib.Topology.Homotopy.Product", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.Homotopy.Product.0.Path.Homotopic._aux_Mathlib_Topology_Homotopy_Product___unexpand_Path_Homotopic_Quotient_trans_1", "kind": "definition", "module": "Mathlib.Topology.Homotopy.Product", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopic.piHomotopy", "kind": "definition", "module": "Mathlib.Topology.Homotopy.Product", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopic.pi", "kind": "definition", "module": "Mathlib.Topology.Homotopy.Product", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopic.pi_lift", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Product", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Path.Homotopic.comp_pi_eq_pi_comp", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Product", "is_tactic_proof": true, "tactics": ["induction", "induction", "simp", "rw", "rfl"], "tactic_count": 5}
{"name": "Path.Homotopic.proj", "kind": "abbrev", "module": "Mathlib.Topology.Homotopy.Product", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopic.proj_pi", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Product", "is_tactic_proof": true, "tactics": ["induction", "simp", "rw", "congr"], "tactic_count": 4}
{"name": "Path.Homotopic.pi_proj", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Product", "is_tactic_proof": true, "tactics": ["induction", "simp_rw", "erw", "congr"], "tactic_count": 4}
{"name": "Path.Homotopic.prodHomotopy", "kind": "definition", "module": "Mathlib.Topology.Homotopy.Product", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopic.prod", "kind": "definition", "module": "Mathlib.Topology.Homotopy.Product", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopic.prod_lift", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Product", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopic.comp_prod_eq_prod_comp", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Product", "is_tactic_proof": true, "tactics": ["induction", "induction", "simp"], "tactic_count": 3}
{"name": "Path.Homotopic.projLeft", "kind": "abbrev", "module": "Mathlib.Topology.Homotopy.Product", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopic.projRight", "kind": "abbrev", "module": "Mathlib.Topology.Homotopy.Product", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.Homotopic.projLeft_prod", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Product", "is_tactic_proof": true, "tactics": ["induction", "rw", "congr"], "tactic_count": 3}
{"name": "Path.Homotopic.projRight_prod", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Product", "is_tactic_proof": true, "tactics": ["induction", "rw", "congr"], "tactic_count": 3}
{"name": "Path.Homotopic.prod_projLeft_projRight", "kind": "theorem", "module": "Mathlib.Topology.Homotopy.Product", "is_tactic_proof": true, "tactics": ["induction", "simp", "congr"], "tactic_count": 3}
{"name": "tendsto_ite", "kind": "theorem", "module": "Mathlib.Topology.IndicatorConstPointwise", "is_tactic_proof": true, "tactics": ["constructor", "by_cases", "simp", "filter_upwards", "simp", "not_forall,", "tauto", "simp", "filter_upwards", "simp", "not_forall,", "tauto", "have", "filter_upwards", "simp", "apply", "by_cases", "simp", "apply", "simp", "simp", "apply", "simp"], "tactic_count": 23}
{"name": "tendsto_indicator_const_apply_iff_eventually'", "kind": "theorem", "module": "Mathlib.Topology.IndicatorConstPointwise", "is_tactic_proof": true, "tactics": ["classical", "have", "convert", "by_cases", "simp", "exact", "simp", "exact"], "tactic_count": 8}
{"name": "tendsto_indicator_const_iff_forall_eventually'", "kind": "theorem", "module": "Mathlib.Topology.IndicatorConstPointwise", "is_tactic_proof": true, "tactics": ["simp_rw", "apply", "exact"], "tactic_count": 3}
{"name": "tendsto_indicator_const_apply_iff_eventually", "kind": "theorem", "module": "Mathlib.Topology.IndicatorConstPointwise", "is_tactic_proof": true, "tactics": ["apply", "simp", "simp"], "tactic_count": 3}
{"name": "tendsto_indicator_const_iff_forall_eventually", "kind": "theorem", "module": "Mathlib.Topology.IndicatorConstPointwise", "is_tactic_proof": true, "tactics": ["apply", "simp", "simp"], "tactic_count": 3}
{"name": "tendsto_indicator_const_iff_tendsto_pi_pure'", "kind": "theorem", "module": "Mathlib.Topology.IndicatorConstPointwise", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "aesop"], "tactic_count": 3}
{"name": "tendsto_indicator_const_iff_tendsto_pi_pure", "kind": "theorem", "module": "Mathlib.Topology.IndicatorConstPointwise", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "aesop"], "tactic_count": 3}
{"name": "specializes_TFAE", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": true, "tactics": ["tfae_have", "tfae_have", "tfae_have", "tfae_have", "tfae_have", "tfae_have", "tfae_have", "refine", "rintro", "rcases", "exact", "tfae_finish"], "tactic_count": 12}
{"name": "specializes_iff_nhds", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Specializes.not_disjoint", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "specializes_iff_pure", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ker_nhds_eq_specializes", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "specializes_iff_forall_open", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Specializes.mem_open", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.not_specializes", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "specializes_iff_forall_closed", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Specializes.mem_closed", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.not_specializes", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "specializes_iff_mem_closure", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "specializes_iff_closure_subset", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "specializes_iff_clusterPt", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.specializes_iff", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "specializes_rfl", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "specializes_refl", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Specializes.trans", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "specializes_of_eq", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "specializes_of_nhdsWithin", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Specializes.map_of_continuousWithinAt", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": true, "tactics": ["rw", "calc", "pure"], "tactic_count": 3}
{"name": "Specializes.map_of_continuousOn", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Specializes.map_of_continuousAt", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Specializes.map", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsInducing.specializes_iff", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "subtype_specializes_iff", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "specializes_prod", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Specializes.prod", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Specializes.fst", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Specializes.snd", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "specializes_pi", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "not_specializes_iff_exists_open", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": true, "tactics": ["rw", "push_neg", "rfl"], "tactic_count": 3}
{"name": "not_specializes_iff_exists_closed", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": true, "tactics": ["rw", "push_neg", "rfl"], "tactic_count": 3}
{"name": "IsOpen.continuous_piecewise_of_specializes", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": true, "tactics": ["have", "rw", "intro", "rw", "exact"], "tactic_count": 5}
{"name": "IsClosed.continuous_piecewise_of_specializes", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Specializes.clusterPt", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.of_subset_of_specializes", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": true, "tactics": ["intro", "obtain", "obtain", "exact"], "tactic_count": 4}
{"name": "Continuous.specialization_monotone", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "closure_singleton_eq_Iic", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StableUnderSpecialization", "kind": "definition", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StableUnderGeneralization", "kind": "definition", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_example", "kind": "example", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_example", "kind": "example", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.stableUnderSpecialization", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.stableUnderGeneralization", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "stableUnderSpecialization_compl_iff", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "stableUnderGeneralization_compl_iff", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "stableUnderSpecialization_univ", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "stableUnderSpecialization_empty", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "stableUnderGeneralization_univ", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "stableUnderGeneralization_empty", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "stableUnderSpecialization_sUnion", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "stableUnderSpecialization_sInter", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "stableUnderGeneralization_sUnion", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "stableUnderGeneralization_sInter", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "stableUnderSpecialization_iUnion", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "stableUnderSpecialization_iInter", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "stableUnderGeneralization_iUnion", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "stableUnderGeneralization_iInter", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Union_closure_singleton_eq_iff", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "stableUnderSpecialization_iff_Union_eq", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "stableUnderSpecialization_iff_exists_sUnion_eq", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": ["refine", "e", "rintro", "conv_rhs", "simp"], "tactic_count": 5}
{"name": "stableUnderGeneralization_iff_exists_sInter_eq", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": ["refine", "rw", "exact", "compl_injective"], "tactic_count": 4}
{"name": "StableUnderSpecialization.preimage", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StableUnderGeneralization.preimage", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SpecializingMap", "kind": "definition", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GeneralizingMap", "kind": "definition", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "specializingMap_iff_closure_singleton_subset", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SpecializingMap.stableUnderSpecialization_image", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "specializingMap_iff_stableUnderSpecialization_image_singleton", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "specializingMap_iff_stableUnderSpecialization_image", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "specializingMap_iff_closure_singleton", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "specializingMap_iff_isClosed_image_closure_singleton", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": ["refine", "specializingMap_iff_stableUnderSpecialization_image_singleton.mpr", "rw", "exact"], "tactic_count": 4}
{"name": "SpecializingMap.comp", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "IsClosedMap.specializingMap", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsInducing.specializingMap", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": true, "tactics": ["intro", "obtain", "exact"], "tactic_count": 3}
{"name": "Topology.IsInducing.generalizingMap", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": true, "tactics": ["intro", "obtain", "exact"], "tactic_count": 3}
{"name": "IsOpenEmbedding.generalizingMap", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SpecializingMap.stableUnderSpecialization_range", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GeneralizingMap.stableUnderGeneralization_image", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GeneralizingMap_iff_stableUnderGeneralization_image", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GeneralizingMap.stableUnderGeneralization_range", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GeneralizingMap.comp", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "_private.Mathlib.Topology.Inseparable.0.term_~ᵢ_", "kind": "definition", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.Inseparable.0._aux_Mathlib_Topology_Inseparable___macroRules__private_Mathlib_Topology_Inseparable_0_term_~ᵢ__1", "kind": "definition", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.Inseparable.0._aux_Mathlib_Topology_Inseparable___unexpand_Inseparable_1", "kind": "definition", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inseparable_def", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inseparable_iff_specializes_and", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Inseparable.specializes", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Inseparable.specializes'", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Specializes.antisymm", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inseparable_iff_forall_isOpen", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "not_inseparable_iff_exists_open", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "inseparable_iff_forall_isClosed", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "inseparable_iff_mem_closure", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inseparable_iff_closure_eq", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "inseparable_of_nhdsWithin_eq", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsInducing.inseparable_iff", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "subtype_inseparable_iff", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inseparable_prod", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Inseparable.prod", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inseparable_pi", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Inseparable.refl", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Inseparable.rfl", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Inseparable.of_eq", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Inseparable.symm", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Inseparable.trans", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Inseparable.nhds_eq", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Inseparable.mem_open_iff", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Inseparable.mem_closed_iff", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Inseparable.map_of_continuousWithinAt", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Inseparable.map_of_continuousOn", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Inseparable.map_of_continuousAt", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Inseparable.map", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.not_inseparable", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.not_inseparable", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instTopologicalSpaceSeparationQuotient", "kind": "instance", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.mk", "kind": "definition", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.isQuotientMap_mk", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.continuous_mk", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.mk_eq_mk", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.forall", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.exists", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.surjective_mk", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.range_mk", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.instNonempty", "kind": "instance", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.instInhabited", "kind": "instance", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.instSubsingleton", "kind": "instance", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.inseparableSetoid_eq_top_iff", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.subsingleton_iff", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.instSubsingletonOfIndiscreteTopology", "kind": "instance", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.nontrivial_iff", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "SeparationQuotient.instNontrivialOfNontrivialTopology", "kind": "instance", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.instOne", "kind": "instance", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.mk_one", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.preimage_image_mk_open", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": true, "tactics": ["refine", "rintro", "exact"], "tactic_count": 3}
{"name": "SeparationQuotient.isOpenMap_mk", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.isOpenQuotientMap_mk", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.preimage_image_mk_closed", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": true, "tactics": ["refine", "rintro", "exact"], "tactic_count": 3}
{"name": "SeparationQuotient.isInducing_mk", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.isClosedMap_mk", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.comap_mk_nhds_mk", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.comap_mk_nhdsSet_image", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.map_mk_nhds", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SeparationQuotient.map_mk_nhdsSet", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SeparationQuotient.comap_mk_nhdsSet", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": true, "tactics": ["conv_lhs"], "tactic_count": 1}
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{"name": "SeparationQuotient.preimage_mk_interior", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.preimage_mk_frontier", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.image_mk_closure", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.map_prod_map_mk_nhds", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SeparationQuotient.map_mk_nhdsWithin_preimage", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SeparationQuotient.isQuotientMap_prodMap_mk", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.lift", "kind": "definition", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.lift_mk", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.lift_comp_mk", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.tendsto_lift_nhds_mk", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SeparationQuotient.tendsto_lift_nhdsWithin_mk", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SeparationQuotient.continuousAt_lift", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.continuousWithinAt_lift", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.continuousOn_lift", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SeparationQuotient.continuous_lift", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "SeparationQuotient.lift₂", "kind": "definition", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.lift₂_mk", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.tendsto_lift₂_nhds", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "SeparationQuotient.tendsto_lift₂_nhdsWithin", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "SeparationQuotient.continuousAt_lift₂", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.continuousWithinAt_lift₂", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.continuousOn_lift₂", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": false, "tactics": ["simp_rw", "rfl"], "tactic_count": 2}
{"name": "SeparationQuotient.continuous_lift₂", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "continuous_congr_of_inseparable", "kind": "theorem", "module": "Mathlib.Topology.Inseparable", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "eventuallyEq_toIcoDiv_nhdsGE", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": true, "tactics": ["simp", "apply", "rw"], "tactic_count": 3}
{"name": "continuousWithinAt_toIcoDiv_Ici", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eventuallyEq_toIocDiv_nhdsLE", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": true, "tactics": ["simp", "apply", "rw"], "tactic_count": 3}
{"name": "continuousWithinAt_toIocDiv_Iic", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousWithinAt_toIcoMod_Ici", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousWithinAt_toIocMod_Iic", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eventuallyEq_toIcoDiv_nhdsLT", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": true, "tactics": ["simp", "apply", "rw"], "tactic_count": 3}
{"name": "eventuallyEq_toIocDiv_nhdsGT", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": true, "tactics": ["simp", "apply", "rw"], "tactic_count": 3}
{"name": "eventuallyEq_toIcoDiv_nhds", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": true, "tactics": ["rw", "refine", "convert", "rwa"], "tactic_count": 4}
{"name": "continuousAt_toIcoDiv", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousOn_toIcoDiv", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eventuallyEq_toIocDiv_nhds", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": true, "tactics": ["rw", "refine", "convert", "rwa"], "tactic_count": 4}
{"name": "continuousAt_toIocDiv", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousOn_toIocDiv", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toIcoMod_eventuallyEq_toIocMod", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact", "rwa"], "tactic_count": 4}
{"name": "continuousAt_toIcoMod", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousAt_toIocMod", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCircle", "kind": "abbrev", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCircle.coe_nsmul", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCircle.coe_zsmul", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCircle.coe_add", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCircle.coe_sub", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCircle.coe_neg", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCircle.coe_zero", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCircle.coe_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AddCircle.coe_period", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCircle.coe_add_period", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AddCircle.continuous_mk'", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCircle.card_torsion_le_of_isSMulRegular", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": false, "tactics": ["have", "obtain", "obtain", "rw", "have", "have", "rw", "set", "use", "simp_rw", "rw", "simp", "choose", "refine", "have", "have", "rw", "rw"], "tactic_count": 18}
{"name": "AddCircle.finite_torsion_of_isSMulRegular", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": true, "tactics": ["nontriviality", "obtain", "exacts"], "tactic_count": 3}
{"name": "AddCircle.card_torsion_le_of_isSMulRegular_int", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": false, "tactics": ["convert", "conv_lhs", "obtain", "simp", "exact", "simp"], "tactic_count": 6}
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{"name": "AddCircle.finite_torsion", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCircle.finite_setOf_addOrderOf_eq", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCircle.coe_eq_zero_of_pos_iff", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": true, "tactics": ["rw", "constructor", "replace", "contrapose", "simpa", "exact", "exact"], "tactic_count": 7}
{"name": "AddCircle.equivIco", "kind": "definition", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCircle.equivIoc", "kind": "definition", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCircle.liftIco", "kind": "definition", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCircle.liftIoc", "kind": "definition", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCircle.equivIco_coe_eq", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AddCircle.equivIoc_coe_eq", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
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{"name": "AddCircle.liftIco_coe_apply", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AddCircle.liftIoc_coe_apply", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AddCircle.liftIco_comp_apply", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCircle.liftIoc_comp_apply", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AddCircle.coe_image_Ico_eq", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "AddCircle.coe_image_Ioc_eq", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "AddCircle.coe_image_Icc_eq", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AddCircle.Ioc_ext", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": true, "tactics": ["rw", "rintro", "exact"], "tactic_count": 3}
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{"name": "AddCircle.equivAddCircle_symm_apply_mk", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AddCircle.homeomorphAddCircle_apply_mk", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCircle.homeomorphAddCircle_symm_apply_mk", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCircle.natCast_div_mul_eq_nsmul", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AddCircle.intCast_div_mul_eq_zsmul", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AddCircle.coe_equivIco_mk_apply", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCircle.instDivisibleByInt", "kind": "instance", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCircle.coe_fract", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AddCircle.addOrderOf_period_div", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": true, "tactics": ["rw", "replace", "refine", "rw", "rw", "rintro", "rw", "exact"], "tactic_count": 8}
{"name": "AddCircle.gcd_mul_addOrderOf_div_eq", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact", "rwa"], "tactic_count": 4}
{"name": "AddCircle.addOrderOf_div_of_gcd_eq_one", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "AddCircle.addOrderOf_div_of_gcd_eq_one'", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": true, "tactics": ["cases", "simp", "exact", "simp", "exact"], "tactic_count": 5}
{"name": "AddCircle.addOrderOf_coe_rat", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": false, "tactics": ["have", "norm_cast", "exact", "rw", "addOrderOf_div_of_gcd_eq_one"], "tactic_count": 5}
{"name": "AddCircle.nsmul_eq_zero_iff", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": true, "tactics": ["refine", "rw", "rintro", "constructor", "exact", "rw", "obtain", "refine", "have", "rw", "rw", "add_eq_right,", "exact"], "tactic_count": 13}
{"name": "AddCircle.addOrderOf_eq_pos_iff", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": true, "tactics": ["refine", "rintro", "exact", "rintro", "obtain", "refine", "convert", "rw", "apply"], "tactic_count": 9}
{"name": "AddCircle.exists_gcd_eq_one_of_isOfFinAddOrder", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCircle.not_isOfFinAddOrder_iff_forall_rat_ne_div", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": false, "tactics": ["simp", "eq_div_iff", "grind"], "tactic_count": 3}
{"name": "AddCircle.isOfFinAddOrder_iff_exists_rat_eq_div", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "AddCircle.addOrderOf_coe_eq_zero_iff_forall_rat_ne_div", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "AddCircle.setAddOrderOfEquiv", "kind": "definition", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCircle.card_addOrderOf_eq_totient", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rcases", "have", "rw", "exact", "exact", "have", "exact", "rw", "simp"], "tactic_count": 11}
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{"name": "_private.Mathlib.Topology.Instances.AddCircle.Defs.0.AddCircle._aux_Mathlib_Topology_Instances_AddCircle_Defs___macroRules__private_Mathlib_Topology_Instances_AddCircle_Defs_0_AddCircle_term𝕋_1", "kind": "definition", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.Instances.AddCircle.Defs.0.AddCircle._aux_Mathlib_Topology_Instances_AddCircle_Defs___unexpand_AddCircle_1", "kind": "definition", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCircle.EndpointIdent", "kind": "inductive", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCircle.equivIccQuot", "kind": "definition", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCircle.equivIccQuot_comp_mk_eq_toIcoMod", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCircle.equivIccQuot_comp_mk_eq_toIocMod", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": true, "tactics": ["rw", "funext", "by_cases", "simp_rw", "exact", "simp_rw"], "tactic_count": 6}
{"name": "AddCircle.homeoIccQuot", "kind": "definition", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCircle.liftIoc_eq_liftIco", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": true, "tactics": ["ext", "obtain", "rw", "obtain", "rw", "exact"], "tactic_count": 6}
{"name": "AddCircle.liftIco_eq_lift_Icc", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCircle.liftIoc_eq_lift_Icc", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "AddCircle.liftIco_zero_coe_apply", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCircle.liftIoc_zero_coe_apply", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCircle.liftIco_continuous", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": true, "tactics": ["rw", "refine", "exact"], "tactic_count": 3}
{"name": "AddCircle.liftIco_zero_continuous", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCircle.liftIoc_continuous", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": true, "tactics": ["rw", "refine", "exact"], "tactic_count": 3}
{"name": "AddCircle.liftIoc_zero_continuous", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dense_addSubgroupClosure_pair_iff", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.DenseSubgroup", "is_tactic_proof": true, "tactics": ["rcases", "rw", "simpa", "constructor", "rintro", "refine", "rw", "pair_subset_iff]", "refine", "simp", "simp", "intro", "contrapose", "rcases", "have", "rw", "apply", "rcases", "simp_all"], "tactic_count": 19}
{"name": "AddCircle.denseRange_zsmul_coe_iff", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.DenseSubgroup", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "AddCircle.denseRange_zsmul_iff", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.DenseSubgroup", "is_tactic_proof": true, "tactics": ["rcases", "simp"], "tactic_count": 2}
{"name": "AddCircle.dense_addSubgroup_iff_ne_zmultiples", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.DenseSubgroup", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "rw", "exact", "intro", "contrapose", "obtain", "rw", "xor_iff_not_iff'.1", "rcases", "use", "rw", "exact", "exact"], "tactic_count": 14}
{"name": "AddCircle.pathConnectedSpace", "kind": "instance", "module": "Mathlib.Topology.Instances.AddCircle.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddCircle.compactSpace", "kind": "instance", "module": "Mathlib.Topology.Instances.AddCircle.Real", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "AddCircle.instProperlyDiscontinuousVAddSubtypeAddOppositeRealMemAddSubgroupOpZmultiples", "kind": "instance", "module": "Mathlib.Topology.Instances.AddCircle.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UnitAddCircle", "kind": "abbrev", "module": "Mathlib.Topology.Instances.AddCircle.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.toAddCircle", "kind": "definition", "module": "Mathlib.Topology.Instances.AddCircle.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.toAddCircle_intCast", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Real", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ZMod.toAddCircle_natCast", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Real", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ZMod.toAddCircle_apply", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Real", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ZMod.toAddCircle_injective", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Real", "is_tactic_proof": true, "tactics": ["intro", "have", "rwa", "exact"], "tactic_count": 4}
{"name": "ZMod.toAddCircle_inj", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.toAddCircle_eq_zero", "kind": "theorem", "module": "Mathlib.Topology.Instances.AddCircle.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "preCantorSet", "kind": "definition", "module": "Mathlib.Topology.Instances.CantorSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "preCantorSet_zero", "kind": "theorem", "module": "Mathlib.Topology.Instances.CantorSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "preCantorSet_succ", "kind": "theorem", "module": "Mathlib.Topology.Instances.CantorSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cantorSet", "kind": "definition", "module": "Mathlib.Topology.Instances.CantorSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "quarters_mem_preCantorSet", "kind": "theorem", "module": "Mathlib.Topology.Instances.CantorSet", "is_tactic_proof": true, "tactics": ["induction", "zero", "simp", "refine", "succ", "apply", "exact", "exact"], "tactic_count": 8}
{"name": "quarter_mem_preCantorSet", "kind": "theorem", "module": "Mathlib.Topology.Instances.CantorSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "quarter_mem_cantorSet", "kind": "theorem", "module": "Mathlib.Topology.Instances.CantorSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zero_mem_preCantorSet", "kind": "theorem", "module": "Mathlib.Topology.Instances.CantorSet", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "zero_mem_cantorSet", "kind": "theorem", "module": "Mathlib.Topology.Instances.CantorSet", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "preCantorSet_antitone", "kind": "theorem", "module": "Mathlib.Topology.Instances.CantorSet", "is_tactic_proof": true, "tactics": ["refine", "simp", "induction"], "tactic_count": 3}
{"name": "preCantorSet_subset_unitInterval", "kind": "theorem", "module": "Mathlib.Topology.Instances.CantorSet", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "cantorSet_subset_unitInterval", "kind": "theorem", "module": "Mathlib.Topology.Instances.CantorSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cantorSet_eq_union_halves", "kind": "theorem", "module": "Mathlib.Topology.Instances.CantorSet", "is_tactic_proof": true, "tactics": ["simp", "rw", "rotate_left", "exact", "exact", "simp_rw", "exact"], "tactic_count": 7}
{"name": "isClosed_preCantorSet", "kind": "theorem", "module": "Mathlib.Topology.Instances.CantorSet", "is_tactic_proof": true, "tactics": ["let", "let", "induction", "zero", "succ", "refine", "simpa", "simpa"], "tactic_count": 8}
{"name": "isClosed_cantorSet", "kind": "theorem", "module": "Mathlib.Topology.Instances.CantorSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCompact_cantorSet", "kind": "theorem", "module": "Mathlib.Topology.Instances.CantorSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofDigits_zero_two_sequence_mem_cantorSet", "kind": "theorem", "module": "Mathlib.Topology.Instances.CantorSet", "is_tactic_proof": true, "tactics": ["simp", "intro", "induction", "zero", "simp", "exact", "succ", "simp", "use", "have", "simp", "specialize", "generalize", "fin_cases"], "tactic_count": 14}
{"name": "ofDigits_zero_two_sequence_unique", "kind": "theorem", "module": "Mathlib.Topology.Instances.CantorSet", "is_tactic_proof": true, "tactics": ["by_contra", "rw", "let", "have", "have", "generalize", "clear", "wlog", "exact", "obtain", "clear", "have", "apply", "grind", "rw", "replace", "ofDigitsTerm", "ring_nf", "linarith", "simp", "pow_succ,", "replace", "rw", "linarith", "linarith"], "tactic_count": 25}
{"name": "cantorStep", "kind": "definition", "module": "Mathlib.Topology.Instances.CantorSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cantorStep_mem_cantorSet", "kind": "theorem", "module": "Mathlib.Topology.Instances.CantorSet", "is_tactic_proof": true, "tactics": ["simp", "obtain", "rw", "grind", "all_goals"], "tactic_count": 5}
{"name": "cantorSequence", "kind": "definition", "module": "Mathlib.Topology.Instances.CantorSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cantorSequence_mem_cantorSet", "kind": "theorem", "module": "Mathlib.Topology.Instances.CantorSet", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "cantorToBinary", "kind": "definition", "module": "Mathlib.Topology.Instances.CantorSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cantorToTernary", "kind": "definition", "module": "Mathlib.Topology.Instances.CantorSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ofDigits_bool_to_fin_three_mem_cantorSet", "kind": "theorem", "module": "Mathlib.Topology.Instances.CantorSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cantorToTernary_ne_one", "kind": "theorem", "module": "Mathlib.Topology.Instances.CantorSet", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "cantorSequence_get_succ", "kind": "theorem", "module": "Mathlib.Topology.Instances.CantorSet", "is_tactic_proof": false, "tactics": ["simp", "split_ifs", "field"], "tactic_count": 3}
{"name": "cantorSequence_eq_self_sub_sum_cantorToTernary", "kind": "theorem", "module": "Mathlib.Topology.Instances.CantorSet", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "ofDigits_cantorToTernary_sum_le", "kind": "theorem", "module": "Mathlib.Topology.Instances.CantorSet", "is_tactic_proof": true, "tactics": ["have", "rw", "apply", "simp", "simpa"], "tactic_count": 5}
{"name": "le_ofDigits_cantorToTernary_sum", "kind": "theorem", "module": "Mathlib.Topology.Instances.CantorSet", "is_tactic_proof": true, "tactics": ["have", "rw", "apply", "simp", "rw", "linarith"], "tactic_count": 6}
{"name": "ofDigits_cantorToTernary", "kind": "theorem", "module": "Mathlib.Topology.Instances.CantorSet", "is_tactic_proof": true, "tactics": ["simp", "rw", "rw", "swap", "simpa", "apply", "rw", "simp", "rw", "exact", "exact", "exact", "exact"], "tactic_count": 13}
{"name": "cantorSet_eq_zero_two_ofDigits", "kind": "theorem", "module": "Mathlib.Topology.Instances.CantorSet", "is_tactic_proof": true, "tactics": ["ext", "refine", "use", "exact", "rw", "exact"], "tactic_count": 6}
{"name": "cantorSetEquivNatToBool", "kind": "definition", "module": "Mathlib.Topology.Instances.CantorSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cantorSetHomeomorphNatToBool", "kind": "definition", "module": "Mathlib.Topology.Instances.CantorSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cantorSpaceHomeomorphNatToCantorSpace", "kind": "definition", "module": "Mathlib.Topology.Instances.CantorSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Complex.subfield_eq_of_closed", "kind": "theorem", "module": "Mathlib.Topology.Instances.Complex", "is_tactic_proof": false, "tactics": ["suffices", "rw", "have", "simp_rw", "exact", "suffices", "refine", "rw", "apply", "rintro", "simp", "nth_rw", "refine", "rw", "simp", "rfl"], "tactic_count": 16}
{"name": "Complex.uniformContinuous_ringHom_eq_id_or_conj", "kind": "theorem", "module": "Mathlib.Topology.Instances.Complex", "is_tactic_proof": true, "tactics": ["letI", "letI", "set", "have", "rw", "congr⟩", "let", "let", "haveI", "rcases", "left", "let", "let", "have", "simpa", "ext1", "rsuffices", "have", "rw", "erw", "rw", "convert", "exact", "rw", "rfl", "obtain", "exact", "let", "have", "rcases", "left", "ext1", "convert", "exact", "right", "ext1", "convert", "exact", "let", "convert", "simp", "rfl⟩", "convert", "rintro", "use", "convert", "simp", "rfl⟩"], "tactic_count": 48}
{"name": "DiscreteTopology.firstCountableTopology", "kind": "instance", "module": "Mathlib.Topology.Instances.Discrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteTopology.secondCountableTopology_of_countable", "kind": "instance", "module": "Mathlib.Topology.Instances.Discrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearOrder.bot_topologicalSpace_eq_generateFrom", "kind": "theorem", "module": "Mathlib.Topology.Instances.Discrete", "is_tactic_proof": true, "tactics": ["let", "have", "exact"], "tactic_count": 3}
{"name": "discreteTopology_iff_orderTopology_of_pred_succ", "kind": "theorem", "module": "Mathlib.Topology.Instances.Discrete", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "OrderTopology.of_discreteTopology", "kind": "instance", "module": "Mathlib.Topology.Instances.Discrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderTopology.of_linearLocallyFinite", "kind": "instance", "module": "Mathlib.Topology.Instances.Discrete", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.isOpen_ne_top", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.isOpen_Ico_zero", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ENNReal.coe_range_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.continuous_coe", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.tendsto_coe_toNNReal", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": true, "tactics": ["nth_rewrite", "exact"], "tactic_count": 2}
{"name": "ENNReal.continuous_coe_iff", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.nhds_coe", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.tendsto_nhds_coe_iff", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.continuousAt_coe_iff", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.continuous_ofReal", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.tendsto_ofReal", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.tendsto_toNNReal", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": true, "tactics": ["lift", "rw", "exact"], "tactic_count": 3}
{"name": "ENNReal.tendsto_toNNReal_iff", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "ENNReal.tendsto_toNNReal_iff'", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ENNReal.eventuallyEq_of_toReal_eventuallyEq", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": true, "tactics": ["filter_upwards", "rwa"], "tactic_count": 2}
{"name": "ENNReal.continuousOn_toNNReal", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.tendsto_toReal", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.continuousOn_toReal", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.continuousAt_toReal", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.neTopHomeomorphNNReal", "kind": "definition", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.ltTopHomeomorphNNReal", "kind": "definition", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": true, "tactics": ["refine", "simp"], "tactic_count": 2}
{"name": "ENNReal.nhds_top", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.nhds_top'", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.nhds_top_basis", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.tendsto_nhds_top_iff_nnreal", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.tendsto_nhds_top_iff_nat", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.tendsto_nhds_top", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.tendsto_nat_nhds_top", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.tendsto_coe_nhds_top", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.tendsto_ofReal_nhds_top", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.tendsto_ofReal_atTop", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.nhds_zero", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.nhds_zero_basis", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.nhds_zero_basis_Iic", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.nhdsGT_coe_neBot", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.nhdsGT_zero_neBot", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.nhdsGT_one_neBot", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.nhdsGT_nat_neBot", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.nhdsGT_ofNat_neBot", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.nhdsLT_neBot", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.hasBasis_nhds_of_ne_top'", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": true, "tactics": ["rcases", "simp_rw", "exact", "refine", "rintro", "rcases", "rcases", "refine", "exact", "grw", "exact", "exact"], "tactic_count": 12}
{"name": "ENNReal.hasBasis_nhds_of_ne_top", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ENNReal.Icc_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.nhds_of_ne_top", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.biInf_le_nhds", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.tendsto_nhds_of_Icc", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": true, "tactics": ["refine", "simpa"], "tactic_count": 2}
{"name": "ENNReal.tendsto_nhds", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.tendsto_nhds_zero", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.tendsto_const_sub_nhds_zero_iff", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "refine", "filter_upwards", "refine", "rw", "rwa", "filter_upwards", "have", "rw", "rwa"], "tactic_count": 10}
{"name": "ENNReal.tendsto_atTop", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.tendsto_atTop_zero", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.tendsto_atTop_zero_iff_le_of_antitone", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "refine", "obtain", "exact", "obtain", "exact"], "tactic_count": 6}
{"name": "ENNReal.tendsto_atTop_zero_iff_lt_of_antitone", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "constructor", "obtain", "h", "refine", "by_cases", "rw", "exact", "refine", "rw", "conv_lhs", "gcongr", "obtain", "exact"], "tactic_count": 14}
{"name": "ENNReal.tendsto_sub", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.Tendsto.sub", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.tendsto_mul", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": ["have", "refine", "rcases", "have", "refine", "exact", "induction", "top", "coe", "induction", "top", "simp", "simpa", "coe"], "tactic_count": 14}
{"name": "ENNReal.Tendsto.mul", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.ennreal_mul", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.ennreal_mul", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.Tendsto.const_mul", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.Tendsto.mul_const", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ENNReal.tendsto_finset_prod_of_ne_top", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "insert", "simp", "apply", "right", "exact", "exact", "exact"], "tactic_count": 10}
{"name": "ENNReal.continuousAt_const_mul", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.continuousAt_mul_const", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.continuous_const_mul", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.continuous_mul_const", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.continuous_div_const", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.continuous_pow", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "simp_rw", "intro", "refine", "simp", "exact", "simp", "simp"], "tactic_count": 10}
{"name": "ENNReal.continuousOn_sub", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "rintro", "simp", "exact"], "tactic_count": 4}
{"name": "ENNReal.continuous_sub_left", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": true, "tactics": ["change", "refine", "simp"], "tactic_count": 3}
{"name": "ENNReal.continuous_nnreal_sub", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.continuousOn_sub_left", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "apply", "rintro", "exact"], "tactic_count": 4}
{"name": "ENNReal.continuous_sub_right", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "rw", "apply", "intro", "simp"], "tactic_count": 6}
{"name": "ENNReal.Tendsto.pow", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.le_of_forall_lt_one_mul_le", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "ENNReal.inv_limsup", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.inv_liminf", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.continuous_zpow", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.Tendsto.div", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "ENNReal.Tendsto.const_div", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "ENNReal.Tendsto.div_const", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "ENNReal.tendsto_inv_nat_nhds_zero", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.tendsto_coe_sub", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.exists_countable_dense_no_zero_top", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": ["obtain", "exists_countable_dense_no_bot_top", "exact"], "tactic_count": 3}
{"name": "ENNReal.exists_frequently_lt_of_liminf_ne_top", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": true, "tactics": ["by_contra", "refine", "simp", "filter_upwards"], "tactic_count": 4}
{"name": "ENNReal.exists_frequently_lt_of_liminf_ne_top'", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": true, "tactics": ["by_contra", "refine", "simp", "filter_upwards"], "tactic_count": 4}
{"name": "ENNReal.exists_upcrossings_of_not_bounded_under", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "obtain", "obtain", "obtain", "refine", "refine", "filter_upwards", "simp", "refine", "filter_upwards", "obtain", "obtain", "refine", "simp", "refine", "filter_upwards", "refine", "filter_upwards"], "tactic_count": 18}
{"name": "ENNReal.tendsto_toReal_iff", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": true, "tactics": ["lift", "lift", "simp"], "tactic_count": 3}
{"name": "edist_ne_top_of_mem_ball", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "metricSpaceEMetricBall", "kind": "definition", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhds_eq_nhds_emetric_ball", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_iff_edist_tendsto_0", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": true, "tactics": ["simp", "forall_prop_of_false"], "tactic_count": 2}
{"name": "EMetric.cauchySeq_iff_le_tendsto_0", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_of_le_add_edist", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": true, "tactics": ["refine", "rcases", "rw", "filter_upwards", "refine", "exacts"], "tactic_count": 6}
{"name": "continuous_edist", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": true, "tactics": ["apply", "rintro", "calc", "edist", "gcongr"], "tactic_count": 5}
{"name": "Continuous.edist", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.edist", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.isClosed_closedEBall", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.ediam_closure", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": true, "tactics": ["refine", "have", "map_mem_closure₂", "rwa"], "tactic_count": 4}
{"name": "Metric.diam_closure", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "isClosed_setOf_lipschitzOnWith", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": true, "tactics": ["simp", "refine", "exacts"], "tactic_count": 3}
{"name": "isClosed_setOf_lipschitzWith", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LipschitzOnWith.closure", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": true, "tactics": ["have", "refine", "all_goals"], "tactic_count": 3}
{"name": "lipschitzOnWith_closure_iff", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.ediam_eq", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": true, "tactics": ["rcases", "simp", "refine", "exact", "apply", "rw", "calc", "sSup", "dist_le_diam_of_mem"], "tactic_count": 9}
{"name": "Real.diam_eq", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Real.ediam_Ioo", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rw"], "tactic_count": 3}
{"name": "Real.ediam_Icc", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": true, "tactics": ["rcases", "rw", "simp"], "tactic_count": 3}
{"name": "Real.ediam_Ico", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.ediam_Ioc", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.diam_Icc", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.diam_Ico", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.diam_Ioc", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.diam_Ioo", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENNReal.truncateToReal", "kind": "definition", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.truncateToReal_eq_toReal", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": true, "tactics": ["have", "have", "exact"], "tactic_count": 3}
{"name": "ENNReal.truncateToReal_le", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "gcongr", "exacts"], "tactic_count": 3}
{"name": "ENNReal.truncateToReal_nonneg", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.monotone_truncateToReal", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": true, "tactics": ["intro", "simp", "gcongr", "exact"], "tactic_count": 4}
{"name": "ENNReal.continuous_truncateToReal", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "ENNReal.limsup_sub_const", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": true, "tactics": ["rcases", "simp", "exact"], "tactic_count": 3}
{"name": "ENNReal.liminf_sub_const", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.limsup_const_sub", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": true, "tactics": ["rcases", "simp", "exact"], "tactic_count": 3}
{"name": "ENNReal.liminf_const_sub", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.le_limsup_mul", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.limsup_mul_le'", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": true, "tactics": ["refine", "filter_upwards", "exact"], "tactic_count": 3}
{"name": "ENNReal.le_liminf_mul", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": true, "tactics": ["refine", "filter_upwards", "exact"], "tactic_count": 3}
{"name": "ENNReal.liminf_mul_le", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.liminf_toReal_eq", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": ["have", "apply", "intro", "obtain", "exact", "have", "filter_upwards", "simp", "have", "rw", "simp_rw", "have", "rw", "rfl"], "tactic_count": 14}
{"name": "ENNReal.limsup_toReal_eq", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": ["have", "filter_upwards", "simp", "have", "rw", "simp_rw", "have", "rw", "rfl"], "tactic_count": 9}
{"name": "ENNReal.ofNNReal_limsup", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": true, "tactics": ["refine", "rw", "simp"], "tactic_count": 3}
{"name": "ENNReal.ofNNReal_liminf", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": true, "tactics": ["refine", "rw", "simp"], "tactic_count": 3}
{"name": "ENNReal.liminf_add_of_right_tendsto_zero", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": true, "tactics": ["refine", "refine", "rw", "rintro", "filter_upwards", "exact"], "tactic_count": 6}
{"name": "ENNReal.liminf_add_of_left_tendsto_zero", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENNReal.limsup_add_of_right_tendsto_zero", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": true, "tactics": ["refine", "refine", "rw", "rintro", "filter_upwards", "calc", "f"], "tactic_count": 7}
{"name": "ENNReal.limsup_add_of_left_tendsto_zero", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Dense.lipschitzWith_extend", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENNReal.Lemmas", "is_tactic_proof": false, "tactics": ["have", "have", "apply", "exact", "have", "apply", "rintro", "have", "have", "simp", "exact", "simpa"], "tactic_count": 12}
{"name": "ENat.instTopologicalSpace", "kind": "instance", "module": "Mathlib.Topology.Instances.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.instOrderTopology", "kind": "instance", "module": "Mathlib.Topology.Instances.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.range_natCast", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.isEmbedding_natCast", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.isOpenEmbedding_natCast", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.nhds_natCast", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENat.nhds_eq_pure", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENat", "is_tactic_proof": true, "tactics": ["lift", "simp"], "tactic_count": 2}
{"name": "ENat.isOpen_singleton", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ENat.mem_nhds_iff", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ENat.mem_nhds_natCast_iff", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.tendsto_nhds_top_iff_natCast_lt", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENat", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "ENat.instContinuousAdd", "kind": "instance", "module": "Mathlib.Topology.Instances.ENat", "is_tactic_proof": true, "tactics": ["refine"], "tactic_count": 1}
{"name": "ENat.instContinuousMul", "kind": "instance", "module": "Mathlib.Topology.Instances.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENat.continuousAt_sub", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENat", "is_tactic_proof": true, "tactics": ["suffices", "filter_upwards", "suffices", "simpa", "exact"], "tactic_count": 5}
{"name": "Filter.Tendsto.enatSub", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.enatSub", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.enatSub", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.enatSub", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.enatSub", "kind": "theorem", "module": "Mathlib.Topology.Instances.ENat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.isEmbedding_coe", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.isOpenEmbedding_coe", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.tendsto_coe", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_coe_real_ereal", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.continuous_coe_iff", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.nhds_coe", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.nhds_coe_coe", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.tendsto_toReal", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": true, "tactics": ["lift", "rw", "exact"], "tactic_count": 3}
{"name": "EReal.continuousOn_toReal", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.neBotTopHomeomorphReal", "kind": "definition", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.isEmbedding_coe_ennreal", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.isClosedEmbedding_coe_ennreal", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.tendsto_coe_ennreal", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_coe_ennreal_ereal", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.continuous_coe_ennreal_iff", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.nhds_top", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.nhds_top_basis", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": true, "tactics": ["refine", "rcases", "exact"], "tactic_count": 3}
{"name": "EReal.nhds_top'", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.mem_nhds_top_iff", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.tendsto_nhds_top_iff_real", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.nhds_bot", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.nhds_bot_basis", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": false, "tactics": ["refine", "rcases", "exact"], "tactic_count": 3}
{"name": "EReal.nhds_bot'", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.mem_nhds_bot_iff", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.tendsto_nhds_bot_iff_real", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.nhdsWithin_top", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": true, "tactics": ["apply", "simp", "intro", "by_cases", "simp", "lift", "refine", "simp", "simp", "refine", "simp"], "tactic_count": 11}
{"name": "EReal.nhdsWithin_bot", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": true, "tactics": ["apply", "simp", "intro", "by_cases", "simp", "lift", "refine", "simp", "simp", "refine", "simp"], "tactic_count": 11}
{"name": "EReal.tendsto_coe_nhds_top_iff", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EReal.tendsto_coe_atTop", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.tendsto_coe_nhds_bot_iff", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "EReal.tendsto_coe_atBot", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.tendsto_toReal_atTop", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "EReal.tendsto_toReal_atBot", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "EReal.continuous_toENNReal", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": true, "tactics": ["refine", "by_cases", "simp", "refine", "filter_upwards", "exact", "refine", "refine", "by_cases", "refine", "rw", "simpa", "refine", "continuousOn_toReal.continuousAt", "simp_all"], "tactic_count": 15}
{"name": "Continuous.ereal_toENNReal", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.ereal_toENNReal", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.ereal_toENNReal", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.ereal_toENNReal", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.add_iInf_le_iInf_add", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.iSup_add_le_add_iSup", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.liminf_neg", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.limsup_neg", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.le_liminf_add", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": true, "tactics": ["refine", "filter_upwards", "exact"], "tactic_count": 3}
{"name": "EReal.limsup_add_le", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": true, "tactics": ["refine", "filter_upwards", "exact"], "tactic_count": 3}
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{"name": "EReal.liminf_add_le", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.limsup_add_bot_of_ne_top", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": true, "tactics": ["apply", "rw", "rw"], "tactic_count": 3}
{"name": "EReal.limsup_add_le_of_le", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": true, "tactics": ["rcases", "rw", "exact"], "tactic_count": 3}
{"name": "EReal.liminf_add_gt_of_gt", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.liminf_add_top_of_ne_bot", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": true, "tactics": ["apply", "rw"], "tactic_count": 2}
{"name": "EReal.le_limsup_mul", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": true, "tactics": ["rcases", "rw", "have", "have", "le_limsup_of_frequently_le", "refine", "refine", "exact"], "tactic_count": 8}
{"name": "EReal.limsup_mul_le", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": true, "tactics": ["rcases", "rw", "have", "replace", "replace", "h₂.imp_right", "refine", "filter_upwards", "apply", "rcases", "apply", "exact", "exact"], "tactic_count": 13}
{"name": "EReal.le_liminf_mul", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": false, "tactics": ["apply", "mul_le_of_forall_lt_of_nonneg", "refine", "filter_upwards", "exact"], "tactic_count": 5}
{"name": "EReal.liminf_mul_le", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": false, "tactics": ["replace", "refine", "exact", "replace", "refine", "exact", "refine", "refine", "exact"], "tactic_count": 9}
{"name": "EReal.continuousAt_add_coe_coe", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "EReal.continuousAt_add_top_coe", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": true, "tactics": ["simp", "refine", "simpa"], "tactic_count": 3}
{"name": "EReal.continuousAt_add_coe_top", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "EReal.continuousAt_add_top_top", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": true, "tactics": ["simp", "refine", "simpa"], "tactic_count": 3}
{"name": "EReal.continuousAt_add_bot_coe", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": true, "tactics": ["simp", "refine", "simpa"], "tactic_count": 3}
{"name": "EReal.continuousAt_add_coe_bot", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "EReal.continuousAt_add_bot_bot", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": true, "tactics": ["simp", "refine", "simpa"], "tactic_count": 3}
{"name": "EReal.continuousAt_add", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": true, "tactics": ["rcases", "induction", "exact", "exact", "simp", "exact", "exact", "exact", "simp", "exact", "exact"], "tactic_count": 11}
{"name": "EReal.lowerSemicontinuous_add", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": true, "tactics": ["intro", "by_cases", "simp", "by_cases", "simp", "exact"], "tactic_count": 6}
{"name": "_private.Mathlib.Topology.Instances.EReal.Lemmas.0.EReal.continuousAt_mul_swap", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "_private.Mathlib.Topology.Instances.EReal.Lemmas.0.EReal.continuousAt_mul_symm1", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": false, "tactics": ["have", "ext", "simp", "rw", "apply", "simp"], "tactic_count": 6}
{"name": "_private.Mathlib.Topology.Instances.EReal.Lemmas.0.EReal.continuousAt_mul_symm2", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.Instances.EReal.Lemmas.0.EReal.continuousAt_mul_symm3", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.Instances.EReal.Lemmas.0.EReal.continuousAt_mul_coe_coe", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "_private.Mathlib.Topology.Instances.EReal.Lemmas.0.EReal.continuousAt_mul_top_top", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": true, "tactics": ["simp", "intro", "rw", "use", "split_ands", "intro", "simp", "rcases", "have", "rw", "exact", "exact", "simp", "rw"], "tactic_count": 14}
{"name": "_private.Mathlib.Topology.Instances.EReal.Lemmas.0.EReal.continuousAt_mul_top_pos", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": true, "tactics": ["simp", "intro", "rw", "use", "split_ands", "intro", "simp", "rcases", "have", "apply", "rw", "apply", "simp", "have", "have", "have", "replace", "apply", "rw", "mul_div_right_comm]", "simp", "lt_max_iff,", "exact", "simp", "simp"], "tactic_count": 25}
{"name": "_private.Mathlib.Topology.Instances.EReal.Lemmas.0.EReal.continuousAt_mul_top_ne_zero", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": true, "tactics": ["rcases", "exact", "exact"], "tactic_count": 3}
{"name": "EReal.continuousAt_mul", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": true, "tactics": ["rcases", "induction", "exact", "simp", "exact", "exact", "simp", "exact", "exact", "simp", "exact", "exact", "simp", "exact", "exact"], "tactic_count": 15}
{"name": "EReal.tendsto_mul", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.Tendsto.mul", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.Tendsto.const_mul", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.Tendsto.mul_const", "kind": "theorem", "module": "Mathlib.Topology.Instances.EReal.Lemmas", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Int.instDist", "kind": "instance", "module": "Mathlib.Topology.Instances.Int", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.dist_eq", "kind": "theorem", "module": "Mathlib.Topology.Instances.Int", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.dist_eq'", "kind": "theorem", "module": "Mathlib.Topology.Instances.Int", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.dist_cast_real", "kind": "theorem", "module": "Mathlib.Topology.Instances.Int", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.pairwise_one_le_dist", "kind": "theorem", "module": "Mathlib.Topology.Instances.Int", "is_tactic_proof": true, "tactics": ["intro", "rw"], "tactic_count": 2}
{"name": "Int.isUniformEmbedding_coe_real", "kind": "theorem", "module": "Mathlib.Topology.Instances.Int", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.isClosedEmbedding_coe_real", "kind": "theorem", "module": "Mathlib.Topology.Instances.Int", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.instMetricSpace", "kind": "instance", "module": "Mathlib.Topology.Instances.Int", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.preimage_ball", "kind": "theorem", "module": "Mathlib.Topology.Instances.Int", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.preimage_closedBall", "kind": "theorem", "module": "Mathlib.Topology.Instances.Int", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.ball_eq_Ioo", "kind": "theorem", "module": "Mathlib.Topology.Instances.Int", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.closedBall_eq_Icc", "kind": "theorem", "module": "Mathlib.Topology.Instances.Int", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.instProperSpace", "kind": "instance", "module": "Mathlib.Topology.Instances.Int", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.instIsOrderBornology", "kind": "instance", "module": "Mathlib.Topology.Instances.Int", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.cobounded_eq", "kind": "theorem", "module": "Mathlib.Topology.Instances.Int", "is_tactic_proof": true, "tactics": ["simp_rw", "comap_comap]", "rfl"], "tactic_count": 3}
{"name": "Int.cofinite_eq", "kind": "theorem", "module": "Mathlib.Topology.Instances.Int", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsGδ.setOf_irrational", "kind": "theorem", "module": "Mathlib.Topology.Instances.Irrational", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dense_irrational", "kind": "theorem", "module": "Mathlib.Topology.Instances.Irrational", "is_tactic_proof": true, "tactics": ["refine", "simp", "rintro", "rw", "exact"], "tactic_count": 5}
{"name": "eventually_residual_irrational", "kind": "theorem", "module": "Mathlib.Topology.Instances.Irrational", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Irrational.instOrderTopologySubtypeReal", "kind": "instance", "module": "Mathlib.Topology.Instances.Irrational", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Irrational.instNoMaxOrderSubtypeReal", "kind": "instance", "module": "Mathlib.Topology.Instances.Irrational", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Irrational.instNoMinOrderSubtypeReal", "kind": "instance", "module": "Mathlib.Topology.Instances.Irrational", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Irrational.instDenselyOrderedSubtypeReal", "kind": "instance", "module": "Mathlib.Topology.Instances.Irrational", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Irrational.eventually_forall_le_dist_cast_div", "kind": "theorem", "module": "Mathlib.Topology.Instances.Irrational", "is_tactic_proof": false, "tactics": ["have", "have", "rintro", "simp", "rcases", "refine", "rw", "refine", "simp"], "tactic_count": 9}
{"name": "Irrational.eventually_forall_le_dist_cast_div_of_denom_le", "kind": "theorem", "module": "Mathlib.Topology.Instances.Irrational", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Irrational.eventually_forall_le_dist_cast_rat_of_den_le", "kind": "theorem", "module": "Mathlib.Topology.Instances.Irrational", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instTopologicalSpaceMatrix", "kind": "instance", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instT2SpaceMatrix", "kind": "instance", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDiscreteTopologyMatrixOfFinite", "kind": "instance", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.matrix", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.matrix", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instContinuousConstSMulMatrix", "kind": "instance", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instContinuousSMulMatrix", "kind": "instance", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instContinuousAddMatrix", "kind": "instance", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instContinuousNegMatrix", "kind": "instance", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsTopologicalAddGroupMatrix", "kind": "instance", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_matrix", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.matrix_elem", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.matrix_map", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.matrix_transpose", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.matrix_conjTranspose", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instContinuousStarMatrix", "kind": "instance", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.matrix_replicateCol", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.matrix_replicateRow", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.matrix_diagonal", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.dotProduct", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": true, "tactics": ["dsimp", "fun_prop"], "tactic_count": 2}
{"name": "Continuous.matrix_mul", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instContinuousMulMatrixOfContinuousAdd", "kind": "instance", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsTopologicalSemiringMatrix", "kind": "instance", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.topologicalRing", "kind": "instance", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.matrix_vecMulVec", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.matrix_mulVec", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.matrix_vecMul", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.matrix_submatrix", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.matrix_reindex", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.matrix_diag", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_matrix_diag", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.matrix_trace", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.matrix_det", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "exact"], "tactic_count": 3}
{"name": "Continuous.matrix_updateCol", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.matrix_updateRow", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.matrix_cramer", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.matrix_adjugate", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousAt_matrix_inv", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsInducing.matrix_map", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsEmbedding.matrix_map", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsClosedEmbedding.matrix_map", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsOpenEmbedding.matrix_map", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.matrix_fromBlocks", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.matrix_blockDiagonal", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.matrix_blockDiag", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.matrix_blockDiagonal'", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.matrix_blockDiag'", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasSum.matrix_transpose", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Summable.matrix_transpose", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "summable_matrix_transpose", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.transpose_tsum", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasSum.matrix_conjTranspose", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Summable.matrix_conjTranspose", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "summable_matrix_conjTranspose", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.conjTranspose_tsum", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasSum.matrix_diagonal", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Summable.matrix_diagonal", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "summable_matrix_diagonal", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.diagonal_tsum", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasSum.matrix_diag", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Summable.matrix_diag", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasSum.matrix_blockDiagonal", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Summable.matrix_blockDiagonal", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "summable_matrix_blockDiagonal", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.blockDiagonal_tsum", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasSum.matrix_blockDiag", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Summable.matrix_blockDiag", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasSum.matrix_blockDiagonal'", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Summable.matrix_blockDiagonal'", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "summable_matrix_blockDiagonal'", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.blockDiagonal'_tsum", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasSum.matrix_blockDiag'", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Summable.matrix_blockDiag'", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.GeneralLinearGroup.continuous_det", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": true, "tactics": ["simp_rw", "constructor"], "tactic_count": 2}
{"name": "Matrix.GeneralLinearGroup.continuous_upperRightHom", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": ["simp", "continuous_prodMk,", "constructor", "refine", "fin_cases"], "tactic_count": 5}
{"name": "_private.Mathlib.Topology.Instances.Matrix.0.Matrix.SpecialLinearGroup.termSL", "kind": "definition", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.Instances.Matrix.0.Matrix.SpecialLinearGroup._aux_Mathlib_Topology_Instances_Matrix___macroRules__private_Mathlib_Topology_Instances_Matrix_0_Matrix_SpecialLinearGroup_termSL_1", "kind": "definition", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.Instances.Matrix.0.Matrix.SpecialLinearGroup._aux_Mathlib_Topology_Instances_Matrix___unexpand_Matrix_SpecialLinearGroup_1", "kind": "definition", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.SpecialLinearGroup.instTopologicalSpace", "kind": "instance", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.SpecialLinearGroup.instDiscreteTopology", "kind": "instance", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.SpecialLinearGroup.topologicalGroup", "kind": "instance", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.SpecialLinearGroup.continuous_toGL", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": true, "tactics": ["simp_rw", "constructor"], "tactic_count": 2}
{"name": "Matrix.SpecialLinearGroup.isInducing_toGL", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.SpecialLinearGroup.isEmbedding_toGL", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.SpecialLinearGroup.range_toGL", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": true, "tactics": ["ext", "simpa"], "tactic_count": 2}
{"name": "Matrix.SpecialLinearGroup.isClosedEmbedding_toGL", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.SpecialLinearGroup.isInducing_mapGL", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": true, "tactics": ["refine", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "Matrix.SpecialLinearGroup.isEmbedding_mapGL", "kind": "theorem", "module": "Mathlib.Topology.Instances.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.isOpen_Ico_zero", "kind": "theorem", "module": "Mathlib.Topology.Instances.NNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_real_toNNReal", "kind": "theorem", "module": "Mathlib.Topology.Instances.NNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.realToNNReal", "kind": "definition", "module": "Mathlib.Topology.Instances.NNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.map_coe_nhdsGT", "kind": "theorem", "module": "Mathlib.Topology.Instances.NNReal.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NNReal.map_coe_nhdsGE", "kind": "theorem", "module": "Mathlib.Topology.Instances.NNReal.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ContinuousOn.ofReal_map_toNNReal", "kind": "theorem", "module": "Mathlib.Topology.Instances.NNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.tendsto_coe", "kind": "theorem", "module": "Mathlib.Topology.Instances.NNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.tendsto_coe'", "kind": "theorem", "module": "Mathlib.Topology.Instances.NNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.map_coe_atTop", "kind": "theorem", "module": "Mathlib.Topology.Instances.NNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.comap_coe_atTop", "kind": "theorem", "module": "Mathlib.Topology.Instances.NNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.tendsto_coe_atTop", "kind": "theorem", "module": "Mathlib.Topology.Instances.NNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_real_toNNReal", "kind": "theorem", "module": "Mathlib.Topology.Instances.NNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.map_toNNReal_atTop", "kind": "theorem", "module": "Mathlib.Topology.Instances.NNReal.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "tendsto_real_toNNReal_atTop", "kind": "theorem", "module": "Mathlib.Topology.Instances.NNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.comap_toNNReal_atTop", "kind": "theorem", "module": "Mathlib.Topology.Instances.NNReal.Lemmas", "is_tactic_proof": true, "tactics": ["refine", "refine", "filter_upwards", "exact"], "tactic_count": 4}
{"name": "Real.tendsto_toNNReal_atTop_iff", "kind": "theorem", "module": "Mathlib.Topology.Instances.NNReal.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.tendsto_toNNReal_atTop", "kind": "theorem", "module": "Mathlib.Topology.Instances.NNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.nhds_zero", "kind": "theorem", "module": "Mathlib.Topology.Instances.NNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.nhds_zero_basis", "kind": "theorem", "module": "Mathlib.Topology.Instances.NNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.hasSum_coe", "kind": "theorem", "module": "Mathlib.Topology.Instances.NNReal.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HasSum.toNNReal", "kind": "theorem", "module": "Mathlib.Topology.Instances.NNReal.Lemmas", "is_tactic_proof": true, "tactics": ["rcases", "lift", "lift", "simpa", "simp"], "tactic_count": 5}
{"name": "NNReal.hasSum_real_toNNReal_of_nonneg", "kind": "theorem", "module": "Mathlib.Topology.Instances.NNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.summable_coe", "kind": "theorem", "module": "Mathlib.Topology.Instances.NNReal.Lemmas", "is_tactic_proof": true, "tactics": ["rcases", "constructor", "exact", "exact", "simp"], "tactic_count": 5}
{"name": "NNReal.summable_mk", "kind": "theorem", "module": "Mathlib.Topology.Instances.NNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.coe_tsum", "kind": "theorem", "module": "Mathlib.Topology.Instances.NNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.coe_tsum_of_nonneg", "kind": "theorem", "module": "Mathlib.Topology.Instances.NNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.tsum_mul_left", "kind": "theorem", "module": "Mathlib.Topology.Instances.NNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.tsum_mul_right", "kind": "theorem", "module": "Mathlib.Topology.Instances.NNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.summable_comp_injective", "kind": "theorem", "module": "Mathlib.Topology.Instances.NNReal.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "NNReal.summable_nat_add", "kind": "theorem", "module": "Mathlib.Topology.Instances.NNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.summable_nat_add_iff", "kind": "theorem", "module": "Mathlib.Topology.Instances.NNReal.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "NNReal.hasSum_nat_add_iff", "kind": "theorem", "module": "Mathlib.Topology.Instances.NNReal.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "NNReal.sum_add_tsum_nat_add", "kind": "theorem", "module": "Mathlib.Topology.Instances.NNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.iInf_real_pos_eq_iInf_nnreal_pos", "kind": "theorem", "module": "Mathlib.Topology.Instances.NNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.tendsto_cofinite_zero_of_summable", "kind": "theorem", "module": "Mathlib.Topology.Instances.NNReal.Lemmas", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "NNReal.tendsto_atTop_zero_of_summable", "kind": "theorem", "module": "Mathlib.Topology.Instances.NNReal.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "NNReal.tendsto_tsum_compl_atTop_zero", "kind": "theorem", "module": "Mathlib.Topology.Instances.NNReal.Lemmas", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "NNReal.powOrderIso", "kind": "definition", "module": "Mathlib.Topology.Instances.NNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.tendsto_of_bddAbove_monotone", "kind": "theorem", "module": "Mathlib.Topology.Instances.NNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.tendsto_of_bddBelow_antitone", "kind": "theorem", "module": "Mathlib.Topology.Instances.NNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.tendsto_of_antitone", "kind": "theorem", "module": "Mathlib.Topology.Instances.NNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.iSup_pow_of_ne_zero", "kind": "theorem", "module": "Mathlib.Topology.Instances.NNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.iSup_pow", "kind": "theorem", "module": "Mathlib.Topology.Instances.NNReal.Lemmas", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "exact"], "tactic_count": 3}
{"name": "ENNReal.powOrderIso", "kind": "definition", "module": "Mathlib.Topology.Instances.NNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.iSup_pow_of_ne_zero", "kind": "theorem", "module": "Mathlib.Topology.Instances.NNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.iSup_pow", "kind": "theorem", "module": "Mathlib.Topology.Instances.NNReal.Lemmas", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "exact"], "tactic_count": 3}
{"name": "ENNReal.iSup₂_pow_of_ne_zero", "kind": "theorem", "module": "Mathlib.Topology.Instances.NNReal.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.iSup_pow", "kind": "theorem", "module": "Mathlib.Topology.Instances.NNReal.Lemmas", "is_tactic_proof": true, "tactics": ["lift"], "tactic_count": 1}
{"name": "Real.iSup_pow_of_ne_zero", "kind": "theorem", "module": "Mathlib.Topology.Instances.NNReal.Lemmas", "is_tactic_proof": true, "tactics": ["cases", "simp", "exact"], "tactic_count": 3}
{"name": "Nat.instDist", "kind": "instance", "module": "Mathlib.Topology.Instances.Nat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.dist_eq", "kind": "theorem", "module": "Mathlib.Topology.Instances.Nat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.dist_coe_int", "kind": "theorem", "module": "Mathlib.Topology.Instances.Nat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.dist_cast_real", "kind": "theorem", "module": "Mathlib.Topology.Instances.Nat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.pairwise_one_le_dist", "kind": "theorem", "module": "Mathlib.Topology.Instances.Nat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.isUniformEmbedding_coe_real", "kind": "theorem", "module": "Mathlib.Topology.Instances.Nat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.isClosedEmbedding_coe_real", "kind": "theorem", "module": "Mathlib.Topology.Instances.Nat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.instMetricSpace", "kind": "instance", "module": "Mathlib.Topology.Instances.Nat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.preimage_ball", "kind": "theorem", "module": "Mathlib.Topology.Instances.Nat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.preimage_closedBall", "kind": "theorem", "module": "Mathlib.Topology.Instances.Nat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.closedBall_eq_Icc", "kind": "theorem", "module": "Mathlib.Topology.Instances.Nat", "is_tactic_proof": true, "tactics": ["rcases", "rw", "positivity", "rw", "calc", "rw", "linarith"], "tactic_count": 7}
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{"name": "Nat.instNoncompactSpace", "kind": "instance", "module": "Mathlib.Topology.Instances.Nat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.instMetricSpace", "kind": "instance", "module": "Mathlib.Topology.Instances.PNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "PNat.dist_coe", "kind": "theorem", "module": "Mathlib.Topology.Instances.PNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.isUniformEmbedding_coe", "kind": "theorem", "module": "Mathlib.Topology.Instances.PNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PNat.instDiscreteTopology", "kind": "instance", "module": "Mathlib.Topology.Instances.PNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "PNat.instNoncompactSpace", "kind": "instance", "module": "Mathlib.Topology.Instances.PNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.instMetricSpace", "kind": "instance", "module": "Mathlib.Topology.Instances.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Rat.dist_cast", "kind": "theorem", "module": "Mathlib.Topology.Instances.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.uniformContinuous_coe_real", "kind": "theorem", "module": "Mathlib.Topology.Instances.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.isUniformEmbedding_coe_real", "kind": "theorem", "module": "Mathlib.Topology.Instances.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.isDenseEmbedding_coe_real", "kind": "theorem", "module": "Mathlib.Topology.Instances.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.isEmbedding_coe_real", "kind": "theorem", "module": "Mathlib.Topology.Instances.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.continuous_coe_real", "kind": "theorem", "module": "Mathlib.Topology.Instances.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.dist_cast_rat", "kind": "theorem", "module": "Mathlib.Topology.Instances.Rat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Nat.isUniformEmbedding_coe_rat", "kind": "theorem", "module": "Mathlib.Topology.Instances.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.isClosedEmbedding_coe_rat", "kind": "theorem", "module": "Mathlib.Topology.Instances.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.dist_cast_rat", "kind": "theorem", "module": "Mathlib.Topology.Instances.Rat", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Int.isUniformEmbedding_coe_rat", "kind": "theorem", "module": "Mathlib.Topology.Instances.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.isClosedEmbedding_coe_rat", "kind": "theorem", "module": "Mathlib.Topology.Instances.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.instNoncompactSpace", "kind": "instance", "module": "Mathlib.Topology.Instances.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.uniformContinuous_add", "kind": "theorem", "module": "Mathlib.Topology.Instances.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.uniformContinuous_neg", "kind": "theorem", "module": "Mathlib.Topology.Instances.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.instIsUniformAddGroup", "kind": "instance", "module": "Mathlib.Topology.Instances.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.instIsTopologicalAddGroup", "kind": "instance", "module": "Mathlib.Topology.Instances.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.instOrderTopology", "kind": "instance", "module": "Mathlib.Topology.Instances.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.uniformContinuous_abs", "kind": "theorem", "module": "Mathlib.Topology.Instances.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.instIsTopologicalRing", "kind": "instance", "module": "Mathlib.Topology.Instances.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.totallyBounded_Icc", "kind": "theorem", "module": "Mathlib.Topology.Instances.Rat", "is_tactic_proof": true, "tactics": ["simpa", "totallyBounded_preimage"], "tactic_count": 2}
{"name": "NNRat.instMetricSpace", "kind": "instance", "module": "Mathlib.Topology.Instances.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.dist_eq", "kind": "theorem", "module": "Mathlib.Topology.Instances.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.nndist_eq", "kind": "theorem", "module": "Mathlib.Topology.Instances.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.instIsTopologicalSemiring", "kind": "instance", "module": "Mathlib.Topology.Instances.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.instContinuousSub", "kind": "instance", "module": "Mathlib.Topology.Instances.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.instOrderTopology", "kind": "instance", "module": "Mathlib.Topology.Instances.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.instContinuousInv₀", "kind": "instance", "module": "Mathlib.Topology.Instances.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.instContinuousSMulRatReal", "kind": "instance", "module": "Mathlib.Topology.Instances.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.instContinuousSMulOfIsScalarTowerOfRat", "kind": "instance", "module": "Mathlib.Topology.Instances.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNRat.instContinuousSMulNNReal", "kind": "instance", "module": "Mathlib.Topology.Instances.Rat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.Instances.RatLemmas.0.termℚ∞", "kind": "definition", "module": "Mathlib.Topology.Instances.RatLemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "_private.Mathlib.Topology.Instances.RatLemmas.0._aux_Mathlib_Topology_Instances_RatLemmas___unexpand_OnePoint_1", "kind": "definition", "module": "Mathlib.Topology.Instances.RatLemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.interior_compact_eq_empty", "kind": "theorem", "module": "Mathlib.Topology.Instances.RatLemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.dense_compl_compact", "kind": "theorem", "module": "Mathlib.Topology.Instances.RatLemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Rat.cocompact_inf_nhds_neBot", "kind": "instance", "module": "Mathlib.Topology.Instances.RatLemmas", "is_tactic_proof": true, "tactics": ["refine", "rintro", "exact"], "tactic_count": 3}
{"name": "Rat.not_countably_generated_cocompact", "kind": "theorem", "module": "Mathlib.Topology.Instances.RatLemmas", "is_tactic_proof": true, "tactics": ["intro", "rcases", "rw", "obtain", "exact"], "tactic_count": 5}
{"name": "Rat.not_countably_generated_nhds_infty_opc", "kind": "theorem", "module": "Mathlib.Topology.Instances.RatLemmas", "is_tactic_proof": true, "tactics": ["intro", "have", "rw", "exact"], "tactic_count": 4}
{"name": "Rat.not_firstCountableTopology_opc", "kind": "theorem", "module": "Mathlib.Topology.Instances.RatLemmas", "is_tactic_proof": true, "tactics": ["intro", "exact"], "tactic_count": 2}
{"name": "Rat.not_secondCountableTopology_opc", "kind": "theorem", "module": "Mathlib.Topology.Instances.RatLemmas", "is_tactic_proof": true, "tactics": ["intro", "exact"], "tactic_count": 2}
{"name": "Rat.instTotallyDisconnectedSpace", "kind": "instance", "module": "Mathlib.Topology.Instances.RatLemmas", "is_tactic_proof": true, "tactics": ["clear", "refine", "by_contra", "wlog", "apply", "rcases", "have", "rw", "have", "exact"], "tactic_count": 10}
{"name": "map_real_smul", "kind": "theorem", "module": "Mathlib.Topology.Instances.RealVectorSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.toRealLinearMap", "kind": "definition", "module": "Mathlib.Topology.Instances.RealVectorSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddMonoidHom.coe_toRealLinearMap", "kind": "theorem", "module": "Mathlib.Topology.Instances.RealVectorSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AddEquiv.toRealLinearEquiv", "kind": "definition", "module": "Mathlib.Topology.Instances.RealVectorSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.isScalarTower", "kind": "instance", "module": "Mathlib.Topology.Instances.RealVectorSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.isTopologicalBasis_Ioo_rat", "kind": "theorem", "module": "Mathlib.Topology.Instances.Real.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.cobounded_eq", "kind": "theorem", "module": "Mathlib.Topology.Instances.Real.Lemmas", "is_tactic_proof": true, "tactics": ["simp", "lemma", "lemma"], "tactic_count": 3}
{"name": "Real.mem_closure_iff", "kind": "theorem", "module": "Mathlib.Topology.Instances.Real.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.uniformContinuous_inv", "kind": "theorem", "module": "Mathlib.Topology.Instances.Real.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.uniformContinuous_abs", "kind": "theorem", "module": "Mathlib.Topology.Instances.Real.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.continuous_inv", "kind": "theorem", "module": "Mathlib.Topology.Instances.Real.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.uniformContinuous_mul", "kind": "theorem", "module": "Mathlib.Topology.Instances.Real.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.totallyBounded_ball", "kind": "theorem", "module": "Mathlib.Topology.Instances.Real.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.subfield_eq_of_closed", "kind": "theorem", "module": "Mathlib.Topology.Instances.Real.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "refine", "rintro", "exact"], "tactic_count": 4}
{"name": "Real.exists_seq_rat_strictMono_tendsto", "kind": "theorem", "module": "Mathlib.Topology.Instances.Real.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.exists_seq_rat_strictAnti_tendsto", "kind": "theorem", "module": "Mathlib.Topology.Instances.Real.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "closure_ordConnected_inter_rat", "kind": "theorem", "module": "Mathlib.Topology.Instances.Real.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "closure_of_rat_image_lt", "kind": "theorem", "module": "Mathlib.Topology.Instances.Real.Lemmas", "is_tactic_proof": true, "tactics": ["convert", "congr", "exact", "exact", "lemma", "lemma", "closure"], "tactic_count": 7}
{"name": "Function.Periodic.compact_of_continuous", "kind": "theorem", "module": "Mathlib.Topology.Instances.Real.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Function.Periodic.isBounded_of_continuous", "kind": "theorem", "module": "Mathlib.Topology.Instances.Real.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.tendsto_atTop_csSup_of_monotoneOn_bddAbove_nat_Ici", "kind": "theorem", "module": "Mathlib.Topology.Instances.Real.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "rw", "rw", "exact"], "tactic_count": 4}
{"name": "Real.tendsto_atTop_csInf_of_antitoneOn_bddBelow_nat_Ici", "kind": "theorem", "module": "Mathlib.Topology.Instances.Real.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "rw", "rw", "exact"], "tactic_count": 4}
{"name": "Real.isLUB_of_tendsto_monotone_bddAbove", "kind": "theorem", "module": "Mathlib.Topology.Instances.Real.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Real.isGLB_of_tendsto_antitone_bddBelow", "kind": "theorem", "module": "Mathlib.Topology.Instances.Real.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
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{"name": "Shrink.homeomorph", "kind": "definition", "module": "Mathlib.Topology.Instances.Shrink", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instTopologicalSpaceSignType", "kind": "instance", "module": "Mathlib.Topology.Instances.Sign", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDiscreteTopologySignType", "kind": "instance", "module": "Mathlib.Topology.Instances.Sign", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousAt_sign_of_pos", "kind": "theorem", "module": "Mathlib.Topology.Instances.Sign", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
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{"name": "_private.Mathlib.Topology.Instances.TrivSqZeroExt.0._aux_Mathlib_Topology_Instances_TrivSqZeroExt___unexpand_TrivSqZeroExt_1", "kind": "definition", "module": "Mathlib.Topology.Instances.TrivSqZeroExt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TrivSqZeroExt.instTopologicalSpace", "kind": "instance", "module": "Mathlib.Topology.Instances.TrivSqZeroExt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TrivSqZeroExt.instT2Space", "kind": "instance", "module": "Mathlib.Topology.Instances.TrivSqZeroExt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TrivSqZeroExt.nhds_def", "kind": "theorem", "module": "Mathlib.Topology.Instances.TrivSqZeroExt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TrivSqZeroExt.nhds_inl", "kind": "theorem", "module": "Mathlib.Topology.Instances.TrivSqZeroExt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TrivSqZeroExt.nhds_inr", "kind": "theorem", "module": "Mathlib.Topology.Instances.TrivSqZeroExt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TrivSqZeroExt.continuous_fst", "kind": "theorem", "module": "Mathlib.Topology.Instances.TrivSqZeroExt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TrivSqZeroExt.continuous_snd", "kind": "theorem", "module": "Mathlib.Topology.Instances.TrivSqZeroExt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TrivSqZeroExt.continuous_inl", "kind": "theorem", "module": "Mathlib.Topology.Instances.TrivSqZeroExt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TrivSqZeroExt.continuous_inr", "kind": "theorem", "module": "Mathlib.Topology.Instances.TrivSqZeroExt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TrivSqZeroExt.IsEmbedding.inl", "kind": "theorem", "module": "Mathlib.Topology.Instances.TrivSqZeroExt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TrivSqZeroExt.IsEmbedding.inr", "kind": "theorem", "module": "Mathlib.Topology.Instances.TrivSqZeroExt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TrivSqZeroExt.fstCLM", "kind": "definition", "module": "Mathlib.Topology.Instances.TrivSqZeroExt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TrivSqZeroExt.sndCLM", "kind": "definition", "module": "Mathlib.Topology.Instances.TrivSqZeroExt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TrivSqZeroExt.inlCLM", "kind": "definition", "module": "Mathlib.Topology.Instances.TrivSqZeroExt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TrivSqZeroExt.inrCLM", "kind": "definition", "module": "Mathlib.Topology.Instances.TrivSqZeroExt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TrivSqZeroExt.instContinuousAdd", "kind": "instance", "module": "Mathlib.Topology.Instances.TrivSqZeroExt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TrivSqZeroExt.instContinuousMulOfContinuousSMulMulOppositeOfContinuousAdd", "kind": "instance", "module": "Mathlib.Topology.Instances.TrivSqZeroExt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TrivSqZeroExt.instContinuousNeg", "kind": "instance", "module": "Mathlib.Topology.Instances.TrivSqZeroExt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TrivSqZeroExt.topologicalSemiring", "kind": "theorem", "module": "Mathlib.Topology.Instances.TrivSqZeroExt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TrivSqZeroExt.instIsTopologicalRingOfIsTopologicalAddGroupOfContinuousSMulMulOpposite", "kind": "instance", "module": "Mathlib.Topology.Instances.TrivSqZeroExt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TrivSqZeroExt.instContinuousConstSMul", "kind": "instance", "module": "Mathlib.Topology.Instances.TrivSqZeroExt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TrivSqZeroExt.instContinuousSMul", "kind": "instance", "module": "Mathlib.Topology.Instances.TrivSqZeroExt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TrivSqZeroExt.hasSum_inl", "kind": "theorem", "module": "Mathlib.Topology.Instances.TrivSqZeroExt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TrivSqZeroExt.hasSum_inr", "kind": "theorem", "module": "Mathlib.Topology.Instances.TrivSqZeroExt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TrivSqZeroExt.hasSum_fst", "kind": "theorem", "module": "Mathlib.Topology.Instances.TrivSqZeroExt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TrivSqZeroExt.hasSum_snd", "kind": "theorem", "module": "Mathlib.Topology.Instances.TrivSqZeroExt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TrivSqZeroExt.instUniformSpace", "kind": "instance", "module": "Mathlib.Topology.Instances.TrivSqZeroExt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TrivSqZeroExt.instCompleteSpace", "kind": "instance", "module": "Mathlib.Topology.Instances.TrivSqZeroExt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TrivSqZeroExt.instIsUniformAddGroup", "kind": "instance", "module": "Mathlib.Topology.Instances.TrivSqZeroExt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TrivSqZeroExt.uniformity_def", "kind": "theorem", "module": "Mathlib.Topology.Instances.TrivSqZeroExt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TrivSqZeroExt.uniformContinuous_fst", "kind": "theorem", "module": "Mathlib.Topology.Instances.TrivSqZeroExt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TrivSqZeroExt.uniformContinuous_snd", "kind": "theorem", "module": "Mathlib.Topology.Instances.TrivSqZeroExt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TrivSqZeroExt.uniformContinuous_inl", "kind": "theorem", "module": "Mathlib.Topology.Instances.TrivSqZeroExt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TrivSqZeroExt.uniformContinuous_inr", "kind": "theorem", "module": "Mathlib.Topology.Instances.TrivSqZeroExt", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.instTopologicalSpace", "kind": "instance", "module": "Mathlib.Topology.Instances.ZMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ZMod.instDiscreteTopology", "kind": "instance", "module": "Mathlib.Topology.Instances.ZMod", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.instDiscreteTopologySubtypeRealMemAddSubgroupZmultiples", "kind": "instance", "module": "Mathlib.Topology.Instances.ZMultiples", "is_tactic_proof": true, "tactics": ["rcases", "rw", "exact", "rw", "refine", "ext", "obtain", "simp"], "tactic_count": 8}
{"name": "Int.tendsto_coe_cofinite", "kind": "theorem", "module": "Mathlib.Topology.Instances.ZMultiples", "is_tactic_proof": true, "tactics": ["apply", "rw", "infer_instance"], "tactic_count": 3}
{"name": "Int.tendsto_zmultiplesHom_cofinite", "kind": "theorem", "module": "Mathlib.Topology.Instances.ZMultiples", "is_tactic_proof": true, "tactics": ["apply", "rw", "infer_instance"], "tactic_count": 3}
{"name": "AddSubgroup.tendsto_zmultiples_subtype_cofinite", "kind": "theorem", "module": "Mathlib.Topology.Instances.ZMultiples", "is_tactic_proof": true, "tactics": ["refine", "rw", "infer_instance"], "tactic_count": 3}
{"name": "IsPreirreducible", "kind": "definition", "module": "Mathlib.Topology.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIrreducible", "kind": "definition", "module": "Mathlib.Topology.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIrreducible.nonempty", "kind": "theorem", "module": "Mathlib.Topology.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIrreducible.isPreirreducible", "kind": "theorem", "module": "Mathlib.Topology.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isPreirreducible_empty", "kind": "theorem", "module": "Mathlib.Topology.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Subsingleton.isPreirreducible", "kind": "theorem", "module": "Mathlib.Topology.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isPreirreducible_singleton", "kind": "theorem", "module": "Mathlib.Topology.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isIrreducible_singleton", "kind": "theorem", "module": "Mathlib.Topology.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isPreirreducible_iff_closure", "kind": "theorem", "module": "Mathlib.Topology.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isIrreducible_iff_closure", "kind": "theorem", "module": "Mathlib.Topology.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_preirreducible", "kind": "theorem", "module": "Mathlib.Topology.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "irreducibleComponents", "kind": "definition", "module": "Mathlib.Topology.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosed_of_mem_irreducibleComponents", "kind": "theorem", "module": "Mathlib.Topology.Irreducible", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "irreducibleComponents_eq_maximals_closed", "kind": "theorem", "module": "Mathlib.Topology.Irreducible", "is_tactic_proof": true, "tactics": ["ext", "constructor", "intro", "exact", "intro", "refine", "have", "exact"], "tactic_count": 8}
{"name": "exists_mem_irreducibleComponents_subset_of_isIrreducible", "kind": "theorem", "module": "Mathlib.Topology.Irreducible", "is_tactic_proof": true, "tactics": ["obtain", "use", "exact"], "tactic_count": 3}
{"name": "irreducibleComponent", "kind": "definition", "module": "Mathlib.Topology.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "irreducibleComponent_property", "kind": "theorem", "module": "Mathlib.Topology.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_irreducibleComponent", "kind": "theorem", "module": "Mathlib.Topology.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isIrreducible_irreducibleComponent", "kind": "theorem", "module": "Mathlib.Topology.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_irreducibleComponent", "kind": "theorem", "module": "Mathlib.Topology.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "irreducibleComponent_mem_irreducibleComponents", "kind": "theorem", "module": "Mathlib.Topology.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosed_irreducibleComponent", "kind": "theorem", "module": "Mathlib.Topology.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IrreducibleSpace.isIrreducible_univ", "kind": "theorem", "module": "Mathlib.Topology.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "irreducibleSpace_def", "kind": "theorem", "module": "Mathlib.Topology.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nonempty_preirreducible_inter", "kind": "theorem", "module": "Mathlib.Topology.Irreducible", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsOpen.dense", "kind": "theorem", "module": "Mathlib.Topology.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPreirreducible.image", "kind": "theorem", "module": "Mathlib.Topology.Irreducible", "is_tactic_proof": true, "tactics": ["rintro", "rw", "rcases", "rcases", "have", "rw", "rw", "rcases", "refine", "all_goals", "rw", "apply", "show", "simp"], "tactic_count": 14}
{"name": "IsIrreducible.image", "kind": "theorem", "module": "Mathlib.Topology.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.preirreducibleSpace", "kind": "theorem", "module": "Mathlib.Topology.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.irreducibleSpace", "kind": "theorem", "module": "Mathlib.Topology.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPreirreducible.of_subtype", "kind": "theorem", "module": "Mathlib.Topology.Irreducible", "is_tactic_proof": true, "tactics": ["rw", "refine", "exact"], "tactic_count": 3}
{"name": "IsIrreducible.of_subtype", "kind": "theorem", "module": "Mathlib.Topology.Irreducible", "is_tactic_proof": true, "tactics": ["exact"], "tactic_count": 1}
{"name": "isPreirreducible_iff_preirreducibleSpace", "kind": "theorem", "module": "Mathlib.Topology.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isIrreducible_iff_irreducibleSpace", "kind": "theorem", "module": "Mathlib.Topology.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instPreirreducibleSpaceOfSubsingleton", "kind": "instance", "module": "Mathlib.Topology.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIrreducibleSpaceCofiniteTopologyOfInfinite", "kind": "instance", "module": "Mathlib.Topology.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "irreducibleComponents_eq_singleton", "kind": "theorem", "module": "Mathlib.Topology.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isIrreducible_iff_sInter", "kind": "theorem", "module": "Mathlib.Topology.Irreducible", "is_tactic_proof": true, "tactics": ["classical", "refine", "induction", "empty", "insert", "rw", "rw", "exact", "simpa", "intro", "simpa"], "tactic_count": 11}
{"name": "isPreirreducible_iff_isClosed_union_isClosed", "kind": "theorem", "module": "Mathlib.Topology.Irreducible", "is_tactic_proof": false, "tactics": ["refine", "compl_surjective.forall.trans", "simp", "refine", "rw"], "tactic_count": 5}
{"name": "isIrreducible_iff_sUnion_isClosed", "kind": "theorem", "module": "Mathlib.Topology.Irreducible", "is_tactic_proof": true, "tactics": ["simp", "refine", "simp_rw", "refine", "simp", "not_disjoint_iff_nonempty_inter]"], "tactic_count": 6}
{"name": "subset_closure_inter_of_isPreirreducible_of_isOpen", "kind": "theorem", "module": "Mathlib.Topology.Irreducible", "is_tactic_proof": true, "tactics": ["by_contra", "obtain", "exact"], "tactic_count": 3}
{"name": "IsPreirreducible.subset_irreducible", "kind": "theorem", "module": "Mathlib.Topology.Irreducible", "is_tactic_proof": true, "tactics": ["obtain", "replace", "refine", "rintro", "classical", "obtain", "refine", "simp", "intro", "simp", "rcases", "exacts", "replace", "exact"], "tactic_count": 14}
{"name": "IsPreirreducible.open_subset", "kind": "theorem", "module": "Mathlib.Topology.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPreirreducible.interior", "kind": "theorem", "module": "Mathlib.Topology.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPreirreducible.preimage", "kind": "theorem", "module": "Mathlib.Topology.Irreducible", "is_tactic_proof": true, "tactics": ["rintro", "obtain", "ht", "cases", "exact"], "tactic_count": 5}
{"name": "IsPreirreducible.preimage_of_dense_isPreirreducible_fiber", "kind": "theorem", "module": "Mathlib.Topology.Irreducible", "is_tactic_proof": true, "tactics": ["rintro", "obtain", "obtain", "mem_closure_iff.mp", "obtain", "refine"], "tactic_count": 6}
{"name": "IsPreirreducible.preimage_of_isPreirreducible_fiber", "kind": "theorem", "module": "Mathlib.Topology.Irreducible", "is_tactic_proof": true, "tactics": ["refine", "simp"], "tactic_count": 2}
{"name": "preimage_mem_irreducibleComponents_of_isPreirreducible_fiber", "kind": "theorem", "module": "Mathlib.Topology.Irreducible", "is_tactic_proof": true, "tactics": ["obtain", "have", "obtain", "obtain", "exact", "have", "refine", "exact", "hV.2", "rw", "exact"], "tactic_count": 11}
{"name": "image_mem_irreducibleComponents_of_isPreirreducible_fiber", "kind": "theorem", "module": "Mathlib.Topology.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "irreducibleComponentsEquivOfIsPreirreducibleFiber", "kind": "definition", "module": "Mathlib.Topology.Irreducible", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDiscrete.subsingleton_of_isPreirreducible", "kind": "theorem", "module": "Mathlib.Topology.Irreducible", "is_tactic_proof": true, "tactics": ["intro", "obtain", "obtain", "obtain", "exact"], "tactic_count": 5}
{"name": "Topology.reorderRestrictProd", "kind": "definition", "module": "Mathlib.Topology.IsClosedRestrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.reorderRestrictProd_of_mem", "kind": "theorem", "module": "Mathlib.Topology.IsClosedRestrict", "is_tactic_proof": true, "tactics": ["have", "simp"], "tactic_count": 2}
{"name": "Topology.reorderRestrictProd_of_compl", "kind": "theorem", "module": "Mathlib.Topology.IsClosedRestrict", "is_tactic_proof": true, "tactics": ["have", "simp"], "tactic_count": 2}
{"name": "Topology.restrict_compl_reorderRestrictProd", "kind": "theorem", "module": "Mathlib.Topology.IsClosedRestrict", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Topology.continuous_reorderRestrictProd", "kind": "theorem", "module": "Mathlib.Topology.IsClosedRestrict", "is_tactic_proof": true, "tactics": ["refine", "simp", "split_ifs", "fun_prop", "exact"], "tactic_count": 5}
{"name": "Topology.reorderRestrictProd_mem_preimage_image_restrict", "kind": "theorem", "module": "Mathlib.Topology.IsClosedRestrict", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Topology.reorderRestrictProd_restrict_compl", "kind": "theorem", "module": "Mathlib.Topology.IsClosedRestrict", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Homeomorph.preimageImageRestrict", "kind": "definition", "module": "Mathlib.Topology.IsClosedRestrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.image_snd_preimageImageRestrict", "kind": "theorem", "module": "Mathlib.Topology.IsClosedRestrict", "is_tactic_proof": true, "tactics": ["ext", "simp", "exists_prop]", "constructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 8}
{"name": "IsCompact.isClosed_image_restrict", "kind": "theorem", "module": "Mathlib.Topology.IsClosedRestrict", "is_tactic_proof": true, "tactics": ["rw", "have", "refine", "rw", "exact"], "tactic_count": 5}
{"name": "isClosedMap_restrict_of_compactSpace", "kind": "theorem", "module": "Mathlib.Topology.IsClosedRestrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.isClosed_image_eval", "kind": "theorem", "module": "Mathlib.Topology.IsClosedRestrict", "is_tactic_proof": false, "tactics": ["suffices", "have", "rwa", "exact"], "tactic_count": 4}
{"name": "IsLocalHomeomorphOn", "kind": "definition", "module": "Mathlib.Topology.IsLocalHomeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLocalHomeomorphOn_iff_isOpenEmbedding_restrict", "kind": "theorem", "module": "Mathlib.Topology.IsLocalHomeomorph", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact", "obtain", "have", "refine", "rw", "obtain", "haveI", "exact", "mem_interior_iff_mem_nhds.mpr"], "tactic_count": 11}
{"name": "IsLocalHomeomorphOn.discreteTopology_of_image", "kind": "theorem", "module": "Mathlib.Topology.IsLocalHomeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalHomeomorphOn.isDiscrete_of_image", "kind": "theorem", "module": "Mathlib.Topology.IsLocalHomeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalHomeomorphOn.discreteTopology_image_iff", "kind": "theorem", "module": "Mathlib.Topology.IsLocalHomeomorph", "is_tactic_proof": true, "tactics": ["refine", "simp_rw", "rintro", "obtain", "refine", "simpa", "ext"], "tactic_count": 7}
{"name": "IsLocalHomeomorphOn.isDiscrete_image_iff", "kind": "theorem", "module": "Mathlib.Topology.IsLocalHomeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalHomeomorphOn.mk", "kind": "theorem", "module": "Mathlib.Topology.IsLocalHomeomorph", "is_tactic_proof": true, "tactics": ["intro", "obtain", "exact", "toFun", "map_source", "left_inv", "right_inv", "continuousOn_toFun", "hx,"], "tactic_count": 9}
{"name": "IsLocalHomeomorphOn.OpenPartialHomeomorph.isLocalHomeomorphOn", "kind": "theorem", "module": "Mathlib.Topology.IsLocalHomeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalHomeomorphOn.mono", "kind": "theorem", "module": "Mathlib.Topology.IsLocalHomeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalHomeomorphOn.of_comp_left", "kind": "theorem", "module": "Mathlib.Topology.IsLocalHomeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalHomeomorphOn.of_comp_right", "kind": "theorem", "module": "Mathlib.Topology.IsLocalHomeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalHomeomorphOn.map_nhds_eq", "kind": "theorem", "module": "Mathlib.Topology.IsLocalHomeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalHomeomorphOn.continuousAt", "kind": "theorem", "module": "Mathlib.Topology.IsLocalHomeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalHomeomorphOn.continuousOn", "kind": "theorem", "module": "Mathlib.Topology.IsLocalHomeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalHomeomorphOn.comp", "kind": "theorem", "module": "Mathlib.Topology.IsLocalHomeomorph", "is_tactic_proof": true, "tactics": ["intro", "obtain", "obtain", "exact"], "tactic_count": 4}
{"name": "IsLocalHomeomorph", "kind": "definition", "module": "Mathlib.Topology.IsLocalHomeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.isLocalHomeomorph", "kind": "theorem", "module": "Mathlib.Topology.IsLocalHomeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLocalHomeomorph_iff_isLocalHomeomorphOn_univ", "kind": "theorem", "module": "Mathlib.Topology.IsLocalHomeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalHomeomorph.isLocalHomeomorphOn", "kind": "theorem", "module": "Mathlib.Topology.IsLocalHomeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLocalHomeomorph_iff_isOpenEmbedding_restrict", "kind": "theorem", "module": "Mathlib.Topology.IsLocalHomeomorph", "is_tactic_proof": true, "tactics": ["simp_rw", "imp_iff_right"], "tactic_count": 2}
{"name": "Topology.IsOpenEmbedding.isLocalHomeomorph", "kind": "theorem", "module": "Mathlib.Topology.IsLocalHomeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalHomeomorph.comap_discreteTopology", "kind": "theorem", "module": "Mathlib.Topology.IsLocalHomeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalHomeomorph.discreteTopology_range_iff", "kind": "theorem", "module": "Mathlib.Topology.IsLocalHomeomorph", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsLocalHomeomorph.discreteTopology_iff_of_surjective", "kind": "theorem", "module": "Mathlib.Topology.IsLocalHomeomorph", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsLocalHomeomorph.mk", "kind": "theorem", "module": "Mathlib.Topology.IsLocalHomeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalHomeomorph.Homeomorph.isLocalHomeomorph", "kind": "theorem", "module": "Mathlib.Topology.IsLocalHomeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalHomeomorph.isLocallyInjective", "kind": "theorem", "module": "Mathlib.Topology.IsLocalHomeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalHomeomorph.of_comp", "kind": "theorem", "module": "Mathlib.Topology.IsLocalHomeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalHomeomorph.map_nhds_eq", "kind": "theorem", "module": "Mathlib.Topology.IsLocalHomeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalHomeomorph.continuous", "kind": "theorem", "module": "Mathlib.Topology.IsLocalHomeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalHomeomorph.isOpenMap", "kind": "theorem", "module": "Mathlib.Topology.IsLocalHomeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalHomeomorph.comp", "kind": "theorem", "module": "Mathlib.Topology.IsLocalHomeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalHomeomorph.isOpenEmbedding_of_injective", "kind": "theorem", "module": "Mathlib.Topology.IsLocalHomeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalHomeomorph.toHomeomorphOfBijective", "kind": "definition", "module": "Mathlib.Topology.IsLocalHomeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalHomeomorph.isOpenEmbedding_of_comp", "kind": "theorem", "module": "Mathlib.Topology.IsLocalHomeomorph", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalHomeomorph.isTopologicalBasis", "kind": "theorem", "module": "Mathlib.Topology.IsLocalHomeomorph", "is_tactic_proof": true, "tactics": ["refine", "rintro", "refine", "rwa", "obtain", "refine", "ext", "apply", "rw", "f.source_inter_preimage_inv_preimage]"], "tactic_count": 10}
{"name": "closedPoints", "kind": "definition", "module": "Mathlib.Topology.JacobsonSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_closedPoints_iff", "kind": "theorem", "module": "Mathlib.Topology.JacobsonSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "preimage_closedPoints_subset", "kind": "theorem", "module": "Mathlib.Topology.JacobsonSpace", "is_tactic_proof": true, "tactics": ["intro", "rw", "convert", "rw"], "tactic_count": 4}
{"name": "Topology.IsClosedEmbedding.preimage_closedPoints", "kind": "theorem", "module": "Mathlib.Topology.JacobsonSpace", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "closedPoints_eq_univ", "kind": "theorem", "module": "Mathlib.Topology.JacobsonSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "closure_closedPoints", "kind": "theorem", "module": "Mathlib.Topology.JacobsonSpace", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "jacobsonSpace_iff_locallyClosed", "kind": "theorem", "module": "Mathlib.Topology.JacobsonSpace", "is_tactic_proof": true, "tactics": ["rw", "constructor", "simp_rw", "intro", "have", "refine", "nth_rw", "rw", "exact", "rw", "exact", "intro", "refine", "rw", "intro", "have", "rw", "exact"], "tactic_count": 18}
{"name": "nonempty_inter_closedPoints", "kind": "theorem", "module": "Mathlib.Topology.JacobsonSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosed_singleton_of_isLocallyClosed_singleton", "kind": "theorem", "module": "Mathlib.Topology.JacobsonSpace", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Topology.IsOpenEmbedding.preimage_closedPoints", "kind": "theorem", "module": "Mathlib.Topology.JacobsonSpace", "is_tactic_proof": true, "tactics": ["apply", "intro", "apply", "rw", "exact"], "tactic_count": 5}
{"name": "JacobsonSpace.of_isOpenEmbedding", "kind": "theorem", "module": "Mathlib.Topology.JacobsonSpace", "is_tactic_proof": true, "tactics": ["rw", "intro", "obtain", "nonempty_inter_closedPoints", "exact"], "tactic_count": 5}
{"name": "JacobsonSpace.of_isClosedEmbedding", "kind": "theorem", "module": "Mathlib.Topology.JacobsonSpace", "is_tactic_proof": true, "tactics": ["rw", "intro", "obtain", "nonempty_inter_closedPoints", "exact"], "tactic_count": 5}
{"name": "JacobsonSpace.discreteTopology", "kind": "theorem", "module": "Mathlib.Topology.JacobsonSpace", "is_tactic_proof": false, "tactics": ["have", "rw", "exact", "have", "rw", "intro", "rw", "refine", "rw", "trivial"], "tactic_count": 10}
{"name": "instDiscreteTopologyOfFiniteOfJacobsonSpace", "kind": "instance", "module": "Mathlib.Topology.JacobsonSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instJacobsonSpaceOfT1Space", "kind": "instance", "module": "Mathlib.Topology.JacobsonSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.IsOpenCover.jacobsonSpace_iff", "kind": "theorem", "module": "Mathlib.Topology.JacobsonSpace", "is_tactic_proof": true, "tactics": ["refine", "rw", "intro", "rw", "obtain", "obtain", "refine", "by_cases", "convert_to", "ext", "apply", "convert", "continuous_subtype_val", "ext", "simp", "convert", "rw", "intro", "exact"], "tactic_count": 19}
{"name": "topologicalKrullDim", "kind": "definition", "module": "Mathlib.Topology.KrullDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsInducing.topologicalKrullDim_le", "kind": "theorem", "module": "Mathlib.Topology.KrullDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsHomeomorph.topologicalKrullDim_eq", "kind": "theorem", "module": "Mathlib.Topology.KrullDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "topologicalKrullDim_subspace_le", "kind": "theorem", "module": "Mathlib.Topology.KrullDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "topologicalKrullDim_zero_of_discreteTopology", "kind": "theorem", "module": "Mathlib.Topology.KrullDimension", "is_tactic_proof": true, "tactics": ["refine", "obtain", "rwa"], "tactic_count": 3}
{"name": "instTopologicalSpaceList", "kind": "instance", "module": "Mathlib.Topology.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhds_list", "kind": "theorem", "module": "Mathlib.Topology.List", "is_tactic_proof": true, "tactics": ["refine", "intro", "induction", "nil", "cons", "ih", "suffices", "simpa", "exact", "intro", "rcases", "clear", "have", "induction", "nil", "exists", "simp", "exact", "cons", "rcases", "rcases", "exact", "rcases", "have", "refine", "have", "have", "refine", "replace", "simp", "exact", "refine", "exact"], "tactic_count": 33}
{"name": "nhds_nil", "kind": "theorem", "module": "Mathlib.Topology.List", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "nhds_cons", "kind": "theorem", "module": "Mathlib.Topology.List", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.tendsto_cons", "kind": "theorem", "module": "Mathlib.Topology.List", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.Tendsto.cons", "kind": "theorem", "module": "Mathlib.Topology.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.tendsto_cons_iff", "kind": "theorem", "module": "Mathlib.Topology.List", "is_tactic_proof": false, "tactics": ["have", "simp", "simp", "rw"], "tactic_count": 4}
{"name": "List.continuous_cons", "kind": "theorem", "module": "Mathlib.Topology.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.tendsto_nhds", "kind": "theorem", "module": "Mathlib.Topology.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.instDiscreteTopology", "kind": "instance", "module": "Mathlib.Topology.List", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "List.continuousAt_length", "kind": "theorem", "module": "Mathlib.Topology.List", "is_tactic_proof": true, "tactics": ["simp", "refine", "exact", "intro", "dsimp", "refine", "exact"], "tactic_count": 7}
{"name": "List.tendsto_insertIdx'", "kind": "theorem", "module": "Mathlib.Topology.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.tendsto_insertIdx", "kind": "theorem", "module": "Mathlib.Topology.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.continuous_insertIdx", "kind": "theorem", "module": "Mathlib.Topology.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.tendsto_eraseIdx", "kind": "theorem", "module": "Mathlib.Topology.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.continuous_eraseIdx", "kind": "theorem", "module": "Mathlib.Topology.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.tendsto_prod", "kind": "theorem", "module": "Mathlib.Topology.List", "is_tactic_proof": true, "tactics": ["induction", "nil", "cons", "simp_rw", "have", "rw", "exact"], "tactic_count": 7}
{"name": "List.continuous_prod", "kind": "theorem", "module": "Mathlib.Topology.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.instTopologicalSpace", "kind": "instance", "module": "Mathlib.Topology.List", "is_tactic_proof": true, "tactics": ["unfold"], "tactic_count": 1}
{"name": "List.Vector.tendsto_cons", "kind": "theorem", "module": "Mathlib.Topology.List", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "List.Vector.tendsto_insertIdx", "kind": "theorem", "module": "Mathlib.Topology.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.continuous_insertIdx'", "kind": "theorem", "module": "Mathlib.Topology.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.continuous_insertIdx", "kind": "theorem", "module": "Mathlib.Topology.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.continuousAt_eraseIdx", "kind": "theorem", "module": "Mathlib.Topology.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "List.Vector.continuous_eraseIdx", "kind": "theorem", "module": "Mathlib.Topology.List", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.restrictPreimage_isInducing", "kind": "theorem", "module": "Mathlib.Topology.LocalAtTarget", "is_tactic_proof": false, "tactics": ["simp_rw", "intro", "rw"], "tactic_count": 3}
{"name": "Set.restrictPreimage_isEmbedding", "kind": "theorem", "module": "Mathlib.Topology.LocalAtTarget", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.restrictPreimage_isOpenEmbedding", "kind": "theorem", "module": "Mathlib.Topology.LocalAtTarget", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.restrictPreimage_isClosedEmbedding", "kind": "theorem", "module": "Mathlib.Topology.LocalAtTarget", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosedMap.restrictPreimage", "kind": "theorem", "module": "Mathlib.Topology.LocalAtTarget", "is_tactic_proof": true, "tactics": ["intro", "suffices", "simpa", "exact"], "tactic_count": 4}
{"name": "IsOpenMap.restrictPreimage", "kind": "theorem", "module": "Mathlib.Topology.LocalAtTarget", "is_tactic_proof": true, "tactics": ["intro", "suffices", "simpa", "exact"], "tactic_count": 4}
{"name": "GeneralizingMap.restrictPreimage", "kind": "theorem", "module": "Mathlib.Topology.LocalAtTarget", "is_tactic_proof": true, "tactics": ["intro", "obtain", "use", "simp"], "tactic_count": 4}
{"name": "IsProperMap.restrictPreimage", "kind": "theorem", "module": "Mathlib.Topology.LocalAtTarget", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "TopologicalSpace.IsOpenCover.isOpen_iff_inter", "kind": "theorem", "module": "Mathlib.Topology.LocalAtTarget", "is_tactic_proof": true, "tactics": ["constructor", "exact", "intro", "simpa"], "tactic_count": 4}
{"name": "TopologicalSpace.IsOpenCover.isOpen_iff_coe_preimage", "kind": "theorem", "module": "Mathlib.Topology.LocalAtTarget", "is_tactic_proof": true, "tactics": ["simp", "image_preimage_eq_inter_range]"], "tactic_count": 2}
{"name": "TopologicalSpace.IsOpenCover.isClosed_iff_coe_preimage", "kind": "theorem", "module": "Mathlib.Topology.LocalAtTarget", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "TopologicalSpace.IsOpenCover.isLocallyClosed_iff_coe_preimage", "kind": "theorem", "module": "Mathlib.Topology.LocalAtTarget", "is_tactic_proof": false, "tactics": ["have", "simp"], "tactic_count": 2}
{"name": "TopologicalSpace.IsOpenCover.isOpenMap_iff_restrictPreimage", "kind": "theorem", "module": "Mathlib.Topology.LocalAtTarget", "is_tactic_proof": true, "tactics": ["refine", "rw", "intro", "convert", "ext", "suffices", "exact"], "tactic_count": 7}
{"name": "TopologicalSpace.IsOpenCover.isClosedMap_iff_restrictPreimage", "kind": "theorem", "module": "Mathlib.Topology.LocalAtTarget", "is_tactic_proof": true, "tactics": ["refine", "rw", "intro", "convert", "ext", "suffices", "exact"], "tactic_count": 7}
{"name": "TopologicalSpace.IsOpenCover.isInducing_iff_restrictPreimage", "kind": "theorem", "module": "Mathlib.Topology.LocalAtTarget", "is_tactic_proof": false, "tactics": ["simp_rw", "constructor", "intro", "rw", "intro", "obtain", "simpa", "preimage_mem_comap"], "tactic_count": 8}
{"name": "TopologicalSpace.IsOpenCover.isEmbedding_iff_restrictPreimage", "kind": "theorem", "module": "Mathlib.Topology.LocalAtTarget", "is_tactic_proof": true, "tactics": ["simpa", "and_congr"], "tactic_count": 2}
{"name": "TopologicalSpace.IsOpenCover.isOpenEmbedding_iff_restrictPreimage", "kind": "theorem", "module": "Mathlib.Topology.LocalAtTarget", "is_tactic_proof": true, "tactics": ["simp_rw", "apply", "exact", "simp_rw", "exact"], "tactic_count": 5}
{"name": "TopologicalSpace.IsOpenCover.isClosedEmbedding_iff_restrictPreimage", "kind": "theorem", "module": "Mathlib.Topology.LocalAtTarget", "is_tactic_proof": true, "tactics": ["simp_rw", "apply", "exact", "simp_rw", "exact"], "tactic_count": 5}
{"name": "TopologicalSpace.IsOpenCover.isHomeomorph_iff_restrictPreimage", "kind": "theorem", "module": "Mathlib.Topology.LocalAtTarget", "is_tactic_proof": true, "tactics": ["simp_rw", "surjective_iff_surjective_of_iUnion_eq_univ"], "tactic_count": 2}
{"name": "TopologicalSpace.IsOpenCover.denseRange_iff_restrictPreimage", "kind": "theorem", "module": "Mathlib.Topology.LocalAtTarget", "is_tactic_proof": false, "tactics": ["simp_rw", "simp", "rw", "congr", "exact"], "tactic_count": 5}
{"name": "TopologicalSpace.IsOpenCover.generalizingMap_iff_restrictPreimage", "kind": "theorem", "module": "Mathlib.Topology.LocalAtTarget", "is_tactic_proof": true, "tactics": ["refine", "obtain", "have", "rwa", "obtain", "refine", "rwa"], "tactic_count": 7}
{"name": "TopologicalSpace.IsOpenCover.isOpenMap_iff_comp", "kind": "theorem", "module": "Mathlib.Topology.LocalAtTarget", "is_tactic_proof": true, "tactics": ["refine", "intro", "convert", "simp_rw"], "tactic_count": 4}
{"name": "TopologicalSpace.IsOpenCover.generalizingMap_iff_comp", "kind": "theorem", "module": "Mathlib.Topology.LocalAtTarget", "is_tactic_proof": false, "tactics": ["refine", "obtain", "replace", "obtain", "use", "simp"], "tactic_count": 6}
{"name": "isEmbedding_of_iSup_eq_top_of_preimage_subset_range", "kind": "theorem", "module": "Mathlib.Topology.LocalAtTarget", "is_tactic_proof": true, "tactics": ["wlog", "let", "suffices", "have", "rw", "simpa", "refine", "fun_prop", "rw", "exact", "exact", "rw", "intro", "let", "have", "have", "let", "refine", "convert", "ext", "obtain", "simp", "rfl"], "tactic_count": 23}
{"name": "subset_coborder", "kind": "theorem", "module": "Mathlib.Topology.LocallyClosed", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "coborder_inter_closure", "kind": "theorem", "module": "Mathlib.Topology.LocallyClosed", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "closure_inter_coborder", "kind": "theorem", "module": "Mathlib.Topology.LocallyClosed", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "coborder_eq_union_frontier_compl", "kind": "theorem", "module": "Mathlib.Topology.LocallyClosed", "is_tactic_proof": true, "tactics": ["rw", "closure_eq_self_union_frontier]"], "tactic_count": 2}
{"name": "coborder_eq_univ_iff", "kind": "theorem", "module": "Mathlib.Topology.LocallyClosed", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "coborder_eq_compl_frontier_iff", "kind": "theorem", "module": "Mathlib.Topology.LocallyClosed", "is_tactic_proof": true, "tactics": ["simp_rw", "disjoint_frontier_iff_isOpen]"], "tactic_count": 2}
{"name": "coborder_eq_union_closure_compl", "kind": "theorem", "module": "Mathlib.Topology.LocallyClosed", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "dense_coborder", "kind": "theorem", "module": "Mathlib.Topology.LocallyClosed", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp"], "tactic_count": 3}
{"name": "IsOpenMap.coborder_preimage_subset", "kind": "theorem", "module": "Mathlib.Topology.LocallyClosed", "is_tactic_proof": true, "tactics": ["rw", "apply", "exact"], "tactic_count": 3}
{"name": "Continuous.preimage_coborder_subset", "kind": "theorem", "module": "Mathlib.Topology.LocallyClosed", "is_tactic_proof": true, "tactics": ["rw", "apply", "exact"], "tactic_count": 3}
{"name": "coborder_preimage", "kind": "theorem", "module": "Mathlib.Topology.LocallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsOpenEmbedding.coborder_preimage", "kind": "theorem", "module": "Mathlib.Topology.LocallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosed_preimage_val_coborder", "kind": "theorem", "module": "Mathlib.Topology.LocallyClosed", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsLocallyClosed.inter", "kind": "theorem", "module": "Mathlib.Topology.LocallyClosed", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "refine"], "tactic_count": 3}
{"name": "IsLocallyClosed.preimage", "kind": "theorem", "module": "Mathlib.Topology.LocallyClosed", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Topology.IsInducing.isLocallyClosed_iff", "kind": "theorem", "module": "Mathlib.Topology.LocallyClosed", "is_tactic_proof": true, "tactics": ["simp_rw", "constructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 6}
{"name": "Topology.IsEmbedding.isLocallyClosed_iff", "kind": "theorem", "module": "Mathlib.Topology.LocallyClosed", "is_tactic_proof": true, "tactics": ["simp_rw", "image_preimage_eq_inter_range]"], "tactic_count": 2}
{"name": "IsLocallyClosed.image", "kind": "theorem", "module": "Mathlib.Topology.LocallyClosed", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact"], "tactic_count": 3}
{"name": "isLocallyClosed_tfae", "kind": "theorem", "module": "Mathlib.Topology.LocallyClosed", "is_tactic_proof": false, "tactics": ["tfae_have", "rintro", "have", "nth_rw", "rw", "refine", "rw", "exact", "tfae_have", "h,", "tfae_have", "h,", "obtain", "obtain", "rw", "exact", "ht'⟩", "tfae_have", "choose", "refine", "rintro", "exact", "exact", "tfae_have", "convert", "simpa", "tfae_finish"], "tactic_count": 27}
{"name": "isLocallyClosed_iff_isOpen_coborder", "kind": "theorem", "module": "Mathlib.Topology.LocallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocallyClosed.isOpen_preimage_val_closure", "kind": "theorem", "module": "Mathlib.Topology.LocallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.instOne", "kind": "instance", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.coe_one", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.one_apply", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.instInv", "kind": "instance", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.coe_inv", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.inv_apply", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.instMul", "kind": "instance", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.coe_mul", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.mul_apply", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.instMulOneClass", "kind": "instance", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.coeFnMonoidHom", "kind": "definition", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.constMonoidHom", "kind": "definition", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.instMulZeroClass", "kind": "instance", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.instMulZeroOneClass", "kind": "instance", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.charFn", "kind": "definition", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.coe_charFn", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.charFn_eq_one", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.charFn_eq_zero", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.charFn_inj", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.instDiv", "kind": "instance", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.coe_div", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.div_apply", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.instSemigroup", "kind": "instance", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.instSemigroupWithZero", "kind": "instance", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.instCommSemigroup", "kind": "instance", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.smul", "kind": "instance", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.coe_smul", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.smul_apply", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.instPow", "kind": "instance", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.instMonoid", "kind": "instance", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.instNatCast", "kind": "instance", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.instIntCast", "kind": "instance", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.instAddMonoidWithOne", "kind": "instance", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.instCommMonoid", "kind": "instance", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.instGroup", "kind": "instance", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.instCommGroup", "kind": "instance", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.instDistrib", "kind": "instance", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.instNonUnitalNonAssocSemiring", "kind": "instance", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.instNonUnitalSemiring", "kind": "instance", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.instNonAssocSemiring", "kind": "instance", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.constRingHom", "kind": "definition", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.instSemiring", "kind": "instance", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.instNonUnitalCommSemiring", "kind": "instance", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.instCommSemiring", "kind": "instance", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.instNonUnitalNonAssocRing", "kind": "instance", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.instNonUnitalRing", "kind": "instance", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.instNonAssocRing", "kind": "instance", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.instRing", "kind": "instance", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.instNonUnitalCommRing", "kind": "instance", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.instCommRing", "kind": "instance", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.instMulAction", "kind": "instance", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.instDistribMulAction", "kind": "instance", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.instModule", "kind": "instance", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.instAlgebra", "kind": "instance", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.coe_algebraMap", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.coeFnRingHom", "kind": "definition", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.coeFnₗ", "kind": "definition", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.coeFnAlgHom", "kind": "definition", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.evalMonoidHom", "kind": "definition", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.evalₗ", "kind": "definition", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.evalRingHom", "kind": "definition", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.evalₐ", "kind": "definition", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.comapMonoidHom", "kind": "definition", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.comapₗ", "kind": "definition", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.comapRingHom", "kind": "definition", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.comapₐ", "kind": "definition", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.ker_comapₗ", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.congrLeftₗ", "kind": "definition", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.congrLeftRingEquiv", "kind": "definition", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.congrLeftₐ", "kind": "definition", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.mapMonoidHom", "kind": "definition", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.mapₗ", "kind": "definition", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.mapRingHom", "kind": "definition", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.mapₐ", "kind": "definition", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.congrRightₗ", "kind": "definition", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.congrRightRingEquiv", "kind": "definition", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.congrRightₐ", "kind": "definition", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.constₗ", "kind": "definition", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.constₐ", "kind": "definition", "module": "Mathlib.Topology.LocallyConstant.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocallyConstant", "kind": "definition", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocallyConstant.tfae", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": true, "tactics": ["tfae_have", "tfae_have", "tfae_have", "tfae_have", "h,", "rcases", "exact", "tfae_have", "h,", "refine", "rcases", "exact", "tfae_finish"], "tactic_count": 13}
{"name": "IsLocallyConstant.of_discrete", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocallyConstant.isOpen_fiber", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocallyConstant.isClosed_fiber", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocallyConstant.isClopen_fiber", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocallyConstant.iff_exists_open", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocallyConstant.iff_eventually_eq", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocallyConstant.exists_open", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocallyConstant.eventually_eq", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocallyConstant.iff_isOpen_fiber_apply", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocallyConstant.iff_isOpen_fiber", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocallyConstant.continuous", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocallyConstant.iff_continuous", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocallyConstant.of_constant", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocallyConstant.const", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocallyConstant.comp", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocallyConstant.prodMk", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocallyConstant.comp₂", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocallyConstant.comp_continuous", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocallyConstant.apply_eq_of_isPreconnected", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": true, "tactics": ["let", "suffices", "intro", "specialize", "simp", "simp"], "tactic_count": 6}
{"name": "IsLocallyConstant.apply_eq_of_preconnectedSpace", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocallyConstant.eq_const", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocallyConstant.exists_eq_const", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": true, "tactics": ["rcases", "exact", "exact"], "tactic_count": 3}
{"name": "IsLocallyConstant.iff_is_const", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocallyConstant.range_finite", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": true, "tactics": ["letI", "exact"], "tactic_count": 2}
{"name": "IsLocallyConstant.one", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocallyConstant.inv", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocallyConstant.mul", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocallyConstant.div", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocallyConstant.desc", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocallyConstant.of_constant_on_connected_components", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocallyConstant.of_constant_on_connected_clopens", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocallyConstant.of_constant_on_preconnected_clopens", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.instInhabited", "kind": "instance", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.instFunLike", "kind": "instance", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.Simps.apply", "kind": "definition", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.toFun_eq_coe", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.coe_mk", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.congr_fun", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.congr_arg", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.coe_injective", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LocallyConstant.toContinuousMap", "kind": "definition", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.instCoeContinuousMap", "kind": "instance", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LocallyConstant.ofIsClopen", "kind": "definition", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.ofIsClopen_fiber_zero", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp", "tauto"], "tactic_count": 3}
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{"name": "LocallyConstant.apply_eq_of_isPreconnected", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.apply_eq_of_preconnectedSpace", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LocallyConstant.flip", "kind": "definition", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.unflip", "kind": "definition", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.unflip_flip", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.flip_unflip", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.comap", "kind": "definition", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.coe_comap", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.coe_comap_apply", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LocallyConstant.comap_const", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "LocallyConstant.comap_injective", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": true, "tactics": ["intro", "ext", "obtain", "simpa"], "tactic_count": 4}
{"name": "LocallyConstant.desc", "kind": "definition", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.coe_desc", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.mulIndicator", "kind": "definition", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.mulIndicator_apply_eq_if", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.mulIndicator_of_mem", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.mulIndicator_of_notMem", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.congrLeft", "kind": "definition", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.congrRight", "kind": "definition", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.equivClopens", "kind": "definition", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.piecewise", "kind": "definition", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyConstant.piecewise_apply_left", "kind": "theorem", "module": "Mathlib.Topology.LocallyConstant.Basic", "is_tactic_proof": true, "tactics": ["simp", "rw"], "tactic_count": 2}
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{"name": "LocallyFinite", "kind": "definition", "module": "Mathlib.Topology.LocallyFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "locallyFinite_of_finite", "kind": "theorem", "module": "Mathlib.Topology.LocallyFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyFinite.point_finite", "kind": "theorem", "module": "Mathlib.Topology.LocallyFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyFinite.subset", "kind": "theorem", "module": "Mathlib.Topology.LocallyFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyFinite.comp_injOn", "kind": "theorem", "module": "Mathlib.Topology.LocallyFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "locallyFinite_iff_smallSets", "kind": "theorem", "module": "Mathlib.Topology.LocallyFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LocallyFinite.exists_mem_basis", "kind": "theorem", "module": "Mathlib.Topology.LocallyFinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Function.locallyFinsuppWithin.supportWithinDomain", "kind": "theorem", "module": "Mathlib.Topology.LocallyFinsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Function.locallyFinsuppWithin.instIsOrderedAddMonoid", "kind": "instance", "module": "Mathlib.Topology.LocallyFinsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.locallyFinsuppWithin.posPart_add", "kind": "theorem", "module": "Mathlib.Topology.LocallyFinsupp", "is_tactic_proof": true, "tactics": ["repeat", "intro", "simp", "constructor", "simp", "simp"], "tactic_count": 6}
{"name": "Function.locallyFinsuppWithin.negPart_add", "kind": "theorem", "module": "Mathlib.Topology.LocallyFinsupp", "is_tactic_proof": true, "tactics": ["repeat", "intro", "simp", "constructor", "simp", "simp"], "tactic_count": 6}
{"name": "Function.locallyFinsuppWithin.nsmul_posPart", "kind": "theorem", "module": "Mathlib.Topology.LocallyFinsupp", "is_tactic_proof": true, "tactics": ["ext", "simp", "by_cases", "simpa", "simpa"], "tactic_count": 5}
{"name": "Function.locallyFinsuppWithin.nsmul_negPart", "kind": "theorem", "module": "Mathlib.Topology.LocallyFinsupp", "is_tactic_proof": true, "tactics": ["ext", "simp", "by_cases", "simpa", "simpa"], "tactic_count": 5}
{"name": "Function.locallyFinsuppWithin.restrict", "kind": "definition", "module": "Mathlib.Topology.LocallyFinsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.locallyFinsuppWithin.restrict_apply", "kind": "theorem", "module": "Mathlib.Topology.LocallyFinsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.locallyFinsuppWithin.restrict_eqOn", "kind": "theorem", "module": "Mathlib.Topology.LocallyFinsupp", "is_tactic_proof": true, "tactics": ["intro", "simp_all"], "tactic_count": 2}
{"name": "Function.locallyFinsuppWithin.restrict_eqOn_compl", "kind": "theorem", "module": "Mathlib.Topology.LocallyFinsupp", "is_tactic_proof": true, "tactics": ["intro", "simp_all"], "tactic_count": 2}
{"name": "Function.locallyFinsuppWithin.restrictMonoidHom", "kind": "definition", "module": "Mathlib.Topology.LocallyFinsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.locallyFinsuppWithin.restrictMonoidHom_apply", "kind": "theorem", "module": "Mathlib.Topology.LocallyFinsupp", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "Function.locallyFinsuppWithin.restrictLatticeHom", "kind": "definition", "module": "Mathlib.Topology.LocallyFinsupp", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.locallyFinsuppWithin.restrictLatticeHom_apply", "kind": "theorem", "module": "Mathlib.Topology.LocallyFinsupp", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "Function.locallyFinsuppWithin.restrict_posPart", "kind": "theorem", "module": "Mathlib.Topology.LocallyFinsupp", "is_tactic_proof": true, "tactics": ["ext", "simp", "aesop"], "tactic_count": 3}
{"name": "Function.locallyFinsuppWithin.restrict_negPart", "kind": "theorem", "module": "Mathlib.Topology.LocallyFinsupp", "is_tactic_proof": true, "tactics": ["ext", "simp", "aesop"], "tactic_count": 3}
{"name": "Topology.IsInducing.induced", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsInducing.id", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsInducing.comp", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsInducing.of_comp_iff", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "Topology.IsInducing.of_comp", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.isInducing_iff_nhds", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsInducing.nhds_eq_comap", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsInducing.basis_nhds", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsInducing.nhdsSet_eq_comap", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Topology.IsInducing.map_nhds_eq", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsInducing.map_nhds_of_mem", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsInducing.mapClusterPt_iff", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": true, "tactics": ["delta", "rw"], "tactic_count": 2}
{"name": "Topology.IsInducing.image_mem_nhdsWithin", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsInducing.tendsto_nhds_iff", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Topology.IsInducing.continuousAt_iff", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsInducing.continuous_iff", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Topology.IsInducing.continuousAt_iff'", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Topology.IsInducing.continuous", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsInducing.closure_eq_preimage_closure_image", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "Topology.IsInducing.isClosed_iff", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Topology.IsInducing.isClosed_iff'", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Topology.IsInducing.isClosed_preimage", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsInducing.isOpen_iff", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Topology.IsInducing.setOf_isOpen", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsInducing.dense_iff", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Topology.IsInducing.of_subsingleton", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsInducing.indiscreteTopology", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsInducing.nontrivialTopology", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsEmbedding.induced", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsEmbedding.isInducing", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsEmbedding.mk'", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsEmbedding.id", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsEmbedding.comp", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsEmbedding.of_comp_iff", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Topology.IsEmbedding.of_comp", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsEmbedding.of_leftInverse", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsEmbedding.map_nhds_eq", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsEmbedding.map_nhds_of_mem", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsEmbedding.tendsto_nhds_iff", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsEmbedding.continuous_iff", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsEmbedding.continuous", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsEmbedding.closure_eq_preimage_closure_image", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsEmbedding.discreteTopology", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsEmbedding.of_subsingleton", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.isQuotientMap_iff", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.isQuotientMap_iff_isClosed", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsQuotientMap.id", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsQuotientMap.comp", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsQuotientMap.of_comp", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsQuotientMap.of_comp_of_eq_coinduced", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsQuotientMap.of_comp_isQuotientMap", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsQuotientMap.of_inverse", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsQuotientMap.continuous_iff", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Topology.IsQuotientMap.continuous", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsQuotientMap.isOpen_preimage", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsQuotientMap.isClosed_preimage", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpenMap.id", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpenMap.comp", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpenMap.isOpen_range", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsOpenMap.image_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpenMap.range_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpenMap.mapsTo_interior", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpenMap.image_interior_subset", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpenMap.nhds_le", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpenMap.map_nhds_eq", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpenMap.map_nhdsSet_eq", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp_rw"], "tactic_count": 2}
{"name": "IsOpenMap.of_nhds_le", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpenMap.of_sections", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpenMap.of_inverse", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpenMap.isQuotientMap", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpenMap.interior_preimage_subset_preimage_interior", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpenMap.preimage_interior_eq_interior_preimage", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpenMap.preimage_closure_subset_closure_preimage", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "IsOpenMap.preimage_closure_eq_closure_preimage", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpenMap.preimage_frontier_subset_frontier_preimage", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": true, "tactics": ["simpa", "inter_subset_inter"], "tactic_count": 2}
{"name": "IsOpenMap.preimage_frontier_eq_frontier_preimage", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": true, "tactics": ["simp", "hf.preimage_closure_eq_closure_preimage"], "tactic_count": 2}
{"name": "IsOpenMap.of_isEmpty", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpenMap.clusterPt_comap", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "isOpenMap_iff_kernImage", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "isOpenMap_iff_nhds_le", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpenMap_iff_clusterPt_comap", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": true, "tactics": ["refine", "simp", "intro", "contrapose", "rw", "exact"], "tactic_count": 6}
{"name": "isOpenMap_iff_image_interior", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpenMap_iff_closure_kernImage", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Topology.IsInducing.isOpenMap", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dense.preimage", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosedMap.id", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosedMap.comp", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": true, "tactics": ["intro", "rw", "exact"], "tactic_count": 3}
{"name": "IsClosedMap.of_comp_surjective", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": true, "tactics": ["intro", "rw", "exact"], "tactic_count": 3}
{"name": "IsClosedMap.closure_image_subset", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosedMap.of_inverse", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosedMap.of_nonempty", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": true, "tactics": ["intro", "simp_rw", "exact"], "tactic_count": 3}
{"name": "IsClosedMap.isClosed_range", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosedMap.isQuotientMap", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosedMap_iff_kernImage", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Topology.IsInducing.isClosedMap", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": true, "tactics": ["intro", "rcases", "rw", "exact"], "tactic_count": 4}
{"name": "isClosedMap_iff_closure_image", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosedMap_iff_kernImage_interior", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "isClosedMap_iff_clusterPt", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "isClosedMap_iff_comap_nhdsSet_le", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": ["simp_rw", "isClosedMap_iff_kernImage_interior]", "exact"], "tactic_count": 3}
{"name": "isClosedMap_iff_comap_nhds_le", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": true, "tactics": ["rw", "constructor", "exact", "intro", "rw", "simp_rw", "exact"], "tactic_count": 7}
{"name": "IsClosedMap.comap_nhds_eq", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosedMap.comap_nhdsSet_eq", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosedMap.eventually_nhds_fiber", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": true, "tactics": ["rw", "replace", "rwa"], "tactic_count": 3}
{"name": "IsClosedMap.frequently_nhds_fiber", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": true, "tactics": ["and", "contrapose", "exact"], "tactic_count": 3}
{"name": "IsClosedMap.closure_image_eq_of_continuous", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosedMap.lift'_closure_map_eq", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": true, "tactics": ["rw", "congr", "ext", "exact"], "tactic_count": 4}
{"name": "IsClosedMap.mapClusterPt_iff_lift'_closure", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": true, "tactics": ["rw", "map_neBot_iff"], "tactic_count": 2}
{"name": "Topology.IsOpenEmbedding.isEmbedding", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsOpenEmbedding.isInducing", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsOpenEmbedding.isOpenMap", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsOpenEmbedding.map_nhds_eq", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsOpenEmbedding.isOpen_iff_image_isOpen", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsOpenEmbedding.tendsto_nhds_iff", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsOpenEmbedding.tendsto_nhds_iff'", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Topology.IsOpenEmbedding.continuousAt_iff", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsOpenEmbedding.continuous", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsOpenEmbedding.isOpen_iff_preimage_isOpen", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Topology.IsOpenEmbedding.of_isEmbedding_isOpenMap", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsEmbedding.isOpenEmbedding_of_surjective", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.isOpenEmbedding_iff_isEmbedding_isOpenMap", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsOpenEmbedding.of_continuous_injective_isOpenMap", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Topology.isOpenEmbedding_iff_continuous_injective_isOpenMap", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsOpenEmbedding.id", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsOpenEmbedding.comp", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsOpenEmbedding.isOpenMap_iff", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Topology.IsOpenEmbedding.of_comp_iff", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": true, "tactics": ["simp", "hg.injective.of_comp_iff]"], "tactic_count": 2}
{"name": "Topology.IsOpenEmbedding.of_comp", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsOpenEmbedding.of_isEmpty", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsOpenEmbedding.image_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Topology.IsClosedEmbedding.isEmbedding", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsClosedEmbedding.isInducing", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsClosedEmbedding.continuous", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsClosedEmbedding.tendsto_nhds_iff", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsClosedEmbedding.isClosedMap", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsClosedEmbedding.isClosed_iff_image_isClosed", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsClosedEmbedding.isClosed_iff_preimage_isClosed", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Topology.IsClosedEmbedding.of_isEmbedding_isClosedMap", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsClosedEmbedding.of_continuous_injective_isClosedMap", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": true, "tactics": ["refine", "refine", "refine", "rw"], "tactic_count": 4}
{"name": "Topology.IsClosedEmbedding.isClosedEmbedding_iff_continuous_injective_isClosedMap", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsClosedEmbedding.id", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsClosedEmbedding.comp", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsClosedEmbedding.of_comp_iff", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Topology.IsClosedEmbedding.of_comp", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsClosedEmbedding.closure_image_eq", "kind": "theorem", "module": "Mathlib.Topology.Maps.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpenQuotientMap.id", "kind": "theorem", "module": "Mathlib.Topology.Maps.OpenQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpenQuotientMap.isQuotientMap", "kind": "theorem", "module": "Mathlib.Topology.Maps.OpenQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpenQuotientMap.iff_isOpenMap_isQuotientMap", "kind": "theorem", "module": "Mathlib.Topology.Maps.OpenQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpenQuotientMap.of_isOpenMap_isQuotientMap", "kind": "theorem", "module": "Mathlib.Topology.Maps.OpenQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpenQuotientMap.comp", "kind": "theorem", "module": "Mathlib.Topology.Maps.OpenQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpenQuotientMap.map_nhds_eq", "kind": "theorem", "module": "Mathlib.Topology.Maps.OpenQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpenQuotientMap.continuous_comp_iff", "kind": "theorem", "module": "Mathlib.Topology.Maps.OpenQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpenQuotientMap.continuousAt_comp_iff", "kind": "theorem", "module": "Mathlib.Topology.Maps.OpenQuotient", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsOpenQuotientMap.dense_preimage_iff", "kind": "theorem", "module": "Mathlib.Topology.Maps.OpenQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpenQuotientMap.baireSpace", "kind": "theorem", "module": "Mathlib.Topology.Maps.OpenQuotient", "is_tactic_proof": true, "tactics": ["constructor", "intro", "have", "dense_iInter_of_isOpen_nat", "simp_all"], "tactic_count": 5}
{"name": "Topology.IsInducing.isOpenQuotientMap_of_surjective", "kind": "theorem", "module": "Mathlib.Topology.Maps.OpenQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsInducing.isQuotientMap_of_surjective", "kind": "theorem", "module": "Mathlib.Topology.Maps.OpenQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "coinduced_eq_induced_of_isOpenQuotientMap_of_isInducing", "kind": "theorem", "module": "Mathlib.Topology.Maps.OpenQuotient", "is_tactic_proof": true, "tactics": ["ext", "change", "simp_rw", "constructor", "rintro", "refine", "ext", "obtain", "constructor", "rintro", "obtain", "rw", "exact", "intro", "exact", "rintro", "refine", "simp_rw"], "tactic_count": 18}
{"name": "isEmbedding_of_isOpenQuotientMap_of_isInducing", "kind": "theorem", "module": "Mathlib.Topology.Maps.OpenQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isQuotientMap_of_isOpenQuotientMap_of_isInducing", "kind": "theorem", "module": "Mathlib.Topology.Maps.OpenQuotient", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsProperMap.continuous", "kind": "theorem", "module": "Mathlib.Topology.Maps.Proper.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsProperMap.isClosedMap", "kind": "theorem", "module": "Mathlib.Topology.Maps.Proper.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "isProperMap_iff_ultrafilter", "kind": "theorem", "module": "Mathlib.Topology.Maps.Proper.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "constructor", "intro", "simp_rw", "exact", "simp_rw", "intro", "rcases", "exact"], "tactic_count": 10}
{"name": "isProperMap_iff_ultrafilter_of_t2", "kind": "theorem", "module": "Mathlib.Topology.Maps.Proper.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsProperMap.ultrafilter_le_nhds_of_tendsto", "kind": "theorem", "module": "Mathlib.Topology.Maps.Proper.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsProperMap.comp", "kind": "theorem", "module": "Mathlib.Topology.Maps.Proper.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "rcases", "rcases", "use"], "tactic_count": 5}
{"name": "isProperMap_of_comp_of_surj", "kind": "theorem", "module": "Mathlib.Topology.Maps.Proper.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "rcases", "rw", "exact"], "tactic_count": 5}
{"name": "isProperMap_of_comp_of_inj", "kind": "theorem", "module": "Mathlib.Topology.Maps.Proper.Basic", "is_tactic_proof": true, "tactics": ["refine", "rcases", "exact"], "tactic_count": 3}
{"name": "isProperMap_of_comp_of_t2", "kind": "theorem", "module": "Mathlib.Topology.Maps.Proper.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "rcases", "exact"], "tactic_count": 5}
{"name": "IsProperMap.prodMap", "kind": "theorem", "module": "Mathlib.Topology.Maps.Proper.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "constructor", "exact", "hf.1.prodMap", "hg.1", "intro", "simp_rw", "rcases", "rcases", "refine", "rw", "exact"], "tactic_count": 12}
{"name": "IsProperMap.pi_map", "kind": "theorem", "module": "Mathlib.Topology.Maps.Proper.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "constructor", "exact", "continuous_pi", "intro", "have", "choose", "refine", "rwa"], "tactic_count": 9}
{"name": "IsProperMap.isCompact_preimage", "kind": "theorem", "module": "Mathlib.Topology.Maps.Proper.Basic", "is_tactic_proof": false, "tactics": ["rw", "intro", "rw", "rcases", "rcases", "exact"], "tactic_count": 6}
{"name": "isProperMap_iff_isClosedMap_and_compact_fibers", "kind": "theorem", "module": "Mathlib.Topology.Maps.Proper.Basic", "is_tactic_proof": true, "tactics": ["constructor", "exact", "rw", "refine", "rw", "rcases", "refine", "rw", "exact"], "tactic_count": 9}
{"name": "isProperMap_iff_isClosedMap_of_inj", "kind": "theorem", "module": "Mathlib.Topology.Maps.Proper.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "isProperMap_of_isClosedMap_of_inj", "kind": "theorem", "module": "Mathlib.Topology.Maps.Proper.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.isProperMap", "kind": "theorem", "module": "Mathlib.Topology.Maps.Proper.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsHomeomorph.isProperMap", "kind": "theorem", "module": "Mathlib.Topology.Maps.Proper.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isProperMap_id", "kind": "theorem", "module": "Mathlib.Topology.Maps.Proper.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsClosedEmbedding.isProperMap", "kind": "theorem", "module": "Mathlib.Topology.Maps.Proper.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.isProperMap_subtypeVal", "kind": "theorem", "module": "Mathlib.Topology.Maps.Proper.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsProperMap.restrict", "kind": "theorem", "module": "Mathlib.Topology.Maps.Proper.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsProperMap.isClosed_range", "kind": "theorem", "module": "Mathlib.Topology.Maps.Proper.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isProperMap_iff_isClosedMap_and_tendsto_cofinite", "kind": "theorem", "module": "Mathlib.Topology.Maps.Proper.Basic", "is_tactic_proof": false, "tactics": ["simp_rw", "preimage_compl]", "refine", "rcases", "exact"], "tactic_count": 5}
{"name": "Continuous.isProperMap", "kind": "theorem", "module": "Mathlib.Topology.Maps.Proper.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isProperMap_const_iff", "kind": "theorem", "module": "Mathlib.Topology.Maps.Proper.Basic", "is_tactic_proof": true, "tactics": ["classical", "rw", "constructor", "rintro", "exact", "intro", "refine", "simp"], "tactic_count": 8}
{"name": "isProperMap_const", "kind": "theorem", "module": "Mathlib.Topology.Maps.Proper.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isProperMap_fst_of_compactSpace", "kind": "theorem", "module": "Mathlib.Topology.Maps.Proper.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isProperMap_snd_of_compactSpace", "kind": "theorem", "module": "Mathlib.Topology.Maps.Proper.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosedMap_fst_of_compactSpace", "kind": "theorem", "module": "Mathlib.Topology.Maps.Proper.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosedMap_snd_of_compactSpace", "kind": "theorem", "module": "Mathlib.Topology.Maps.Proper.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsProperMap.universally_closed", "kind": "theorem", "module": "Mathlib.Topology.Maps.Proper.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isProperMap_iff_isCompact_preimage", "kind": "theorem", "module": "Mathlib.Topology.Maps.Proper.CompactlyGenerated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isProperMap_iff_tendsto_cocompact", "kind": "theorem", "module": "Mathlib.Topology.Maps.Proper.CompactlyGenerated", "is_tactic_proof": false, "tactics": ["simp_rw", "preimage_compl]", "refine", "rcases", "exact"], "tactic_count": 5}
{"name": "isProperMap_iff_isClosedMap_filter", "kind": "theorem", "module": "Mathlib.Topology.Maps.Proper.UniversallyClosed", "is_tactic_proof": true, "tactics": ["constructor", "exact", "rw", "refine", "let", "closure", "have", "have", "this.mem_of_tendsto", "rcases", "refine", "rw", "rcases", "exact"], "tactic_count": 14}
{"name": "isProperMap_iff_isClosedMap_ultrafilter", "kind": "theorem", "module": "Mathlib.Topology.Maps.Proper.UniversallyClosed", "is_tactic_proof": true, "tactics": ["constructor", "exact", "rw", "refine", "let", "have", "have", "this.mem_of_tendsto", "rcases", "refine", "rw", "rcases", "exact"], "tactic_count": 13}
{"name": "isProperMap_iff_universally_closed", "kind": "theorem", "module": "Mathlib.Topology.Maps.Proper.UniversallyClosed", "is_tactic_proof": true, "tactics": ["constructor", "exact", "rw", "exact"], "tactic_count": 4}
{"name": "LipschitzMul.C", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lipschitzWith_lipschitz_const_mul_edist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lipschitz_with_lipschitz_const_mul", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Algebra", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "LipschitzMul.continuousMul", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Submonoid.lipschitzMul", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.lipschitzMul", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.hasLipschitzAdd", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.hasLipschitzAdd", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dist_smul_pair", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dist_pair_smul", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.IsBounded.uniformContinuousOn_smul", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Algebra", "is_tactic_proof": true, "tactics": ["rcases", "rw", "intro", "refine", "grw", "rw", "dsimp", "grw", "field_simp", "norm_num1"], "tactic_count": 10}
{"name": "IsBoundedSMul.continuousSMul", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBoundedSMul.toUniformContinuousConstSMul", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TendstoLocallyUniformlyOn.smul₀_of_isBoundedUnder", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Algebra", "is_tactic_proof": true, "tactics": ["have", "rw", "intro", "rcases", "simp_rw", "refine", "filter_upwards", "tendsto_snd", "simp", "mem_setOf]", "grw", "constructor"], "tactic_count": 12}
{"name": "TendstoLocallyUniformlyOn.mul₀_of_isBoundedUnder", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TendstoLocallyUniformly.smul₀_of_isBoundedUnder", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Algebra", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "TendstoLocallyUniformly.mul₀_of_isBoundedUnder", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TendstoLocallyUniformlyOn.smul₀", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TendstoLocallyUniformlyOn.mul₀", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TendstoLocallyUniformly.smul₀", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TendstoLocallyUniformly.mul₀", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.isBoundedSMul", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.isBoundedSMul", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsBoundedSMul.op", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instLipschitzAddAdditiveOfLipschitzMul", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instLipschitzMulMultiplicativeOfLipschitzAdd", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instLipschitzMulOrderDual", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instIsBoundedSMul", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instIsBoundedSMul'", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instIsBoundedSMul", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsBoundedSMulSeparationQuotient", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Algebra", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntilipschitzWith", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Antilipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntilipschitzWith.edist_lt_top", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Antilipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntilipschitzWith.edist_ne_top", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Antilipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "antilipschitzWith_iff_le_mul_nndist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Antilipschitz", "is_tactic_proof": true, "tactics": ["simp", "norm_cast"], "tactic_count": 2}
{"name": "antilipschitzWith_iff_le_mul_dist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Antilipschitz", "is_tactic_proof": true, "tactics": ["simp", "norm_cast"], "tactic_count": 2}
{"name": "AntilipschitzWith.mul_le_nndist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Antilipschitz", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "AntilipschitzWith.mul_le_dist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Antilipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntilipschitzWith.k", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Antilipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntilipschitzWith.injective", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Antilipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntilipschitzWith.mul_le_edist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Antilipschitz", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "AntilipschitzWith.ediam_preimage_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Antilipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntilipschitzWith.le_mul_ediam_image", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Antilipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntilipschitzWith.id", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Antilipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntilipschitzWith.comp", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Antilipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntilipschitzWith.restrict", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Antilipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntilipschitzWith.codRestrict", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Antilipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntilipschitzWith.to_rightInvOn'", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Antilipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntilipschitzWith.to_rightInvOn", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Antilipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntilipschitzWith.to_rightInverse", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Antilipschitz", "is_tactic_proof": true, "tactics": ["intro", "have", "rwa"], "tactic_count": 3}
{"name": "AntilipschitzWith.comap_uniformity_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Antilipschitz", "is_tactic_proof": true, "tactics": ["refine", "refine", "refine", "rw", "rw", "exact"], "tactic_count": 6}
{"name": "AntilipschitzWith.isUniformInducing", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Antilipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntilipschitzWith.isUniformEmbedding", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Antilipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntilipschitzWith.isComplete_range", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Antilipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntilipschitzWith.isClosed_range", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Antilipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntilipschitzWith.isClosedEmbedding", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Antilipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntilipschitzWith.subtype_coe", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Antilipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntilipschitzWith.of_subsingleton", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Antilipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntilipschitzWith.subsingleton", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Antilipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntilipschitzWith.isBounded_preimage", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Antilipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntilipschitzWith.tendsto_cobounded", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Antilipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntilipschitzWith.properSpace", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Antilipschitz", "is_tactic_proof": true, "tactics": ["refine", "let", "have", "have", "have", "convert", "exact"], "tactic_count": 7}
{"name": "AntilipschitzWith.isBounded_of_image2_left", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Antilipschitz", "is_tactic_proof": true, "tactics": ["contrapose", "obtain", "have", "intro", "apply", "rw", "replace", "exact", "exact"], "tactic_count": 9}
{"name": "AntilipschitzWith.isBounded_of_image2_right", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Antilipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzWith.to_rightInverse", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Antilipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MetricSpace.instT0Space", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.isUniformEmbedding_iff'", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MetricSpace.ofT0PseudoMetricSpace", "kind": "abbrev", "module": "Mathlib.Topology.MetricSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MetricSpace.toEMetricSpace", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.isClosed_of_pairwise_le_dist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.isClosedEmbedding_of_pairwise_le_dist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.isUniformEmbedding_bot_of_pairwise_le_dist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EMetricSpace.toMetricSpaceOfDist", "kind": "abbrev", "module": "Mathlib.Topology.MetricSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EMetricSpace.toMetricSpace", "kind": "abbrev", "module": "Mathlib.Topology.MetricSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MetricSpace.induced", "kind": "abbrev", "module": "Mathlib.Topology.MetricSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUniformEmbedding.comapMetricSpace", "kind": "abbrev", "module": "Mathlib.Topology.MetricSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsEmbedding.comapMetricSpace", "kind": "abbrev", "module": "Mathlib.Topology.MetricSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.metricSpace", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.instMetricSpace", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.metricSpace", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instMetricSpaceNNReal", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.isUniformEmbedding_coe", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.isEmbedding_coe", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instMetricSpaceULift", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.metricSpaceMax", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "metricSpacePi", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.secondCountable_of_countable_discretization", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Basic", "is_tactic_proof": true, "tactics": ["refine", "rcases", "let", "refine", "let", "have", "exact"], "tactic_count": 7}
{"name": "SeparationQuotient.instDist", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.dist_mk", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.instMetricSpace", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoEMetricSpace.replaceEDist", "kind": "abbrev", "module": "Mathlib.Topology.MetricSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoEMetricSpace.replaceEDist_eq", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "PseudoEMetricSpace._example", "kind": "example", "module": "Mathlib.Topology.MetricSpace.Basic", "is_tactic_proof": true, "tactics": ["with_reducible"], "tactic_count": 1}
{"name": "PseudoMetricSpace.replaceDist", "kind": "abbrev", "module": "Mathlib.Topology.MetricSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoMetricSpace.replaceDist_eq", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "PseudoMetricSpace._example", "kind": "example", "module": "Mathlib.Topology.MetricSpace.Basic", "is_tactic_proof": true, "tactics": ["with_reducible", "dsimp"], "tactic_count": 2}
{"name": "PseudoMetricSpace._example", "kind": "example", "module": "Mathlib.Topology.MetricSpace.Basic", "is_tactic_proof": true, "tactics": ["with_reducible"], "tactic_count": 1}
{"name": "EMetricSpace.replaceEDist", "kind": "abbrev", "module": "Mathlib.Topology.MetricSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EMetricSpace.replaceEDist_eq", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "EMetricSpace._example", "kind": "example", "module": "Mathlib.Topology.MetricSpace.Basic", "is_tactic_proof": true, "tactics": ["with_reducible"], "tactic_count": 1}
{"name": "MetricSpace.replaceDist", "kind": "abbrev", "module": "Mathlib.Topology.MetricSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MetricSpace.replaceDist_eq", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "MetricSpace._example", "kind": "example", "module": "Mathlib.Topology.MetricSpace.Basic", "is_tactic_proof": true, "tactics": ["with_reducible", "simp"], "tactic_count": 2}
{"name": "MetricSpace._example", "kind": "example", "module": "Mathlib.Topology.MetricSpace.Basic", "is_tactic_proof": true, "tactics": ["with_reducible"], "tactic_count": 1}
{"name": "uniformity_eq_of_bilipschitz", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bilipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bornology_eq_of_bilipschitz", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bilipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isBounded_iff_of_bilipschitz", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bilipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "totallyBounded_Icc", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "totallyBounded_Ico", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "totallyBounded_Ioc", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "totallyBounded_Ioo", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.isBounded_closedBall", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.isBounded_ball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.isBounded_sphere", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.isBounded_iff_subset_closedBall", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.IsBounded.subset_closedBall", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.IsBounded.subset_ball_lt", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.IsBounded.subset_ball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.isBounded_iff_subset_ball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.IsBounded.subset_closedBall_lt", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.isBounded_closure_of_isBounded", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.IsBounded.closure", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.isBounded_closure_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.hasBasis_cobounded_compl_closedBall", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.hasAntitoneBasis_cobounded_compl_closedBall", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.hasBasis_cobounded_compl_ball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.hasAntitoneBasis_cobounded_compl_ball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.comap_dist_right_atTop", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.comap_dist_left_atTop", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Metric.tendsto_dist_right_atTop_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Metric.tendsto_dist_left_atTop_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Metric.tendsto_dist_right_cobounded_atTop", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.tendsto_dist_left_cobounded_atTop", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TotallyBounded.isBounded", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.isBounded", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.cobounded_le_cocompact", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.isCobounded_iff_closedBall_compl_subset", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": true, "tactics": ["rw", "apply", "intro", "rw"], "tactic_count": 4}
{"name": "Bornology.IsCobounded.closedBall_compl_subset", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.closedBall_compl_subset_of_mem_cocompact", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.mem_cocompact_of_closedBall_compl_subset", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": true, "tactics": ["rcases", "rw", "exact"], "tactic_count": 3}
{"name": "Metric.mem_cocompact_iff_closedBall_compl_subset", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.isBounded_range_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.isBounded_image_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.isBounded_range_of_tendsto_cofinite_uniformity", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": true, "tactics": ["rcases", "rw", "refine", "exact"], "tactic_count": 4}
{"name": "Metric.isBounded_range_of_cauchy_map_cofinite", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauchySeq.isBounded_range", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.isBounded_range_of_tendsto_cofinite", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.isBounded_of_compactSpace", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.isBounded_range_of_tendsto", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.disjoint_nhds_cobounded", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.disjoint_cobounded_nhds", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.disjoint_nhdsSet_cobounded", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.disjoint_cobounded_nhdsSet", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.exists_isBounded_image_of_tendsto", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.exists_isOpen_isBounded_image_inter_of_isCompact_of_forall_continuousWithinAt", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": ["have", "rw", "exact", "rcases", "refine", "rwa"], "tactic_count": 6}
{"name": "Metric.exists_isOpen_isBounded_image_of_isCompact_of_forall_continuousAt", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": true, "tactics": ["simp_rw", "simpa"], "tactic_count": 2}
{"name": "Metric.exists_isOpen_isBounded_image_inter_of_isCompact_of_continuousOn", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.exists_isOpen_isBounded_image_of_isCompact_of_continuousOn", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.isCompact_of_isClosed_isBounded", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": true, "tactics": ["rcases", "exact", "rcases", "exact"], "tactic_count": 4}
{"name": "Bornology.IsBounded.isCompact_closure", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.isCompact_iff_isClosed_bounded", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.compactSpace_iff_isBounded_univ", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.isBounded_Icc", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.isBounded_Ico", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.isBounded_Ioc", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.isBounded_Ioo", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.isBounded_of_bddAbove_of_bddBelow", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOrderBornology.of_isCompactIcc", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.isBounded_of_abs_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": true, "tactics": ["convert", "ext1", "simp"], "tactic_count": 3}
{"name": "Metric.isBounded_of_abs_lt", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": true, "tactics": ["convert", "ext1", "simp"], "tactic_count": 3}
{"name": "Metric.diam", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.diam_nonneg", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.diam_subsingleton", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Metric.diam_empty", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.diam_singleton", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.diam_one", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.diam_pair", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Metric.diam_triple", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": true, "tactics": ["simp", "rw"], "tactic_count": 2}
{"name": "Metric.ediam_le_of_forall_dist_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.diam_le_of_forall_dist_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.diam_le_of_forall_dist_le_of_nonempty", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.dist_le_diam_of_mem'", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Metric.isBounded_iff_ediam_ne_top", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.ediam_eq_top_iff_unbounded", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.ediam_univ_eq_top_iff_noncompact", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Metric.ediam_univ_of_noncompact", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.diam_univ_of_noncompact", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Metric.dist_le_diam_of_mem", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.ediam_of_unbounded", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.diam_eq_zero_of_unbounded", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Metric.diam_mono", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.diam_union", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": true, "tactics": ["simp", "grw", "simp", "exact", "exact"], "tactic_count": 5}
{"name": "Metric.diam_union'", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": true, "tactics": ["rcases", "simpa"], "tactic_count": 2}
{"name": "Metric.diam_le_of_subset_closedBall", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.diam_closedBall", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.diam_ball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsComplete.nonempty_iInter_of_nonempty_biInter", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": true, "tactics": ["let", "have", "intro", "apply", "intro", "simp", "exact", "have", "apply", "intro", "exact", "obtain", "cauchySeq_tendsto_of_isComplete", "refine", "apply", "filter_upwards", "exact"], "tactic_count": 17}
{"name": "Metric.nonempty_iInter_of_nonempty_biInter", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.diam_pos", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "Mathlib.Meta.Positivity.evalDiam", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.cobounded_eq_cocompact", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": true, "tactics": ["nontriviality", "exact", "cobounded_le_cocompact.antisymm"], "tactic_count": 3}
{"name": "tendsto_dist_right_cocompact_atTop", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_dist_left_cocompact_atTop", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "comap_dist_left_atTop_eq_cocompact", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "tendsto_cocompact_of_tendsto_dist_comp_atTop", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.finite_isBounded_inter_isClosed", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": true, "tactics": ["refine", "exact", "exact"], "tactic_count": 3}
{"name": "Continuous.exists_forall_le_of_isBounded", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": true, "tactics": ["refine", "have", "refine", "simp", "exact", "filter_upwards"], "tactic_count": 6}
{"name": "Continuous.exists_forall_ge_of_isBounded", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Bounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoMetric.instFunLikeForall", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.BundledFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoMetric.coe_mk", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.BundledFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoMetric.mk_apply", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.BundledFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoMetric.refl", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.BundledFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoMetric.symm", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.BundledFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoMetric.triangle", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.BundledFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoMetric.instLE", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.BundledFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoMetric.coe_le_coe", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.BundledFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoMetric.instPartialOrder", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.BundledFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoMetric.instBot", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.BundledFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoMetric.coe_bot", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.BundledFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoMetric.bot_apply", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.BundledFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoMetric.instMaxOfAddLeftMonoOfAddRightMono", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.BundledFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoMetric.coe_sup", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.BundledFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoMetric.sup_apply", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.BundledFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoMetric.instSemilatticeSupOfAddLeftMonoOfAddRightMono", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.BundledFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoMetric.nonneg", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.BundledFun", "is_tactic_proof": true, "tactics": ["by_contra", "have", "calc", "d", "exact"], "tactic_count": 5}
{"name": "PseudoMetric.instOrderBot", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.BundledFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoMetric.coe_finsetSup", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.BundledFun", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "PseudoMetric.finsetSup_apply", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.BundledFun", "is_tactic_proof": true, "tactics": ["induction", "singleton", "cons"], "tactic_count": 3}
{"name": "PseudoMetric.IsUltra.le_sup", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.BundledFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoMetric.IsUltra.bot", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.BundledFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoMetric.IsUltra.sup", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.BundledFun", "is_tactic_proof": true, "tactics": ["constructor", "intro", "simp", "calc", "d"], "tactic_count": 5}
{"name": "PseudoMetric.IsUltra.finsetSup", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.BundledFun", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rcases", "simp", "simp_rw", "apply", "simp", "intro", "have", "simp", "refine"], "tactic_count": 11}
{"name": "PseudoMetric.isSymm_ball", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.BundledFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoMetric.isSymm_closedBall", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.BundledFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoMetric.IsUltra.isTrans_ball", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.BundledFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoMetric.IsUltra.isTrans_closedBall", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.BundledFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CantorScheme.inducedMap", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.CantorScheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CantorScheme.Antitone", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.CantorScheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CantorScheme.ClosureAntitone", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.CantorScheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CantorScheme.Disjoint", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.CantorScheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CantorScheme.map_mem", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.CantorScheme", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "CantorScheme.ClosureAntitone.antitone", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.CantorScheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CantorScheme.Antitone.closureAntitone", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.CantorScheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CantorScheme.Disjoint.map_injective", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.CantorScheme", "is_tactic_proof": true, "tactics": ["rintro", "refine", "dsimp", "ext", "induction", "zero", "succ", "simp", "refine", "contrapose", "simp", "refine", "rw", "refine", "rw", "apply", "rw", "apply"], "tactic_count": 18}
{"name": "CantorScheme.VanishingDiam", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.CantorScheme", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CantorScheme.VanishingDiam.dist_lt", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.CantorScheme", "is_tactic_proof": true, "tactics": ["specialize", "rw", "obtain", "use", "intro", "rw", "apply", "apply", "rw", "linarith"], "tactic_count": 10}
{"name": "CantorScheme.VanishingDiam.map_continuous", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.CantorScheme", "is_tactic_proof": true, "tactics": ["rw", "rintro", "obtain", "rw", "refine", "rintro", "rw", "apply", "rw", "apply", "apply", "apply", "apply"], "tactic_count": 13}
{"name": "CantorScheme.ClosureAntitone.map_of_vanishingDiam", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.CantorScheme", "is_tactic_proof": true, "tactics": ["rw", "intro", "choose", "have", "have", "refine", "intro", "apply", "intro", "exact", "have", "rw", "intro", "obtain", "use", "intro", "apply", "obtain", "use", "rw", "intro", "apply", "apply", "rw", "exact"], "tactic_count": 25}
{"name": "CauSeq.tendsto_limit", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.CauSeqFilter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauchySeq.isCauSeq", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.CauSeqFilter", "is_tactic_proof": true, "tactics": ["obtain", "intro", "rcases", "simp", "exists", "intro", "rw", "apply", "apply"], "tactic_count": 9}
{"name": "CauSeq.cauchySeq", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.CauSeqFilter", "is_tactic_proof": true, "tactics": ["refine", "rcases", "obtain", "exists", "simp", "constructor", "exists", "intro", "exists", "rintro", "dsimp", "rw", "apply", "rw", "apply"], "tactic_count": 15}
{"name": "isCauSeq_iff_cauchySeq", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.CauSeqFilter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "completeSpace_of_cauSeq_isComplete", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.CauSeqFilter", "is_tactic_proof": true, "tactics": ["apply", "intro", "have", "exists", "rw", "intro", "obtain", "exists", "simpa"], "tactic_count": 9}
{"name": "Metric.complete_of_convergent_controlled_sequences", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.complete_of_cauchySeq_tendsto", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.cauchySeq_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.cauchySeq_iff'", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.uniformCauchySeqOn_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Cauchy", "is_tactic_proof": true, "tactics": ["constructor", "intro", "let", "have", "rw", "specialize", "rw", "exact", "intro", "rcases", "rcases", "rw", "use", "intro", "rcases", "exact"], "tactic_count": 16}
{"name": "cauchySeq_of_le_tendsto_0'", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Metric.exists_subseq_bounded_of_cauchySeq", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Cauchy", "is_tactic_proof": true, "tactics": ["rw", "have", "intro", "rw", "obtain", "exact", "exact"], "tactic_count": 7}
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{"name": "TopologicalSpace.Closeds.continuous_infEDist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Closeds", "is_tactic_proof": true, "tactics": ["refine", "rintro", "calc", "infEDist", "gcongr"], "tactic_count": 5}
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{"name": "TopologicalSpace.Closeds.isometry_singleton", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Metric.NonemptyCompacts.instMetricSpace", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Metric.lipschitz_infDist_set", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Metric.uniformContinuous_infDist_Hausdorff_dist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LipschitzWith.completion_extension", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "ContractingWith.fixedPoint_isFixedPt", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Contracting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContractingWith.fixedPoint_unique", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Contracting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContractingWith.dist_fixedPoint_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Contracting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContractingWith.aposteriori_dist_iterate_fixedPoint_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Contracting", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "ContractingWith.apriori_dist_iterate_fixedPoint_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Contracting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContractingWith.tendsto_iterate_fixedPoint", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Contracting", "is_tactic_proof": true, "tactics": ["convert", "refine", "apply"], "tactic_count": 3}
{"name": "ContractingWith.fixedPoint_lipschitz_in_map", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Contracting", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContractingWith.isFixedPt_fixedPoint_iterate", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Contracting", "is_tactic_proof": true, "tactics": ["set", "have", "have", "rw", "contrapose", "simpa"], "tactic_count": 6}
{"name": "Metric.instIsReflSetOfProdMatch_1PropLeENNRealEdistOfNNReal", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.instIsSymmSetOfProdMatch_1PropLeENNRealEdistOfNNReal._@.Mathlib.Topology.MetricSpace.Cover.675959687._hygCtx._hyg.63", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.IsCover", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.IsCover.empty", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.isCover_empty_right", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.IsCover.nonempty", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.IsCover.refl", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.IsCover.rfl", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.IsCover.mono", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.IsCover.anti", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.IsCover.mono_radius", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.IsCover.singleton_of_ediam_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.isCover_iff_subset_iUnion_closedEBall", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Cover", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Metric.IsCover.of_maximal_isSeparated", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.exists_finite_isCover_of_totallyBounded", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Cover", "is_tactic_proof": true, "tactics": ["rw", "obtain", "simp", "refine", "refine", "simp", "obtain", "exact"], "tactic_count": 8}
{"name": "Metric.exists_finite_isCover_of_isCompact_closure", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.exists_finite_isCover_of_isCompact", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.isCover_iff_subset_iUnion_closedBall", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Cover", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Metric.IsCover.of_subset_cthickening_of_lt", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.isCover_iff_subset_cthickening", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Cover", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Metric.isCover_closure", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Cover", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Metric.isCover_zero", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Cover", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Metric.IsCover.isCompact", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.IsCover.isCompact_closure", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.isCompact_closure_iff_exists_finite_isCover", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Cover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.externalCoveringNumber", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.CoveringNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.coveringNumber", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.CoveringNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.packingNumber", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.CoveringNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.externalCoveringNumber_empty", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.CoveringNumbers", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Metric.coveringNumber_empty", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.CoveringNumbers", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Metric.packingNumber_empty", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.CoveringNumbers", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Metric.externalCoveringNumber_eq_zero", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.CoveringNumbers", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Metric.externalCoveringNumber_pos_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.CoveringNumbers", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Metric.coveringNumber_eq_zero", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.CoveringNumbers", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Metric.coveringNumber_pos_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.CoveringNumbers", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Metric.packingNumber_eq_zero", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.CoveringNumbers", "is_tactic_proof": true, "tactics": ["simp", "refine", "by_contra", "obtain", "simpa"], "tactic_count": 5}
{"name": "Metric.packingNumber_pos_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.CoveringNumbers", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Metric.externalCoveringNumber_le_coveringNumber", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.CoveringNumbers", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Metric.IsCover.externalCoveringNumber_le_encard", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.CoveringNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.IsCover.coveringNumber_le_encard", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.CoveringNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.IsSeparated.encard_le_packingNumber", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.CoveringNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.externalCoveringNumber_le_encard_self", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.CoveringNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.coveringNumber_le_encard_self", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.CoveringNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.packingNumber_le_encard_self", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.CoveringNumbers", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Metric.externalCoveringNumber_anti", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.CoveringNumbers", "is_tactic_proof": true, "tactics": ["simp_rw", "gcongr", "exact"], "tactic_count": 3}
{"name": "Metric.coveringNumber_anti", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.CoveringNumbers", "is_tactic_proof": true, "tactics": ["simp_rw", "gcongr", "exact"], "tactic_count": 3}
{"name": "Metric.externalCoveringNumber_mono_set", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.CoveringNumbers", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Metric.externalCoveringNumber_zero", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.CoveringNumbers", "is_tactic_proof": true, "tactics": ["refine", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "Metric.coveringNumber_zero", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.CoveringNumbers", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "Metric.packingNumber_zero", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.CoveringNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.coveringNumber_eq_one_of_ediam_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.CoveringNumbers", "is_tactic_proof": true, "tactics": ["refine", "have", "calc", "coveringNumber", "simpa"], "tactic_count": 5}
{"name": "Metric.externalCoveringNumber_eq_one_of_ediam_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.CoveringNumbers", "is_tactic_proof": true, "tactics": ["refine", "exact", "simpa"], "tactic_count": 3}
{"name": "Metric.externalCoveringNumber_le_one_of_ediam_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.CoveringNumbers", "is_tactic_proof": true, "tactics": ["rcases", "rw", "simp", "exact"], "tactic_count": 4}
{"name": "Metric.coveringNumber_le_one_of_ediam_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.CoveringNumbers", "is_tactic_proof": true, "tactics": ["rcases", "rw", "simp", "exact"], "tactic_count": 4}
{"name": "Metric.coveringNumber_singleton", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.CoveringNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.externalCoveringNumber_singleton", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.CoveringNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.packingNumber_singleton", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.CoveringNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.exists_set_encard_eq_coveringNumber", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.CoveringNumbers", "is_tactic_proof": true, "tactics": ["simp", "obtain", "have", "let", "obtain", "refine", "refine", "simp", "exact", "rw", "simp_rw", "rfl"], "tactic_count": 12}
{"name": "Metric.minimalCover", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.CoveringNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.minimalCover_subset", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.CoveringNumbers", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Metric.finite_minimalCover", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.CoveringNumbers", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Metric.isCover_minimalCover", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.CoveringNumbers", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Metric.encard_minimalCover", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.CoveringNumbers", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Metric.exists_set_encard_eq_packingNumber", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.CoveringNumbers", "is_tactic_proof": true, "tactics": ["rcases", "simp", "have", "obtain", "exact", "let", "simp_rw", "simp_rw", "specialize", "obtain", "refine", "refine", "rwa", "rw"], "tactic_count": 14}
{"name": "Metric.maximalSeparatedSet", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.CoveringNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.maximalSeparatedSet_subset", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.CoveringNumbers", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Metric.isSeparated_maximalSeparatedSet", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.CoveringNumbers", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Metric.encard_maximalSeparatedSet", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.CoveringNumbers", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Metric.encard_le_of_isSeparated", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.CoveringNumbers", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Metric.isCover_maximalSeparatedSet", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.CoveringNumbers", "is_tactic_proof": true, "tactics": ["intro", "by_contra", "let", "have", "suffices", "refine", "simp", "constructor", "simp", "exact"], "tactic_count": 10}
{"name": "Metric.packingNumber_two_mul_le_externalCoveringNumber", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.CoveringNumbers", "is_tactic_proof": true, "tactics": ["simp", "intro", "let", "have", "simp", "gcongr", "refine", "apply", "simp", "calc", "edist", "rw", "gcongr", "exact", "simpa"], "tactic_count": 15}
{"name": "Metric.coveringNumber_le_packingNumber", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.CoveringNumbers", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "exact", "simp"], "tactic_count": 4}
{"name": "Metric.coveringNumber_two_mul_le_externalCoveringNumber", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.CoveringNumbers", "is_tactic_proof": true, "tactics": ["rcases", "simp", "refine", "exact"], "tactic_count": 4}
{"name": "Metric.coveringNumber_subset_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.CoveringNumbers", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MetricSpace.ext", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Defs", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "MetricSpace.ofDistTopology", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_of_dist_eq_zero", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dist_eq_zero", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "zero_eq_dist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "dist_ne_zero", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "dist_le_zero", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "dist_pos", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "eq_of_forall_dist_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_of_nndist_eq_zero", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "nndist_eq_zero", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "zero_eq_nndist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Metric.closedBall_zero", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.sphere_zero", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.subsingleton_closedBall", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Defs", "is_tactic_proof": true, "tactics": ["rcases", "rw", "exact", "rw", "exact"], "tactic_count": 5}
{"name": "Metric.subsingleton_sphere", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MetricSpace.replaceUniformity", "kind": "abbrev", "module": "Mathlib.Topology.MetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MetricSpace.replaceUniformity_eq", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Defs", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "MetricSpace.replaceTopology", "kind": "abbrev", "module": "Mathlib.Topology.MetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MetricSpace.replaceTopology_eq", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Defs", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "MetricSpace.replaceBornology", "kind": "abbrev", "module": "Mathlib.Topology.MetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MetricSpace.replaceBornology_eq", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Defs", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "instMetricSpaceEmpty", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instMetricSpacePUnit", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDistAdditive", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDistMultiplicative", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dist_ofMul", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dist_ofAdd", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dist_toMul", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dist_toAdd", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instMetricSpaceAdditive", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instMetricSpaceMultiplicative", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDistOrderDual", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dist_toDual", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dist_ofDual", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instMetricSpaceOrderDual", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "term_→ᵈ_", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Topology_MetricSpace_Dilation___macroRules_term_→ᵈ__1", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Topology_MetricSpace_Dilation___unexpand_Dilation_1", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dilation.funLike", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dilation.toDilationClass", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dilation.toFun_eq_coe", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dilation.coe_mk", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dilation.congr_fun", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dilation.congr_arg", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dilation.ext", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dilation.mk_coe", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dilation.copy", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dilation.copy_eq_self", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dilation.ratio", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dilation.ratio_of_trivial", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dilation.ratio_of_subsingleton", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dilation.ratio_ne_zero", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": true, "tactics": ["rw", "exact", "exact"], "tactic_count": 3}
{"name": "Dilation.ratio_pos", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dilation.edist_eq", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": true, "tactics": ["rw", "rcases", "replace", "rcases", "simp", "simp", "exact"], "tactic_count": 7}
{"name": "Dilation.nndist_eq", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Dilation.dist_eq", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Dilation.ratio_unique", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Dilation.ratio_unique_of_nndist_ne_zero", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dilation.ratio_unique_of_dist_ne_zero", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dilation.mkOfNNDistEq", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dilation.coe_mkOfNNDistEq", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dilation.mk_coe_of_nndist_eq", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dilation.mkOfDistEq", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dilation.coe_mkOfDistEq", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dilation.mk_coe_of_dist_eq", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Isometry.toDilation", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Isometry.toDilation_ratio", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "obtain", "exact"], "tactic_count": 4}
{"name": "Dilation.lipschitz", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dilation.antilipschitz", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dilation.injective", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dilation.id", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dilation.instInhabited", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dilation.coe_id", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dilation.ratio_id", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "rcases", "refine", "simp"], "tactic_count": 5}
{"name": "Dilation.comp", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dilation.comp_assoc", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dilation.coe_comp", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dilation.comp_apply", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dilation.ratio_comp'", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": true, "tactics": ["rcases", "have", "simp_rw", "rwa"], "tactic_count": 4}
{"name": "Dilation.comp_id", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dilation.id_comp", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dilation.instMonoid", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dilation.one_def", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dilation.mul_def", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dilation.coe_one", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dilation.coe_mul", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dilation.ratio_one", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dilation.ratio_mul", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "exact"], "tactic_count": 3}
{"name": "Dilation.ratioHom", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dilation.ratio_pow", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dilation.cancel_right", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dilation.cancel_left", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dilation.isUniformInducing", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dilation.tendsto_nhds_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dilation.toContinuous", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dilation.ediam_image", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": true, "tactics": ["refine", "apply", "rw", "exacts"], "tactic_count": 4}
{"name": "Dilation.ediam_range", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Dilation.mapsTo_eball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dilation.mapsTo_closedEBall", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dilation.comp_continuousOn_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dilation.comp_continuous_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dilation.isUniformEmbedding", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dilation.isEmbedding", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dilation.isClosedEmbedding", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dilation.ratio_comp", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dilation.diam_image", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Dilation.diam_range", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Dilation.mapsTo_ball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dilation.mapsTo_sphere", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dilation.mapsTo_closedBall", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dilation.tendsto_cobounded", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dilation.comap_cobounded", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Dilation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDilationClassOfDilationEquivClass", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.DilationEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "term_≃ᵈ_", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.DilationEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Topology_MetricSpace_DilationEquiv___macroRules_term_≃ᵈ__1", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.DilationEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Topology_MetricSpace_DilationEquiv___unexpand_DilationEquiv_1", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.DilationEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DilationEquiv.instEquivLike", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.DilationEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DilationEquiv.instDilationEquivClass", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.DilationEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DilationEquiv.coe_toEquiv", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.DilationEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DilationEquiv.ext", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.DilationEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DilationEquiv.symm", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.DilationEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DilationEquiv.symm_symm", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.DilationEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DilationEquiv.symm_bijective", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.DilationEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DilationEquiv.apply_symm_apply", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.DilationEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DilationEquiv.symm_apply_apply", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.DilationEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DilationEquiv.Simps.symm_apply", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.DilationEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DilationEquiv.ratio_toDilation", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.DilationEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DilationEquiv.refl", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.DilationEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DilationEquiv.refl_symm", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.DilationEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DilationEquiv.ratio_refl", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.DilationEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DilationEquiv.trans", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.DilationEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DilationEquiv.refl_trans", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.DilationEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DilationEquiv.trans_refl", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.DilationEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DilationEquiv.symm_trans_self", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.DilationEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DilationEquiv.self_trans_symm", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.DilationEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DilationEquiv.surjective", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.DilationEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DilationEquiv.bijective", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.DilationEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DilationEquiv.injective", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.DilationEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DilationEquiv.ratio_trans", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.DilationEquiv", "is_tactic_proof": true, "tactics": ["by_cases", "have", "e.surjective.forall₂.2", "refine", "simp", "exact"], "tactic_count": 6}
{"name": "DilationEquiv.ratio_symm", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.DilationEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DilationEquiv.instGroup", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.DilationEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DilationEquiv.mul_def", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.DilationEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DilationEquiv.one_def", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.DilationEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DilationEquiv.inv_def", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.DilationEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DilationEquiv.coe_mul", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.DilationEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DilationEquiv.coe_one", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.DilationEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DilationEquiv.coe_inv", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.DilationEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DilationEquiv.ratioHom", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.DilationEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DilationEquiv.ratio_inv", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.DilationEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DilationEquiv.ratio_pow", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.DilationEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DilationEquiv.ratio_zpow", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.DilationEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DilationEquiv.toPerm", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.DilationEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DilationEquiv.coe_pow", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.DilationEquiv", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "IsometryEquiv.toDilationEquiv", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.DilationEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.toDilationEquiv_apply", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.DilationEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.toDilationEquiv_symm", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.DilationEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.coe_toDilationEquiv", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.DilationEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.coe_symm_toDilationEquiv", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.DilationEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.toDilationEquiv_toDilation", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.DilationEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.toDilationEquiv_ratio", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.DilationEquiv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "DilationEquiv.toHomeomorph", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.DilationEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DilationEquiv.toHomeomorph_symm", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.DilationEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DilationEquiv.coe_toHomeomorph", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.DilationEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DilationEquiv.coe_symm_toHomeomorph", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.DilationEquiv", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DilationEquiv.map_cobounded", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.DilationEquiv", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Metric.equicontinuousAt_iff_right", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.equicontinuousAt_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.equicontinuousAt_iff_pair", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Equicontinuity", "is_tactic_proof": true, "tactics": ["rw", "constructor", "intro", "exact", "intro", "rcases", "refine", "exact"], "tactic_count": 8}
{"name": "Metric.uniformEquicontinuous_iff_right", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.uniformEquicontinuous_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.equicontinuousAt_of_continuity_modulus", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Equicontinuity", "is_tactic_proof": true, "tactics": ["rw", "intro", "filter_upwards"], "tactic_count": 3}
{"name": "Metric.uniformEquicontinuous_of_continuity_modulus", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Equicontinuity", "is_tactic_proof": true, "tactics": ["rw", "intro", "rcases", "refine", "calc", "dist"], "tactic_count": 6}
{"name": "Metric.equicontinuous_of_continuity_modulus", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.glueDist", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Gluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.MetricSpace.Gluing.0.Metric.glueDist_self", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Gluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.glueDist_glued_points", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Gluing", "is_tactic_proof": false, "tactics": ["have", "have", "refine", "have", "rw", "exact", "simp"], "tactic_count": 7}
{"name": "_private.Mathlib.Topology.MetricSpace.Gluing.0.Metric.glueDist_comm", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Gluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.glueDist_swap", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Gluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.le_glueDist_inl_inr", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Gluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.le_glueDist_inr_inl", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Gluing", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "_private.Mathlib.Topology.MetricSpace.Gluing.0.Metric.glueDist_triangle_inl_inr_inr", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Gluing", "is_tactic_proof": true, "tactics": ["simp", "rw", "refine", "exact", "linarith"], "tactic_count": 5}
{"name": "_private.Mathlib.Topology.MetricSpace.Gluing.0.Metric.glueDist_triangle_inl_inr_inl", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Gluing", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "rw", "refine", "rw", "linarith"], "tactic_count": 6}
{"name": "_private.Mathlib.Topology.MetricSpace.Gluing.0.Metric.glueDist_triangle", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Gluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.MetricSpace.Gluing.0.Metric.eq_of_glueDist_eq_zero", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Gluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.Sum.mem_uniformity_iff_glueDist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Gluing", "is_tactic_proof": true, "tactics": ["simp", "constructor", "rintro", "refine", "rintro", "exact", "exact", "exact", "exact", "rintro", "constructor"], "tactic_count": 11}
{"name": "Metric.glueMetricApprox", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Gluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.Sum.dist", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Gluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.Sum.dist_eq_glueDist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Gluing", "is_tactic_proof": true, "tactics": ["cases", "first", "rfl", "simp"], "tactic_count": 4}
{"name": "_private.Mathlib.Topology.MetricSpace.Gluing.0.Metric.Sum.dist_comm", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Gluing", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Metric.Sum.one_le_dist_inl_inr", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Gluing", "is_tactic_proof": true, "tactics": ["grw"], "tactic_count": 1}
{"name": "Metric.Sum.one_le_dist_inr_inl", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Gluing", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "_private.Mathlib.Topology.MetricSpace.Gluing.0.Metric.Sum.mem_uniformity", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Gluing", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "rcases", "rcases", "refine", "rintro", "exact", "cases", "cases", "exact", "rintro", "constructor"], "tactic_count": 12}
{"name": "Metric.metricSpaceSum", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Gluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.Sum.dist_eq", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Gluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.isometry_inl", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Gluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.isometry_inr", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Gluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.Sigma.dist", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Gluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.Sigma.instDist", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Gluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.Sigma.dist_same", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Gluing", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Metric.Sigma.dist_ne", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Gluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.Sigma.one_le_dist_of_ne", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Gluing", "is_tactic_proof": true, "tactics": ["rw", "linarith"], "tactic_count": 2}
{"name": "Metric.Sigma.fst_eq_of_dist_lt_one", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Gluing", "is_tactic_proof": true, "tactics": ["cases", "contrapose", "apply"], "tactic_count": 3}
{"name": "Metric.Sigma.dist_triangle", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Gluing", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "rcases", "simpa", "simp", "calc", "dist", "simpa", "rcases", "simp", "calc", "dist", "dist", "rcases", "simp", "calc", "dist", "dist", "simp", "calc", "dist", "dist"], "tactic_count": 22}
{"name": "Metric.Sigma.isOpen_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Gluing", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "obtain", "refine", "rintro", "rcases", "simp", "exact", "apply", "calc", "refine", "obtain", "refine", "apply", "rw", "exact"], "tactic_count": 16}
{"name": "Metric.Sigma.metricSpace", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Gluing", "is_tactic_proof": true, "tactics": ["refine", "rintro", "simp", "rintro", "rcases", "simp", "simp", "abel", "rintro", "rcases", "simp", "intro", "apply", "calc"], "tactic_count": 14}
{"name": "Metric.Sigma.isometry_mk", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Gluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.Sigma.completeSpace", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Gluing", "is_tactic_proof": true, "tactics": ["set", "set", "have", "simp", "exact", "have", "refine", "convert", "simp"], "tactic_count": 9}
{"name": "Metric.gluePremetric", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Gluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.GlueSpace", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Gluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.instMetricSpaceGlueSpace", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Gluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.toGlueL", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Gluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.toGlueR", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Gluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.inhabitedLeft", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Gluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.inhabitedRight", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Gluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.toGlue_commute", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Gluing", "is_tactic_proof": true, "tactics": ["let", "let", "funext", "simp", "refine", "exact"], "tactic_count": 6}
{"name": "Metric.toGlueL_isometry", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Gluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.toGlueR_isometry", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Gluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.inductiveLimitDist", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Gluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.inductiveLimitDist_eq_dist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Gluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.inductivePremetric", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Gluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.InductiveLimit", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Gluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.instMetricSpaceInductiveLimit", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Gluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.toInductiveLimit", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Gluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.instInhabitedInductiveLimitOfOfNatNat", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Gluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.toInductiveLimit_isometry", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Gluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.toInductiveLimit_commute", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Gluing", "is_tactic_proof": true, "tactics": ["let", "let", "funext", "simp", "refine", "change", "rw", "rfl", "rfl", "exact"], "tactic_count": 10}
{"name": "Metric.dense_iUnion_range_toInductiveLimit", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Gluing", "is_tactic_proof": true, "tactics": ["refine", "rintro", "refine"], "tactic_count": 3}
{"name": "Metric.separableSpaceInductiveLimit_of_separableSpace", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Gluing", "is_tactic_proof": true, "tactics": ["choose", "let", "refine", "refine", "calc", "range"], "tactic_count": 6}
{"name": "_private.Mathlib.Topology.MetricSpace.GromovHausdorff.0.termℓ_infty_ℝ", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.GromovHausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.MetricSpace.GromovHausdorff.0._aux_Mathlib_Topology_MetricSpace_GromovHausdorff___macroRules__private_Mathlib_Topology_MetricSpace_GromovHausdorff_0_termℓ_infty_ℝ_1", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.GromovHausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.MetricSpace.GromovHausdorff.0._aux_Mathlib_Topology_MetricSpace_GromovHausdorff___unexpand_lp_1", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.GromovHausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.MetricSpace.GromovHausdorff.0.GromovHausdorff.IsometryRel", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.GromovHausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.MetricSpace.GromovHausdorff.0.GromovHausdorff.equivalence_isometryRel", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.GromovHausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GromovHausdorff.IsometryRel.setoid", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.GromovHausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GromovHausdorff.GHSpace", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.GromovHausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GromovHausdorff.toGHSpace", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.GromovHausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GromovHausdorff.instInhabitedGHSpace", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.GromovHausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GromovHausdorff.GHSpace.Rep", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.GromovHausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GromovHausdorff.eq_toGHSpace_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.GromovHausdorff", "is_tactic_proof": true, "tactics": ["simp", "refine", "rcases", "have", "use", "rw", "rintro", "have", "have", "dsimp", "exact"], "tactic_count": 11}
{"name": "GromovHausdorff.eq_toGHSpace", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.GromovHausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GromovHausdorff.repGHSpaceMetricSpace", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.GromovHausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GromovHausdorff.rep_gHSpace_compactSpace", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.GromovHausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GromovHausdorff.rep_gHSpace_nonempty", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.GromovHausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GromovHausdorff.GHSpace.toGHSpace_rep", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.GromovHausdorff", "is_tactic_proof": true, "tactics": ["change", "rw", "exact"], "tactic_count": 3}
{"name": "GromovHausdorff.toGHSpace_eq_toGHSpace_iff_isometryEquiv", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.GromovHausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GromovHausdorff.instDistGHSpace", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.GromovHausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GromovHausdorff.ghDist", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.GromovHausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GromovHausdorff.dist_ghDist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.GromovHausdorff", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "GromovHausdorff.ghDist_le_hausdorffDist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.GromovHausdorff", "is_tactic_proof": true, "tactics": ["in", "separable", "separable", "rcases", "let", "let", "let", "have", "have", "have", "let", "have", "have", "have", "have", "rw", "exact", "rw", "let", "have", "hausdorffDist_image", "rw", "let", "let", "have", "rw", "exact", "have", "rw", "exact", "refine", "simp", "intro", "rw", "exact", "apply", "exists"], "tactic_count": 37}
{"name": "GromovHausdorff.hausdorffDist_optimal", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.GromovHausdorff", "is_tactic_proof": true, "tactics": ["inhabit", "have", "hausdorffDist", "hausdorffDist", "hausdorffDist", "intro", "rcases", "rcases", "have", "rcases", "have", "rw", "have", "exact", "exists_dist_lt_of_hausdorffDist_lt", "q.isCompact.isBounded)", "rcases", "rcases", "rw", "have", "have", "calc", "diam", "diam_union", "rw", "gcongr", "let", "inl", "inr", "let", "dist", "have", "simp", "repeat", "exact", "calc", "exact", "calc", "exact", "exact", "exact", "calc", "have", "intro", "cases", "apply", "apply", "refine", "rw", "exact", "let", "have", "hausdorffDist_optimal_le_HD", "refine", "have", "intro", "have", "rcases", "exists_dist_lt_of_hausdorffDist_lt", "q.isCompact.isBounded)", "have", "rcases", "calc", "have", "intro", "have", "rcases", "exists_dist_lt_of_hausdorffDist_lt", "q.isCompact.isBounded)", "have", "rcases", "calc", "simp", "inequality", "have", "hausdorffDist", "intro", "by_cases", "exact", "calc", "hausdorffDist", "hausdorffDist_optimal_le_HD", "refine", "apply", "refine", "rintro", "exact", "exact"], "tactic_count": 88}
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{"name": "TopologicalSpace.NonemptyCompacts.toGHSpace", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.GromovHausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GromovHausdorff.ghDist_le_nonemptyCompacts_dist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.GromovHausdorff", "is_tactic_proof": true, "tactics": ["have", "have", "have", "have", "have", "rw", "exact"], "tactic_count": 7}
{"name": "GromovHausdorff.toGHSpace_lipschitz", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.GromovHausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "GromovHausdorff.instInhabitedAuxGluingStruct", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.GromovHausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GromovHausdorff.auxGluing", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.GromovHausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GromovHausdorff.instCompleteSpaceGHSpace", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.GromovHausdorff", "is_tactic_proof": true, "tactics": ["set", "have", "positivity", "refine", "let", "let", "have", "dsimp", "let", "have", "let", "c", "have", "let", "let", "let", "let", "let", "have", "intro", "refine", "exact", "have", "range", "optimalGHInjl", "intro", "change", "range", "c", "simp", "rw", "simp", "have", "range", "optimalGHInjr", "intro", "rfl", "have", "rw", "exact", "apply", "exact", "let", "have", "refine", "rw", "exact", "le_of_lt", "rcases", "have", "intro", "rw", "toGHSpace_eq_toGHSpace_iff_isometryEquiv]", "constructor", "convert", "use", "apply", "refine", "apply"], "tactic_count": 59}
{"name": "_private.Mathlib.Topology.MetricSpace.GromovHausdorffRealized.0.GromovHausdorff.ProdSpaceFun", "kind": "abbrev", "module": "Mathlib.Topology.MetricSpace.GromovHausdorffRealized", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.MetricSpace.GromovHausdorffRealized.0.GromovHausdorff.Cb", "kind": "abbrev", "module": "Mathlib.Topology.MetricSpace.GromovHausdorffRealized", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.MetricSpace.GromovHausdorffRealized.0.GromovHausdorff.maxVar", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.GromovHausdorffRealized", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.MetricSpace.GromovHausdorffRealized.0.GromovHausdorff.one_le_maxVar", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.GromovHausdorffRealized", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GromovHausdorff.candidates", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.GromovHausdorffRealized", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.MetricSpace.GromovHausdorffRealized.0.GromovHausdorff.candidatesB", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.GromovHausdorffRealized", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.MetricSpace.GromovHausdorffRealized.0.GromovHausdorff.maxVar_bound", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.GromovHausdorffRealized", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.MetricSpace.GromovHausdorffRealized.0.GromovHausdorff.candidates_symm", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.GromovHausdorffRealized", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.MetricSpace.GromovHausdorffRealized.0.GromovHausdorff.candidates_triangle", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.GromovHausdorffRealized", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.MetricSpace.GromovHausdorffRealized.0.GromovHausdorff.candidates_refl", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.GromovHausdorffRealized", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.MetricSpace.GromovHausdorffRealized.0.GromovHausdorff.candidates_nonneg", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.GromovHausdorffRealized", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "_private.Mathlib.Topology.MetricSpace.GromovHausdorffRealized.0.GromovHausdorff.candidates_dist_inl", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.GromovHausdorffRealized", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.MetricSpace.GromovHausdorffRealized.0.GromovHausdorff.candidates_dist_inr", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.GromovHausdorffRealized", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.MetricSpace.GromovHausdorffRealized.0.GromovHausdorff.candidates_le_maxVar", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.GromovHausdorffRealized", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.MetricSpace.GromovHausdorffRealized.0.GromovHausdorff.candidates_dist_bound", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.GromovHausdorffRealized", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.MetricSpace.GromovHausdorffRealized.0.GromovHausdorff.candidates_lipschitz_aux", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.GromovHausdorffRealized", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.MetricSpace.GromovHausdorffRealized.0.GromovHausdorff.candidates_lipschitz", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.GromovHausdorffRealized", "is_tactic_proof": true, "tactics": ["apply", "rintro", "rw", "use", "rw", "exact"], "tactic_count": 6}
{"name": "_private.Mathlib.Topology.MetricSpace.GromovHausdorffRealized.0.GromovHausdorff.closed_candidatesB", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.GromovHausdorffRealized", "is_tactic_proof": false, "tactics": ["have", "isClosed_eq", "have", "isClosed_eq", "have", "isClosed_eq", "have", "isClosed_le", "have", "have", "isClosed_le", "have", "candidatesB", "ext", "simp", "rw", "repeat", "first", "apply", "apply", "apply", "apply", "apply", "apply", "apply", "apply", "intro"], "tactic_count": 27}
{"name": "GromovHausdorff.HD", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.GromovHausdorffRealized", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GromovHausdorff.HD_below_aux1", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.GromovHausdorffRealized", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.MetricSpace.GromovHausdorffRealized.0.GromovHausdorff.HD_bound_aux1", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.GromovHausdorffRealized", "is_tactic_proof": true, "tactics": ["obtain", "refine", "calc"], "tactic_count": 3}
{"name": "GromovHausdorff.HD_below_aux2", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.GromovHausdorffRealized", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.MetricSpace.GromovHausdorffRealized.0.GromovHausdorff.HD_bound_aux2", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.GromovHausdorffRealized", "is_tactic_proof": true, "tactics": ["obtain", "refine", "calc"], "tactic_count": 3}
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{"name": "_private.Mathlib.Topology.MetricSpace.GromovHausdorffRealized.0.GromovHausdorff.HD_lipschitz_aux2", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.GromovHausdorffRealized", "is_tactic_proof": true, "tactics": ["obtain", "have", "obtain", "have", "hcf", "have", "ciSup_mono", "ciInf_mono", "have", "intro", "refine", "intro", "simpa", "change", "exact", "have", "refine", "intro", "simpa", "simpa", "simpa"], "tactic_count": 21}
{"name": "_private.Mathlib.Topology.MetricSpace.GromovHausdorffRealized.0.GromovHausdorff.HD_lipschitz_aux3", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.GromovHausdorffRealized", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.MetricSpace.GromovHausdorffRealized.0.GromovHausdorff.HD_continuous", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.GromovHausdorffRealized", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.MetricSpace.GromovHausdorffRealized.0.GromovHausdorff.isCompact_candidatesB", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.GromovHausdorffRealized", "is_tactic_proof": true, "tactics": ["refine", "rintro", "simp", "exact", "refine", "have", "tendsto_const_nhds.mul", "simpa", "rintro", "exact"], "tactic_count": 10}
{"name": "GromovHausdorff.candidatesBOfCandidates", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.GromovHausdorffRealized", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GromovHausdorff.candidatesBOfCandidates_mem", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.GromovHausdorffRealized", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.MetricSpace.GromovHausdorffRealized.0.GromovHausdorff.dist_mem_candidates", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.GromovHausdorffRealized", "is_tactic_proof": false, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "GromovHausdorff.candidatesBDist", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.GromovHausdorffRealized", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GromovHausdorff.candidatesBDist_mem_candidatesB", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.GromovHausdorffRealized", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.MetricSpace.GromovHausdorffRealized.0.GromovHausdorff.candidatesB_nonempty", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.GromovHausdorffRealized", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GromovHausdorff.HD_candidatesBDist_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.GromovHausdorffRealized", "is_tactic_proof": true, "tactics": ["refine", "have", "ciInf_le", "have", "calc", "dist", "gcongr", "exact", "have", "ciInf_le", "have", "calc", "dist", "gcongr", "exact"], "tactic_count": 15}
{"name": "_private.Mathlib.Topology.MetricSpace.GromovHausdorffRealized.0.GromovHausdorff.exists_minimizer", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.GromovHausdorffRealized", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.MetricSpace.GromovHausdorffRealized.0.GromovHausdorff.optimalGHDist", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.GromovHausdorffRealized", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.MetricSpace.GromovHausdorffRealized.0.GromovHausdorff.optimalGHDist_mem_candidatesB", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.GromovHausdorffRealized", "is_tactic_proof": true, "tactics": ["cases", "assumption"], "tactic_count": 2}
{"name": "_private.Mathlib.Topology.MetricSpace.GromovHausdorffRealized.0.GromovHausdorff.HD_optimalGHDist_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.GromovHausdorffRealized", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GromovHausdorff.premetricOptimalGHDist", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.GromovHausdorffRealized", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GromovHausdorff.OptimalGHCoupling", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.GromovHausdorffRealized", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GromovHausdorff.instMetricSpaceOptimalGHCoupling", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.GromovHausdorffRealized", "is_tactic_proof": true, "tactics": ["unfold", "infer_instance"], "tactic_count": 2}
{"name": "GromovHausdorff.optimalGHInjl", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.GromovHausdorffRealized", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GromovHausdorff.isometry_optimalGHInjl", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.GromovHausdorffRealized", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GromovHausdorff.optimalGHInjr", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.GromovHausdorffRealized", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GromovHausdorff.isometry_optimalGHInjr", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.GromovHausdorffRealized", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GromovHausdorff.compactSpace_optimalGHCoupling", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.GromovHausdorffRealized", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "GromovHausdorff.hausdorffDist_optimal_le_HD", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.GromovHausdorffRealized", "is_tactic_proof": true, "tactics": ["refine", "have", "rintro", "have", "have", "le_csSup", "have", "rcases", "exact", "refine", "inhabit", "rcases", "exact", "rintro", "have", "have", "le_csSup", "have", "rcases", "refine", "rwa"], "tactic_count": 21}
{"name": "Real.fromBinary", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.HausdorffAlexandroff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.fromBinary_continuous", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffAlexandroff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.fromBinary_surjective", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffAlexandroff", "is_tactic_proof": true, "tactics": ["refine", "simp"], "tactic_count": 2}
{"name": "cantorToHilbert", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.HausdorffAlexandroff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cantorToHilbert_continuous", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffAlexandroff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cantorToHilbert_surjective", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffAlexandroff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_retractionCantorSet", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffAlexandroff", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "exists_nat_bool_continuous_surjective_of_compact", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffAlexandroff", "is_tactic_proof": true, "tactics": ["let", "obtain", "let", "let", "let", "have", "obtain", "exists_retractionCantorSet", "let", "have", "let", "have", "have", "exact"], "tactic_count": 14}
{"name": "dimH", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.HausdorffDimension", "is_tactic_proof": true, "tactics": ["borelize"], "tactic_count": 1}
{"name": "dimH_def", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDimension", "is_tactic_proof": true, "tactics": ["borelize"], "tactic_count": 1}
{"name": "hausdorffMeasure_of_lt_dimH", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDimension", "is_tactic_proof": true, "tactics": ["simp", "rcases", "rw", "exact"], "tactic_count": 4}
{"name": "dimH_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dimH_le_of_hausdorffMeasure_ne_top", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_dimH_of_hausdorffMeasure_eq_top", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDimension", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "hausdorffMeasure_of_dimH_lt", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDimension", "is_tactic_proof": true, "tactics": ["rw", "rcases", "rw", "exact"], "tactic_count": 4}
{"name": "measure_zero_of_dimH_lt", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_dimH_of_hausdorffMeasure_ne_zero", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dimH_of_hausdorffMeasure_ne_zero_ne_top", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dimH_eq_iInf", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDimension", "is_tactic_proof": true, "tactics": ["apply", "rw", "simp", "intro", "by_contra", "simpa", "by_contra", "rcases", "have", "exact"], "tactic_count": 10}
{"name": "dimH_mono", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDimension", "is_tactic_proof": true, "tactics": ["borelize", "exact"], "tactic_count": 2}
{"name": "dimH_subsingleton", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDimension", "is_tactic_proof": true, "tactics": ["borelize", "apply", "refine", "exact"], "tactic_count": 4}
{"name": "dimH_empty", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dimH_singleton", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dimH_iUnion", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDimension", "is_tactic_proof": true, "tactics": ["borelize", "refine", "contrapose", "have", "rw", "exact"], "tactic_count": 6}
{"name": "dimH_bUnion", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDimension", "is_tactic_proof": true, "tactics": ["haveI", "rw"], "tactic_count": 2}
{"name": "dimH_sUnion", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDimension", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "dimH_union", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDimension", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "dimH_countable", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dimH_finite", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dimH_coe_finset", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_mem_nhdsWithin_lt_dimH_of_lt_dimH", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDimension", "is_tactic_proof": true, "tactics": ["contrapose", "rcases", "calc", "dimH"], "tactic_count": 4}
{"name": "bsupr_limsup_dimH", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDimension", "is_tactic_proof": true, "tactics": ["refine", "refine", "exact", "refine", "rcases", "refine", "rcases", "exact"], "tactic_count": 8}
{"name": "iSup_limsup_dimH", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDimension", "is_tactic_proof": true, "tactics": ["refine", "refine", "exact", "rw"], "tactic_count": 4}
{"name": "HolderOnWith.dimH_image_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDimension", "is_tactic_proof": true, "tactics": ["borelize", "refine", "have", "rw", "have", "contrapose", "finiteness", "rw", "exacts"], "tactic_count": 9}
{"name": "HolderWith.dimH_image_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HolderWith.dimH_range_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dimH_image_le_of_locally_holder_on", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDimension", "is_tactic_proof": true, "tactics": ["choose", "rcases", "replace", "rw", "exact"], "tactic_count": 5}
{"name": "dimH_range_le_of_locally_holder_on", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDimension", "is_tactic_proof": true, "tactics": ["rw", "refine", "simpa"], "tactic_count": 3}
{"name": "LipschitzOnWith.dimH_image_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDimension", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "LipschitzWith.dimH_image_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzWith.dimH_range_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dimH_image_le_of_locally_lipschitzOn", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDimension", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "dimH_range_le_of_locally_lipschitzOn", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDimension", "is_tactic_proof": true, "tactics": ["rw", "refine", "simpa"], "tactic_count": 3}
{"name": "AntilipschitzWith.dimH_preimage_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDimension", "is_tactic_proof": true, "tactics": ["borelize", "refine", "have", "rw", "contrapose", "exact"], "tactic_count": 6}
{"name": "AntilipschitzWith.le_dimH_image", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Isometry.dimH_image", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.dimH_image", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.dimH_preimage", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDimension", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsometryEquiv.dimH_univ", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDimension", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ContinuousLinearEquiv.dimH_image", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearEquiv.dimH_preimage", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDimension", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ContinuousLinearEquiv.dimH_univ", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDimension", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.dimH_ball_pi", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDimension", "is_tactic_proof": true, "tactics": ["cases", "rwa", "exact", "rw", "have", "rw", "refine", "simp", "exact"], "tactic_count": 9}
{"name": "Real.dimH_ball_pi_fin", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDimension", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.dimH_univ_pi", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDimension", "is_tactic_proof": true, "tactics": ["simp", "iSup_const]"], "tactic_count": 2}
{"name": "Real.dimH_univ_pi_fin", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDimension", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.dimH_of_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDimension", "is_tactic_proof": true, "tactics": ["have", "rw", "refine", "exact", "have", "rcases", "simpa"], "tactic_count": 7}
{"name": "Real.dimH_of_nonempty_interior", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.Convex.dimH_eq_finrank_vectorSpan", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDimension", "is_tactic_proof": true, "tactics": ["have", "let", "have", "rw", "direction_affineSpan", "simp_rw", "simpa"], "tactic_count": 7}
{"name": "Real.dimH_univ_eq_finrank", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.dimH_univ", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDimension", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Real.dimH_lt_top", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDimension", "is_tactic_proof": true, "tactics": ["calc", "dimH"], "tactic_count": 2}
{"name": "Real.dimH_ne_top", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.hausdorffMeasure_of_finrank_lt", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDimension", "is_tactic_proof": true, "tactics": ["lift", "rw", "apply", "rw", "exact"], "tactic_count": 5}
{"name": "dense_compl_of_dimH_lt_finrank", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDimension", "is_tactic_proof": true, "tactics": ["refine", "rw", "rw", "exact"], "tactic_count": 4}
{"name": "ContDiffOn.dimH_image_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.dimH_range_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiffOn.dense_compl_image_of_dimH_lt_finrank", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContDiff.dense_compl_range_of_finrank_lt_finrank", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dimH_orthogonalProjection_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDimension", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.infEDist", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.infEDist_empty", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.le_infEDist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Metric.infEDist_union", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.infEDist_iUnion", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.infEDist_biUnion", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Metric.infEDist_singleton", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.infEDist_le_edist_of_mem", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.infEDist_zero_of_mem", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.infEDist_anti", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.infEDist_lt_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Metric.infEDist_le_infEDist_add_edist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.infEDist_le_edist_add_infEDist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Metric.edist_le_infEDist_add_ediam", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "calc", "edist"], "tactic_count": 4}
{"name": "Metric.continuous_infEDist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.infEDist_closure", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["refine", "refine", "have", "have", "obtain", "obtain", "calc", "infEDist"], "tactic_count": 8}
{"name": "Metric.mem_closure_iff_infEDist_zero", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.mem_iff_infEDist_zero_of_closed", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Metric.infEDist_pos_iff_notMem_closure", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Metric.infEDist_closure_pos_iff_notMem_closure", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Metric.exists_real_pos_lt_infEDist_of_notMem_closure", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["rw", "rcases", "exact"], "tactic_count": 3}
{"name": "Metric.disjoint_closedEBall_of_lt_infEDist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["rw", "intro", "apply", "calc", "infEDist"], "tactic_count": 5}
{"name": "Metric.infEDist_image", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Metric.infEDist_smul", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.exists_iUnion_isClosed", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["obtain", "let", "have", "by_contra", "have", "exact", "refine", "show", "refine", "have", "rw", "have", "have", "rcases", "simp", "exact", "show", "intro", "simp", "apply"], "tactic_count": 20}
{"name": "IsCompact.exists_infEDist_eq_edist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["have", "obtain", "exact"], "tactic_count": 3}
{"name": "Metric.exists_pos_forall_lt_edist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["rcases", "use", "simp", "obtain", "have", "rcases", "exact"], "tactic_count": 7}
{"name": "Metric.infEDist_prod", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["simp_rw", "iInf_sup_eq,"], "tactic_count": 2}
{"name": "Metric.definition._@.Mathlib.Topology.MetricSpace.HausdorffDistance.433595793._hygCtx._hyg.2", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.wrapped._@.Mathlib.Topology.MetricSpace.HausdorffDistance.433595793._hygCtx._hyg.2", "kind": "opaque", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.hausdorffEDist", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.hausdorffEDist_def", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["intros", "delta", "rw", "rfl"], "tactic_count": 4}
{"name": "Metric.hausdorffEDist_self", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Metric.hausdorffEDist_comm", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Metric.hausdorffEDist_le_of_infEDist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Metric.hausdorffEDist_le_of_mem_edist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["refine", "rcases", "exact", "rcases", "exact"], "tactic_count": 5}
{"name": "Metric.infEDist_le_hausdorffEDist_of_mem", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["rw", "refine", "exact"], "tactic_count": 3}
{"name": "Metric.exists_edist_lt_of_hausdorffEDist_lt", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.infEDist_le_infEDist_add_hausdorffEDist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.hausdorffEDist_image", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Metric.hausdorffEDist_le_ediam", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "refine", "intro", "exact", "intro", "exact"], "tactic_count": 7}
{"name": "Metric.hausdorffEDist_triangle", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["rw", "simp", "constructor", "change", "exact", "calc", "infEDist", "change", "exact", "calc", "infEDist"], "tactic_count": 11}
{"name": "Metric.hausdorffEDist_zero_iff_closure_eq_closure", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Metric.hausdorffEDist_self_closure", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Metric.hausdorffEDist_closure_left", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["refine", "calc", "calc"], "tactic_count": 3}
{"name": "Metric.hausdorffEDist_closure_right", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Metric.hausdorffEDist_closure", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsClosed.hausdorffEDist_zero_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Metric.hausdorffEDist_empty", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["rcases", "have", "simpa"], "tactic_count": 3}
{"name": "Metric.nonempty_of_hausdorffEDist_ne_top", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.empty_or_nonempty_of_hausdorffEDist_ne_top", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "exact", "rw", "exact", "exact"], "tactic_count": 6}
{"name": "Metric.hausdorffEDist_singleton", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["simp_rw", "nth_rw", "exact"], "tactic_count": 3}
{"name": "Metric.hausdorffEDist_iUnion_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["simp_rw", "constructor", "exact", "exact"], "tactic_count": 4}
{"name": "Metric.hausdorffEDist_union_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["simp_rw", "convert"], "tactic_count": 2}
{"name": "Metric.hausdorffEDist_prod_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["refine", "simp_all"], "tactic_count": 2}
{"name": "Metric.infDist", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.infDist_eq_iInf", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["rw", "simp", "finiteness"], "tactic_count": 3}
{"name": "Metric.infDist_nonneg", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.infDist_empty", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Metric.isGLB_infDist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Metric.infEDist_ne_top", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "Metric.infEDist_eq_top_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "Metric.infDist_zero_of_mem", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Metric.infDist_singleton", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Metric.infDist_le_dist_of_mem", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Metric.infDist_le_infDist_of_subset", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.le_infDist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Metric.infDist_lt_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Metric.infDist_le_infDist_add_dist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp"], "tactic_count": 3}
{"name": "Metric.notMem_of_dist_lt_infDist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.disjoint_ball_infDist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.ball_infDist_subset_compl", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.ball_infDist_compl_subset", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.disjoint_closedBall_of_lt_infDist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.dist_le_infDist_add_diam", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Metric.lipschitz_infDist_pt", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.uniformContinuous_infDist_pt", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.continuous_infDist_pt", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.infDist_closure", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Metric.infDist_zero_of_mem_closure", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Metric.mem_closure_iff_infDist_zero", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Metric.infDist_pos_iff_notMem_closure", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.mem_iff_infDist_zero", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsClosed.notMem_iff_infDist_pos", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Metric.continuousAt_inv_infDist_pt", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["rcases", "simp", "refine", "rwa"], "tactic_count": 4}
{"name": "Metric.infDist_image", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Metric.infDist_inter_closedBall_of_mem", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["replace", "refine", "refine", "rcases", "rcases", "exact", "rw", "exact"], "tactic_count": 8}
{"name": "IsCompact.exists_infDist_eq_dist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.exists_infDist_eq_dist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["rcases", "rw", "set", "have", "have", "obtain", "exact"], "tactic_count": 7}
{"name": "Metric.exists_mem_closure_infDist_eq_dist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Metric.infNndist", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.coe_infNndist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.lipschitz_infNndist_pt", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.uniformContinuous_infNndist_pt", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.continuous_infNndist_pt", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.hausdorffDist", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.hausdorffDist_nonneg", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Metric.hausdorffEDist_ne_top_of_nonempty_of_bounded", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "rcases", "rcases", "have", "apply", "intro", "exists", "have", "rwa", "exact", "intro", "exists", "have", "rwa", "exact", "exact"], "tactic_count": 17}
{"name": "Metric.hausdorffDist_self_zero", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Metric.hausdorffDist_comm", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Metric.hausdorffDist_empty", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simp"], "tactic_count": 3}
{"name": "Metric.hausdorffDist_empty'", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Metric.hausdorffDist_le_of_infDist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["rcases", "rwa", "rcases", "rwa", "have", "apply", "simpa", "simpa", "exact"], "tactic_count": 9}
{"name": "Metric.hausdorffDist_le_of_mem_dist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["apply", "intro", "rcases", "exact", "intro", "rcases", "exact"], "tactic_count": 7}
{"name": "Metric.hausdorffDist_le_diam", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "refine", "exact", "exact"], "tactic_count": 5}
{"name": "Metric.infDist_le_hausdorffDist_of_mem", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.exists_dist_lt_of_hausdorffDist_lt", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["have", "have", "rwa", "rcases", "rw", "exact"], "tactic_count": 6}
{"name": "Metric.exists_dist_lt_of_hausdorffDist_lt'", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["rw", "rw", "simpa"], "tactic_count": 3}
{"name": "Metric.infDist_le_infDist_add_hausdorffDist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["refine", "rw", "rw", "exact"], "tactic_count": 4}
{"name": "Metric.hausdorffDist_image", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Metric.hausdorffDist_triangle", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "Metric.hausdorffDist_triangle'", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["rw", "have", "simpa"], "tactic_count": 3}
{"name": "Metric.hausdorffDist_self_closure", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Metric.hausdorffDist_closure₁", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Metric.hausdorffDist_closure₂", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Metric.hausdorffDist_closure", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Metric.hausdorffDist_zero_iff_closure_eq_closure", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsClosed.hausdorffDist_zero_iff_eq", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Metric.hausdorffDist_singleton", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HausdorffDistance", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "HolderWith", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HolderOnWith", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "holderOnWith_empty", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "holderOnWith_singleton", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Holder", "is_tactic_proof": true, "tactics": ["rintro", "rw", "exact"], "tactic_count": 3}
{"name": "Set.Subsingleton.holderOnWith", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "holderOnWith_univ", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Holder", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "holderOnWith_one", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Holder", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "holderWith_one", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "holderWith_id", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HolderWith.holderOnWith", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HolderOnWith.edist_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HolderOnWith.edist_le_of_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HolderOnWith.comp", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Holder", "is_tactic_proof": true, "tactics": ["intro", "rw", "exact"], "tactic_count": 3}
{"name": "HolderOnWith.comp_holderWith", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HolderOnWith.uniformContinuousOn", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Holder", "is_tactic_proof": true, "tactics": ["refine", "have", "rcases", "exact"], "tactic_count": 4}
{"name": "HolderOnWith.continuousOn", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HolderOnWith.mono", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HolderOnWith.ediam_image_le_of_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HolderOnWith.ediam_image_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HolderOnWith.ediam_image_le_of_subset", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HolderOnWith.ediam_image_le_of_subset_of_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HolderOnWith.ediam_image_inter_le_of_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HolderOnWith.ediam_image_inter_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HolderOnWith.interpolate", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Holder", "is_tactic_proof": true, "tactics": ["intro", "calc", "edist", "simp", "nth_grw", "push_cast", "simp", "ring"], "tactic_count": 8}
{"name": "HolderOnWith.holderOnWith_zero_of_bounded", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Holder", "is_tactic_proof": true, "tactics": ["intro", "simp", "grw"], "tactic_count": 3}
{"name": "HolderOnWith.of_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Holder", "is_tactic_proof": true, "tactics": ["obtain", "simpa", "have", "rw", "rw", "set", "set", "have", "have", "have", "simp", "congr", "simp", "rw", "exact"], "tactic_count": 15}
{"name": "HolderOnWith.mono_const", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Holder", "is_tactic_proof": true, "tactics": ["intro", "grw", "exact"], "tactic_count": 3}
{"name": "HolderOnWith.interpolate_const", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Holder", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "convex_setOf_holderOnWith", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Holder", "is_tactic_proof": true, "tactics": ["intro", "rw", "exact"], "tactic_count": 3}
{"name": "HolderOnWith.of_le_of_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Holder", "is_tactic_proof": true, "tactics": ["replace", "replace", "exact"], "tactic_count": 3}
{"name": "HolderWith.restrict_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Holder", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "HolderWith.edist_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HolderWith.edist_le_of_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HolderWith.comp", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HolderWith.comp_holderOnWith", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HolderWith.uniformContinuous", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HolderWith.continuous", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HolderWith.ediam_image_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HolderWith.const", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HolderWith.zero", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HolderWith.of_isEmpty", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HolderWith.mono", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HolderWith.interpolate", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HolderWith.holderWith_zero_of_bounded", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HolderWith.of_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HolderWith.interpolate_const", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "convex_setOf_holderWith", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Holder", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "HolderWith.of_le_of_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HolderOnWith.nndist_le_of_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Holder", "is_tactic_proof": true, "tactics": ["rw", "apply", "rwa"], "tactic_count": 3}
{"name": "HolderOnWith.nndist_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HolderOnWith.dist_le_of_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Holder", "is_tactic_proof": true, "tactics": ["lift", "rw", "norm_cast", "exact"], "tactic_count": 4}
{"name": "HolderOnWith.dist_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HolderWith.nndist_le_of_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HolderWith.nndist_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HolderWith.dist_le_of_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HolderWith.dist_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "holderWith_zero_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Holder", "is_tactic_proof": true, "tactics": ["refine", "specialize", "simp", "assumption", "simp"], "tactic_count": 5}
{"name": "HolderWith.add", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Holder", "is_tactic_proof": true, "tactics": ["intro", "simp", "grw", "rw"], "tactic_count": 4}
{"name": "HolderWith.smul", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Holder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HolderWith.smul_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Holder", "is_tactic_proof": true, "tactics": ["simp_rw", "mul_assoc,"], "tactic_count": 2}
{"name": "eHolderNorm", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.HolderNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nnHolderNorm", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.HolderNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MemHolder", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.HolderNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HolderWith.memHolder", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HolderNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eHolderNorm_lt_top", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HolderNorm", "is_tactic_proof": false, "tactics": ["refine", "let", "iInf_lt_top.2", "simp_rw", "let", "exact"], "tactic_count": 6}
{"name": "eHolderNorm_ne_top", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HolderNorm", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "eHolderNorm_eq_top", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HolderNorm", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "coe_nnHolderNorm_le_eHolderNorm", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HolderNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eHolderNorm_const", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HolderNorm", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "eHolderNorm_zero", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HolderNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nnHolderNorm_const", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HolderNorm", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "nnHolderNorm_zero", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HolderNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eHolderNorm_of_isEmpty", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HolderNorm", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "HolderWith.eHolderNorm_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HolderNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "memHolder_const", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HolderNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "memHolder_const'", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HolderNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "memHolder_zero", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HolderNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MemHolder.of_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HolderNorm", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "exact"], "tactic_count": 3}
{"name": "MemHolder.of_le'", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HolderNorm", "is_tactic_proof": true, "tactics": ["obtain", "letI", "have", "exact"], "tactic_count": 4}
{"name": "HolderOnWith.exists_holderOnWith_of_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HolderNorm", "is_tactic_proof": true, "tactics": ["simp_rw", "have", "exact"], "tactic_count": 3}
{"name": "HolderOnWith.exists_holderOnWith_of_le'", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HolderNorm", "is_tactic_proof": true, "tactics": ["simp_rw", "letI", "have", "exact"], "tactic_count": 4}
{"name": "HolderOnWith.exists_holderOnWith_of_le_of_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HolderNorm", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "exact"], "tactic_count": 3}
{"name": "MemHolder.memHolder_of_le_of_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HolderNorm", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "eHolderNorm_eq_zero", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HolderNorm", "is_tactic_proof": true, "tactics": ["constructor", "refine", "by_cases", "rw", "rw", "rw", "refine", "obtain", "h", "exact", "intro", "rcases", "exact", "rw", "congr", "simp"], "tactic_count": 16}
{"name": "MemHolder.holderWith", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HolderNorm", "is_tactic_proof": true, "tactics": ["intro", "by_cases", "simp", "rw", "on_goal", "have", "have", "rw", "refine", "rw", "exact"], "tactic_count": 11}
{"name": "memHolder_iff_holderWith", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HolderNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MemHolder.coe_nnHolderNorm_eq_eHolderNorm", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HolderNorm", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "HolderWith.nnholderNorm_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HolderNorm", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "MemHolder.comp", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HolderNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MemHolder.nnHolderNorm_eq_zero", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HolderNorm", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MemHolder.add", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HolderNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MemHolder.smul", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HolderNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MemHolder.smul_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HolderNorm", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "MemHolder.nsmul", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HolderNorm", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MemHolder.nnHolderNorm_add_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HolderNorm", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eHolderNorm_add_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HolderNorm", "is_tactic_proof": true, "tactics": ["by_cases", "obtain", "rw", "exact", "rw", "obtain", "all_goals"], "tactic_count": 7}
{"name": "eHolderNorm_smul", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HolderNorm", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "simp", "by_cases", "refine", "rw", "rw", "refine", "rw", "exact", "rw", "rw", "rw", "intro", "exact"], "tactic_count": 15}
{"name": "MemHolder.nnHolderNorm_smul", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HolderNorm", "is_tactic_proof": true, "tactics": ["rw", "eHolderNorm_smul]"], "tactic_count": 2}
{"name": "eHolderNorm_nsmul", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HolderNorm", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "MemHolder.nnHolderNorm_nsmul", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.HolderNorm", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.einfsep", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.le_einfsep_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.einfsep_zero", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.einfsep_pos", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Set.einfsep_top", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.einfsep_lt_top", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.einfsep_ne_top", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.einfsep_lt_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.nontrivial_of_einfsep_lt_top", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "Set.nontrivial_of_einfsep_ne_top", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Subsingleton.einfsep", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.le_einfsep_image_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.le_edist_of_le_einfsep", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.einfsep_le_edist_of_mem", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.einfsep_le_of_mem_of_edist_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.le_einfsep", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.einfsep_empty", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.einfsep_singleton", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.einfsep_iUnion_mem_option", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Set.einfsep_anti", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.einfsep_insert_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Set.le_einfsep_pair", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": true, "tactics": ["simp_rw", "rintro"], "tactic_count": 2}
{"name": "Set.einfsep_pair_le_left", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.einfsep_pair_le_right", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.einfsep_pair_eq_inf", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.einfsep_eq_iInf", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": true, "tactics": ["refine", "simp_rw", "and_imp]"], "tactic_count": 3}
{"name": "Set.einfsep_of_fintype", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": true, "tactics": ["refine", "simp_rw", "uncurry_apply_pair,"], "tactic_count": 3}
{"name": "Set.Finite.einfsep", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": true, "tactics": ["refine", "simp_rw", "uncurry_apply_pair,"], "tactic_count": 3}
{"name": "Set.Finset.coe_einfsep", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Set.Nontrivial.einfsep_exists_of_finite", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": true, "tactics": ["classical", "cases", "simp_rw", "rcases", "simp_rw", "exact"], "tactic_count": 6}
{"name": "Set.Finite.einfsep_exists_of_nontrivial", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.einfsep_pair", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": true, "tactics": ["nth_rw", "convert", "rw"], "tactic_count": 3}
{"name": "Set.einfsep_insert", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": true, "tactics": ["refine", "simp_rw", "rintro", "exact", "exact", "rw", "exact", "exact"], "tactic_count": 8}
{"name": "Set.einfsep_triple", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": true, "tactics": ["simp_rw", "ciInf_pos"], "tactic_count": 2}
{"name": "Set.le_einfsep_pi_of_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": true, "tactics": ["refine", "rw", "rcases", "exact"], "tactic_count": 4}
{"name": "Set.subsingleton_of_einfsep_eq_top", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.einfsep_eq_top_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Nontrivial.einfsep_ne_top", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": true, "tactics": ["contrapose", "exact"], "tactic_count": 2}
{"name": "Set.Nontrivial.einfsep_lt_top", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.einfsep_lt_top_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.einfsep_ne_top_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.le_einfsep_of_forall_dist_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.einfsep_pos_of_finite", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": true, "tactics": ["cases", "by_cases", "rcases", "exact", "rw", "exact"], "tactic_count": 6}
{"name": "Set.relatively_discrete_of_finite", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.Finite.einfsep_pos", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.relatively_discrete", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.infsep", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.infsep_zero", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.infsep_nonneg", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.infsep_pos", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.Subsingleton.infsep_zero", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.nontrivial_of_infsep_pos", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": true, "tactics": ["contrapose", "rw", "exact"], "tactic_count": 3}
{"name": "Set.infsep_empty", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.infsep_singleton", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.infsep_pair_le_toReal_inf", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": true, "tactics": ["simp_rw", "simp"], "tactic_count": 2}
{"name": "Set.infsep_pair_eq_toReal", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "simp", "rw"], "tactic_count": 4}
{"name": "Set.Nontrivial.le_infsep_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Set.Nontrivial.infsep_lt_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": true, "tactics": ["contrapose"], "tactic_count": 1}
{"name": "Set.Nontrivial.le_infsep", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.le_edist_of_le_infsep", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "rw", "rw", "exact"], "tactic_count": 5}
{"name": "Set.infsep_le_dist_of_mem", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.infsep_le_of_mem_of_edist_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.infsep_pair", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.infsep_triple", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": true, "tactics": ["simp", "edist_ne_top"], "tactic_count": 2}
{"name": "Set.Nontrivial.infsep_anti", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.infsep_eq_iInf", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": true, "tactics": ["split_ifs", "have", "refine", "simp_rw", "rcases", "exact", "refine", "simp_rw", "uncurry_apply_pair,", "exact"], "tactic_count": 10}
{"name": "Set.Nontrivial.infsep_eq_iInf", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Set.infsep_of_fintype", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": true, "tactics": ["split_ifs", "refine", "simp_rw", "uncurry_apply_pair,", "rw", "exact"], "tactic_count": 6}
{"name": "Set.Nontrivial.infsep_of_fintype", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Set.Finite.infsep", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": true, "tactics": ["split_ifs", "refine", "simp_rw", "uncurry_apply_pair,", "rw", "exact"], "tactic_count": 6}
{"name": "Set.Finite.infsep_of_nontrivial", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "Finset.coe_infsep", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": false, "tactics": ["have", "rw", "split_ifs", "classical", "exact"], "tactic_count": 5}
{"name": "Finset.coe_infsep_of_offDiag_nonempty", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Finset.coe_infsep_of_offDiag_empty", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": true, "tactics": ["rw", "rw"], "tactic_count": 2}
{"name": "Set.Nontrivial.infsep_exists_of_finite", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": true, "tactics": ["classical", "cases", "simp_rw", "rcases", "simp_rw", "exact"], "tactic_count": 6}
{"name": "Set.Finite.infsep_exists_of_nontrivial", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.infsep_zero_iff_subsingleton_of_finite", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.infsep_pos_iff_nontrivial_of_finite", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.Finite.infsep_zero_iff_subsingleton", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.infsep_pos_iff_nontrivial", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.infsep_zero_iff_subsingleton", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.infsep_pos_iff_nontrivial", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Infsep", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIsometricSMul.to_continuousConstSMul", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIsometricSMul.opposite_of_comm", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "edist_smul_left", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ediam_smul", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isometry_mul_left", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "edist_mul_left", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isometry_mul_right", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "edist_mul_right", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "edist_div_right", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "edist_inv_inv", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "isometry_inv", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "edist_inv", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "edist_div_left", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsometryEquiv.constSMul", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.constSMul_symm", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.mulLeft", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.mulLeft_symm", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.mulRight", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.mulRight_symm", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.divRight", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.divRight_symm", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.divLeft", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.inv", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.inv_symm", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.smul_eball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.preimage_smul_eball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Metric.smul_closedEBall", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.preimage_smul_closedEBall", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Metric.preimage_mul_left_eball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.preimage_mul_right_eball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Metric.preimage_mul_left_closedEBall", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.preimage_mul_right_closedEBall", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "dist_smul", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nndist_smul", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "diam_smul", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dist_mul_left", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nndist_mul_left", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dist_mul_right", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nndist_mul_right", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dist_div_right", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "nndist_div_right", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "dist_inv_inv", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nndist_inv_inv", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dist_div_left", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "nndist_div_left", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Bornology.IsBounded.smul", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.smul_ball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.preimage_smul_ball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Metric.smul_closedBall", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.preimage_smul_closedBall", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Metric.smul_sphere", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.preimage_smul_sphere", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Metric.preimage_mul_left_ball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.preimage_mul_right_ball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Metric.preimage_mul_left_closedBall", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.preimage_mul_right_closedBall", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Prod.instIsIsometricSMul", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.isIsometricSMul'", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.isIsometricSMul''", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Units.isIsometricSMul", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsIsometricSMulMulOpposite", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.isIsometricSMul", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.isIsometricSMul'", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsIsometricSMulForall", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.isIsometricSMul'", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.isIsometricSMul''", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Additive.isIsIsometricVAdd", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Additive.isIsIsometricVAdd'", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Additive.isIsIsometricVAdd''", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiplicative.isIsometricSMul", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiplicative.isIsometricSMul'", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Multiplicative.isIsIsometricVAdd''", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.IsometricSMul", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Isometry", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isometry_iff_nndist_eq", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "isometry_iff_dist_eq", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Isometry.edist_eq", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Isometry.lipschitz", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Isometry.antilipschitz", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isometry_subsingleton", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isometry_id", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Isometry.prodMap", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Isometry.piMap", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Isometry.single", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": true, "tactics": ["intro", "rw", "refine", "obtain", "simp", "simp"], "tactic_count": 6}
{"name": "Isometry.inl", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": true, "tactics": ["intro", "rw", "simp"], "tactic_count": 3}
{"name": "Isometry.inr", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": true, "tactics": ["intro", "rw", "simp"], "tactic_count": 3}
{"name": "Isometry.comp", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Isometry.uniformContinuous", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Isometry.isUniformInducing", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Isometry.tendsto_nhds_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Isometry.continuous", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Isometry.right_inv", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Isometry.preimage_closedEBall", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Isometry.preimage_eball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Isometry.ediam_image", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Isometry.ediam_range", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Isometry.mapsTo_eball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Isometry.mapsTo_closedEBall", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isometry_subtype_coe", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Isometry.comp_continuousOn_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Isometry.comp_continuous_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Isometry.injective", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Isometry.isUniformEmbedding", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Isometry.isEmbedding", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Isometry.isClosedEmbedding", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Isometry.diam_image", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Isometry.diam_range", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Isometry.preimage_setOf_dist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Isometry.preimage_closedBall", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Isometry.preimage_ball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Isometry.preimage_sphere", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Isometry.mapsTo_ball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Isometry.mapsTo_sphere", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Isometry.mapsTo_closedBall", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUniformEmbedding.to_isometry", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsEmbedding.to_isometry", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoEMetricSpace.isometry_induced", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoMetricSpace.isometry_induced", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EMetricSpace.isometry_induced", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MetricSpace.isometry_induced", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryClass.edist_eq", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryClass.continuous", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryClass.lipschitz", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryClass.antilipschitz", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryClass.ediam_image", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryClass.ediam_range", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryClass.toContinuousMapClass", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryClass.toHomeomorphClass", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryClass.dist_eq", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryClass.nndist_eq", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryClass.diam_image", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryClass.diam_range", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "term_≃ᵢ_", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Topology_MetricSpace_Isometry___macroRules_term_≃ᵢ__1", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Topology_MetricSpace_Isometry___unexpand_IsometryEquiv_1", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.toEquiv_injective", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.toEquiv_inj", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.instEquivLike", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.instIsometryClass", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.coe_eq_toEquiv", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.coe_toEquiv", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.coe_mk", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.isometry", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.bijective", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.injective", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.surjective", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.edist_eq", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.dist_eq", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.nndist_eq", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.continuous", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.ediam_image", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.ext", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.mk'", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.refl", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.trans", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.trans_apply", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.symm", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.Simps.apply", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.Simps.symm_apply", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.coe_symm_toEquiv", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.symm_symm", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.symm_bijective", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.apply_symm_apply", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.symm_apply_apply", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.symm_apply_eq", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.eq_symm_apply", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.symm_comp_self", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.self_comp_symm", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.range_eq_univ", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsometryEquiv.image_symm", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.preimage_symm", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.symm_trans_apply", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.ediam_univ", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsometryEquiv.ediam_preimage", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsometryEquiv.preimage_eball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsometryEquiv.preimage_closedEBall", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsometryEquiv.image_eball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsometryEquiv.image_closedEBall", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsometryEquiv.toHomeomorph", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.coe_toHomeomorph", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.coe_toHomeomorph_symm", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.comp_continuousOn_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.comp_continuous_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.comp_continuous_iff'", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.instGroup", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.coe_one", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.coe_mul", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.mul_apply", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.inv_apply_self", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.apply_inv_self", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.completeSpace_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": true, "tactics": ["simp", "isComplete_image_iff"], "tactic_count": 2}
{"name": "IsometryEquiv.completeSpace", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.piCongrLeft'", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.piCongrLeft", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.sumArrowIsometryEquivProdArrow", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.sumArrowIsometryEquivProdArrow_toHomeomorph", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.edist_append_eq_max_edist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Fin.appendIsometry", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.appendIsometry_toHomeomorph", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.appendIsometryOfEq", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.funUnique", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.piFinTwo", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.diam_image", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.diam_preimage", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsometryEquiv.diam_univ", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryEquiv.preimage_ball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsometryEquiv.preimage_sphere", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsometryEquiv.preimage_closedBall", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsometryEquiv.image_ball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsometryEquiv.image_sphere", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsometryEquiv.image_closedBall", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Isometry.isometryEquivOnRange", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Isometry.lipschitzWith_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsometryClass.toIsometryEquiv", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryClass.coe_coe", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryClass.instCoeOutIsometryEquiv", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsometryClass.toIsometryEquiv_injective", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Isometry", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "KuratowskiEmbedding.embeddingOfSubset", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Kuratowski", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "KuratowskiEmbedding.embeddingOfSubset_coe", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Kuratowski", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "KuratowskiEmbedding.embeddingOfSubset_dist_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Kuratowski", "is_tactic_proof": true, "tactics": ["refine", "simp", "convert", "ring"], "tactic_count": 4}
{"name": "KuratowskiEmbedding.embeddingOfSubset_isometry", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Kuratowski", "is_tactic_proof": true, "tactics": ["refine", "refine", "rcases", "have", "simp", "have", "calc", "dist", "rw", "gcongr", "gcongr", "simp", "exact", "simpa"], "tactic_count": 14}
{"name": "KuratowskiEmbedding.exists_isometric_embedding", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Kuratowski", "is_tactic_proof": true, "tactics": ["rcases", "use", "rcases", "haveI", "have", "rcases", "rcases", "exact"], "tactic_count": 8}
{"name": "kuratowskiEmbedding", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Kuratowski", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "kuratowskiEmbedding.isometry", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Kuratowski", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NonemptyCompacts.kuratowskiEmbedding", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Kuratowski", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzOnWith.extend_lp_infty", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Kuratowski", "is_tactic_proof": true, "tactics": ["rw", "have", "choose", "rcases", "exact", "have", "apply", "use", "rintro", "simp_rw", "exact", "let", "refine", "rw", "exact", "intro", "ext", "exact"], "tactic_count": 18}
{"name": "lipschitzWith_iff_dist_le_mul", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Lipschitz", "is_tactic_proof": true, "tactics": ["simp", "norm_cast"], "tactic_count": 2}
{"name": "lipschitzOnWith_iff_dist_le_mul", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Lipschitz", "is_tactic_proof": true, "tactics": ["simp", "norm_cast"], "tactic_count": 2}
{"name": "LipschitzWith.of_dist_le'", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzWith.mk_one", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzWith.of_le_add_mul'", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzWith.of_le_add_mul", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Lipschitz", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "LipschitzWith.of_le_add", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzWith.le_add_mul", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzWith.iff_le_add_mul", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzWith.nndist_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzWith.dist_le_mul_of_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzWith.mapsTo_closedBall", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzWith.dist_lt_mul_of_lt", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzWith.mapsTo_ball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzWith.toLocallyBoundedMap", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzWith.coe_toLocallyBoundedMap", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzWith.comap_cobounded_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzWith.isBounded_image", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzWith.diam_image_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzWith.dist_left", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzWith.dist_right", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzWith.dist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Lipschitz", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "LipschitzWith.dist_iterate_succ_le_geometric", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Lipschitz", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "lipschitzWith_max", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lipschitzWith_min", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.lipschitzWith_toNNReal", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Lipschitz", "is_tactic_proof": true, "tactics": ["refine", "simpa", "lipschitzWith_iff_dist_le_mul.mp"], "tactic_count": 3}
{"name": "LipschitzWith.max", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Lipschitz", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "LipschitzWith.min", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Lipschitz", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "LipschitzWith.max_const", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Lipschitz", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "LipschitzWith.const_max", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Lipschitz", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
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{"name": "LipschitzWith.const_min", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Lipschitz", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "LipschitzWith.projIcc", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzWith.properSpace", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzOnWith.of_dist_le'", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzOnWith.mk_one", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzOnWith.of_le_add_mul'", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzOnWith.of_le_add_mul", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Lipschitz", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "LipschitzOnWith.of_le_add", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzOnWith.le_add_mul", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzOnWith.iff_le_add_mul", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzOnWith.isBounded_image2", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyLipschitz.min", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyLipschitz.max", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyLipschitz.max_const", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyLipschitz.const_max", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Lipschitz", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "LocallyLipschitz.min_const", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LocallyLipschitz.const_min", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Lipschitz", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "LipschitzOnWith.extend_real", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Lipschitz", "is_tactic_proof": true, "tactics": ["cannot", "the", "rcases", "exact", "have", "let", "have", "rcases", "refine", "rintro", "dsimp", "rw", "calc", "f", "have", "refine", "simpa", "refine", "rw", "refine", "rw", "calc", "g", "rw", "gcongr", "apply"], "tactic_count": 26}
{"name": "LipschitzOnWith.extend_pi", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Lipschitz", "is_tactic_proof": false, "tactics": ["have", "have", "exact", "choose", "refine", "exact", "ext1", "exact"], "tactic_count": 8}
{"name": "Metric.IsSeparated", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.MetricSeparated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.isSeparated_iff_setRelIsSeparated", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.MetricSeparated", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Metric.IsSeparated.empty", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.MetricSeparated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.IsSeparated.singleton", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.MetricSeparated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.IsSeparated.of_subsingleton", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.MetricSeparated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.IsSeparated.anti", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.MetricSeparated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.IsSeparated.subset", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.MetricSeparated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.isSeparated_insert", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.MetricSeparated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.isSeparated_insert_of_notMem", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.MetricSeparated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.IsSeparated.insert", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.MetricSeparated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.isSeparated_zero", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.MetricSeparated", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Metric.AreSeparated", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.MetricSeparated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.AreSeparated.symm", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.MetricSeparated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.AreSeparated.comm", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.MetricSeparated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.AreSeparated.empty_left", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.MetricSeparated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.AreSeparated.empty_right", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.MetricSeparated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.AreSeparated.disjoint", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.MetricSeparated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.AreSeparated.subset_compl_right", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.MetricSeparated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.AreSeparated.mono", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.MetricSeparated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.AreSeparated.mono_left", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.MetricSeparated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.AreSeparated.mono_right", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.MetricSeparated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.AreSeparated.union_left", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.MetricSeparated", "is_tactic_proof": true, "tactics": ["rcases", "refine", "rw", "exact", "exact", "exact"], "tactic_count": 6}
{"name": "Metric.AreSeparated.union_left_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.MetricSeparated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.AreSeparated.union_right", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.MetricSeparated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.AreSeparated.union_right_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.MetricSeparated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.AreSeparated.finite_iUnion_left_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.MetricSeparated", "is_tactic_proof": true, "tactics": ["induction", "empty", "insert"], "tactic_count": 3}
{"name": "Metric.AreSeparated.finite_iUnion_right_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.MetricSeparated", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Metric.AreSeparated.finset_iUnion_left_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.MetricSeparated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.AreSeparated.finset_iUnion_right_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.MetricSeparated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.eventually_nhds_zero_forall_closedEBall_subset", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PartitionOfUnity", "is_tactic_proof": false, "tactics": ["suffices", "apply", "mp_mem", "apply", "rintro", "simp", "exact", "intro", "rcases", "rcases", "filter_upwards", "hz", "apply", "calc", "edist"], "tactic_count": 15}
{"name": "Metric.exists_forall_closedEBall_subset_aux₁", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PartitionOfUnity", "is_tactic_proof": false, "tactics": ["have", "rcases", "refine", "rwa"], "tactic_count": 4}
{"name": "Metric.exists_forall_closedEBall_subset_aux₂", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PartitionOfUnity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.exists_continuous_real_forall_closedEBall_subset", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PartitionOfUnity", "is_tactic_proof": true, "tactics": ["simpa", "exists_continuous_forall_mem_convex_of_local_const"], "tactic_count": 2}
{"name": "Metric.exists_continuous_nnreal_forall_closedEBall_subset", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PartitionOfUnity", "is_tactic_proof": true, "tactics": ["rcases", "lift", "refine", "simpa"], "tactic_count": 4}
{"name": "Metric.exists_continuous_ennreal_forall_closedEBall_subset", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PartitionOfUnity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.exists_continuous_nnreal_forall_closedBall_subset", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PartitionOfUnity", "is_tactic_proof": true, "tactics": ["rcases", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "Metric.exists_continuous_real_forall_closedBall_subset", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PartitionOfUnity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.MetricSpace.Perfect.0.Perfect.small_diam_aux", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Perfect", "is_tactic_proof": false, "tactics": ["have", "apply", "rw", "exact", "have", "refine", "rw", "apply", "rw", "apply", "convert", "rw"], "tactic_count": 12}
{"name": "Perfect.small_diam_splitting", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Perfect", "is_tactic_proof": true, "tactics": ["rcases", "obtain", "obtain", "rcases", "rcases", "refine", "apply"], "tactic_count": 7}
{"name": "Perfect.exists_nat_bool_injection", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Perfect", "is_tactic_proof": true, "tactics": ["obtain", "have", "let", "choose", "hC.small_diam_splitting", "let", "induction", "nil", "cons", "cases", "use", "exact", "use", "exact", "let", "have", "refine", "intro", "cases", "exact", "exact", "have", "intro", "apply", "simp", "rw", "refine", "rw", "rcases", "dsimp", "cases", "convert", "rw", "convert", "rw", "have", "rintro", "exact", "exact", "have", "rw", "apply", "refine", "rintro", "exact", "apply", "fun_prop", "intro", "simpa"], "tactic_count": 49}
{"name": "IsClosed.exists_nat_bool_injection_of_not_countable", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Perfect", "is_tactic_proof": true, "tactics": ["letI", "obtain", "obtain", "exact"], "tactic_count": 4}
{"name": "PiNat.definition._@.Mathlib.Topology.MetricSpace.PiNat.3303004985._hygCtx._hyg.8", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "PiNat.firstDiff", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiNat.firstDiff_def", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": true, "tactics": ["intros", "delta", "rw", "rfl"], "tactic_count": 4}
{"name": "PiNat.apply_firstDiff_ne", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": true, "tactics": ["rw", "classical"], "tactic_count": 2}
{"name": "PiNat.apply_eq_of_lt_firstDiff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": true, "tactics": ["rw", "split_ifs", "convert", "simp", "exact"], "tactic_count": 5}
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{"name": "PiNat.min_firstDiff_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": true, "tactics": ["by_contra", "rw", "refine", "calc", "x"], "tactic_count": 5}
{"name": "PiNat.cylinder", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiNat.cylinder_eq_pi", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "PiNat.cylinder_zero", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PiNat.cylinder_anti", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiNat.mem_cylinder_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiNat.self_mem_cylinder", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PiNat.mem_cylinder_iff_eq", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": true, "tactics": ["constructor", "intro", "apply", "intro", "rw", "exact", "intro", "rw", "exact", "intro", "rw", "exact"], "tactic_count": 12}
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{"name": "PiNat.mem_cylinder_iff_le_firstDiff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": true, "tactics": ["constructor", "intro", "by_contra", "exact", "intro", "exact"], "tactic_count": 6}
{"name": "PiNat.mem_cylinder_firstDiff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiNat.cylinder_eq_cylinder_of_le_firstDiff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": true, "tactics": ["rw", "intro", "exact"], "tactic_count": 3}
{"name": "PiNat.iUnion_cylinder_update", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": true, "tactics": ["ext", "simp", "constructor", "rintro", "simpa", "intro", "refine", "rcases", "simp", "simp"], "tactic_count": 10}
{"name": "PiNat.update_mem_cylinder", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiNat.res", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiNat.res_zero", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiNat.res_succ", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiNat.res_length", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": true, "tactics": ["induction"], "tactic_count": 1}
{"name": "PiNat.res_eq_res", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": true, "tactics": ["constructor", "induction", "zero", "succ", "intro", "rw", "simp", "rcases", "exact", "rw", "exact", "induction", "zero", "succ", "simp", "refine", "exact"], "tactic_count": 17}
{"name": "PiNat.res_injective", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": true, "tactics": ["intro", "ext", "apply", "rw"], "tactic_count": 4}
{"name": "PiNat.cylinder_eq_res", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "rw"], "tactic_count": 3}
{"name": "PiNat.dist", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiNat.dist_eq_of_ne", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PiNat.dist_self", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PiNat.dist_comm", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "PiNat.dist_nonneg", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simp"], "tactic_count": 3}
{"name": "PiNat.dist_triangle_nonarch", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rcases", "simp", "rcases", "simp", "simp", "pow_le_pow_iff_right₀,"], "tactic_count": 8}
{"name": "PiNat.dist_triangle", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiNat.eq_of_dist_eq_zero", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": true, "tactics": ["rcases", "simp"], "tactic_count": 2}
{"name": "PiNat.mem_cylinder_iff_dist_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": true, "tactics": ["rcases", "simp", "suffices", "constructor", "intro", "by_contra", "exact", "intro", "exact"], "tactic_count": 9}
{"name": "PiNat.apply_eq_of_dist_lt", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": true, "tactics": ["rcases", "rfl", "have", "exact"], "tactic_count": 4}
{"name": "PiNat.lipschitz_with_one_iff_forall_dist_image_le_of_mem_cylinder", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": true, "tactics": ["constructor", "intro", "apply", "rw", "exact", "intro", "rcases", "simp", "rw", "apply", "rw", "exact"], "tactic_count": 12}
{"name": "PiNat.isOpen_cylinder", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "PiNat.isTopologicalBasis_cylinders", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": true, "tactics": ["apply", "rintro", "apply", "intro", "obtain", "v", "x", "rcases", "refine", "intro", "suffices", "intro", "have", "rw", "simp", "exact"], "tactic_count": 16}
{"name": "PiNat.isOpen_iff_dist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": true, "tactics": ["constructor", "intro", "obtain", "rw", "exact", "intro", "refine", "rcases", "obtain", "refine", "rw", "exact"], "tactic_count": 12}
{"name": "PiNat.metricSpace", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiNat.metricSpaceOfDiscreteUniformity", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiNat.metricSpaceNatNat", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiNat.completeSpace", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": true, "tactics": ["refine", "intro", "refine", "refine", "filter_upwards", "exact"], "tactic_count": 6}
{"name": "PiNat.exists_disjoint_cylinder", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": true, "tactics": ["rcases", "exact", "have", "obtain", "refine", "apply", "calc", "infDist", "rw", "exact"], "tactic_count": 10}
{"name": "PiNat.shortestPrefixDiff", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiNat.firstDiff_lt_shortestPrefixDiff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": true, "tactics": ["have", "rw", "classical", "have", "contrapose", "rw", "refine", "rw", "exact"], "tactic_count": 9}
{"name": "PiNat.shortestPrefixDiff_pos", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "PiNat.longestPrefix", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiNat.firstDiff_le_longestPrefix", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": true, "tactics": ["rw", "exact", "exact"], "tactic_count": 3}
{"name": "PiNat.inter_cylinder_longestPrefix_nonempty", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "have", "have", "rw", "classical", "obtain", "simpa", "refine", "rw", "rw"], "tactic_count": 11}
{"name": "PiNat.disjoint_cylinder_of_longestPrefix_lt", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": true, "tactics": ["contrapose", "rcases", "apply", "apply", "rwa"], "tactic_count": 5}
{"name": "PiNat.cylinder_longestPrefix_eq_of_longestPrefix_lt_firstDiff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": false, "tactics": ["have", "rcases", "have", "have", "rw", "rw", "exact", "exact", "have", "have", "have", "rw", "exact", "rw", "exact"], "tactic_count": 15}
{"name": "PiNat.exists_lipschitz_retraction_of_isClosed", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": true, "tactics": ["prefix", "of", "that", "length", "same", "length", "classical", "set", "have", "refine", "apply", "rintro", "by_cases", "rwa", "simpa", "intro", "rw", "exact", "mem_range_self", "refine", "rcases", "simp", "rcases", "simp", "have", "rw", "apply", "suffices", "simpa", "by_cases", "rw", "xs]", "by_cases", "rw", "have", "have", "have", "rw", "apply", "exact", "rwa", "by_cases", "have", "have", "have", "rw", "apply", "apply", "rw", "rwa", "have", "have", "have", "have", "simp_rw", "by_cases", "have", "rcases", "exact", "symm", "rw", "exact", "rw", "apply", "congr", "have", "rw", "exact", "have", "rw", "exact", "have", "rw", "exact"], "tactic_count": 74}
{"name": "PiNat.exists_retraction_of_isClosed", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "PiNat.exists_retraction_subtype_of_isClosed", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": false, "tactics": ["obtain", "exists_retraction_of_isClosed", "have", "exact"], "tactic_count": 4}
{"name": "exists_nat_nat_continuous_surjective_of_completeSpace", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": true, "tactics": ["this", "balls", "and", "letI", "have", "have", "rcases", "let", "let", "have", "have", "refine", "refine", "rcases", "simp", "have", "have", "let", "have", "by_contra", "apply", "rw", "apply", "rw", "exact", "have", "rw", "have", "calc", "dist", "have", "have", "rcases", "exact", "choose", "have", "refine", "refine", "have", "calc", "dist", "have", "rw", "exact", "have", "refine", "have", "have", "rw", "exact", "refine", "nonempty_iInter_of_nonempty_biInter", "obtain", "clusterPt_principal_iff.1", "have", "refine", "have", "rw", "rw", "apply", "apply", "obtain", "apply", "simpa", "exact"], "tactic_count": 65}
{"name": "PiCountable.edist", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiCountable.edist_eq_tsum", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiCountable.min_edist_le_edist_pi", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiCountable.edist_le_two", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiCountable.edist_lt_top", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiCountable.edist_le_edist_pi_of_edist_lt", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "PiCountable.pseudoEMetricSpace", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiCountable.emetricSpace", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiCountable.dist", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiCountable.dist_eq_tsum", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiCountable.dist_summable", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": false, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "PiCountable.min_dist_le_dist_pi", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiCountable.dist_le_dist_pi_of_dist_lt", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": true, "tactics": ["simpa", "min_le_iff.1"], "tactic_count": 2}
{"name": "PiCountable.pseudoMetricSpace", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PiCountable.metricSpace", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.PiNatEmbed.ext", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Metric.PiNatEmbed.toPiNatEquiv", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.PiNatEmbed.ofPiNat_inj", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.PiNatEmbed.forall", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.PiNatEmbed.embed", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.PiNatEmbed.embed_injective", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Metric.PiNatEmbed.instPseudoEMetricSpace", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.PiNatEmbed.edist_def", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.PiNatEmbed.isometry_embed", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.PiNatEmbed.instPseudoMetricSpace", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.PiNatEmbed.dist_def", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.PiNatEmbed.continuous_toPiNat", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": true, "tactics": ["rw", "simp", "apply"], "tactic_count": 3}
{"name": "Metric.PiNatEmbed.emetricSpace", "kind": "abbrev", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.PiNatEmbed.isUniformEmbedding_embed", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.PiNatEmbed.metricSpace", "kind": "abbrev", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.PiNatEmbed.isHomeomorph_toPiNat", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": true, "tactics": ["letI", "rw", "exact"], "tactic_count": 3}
{"name": "Metric.PiNatEmbed.toPiNatHomeo", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.PiNatEmbed.TopologicalSpace.MetrizableSpace.of_countable_separating", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.PiNatEmbed.distDenseSeq", "kind": "abbrev", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.PiNatEmbed.continuous_distDenseSeq", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": true, "tactics": ["cases", "exact", "refine", "convert"], "tactic_count": 4}
{"name": "Metric.PiNatEmbed.separation", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": true, "tactics": ["let", "obtain", "simp_all", "have", "obtain", "denseRange_iff.mp", "refine", "simp", "intro", "replace", "simpa", "have", "simpa"], "tactic_count": 13}
{"name": "Metric.PiNatEmbed.injective_distDenseSeq", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Metric.PiNatEmbed.continuous_distDenseSeq_inv", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": true, "tactics": ["refine", "obtain", "rw", "exact"], "tactic_count": 4}
{"name": "Metric.PiNatEmbed.exists_embedding_to_hilbert_cube", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.PiNat", "is_tactic_proof": false, "tactics": ["let", "invFun", "left_inv", "right_inv", "continuous_toFun", "continuous_invFun", "let", "let", "exact"], "tactic_count": 9}
{"name": "instPolishSpaceOfSeparableSpaceOfIsCompletelyMetrizableSpace", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Polish", "is_tactic_proof": true, "tactics": ["letI", "haveI", "constructor"], "tactic_count": 3}
{"name": "PolishSpace.exists_nat_nat_continuous_surjective", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Polish", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsClosedEmbedding.polishSpace", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Polish", "is_tactic_proof": true, "tactics": ["letI", "letI", "haveI", "have", "rw", "exact", "infer_instance"], "tactic_count": 7}
{"name": "Equiv.polishSpace_induced", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Polish", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.polishSpace", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Polish", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompletePseudometrizable.iInf", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Polish", "is_tactic_proof": true, "tactics": ["choose", "obtain", "refine", "rw", "infer_instance"], "tactic_count": 5}
{"name": "PolishSpace.iInf", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Polish", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "letI", "haveI", "inferInstance,", "hi₀⟩", "letI", "haveI", "letI", "rw", "have", "htop.symm", "secondCountableTopology_iInf", "letI", "have", "htop.symm", "infer_instance"], "tactic_count": 17}
{"name": "PolishSpace.exists_polishSpace_forall_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Polish", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PolishSpace.instENNReal", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Polish", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.CompleteCopy", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Polish", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.CompleteCopy.instDist", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Polish", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.CompleteCopy.dist_eq", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Polish", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.CompleteCopy.dist_val_le_dist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Polish", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.CompleteCopy.inst", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Polish", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.CompleteCopy.instSecondCountableTopology", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Polish", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.CompleteCopy.instT0Space", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Polish", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.CompleteCopy.instMetricSpace", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Polish", "is_tactic_proof": false, "tactics": ["refine", "simp", "simp", "calc", "dist", "dist", "refine", "rcases", "exact", "rcases", "simp", "have", "refine", "refine", "rw", "exact", "simp", "exact"], "tactic_count": 18}
{"name": "TopologicalSpace.Opens.CompleteCopy.instCompleteSpace", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Polish", "is_tactic_proof": true, "tactics": ["refine", "have", "refine", "exact", "exact", "obtain", "by_cases", "exact", "obtain", "refine", "rw", "calc", "have", "have", "rw", "have", "have", "rw", "exact", "have", "have", "ge_of_tendsto", "exact"], "tactic_count": 23}
{"name": "IsOpen.polishSpace", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Polish", "is_tactic_proof": true, "tactics": ["letI", "lift", "exact"], "tactic_count": 3}
{"name": "PolishSpace.IsClopenable", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Polish", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.isClopenable", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Polish", "is_tactic_proof": true, "tactics": ["topology", "classical", "haveI", "let", "haveI", "let", "have", "simp", "exact", "refine", "rw", "exact", "rw", "simp", "have", "have", "simp_rw", "simp", "rw", "simp"], "tactic_count": 20}
{"name": "PolishSpace.IsClopenable.compl", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Polish", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "IsOpen.isClopenable", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Polish", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "PolishSpace.IsClopenable.iUnion", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Polish", "is_tactic_proof": true, "tactics": ["choose", "obtain", "exists_polishSpace_forall_le", "have", "apply", "intro", "apply", "exact", "obtain", "exact"], "tactic_count": 10}
{"name": "isCompact_sphere", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.ProperSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCompactSpaceElemClosedBallOfProperSpace", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.ProperSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.sphere.compactSpace", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.ProperSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "secondCountable_of_proper", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.ProperSpace", "is_tactic_proof": true, "tactics": ["suffices", "rcases", "exact", "exact"], "tactic_count": 4}
{"name": "ProperSpace.of_isCompact_closedBall_of_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.ProperSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ProperSpace.of_seq_closedBall", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.ProperSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "proper_of_compact", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.ProperSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "locallyCompact_of_proper", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.ProperSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "complete_of_proper", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.ProperSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instProperSpaceReal", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.ProperSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instSecondCountableTopologyReal", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.ProperSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "prod_properSpace", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.ProperSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pi_properSpace", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.ProperSpace", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "ProperSpace.of_isClosed", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.ProperSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instProperSpaceAdditive", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.ProperSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instProperSpaceMultiplicative", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.ProperSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instProperSpaceOrderDual", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.ProperSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_pos_lt_subset_ball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.ProperSpace.Lemmas", "is_tactic_proof": true, "tactics": ["rcases", "exact", "have", "obtain", "have", "rcases", "exact"], "tactic_count": 7}
{"name": "exists_lt_subset_ball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.ProperSpace.Lemmas", "is_tactic_proof": true, "tactics": ["rcases", "rw", "subst", "exact", "exact"], "tactic_count": 5}
{"name": "Metric.exists_isLocalMin_mem_ball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.ProperSpace.Lemmas", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "isProperMap_dist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.ProperSpace.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "properSpace_iff_isProperMap_dist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.ProperSpace.Lemmas", "is_tactic_proof": true, "tactics": ["refine", "convert", "ext", "simp"], "tactic_count": 4}
{"name": "isClosedMap_dist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.ProperSpace.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isProperMap_nndist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.ProperSpace.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosedMap_nndist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.ProperSpace.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.instSecondCountableTopology", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.ProperSpace.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.instSecondCountableTopology", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.ProperSpace.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.instProperSpace", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.ProperSpace.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.instSecondCountableTopology", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.ProperSpace.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dist_le_Ico_sum_dist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Basic", "is_tactic_proof": true, "tactics": ["induction", "base", "succ", "calc", "dist", "rw"], "tactic_count": 6}
{"name": "dist_le_range_sum_dist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dist_le_Ico_sum_of_dist_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dist_le_range_sum_of_dist_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.isUniformInducing_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.isUniformEmbedding_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Metric.controlled_of_isUniformEmbedding", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.totallyBounded_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.totallyBounded_of_finite_discretization", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Basic", "is_tactic_proof": true, "tactics": ["rcases", "rw", "exact", "rcases", "haveI", "refine", "rcases", "let", "refine", "let", "have", "simp", "exact"], "tactic_count": 13}
{"name": "Metric.finite_approx_of_totallyBounded", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Basic", "is_tactic_proof": true, "tactics": ["intro", "rw", "exact"], "tactic_count": 3}
{"name": "Metric.tendstoUniformlyOnFilter_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Basic", "is_tactic_proof": true, "tactics": ["refine", "rcases", "exact"], "tactic_count": 3}
{"name": "Metric.tendstoLocallyUniformlyOn_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Basic", "is_tactic_proof": true, "tactics": ["refine", "rcases", "rcases", "exact"], "tactic_count": 4}
{"name": "Metric.tendstoUniformlyOn_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Basic", "is_tactic_proof": true, "tactics": ["refine", "rcases", "exact"], "tactic_count": 3}
{"name": "Metric.tendstoLocallyUniformly_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Metric.tendstoUniformly_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Metric.cauchy_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.exists_ball_inter_eq_singleton_of_mem_discrete", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.exists_closedBall_inter_eq_singleton_of_discrete", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.inseparable_iff_nndist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Metric.inseparable_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "tendsto_nhds_unique_dist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cauchySeq_iff_tendsto_dist_atTop_0", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp_rw"], "tactic_count": 2}
{"name": "Topology.IsInducing.isSeparable_preimage", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Basic", "is_tactic_proof": true, "tactics": ["letI", "have", "have", "have", "have", "have", "exact"], "tactic_count": 7}
{"name": "Topology.IsEmbedding.isSeparable_preimage", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.isSeparable", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.secondCountable_of_almost_dense_set", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Basic", "is_tactic_proof": true, "tactics": ["refine", "rcases", "choose", "refine", "exact"], "tactic_count": 5}
{"name": "finite_cover_balls_of_compact", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_finite_cover_balls_of_isCompact_closure", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Basic", "is_tactic_proof": false, "tactics": ["obtain", "hs.elim_finite_subcover", "let", "mem_iUnion.2", "refine", "simpa"], "tactic_count": 6}
{"name": "ContinuousOn.isSeparable_image", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "PseudoMetricSpace.induced", "kind": "abbrev", "module": "Mathlib.Topology.MetricSpace.Pseudo.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsInducing.comapPseudoMetricSpace", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Pseudo.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUniformInducing.comapPseudoMetricSpace", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Pseudo.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.pseudoMetricSpace", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Pseudo.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.dist_eq", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.nndist_eq", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.preimage_ball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.preimage_closedBall", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.image_ball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Constructions", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Subtype.image_closedBall", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Constructions", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MulOpposite.instPseudoMetricSpace", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Pseudo.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.dist_unop", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.dist_op", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.nndist_unop", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.nndist_op", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instPseudoMetricSpaceNNReal", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Pseudo.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.dist_eq", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.nndist_eq", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.nndist_zero_eq_val", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Constructions", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "NNReal.nndist_zero_eq_val'", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Constructions", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "NNReal.le_add_nndist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Constructions", "is_tactic_proof": true, "tactics": ["suffices", "rw", "exact"], "tactic_count": 3}
{"name": "NNReal.ball_zero_eq_Ico'", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Constructions", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "NNReal.ball_zero_eq_Ico", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Constructions", "is_tactic_proof": true, "tactics": ["by_cases", "convert", "simp", "simp"], "tactic_count": 4}
{"name": "NNReal.closedBall_zero_eq_Icc'", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Constructions", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "NNReal.closedBall_zero_eq_Icc", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Constructions", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "ULift.instPseudoMetricSpace", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Pseudo.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.dist_eq", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.nndist_eq", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.dist_up_up", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.nndist_up_up", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.pseudoMetricSpaceMax", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Pseudo.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.dist_eq", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dist_prod_same_left", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Constructions", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "dist_prod_same_right", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Constructions", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ball_prod_same", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "closedBall_prod_same", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sphere_prod", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Constructions", "is_tactic_proof": true, "tactics": ["obtain", "simp", "cases", "simp_rw", "ext", "simp_rw", "refine", "all_goals"], "tactic_count": 8}
{"name": "uniformContinuous_dist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformContinuous.dist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_dist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.dist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.dist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_iff_continuous_dist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformContinuous_nndist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformContinuous.nndist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_nndist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.nndist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.nndist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.ofDist_aux", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.ofDist", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.ofDist", "kind": "abbrev", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.MetricSpace.Pseudo.Defs.0.dist_nonneg'", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoMetricSpace.ext", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["let", "obtain", "let", "obtain", "obtain", "congr", "ext", "rw", "exact", "ext", "rw"], "tactic_count": 11}
{"name": "PseudoMetricSpace.toEDist", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoMetricSpace.ofDistTopology", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dist_self", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dist_comm", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "edist_dist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dist_triangle", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dist_triangle_left", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "dist_triangle_right", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "dist_triangle4", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dist_triangle4_left", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "dist_triangle4_right", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "dist_triangle8", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["apply", "gcongr", "apply", "gcongr", "exact"], "tactic_count": 5}
{"name": "swap_dist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["funext"], "tactic_count": 1}
{"name": "abs_dist_sub_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dist_nonneg", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Mathlib.Meta.Positivity.evalDist", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_example", "kind": "example", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["positivity"], "tactic_count": 1}
{"name": "abs_dist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoMetricSpace.toNNDist", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dist_nndist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "coe_nndist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "edist_nndist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "nndist_edist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "coe_nnreal_ennreal_nndist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "edist_lt_coe", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "edist_le_coe", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "edist_lt_top", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "edist_ne_top", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nndist_self", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dist_lt_coe", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dist_le_coe", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "edist_lt_ofReal", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "edist_le_ofReal", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "nndist_dist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "nndist_comm", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nndist_triangle", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nndist_triangle_left", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nndist_triangle_right", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dist_edist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Metric.ball", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.mem_ball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.mem_ball'", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Metric.pos_of_mem_ball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.mem_ball_self", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Metric.nonempty_ball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.ball_eq_empty", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Metric.ball_zero", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Metric.exists_lt_mem_ball_of_mem_ball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Metric.ball_eq_ball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.ball_eq_ball'", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Metric.iUnion_ball_nat", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.iUnion_ball_nat_succ", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.closedBall", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.mem_closedBall", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.mem_closedBall'", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Metric.sphere", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.mem_sphere", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.mem_sphere'", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Metric.ne_of_mem_sphere", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.nonneg_of_mem_sphere", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.sphere_eq_empty_of_neg", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.sphere_eq_empty_of_subsingleton", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.sphere_isEmpty_of_subsingleton", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Metric.closedBall_eq_singleton_of_subsingleton", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["ext", "simpa"], "tactic_count": 2}
{"name": "Metric.ball_eq_singleton_of_subsingleton", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["ext", "simpa"], "tactic_count": 2}
{"name": "Metric.mem_closedBall_self", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "Metric.nonempty_closedBall", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.closedBall_eq_empty", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Metric.closedBall_eq_sphere_of_nonpos", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.ball_subset_closedBall", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.sphere_subset_closedBall", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.sphere_subset_ball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.closedBall_disjoint_ball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.ball_disjoint_closedBall", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.ball_disjoint_ball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.closedBall_disjoint_closedBall", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.sphere_disjoint_ball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.ball_union_sphere", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.sphere_union_ball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Metric.closedBall_diff_sphere", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Metric.closedBall_diff_ball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Metric.mem_ball_comm", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Metric.mem_closedBall_comm", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Metric.mem_sphere_comm", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Metric.ball_subset_ball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.closedBall_eq_bInter_ball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Metric.ball_subset_ball'", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.closedBall_subset_closedBall", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.closedBall_subset_closedBall'", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.closedBall_subset_ball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.closedBall_subset_ball'", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.dist_le_add_of_nonempty_closedBall_inter_closedBall", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.dist_lt_add_of_nonempty_closedBall_inter_ball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.dist_lt_add_of_nonempty_ball_inter_closedBall", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "Metric.dist_lt_add_of_nonempty_ball_inter_ball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.iUnion_closedBall_nat", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.iUnion_inter_closedBall_nat", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Metric.ball_subset", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.ball_half_subset", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.exists_ball_subset_ball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.forall_of_forall_mem_closedBall", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Metric.forall_of_forall_mem_ball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Metric.isBounded_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Metric.boundedSpace_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Metric.isBounded_iff_eventually", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.isBounded_iff_exists_ge", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.isBounded_iff_nndist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Metric.boundedSpace_iff_nndist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Metric.boundedSpace_iff_edist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Metric.toUniformSpace_eq", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.uniformity_basis_dist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Metric.mk_uniformity_basis", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["refine", "constructor", "rintro", "rcases", "exact", "exact"], "tactic_count": 6}
{"name": "Metric.uniformity_basis_dist_rat", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.uniformity_basis_dist_inv_nat_succ", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.uniformity_basis_dist_inv_nat_pos", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.uniformity_basis_dist_pow", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.uniformity_basis_dist_lt", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.mk_uniformity_basis_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["refine", "constructor", "rintro", "rcases", "rcases", "exact", "exact"], "tactic_count": 7}
{"name": "Metric.uniformity_basis_dist_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.uniformity_basis_dist_le_pow", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.mem_uniformity_dist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.dist_mem_uniformity", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.uniformContinuous_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.uniformContinuousOn_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.uniformContinuous_iff_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.uniformContinuousOn_iff_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.nhds_basis_ball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.mem_nhds_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.eventually_nhds_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.eventually_nhds_iff_ball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.eventually_nhds_prod_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["refine", "simp", "rfl"], "tactic_count": 3}
{"name": "Metric.eventually_prod_nhds_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["rw", "constructor", "rintro", "exact"], "tactic_count": 4}
{"name": "Metric.nhds_basis_closedBall", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.nhds_basis_ball_inv_nat_succ", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.nhds_basis_ball_inv_nat_pos", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.nhds_basis_ball_pow", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.nhds_basis_closedBall_pow", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.isOpen_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Metric.isOpen_ball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.ball_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.closedBall_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.closedBall_mem_nhds_of_mem", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.nhdsWithin_basis_ball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.mem_nhdsWithin_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.tendsto_nhdsWithin_nhdsWithin", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.tendsto_nhdsWithin_nhds", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Metric.tendsto_nhds_nhds", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.continuousAt_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Metric.continuousWithinAt_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Metric.continuousOn_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Metric.continuous_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.tendsto_nhds", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.continuousAt_iff'", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Metric.continuousWithinAt_iff'", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Metric.continuousOn_iff'", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Metric.continuous_iff'", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.tendsto_atTop", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.tendsto_atTop'", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.isOpen_singleton_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Dense.exists_dist_lt", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "DenseRange.exists_dist_lt", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.uniformSpace_eq_bot", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DiscreteTopology.of_forall_le_dist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.uniformity_edist_aux", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["simp", "refine", "rcases", "refine", "exact", "lift", "refine", "exact"], "tactic_count": 8}
{"name": "Metric.uniformity_edist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PseudoMetricSpace.toPseudoEMetricSpace", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.eball_top_eq_univ", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.eball_ofReal", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["ext", "simp", "exact"], "tactic_count": 3}
{"name": "Metric.eball_coe", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Metric.closedEBall_ofReal", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Metric.closedEBall_coe", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Metric.eball_top", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoMetricSpace.replaceUniformity", "kind": "abbrev", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoMetricSpace.replaceUniformity_eq", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "_example", "kind": "example", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["with_reducible_and_instances"], "tactic_count": 1}
{"name": "PseudoMetricSpace.replaceTopology", "kind": "abbrev", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoMetricSpace.replaceTopology_eq", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "PseudoEMetricSpace.toPseudoMetricSpaceOfDist", "kind": "abbrev", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoEMetricSpace.toPseudoMetricSpace", "kind": "abbrev", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoMetricSpace.replaceBornology", "kind": "abbrev", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoMetricSpace.replaceBornology_eq", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "_example", "kind": "example", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["with_reducible_and_instances"], "tactic_count": 1}
{"name": "Real.pseudoMetricSpace", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.dist_eq", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.nndist_eq", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.nndist_eq'", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.dist_0_eq_abs", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.sub_le_dist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Real.ball_eq_Ioo", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.ball_zero_eq_Ioo", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.closedBall_eq_Icc", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "Real.closedBall_zero_eq_Icc", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.Ioo_eq_ball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["rw", "add_sub_cancel,"], "tactic_count": 2}
{"name": "Real.Icc_eq_closedBall", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["rw", "add_assoc,"], "tactic_count": 2}
{"name": "Metric.uniformity_eq_comap_nhds_zero", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["ext", "simp", "simp"], "tactic_count": 3}
{"name": "tendsto_uniformity_iff_dist_tendsto_zero", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.Tendsto.congr_dist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_iff_of_dist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoMetricSpace.dist_eq_of_dist_zero", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dist_dist_dist_le_left", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dist_dist_dist_le_right", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "dist_dist_dist_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhds_comap_dist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["simp", "dist_comm]"], "tactic_count": 2}
{"name": "tendsto_iff_dist_tendsto_zero", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Metric.ball_subset_interior_closedBall", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.mem_closure_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.mem_closure_range_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Metric.mem_closure_range_iff_nat", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.mem_of_closed'", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Metric.dense_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.dense_iff_iUnion_ball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Metric.denseRange_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instPseudoMetricSpaceAdditive", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instPseudoMetricSpaceMultiplicative", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nndist_ofMul", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nndist_ofAdd", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nndist_toMul", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nndist_toAdd", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instPseudoMetricSpaceOrderDual", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nndist_toDual", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nndist_ofDual", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instOrderTopologyReal", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Pseudo.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.singleton_eq_inter_Icc", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Lemmas", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "squeeze_zero'", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "squeeze_zero", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eventually_closedBall_subset", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Lemmas", "is_tactic_proof": true, "tactics": ["obtain", "have", "filter_upwards"], "tactic_count": 3}
{"name": "tendsto_closedBall_smallSets", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eventually_ball_subset", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.isClosed_closedBall", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.isClosed_sphere", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.closure_closedBall", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.closure_sphere", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.closure_ball_subset_closedBall", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.frontier_ball_subset_sphere", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.frontier_closedBall_subset_sphere", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.closedBall_zero'", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.eventually_isCompact_closedBall", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Lemmas", "is_tactic_proof": true, "tactics": ["rcases", "filter_upwards", "exact"], "tactic_count": 3}
{"name": "Metric.exists_isCompact_closedBall", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Lemmas", "is_tactic_proof": false, "tactics": ["have", "eventually_nhdsWithin_of_eventually_nhds", "simpa"], "tactic_count": 3}
{"name": "Metric.biInter_gt_closedBall", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Lemmas", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Metric.biInter_gt_ball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Lemmas", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Metric.biUnion_lt_ball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Lemmas", "is_tactic_proof": true, "tactics": ["ext", "rw", "simp"], "tactic_count": 3}
{"name": "Metric.biUnion_lt_closedBall", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Lemmas", "is_tactic_proof": true, "tactics": ["ext", "rw", "simp"], "tactic_count": 3}
{"name": "lebesgue_number_lemma_of_metric", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Lemmas", "is_tactic_proof": true, "tactics": ["simpa", "uniformity_basis_dist.lebesgue_number_lemma"], "tactic_count": 2}
{"name": "lebesgue_number_lemma_of_metric_sUnion", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Lemmas", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "pseudoMetricSpacePi", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Pseudo.Pi", "is_tactic_proof": true, "tactics": ["the", "formula", "let", "refine", "simp", "refine", "lift", "refine", "simpa"], "tactic_count": 9}
{"name": "nndist_pi_def", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dist_pi_def", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nndist_pi_le_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Pi", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "nndist_pi_lt_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Pi", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "nndist_pi_eq_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Pi", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "intro", "refine", "apply"], "tactic_count": 5}
{"name": "dist_pi_lt_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Pi", "is_tactic_proof": true, "tactics": ["lift", "exact"], "tactic_count": 2}
{"name": "dist_pi_le_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Pi", "is_tactic_proof": true, "tactics": ["lift", "exact"], "tactic_count": 2}
{"name": "dist_pi_eq_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Pi", "is_tactic_proof": true, "tactics": ["lift", "simp_rw"], "tactic_count": 2}
{"name": "dist_pi_le_iff'", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Pi", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "exact", "iff_of_false"], "tactic_count": 4}
{"name": "dist_pi_const_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nndist_pi_const_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dist_pi_const", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Pi", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "nndist_pi_const", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nndist_le_pi_nndist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Pi", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "dist_le_pi_dist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Pi", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ball_pi", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Pi", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "ball_pi'", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "closedBall_pi", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Pi", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "closedBall_pi'", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sphere_pi", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Pi", "is_tactic_proof": true, "tactics": ["obtain", "simp", "rw", "letI", "inhabit", "refine", "intro", "replace", "rw", "exact", "ext", "simp"], "tactic_count": 12}
{"name": "Fin.nndist_insertNth_insertNth", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Fin.dist_insertNth_insertNth", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Pi", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "nndist_single_single", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Pi", "is_tactic_proof": true, "tactics": ["refine", "simp", "by_cases", "simpa", "simpa"], "tactic_count": 5}
{"name": "dist_single_single", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Pi", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Real.dist_left_le_of_mem_uIcc", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Real", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.dist_right_le_of_mem_uIcc", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Real", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.dist_le_of_mem_uIcc", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.dist_le_of_mem_Icc", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Real", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.dist_le_of_mem_Icc_01", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Real", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Real.dist_le_of_mem_pi_Icc", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Pseudo.Real", "is_tactic_proof": false, "tactics": ["refine", "refine", "exacts"], "tactic_count": 3}
{"name": "tendsto_subseq_of_frequently_bounded", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Sequences", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_subseq_of_bounded", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Sequences", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_subset_iUnion_ball_radius_lt", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.ShrinkingLemma", "is_tactic_proof": false, "tactics": ["rcases", "have", "choose", "exact"], "tactic_count": 4}
{"name": "exists_iUnion_ball_eq_radius_lt", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.ShrinkingLemma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_subset_iUnion_ball_radius_pos_lt", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.ShrinkingLemma", "is_tactic_proof": false, "tactics": ["rcases", "have", "choose", "exact"], "tactic_count": 4}
{"name": "exists_iUnion_ball_eq_radius_pos_lt", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.ShrinkingLemma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_locallyFinite_subset_iUnion_ball_radius_lt", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.ShrinkingLemma", "is_tactic_proof": false, "tactics": ["have", "nhds_basis_uniformity", "rcases", "rcases", "exact"], "tactic_count": 5}
{"name": "exists_locallyFinite_iUnion_eq_ball_radius_lt", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.ShrinkingLemma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Similar", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Similarity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Similar.term_∼_", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Similarity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Similar._aux_Mathlib_Topology_MetricSpace_Similarity___macroRules_Similar_term_∼__1", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Similarity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Similar._aux_Mathlib_Topology_MetricSpace_Similarity___unexpand_Similar_1", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Similarity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "similar_iff_exists_edist_eq", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Similarity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "similar_iff_exists_pairwise_edist_eq", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Similarity", "is_tactic_proof": true, "tactics": ["rw", "refine", "exact", "by_cases", "simp", "exact"], "tactic_count": 6}
{"name": "Congruent.similar", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Similarity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Similar.refl", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Similarity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Similar.symm", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Similarity", "is_tactic_proof": true, "tactics": ["rcases", "refine", "rw", "norm_cast"], "tactic_count": 4}
{"name": "similar_comm", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Similarity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Similar.trans", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Similarity", "is_tactic_proof": true, "tactics": ["rcases", "refine", "rw"], "tactic_count": 3}
{"name": "Similar.index_map", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Similarity", "is_tactic_proof": true, "tactics": ["rcases", "refine", "apply"], "tactic_count": 3}
{"name": "Similar.index_equiv", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Similarity", "is_tactic_proof": true, "tactics": ["refine", "rcases", "refine", "simpa"], "tactic_count": 4}
{"name": "Similar.of_subsingleton_index", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Similarity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Similar.comp_left", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Similarity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Similar.comp_right", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Similarity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Similar.comp_left_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Similarity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Similar.comp_right_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Similarity", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Similar.comp_isometry_left", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Similarity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Similar.comp_isometry_right", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Similarity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Similar.comp_isometry_left_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Similarity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Similar.comp_isometry_right_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Similarity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Similar.comm_left", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Similarity", "is_tactic_proof": false, "tactics": ["have", "ext", "fin_cases", "have", "ext", "fin_cases", "grind"], "tactic_count": 7}
{"name": "Similar.comm_right", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Similarity", "is_tactic_proof": false, "tactics": ["have", "ext", "fin_cases", "have", "ext", "fin_cases", "grind"], "tactic_count": 7}
{"name": "Similar.reverse_of_three", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Similarity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "similar_iff_exists_nndist_eq", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Similarity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "similar_iff_exists_pairwise_nndist_eq", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Similarity", "is_tactic_proof": true, "tactics": ["simp_rw", "exact_mod_cast"], "tactic_count": 2}
{"name": "similar_iff_exists_dist_eq", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Similarity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "similar_iff_exists_pairwise_dist_eq", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Similarity", "is_tactic_proof": true, "tactics": ["simp_rw", "exact_mod_cast"], "tactic_count": 2}
{"name": "similar_iff_exists_pos_dist_eq", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Similarity", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "grind"], "tactic_count": 3}
{"name": "similar_iff_exists_pos_pairwise_dist_eq", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Similarity", "is_tactic_proof": true, "tactics": ["simp_rw", "simp_rw", "grind"], "tactic_count": 3}
{"name": "similar_of_dist_mul_eq_dist_mul_eq", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Similarity", "is_tactic_proof": true, "tactics": ["set", "have", "apply", "use", "refine", "intro", "fin_cases", "try", "all_goals"], "tactic_count": 9}
{"name": "Metric.Snowflaking.ofSnowflaking", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Snowflaking", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.Snowflaking.toSnowflaking", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Snowflaking", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.Snowflaking.toSnowflaking.sizeOf_spec", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Snowflaking", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.Snowflaking.casesOn_toSnowflaking", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Snowflaking", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.Snowflaking.mk_eq_toSnowflaking", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Snowflaking", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.Snowflaking.val_eq_ofSnowflaking", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Snowflaking", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.Snowflaking.symm_toSnowflaking", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Snowflaking", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.Snowflaking.symm_ofSnowflaking", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Snowflaking", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.Snowflaking.toSnowflaking_ofSnowflaking", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Snowflaking", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.Snowflaking.ofSnowflaking_toSnowflaking", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Snowflaking", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.Snowflaking.ofSnowflaking_comp_toSnowflaking", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Snowflaking", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.Snowflaking.toSnowflaking_comp_ofSnowflaking", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Snowflaking", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.Snowflaking.image_toSnowflaking_eq_preimage", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Snowflaking", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.Snowflaking.image_ofSnowflaking_eq_preimage", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Snowflaking", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.Snowflaking.image_toSnowflaking_image_ofSnowflaking", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Snowflaking", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.Snowflaking.image_ofSnowflaking_image_toSnowflaking", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Snowflaking", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.Snowflaking.instTopologicalSpace", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Snowflaking", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.Snowflaking.continuous_ofSnowflaking", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Snowflaking", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.Snowflaking.continuous_toSnowflaking", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Snowflaking", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.Snowflaking.homeomorph", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Snowflaking", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.Snowflaking.instT0Space", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Snowflaking", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.Snowflaking.instT2Space", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Snowflaking", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.Snowflaking.instSecondCountableTopology", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Snowflaking", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.Snowflaking.instBornology", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Snowflaking", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.Snowflaking.isBounded_image_ofSnowflaking_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Snowflaking", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.Snowflaking.isBounded_preimage_toSnowflaking_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Snowflaking", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Metric.Snowflaking.isBounded_image_toSnowflaking_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Snowflaking", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Metric.Snowflaking.isBounded_preimage_ofSnowflaking_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Snowflaking", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Metric.Snowflaking.instUniformSpace", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Snowflaking", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.Snowflaking.uniformContinuous_ofSnowflaking", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Snowflaking", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.Snowflaking.uniformContinuous_toSnowflaking", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Snowflaking", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.Snowflaking.uniformEquiv", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Snowflaking", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.Snowflaking.instEDist", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Snowflaking", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.Snowflaking.edist_def", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Snowflaking", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.Snowflaking.edist_toSnowflaking_toSnowflaking", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Snowflaking", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.Snowflaking.edist_ofSnowflaking_ofSnowflaking", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Snowflaking", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Metric.Snowflaking.instPseudoEMetricSpace", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Snowflaking", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.Snowflaking.preimage_ofSnowflaking_eball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Snowflaking", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Metric.Snowflaking.image_toSnowflaking_eball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Snowflaking", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Metric.Snowflaking.preimage_toSnowflaking_eball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Snowflaking", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Metric.Snowflaking.image_ofSnowflaking_eball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Snowflaking", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Metric.Snowflaking.preimage_ofSnowflaking_closedEBall", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Snowflaking", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Metric.Snowflaking.image_toSnowflaking_closedEBall", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Snowflaking", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Metric.Snowflaking.preimage_toSnowflaking_closedEBall", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Snowflaking", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Metric.Snowflaking.image_ofSnowflaking_closedEBall", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Snowflaking", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Metric.Snowflaking.ediam_image_ofSnowflaking", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Snowflaking", "is_tactic_proof": true, "tactics": ["refine", "simp"], "tactic_count": 2}
{"name": "Metric.Snowflaking.ediam_preimage_toSnowflaking", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Snowflaking", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Metric.Snowflaking.ediam_preimage_ofSnowflaking", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Snowflaking", "is_tactic_proof": true, "tactics": ["rw", "ofSnowflaking_comp_toSnowflaking,"], "tactic_count": 2}
{"name": "Metric.Snowflaking.ediam_image_toSnowflaking", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Snowflaking", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Metric.Snowflaking.instEMetricSpace", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Snowflaking", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.Snowflaking.instDist", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Snowflaking", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.Snowflaking.dist_toSnowflaking_toSnowflaking", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Snowflaking", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.Snowflaking.instPseudoMetricSpace", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Snowflaking", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.Snowflaking.dist_ofSnowflaking_ofSnowflaking", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Snowflaking", "is_tactic_proof": true, "tactics": ["cases", "simp"], "tactic_count": 2}
{"name": "Metric.Snowflaking.preimage_ofSnowflaking_ball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Snowflaking", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Metric.Snowflaking.image_toSnowflaking_ball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Snowflaking", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Metric.Snowflaking.preimage_toSnowflaking_ball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Snowflaking", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Metric.Snowflaking.image_ofSnowflaking_ball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Snowflaking", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Metric.Snowflaking.preimage_ofSnowflaking_closedBall", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Snowflaking", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Metric.Snowflaking.image_toSnowflaking_closedBall", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Snowflaking", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Metric.Snowflaking.preimage_toSnowflaking_closedBall", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Snowflaking", "is_tactic_proof": true, "tactics": ["rw", "toSnowflaking_ofSnowflaking,"], "tactic_count": 2}
{"name": "Metric.Snowflaking.image_ofSnowflaking_closedBall", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Snowflaking", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Metric.Snowflaking.instMetricSpace", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Snowflaking", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "thickenedIndicatorAux", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.ThickenedIndicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_thickenedIndicatorAux", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.ThickenedIndicator", "is_tactic_proof": true, "tactics": ["unfold", "let", "let", "rw", "apply", "apply", "norm_num"], "tactic_count": 7}
{"name": "thickenedIndicatorAux_le_one", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.ThickenedIndicator", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "thickenedIndicatorAux_lt_top", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.ThickenedIndicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "thickenedIndicatorAux_closure_eq", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.ThickenedIndicator", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "thickenedIndicatorAux_one", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.ThickenedIndicator", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "thickenedIndicatorAux_one_of_mem_closure", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.ThickenedIndicator", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "thickenedIndicatorAux_zero", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.ThickenedIndicator", "is_tactic_proof": true, "tactics": ["rw", "unfold", "apply", "have", "rw", "simpa"], "tactic_count": 6}
{"name": "thickenedIndicatorAux_mono", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.ThickenedIndicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "indicator_le_thickenedIndicatorAux", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.ThickenedIndicator", "is_tactic_proof": true, "tactics": ["intro", "by_cases", "simp", "simp"], "tactic_count": 4}
{"name": "thickenedIndicatorAux_subset", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.ThickenedIndicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "thickenedIndicatorAux_mono_infEDist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.ThickenedIndicator", "is_tactic_proof": true, "tactics": ["simp", "rcases", "rw", "gcongr", "rw", "exact"], "tactic_count": 6}
{"name": "thickenedIndicatorAux_tendsto_indicator_closure", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.ThickenedIndicator", "is_tactic_proof": true, "tactics": ["rw", "intro", "by_cases", "simp_rw", "rw", "exact", "rw", "simp", "rcases", "rw", "specialize", "simp", "rcases", "apply", "intro", "have", "refine", "apply", "exact"], "tactic_count": 19}
{"name": "thickenedIndicator", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.ThickenedIndicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "thickenedIndicator.coeFn_eq_comp", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.ThickenedIndicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "thickenedIndicator_le_one", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.ThickenedIndicator", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "thickenedIndicator_one_of_mem_closure", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.ThickenedIndicator", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "one_le_thickenedIndicator_apply'", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.ThickenedIndicator", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "one_le_thickenedIndicator_apply", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.ThickenedIndicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "thickenedIndicator_one", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.ThickenedIndicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "thickenedIndicator_zero", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.ThickenedIndicator", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "indicator_le_thickenedIndicator", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.ThickenedIndicator", "is_tactic_proof": true, "tactics": ["intro", "by_cases", "simp", "simp"], "tactic_count": 4}
{"name": "thickenedIndicator_mono", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.ThickenedIndicator", "is_tactic_proof": true, "tactics": ["intro", "apply", "apply"], "tactic_count": 3}
{"name": "thickenedIndicator_subset", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.ThickenedIndicator", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "thickenedIndicator_mono_infEDist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.ThickenedIndicator", "is_tactic_proof": true, "tactics": ["simp", "gcongr", "finiteness", "exact"], "tactic_count": 4}
{"name": "thickenedIndicator_tendsto_indicator_closure", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.ThickenedIndicator", "is_tactic_proof": true, "tactics": ["have", "rw", "intro", "rw", "refine", "refine", "by_cases"], "tactic_count": 7}
{"name": "lipschitzWith_thickenedIndicator", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.ThickenedIndicator", "is_tactic_proof": true, "tactics": ["intro", "wlog", "specialize", "rwa", "simp_rw", "rw", "simp", "and_true,", "rw", "by_cases", "calc", "rw", "rw", "gcongr", "simp", "exact", "simp", "rw", "calc", "rw", "gcongr", "exact"], "tactic_count": 22}
{"name": "mulIndicator_thickening_eventually_eq_mulIndicator_closure", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.ThickenedIndicator", "is_tactic_proof": true, "tactics": ["by_cases", "filter_upwards", "simp", "have", "filter_upwards", "simp"], "tactic_count": 6}
{"name": "mulIndicator_cthickening_eventually_eq_mulIndicator_closure", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.ThickenedIndicator", "is_tactic_proof": true, "tactics": ["by_cases", "filter_upwards", "have", "rw", "filter_upwards", "simp"], "tactic_count": 6}
{"name": "tendsto_mulIndicator_thickening_mulIndicator_closure", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.ThickenedIndicator", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "apply"], "tactic_count": 4}
{"name": "tendsto_mulIndicator_cthickening_mulIndicator_closure", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.ThickenedIndicator", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "apply"], "tactic_count": 4}
{"name": "Metric.thickening", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.mem_thickening_iff_infEDist_lt", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.eventually_notMem_thickening_of_infEDist_pos", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": true, "tactics": ["obtain", "filter_upwards", "simp", "exact"], "tactic_count": 4}
{"name": "Metric.thickening_eq_preimage_infEDist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.isOpen_thickening", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.thickening_empty", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Metric.thickening_of_nonpos", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.thickening_mono", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.thickening_subset_of_subset", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.mem_thickening_iff_exists_edist_lt", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.frontier_thickening_subset", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.frontier_thickening_disjoint", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": true, "tactics": ["refine", "rcases", "simp", "refine", "apply_fun", "rwa"], "tactic_count": 6}
{"name": "Metric.subset_compl_thickening_compl_thickening_self", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": true, "tactics": ["intro", "simp", "apply", "simp", "simpa"], "tactic_count": 5}
{"name": "Metric.thickening_compl_thickening_self_subset_compl", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": true, "tactics": ["apply", "simpa"], "tactic_count": 2}
{"name": "Metric.mem_thickening_iff_infDist_lt", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.mem_thickening_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": false, "tactics": ["have", "rw", "simp_rw"], "tactic_count": 3}
{"name": "Metric.thickening_singleton", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Metric.ball_subset_thickening", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.thickening_eq_biUnion_ball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": true, "tactics": ["ext", "simp", "exact"], "tactic_count": 3}
{"name": "Bornology.IsBounded.thickening", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": true, "tactics": ["rcases", "simp", "refine", "calc", "dist"], "tactic_count": 5}
{"name": "Metric.cthickening", "kind": "definition", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.mem_cthickening_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.eventually_notMem_cthickening_of_infEDist_pos", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": true, "tactics": ["obtain", "filter_upwards", "simp", "exact"], "tactic_count": 4}
{"name": "Metric.mem_cthickening_of_edist_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.mem_cthickening_of_dist_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": true, "tactics": ["apply", "rw", "exact"], "tactic_count": 3}
{"name": "Metric.cthickening_eq_preimage_infEDist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.isClosed_cthickening", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.cthickening_empty", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Metric.cthickening_of_nonpos", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Metric.cthickening_zero", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.cthickening_max_zero", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "Metric.cthickening_mono", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.cthickening_singleton", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Metric.closedBall_subset_cthickening_singleton", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": true, "tactics": ["rcases", "simp", "simp"], "tactic_count": 3}
{"name": "Metric.cthickening_subset_of_subset", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.cthickening_subset_thickening", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.cthickening_subset_thickening'", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.thickening_subset_cthickening", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": true, "tactics": ["intro", "rw", "exact"], "tactic_count": 3}
{"name": "Metric.thickening_subset_cthickening_of_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.IsBounded.cthickening", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": true, "tactics": ["have", "apply", "exact", "cthickening_subset_thickening"], "tactic_count": 4}
{"name": "IsCompact.cthickening", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.thickening_subset_interior_cthickening", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.closure_thickening_subset_cthickening", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.closure_subset_cthickening", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Metric.closure_subset_thickening", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Metric.self_subset_thickening", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.self_subset_cthickening", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.thickening_mem_nhdsSet", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.cthickening_mem_nhdsSet", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.thickening_union", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Metric.cthickening_union", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Metric.thickening_iUnion", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Metric.thickening_biUnion", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Metric.ediam_cthickening_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": true, "tactics": ["refine", "rw", "have", "replace", "obtain", "calc", "edist"], "tactic_count": 7}
{"name": "Metric.ediam_thickening_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.diam_cthickening_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": true, "tactics": ["lift", "refine", "exact", "simp", "simp"], "tactic_count": 5}
{"name": "Metric.diam_thickening_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "obtain", "simp", "rw", "positivity"], "tactic_count": 6}
{"name": "Metric.thickening_closure", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Metric.cthickening_closure", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Metric.thickening_eq_empty_iff_of_pos", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.thickening_nonempty_iff_of_pos", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Metric.thickening_eq_empty_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": true, "tactics": ["obtain", "simp", "simp"], "tactic_count": 3}
{"name": "Metric.thickening_nonempty_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Disjoint.exists_thickenings", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": true, "tactics": ["obtain", "refine", "rw", "rintro", "rw", "rw", "obtain", "obtain", "refine", "calc", "edist"], "tactic_count": 11}
{"name": "Disjoint.exists_cthickenings", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": true, "tactics": ["obtain", "refine"], "tactic_count": 2}
{"name": "IsCompact.exists_cthickening_subset_open", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.exists_isCompact_cthickening", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "refine", "exact"], "tactic_count": 4}
{"name": "IsCompact.exists_thickening_subset_open", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.hasBasis_nhdsSet_thickening", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.hasBasis_nhdsSet_cthickening", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.cthickening_eq_iInter_cthickening'", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": true, "tactics": ["apply", "exact", "unfold", "intro", "simp", "apply", "intro", "rcases", "apply", "rw", "exact"], "tactic_count": 11}
{"name": "Metric.cthickening_eq_iInter_cthickening", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": true, "tactics": ["apply", "simp_rw", "exact"], "tactic_count": 3}
{"name": "Metric.cthickening_eq_iInter_thickening'", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": true, "tactics": ["refine", "obtain", "have", "exact", "rw", "exact"], "tactic_count": 6}
{"name": "Metric.cthickening_eq_iInter_thickening", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": true, "tactics": ["apply", "simp_rw", "exact"], "tactic_count": 3}
{"name": "Metric.cthickening_eq_iInter_thickening''", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Metric.closure_eq_iInter_cthickening'", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "apply", "obtain", "rw", "apply", "exact", "rw", "exact"], "tactic_count": 9}
{"name": "Metric.closure_eq_iInter_cthickening", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Metric.closure_eq_iInter_thickening'", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "Metric.closure_eq_iInter_thickening", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Metric.frontier_cthickening_subset", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.closedBall_subset_cthickening", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": true, "tactics": ["refine", "simpa"], "tactic_count": 2}
{"name": "Metric.cthickening_subset_iUnion_closedBall_of_lt", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": true, "tactics": ["refine", "obtain", "exact"], "tactic_count": 3}
{"name": "IsCompact.cthickening_eq_biUnion_closedBall", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": true, "tactics": ["rcases", "simp", "refine", "obtain", "have", "have", "rw", "exact", "exact"], "tactic_count": 9}
{"name": "Metric.cthickening_eq_biUnion_closedBall", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rw", "refine", "obtain", "isClosed_closure.exists_infDist_eq_dist", "replace", "exact"], "tactic_count": 8}
{"name": "IsClosed.cthickening_eq_biUnion_closedBall", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Metric.infEDist_le_infEDist_cthickening_add", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": true, "tactics": ["refine", "simp_rw", "obtain", "exact", "infEDist_le_edist_add_infEDist.trans_lt"], "tactic_count": 5}
{"name": "Metric.infEDist_le_infEDist_thickening_add", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.thickening_thickening_subset", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": true, "tactics": ["obtain", "simp", "obtain", "simp", "intro", "simp_rw", "exact"], "tactic_count": 7}
{"name": "Metric.thickening_cthickening_subset", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": true, "tactics": ["obtain", "simp", "intro", "simp_rw", "rintro", "exact", "infEDist_le_edist_add_infEDist.trans_lt"], "tactic_count": 7}
{"name": "Metric.cthickening_thickening_subset", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": true, "tactics": ["obtain", "simp", "intro", "simp_rw", "exact"], "tactic_count": 5}
{"name": "Metric.cthickening_cthickening_subset", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": true, "tactics": ["intro", "simp_rw", "exact"], "tactic_count": 3}
{"name": "Metric.frontier_cthickening_disjoint", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Metric.thickening_ball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "IsClopen.of_thickening_subset_self", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": true, "tactics": ["replace", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "IsClopen.of_cthickening_subset_self", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.exists_thickening_image_subset", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Thickening", "is_tactic_proof": true, "tactics": ["apply", "use", "exact", "rintro", "refine", "rw", "calc", "thickening", "intro", "have", "obtain", "let", "have", "apply", "apply", "exact", "refine", "rw", "calc", "thickening"], "tactic_count": 20}
{"name": "Equiv.dist", "kind": "abbrev", "module": "Mathlib.Topology.MetricSpace.TransferInstance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.pseudometricSpace", "kind": "abbrev", "module": "Mathlib.Topology.MetricSpace.TransferInstance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.metricSpace", "kind": "abbrev", "module": "Mathlib.Topology.MetricSpace.TransferInstance", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dist_triangle_max", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Ultra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUltrametricDist.dist_eq_max_of_dist_ne_dist", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Ultra.Basic", "is_tactic_proof": true, "tactics": ["apply", "rcases", "rw", "apply", "simpa", "rw", "apply", "simpa"], "tactic_count": 8}
{"name": "IsUltrametricDist.subtype", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Ultra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUltrametricDist.ball_eq_of_mem", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Ultra.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp_rw", "constructor"], "tactic_count": 3}
{"name": "IsUltrametricDist.ball_subset_trichotomy", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Ultra.Basic", "is_tactic_proof": true, "tactics": ["wlog", "rw", "exact", "refine", "obtain", "have", "rwa"], "tactic_count": 7}
{"name": "IsUltrametricDist.ball_eq_or_disjoint", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Ultra.Basic", "is_tactic_proof": true, "tactics": ["refine", "have", "have", "exact"], "tactic_count": 4}
{"name": "IsUltrametricDist.closedBall_eq_of_mem", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Ultra.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp_rw", "constructor"], "tactic_count": 3}
{"name": "IsUltrametricDist.closedBall_subset_trichotomy", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Ultra.Basic", "is_tactic_proof": true, "tactics": ["wlog", "rw", "exact", "refine", "obtain", "have", "rwa"], "tactic_count": 7}
{"name": "IsUltrametricDist.isClosed_ball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Ultra.Basic", "is_tactic_proof": true, "tactics": ["cases", "inl", "inr", "rw", "push", "intro", "cases", "inl", "rw", "simp", "inr", "use", "simp"], "tactic_count": 13}
{"name": "IsUltrametricDist.isClopen_ball", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Ultra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUltrametricDist.frontier_ball_eq_empty", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Ultra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUltrametricDist.closedBall_eq_or_disjoint", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Ultra.Basic", "is_tactic_proof": true, "tactics": ["refine", "have", "have", "exact"], "tactic_count": 4}
{"name": "IsUltrametricDist.isOpen_closedBall", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Ultra.Basic", "is_tactic_proof": true, "tactics": ["cases", "inl", "inr", "rw", "simp", "intro", "cases", "inl", "use", "simp", "inr"], "tactic_count": 11}
{"name": "IsUltrametricDist.isClopen_closedBall", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Ultra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUltrametricDist.frontier_closedBall_eq_empty", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Ultra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUltrametricDist.isOpen_sphere", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Ultra.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsUltrametricDist.isClopen_sphere", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.Ultra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.isUltrametricDist", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Ultra.ContinuousMaps", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "refine", "exact"], "tactic_count": 5}
{"name": "Pi.instIsUltrametricDist", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Ultra.Pi", "is_tactic_proof": true, "tactics": ["constructor", "intro", "simp", "exact"], "tactic_count": 4}
{"name": "instTotallySeparatedSpaceOfIsUltrametricDist", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.Ultra.TotallySeparated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_example", "kind": "example", "module": "Mathlib.Topology.MetricSpace.Ultra.TotallySeparated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformFun.instEDist", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformFun.edist_def", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformFun.edist_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformFun.instPseudoEMetricSpace", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformFun.instEMetricSpace", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformFun.lipschitzWith_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.UniformConvergence", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "UniformFun.lipschitzWith_ofFun_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzWith.uniformEquicontinuous", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.UniformConvergence", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "UniformFun.lipschitzOnWith_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.UniformConvergence", "is_tactic_proof": true, "tactics": ["simp", "rfl"], "tactic_count": 2}
{"name": "UniformFun.lipschitzOnWith_ofFun_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LipschitzOnWith.uniformEquicontinuousOn", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.UniformConvergence", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "UniformFun.edist_eval_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformFun.lipschitzWith_eval", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.UniformConvergence", "is_tactic_proof": true, "tactics": ["intro", "simpa"], "tactic_count": 2}
{"name": "UniformFun.instPseudoMetricSpaceOfBoundedSpace", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformFun.dist_def", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformFun.dist_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.UniformConvergence", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "UniformFun.instBoundedSpace", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformFun.instMetricSpaceOfBoundedSpace", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformFun.isometry_ofFun_boundedContinuousFunction", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.UniformConvergence", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "UniformFun.isometry_ofFun_continuousMap", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformFun.edist_continuousMapMk", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.UniformConvergence", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "UniformOnFun.continuous_of_forall_lipschitzWith", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.UniformConvergence", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "rintro", "exact"], "tactic_count": 5}
{"name": "UniformOnFun.instEDistOfFiniteElemSet", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformOnFun.edist_def", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformOnFun.edist_def'", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.UniformConvergence", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "UniformOnFun.edist_eq_restrict_sUnion", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformOnFun.edist_eq_pi_restrict", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.UniformConvergence", "is_tactic_proof": true, "tactics": ["simp_rw", "rfl"], "tactic_count": 2}
{"name": "UniformOnFun.instPseudoEMetricSpace", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformOnFun.edist_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.UniformConvergence", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "UniformOnFun.lipschitzWith_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.UniformConvergence", "is_tactic_proof": true, "tactics": ["simp", "tauto"], "tactic_count": 2}
{"name": "UniformOnFun.lipschitzOnWith_iff", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.UniformConvergence", "is_tactic_proof": true, "tactics": ["simp", "rfl"], "tactic_count": 2}
{"name": "UniformOnFun.edist_eval_le", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformOnFun.lipschitzWith_eval", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.UniformConvergence", "is_tactic_proof": true, "tactics": ["intro", "simpa"], "tactic_count": 2}
{"name": "UniformOnFun.lipschitzWith_one_ofFun_toFun", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformOnFun.lipschitzWith_one_ofFun_toFun'", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformOnFun.lipschitzWith_restrict", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformOnFun.isometry_restrict", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.UniformConvergence", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "UniformOnFun.instPseudoMetricSpaceOfBoundedSpace", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformOnFun.instBoundedSpace", "kind": "instance", "module": "Mathlib.Topology.MetricSpace.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformOnFun.edist_continuousRestrict", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.UniformConvergence", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "UniformOnFun.edist_continuousRestrict_of_singleton", "kind": "theorem", "module": "Mathlib.Topology.MetricSpace.UniformConvergence", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "UniformSpace.pseudoMetrizableSpace", "kind": "instance", "module": "Mathlib.Topology.Metrizable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.pseudoMetrizableSpaceUniformity", "kind": "abbrev", "module": "Mathlib.Topology.Metrizable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace._example", "kind": "example", "module": "Mathlib.Topology.Metrizable.Basic", "is_tactic_proof": true, "tactics": ["with_reducible_and_instances"], "tactic_count": 1}
{"name": "TopologicalSpace.pseudoMetrizableSpaceUniformity_countably_generated", "kind": "theorem", "module": "Mathlib.Topology.Metrizable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.pseudoMetrizableSpace_prod", "kind": "instance", "module": "Mathlib.Topology.Metrizable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsInducing.pseudoMetrizableSpace", "kind": "theorem", "module": "Mathlib.Topology.Metrizable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.PseudoMetrizableSpace.firstCountableTopology", "kind": "instance", "module": "Mathlib.Topology.Metrizable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.PseudoMetrizableSpace.subtype", "kind": "instance", "module": "Mathlib.Topology.Metrizable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.pseudoMetrizableSpace_pi", "kind": "instance", "module": "Mathlib.Topology.Metrizable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.PseudoMetrizableSpace.regularSpace", "kind": "instance", "module": "Mathlib.Topology.Metrizable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.PseudoMetrizableSpace.toMetrizableSpace", "kind": "instance", "module": "Mathlib.Topology.Metrizable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.t2Space_of_metrizableSpace", "kind": "instance", "module": "Mathlib.Topology.Metrizable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.metrizableSpace_prod", "kind": "instance", "module": "Mathlib.Topology.Metrizable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsEmbedding.metrizableSpace", "kind": "theorem", "module": "Mathlib.Topology.Metrizable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.MetrizableSpace.subtype", "kind": "instance", "module": "Mathlib.Topology.Metrizable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.metrizableSpace_pi", "kind": "instance", "module": "Mathlib.Topology.Metrizable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.IsSeparable.secondCountableTopology", "kind": "theorem", "module": "Mathlib.Topology.Metrizable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.instSecondCountableTopologyOfLindelofSpaceOfPseudoMetrizableSpace", "kind": "instance", "module": "Mathlib.Topology.Metrizable.Basic", "is_tactic_proof": true, "tactics": ["let", "have", "suffices", "obtain", "choose", "refine", "rw", "intro", "obtain", "rw", "exact"], "tactic_count": 11}
{"name": "TopologicalSpace.IsSeparable.exists_countable_dense_subset", "kind": "theorem", "module": "Mathlib.Topology.Metrizable.Basic", "is_tactic_proof": true, "tactics": ["let", "have", "apply", "intro", "obtain", "refine", "obtain", "exact"], "tactic_count": 8}
{"name": "TopologicalSpace.IsSeparable.separableSpace", "kind": "theorem", "module": "Mathlib.Topology.Metrizable.Basic", "is_tactic_proof": true, "tactics": ["rcases", "lift", "refine", "rwa"], "tactic_count": 4}
{"name": "TopologicalSpace.DiscreteTopology.metrizableSpace", "kind": "instance", "module": "Mathlib.Topology.Metrizable.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoMetricSpace.toIsCompletelPseudoMetrizableSpace", "kind": "instance", "module": "Mathlib.Topology.Metrizable.CompletelyMetrizable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.IsCompletelyPseudoMetrizableSpace.of_completeSpace_pseudometrizable", "kind": "instance", "module": "Mathlib.Topology.Metrizable.CompletelyMetrizable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.completelyPseudoMetrizableMetric", "kind": "definition", "module": "Mathlib.Topology.Metrizable.CompletelyMetrizable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.complete_completelyPseudoMetrizableMetric", "kind": "theorem", "module": "Mathlib.Topology.Metrizable.CompletelyMetrizable", "is_tactic_proof": true, "tactics": ["convert", "exact"], "tactic_count": 2}
{"name": "TopologicalSpace.upgradeIsCompletelyPseudoMetrizable", "kind": "definition", "module": "Mathlib.Topology.Metrizable.CompletelyMetrizable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.IsCompletelyPseudoMetrizableSpace.PseudoMetrizableSpace", "kind": "instance", "module": "Mathlib.Topology.Metrizable.CompletelyMetrizable", "is_tactic_proof": true, "tactics": ["letI", "infer_instance"], "tactic_count": 2}
{"name": "TopologicalSpace.IsCompletelyPseudoMetrizableSpace.pi_countable", "kind": "instance", "module": "Mathlib.Topology.Metrizable.CompletelyMetrizable", "is_tactic_proof": true, "tactics": ["letI", "infer_instance"], "tactic_count": 2}
{"name": "TopologicalSpace.IsCompletelyPseudoMetrizableSpace.prod", "kind": "instance", "module": "Mathlib.Topology.Metrizable.CompletelyMetrizable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.IsCompletelyPseudoMetrizableSpace.sum", "kind": "instance", "module": "Mathlib.Topology.Metrizable.CompletelyMetrizable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsClosedEmbedding.IsCompletelyPseudoMetrizableSpace", "kind": "theorem", "module": "Mathlib.Topology.Metrizable.CompletelyMetrizable", "is_tactic_proof": true, "tactics": ["letI", "letI", "have", "rw", "exact", "infer_instance"], "tactic_count": 6}
{"name": "IsClosed.isCompletelyPseudoMetrizableSpace", "kind": "theorem", "module": "Mathlib.Topology.Metrizable.CompletelyMetrizable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.IsCompletelyMetrizableSpace.toIsCompletelyPseudoMetrizableSpace", "kind": "instance", "module": "Mathlib.Topology.Metrizable.CompletelyMetrizable", "is_tactic_proof": true, "tactics": ["obtain", "use"], "tactic_count": 2}
{"name": "TopologicalSpace.IsCompletelyMetrizableSpace_of_isCompletelyPseudoMetrizableSpace", "kind": "theorem", "module": "Mathlib.Topology.Metrizable.CompletelyMetrizable", "is_tactic_proof": true, "tactics": ["letI", "use", "exact"], "tactic_count": 3}
{"name": "MetricSpace.toIsCompletelyMetrizableSpace", "kind": "instance", "module": "Mathlib.Topology.Metrizable.CompletelyMetrizable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.IsCompletelyMetrizableSpace.of_completeSpace_metrizable", "kind": "instance", "module": "Mathlib.Topology.Metrizable.CompletelyMetrizable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.completelyMetrizableMetric", "kind": "definition", "module": "Mathlib.Topology.Metrizable.CompletelyMetrizable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.complete_completelyMetrizableMetric", "kind": "theorem", "module": "Mathlib.Topology.Metrizable.CompletelyMetrizable", "is_tactic_proof": true, "tactics": ["convert", "exact"], "tactic_count": 2}
{"name": "TopologicalSpace.upgradeIsCompletelyMetrizable", "kind": "definition", "module": "Mathlib.Topology.Metrizable.CompletelyMetrizable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.IsCompletelyMetrizableSpace.MetrizableSpace", "kind": "instance", "module": "Mathlib.Topology.Metrizable.CompletelyMetrizable", "is_tactic_proof": true, "tactics": ["letI", "infer_instance"], "tactic_count": 2}
{"name": "TopologicalSpace.IsCompletelyMetrizableSpace.pi_countable", "kind": "instance", "module": "Mathlib.Topology.Metrizable.CompletelyMetrizable", "is_tactic_proof": true, "tactics": ["letI", "infer_instance"], "tactic_count": 2}
{"name": "TopologicalSpace.IsCompletelyMetrizableSpace.sigma", "kind": "instance", "module": "Mathlib.Topology.Metrizable.CompletelyMetrizable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.IsCompletelyMetrizableSpace.prod", "kind": "instance", "module": "Mathlib.Topology.Metrizable.CompletelyMetrizable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.IsCompletelyMetrizableSpace.sum", "kind": "instance", "module": "Mathlib.Topology.Metrizable.CompletelyMetrizable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsClosedEmbedding.IsCompletelyMetrizableSpace", "kind": "theorem", "module": "Mathlib.Topology.Metrizable.CompletelyMetrizable", "is_tactic_proof": true, "tactics": ["letI", "letI", "have", "rw", "exact", "infer_instance"], "tactic_count": 6}
{"name": "TopologicalSpace.IsCompletelyMetrizableSpace.discrete", "kind": "instance", "module": "Mathlib.Topology.Metrizable.CompletelyMetrizable", "is_tactic_proof": true, "tactics": ["classical", "let", "dist_self", "dist_comm", "y", "obtain", "simp", "simp", "dist_triangle", "eq_of_dist_eq_zero", "refine", "rw", "refine", "convert", "refine", "simp", "by_contra", "change", "simp_all", "refine", "rw", "obtain", "refine", "specialize", "by_contra", "change", "simp_all"], "tactic_count": 27}
{"name": "IsClosed.isCompletelyMetrizableSpace", "kind": "theorem", "module": "Mathlib.Topology.Metrizable.CompletelyMetrizable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.IsCompletelyMetrizableSpace.univ", "kind": "instance", "module": "Mathlib.Topology.Metrizable.CompletelyMetrizable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instPseudoMetrizableSpace", "kind": "instance", "module": "Mathlib.Topology.Metrizable.ContinuousMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instMetrizableSpace", "kind": "instance", "module": "Mathlib.Topology.Metrizable.ContinuousMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.instMetrizableSpace", "kind": "instance", "module": "Mathlib.Topology.Metrizable.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoMetricSpace.ofPreNNDist", "kind": "definition", "module": "Mathlib.Topology.Metrizable.Uniformity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoMetricSpace.dist_ofPreNNDist", "kind": "theorem", "module": "Mathlib.Topology.Metrizable.Uniformity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoMetricSpace.dist_ofPreNNDist_le", "kind": "theorem", "module": "Mathlib.Topology.Metrizable.Uniformity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoMetricSpace.le_two_mul_dist_ofPreNNDist", "kind": "theorem", "module": "Mathlib.Topology.Metrizable.Uniformity", "is_tactic_proof": true, "tactics": ["splits", "rw", "refine", "have", "intro", "rw", "simpa", "haveI", "suffices", "intro", "induction", "h", "simp", "subst", "set", "have", "rcases", "simp", "rsuffices", "grw", "set", "have", "have", "obtain", "have", "intro", "rw", "intro", "rw", "forall_iff_forall_mem,", "exact", "have", "exact", "have", "have", "have", "refine", "cases", "zero", "succ", "rw", "have", "refine", "convert", "rw", "exact", "rcases", "simp", "rw", "have", "have", "refine", "rw", "have", "rw", "sum_take_add_sum_drop,", "convert", "rwa"], "tactic_count": 58}
{"name": "UniformSpace.metrizable_uniformity", "kind": "theorem", "module": "Mathlib.Topology.Metrizable.Uniformity", "is_tactic_proof": true, "tactics": ["classical", "separates", "satisfies", "pseudometric", "to", "obtain", "rcases", "rcases", "hB.subbasis_with_rel", "hB.tendsto_smallSets.eventually", "exact", "set", "have", "intro", "refine", "simp", "split_ifs", "simp", "simpa", "have", "have", "letI", "have", "have", "intro", "dsimp", "split_ifs", "rw", "exact", "push_neg", "simp", "have", "refine", "by_cases", "refine", "rw", "simp", "rintro", "refine", "exact", "exact", "rw", "refine", "refine", "rwa", "refine", "rw", "contrapose", "refine", "rwa", "div_le_iff₀"], "tactic_count": 51}
{"name": "UniformSpace.pseudoMetricSpace", "kind": "abbrev", "module": "Mathlib.Topology.Metrizable.Uniformity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.metricSpace", "kind": "abbrev", "module": "Mathlib.Topology.Metrizable.Uniformity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.metrizableSpace", "kind": "theorem", "module": "Mathlib.Topology.Metrizable.Uniformity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.pseudoMetrizableSpacePseudoMetric", "kind": "abbrev", "module": "Mathlib.Topology.Metrizable.Uniformity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_example", "kind": "example", "module": "Mathlib.Topology.Metrizable.Uniformity", "is_tactic_proof": true, "tactics": ["with_reducible_and_instances"], "tactic_count": 1}
{"name": "TopologicalSpace.metrizableSpaceMetric", "kind": "abbrev", "module": "Mathlib.Topology.Metrizable.Uniformity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_example", "kind": "example", "module": "Mathlib.Topology.Metrizable.Uniformity", "is_tactic_proof": true, "tactics": ["with_reducible_and_instances"], "tactic_count": 1}
{"name": "PseudoEMetricSpace.pseudoMetrizableSpace", "kind": "instance", "module": "Mathlib.Topology.Metrizable.Uniformity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EMetricSpace.metrizableSpace", "kind": "instance", "module": "Mathlib.Topology.Metrizable.Uniformity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.exists_isInducing_l_infty", "kind": "theorem", "module": "Mathlib.Topology.Metrizable.Urysohn", "is_tactic_proof": true, "tactics": ["rcases", "let", "haveI", "letI", "haveI", "rsuffices", "exact", "have", "disjoint_compl_right.mono_right", "obtain", "rcases", "refine", "exact", "have", "intro", "rcases", "exact", "choose", "have", "set", "have", "refine", "such", "we", "refine", "have", "have", "refine", "exact", "refine", "rcases", "exacts", "includes", "refine", "rintro", "rcases", "set", "refine", "replace", "contrapose", "rw", "exact"], "tactic_count": 42}
{"name": "TopologicalSpace.PseudoMetrizableSpace.of_regularSpace_secondCountableTopology", "kind": "instance", "module": "Mathlib.Topology.Metrizable.Urysohn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.exists_embedding_l_infty", "kind": "theorem", "module": "Mathlib.Topology.Metrizable.Urysohn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.metrizableSpace_of_t3_secondCountable", "kind": "instance", "module": "Mathlib.Topology.Metrizable.Urysohn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_seq_infinite_isOpen_pairwise_disjoint", "kind": "theorem", "module": "Mathlib.Topology.NatEmbedding", "is_tactic_proof": false, "tactics": ["suffices", "rcases", "refine", "refine", "suffices", "apply", "simpa", "refine", "simp", "by_cases", "refine", "simpa", "simp", "rcases", "suffices", "rcases", "exact", "have", "refine", "have", "inter_mem_inf", "rcases", "rcases", "refine", "exact", "refine", "exact", "exact"], "tactic_count": 28}
{"name": "exists_topology_isEmbedding_nat", "kind": "theorem", "module": "Mathlib.Topology.NatEmbedding", "is_tactic_proof": true, "tactics": ["rcases", "choose", "refine", "refine", "exact"], "tactic_count": 5}
{"name": "exists_infinite_discreteTopology", "kind": "theorem", "module": "Mathlib.Topology.NatEmbedding", "is_tactic_proof": true, "tactics": ["rcases", "refine", "exact"], "tactic_count": 3}
{"name": "nhds_def'", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "nhds_basis_opens", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": true, "tactics": ["rw", "exact", "hasBasis_biInf_principal"], "tactic_count": 3}
{"name": "nhds_basis_closeds", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lift'_nhds_interior", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.nhds_interior", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_nhds_iff", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "nhds_le_of_le", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mem_nhds_iff", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eventually_nhds_iff", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "frequently_nhds_iff", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_interior_iff_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "map_nhds", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_of_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Eventually.self_of_nhds", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.mem_nhds_iff", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.compl_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.eventually_mem", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhds_basis_opens'", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": true, "tactics": ["convert", "exact"], "tactic_count": 2}
{"name": "exists_open_set_nhds", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_open_set_nhds'", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Eventually.eventually_nhds", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eventually_eventually_nhds", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "frequently_frequently_nhds", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "eventually_mem_nhds_iff", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhds_bind_nhds", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eventually_eventuallyEq_nhds", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.eq_of_nhds", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eventually_eventuallyLE_nhds", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.eventuallyEq_nhds", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyLE.eventuallyLE_nhds", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "all_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "all_mem_nhds_filter", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_nhds", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_atTop_nhds", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_const_nhds", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_atTop_of_eventually_const", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_atBot_of_eventually_const", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pure_le_nhds", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_pure_nhds", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderTop.tendsto_atTop_nhds", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhds_neBot", "kind": "instance", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_nhds_of_eventually_eq", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.tendsto", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "interior_eq_nhds'", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "interior_eq_nhds", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "interior_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "interior_setOf_eq", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpen_setOf_eventually_nhds", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "subset_interior_iff_nhds", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "isOpen_iff_nhds", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.ext_iff_nhds", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpen_iff_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpen_iff_eventually", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpen_singleton_iff_nhds_eq_pure", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "isOpen_singleton_iff_punctured_nhds", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "mem_closure_iff_frequently", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": true, "tactics": ["rw", "compl_def]"], "tactic_count": 2}
{"name": "isClosed_iff_frequently", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw"], "tactic_count": 3}
{"name": "nhdsWithin_neBot", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": true, "tactics": ["rw", "exact", "forall₂_congr"], "tactic_count": 3}
{"name": "nhdsWithin_mono", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.interior_union_left", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.interior_union_right", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsOpen.inter_closure", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.closure_inter", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Dense.open_subset_closure_inter", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dense.inter_of_isOpen_left", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dense.inter_of_isOpen_right", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dense.inter_nhds_nonempty", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "closure_diff", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Frequently.mem_of_closed", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.mem_of_frequently_of_tendsto", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.mem_of_tendsto", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_closure_of_frequently_of_tendsto", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_closure_of_tendsto", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_inf_principal_nhds_iff_of_forall_eq", "kind": "theorem", "module": "Mathlib.Topology.Neighborhoods", "is_tactic_proof": true, "tactics": ["rw", "replace", "rintro", "have", "exact", "refine", "have", "rw", "exact"], "tactic_count": 9}
{"name": "nhdsKer_singleton_eq_ker_nhds", "kind": "theorem", "module": "Mathlib.Topology.NhdsKer", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "mem_nhdsKer_singleton", "kind": "theorem", "module": "Mathlib.Topology.NhdsKer", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "nhdsKer_def", "kind": "theorem", "module": "Mathlib.Topology.NhdsKer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_nhdsKer", "kind": "theorem", "module": "Mathlib.Topology.NhdsKer", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "subset_nhdsKer_iff", "kind": "theorem", "module": "Mathlib.Topology.NhdsKer", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "subset_nhdsKer", "kind": "theorem", "module": "Mathlib.Topology.NhdsKer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsKer_minimal", "kind": "theorem", "module": "Mathlib.Topology.NhdsKer", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsOpen.nhdsKer_eq", "kind": "theorem", "module": "Mathlib.Topology.NhdsKer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.nhdsKer_subset", "kind": "theorem", "module": "Mathlib.Topology.NhdsKer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsKer_iUnion", "kind": "theorem", "module": "Mathlib.Topology.NhdsKer", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "nhdsKer_biUnion", "kind": "theorem", "module": "Mathlib.Topology.NhdsKer", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "nhdsKer_union", "kind": "theorem", "module": "Mathlib.Topology.NhdsKer", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "nhdsKer_sUnion", "kind": "theorem", "module": "Mathlib.Topology.NhdsKer", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "mem_nhdsKer_iff_specializes", "kind": "theorem", "module": "Mathlib.Topology.NhdsKer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsKer_mono", "kind": "theorem", "module": "Mathlib.Topology.NhdsKer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsKer_subset_nhdsKer", "kind": "theorem", "module": "Mathlib.Topology.NhdsKer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsKer_subset_nhdsKer_iff_nhdsSet", "kind": "theorem", "module": "Mathlib.Topology.NhdsKer", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "nhdsKer_eq_nhdsKer_iff_nhdsSet", "kind": "theorem", "module": "Mathlib.Topology.NhdsKer", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "specializes_iff_nhdsKer_subset", "kind": "theorem", "module": "Mathlib.Topology.NhdsKer", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "nhdsKer_iInter_subset", "kind": "theorem", "module": "Mathlib.Topology.NhdsKer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsKer_inter_subset", "kind": "theorem", "module": "Mathlib.Topology.NhdsKer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsKer_sInter_subset", "kind": "theorem", "module": "Mathlib.Topology.NhdsKer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsKer_empty", "kind": "theorem", "module": "Mathlib.Topology.NhdsKer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsKer_univ", "kind": "theorem", "module": "Mathlib.Topology.NhdsKer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsKer_eq_empty", "kind": "theorem", "module": "Mathlib.Topology.NhdsKer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsSet_nhdsKer", "kind": "theorem", "module": "Mathlib.Topology.NhdsKer", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "nhdsKer_nhdsKer", "kind": "theorem", "module": "Mathlib.Topology.NhdsKer", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "nhdsKer_pair", "kind": "theorem", "module": "Mathlib.Topology.NhdsKer", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "nhdsKer_prod", "kind": "theorem", "module": "Mathlib.Topology.NhdsKer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsKer_singleton_pi", "kind": "theorem", "module": "Mathlib.Topology.NhdsKer", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "nhdsKer_pi", "kind": "theorem", "module": "Mathlib.Topology.NhdsKer", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsSet_diagonal", "kind": "theorem", "module": "Mathlib.Topology.NhdsSet", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "mem_nhdsSet_iff_forall", "kind": "theorem", "module": "Mathlib.Topology.NhdsSet", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "nhdsSet_le", "kind": "theorem", "module": "Mathlib.Topology.NhdsSet", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "bUnion_mem_nhdsSet", "kind": "theorem", "module": "Mathlib.Topology.NhdsSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "subset_interior_iff_mem_nhdsSet", "kind": "theorem", "module": "Mathlib.Topology.NhdsSet", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "disjoint_principal_nhdsSet", "kind": "theorem", "module": "Mathlib.Topology.NhdsSet", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "disjoint_nhdsSet_principal", "kind": "theorem", "module": "Mathlib.Topology.NhdsSet", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mem_nhdsSet_iff_exists", "kind": "theorem", "module": "Mathlib.Topology.NhdsSet", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "eventually_nhdsSet_iff_exists", "kind": "theorem", "module": "Mathlib.Topology.NhdsSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eventually_nhdsSet_iff_forall", "kind": "theorem", "module": "Mathlib.Topology.NhdsSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasBasis_nhdsSet", "kind": "theorem", "module": "Mathlib.Topology.NhdsSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lift'_nhdsSet_interior", "kind": "theorem", "module": "Mathlib.Topology.NhdsSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.nhdsSet_interior", "kind": "theorem", "module": "Mathlib.Topology.NhdsSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.mem_nhdsSet", "kind": "theorem", "module": "Mathlib.Topology.NhdsSet", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsOpen.mem_nhdsSet_self", "kind": "theorem", "module": "Mathlib.Topology.NhdsSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "principal_le_nhdsSet", "kind": "theorem", "module": "Mathlib.Topology.NhdsSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "subset_of_mem_nhdsSet", "kind": "theorem", "module": "Mathlib.Topology.NhdsSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Eventually.self_of_nhdsSet", "kind": "theorem", "module": "Mathlib.Topology.NhdsSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.self_of_nhdsSet", "kind": "theorem", "module": "Mathlib.Topology.NhdsSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsSet_eq_principal_iff", "kind": "theorem", "module": "Mathlib.Topology.NhdsSet", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "nhdsSet_interior", "kind": "theorem", "module": "Mathlib.Topology.NhdsSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsSet_singleton", "kind": "theorem", "module": "Mathlib.Topology.NhdsSet", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "mem_nhdsSet_interior", "kind": "theorem", "module": "Mathlib.Topology.NhdsSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsSet_empty", "kind": "theorem", "module": "Mathlib.Topology.NhdsSet", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mem_nhdsSet_empty", "kind": "theorem", "module": "Mathlib.Topology.NhdsSet", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "nhdsSet_eq_bot_iff", "kind": "theorem", "module": "Mathlib.Topology.NhdsSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsSet_neBot_iff", "kind": "theorem", "module": "Mathlib.Topology.NhdsSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsSet_univ", "kind": "theorem", "module": "Mathlib.Topology.NhdsSet", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "nhdsSet_mono", "kind": "theorem", "module": "Mathlib.Topology.NhdsSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "monotone_nhdsSet", "kind": "theorem", "module": "Mathlib.Topology.NhdsSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhds_le_nhdsSet", "kind": "theorem", "module": "Mathlib.Topology.NhdsSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsSet_union", "kind": "theorem", "module": "Mathlib.Topology.NhdsSet", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "union_mem_nhdsSet", "kind": "theorem", "module": "Mathlib.Topology.NhdsSet", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "nhdsSet_insert", "kind": "theorem", "module": "Mathlib.Topology.NhdsSet", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "nhdsSet_inter_le", "kind": "theorem", "module": "Mathlib.Topology.NhdsSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsSet_iInter_le", "kind": "theorem", "module": "Mathlib.Topology.NhdsSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsSet_sInter_le", "kind": "theorem", "module": "Mathlib.Topology.NhdsSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.nhdsSet_le_sup", "kind": "theorem", "module": "Mathlib.Topology.NhdsSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.nhdsSet_le_sup'", "kind": "theorem", "module": "Mathlib.Topology.NhdsSet", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.Eventually.eventually_nhdsSet", "kind": "theorem", "module": "Mathlib.Topology.NhdsSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Eventually.union_nhdsSet", "kind": "theorem", "module": "Mathlib.Topology.NhdsSet", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.Eventually.union", "kind": "theorem", "module": "Mathlib.Topology.NhdsSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsSet_iUnion", "kind": "theorem", "module": "Mathlib.Topology.NhdsSet", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "eventually_nhdsSet_iUnion₂", "kind": "theorem", "module": "Mathlib.Topology.NhdsSet", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "eventually_nhdsSet_iUnion", "kind": "theorem", "module": "Mathlib.Topology.NhdsSet", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "nhds_bind_nhdsWithin", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eventually_nhds_nhdsWithin", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eventually_nhdsWithin_iff", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "frequently_nhdsWithin_iff", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_closure_ne_iff_frequently_within", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "eventually_eventually_nhdsWithin", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": true, "tactics": ["refine", "simp", "exact"], "tactic_count": 3}
{"name": "eventually_mem_nhdsWithin_iff", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsWithin_eq", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsWithin_univ", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "nhdsWithin_hasBasis", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsWithin_basis_open", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_nhdsWithin", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "mem_nhdsWithin_iff_exists_mem_nhds_inter", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "diff_mem_nhdsWithin_compl", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "diff_mem_nhdsWithin_diff", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "nhds_of_nhdsWithin_of_nhds", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "mem_nhdsWithin_iff_eventually", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_nhdsWithin_iff_eventuallyEq", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "mem_nhdsWithin_inter_self", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_nhdsWithin_self_inter", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsWithin_eq_iff_eventuallyEq", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsWithin_le_iff", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "preimage_nhdsWithin_coinduced'", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": true, "tactics": ["lift", "replace", "rwa"], "tactic_count": 3}
{"name": "mem_nhdsWithin_of_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "self_mem_nhdsWithin", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eventually_mem_nhdsWithin", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inter_mem_nhdsWithin", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pure_le_nhdsWithin", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_of_mem_nhdsWithin", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Eventually.self_of_nhdsWithin", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_const_nhdsWithin", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsWithin_restrict''", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsWithin_restrict'", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsWithin_restrict", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsWithin_le_of_mem", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsWithin_le_nhds", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": true, "tactics": ["rw", "apply", "exact"], "tactic_count": 3}
{"name": "nhdsWithin_eq_nhdsWithin'", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "nhdsWithin_eq_nhdsWithin", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "nhdsWithin_eq_nhds", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.nhdsWithin_eq", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "preimage_nhds_within_coinduced", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "nhdsWithin_empty", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "nhdsWithin_union", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": true, "tactics": ["delta", "rw"], "tactic_count": 2}
{"name": "nhds_eq_nhdsWithin_sup_nhdsWithin", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "inter_mem_nhdsWithin_inter", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "union_mem_nhds_of_mem_nhdsWithin", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "punctured_nhds_eq_nhdsWithin_sup_nhdsWithin", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "nhds_of_Ici_Iic", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsWithin_biUnion", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": true, "tactics": ["induction", "empty", "insert"], "tactic_count": 3}
{"name": "nhdsWithin_sUnion", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "nhdsWithin_iUnion", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "nhdsWithin_inter", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": true, "tactics": ["delta", "rw"], "tactic_count": 2}
{"name": "nhdsWithin_inter'", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": true, "tactics": ["delta", "rw"], "tactic_count": 2}
{"name": "nhdsWithin_inter_of_mem", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "nhdsWithin_inter_of_mem'", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "nhdsWithin_singleton", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "nhdsWithin_insert", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mem_nhdsWithin_insert", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "insert_mem_nhdsWithin_insert", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "insert_mem_nhds_iff", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "nhdsNE_sup_pure", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "pure_sup_nhdsNE", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "continuousAt_iff_punctured_nhds", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "nhdsWithin_prod", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Filter.EventuallyEq.mem_interior", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "Filter.EventuallyEq.mem_interior_iff", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsWithin_pi_eq'", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "nhdsWithin_pi_eq", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": true, "tactics": ["simp", "rw", "simp"], "tactic_count": 3}
{"name": "nhdsWithin_pi_univ_eq", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "nhdsWithin_pi_eq_bot", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "nhdsWithin_pi_neBot", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "instNeBotNhdsWithinUnivPi", "kind": "instance", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Pi.instNeBotNhdsWithinIio", "kind": "instance", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instNeBotNhdsWithinIoi", "kind": "instance", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.piecewise_nhdsWithin", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "Filter.Tendsto.if_nhdsWithin", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "map_nhdsWithin", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_nhdsWithin_mono_left", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_nhdsWithin_mono_right", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_nhdsWithin_of_tendsto_nhds", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eventually_mem_of_tendsto_nhdsWithin", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "tendsto_nhds_of_tendsto_nhdsWithin", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsWithin_neBot_of_mem", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.mem_of_nhdsWithin_neBot", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DenseRange.nhdsWithin_neBot", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_closure_pi", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "closure_pi_set", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dense_pi", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DenseRange.piMap", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "eventuallyEq_nhdsWithin_iff", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eventuallyEq_nhds_of_eventuallyEq_nhdsNE", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": true, "tactics": ["filter_upwards", "grind"], "tactic_count": 2}
{"name": "eventuallyEq_nhdsWithin_of_eqOn", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.EqOn.eventuallyEq_nhdsWithin", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_nhdsWithin_congr", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eventually_nhdsWithin_of_forall", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_nhdsWithin_of_tendsto_nhds_of_eventually_within", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_nhdsWithin_iff", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_nhdsWithin_range", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.eq_of_nhdsWithin", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eventually_nhdsWithin_of_eventually_nhds", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.MapsTo.preimage_mem_nhdsWithin", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_nhdsWithin_subtype", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "nhdsWithin_subtype", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsWithin_eq_map_subtype_coe", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_nhds_subtype_iff_nhdsWithin", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "preimage_coe_mem_nhds_subtype", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "eventually_nhds_subtype_iff", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "frequently_nhds_subtype_iff", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_nhdsWithin_iff_subtype", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "nhdsSetWithin_mono_left", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsSetWithin_mono_right", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsSetWithin_hasBasis", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsSetWithin_basis_open", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_nhdsSetWithin", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "nhdsSetWithin_singleton", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "nhdsSetWithin_univ", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "mem_nhdsSet", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "nhdsSetWithin_univ'", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "nhdsSetWithin_self", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "nhdsSetWithin_eq_principal_of_subset", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "nhdsSetWithin_empty", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "nhdsSetWithin_empty'", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "principal_inter_le_nhdsSetWithin", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "nhdsSetWithin_prod_le", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "mem_nhdsSet_induced", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": true, "tactics": ["letI", "simp_rw", "refine", "refine", "exact", "exact"], "tactic_count": 6}
{"name": "nhdsSet_induced", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "map_nhdsSet_induced_eq", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Topology.IsInducing.map_nhdsSet_eq", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "map_nhdsSet_subtype_val", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mem_nhdsSet_subtype_iff_nhdsSetWithin", "kind": "theorem", "module": "Mathlib.Topology.NhdsWithin", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "TopologicalSpace.NoetherianSpace", "kind": "abbrev", "module": "Mathlib.Topology.NoetherianSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.noetherianSpace_iff_opens", "kind": "theorem", "module": "Mathlib.Topology.NoetherianSpace", "is_tactic_proof": false, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "TopologicalSpace.NoetherianSpace.compactSpace", "kind": "instance", "module": "Mathlib.Topology.NoetherianSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NoetherianSpace.isCompact", "kind": "theorem", "module": "Mathlib.Topology.NoetherianSpace", "is_tactic_proof": true, "tactics": ["refine", "rcases", "exact"], "tactic_count": 3}
{"name": "Topology.IsInducing.noetherianSpace", "kind": "theorem", "module": "Mathlib.Topology.NoetherianSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NoetherianSpace.set", "kind": "instance", "module": "Mathlib.Topology.NoetherianSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.noetherianSpace_TFAE", "kind": "theorem", "module": "Mathlib.Topology.NoetherianSpace", "is_tactic_proof": false, "tactics": ["tfae_have", "simp_rw", "exact", "tfae_have", "tfae_have", "tfae_have", "tfae_finish"], "tactic_count": 7}
{"name": "TopologicalSpace.noetherianSpace_iff_isCompact", "kind": "theorem", "module": "Mathlib.Topology.NoetherianSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.instWellFoundedLTClosedsOfNoetherianSpace", "kind": "instance", "module": "Mathlib.Topology.NoetherianSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.instNoetherianSpaceCofiniteTopology", "kind": "instance", "module": "Mathlib.Topology.NoetherianSpace", "is_tactic_proof": false, "tactics": ["simp", "intro", "rcases", "rcases", "exact", "exact"], "tactic_count": 6}
{"name": "TopologicalSpace.noetherianSpace_of_surjective", "kind": "theorem", "module": "Mathlib.Topology.NoetherianSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.noetherianSpace_iff_of_homeomorph", "kind": "theorem", "module": "Mathlib.Topology.NoetherianSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NoetherianSpace.range", "kind": "theorem", "module": "Mathlib.Topology.NoetherianSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.noetherianSpace_set_iff", "kind": "theorem", "module": "Mathlib.Topology.NoetherianSpace", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "TopologicalSpace.noetherian_univ_iff", "kind": "theorem", "module": "Mathlib.Topology.NoetherianSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NoetherianSpace.iUnion", "kind": "theorem", "module": "Mathlib.Topology.NoetherianSpace", "is_tactic_proof": true, "tactics": ["simp_rw", "intro", "rw", "exact"], "tactic_count": 4}
{"name": "TopologicalSpace.NoetherianSpace.discrete", "kind": "theorem", "module": "Mathlib.Topology.NoetherianSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NoetherianSpace.finite", "kind": "theorem", "module": "Mathlib.Topology.NoetherianSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Finite.to_noetherianSpace", "kind": "instance", "module": "Mathlib.Topology.NoetherianSpace", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NoetherianSpace.exists_finite_set_closeds_irreducible", "kind": "theorem", "module": "Mathlib.Topology.NoetherianSpace", "is_tactic_proof": true, "tactics": ["apply", "intro", "rcases", "use", "by_cases", "replace", "use", "simp", "obtain", "lift", "lift", "rcases", "rcases", "refine", "rwa"], "tactic_count": 15}
{"name": "TopologicalSpace.NoetherianSpace.exists_finite_set_isClosed_irreducible", "kind": "theorem", "module": "Mathlib.Topology.NoetherianSpace", "is_tactic_proof": true, "tactics": ["lift", "rcases", "refine", "lift", "simp"], "tactic_count": 5}
{"name": "TopologicalSpace.NoetherianSpace.exists_finset_irreducible", "kind": "theorem", "module": "Mathlib.Topology.NoetherianSpace", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "TopologicalSpace.NoetherianSpace.finite_irreducibleComponents", "kind": "theorem", "module": "Mathlib.Topology.NoetherianSpace", "is_tactic_proof": false, "tactics": ["obtain", "refine", "lift", "rcases", "rwa"], "tactic_count": 5}
{"name": "TopologicalSpace.NoetherianSpace.exists_isOpen_nonempty_subset_irreducibleComponent", "kind": "theorem", "module": "Mathlib.Topology.NoetherianSpace", "is_tactic_proof": true, "tactics": ["classical", "let", "have", "have", "let", "have", "obtain", "isIrreducible_iff_sUnion_isClosed.mp", "rw", "exact", "have", "rw", "refine", "rw", "refine", "rw", "rintro", "by_cases", "exact", "rw", "rcases", "refine", "simp", "refine", "rintro", "exact", "exact", "refine", "exact"], "tactic_count": 29}
{"name": "TopologicalSpace.NoetherianSpace.exists_open_ne_empty_le_irreducibleComponent", "kind": "theorem", "module": "Mathlib.Topology.NoetherianSpace", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Topology.IsScott.ωScottContinuous_iff_continuous", "kind": "theorem", "module": "Mathlib.Topology.OmegaCompletePartialOrder", "is_tactic_proof": true, "tactics": ["rw", "scottContinuousOn_iff_continuous"], "tactic_count": 2}
{"name": "Scott.IsωSup", "kind": "definition", "module": "Mathlib.Topology.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Scott.isωSup_iff_isLUB", "kind": "theorem", "module": "Mathlib.Topology.OmegaCompletePartialOrder", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Scott.IsOpen", "kind": "definition", "module": "Mathlib.Topology.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Scott.isOpen_univ", "kind": "theorem", "module": "Mathlib.Topology.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Scott.IsOpen.inter", "kind": "theorem", "module": "Mathlib.Topology.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Scott.isOpen_sUnion", "kind": "theorem", "module": "Mathlib.Topology.OmegaCompletePartialOrder", "is_tactic_proof": true, "tactics": ["simp", "convert", "aesop"], "tactic_count": 3}
{"name": "Scott.IsOpen.isUpperSet", "kind": "theorem", "module": "Mathlib.Topology.OmegaCompletePartialOrder", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isωSup_ωSup", "kind": "theorem", "module": "Mathlib.Topology.OmegaCompletePartialOrder", "is_tactic_proof": true, "tactics": ["constructor", "apply", "apply"], "tactic_count": 3}
{"name": "OpenPartialHomeomorph.refl", "kind": "definition", "module": "Mathlib.Topology.OpenPartialHomeomorph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.refl_partialEquiv", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.refl_symm", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.source_preimage_target", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.image_eq_target_inter_inv_preimage", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.image_source_inter_eq'", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.image_source_inter_eq", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.symm_image_eq_source_inter_preimage", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.symm_image_target_inter_eq", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.source_inter_preimage_inv_preimage", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.target_inter_inv_preimage_preimage", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.source_inter_preimage_target_inter", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.image_source_eq_target", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.symm_image_target_eq_source", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.isOpen_inter_preimage", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.isOpen_inter_preimage_symm", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.isOpen_image_of_subset_source", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "OpenPartialHomeomorph.isOpen_image_source_inter", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.isOpen_image_symm_of_subset_target", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.isOpen_symm_image_iff_of_subset_target", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Basic", "is_tactic_proof": true, "tactics": ["refine", "have", "rw", "apply", "rw", "exact"], "tactic_count": 6}
{"name": "OpenPartialHomeomorph.isOpen_image_iff_of_subset_source", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "OpenPartialHomeomorph.ofContinuousOpenRestrict", "kind": "definition", "module": "Mathlib.Topology.OpenPartialHomeomorph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.coe_ofContinuousOpenRestrict", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.coe_ofContinuousOpenRestrict_symm", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.ofContinuousOpen", "kind": "definition", "module": "Mathlib.Topology.OpenPartialHomeomorph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.coe_ofContinuousOpen", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.coe_ofContinuousOpen_symm", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.homeomorphOfImageSubsetSource", "kind": "definition", "module": "Mathlib.Topology.OpenPartialHomeomorph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.toHomeomorphSourceTarget", "kind": "definition", "module": "Mathlib.Topology.OpenPartialHomeomorph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.secondCountableTopology_source", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.nhds_eq_comap_inf_principal", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Basic", "is_tactic_proof": true, "tactics": ["lift", "rw", "e.toHomeomorphSourceTarget.nhds_eq_comap,", "simp"], "tactic_count": 4}
{"name": "OpenPartialHomeomorph.toHomeomorphOfSourceEqUnivTargetEqUniv", "kind": "definition", "module": "Mathlib.Topology.OpenPartialHomeomorph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.isOpenEmbedding_restrict", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Basic", "is_tactic_proof": false, "tactics": ["refine", "e.injOn.injective", "rw", "exact"], "tactic_count": 4}
{"name": "OpenPartialHomeomorph.to_isOpenEmbedding", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsOpenEmbedding.toOpenPartialHomeomorph", "kind": "definition", "module": "Mathlib.Topology.OpenPartialHomeomorph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsOpenEmbedding.toOpenPartialHomeomorph_left_inv", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Topology.IsOpenEmbedding.toOpenPartialHomeomorph_right_inv", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Basic", "is_tactic_proof": true, "tactics": ["rw", "rwa"], "tactic_count": 2}
{"name": "TopologicalSpace.Opens.openPartialHomeomorphSubtypeCoe", "kind": "definition", "module": "Mathlib.Topology.OpenPartialHomeomorph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.openPartialHomeomorphSubtypeCoe_coe", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.openPartialHomeomorphSubtypeCoe_source", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.openPartialHomeomorphSubtypeCoe_target", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Basic", "is_tactic_proof": true, "tactics": ["simp", "rfl"], "tactic_count": 2}
{"name": "OpenPartialHomeomorph.trans'", "kind": "definition", "module": "Mathlib.Topology.OpenPartialHomeomorph.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.trans", "kind": "definition", "module": "Mathlib.Topology.OpenPartialHomeomorph.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.trans_toPartialEquiv", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.coe_trans", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.coe_trans_symm", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.trans_apply", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.trans_symm_eq_symm_trans_symm", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.trans_source", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.trans_source'", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.trans_source''", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.image_trans_source", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.trans_target", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.trans_target'", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.trans_target''", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.inv_image_trans_target", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.trans_assoc", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.trans_refl", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.refl_trans", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.trans_ofSet", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.trans_of_set'", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Composition", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "OpenPartialHomeomorph.ofSet_trans", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.ofSet_trans'", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Composition", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "OpenPartialHomeomorph.ofSet_trans_ofSet", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Composition", "is_tactic_proof": true, "tactics": ["rw", "ext"], "tactic_count": 2}
{"name": "OpenPartialHomeomorph.restr_trans", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.EqOnSource.trans'", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.self_trans_symm", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.symm_trans_self", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.restr_symm_trans", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Composition", "is_tactic_proof": true, "tactics": ["refine", "simp", "rw", "rw", "congr", "rw", "refine", "intro", "rw", "simp_rw", "intro", "simp"], "tactic_count": 12}
{"name": "OpenPartialHomeomorph.symm_trans_restr", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Composition", "is_tactic_proof": false, "tactics": ["have", "rw", "exact", "refine", "simp", "rw", "congr", "nth_rw", "rw", "simp"], "tactic_count": 10}
{"name": "Homeomorph.trans_toOpenPartialHomeomorph", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.transOpenPartialHomeomorph", "kind": "definition", "module": "Mathlib.Topology.OpenPartialHomeomorph.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.transOpenPartialHomeomorph_eq_trans", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Composition", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.transOpenPartialHomeomorph_trans", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Composition", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Homeomorph.trans_transOpenPartialHomeomorph", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Composition", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "OpenPartialHomeomorph.const", "kind": "definition", "module": "Mathlib.Topology.OpenPartialHomeomorph.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.const_apply", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.const_source", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.const_target", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.prod", "kind": "definition", "module": "Mathlib.Topology.OpenPartialHomeomorph.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.prod_symm", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.refl_prod_refl", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.prod_trans", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.prod_eq_prod_of_nonempty", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Constructions", "is_tactic_proof": true, "tactics": ["obtain", "haveI", "haveI", "haveI", "haveI", "simp_rw"], "tactic_count": 6}
{"name": "OpenPartialHomeomorph.prod_eq_prod_of_nonempty'", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Constructions", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "OpenPartialHomeomorph.prod_symm_trans_prod", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Constructions", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "OpenPartialHomeomorph.pi", "kind": "definition", "module": "Mathlib.Topology.OpenPartialHomeomorph.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.piecewise", "kind": "definition", "module": "Mathlib.Topology.OpenPartialHomeomorph.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.symm_piecewise", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.disjointUnion", "kind": "definition", "module": "Mathlib.Topology.OpenPartialHomeomorph.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.transHomeomorph", "kind": "definition", "module": "Mathlib.Topology.OpenPartialHomeomorph.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.transHomeomorph_eq_trans", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.transHomeomorph_transHomeomorph", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Constructions", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "OpenPartialHomeomorph.trans_transHomeomorph", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Constructions", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "OpenPartialHomeomorph.subtypeRestr", "kind": "definition", "module": "Mathlib.Topology.OpenPartialHomeomorph.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.subtypeRestr_def", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.subtypeRestr_coe", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.subtypeRestr_source", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Constructions", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "OpenPartialHomeomorph.map_subtype_source", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Constructions", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "OpenPartialHomeomorph.subtypeRestr_target_subset", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Constructions", "is_tactic_proof": true, "tactics": ["rw", "rintro", "use", "simpa"], "tactic_count": 4}
{"name": "OpenPartialHomeomorph.subtypeRestr_symm_trans_subtypeRestr", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Constructions", "is_tactic_proof": true, "tactics": ["simp", "have", "rw", "refine", "have", "have", "rw", "refine", "refine", "simp"], "tactic_count": 10}
{"name": "OpenPartialHomeomorph.subtypeRestr_symm_apply", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Constructions", "is_tactic_proof": true, "tactics": ["rw", "change", "rw", "have", "rwa"], "tactic_count": 5}
{"name": "OpenPartialHomeomorph.subtypeRestr_symm_eqOn", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.subtypeRestr_symm_eqOn_of_le", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Constructions", "is_tactic_proof": true, "tactics": ["set", "intro", "dsimp", "have", "rw", "exact", "refine", "rw", "apply", "rw", "exact", "rw", "change", "rw"], "tactic_count": 14}
{"name": "OpenPartialHomeomorph.lift_openEmbedding", "kind": "definition", "module": "Mathlib.Topology.OpenPartialHomeomorph.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.lift_openEmbedding_toFun", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.lift_openEmbedding_apply", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Constructions", "is_tactic_proof": true, "tactics": ["simp_rw", "apply"], "tactic_count": 2}
{"name": "OpenPartialHomeomorph.lift_openEmbedding_source", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.lift_openEmbedding_target", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.lift_openEmbedding_symm", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.lift_openEmbedding_symm_source", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.lift_openEmbedding_symm_target", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Constructions", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "OpenPartialHomeomorph.lift_openEmbedding_trans_apply", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Constructions", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "OpenPartialHomeomorph.lift_openEmbedding_trans", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Constructions", "is_tactic_proof": true, "tactics": ["ext", "exact", "simp", "simp_rw", "e.lift_openEmbedding_symm,", "refine", "rw", "exact"], "tactic_count": 8}
{"name": "OpenPartialHomeomorph.eventually_left_inverse", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Continuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.eventually_left_inverse'", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Continuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.eventually_right_inverse", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Continuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.eventually_right_inverse'", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Continuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.eventually_ne_nhdsWithin", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Continuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.nhdsWithin_source_inter", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Continuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.nhdsWithin_target_inter", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Continuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.continuousAt", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Continuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.continuousAt_symm", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Continuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.tendsto_symm", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Continuity", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "OpenPartialHomeomorph.map_nhds_eq", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Continuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.symm_map_nhds_eq", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Continuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.image_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Continuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.map_nhdsWithin_eq", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Continuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.map_nhdsWithin_preimage_eq", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Continuity", "is_tactic_proof": true, "tactics": ["rw", "e.nhdsWithin_target_inter"], "tactic_count": 2}
{"name": "OpenPartialHomeomorph.eventually_nhds", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Continuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.eventually_nhds'", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Continuity", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw"], "tactic_count": 3}
{"name": "OpenPartialHomeomorph.eventually_nhdsWithin", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Continuity", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "OpenPartialHomeomorph.eventually_nhdsWithin'", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Continuity", "is_tactic_proof": true, "tactics": ["rw", "refine", "eventually_congr", "rw"], "tactic_count": 4}
{"name": "OpenPartialHomeomorph.preimage_eventuallyEq_target_inter_preimage_inter", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Continuity", "is_tactic_proof": true, "tactics": ["rw", "filter_upwards", "intro", "simp_rw", "iff_true_intro"], "tactic_count": 5}
{"name": "OpenPartialHomeomorph.continuousWithinAt_iff_continuousWithinAt_comp_right", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Continuity", "is_tactic_proof": true, "tactics": ["simp_rw", "e.right_inv"], "tactic_count": 2}
{"name": "OpenPartialHomeomorph.continuousAt_iff_continuousAt_comp_right", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Continuity", "is_tactic_proof": true, "tactics": ["rw", "continuousWithinAt_univ]"], "tactic_count": 2}
{"name": "OpenPartialHomeomorph.continuousOn_iff_continuousOn_comp_right", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Continuity", "is_tactic_proof": true, "tactics": ["simp", "refine", "rw", "inter_comm,", "exact"], "tactic_count": 5}
{"name": "OpenPartialHomeomorph.continuousWithinAt_iff_continuousWithinAt_comp_left", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Continuity", "is_tactic_proof": true, "tactics": ["refine", "rw", "have", "haveI", "exact"], "tactic_count": 5}
{"name": "OpenPartialHomeomorph.continuousAt_iff_continuousAt_comp_left", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Continuity", "is_tactic_proof": true, "tactics": ["have", "have", "rw"], "tactic_count": 3}
{"name": "OpenPartialHomeomorph.continuousOn_iff_continuousOn_comp_left", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Continuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.continuous_iff_continuous_comp_left", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Continuity", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "OpenPartialHomeomorph.toFun'", "kind": "definition", "module": "Mathlib.Topology.OpenPartialHomeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.instCoeFunForall", "kind": "instance", "module": "Mathlib.Topology.OpenPartialHomeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.symm", "kind": "definition", "module": "Mathlib.Topology.OpenPartialHomeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.Simps.apply", "kind": "definition", "module": "Mathlib.Topology.OpenPartialHomeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.Simps.symm_apply", "kind": "definition", "module": "Mathlib.Topology.OpenPartialHomeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.continuousOn", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.continuousOn_symm", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.mk_coe", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.mk_coe_symm", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.toPartialEquiv_injective", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.toFun_eq_coe", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.invFun_eq_coe", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.coe_coe", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.coe_coe_symm", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.map_source", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.map_source''", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.map_target", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.left_inv", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.right_inv", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.eq_symm_apply", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.mapsTo", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.symm_mapsTo", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.leftInvOn", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.rightInvOn", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.invOn", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.injOn", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.bijOn", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.surjOn", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.toOpenPartialHomeomorphOfImageEq", "kind": "definition", "module": "Mathlib.Topology.OpenPartialHomeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.toOpenPartialHomeomorph", "kind": "definition", "module": "Mathlib.Topology.OpenPartialHomeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.replaceEquiv", "kind": "definition", "module": "Mathlib.Topology.OpenPartialHomeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.replaceEquiv_eq_self", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Defs", "is_tactic_proof": true, "tactics": ["cases", "subst", "rfl"], "tactic_count": 3}
{"name": "OpenPartialHomeomorph.ext", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.symm_toPartialEquiv", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.symm_source", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.symm_target", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.symm_symm", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.symm_bijective", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.IsImage", "kind": "definition", "module": "Mathlib.Topology.OpenPartialHomeomorph.IsImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.IsImage.toPartialEquiv", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.IsImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.IsImage.apply_mem_iff", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.IsImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.IsImage.symm", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.IsImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.IsImage.symm_apply_mem_iff", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.IsImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.IsImage.symm_iff", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.IsImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.IsImage.mapsTo", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.IsImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.IsImage.symm_mapsTo", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.IsImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.IsImage.image_eq", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.IsImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.IsImage.symm_image_eq", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.IsImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.IsImage.iff_preimage_eq", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.IsImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.IsImage.iff_symm_preimage_eq", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.IsImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.IsImage.iff_symm_preimage_eq'", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.IsImage", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "OpenPartialHomeomorph.IsImage.iff_preimage_eq'", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.IsImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.IsImage.of_image_eq", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.IsImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.IsImage.of_symm_image_eq", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.IsImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.IsImage.compl", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.IsImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.IsImage.inter", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.IsImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.IsImage.union", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.IsImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.IsImage.diff", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.IsImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.IsImage.leftInvOn_piecewise", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.IsImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.IsImage.inter_eq_of_inter_eq_of_eqOn", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.IsImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.IsImage.symm_eqOn_of_inter_eq_of_eqOn", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.IsImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.IsImage.map_nhdsWithin_eq", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.IsImage", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "OpenPartialHomeomorph.IsImage.closure", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.IsImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.IsImage.interior", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.IsImage", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "OpenPartialHomeomorph.IsImage.frontier", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.IsImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.IsImage.isOpen_iff", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.IsImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.IsImage.restr", "kind": "definition", "module": "Mathlib.Topology.OpenPartialHomeomorph.IsImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.isImage_source_target", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.IsImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.isImage_source_target_of_disjoint", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.IsImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.preimage_interior", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.IsImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.preimage_closure", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.IsImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.preimage_frontier", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.IsImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.restrOpen", "kind": "definition", "module": "Mathlib.Topology.OpenPartialHomeomorph.IsImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.restrOpen_toPartialEquiv", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.IsImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.restrOpen_source", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.IsImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.coe_restrOpen", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.IsImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.coe_restrOpen_symm", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.IsImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.restr", "kind": "definition", "module": "Mathlib.Topology.OpenPartialHomeomorph.IsImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.restr_toPartialEquiv", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.IsImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.restr_source'", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.IsImage", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "OpenPartialHomeomorph.restr_toPartialEquiv'", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.IsImage", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "OpenPartialHomeomorph.restr_eq_of_source_subset", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.IsImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.restr_univ", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.IsImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.restr_source_inter", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.IsImage", "is_tactic_proof": true, "tactics": ["refine", "simp"], "tactic_count": 2}
{"name": "OpenPartialHomeomorph.ofSet", "kind": "definition", "module": "Mathlib.Topology.OpenPartialHomeomorph.IsImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.ofSet_toPartialEquiv", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.IsImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.ofSet_symm", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.IsImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.ofSet_univ_eq_refl", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.IsImage", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "OpenPartialHomeomorph.EqOnSource", "kind": "definition", "module": "Mathlib.Topology.OpenPartialHomeomorph.IsImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.eqOnSource_iff", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.IsImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.eqOnSourceSetoid", "kind": "instance", "module": "Mathlib.Topology.OpenPartialHomeomorph.IsImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.eqOnSource_refl", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.IsImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.EqOnSource.symm'", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.IsImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.EqOnSource.source_eq", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.IsImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.EqOnSource.target_eq", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.IsImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.EqOnSource.eqOn", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.IsImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.EqOnSource.symm_eqOn_target", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.IsImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.EqOnSource.restr", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.IsImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.Set.EqOn.restr_eqOn_source", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.IsImage", "is_tactic_proof": true, "tactics": ["constructor", "rw", "rw", "exact", "rw", "refine"], "tactic_count": 6}
{"name": "OpenPartialHomeomorph.eq_of_eqOnSource_univ", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.IsImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OpenPartialHomeomorph.restr_eqOnSource_restr", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.IsImage", "is_tactic_proof": true, "tactics": ["constructor", "simpa", "simp"], "tactic_count": 3}
{"name": "OpenPartialHomeomorph.restr_inter_source", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.IsImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.refl_toOpenPartialHomeomorph", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.IsImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.symm_toOpenPartialHomeomorph", "kind": "theorem", "module": "Mathlib.Topology.OpenPartialHomeomorph.IsImage", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.GenerateOpen", "kind": "inductive", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.generateFrom", "kind": "definition", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.isOpen_generateFrom_of_mem", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.nhds_generateFrom", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": true, "tactics": ["letI", "rw", "refine", "rintro", "induction", "basic", "univ", "inter", "sUnion", "let", "exact"], "tactic_count": 11}
{"name": "TopologicalSpace.tendsto_nhds_generateFrom_iff", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "TopologicalSpace.mkOfNhds", "kind": "definition", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.nhds_mkOfNhds_of_hasBasis", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": true, "tactics": ["let", "apply", "intro", "replace", "refine", "rcases", "exact", "exact"], "tactic_count": 8}
{"name": "TopologicalSpace.nhds_mkOfNhds", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.nhds_mkOfNhds_single", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": true, "tactics": ["refine", "rcases", "filter_upwards", "rcases", "exact", "rwa", "simpa"], "tactic_count": 7}
{"name": "TopologicalSpace.nhds_mkOfNhds_filterBasis", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.instPartialOrder", "kind": "instance", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.le_def", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.le_generateFrom_iff_subset_isOpen", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.mkOfClosure", "kind": "definition", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.mkOfClosure_sets", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.gc_generateFrom", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.gciGenerateFrom", "kind": "definition", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.instCompleteLattice", "kind": "instance", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.generateFrom_anti", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.generateFrom_setOf_isOpen", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.leftInverse_generateFrom", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.generateFrom_surjective", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.setOf_isOpen_injective", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.mono", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.mono", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "closure.mono", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpen_implies_isOpen_iff", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIndiscreteTopology", "kind": "instance", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.indiscrete_or_nontrivial", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.not_indiscrete_iff", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.not_nontrivial_iff", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IndiscreteTopology.isOpen_iff", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": true, "tactics": ["cases", "refine", "induction", "basic", "univ", "inter", "sUnion", "rintro", "exacts"], "tactic_count": 9}
{"name": "TopologicalSpace.isOpen_top_iff", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "discreteTopology_bot", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpen_discrete", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosed_discrete", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "closure_discrete", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dense_discrete", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "denseRange_discrete", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "continuous_of_discreteTopology", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_discrete_rng", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhds_discrete", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_nhds_discrete", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "le_of_nhds_le_nhds", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_bot_of_singletons_open", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "discreteTopology_iff_forall_isOpen", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "forall_open_iff_discrete", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "discreteTopology_iff_forall_isClosed", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "discreteTopology_iff_isOpen_singleton", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "singletons_open_iff_discrete", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteTopology.of_finite_of_isClosed_singleton", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "discreteTopology_iff_singleton_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "discreteTopology_iff_nhds", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": true, "tactics": ["simp", "apply", "simp"], "tactic_count": 3}
{"name": "discreteTopology_iff_nhds_ne", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DiscreteTopology.of_continuous_injective", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpen_induced_iff", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosed_induced_iff", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": true, "tactics": ["letI", "simp", "exact"], "tactic_count": 3}
{"name": "isOpen_coinduced", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosed_coinduced", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "preimage_nhds_coinduced", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": true, "tactics": ["letI", "rcases", "exact"], "tactic_count": 3}
{"name": "Continuous.coinduced_le", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "coinduced_le_iff_le_induced", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.le_induced", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "gc_coinduced_induced", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "induced_mono", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "coinduced_mono", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "induced_top", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "induced_inf", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "induced_iInf", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "induced_sInf", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "coinduced_bot", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "coinduced_sup", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "coinduced_iSup", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "coinduced_sSup", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "induced_id", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "induced_compose", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "induced_const", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "coinduced_id", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "coinduced_compose", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equiv.induced_symm", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": true, "tactics": ["ext", "rw", "simp"], "tactic_count": 3}
{"name": "Equiv.coinduced_symm", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inhabitedTopologicalSpace", "kind": "instance", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsingleton.uniqueTopologicalSpace", "kind": "instance", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subsingleton.discreteTopology", "kind": "instance", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIndiscreteTopologyOfSubsingleton", "kind": "instance", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instTopologicalSpaceEmpty", "kind": "instance", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDiscreteTopologyEmpty", "kind": "instance", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIndiscreteTopologyEmpty", "kind": "instance", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instTopologicalSpacePEmpty", "kind": "instance", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDiscreteTopologyPEmpty", "kind": "instance", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIndiscreteTopologyPEmpty", "kind": "instance", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instTopologicalSpacePUnit", "kind": "instance", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDiscreteTopologyPUnit", "kind": "instance", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIndiscreteTopologyPUnit", "kind": "instance", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instTopologicalSpaceBool", "kind": "instance", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDiscreteTopologyBool", "kind": "instance", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instTopologicalSpaceNat", "kind": "instance", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDiscreteTopologyNat", "kind": "instance", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instTopologicalSpaceInt", "kind": "instance", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDiscreteTopologyInt", "kind": "instance", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instTopologicalSpaceFin", "kind": "instance", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instDiscreteTopologyFin", "kind": "instance", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Nat.cast_continuous", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Int.cast_continuous", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sierpinskiSpace", "kind": "instance", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_empty_function", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_generateFrom", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "induced_generateFrom_eq", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_induced_generateFrom", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": true, "tactics": ["rw", "apply", "simp", "exact"], "tactic_count": 4}
{"name": "generateFrom_insert_of_generateOpen", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": true, "tactics": ["refine", "rintro", "exact", "exact"], "tactic_count": 4}
{"name": "generateFrom_insert_univ", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "generateFrom_insert_empty", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "nhdsAdjoint", "kind": "definition", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "gc_nhds", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhds_mono", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_iff_nhds", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpen_singleton_nhdsAdjoint", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhds_nhdsAdjoint_same", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": true, "tactics": ["let", "apply", "rintro", "exact", "exact"], "tactic_count": 5}
{"name": "nhds_nhdsAdjoint_of_ne", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhds_nhdsAdjoint", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_nhdsAdjoint_iff'", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "le_nhdsAdjoint_iff", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "nhds_iInf", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhds_sInf", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhds_inf", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhds_top", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpen_sup", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IndiscreteTopology.nhds_eq", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": true, "tactics": ["cases", "exact"], "tactic_count": 2}
{"name": "Inseparable.all", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IndiscreteTopology.of_forall_inseparable", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.indiscrete_iff_forall_inseparable", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.nontrivial_iff_exists_not_inseparable", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "inseparable_top", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.eq_top_iff_forall_inseparable", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "TopologicalSpace.ne_top_iff_exists_not_inseparable", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "continuous_iff_coinduced_le", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_iff_le_induced", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_generateFrom_iff", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "continuous_induced_dom", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_induced_rng", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "continuous_coinduced_rng", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_coinduced_dom", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "continuous_le_dom", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "continuous_le_rng", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "continuous_sup_dom", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "continuous_sup_rng_left", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_sup_rng_right", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_sSup_dom", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "continuous_sSup_rng", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_iSup_dom", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "continuous_iSup_rng", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_inf_rng", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "continuous_inf_dom_left", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_inf_dom_right", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_sInf_dom", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_sInf_rng", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "continuous_iInf_dom", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_iInf_rng", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "continuous_bot", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_top", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_id_iff_le", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_id_of_le", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_nhds_induced", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": true, "tactics": ["letI", "simp_rw", "constructor", "rintro", "exact", "rintro", "exact"], "tactic_count": 7}
{"name": "nhds_induced", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "induced_iff_nhds_eq", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "map_nhds_induced_of_surjective", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "continuous_nhdsAdjoint_dom", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "coinduced_nhdsAdjoint", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpen_induced_eq", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpen_induced", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosed_induced", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "map_nhds_induced_eq", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "map_nhds_induced_of_mem", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "closure_induced", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "isClosed_induced_iff'", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "isOpen_singleton_true", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhds_true", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhds_false", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_nhds_true", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "tendsto_nhds_Prop", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": true, "tactics": ["by_cases"], "tactic_count": 1}
{"name": "continuous_Prop", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "isOpen_iff_continuous_mem", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "generateFrom_union", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "setOf_isOpen_sup", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "generateFrom_iUnion", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "setOf_isOpen_iSup", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "generateFrom_sUnion", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "setOf_isOpen_sSup", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "generateFrom_union_isOpen", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "generateFrom_iUnion_isOpen", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "generateFrom_inter", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "generateFrom_iInter", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "generateFrom_iInter_of_generateFrom_eq_self", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpen_iSup_iff", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpen_sSup_iff", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "isClosed_iSup_iff", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "isClosed_sSup_iff", "kind": "theorem", "module": "Mathlib.Topology.Order", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "comap_coe_nhdsLT_eq_atTop_iff", "kind": "theorem", "module": "Mathlib.Topology.Order.AtTopBotIxx", "is_tactic_proof": true, "tactics": ["rcases", "simp", "have", "simp", "by_cases", "simp", "constructor", "intro", "have", "rw", "rcases", "exact", "intro", "refine", "intro", "rcases", "use", "simp_all", "rintro", "use", "simp_all", "suffices", "contrapose", "simp_all", "intro", "rcases", "rcases", "apply", "calc", "a"], "tactic_count": 30}
{"name": "comap_coe_nhdsGT_eq_atBot_iff", "kind": "theorem", "module": "Mathlib.Topology.Order.AtTopBotIxx", "is_tactic_proof": false, "tactics": ["refine", "comap_coe_nhdsLT_eq_atTop_iff", "rw", "rfl"], "tactic_count": 4}
{"name": "Preorder.topology", "kind": "definition", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instSecondCountableTopologyOfOrderTopologyOfCountable", "kind": "instance", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": true, "tactics": ["refine", "let", "let", "exact", "simp"], "tactic_count": 5}
{"name": "instOrderTopologyOrderDual", "kind": "instance", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderTopology.continuous_iff", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "aesop"], "tactic_count": 2}
{"name": "isOpen_iff_generate_intervals", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "isOpen_lt'", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpen_Ioi'", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpen_gt'", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpen_Iio'", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lt_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "gt_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ge_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhds_eq_order", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "iInf_comm"], "tactic_count": 3}
{"name": "tendsto_order", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "tendstoIccClassNhds", "kind": "instance", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": true, "tactics": ["simp", "refine", "refine", "exacts"], "tactic_count": 4}
{"name": "tendstoIcoClassNhds", "kind": "instance", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendstoIocClassNhds", "kind": "instance", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendstoIooClassNhds", "kind": "instance", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_countable_generateFrom_Ioi_Iio", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": true, "tactics": ["rcases", "exact", "obtain", "exists_countable_of_generateFrom", "have", "choose", "refine", "apply", "apply", "simp", "grind", "rw", "apply", "grind"], "tactic_count": 14}
{"name": "isTopologicalBasis_biInter_Ioi_Iio_of_generateFrom", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": true, "tactics": ["refine", "rintro", "apply", "apply", "rw", "exact", "apply", "rw", "exact", "simp", "intro", "let", "let", "have", "have", "ext", "grind", "have", "have", "have", "choose", "have", "choose", "refine", "finite_range", "rw", "simp"], "tactic_count": 27}
{"name": "tendsto_of_tendsto_of_tendsto_of_le_of_le'", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_of_tendsto_of_tendsto_of_le_of_le", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhds_order_unbounded", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "tendsto_order_unbounded", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "tendstoIxxNhdsWithin", "kind": "instance", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendstoIccClassNhdsPi", "kind": "instance", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": true, "tactics": ["constructor", "conv", "simp", "intro", "have", "refine", "filter_upwards"], "tactic_count": 7}
{"name": "induced_topology_le_preorder", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": true, "tactics": ["let", "refine", "simp", "refine", "exacts"], "tactic_count": 5}
{"name": "induced_topology_eq_preorder", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": true, "tactics": ["let", "refine", "refine", "simp", "refine", "by_cases", "rcases", "rcases", "exact", "exact", "by_cases", "rcases", "rcases", "exact", "exact"], "tactic_count": 15}
{"name": "induced_orderTopology'", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "induced_orderTopology", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMono.induced_topology_eq_preorder", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": true, "tactics": ["refine", "rcases", "exact", "rcases", "exact"], "tactic_count": 5}
{"name": "StrictMono.isEmbedding_of_ordConnected", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderEmbedding.isEmbedding_of_ordConnected", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "orderTopology_of_ordConnected", "kind": "instance", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsGE_eq_iInf_inf_principal", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "exact"], "tactic_count": 3}
{"name": "nhdsLE_eq_iInf_inf_principal", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsGE_eq_iInf_principal", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "nhdsLE_eq_iInf_principal", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "nhdsGE_basis_of_exists_gt", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsLE_basis_of_exists_lt", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": true, "tactics": ["convert", "exact"], "tactic_count": 2}
{"name": "nhdsGE_basis", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsLE_basis", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhds_top_order", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "nhds_bot_order", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "nhds_top_basis", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "nhds_bot_basis", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhds_top_basis_Ici", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhds_bot_basis_Iic", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_nhds_top_mono", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": true, "tactics": ["simp", "intro", "filter_upwards"], "tactic_count": 3}
{"name": "tendsto_nhds_bot_mono", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_nhds_top_mono'", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_nhds_bot_mono'", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "order_separated", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderTopology.to_orderClosedTopology", "kind": "instance", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_Ioc_subset_of_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_Ioc_subset_of_mem_nhds'", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_Ico_subset_of_mem_nhds'", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": true, "tactics": ["simpa", "exists_Ioc_subset_of_mem_nhds"], "tactic_count": 2}
{"name": "exists_Ico_subset_of_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_Icc_mem_subset_of_mem_nhdsGE", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": true, "tactics": ["rcases", "use", "simpa", "rcases", "rcases", "have", "exact", "refine", "exact"], "tactic_count": 9}
{"name": "exists_Icc_mem_subset_of_mem_nhdsLE", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": true, "tactics": ["simpa", "exists_Icc_mem_subset_of_mem_nhdsGE"], "tactic_count": 2}
{"name": "exists_Icc_mem_subset_of_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "refine", "rw", "exact"], "tactic_count": 5}
{"name": "IsOpen.exists_Ioo_subset", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "rcases", "obtain", "exact", "exact", "obtain", "exact"], "tactic_count": 8}
{"name": "dense_of_exists_between", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": true, "tactics": ["refine", "obtain", "obtain", "exact"], "tactic_count": 4}
{"name": "IsUpperSet.isClosed", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": true, "tactics": ["obtain", "exacts"], "tactic_count": 2}
{"name": "IsLowerSet.isClosed", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLowerSet.isOpen", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsUpperSet.isOpen", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dense_iff_exists_between", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_nhds_iff_exists_Ioo_subset'", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rcases", "rcases", "exact", "rintro", "apply"], "tactic_count": 7}
{"name": "mem_nhds_iff_exists_Ioo_subset", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhds_basis_Ioo'", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhds_basis_Ioo", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Eventually.exists_Ioo_subset", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dense.topology_eq_generateFrom", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": true, "tactics": ["refine", "refine", "simp", "exact", "rintro", "rw", "let", "exact", "rw", "let", "exact"], "tactic_count": 11}
{"name": "PredOrder.hasBasis_nhds_Ioc_of_exists_gt", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PredOrder.hasBasis_nhds_Ioc", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SuccOrder.hasBasis_nhds_Ioc_of_exists_lt", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SuccOrder.hasBasis_nhds_Ioc", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SecondCountableTopology.of_separableSpace_orderTopology", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": true, "tactics": ["rcases", "refine", "exact"], "tactic_count": 3}
{"name": "countable_setOf_covBy_right", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": true, "tactics": ["nontriviality", "let", "have", "choose", "have", "suffices", "have", "rcases", "exact", "refine", "refine", "exact", "intro", "suffices", "simp", "let", "have", "intro", "apply", "simpa", "choose", "have", "rcases", "refine", "refine", "by_contra", "exact", "refine", "refine", "by_contra", "exact", "refine", "suffices", "rw", "exact", "exact"], "tactic_count": 36}
{"name": "countable_setOf_covBy_left", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": true, "tactics": ["convert", "exact"], "tactic_count": 2}
{"name": "countable_of_isolated_left'", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.PairwiseDisjoint.countable_of_Ioo", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "countable_image_lt_image_Ioi_within", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": true, "tactics": ["which", "family", "nontriviality", "have", "let", "have", "hx.2", "choose", "have", "apply", "intro", "calc", "f", "have", "have", "rintro", "wlog", "exact", "have", "apply", "rintro", "simp", "exact", "apply", "rintro", "simpa", "exact"], "tactic_count": 27}
{"name": "countable_image_lt_image_Ioi", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "countable_image_gt_image_Ioi_within", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "countable_image_gt_image_Ioi", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "countable_image_lt_image_Iio_within", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "countable_image_lt_image_Iio", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "countable_image_gt_image_Iio_within", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "countable_image_gt_image_Iio", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsCountablyGenerated_atTop", "kind": "instance", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "have", "refine", "simp", "obtain", "exact", "rw", "exact", "rw", "exact"], "tactic_count": 11}
{"name": "instIsCountablyGenerated_atBot", "kind": "instance", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pi_Iic_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pi_Iic_mem_nhds'", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pi_Ici_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pi_Ici_mem_nhds'", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pi_Icc_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pi_Icc_mem_nhds'", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pi_Iio_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pi_Iio_mem_nhds'", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pi_Ioi_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pi_Ioi_mem_nhds'", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pi_Ioc_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "pi_Ioc_mem_nhds'", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pi_Ico_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "pi_Ico_mem_nhds'", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pi_Ioo_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "pi_Ioo_mem_nhds'", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LeftOrdContinuous.continuousWithinAt_Iic", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "rintro", "obtain", "exact", "exact"], "tactic_count": 6}
{"name": "RightOrdContinuous.continuousWithinAt_Ici", "kind": "theorem", "module": "Mathlib.Topology.Order.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "orderBornology", "kind": "definition", "module": "Mathlib.Topology.Order.Bornology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "orderBornology_isBounded", "kind": "theorem", "module": "Mathlib.Topology.Order.Bornology", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "isOrderBornology_iff_eq_orderBornology", "kind": "theorem", "module": "Mathlib.Topology.Order.Bornology", "is_tactic_proof": true, "tactics": ["refine", "ext", "exact"], "tactic_count": 3}
{"name": "isBounded_iff_bddBelow_bddAbove", "kind": "theorem", "module": "Mathlib.Topology.Order.Bornology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.IsBounded.bddBelow", "kind": "theorem", "module": "Mathlib.Topology.Order.Bornology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.IsBounded.bddAbove", "kind": "theorem", "module": "Mathlib.Topology.Order.Bornology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddBelow.isBounded", "kind": "theorem", "module": "Mathlib.Topology.Order.Bornology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddAbove.isBounded", "kind": "theorem", "module": "Mathlib.Topology.Order.Bornology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddBelow.isBounded_inter", "kind": "theorem", "module": "Mathlib.Topology.Order.Bornology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddAbove.isBounded_inter", "kind": "theorem", "module": "Mathlib.Topology.Order.Bornology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instIsOrderBornology", "kind": "instance", "module": "Mathlib.Topology.Order.Bornology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instIsOrderBornology", "kind": "instance", "module": "Mathlib.Topology.Order.Bornology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instIsOrderBornology", "kind": "instance", "module": "Mathlib.Topology.Order.Bornology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.IsBounded.subset_Icc_sInf_sSup", "kind": "theorem", "module": "Mathlib.Topology.Order.Bornology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlexDisc.instCoeSortType", "kind": "instance", "module": "Mathlib.Topology.Order.Category.AlexDisc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlexDisc.category", "kind": "instance", "module": "Mathlib.Topology.Order.Category.AlexDisc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlexDisc.concreteCategory", "kind": "instance", "module": "Mathlib.Topology.Order.Category.AlexDisc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlexDisc.instHasForgetToTop", "kind": "instance", "module": "Mathlib.Topology.Order.Category.AlexDisc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlexDisc.forgetToTop_full", "kind": "instance", "module": "Mathlib.Topology.Order.Category.AlexDisc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlexDisc.forgetToTop_faithful", "kind": "instance", "module": "Mathlib.Topology.Order.Category.AlexDisc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlexDisc.of", "kind": "abbrev", "module": "Mathlib.Topology.Order.Category.AlexDisc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlexDisc.coe_of", "kind": "theorem", "module": "Mathlib.Topology.Order.Category.AlexDisc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlexDisc.forgetToTop_of", "kind": "theorem", "module": "Mathlib.Topology.Order.Category.AlexDisc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlexDisc.coe_forgetToTop", "kind": "theorem", "module": "Mathlib.Topology.Order.Category.AlexDisc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AlexDisc.Iso.mk", "kind": "definition", "module": "Mathlib.Topology.Order.Category.AlexDisc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "alexDiscEquivPreord", "kind": "definition", "module": "Mathlib.Topology.Order.Category.AlexDisc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Locale.PT", "kind": "abbrev", "module": "Mathlib.Topology.Order.Category.FrameAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Locale.openOfElementHom", "kind": "definition", "module": "Mathlib.Topology.Order.Category.FrameAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Locale.PT.instTopologicalSpace", "kind": "instance", "module": "Mathlib.Topology.Order.Category.FrameAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Locale.PT.isOpen_iff", "kind": "theorem", "module": "Mathlib.Topology.Order.Category.FrameAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Locale.pt", "kind": "definition", "module": "Mathlib.Topology.Order.Category.FrameAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Locale.localePointOfSpacePoint", "kind": "definition", "module": "Mathlib.Topology.Order.Category.FrameAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Locale.counitAppCont", "kind": "definition", "module": "Mathlib.Topology.Order.Category.FrameAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Locale.adjunctionTopToLocalePT", "kind": "definition", "module": "Mathlib.Topology.Order.Category.FrameAdjunction", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompactIccSpace.mk'", "kind": "theorem", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompactIccSpace.mk''", "kind": "theorem", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCompactIccSpaceOrderDual", "kind": "instance", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConditionallyCompleteLinearOrder.toCompactIccSpace", "kind": "instance", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCompactIccSpaceForall", "kind": "instance", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.compact_Icc_space'", "kind": "instance", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCompactIccSpaceProd", "kind": "instance", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCompact_uIcc", "kind": "theorem", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "compactSpace_of_completeLinearOrder", "kind": "instance", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "compactSpace_Icc", "kind": "instance", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCompact_Ico_iff", "kind": "theorem", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCompact_Ioc_iff", "kind": "theorem", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCompact_Ioo_iff", "kind": "theorem", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.exists_isLeast", "kind": "theorem", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": true, "tactics": ["haveI", "suffices", "rw", "by_contra", "rw", "rcases", "hs.elim_directed_family_closed", "exact"], "tactic_count": 8}
{"name": "IsCompact.exists_isGreatest", "kind": "theorem", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.exists_isGLB", "kind": "theorem", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.exists_isLUB", "kind": "theorem", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cocompact_le_atBot_atTop", "kind": "theorem", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": true, "tactics": ["refine", "exact", "obtain", "obtain", "refine", "exact"], "tactic_count": 6}
{"name": "cocompact_le_atBot", "kind": "theorem", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": true, "tactics": ["refine", "exact", "obtain", "refine", "exact"], "tactic_count": 5}
{"name": "cocompact_le_atTop", "kind": "theorem", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "atBot_le_cocompact", "kind": "theorem", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": true, "tactics": ["refine", "obtain", "refine", "rewrite", "convert", "haveI", "obtain", "obtain", "exact", "hts"], "tactic_count": 10}
{"name": "atTop_le_cocompact", "kind": "theorem", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "atBot_atTop_le_cocompact", "kind": "theorem", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cocompact_eq_atBot_atTop", "kind": "theorem", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cocompact_eq_atBot", "kind": "theorem", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cocompact_eq_atTop", "kind": "theorem", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.exists_isMinOn", "kind": "theorem", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": true, "tactics": ["rcases", "refine", "rwa"], "tactic_count": 3}
{"name": "IsCompact.exists_forall_le'", "kind": "theorem", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": true, "tactics": ["rcases", "obtain", "exact", "obtain", "exact"], "tactic_count": 5}
{"name": "IsCompact.exists_isMaxOn", "kind": "theorem", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.exists_isMinOn'", "kind": "theorem", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": true, "tactics": ["rcases", "have", "obtain", "refine", "by_cases", "exacts"], "tactic_count": 6}
{"name": "ContinuousOn.exists_isMaxOn'", "kind": "theorem", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.exists_forall_le'", "kind": "theorem", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.exists_forall_ge'", "kind": "theorem", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.exists_forall_le", "kind": "theorem", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": true, "tactics": ["inhabit", "exact"], "tactic_count": 2}
{"name": "Continuous.exists_forall_ge", "kind": "theorem", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.exists_forall_le_of_hasCompactMulSupport", "kind": "theorem", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": true, "tactics": ["obtain", "rw", "exact"], "tactic_count": 3}
{"name": "Continuous.exists_forall_ge_of_hasCompactMulSupport", "kind": "theorem", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.bddBelow", "kind": "theorem", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": true, "tactics": ["rcases", "exact", "obtain", "exact"], "tactic_count": 4}
{"name": "IsCompact.bddAbove", "kind": "theorem", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.bddBelow_image", "kind": "theorem", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.bddAbove_image", "kind": "theorem", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.bddBelow_range_of_hasCompactMulSupport", "kind": "theorem", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.bddAbove_range_of_hasCompactMulSupport", "kind": "theorem", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.sSup_lt_iff_of_continuous", "kind": "theorem", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": true, "tactics": ["refine", "obtain", "refine", "rintro"], "tactic_count": 4}
{"name": "IsCompact.lt_sInf_iff_of_continuous", "kind": "theorem", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.sInf_mem", "kind": "theorem", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.sSup_mem", "kind": "theorem", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.isGLB_sInf", "kind": "theorem", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.isLUB_sSup", "kind": "theorem", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.isLeast_sInf", "kind": "theorem", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.isGreatest_sSup", "kind": "theorem", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.exists_sInf_image_eq_and_le", "kind": "theorem", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.exists_sSup_image_eq_and_ge", "kind": "theorem", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.exists_sInf_image_eq", "kind": "theorem", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.exists_sSup_image_eq", "kind": "theorem", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.exists_isMinOn_mem_subset", "kind": "theorem", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.exists_isMaxOn_mem_subset", "kind": "theorem", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.exists_isLocalMin_mem_open", "kind": "theorem", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.exists_isLocalMax_mem_open", "kind": "theorem", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_Icc_of_connected_compact", "kind": "theorem", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.continuous_sSup", "kind": "theorem", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": true, "tactics": ["rcases", "simp_rw", "exact", "rw", "intro", "obtain", "hK.exists_sSup_image_eq_and_ge", "rw", "have", "refine", "refine", "exact", "have", "rintro", "exact", "obtain", "refine", "rw", "exact"], "tactic_count": 19}
{"name": "IsCompact.continuous_sInf", "kind": "theorem", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.image_Icc", "kind": "theorem", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.image_uIcc_eq_Icc", "kind": "theorem", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.image_uIcc", "kind": "theorem", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": true, "tactics": ["refine", "refine", "exacts"], "tactic_count": 3}
{"name": "ContinuousOn.sInf_image_Icc_le", "kind": "theorem", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "ContinuousOn.le_sSup_image_Icc", "kind": "theorem", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "ContinuousOn.image_Icc_of_monotoneOn", "kind": "theorem", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": true, "tactics": ["rw", "congr", "exact", "exact"], "tactic_count": 4}
{"name": "ContinuousOn.image_Icc_of_antitoneOn", "kind": "theorem", "module": "Mathlib.Topology.Order.Compact", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "HasCountableSeparatingOn.range_Iio", "kind": "instance", "module": "Mathlib.Topology.Order.CountableSeparating", "is_tactic_proof": true, "tactics": ["constructor", "rcases", "set", "refine", "exact", "exact", "rintro", "by_contra", "wlog", "refine", "simpa", "cases", "inl", "specialize", "simp", "inr", "rcases", "simpa"], "tactic_count": 18}
{"name": "HasCountableSeparatingOn.range_Ioi", "kind": "instance", "module": "Mathlib.Topology.Order.CountableSeparating", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasCountableSeparatingOn.range_Iic", "kind": "instance", "module": "Mathlib.Topology.Order.CountableSeparating", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasCountableSeparatingOn.range_Ici", "kind": "instance", "module": "Mathlib.Topology.Order.CountableSeparating", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.of_forall_eventually_lt_iff", "kind": "theorem", "module": "Mathlib.Topology.Order.CountableSeparating", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.of_forall_eventually_le_iff", "kind": "theorem", "module": "Mathlib.Topology.Order.CountableSeparating", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.of_forall_eventually_gt_iff", "kind": "theorem", "module": "Mathlib.Topology.Order.CountableSeparating", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.of_forall_eventually_ge_iff", "kind": "theorem", "module": "Mathlib.Topology.Order.CountableSeparating", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "closure_Ioi'", "kind": "theorem", "module": "Mathlib.Topology.Order.DenselyOrdered", "is_tactic_proof": true, "tactics": ["apply", "exact", "rw", "exact"], "tactic_count": 4}
{"name": "closure_Ioi", "kind": "theorem", "module": "Mathlib.Topology.Order.DenselyOrdered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "closure_Iio'", "kind": "theorem", "module": "Mathlib.Topology.Order.DenselyOrdered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "closure_Iio", "kind": "theorem", "module": "Mathlib.Topology.Order.DenselyOrdered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "closure_Ioo", "kind": "theorem", "module": "Mathlib.Topology.Order.DenselyOrdered", "is_tactic_proof": true, "tactics": ["apply", "exact", "rcases", "rw", "have", "simp", "exact", "rw", "exact"], "tactic_count": 9}
{"name": "closure_uIoo", "kind": "theorem", "module": "Mathlib.Topology.Order.DenselyOrdered", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "closure_Ioc", "kind": "theorem", "module": "Mathlib.Topology.Order.DenselyOrdered", "is_tactic_proof": true, "tactics": ["apply", "exact", "apply", "rw"], "tactic_count": 4}
{"name": "closure_uIoc", "kind": "theorem", "module": "Mathlib.Topology.Order.DenselyOrdered", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "closure_Ico", "kind": "theorem", "module": "Mathlib.Topology.Order.DenselyOrdered", "is_tactic_proof": true, "tactics": ["apply", "exact", "apply", "rw"], "tactic_count": 4}
{"name": "interior_Ici'", "kind": "theorem", "module": "Mathlib.Topology.Order.DenselyOrdered", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "interior_Ici", "kind": "theorem", "module": "Mathlib.Topology.Order.DenselyOrdered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "interior_Iic'", "kind": "theorem", "module": "Mathlib.Topology.Order.DenselyOrdered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "interior_Iic", "kind": "theorem", "module": "Mathlib.Topology.Order.DenselyOrdered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "interior_Icc", "kind": "theorem", "module": "Mathlib.Topology.Order.DenselyOrdered", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Icc_mem_nhds_iff", "kind": "theorem", "module": "Mathlib.Topology.Order.DenselyOrdered", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "interior_Ico", "kind": "theorem", "module": "Mathlib.Topology.Order.DenselyOrdered", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ico_mem_nhds_iff", "kind": "theorem", "module": "Mathlib.Topology.Order.DenselyOrdered", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "interior_Ioc", "kind": "theorem", "module": "Mathlib.Topology.Order.DenselyOrdered", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ioc_mem_nhds_iff", "kind": "theorem", "module": "Mathlib.Topology.Order.DenselyOrdered", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "closure_interior_Icc", "kind": "theorem", "module": "Mathlib.Topology.Order.DenselyOrdered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ioc_subset_closure_interior", "kind": "theorem", "module": "Mathlib.Topology.Order.DenselyOrdered", "is_tactic_proof": true, "tactics": ["rcases", "simp", "calc"], "tactic_count": 3}
{"name": "Ico_subset_closure_interior", "kind": "theorem", "module": "Mathlib.Topology.Order.DenselyOrdered", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "frontier_Ici'", "kind": "theorem", "module": "Mathlib.Topology.Order.DenselyOrdered", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "frontier_Ici", "kind": "theorem", "module": "Mathlib.Topology.Order.DenselyOrdered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "frontier_Iic'", "kind": "theorem", "module": "Mathlib.Topology.Order.DenselyOrdered", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "frontier_Iic", "kind": "theorem", "module": "Mathlib.Topology.Order.DenselyOrdered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "frontier_Ioi'", "kind": "theorem", "module": "Mathlib.Topology.Order.DenselyOrdered", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "frontier_Ioi", "kind": "theorem", "module": "Mathlib.Topology.Order.DenselyOrdered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "frontier_Iio'", "kind": "theorem", "module": "Mathlib.Topology.Order.DenselyOrdered", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "frontier_Iio", "kind": "theorem", "module": "Mathlib.Topology.Order.DenselyOrdered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "frontier_Icc", "kind": "theorem", "module": "Mathlib.Topology.Order.DenselyOrdered", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "frontier_Ioo", "kind": "theorem", "module": "Mathlib.Topology.Order.DenselyOrdered", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "frontier_Ico", "kind": "theorem", "module": "Mathlib.Topology.Order.DenselyOrdered", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "frontier_Ioc", "kind": "theorem", "module": "Mathlib.Topology.Order.DenselyOrdered", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "nhdsWithin_Ioi_neBot'", "kind": "theorem", "module": "Mathlib.Topology.Order.DenselyOrdered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsWithin_Ioi_neBot", "kind": "theorem", "module": "Mathlib.Topology.Order.DenselyOrdered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsGT_neBot_of_exists_gt", "kind": "theorem", "module": "Mathlib.Topology.Order.DenselyOrdered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsGT_neBot", "kind": "instance", "module": "Mathlib.Topology.Order.DenselyOrdered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsWithin_Iio_neBot'", "kind": "theorem", "module": "Mathlib.Topology.Order.DenselyOrdered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsWithin_Iio_neBot", "kind": "theorem", "module": "Mathlib.Topology.Order.DenselyOrdered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsLT_neBot_of_exists_lt", "kind": "theorem", "module": "Mathlib.Topology.Order.DenselyOrdered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsLT_neBot", "kind": "instance", "module": "Mathlib.Topology.Order.DenselyOrdered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "right_nhdsWithin_Ico_neBot", "kind": "theorem", "module": "Mathlib.Topology.Order.DenselyOrdered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "left_nhdsWithin_Ioc_neBot", "kind": "theorem", "module": "Mathlib.Topology.Order.DenselyOrdered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "left_nhdsWithin_Ioo_neBot", "kind": "theorem", "module": "Mathlib.Topology.Order.DenselyOrdered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "right_nhdsWithin_Ioo_neBot", "kind": "theorem", "module": "Mathlib.Topology.Order.DenselyOrdered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instNeBotNhdsWithinComplSetSingletonOfNontrivial", "kind": "instance", "module": "Mathlib.Topology.Order.DenselyOrdered", "is_tactic_proof": true, "tactics": ["refine", "obtain", "obtain", "obtain", "rcases", "exact", "obtain", "exact"], "tactic_count": 8}
{"name": "DenselyOrdered.subsingleton_of_discreteTopology", "kind": "theorem", "module": "Mathlib.Topology.Order.DenselyOrdered", "is_tactic_proof": true, "tactics": ["suffices", "intro", "by_contra", "suffices", "simp_all", "rw", "grind"], "tactic_count": 7}
{"name": "Dense.exists_countable_dense_subset_no_bot_top", "kind": "theorem", "module": "Mathlib.Topology.Order.DenselyOrdered", "is_tactic_proof": true, "tactics": ["rcases", "refine", "exact", "exact", "exact", "simp", "simp"], "tactic_count": 7}
{"name": "exists_countable_dense_no_bot_top", "kind": "theorem", "module": "Mathlib.Topology.Order.DenselyOrdered", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "isClosed_Ico_iff", "kind": "theorem", "module": "Mathlib.Topology.Order.DenselyOrdered", "is_tactic_proof": true, "tactics": ["refine", "have", "rw", "exact"], "tactic_count": 4}
{"name": "isClosed_Ioc_iff", "kind": "theorem", "module": "Mathlib.Topology.Order.DenselyOrdered", "is_tactic_proof": true, "tactics": ["refine", "have", "rw", "exact"], "tactic_count": 4}
{"name": "isClosed_Ioo_iff", "kind": "theorem", "module": "Mathlib.Topology.Order.DenselyOrdered", "is_tactic_proof": true, "tactics": ["refine", "have", "rw", "exact"], "tactic_count": 4}
{"name": "continuousOn_Icc_extendFrom_Ioo", "kind": "theorem", "module": "Mathlib.Topology.Order.ExtendFrom", "is_tactic_proof": true, "tactics": ["apply", "rw", "intro", "rcases", "exact", "exact", "exact"], "tactic_count": 7}
{"name": "continuousOn_uIcc_extendFrom_uIoo", "kind": "theorem", "module": "Mathlib.Topology.Order.ExtendFrom", "is_tactic_proof": true, "tactics": ["obtain", "simp", "exact", "simp", "exact"], "tactic_count": 5}
{"name": "continuousOn_Ico_extendFrom_Ioo", "kind": "theorem", "module": "Mathlib.Topology.Order.ExtendFrom", "is_tactic_proof": true, "tactics": ["apply", "rw", "exact", "intro", "rcases", "use", "simpa", "exact"], "tactic_count": 8}
{"name": "continuousOn_Ioc_extendFrom_Ioo", "kind": "theorem", "module": "Mathlib.Topology.Order.ExtendFrom", "is_tactic_proof": true, "tactics": ["have", "rw", "exact"], "tactic_count": 3}
{"name": "eq_lim_at_left_extendFrom_Ioo", "kind": "theorem", "module": "Mathlib.Topology.Order.ExtendFrom", "is_tactic_proof": true, "tactics": ["apply", "rw", "simp", "simpa"], "tactic_count": 4}
{"name": "eq_lim_at_right_extendFrom_Ioo", "kind": "theorem", "module": "Mathlib.Topology.Order.ExtendFrom", "is_tactic_proof": true, "tactics": ["apply", "rw", "simp", "simpa"], "tactic_count": 4}
{"name": "eq_lim_at_left_extendFrom_uIoo", "kind": "theorem", "module": "Mathlib.Topology.Order.ExtendFrom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_lim_at_right_extendFrom_uIoo", "kind": "theorem", "module": "Mathlib.Topology.Order.ExtendFrom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMaxOn.closure", "kind": "theorem", "module": "Mathlib.Topology.Order.ExtrClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMinOn.closure", "kind": "theorem", "module": "Mathlib.Topology.Order.ExtrClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsExtrOn.closure", "kind": "theorem", "module": "Mathlib.Topology.Order.ExtrClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMaxOn.closure", "kind": "theorem", "module": "Mathlib.Topology.Order.ExtrClosure", "is_tactic_proof": true, "tactics": ["rcases", "refine", "rintro", "refine", "rwa", "exact", "exact"], "tactic_count": 7}
{"name": "IsLocalMinOn.closure", "kind": "theorem", "module": "Mathlib.Topology.Order.ExtrClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalExtrOn.closure", "kind": "theorem", "module": "Mathlib.Topology.Order.ExtrClosure", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_nhds_atTop", "kind": "theorem", "module": "Mathlib.Topology.Order.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_nhds_atBot", "kind": "theorem", "module": "Mathlib.Topology.Order.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.nhds_atTop", "kind": "theorem", "module": "Mathlib.Topology.Order.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.nhds_atBot", "kind": "theorem", "module": "Mathlib.Topology.Order.Filter", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "term_→Co_", "kind": "definition", "module": "Mathlib.Topology.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Topology_Order_Hom_Basic___macroRules_term_→Co__1", "kind": "definition", "module": "Mathlib.Topology.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_aux_Mathlib_Topology_Order_Hom_Basic___unexpand_ContinuousOrderHom_1", "kind": "definition", "module": "Mathlib.Topology.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOrderHomClass.toOrderHomClass", "kind": "instance", "module": "Mathlib.Topology.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOrderHomClass.toContinuousOrderHom", "kind": "definition", "module": "Mathlib.Topology.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOrderHomClass.instCoeTCContinuousOrderHom", "kind": "instance", "module": "Mathlib.Topology.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOrderHom.toContinuousMap", "kind": "definition", "module": "Mathlib.Topology.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOrderHom.instFunLike", "kind": "instance", "module": "Mathlib.Topology.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOrderHom.instContinuousOrderHomClass", "kind": "instance", "module": "Mathlib.Topology.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOrderHom.coe_toOrderHom", "kind": "theorem", "module": "Mathlib.Topology.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOrderHom.toFun_eq_coe", "kind": "theorem", "module": "Mathlib.Topology.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOrderHom.ext", "kind": "theorem", "module": "Mathlib.Topology.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOrderHom.copy", "kind": "definition", "module": "Mathlib.Topology.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOrderHom.coe_copy", "kind": "theorem", "module": "Mathlib.Topology.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOrderHom.copy_eq", "kind": "theorem", "module": "Mathlib.Topology.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOrderHom.id", "kind": "definition", "module": "Mathlib.Topology.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOrderHom.instInhabited", "kind": "instance", "module": "Mathlib.Topology.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOrderHom.coe_id", "kind": "theorem", "module": "Mathlib.Topology.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOrderHom.id_apply", "kind": "theorem", "module": "Mathlib.Topology.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOrderHom.comp", "kind": "definition", "module": "Mathlib.Topology.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOrderHom.coe_comp", "kind": "theorem", "module": "Mathlib.Topology.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOrderHom.comp_apply", "kind": "theorem", "module": "Mathlib.Topology.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOrderHom.comp_assoc", "kind": "theorem", "module": "Mathlib.Topology.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOrderHom.comp_id", "kind": "theorem", "module": "Mathlib.Topology.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOrderHom.id_comp", "kind": "theorem", "module": "Mathlib.Topology.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOrderHom.cancel_right", "kind": "theorem", "module": "Mathlib.Topology.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOrderHom.cancel_left", "kind": "theorem", "module": "Mathlib.Topology.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOrderHom.instPreorder", "kind": "instance", "module": "Mathlib.Topology.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOrderHom.instPartialOrder", "kind": "instance", "module": "Mathlib.Topology.Order.Hom.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoEpimorphismClass.toTopHomClass", "kind": "instance", "module": "Mathlib.Topology.Order.Hom.Esakia", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EsakiaHomClass.toPseudoEpimorphismClass", "kind": "instance", "module": "Mathlib.Topology.Order.Hom.Esakia", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCoeTCPseudoEpimorphismOfPseudoEpimorphismClass", "kind": "instance", "module": "Mathlib.Topology.Order.Hom.Esakia", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCoeTCEsakiaHomOfEsakiaHomClass", "kind": "instance", "module": "Mathlib.Topology.Order.Hom.Esakia", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIsoClass.toPseudoEpimorphismClass", "kind": "instance", "module": "Mathlib.Topology.Order.Hom.Esakia", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoEpimorphism.instFunLike", "kind": "instance", "module": "Mathlib.Topology.Order.Hom.Esakia", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoEpimorphism.instPseudoEpimorphismClass", "kind": "instance", "module": "Mathlib.Topology.Order.Hom.Esakia", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoEpimorphism.toOrderHom_eq_coe", "kind": "theorem", "module": "Mathlib.Topology.Order.Hom.Esakia", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoEpimorphism.toFun_eq_coe", "kind": "theorem", "module": "Mathlib.Topology.Order.Hom.Esakia", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoEpimorphism.ext", "kind": "theorem", "module": "Mathlib.Topology.Order.Hom.Esakia", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoEpimorphism.copy", "kind": "definition", "module": "Mathlib.Topology.Order.Hom.Esakia", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoEpimorphism.coe_copy", "kind": "theorem", "module": "Mathlib.Topology.Order.Hom.Esakia", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoEpimorphism.copy_eq", "kind": "theorem", "module": "Mathlib.Topology.Order.Hom.Esakia", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoEpimorphism.id", "kind": "definition", "module": "Mathlib.Topology.Order.Hom.Esakia", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoEpimorphism.instInhabited", "kind": "instance", "module": "Mathlib.Topology.Order.Hom.Esakia", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoEpimorphism.coe_id", "kind": "theorem", "module": "Mathlib.Topology.Order.Hom.Esakia", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoEpimorphism.coe_id_orderHom", "kind": "theorem", "module": "Mathlib.Topology.Order.Hom.Esakia", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoEpimorphism.id_apply", "kind": "theorem", "module": "Mathlib.Topology.Order.Hom.Esakia", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoEpimorphism.comp", "kind": "definition", "module": "Mathlib.Topology.Order.Hom.Esakia", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoEpimorphism.coe_comp", "kind": "theorem", "module": "Mathlib.Topology.Order.Hom.Esakia", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoEpimorphism.coe_comp_orderHom", "kind": "theorem", "module": "Mathlib.Topology.Order.Hom.Esakia", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoEpimorphism.comp_apply", "kind": "theorem", "module": "Mathlib.Topology.Order.Hom.Esakia", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoEpimorphism.comp_assoc", "kind": "theorem", "module": "Mathlib.Topology.Order.Hom.Esakia", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoEpimorphism.comp_id", "kind": "theorem", "module": "Mathlib.Topology.Order.Hom.Esakia", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoEpimorphism.id_comp", "kind": "theorem", "module": "Mathlib.Topology.Order.Hom.Esakia", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoEpimorphism.cancel_right", "kind": "theorem", "module": "Mathlib.Topology.Order.Hom.Esakia", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PseudoEpimorphism.cancel_left", "kind": "theorem", "module": "Mathlib.Topology.Order.Hom.Esakia", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EsakiaHom.toPseudoEpimorphism", "kind": "definition", "module": "Mathlib.Topology.Order.Hom.Esakia", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EsakiaHom.instFunLike", "kind": "instance", "module": "Mathlib.Topology.Order.Hom.Esakia", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EsakiaHom.instEsakiaHomClass", "kind": "instance", "module": "Mathlib.Topology.Order.Hom.Esakia", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EsakiaHom.toContinuousOrderHom_coe", "kind": "theorem", "module": "Mathlib.Topology.Order.Hom.Esakia", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EsakiaHom.toFun_eq_coe", "kind": "theorem", "module": "Mathlib.Topology.Order.Hom.Esakia", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EsakiaHom.ext", "kind": "theorem", "module": "Mathlib.Topology.Order.Hom.Esakia", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EsakiaHom.copy", "kind": "definition", "module": "Mathlib.Topology.Order.Hom.Esakia", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EsakiaHom.coe_copy", "kind": "theorem", "module": "Mathlib.Topology.Order.Hom.Esakia", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EsakiaHom.copy_eq", "kind": "theorem", "module": "Mathlib.Topology.Order.Hom.Esakia", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EsakiaHom.id", "kind": "definition", "module": "Mathlib.Topology.Order.Hom.Esakia", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EsakiaHom.instInhabited", "kind": "instance", "module": "Mathlib.Topology.Order.Hom.Esakia", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EsakiaHom.coe_id", "kind": "theorem", "module": "Mathlib.Topology.Order.Hom.Esakia", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EsakiaHom.coe_id_pseudoEpimorphism", "kind": "theorem", "module": "Mathlib.Topology.Order.Hom.Esakia", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EsakiaHom.id_apply", "kind": "theorem", "module": "Mathlib.Topology.Order.Hom.Esakia", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EsakiaHom.coe_id_continuousOrderHom", "kind": "theorem", "module": "Mathlib.Topology.Order.Hom.Esakia", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EsakiaHom.comp", "kind": "definition", "module": "Mathlib.Topology.Order.Hom.Esakia", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EsakiaHom.coe_comp_continuousOrderHom", "kind": "theorem", "module": "Mathlib.Topology.Order.Hom.Esakia", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EsakiaHom.coe_comp_pseudoEpimorphism", "kind": "theorem", "module": "Mathlib.Topology.Order.Hom.Esakia", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EsakiaHom.coe_comp", "kind": "theorem", "module": "Mathlib.Topology.Order.Hom.Esakia", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EsakiaHom.comp_apply", "kind": "theorem", "module": "Mathlib.Topology.Order.Hom.Esakia", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EsakiaHom.comp_assoc", "kind": "theorem", "module": "Mathlib.Topology.Order.Hom.Esakia", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EsakiaHom.comp_id", "kind": "theorem", "module": "Mathlib.Topology.Order.Hom.Esakia", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EsakiaHom.id_comp", "kind": "theorem", "module": "Mathlib.Topology.Order.Hom.Esakia", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EsakiaHom.cancel_right", "kind": "theorem", "module": "Mathlib.Topology.Order.Hom.Esakia", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EsakiaHom.cancel_left", "kind": "theorem", "module": "Mathlib.Topology.Order.Hom.Esakia", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimitiveSpectrum.hull", "kind": "abbrev", "module": "Mathlib.Topology.Order.HullKernel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimitiveSpectrum.hull_inf", "kind": "theorem", "module": "Mathlib.Topology.Order.HullKernel", "is_tactic_proof": true, "tactics": ["ext", "constructor", "exact", "rcases", "exact", "exact"], "tactic_count": 6}
{"name": "PrimitiveSpectrum.hull_finsetInf", "kind": "theorem", "module": "Mathlib.Topology.Order.HullKernel", "is_tactic_proof": true, "tactics": ["rw", "induction", "empty", "simp", "by_contra", "rw", "obtain", "exact", "cons", "simp", "set"], "tactic_count": 11}
{"name": "PrimitiveSpectrum.preimage_upperClosure_compl_finset", "kind": "theorem", "module": "Mathlib.Topology.Order.HullKernel", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PrimitiveSpectrum.isTopologicalBasis_relativeLower", "kind": "theorem", "module": "Mathlib.Topology.Order.HullKernel", "is_tactic_proof": true, "tactics": ["convert", "ext", "simp", "constructor", "obtain", "use", "rw", "simp", "diff_self_inter,", "exact", "obtain", "lift", "use", "ext", "simp"], "tactic_count": 15}
{"name": "PrimitiveSpectrum.hull_iSup", "kind": "theorem", "module": "Mathlib.Topology.Order.HullKernel", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "PrimitiveSpectrum.hull_sSup", "kind": "theorem", "module": "Mathlib.Topology.Order.HullKernel", "is_tactic_proof": true, "tactics": ["aesop"], "tactic_count": 1}
{"name": "PrimitiveSpectrum.isOpen_iff", "kind": "theorem", "module": "Mathlib.Topology.Order.HullKernel", "is_tactic_proof": true, "tactics": ["constructor", "let", "use", "rw", "aesop", "obtain", "exact", "form"], "tactic_count": 8}
{"name": "PrimitiveSpectrum.isClosed_iff", "kind": "theorem", "module": "Mathlib.Topology.Order.HullKernel", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PrimitiveSpectrum.kernel", "kind": "abbrev", "module": "Mathlib.Topology.Order.HullKernel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimitiveSpectrum.gc", "kind": "theorem", "module": "Mathlib.Topology.Order.HullKernel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimitiveSpectrum.gc_closureOperator", "kind": "theorem", "module": "Mathlib.Topology.Order.HullKernel", "is_tactic_proof": true, "tactics": ["simp", "rw"], "tactic_count": 2}
{"name": "PrimitiveSpectrum.OrderGenerates", "kind": "definition", "module": "Mathlib.Topology.Order.HullKernel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimitiveSpectrum.gi", "kind": "definition", "module": "Mathlib.Topology.Order.HullKernel", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrimitiveSpectrum.kernel_hull", "kind": "theorem", "module": "Mathlib.Topology.Order.HullKernel", "is_tactic_proof": true, "tactics": ["conv_rhs", "rfl"], "tactic_count": 2}
{"name": "PrimitiveSpectrum.hull_kernel_of_isClosed", "kind": "theorem", "module": "Mathlib.Topology.Order.HullKernel", "is_tactic_proof": true, "tactics": ["obtain", "rw"], "tactic_count": 2}
{"name": "PrimitiveSpectrum.closedsGC_closureOperator", "kind": "theorem", "module": "Mathlib.Topology.Order.HullKernel", "is_tactic_proof": true, "tactics": ["simp", "constructor", "exact", "a", "image_subset_iff.mp", "simp_rw", "intro", "rw", "exact"], "tactic_count": 9}
{"name": "intermediate_value_univ₂", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": ["obtain", "isPreconnected_closed_iff.1", "exact"], "tactic_count": 3}
{"name": "intermediate_value_univ₂_eventually₁", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intermediate_value_univ₂_eventually₂", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPreconnected.intermediate_value₂", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPreconnected.intermediate_value₂_eventually₁", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": true, "tactics": ["rw", "obtain", "exact"], "tactic_count": 3}
{"name": "IsPreconnected.intermediate_value₂_eventually₂", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": true, "tactics": ["rw", "obtain", "exact"], "tactic_count": 3}
{"name": "IsPreconnected.intermediate_value", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPreconnected.intermediate_value_Ico", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPreconnected.intermediate_value_Ioc", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPreconnected.intermediate_value_Ioo", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPreconnected.intermediate_value_Ici", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPreconnected.intermediate_value_Iic", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPreconnected.intermediate_value_Ioi", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPreconnected.intermediate_value_Iio", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPreconnected.intermediate_value_Iii", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intermediate_value_univ", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_range_of_exists_le_of_exists_ge", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPreconnected.Icc_subset", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsPreconnected.ordConnected", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsConnected.Icc_subset", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPreconnected.eq_univ_of_unbounded", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": true, "tactics": ["refine", "obtain", "obtain", "exact"], "tactic_count": 4}
{"name": "IsConnected.Ioo_csInf_csSup_subset", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_Icc_csInf_csSup_of_connected_bdd_closed", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPreconnected.Ioi_csInf_subset", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPreconnected.Iio_csSup_subset", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPreconnected.mem_intervals", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": true, "tactics": ["rcases", "apply_rules", "have", "by_cases", "refine", "mem_of_subset_of_mem", "mem_Icc_Ico_Ioc_Ioo_of_subset_of_subset", "simp", "refine", "rcases", "exact", "exact", "iterate", "rcases", "exact", "exact", "iterate", "exact"], "tactic_count": 18}
{"name": "setOf_isPreconnected_subset_of_ordered", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": true, "tactics": ["intro", "rcases", "simp", "exists_apply_eq_apply,"], "tactic_count": 4}
{"name": "IsClosed.mem_of_ge_of_forall_exists_gt", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": true, "tactics": ["let", "replace", "have", "let", "have", "have", "rcases", "exact", "exfalso", "rcases", "exact"], "tactic_count": 11}
{"name": "IsClosed.Icc_subset_of_forall_exists_gt", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": true, "tactics": ["intro", "have", "suffices", "grind", "exact"], "tactic_count": 5}
{"name": "IsClosed.mem_of_ge_of_forall_exists_lt", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": true, "tactics": ["suffices", "have", "rw", "apply", "rw", "aesop"], "tactic_count": 6}
{"name": "IsClosed.Icc_subset_of_forall_exists_lt", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": true, "tactics": ["intro", "have", "suffices", "grind", "exact"], "tactic_count": 5}
{"name": "IsClosed.Icc_subset_of_forall_mem_nhdsGT_of_Icc_subset", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": true, "tactics": ["rcases", "simp_all", "set", "have", "have", "set", "have", "obtain", "refine", "rcases", "have", "apply", "have", "exact", "apply", "exact", "obtain", "apply", "exact", "suffices", "apply", "obtain", "obtain", "have", "refine", "rcases", "exact", "exact", "have", "order"], "tactic_count": 30}
{"name": "IsClosed.Icc_subset_of_forall_mem_nhdsWithin", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isPreconnected_Icc_aux", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": true, "tactics": ["have", "by_contra", "suffices", "apply", "rintro", "have", "have", "rw", "exact", "apply", "have", "exact"], "tactic_count": 12}
{"name": "isPreconnected_Icc", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isPreconnected_uIcc", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.OrdConnected.isPreconnected", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isPreconnected_iff_ordConnected", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isPreconnected_Ici", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isPreconnected_Iic", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isPreconnected_Iio", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isPreconnected_Ioi", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isPreconnected_Ioo", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isPreconnected_uIoo", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isPreconnected_Ioc", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isPreconnected_uIoc", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isPreconnected_Ico", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isConnected_Ici", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isConnected_Iic", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isConnected_Ioi", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isConnected_Iio", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isConnected_Icc", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isConnected_Ioo", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isConnected_uIoo", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isConnected_Ioc", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isConnected_uIoc", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isConnected_Ico", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ordered_connected_space", "kind": "instance", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "setOf_isPreconnected_eq_of_ordered", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": true, "tactics": ["refine", "simp", "mem_singleton_iff,", "isPreconnected_Ioo,", "isPreconnected_univ,"], "tactic_count": 5}
{"name": "isTotallyDisconnected_iff_lt", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": ["simp", "not_exists,", "refine", "simp_rw", "exact", "obtain", "exact"], "tactic_count": 7}
{"name": "intermediate_value_Icc", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intermediate_value_Icc'", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intermediate_value_uIcc", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": true, "tactics": ["cases"], "tactic_count": 1}
{"name": "exists_mem_uIcc_isFixedPt", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_mem_Icc_isFixedPt", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_mem_Icc_isFixedPt_of_mapsTo", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intermediate_value_Ico", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intermediate_value_Ico'", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intermediate_value_Ioc", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intermediate_value_Ioc'", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intermediate_value_Ioo", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "intermediate_value_Ioo'", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.surjOn_Icc", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.surjOn_uIcc", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": true, "tactics": ["rcases"], "tactic_count": 1}
{"name": "Continuous.surjective", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.surjective'", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.surjOn_of_tendsto", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.surjOn_of_tendsto'", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.strictMono_of_inj_boundedOrder", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": true, "tactics": ["intro", "by_contra", "have", "by_cases", "obtain", "have", "simp_all", "by_cases", "obtain", "rw", "exact", "replace", "obtain", "have", "simp_all"], "tactic_count": 15}
{"name": "Continuous.strictAnti_of_inj_boundedOrder", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.strictMono_of_inj_boundedOrder'", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.strictMonoOn_of_inj_rigidity", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": true, "tactics": ["intro", "let", "let", "have", "have", "have", "have", "have", "hf_i.injOn.injective", "exact", "have", "have", "replace", "replace", "exact", "replace", "have", "have", "replace", "replace", "exact"], "tactic_count": 21}
{"name": "ContinuousOn.strictMonoOn_of_injOn_Icc", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": true, "tactics": ["have", "refine", "set", "have", "exact"], "tactic_count": 5}
{"name": "ContinuousOn.strictAntiOn_of_injOn_Icc", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.strictMonoOn_of_injOn_Icc'", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.strictMono_of_inj", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": false, "tactics": ["have", "cases", "inl", "inr", "obtain", "exact"], "tactic_count": 6}
{"name": "ContinuousOn.strictMonoOn_of_injOn_Ioo", "kind": "theorem", "module": "Mathlib.Topology.Order.IntermediateValue", "is_tactic_proof": true, "tactics": ["haveI", "let", "have", "exact"], "tactic_count": 4}
{"name": "IsLUB.frequently_mem", "kind": "theorem", "module": "Mathlib.Topology.Order.IsLUB", "is_tactic_proof": true, "tactics": ["rcases", "intro", "rcases", "exact", "rcases", "rcases", "exact"], "tactic_count": 7}
{"name": "IsLUB.frequently_nhds_mem", "kind": "theorem", "module": "Mathlib.Topology.Order.IsLUB", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGLB.frequently_mem", "kind": "theorem", "module": "Mathlib.Topology.Order.IsLUB", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGLB.frequently_nhds_mem", "kind": "theorem", "module": "Mathlib.Topology.Order.IsLUB", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLUB.mem_closure", "kind": "theorem", "module": "Mathlib.Topology.Order.IsLUB", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGLB.mem_closure", "kind": "theorem", "module": "Mathlib.Topology.Order.IsLUB", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLUB.nhdsWithin_neBot", "kind": "theorem", "module": "Mathlib.Topology.Order.IsLUB", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGLB.nhdsWithin_neBot", "kind": "theorem", "module": "Mathlib.Topology.Order.IsLUB", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLUB_of_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Order.IsLUB", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLUB_of_mem_closure", "kind": "theorem", "module": "Mathlib.Topology.Order.IsLUB", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "isGLB_of_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Order.IsLUB", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isGLB_of_mem_closure", "kind": "theorem", "module": "Mathlib.Topology.Order.IsLUB", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLUB.mem_upperBounds_of_tendsto", "kind": "theorem", "module": "Mathlib.Topology.Order.IsLUB", "is_tactic_proof": true, "tactics": ["rintro", "replace", "haveI", "refine", "exact", "mem_of_superset", "hf", "hy.2"], "tactic_count": 8}
{"name": "IsLUB.isLUB_of_tendsto", "kind": "theorem", "module": "Mathlib.Topology.Order.IsLUB", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGLB.mem_lowerBounds_of_tendsto", "kind": "theorem", "module": "Mathlib.Topology.Order.IsLUB", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGLB.isGLB_of_tendsto", "kind": "theorem", "module": "Mathlib.Topology.Order.IsLUB", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLUB.mem_lowerBounds_of_tendsto", "kind": "theorem", "module": "Mathlib.Topology.Order.IsLUB", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLUB.isGLB_of_tendsto", "kind": "theorem", "module": "Mathlib.Topology.Order.IsLUB", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGLB.mem_upperBounds_of_tendsto", "kind": "theorem", "module": "Mathlib.Topology.Order.IsLUB", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGLB.isLUB_of_tendsto", "kind": "theorem", "module": "Mathlib.Topology.Order.IsLUB", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLUB.mem_of_isClosed", "kind": "theorem", "module": "Mathlib.Topology.Order.IsLUB", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGLB.mem_of_isClosed", "kind": "theorem", "module": "Mathlib.Topology.Order.IsLUB", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLUB_iff_of_subset_of_subset_closure", "kind": "theorem", "module": "Mathlib.Topology.Order.IsLUB", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isGLB_iff_of_subset_of_subset_closure", "kind": "theorem", "module": "Mathlib.Topology.Order.IsLUB", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dense.isLUB_inter_iff", "kind": "theorem", "module": "Mathlib.Topology.Order.IsLUB", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dense.isGLB_inter_iff", "kind": "theorem", "module": "Mathlib.Topology.Order.IsLUB", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dense.upperBounds_image", "kind": "theorem", "module": "Mathlib.Topology.Order.IsLUB", "is_tactic_proof": true, "tactics": ["refine", "refine", "intro", "rw", "exact"], "tactic_count": 5}
{"name": "Dense.lowerBounds_image", "kind": "theorem", "module": "Mathlib.Topology.Order.IsLUB", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dense.ciSup", "kind": "theorem", "module": "Mathlib.Topology.Order.IsLUB", "is_tactic_proof": true, "tactics": ["rw", "obtain", "simp", "refine", "refine", "exact"], "tactic_count": 6}
{"name": "Dense.ciInf", "kind": "theorem", "module": "Mathlib.Topology.Order.IsLUB", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dense.ciSup'", "kind": "theorem", "module": "Mathlib.Topology.Order.IsLUB", "is_tactic_proof": true, "tactics": ["by_cases", "refine", "simpa", "suffices", "contrapose", "grind"], "tactic_count": 6}
{"name": "Dense.ciInf'", "kind": "theorem", "module": "Mathlib.Topology.Order.IsLUB", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConditionallyCompleteLinearOrder.isCompact_Icc", "kind": "theorem", "module": "Mathlib.Topology.Order.IsLUB", "is_tactic_proof": true, "tactics": ["simp", "refine", "by_contra", "have", "set", "have", "have", "let", "have", "have", "have", "have", "filter_upwards", "have", "have", "have", "have", "exact"], "tactic_count": 18}
{"name": "upperClosure_eq_Ici_csInf", "kind": "theorem", "module": "Mathlib.Topology.Order.IsLUB", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lowerClosure_eq_Iic_csSup", "kind": "theorem", "module": "Mathlib.Topology.Order.IsLUB", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.upperClosure", "kind": "theorem", "module": "Mathlib.Topology.Order.IsLUB", "is_tactic_proof": true, "tactics": ["obtain", "simp", "by_cases", "exact", "exact"], "tactic_count": 5}
{"name": "IsClosed.lowerClosure", "kind": "theorem", "module": "Mathlib.Topology.Order.IsLUB", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLUB.exists_seq_strictMono_tendsto_of_notMem", "kind": "theorem", "module": "Mathlib.Topology.Order.IsLUB", "is_tactic_proof": true, "tactics": ["obtain", "replace", "have", "have", "choose", "refine", "hvx.comp", "rw", "rw"], "tactic_count": 9}
{"name": "IsLUB.exists_seq_monotone_tendsto", "kind": "theorem", "module": "Mathlib.Topology.Order.IsLUB", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "rcases", "exact"], "tactic_count": 4}
{"name": "exists_seq_strictMono_tendsto'", "kind": "theorem", "module": "Mathlib.Topology.Order.IsLUB", "is_tactic_proof": true, "tactics": ["have", "have", "rcases", "exact"], "tactic_count": 4}
{"name": "exists_seq_strictMono_tendsto", "kind": "theorem", "module": "Mathlib.Topology.Order.IsLUB", "is_tactic_proof": true, "tactics": ["obtain", "rcases", "exact"], "tactic_count": 3}
{"name": "exists_seq_strictMono_tendsto_nhdsWithin", "kind": "theorem", "module": "Mathlib.Topology.Order.IsLUB", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_seq_tendsto_sSup", "kind": "theorem", "module": "Mathlib.Topology.Order.IsLUB", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "Dense.exists_seq_strictMono_tendsto_of_lt", "kind": "theorem", "module": "Mathlib.Topology.Order.IsLUB", "is_tactic_proof": false, "tactics": ["have", "obtain", "exact", "have", "apply", "simp_all"], "tactic_count": 6}
{"name": "Dense.exists_seq_strictMono_tendsto", "kind": "theorem", "module": "Mathlib.Topology.Order.IsLUB", "is_tactic_proof": true, "tactics": ["obtain", "apply", "simp_all"], "tactic_count": 3}
{"name": "DenseRange.exists_seq_strictMono_tendsto_of_lt", "kind": "theorem", "module": "Mathlib.Topology.Order.IsLUB", "is_tactic_proof": true, "tactics": ["rcases", "have", "have", "choose", "obtain", "exact"], "tactic_count": 6}
{"name": "DenseRange.exists_seq_strictMono_tendsto", "kind": "theorem", "module": "Mathlib.Topology.Order.IsLUB", "is_tactic_proof": true, "tactics": ["rcases", "have", "have", "choose", "obtain", "exact"], "tactic_count": 6}
{"name": "IsGLB.exists_seq_strictAnti_tendsto_of_notMem", "kind": "theorem", "module": "Mathlib.Topology.Order.IsLUB", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGLB.exists_seq_antitone_tendsto", "kind": "theorem", "module": "Mathlib.Topology.Order.IsLUB", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_seq_strictAnti_tendsto'", "kind": "theorem", "module": "Mathlib.Topology.Order.IsLUB", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "exists_seq_strictAnti_tendsto", "kind": "theorem", "module": "Mathlib.Topology.Order.IsLUB", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_seq_strictAnti_tendsto_nhdsWithin", "kind": "theorem", "module": "Mathlib.Topology.Order.IsLUB", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_seq_strictAnti_strictMono_tendsto", "kind": "theorem", "module": "Mathlib.Topology.Order.IsLUB", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "exact"], "tactic_count": 3}
{"name": "exists_seq_tendsto_sInf", "kind": "theorem", "module": "Mathlib.Topology.Order.IsLUB", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dense.exists_seq_strictAnti_tendsto_of_lt", "kind": "theorem", "module": "Mathlib.Topology.Order.IsLUB", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Dense.exists_seq_strictAnti_tendsto", "kind": "theorem", "module": "Mathlib.Topology.Order.IsLUB", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DenseRange.exists_seq_strictAnti_tendsto_of_lt", "kind": "theorem", "module": "Mathlib.Topology.Order.IsLUB", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "DenseRange.exists_seq_strictAnti_tendsto", "kind": "theorem", "module": "Mathlib.Topology.Order.IsLUB", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLocallyClosed_Icc", "kind": "theorem", "module": "Mathlib.Topology.Order.IsLocallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLocallyClosed_Ioo", "kind": "theorem", "module": "Mathlib.Topology.Order.IsLocallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLocallyClosed_Ici", "kind": "theorem", "module": "Mathlib.Topology.Order.IsLocallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLocallyClosed_Iic", "kind": "theorem", "module": "Mathlib.Topology.Order.IsLocallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLocallyClosed_Ioi", "kind": "theorem", "module": "Mathlib.Topology.Order.IsLocallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLocallyClosed_Iio", "kind": "theorem", "module": "Mathlib.Topology.Order.IsLocallyClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLocallyClosed_Ioc", "kind": "theorem", "module": "Mathlib.Topology.Order.IsLocallyClosed", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "isLocallyClosed_Ico", "kind": "theorem", "module": "Mathlib.Topology.Order.IsLocallyClosed", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Order.IsNormal.continuous", "kind": "theorem", "module": "Mathlib.Topology.Order.IsNormal", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "obtain", "exact", "obtain", "exact", "have", "have", "rw", "exact"], "tactic_count": 11}
{"name": "Order.isNormal_iff_strictMono_and_continuous", "kind": "theorem", "module": "Mathlib.Topology.Order.IsNormal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.continuousSup", "kind": "instance", "module": "Mathlib.Topology.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.continuousInf", "kind": "instance", "module": "Mathlib.Topology.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.topologicalLattice", "kind": "instance", "module": "Mathlib.Topology.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearOrder.topologicalLattice", "kind": "instance", "module": "Mathlib.Topology.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_inf", "kind": "theorem", "module": "Mathlib.Topology.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.inf", "kind": "theorem", "module": "Mathlib.Topology.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_sup", "kind": "theorem", "module": "Mathlib.Topology.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.sup", "kind": "theorem", "module": "Mathlib.Topology.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.sup_nhds'", "kind": "theorem", "module": "Mathlib.Topology.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.sup_nhds", "kind": "theorem", "module": "Mathlib.Topology.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.inf_nhds'", "kind": "theorem", "module": "Mathlib.Topology.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.inf_nhds", "kind": "theorem", "module": "Mathlib.Topology.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.finset_sup'_nhds", "kind": "theorem", "module": "Mathlib.Topology.Order.Lattice", "is_tactic_proof": true, "tactics": ["induction", "singleton", "cons", "rw", "simp", "exact"], "tactic_count": 6}
{"name": "Filter.Tendsto.finset_sup'_nhds_apply", "kind": "theorem", "module": "Mathlib.Topology.Order.Lattice", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Filter.Tendsto.finset_inf'_nhds", "kind": "theorem", "module": "Mathlib.Topology.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.finset_inf'_nhds_apply", "kind": "theorem", "module": "Mathlib.Topology.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.finset_sup_nhds", "kind": "theorem", "module": "Mathlib.Topology.Order.Lattice", "is_tactic_proof": true, "tactics": ["rcases", "simpa", "simp", "exact"], "tactic_count": 4}
{"name": "Filter.Tendsto.finset_sup_nhds_apply", "kind": "theorem", "module": "Mathlib.Topology.Order.Lattice", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Filter.Tendsto.finset_inf_nhds", "kind": "theorem", "module": "Mathlib.Topology.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.finset_inf_nhds_apply", "kind": "theorem", "module": "Mathlib.Topology.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.sup'", "kind": "theorem", "module": "Mathlib.Topology.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.sup", "kind": "theorem", "module": "Mathlib.Topology.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.sup'", "kind": "theorem", "module": "Mathlib.Topology.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.sup", "kind": "theorem", "module": "Mathlib.Topology.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.sup'", "kind": "theorem", "module": "Mathlib.Topology.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.sup", "kind": "theorem", "module": "Mathlib.Topology.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.sup'", "kind": "theorem", "module": "Mathlib.Topology.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.inf'", "kind": "theorem", "module": "Mathlib.Topology.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.inf", "kind": "theorem", "module": "Mathlib.Topology.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.inf'", "kind": "theorem", "module": "Mathlib.Topology.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.inf", "kind": "theorem", "module": "Mathlib.Topology.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.inf'", "kind": "theorem", "module": "Mathlib.Topology.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.inf", "kind": "theorem", "module": "Mathlib.Topology.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.inf'", "kind": "theorem", "module": "Mathlib.Topology.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.finset_sup'_apply", "kind": "theorem", "module": "Mathlib.Topology.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.finset_sup'", "kind": "theorem", "module": "Mathlib.Topology.Order.Lattice", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ContinuousWithinAt.finset_sup'_apply", "kind": "theorem", "module": "Mathlib.Topology.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.finset_sup'", "kind": "theorem", "module": "Mathlib.Topology.Order.Lattice", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ContinuousOn.finset_sup'_apply", "kind": "theorem", "module": "Mathlib.Topology.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.finset_sup'", "kind": "theorem", "module": "Mathlib.Topology.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.finset_sup'_apply", "kind": "theorem", "module": "Mathlib.Topology.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.finset_sup'", "kind": "theorem", "module": "Mathlib.Topology.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.finset_sup_apply", "kind": "theorem", "module": "Mathlib.Topology.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.finset_sup", "kind": "theorem", "module": "Mathlib.Topology.Order.Lattice", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ContinuousWithinAt.finset_sup_apply", "kind": "theorem", "module": "Mathlib.Topology.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.finset_sup", "kind": "theorem", "module": "Mathlib.Topology.Order.Lattice", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ContinuousOn.finset_sup_apply", "kind": "theorem", "module": "Mathlib.Topology.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.finset_sup", "kind": "theorem", "module": "Mathlib.Topology.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.finset_sup_apply", "kind": "theorem", "module": "Mathlib.Topology.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.finset_sup", "kind": "theorem", "module": "Mathlib.Topology.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.finset_inf'_apply", "kind": "theorem", "module": "Mathlib.Topology.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.finset_inf'", "kind": "theorem", "module": "Mathlib.Topology.Order.Lattice", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ContinuousWithinAt.finset_inf'_apply", "kind": "theorem", "module": "Mathlib.Topology.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.finset_inf'", "kind": "theorem", "module": "Mathlib.Topology.Order.Lattice", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ContinuousOn.finset_inf'_apply", "kind": "theorem", "module": "Mathlib.Topology.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.finset_inf'", "kind": "theorem", "module": "Mathlib.Topology.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.finset_inf'_apply", "kind": "theorem", "module": "Mathlib.Topology.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.finset_inf'", "kind": "theorem", "module": "Mathlib.Topology.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.finset_inf_apply", "kind": "theorem", "module": "Mathlib.Topology.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.finset_inf", "kind": "theorem", "module": "Mathlib.Topology.Order.Lattice", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ContinuousWithinAt.finset_inf_apply", "kind": "theorem", "module": "Mathlib.Topology.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.finset_inf", "kind": "theorem", "module": "Mathlib.Topology.Order.Lattice", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ContinuousOn.finset_inf_apply", "kind": "theorem", "module": "Mathlib.Topology.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.finset_inf", "kind": "theorem", "module": "Mathlib.Topology.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.finset_inf_apply", "kind": "theorem", "module": "Mathlib.Topology.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.finset_inf", "kind": "theorem", "module": "Mathlib.Topology.Order.Lattice", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.lawson", "kind": "definition", "module": "Mathlib.Topology.Order.LawsonTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsLawson.lawsonBasis", "kind": "definition", "module": "Mathlib.Topology.Order.LawsonTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsLawson.isTopologicalBasis", "kind": "theorem", "module": "Mathlib.Topology.Order.LawsonTopology", "is_tactic_proof": false, "tactics": ["have", "lawsonBasis", "rw", "simp_rw", "aesop", "rw", "convert", "rw", "apply", "letI", "exact", "letI", "exact"], "tactic_count": 13}
{"name": "Topology.WithLawson", "kind": "definition", "module": "Mathlib.Topology.Order.LawsonTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithLawson.toLawson", "kind": "definition", "module": "Mathlib.Topology.Order.LawsonTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithLawson.ofLawson", "kind": "definition", "module": "Mathlib.Topology.Order.LawsonTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithLawson.to_Lawson_symm_eq", "kind": "theorem", "module": "Mathlib.Topology.Order.LawsonTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithLawson.of_Lawson_symm_eq", "kind": "theorem", "module": "Mathlib.Topology.Order.LawsonTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithLawson.toLawson_ofLawson", "kind": "theorem", "module": "Mathlib.Topology.Order.LawsonTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithLawson.ofLawson_toLawson", "kind": "theorem", "module": "Mathlib.Topology.Order.LawsonTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithLawson.toLawson_inj", "kind": "theorem", "module": "Mathlib.Topology.Order.LawsonTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithLawson.ofLawson_inj", "kind": "theorem", "module": "Mathlib.Topology.Order.LawsonTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithLawson.rec", "kind": "definition", "module": "Mathlib.Topology.Order.LawsonTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithLawson.instNonempty", "kind": "instance", "module": "Mathlib.Topology.Order.LawsonTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithLawson.instInhabited", "kind": "instance", "module": "Mathlib.Topology.Order.LawsonTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithLawson.instPreorder", "kind": "instance", "module": "Mathlib.Topology.Order.LawsonTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithLawson.instTopologicalSpace", "kind": "instance", "module": "Mathlib.Topology.Order.LawsonTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithLawson.instIsLawson", "kind": "instance", "module": "Mathlib.Topology.Order.LawsonTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithLawson.homeomorph", "kind": "definition", "module": "Mathlib.Topology.Order.LawsonTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithLawson.isOpen_preimage_ofLawson", "kind": "theorem", "module": "Mathlib.Topology.Order.LawsonTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithLawson.isClosed_preimage_ofLawson", "kind": "theorem", "module": "Mathlib.Topology.Order.LawsonTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithLawson.isOpen_def", "kind": "theorem", "module": "Mathlib.Topology.Order.LawsonTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.lawson_le_scott", "kind": "theorem", "module": "Mathlib.Topology.Order.LawsonTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.lawson_le_lower", "kind": "theorem", "module": "Mathlib.Topology.Order.LawsonTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.scottHausdorff_le_lawson", "kind": "theorem", "module": "Mathlib.Topology.Order.LawsonTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.lawsonClosed_of_scottClosed", "kind": "theorem", "module": "Mathlib.Topology.Order.LawsonTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.lawsonClosed_of_lowerClosed", "kind": "theorem", "module": "Mathlib.Topology.Order.LawsonTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.lawsonOpen_iff_scottOpen_of_isUpperSet", "kind": "theorem", "module": "Mathlib.Topology.Order.LawsonTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.isLawson_le_isScott", "kind": "theorem", "module": "Mathlib.Topology.Order.LawsonTopology", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Topology.scottHausdorff_le_isLawson", "kind": "theorem", "module": "Mathlib.Topology.Order.LawsonTopology", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Topology.lawsonOpen_iff_scottOpen_of_isUpperSet'", "kind": "theorem", "module": "Mathlib.Topology.Order.LawsonTopology", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Topology.lawsonClosed_iff_scottClosed_of_isLowerSet", "kind": "theorem", "module": "Mathlib.Topology.Order.LawsonTopology", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Topology.lawsonClosed_iff_dirSupClosed_of_isLowerSet", "kind": "theorem", "module": "Mathlib.Topology.Order.LawsonTopology", "is_tactic_proof": true, "tactics": ["rw", "simp_all"], "tactic_count": 2}
{"name": "Topology.IsLawson.toT1Space", "kind": "instance", "module": "Mathlib.Topology.Order.LawsonTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "frequently_lt_nhds", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRight", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "frequently_gt_nhds", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRight", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Eventually.exists_lt", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRight", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Eventually.exists_gt", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRight", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsWithin_Ici_neBot", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRight", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsGE_neBot", "kind": "instance", "module": "Mathlib.Topology.Order.LeftRight", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsWithin_Iic_neBot", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRight", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsLE_neBot", "kind": "instance", "module": "Mathlib.Topology.Order.LeftRight", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsLT_le_nhdsNE", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRight", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsGT_le_nhdsNE", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRight", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsAntichain.interior_eq_empty", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRight", "is_tactic_proof": true, "tactics": ["refine", "have", "rcases", "exact"], "tactic_count": 4}
{"name": "IsAntichain.interior_eq_empty'", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRight", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousWithinAt_Ioi_iff_Ici", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRight", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "continuousWithinAt_Iio_iff_Iic", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRight", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousWithinAt_inter_Ioi_iff_Ici", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRight", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "continuousWithinAt_inter_Iio_iff_Iic", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRight", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsLE_sup_nhdsGE", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRight", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "nhdsWithinLE_sup_nhdsWithinGE", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRight", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "nhdsLT_sup_nhdsGE", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRight", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "nhdsWithinLT_sup_nhdsWithinGE", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRight", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "nhdsLE_sup_nhdsGT", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRight", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "nhdsWithinLE_sup_nhdsWithinGT", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRight", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "nhdsLT_sup_nhdsGT", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRight", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "nhdsWithinLT_sup_nhdsWithinGT", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRight", "is_tactic_proof": true, "tactics": ["rw", "univ_inter]"], "tactic_count": 2}
{"name": "nhdsGT_sup_nhdsWithin_singleton", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRight", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "nhdsWithin_uIoo_left_le_nhdsNE", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRight", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsWithin_uIoo_right_le_nhdsNE", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRight", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousAt_iff_continuous_left_right", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRight", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "continuousAt_iff_continuous_left'_right'", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRight", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "continuousWithinAt_iff_continuous_left_right", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRight", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "continuousWithinAt_iff_continuous_left'_right'", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRight", "is_tactic_proof": true, "tactics": ["rw", "continuousWithinAt_iff_continuous_left_right]"], "tactic_count": 2}
{"name": "Function.leftLim", "kind": "definition", "module": "Mathlib.Topology.Order.LeftRightLim", "is_tactic_proof": true, "tactics": ["classical", "haveI", "letI", "exact"], "tactic_count": 4}
{"name": "Function.rightLim", "kind": "definition", "module": "Mathlib.Topology.Order.LeftRightLim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "leftLim_eq_of_tendsto", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightLim", "is_tactic_proof": true, "tactics": ["have", "rw", "simp", "haveI", "exact"], "tactic_count": 5}
{"name": "rightLim_eq_of_tendsto", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightLim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "leftLim_eq_of_eq_bot", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightLim", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "rightLim_eq_of_eq_bot", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightLim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "leftLim_eq_of_not_tendsto", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightLim", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "rightLim_eq_of_not_tendsto", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightLim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "leftLim_eq_of_isBot", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightLim", "is_tactic_proof": true, "tactics": ["let", "have", "apply", "have", "simp"], "tactic_count": 5}
{"name": "rightLim_eq_of_isTop", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightLim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.leftLim_eq", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightLim", "is_tactic_proof": true, "tactics": ["rcases", "simp", "apply", "exact"], "tactic_count": 4}
{"name": "ContinuousWithinAt.rightLim_eq", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightLim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_leftLim_of_tendsto", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightLim", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rw", "simp", "exact"], "tactic_count": 5}
{"name": "tendsto_rightLim_of_tendsto", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightLim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mapClusterPt_leftLim", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightLim", "is_tactic_proof": false, "tactics": ["have", "refine", "refine", "simp", "apply", "rcases", "simp", "by_cases", "simp", "have", "exact"], "tactic_count": 11}
{"name": "mapClusterPt_rightLim", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightLim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousWithinAt_leftLim_Iic", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightLim", "is_tactic_proof": false, "tactics": ["have", "rw", "simp", "rw", "simp", "apply", "rintro", "rcases", "simp", "obtain", "obtain", "have", "simpa", "filter_upwards", "rcases", "simpa", "by_cases", "simpa", "apply", "filter_upwards"], "tactic_count": 20}
{"name": "leftLim_leftLim", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightLim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousWithinAt_rightLim_Ici", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightLim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "rightLim_rightLim", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightLim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "leftLim_rightLim", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightLim", "is_tactic_proof": true, "tactics": ["obtain", "apply", "apply", "rintro", "obtain", "have", "simpa", "filter_upwards", "rcases", "simpa", "by_cases", "simpa", "apply", "filter_upwards"], "tactic_count": 14}
{"name": "rightLim_leftLim", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightLim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_atTop_of_mapClusterPt", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightLim", "is_tactic_proof": true, "tactics": ["rcases", "simp", "apply", "rintro", "obtain", "simpa", "filter_upwards", "apply", "filter_upwards"], "tactic_count": 9}
{"name": "tendsto_atBot_of_mapClusterPt", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightLim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_leftLim_atTop_of_tendsto", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightLim", "is_tactic_proof": true, "tactics": ["apply", "exact"], "tactic_count": 2}
{"name": "tendsto_rightLim_atTop_of_tendsto", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightLim", "is_tactic_proof": true, "tactics": ["cases", "simp", "have", "rw", "apply", "apply", "exact"], "tactic_count": 7}
{"name": "tendsto_rightLim_atBot_of_tendsto", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightLim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_leftLim_atBot_of_tendsto", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightLim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.leftLim_eq_sSup", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightLim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.rightLim_eq_sInf", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightLim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.leftLim_le", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightLim", "is_tactic_proof": true, "tactics": ["letI", "haveI", "rcases", "simpa", "haveI", "rw", "refine", "simp", "exact", "simp", "intro", "exact"], "tactic_count": 12}
{"name": "Monotone.le_leftLim", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightLim", "is_tactic_proof": true, "tactics": ["letI", "haveI", "rcases", "rw", "exact", "rw", "refine", "simp", "intro", "exact"], "tactic_count": 10}
{"name": "Monotone.leftLim", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightLim", "is_tactic_proof": true, "tactics": ["intro", "rcases", "exact", "exact"], "tactic_count": 4}
{"name": "Monotone.le_rightLim", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightLim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.rightLim_le", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightLim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.rightLim", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightLim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.leftLim_le_rightLim", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightLim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.rightLim_le_leftLim", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightLim", "is_tactic_proof": true, "tactics": ["letI", "haveI", "rcases", "simpa", "obtain", "calc", "rightLim"], "tactic_count": 7}
{"name": "Monotone.tendsto_leftLim", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightLim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.tendsto_leftLim_within", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightLim", "is_tactic_proof": true, "tactics": ["apply", "filter_upwards"], "tactic_count": 2}
{"name": "Monotone.tendsto_rightLim", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightLim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.tendsto_rightLim_within", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightLim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.continuousWithinAt_Iio_iff_leftLim_eq", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightLim", "is_tactic_proof": true, "tactics": ["rcases", "simp", "haveI", "refine", "have", "rwa"], "tactic_count": 6}
{"name": "Monotone.continuousWithinAt_Ioi_iff_rightLim_eq", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightLim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.continuousAt_iff_leftLim_eq_rightLim", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightLim", "is_tactic_proof": true, "tactics": ["refine", "have", "have", "exact", "have", "apply", "rw", "exact", "refine", "exact", "rw", "exact"], "tactic_count": 12}
{"name": "Antitone.le_leftLim", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightLim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.leftLim_le", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightLim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.leftLim", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightLim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.rightLim_le", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightLim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.le_rightLim", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightLim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.rightLim", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightLim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.rightLim_le_leftLim", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightLim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.leftLim_le_rightLim", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightLim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.tendsto_leftLim", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightLim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.tendsto_leftLim_within", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightLim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.tendsto_rightLim", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightLim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.tendsto_rightLim_within", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightLim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.continuousWithinAt_Iio_iff_leftLim_eq", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightLim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.continuousWithinAt_Ioi_iff_rightLim_eq", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightLim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.continuousAt_iff_leftLim_eq_rightLim", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightLim", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TFAE_mem_nhdsGT", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightNhds", "is_tactic_proof": true, "tactics": ["tfae_have", "tfae_have", "tfae_have", "tfae_have", "tfae_have", "h", "rcases", "rcases", "exact", "tfae_finish"], "tactic_count": 10}
{"name": "mem_nhdsGT_iff_exists_mem_Ioc_Ioo_subset", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_nhdsGT_iff_exists_Ioo_subset'", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsGT_basis_of_exists_gt", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsGT_basis", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsGT_eq_bot_iff", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightNhds", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "simp", "rw", "simp"], "tactic_count": 5}
{"name": "mem_nhdsGT_iff_exists_Ioo_subset", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "countable_setOf_isolated_right", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightNhds", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "countable_setOf_isolated_left", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "countable_setOf_isolated_right_within", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightNhds", "is_tactic_proof": true, "tactics": ["is", "topology.", "let", "suffices", "have", "intro", "by_cases", "simp", "simpa", "apply", "simp", "have", "simp", "not_le,", "rcases", "obtain", "refine", "contrapose", "apply", "intro", "exact", "choose", "apply", "simp", "intro", "wlog", "have", "exact", "have", "by_contra", "have", "simp", "rw", "exact"], "tactic_count": 34}
{"name": "countable_setOf_isolated_left_within", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_nhdsGT_iff_exists_Ioc_subset", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightNhds", "is_tactic_proof": true, "tactics": ["rw", "constructor", "rintro", "rcases", "exact", "rintro", "exact"], "tactic_count": 7}
{"name": "TFAE_mem_nhdsLT", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightNhds", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "mem_nhdsLT_iff_exists_mem_Ico_Ioo_subset", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_nhdsLT_iff_exists_Ioo_subset'", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_nhdsLT_iff_exists_Ioo_subset", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_nhdsLT_iff_exists_Ico_subset", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightNhds", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "nhdsLT_basis_of_exists_lt", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsLT_basis", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsLT_eq_bot_iff", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightNhds", "is_tactic_proof": true, "tactics": ["convert", "exact"], "tactic_count": 2}
{"name": "TFAE_mem_nhdsGE", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightNhds", "is_tactic_proof": true, "tactics": ["tfae_have", "tfae_have", "tfae_have", "tfae_have", "tfae_have", "tfae_finish"], "tactic_count": 6}
{"name": "mem_nhdsGE_iff_exists_mem_Ioc_Ico_subset", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_nhdsGE_iff_exists_Ico_subset'", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_nhdsGE_iff_exists_Ico_subset", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsGE_basis_Ico", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsGE_basis_Icc", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_nhdsGE_iff_exists_Icc_subset", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TFAE_mem_nhdsLE", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightNhds", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "mem_nhdsLE_iff_exists_mem_Ico_Ioc_subset", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_nhdsLE_iff_exists_Ioc_subset'", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_nhdsLE_iff_exists_Ioc_subset", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_nhdsLE_iff_exists_Icc_subset", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsLE_basis_Icc", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhds_eq_iInf_mabs_div", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightNhds", "is_tactic_proof": true, "tactics": ["simp", "refine", "refine", "refine"], "tactic_count": 4}
{"name": "orderTopology_of_nhds_mabs", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightNhds", "is_tactic_proof": true, "tactics": ["refine", "rw", "letI", "exact"], "tactic_count": 4}
{"name": "LinearOrderedCommGroup.tendsto_nhds", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightNhds", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "eventually_mabs_div_lt", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.mul_atTop'", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightNhds", "is_tactic_proof": true, "tactics": ["nontriviality", "obtain", "refine", "exact"], "tactic_count": 4}
{"name": "Filter.Tendsto.mul_atBot'", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.atTop_mul'", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightNhds", "is_tactic_proof": true, "tactics": ["conv", "exact"], "tactic_count": 2}
{"name": "Filter.Tendsto.atBot_mul'", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightNhds", "is_tactic_proof": true, "tactics": ["conv", "exact"], "tactic_count": 2}
{"name": "nhds_basis_mabs_div_lt", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightNhds", "is_tactic_proof": true, "tactics": ["simp", "refine", "exact"], "tactic_count": 3}
{"name": "nhds_basis_Ioo_one_lt", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightNhds", "is_tactic_proof": true, "tactics": ["convert", "simp"], "tactic_count": 2}
{"name": "nhds_basis_Icc_one_lt", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhds_basis_one_mabs_lt", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightNhds", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "nhds_basis_Ioo_one_lt_of_one_lt", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.OrdConnected.mem_nhdsGE", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.OrdConnected.mem_nhdsGT", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.OrdConnected.mem_nhdsLE", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.OrdConnected.mem_nhdsLT", "kind": "theorem", "module": "Mathlib.Topology.Order.LeftRightNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isBounded_le_nhds", "kind": "theorem", "module": "Mathlib.Topology.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.isBoundedUnder_le", "kind": "theorem", "module": "Mathlib.Topology.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.bddAbove_range_of_cofinite", "kind": "theorem", "module": "Mathlib.Topology.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.bddAbove_range", "kind": "theorem", "module": "Mathlib.Topology.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCobounded_ge_nhds", "kind": "theorem", "module": "Mathlib.Topology.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.isCoboundedUnder_ge", "kind": "theorem", "module": "Mathlib.Topology.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instBoundedGENhdsClassOrderDual", "kind": "instance", "module": "Mathlib.Topology.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instBoundedLENhdsClass", "kind": "instance", "module": "Mathlib.Topology.Order.LiminfLimsup", "is_tactic_proof": true, "tactics": ["refine", "obtain", "obtain", "rw", "exact"], "tactic_count": 5}
{"name": "Pi.instBoundedLENhdsClass", "kind": "instance", "module": "Mathlib.Topology.Order.LiminfLimsup", "is_tactic_proof": true, "tactics": ["refine", "rw", "choose", "exact"], "tactic_count": 4}
{"name": "isBounded_ge_nhds", "kind": "theorem", "module": "Mathlib.Topology.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.isBoundedUnder_ge", "kind": "theorem", "module": "Mathlib.Topology.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.bddBelow_range_of_cofinite", "kind": "theorem", "module": "Mathlib.Topology.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.bddBelow_range", "kind": "theorem", "module": "Mathlib.Topology.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCobounded_le_nhds", "kind": "theorem", "module": "Mathlib.Topology.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.isCoboundedUnder_le", "kind": "theorem", "module": "Mathlib.Topology.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instBoundedLENhdsClassOrderDual", "kind": "instance", "module": "Mathlib.Topology.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.instBoundedGENhdsClass", "kind": "instance", "module": "Mathlib.Topology.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instBoundedGENhdsClass", "kind": "instance", "module": "Mathlib.Topology.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderTop.to_BoundedLENhdsClass", "kind": "instance", "module": "Mathlib.Topology.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderBot.to_BoundedGENhdsClass", "kind": "instance", "module": "Mathlib.Topology.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedLENhdsClass.of_closedIciTopology", "kind": "instance", "module": "Mathlib.Topology.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BoundedGENhdsClass.of_closedIicTopology", "kind": "instance", "module": "Mathlib.Topology.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_nhds_of_limsSup_eq_limsInf", "kind": "theorem", "module": "Mathlib.Topology.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "limsSup_nhds", "kind": "theorem", "module": "Mathlib.Topology.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "limsInf_nhds", "kind": "theorem", "module": "Mathlib.Topology.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "limsInf_eq_of_le_nhds", "kind": "theorem", "module": "Mathlib.Topology.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "limsSup_eq_of_le_nhds", "kind": "theorem", "module": "Mathlib.Topology.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.limsup_eq", "kind": "theorem", "module": "Mathlib.Topology.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.liminf_eq", "kind": "theorem", "module": "Mathlib.Topology.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "limsup_eq_bot", "kind": "theorem", "module": "Mathlib.Topology.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "liminf_eq_top", "kind": "theorem", "module": "Mathlib.Topology.Order.LiminfLimsup", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMinOn", "kind": "definition", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMaxOn", "kind": "definition", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalExtrOn", "kind": "definition", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMin", "kind": "definition", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMax", "kind": "definition", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalExtr", "kind": "definition", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalExtrOn.elim", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalExtr.elim", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMin.on", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMax.on", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalExtr.on", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMinOn.on_subset", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMaxOn.on_subset", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalExtrOn.on_subset", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMinOn.inter", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMaxOn.inter", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalExtrOn.inter", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMinOn.localize", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMaxOn.localize", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsExtrOn.localize", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMinOn.isLocalMin", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMaxOn.isLocalMax", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalExtrOn.isLocalExtr", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLocalMinOn_univ_iff", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "isLocalMaxOn_univ_iff", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "isLocalExtrOn_univ_iff", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMinOn.isLocalMin", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsMaxOn.isLocalMax", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsExtrOn.isLocalExtr", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMinOn.not_nhds_le_map", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMaxOn.not_nhds_le_map", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalExtrOn.not_nhds_le_map", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLocalMinOn_const", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLocalMaxOn_const", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLocalExtrOn_const", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLocalMin_const", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLocalMax_const", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLocalExtr_const", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMin.comp_mono", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMax.comp_mono", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalExtr.comp_mono", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMin.comp_antitone", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMax.comp_antitone", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalExtr.comp_antitone", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMinOn.comp_mono", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMaxOn.comp_mono", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalExtrOn.comp_mono", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMinOn.comp_antitone", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMaxOn.comp_antitone", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalExtrOn.comp_antitone", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMin.bicomp_mono", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMax.bicomp_mono", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMinOn.bicomp_mono", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMaxOn.bicomp_mono", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMin.comp_continuous", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMax.comp_continuous", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalExtr.comp_continuous", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMin.comp_continuousOn", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMax.comp_continuousOn", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalExtr.comp_continuousOn", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMinOn.comp_continuousOn", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMaxOn.comp_continuousOn", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalExtrOn.comp_continuousOn", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMin.add", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMax.add", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMinOn.add", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMaxOn.add", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMin.neg", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMax.neg", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalExtr.neg", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMinOn.neg", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMaxOn.neg", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalExtrOn.neg", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMin.sub", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMax.sub", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMinOn.sub", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMaxOn.sub", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMin.sup", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMax.sup", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMinOn.sup", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMaxOn.sup", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMin.inf", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMax.inf", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMinOn.inf", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMaxOn.inf", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMin.min", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMax.min", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMinOn.min", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMaxOn.min", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMin.max", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMax.max", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMinOn.max", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMaxOn.max", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyLE.isLocalMaxOn", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMaxOn.congr", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.isLocalMaxOn_iff", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyLE.isLocalMinOn", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMinOn.congr", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.isLocalMinOn_iff", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalExtrOn.congr", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.isLocalExtrOn_iff", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyLE.isLocalMax", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMax.congr", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.isLocalMax_iff", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyLE.isLocalMin", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalMin.congr", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.isLocalMin_iff", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocalExtr.congr", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.EventuallyEq.isLocalExtr_iff", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLocalMax_of_mono_anti'", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLocalMin_of_anti_mono'", "kind": "theorem", "module": "Mathlib.Topology.Order.LocalExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.lower", "kind": "definition", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.upper", "kind": "definition", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithLower", "kind": "definition", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithLower.toLower", "kind": "definition", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithLower.ofLower", "kind": "definition", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithLower.toLower_symm", "kind": "theorem", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithLower.ofLower_symm", "kind": "theorem", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithLower.toLower_ofLower", "kind": "theorem", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithLower.ofLower_toLower", "kind": "theorem", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithLower.toLower_inj", "kind": "theorem", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithLower.ofLower_inj", "kind": "theorem", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithLower.rec", "kind": "definition", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithLower.instNonempty", "kind": "instance", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithLower.instInhabited", "kind": "instance", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithLower.instPreorder", "kind": "instance", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithLower.instTopologicalSpace", "kind": "instance", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithLower.toLower_le_toLower", "kind": "theorem", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithLower.toLower_lt_toLower", "kind": "theorem", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithLower.ofLower_le_ofLower", "kind": "theorem", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithLower.ofLower_lt_ofLower", "kind": "theorem", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithLower.isOpen_preimage_ofLower", "kind": "theorem", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithLower.isOpen_def", "kind": "theorem", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithLower.continuous_toLower", "kind": "theorem", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithLower.instPartialOrder", "kind": "instance", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithLower.instLinearOrder", "kind": "instance", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithUpper", "kind": "definition", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithUpper.toUpper", "kind": "definition", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithUpper.ofUpper", "kind": "definition", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithUpper.toUpper_symm", "kind": "theorem", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithUpper.ofUpper_symm", "kind": "theorem", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithUpper.toUpper_ofUpper", "kind": "theorem", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithUpper.ofUpper_toUpper", "kind": "theorem", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithUpper.toUpper_inj", "kind": "theorem", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithUpper.ofUpper_inj", "kind": "theorem", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithUpper.rec", "kind": "definition", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithUpper.instNonempty", "kind": "instance", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithUpper.instInhabited", "kind": "instance", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithUpper.instPreorder", "kind": "instance", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithUpper.instTopologicalSpace", "kind": "instance", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithUpper.toUpper_le_toUpper", "kind": "theorem", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithUpper.toUpper_lt_toUpper", "kind": "theorem", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithUpper.ofUpper_le_ofUpper", "kind": "theorem", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithUpper.ofUpper_lt_ofUpper", "kind": "theorem", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithUpper.isOpen_preimage_ofUpper", "kind": "theorem", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithUpper.isOpen_def", "kind": "theorem", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithUpper.continuous_toUpper", "kind": "theorem", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithUpper.instPartialOrder", "kind": "instance", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithUpper.instLinearOrder", "kind": "instance", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.instIsLowerWithLower", "kind": "instance", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.instIsUpperWithUpper", "kind": "instance", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithLower.toDualHomeomorph", "kind": "definition", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsLower.lowerBasis", "kind": "definition", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsLower.topology_eq", "kind": "theorem", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsLower.withLowerHomeomorph", "kind": "definition", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsLower.isOpen_iff_generate_Ici_compl", "kind": "theorem", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "OrderDual.instIsUpper", "kind": "instance", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsLower.instClosedIciTopology", "kind": "instance", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsLower.isClosed_upperClosure", "kind": "theorem", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Topology.IsLower.isLowerSet_of_isOpen", "kind": "theorem", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": true, "tactics": ["replace", "induction", "basic", "univ", "inter", "sUnion"], "tactic_count": 6}
{"name": "Topology.IsLower.isUpperSet_of_isClosed", "kind": "theorem", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsLower.tendsto_nhds_iff_not_le", "kind": "theorem", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Topology.IsLower.closure_singleton", "kind": "theorem", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsLower.isTopologicalBasis", "kind": "theorem", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": true, "tactics": ["convert", "simp_rw", "ext", "constructor", "rintro", "refine", "simp", "rintro", "haveI", "rw", "choose", "exact"], "tactic_count": 12}
{"name": "Topology.IsLower.continuous_iff_Ici", "kind": "theorem", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": true, "tactics": ["obtain", "simp"], "tactic_count": 2}
{"name": "Topology.IsLower.t0Space", "kind": "instance", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsLower.isTopologicalBasis_insert_univ_subbasis", "kind": "theorem", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsLower.tendsto_nhds_iff_lt", "kind": "theorem", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Topology.IsLower.isTopologicalSpace_basis", "kind": "theorem", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": true, "tactics": ["by_cases", "simp", "refine", "intro", "apply", "convert", "constructor", "intro", "use", "constructor", "apply", "use", "rw", "intro", "have", "by_contra", "apply", "rw", "exact", "use", "rw", "apply", "intro", "simp", "intro", "obtain", "subst", "simp_all", "intro", "rw", "intro", "simp", "rw", "exact"], "tactic_count": 34}
{"name": "Topology.IsUpper.upperBasis", "kind": "definition", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsUpper.topology_eq", "kind": "theorem", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsUpper.withUpperHomeomorph", "kind": "definition", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsUpper.isOpen_iff_generate_Iic_compl", "kind": "theorem", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "OrderDual.instIsLower", "kind": "instance", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsUpper.instClosedIicTopology", "kind": "instance", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsUpper.isClosed_lowerClosure", "kind": "theorem", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsUpper.isUpperSet_of_isOpen", "kind": "theorem", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsUpper.isLowerSet_of_isClosed", "kind": "theorem", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsUpper.tendsto_nhds_iff_not_le", "kind": "theorem", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsUpper.closure_singleton", "kind": "theorem", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsUpper.isTopologicalBasis", "kind": "theorem", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsUpper.continuous_iff_Iic", "kind": "theorem", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsUpper.t0Space", "kind": "instance", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsUpper.isTopologicalBasis_insert_univ_subbasis", "kind": "theorem", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsUpper.tendsto_nhds_iff_lt", "kind": "theorem", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsUpper.isTopologicalSpace_basis", "kind": "theorem", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.instIsLowerProd", "kind": "instance", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.instIsUpperProd", "kind": "instance", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sInfHom.continuous", "kind": "theorem", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": true, "tactics": ["refine", "convert", "refine", "refine", "simp"], "tactic_count": 5}
{"name": "Topology.IsLower.toContinuousInf", "kind": "instance", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sSupHom.continuous", "kind": "theorem", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsUpper.toContinuousInf", "kind": "instance", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.isUpper_orderDual", "kind": "theorem", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": true, "tactics": ["constructor", "apply", "apply"], "tactic_count": 3}
{"name": "Topology.isLower_orderDual", "kind": "theorem", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsUpperProp", "kind": "instance", "module": "Mathlib.Topology.Order.LowerUpperTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonotoneOn.insert_of_continuousWithinAt", "kind": "theorem", "module": "Mathlib.Topology.Order.Monotone", "is_tactic_proof": true, "tactics": ["have", "apply", "rcases", "exact", "simp", "apply", "have", "filter_upwards", "rcases", "exact", "simp", "apply", "have", "filter_upwards", "exact"], "tactic_count": 15}
{"name": "MonotoneOn.countable_setOf_two_preimages", "kind": "theorem", "module": "Mathlib.Topology.Order.Monotone", "is_tactic_proof": true, "tactics": ["nontriviality", "let", "have", "choose", "let", "suffices", "have", "intro", "have", "rwa", "exact", "apply", "rintro", "rw", "exact", "simp", "intro", "wlog", "apply", "have", "order", "simp", "rintro", "rw", "have", "have", "rw", "exact"], "tactic_count": 28}
{"name": "Monotone.countable_setOf_two_preimages", "kind": "theorem", "module": "Mathlib.Topology.Order.Monotone", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "AntitoneOn.countable_setOf_two_preimages", "kind": "theorem", "module": "Mathlib.Topology.Order.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.countable_setOf_two_preimages", "kind": "theorem", "module": "Mathlib.Topology.Order.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonotoneOn.countable_not_continuousWithinAt_Ioi", "kind": "theorem", "module": "Mathlib.Topology.Order.Monotone", "is_tactic_proof": true, "tactics": ["apply", "rintro", "dsimp", "contrapose", "refine", "filter_upwards", "exact", "rcases", "have", "simp", "filter_upwards", "exact"], "tactic_count": 12}
{"name": "MonotoneOn.countable_not_continuousWithinAt_Iio", "kind": "theorem", "module": "Mathlib.Topology.Order.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonotoneOn.countable_not_continuousWithinAt", "kind": "theorem", "module": "Mathlib.Topology.Order.Monotone", "is_tactic_proof": true, "tactics": ["apply", "refine", "simp", "rintro", "simp", "intro", "exact"], "tactic_count": 7}
{"name": "Monotone.countable_not_continuousAt", "kind": "theorem", "module": "Mathlib.Topology.Order.Monotone", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "AntitoneOn.countable_not_continuousWithinAt", "kind": "theorem", "module": "Mathlib.Topology.Order.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.countable_not_continuousAt", "kind": "theorem", "module": "Mathlib.Topology.Order.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sSup_mem_closure", "kind": "theorem", "module": "Mathlib.Topology.Order.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "sInf_mem_closure", "kind": "theorem", "module": "Mathlib.Topology.Order.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.sSup_mem", "kind": "theorem", "module": "Mathlib.Topology.Order.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.sInf_mem", "kind": "theorem", "module": "Mathlib.Topology.Order.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonotoneOn.map_sSup_of_continuousWithinAt", "kind": "theorem", "module": "Mathlib.Topology.Order.Monotone", "is_tactic_proof": true, "tactics": ["rcases", "simp", "exact"], "tactic_count": 3}
{"name": "Monotone.map_sSup_of_continuousAt", "kind": "theorem", "module": "Mathlib.Topology.Order.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.map_iSup_of_continuousAt", "kind": "theorem", "module": "Mathlib.Topology.Order.Monotone", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "MonotoneOn.map_sInf_of_continuousWithinAt", "kind": "theorem", "module": "Mathlib.Topology.Order.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.map_sInf_of_continuousAt", "kind": "theorem", "module": "Mathlib.Topology.Order.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.map_iInf_of_continuousAt", "kind": "theorem", "module": "Mathlib.Topology.Order.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntitoneOn.map_sSup_of_continuousWithinAt", "kind": "theorem", "module": "Mathlib.Topology.Order.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.map_sSup_of_continuousAt", "kind": "theorem", "module": "Mathlib.Topology.Order.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.map_iSup_of_continuousAt", "kind": "theorem", "module": "Mathlib.Topology.Order.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntitoneOn.map_sInf_of_continuousWithinAt", "kind": "theorem", "module": "Mathlib.Topology.Order.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.map_sInf_of_continuousAt", "kind": "theorem", "module": "Mathlib.Topology.Order.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.map_iInf_of_continuousAt", "kind": "theorem", "module": "Mathlib.Topology.Order.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csSup_mem_closure", "kind": "theorem", "module": "Mathlib.Topology.Order.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "csInf_mem_closure", "kind": "theorem", "module": "Mathlib.Topology.Order.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.csSup_mem", "kind": "theorem", "module": "Mathlib.Topology.Order.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.csInf_mem", "kind": "theorem", "module": "Mathlib.Topology.Order.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.isLeast_csInf", "kind": "theorem", "module": "Mathlib.Topology.Order.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.isGreatest_csSup", "kind": "theorem", "module": "Mathlib.Topology.Order.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MonotoneOn.tendsto_nhdsWithin_Ioo_left", "kind": "theorem", "module": "Mathlib.Topology.Order.Monotone", "is_tactic_proof": true, "tactics": ["refine", "obtain", "simpa", "filter_upwards", "exact", "rcases", "filter_upwards", "exact"], "tactic_count": 8}
{"name": "MonotoneOn.tendsto_nhdsWithin_Ioo_right", "kind": "theorem", "module": "Mathlib.Topology.Order.Monotone", "is_tactic_proof": true, "tactics": ["refine", "rcases", "filter_upwards", "exact", "obtain", "simpa", "filter_upwards", "exact"], "tactic_count": 8}
{"name": "MonotoneOn.tendsto_nhdsLT", "kind": "theorem", "module": "Mathlib.Topology.Order.Monotone", "is_tactic_proof": true, "tactics": ["rcases", "refine", "obtain", "simpa", "filter_upwards", "refine", "exact"], "tactic_count": 7}
{"name": "MonotoneOn.tendsto_nhdsGT", "kind": "theorem", "module": "Mathlib.Topology.Order.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.tendsto_nhdsLT", "kind": "theorem", "module": "Mathlib.Topology.Order.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.tendsto_nhdsGT", "kind": "theorem", "module": "Mathlib.Topology.Order.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntitoneOn.tendsto_nhdsWithin_Ioo_left", "kind": "theorem", "module": "Mathlib.Topology.Order.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntitoneOn.tendsto_nhdsWithin_Ioo_right", "kind": "theorem", "module": "Mathlib.Topology.Order.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntitoneOn.tendsto_nhdsLT", "kind": "theorem", "module": "Mathlib.Topology.Order.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "AntitoneOn.tendsto_nhdsGT", "kind": "theorem", "module": "Mathlib.Topology.Order.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.tendsto_nhdsLT", "kind": "theorem", "module": "Mathlib.Topology.Order.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.tendsto_nhdsGT", "kind": "theorem", "module": "Mathlib.Topology.Order.Monotone", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMonoOn.continuousWithinAt_right_of_exists_between", "kind": "theorem", "module": "Mathlib.Topology.Order.MonotoneContinuity", "is_tactic_proof": true, "tactics": ["have", "refine", "filter_upwards", "hb.trans_le", "rcases", "rw", "filter_upwards", "rintro", "exact"], "tactic_count": 9}
{"name": "continuousWithinAt_right_of_monotoneOn_of_exists_between", "kind": "theorem", "module": "Mathlib.Topology.Order.MonotoneContinuity", "is_tactic_proof": true, "tactics": ["have", "refine", "filter_upwards", "rcases", "have", "filter_upwards", "rintro", "exact"], "tactic_count": 8}
{"name": "continuousWithinAt_right_of_monotoneOn_of_closure_image_mem_nhdsWithin", "kind": "theorem", "module": "Mathlib.Topology.Order.MonotoneContinuity", "is_tactic_proof": true, "tactics": ["refine", "rcases", "rcases", "rcases", "exact"], "tactic_count": 5}
{"name": "continuousWithinAt_right_of_monotoneOn_of_image_mem_nhdsWithin", "kind": "theorem", "module": "Mathlib.Topology.Order.MonotoneContinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMonoOn.continuousWithinAt_right_of_closure_image_mem_nhdsWithin", "kind": "theorem", "module": "Mathlib.Topology.Order.MonotoneContinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMonoOn.continuousWithinAt_right_of_image_mem_nhdsWithin", "kind": "theorem", "module": "Mathlib.Topology.Order.MonotoneContinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMonoOn.continuousWithinAt_right_of_surjOn", "kind": "theorem", "module": "Mathlib.Topology.Order.MonotoneContinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMonoOn.continuousWithinAt_left_of_exists_between", "kind": "theorem", "module": "Mathlib.Topology.Order.MonotoneContinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousWithinAt_left_of_monotoneOn_of_exists_between", "kind": "theorem", "module": "Mathlib.Topology.Order.MonotoneContinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousWithinAt_left_of_monotoneOn_of_closure_image_mem_nhdsWithin", "kind": "theorem", "module": "Mathlib.Topology.Order.MonotoneContinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousWithinAt_left_of_monotoneOn_of_image_mem_nhdsWithin", "kind": "theorem", "module": "Mathlib.Topology.Order.MonotoneContinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMonoOn.continuousWithinAt_left_of_closure_image_mem_nhdsWithin", "kind": "theorem", "module": "Mathlib.Topology.Order.MonotoneContinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMonoOn.continuousWithinAt_left_of_image_mem_nhdsWithin", "kind": "theorem", "module": "Mathlib.Topology.Order.MonotoneContinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMonoOn.continuousWithinAt_left_of_surjOn", "kind": "theorem", "module": "Mathlib.Topology.Order.MonotoneContinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMonoOn.continuousAt_of_exists_between", "kind": "theorem", "module": "Mathlib.Topology.Order.MonotoneContinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMonoOn.continuousAt_of_closure_image_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Order.MonotoneContinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StrictMonoOn.continuousAt_of_image_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Order.MonotoneContinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousAt_of_monotoneOn_of_exists_between", "kind": "theorem", "module": "Mathlib.Topology.Order.MonotoneContinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousAt_of_monotoneOn_of_closure_image_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Order.MonotoneContinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousAt_of_monotoneOn_of_image_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Order.MonotoneContinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.continuous_of_denseRange", "kind": "theorem", "module": "Mathlib.Topology.Order.MonotoneContinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.continuous_of_surjective", "kind": "theorem", "module": "Mathlib.Topology.Order.MonotoneContinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.continuous", "kind": "theorem", "module": "Mathlib.Topology.Order.MonotoneContinuity", "is_tactic_proof": true, "tactics": ["rw", "rintro", "rw", "apply", "rw", "apply"], "tactic_count": 6}
{"name": "OrderIso.instHomeomorphClass", "kind": "instance", "module": "Mathlib.Topology.Order.MonotoneContinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.toHomeomorph", "kind": "abbrev", "module": "Mathlib.Topology.Order.MonotoneContinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.coe_toHomeomorph", "kind": "theorem", "module": "Mathlib.Topology.Order.MonotoneContinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderIso.coe_toHomeomorph_symm", "kind": "theorem", "module": "Mathlib.Topology.Order.MonotoneContinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.supConvergenceClass", "kind": "instance", "module": "Mathlib.Topology.Order.MonotoneConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.infConvergenceClass", "kind": "instance", "module": "Mathlib.Topology.Order.MonotoneConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LinearOrder.supConvergenceClass", "kind": "instance", "module": "Mathlib.Topology.Order.MonotoneConvergence", "is_tactic_proof": true, "tactics": ["refine", "rcases", "lift", "exact", "exact"], "tactic_count": 5}
{"name": "LinearOrder.infConvergenceClass", "kind": "instance", "module": "Mathlib.Topology.Order.MonotoneConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_atTop_isLUB", "kind": "theorem", "module": "Mathlib.Topology.Order.MonotoneConvergence", "is_tactic_proof": false, "tactics": ["suffices", "exact"], "tactic_count": 2}
{"name": "tendsto_atBot_isLUB", "kind": "theorem", "module": "Mathlib.Topology.Order.MonotoneConvergence", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "tendsto_atBot_isGLB", "kind": "theorem", "module": "Mathlib.Topology.Order.MonotoneConvergence", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "tendsto_atTop_isGLB", "kind": "theorem", "module": "Mathlib.Topology.Order.MonotoneConvergence", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "tendsto_atTop_ciSup", "kind": "theorem", "module": "Mathlib.Topology.Order.MonotoneConvergence", "is_tactic_proof": true, "tactics": ["cases", "exacts"], "tactic_count": 2}
{"name": "tendsto_atBot_ciSup", "kind": "theorem", "module": "Mathlib.Topology.Order.MonotoneConvergence", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "tendsto_atBot_ciInf", "kind": "theorem", "module": "Mathlib.Topology.Order.MonotoneConvergence", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "tendsto_atTop_ciInf", "kind": "theorem", "module": "Mathlib.Topology.Order.MonotoneConvergence", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "tendsto_atTop_iSup", "kind": "theorem", "module": "Mathlib.Topology.Order.MonotoneConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_atBot_iSup", "kind": "theorem", "module": "Mathlib.Topology.Order.MonotoneConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_atBot_iInf", "kind": "theorem", "module": "Mathlib.Topology.Order.MonotoneConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_atTop_iInf", "kind": "theorem", "module": "Mathlib.Topology.Order.MonotoneConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.supConvergenceClass", "kind": "instance", "module": "Mathlib.Topology.Order.MonotoneConvergence", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "rw", "have", "have", "exact"], "tactic_count": 6}
{"name": "instInfConvergenceClassProd", "kind": "instance", "module": "Mathlib.Topology.Order.MonotoneConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.supConvergenceClass", "kind": "instance", "module": "Mathlib.Topology.Order.MonotoneConvergence", "is_tactic_proof": true, "tactics": ["refine", "simp", "exact"], "tactic_count": 3}
{"name": "Pi.infConvergenceClass", "kind": "instance", "module": "Mathlib.Topology.Order.MonotoneConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.supConvergenceClass'", "kind": "instance", "module": "Mathlib.Topology.Order.MonotoneConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.infConvergenceClass'", "kind": "instance", "module": "Mathlib.Topology.Order.MonotoneConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_atTop_of_monotone", "kind": "theorem", "module": "Mathlib.Topology.Order.MonotoneConvergence", "is_tactic_proof": true, "tactics": ["classical", "exact"], "tactic_count": 2}
{"name": "tendsto_atTop_of_antitone", "kind": "theorem", "module": "Mathlib.Topology.Order.MonotoneConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_atBot_of_monotone", "kind": "theorem", "module": "Mathlib.Topology.Order.MonotoneConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_atBot_of_antitone", "kind": "theorem", "module": "Mathlib.Topology.Order.MonotoneConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_iff_tendsto_subseq_of_monotone", "kind": "theorem", "module": "Mathlib.Topology.Order.MonotoneConvergence", "is_tactic_proof": true, "tactics": ["constructor", "exact", "rcases", "exact", "rwa"], "tactic_count": 5}
{"name": "tendsto_iff_tendsto_subseq_of_antitone", "kind": "theorem", "module": "Mathlib.Topology.Order.MonotoneConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.ge_of_tendsto", "kind": "theorem", "module": "Mathlib.Topology.Order.MonotoneConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.le_of_tendsto", "kind": "theorem", "module": "Mathlib.Topology.Order.MonotoneConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.le_of_tendsto", "kind": "theorem", "module": "Mathlib.Topology.Order.MonotoneConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.ge_of_tendsto", "kind": "theorem", "module": "Mathlib.Topology.Order.MonotoneConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLUB_of_tendsto_atTop", "kind": "theorem", "module": "Mathlib.Topology.Order.MonotoneConvergence", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "exact", "exact"], "tactic_count": 4}
{"name": "isGLB_of_tendsto_atBot", "kind": "theorem", "module": "Mathlib.Topology.Order.MonotoneConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLUB_of_tendsto_atBot", "kind": "theorem", "module": "Mathlib.Topology.Order.MonotoneConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isGLB_of_tendsto_atTop", "kind": "theorem", "module": "Mathlib.Topology.Order.MonotoneConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_eq_of_tendsto", "kind": "theorem", "module": "Mathlib.Topology.Order.MonotoneConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iInf_eq_of_tendsto", "kind": "theorem", "module": "Mathlib.Topology.Order.MonotoneConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_eq_iSup_subseq_of_monotone", "kind": "theorem", "module": "Mathlib.Topology.Order.MonotoneConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_eq_iSup_subseq_of_antitone", "kind": "theorem", "module": "Mathlib.Topology.Order.MonotoneConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iInf_eq_iInf_subseq_of_monotone", "kind": "theorem", "module": "Mathlib.Topology.Order.MonotoneConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iInf_eq_iInf_subseq_of_antitone", "kind": "theorem", "module": "Mathlib.Topology.Order.MonotoneConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsSet_Ioi", "kind": "theorem", "module": "Mathlib.Topology.Order.NhdsSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsSet_Iio", "kind": "theorem", "module": "Mathlib.Topology.Order.NhdsSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsSet_Ioo", "kind": "theorem", "module": "Mathlib.Topology.Order.NhdsSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsSet_Ici", "kind": "theorem", "module": "Mathlib.Topology.Order.NhdsSet", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "nhdsSet_Iic", "kind": "theorem", "module": "Mathlib.Topology.Order.NhdsSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsSet_Ico", "kind": "theorem", "module": "Mathlib.Topology.Order.NhdsSet", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "nhdsSet_Ioc", "kind": "theorem", "module": "Mathlib.Topology.Order.NhdsSet", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "nhdsSet_Icc", "kind": "theorem", "module": "Mathlib.Topology.Order.NhdsSet", "is_tactic_proof": true, "tactics": ["rcases", "simp", "rw"], "tactic_count": 3}
{"name": "Ioi_mem_nhdsSet_Ici_iff", "kind": "theorem", "module": "Mathlib.Topology.Order.NhdsSet", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ici_mem_nhdsSet_Ici", "kind": "theorem", "module": "Mathlib.Topology.Order.NhdsSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Iio_mem_nhdsSet_Iic_iff", "kind": "theorem", "module": "Mathlib.Topology.Order.NhdsSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Iic_mem_nhdsSet_Iic", "kind": "theorem", "module": "Mathlib.Topology.Order.NhdsSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ioi_mem_nhdsSet_Icc", "kind": "theorem", "module": "Mathlib.Topology.Order.NhdsSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ici_mem_nhdsSet_Icc", "kind": "theorem", "module": "Mathlib.Topology.Order.NhdsSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Iio_mem_nhdsSet_Icc", "kind": "theorem", "module": "Mathlib.Topology.Order.NhdsSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Iic_mem_nhdsSet_Icc", "kind": "theorem", "module": "Mathlib.Topology.Order.NhdsSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ioo_mem_nhdsSet_Icc", "kind": "theorem", "module": "Mathlib.Topology.Order.NhdsSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ico_mem_nhdsSet_Icc", "kind": "theorem", "module": "Mathlib.Topology.Order.NhdsSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ioc_mem_nhdsSet_Icc", "kind": "theorem", "module": "Mathlib.Topology.Order.NhdsSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Icc_mem_nhdsSet_Icc", "kind": "theorem", "module": "Mathlib.Topology.Order.NhdsSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ici_mem_nhdsSet_Ico", "kind": "theorem", "module": "Mathlib.Topology.Order.NhdsSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ioi_mem_nhdsSet_Ico", "kind": "theorem", "module": "Mathlib.Topology.Order.NhdsSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Iio_mem_nhdsSet_Ico", "kind": "theorem", "module": "Mathlib.Topology.Order.NhdsSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Iic_mem_nhdsSet_Ico", "kind": "theorem", "module": "Mathlib.Topology.Order.NhdsSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ioo_mem_nhdsSet_Ico", "kind": "theorem", "module": "Mathlib.Topology.Order.NhdsSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Icc_mem_nhdsSet_Ico", "kind": "theorem", "module": "Mathlib.Topology.Order.NhdsSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ioc_mem_nhdsSet_Ico", "kind": "theorem", "module": "Mathlib.Topology.Order.NhdsSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ico_mem_nhdsSet_Ico", "kind": "theorem", "module": "Mathlib.Topology.Order.NhdsSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ioi_mem_nhdsSet_Ioc", "kind": "theorem", "module": "Mathlib.Topology.Order.NhdsSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Iio_mem_nhdsSet_Ioc", "kind": "theorem", "module": "Mathlib.Topology.Order.NhdsSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ici_mem_nhdsSet_Ioc", "kind": "theorem", "module": "Mathlib.Topology.Order.NhdsSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Iic_mem_nhdsSet_Ioc", "kind": "theorem", "module": "Mathlib.Topology.Order.NhdsSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ioo_mem_nhdsSet_Ioc", "kind": "theorem", "module": "Mathlib.Topology.Order.NhdsSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Icc_mem_nhdsSet_Ioc", "kind": "theorem", "module": "Mathlib.Topology.Order.NhdsSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ioc_mem_nhdsSet_Ioc", "kind": "theorem", "module": "Mathlib.Topology.Order.NhdsSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ico_mem_nhdsSet_Ioc", "kind": "theorem", "module": "Mathlib.Topology.Order.NhdsSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasBasis_nhdsSet_Iic_Iio", "kind": "theorem", "module": "Mathlib.Topology.Order.NhdsSet", "is_tactic_proof": true, "tactics": ["refine", "rw", "rcases", "exact"], "tactic_count": 4}
{"name": "hasBasis_nhdsSet_Iic_Iic", "kind": "theorem", "module": "Mathlib.Topology.Order.NhdsSet", "is_tactic_proof": true, "tactics": ["have", "refine", "simpa"], "tactic_count": 3}
{"name": "Iic_mem_nhdsSet_Iic_iff", "kind": "theorem", "module": "Mathlib.Topology.Order.NhdsSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasBasis_nhdsSet_Ici_Ioi", "kind": "theorem", "module": "Mathlib.Topology.Order.NhdsSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasBasis_nhdsSet_Ici_Ici", "kind": "theorem", "module": "Mathlib.Topology.Order.NhdsSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ici_mem_nhdsSet_Ici_iff", "kind": "theorem", "module": "Mathlib.Topology.Order.NhdsSet", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instFirstCountableTopologyOrderDual", "kind": "instance", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instSecondCountableTopologyOrderDual", "kind": "instance", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instSeparableSpaceOrderDual", "kind": "instance", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dense.orderDual", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddAbove.of_closure", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BddBelow.of_closure", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosed_Iic", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instClosedIciTopologyOrderDual", "kind": "instance", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "closure_Iic", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_of_tendsto_of_frequently", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_of_tendsto", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_of_tendsto'", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "upperBounds_closure", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bddAbove_closure", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "disjoint_nhds_atBot_iff", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rw", "exact", "simp", "rintro", "refine", "exact"], "tactic_count": 8}
{"name": "IsLUB.range_of_tendsto", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "disjoint_nhds_atBot", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "inf_nhds_atBot", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_tendsto_nhds_of_tendsto_atBot", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_tendsto_atBot_of_tendsto_nhds", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iSup_eq_of_forall_le_of_tendsto", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iUnion_Iic_eq_Iio_of_lt_of_tendsto", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": ["have", "rw", "rintro", "exact", "rw"], "tactic_count": 5}
{"name": "isOpen_Ioi", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "interior_Ioi", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ioi_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eventually_gt_nhds", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ici_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eventually_ge_nhds", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.eventually_const_lt", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.eventually_const_le", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dense.exists_gt", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dense.exists_ge", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dense.exists_ge'", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": true, "tactics": ["by_cases", "exact", "simp", "rcases", "exact"], "tactic_count": 5}
{"name": "Ioo_mem_nhdsLT", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Ioo_mem_nhdsLT_of_mem", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CovBy.nhdsLT", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PredOrder.nhdsLT", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": true, "tactics": [], "tactic_count": 0}
{"name": "PredOrder.nhdsGT_eq_nhdsNE", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PredOrder.nhdsGE_eq_nhds", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ico_mem_nhdsLT_of_mem", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ico_mem_nhdsLT", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ioc_mem_nhdsLT_of_mem", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ioc_mem_nhdsLT", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Icc_mem_nhdsLT_of_mem", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Icc_mem_nhdsLT", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsWithin_Ico_eq_nhdsLT", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsWithin_Ioo_eq_nhdsLT", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousWithinAt_Ico_iff_Iio", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "continuousWithinAt_Ioo_iff_Iio", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CovBy.nhdsLE", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PredOrder.nhdsLE", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Ioc_mem_nhdsLE", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ioo_mem_nhdsLE_of_mem", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ico_mem_nhdsLE_of_mem", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ioc_mem_nhdsLE_of_mem", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Icc_mem_nhdsLE_of_mem", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Icc_mem_nhdsLE", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsWithin_Icc_eq_nhdsLE", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsWithin_Ioc_eq_nhdsLE", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousWithinAt_Icc_iff_Iic", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "continuousWithinAt_Ioc_iff_Iic", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "isClosed_Ici", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instClosedIicTopologyOrderDual", "kind": "instance", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "closure_Ici", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ge_of_tendsto_of_frequently", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ge_of_tendsto", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ge_of_tendsto'", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lowerBounds_closure", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bddBelow_closure", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "disjoint_nhds_atTop_iff", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGLB.range_of_tendsto", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "disjoint_nhds_atTop", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inf_nhds_atTop", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_tendsto_nhds_of_tendsto_atTop", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "not_tendsto_atTop_of_tendsto_nhds", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iInf_eq_of_forall_le_of_tendsto", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iUnion_Ici_eq_Ioi_of_lt_of_tendsto", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpen_Iio", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "interior_Iio", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Iio_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eventually_lt_nhds", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Iic_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eventually_le_nhds", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.eventually_lt_const", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.eventually_le_const", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dense.exists_lt", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dense.exists_le", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dense.exists_le'", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ioo_mem_nhdsGT_of_mem", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ioo_mem_nhdsGT", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CovBy.nhdsGT", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SuccOrder.nhdsGT", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SuccOrder.nhdsLT_eq_nhdsNE", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SuccOrder.nhdsLE_eq_nhds", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ioc_mem_nhdsGT_of_mem", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ioc_mem_nhdsGT", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ico_mem_nhdsGT_of_mem", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ico_mem_nhdsGT", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Icc_mem_nhdsGT_of_mem", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Icc_mem_nhdsGT", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsWithin_Ioc_eq_nhdsGT", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsWithin_Ioo_eq_nhdsGT", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousWithinAt_Ioc_iff_Ioi", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "continuousWithinAt_Ioo_iff_Ioi", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CovBy.nhdsGE", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SuccOrder.nhdsGE", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ico_mem_nhdsGE", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ico_mem_nhdsGE_of_mem", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ioo_mem_nhdsGE_of_mem", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ioc_mem_nhdsGE_of_mem", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Icc_mem_nhdsGE_of_mem", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Icc_mem_nhdsGE", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsWithin_Icc_eq_nhdsGE", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsWithin_Ico_eq_nhdsGE", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousWithinAt_Icc_iff_Ici", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "continuousWithinAt_Ico_iff_Ici", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Subtype.instOrderClosedTopology", "kind": "instance", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosed_le_prod", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosed_le", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instClosedIicTopology", "kind": "instance", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instClosedIciTopology", "kind": "instance", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instOrderClosedTopologyOrderDual", "kind": "instance", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosed_Icc", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "closure_Icc", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_of_tendsto_of_tendsto_of_frequently", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_of_tendsto_of_tendsto", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_of_tendsto_of_tendsto'", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "closure_le_eq", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "closure_lt_subset_le", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.closure_le", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.isClosed_le", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_on_closure", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.epigraph", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.hypograph", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosed_monotoneOn", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": true, "tactics": ["simp", "intro", "have", "exact"], "tactic_count": 4}
{"name": "isClosed_monotone", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "isClosed_antitoneOn", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosed_antitone", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderClosedTopology.to_t2Space", "kind": "instance", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpen_lt", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "isOpen_lt_prod", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpen_Ioo", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "interior_Ioo", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ioo_subset_closure_interior", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Ioo_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ioc_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ico_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Icc_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteTopology.of_predOrder_succOrder", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "lt_subset_interior_le", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "frontier_le_subset_eq", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": true, "tactics": ["rw", "rintro", "refine", "convert"], "tactic_count": 4}
{"name": "frontier_Iic_subset", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "frontier_Ici_subset", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "frontier_lt_subset_eq", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "continuous_if_le", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": true, "tactics": ["refine", "rwa", "simp", "exact"], "tactic_count": 4}
{"name": "Continuous.if_le", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.eventually_lt", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.eventually_lt", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.min", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Continuous.max", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_min", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_max", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.max", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.min", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.max_right", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Filter.Tendsto.max_left", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Filter.tendsto_nhds_max_right", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "Filter.tendsto_nhds_max_left", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Filter.Tendsto.min_right", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.min_left", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_nhds_min_right", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.tendsto_nhds_min_left", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dense.exists_between", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dense.Ioi_eq_biUnion", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": true, "tactics": ["refine", "rcases", "exact"], "tactic_count": 3}
{"name": "Dense.Iio_eq_biUnion", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instOrderClosedTopologyProd", "kind": "instance", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instOrderClosedTopologyForall", "kind": "instance", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": true, "tactics": ["constructor", "simp", "exact"], "tactic_count": 3}
{"name": "Pi.orderClosedTopology'", "kind": "instance", "module": "Mathlib.Topology.Order.OrderClosed", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLocalMax_of_mono_anti", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosedExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLocalMin_of_anti_mono", "kind": "theorem", "module": "Mathlib.Topology.Order.OrderClosedExtr", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.partialSups", "kind": "theorem", "module": "Mathlib.Topology.Order.PartialSups", "is_tactic_proof": true, "tactics": ["simp", "refine", "simpa"], "tactic_count": 3}
{"name": "Filter.Tendsto.partialSups_apply", "kind": "theorem", "module": "Mathlib.Topology.Order.PartialSups", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ContinuousAt.partialSups_apply", "kind": "theorem", "module": "Mathlib.Topology.Order.PartialSups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.partialSups", "kind": "theorem", "module": "Mathlib.Topology.Order.PartialSups", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ContinuousWithinAt.partialSups_apply", "kind": "theorem", "module": "Mathlib.Topology.Order.PartialSups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.partialSups", "kind": "theorem", "module": "Mathlib.Topology.Order.PartialSups", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "ContinuousOn.partialSups_apply", "kind": "theorem", "module": "Mathlib.Topology.Order.PartialSups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.partialSups", "kind": "theorem", "module": "Mathlib.Topology.Order.PartialSups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.partialSups_apply", "kind": "theorem", "module": "Mathlib.Topology.Order.PartialSups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.partialSups", "kind": "theorem", "module": "Mathlib.Topology.Order.PartialSups", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_isClopen_upper_of_not_le", "kind": "theorem", "module": "Mathlib.Topology.Order.Priestley", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_isClopen_lower_of_not_le", "kind": "theorem", "module": "Mathlib.Topology.Order.Priestley", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_isClopen_upper_or_lower_of_ne", "kind": "theorem", "module": "Mathlib.Topology.Order.Priestley", "is_tactic_proof": true, "tactics": ["obtain", "exact", "obtain", "exact"], "tactic_count": 4}
{"name": "PriestleySpace.toTotallySeparatedSpace", "kind": "instance", "module": "Mathlib.Topology.Order.Priestley", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.IccExtend", "kind": "theorem", "module": "Mathlib.Topology.Order.ProjIcc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_projIcc", "kind": "theorem", "module": "Mathlib.Topology.Order.ProjIcc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isQuotientMap_projIcc", "kind": "theorem", "module": "Mathlib.Topology.Order.ProjIcc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_IccExtend_iff", "kind": "theorem", "module": "Mathlib.Topology.Order.ProjIcc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.IccExtend", "kind": "theorem", "module": "Mathlib.Topology.Order.ProjIcc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.Icc_extend'", "kind": "theorem", "module": "Mathlib.Topology.Order.ProjIcc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.IccExtend", "kind": "theorem", "module": "Mathlib.Topology.Order.ProjIcc", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.instTopologicalSpace", "kind": "instance", "module": "Mathlib.Topology.Order.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.instOrderTopology", "kind": "instance", "module": "Mathlib.Topology.Order.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.instT5Space", "kind": "instance", "module": "Mathlib.Topology.Order.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.instT2Space", "kind": "instance", "module": "Mathlib.Topology.Order.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EReal.denseRange_ratCast", "kind": "theorem", "module": "Mathlib.Topology.Order.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.instTopologicalSpace", "kind": "instance", "module": "Mathlib.Topology.Order.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.instOrderTopology", "kind": "instance", "module": "Mathlib.Topology.Order.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.instT2Space", "kind": "instance", "module": "Mathlib.Topology.Order.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.instT5Space", "kind": "instance", "module": "Mathlib.Topology.Order.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ENNReal.instT4Space", "kind": "instance", "module": "Mathlib.Topology.Order.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_Ioo_extr_on_Icc", "kind": "theorem", "module": "Mathlib.Topology.Order.Rolle", "is_tactic_proof": false, "tactics": ["have", "nonempty_Icc.2", "obtain", "obtain", "by_cases", "by_cases", "have", "le_antisymm", "rcases", "refine", "simp", "refine", "exacts", "refine", "exacts"], "tactic_count": 15}
{"name": "exists_isLocalExtr_Ioo", "kind": "theorem", "module": "Mathlib.Topology.Order.Rolle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_isExtrOn_Ioo_of_tendsto", "kind": "theorem", "module": "Mathlib.Topology.Order.Rolle", "is_tactic_proof": true, "tactics": ["have", "obtain", "exists_Ioo_extr_on_Icc", "exact"], "tactic_count": 4}
{"name": "exists_isLocalExtr_Ioo_of_tendsto", "kind": "theorem", "module": "Mathlib.Topology.Order.Rolle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_uIoo_isExtrOn_uIcc", "kind": "theorem", "module": "Mathlib.Topology.Order.Rolle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_isLocalExtr_uIoo", "kind": "theorem", "module": "Mathlib.Topology.Order.Rolle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_isExtrOn_uIoo_of_tendsto", "kind": "theorem", "module": "Mathlib.Topology.Order.Rolle", "is_tactic_proof": true, "tactics": ["have", "obtain", "exists_uIoo_isExtrOn_uIcc", "exact"], "tactic_count": 4}
{"name": "exists_isLocalExtr_uIoo_of_tendsto", "kind": "theorem", "module": "Mathlib.Topology.Order.Rolle", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirSupInaccOn", "kind": "definition", "module": "Mathlib.Topology.Order.ScottTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirSupInacc", "kind": "definition", "module": "Mathlib.Topology.Order.ScottTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dirSupInaccOn_univ", "kind": "theorem", "module": "Mathlib.Topology.Order.ScottTopology", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DirSupInacc.dirSupInaccOn", "kind": "theorem", "module": "Mathlib.Topology.Order.ScottTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirSupInaccOn.mono", "kind": "theorem", "module": "Mathlib.Topology.Order.ScottTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirSupClosed", "kind": "definition", "module": "Mathlib.Topology.Order.ScottTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dirSupInacc_compl", "kind": "theorem", "module": "Mathlib.Topology.Order.ScottTopology", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "dirSupClosed_compl", "kind": "theorem", "module": "Mathlib.Topology.Order.ScottTopology", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "DirSupClosed.inter", "kind": "theorem", "module": "Mathlib.Topology.Order.ScottTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DirSupInacc.union", "kind": "theorem", "module": "Mathlib.Topology.Order.ScottTopology", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsUpperSet.dirSupClosed", "kind": "theorem", "module": "Mathlib.Topology.Order.ScottTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLowerSet.dirSupInacc", "kind": "theorem", "module": "Mathlib.Topology.Order.ScottTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dirSupClosed_Iic", "kind": "theorem", "module": "Mathlib.Topology.Order.ScottTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "dirSupInacc_iff_forall_sSup", "kind": "theorem", "module": "Mathlib.Topology.Order.ScottTopology", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "dirSupClosed_iff_forall_sSup", "kind": "theorem", "module": "Mathlib.Topology.Order.ScottTopology", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Topology.scottHausdorff", "kind": "definition", "module": "Mathlib.Topology.Order.ScottTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.instIsScottHausdorff", "kind": "instance", "module": "Mathlib.Topology.Order.ScottTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsScottHausdorff.topology_eq", "kind": "theorem", "module": "Mathlib.Topology.Order.ScottTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsScottHausdorff.isOpen_iff", "kind": "theorem", "module": "Mathlib.Topology.Order.ScottTopology", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Topology.IsScottHausdorff.dirSupInaccOn_of_isOpen", "kind": "theorem", "module": "Mathlib.Topology.Order.ScottTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsScottHausdorff.dirSupClosed_of_isClosed", "kind": "theorem", "module": "Mathlib.Topology.Order.ScottTopology", "is_tactic_proof": true, "tactics": ["apply", "rw", "exact"], "tactic_count": 3}
{"name": "Topology.IsScottHausdorff.isOpen_of_isLowerSet", "kind": "theorem", "module": "Mathlib.Topology.Order.ScottTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsScottHausdorff.isClosed_of_isUpperSet", "kind": "theorem", "module": "Mathlib.Topology.Order.ScottTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.scott", "kind": "definition", "module": "Mathlib.Topology.Order.ScottTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.upperSet_le_scott", "kind": "theorem", "module": "Mathlib.Topology.Order.ScottTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.scottHausdorff_le_scott", "kind": "theorem", "module": "Mathlib.Topology.Order.ScottTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsScott.topology_eq", "kind": "theorem", "module": "Mathlib.Topology.Order.ScottTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsScott.isOpen_iff_isUpperSet_and_scottHausdorff_open", "kind": "theorem", "module": "Mathlib.Topology.Order.ScottTopology", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Topology.IsScott.isOpen_iff_isUpperSet_and_dirSupInaccOn", "kind": "theorem", "module": "Mathlib.Topology.Order.ScottTopology", "is_tactic_proof": true, "tactics": ["rw", "refine", "and_congr_right", "obtain", "exact"], "tactic_count": 5}
{"name": "Topology.IsScott.isClosed_iff_isLowerSet_and_dirSupClosed", "kind": "theorem", "module": "Mathlib.Topology.Order.ScottTopology", "is_tactic_proof": true, "tactics": ["rw", "dirSupInacc_compl]"], "tactic_count": 2}
{"name": "Topology.IsScott.isUpperSet_of_isOpen", "kind": "theorem", "module": "Mathlib.Topology.Order.ScottTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsScott.isLowerSet_of_isClosed", "kind": "theorem", "module": "Mathlib.Topology.Order.ScottTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsScott.dirSupClosed_of_isClosed", "kind": "theorem", "module": "Mathlib.Topology.Order.ScottTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsScott.lowerClosure_subset_closure", "kind": "theorem", "module": "Mathlib.Topology.Order.ScottTopology", "is_tactic_proof": true, "tactics": ["convert", "rw", "infer_instance", "exact"], "tactic_count": 4}
{"name": "Topology.IsScott.instClosedIicTopologyOfUnivSet", "kind": "instance", "module": "Mathlib.Topology.Order.ScottTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsScott.closure_singleton", "kind": "theorem", "module": "Mathlib.Topology.Order.ScottTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsScott.monotone_of_continuous", "kind": "theorem", "module": "Mathlib.Topology.Order.ScottTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsScott.scottContinuousOn_iff_continuous", "kind": "theorem", "module": "Mathlib.Topology.Order.ScottTopology", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact", "image_inter_nonempty_iff.mp", "refine", "by_contra", "let", "have", "rw", "obtain", "simp", "exact"], "tactic_count": 12}
{"name": "Topology.IsScott.instT0Space", "kind": "instance", "module": "Mathlib.Topology.Order.ScottTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsScott.isOpen_iff_Iic_compl_or_univ", "kind": "theorem", "module": "Mathlib.Topology.Order.ScottTopology", "is_tactic_proof": true, "tactics": ["constructor", "intro", "rcases", "exact", "apply", "use", "rw", "exact", "rintro", "exact", "exact"], "tactic_count": 11}
{"name": "Topology.IsScott.scott_eq_upper_of_completeLinearOrder", "kind": "theorem", "module": "Mathlib.Topology.Order.ScottTopology", "is_tactic_proof": true, "tactics": ["letI", "ext", "rw", "letI", "rw"], "tactic_count": 5}
{"name": "Topology.IsScott.instUnivSetOfIsUpper", "kind": "instance", "module": "Mathlib.Topology.Order.ScottTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsScott.isOpen_iff_scottContinuous_mem", "kind": "theorem", "module": "Mathlib.Topology.Order.ScottTopology", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Topology.WithScott", "kind": "definition", "module": "Mathlib.Topology.Order.ScottTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithScott.toScott", "kind": "definition", "module": "Mathlib.Topology.Order.ScottTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithScott.ofScott", "kind": "definition", "module": "Mathlib.Topology.Order.ScottTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithScott.toScott_symm_eq", "kind": "theorem", "module": "Mathlib.Topology.Order.ScottTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithScott.ofScott_symm_eq", "kind": "theorem", "module": "Mathlib.Topology.Order.ScottTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithScott.toScott_ofScott", "kind": "theorem", "module": "Mathlib.Topology.Order.ScottTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithScott.ofScott_toScott", "kind": "theorem", "module": "Mathlib.Topology.Order.ScottTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithScott.toScott_inj", "kind": "theorem", "module": "Mathlib.Topology.Order.ScottTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithScott.ofScott_inj", "kind": "theorem", "module": "Mathlib.Topology.Order.ScottTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithScott.rec", "kind": "definition", "module": "Mathlib.Topology.Order.ScottTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithScott.instNonempty", "kind": "instance", "module": "Mathlib.Topology.Order.ScottTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithScott.instInhabited", "kind": "instance", "module": "Mathlib.Topology.Order.ScottTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithScott.instPreorder", "kind": "instance", "module": "Mathlib.Topology.Order.ScottTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithScott.instTopologicalSpace", "kind": "instance", "module": "Mathlib.Topology.Order.ScottTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithScott.instIsScottUnivSet", "kind": "instance", "module": "Mathlib.Topology.Order.ScottTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithScott.isOpen_iff_isUpperSet_and_scottHausdorff_open'", "kind": "theorem", "module": "Mathlib.Topology.Order.ScottTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.scottHausdorff_le_lower", "kind": "theorem", "module": "Mathlib.Topology.Order.ScottTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsScott.withScottHomeomorph", "kind": "definition", "module": "Mathlib.Topology.Order.ScottTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsScott.scottHausdorff_le", "kind": "theorem", "module": "Mathlib.Topology.Order.ScottTopology", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Topology.IsLower.scottHausdorff_le", "kind": "theorem", "module": "Mathlib.Topology.Order.ScottTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.ordConnectedComponent_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Order.T5", "is_tactic_proof": true, "tactics": ["refine", "rcases", "exact"], "tactic_count": 3}
{"name": "Set.compl_ordConnectedSection_ordSeparatingSet_mem_nhdsGE", "kind": "theorem", "module": "Mathlib.Topology.Order.T5", "is_tactic_proof": false, "tactics": ["have", "refine", "rw", "exact", "rcases", "by_cases", "exact", "simp", "rcases", "have", "have", "disjoint_left_ordSeparatingSet.mono_right", "replace", "filter_upwards", "refine", "refine", "exact", "rcases", "refine", "refine", "suffices", "rw", "exact", "refine", "have", "exact"], "tactic_count": 26}
{"name": "Set.compl_ordConnectedSection_ordSeparatingSet_mem_nhdsLE", "kind": "theorem", "module": "Mathlib.Topology.Order.T5", "is_tactic_proof": true, "tactics": ["have", "have", "simpa", "compl_ordConnectedSection_ordSeparatingSet_mem_nhdsGE"], "tactic_count": 4}
{"name": "Set.compl_ordConnectedSection_ordSeparatingSet_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Order.T5", "is_tactic_proof": true, "tactics": ["rw", "exact", "compl_ordConnectedSection_ordSeparatingSet_mem_nhdsGE"], "tactic_count": 3}
{"name": "Set.ordT5Nhd_mem_nhdsSet", "kind": "theorem", "module": "Mathlib.Topology.Order.T5", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderTopology.completelyNormalSpace", "kind": "instance", "module": "Mathlib.Topology.Order.T5", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderTopology.t5Space", "kind": "instance", "module": "Mathlib.Topology.Order.T5", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.upperSet", "kind": "definition", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.lowerSet", "kind": "definition", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithUpperSet", "kind": "definition", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithUpperSet.toUpperSet", "kind": "definition", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithUpperSet.ofUpperSet", "kind": "definition", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithUpperSet.toUpperSet_symm", "kind": "theorem", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithUpperSet.ofUpperSet_symm", "kind": "theorem", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithUpperSet.toUpperSet_ofUpperSet", "kind": "theorem", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithUpperSet.ofUpperSet_toUpperSet", "kind": "theorem", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithUpperSet.toUpperSet_inj", "kind": "theorem", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithUpperSet.ofUpperSet_inj", "kind": "theorem", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithUpperSet.rec", "kind": "definition", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithUpperSet.instNonempty", "kind": "instance", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithUpperSet.instInhabited", "kind": "instance", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithUpperSet.instPreorder", "kind": "instance", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithUpperSet.instTopologicalSpace", "kind": "instance", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithUpperSet.ofUpperSet_le_iff", "kind": "theorem", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithUpperSet.toUpperSet_le_iff", "kind": "theorem", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithUpperSet.ofUpperSetOrderIso", "kind": "definition", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithUpperSet.toUpperSetOrderIso", "kind": "definition", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithLowerSet", "kind": "definition", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithLowerSet.toLowerSet", "kind": "definition", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithLowerSet.ofLowerSet", "kind": "definition", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithLowerSet.toLowerSet_symm", "kind": "theorem", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithLowerSet.ofLowerSet_symm", "kind": "theorem", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithLowerSet.toLowerSet_ofLowerSet", "kind": "theorem", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithLowerSet.ofLowerSet_toLowerSet", "kind": "theorem", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithLowerSet.toLowerSet_inj", "kind": "theorem", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithLowerSet.ofLowerSet_inj", "kind": "theorem", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithLowerSet.rec", "kind": "definition", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithLowerSet.instNonempty", "kind": "instance", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithLowerSet.instInhabited", "kind": "instance", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithLowerSet.instPreorder", "kind": "instance", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithLowerSet.instTopologicalSpace", "kind": "instance", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithLowerSet.ofLowerSet_le_iff", "kind": "theorem", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithLowerSet.toLowerSet_le_iff", "kind": "theorem", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithLowerSet.ofLowerSetOrderIso", "kind": "definition", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithLowerSet.toLowerSetOrderIso", "kind": "definition", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithUpperSet.toDualHomeomorph", "kind": "definition", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.instIsUpperSetWithUpperSet", "kind": "instance", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.instIsUpperSet", "kind": "instance", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": true, "tactics": ["letI", "exact"], "tactic_count": 2}
{"name": "Topology.instIsLowerSetWithLowerSet", "kind": "instance", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.instIsLowerSet", "kind": "instance", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": true, "tactics": ["letI", "exact"], "tactic_count": 2}
{"name": "Topology.IsUpperSet.topology_eq", "kind": "theorem", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instIsLowerSet", "kind": "instance", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsUpperSet.WithUpperSetHomeomorph", "kind": "definition", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsUpperSet.isOpen_iff_isUpperSet", "kind": "theorem", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Topology.IsUpperSet.toAlexandrovDiscrete", "kind": "instance", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsUpperSet.isClosed_iff_isLower", "kind": "theorem", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Topology.IsUpperSet.closure_eq_lowerClosure", "kind": "theorem", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": true, "tactics": ["rw", "refine", "apply", "rw", "exact"], "tactic_count": 5}
{"name": "Topology.IsUpperSet.closure_singleton", "kind": "theorem", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Topology.IsUpperSet.specializes_iff_le", "kind": "theorem", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Topology.IsUpperSet.nhdsKer_eq_upperClosure", "kind": "theorem", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Topology.IsUpperSet.nhdsKer_singleton", "kind": "theorem", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Topology.IsUpperSet.nhds_eq_principal_Ici", "kind": "theorem", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Topology.IsUpperSet.nhdsSet_eq_principal_upperClosure", "kind": "theorem", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Topology.isUpperSet_iff_nhds", "kind": "theorem", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsUpperSet.instProp", "kind": "instance", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Topology.IsUpperSet.monotone_iff_continuous", "kind": "theorem", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": true, "tactics": ["constructor", "intro", "simp_rw", "exact", "intro", "rw", "apply", "apply", "apply", "rw"], "tactic_count": 10}
{"name": "Topology.IsUpperSet.monotone_to_upperTopology_continuous", "kind": "theorem", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": true, "tactics": ["simp_rw", "intro", "exact"], "tactic_count": 3}
{"name": "Topology.IsUpperSet.upperSet_le_upper", "kind": "theorem", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsLowerSet.topology_eq", "kind": "theorem", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instIsUpperSet", "kind": "instance", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsLowerSet.WithLowerSetHomeomorph", "kind": "definition", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsLowerSet.isOpen_iff_isLowerSet", "kind": "theorem", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Topology.IsLowerSet.toAlexandrovDiscrete", "kind": "instance", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsLowerSet.isClosed_iff_isUpper", "kind": "theorem", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Topology.IsLowerSet.closure_eq_upperClosure", "kind": "theorem", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsLowerSet.closure_singleton", "kind": "theorem", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Topology.IsLowerSet.specializes_iff_le", "kind": "theorem", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Topology.IsLowerSet.nhdsKer_eq_lowerClosure", "kind": "theorem", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Topology.IsLowerSet.nhdsKer_singleton", "kind": "theorem", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Topology.IsLowerSet.nhds_eq_principal_Iic", "kind": "theorem", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Topology.IsLowerSet.nhdsSet_eq_principal_lowerClosure", "kind": "theorem", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Topology.isLowerSet_iff_nhds", "kind": "theorem", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsLowerSet.monotone_iff_continuous", "kind": "theorem", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Topology.IsLowerSet.monotone_to_lowerTopology_continuous", "kind": "theorem", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsLowerSet.lowerSet_le_lower", "kind": "theorem", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.isUpperSet_orderDual", "kind": "theorem", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": true, "tactics": ["constructor", "apply", "apply"], "tactic_count": 3}
{"name": "Topology.isLowerSet_orderDual", "kind": "theorem", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithUpperSet.map", "kind": "definition", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithUpperSet.map_id", "kind": "theorem", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithUpperSet.map_comp", "kind": "theorem", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithUpperSet.toUpperSet_specializes_toUpperSet", "kind": "theorem", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Topology.WithUpperSet.ofUpperSet_le_ofUpperSet", "kind": "theorem", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithUpperSet.isUpperSet_toUpperSet_preimage", "kind": "theorem", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithUpperSet.isOpen_ofUpperSet_preimage", "kind": "theorem", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithLowerSet.map", "kind": "definition", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithLowerSet.map_id", "kind": "theorem", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithLowerSet.map_comp", "kind": "theorem", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithLowerSet.toLowerSet_specializes_toLowerSet", "kind": "theorem", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Topology.WithLowerSet.ofLowerSet_le_ofLowerSet", "kind": "theorem", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithLowerSet.isLowerSet_toLowerSet_preimage", "kind": "theorem", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.WithLowerSet.isOpen_ofLowerSet_preimage", "kind": "theorem", "module": "Mathlib.Topology.Order.UpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.instWithTopOfOrderTopology", "kind": "instance", "module": "Mathlib.Topology.Order.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.instOrderTopologyWithTop", "kind": "instance", "module": "Mathlib.Topology.Order.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.instSecondCountableTopologyWithTop", "kind": "instance", "module": "Mathlib.Topology.Order.WithTop", "is_tactic_proof": true, "tactics": ["classical", "rcases", "infer_instance", "and", "second-countability.", "for", "obtain", "exists_countable_generateFrom_Ioi_Iio", "obtain", "let", "let", "suffices", "refine", "have", "have", "rw", "exact", "apply", "apply", "grind", "generated", "half-infinite", "let", "have", "rw", "apply", "simp", "rintro", "induction", "top", "apply", "exact", "coe", "rw", "intro", "induction", "top", "rcases", "refine", "have", "have", "simp", "exact", "simp", "apply", "simp", "obtain", "refine", "apply", "simpa", "apply", "exact", "coe", "simp", "obtain", "h_basis.isOpen_iff.1", "refine", "intro", "induction", "top", "coe", "simp", "apply", "simpa", "apply", "apply", "exact", "intro", "apply", "grind", "apply", "exact", "intro", "apply", "grind", "induction", "top", "apply", "exact", "coe", "rw", "intro", "induction", "top", "coe", "simp", "obtain", "h_basis.isOpen_iff.1", "refine", "intro", "induction", "top", "coe", "simp", "apply", "simpa", "apply", "apply", "simp", "apply", "apply", "exact", "intro", "apply", "grind", "apply", "exact", "intro", "apply", "grind"], "tactic_count": 110}
{"name": "WithTop.isEmbedding_coe", "kind": "theorem", "module": "Mathlib.Topology.Order.WithTop", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "WithTop.isOpenEmbedding_coe", "kind": "theorem", "module": "Mathlib.Topology.Order.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.nhds_coe", "kind": "theorem", "module": "Mathlib.Topology.Order.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.continuous_coe", "kind": "theorem", "module": "Mathlib.Topology.Order.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.tendsto_untopD", "kind": "theorem", "module": "Mathlib.Topology.Order.WithTop", "is_tactic_proof": true, "tactics": ["lift", "rw", "exact"], "tactic_count": 3}
{"name": "WithTop.continuousOn_untopD", "kind": "theorem", "module": "Mathlib.Topology.Order.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.tendsto_untopA", "kind": "theorem", "module": "Mathlib.Topology.Order.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.continuousOn_untopA", "kind": "theorem", "module": "Mathlib.Topology.Order.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.tendsto_untop", "kind": "theorem", "module": "Mathlib.Topology.Order.WithTop", "is_tactic_proof": true, "tactics": ["have", "simp", "exact"], "tactic_count": 3}
{"name": "WithTop.continuous_untop", "kind": "theorem", "module": "Mathlib.Topology.Order.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.neTopHomeomorph", "kind": "definition", "module": "Mathlib.Topology.Order.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.sumHomeomorph", "kind": "definition", "module": "Mathlib.Topology.Order.WithTop", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WithTop.tendsto_nhds_top_iff", "kind": "theorem", "module": "Mathlib.Topology.Order.WithTop", "is_tactic_proof": true, "tactics": ["obtain", "simpa", "refine", "rw", "simp"], "tactic_count": 5}
{"name": "WithTop.tendsto_coe_atTop", "kind": "theorem", "module": "Mathlib.Topology.Order.WithTop", "is_tactic_proof": true, "tactics": ["obtain", "simpa", "rw", "intro", "filter_upwards", "simp"], "tactic_count": 6}
{"name": "rtendsto_nhds", "kind": "theorem", "module": "Mathlib.Topology.Partial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "rtendsto'_nhds", "kind": "theorem", "module": "Mathlib.Topology.Partial", "is_tactic_proof": true, "tactics": ["rw", "apply", "apply"], "tactic_count": 3}
{"name": "ptendsto_nhds", "kind": "theorem", "module": "Mathlib.Topology.Partial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ptendsto'_nhds", "kind": "theorem", "module": "Mathlib.Topology.Partial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PContinuous", "kind": "definition", "module": "Mathlib.Topology.Partial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "open_dom_of_pcontinuous", "kind": "theorem", "module": "Mathlib.Topology.Partial", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "pcontinuous_iff'", "kind": "theorem", "module": "Mathlib.Topology.Partial", "is_tactic_proof": true, "tactics": ["constructor", "intro", "simp", "rintro", "exact", "intro", "rw", "rintro", "rw", "intro", "apply", "have", "intro", "have", "rw", "exact", "change", "apply", "rw", "exact"], "tactic_count": 20}
{"name": "continuousWithinAt_iff_ptendsto_res", "kind": "theorem", "module": "Mathlib.Topology.Partial", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartitionOfUnity.instFunLikeContinuousMapReal", "kind": "instance", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartitionOfUnity.locallyFinite", "kind": "theorem", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartitionOfUnity.locallyFinite_tsupport", "kind": "theorem", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartitionOfUnity.nonneg", "kind": "theorem", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartitionOfUnity.sum_eq_one", "kind": "theorem", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartitionOfUnity.exists_pos", "kind": "theorem", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": true, "tactics": ["have", "contrapose", "simpa"], "tactic_count": 3}
{"name": "PartitionOfUnity.sum_le_one", "kind": "theorem", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartitionOfUnity.sum_nonneg", "kind": "theorem", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartitionOfUnity.le_one", "kind": "theorem", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartitionOfUnity.finsupport", "kind": "definition", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartitionOfUnity.mem_finsupport", "kind": "theorem", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PartitionOfUnity.coe_finsupport", "kind": "theorem", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "PartitionOfUnity.sum_finsupport", "kind": "theorem", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "PartitionOfUnity.sum_finsupport'", "kind": "theorem", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": true, "tactics": ["classical", "rw", "suffices", "rw", "apply", "rintro", "simp", "exact"], "tactic_count": 8}
{"name": "PartitionOfUnity.sum_finsupport_smul_eq_finsum", "kind": "theorem", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": true, "tactics": ["apply", "have", "funext", "rw", "exact"], "tactic_count": 5}
{"name": "PartitionOfUnity.finite_tsupport", "kind": "theorem", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": true, "tactics": ["rcases", "apply", "rintro", "simp", "exact"], "tactic_count": 5}
{"name": "PartitionOfUnity.fintsupport", "kind": "definition", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartitionOfUnity.mem_fintsupport_iff", "kind": "theorem", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartitionOfUnity.eventually_fintsupport_subset", "kind": "theorem", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": true, "tactics": ["apply", "intro", "rw", "exact"], "tactic_count": 4}
{"name": "PartitionOfUnity.finsupport_subset_fintsupport", "kind": "theorem", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartitionOfUnity.eventually_finsupport_subset", "kind": "theorem", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartitionOfUnity.continuous_smul", "kind": "theorem", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartitionOfUnity.continuous_finsum_smul", "kind": "theorem", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartitionOfUnity.IsSubordinate", "kind": "definition", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartitionOfUnity.exists_finset_nhds'", "kind": "theorem", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": true, "tactics": ["rcases", "refine", "have", "rwa"], "tactic_count": 4}
{"name": "PartitionOfUnity.exists_finset_nhds", "kind": "theorem", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": true, "tactics": ["rcases", "use", "rwa"], "tactic_count": 3}
{"name": "PartitionOfUnity.exists_finset_nhds_support_subset", "kind": "theorem", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartitionOfUnity.IsSubordinate.continuous_finsum_smul", "kind": "theorem", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BumpCovering.instFunLikeContinuousMapReal", "kind": "instance", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BumpCovering.toFun_eq_coe", "kind": "theorem", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BumpCovering.locallyFinite", "kind": "theorem", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BumpCovering.locallyFinite_tsupport", "kind": "theorem", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BumpCovering.point_finite", "kind": "theorem", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BumpCovering.nonneg", "kind": "theorem", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BumpCovering.le_one", "kind": "theorem", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BumpCovering.single", "kind": "definition", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BumpCovering.coe_single", "kind": "theorem", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "BumpCovering.instInhabited", "kind": "instance", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BumpCovering.IsSubordinate", "kind": "definition", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BumpCovering.IsSubordinate.mono", "kind": "theorem", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BumpCovering.exists_isSubordinate_of_locallyFinite_of_prop", "kind": "theorem", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": true, "tactics": ["rcases", "have", "rcases", "choose", "h01", "have", "refine", "hfp,", "rcases", "exact"], "tactic_count": 10}
{"name": "BumpCovering.exists_isSubordinate_of_locallyFinite", "kind": "theorem", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BumpCovering.exists_isSubordinate_of_prop", "kind": "theorem", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "exact"], "tactic_count": 3}
{"name": "BumpCovering.exists_isSubordinate", "kind": "theorem", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "exact"], "tactic_count": 3}
{"name": "BumpCovering.exists_isSubordinate_of_locallyFinite_of_prop_t2space", "kind": "theorem", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": false, "tactics": ["rcases", "have", "rcases", "choose", "h01", "have", "refine", "hfp,", "rcases", "exact"], "tactic_count": 10}
{"name": "BumpCovering.exists_isSubordinate_hasCompactSupport_of_locallyFinite_t2space", "kind": "theorem", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": true, "tactics": ["simpa", "exists_isSubordinate_of_locallyFinite_of_prop_t2space", "ho"], "tactic_count": 3}
{"name": "BumpCovering.ind", "kind": "definition", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BumpCovering.eventuallyEq_one", "kind": "theorem", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BumpCovering.ind_apply", "kind": "theorem", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BumpCovering.toPOUFun", "kind": "definition", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BumpCovering.toPOUFun_zero_of_zero", "kind": "theorem", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "BumpCovering.support_toPOUFun_subset", "kind": "theorem", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BumpCovering.toPOUFun_eq_mul_prod", "kind": "theorem", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": true, "tactics": ["refine", "rw", "rw", "exact"], "tactic_count": 4}
{"name": "BumpCovering.sum_toPOUFun_eq", "kind": "theorem", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": true, "tactics": ["set", "have", "have", "rw", "exact", "have", "rw", "exact", "classical", "letI", "rw", "sub_sub_cancel]", "refine", "convert", "rwa"], "tactic_count": 15}
{"name": "BumpCovering.exists_finset_toPOUFun_eventuallyEq", "kind": "theorem", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": true, "tactics": ["rcases", "use", "filter_upwards", "simp", "apply", "intro", "exact"], "tactic_count": 7}
{"name": "BumpCovering.continuous_toPOUFun", "kind": "theorem", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": true, "tactics": ["refine", "simp", "exact"], "tactic_count": 3}
{"name": "BumpCovering.toPartitionOfUnity", "kind": "definition", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BumpCovering.toPartitionOfUnity_apply", "kind": "theorem", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BumpCovering.toPartitionOfUnity_eq_mul_prod", "kind": "theorem", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BumpCovering.exists_finset_toPartitionOfUnity_eventuallyEq", "kind": "theorem", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BumpCovering.toPartitionOfUnity_zero_of_zero", "kind": "theorem", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BumpCovering.support_toPartitionOfUnity_subset", "kind": "theorem", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BumpCovering.sum_toPartitionOfUnity_eq", "kind": "theorem", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "BumpCovering.IsSubordinate.toPartitionOfUnity", "kind": "theorem", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartitionOfUnity.instInhabited", "kind": "instance", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartitionOfUnity.exists_isSubordinate_of_locallyFinite", "kind": "theorem", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartitionOfUnity.exists_isSubordinate", "kind": "theorem", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PartitionOfUnity.exists_isSubordinate_of_locallyFinite_t2space", "kind": "theorem", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_continuous_sum_one_of_isOpen_isCompact", "kind": "theorem", "module": "Mathlib.Topology.PartitionOfUnity", "is_tactic_proof": false, "tactics": ["obtain", "use", "refine", "intro", "simp", "have", "rw", "rwa", "intro", "exact"], "tactic_count": 10}
{"name": "Path.instFunLike", "kind": "instance", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.continuousMapClass", "kind": "instance", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.ext", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": true, "tactics": ["rintro", "rfl"], "tactic_count": 2}
{"name": "Path.coe_mk'", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.coe_mk_mk", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.continuous", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.source", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.target", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.simps.apply", "kind": "definition", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.coe_toContinuousMap", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.range_coe", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.instHasUncurryPath", "kind": "instance", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.source_mem_range", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.target_mem_range", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.id", "kind": "definition", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.refl", "kind": "definition", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.refl_range", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.symm", "kind": "definition", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.symm_symm", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Path.symm_bijective", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.refl_symm", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.symm_range", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.instTopologicalSpace", "kind": "instance", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.instContinuousEvalElemRealUnitInterval", "kind": "instance", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.continuous_uncurry_iff", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.extend", "kind": "definition", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.pathExtend", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.continuous_extend", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.pathExtend", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.pathExtend", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.extend_apply", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.extend_zero", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Path.extend_one", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Path.extend_extends'", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.extend_range", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.image_extend_of_subset", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.extend_of_le_zero", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.extend_of_one_le", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.refl_extend", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.extend_symm_apply", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.extend_symm", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.ofLine", "kind": "definition", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.ofLine_mem", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.ofLine_extend", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Path.trans", "kind": "definition", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.trans_apply", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.trans_symm", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": true, "tactics": ["ext", "simp", "split_ifs", "have", "norm_num", "refine", "norm_num", "refine", "simp", "ring", "exfalso", "linarith"], "tactic_count": 12}
{"name": "Path.extend_trans_of_le_half", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": true, "tactics": ["obtain", "repeat", "rwa"], "tactic_count": 3}
{"name": "Path.extend_trans_of_half_le", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": true, "tactics": ["conv_lhs", "rw", "congr", "linarith"], "tactic_count": 4}
{"name": "Path.refl_trans_refl", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "Path.trans_range", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": ["rw", "image_image", "norm_num"], "tactic_count": 3}
{"name": "Path.map'", "kind": "definition", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.map", "kind": "definition", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.map_coe", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "Path.map_symm", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.map_trans", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": true, "tactics": ["ext", "rw", "grind"], "tactic_count": 3}
{"name": "Path.map_id", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "Path.map_map", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "Path.cast", "kind": "definition", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.cast_rfl_rfl", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.cast_symm", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.symm_cast", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.cast_trans", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.trans_cast", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.extend_cast", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.cast_coe", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.bijective_cast", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": true, "tactics": ["subst_vars"], "tactic_count": 1}
{"name": "Path.exists_congr", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.symm_continuous_family", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.continuous_symm", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.continuous_uncurry_extend_of_continuous_family", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": true, "tactics": ["apply", "exact"], "tactic_count": 2}
{"name": "Path.trans_continuous_family", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": true, "tactics": ["have", "have", "simp", "refine", "change", "exact", "change", "exact", "rintro", "simp"], "tactic_count": 10}
{"name": "Continuous.path_trans", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": true, "tactics": ["intro", "apply", "exact"], "tactic_count": 3}
{"name": "Path.continuous_trans", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": true, "tactics": ["fun_prop"], "tactic_count": 1}
{"name": "Path.prod", "kind": "definition", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.prod_coe", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.trans_prod_eq_prod_trans", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Path.pi", "kind": "definition", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.pi_coe", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.trans_pi_eq_pi_trans", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": true, "tactics": ["ext", "unfold", "simp", "split_ifs", "rfl", "rfl"], "tactic_count": 6}
{"name": "Path.mul", "kind": "definition", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.inv", "kind": "definition", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.truncate", "kind": "definition", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.truncateOfLE", "kind": "definition", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.truncate_range", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": true, "tactics": ["rw", "simp", "intro", "simp"], "tactic_count": 4}
{"name": "Path.truncate_continuous_family", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.truncate_const_continuous_family", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "Path.truncate_self", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": true, "tactics": ["ext", "by_cases"], "tactic_count": 2}
{"name": "Path.truncate_zero_zero", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "Path.truncate_one_one", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "Path.truncate_zero_one", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": true, "tactics": ["ext", "rw", "have", "rw"], "tactic_count": 4}
{"name": "Path.reparam", "kind": "definition", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.coe_reparam", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.reparam_id", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": true, "tactics": ["ext", "rfl"], "tactic_count": 2}
{"name": "Path.range_reparam", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": true, "tactics": ["change", "have", "rw", "intro", "have", "have", "rw", "rcases", "rw", "exact", "rw"], "tactic_count": 11}
{"name": "Path.refl_reparam", "kind": "theorem", "module": "Mathlib.Topology.Path", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "AccPt.nhds_inter", "kind": "theorem", "module": "Mathlib.Topology.Perfect", "is_tactic_proof": false, "tactics": ["have", "rw", "exact", "rw", "exact"], "tactic_count": 5}
{"name": "Preperfect", "kind": "definition", "module": "Mathlib.Topology.Perfect", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "preperfect_iff_nhds", "kind": "theorem", "module": "Mathlib.Topology.Perfect", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PerfectSpace.univ_perfect", "kind": "theorem", "module": "Mathlib.Topology.Perfect", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Preperfect.open_inter", "kind": "theorem", "module": "Mathlib.Topology.Perfect", "is_tactic_proof": true, "tactics": ["rintro", "apply", "exact"], "tactic_count": 3}
{"name": "Preperfect.perfect_closure", "kind": "theorem", "module": "Mathlib.Topology.Perfect", "is_tactic_proof": true, "tactics": ["constructor", "intro", "by_cases", "exact", "have", "rw", "rw", "exact"], "tactic_count": 8}
{"name": "preperfect_iff_perfect_closure", "kind": "theorem", "module": "Mathlib.Topology.Perfect", "is_tactic_proof": true, "tactics": ["constructor", "exact", "intro", "have", "rw", "have", "rintro", "simp", "exact", "rw", "exact"], "tactic_count": 11}
{"name": "Perfect.closure_nhds_inter", "kind": "theorem", "module": "Mathlib.Topology.Perfect", "is_tactic_proof": true, "tactics": ["constructor", "apply", "exact", "apply", "exact"], "tactic_count": 5}
{"name": "Perfect.splitting", "kind": "theorem", "module": "Mathlib.Topology.Perfect", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "have", "rw", "rcases", "exact", "obtain", "use", "constructor", "refine", "rw", "exact", "constructor", "refine", "rw", "exact", "apply"], "tactic_count": 17}
{"name": "IsPreconnected.preperfect_of_nontrivial", "kind": "theorem", "module": "Mathlib.Topology.Perfect", "is_tactic_proof": true, "tactics": ["intro", "rw", "specialize", "trans", "simp", "apply", "exact", "exact", "obtain", "use", "simp", "apply", "simp", "apply", "rw", "exact"], "tactic_count": 16}
{"name": "instPerfectSpaceOfT1SpaceOfConnectedSpaceOfNontrivial", "kind": "instance", "module": "Mathlib.Topology.Perfect", "is_tactic_proof": true, "tactics": ["constructor", "apply", "rw", "infer_instance"], "tactic_count": 4}
{"name": "exists_countable_union_perfect_of_isClosed", "kind": "theorem", "module": "Mathlib.Topology.Perfect", "is_tactic_proof": true, "tactics": ["obtain", "let", "let", "let", "have", "simp", "apply", "exact", "exact", "refine", "refine", "exact", "rw", "intro", "have", "intro", "obtain", "have", "apply", "rintro", "by_cases", "exact", "exact", "exact", "have", "apply", "exact", "by_contra", "exact", "rw"], "tactic_count": 30}
{"name": "exists_perfect_nonempty_of_isClosed_of_not_countable", "kind": "theorem", "module": "Mathlib.Topology.Perfect", "is_tactic_proof": true, "tactics": ["rcases", "refine", "constructor", "rw", "by_contra", "rw", "rw", "contradiction", "rw", "exact"], "tactic_count": 10}
{"name": "perfectSpace_iff_forall_not_isolated", "kind": "theorem", "module": "Mathlib.Topology.Perfect", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "PerfectSpace.not_isolated", "kind": "instance", "module": "Mathlib.Topology.Perfect", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousWithinAt_update_same", "kind": "theorem", "module": "Mathlib.Topology.Piecewise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousAt_update_same", "kind": "theorem", "module": "Mathlib.Topology.Piecewise", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ContinuousOn.if'", "kind": "theorem", "module": "Mathlib.Topology.Piecewise", "is_tactic_proof": true, "tactics": ["intro", "by_cases", "exact", "rw", "rcases", "apply", "exact", "have", "exact", "apply", "have", "exact", "exact"], "tactic_count": 13}
{"name": "ContinuousOn.piecewise'", "kind": "theorem", "module": "Mathlib.Topology.Piecewise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.if", "kind": "theorem", "module": "Mathlib.Topology.Piecewise", "is_tactic_proof": true, "tactics": ["apply", "rintro", "simp", "apply", "exact", "rintro", "simp", "apply", "rcases", "rw", "apply", "exact", "exact"], "tactic_count": 13}
{"name": "ContinuousOn.piecewise", "kind": "theorem", "module": "Mathlib.Topology.Piecewise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_if'", "kind": "theorem", "module": "Mathlib.Topology.Piecewise", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "continuous_if", "kind": "theorem", "module": "Mathlib.Topology.Piecewise", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "Continuous.if", "kind": "theorem", "module": "Mathlib.Topology.Piecewise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_if_const", "kind": "theorem", "module": "Mathlib.Topology.Piecewise", "is_tactic_proof": true, "tactics": ["split_ifs", "exacts"], "tactic_count": 2}
{"name": "Continuous.if_const", "kind": "theorem", "module": "Mathlib.Topology.Piecewise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_piecewise", "kind": "theorem", "module": "Mathlib.Topology.Piecewise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.piecewise", "kind": "theorem", "module": "Mathlib.Topology.Piecewise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.ite'", "kind": "theorem", "module": "Mathlib.Topology.Piecewise", "is_tactic_proof": true, "tactics": ["classical", "simp", "convert", "rename_i", "by_cases"], "tactic_count": 5}
{"name": "IsOpen.ite", "kind": "theorem", "module": "Mathlib.Topology.Piecewise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ite_inter_closure_eq_of_inter_frontier_eq", "kind": "theorem", "module": "Mathlib.Topology.Piecewise", "is_tactic_proof": true, "tactics": ["rw", "ite_inter_of_inter_eq"], "tactic_count": 2}
{"name": "ite_inter_closure_compl_eq_of_inter_frontier_eq", "kind": "theorem", "module": "Mathlib.Topology.Piecewise", "is_tactic_proof": true, "tactics": ["rw", "rwa"], "tactic_count": 2}
{"name": "continuousOn_piecewise_ite'", "kind": "theorem", "module": "Mathlib.Topology.Piecewise", "is_tactic_proof": true, "tactics": ["apply", "rwa", "rwa", "rwa"], "tactic_count": 4}
{"name": "continuousOn_piecewise_ite", "kind": "theorem", "module": "Mathlib.Topology.Piecewise", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Preorder.continuous_restrictLe", "kind": "theorem", "module": "Mathlib.Topology.PreorderRestrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Preorder.continuous_restrictLe₂", "kind": "theorem", "module": "Mathlib.Topology.PreorderRestrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Preorder.continuous_frestrictLe", "kind": "theorem", "module": "Mathlib.Topology.PreorderRestrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Preorder.continuous_frestrictLe₂", "kind": "theorem", "module": "Mathlib.Topology.PreorderRestrict", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsQuasiSeparated", "kind": "definition", "module": "Mathlib.Topology.QuasiSeparated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isQuasiSeparated_univ_iff", "kind": "theorem", "module": "Mathlib.Topology.QuasiSeparated", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "isQuasiSeparated_univ", "kind": "theorem", "module": "Mathlib.Topology.QuasiSeparated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsQuasiSeparated.image_of_isEmbedding", "kind": "theorem", "module": "Mathlib.Topology.QuasiSeparated", "is_tactic_proof": true, "tactics": ["intro", "convert", "symm", "rw", "exact", "intro", "rw", "exact", "rw", "convert", "rw", "exact", "intro", "rw", "exact", "rw", "convert", "rw", "exact"], "tactic_count": 19}
{"name": "IsQuasiSeparated.of_subset", "kind": "theorem", "module": "Mathlib.Topology.QuasiSeparated", "is_tactic_proof": true, "tactics": ["intro", "exact"], "tactic_count": 2}
{"name": "Topology.IsOpenEmbedding.isQuasiSeparated_iff", "kind": "theorem", "module": "Mathlib.Topology.QuasiSeparated", "is_tactic_proof": true, "tactics": ["refine", "intro", "rw", "exact"], "tactic_count": 4}
{"name": "Topology.IsOpenEmbedding.quasiSeparatedSpace", "kind": "theorem", "module": "Mathlib.Topology.QuasiSeparated", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "isQuasiSeparated_iff_quasiSeparatedSpace", "kind": "theorem", "module": "Mathlib.Topology.QuasiSeparated", "is_tactic_proof": true, "tactics": ["rw", "convert", "simp"], "tactic_count": 3}
{"name": "T2Space.to_quasiSeparatedSpace", "kind": "instance", "module": "Mathlib.Topology.QuasiSeparated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NoetherianSpace.to_quasiSeparatedSpace", "kind": "instance", "module": "Mathlib.Topology.QuasiSeparated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuasiSeparatedSpace.of_isTopologicalBasis", "kind": "theorem", "module": "Mathlib.Topology.QuasiSeparated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsQuasiSeparated.of_quasiSeparatedSpace", "kind": "theorem", "module": "Mathlib.Topology.QuasiSeparated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "QuasiSeparatedSpace.of_isOpenEmbedding", "kind": "theorem", "module": "Mathlib.Topology.QuasiSeparated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.inter_of_isOpen", "kind": "theorem", "module": "Mathlib.Topology.QuasiSeparated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "quasiSeparatedSpace_congr", "kind": "theorem", "module": "Mathlib.Topology.QuasiSeparated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSemicontinuousOn.exists_isMinOn", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Basic", "is_tactic_proof": true, "tactics": ["simp", "have", "have", "let", "let", "have", "apply", "change", "exact", "intro", "have", "exact", "have", "have", "obtain", "refine", "let", "suffices", "filter_upwards"], "tactic_count": 19}
{"name": "LowerSemicontinuousOn.bddBelow_of_isCompact", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Basic", "is_tactic_proof": true, "tactics": ["cases", "inl", "simp", "exact", "inr", "obtain", "exact"], "tactic_count": 7}
{"name": "IsOpen.lowerSemicontinuous_indicator", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Basic", "is_tactic_proof": true, "tactics": ["intro", "by_cases", "filter_upwards", "simp", "refine", "by_cases"], "tactic_count": 6}
{"name": "IsOpen.lowerSemicontinuousOn_indicator", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.lowerSemicontinuousAt_indicator", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.lowerSemicontinuousWithinAt_indicator", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.lowerSemicontinuous_indicator", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Basic", "is_tactic_proof": true, "tactics": ["intro", "by_cases", "refine", "by_cases", "filter_upwards", "simp"], "tactic_count": 6}
{"name": "IsClosed.lowerSemicontinuousOn_indicator", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.lowerSemicontinuousAt_indicator", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.lowerSemicontinuousWithinAt_indicator", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lowerSemicontinuous_iff_isOpen_preimage", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSemicontinuous.isOpen_preimage", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lowerSemicontinuousOn_iff_preimage_Ioi", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Basic", "is_tactic_proof": true, "tactics": ["simp", "isOpen_induced_iff,"], "tactic_count": 2}
{"name": "lowerSemicontinuous_iff_isClosed_preimage", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "LowerSemicontinuous.isClosed_preimage", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lowerSemicontinuousOn_iff_preimage_Iic", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Basic", "is_tactic_proof": true, "tactics": ["simp", "isClosed_induced_iff,"], "tactic_count": 2}
{"name": "ContinuousWithinAt.lowerSemicontinuousWithinAt", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.lowerSemicontinuousAt", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.lowerSemicontinuousOn", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.lowerSemicontinuous", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lowerSemicontinuousWithinAt_iff_le_liminf", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Basic", "is_tactic_proof": true, "tactics": ["constructor", "intro", "by_contra", "obtain", "exact", "ltz.not_ge", "exact"], "tactic_count": 7}
{"name": "lowerSemicontinuousAt_iff_le_liminf", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "lowerSemicontinuous_iff_le_liminf", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "lowerSemicontinuousOn_iff_le_liminf", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LowerSemicontinuousOn.isCompact_inter_preimage_Iic", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Basic", "is_tactic_proof": true, "tactics": ["rw", "obtain", "exact"], "tactic_count": 3}
{"name": "LowerSemicontinuousOn.inter_biInter_preimage_Iic_eq_empty_iff_exists_finset", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Basic", "is_tactic_proof": true, "tactics": ["refine", "suffices", "simpa", "exact", "rw", "simp", "grind"], "tactic_count": 7}
{"name": "lowerSemicontinuousOn_iff_isClosed_epigraph", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Basic", "is_tactic_proof": false, "tactics": ["simp_rw", "compl_setOf,", "constructor", "intro", "by_cases", "have", "filter_upwards", "filter_upwards", "intro", "exact"], "tactic_count": 10}
{"name": "lowerSemicontinuous_iff_isClosed_epigraph", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousAt.comp_lowerSemicontinuousWithinAt", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Basic", "is_tactic_proof": true, "tactics": ["intro", "by_cases", "obtain", "filter_upwards", "calc", "y", "exact"], "tactic_count": 7}
{"name": "ContinuousAt.comp_lowerSemicontinuousAt", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Basic", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Continuous.comp_lowerSemicontinuousOn", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.comp_lowerSemicontinuous", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.comp_lowerSemicontinuousWithinAt_antitone", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.comp_lowerSemicontinuousAt_antitone", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.comp_lowerSemicontinuousOn_antitone", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.comp_lowerSemicontinuous_antitone", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSemicontinuousWithinAt.add'", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Basic", "is_tactic_proof": true, "tactics": ["intro", "obtain", "mem_nhds_prod_iff'.1", "by_cases", "obtain", "by_cases", "obtain", "filter_upwards", "have", "by_cases", "simpa", "simpa", "have", "by_cases", "simpa", "simpa", "have", "calc", "y", "simp", "filter_upwards", "have", "by_cases", "simpa", "simpa", "have", "calc", "y", "simp", "by_cases", "obtain", "filter_upwards", "have", "by_cases", "simpa", "simpa", "have", "calc", "y", "simp", "apply", "intro", "have", "calc", "y"], "tactic_count": 45}
{"name": "LowerSemicontinuousAt.add'", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "LowerSemicontinuousOn.add'", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSemicontinuous.add'", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSemicontinuousWithinAt.add", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSemicontinuousAt.add", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSemicontinuousOn.add", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSemicontinuous.add", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lowerSemicontinuousWithinAt_sum", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Basic", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "insert", "simp", "exact"], "tactic_count": 6}
{"name": "lowerSemicontinuousAt_sum", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "lowerSemicontinuousOn_sum", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lowerSemicontinuous_sum", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSemicontinuousWithinAt.sup", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Basic", "is_tactic_proof": true, "tactics": ["intro", "simp", "rcases", "filter_upwards", "filter_upwards"], "tactic_count": 5}
{"name": "LowerSemicontinuousAt.sup", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "LowerSemicontinuousOn.sup", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "LowerSemicontinuousWithinAt.inf", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Basic", "is_tactic_proof": true, "tactics": ["intro", "simp", "exact"], "tactic_count": 3}
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{"name": "lowerSemicontinuousWithinAt_ciSup", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Basic", "is_tactic_proof": true, "tactics": ["cases", "simpa", "intro", "rcases", "filter_upwards"], "tactic_count": 5}
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{"name": "UpperSemicontinuousOn.exists_isMaxOn", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "upperSemicontinuousWithinAt_iff_limsup_le", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SemicontinuousAt.comp", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Semicontinuous.comp", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_example", "kind": "example", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "LowerSemicontinuousWithinAt", "kind": "abbrev", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSemicontinuousOn", "kind": "abbrev", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSemicontinuousAt", "kind": "abbrev", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSemicontinuous", "kind": "abbrev", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSemicontinuousWithinAt", "kind": "abbrev", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSemicontinuousOn", "kind": "abbrev", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSemicontinuousAt", "kind": "abbrev", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSemicontinuous", "kind": "abbrev", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lowerSemicontinuousWithinAt_iff", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lowerSemicontinuousOn_iff", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lowerSemicontinuousAt_iff", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lowerSemicontinuous_iff", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "upperSemicontinuousWithinAt_iff", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "upperSemicontinuousOn_iff", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "upperSemicontinuousAt_iff", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "upperSemicontinuous_iff", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSemicontinuousWithinAt.mono", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSemicontinuousWithinAt.congr_of_eventuallyEq", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lowerSemicontinuousWithinAt_univ_iff", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSemicontinuousAt.lowerSemicontinuousWithinAt", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSemicontinuousOn.lowerSemicontinuousWithinAt", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSemicontinuousOn.mono", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lowerSemicontinuousOn_univ_iff", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lowerSemicontinuous_restrict_iff", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSemicontinuous.lowerSemicontinuousAt", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSemicontinuous.lowerSemicontinuousWithinAt", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSemicontinuous.lowerSemicontinuousOn", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lowerSemicontinuousWithinAt_const", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lowerSemicontinuousAt_const", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lowerSemicontinuousOn_const", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lowerSemicontinuous_const", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSemicontinuousWithinAt.comp", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSemicontinuousAt.comp", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSemicontinuousOn.comp", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerSemicontinuous.comp", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSemicontinuousWithinAt.mono", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSemicontinuousWithinAt.congr_of_eventuallyEq", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "upperSemicontinuousWithinAt_univ_iff", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "upperSemicontinuousOn_iff_restrict", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSemicontinuousAt.upperSemicontinuousWithinAt", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSemicontinuousOn.upperSemicontinuousWithinAt", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSemicontinuousOn.mono", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "upperSemicontinuousOn_univ_iff", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSemicontinuous.upperSemicontinuousAt", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSemicontinuous.upperSemicontinuousWithinAt", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSemicontinuous.upperSemicontinuousOn", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "upperSemicontinuousWithinAt_const", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "upperSemicontinuousAt_const", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "upperSemicontinuousOn_const", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "upperSemicontinuous_const", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSemicontinuousWithinAt.comp", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSemicontinuousAt.comp", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSemicontinuousOn.comp", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperSemicontinuous.comp", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lowerSemicontinuousWithinAt_iff_frequently", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "lowerSemicontinuousOn_iff_frequently", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "lowerSemicontinuousAt_iff_frequently", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "lowerSemicontinuous_iff_frequently", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "upperSemicontinuousWithinAt_iff_frequently", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "upperSemicontinuousOn_iff_frequently", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "upperSemicontinuousAt_iff_frequently", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "upperSemicontinuous_iff_frequently", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "LowerHemicontinuousWithinAt", "kind": "abbrev", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerHemicontinuousOn", "kind": "abbrev", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerHemicontinuousAt", "kind": "abbrev", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerHemicontinuous", "kind": "abbrev", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHemicontinuousWithinAt", "kind": "abbrev", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHemicontinuousOn", "kind": "abbrev", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHemicontinuousAt", "kind": "abbrev", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHemicontinuous", "kind": "abbrev", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lowerHemicontinuousWithinAt_iff", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "lowerHemicontinuousOn_iff", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lowerHemicontinuousAt_iff", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "lowerHemicontinuous_iff", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "upperHemicontinuousWithinAt_iff", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "upperHemicontinuousOn_iff", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "upperHemicontinuousAt_iff", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "upperHemicontinuous_iff", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerHemicontinuousWithinAt.mono", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerHemicontinuousWithinAt.congr_of_eventuallyEq", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lowerHemicontinuousWithinAt_univ_iff", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerHemicontinuousAt.lowerHemicontinuousWithinAt", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerHemicontinuousOn.lowerHemicontinuousWithinAt", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerHemicontinuousOn.mono", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lowerHemicontinuousOn_univ_iff", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lowerHemicontinuous_restrict_iff", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerHemicontinuous.lowerHemicontinuousAt", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerHemicontinuous.lowerHemicontinuousWithinAt", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerHemicontinuous.lowerHemicontinuousOn", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lowerHemicontinuousWithinAt_iff_frequently", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": true, "tactics": ["rw", "simp", "refine", "rw", "simp"], "tactic_count": 5}
{"name": "lowerHemicontinuousOn_iff_frequently", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "lowerHemicontinuousAt_iff_frequently", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "lowerHemicontinuous_iff_frequently", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "LowerHemicontinuousWithinAt.const", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerHemicontinuousAt.const", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerHemicontinuousOn.const", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerHemicontinuous.const", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerHemicontinuousWithinAt.comp", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerHemicontinuousAt.comp", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerHemicontinuousOn.comp", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "LowerHemicontinuous.comp", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHemicontinuousWithinAt.mono", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHemicontinuousWithinAt.congr_of_eventuallyEq", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "upperHemicontinuousWithinAt_univ_iff", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "upperHemicontinuousOn_iff_restrict", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHemicontinuousAt.upperHemicontinuousWithinAt", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHemicontinuousOn.upperHemicontinuousWithinAt", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHemicontinuousOn.mono", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "upperHemicontinuousOn_univ_iff", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHemicontinuous.upperHemicontinuousAt", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHemicontinuous.upperHemicontinuousWithinAt", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHemicontinuous.upperHemicontinuousOn", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "upperHemicontinuousWithinAt_iff_frequently", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "upperHemicontinuousOn_iff_frequently", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "upperHemicontinuousAt_iff_frequently", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "upperHemicontinuous_iff_frequently", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "UpperHemicontinuousWithinAt.const", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHemicontinuousAt.const", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHemicontinuousOn.const", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHemicontinuous.const", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHemicontinuousWithinAt.comp", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHemicontinuousAt.comp", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHemicontinuousOn.comp", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UpperHemicontinuous.comp", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "upperHemicontinuousWithinAt_iff_forall_isOpen", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Hemicontinuity", "is_tactic_proof": true, "tactics": ["rw", "exact", "simp", "apply", "simp"], "tactic_count": 5}
{"name": "upperHemicontinuousOn_iff_forall_isOpen", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Hemicontinuity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "upperHemicontinuousAt_iff_forall_isOpen", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Hemicontinuity", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "upperHemicontinuous_iff_forall_isOpen", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Hemicontinuity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "upperHemicontinuousWithinAt_iff_preimage_Iic", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Hemicontinuity", "is_tactic_proof": true, "tactics": ["simp_rw", "rw", "refine", "gcongr", "exact", "intro", "filter_upwards", "exact", "refine", "simp"], "tactic_count": 10}
{"name": "upperHemicontinuousAt_iff_preimage_Iic", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Hemicontinuity", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "upperHemicontinuousOn_iff_preimage_Iic", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Hemicontinuity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "upperHemicontinuous_iff_preimage_Iic", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Hemicontinuity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "upperHemicontinuous_iff_isOpen_preimage_Iic", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Hemicontinuity", "is_tactic_proof": true, "tactics": ["simp_rw", "conv", "enter", "rw", "simp"], "tactic_count": 5}
{"name": "upperHemicontinuous_iff_isClosed_compl_preimage_Iic_compl", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Hemicontinuity", "is_tactic_proof": false, "tactics": ["conv_rhs", "rw", "simp", "exact"], "tactic_count": 4}
{"name": "isClosedMap_iff_upperHemicontinuous", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Hemicontinuity", "is_tactic_proof": true, "tactics": ["rw", "aesop"], "tactic_count": 2}
{"name": "lowerHemicontinuous_iff_isOpen_compl_preimage_Iic_compl", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Hemicontinuity", "is_tactic_proof": false, "tactics": ["have", "simp", "simp_rw", "mem_setOf,"], "tactic_count": 4}
{"name": "lowerHemicontinuous_iff_isClosed_preimage_Iic", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Hemicontinuity", "is_tactic_proof": false, "tactics": ["conv_rhs", "rw", "simp", "exact"], "tactic_count": 4}
{"name": "isOpenMap_iff_lowerHemicontinuous", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Hemicontinuity", "is_tactic_proof": true, "tactics": ["rw", "aesop"], "tactic_count": 2}
{"name": "upperHemicontinuous_singleton_id", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Hemicontinuity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "upperHemicontinuousWithinAt_singleton_iff", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Hemicontinuity", "is_tactic_proof": false, "tactics": ["refine", "simp", "intro", "filter_upwards", "exact"], "tactic_count": 5}
{"name": "upperHemicontinuousAt_singleton_iff", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Hemicontinuity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "upperHemicontinuousOn_singleton_iff", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Hemicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "upperHemicontinuous_singleton_iff", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Hemicontinuity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "UpperHemicontinuousWithinAt.union", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Hemicontinuity", "is_tactic_proof": true, "tactics": ["rw", "aesop"], "tactic_count": 2}
{"name": "UpperHemicontinuousOn.union", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Hemicontinuity", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "UpperHemicontinuousAt.union", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Hemicontinuity", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "UpperHemicontinuous.union", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Hemicontinuity", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "UpperHemicontinuousWithinAt.inter", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Hemicontinuity", "is_tactic_proof": true, "tactics": ["rw", "intro", "specialize", "grind"], "tactic_count": 4}
{"name": "UpperHemicontinuousOn.inter", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Hemicontinuity", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "UpperHemicontinuousAt.inter", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Hemicontinuity", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "UpperHemicontinuous.inter", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Hemicontinuity", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "UpperHemicontinuousWithinAt.isInducing_comp", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Hemicontinuity", "is_tactic_proof": true, "tactics": ["refine", "obtain", "simp_rw", "exact"], "tactic_count": 4}
{"name": "UpperHemicontinuousOn.isInducing_comp", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Hemicontinuity", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "UpperHemicontinuousAt.isInducing_comp", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Hemicontinuity", "is_tactic_proof": true, "tactics": ["simpa", "hf.upperHemicontinuousWithinAt"], "tactic_count": 2}
{"name": "UpperHemicontinuous.isInducing_comp", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Hemicontinuity", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "UpperHemicontinuous.isClosed_domain", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Hemicontinuity", "is_tactic_proof": true, "tactics": ["simp", "intro", "simp_rw", "simpa"], "tactic_count": 4}
{"name": "UpperHemicontinuousAt.of_sequences", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Hemicontinuity", "is_tactic_proof": true, "tactics": ["refine", "obtain", "choose", "obtain", "hK.subseq_of_frequently_in", "refine", "filter_upwards", "exact", "specialize", "exact"], "tactic_count": 10}
{"name": "UpperHemicontinuousAt.mem_of_tendsto", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Hemicontinuity", "is_tactic_proof": true, "tactics": ["by_contra", "obtain", "suffices", "apply", "filter_upwards", "exact", "apply", "filter_upwards", "simp", "exact"], "tactic_count": 10}
{"name": "exists_countable_upperSemicontinuous_isGLB", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Lindelof", "is_tactic_proof": true, "tactics": ["simp_rw", "rcases", "let", "have", "have", "ext", "simp", "have", "simp_rw", "rcases", "use", "rw", "choose", "set", "have", "use", "refine", "by_contra", "rcases", "obtain", "have", "simpa", "suffices", "exact"], "tactic_count": 24}
{"name": "exists_countable_lowerSemicontinuous_isLUB", "kind": "theorem", "module": "Mathlib.Topology.Semicontinuity.Lindelof", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsEmbedding.toPullbackDiag", "kind": "theorem", "module": "Mathlib.Topology.SeparatedMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.mapPullback", "kind": "theorem", "module": "Mathlib.Topology.SeparatedMap", "is_tactic_proof": true, "tactics": ["refine", "apply_rules"], "tactic_count": 2}
{"name": "IsSeparatedMap", "kind": "definition", "module": "Mathlib.Topology.SeparatedMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "t2space_iff_isSeparatedMap", "kind": "theorem", "module": "Mathlib.Topology.SeparatedMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "T2Space.isSeparatedMap", "kind": "theorem", "module": "Mathlib.Topology.SeparatedMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.isSeparatedMap", "kind": "theorem", "module": "Mathlib.Topology.SeparatedMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isSeparatedMap_iff_disjoint_nhds", "kind": "theorem", "module": "Mathlib.Topology.SeparatedMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isSeparatedMap_iff_nhds", "kind": "theorem", "module": "Mathlib.Topology.SeparatedMap", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "isSeparatedMap_iff_isClosed_diagonal", "kind": "theorem", "module": "Mathlib.Topology.SeparatedMap", "is_tactic_proof": false, "tactics": ["simp_rw", "nhds_prod_eq]", "refine", "simp_rw", "exact", "obtain", "exact"], "tactic_count": 7}
{"name": "isSeparatedMap_iff_isClosedEmbedding", "kind": "theorem", "module": "Mathlib.Topology.SeparatedMap", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "isSeparatedMap_iff_isClosedMap", "kind": "theorem", "module": "Mathlib.Topology.SeparatedMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSeparatedMap.pullback", "kind": "theorem", "module": "Mathlib.Topology.SeparatedMap", "is_tactic_proof": true, "tactics": ["rw", "rw", "refine", "apply_rules"], "tactic_count": 4}
{"name": "IsSeparatedMap.comp_left", "kind": "theorem", "module": "Mathlib.Topology.SeparatedMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSeparatedMap.comp_right", "kind": "theorem", "module": "Mathlib.Topology.SeparatedMap", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "IsLocallyInjective", "kind": "definition", "module": "Mathlib.Topology.SeparatedMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Injective.IsLocallyInjective", "kind": "theorem", "module": "Mathlib.Topology.SeparatedMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isLocallyInjective_iff_nhds", "kind": "theorem", "module": "Mathlib.Topology.SeparatedMap", "is_tactic_proof": true, "tactics": ["constructor", "obtain", "obtain", "exact"], "tactic_count": 4}
{"name": "isLocallyInjective_iff_isOpen_diagonal", "kind": "theorem", "module": "Mathlib.Topology.SeparatedMap", "is_tactic_proof": false, "tactics": ["simp_rw", "refine", "rintro", "obtain", "exact", "obtain", "obtain", "exact"], "tactic_count": 8}
{"name": "IsLocallyInjective_iff_isOpenEmbedding", "kind": "theorem", "module": "Mathlib.Topology.SeparatedMap", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "isLocallyInjective_iff_isOpenMap", "kind": "theorem", "module": "Mathlib.Topology.SeparatedMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "discreteTopology_iff_locallyInjective", "kind": "theorem", "module": "Mathlib.Topology.SeparatedMap", "is_tactic_proof": true, "tactics": ["rw", "refine", "convert", "rintro"], "tactic_count": 4}
{"name": "IsLocallyInjective.comp_left", "kind": "theorem", "module": "Mathlib.Topology.SeparatedMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocallyInjective.comp_right", "kind": "theorem", "module": "Mathlib.Topology.SeparatedMap", "is_tactic_proof": true, "tactics": ["rw", "rw", "apply"], "tactic_count": 3}
{"name": "IsSeparatedMap.isClosed_eqLocus", "kind": "theorem", "module": "Mathlib.Topology.SeparatedMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsLocallyInjective.isOpen_eqLocus", "kind": "theorem", "module": "Mathlib.Topology.SeparatedMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSeparatedMap.eq_of_comp_eq", "kind": "theorem", "module": "Mathlib.Topology.SeparatedMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSeparatedMap.eqOn_of_comp_eqOn", "kind": "theorem", "module": "Mathlib.Topology.SeparatedMap", "is_tactic_proof": true, "tactics": ["rw", "rw", "rw", "exact"], "tactic_count": 4}
{"name": "IsSeparatedMap.const_of_comp", "kind": "theorem", "module": "Mathlib.Topology.SeparatedMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSeparatedMap.constOn_of_comp", "kind": "theorem", "module": "Mathlib.Topology.SeparatedMap", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsKer_eq_of_t1Space", "kind": "theorem", "module": "Mathlib.Topology.Separation.AlexandrovDiscrete", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "instDiscreteTopologyOfAlexandrovDiscreteOfT1Space", "kind": "instance", "module": "Mathlib.Topology.Separation.AlexandrovDiscrete", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "t0Space_iff_inseparable", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "t0Space_iff_not_inseparable", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Inseparable.eq", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsInducing.injective", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsInducing.isEmbedding", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isEmbedding_iff_isInducing", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "t0Space_iff_nhds_injective", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhds_injective", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inseparable_iff_eq", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhds_eq_nhds_iff", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inseparable_eq_eq", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.IsTopologicalBasis.inseparable_iff", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.IsTopologicalBasis.eq_iff", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "t0Space_iff_exists_isOpen_xor'_mem", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "exists_isOpen_xor'_mem", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "specializationOrder", "kind": "definition", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.instT0Space", "kind": "instance", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "minimal_nonempty_closed_subsingleton", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": true, "tactics": ["refine", "rcases", "wlog", "refine", "obtain", "have", "exact"], "tactic_count": 7}
{"name": "minimal_nonempty_closed_eq_singleton", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.exists_closed_singleton", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": true, "tactics": ["obtain", "rcases", "exact"], "tactic_count": 3}
{"name": "minimal_nonempty_open_subsingleton", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": true, "tactics": ["refine", "rcases", "wlog", "exact", "obtain", "have", "exact"], "tactic_count": 7}
{"name": "minimal_nonempty_open_eq_singleton", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_isOpen_singleton_of_isOpen_finite", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": true, "tactics": ["lift", "induction", "rename_i", "rcases", "rcases", "exact", "rsuffices", "exact", "refine", "refine", "lift", "exact"], "tactic_count": 12}
{"name": "exists_open_singleton_of_finite", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "t0Space_of_injective_of_continuous", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsEmbedding.t0Space", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.t0Space", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.t0Space", "kind": "instance", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "t0Space_iff_or_notMem_closure", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Prod.instT0Space", "kind": "instance", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.instT0Space", "kind": "instance", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.instT0Space", "kind": "instance", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "T0Space.of_cover", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": true, "tactics": ["refine", "rcases", "lift", "rw", "exact"], "tactic_count": 5}
{"name": "T0Space.of_open_cover", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Specializes.symm", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "specializes_comm", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "specializes_iff_inseparable", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsInducing.r0Space", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instR0SpaceSubtype", "kind": "instance", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instR0SpaceProd", "kind": "instance", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instR0SpaceForall", "kind": "instance", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "R0Space.closure_singleton", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "isCompact_closure_singleton", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": true, "tactics": ["refine", "obtain", "refine", "rw", "simpa"], "tactic_count": 5}
{"name": "Filter.coclosedCompact_le_cofinite", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.relativelyCompact", "kind": "definition", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bornology.relativelyCompact.isBounded_iff", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.isCompact_closure", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosed_singleton", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpen_compl_singleton", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpen_ne", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.isOpen_mulSupport", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ne.nhdsWithin_compl_singleton", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ne.nhdsWithin_diff_singleton", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "nhdsWithin_compl_singleton_le", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": true, "tactics": ["rcases", "exact", "rw", "exact"], "tactic_count": 4}
{"name": "isOpen_setOf_eventually_nhdsWithin", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": true, "tactics": ["refine", "filter_upwards", "rcases", "exact", "rw", "exact"], "tactic_count": 6}
{"name": "Set.Finite.isClosed", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "TopologicalSpace.IsTopologicalBasis.exists_mem_of_ne", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "Finset.isClosed", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "t1Space_TFAE", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": true, "tactics": ["tfae_have", "tfae_have", "tfae_have", "refine", "simp", "tfae_have", "tfae_have", "tfae_have", "tfae_have", "tfae_have", "simp", "rintro", "exacts", "tfae_have", "tfae_have", "simp", "tfae_have", "tfae_finish"], "tactic_count": 18}
{"name": "t1Space_iff_continuous_cofinite_of", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CofiniteTopology.continuous_of", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "t1Space_iff_exists_open", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "t1Space_iff_disjoint_pure_nhds", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "t1Space_iff_disjoint_nhds_pure", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "t1Space_iff_specializes_imp_eq", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "t1Space_iff_t0Space_and_r0Space", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "disjoint_pure_nhds", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "disjoint_nhds_pure", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Specializes.eq", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "specializes_iff_eq", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "specializes_eq_eq", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pure_le_nhds_iff", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhds_le_nhds_iff", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instR0SpaceOfT1Space", "kind": "instance", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instT1SpaceCofiniteTopology", "kind": "instance", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instT1SpaceOfT0SpaceOfR0Space", "kind": "instance", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "t1Space_antitone", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousWithinAt_update_of_ne", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousAt_update_of_ne", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "continuousOn_update_iff", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": true, "tactics": ["rw", "refine", "specialize", "rw", "exact", "rw", "refine", "exact", "exact"], "tactic_count": 9}
{"name": "t1Space_of_injective_of_continuous", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsEmbedding.t1Space", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.t1Space", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.t1Space", "kind": "instance", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instT1SpaceProd", "kind": "instance", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instT1SpaceForall", "kind": "instance", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.instT1Space", "kind": "instance", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "T1Space.t0Space", "kind": "instance", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "compl_singleton_mem_nhds_iff", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "compl_singleton_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "closure_singleton", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Subsingleton.isClosed", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": true, "tactics": ["rcases", "exact", "exact"], "tactic_count": 3}
{"name": "Set.Subsingleton.closure_eq", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Subsingleton.closure", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "subsingleton_closure", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosedMap_const", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosedMap_prodMk_left", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosedMap_prodMk_right", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsWithin_insert_of_ne", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": true, "tactics": ["refine", "obtain", "refine", "rw", "exact"], "tactic_count": 5}
{"name": "insert_mem_nhdsWithin_of_subset_insert", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": true, "tactics": ["rcases", "exact", "refine", "rw", "exact"], "tactic_count": 5}
{"name": "eventuallyEq_insert", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "simp_rw", "nhdsWithin_singleton,", "filter_upwards"], "tactic_count": 4}
{"name": "ker_nhds", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "biInter_basis_nhds", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "compl_singleton_mem_nhdsSet_iff", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "nhdsSet_le_iff", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": true, "tactics": ["refine", "simp_rw", "specialize", "simp_rw", "by_contra", "exact"], "tactic_count": 6}
{"name": "nhdsSet_inj_iff", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "injective_nhdsSet", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "strictMono_nhdsSet", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhds_le_nhdsSet_iff", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Dense.diff_singleton", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dense.diff_finset", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "insert", "rw", "exact"], "tactic_count": 6}
{"name": "Dense.diff_finite", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": true, "tactics": ["convert", "exact"], "tactic_count": 2}
{"name": "eq_of_tendsto_nhds", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": ["have", "have", "fact₂"], "tactic_count": 3}
{"name": "Filter.Tendsto.eventually_ne", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.eventually_ne", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eventually_ne_nhds", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eventually_ne_nhdsWithin", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eventually_nhdsWithin_eventually_nhds_iff_of_isOpen", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": true, "tactics": ["nth_rw", "constructor", "intro", "filter_upwards", "exact", "intro", "filter_upwards", "simp_all"], "tactic_count": 8}
{"name": "eventually_nhdsNE_eventually_nhds_iff", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousWithinAt_insert", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": true, "tactics": ["rcases", "exact", "simp_rw"], "tactic_count": 3}
{"name": "continuousWithinAt_diff_singleton", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "continuousWithinAt_congr_set'", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ContinuousWithinAt.eq_const_of_mem_closure", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ContinuousWithinAt.eqOn_const_closure", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": true, "tactics": ["intro", "apply"], "tactic_count": 2}
{"name": "continuousAt_of_tendsto_nhds", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "tendsto_const_nhds_iff", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "isOpen_singleton_of_finite_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": true, "tactics": ["have", "have", "have", "have", "rwa"], "tactic_count": 5}
{"name": "infinite_of_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "instT1SpaceOfDiscreteTopology", "kind": "instance", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finite.instDiscreteTopology", "kind": "instance", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.isDiscrete", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.continuousOn", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": true, "tactics": ["rw", "have", "fun_prop"], "tactic_count": 3}
{"name": "SeparationQuotient.t1Space_iff", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": true, "tactics": ["rw", "constructor", "intro", "rw", "rintro", "change", "have", "have", "rw", "exact"], "tactic_count": 10}
{"name": "isClosed_inter_singleton", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosed_singleton_inter", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "singleton_mem_nhdsWithin_of_mem_discrete", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": true, "tactics": ["rw", "have", "simpa"], "tactic_count": 3}
{"name": "nhdsWithin_of_mem_discrete", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.exists_inter_eq_singleton_of_mem_discrete", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "nhds_inter_eq_singleton_of_mem_discrete", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "isOpen_inter_eq_singleton_of_mem_discrete", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "grind"], "tactic_count": 3}
{"name": "disjoint_nhdsWithin_of_mem_discrete", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosedEmbedding_update", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": ["refine", "rw", "apply", "simp"], "tactic_count": 4}
{"name": "nhdsNE_le_cofinite", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": true, "tactics": ["refine", "rcases", "exacts"], "tactic_count": 3}
{"name": "Function.update_eventuallyEq_nhdsNE", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instR0Space", "kind": "instance", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "disjoint_nhds_nhds_iff_not_specializes", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "specializes_iff_not_disjoint", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "disjoint_nhds_nhds_iff_not_inseparable", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "r1Space_iff_inseparable_or_disjoint_nhds", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Inseparable.of_nhds_neBot", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "r1_separation", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": true, "tactics": ["rw", "obtain", "exact"], "tactic_count": 3}
{"name": "tendsto_nhds_unique_inseparable", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosed_setOf_specializes", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "isClosed_setOf_inseparable", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsCompact.mem_closure_iff_exists_inseparable", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": true, "tactics": ["refine", "contrapose", "have", "hK.disjoint_nhdsSet_right.2", "simpa"], "tactic_count": 5}
{"name": "IsCompact.closure_eq_biUnion_inseparable", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "IsCompact.closure_eq_biUnion_closure_singleton", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": true, "tactics": ["simp", "setOf_mem_eq]"], "tactic_count": 2}
{"name": "IsCompact.closure_subset_of_isOpen", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsCompact.closure", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": true, "tactics": ["refine", "rcases", "exact"], "tactic_count": 3}
{"name": "IsCompact.closure_of_subset", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_isCompact_superset_iff", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparatedNhds.of_isCompact_isCompact_isClosed", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": ["simp_rw", "disjoint_nhds_nhds_iff_not_inseparable]", "intro", "exact"], "tactic_count": 4}
{"name": "IsCompact.binary_compact_cover", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": true, "tactics": ["have", "have", "apply", "rw", "exact", "have", "this.mono", "rcases", "exact", "rw"], "tactic_count": 10}
{"name": "IsCompact.finite_compact_cover", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "refine", "simpa", "insert", "simp", "simp", "have", "rcases", "rcases", "refine", "intro", "rcases", "simp", "simp", "intro", "rcases", "simp", "simp", "simp"], "tactic_count": 21}
{"name": "R1Space.of_continuous_specializes_imp", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsInducing.r1Space", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "R1Space.induced", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instR1SpaceSubtype", "kind": "instance", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "R1Space.sInf", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": true, "tactics": ["let", "refine", "simp", "by_cases", "rcases", "exact", "exact"], "tactic_count": 7}
{"name": "R1Space.iInf", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "R1Space.inf", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply", "simp"], "tactic_count": 3}
{"name": "instR1SpaceProd", "kind": "instance", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instR1SpaceForall", "kind": "instance", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_mem_nhds_isCompact_mapsTo_of_isCompact_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": true, "tactics": ["have", "obtain", "simp_rw", "disjoint_nhds_nhds_iff_not_inseparable]", "rintro", "refine", "rwa", "refine", "filter_upwards", "by_contra", "exact"], "tactic_count": 11}
{"name": "instLocallyCompactPairOfWeaklyLocallyCompactSpaceOfR1Space", "kind": "instance", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.isCompact_isClosed_basis_nhds", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.coclosedCompact_eq_cocompact", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "Bornology.relativelyCompact_eq_inCompact", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCompact_isClosed_basis_nhds", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_mem_nhds_isCompact_isClosed", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "WeaklyLocallyCompactSpace.locallyCompactSpace", "kind": "instance", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_isOpen_superset_and_isCompact_closure", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "exists_isOpen_mem_isCompact_closure", "kind": "theorem", "module": "Mathlib.Topology.Separation.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "completelyRegularSpace_iff_isOpen", "kind": "theorem", "module": "Mathlib.Topology.Separation.CompletelyRegular", "is_tactic_proof": true, "tactics": ["conv_lhs", "tactic", "simp_rw", "not_not]"], "tactic_count": 4}
{"name": "CompletelyRegularSpace.completely_regular_isOpen", "kind": "theorem", "module": "Mathlib.Topology.Separation.CompletelyRegular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompletelyRegularSpace.instRegularSpace", "kind": "instance", "module": "Mathlib.Topology.Separation.CompletelyRegular", "is_tactic_proof": true, "tactics": ["rw", "intro", "obtain", "apply", "apply", "exact"], "tactic_count": 6}
{"name": "NormalSpace.instCompletelyRegularSpace", "kind": "instance", "module": "Mathlib.Topology.Separation.CompletelyRegular", "is_tactic_proof": true, "tactics": ["rw", "intro", "have", "have", "rw", "intro", "exact", "let", "let", "have", "have", "have", "exact"], "tactic_count": 13}
{"name": "Topology.IsInducing.completelyRegularSpace", "kind": "theorem", "module": "Mathlib.Topology.Separation.CompletelyRegular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCompletelyRegularSpaceSubtype", "kind": "instance", "module": "Mathlib.Topology.Separation.CompletelyRegular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "completelyRegularSpace_induced", "kind": "theorem", "module": "Mathlib.Topology.Separation.CompletelyRegular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "completelyRegularSpace_iInf", "kind": "theorem", "module": "Mathlib.Topology.Separation.CompletelyRegular", "is_tactic_proof": false, "tactics": ["letI", "rw", "intro", "simp_rw", "obtain", "simp", "choose", "replace", "clear", "choose", "use", "constructorm*", "solve_by_elim", "simpa", "simp", "conv", "intro", "specialize", "exists"], "tactic_count": 19}
{"name": "completelyRegularSpace_inf", "kind": "theorem", "module": "Mathlib.Topology.Separation.CompletelyRegular", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "instCompletelyRegularSpaceForall", "kind": "instance", "module": "Mathlib.Topology.Separation.CompletelyRegular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCompletelyRegularSpaceProd", "kind": "instance", "module": "Mathlib.Topology.Separation.CompletelyRegular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isInducing_stoneCechUnit", "kind": "theorem", "module": "Mathlib.Topology.Separation.CompletelyRegular", "is_tactic_proof": true, "tactics": ["rw", "intro", "apply", "rw", "simp_rw", "intro", "obtain", "conv", "rw", "refine", "rw", "simp"], "tactic_count": 12}
{"name": "isDenseInducing_stoneCechUnit", "kind": "theorem", "module": "Mathlib.Topology.Separation.CompletelyRegular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "completelyRegularSpace_iff_isInducing_stoneCechUnit", "kind": "theorem", "module": "Mathlib.Topology.Separation.CompletelyRegular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompletelyRegularSpace.isTopologicalBasis_clopens_of_cardinalMk_lt_continuum", "kind": "theorem", "module": "Mathlib.Topology.Separation.CompletelyRegular", "is_tactic_proof": true, "tactics": ["refine", "choose", "obtain", "let", "have", "simpa", "rw", "obtain", "have", "have", "refine", "simp", "refine", "contrapose", "simpa"], "tactic_count": 15}
{"name": "T35Space.instT3space", "kind": "instance", "module": "Mathlib.Topology.Separation.CompletelyRegular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "T4Space.instT35Space", "kind": "instance", "module": "Mathlib.Topology.Separation.CompletelyRegular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsEmbedding.t35Space", "kind": "theorem", "module": "Mathlib.Topology.Separation.CompletelyRegular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instT35SpaceSubtype", "kind": "instance", "module": "Mathlib.Topology.Separation.CompletelyRegular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instT35SpaceForall", "kind": "instance", "module": "Mathlib.Topology.Separation.CompletelyRegular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instT35SpaceProd", "kind": "instance", "module": "Mathlib.Topology.Separation.CompletelyRegular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "separatesPoints_continuous_of_t35Space", "kind": "theorem", "module": "Mathlib.Topology.Separation.CompletelyRegular", "is_tactic_proof": true, "tactics": ["intro", "obtain", "exact"], "tactic_count": 3}
{"name": "separatesPoints_continuous_of_t35Space_Icc", "kind": "theorem", "module": "Mathlib.Topology.Separation.CompletelyRegular", "is_tactic_proof": true, "tactics": ["intro", "obtain", "exact"], "tactic_count": 3}
{"name": "injective_stoneCechUnit_of_t35Space", "kind": "theorem", "module": "Mathlib.Topology.Separation.CompletelyRegular", "is_tactic_proof": true, "tactics": ["intro", "contrapose", "obtain", "exact"], "tactic_count": 4}
{"name": "isEmbedding_stoneCechUnit", "kind": "theorem", "module": "Mathlib.Topology.Separation.CompletelyRegular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isDenseEmbedding_stoneCechUnit", "kind": "theorem", "module": "Mathlib.Topology.Separation.CompletelyRegular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "t35Space_iff_isEmbedding_stoneCechUnit", "kind": "theorem", "module": "Mathlib.Topology.Separation.CompletelyRegular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TotallyDisconnectedSpace.t1Space", "kind": "instance", "module": "Mathlib.Topology.Separation.Connected", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "exact"], "tactic_count": 4}
{"name": "PreconnectedSpace.trivial_of_discrete", "kind": "theorem", "module": "Mathlib.Topology.Separation.Connected", "is_tactic_proof": true, "tactics": ["by_contra", "rw", "exact"], "tactic_count": 3}
{"name": "IsPreconnected.infinite_of_nontrivial", "kind": "theorem", "module": "Mathlib.Topology.Separation.Connected", "is_tactic_proof": true, "tactics": ["refine", "haveI", "exact"], "tactic_count": 3}
{"name": "PreconnectedSpace.infinite", "kind": "theorem", "module": "Mathlib.Topology.Separation.Connected", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ConnectedSpace.neBot_nhdsWithin_compl_of_nontrivial_of_t1space", "kind": "instance", "module": "Mathlib.Topology.Separation.Connected", "is_tactic_proof": true, "tactics": ["by_contra", "rw", "replace", "nonempty_inter", "simp"], "tactic_count": 5}
{"name": "instHasCountableSeparatingOnIsOpenOfT0SpaceOfSecondCountableTopologyElem", "kind": "instance", "module": "Mathlib.Topology.Separation.CountableSeparatingOn", "is_tactic_proof": true, "tactics": ["suffices", "refine", "exact"], "tactic_count": 3}
{"name": "instHasCountableSeparatingOnIsClosedOfIsOpen", "kind": "instance", "module": "Mathlib.Topology.Separation.CountableSeparatingOn", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.IsOpenCover.exists_finite_clopen_cover", "kind": "theorem", "module": "Mathlib.Topology.Separation.DisjointCover", "is_tactic_proof": true, "tactics": ["choose", "choose", "compact_exists_isClopen_in_isOpen", "obtain", "isCompact_univ.elim_finite_subcover", "refine", "obtain", "exact"], "tactic_count": 8}
{"name": "TopologicalSpace.IsOpenCover.exists_finite_nonempty_disjoint_clopen_cover", "kind": "theorem", "module": "Mathlib.Topology.Separation.DisjointCover", "is_tactic_proof": true, "tactics": ["classical", "obtain", "obtain", "simp", "let", "refine", "exact", "exact", "obtain", "have", "exact", "exact"], "tactic_count": 12}
{"name": "TopologicalSpace.exists_open_prod_subset_of_mem_nhds_diagonal", "kind": "theorem", "module": "Mathlib.Topology.Separation.DisjointCover", "is_tactic_proof": true, "tactics": ["have", "obtain", "exact"], "tactic_count": 3}
{"name": "TopologicalSpace.exists_finite_open_cover_prod_subset_of_mem_nhds_diagonal_of_compact", "kind": "theorem", "module": "Mathlib.Topology.Separation.DisjointCover", "is_tactic_proof": true, "tactics": ["choose", "obtain", "refine", "simpa"], "tactic_count": 4}
{"name": "_private.Mathlib.Topology.Separation.DisjointCover.0.TopologicalSpace.exists_finite_disjoint_nonempty_clopen_cover_of_mem_nhds_diagonal_of_profinite", "kind": "theorem", "module": "Mathlib.Topology.Separation.DisjointCover", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "refine", "exact"], "tactic_count": 4}
{"name": "ContinuousMap.exists_disjoint_nonempty_clopen_cover_of_mem_nhds_diagonal", "kind": "theorem", "module": "Mathlib.Topology.Separation.DisjointCover", "is_tactic_proof": false, "tactics": ["have", "rw", "rintro", "exact", "exact"], "tactic_count": 5}
{"name": "ContinuousMap.exists_finite_approximation_of_mem_nhds_diagonal", "kind": "theorem", "module": "Mathlib.Topology.Separation.DisjointCover", "is_tactic_proof": true, "tactics": ["obtain", "have", "refine", "simpa", "choose", "have", "choose", "refine", "convert", "exact"], "tactic_count": 10}
{"name": "ContinuousMap.exists_finite_sum_const_mulIndicator_approximation_of_mem_nhds_diagonal", "kind": "theorem", "module": "Mathlib.Topology.Separation.DisjointCover", "is_tactic_proof": true, "tactics": ["obtain", "refine", "convert", "exact"], "tactic_count": 4}
{"name": "IsGδ.compl_singleton", "kind": "theorem", "module": "Mathlib.Topology.Separation.GDelta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Countable.isGδ_compl", "kind": "theorem", "module": "Mathlib.Topology.Separation.GDelta", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.Finite.isGδ_compl", "kind": "theorem", "module": "Mathlib.Topology.Separation.GDelta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Subsingleton.isGδ_compl", "kind": "theorem", "module": "Mathlib.Topology.Separation.GDelta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Finset.isGδ_compl", "kind": "theorem", "module": "Mathlib.Topology.Separation.GDelta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGδ.singleton", "kind": "theorem", "module": "Mathlib.Topology.Separation.GDelta", "is_tactic_proof": true, "tactics": ["rcases", "rw", "exact"], "tactic_count": 3}
{"name": "Set.Finite.isGδ", "kind": "theorem", "module": "Mathlib.Topology.Separation.GDelta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Disjoint.hasSeparatingCover_closed_gdelta_right", "kind": "theorem", "module": "Mathlib.Topology.Separation.GDelta", "is_tactic_proof": true, "tactics": ["obtain", "rcases", "rw", "rw", "exact", "obtain", "choose", "apply", "rw", "exact", "have", "apply", "rw", "refine", "obtain", "refine", "rw", "use", "constructor", "rw", "exact", "refine", "simp", "rw", "exact"], "tactic_count": 25}
{"name": "PerfectlyNormalSpace.toCompletelyNormalSpace", "kind": "instance", "module": "Mathlib.Topology.Separation.GDelta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.isGδ", "kind": "theorem", "module": "Mathlib.Topology.Separation.GDelta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instR0SpaceOfPerfectlyNormalSpace", "kind": "instance", "module": "Mathlib.Topology.Separation.GDelta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "T6Space.toT5Space", "kind": "instance", "module": "Mathlib.Topology.Separation.GDelta", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "t2_separation", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "t2Space_iff_disjoint_nhds", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": true, "tactics": ["refine", "simp", "and_left_comm]"], "tactic_count": 3}
{"name": "disjoint_nhds_nhds", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "pairwise_disjoint_nhds", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.pairwiseDisjoint_nhds", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Finite.t2_separation", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "T2Space.t1Space", "kind": "instance", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "T2Space.r1Space", "kind": "instance", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.t2Space_iff", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": true, "tactics": ["simp", "r1Space_iff_inseparable_or_disjoint_nhds,"], "tactic_count": 2}
{"name": "SeparationQuotient.t2Space", "kind": "instance", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instT2SpaceOfR1SpaceOfT0Space", "kind": "instance", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "R1Space.t2Space_iff_t0Space", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": true, "tactics": ["constructor"], "tactic_count": 1}
{"name": "t2_iff_nhds", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "eq_of_nhds_neBot", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "t2Space_iff_nhds", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "t2_separation_nhds", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "t2_separation_compact_nhds", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "t2_iff_ultrafilter", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "t2_iff_isClosed_diagonal", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": true, "tactics": ["simp", "compl_diagonal_mem_prod,"], "tactic_count": 2}
{"name": "isClosed_diagonal", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "t2Space_iff_of_isOpenQuotientMap", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": true, "tactics": ["rw", "replace", "refine", "simp_rw", "convert", "exact"], "tactic_count": 6}
{"name": "tendsto_nhds_unique", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_nhds_unique'", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_nhds_unique_of_eventuallyEq", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_nhds_unique_of_frequently_eq", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.nhdsSet_inter_eq", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": true, "tactics": ["refine", "simp_rw", "refine", "rcases", "exact", "exact"], "tactic_count": 6}
{"name": "IsCompact.separation_of_notMem", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": true, "tactics": ["simpa", "disjoint_singleton_right.mpr"], "tactic_count": 2}
{"name": "IsCompact.disjoint_nhdsSet_nhds", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Set.InjOn.exists_mem_nhdsSet", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": ["have", "rcases", "rcases", "exact", "suffices", "refine", "exact", "rw", "exact"], "tactic_count": 9}
{"name": "Set.InjOn.exists_isOpen_superset", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lim_eq", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lim_eq_iff", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ultrafilter.lim_eq_iff_le_nhds", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpen_iff_ultrafilter'", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": true, "tactics": ["rw", "refine", "intro", "rw", "exact"], "tactic_count": 5}
{"name": "Filter.Tendsto.limUnder_eq", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.limUnder_eq_iff", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.limUnder_eq", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lim_nhds", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "limUnder_nhds_id", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lim_nhdsWithin", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "limUnder_nhdsWithin_id", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteTopology.toT2Space", "kind": "instance", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "separated_by_continuous", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "separated_by_isOpenEmbedding", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instT2SpaceSubtype", "kind": "instance", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Prod.t2Space", "kind": "instance", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "T2Space.of_injective_continuous", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsEmbedding.t2Space", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.t2Space", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.instT2Space", "kind": "instance", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instT2SpaceSum", "kind": "instance", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "exact", "exact", "exact", "exact"], "tactic_count": 6}
{"name": "Pi.t2Space", "kind": "instance", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.t2Space", "kind": "instance", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "rcases", "replace", "exact", "let", "exact"], "tactic_count": 7}
{"name": "t2Setoid", "kind": "definition", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "T2Quotient", "kind": "definition", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "T2Quotient.instTopologicalSpace", "kind": "instance", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "T2Quotient.mk", "kind": "definition", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "T2Quotient.mk_eq", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "T2Quotient.surjective_mk", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "T2Quotient.continuous_mk", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "T2Quotient.inductionOn", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "T2Quotient.inductionOn₂", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "T2Quotient.instT2Space", "kind": "instance", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": true, "tactics": ["rw", "rintro", "obtain", "simpa", "exact"], "tactic_count": 5}
{"name": "T2Quotient.compatible", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": true, "tactics": ["change", "exact"], "tactic_count": 2}
{"name": "T2Quotient.lift", "kind": "definition", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "T2Quotient.continuous_lift", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "T2Quotient.lift_mk", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "T2Quotient.unique_lift", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": true, "tactics": ["apply", "simp"], "tactic_count": 2}
{"name": "isClosed_eq", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.isClosed_eq", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpen_ne_fun", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.EqOn.closure", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.ext_on", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eqOn_closure₂'", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eqOn_closure₂", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.EqOn.of_subset_closure", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": true, "tactics": ["intro", "have", "exact", "tendsto_nhds_unique_of_eventuallyEq"], "tactic_count": 4}
{"name": "Function.LeftInverse.isClosed_range", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.LeftInverse.isClosedEmbedding", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparatedNhds.of_isCompact_isCompact", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "SeparatedNhds.of_isClosed_isCompact_closure_compl_isClosed", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": true, "tactics": ["have", "rw", "refine", "disjoint_compl_right.mono_left", "rw", "refine", "exact"], "tactic_count": 7}
{"name": "SeparatedNhds.of_finset_finset", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparatedNhds.of_singleton_finset", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.isClosed", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.preimage_continuous", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.isCompact_iff", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": true, "tactics": ["constructor", "exact", "exact"], "tactic_count": 3}
{"name": "Pi.isCompact_closure_iff", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "exists_subset_nhds_of_isCompact", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompactExhaustion.isClosed", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.inter", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "image_closure_of_isCompact", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousAt.ne_iff_eventually_ne", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": true, "tactics": ["constructor", "obtain", "rw", "filter_upwards", "intro", "simp", "by_contra", "rw", "have", "simp", "obtain", "exact"], "tactic_count": 12}
{"name": "ContinuousAt.eventuallyEq_nhds_iff_eventuallyEq_nhdsNE", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": true, "tactics": ["constructor", "apply", "by_contra", "obtain", "have", "have", "simp_all", "simp", "exact"], "tactic_count": 9}
{"name": "Continuous.isClosedMap", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.isClosedEmbedding", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsQuotientMap.of_surjective_continuous", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isPreirreducible_iff_forall_mem_subset_closure_singleton", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": true, "tactics": ["constructor", "intro", "by_contra", "obtain", "exact", "intro", "exact"], "tactic_count": 7}
{"name": "isPreirreducible_iff_subsingleton", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsPreirreducible.subsingleton", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isIrreducible_iff_singleton", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "not_preirreducible_nontrivial_t2", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "t2Space_antitone", "kind": "theorem", "module": "Mathlib.Topology.Separation.Hausdorff", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompletelyRegularSpace.totallySeparatedSpace_of_cardinalMk_lt_continuum", "kind": "theorem", "module": "Mathlib.Topology.Separation.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompletelyRegularSpace.instTotallySeparatedSpaceOfCountable", "kind": "instance", "module": "Mathlib.Topology.Separation.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Countable.totallySeparatedSpace", "kind": "theorem", "module": "Mathlib.Topology.Separation.Lemmas", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Countable.isTotallyDisconnected", "kind": "theorem", "module": "Mathlib.Topology.Separation.Lemmas", "is_tactic_proof": true, "tactics": ["rw", "have", "infer_instance"], "tactic_count": 3}
{"name": "instCompletelyNormalSpaceOfIsUpperSet", "kind": "instance", "module": "Mathlib.Topology.Separation.LinearUpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCompletelyNormalSpaceOfIsLowerSet", "kind": "instance", "module": "Mathlib.Topology.Separation.LinearUpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCompletelyNormalSpaceProp", "kind": "instance", "module": "Mathlib.Topology.Separation.LinearUpperLowerSetTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.two_pow_mk_le_two_pow_mk_dense", "kind": "theorem", "module": "Mathlib.Topology.Separation.NotNormal", "is_tactic_proof": false, "tactics": ["have", "rw", "exact", "choose", "normal_separation", "have", "by_contra", "rw", "have", "hd.inter_open_nonempty", "ht.mono", "rw", "exact", "have", "rw", "apply", "rw", "intro", "exact"], "tactic_count": 19}
{"name": "IsClosed.mk_lt_two_pow_mk_dense", "kind": "theorem", "module": "Mathlib.Topology.Separation.NotNormal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.two_pow_mk_lt_continuum", "kind": "theorem", "module": "Mathlib.Topology.Separation.NotNormal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.mk_lt_continuum", "kind": "theorem", "module": "Mathlib.Topology.Separation.NotNormal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.not_normal_of_continuum_le_mk", "kind": "theorem", "module": "Mathlib.Topology.Separation.NotNormal", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "totallySeparatedSpace_of_t0_of_basis_clopen", "kind": "theorem", "module": "Mathlib.Topology.Separation.Profinite", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "choose", "obtain", "rcases", "choose", "exact", "disjoint_compl_right⟩", "choose", "exact"], "tactic_count": 10}
{"name": "nhds_basis_clopen", "kind": "theorem", "module": "Mathlib.Topology.Separation.Profinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isTopologicalBasis_isClopen", "kind": "theorem", "module": "Mathlib.Topology.Separation.Profinite", "is_tactic_proof": true, "tactics": ["apply", "intro", "have", "rcases", "use", "tauto"], "tactic_count": 6}
{"name": "compact_exists_isClopen_in_isOpen", "kind": "theorem", "module": "Mathlib.Topology.Separation.Profinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "loc_compact_Haus_tot_disc_of_zero_dim", "kind": "theorem", "module": "Mathlib.Topology.Separation.Profinite", "is_tactic_proof": true, "tactics": ["refine", "obtain", "let", "have", "lift", "haveI", "obtain", "have", "refine", "let", "have", "have", "have", "refine", "have", "rw", "apply", "rw", "apply", "have", "have", "rw", "rw", "apply", "use"], "tactic_count": 25}
{"name": "loc_compact_t2_tot_disc_iff_tot_sep", "kind": "theorem", "module": "Mathlib.Topology.Separation.Profinite", "is_tactic_proof": true, "tactics": ["constructor", "intro", "exact", "apply"], "tactic_count": 4}
{"name": "instTotallySeparatedSpaceOfTotallyDisconnectedSpace", "kind": "instance", "module": "Mathlib.Topology.Separation.Profinite", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_clopen_of_closed_subset_open", "kind": "theorem", "module": "Mathlib.Topology.Separation.Profinite", "is_tactic_proof": true, "tactics": ["choose", "compact_exists_isClopen_in_isOpen", "have", "mem_iUnion.mpr", "choose", "exact"], "tactic_count": 6}
{"name": "exists_clopen_partition_of_clopen_cover", "kind": "theorem", "module": "Mathlib.Topology.Separation.Profinite", "is_tactic_proof": true, "tactics": ["induction", "of_equiv", "obtain", "refine", "simp", "simpa", "h_empty", "let", "have", "have", "rw", "exact", "let", "have", "have", "rw", "simpa", "obtain", "exists_clopen_of_closed_subset_open", "have", "let", "have", "have", "rw", "refine", "exact", "obtain", "let", "have", "have", "simp", "exact", "let", "refine", "all_goals", "intro", "rw", "by_cases", "by_cases", "have", "obtain", "exact", "obtain", "have", "obtain", "exact", "rw", "rintro", "simp", "simpa", "simpa", "simpa"], "tactic_count": 52}
{"name": "regularSpace_TFAE", "kind": "theorem", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": false, "tactics": ["tfae_have", "rw", "simp", "tfae_have", "tfae_have", "rw", "rcases", "exact", "tfae_have", "have", "rcases", "refine", "rwa", "tfae_have", "refine", "exact", "tfae_have", "tfae_finish"], "tactic_count": 18}
{"name": "RegularSpace.of_lift'_closure_le", "kind": "theorem", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RegularSpace.of_lift'_closure", "kind": "theorem", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RegularSpace.of_hasBasis", "kind": "theorem", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RegularSpace.of_exists_mem_nhds_isClosed_subset", "kind": "theorem", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instRegularSpaceOfWeaklyLocallyCompactSpaceOfR1Space", "kind": "instance", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "regularSpace_generateFrom", "kind": "theorem", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": false, "tactics": ["refine", "obtain", "rw", "rw", "induction", "basic", "univ", "inter", "sUnion", "obtain", "grw", "exact"], "tactic_count": 12}
{"name": "disjoint_nhdsSet_nhds", "kind": "theorem", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "disjoint_nhds_nhdsSet", "kind": "theorem", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instR1Space", "kind": "instance", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_mem_nhds_isClosed_subset", "kind": "theorem", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "closed_nhds_basis", "kind": "theorem", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lift'_nhds_closure", "kind": "theorem", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.nhds_closure", "kind": "theorem", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasBasis_nhds_closure", "kind": "theorem", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasBasis_opens_closure", "kind": "theorem", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.exists_isOpen_closure_subset", "kind": "theorem", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": false, "tactics": ["have", "simpa", "rcases", "refine", "exact"], "tactic_count": 5}
{"name": "IsCompact.lift'_closure_nhdsSet", "kind": "theorem", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": true, "tactics": ["refine", "rcases", "exact"], "tactic_count": 3}
{"name": "TopologicalSpace.IsTopologicalBasis.nhds_basis_closure", "kind": "theorem", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "TopologicalSpace.IsTopologicalBasis.exists_closure_subset", "kind": "theorem", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Topology.IsInducing.regularSpace", "kind": "theorem", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "regularSpace_induced", "kind": "theorem", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "regularSpace_sInf", "kind": "theorem", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": true, "tactics": ["let", "have", "rw", "exact", "refine", "exact"], "tactic_count": 6}
{"name": "regularSpace_iInf", "kind": "theorem", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RegularSpace.inf", "kind": "theorem", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "instRegularSpaceSubtype", "kind": "instance", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instRegularSpaceProd", "kind": "instance", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instRegularSpaceForall", "kind": "instance", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparatedNhds.of_isCompact_isClosed", "kind": "theorem", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": true, "tactics": ["simpa", "disjoint_left]"], "tactic_count": 2}
{"name": "IsClosed.HasSeparatingCover", "kind": "theorem", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": true, "tactics": ["rcases", "rw", "exact", "hasSeparatingCovers_iff_separatedNhds.mpr", "have", "wlog", "exact", "obtain", "exact", "disjoint_left.mpr", "mem_interior_iff_mem_nhds.mpr", "choose", "obtain", "s_cl.isLindelof.indexed_countable_subcover", "exact"], "tactic_count": 15}
{"name": "disjoint_nested_nhds_of_not_inseparable", "kind": "theorem", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "rcases", "exact"], "tactic_count": 4}
{"name": "exists_compact_closed_between", "kind": "theorem", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.nhdsSet_basis_isCompact_isClosed", "kind": "theorem", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": true, "tactics": ["rw", "intro", "obtain", "exact"], "tactic_count": 4}
{"name": "exists_open_between_and_isCompact_closure", "kind": "theorem", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": true, "tactics": ["rcases", "have", "refine", "exact"], "tactic_count": 4}
{"name": "IsCompact.closure_eq_nhdsKer", "kind": "theorem", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": true, "tactics": ["apply", "rw", "simp", "intro", "by_contra", "rw", "obtain", "exact"], "tactic_count": 8}
{"name": "disjoint_lift'_closure_nhds", "kind": "theorem", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "T25Space.t2Space", "kind": "instance", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_nhds_disjoint_closure", "kind": "theorem", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_open_nhds_disjoint_closure", "kind": "theorem", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "T25Space.of_injective_continuous", "kind": "theorem", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsEmbedding.t25Space", "kind": "theorem", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.t25Space", "kind": "theorem", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.instT25Space", "kind": "instance", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instT3Space", "kind": "instance", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "RegularSpace.t3Space_iff_t0Space", "kind": "theorem", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": true, "tactics": ["constructor", "infer_instance"], "tactic_count": 2}
{"name": "T3Space.t25Space", "kind": "instance", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": true, "tactics": ["refine", "rw", "have", "simp", "exact"], "tactic_count": 5}
{"name": "Topology.IsEmbedding.t3Space", "kind": "theorem", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.t3Space", "kind": "theorem", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.t3Space", "kind": "instance", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.instT3Space", "kind": "instance", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instT3SpaceProd", "kind": "instance", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instT3SpaceForall", "kind": "instance", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "disjoint_nested_nhds", "kind": "theorem", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instT3SpaceSeparationQuotientOfRegularSpace", "kind": "instance", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "normal_separation", "kind": "theorem", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "disjoint_nhdsSet_nhdsSet", "kind": "theorem", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "normal_exists_closure_subset", "kind": "theorem", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": true, "tactics": ["have", "rcases", "refine", "exact"], "tactic_count": 4}
{"name": "Topology.IsClosedEmbedding.normalSpace", "kind": "theorem", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.normalSpace", "kind": "theorem", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormalSpace.of_compactSpace_r1Space", "kind": "instance", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormalSpace.of_regularSpace_lindelofSpace", "kind": "instance", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NormalSpace.of_regularSpace_secondCountableTopology", "kind": "instance", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instT4SpaceOfT1SpaceOfNormalSpace", "kind": "instance", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "T4Space.t3Space", "kind": "instance", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsClosedEmbedding.t4Space", "kind": "theorem", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.t4Space", "kind": "theorem", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.instT4Space", "kind": "instance", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.instNormalSpace", "kind": "instance", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompletelyNormalSpace.toNormalSpace", "kind": "instance", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsEmbedding.completelyNormalSpace", "kind": "theorem", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": true, "tactics": ["refine", "simp", "refine", "rwa", "subset_compl_iff_disjoint_left]", "rwa", "subset_compl_iff_disjoint_right]"], "tactic_count": 7}
{"name": "instCompletelyNormalSpaceSubtype", "kind": "instance", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.instCompletelyNormalSpace", "kind": "instance", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "completelyNormalSpace_iff_forall_isOpen_normalSpace", "kind": "theorem", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": true, "tactics": ["refine", "let", "have", "specialize", "have", "rw", "intro", "exact", "obtain", "normal_separation", "rw", "obtain", "obtain", "rw", "rw", "refine", "intro", "exact", "intro", "exact", "rw", "intro", "exact"], "tactic_count": 23}
{"name": "completelyNormalSpace_iff_forall_normalSpace", "kind": "theorem", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompletelyNormalSpace.of_regularSpace_secondCountableTopology", "kind": "instance", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsEmbedding.t5Space", "kind": "theorem", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.t5Space", "kind": "theorem", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "T5Space.toT4Space", "kind": "instance", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instT5SpaceSubtype", "kind": "instance", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.instT5Space", "kind": "instance", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "t5Space_iff_forall_isOpen_t4Space", "kind": "theorem", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "t5Space_iff_forall_t4Space", "kind": "theorem", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instT5SpaceSeparationQuotientOfCompletelyNormalSpaceOfR0Space", "kind": "instance", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "connectedComponent_eq_iInter_isClopen", "kind": "theorem", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": true, "tactics": ["apply", "refine", "have", "rw", "intro", "rcases", "obtain", "of", "so", "have", "rw", "obtain", "refine", "exact", "exact", "rwa", "have", "rw", "have", "by_cases", "suffices", "apply", "exact", "iInter_subset", "have", "suffices", "refine", "exact"], "tactic_count": 28}
{"name": "ConnectedComponents.t2", "kind": "instance", "module": "Mathlib.Topology.Separation.Regular", "is_tactic_proof": true, "tactics": ["refine", "rw", "have", "rw", "obtain", "have", "obtain", "set", "have", "exact", "rw", "refine", "exact"], "tactic_count": 13}
{"name": "SeparatedNhds", "kind": "definition", "module": "Mathlib.Topology.Separation.SeparatedNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "separatedNhds_iff_disjoint", "kind": "theorem", "module": "Mathlib.Topology.Separation.SeparatedNhds", "is_tactic_proof": true, "tactics": ["simp", "and_comm,"], "tactic_count": 2}
{"name": "HasSeparatingCover", "kind": "definition", "module": "Mathlib.Topology.Separation.SeparatedNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hasSeparatingCovers_iff_separatedNhds", "kind": "theorem", "module": "Mathlib.Topology.Separation.SeparatedNhds", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "have", "have", "rcases", "simp", "refine", "simp_all", "refine", "open_lemma", "open_lemma", "cover_lemma", "rw", "rintro", "suffices", "intro", "have", "by_contra", "exact", "exact", "rintro", "exact"], "tactic_count": 22}
{"name": "Set.hasSeparatingCover_empty_left", "kind": "theorem", "module": "Mathlib.Topology.Separation.SeparatedNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.hasSeparatingCover_empty_right", "kind": "theorem", "module": "Mathlib.Topology.Separation.SeparatedNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "HasSeparatingCover.mono", "kind": "theorem", "module": "Mathlib.Topology.Separation.SeparatedNhds", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "SeparatedNhds.symm", "kind": "theorem", "module": "Mathlib.Topology.Separation.SeparatedNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparatedNhds.comm", "kind": "theorem", "module": "Mathlib.Topology.Separation.SeparatedNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparatedNhds.preimage", "kind": "theorem", "module": "Mathlib.Topology.Separation.SeparatedNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparatedNhds.disjoint", "kind": "theorem", "module": "Mathlib.Topology.Separation.SeparatedNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparatedNhds.disjoint_closure_left", "kind": "theorem", "module": "Mathlib.Topology.Separation.SeparatedNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparatedNhds.disjoint_closure_right", "kind": "theorem", "module": "Mathlib.Topology.Separation.SeparatedNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparatedNhds.empty_right", "kind": "theorem", "module": "Mathlib.Topology.Separation.SeparatedNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparatedNhds.empty_left", "kind": "theorem", "module": "Mathlib.Topology.Separation.SeparatedNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparatedNhds.mono", "kind": "theorem", "module": "Mathlib.Topology.Separation.SeparatedNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparatedNhds.union_left", "kind": "theorem", "module": "Mathlib.Topology.Separation.SeparatedNhds", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "SeparatedNhds.union_right", "kind": "theorem", "module": "Mathlib.Topology.Separation.SeparatedNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparatedNhds.isOpen_left_of_isOpen_union", "kind": "theorem", "module": "Mathlib.Topology.Separation.SeparatedNhds", "is_tactic_proof": true, "tactics": ["obtain", "suffices", "rw"], "tactic_count": 3}
{"name": "SeparatedNhds.isOpen_right_of_isOpen_union", "kind": "theorem", "module": "Mathlib.Topology.Separation.SeparatedNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparatedNhds.isOpen_union_iff", "kind": "theorem", "module": "Mathlib.Topology.Separation.SeparatedNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparatedNhds.isClosed_left_of_isClosed_union", "kind": "theorem", "module": "Mathlib.Topology.Separation.SeparatedNhds", "is_tactic_proof": true, "tactics": ["obtain", "rw", "suffices", "rw", "exact"], "tactic_count": 5}
{"name": "SeparatedNhds.isClosed_right_of_isClosed_union", "kind": "theorem", "module": "Mathlib.Topology.Separation.SeparatedNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparatedNhds.isClosed_union_iff", "kind": "theorem", "module": "Mathlib.Topology.Separation.SeparatedNhds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "subset_seqClosure", "kind": "theorem", "module": "Mathlib.Topology.Sequences", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "seqClosure_subset_closure", "kind": "theorem", "module": "Mathlib.Topology.Sequences", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSeqClosed.seqClosure_eq", "kind": "theorem", "module": "Mathlib.Topology.Sequences", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isSeqClosed_of_seqClosure_eq", "kind": "theorem", "module": "Mathlib.Topology.Sequences", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isSeqClosed_iff", "kind": "theorem", "module": "Mathlib.Topology.Sequences", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.isSeqClosed", "kind": "theorem", "module": "Mathlib.Topology.Sequences", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "seqClosure_eq_closure", "kind": "theorem", "module": "Mathlib.Topology.Sequences", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_closure_iff_seq_limit", "kind": "theorem", "module": "Mathlib.Topology.Sequences", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "tendsto_nhds_iff_seq_tendsto", "kind": "theorem", "module": "Mathlib.Topology.Sequences", "is_tactic_proof": true, "tactics": ["refine", "rintro", "refine", "rw", "rintro", "exact"], "tactic_count": 6}
{"name": "FrechetUrysohnSpace.of_seq_tendsto_imp_tendsto", "kind": "theorem", "module": "Mathlib.Topology.Sequences", "is_tactic_proof": true, "tactics": ["refine", "by_cases", "exact", "obtain", "simpa", "h", "rcases", "exact"], "tactic_count": 8}
{"name": "FirstCountableTopology.frechetUrysohnSpace", "kind": "instance", "module": "Mathlib.Topology.Sequences", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FrechetUrysohnSpace.to_sequentialSpace", "kind": "instance", "module": "Mathlib.Topology.Sequences", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsInducing.frechetUrysohnSpace", "kind": "theorem", "module": "Mathlib.Topology.Sequences", "is_tactic_proof": true, "tactics": ["refine", "rw", "rcases", "choose", "refine", "simpa"], "tactic_count": 6}
{"name": "Subtype.instFrechetUrysohnSpace", "kind": "instance", "module": "Mathlib.Topology.Sequences", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isSeqClosed_iff_isClosed", "kind": "theorem", "module": "Mathlib.Topology.Sequences", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSeqClosed.preimage", "kind": "theorem", "module": "Mathlib.Topology.Sequences", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.seqContinuous", "kind": "theorem", "module": "Mathlib.Topology.Sequences", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeqContinuous.continuous", "kind": "theorem", "module": "Mathlib.Topology.Sequences", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_iff_seqContinuous", "kind": "theorem", "module": "Mathlib.Topology.Sequences", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SequentialSpace.coinduced", "kind": "theorem", "module": "Mathlib.Topology.Sequences", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SequentialSpace.iSup", "kind": "theorem", "module": "Mathlib.Topology.Sequences", "is_tactic_proof": true, "tactics": ["letI", "refine", "letI", "exact"], "tactic_count": 4}
{"name": "SequentialSpace.sup", "kind": "theorem", "module": "Mathlib.Topology.Sequences", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Topology.IsQuotientMap.sequentialSpace", "kind": "theorem", "module": "Mathlib.Topology.Sequences", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Quotient.instSequentialSpace", "kind": "instance", "module": "Mathlib.Topology.Sequences", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.instSequentialSpace", "kind": "instance", "module": "Mathlib.Topology.Sequences", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sigma.instSequentialSpace", "kind": "instance", "module": "Mathlib.Topology.Sequences", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSeqCompact.subseq_of_frequently_in", "kind": "theorem", "module": "Mathlib.Topology.Sequences", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeqCompactSpace.tendsto_subseq", "kind": "theorem", "module": "Mathlib.Topology.Sequences", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.isSeqCompact", "kind": "theorem", "module": "Mathlib.Topology.Sequences", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.tendsto_subseq'", "kind": "theorem", "module": "Mathlib.Topology.Sequences", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.tendsto_subseq", "kind": "theorem", "module": "Mathlib.Topology.Sequences", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "FirstCountableTopology.seq_compact_of_compact", "kind": "instance", "module": "Mathlib.Topology.Sequences", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompactSpace.tendsto_subseq", "kind": "theorem", "module": "Mathlib.Topology.Sequences", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSeqCompact.image", "kind": "theorem", "module": "Mathlib.Topology.Sequences", "is_tactic_proof": true, "tactics": ["intro", "choose", "obtain", "refine", "exact"], "tactic_count": 5}
{"name": "IsSeqCompact.range", "kind": "theorem", "module": "Mathlib.Topology.Sequences", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "IsSeqCompact.exists_tendsto_of_frequently_mem", "kind": "theorem", "module": "Mathlib.Topology.Sequences", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSeqCompact.exists_tendsto", "kind": "theorem", "module": "Mathlib.Topology.Sequences", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSeqCompact.totallyBounded", "kind": "theorem", "module": "Mathlib.Topology.Sequences", "is_tactic_proof": true, "tactics": ["intro", "unfold", "contrapose", "obtain", "simp", "simpa", "refine", "obtain", "exact"], "tactic_count": 9}
{"name": "IsSeqCompact.isComplete", "kind": "theorem", "module": "Mathlib.Topology.Sequences", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSeqCompact.isCompact", "kind": "theorem", "module": "Mathlib.Topology.Sequences", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isCompact_iff_isSeqCompact", "kind": "theorem", "module": "Mathlib.Topology.Sequences", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "compactSpace_iff_seqCompactSpace", "kind": "theorem", "module": "Mathlib.Topology.Sequences", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "TopologicalSpace.Closeds.instSetLike", "kind": "instance", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Closeds.instPartialOrder", "kind": "instance", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Closeds.instCanLiftSetCoeIsClosed", "kind": "instance", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Closeds.isClosed", "kind": "theorem", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Closeds.Simps.coe", "kind": "definition", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Closeds.carrier_eq_coe", "kind": "theorem", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Closeds.ext", "kind": "theorem", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Closeds.coe_mk", "kind": "theorem", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Closeds.mem_mk", "kind": "theorem", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Closeds.closure", "kind": "definition", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Closeds.mem_closure", "kind": "theorem", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Closeds.gc", "kind": "theorem", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Closeds.closure_le", "kind": "theorem", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Closeds.gi", "kind": "definition", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Closeds.instCompleteLattice", "kind": "instance", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Closeds.instInhabited", "kind": "instance", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Closeds.coe_sup", "kind": "theorem", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "TopologicalSpace.Closeds.coe_inf", "kind": "theorem", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Closeds.coe_top", "kind": "theorem", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Closeds.coe_eq_univ", "kind": "theorem", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Closeds.coe_bot", "kind": "theorem", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Closeds.coe_eq_empty", "kind": "theorem", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Closeds.coe_nonempty", "kind": "theorem", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Closeds.coe_sInf", "kind": "theorem", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Closeds.coe_sSup", "kind": "theorem", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": true, "tactics": ["rfl"], "tactic_count": 1}
{"name": "TopologicalSpace.Closeds.coe_finset_sup", "kind": "theorem", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Closeds.coe_finset_inf", "kind": "theorem", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Closeds.mem_sInf", "kind": "theorem", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Closeds.mem_iInf", "kind": "theorem", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "TopologicalSpace.Closeds.coe_iInf", "kind": "theorem", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "TopologicalSpace.Closeds.iInf_def", "kind": "theorem", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": true, "tactics": ["ext1"], "tactic_count": 1}
{"name": "TopologicalSpace.Closeds.iInf_mk", "kind": "theorem", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Closeds.coframeMinimalAxioms", "kind": "definition", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Closeds.instCoframe", "kind": "instance", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Closeds.instSingletonOfT1Space", "kind": "instance", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Closeds.singleton", "kind": "abbrev", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Closeds.mk_singleton", "kind": "theorem", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Closeds.mem_singleton", "kind": "theorem", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Closeds.singleton_injective", "kind": "theorem", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Closeds.singleton_inj", "kind": "theorem", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Closeds.preimage", "kind": "definition", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Closeds.compl", "kind": "definition", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.compl", "kind": "definition", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Closeds.compl_compl", "kind": "theorem", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.compl_compl", "kind": "theorem", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Closeds.compl_bijective", "kind": "theorem", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.compl_bijective", "kind": "theorem", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Closeds.complOrderIso", "kind": "definition", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.complOrderIso", "kind": "definition", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Closeds.coe_eq_singleton_of_isAtom", "kind": "theorem", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": true, "tactics": ["refine", "lift", "exact"], "tactic_count": 3}
{"name": "TopologicalSpace.Closeds.isAtom_coe", "kind": "theorem", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Closeds.isAtom_iff", "kind": "theorem", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "TopologicalSpace.Opens.isCoatom_iff", "kind": "theorem", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": true, "tactics": ["rw", "change", "simp"], "tactic_count": 3}
{"name": "TopologicalSpace.Clopens.instSetLike", "kind": "instance", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Clopens.instPartialOrder", "kind": "instance", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Clopens.isClopen", "kind": "theorem", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Clopens.isOpen", "kind": "theorem", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Clopens.isClosed", "kind": "theorem", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Clopens.Simps.coe", "kind": "definition", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Clopens.toOpens", "kind": "definition", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Clopens.toCloseds", "kind": "definition", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Clopens.ext", "kind": "theorem", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Clopens.coe_mk", "kind": "theorem", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Clopens.mem_mk", "kind": "theorem", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Clopens.instMax", "kind": "instance", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Clopens.instMin", "kind": "instance", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Clopens.instTop", "kind": "instance", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Clopens.instBot", "kind": "instance", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Clopens.instSDiff", "kind": "instance", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Clopens.instHImp", "kind": "instance", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Clopens.instCompl", "kind": "instance", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Clopens.coe_sup", "kind": "theorem", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Clopens.coe_inf", "kind": "theorem", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Clopens.coe_top", "kind": "theorem", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Clopens.coe_bot", "kind": "theorem", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Clopens.coe_sdiff", "kind": "theorem", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Clopens.coe_himp", "kind": "theorem", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Clopens.coe_compl", "kind": "theorem", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Clopens.instBooleanAlgebra", "kind": "instance", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Clopens.instInhabited", "kind": "instance", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Clopens.instSProdProd", "kind": "instance", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Clopens.mem_prod", "kind": "theorem", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Clopens.coe_finset_sup", "kind": "theorem", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": true, "tactics": ["classical", "induction", "empty", "insert"], "tactic_count": 4}
{"name": "TopologicalSpace.Clopens.coe_disjoint", "kind": "theorem", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "TopologicalSpace.IrreducibleCloseds.instSetLike", "kind": "instance", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.IrreducibleCloseds.instPartialOrder", "kind": "instance", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.IrreducibleCloseds.instCanLiftSetCoeAndIsIrreducibleIsClosed", "kind": "instance", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.IrreducibleCloseds.isIrreducible", "kind": "theorem", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.IrreducibleCloseds.isClosed", "kind": "theorem", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.IrreducibleCloseds.Simps.coe", "kind": "definition", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.IrreducibleCloseds.ext", "kind": "theorem", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.IrreducibleCloseds.coe_mk", "kind": "theorem", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.IrreducibleCloseds.instSingletonOfT1Space", "kind": "instance", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.IrreducibleCloseds.singleton", "kind": "abbrev", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.IrreducibleCloseds.mk_singleton", "kind": "theorem", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.IrreducibleCloseds.mem_singleton", "kind": "theorem", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.IrreducibleCloseds.singleton_injective", "kind": "theorem", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.IrreducibleCloseds.singleton_inj", "kind": "theorem", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.IrreducibleCloseds.equivSubtype", "kind": "definition", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.IrreducibleCloseds.equivSubtype'", "kind": "definition", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.IrreducibleCloseds.orderIsoSubtype", "kind": "definition", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.IrreducibleCloseds.orderIsoSubtype'", "kind": "definition", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.IrreducibleCloseds.map", "kind": "definition", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.IrreducibleCloseds.coe_map", "kind": "theorem", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.IrreducibleCloseds.map_mono", "kind": "theorem", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.IrreducibleCloseds.map_injective_of_isInducing", "kind": "theorem", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": true, "tactics": ["intro", "apply", "replace", "rw", "hf.closure_eq_preimage_closure_image,"], "tactic_count": 5}
{"name": "TopologicalSpace.IrreducibleCloseds.map_strictMono_of_isInducing", "kind": "theorem", "module": "Mathlib.Topology.Sets.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompactOpenCovered", "kind": "definition", "module": "Mathlib.Topology.Sets.CompactOpenCovered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompactOpenCovered.empty", "kind": "theorem", "module": "Mathlib.Topology.Sets.CompactOpenCovered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompactOpenCovered.iff_of_unique", "kind": "theorem", "module": "Mathlib.Topology.Sets.CompactOpenCovered", "is_tactic_proof": true, "tactics": ["refine", "by_cases", "aesop", "obtain", "rw", "aesop", "refine", "rintro", "simpa"], "tactic_count": 9}
{"name": "IsCompactOpenCovered.id_iff_isOpen_and_isCompact", "kind": "theorem", "module": "Mathlib.Topology.Sets.CompactOpenCovered", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp", "exact"], "tactic_count": 4}
{"name": "IsCompactOpenCovered.iff_isCompactOpenCovered_sigmaMk", "kind": "theorem", "module": "Mathlib.Topology.Sets.CompactOpenCovered", "is_tactic_proof": true, "tactics": ["classical", "rw", "refine", "refine", "intro", "by_cases", "simpa", "simp", "dsimp", "exact", "aesop", "obtain", "have", "rw", "exact", "refine", "simp_rw"], "tactic_count": 17}
{"name": "IsCompactOpenCovered.of_iUnion_eq_of_finite", "kind": "theorem", "module": "Mathlib.Topology.Sets.CompactOpenCovered", "is_tactic_proof": true, "tactics": ["rw", "have", "rw", "choose", "exact"], "tactic_count": 5}
{"name": "IsCompactOpenCovered.of_biUnion_eq_of_finite", "kind": "theorem", "module": "Mathlib.Topology.Sets.CompactOpenCovered", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "IsCompactOpenCovered.of_biUnion_eq_of_isCompact", "kind": "theorem", "module": "Mathlib.Topology.Sets.CompactOpenCovered", "is_tactic_proof": true, "tactics": ["classical", "obtain", "refine", "exact", "exact", "grind"], "tactic_count": 6}
{"name": "IsCompactOpenCovered.of_isCompact_of_forall_exists_isCompactOpenCovered", "kind": "theorem", "module": "Mathlib.Topology.Sets.CompactOpenCovered", "is_tactic_proof": true, "tactics": ["choose", "refine", "refine", "simp", "aesop", "simpa", "grind"], "tactic_count": 7}
{"name": "IsCompactOpenCovered.image", "kind": "theorem", "module": "Mathlib.Topology.Sets.CompactOpenCovered", "is_tactic_proof": true, "tactics": ["refine"], "tactic_count": 1}
{"name": "IsCompactOpenCovered.of_finite", "kind": "theorem", "module": "Mathlib.Topology.Sets.CompactOpenCovered", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompactOpenCovered.exists_mem_of_isBasis", "kind": "theorem", "module": "Mathlib.Topology.Sets.CompactOpenCovered", "is_tactic_proof": false, "tactics": ["suffices", "obtain", "cases", "refine", "simp", "obtain", "choose", "let", "have", "have", "refine", "rw", "ext", "simp_rw", "refine", "rw", "obtain", "simp", "use"], "tactic_count": 19}
{"name": "IsCompactOpenCovered.of_finite_of_isSpectralMap", "kind": "theorem", "module": "Mathlib.Topology.Sets.CompactOpenCovered", "is_tactic_proof": false, "tactics": ["refine", "subset_antisymm", "obtain", "simpa"], "tactic_count": 4}
{"name": "IsCompactOpenCovered.of_isOpenMap", "kind": "theorem", "module": "Mathlib.Topology.Sets.CompactOpenCovered", "is_tactic_proof": true, "tactics": ["rw", "refine", "hc", "simpa"], "tactic_count": 4}
{"name": "IsCompactOpenCovered.of_comp", "kind": "theorem", "module": "Mathlib.Topology.Sets.CompactOpenCovered", "is_tactic_proof": true, "tactics": ["rw", "let", "have", "ext", "simp", "have", "have", "obtain", "obtain", "simp", "refine", "rw", "exact"], "tactic_count": 13}
{"name": "TopologicalSpace.Compacts.instSetLike", "kind": "instance", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.instPartialOrder", "kind": "instance", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.Simps.coe", "kind": "definition", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.isCompact", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.instCompactSpaceSubtypeMem", "kind": "instance", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.toCloseds", "kind": "definition", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.mem_toCloseds", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.toCloseds_injective", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.instCanLiftSetCoeIsCompact", "kind": "instance", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.ext", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.coe_mk", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.carrier_eq_coe", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.instMax", "kind": "instance", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.instMinOfT2Space", "kind": "instance", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.instTopOfCompactSpace", "kind": "instance", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.instBot", "kind": "instance", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.instSemilatticeSup", "kind": "instance", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.instDistribLatticeOfT2Space", "kind": "instance", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.instOrderBot", "kind": "instance", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.instBoundedOrderOfCompactSpace", "kind": "instance", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.instInhabited", "kind": "instance", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.instUniqueOfIsEmpty", "kind": "instance", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.coe_sup", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.coe_inf", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.coe_top", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.coe_bot", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.coe_eq_empty", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.coe_nonempty", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.coe_finset_sup", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": true, "tactics": ["refine", "simp_rw", "congr"], "tactic_count": 3}
{"name": "TopologicalSpace.Compacts.instSingleton", "kind": "instance", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.mem_singleton", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.toCloseds_singleton", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.singleton_injective", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.singleton_inj", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.instNontrivialOfNonempty", "kind": "instance", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": true, "tactics": ["constructor", "obtain", "exact"], "tactic_count": 3}
{"name": "TopologicalSpace.Compacts.subsingleton_iff", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": true, "tactics": ["refine", "contrapose", "infer_instance"], "tactic_count": 3}
{"name": "TopologicalSpace.Compacts.nontrivial_iff", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "TopologicalSpace.Compacts.map", "kind": "definition", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.coe_map", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.map_id", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.map_comp", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.map_injective", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.map_singleton", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.map_injective_iff", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": true, "tactics": ["refine", "simp_rw", "exact"], "tactic_count": 3}
{"name": "TopologicalSpace.Compacts.range_map", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.equiv", "kind": "definition", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.equiv_refl", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.equiv_trans", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.equiv_symm", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.coe_equiv_apply_eq_preimage", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.instSProdProd", "kind": "instance", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.prod", "kind": "abbrev", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.coe_prod", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.singleton_prod_singleton", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.instSetLike", "kind": "instance", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.instPartialOrder", "kind": "instance", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.Simps.coe", "kind": "definition", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.isCompact", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.nonempty", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.toCloseds", "kind": "definition", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.toCloseds_toCompacts", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.mem_toCloseds", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.toCloseds_injective", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.ext", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.coe_mk", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.carrier_eq_coe", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.coe_toCompacts", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.mem_toCompacts", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.toCompacts_injective", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.range_toCompacts", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": true, "tactics": ["ext", "rw", "refine", "rintro", "exact"], "tactic_count": 5}
{"name": "TopologicalSpace.NonemptyCompacts.instMax", "kind": "instance", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.instTopOfCompactSpaceOfNonempty", "kind": "instance", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.instSemilatticeSup", "kind": "instance", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.instOrderTopOfCompactSpaceOfNonempty", "kind": "instance", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.coe_sup", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.coe_top", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.instSingleton", "kind": "instance", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.mem_singleton", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.toCloseds_singleton", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.singleton_injective", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.singleton_inj", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.instInhabited", "kind": "instance", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.instIsEmpty", "kind": "instance", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.isEmpty_iff", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.instNonempty", "kind": "instance", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.nonempty_iff", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "TopologicalSpace.NonemptyCompacts.instSubsingleton", "kind": "instance", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "TopologicalSpace.NonemptyCompacts.subsingleton_iff", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.instUnique", "kind": "instance", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.instNontrivial", "kind": "instance", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.nontrivial_iff", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "TopologicalSpace.NonemptyCompacts.map", "kind": "definition", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.coe_map", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.map_id", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "TopologicalSpace.NonemptyCompacts.map_comp", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "TopologicalSpace.NonemptyCompacts.map_singleton", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "TopologicalSpace.NonemptyCompacts.map_injective", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.map_injective_iff", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.range_map", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.toCompactSpace", "kind": "instance", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.toNonempty", "kind": "instance", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.instSProdProd", "kind": "instance", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.prod", "kind": "abbrev", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.coe_prod", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.singleton_prod_singleton", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.PositiveCompacts.instSetLike", "kind": "instance", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.PositiveCompacts.instPartialOrder", "kind": "instance", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.PositiveCompacts.Simps.coe", "kind": "definition", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.PositiveCompacts.isCompact", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.PositiveCompacts.interior_nonempty", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.PositiveCompacts.nonempty", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.PositiveCompacts.toNonemptyCompacts", "kind": "definition", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.PositiveCompacts.ext", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.PositiveCompacts.coe_mk", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.PositiveCompacts.carrier_eq_coe", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.PositiveCompacts.coe_toCompacts", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.PositiveCompacts.instMax", "kind": "instance", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.PositiveCompacts.instTopOfCompactSpaceOfNonempty", "kind": "instance", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.PositiveCompacts.instSemilatticeSup", "kind": "instance", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.PositiveCompacts.instOrderTopOfCompactSpaceOfNonempty", "kind": "instance", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.PositiveCompacts.coe_sup", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.PositiveCompacts.coe_top", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.PositiveCompacts.map", "kind": "definition", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.PositiveCompacts.coe_map", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.PositiveCompacts.map_id", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.PositiveCompacts.map_comp", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_positiveCompacts_subset", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.exists_positiveCompacts_closure_subset", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.PositiveCompacts.instInhabitedOfCompactSpaceOfNonempty", "kind": "instance", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.PositiveCompacts.nonempty'", "kind": "instance", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": true, "tactics": ["inhabit", "rcases", "exact"], "tactic_count": 3}
{"name": "TopologicalSpace.PositiveCompacts.instSProdProd", "kind": "instance", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.PositiveCompacts.prod", "kind": "abbrev", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.PositiveCompacts.coe_prod", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.CompactOpens.instSetLike", "kind": "instance", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.CompactOpens.instPartialOrder", "kind": "instance", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.CompactOpens.Simps.coe", "kind": "definition", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.CompactOpens.isCompact", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.CompactOpens.isOpen", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.CompactOpens.toOpens", "kind": "definition", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.CompactOpens.toClopens", "kind": "definition", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.CompactOpens.ext", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.CompactOpens.coe_mk", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.CompactOpens.instMax", "kind": "instance", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.CompactOpens.instBot", "kind": "instance", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.CompactOpens.coe_sup", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.CompactOpens.coe_bot", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.CompactOpens.instSemilatticeSup", "kind": "instance", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.CompactOpens.instOrderBot", "kind": "instance", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.CompactOpens.coe_finsetSup", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "TopologicalSpace.CompactOpens.instInhabited", "kind": "instance", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.CompactOpens.instInf", "kind": "instance", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.CompactOpens.coe_inf", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.CompactOpens.instSemilatticeInf", "kind": "instance", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.CompactOpens.instSDiff", "kind": "instance", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.CompactOpens.coe_sdiff", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.CompactOpens.instGeneralizedBooleanAlgebra", "kind": "instance", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.CompactOpens.instTop", "kind": "instance", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.CompactOpens.coe_top", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.CompactOpens.instBoundedOrder", "kind": "instance", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.CompactOpens.instCompl", "kind": "instance", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.CompactOpens.instHImp", "kind": "instance", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.CompactOpens.coe_compl", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.CompactOpens.coe_himp", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.CompactOpens.instBooleanAlgebra", "kind": "instance", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.CompactOpens.map", "kind": "definition", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.CompactOpens.coe_map", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.CompactOpens.map_id", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.CompactOpens.map_comp", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.CompactOpens.instSProdProd", "kind": "instance", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.CompactOpens.prod", "kind": "abbrev", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.CompactOpens.coe_prod", "kind": "theorem", "module": "Mathlib.Topology.Sets.Compacts", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.IsOpenCover", "kind": "definition", "module": "Mathlib.Topology.Sets.OpenCover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.IsOpenCover.mk", "kind": "theorem", "module": "Mathlib.Topology.Sets.OpenCover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.IsOpenCover.of_sets", "kind": "theorem", "module": "Mathlib.Topology.Sets.OpenCover", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "TopologicalSpace.IsOpenCover.iSup_eq_top", "kind": "theorem", "module": "Mathlib.Topology.Sets.OpenCover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.IsOpenCover.iSup_set_eq_univ", "kind": "theorem", "module": "Mathlib.Topology.Sets.OpenCover", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "TopologicalSpace.IsOpenCover.comap", "kind": "theorem", "module": "Mathlib.Topology.Sets.OpenCover", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "TopologicalSpace.IsOpenCover.exists_mem", "kind": "theorem", "module": "Mathlib.Topology.Sets.OpenCover", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "TopologicalSpace.IsOpenCover.exists_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.Sets.OpenCover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.IsOpenCover.iUnion_inter", "kind": "theorem", "module": "Mathlib.Topology.Sets.OpenCover", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "TopologicalSpace.IsOpenCover.isTopologicalBasis", "kind": "theorem", "module": "Mathlib.Topology.Sets.OpenCover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsPreirreducible.of_subset_iUnion", "kind": "theorem", "module": "Mathlib.Topology.Sets.OpenCover", "is_tactic_proof": true, "tactics": ["rcases", "rw", "choose", "choose", "rcases", "by_cases", "exact", "have", "rcases", "choose", "have", "rcases", "inter_nonempty_iff_exists_left.mp", "exfalso"], "tactic_count": 14}
{"name": "PreirreducibleSpace.of_isOpenCover", "kind": "theorem", "module": "Mathlib.Topology.Sets.OpenCover", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.instSetLike", "kind": "instance", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.instPartialOrder", "kind": "instance", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.instCanLiftSetCoeIsOpen", "kind": "instance", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.instSecondCountableOpens", "kind": "instance", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.forall", "kind": "theorem", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.carrier_eq_coe", "kind": "theorem", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.coe_mk", "kind": "theorem", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.mem_mk", "kind": "theorem", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.nonempty_coeSort", "kind": "theorem", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.nonempty_coe", "kind": "theorem", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.ext", "kind": "theorem", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.coe_inj", "kind": "theorem", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.inclusion", "kind": "abbrev", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.isOpen", "kind": "theorem", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.mk_coe", "kind": "theorem", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.Simps.coe", "kind": "definition", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.interior", "kind": "definition", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.mem_interior", "kind": "theorem", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.gc", "kind": "theorem", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.gi", "kind": "definition", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.instCompleteLattice", "kind": "instance", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.mk_inf_mk", "kind": "theorem", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.coe_inf", "kind": "theorem", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.mem_inf", "kind": "theorem", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.coe_sup", "kind": "theorem", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.mem_sup", "kind": "theorem", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.coe_bot", "kind": "theorem", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.mem_bot", "kind": "theorem", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.mk_empty", "kind": "theorem", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.coe_eq_empty", "kind": "theorem", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.mem_top", "kind": "theorem", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.coe_top", "kind": "theorem", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.mk_univ", "kind": "theorem", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.coe_eq_univ", "kind": "theorem", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.coe_sSup", "kind": "theorem", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.coe_finset_sup", "kind": "theorem", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.coe_finset_inf", "kind": "theorem", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.coe_disjoint", "kind": "theorem", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "TopologicalSpace.Opens.instInhabited", "kind": "instance", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.instUniqueOfIsEmpty", "kind": "instance", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.instNontrivialOfNonempty", "kind": "instance", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.coe_iSup", "kind": "theorem", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "TopologicalSpace.Opens.iSup_def", "kind": "theorem", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.iSup_mk", "kind": "theorem", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.mem_iSup", "kind": "theorem", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "TopologicalSpace.Opens.mem_sSup", "kind": "theorem", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "TopologicalSpace.Opens.frameMinimalAxioms", "kind": "definition", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.instFrame", "kind": "instance", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.isOpenEmbedding'", "kind": "theorem", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.isOpenEmbedding_of_le", "kind": "theorem", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.not_nonempty_iff_eq_bot", "kind": "theorem", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "TopologicalSpace.Opens.ne_bot_iff_nonempty", "kind": "theorem", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "TopologicalSpace.Opens.eq_bot_or_top", "kind": "theorem", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "TopologicalSpace.Opens.instIsSimpleOrderOfNonemptyOfIndiscreteTopology", "kind": "instance", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.IsBasis", "kind": "definition", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.isBasis_iff_nbhd", "kind": "theorem", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "rcases", "refine", "cases", "dsimp", "subst", "exact", "refine", "rintro", "exact", "intro", "rcases", "exact"], "tactic_count": 14}
{"name": "TopologicalSpace.Opens.isBasis_iff_cover", "kind": "theorem", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": true, "tactics": ["constructor", "intro", "refine", "rw", "simp_rw", "rfl", "intro", "rw", "intro", "rcases", "rcases", "exact"], "tactic_count": 12}
{"name": "TopologicalSpace.Opens.IsBasis.isCompact_open_iff_eq_finite_iUnion", "kind": "theorem", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": true, "tactics": ["apply", "convert", "ext", "simp", "exact"], "tactic_count": 5}
{"name": "TopologicalSpace.Opens.IsBasis.exists_finite_of_isCompact", "kind": "theorem", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": true, "tactics": ["classical", "obtain", "obtain", "refine", "exact"], "tactic_count": 5}
{"name": "TopologicalSpace.Opens.IsBasis.le_iff", "kind": "theorem", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": true, "tactics": ["conv_lhs", "simp"], "tactic_count": 2}
{"name": "TopologicalSpace.Opens.isBasis_sigma", "kind": "theorem", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": true, "tactics": ["convert", "simp", "simp"], "tactic_count": 3}
{"name": "TopologicalSpace.Opens.IsBasis.of_isInducing", "kind": "theorem", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": true, "tactics": ["simp", "convert", "ext"], "tactic_count": 3}
{"name": "TopologicalSpace.Opens.isCompactElement_iff", "kind": "theorem", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": true, "tactics": ["rw", "refine", "introv", "obtain", "refine", "rw", "rfl", "obtain", "refine", "simp", "change", "exact"], "tactic_count": 12}
{"name": "TopologicalSpace.Opens.comap", "kind": "definition", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.comap_id", "kind": "theorem", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.comap_mono", "kind": "theorem", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.coe_comap", "kind": "theorem", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.mem_comap", "kind": "theorem", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.comap_comp", "kind": "theorem", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.comap_comap", "kind": "theorem", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.comap_injective", "kind": "theorem", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.opensCongr", "kind": "definition", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Homeomorph.opensCongr_symm", "kind": "theorem", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.instFinite", "kind": "instance", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.OpenNhdsOf.toOpens_injective", "kind": "theorem", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.OpenNhdsOf.instSetLike", "kind": "instance", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.OpenNhdsOf.instPartialOrder", "kind": "instance", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.OpenNhdsOf.canLiftSet", "kind": "instance", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.OpenNhdsOf.mem", "kind": "theorem", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.OpenNhdsOf.isOpen", "kind": "theorem", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.OpenNhdsOf.instOrderTop", "kind": "instance", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.OpenNhdsOf.instInhabited", "kind": "instance", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.OpenNhdsOf.instMin", "kind": "instance", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.OpenNhdsOf.instMax", "kind": "instance", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.OpenNhdsOf.instUniqueOfSubsingleton", "kind": "instance", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.OpenNhdsOf.instDistribLattice", "kind": "instance", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.OpenNhdsOf.basis_nhds", "kind": "theorem", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.OpenNhdsOf.comap", "kind": "definition", "module": "Mathlib.Topology.Sets.Opens", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClopenUpperSet.instSetLike", "kind": "instance", "module": "Mathlib.Topology.Sets.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClopenUpperSet.instPartialOrder", "kind": "instance", "module": "Mathlib.Topology.Sets.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClopenUpperSet.Simps.coe", "kind": "definition", "module": "Mathlib.Topology.Sets.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClopenUpperSet.upper", "kind": "theorem", "module": "Mathlib.Topology.Sets.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClopenUpperSet.isClopen", "kind": "theorem", "module": "Mathlib.Topology.Sets.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClopenUpperSet.toUpperSet", "kind": "definition", "module": "Mathlib.Topology.Sets.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClopenUpperSet.ext", "kind": "theorem", "module": "Mathlib.Topology.Sets.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClopenUpperSet.coe_mk", "kind": "theorem", "module": "Mathlib.Topology.Sets.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClopenUpperSet.instMax", "kind": "instance", "module": "Mathlib.Topology.Sets.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClopenUpperSet.instMin", "kind": "instance", "module": "Mathlib.Topology.Sets.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClopenUpperSet.instTop", "kind": "instance", "module": "Mathlib.Topology.Sets.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClopenUpperSet.instBot", "kind": "instance", "module": "Mathlib.Topology.Sets.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClopenUpperSet.instLattice", "kind": "instance", "module": "Mathlib.Topology.Sets.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClopenUpperSet.instBoundedOrder", "kind": "instance", "module": "Mathlib.Topology.Sets.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClopenUpperSet.coe_sup", "kind": "theorem", "module": "Mathlib.Topology.Sets.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClopenUpperSet.coe_inf", "kind": "theorem", "module": "Mathlib.Topology.Sets.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClopenUpperSet.coe_top", "kind": "theorem", "module": "Mathlib.Topology.Sets.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClopenUpperSet.coe_bot", "kind": "theorem", "module": "Mathlib.Topology.Sets.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ClopenUpperSet.instInhabited", "kind": "instance", "module": "Mathlib.Topology.Sets.Order", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.vietoris", "kind": "definition", "module": "Mathlib.Topology.Sets.VietorisTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsOpen.powerset_vietoris", "kind": "theorem", "module": "Mathlib.Topology.Sets.VietorisTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.vietoris.isOpen_inter_nonempty_of_isOpen", "kind": "theorem", "module": "Mathlib.Topology.Sets.VietorisTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.powerset_vietoris", "kind": "theorem", "module": "Mathlib.Topology.Sets.VietorisTopology", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "TopologicalSpace.vietoris.isClosed_inter_nonempty_of_isClosed", "kind": "theorem", "module": "Mathlib.Topology.Sets.VietorisTopology", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "TopologicalSpace.vietoris.isClopen_singleton_empty", "kind": "theorem", "module": "Mathlib.Topology.Sets.VietorisTopology", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "_private.Mathlib.Topology.Sets.VietorisTopology.0.TopologicalSpace.vietoris.isCompact_aux", "kind": "theorem", "module": "Mathlib.Topology.Sets.VietorisTopology", "is_tactic_proof": true, "tactics": ["refine", "let", "by_cases", "obtain", "rw", "obtain", "refine", "simp_rw", "grw", "grind", "simp_rw", "replace", "obtain", "rcases", "rw", "obtain", "refine", "insert_subset", "rw", "rintro", "rw", "obtain", "obtain", "exact", "obtain", "cases"], "tactic_count": 26}
{"name": "IsCompact.powerset_vietoris", "kind": "theorem", "module": "Mathlib.Topology.Sets.VietorisTopology", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "TopologicalSpace.vietoris.instCompactSpaceSet", "kind": "instance", "module": "Mathlib.Topology.Sets.VietorisTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.vietoris.specializes_of_subset_closure", "kind": "theorem", "module": "Mathlib.Topology.Sets.VietorisTopology", "is_tactic_proof": true, "tactics": ["simp_rw", "rintro", "exact", "obtain", "obtain", "exact"], "tactic_count": 6}
{"name": "TopologicalSpace.vietoris.specializes_closure", "kind": "theorem", "module": "Mathlib.Topology.Sets.VietorisTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.topology", "kind": "instance", "module": "Mathlib.Topology.Sets.VietorisTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.isEmbedding_coe", "kind": "theorem", "module": "Mathlib.Topology.Sets.VietorisTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.continuous_coe", "kind": "theorem", "module": "Mathlib.Topology.Sets.VietorisTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.isOpen_subsets_of_isOpen", "kind": "theorem", "module": "Mathlib.Topology.Sets.VietorisTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.isOpen_inter_nonempty_of_isOpen", "kind": "theorem", "module": "Mathlib.Topology.Sets.VietorisTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.isClosed_subsets_of_isClosed", "kind": "theorem", "module": "Mathlib.Topology.Sets.VietorisTopology", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "TopologicalSpace.Compacts.isClosed_inter_nonempty_of_isClosed", "kind": "theorem", "module": "Mathlib.Topology.Sets.VietorisTopology", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "TopologicalSpace.Compacts.isClopen_singleton_bot", "kind": "theorem", "module": "Mathlib.Topology.Sets.VietorisTopology", "is_tactic_proof": true, "tactics": ["convert", "rw"], "tactic_count": 2}
{"name": "TopologicalSpace.Compacts.isCompact_subsets_of_isCompact", "kind": "theorem", "module": "Mathlib.Topology.Sets.VietorisTopology", "is_tactic_proof": true, "tactics": ["rw", "refine", "let", "exact", "vietoris.specializes_of_subset_closure"], "tactic_count": 5}
{"name": "TopologicalSpace.Compacts.instCompactSpace", "kind": "instance", "module": "Mathlib.Topology.Sets.VietorisTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.isCompact_biUnion_coe_of_isCompact", "kind": "theorem", "module": "Mathlib.Topology.Sets.VietorisTopology", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "obtain", "hS.elim_finite_subcover", "classical", "refine", "simp_rw", "exact"], "tactic_count": 9}
{"name": "TopologicalSpace.Compacts.compactSpace_iff", "kind": "theorem", "module": "Mathlib.Topology.Sets.VietorisTopology", "is_tactic_proof": true, "tactics": ["refine", "convert", "symm", "simp_rw", "exact"], "tactic_count": 5}
{"name": "TopologicalSpace.Compacts.noncompactSpace_iff", "kind": "theorem", "module": "Mathlib.Topology.Sets.VietorisTopology", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "TopologicalSpace.Compacts.instNoncompactSpace", "kind": "instance", "module": "Mathlib.Topology.Sets.VietorisTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.topology", "kind": "instance", "module": "Mathlib.Topology.Sets.VietorisTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.isEmbedding_coe", "kind": "theorem", "module": "Mathlib.Topology.Sets.VietorisTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.continuous_coe", "kind": "theorem", "module": "Mathlib.Topology.Sets.VietorisTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.isEmbedding_toCompacts", "kind": "theorem", "module": "Mathlib.Topology.Sets.VietorisTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.continuous_toCompacts", "kind": "theorem", "module": "Mathlib.Topology.Sets.VietorisTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.isClosedEmbedding_toCompacts", "kind": "theorem", "module": "Mathlib.Topology.Sets.VietorisTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.isOpenEmbedding_toCompacts", "kind": "theorem", "module": "Mathlib.Topology.Sets.VietorisTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.isOpen_subsets_of_isOpen", "kind": "theorem", "module": "Mathlib.Topology.Sets.VietorisTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.isOpen_inter_nonempty_of_isOpen", "kind": "theorem", "module": "Mathlib.Topology.Sets.VietorisTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.isClosed_subsets_of_isClosed", "kind": "theorem", "module": "Mathlib.Topology.Sets.VietorisTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.isClosed_inter_nonempty_of_isClosed", "kind": "theorem", "module": "Mathlib.Topology.Sets.VietorisTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.instCompactSpace", "kind": "instance", "module": "Mathlib.Topology.Sets.VietorisTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.isCompact_subsets_of_isCompact", "kind": "theorem", "module": "Mathlib.Topology.Sets.VietorisTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.isCompact_biUnion_coe_of_isCompact", "kind": "theorem", "module": "Mathlib.Topology.Sets.VietorisTopology", "is_tactic_proof": true, "tactics": ["convert", "simp_rw"], "tactic_count": 2}
{"name": "TopologicalSpace.NonemptyCompacts.compactSpace_iff", "kind": "theorem", "module": "Mathlib.Topology.Sets.VietorisTopology", "is_tactic_proof": true, "tactics": ["refine", "convert", "symm", "simp_rw", "exact"], "tactic_count": 5}
{"name": "TopologicalSpace.NonemptyCompacts.noncompactSpace_iff", "kind": "theorem", "module": "Mathlib.Topology.Sets.VietorisTopology", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "TopologicalSpace.NonemptyCompacts.instNoncompactSpace", "kind": "instance", "module": "Mathlib.Topology.Sets.VietorisTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Alexandrov.principalOpen", "kind": "definition", "module": "Mathlib.Topology.Sheaves.Alexandrov", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Alexandrov.self_mem_principalOpen", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Alexandrov", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Alexandrov.principalOpen_le_iff", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Alexandrov", "is_tactic_proof": true, "tactics": ["refine", "have", "rw", "exact"], "tactic_count": 4}
{"name": "Alexandrov.principalOpen_le", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Alexandrov", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Alexandrov.principals", "kind": "definition", "module": "Mathlib.Topology.Sheaves.Alexandrov", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Alexandrov.exists_le_of_le_sup", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Alexandrov", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "Alexandrov.principalsKanExtension", "kind": "abbrev", "module": "Mathlib.Topology.Sheaves.Alexandrov", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Alexandrov.generator", "kind": "abbrev", "module": "Mathlib.Topology.Sheaves.Alexandrov", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Alexandrov.projSup", "kind": "definition", "module": "Mathlib.Topology.Sheaves.Alexandrov", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Alexandrov.lowerCone", "kind": "definition", "module": "Mathlib.Topology.Sheaves.Alexandrov", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Alexandrov.isLimit", "kind": "definition", "module": "Mathlib.Topology.Sheaves.Alexandrov", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Alexandrov.isSheaf_principalsKanExtension", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Alexandrov", "is_tactic_proof": true, "tactics": ["rw", "intro", "constructor", "apply"], "tactic_count": 4}
{"name": "Topology.IsUpperSet.isSheaf_of_isRightKanExtension", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Alexandrov", "is_tactic_proof": true, "tactics": ["let", "let", "have", "change", "rw", "let", "have", "exact"], "tactic_count": 8}
{"name": "TopCat.Presheaf._example", "kind": "example", "module": "Mathlib.Topology.Sheaves.CommRingCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.SubmonoidPresheaf.localizationPresheaf", "kind": "definition", "module": "Mathlib.Topology.Sheaves.CommRingCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.instAlgebraCarrierObjOppositeOpensCarrierCommRingCatLocalizationPresheaf", "kind": "instance", "module": "Mathlib.Topology.Sheaves.CommRingCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.instIsLocalizationCarrierObjOppositeOpensCarrierCommRingCatObjLocalizationPresheaf", "kind": "instance", "module": "Mathlib.Topology.Sheaves.CommRingCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.SubmonoidPresheaf.toLocalizationPresheaf", "kind": "definition", "module": "Mathlib.Topology.Sheaves.CommRingCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.epi_toLocalizationPresheaf", "kind": "instance", "module": "Mathlib.Topology.Sheaves.CommRingCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.submonoidPresheafOfStalk", "kind": "definition", "module": "Mathlib.Topology.Sheaves.CommRingCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.instInhabitedSubmonoidPresheaf", "kind": "instance", "module": "Mathlib.Topology.Sheaves.CommRingCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.totalQuotientPresheaf", "kind": "definition", "module": "Mathlib.Topology.Sheaves.CommRingCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.toTotalQuotientPresheaf", "kind": "definition", "module": "Mathlib.Topology.Sheaves.CommRingCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.instMonoCommRingCatToTotalQuotientPresheafPresheaf", "kind": "instance", "module": "Mathlib.Topology.Sheaves.CommRingCat", "is_tactic_proof": true, "tactics": ["apply", "intro", "apply", "dsimp", "set", "change", "refine", "rw", "intro", "apply", "intro", "rw", "apply", "rw"], "tactic_count": 14}
{"name": "TopCat.instNatCastHomObjTopCommRingCatForget₂", "kind": "instance", "module": "Mathlib.Topology.Sheaves.CommRingCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.instIntCastHomObjTopCommRingCatForget₂", "kind": "instance", "module": "Mathlib.Topology.Sheaves.CommRingCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.instZeroHomObjTopCommRingCatForget₂", "kind": "instance", "module": "Mathlib.Topology.Sheaves.CommRingCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.instOneHomObjTopCommRingCatForget₂", "kind": "instance", "module": "Mathlib.Topology.Sheaves.CommRingCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.instNegHomObjTopCommRingCatForget₂", "kind": "instance", "module": "Mathlib.Topology.Sheaves.CommRingCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.instSubHomObjTopCommRingCatForget₂", "kind": "instance", "module": "Mathlib.Topology.Sheaves.CommRingCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.instAddHomObjTopCommRingCatForget₂", "kind": "instance", "module": "Mathlib.Topology.Sheaves.CommRingCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.instMulHomObjTopCommRingCatForget₂", "kind": "instance", "module": "Mathlib.Topology.Sheaves.CommRingCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.instSMulNatHomObjTopCommRingCatForget₂", "kind": "instance", "module": "Mathlib.Topology.Sheaves.CommRingCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.instSMulIntHomObjTopCommRingCatForget₂", "kind": "instance", "module": "Mathlib.Topology.Sheaves.CommRingCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.instPowHomObjTopCommRingCatForget₂Nat", "kind": "instance", "module": "Mathlib.Topology.Sheaves.CommRingCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.instCommRingHomObjTopCommRingCatForget₂", "kind": "instance", "module": "Mathlib.Topology.Sheaves.CommRingCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.continuousFunctions", "kind": "definition", "module": "Mathlib.Topology.Sheaves.CommRingCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.continuousFunctions.pullback", "kind": "definition", "module": "Mathlib.Topology.Sheaves.CommRingCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.continuousFunctions.map", "kind": "definition", "module": "Mathlib.Topology.Sheaves.CommRingCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.commRingYoneda", "kind": "definition", "module": "Mathlib.Topology.Sheaves.CommRingCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.presheafToTopCommRing", "kind": "definition", "module": "Mathlib.Topology.Sheaves.CommRingCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.algebra_section_stalk", "kind": "instance", "module": "Mathlib.Topology.Sheaves.CommRingCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.stalk_open_algebraMap", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.CommRingCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Sheaf.objSupIsoProdEqLocus", "kind": "definition", "module": "Mathlib.Topology.Sheaves.CommRingCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Sheaf.objSupIsoProdEqLocus_hom_fst", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.CommRingCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Sheaf.objSupIsoProdEqLocus_hom_snd", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.CommRingCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Sheaf.objSupIsoProdEqLocus_inv_fst", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.CommRingCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Sheaf.objSupIsoProdEqLocus_inv_snd", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.CommRingCat", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Sheaf.objSupIsoProdEqLocus_inv_eq_iff", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.CommRingCat", "is_tactic_proof": true, "tactics": ["subst", "constructor", "rintro", "rw", "simp", "rintro", "refine", "rw", "exact", "rw", "simp", "rw", "simp"], "tactic_count": 13}
{"name": "TopCat.Presheaf.isSheaf_iff_isSheaf_comp'", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Forget", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.isSheaf_iff_isSheaf_comp", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Forget", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Sheaf.pushforward_sheaf_of_sheaf", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Functors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Sheaf.pushforward", "kind": "definition", "module": "Mathlib.Topology.Sheaves.Functors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Sheaf.pushforward_forget", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Functors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Sheaf.pushforwardForgetIso", "kind": "definition", "module": "Mathlib.Topology.Sheaves.Functors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Sheaf.pushforward_obj_val", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Functors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Sheaf.pushforward_map", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Functors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Sheaf.pullback", "kind": "definition", "module": "Mathlib.Topology.Sheaves.Functors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Sheaf.pullbackIso", "kind": "definition", "module": "Mathlib.Topology.Sheaves.Functors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Sheaf.pullbackPushforwardAdjunction", "kind": "definition", "module": "Mathlib.Topology.Sheaves.Functors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Sheaf.instIsLeftAdjointPullback", "kind": "instance", "module": "Mathlib.Topology.Sheaves.Functors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Sheaf.instIsRightAdjointPushforward", "kind": "instance", "module": "Mathlib.Topology.Sheaves.Functors", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "initFn._@.Mathlib.Topology.Sheaves.Init.2127643879._hygCtx._hyg.3", "kind": "definition", "module": "Mathlib.Topology.Sheaves.Init", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.instHasLimitsOfShapePresheaf", "kind": "instance", "module": "Mathlib.Topology.Sheaves.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.instHasLimitsPresheaf", "kind": "instance", "module": "Mathlib.Topology.Sheaves.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.instHasColimitsOfShapePresheaf", "kind": "instance", "module": "Mathlib.Topology.Sheaves.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.instHasColimitsOfSizePresheafOfHasColimits", "kind": "instance", "module": "Mathlib.Topology.Sheaves.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.instCreatesLimitsOfShapeSheafPresheafForgetOfHasLimitsOfShape", "kind": "instance", "module": "Mathlib.Topology.Sheaves.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.instHasLimitsOfShapeSheaf", "kind": "instance", "module": "Mathlib.Topology.Sheaves.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.instCreatesLimitsSheafPresheafForgetOfHasLimits", "kind": "instance", "module": "Mathlib.Topology.Sheaves.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.instHasLimitsOfSizeSheafOfHasLimits", "kind": "instance", "module": "Mathlib.Topology.Sheaves.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.isSheaf_of_isLimit", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Limits", "is_tactic_proof": false, "tactics": ["let", "map", "let", "exact"], "tactic_count": 4}
{"name": "TopCat.limit_isSheaf", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Limits", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.continuousPrelocal", "kind": "definition", "module": "Mathlib.Topology.Sheaves.LocalPredicate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.inhabitedPrelocalPredicate", "kind": "instance", "module": "Mathlib.Topology.Sheaves.LocalPredicate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.continuousLocal", "kind": "definition", "module": "Mathlib.Topology.Sheaves.LocalPredicate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.inhabitedLocalPredicate", "kind": "instance", "module": "Mathlib.Topology.Sheaves.LocalPredicate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.PrelocalPredicate.and", "kind": "definition", "module": "Mathlib.Topology.Sheaves.LocalPredicate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.LocalPredicate.and", "kind": "definition", "module": "Mathlib.Topology.Sheaves.LocalPredicate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.isSection", "kind": "definition", "module": "Mathlib.Topology.Sheaves.LocalPredicate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.PrelocalPredicate.sheafify", "kind": "definition", "module": "Mathlib.Topology.Sheaves.LocalPredicate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.PrelocalPredicate.sheafifyOf", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.LocalPredicate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.PrelocalPredicate.sheafify_inductionOn", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.LocalPredicate", "is_tactic_proof": true, "tactics": ["intro", "rcases", "rcases", "exact"], "tactic_count": 4}
{"name": "TopCat.PrelocalPredicate.sheafify_inductionOn'", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.LocalPredicate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.PrelocalPredicate.sheafify_inductionOn₂", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.LocalPredicate", "is_tactic_proof": true, "tactics": ["intro", "rcases", "rcases", "rcases", "exact"], "tactic_count": 5}
{"name": "TopCat.PrelocalPredicate.sheafify_inductionOn₂'", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.LocalPredicate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.subpresheafToTypes", "kind": "definition", "module": "Mathlib.Topology.Sheaves.LocalPredicate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.subpresheafToTypes.subtype", "kind": "definition", "module": "Mathlib.Topology.Sheaves.LocalPredicate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.subpresheafToTypes.isSheaf", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.LocalPredicate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.subsheafToTypes", "kind": "definition", "module": "Mathlib.Topology.Sheaves.LocalPredicate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.stalkToFiber", "kind": "definition", "module": "Mathlib.Topology.Sheaves.LocalPredicate", "is_tactic_proof": false, "tactics": ["refine", "colimit.desc", "ι", "naturality", "exact", "aesop"], "tactic_count": 6}
{"name": "TopCat.stalkToFiber_germ", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.LocalPredicate", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "TopCat.stalkToFiber_surjective", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.LocalPredicate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.stalkToFiber_injective", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.LocalPredicate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.subpresheafContinuousPrelocalIsoPresheafToTop", "kind": "definition", "module": "Mathlib.Topology.Sheaves.LocalPredicate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.sheafToTop", "kind": "definition", "module": "Mathlib.Topology.Sheaves.LocalPredicate", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.IsLocallySurjective", "kind": "definition", "module": "Mathlib.Topology.Sheaves.LocallySurjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.isLocallySurjective_iff", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.LocallySurjective", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.locally_surjective_iff_surjective_on_stalks", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.LocallySurjective", "is_tactic_proof": true, "tactics": ["constructor", "as", "on", "intro", "obtain", "rcases", "use", "simp", "some", "we", "constructor", "intro", "set", "obtain", "obtain", "have", "convert", "symm", "convert", "obtain", "refine", "convert", "simp"], "tactic_count": 23}
{"name": "Opens.mayerVietorisSquare'", "kind": "definition", "module": "Mathlib.Topology.Sheaves.MayerVietoris", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Opens.mayerVietorisSquare", "kind": "definition", "module": "Mathlib.Topology.Sheaves.MayerVietoris", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Opens.overEquivalence", "kind": "definition", "module": "Mathlib.Topology.Sheaves.Over", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.isSheaf_of_isTerminal_of_indiscrete", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.PUnit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.isSheaf_iff_isTerminal_of_indiscrete", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.PUnit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.isSheaf_on_punit_of_isTerminal", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.PUnit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.isSheaf_on_punit_iff_isTerminal", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.PUnit", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf", "kind": "definition", "module": "Mathlib.Topology.Sheaves.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.instCategoryPresheaf", "kind": "instance", "module": "Mathlib.Topology.Sheaves.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.comp_app", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.ext", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Presheaf", "is_tactic_proof": true, "tactics": ["apply", "ext", "induction", "apply"], "tactic_count": 4}
{"name": "TopCat.Presheaf.attrSheaf_restrict", "kind": "definition", "module": "Mathlib.Topology.Sheaves.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "AlgebraicGeometry.term_|_ₕ_", "kind": "definition", "module": "Mathlib.Topology.Sheaves.Presheaf", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "TopCat.Presheaf.isLimitOpensLeCoverEquivPairwise", "kind": "definition", "module": "Mathlib.Topology.Sheaves.SheafCondition.PairwiseIntersections", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.isSheafOpensLeCover_iff_isSheafPairwiseIntersections", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.SheafCondition.PairwiseIntersections", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.IsSheaf.isSheafPairwiseIntersections", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.SheafCondition.PairwiseIntersections", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.isSheaf_iff_isSheafPairwiseIntersections", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.SheafCondition.PairwiseIntersections", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "TopCat.Presheaf.IsSheaf.isSheafPreservesLimitPairwiseIntersections", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.SheafCondition.PairwiseIntersections", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.isSheaf_iff_isSheafPreservesLimitPairwiseIntersections", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.SheafCondition.PairwiseIntersections", "is_tactic_proof": false, "tactics": ["refine", "haveI", "exact"], "tactic_count": 3}
{"name": "TopCat.Sheaf.interUnionPullbackCone", "kind": "definition", "module": "Mathlib.Topology.Sheaves.SheafCondition.PairwiseIntersections", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Sheaf.interUnionPullbackCone_pt", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.SheafCondition.PairwiseIntersections", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Sheaf.interUnionPullbackCone_fst", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.SheafCondition.PairwiseIntersections", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Sheaf.interUnionPullbackCone_snd", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.SheafCondition.PairwiseIntersections", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Sheaf.interUnionPullbackConeLift", "kind": "definition", "module": "Mathlib.Topology.Sheaves.SheafCondition.PairwiseIntersections", "is_tactic_proof": true, "tactics": ["let", "have", "ext", "rw", "constructor", "rintro", "exacts", "rintro", "exacts", "refine", "naturality", "rintro", "exacts", "rintro", "let", "have", "clear_value", "subst", "rcases", "dsimp", "simp", "rw", "exact"], "tactic_count": 23}
{"name": "TopCat.Sheaf.interUnionPullbackConeLift_left", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.SheafCondition.PairwiseIntersections", "is_tactic_proof": true, "tactics": ["erw", "simp_rw", "exact", "op"], "tactic_count": 4}
{"name": "TopCat.Sheaf.interUnionPullbackConeLift_right", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.SheafCondition.PairwiseIntersections", "is_tactic_proof": true, "tactics": ["erw", "simp_rw", "exact", "op"], "tactic_count": 4}
{"name": "TopCat.Sheaf.isLimitPullbackCone", "kind": "definition", "module": "Mathlib.Topology.Sheaves.SheafCondition.PairwiseIntersections", "is_tactic_proof": true, "tactics": ["let", "have", "ext", "rw", "constructor", "rintro", "exacts", "rintro", "exacts", "apply", "intro", "use", "refine", "apply", "apply", "intro", "rw", "apply", "rintro", "erw", "convert", "apply", "erw", "convert", "apply", "all_goals", "dsimp", "op_comp,", "simp_rw", "congr", "simp_rw", "convert", "apply", "convert", "apply"], "tactic_count": 35}
{"name": "TopCat.Sheaf.isProductOfDisjoint", "kind": "definition", "module": "Mathlib.Topology.Sheaves.SheafCondition.PairwiseIntersections", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.coveringOfPresieve", "kind": "definition", "module": "Mathlib.Topology.Sheaves.SheafCondition.Sites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.coveringOfPresieve_apply", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.SheafCondition.Sites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.coveringOfPresieve.iSup_eq_of_mem_grothendieck", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.SheafCondition.Sites", "is_tactic_proof": true, "tactics": ["apply", "refine", "intro", "exact", "intro", "rw", "obtain", "exact"], "tactic_count": 8}
{"name": "TopCat.Presheaf.presieveOfCoveringAux", "kind": "definition", "module": "Mathlib.Topology.Sheaves.SheafCondition.Sites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.presieveOfCovering", "kind": "definition", "module": "Mathlib.Topology.Sheaves.SheafCondition.Sites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.covering_presieve_eq_self", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.SheafCondition.Sites", "is_tactic_proof": true, "tactics": ["funext", "ext", "exact"], "tactic_count": 3}
{"name": "TopCat.Presheaf.presieveOfCovering.mem_grothendieckTopology", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.SheafCondition.Sites", "is_tactic_proof": true, "tactics": ["intro", "obtain", "exact"], "tactic_count": 3}
{"name": "TopCat.Presheaf.presieveOfCovering.homOfIndex", "kind": "definition", "module": "Mathlib.Topology.Sheaves.SheafCondition.Sites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.presieveOfCovering.indexOfHom", "kind": "definition", "module": "Mathlib.Topology.Sheaves.SheafCondition.Sites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.presieveOfCovering.indexOfHom_spec", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.SheafCondition.Sites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Opens.coverDense_iff_isBasis", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.SheafCondition.Sites", "is_tactic_proof": true, "tactics": ["rw", "constructor", "intro", "exact", "intro", "exact"], "tactic_count": 6}
{"name": "TopCat.Opens.coverDense_inducedFunctor", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.SheafCondition.Sites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsOpenEmbedding.compatiblePreserving", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.SheafCondition.Sites", "is_tactic_proof": true, "tactics": ["haveI", "apply", "intro", "refine", "obtain", "exact"], "tactic_count": 6}
{"name": "IsOpenMap.coverPreserving", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.SheafCondition.Sites", "is_tactic_proof": true, "tactics": ["constructor", "rintro", "obtain", "exact"], "tactic_count": 4}
{"name": "Topology.IsOpenEmbedding.functor_isContinuous", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.SheafCondition.Sites", "is_tactic_proof": true, "tactics": ["apply", "exact", "exact"], "tactic_count": 3}
{"name": "TopCat.Presheaf.isSheaf_of_isOpenEmbedding", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.SheafCondition.Sites", "is_tactic_proof": true, "tactics": ["have", "exact"], "tactic_count": 2}
{"name": "instRepresentablyFlatOpensCarrierMap", "kind": "instance", "module": "Mathlib.Topology.Sheaves.SheafCondition.Sites", "is_tactic_proof": true, "tactics": ["constructor", "intro", "refine", "constructor", "intro", "exact", "exact", "exact"], "tactic_count": 8}
{"name": "compatiblePreserving_opens_map", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.SheafCondition.Sites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "coverPreserving_opens_map", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.SheafCondition.Sites", "is_tactic_proof": true, "tactics": ["constructor", "intro", "obtain", "exact"], "tactic_count": 4}
{"name": "instIsContinuousOpensCarrierMapGrothendieckTopology", "kind": "instance", "module": "Mathlib.Topology.Sheaves.SheafCondition.Sites", "is_tactic_proof": true, "tactics": ["apply", "exact", "exact"], "tactic_count": 3}
{"name": "TopCat.Sheaf.isTerminalOfEmpty", "kind": "definition", "module": "Mathlib.Topology.Sheaves.SheafCondition.Sites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Sheaf.isTerminalOfEqEmpty", "kind": "definition", "module": "Mathlib.Topology.Sheaves.SheafCondition.Sites", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "TopCat.Sheaf.restrictHomEquivHom", "kind": "definition", "module": "Mathlib.Topology.Sheaves.SheafCondition.Sites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Sheaf.extend_hom_app", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.SheafCondition.Sites", "is_tactic_proof": true, "tactics": ["nth_rw", "rfl"], "tactic_count": 2}
{"name": "TopCat.Sheaf.hom_ext", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.SheafCondition.Sites", "is_tactic_proof": true, "tactics": ["apply", "ext", "exact"], "tactic_count": 3}
{"name": "TopologicalSpace.Opens.instIsContinuousCompGrothendieckTopology", "kind": "instance", "module": "Mathlib.Topology.Sheaves.SheafCondition.Sites", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.IsCompatible", "kind": "definition", "module": "Mathlib.Topology.Sheaves.SheafCondition.UniqueGluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.IsGluing", "kind": "definition", "module": "Mathlib.Topology.Sheaves.SheafCondition.UniqueGluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.IsSheafUniqueGluing", "kind": "definition", "module": "Mathlib.Topology.Sheaves.SheafCondition.UniqueGluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.objPairwiseOfFamily", "kind": "definition", "module": "Mathlib.Topology.Sheaves.SheafCondition.UniqueGluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.IsCompatible.sectionPairwise", "kind": "definition", "module": "Mathlib.Topology.Sheaves.SheafCondition.UniqueGluing", "is_tactic_proof": true, "tactics": ["refine", "let", "rintro", "exact", "rfl", "exact", "exact"], "tactic_count": 7}
{"name": "TopCat.Presheaf.isGluing_iff_pairwise", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.SheafCondition.UniqueGluing", "is_tactic_proof": true, "tactics": ["refine", "rintro", "exact", "rw", "exact"], "tactic_count": 5}
{"name": "TopCat.Presheaf.IsSheaf.isSheafUniqueGluing_types", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.SheafCondition.UniqueGluing", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "TopCat.Presheaf.isSheaf_iff_isSheafUniqueGluing_types", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.SheafCondition.UniqueGluing", "is_tactic_proof": false, "tactics": ["simp_rw", "refine", "exact", "specialize", "h", "convert", "rfl", "exact"], "tactic_count": 8}
{"name": "TopCat.Presheaf.isSheaf_of_isSheafUniqueGluing_types", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.SheafCondition.UniqueGluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.IsSheaf.isSheafUniqueGluing", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.SheafCondition.UniqueGluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.isSheaf_iff_isSheafUniqueGluing", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.SheafCondition.UniqueGluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Sheaf.existsUnique_gluing", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.SheafCondition.UniqueGluing", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Sheaf.existsUnique_gluing'", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.SheafCondition.UniqueGluing", "is_tactic_proof": true, "tactics": ["have", "obtain", "refine", "intro", "rw", "exact", "intro", "convert", "rw", "rw", "exact"], "tactic_count": 11}
{"name": "TopCat.Sheaf.eq_of_locally_eq", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.SheafCondition.UniqueGluing", "is_tactic_proof": true, "tactics": ["let", "have", "intro", "simp_rw", "rfl", "obtain", "trans", "apply", "intro", "rfl", "symm", "apply", "intro", "rw"], "tactic_count": 14}
{"name": "TopCat.Sheaf.eq_of_locally_eq'", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.SheafCondition.UniqueGluing", "is_tactic_proof": true, "tactics": ["have", "suffices", "convert", "rw", "apply", "intro", "rw", "exact"], "tactic_count": 8}
{"name": "TopCat.Sheaf.eq_of_locally_eq₂", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.SheafCondition.UniqueGluing", "is_tactic_proof": true, "tactics": ["classical", "fapply", "exact", "refine", "rw", "constructor", "exact", "exact", "rintro", "any_goals", "any_goals"], "tactic_count": 11}
{"name": "TopCat.Presheaf.toTypes_isSheaf", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.SheafOfFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.toType_isSheaf", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.SheafOfFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.sheafToTypes", "kind": "definition", "module": "Mathlib.Topology.Sheaves.SheafOfFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.sheafToType", "kind": "definition", "module": "Mathlib.Topology.Sheaves.SheafOfFunctions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.Sheafify.isGerm", "kind": "definition", "module": "Mathlib.Topology.Sheaves.Sheafify", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.Sheafify.isLocallyGerm", "kind": "definition", "module": "Mathlib.Topology.Sheaves.Sheafify", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.sheafify", "kind": "definition", "module": "Mathlib.Topology.Sheaves.Sheafify", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.toSheafify", "kind": "definition", "module": "Mathlib.Topology.Sheaves.Sheafify", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.stalkToFiber", "kind": "definition", "module": "Mathlib.Topology.Sheaves.Sheafify", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.stalkToFiber_surjective", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Sheafify", "is_tactic_proof": true, "tactics": ["apply", "intro", "obtain", "use", "fconstructor", "exact", "exact"], "tactic_count": 7}
{"name": "TopCat.Presheaf.stalkToFiber_injective", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Sheafify", "is_tactic_proof": true, "tactics": ["apply", "intro", "rcases", "rcases", "have", "dsimp", "have", "dsimp", "rcases", "use", "refine", "change", "exact", "change", "exact", "intro", "specialize", "specialize", "refine", "rw"], "tactic_count": 20}
{"name": "TopCat.Presheaf.sheafifyStalkIso", "kind": "definition", "module": "Mathlib.Topology.Sheaves.Sheafify", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "skyscraperPresheaf", "kind": "definition", "module": "Mathlib.Topology.Sheaves.Skyscraper", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "skyscraperPresheaf_eq_pushforward", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Skyscraper", "is_tactic_proof": true, "tactics": ["convert_to", "congr"], "tactic_count": 2}
{"name": "SkyscraperPresheafFunctor.map'", "kind": "definition", "module": "Mathlib.Topology.Sheaves.Skyscraper", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SkyscraperPresheafFunctor.map'_id", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Skyscraper", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "SkyscraperPresheafFunctor.map'_comp", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Skyscraper", "is_tactic_proof": true, "tactics": ["ext", "simp", "split_ifs"], "tactic_count": 3}
{"name": "skyscraperPresheafFunctor", "kind": "definition", "module": "Mathlib.Topology.Sheaves.Skyscraper", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "skyscraperPresheafCoconeOfSpecializes", "kind": "definition", "module": "Mathlib.Topology.Sheaves.Skyscraper", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "skyscraperPresheafCoconeIsColimitOfSpecializes", "kind": "definition", "module": "Mathlib.Topology.Sheaves.Skyscraper", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "skyscraperPresheafStalkOfSpecializes", "kind": "definition", "module": "Mathlib.Topology.Sheaves.Skyscraper", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "germ_skyscraperPresheafStalkOfSpecializes_hom", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Skyscraper", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "skyscraperPresheafCocone", "kind": "definition", "module": "Mathlib.Topology.Sheaves.Skyscraper", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "skyscraperPresheafCoconeIsColimitOfNotSpecializes", "kind": "definition", "module": "Mathlib.Topology.Sheaves.Skyscraper", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "skyscraperPresheafStalkOfNotSpecializes", "kind": "definition", "module": "Mathlib.Topology.Sheaves.Skyscraper", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "skyscraperPresheafStalkOfNotSpecializesIsTerminal", "kind": "definition", "module": "Mathlib.Topology.Sheaves.Skyscraper", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "skyscraperPresheaf_isSheaf", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Skyscraper", "is_tactic_proof": true, "tactics": ["classical", "exact", "dsimp", "rw", "exact", "exact"], "tactic_count": 6}
{"name": "skyscraperSheaf", "kind": "definition", "module": "Mathlib.Topology.Sheaves.Skyscraper", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "skyscraperSheafFunctor", "kind": "definition", "module": "Mathlib.Topology.Sheaves.Skyscraper", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StalkSkyscraperPresheafAdjunctionAuxs.toSkyscraperPresheaf", "kind": "definition", "module": "Mathlib.Topology.Sheaves.Skyscraper", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StalkSkyscraperPresheafAdjunctionAuxs.fromStalk", "kind": "definition", "module": "Mathlib.Topology.Sheaves.Skyscraper", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StalkSkyscraperPresheafAdjunctionAuxs.germ_fromStalk", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Skyscraper", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StalkSkyscraperPresheafAdjunctionAuxs.to_skyscraper_fromStalk", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Skyscraper", "is_tactic_proof": true, "tactics": ["apply", "ext", "dsimp", "split_ifs", "rw", "exact"], "tactic_count": 6}
{"name": "StalkSkyscraperPresheafAdjunctionAuxs.fromStalk_to_skyscraper", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Skyscraper", "is_tactic_proof": true, "tactics": ["refine", "rw", "eqToHom_refl,"], "tactic_count": 3}
{"name": "StalkSkyscraperPresheafAdjunctionAuxs.unit", "kind": "definition", "module": "Mathlib.Topology.Sheaves.Skyscraper", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "StalkSkyscraperPresheafAdjunctionAuxs.counit", "kind": "definition", "module": "Mathlib.Topology.Sheaves.Skyscraper", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "skyscraperPresheafStalkAdjunction", "kind": "definition", "module": "Mathlib.Topology.Sheaves.Skyscraper", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsRightAdjointPresheafSkyscraperPresheafFunctorOfHasColimits", "kind": "instance", "module": "Mathlib.Topology.Sheaves.Skyscraper", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsLeftAdjointPresheafStalkFunctor", "kind": "instance", "module": "Mathlib.Topology.Sheaves.Skyscraper", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "stalkSkyscraperSheafAdjunction", "kind": "definition", "module": "Mathlib.Topology.Sheaves.Skyscraper", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsRightAdjointSheafSkyscraperSheafFunctorOfHasColimits", "kind": "instance", "module": "Mathlib.Topology.Sheaves.Skyscraper", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.stalkFunctor", "kind": "definition", "module": "Mathlib.Topology.Sheaves.Stalks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.stalk", "kind": "definition", "module": "Mathlib.Topology.Sheaves.Stalks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.stalkFunctor_obj", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Stalks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.germ", "kind": "definition", "module": "Mathlib.Topology.Sheaves.Stalks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.Γgerm", "kind": "definition", "module": "Mathlib.Topology.Sheaves.Stalks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.germ_res", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Stalks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.germ_res'", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Stalks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.map_germ_eq_Γgerm", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Stalks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.germ_res_apply", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Stalks", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "TopCat.Presheaf.germ_res_apply'", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Stalks", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "TopCat.Presheaf.Γgerm_res_apply", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Stalks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.stalk_hom_ext", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Stalks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.stalkFunctor_map_germ", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Stalks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.stalkFunctor_map_germ_apply", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Stalks", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "TopCat.Presheaf.stalkFunctor_map_germ_apply'", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Stalks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.stalkPushforward", "kind": "definition", "module": "Mathlib.Topology.Sheaves.Stalks", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "TopCat.Presheaf.stalkPushforward_germ", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Stalks", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "TopCat.Presheaf.stalkPushforward.id", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Stalks", "is_tactic_proof": true, "tactics": ["ext", "simp", "erw", "simp"], "tactic_count": 4}
{"name": "TopCat.Presheaf.stalkPushforward.comp", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Stalks", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "TopCat.Presheaf.stalkPushforward.stalkPushforward_iso_of_isInducing", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Stalks", "is_tactic_proof": true, "tactics": ["haveI", "convert", "refine", "symm", "exact"], "tactic_count": 5}
{"name": "TopCat.Presheaf.stalkPullbackHom", "kind": "definition", "module": "Mathlib.Topology.Sheaves.Stalks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.germ_stalkPullbackHom", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Stalks", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "TopCat.Presheaf.germToPullbackStalk", "kind": "definition", "module": "Mathlib.Topology.Sheaves.Stalks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.pullback_obj_obj_ext", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Stalks", "is_tactic_proof": true, "tactics": ["apply", "rintro", "simpa"], "tactic_count": 3}
{"name": "TopCat.Presheaf.pushforwardPullbackAdjunction_unit_pullback_map_germToPullbackStalk", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Stalks", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "TopCat.Presheaf.germToPullbackStalk_stalkPullbackHom", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Stalks", "is_tactic_proof": true, "tactics": ["ext", "dsimp", "simp"], "tactic_count": 3}
{"name": "TopCat.Presheaf.pushforwardPullbackAdjunction_unit_app_app_germToPullbackStalk", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Stalks", "is_tactic_proof": true, "tactics": ["simpa", "pushforwardPullbackAdjunction_unit_pullback_map_germToPullbackStalk"], "tactic_count": 2}
{"name": "TopCat.Presheaf.stalkPullbackInv", "kind": "definition", "module": "Mathlib.Topology.Sheaves.Stalks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.germ_stalkPullbackInv", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Stalks", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "TopCat.Presheaf.stalkPullbackIso", "kind": "definition", "module": "Mathlib.Topology.Sheaves.Stalks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.stalkSpecializes", "kind": "definition", "module": "Mathlib.Topology.Sheaves.Stalks", "is_tactic_proof": true, "tactics": ["refine", "exact", "colimit.ι", "intro", "dsimp", "rw", "let", "let", "exact"], "tactic_count": 9}
{"name": "TopCat.Presheaf.germ_stalkSpecializes", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Stalks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.stalkSpecializes_refl", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Stalks", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "TopCat.Presheaf.stalkSpecializes_comp", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Stalks", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "TopCat.Presheaf.stalkSpecializes_stalkFunctor_map", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Stalks", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "TopCat.Presheaf.stalkSpecializes_stalkPushforward", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Stalks", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "TopCat.Presheaf.stalkCongr", "kind": "definition", "module": "Mathlib.Topology.Sheaves.Stalks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.germ_ext", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Stalks", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "TopCat.Presheaf.germ_exist", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Stalks", "is_tactic_proof": true, "tactics": ["obtain", "revert", "induction", "op", "obtain", "intro", "exact"], "tactic_count": 7}
{"name": "TopCat.Presheaf.germ_eq", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Stalks", "is_tactic_proof": false, "tactics": ["obtain", "h", "exact"], "tactic_count": 3}
{"name": "TopCat.Presheaf.stalkFunctor_map_injective_of_app_injective", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Stalks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.germ_exist_of_isBasis", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Stalks", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "exact"], "tactic_count": 3}
{"name": "TopCat.Presheaf.germ_eq_of_isBasis", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Stalks", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "refine", "simpa"], "tactic_count": 4}
{"name": "TopCat.Presheaf.stalkFunctor_map_injective_of_isBasis", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Stalks", "is_tactic_proof": true, "tactics": ["intro", "obtain", "obtain", "rw", "obtain", "simp", "simpa"], "tactic_count": 7}
{"name": "TopCat.Presheaf.section_ext", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Stalks", "is_tactic_proof": true, "tactics": ["choose", "apply", "intro", "simp", "exact", "intro", "rw", "imply", "is"], "tactic_count": 9}
{"name": "TopCat.Presheaf.app_injective_of_stalkFunctor_map_injective", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Stalks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.app_injective_iff_stalkFunctor_map_injective", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Stalks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.stalkFunctor_preserves_mono", "kind": "instance", "module": "Mathlib.Topology.Sheaves.Stalks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.stalk_mono_of_mono", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Stalks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.mono_of_stalk_mono", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Stalks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.mono_iff_stalk_mono", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Stalks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.app_surjective_of_injective_of_locally_surjective", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Stalks", "is_tactic_proof": false, "tactics": ["conv", "enter", "rw", "intro", "choose", "have", "intro", "simp", "exact", "suffices", "obtain", "use", "apply", "intro", "rw", "intro", "apply", "intro", "apply", "dsimp", "rw", "simp_rw", "rfl"], "tactic_count": 23}
{"name": "TopCat.Presheaf.app_surjective_of_stalkFunctor_map_bijective", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Stalks", "is_tactic_proof": false, "tactics": ["refine", "app_surjective_of_injective_of_locally_surjective", "obtain", "obtain", "subst", "rw", "obtain", "use", "rw"], "tactic_count": 9}
{"name": "TopCat.Presheaf.app_bijective_of_stalkFunctor_map_bijective", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Stalks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopCat.Presheaf.app_isIso_of_stalkFunctor_map_iso", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Stalks", "is_tactic_proof": true, "tactics": ["suffices", "rw", "apply", "intro", "apply", "exact"], "tactic_count": 6}
{"name": "TopCat.Presheaf.isIso_of_stalkFunctor_map_iso", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Stalks", "is_tactic_proof": true, "tactics": ["suffices", "suffices", "intro", "apply"], "tactic_count": 4}
{"name": "TopCat.Presheaf.isIso_iff_stalkFunctor_map_iso", "kind": "theorem", "module": "Mathlib.Topology.Sheaves.Stalks", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ShrinkingLemma.PartialRefinement.instCoeFunForallSet", "kind": "instance", "module": "Mathlib.Topology.ShrinkingLemma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ShrinkingLemma.PartialRefinement.subset", "kind": "theorem", "module": "Mathlib.Topology.ShrinkingLemma", "is_tactic_proof": true, "tactics": ["classical"], "tactic_count": 1}
{"name": "ShrinkingLemma.PartialRefinement.instPartialOrder", "kind": "instance", "module": "Mathlib.Topology.ShrinkingLemma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ShrinkingLemma.PartialRefinement.apply_eq_of_chain", "kind": "theorem", "module": "Mathlib.Topology.ShrinkingLemma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ShrinkingLemma.PartialRefinement.chainSupCarrier", "kind": "definition", "module": "Mathlib.Topology.ShrinkingLemma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ShrinkingLemma.PartialRefinement.find", "kind": "definition", "module": "Mathlib.Topology.ShrinkingLemma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ShrinkingLemma.PartialRefinement.find_mem", "kind": "theorem", "module": "Mathlib.Topology.ShrinkingLemma", "is_tactic_proof": true, "tactics": ["rw", "split_ifs", "exacts"], "tactic_count": 3}
{"name": "ShrinkingLemma.PartialRefinement.mem_find_carrier_iff", "kind": "theorem", "module": "Mathlib.Topology.ShrinkingLemma", "is_tactic_proof": true, "tactics": ["rw", "split_ifs", "have", "exact", "push_neg", "refine", "simpa"], "tactic_count": 7}
{"name": "ShrinkingLemma.PartialRefinement.find_apply_of_mem", "kind": "theorem", "module": "Mathlib.Topology.ShrinkingLemma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ShrinkingLemma.PartialRefinement.chainSup", "kind": "definition", "module": "Mathlib.Topology.ShrinkingLemma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ShrinkingLemma.PartialRefinement.le_chainSup", "kind": "theorem", "module": "Mathlib.Topology.ShrinkingLemma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ShrinkingLemma.PartialRefinement.exists_gt", "kind": "theorem", "module": "Mathlib.Topology.ShrinkingLemma", "is_tactic_proof": false, "tactics": ["have", "simp", "intro", "rcases", "exact", "have", "rcases", "classical", "refine", "intro", "rcases", "refine", "by_cases", "rcases", "use", "rwa", "use", "rw", "exact", "rintro", "rwa", "rw", "exact", "exact", "intro", "rw", "rw", "refine", "exact", "exact"], "tactic_count": 30}
{"name": "exists_subset_iUnion_closure_subset", "kind": "theorem", "module": "Mathlib.Topology.ShrinkingLemma", "is_tactic_proof": true, "tactics": ["haveI", "have", "rcases", "suffices", "intro", "rcases", "exact"], "tactic_count": 7}
{"name": "exists_subset_iUnion_closed_subset", "kind": "theorem", "module": "Mathlib.Topology.ShrinkingLemma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_iUnion_eq_closure_subset", "kind": "theorem", "module": "Mathlib.Topology.ShrinkingLemma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_iUnion_eq_closed_subset", "kind": "theorem", "module": "Mathlib.Topology.ShrinkingLemma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_gt_t2space", "kind": "theorem", "module": "Mathlib.Topology.ShrinkingLemma", "is_tactic_proof": true, "tactics": ["set", "simp", "have", "apply", "have", "apply", "intro", "exact", "exact", "have", "intro", "have", "rw", "apply", "have", "rw", "rw", "exact", "obtain", "obtain", "by_contra", "exact", "exact", "obtain", "classical", "refine", "intro", "rcases", "refine", "by_cases", "rcases", "use", "rwa", "use", "rw", "apply", "rw", "exact", "rintro", "rw", "exact", "rw", "exact", "intro", "rw", "by_cases", "rw", "simp", "exact", "apply", "intro", "exact", "intro", "rw", "exact", "intro", "rw", "rw", "refine", "exact", "exact", "simp", "exact"], "tactic_count": 63}
{"name": "exists_subset_iUnion_closure_subset_t2space", "kind": "theorem", "module": "Mathlib.Topology.ShrinkingLemma", "is_tactic_proof": false, "tactics": ["haveI", "have", "rcases", "suffices", "intro", "exact", "intro", "by_contra", "rcases", "exact"], "tactic_count": 10}
{"name": "exists_subset_iUnion_compact_subset_t2space", "kind": "theorem", "module": "Mathlib.Topology.ShrinkingLemma", "is_tactic_proof": true, "tactics": ["let", "use", "refine", "exact", "simp"], "tactic_count": 5}
{"name": "IsGenericPoint", "kind": "definition", "module": "Mathlib.Topology.Sober", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isGenericPoint_def", "kind": "theorem", "module": "Mathlib.Topology.Sober", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGenericPoint.def", "kind": "theorem", "module": "Mathlib.Topology.Sober", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isGenericPoint_closure", "kind": "theorem", "module": "Mathlib.Topology.Sober", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isGenericPoint_iff_specializes", "kind": "theorem", "module": "Mathlib.Topology.Sober", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsGenericPoint.specializes_iff_mem", "kind": "theorem", "module": "Mathlib.Topology.Sober", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGenericPoint.specializes", "kind": "theorem", "module": "Mathlib.Topology.Sober", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGenericPoint.mem", "kind": "theorem", "module": "Mathlib.Topology.Sober", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGenericPoint.isClosed", "kind": "theorem", "module": "Mathlib.Topology.Sober", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGenericPoint.isIrreducible", "kind": "theorem", "module": "Mathlib.Topology.Sober", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGenericPoint.inseparable", "kind": "theorem", "module": "Mathlib.Topology.Sober", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGenericPoint.eq", "kind": "theorem", "module": "Mathlib.Topology.Sober", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGenericPoint.mem_open_set_iff", "kind": "theorem", "module": "Mathlib.Topology.Sober", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsGenericPoint.disjoint_iff", "kind": "theorem", "module": "Mathlib.Topology.Sober", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsGenericPoint.mem_closed_set_iff", "kind": "theorem", "module": "Mathlib.Topology.Sober", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsGenericPoint.image", "kind": "theorem", "module": "Mathlib.Topology.Sober", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "isGenericPoint_iff_forall_closed", "kind": "theorem", "module": "Mathlib.Topology.Sober", "is_tactic_proof": true, "tactics": ["have", "simp_rw", "singleton_subset_iff]"], "tactic_count": 3}
{"name": "IsIrreducible.genericPoint", "kind": "definition", "module": "Mathlib.Topology.Sober", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIrreducible.isGenericPoint_genericPoint_closure", "kind": "theorem", "module": "Mathlib.Topology.Sober", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIrreducible.isGenericPoint_genericPoint", "kind": "theorem", "module": "Mathlib.Topology.Sober", "is_tactic_proof": true, "tactics": ["convert"], "tactic_count": 1}
{"name": "IsIrreducible.genericPoint_closure_eq", "kind": "theorem", "module": "Mathlib.Topology.Sober", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsIrreducible.closure_genericPoint", "kind": "theorem", "module": "Mathlib.Topology.Sober", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "genericPoint", "kind": "definition", "module": "Mathlib.Topology.Sober", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "genericPoint_spec", "kind": "theorem", "module": "Mathlib.Topology.Sober", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "genericPoint_closure", "kind": "theorem", "module": "Mathlib.Topology.Sober", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "genericPoint_specializes", "kind": "theorem", "module": "Mathlib.Topology.Sober", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "irreducibleSetEquivPoints", "kind": "definition", "module": "Mathlib.Topology.Sober", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsClosedEmbedding.quasiSober", "kind": "theorem", "module": "Mathlib.Topology.Sober", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsOpenEmbedding.quasiSober", "kind": "theorem", "module": "Mathlib.Topology.Sober", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.IsOpenCover.quasiSober_iff_forall", "kind": "theorem", "module": "Mathlib.Topology.Sober", "is_tactic_proof": true, "tactics": ["refine", "rintro", "obtain", "have", "use", "apply", "simpa", "continuous_subtype_val.closure_preimage_subset", "rw", "refine", "simpa"], "tactic_count": 11}
{"name": "TopologicalSpace.IsOpenCover.quasiSober", "kind": "theorem", "module": "Mathlib.Topology.Sober", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "quasiSober_of_open_cover", "kind": "theorem", "module": "Mathlib.Topology.Sober", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "R1Space.quasiSober", "kind": "instance", "module": "Mathlib.Topology.Sober", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "genericPoints", "kind": "definition", "module": "Mathlib.Topology.Sober", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "genericPoints.component", "kind": "definition", "module": "Mathlib.Topology.Sober", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "genericPoints.isGenericPoint", "kind": "theorem", "module": "Mathlib.Topology.Sober", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "genericPoints.component_injective", "kind": "theorem", "module": "Mathlib.Topology.Sober", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "genericPoints.ofComponent", "kind": "definition", "module": "Mathlib.Topology.Sober", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "genericPoints.isGenericPoint_ofComponent", "kind": "theorem", "module": "Mathlib.Topology.Sober", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "genericPoints.component_ofComponent", "kind": "theorem", "module": "Mathlib.Topology.Sober", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "genericPoints.ofComponent_component", "kind": "theorem", "module": "Mathlib.Topology.Sober", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "genericPoints.component_surjective", "kind": "theorem", "module": "Mathlib.Topology.Sober", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "genericPoints.finite", "kind": "theorem", "module": "Mathlib.Topology.Sober", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "genericPoints.equiv", "kind": "definition", "module": "Mathlib.Topology.Sober", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "genericPoints.closure", "kind": "theorem", "module": "Mathlib.Topology.Sober", "is_tactic_proof": true, "tactics": ["refine", "refine", "exact"], "tactic_count": 3}
{"name": "genericPoints_eq_singleton", "kind": "theorem", "module": "Mathlib.Topology.Sober", "is_tactic_proof": true, "tactics": ["ext", "rw", "exact"], "tactic_count": 3}
{"name": "Specialization", "kind": "definition", "module": "Mathlib.Topology.Specialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Specialization.ofEquiv", "kind": "definition", "module": "Mathlib.Topology.Specialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Specialization.toEquiv_symm", "kind": "theorem", "module": "Mathlib.Topology.Specialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Specialization.ofEquiv_symm", "kind": "theorem", "module": "Mathlib.Topology.Specialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Specialization.toEquiv_ofEquiv", "kind": "theorem", "module": "Mathlib.Topology.Specialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Specialization.toEquiv_le_toEquiv", "kind": "theorem", "module": "Mathlib.Topology.Specialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Specialization.isOpen_toEquiv_preimage", "kind": "theorem", "module": "Mathlib.Topology.Specialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Specialization.isUpperSet_ofEquiv_preimage", "kind": "theorem", "module": "Mathlib.Topology.Specialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Specialization.map", "kind": "definition", "module": "Mathlib.Topology.Specialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "orderIsoSpecializationWithUpperSetTopology", "kind": "definition", "module": "Mathlib.Topology.Specialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "homeoWithUpperSetTopologyorderIso", "kind": "definition", "module": "Mathlib.Topology.Specialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "topToPreord", "kind": "definition", "module": "Mathlib.Topology.Specialization", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsOpenEmbedding.spectralSpace", "kind": "theorem", "module": "Mathlib.Topology.Spectral.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.preimage_of_isOpen", "kind": "theorem", "module": "Mathlib.Topology.Spectral.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSpectralMap.continuous", "kind": "theorem", "module": "Mathlib.Topology.Spectral.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isSpectralMap_id", "kind": "theorem", "module": "Mathlib.Topology.Spectral.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "IsProperMap.isSpectralMap", "kind": "theorem", "module": "Mathlib.Topology.Spectral.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SpectralMapClass.toContinuousMapClass", "kind": "instance", "module": "Mathlib.Topology.Spectral.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCoeTCSpectralMapOfSpectralMapClass", "kind": "instance", "module": "Mathlib.Topology.Spectral.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SpectralMap.instFunLike", "kind": "instance", "module": "Mathlib.Topology.Spectral.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SpectralMap.instSpectralMapClass", "kind": "instance", "module": "Mathlib.Topology.Spectral.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SpectralMap.toFun_eq_coe", "kind": "theorem", "module": "Mathlib.Topology.Spectral.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SpectralMap.id", "kind": "definition", "module": "Mathlib.Topology.Spectral.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SpectralMap.instInhabited", "kind": "instance", "module": "Mathlib.Topology.Spectral.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SpectralMap.id_apply", "kind": "theorem", "module": "Mathlib.Topology.Spectral.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SpectralMap.comp", "kind": "definition", "module": "Mathlib.Topology.Spectral.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SpectralMap.coe_comp_continuousMap", "kind": "theorem", "module": "Mathlib.Topology.Spectral.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "SpectralMap.comp_assoc", "kind": "theorem", "module": "Mathlib.Topology.Spectral.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "instPrespectralSpaceOfNoetherianSpace", "kind": "instance", "module": "Mathlib.Topology.Spectral.Prespectral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instLocallyCompactSpaceOfPrespectralSpace", "kind": "instance", "module": "Mathlib.Topology.Spectral.Prespectral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instTotallySeparatedSpaceOfT2SpaceOfPrespectralSpace", "kind": "instance", "module": "Mathlib.Topology.Spectral.Prespectral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "PrespectralSpace.of_isOpenCover", "kind": "theorem", "module": "Mathlib.Topology.Spectral.Prespectral", "is_tactic_proof": true, "tactics": ["refine", "simp", "forall_apply_eq_imp_iff₂]", "exact"], "tactic_count": 4}
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{"name": "PrespectralSpace.sigma", "kind": "instance", "module": "Mathlib.Topology.Spectral.Prespectral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "PrespectralSpace.opensEquiv", "kind": "definition", "module": "Mathlib.Topology.Spectral.Prespectral", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "Path.Homotopic.concat_subpath", "kind": "theorem", "module": "Mathlib.Topology.Subpath", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "IsClosed.relInv", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.relImage_of_finite", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "IsClosed.relPreimage_of_finite", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eventually_uniformity_iterate_comp_subset", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": true, "tactics": ["suffices", "induction", "zero", "succ", "rcases", "refine", "rw", "have", "exact"], "tactic_count": 9}
{"name": "eventually_uniformity_comp_subset", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.isOpen_ball", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.isClosed_ball", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.hasBasis_nhds_prod", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": true, "tactics": ["rw", "apply", "rintro", "exact"], "tactic_count": 4}
{"name": "nhds_eq_uniformity_prod", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact", "refine", "exact"], "tactic_count": 4}
{"name": "nhdset_of_mem_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": true, "tactics": ["let", "have", "mem_nhds_iff.mp", "show", "rw", "exact", "exact", "choose", "exact", "isOpen_iUnion", "simp", "iUnion_subset"], "tactic_count": 12}
{"name": "nhds_le_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": true, "tactics": ["intro", "rcases", "have", "rw", "exact", "apply", "rintro", "exact"], "tactic_count": 8}
{"name": "iSup_nhds_le_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsSet_diagonal_le_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.has_seq_basis", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "closure_eq_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp", "and_imp,"], "tactic_count": 3}
{"name": "uniformity_hasBasis_closed", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": true, "tactics": ["refine", "rcases", "refine", "refine", "rw", "apply", "apply", "exact"], "tactic_count": 8}
{"name": "uniformity_eq_uniformity_closure", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.uniformity_closure", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformity_hasBasis_closure", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "closure_eq_inter_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformity_eq_uniformity_interior", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "interior_mem_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mem_uniformity_isClosed", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpen_iff_isOpen_ball_subset", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": true, "tactics": ["rw", "constructor", "obtain", "exact", "obtain", "exact"], "tactic_count": 6}
{"name": "closure_ball_subset", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dense.biUnion_uniformity_ball", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": true, "tactics": ["refine", "rcases", "exact"], "tactic_count": 3}
{"name": "DenseRange.iUnion_uniformity_ball", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "uniformity_hasBasis_open", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.mem_uniformity_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformity_hasBasis_open_symmetric", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": true, "tactics": ["simp", "refine", "exact"], "tactic_count": 3}
{"name": "comp_open_symm_mem_uniformity_sets", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "exact"], "tactic_count": 3}
{"name": "instPartialOrderUniformSpace", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.le_def", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInfSetUniformSpace", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.sInf_le", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.le_sInf", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instTopUniformSpace", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instBotUniformSpace", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instMinUniformSpace", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instCompleteLatticeUniformSpace", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iInf_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inf_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "bot_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "top_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inhabitedUniformSpace", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inhabitedUniformSpaceCore", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instUniqueUniformSpaceOfSubsingleton", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.comap", "kind": "abbrev", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformity_comap", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ball_preimage", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "uniformSpace_comap_id", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": true, "tactics": ["ext", "rw"], "tactic_count": 2}
{"name": "UniformSpace.comap_comap", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": true, "tactics": ["ext1", "simp"], "tactic_count": 2}
{"name": "UniformSpace.comap_inf", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.comap_iInf", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "UniformSpace.comap_mono", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformContinuous_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_iff_uniformContinuous_id", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "uniformContinuous_comap", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformContinuous_comap'", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.to_nhds_mono", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "UniformSpace.toTopologicalSpace_mono", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.toTopologicalSpace_comap", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.uniformSpace_eq_bot", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.uniformSpace_eq_bot", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "UniformSpace.toTopologicalSpace_bot", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.toTopologicalSpace_top", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.toTopologicalSpace_iInf", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.toTopologicalSpace_sInf", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "UniformSpace.toTopologicalSpace_inf", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformContinuous.continuous", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformContinuous.uniformContinuousOn", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformContinuousOn.mono", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformContinuousOn.congr", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": true, "tactics": ["apply", "apply", "filter_upwards"], "tactic_count": 3}
{"name": "UniformContinuousOn.comp", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": true, "tactics": ["change", "apply", "refine", "simp", "exact"], "tactic_count": 5}
{"name": "UniformContinuous.comp_uniformContinuousOn", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.uniformSpace", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "OrderDual.instUniformSpace", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformContinuous.inf_rng", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformContinuous.inf_dom_left", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformContinuous.inf_dom_right", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformContinuous_sInf_dom", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": true, "tactics": ["delta", "rw", "exact"], "tactic_count": 3}
{"name": "uniformContinuous_sInf_rng", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": true, "tactics": ["delta", "rw"], "tactic_count": 2}
{"name": "uniformContinuous_iInf_dom", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": true, "tactics": ["delta", "rw", "exact"], "tactic_count": 3}
{"name": "uniformContinuous_iInf_rng", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": true, "tactics": ["delta", "rw"], "tactic_count": 2}
{"name": "discreteTopology_of_discrete_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instUniformSpaceEmpty", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instUniformSpacePUnit", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instUniformSpaceBool", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instUniformSpaceNat", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instUniformSpaceInt", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instUniformSpaceAdditive", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instUniformSpaceMultiplicative", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformContinuous_ofMul", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformContinuous_toMul", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformContinuous_ofAdd", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformContinuous_toAdd", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformity_additive", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformity_multiplicative", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instUniformSpaceSubtype", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformity_subtype", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformity_setCoe", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "map_uniformity_set_coe", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "uniformContinuous_subtype_val", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformContinuous.subtype_mk", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformContinuous.subtype_map", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformContinuousOn_iff_restrict", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": true, "tactics": ["delta", "rw"], "tactic_count": 2}
{"name": "tendsto_of_uniformContinuous_subtype", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "UniformContinuousOn.continuousOn", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "instIsCountablyGeneratedProdElemUniformity", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instUniformSpaceMulOpposite", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformity_mulOpposite", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "comap_uniformity_mulOpposite", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "MulOpposite.uniformContinuous_unop", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "MulOpposite.uniformContinuous_op", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instUniformSpaceProd", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_example", "kind": "example", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": true, "tactics": ["with_reducible_and_instances"], "tactic_count": 1}
{"name": "uniformity_prod", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsCountablyGeneratedProdUniformity", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "uniformity_prod_eq_comap_prod", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "uniformity_prod_eq_prod", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "mem_uniformity_of_uniformContinuous_invariant", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": true, "tactics": ["rw", "rcases", "exact"], "tactic_count": 3}
{"name": "entourageProd", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_entourageProd", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "entourageProd_mem_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "ball_entourageProd", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "IsSymm_entourageProd", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_entourageProd", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "image_entourageProd_prod", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp", "grind"], "tactic_count": 3}
{"name": "preimage_entourageProd_prod", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.uniformity_prod", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "entourageProd_subset", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": true, "tactics": ["rcases", "use"], "tactic_count": 2}
{"name": "tendsto_prod_uniformity_fst", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_prod_uniformity_snd", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformContinuous_fst", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformContinuous_snd", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformContinuous.prodMk", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "UniformContinuous.prodMk_left", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformContinuous.prodMk_right", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformContinuous.prodMap", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformContinuous_swap", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toTopologicalSpace_prod", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformContinuous_inf_dom_left₂", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": true, "tactics": ["have", "have", "have", "exact"], "tactic_count": 4}
{"name": "uniformContinuous_inf_dom_right₂", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": true, "tactics": ["have", "have", "have", "exact"], "tactic_count": 4}
{"name": "uniformContinuous_sInf_dom₂", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": true, "tactics": ["let", "have", "have", "have", "exact"], "tactic_count": 5}
{"name": "_private.Mathlib.Topology.UniformSpace.Basic.0.term_∘₂_", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.UniformSpace.Basic.0._aux_Mathlib_Topology_UniformSpace_Basic___macroRules__private_Mathlib_Topology_UniformSpace_Basic_0_term_∘₂__1", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.UniformSpace.Basic.0._aux_Mathlib_Topology_UniformSpace_Basic___unexpand_Function_bicompr_1", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformContinuous₂", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformContinuous₂_def", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformContinuous₂.uniformContinuous", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformContinuous₂_curry", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "UniformContinuous₂.comp", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformContinuous₂.bicompl", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "toTopologicalSpace_subtype", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.instUniformSpace", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "union_mem_uniformity_sum", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Sum.uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformContinuous_inl", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformContinuous_inr", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsCountablyGeneratedProdSumUniformity", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "Uniform.tendsto_nhds_right", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Uniform.tendsto_nhds_left", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Uniform.continuousAt_iff'_right", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Uniform.continuousAt_iff'_left", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Uniform.continuousAt_iff_prod", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Uniform.continuousWithinAt_iff'_right", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Uniform.continuousWithinAt_iff'_left", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Uniform.continuousOn_iff'_right", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Uniform.continuousOn_iff'_left", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Uniform.continuous_iff'_right", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Uniform.continuous_iff'_left", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Uniform.exists_is_open_mem_uniformity_of_forall_mem_eq", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": ["have", "intro", "obtain", "have", "have", "rcases", "refine", "have", "have", "rw", "exact", "choose", "refine", "rintro", "simp", "rcases", "exact"], "tactic_count": 17}
{"name": "Filter.Tendsto.congr_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Uniform.tendsto_congr", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cauchy", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsComplete", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.cauchy_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cauchy_iff'", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cauchy_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cauchy_iff_le", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Cauchy.ultrafilter_of", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": true, "tactics": ["haveI", "have", "exact"], "tactic_count": 3}
{"name": "cauchy_map_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "cauchy_map_iff'", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cauchy.mono", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cauchy.mono'", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cauchy_nhds", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cauchy_pure", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.cauchy_map", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cauchy.mono_uniformSpace", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cauchy_inf_uniformSpace", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": true, "tactics": ["unfold", "rw"], "tactic_count": 2}
{"name": "cauchy_iInf_uniformSpace", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": true, "tactics": ["unfold", "rw"], "tactic_count": 2}
{"name": "cauchy_iInf_uniformSpace'", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "cauchy_comap_uniformSpace", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": true, "tactics": ["simp", "rfl"], "tactic_count": 2}
{"name": "cauchy_prod_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Cauchy.prod", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "le_nhds_of_cauchy_adhp_aux", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": true, "tactics": ["intro", "rcases", "rcases", "apply", "exact"], "tactic_count": 5}
{"name": "le_nhds_of_cauchy_adhp", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "le_nhds_iff_adhp_of_cauchy", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cauchy.map", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cauchy.comap", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cauchy.comap'", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauchySeq", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauchySeq.tendsto_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CauchySeq.nonempty", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauchySeq.mem_entourage", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": true, "tactics": ["haveI", "have", "simpa"], "tactic_count": 3}
{"name": "Filter.Tendsto.cauchySeq", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cauchySeq_const", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cauchySeq_iff_tendsto", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauchySeq.comp_tendsto", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauchySeq.comp_injective", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Function.Bijective.cauchySeq_comp_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": true, "tactics": ["refine", "lift", "simpa"], "tactic_count": 3}
{"name": "CauchySeq.subseq_subseq_mem", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "cauchySeq_iff'", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cauchySeq_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CauchySeq.prodMap", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "CauchySeq.prodMk", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauchySeq.eventually_eventually", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformContinuous.comp_cauchySeq", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauchySeq.subseq_mem", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": ["have", "rw", "rcases", "exact", "obtain", "extraction_forall_of_eventually", "exact"], "tactic_count": 7}
{"name": "Filter.Tendsto.subseq_mem_entourage", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "exact"], "tactic_count": 3}
{"name": "tendsto_nhds_of_cauchySeq_of_subseq", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cauchySeq_shift", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": true, "tactics": ["constructor", "rw", "intro", "obtain", "use", "intro", "convert", "exact"], "tactic_count": 8}
{"name": "Filter.HasBasis.cauchySeq_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": true, "tactics": ["rw", "refine", "simp"], "tactic_count": 3}
{"name": "Filter.HasBasis.cauchySeq_iff'", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": true, "tactics": ["refine", "exact", "rcases", "rcases", "refine", "exacts"], "tactic_count": 6}
{"name": "cauchySeq_of_controlled", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isComplete_iff_clusterPt", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isComplete_iff_ultrafilter", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": true, "tactics": ["refine", "haveI", "rcases", "exact"], "tactic_count": 4}
{"name": "isComplete_iff_ultrafilter'", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsComplete.union", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "isComplete_iUnion_separated", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": true, "tactics": ["set", "intro", "rw", "obtain", "obtain", "rcases", "refine", "gcongr", "obtain", "rcases", "rcases", "refine", "rcases", "rwa", "rcases", "exact"], "tactic_count": 16}
{"name": "complete_univ", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteSpace.prod", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteSpace.fst_of_prod", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteSpace.snd_of_prod", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "completeSpace_prod_of_nonempty", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteSpace.mulOpposite", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "completeSpace_of_isComplete_univ", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "completeSpace_iff_isComplete_univ", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "completeSpace_iff_ultrafilter", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "cauchy_iff_exists_le_nhds", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cauchy_map_iff_exists_tendsto", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cauchySeq_tendsto_of_complete", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "cauchySeq_tendsto_of_isComplete", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Cauchy.le_nhds_lim", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauchySeq.tendsto_limUnder", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsClosed.isComplete", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteUniformity.eq_pure_of_cauchy", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": true, "tactics": ["rcases", "simp", "obtain", "obtain", "exact"], "tactic_count": 5}
{"name": "DiscreteUniformity.instCompleteSpace", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteUniformity.cauchyConst", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteUniformity.eq_pure_cauchyConst", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TotallyBounded", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.TotallyBounded", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.totallyBounded_principal_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.TotallyBounded.exists_subset_of_mem", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "let", "choose", "refine", "exact", "haveI", "exact", "filter_upwards", "simp_rw", "set", "exact"], "tactic_count": 12}
{"name": "TotallyBounded.exists_subset", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "exact"], "tactic_count": 3}
{"name": "totallyBounded_iff_subset", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.totallyBounded_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.filter_totallyBounded_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "totallyBounded_of_forall_isSymm", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TotallyBounded.subset", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.TotallyBounded.mono", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.TotallyBounded.totallyBounded_setOf_clusterPt", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": true, "tactics": ["refine", "obtain", "refine", "rw", "exact"], "tactic_count": 5}
{"name": "TotallyBounded.closure", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "totallyBounded_closure", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.totallyBounded_iSup", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": true, "tactics": ["refine", "choose", "refine", "simp_rw", "gcongr"], "tactic_count": 5}
{"name": "Filter.totallyBounded_biSup", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "totallyBounded_sSup", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "totallyBounded_iUnion", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "totallyBounded_biUnion", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": true, "tactics": ["have", "rw"], "tactic_count": 2}
{"name": "totallyBounded_sUnion", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.Finite.totallyBounded", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Subsingleton.totallyBounded", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "totallyBounded_singleton", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "totallyBounded_empty", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.totallyBounded_bot", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "totallyBounded_union", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "TotallyBounded.union", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "totallyBounded_insert", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Filter.totallyBounded_sup", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "Filter.TotallyBounded.sup", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.TotallyBounded.map", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TotallyBounded.image", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "Ultrafilter.cauchy_of_totallyBounded'", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Ultrafilter.cauchy_of_totallyBounded", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.totallyBounded_iff_filter", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": true, "tactics": ["constructor", "exact", "intro", "contrapose", "set", "have", "have", "have", "refine", "rcases", "rcases", "have", "rcases", "exact"], "tactic_count": 14}
{"name": "Filter.totallyBounded_iff_ultrafilter", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": true, "tactics": ["refine", "intro", "exact"], "tactic_count": 3}
{"name": "totallyBounded_iff_filter", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "totallyBounded_iff_ultrafilter", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "isCompact_iff_totallyBounded_isComplete", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.totallyBounded", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsCompact.isComplete", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "complete_of_compact", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TotallyBounded.isCompact_of_isComplete", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TotallyBounded.isCompact_of_isClosed", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.TotallyBounded.isCompact_setOf_clusterPt", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.TotallyBounded.exists_clusterPt", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": true, "tactics": ["let", "have", "have", "obtain", "rw", "exact"], "tactic_count": 6}
{"name": "CauchySeq.totallyBounded_range", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": true, "tactics": ["intro", "obtain", "refine", "rw", "intro", "rw", "rcases", "exacts"], "tactic_count": 8}
{"name": "interUnionBalls", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "totallyBounded_interUnionBalls", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": true, "tactics": ["rw", "intro", "have", "classical", "refine", "simp", "iUnion_iUnion_eq_right,", "exact"], "tactic_count": 8}
{"name": "isCompact_closure_interUnionBalls", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": true, "tactics": ["rw", "refine", "exact"], "tactic_count": 3}
{"name": "SequentiallyComplete.setSeqAux", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SequentiallyComplete.setSeq", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SequentiallyComplete.setSeq_mem", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SequentiallyComplete.setSeq_mono", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SequentiallyComplete.setSeq_sub_aux", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SequentiallyComplete.setSeq_prod_subset", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SequentiallyComplete.seq", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SequentiallyComplete.seq_mem", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SequentiallyComplete.seq_pair_mem", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SequentiallyComplete.seq_is_cauchySeq", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SequentiallyComplete.le_nhds_of_seq_tendsto_nhds", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.complete_of_convergent_controlled_sequences", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": true, "tactics": ["obtain", "have", "refine", "exact", "rcases", "exact"], "tactic_count": 6}
{"name": "UniformSpace.complete_of_cauchySeq_tendsto", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.firstCountableTopology", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.secondCountable_of_separable", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": true, "tactics": ["rcases", "obtain", "choose", "refine", "refine", "simp", "rintro", "exact", "intro", "simp", "rcases", "rcases", "rcases", "rcases", "hsd.inter_open_nonempty", "refine", "exact"], "tactic_count": 17}
{"name": "UniformSpace.subset_countable_closure_of_almost_dense_set", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": true, "tactics": ["obtain", "replace", "choose", "have", "choose", "refine", "countable_iUnion", "rw", "intro", "obtain", "obtain", "specialize", "rw", "obtain", "refine", "apply", "exact", "exact"], "tactic_count": 18}
{"name": "UniformSpace.secondCountable_of_almost_dense_set", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": true, "tactics": ["suffices", "have", "rcases", "exact"], "tactic_count": 4}
{"name": "TotallyBounded.isSeparable", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Cauchy", "is_tactic_proof": false, "tactics": ["obtain", "subset_countable_closure_of_almost_dense_set", "obtain", "h", "exact", "exact"], "tactic_count": 6}
{"name": "hausdorffEntourage", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_hausdorffEntourage", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hausdorffEntourage_mono", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": true, "tactics": ["unfold", "gcongr"], "tactic_count": 2}
{"name": "monotone_hausdorffEntourage", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hausdorffEntourage_id", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "isRefl_hausdorffEntourage", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inv_hausdorffEntourage", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isSymm_hausdorffEntourage", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "hausdorffEntourage_comp", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": true, "tactics": ["apply", "intro", "simp", "refine", "intro", "obtain", "exact", "intro", "obtain", "exact", "intro", "simp", "grw", "exact"], "tactic_count": 14}
{"name": "isTrans_hausdorffEntourage", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": true, "tactics": ["grw"], "tactic_count": 1}
{"name": "singleton_mem_hausdorffEntourage", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "union_mem_hausdorffEntourage", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": true, "tactics": ["grind"], "tactic_count": 1}
{"name": "TotallyBounded.exists_prodMk_finset_mem_hausdorffEntourage", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": true, "tactics": ["obtain", "lift", "classical", "refine", "rw", "refine", "obtain", "exact"], "tactic_count": 8}
{"name": "UniformSpace.hausdorff", "kind": "abbrev", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.uniformity_hausdorff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.hausdorff.isOpen_inter_nonempty_of_isOpen", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "obtain", "rw", "refine", "rintro", "obtain", "exact"], "tactic_count": 9}
{"name": "IsClosed.powerset_hausdorff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "UniformSpace.hausdorff.isClopen_singleton_empty", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": true, "tactics": ["constructor", "rw", "exact", "simp_rw", "filter_upwards", "simpa"], "tactic_count": 6}
{"name": "UniformSpace.hausdorff.isUniformEmbedding_singleton", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.hausdorff.isClosedEmbedding_singleton", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.hausdorff.uniformContinuous_union", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": true, "tactics": ["refine", "filter_upwards", "union_mem_hausdorffEntourage"], "tactic_count": 3}
{"name": "UniformSpace.hausdorff.uniformContinuous_closure", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": ["simp_rw", "intro", "obtain", "refine", "simp", "constructor", "grw", "grw"], "tactic_count": 8}
{"name": "UniformSpace.hausdorff.continuous_closure", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.hausdorff.isUniformInducing_closure", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": true, "tactics": ["refine", "rw", "intro", "obtain", "refine", "simp", "constructor", "grw", "grw"], "tactic_count": 9}
{"name": "UniformSpace.hausdorff.nhds_closure", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "UniformSpace.hausdorff.instDiscreteUniformitySet", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": true, "tactics": ["rw", "convert", "rw"], "tactic_count": 3}
{"name": "UniformContinuous.image_hausdorff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": true, "tactics": ["refine", "filter_upwards", "simp_rw", "exact", "h₂.trans"], "tactic_count": 5}
{"name": "IsUniformInducing.image_hausdorff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": true, "tactics": ["constructor", "change", "rw", "congr", "simp"], "tactic_count": 5}
{"name": "IsUniformEmbedding.image_hausdorff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TotallyBounded.powerset_hausdorff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": ["simp_rw", "intro", "obtain", "refine", "obtain", "exact"], "tactic_count": 6}
{"name": "TotallyBounded.nhds_vietoris_le_nhds_hausdorff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": true, "tactics": ["open", "simp_rw", "intro", "have", "let", "refine", "obtain", "obtain", "dsimp", "filter_upwards", "isOpen_inter_nonempty_of_isOpen", "u", "grw"], "tactic_count": 13}
{"name": "IsCompact.nhds_hausdorff_eq_nhds_vietoris", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": true, "tactics": ["refine", "simp_rw", "rintro", "obtain", "hs.nhdsSet_basis_uniformity", "filter_upwards", "exact", "exact"], "tactic_count": 8}
{"name": "TopologicalSpace.Closeds.uniformSpace", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Closeds.uniformity_def", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.uniformity_closeds", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Closeds.isUniformEmbedding_coe", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Closeds.uniformContinuous_coe", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Closeds.isOpen_inter_nonempty_of_isOpen", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Closeds.isClosed_subsets_of_isClosed", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Closeds.totallyBounded_subsets_of_totallyBounded", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Closeds.instDiscreteUniformity", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Closeds.isUniformEmbedding_singleton", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Closeds.uniformContinuous_singleton", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Closeds.isEmbedding_singleton", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Closeds.continuous_singleton", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Closeds.isClosedEmbedding_singleton", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Closeds.discreteUniformity_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Closeds.uniformContinuous_sup", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformContinuous.sup_closeds", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Closeds.instContinuousSup", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Closeds.instT0Space", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": ["suffices", "refine", "rw", "intro", "obtain", "mem_of_mem_nhds", "obtain", "exact"], "tactic_count": 8}
{"name": "TopologicalSpace.Closeds.isUniformInducing_closure", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Closeds.uniformContinuous_closure", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Closeds.continuous_closure", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.uniformSpace", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.uniformity_def", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.uniformity_compacts", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.isUniformEmbedding_coe", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.uniformContinuous_coe", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.isUniformEmbedding_toCloseds", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.uniformContinuous_toCloseds", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.isEmbedding_toCloseds", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.continuous_toCloseds", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.totallyBounded_subsets_of_totallyBounded", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.isUniformEmbedding_singleton", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.uniformContinuous_singleton", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.uniformContinuous_sup", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformContinuous.sup_compacts", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformContinuous.compacts_map", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUniformInducing.compacts_map", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUniformEmbedding.compacts_map", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.instDiscreteUniformity", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.Compacts.discreteUniformity_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.uniformSpace", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.uniformity_def", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.uniformity_nonemptyCompacts", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.isUniformEmbedding_coe", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.uniformContinuous_coe", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.isUniformEmbedding_toCloseds", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.uniformContinuous_toCloseds", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.isEmbedding_toCloseds", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.continuous_toCloseds", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.isUniformEmbedding_toCompacts", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.uniformContinuous_toCompacts", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.totallyBounded_subsets_of_totallyBounded", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.isUniformEmbedding_singleton", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.uniformContinuous_singleton", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.uniformContinuous_sup", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformContinuous.sup_nonemptyCompacts", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformContinuous.nonemptyCompacts_map", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUniformInducing.nonemptyCompacts_map", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUniformEmbedding.nonemptyCompacts_map", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.instDiscreteUniformity", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TopologicalSpace.NonemptyCompacts.discreteUniformity_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Closeds", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lebesgue_number_lemma", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Compact", "is_tactic_proof": false, "tactics": ["have", "obtain", "rw", "exact", "choose", "rcases", "refine", "rcases", "exact"], "tactic_count": 9}
{"name": "lebesgue_number_lemma_nhds'", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Compact", "is_tactic_proof": false, "tactics": ["rcases", "lebesgue_number_lemma", "exact"], "tactic_count": 3}
{"name": "lebesgue_number_lemma_nhds", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Compact", "is_tactic_proof": false, "tactics": ["rcases", "lebesgue_number_lemma", "exact"], "tactic_count": 3}
{"name": "lebesgue_number_lemma_nhdsWithin'", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lebesgue_number_lemma_nhdsWithin", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.lebesgue_number_lemma", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Compact", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "Filter.HasBasis.lebesgue_number_lemma_nhds'", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Compact", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "Filter.HasBasis.lebesgue_number_lemma_nhds", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Compact", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "Filter.HasBasis.lebesgue_number_lemma_nhdsWithin'", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Compact", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "Filter.HasBasis.lebesgue_number_lemma_nhdsWithin", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Compact", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "lebesgue_number_lemma_sUnion", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Compact", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "IsCompact.nhdsSet_basis_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Disjoint.exists_uniform_thickening", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Compact", "is_tactic_proof": true, "tactics": ["have", "rw", "rcases", "rcases", "refine", "simp", "rintro", "rw", "exact"], "tactic_count": 9}
{"name": "Disjoint.exists_uniform_thickening_of_basis", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Compact", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "exact"], "tactic_count": 3}
{"name": "lebesgue_number_of_compact_open", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhdsSet_diagonal_eq_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Compact", "is_tactic_proof": true, "tactics": ["refine", "have", "rw", "exact", "refine", "exact"], "tactic_count": 6}
{"name": "compactSpace_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unique_uniformity_of_compact", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Compact", "is_tactic_proof": true, "tactics": ["refine", "have", "have", "rw"], "tactic_count": 4}
{"name": "IsClosed.relPreimage_of_isCompact", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Compact", "is_tactic_proof": true, "tactics": ["rw", "simp_rw", "exact"], "tactic_count": 3}
{"name": "IsClosed.relImage_of_isCompact", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Compact", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.tendsto_iff_forall_isCompact_tendstoUniformlyOn", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.CompactConvergence", "is_tactic_proof": true, "tactics": ["rw", "constructor", "intro", "rw", "intro", "rcases", "rcases", "set", "have", "inter_mem_nhdsWithin", "f.continuousAt", "have", "have", "use", "refine", "exact", "intro", "rcases", "filter_upwards"], "tactic_count": 19}
{"name": "ContinuousMap.toUniformOnFunIsCompact", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.CompactConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.toUniformOnFun_toFun", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.CompactConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.range_toUniformOnFunIsCompact", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.CompactConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.compactConvergenceUniformSpace", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.CompactConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.isUniformEmbedding_toUniformOnFunIsCompact", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.CompactConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.continuous_iff_continuous_uniformOnFun", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.CompactConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.compactConvergenceUniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.CompactConvergence", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "ContinuousMap.hasBasis_compactConvergenceUniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.CompactConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.mem_compactConvergence_entourage_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.CompactConvergence", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "CompactExhaustion.hasBasis_compactConvergenceUniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.CompactConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompactExhaustion.hasAntitoneBasis_compactConvergenceUniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.CompactConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.instIsCountablyGeneratedProdUniformityOfWeaklyLocallyCompactSpaceOfSigmaCompactSpace", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.CompactConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.tendsto_of_tendstoLocallyUniformly", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.CompactConvergence", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "exact"], "tactic_count": 4}
{"name": "ContinuousMap.tendsto_iff_tendstoLocallyUniformly", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.CompactConvergence", "is_tactic_proof": true, "tactics": ["refine", "rw", "obtain", "exact"], "tactic_count": 4}
{"name": "ContinuousMap.uniformContinuous_comp", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.CompactConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.isUniformInducing_comp", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.CompactConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.isUniformEmbedding_comp", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.CompactConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.uniformContinuous_comp_left", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.CompactConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformEquiv.arrowCongr", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.CompactConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.hasBasis_compactConvergenceUniformity_of_compact", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.CompactConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.compactConvergenceUniformity_of_compact", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.CompactConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.isUniformEmbedding_uniformFunOfFun", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.CompactConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.tendsto_iff_tendstoUniformly", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.CompactConvergence", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "ContinuousMap.continuous_iff_continuous_uniformFun", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.CompactConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousOn.tendsto_restrict_iff_tendstoUniformlyOn", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.CompactConvergence", "is_tactic_proof": true, "tactics": ["rw", "congr"], "tactic_count": 2}
{"name": "ContinuousOn.continuous_restrict_iff_continuous_uniformOnFun", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.CompactConvergence", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "ContinuousMap.uniformSpace_eq_inf_precomp_of_cover", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.CompactConvergence", "is_tactic_proof": true, "tactics": ["set", "set", "set", "have", "have", "have", "have", "have", "h_cover", "subset_univ", "simp_rw", "rfl"], "tactic_count": 12}
{"name": "ContinuousMap.uniformSpace_eq_iInf_precomp_of_cover", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.CompactConvergence", "is_tactic_proof": true, "tactics": ["set", "set", "have", "have", "have", "refine", "simp_rw", "simp_rw", "rfl"], "tactic_count": 9}
{"name": "ContinuousMap.instCompleteSpaceOfCompactlyCoherentSpace", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.CompactConvergence", "is_tactic_proof": false, "tactics": ["rw", "range_toUniformOnFunIsCompact,", "exact"], "tactic_count": 3}
{"name": "ContinuousMap.isComplete_setOf_eqOn", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.CompactConvergence", "is_tactic_proof": true, "tactics": ["classical", "intro", "rcases", "have", "have", "refine", "refine", "exact", "have", "set", "refine", "rwa"], "tactic_count": 12}
{"name": "Rat.uniformSpace_eq", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.CompareReals", "is_tactic_proof": true, "tactics": ["ext", "rw", "simp"], "tactic_count": 3}
{"name": "rationalCauSeqPkg", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.CompareReals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompareReals.Q", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.CompareReals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompareReals.uniformSpace", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.CompareReals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompareReals.Bourbakiℝ", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.CompareReals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompareReals.Bourbaki.uniformSpace", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.CompareReals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompareReals.bourbakiPkg", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.CompareReals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompareReals.compareEquiv", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.CompareReals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompareReals.compare_uc", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.CompareReals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompareReals.compare_uc_symm", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.CompareReals", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsComplete.isClosed", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.CompleteSeparated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUniformEmbedding.isClosedEmbedding", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.CompleteSeparated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDenseInducing.continuous_extend_of_cauchy", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.CompleteSeparated", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauchyFilter", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauchyFilter.instNeBotValFilterCauchy", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauchyFilter.gen", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauchyFilter.monotone_gen", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.UniformSpace.Completion.0.CauchyFilter.symm_gen", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": ["let", "have", "delta", "simp", "have", "uniformity_lift_le_swap", "have", "simp", "exact", "exact"], "tactic_count": 10}
{"name": "_private.Mathlib.Topology.UniformSpace.Completion.0.CauchyFilter.subset_gen_relComp", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.UniformSpace.Completion.0.CauchyFilter.comp_gen", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauchyFilter.instUniformSpace", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauchyFilter.mem_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauchyFilter.basis_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauchyFilter.mem_uniformity'", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": true, "tactics": ["refine", "exact"], "tactic_count": 2}
{"name": "CauchyFilter.pureCauchy", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauchyFilter.isUniformInducing_pureCauchy", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauchyFilter.isUniformEmbedding_pureCauchy", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauchyFilter.denseRange_pureCauchy", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauchyFilter.isDenseInducing_pureCauchy", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauchyFilter.isDenseEmbedding_pureCauchy", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauchyFilter.nonempty_cauchyFilter_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": true, "tactics": ["constructor", "have", "obtain", "exact", "exact"], "tactic_count": 5}
{"name": "CauchyFilter.instCompleteSpace", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauchyFilter.instInhabited", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauchyFilter.instNonempty", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauchyFilter.extend", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauchyFilter.extend_pureCauchy", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "CauchyFilter.uniformContinuous_extend", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": true, "tactics": ["by_cases", "rw", "exact", "rw", "exact"], "tactic_count": 5}
{"name": "CauchyFilter.inseparable_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauchyFilter.inseparable_iff_of_le_nhds", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": true, "tactics": ["rw", "rw", "simp"], "tactic_count": 3}
{"name": "CauchyFilter.inseparable_lim_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauchyFilter.cauchyFilter_eq", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "CauchyFilter.separated_pureCauchy_injective", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.inhabited", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.uniformSpace", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.completeSpace", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.t0Space", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.coe'", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.instCoe", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.coe_eq", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.isUniformInducing_coe", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.comap_coe_eq_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.denseRange_coe", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.cPkg", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.AbstractCompletion.inhabited", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.nonempty_completion_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.uniformContinuous_coe", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.continuous_coe", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.isUniformEmbedding_coe", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.coe_injective", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.coe_inj", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.isDenseInducing_coe", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.UniformCompletion.completeEquivSelf", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.separableSpace_completion", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.isDenseEmbedding_coe", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.denseRange_coe₂", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.denseRange_coe₃", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.induction_on", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.induction_on₂", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.induction_on₃", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.ext", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.ext'", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.extension", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.uniformContinuous_extension", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.continuous_extension", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.extension_coe", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.inseparable_extension_coe", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.isUniformInducing_extension", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.extension_unique", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.extension_comp_coe", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.map", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.uniformContinuous_map", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.continuous_map", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.map_coe", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.map_unique", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.map_id", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.extension_map", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.map_comp", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.mapEquiv", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.mapEquiv_symm", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.mapEquiv_coe", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.completionSeparationQuotientEquiv", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": ["refine", "refine", "refine", "rw", "refine", "rw"], "tactic_count": 6}
{"name": "UniformSpace.Completion.uniformContinuous_completionSeparationQuotientEquiv", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.uniformContinuous_completionSeparationQuotientEquiv_symm", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.extension₂", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.extension₂_coe_coe", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.uniformContinuous_extension₂", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.map₂", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.uniformContinuous_map₂", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.continuous_map₂", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Completion.map₂_coe_coe", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "idRel", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_idRel", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "idRel_subset", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "eq_singleton_left_of_prod_subset_idRel", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "eq_singleton_right_prod_subset_idRel", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": true, "tactics": ["obtain"], "tactic_count": 1}
{"name": "compRel", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_compRel", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "swap_idRel", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.compRel", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "id_compRel", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "compRel_assoc", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "left_subset_compRel", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "right_subset_compRel", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "subset_comp_self", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "subset_iterate_compRel", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "IsSymmetricRel", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "symmetrizeRel", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "symmetric_symmetrizeRel", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "symmetrizeRel_subset_self", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "symmetrize_mono", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSymmetricRel.mk_mem_comm", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSymmetricRel.eq", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSymmetricRel.inter", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsSymmetricRel.iInter", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "IsSymmetricRel.sInter", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "isSymmetricRel_idRel", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "isSymmetricRel_univ", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsSymmetricRel.preimage_prodMap", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsSymmetricRel.image_prodMap", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": true, "tactics": ["rw", "image_swap_eq_preimage_swap,"], "tactic_count": 2}
{"name": "IsSymmetricRel.prod_subset_comm", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SetRel.mem_filter_prod_comm", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsSymmetricRel.mem_filter_prod_comm", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "UniformSpace.Core.comp_mem_uniformity_sets", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Core.mk'", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Core.mkOfBasis", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Core.toTopologicalSpace", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Core.ext", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.Core.nhds_toTopologicalSpace", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": true, "tactics": ["apply", "exact", "intro", "rcases", "filter_upwards", "filter_upwards", "exact", "hVU"], "tactic_count": 8}
{"name": "uniformity", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Uniformity.term𝓤[_]", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Uniformity._aux_Mathlib_Topology_UniformSpace_Defs___macroRules_Uniformity_term𝓤[_]_1", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Uniformity.term𝓤", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Uniformity._aux_Mathlib_Topology_UniformSpace_Defs___macroRules_Uniformity_term𝓤_1", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Uniformity._aux_Mathlib_Topology_UniformSpace_Defs___unexpand_uniformity_1", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.ofCoreEq", "kind": "abbrev", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.ofCore", "kind": "abbrev", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.toCore", "kind": "abbrev", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.toCore_toTopologicalSpace", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.mem_uniformity_ofCore_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.ext", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": ["have", "rw", "exact", "cases"], "tactic_count": 4}
{"name": "UniformSpace.ext_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.ofCoreEq_toCore", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.replaceTopology", "kind": "abbrev", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.replaceTopology_eq", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhds_eq_comap_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpen_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "refl_le_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformity.neBot", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "refl_mem_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isRefl_of_mem_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_uniformity_of_eq", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "symm_le_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "comp_le_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lift'_comp_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_swap_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "comp_mem_uniformity_sets", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.uniformity_trans", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": true, "tactics": ["refine", "filter_upwards"], "tactic_count": 2}
{"name": "Filter.Tendsto.uniformity_symm", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_diag_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_const_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "symm_of_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "comp_symm_of_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformity_le_symm", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "uniformity_eq_symm", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "comap_swap_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "symmetrize_mem_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": true, "tactics": ["apply", "rw", "exact"], "tactic_count": 3}
{"name": "UniformSpace.hasBasis_symmetric", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformity_lift_le_swap", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformity_lift_le_comp", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "comp3_mem_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "comp_le_uniformity3", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "comp_symm_mem_uniformity_sets", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": true, "tactics": ["obtain", "use", "have", "calc"], "tactic_count": 4}
{"name": "subset_comp_self_of_mem_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "comp_comp_symm_mem_uniformity_sets", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "use", "have", "calc", "t"], "tactic_count": 6}
{"name": "UniformSpace.ball", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.mem_ball_self", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.mem_ball_comp", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.ball_subset_of_comp_subset", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.ball_mono", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.ball_inter", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.ball_inter_left", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.ball_inter_right", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.ball_iInter", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.mem_ball_symmetry", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.ball_eq_of_symmetry", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": true, "tactics": ["ext", "rw", "exact"], "tactic_count": 3}
{"name": "UniformSpace.mem_comp_of_mem_ball", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "UniformSpace.mem_comp_comp", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": true, "tactics": ["obtain", "constructor", "rintro", "exact", "rintro", "rw", "exact"], "tactic_count": 7}
{"name": "UniformSpace.isCover_iff_subset_iUnion_ball", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "mem_nhds_uniformity_iff_right", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "mem_nhds_uniformity_iff_left", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "nhdsWithin_eq_comap_uniformity_of_mem", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "nhdsWithin_eq_comap_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isOpen_iff_ball_subset", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "nhds_basis_uniformity'", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "nhds_basis_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": true, "tactics": ["replace", "rw", "exact"], "tactic_count": 3}
{"name": "nhds_eq_comap_uniformity'", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.mem_nhds_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": true, "tactics": ["rw", "simp_rw"], "tactic_count": 2}
{"name": "UniformSpace.ball_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "UniformSpace.ball_mem_nhdsWithin", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "UniformSpace.mem_nhds_iff_symm", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": true, "tactics": ["rw", "constructor", "rintro", "use", "exact", "rintro", "exact"], "tactic_count": 7}
{"name": "UniformSpace.hasBasis_nhds", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.mem_closure_iff_symm_ball", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "UniformSpace.mem_closure_iff_ball", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "UniformSpace.closure_subset_preimage", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": true, "tactics": ["intro", "obtain", "exact"], "tactic_count": 3}
{"name": "UniformSpace.closure_subset_image", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhds_eq_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "nhds_eq_uniformity'", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_nhds_left", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "mem_nhds_right", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_mem_nhds_ball_subset_of_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_right_nhds_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_left_nhds_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "lift_nhds_left", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": true, "tactics": ["rw", "simp_rw"], "tactic_count": 2}
{"name": "lift_nhds_right", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": true, "tactics": ["rw", "simp_rw"], "tactic_count": 2}
{"name": "nhds_nhds_eq_uniformity_uniformity_prod", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": true, "tactics": ["rw", "exacts"], "tactic_count": 2}
{"name": "Filter.HasBasis.biInter_biUnion_ball", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": true, "tactics": ["ext", "simp"], "tactic_count": 2}
{"name": "UniformContinuous", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Uniformity.termUniformContinuous[_,_]", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Uniformity._aux_Mathlib_Topology_UniformSpace_Defs___macroRules_Uniformity_termUniformContinuous[_,_]_1", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformContinuousOn", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformContinuous_def", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformContinuous_iff_eventually", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformContinuousOn_univ", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "uniformContinuous_of_const", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformContinuous_id", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformContinuous_const", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformContinuous.comp", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformContinuous.iterate", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ"], "tactic_count": 3}
{"name": "Filter.HasBasis.uniformContinuous_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.uniformContinuousOn_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUniformEmbedding.isUniformInducing", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Defs", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.tendstoLocallyUniformly_of_forall_tendsto", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Dini", "is_tactic_proof": true, "tactics": ["refine", "simp", "have", "refine", "filter_upwards", "exact", "simp_rw", "intro", "simp_rw", "obtain", "refine", "filter_upwards", "refine", "simp", "exact"], "tactic_count": 15}
{"name": "Monotone.tendstoLocallyUniformlyOn_of_forall_tendsto", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Dini", "is_tactic_proof": true, "tactics": ["rw", "exact", "tendstoLocallyUniformly_of_forall_tendsto"], "tactic_count": 3}
{"name": "Monotone.tendstoUniformly_of_forall_tendsto", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Dini", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Monotone.tendstoUniformlyOn_of_forall_tendsto", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Dini", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.tendstoLocallyUniformly_of_forall_tendsto", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Dini", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.tendstoLocallyUniformlyOn_of_forall_tendsto", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Dini", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.tendstoUniformly_of_forall_tendsto", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Dini", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Antitone.tendstoUniformlyOn_of_forall_tendsto", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Dini", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.tendsto_of_monotone_of_pointwise", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Dini", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.tendsto_of_antitone_of_pointwise", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Dini", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteUniformity.inst", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.DiscreteUniformity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "discreteUniformity_iff_eq_principal_setRelId", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.DiscreteUniformity", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "DiscreteUniformity.eq_principal_setRelId", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.DiscreteUniformity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteUniformity.instDiscreteTopology", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.DiscreteUniformity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "discreteUniformity_iff_setRelId_mem_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.DiscreteUniformity", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "DiscreteUniformity.relId_mem_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.DiscreteUniformity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "DiscreteUniformity.instProd", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.DiscreteUniformity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "DiscreteUniformity.uniformContinuous", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.DiscreteUniformity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "EquicontinuousAt", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.EquicontinuousAt", "kind": "abbrev", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EquicontinuousWithinAt", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.EquicontinuousWithinAt", "kind": "abbrev", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equicontinuous", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Equicontinuous", "kind": "abbrev", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EquicontinuousOn", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.EquicontinuousOn", "kind": "abbrev", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformEquicontinuous", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.UniformEquicontinuous", "kind": "abbrev", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformEquicontinuousOn", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.UniformEquicontinuousOn", "kind": "abbrev", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EquicontinuousAt.equicontinuousWithinAt", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EquicontinuousWithinAt.mono", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "equicontinuousWithinAt_univ", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "equicontinuousAt_restrict_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Equicontinuous.equicontinuousOn", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EquicontinuousOn.mono", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "equicontinuousOn_univ", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "equicontinuous_restrict_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "UniformEquicontinuous.uniformEquicontinuousOn", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformEquicontinuousOn.mono", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformEquicontinuousOn_univ", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "uniformEquicontinuous_restrict_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": true, "tactics": ["rw", "conv", "rfl"], "tactic_count": 3}
{"name": "equicontinuousAt_empty", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "equicontinuousWithinAt_empty", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "equicontinuous_empty", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "equicontinuousOn_empty", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformEquicontinuous_empty", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformEquicontinuousOn_empty", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "equicontinuousAt_finite", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "equicontinuousWithinAt_finite", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "equicontinuous_finite", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "equicontinuousOn_finite", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "uniformEquicontinuous_finite", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "uniformEquicontinuousOn_finite", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "equicontinuousAt_unique", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "equicontinuousWithinAt_unique", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "equicontinuous_unique", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "equicontinuousOn_unique", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformEquicontinuous_unique", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformEquicontinuousOn_unique", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "equicontinuousWithinAt_iff_pair", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": true, "tactics": ["constructor", "rcases", "refine", "exact", "rcases", "filter_upwards"], "tactic_count": 6}
{"name": "equicontinuousAt_iff_pair", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "UniformEquicontinuous.equicontinuous", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformEquicontinuousOn.equicontinuousOn", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EquicontinuousAt.continuousAt", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EquicontinuousWithinAt.continuousWithinAt", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.EquicontinuousAt.continuousAt_of_mem", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.EquicontinuousWithinAt.continuousWithinAt_of_mem", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equicontinuous.continuous", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EquicontinuousOn.continuousOn", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Equicontinuous.continuous_of_mem", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.EquicontinuousOn.continuousOn_of_mem", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformEquicontinuous.uniformContinuous", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformEquicontinuousOn.uniformContinuousOn", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.UniformEquicontinuous.uniformContinuous_of_mem", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.UniformEquicontinuousOn.uniformContinuousOn_of_mem", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EquicontinuousAt.comp", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EquicontinuousWithinAt.comp", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.EquicontinuousAt.mono", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.EquicontinuousWithinAt.mono", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Equicontinuous.comp", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "EquicontinuousOn.comp", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Equicontinuous.mono", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.EquicontinuousOn.mono", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformEquicontinuous.comp", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformEquicontinuousOn.comp", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.UniformEquicontinuous.mono", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.UniformEquicontinuousOn.mono", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "equicontinuousAt_iff_range", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "equicontinuousWithinAt_iff_range", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "equicontinuous_iff_range", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "equicontinuousOn_iff_range", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformEquicontinuous_iff_range", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformEquicontinuousOn_iff_range", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "equicontinuousAt_iff_continuousAt", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "equicontinuousWithinAt_iff_continuousWithinAt", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "equicontinuous_iff_continuous", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "equicontinuousOn_iff_continuousOn", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "uniformEquicontinuous_iff_uniformContinuous", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "uniformEquicontinuousOn_iff_uniformContinuousOn", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "equicontinuousWithinAt_iInf_rng", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": true, "tactics": ["simp", "unfold", "rw"], "tactic_count": 3}
{"name": "equicontinuousAt_iInf_rng", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "equicontinuous_iInf_rng", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": true, "tactics": ["simp_rw", "rw"], "tactic_count": 2}
{"name": "equicontinuousOn_iInf_rng", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "uniformEquicontinuous_iInf_rng", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": true, "tactics": ["simp_rw", "rw"], "tactic_count": 2}
{"name": "uniformEquicontinuousOn_iInf_rng", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": true, "tactics": ["simp_rw", "unfold", "rw"], "tactic_count": 3}
{"name": "equicontinuousWithinAt_iInf_dom", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": true, "tactics": ["simp", "unfold", "rw", "exact"], "tactic_count": 4}
{"name": "equicontinuousAt_iInf_dom", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "equicontinuous_iInf_dom", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "equicontinuousOn_iInf_dom", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformEquicontinuous_iInf_dom", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "uniformEquicontinuousOn_iInf_dom", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": true, "tactics": ["simp_rw", "unfold", "rw", "exact"], "tactic_count": 4}
{"name": "Filter.HasBasis.equicontinuousAt_iff_left", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Filter.HasBasis.equicontinuousWithinAt_iff_left", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": ["rw", "hX.tendsto_iff", "rfl"], "tactic_count": 3}
{"name": "Filter.HasBasis.equicontinuousAt_iff_right", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Filter.HasBasis.equicontinuousWithinAt_iff_right", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Filter.HasBasis.equicontinuousAt_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Filter.HasBasis.equicontinuousWithinAt_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": ["rw", "hX.tendsto_iff", "rfl"], "tactic_count": 3}
{"name": "Filter.HasBasis.uniformEquicontinuous_iff_left", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": ["rw", "hβ.tendsto_iff", "simp", "rfl"], "tactic_count": 4}
{"name": "Filter.HasBasis.uniformEquicontinuousOn_iff_left", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": ["rw", "hβ.tendsto_iff", "simp", "rfl"], "tactic_count": 4}
{"name": "Filter.HasBasis.uniformEquicontinuous_iff_right", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Filter.HasBasis.uniformEquicontinuousOn_iff_right", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "Filter.HasBasis.uniformEquicontinuous_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": ["rw", "hβ.tendsto_iff", "simp", "rfl"], "tactic_count": 4}
{"name": "Filter.HasBasis.uniformEquicontinuousOn_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": ["rw", "hβ.tendsto_iff", "simp", "rfl"], "tactic_count": 4}
{"name": "IsUniformInducing.equicontinuousAt_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": true, "tactics": ["have", "rw", "rfl"], "tactic_count": 3}
{"name": "IsUniformInducing.equicontinuousWithinAt_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": true, "tactics": ["have", "simp", "rfl"], "tactic_count": 3}
{"name": "IsUniformInducing.equicontinuous_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": true, "tactics": ["congrm", "rw"], "tactic_count": 2}
{"name": "IsUniformInducing.equicontinuousOn_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": true, "tactics": ["congrm", "rw"], "tactic_count": 2}
{"name": "IsUniformInducing.uniformEquicontinuous_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": true, "tactics": ["have", "simp", "rfl"], "tactic_count": 3}
{"name": "IsUniformInducing.uniformEquicontinuousOn_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": true, "tactics": ["have", "simp", "rfl"], "tactic_count": 3}
{"name": "EquicontinuousWithinAt.closure'", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": true, "tactics": ["intro", "rcases", "filter_upwards", "rw", "change", "refine", "exact"], "tactic_count": 7}
{"name": "EquicontinuousAt.closure'", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.EquicontinuousAt.closure", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.EquicontinuousWithinAt.closure", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Equicontinuity", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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{"name": "TendstoLocallyUniformlyOn.prodMk", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.LocallyUniformConvergence", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "exact"], "tactic_count": 4}
{"name": "TendstoLocallyUniformlyOn.piProd", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.LocallyUniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TendstoLocallyUniformly.prodMk", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.LocallyUniformConvergence", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "TendstoLocallyUniformly.piProd", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.LocallyUniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendstoLocallyUniformlyOn_of_forall_exists_nhds", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.LocallyUniformConvergence", "is_tactic_proof": true, "tactics": ["refine", "obtain", "rw", "exact"], "tactic_count": 4}
{"name": "tendstoLocallyUniformly_of_forall_exists_nhds", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.LocallyUniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendstoLocallyUniformlyOn_TFAE", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.LocallyUniformConvergence", "is_tactic_proof": false, "tactics": ["tfae_have", "h,", "tfae_have", "h,", "obtain", "exact", "tfae_have", "h,", "obtain", "exact", "tfae_finish"], "tactic_count": 11}
{"name": "tendstoLocallyUniformlyOn_iff_forall_isCompact", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.LocallyUniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendstoLocallyUniformly_iff_forall_isCompact", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.LocallyUniformConvergence", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "tendstoLocallyUniformlyOn_iff_filter", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.LocallyUniformConvergence", "is_tactic_proof": true, "tactics": ["simp", "constructor", "rintro", "obtain", "exact", "rintro", "obtain", "exact"], "tactic_count": 8}
{"name": "tendstoLocallyUniformly_iff_filter", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.LocallyUniformConvergence", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "TendstoLocallyUniformlyOn.tendsto_at", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.LocallyUniformConvergence", "is_tactic_proof": true, "tactics": ["refine", "simpa"], "tactic_count": 2}
{"name": "TendstoLocallyUniformlyOn.unique", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.LocallyUniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TendstoLocallyUniformlyOn.congr_inseparable", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.LocallyUniformConvergence", "is_tactic_proof": false, "tactics": ["have", "rw", "refine", "rw", "exact"], "tactic_count": 5}
{"name": "TendstoLocallyUniformlyOn.congr", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.LocallyUniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TendstoLocallyUniformlyOn.congr_inseparable_right", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.LocallyUniformConvergence", "is_tactic_proof": false, "tactics": ["have", "rw", "exact", "rw", "refine", "rw", "exact"], "tactic_count": 7}
{"name": "TendstoLocallyUniformlyOn.congr_right", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.LocallyUniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TendstoLocallyUniformly.congr_inseparable", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.LocallyUniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TendstoLocallyUniformly.congr", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.LocallyUniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TendstoLocallyUniformly.congr_inseparable_right", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.LocallyUniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TendstoLocallyUniformly.congr_right", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.LocallyUniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.instUniformSpace", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.instIsUniformAddGroup", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Matrix", "is_tactic_proof": true, "tactics": ["erw", "simp_rw", "rfl"], "tactic_count": 3}
{"name": "Matrix.uniformContinuous", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Matrix", "is_tactic_proof": true, "tactics": ["simp", "apply"], "tactic_count": 2}
{"name": "Matrix.instCompleteSpace", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Matrix.instT0Space", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Matrix", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformSpaceOfCompactR1", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.OfCompactT2", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.ofFun", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.OfFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.hasBasis_ofFun", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.OfFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.ofFunOfHasBasis", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.OfFun", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.instUniformSpace", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.isUniformEmbedding_coe", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.uniformContinuous", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.uniformContinuous_extend", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.uniformContinuous_extend_left", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.uniformityPath", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.hasBasis_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.uniformContinuous_symm", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.uniformContinuous_trans", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Path.instCompleteSpace", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Path", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.uniformSpace", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.uniformSpace_eq", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Pi", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Pi.uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instIsCountablyGeneratedProdForallUniformityOfCountable", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Pi", "is_tactic_proof": true, "tactics": ["rw", "infer_instance"], "tactic_count": 2}
{"name": "uniformContinuous_pi", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Pi", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Pi.uniformContinuous_proj", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.uniformContinuous_precomp'", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.uniformContinuous_precomp", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.uniformContinuous_postcomp'", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.uniformContinuous_postcomp", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.uniformSpace_comap_precomp'", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Pi", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Pi.uniformSpace_comap_precomp", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.uniformContinuous_restrict", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.uniformSpace_comap_restrict", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Pi", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "cauchy_pi_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Pi", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "cauchy_pi_iff'", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Pi", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Cauchy.pi", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Pi", "is_tactic_proof": true, "tactics": ["have", "simpa"], "tactic_count": 2}
{"name": "Pi.complete", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Pi", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pi.uniformSpace_comap_restrict_sUnion", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Pi", "is_tactic_proof": true, "tactics": ["simp_rw", "as"], "tactic_count": 2}
{"name": "CompleteSpace.iInf", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Pi", "is_tactic_proof": true, "tactics": ["nontriviality", "rcases", "have", "simp_rw", "const,", "simp_rw", "have", "iInf_mono", "refine", "exact"], "tactic_count": 10}
{"name": "ContinuousMap.exists_finite_sum_smul_approximation_of_mem_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.ProdApproximation", "is_tactic_proof": false, "tactics": ["have", "obtain", "exists_finite_sum_const_indicator_approximation_of_mem_nhds_diagonal", "refine", "convert", "simp", "congr", "by_cases"], "tactic_count": 8}
{"name": "ContinuousMap.exists_finite_sum_mul_approximation_of_mem_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.ProdApproximation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Real.instCompleteSpace", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Real", "is_tactic_proof": true, "tactics": ["apply", "intro", "let", "refine", "rcases", "have", "simp", "exact"], "tactic_count": 8}
{"name": "NNReal.instTopologicalSpace", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.instCompleteSpace", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.continuous_coe", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousMap.coeNNRealReal", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.coeNNRealReal_zero", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "NNReal.ContinuousMap.canLift", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Real", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.to_regularSpace", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Separation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.completelyNormalSpace_of_hasAntitoneBasis", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Separation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.completelyNormalSpace_of_isCountablyGenerated_uniformity", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Separation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.specializes_iff_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Separation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.inseparable_iff_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Separation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "inseparable_iff_ker_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Separation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Inseparable.nhds_le_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Separation", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "inseparable_iff_clusterPt_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Separation", "is_tactic_proof": true, "tactics": ["refine", "simp_rw", "exact"], "tactic_count": 3}
{"name": "t0Space_iff_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Separation", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "t0Space_iff_uniformity'", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Separation", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "t0Space_iff_ker_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Separation", "is_tactic_proof": false, "tactics": ["simp_rw", "mem_diagonal_iff,", "exact"], "tactic_count": 3}
{"name": "eq_of_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Separation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_of_uniformity_basis", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Separation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_of_forall_symmetric", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Separation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "eq_of_clusterPt_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Separation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.Tendsto.inseparable_iff_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Separation", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "isClosed_of_spaced_out", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Separation", "is_tactic_proof": true, "tactics": ["rcases", "apply", "intro", "rw", "rcases", "suffices", "apply", "intro", "rcases", "obtain", "by_contra", "exact", "exact"], "tactic_count": 13}
{"name": "isClosed_range_of_spaced_out", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Separation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.comap_map_mk_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Separation", "is_tactic_proof": true, "tactics": ["refine", "refine", "refine", "simp", "exact"], "tactic_count": 5}
{"name": "SeparationQuotient.instUniformSpace", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Separation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.uniformity_eq", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Separation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.uniformContinuous_mk", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Separation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.uniformContinuous_dom", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Separation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.uniformContinuous_dom₂", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Separation", "is_tactic_proof": true, "tactics": ["simp", "rfl"], "tactic_count": 2}
{"name": "SeparationQuotient.uniformContinuous_lift", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Separation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.uniformContinuous_uncurry_lift₂", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Separation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.comap_mk_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Separation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.lift'", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.Separation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.lift'_mk", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Separation", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SeparationQuotient.uniformContinuous_lift'", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Separation", "is_tactic_proof": true, "tactics": ["by_cases", "rwa", "rw", "exact"], "tactic_count": 4}
{"name": "SeparationQuotient.map", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.Separation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.map_mk", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Separation", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SeparationQuotient.uniformContinuous_map", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Separation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.map_unique", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Separation", "is_tactic_proof": true, "tactics": ["ext", "calc", "map"], "tactic_count": 3}
{"name": "SeparationQuotient.map_id", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Separation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.map_comp", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Separation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsTransitiveRel", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.Ultra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsTransitiveRel.comp_subset_self", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Ultra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isTransitiveRel_iff_comp_subset_self", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Ultra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isTransitiveRel_empty", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Ultra.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "isTransitiveRel_univ", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Ultra.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "isTransitiveRel_singleton", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Ultra.Basic", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsTransitiveRel.inter", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Ultra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsTransitiveRel.iInter", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Ultra.Basic", "is_tactic_proof": true, "tactics": ["intro", "simp", "intro", "exact"], "tactic_count": 4}
{"name": "IsTransitiveRel.sInter", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Ultra.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsTransitiveRel.preimage_prodMap", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Ultra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsTransitiveRel.symmetrizeRel", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Ultra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsTransitiveRel.comp_eq_of_idRel_subset", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Ultra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsTransitiveRel.prod_subset_trans", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Ultra.Basic", "is_tactic_proof": true, "tactics": ["rintro", "simp", "obtain", "exact"], "tactic_count": 4}
{"name": "IsTransitiveRel.mem_filter_prod_trans", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Ultra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ball_subset_of_mem", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Ultra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ball_eq_of_mem", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Ultra.Basic", "is_tactic_proof": true, "tactics": ["refine", "rwa"], "tactic_count": 2}
{"name": "IsUltraUniformity.mk_of_hasBasis", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Ultra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUltraUniformity.mem_nhds_iff_symm_trans", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Ultra.Basic", "is_tactic_proof": true, "tactics": ["rw", "constructor", "rintro", "rw", "obtain", "refine", "rintro", "exact"], "tactic_count": 8}
{"name": "UniformSpace.isOpen_ball_of_mem_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Ultra.Basic", "is_tactic_proof": true, "tactics": ["rw", "intro", "exact"], "tactic_count": 3}
{"name": "UniformSpace.isClosed_ball_of_isSymm_of_isTrans_of_mem_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Ultra.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "UniformSpace.isClopen_ball_of_isSymm_of_isTrans_of_mem_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Ultra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformSpace.nhds_basis_clopens", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Ultra.Basic", "is_tactic_proof": true, "tactics": ["refine", "intro", "exact", "rintro", "simp"], "tactic_count": 5}
{"name": "TopologicalSpace.isTopologicalBasis_clopens", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Ultra.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUniformInducing.isUltraUniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Ultra.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauchyFilter.isSymm_gen", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Ultra.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CauchyFilter.isTrans_gen", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Ultra.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUltraUniformity.cauchyFilter", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Ultra.Completion", "is_tactic_proof": true, "tactics": ["apply", "exact", "exact"], "tactic_count": 3}
{"name": "IsUltraUniformity.cauchyFilter_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Ultra.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUltraUniformity.separationQuotient", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Ultra.Completion", "is_tactic_proof": true, "tactics": ["have", "rw", "apply", "exact", "rintro", "constructor", "rintro", "simp", "rintro", "have", "rw", "exact", "exact"], "tactic_count": 13}
{"name": "IsUltraUniformity.separationQuotient_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Ultra.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUltraUniformity.completion_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Ultra.Completion", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "IsUltraUniformity.completion", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Ultra.Completion", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SetRel.isTrans_entourageProd", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Ultra.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUltraUniformity.comap", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Ultra.Constructions", "is_tactic_proof": true, "tactics": ["letI", "refine", "dsimp", "rintro", "infer_instance"], "tactic_count": 5}
{"name": "IsUltraUniformity.inf", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Ultra.Constructions", "is_tactic_proof": true, "tactics": ["letI", "refine", "dsimp", "rintro", "infer_instance"], "tactic_count": 5}
{"name": "IsUltraUniformity.prod", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Ultra.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUltraUniformity.iInf", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Ultra.Constructions", "is_tactic_proof": true, "tactics": ["letI", "refine", "simp", "rintro", "infer_instance"], "tactic_count": 5}
{"name": "IsUltraUniformity.pi", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Ultra.Constructions", "is_tactic_proof": false, "tactics": ["suffices", "simpa", "exact"], "tactic_count": 3}
{"name": "IsUltraUniformity.bot", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Ultra.Constructions", "is_tactic_proof": true, "tactics": ["have", "rw", "apply"], "tactic_count": 3}
{"name": "IsUltraUniformity.top", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Ultra.Constructions", "is_tactic_proof": true, "tactics": ["letI", "have", "rw", "apply"], "tactic_count": 4}
{"name": "continuousWithinAt_of_locally_uniform_approx_of_continuousWithinAt", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformApproximation", "is_tactic_proof": true, "tactics": ["refine", "obtain", "obtain", "rcases", "have", "have", "have", "have", "exact"], "tactic_count": 9}
{"name": "continuousAt_of_locally_uniform_approx_of_continuousAt", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformApproximation", "is_tactic_proof": true, "tactics": ["rw", "apply", "simpa"], "tactic_count": 3}
{"name": "continuousOn_of_locally_uniform_approx_of_continuousWithinAt", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformApproximation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousOn_of_uniform_approx_of_continuousOn", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformApproximation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_of_locally_uniform_approx_of_continuousAt", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformApproximation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuous_of_uniform_approx_of_continuous", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformApproximation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TendstoLocallyUniformlyOn.continuousOn", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformApproximation", "is_tactic_proof": true, "tactics": ["refine", "rcases", "rcases", "exact"], "tactic_count": 4}
{"name": "TendstoUniformlyOn.continuousOn", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformApproximation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TendstoLocallyUniformly.continuous", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformApproximation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TendstoUniformly.continuous", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformApproximation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_comp_of_locally_uniform_limit_within", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformApproximation", "is_tactic_proof": true, "tactics": ["refine", "obtain", "rcases", "have", "have", "exact"], "tactic_count": 6}
{"name": "tendsto_comp_of_locally_uniform_limit", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformApproximation", "is_tactic_proof": true, "tactics": ["rw", "rw", "exact"], "tactic_count": 3}
{"name": "TendstoLocallyUniformlyOn.tendsto_comp", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformApproximation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TendstoUniformlyOn.tendsto_comp", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformApproximation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TendstoLocallyUniformly.tendsto_comp", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformApproximation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TendstoUniformly.tendsto_comp", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformApproximation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformContinuousOn_of_uniform_approx_of_uniformContinuousOn", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformApproximation", "is_tactic_proof": true, "tactics": ["simp_rw", "intro", "obtain", "obtain", "filter_upwards", "exact"], "tactic_count": 6}
{"name": "uniformContinuous_of_uniform_approx_of_uniformContinuous", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformApproximation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TendstoUniformlyOn.uniformContinuousOn", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformApproximation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TendstoUniformly.uniformContinuous", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformApproximation", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TendstoUniformlyOnFilter", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendstoUniformlyOnFilter_iff_tendsto", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TendstoUniformlyOn", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendstoUniformlyOn_iff_tendstoUniformlyOnFilter", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": true, "tactics": ["simp", "apply", "simp_rw", "simp"], "tactic_count": 4}
{"name": "tendstoUniformlyOn_iff_tendsto", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "TendstoUniformly", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendstoUniformlyOn_univ", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "tendstoUniformly_iff_tendstoUniformlyOnFilter", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "TendstoUniformly.tendstoUniformlyOnFilter", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "tendstoUniformlyOn_iff_tendstoUniformly_comp_coe", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendstoUniformlyOn_iff_restrict", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendstoUniformly_iff_tendsto", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "TendstoUniformlyOnFilter.tendsto_at", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": true, "tactics": ["refine", "filter_upwards", "intro", "simpa"], "tactic_count": 4}
{"name": "TendstoUniformlyOn.tendsto_at", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TendstoUniformly.tendsto_at", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TendstoUniformlyOnFilter.mono_left", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TendstoUniformlyOnFilter.mono_right", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TendstoUniformlyOn.mono", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TendstoUniformlyOnFilter.congr_inseparable", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "TendstoUniformlyOnFilter.congr", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TendstoUniformlyOn.congr_inseparable", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": true, "tactics": ["rw", "refine", "rwa"], "tactic_count": 3}
{"name": "TendstoUniformlyOn.congr", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendstoUniformly_congr_inseparable", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": true, "tactics": ["rw", "exact", "h.congr_inseparable"], "tactic_count": 3}
{"name": "tendstoUniformly_congr", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TendstoUniformlyOn.congr_inseparable_right", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": true, "tactics": ["rw", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "TendstoUniformlyOn.congr_right", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TendstoUniformly.tendstoUniformlyOn", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TendstoUniformlyOnFilter.comp", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "TendstoUniformlyOn.comp", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "TendstoUniformly.comp", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "UniformContinuous.comp_tendstoUniformlyOnFilter", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformContinuous.comp_tendstoUniformlyOn", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformContinuous.comp_tendstoUniformly", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TendstoUniformlyOnFilter.prodMap", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": true, "tactics": ["rw", "rw", "simpa"], "tactic_count": 3}
{"name": "TendstoUniformlyOn.prodMap", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "TendstoUniformly.prodMap", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "TendstoUniformlyOnFilter.prodMk", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TendstoUniformlyOn.prodMk", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "TendstoUniformly.prodMk", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendsto_prod_filter_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": true, "tactics": ["simp_rw", "rfl"], "tactic_count": 2}
{"name": "tendsto_prod_principal_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "tendsto_prod_top_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "tendstoUniformlyOn_empty", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendstoUniformlyOn_singleton_iff_tendsto", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "Filter.Tendsto.tendstoUniformlyOnFilter_const", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Filter.Tendsto.tendstoUniformlyOn_const", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformContinuousOn.tendstoUniformlyOn", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": true, "tactics": ["set", "rw", "change", "simp", "refine", "simp", "exact"], "tactic_count": 7}
{"name": "UniformContinuousOn.tendstoUniformly", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "UniformContinuous₂.tendstoUniformly", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.HasBasis.tendstoUniformlyOnFilter_iff_of_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.HasBasis.tendstoUniformlyOnFilter_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.HasBasis.tendstoUniformlyOn_iff_of_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Filter.HasBasis.tendstoUniformlyOn_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Filter.HasBasis.tendstoUniformly_iff_of_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Filter.HasBasis.tendstoUniformly_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "UniformCauchySeqOnFilter", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformCauchySeqOn", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformCauchySeqOn_iff_uniformCauchySeqOnFilter", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": true, "tactics": ["simp", "refine", "rw"], "tactic_count": 3}
{"name": "UniformCauchySeqOn.uniformCauchySeqOnFilter", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": true, "tactics": ["rwa"], "tactic_count": 1}
{"name": "TendstoUniformlyOnFilter.uniformCauchySeqOnFilter", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": true, "tactics": ["intro", "rcases", "have", "apply", "simp", "intro", "exact"], "tactic_count": 7}
{"name": "TendstoUniformlyOn.uniformCauchySeqOn", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformCauchySeqOnFilter.tendstoUniformlyOnFilter_of_tendsto", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": true, "tactics": ["rcases", "simp", "intro", "rcases", "have", "rw", "exact", "rw", "have", "apply", "simp", "intro", "refine", "rw", "have", "obtain", "exact"], "tactic_count": 17}
{"name": "UniformCauchySeqOn.tendstoUniformlyOn_of_tendsto", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformCauchySeqOnFilter.mono_left", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformCauchySeqOnFilter.mono_right", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformCauchySeqOn.mono", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "UniformCauchySeqOnFilter.comp", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformCauchySeqOn.comp", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": true, "tactics": ["rw", "simpa"], "tactic_count": 2}
{"name": "UniformContinuous.comp_uniformCauchySeqOn", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformCauchySeqOn.prodMap", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": true, "tactics": ["intro", "rw", "obtain", "simp_rw", "rw", "apply", "intro", "exact"], "tactic_count": 8}
{"name": "UniformCauchySeqOn.prod", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformCauchySeqOn.prod'", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformCauchySeqOn.cauchy_map", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": true, "tactics": ["simp", "intro", "rw", "filter_upwards"], "tactic_count": 4}
{"name": "UniformCauchySeqOn.cauchySeq", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendstoUniformlyOn_of_seq_tendstoUniformlyOn", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "specialize", "rw", "exact"], "tactic_count": 6}
{"name": "TendstoUniformlyOn.seq_tendstoUniformlyOn", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "tendstoUniformlyOn_iff_seq_tendstoUniformlyOn", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "tendstoUniformly_iff_seq_tendstoUniformly", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "TendstoUniformlyOnFilter.tendsto_of_eventually_tendsto", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": true, "tactics": ["rw", "intro", "rw", "obtain", "have", "have", "have", "obtain", "filter_upwards"], "tactic_count": 9}
{"name": "TendstoUniformly.tendsto_of_eventually_tendsto", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergence", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformFun", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformOnFun", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformConvergence.term_→ᵤ_", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformConvergence._aux_Mathlib_Topology_UniformSpace_UniformConvergenceTopology___macroRules_UniformConvergence_term_→ᵤ__1", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformConvergence._aux_Mathlib_Topology_UniformSpace_UniformConvergenceTopology___unexpand_UniformFun_1", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformConvergence.term_→ᵤ[_]_", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformConvergence._aux_Mathlib_Topology_UniformSpace_UniformConvergenceTopology___macroRules_UniformConvergence_term_→ᵤ[_]__1", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformConvergence._aux_Mathlib_Topology_UniformSpace_UniformConvergenceTopology___unexpand_UniformOnFun_1", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instNonemptyUniformFun", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instNonemptyUniformOnFun", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instSubsingletonUniformFun", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instSubsingletonUniformOnFun", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformFun.ofFun", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformOnFun.ofFun", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformFun.toFun", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformOnFun.toFun", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformFun.toFun_ofFun", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformFun.ofFun_toFun", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformOnFun.toFun_ofFun", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformOnFun.ofFun_toFun", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformFun.gen", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformFun.isBasis_gen", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformFun.basis", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformFun.filter", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformFun.phi", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.UniformSpace.UniformConvergenceTopology.0.UniformFun.termLowerAdjoint", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.UniformSpace.UniformConvergenceTopology.0.UniformFun._aux_Mathlib_Topology_UniformSpace_UniformConvergenceTopology___macroRules__private_Mathlib_Topology_UniformSpace_UniformConvergenceTopology_0_UniformFun_termLowerAdjoint_1", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformFun.gc", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": true, "tactics": ["intro", "symm", "calc", "rw"], "tactic_count": 4}
{"name": "UniformFun.uniformCore", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformFun.uniformSpace", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformFun.topologicalSpace", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.UniformSpace.UniformConvergenceTopology.0.UniformFun.term𝒰(_,_,_)", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.UniformSpace.UniformConvergenceTopology.0.UniformFun._aux_Mathlib_Topology_UniformSpace_UniformConvergenceTopology___macroRules__private_Mathlib_Topology_UniformSpace_UniformConvergenceTopology_0_UniformFun_term𝒰(_,_,_)_1", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformFun.hasBasis_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformFun.hasBasis_uniformity_of_basis", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformFun.hasBasis_nhds_of_basis", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformFun.hasBasis_nhds", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformFun.uniformContinuous_eval", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": true, "tactics": ["change", "rw", "exact"], "tactic_count": 3}
{"name": "UniformFun.mem_gen", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformFun.mono", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformFun.iInf_eq", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": true, "tactics": ["ext", "change", "rw", "exact"], "tactic_count": 4}
{"name": "UniformFun.inf_eq", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": true, "tactics": ["rw", "refine", "cases"], "tactic_count": 3}
{"name": "UniformFun.postcomp_isUniformInducing", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformFun.postcomp_isUniformEmbedding", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformFun.comap_eq", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": true, "tactics": ["letI", "exact"], "tactic_count": 2}
{"name": "UniformFun.postcomp_uniformContinuous", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": true, "tactics": ["refine", "calc"], "tactic_count": 2}
{"name": "UniformFun.congrRight", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformFun.precomp_uniformContinuous", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "UniformFun.congrLeft", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformFun.uniformContinuous_toFun", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": true, "tactics": ["rw", "intro", "exact"], "tactic_count": 3}
{"name": "UniformFun.instT2Space", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformFun.tendsto_iff_tendstoUniformly", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": true, "tactics": ["rw", "simp"], "tactic_count": 2}
{"name": "UniformFun.uniformEquivProdArrow", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformFun.uniformEquivPiComm", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformFun.isClosed_setOf_continuous", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "UniformFun.uniformSpace_eq_inf_precomp_of_cover", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": true, "tactics": ["ext", "refine", "exact", "exact", "refine", "rcases", "exact", "exact"], "tactic_count": 8}
{"name": "UniformFun.uniformSpace_eq_iInf_precomp_of_cover", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": true, "tactics": ["ext", "simp_rw", "refine", "rcases", "refine", "rcases", "exact"], "tactic_count": 7}
{"name": "_private.Mathlib.Topology.UniformSpace.UniformConvergenceTopology.0.UniformOnFun.term𝒰(_,_,_)", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.UniformSpace.UniformConvergenceTopology.0.UniformOnFun._aux_Mathlib_Topology_UniformSpace_UniformConvergenceTopology___macroRules__private_Mathlib_Topology_UniformSpace_UniformConvergenceTopology_0_UniformOnFun_term𝒰(_,_,_)_1", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformOnFun.gen", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformOnFun.gen_eq_preimage_restrict", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": true, "tactics": ["ext", "exact"], "tactic_count": 2}
{"name": "UniformOnFun.gen_mono", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformOnFun.isBasis_gen", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformOnFun.uniformSpace", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.UniformSpace.UniformConvergenceTopology.0.UniformOnFun.term𝒱(_,_,_,_)", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.UniformSpace.UniformConvergenceTopology.0.UniformOnFun._aux_Mathlib_Topology_UniformSpace_UniformConvergenceTopology___macroRules__private_Mathlib_Topology_UniformSpace_UniformConvergenceTopology_0_UniformOnFun_term𝒱(_,_,_,_)_1", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformOnFun.topologicalSpace", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformOnFun.topologicalSpace_eq", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": true, "tactics": ["simp", "rfl"], "tactic_count": 2}
{"name": "UniformOnFun.hasBasis_uniformity_of_basis_aux₁", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "UniformOnFun.hasBasis_uniformity_of_basis_aux₂", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformOnFun.hasBasis_uniformity_of_basis", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": true, "tactics": ["simp", "exact", "hasBasis_biInf_of_directed"], "tactic_count": 3}
{"name": "UniformOnFun.hasBasis_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformOnFun.hasBasis_uniformity_of_covering_of_basis", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": true, "tactics": ["have", "have", "rcases", "rcases", "exact", "refine", "rcases", "exact"], "tactic_count": 8}
{"name": "UniformOnFun.hasAntitoneBasis_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": true, "tactics": ["have", "refine", "rintro", "rcases", "exact", "exact"], "tactic_count": 6}
{"name": "UniformOnFun.isCountablyGenerated_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformOnFun.hasBasis_nhds_of_basis", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformOnFun.hasBasis_nhds", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformOnFun.uniformContinuous_restrict", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": true, "tactics": ["change", "simp", "exact"], "tactic_count": 3}
{"name": "UniformOnFun.isUniformEmbedding_toFun_finite", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": true, "tactics": ["refine", "simp_rw", "refine"], "tactic_count": 3}
{"name": "UniformOnFun.isEmbedding_toFun_finite", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformOnFun.uniformity_eq_of_basis", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": true, "tactics": ["simp_rw", "comap_principal,"], "tactic_count": 2}
{"name": "UniformOnFun.uniformity_eq", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformOnFun.gen_mem_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": true, "tactics": ["rw", "apply_rules"], "tactic_count": 2}
{"name": "UniformOnFun.nhds_eq_of_basis", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "UniformOnFun.nhds_eq", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformOnFun.gen_mem_nhds", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": true, "tactics": ["rw", "apply_rules"], "tactic_count": 2}
{"name": "UniformOnFun.uniformContinuous_ofUniformFun", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "UniformOnFun.uniformEquivUniformFun", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformOnFun.uniformContinuous_ofFun_toFun", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": true, "tactics": ["simp", "refine", "simp", "intro", "obtain", "refine", "simp", "intro", "obtain", "exact"], "tactic_count": 10}
{"name": "UniformOnFun.mono", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformOnFun.uniformContinuous_eval_of_mem", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformOnFun.uniformContinuous_eval_of_mem_sUnion", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformOnFun.uniformContinuous_eval", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformOnFun.iInf_eq", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": true, "tactics": ["simp_rw", "rw", "exact"], "tactic_count": 3}
{"name": "UniformOnFun.inf_eq", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": true, "tactics": ["rw", "refine", "cases"], "tactic_count": 3}
{"name": "UniformOnFun.comap_eq", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": true, "tactics": ["simp_rw", "rfl"], "tactic_count": 2}
{"name": "UniformOnFun.postcomp_uniformContinuous", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "UniformOnFun.postcomp_isUniformInducing", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": true, "tactics": ["constructor", "replace", "change", "rw", "congr", "rw", "rfl"], "tactic_count": 7}
{"name": "UniformOnFun.postcomp_isUniformEmbedding", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformOnFun.congrRight", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformOnFun.precomp_uniformContinuous", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": true, "tactics": ["simp_rw", "refine", "simpa"], "tactic_count": 3}
{"name": "UniformOnFun.congrLeft", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformOnFun.t2Space_of_covering", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformOnFun.uniformContinuous_restrict_toFun", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": true, "tactics": ["rw", "intro", "obtain", "exact"], "tactic_count": 4}
{"name": "UniformOnFun.isUniformInducing_pi_restrict", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": ["simp_rw", "iInf_subtype]", "rfl"], "tactic_count": 3}
{"name": "UniformOnFun.uniformContinuous_toFun", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "UniformOnFun.continuousAt_eval₂", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": true, "tactics": ["rw", "intro", "rcases", "filter_upwards"], "tactic_count": 4}
{"name": "UniformOnFun.continuousOn_eval₂", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformOnFun.tendsto_iff_tendstoUniformlyOn", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "UniformOnFun.continuous_rng_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "UniformOnFun.instCompleteSpace", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": true, "tactics": ["rcases", "infer_instance", "refine", "have", "have", "choose", "use", "simp_rw", "intro", "rcases", "filter_upwards", "refine", "filter_upwards"], "tactic_count": 13}
{"name": "UniformOnFun.uniformEquivProdArrow", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformOnFun.uniformEquivPiComm", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformOnFun.isClosed_setOf_continuous", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "UniformOnFun.uniformSpace_eq_inf_precomp_of_cover", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": true, "tactics": ["set", "set", "have", "refine", "simpa", "refine", "rw", "exact", "rw", "exact", "simp_rw", "exact"], "tactic_count": 12}
{"name": "UniformOnFun.uniformSpace_eq_iInf_precomp_of_cover", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": true, "tactics": ["set", "have", "rcases", "refine", "simpa", "refine", "rw", "exact", "simp_rw", "exact"], "tactic_count": 10}
{"name": "UniformFun.instCompleteSpace", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformContinuousOn.comp_tendstoUniformly", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": true, "tactics": ["rw", "lift", "lift", "rw", "have", "h.of_tendsto_comp", "apply", "rwa"], "tactic_count": 8}
{"name": "UniformContinuousOn.comp_tendstoUniformly_eventually", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": true, "tactics": ["classical", "obtain", "let", "have", "rw", "refine", "have", "apply", "rw", "refine"], "tactic_count": 10}
{"name": "UniformContinuousOn.comp_tendstoUniformlyOn_eventually", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformConvergenceTopology", "is_tactic_proof": true, "tactics": ["rw", "apply"], "tactic_count": 2}
{"name": "isUniformInducing_iff_uniformSpace", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": true, "tactics": ["rw", "rfl"], "tactic_count": 2}
{"name": "isUniformInducing_iff'", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.HasBasis.isUniformInducing_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsUniformInducing.mk'", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUniformInducing.id", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUniformInducing.comp", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUniformInducing.of_comp_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": true, "tactics": ["refine", "rw"], "tactic_count": 2}
{"name": "IsUniformInducing.basis_uniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUniformInducing.cauchy_map_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsUniformInducing.of_comp", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": true, "tactics": ["refine", "rw", "exact"], "tactic_count": 3}
{"name": "IsUniformInducing.uniformContinuous", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUniformInducing.uniformContinuous_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": true, "tactics": ["dsimp", "simp"], "tactic_count": 2}
{"name": "IsUniformInducing.isUniformInducing_comp_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "IsUniformInducing.uniformContinuousOn_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": true, "tactics": ["dsimp", "rw"], "tactic_count": 2}
{"name": "IsUniformInducing.isInducing", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": true, "tactics": ["obtain", "exact"], "tactic_count": 2}
{"name": "IsUniformInducing.prod", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUniformInducing.isDenseInducing", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.isUniformInducing_mk", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUniformInducing.injective", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isUniformEmbedding_iff'", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.HasBasis.isUniformEmbedding_iff'", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Filter.HasBasis.isUniformEmbedding_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "isUniformEmbedding_subtype_val", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isUniformEmbedding_set_inclusion", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUniformEmbedding.comp", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUniformEmbedding.of_comp_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Equiv.isUniformEmbedding", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isUniformEmbedding_inl", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isUniformEmbedding_inr", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUniformInducing.isUniformEmbedding", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isUniformEmbedding_iff_isUniformInducing", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "comap_uniformity_of_spaced_out", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": true, "tactics": ["refine", "calc", "comap", "rintro"], "tactic_count": 4}
{"name": "isUniformEmbedding_of_spaced_out", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": true, "tactics": ["let", "exact"], "tactic_count": 2}
{"name": "IsUniformEmbedding.isEmbedding", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUniformEmbedding.isDenseEmbedding", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isClosedEmbedding_of_spaced_out", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": true, "tactics": ["rcases", "exact"], "tactic_count": 2}
{"name": "closure_image_mem_nhds_of_isUniformInducing", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": false, "tactics": ["obtain", "rwa", "rcases", "refine", "have", "refine", "refine", "rcases", "exact"], "tactic_count": 9}
{"name": "isUniformEmbedding_subtypeEmb", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUniformEmbedding.prod", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isComplete_image_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": true, "tactics": ["have", "have", "simp_rw", "exists_mem_image,"], "tactic_count": 4}
{"name": "IsUniformInducing.isComplete_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUniformEmbedding.isComplete_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Subtype.isComplete_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "completeSpace_iff_isComplete_range", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsUniformInducing.isComplete_range", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUniformInducing.completeSpace_congr", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "SeparationQuotient.completeSpace_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "SeparationQuotient.instCompleteSpace", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "completeSpace_congr", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "completeSpace_coe_iff_isComplete", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "IsClosed.completeSpace_coe", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "completeSpace_ulift_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ULift.instCompleteSpace", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "completeSpace_extension", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.totallyBounded_map_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": true, "tactics": ["refine", "simp_rw", "intro", "rcases", "use", "simp_rw", "exact"], "tactic_count": 7}
{"name": "totallyBounded_image_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "totallyBounded_preimage", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Filter.totallyBounded_comap", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompleteSpace.sum", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": true, "tactics": ["rw", "exact", "isUniformEmbedding_inl.isUniformInducing.isComplete_range.union", "isUniformEmbedding_inr.isUniformInducing.isComplete_range"], "tactic_count": 4}
{"name": "IsUniformEmbedding.discreteUniformity", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "isUniformEmbedding_comap", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Topology.IsEmbedding.comapUniformSpace", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Embedding.to_isUniformEmbedding", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.UniformSpace.UniformEmbedding.0.termψ", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.UniformSpace.UniformEmbedding.0._aux_Mathlib_Topology_UniformSpace_UniformEmbedding___macroRules__private_Mathlib_Topology_UniformSpace_UniformEmbedding_0_termψ_1", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "_private.Mathlib.Topology.UniformSpace.UniformEmbedding.0._aux_Mathlib_Topology_UniformSpace_UniformEmbedding___unexpand_IsDenseInducing_extend_1", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformly_extend_exists", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniform_extend_subtype", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": true, "tactics": ["have", "have", "have", "have", "let", "replace", "simpa", "refine", "rw", "exact"], "tactic_count": 10}
{"name": "uniformly_extend_spec", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "uniformContinuous_uniformly_extend", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformly_extend_of_ind", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformly_extend_unique", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isUniformInducing_val", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "uniformContinuous_rangeFactorization_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "UniformContinuous.rangeFactorization", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "isUniformInducing_rangeFactorization_iff", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsUniformInducing.rangeFactorization", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dense.extend_exists", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dense.extend_spec", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dense.uniformContinuous_extend", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Dense.extend_of_ind", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "IsDenseInducing.isUniformInducing_extend", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.UniformEmbedding", "is_tactic_proof": true, "tactics": ["let", "have", "let", "have", "have", "have", "let", "have", "have", "have", "ext", "induction", "exact", "isClosed_eq", "simpa", "hg.inseparable_extend", "have", "refine", "rw", "exact", "have", "refine", "h.uniformContinuous).continuous).range_subset_closure_image_dense", "hid.dense).trans", "rw", "apply", "funext", "simpa", "suffices", "rw", "exact", "rw", "refine", "simp", "exact"], "tactic_count": 35}
{"name": "IsThickening", "kind": "definition", "module": "Mathlib.Topology.UniformSpace.Uniformizable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "urysohns_main", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Uniformizable", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "have", "have", "calc", "ds", "replace", "have", "refine", "refine", "rw", "exact"], "tactic_count": 12}
{"name": "UniformSpace.toCompletelyRegularSpace", "kind": "instance", "module": "Mathlib.Topology.UniformSpace.Uniformizable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "CompletelyRegularSpace.of_exists_uniformSpace", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Uniformizable", "is_tactic_proof": true, "tactics": ["obtain", "infer_instance"], "tactic_count": 2}
{"name": "CompletelyRegularSpace.exists_uniformSpace", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Uniformizable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "completelyRegularSpace_iff_exists_uniformSpace", "kind": "theorem", "module": "Mathlib.Topology.UniformSpace.Uniformizable", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval", "kind": "abbrev", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.termI", "kind": "definition", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval._aux_Mathlib_Topology_UnitInterval___macroRules_unitInterval_termI_1", "kind": "definition", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval._aux_Mathlib_Topology_UnitInterval___unexpand_unitInterval_1", "kind": "definition", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.zero_mem", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.one_mem", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.mul_mem", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.div_mem", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.fract_mem", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.univ_eq_Icc", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.coe_ne_zero", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.coe_ne_one", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.coe_pos", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.coe_lt_one", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.mul_le_left", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.mul_le_right", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.eq_closedBall", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": true, "tactics": ["norm_num"], "tactic_count": 1}
{"name": "unitInterval.symm", "kind": "definition", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.termσ", "kind": "definition", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval._aux_Mathlib_Topology_UnitInterval___macroRules_unitInterval_termσ_1", "kind": "definition", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval._aux_Mathlib_Topology_UnitInterval___unexpand_unitInterval_symm_1", "kind": "definition", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.symm_zero", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.symm_one", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.symm_symm", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.symm_involutive", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.symm_bijective", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.coe_symm_eq", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.image_coe_preimage_symm", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "unitInterval.symm_projIcc", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": true, "tactics": ["ext", "rcases", "simp", "rcases", "lift", "simp_rw", "simp"], "tactic_count": 7}
{"name": "unitInterval.continuous_symm", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.symmHomeomorph", "kind": "definition", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.strictAnti_symm", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.symm_inj", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.half_le_symm_iff", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "unitInterval.symm_eq_one", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "unitInterval.symm_eq_zero", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "unitInterval.symm_le_symm", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "unitInterval.le_symm_comm", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "unitInterval.symm_le_comm", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "unitInterval.symm_lt_symm", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "unitInterval.lt_symm_comm", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "unitInterval.symm_lt_comm", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "unitInterval.instConnectedSpaceElemReal", "kind": "instance", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval._example", "kind": "example", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": true, "tactics": ["infer_instance"], "tactic_count": 1}
{"name": "unitInterval.nonneg", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.one_minus_nonneg", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "unitInterval.le_one", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.one_minus_le_one", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "unitInterval.add_pos", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.nonneg'", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.le_one'", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.pos_iff_ne_zero", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.lt_one_iff_ne_one", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.eq_one_or_eq_zero_of_le_mul", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": true, "tactics": ["contrapose", "rw", "rw", "simpa"], "tactic_count": 4}
{"name": "unitInterval.instNontrivialElemReal", "kind": "instance", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.mul_pos_mem_iff", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": true, "tactics": ["constructor", "exact", "rwa", "exact", "rwa"], "tactic_count": 5}
{"name": "unitInterval.two_mul_sub_one_mem_iff", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": true, "tactics": ["constructor"], "tactic_count": 1}
{"name": "unitInterval.submonoid", "kind": "definition", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.coe_unitIntervalSubmonoid", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.mem_unitIntervalSubmonoid", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.prod_mem", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.instLinearOrderedCommMonoidWithZeroElemReal", "kind": "instance", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.subtype_Iic_eq_Icc", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "unitInterval.subtype_Iio_eq_Ico", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "unitInterval.subtype_Ici_eq_Icc", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "unitInterval.subtype_Ioi_eq_Ioc", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Set.abs_projIcc_sub_projIcc", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": true, "tactics": ["wlog", "rw", "rw", "rw", "refine", "refine", "rwa", "exact"], "tactic_count": 8}
{"name": "Set.Icc.addNSMul", "kind": "definition", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc.addNSMul_zero", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Set.Icc.addNSMul_eq_right", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": true, "tactics": ["obtain", "refine", "rw", "exact"], "tactic_count": 4}
{"name": "Set.Icc.monotone_addNSMul", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc.abs_sub_addNSMul_le", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc.convexCombo", "kind": "definition", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc.coe_convexCombo", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc.convexCombo_zero", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.Icc.convexCombo_one", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Set.Icc.convexCombo_symm", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": true, "tactics": ["simp", "abel"], "tactic_count": 2}
{"name": "Set.Icc.le_convexCombo", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": true, "tactics": ["rw", "simp", "nlinarith"], "tactic_count": 3}
{"name": "Set.Icc.convexCombo_le", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": true, "tactics": ["rw", "simp", "nlinarith"], "tactic_count": 3}
{"name": "Set.Icc.convexCombo_assoc_coeff₁", "kind": "abbrev", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc.convexCombo_assoc_coeff₂", "kind": "abbrev", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc.convexCombo_assoc", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": true, "tactics": ["simp", "by_cases", "simp", "by_cases", "simp", "have", "field_simp", "simp", "by_cases", "simp", "have", "intro", "have", "grind", "field_simp", "ring_nf"], "tactic_count": 16}
{"name": "Set.Icc.convexCombo_assoc_coeff₁'", "kind": "abbrev", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc.convexCombo_assoc_coeff₂'", "kind": "abbrev", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Set.Icc.convexCombo_assoc'", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": false, "tactics": ["rw", "rw"], "tactic_count": 2}
{"name": "_private.Mathlib.Topology.UnitInterval.0.Set.Icc.eq_convexCombo.zero_le", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": true, "tactics": ["by_cases", "simp_all", "replace", "replace", "apply"], "tactic_count": 5}
{"name": "_private.Mathlib.Topology.UnitInterval.0.Set.Icc.eq_convexCombo.le_one", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": true, "tactics": ["by_cases", "simp_all", "replace", "replace", "apply"], "tactic_count": 5}
{"name": "Set.Icc.eq_convexCombo", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": true, "tactics": ["ext", "simp", "by_cases", "simp_all", "replace", "replace", "linarith", "field_simp", "ring_nf"], "tactic_count": 9}
{"name": "exists_monotone_Icc_subset_open_cover_Icc", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": true, "tactics": ["obtain", "have", "refine", "obtain", "exact"], "tactic_count": 5}
{"name": "exists_monotone_Icc_subset_open_cover_unitInterval", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": true, "tactics": ["simp_rw", "exact"], "tactic_count": 2}
{"name": "exists_monotone_Icc_subset_open_cover_unitInterval_prod_self", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": true, "tactics": ["obtain", "have", "simp_rw", "have", "refine", "obtain", "exact", "hsub", "half_lt_self"], "tactic_count": 9}
{"name": "projIcc_eq_zero", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "projIcc_eq_one", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.Interactive.tacticUnit_interval", "kind": "definition", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.Interactive._aux_Mathlib_Topology_UnitInterval___macroRules_Tactic_Interactive_tacticUnit_interval_1", "kind": "definition", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Tactic.Interactive._example", "kind": "example", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": true, "tactics": ["unit_interval"], "tactic_count": 1}
{"name": "affineHomeomorph_image_I", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "iccHomeoI", "kind": "definition", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": true, "tactics": ["let", "refine", "apply", "rw", "simp"], "tactic_count": 5}
{"name": "iccHomeoI_apply_coe", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "iccHomeoI_symm_apply_coe", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.toNNReal", "kind": "definition", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.toNNReal_zero", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.toNNReal_one", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.toNNReal_continuous", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": true, "tactics": ["delta"], "tactic_count": 1}
{"name": "unitInterval.coe_toNNReal", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "unitInterval.toNNReal_add_toNNReal_symm", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "unitInterval.toNNReal_symm_add_toNNReal", "kind": "theorem", "module": "Mathlib.Topology.UnitInterval", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "exists_bounded_zero_one_of_closed", "kind": "theorem", "module": "Mathlib.Topology.UrysohnsBounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "exists_bounded_mem_Icc_of_closed_of_le", "kind": "theorem", "module": "Mathlib.Topology.UrysohnsBounded", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Urysohns.CU.left", "kind": "definition", "module": "Mathlib.Topology.UrysohnsLemma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Urysohns.CU.right", "kind": "definition", "module": "Mathlib.Topology.UrysohnsLemma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Urysohns.CU.left_U_subset_right_C", "kind": "theorem", "module": "Mathlib.Topology.UrysohnsLemma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Urysohns.CU.left_U_subset", "kind": "theorem", "module": "Mathlib.Topology.UrysohnsLemma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Urysohns.CU.subset_right_C", "kind": "theorem", "module": "Mathlib.Topology.UrysohnsLemma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Urysohns.CU.approx", "kind": "definition", "module": "Mathlib.Topology.UrysohnsLemma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Urysohns.CU.approx_of_mem_C", "kind": "theorem", "module": "Mathlib.Topology.UrysohnsLemma", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "simp", "rw", "exacts"], "tactic_count": 6}
{"name": "Urysohns.CU.approx_of_notMem_U", "kind": "theorem", "module": "Mathlib.Topology.UrysohnsLemma", "is_tactic_proof": true, "tactics": ["induction", "zero", "rw", "exact", "succ", "simp", "rw", "exacts"], "tactic_count": 8}
{"name": "Urysohns.CU.approx_nonneg", "kind": "theorem", "module": "Mathlib.Topology.UrysohnsLemma", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "simp", "refine"], "tactic_count": 5}
{"name": "Urysohns.CU.approx_le_one", "kind": "theorem", "module": "Mathlib.Topology.UrysohnsLemma", "is_tactic_proof": true, "tactics": ["induction", "zero", "succ", "simp", "have", "norm_num", "exact"], "tactic_count": 7}
{"name": "Urysohns.CU.bddAbove_range_approx", "kind": "theorem", "module": "Mathlib.Topology.UrysohnsLemma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Urysohns.CU.approx_le_approx_of_U_sub_C", "kind": "theorem", "module": "Mathlib.Topology.UrysohnsLemma", "is_tactic_proof": true, "tactics": ["by_cases", "calc", "approx", "calc", "approx"], "tactic_count": 5}
{"name": "Urysohns.CU.approx_mem_Icc_right_left", "kind": "theorem", "module": "Mathlib.Topology.UrysohnsLemma", "is_tactic_proof": true, "tactics": ["induction", "zero", "simp", "refine", "grw", "rw", "positivity", "succ", "simp", "refine", "exacts"], "tactic_count": 11}
{"name": "Urysohns.CU.approx_le_succ", "kind": "theorem", "module": "Mathlib.Topology.UrysohnsLemma", "is_tactic_proof": true, "tactics": ["induction", "zero", "simp", "exact", "succ", "rw", "exact"], "tactic_count": 7}
{"name": "Urysohns.CU.approx_mono", "kind": "theorem", "module": "Mathlib.Topology.UrysohnsLemma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Urysohns.CU.lim", "kind": "definition", "module": "Mathlib.Topology.UrysohnsLemma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Urysohns.CU.tendsto_approx_atTop", "kind": "theorem", "module": "Mathlib.Topology.UrysohnsLemma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Urysohns.CU.lim_of_mem_C", "kind": "theorem", "module": "Mathlib.Topology.UrysohnsLemma", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Urysohns.CU.disjoint_C_support_lim", "kind": "theorem", "module": "Mathlib.Topology.UrysohnsLemma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Urysohns.CU.lim_of_notMem_U", "kind": "theorem", "module": "Mathlib.Topology.UrysohnsLemma", "is_tactic_proof": true, "tactics": ["simp"], "tactic_count": 1}
{"name": "Urysohns.CU.lim_eq_midpoint", "kind": "theorem", "module": "Mathlib.Topology.UrysohnsLemma", "is_tactic_proof": true, "tactics": ["refine", "simp", "exact"], "tactic_count": 3}
{"name": "Urysohns.CU.approx_le_lim", "kind": "theorem", "module": "Mathlib.Topology.UrysohnsLemma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Urysohns.CU.lim_nonneg", "kind": "theorem", "module": "Mathlib.Topology.UrysohnsLemma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Urysohns.CU.lim_le_one", "kind": "theorem", "module": "Mathlib.Topology.UrysohnsLemma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Urysohns.CU.lim_mem_Icc", "kind": "theorem", "module": "Mathlib.Topology.UrysohnsLemma", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Urysohns.CU.continuous_lim", "kind": "theorem", "module": "Mathlib.Topology.UrysohnsLemma", "is_tactic_proof": true, "tactics": ["obtain", "refine", "continuous_iff_continuousAt.2", "simp", "induction", "zero", "filter_upwards", "rw", "exact", "succ", "by_cases", "filter_upwards", "rw", "c.right.lim_of_mem_C", "refine", "rw", "gcongr", "replace", "filter_upwards", "ihn", "replace", "replace", "simp", "c.left.left.lim_of_notMem_U", "grw", "set", "calc"], "tactic_count": 27}
{"name": "exists_continuous_zero_one_of_isClosed", "kind": "theorem", "module": "Mathlib.Topology.UrysohnsLemma", "is_tactic_proof": true, "tactics": ["let", "set", "closed_C", "open_U", "subset", "hP", "rintro", "rcases", "exact", "exact"], "tactic_count": 10}
{"name": "exists_continuous_zero_one_of_isCompact", "kind": "theorem", "module": "Mathlib.Topology.UrysohnsLemma", "is_tactic_proof": false, "tactics": ["obtain", "exists_compact_closed_between", "let", "set", "closed_C", "open_U", "subset", "hP", "rintro", "rcases", "have", "refine", "exact", "c.lim_of_notMem_U"], "tactic_count": 14}
{"name": "exists_continuous_zero_one_of_isCompact'", "kind": "theorem", "module": "Mathlib.Topology.UrysohnsLemma", "is_tactic_proof": true, "tactics": ["obtain", "use", "refine", "intro", "simp", "exact", "intro", "simp", "exact", "intro", "simpa"], "tactic_count": 11}
{"name": "exists_continuous_one_zero_of_isCompact", "kind": "theorem", "module": "Mathlib.Topology.UrysohnsLemma", "is_tactic_proof": false, "tactics": ["obtain", "exists_compact_closed_between", "rcases", "exists_continuous_zero_one_of_isCompact", "have", "refine", "simpa", "apply", "simp", "apply", "contrapose", "simp", "exact", "have", "simp"], "tactic_count": 15}
{"name": "exists_continuous_one_zero_of_isCompact_of_isGδ", "kind": "theorem", "module": "Mathlib.Topology.UrysohnsLemma", "is_tactic_proof": true, "tactics": ["rcases", "obtain", "exists_compact_closed_between", "have", "apply", "rw", "exact", "choose", "obtain", "let", "have", "intro", "have", "have", "exact", "simp", "have", "have", "refine", "apply", "simpa", "apply", "apply", "intro", "obtain", "have", "have", "apply", "exact", "simpa", "exact", "exact", "apply", "exact"], "tactic_count": 34}
{"name": "exists_tsupport_one_of_isOpen_isClosed", "kind": "theorem", "module": "Mathlib.Topology.UrysohnsLemma", "is_tactic_proof": true, "tactics": ["rw", "obtain", "rw", "have", "let", "set", "closed_C", "open_U", "subset", "hP", "intro", "obtain", "simp_rw", "obtain", "refine", "exact", "use", "simp", "refine", "apply", "rw", "apply", "exact", "intro", "apply", "exact"], "tactic_count": 26}
{"name": "exists_continuousMap_one_of_isCompact_subset_isOpen", "kind": "theorem", "module": "Mathlib.Topology.UrysohnsLemma", "is_tactic_proof": true, "tactics": ["obtain", "obtain", "exists_tsupport_one_of_isOpen_isClosed", "have", "exact"], "tactic_count": 5}
{"name": "exists_continuous_nonneg_pos", "kind": "theorem", "module": "Mathlib.Topology.UrysohnsLemma", "is_tactic_proof": true, "tactics": ["rcases", "rcases", "refine", "have", "simp", "simp"], "tactic_count": 6}
{"name": "Pretrivialization.linear", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pretrivialization.symmₗ", "kind": "definition", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": true, "tactics": ["refine", "by_cases", "exact", "congr_arg", "rw", "exact"], "tactic_count": 6}
{"name": "Pretrivialization.linearEquivAt", "kind": "definition", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pretrivialization.linearMapAt", "kind": "definition", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pretrivialization.coe_linearMapAt", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": true, "tactics": ["rw", "split_ifs"], "tactic_count": 2}
{"name": "Pretrivialization.coe_linearMapAt_of_mem", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Pretrivialization.linearMapAt_apply", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Pretrivialization.linearMapAt_def_of_mem", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pretrivialization.linearMapAt_def_of_notMem", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pretrivialization.linearMapAt_eq_zero", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pretrivialization.symmₗ_linearMapAt", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Pretrivialization.linearMapAt_symmₗ", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "Trivialization.linear", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.toPretrivialization.isLinear", "kind": "instance", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.linearEquivAt", "kind": "definition", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.linearEquivAt_apply", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.linearEquivAt_symm_apply", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.symmₗ", "kind": "definition", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.coe_symmₗ", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.linearMapAt", "kind": "definition", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.coe_linearMapAt", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.coe_linearMapAt_of_mem", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Trivialization.linearMapAt_apply", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Trivialization.linearMapAt_def_of_mem", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.linearMapAt_def_of_notMem", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.symmₗ_linearMapAt", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.linearMapAt_symmₗ", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.coordChangeL", "kind": "definition", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.coe_coordChangeL", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.coe_coordChangeL'", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.symm_coordChangeL", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": true, "tactics": ["apply", "rw"], "tactic_count": 2}
{"name": "Trivialization.coordChangeL_apply", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.mk_coordChangeL", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": true, "tactics": ["ext", "rw", "rw", "exact", "exact"], "tactic_count": 5}
{"name": "Trivialization.apply_symm_apply_eq_coordChangeL", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Trivialization.coordChangeL_apply'", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": true, "tactics": ["rw"], "tactic_count": 1}
{"name": "Trivialization.coordChangeL_symm_apply", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bundle.zeroSection", "kind": "definition", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bundle.zeroSection_proj", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bundle.zeroSection_snd", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "trivialization_linear", "kind": "instance", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousOn_coordChange", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.continuousLinearMapAt", "kind": "definition", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.symmL", "kind": "definition", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.symmL_continuousLinearMapAt", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.continuousLinearMapAt_symmL", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.continuousLinearEquivAt", "kind": "definition", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.coe_continuousLinearEquivAt_eq", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.symm_continuousLinearEquivAt_eq", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.continuousLinearEquivAt_apply'", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.apply_eq_prod_continuousLinearEquivAt", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": true, "tactics": ["ext", "refine", "rw", "exact", "simp"], "tactic_count": 5}
{"name": "Trivialization.zeroSection", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Trivialization.symm_apply_eq_mk_continuousLinearEquivAt_symm", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": true, "tactics": ["simpa"], "tactic_count": 1}
{"name": "Trivialization.comp_continuousLinearEquivAt_eq_coord_change", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": true, "tactics": ["ext", "rw", "rfl"], "tactic_count": 3}
{"name": "trivialVectorBundleCore", "kind": "definition", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instInhabitedVectorBundleCore", "kind": "instance", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorBundleCore.toFiberBundleCore", "kind": "definition", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorBundleCore.coordChange_linear_comp", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorBundleCore.Index", "kind": "definition", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorBundleCore.Base", "kind": "definition", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorBundleCore.Fiber", "kind": "definition", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorBundleCore.topologicalSpaceFiber", "kind": "instance", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorBundleCore.addCommGroupFiber", "kind": "instance", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorBundleCore.moduleFiber", "kind": "instance", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorBundleCore.proj", "kind": "definition", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorBundleCore.TotalSpace", "kind": "definition", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorBundleCore.trivChange", "kind": "definition", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorBundleCore.mem_trivChange_source", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorBundleCore.toTopologicalSpace", "kind": "instance", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorBundleCore.coe_coordChange", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorBundleCore.localTriv", "kind": "definition", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorBundleCore.localTriv_apply", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorBundleCore.localTriv.isLinear", "kind": "instance", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorBundleCore.mem_localTriv_source", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorBundleCore.baseSet_at", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorBundleCore.mem_localTriv_target", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorBundleCore.localTriv_symm_fst", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorBundleCore.localTriv_symm_apply", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": true, "tactics": ["apply"], "tactic_count": 1}
{"name": "VectorBundleCore.localTriv_coordChange_eq", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": true, "tactics": ["rw", "exacts"], "tactic_count": 2}
{"name": "VectorBundleCore.localTrivAt", "kind": "definition", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorBundleCore.localTrivAt_def", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorBundleCore.mem_source_at", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": true, "tactics": ["rw", "exact"], "tactic_count": 2}
{"name": "VectorBundleCore.localTrivAt_apply", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorBundleCore.localTrivAt_apply_mk", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorBundleCore.mem_localTrivAt_baseSet", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorBundleCore.fiberBundle", "kind": "instance", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorBundleCore.trivializationAt", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorBundleCore.vectorBundle", "kind": "instance", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorBundleCore.continuous_proj", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorBundleCore.isOpenMap_proj", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorBundleCore.localTriv_continuousLinearMapAt", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": true, "tactics": ["ext1", "rw", "exacts"], "tactic_count": 3}
{"name": "VectorBundleCore.trivializationAt_continuousLinearMapAt", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorBundleCore.localTriv_symmL", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": true, "tactics": ["ext1", "rw", "exacts"], "tactic_count": 3}
{"name": "VectorBundleCore.trivializationAt_symmL", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorBundleCore.trivializationAt_coordChange_eq", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorPrebundle.coordChange", "kind": "definition", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorPrebundle.continuousOn_coordChange", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorPrebundle.coordChange_apply", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorPrebundle.mk_coordChange", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": true, "tactics": ["ext", "rw", "rw", "exact", "exact"], "tactic_count": 5}
{"name": "VectorPrebundle.toFiberPrebundle", "kind": "definition", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorPrebundle.totalSpaceTopology", "kind": "definition", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorPrebundle.trivializationOfMemPretrivializationAtlas", "kind": "definition", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorPrebundle.linear_trivializationOfMemPretrivializationAtlas", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorPrebundle.mem_trivialization_at_source", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorPrebundle.totalSpaceMk_preimage_source", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorPrebundle.continuous_totalSpaceMk", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorPrebundle.toFiberBundle", "kind": "definition", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorPrebundle.toVectorBundle", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.inCoordinates", "kind": "definition", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousLinearMap.inCoordinates_eq", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": true, "tactics": ["ext", "simp_rw"], "tactic_count": 2}
{"name": "VectorBundleCore.inCoordinates_eq", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Basic", "is_tactic_proof": true, "tactics": ["simp_rw"], "tactic_count": 1}
{"name": "Bundle.Trivial.trivialization.isLinear", "kind": "instance", "module": "Mathlib.Topology.VectorBundle.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bundle.Trivial.trivialization.coordChangeL", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Constructions", "is_tactic_proof": true, "tactics": ["ext", "rw", "exacts"], "tactic_count": 3}
{"name": "Bundle.Trivial.vectorBundle", "kind": "instance", "module": "Mathlib.Topology.VectorBundle.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bundle.Trivial.linearMapAt_trivialization", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Constructions", "is_tactic_proof": true, "tactics": ["ext", "rw", "rfl"], "tactic_count": 3}
{"name": "Bundle.Trivial.continuousLinearMapAt_trivialization", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Constructions", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Bundle.Trivial.symmₗ_trivialization", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Constructions", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Bundle.Trivial.symmL_trivialization", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Constructions", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Bundle.Trivial.continuousLinearEquivAt_trivialization", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Constructions", "is_tactic_proof": true, "tactics": ["ext"], "tactic_count": 1}
{"name": "Trivialization.prod.isLinear", "kind": "instance", "module": "Mathlib.Topology.VectorBundle.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.coordChangeL_prod", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Constructions", "is_tactic_proof": true, "tactics": ["rw", "rintro", "change", "rw", "exacts"], "tactic_count": 5}
{"name": "Trivialization.prod_apply'", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorBundle.prod", "kind": "instance", "module": "Mathlib.Topology.VectorBundle.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.continuousLinearEquivAt_prod", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Constructions", "is_tactic_proof": true, "tactics": ["ext", "obtain", "rw", "exact"], "tactic_count": 4}
{"name": "instAddCommMonoidPullback", "kind": "instance", "module": "Mathlib.Topology.VectorBundle.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "instModulePullback", "kind": "instance", "module": "Mathlib.Topology.VectorBundle.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.pullback_linear", "kind": "instance", "module": "Mathlib.Topology.VectorBundle.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "VectorBundle.pullback", "kind": "instance", "module": "Mathlib.Topology.VectorBundle.Constructions", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pretrivialization.continuousLinearMapCoordChange", "kind": "definition", "module": "Mathlib.Topology.VectorBundle.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pretrivialization.continuousOn_continuousLinearMapCoordChange", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Hom", "is_tactic_proof": true, "tactics": ["have", "have", "have", "have", "refine", "mfld_set_tac", "mfld_set_tac", "intro", "ext", "dsimp"], "tactic_count": 10}
{"name": "Pretrivialization.continuousLinearMap", "kind": "definition", "module": "Mathlib.Topology.VectorBundle.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pretrivialization.continuousLinearMap.isLinear", "kind": "instance", "module": "Mathlib.Topology.VectorBundle.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pretrivialization.continuousLinearMap_apply", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pretrivialization.continuousLinearMap_symm_apply", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Pretrivialization.continuousLinearMap_symm_apply'", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Hom", "is_tactic_proof": true, "tactics": ["rw", "rfl", "exact"], "tactic_count": 3}
{"name": "Pretrivialization.continuousLinearMapCoordChange_apply", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Hom", "is_tactic_proof": true, "tactics": ["ext", "simp_rw", "continuousLinearMap_apply,", "rw", "e₂'.coe_linearMapAt_of_mem", "exacts"], "tactic_count": 6}
{"name": "Bundle.ContinuousLinearMap.vectorPrebundle", "kind": "definition", "module": "Mathlib.Topology.VectorBundle.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bundle.ContinuousLinearMap.topologicalSpaceTotalSpace", "kind": "instance", "module": "Mathlib.Topology.VectorBundle.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bundle.ContinuousLinearMap.fiberBundle", "kind": "instance", "module": "Mathlib.Topology.VectorBundle.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bundle.ContinuousLinearMap.vectorBundle", "kind": "instance", "module": "Mathlib.Topology.VectorBundle.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.continuousLinearMap", "kind": "definition", "module": "Mathlib.Topology.VectorBundle.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Bundle.ContinuousLinearMap.memTrivializationAtlas", "kind": "instance", "module": "Mathlib.Topology.VectorBundle.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.baseSet_continuousLinearMap", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Trivialization.continuousLinearMap_apply", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hom_trivializationAt", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hom_trivializationAt_apply", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hom_trivializationAt_source", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hom_trivializationAt_target", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "hom_trivializationAt_baseSet", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousWithinAt_hom_bundle", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "continuousAt_hom_bundle", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "ContinuousWithinAt.clm_apply_of_inCoordinates", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Hom", "is_tactic_proof": true, "tactics": ["rw", "rw", "refine", "apply", "have", "apply", "apply", "exact", "have", "apply", "apply", "exact", "filter_upwards", "simp"], "tactic_count": 14}
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{"name": "ContinuousAt.clm_bundle_apply", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Hom", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
{"name": "ContinuousOn.clm_bundle_apply", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
{"name": "Continuous.clm_bundle_apply", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Hom", "is_tactic_proof": true, "tactics": ["simp", "exact"], "tactic_count": 2}
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{"name": "ContinuousAt.clm_bundle_apply₂", "kind": "theorem", "module": "Mathlib.Topology.VectorBundle.Hom", "is_tactic_proof": false, "tactics": [], "tactic_count": 0}
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